Properties

Label 1148.2.k.b.337.17
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 337.17
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.86437 + 1.86437i) q^{3} -2.96253i q^{5} +(0.707107 + 0.707107i) q^{7} +3.95177i q^{9} +O(q^{10})\) \(q+(1.86437 + 1.86437i) q^{3} -2.96253i q^{5} +(0.707107 + 0.707107i) q^{7} +3.95177i q^{9} +(2.99130 + 2.99130i) q^{11} +(0.619012 + 0.619012i) q^{13} +(5.52326 - 5.52326i) q^{15} +(1.08301 - 1.08301i) q^{17} +(-1.93662 + 1.93662i) q^{19} +2.63662i q^{21} -1.66835 q^{23} -3.77657 q^{25} +(-1.77446 + 1.77446i) q^{27} +(-2.85131 - 2.85131i) q^{29} +10.4509 q^{31} +11.1538i q^{33} +(2.09482 - 2.09482i) q^{35} +5.67577 q^{37} +2.30814i q^{39} +(-2.65185 + 5.82818i) q^{41} +0.246878i q^{43} +11.7072 q^{45} +(1.86462 - 1.86462i) q^{47} +1.00000i q^{49} +4.03826 q^{51} +(-2.37754 - 2.37754i) q^{53} +(8.86182 - 8.86182i) q^{55} -7.22118 q^{57} +12.0601 q^{59} +2.07952i q^{61} +(-2.79432 + 2.79432i) q^{63} +(1.83384 - 1.83384i) q^{65} +(-3.35588 + 3.35588i) q^{67} +(-3.11043 - 3.11043i) q^{69} +(-7.87049 - 7.87049i) q^{71} +2.12655i q^{73} +(-7.04094 - 7.04094i) q^{75} +4.23034i q^{77} +(-3.02140 - 3.02140i) q^{79} +5.23882 q^{81} -2.75282 q^{83} +(-3.20844 - 3.20844i) q^{85} -10.6318i q^{87} +(-9.71983 - 9.71983i) q^{89} +0.875415i q^{91} +(19.4843 + 19.4843i) q^{93} +(5.73730 + 5.73730i) q^{95} +(-11.1964 + 11.1964i) q^{97} +(-11.8210 + 11.8210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

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
\(3\) 1.86437 + 1.86437i 1.07640 + 1.07640i 0.996830 + 0.0795665i \(0.0253536\pi\)
0.0795665 + 0.996830i \(0.474646\pi\)
\(4\) 0 0
\(5\) 2.96253i 1.32488i −0.749114 0.662441i \(-0.769520\pi\)
0.749114 0.662441i \(-0.230480\pi\)
\(6\) 0 0
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0 0
\(9\) 3.95177i 1.31726i
\(10\) 0 0
\(11\) 2.99130 + 2.99130i 0.901912 + 0.901912i 0.995601 0.0936893i \(-0.0298660\pi\)
−0.0936893 + 0.995601i \(0.529866\pi\)
\(12\) 0 0
\(13\) 0.619012 + 0.619012i 0.171683 + 0.171683i 0.787718 0.616035i \(-0.211262\pi\)
−0.616035 + 0.787718i \(0.711262\pi\)
\(14\) 0 0
\(15\) 5.52326 5.52326i 1.42610 1.42610i
\(16\) 0 0
\(17\) 1.08301 1.08301i 0.262668 0.262668i −0.563469 0.826137i \(-0.690534\pi\)
0.826137 + 0.563469i \(0.190534\pi\)
\(18\) 0 0
\(19\) −1.93662 + 1.93662i −0.444292 + 0.444292i −0.893452 0.449160i \(-0.851723\pi\)
0.449160 + 0.893452i \(0.351723\pi\)
\(20\) 0 0
\(21\) 2.63662i 0.575358i
\(22\) 0 0
\(23\) −1.66835 −0.347875 −0.173938 0.984757i \(-0.555649\pi\)
−0.173938 + 0.984757i \(0.555649\pi\)
\(24\) 0 0
\(25\) −3.77657 −0.755314
\(26\) 0 0
\(27\) −1.77446 + 1.77446i −0.341494 + 0.341494i
\(28\) 0 0
\(29\) −2.85131 2.85131i −0.529475 0.529475i 0.390941 0.920416i \(-0.372150\pi\)
−0.920416 + 0.390941i \(0.872150\pi\)
\(30\) 0 0
\(31\) 10.4509 1.87703 0.938515 0.345238i \(-0.112202\pi\)
0.938515 + 0.345238i \(0.112202\pi\)
\(32\) 0 0
\(33\) 11.1538i 1.94163i
\(34\) 0 0
\(35\) 2.09482 2.09482i 0.354090 0.354090i
\(36\) 0 0
\(37\) 5.67577 0.933090 0.466545 0.884497i \(-0.345499\pi\)
0.466545 + 0.884497i \(0.345499\pi\)
\(38\) 0 0
\(39\) 2.30814i 0.369598i
\(40\) 0 0
\(41\) −2.65185 + 5.82818i −0.414150 + 0.910209i
\(42\) 0 0
\(43\) 0.246878i 0.0376486i 0.999823 + 0.0188243i \(0.00599231\pi\)
−0.999823 + 0.0188243i \(0.994008\pi\)
\(44\) 0 0
\(45\) 11.7072 1.74521
\(46\) 0 0
\(47\) 1.86462 1.86462i 0.271983 0.271983i −0.557915 0.829898i \(-0.688399\pi\)
0.829898 + 0.557915i \(0.188399\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 4.03826 0.565470
\(52\) 0 0
\(53\) −2.37754 2.37754i −0.326581 0.326581i 0.524704 0.851285i \(-0.324176\pi\)
−0.851285 + 0.524704i \(0.824176\pi\)
\(54\) 0 0
\(55\) 8.86182 8.86182i 1.19493 1.19493i
\(56\) 0 0
\(57\) −7.22118 −0.956468
\(58\) 0 0
\(59\) 12.0601 1.57010 0.785048 0.619436i \(-0.212638\pi\)
0.785048 + 0.619436i \(0.212638\pi\)
\(60\) 0 0
