Properties

Label 1232.2.q.f.177.1
Level $1232$
Weight $2$
Character 1232.177
Analytic conductor $9.838$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.83756952902\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1232.177
Dual form 1232.2.q.f.529.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20711 - 2.09077i) q^{3} +(0.292893 - 0.507306i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+(-1.20711 - 2.09077i) q^{3} +(0.292893 - 0.507306i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(0.500000 + 0.866025i) q^{11} -3.82843 q^{13} -1.41421 q^{15} +(-1.82843 - 3.16693i) q^{17} +(-0.292893 + 0.507306i) q^{19} +(-2.41421 + 5.91359i) q^{21} +(-3.12132 + 5.40629i) q^{23} +(2.32843 + 4.03295i) q^{25} -0.414214 q^{27} +2.65685 q^{29} +(-2.00000 - 3.46410i) q^{31} +(1.20711 - 2.09077i) q^{33} +(-1.53553 + 0.210133i) q^{35} +(4.70711 - 8.15295i) q^{37} +(4.62132 + 8.00436i) q^{39} -5.41421 q^{41} +5.65685 q^{43} +(0.828427 + 1.43488i) q^{45} +(-5.24264 + 9.08052i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-4.41421 + 7.64564i) q^{51} +(-3.94975 - 6.84116i) q^{53} +0.585786 q^{55} +1.41421 q^{57} +(-2.79289 - 4.83743i) q^{59} +(-5.91421 + 10.2437i) q^{61} +(7.41421 - 1.01461i) q^{63} +(-1.12132 + 1.94218i) q^{65} +(1.37868 + 2.38794i) q^{67} +15.0711 q^{69} +11.0711 q^{71} +(4.70711 + 8.15295i) q^{73} +(5.62132 - 9.73641i) q^{75} +(1.00000 - 2.44949i) q^{77} +(-6.62132 + 11.4685i) q^{79} +(4.74264 + 8.21449i) q^{81} +12.1421 q^{83} -2.14214 q^{85} +(-3.20711 - 5.55487i) q^{87} +(-6.24264 + 10.8126i) q^{89} +(6.20711 + 8.00436i) q^{91} +(-4.82843 + 8.36308i) q^{93} +(0.171573 + 0.297173i) q^{95} -3.82843 q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 4 q^{5} + 2 q^{7} + O(q^{10}) \) \( 4 q - 2 q^{3} + 4 q^{5} + 2 q^{7} + 2 q^{11} - 4 q^{13} + 4 q^{17} - 4 q^{19} - 4 q^{21} - 4 q^{23} - 2 q^{25} + 4 q^{27} - 12 q^{29} - 8 q^{31} + 2 q^{33} + 8 q^{35} + 16 q^{37} + 10 q^{39} - 16 q^{41} - 8 q^{45} - 4 q^{47} + 10 q^{49} - 12 q^{51} + 4 q^{53} + 8 q^{55} - 14 q^{59} - 18 q^{61} + 24 q^{63} + 4 q^{65} + 14 q^{67} + 32 q^{69} + 16 q^{71} + 16 q^{73} + 14 q^{75} + 4 q^{77} - 18 q^{79} + 2 q^{81} - 8 q^{83} + 48 q^{85} - 10 q^{87} - 8 q^{89} + 22 q^{91} - 8 q^{93} + 12 q^{95} - 4 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).

\(n\) \(309\) \(353\) \(463\) \(673\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.20711 2.09077i −0.696923 1.20711i −0.969528 0.244981i \(-0.921218\pi\)
0.272605 0.962126i \(-0.412115\pi\)
\(4\) 0 0
\(5\) 0.292893 0.507306i 0.130986 0.226874i −0.793071 0.609129i \(-0.791519\pi\)
0.924057 + 0.382255i \(0.124852\pi\)
\(6\) 0 0
\(7\) −1.62132 2.09077i −0.612801 0.790237i
\(8\) 0 0
\(9\) −1.41421 + 2.44949i −0.471405 + 0.816497i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0 0
\(13\) −3.82843 −1.06181 −0.530907 0.847430i \(-0.678149\pi\)
−0.530907 + 0.847430i \(0.678149\pi\)
\(14\) 0 0
\(15\) −1.41421 −0.365148
\(16\) 0 0
\(17\) −1.82843 3.16693i −0.443459 0.768093i 0.554485 0.832194i \(-0.312915\pi\)
−0.997943 + 0.0641009i \(0.979582\pi\)
\(18\) 0 0
\(19\) −0.292893 + 0.507306i −0.0671943 + 0.116384i −0.897665 0.440678i \(-0.854738\pi\)
0.830471 + 0.557062i \(0.188071\pi\)
\(20\) 0 0
\(21\) −2.41421 + 5.91359i −0.526825 + 1.29045i
\(22\) 0 0
\(23\) −3.12132 + 5.40629i −0.650840 + 1.12729i 0.332079 + 0.943252i \(0.392250\pi\)
−0.982919 + 0.184037i \(0.941083\pi\)
\(24\) 0 0
\(25\) 2.32843 + 4.03295i 0.465685 + 0.806591i
\(26\) 0 0
\(27\) −0.414214 −0.0797154
\(28\) 0 0
\(29\) 2.65685 0.493365 0.246683 0.969096i \(-0.420659\pi\)
0.246683 + 0.969096i \(0.420659\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0 0
\(33\) 1.20711 2.09077i 0.210130 0.363956i
\(34\) 0 0
\(35\) −1.53553 + 0.210133i −0.259553 + 0.0355190i
\(36\) 0 0
\(37\) 4.70711 8.15295i 0.773844 1.34034i −0.161599 0.986857i \(-0.551665\pi\)
0.935442 0.353480i \(-0.115002\pi\)
\(38\) 0 0
\(39\) 4.62132 + 8.00436i 0.740003 + 1.28172i
\(40\) 0 0
\(41\) −5.41421 −0.845558 −0.422779 0.906233i \(-0.638945\pi\)
−0.422779 + 0.906233i \(0.638945\pi\)
\(42\) 0 0
\(43\) 5.65685 0.862662 0.431331 0.902194i \(-0.358044\pi\)
