Properties

Label 1148.2.k.b.337.13
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.13
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.46058 + 1.46058i) q^{3} -2.07990i q^{5} +(-0.707107 - 0.707107i) q^{7} +1.26660i q^{9} +O(q^{10})\) \(q+(1.46058 + 1.46058i) q^{3} -2.07990i q^{5} +(-0.707107 - 0.707107i) q^{7} +1.26660i q^{9} +(3.13374 + 3.13374i) q^{11} +(-1.44357 - 1.44357i) q^{13} +(3.03787 - 3.03787i) q^{15} +(-2.75344 + 2.75344i) q^{17} +(3.62637 - 3.62637i) q^{19} -2.06558i q^{21} +8.09052 q^{23} +0.674015 q^{25} +(2.53177 - 2.53177i) q^{27} +(6.51134 + 6.51134i) q^{29} -6.43870 q^{31} +9.15418i q^{33} +(-1.47071 + 1.47071i) q^{35} +3.66193 q^{37} -4.21689i q^{39} +(5.32231 - 3.55991i) q^{41} +0.897994i q^{43} +2.63441 q^{45} +(8.63929 - 8.63929i) q^{47} +1.00000i q^{49} -8.04324 q^{51} +(-7.62335 - 7.62335i) q^{53} +(6.51787 - 6.51787i) q^{55} +10.5932 q^{57} -10.3975 q^{59} -1.15180i q^{61} +(0.895623 - 0.895623i) q^{63} +(-3.00247 + 3.00247i) q^{65} +(0.147560 - 0.147560i) q^{67} +(11.8169 + 11.8169i) q^{69} +(2.99467 + 2.99467i) q^{71} +8.52008i q^{73} +(0.984454 + 0.984454i) q^{75} -4.43178i q^{77} +(-5.31233 - 5.31233i) q^{79} +11.1955 q^{81} -13.1465 q^{83} +(5.72687 + 5.72687i) q^{85} +19.0207i q^{87} +(0.506568 + 0.506568i) q^{89} +2.04151i q^{91} +(-9.40426 - 9.40426i) q^{93} +(-7.54248 - 7.54248i) q^{95} +(-10.8950 + 10.8950i) q^{97} +(-3.96921 + 3.96921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.46058 + 1.46058i 0.843268 + 0.843268i 0.989282 0.146015i \(-0.0466447\pi\)
−0.146015 + 0.989282i \(0.546645\pi\)
\(4\) 0 0
\(5\) 2.07990i 0.930160i −0.885269 0.465080i \(-0.846026\pi\)
0.885269 0.465080i \(-0.153974\pi\)
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 0 0
\(9\) 1.26660i 0.422201i
\(10\) 0 0
\(11\) 3.13374 + 3.13374i 0.944859 + 0.944859i 0.998557 0.0536980i \(-0.0171008\pi\)
−0.0536980 + 0.998557i \(0.517101\pi\)
\(12\) 0 0
\(13\) −1.44357 1.44357i −0.400373 0.400373i 0.477991 0.878364i \(-0.341365\pi\)
−0.878364 + 0.477991i \(0.841365\pi\)
\(14\) 0 0
\(15\) 3.03787 3.03787i 0.784374 0.784374i
\(16\) 0 0
\(17\) −2.75344 + 2.75344i −0.667806 + 0.667806i −0.957208 0.289402i \(-0.906544\pi\)
0.289402 + 0.957208i \(0.406544\pi\)
\(18\) 0 0
\(19\) 3.62637 3.62637i 0.831946 0.831946i −0.155837 0.987783i \(-0.549807\pi\)
0.987783 + 0.155837i \(0.0498074\pi\)
\(20\) 0 0
\(21\) 2.06558i 0.450746i
\(22\) 0 0
\(23\) 8.09052 1.68699 0.843496 0.537136i \(-0.180494\pi\)
0.843496 + 0.537136i \(0.180494\pi\)
\(24\) 0 0
\(25\) 0.674015 0.134803
\(26\) 0 0
\(27\) 2.53177 2.53177i 0.487239 0.487239i
\(28\) 0 0
\(29\) 6.51134 + 6.51134i 1.20913 + 1.20913i 0.971310 + 0.237815i \(0.0764313\pi\)
0.237815 + 0.971310i \(0.423569\pi\)
\(30\) 0 0
\(31\) −6.43870 −1.15642 −0.578212 0.815886i \(-0.696250\pi\)
−0.578212 + 0.815886i \(0.696250\pi\)
\(32\) 0 0
\(33\) 9.15418i 1.59354i
\(34\) 0 0
\(35\) −1.47071 + 1.47071i −0.248596 + 0.248596i
\(36\) 0 0
\(37\) 3.66193 0.602018 0.301009 0.953621i \(-0.402677\pi\)
0.301009 + 0.953621i \(0.402677\pi\)
\(38\) 0 0
\(39\) 4.21689i 0.675243i
\(40\) 0 0
\(41\) 5.32231 3.55991i 0.831206 0.555965i
\(42\) 0 0
\(43\) 0.897994i 0.136943i 0.997653 + 0.0684714i \(0.0218122\pi\)
−0.997653 + 0.0684714i \(0.978188\pi\)
\(44\) 0 0
\(45\) 2.63441 0.392714
\(46\) 0 0
\(47\) 8.63929 8.63929i 1.26017 1.26017i 0.309160 0.951010i \(-0.399952\pi\)
0.951010 0.309160i \(-0.100048\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −8.04324 −1.12628
\(52\) 0 0
\(53\) −7.62335 7.62335i −1.04715 1.04715i −0.998832 0.0483150i \(-0.984615\pi\)
−0.0483150 0.998832i \(-0.515385\pi\)
\(54\) 0 0
\(55\) 6.51787 6.51787i 0.878870 0.878870i
\(56\) 0 0
\(57\) 10.5932 1.40311
\(58\) 0 0
\(59\) −10.3975 −1.35364 −0.676822 0.736146i \(-0.736643\pi\)
−0.676822 + 0.736146i \(0.736643\pi\)
\(60\) 0 0
\(61\) 1.15180i 0.147473i −0.997278 0.0737367i \(-0.976508\pi\)
