Properties

Label 1152.2.w.b.1007.7
Level $1152$
Weight $2$
Character 1152.1007
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 1007.7
Character \(\chi\) \(=\) 1152.1007
Dual form 1152.2.w.b.143.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.11994 + 2.70378i) q^{5} +(-1.57144 - 1.57144i) q^{7} +O(q^{10})\) \(q+(1.11994 + 2.70378i) q^{5} +(-1.57144 - 1.57144i) q^{7} +(-1.00153 - 2.41791i) q^{11} +(-6.48559 - 2.68642i) q^{13} -0.520719 q^{17} +(-2.95774 + 7.14062i) q^{19} +(-1.35340 - 1.35340i) q^{23} +(-2.52064 + 2.52064i) q^{25} +(-5.31381 - 2.20105i) q^{29} +1.54505i q^{31} +(2.48892 - 6.00877i) q^{35} +(-3.79897 + 1.57359i) q^{37} +(-1.08917 + 1.08917i) q^{41} +(2.71012 - 1.12257i) q^{43} -11.1855i q^{47} -2.06113i q^{49} +(3.70104 - 1.53302i) q^{53} +(5.41584 - 5.41584i) q^{55} +(3.19376 - 1.32290i) q^{59} +(-3.78169 + 9.12981i) q^{61} -20.5443i q^{65} +(-10.9492 - 4.53532i) q^{67} +(-6.83579 + 6.83579i) q^{71} +(2.94667 + 2.94667i) q^{73} +(-2.22576 + 5.37346i) q^{77} -8.79533 q^{79} +(13.9866 + 5.79342i) q^{83} +(-0.583176 - 1.40791i) q^{85} +(-7.09089 - 7.09089i) q^{89} +(5.97019 + 14.4133i) q^{91} -22.6192 q^{95} -5.91713 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{7}{8}\right)\)

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
\(5\) 1.11994 + 2.70378i 0.500854 + 1.20917i 0.949019 + 0.315218i \(0.102078\pi\)
−0.448165 + 0.893951i \(0.647922\pi\)
\(6\) 0 0
\(7\) −1.57144 1.57144i −0.593950 0.593950i 0.344746 0.938696i \(-0.387965\pi\)
−0.938696 + 0.344746i \(0.887965\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00153 2.41791i −0.301973 0.729027i −0.999917 0.0128746i \(-0.995902\pi\)
0.697944 0.716152i \(-0.254098\pi\)
\(12\) 0 0
\(13\) −6.48559 2.68642i −1.79878 0.745079i −0.986917 0.161230i \(-0.948454\pi\)
−0.811863 0.583848i \(-0.801546\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.520719 −0.126293 −0.0631465 0.998004i \(-0.520114\pi\)
−0.0631465 + 0.998004i \(0.520114\pi\)
\(18\) 0 0
\(19\) −2.95774 + 7.14062i −0.678552 + 1.63817i 0.0881038 + 0.996111i \(0.471919\pi\)
−0.766656 + 0.642058i \(0.778081\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.35340 1.35340i −0.282204 0.282204i 0.551784 0.833987i \(-0.313947\pi\)
−0.833987 + 0.551784i \(0.813947\pi\)
\(24\) 0 0
\(25\) −2.52064 + 2.52064i −0.504128 + 0.504128i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5.31381 2.20105i −0.986750 0.408725i −0.169828 0.985474i \(-0.554321\pi\)
−0.816922 + 0.576748i \(0.804321\pi\)
\(30\) 0 0
\(31\) 1.54505i 0.277498i 0.990328 + 0.138749i \(0.0443082\pi\)
−0.990328 + 0.138749i \(0.955692\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.48892 6.00877i 0.420704 1.01567i
\(36\) 0 0
\(37\) −3.79897 + 1.57359i −0.624548 + 0.258696i −0.672434 0.740157i \(-0.734751\pi\)
0.0478869 + 0.998853i \(0.484751\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.08917 + 1.08917i −0.170100 + 0.170100i −0.787023 0.616923i \(-0.788379\pi\)
0.616923 + 0.787023i \(0.288379\pi\)
\(42\) 0 0
\(43\) 2.71012 1.12257i 0.413290 0.171190i −0.166343 0.986068i \(-0.553196\pi\)
0.579633 + 0.814878i \(0.303196\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.1855i 1.63157i −0.578358 0.815783i \(-0.696306\pi\)
0.578358 0.815783i \(-0.303694\pi\)
\(48\) 0 0
\(49\) 2.06113i 0.294447i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.70104 1.53302i 0.508377 0.210577i −0.113726 0.993512i \(-0.536279\pi\)
0.622103 + 0.782936i \(0.286279\pi\)
\(54\) 0 0
\(55\) 5.41584 5.41584i 0.730272 0.730272i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.19376 1.32290i 0.415792 0.172227i −0.164973 0.986298i \(-0.552754\pi\)
0.580765 + 0.814071i \(0.302754\pi\)
\(60\) 0 0
\(61\) −3.78169 + 9.12981i −0.484196 + 1.16895i 0.473403 + 0.880846i \(0.343026\pi\)
