Properties

Label 1792.2.m.h.1345.8
Level $1792$
Weight $2$
Character 1792.1345
Analytic conductor $14.309$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.3091920422\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1345.8
Root \(0.117630 + 0.893490i\) of defining polynomial
Character \(\chi\) \(=\) 1792.1345
Dual form 1792.2.m.h.449.8

$q$-expansion

\(f(q)\) \(=\) \(q+(2.41958 + 2.41958i) q^{3} +(2.54136 - 2.54136i) q^{5} -1.00000i q^{7} +8.70871i q^{9} +O(q^{10})\) \(q+(2.41958 + 2.41958i) q^{3} +(2.54136 - 2.54136i) q^{5} -1.00000i q^{7} +8.70871i q^{9} +(-0.764739 + 0.764739i) q^{11} +(1.26582 + 1.26582i) q^{13} +12.2980 q^{15} +5.65390 q^{17} +(-0.0445673 - 0.0445673i) q^{19} +(2.41958 - 2.41958i) q^{21} +1.46467i q^{23} -7.91700i q^{25} +(-13.8127 + 13.8127i) q^{27} +(-3.56633 - 3.56633i) q^{29} -4.75455 q^{31} -3.70069 q^{33} +(-2.54136 - 2.54136i) q^{35} +(5.09082 - 5.09082i) q^{37} +6.12551i q^{39} -7.50243i q^{41} +(-3.22558 + 3.22558i) q^{43} +(22.1320 + 22.1320i) q^{45} +1.52393 q^{47} -1.00000 q^{49} +(13.6800 + 13.6800i) q^{51} +(-4.66114 + 4.66114i) q^{53} +3.88695i q^{55} -0.215668i q^{57} +(5.38865 - 5.38865i) q^{59} +(6.80717 + 6.80717i) q^{61} +8.70871 q^{63} +6.43381 q^{65} +(-4.92858 - 4.92858i) q^{67} +(-3.54387 + 3.54387i) q^{69} +6.19187i q^{71} +8.59924i q^{73} +(19.1558 - 19.1558i) q^{75} +(0.764739 + 0.764739i) q^{77} -7.84435 q^{79} -40.7155 q^{81} +(7.43857 + 7.43857i) q^{83} +(14.3686 - 14.3686i) q^{85} -17.2580i q^{87} -9.32780i q^{89} +(1.26582 - 1.26582i) q^{91} +(-11.5040 - 11.5040i) q^{93} -0.226523 q^{95} +0.485578 q^{97} +(-6.65990 - 6.65990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{3} + 4q^{5} + O(q^{10}) \) \( 16q + 4q^{3} + 4q^{5} - 8q^{11} - 12q^{13} - 8q^{17} + 4q^{19} + 4q^{21} - 56q^{27} - 8q^{31} + 16q^{33} - 4q^{35} + 8q^{37} - 24q^{43} + 36q^{45} - 40q^{47} - 16q^{49} + 24q^{51} + 32q^{53} - 4q^{59} + 20q^{61} + 24q^{63} + 72q^{65} + 32q^{67} - 56q^{69} - 28q^{75} + 8q^{77} - 40q^{81} + 36q^{83} - 12q^{91} - 8q^{93} - 80q^{95} - 72q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 2.41958 + 2.41958i 1.39694 + 1.39694i 0.808640 + 0.588304i \(0.200204\pi\)
0.588304 + 0.808640i \(0.299796\pi\)
\(4\) 0 0
\(5\) 2.54136 2.54136i 1.13653 1.13653i 0.147462 0.989068i \(-0.452890\pi\)
0.989068 0.147462i \(-0.0471104\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 8.70871i 2.90290i
\(10\) 0 0
\(11\) −0.764739 + 0.764739i −0.230578 + 0.230578i −0.812934 0.582356i \(-0.802131\pi\)
0.582356 + 0.812934i \(0.302131\pi\)
\(12\) 0 0
\(13\) 1.26582 + 1.26582i 0.351076 + 0.351076i 0.860510 0.509434i \(-0.170145\pi\)
−0.509434 + 0.860510i \(0.670145\pi\)
\(14\) 0 0
\(15\) 12.2980 3.17534
\(16\) 0 0
\(17\) 5.65390 1.37127 0.685636 0.727945i \(-0.259524\pi\)
0.685636 + 0.727945i \(0.259524\pi\)
\(18\) 0 0
\(19\) −0.0445673 0.0445673i −0.0102244 0.0102244i 0.701976 0.712201i \(-0.252301\pi\)
−0.712201 + 0.701976i \(0.752301\pi\)
\(20\) 0 0
\(21\) 2.41958 2.41958i 0.527995 0.527995i
\(22\) 0 0
\(23\) 1.46467i 0.305404i 0.988272 + 0.152702i \(0.0487975\pi\)
−0.988272 + 0.152702i \(0.951203\pi\)
\(24\) 0 0
\(25\) 7.91700i 1.58340i
\(26\) 0 0
\(27\) −13.8127 + 13.8127i −2.65825 + 2.65825i
\(28\) 0 0
\(29\) −3.56633 3.56633i −0.662251 0.662251i 0.293659 0.955910i \(-0.405127\pi\)
−0.955910 + 0.293659i \(0.905127\pi\)
\(30\) 0 0
\(31\) −4.75455 −0.853943 −0.426971 0.904265i \(-0.640419\pi\)
−0.426971 + 0.904265i \(0.640419\pi\)
\(32\) 0 0
\(33\) −3.70069 −0.644208
\(34\) 0 0
\(35\) −2.54136 2.54136i −0.429568 0.429568i
\(36\) 0 0
\(37\) 5.09082 5.09082i 0.836926 0.836926i −0.151527 0.988453i \(-0.548419\pi\)
0.988453 + 0.151527i \(0.0484190\pi\)
\(38\) 0 0
\(39\) 6.12551i 0.980867i
\(40\) 0 0
\(41\) 7.50243i 1.17168i −0.810426 0.585841i \(-0.800764\pi\)
0.810426 0.585841i \(-0.199236\pi\)
\(42\) 0 0
\(43\) −3.22558 + 3.22558i −0.491897 + 0.491897i −0.908903 0.417007i \(-0.863079\pi\)
0.417007 + 0.908903i \(0.363079\pi\)
