Properties

Label 384.2.n.a.241.4
Level $384$
Weight $2$
Character 384.241
Analytic conductor $3.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.n (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 241.4
Character \(\chi\) \(=\) 384.241
Dual form 384.2.n.a.145.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.382683 - 0.923880i) q^{3} +(3.68816 + 1.52768i) q^{5} +(1.63704 + 1.63704i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.382683 - 0.923880i) q^{3} +(3.68816 + 1.52768i) q^{5} +(1.63704 + 1.63704i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(-1.20420 + 2.90719i) q^{11} +(-3.30127 + 1.36743i) q^{13} -3.99203i q^{15} -0.511560i q^{17} +(0.254077 - 0.105242i) q^{19} +(0.885960 - 2.13890i) q^{21} +(3.17185 - 3.17185i) q^{23} +(7.73315 + 7.73315i) q^{25} +(0.923880 + 0.382683i) q^{27} +(-2.75087 - 6.64118i) q^{29} +5.82083 q^{31} +3.14672 q^{33} +(3.53678 + 8.53855i) q^{35} +(-5.53467 - 2.29253i) q^{37} +(2.52668 + 2.52668i) q^{39} +(3.94823 - 3.94823i) q^{41} +(-1.30801 + 3.15781i) q^{43} +(-3.68816 + 1.52768i) q^{45} -9.41403i q^{47} -1.64019i q^{49} +(-0.472620 + 0.195765i) q^{51} +(2.50482 - 6.04717i) q^{53} +(-8.88255 + 8.88255i) q^{55} +(-0.194462 - 0.194462i) q^{57} +(-13.3423 - 5.52657i) q^{59} +(3.35835 + 8.10777i) q^{61} -2.31513 q^{63} -14.2646 q^{65} +(1.11643 + 2.69530i) q^{67} +(-4.14422 - 1.71659i) q^{69} +(-1.26611 - 1.26611i) q^{71} +(-7.51616 + 7.51616i) q^{73} +(4.18515 - 10.1038i) q^{75} +(-6.73052 + 2.78787i) q^{77} -0.709730i q^{79} -1.00000i q^{81} +(1.40823 - 0.583309i) q^{83} +(0.781502 - 1.88671i) q^{85} +(-5.08294 + 5.08294i) q^{87} +(-0.0856897 - 0.0856897i) q^{89} +(-7.64285 - 3.16577i) q^{91} +(-2.22754 - 5.37775i) q^{93} +1.09785 q^{95} -0.677647 q^{97} +(-1.20420 - 2.90719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} + 48q^{35} + 16q^{43} - 16q^{51} - 32q^{53} - 32q^{55} - 64q^{59} - 32q^{61} - 16q^{63} - 16q^{67} - 32q^{69} - 64q^{71} - 32q^{75} - 32q^{77} + 48q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.382683 0.923880i −0.220942 0.533402i
\(4\) 0 0
\(5\) 3.68816 + 1.52768i 1.64939 + 0.683201i 0.997195 0.0748462i \(-0.0238466\pi\)
0.652199 + 0.758048i \(0.273847\pi\)
\(6\) 0 0
\(7\) 1.63704 + 1.63704i 0.618743 + 0.618743i 0.945209 0.326466i \(-0.105858\pi\)
−0.326466 + 0.945209i \(0.605858\pi\)
\(8\) 0 0
\(9\) −0.707107 + 0.707107i −0.235702 + 0.235702i
\(10\) 0 0
\(11\) −1.20420 + 2.90719i −0.363080 + 0.876552i 0.631767 + 0.775158i \(0.282330\pi\)
−0.994846 + 0.101393i \(0.967670\pi\)
\(12\) 0 0
\(13\) −3.30127 + 1.36743i −0.915607 + 0.379257i −0.790200 0.612849i \(-0.790024\pi\)
−0.125407 + 0.992105i \(0.540024\pi\)
\(14\) 0 0
\(15\) 3.99203i 1.03074i
\(16\) 0 0
\(17\) 0.511560i 0.124071i −0.998074 0.0620357i \(-0.980241\pi\)
0.998074 0.0620357i \(-0.0197593\pi\)
\(18\) 0 0
\(19\) 0.254077 0.105242i 0.0582894 0.0241442i −0.353348 0.935492i \(-0.614957\pi\)
0.411638 + 0.911348i \(0.364957\pi\)
\(20\) 0 0
\(21\) 0.885960 2.13890i 0.193332 0.466746i
\(22\) 0 0
\(23\) 3.17185 3.17185i 0.661376 0.661376i −0.294329 0.955704i \(-0.595096\pi\)
0.955704 + 0.294329i \(0.0950960\pi\)
\(24\) 0 0
\(25\) 7.73315 + 7.73315i 1.54663 + 1.54663i
\(26\) 0 0
\(27\) 0.923880 + 0.382683i 0.177801 + 0.0736475i
\(28\) 0 0
\(29\) −2.75087 6.64118i −0.510823 1.23324i −0.943405 0.331642i \(-0.892397\pi\)
0.432582 0.901595i \(-0.357603\pi\)
\(30\) 0 0
\(31\) 5.82083 1.04545 0.522726 0.852501i \(-0.324915\pi\)
0.522726 + 0.852501i \(0.324915\pi\)
\(32\) 0 0
\(33\) 3.14672 0.547774
\(34\) 0 0
\(35\) 3.53678 + 8.53855i 0.597825 + 1.44328i
\(36\) 0 0
\(37\) −5.53467 2.29253i −0.909894 0.376890i −0.121878 0.992545i \(-0.538892\pi\)
−0.788016 + 0.615655i \(0.788892\pi\)
\(38\) 0 0
\(39\) 2.52668 + 2.52668i 0.404593 + 0.404593i
\(40\) 0 0
\(41\) 3.94823 3.94823i 0.616610 0.616610i −0.328050 0.944660i \(-0.606392\pi\)
0.944660 + 0.328050i \(0.106392\pi\)
\(42\) 0 0
\(43\) −1.30801 + 3.15781i −0.199469 + 0.481561i −0.991686 0.128678i \(-0.958927\pi\)
0.792217 + 0.610239i \(0.208927\pi\)
\(44\) 0 0
\(45\) −3.68816 + 1.52768i −0.549798 + 0.227734i
\(46\) 0 0
\(47\) 9.41403i 1.37318i −0.727046 0.686589i \(-0.759107\pi\)
0.727046 0.686589i \(-0.240893\pi\)
\(48\) 0 0
\(49\) 1.64019i 0.234313i