0.431331 + 0.902194i \(0.358044\pi\)
\(44\) 0 0
\(45\) 0.828427 + 1.43488i 0.123495 + 0.213899i
\(46\) 0 0
\(47\) −5.24264 + 9.08052i −0.764718 + 1.32453i 0.175678 + 0.984448i \(0.443788\pi\)
−0.940396 + 0.340082i \(0.889545\pi\)
\(48\) 0 0
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) 0 0
\(51\) −4.41421 + 7.64564i −0.618114 + 1.07060i
\(52\) 0 0
\(53\) −3.94975 6.84116i −0.542540 0.939706i −0.998757 0.0498379i \(-0.984130\pi\)
0.456218 0.889868i \(-0.349204\pi\)
\(54\) 0 0
\(55\) 0.585786 0.0789874
\(56\) 0 0
\(57\) 1.41421 0.187317
\(58\) 0 0
\(59\) −2.79289 4.83743i −0.363604 0.629780i 0.624947 0.780667i \(-0.285120\pi\)
−0.988551 + 0.150887i \(0.951787\pi\)
\(60\) 0 0
\(61\) −5.91421 + 10.2437i −0.757237 + 1.31157i 0.187017 + 0.982357i \(0.440118\pi\)
−0.944254 + 0.329217i \(0.893215\pi\)
\(62\) 0 0
\(63\) 7.41421 1.01461i 0.934103 0.127829i
\(64\) 0 0
\(65\) −1.12132 + 1.94218i −0.139083 + 0.240898i
\(66\) 0 0
\(67\) 1.37868 + 2.38794i 0.168433 + 0.291734i 0.937869 0.346990i \(-0.112796\pi\)
−0.769436 + 0.638723i \(0.779463\pi\)
\(68\) 0 0
\(69\) 15.0711 1.81434
\(70\) 0 0
\(71\) 11.0711 1.31389 0.656947 0.753937i \(-0.271848\pi\)
0.656947 + 0.753937i \(0.271848\pi\)
\(72\) 0 0
\(73\) 4.70711 + 8.15295i 0.550925 + 0.954230i 0.998208 + 0.0598379i \(0.0190584\pi\)
−0.447283 + 0.894393i \(0.647608\pi\)
\(74\) 0 0
\(75\) 5.62132 9.73641i 0.649094 1.12426i
\(76\) 0 0
\(77\) 1.00000 2.44949i 0.113961 0.279145i
\(78\) 0 0
\(79\) −6.62132 + 11.4685i −0.744957 + 1.29030i 0.205258 + 0.978708i \(0.434197\pi\)
−0.950215 + 0.311595i \(0.899137\pi\)
\(80\) 0 0
\(81\) 4.74264 + 8.21449i 0.526960 + 0.912722i
\(82\) 0 0
\(83\) 12.1421 1.33277 0.666386 0.745607i \(-0.267840\pi\)
0.666386 + 0.745607i \(0.267840\pi\)
\(84\) 0 0
\(85\) −2.14214 −0.232347
\(86\) 0 0
\(87\) −3.20711 5.55487i −0.343838 0.595545i
\(88\) 0 0
\(89\) −6.24264 + 10.8126i −0.661719 + 1.14613i 0.318445 + 0.947941i \(0.396839\pi\)
−0.980164 + 0.198189i \(0.936494\pi\)
\(90\) 0 0
\(91\) 6.20711 + 8.00436i 0.650682 + 0.839085i
\(92\) 0 0
\(93\) −4.82843 + 8.36308i −0.500685 + 0.867211i
\(94\) 0 0
\(95\) 0.171573 + 0.297173i 0.0176030 + 0.0304893i
\(96\) 0 0
\(97\) −3.82843 −0.388718 −0.194359 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(98\) 0 0
\(99\) −2.82843 −0.284268
\(100\) 0 0
\(101\) −3.08579 5.34474i −0.307047 0.531821i 0.670668 0.741758i \(-0.266008\pi\)
−0.977715 + 0.209936i \(0.932674\pi\)
\(102\) 0 0
\(103\) 6.70711 11.6170i 0.660871 1.14466i −0.319516 0.947581i \(-0.603520\pi\)
0.980387 0.197081i \(-0.0631462\pi\)
\(104\) 0 0
\(105\) 2.29289 + 2.95680i 0.223763 + 0.288554i
\(106\) 0 0
\(107\) −1.53553 + 2.65962i −0.148446 + 0.257115i −0.930653 0.365903i \(-0.880760\pi\)
0.782207 + 0.623018i \(0.214094\pi\)
\(108\) 0 0
\(109\) −8.24264 14.2767i −0.789502 1.36746i −0.926272 0.376854i \(-0.877006\pi\)
0.136771 0.990603i \(-0.456328\pi\)
\(110\) 0 0
\(111\) −22.7279 −2.15724
\(112\) 0 0
\(113\) −8.17157 −0.768717 −0.384358 0.923184i \(-0.625577\pi\)
−0.384358 + 0.923184i \(0.625577\pi\)
\(114\) 0 0
\(115\) 1.82843 + 3.16693i 0.170502 + 0.295318i
\(116\) 0 0
\(117\) 5.41421 9.37769i 0.500544 0.866968i
\(118\) 0 0
\(119\) −3.65685 + 8.95743i −0.335223 + 0.821126i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 0 0
\(123\) 6.53553 + 11.3199i 0.589289 + 1.02068i
\(124\) 0 0
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) −15.7279 −1.39563 −0.697814 0.716279i \(-0.745844\pi\)
−0.697814 + 0.716279i \(0.745844\pi\)
\(128\) 0 0
\(129\) −6.82843 11.8272i −0.601209 1.04133i
\(130\) 0 0
\(131\) −0.292893 + 0.507306i −0.0255902 + 0.0443235i −0.878537 0.477674i \(-0.841480\pi\)
0.852947 + 0.521998i \(0.174813\pi\)
\(132\) 0 0
\(133\) 1.53553 0.210133i 0.133148 0.0182208i
\(134\) 0 0
\(135\) −0.121320 + 0.210133i −0.0104416 + 0.0180854i
\(136\) 0 0
\(137\) 8.32843 + 14.4253i 0.711546 + 1.23243i 0.964277 + 0.264897i \(0.0853378\pi\)
−0.252731 + 0.967537i \(0.581329\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 25.3137 2.13180
\(142\) 0 0
\(143\) −1.91421 3.31552i −0.160075 0.277257i
\(144\) 0 0
\(145\) 0.778175 1.34784i 0.0646239 0.111932i
\(146\) 0 0