\(44\) 0 0
\(45\) 22.1320 + 22.1320i 3.29924 + 3.29924i
\(46\) 0 0
\(47\) 1.52393 0.222287 0.111144 0.993804i \(-0.464549\pi\)
0.111144 + 0.993804i \(0.464549\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 13.6800 + 13.6800i 1.91559 + 1.91559i
\(52\) 0 0
\(53\) −4.66114 + 4.66114i −0.640257 + 0.640257i −0.950619 0.310362i \(-0.899550\pi\)
0.310362 + 0.950619i \(0.399550\pi\)
\(54\) 0 0
\(55\) 3.88695i 0.524117i
\(56\) 0 0
\(57\) 0.215668i 0.0285659i
\(58\) 0 0
\(59\) 5.38865 5.38865i 0.701543 0.701543i −0.263199 0.964742i \(-0.584777\pi\)
0.964742 + 0.263199i \(0.0847775\pi\)
\(60\) 0 0
\(61\) 6.80717 + 6.80717i 0.871569 + 0.871569i 0.992643 0.121074i \(-0.0386339\pi\)
−0.121074 + 0.992643i \(0.538634\pi\)
\(62\) 0 0
\(63\) 8.70871 1.09719
\(64\) 0 0
\(65\) 6.43381 0.798016
\(66\) 0 0
\(67\) −4.92858 4.92858i −0.602122 0.602122i 0.338754 0.940875i \(-0.389995\pi\)
−0.940875 + 0.338754i \(0.889995\pi\)
\(68\) 0 0
\(69\) −3.54387 + 3.54387i −0.426632 + 0.426632i
\(70\) 0 0
\(71\) 6.19187i 0.734839i 0.930055 + 0.367420i \(0.119759\pi\)
−0.930055 + 0.367420i \(0.880241\pi\)
\(72\) 0 0
\(73\) 8.59924i 1.00647i 0.864151 + 0.503233i \(0.167856\pi\)
−0.864151 + 0.503233i \(0.832144\pi\)
\(74\) 0 0
\(75\) 19.1558 19.1558i 2.21192 2.21192i
\(76\) 0 0
\(77\) 0.764739 + 0.764739i 0.0871502 + 0.0871502i
\(78\) 0 0
\(79\) −7.84435 −0.882558 −0.441279 0.897370i \(-0.645475\pi\)
−0.441279 + 0.897370i \(0.645475\pi\)
\(80\) 0 0
\(81\) −40.7155 −4.52395
\(82\) 0 0
\(83\) 7.43857 + 7.43857i 0.816489 + 0.816489i 0.985598 0.169108i \(-0.0540887\pi\)
−0.169108 + 0.985598i \(0.554089\pi\)
\(84\) 0 0
\(85\) 14.3686 14.3686i 1.55849 1.55849i
\(86\) 0 0
\(87\) 17.2580i 1.85026i
\(88\) 0 0
\(89\) 9.32780i 0.988745i −0.869250 0.494373i \(-0.835398\pi\)
0.869250 0.494373i \(-0.164602\pi\)
\(90\) 0 0
\(91\) 1.26582 1.26582i 0.132694 0.132694i
\(92\) 0 0
\(93\) −11.5040 11.5040i −1.19291 1.19291i
\(94\) 0 0
\(95\) −0.226523 −0.0232407
\(96\) 0 0
\(97\) 0.485578 0.0493030 0.0246515 0.999696i \(-0.492152\pi\)
0.0246515 + 0.999696i \(0.492152\pi\)
\(98\) 0 0
\(99\) −6.65990 6.65990i −0.669345 0.669345i
\(100\) 0 0
\(101\) 4.55780 4.55780i 0.453518 0.453518i −0.443002 0.896521i \(-0.646087\pi\)
0.896521 + 0.443002i \(0.146087\pi\)
\(102\) 0 0
\(103\) 4.26862i 0.420599i −0.977637 0.210300i \(-0.932556\pi\)
0.977637 0.210300i \(-0.0674440\pi\)
\(104\) 0 0
\(105\) 12.2980i 1.20016i
\(106\) 0 0
\(107\) −1.80860 + 1.80860i −0.174844 + 0.174844i −0.789104 0.614260i \(-0.789455\pi\)
0.614260 + 0.789104i \(0.289455\pi\)
\(108\) 0 0
\(109\) −11.0153 11.0153i −1.05507 1.05507i −0.998392 0.0566812i \(-0.981948\pi\)
−0.0566812 0.998392i \(-0.518052\pi\)
\(110\) 0 0
\(111\) 24.6353 2.33828
\(112\) 0 0
\(113\) −11.6345 −1.09449 −0.547243 0.836974i \(-0.684323\pi\)
−0.547243 + 0.836974i \(0.684323\pi\)
\(114\) 0 0
\(115\) 3.72224 + 3.72224i 0.347101 + 0.347101i
\(116\) 0 0
\(117\) −11.0237 + 11.0237i −1.01914 + 1.01914i
\(118\) 0 0
\(119\) 5.65390i 0.518292i
\(120\) 0 0
\(121\) 9.83035i 0.893668i
\(122\) 0 0
\(123\) 18.1527 18.1527i 1.63677 1.63677i
\(124\) 0 0
\(125\) −7.41313 7.41313i −0.663051 0.663051i
\(126\) 0 0
\(127\) −11.7630 −1.04380 −0.521899 0.853007i \(-0.674776\pi\)
−0.521899 + 0.853007i \(0.674776\pi\)
\(128\) 0 0
\(129\) −15.6091 −1.37430
\(130\) 0 0
\(131\) 11.0924 + 11.0924i 0.969152 + 0.969152i 0.999538 0.0303864i \(-0.00967378\pi\)
−0.0303864 + 0.999538i \(0.509674\pi\)
\(132\) 0 0
\(133\) −0.0445673 + 0.0445673i −0.00386447 + 0.00386447i
\(134\) 0 0
\(135\) 70.2059i 6.04236i
\(136\) 0 0
\(137\) 7.47159i 0.638341i −0.947697 0.319170i \(-0.896596\pi\)
0.947697 0.319170i \(-0.103404\pi\)
\(138\) 0 0
\(139\) −0.249091 + 0.249091i −0.0211277 + 0.0211277i −0.717592 0.696464i \(-0.754756\pi\)
0.696464 + 0.717592i \(0.254756\pi\)
\(140\) 0 0
\(141\) 3.68726 + 3.68726i 0.310523 + 0.310523i
\(142\) 0 0
\(143\) −1.93605 −0.161901
\(144\) 0 0
\(145\) −18.1267 −1.50534
\(146\) 0 0