\(50\) 0 0
\(51\) −0.472620 + 0.195765i −0.0661800 + 0.0274127i
\(52\) 0 0
\(53\) 2.50482 6.04717i 0.344063 0.830642i −0.653233 0.757157i \(-0.726588\pi\)
0.997296 0.0734852i \(-0.0234122\pi\)
\(54\) 0 0
\(55\) −8.88255 + 8.88255i −1.19772 + 1.19772i
\(56\) 0 0
\(57\) −0.194462 0.194462i −0.0257572 0.0257572i
\(58\) 0 0
\(59\) −13.3423 5.52657i −1.73702 0.719498i −0.998999 0.0447232i \(-0.985759\pi\)
−0.738023 0.674775i \(-0.764241\pi\)
\(60\) 0 0
\(61\) 3.35835 + 8.10777i 0.429992 + 1.03809i 0.979289 + 0.202466i \(0.0648955\pi\)
−0.549297 + 0.835627i \(0.685104\pi\)
\(62\) 0 0
\(63\) −2.31513 −0.291678
\(64\) 0 0
\(65\) −14.2646 −1.76931
\(66\) 0 0
\(67\) 1.11643 + 2.69530i 0.136394 + 0.329283i 0.977288 0.211916i \(-0.0679704\pi\)
−0.840894 + 0.541199i \(0.817970\pi\)
\(68\) 0 0
\(69\) −4.14422 1.71659i −0.498905 0.206653i
\(70\) 0 0
\(71\) −1.26611 1.26611i −0.150259 0.150259i 0.627975 0.778234i \(-0.283884\pi\)
−0.778234 + 0.627975i \(0.783884\pi\)
\(72\) 0 0
\(73\) −7.51616 + 7.51616i −0.879700 + 0.879700i −0.993503 0.113804i \(-0.963697\pi\)
0.113804 + 0.993503i \(0.463697\pi\)
\(74\) 0 0
\(75\) 4.18515 10.1038i 0.483260 1.16669i
\(76\) 0 0
\(77\) −6.73052 + 2.78787i −0.767014 + 0.317707i
\(78\) 0 0
\(79\) 0.709730i 0.0798509i −0.999203 0.0399254i \(-0.987288\pi\)
0.999203 0.0399254i \(-0.0127120\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 1.40823 0.583309i 0.154574 0.0640265i −0.304055 0.952654i \(-0.598341\pi\)
0.458629 + 0.888628i \(0.348341\pi\)
\(84\) 0 0
\(85\) 0.781502 1.88671i 0.0847658 0.204643i
\(86\) 0 0
\(87\) −5.08294 + 5.08294i −0.544949 + 0.544949i
\(88\) 0 0
\(89\) −0.0856897 0.0856897i −0.00908309 0.00908309i 0.702551 0.711634i \(-0.252044\pi\)
−0.711634 + 0.702551i \(0.752044\pi\)
\(90\) 0 0
\(91\) −7.64285 3.16577i −0.801188 0.331863i
\(92\) 0 0
\(93\) −2.22754 5.37775i −0.230985 0.557646i
\(94\) 0 0
\(95\) 1.09785 0.112638
\(96\) 0 0
\(97\) −0.677647 −0.0688046 −0.0344023 0.999408i \(-0.510953\pi\)
−0.0344023 + 0.999408i \(0.510953\pi\)
\(98\) 0 0
\(99\) −1.20420 2.90719i −0.121027 0.292184i
\(100\) 0 0
\(101\) 10.0095 + 4.14605i 0.995978 + 0.412548i 0.820321 0.571904i \(-0.193795\pi\)
0.175657 + 0.984451i \(0.443795\pi\)
\(102\) 0 0
\(103\) −8.25191 8.25191i −0.813085 0.813085i 0.172010 0.985095i \(-0.444974\pi\)
−0.985095 + 0.172010i \(0.944974\pi\)
\(104\) 0 0
\(105\) 6.53512 6.53512i 0.637763 0.637763i
\(106\) 0 0
\(107\) 0.162056 0.391238i 0.0156665 0.0378224i −0.915853 0.401514i \(-0.868484\pi\)
0.931519 + 0.363692i \(0.118484\pi\)
\(108\) 0 0
\(109\) 5.41943 2.24480i 0.519087 0.215013i −0.107729 0.994180i \(-0.534358\pi\)
0.626816 + 0.779167i \(0.284358\pi\)
\(110\) 0 0
\(111\) 5.99068i 0.568610i
\(112\) 0 0
\(113\) 3.60406i 0.339041i −0.985527 0.169521i \(-0.945778\pi\)
0.985527 0.169521i \(-0.0542219\pi\)
\(114\) 0 0
\(115\) 16.5438 6.85269i 1.54272 0.639016i
\(116\) 0 0
\(117\) 1.36743 3.30127i 0.126419 0.305202i
\(118\) 0 0
\(119\) 0.837445 0.837445i 0.0767684 0.0767684i
\(120\) 0 0
\(121\) 0.776498 + 0.776498i 0.0705908 + 0.0705908i
\(122\) 0 0
\(123\) −5.15861 2.13677i −0.465136 0.192666i
\(124\) 0 0
\(125\) 9.06884 + 21.8941i 0.811142 + 1.95827i
\(126\) 0 0
\(127\) 0.146652 0.0130133 0.00650663 0.999979i \(-0.497929\pi\)
0.00650663 + 0.999979i \(0.497929\pi\)
\(128\) 0 0
\(129\) 3.41799 0.300937
\(130\) 0 0
\(131\) −1.16280 2.80726i −0.101595 0.245271i 0.864907 0.501933i \(-0.167377\pi\)
−0.966501 + 0.256661i \(0.917377\pi\)
\(132\) 0 0
\(133\) 0.588221 + 0.243649i 0.0510053 + 0.0211271i
\(134\) 0 0
\(135\) 2.82279 + 2.82279i 0.242947 + 0.242947i
\(136\) 0 0
\(137\) −11.6890 + 11.6890i −0.998662 + 0.998662i −0.999999 0.00133685i \(-0.999574\pi\)
0.00133685 + 0.999999i \(0.499574\pi\)
\(138\) 0 0
\(139\) −7.96071 + 19.2188i −0.675218 + 1.63012i 0.0973963 + 0.995246i \(0.468949\pi\)
−0.772615 + 0.634875i \(0.781051\pi\)
\(140\) 0 0
\(141\) −8.69743 + 3.60259i −0.732456 + 0.303393i
\(142\) 0 0
\(143\) 11.2441i 0.940277i
\(144\) 0 0
\(145\) 28.6962i 2.38309i
\(146\) 0 0
\(147\) −1.51534 + 0.627674i −0.124983 + 0.0517697i
\(148\) 0 0
\(149\) −0.110593 + 0.266995i −0.00906011 + 0.0218730i −0.928345 0.371720i \(-0.878768\pi\)
0.919285 + 0.393593i \(0.128768\pi\)
\(150\) 0 0