0.997278 0.0737367i \(-0.0234924\pi\)
\(62\) 0 0
\(63\) 0.895623 0.895623i 0.112838 0.112838i
\(64\) 0 0
\(65\) −3.00247 + 3.00247i −0.372411 + 0.372411i
\(66\) 0 0
\(67\) 0.147560 0.147560i 0.0180273 0.0180273i −0.698036 0.716063i \(-0.745942\pi\)
0.716063 + 0.698036i \(0.245942\pi\)
\(68\) 0 0
\(69\) 11.8169 + 11.8169i 1.42259 + 1.42259i
\(70\) 0 0
\(71\) 2.99467 + 2.99467i 0.355402 + 0.355402i 0.862115 0.506713i \(-0.169140\pi\)
−0.506713 + 0.862115i \(0.669140\pi\)
\(72\) 0 0
\(73\) 8.52008i 0.997200i 0.866832 + 0.498600i \(0.166152\pi\)
−0.866832 + 0.498600i \(0.833848\pi\)
\(74\) 0 0
\(75\) 0.984454 + 0.984454i 0.113675 + 0.113675i
\(76\) 0 0
\(77\) 4.43178i 0.505049i
\(78\) 0 0
\(79\) −5.31233 5.31233i −0.597684 0.597684i 0.342012 0.939696i \(-0.388892\pi\)
−0.939696 + 0.342012i \(0.888892\pi\)
\(80\) 0 0
\(81\) 11.1955 1.24395
\(82\) 0 0
\(83\) −13.1465 −1.44302 −0.721510 0.692404i \(-0.756552\pi\)
−0.721510 + 0.692404i \(0.756552\pi\)
\(84\) 0 0
\(85\) 5.72687 + 5.72687i 0.621166 + 0.621166i
\(86\) 0 0
\(87\) 19.0207i 2.03923i
\(88\) 0 0
\(89\) 0.506568 + 0.506568i 0.0536961 + 0.0536961i 0.733445 0.679749i \(-0.237911\pi\)
−0.679749 + 0.733445i \(0.737911\pi\)
\(90\) 0 0
\(91\) 2.04151i 0.214008i
\(92\) 0 0
\(93\) −9.40426 9.40426i −0.975176 0.975176i
\(94\) 0 0
\(95\) −7.54248 7.54248i −0.773843 0.773843i
\(96\) 0 0
\(97\) −10.8950 + 10.8950i −1.10622 + 1.10622i −0.112579 + 0.993643i \(0.535911\pi\)
−0.993643 + 0.112579i \(0.964089\pi\)
\(98\) 0 0
\(99\) −3.96921 + 3.96921i −0.398920 + 0.398920i
\(100\) 0 0
\(101\) 10.4719 10.4719i 1.04200 1.04200i 0.0429187 0.999079i \(-0.486334\pi\)
0.999079 0.0429187i \(-0.0136657\pi\)
\(102\) 0 0
\(103\) 13.1568i 1.29638i 0.761480 + 0.648188i \(0.224473\pi\)
−0.761480 + 0.648188i \(0.775527\pi\)
\(104\) 0 0
\(105\) −4.29619 −0.419265
\(106\) 0 0
\(107\) −5.74222 −0.555121 −0.277561 0.960708i \(-0.589526\pi\)
−0.277561 + 0.960708i \(0.589526\pi\)
\(108\) 0 0
\(109\) −11.1358 + 11.1358i −1.06661 + 1.06661i −0.0689967 + 0.997617i \(0.521980\pi\)
−0.997617 + 0.0689967i \(0.978020\pi\)
\(110\) 0 0
\(111\) 5.34856 + 5.34856i 0.507662 + 0.507662i
\(112\) 0 0
\(113\) −16.0102 −1.50611 −0.753056 0.657957i \(-0.771421\pi\)
−0.753056 + 0.657957i \(0.771421\pi\)
\(114\) 0 0
\(115\) 16.8275i 1.56917i
\(116\) 0 0
\(117\) 1.82842 1.82842i 0.169038 0.169038i
\(118\) 0 0
\(119\) 3.89395 0.356957
\(120\) 0 0
\(121\) 8.64070i 0.785518i
\(122\) 0 0
\(123\) 12.9732 + 2.57413i 1.16976 + 0.232102i
\(124\) 0 0
\(125\) 11.8014i 1.05555i
\(126\) 0 0
\(127\) 18.0589 1.60247 0.801234 0.598350i \(-0.204177\pi\)
0.801234 + 0.598350i \(0.204177\pi\)
\(128\) 0 0
\(129\) −1.31159 + 1.31159i −0.115479 + 0.115479i
\(130\) 0 0
\(131\) 21.0436i 1.83858i 0.393577 + 0.919292i \(0.371238\pi\)
−0.393577 + 0.919292i \(0.628762\pi\)
\(132\) 0 0
\(133\) −5.12846 −0.444694
\(134\) 0 0
\(135\) −5.26583 5.26583i −0.453210 0.453210i
\(136\) 0 0
\(137\) −11.6271 + 11.6271i −0.993368 + 0.993368i −0.999978 0.00660984i \(-0.997896\pi\)
0.00660984 + 0.999978i \(0.497896\pi\)
\(138\) 0 0
\(139\) 1.88786 0.160126 0.0800629 0.996790i \(-0.474488\pi\)
0.0800629 + 0.996790i \(0.474488\pi\)
\(140\) 0 0
\(141\) 25.2368 2.12532
\(142\) 0 0
\(143\) 9.04753i 0.756592i
\(144\) 0 0
\(145\) 13.5429 13.5429i 1.12468 1.12468i
\(146\) 0 0
\(147\) −1.46058 + 1.46058i −0.120467 + 0.120467i
\(148\) 0 0
\(149\) −14.7204 + 14.7204i −1.20594 + 1.20594i −0.233608 + 0.972331i \(0.575053\pi\)
−0.972331 + 0.233608i \(0.924947\pi\)
\(150\) 0 0
\(151\) −3.57223 3.57223i −0.290704 0.290704i 0.546654 0.837358i \(-0.315901\pi\)
−0.837358 + 0.546654i \(0.815901\pi\)
\(152\) 0 0
\(153\) −3.48751 3.48751i −0.281948 0.281948i
\(154\) 0 0
\(155\) 13.3919i 1.07566i
\(156\) 0 0
\(157\) 9.44146 + 9.44146i 0.753510 + 0.753510i 0.975133 0.221622i \(-0.0711352\pi\)
−0.221622 + 0.975133i \(0.571135\pi\)
\(158\) 0 0
\(159\) 22.2691i 1.76605i
\(160\) 0 0