\(147\) −2.41958 2.41958i −0.199563 0.199563i
\(148\) 0 0
\(149\) −4.43030 + 4.43030i −0.362944 + 0.362944i −0.864896 0.501951i \(-0.832616\pi\)
0.501951 + 0.864896i \(0.332616\pi\)
\(150\) 0 0
\(151\) 12.4475i 1.01297i −0.862250 0.506483i \(-0.830945\pi\)
0.862250 0.506483i \(-0.169055\pi\)
\(152\) 0 0
\(153\) 49.2382i 3.98067i
\(154\) 0 0
\(155\) −12.0830 + 12.0830i −0.970531 + 0.970531i
\(156\) 0 0
\(157\) −3.71095 3.71095i −0.296166 0.296166i 0.543344 0.839510i \(-0.317158\pi\)
−0.839510 + 0.543344i \(0.817158\pi\)
\(158\) 0 0
\(159\) −22.5560 −1.78881
\(160\) 0 0
\(161\) 1.46467 0.115432
\(162\) 0 0
\(163\) −5.46072 5.46072i −0.427717 0.427717i 0.460133 0.887850i \(-0.347802\pi\)
−0.887850 + 0.460133i \(0.847802\pi\)
\(164\) 0 0
\(165\) −9.40479 + 9.40479i −0.732162 + 0.732162i
\(166\) 0 0
\(167\) 8.39368i 0.649523i −0.945796 0.324761i \(-0.894716\pi\)
0.945796 0.324761i \(-0.105284\pi\)
\(168\) 0 0
\(169\) 9.79539i 0.753491i
\(170\) 0 0
\(171\) 0.388124 0.388124i 0.0296806 0.0296806i
\(172\) 0 0
\(173\) 8.17036 + 8.17036i 0.621181 + 0.621181i 0.945833 0.324653i \(-0.105247\pi\)
−0.324653 + 0.945833i \(0.605247\pi\)
\(174\) 0 0
\(175\) −7.91700 −0.598469
\(176\) 0 0
\(177\) 26.0765 1.96003
\(178\) 0 0
\(179\) 13.7656 + 13.7656i 1.02889 + 1.02889i 0.999570 + 0.0293209i \(0.00933448\pi\)
0.0293209 + 0.999570i \(0.490666\pi\)
\(180\) 0 0
\(181\) 8.11694 8.11694i 0.603327 0.603327i −0.337867 0.941194i \(-0.609705\pi\)
0.941194 + 0.337867i \(0.109705\pi\)
\(182\) 0 0
\(183\) 32.9410i 2.43507i
\(184\) 0 0
\(185\) 25.8752i 1.90238i
\(186\) 0 0
\(187\) −4.32376 + 4.32376i −0.316185 + 0.316185i
\(188\) 0 0
\(189\) 13.8127 + 13.8127i 1.00472 + 1.00472i
\(190\) 0 0
\(191\) −16.5900 −1.20041 −0.600206 0.799846i \(-0.704915\pi\)
−0.600206 + 0.799846i \(0.704915\pi\)
\(192\) 0 0
\(193\) −1.32261 −0.0952033 −0.0476016 0.998866i \(-0.515158\pi\)
−0.0476016 + 0.998866i \(0.515158\pi\)
\(194\) 0 0
\(195\) 15.5671 + 15.5671i 1.11478 + 1.11478i
\(196\) 0 0
\(197\) −11.5578 + 11.5578i −0.823457 + 0.823457i −0.986602 0.163145i \(-0.947836\pi\)
0.163145 + 0.986602i \(0.447836\pi\)
\(198\) 0 0
\(199\) 26.1422i 1.85317i −0.376081 0.926587i \(-0.622728\pi\)
0.376081 0.926587i \(-0.377272\pi\)
\(200\) 0 0
\(201\) 23.8502i 1.68226i
\(202\) 0 0
\(203\) −3.56633 + 3.56633i −0.250307 + 0.250307i
\(204\) 0 0
\(205\) −19.0664 19.0664i −1.33165 1.33165i
\(206\) 0 0
\(207\) −12.7554 −0.886559
\(208\) 0 0
\(209\) 0.0681647 0.00471505
\(210\) 0 0
\(211\) 17.4835 + 17.4835i 1.20361 + 1.20361i 0.973060 + 0.230551i \(0.0740527\pi\)
0.230551 + 0.973060i \(0.425947\pi\)
\(212\) 0 0
\(213\) −14.9817 + 14.9817i −1.02653 + 1.02653i
\(214\) 0 0
\(215\) 16.3947i 1.11811i
\(216\) 0 0
\(217\) 4.75455i 0.322760i
\(218\) 0 0
\(219\) −20.8065 + 20.8065i −1.40598 + 1.40598i
\(220\) 0 0
\(221\) 7.15683 + 7.15683i 0.481420 + 0.481420i
\(222\) 0 0
\(223\) −9.70637 −0.649987 −0.324993 0.945716i \(-0.605362\pi\)
−0.324993 + 0.945716i \(0.605362\pi\)
\(224\) 0 0
\(225\) 68.9469 4.59646
\(226\) 0 0
\(227\) −16.7964 16.7964i −1.11481 1.11481i −0.992490 0.122323i \(-0.960966\pi\)
−0.122323 0.992490i \(-0.539034\pi\)
\(228\) 0 0
\(229\) 13.1587 13.1587i 0.869555 0.869555i −0.122868 0.992423i \(-0.539209\pi\)
0.992423 + 0.122868i \(0.0392093\pi\)
\(230\) 0 0
\(231\) 3.70069i 0.243488i
\(232\) 0 0
\(233\) 10.7832i 0.706431i −0.935542 0.353216i \(-0.885088\pi\)
0.935542 0.353216i \(-0.114912\pi\)
\(234\) 0 0
\(235\) 3.87284 3.87284i 0.252636 0.252636i
\(236\) 0 0
\(237\) −18.9800 18.9800i −1.23288 1.23288i
\(238\) 0 0
\(239\) 2.08310 0.134745 0.0673724 0.997728i \(-0.478538\pi\)
0.0673724 + 0.997728i \(0.478538\pi\)
\(240\) 0 0
\(241\) −15.8817 −1.02303 −0.511516 0.859274i \(-0.670916\pi\)
−0.511516 + 0.859274i \(0.670916\pi\)
\(242\) 0 0
\(243\) −57.0764 57.0764i −3.66145 3.66145i
\(244\) 0 0
\(245\) −2.54136 + 2.54136i −0.162361 + 0.162361i
\(246\) 0 0
\(247\) 0.112828i 0.00717911i
\(248\) 0 0
\(249\) 35.9964i 2.28118i
\(250\) 0 0