\(147\) 16.2782 4.54026i 1.34260 0.374474i
\(148\) 0 0
\(149\) −8.82843 + 15.2913i −0.723253 + 1.25271i 0.236436 + 0.971647i \(0.424021\pi\)
−0.959689 + 0.281064i \(0.909313\pi\)
\(150\) 0 0
\(151\) −7.86396 13.6208i −0.639960 1.10844i −0.985441 0.170018i \(-0.945618\pi\)
0.345481 0.938426i \(-0.387716\pi\)
\(152\) 0 0
\(153\) 10.3431 0.836194
\(154\) 0 0
\(155\) −2.34315 −0.188206
\(156\) 0 0
\(157\) −8.82843 15.2913i −0.704585 1.22038i −0.966841 0.255379i \(-0.917800\pi\)
0.262256 0.964998i \(-0.415534\pi\)
\(158\) 0 0
\(159\) −9.53553 + 16.5160i −0.756217 + 1.30981i
\(160\) 0 0
\(161\) 16.3640 2.23936i 1.28966 0.176486i
\(162\) 0 0
\(163\) 4.86396 8.42463i 0.380975 0.659868i −0.610227 0.792227i \(-0.708922\pi\)
0.991202 + 0.132359i \(0.0422551\pi\)
\(164\) 0 0
\(165\) −0.707107 1.22474i −0.0550482 0.0953463i
\(166\) 0 0
\(167\) −13.7279 −1.06230 −0.531149 0.847278i \(-0.678240\pi\)
−0.531149 + 0.847278i \(0.678240\pi\)
\(168\) 0 0
\(169\) 1.65685 0.127450
\(170\) 0 0
\(171\) −0.828427 1.43488i −0.0633514 0.109728i
\(172\) 0 0
\(173\) 4.91421 8.51167i 0.373621 0.647130i −0.616499 0.787356i \(-0.711449\pi\)
0.990120 + 0.140226i \(0.0447828\pi\)
\(174\) 0 0
\(175\) 4.65685 11.4069i 0.352025 0.862282i
\(176\) 0 0
\(177\) −6.74264 + 11.6786i −0.506808 + 0.877817i
\(178\) 0 0
\(179\) 0.449747 + 0.778985i 0.0336157 + 0.0582241i 0.882344 0.470605i \(-0.155964\pi\)
−0.848728 + 0.528829i \(0.822631\pi\)
\(180\) 0 0
\(181\) −7.65685 −0.569129 −0.284565 0.958657i \(-0.591849\pi\)
−0.284565 + 0.958657i \(0.591849\pi\)
\(182\) 0 0
\(183\) 28.5563 2.11095
\(184\) 0 0
\(185\) −2.75736 4.77589i −0.202725 0.351130i
\(186\) 0 0
\(187\) 1.82843 3.16693i 0.133708 0.231589i
\(188\) 0 0
\(189\) 0.671573 + 0.866025i 0.0488497 + 0.0629941i
\(190\) 0 0
\(191\) −3.58579 + 6.21076i −0.259458 + 0.449395i −0.966097 0.258180i \(-0.916877\pi\)
0.706639 + 0.707575i \(0.250211\pi\)
\(192\) 0 0
\(193\) −10.9497 18.9655i −0.788180 1.36517i −0.927081 0.374862i \(-0.877690\pi\)
0.138901 0.990306i \(-0.455643\pi\)
\(194\) 0 0
\(195\) 5.41421 0.387720
\(196\) 0 0
\(197\) −0.514719 −0.0366722 −0.0183361 0.999832i \(-0.505837\pi\)
−0.0183361 + 0.999832i \(0.505837\pi\)
\(198\) 0 0
\(199\) 0.0502525 + 0.0870399i 0.00356231 + 0.00617010i 0.867801 0.496912i \(-0.165533\pi\)
−0.864239 + 0.503082i \(0.832199\pi\)
\(200\) 0 0
\(201\) 3.32843 5.76500i 0.234769 0.406632i
\(202\) 0 0
\(203\) −4.30761 5.55487i −0.302335 0.389876i
\(204\) 0 0
\(205\) −1.58579 + 2.74666i −0.110756 + 0.191835i
\(206\) 0 0
\(207\) −8.82843 15.2913i −0.613618 1.06282i
\(208\) 0 0
\(209\) −0.585786 −0.0405197
\(210\) 0 0
\(211\) −7.41421 −0.510416 −0.255208 0.966886i \(-0.582144\pi\)
−0.255208 + 0.966886i \(0.582144\pi\)
\(212\) 0 0
\(213\) −13.3640 23.1471i −0.915684 1.58601i
\(214\) 0 0
\(215\) 1.65685 2.86976i 0.112997 0.195716i
\(216\) 0 0
\(217\) −4.00000 + 9.79796i −0.271538 + 0.665129i
\(218\) 0 0
\(219\) 11.3640 19.6830i 0.767905 1.33005i
\(220\) 0 0
\(221\) 7.00000 + 12.1244i 0.470871 + 0.815572i
\(222\) 0 0
\(223\) −8.58579 −0.574947 −0.287473 0.957789i \(-0.592815\pi\)
−0.287473 + 0.957789i \(0.592815\pi\)
\(224\) 0 0
\(225\) −13.1716 −0.878105
\(226\) 0 0
\(227\) −14.4142 24.9662i −0.956705 1.65706i −0.730417 0.683001i \(-0.760674\pi\)
−0.226288 0.974061i \(-0.572659\pi\)
\(228\) 0 0
\(229\) −11.6569 + 20.1903i −0.770307 + 1.33421i 0.167088 + 0.985942i \(0.446564\pi\)
−0.937395 + 0.348268i \(0.886770\pi\)
\(230\) 0 0
\(231\) −6.32843 + 0.866025i −0.416380 + 0.0569803i
\(232\) 0 0
\(233\) −0.707107 + 1.22474i −0.0463241 + 0.0802357i −0.888258 0.459345i \(-0.848084\pi\)
0.841934 + 0.539581i \(0.181417\pi\)
\(234\) 0 0
\(235\) 3.07107 + 5.31925i 0.200334 + 0.346989i
\(236\) 0 0
\(237\) 31.9706 2.07671
\(238\) 0 0
\(239\) −20.2132 −1.30748 −0.653742 0.756718i \(-0.726802\pi\)
−0.653742 + 0.756718i \(0.726802\pi\)
\(240\) 0 0
\(241\) −6.12132 10.6024i −0.394309 0.682963i 0.598704 0.800971i \(-0.295683\pi\)
−0.993013 + 0.118007i \(0.962349\pi\)
\(242\) 0 0
\(243\) 10.8284 18.7554i 0.694644 1.20316i
\(244\) 0 0
\(245\) 2.92893 + 2.86976i 0.187123 + 0.183342i
\(246\) 0 0
\(247\) 1.12132 1.94218i 0.0713479 0.123578i
\(248\) 0 0