\(151\) 4.70680 4.70680i 0.383034 0.383034i −0.489160 0.872194i \(-0.662697\pi\)
0.872194 + 0.489160i \(0.162697\pi\)
\(152\) 0 0
\(153\) 0.361727 + 0.361727i 0.0292439 + 0.0292439i
\(154\) 0 0
\(155\) 21.4681 + 8.89240i 1.72436 + 0.714255i
\(156\) 0 0
\(157\) −7.43264 17.9440i −0.593189 1.43208i −0.880407 0.474220i \(-0.842730\pi\)
0.287218 0.957865i \(-0.407270\pi\)
\(158\) 0 0
\(159\) −6.54540 −0.519084
\(160\) 0 0
\(161\) 10.3849 0.818444
\(162\) 0 0
\(163\) −5.94686 14.3570i −0.465794 1.12453i −0.965982 0.258609i \(-0.916736\pi\)
0.500188 0.865917i \(-0.333264\pi\)
\(164\) 0 0
\(165\) 11.6056 + 4.80720i 0.903496 + 0.374240i
\(166\) 0 0
\(167\) 10.7086 + 10.7086i 0.828655 + 0.828655i 0.987331 0.158676i \(-0.0507225\pi\)
−0.158676 + 0.987331i \(0.550723\pi\)
\(168\) 0 0
\(169\) −0.163883 + 0.163883i −0.0126064 + 0.0126064i
\(170\) 0 0
\(171\) −0.105242 + 0.254077i −0.00804808 + 0.0194298i
\(172\) 0 0
\(173\) 2.46513 1.02109i 0.187420 0.0776320i −0.287000 0.957931i \(-0.592658\pi\)
0.474420 + 0.880299i \(0.342658\pi\)
\(174\) 0 0
\(175\) 25.3190i 1.91393i
\(176\) 0 0
\(177\) 14.4416i 1.08550i
\(178\) 0 0
\(179\) −9.77295 + 4.04809i −0.730465 + 0.302568i −0.716743 0.697337i \(-0.754368\pi\)
−0.0137219 + 0.999906i \(0.504368\pi\)
\(180\) 0 0
\(181\) −7.36413 + 17.7786i −0.547371 + 1.32147i 0.372056 + 0.928210i \(0.378653\pi\)
−0.919427 + 0.393261i \(0.871347\pi\)
\(182\) 0 0
\(183\) 6.20542 6.20542i 0.458718 0.458718i
\(184\) 0 0
\(185\) −16.9105 16.9105i −1.24328 1.24328i
\(186\) 0 0
\(187\) 1.48720 + 0.616020i 0.108755 + 0.0450478i
\(188\) 0 0
\(189\) 0.885960 + 2.13890i 0.0644441 + 0.155582i
\(190\) 0 0
\(191\) −10.1764 −0.736335 −0.368168 0.929759i \(-0.620015\pi\)
−0.368168 + 0.929759i \(0.620015\pi\)
\(192\) 0 0
\(193\) −7.17480 −0.516454 −0.258227 0.966084i \(-0.583138\pi\)
−0.258227 + 0.966084i \(0.583138\pi\)
\(194\) 0 0
\(195\) 5.45883 + 13.1788i 0.390915 + 0.943751i
\(196\) 0 0
\(197\) 9.81153 + 4.06407i 0.699042 + 0.289553i 0.703762 0.710436i \(-0.251502\pi\)
−0.00471943 + 0.999989i \(0.501502\pi\)
\(198\) 0 0
\(199\) 7.92887 + 7.92887i 0.562063 + 0.562063i 0.929893 0.367830i \(-0.119899\pi\)
−0.367830 + 0.929893i \(0.619899\pi\)
\(200\) 0 0
\(201\) 2.06289 2.06289i 0.145505 0.145505i
\(202\) 0 0
\(203\) 6.36861 15.3752i 0.446989 1.07913i
\(204\) 0 0
\(205\) 20.5933 8.53004i 1.43830 0.595764i
\(206\) 0 0
\(207\) 4.48567i 0.311775i
\(208\) 0 0
\(209\) 0.865385i 0.0598599i
\(210\) 0 0
\(211\) 23.9700 9.92869i 1.65016 0.683519i 0.652898 0.757446i \(-0.273553\pi\)
0.997264 + 0.0739270i \(0.0235532\pi\)
\(212\) 0 0
\(213\) −0.685213 + 1.65425i −0.0469500 + 0.113347i
\(214\) 0 0
\(215\) −9.64827 + 9.64827i −0.658007 + 0.658007i
\(216\) 0 0
\(217\) 9.52894 + 9.52894i 0.646867 + 0.646867i
\(218\) 0 0
\(219\) 9.82033 + 4.06771i 0.663597 + 0.274871i
\(220\) 0 0
\(221\) 0.699522 + 1.68880i 0.0470550 + 0.113601i
\(222\) 0 0
\(223\) 0.573216 0.0383854 0.0191927 0.999816i \(-0.493890\pi\)
0.0191927 + 0.999816i \(0.493890\pi\)
\(224\) 0 0
\(225\) −10.9363 −0.729089
\(226\) 0 0
\(227\) 1.44349 + 3.48488i 0.0958075 + 0.231300i 0.964516 0.264023i \(-0.0850496\pi\)
−0.868709 + 0.495323i \(0.835050\pi\)
\(228\) 0 0
\(229\) −7.10429 2.94269i −0.469465 0.194459i 0.135393 0.990792i \(-0.456770\pi\)
−0.604858 + 0.796333i \(0.706770\pi\)
\(230\) 0 0
\(231\) 5.15132 + 5.15132i 0.338932 + 0.338932i
\(232\) 0 0
\(233\) 1.38129 1.38129i 0.0904912 0.0904912i −0.660412 0.750903i \(-0.729618\pi\)
0.750903 + 0.660412i \(0.229618\pi\)
\(234\) 0 0
\(235\) 14.3817 34.7204i 0.938157 2.26491i
\(236\) 0 0
\(237\) −0.655705 + 0.271602i −0.0425926 + 0.0176424i
\(238\) 0 0
\(239\) 4.58455i 0.296550i 0.988946 + 0.148275i \(0.0473721\pi\)
−0.988946 + 0.148275i \(0.952628\pi\)
\(240\) 0 0
\(241\) 15.9551i 1.02776i 0.857862 + 0.513880i \(0.171792\pi\)
−0.857862 + 0.513880i \(0.828208\pi\)
\(242\) 0 0
\(243\) −0.923880 + 0.382683i −0.0592669 + 0.0245492i
\(244\) 0 0
\(245\) 2.50570 6.04929i 0.160083 0.386475i
\(246\) 0 0
\(247\) −0.694866 + 0.694866i −0.0442133 + 0.0442133i
\(248\) 0 0
\(249\) −1.07781 1.07781i −0.0683037 0.0683037i
\(250\) 0 0
\(251\) 20.0790 + 8.31700i 1.26738 + 0.524964i 0.912166 0.409822i \(-0.134409\pi\)
0.355211 + 0.934786i \(0.384409\pi\)
\(252\) 0 0
