Properties

Label 756.2.ck.a.5.16
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.16
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.727904 - 1.57167i) q^{3} +(-0.591212 + 3.35293i) q^{5} +(-1.25160 - 2.33098i) q^{7} +(-1.94031 - 2.28805i) q^{9} +O(q^{10})\) \(q+(0.727904 - 1.57167i) q^{3} +(-0.591212 + 3.35293i) q^{5} +(-1.25160 - 2.33098i) q^{7} +(-1.94031 - 2.28805i) q^{9} +(-5.13559 + 0.905544i) q^{11} +(2.56808 - 3.06052i) q^{13} +(4.83937 + 3.36980i) q^{15} -3.67787 q^{17} -7.57664i q^{19} +(-4.57459 + 0.270382i) q^{21} +(3.17546 - 3.78437i) q^{23} +(-6.19416 - 2.25449i) q^{25} +(-5.00843 + 1.38405i) q^{27} +(-5.50806 - 6.56425i) q^{29} +(-1.36807 - 3.75873i) q^{31} +(-2.31500 + 8.73062i) q^{33} +(8.55559 - 2.81844i) q^{35} +(3.11270 + 5.39136i) q^{37} +(-2.94082 - 6.26394i) q^{39} +(3.29135 + 2.76177i) q^{41} +(8.46720 + 3.08181i) q^{43} +(8.81882 - 5.15301i) q^{45} +(0.0867629 + 0.0315791i) q^{47} +(-3.86697 + 5.83494i) q^{49} +(-2.67714 + 5.78041i) q^{51} +(-0.822872 + 0.475085i) q^{53} -17.7547i q^{55} +(-11.9080 - 5.51507i) q^{57} +(0.157848 + 0.132450i) q^{59} +(-3.75967 + 10.3296i) q^{61} +(-2.90491 + 7.38658i) q^{63} +(8.74342 + 10.4200i) q^{65} +(0.114606 - 0.649962i) q^{67} +(-3.63636 - 7.74545i) q^{69} +(-4.63188 - 2.67422i) q^{71} +(-8.35033 - 4.82106i) q^{73} +(-8.05207 + 8.09414i) q^{75} +(8.53854 + 10.8376i) q^{77} +(-0.401358 - 2.27621i) q^{79} +(-1.47037 + 8.87908i) q^{81} +(-5.15096 + 4.32216i) q^{83} +(2.17440 - 12.3317i) q^{85} +(-14.3262 + 3.87873i) q^{87} +1.57358 q^{89} +(-10.3482 - 2.15559i) q^{91} +(-6.90332 - 0.585841i) q^{93} +(25.4040 + 4.47941i) q^{95} +(-1.25237 + 3.44085i) q^{97} +(12.0366 + 9.99347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) 0.727904 1.57167i 0.420255 0.907406i
\(4\) 0 0
\(5\) −0.591212 + 3.35293i −0.264398 + 1.49948i 0.506345 + 0.862331i \(0.330996\pi\)
−0.770743 + 0.637146i \(0.780115\pi\)
\(6\) 0 0
\(7\) −1.25160 2.33098i −0.473062 0.881029i
\(8\) 0 0
\(9\) −1.94031 2.28805i −0.646771 0.762684i
\(10\) 0 0
\(11\) −5.13559 + 0.905544i −1.54844 + 0.273032i −0.881538 0.472114i \(-0.843491\pi\)
−0.666902 + 0.745146i \(0.732380\pi\)
\(12\) 0 0
\(13\) 2.56808 3.06052i 0.712256 0.848834i −0.281598 0.959533i \(-0.590864\pi\)
0.993854 + 0.110698i \(0.0353088\pi\)
\(14\) 0 0
\(15\) 4.83937 + 3.36980i 1.24952 + 0.870080i
\(16\) 0 0
\(17\) −3.67787 −0.892015 −0.446008 0.895029i \(-0.647155\pi\)
−0.446008 + 0.895029i \(0.647155\pi\)