\(161\) −5.72086 5.72086i −0.450867 0.450867i
\(162\) 0 0
\(163\) 0.847363 0.0663706 0.0331853 0.999449i \(-0.489435\pi\)
0.0331853 + 0.999449i \(0.489435\pi\)
\(164\) 0 0
\(165\) 19.0398 1.48225
\(166\) 0 0
\(167\) −15.9122 15.9122i −1.23132 1.23132i −0.963457 0.267863i \(-0.913683\pi\)
−0.267863 0.963457i \(-0.586317\pi\)
\(168\) 0 0
\(169\) 8.83224i 0.679403i
\(170\) 0 0
\(171\) 4.59317 + 4.59317i 0.351248 + 0.351248i
\(172\) 0 0
\(173\) 11.3635i 0.863949i −0.901886 0.431975i \(-0.857817\pi\)
0.901886 0.431975i \(-0.142183\pi\)
\(174\) 0 0
\(175\) −0.476600 0.476600i −0.0360276 0.0360276i
\(176\) 0 0
\(177\) −15.1865 15.1865i −1.14148 1.14148i
\(178\) 0 0
\(179\) −2.51734 + 2.51734i −0.188155 + 0.188155i −0.794898 0.606743i \(-0.792476\pi\)
0.606743 + 0.794898i \(0.292476\pi\)
\(180\) 0 0
\(181\) 10.7989 10.7989i 0.802677 0.802677i −0.180836 0.983513i \(-0.557880\pi\)
0.983513 + 0.180836i \(0.0578804\pi\)
\(182\) 0 0
\(183\) 1.68230 1.68230i 0.124359 0.124359i
\(184\) 0 0
\(185\) 7.61646i 0.559973i
\(186\) 0 0
\(187\) −17.2571 −1.26197
\(188\) 0 0
\(189\) −3.58046 −0.260440
\(190\) 0 0
\(191\) 17.5344 17.5344i 1.26875 1.26875i 0.322009 0.946737i \(-0.395642\pi\)
0.946737 0.322009i \(-0.104358\pi\)
\(192\) 0 0
\(193\) 5.28816 + 5.28816i 0.380650 + 0.380650i 0.871336 0.490686i \(-0.163254\pi\)
−0.490686 + 0.871336i \(0.663254\pi\)
\(194\) 0 0
\(195\) −8.77072 −0.628084
\(196\) 0 0
\(197\) 7.36967i 0.525067i −0.964923 0.262534i \(-0.915442\pi\)
0.964923 0.262534i \(-0.0845580\pi\)
\(198\) 0 0
\(199\) −6.26753 + 6.26753i −0.444293 + 0.444293i −0.893452 0.449159i \(-0.851724\pi\)
0.449159 + 0.893452i \(0.351724\pi\)
\(200\) 0 0
\(201\) 0.431046 0.0304037
\(202\) 0 0
\(203\) 9.20843i 0.646305i
\(204\) 0 0
\(205\) −7.40426 11.0699i −0.517136 0.773154i
\(206\) 0 0
\(207\) 10.2475i 0.712249i
\(208\) 0 0
\(209\) 22.7282 1.57214
\(210\) 0 0
\(211\) −12.7875 + 12.7875i −0.880328 + 0.880328i −0.993568 0.113240i \(-0.963877\pi\)
0.113240 + 0.993568i \(0.463877\pi\)
\(212\) 0 0
\(213\) 8.74793i 0.599399i
\(214\) 0 0
\(215\) 1.86774 0.127379
\(216\) 0 0
\(217\) 4.55285 + 4.55285i 0.309068 + 0.309068i
\(218\) 0 0
\(219\) −12.4443 + 12.4443i −0.840907 + 0.840907i
\(220\) 0 0
\(221\) 7.94953 0.534743
\(222\) 0 0
\(223\) −26.4926 −1.77408 −0.887038 0.461697i \(-0.847241\pi\)
−0.887038 + 0.461697i \(0.847241\pi\)
\(224\) 0 0
\(225\) 0.853709i 0.0569139i
\(226\) 0 0
\(227\) −1.06921 + 1.06921i −0.0709656 + 0.0709656i −0.741699 0.670733i \(-0.765980\pi\)
0.670733 + 0.741699i \(0.265980\pi\)
\(228\) 0 0
\(229\) 6.38701 6.38701i 0.422065 0.422065i −0.463849 0.885914i \(-0.653532\pi\)
0.885914 + 0.463849i \(0.153532\pi\)
\(230\) 0 0
\(231\) 6.47298 6.47298i 0.425891 0.425891i
\(232\) 0 0
\(233\) −4.17317 4.17317i −0.273393 0.273393i 0.557071 0.830465i \(-0.311925\pi\)
−0.830465 + 0.557071i \(0.811925\pi\)
\(234\) 0 0
\(235\) −17.9689 17.9689i −1.17216 1.17216i
\(236\) 0 0
\(237\) 15.5182i 1.00802i
\(238\) 0 0
\(239\) −6.29633 6.29633i −0.407276 0.407276i 0.473512 0.880787i \(-0.342986\pi\)
−0.880787 + 0.473512i \(0.842986\pi\)
\(240\) 0 0
\(241\) 14.8553i 0.956912i 0.878111 + 0.478456i \(0.158803\pi\)
−0.878111 + 0.478456i \(0.841197\pi\)
\(242\) 0 0
\(243\) 8.75668 + 8.75668i 0.561741 + 0.561741i
\(244\) 0 0
\(245\) 2.07990 0.132880
\(246\) 0 0
\(247\) −10.4698 −0.666177
\(248\) 0 0
\(249\) −19.2016 19.2016i −1.21685 1.21685i
\(250\) 0 0
\(251\) 19.3759i 1.22299i −0.791247 0.611496i \(-0.790568\pi\)
0.791247 0.611496i \(-0.209432\pi\)
\(252\) 0 0
\(253\) 25.3536 + 25.3536i 1.59397 + 1.59397i
\(254\) 0 0
\(255\) 16.7291i 1.04762i
\(256\) 0 0
\(257\) −0.0866284 0.0866284i −0.00540373 0.00540373i 0.704400 0.709803i \(-0.251216\pi\)
−0.709803 + 0.704400i \(0.751216\pi\)
\(258\) 0 0
\(259\) −2.58938 2.58938i −0.160896 0.160896i
\(260\) 0 0
\(261\) −8.24728 + 8.24728i −0.510494 + 0.510494i
\(262\) 0 0
