Properties

Label 864.2.v.b.109.4
Level $864$
Weight $2$
Character 864.109
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 109.4
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.b.325.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23997 + 0.680049i) q^{2} +(1.07507 - 1.68649i) q^{4} +(1.02237 - 0.423478i) q^{5} +(0.485592 - 0.485592i) q^{7} +(-0.186159 + 2.82229i) q^{8} +O(q^{10})\) \(q+(-1.23997 + 0.680049i) q^{2} +(1.07507 - 1.68649i) q^{4} +(1.02237 - 0.423478i) q^{5} +(0.485592 - 0.485592i) q^{7} +(-0.186159 + 2.82229i) q^{8} +(-0.979722 + 1.22036i) q^{10} +(1.70905 + 4.12601i) q^{11} +(-2.03122 - 0.841358i) q^{13} +(-0.271894 + 0.932347i) q^{14} +(-1.68847 - 3.62617i) q^{16} +4.47838i q^{17} +(2.51262 + 1.04076i) q^{19} +(0.384922 - 2.17947i) q^{20} +(-4.92507 - 3.95390i) q^{22} +(-1.15719 - 1.15719i) q^{23} +(-2.66963 + 2.66963i) q^{25} +(3.09082 - 0.338067i) q^{26} +(-0.296901 - 1.34099i) q^{28} +(-1.62983 + 3.93476i) q^{29} +6.62389 q^{31} +(4.55963 + 3.34811i) q^{32} +(-3.04552 - 5.55306i) q^{34} +(0.290816 - 0.702091i) q^{35} +(9.60845 - 3.97995i) q^{37} +(-3.82335 + 0.418190i) q^{38} +(1.00486 + 2.96426i) q^{40} +(3.06238 + 3.06238i) q^{41} +(-2.15582 - 5.20462i) q^{43} +(8.79580 + 1.55345i) q^{44} +(2.22184 + 0.647940i) q^{46} -8.66512i q^{47} +6.52840i q^{49} +(1.49479 - 5.12575i) q^{50} +(-3.60263 + 2.52110i) q^{52} +(2.26817 + 5.47584i) q^{53} +(3.49455 + 3.49455i) q^{55} +(1.28009 + 1.46088i) q^{56} +(-0.654885 - 5.98736i) q^{58} +(7.36470 - 3.05056i) q^{59} +(-1.16848 + 2.82095i) q^{61} +(-8.21344 + 4.50457i) q^{62} +(-7.93069 - 1.05079i) q^{64} -2.43295 q^{65} +(-1.63065 + 3.93673i) q^{67} +(7.55272 + 4.81455i) q^{68} +(0.116853 + 1.06834i) q^{70} +(-2.11730 + 2.11730i) q^{71} +(6.06373 + 6.06373i) q^{73} +(-9.20765 + 11.4692i) q^{74} +(4.45646 - 3.11861i) q^{76} +(2.83346 + 1.17366i) q^{77} +5.65785i q^{79} +(-3.26184 - 2.99224i) q^{80} +(-5.87983 - 1.71470i) q^{82} +(-1.59099 - 0.659009i) q^{83} +(1.89650 + 4.57854i) q^{85} +(6.21256 + 4.98752i) q^{86} +(-11.9630 + 4.05535i) q^{88} +(0.998730 - 0.998730i) q^{89} +(-1.39490 + 0.577786i) q^{91} +(-3.19565 + 0.707531i) q^{92} +(5.89271 + 10.7445i) q^{94} +3.00956 q^{95} +9.78679 q^{97} +(-4.43963 - 8.09504i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23997 + 0.680049i −0.876793 + 0.480867i
\(3\) 0 0
\(4\) 1.07507 1.68649i 0.537533 0.843243i
\(5\) 1.02237 0.423478i 0.457217 0.189385i −0.142175 0.989842i \(-0.545409\pi\)
0.599391 + 0.800456i \(0.295409\pi\)
\(6\) 0 0
\(7\) 0.485592 0.485592i 0.183537 0.183537i −0.609358 0.792895i \(-0.708573\pi\)
0.792895 + 0.609358i \(0.208573\pi\)
\(8\) −0.186159 + 2.82229i −0.0658172 + 0.997832i
\(9\) 0 0
\(10\) −0.979722 + 1.22036i −0.309815 + 0.385912i
\(11\) 1.70905 + 4.12601i 0.515298 + 1.24404i 0.940763 + 0.339064i \(0.110110\pi\)
−0.425465 + 0.904975i \(0.639890\pi\)
\(12\) 0 0
\(13\) −2.03122 0.841358i −0.563358 0.233351i 0.0827840 0.996568i \(-0.473619\pi\)
−0.646142 + 0.763217i \(0.723619\pi\)
\(14\) −0.271894 + 0.932347i −0.0726668 + 0.249180i
\(15\) 0 0
\(16\) −1.68847 3.62617i −0.422117 0.906541i
\(17\) 4.47838i 1.08617i 0.839679 + 0.543083i \(0.182743\pi\)
−0.839679 + 0.543083i \(0.817257\pi\)
\(18\) 0 0
\(19\) 2.51262 + 1.04076i 0.576434 + 0.238767i 0.651802 0.758389i \(-0.274013\pi\)
−0.0753681 + 0.997156i \(0.524013\pi\)
\(20\) 0.384922 2.17947i 0.0860711 0.487345i
\(21\) 0 0
\(22\) −4.92507 3.95390i −1.05003 0.842975i
\(23\) −1.15719 1.15719i −0.241291 0.241291i 0.576093 0.817384i \(-0.304577\pi\)
−0.817384 + 0.576093i \(0.804577\pi\)
\(24\) 0 0
\(25\) −2.66963 + 2.66963i −0.533927 + 0.533927i
\(26\) 3.09082 0.338067i 0.606160 0.0663004i
\(27\) 0 0
\(28\) −0.296901 1.34099i −0.0561089 0.253423i
\(29\) −1.62983 + 3.93476i −0.302652 + 0.730667i 0.697252 + 0.716826i \(0.254406\pi\)
−0.999904 + 0.0138407i \(0.995594\pi\)
\(30\) 0 0
\(31\) 6.62389 1.18969 0.594843 0.803842i \(-0.297214\pi\)
0.594843 + 0.803842i \(0.297214\pi\)
\(32\) 4.55963 + 3.34811i 0.806035 + 0.591867i
\(33\) 0 0
\(34\) −3.04552 5.55306i −0.522302 0.952343i
\(35\) 0.290816 0.702091i 0.0491568 0.118675i
\(36\) 0 0
\(37\) 9.60845 3.97995i 1.57962 0.654300i 0.591266 0.806477i \(-0.298628\pi\)
0.988353 + 0.152177i \(0.0486284\pi\)
\(38\) −3.82335 + 0.418190i −0.620229 + 0.0678393i
\(39\) 0 0
\(40\) 1.00486 + 2.96426i 0.158882 + 0.468690i
\(41\) 3.06238 + 3.06238i 0.478263 + 0.478263i 0.904576 0.426313i \(-0.140188\pi\)
−0.426313 + 0.904576i \(0.640188\pi\)
\(42\) 0 0
\(43\) −2.15582 5.20462i −0.328760 0.793696i −0.998685 0.0512678i \(-0.983674\pi\)
0.669925 0.742429i \(-0.266326\pi\)
\(44\) 8.79580 + 1.55345i 1.32602 + 0.234191i
\(45\) 0 0
\(46\) 2.22184 + 0.647940i 0.327592 + 0.0955335i
\(47\) 8.66512i 1.26394i −0.774994 0.631969i \(-0.782247\pi\)
0.774994 0.631969i \(-0.217753\pi\)
\(48\) 0 0
\(49\) 6.52840i 0.932629i
\(50\) 1.49479 5.12575i 0.211395 0.724891i
