Properties

Label 4020.2.q.k.841.5
Level 4020
Weight 2
Character 4020.841
Analytic conductor 32.100
Analytic rank 0
Dimension 14
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.q (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 841.5
Root \(1.24942 - 2.16407i\)
Character \(\chi\) = 4020.841
Dual form 4020.2.q.k.3781.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +(1.07806 - 1.86725i) q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} +(1.07806 - 1.86725i) q^{7} +1.00000 q^{9} +(2.31297 - 4.00618i) q^{11} +(2.99885 + 5.19416i) q^{13} -1.00000 q^{15} +(3.06661 + 5.31152i) q^{17} +(2.62213 + 4.54165i) q^{19} +(-1.07806 + 1.86725i) q^{21} +(-0.436687 - 0.756365i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-2.60303 + 4.50859i) q^{29} +(1.56927 - 2.71805i) q^{31} +(-2.31297 + 4.00618i) q^{33} +(1.07806 - 1.86725i) q^{35} +(1.89501 + 3.28225i) q^{37} +(-2.99885 - 5.19416i) q^{39} +(-4.79372 + 8.30297i) q^{41} -5.46495 q^{43} +1.00000 q^{45} +(-3.90018 + 6.75530i) q^{47} +(1.17558 + 2.03617i) q^{49} +(-3.06661 - 5.31152i) q^{51} -6.77213 q^{53} +(2.31297 - 4.00618i) q^{55} +(-2.62213 - 4.54165i) q^{57} +5.61145 q^{59} +(-1.75300 - 3.03629i) q^{61} +(1.07806 - 1.86725i) q^{63} +(2.99885 + 5.19416i) q^{65} +(3.47231 - 7.41236i) q^{67} +(0.436687 + 0.756365i) q^{69} +(2.58722 - 4.48120i) q^{71} +(-0.841448 - 1.45743i) q^{73} -1.00000 q^{75} +(-4.98703 - 8.63778i) q^{77} +(-2.70536 + 4.68582i) q^{79} +1.00000 q^{81} +(7.83527 + 13.5711i) q^{83} +(3.06661 + 5.31152i) q^{85} +(2.60303 - 4.50859i) q^{87} -7.97892 q^{89} +12.9317 q^{91} +(-1.56927 + 2.71805i) q^{93} +(2.62213 + 4.54165i) q^{95} +(5.01466 + 8.68565i) q^{97} +(2.31297 - 4.00618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + 6q^{11} + 9q^{13} - 14q^{15} - 12q^{17} + 14q^{19} - 3q^{21} + 6q^{23} + 14q^{25} - 14q^{27} - q^{29} + 7q^{31} - 6q^{33} + 3q^{35} - 2q^{37} - 9q^{39} - 18q^{41} - 6q^{43} + 14q^{45} + 7q^{47} + 12q^{51} - 12q^{53} + 6q^{55} - 14q^{57} - 2q^{59} + 3q^{63} + 9q^{65} + 25q^{67} - 6q^{69} + 22q^{71} - 15q^{73} - 14q^{75} + q^{77} + 9q^{79} + 14q^{81} - q^{83} - 12q^{85} + q^{87} - 12q^{89} - 38q^{91} - 7q^{93} + 14q^{95} + 16q^{97} + 6q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.07806 1.86725i 0.407468 0.705755i −0.587138 0.809487i \(-0.699745\pi\)
0.994605 + 0.103732i \(0.0330786\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.31297 4.00618i 0.697386 1.20791i −0.271984 0.962302i \(-0.587680\pi\)
0.969370 0.245606i \(-0.0789869\pi\)
\(12\) 0 0
\(13\) 2.99885 + 5.19416i 0.831731 + 1.44060i 0.896664 + 0.442711i \(0.145983\pi\)
−0.0649329 + 0.997890i \(0.520683\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 3.06661 + 5.31152i 0.743761 + 1.28823i 0.950771 + 0.309893i \(0.100293\pi\)
−0.207010 + 0.978339i \(0.566373\pi\)
\(18\) 0 0
\(19\) 2.62213 + 4.54165i 0.601557 + 1.04193i 0.992585 + 0.121549i \(0.0387860\pi\)
−0.391029 + 0.920379i \(0.627881\pi\)
\(20\) 0 0
\(21\) −1.07806 + 1.86725i −0.235252 + 0.407468i
\(22\) 0 0
\(23\) −0.436687 0.756365i −0.0910556 0.157713i 0.816900 0.576779i \(-0.195691\pi\)
−0.907956 + 0.419066i \(0.862357\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.60303 + 4.50859i −0.483371 + 0.837223i −0.999818 0.0190961i \(-0.993921\pi\)
0.516447 + 0.856319i \(0.327254\pi\)
\(30\) 0 0
\(31\) 1.56927 2.71805i 0.281849 0.488176i −0.689991 0.723818i \(-0.742386\pi\)
0.971840 + 0.235641i \(0.0757190\pi\)
\(32\) 0 0
\(33\) −2.31297 + 4.00618i −0.402636 + 0.697386i
\(34\) 0 0
\(35\) 1.07806 1.86725i 0.182225 0.315623i
\(36\) 0 0
\(37\) 1.89501 + 3.28225i 0.311538 + 0.539599i 0.978695 0.205317i \(-0.0658226\pi\)
−0.667158 + 0.744917i \(0.732489\pi\)
\(38\) 0 0
\(39\) −2.99885 5.19416i −0.480200 0.831731i
\(40\) 0 0
\(41\) −4.79372 + 8.30297i −0.748654 + 1.29671i 0.199815 + 0.979834i \(0.435966\pi\)
−0.948468 + 0.316872i \(0.897367\pi\)
\(42\) 0 0
\(43\) −5.46495 −0.833396 −0.416698 0.909045i \(-0.636813\pi\)
−0.416698 + 0.909045i \(0.636813\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −3.90018 + 6.75530i −0.568899 + 0.985362i 0.427776 + 0.903885i \(0.359297\pi\)
