Properties

Label 384.2.n.a.145.4
Level $384$
Weight $2$
Character 384.145
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 145.4
Character \(\chi\) \(=\) 384.145
Dual form 384.2.n.a.241.4

$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(1\)

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 0.652199 0.758048i \(-0.273847\pi\)
0.997195 + 0.0748462i \(0.0238466\pi\)
\(6\) 0 0
\(7\) 1.63704 1.63704i 0.618743 0.618743i −0.326466 0.945209i \(-0.605858\pi\)
0.945209 + 0.326466i \(0.105858\pi\)
\(8\) 0 0
\(9\) −0.707107 0.707107i −0.235702 0.235702i
\(10\) 0 0
\(11\) −1.20420 2.90719i −0.363080 0.876552i −0.994846 0.101393i \(-0.967670\pi\)
0.631767 0.775158i \(-0.282330\pi\)
\(12\) 0 0
\(13\) −3.30127 1.36743i −0.915607 0.379257i −0.125407 0.992105i \(-0.540024\pi\)
−0.790200 + 0.612849i \(0.790024\pi\)
\(14\) 0 0
\(15\) 3.99203i 1.03074i
\(16\) 0 0
\(17\) 0.511560i 0.124071i 0.998074 + 0.0620357i \(0.0197593\pi\)
−0.998074 + 0.0620357i \(0.980241\pi\)
\(18\) 0 0
\(19\) 0.254077 + 0.105242i 0.0582894 + 0.0241442i 0.411638 0.911348i \(-0.364957\pi\)
−0.353348 + 0.935492i \(0.614957\pi\)
\(20\) 0 0
\(21\) 0.885960 + 2.13890i 0.193332 + 0.466746i
\(22\) 0 0
\(23\) 3.17185 + 3.17185i 0.661376 + 0.661376i 0.955704 0.294329i \(-0.0950960\pi\)
−0.294329 + 0.955704i \(0.595096\pi\)
\(24\) 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 0.432582 + 0.901595i \(0.357603\pi\)
−0.943405 + 0.331642i \(0.892397\pi\)
\(30\) 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 −0.788016 0.615655i \(-0.788892\pi\)
−0.121878 + 0.992545i \(0.538892\pi\)
\(38\) 0 0
\(39\) 2.52668 2.52668i 0.404593 0.404593i
\(40\) 0 0
\(41\) 3.94823 + 3.94823i 0.616610 + 0.616610i 0.944660 0.328050i \(-0.106392\pi\)
−0.328050 + 0.944660i \(0.606392\pi\)
\(42\) 0 0
\(43\) −1.30801 3.15781i −0.199469 0.481561i 0.792217 0.610239i \(-0.208927\pi\)
−0.991686 + 0.128678i \(0.958927\pi\)
\(44\) 0 0
\(45\) −3.68816 1.52768i −0.549798 0.227734i
\(46\) 0 0
\(47\) 9.41403i 1.37318i 0.727046 + 0.686589i \(0.240893\pi\)
−0.727046 + 0.686589i \(0.759107\pi\)
\(48\) 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 0.997296 + 0.0734852i \(0.0234122\pi\)
−0.653233 + 0.757157i \(0.726588\pi\)
\(54\) 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 −0.738023 + 0.674775i \(0.764241\pi\)
−0.998999 + 0.0447232i \(0.985759\pi\)
\(60\) 0 0
\(61\) 3.35835 8.10777i 0.429992 1.03809i −0.549297 0.835627i \(-0.685104\pi\)
0.979289 0.202466i \(-0.0648955\pi\)
\(62\) 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 −0.840894 0.541199i \(-0.817970\pi\)
0.977288 + 0.211916i \(0.0679704\pi\)
\(68\) 0 0
\(69\) −4.14422 + 1.71659i −0.498905 + 0.206653i
\(70\) 0 0
\(71\) −1.26611 + 1.26611i −0.150259 + 0.150259i −0.778234 0.627975i \(-0.783884\pi\)
0.627975 + 0.778234i \(0.283884\pi\)
\(72\) 0 0
\(73\) −7.51616 7.51616i −0.879700 0.879700i 0.113804 0.993503i \(-0.463697\pi\)
−0.993503 + 0.113804i \(0.963697\pi\)
\(74\) 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 \(0.0127120\pi\)
−0.999203 + 0.0399254i \(0.987288\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 1.40823 + 0.583309i 0.154574 + 0.0640265i 0.458629 0.888628i \(-0.348341\pi\)
−0.304055 + 0.952654i \(0.598341\pi\)
\(84\) 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 −0.711634 0.702551i \(-0.752044\pi\)
0.702551 + 0.711634i \(0.252044\pi\)
\(90\) 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 0.175657 0.984451i \(-0.443795\pi\)
0.820321 + 0.571904i \(0.193795\pi\)
\(102\) 0 0