\(249\) −14.6569 25.3864i −0.928840 1.60880i
\(250\) 0 0
\(251\) 26.1421 1.65008 0.825038 0.565077i \(-0.191153\pi\)
0.825038 + 0.565077i \(0.191153\pi\)
\(252\) 0 0
\(253\) −6.24264 −0.392471
\(254\) 0 0
\(255\) 2.58579 + 4.47871i 0.161928 + 0.280468i
\(256\) 0 0
\(257\) 12.5711 21.7737i 0.784162 1.35821i −0.145337 0.989382i \(-0.546427\pi\)
0.929499 0.368826i \(-0.120240\pi\)
\(258\) 0 0
\(259\) −24.6777 + 3.37706i −1.53340 + 0.209840i
\(260\) 0 0
\(261\) −3.75736 + 6.50794i −0.232575 + 0.402831i
\(262\) 0 0
\(263\) −8.52082 14.7585i −0.525416 0.910047i −0.999562 0.0296008i \(-0.990576\pi\)
0.474146 0.880446i \(-0.342757\pi\)
\(264\) 0 0
\(265\) −4.62742 −0.284260
\(266\) 0 0
\(267\) 30.1421 1.84467
\(268\) 0 0
\(269\) −1.17157 2.02922i −0.0714321 0.123724i 0.828097 0.560585i \(-0.189424\pi\)
−0.899529 + 0.436861i \(0.856090\pi\)
\(270\) 0 0
\(271\) 2.27817 3.94591i 0.138389 0.239697i −0.788498 0.615038i \(-0.789141\pi\)
0.926887 + 0.375340i \(0.122474\pi\)
\(272\) 0 0
\(273\) 9.24264 22.6398i 0.559390 1.37022i
\(274\) 0 0
\(275\) −2.32843 + 4.03295i −0.140409 + 0.243196i
\(276\) 0 0
\(277\) −0.914214 1.58346i −0.0549298 0.0951412i 0.837253 0.546816i \(-0.184160\pi\)
−0.892183 + 0.451675i \(0.850827\pi\)
\(278\) 0 0
\(279\) 11.3137 0.677334
\(280\) 0 0
\(281\) 8.72792 0.520664 0.260332 0.965519i \(-0.416168\pi\)
0.260332 + 0.965519i \(0.416168\pi\)
\(282\) 0 0
\(283\) −11.7071 20.2773i −0.695915 1.20536i −0.969871 0.243618i \(-0.921666\pi\)
0.273956 0.961742i \(-0.411668\pi\)
\(284\) 0 0
\(285\) 0.414214 0.717439i 0.0245359 0.0424974i
\(286\) 0 0
\(287\) 8.77817 + 11.3199i 0.518159 + 0.668191i
\(288\) 0 0
\(289\) 1.81371 3.14144i 0.106689 0.184790i
\(290\) 0 0
\(291\) 4.62132 + 8.00436i 0.270907 + 0.469224i
\(292\) 0 0
\(293\) −10.8284 −0.632603 −0.316302 0.948659i \(-0.602441\pi\)
−0.316302 + 0.948659i \(0.602441\pi\)
\(294\) 0 0
\(295\) −3.27208 −0.190508
\(296\) 0 0
\(297\) −0.207107 0.358719i −0.0120176 0.0208150i
\(298\) 0 0
\(299\) 11.9497 20.6976i 0.691072 1.19697i
\(300\) 0 0
\(301\) −9.17157 11.8272i −0.528641 0.681707i
\(302\) 0 0
\(303\) −7.44975 + 12.9033i −0.427977 + 0.741278i
\(304\) 0 0
\(305\) 3.46447 + 6.00063i 0.198375 + 0.343595i
\(306\) 0 0
\(307\) −9.89949 −0.564994 −0.282497 0.959268i \(-0.591163\pi\)
−0.282497 + 0.959268i \(0.591163\pi\)
\(308\) 0 0
\(309\) −32.3848 −1.84231
\(310\) 0 0
\(311\) 8.36396 + 14.4868i 0.474277 + 0.821471i 0.999566 0.0294522i \(-0.00937629\pi\)
−0.525289 + 0.850924i \(0.676043\pi\)
\(312\) 0 0
\(313\) 10.3284 17.8894i 0.583797 1.01117i −0.411227 0.911533i \(-0.634900\pi\)
0.995024 0.0996335i \(-0.0317670\pi\)
\(314\) 0 0
\(315\) 1.65685 4.05845i 0.0933532 0.228668i
\(316\) 0 0
\(317\) −4.34315 + 7.52255i −0.243935 + 0.422508i −0.961832 0.273642i \(-0.911772\pi\)
0.717896 + 0.696150i \(0.245105\pi\)
\(318\) 0 0
\(319\) 1.32843 + 2.30090i 0.0743776 + 0.128826i
\(320\) 0 0
\(321\) 7.41421 0.413821
\(322\) 0 0
\(323\) 2.14214 0.119192
\(324\) 0 0
\(325\) −8.91421 15.4399i −0.494472 0.856450i
\(326\) 0 0
\(327\) −19.8995 + 34.4669i −1.10044 + 1.90603i
\(328\) 0 0
\(329\) 27.4853 3.76127i 1.51531 0.207366i
\(330\) 0 0
\(331\) −12.0355 + 20.8462i −0.661533 + 1.14581i 0.318680 + 0.947862i \(0.396760\pi\)
−0.980213 + 0.197946i \(0.936573\pi\)
\(332\) 0 0
\(333\) 13.3137 + 23.0600i 0.729587 + 1.26368i
\(334\) 0 0
\(335\) 1.61522 0.0882491
\(336\) 0 0
\(337\) −28.2426 −1.53847 −0.769237 0.638963i \(-0.779364\pi\)
−0.769237 + 0.638963i \(0.779364\pi\)
\(338\) 0 0
\(339\) 9.86396 + 17.0849i 0.535737 + 0.927923i
\(340\) 0 0
\(341\) 2.00000 3.46410i 0.108306 0.187592i
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 0 0
\(345\) 4.41421 7.64564i 0.237653 0.411628i
\(346\) 0 0
\(347\) 8.70711 + 15.0812i 0.467422 + 0.809599i 0.999307 0.0372179i \(-0.0118495\pi\)
−0.531885 + 0.846816i \(0.678516\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 1.58579 0.0846430
\(352\) 0 0
\(353\) 1.34315 + 2.32640i 0.0714884 + 0.123822i 0.899554 0.436810i \(-0.143892\pi\)
−0.828065 + 0.560632i \(0.810558\pi\)
\(354\) 0 0
\(355\) 3.24264 5.61642i 0.172101 0.298089i
\(356\) 0 0
\(357\) 23.1421 3.16693i 1.22481 0.167612i
\(358\) 0 0