−0.996675 + 0.0814776i \(0.974036\pi\)
\(48\) 0 0
\(49\) 1.17558 + 2.03617i 0.167940 + 0.290881i
\(50\) 0 0
\(51\) −3.06661 5.31152i −0.429411 0.743761i
\(52\) 0 0
\(53\) −6.77213 −0.930224 −0.465112 0.885252i \(-0.653986\pi\)
−0.465112 + 0.885252i \(0.653986\pi\)
\(54\) 0 0
\(55\) 2.31297 4.00618i 0.311880 0.540193i
\(56\) 0 0
\(57\) −2.62213 4.54165i −0.347309 0.601557i
\(58\) 0 0
\(59\) 5.61145 0.730549 0.365274 0.930900i \(-0.380975\pi\)
0.365274 + 0.930900i \(0.380975\pi\)
\(60\) 0 0
\(61\) −1.75300 3.03629i −0.224449 0.388757i 0.731705 0.681622i \(-0.238725\pi\)
−0.956154 + 0.292864i \(0.905392\pi\)
\(62\) 0 0
\(63\) 1.07806 1.86725i 0.135823 0.235252i
\(64\) 0 0
\(65\) 2.99885 + 5.19416i 0.371962 + 0.644256i
\(66\) 0 0
\(67\) 3.47231 7.41236i 0.424210 0.905564i
\(68\) 0 0
\(69\) 0.436687 + 0.756365i 0.0525710 + 0.0910556i
\(70\) 0 0
\(71\) 2.58722 4.48120i 0.307047 0.531820i −0.670668 0.741757i \(-0.733993\pi\)
0.977715 + 0.209937i \(0.0673259\pi\)
\(72\) 0 0
\(73\) −0.841448 1.45743i −0.0984840 0.170579i 0.812573 0.582859i \(-0.198066\pi\)
−0.911057 + 0.412280i \(0.864733\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) −4.98703 8.63778i −0.568324 0.984367i
\(78\) 0 0
\(79\) −2.70536 + 4.68582i −0.304377 + 0.527196i −0.977122 0.212678i \(-0.931782\pi\)
0.672745 + 0.739874i \(0.265115\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 7.83527 + 13.5711i 0.860033 + 1.48962i 0.871896 + 0.489690i \(0.162890\pi\)
−0.0118638 + 0.999930i \(0.503776\pi\)
\(84\) 0 0
\(85\) 3.06661 + 5.31152i 0.332620 + 0.576115i
\(86\) 0 0
\(87\) 2.60303 4.50859i 0.279074 0.483371i
\(88\) 0 0
\(89\) −7.97892 −0.845764 −0.422882 0.906185i \(-0.638982\pi\)
−0.422882 + 0.906185i \(0.638982\pi\)
\(90\) 0 0
\(91\) 12.9317 1.35561
\(92\) 0 0
\(93\) −1.56927 + 2.71805i −0.162725 + 0.281849i
\(94\) 0 0
\(95\) 2.62213 + 4.54165i 0.269024 + 0.465964i
\(96\) 0 0
\(97\) 5.01466 + 8.68565i 0.509162 + 0.881894i 0.999944 + 0.0106116i \(0.00337785\pi\)
−0.490782 + 0.871282i \(0.663289\pi\)
\(98\) 0 0
\(99\) 2.31297 4.00618i 0.232462 0.402636i
\(100\) 0 0
\(101\) 9.06051 15.6933i 0.901555 1.56154i 0.0760781 0.997102i \(-0.475760\pi\)
0.825476 0.564436i \(-0.190906\pi\)
\(102\) 0 0
\(103\) −4.74446 + 8.21765i −0.467485 + 0.809709i −0.999310 0.0371461i \(-0.988173\pi\)
0.531824 + 0.846855i \(0.321507\pi\)
\(104\) 0 0
\(105\) −1.07806 + 1.86725i −0.105208 + 0.182225i
\(106\) 0 0
\(107\) −15.3498 −1.48392 −0.741960 0.670445i \(-0.766103\pi\)
−0.741960 + 0.670445i \(0.766103\pi\)
\(108\) 0 0
\(109\) −6.26073 −0.599669 −0.299834 0.953991i \(-0.596931\pi\)
−0.299834 + 0.953991i \(0.596931\pi\)
\(110\) 0 0
\(111\) −1.89501 3.28225i −0.179866 0.311538i
\(112\) 0 0
\(113\) 6.08157 10.5336i 0.572106 0.990917i −0.424243 0.905548i \(-0.639460\pi\)
0.996349 0.0853686i \(-0.0272068\pi\)
\(114\) 0 0
\(115\) −0.436687 0.756365i −0.0407213 0.0705314i
\(116\) 0 0
\(117\) 2.99885 + 5.19416i 0.277244 + 0.480200i
\(118\) 0 0
\(119\) 13.2239 1.21223
\(120\) 0 0
\(121\) −5.19963 9.00603i −0.472694 0.818730i
\(122\) 0 0
\(123\) 4.79372 8.30297i 0.432235 0.748654i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 6.63481 11.4918i 0.588744 1.01973i −0.405653 0.914027i \(-0.632956\pi\)
0.994397 0.105707i \(-0.0337107\pi\)
\(128\) 0 0
\(129\) 5.46495 0.481162
\(130\) 0 0
\(131\) −0.697341 −0.0609270 −0.0304635 0.999536i \(-0.509698\pi\)
−0.0304635 + 0.999536i \(0.509698\pi\)
\(132\) 0 0
\(133\) 11.3072 0.980460
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 11.5162 0.983892 0.491946 0.870626i \(-0.336286\pi\)
0.491946 + 0.870626i \(0.336286\pi\)
\(138\) 0 0
\(139\) −2.18220 −0.185092 −0.0925460 0.995708i \(-0.529501\pi\)
−0.0925460 + 0.995708i \(0.529501\pi\)
\(140\) 0 0
\(141\) 3.90018 6.75530i 0.328454 0.568899i
\(142\) 0 0
\(143\) 27.7450 2.32015
\(144\) 0 0
\(145\) −2.60303 + 4.50859i −0.216170 + 0.374418i
\(146\) 0 0
\(147\) −1.17558 2.03617i −0.0969603 0.167940i
\(148\) 0 0
\(149\) −8.90881 −0.729838 −0.364919 0.931039i \(-0.618903\pi\)
−0.364919 + 0.931039i \(0.618903\pi\)
\(150\) 0 0