\(103\) −8.25191 + 8.25191i −0.813085 + 0.813085i −0.985095 0.172010i \(-0.944974\pi\)
0.172010 + 0.985095i \(0.444974\pi\)
\(104\) 0 0
\(105\) 6.53512 + 6.53512i 0.637763 + 0.637763i
\(106\) 0 0
\(107\) 0.162056 + 0.391238i 0.0156665 + 0.0378224i 0.931519 0.363692i \(-0.118484\pi\)
−0.915853 + 0.401514i \(0.868484\pi\)
\(108\) 0 0
\(109\) 5.41943 + 2.24480i 0.519087 + 0.215013i 0.626816 0.779167i \(-0.284358\pi\)
−0.107729 + 0.994180i \(0.534358\pi\)
\(110\) 0 0
\(111\) 5.99068i 0.568610i
\(112\) 0 0
\(113\) 3.60406i 0.339041i 0.985527 + 0.169521i \(0.0542219\pi\)
−0.985527 + 0.169521i \(0.945778\pi\)
\(114\) 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 −0.966501 0.256661i \(-0.917377\pi\)
0.864907 + 0.501933i \(0.167377\pi\)
\(132\) 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 0.00133685 0.999999i \(-0.499574\pi\)
−0.999999 + 0.00133685i \(0.999574\pi\)
\(138\) 0 0
\(139\) −7.96071 19.2188i −0.675218 1.63012i −0.772615 0.634875i \(-0.781051\pi\)
0.0973963 0.995246i \(-0.468949\pi\)
\(140\) 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 0.919285 0.393593i \(-0.128768\pi\)
−0.928345 + 0.371720i \(0.878768\pi\)
\(150\) 0 0
\(151\) 4.70680 + 4.70680i 0.383034 + 0.383034i 0.872194 0.489160i \(-0.162697\pi\)
−0.489160 + 0.872194i \(0.662697\pi\)
\(152\) 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 0.287218 + 0.957865i \(0.407270\pi\)
−0.880407 + 0.474220i \(0.842730\pi\)
\(158\) 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 0.500188 + 0.865917i \(0.333264\pi\)
−0.965982 + 0.258609i \(0.916736\pi\)
\(164\) 0 0
\(165\) 11.6056 4.80720i 0.903496 0.374240i
\(166\) 0 0
\(167\) 10.7086 10.7086i 0.828655 0.828655i −0.158676 0.987331i \(-0.550723\pi\)
0.987331 + 0.158676i \(0.0507225\pi\)
\(168\) 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 0.474420 0.880299i \(-0.342658\pi\)
−0.287000 + 0.957931i \(0.592658\pi\)
\(174\) 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 −0.0137219 0.999906i \(-0.504368\pi\)
−0.716743 + 0.697337i \(0.754368\pi\)
\(180\) 0 0
\(181\) −7.36413 17.7786i −0.547371 1.32147i −0.919427 0.393261i \(-0.871347\pi\)
0.372056 0.928210i \(-0.378653\pi\)
\(182\) 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 −0.00471943 0.999989i \(-0.501502\pi\)
0.703762 + 0.710436i \(0.251502\pi\)
\(198\) 0 0
\(199\) 7.92887 7.92887i 0.562063 0.562063i −0.367830 0.929893i \(-0.619899\pi\)
0.929893 + 0.367830i \(0.119899\pi\)
\(200\) 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 0.997264 0.0739270i \(-0.0235532\pi\)
0.652898 + 0.757446i \(0.273553\pi\)
\(212\) 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 −0.868709 0.495323i \(-0.835050\pi\)
0.964516 + 0.264023i \(0.0850496\pi\)
\(228\) 0 0
\(229\) −7.10429 + 2.94269i −0.469465 + 0.194459i −0.604858 0.796333i \(-0.706770\pi\)
0.135393 + 0.990792i \(0.456770\pi\)
\(230\) 0 0
\(231\) 5.15132 5.15132i 0.338932 0.338932i
\(232\) 0 0
\(233\) 1.38129 + 1.38129i 0.0904912 + 0.0904912i 0.750903 0.660412i \(-0.229618\pi\)
−0.660412 + 0.750903i \(0.729618\pi\)
\(234\) 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 \(-0.952628\pi\)
0.988946 0.148275i \(-0.0473721\pi\)
\(240\) 0 0
\(241\) 15.9551i 1.02776i −0.857862 0.513880i \(-0.828208\pi\)
0.857862 0.513880i \(-0.171792\pi\)
\(242\) 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 0.355211 0.934786i \(-0.384409\pi\)
0.912166 + 0.409822i \(0.134409\pi\)
\(252\) 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 −0.902940 0.429767i \(-0.858596\pi\)
0.429767 + 0.902940i \(0.358596\pi\)