−0.957598 + 0.288106i \(0.906974\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 20.5443i 2.54820i
\(66\) 0 0
\(67\) −10.9492 4.53532i −1.33766 0.554077i −0.404830 0.914392i \(-0.632669\pi\)
−0.932831 + 0.360314i \(0.882669\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.83579 + 6.83579i −0.811259 + 0.811259i −0.984823 0.173564i \(-0.944472\pi\)
0.173564 + 0.984823i \(0.444472\pi\)
\(72\) 0 0
\(73\) 2.94667 + 2.94667i 0.344882 + 0.344882i 0.858199 0.513317i \(-0.171584\pi\)
−0.513317 + 0.858199i \(0.671584\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.22576 + 5.37346i −0.253649 + 0.612362i
\(78\) 0 0
\(79\) −8.79533 −0.989552 −0.494776 0.869021i \(-0.664750\pi\)
−0.494776 + 0.869021i \(0.664750\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 13.9866 + 5.79342i 1.53522 + 0.635911i 0.980570 0.196170i \(-0.0628504\pi\)
0.554655 + 0.832081i \(0.312850\pi\)
\(84\) 0 0
\(85\) −0.583176 1.40791i −0.0632544 0.152710i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.09089 7.09089i −0.751633 0.751633i 0.223151 0.974784i \(-0.428366\pi\)
−0.974784 + 0.223151i \(0.928366\pi\)
\(90\) 0 0
\(91\) 5.97019 + 14.4133i 0.625846 + 1.51092i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −22.6192 −2.32068
\(96\) 0 0
\(97\) −5.91713 −0.600793 −0.300397 0.953814i \(-0.597119\pi\)
−0.300397 + 0.953814i \(0.597119\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.62448 + 11.1645i 0.460153 + 1.11091i 0.968334 + 0.249657i \(0.0803178\pi\)
−0.508182 + 0.861250i \(0.669682\pi\)
\(102\) 0 0
\(103\) −12.0132 12.0132i −1.18369 1.18369i −0.978780 0.204913i \(-0.934309\pi\)
−0.204913 0.978780i \(-0.565691\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.56773 + 13.4417i 0.538253 + 1.29946i 0.925941 + 0.377667i \(0.123274\pi\)
−0.387688 + 0.921791i \(0.626726\pi\)
\(108\) 0 0
\(109\) −5.97381 2.47443i −0.572187 0.237008i 0.0777792 0.996971i \(-0.475217\pi\)
−0.649966 + 0.759963i \(0.725217\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.0445 0.944908 0.472454 0.881355i \(-0.343368\pi\)
0.472454 + 0.881355i \(0.343368\pi\)
\(114\) 0 0
\(115\) 2.14357 5.17504i 0.199889 0.482575i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.818281 + 0.818281i 0.0750117 + 0.0750117i
\(120\) 0 0
\(121\) 2.93496 2.93496i 0.266815 0.266815i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.88069 + 1.60743i 0.347099 + 0.143773i
\(126\) 0 0
\(127\) 12.2276i 1.08503i 0.840047 + 0.542513i \(0.182527\pi\)
−0.840047 + 0.542513i \(0.817473\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.18881 5.28425i 0.191237 0.461687i −0.798957 0.601389i \(-0.794614\pi\)
0.990194 + 0.139702i \(0.0446144\pi\)
\(132\) 0 0
\(133\) 15.8690 6.57316i 1.37602 0.569965i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.53314 3.53314i 0.301856 0.301856i −0.539883 0.841740i \(-0.681532\pi\)
0.841740 + 0.539883i \(0.181532\pi\)
\(138\) 0 0
\(139\) −4.17495 + 1.72932i −0.354115 + 0.146679i −0.552648 0.833415i \(-0.686382\pi\)
0.198533 + 0.980094i \(0.436382\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 18.3721i 1.53635i
\(144\) 0 0
\(145\) 16.8325i 1.39786i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −15.4396 + 6.39531i −1.26486 + 0.523924i −0.911399 0.411524i \(-0.864997\pi\)
−0.353465 + 0.935448i \(0.614997\pi\)
\(150\) 0 0
\(151\) −0.199339 + 0.199339i −0.0162220 + 0.0162220i −0.715171 0.698949i \(-0.753651\pi\)
0.698949 + 0.715171i \(0.253651\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.17747 + 1.73036i −0.335542 + 0.138986i
\(156\) 0 0
\(157\) −2.24745 + 5.42583i −0.179366 + 0.433028i −0.987834 0.155512i \(-0.950297\pi\)
0.808468 + 0.588540i \(0.200297\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.25359i 0.335230i