\(263\) −9.10876 + 9.10876i −0.561670 + 0.561670i −0.929782 0.368112i \(-0.880004\pi\)
0.368112 + 0.929782i \(0.380004\pi\)
\(264\) 0 0
\(265\) −15.8558 + 15.8558i −0.974014 + 0.974014i
\(266\) 0 0
\(267\) 1.47977i 0.0905603i
\(268\) 0 0
\(269\) −12.8010 −0.780491 −0.390245 0.920711i \(-0.627610\pi\)
−0.390245 + 0.920711i \(0.627610\pi\)
\(270\) 0 0
\(271\) 0.850365 0.0516560 0.0258280 0.999666i \(-0.491778\pi\)
0.0258280 + 0.999666i \(0.491778\pi\)
\(272\) 0 0
\(273\) −2.98179 + 2.98179i −0.180466 + 0.180466i
\(274\) 0 0
\(275\) 2.11219 + 2.11219i 0.127370 + 0.127370i
\(276\) 0 0
\(277\) 8.62452 0.518197 0.259099 0.965851i \(-0.416575\pi\)
0.259099 + 0.965851i \(0.416575\pi\)
\(278\) 0 0
\(279\) 8.15528i 0.488244i
\(280\) 0 0
\(281\) 5.20382 5.20382i 0.310434 0.310434i −0.534644 0.845078i \(-0.679554\pi\)
0.845078 + 0.534644i \(0.179554\pi\)
\(282\) 0 0
\(283\) −3.91912 −0.232967 −0.116484 0.993193i \(-0.537162\pi\)
−0.116484 + 0.993193i \(0.537162\pi\)
\(284\) 0 0
\(285\) 22.0328i 1.30511i
\(286\) 0 0
\(287\) −6.28068 1.24621i −0.370737 0.0735612i
\(288\) 0 0
\(289\) 1.83719i 0.108070i
\(290\) 0 0
\(291\) −31.8262 −1.86568
\(292\) 0 0
\(293\) 6.13507 6.13507i 0.358414 0.358414i −0.504814 0.863228i \(-0.668439\pi\)
0.863228 + 0.504814i \(0.168439\pi\)
\(294\) 0 0
\(295\) 21.6259i 1.25911i
\(296\) 0 0
\(297\) 15.8678 0.920745
\(298\) 0 0
\(299\) −11.6792 11.6792i −0.675426 0.675426i
\(300\) 0 0
\(301\) 0.634977 0.634977i 0.0365995 0.0365995i
\(302\) 0 0
\(303\) 30.5903 1.75737
\(304\) 0 0
\(305\) −2.39564 −0.137174
\(306\) 0 0
\(307\) 5.36025i 0.305926i 0.988232 + 0.152963i \(0.0488815\pi\)
−0.988232 + 0.152963i \(0.951118\pi\)
\(308\) 0 0
\(309\) −19.2166 + 19.2166i −1.09319 + 1.09319i
\(310\) 0 0
\(311\) 7.92997 7.92997i 0.449667 0.449667i −0.445577 0.895244i \(-0.647001\pi\)
0.895244 + 0.445577i \(0.147001\pi\)
\(312\) 0 0
\(313\) 3.30950 3.30950i 0.187064 0.187064i −0.607362 0.794425i \(-0.707772\pi\)
0.794425 + 0.607362i \(0.207772\pi\)
\(314\) 0 0
\(315\) −1.86281 1.86281i −0.104957 0.104957i
\(316\) 0 0
\(317\) −3.89022 3.89022i −0.218497 0.218497i 0.589368 0.807865i \(-0.299377\pi\)
−0.807865 + 0.589368i \(0.799377\pi\)
\(318\) 0 0
\(319\) 40.8097i 2.28491i
\(320\) 0 0
\(321\) −8.38698 8.38698i −0.468116 0.468116i
\(322\) 0 0
\(323\) 19.9699i 1.11116i
\(324\) 0 0
\(325\) −0.972984 0.972984i −0.0539715 0.0539715i
\(326\) 0 0
\(327\) −32.5294 −1.79888
\(328\) 0 0
\(329\) −12.2178 −0.673589
\(330\) 0 0
\(331\) 0.742152 + 0.742152i 0.0407924 + 0.0407924i 0.727209 0.686416i \(-0.240817\pi\)
−0.686416 + 0.727209i \(0.740817\pi\)
\(332\) 0 0
\(333\) 4.63822i 0.254173i
\(334\) 0 0
\(335\) −0.306909 0.306909i −0.0167683 0.0167683i
\(336\) 0 0
\(337\) 6.77218i 0.368904i 0.982841 + 0.184452i \(0.0590511\pi\)
−0.982841 + 0.184452i \(0.940949\pi\)
\(338\) 0 0
\(339\) −23.3842 23.3842i −1.27005 1.27005i
\(340\) 0 0
\(341\) −20.1772 20.1772i −1.09266 1.09266i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 0 0
\(345\) 24.5779 24.5779i 1.32323 1.32323i
\(346\) 0 0
\(347\) 3.29604 3.29604i 0.176941 0.176941i −0.613080 0.790021i \(-0.710070\pi\)
0.790021 + 0.613080i \(0.210070\pi\)
\(348\) 0 0
\(349\) 34.5405i 1.84891i 0.381290 + 0.924456i \(0.375480\pi\)
−0.381290 + 0.924456i \(0.624520\pi\)
\(350\) 0 0
\(351\) −7.30955 −0.390155
\(352\) 0 0
\(353\) 25.5874 1.36188 0.680939 0.732340i \(-0.261572\pi\)
0.680939 + 0.732340i \(0.261572\pi\)
\(354\) 0 0
\(355\) 6.22862 6.22862i 0.330581 0.330581i
\(356\) 0 0
\(357\) 5.68743 + 5.68743i 0.301011 + 0.301011i
\(358\) 0 0
\(359\) 23.5577 1.24333 0.621663 0.783285i \(-0.286457\pi\)
0.621663 + 0.783285i \(0.286457\pi\)
\(360\) 0 0
\(361\) 7.30109i 0.384268i
\(362\) 0 0
\(363\) −12.6205 + 12.6205i −0.662402 + 0.662402i
\(364\) 0 0
\(365\) 17.7209 0.927556
\(366\) 0 0
\(367\) 27.6733i 1.44453i −0.691615 0.722267i \(-0.743100\pi\)
0.691615 0.722267i \(-0.256900\pi\)
\(368\) 0 0