\(253\) 5.40164 + 13.0407i 0.339598 + 0.819862i
\(254\) 0 0
\(255\) −2.04216 −0.127885
\(256\) 0 0
\(257\) 0.677979 0.0422912 0.0211456 0.999776i \(-0.493269\pi\)
0.0211456 + 0.999776i \(0.493269\pi\)
\(258\) 0 0
\(259\) −5.30750 12.8134i −0.329792 0.796189i
\(260\) 0 0
\(261\) 6.64118 + 2.75087i 0.411079 + 0.170274i
\(262\) 0 0
\(263\) −7.67357 7.67357i −0.473173 0.473173i 0.429767 0.902940i \(-0.358596\pi\)
−0.902940 + 0.429767i \(0.858596\pi\)
\(264\) 0 0
\(265\) 18.4763 18.4763i 1.13499 1.13499i
\(266\) 0 0
\(267\) −0.0463749 + 0.111959i −0.00283810 + 0.00685178i
\(268\) 0 0
\(269\) 22.0482 9.13266i 1.34430 0.556828i 0.409602 0.912264i \(-0.365668\pi\)
0.934701 + 0.355436i \(0.115668\pi\)
\(270\) 0 0
\(271\) 0.778886i 0.0473140i −0.999720 0.0236570i \(-0.992469\pi\)
0.999720 0.0236570i \(-0.00753096\pi\)
\(272\) 0 0
\(273\) 8.27256i 0.500678i
\(274\) 0 0
\(275\) −31.7940 + 13.1695i −1.91725 + 0.794151i
\(276\) 0 0
\(277\) 1.47054 3.55020i 0.0883564 0.213311i −0.873524 0.486780i \(-0.838171\pi\)
0.961881 + 0.273469i \(0.0881712\pi\)
\(278\) 0 0
\(279\) −4.11595 + 4.11595i −0.246415 + 0.246415i
\(280\) 0 0
\(281\) −3.60771 3.60771i −0.215218 0.215218i 0.591262 0.806480i \(-0.298630\pi\)
−0.806480 + 0.591262i \(0.798630\pi\)
\(282\) 0 0
\(283\) −12.3134 5.10036i −0.731953 0.303185i −0.0145986 0.999893i \(-0.504647\pi\)
−0.717354 + 0.696709i \(0.754647\pi\)
\(284\) 0 0
\(285\) −0.420131 1.01429i −0.0248864 0.0600811i
\(286\) 0 0
\(287\) 12.9268 0.763047
\(288\) 0 0
\(289\) 16.7383 0.984606
\(290\) 0 0
\(291\) 0.259324 + 0.626064i 0.0152019 + 0.0367005i
\(292\) 0 0
\(293\) −21.1509 8.76099i −1.23565 0.511822i −0.333297 0.942822i \(-0.608161\pi\)
−0.902352 + 0.431000i \(0.858161\pi\)
\(294\) 0 0
\(295\) −40.7657 40.7657i −2.37347 2.37347i
\(296\) 0 0
\(297\) −2.22507 + 2.22507i −0.129112 + 0.129112i
\(298\) 0 0
\(299\) −6.13384 + 14.8084i −0.354729 + 0.856391i
\(300\) 0 0
\(301\) −7.31072 + 3.02820i −0.421383 + 0.174543i
\(302\) 0 0
\(303\) 10.8342i 0.622406i
\(304\) 0 0
\(305\) 35.0332i 2.00600i
\(306\) 0 0
\(307\) −29.7333 + 12.3159i −1.69697 + 0.702908i −0.999901 0.0140946i \(-0.995513\pi\)
−0.697070 + 0.717003i \(0.745513\pi\)
\(308\) 0 0
\(309\) −4.46590 + 10.7816i −0.254056 + 0.613346i
\(310\) 0 0
\(311\) 5.08789 5.08789i 0.288508 0.288508i −0.547982 0.836490i \(-0.684604\pi\)
0.836490 + 0.547982i \(0.184604\pi\)
\(312\) 0 0
\(313\) −10.3695 10.3695i −0.586117 0.586117i 0.350460 0.936578i \(-0.386025\pi\)
−0.936578 + 0.350460i \(0.886025\pi\)
\(314\) 0 0
\(315\) −8.53855 3.53678i −0.481093 0.199275i
\(316\) 0 0
\(317\) −6.18851 14.9404i −0.347582 0.839136i −0.996904 0.0786232i \(-0.974948\pi\)
0.649323 0.760513i \(-0.275052\pi\)
\(318\) 0 0
\(319\) 22.6198 1.26647
\(320\) 0 0
\(321\) −0.423473 −0.0236359
\(322\) 0 0
\(323\) −0.0538378 0.129976i −0.00299561 0.00723205i
\(324\) 0 0
\(325\) −36.1037 14.9547i −2.00268 0.829535i
\(326\) 0 0
\(327\) −4.14785 4.14785i −0.229377 0.229377i
\(328\) 0 0
\(329\) 15.4112 15.4112i 0.849645 0.849645i
\(330\) 0 0
\(331\) −12.0185 + 29.0153i −0.660599 + 1.59483i 0.136268 + 0.990672i \(0.456489\pi\)
−0.796867 + 0.604155i \(0.793511\pi\)
\(332\) 0 0
\(333\) 5.53467 2.29253i 0.303298 0.125630i
\(334\) 0 0
\(335\) 11.6462i 0.636302i
\(336\) 0 0
\(337\) 2.12023i 0.115496i −0.998331 0.0577480i \(-0.981608\pi\)
0.998331 0.0577480i \(-0.0183920\pi\)
\(338\) 0 0
\(339\) −3.32971 + 1.37921i −0.180845 + 0.0749085i
\(340\) 0 0
\(341\) −7.00944 + 16.9223i −0.379582 + 0.916393i
\(342\) 0 0
\(343\) 14.1444 14.1444i 0.763723 0.763723i
\(344\) 0 0
\(345\) −12.6621 12.6621i −0.681705 0.681705i
\(346\) 0 0
\(347\) −15.6587 6.48607i −0.840606 0.348190i −0.0795133 0.996834i \(-0.525337\pi\)
−0.761092 + 0.648644i \(0.775337\pi\)
\(348\) 0 0
\(349\) −2.54342 6.14035i −0.136146 0.328685i 0.841072 0.540923i \(-0.181925\pi\)
−0.977218 + 0.212238i \(0.931925\pi\)
\(350\) 0 0
\(351\) −3.57327 −0.190727
\(352\) 0 0
\(353\) 26.7822 1.42547 0.712737 0.701431i \(-0.247455\pi\)
0.712737 + 0.701431i \(0.247455\pi\)
\(354\) 0 0
\(355\) −2.73539 6.60382i −0.145179 0.350494i
\(356\) 0 0
\(357\) −1.09417 0.453222i −0.0579098 0.0239870i
\(358\) 0 0
\(359\) 21.9626 + 21.9626i 1.15914 + 1.15914i 0.984661 + 0.174480i \(0.0558243\pi\)
0.174480 + 0.984661i \(0.444176\pi\)
