Properties

Label 1148.2.k.b.729.1
Level $1148$
Weight $2$
Character 1148.729
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 729.1
Character \(\chi\) \(=\) 1148.729
Dual form 1148.2.k.b.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.33489 + 2.33489i) q^{3} -3.90568i q^{5} +(-0.707107 + 0.707107i) q^{7} -7.90342i q^{9} +O(q^{10})\) \(q+(-2.33489 + 2.33489i) q^{3} -3.90568i q^{5} +(-0.707107 + 0.707107i) q^{7} -7.90342i q^{9} +(0.604261 - 0.604261i) q^{11} +(0.252118 - 0.252118i) q^{13} +(9.11934 + 9.11934i) q^{15} +(2.82692 + 2.82692i) q^{17} +(-1.41581 - 1.41581i) q^{19} -3.30203i q^{21} -8.08621 q^{23} -10.2544 q^{25} +(11.4489 + 11.4489i) q^{27} +(-5.73525 + 5.73525i) q^{29} +10.8735 q^{31} +2.82177i q^{33} +(2.76174 + 2.76174i) q^{35} +0.470242 q^{37} +1.17734i q^{39} +(-5.11381 - 3.85343i) q^{41} +11.3006i q^{43} -30.8682 q^{45} +(1.33189 + 1.33189i) q^{47} -1.00000i q^{49} -13.2011 q^{51} +(-4.21493 + 4.21493i) q^{53} +(-2.36005 - 2.36005i) q^{55} +6.61154 q^{57} -10.4168 q^{59} -8.63089i q^{61} +(5.58856 + 5.58856i) q^{63} +(-0.984695 - 0.984695i) q^{65} +(-5.76041 - 5.76041i) q^{67} +(18.8804 - 18.8804i) q^{69} +(1.36090 - 1.36090i) q^{71} +1.88354i q^{73} +(23.9428 - 23.9428i) q^{75} +0.854555i q^{77} +(-5.15390 + 5.15390i) q^{79} -29.7537 q^{81} -8.02941 q^{83} +(11.0411 - 11.0411i) q^{85} -26.7823i q^{87} +(1.89785 - 1.89785i) q^{89} +0.356549i q^{91} +(-25.3885 + 25.3885i) q^{93} +(-5.52972 + 5.52972i) q^{95} +(3.77435 + 3.77435i) q^{97} +(-4.77573 - 4.77573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.33489 + 2.33489i −1.34805 + 1.34805i −0.460270 + 0.887779i \(0.652247\pi\)
−0.887779 + 0.460270i \(0.847753\pi\)
\(4\) 0 0
\(5\) 3.90568i 1.74668i −0.487116 0.873338i \(-0.661951\pi\)
0.487116 0.873338i \(-0.338049\pi\)
\(6\) 0 0
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 0 0
\(9\) 7.90342i 2.63447i
\(10\) 0 0
\(11\) 0.604261 0.604261i 0.182192 0.182192i −0.610119 0.792310i \(-0.708878\pi\)
0.792310 + 0.610119i \(0.208878\pi\)
\(12\) 0 0
\(13\) 0.252118 0.252118i 0.0699251 0.0699251i −0.671279 0.741204i \(-0.734255\pi\)
0.741204 + 0.671279i \(0.234255\pi\)
\(14\) 0 0
\(15\) 9.11934 + 9.11934i 2.35460 + 2.35460i
\(16\) 0 0
\(17\) 2.82692 + 2.82692i 0.685629 + 0.685629i 0.961263 0.275633i \(-0.0888876\pi\)
−0.275633 + 0.961263i \(0.588888\pi\)
\(18\) 0 0
\(19\) −1.41581 1.41581i −0.324810 0.324810i 0.525799 0.850609i \(-0.323766\pi\)
−0.850609 + 0.525799i \(0.823766\pi\)
\(20\) 0 0
\(21\) 3.30203i 0.720562i
\(22\) 0 0
\(23\) −8.08621 −1.68609 −0.843045 0.537843i \(-0.819239\pi\)
−0.843045 + 0.537843i \(0.819239\pi\)
\(24\) 0 0
\(25\) −10.2544 −2.05087
\(26\) 0 0
\(27\) 11.4489 + 11.4489i 2.20335 + 2.20335i
\(28\) 0 0
\(29\) −5.73525 + 5.73525i −1.06501 + 1.06501i −0.0672747 + 0.997734i \(0.521430\pi\)
−0.997734 + 0.0672747i \(0.978570\pi\)
\(30\) 0 0
\(31\) 10.8735 1.95294 0.976471 0.215647i \(-0.0691862\pi\)
0.976471 + 0.215647i \(0.0691862\pi\)
\(32\) 0 0
\(33\) 2.82177i 0.491206i
\(34\) 0 0
\(35\) 2.76174 + 2.76174i 0.466819 + 0.466819i
\(36\) 0 0
\(37\) 0.470242 0.0773073 0.0386537 0.999253i \(-0.487693\pi\)
0.0386537 + 0.999253i \(0.487693\pi\)
\(38\) 0 0
\(39\) 1.17734i 0.188525i
\(40\) 0 0
\(41\) −5.11381 3.85343i −0.798643 0.601805i
\(42\) 0 0
\(43\) 11.3006i 1.72332i 0.507482 + 0.861662i \(0.330576\pi\)
−0.507482 + 0.861662i \(0.669424\pi\)
\(44\) 0 0
\(45\) −30.8682 −4.60157
\(46\) 0 0
\(47\) 1.33189 + 1.33189i 0.194276 + 0.194276i 0.797541 0.603265i \(-0.206134\pi\)
−0.603265 + 0.797541i \(0.706134\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −13.2011 −1.84852
\(52\) 0 0
\(53\) −4.21493 + 4.21493i −0.578964 + 0.578964i −0.934618 0.355653i \(-0.884258\pi\)
0.355653 + 0.934618i \(0.384258\pi\)
\(54\) 0 0
\(55\) −2.36005 2.36005i −0.318230 0.318230i
\(56\) 0 0
\(57\) 6.61154 0.875719
\(58\) 0 0
\(59\) −10.4168 −1.35615 −0.678076 0.734992i \(-0.737186\pi\)