\(51\) 0 0
\(52\) −3.60263 + 2.52110i −0.499595 + 0.349614i
\(53\) 2.26817 + 5.47584i 0.311557 + 0.752165i 0.999648 + 0.0265403i \(0.00844902\pi\)
−0.688091 + 0.725625i \(0.741551\pi\)
\(54\) 0 0
\(55\) 3.49455 + 3.49455i 0.471205 + 0.471205i
\(56\) 1.28009 + 1.46088i 0.171059 + 0.195218i
\(57\) 0 0
\(58\) −0.654885 5.98736i −0.0859906 0.786179i
\(59\) 7.36470 3.05056i 0.958802 0.397149i 0.152270 0.988339i \(-0.451342\pi\)
0.806532 + 0.591190i \(0.201342\pi\)
\(60\) 0 0
\(61\) −1.16848 + 2.82095i −0.149608 + 0.361186i −0.980861 0.194708i \(-0.937624\pi\)
0.831253 + 0.555894i \(0.187624\pi\)
\(62\) −8.21344 + 4.50457i −1.04311 + 0.572081i
\(63\) 0 0
\(64\) −7.93069 1.05079i −0.991336 0.131349i
\(65\) −2.43295 −0.301770
\(66\) 0 0
\(67\) −1.63065 + 3.93673i −0.199215 + 0.480948i −0.991642 0.129019i \(-0.958817\pi\)
0.792427 + 0.609967i \(0.208817\pi\)
\(68\) 7.55272 + 4.81455i 0.915901 + 0.583850i
\(69\) 0 0
\(70\) 0.116853 + 1.06834i 0.0139666 + 0.127691i
\(71\) −2.11730 + 2.11730i −0.251277 + 0.251277i −0.821494 0.570217i \(-0.806859\pi\)
0.570217 + 0.821494i \(0.306859\pi\)
\(72\) 0 0
\(73\) 6.06373 + 6.06373i 0.709706 + 0.709706i 0.966473 0.256767i \(-0.0826573\pi\)
−0.256767 + 0.966473i \(0.582657\pi\)
\(74\) −9.20765 + 11.4692i −1.07037 + 1.33327i
\(75\) 0 0
\(76\) 4.45646 3.11861i 0.511191 0.357729i
\(77\) 2.83346 + 1.17366i 0.322903 + 0.133751i
\(78\) 0 0
\(79\) 5.65785i 0.636558i 0.947997 + 0.318279i \(0.103105\pi\)
−0.947997 + 0.318279i \(0.896895\pi\)
\(80\) −3.26184 2.99224i −0.364684 0.334543i
\(81\) 0 0
\(82\) −5.87983 1.71470i −0.649319 0.189357i
\(83\) −1.59099 0.659009i −0.174634 0.0723356i 0.293654 0.955912i \(-0.405129\pi\)
−0.468287 + 0.883576i \(0.655129\pi\)
\(84\) 0 0
\(85\) 1.89650 + 4.57854i 0.205704 + 0.496613i
\(86\) 6.21256 + 4.98752i 0.669917 + 0.537818i
\(87\) 0 0
\(88\) −11.9630 + 4.05535i −1.27526 + 0.432301i
\(89\) 0.998730 0.998730i 0.105865 0.105865i −0.652190 0.758055i \(-0.726150\pi\)
0.758055 + 0.652190i \(0.226150\pi\)
\(90\) 0 0
\(91\) −1.39490 + 0.577786i −0.146225 + 0.0605685i
\(92\) −3.19565 + 0.707531i −0.333169 + 0.0737652i
\(93\) 0 0
\(94\) 5.89271 + 10.7445i 0.607787 + 1.10821i
\(95\) 3.00956 0.308774
\(96\) 0 0
\(97\) 9.78679 0.993698 0.496849 0.867837i \(-0.334490\pi\)
0.496849 + 0.867837i \(0.334490\pi\)
\(98\) −4.43963 8.09504i −0.448471 0.817723i
\(99\) 0 0
\(100\) 1.63227 + 7.37233i 0.163227 + 0.737233i
\(101\) −9.75718 + 4.04156i −0.970876 + 0.402150i −0.811038 0.584993i \(-0.801097\pi\)
−0.159838 + 0.987143i \(0.551097\pi\)
\(102\) 0 0
\(103\) −6.84442 + 6.84442i −0.674400 + 0.674400i −0.958727 0.284327i \(-0.908230\pi\)
0.284327 + 0.958727i \(0.408230\pi\)
\(104\) 2.75269 5.57607i 0.269923 0.546778i
\(105\) 0 0
\(106\) −6.53631 5.24743i −0.634863 0.509675i
\(107\) −7.22263 17.4370i −0.698238 1.68570i −0.727485 0.686123i \(-0.759311\pi\)
0.0292471 0.999572i \(-0.490689\pi\)
\(108\) 0 0
\(109\) 2.61835 + 1.08456i 0.250793 + 0.103882i 0.504539 0.863389i \(-0.331663\pi\)
−0.253746 + 0.967271i \(0.581663\pi\)
\(110\) −6.70962 1.95668i −0.639737 0.186562i
\(111\) 0 0
\(112\) −2.58074 0.940931i −0.243857 0.0889096i
\(113\) 9.73367i 0.915667i 0.889038 + 0.457833i \(0.151374\pi\)
−0.889038 + 0.457833i \(0.848626\pi\)
\(114\) 0 0
\(115\) −1.67312 0.693030i −0.156019 0.0646254i
\(116\) 4.88374 + 6.97881i 0.453444 + 0.647966i
\(117\) 0 0
\(118\) −7.05750 + 8.79097i −0.649695 + 0.809274i
\(119\) 2.17466 + 2.17466i 0.199351 + 0.199351i
\(120\) 0 0
\(121\) −6.32494 + 6.32494i −0.574994 + 0.574994i
\(122\) −0.469507 4.29252i −0.0425072 0.388627i
\(123\) 0 0
\(124\) 7.12112 11.1711i 0.639495 1.00319i
\(125\) −3.71621 + 8.97171i −0.332388 + 0.802454i
\(126\) 0 0
\(127\) 15.1424 1.34367 0.671834 0.740702i \(-0.265507\pi\)
0.671834 + 0.740702i \(0.265507\pi\)
\(128\) 10.5484 4.09031i 0.932358 0.361535i
\(129\) 0 0
\(130\) 3.01679 1.65452i 0.264590 0.145111i
\(131\) 1.28871 3.11121i 0.112595 0.271828i −0.857530 0.514434i \(-0.828002\pi\)
0.970125 + 0.242606i \(0.0780021\pi\)
\(132\) 0 0
\(133\) 1.72549 0.714722i 0.149619 0.0619743i
\(134\) −0.655213 5.99036i −0.0566018 0.517488i
\(135\) 0 0
\(136\) −12.6393 0.833690i −1.08381 0.0714884i
\(137\) −6.62181 6.62181i −0.565739 0.565739i 0.365193 0.930932i \(-0.381003\pi\)
−0.930932 + 0.365193i \(0.881003\pi\)
\(138\) 0 0
\(139\) 4.72217 + 11.4003i 0.400529 + 0.966963i 0.987538 + 0.157382i \(0.0503054\pi\)
−0.587009 + 0.809581i \(0.699695\pi\)
\(140\) −0.871420 1.24525i −0.0736485 0.105243i
\(141\) 0 0
\(142\) 1.18552 4.06525i 0.0994869 0.341149i
\(143\) 9.81875i 0.821085i
\(144\) 0 0
\(145\) 4.71297i 0.391391i
\(146\) −11.6425 3.39523i −0.963540 0.280991i
\(147\) 0 0
\(148\) 3.61759 20.4832i 0.297364 1.68371i
\(149\) 5.42967 + 13.1084i 0.444816 + 1.07388i 0.974238 + 0.225522i \(0.0724086\pi\)
−0.529423 + 0.848358i \(0.677591\pi\)
\(150\) 0 0
\(151\) 7.50713 + 7.50713i 0.610921 + 0.610921i 0.943186 0.332265i \(-0.107813\pi\)