\(359\) 9.62132 16.6646i 0.507794 0.879525i −0.492165 0.870502i \(-0.663794\pi\)
0.999959 0.00902308i \(-0.00287218\pi\)
\(360\) 0 0
\(361\) 9.32843 + 16.1573i 0.490970 + 0.850385i
\(362\) 0 0
\(363\) 2.41421 0.126713
\(364\) 0 0
\(365\) 5.51472 0.288654
\(366\) 0 0
\(367\) −5.36396 9.29065i −0.279996 0.484968i 0.691387 0.722485i \(-0.257000\pi\)
−0.971384 + 0.237516i \(0.923667\pi\)
\(368\) 0 0
\(369\) 7.65685 13.2621i 0.398600 0.690395i
\(370\) 0 0
\(371\) −7.89949 + 19.3497i −0.410121 + 1.00459i
\(372\) 0 0
\(373\) 9.98528 17.2950i 0.517018 0.895502i −0.482786 0.875738i \(-0.660375\pi\)
0.999805 0.0197638i \(-0.00629142\pi\)
\(374\) 0 0
\(375\) −6.82843 11.8272i −0.352618 0.610753i
\(376\) 0 0
\(377\) −10.1716 −0.523863
\(378\) 0 0
\(379\) −27.8701 −1.43159 −0.715794 0.698311i \(-0.753935\pi\)
−0.715794 + 0.698311i \(0.753935\pi\)
\(380\) 0 0
\(381\) 18.9853 + 32.8835i 0.972645 + 1.68467i
\(382\) 0 0
\(383\) −3.19239 + 5.52938i −0.163123 + 0.282538i −0.935987 0.352034i \(-0.885490\pi\)
0.772864 + 0.634572i \(0.218824\pi\)
\(384\) 0 0
\(385\) −0.949747 1.22474i −0.0484036 0.0624188i
\(386\) 0 0
\(387\) −8.00000 + 13.8564i −0.406663 + 0.704361i
\(388\) 0 0
\(389\) 11.3640 + 19.6830i 0.576176 + 0.997966i 0.995913 + 0.0903199i \(0.0287889\pi\)
−0.419737 + 0.907646i \(0.637878\pi\)
\(390\) 0 0
\(391\) 22.8284 1.15448
\(392\) 0 0
\(393\) 1.41421 0.0713376
\(394\) 0 0
\(395\) 3.87868 + 6.71807i 0.195158 + 0.338023i
\(396\) 0 0
\(397\) −11.0000 + 19.0526i −0.552074 + 0.956221i 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 0 0
\(399\) −2.29289 2.95680i −0.114788 0.148025i
\(400\) 0 0
\(401\) −9.15685 + 15.8601i −0.457271 + 0.792017i −0.998816 0.0486549i \(-0.984507\pi\)
0.541544 + 0.840672i \(0.317840\pi\)
\(402\) 0 0
\(403\) 7.65685 + 13.2621i 0.381415 + 0.660630i
\(404\) 0 0
\(405\) 5.55635 0.276097
\(406\) 0 0
\(407\) 9.41421 0.466645
\(408\) 0 0
\(409\) −1.36396 2.36245i −0.0674435 0.116816i 0.830332 0.557269i \(-0.188151\pi\)
−0.897775 + 0.440454i \(0.854818\pi\)
\(410\) 0 0
\(411\) 20.1066 34.8257i 0.991786 1.71782i
\(412\) 0 0
\(413\) −5.58579 + 13.6823i −0.274859 + 0.673263i
\(414\) 0 0
\(415\) 3.55635 6.15978i 0.174574 0.302372i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 26.1421 1.27713 0.638563 0.769569i \(-0.279529\pi\)
0.638563 + 0.769569i \(0.279529\pi\)
\(420\) 0 0
\(421\) 0.686292 0.0334478 0.0167239 0.999860i \(-0.494676\pi\)
0.0167239 + 0.999860i \(0.494676\pi\)
\(422\) 0 0
\(423\) −14.8284 25.6836i −0.720983 1.24878i
\(424\) 0 0
\(425\) 8.51472 14.7479i 0.413025 0.715379i
\(426\) 0 0
\(427\) 31.0061 4.24309i 1.50049 0.205337i
\(428\) 0 0
\(429\) −4.62132 + 8.00436i −0.223119 + 0.386454i
\(430\) 0 0
\(431\) −8.79289 15.2297i −0.423539 0.733591i 0.572744 0.819734i \(-0.305879\pi\)
−0.996283 + 0.0861437i \(0.972546\pi\)
\(432\) 0 0
\(433\) 26.1421 1.25631 0.628155 0.778088i \(-0.283810\pi\)
0.628155 + 0.778088i \(0.283810\pi\)
\(434\) 0 0
\(435\) −3.75736 −0.180152
\(436\) 0 0
\(437\) −1.82843 3.16693i −0.0874655 0.151495i
\(438\) 0 0
\(439\) −13.6924 + 23.7159i −0.653502 + 1.13190i 0.328765 + 0.944412i \(0.393368\pi\)
−0.982267 + 0.187487i \(0.939966\pi\)
\(440\) 0 0
\(441\) −14.1421 13.8564i −0.673435 0.659829i
\(442\) 0 0
\(443\) 6.31371 10.9357i 0.299973 0.519569i −0.676156 0.736758i \(-0.736356\pi\)
0.976130 + 0.217189i \(0.0696889\pi\)
\(444\) 0 0
\(445\) 3.65685 + 6.33386i 0.173352 + 0.300254i
\(446\) 0 0
\(447\) 42.6274 2.01621
\(448\) 0 0
\(449\) 22.3431 1.05444 0.527219 0.849729i \(-0.323235\pi\)
0.527219 + 0.849729i \(0.323235\pi\)
\(450\) 0 0
\(451\) −2.70711 4.68885i −0.127473 0.220789i
\(452\) 0 0
\(453\) −18.9853 + 32.8835i −0.892006 + 1.54500i
\(454\) 0 0
\(455\) 5.87868 0.804479i 0.275597 0.0377146i
\(456\) 0 0
\(457\) 5.82843 10.0951i 0.272642 0.472230i −0.696895 0.717173i \(-0.745436\pi\)
0.969538 + 0.244943i \(0.0787691\pi\)
\(458\) 0 0
\(459\) 0.757359 + 1.31178i 0.0353505 + 0.0612289i
\(460\) 0 0
\(461\) −8.31371 −0.387208 −0.193604 0.981080i \(-0.562018\pi\)
−0.193604 + 0.981080i \(0.562018\pi\)
\(462\) 0 0
\(463\) −12.8284 −0.596188 −0.298094 0.954537i \(-0.596351\pi\)
−0.298094 + 0.954537i \(0.596351\pi\)