−0.678076 + 0.734992i \(0.737186\pi\)
\(60\) 0 0
\(61\) 8.63089i 1.10507i −0.833489 0.552536i \(-0.813660\pi\)
0.833489 0.552536i \(-0.186340\pi\)
\(62\) 0 0
\(63\) 5.58856 + 5.58856i 0.704092 + 0.704092i
\(64\) 0 0
\(65\) −0.984695 0.984695i −0.122136 0.122136i
\(66\) 0 0
\(67\) −5.76041 5.76041i −0.703746 0.703746i 0.261467 0.965212i \(-0.415794\pi\)
−0.965212 + 0.261467i \(0.915794\pi\)
\(68\) 0 0
\(69\) 18.8804 18.8804i 2.27293 2.27293i
\(70\) 0 0
\(71\) 1.36090 1.36090i 0.161509 0.161509i −0.621726 0.783235i \(-0.713568\pi\)
0.783235 + 0.621726i \(0.213568\pi\)
\(72\) 0 0
\(73\) 1.88354i 0.220452i 0.993907 + 0.110226i \(0.0351574\pi\)
−0.993907 + 0.110226i \(0.964843\pi\)
\(74\) 0 0
\(75\) 23.9428 23.9428i 2.76468 2.76468i
\(76\) 0 0
\(77\) 0.854555i 0.0973855i
\(78\) 0 0
\(79\) −5.15390 + 5.15390i −0.579859 + 0.579859i −0.934864 0.355005i \(-0.884479\pi\)
0.355005 + 0.934864i \(0.384479\pi\)
\(80\) 0 0
\(81\) −29.7537 −3.30597
\(82\) 0 0
\(83\) −8.02941 −0.881343 −0.440671 0.897669i \(-0.645260\pi\)
−0.440671 + 0.897669i \(0.645260\pi\)
\(84\) 0 0
\(85\) 11.0411 11.0411i 1.19757 1.19757i
\(86\) 0 0
\(87\) 26.7823i 2.87137i
\(88\) 0 0
\(89\) 1.89785 1.89785i 0.201171 0.201171i −0.599330 0.800502i \(-0.704566\pi\)
0.800502 + 0.599330i \(0.204566\pi\)
\(90\) 0 0
\(91\) 0.356549i 0.0373765i
\(92\) 0 0
\(93\) −25.3885 + 25.3885i −2.63266 + 2.63266i
\(94\) 0 0
\(95\) −5.52972 + 5.52972i −0.567337 + 0.567337i
\(96\) 0 0
\(97\) 3.77435 + 3.77435i 0.383227 + 0.383227i 0.872263 0.489036i \(-0.162651\pi\)
−0.489036 + 0.872263i \(0.662651\pi\)
\(98\) 0 0
\(99\) −4.77573 4.77573i −0.479979 0.479979i
\(100\) 0 0
\(101\) −1.27902 1.27902i −0.127267 0.127267i 0.640604 0.767871i \(-0.278684\pi\)
−0.767871 + 0.640604i \(0.778684\pi\)
\(102\) 0 0
\(103\) 3.35602i 0.330678i 0.986237 + 0.165339i \(0.0528719\pi\)
−0.986237 + 0.165339i \(0.947128\pi\)
\(104\) 0 0
\(105\) −12.8967 −1.25859
\(106\) 0 0
\(107\) −7.99339 −0.772750 −0.386375 0.922342i \(-0.626273\pi\)
−0.386375 + 0.922342i \(0.626273\pi\)
\(108\) 0 0
\(109\) 4.40084 + 4.40084i 0.421524 + 0.421524i 0.885728 0.464204i \(-0.153660\pi\)
−0.464204 + 0.885728i \(0.653660\pi\)
\(110\) 0 0
\(111\) −1.09796 + 1.09796i −0.104214 + 0.104214i
\(112\) 0 0
\(113\) −16.8928 −1.58914 −0.794569 0.607174i \(-0.792303\pi\)
−0.794569 + 0.607174i \(0.792303\pi\)
\(114\) 0 0
\(115\) 31.5822i 2.94505i
\(116\) 0 0
\(117\) −1.99260 1.99260i −0.184216 0.184216i
\(118\) 0 0
\(119\) −3.99787 −0.366484
\(120\) 0 0
\(121\) 10.2697i 0.933612i
\(122\) 0 0
\(123\) 20.9375 2.94286i 1.88787 0.265348i
\(124\) 0 0
\(125\) 20.5219i 1.83554i
\(126\) 0 0
\(127\) 8.28929 0.735555 0.367778 0.929914i \(-0.380119\pi\)
0.367778 + 0.929914i \(0.380119\pi\)
\(128\) 0 0
\(129\) −26.3856 26.3856i −2.32313 2.32313i
\(130\) 0 0
\(131\) 19.8121i 1.73099i 0.500915 + 0.865496i \(0.332997\pi\)
−0.500915 + 0.865496i \(0.667003\pi\)
\(132\) 0 0
\(133\) 2.00226 0.173618
\(134\) 0 0
\(135\) 44.7159 44.7159i 3.84853 3.84853i
\(136\) 0 0
\(137\) 15.6890 + 15.6890i 1.34040 + 1.34040i 0.895658 + 0.444743i \(0.146705\pi\)
0.444743 + 0.895658i \(0.353295\pi\)
\(138\) 0 0
\(139\) −5.57897 −0.473202 −0.236601 0.971607i \(-0.576033\pi\)
−0.236601 + 0.971607i \(0.576033\pi\)
\(140\) 0 0
\(141\) −6.21962 −0.523786
\(142\) 0 0
\(143\) 0.304691i 0.0254795i
\(144\) 0 0
\(145\) 22.4001 + 22.4001i 1.86023 + 1.86023i
\(146\) 0 0
\(147\) 2.33489 + 2.33489i 0.192578 + 0.192578i
\(148\) 0 0
\(149\) −9.93354 9.93354i −0.813787 0.813787i 0.171412 0.985199i \(-0.445167\pi\)
−0.985199 + 0.171412i \(0.945167\pi\)
\(150\) 0 0
\(151\) −2.22594 + 2.22594i −0.181144 + 0.181144i −0.791854 0.610710i \(-0.790884\pi\)
0.610710 + 0.791854i \(0.290884\pi\)
\(152\) 0 0
\(153\) 22.3423 22.3423i 1.80627 1.80627i
\(154\) 0 0
\(155\) 42.4686i 3.41116i
\(156\) 0 0
\(157\) −1.46203 + 1.46203i −0.116683 + 0.116683i −0.763037 0.646354i \(-0.776293\pi\)
