Properties

Label 1900.2.l.b.1557.2
Level $1900$
Weight $2$
Character 1900.1557
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 4 x^{11} + 28 x^{10} - 64 x^{9} + 236 x^{8} - 420 x^{7} + 946 x^{6} - 1216 x^{5} + 1896 x^{4} - 1564 x^{3} + 2284 x^{2} - 1088 x + 1370\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1557.2
Root \(-0.585043 + 2.22350i\) of defining polynomial
Character \(\chi\) \(=\) 1900.1557
Dual form 1900.2.l.b.493.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.63846 - 1.63846i) q^{3} +(-2.17009 - 2.17009i) q^{7} +2.36910i q^{9} +O(q^{10})\) \(q+(-1.63846 - 1.63846i) q^{3} +(-2.17009 - 2.17009i) q^{7} +2.36910i q^{9} -1.70928 q^{11} +(4.43904 + 4.43904i) q^{13} +(1.63090 + 1.63090i) q^{17} +(-2.80058 - 3.34017i) q^{19} +7.11120i q^{21} +(-3.24846 + 3.24846i) q^{23} +(-1.03370 + 1.03370i) q^{27} -3.27692 q^{29} +7.11120i q^{31} +(2.80058 + 2.80058i) q^{33} +(-0.128419 + 0.128419i) q^{37} -14.5464i q^{39} +3.83428i q^{41} +(5.24846 - 5.24846i) q^{43} +(-0.908291 - 0.908291i) q^{47} +2.41855i q^{49} -5.34432i q^{51} +(5.47274 + 5.47274i) q^{53} +(-0.884103 + 10.0614i) q^{57} +13.9219 q^{59} +2.63090 q^{61} +(5.14116 - 5.14116i) q^{63} +(-7.71596 + 7.71596i) q^{67} +10.6450 q^{69} -1.51004i q^{71} +(8.70928 - 8.70928i) q^{73} +(3.70928 + 3.70928i) q^{77} -4.78696 q^{79} +10.4947 q^{81} +(-6.46081 + 6.46081i) q^{83} +(5.36910 + 5.36910i) q^{87} +5.34432 q^{89} -19.2662i q^{91} +(11.6514 - 11.6514i) q^{93} +(10.2597 - 10.2597i) q^{97} -4.04945i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{7} + O(q^{10}) \) \( 12q - 4q^{7} + 8q^{11} + 4q^{17} - 4q^{23} + 28q^{43} - 20q^{47} - 24q^{57} + 16q^{61} - 20q^{63} + 76q^{73} + 16q^{77} + 4q^{81} - 84q^{83} + 80q^{87} - 8q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.63846 1.63846i −0.945965 0.945965i 0.0526478 0.998613i \(-0.483234\pi\)
−0.998613 + 0.0526478i \(0.983234\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.17009 2.17009i −0.820216 0.820216i 0.165923 0.986139i \(-0.446940\pi\)
−0.986139 + 0.165923i \(0.946940\pi\)
\(8\) 0 0
\(9\) 2.36910i 0.789701i
\(10\) 0 0
\(11\) −1.70928 −0.515366 −0.257683 0.966230i \(-0.582959\pi\)
−0.257683 + 0.966230i \(0.582959\pi\)
\(12\) 0 0
\(13\) 4.43904 + 4.43904i 1.23117 + 1.23117i 0.963516 + 0.267652i \(0.0862479\pi\)
0.267652 + 0.963516i \(0.413752\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.63090 + 1.63090i 0.395551 + 0.395551i 0.876660 0.481110i \(-0.159766\pi\)
−0.481110 + 0.876660i \(0.659766\pi\)
\(18\) 0 0
\(19\) −2.80058 3.34017i −0.642497 0.766288i
\(20\) 0 0
\(21\) 7.11120i 1.55179i
\(22\) 0 0
\(23\) −3.24846 + 3.24846i −0.677352 + 0.677352i −0.959400 0.282049i \(-0.908986\pi\)
0.282049 + 0.959400i \(0.408986\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.03370 + 1.03370i −0.198936 + 0.198936i
\(28\) 0 0
\(29\) −3.27692 −0.608509 −0.304254 0.952591i \(-0.598407\pi\)
−0.304254 + 0.952591i \(0.598407\pi\)
\(30\) 0 0
\(31\) 7.11120i 1.27721i 0.769535 + 0.638605i \(0.220488\pi\)
−0.769535 + 0.638605i \(0.779512\pi\)
\(32\) 0 0
\(33\) 2.80058 + 2.80058i 0.487518 + 0.487518i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.128419 + 0.128419i −0.0211119 + 0.0211119i −0.717584 0.696472i \(-0.754752\pi\)
0.696472 + 0.717584i \(0.254752\pi\)
\(38\) 0 0
\(39\) 14.5464i 2.32928i
\(40\) 0 0
\(41\) 3.83428i 0.598814i 0.954126 + 0.299407i \(0.0967888\pi\)
−0.954126 + 0.299407i \(0.903211\pi\)
\(42\) 0 0
\(43\) 5.24846 5.24846i 0.800383 0.800383i −0.182772 0.983155i \(-0.558507\pi\)
0.983155 + 0.182772i \(0.0585070\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.908291 0.908291i −0.132488 0.132488i 0.637753 0.770241i \(-0.279864\pi\)
−0.770241 + 0.637753i \(0.779864\pi\)
\(48\) 0 0
\(49\) 2.41855i 0.345507i
\(50\) 0 0
\(51\) 5.34432i 0.748355i