\(464\) 0 0
\(465\) 2.82843 + 4.89898i 0.131165 + 0.227185i
\(466\) 0 0
\(467\) −17.0000 + 29.4449i −0.786666 + 1.36255i 0.141332 + 0.989962i \(0.454861\pi\)
−0.927999 + 0.372584i \(0.878472\pi\)
\(468\) 0 0
\(469\) 2.75736 6.75412i 0.127323 0.311876i
\(470\) 0 0
\(471\) −21.3137 + 36.9164i −0.982084 + 1.70102i
\(472\) 0 0
\(473\) 2.82843 + 4.89898i 0.130051 + 0.225255i
\(474\) 0 0
\(475\) −2.72792 −0.125166
\(476\) 0 0
\(477\) 22.3431 1.02302
\(478\) 0 0
\(479\) −5.96447 10.3308i −0.272523 0.472024i 0.696984 0.717087i \(-0.254525\pi\)
−0.969507 + 0.245062i \(0.921192\pi\)
\(480\) 0 0
\(481\) −18.0208 + 31.2130i −0.821678 + 1.42319i
\(482\) 0 0
\(483\) −24.4350 31.5101i −1.11183 1.43376i
\(484\) 0 0
\(485\) −1.12132 + 1.94218i −0.0509165 + 0.0881900i
\(486\) 0 0
\(487\) −4.82843 8.36308i −0.218797 0.378967i 0.735644 0.677369i \(-0.236880\pi\)
−0.954440 + 0.298402i \(0.903547\pi\)
\(488\) 0 0
\(489\) −23.4853 −1.06204
\(490\) 0 0
\(491\) −19.1716 −0.865201 −0.432600 0.901586i \(-0.642404\pi\)
−0.432600 + 0.901586i \(0.642404\pi\)
\(492\) 0 0
\(493\) −4.85786 8.41407i −0.218787 0.378951i
\(494\) 0 0
\(495\) −0.828427 + 1.43488i −0.0372350 + 0.0644930i
\(496\) 0 0
\(497\) −17.9497 23.1471i −0.805156 1.03829i
\(498\) 0 0
\(499\) 11.0711 19.1757i 0.495609 0.858420i −0.504378 0.863483i \(-0.668278\pi\)
0.999987 + 0.00506282i \(0.00161155\pi\)
\(500\) 0 0
\(501\) 16.5711 + 28.7019i 0.740341 + 1.28231i
\(502\) 0 0
\(503\) −4.21320 −0.187857 −0.0939287 0.995579i \(-0.529943\pi\)
−0.0939287 + 0.995579i \(0.529943\pi\)
\(504\) 0 0
\(505\) −3.61522 −0.160875
\(506\) 0 0
\(507\) −2.00000 3.46410i −0.0888231 0.153846i
\(508\) 0 0
\(509\) −4.65685 + 8.06591i −0.206411 + 0.357515i −0.950582 0.310475i \(-0.899512\pi\)
0.744170 + 0.667990i \(0.232845\pi\)
\(510\) 0 0
\(511\) 9.41421 23.0600i 0.416460 1.02012i
\(512\) 0 0
\(513\) 0.121320 0.210133i 0.00535642 0.00927760i
\(514\) 0 0
\(515\) −3.92893 6.80511i −0.173129 0.299869i
\(516\) 0 0
\(517\) −10.4853 −0.461142
\(518\) 0 0
\(519\) −23.7279 −1.04154
\(520\) 0 0
\(521\) 14.1421 + 24.4949i 0.619578 + 1.07314i 0.989563 + 0.144103i \(0.0460297\pi\)
−0.369984 + 0.929038i \(0.620637\pi\)
\(522\) 0 0
\(523\) −6.36396 + 11.0227i −0.278277 + 0.481989i −0.970957 0.239256i \(-0.923097\pi\)
0.692680 + 0.721245i \(0.256430\pi\)
\(524\) 0 0
\(525\) −29.4706 + 4.03295i −1.28620 + 0.176013i
\(526\) 0 0
\(527\) −7.31371 + 12.6677i −0.318590 + 0.551814i
\(528\) 0 0
\(529\) −7.98528 13.8309i −0.347186 0.601344i
\(530\) 0 0
\(531\) 15.7990 0.685618
\(532\) 0 0
\(533\) 20.7279 0.897826
\(534\) 0 0
\(535\) 0.899495 + 1.55797i 0.0388886 + 0.0673570i
\(536\) 0 0
\(537\) 1.08579 1.88064i 0.0468551 0.0811555i
\(538\) 0 0
\(539\) −6.74264 + 1.88064i −0.290426 + 0.0810048i
\(540\) 0 0
\(541\) 6.42893 11.1352i 0.276401 0.478741i −0.694086 0.719892i \(-0.744191\pi\)
0.970488 + 0.241151i \(0.0775248\pi\)
\(542\) 0 0
\(543\) 9.24264 + 16.0087i 0.396640 + 0.687000i
\(544\) 0 0
\(545\) −9.65685 −0.413654
\(546\) 0 0
\(547\) −34.8701 −1.49094 −0.745468 0.666541i \(-0.767774\pi\)
−0.745468 + 0.666541i \(0.767774\pi\)
\(548\) 0 0
\(549\) −16.7279 28.9736i −0.713930 1.23656i
\(550\) 0 0
\(551\) −0.778175 + 1.34784i −0.0331514 + 0.0574198i
\(552\) 0 0
\(553\) 34.7132 4.75039i 1.47616 0.202007i
\(554\) 0 0
\(555\) −6.65685 + 11.5300i −0.282568 + 0.489422i
\(556\) 0 0
\(557\) −3.75736 6.50794i −0.159204 0.275750i 0.775378 0.631498i \(-0.217560\pi\)
−0.934582 + 0.355748i \(0.884226\pi\)
\(558\) 0 0
\(559\) −21.6569 −0.915987
\(560\) 0 0
\(561\) −8.82843 −0.372736
\(562\) 0 0
\(563\) 4.53553 + 7.85578i 0.191150 + 0.331081i 0.945632 0.325240i \(-0.105445\pi\)
−0.754482 + 0.656321i \(0.772112\pi\)
\(564\) 0 0
\(565\) −2.39340 + 4.14549i −0.100691 + 0.174402i
\(566\) 0 0
\(567\) 9.48528 23.2341i 0.398344 0.975740i
\(568\) 0 0
\(569\) 2.00000 3.46410i 0.0838444 0.145223i −0.821054 0.570851i \(-0.806613\pi\)
0.904898 + 0.425628i \(0.139947\pi\)
\(570\) 0 0
\(571\) 13.1924 + 22.8499i 0.552084 + 0.956238i 0.998124 + 0.0612248i \(0.0195007\pi\)
−0.446040 + 0.895013i \(0.647166\pi\)
\(572\) 0 0
\(573\) 17.3137 0.723291
\(574\) 0 0
\(575\) −29.0711 −1.21235