0.646354 + 0.763037i \(0.276293\pi\)
\(158\) 0 0
\(159\) 19.6828i 1.56094i
\(160\) 0 0
\(161\) 5.71781 5.71781i 0.450627 0.450627i
\(162\) 0 0
\(163\) −6.76472 −0.529854 −0.264927 0.964269i \(-0.585348\pi\)
−0.264927 + 0.964269i \(0.585348\pi\)
\(164\) 0 0
\(165\) 11.0209 0.857978
\(166\) 0 0
\(167\) −10.1354 + 10.1354i −0.784297 + 0.784297i −0.980553 0.196256i \(-0.937122\pi\)
0.196256 + 0.980553i \(0.437122\pi\)
\(168\) 0 0
\(169\) 12.8729i 0.990221i
\(170\) 0 0
\(171\) −11.1898 + 11.1898i −0.855703 + 0.855703i
\(172\) 0 0
\(173\) 1.61515i 0.122797i 0.998113 + 0.0613987i \(0.0195561\pi\)
−0.998113 + 0.0613987i \(0.980444\pi\)
\(174\) 0 0
\(175\) 7.25093 7.25093i 0.548119 0.548119i
\(176\) 0 0
\(177\) 24.3221 24.3221i 1.82816 1.82816i
\(178\) 0 0
\(179\) −11.4527 11.4527i −0.856015 0.856015i 0.134851 0.990866i \(-0.456944\pi\)
−0.990866 + 0.134851i \(0.956944\pi\)
\(180\) 0 0
\(181\) 8.29754 + 8.29754i 0.616751 + 0.616751i 0.944697 0.327945i \(-0.106356\pi\)
−0.327945 + 0.944697i \(0.606356\pi\)
\(182\) 0 0
\(183\) 20.1522 + 20.1522i 1.48969 + 1.48969i
\(184\) 0 0
\(185\) 1.83662i 0.135031i
\(186\) 0 0
\(187\) 3.41640 0.249832
\(188\) 0 0
\(189\) −16.1912 −1.17774
\(190\) 0 0
\(191\) 8.41481 + 8.41481i 0.608874 + 0.608874i 0.942652 0.333778i \(-0.108324\pi\)
−0.333778 + 0.942652i \(0.608324\pi\)
\(192\) 0 0
\(193\) 11.1471 11.1471i 0.802384 0.802384i −0.181083 0.983468i \(-0.557960\pi\)
0.983468 + 0.181083i \(0.0579604\pi\)
\(194\) 0 0
\(195\) 4.59831 0.329292
\(196\) 0 0
\(197\) 9.13567i 0.650889i 0.945561 + 0.325445i \(0.105514\pi\)
−0.945561 + 0.325445i \(0.894486\pi\)
\(198\) 0 0
\(199\) 7.25035 + 7.25035i 0.513964 + 0.513964i 0.915739 0.401775i \(-0.131606\pi\)
−0.401775 + 0.915739i \(0.631606\pi\)
\(200\) 0 0
\(201\) 26.8998 1.89737
\(202\) 0 0
\(203\) 8.11087i 0.569271i
\(204\) 0 0
\(205\) −15.0503 + 19.9729i −1.05116 + 1.39497i
\(206\) 0 0
\(207\) 63.9086i 4.44196i
\(208\) 0 0
\(209\) −1.71104 −0.118355
\(210\) 0 0
\(211\) −17.1559 17.1559i −1.18106 1.18106i −0.979470 0.201590i \(-0.935389\pi\)
−0.201590 0.979470i \(-0.564611\pi\)
\(212\) 0 0
\(213\) 6.35509i 0.435444i
\(214\) 0 0
\(215\) 44.1366 3.01009
\(216\) 0 0
\(217\) −7.68874 + 7.68874i −0.521946 + 0.521946i
\(218\) 0 0
\(219\) −4.39786 4.39786i −0.297180 0.297180i
\(220\) 0 0
\(221\) 1.42544 0.0958854
\(222\) 0 0
\(223\) −5.80697 −0.388864 −0.194432 0.980916i \(-0.562286\pi\)
−0.194432 + 0.980916i \(0.562286\pi\)
\(224\) 0 0
\(225\) 81.0445i 5.40297i
\(226\) 0 0
\(227\) 2.50663 + 2.50663i 0.166371 + 0.166371i 0.785382 0.619011i \(-0.212466\pi\)
−0.619011 + 0.785382i \(0.712466\pi\)
\(228\) 0 0
\(229\) 1.37349 + 1.37349i 0.0907628 + 0.0907628i 0.751030 0.660268i \(-0.229557\pi\)
−0.660268 + 0.751030i \(0.729557\pi\)
\(230\) 0 0
\(231\) −1.99529 1.99529i −0.131280 0.131280i
\(232\) 0 0
\(233\) 8.00299 8.00299i 0.524293 0.524293i −0.394572 0.918865i \(-0.629107\pi\)
0.918865 + 0.394572i \(0.129107\pi\)
\(234\) 0 0
\(235\) 5.20193 5.20193i 0.339337 0.339337i
\(236\) 0 0
\(237\) 24.0676i 1.56336i
\(238\) 0 0
\(239\) −4.43313 + 4.43313i −0.286755 + 0.286755i −0.835796 0.549041i \(-0.814993\pi\)
0.549041 + 0.835796i \(0.314993\pi\)
\(240\) 0 0
\(241\) 6.25570i 0.402965i −0.979492 0.201482i \(-0.935424\pi\)
0.979492 0.201482i \(-0.0645759\pi\)
\(242\) 0 0
\(243\) 35.1249 35.1249i 2.25326 2.25326i
\(244\) 0 0
\(245\) −3.90568 −0.249525
\(246\) 0 0
\(247\) −0.713905 −0.0454247
\(248\) 0 0
\(249\) 18.7478 18.7478i 1.18809 1.18809i
\(250\) 0 0
\(251\) 12.9520i 0.817524i −0.912641 0.408762i \(-0.865961\pi\)
0.912641 0.408762i \(-0.134039\pi\)
\(252\) 0 0
\(253\) −4.88618 + 4.88618i −0.307192 + 0.307192i
\(254\) 0 0
\(255\) 51.5593i 3.22877i
\(256\) 0 0
\(257\) 13.4896 13.4896i 0.841457 0.841457i −0.147591 0.989048i \(-0.547152\pi\)
0.989048 + 0.147591i \(0.0471520\pi\)
\(258\) 0 0
\(259\) −0.332511 + 0.332511i −0.0206613 + 0.0206613i