−0.332265 + 0.943186i \(0.607813\pi\)
\(152\) −3.40508 + 6.89760i −0.276188 + 0.559469i
\(153\) 0 0
\(154\) −4.31156 + 0.471589i −0.347435 + 0.0380017i
\(155\) 6.77205 2.80507i 0.543944 0.225309i
\(156\) 0 0
\(157\) 7.85968 18.9749i 0.627270 1.51436i −0.215731 0.976453i \(-0.569213\pi\)
0.843001 0.537912i \(-0.180787\pi\)
\(158\) −3.84762 7.01558i −0.306100 0.558130i
\(159\) 0 0
\(160\) 6.07946 + 1.49209i 0.480624 + 0.117960i
\(161\) −1.12385 −0.0885716
\(162\) 0 0
\(163\) 4.90975 11.8532i 0.384561 0.928413i −0.606510 0.795076i \(-0.707431\pi\)
0.991071 0.133337i \(-0.0425692\pi\)
\(164\) 8.45691 1.87240i 0.660374 0.146210i
\(165\) 0 0
\(166\) 2.42094 0.264797i 0.187901 0.0205523i
\(167\) 6.25647 6.25647i 0.484140 0.484140i −0.422311 0.906451i \(-0.638781\pi\)
0.906451 + 0.422311i \(0.138781\pi\)
\(168\) 0 0
\(169\) −5.77443 5.77443i −0.444187 0.444187i
\(170\) −5.46524 4.38756i −0.419165 0.336511i
\(171\) 0 0
\(172\) −11.0952 1.95954i −0.845998 0.149414i
\(173\) −19.6250 8.12896i −1.49206 0.618033i −0.520300 0.853984i \(-0.674180\pi\)
−0.971765 + 0.235950i \(0.924180\pi\)
\(174\) 0 0
\(175\) 2.59270i 0.195990i
\(176\) 12.0759 13.1639i 0.910257 0.992269i
\(177\) 0 0
\(178\) −0.559212 + 1.91758i −0.0419147 + 0.143729i
\(179\) −17.6010 7.29058i −1.31556 0.544923i −0.389059 0.921213i \(-0.627200\pi\)
−0.926502 + 0.376289i \(0.877200\pi\)
\(180\) 0 0
\(181\) −5.96863 14.4095i −0.443644 1.07105i −0.974660 0.223691i \(-0.928189\pi\)
0.531016 0.847362i \(-0.321811\pi\)
\(182\) 1.33671 1.66504i 0.0990839 0.123421i
\(183\) 0 0
\(184\) 3.48136 3.05052i 0.256649 0.224887i
\(185\) 8.13794 8.13794i 0.598313 0.598313i
\(186\) 0 0
\(187\) −18.4778 + 7.65377i −1.35123 + 0.559699i
\(188\) −14.6136 9.31557i −1.06581 0.679408i
\(189\) 0 0
\(190\) −3.73177 + 2.04665i −0.270731 + 0.148479i
\(191\) −1.13157 −0.0818774 −0.0409387 0.999162i \(-0.513035\pi\)
−0.0409387 + 0.999162i \(0.513035\pi\)
\(192\) 0 0
\(193\) −24.9180 −1.79363 −0.896817 0.442401i \(-0.854127\pi\)
−0.896817 + 0.442401i \(0.854127\pi\)
\(194\) −12.1354 + 6.65550i −0.871268 + 0.477837i
\(195\) 0 0
\(196\) 11.0101 + 7.01846i 0.786432 + 0.501319i
\(197\) 13.0772 5.41675i 0.931711 0.385927i 0.135384 0.990793i \(-0.456773\pi\)
0.796327 + 0.604866i \(0.206773\pi\)
\(198\) 0 0
\(199\) 13.5340 13.5340i 0.959398 0.959398i −0.0398095 0.999207i \(-0.512675\pi\)
0.999207 + 0.0398095i \(0.0126751\pi\)
\(200\) −7.03751 8.03147i −0.497627 0.567910i
\(201\) 0 0
\(202\) 9.35018 11.6468i 0.657877 0.819465i
\(203\) 1.11926 + 2.70212i 0.0785563 + 0.189652i
\(204\) 0 0
\(205\) 4.42772 + 1.83402i 0.309246 + 0.128094i
\(206\) 3.83235 13.1414i 0.267013 0.915607i
\(207\) 0 0
\(208\) 0.378741 + 8.78614i 0.0262610 + 0.609209i
\(209\) 12.1458i 0.840143i
\(210\) 0 0
\(211\) −22.1970 9.19431i −1.52811 0.632962i −0.548910 0.835881i \(-0.684957\pi\)
−0.979196 + 0.202919i \(0.934957\pi\)
\(212\) 11.6734 + 2.06166i 0.801730 + 0.141595i
\(213\) 0 0
\(214\) 20.8139 + 16.7096i 1.42281 + 1.14225i
\(215\) −4.40808 4.40808i −0.300629 0.300629i
\(216\) 0 0
\(217\) 3.21651 3.21651i 0.218351 0.218351i
\(218\) −3.98424 + 0.435788i −0.269847 + 0.0295153i
\(219\) 0 0
\(220\) 9.65039 2.13664i 0.650629 0.144052i
\(221\) 3.76792 9.09656i 0.253458 0.611901i
\(222\) 0 0
\(223\) 11.4842 0.769038 0.384519 0.923117i \(-0.374367\pi\)
0.384519 + 0.923117i \(0.374367\pi\)
\(224\) 3.83993 0.588304i 0.256566 0.0393077i
\(225\) 0 0
\(226\) −6.61938 12.0695i −0.440314 0.802850i
\(227\) 1.61220 3.89220i 0.107006 0.258335i −0.861303 0.508092i \(-0.830351\pi\)
0.968308 + 0.249758i \(0.0803509\pi\)
\(228\) 0 0
\(229\) 5.52685 2.28930i 0.365225 0.151281i −0.192521 0.981293i \(-0.561666\pi\)
0.557746 + 0.830012i \(0.311666\pi\)
\(230\) 2.54592 0.278467i 0.167873 0.0183616i
\(231\) 0 0
\(232\) −10.8016 5.33235i −0.709163 0.350086i
\(233\) 16.1535 + 16.1535i 1.05825 + 1.05825i 0.998195 + 0.0600537i \(0.0191272\pi\)
0.0600537 + 0.998195i \(0.480873\pi\)
\(234\) 0 0
\(235\) −3.66949 8.85893i −0.239371 0.577893i
\(236\) 2.77281 15.7000i 0.180495 1.02198i
\(237\) 0 0
\(238\) −4.17540 1.21765i −0.270651 0.0789282i
\(239\) 26.7053i 1.72742i −0.503985 0.863712i \(-0.668133\pi\)
0.503985 0.863712i \(-0.331867\pi\)
\(240\) 0 0
\(241\) 14.7649i 0.951088i 0.879692 + 0.475544i \(0.157749\pi\)
−0.879692 + 0.475544i \(0.842251\pi\)
\(242\) 3.54148 12.1440i 0.227655 0.780647i
\(243\) 0 0
\(244\) 3.50130 + 5.00332i 0.224148 + 0.320305i
\(245\) 2.76464 + 6.67442i 0.176626 + 0.426413i
\(246\) 0 0
\(247\) −4.22802 4.22802i −0.269023 0.269023i
\(248\) −1.23310 + 18.6946i −0.0783018 + 1.18711i
\(249\) 0 0
\(250\) −1.49321 13.6519i −0.0944391 0.863421i
\(251\) 16.6808 6.90939i 1.05288 0.436117i 0.211961 0.977278i \(-0.432015\pi\)
0.840919 + 0.541161i \(0.182015\pi\)
\(252\) 0 0
\(253\) 2.79689 6.75229i 0.175839 0.424513i
\(254\) −18.7761 + 10.2976i −1.17812 + 0.646126i