\(360\) 0 0
\(361\) −13.3815 + 13.3815i −0.704292 + 0.704292i
\(362\) 0 0
\(363\) 0.420238 1.01454i 0.0220568 0.0532498i
\(364\) 0 0
\(365\) −39.2031 + 16.2385i −2.05198 + 0.849959i
\(366\) 0 0
\(367\) 20.1290i 1.05073i −0.850878 0.525363i \(-0.823929\pi\)
0.850878 0.525363i \(-0.176071\pi\)
\(368\) 0 0
\(369\) 5.58364i 0.290673i
\(370\) 0 0
\(371\) 13.9999 5.79897i 0.726841 0.301067i
\(372\) 0 0
\(373\) 0.278651 0.672724i 0.0144280 0.0348323i −0.916501 0.400032i \(-0.868999\pi\)
0.930929 + 0.365199i \(0.118999\pi\)
\(374\) 0 0
\(375\) 16.7570 16.7570i 0.865329 0.865329i
\(376\) 0 0
\(377\) 18.1627 + 18.1627i 0.935427 + 0.935427i
\(378\) 0 0
\(379\) 33.2934 + 13.7906i 1.71017 + 0.708375i 0.999991 + 0.00435195i \(0.00138527\pi\)
0.710177 + 0.704023i \(0.248615\pi\)
\(380\) 0 0
\(381\) −0.0561213 0.135489i −0.00287518 0.00694130i
\(382\) 0 0
\(383\) −30.6643 −1.56687 −0.783435 0.621473i \(-0.786534\pi\)
−0.783435 + 0.621473i \(0.786534\pi\)
\(384\) 0 0
\(385\) −29.0822 −1.48217
\(386\) 0 0
\(387\) −1.30801 3.15781i −0.0664897 0.160520i
\(388\) 0 0
\(389\) −9.95840 4.12490i −0.504911 0.209141i 0.115664 0.993288i \(-0.463101\pi\)
−0.620575 + 0.784147i \(0.713101\pi\)
\(390\) 0 0
\(391\) −1.62259 1.62259i −0.0820579 0.0820579i
\(392\) 0 0
\(393\) −2.14858 + 2.14858i −0.108382 + 0.108382i
\(394\) 0 0
\(395\) 1.08424 2.61760i 0.0545542 0.131706i
\(396\) 0 0
\(397\) 33.1225 13.7198i 1.66237 0.688577i 0.664118 0.747628i \(-0.268807\pi\)
0.998255 + 0.0590504i \(0.0188073\pi\)
\(398\) 0 0
\(399\) 0.636686i 0.0318742i
\(400\) 0 0
\(401\) 1.21160i 0.0605046i 0.999542 + 0.0302523i \(0.00963107\pi\)
−0.999542 + 0.0302523i \(0.990369\pi\)
\(402\) 0 0
\(403\) −19.2161 + 7.95958i −0.957224 + 0.396495i
\(404\) 0 0
\(405\) 1.52768 3.68816i 0.0759113 0.183266i
\(406\) 0 0
\(407\) 13.3297 13.3297i 0.660728 0.660728i
\(408\) 0 0
\(409\) −20.0380 20.0380i −0.990817 0.990817i 0.00914144 0.999958i \(-0.497090\pi\)
−0.999958 + 0.00914144i \(0.997090\pi\)
\(410\) 0 0
\(411\) 15.2725 + 6.32606i 0.753335 + 0.312042i
\(412\) 0 0
\(413\) −12.7947 30.8892i −0.629587 1.51996i
\(414\) 0 0
\(415\) 6.08490 0.298696
\(416\) 0 0
\(417\) 20.8023 1.01869
\(418\) 0 0
\(419\) −1.34843 3.25539i −0.0658749 0.159036i 0.887514 0.460781i \(-0.152431\pi\)
−0.953389 + 0.301745i \(0.902431\pi\)
\(420\) 0 0
\(421\) 10.4207 + 4.31639i 0.507873 + 0.210368i 0.621881 0.783112i \(-0.286369\pi\)
−0.114008 + 0.993480i \(0.536369\pi\)
\(422\) 0 0
\(423\) 6.65673 + 6.65673i 0.323661 + 0.323661i
\(424\) 0 0
\(425\) 3.95597 3.95597i 0.191893 0.191893i
\(426\) 0 0
\(427\) −7.77500 + 18.7705i −0.376258 + 0.908368i
\(428\) 0 0
\(429\) −10.3882 + 4.30292i −0.501546 + 0.207747i
\(430\) 0 0
\(431\) 35.6433i 1.71688i 0.512914 + 0.858440i \(0.328566\pi\)
−0.512914 + 0.858440i \(0.671434\pi\)
\(432\) 0 0
\(433\) 9.75449i 0.468771i −0.972144 0.234385i \(-0.924692\pi\)
0.972144 0.234385i \(-0.0753078\pi\)
\(434\) 0 0
\(435\) −26.5118 + 10.9816i −1.27114 + 0.526525i
\(436\) 0 0
\(437\) 0.472082 1.13971i 0.0225828 0.0545196i
\(438\) 0 0
\(439\) 11.2645 11.2645i 0.537625 0.537625i −0.385206 0.922831i \(-0.625870\pi\)
0.922831 + 0.385206i \(0.125870\pi\)
\(440\) 0 0
\(441\) 1.15979 + 1.15979i 0.0552281 + 0.0552281i
\(442\) 0 0
\(443\) −22.1985 9.19492i −1.05468 0.436864i −0.213122 0.977026i \(-0.568363\pi\)
−0.841561 + 0.540162i \(0.818363\pi\)
\(444\) 0 0
\(445\) −0.185130 0.446944i −0.00877601 0.0211872i
\(446\) 0 0
\(447\) 0.288993 0.0136689
\(448\) 0 0
\(449\) −12.5831 −0.593834 −0.296917 0.954903i \(-0.595958\pi\)
−0.296917 + 0.954903i \(0.595958\pi\)
\(450\) 0 0
\(451\) 6.72381 + 16.2327i 0.316612 + 0.764369i
\(452\) 0 0
\(453\) −6.14974 2.54730i −0.288940 0.119683i
\(454\) 0 0
\(455\) −23.3517 23.3517i −1.09475 1.09475i
\(456\) 0 0
\(457\) −28.8488 + 28.8488i −1.34949 + 1.34949i −0.463273 + 0.886216i \(0.653325\pi\)
−0.886216 + 0.463273i \(0.846675\pi\)
\(458\) 0 0
\(459\) 0.195765 0.472620i 0.00913755 0.0220600i
\(460\) 0 0
\(461\) 11.8188 4.89549i 0.550454 0.228006i −0.0900809 0.995934i \(-0.528713\pi\)
0.640535 + 0.767929i \(0.278713\pi\)
\(462\) 0 0
\(463\) 18.0311i 0.837976i 0.907992 + 0.418988i \(0.137615\pi\)
−0.907992 + 0.418988i \(0.862385\pi\)
\(464\) 0 0
\(465\) 23.2370i 1.07759i
\(466\) 0 0