\(251\) −17.1226 + 17.1226i −1.08077 + 1.08077i −0.0843330 + 0.996438i \(0.526876\pi\)
−0.996438 + 0.0843330i \(0.973124\pi\)
\(252\) 0 0
\(253\) −1.12009 1.12009i −0.0704194 0.0704194i
\(254\) 0 0
\(255\) 69.5318 4.35425
\(256\) 0 0
\(257\) −16.3998 −1.02299 −0.511497 0.859285i \(-0.670909\pi\)
−0.511497 + 0.859285i \(0.670909\pi\)
\(258\) 0 0
\(259\) −5.09082 5.09082i −0.316328 0.316328i
\(260\) 0 0
\(261\) 31.0582 31.0582i 1.92245 1.92245i
\(262\) 0 0
\(263\) 24.4978i 1.51060i −0.655379 0.755300i \(-0.727491\pi\)
0.655379 0.755300i \(-0.272509\pi\)
\(264\) 0 0
\(265\) 23.6912i 1.45534i
\(266\) 0 0
\(267\) 22.5693 22.5693i 1.38122 1.38122i
\(268\) 0 0
\(269\) 1.05278 + 1.05278i 0.0641889 + 0.0641889i 0.738472 0.674284i \(-0.235547\pi\)
−0.674284 + 0.738472i \(0.735547\pi\)
\(270\) 0 0
\(271\) 28.0458 1.70366 0.851829 0.523820i \(-0.175493\pi\)
0.851829 + 0.523820i \(0.175493\pi\)
\(272\) 0 0
\(273\) 6.12551 0.370733
\(274\) 0 0
\(275\) 6.05444 + 6.05444i 0.365096 + 0.365096i
\(276\) 0 0
\(277\) −3.59707 + 3.59707i −0.216127 + 0.216127i −0.806864 0.590737i \(-0.798837\pi\)
0.590737 + 0.806864i \(0.298837\pi\)
\(278\) 0 0
\(279\) 41.4060i 2.47891i
\(280\) 0 0
\(281\) 2.33236i 0.139137i −0.997577 0.0695683i \(-0.977838\pi\)
0.997577 0.0695683i \(-0.0221622\pi\)
\(282\) 0 0
\(283\) −4.49397 + 4.49397i −0.267139 + 0.267139i −0.827946 0.560807i \(-0.810491\pi\)
0.560807 + 0.827946i \(0.310491\pi\)
\(284\) 0 0
\(285\) −0.548089 0.548089i −0.0324660 0.0324660i
\(286\) 0 0
\(287\) −7.50243 −0.442854
\(288\) 0 0
\(289\) 14.9666 0.880386
\(290\) 0 0
\(291\) 1.17489 + 1.17489i 0.0688736 + 0.0688736i
\(292\) 0 0
\(293\) −1.02932 + 1.02932i −0.0601334 + 0.0601334i −0.736534 0.676401i \(-0.763539\pi\)
0.676401 + 0.736534i \(0.263539\pi\)
\(294\) 0 0
\(295\) 27.3890i 1.59465i
\(296\) 0 0
\(297\) 21.1262i 1.22587i
\(298\) 0 0
\(299\) −1.85401 + 1.85401i −0.107220 + 0.107220i
\(300\) 0 0
\(301\) 3.22558 + 3.22558i 0.185920 + 0.185920i
\(302\) 0 0
\(303\) 22.0559 1.26708
\(304\) 0 0
\(305\) 34.5989 1.98113
\(306\) 0 0
\(307\) 5.26150 + 5.26150i 0.300290 + 0.300290i 0.841127 0.540837i \(-0.181893\pi\)
−0.540837 + 0.841127i \(0.681893\pi\)
\(308\) 0 0
\(309\) 10.3282 10.3282i 0.587554 0.587554i
\(310\) 0 0
\(311\) 8.74660i 0.495974i −0.968763 0.247987i \(-0.920231\pi\)
0.968763 0.247987i \(-0.0797690\pi\)
\(312\) 0 0
\(313\) 8.77036i 0.495730i 0.968795 + 0.247865i \(0.0797289\pi\)
−0.968795 + 0.247865i \(0.920271\pi\)
\(314\) 0 0
\(315\) 22.1320 22.1320i 1.24699 1.24699i
\(316\) 0 0
\(317\) −15.2046 15.2046i −0.853975 0.853975i 0.136645 0.990620i \(-0.456368\pi\)
−0.990620 + 0.136645i \(0.956368\pi\)
\(318\) 0 0
\(319\) 5.45463 0.305401
\(320\) 0 0
\(321\) −8.75210 −0.488495
\(322\) 0 0
\(323\) −0.251979 0.251979i −0.0140205 0.0140205i
\(324\) 0 0
\(325\) 10.0215 10.0215i 0.555893 0.555893i
\(326\) 0 0
\(327\) 53.3047i 2.94776i
\(328\) 0 0
\(329\) 1.52393i 0.0840167i
\(330\) 0 0
\(331\) −4.92777 + 4.92777i −0.270854 + 0.270854i −0.829444 0.558590i \(-0.811343\pi\)
0.558590 + 0.829444i \(0.311343\pi\)
\(332\) 0 0
\(333\) 44.3345 + 44.3345i 2.42952 + 2.42952i
\(334\) 0 0
\(335\) −25.0506 −1.36866
\(336\) 0 0
\(337\) −12.5793 −0.685237 −0.342619 0.939475i \(-0.611314\pi\)
−0.342619 + 0.939475i \(0.611314\pi\)
\(338\) 0 0
\(339\) −28.1507 28.1507i −1.52893 1.52893i
\(340\) 0 0
\(341\) 3.63599 3.63599i 0.196900 0.196900i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 18.0125i 0.969761i
\(346\) 0 0
\(347\) 3.38504 3.38504i 0.181718 0.181718i −0.610386 0.792104i \(-0.708986\pi\)
0.792104 + 0.610386i \(0.208986\pi\)
\(348\) 0 0
\(349\) 24.8531 + 24.8531i 1.33035 + 1.33035i 0.905051 + 0.425303i \(0.139832\pi\)
0.425303 + 0.905051i \(0.360168\pi\)
\(350\) 0 0
\(351\) −34.9688 −1.86650
\(352\) 0 0
\(353\) 8.70479 0.463309 0.231655 0.972798i \(-0.425586\pi\)
0.231655 + 0.972798i \(0.425586\pi\)
\(354\) 0 0
\(355\) 15.7357 + 15.7357i 0.835167 + 0.835167i
\(356\) 0 0
\(357\) 13.6800 13.6800i 0.724025 0.724025i