\(162\) 0 0
\(163\) −4.85740 2.01200i −0.380461 0.157592i 0.184253 0.982879i \(-0.441013\pi\)
−0.564714 + 0.825287i \(0.691013\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.1373 14.1373i 1.09397 1.09397i 0.0988739 0.995100i \(-0.468476\pi\)
0.995100 0.0988739i \(-0.0315240\pi\)
\(168\) 0 0
\(169\) 25.6537 + 25.6537i 1.97336 + 1.97336i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.98598 9.62302i 0.303049 0.731625i −0.696847 0.717219i \(-0.745415\pi\)
0.999896 0.0144051i \(-0.00458545\pi\)
\(174\) 0 0
\(175\) 7.92208 0.598853
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −17.3296 7.17815i −1.29527 0.536520i −0.374721 0.927138i \(-0.622261\pi\)
−0.920553 + 0.390618i \(0.872261\pi\)
\(180\) 0 0
\(181\) −1.80823 4.36545i −0.134404 0.324481i 0.842320 0.538977i \(-0.181189\pi\)
−0.976725 + 0.214496i \(0.931189\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −8.50928 8.50928i −0.625614 0.625614i
\(186\) 0 0
\(187\) 0.521516 + 1.25905i 0.0381370 + 0.0920709i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.95000 −0.502885 −0.251442 0.967872i \(-0.580905\pi\)
−0.251442 + 0.967872i \(0.580905\pi\)
\(192\) 0 0
\(193\) 10.4125 0.749511 0.374756 0.927124i \(-0.377727\pi\)
0.374756 + 0.927124i \(0.377727\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.52349 + 8.50645i 0.251038 + 0.606059i 0.998288 0.0584832i \(-0.0186264\pi\)
−0.747250 + 0.664543i \(0.768626\pi\)
\(198\) 0 0
\(199\) 5.74862 + 5.74862i 0.407509 + 0.407509i 0.880869 0.473360i \(-0.156959\pi\)
−0.473360 + 0.880869i \(0.656959\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.89153 + 11.8092i 0.343318 + 0.828843i
\(204\) 0 0
\(205\) −4.16470 1.72507i −0.290875 0.120484i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 20.2276 1.39917
\(210\) 0 0
\(211\) −3.53929 + 8.54461i −0.243655 + 0.588235i −0.997640 0.0686560i \(-0.978129\pi\)
0.753985 + 0.656891i \(0.228129\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.07037 + 6.07037i 0.413996 + 0.413996i
\(216\) 0 0
\(217\) 2.42795 2.42795i 0.164820 0.164820i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.37717 + 1.39887i 0.227173 + 0.0940982i
\(222\) 0 0
\(223\) 11.5406i 0.772814i −0.922328 0.386407i \(-0.873716\pi\)
0.922328 0.386407i \(-0.126284\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.48691 13.2466i 0.364179 0.879205i −0.630501 0.776188i \(-0.717151\pi\)
0.994680 0.103017i \(-0.0328495\pi\)
\(228\) 0 0
\(229\) 4.29256 1.77804i 0.283661 0.117496i −0.236317 0.971676i \(-0.575940\pi\)
0.519977 + 0.854180i \(0.325940\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.05679 + 9.05679i −0.593330 + 0.593330i −0.938529 0.345199i \(-0.887811\pi\)
0.345199 + 0.938529i \(0.387811\pi\)
\(234\) 0 0
\(235\) 30.2430 12.5271i 1.97284 0.817177i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.04485i 0.520378i 0.965558 + 0.260189i \(0.0837849\pi\)
−0.965558 + 0.260189i \(0.916215\pi\)
\(240\) 0 0
\(241\) 19.0228i 1.22536i −0.790329 0.612682i \(-0.790091\pi\)
0.790329 0.612682i \(-0.209909\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5.57284 2.30835i 0.356036 0.147475i
\(246\) 0 0
\(247\) 38.3654 38.3654i 2.44113 2.44113i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7.25290 3.00425i 0.457799 0.189626i −0.141853 0.989888i \(-0.545306\pi\)
0.599651 + 0.800261i \(0.295306\pi\)
\(252\) 0 0
\(253\) −1.91693 + 4.62787i −0.120516 + 0.290952i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 23.0041i 1.43496i 0.696581 + 0.717478i \(0.254703\pi\)
−0.696581 + 0.717478i \(0.745297\pi\)
\(258\) 0 0
\(259\) 8.44268 + 3.49707i 0.524603 + 0.217298i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.44247 + 1.44247i −0.0889468 + 0.0889468i −0.750180 0.661233i \(-0.770033\pi\)