\(18\) 0 0
\(19\) 7.57664i 1.73820i −0.494635 0.869101i \(-0.664698\pi\)
0.494635 0.869101i \(-0.335302\pi\)
\(20\) 0 0
\(21\) −4.57459 + 0.270382i −0.998258 + 0.0590022i
\(22\) 0 0
\(23\) 3.17546 3.78437i 0.662130 0.789096i −0.325560 0.945521i \(-0.605553\pi\)
0.987690 + 0.156426i \(0.0499972\pi\)
\(24\) 0 0
\(25\) −6.19416 2.25449i −1.23883 0.450898i
\(26\) 0 0
\(27\) −5.00843 + 1.38405i −0.963873 + 0.266361i
\(28\) 0 0
\(29\) −5.50806 6.56425i −1.02282 1.21895i −0.975484 0.220072i \(-0.929371\pi\)
−0.0473381 0.998879i \(-0.515074\pi\)
\(30\) 0 0
\(31\) −1.36807 3.75873i −0.245712 0.675088i −0.999832 0.0183509i \(-0.994158\pi\)
0.754120 0.656737i \(-0.228064\pi\)
\(32\) 0 0
\(33\) −2.31500 + 8.73062i −0.402989 + 1.51981i
\(34\) 0 0
\(35\) 8.55559 2.81844i 1.44616 0.476403i
\(36\) 0 0
\(37\) 3.11270 + 5.39136i 0.511725 + 0.886334i 0.999908 + 0.0135926i \(0.00432679\pi\)
−0.488182 + 0.872742i \(0.662340\pi\)
\(38\) 0 0
\(39\) −2.94082 6.26394i −0.470908 1.00303i
\(40\) 0 0
\(41\) 3.29135 + 2.76177i 0.514022 + 0.431315i 0.862542 0.505986i \(-0.168871\pi\)
−0.348520 + 0.937301i \(0.613316\pi\)
\(42\) 0 0
\(43\) 8.46720 + 3.08181i 1.29124 + 0.469971i 0.894132 0.447803i \(-0.147793\pi\)
0.397103 + 0.917774i \(0.370015\pi\)
\(44\) 0 0
\(45\) 8.81882 5.15301i 1.31463 0.768165i
\(46\) 0 0
\(47\) 0.0867629 + 0.0315791i 0.0126557 + 0.00460629i 0.348340 0.937368i \(-0.386745\pi\)
−0.335685 + 0.941974i \(0.608968\pi\)
\(48\) 0 0
\(49\) −3.86697 + 5.83494i −0.552424 + 0.833563i
\(50\) 0 0
\(51\) −2.67714 + 5.78041i −0.374874 + 0.809420i
\(52\) 0 0
\(53\) −0.822872 + 0.475085i −0.113030 + 0.0652580i −0.555449 0.831550i \(-0.687454\pi\)
0.442419 + 0.896808i \(0.354120\pi\)
\(54\) 0 0
\(55\) 17.7547i 2.39404i
\(56\) 0 0
\(57\) −11.9080 5.51507i −1.57725 0.730488i
\(58\) 0 0
\(59\) 0.157848 + 0.132450i 0.0205500 + 0.0172435i 0.653005 0.757354i \(-0.273508\pi\)
−0.632455 + 0.774597i \(0.717953\pi\)
\(60\) 0 0
\(61\) −3.75967 + 10.3296i −0.481376 + 1.32257i 0.426938 + 0.904281i \(0.359592\pi\)
−0.908314 + 0.418289i \(0.862630\pi\)
\(62\) 0 0
\(63\) −2.90491 + 7.38658i −0.365984 + 0.930621i
\(64\) 0 0
\(65\) 8.74342 + 10.4200i 1.08449 + 1.29244i
\(66\) 0 0
\(67\) 0.114606 0.649962i 0.0140013 0.0794055i −0.977006 0.213210i \(-0.931608\pi\)
0.991008 + 0.133804i \(0.0427193\pi\)
\(68\) 0 0
\(69\) −3.63636 7.74545i −0.437766 0.932442i
\(70\) 0 0
\(71\) −4.63188 2.67422i −0.549703 0.317371i 0.199299 0.979939i \(-0.436133\pi\)