\(358\) 0 0
\(359\) 4.04735i 0.213611i 0.994280 + 0.106805i \(0.0340622\pi\)
−0.994280 + 0.106805i \(0.965938\pi\)
\(360\) 0 0
\(361\) 18.9960i 0.999791i
\(362\) 0 0
\(363\) −23.7853 + 23.7853i −1.24840 + 1.24840i
\(364\) 0 0
\(365\) 21.8537 + 21.8537i 1.14388 + 1.14388i
\(366\) 0 0
\(367\) −31.6904 −1.65423 −0.827113 0.562036i \(-0.810018\pi\)
−0.827113 + 0.562036i \(0.810018\pi\)
\(368\) 0 0
\(369\) 65.3365 3.40128
\(370\) 0 0
\(371\) 4.66114 + 4.66114i 0.241994 + 0.241994i
\(372\) 0 0
\(373\) −15.1383 + 15.1383i −0.783830 + 0.783830i −0.980475 0.196645i \(-0.936995\pi\)
0.196645 + 0.980475i \(0.436995\pi\)
\(374\) 0 0
\(375\) 35.8733i 1.85249i
\(376\) 0 0
\(377\) 9.02869i 0.465001i
\(378\) 0 0
\(379\) 13.8140 13.8140i 0.709580 0.709580i −0.256867 0.966447i \(-0.582690\pi\)
0.966447 + 0.256867i \(0.0826903\pi\)
\(380\) 0 0
\(381\) −28.4615 28.4615i −1.45813 1.45813i
\(382\) 0 0
\(383\) 17.3513 0.886610 0.443305 0.896371i \(-0.353806\pi\)
0.443305 + 0.896371i \(0.353806\pi\)
\(384\) 0 0
\(385\) 3.88695 0.198097
\(386\) 0 0
\(387\) −28.0907 28.0907i −1.42793 1.42793i
\(388\) 0 0
\(389\) −17.8880 + 17.8880i −0.906958 + 0.906958i −0.996026 0.0890675i \(-0.971611\pi\)
0.0890675 + 0.996026i \(0.471611\pi\)
\(390\) 0 0
\(391\) 8.28108i 0.418792i
\(392\) 0 0
\(393\) 53.6781i 2.70770i
\(394\) 0 0
\(395\) −19.9353 + 19.9353i −1.00305 + 1.00305i
\(396\) 0 0
\(397\) −4.35521 4.35521i −0.218582 0.218582i 0.589319 0.807900i \(-0.299396\pi\)
−0.807900 + 0.589319i \(0.799396\pi\)
\(398\) 0 0
\(399\) −0.215668 −0.0107969
\(400\) 0 0
\(401\) 17.6318 0.880492 0.440246 0.897877i \(-0.354891\pi\)
0.440246 + 0.897877i \(0.354891\pi\)
\(402\) 0 0
\(403\) −6.01842 6.01842i −0.299799 0.299799i
\(404\) 0 0
\(405\) −103.473 + 103.473i −5.14160 + 5.14160i
\(406\) 0 0
\(407\) 7.78631i 0.385953i
\(408\) 0 0
\(409\) 24.7264i 1.22264i −0.791383 0.611320i \(-0.790639\pi\)
0.791383 0.611320i \(-0.209361\pi\)
\(410\) 0 0
\(411\) 18.0781 18.0781i 0.891726 0.891726i
\(412\) 0 0
\(413\) −5.38865 5.38865i −0.265158 0.265158i
\(414\) 0 0
\(415\) 37.8081 1.85593
\(416\) 0 0
\(417\) −1.20539 −0.0590283
\(418\) 0 0
\(419\) −1.67364 1.67364i −0.0817626 0.0817626i 0.665043 0.746805i \(-0.268413\pi\)
−0.746805 + 0.665043i \(0.768413\pi\)
\(420\) 0 0
\(421\) 22.2705 22.2705i 1.08540 1.08540i 0.0894016 0.995996i \(-0.471505\pi\)
0.995996 0.0894016i \(-0.0284955\pi\)
\(422\) 0 0
\(423\) 13.2714i 0.645279i
\(424\) 0 0
\(425\) 44.7619i 2.17127i
\(426\) 0 0
\(427\) 6.80717 6.80717i 0.329422 0.329422i
\(428\) 0 0
\(429\) −4.68442 4.68442i −0.226166 0.226166i
\(430\) 0 0
\(431\) −23.0028 −1.10800 −0.554002 0.832515i \(-0.686900\pi\)
−0.554002 + 0.832515i \(0.686900\pi\)
\(432\) 0 0
\(433\) −1.31078 −0.0629921 −0.0314960 0.999504i \(-0.510027\pi\)
−0.0314960 + 0.999504i \(0.510027\pi\)
\(434\) 0 0
\(435\) −43.8588 43.8588i −2.10287 2.10287i
\(436\) 0 0
\(437\) 0.0652762 0.0652762i 0.00312258 0.00312258i
\(438\) 0 0
\(439\) 36.2799i 1.73155i 0.500437 + 0.865773i \(0.333173\pi\)
−0.500437 + 0.865773i \(0.666827\pi\)
\(440\) 0 0
\(441\) 8.70871i 0.414701i
\(442\) 0 0
\(443\) 9.57493 9.57493i 0.454918 0.454918i −0.442065 0.896983i \(-0.645754\pi\)
0.896983 + 0.442065i \(0.145754\pi\)
\(444\) 0 0
\(445\) −23.7053 23.7053i −1.12374 1.12374i
\(446\) 0 0
\(447\) −21.4389 −1.01403
\(448\) 0 0
\(449\) −3.60363 −0.170066 −0.0850329 0.996378i \(-0.527100\pi\)
−0.0850329 + 0.996378i \(0.527100\pi\)
\(450\) 0 0
\(451\) 5.73740 + 5.73740i 0.270164 + 0.270164i
\(452\) 0 0
\(453\) 30.1178 30.1178i 1.41506 1.41506i
\(454\) 0 0
\(455\) 6.43381i 0.301622i
\(456\) 0 0
\(457\) 6.35277i 0.297170i −0.988900 0.148585i \(-0.952528\pi\)
0.988900 0.148585i \(-0.0474719\pi\)
\(458\) 0 0
\(459\) −78.0955 + 78.0955i −3.64518 + 3.64518i
\(460\) 0 0
\(461\) −4.16339 4.16339i −0.193908 0.193908i 0.603474 0.797383i \(-0.293783\pi\)
−0.797383 + 0.603474i \(0.793783\pi\)
\(462\) 0 0
\(463\) −12.7205 −0.591171 −0.295585 0.955316i \(-0.595515\pi\)