0.661233 + 0.750180i \(0.270033\pi\)
\(264\) 0 0
\(265\) 8.28991 + 8.28991i 0.509245 + 0.509245i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.77582 4.28722i 0.108274 0.261396i −0.860451 0.509533i \(-0.829818\pi\)
0.968725 + 0.248137i \(0.0798182\pi\)
\(270\) 0 0
\(271\) −2.52337 −0.153284 −0.0766419 0.997059i \(-0.524420\pi\)
−0.0766419 + 0.997059i \(0.524420\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 8.61916 + 3.57017i 0.519755 + 0.215290i
\(276\) 0 0
\(277\) −3.50691 8.46643i −0.210710 0.508699i 0.782823 0.622245i \(-0.213779\pi\)
−0.993533 + 0.113546i \(0.963779\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.34778 + 5.34778i 0.319022 + 0.319022i 0.848391 0.529369i \(-0.177571\pi\)
−0.529369 + 0.848391i \(0.677571\pi\)
\(282\) 0 0
\(283\) 10.0243 + 24.2009i 0.595885 + 1.43859i 0.877741 + 0.479136i \(0.159050\pi\)
−0.281856 + 0.959457i \(0.590950\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.42315 0.202062
\(288\) 0 0
\(289\) −16.7289 −0.984050
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.12975 + 14.7985i 0.358104 + 0.864539i 0.995567 + 0.0940580i \(0.0299839\pi\)
−0.637463 + 0.770481i \(0.720016\pi\)
\(294\) 0 0
\(295\) 7.15366 + 7.15366i 0.416502 + 0.416502i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.14180 + 12.4134i 0.297358 + 0.717886i
\(300\) 0 0
\(301\) −6.02286 2.49475i −0.347152 0.143795i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −28.9203 −1.65597
\(306\) 0 0
\(307\) 6.63881 16.0275i 0.378897 0.914738i −0.613276 0.789869i \(-0.710149\pi\)
0.992173 0.124870i \(-0.0398513\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 15.0561 + 15.0561i 0.853754 + 0.853754i 0.990593 0.136839i \(-0.0436942\pi\)
−0.136839 + 0.990593i \(0.543694\pi\)
\(312\) 0 0
\(313\) 4.19455 4.19455i 0.237090 0.237090i −0.578554 0.815644i \(-0.696383\pi\)
0.815644 + 0.578554i \(0.196383\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.3097 5.51307i −0.747549 0.309645i −0.0238078 0.999717i \(-0.507579\pi\)
−0.723741 + 0.690072i \(0.757579\pi\)
\(318\) 0 0
\(319\) 15.0527i 0.842791i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.54015 3.71826i 0.0856964 0.206889i
\(324\) 0 0
\(325\) 23.1193 9.57633i 1.28243 0.531199i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −17.5773 + 17.5773i −0.969069 + 0.969069i
\(330\) 0 0
\(331\) −5.98959 + 2.48097i −0.329218 + 0.136366i −0.541169 0.840914i \(-0.682018\pi\)
0.211951 + 0.977280i \(0.432018\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 34.6836i 1.89497i
\(336\) 0 0
\(337\) 29.6988i 1.61779i 0.587950 + 0.808897i \(0.299935\pi\)
−0.587950 + 0.808897i \(0.700065\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.73578 1.54741i 0.202304 0.0837969i
\(342\) 0 0
\(343\) −14.2391 + 14.2391i −0.768837 + 0.768837i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −29.8947 + 12.3828i −1.60483 + 0.664744i −0.992089 0.125537i \(-0.959935\pi\)
−0.612745 + 0.790281i \(0.709935\pi\)
\(348\) 0 0
\(349\) −8.37790 + 20.2260i −0.448459 + 1.08268i 0.524441 + 0.851447i \(0.324274\pi\)
−0.972899 + 0.231228i \(0.925726\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.58104i 0.137375i 0.997638 + 0.0686874i \(0.0218811\pi\)
−0.997638 + 0.0686874i \(0.978119\pi\)
\(354\) 0 0
\(355\) −26.1382 10.8268i −1.38727 0.574627i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.3463 11.3463i 0.598834 0.598834i −0.341168 0.940002i \(-0.610823\pi\)
0.940002 + 0.341168i \(0.110823\pi\)
\(360\) 0 0
\(361\) −28.8051 28.8051i −1.51606 1.51606i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.66705 + 11.2673i −0.244285 + 0.589755i
\(366\) 0 0
\(367\) −8.71339 −0.454835 −0.227418 0.973797i \(-0.573028\pi\)
−0.227418 + 0.973797i \(0.573028\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8.22503 3.40692i −0.427022 0.176878i