\(61\) 2.07952i 0.266255i 0.991099 + 0.133128i \(0.0425020\pi\)
−0.991099 + 0.133128i \(0.957498\pi\)
\(62\) 0 0
\(63\) −2.79432 + 2.79432i −0.352052 + 0.352052i
\(64\) 0 0
\(65\) 1.83384 1.83384i 0.227460 0.227460i
\(66\) 0 0
\(67\) −3.35588 + 3.35588i −0.409986 + 0.409986i −0.881734 0.471748i \(-0.843623\pi\)
0.471748 + 0.881734i \(0.343623\pi\)
\(68\) 0 0
\(69\) −3.11043 3.11043i −0.374452 0.374452i
\(70\) 0 0
\(71\) −7.87049 7.87049i −0.934055 0.934055i 0.0639014 0.997956i \(-0.479646\pi\)
−0.997956 + 0.0639014i \(0.979646\pi\)
\(72\) 0 0
\(73\) 2.12655i 0.248894i 0.992226 + 0.124447i \(0.0397156\pi\)
−0.992226 + 0.124447i \(0.960284\pi\)
\(74\) 0 0
\(75\) −7.04094 7.04094i −0.813017 0.813017i
\(76\) 0 0
\(77\) 4.23034i 0.482092i
\(78\) 0 0
\(79\) −3.02140 3.02140i −0.339934 0.339934i 0.516408 0.856342i \(-0.327269\pi\)
−0.856342 + 0.516408i \(0.827269\pi\)
\(80\) 0 0
\(81\) 5.23882 0.582091
\(82\) 0 0
\(83\) −2.75282 −0.302162 −0.151081 0.988521i \(-0.548275\pi\)
−0.151081 + 0.988521i \(0.548275\pi\)
\(84\) 0 0
\(85\) −3.20844 3.20844i −0.348004 0.348004i
\(86\) 0 0
\(87\) 10.6318i 1.13985i
\(88\) 0 0
\(89\) −9.71983 9.71983i −1.03030 1.03030i −0.999526 0.0307731i \(-0.990203\pi\)
−0.0307731 0.999526i \(-0.509797\pi\)
\(90\) 0 0
\(91\) 0.875415i 0.0917684i
\(92\) 0 0
\(93\) 19.4843 + 19.4843i 2.02043 + 2.02043i
\(94\) 0 0
\(95\) 5.73730 + 5.73730i 0.588635 + 0.588635i
\(96\) 0 0
\(97\) −11.1964 + 11.1964i −1.13682 + 1.13682i −0.147806 + 0.989016i \(0.547221\pi\)
−0.989016 + 0.147806i \(0.952779\pi\)
\(98\) 0 0
\(99\) −11.8210 + 11.8210i −1.18805 + 1.18805i
\(100\) 0 0
\(101\) −11.9754 + 11.9754i −1.19160 + 1.19160i −0.214977 + 0.976619i \(0.568968\pi\)
−0.976619 + 0.214977i \(0.931032\pi\)
\(102\) 0 0
\(103\) 4.53596i 0.446941i −0.974711 0.223470i \(-0.928261\pi\)
0.974711 0.223470i \(-0.0717386\pi\)
\(104\) 0 0
\(105\) 7.81106 0.762282
\(106\) 0 0
\(107\) −5.03676 −0.486922 −0.243461 0.969911i \(-0.578283\pi\)
−0.243461 + 0.969911i \(0.578283\pi\)
\(108\) 0 0
\(109\) −7.55793 + 7.55793i −0.723918 + 0.723918i −0.969401 0.245483i \(-0.921054\pi\)
0.245483 + 0.969401i \(0.421054\pi\)
\(110\) 0 0
\(111\) 10.5817 + 10.5817i 1.00437 + 1.00437i
\(112\) 0 0
\(113\) −15.4571 −1.45408 −0.727041 0.686594i \(-0.759105\pi\)
−0.727041 + 0.686594i \(0.759105\pi\)
\(114\) 0 0
\(115\) 4.94254i 0.460894i
\(116\) 0 0
\(117\) −2.44619 + 2.44619i −0.226151 + 0.226151i
\(118\) 0 0
\(119\) 1.53160 0.140402
\(120\) 0 0
\(121\) 6.89580i 0.626891i
\(122\) 0 0
\(123\) −15.8099 + 5.92185i −1.42553 + 0.533956i
\(124\) 0 0
\(125\) 3.62444i 0.324180i
\(126\) 0 0
\(127\) 3.48488 0.309233 0.154616 0.987975i \(-0.450586\pi\)
0.154616 + 0.987975i \(0.450586\pi\)
\(128\) 0 0
\(129\) −0.460273 + 0.460273i −0.0405248 + 0.0405248i
\(130\) 0 0
\(131\) 8.94915i 0.781891i −0.920414 0.390946i \(-0.872148\pi\)
0.920414 0.390946i \(-0.127852\pi\)
\(132\) 0 0
\(133\) −2.73880 −0.237484
\(134\) 0 0
\(135\) 5.25688 + 5.25688i 0.452440 + 0.452440i
\(136\) 0 0
\(137\) 9.10060 9.10060i 0.777517 0.777517i −0.201891 0.979408i \(-0.564709\pi\)
0.979408 + 0.201891i \(0.0647088\pi\)
\(138\) 0 0
\(139\) −22.6023 −1.91710 −0.958552 0.284919i \(-0.908033\pi\)
−0.958552 + 0.284919i \(0.908033\pi\)
\(140\) 0 0
\(141\) 6.95269 0.585522
\(142\) 0 0
\(143\) 3.70330i 0.309686i
\(144\) 0 0
\(145\) −8.44708 + 8.44708i −0.701492 + 0.701492i
\(146\) 0 0
\(147\) −1.86437 + 1.86437i −0.153771 + 0.153771i
\(148\) 0 0
\(149\) 17.0991 17.0991i 1.40081 1.40081i 0.603292 0.797520i \(-0.293855\pi\)
0.797520 0.603292i \(-0.206145\pi\)
\(150\) 0 0
\(151\) 3.55269 + 3.55269i 0.289114 + 0.289114i 0.836730 0.547616i \(-0.184464\pi\)
−0.547616 + 0.836730i \(0.684464\pi\)
\(152\) 0 0
\(153\) 4.27980 + 4.27980i 0.346001 + 0.346001i
\(154\) 0 0
\(155\) 30.9610i 2.48684i
\(156\) 0 0
\(157\) −3.45235 3.45235i −0.275527 0.275527i 0.555793 0.831321i \(-0.312415\pi\)
−0.831321 + 0.555793i \(0.812415\pi\)