\(255\) 0 0
\(256\) −10.2982 + 12.2453i −0.643635 + 0.765333i
\(257\) −18.9756 −1.18367 −0.591833 0.806061i \(-0.701595\pi\)
−0.591833 + 0.806061i \(0.701595\pi\)
\(258\) 0 0
\(259\) 2.73315 6.59842i 0.169830 0.410006i
\(260\) −2.61558 + 4.10313i −0.162211 + 0.254465i
\(261\) 0 0
\(262\) 0.517817 + 4.73421i 0.0319909 + 0.292480i
\(263\) −0.267788 + 0.267788i −0.0165125 + 0.0165125i −0.715315 0.698802i \(-0.753717\pi\)
0.698802 + 0.715315i \(0.253717\pi\)
\(264\) 0 0
\(265\) 4.63780 + 4.63780i 0.284898 + 0.284898i
\(266\) −1.65352 + 2.05966i −0.101384 + 0.126286i
\(267\) 0 0
\(268\) 4.88619 + 6.98231i 0.298471 + 0.426512i
\(269\) −11.2094 4.64308i −0.683449 0.283094i 0.0138189 0.999905i \(-0.495601\pi\)
−0.697268 + 0.716811i \(0.745601\pi\)
\(270\) 0 0
\(271\) 6.73779i 0.409292i 0.978836 + 0.204646i \(0.0656043\pi\)
−0.978836 + 0.204646i \(0.934396\pi\)
\(272\) 16.2393 7.56159i 0.984654 0.458489i
\(273\) 0 0
\(274\) 12.7140 + 3.70771i 0.768082 + 0.223991i
\(275\) −15.5775 6.45240i −0.939357 0.389094i
\(276\) 0 0
\(277\) −4.41073 10.6484i −0.265015 0.639803i 0.734220 0.678912i \(-0.237548\pi\)
−0.999235 + 0.0391089i \(0.987548\pi\)
\(278\) −13.6081 10.9248i −0.816162 0.655225i
\(279\) 0 0
\(280\) 1.92737 + 0.951468i 0.115182 + 0.0568611i
\(281\) −2.44614 + 2.44614i −0.145925 + 0.145925i −0.776295 0.630370i \(-0.782903\pi\)
0.630370 + 0.776295i \(0.282903\pi\)
\(282\) 0 0
\(283\) −6.00045 + 2.48547i −0.356690 + 0.147746i −0.553831 0.832629i \(-0.686834\pi\)
0.197141 + 0.980375i \(0.436834\pi\)
\(284\) 1.29456 + 5.84702i 0.0768178 + 0.346957i
\(285\) 0 0
\(286\) 6.67723 + 12.1750i 0.394833 + 0.719922i
\(287\) 2.97413 0.175557
\(288\) 0 0
\(289\) −3.05585 −0.179756
\(290\) −3.20505 5.84395i −0.188207 0.343169i
\(291\) 0 0
\(292\) 16.7453 3.70749i 0.979945 0.216964i
\(293\) −1.19634 + 0.495540i −0.0698909 + 0.0289498i −0.417355 0.908744i \(-0.637043\pi\)
0.347464 + 0.937693i \(0.387043\pi\)
\(294\) 0 0
\(295\) 6.23758 6.23758i 0.363166 0.363166i
\(296\) 9.44389 + 27.8588i 0.548915 + 1.61926i
\(297\) 0 0
\(298\) −15.6470 12.5616i −0.906405 0.727673i
\(299\) 1.37690 + 3.32412i 0.0796280 + 0.192239i
\(300\) 0 0
\(301\) −3.57417 1.48047i −0.206012 0.0853328i
\(302\) −14.4138 4.20342i −0.829424 0.241879i
\(303\) 0 0
\(304\) −0.468503 10.8685i −0.0268705 0.623349i
\(305\) 3.37887i 0.193474i
\(306\) 0 0
\(307\) −26.8795 11.1339i −1.53410 0.635444i −0.553742 0.832688i \(-0.686801\pi\)
−0.980354 + 0.197245i \(0.936801\pi\)
\(308\) 5.02551 3.51683i 0.286355 0.200390i
\(309\) 0 0
\(310\) −6.48957 + 8.08354i −0.368583 + 0.459114i
\(311\) 11.0006 + 11.0006i 0.623786 + 0.623786i 0.946497 0.322711i \(-0.104594\pi\)
−0.322711 + 0.946497i \(0.604594\pi\)
\(312\) 0 0
\(313\) −0.444422 + 0.444422i −0.0251202 + 0.0251202i −0.719555 0.694435i \(-0.755654\pi\)
0.694435 + 0.719555i \(0.255654\pi\)
\(314\) 3.15811 + 28.8734i 0.178222 + 1.62942i
\(315\) 0 0
\(316\) 9.54189 + 6.08256i 0.536773 + 0.342171i
\(317\) 7.05034 17.0210i 0.395986 0.955995i −0.592622 0.805481i \(-0.701907\pi\)
0.988608 0.150514i \(-0.0480930\pi\)
\(318\) 0 0
\(319\) −19.0203 −1.06493
\(320\) −8.55306 + 2.28418i −0.478131 + 0.127690i
\(321\) 0 0
\(322\) 1.39354 0.764272i 0.0776590 0.0425912i
\(323\) −4.66092 + 11.2525i −0.259340 + 0.626103i
\(324\) 0 0
\(325\) 7.66872 3.17649i 0.425384 0.176200i
\(326\) 1.97279 + 18.0365i 0.109263 + 0.998949i
\(327\) 0 0
\(328\) −9.21302 + 8.07284i −0.508704 + 0.445748i
\(329\) −4.20771 4.20771i −0.231979 0.231979i
\(330\) 0 0
\(331\) −9.72879 23.4874i −0.534743 1.29098i −0.928351 0.371705i \(-0.878773\pi\)
0.393608 0.919278i \(-0.371227\pi\)
\(332\) −2.82183 + 1.97470i −0.154868 + 0.108376i
\(333\) 0 0
\(334\) −3.50315 + 12.0126i −0.191684 + 0.657298i
\(335\) 4.71533i 0.257626i
\(336\) 0 0
\(337\) 29.5844i 1.61157i 0.592210 + 0.805784i \(0.298256\pi\)
−0.592210 + 0.805784i \(0.701744\pi\)
\(338\) 11.0870 + 3.23324i 0.603055 + 0.175865i
\(339\) 0 0
\(340\) 9.76051 + 1.72382i 0.529338 + 0.0934875i
\(341\) 11.3206 + 27.3302i 0.613042 + 1.48002i
\(342\) 0 0
\(343\) 6.56928 + 6.56928i 0.354708 + 0.354708i
\(344\) 15.0903 5.11548i 0.813614 0.275808i
\(345\) 0 0
\(346\) 29.8626 3.26631i 1.60542 0.175598i
\(347\) 2.09304 0.866967i 0.112360 0.0465412i −0.325795 0.945440i \(-0.605632\pi\)
0.438155 + 0.898899i \(0.355632\pi\)
\(348\) 0 0
\(349\) 1.65875 4.00459i 0.0887910 0.214361i −0.873246 0.487280i \(-0.837989\pi\)
0.962037 + 0.272919i \(0.0879892\pi\)
\(350\) −1.76317 3.21488i −0.0942453 0.171843i
\(351\) 0 0
\(352\) −6.02170 + 24.5351i −0.320958 + 1.30773i
\(353\) −35.4920 −1.88905 −0.944524 0.328444i \(-0.893476\pi\)
−0.944524 + 0.328444i \(0.893476\pi\)
\(354\) 0 0
\(355\) −1.26802 + 3.06128i −0.0672998 + 0.162476i
\(356\) −0.610643 2.75804i −0.0323640 0.146176i
\(357\) 0 0
\(358\) 26.7827 2.92944i 1.41551 0.154826i
\(359\) −20.6647 + 20.6647i −1.09064 + 1.09064i −0.0951815 + 0.995460i \(0.530343\pi\)