\(52\) 0 0
\(53\) 5.47274 + 5.47274i 0.751739 + 0.751739i 0.974804 0.223065i \(-0.0716062\pi\)
−0.223065 + 0.974804i \(0.571606\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.884103 + 10.0614i −0.117102 + 1.33266i
\(58\) 0 0
\(59\) 13.9219 1.81247 0.906237 0.422770i \(-0.138942\pi\)
0.906237 + 0.422770i \(0.138942\pi\)
\(60\) 0 0
\(61\) 2.63090 0.336852 0.168426 0.985714i \(-0.446132\pi\)
0.168426 + 0.985714i \(0.446132\pi\)
\(62\) 0 0
\(63\) 5.14116 5.14116i 0.647725 0.647725i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.71596 + 7.71596i −0.942654 + 0.942654i −0.998443 0.0557882i \(-0.982233\pi\)
0.0557882 + 0.998443i \(0.482233\pi\)
\(68\) 0 0
\(69\) 10.6450 1.28150
\(70\) 0 0
\(71\) 1.51004i 0.179209i −0.995977 0.0896045i \(-0.971440\pi\)
0.995977 0.0896045i \(-0.0285603\pi\)
\(72\) 0 0
\(73\) 8.70928 8.70928i 1.01934 1.01934i 0.0195344 0.999809i \(-0.493782\pi\)
0.999809 0.0195344i \(-0.00621839\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.70928 + 3.70928i 0.422711 + 0.422711i
\(78\) 0 0
\(79\) −4.78696 −0.538575 −0.269288 0.963060i \(-0.586788\pi\)
−0.269288 + 0.963060i \(0.586788\pi\)
\(80\) 0 0
\(81\) 10.4947 1.16607
\(82\) 0 0
\(83\) −6.46081 + 6.46081i −0.709166 + 0.709166i −0.966360 0.257194i \(-0.917202\pi\)
0.257194 + 0.966360i \(0.417202\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 5.36910 + 5.36910i 0.575628 + 0.575628i
\(88\) 0 0
\(89\) 5.34432 0.566497 0.283248 0.959047i \(-0.408588\pi\)
0.283248 + 0.959047i \(0.408588\pi\)
\(90\) 0 0
\(91\) 19.2662i 2.01965i
\(92\) 0 0
\(93\) 11.6514 11.6514i 1.20820 1.20820i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.2597 10.2597i 1.04171 1.04171i 0.0426236 0.999091i \(-0.486428\pi\)
0.999091 0.0426236i \(-0.0135716\pi\)
\(98\) 0 0
\(99\) 4.04945i 0.406985i
\(100\) 0 0
\(101\) −15.3112 −1.52353 −0.761763 0.647856i \(-0.775666\pi\)
−0.761763 + 0.647856i \(0.775666\pi\)
\(102\) 0 0
\(103\) 13.3171 + 13.3171i 1.31217 + 1.31217i 0.919810 + 0.392365i \(0.128343\pi\)
0.392365 + 0.919810i \(0.371657\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.67216 2.67216i 0.258328 0.258328i −0.566046 0.824374i \(-0.691528\pi\)
0.824374 + 0.566046i \(0.191528\pi\)
\(108\) 0 0
\(109\) 6.15852 0.589879 0.294940 0.955516i \(-0.404700\pi\)
0.294940 + 0.955516i \(0.404700\pi\)
\(110\) 0 0
\(111\) 0.420818 0.0399423
\(112\) 0 0
\(113\) −11.5502 11.5502i −1.08656 1.08656i −0.995881 0.0906745i \(-0.971098\pi\)
−0.0906745 0.995881i \(-0.528902\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −10.5165 + 10.5165i −0.972254 + 0.972254i
\(118\) 0 0
\(119\) 7.07838i 0.648874i
\(120\) 0 0
\(121\) −8.07838 −0.734398
\(122\) 0 0
\(123\) 6.28231 6.28231i 0.566457 0.566457i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 3.40534 3.40534i 0.302175 0.302175i −0.539689 0.841864i \(-0.681458\pi\)
0.841864 + 0.539689i \(0.181458\pi\)
\(128\) 0 0
\(129\) −17.1988 −1.51427
\(130\) 0 0
\(131\) 15.5174 1.35577 0.677883 0.735170i \(-0.262898\pi\)
0.677883 + 0.735170i \(0.262898\pi\)
\(132\) 0 0
\(133\) −1.17096 + 13.3260i −0.101536 + 1.15551i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.1773 + 14.1773i 1.21125 + 1.21125i 0.970617 + 0.240629i \(0.0773538\pi\)
0.240629 + 0.970617i \(0.422646\pi\)
\(138\) 0 0
\(139\) 10.9444i 0.928293i 0.885759 + 0.464146i \(0.153639\pi\)
−0.885759 + 0.464146i \(0.846361\pi\)
\(140\) 0 0
\(141\) 2.97640i 0.250658i
\(142\) 0 0
\(143\) −7.58754 7.58754i −0.634502 0.634502i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.96270 3.96270i 0.326838 0.326838i
\(148\) 0 0
\(149\) 0.532001i 0.0435832i −0.999763 0.0217916i \(-0.993063\pi\)
0.999763 0.0217916i \(-0.00693703\pi\)
\(150\) 0 0
\(151\) 11.8982i 0.968259i 0.874996 + 0.484129i \(0.160864\pi\)
−0.874996 + 0.484129i \(0.839136\pi\)