\(158\) 0 0
\(159\) 8.86526i 0.703061i
\(160\) 0 0
\(161\) −1.17970 1.17970i −0.0929736 0.0929736i
\(162\) 0 0
\(163\) −12.9288 −1.01266 −0.506332 0.862339i \(-0.668999\pi\)
−0.506332 + 0.862339i \(0.668999\pi\)
\(164\) 0 0
\(165\) 33.0435 2.57243
\(166\) 0 0
\(167\) 6.02429 + 6.02429i 0.466173 + 0.466173i 0.900672 0.434499i \(-0.143075\pi\)
−0.434499 + 0.900672i \(0.643075\pi\)
\(168\) 0 0
\(169\) 12.2336i 0.941050i
\(170\) 0 0
\(171\) −7.65309 7.65309i −0.585247 0.585247i
\(172\) 0 0
\(173\) 10.8343i 0.823714i −0.911249 0.411857i \(-0.864880\pi\)
0.911249 0.411857i \(-0.135120\pi\)
\(174\) 0 0
\(175\) −2.67044 2.67044i −0.201866 0.201866i
\(176\) 0 0
\(177\) 22.4846 + 22.4846i 1.69004 + 1.69004i
\(178\) 0 0
\(179\) 11.4482 11.4482i 0.855679 0.855679i −0.135147 0.990826i \(-0.543151\pi\)
0.990826 + 0.135147i \(0.0431506\pi\)
\(180\) 0 0
\(181\) 13.7929 13.7929i 1.02521 1.02521i 0.0255409 0.999674i \(-0.491869\pi\)
0.999674 0.0255409i \(-0.00813081\pi\)
\(182\) 0 0
\(183\) −3.87700 + 3.87700i −0.286596 + 0.286596i
\(184\) 0 0
\(185\) 16.8146i 1.23623i
\(186\) 0 0
\(187\) 6.47921 0.473807
\(188\) 0 0
\(189\) −2.50946 −0.182536
\(190\) 0 0
\(191\) −11.9361 + 11.9361i −0.863665 + 0.863665i −0.991762 0.128097i \(-0.959113\pi\)
0.128097 + 0.991762i \(0.459113\pi\)
\(192\) 0 0
\(193\) 0.740264 + 0.740264i 0.0532854 + 0.0532854i 0.733247 0.679962i \(-0.238004\pi\)
−0.679962 + 0.733247i \(0.738004\pi\)
\(194\) 0 0
\(195\) 6.83792 0.489674
\(196\) 0 0
\(197\) 10.4556i 0.744933i −0.928046 0.372466i \(-0.878512\pi\)
0.928046 0.372466i \(-0.121488\pi\)
\(198\) 0 0
\(199\) 4.72768 4.72768i 0.335137 0.335137i −0.519397 0.854533i \(-0.673843\pi\)
0.854533 + 0.519397i \(0.173843\pi\)
\(200\) 0 0
\(201\) −12.5132 −0.882615
\(202\) 0 0
\(203\) 4.03236i 0.283016i
\(204\) 0 0
\(205\) 17.2661 + 7.85619i 1.20592 + 0.548700i
\(206\) 0 0
\(207\) 6.59295i 0.458241i
\(208\) 0 0
\(209\) −11.5861 −0.801424
\(210\) 0 0
\(211\) −1.37936 + 1.37936i −0.0949588 + 0.0949588i −0.752990 0.658032i \(-0.771389\pi\)
0.658032 + 0.752990i \(0.271389\pi\)
\(212\) 0 0
\(213\) 29.3470i 2.01083i
\(214\) 0 0
\(215\) 0.731384 0.0498800
\(216\) 0 0
\(217\) 7.38987 + 7.38987i 0.501657 + 0.501657i
\(218\) 0 0
\(219\) −3.96468 + 3.96468i −0.267908 + 0.267908i
\(220\) 0 0
\(221\) 1.34079 0.0901912
\(222\) 0 0
\(223\) −3.79309 −0.254004 −0.127002 0.991902i \(-0.540535\pi\)
−0.127002 + 0.991902i \(0.540535\pi\)
\(224\) 0 0
\(225\) 14.9241i 0.994943i
\(226\) 0 0
\(227\) −13.0020 + 13.0020i −0.862975 + 0.862975i −0.991683 0.128707i \(-0.958917\pi\)
0.128707 + 0.991683i \(0.458917\pi\)
\(228\) 0 0
\(229\) −10.9076 + 10.9076i −0.720797 + 0.720797i −0.968768 0.247970i \(-0.920236\pi\)
0.247970 + 0.968768i \(0.420236\pi\)
\(230\) 0 0
\(231\) −7.88694 + 7.88694i −0.518922 + 0.518922i
\(232\) 0 0
\(233\) −8.61461 8.61461i −0.564362 0.564362i 0.366181 0.930543i \(-0.380665\pi\)
−0.930543 + 0.366181i \(0.880665\pi\)
\(234\) 0 0
\(235\) −5.52399 5.52399i −0.360345 0.360345i
\(236\) 0 0
\(237\) 11.2660i 0.731807i
\(238\) 0 0
\(239\) 4.44216 + 4.44216i 0.287340 + 0.287340i 0.836027 0.548688i \(-0.184872\pi\)
−0.548688 + 0.836027i \(0.684872\pi\)
\(240\) 0 0
\(241\) 8.60928i 0.554573i 0.960787 + 0.277286i \(0.0894350\pi\)
−0.960787 + 0.277286i \(0.910565\pi\)
\(242\) 0 0
\(243\) 15.0905 + 15.0905i 0.968055 + 0.968055i
\(244\) 0 0
\(245\) 2.96253 0.189269
\(246\) 0 0
\(247\) −2.39759 −0.152555
\(248\) 0 0
\(249\) −5.13229 5.13229i −0.325246 0.325246i
\(250\) 0 0
\(251\) 6.75004i 0.426059i 0.977046 + 0.213029i \(0.0683330\pi\)
−0.977046 + 0.213029i \(0.931667\pi\)
\(252\) 0 0
\(253\) −4.99055 4.99055i −0.313753 0.313753i
\(254\) 0 0
\(255\) 11.9635i 0.749181i
\(256\) 0 0
\(257\) 9.70135 + 9.70135i 0.605154 + 0.605154i 0.941676 0.336522i \(-0.109251\pi\)
−0.336522 + 0.941676i \(0.609251\pi\)
\(258\) 0 0
\(259\) 4.01337 + 4.01337i 0.249379 + 0.249379i
\(260\) 0 0