\(260\) 0 0
\(261\) 45.3281 + 45.3281i 2.80574 + 2.80574i
\(262\) 0 0
\(263\) 11.2174 + 11.2174i 0.691694 + 0.691694i 0.962605 0.270910i \(-0.0873246\pi\)
−0.270910 + 0.962605i \(0.587325\pi\)
\(264\) 0 0
\(265\) 16.4622 + 16.4622i 1.01126 + 1.01126i
\(266\) 0 0
\(267\) 8.86253i 0.542378i
\(268\) 0 0
\(269\) 9.92609 0.605204 0.302602 0.953117i \(-0.402145\pi\)
0.302602 + 0.953117i \(0.402145\pi\)
\(270\) 0 0
\(271\) −31.0940 −1.88883 −0.944413 0.328761i \(-0.893369\pi\)
−0.944413 + 0.328761i \(0.893369\pi\)
\(272\) 0 0
\(273\) −0.832503 0.832503i −0.0503854 0.0503854i
\(274\) 0 0
\(275\) −6.19632 + 6.19632i −0.373652 + 0.373652i
\(276\) 0 0
\(277\) −8.93861 −0.537069 −0.268534 0.963270i \(-0.586539\pi\)
−0.268534 + 0.963270i \(0.586539\pi\)
\(278\) 0 0
\(279\) 85.9380i 5.14497i
\(280\) 0 0
\(281\) −14.5726 14.5726i −0.869330 0.869330i 0.123068 0.992398i \(-0.460727\pi\)
−0.992398 + 0.123068i \(0.960727\pi\)
\(282\) 0 0
\(283\) −0.0724424 −0.00430625 −0.00215313 0.999998i \(-0.500685\pi\)
−0.00215313 + 0.999998i \(0.500685\pi\)
\(284\) 0 0
\(285\) 25.8226i 1.52960i
\(286\) 0 0
\(287\) 6.34080 0.891226i 0.374285 0.0526074i
\(288\) 0 0
\(289\) 1.01702i 0.0598246i
\(290\) 0 0
\(291\) −17.6254 −1.03322
\(292\) 0 0
\(293\) −12.4244 12.4244i −0.725839 0.725839i 0.243949 0.969788i \(-0.421557\pi\)
−0.969788 + 0.243949i \(0.921557\pi\)
\(294\) 0 0
\(295\) 40.6848i 2.36876i
\(296\) 0 0
\(297\) 13.8363 0.802863
\(298\) 0 0
\(299\) −2.03868 + 2.03868i −0.117900 + 0.117900i
\(300\) 0 0
\(301\) −7.99073 7.99073i −0.460578 0.460578i
\(302\) 0 0
\(303\) 5.97274 0.343125
\(304\) 0 0
\(305\) −33.7095 −1.93020
\(306\) 0 0
\(307\) 22.8144i 1.30208i −0.759042 0.651042i \(-0.774332\pi\)
0.759042 0.651042i \(-0.225668\pi\)
\(308\) 0 0
\(309\) −7.83593 7.83593i −0.445771 0.445771i
\(310\) 0 0
\(311\) 13.4277 + 13.4277i 0.761414 + 0.761414i 0.976578 0.215164i \(-0.0690286\pi\)
−0.215164 + 0.976578i \(0.569029\pi\)
\(312\) 0 0
\(313\) 1.64313 + 1.64313i 0.0928753 + 0.0928753i 0.752018 0.659143i \(-0.229081\pi\)
−0.659143 + 0.752018i \(0.729081\pi\)
\(314\) 0 0
\(315\) 21.8271 21.8271i 1.22982 1.22982i
\(316\) 0 0
\(317\) −8.33677 + 8.33677i −0.468240 + 0.468240i −0.901344 0.433104i \(-0.857418\pi\)
0.433104 + 0.901344i \(0.357418\pi\)
\(318\) 0 0
\(319\) 6.93118i 0.388072i
\(320\) 0 0
\(321\) 18.6637 18.6637i 1.04170 1.04170i
\(322\) 0 0
\(323\) 8.00479i 0.445399i
\(324\) 0 0
\(325\) −2.58532 + 2.58532i −0.143408 + 0.143408i
\(326\) 0 0
\(327\) −20.5510 −1.13647
\(328\) 0 0
\(329\) −1.88357 −0.103845
\(330\) 0 0
\(331\) −4.74328 + 4.74328i −0.260714 + 0.260714i −0.825344 0.564630i \(-0.809019\pi\)
0.564630 + 0.825344i \(0.309019\pi\)
\(332\) 0 0
\(333\) 3.71652i 0.203664i
\(334\) 0 0
\(335\) −22.4983 + 22.4983i −1.22922 + 1.22922i
\(336\) 0 0
\(337\) 22.7509i 1.23932i 0.784871 + 0.619659i \(0.212729\pi\)
−0.784871 + 0.619659i \(0.787271\pi\)
\(338\) 0 0
\(339\) 39.4427 39.4427i 2.14224 2.14224i
\(340\) 0 0
\(341\) 6.57045 6.57045i 0.355810 0.355810i
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) −73.7409 73.7409i −3.97007 3.97007i
\(346\) 0 0
\(347\) −2.64443 2.64443i −0.141961 0.141961i 0.632555 0.774515i \(-0.282006\pi\)
−0.774515 + 0.632555i \(0.782006\pi\)
\(348\) 0 0
\(349\) 19.3625i 1.03645i 0.855244 + 0.518226i \(0.173407\pi\)
−0.855244 + 0.518226i \(0.826593\pi\)
\(350\) 0 0
\(351\) 5.77297 0.308139
\(352\) 0 0
\(353\) 4.90514 0.261074 0.130537 0.991443i \(-0.458330\pi\)
0.130537 + 0.991443i \(0.458330\pi\)
\(354\) 0 0
\(355\) −5.31524 5.31524i −0.282103 0.282103i
\(356\) 0 0
\(357\) 9.33459 9.33459i 0.494039 0.494039i
\(358\) 0 0
\(359\) 17.2354 0.909648 0.454824 0.890581i \(-0.349702\pi\)
0.454824 + 0.890581i \(0.349702\pi\)
\(360\) 0 0
\(361\) 14.9909i 0.788997i
\(362\) 0 0
\(363\) −23.9787 23.9787i −1.25856 1.25856i
\(364\) 0 0
\(365\) 7.35651 0.385057
\(366\) 0 0
\(367\) 22.8287i 1.19165i −0.803116 0.595823i \(-0.796826\pi\)
