Properties

Label 1792.2.m.h.449.8
Level $1792$
Weight $2$
Character 1792.449
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 449.8
Root \(0.117630 - 0.893490i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.h.1345.8

$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

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

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 0.588304 0.808640i \(-0.299796\pi\)
0.808640 0.588304i \(-0.200204\pi\)
\(4\) 0 0
\(5\) 2.54136 + 2.54136i 1.13653 + 1.13653i 0.989068 + 0.147462i \(0.0471104\pi\)
0.147462 + 0.989068i \(0.452890\pi\)
\(6\) 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 0.582356 0.812934i \(-0.302131\pi\)
−0.812934 + 0.582356i \(0.802131\pi\)
\(12\) 0 0
\(13\) 1.26582 1.26582i 0.351076 0.351076i −0.509434 0.860510i \(-0.670145\pi\)
0.860510 + 0.509434i \(0.170145\pi\)
\(14\) 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 −0.712201 0.701976i \(-0.752301\pi\)
0.701976 + 0.712201i \(0.252301\pi\)
\(20\) 0 0
\(21\) 2.41958 + 2.41958i 0.527995 + 0.527995i
\(22\) 0 0
\(23\) 1.46467i 0.305404i −0.988272 0.152702i \(-0.951203\pi\)
0.988272 0.152702i \(-0.0487975\pi\)
\(24\) 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 −0.955910 0.293659i \(-0.905127\pi\)
0.293659 + 0.955910i \(0.405127\pi\)
\(30\) 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 0.988453 0.151527i \(-0.0484190\pi\)
−0.151527 + 0.988453i \(0.548419\pi\)
\(38\) 0 0
\(39\) 6.12551i 0.980867i
\(40\) 0 0
\(41\) 7.50243i 1.17168i 0.810426 + 0.585841i \(0.199236\pi\)
−0.810426 + 0.585841i \(0.800764\pi\)
\(42\) 0 0
\(43\) −3.22558 3.22558i −0.491897 0.491897i 0.417007 0.908903i \(-0.363079\pi\)
−0.908903 + 0.417007i \(0.863079\pi\)
\(44\) 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 0.310362 0.950619i \(-0.399550\pi\)
−0.950619 + 0.310362i \(0.899550\pi\)
\(54\) 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 0.964742 0.263199i \(-0.0847775\pi\)
−0.263199 + 0.964742i \(0.584777\pi\)
\(60\) 0 0
\(61\) 6.80717 6.80717i 0.871569 0.871569i −0.121074 0.992643i \(-0.538634\pi\)
0.992643 + 0.121074i \(0.0386339\pi\)
\(62\) 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 −0.940875 0.338754i \(-0.889995\pi\)
0.338754 + 0.940875i \(0.389995\pi\)
\(68\) 0 0
\(69\) −3.54387 3.54387i −0.426632 0.426632i
\(70\) 0 0
\(71\) 6.19187i 0.734839i −0.930055 0.367420i \(-0.880241\pi\)
0.930055 0.367420i \(-0.119759\pi\)
\(72\) 0 0
\(73\) 8.59924i 1.00647i −0.864151 0.503233i \(-0.832144\pi\)
0.864151 0.503233i \(-0.167856\pi\)
\(74\) 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 −0.169108 0.985598i \(-0.554089\pi\)
0.985598 + 0.169108i \(0.0540887\pi\)
\(84\) 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 \(0.164602\pi\)
−0.869250 + 0.494373i \(0.835398\pi\)
\(90\) 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 0.896521 0.443002i \(-0.146087\pi\)
−0.443002 + 0.896521i \(0.646087\pi\)
\(102\) 0 0
\(103\) 4.26862i 0.420599i 0.977637 + 0.210300i \(0.0674440\pi\)
−0.977637 + 0.210300i \(0.932556\pi\)
\(104\) 0 0
\(105\) 12.2980i 1.20016i
\(106\) 0 0
\(107\) −1.80860 1.80860i −0.174844 0.174844i 0.614260 0.789104i \(-0.289455\pi\)
−0.789104 + 0.614260i \(0.789455\pi\)
\(108\) 0 0
\(109\) −11.0153 + 11.0153i −1.05507 + 1.05507i −0.0566812 + 0.998392i \(0.518052\pi\)
−0.998392 + 0.0566812i \(0.981948\pi\)
\(110\) 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 −0.0303864 0.999538i \(-0.509674\pi\)
0.999538 + 0.0303864i \(0.00967378\pi\)
\(132\) 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 \(0.103404\pi\)
−0.947697 + 0.319170i \(0.896596\pi\)
\(138\) 0 0
\(139\) −0.249091 0.249091i −0.0211277 0.0211277i 0.696464 0.717592i \(-0.254756\pi\)