\(261\) 11.2677 11.2677i 0.697454 0.697454i
\(262\) 0 0
\(263\) 17.8681 17.8681i 1.10179 1.10179i 0.107601 0.994194i \(-0.465683\pi\)
0.994194 0.107601i \(-0.0343168\pi\)
\(264\) 0 0
\(265\) −7.04354 + 7.04354i −0.432681 + 0.432681i
\(266\) 0 0
\(267\) 36.2428i 2.21802i
\(268\) 0 0
\(269\) 6.55438 0.399628 0.199814 0.979834i \(-0.435966\pi\)
0.199814 + 0.979834i \(0.435966\pi\)
\(270\) 0 0
\(271\) −13.8236 −0.839724 −0.419862 0.907588i \(-0.637922\pi\)
−0.419862 + 0.907588i \(0.637922\pi\)
\(272\) 0 0
\(273\) −1.63210 + 1.63210i −0.0987792 + 0.0987792i
\(274\) 0 0
\(275\) −11.2969 11.2969i −0.681227 0.681227i
\(276\) 0 0
\(277\) 11.2742 0.677403 0.338701 0.940894i \(-0.390012\pi\)
0.338701 + 0.940894i \(0.390012\pi\)
\(278\) 0 0
\(279\) 41.2994i 2.47253i
\(280\) 0 0
\(281\) 15.9759 15.9759i 0.953043 0.953043i −0.0459031 0.998946i \(-0.514617\pi\)
0.998946 + 0.0459031i \(0.0146165\pi\)
\(282\) 0 0
\(283\) −12.9982 −0.772663 −0.386332 0.922360i \(-0.626258\pi\)
−0.386332 + 0.922360i \(0.626258\pi\)
\(284\) 0 0
\(285\) 21.3929i 1.26721i
\(286\) 0 0
\(287\) −5.99629 + 2.24600i −0.353950 + 0.132577i
\(288\) 0 0
\(289\) 14.6542i 0.862011i
\(290\) 0 0
\(291\) −41.7485 −2.44734
\(292\) 0 0
\(293\) −14.9236 + 14.9236i −0.871843 + 0.871843i −0.992673 0.120830i \(-0.961444\pi\)
0.120830 + 0.992673i \(0.461444\pi\)
\(294\) 0 0
\(295\) 35.7285i 2.08019i
\(296\) 0 0
\(297\) −10.6159 −0.615996
\(298\) 0 0
\(299\) −1.03273 1.03273i −0.0597243 0.0597243i
\(300\) 0 0
\(301\) −0.174569 + 0.174569i −0.0100620 + 0.0100620i
\(302\) 0 0
\(303\) −44.6532 −2.56526
\(304\) 0 0
\(305\) 6.16064 0.352757
\(306\) 0 0
\(307\) 23.2534i 1.32714i −0.748113 0.663571i \(-0.769040\pi\)
0.748113 0.663571i \(-0.230960\pi\)
\(308\) 0 0
\(309\) 8.45671 8.45671i 0.481085 0.481085i
\(310\) 0 0
\(311\) −9.99104 + 9.99104i −0.566540 + 0.566540i −0.931157 0.364618i \(-0.881200\pi\)
0.364618 + 0.931157i \(0.381200\pi\)
\(312\) 0 0
\(313\) 6.24374 6.24374i 0.352917 0.352917i −0.508277 0.861194i \(-0.669717\pi\)
0.861194 + 0.508277i \(0.169717\pi\)
\(314\) 0 0
\(315\) 8.27826 + 8.27826i 0.466427 + 0.466427i
\(316\) 0 0
\(317\) −6.18228 6.18228i −0.347231 0.347231i 0.511846 0.859077i \(-0.328962\pi\)
−0.859077 + 0.511846i \(0.828962\pi\)
\(318\) 0 0
\(319\) 17.0583i 0.955079i
\(320\) 0 0
\(321\) −9.39040 9.39040i −0.524121 0.524121i
\(322\) 0 0
\(323\) 4.19476i 0.233402i
\(324\) 0 0
\(325\) −2.33774 2.33774i −0.129675 0.129675i
\(326\) 0 0
\(327\) −28.1816 −1.55845
\(328\) 0 0
\(329\) 2.63697 0.145381
\(330\) 0 0
\(331\) 1.41693 + 1.41693i 0.0778817 + 0.0778817i 0.744975 0.667093i \(-0.232462\pi\)
−0.667093 + 0.744975i \(0.732462\pi\)
\(332\) 0 0
\(333\) 22.4293i 1.22912i
\(334\) 0 0
\(335\) 9.94189 + 9.94189i 0.543183 + 0.543183i
\(336\) 0 0
\(337\) 20.9764i 1.14266i 0.820721 + 0.571329i \(0.193572\pi\)
−0.820721 + 0.571329i \(0.806428\pi\)
\(338\) 0 0
\(339\) −28.8178 28.8178i −1.56517 1.56517i
\(340\) 0 0
\(341\) 31.2617 + 31.2617i 1.69292 + 1.69292i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) −9.21474 + 9.21474i −0.496105 + 0.496105i
\(346\) 0 0
\(347\) 10.4052 10.4052i 0.558578 0.558578i −0.370325 0.928902i \(-0.620754\pi\)
0.928902 + 0.370325i \(0.120754\pi\)
\(348\) 0 0
\(349\) 4.66785i 0.249864i −0.992165 0.124932i \(-0.960129\pi\)
0.992165 0.124932i \(-0.0398713\pi\)
\(350\) 0 0
\(351\) −2.19682 −0.117258
\(352\) 0 0
\(353\) −0.537690 −0.0286184 −0.0143092 0.999898i \(-0.504555\pi\)
−0.0143092 + 0.999898i \(0.504555\pi\)
\(354\) 0 0
\(355\) −23.3165 + 23.3165i −1.23751 + 1.23751i
\(356\) 0 0
\(357\) 2.85548 + 2.85548i 0.151128 + 0.151128i
\(358\) 0 0
\(359\) −21.2692 −1.12255 −0.561273 0.827631i \(-0.689688\pi\)
−0.561273 + 0.827631i \(0.689688\pi\)
\(360\) 0 0
\(361\) 11.4990i 0.605209i
\(362\) 0 0
\(363\) −12.8563 + 12.8563i −0.674783 + 0.674783i
\(364\) 0 0
\(365\) 6.29996 0.329755
\(366\) 0 0
\(367\) 4.93875i 0.257801i 0.991658 + 0.128900i \(0.0411447\pi\)