\(372\) 0 0
\(373\) 1.56395 + 3.77570i 0.0809781 + 0.195498i 0.959183 0.282786i \(-0.0912587\pi\)
−0.878205 + 0.478285i \(0.841259\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 28.5503 + 28.5503i 1.47041 + 1.47041i
\(378\) 0 0
\(379\) −8.85643 21.3813i −0.454925 1.09828i −0.970427 0.241397i \(-0.922395\pi\)
0.515502 0.856888i \(-0.327605\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.90996 0.199790 0.0998949 0.994998i \(-0.468149\pi\)
0.0998949 + 0.994998i \(0.468149\pi\)
\(384\) 0 0
\(385\) −17.0214 −0.867490
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.92740 9.48159i −0.199127 0.480736i 0.792500 0.609872i \(-0.208779\pi\)
−0.991627 + 0.129137i \(0.958779\pi\)
\(390\) 0 0
\(391\) 0.704742 + 0.704742i 0.0356403 + 0.0356403i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −9.85028 23.7807i −0.495621 1.19654i
\(396\) 0 0
\(397\) 15.8590 + 6.56903i 0.795942 + 0.329690i 0.743330 0.668925i \(-0.233245\pi\)
0.0526124 + 0.998615i \(0.483245\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 18.8741 0.942529 0.471265 0.881992i \(-0.343798\pi\)
0.471265 + 0.881992i \(0.343798\pi\)
\(402\) 0 0
\(403\) 4.15064 10.0205i 0.206758 0.499158i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.60957 + 7.60957i 0.377193 + 0.377193i
\(408\) 0 0
\(409\) −9.68899 + 9.68899i −0.479089 + 0.479089i −0.904840 0.425751i \(-0.860010\pi\)
0.425751 + 0.904840i \(0.360010\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −7.09768 2.93995i −0.349254 0.144666i
\(414\) 0 0
\(415\) 44.3049i 2.17484i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13.8806 + 33.5108i −0.678114 + 1.63711i 0.0893350 + 0.996002i \(0.471526\pi\)
−0.767449 + 0.641110i \(0.778474\pi\)
\(420\) 0 0
\(421\) 23.7882 9.85339i 1.15937 0.480225i 0.281702 0.959502i \(-0.409101\pi\)
0.877664 + 0.479277i \(0.159101\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.31254 1.31254i 0.0636678 0.0636678i
\(426\) 0 0
\(427\) 20.2897 8.40427i 0.981887 0.406711i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.02776i 0.0495056i 0.999694 + 0.0247528i \(0.00787987\pi\)
−0.999694 + 0.0247528i \(0.992120\pi\)
\(432\) 0 0
\(433\) 21.3662i 1.02680i −0.858151 0.513398i \(-0.828386\pi\)
0.858151 0.513398i \(-0.171614\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 13.6671 5.66111i 0.653787 0.270807i
\(438\) 0 0
\(439\) −13.4689 + 13.4689i −0.642835 + 0.642835i −0.951251 0.308417i \(-0.900201\pi\)
0.308417 + 0.951251i \(0.400201\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.92612 2.04047i 0.234047 0.0969454i −0.262578 0.964911i \(-0.584573\pi\)
0.496625 + 0.867965i \(0.334573\pi\)
\(444\) 0 0
\(445\) 11.2308 27.1136i 0.532393 1.28531i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.2980i 1.05231i −0.850390 0.526153i \(-0.823634\pi\)
0.850390 0.526153i \(-0.176366\pi\)
\(450\) 0 0
\(451\) 3.72436 + 1.54268i 0.175373 + 0.0726419i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −32.2842 + 32.2842i −1.51351 + 1.51351i
\(456\) 0 0
\(457\) −6.58505 6.58505i −0.308035 0.308035i 0.536112 0.844147i \(-0.319893\pi\)
−0.844147 + 0.536112i \(0.819893\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14.3380 34.6150i 0.667788 1.61218i −0.117515 0.993071i \(-0.537493\pi\)
0.785303 0.619112i \(-0.212507\pi\)
\(462\) 0 0
\(463\) 14.4728 0.672607 0.336304 0.941754i \(-0.390823\pi\)
0.336304 + 0.941754i \(0.390823\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.73511 4.03241i −0.450487 0.186598i 0.145892 0.989300i \(-0.453395\pi\)
−0.596380 + 0.802703i \(0.703395\pi\)
\(468\) 0 0
\(469\) 10.0791 + 24.3331i 0.465410 + 1.12360i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.42854 5.42854i −0.249605 0.249605i