\(152\) 0 0
\(153\) −3.86376 + 3.86376i −0.312367 + 0.312367i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.94441 + 5.94441i 0.474415 + 0.474415i 0.903340 0.428925i \(-0.141107\pi\)
−0.428925 + 0.903340i \(0.641107\pi\)
\(158\) 0 0
\(159\) 17.9337i 1.42224i
\(160\) 0 0
\(161\) 14.0989 1.11115
\(162\) 0 0
\(163\) 12.0361 12.0361i 0.942741 0.942741i −0.0557058 0.998447i \(-0.517741\pi\)
0.998447 + 0.0557058i \(0.0177409\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.74966 + 8.74966i −0.677069 + 0.677069i −0.959336 0.282267i \(-0.908914\pi\)
0.282267 + 0.959336i \(0.408914\pi\)
\(168\) 0 0
\(169\) 26.4101i 2.03155i
\(170\) 0 0
\(171\) 7.91321 6.63486i 0.605138 0.507380i
\(172\) 0 0
\(173\) −1.16212 1.16212i −0.0883543 0.0883543i 0.661548 0.749903i \(-0.269900\pi\)
−0.749903 + 0.661548i \(0.769900\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −22.8104 22.8104i −1.71454 1.71454i
\(178\) 0 0
\(179\) 25.5632 1.91068 0.955342 0.295503i \(-0.0954874\pi\)
0.955342 + 0.295503i \(0.0954874\pi\)
\(180\) 0 0
\(181\) 13.1077i 0.974286i −0.873322 0.487143i \(-0.838039\pi\)
0.873322 0.487143i \(-0.161961\pi\)
\(182\) 0 0
\(183\) −4.31062 4.31062i −0.318650 0.318650i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.78765 2.78765i −0.203853 0.203853i
\(188\) 0 0
\(189\) 4.48644 0.326340
\(190\) 0 0
\(191\) −2.65368 −0.192014 −0.0960069 0.995381i \(-0.530607\pi\)
−0.0960069 + 0.995381i \(0.530607\pi\)
\(192\) 0 0
\(193\) −8.74966 8.74966i −0.629814 0.629814i 0.318207 0.948021i \(-0.396919\pi\)
−0.948021 + 0.318207i \(0.896919\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.46800 + 4.46800i 0.318332 + 0.318332i 0.848126 0.529794i \(-0.177731\pi\)
−0.529794 + 0.848126i \(0.677731\pi\)
\(198\) 0 0
\(199\) 15.9421i 1.13011i 0.825054 + 0.565054i \(0.191145\pi\)
−0.825054 + 0.565054i \(0.808855\pi\)
\(200\) 0 0
\(201\) 25.2846 1.78344
\(202\) 0 0
\(203\) 7.11120 + 7.11120i 0.499108 + 0.499108i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −7.69594 7.69594i −0.534905 0.534905i
\(208\) 0 0
\(209\) 4.78696 + 5.70928i 0.331121 + 0.394919i
\(210\) 0 0
\(211\) 16.3846i 1.12796i 0.825788 + 0.563981i \(0.190731\pi\)
−0.825788 + 0.563981i \(0.809269\pi\)
\(212\) 0 0
\(213\) −2.47414 + 2.47414i −0.169525 + 0.169525i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 15.4319 15.4319i 1.04759 1.04759i
\(218\) 0 0
\(219\) −28.5396 −1.92853
\(220\) 0 0
\(221\) 14.4792i 0.973979i
\(222\) 0 0
\(223\) 2.19582 + 2.19582i 0.147043 + 0.147043i 0.776796 0.629753i \(-0.216844\pi\)
−0.629753 + 0.776796i \(0.716844\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.16212 + 1.16212i −0.0771326 + 0.0771326i −0.744621 0.667488i \(-0.767370\pi\)
0.667488 + 0.744621i \(0.267370\pi\)
\(228\) 0 0
\(229\) 9.89269i 0.653728i −0.945071 0.326864i \(-0.894008\pi\)
0.945071 0.326864i \(-0.105992\pi\)
\(230\) 0 0
\(231\) 12.1550i 0.799740i
\(232\) 0 0
\(233\) −20.8576 + 20.8576i −1.36643 + 1.36643i −0.500955 + 0.865474i \(0.667018\pi\)
−0.865474 + 0.500955i \(0.832982\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 7.84324 + 7.84324i 0.509473 + 0.509473i
\(238\) 0 0
\(239\) 8.65368i 0.559760i −0.960035 0.279880i \(-0.909705\pi\)
0.960035 0.279880i \(-0.0902947\pi\)
\(240\) 0 0
\(241\) 1.25320i 0.0807259i 0.999185 + 0.0403630i \(0.0128514\pi\)
−0.999185 + 0.0403630i \(0.987149\pi\)
\(242\) 0 0
\(243\) −14.0940 14.0940i −0.904129 0.904129i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.39528 27.2590i 0.152408 1.73445i
\(248\) 0 0
\(249\) 21.1716 1.34169
\(250\) 0 0
\(251\) 1.65983 0.104767 0.0523837 0.998627i \(-0.483318\pi\)
0.0523837 + 0.998627i \(0.483318\pi\)
\(252\) 0 0
\(253\) 5.55252 5.55252i 0.349084 0.349084i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.91538 + 4.91538i −0.306613 + 0.306613i −0.843594 0.536981i \(-0.819565\pi\)