−0.991658 + 0.128900i \(0.958855\pi\)
\(368\) 0 0
\(369\) −23.0316 10.4795i −1.19898 0.545542i
\(370\) 0 0
\(371\) 3.36236i 0.174565i
\(372\) 0 0
\(373\) −28.1009 −1.45501 −0.727506 0.686102i \(-0.759320\pi\)
−0.727506 + 0.686102i \(0.759320\pi\)
\(374\) 0 0
\(375\) 6.75731 6.75731i 0.348946 0.348946i
\(376\) 0 0
\(377\) 3.52999i 0.181804i
\(378\) 0 0
\(379\) −0.0435824 −0.00223868 −0.00111934 0.999999i \(-0.500356\pi\)
−0.00111934 + 0.999999i \(0.500356\pi\)
\(380\) 0 0
\(381\) 6.49711 + 6.49711i 0.332857 + 0.332857i
\(382\) 0 0
\(383\) 2.20923 2.20923i 0.112886 0.112886i −0.648407 0.761294i \(-0.724565\pi\)
0.761294 + 0.648407i \(0.224565\pi\)
\(384\) 0 0
\(385\) 12.5325 0.638716
\(386\) 0 0
\(387\) −0.975607 −0.0495929
\(388\) 0 0
\(389\) 12.5762i 0.637638i 0.947816 + 0.318819i \(0.103286\pi\)
−0.947816 + 0.318819i \(0.896714\pi\)
\(390\) 0 0
\(391\) −1.80684 + 1.80684i −0.0913757 + 0.0913757i
\(392\) 0 0
\(393\) 16.6846 16.6846i 0.841625 0.841625i
\(394\) 0 0
\(395\) −8.95098 + 8.95098i −0.450373 + 0.450373i
\(396\) 0 0
\(397\) 6.83348 + 6.83348i 0.342962 + 0.342962i 0.857480 0.514517i \(-0.172029\pi\)
−0.514517 + 0.857480i \(0.672029\pi\)
\(398\) 0 0
\(399\) −5.10614 5.10614i −0.255627 0.255627i
\(400\) 0 0
\(401\) 18.3776i 0.917732i −0.888505 0.458866i \(-0.848256\pi\)
0.888505 0.458866i \(-0.151744\pi\)
\(402\) 0 0
\(403\) 6.46921 + 6.46921i 0.322254 + 0.322254i
\(404\) 0 0
\(405\) 15.5201i 0.771202i
\(406\) 0 0
\(407\) 16.9779 + 16.9779i 0.841565 + 0.841565i
\(408\) 0 0
\(409\) −32.3286 −1.59855 −0.799273 0.600968i \(-0.794782\pi\)
−0.799273 + 0.600968i \(0.794782\pi\)
\(410\) 0 0
\(411\) 33.9338 1.67383
\(412\) 0 0
\(413\) 8.52780 + 8.52780i 0.419626 + 0.419626i
\(414\) 0 0
\(415\) 8.15532i 0.400329i
\(416\) 0 0
\(417\) −42.1391 42.1391i −2.06356 2.06356i
\(418\) 0 0
\(419\) 30.0922i 1.47010i 0.678014 + 0.735049i \(0.262841\pi\)
−0.678014 + 0.735049i \(0.737159\pi\)
\(420\) 0 0
\(421\) 0.865599 + 0.865599i 0.0421867 + 0.0421867i 0.727885 0.685699i \(-0.240503\pi\)
−0.685699 + 0.727885i \(0.740503\pi\)
\(422\) 0 0
\(423\) 7.36855 + 7.36855i 0.358271 + 0.358271i
\(424\) 0 0
\(425\) −4.09006 + 4.09006i −0.198397 + 0.198397i
\(426\) 0 0
\(427\) −1.47044 + 1.47044i −0.0711598 + 0.0711598i
\(428\) 0 0
\(429\) −6.90434 + 6.90434i −0.333345 + 0.333345i
\(430\) 0 0
\(431\) 11.4284i 0.550488i −0.961374 0.275244i \(-0.911241\pi\)
0.961374 0.275244i \(-0.0887586\pi\)
\(432\) 0 0
\(433\) 27.5678 1.32482 0.662412 0.749140i \(-0.269533\pi\)
0.662412 + 0.749140i \(0.269533\pi\)
\(434\) 0 0
\(435\) −31.4970 −1.51017
\(436\) 0 0
\(437\) 3.23097 3.23097i 0.154558 0.154558i
\(438\) 0 0
\(439\) −17.3450 17.3450i −0.827829 0.827829i 0.159387 0.987216i \(-0.449048\pi\)
−0.987216 + 0.159387i \(0.949048\pi\)
\(440\) 0 0
\(441\) −3.95177 −0.188180
\(442\) 0 0
\(443\) 35.3005i 1.67718i −0.544763 0.838590i \(-0.683381\pi\)
0.544763 0.838590i \(-0.316619\pi\)
\(444\) 0 0
\(445\) −28.7953 + 28.7953i −1.36503 + 1.36503i
\(446\) 0 0
\(447\) 63.7582 3.01566
\(448\) 0 0
\(449\) 0.647504i 0.0305576i −0.999883 0.0152788i \(-0.995136\pi\)
0.999883 0.0152788i \(-0.00486358\pi\)
\(450\) 0 0
\(451\) −25.3664 + 9.50136i −1.19446 + 0.447401i
\(452\) 0 0
\(453\) 13.2471i 0.622402i
\(454\) 0 0
\(455\) 2.59344 0.121582
\(456\) 0 0
\(457\) −12.1129 + 12.1129i −0.566616 + 0.566616i −0.931179 0.364563i \(-0.881218\pi\)
0.364563 + 0.931179i \(0.381218\pi\)
\(458\) 0 0
\(459\) 3.84350i 0.179399i
\(460\) 0 0
\(461\) 24.3612 1.13462 0.567308 0.823506i \(-0.307985\pi\)
0.567308 + 0.823506i \(0.307985\pi\)
\(462\) 0 0
\(463\) −5.63968 5.63968i −0.262098 0.262098i 0.563808 0.825906i \(-0.309336\pi\)
−0.825906 + 0.563808i \(0.809336\pi\)
\(464\) 0 0
\(465\) 57.7228 57.7228i 2.67683 2.67683i
\(466\) 0 0
\(467\) 33.0389 1.52886 0.764430 0.644707i \(-0.223021\pi\)
0.764430 + 0.644707i \(0.223021\pi\)
\(468\) 0 0
\(469\) −4.74593 −0.219147
\(470\) 0 0