\(474\) 0 0
\(475\) −10.5435 25.4543i −0.483770 1.16792i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 30.2779 1.38343 0.691717 0.722169i \(-0.256855\pi\)
0.691717 + 0.722169i \(0.256855\pi\)
\(480\) 0 0
\(481\) 28.8659 1.31617
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.62685 15.9986i −0.300910 0.726461i
\(486\) 0 0
\(487\) −11.6078 11.6078i −0.526000 0.526000i 0.393377 0.919377i \(-0.371307\pi\)
−0.919377 + 0.393377i \(0.871307\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.08448 9.86082i −0.184330 0.445012i 0.804520 0.593925i \(-0.202423\pi\)
−0.988850 + 0.148913i \(0.952423\pi\)
\(492\) 0 0
\(493\) 2.76700 + 1.14613i 0.124620 + 0.0516191i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 21.4841 0.963695
\(498\) 0 0
\(499\) −10.5238 + 25.4066i −0.471109 + 1.13736i 0.492565 + 0.870276i \(0.336059\pi\)
−0.963674 + 0.267082i \(0.913941\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −16.9786 16.9786i −0.757040 0.757040i 0.218742 0.975783i \(-0.429805\pi\)
−0.975783 + 0.218742i \(0.929805\pi\)
\(504\) 0 0
\(505\) −25.0072 + 25.0072i −1.11280 + 1.11280i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −25.0892 10.3923i −1.11206 0.460630i −0.250413 0.968139i \(-0.580566\pi\)
−0.861646 + 0.507509i \(0.830566\pi\)
\(510\) 0 0
\(511\) 9.26105i 0.409685i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 19.0269 45.9351i 0.838427 2.02414i
\(516\) 0 0
\(517\) −27.0454 + 11.2026i −1.18946 + 0.492688i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3.51029 3.51029i 0.153789 0.153789i −0.626019 0.779808i \(-0.715317\pi\)
0.779808 + 0.626019i \(0.215317\pi\)
\(522\) 0 0
\(523\) 2.65762 1.10082i 0.116209 0.0481355i −0.323821 0.946118i \(-0.604968\pi\)
0.440031 + 0.897983i \(0.354968\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.804535i 0.0350461i
\(528\) 0 0
\(529\) 19.3366i 0.840722i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9.98990 4.13795i 0.432711 0.179235i
\(534\) 0 0
\(535\) −30.1079 + 30.1079i −1.30168 + 1.30168i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.98361 + 2.06428i −0.214659 + 0.0889148i
\(540\) 0 0
\(541\) 8.33435 20.1209i 0.358322 0.865066i −0.637214 0.770687i \(-0.719913\pi\)
0.995536 0.0943790i \(-0.0300866\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 18.9231i 0.810577i
\(546\) 0 0
\(547\) −15.3897 6.37463i −0.658017 0.272560i 0.0285868 0.999591i \(-0.490899\pi\)
−0.686604 + 0.727032i \(0.740899\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 31.4337 31.4337i 1.33912 1.33912i
\(552\) 0 0
\(553\) 13.8214 + 13.8214i 0.587744 + 0.587744i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.13010 + 7.55673i −0.132627 + 0.320189i −0.976216 0.216800i \(-0.930438\pi\)
0.843590 + 0.536989i \(0.180438\pi\)
\(558\) 0 0
\(559\) −20.5924 −0.870968
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −0.345832 0.143248i −0.0145751 0.00603719i 0.375384 0.926869i \(-0.377511\pi\)
−0.389959 + 0.920832i \(0.627511\pi\)
\(564\) 0 0
\(565\) 11.2493 + 27.1582i 0.473261 + 1.14255i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −31.8289 31.8289i −1.33434 1.33434i −0.901447 0.432890i \(-0.857494\pi\)
−0.432890 0.901447i \(-0.642506\pi\)
\(570\) 0 0
\(571\) −7.49818 18.1022i −0.313789 0.757554i −0.999558 0.0297343i \(-0.990534\pi\)
0.685769 0.727819i \(-0.259466\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.82287 0.284533
\(576\) 0 0
\(577\) −19.6358 −0.817447 −0.408724 0.912658i \(-0.634026\pi\)
−0.408724 + 0.912658i \(0.634026\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12.8751 31.0831i −0.534147 1.28955i
\(582\) 0 0
\(583\) −7.41340 7.41340i −0.307032 0.307032i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.01640 19.3533i −0.330872 0.798796i −0.998523 0.0543221i \(-0.982700\pi\)