\(151\) −0.0253744 0.0439498i −0.00206494 0.00357659i 0.864991 0.501787i \(-0.167324\pi\)
−0.867056 + 0.498211i \(0.833991\pi\)
\(152\) 0 0
\(153\) 3.06661 + 5.31152i 0.247920 + 0.429411i
\(154\) 0 0
\(155\) 1.56927 2.71805i 0.126047 0.218319i
\(156\) 0 0
\(157\) 8.62937 + 14.9465i 0.688698 + 1.19286i 0.972259 + 0.233906i \(0.0751509\pi\)
−0.283561 + 0.958954i \(0.591516\pi\)
\(158\) 0 0
\(159\) 6.77213 0.537065
\(160\) 0 0
\(161\) −1.88310 −0.148409
\(162\) 0 0
\(163\) −9.40567 + 16.2911i −0.736709 + 1.27602i 0.217261 + 0.976114i \(0.430288\pi\)
−0.953969 + 0.299904i \(0.903045\pi\)
\(164\) 0 0
\(165\) −2.31297 + 4.00618i −0.180064 + 0.311880i
\(166\) 0 0
\(167\) −1.29815 + 2.24847i −0.100454 + 0.173991i −0.911872 0.410475i \(-0.865363\pi\)
0.811418 + 0.584467i \(0.198696\pi\)
\(168\) 0 0
\(169\) −11.4862 + 19.8947i −0.883554 + 1.53036i
\(170\) 0 0
\(171\) 2.62213 + 4.54165i 0.200519 + 0.347309i
\(172\) 0 0
\(173\) −9.80640 16.9852i −0.745567 1.29136i −0.949929 0.312465i \(-0.898845\pi\)
0.204362 0.978895i \(-0.434488\pi\)
\(174\) 0 0
\(175\) 1.07806 1.86725i 0.0814935 0.141151i
\(176\) 0 0
\(177\) −5.61145 −0.421782
\(178\) 0 0
\(179\) −8.75619 −0.654469 −0.327234 0.944943i \(-0.606117\pi\)
−0.327234 + 0.944943i \(0.606117\pi\)
\(180\) 0 0
\(181\) 2.68166 4.64477i 0.199326 0.345243i −0.748984 0.662588i \(-0.769458\pi\)
0.948310 + 0.317345i \(0.102791\pi\)
\(182\) 0 0
\(183\) 1.75300 + 3.03629i 0.129586 + 0.224449i
\(184\) 0 0
\(185\) 1.89501 + 3.28225i 0.139324 + 0.241316i
\(186\) 0 0
\(187\) 28.3718 2.07475
\(188\) 0 0
\(189\) −1.07806 + 1.86725i −0.0784172 + 0.135823i
\(190\) 0 0
\(191\) −7.83945 13.5783i −0.567242 0.982493i −0.996837 0.0794708i \(-0.974677\pi\)
0.429595 0.903022i \(-0.358656\pi\)
\(192\) 0 0
\(193\) 3.33316 0.239926 0.119963 0.992778i \(-0.461722\pi\)
0.119963 + 0.992778i \(0.461722\pi\)
\(194\) 0 0
\(195\) −2.99885 5.19416i −0.214752 0.371962i
\(196\) 0 0
\(197\) −10.9023 + 18.8833i −0.776756 + 1.34538i 0.157047 + 0.987591i \(0.449803\pi\)
−0.933802 + 0.357789i \(0.883531\pi\)
\(198\) 0 0
\(199\) 12.6316 + 21.8786i 0.895430 + 1.55093i 0.833271 + 0.552865i \(0.186465\pi\)
0.0621595 + 0.998066i \(0.480201\pi\)
\(200\) 0 0
\(201\) −3.47231 + 7.41236i −0.244918 + 0.522828i
\(202\) 0 0
\(203\) 5.61244 + 9.72104i 0.393916 + 0.682283i
\(204\) 0 0
\(205\) −4.79372 + 8.30297i −0.334808 + 0.579905i
\(206\) 0 0
\(207\) −0.436687 0.756365i −0.0303519 0.0525710i
\(208\) 0 0
\(209\) 24.2596 1.67807
\(210\) 0 0
\(211\) 2.44395 + 4.23305i 0.168249 + 0.291415i 0.937804 0.347165i \(-0.112856\pi\)
−0.769556 + 0.638580i \(0.779522\pi\)
\(212\) 0 0
\(213\) −2.58722 + 4.48120i −0.177273 + 0.307047i
\(214\) 0 0
\(215\) −5.46495 −0.372706
\(216\) 0 0
\(217\) −3.38352 5.86043i −0.229689 0.397832i
\(218\) 0 0
\(219\) 0.841448 + 1.45743i 0.0568598 + 0.0984840i
\(220\) 0 0
\(221\) −18.3926 + 31.8569i −1.23722 + 2.14293i
\(222\) 0 0
\(223\) 11.1873 0.749156 0.374578 0.927195i \(-0.377788\pi\)
0.374578 + 0.927195i \(0.377788\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −6.85934 + 11.8807i −0.455271 + 0.788552i −0.998704 0.0509006i \(-0.983791\pi\)
0.543433 + 0.839452i \(0.317124\pi\)
\(228\) 0 0
\(229\) −2.91018 5.04057i −0.192310 0.333090i 0.753705 0.657212i \(-0.228265\pi\)
−0.946015 + 0.324122i \(0.894931\pi\)
\(230\) 0 0
\(231\) 4.98703 + 8.63778i 0.328122 + 0.568324i
\(232\) 0 0
\(233\) 3.33684 5.77957i 0.218603 0.378632i −0.735778 0.677223i \(-0.763183\pi\)
0.954381 + 0.298591i \(0.0965166\pi\)
\(234\) 0 0
\(235\) −3.90018 + 6.75530i −0.254419 + 0.440667i
\(236\) 0 0
\(237\) 2.70536 4.68582i 0.175732 0.304377i
\(238\) 0 0
\(239\) 9.78623 16.9502i 0.633019 1.09642i −0.353913 0.935278i \(-0.615149\pi\)
0.986931 0.161142i \(-0.0515177\pi\)
\(240\) 0 0
\(241\) −3.36061 −0.216476 −0.108238 0.994125i \(-0.534521\pi\)
−0.108238 + 0.994125i \(0.534521\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 1.17558 + 2.03617i 0.0751051 + 0.130086i
\(246\) 0 0
\(247\) −15.7267 + 27.2395i −1.00067 + 1.73321i
\(248\) 0 0
\(249\) −7.83527 13.5711i −0.496540 0.860033i
\(250\) 0 0
\(251\) −4.15611 7.19859i −0.262331 0.454371i 0.704530 0.709675i \(-0.251158\pi\)