\(369\) 4.50899 + 6.74126i 0.234729 + 0.350936i
\(370\) 0 0
\(371\) 10.7810i 0.559724i
\(372\) 0 0
\(373\) −16.5781 −0.858380 −0.429190 0.903214i \(-0.641201\pi\)
−0.429190 + 0.903214i \(0.641201\pi\)
\(374\) 0 0
\(375\) 17.2369 17.2369i 0.890110 0.890110i
\(376\) 0 0
\(377\) 18.7991i 0.968203i
\(378\) 0 0
\(379\) −20.3072 −1.04311 −0.521555 0.853218i \(-0.674648\pi\)
−0.521555 + 0.853218i \(0.674648\pi\)
\(380\) 0 0
\(381\) 26.3765 + 26.3765i 1.35131 + 1.35131i
\(382\) 0 0
\(383\) −21.4939 + 21.4939i −1.09829 + 1.09829i −0.103678 + 0.994611i \(0.533061\pi\)
−0.994611 + 0.103678i \(0.966939\pi\)
\(384\) 0 0
\(385\) −9.21767 −0.469776
\(386\) 0 0
\(387\) −1.13740 −0.0578174
\(388\) 0 0
\(389\) 18.5132i 0.938657i 0.883024 + 0.469328i \(0.155504\pi\)
−0.883024 + 0.469328i \(0.844496\pi\)
\(390\) 0 0
\(391\) −22.2767 + 22.2767i −1.12658 + 1.12658i
\(392\) 0 0
\(393\) −30.7358 + 30.7358i −1.55042 + 1.55042i
\(394\) 0 0
\(395\) −11.0491 + 11.0491i −0.555942 + 0.555942i
\(396\) 0 0
\(397\) −18.0383 18.0383i −0.905317 0.905317i 0.0905730 0.995890i \(-0.471130\pi\)
−0.995890 + 0.0905730i \(0.971130\pi\)
\(398\) 0 0
\(399\) −7.49054 7.49054i −0.374996 0.374996i
\(400\) 0 0
\(401\) 19.6451i 0.981027i −0.871433 0.490514i \(-0.836809\pi\)
0.871433 0.490514i \(-0.163191\pi\)
\(402\) 0 0
\(403\) 9.29469 + 9.29469i 0.463001 + 0.463001i
\(404\) 0 0
\(405\) 23.2856i 1.15707i
\(406\) 0 0
\(407\) 11.4756 + 11.4756i 0.568822 + 0.568822i
\(408\) 0 0
\(409\) 11.3486 0.561153 0.280576 0.959832i \(-0.409474\pi\)
0.280576 + 0.959832i \(0.409474\pi\)
\(410\) 0 0
\(411\) −33.9646 −1.67535
\(412\) 0 0
\(413\) 7.35217 + 7.35217i 0.361777 + 0.361777i
\(414\) 0 0
\(415\) 27.3435i 1.34224i
\(416\) 0 0
\(417\) 2.75737 + 2.75737i 0.135029 + 0.135029i
\(418\) 0 0
\(419\) 2.51864i 0.123044i 0.998106 + 0.0615218i \(0.0195954\pi\)
−0.998106 + 0.0615218i \(0.980405\pi\)
\(420\) 0 0
\(421\) 27.2063 + 27.2063i 1.32595 + 1.32595i 0.908868 + 0.417084i \(0.136948\pi\)
0.417084 + 0.908868i \(0.363052\pi\)
\(422\) 0 0
\(423\) 10.9425 + 10.9425i 0.532045 + 0.532045i
\(424\) 0 0
\(425\) −1.85586 + 1.85586i −0.0900222 + 0.0900222i
\(426\) 0 0
\(427\) −0.814448 + 0.814448i −0.0394139 + 0.0394139i
\(428\) 0 0
\(429\) 13.2147 13.2147i 0.638010 0.638010i
\(430\) 0 0
\(431\) 26.9611i 1.29867i 0.760502 + 0.649335i \(0.224953\pi\)
−0.760502 + 0.649335i \(0.775047\pi\)
\(432\) 0 0
\(433\) −1.99421 −0.0958356 −0.0479178 0.998851i \(-0.515259\pi\)
−0.0479178 + 0.998851i \(0.515259\pi\)
\(434\) 0 0
\(435\) 39.5612 1.89681
\(436\) 0 0
\(437\) 29.3392 29.3392i 1.40349 1.40349i
\(438\) 0 0
\(439\) −23.0565 23.0565i −1.10043 1.10043i −0.994359 0.106068i \(-0.966174\pi\)
−0.106068 0.994359i \(-0.533826\pi\)
\(440\) 0 0
\(441\) −1.26660 −0.0603144
\(442\) 0 0
\(443\) 36.8966i 1.75301i −0.481393 0.876505i \(-0.659869\pi\)
0.481393 0.876505i \(-0.340131\pi\)
\(444\) 0 0
\(445\) 1.05361 1.05361i 0.0499459 0.0499459i
\(446\) 0 0
\(447\) −43.0006 −2.03386
\(448\) 0 0
\(449\) 3.55024i 0.167546i 0.996485 + 0.0837730i \(0.0266971\pi\)
−0.996485 + 0.0837730i \(0.973303\pi\)
\(450\) 0 0
\(451\) 27.8346 + 5.52292i 1.31068 + 0.260064i
\(452\) 0 0
\(453\) 10.4351i 0.490283i
\(454\) 0 0
\(455\) 4.24614 0.199062
\(456\) 0 0
\(457\) 5.23465 5.23465i 0.244867 0.244867i −0.573993 0.818860i \(-0.694606\pi\)
0.818860 + 0.573993i \(0.194606\pi\)
\(458\) 0 0
\(459\) 13.9421i 0.650763i
\(460\) 0 0
\(461\) −1.11794 −0.0520675 −0.0260337 0.999661i \(-0.508288\pi\)
−0.0260337 + 0.999661i \(0.508288\pi\)
\(462\) 0 0
\(463\) −12.7319 12.7319i −0.591702 0.591702i 0.346389 0.938091i \(-0.387408\pi\)
−0.938091 + 0.346389i \(0.887408\pi\)
\(464\) 0 0
\(465\) −19.5599 + 19.5599i −0.907069 + 0.907069i
\(466\) 0 0
\(467\) 33.8870 1.56810 0.784051 0.620697i \(-0.213150\pi\)
0.784051 + 0.620697i \(0.213150\pi\)
\(468\) 0 0
\(469\) −0.208681 −0.00963599
\(470\) 0 0
\(471\) 27.5801i 1.27082i
\(472\) 0 0