−0.749002 + 0.662568i \(0.769467\pi\)
\(72\) 0 0
\(73\) −8.35033 4.82106i −0.977332 0.564263i −0.0758684 0.997118i \(-0.524173\pi\)
−0.901464 + 0.432855i \(0.857506\pi\)
\(74\) 0 0
\(75\) −8.05207 + 8.09414i −0.929773 + 0.934631i
\(76\) 0 0
\(77\) 8.53854 + 10.8376i 0.973057 + 1.23506i
\(78\) 0 0
\(79\) −0.401358 2.27621i −0.0451563 0.256094i 0.953870 0.300221i \(-0.0970605\pi\)
−0.999026 + 0.0441271i \(0.985949\pi\)
\(80\) 0 0
\(81\) −1.47037 + 8.87908i −0.163375 + 0.986564i
\(82\) 0 0
\(83\) −5.15096 + 4.32216i −0.565391 + 0.474419i −0.880113 0.474765i \(-0.842533\pi\)
0.314722 + 0.949184i \(0.398089\pi\)
\(84\) 0 0
\(85\) 2.17440 12.3317i 0.235847 1.33756i
\(86\) 0 0
\(87\) −14.3262 + 3.87873i −1.53593 + 0.415844i
\(88\) 0 0
\(89\) 1.57358 0.166799 0.0833997 0.996516i \(-0.473422\pi\)
0.0833997 + 0.996516i \(0.473422\pi\)
\(90\) 0 0
\(91\) −10.3482 2.15559i −1.08479 0.225967i
\(92\) 0 0
\(93\) −6.90332 0.585841i −0.715840 0.0607489i
\(94\) 0 0
\(95\) 25.4040 + 4.47941i 2.60639 + 0.459577i
\(96\) 0 0
\(97\) −1.25237 + 3.44085i −0.127159 + 0.349365i −0.986893 0.161376i \(-0.948407\pi\)
0.859734 + 0.510741i \(0.170629\pi\)
\(98\) 0 0
\(99\) 12.0366 + 9.99347i 1.20972 + 1.00438i
\(100\) 0 0
\(101\) 1.45113 1.21764i 0.144393 0.121160i −0.567730 0.823215i \(-0.692178\pi\)
0.712123 + 0.702055i \(0.247734\pi\)
\(102\) 0 0
\(103\) −5.01468 0.884223i −0.494111 0.0871251i −0.0789603 0.996878i \(-0.525160\pi\)
−0.415151 + 0.909753i \(0.636271\pi\)
\(104\) 0 0
\(105\) 1.79798 15.4981i 0.175465 1.51246i
\(106\) 0 0
\(107\) 5.57533 + 3.21892i 0.538987 + 0.311184i 0.744668 0.667435i \(-0.232608\pi\)
−0.205681 + 0.978619i \(0.565941\pi\)
\(108\) 0 0
\(109\) −1.33104 2.30543i −0.127491 0.220820i 0.795213 0.606330i \(-0.207359\pi\)
−0.922704 + 0.385510i \(0.874026\pi\)
\(110\) 0 0
\(111\) 10.7392 0.967761i 1.01932 0.0918558i
\(112\) 0 0
\(113\) −1.42760 3.92229i −0.134297 0.368978i 0.854256 0.519853i \(-0.174013\pi\)
−0.988553 + 0.150875i \(0.951791\pi\)
\(114\) 0 0
\(115\) 10.8114 + 12.8845i 1.00816 + 1.20148i
\(116\) 0 0
\(117\) −11.9855 + 0.0624590i −1.10806 + 0.00577434i
\(118\) 0 0
\(119\) 4.60324 + 8.57306i 0.421979 + 0.785891i
\(120\) 0 0
\(121\) 15.2177 5.53878i 1.38343 0.503526i
\(122\) 0 0
\(123\) 6.73638 3.16262i 0.607399 0.285164i
\(124\) 0 0
\(125\) 2.70957 4.69311i 0.242351 0.419765i
\(126\) 0 0
\(127\) −1.14708 1.98680i −0.101787 0.176300i 0.810634 0.585553i \(-0.199123\pi\)
−0.912421 + 0.409253i \(0.865789\pi\)