−0.966861 + 0.255303i \(0.917825\pi\)
\(252\) 0 0
\(253\) −4.04017 −0.254003
\(254\) 0 0
\(255\) −3.06661 5.31152i −0.192038 0.332620i
\(256\) 0 0
\(257\) 4.67272 8.09339i 0.291476 0.504852i −0.682683 0.730715i \(-0.739187\pi\)
0.974159 + 0.225863i \(0.0725203\pi\)
\(258\) 0 0
\(259\) 8.17173 0.507766
\(260\) 0 0
\(261\) −2.60303 + 4.50859i −0.161124 + 0.279074i
\(262\) 0 0
\(263\) 19.2383 1.18629 0.593144 0.805097i \(-0.297887\pi\)
0.593144 + 0.805097i \(0.297887\pi\)
\(264\) 0 0
\(265\) −6.77213 −0.416009
\(266\) 0 0
\(267\) 7.97892 0.488302
\(268\) 0 0
\(269\) −7.46217 −0.454977 −0.227488 0.973781i \(-0.573051\pi\)
−0.227488 + 0.973781i \(0.573051\pi\)
\(270\) 0 0
\(271\) −18.2280 −1.10727 −0.553637 0.832758i \(-0.686760\pi\)
−0.553637 + 0.832758i \(0.686760\pi\)
\(272\) 0 0
\(273\) −12.9317 −0.782664
\(274\) 0 0
\(275\) 2.31297 4.00618i 0.139477 0.241582i
\(276\) 0 0
\(277\) 14.6155 0.878158 0.439079 0.898448i \(-0.355305\pi\)
0.439079 + 0.898448i \(0.355305\pi\)
\(278\) 0 0
\(279\) 1.56927 2.71805i 0.0939496 0.162725i
\(280\) 0 0
\(281\) −4.47857 7.75710i −0.267169 0.462750i 0.700961 0.713200i \(-0.252755\pi\)
−0.968130 + 0.250450i \(0.919421\pi\)
\(282\) 0 0
\(283\) 12.3644 0.734988 0.367494 0.930026i \(-0.380216\pi\)
0.367494 + 0.930026i \(0.380216\pi\)
\(284\) 0 0
\(285\) −2.62213 4.54165i −0.155321 0.269024i
\(286\) 0 0
\(287\) 10.3358 + 17.9022i 0.610104 + 1.05673i
\(288\) 0 0
\(289\) −10.3081 + 17.8542i −0.606362 + 1.05025i
\(290\) 0 0
\(291\) −5.01466 8.68565i −0.293965 0.509162i
\(292\) 0 0
\(293\) 29.0024 1.69434 0.847170 0.531322i \(-0.178304\pi\)
0.847170 + 0.531322i \(0.178304\pi\)
\(294\) 0 0
\(295\) 5.61145 0.326711
\(296\) 0 0
\(297\) −2.31297 + 4.00618i −0.134212 + 0.232462i
\(298\) 0 0
\(299\) 2.61912 4.53645i 0.151468 0.262350i
\(300\) 0 0
\(301\) −5.89153 + 10.2044i −0.339582 + 0.588173i
\(302\) 0 0
\(303\) −9.06051 + 15.6933i −0.520513 + 0.901555i
\(304\) 0 0
\(305\) −1.75300 3.03629i −0.100377 0.173858i
\(306\) 0 0
\(307\) 7.73403 + 13.3957i 0.441404 + 0.764535i 0.997794 0.0663868i \(-0.0211471\pi\)
−0.556390 + 0.830922i \(0.687814\pi\)
\(308\) 0 0
\(309\) 4.74446 8.21765i 0.269903 0.467485i
\(310\) 0 0
\(311\) −18.5549 −1.05215 −0.526076 0.850437i \(-0.676337\pi\)
−0.526076 + 0.850437i \(0.676337\pi\)
\(312\) 0 0
\(313\) 34.3221 1.94000 0.970000 0.243106i \(-0.0781661\pi\)
0.970000 + 0.243106i \(0.0781661\pi\)
\(314\) 0 0
\(315\) 1.07806 1.86725i 0.0607417 0.105208i
\(316\) 0 0
\(317\) −7.87420 13.6385i −0.442259 0.766015i 0.555598 0.831451i \(-0.312490\pi\)
−0.997857 + 0.0654359i \(0.979156\pi\)
\(318\) 0 0
\(319\) 12.0415 + 20.8564i 0.674192 + 1.16774i
\(320\) 0 0
\(321\) 15.3498 0.856741
\(322\) 0 0
\(323\) −16.0821 + 27.8549i −0.894829 + 1.54989i
\(324\) 0 0
\(325\) 2.99885 + 5.19416i 0.166346 + 0.288120i
\(326\) 0 0
\(327\) 6.26073 0.346219
\(328\) 0 0
\(329\) 8.40924 + 14.5652i 0.463616 + 0.803007i
\(330\) 0 0
\(331\) 14.2382 24.6612i 0.782601 1.35550i −0.147821 0.989014i \(-0.547226\pi\)
0.930422 0.366490i \(-0.119441\pi\)
\(332\) 0 0
\(333\) 1.89501 + 3.28225i 0.103846 + 0.179866i
\(334\) 0 0
\(335\) 3.47231 7.41236i 0.189712 0.404980i
\(336\) 0 0
\(337\) −15.6567 27.1183i −0.852877 1.47723i −0.878600 0.477558i \(-0.841522\pi\)
0.0257228 0.999669i \(-0.491811\pi\)
\(338\) 0 0
\(339\) −6.08157 + 10.5336i −0.330306 + 0.572106i
\(340\) 0 0
\(341\) −7.25933 12.5735i −0.393115 0.680895i
\(342\) 0 0
\(343\) 20.1622 1.08866
\(344\) 0 0
\(345\) 0.436687 + 0.756365i 0.0235105 + 0.0407213i
\(346\) 0 0
\(347\) 5.21446 9.03171i 0.279927 0.484848i −0.691439 0.722434i \(-0.743023\pi\)
0.971366 + 0.237587i \(0.0763564\pi\)
\(348\) 0 0
\(349\) 17.6385 0.944166 0.472083 0.881554i \(-0.343502\pi\)
0.472083 + 0.881554i \(0.343502\pi\)
\(350\) 0 0
\(351\) −2.99885 5.19416i −0.160067 0.277244i
\(352\) 0 0
\(353\) 3.33685 + 5.77959i 0.177603 + 0.307617i 0.941059 0.338243i \(-0.109832\pi\)
−0.763456 + 0.645860i \(0.776499\pi\)
\(354\) 0 0
\(355\) 2.58722 4.48120i 0.137315 0.237837i
\(356\) 0 0
\(357\) −13.2239 −0.699884
\(358\) 0 0