\(471\) 12.8729i 0.593153i
\(472\) 0 0
\(473\) −0.738488 + 0.738488i −0.0339557 + 0.0339557i
\(474\) 0 0
\(475\) 7.31380 7.31380i 0.335580 0.335580i
\(476\) 0 0
\(477\) 9.39551 9.39551i 0.430191 0.430191i
\(478\) 0 0
\(479\) 10.6584 + 10.6584i 0.486993 + 0.486993i 0.907356 0.420363i \(-0.138097\pi\)
−0.420363 + 0.907356i \(0.638097\pi\)
\(480\) 0 0
\(481\) 3.51337 + 3.51337i 0.160196 + 0.160196i
\(482\) 0 0
\(483\) 4.39881i 0.200153i
\(484\) 0 0
\(485\) 33.1696 + 33.1696i 1.50616 + 1.50616i
\(486\) 0 0
\(487\) 30.6853i 1.39048i −0.718776 0.695242i \(-0.755297\pi\)
0.718776 0.695242i \(-0.244703\pi\)
\(488\) 0 0
\(489\) −24.1041 24.1041i −1.09003 1.09003i
\(490\) 0 0
\(491\) −3.89308 −0.175692 −0.0878461 0.996134i \(-0.527998\pi\)
−0.0878461 + 0.996134i \(0.527998\pi\)
\(492\) 0 0
\(493\) −6.17598 −0.278152
\(494\) 0 0
\(495\) 35.0199 + 35.0199i 1.57403 + 1.57403i
\(496\) 0 0
\(497\) 11.1305i 0.499273i
\(498\) 0 0
\(499\) 3.34648 + 3.34648i 0.149809 + 0.149809i 0.778033 0.628224i \(-0.216218\pi\)
−0.628224 + 0.778033i \(0.716218\pi\)
\(500\) 0 0
\(501\) 22.4630i 1.00357i
\(502\) 0 0
\(503\) −16.0237 16.0237i −0.714460 0.714460i 0.253005 0.967465i \(-0.418581\pi\)
−0.967465 + 0.253005i \(0.918581\pi\)
\(504\) 0 0
\(505\) 35.4774 + 35.4774i 1.57873 + 1.57873i
\(506\) 0 0
\(507\) 22.8081 22.8081i 1.01294 1.01294i
\(508\) 0 0
\(509\) −20.4686 + 20.4686i −0.907257 + 0.907257i −0.996050 0.0887935i \(-0.971699\pi\)
0.0887935 + 0.996050i \(0.471699\pi\)
\(510\) 0 0
\(511\) −1.50370 + 1.50370i −0.0665196 + 0.0665196i
\(512\) 0 0
\(513\) 6.87291i 0.303446i
\(514\) 0 0
\(515\) −13.4379 −0.592144
\(516\) 0 0
\(517\) 11.1553 0.490609
\(518\) 0 0
\(519\) 20.1991 20.1991i 0.886642 0.886642i
\(520\) 0 0
\(521\) −3.70892 3.70892i −0.162491 0.162491i 0.621179 0.783669i \(-0.286654\pi\)
−0.783669 + 0.621179i \(0.786654\pi\)
\(522\) 0 0
\(523\) 31.5018 1.37748 0.688738 0.725010i \(-0.258165\pi\)
0.688738 + 0.725010i \(0.258165\pi\)
\(524\) 0 0
\(525\) 9.95739i 0.434576i
\(526\) 0 0
\(527\) 11.3184 11.3184i 0.493036 0.493036i
\(528\) 0 0
\(529\) −20.2166 −0.878983
\(530\) 0 0
\(531\) 47.6589i 2.06822i
\(532\) 0 0
\(533\) −5.24924 + 1.96618i −0.227370 + 0.0851648i
\(534\) 0 0
\(535\) 14.9215i 0.645114i
\(536\) 0 0
\(537\) 42.6874 1.84210
\(538\) 0 0
\(539\) −2.99130 + 2.99130i −0.128845 + 0.128845i
\(540\) 0 0
\(541\) 19.6275i 0.843852i 0.906630 + 0.421926i \(0.138646\pi\)
−0.906630 + 0.421926i \(0.861354\pi\)
\(542\) 0 0
\(543\) 51.4300 2.20707
\(544\) 0 0
\(545\) 22.3906 + 22.3906i 0.959107 + 0.959107i
\(546\) 0 0
\(547\) −13.7488 + 13.7488i −0.587858 + 0.587858i −0.937051 0.349193i \(-0.886456\pi\)
0.349193 + 0.937051i \(0.386456\pi\)
\(548\) 0 0
\(549\) −8.21779 −0.350727
\(550\) 0 0
\(551\) 11.0438 0.470483
\(552\) 0 0
\(553\) 4.27290i 0.181702i
\(554\) 0 0
\(555\) 31.3487 31.3487i 1.33068 1.33068i
\(556\) 0 0
\(557\) −0.950248 + 0.950248i −0.0402633 + 0.0402633i −0.726952 0.686688i \(-0.759064\pi\)
0.686688 + 0.726952i \(0.259064\pi\)
\(558\) 0 0
\(559\) −0.152821 + 0.152821i −0.00646362 + 0.00646362i
\(560\) 0 0
\(561\) 12.0797 + 12.0797i 0.510004 + 0.510004i
\(562\) 0 0
\(563\) 29.8627 + 29.8627i 1.25856 + 1.25856i 0.951780 + 0.306781i \(0.0992520\pi\)
0.306781 + 0.951780i \(0.400748\pi\)
\(564\) 0 0
\(565\) 45.7921i 1.92649i
\(566\) 0 0
\(567\) 3.70440 + 3.70440i 0.155570 + 0.155570i
\(568\) 0 0
\(569\) 30.1543i 1.26413i 0.774914 + 0.632067i \(0.217793\pi\)
−0.774914 + 0.632067i \(0.782207\pi\)
\(570\) 0 0
\(571\) −0.0634064 0.0634064i −0.00265348 0.00265348i 0.705779 0.708432i \(-0.250597\pi\)
−0.708432 + 0.705779i \(0.750597\pi\)
\(572\) 0 0
\(573\) −44.5066 −1.85929
\(574\) 0 0
\(575\) 6.30065 0.262755
\(576\) 0 0
\(577\) −25.1147 25.1147i −1.04554 1.04554i −0.998912 0.0466249i \(-0.985153\pi\)
−0.0466249 0.998912i \(-0.514847\pi\)
\(578\) 0 0
\(579\) 2.76026i 0.114712i
\(580\) 0 0
\(581\) −1.94654 1.94654i −0.0807561 0.0807561i
\(582\) 0 0