−0.995460 + 0.0951815i \(0.969657\pi\)
\(360\) 0 0
\(361\) −8.20496 8.20496i −0.431840 0.431840i
\(362\) 17.2001 + 13.8085i 0.904019 + 0.725757i
\(363\) 0 0
\(364\) −0.525181 + 2.97364i −0.0275269 + 0.155861i
\(365\) 8.76722 + 3.63150i 0.458897 + 0.190081i
\(366\) 0 0
\(367\) 9.73373i 0.508096i 0.967192 + 0.254048i \(0.0817622\pi\)
−0.967192 + 0.254048i \(0.918238\pi\)
\(368\) −2.24229 + 6.15006i −0.116888 + 0.320594i
\(369\) 0 0
\(370\) −4.55662 + 15.6250i −0.236888 + 0.812306i
\(371\) 3.76043 + 1.55762i 0.195232 + 0.0808676i
\(372\) 0 0
\(373\) −9.81708 23.7005i −0.508309 1.22717i −0.944856 0.327486i \(-0.893799\pi\)
0.436547 0.899681i \(-0.356201\pi\)
\(374\) 17.7071 22.0563i 0.915611 1.14050i
\(375\) 0 0
\(376\) 24.4555 + 1.61309i 1.26120 + 0.0831888i
\(377\) 6.62108 6.62108i 0.341003 0.341003i
\(378\) 0 0
\(379\) 7.55314 3.12861i 0.387979 0.160706i −0.180163 0.983637i \(-0.557663\pi\)
0.568142 + 0.822931i \(0.307663\pi\)
\(380\) 3.23547 5.07558i 0.165976 0.260372i
\(381\) 0 0
\(382\) 1.40311 0.769522i 0.0717895 0.0393722i
\(383\) −37.2848 −1.90516 −0.952582 0.304283i \(-0.901583\pi\)
−0.952582 + 0.304283i \(0.901583\pi\)
\(384\) 0 0
\(385\) 3.39385 0.172967
\(386\) 30.8976 16.9454i 1.57265 0.862501i
\(387\) 0 0
\(388\) 10.5214 16.5053i 0.534145 0.837929i
\(389\) 18.9989 7.86962i 0.963284 0.399005i 0.155076 0.987903i \(-0.450438\pi\)
0.808208 + 0.588897i \(0.200438\pi\)
\(390\) 0 0
\(391\) 5.18234 5.18234i 0.262082 0.262082i
\(392\) −18.4251 1.21532i −0.930606 0.0613830i
\(393\) 0 0
\(394\) −12.5317 + 15.6098i −0.631338 + 0.786408i
\(395\) 2.39598 + 5.78440i 0.120555 + 0.291045i
\(396\) 0 0
\(397\) −0.456018 0.188889i −0.0228869 0.00948006i 0.371211 0.928549i \(-0.378943\pi\)
−0.394098 + 0.919069i \(0.628943\pi\)
\(398\) −7.57799 + 25.9855i −0.379850 + 1.30254i
\(399\) 0 0
\(400\) 14.1881 + 5.17294i 0.709406 + 0.258647i
\(401\) 34.6938i 1.73252i 0.499590 + 0.866262i \(0.333484\pi\)
−0.499590 + 0.866262i \(0.666516\pi\)
\(402\) 0 0
\(403\) −13.4546 5.57306i −0.670219 0.277614i
\(404\) −3.67358 + 20.8003i −0.182768 + 1.03485i
\(405\) 0 0
\(406\) −3.22542 2.58941i −0.160075 0.128510i
\(407\) 32.8426 + 32.8426i 1.62795 + 1.62795i
\(408\) 0 0
\(409\) −26.3301 + 26.3301i −1.30194 + 1.30194i −0.374860 + 0.927081i \(0.622309\pi\)
−0.927081 + 0.374860i \(0.877691\pi\)
\(410\) −6.73748 + 0.736931i −0.332741 + 0.0363944i
\(411\) 0 0
\(412\) 4.18481 + 18.9012i 0.206171 + 0.931196i
\(413\) 2.09491 5.05756i 0.103084 0.248866i
\(414\) 0 0
\(415\) −1.90565 −0.0935447
\(416\) −6.44464 10.6370i −0.315974 0.521522i
\(417\) 0 0
\(418\) −8.25975 15.0605i −0.403997 0.736632i
\(419\) −2.41226 + 5.82370i −0.117846 + 0.284506i −0.971785 0.235867i \(-0.924207\pi\)
0.853939 + 0.520373i \(0.174207\pi\)
\(420\) 0 0
\(421\) −29.8254 + 12.3541i −1.45360 + 0.602101i −0.963053 0.269314i \(-0.913203\pi\)
−0.490547 + 0.871414i \(0.663203\pi\)
\(422\) 33.7763 3.69438i 1.64420 0.179839i
\(423\) 0 0
\(424\) −15.8767 + 5.38206i −0.771040 + 0.261376i
\(425\) −11.9556 11.9556i −0.579933 0.579933i
\(426\) 0 0
\(427\) 0.802428 + 1.93723i 0.0388322 + 0.0937493i
\(428\) −37.1720 6.56503i −1.79678 0.317333i
\(429\) 0 0
\(430\) 8.46362 + 2.46819i 0.408152 + 0.119027i
\(431\) 34.6034i 1.66679i −0.552680 0.833394i \(-0.686395\pi\)
0.552680 0.833394i \(-0.313605\pi\)
\(432\) 0 0
\(433\) 15.1909i 0.730027i −0.931002 0.365013i \(-0.881064\pi\)
0.931002 0.365013i \(-0.118936\pi\)
\(434\) −1.80100 + 6.17577i −0.0864507 + 0.296446i
\(435\) 0 0
\(436\) 4.64400 3.24985i 0.222407 0.155639i
\(437\) −1.70322 4.11195i −0.0814762 0.196701i
\(438\) 0 0
\(439\) 25.6561 + 25.6561i 1.22450 + 1.22450i 0.966015 + 0.258486i \(0.0832235\pi\)
0.258486 + 0.966015i \(0.416776\pi\)
\(440\) −10.5132 + 9.21211i −0.501197 + 0.439170i
\(441\) 0 0
\(442\) 1.51399 + 13.8419i 0.0720133 + 0.658390i
\(443\) 32.9101 13.6318i 1.56361 0.647667i 0.577896 0.816110i \(-0.303874\pi\)
0.985711 + 0.168443i \(0.0538739\pi\)
\(444\) 0 0
\(445\) 0.598128 1.44401i 0.0283540 0.0684526i
\(446\) −14.2401 + 7.80981i −0.674287 + 0.369805i
\(447\) 0 0
\(448\) −4.36134 + 3.34082i −0.206054 + 0.157839i
\(449\) 27.6838 1.30648 0.653240 0.757151i \(-0.273409\pi\)
0.653240 + 0.757151i \(0.273409\pi\)
\(450\) 0 0
\(451\) −7.40164 + 17.8691i −0.348530 + 0.841425i
\(452\) 16.4157 + 10.4643i 0.772129 + 0.492201i
\(453\) 0 0
\(454\) 0.647802 + 5.92260i 0.0304028 + 0.277962i
\(455\) −1.18142 + 1.18142i −0.0553858 + 0.0553858i
\(456\) 0 0
\(457\) −1.63136 1.63136i −0.0763119 0.0763119i 0.667921 0.744233i \(-0.267185\pi\)
−0.744233 + 0.667921i \(0.767185\pi\)
\(458\) −5.29631 + 6.59720i −0.247481 + 0.308267i
\(459\) 0 0
\(460\) −2.96750 + 2.07664i −0.138360 + 0.0968240i
\(461\) −9.64566 3.99536i −0.449243 0.186083i 0.146579 0.989199i \(-0.453174\pi\)
−0.595822 + 0.803116i \(0.703174\pi\)
\(462\) 0 0
\(463\) 27.9841i 1.30053i −0.759707 0.650266i \(-0.774658\pi\)