\(359\) 35.0431 1.84950 0.924752 0.380570i \(-0.124272\pi\)
0.924752 + 0.380570i \(0.124272\pi\)
\(360\) 0 0
\(361\) −4.25109 + 7.36310i −0.223741 + 0.387531i
\(362\) 0 0
\(363\) 5.19963 + 9.00603i 0.272910 + 0.472694i
\(364\) 0 0
\(365\) −0.841448 1.45743i −0.0440434 0.0762854i
\(366\) 0 0
\(367\) 8.12012 14.0645i 0.423867 0.734159i −0.572447 0.819942i \(-0.694006\pi\)
0.996314 + 0.0857828i \(0.0273391\pi\)
\(368\) 0 0
\(369\) −4.79372 + 8.30297i −0.249551 + 0.432235i
\(370\) 0 0
\(371\) −7.30075 + 12.6453i −0.379036 + 0.656510i
\(372\) 0 0
\(373\) 10.0833 17.4648i 0.522093 0.904291i −0.477577 0.878590i \(-0.658485\pi\)
0.999670 0.0257011i \(-0.00818181\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −31.2244 −1.60814
\(378\) 0 0
\(379\) 4.69017 + 8.12361i 0.240918 + 0.417282i 0.960976 0.276632i \(-0.0892182\pi\)
−0.720058 + 0.693914i \(0.755885\pi\)
\(380\) 0 0
\(381\) −6.63481 + 11.4918i −0.339911 + 0.588744i
\(382\) 0 0
\(383\) −7.72118 13.3735i −0.394534 0.683353i 0.598508 0.801117i \(-0.295761\pi\)
−0.993042 + 0.117764i \(0.962427\pi\)
\(384\) 0 0
\(385\) −4.98703 8.63778i −0.254162 0.440222i
\(386\) 0 0
\(387\) −5.46495 −0.277799
\(388\) 0 0
\(389\) −5.36740 9.29661i −0.272138 0.471357i 0.697271 0.716808i \(-0.254397\pi\)
−0.969409 + 0.245451i \(0.921064\pi\)
\(390\) 0 0
\(391\) 2.67830 4.63894i 0.135447 0.234601i
\(392\) 0 0
\(393\) 0.697341 0.0351762
\(394\) 0 0
\(395\) −2.70536 + 4.68582i −0.136122 + 0.235769i
\(396\) 0 0
\(397\) 24.0836 1.20872 0.604360 0.796712i \(-0.293429\pi\)
0.604360 + 0.796712i \(0.293429\pi\)
\(398\) 0 0
\(399\) −11.3072 −0.566069
\(400\) 0 0
\(401\) −17.5499 −0.876402 −0.438201 0.898877i \(-0.644384\pi\)
−0.438201 + 0.898877i \(0.644384\pi\)
\(402\) 0 0
\(403\) 18.8240 0.937690
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 17.5324 0.869048
\(408\) 0 0
\(409\) −4.55440 + 7.88845i −0.225200 + 0.390059i −0.956380 0.292127i \(-0.905637\pi\)
0.731179 + 0.682185i \(0.238970\pi\)
\(410\) 0 0
\(411\) −11.5162 −0.568051
\(412\) 0 0
\(413\) 6.04947 10.4780i 0.297675 0.515588i
\(414\) 0 0
\(415\) 7.83527 + 13.5711i 0.384618 + 0.666178i
\(416\) 0 0
\(417\) 2.18220 0.106863
\(418\) 0 0
\(419\) −11.1051 19.2346i −0.542519 0.939670i −0.998759 0.0498132i \(-0.984137\pi\)
0.456240 0.889857i \(-0.349196\pi\)
\(420\) 0 0
\(421\) −3.36595 5.82999i −0.164046 0.284136i 0.772270 0.635295i \(-0.219121\pi\)
−0.936316 + 0.351158i \(0.885788\pi\)
\(422\) 0 0
\(423\) −3.90018 + 6.75530i −0.189633 + 0.328454i
\(424\) 0 0
\(425\) 3.06661 + 5.31152i 0.148752 + 0.257646i
\(426\) 0 0
\(427\) −7.55936 −0.365823
\(428\) 0 0
\(429\) −27.7450 −1.33954
\(430\) 0 0
\(431\) 9.81730 17.0041i 0.472883 0.819057i −0.526636 0.850091i \(-0.676547\pi\)
0.999518 + 0.0310343i \(0.00988011\pi\)
\(432\) 0 0
\(433\) 12.5754 21.7813i 0.604337 1.04674i −0.387818 0.921736i \(-0.626771\pi\)
0.992156 0.125007i \(-0.0398954\pi\)
\(434\) 0 0
\(435\) 2.60303 4.50859i 0.124806 0.216170i
\(436\) 0 0
\(437\) 2.29010 3.96657i 0.109550 0.189747i
\(438\) 0 0
\(439\) −0.513094 0.888705i −0.0244886 0.0424156i 0.853521 0.521058i \(-0.174462\pi\)
−0.878010 + 0.478642i \(0.841129\pi\)
\(440\) 0 0
\(441\) 1.17558 + 2.03617i 0.0559801 + 0.0969603i
\(442\) 0 0
\(443\) 10.9969 19.0473i 0.522481 0.904963i −0.477177 0.878807i \(-0.658340\pi\)
0.999658 0.0261562i \(-0.00832671\pi\)
\(444\) 0 0
\(445\) −7.97892 −0.378237
\(446\) 0 0
\(447\) 8.90881 0.421372
\(448\) 0 0
\(449\) −11.2522 + 19.4894i −0.531024 + 0.919760i 0.468321 + 0.883559i \(0.344859\pi\)
−0.999345 + 0.0362017i \(0.988474\pi\)
\(450\) 0 0
\(451\) 22.1754 + 38.4090i 1.04420 + 1.80861i
\(452\) 0 0
\(453\) 0.0253744 + 0.0439498i 0.00119220 + 0.00206494i
\(454\) 0 0
\(455\) 12.9317 0.606249
\(456\) 0 0
\(457\) 15.1792 26.2912i 0.710055 1.22985i −0.254782 0.966999i \(-0.582004\pi\)
0.964836 0.262852i \(-0.0846631\pi\)
\(458\) 0 0
\(459\) −3.06661 5.31152i −0.143137 0.247920i
\(460\) 0 0
\(461\) 13.2096 0.615230 0.307615 0.951511i \(-0.400469\pi\)
0.307615 + 0.951511i \(0.400469\pi\)
\(462\) 0 0
\(463\) 8.62771 + 14.9436i 0.400964 + 0.694490i 0.993842 0.110802i \(-0.0353420\pi\)