\(473\) −2.81408 + 2.81408i −0.129392 + 0.129392i
\(474\) 0 0
\(475\) 2.44423 2.44423i 0.112149 0.112149i
\(476\) 0 0
\(477\) 9.65575 9.65575i 0.442107 0.442107i
\(478\) 0 0
\(479\) −11.6403 11.6403i −0.531859 0.531859i 0.389266 0.921125i \(-0.372729\pi\)
−0.921125 + 0.389266i \(0.872729\pi\)
\(480\) 0 0
\(481\) −5.28624 5.28624i −0.241032 0.241032i
\(482\) 0 0
\(483\) 16.7116i 0.760404i
\(484\) 0 0
\(485\) 22.6606 + 22.6606i 1.02896 + 1.02896i
\(486\) 0 0
\(487\) 31.9191i 1.44639i −0.690643 0.723196i \(-0.742672\pi\)
0.690643 0.723196i \(-0.257328\pi\)
\(488\) 0 0
\(489\) 1.23764 + 1.23764i 0.0559682 + 0.0559682i
\(490\) 0 0
\(491\) 27.8592 1.25727 0.628633 0.777702i \(-0.283615\pi\)
0.628633 + 0.777702i \(0.283615\pi\)
\(492\) 0 0
\(493\) −35.8571 −1.61492
\(494\) 0 0
\(495\) 8.25556 + 8.25556i 0.371060 + 0.371060i
\(496\) 0 0
\(497\) 4.23511i 0.189971i
\(498\) 0 0
\(499\) −0.964813 0.964813i −0.0431910 0.0431910i 0.685181 0.728372i \(-0.259723\pi\)
−0.728372 + 0.685181i \(0.759723\pi\)
\(500\) 0 0
\(501\) 46.4820i 2.07666i
\(502\) 0 0
\(503\) −12.8206 12.8206i −0.571643 0.571643i 0.360944 0.932587i \(-0.382454\pi\)
−0.932587 + 0.360944i \(0.882454\pi\)
\(504\) 0 0
\(505\) −21.7806 21.7806i −0.969224 0.969224i
\(506\) 0 0
\(507\) 12.9002 12.9002i 0.572919 0.572919i
\(508\) 0 0
\(509\) −20.0927 + 20.0927i −0.890595 + 0.890595i −0.994579 0.103984i \(-0.966841\pi\)
0.103984 + 0.994579i \(0.466841\pi\)
\(510\) 0 0
\(511\) 6.02461 6.02461i 0.266513 0.266513i
\(512\) 0 0
\(513\) 18.3623i 0.810714i
\(514\) 0 0
\(515\) 27.3648 1.20584
\(516\) 0 0
\(517\) 54.1466 2.38137
\(518\) 0 0
\(519\) 16.5973 16.5973i 0.728540 0.728540i
\(520\) 0 0
\(521\) −2.46015 2.46015i −0.107781 0.107781i 0.651160 0.758941i \(-0.274283\pi\)
−0.758941 + 0.651160i \(0.774283\pi\)
\(522\) 0 0
\(523\) −6.88317 −0.300980 −0.150490 0.988612i \(-0.548085\pi\)
−0.150490 + 0.988612i \(0.548085\pi\)
\(524\) 0 0
\(525\) 1.39223i 0.0607618i
\(526\) 0 0
\(527\) 17.7285 17.7285i 0.772268 0.772268i
\(528\) 0 0
\(529\) 42.4566 1.84594
\(530\) 0 0
\(531\) 13.1696i 0.571510i
\(532\) 0 0
\(533\) −12.8221 2.54414i −0.555386 0.110199i
\(534\) 0 0
\(535\) 11.9432i 0.516351i
\(536\) 0 0
\(537\) −7.35356 −0.317330
\(538\) 0 0
\(539\) −3.13374 + 3.13374i −0.134980 + 0.134980i
\(540\) 0 0
\(541\) 40.4359i 1.73847i 0.494395 + 0.869237i \(0.335390\pi\)
−0.494395 + 0.869237i \(0.664610\pi\)
\(542\) 0 0
\(543\) 31.5454 1.35374
\(544\) 0 0
\(545\) 23.1613 + 23.1613i 0.992121 + 0.992121i
\(546\) 0 0
\(547\) 18.2571 18.2571i 0.780618 0.780618i −0.199317 0.979935i \(-0.563872\pi\)
0.979935 + 0.199317i \(0.0638723\pi\)
\(548\) 0 0
\(549\) 1.45888 0.0622634
\(550\) 0 0
\(551\) 47.2250 2.01185
\(552\) 0 0
\(553\) 7.51277i 0.319476i
\(554\) 0 0
\(555\) 11.1245 11.1245i 0.472207 0.472207i
\(556\) 0 0
\(557\) 16.9196 16.9196i 0.716908 0.716908i −0.251063 0.967971i \(-0.580780\pi\)
0.967971 + 0.251063i \(0.0807802\pi\)
\(558\) 0 0
\(559\) 1.29631 1.29631i 0.0548282 0.0548282i
\(560\) 0 0
\(561\) −25.2054 25.2054i −1.06417 1.06417i
\(562\) 0 0
\(563\) 14.3657 + 14.3657i 0.605441 + 0.605441i 0.941751 0.336310i \(-0.109179\pi\)
−0.336310 + 0.941751i \(0.609179\pi\)
\(564\) 0 0
\(565\) 33.2996i 1.40092i
\(566\) 0 0
\(567\) −7.91643 7.91643i −0.332459 0.332459i
\(568\) 0 0
\(569\) 19.1050i 0.800922i 0.916314 + 0.400461i \(0.131150\pi\)
−0.916314 + 0.400461i \(0.868850\pi\)
\(570\) 0 0
\(571\) 17.7211 + 17.7211i 0.741606 + 0.741606i 0.972887 0.231281i \(-0.0742917\pi\)
−0.231281 + 0.972887i \(0.574292\pi\)
\(572\) 0 0
\(573\) 51.2209 2.13978
\(574\) 0 0
\(575\) 5.45313 0.227411
\(576\) 0 0
\(577\) 12.1528 + 12.1528i 0.505929 + 0.505929i 0.913274 0.407346i \(-0.133546\pi\)
−0.407346 + 0.913274i \(0.633546\pi\)
\(578\) 0 0
\(579\) 15.4476i 0.641980i
\(580\) 0 0
\(581\) 9.29601 + 9.29601i 0.385663 + 0.385663i
\(582\) 0 0
\(583\) 47.7792i 1.97881i
\(584\) 0 0
\(585\) −3.80294 3.80294i −0.157232 0.157232i