0.536981 + 0.843594i \(0.319565\pi\)
\(258\) 0 0
\(259\) 0.557360 0.0346327
\(260\) 0 0
\(261\) 7.76336i 0.480540i
\(262\) 0 0
\(263\) 12.8010 12.8010i 0.789342 0.789342i −0.192044 0.981386i \(-0.561512\pi\)
0.981386 + 0.192044i \(0.0615116\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −8.75646 8.75646i −0.535886 0.535886i
\(268\) 0 0
\(269\) −17.1988 −1.04863 −0.524315 0.851525i \(-0.675678\pi\)
−0.524315 + 0.851525i \(0.675678\pi\)
\(270\) 0 0
\(271\) −11.2846 −0.685490 −0.342745 0.939429i \(-0.611357\pi\)
−0.342745 + 0.939429i \(0.611357\pi\)
\(272\) 0 0
\(273\) −31.5669 + 31.5669i −1.91052 + 1.91052i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.29072 + 7.29072i 0.438057 + 0.438057i 0.891358 0.453301i \(-0.149754\pi\)
−0.453301 + 0.891358i \(0.649754\pi\)
\(278\) 0 0
\(279\) −16.8472 −1.00861
\(280\) 0 0
\(281\) 25.1242i 1.49878i 0.662127 + 0.749392i \(0.269654\pi\)
−0.662127 + 0.749392i \(0.730346\pi\)
\(282\) 0 0
\(283\) 4.01333 4.01333i 0.238568 0.238568i −0.577689 0.816257i \(-0.696045\pi\)
0.816257 + 0.577689i \(0.196045\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.32072 8.32072i 0.491157 0.491157i
\(288\) 0 0
\(289\) 11.6803i 0.687079i
\(290\) 0 0
\(291\) −33.6202 −1.97085
\(292\) 0 0
\(293\) 0.824263 + 0.824263i 0.0481539 + 0.0481539i 0.730774 0.682620i \(-0.239159\pi\)
−0.682620 + 0.730774i \(0.739159\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.76688 1.76688i 0.102525 0.102525i
\(298\) 0 0
\(299\) −28.8401 −1.66787
\(300\) 0 0
\(301\) −22.7792 −1.31297
\(302\) 0 0
\(303\) 25.0869 + 25.0869i 1.44120 + 1.44120i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 7.32064 7.32064i 0.417811 0.417811i −0.466638 0.884449i \(-0.654535\pi\)
0.884449 + 0.466638i \(0.154535\pi\)
\(308\) 0 0
\(309\) 43.6391i 2.48254i
\(310\) 0 0
\(311\) −11.3835 −0.645498 −0.322749 0.946485i \(-0.604607\pi\)
−0.322749 + 0.946485i \(0.604607\pi\)
\(312\) 0 0
\(313\) 5.09890 5.09890i 0.288207 0.288207i −0.548164 0.836371i \(-0.684673\pi\)
0.836371 + 0.548164i \(0.184673\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −17.1514 + 17.1514i −0.963318 + 0.963318i −0.999351 0.0360322i \(-0.988528\pi\)
0.0360322 + 0.999351i \(0.488528\pi\)
\(318\) 0 0
\(319\) 5.60116 0.313605
\(320\) 0 0
\(321\) −8.75646 −0.488738
\(322\) 0 0
\(323\) 0.880022 10.0149i 0.0489657 0.557246i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −10.0905 10.0905i −0.558005 0.558005i
\(328\) 0 0
\(329\) 3.94214i 0.217337i
\(330\) 0 0
\(331\) 8.36440i 0.459749i 0.973220 + 0.229875i \(0.0738316\pi\)
−0.973220 + 0.229875i \(0.926168\pi\)
\(332\) 0 0
\(333\) −0.304237 0.304237i −0.0166721 0.0166721i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −24.6579 + 24.6579i −1.34320 + 1.34320i −0.450351 + 0.892852i \(0.648701\pi\)
−0.892852 + 0.450351i \(0.851299\pi\)
\(338\) 0 0
\(339\) 37.8492i 2.05569i
\(340\) 0 0
\(341\) 12.1550i 0.658230i
\(342\) 0 0
\(343\) −9.94214 + 9.94214i −0.536825 + 0.536825i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.68753 + 9.68753i 0.520054 + 0.520054i 0.917588 0.397534i \(-0.130134\pi\)
−0.397534 + 0.917588i \(0.630134\pi\)
\(348\) 0 0
\(349\) 0.130094i 0.00696375i −0.999994 0.00348187i \(-0.998892\pi\)
0.999994 0.00348187i \(-0.00110832\pi\)
\(350\) 0 0
\(351\) −9.17727 −0.489847
\(352\) 0 0
\(353\) −17.8865 + 17.8865i −0.952005 + 0.952005i −0.998900 0.0468948i \(-0.985067\pi\)
0.0468948 + 0.998900i \(0.485067\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −11.5976 + 11.5976i −0.613812 + 0.613812i
\(358\) 0 0
\(359\) 15.2579i 0.805282i 0.915358 + 0.402641i \(0.131908\pi\)
−0.915358 + 0.402641i \(0.868092\pi\)
\(360\) 0 0
\(361\) −3.31351 + 18.7088i −0.174395 + 0.984676i
\(362\) 0 0