\(583\) 14.2239i 0.589094i
\(584\) 0 0
\(585\) 7.24691 + 7.24691i 0.299623 + 0.299623i
\(586\) 0 0
\(587\) 27.8322 + 27.8322i 1.14876 + 1.14876i 0.986797 + 0.161961i \(0.0517817\pi\)
0.161961 + 0.986797i \(0.448218\pi\)
\(588\) 0 0
\(589\) −20.2394 + 20.2394i −0.833949 + 0.833949i
\(590\) 0 0
\(591\) 19.4932 19.4932i 0.801842 0.801842i
\(592\) 0 0
\(593\) 8.79150 8.79150i 0.361023 0.361023i −0.503166 0.864190i \(-0.667832\pi\)
0.864190 + 0.503166i \(0.167832\pi\)
\(594\) 0 0
\(595\) 4.53742i 0.186016i
\(596\) 0 0
\(597\) 17.6283 0.721480
\(598\) 0 0
\(599\) −32.6899 −1.33567 −0.667837 0.744308i \(-0.732780\pi\)
−0.667837 + 0.744308i \(0.732780\pi\)
\(600\) 0 0
\(601\) 28.8995 28.8995i 1.17883 1.17883i 0.198792 0.980042i \(-0.436298\pi\)
0.980042 0.198792i \(-0.0637020\pi\)
\(602\) 0 0
\(603\) −13.2617 13.2617i −0.540057 0.540057i
\(604\) 0 0
\(605\) 20.4290 0.830557
\(606\) 0 0
\(607\) 1.35383i 0.0549502i 0.999622 + 0.0274751i \(0.00874670\pi\)
−0.999622 + 0.0274751i \(0.991253\pi\)
\(608\) 0 0
\(609\) 7.51782 7.51782i 0.304637 0.304637i
\(610\) 0 0
\(611\) 2.30844 0.0933896
\(612\) 0 0
\(613\) 43.1444i 1.74259i −0.490764 0.871293i \(-0.663282\pi\)
0.490764 0.871293i \(-0.336718\pi\)
\(614\) 0 0
\(615\) 17.5437 + 46.8374i 0.707429 + 1.88867i
\(616\) 0 0
\(617\) 39.3454i 1.58399i −0.610529 0.791994i \(-0.709043\pi\)
0.610529 0.791994i \(-0.290957\pi\)
\(618\) 0 0
\(619\) −37.3816 −1.50249 −0.751246 0.660022i \(-0.770547\pi\)
−0.751246 + 0.660022i \(0.770547\pi\)
\(620\) 0 0
\(621\) 2.96042 2.96042i 0.118798 0.118798i
\(622\) 0 0
\(623\) 13.7459i 0.550718i
\(624\) 0 0
\(625\) −29.6204 −1.18481
\(626\) 0 0
\(627\) −21.6007 21.6007i −0.862650 0.862650i
\(628\) 0 0
\(629\) 6.14690 6.14690i 0.245093 0.245093i
\(630\) 0 0
\(631\) 27.9832 1.11399 0.556997 0.830515i \(-0.311954\pi\)
0.556997 + 0.830515i \(0.311954\pi\)
\(632\) 0 0
\(633\) −5.14327 −0.204426
\(634\) 0 0
\(635\) 10.3240i 0.409697i
\(636\) 0 0
\(637\) −0.619012 + 0.619012i −0.0245261 + 0.0245261i
\(638\) 0 0
\(639\) 31.1024 31.1024i 1.23039 1.23039i
\(640\) 0 0
\(641\) 4.77628 4.77628i 0.188652 0.188652i −0.606461 0.795113i \(-0.707411\pi\)
0.795113 + 0.606461i \(0.207411\pi\)
\(642\) 0 0
\(643\) 35.3684 + 35.3684i 1.39480 + 1.39480i 0.814173 + 0.580622i \(0.197191\pi\)
0.580622 + 0.814173i \(0.302809\pi\)
\(644\) 0 0
\(645\) 1.36357 + 1.36357i 0.0536906 + 0.0536906i
\(646\) 0 0
\(647\) 12.9182i 0.507868i −0.967221 0.253934i \(-0.918275\pi\)
0.967221 0.253934i \(-0.0817247\pi\)
\(648\) 0 0
\(649\) 36.0755 + 36.0755i 1.41609 + 1.41609i
\(650\) 0 0
\(651\) 27.5550i 1.07996i
\(652\) 0 0
\(653\) −12.7030 12.7030i −0.497109 0.497109i 0.413428 0.910537i \(-0.364331\pi\)
−0.910537 + 0.413428i \(0.864331\pi\)
\(654\) 0 0
\(655\) −26.5121 −1.03591
\(656\) 0 0
\(657\) −8.40363 −0.327857
\(658\) 0 0
\(659\) 22.0826 + 22.0826i 0.860216 + 0.860216i 0.991363 0.131147i \(-0.0418659\pi\)
−0.131147 + 0.991363i \(0.541866\pi\)
\(660\) 0 0
\(661\) 43.6695i 1.69855i 0.527953 + 0.849274i \(0.322960\pi\)
−0.527953 + 0.849274i \(0.677040\pi\)
\(662\) 0 0
\(663\) 2.49973 + 2.49973i 0.0970815 + 0.0970815i
\(664\) 0 0
\(665\) 8.11377i 0.314638i
\(666\) 0 0
\(667\) 4.75699 + 4.75699i 0.184191 + 0.184191i
\(668\) 0 0
\(669\) −7.07174 7.07174i −0.273409 0.273409i
\(670\) 0 0
\(671\) −6.22048 + 6.22048i −0.240139 + 0.240139i
\(672\) 0 0
\(673\) 11.6853 11.6853i 0.450437 0.450437i −0.445063 0.895499i \(-0.646819\pi\)
0.895499 + 0.445063i \(0.146819\pi\)
\(674\) 0 0
\(675\) 6.70136 6.70136i 0.257936 0.257936i
\(676\) 0 0
\(677\) 10.4067i 0.399963i 0.979800 + 0.199981i \(0.0640882\pi\)
−0.979800 + 0.199981i \(0.935912\pi\)
\(678\) 0 0
\(679\) −15.8341 −0.607657
\(680\) 0 0
\(681\) −48.4813 −1.85781
\(682\) 0 0
\(683\) −5.00945 + 5.00945i −0.191681 + 0.191681i −0.796422 0.604741i \(-0.793277\pi\)
0.604741 + 0.796422i \(0.293277\pi\)
\(684\) 0 0
\(685\) −26.9608 26.9608i −1.03012 1.03012i