\(264\) 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 0.934701 0.355436i \(-0.115668\pi\)
0.409602 + 0.912264i \(0.365668\pi\)
\(270\) 0 0
\(271\) 0.778886i 0.0473140i 0.999720 + 0.0236570i \(0.00753096\pi\)
−0.999720 + 0.0236570i \(0.992469\pi\)
\(272\) 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 0.961881 0.273469i \(-0.0881712\pi\)
−0.873524 + 0.486780i \(0.838171\pi\)
\(278\) 0 0
\(279\) −4.11595 4.11595i −0.246415 0.246415i
\(280\) 0 0
\(281\) −3.60771 + 3.60771i −0.215218 + 0.215218i −0.806480 0.591262i \(-0.798630\pi\)
0.591262 + 0.806480i \(0.298630\pi\)
\(282\) 0 0
\(283\) −12.3134 + 5.10036i −0.731953 + 0.303185i −0.717354 0.696709i \(-0.754647\pi\)
−0.0145986 + 0.999893i \(0.504647\pi\)
\(284\) 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 −0.902352 0.431000i \(-0.858161\pi\)
−0.333297 + 0.942822i \(0.608161\pi\)
\(294\) 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 −0.697070 0.717003i \(-0.745513\pi\)
−0.999901 + 0.0140946i \(0.995513\pi\)
\(308\) 0 0
\(309\) −4.46590 10.7816i −0.254056 0.613346i
\(310\) 0 0
\(311\) 5.08789 + 5.08789i 0.288508 + 0.288508i 0.836490 0.547982i \(-0.184604\pi\)
−0.547982 + 0.836490i \(0.684604\pi\)
\(312\) 0 0
\(313\) −10.3695 + 10.3695i −0.586117 + 0.586117i −0.936578 0.350460i \(-0.886025\pi\)
0.350460 + 0.936578i \(0.386025\pi\)
\(314\) 0 0
\(315\) −8.53855 + 3.53678i −0.481093 + 0.199275i
\(316\) 0 0
\(317\) −6.18851 + 14.9404i −0.347582 + 0.839136i 0.649323 + 0.760513i \(0.275052\pi\)
−0.996904 + 0.0786232i \(0.974948\pi\)
\(318\) 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 −0.796867 0.604155i \(-0.793511\pi\)
0.136268 0.990672i \(-0.456489\pi\)
\(332\) 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 \(0.0183920\pi\)
−0.998331 + 0.0577480i \(0.981608\pi\)
\(338\) 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 −0.761092 0.648644i \(-0.775337\pi\)
−0.0795133 + 0.996834i \(0.525337\pi\)
\(348\) 0 0
\(349\) −2.54342 + 6.14035i −0.136146 + 0.328685i −0.977218 0.212238i \(-0.931925\pi\)
0.841072 + 0.540923i \(0.181925\pi\)
\(350\) 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 0.174480 0.984661i \(-0.444176\pi\)
0.984661 0.174480i \(-0.0558243\pi\)
\(360\) 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 \(0.176071\pi\)
−0.850878 + 0.525363i \(0.823929\pi\)
\(368\) 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 0.930929 0.365199i \(-0.118999\pi\)
−0.916501 + 0.400032i \(0.868999\pi\)
\(374\) 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 0.710177 0.704023i \(-0.248615\pi\)
0.999991 0.00435195i \(-0.00138527\pi\)
\(380\) 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 −0.620575 0.784147i \(-0.713101\pi\)
0.115664 + 0.993288i \(0.463101\pi\)
\(390\) 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 0.998255 0.0590504i \(-0.0188073\pi\)
0.664118 + 0.747628i \(0.268807\pi\)
\(398\) 0 0
\(399\) 0.636686i 0.0318742i
\(400\) 0 0
\(401\) 1.21160i 0.0605046i −0.999542 0.0302523i \(-0.990369\pi\)
0.999542 0.0302523i \(-0.00963107\pi\)
\(402\) 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 −0.999958 0.00914144i \(-0.997090\pi\)
0.00914144 + 0.999958i \(0.497090\pi\)
\(410\) 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 −0.953389 0.301745i \(-0.902431\pi\)
0.887514 + 0.460781i \(0.152431\pi\)
\(420\) 0 0
\(421\) 10.4207 4.31639i 0.507873 0.210368i −0.114008 0.993480i \(-0.536369\pi\)
0.621881 + 0.783112i \(0.286369\pi\)
\(422\) 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 \(-0.671434\pi\)
0.512914 0.858440i \(-0.328566\pi\)
\(432\) 0 0