0.803116 0.595823i \(-0.203174\pi\)
\(368\) 0 0
\(369\) −30.4552 + 40.4166i −1.58544 + 2.10400i
\(370\) 0 0
\(371\) 5.96080i 0.309470i
\(372\) 0 0
\(373\) −0.870831 −0.0450899 −0.0225450 0.999746i \(-0.507177\pi\)
−0.0225450 + 0.999746i \(0.507177\pi\)
\(374\) 0 0
\(375\) −47.9164 47.9164i −2.47439 2.47439i
\(376\) 0 0
\(377\) 2.89192i 0.148942i
\(378\) 0 0
\(379\) −19.3295 −0.992891 −0.496445 0.868068i \(-0.665362\pi\)
−0.496445 + 0.868068i \(0.665362\pi\)
\(380\) 0 0
\(381\) −19.3546 + 19.3546i −0.991564 + 0.991564i
\(382\) 0 0
\(383\) 9.33099 + 9.33099i 0.476791 + 0.476791i 0.904104 0.427313i \(-0.140540\pi\)
−0.427313 + 0.904104i \(0.640540\pi\)
\(384\) 0 0
\(385\) 3.33762 0.170101
\(386\) 0 0
\(387\) 89.3133 4.54005
\(388\) 0 0
\(389\) 24.2825i 1.23117i −0.788069 0.615587i \(-0.788919\pi\)
0.788069 0.615587i \(-0.211081\pi\)
\(390\) 0 0
\(391\) −22.8591 22.8591i −1.15603 1.15603i
\(392\) 0 0
\(393\) −46.2591 46.2591i −2.33346 2.33346i
\(394\) 0 0
\(395\) 20.1295 + 20.1295i 1.01283 + 1.01283i
\(396\) 0 0
\(397\) 6.71206 6.71206i 0.336869 0.336869i −0.518319 0.855187i \(-0.673442\pi\)
0.855187 + 0.518319i \(0.173442\pi\)
\(398\) 0 0
\(399\) −4.67506 + 4.67506i −0.234046 + 0.234046i
\(400\) 0 0
\(401\) 32.7023i 1.63307i −0.577293 0.816537i \(-0.695891\pi\)
0.577293 0.816537i \(-0.304109\pi\)
\(402\) 0 0
\(403\) 2.74142 2.74142i 0.136560 0.136560i
\(404\) 0 0
\(405\) 116.209i 5.77445i
\(406\) 0 0
\(407\) 0.284149 0.284149i 0.0140847 0.0140847i
\(408\) 0 0
\(409\) 6.26430 0.309750 0.154875 0.987934i \(-0.450503\pi\)
0.154875 + 0.987934i \(0.450503\pi\)
\(410\) 0 0
\(411\) −73.2641 −3.61385
\(412\) 0 0
\(413\) 7.36579 7.36579i 0.362447 0.362447i
\(414\) 0 0
\(415\) 31.3604i 1.53942i
\(416\) 0 0
\(417\) 13.0263 13.0263i 0.637900 0.637900i
\(418\) 0 0
\(419\) 14.1392i 0.690745i −0.938466 0.345373i \(-0.887752\pi\)
0.938466 0.345373i \(-0.112248\pi\)
\(420\) 0 0
\(421\) −2.79838 + 2.79838i −0.136385 + 0.136385i −0.772003 0.635619i \(-0.780745\pi\)
0.635619 + 0.772003i \(0.280745\pi\)
\(422\) 0 0
\(423\) 10.5265 10.5265i 0.511814 0.511814i
\(424\) 0 0
\(425\) −28.9883 28.9883i −1.40614 1.40614i
\(426\) 0 0
\(427\) 6.10296 + 6.10296i 0.295343 + 0.295343i
\(428\) 0 0
\(429\) 0.711419 + 0.711419i 0.0343476 + 0.0343476i
\(430\) 0 0
\(431\) 3.13515i 0.151015i 0.997145 + 0.0755074i \(0.0240576\pi\)
−0.997145 + 0.0755074i \(0.975942\pi\)
\(432\) 0 0
\(433\) 4.38905 0.210924 0.105462 0.994423i \(-0.466368\pi\)
0.105462 + 0.994423i \(0.466368\pi\)
\(434\) 0 0
\(435\) −104.603 −5.01535
\(436\) 0 0
\(437\) 11.4486 + 11.4486i 0.547659 + 0.547659i
\(438\) 0 0
\(439\) 0.742883 0.742883i 0.0354559 0.0354559i −0.689157 0.724612i \(-0.742019\pi\)
0.724612 + 0.689157i \(0.242019\pi\)
\(440\) 0 0
\(441\) −7.90342 −0.376353
\(442\) 0 0
\(443\) 34.6887i 1.64811i −0.566511 0.824054i \(-0.691707\pi\)
0.566511 0.824054i \(-0.308293\pi\)
\(444\) 0 0
\(445\) −7.41239 7.41239i −0.351381 0.351381i
\(446\) 0 0
\(447\) 46.3874 2.19405
\(448\) 0 0
\(449\) 22.7931i 1.07567i −0.843050 0.537835i \(-0.819242\pi\)
0.843050 0.537835i \(-0.180758\pi\)
\(450\) 0 0
\(451\) −5.41856 + 0.761601i −0.255150 + 0.0358624i
\(452\) 0 0
\(453\) 10.3946i 0.488383i
\(454\) 0 0
\(455\) 1.39257 0.0652846
\(456\) 0 0
\(457\) 20.1099 + 20.1099i 0.940702 + 0.940702i 0.998338 0.0576354i \(-0.0183561\pi\)
−0.0576354 + 0.998338i \(0.518356\pi\)
\(458\) 0 0
\(459\) 64.7305i 3.02136i
\(460\) 0 0
\(461\) 28.9855 1.34999 0.674995 0.737823i \(-0.264146\pi\)
0.674995 + 0.737823i \(0.264146\pi\)
\(462\) 0 0
\(463\) 15.5420 15.5420i 0.722299 0.722299i −0.246774 0.969073i \(-0.579370\pi\)
0.969073 + 0.246774i \(0.0793705\pi\)
\(464\) 0 0
\(465\) 99.1594 + 99.1594i 4.59841 + 4.59841i
\(466\) 0 0
\(467\) −7.72154 −0.357310 −0.178655 0.983912i \(-0.557175\pi\)
−0.178655 + 0.983912i \(0.557175\pi\)
\(468\) 0 0
\(469\) 8.14645 0.376168
\(470\) 0 0
\(471\) 6.82736i 0.314588i