\(363\) 13.2361 + 13.2361i 0.694715 + 0.694715i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −23.2401 23.2401i −1.21312 1.21312i −0.969995 0.243126i \(-0.921827\pi\)
−0.243126 0.969995i \(-0.578173\pi\)
\(368\) 0 0
\(369\) −9.08380 −0.472884
\(370\) 0 0
\(371\) 23.7526i 1.23318i
\(372\) 0 0
\(373\) 3.70586 + 3.70586i 0.191882 + 0.191882i 0.796509 0.604627i \(-0.206678\pi\)
−0.604627 + 0.796509i \(0.706678\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −14.5464 14.5464i −0.749177 0.749177i
\(378\) 0 0
\(379\) 9.57392 0.491779 0.245890 0.969298i \(-0.420920\pi\)
0.245890 + 0.969298i \(0.420920\pi\)
\(380\) 0 0
\(381\) −11.1590 −0.571694
\(382\) 0 0
\(383\) 8.01648 + 8.01648i 0.409623 + 0.409623i 0.881607 0.471984i \(-0.156462\pi\)
−0.471984 + 0.881607i \(0.656462\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 12.4341 + 12.4341i 0.632063 + 0.632063i
\(388\) 0 0
\(389\) 30.5692i 1.54992i 0.632011 + 0.774959i \(0.282230\pi\)
−0.632011 + 0.774959i \(0.717770\pi\)
\(390\) 0 0
\(391\) −10.5958 −0.535854
\(392\) 0 0
\(393\) −25.4247 25.4247i −1.28251 1.28251i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 15.0494 + 15.0494i 0.755310 + 0.755310i 0.975465 0.220155i \(-0.0706562\pi\)
−0.220155 + 0.975465i \(0.570656\pi\)
\(398\) 0 0
\(399\) 23.7526 19.9155i 1.18912 0.997021i
\(400\) 0 0
\(401\) 2.06740i 0.103241i −0.998667 0.0516205i \(-0.983561\pi\)
0.998667 0.0516205i \(-0.0164386\pi\)
\(402\) 0 0
\(403\) −31.5669 + 31.5669i −1.57246 + 1.57246i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.219503 0.219503i 0.0108804 0.0108804i
\(408\) 0 0
\(409\) −14.6177 −0.722800 −0.361400 0.932411i \(-0.617701\pi\)
−0.361400 + 0.932411i \(0.617701\pi\)
\(410\) 0 0
\(411\) 46.4578i 2.29159i
\(412\) 0 0
\(413\) −30.2117 30.2117i −1.48662 1.48662i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 17.9320 17.9320i 0.878133 0.878133i
\(418\) 0 0
\(419\) 3.29299i 0.160873i −0.996760 0.0804366i \(-0.974369\pi\)
0.996760 0.0804366i \(-0.0256315\pi\)
\(420\) 0 0
\(421\) 27.6306i 1.34663i −0.739354 0.673317i \(-0.764869\pi\)
0.739354 0.673317i \(-0.235131\pi\)
\(422\) 0 0
\(423\) 2.15183 2.15183i 0.104626 0.104626i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −5.70928 5.70928i −0.276291 0.276291i
\(428\) 0 0
\(429\) 24.8638i 1.20043i
\(430\) 0 0
\(431\) 34.3028i 1.65231i 0.563445 + 0.826154i \(0.309476\pi\)
−0.563445 + 0.826154i \(0.690524\pi\)
\(432\) 0 0
\(433\) −4.69588 4.69588i −0.225669 0.225669i 0.585211 0.810881i \(-0.301012\pi\)
−0.810881 + 0.585211i \(0.801012\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 19.9480 + 1.75285i 0.954243 + 0.0838502i
\(438\) 0 0
\(439\) −12.0165 −0.573517 −0.286758 0.958003i \(-0.592578\pi\)
−0.286758 + 0.958003i \(0.592578\pi\)
\(440\) 0 0
\(441\) −5.72979 −0.272847
\(442\) 0 0
\(443\) 16.8999 16.8999i 0.802938 0.802938i −0.180616 0.983554i \(-0.557809\pi\)
0.983554 + 0.180616i \(0.0578092\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −0.871662 + 0.871662i −0.0412282 + 0.0412282i
\(448\) 0 0
\(449\) −39.6034 −1.86900 −0.934501 0.355961i \(-0.884154\pi\)
−0.934501 + 0.355961i \(0.884154\pi\)
\(450\) 0 0
\(451\) 6.55384i 0.308608i
\(452\) 0 0
\(453\) 19.4947 19.4947i 0.915939 0.915939i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 10.5174 + 10.5174i 0.491985 + 0.491985i 0.908931 0.416946i \(-0.136900\pi\)
−0.416946 + 0.908931i \(0.636900\pi\)
\(458\) 0 0
\(459\) −3.37172 −0.157378
\(460\) 0 0
\(461\) 25.6163 1.19307 0.596536 0.802586i \(-0.296543\pi\)
0.596536 + 0.802586i \(0.296543\pi\)
\(462\) 0 0
\(463\) −9.58864 + 9.58864i −0.445622 + 0.445622i −0.893896 0.448274i \(-0.852039\pi\)
0.448274 + 0.893896i \(0.352039\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9.27513 + 9.27513i 0.429202 + 0.429202i 0.888356 0.459155i \(-0.151848\pi\)