\(467\) 22.2527 9.21739i 1.02973 0.426530i 0.197118 0.980380i \(-0.436842\pi\)
0.832616 + 0.553850i \(0.186842\pi\)
\(468\) 0 0
\(469\) −2.58467 + 6.23995i −0.119349 + 0.288134i
\(470\) 0 0
\(471\) −13.7337 + 13.7337i −0.632817 + 0.632817i
\(472\) 0 0
\(473\) −7.60526 7.60526i −0.349690 0.349690i
\(474\) 0 0
\(475\) 2.77867 + 1.15096i 0.127494 + 0.0528099i
\(476\) 0 0
\(477\) 2.50482 + 6.04717i 0.114688 + 0.276881i
\(478\) 0 0
\(479\) −11.2525 −0.514141 −0.257070 0.966393i \(-0.582757\pi\)
−0.257070 + 0.966393i \(0.582757\pi\)
\(480\) 0 0
\(481\) 21.4063 0.976043
\(482\) 0 0
\(483\) −3.97412 9.59438i −0.180829 0.436560i
\(484\) 0 0
\(485\) −2.49927 1.03523i −0.113486 0.0470074i
\(486\) 0 0
\(487\) 23.1247 + 23.1247i 1.04788 + 1.04788i 0.998795 + 0.0490867i \(0.0156311\pi\)
0.0490867 + 0.998795i \(0.484369\pi\)
\(488\) 0 0
\(489\) −10.9884 + 10.9884i −0.496911 + 0.496911i
\(490\) 0 0
\(491\) 9.92916 23.9711i 0.448097 1.08180i −0.524937 0.851141i \(-0.675911\pi\)
0.973034 0.230661i \(-0.0740888\pi\)
\(492\) 0 0
\(493\) −3.39736 + 1.40723i −0.153010 + 0.0633786i
\(494\) 0 0
\(495\) 12.5618i 0.564612i
\(496\) 0 0
\(497\) 4.14534i 0.185944i
\(498\) 0 0
\(499\) 0.662766 0.274527i 0.0296695 0.0122895i −0.367799 0.929905i \(-0.619889\pi\)
0.397469 + 0.917616i \(0.369889\pi\)
\(500\) 0 0
\(501\) 5.79544 13.9914i 0.258921 0.625091i
\(502\) 0 0
\(503\) 5.46400 5.46400i 0.243628 0.243628i −0.574721 0.818349i \(-0.694890\pi\)
0.818349 + 0.574721i \(0.194890\pi\)
\(504\) 0 0
\(505\) 30.5826 + 30.5826i 1.36091 + 1.36091i
\(506\) 0 0
\(507\) 0.214123 + 0.0886927i 0.00950954 + 0.00393898i
\(508\) 0 0
\(509\) −3.15891 7.62628i −0.140016 0.338029i 0.838280 0.545240i \(-0.183561\pi\)
−0.978296 + 0.207211i \(0.933561\pi\)
\(510\) 0 0
\(511\) −24.6085 −1.08862
\(512\) 0 0
\(513\) 0.275011 0.0121421
\(514\) 0 0
\(515\) −17.8280 43.0407i −0.785597 1.89660i
\(516\) 0 0
\(517\) 27.3684 + 11.3364i 1.20366 + 0.498573i
\(518\) 0 0
\(519\) −1.88673 1.88673i −0.0828182 0.0828182i
\(520\) 0 0
\(521\) 17.3737 17.3737i 0.761157 0.761157i −0.215375 0.976531i \(-0.569097\pi\)
0.976531 + 0.215375i \(0.0690973\pi\)
\(522\) 0 0
\(523\) −6.26194 + 15.1177i −0.273816 + 0.661049i −0.999640 0.0268308i \(-0.991458\pi\)
0.725824 + 0.687880i \(0.241458\pi\)
\(524\) 0 0
\(525\) 23.3917 9.68915i 1.02090 0.422869i
\(526\) 0 0
\(527\) 2.97770i 0.129711i
\(528\) 0 0
\(529\) 2.87879i 0.125165i
\(530\) 0 0
\(531\) 13.3423 5.52657i 0.579008 0.239833i
\(532\) 0 0
\(533\) −7.63524 + 18.4331i −0.330719 + 0.798426i
\(534\) 0 0
\(535\) 1.19538 1.19538i 0.0516806 0.0516806i
\(536\) 0 0
\(537\) 7.47990 + 7.47990i 0.322781 + 0.322781i
\(538\) 0 0
\(539\) 4.76835 + 1.97512i 0.205388 + 0.0850743i
\(540\) 0 0
\(541\) 10.7750 + 26.0132i 0.463255 + 1.11840i 0.967053 + 0.254574i \(0.0819354\pi\)
−0.503799 + 0.863821i \(0.668065\pi\)
\(542\) 0 0
\(543\) 19.2434 0.825813
\(544\) 0 0
\(545\) 23.4171 1.00308
\(546\) 0 0
\(547\) 13.7101 + 33.0991i 0.586201 + 1.41521i 0.887109 + 0.461561i \(0.152710\pi\)
−0.300908 + 0.953653i \(0.597290\pi\)
\(548\) 0 0
\(549\) −8.10777 3.35835i −0.346031 0.143331i
\(550\) 0 0
\(551\) −1.39787 1.39787i −0.0595512 0.0595512i
\(552\) 0 0
\(553\) 1.16186 1.16186i 0.0494072 0.0494072i
\(554\) 0 0
\(555\) −9.15187 + 22.0946i −0.388475 + 0.937862i
\(556\) 0 0
\(557\) −21.4363 + 8.87921i −0.908286 + 0.376224i −0.787400 0.616442i \(-0.788573\pi\)
−0.120886 + 0.992666i \(0.538573\pi\)
\(558\) 0 0
\(559\) 12.2134i 0.516571i
\(560\) 0 0
\(561\) 1.60974i 0.0679632i
\(562\) 0 0
\(563\) 41.3211 17.1158i 1.74148 0.721343i 0.742822 0.669489i \(-0.233487\pi\)
0.998655 0.0518544i \(-0.0165132\pi\)
\(564\) 0 0
\(565\) 5.50586 13.2923i 0.231633 0.559212i
\(566\) 0 0
\(567\) 1.63704 1.63704i 0.0687493 0.0687493i
\(568\) 0 0
\(569\) 29.0924 + 29.0924i 1.21962 + 1.21962i 0.967767 + 0.251848i \(0.0810384\pi\)
0.251848 + 0.967767i \(0.418962\pi\)
\(570\) 0 0
\(571\) −0.414172 0.171556i −0.0173326 0.00717938i 0.374000 0.927429i \(-0.377986\pi\)
−0.391333 + 0.920249i \(0.627986\pi\)
\(572\) 0 0
\(573\) 3.89432 + 9.40172i 0.162688 + 0.392763i
\(574\) 0 0
\(575\) 49.0567 2.04581
\(576\) 0 0
\(577\) 23.7041 0.986813 0.493406 0.869799i \(-0.335752\pi\)
0.493406 + 0.869799i \(0.335752\pi\)
\(578\) 0 0