0.667651 0.744474i \(-0.267300\pi\)
\(588\) 0 0
\(589\) −11.0326 4.56984i −0.454589 0.188297i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −26.2206 −1.07675 −0.538376 0.842704i \(-0.680962\pi\)
−0.538376 + 0.842704i \(0.680962\pi\)
\(594\) 0 0
\(595\) −1.29603 + 3.12888i −0.0531319 + 0.128272i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13.4497 + 13.4497i 0.549542 + 0.549542i 0.926308 0.376767i \(-0.122964\pi\)
−0.376767 + 0.926308i \(0.622964\pi\)
\(600\) 0 0
\(601\) −10.7760 + 10.7760i −0.439562 + 0.439562i −0.891864 0.452303i \(-0.850603\pi\)
0.452303 + 0.891864i \(0.350603\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 11.2225 + 4.64851i 0.456259 + 0.188989i
\(606\) 0 0
\(607\) 5.71428i 0.231936i −0.993253 0.115968i \(-0.963003\pi\)
0.993253 0.115968i \(-0.0369969\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −30.0488 + 72.5443i −1.21565 + 2.93483i
\(612\) 0 0
\(613\) −25.0980 + 10.3959i −1.01370 + 0.419887i −0.826802 0.562493i \(-0.809842\pi\)
−0.186895 + 0.982380i \(0.559842\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.07388 + 7.07388i −0.284784 + 0.284784i −0.835013 0.550230i \(-0.814540\pi\)
0.550230 + 0.835013i \(0.314540\pi\)
\(618\) 0 0
\(619\) −32.9781 + 13.6600i −1.32550 + 0.549041i −0.929369 0.369151i \(-0.879648\pi\)
−0.396134 + 0.918193i \(0.629648\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 22.2859i 0.892865i
\(624\) 0 0
\(625\) 30.1164i 1.20465i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.97820 0.819397i 0.0788760 0.0326715i
\(630\) 0 0
\(631\) 2.15849 2.15849i 0.0859280 0.0859280i −0.662836 0.748764i \(-0.730647\pi\)
0.748764 + 0.662836i \(0.230647\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −33.0608 + 13.6943i −1.31198 + 0.543440i
\(636\) 0 0
\(637\) −5.53705 + 13.3676i −0.219386 + 0.529645i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 38.0487i 1.50283i 0.659827 + 0.751417i \(0.270629\pi\)
−0.659827 + 0.751417i \(0.729371\pi\)
\(642\) 0 0
\(643\) 16.7464 + 6.93660i 0.660414 + 0.273553i 0.687613 0.726077i \(-0.258659\pi\)
−0.0271985 + 0.999630i \(0.508659\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.77745 1.77745i 0.0698786 0.0698786i −0.671304 0.741182i \(-0.734265\pi\)
0.741182 + 0.671304i \(0.234265\pi\)
\(648\) 0 0
\(649\) −6.39729 6.39729i −0.251116 0.251116i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.13694 19.6443i 0.318423 0.768742i −0.680915 0.732363i \(-0.738418\pi\)
0.999338 0.0363791i \(-0.0115824\pi\)
\(654\) 0 0
\(655\) 16.7388 0.654039
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −5.72478 2.37128i −0.223006 0.0923720i 0.268383 0.963312i \(-0.413511\pi\)
−0.491389 + 0.870940i \(0.663511\pi\)
\(660\) 0 0
\(661\) −14.6754 35.4296i −0.570808 1.37805i −0.900868 0.434092i \(-0.857069\pi\)
0.330061 0.943960i \(-0.392931\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 35.5448 + 35.5448i 1.37837 + 1.37837i
\(666\) 0 0
\(667\) 4.21281 + 10.1706i 0.163121 + 0.393808i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 25.8625 0.998411
\(672\) 0 0
\(673\) −32.6272 −1.25768 −0.628842 0.777533i \(-0.716471\pi\)
−0.628842 + 0.777533i \(0.716471\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −11.1224 26.8518i −0.427468 1.03200i −0.980088 0.198565i \(-0.936372\pi\)
0.552620 0.833433i \(-0.313628\pi\)
\(678\) 0 0
\(679\) 9.29844 + 9.29844i 0.356841 + 0.356841i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.38525 3.34428i −0.0530050 0.127965i 0.895159 0.445747i \(-0.147062\pi\)
−0.948164 + 0.317782i \(0.897062\pi\)
\(684\) 0 0
\(685\) 13.5098 + 5.59593i 0.516181 + 0.213809i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −28.1218 −1.07135
\(690\) 0 0
\(691\) 13.4910 32.5702i 0.513223 1.23903i −0.428775 0.903411i \(-0.641055\pi\)