\(472\) 0 0
\(473\) 6.82851 + 6.82851i 0.313975 + 0.313975i
\(474\) 0 0
\(475\) 14.5183 + 14.5183i 0.666144 + 0.666144i
\(476\) 0 0
\(477\) 33.3123 + 33.3123i 1.52527 + 1.52527i
\(478\) 0 0
\(479\) −18.0696 + 18.0696i −0.825620 + 0.825620i −0.986907 0.161288i \(-0.948435\pi\)
0.161288 + 0.986907i \(0.448435\pi\)
\(480\) 0 0
\(481\) 0.118557 0.118557i 0.00540572 0.00540572i
\(482\) 0 0
\(483\) 26.7009i 1.21493i
\(484\) 0 0
\(485\) 14.7414 14.7414i 0.669373 0.669373i
\(486\) 0 0
\(487\) 10.9869i 0.497865i 0.968521 + 0.248932i \(0.0800797\pi\)
−0.968521 + 0.248932i \(0.919920\pi\)
\(488\) 0 0
\(489\) 15.7949 15.7949i 0.714269 0.714269i
\(490\) 0 0
\(491\) 12.8301 0.579015 0.289507 0.957176i \(-0.406508\pi\)
0.289507 + 0.957176i \(0.406508\pi\)
\(492\) 0 0
\(493\) −32.4262 −1.46040
\(494\) 0 0
\(495\) −18.6525 + 18.6525i −0.838367 + 0.838367i
\(496\) 0 0
\(497\) 1.92460i 0.0863301i
\(498\) 0 0
\(499\) −28.2708 + 28.2708i −1.26557 + 1.26557i −0.317224 + 0.948351i \(0.602751\pi\)
−0.948351 + 0.317224i \(0.897249\pi\)
\(500\) 0 0
\(501\) 47.3298i 2.11454i
\(502\) 0 0
\(503\) −27.4481 + 27.4481i −1.22385 + 1.22385i −0.257598 + 0.966252i \(0.582931\pi\)
−0.966252 + 0.257598i \(0.917069\pi\)
\(504\) 0 0
\(505\) −4.99545 + 4.99545i −0.222295 + 0.222295i
\(506\) 0 0
\(507\) −30.0567 30.0567i −1.33487 1.33487i
\(508\) 0 0
\(509\) −15.3085 15.3085i −0.678538 0.678538i 0.281132 0.959669i \(-0.409290\pi\)
−0.959669 + 0.281132i \(0.909290\pi\)
\(510\) 0 0
\(511\) −1.33186 1.33186i −0.0589182 0.0589182i
\(512\) 0 0
\(513\) 32.4191i 1.43134i
\(514\) 0 0
\(515\) 13.1076 0.577588
\(516\) 0 0
\(517\) 1.60962 0.0707908
\(518\) 0 0
\(519\) −3.77119 3.77119i −0.165537 0.165537i
\(520\) 0 0
\(521\) −9.52829 + 9.52829i −0.417442 + 0.417442i −0.884321 0.466879i \(-0.845378\pi\)
0.466879 + 0.884321i \(0.345378\pi\)
\(522\) 0 0
\(523\) −7.33546 −0.320757 −0.160379 0.987056i \(-0.551272\pi\)
−0.160379 + 0.987056i \(0.551272\pi\)
\(524\) 0 0
\(525\) 33.8603i 1.47778i
\(526\) 0 0
\(527\) 30.7386 + 30.7386i 1.33899 + 1.33899i
\(528\) 0 0
\(529\) 42.3867 1.84290
\(530\) 0 0
\(531\) 82.3283i 3.57275i
\(532\) 0 0
\(533\) −2.26081 + 0.317766i −0.0979264 + 0.0137640i
\(534\) 0 0
\(535\) 31.2197i 1.34974i
\(536\) 0 0
\(537\) 53.4816 2.30790
\(538\) 0 0
\(539\) −0.604261 0.604261i −0.0260274 0.0260274i
\(540\) 0 0
\(541\) 30.9228i 1.32948i 0.747077 + 0.664738i \(0.231457\pi\)
−0.747077 + 0.664738i \(0.768543\pi\)
\(542\) 0 0
\(543\) −38.7477 −1.66282
\(544\) 0 0
\(545\) 17.1883 17.1883i 0.736266 0.736266i
\(546\) 0 0
\(547\) −12.5722 12.5722i −0.537547 0.537547i 0.385261 0.922808i \(-0.374112\pi\)
−0.922808 + 0.385261i \(0.874112\pi\)
\(548\) 0 0
\(549\) −68.2135 −2.91128
\(550\) 0 0
\(551\) 16.2401 0.691851
\(552\) 0 0
\(553\) 7.28872i 0.309948i
\(554\) 0 0
\(555\) 4.28830 + 4.28830i 0.182028 + 0.182028i
\(556\) 0 0
\(557\) −17.9650 17.9650i −0.761202 0.761202i 0.215337 0.976540i \(-0.430915\pi\)
−0.976540 + 0.215337i \(0.930915\pi\)
\(558\) 0 0
\(559\) 2.84909 + 2.84909i 0.120504 + 0.120504i
\(560\) 0 0
\(561\) −7.97691 + 7.97691i −0.336786 + 0.336786i
\(562\) 0 0
\(563\) 18.2877 18.2877i 0.770733 0.770733i −0.207502 0.978235i \(-0.566533\pi\)
0.978235 + 0.207502i \(0.0665333\pi\)
\(564\) 0 0
\(565\) 65.9778i 2.77571i
\(566\) 0 0
\(567\) 21.0391 21.0391i 0.883557 0.883557i
\(568\) 0 0
\(569\) 11.9030i 0.498998i 0.968375 + 0.249499i \(0.0802659\pi\)
−0.968375 + 0.249499i \(0.919734\pi\)
\(570\) 0 0
\(571\) −17.9514 + 17.9514i −0.751242 + 0.751242i −0.974711 0.223469i \(-0.928262\pi\)
0.223469 + 0.974711i \(0.428262\pi\)
\(572\) 0 0
\(573\) −39.2953 −1.64158
\(574\) 0 0
\(575\) 82.9189 3.45796
\(576\) 0 0
\(577\) −7.97498 + 7.97498i −0.332003 + 0.332003i −0.853347 0.521344i \(-0.825431\pi\)
0.521344 + 0.853347i \(0.325431\pi\)
\(578\) 0 0
\(579\) 52.0544i 2.16331i
\(580\) 0 0
\(581\) 5.67765 5.67765i 0.235549 0.235549i
\(582\) 0 0