\(686\) 0 0
\(687\) −40.6718 −1.55173
\(688\) 0 0
\(689\) 2.94346i 0.112137i
\(690\) 0 0
\(691\) −9.29478 + 9.29478i −0.353590 + 0.353590i −0.861444 0.507853i \(-0.830439\pi\)
0.507853 + 0.861444i \(0.330439\pi\)
\(692\) 0 0
\(693\) −16.7173 −0.635040
\(694\) 0 0
\(695\) 66.9600i 2.53994i
\(696\) 0 0
\(697\) 3.43998 + 9.18394i 0.130299 + 0.347867i
\(698\) 0 0
\(699\) 32.1217i 1.21495i
\(700\) 0 0
\(701\) 21.6512 0.817755 0.408878 0.912589i \(-0.365920\pi\)
0.408878 + 0.912589i \(0.365920\pi\)
\(702\) 0 0
\(703\) −10.9918 + 10.9918i −0.414564 + 0.414564i
\(704\) 0 0
\(705\) 20.5975i 0.775748i
\(706\) 0 0
\(707\) −16.9358 −0.636935
\(708\) 0 0
\(709\) 23.2112 + 23.2112i 0.871717 + 0.871717i 0.992659 0.120943i \(-0.0385918\pi\)
−0.120943 + 0.992659i \(0.538592\pi\)
\(710\) 0 0
\(711\) 11.9399 11.9399i 0.447780 0.447780i
\(712\) 0 0
\(713\) −17.4357 −0.652973
\(714\) 0 0
\(715\) 10.9711 0.410297
\(716\) 0 0
\(717\) 16.5637i 0.618582i
\(718\) 0 0
\(719\) 1.30997 1.30997i 0.0488537 0.0488537i −0.682258 0.731112i \(-0.739002\pi\)
0.731112 + 0.682258i \(0.239002\pi\)
\(720\) 0 0
\(721\) 3.20740 3.20740i 0.119450 0.119450i
\(722\) 0 0
\(723\) −16.0509 + 16.0509i −0.596940 + 0.596940i
\(724\) 0 0
\(725\) 10.7682 + 10.7682i 0.399920 + 0.399920i
\(726\) 0 0
\(727\) 25.9337 + 25.9337i 0.961828 + 0.961828i 0.999298 0.0374696i \(-0.0119297\pi\)
−0.0374696 + 0.999298i \(0.511930\pi\)
\(728\) 0 0
\(729\) 40.5521i 1.50193i
\(730\) 0 0
\(731\) 0.267371 + 0.267371i 0.00988908 + 0.00988908i
\(732\) 0 0
\(733\) 34.9903i 1.29240i 0.763170 + 0.646198i \(0.223642\pi\)
−0.763170 + 0.646198i \(0.776358\pi\)
\(734\) 0 0
\(735\) 5.52326 + 5.52326i 0.203728 + 0.203728i
\(736\) 0 0
\(737\) −20.0769 −0.739543
\(738\) 0 0
\(739\) 51.9176 1.90982 0.954910 0.296895i \(-0.0959511\pi\)
0.954910 + 0.296895i \(0.0959511\pi\)
\(740\) 0 0
\(741\) −4.46999 4.46999i −0.164209 0.164209i
\(742\) 0 0
\(743\) 48.7958i 1.79015i −0.445920 0.895073i \(-0.647123\pi\)
0.445920 0.895073i \(-0.352877\pi\)
\(744\) 0 0
\(745\) −50.6565 50.6565i −1.85591 1.85591i
\(746\) 0 0
\(747\) 10.8785i 0.398025i
\(748\) 0 0
\(749\) −3.56153 3.56153i −0.130135 0.130135i
\(750\) 0 0
\(751\) 25.3074 + 25.3074i 0.923478 + 0.923478i 0.997273 0.0737950i \(-0.0235110\pi\)
−0.0737950 + 0.997273i \(0.523511\pi\)
\(752\) 0 0
\(753\) −12.5846 + 12.5846i −0.458608 + 0.458608i
\(754\) 0 0
\(755\) 10.5249 10.5249i 0.383042 0.383042i
\(756\) 0 0
\(757\) 10.7127 10.7127i 0.389360 0.389360i −0.485099 0.874459i \(-0.661217\pi\)
0.874459 + 0.485099i \(0.161217\pi\)
\(758\) 0 0
\(759\) 18.6085i 0.675445i
\(760\) 0 0
\(761\) −37.3994 −1.35573 −0.677864 0.735187i \(-0.737094\pi\)
−0.677864 + 0.735187i \(0.737094\pi\)
\(762\) 0 0
\(763\) −10.6885 −0.386951
\(764\) 0 0
\(765\) 12.6790 12.6790i 0.458411 0.458411i
\(766\) 0 0
\(767\) 7.46536 + 7.46536i 0.269559 + 0.269559i
\(768\) 0 0
\(769\) −45.7162 −1.64857 −0.824283 0.566178i \(-0.808422\pi\)
−0.824283 + 0.566178i \(0.808422\pi\)
\(770\) 0 0
\(771\) 36.1739i 1.30277i
\(772\) 0 0
\(773\) −4.26643 + 4.26643i −0.153453 + 0.153453i −0.779658 0.626205i \(-0.784607\pi\)
0.626205 + 0.779658i \(0.284607\pi\)
\(774\) 0 0
\(775\) −39.4684 −1.41775
\(776\) 0 0
\(777\) 14.9648i 0.536861i
\(778\) 0 0
\(779\) −6.15135 16.4226i −0.220395 0.588402i
\(780\) 0 0
\(781\) 47.0860i 1.68487i
\(782\) 0 0
\(783\) 10.1190 0.361625
\(784\) 0 0
\(785\) −10.2277 + 10.2277i −0.365041 + 0.365041i
\(786\) 0 0
\(787\) 13.7853i 0.491394i 0.969347 + 0.245697i \(0.0790168\pi\)
−0.969347 + 0.245697i \(0.920983\pi\)
\(788\) 0 0
\(789\) 66.6256 2.37194
\(790\) 0 0
\(791\) −10.9298 10.9298i −0.388620 0.388620i
\(792\) 0 0
\(793\) −1.28725 + 1.28725i −0.0457115 + 0.0457115i
\(794\) 0 0
\(795\) −26.2636 −0.931473
\(796\) 0 0
\(797\) −40.6666 −1.44049 −0.720243 0.693722i \(-0.755970\pi\)
−0.720243 + 0.693722i \(0.755970\pi\)
\(798\) 0 0
\(799\) 4.03879i 0.142882i
\(800\) 0 0
\(801\) 38.4105 38