\(128\) 0 0
\(129\) 11.0069 11.0644i 0.969104 0.974167i
\(130\) 0 0
\(131\) 14.4895 + 12.1582i 1.26596 + 1.06226i 0.995021 + 0.0996665i \(0.0317776\pi\)
0.270936 + 0.962597i \(0.412667\pi\)
\(132\) 0 0
\(133\) −17.6610 + 9.48296i −1.53141 + 0.822277i
\(134\) 0 0
\(135\) −1.67959 17.6112i −0.144556 1.51573i
\(136\) 0 0
\(137\) 6.88509 18.9166i 0.588233 1.61616i −0.185499 0.982644i \(-0.559390\pi\)
0.773732 0.633513i \(-0.218388\pi\)
\(138\) 0 0
\(139\) 8.88650 + 1.56693i 0.753743 + 0.132905i 0.537302 0.843390i \(-0.319444\pi\)
0.216442 + 0.976296i \(0.430555\pi\)
\(140\) 0 0
\(141\) 0.112787 0.113376i 0.00949838 0.00954801i
\(142\) 0 0
\(143\) −10.4172 + 18.0431i −0.871127 + 1.50884i
\(144\) 0 0
\(145\) 25.2659 14.5873i 2.09822 1.21141i
\(146\) 0 0
\(147\) 6.35584 + 10.3249i 0.524221 + 0.851582i
\(148\) 0 0
\(149\) −5.94231 16.3264i −0.486813 1.33751i −0.903551 0.428482i \(-0.859049\pi\)
0.416737 0.909027i \(-0.363174\pi\)
\(150\) 0 0
\(151\) −3.04228 17.2537i −0.247578 1.40408i −0.814430 0.580262i \(-0.802950\pi\)
0.566852 0.823820i \(-0.308161\pi\)
\(152\) 0 0
\(153\) 7.13622 + 8.41517i 0.576930 + 0.680326i
\(154\) 0 0
\(155\) 13.4116 2.36482i 1.07724 0.189947i
\(156\) 0 0
\(157\) −11.4237 + 13.6142i −0.911709 + 1.08653i 0.0842255 + 0.996447i \(0.473158\pi\)
−0.995934 + 0.0900852i \(0.971286\pi\)
\(158\) 0 0
\(159\) 0.147707 + 1.63910i 0.0117139 + 0.129989i
\(160\) 0 0
\(161\) −12.7957 2.66542i −1.00844 0.210064i
\(162\) 0 0
\(163\) 1.26841 2.19695i 0.0993497 0.172079i −0.812066 0.583566i \(-0.801657\pi\)
0.911416 + 0.411487i \(0.134990\pi\)
\(164\) 0 0
\(165\) −27.9045 12.9237i −2.17236 1.00611i
\(166\) 0 0
\(167\) −9.64872 + 3.51185i −0.746640 + 0.271755i −0.687191 0.726477i \(-0.741157\pi\)
−0.0594489 + 0.998231i \(0.518934\pi\)
\(168\) 0 0
\(169\) −0.514306 2.91678i −0.0395620 0.224367i
\(170\) 0 0
\(171\) −17.3358 + 14.7011i −1.32570 + 1.12422i
\(172\) 0 0
\(173\) 17.4211 14.6180i 1.32450 1.11139i 0.339170 0.940725i \(-0.389854\pi\)
0.985330 0.170662i \(-0.0545905\pi\)
\(174\) 0 0
\(175\) 2.49746 + 17.2602i 0.188790 + 1.30475i
\(176\) 0 0
\(177\) 0.323066 0.151674i 0.0242831 0.0114005i
\(178\) 0 0
\(179\) 8.20144i 0.613004i −0.951870 0.306502i \(-0.900841\pi\)
0.951870 0.306502i \(-0.0991586\pi\)
\(180\) 0 0
\(181\) 18.4566 10.6559i 1.37187 0.792050i 0.380708 0.924695i \(-0.375680\pi\)
0.991164 + 0.132645i \(0.0423471\pi\)
\(182\) 0 0
\(183\) 13.4981 + 13.4279i 0.997807 + 0.992621i