\(586\) 0 0
\(587\) −24.6953 24.6953i −1.01928 1.01928i −0.999810 0.0194733i \(-0.993801\pi\)
−0.0194733 0.999810i \(-0.506199\pi\)
\(588\) 0 0
\(589\) −23.3491 + 23.3491i −0.962083 + 0.962083i
\(590\) 0 0
\(591\) 10.7640 10.7640i 0.442772 0.442772i
\(592\) 0 0
\(593\) −22.9185 + 22.9185i −0.941151 + 0.941151i −0.998362 0.0572107i \(-0.981779\pi\)
0.0572107 + 0.998362i \(0.481779\pi\)
\(594\) 0 0
\(595\) 8.09902i 0.332027i
\(596\) 0 0
\(597\) −18.3085 −0.749316
\(598\) 0 0
\(599\) 4.17456 0.170568 0.0852839 0.996357i \(-0.472820\pi\)
0.0852839 + 0.996357i \(0.472820\pi\)
\(600\) 0 0
\(601\) −5.08430 + 5.08430i −0.207393 + 0.207393i −0.803158 0.595765i \(-0.796849\pi\)
0.595765 + 0.803158i \(0.296849\pi\)
\(602\) 0 0
\(603\) 0.186900 + 0.186900i 0.00761114 + 0.00761114i
\(604\) 0 0
\(605\) 17.9718 0.730657
\(606\) 0 0
\(607\) 4.41771i 0.179309i 0.995973 + 0.0896547i \(0.0285763\pi\)
−0.995973 + 0.0896547i \(0.971424\pi\)
\(608\) 0 0
\(609\) 13.4497 13.4497i 0.545008 0.545008i
\(610\) 0 0
\(611\) −24.9428 −1.00908
\(612\) 0 0
\(613\) 17.7771i 0.718009i 0.933336 + 0.359004i \(0.116884\pi\)
−0.933336 + 0.359004i \(0.883116\pi\)
\(614\) 0 0
\(615\) 5.35394 26.9830i 0.215892 1.08806i
\(616\) 0 0
\(617\) 26.1370i 1.05224i 0.850411 + 0.526119i \(0.176353\pi\)
−0.850411 + 0.526119i \(0.823647\pi\)
\(618\) 0 0
\(619\) 43.9659 1.76714 0.883570 0.468299i \(-0.155133\pi\)
0.883570 + 0.468299i \(0.155133\pi\)
\(620\) 0 0
\(621\) 20.4833 20.4833i 0.821968 0.821968i
\(622\) 0 0
\(623\) 0.716395i 0.0287018i
\(624\) 0 0
\(625\) −21.1756 −0.847025
\(626\) 0 0
\(627\) 33.1964 + 33.1964i 1.32574 + 1.32574i
\(628\) 0 0
\(629\) −10.0829 + 10.0829i −0.402031 + 0.402031i
\(630\) 0 0
\(631\) −33.3447 −1.32743 −0.663717 0.747984i \(-0.731022\pi\)
−0.663717 + 0.747984i \(0.731022\pi\)
\(632\) 0 0
\(633\) −37.3544 −1.48470
\(634\) 0 0
\(635\) 37.5607i 1.49055i
\(636\) 0 0
\(637\) 1.44357 1.44357i 0.0571961 0.0571961i
\(638\) 0 0
\(639\) −3.79306 + 3.79306i −0.150051 + 0.150051i
\(640\) 0 0
\(641\) −13.8479 + 13.8479i −0.546960 + 0.546960i −0.925560 0.378601i \(-0.876405\pi\)
0.378601 + 0.925560i \(0.376405\pi\)
\(642\) 0 0
\(643\) −15.4069 15.4069i −0.607588 0.607588i 0.334727 0.942315i \(-0.391356\pi\)
−0.942315 + 0.334727i \(0.891356\pi\)
\(644\) 0 0
\(645\) 2.72798 + 2.72798i 0.107414 + 0.107414i
\(646\) 0 0
\(647\) 1.18670i 0.0466541i 0.999728 + 0.0233271i \(0.00742591\pi\)
−0.999728 + 0.0233271i \(0.992574\pi\)
\(648\) 0 0
\(649\) −32.5832 32.5832i −1.27900 1.27900i
\(650\) 0 0
\(651\) 13.2996i 0.521253i
\(652\) 0 0
\(653\) 22.2416 + 22.2416i 0.870383 + 0.870383i 0.992514 0.122131i \(-0.0389729\pi\)
−0.122131 + 0.992514i \(0.538973\pi\)
\(654\) 0 0
\(655\) 43.7685 1.71018
\(656\) 0 0
\(657\) −10.7916 −0.421019
\(658\) 0 0
\(659\) 16.7069 + 16.7069i 0.650809 + 0.650809i 0.953188 0.302379i \(-0.0977807\pi\)
−0.302379 + 0.953188i \(0.597781\pi\)
\(660\) 0 0
\(661\) 31.3617i 1.21983i 0.792467 + 0.609914i \(0.208796\pi\)
−0.792467 + 0.609914i \(0.791204\pi\)
\(662\) 0 0
\(663\) 11.6109 + 11.6109i 0.450932 + 0.450932i
\(664\) 0 0
\(665\) 10.6667i 0.413636i
\(666\) 0 0
\(667\) 52.6802 + 52.6802i 2.03978 + 2.03978i
\(668\) 0 0
\(669\) −38.6946 38.6946i −1.49602 1.49602i
\(670\) 0 0
\(671\) 3.60946 3.60946i 0.139342 0.139342i
\(672\) 0 0
\(673\) 12.0018 12.0018i 0.462636 0.462636i −0.436883 0.899518i \(-0.643918\pi\)
0.899518 + 0.436883i \(0.143918\pi\)
\(674\) 0 0
\(675\) 1.70645 1.70645i 0.0656813 0.0656813i
\(676\) 0 0
\(677\) 24.8177i 0.953820i −0.878952 0.476910i \(-0.841757\pi\)
0.878952 0.476910i \(-0.158243\pi\)
\(678\) 0 0
\(679\) 15.4079 0.591301
\(680\) 0 0
\(681\) −3.12332 −0.119686
\(682\) 0 0
\(683\) −14.2128 + 14.2128i −0.543836 + 0.543836i −0.924651 0.380815i \(-0.875643\pi\)
0.380815 + 0.924651i \(0.375643\pi\)
\(684\) 0 0
\(685\) 24.1832 + 24.1832i 0.923991 + 0.923991i
\(686\) 0 0
\(687\) 18.6575 0.711828