\(583\) 5.09383i 0.210965i
\(584\) 0 0
\(585\) −7.78245 + 7.78245i −0.321765 + 0.321765i
\(586\) 0 0
\(587\) −2.68198 + 2.68198i −0.110697 + 0.110697i −0.760286 0.649589i \(-0.774941\pi\)
0.649589 + 0.760286i \(0.274941\pi\)
\(588\) 0 0
\(589\) −15.3949 15.3949i −0.634335 0.634335i
\(590\) 0 0
\(591\) −21.3308 21.3308i −0.877431 0.877431i
\(592\) 0 0
\(593\) −19.4170 19.4170i −0.797362 0.797362i 0.185317 0.982679i \(-0.440669\pi\)
−0.982679 + 0.185317i \(0.940669\pi\)
\(594\) 0 0
\(595\) 15.6144i 0.640129i
\(596\) 0 0
\(597\) −33.8575 −1.38570
\(598\) 0 0
\(599\) −5.81743 −0.237694 −0.118847 0.992913i \(-0.537920\pi\)
−0.118847 + 0.992913i \(0.537920\pi\)
\(600\) 0 0
\(601\) −25.5731 25.5731i −1.04315 1.04315i −0.999026 0.0441241i \(-0.985950\pi\)
−0.0441241 0.999026i \(-0.514050\pi\)
\(602\) 0 0
\(603\) −45.5269 + 45.5269i −1.85400 + 1.85400i
\(604\) 0 0
\(605\) 40.1103 1.63072
\(606\) 0 0
\(607\) 28.3183i 1.14941i −0.818362 0.574703i \(-0.805118\pi\)
0.818362 0.574703i \(-0.194882\pi\)
\(608\) 0 0
\(609\) 18.9380 + 18.9380i 0.767406 + 0.767406i
\(610\) 0 0
\(611\) 0.671587 0.0271695
\(612\) 0 0
\(613\) 6.73353i 0.271965i 0.990711 + 0.135982i \(0.0434190\pi\)
−0.990711 + 0.135982i \(0.956581\pi\)
\(614\) 0 0
\(615\) −11.4939 81.7753i −0.463478 3.29750i
\(616\) 0 0
\(617\) 4.05005i 0.163049i 0.996671 + 0.0815245i \(0.0259789\pi\)
−0.996671 + 0.0815245i \(0.974021\pi\)
\(618\) 0 0
\(619\) 30.0767 1.20889 0.604443 0.796649i \(-0.293396\pi\)
0.604443 + 0.796649i \(0.293396\pi\)
\(620\) 0 0
\(621\) −92.5784 92.5784i −3.71504 3.71504i
\(622\) 0 0
\(623\) 2.68396i 0.107531i
\(624\) 0 0
\(625\) 28.8802 1.15521
\(626\) 0 0
\(627\) 3.99510 3.99510i 0.159549 0.159549i
\(628\) 0 0
\(629\) 1.32934 + 1.32934i 0.0530042 + 0.0530042i
\(630\) 0 0
\(631\) 33.0127 1.31421 0.657107 0.753797i \(-0.271780\pi\)
0.657107 + 0.753797i \(0.271780\pi\)
\(632\) 0 0
\(633\) 80.1142 3.18425
\(634\) 0 0
\(635\) 32.3753i 1.28478i
\(636\) 0 0
\(637\) −0.252118 0.252118i −0.00998930 0.00998930i
\(638\) 0 0
\(639\) −10.7557 10.7557i −0.425490 0.425490i
\(640\) 0 0
\(641\) −15.0452 15.0452i −0.594249 0.594249i 0.344528 0.938776i \(-0.388039\pi\)
−0.938776 + 0.344528i \(0.888039\pi\)
\(642\) 0 0
\(643\) 8.27521 8.27521i 0.326343 0.326343i −0.524851 0.851194i \(-0.675879\pi\)
0.851194 + 0.524851i \(0.175879\pi\)
\(644\) 0 0
\(645\) −103.054 + 103.054i −4.05775 + 4.05775i
\(646\) 0 0
\(647\) 32.4186i 1.27451i −0.770654 0.637254i \(-0.780070\pi\)
0.770654 0.637254i \(-0.219930\pi\)
\(648\) 0 0
\(649\) −6.29447 + 6.29447i −0.247080 + 0.247080i
\(650\) 0 0
\(651\) 35.9047i 1.40722i
\(652\) 0 0
\(653\) −7.86295 + 7.86295i −0.307701 + 0.307701i −0.844017 0.536316i \(-0.819816\pi\)
0.536316 + 0.844017i \(0.319816\pi\)
\(654\) 0 0
\(655\) 77.3799 3.02348
\(656\) 0 0
\(657\) 14.8864 0.580773
\(658\) 0 0
\(659\) 23.4608 23.4608i 0.913904 0.913904i −0.0826724 0.996577i \(-0.526346\pi\)
0.996577 + 0.0826724i \(0.0263455\pi\)
\(660\) 0 0
\(661\) 32.8166i 1.27642i −0.769863 0.638209i \(-0.779676\pi\)
0.769863 0.638209i \(-0.220324\pi\)
\(662\) 0 0
\(663\) −3.32824 + 3.32824i −0.129258 + 0.129258i
\(664\) 0 0
\(665\) 7.82021i 0.303255i
\(666\) 0 0
\(667\) 46.3764 46.3764i 1.79570 1.79570i
\(668\) 0 0
\(669\) 13.5586 13.5586i 0.524207 0.524207i
\(670\) 0 0
\(671\) −5.21531 5.21531i −0.201335 0.201335i
\(672\) 0 0
\(673\) −32.8830 32.8830i −1.26755 1.26755i −0.947352 0.320195i \(-0.896252\pi\)
−0.320195 0.947352i \(-0.603748\pi\)
\(674\) 0 0
\(675\) −117.402 117.402i −4.51879 4.51879i
\(676\) 0 0
\(677\) 39.9439i 1.53517i 0.640948 + 0.767584i \(0.278541\pi\)
−0.640948 + 0.767584i \(0.721459\pi\)
\(678\) 0 0
\(679\) −5.33774 −0.204844
\(680\) 0 0
\(681\) −11.7054 −0.448552
\(682\) 0 0
\(683\) 22.2556 + 22.2556i 0.851586 + 0.851586i 0.990329 0.138742i \(-0.0443060\pi\)
−0.138742 + 0.990329i \(0.544306\pi\)
\(684\) 0 0
\(685\) 61.2763 61.2763i 2.34125 2.34125i