\(184\) 0 0
\(185\) −19.9171 + 7.24924i −1.46434 + 0.532975i
\(186\) 0 0
\(187\) 18.8881 3.33047i 1.38123 0.243548i
\(188\) 0 0
\(189\) 9.49479 + 9.94228i 0.690644 + 0.723195i
\(190\) 0 0
\(191\) 22.4547 3.95937i 1.62477 0.286490i 0.714228 0.699913i \(-0.246778\pi\)
0.910539 + 0.413423i \(0.135667\pi\)
\(192\) 0 0
\(193\) 18.1474 6.60512i 1.30628 0.475447i 0.407243 0.913320i \(-0.366490\pi\)
0.899037 + 0.437873i \(0.144268\pi\)
\(194\) 0 0
\(195\) 22.7412 6.15704i 1.62853 0.440915i
\(196\) 0 0
\(197\) −1.31379 + 0.758514i −0.0936033 + 0.0540419i −0.546071 0.837739i \(-0.683877\pi\)
0.452468 + 0.891781i \(0.350544\pi\)
\(198\) 0 0
\(199\) 10.5673i 0.749099i 0.927207 + 0.374549i \(0.122203\pi\)
−0.927207 + 0.374549i \(0.877797\pi\)
\(200\) 0 0
\(201\) −0.938106 0.653233i −0.0661689 0.0460755i
\(202\) 0 0
\(203\) −8.40725 + 21.0551i −0.590073 + 1.47778i
\(204\) 0 0
\(205\) −11.2059 + 9.40287i −0.782654 + 0.656725i
\(206\) 0 0
\(207\) −14.8202 + 0.0772315i −1.03008 + 0.00536796i
\(208\) 0 0
\(209\) 6.86098 + 38.9106i 0.474584 + 2.69150i
\(210\) 0 0
\(211\) 11.7963 4.29351i 0.812093 0.295578i 0.0976050 0.995225i \(-0.468882\pi\)
0.714488 + 0.699647i \(0.246660\pi\)
\(212\) 0 0
\(213\) −7.57456 + 5.33323i −0.519000 + 0.365427i
\(214\) 0 0
\(215\) −15.3390 + 26.5679i −1.04611 + 1.81192i
\(216\) 0 0
\(217\) −7.04926 + 7.89338i −0.478535 + 0.535838i
\(218\) 0 0
\(219\) −13.6554 + 9.61472i −0.922744 + 0.649702i
\(220\) 0 0
\(221\) −9.44506 + 11.2562i −0.635344 + 0.757173i
\(222\) 0 0
\(223\) −17.7911 + 3.13705i −1.19138 + 0.210073i −0.733970 0.679182i \(-0.762335\pi\)
−0.457412 + 0.889255i \(0.651223\pi\)
\(224\) 0 0
\(225\) 6.86021 + 18.5470i 0.457347 + 1.23646i
\(226\) 0 0
\(227\) −4.22816 23.9791i −0.280633 1.59155i −0.720481 0.693474i \(-0.756079\pi\)
0.439849 0.898072i \(-0.355032\pi\)
\(228\) 0 0
\(229\) 3.04053 + 8.35380i 0.200924 + 0.552034i 0.998703 0.0509157i \(-0.0162140\pi\)
−0.797779 + 0.602950i \(0.793992\pi\)
\(230\) 0 0
\(231\) 23.2484 5.53106i 1.52963 0.363917i
\(232\) 0 0
\(233\) −3.32605 + 1.92030i −0.217897 + 0.125803i −0.604976 0.796244i \(-0.706817\pi\)
0.387079 + 0.922046i \(0.373484\pi\)
\(234\) 0 0
\(235\) −0.157178 + 0.272240i −0.0102532 + 0.0177590i
\(236\) 0 0
\(237\) −3.86961 1.02606i −0.251358 0.0666498i
\(238\) 0 0
\(239\) 3.15316 + 0.555987i 0.203961 + 0.0359638i 0.274695 0.961531i \(-0.411423\pi\)
−0.0707342 + 0.997495i \(0.522534\pi\)
\(240\) 0 0