−0.592879 + 0.805292i \(0.702009\pi\)
\(464\) 0 0
\(465\) −1.56927 + 2.71805i −0.0727730 + 0.126047i
\(466\) 0 0
\(467\) 12.3804 + 21.4434i 0.572895 + 0.992283i 0.996267 + 0.0863268i \(0.0275129\pi\)
−0.423372 + 0.905956i \(0.639154\pi\)
\(468\) 0 0
\(469\) −10.0974 14.4746i −0.466254 0.668376i
\(470\) 0 0
\(471\) −8.62937 14.9465i −0.397620 0.688698i
\(472\) 0 0
\(473\) −12.6402 + 21.8935i −0.581199 + 1.00667i
\(474\) 0 0
\(475\) 2.62213 + 4.54165i 0.120311 + 0.208385i
\(476\) 0 0
\(477\) −6.77213 −0.310075
\(478\) 0 0
\(479\) −7.05677 12.2227i −0.322432 0.558469i 0.658557 0.752531i \(-0.271167\pi\)
−0.980989 + 0.194062i \(0.937834\pi\)
\(480\) 0 0
\(481\) −11.3657 + 19.6860i −0.518231 + 0.897603i
\(482\) 0 0
\(483\) 1.88310 0.0856839
\(484\) 0 0
\(485\) 5.01466 + 8.68565i 0.227704 + 0.394395i
\(486\) 0 0
\(487\) −10.0847 17.4672i −0.456981 0.791514i 0.541819 0.840495i \(-0.317736\pi\)
−0.998800 + 0.0489814i \(0.984403\pi\)
\(488\) 0 0
\(489\) 9.40567 16.2911i 0.425339 0.736709i
\(490\) 0 0
\(491\) −27.6864 −1.24947 −0.624736 0.780836i \(-0.714793\pi\)
−0.624736 + 0.780836i \(0.714793\pi\)
\(492\) 0 0
\(493\) −31.9299 −1.43805
\(494\) 0 0
\(495\) 2.31297 4.00618i 0.103960 0.180064i
\(496\) 0 0
\(497\) −5.57835 9.66198i −0.250223 0.433399i
\(498\) 0 0
\(499\) 6.02828 + 10.4413i 0.269863 + 0.467416i 0.968826 0.247741i \(-0.0796883\pi\)
−0.698963 + 0.715157i \(0.746355\pi\)
\(500\) 0 0
\(501\) 1.29815 2.24847i 0.0579972 0.100454i
\(502\) 0 0
\(503\) −3.75145 + 6.49770i −0.167269 + 0.289718i −0.937459 0.348096i \(-0.886828\pi\)
0.770190 + 0.637815i \(0.220161\pi\)
\(504\) 0 0
\(505\) 9.06051 15.6933i 0.403187 0.698341i
\(506\) 0 0
\(507\) 11.4862 19.8947i 0.510120 0.883554i
\(508\) 0 0
\(509\) −14.9289 −0.661711 −0.330856 0.943681i \(-0.607337\pi\)
−0.330856 + 0.943681i \(0.607337\pi\)
\(510\) 0 0
\(511\) −3.62852 −0.160516
\(512\) 0 0
\(513\) −2.62213 4.54165i −0.115770 0.200519i
\(514\) 0 0
\(515\) −4.74446 + 8.21765i −0.209066 + 0.362113i
\(516\) 0 0
\(517\) 18.0420 + 31.2496i 0.793484 + 1.37436i
\(518\) 0 0
\(519\) 9.80640 + 16.9852i 0.430453 + 0.745567i
\(520\) 0 0
\(521\) −35.4177 −1.55168 −0.775839 0.630931i \(-0.782673\pi\)
−0.775839 + 0.630931i \(0.782673\pi\)
\(522\) 0 0
\(523\) −1.34658 2.33235i −0.0588819 0.101987i 0.835082 0.550126i \(-0.185420\pi\)
−0.893964 + 0.448139i \(0.852087\pi\)
\(524\) 0 0
\(525\) −1.07806 + 1.86725i −0.0470503 + 0.0814935i
\(526\) 0 0
\(527\) 19.2493 0.838513
\(528\) 0 0
\(529\) 11.1186 19.2580i 0.483418 0.837304i
\(530\) 0 0
\(531\) 5.61145 0.243516
\(532\) 0 0
\(533\) −57.5026 −2.49071
\(534\) 0 0
\(535\) −15.3498 −0.663629
\(536\) 0 0
\(537\) 8.75619 0.377858
\(538\) 0 0
\(539\) 10.8763 0.468476
\(540\) 0 0
\(541\) −9.30439 −0.400027 −0.200013 0.979793i \(-0.564099\pi\)
−0.200013 + 0.979793i \(0.564099\pi\)
\(542\) 0 0
\(543\) −2.68166 + 4.64477i −0.115081 + 0.199326i
\(544\) 0 0
\(545\) −6.26073 −0.268180
\(546\) 0 0
\(547\) 20.6416 35.7523i 0.882572 1.52866i 0.0341001 0.999418i \(-0.489143\pi\)
0.848472 0.529241i \(-0.177523\pi\)
\(548\) 0 0
\(549\) −1.75300 3.03629i −0.0748164 0.129586i
\(550\) 0 0
\(551\) −27.3019 −1.16310
\(552\) 0 0
\(553\) 5.83307 + 10.1032i 0.248048 + 0.429631i
\(554\) 0 0
\(555\) −1.89501 3.28225i −0.0804387 0.139324i
\(556\) 0 0
\(557\) −14.6561 + 25.3851i −0.621000 + 1.07560i 0.368300 + 0.929707i \(0.379940\pi\)
−0.989300 + 0.145896i \(0.953393\pi\)
\(558\) 0 0
\(559\) −16.3886 28.3858i −0.693162 1.20059i
\(560\) 0 0
\(561\) −28.3718 −1.19786
\(562\) 0 0
\(563\) 10.2565 0.432260 0.216130 0.976365i \(-0.430656\pi\)
0.216130 + 0.976365i \(0.430656\pi\)
\(564\) 0 0
\(565\) 6.08157 10.5336i 0.255854 0.443151i
\(566\) 0 0
\(567\) 1.07806 1.86725i 0.0452742 0.0784172i
\(568\) 0 0
\(569\) −1.04247 + 1.80560i −0.0437024 + 0.0756948i −0.887049 0.461675i \(-0.847249\pi\)
0.843347 + 0.537370i \(0.180582\pi\)
\(570\) 0 0
\(571\) −2.13139 + 3.69167i −0.0891958 + 0.154492i −0.907171 0.420761i \(-0.861763\pi\)
0.817976 + 0.575253i \(0.195096\pi\)
\(572\) 0 0
\(573\) 7.83945 + 13.5783i 0.327498 + 0.567242i
\(574\) 0 0
\(575\) −0.436687 0.756365i −0.0182111 0.0315426i