−0.295585 + 0.955316i \(0.595515\pi\)
\(464\) 0 0
\(465\) −58.4716 −2.71156
\(466\) 0 0
\(467\) 15.4085 + 15.4085i 0.713022 + 0.713022i 0.967166 0.254145i \(-0.0817939\pi\)
−0.254145 + 0.967166i \(0.581794\pi\)
\(468\) 0 0
\(469\) −4.92858 + 4.92858i −0.227581 + 0.227581i
\(470\) 0 0
\(471\) 17.9579i 0.827455i
\(472\) 0 0
\(473\) 4.93346i 0.226841i
\(474\) 0 0
\(475\) −0.352839 + 0.352839i −0.0161894 + 0.0161894i
\(476\) 0 0
\(477\) −40.5925 40.5925i −1.85860 1.85860i
\(478\) 0 0
\(479\) −26.3235 −1.20275 −0.601375 0.798967i \(-0.705380\pi\)
−0.601375 + 0.798967i \(0.705380\pi\)
\(480\) 0 0
\(481\) 12.8882 0.587649
\(482\) 0 0
\(483\) 3.54387 + 3.54387i 0.161252 + 0.161252i
\(484\) 0 0
\(485\) 1.23403 1.23403i 0.0560343 0.0560343i
\(486\) 0 0
\(487\) 4.62575i 0.209613i −0.994493 0.104806i \(-0.966578\pi\)
0.994493 0.104806i \(-0.0334223\pi\)
\(488\) 0 0
\(489\) 26.4253i 1.19499i
\(490\) 0 0
\(491\) 2.74222 2.74222i 0.123754 0.123754i −0.642517 0.766271i \(-0.722110\pi\)
0.766271 + 0.642517i \(0.222110\pi\)
\(492\) 0 0
\(493\) −20.1637 20.1637i −0.908126 0.908126i
\(494\) 0 0
\(495\) −33.8504 −1.52146
\(496\) 0 0
\(497\) 6.19187 0.277743
\(498\) 0 0
\(499\) 0.703246 + 0.703246i 0.0314816 + 0.0314816i 0.722672 0.691191i \(-0.242914\pi\)
−0.691191 + 0.722672i \(0.742914\pi\)
\(500\) 0 0
\(501\) 20.3092 20.3092i 0.907347 0.907347i
\(502\) 0 0
\(503\) 23.3204i 1.03980i 0.854226 + 0.519902i \(0.174032\pi\)
−0.854226 + 0.519902i \(0.825968\pi\)
\(504\) 0 0
\(505\) 23.1660i 1.03087i
\(506\) 0 0
\(507\) 23.7007 23.7007i 1.05259 1.05259i
\(508\) 0 0
\(509\) 4.80305 + 4.80305i 0.212891 + 0.212891i 0.805495 0.592603i \(-0.201900\pi\)
−0.592603 + 0.805495i \(0.701900\pi\)
\(510\) 0 0
\(511\) 8.59924 0.380408
\(512\) 0 0
\(513\) 1.23119 0.0543582
\(514\) 0 0
\(515\) −10.8481 10.8481i −0.478024 0.478024i
\(516\) 0 0
\(517\) −1.16541 + 1.16541i −0.0512545 + 0.0512545i
\(518\) 0 0
\(519\) 39.5376i 1.73551i
\(520\) 0 0
\(521\) 33.2330i 1.45596i 0.685596 + 0.727982i \(0.259542\pi\)
−0.685596 + 0.727982i \(0.740458\pi\)
\(522\) 0 0
\(523\) 20.4284 20.4284i 0.893271 0.893271i −0.101559 0.994830i \(-0.532383\pi\)
0.994830 + 0.101559i \(0.0323830\pi\)
\(524\) 0 0
\(525\) −19.1558 19.1558i −0.836027 0.836027i
\(526\) 0 0
\(527\) −26.8818 −1.17099
\(528\) 0 0
\(529\) 20.8548 0.906728
\(530\) 0 0
\(531\) 46.9282 + 46.9282i 2.03651 + 2.03651i
\(532\) 0 0
\(533\) 9.49674 9.49674i 0.411350 0.411350i
\(534\) 0 0
\(535\) 9.19260i 0.397431i
\(536\) 0 0
\(537\) 66.6140i 2.87461i
\(538\) 0 0
\(539\) 0.764739 0.764739i 0.0329397 0.0329397i
\(540\) 0 0
\(541\) 3.50325 + 3.50325i 0.150617 + 0.150617i 0.778393 0.627777i \(-0.216035\pi\)
−0.627777 + 0.778393i \(0.716035\pi\)
\(542\) 0 0
\(543\) 39.2791 1.68563
\(544\) 0 0
\(545\) −55.9876 −2.39824
\(546\) 0 0
\(547\) 21.9766 + 21.9766i 0.939652 + 0.939652i 0.998280 0.0586277i \(-0.0186725\pi\)
−0.0586277 + 0.998280i \(0.518672\pi\)
\(548\) 0 0
\(549\) −59.2817 + 59.2817i −2.53008 + 2.53008i
\(550\) 0 0
\(551\) 0.317883i 0.0135423i
\(552\) 0 0
\(553\) 7.84435i 0.333576i
\(554\) 0 0
\(555\) 62.6071 62.6071i 2.65752 2.65752i
\(556\) 0 0
\(557\) 4.25629 + 4.25629i 0.180345 + 0.180345i 0.791506 0.611161i \(-0.209297\pi\)
−0.611161 + 0.791506i \(0.709297\pi\)
\(558\) 0 0
\(559\) −8.16603 −0.345386
\(560\) 0 0
\(561\) −20.9233 −0.883384
\(562\) 0 0
\(563\) −8.97634 8.97634i −0.378307 0.378307i 0.492184 0.870491i \(-0.336199\pi\)
−0.870491 + 0.492184i \(0.836199\pi\)
\(564\) 0 0
\(565\) −29.5675 + 29.5675i −1.24392 + 1.24392i
\(566\) 0 0
\(567\) 40.7155i 1.70989i
\(568\) 0 0
\(569\) 12.3968i 0.519701i −0.965649 0.259851i \(-0.916327\pi\)
0.965649 0.259851i \(-0.0836733\pi\)
\(570\) 0 0
\(571\) 5.24097 5.24097i 0.219328 0.219328i −0.588887 0.808215i \(-0.700434\pi\)
0.808215 + 0.588887i \(0.200434\pi\)
\(572\) 0 0
\(573\) −40.1408 40.1408i −1.67691 1.67691i
\(574\) 0 0
\(575\) 11.5958 0.483577
\(576\) 0 0
\(577\) 43.5232 1.81189 0.905947 0.423390i \(-0.139160\pi\)