−0.459155 + 0.888356i \(0.651848\pi\)
\(468\) 0 0
\(469\) 33.4886 1.54636
\(470\) 0 0
\(471\) 19.4794i 0.897561i
\(472\) 0 0
\(473\) −8.97107 + 8.97107i −0.412490 + 0.412490i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −12.9655 + 12.9655i −0.593649 + 0.593649i
\(478\) 0 0
\(479\) 32.6719i 1.49282i 0.665487 + 0.746409i \(0.268224\pi\)
−0.665487 + 0.746409i \(0.731776\pi\)
\(480\) 0 0
\(481\) −1.14011 −0.0519846
\(482\) 0 0
\(483\) −23.1005 23.1005i −1.05111 1.05111i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −0.347922 + 0.347922i −0.0157658 + 0.0157658i −0.714946 0.699180i \(-0.753549\pi\)
0.699180 + 0.714946i \(0.253549\pi\)
\(488\) 0 0
\(489\) −39.4414 −1.78360
\(490\) 0 0
\(491\) 1.17727 0.0531297 0.0265648 0.999647i \(-0.491543\pi\)
0.0265648 + 0.999647i \(0.491543\pi\)
\(492\) 0 0
\(493\) −5.34432 5.34432i −0.240696 0.240696i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.27692 + 3.27692i −0.146990 + 0.146990i
\(498\) 0 0
\(499\) 18.4163i 0.824426i −0.911087 0.412213i \(-0.864756\pi\)
0.911087 0.412213i \(-0.135244\pi\)
\(500\) 0 0
\(501\) 28.6719 1.28097
\(502\) 0 0
\(503\) −10.9493 + 10.9493i −0.488206 + 0.488206i −0.907740 0.419533i \(-0.862194\pi\)
0.419533 + 0.907740i \(0.362194\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 43.2720 43.2720i 1.92178 1.92178i
\(508\) 0 0
\(509\) −29.1406 −1.29164 −0.645818 0.763491i \(-0.723484\pi\)
−0.645818 + 0.763491i \(0.723484\pi\)
\(510\) 0 0
\(511\) −37.7998 −1.67216
\(512\) 0 0
\(513\) 6.34770 + 0.557778i 0.280258 + 0.0246265i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.55252 + 1.55252i 0.0682797 + 0.0682797i
\(518\) 0 0
\(519\) 3.80817i 0.167160i
\(520\) 0 0
\(521\) 36.9040i 1.61679i 0.588638 + 0.808397i \(0.299664\pi\)
−0.588638 + 0.808397i \(0.700336\pi\)
\(522\) 0 0
\(523\) −6.72594 6.72594i −0.294105 0.294105i 0.544595 0.838699i \(-0.316684\pi\)
−0.838699 + 0.544595i \(0.816684\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11.5976 + 11.5976i −0.505201 + 0.505201i
\(528\) 0 0
\(529\) 1.89496i 0.0823896i
\(530\) 0 0
\(531\) 32.9824i 1.43131i
\(532\) 0 0
\(533\) −17.0205 + 17.0205i −0.737241 + 0.737241i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −41.8843 41.8843i −1.80744 1.80744i
\(538\) 0 0
\(539\) 4.13397i 0.178063i
\(540\) 0 0
\(541\) 32.5197 1.39813 0.699066 0.715057i \(-0.253599\pi\)
0.699066 + 0.715057i \(0.253599\pi\)
\(542\) 0 0
\(543\) −21.4764 + 21.4764i −0.921641 + 0.921641i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 23.2289 23.2289i 0.993196 0.993196i −0.00678109 0.999977i \(-0.502159\pi\)
0.999977 + 0.00678109i \(0.00215850\pi\)
\(548\) 0 0
\(549\) 6.23287i 0.266012i
\(550\) 0 0
\(551\) 9.17727 + 10.9455i 0.390965 + 0.466293i
\(552\) 0 0
\(553\) 10.3881 + 10.3881i 0.441748 + 0.441748i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.14834 + 5.14834i 0.218142 + 0.218142i 0.807715 0.589573i \(-0.200704\pi\)
−0.589573 + 0.807715i \(0.700704\pi\)
\(558\) 0 0
\(559\) 46.5963 1.97081
\(560\) 0 0
\(561\) 9.13492i 0.385676i
\(562\) 0 0
\(563\) 11.4692 + 11.4692i 0.483370 + 0.483370i 0.906206 0.422836i \(-0.138965\pi\)
−0.422836 + 0.906206i \(0.638965\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −22.7743 22.7743i −0.956432 0.956432i
\(568\) 0 0
\(569\) 31.8602 1.33565 0.667825 0.744319i \(-0.267226\pi\)
0.667825 + 0.744319i \(0.267226\pi\)
\(570\) 0 0
\(571\) 23.5981 0.987549 0.493775 0.869590i \(-0.335617\pi\)
0.493775 + 0.869590i \(0.335617\pi\)
\(572\) 0 0
\(573\) 4.34796 + 4.34796i 0.181638 + 0.181638i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −24.2762 24.2762i −1.01063 1.01063i −0.999943 0.0106873i \(-0.996598\pi\)
−0.0106873 0.999943i \(-0.503402\pi\)
\(578\) 0 0
\(579\) 28.6719i 1.19156i
\(580\) 0 0
\(581\) 28.0410 1.16334