\(241\) −0.279960 + 0.769183i −0.0180338 + 0.0495474i −0.948383 0.317128i \(-0.897282\pi\)
0.930349 + 0.366675i \(0.119504\pi\)
\(242\) 0 0
\(243\) 12.8847 + 8.77406i 0.826555 + 0.562856i
\(244\) 0 0
\(245\) −17.2780 16.4154i −1.10385 1.04874i
\(246\) 0 0
\(247\) −23.1884 19.4574i −1.47544 1.23805i
\(248\) 0 0
\(249\) 3.04363 + 11.2417i 0.192882 + 0.712416i
\(250\) 0 0
\(251\) −1.58268 2.74129i −0.0998981 0.173029i 0.811744 0.584013i \(-0.198518\pi\)
−0.911642 + 0.410985i \(0.865185\pi\)
\(252\) 0 0
\(253\) −12.8810 + 22.3105i −0.809820 + 1.40265i
\(254\) 0 0
\(255\) −17.7986 12.3937i −1.11459 0.776124i
\(256\) 0 0
\(257\) −7.10354 + 2.58548i −0.443107 + 0.161278i −0.553931 0.832562i \(-0.686873\pi\)
0.110825 + 0.993840i \(0.464651\pi\)
\(258\) 0 0
\(259\) 8.67130 14.0035i 0.538808 0.870136i
\(260\) 0 0
\(261\) −4.33200 + 25.3394i −0.268144 + 1.56847i
\(262\) 0 0
\(263\) −11.3794 13.5615i −0.701686 0.836237i 0.291030 0.956714i \(-0.406002\pi\)
−0.992716 + 0.120477i \(0.961558\pi\)
\(264\) 0 0
\(265\) −1.10644 3.03991i −0.0679678 0.186740i
\(266\) 0 0
\(267\) 1.14542 2.47316i 0.0700983 0.151355i
\(268\) 0 0
\(269\) 4.49490 + 7.78539i 0.274059 + 0.474683i 0.969897 0.243515i \(-0.0783004\pi\)
−0.695839 + 0.718198i \(0.744967\pi\)
\(270\) 0 0
\(271\) −28.2099 16.2870i −1.71363 0.989364i −0.929545 0.368708i \(-0.879800\pi\)
−0.784083 0.620656i \(-0.786866\pi\)
\(272\) 0 0
\(273\) −10.9204 + 14.6950i −0.660932 + 0.889380i
\(274\) 0 0
\(275\) 33.8522 + 5.96906i 2.04136 + 0.359948i
\(276\) 0 0
\(277\) 22.9194 19.2317i 1.37709 1.15552i 0.406819 0.913509i \(-0.366638\pi\)
0.970274 0.242009i \(-0.0778064\pi\)
\(278\) 0 0
\(279\) −5.94570 + 10.4233i −0.355960 + 0.624028i
\(280\) 0 0
\(281\) −4.56329 + 12.5375i −0.272223 + 0.747926i 0.725964 + 0.687733i \(0.241394\pi\)
−0.998187 + 0.0601934i \(0.980828\pi\)
\(282\) 0 0
\(283\) 15.2606 + 2.69085i 0.907148 + 0.159955i 0.607708 0.794160i \(-0.292089\pi\)
0.299440 + 0.954115i \(0.403200\pi\)
\(284\) 0 0
\(285\) 25.5318 36.6662i 1.51237 2.17192i
\(286\) 0 0
\(287\) 2.31817 11.1287i 0.136837 0.656907i
\(288\) 0 0
\(289\) −3.47325 −0.204309
\(290\) 0 0
\(291\) 4.49629 + 4.47292i 0.263577 + 0.262207i
\(292\) 0 0
\(293\) 1.97923 11.2248i 0.115628 0.655760i −0.870809 0.491621i \(-0.836405\pi\)
0.986437 0.164138i \(-0.0524844\pi\)
\(294\) 0 0
\(295\) −0.537417 + 0.450946i −0.0312896 + 0.0262551i
\(296\) 0 0
\(297\) 24.4679 11.6433i 1.41977 0.675612i
\(298\) 0 0
\(299\) −3.42729 19.4371i −0.198205 1.12408i