0.941998 0.335618i \(-0.108945\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.35143 9.35143i −0.354720 0.354720i
\(696\) 0 0
\(697\) 0.567153 0.567153i 0.0214825 0.0214825i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 3.25729 + 1.34921i 0.123026 + 0.0509590i 0.443347 0.896350i \(-0.353791\pi\)
−0.320321 + 0.947309i \(0.603791\pi\)
\(702\) 0 0
\(703\) 31.7813i 1.19865i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 10.2772 24.8115i 0.386515 0.933131i
\(708\) 0 0
\(709\) −27.0551 + 11.2066i −1.01607 + 0.420872i −0.827667 0.561219i \(-0.810332\pi\)
−0.188407 + 0.982091i \(0.560332\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.09107 2.09107i 0.0783110 0.0783110i
\(714\) 0 0
\(715\) −49.6742 + 20.5757i −1.85771 + 0.769488i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.87831i 0.256518i 0.991741 + 0.128259i \(0.0409389\pi\)
−0.991741 + 0.128259i \(0.959061\pi\)
\(720\) 0 0
\(721\) 37.7561i 1.40611i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 18.9422 7.84614i 0.703497 0.291398i
\(726\) 0 0
\(727\) −8.61474 + 8.61474i −0.319503 + 0.319503i −0.848576 0.529073i \(-0.822540\pi\)
0.529073 + 0.848576i \(0.322540\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.41121 + 0.584544i −0.0521956 + 0.0216201i
\(732\) 0 0
\(733\) 6.86842 16.5818i 0.253691 0.612464i −0.744806 0.667282i \(-0.767458\pi\)
0.998496 + 0.0548178i \(0.0174578\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31.0165i 1.14251i
\(738\) 0 0
\(739\) −8.65828 3.58638i −0.318500 0.131927i 0.217706 0.976014i \(-0.430143\pi\)
−0.536205 + 0.844088i \(0.680143\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5.87413 5.87413i 0.215501 0.215501i −0.591098 0.806599i \(-0.701306\pi\)
0.806599 + 0.591098i \(0.201306\pi\)
\(744\) 0 0
\(745\) −34.5830 34.5830i −1.26702 1.26702i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 12.3735 29.8723i 0.452118 1.09151i
\(750\) 0 0
\(751\) −3.89687 −0.142199 −0.0710993 0.997469i \(-0.522651\pi\)
−0.0710993 + 0.997469i \(0.522651\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.762219 0.315721i −0.0277400 0.0114903i
\(756\) 0 0
\(757\) −4.04702 9.77036i −0.147091 0.355110i 0.833112 0.553105i \(-0.186557\pi\)
−0.980203 + 0.197995i \(0.936557\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.3848 + 13.3848i 0.485198 + 0.485198i 0.906787 0.421589i \(-0.138528\pi\)
−0.421589 + 0.906787i \(0.638528\pi\)
\(762\) 0 0
\(763\) 5.49908 + 13.2759i 0.199080 + 0.480621i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −24.2673 −0.876241
\(768\) 0 0
\(769\) 5.94152 0.214257 0.107128 0.994245i \(-0.465834\pi\)
0.107128 + 0.994245i \(0.465834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.97648 9.60006i −0.143024 0.345290i 0.836093 0.548588i \(-0.184834\pi\)
−0.979117 + 0.203297i \(0.934834\pi\)
\(774\) 0 0
\(775\) −3.89450 3.89450i −0.139895 0.139895i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.55587 10.9988i −0.163231 0.394075i
\(780\) 0 0
\(781\) 23.3746 + 9.68206i 0.836408 + 0.346451i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −17.1873 −0.613440
\(786\) 0 0
\(787\) −6.79001 + 16.3925i −0.242038 + 0.584331i −0.997485 0.0708787i \(-0.977420\pi\)
0.755447 + 0.655210i \(0.227420\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15.7844 15.7844i −0.561228 0.561228i
\(792\) 0 0
\(793\) 49.0530 49.0530i 1.74192 1.74192i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.96338 + 3.71275i 0.317499 + 0.131512i 0.535741 0.844382i \(-0.320032\pi\)
−0.218242 + 0.975895i \(0.570032\pi\)
\(798\) 0 0
\(799\) 5.82448i 0.206055i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.17360 10.0760i 0.147283 0.355573i
\(804\) 0 0
\(805\) −11.5008 + 4.76378i −0.405349