\(579\) 2.74568 + 6.62865i 0.114107 + 0.275477i
\(580\) 0 0
\(581\) 3.26024 + 1.35043i 0.135257 + 0.0560255i
\(582\) 0 0
\(583\) 14.5640 + 14.5640i 0.603178 + 0.603178i
\(584\) 0 0
\(585\) 10.0866 10.0866i 0.417029 0.417029i
\(586\) 0 0
\(587\) 6.09999 14.7267i 0.251773 0.607835i −0.746574 0.665302i \(-0.768303\pi\)
0.998347 + 0.0574676i \(0.0183026\pi\)
\(588\) 0 0
\(589\) 1.47894 0.612598i 0.0609388 0.0252417i
\(590\) 0 0
\(591\) 10.6199i 0.436845i
\(592\) 0 0
\(593\) 6.36035i 0.261188i −0.991436 0.130594i \(-0.958312\pi\)
0.991436 0.130594i \(-0.0416885\pi\)
\(594\) 0 0
\(595\) 4.36798 1.80928i 0.179070 0.0741731i
\(596\) 0 0
\(597\) 4.29107 10.3596i 0.175622 0.423989i
\(598\) 0 0
\(599\) 4.61895 4.61895i 0.188725 0.188725i −0.606420 0.795145i \(-0.707395\pi\)
0.795145 + 0.606420i \(0.207395\pi\)
\(600\) 0 0
\(601\) −10.9077 10.9077i −0.444936 0.444936i 0.448731 0.893667i \(-0.351876\pi\)
−0.893667 + 0.448731i \(0.851876\pi\)
\(602\) 0 0
\(603\) −2.69530 1.11643i −0.109761 0.0454645i
\(604\) 0 0
\(605\) 1.67760 + 4.05009i 0.0682043 + 0.164660i
\(606\) 0 0
\(607\) 0.957019 0.0388442 0.0194221 0.999811i \(-0.493817\pi\)
0.0194221 + 0.999811i \(0.493817\pi\)
\(608\) 0 0
\(609\) −16.6420 −0.674367
\(610\) 0 0
\(611\) 12.8730 + 31.0782i 0.520787 + 1.25729i
\(612\) 0 0
\(613\) −2.24424 0.929594i −0.0906440 0.0375460i 0.336901 0.941540i \(-0.390621\pi\)
−0.427545 + 0.903994i \(0.640621\pi\)
\(614\) 0 0
\(615\) −15.7615 15.7615i −0.635564 0.635564i
\(616\) 0 0
\(617\) −22.5163 + 22.5163i −0.906472 + 0.906472i −0.995986 0.0895138i \(-0.971469\pi\)
0.0895138 + 0.995986i \(0.471469\pi\)
\(618\) 0 0
\(619\) 3.44381 8.31410i 0.138419 0.334172i −0.839436 0.543459i \(-0.817114\pi\)
0.977854 + 0.209287i \(0.0671143\pi\)
\(620\) 0 0
\(621\) 4.14422 1.71659i 0.166302 0.0688844i
\(622\) 0 0
\(623\) 0.280555i 0.0112402i
\(624\) 0 0
\(625\) 39.9216i 1.59687i
\(626\) 0 0
\(627\) 0.799511 0.331168i 0.0319294 0.0132256i
\(628\) 0 0
\(629\) −1.17277 + 2.83131i −0.0467613 + 0.112892i
\(630\) 0 0
\(631\) −28.2240 + 28.2240i −1.12358 + 1.12358i −0.132379 + 0.991199i \(0.542262\pi\)
−0.991199 + 0.132379i \(0.957738\pi\)
\(632\) 0 0
\(633\) −18.3458 18.3458i −0.729181 0.729181i
\(634\) 0 0
\(635\) 0.540876 + 0.224038i 0.0214640 + 0.00889068i
\(636\) 0 0
\(637\) 2.24285 + 5.41471i 0.0888649 + 0.214539i
\(638\) 0 0
\(639\) 1.79055 0.0708329
\(640\) 0 0
\(641\) −30.2846 −1.19617 −0.598084 0.801433i \(-0.704071\pi\)
−0.598084 + 0.801433i \(0.704071\pi\)
\(642\) 0 0
\(643\) −0.944867 2.28111i −0.0372619 0.0899582i 0.904153 0.427209i \(-0.140503\pi\)
−0.941415 + 0.337251i \(0.890503\pi\)
\(644\) 0 0
\(645\) 12.6061 + 5.22161i 0.496364 + 0.205601i
\(646\) 0 0
\(647\) −8.32184 8.32184i −0.327165 0.327165i 0.524342 0.851508i \(-0.324311\pi\)
−0.851508 + 0.524342i \(0.824311\pi\)
\(648\) 0 0
\(649\) 32.1336 32.1336i 1.26136 1.26136i
\(650\) 0 0
\(651\) 5.15703 12.4502i 0.202120 0.487960i
\(652\) 0 0
\(653\) 19.1159 7.91806i 0.748062 0.309858i 0.0241116 0.999709i \(-0.492324\pi\)
0.723951 + 0.689852i \(0.242324\pi\)
\(654\) 0 0
\(655\) 12.1300i 0.473959i
\(656\) 0 0
\(657\) 10.6295i 0.414694i
\(658\) 0 0
\(659\) −29.0382 + 12.0280i −1.13117 + 0.468546i −0.868178 0.496253i \(-0.834709\pi\)
−0.262991 + 0.964798i \(0.584709\pi\)
\(660\) 0 0
\(661\) −6.92538 + 16.7193i −0.269366 + 0.650307i −0.999454 0.0330463i \(-0.989479\pi\)
0.730088 + 0.683353i \(0.239479\pi\)
\(662\) 0 0
\(663\) 1.29255 1.29255i 0.0501984 0.0501984i
\(664\) 0 0
\(665\) 1.79723 + 1.79723i 0.0696937 + 0.0696937i
\(666\) 0 0
\(667\) −29.7901 12.3395i −1.15348 0.477787i
\(668\) 0 0
\(669\) −0.219360 0.529583i −0.00848096 0.0204749i
\(670\) 0 0
\(671\) −27.6150 −1.06606
\(672\) 0 0
\(673\) −19.3968 −0.747691 −0.373846 0.927491i \(-0.621961\pi\)
−0.373846 + 0.927491i \(0.621961\pi\)
\(674\) 0 0
\(675\) 4.18515 + 10.1038i 0.161087 + 0.388897i
\(676\) 0 0
\(677\) −1.10973 0.459664i −0.0426503 0.0176663i 0.361256 0.932467i \(-0.382348\pi\)
−0.403907 + 0.914800i \(0.632348\pi\)
\(678\) 0 0
\(679\) −1.10934 1.10934i −0.0425724 0.0425724i
\(680\) 0 0
\(681\) 2.66721 2.66721i 0.102208 0.102208i
\(682\) 0 0
\(683\) 2.49553 6.02475i 0.0954889 0.230531i −0.868916 0.494959i \(-0.835183\pi\)
0.964405 + 0.264428i \(0.0851832\pi\)