0.759707 0.650266i \(-0.225342\pi\)
\(464\) 17.0200 0.733675i 0.790134 0.0340600i
\(465\) 0 0
\(466\) −31.0150 9.04471i −1.43674 0.418988i
\(467\) −0.710835 0.294438i −0.0328935 0.0136250i 0.366176 0.930546i \(-0.380667\pi\)
−0.399070 + 0.916921i \(0.630667\pi\)
\(468\) 0 0
\(469\) 1.11982 + 2.70347i 0.0517083 + 0.124835i
\(470\) 10.5746 + 8.48940i 0.487769 + 0.391587i
\(471\) 0 0
\(472\) 7.23857 + 21.3532i 0.333182 + 0.982862i
\(473\) 17.7899 17.7899i 0.817980 0.817980i
\(474\) 0 0
\(475\) −9.48622 + 3.92932i −0.435258 + 0.180290i
\(476\) 6.00544 1.32963i 0.275259 0.0609436i
\(477\) 0 0
\(478\) 18.1609 + 33.1139i 0.830662 + 1.51459i
\(479\) 39.4950 1.80457 0.902285 0.431139i \(-0.141888\pi\)
0.902285 + 0.431139i \(0.141888\pi\)
\(480\) 0 0
\(481\) −22.8654 −1.04257
\(482\) −10.0408 18.3080i −0.457347 0.833908i
\(483\) 0 0
\(484\) 3.86719 + 17.4666i 0.175781 + 0.793938i
\(485\) 10.0057 4.14449i 0.454335 0.188192i
\(486\) 0 0
\(487\) 1.03654 1.03654i 0.0469700 0.0469700i −0.683232 0.730202i \(-0.739426\pi\)
0.730202 + 0.683232i \(0.239426\pi\)
\(488\) −7.74403 3.82293i −0.350556 0.173056i
\(489\) 0 0
\(490\) −7.96701 6.39601i −0.359913 0.288942i
\(491\) 8.81350 + 21.2777i 0.397748 + 0.960248i 0.988199 + 0.153174i \(0.0489497\pi\)
−0.590452 + 0.807073i \(0.701050\pi\)
\(492\) 0 0
\(493\) −17.6213 7.29900i −0.793625 0.328730i
\(494\) 8.11790 + 2.36737i 0.365242 + 0.106513i
\(495\) 0 0
\(496\) −11.1842 24.0193i −0.502186 1.07850i
\(497\) 2.05628i 0.0922369i
\(498\) 0 0
\(499\) 31.2067 + 12.9263i 1.39701 + 0.578659i 0.948973 0.315359i \(-0.102125\pi\)
0.448033 + 0.894017i \(0.352125\pi\)
\(500\) 11.1355 + 15.9125i 0.497995 + 0.711629i
\(501\) 0 0
\(502\) −15.9850 + 19.9112i −0.713443 + 0.888680i
\(503\) −1.63550 1.63550i −0.0729233 0.0729233i 0.669704 0.742628i \(-0.266421\pi\)
−0.742628 + 0.669704i \(0.766421\pi\)
\(504\) 0 0
\(505\) −8.26391 + 8.26391i −0.367739 + 0.367739i
\(506\) 1.12382 + 10.2747i 0.0499600 + 0.456765i
\(507\) 0 0
\(508\) 16.2790 25.5374i 0.722266 1.13304i
\(509\) −7.48659 + 18.0742i −0.331837 + 0.801126i 0.666609 + 0.745407i \(0.267745\pi\)
−0.998447 + 0.0557188i \(0.982255\pi\)
\(510\) 0 0
\(511\) 5.88900 0.260514
\(512\) 4.44201 22.1871i 0.196311 0.980542i
\(513\) 0 0
\(514\) 23.5292 12.9043i 1.03783 0.569186i
\(515\) −4.09904 + 9.89597i −0.180626 + 0.436069i
\(516\) 0 0
\(517\) 35.7524 14.8091i 1.57239 0.651304i
\(518\) 1.09821 + 10.0405i 0.0482527 + 0.441156i
\(519\) 0 0
\(520\) 0.452915 6.86649i 0.0198617 0.301116i
\(521\) 3.96008 + 3.96008i 0.173494 + 0.173494i 0.788513 0.615018i \(-0.210851\pi\)
−0.615018 + 0.788513i \(0.710851\pi\)
\(522\) 0 0
\(523\) −8.21965 19.8440i −0.359420 0.867717i −0.995382 0.0959961i \(-0.969396\pi\)
0.635962 0.771721i \(-0.280604\pi\)
\(524\) −3.86157 5.51815i −0.168694 0.241061i
\(525\) 0 0
\(526\) 0.149941 0.514158i 0.00653772 0.0224184i
\(527\) 29.6643i 1.29220i
\(528\) 0 0
\(529\) 20.3218i 0.883557i
\(530\) −8.90468 2.59681i −0.386795 0.112798i
\(531\) 0 0
\(532\) 0.649649 3.67839i 0.0281659 0.159479i
\(533\) −3.64380 8.79691i −0.157830 0.381036i
\(534\) 0 0
\(535\) −14.7684 14.7684i −0.638492 0.638492i
\(536\) −10.8071 5.33503i −0.466794 0.230438i
\(537\) 0 0
\(538\) 17.0569 1.86564i 0.735374 0.0804336i
\(539\) −26.9363 + 11.1574i −1.16023 + 0.480582i
\(540\) 0 0
\(541\) 6.31469 15.2450i 0.271490 0.655435i −0.728058 0.685516i \(-0.759577\pi\)
0.999547 + 0.0300814i \(0.00957665\pi\)
\(542\) −4.58203 8.35468i −0.196815 0.358864i
\(543\) 0 0
\(544\) −14.9941 + 20.4197i −0.642866 + 0.875488i
\(545\) 3.13621 0.134340
\(546\) 0 0
\(547\) 1.21894 2.94279i 0.0521182 0.125825i −0.895676 0.444707i \(-0.853308\pi\)
0.947794 + 0.318883i \(0.103308\pi\)
\(548\) −18.2865 + 4.04871i −0.781159 + 0.172952i
\(549\) 0 0
\(550\) 23.7036 2.59265i 1.01072 0.110551i
\(551\) −8.19029 + 8.19029i −0.348918 + 0.348918i
\(552\) 0 0
\(553\) 2.74741 + 2.74741i 0.116832 + 0.116832i
\(554\) 12.7106 + 10.2043i 0.540024 + 0.433538i
\(555\) 0 0
\(556\) 24.3031 + 4.29223i 1.03068 + 0.182031i
\(557\) −30.1821 12.5018i −1.27886 0.529719i −0.363211 0.931707i \(-0.618319\pi\)
−0.915645 + 0.401988i \(0.868319\pi\)
\(558\) 0 0
\(559\) 12.3855i 0.523852i
\(560\) −3.03693 + 0.130912i −0.128334 + 0.00553204i
\(561\) 0 0
\(562\) 1.36965 4.69665i 0.0577753 0.198116i
\(563\) −35.5009 14.7050i −1.49618 0.619740i −0.523532 0.852006i \(-0.675386\pi\)
−0.972652 + 0.232266i \(0.925386\pi\)
\(564\) 0 0
\(565\) 4.12200 + 9.95138i 0.173414 + 0.418658i
\(566\) 5.75016 7.16252i 0.241697 0.301063i
\(567\) 0 0
\(568\) −5.58148 6.36978i −0.234194 0.267270i
\(569\) 25.8368 25.8368i 1.08313 1.08313i 0.0869193 0.996215i \(-0.472298\pi\)
0.996215 0.0869193i \(-0.0277022\pi\)
\(570\) 0 0
\(571\) −2.57652 + 1.06723i −0.107824 + 0.0446621i −0.435943 0.899974i \(-0.643585\pi\)
0.328119 + 0.944636i \(0.393585\pi\)
\(572\) −16.5592 10.5558i −0.692374 0.441360i
\(573\) 0 0