\(300\) 0 0
\(301\) −3.41394 23.5941i −0.196776 1.35994i
\(302\) 0 0
\(303\) −0.857453 3.16703i −0.0492594 0.181941i
\(304\) 0 0
\(305\) −32.4117 18.7129i −1.85589 1.07150i
\(306\) 0 0
\(307\) −2.53824 1.46546i −0.144865 0.0836380i 0.425815 0.904810i \(-0.359987\pi\)
−0.570681 + 0.821172i \(0.693321\pi\)
\(308\) 0 0
\(309\) −5.03991 + 7.23781i −0.286711 + 0.411744i
\(310\) 0 0
\(311\) 1.51071 8.56764i 0.0856643 0.485826i −0.911547 0.411196i \(-0.865111\pi\)
0.997211 0.0746305i \(-0.0237777\pi\)
\(312\) 0 0
\(313\) 3.79403 + 4.52155i 0.214451 + 0.255573i 0.862537 0.505995i \(-0.168874\pi\)
−0.648085 + 0.761568i \(0.724430\pi\)
\(314\) 0 0
\(315\) −23.0493 14.1070i −1.29868 0.794839i
\(316\) 0 0
\(317\) 11.6009 31.8731i 0.651569 1.79017i 0.0396997 0.999212i \(-0.487360\pi\)
0.611869 0.790959i \(-0.290418\pi\)
\(318\) 0 0
\(319\) 34.2314 + 28.7235i 1.91659 + 1.60821i
\(320\) 0 0
\(321\) 9.11738 6.41953i 0.508883 0.358303i
\(322\) 0 0
\(323\) 27.8659i 1.55050i
\(324\) 0 0
\(325\) −22.8070 + 13.1676i −1.26510 + 0.730408i
\(326\) 0 0
\(327\) −4.59225 + 0.413830i −0.253952 + 0.0228848i
\(328\) 0 0
\(329\) −0.0349825 0.241767i −0.00192865 0.0133291i
\(330\) 0 0
\(331\) −23.4513 8.53558i −1.28900 0.469158i −0.395601 0.918422i \(-0.629464\pi\)
−0.893399 + 0.449265i \(0.851686\pi\)
\(332\) 0 0
\(333\) 6.29610 17.5830i 0.345024 0.963540i
\(334\) 0 0
\(335\) 2.11152 + 0.768531i 0.115365 + 0.0419894i
\(336\) 0 0
\(337\) 14.2082 + 11.9221i 0.773968 + 0.649436i 0.941722 0.336393i \(-0.109207\pi\)
−0.167754 + 0.985829i \(0.553651\pi\)
\(338\) 0 0
\(339\) −7.20371 0.611333i −0.391252 0.0332031i
\(340\) 0 0
\(341\) 10.4295 + 18.0645i 0.564790 + 0.978246i
\(342\) 0 0
\(343\) 18.4411 + 1.71081i 0.995724 + 0.0923748i
\(344\) 0 0
\(345\) 28.1198 7.61327i 1.51392 0.409885i
\(346\) 0 0
\(347\) 8.00581 + 21.9958i 0.429774 + 1.18080i 0.945950 + 0.324313i \(0.105133\pi\)
−0.516175 + 0.856483i \(0.672645\pi\)
\(348\) 0 0
\(349\) −14.0653 16.7624i −0.752899 0.897270i 0.244478 0.969655i \(-0.421383\pi\)
−0.997377 + 0.0723850i \(0.976939\pi\)
\(350\) 0 0
\(351\) −8.62612 + 18.8827i −0.460428 + 1.00789i
\(352\) 0 0
\(353\) −21.2118 7.72046i −1.12899 0.410919i −0.291064 0.956703i \(-0.594009\pi\)
−0.837925 + 0.545785i \(0.816232\pi\)
\(354\) 0 0
\(355\) 11.7049 13.9493i 0.621231 0.740354i
\(356\) 0 0
\(357\) 16.8248 0.994431i 0.890461 0.0526309i
\(358\) 0 0
\(359\) 26.0175i 1.37315i −0.727057 0.686577i \(-0.759113\pi\)