\(684\) 0 0
\(685\) −60.9682 + 25.2539i −2.32948 + 0.964900i
\(686\) 0 0
\(687\) 7.68963i 0.293378i
\(688\) 0 0
\(689\) 23.3885i 0.891030i
\(690\) 0 0
\(691\) 12.2382 5.06922i 0.465563 0.192842i −0.137556 0.990494i \(-0.543925\pi\)
0.603118 + 0.797652i \(0.293925\pi\)
\(692\) 0 0
\(693\) 2.78787 6.73052i 0.105902 0.255671i
\(694\) 0 0
\(695\) −58.7207 + 58.7207i −2.22740 + 2.22740i
\(696\) 0 0
\(697\) −2.01976 2.01976i −0.0765037 0.0765037i
\(698\) 0 0
\(699\) −1.80474 0.747548i −0.0682615 0.0282748i
\(700\) 0 0
\(701\) 14.9505 + 36.0936i 0.564671 + 1.36324i 0.905994 + 0.423291i \(0.139125\pi\)
−0.341322 + 0.939946i \(0.610875\pi\)
\(702\) 0 0
\(703\) −1.64751 −0.0621369
\(704\) 0 0
\(705\) −37.5811 −1.41539
\(706\) 0 0
\(707\) 9.59863 + 23.1731i 0.360994 + 0.871516i
\(708\) 0 0
\(709\) 31.0545 + 12.8632i 1.16627 + 0.483087i 0.879959 0.475049i \(-0.157570\pi\)
0.286315 + 0.958136i \(0.407570\pi\)
\(710\) 0 0
\(711\) 0.501855 + 0.501855i 0.0188210 + 0.0188210i
\(712\) 0 0
\(713\) 18.4628 18.4628i 0.691437 0.691437i
\(714\) 0 0
\(715\) 17.1774 41.4699i 0.642399 1.55089i
\(716\) 0 0
\(717\) 4.23557 1.75443i 0.158180 0.0655205i
\(718\) 0 0
\(719\) 12.6636i 0.472274i 0.971720 + 0.236137i \(0.0758815\pi\)
−0.971720 + 0.236137i \(0.924119\pi\)
\(720\) 0 0
\(721\) 27.0174i 1.00618i
\(722\) 0 0
\(723\) 14.7406 6.10576i 0.548209 0.227076i
\(724\) 0 0
\(725\) 30.0844 72.6302i 1.11731 2.69742i
\(726\) 0 0
\(727\) −33.0425 + 33.0425i −1.22548 + 1.22548i −0.259821 + 0.965657i \(0.583664\pi\)
−0.965657 + 0.259821i \(0.916336\pi\)
\(728\) 0 0
\(729\) 0.707107 + 0.707107i 0.0261891 + 0.0261891i
\(730\) 0 0
\(731\) 1.61541 + 0.669124i 0.0597480 + 0.0247484i
\(732\) 0 0
\(733\) 1.87261 + 4.52088i 0.0691664 + 0.166982i 0.954682 0.297626i \(-0.0961950\pi\)
−0.885516 + 0.464609i \(0.846195\pi\)
\(734\) 0 0
\(735\) −6.54770 −0.241516
\(736\) 0 0
\(737\) −9.18015 −0.338155
\(738\) 0 0
\(739\) −15.0628 36.3648i −0.554093 1.33770i −0.914380 0.404857i \(-0.867321\pi\)
0.360287 0.932842i \(-0.382679\pi\)
\(740\) 0 0
\(741\) 0.907887 + 0.376059i 0.0333520 + 0.0138149i
\(742\) 0 0
\(743\) 20.9250 + 20.9250i 0.767664 + 0.767664i 0.977695 0.210031i \(-0.0673563\pi\)
−0.210031 + 0.977695i \(0.567356\pi\)
\(744\) 0 0
\(745\) −0.815767 + 0.815767i −0.0298874 + 0.0298874i
\(746\) 0 0
\(747\) −0.583309 + 1.40823i −0.0213422 + 0.0515246i
\(748\) 0 0
\(749\) 0.905765 0.375180i 0.0330959 0.0137088i
\(750\) 0 0
\(751\) 2.47050i 0.0901497i −0.998984 0.0450749i \(-0.985647\pi\)
0.998984 0.0450749i \(-0.0143526\pi\)
\(752\) 0 0
\(753\) 21.7334i 0.792008i
\(754\) 0 0
\(755\) 24.5499 10.1689i 0.893464 0.370085i
\(756\) 0 0
\(757\) 2.84324 6.86420i 0.103339 0.249483i −0.863750 0.503921i \(-0.831890\pi\)
0.967089 + 0.254437i \(0.0818903\pi\)
\(758\) 0 0
\(759\) 9.98092 9.98092i 0.362284 0.362284i
\(760\) 0 0
\(761\) −29.8039 29.8039i −1.08039 1.08039i −0.996473 0.0839198i \(-0.973256\pi\)
−0.0839198 0.996473i \(-0.526744\pi\)
\(762\) 0 0
\(763\) 12.5467 + 5.19700i 0.454220 + 0.188144i
\(764\) 0 0
\(765\) 0.781502 + 1.88671i 0.0282553 + 0.0682143i
\(766\) 0 0
\(767\) 51.6038 1.86330
\(768\) 0 0
\(769\) −50.3024 −1.81395 −0.906976 0.421182i \(-0.861615\pi\)
−0.906976 + 0.421182i \(0.861615\pi\)
\(770\) 0 0
\(771\) −0.259451 0.626371i −0.00934391 0.0225582i
\(772\) 0 0
\(773\) −0.373623 0.154760i −0.0134383 0.00556632i 0.375954 0.926638i \(-0.377315\pi\)
−0.389392 + 0.921072i \(0.627315\pi\)
\(774\) 0 0
\(775\) 45.0134 + 45.0134i 1.61693 + 1.61693i
\(776\) 0 0
\(777\) −9.80699 + 9.80699i −0.351824 + 0.351824i
\(778\) 0 0
\(779\) 0.587635 1.41868i 0.0210542 0.0508294i
\(780\) 0 0
\(781\) 5.20546 2.15617i 0.186266 0.0771540i
\(782\) 0 0
\(783\) 7.18837i 0.256891i
\(784\) 0 0
\(785\) 77.5349i 2.76734i
\(786\) 0 0
\(787\) 13.9620 5.78325i 0.497692 0.206151i −0.119695 0.992811i \(-0.538192\pi\)
0.617386 + 0.786660i \(0.288192\pi\)
\(788\) 0 0
\(789\) −4.15291 + 10.0260i −0.147847 + 0.356935i
\(790\) 0 0
\(791\) 5.89999 5.89999i 0.209779 0.209779i
\(792\) 0 0
\(793\) −22.1736 22.1736i −0.787408 0.787408i
\(794\) 0 0
\(795\) −24.1405 9.99932i −0.856175 0.354639i
\(796\) 0 0
\(797\) −1.14025 2.75280i −0.0403896 0.0975092i 0.902397 0.430905i \(-0.141806\pi\)
−0.942787 + 0.333396i \(0.891806\pi\)