\(574\) −3.68784 + 2.02256i −0.153928 + 0.0844198i
\(575\) 6.17856 0.257664
\(576\) 0 0
\(577\) 13.8404 0.576184 0.288092 0.957603i \(-0.406979\pi\)
0.288092 + 0.957603i \(0.406979\pi\)
\(578\) 3.78917 2.07813i 0.157609 0.0864387i
\(579\) 0 0
\(580\) 7.94835 + 5.06675i 0.330037 + 0.210385i
\(581\) −1.09258 + 0.452562i −0.0453279 + 0.0187754i
\(582\) 0 0
\(583\) −18.7170 + 18.7170i −0.775178 + 0.775178i
\(584\) −18.2425 + 15.9848i −0.754878 + 0.661456i
\(585\) 0 0
\(586\) 1.14644 1.42803i 0.0473589 0.0589912i
\(587\) 16.7762 + 40.5013i 0.692427 + 1.67167i 0.739832 + 0.672791i \(0.234905\pi\)
−0.0474052 + 0.998876i \(0.515095\pi\)
\(588\) 0 0
\(589\) 16.6433 + 6.89388i 0.685776 + 0.284058i
\(590\) −3.49257 + 11.9763i −0.143787 + 0.493056i
\(591\) 0 0
\(592\) −30.6555 28.1218i −1.25993 1.15580i
\(593\) 14.3003i 0.587243i −0.955922 0.293621i \(-0.905139\pi\)
0.955922 0.293621i \(-0.0948605\pi\)
\(594\) 0 0
\(595\) 3.14423 + 1.30238i 0.128901 + 0.0533924i
\(596\) 27.9443 + 4.93531i 1.14464 + 0.202158i
\(597\) 0 0
\(598\) −3.96788 3.18547i −0.162259 0.130263i
\(599\) 5.98650 + 5.98650i 0.244602 + 0.244602i 0.818751 0.574149i \(-0.194667\pi\)
−0.574149 + 0.818751i \(0.694667\pi\)
\(600\) 0 0
\(601\) 14.6645 14.6645i 0.598179 0.598179i −0.341649 0.939828i \(-0.610985\pi\)
0.939828 + 0.341649i \(0.110985\pi\)
\(602\) 5.43867 0.594870i 0.221663 0.0242451i
\(603\) 0 0
\(604\) 20.7313 4.59001i 0.843545 0.186765i
\(605\) −3.78794 + 9.14489i −0.154001 + 0.371792i
\(606\) 0 0
\(607\) −5.96144 −0.241967 −0.120984 0.992654i \(-0.538605\pi\)
−0.120984 + 0.992654i \(0.538605\pi\)
\(608\) 7.97202 + 13.1580i 0.323308 + 0.533627i
\(609\) 0 0
\(610\) −2.29780 4.18971i −0.0930352 0.169636i
\(611\) −7.29047 + 17.6007i −0.294941 + 0.712050i
\(612\) 0 0
\(613\) −5.23798 + 2.16964i −0.211560 + 0.0876310i −0.485947 0.873988i \(-0.661525\pi\)
0.274387 + 0.961619i \(0.411525\pi\)
\(614\) 40.9015 4.47372i 1.65065 0.180544i
\(615\) 0 0
\(616\) −3.83988 + 7.77837i −0.154713 + 0.313399i
\(617\) −9.39267 9.39267i −0.378135 0.378135i 0.492294 0.870429i \(-0.336158\pi\)
−0.870429 + 0.492294i \(0.836158\pi\)
\(618\) 0 0
\(619\) −7.90970 19.0957i −0.317918 0.767521i −0.999364 0.0356533i \(-0.988649\pi\)
0.681447 0.731868i \(-0.261351\pi\)
\(620\) 2.54968 14.4366i 0.102398 0.579788i
\(621\) 0 0
\(622\) −21.1214 6.15949i −0.846890 0.246973i
\(623\) 0.969950i 0.0388602i
\(624\) 0 0
\(625\) 8.13104i 0.325242i
\(626\) 0.248843 0.853301i 0.00994575 0.0341048i
\(627\) 0 0
\(628\) −23.5513 33.6545i −0.939799 1.34296i
\(629\) 17.8237 + 43.0302i 0.710678 + 1.71573i
\(630\) 0 0
\(631\) −7.71198 7.71198i −0.307009 0.307009i 0.536739 0.843748i \(-0.319656\pi\)
−0.843748 + 0.536739i \(0.819656\pi\)
\(632\) −15.9681 1.05326i −0.635178 0.0418965i
\(633\) 0 0
\(634\) 2.83291 + 25.9002i 0.112509 + 1.02863i
\(635\) 15.4811 6.41247i 0.614347 0.254471i
\(636\) 0 0
\(637\) 5.49272 13.2606i 0.217630 0.525404i
\(638\) 23.5847 12.9348i 0.933727 0.512092i
\(639\) 0 0
\(640\) 9.05221 8.64883i 0.357820 0.341875i
\(641\) 12.0769 0.477008 0.238504 0.971141i \(-0.423343\pi\)
0.238504 + 0.971141i \(0.423343\pi\)
\(642\) 0 0
\(643\) −4.69996 + 11.3467i −0.185348 + 0.447470i −0.989054 0.147557i \(-0.952859\pi\)
0.803705 + 0.595028i \(0.202859\pi\)
\(644\) −1.20821 + 1.89535i −0.0476101 + 0.0746873i
\(645\) 0 0
\(646\) −1.87281 17.1224i −0.0736847 0.673671i
\(647\) −25.6699 + 25.6699i −1.00919 + 1.00919i −0.00923049 + 0.999957i \(0.502938\pi\)
−0.999957 + 0.00923049i \(0.997062\pi\)
\(648\) 0 0
\(649\) 25.1733 + 25.1733i 0.988137 + 0.988137i
\(650\) −7.34884 + 9.15387i −0.288245 + 0.359044i
\(651\) 0 0
\(652\) −14.7119 21.0232i −0.576163 0.823331i
\(653\) −44.9438 18.6163i −1.75879 0.728513i −0.996712 0.0810226i \(-0.974181\pi\)
−0.762074 0.647490i \(-0.775819\pi\)
\(654\) 0 0
\(655\) 3.72654i 0.145608i
\(656\) 5.93396 16.2754i 0.231682 0.635448i
\(657\) 0 0
\(658\) 8.07890 + 2.35600i 0.314948 + 0.0918464i
\(659\) −19.3749 8.02536i −0.754740 0.312623i −0.0280660 0.999606i \(-0.508935\pi\)
−0.726674 + 0.686983i \(0.758935\pi\)
\(660\) 0 0
\(661\) −2.55430 6.16663i −0.0993509 0.239854i 0.866387 0.499373i \(-0.166436\pi\)
−0.965738 + 0.259518i \(0.916436\pi\)
\(662\) 28.0360 + 22.5077i 1.08965 + 0.874785i
\(663\) 0 0
\(664\) 2.15609 4.36756i 0.0836727 0.169494i
\(665\) 1.46142 1.46142i 0.0566713 0.0566713i
\(666\) 0 0
\(667\) 6.43931 2.66725i 0.249331 0.103276i
\(668\) −3.82533 17.2776i −0.148006 0.668489i
\(669\) 0 0
\(670\) −3.20666 5.84688i −0.123884 0.225885i
\(671\) −13.6363 −0.526422
\(672\) 0 0
\(673\) −5.63737 −0.217305 −0.108652 0.994080i \(-0.534654\pi\)
−0.108652 + 0.994080i \(0.534654\pi\)
\(674\) −20.1189 36.6839i −0.774950 1.41301i
\(675\) 0 0
\(676\) −15.9464 + 3.53060i −0.613322 + 0.135792i
\(677\) −0.110383 + 0.0457221i −0.00424236 + 0.00175724i −0.384804 0.922998i \(-0.625731\pi\)
0.380561 + 0.924756i \(0.375731\pi\)
\(678\) 0 0