\(433\) 9.75449i 0.468771i 0.972144 + 0.234385i \(0.0753078\pi\)
−0.972144 + 0.234385i \(0.924692\pi\)
\(434\) 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 0.922831 0.385206i \(-0.125870\pi\)
−0.385206 + 0.922831i \(0.625870\pi\)
\(440\) 0 0
\(441\) 1.15979 1.15979i 0.0552281 0.0552281i
\(442\) 0 0
\(443\) −22.1985 + 9.19492i −1.05468 + 0.436864i −0.841561 0.540162i \(-0.818363\pi\)
−0.213122 + 0.977026i \(0.568363\pi\)
\(444\) 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 −0.886216 0.463273i \(-0.846675\pi\)
−0.463273 0.886216i \(-0.653325\pi\)
\(458\) 0 0
\(459\) 0.195765 + 0.472620i 0.00913755 + 0.0220600i
\(460\) 0 0
\(461\) 11.8188 + 4.89549i 0.550454 + 0.228006i 0.640535 0.767929i \(-0.278713\pi\)
−0.0900809 + 0.995934i \(0.528713\pi\)
\(462\) 0 0
\(463\) 18.0311i 0.837976i −0.907992 0.418988i \(-0.862385\pi\)
0.907992 0.418988i \(-0.137615\pi\)
\(464\) 0 0
\(465\) 23.2370i 1.07759i
\(466\) 0 0
\(467\) 22.2527 + 9.21739i 1.02973 + 0.426530i 0.832616 0.553850i \(-0.186842\pi\)
0.197118 + 0.980380i \(0.436842\pi\)
\(468\) 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 0.0490867 0.998795i \(-0.484369\pi\)
0.998795 0.0490867i \(-0.0156311\pi\)
\(488\) 0 0
\(489\) −10.9884 10.9884i −0.496911 0.496911i
\(490\) 0 0
\(491\) 9.92916 + 23.9711i 0.448097 + 1.08180i 0.973034 + 0.230661i \(0.0740888\pi\)
−0.524937 + 0.851141i \(0.675911\pi\)
\(492\) 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 0.397469 0.917616i \(-0.369889\pi\)
−0.367799 + 0.929905i \(0.619889\pi\)
\(500\) 0 0
\(501\) 5.79544 + 13.9914i 0.258921 + 0.625091i
\(502\) 0 0
\(503\) 5.46400 + 5.46400i 0.243628 + 0.243628i 0.818349 0.574721i \(-0.194890\pi\)
−0.574721 + 0.818349i \(0.694890\pi\)
\(504\) 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 −0.978296 0.207211i \(-0.933561\pi\)
0.838280 + 0.545240i \(0.183561\pi\)
\(510\) 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 0.976531 0.215375i \(-0.0690973\pi\)
−0.215375 + 0.976531i \(0.569097\pi\)
\(522\) 0 0
\(523\) −6.26194 15.1177i −0.273816 0.661049i 0.725824 0.687880i \(-0.241458\pi\)
−0.999640 + 0.0268308i \(0.991458\pi\)
\(524\) 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 −0.503799 0.863821i \(-0.668065\pi\)
0.967053 0.254574i \(-0.0819354\pi\)
\(542\) 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 −0.300908 0.953653i \(-0.597290\pi\)
0.887109 0.461561i \(-0.152710\pi\)
\(548\) 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 −0.120886 0.992666i \(-0.538573\pi\)
−0.787400 + 0.616442i \(0.788573\pi\)
\(558\) 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 0.998655 + 0.0518544i \(0.0165132\pi\)
0.742822 + 0.669489i \(0.233487\pi\)
\(564\) 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 0.251848 0.967767i \(-0.418962\pi\)
0.967767 0.251848i \(-0.0810384\pi\)
\(570\) 0 0
\(571\) −0.414172 + 0.171556i −0.0173326 + 0.00717938i −0.391333 0.920249i \(-0.627986\pi\)
0.374000 + 0.927429i \(0.377986\pi\)
\(572\) 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 0.998347 0.0574676i \(-0.0183026\pi\)
−0.746574 + 0.665302i \(0.768303\pi\)
\(588\) 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 \(0.0416885\pi\)
−0.991436 + 0.130594i \(0.958312\pi\)
\(594\) 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 0.795145 0.606420i \(-0.207395\pi\)
−0.606420 + 0.795145i \(0.707395\pi\)
\(600\) 0 0
\(601\) −10.9077 + 10.9077i −0.444936 + 0.444936i −0.893667 0.448731i \(-0.851876\pi\)
0.448731 + 0.893667i \(0.351876\pi\)
\(602\) 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 −0.427545 0.903994i \(-0.640621\pi\)