\(686\) 0 0
\(687\) −6.41390 −0.244705
\(688\) 0 0
\(689\) 2.12532i 0.0809683i
\(690\) 0 0
\(691\) 28.8143 + 28.8143i 1.09615 + 1.09615i 0.994857 + 0.101292i \(0.0322977\pi\)
0.101292 + 0.994857i \(0.467702\pi\)
\(692\) 0 0
\(693\) 6.75390 0.256559
\(694\) 0 0
\(695\) 21.7897i 0.826531i
\(696\) 0 0
\(697\) −3.56301 25.3497i −0.134959 0.960188i
\(698\) 0 0
\(699\) 37.3722i 1.41355i
\(700\) 0 0
\(701\) −47.1718 −1.78166 −0.890828 0.454341i \(-0.849875\pi\)
−0.890828 + 0.454341i \(0.849875\pi\)
\(702\) 0 0
\(703\) −0.665775 0.665775i −0.0251102 0.0251102i
\(704\) 0 0
\(705\) 24.2919i 0.914885i
\(706\) 0 0
\(707\) 1.80881 0.0680273
\(708\) 0 0
\(709\) 21.5351 21.5351i 0.808766 0.808766i −0.175681 0.984447i \(-0.556213\pi\)
0.984447 + 0.175681i \(0.0562127\pi\)
\(710\) 0 0
\(711\) 40.7334 + 40.7334i 1.52762 + 1.52762i
\(712\) 0 0
\(713\) −87.9256 −3.29284
\(714\) 0 0
\(715\) −1.19003 −0.0445045
\(716\) 0 0
\(717\) 20.7017i 0.773120i
\(718\) 0 0
\(719\) −24.1944 24.1944i −0.902299 0.902299i 0.0933355 0.995635i \(-0.470247\pi\)
−0.995635 + 0.0933355i \(0.970247\pi\)
\(720\) 0 0
\(721\) −2.37306 2.37306i −0.0883775 0.0883775i
\(722\) 0 0
\(723\) 14.6064 + 14.6064i 0.543216 + 0.543216i
\(724\) 0 0
\(725\) 58.8114 58.8114i 2.18420 2.18420i
\(726\) 0 0
\(727\) 6.53856 6.53856i 0.242502 0.242502i −0.575383 0.817884i \(-0.695147\pi\)
0.817884 + 0.575383i \(0.195147\pi\)
\(728\) 0 0
\(729\) 74.7641i 2.76904i
\(730\) 0 0
\(731\) −31.9459 + 31.9459i −1.18156 + 1.18156i
\(732\) 0 0
\(733\) 28.9164i 1.06805i 0.845469 + 0.534025i \(0.179321\pi\)
−0.845469 + 0.534025i \(0.820679\pi\)
\(734\) 0 0
\(735\) 9.11934 9.11934i 0.336372 0.336372i
\(736\) 0 0
\(737\) −6.96158 −0.256433
\(738\) 0 0
\(739\) −19.2957 −0.709804 −0.354902 0.934904i \(-0.615486\pi\)
−0.354902 + 0.934904i \(0.615486\pi\)
\(740\) 0 0
\(741\) 1.66689 1.66689i 0.0612347 0.0612347i
\(742\) 0 0
\(743\) 9.23639i 0.338850i 0.985543 + 0.169425i \(0.0541911\pi\)
−0.985543 + 0.169425i \(0.945809\pi\)
\(744\) 0 0
\(745\) −38.7973 + 38.7973i −1.42142 + 1.42142i
\(746\) 0 0
\(747\) 63.4598i 2.32187i
\(748\) 0 0
\(749\) 5.65218 5.65218i 0.206526 0.206526i
\(750\) 0 0
\(751\) 18.9416 18.9416i 0.691187 0.691187i −0.271306 0.962493i \(-0.587456\pi\)
0.962493 + 0.271306i \(0.0874556\pi\)
\(752\) 0 0
\(753\) 30.2415 + 30.2415i 1.10206 + 1.10206i
\(754\) 0 0
\(755\) 8.69381 + 8.69381i 0.316400 + 0.316400i
\(756\) 0 0
\(757\) 25.0860 + 25.0860i 0.911768 + 0.911768i 0.996411 0.0846433i \(-0.0269751\pi\)
−0.0846433 + 0.996411i \(0.526975\pi\)
\(758\) 0 0
\(759\) 22.8174i 0.828219i
\(760\) 0 0
\(761\) 5.10912 0.185205 0.0926027 0.995703i \(-0.470481\pi\)
0.0926027 + 0.995703i \(0.470481\pi\)
\(762\) 0 0
\(763\) −6.22373 −0.225314
\(764\) 0 0
\(765\) −87.2621 87.2621i −3.15497 3.15497i
\(766\) 0 0
\(767\) −2.62627 + 2.62627i −0.0948291 + 0.0948291i
\(768\) 0 0
\(769\) 50.1889 1.80986 0.904928 0.425564i \(-0.139924\pi\)
0.904928 + 0.425564i \(0.139924\pi\)
\(770\) 0 0
\(771\) 62.9934i 2.26865i
\(772\) 0 0
\(773\) −2.49807 2.49807i −0.0898492 0.0898492i 0.660754 0.750603i \(-0.270237\pi\)
−0.750603 + 0.660754i \(0.770237\pi\)
\(774\) 0 0
\(775\) −111.501 −4.00524
\(776\) 0 0
\(777\) 1.55275i 0.0557048i
\(778\) 0 0
\(779\) 1.78447 + 12.6959i 0.0639352 + 0.454879i
\(780\) 0 0
\(781\) 1.64468i 0.0588511i
\(782\) 0 0
\(783\) −131.325 −4.69317
\(784\) 0 0
\(785\) 5.71023 + 5.71023i 0.203807 + 0.203807i
\(786\) 0 0
\(787\) 16.8884i 0.602008i 0.953623 + 0.301004i \(0.0973217\pi\)
−0.953623 + 0.301004i \(0.902678\pi\)
\(788\) 0 0
\(789\) −52.3828 −1.86488
\(790\) 0 0
\(791\) 11.9450 11.9450i 0.424715 0.424715i
\(792\) 0 0
\(793\) −2.17601 2.17601i −0.0772723 0.0772723i
\(794\) 0 0
\(795\) −76.8747 −2.72646
\(796\) 0 0
\(797\) 23.7983 0.842979 0.421490 0.906833i \(-0.361507\pi\)
0.421490 + 0.906833i \(0.361507\pi\)
\(798\) 0 0
\(799\) 7.53029i 0.266402i
\(800\) 0 0
\(801\) −14.9995