\(679\) 4.75239 4.75239i 0.182380 0.182380i
\(680\) −13.2750 + 4.50013i −0.509075 + 0.172572i
\(681\) 0 0
\(682\) −32.6231 26.1902i −1.24920 1.00288i
\(683\) −10.5093 25.3717i −0.402127 0.970820i −0.987149 0.159803i \(-0.948914\pi\)
0.585022 0.811017i \(-0.301086\pi\)
\(684\) 0 0
\(685\) −9.57412 3.96573i −0.365808 0.151523i
\(686\) −12.6132 3.67830i −0.481573 0.140438i
\(687\) 0 0
\(688\) −15.2328 + 16.6052i −0.580744 + 0.633067i
\(689\) 13.0310i 0.496440i
\(690\) 0 0
\(691\) −35.2220 14.5894i −1.33991 0.555008i −0.406443 0.913676i \(-0.633231\pi\)
−0.933465 + 0.358668i \(0.883231\pi\)
\(692\) −34.8076 + 24.3582i −1.32319 + 0.925959i
\(693\) 0 0
\(694\) −2.00574 + 2.49839i −0.0761367 + 0.0948375i
\(695\) 9.65558 + 9.65558i 0.366257 + 0.366257i
\(696\) 0 0
\(697\) −13.7145 + 13.7145i −0.519473 + 0.519473i
\(698\) 0.666506 + 6.09361i 0.0252276 + 0.230647i
\(699\) 0 0
\(700\) 4.37256 + 2.78733i 0.165267 + 0.105351i
\(701\) 14.7113 35.5162i 0.555638 1.34143i −0.357552 0.933893i \(-0.616388\pi\)
0.913190 0.407535i \(-0.133612\pi\)
\(702\) 0 0
\(703\) 28.2845 1.06677
\(704\) −9.21836 34.5180i −0.347430 1.30094i
\(705\) 0 0
\(706\) 44.0091 24.1363i 1.65630 0.908381i
\(707\) −2.77546 + 6.70056i −0.104382 + 0.252000i
\(708\) 0 0
\(709\) 12.3798 5.12787i 0.464932 0.192581i −0.137905 0.990445i \(-0.544037\pi\)
0.602837 + 0.797864i \(0.294037\pi\)
\(710\) −0.509507 4.65823i −0.0191214 0.174820i
\(711\) 0 0
\(712\) 2.63279 + 3.00463i 0.0986678 + 0.112603i
\(713\) −7.66512 7.66512i −0.287061 0.287061i
\(714\) 0 0
\(715\) −4.15803 10.0384i −0.155501 0.375414i
\(716\) −31.2177 + 21.8460i −1.16666 + 0.816423i
\(717\) 0 0
\(718\) 11.5707 39.6767i 0.431813 1.48072i
\(719\) 32.5496i 1.21390i −0.794741 0.606948i \(-0.792393\pi\)
0.794741 0.606948i \(-0.207607\pi\)
\(720\) 0 0
\(721\) 6.64719i 0.247554i
\(722\) 15.7537 + 4.59415i 0.586292 + 0.170977i
\(723\) 0 0
\(724\) −30.7181 5.42520i −1.14163 0.201626i
\(725\) −6.15332 14.8554i −0.228528 0.551716i
\(726\) 0 0
\(727\) 7.49561 + 7.49561i 0.277997 + 0.277997i 0.832309 0.554312i \(-0.187019\pi\)
−0.554312 + 0.832309i \(0.687019\pi\)
\(728\) −1.37101 4.04438i −0.0508130 0.149895i
\(729\) 0 0
\(730\) −13.3407 + 1.45918i −0.493762 + 0.0540066i
\(731\) 23.3082 9.65458i 0.862086 0.357088i
\(732\) 0 0
\(733\) 6.16287 14.8785i 0.227631 0.549550i −0.768257 0.640141i \(-0.778876\pi\)
0.995888 + 0.0905917i \(0.0288758\pi\)
\(734\) −6.61942 12.0696i −0.244327 0.445496i
\(735\) 0 0
\(736\) −1.40196 9.15077i −0.0516770 0.337302i
\(737\) −19.0299 −0.700974
\(738\) 0 0
\(739\) −1.76773 + 4.26769i −0.0650272 + 0.156989i −0.953053 0.302805i \(-0.902077\pi\)
0.888025 + 0.459794i \(0.152077\pi\)
\(740\) −4.97570 22.4733i −0.182910 0.826136i
\(741\) 0 0
\(742\) −5.72209 + 0.625870i −0.210065 + 0.0229764i
\(743\) −9.36119 + 9.36119i −0.343429 + 0.343429i −0.857655 0.514226i \(-0.828079\pi\)
0.514226 + 0.857655i \(0.328079\pi\)
\(744\) 0 0
\(745\) 11.1022 + 11.1022i 0.406754 + 0.406754i
\(746\) 28.2904 + 22.7119i 1.03579 + 0.831542i
\(747\) 0 0
\(748\) −6.95691 + 39.3909i −0.254370 + 1.44027i
\(749\) −11.9745 4.96000i −0.437539 0.181235i
\(750\) 0 0
\(751\) 1.39834i 0.0510263i 0.999674 + 0.0255131i \(0.00812196\pi\)
−0.999674 + 0.0255131i \(0.991878\pi\)
\(752\) −31.4212 + 14.6308i −1.14581 + 0.533529i
\(753\) 0 0
\(754\) −3.70730 + 12.7126i −0.135012 + 0.462967i
\(755\) 10.8541 + 4.49593i 0.395023 + 0.163624i
\(756\) 0 0
\(757\) 8.78917 + 21.2189i 0.319448 + 0.771216i 0.999283 + 0.0378509i \(0.0120512\pi\)
−0.679835 + 0.733365i \(0.737949\pi\)
\(758\) −7.23808 + 9.01590i −0.262899 + 0.327472i
\(759\) 0 0
\(760\) −0.560257 + 8.49386i −0.0203227 + 0.308105i
\(761\) 29.1747 29.1747i 1.05758 1.05758i 0.0593461 0.998237i \(-0.481098\pi\)
0.998237 0.0593461i \(-0.0189015\pi\)
\(762\) 0 0
\(763\) 1.79810 0.744799i 0.0650958 0.0269635i
\(764\) −1.21651 + 1.90837i −0.0440118 + 0.0690425i
\(765\) 0 0
\(766\) 46.2321 25.3555i 1.67043 0.916131i
\(767\) −17.5259 −0.632824
\(768\) 0 0
\(769\) 32.4734 1.17102 0.585509 0.810666i \(-0.300894\pi\)
0.585509 + 0.810666i \(0.300894\pi\)
\(770\) −4.20829 + 2.30799i −0.151656 + 0.0831741i
\(771\) 0 0
\(772\) −26.7885 + 42.0238i −0.964138 + 1.51247i
\(773\) 46.7641 19.3703i 1.68199 0.696702i 0.682570 0.730820i \(-0.260862\pi\)
0.999418 + 0.0341178i \(0.0108621\pi\)
\(774\) 0 0
\(775\) −17.6834 + 17.6834i −0.635205 + 0.635205i
\(776\) −1.82190 + 27.6212i −0.0654024 + 0.991543i
\(777\) 0 0
\(778\) −18.2064 + 22.6783i −0.652732 + 0.813057i
\(779\) 4.50738 + 10.8818i 0.161494 + 0.389880i
\(780\) 0 0
\(781\) −12.3545 5.11742i −0.442080 0.183116i
\(782\) −2.90172 + 9.95022i −0.103765 + 0.355819i
\(783\) 0 0
\(784\) 23.6731 11.0230i 0.845467 0.393678i
\(785\) 22.7278i 0.811188i
\(786\) 0 0
\(787\) 50.0612 + 20.7360i 1.78449 + 0.739160i 0.991529 + 0.129886i \(0.0414612\pi\)
0.792960 + 0.609273i \(0.208539\pi\)
\(788\) 4.92357 27.8779i 0.175395 0.993108i