\(582\) 0 0
\(583\) −9.35442 9.35442i −0.387420 0.387420i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.7165 18.7165i −0.772511 0.772511i 0.206034 0.978545i \(-0.433944\pi\)
−0.978545 + 0.206034i \(0.933944\pi\)
\(588\) 0 0
\(589\) 23.7526 19.9155i 0.978710 0.820603i
\(590\) 0 0
\(591\) 14.6413i 0.602262i
\(592\) 0 0
\(593\) −1.26794 + 1.26794i −0.0520680 + 0.0520680i −0.732661 0.680593i \(-0.761722\pi\)
0.680593 + 0.732661i \(0.261722\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 26.1206 26.1206i 1.06904 1.06904i
\(598\) 0 0
\(599\) 10.5502 0.431068 0.215534 0.976496i \(-0.430851\pi\)
0.215534 + 0.976496i \(0.430851\pi\)
\(600\) 0 0
\(601\) 38.8329i 1.58403i −0.610503 0.792014i \(-0.709033\pi\)
0.610503 0.792014i \(-0.290967\pi\)
\(602\) 0 0
\(603\) −18.2799 18.2799i −0.744415 0.744415i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 7.97280 7.97280i 0.323606 0.323606i −0.526543 0.850149i \(-0.676512\pi\)
0.850149 + 0.526543i \(0.176512\pi\)
\(608\) 0 0
\(609\) 23.3028i 0.944278i
\(610\) 0 0
\(611\) 8.06388i 0.326230i
\(612\) 0 0
\(613\) 18.1194 18.1194i 0.731836 0.731836i −0.239147 0.970983i \(-0.576868\pi\)
0.970983 + 0.239147i \(0.0768678\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16.2123 + 16.2123i 0.652685 + 0.652685i 0.953639 0.300954i \(-0.0973051\pi\)
−0.300954 + 0.953639i \(0.597305\pi\)
\(618\) 0 0
\(619\) 8.73433i 0.351062i 0.984474 + 0.175531i \(0.0561643\pi\)
−0.984474 + 0.175531i \(0.943836\pi\)
\(620\) 0 0
\(621\) 6.71588i 0.269499i
\(622\) 0 0
\(623\) −11.5976 11.5976i −0.464650 0.464650i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.51117 17.1977i 0.0603505 0.686809i
\(628\) 0 0
\(629\) −0.418876 −0.0167017
\(630\) 0 0
\(631\) 29.7093 1.18271 0.591354 0.806412i \(-0.298594\pi\)
0.591354 + 0.806412i \(0.298594\pi\)
\(632\) 0 0
\(633\) 26.8455 26.8455i 1.06701 1.06701i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −10.7360 + 10.7360i −0.425377 + 0.425377i
\(638\) 0 0
\(639\) 3.57744 0.141521
\(640\) 0 0
\(641\) 40.2993i 1.59173i −0.605477 0.795863i \(-0.707018\pi\)
0.605477 0.795863i \(-0.292982\pi\)
\(642\) 0 0
\(643\) −1.57426 + 1.57426i −0.0620828 + 0.0620828i −0.737467 0.675384i \(-0.763978\pi\)
0.675384 + 0.737467i \(0.263978\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.79484 + 5.79484i 0.227819 + 0.227819i 0.811781 0.583962i \(-0.198498\pi\)
−0.583962 + 0.811781i \(0.698498\pi\)
\(648\) 0 0
\(649\) −23.7963 −0.934087
\(650\) 0 0
\(651\) −50.5692 −1.98196
\(652\) 0 0
\(653\) 21.6537 21.6537i 0.847374 0.847374i −0.142431 0.989805i \(-0.545492\pi\)
0.989805 + 0.142431i \(0.0454918\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 20.6332 + 20.6332i 0.804976 + 0.804976i
\(658\) 0 0
\(659\) 16.9420 0.659965 0.329983 0.943987i \(-0.392957\pi\)
0.329983 + 0.943987i \(0.392957\pi\)
\(660\) 0 0
\(661\) 27.1916i 1.05763i 0.848737 + 0.528815i \(0.177364\pi\)
−0.848737 + 0.528815i \(0.822636\pi\)
\(662\) 0 0
\(663\) 23.7237 23.7237i 0.921350 0.921350i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.6450 10.6450i 0.412174 0.412174i
\(668\) 0 0
\(669\) 7.19553i 0.278195i
\(670\) 0 0
\(671\) −4.49693 −0.173602
\(672\) 0 0
\(673\) −1.97632 1.97632i −0.0761814 0.0761814i 0.667989 0.744171i \(-0.267155\pi\)
−0.744171 + 0.667989i \(0.767155\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −21.7189 + 21.7189i −0.834723 + 0.834723i −0.988159 0.153435i \(-0.950966\pi\)
0.153435 + 0.988159i \(0.450966\pi\)
\(678\) 0 0
\(679\) −44.5289 −1.70886
\(680\) 0 0
\(681\) 3.80817 0.145929
\(682\) 0 0
\(683\) 22.3710 + 22.3710i 0.856003 + 0.856003i 0.990864 0.134861i \(-0.0430589\pi\)
−0.134861 + 0.990864i \(0.543059\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −16.2088 + 16.2088i −0.618404 + 0.618404i
\(688\) 0 0