\(576\) 0 0
\(577\) 4.84315 + 8.38857i 0.201623 + 0.349221i 0.949051 0.315121i \(-0.102045\pi\)
−0.747429 + 0.664342i \(0.768712\pi\)
\(578\) 0 0
\(579\) −26.4350 + 45.7868i −1.09860 + 1.90284i
\(580\) 0 0
\(581\) −19.6863 25.3864i −0.816725 1.05321i
\(582\) 0 0
\(583\) 3.94975 6.84116i 0.163582 0.283332i
\(584\) 0 0
\(585\) −3.17157 5.49333i −0.131128 0.227121i
\(586\) 0 0
\(587\) 25.1005 1.03601 0.518004 0.855378i \(-0.326675\pi\)
0.518004 + 0.855378i \(0.326675\pi\)
\(588\) 0 0
\(589\) 2.34315 0.0965476
\(590\) 0 0
\(591\) 0.621320 + 1.07616i 0.0255577 + 0.0442672i
\(592\) 0 0
\(593\) −11.8492 + 20.5235i −0.486590 + 0.842799i −0.999881 0.0154159i \(-0.995093\pi\)
0.513291 + 0.858215i \(0.328426\pi\)
\(594\) 0 0
\(595\) 3.47309 + 4.47871i 0.142383 + 0.183609i
\(596\) 0 0
\(597\) 0.121320 0.210133i 0.00496531 0.00860017i
\(598\) 0 0
\(599\) 21.3137 + 36.9164i 0.870855 + 1.50836i 0.861114 + 0.508412i \(0.169767\pi\)
0.00974040 + 0.999953i \(0.496899\pi\)
\(600\) 0 0
\(601\) 31.9411 1.30291 0.651453 0.758689i \(-0.274160\pi\)
0.651453 + 0.758689i \(0.274160\pi\)
\(602\) 0 0
\(603\) −7.79899 −0.317599
\(604\) 0 0
\(605\) 0.292893 + 0.507306i 0.0119078 + 0.0206249i
\(606\) 0 0
\(607\) −21.4853 + 37.2136i −0.872061 + 1.51045i −0.0121994 + 0.999926i \(0.503883\pi\)
−0.859861 + 0.510528i \(0.829450\pi\)
\(608\) 0 0
\(609\) −6.41421 + 15.7116i −0.259917 + 0.636664i
\(610\) 0 0
\(611\) 20.0711 34.7641i 0.811988 1.40641i
\(612\) 0 0
\(613\) −14.3137 24.7921i −0.578125 1.00134i −0.995694 0.0926971i \(-0.970451\pi\)
0.417569 0.908645i \(-0.362882\pi\)
\(614\) 0 0
\(615\) 7.65685 0.308754
\(616\) 0 0
\(617\) −41.9706 −1.68967 −0.844836 0.535026i \(-0.820302\pi\)
−0.844836 + 0.535026i \(0.820302\pi\)
\(618\) 0 0
\(619\) −10.9706 19.0016i −0.440944 0.763738i 0.556816 0.830636i \(-0.312023\pi\)
−0.997760 + 0.0668984i \(0.978690\pi\)
\(620\) 0 0
\(621\) 1.29289 2.23936i 0.0518820 0.0898623i
\(622\) 0 0
\(623\) 32.7279 4.47871i 1.31122 0.179436i
\(624\) 0 0
\(625\) −9.98528 + 17.2950i −0.399411 + 0.691801i
\(626\) 0 0
\(627\) 0.707107 + 1.22474i 0.0282391 + 0.0489116i
\(628\) 0 0
\(629\) −34.4264 −1.37267
\(630\) 0 0
\(631\) −23.2721 −0.926447 −0.463223 0.886242i \(-0.653307\pi\)
−0.463223 + 0.886242i \(0.653307\pi\)
\(632\) 0 0
\(633\) 8.94975 + 15.5014i 0.355721 + 0.616126i
\(634\) 0 0
\(635\) −4.60660 + 7.97887i −0.182807 + 0.316632i
\(636\) 0 0
\(637\) 6.67157 25.9553i 0.264337 1.02839i
\(638\) 0 0
\(639\) −15.6569 + 27.1185i −0.619376 + 1.07279i
\(640\) 0 0
\(641\) −7.64214 13.2366i −0.301846 0.522813i 0.674708 0.738085i \(-0.264270\pi\)
−0.976554 + 0.215272i \(0.930936\pi\)
\(642\) 0 0
\(643\) −1.58579 −0.0625373 −0.0312687 0.999511i \(-0.509955\pi\)
−0.0312687 + 0.999511i \(0.509955\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) 15.0919 + 26.1399i 0.593323 + 1.02767i 0.993781 + 0.111351i \(0.0355177\pi\)
−0.400458 + 0.916315i \(0.631149\pi\)
\(648\) 0 0
\(649\) 2.79289 4.83743i 0.109631 0.189886i
\(650\) 0 0
\(651\) 25.3137 3.46410i 0.992122 0.135769i
\(652\) 0 0
\(653\) 9.19239 15.9217i 0.359726 0.623064i −0.628189 0.778061i \(-0.716204\pi\)
0.987915 + 0.154997i \(0.0495369\pi\)
\(654\) 0 0
\(655\) 0.171573 + 0.297173i 0.00670391 + 0.0116115i
\(656\) 0 0
\(657\) −26.6274 −1.03883
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −9.48528 16.4290i −0.368935 0.639014i 0.620465 0.784234i \(-0.286944\pi\)
−0.989399 + 0.145221i \(0.953611\pi\)
\(662\) 0 0
\(663\) 16.8995 29.2708i 0.656322 1.13678i
\(664\) 0 0
\(665\) 0.343146 0.840532i 0.0133066 0.0325944i
\(666\) 0 0
\(667\) −8.29289 + 14.3637i −0.321102 + 0.556165i
\(668\) 0 0
\(669\) 10.3640 + 17.9509i 0.400694 + 0.694022i
\(670\) 0 0
\(671\) −11.8284 −0.456631
\(672\) 0 0
\(673\) 5.55635 0.214182 0.107091 0.994249i \(-0.465846\pi\)
0.107091 + 0.994249i \(0.465846\pi\)
\(674\) 0 0
\(675\) −0.964466 1.67050i −0.0371223 0.0642977i
\(676\) 0 0
\(677\) 17.6569 30.5826i 0.678608 1.17538i −0.296792 0.954942i \(-0.595917\pi\)
0.975400 0.220441i \(-0.0707498\pi\)
\(678\) 0 0
\(679\) 6.20711 + 8.00436i 0.238207 + 0.307179i
\(680\) 0 0
\(681\) −34.7990 + 60.2736i −1.33350 + 2.30969i
\(682\) 0 0