0.336901 + 0.941540i \(0.390621\pi\)
\(614\) 0 0
\(615\) −15.7615 + 15.7615i −0.635564 + 0.635564i
\(616\) 0 0
\(617\) −22.5163 22.5163i −0.906472 0.906472i 0.0895138 0.995986i \(-0.471469\pi\)
−0.995986 + 0.0895138i \(0.971469\pi\)
\(618\) 0 0
\(619\) 3.44381 + 8.31410i 0.138419 + 0.334172i 0.977854 0.209287i \(-0.0671143\pi\)
−0.839436 + 0.543459i \(0.817114\pi\)
\(620\) 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 −0.991199 0.132379i \(-0.957738\pi\)
−0.132379 0.991199i \(-0.542262\pi\)
\(632\) 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 −0.941415 0.337251i \(-0.890503\pi\)
0.904153 + 0.427209i \(0.140503\pi\)
\(644\) 0 0
\(645\) 12.6061 5.22161i 0.496364 0.205601i
\(646\) 0 0
\(647\) −8.32184 + 8.32184i −0.327165 + 0.327165i −0.851508 0.524342i \(-0.824311\pi\)
0.524342 + 0.851508i \(0.324311\pi\)
\(648\) 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 0.723951 0.689852i \(-0.242324\pi\)
0.0241116 + 0.999709i \(0.492324\pi\)
\(654\) 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 −0.262991 0.964798i \(-0.584709\pi\)
−0.868178 + 0.496253i \(0.834709\pi\)
\(660\) 0 0
\(661\) −6.92538 16.7193i −0.269366 0.650307i 0.730088 0.683353i \(-0.239479\pi\)
−0.999454 + 0.0330463i \(0.989479\pi\)
\(662\) 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 −0.403907 0.914800i \(-0.632348\pi\)
0.361256 + 0.932467i \(0.382348\pi\)
\(678\) 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 0.964405 0.264428i \(-0.0851832\pi\)
−0.868916 + 0.494959i \(0.835183\pi\)
\(684\) 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 0.603118 0.797652i \(-0.293925\pi\)
−0.137556 + 0.990494i \(0.543925\pi\)
\(692\) 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 −0.341322 0.939946i \(-0.610875\pi\)
0.905994 0.423291i \(-0.139125\pi\)
\(702\) 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 0.286315 0.958136i \(-0.407570\pi\)
0.879959 + 0.475049i \(0.157570\pi\)
\(710\) 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 \(-0.924119\pi\)
0.971720 0.236137i \(-0.0758815\pi\)
\(720\) 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 −0.965657 0.259821i \(-0.916336\pi\)
−0.259821 0.965657i \(-0.583664\pi\)
\(728\) 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 −0.885516 0.464609i \(-0.846195\pi\)
0.954682 + 0.297626i \(0.0961950\pi\)
\(734\) 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 0.360287 + 0.932842i \(0.382679\pi\)
−0.914380 + 0.404857i \(0.867321\pi\)
\(740\) 0 0
\(741\) 0.907887 0.376059i 0.0333520 0.0138149i
\(742\) 0 0
\(743\) 20.9250 20.9250i 0.767664 0.767664i −0.210031 0.977695i \(-0.567356\pi\)
0.977695 + 0.210031i \(0.0673563\pi\)
\(744\) 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 \(0.0143526\pi\)
−0.998984 + 0.0450749i \(0.985647\pi\)
\(752\) 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 0.967089 0.254437i \(-0.0818903\pi\)
−0.863750 + 0.503921i \(0.831890\pi\)
\(758\) 0 0
\(759\) 9.98092 + 9.98092i 0.362284 + 0.362284i
\(760\) 0 0
\(761\) −29.8039 + 29.8039i −1.08039 + 1.08039i −0.0839198 + 0.996473i \(0.526744\pi\)
−0.996473 + 0.0839198i \(0.973256\pi\)
\(762\) 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 −0.389392 0.921072i \(-0.627315\pi\)
0.375954 + 0.926638i \(0.377315\pi\)
\(774\) 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 0.617386 0.786660i \(-0.288192\pi\)
−0.119695 + 0.992811i \(0.538192\pi\)
\(788\) 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 −0.942787 0.333396i \(-0.891806\pi\)
0.902397 + 0.430905i \(0.141806\pi\)
\(798\) 0 0