−0.717592 + 0.696464i \(0.754756\pi\)
\(140\) 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 0.501951 0.864896i \(-0.332616\pi\)
−0.864896 + 0.501951i \(0.832616\pi\)
\(150\) 0 0
\(151\) 12.4475i 1.01297i 0.862250 + 0.506483i \(0.169055\pi\)
−0.862250 + 0.506483i \(0.830945\pi\)
\(152\) 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 −0.839510 0.543344i \(-0.817158\pi\)
0.543344 + 0.839510i \(0.317158\pi\)
\(158\) 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 −0.887850 0.460133i \(-0.847802\pi\)
0.460133 + 0.887850i \(0.347802\pi\)
\(164\) 0 0
\(165\) −9.40479 9.40479i −0.732162 0.732162i
\(166\) 0 0
\(167\) 8.39368i 0.649523i 0.945796 + 0.324761i \(0.105284\pi\)
−0.945796 + 0.324761i \(0.894716\pi\)
\(168\) 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 −0.324653 0.945833i \(-0.605247\pi\)
0.945833 + 0.324653i \(0.105247\pi\)
\(174\) 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 0.0293209 0.999570i \(-0.490666\pi\)
0.999570 0.0293209i \(-0.00933448\pi\)
\(180\) 0 0
\(181\) 8.11694 + 8.11694i 0.603327 + 0.603327i 0.941194 0.337867i \(-0.109705\pi\)
−0.337867 + 0.941194i \(0.609705\pi\)
\(182\) 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 0.163145 0.986602i \(-0.447836\pi\)
−0.986602 + 0.163145i \(0.947836\pi\)
\(198\) 0 0
\(199\) 26.1422i 1.85317i 0.376081 + 0.926587i \(0.377272\pi\)
−0.376081 + 0.926587i \(0.622728\pi\)
\(200\) 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 0.230551 0.973060i \(-0.425947\pi\)
0.973060 0.230551i \(-0.0740527\pi\)
\(212\) 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 −0.122323 + 0.992490i \(0.539034\pi\)
−0.992490 + 0.122323i \(0.960966\pi\)
\(228\) 0 0
\(229\) 13.1587 + 13.1587i 0.869555 + 0.869555i 0.992423 0.122868i \(-0.0392093\pi\)
−0.122868 + 0.992423i \(0.539209\pi\)
\(230\) 0 0
\(231\) 3.70069i 0.243488i
\(232\) 0 0
\(233\) 10.7832i 0.706431i 0.935542 + 0.353216i \(0.114912\pi\)
−0.935542 + 0.353216i \(0.885088\pi\)
\(234\) 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 −0.996438 0.0843330i \(-0.973124\pi\)
−0.0843330 0.996438i \(-0.526876\pi\)
\(252\) 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 \(0.272509\pi\)
−0.655379 + 0.755300i \(0.727491\pi\)
\(264\) 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 −0.674284 0.738472i \(-0.735547\pi\)
0.738472 + 0.674284i \(0.235547\pi\)
\(270\) 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 0.590737 0.806864i \(-0.298837\pi\)
−0.806864 + 0.590737i \(0.798837\pi\)
\(278\) 0 0
\(279\) 41.4060i 2.47891i
\(280\) 0 0
\(281\) 2.33236i 0.139137i 0.997577 + 0.0695683i \(0.0221622\pi\)
−0.997577 + 0.0695683i \(0.977838\pi\)
\(282\) 0 0
\(283\) −4.49397 4.49397i −0.267139 0.267139i 0.560807 0.827946i \(-0.310491\pi\)
−0.827946 + 0.560807i \(0.810491\pi\)
\(284\) 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 0.676401 0.736534i \(-0.263539\pi\)
−0.736534 + 0.676401i \(0.763539\pi\)
\(294\) 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 −0.540837 0.841127i \(-0.681893\pi\)
0.841127 + 0.540837i \(0.181893\pi\)
\(308\) 0 0
\(309\) 10.3282 + 10.3282i 0.587554 + 0.587554i
\(310\) 0 0
\(311\) 8.74660i 0.495974i 0.968763 + 0.247987i \(0.0797690\pi\)
−0.968763 + 0.247987i \(0.920231\pi\)
\(312\) 0 0
\(313\) 8.77036i 0.495730i −0.968795 0.247865i \(-0.920271\pi\)
0.968795 0.247865i \(-0.0797289\pi\)
\(314\) 0 0
\(315\) 22.1320 + 22.1320i 1.24699 + 1.24699i
\(316\) 0 0
\(317\) −15.2046 + 15.2046i −0.853975 + 0.853975i −0.990620 0.136645i \(-0.956368\pi\)
0.136645 + 0.990620i \(0.456368\pi\)
\(318\) 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 0.558590 0.829444i \(-0.311343\pi\)
−0.829444 + 0.558590i \(0.811343\pi\)