\(688\) 0 0
\(689\) 22.0096i 0.838499i
\(690\) 0 0
\(691\) −0.580666 + 0.580666i −0.0220896 + 0.0220896i −0.718065 0.695976i \(-0.754972\pi\)
0.695976 + 0.718065i \(0.254972\pi\)
\(692\) 0 0
\(693\) 5.61331 0.213232
\(694\) 0 0
\(695\) 3.92655i 0.148943i
\(696\) 0 0
\(697\) −4.85266 + 24.4566i −0.183808 + 0.926361i
\(698\) 0 0
\(699\) 12.1905i 0.461088i
\(700\) 0 0
\(701\) 26.2027 0.989661 0.494831 0.868989i \(-0.335230\pi\)
0.494831 + 0.868989i \(0.335230\pi\)
\(702\) 0 0
\(703\) 13.2795 13.2795i 0.500847 0.500847i
\(704\) 0 0
\(705\) 52.4900i 1.97689i
\(706\) 0 0
\(707\) −14.8096 −0.556971
\(708\) 0 0
\(709\) −33.7554 33.7554i −1.26771 1.26771i −0.947268 0.320444i \(-0.896168\pi\)
−0.320444 0.947268i \(-0.603832\pi\)
\(710\) 0 0
\(711\) 6.72862 6.72862i 0.252343 0.252343i
\(712\) 0 0
\(713\) −52.0925 −1.95088
\(714\) 0 0
\(715\) −18.8180 −0.703752
\(716\) 0 0
\(717\) 18.3926i 0.686885i
\(718\) 0 0
\(719\) −10.5268 + 10.5268i −0.392584 + 0.392584i −0.875607 0.483024i \(-0.839539\pi\)
0.483024 + 0.875607i \(0.339539\pi\)
\(720\) 0 0
\(721\) 9.30325 9.30325i 0.346471 0.346471i
\(722\) 0 0
\(723\) −21.6974 + 21.6974i −0.806933 + 0.806933i
\(724\) 0 0
\(725\) 4.38874 + 4.38874i 0.162994 + 0.162994i
\(726\) 0 0
\(727\) −10.3018 10.3018i −0.382074 0.382074i 0.489775 0.871849i \(-0.337079\pi\)
−0.871849 + 0.489775i \(0.837079\pi\)
\(728\) 0 0
\(729\) 8.00687i 0.296551i
\(730\) 0 0
\(731\) −2.47257 2.47257i −0.0914512 0.0914512i
\(732\) 0 0
\(733\) 14.1714i 0.523432i 0.965145 + 0.261716i \(0.0842883\pi\)
−0.965145 + 0.261716i \(0.915712\pi\)
\(734\) 0 0
\(735\) 3.03787 + 3.03787i 0.112053 + 0.112053i
\(736\) 0 0
\(737\) 0.924829 0.0340665
\(738\) 0 0
\(739\) 1.86058 0.0684426 0.0342213 0.999414i \(-0.489105\pi\)
0.0342213 + 0.999414i \(0.489105\pi\)
\(740\) 0 0
\(741\) −15.2920 15.2920i −0.561766 0.561766i
\(742\) 0 0
\(743\) 0.482928i 0.0177169i 0.999961 + 0.00885845i \(0.00281977\pi\)
−0.999961 + 0.00885845i \(0.997180\pi\)
\(744\) 0 0
\(745\) 30.6169 + 30.6169i 1.12172 + 1.12172i
\(746\) 0 0
\(747\) 16.6514i 0.609245i
\(748\) 0 0
\(749\) 4.06036 + 4.06036i 0.148362 + 0.148362i
\(750\) 0 0
\(751\) −1.25608 1.25608i −0.0458350 0.0458350i 0.683818 0.729653i \(-0.260318\pi\)
−0.729653 + 0.683818i \(0.760318\pi\)
\(752\) 0 0
\(753\) 28.3000 28.3000i 1.03131 1.03131i
\(754\) 0 0
\(755\) −7.42989 + 7.42989i −0.270401 + 0.270401i
\(756\) 0 0
\(757\) −18.3163 + 18.3163i −0.665717 + 0.665717i −0.956722 0.291004i \(-0.906011\pi\)
0.291004 + 0.956722i \(0.406011\pi\)
\(758\) 0 0
\(759\) 74.0621i 2.68829i
\(760\) 0 0
\(761\) −19.4530 −0.705172 −0.352586 0.935779i \(-0.614698\pi\)
−0.352586 + 0.935779i \(0.614698\pi\)
\(762\) 0 0
\(763\) 15.7484 0.570129
\(764\) 0 0
\(765\) −7.25367 + 7.25367i −0.262257 + 0.262257i
\(766\) 0 0
\(767\) 15.0095 + 15.0095i 0.541963 + 0.541963i
\(768\) 0 0
\(769\) 24.8729 0.896940 0.448470 0.893798i \(-0.351969\pi\)
0.448470 + 0.893798i \(0.351969\pi\)
\(770\) 0 0
\(771\) 0.253056i 0.00911358i
\(772\) 0 0
\(773\) 8.54580 8.54580i 0.307371 0.307371i −0.536518 0.843889i \(-0.680261\pi\)
0.843889 + 0.536518i \(0.180261\pi\)
\(774\) 0 0
\(775\) −4.33978 −0.155889
\(776\) 0 0
\(777\) 7.56400i 0.271357i
\(778\) 0 0
\(779\) 6.39112 32.2102i 0.228986 1.15405i
\(780\) 0 0
\(781\) 18.7691i 0.671610i
\(782\) 0 0
\(783\) 32.9704 1.17827
\(784\) 0 0
\(785\) 19.6373 19.6373i 0.700885 0.700885i
\(786\) 0 0
\(787\) 3.13834i 0.111870i 0.998434 + 0.0559349i \(0.0178139\pi\)
−0.998434 + 0.0559349i \(0.982186\pi\)
\(788\) 0 0
\(789\) −26.6082 −0.947276
\(790\) 0 0
\(791\) 11.3209 + 11.3209i 0.402525 + 0.402525i
\(792\) 0 0
\(793\) −1.66270 + 1.66270i −0.0590443 + 0.0590443i
\(794\) 0 0
\(795\) −46.3174 −1.64271
\(796\) 0 0
\(797\) −2.93668 −0.104022 −0.0520112 0.998647i \(-0.516563\pi\)
−0.0520112 + 0.998647i \(0.516563\pi\)
\(798\) 0 0
\(799\) 47.5755i 1.68310i
\(800\) 0 0
\(801\) −0.641620 + 0.641620i <