\(683\) 6.79289 + 11.7656i 0.259923 + 0.450200i 0.966221 0.257715i \(-0.0829695\pi\)
−0.706298 + 0.707914i \(0.749636\pi\)
\(684\) 0 0
\(685\) 9.75736 0.372810
\(686\) 0 0
\(687\) 56.2843 2.14738
\(688\) 0 0
\(689\) 15.1213 + 26.1909i 0.576076 + 0.997794i
\(690\) 0 0
\(691\) 14.0355 24.3103i 0.533937 0.924806i −0.465277 0.885165i \(-0.654045\pi\)
0.999214 0.0396407i \(-0.0126213\pi\)
\(692\) 0 0
\(693\) 4.58579 + 5.91359i 0.174200 + 0.224639i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 9.89949 + 17.1464i 0.374970 + 0.649467i
\(698\) 0 0
\(699\) 3.41421 0.129137
\(700\) 0 0
\(701\) −26.1127 −0.986263 −0.493132 0.869955i \(-0.664148\pi\)
−0.493132 + 0.869955i \(0.664148\pi\)
\(702\) 0 0
\(703\) 2.75736 + 4.77589i 0.103996 + 0.180126i
\(704\) 0 0
\(705\) 7.41421 12.8418i 0.279235 0.483650i
\(706\) 0 0
\(707\) −6.17157 + 15.1172i −0.232106 + 0.568541i
\(708\) 0 0
\(709\) 6.02082 10.4284i 0.226116 0.391645i −0.730537 0.682873i \(-0.760730\pi\)
0.956654 + 0.291228i \(0.0940637\pi\)
\(710\) 0 0
\(711\) −18.7279 32.4377i −0.702352 1.21651i
\(712\) 0 0
\(713\) 24.9706 0.935155
\(714\) 0 0
\(715\) −2.24264 −0.0838700
\(716\) 0 0
\(717\) 24.3995 + 42.2612i 0.911216 + 1.57827i
\(718\) 0 0
\(719\) −0.757359 + 1.31178i −0.0282447 + 0.0489213i −0.879802 0.475340i \(-0.842325\pi\)
0.851558 + 0.524261i \(0.175658\pi\)
\(720\) 0 0
\(721\) −35.1630 + 4.81194i −1.30954 + 0.179206i
\(722\) 0 0
\(723\) −14.7782 + 25.5965i −0.549606 + 0.951946i
\(724\) 0 0
\(725\) 6.18629 + 10.7150i 0.229753 + 0.397944i
\(726\) 0 0
\(727\) −36.4264 −1.35098 −0.675490 0.737369i \(-0.736068\pi\)
−0.675490 + 0.737369i \(0.736068\pi\)
\(728\) 0 0
\(729\) −23.8284 −0.882534
\(730\) 0 0
\(731\) −10.3431 17.9149i −0.382555 0.662605i
\(732\) 0 0
\(733\) 6.50000 11.2583i 0.240083 0.415836i −0.720655 0.693294i \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894920\pi\)
\(734\) 0 0
\(735\) 2.46447 9.58783i 0.0909032 0.353652i
\(736\) 0 0
\(737\) −1.37868 + 2.38794i −0.0507843 + 0.0879610i
\(738\) 0 0
\(739\) −26.2132 45.4026i −0.964268 1.67016i −0.711568 0.702617i \(-0.752015\pi\)
−0.252700 0.967545i \(-0.581319\pi\)
\(740\) 0 0
\(741\) −5.41421 −0.198896
\(742\) 0 0
\(743\) 13.3137 0.488433 0.244216 0.969721i \(-0.421469\pi\)
0.244216 + 0.969721i \(0.421469\pi\)
\(744\) 0 0
\(745\) 5.17157 + 8.95743i 0.189472 + 0.328175i
\(746\) 0 0
\(747\) −17.1716 + 29.7420i −0.628275 + 1.08820i
\(748\) 0 0
\(749\) 8.05025 1.10165i 0.294150 0.0402535i
\(750\) 0 0
\(751\) 22.8284 39.5400i 0.833021 1.44283i −0.0626103 0.998038i \(-0.519943\pi\)
0.895631 0.444797i \(-0.146724\pi\)
\(752\) 0 0
\(753\) −31.5563 54.6572i −1.14998 1.99182i
\(754\) 0 0
\(755\) −9.21320 −0.335303
\(756\) 0 0
\(757\) 8.34315 0.303237 0.151618 0.988439i \(-0.451552\pi\)
0.151618 + 0.988439i \(0.451552\pi\)
\(758\) 0 0
\(759\) 7.53553 + 13.0519i 0.273523 + 0.473755i
\(760\) 0 0
\(761\) −15.4853 + 26.8213i −0.561341 + 0.972271i 0.436039 + 0.899928i \(0.356381\pi\)
−0.997380 + 0.0723433i \(0.976952\pi\)
\(762\) 0 0
\(763\) −16.4853 + 40.3805i −0.596807 + 1.46187i
\(764\) 0 0
\(765\) 3.02944 5.24714i 0.109530 0.189711i
\(766\) 0 0
\(767\) 10.6924 + 18.5198i 0.386080 + 0.668710i
\(768\) 0 0
\(769\) 22.9706 0.828340 0.414170 0.910200i \(-0.364072\pi\)
0.414170 + 0.910200i \(0.364072\pi\)
\(770\) 0 0
\(771\) −60.6985 −2.18600
\(772\) 0 0
\(773\) 10.9706 + 19.0016i 0.394584 + 0.683439i 0.993048 0.117710i \(-0.0375555\pi\)
−0.598464 + 0.801150i \(0.704222\pi\)
\(774\) 0 0
\(775\) 9.31371 16.1318i 0.334558 0.579472i
\(776\) 0 0
\(777\) 36.8492 + 47.5189i 1.32196 + 1.70473i
\(778\) 0 0
\(779\) 1.58579 2.74666i 0.0568167 0.0984094i
\(780\) 0 0
\(781\) 5.53553 + 9.58783i 0.198077 + 0.343079i
\(782\) 0 0
\(783\) −1.10051 −0.0393288
\(784\) 0 0
\(785\) −10.3431 −0.369163
\(786\) 0 0
\(787\) 6.77817 + 11.7401i 0.241616 + 0.418491i 0.961175 0.275941i \(-0.0889893\pi\)
−0.719559 + 0.694431i \(0.755656\pi\)
\(788\) 0 0
\(789\) −20.5711 + 35.6301i −0.732349 + 1.26847i
\(790\) 0 0
\(791\) 13.2487 + 17.0849i 0.471071 + 0.607468i
\(792\) 0 0
\(793\) 22.6421 39.2173i 0.804046 1.39265i
\(794\) 0 0
\(795\) 5.58579 + 9.67487i 0.198107 + 0.343132i
\(796\) 0 0