\(332\) 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 0.792104 0.610386i \(-0.208986\pi\)
−0.610386 + 0.792104i \(0.708986\pi\)
\(348\) 0 0
\(349\) 24.8531 24.8531i 1.33035 1.33035i 0.425303 0.905051i \(-0.360168\pi\)
0.905051 0.425303i \(-0.139832\pi\)
\(350\) 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 \(-0.965938\pi\)
0.994280 0.106805i \(-0.0340622\pi\)
\(360\) 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 0.196645 0.980475i \(-0.436995\pi\)
−0.980475 + 0.196645i \(0.936995\pi\)
\(374\) 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 0.966447 0.256867i \(-0.0826903\pi\)
−0.256867 + 0.966447i \(0.582690\pi\)
\(380\) 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 0.0890675 0.996026i \(-0.471611\pi\)
−0.996026 + 0.0890675i \(0.971611\pi\)
\(390\) 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 −0.807900 0.589319i \(-0.799396\pi\)
0.589319 + 0.807900i \(0.299396\pi\)
\(398\) 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 \(0.209361\pi\)
−0.791383 + 0.611320i \(0.790639\pi\)
\(410\) 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 −0.746805 0.665043i \(-0.768413\pi\)
0.665043 + 0.746805i \(0.268413\pi\)
\(420\) 0 0
\(421\) 22.2705 + 22.2705i 1.08540 + 1.08540i 0.995996 + 0.0894016i \(0.0284955\pi\)
0.0894016 + 0.995996i \(0.471505\pi\)
\(422\) 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 \(-0.666827\pi\)
0.500437 0.865773i \(-0.333173\pi\)
\(440\) 0 0
\(441\) 8.70871i 0.414701i
\(442\) 0 0
\(443\) 9.57493 + 9.57493i 0.454918 + 0.454918i 0.896983 0.442065i \(-0.145754\pi\)
−0.442065 + 0.896983i \(0.645754\pi\)
\(444\) 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 \(0.0474719\pi\)
−0.988900 + 0.148585i \(0.952528\pi\)
\(458\) 0 0
\(459\) −78.0955 78.0955i −3.64518 3.64518i
\(460\) 0 0
\(461\) −4.16339 + 4.16339i −0.193908 + 0.193908i −0.797383 0.603474i \(-0.793783\pi\)
0.603474 + 0.797383i \(0.293783\pi\)
\(462\) 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 −0.254145 0.967166i \(-0.581794\pi\)
0.967166 + 0.254145i \(0.0817939\pi\)
\(468\) 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 \(0.0334223\pi\)
−0.994493 + 0.104806i \(0.966578\pi\)
\(488\) 0 0
\(489\) 26.4253i 1.19499i
\(490\) 0 0
\(491\) 2.74222 + 2.74222i 0.123754 + 0.123754i 0.766271 0.642517i \(-0.222110\pi\)
−0.642517 + 0.766271i \(0.722110\pi\)
\(492\) 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 −0.691191 0.722672i \(-0.742914\pi\)
0.722672 + 0.691191i \(0.242914\pi\)
\(500\) 0 0
\(501\) 20.3092 + 20.3092i 0.907347 + 0.907347i
\(502\) 0 0
\(503\) 23.3204i 1.03980i −0.854226 0.519902i \(-0.825968\pi\)
0.854226 0.519902i \(-0.174032\pi\)
\(504\) 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 −0.592603 0.805495i \(-0.701900\pi\)
0.805495 + 0.592603i \(0.201900\pi\)
\(510\) 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 \(-0.740458\pi\)
0.685596 0.727982i \(-0.259542\pi\)
\(522\) 0 0
\(523\) 20.4284 + 20.4284i 0.893271 + 0.893271i 0.994830 0.101559i \(-0.0323830\pi\)
−0.101559 + 0.994830i \(0.532383\pi\)
\(524\) 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 −0.627777 0.778393i \(-0.716035\pi\)
0.778393 + 0.627777i \(0.216035\pi\)
\(542\) 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 −0.0586277 0.998280i \(-0.518672\pi\)
0.998280 + 0.0586277i \(0.0186725\pi\)
\(548\) 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 −0.611161 0.791506i \(-0.709297\pi\)
0.791506 + 0.611161i \(0.209297\pi\)
\(558\) 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 −0.870491 0.492184i \(-0.836199\pi\)
0.492184 + 0.870491i \(0.336199\pi\)
\(564\) 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 \(0.0836733\pi\)
−0.965649 + 0.259851i \(0.916327\pi\)
\(570\) 0 0