\(576\) 0 0
\(577\) −18.6289 + 32.2661i −0.775529 + 1.34326i 0.158967 + 0.987284i \(0.449184\pi\)
−0.934496 + 0.355972i \(0.884150\pi\)
\(578\) 0 0
\(579\) −3.33316 −0.138522
\(580\) 0 0
\(581\) 33.7875 1.40174
\(582\) 0 0
\(583\) −15.6637 + 27.1304i −0.648725 + 1.12362i
\(584\) 0 0
\(585\) 2.99885 + 5.19416i 0.123987 + 0.214752i
\(586\) 0 0
\(587\) 6.18285 + 10.7090i 0.255194 + 0.442008i 0.964948 0.262441i \(-0.0845274\pi\)
−0.709754 + 0.704449i \(0.751194\pi\)
\(588\) 0 0
\(589\) 16.4593 0.678192
\(590\) 0 0
\(591\) 10.9023 18.8833i 0.448460 0.776756i
\(592\) 0 0
\(593\) 16.0411 + 27.7840i 0.658730 + 1.14095i 0.980945 + 0.194287i \(0.0622392\pi\)
−0.322215 + 0.946666i \(0.604427\pi\)
\(594\) 0 0
\(595\) 13.2239 0.542128
\(596\) 0 0
\(597\) −12.6316 21.8786i −0.516977 0.895430i
\(598\) 0 0
\(599\) 18.1471 31.4317i 0.741471 1.28426i −0.210355 0.977625i \(-0.567462\pi\)
0.951826 0.306640i \(-0.0992047\pi\)
\(600\) 0 0
\(601\) −7.43597 12.8795i −0.303320 0.525365i 0.673566 0.739127i \(-0.264762\pi\)
−0.976886 + 0.213762i \(0.931428\pi\)
\(602\) 0 0
\(603\) 3.47231 7.41236i 0.141403 0.301855i
\(604\) 0 0
\(605\) −5.19963 9.00603i −0.211395 0.366147i
\(606\) 0 0
\(607\) −8.36045 + 14.4807i −0.339340 + 0.587754i −0.984309 0.176455i \(-0.943537\pi\)
0.644969 + 0.764209i \(0.276870\pi\)
\(608\) 0 0
\(609\) −5.61244 9.72104i −0.227428 0.393916i
\(610\) 0 0
\(611\) −46.7842 −1.89269
\(612\) 0 0
\(613\) 23.6061 + 40.8870i 0.953442 + 1.65141i 0.737893 + 0.674917i \(0.235821\pi\)
0.215549 + 0.976493i \(0.430846\pi\)
\(614\) 0 0
\(615\) 4.79372 8.30297i 0.193302 0.334808i
\(616\) 0 0
\(617\) −17.4036 −0.700641 −0.350321 0.936630i \(-0.613927\pi\)
−0.350321 + 0.936630i \(0.613927\pi\)
\(618\) 0 0
\(619\) −2.13529 3.69843i −0.0858246 0.148653i 0.819918 0.572481i \(-0.194019\pi\)
−0.905742 + 0.423829i \(0.860686\pi\)
\(620\) 0 0
\(621\) 0.436687 + 0.756365i 0.0175237 + 0.0303519i
\(622\) 0 0
\(623\) −8.60174 + 14.8987i −0.344622 + 0.596902i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −24.2596 −0.968833
\(628\) 0 0
\(629\) −11.6225 + 20.1308i −0.463419 + 0.802666i
\(630\) 0 0
\(631\) −20.6879 35.8324i −0.823571 1.42647i −0.903007 0.429626i \(-0.858645\pi\)
0.0794361 0.996840i \(-0.474688\pi\)
\(632\) 0 0
\(633\) −2.44395 4.23305i −0.0971384 0.168249i
\(634\) 0 0
\(635\) 6.63481 11.4918i 0.263294 0.456039i
\(636\) 0 0
\(637\) −7.05078 + 12.2123i −0.279362 + 0.483870i
\(638\) 0 0
\(639\) 2.58722 4.48120i 0.102349 0.177273i
\(640\) 0 0
\(641\) 17.9342 31.0629i 0.708357 1.22691i −0.257109 0.966382i \(-0.582770\pi\)
0.965466 0.260528i \(-0.0838967\pi\)
\(642\) 0 0
\(643\) 35.3879 1.39556 0.697781 0.716311i \(-0.254171\pi\)
0.697781 + 0.716311i \(0.254171\pi\)
\(644\) 0 0
\(645\) 5.46495 0.215182
\(646\) 0 0
\(647\) −17.6557 30.5805i −0.694116 1.20224i −0.970478 0.241191i \(-0.922462\pi\)
0.276361 0.961054i \(-0.410871\pi\)
\(648\) 0 0
\(649\) 12.9791 22.4805i 0.509474 0.882435i
\(650\) 0 0
\(651\) 3.38352 + 5.86043i 0.132611 + 0.229689i
\(652\) 0 0
\(653\) −6.25811 10.8394i −0.244899 0.424177i 0.717204 0.696863i \(-0.245421\pi\)
−0.962103 + 0.272686i \(0.912088\pi\)
\(654\) 0 0
\(655\) −0.697341 −0.0272474
\(656\) 0 0
\(657\) −0.841448 1.45743i −0.0328280 0.0568598i
\(658\) 0 0
\(659\) 15.9834 27.6840i 0.622623 1.07841i −0.366372 0.930468i \(-0.619400\pi\)
0.988995 0.147947i \(-0.0472664\pi\)
\(660\) 0 0
\(661\) 24.4287 0.950165 0.475083 0.879941i \(-0.342418\pi\)
0.475083 + 0.879941i \(0.342418\pi\)
\(662\) 0 0
\(663\) 18.3926 31.8569i 0.714309 1.23722i
\(664\) 0 0
\(665\) 11.3072 0.438475
\(666\) 0 0
\(667\) 4.54685 0.176055
\(668\) 0 0
\(669\) −11.1873 −0.432526
\(670\) 0 0
\(671\) −16.2186 −0.626111
\(672\) 0 0
\(673\) −12.4012 −0.478032 −0.239016 0.971016i \(-0.576825\pi\)
−0.239016 + 0.971016i \(0.576825\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) −5.01938 + 8.69382i −0.192910 + 0.334131i −0.946214 0.323543i \(-0.895126\pi\)
0.753303 + 0.657674i \(0.228459\pi\)
\(678\) 0 0
\(679\) 21.6244 0.829868
\(680\) 0 0
\(681\) 6.85934 11.8807i 0.262851 0.455271i
\(682\) 0 0