0.905947 + 0.423390i \(0.139160\pi\)
\(578\) 0 0
\(579\) −3.20015 3.20015i −0.132994 0.132994i
\(580\) 0 0
\(581\) 7.43857 7.43857i 0.308604 0.308604i
\(582\) 0 0
\(583\) 7.12912i 0.295258i
\(584\) 0 0
\(585\) 56.0302i 2.31657i
\(586\) 0 0
\(587\) −2.64923 + 2.64923i −0.109346 + 0.109346i −0.759663 0.650317i \(-0.774636\pi\)
0.650317 + 0.759663i \(0.274636\pi\)
\(588\) 0 0
\(589\) 0.211897 + 0.211897i 0.00873108 + 0.00873108i
\(590\) 0 0
\(591\) −55.9299 −2.30065
\(592\) 0 0
\(593\) 5.12318 0.210384 0.105192 0.994452i \(-0.466454\pi\)
0.105192 + 0.994452i \(0.466454\pi\)
\(594\) 0 0
\(595\) −14.3686 14.3686i −0.589054 0.589054i
\(596\) 0 0
\(597\) 63.2532 63.2532i 2.58878 2.58878i
\(598\) 0 0
\(599\) 39.6945i 1.62187i 0.585135 + 0.810936i \(0.301041\pi\)
−0.585135 + 0.810936i \(0.698959\pi\)
\(600\) 0 0
\(601\) 19.6274i 0.800620i 0.916380 + 0.400310i \(0.131097\pi\)
−0.916380 + 0.400310i \(0.868903\pi\)
\(602\) 0 0
\(603\) 42.9216 42.9216i 1.74790 1.74790i
\(604\) 0 0
\(605\) 24.9824 + 24.9824i 1.01568 + 1.01568i
\(606\) 0 0
\(607\) 25.7837 1.04653 0.523264 0.852170i \(-0.324714\pi\)
0.523264 + 0.852170i \(0.324714\pi\)
\(608\) 0 0
\(609\) −17.2580 −0.699331
\(610\) 0 0
\(611\) 1.92902 + 1.92902i 0.0780397 + 0.0780397i
\(612\) 0 0
\(613\) −4.09160 + 4.09160i −0.165258 + 0.165258i −0.784891 0.619633i \(-0.787281\pi\)
0.619633 + 0.784891i \(0.287281\pi\)
\(614\) 0 0
\(615\) 92.2651i 3.72049i
\(616\) 0 0
\(617\) 10.4658i 0.421337i −0.977558 0.210668i \(-0.932436\pi\)
0.977558 0.210668i \(-0.0675640\pi\)
\(618\) 0 0
\(619\) 21.5251 21.5251i 0.865166 0.865166i −0.126766 0.991933i \(-0.540460\pi\)
0.991933 + 0.126766i \(0.0404599\pi\)
\(620\) 0 0
\(621\) −20.2310 20.2310i −0.811841 0.811841i
\(622\) 0 0
\(623\) −9.32780 −0.373711
\(624\) 0 0
\(625\) 1.90615 0.0762459
\(626\) 0 0
\(627\) 0.164930 + 0.164930i 0.00658666 + 0.00658666i
\(628\) 0 0
\(629\) 28.7830 28.7830i 1.14765 1.14765i
\(630\) 0 0
\(631\) 0.948167i 0.0377459i −0.999822 0.0188730i \(-0.993992\pi\)
0.999822 0.0188730i \(-0.00600781\pi\)
\(632\) 0 0
\(633\) 84.6052i 3.36275i
\(634\) 0 0
\(635\) −29.8940 + 29.8940i −1.18631 + 1.18631i
\(636\) 0 0
\(637\) −1.26582 1.26582i −0.0501537 0.0501537i
\(638\) 0 0
\(639\) −53.9232 −2.13317
\(640\) 0 0
\(641\) 12.1984 0.481808 0.240904 0.970549i \(-0.422556\pi\)
0.240904 + 0.970549i \(0.422556\pi\)
\(642\) 0 0
\(643\) −35.6860 35.6860i −1.40732 1.40732i −0.773402 0.633916i \(-0.781446\pi\)
−0.633916 0.773402i \(-0.718554\pi\)
\(644\) 0 0
\(645\) −39.6683 + 39.6683i −1.56194 + 1.56194i
\(646\) 0 0
\(647\) 29.4906i 1.15939i 0.814832 + 0.579697i \(0.196829\pi\)
−0.814832 + 0.579697i \(0.803171\pi\)
\(648\) 0 0
\(649\) 8.24183i 0.323520i
\(650\) 0 0
\(651\) −11.5040 + 11.5040i −0.450878 + 0.450878i
\(652\) 0 0
\(653\) 30.8952 + 30.8952i 1.20902 + 1.20902i 0.971344 + 0.237679i \(0.0763868\pi\)
0.237679 + 0.971344i \(0.423613\pi\)
\(654\) 0 0
\(655\) 56.3798 2.20294
\(656\) 0 0
\(657\) −74.8883 −2.92167
\(658\) 0 0
\(659\) −12.6158 12.6158i −0.491443 0.491443i 0.417317 0.908761i \(-0.362970\pi\)
−0.908761 + 0.417317i \(0.862970\pi\)
\(660\) 0 0
\(661\) 20.5214 20.5214i 0.798189 0.798189i −0.184621 0.982810i \(-0.559106\pi\)
0.982810 + 0.184621i \(0.0591057\pi\)
\(662\) 0 0
\(663\) 34.6330i 1.34503i
\(664\) 0 0
\(665\) 0.226523i 0.00878418i
\(666\) 0 0
\(667\) 5.22349 5.22349i 0.202254 0.202254i
\(668\) 0 0
\(669\) −23.4853 23.4853i −0.907995 0.907995i
\(670\) 0 0
\(671\) −10.4114 −0.401929
\(672\) 0 0
\(673\) 19.4620 0.750205 0.375103 0.926983i \(-0.377607\pi\)
0.375103 + 0.926983i \(0.377607\pi\)
\(674\) 0 0
\(675\) 109.355 + 109.355i 4.20907 + 4.20907i
\(676\) 0 0
\(677\) 3.68505 3.68505i 0.141628 0.141628i −0.632738 0.774366i \(-0.718069\pi\)
0.774366 + 0.632738i \(0.218069\pi\)
\(678\) 0 0
\(679\) 0.485578i 0.0186348i
\(680\) 0 0
\(681\) 81.2802i 3.11466i
\(682\) 0 0
\(683\) 0.819191 0.819191i 0.0313455 0.0313455i −0.691260 0.722606i \(-0.742944\pi\)
0.722606 + 0.691260i \(0.242944\pi\)