\(571\) 5.24097 + 5.24097i 0.219328 + 0.219328i 0.808215 0.588887i \(-0.200434\pi\)
−0.588887 + 0.808215i \(0.700434\pi\)
\(572\) 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 0.650317 0.759663i \(-0.274636\pi\)
−0.759663 + 0.650317i \(0.774636\pi\)
\(588\) 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 \(-0.698959\pi\)
0.585135 0.810936i \(-0.301041\pi\)
\(600\) 0 0
\(601\) 19.6274i 0.800620i −0.916380 0.400310i \(-0.868903\pi\)
0.916380 0.400310i \(-0.131097\pi\)
\(602\) 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 0.619633 0.784891i \(-0.287281\pi\)
−0.784891 + 0.619633i \(0.787281\pi\)
\(614\) 0 0
\(615\) 92.2651i 3.72049i
\(616\) 0 0
\(617\) 10.4658i 0.421337i 0.977558 + 0.210668i \(0.0675640\pi\)
−0.977558 + 0.210668i \(0.932436\pi\)
\(618\) 0 0
\(619\) 21.5251 + 21.5251i 0.865166 + 0.865166i 0.991933 0.126766i \(-0.0404599\pi\)
−0.126766 + 0.991933i \(0.540460\pi\)
\(620\) 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 \(0.00600781\pi\)
−0.999822 + 0.0188730i \(0.993992\pi\)
\(632\) 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 −0.633916 + 0.773402i \(0.718554\pi\)
−0.773402 + 0.633916i \(0.781446\pi\)
\(644\) 0 0
\(645\) −39.6683 39.6683i −1.56194 1.56194i
\(646\) 0 0
\(647\) 29.4906i 1.15939i −0.814832 0.579697i \(-0.803171\pi\)
0.814832 0.579697i \(-0.196829\pi\)
\(648\) 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 0.237679 0.971344i \(-0.423613\pi\)
0.971344 0.237679i \(-0.0763868\pi\)
\(654\) 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 −0.908761 0.417317i \(-0.862970\pi\)
0.417317 + 0.908761i \(0.362970\pi\)
\(660\) 0 0
\(661\) 20.5214 + 20.5214i 0.798189 + 0.798189i 0.982810 0.184621i \(-0.0591057\pi\)
−0.184621 + 0.982810i \(0.559106\pi\)
\(662\) 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 0.774366 0.632738i \(-0.218069\pi\)
−0.632738 + 0.774366i \(0.718069\pi\)
\(678\) 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 0.722606 0.691260i \(-0.242944\pi\)
−0.691260 + 0.722606i \(0.742944\pi\)
\(684\) 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 −0.858334 0.513091i \(-0.828500\pi\)
0.513091 + 0.858334i \(0.328500\pi\)
\(692\) 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 −0.990536 0.137250i \(-0.956173\pi\)
0.137250 + 0.990536i \(0.456173\pi\)
\(702\) 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 0.403464 0.914996i \(-0.367806\pi\)
−0.914996 + 0.403464i \(0.867806\pi\)
\(710\) 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 \(0.170864\pi\)
−0.859358 + 0.511375i \(0.829136\pi\)
\(728\) 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 0.123029 0.992403i \(-0.460739\pi\)
0.992403 0.123029i \(-0.0392609\pi\)
\(734\) 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 0.452592 0.891718i \(-0.350499\pi\)
0.891718 0.452592i \(-0.149501\pi\)
\(740\) 0 0
\(741\) 0.272997 + 0.272997i 0.0100288 + 0.0100288i
\(742\) 0 0
\(743\) 43.1375i 1.58256i −0.611452 0.791281i \(-0.709414\pi\)
0.611452 0.791281i \(-0.290586\pi\)
\(744\) 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 0.726362 0.687312i \(-0.241209\pi\)
−0.687312 + 0.726362i \(0.741209\pi\)
\(758\) 0 0
\(759\) 5.42028i 0.196744i
\(760\) 0 0
\(761\) 34.1138i 1.23662i 0.785932 + 0.618312i \(0.212183\pi\)
−0.785932 + 0.618312i \(0.787817\pi\)
\(762\) 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 0.0737087 0.997280i \(-0.476516\pi\)
−0.997280 + 0.0737087i \(0.976516\pi\)
\(774\) 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 −0.352914 0.935656i \(-0.614809\pi\)
0.935656 + 0.352914i \(0.114809\pi\)
\(788\) 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 0.0580002 0.998317i \(-0.481528\pi\)
0.998317 0.0580002i \(-0.0184724\pi\)
\(798\) 0 0
\(799\) 8.61612 0.304816