\(689\) 48.5874i 1.85103i
\(690\) 0 0
\(691\) 13.7093 0.521525 0.260763 0.965403i \(-0.416026\pi\)
0.260763 + 0.965403i \(0.416026\pi\)
\(692\) 0 0
\(693\) −8.78765 + 8.78765i −0.333815 + 0.333815i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −6.25332 + 6.25332i −0.236861 + 0.236861i
\(698\) 0 0
\(699\) 68.3488 2.58519
\(700\) 0 0
\(701\) 47.8225 1.80623 0.903116 0.429396i \(-0.141273\pi\)
0.903116 + 0.429396i \(0.141273\pi\)
\(702\) 0 0
\(703\) 0.788588 + 0.0692940i 0.0297422 + 0.00261347i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 33.2267 + 33.2267i 1.24962 + 1.24962i
\(708\) 0 0
\(709\) 0.0143758i 0.000539896i 1.00000 0.000269948i \(8.59272e-5\pi\)
−1.00000 0.000269948i \(0.999914\pi\)
\(710\) 0 0
\(711\) 11.3408i 0.425313i
\(712\) 0 0
\(713\) −23.1005 23.1005i −0.865120 0.865120i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −14.1787 + 14.1787i −0.529514 + 0.529514i
\(718\) 0 0
\(719\) 11.7237i 0.437218i −0.975812 0.218609i \(-0.929848\pi\)
0.975812 0.218609i \(-0.0701520\pi\)
\(720\) 0 0
\(721\) 57.7986i 2.15253i
\(722\) 0 0
\(723\) 2.05332 2.05332i 0.0763639 0.0763639i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 3.87936 + 3.87936i 0.143878 + 0.143878i 0.775377 0.631499i \(-0.217560\pi\)
−0.631499 + 0.775377i \(0.717560\pi\)
\(728\) 0 0
\(729\) 14.7009i 0.544476i
\(730\) 0 0
\(731\) 17.1194 0.633184
\(732\) 0 0
\(733\) −3.97948 + 3.97948i −0.146985 + 0.146985i −0.776770 0.629784i \(-0.783143\pi\)
0.629784 + 0.776770i \(0.283143\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.1887 13.1887i 0.485812 0.485812i
\(738\) 0 0
\(739\) 30.6270i 1.12663i −0.826241 0.563317i \(-0.809525\pi\)
0.826241 0.563317i \(-0.190475\pi\)
\(740\) 0 0
\(741\) −48.5874 + 40.7383i −1.78490 + 1.49656i
\(742\) 0 0
\(743\) 7.93546 + 7.93546i 0.291124 + 0.291124i 0.837524 0.546400i \(-0.184002\pi\)
−0.546400 + 0.837524i \(0.684002\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −15.3063 15.3063i −0.560029 0.560029i
\(748\) 0 0
\(749\) −11.5976 −0.423769
\(750\) 0 0
\(751\) 7.92540i 0.289202i 0.989490 + 0.144601i \(0.0461898\pi\)
−0.989490 + 0.144601i \(0.953810\pi\)
\(752\) 0 0
\(753\) −2.71956 2.71956i −0.0991063 0.0991063i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −2.58372 2.58372i −0.0939068 0.0939068i 0.658593 0.752500i \(-0.271152\pi\)
−0.752500 + 0.658593i \(0.771152\pi\)
\(758\) 0 0
\(759\) −18.1952 −0.660443
\(760\) 0 0
\(761\) −33.4680 −1.21321 −0.606607 0.795002i \(-0.707470\pi\)
−0.606607 + 0.795002i \(0.707470\pi\)
\(762\) 0 0
\(763\) −13.3645 13.3645i −0.483828 0.483828i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 61.7998 + 61.7998i 2.23146 + 2.23146i
\(768\) 0 0
\(769\) 49.4557i 1.78342i −0.452609 0.891709i \(-0.649506\pi\)
0.452609 0.891709i \(-0.350494\pi\)
\(770\) 0 0
\(771\) 16.1073 0.580090
\(772\) 0 0
\(773\) 37.0698 + 37.0698i 1.33331 + 1.33331i 0.902394 + 0.430913i \(0.141808\pi\)
0.430913 + 0.902394i \(0.358192\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −0.913212 0.913212i −0.0327613 0.0327613i
\(778\) 0 0
\(779\) 12.8072 10.7382i 0.458864 0.384736i
\(780\) 0 0
\(781\) 2.58108i 0.0923582i
\(782\) 0 0
\(783\) 3.38735 3.38735i 0.121054 0.121054i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −13.3981 + 13.3981i −0.477592 + 0.477592i −0.904361 0.426769i \(-0.859652\pi\)
0.426769 + 0.904361i \(0.359652\pi\)
\(788\) 0 0
\(789\) −41.9478 −1.49338
\(790\) 0 0
\(791\) 50.1300i 1.78242i
\(792\) 0 0
\(793\) 11.6787 + 11.6787i 0.414721 + 0.414721i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5.61122 5.61122i 0.198760 0.198760i −0.600708 0.799468i \(-0.705115\pi\)
0.799468 + 0.600708i \(0.205115\pi\)
\(798\) 0 0
\(799\) 2.96266i 0.104811i
\(800\) 0 0
\(801\) 12.6612i 0.447363i
\(802\) 0 0
\(803\) −14.8865 + 14.8865i −0.525335 +