\(683\) −18.2393 31.5915i −0.697909 1.20881i −0.969190 0.246314i \(-0.920781\pi\)
0.271281 0.962500i \(-0.412553\pi\)
\(684\) 0 0
\(685\) 11.5162 0.440010
\(686\) 0 0
\(687\) 2.91018 + 5.04057i 0.111030 + 0.192310i
\(688\) 0 0
\(689\) −20.3086 35.1755i −0.773697 1.34008i
\(690\) 0 0
\(691\) −7.05955 + 12.2275i −0.268558 + 0.465156i −0.968490 0.249054i \(-0.919880\pi\)
0.699932 + 0.714210i \(0.253214\pi\)
\(692\) 0 0
\(693\) −4.98703 8.63778i −0.189441 0.328122i
\(694\) 0 0
\(695\) −2.18220 −0.0827757
\(696\) 0 0
\(697\) −58.8018 −2.22728
\(698\) 0 0
\(699\) −3.33684 + 5.77957i −0.126211 + 0.218603i
\(700\) 0 0
\(701\) −8.35311 + 14.4680i −0.315493 + 0.546449i −0.979542 0.201239i \(-0.935503\pi\)
0.664049 + 0.747689i \(0.268836\pi\)
\(702\) 0 0
\(703\) −9.93791 + 17.2130i −0.374815 + 0.649199i
\(704\) 0 0
\(705\) 3.90018 6.75530i 0.146889 0.254419i
\(706\) 0 0
\(707\) −19.5355 33.8365i −0.734709 1.27255i
\(708\) 0 0
\(709\) −3.35461 5.81036i −0.125985 0.218213i 0.796132 0.605122i \(-0.206876\pi\)
−0.922118 + 0.386910i \(0.873542\pi\)
\(710\) 0 0
\(711\) −2.70536 + 4.68582i −0.101459 + 0.175732i
\(712\) 0 0
\(713\) −2.74112 −0.102656
\(714\) 0 0
\(715\) 27.7450 1.03760
\(716\) 0 0
\(717\) −9.78623 + 16.9502i −0.365473 + 0.633019i
\(718\) 0 0
\(719\) 17.1607 + 29.7233i 0.639988 + 1.10849i 0.985435 + 0.170053i \(0.0543939\pi\)
−0.345447 + 0.938438i \(0.612273\pi\)
\(720\) 0 0
\(721\) 10.2296 + 17.7182i 0.380970 + 0.659860i
\(722\) 0 0
\(723\) 3.36061 0.124982
\(724\) 0 0
\(725\) −2.60303 + 4.50859i −0.0966742 + 0.167445i
\(726\) 0 0
\(727\) −17.8567 30.9287i −0.662269 1.14708i −0.980018 0.198908i \(-0.936260\pi\)
0.317749 0.948175i \(-0.397073\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −16.7588 29.0272i −0.619848 1.07361i
\(732\) 0 0
\(733\) −20.7429 + 35.9278i −0.766157 + 1.32702i 0.173475 + 0.984838i \(0.444500\pi\)
−0.939633 + 0.342185i \(0.888833\pi\)
\(734\) 0 0
\(735\) −1.17558 2.03617i −0.0433620 0.0751051i
\(736\) 0 0
\(737\) −21.6639 31.0552i −0.798000 1.14393i
\(738\) 0 0
\(739\) −18.0162 31.2050i −0.662737 1.14789i −0.979894 0.199521i \(-0.936061\pi\)
0.317157 0.948373i \(-0.397272\pi\)
\(740\) 0 0
\(741\) 15.7267 27.2395i 0.577736 1.00067i
\(742\) 0 0
\(743\) −17.6137 30.5078i −0.646183 1.11922i −0.984027 0.178020i \(-0.943031\pi\)
0.337844 0.941202i \(-0.390302\pi\)
\(744\) 0 0
\(745\) −8.90881 −0.326394
\(746\) 0 0
\(747\) 7.83527 + 13.5711i 0.286678 + 0.496540i
\(748\) 0 0
\(749\) −16.5480 + 28.6619i −0.604649 + 1.04728i
\(750\) 0 0
\(751\) 6.11344 0.223083 0.111541 0.993760i \(-0.464421\pi\)
0.111541 + 0.993760i \(0.464421\pi\)
\(752\) 0 0
\(753\) 4.15611 + 7.19859i 0.151457 + 0.262331i
\(754\) 0 0
\(755\) −0.0253744 0.0439498i −0.000923471 0.00159950i
\(756\) 0 0
\(757\) −25.2580 + 43.7481i −0.918017 + 1.59005i −0.115595 + 0.993296i \(0.536877\pi\)
−0.802423 + 0.596756i \(0.796456\pi\)
\(758\) 0 0
\(759\) 4.04017 0.146649
\(760\) 0 0
\(761\) 25.7993 0.935224 0.467612 0.883934i \(-0.345114\pi\)
0.467612 + 0.883934i \(0.345114\pi\)
\(762\) 0 0
\(763\) −6.74943 + 11.6904i −0.244346 + 0.423219i
\(764\) 0 0
\(765\) 3.06661 + 5.31152i 0.110873 + 0.192038i
\(766\) 0 0
\(767\) 16.8279 + 29.1468i 0.607620 + 1.05243i
\(768\) 0 0
\(769\) 4.37865 7.58404i 0.157898 0.273487i −0.776212 0.630471i \(-0.782862\pi\)
0.934110 + 0.356984i \(0.116195\pi\)
\(770\) 0 0
\(771\) −4.67272 + 8.09339i −0.168284 + 0.291476i
\(772\) 0 0
\(773\) 4.04053 6.99840i 0.145328 0.251715i −0.784168 0.620549i \(-0.786910\pi\)
0.929495 + 0.368834i \(0.120243\pi\)
\(774\) 0 0
\(775\) 1.56927 2.71805i 0.0563698 0.0976353i
\(776\) 0 0
\(777\) −8.17173 −0.293159
\(778\) 0 0
\(779\) −50.2790 −1.80143
\(780\) 0 0
\(781\) −11.9683 20.7297i −0.428260 0.741768i
\(782\) 0 0
\(783\) 2.60303 4.50859i 0.0930248 0.161124i
\(784\) 0 0
\(785\) 8.62937 + 14.9465i 0.307995 + 0.533464i
\(786\) 0 0
\(787\) −19.9342 34.5271i −0.710578 1.23076i −0.964640 0.263570i \(-0.915100\pi\)
0.254062 0.967188i \(-0.418233\pi\)
\(788\) 0 0
\(789\) −19.2383 −0.684903
\(790\) 0 0
\(791\) −13.1126 22.7116i −0.466229 0.807533i
\(792\) 0 0
\(793\) 10.5140 18.2108i 0.373363