\(684\) 0 0
\(685\) −18.9880 18.9880i −0.725493 0.725493i
\(686\) 0 0
\(687\) 63.6772 2.42944
\(688\) 0 0
\(689\) −11.8003 −0.449558
\(690\) 0 0
\(691\) −9.07535 9.07535i −0.345243 0.345243i 0.513091 0.858334i \(-0.328500\pi\)
−0.858334 + 0.513091i \(0.828500\pi\)
\(692\) 0 0
\(693\) −6.65990 + 6.65990i −0.252989 + 0.252989i
\(694\) 0 0
\(695\) 1.26606i 0.0480244i
\(696\) 0 0
\(697\) 42.4180i 1.60670i
\(698\) 0 0
\(699\) 26.0908 26.0908i 0.986845 0.986845i
\(700\) 0 0
\(701\) −22.5919 22.5919i −0.853286 0.853286i 0.137250 0.990536i \(-0.456173\pi\)
−0.990536 + 0.137250i \(0.956173\pi\)
\(702\) 0 0
\(703\) −0.453768 −0.0171142
\(704\) 0 0
\(705\) 18.7413 0.705837
\(706\) 0 0
\(707\) −4.55780 4.55780i −0.171414 0.171414i
\(708\) 0 0
\(709\) −13.6206 + 13.6206i −0.511532 + 0.511532i −0.914996 0.403464i \(-0.867806\pi\)
0.403464 + 0.914996i \(0.367806\pi\)
\(710\) 0 0
\(711\) 68.3142i 2.56198i
\(712\) 0 0
\(713\) 6.96383i 0.260798i
\(714\) 0 0
\(715\) −4.92019 + 4.92019i −0.184005 + 0.184005i
\(716\) 0 0
\(717\) 5.04023 + 5.04023i 0.188231 + 0.188231i
\(718\) 0 0
\(719\) −25.9785 −0.968836 −0.484418 0.874837i \(-0.660969\pi\)
−0.484418 + 0.874837i \(0.660969\pi\)
\(720\) 0 0
\(721\) −4.26862 −0.158972
\(722\) 0 0
\(723\) −38.4271 38.4271i −1.42912 1.42912i
\(724\) 0 0
\(725\) −28.2346 + 28.2346i −1.04861 + 1.04861i
\(726\) 0 0
\(727\) 27.5763i 1.02275i −0.859358 0.511375i \(-0.829136\pi\)
0.859358 0.511375i \(-0.170864\pi\)
\(728\) 0 0
\(729\) 154.055i 5.70574i
\(730\) 0 0
\(731\) −18.2371 + 18.2371i −0.674524 + 0.674524i
\(732\) 0 0
\(733\) 30.1992 + 30.1992i 1.11543 + 1.11543i 0.992403 + 0.123029i \(0.0392609\pi\)
0.123029 + 0.992403i \(0.460739\pi\)
\(734\) 0 0
\(735\) −12.2980 −0.453619
\(736\) 0 0
\(737\) 7.53816 0.277672
\(738\) 0 0
\(739\) 36.5445 + 36.5445i 1.34431 + 1.34431i 0.891718 + 0.452592i \(0.149501\pi\)
0.452592 + 0.891718i \(0.350499\pi\)
\(740\) 0 0
\(741\) 0.272997 0.272997i 0.0100288 0.0100288i
\(742\) 0 0
\(743\) 43.1375i 1.58256i 0.611452 + 0.791281i \(0.290586\pi\)
−0.611452 + 0.791281i \(0.709414\pi\)
\(744\) 0 0
\(745\) 22.5180i 0.824994i
\(746\) 0 0
\(747\) −64.7804 + 64.7804i −2.37019 + 2.37019i
\(748\) 0 0
\(749\) 1.80860 + 1.80860i 0.0660848 + 0.0660848i
\(750\) 0 0
\(751\) 9.04305 0.329986 0.164993 0.986295i \(-0.447240\pi\)
0.164993 + 0.986295i \(0.447240\pi\)
\(752\) 0 0
\(753\) −82.8591 −3.01955
\(754\) 0 0
\(755\) −31.6336 31.6336i −1.15126 1.15126i
\(756\) 0 0
\(757\) 1.07442 1.07442i 0.0390505 0.0390505i −0.687312 0.726362i \(-0.741209\pi\)
0.726362 + 0.687312i \(0.241209\pi\)
\(758\) 0 0
\(759\) 5.42028i 0.196744i
\(760\) 0 0
\(761\) 34.1138i 1.23662i −0.785932 0.618312i \(-0.787817\pi\)
0.785932 0.618312i \(-0.212183\pi\)
\(762\) 0 0
\(763\) −11.0153 + 11.0153i −0.398780 + 0.398780i
\(764\) 0 0
\(765\) 125.132 + 125.132i 4.52415 + 4.52415i
\(766\) 0 0
\(767\) 13.6422 0.492590
\(768\) 0 0
\(769\) −54.2612 −1.95671 −0.978354 0.206939i \(-0.933650\pi\)
−0.978354 + 0.206939i \(0.933650\pi\)
\(770\) 0 0
\(771\) −39.6807 39.6807i −1.42906 1.42906i
\(772\) 0 0
\(773\) −25.6779 + 25.6779i −0.923571 + 0.923571i −0.997280 0.0737087i \(-0.976516\pi\)
0.0737087 + 0.997280i \(0.476516\pi\)
\(774\) 0 0
\(775\) 37.6418i 1.35213i
\(776\) 0 0
\(777\) 24.6353i 0.883786i
\(778\) 0 0
\(779\) −0.334363 + 0.334363i −0.0119798 + 0.0119798i
\(780\) 0 0
\(781\) −4.73517 4.73517i −0.169438 0.169438i
\(782\) 0 0
\(783\) 98.5212 3.52086
\(784\) 0 0
\(785\) −18.8617 −0.673203
\(786\) 0 0
\(787\) 16.3479 + 16.3479i 0.582741 + 0.582741i 0.935656 0.352914i \(-0.114809\pi\)
−0.352914 + 0.935656i \(0.614809\pi\)
\(788\) 0 0
\(789\) 59.2744 59.2744i 2.11022 2.11022i
\(790\) 0 0
\(791\) 11.6345i 0.413677i
\(792\) 0 0
\(793\) 17.2333i 0.611974i
\(794\) 0 0
\(795\) −57.3228 + 57.3228i −2.03303 + 2.03303i
\(796\) 0 0
\(797\) 29.8211 + 29.8211i 1.05632 + 1.05632i 0.998317 + 0.0580002i \(0.0184724\pi\)
0.0580002 + 0.998317i \(0.481528\pi\)
\(798\) 0 0
\(799\) 8.61612