0.727057 0.686577i \(-0.240887\pi\)
\(360\) 0 0
\(361\) −38.4055 −2.02134
\(362\) 0 0
\(363\) 2.37185 27.9489i 0.124490 1.46694i
\(364\) 0 0
\(365\) 21.1015 25.1478i 1.10450 1.31630i
\(366\) 0 0
\(367\) −20.7174 + 3.65303i −1.08144 + 0.190687i −0.685852 0.727741i \(-0.740570\pi\)
−0.395587 + 0.918428i \(0.629459\pi\)
\(368\) 0 0
\(369\) −0.0671698 12.8895i −0.00349672 0.670999i
\(370\) 0 0
\(371\) 2.13733 + 1.32348i 0.110964 + 0.0687117i
\(372\) 0 0
\(373\) 1.91950 10.8860i 0.0993881 0.563658i −0.893926 0.448215i \(-0.852060\pi\)
0.993314 0.115443i \(-0.0368288\pi\)
\(374\) 0 0
\(375\) −5.40373 7.67469i −0.279047 0.396319i
\(376\) 0 0
\(377\) −34.2351 −1.76320
\(378\) 0 0
\(379\) 18.1091 0.930203 0.465102 0.885257i \(-0.346018\pi\)
0.465102 + 0.885257i \(0.346018\pi\)
\(380\) 0 0
\(381\) −3.95757 + 0.356635i −0.202752 + 0.0182710i
\(382\) 0 0
\(383\) 0.256321 1.45367i 0.0130974 0.0742791i −0.977558 0.210664i \(-0.932437\pi\)
0.990656 + 0.136385i \(0.0435485\pi\)
\(384\) 0 0
\(385\) −41.3858 + 22.2218i −2.10922 + 1.13253i
\(386\) 0 0
\(387\) −9.37767 25.3531i −0.476694 1.28877i
\(388\) 0 0
\(389\) −11.7473 + 2.07137i −0.595614 + 0.105023i −0.463325 0.886189i \(-0.653344\pi\)
−0.132289 + 0.991211i \(0.542233\pi\)
\(390\) 0 0
\(391\) −11.6790 + 13.9184i −0.590630 + 0.703886i
\(392\) 0 0
\(393\) 29.6557 13.9228i 1.49593 0.702315i
\(394\) 0 0
\(395\) 7.86928 0.395946
\(396\) 0 0
\(397\) 6.36679i 0.319540i 0.987154 + 0.159770i \(0.0510753\pi\)
−0.987154 + 0.159770i \(0.948925\pi\)
\(398\) 0 0
\(399\) 2.04859 + 34.6601i 0.102558 + 1.73517i
\(400\) 0 0
\(401\) −16.3873 + 19.5296i −0.818341 + 0.975261i −0.999967 0.00810645i \(-0.997420\pi\)
0.181626 + 0.983368i \(0.441864\pi\)
\(402\) 0 0
\(403\) −15.0170 5.46572i −0.748048 0.272267i
\(404\) 0 0
\(405\) −28.9016 10.1795i −1.43613 0.505823i
\(406\) 0 0
\(407\) −20.8677 24.8691i −1.03437 1.23272i
\(408\) 0 0
\(409\) 6.72474 + 18.4761i 0.332517 + 0.913583i 0.987455 + 0.157901i \(0.0504726\pi\)
−0.654938 + 0.755683i \(0.727305\pi\)
\(410\) 0 0
\(411\) −24.7191 24.5906i −1.21930 1.21296i
\(412\) 0 0
\(413\) 0.111176 0.533715i 0.00547060 0.0262624i
\(414\) 0 0
\(415\) −11.4466 19.8261i −0.561892 0.973226i
\(416\) 0 0
\(417\) 8.93122 12.8261i 0.437364 0.628097i
\(418\) 0 0
\(419\) −5.01894 4.21139i −0.245191 0.205740i 0.511907 0.859041i \(-0.328939\pi\)
−0.757098 + 0.653301i \(0.773384\pi\)
\(420\) 0 0
\(421\) 27.0755 + 9.85467i 1.31958 + 0.480287i 0.903323 0.428960i \(-0.141120\pi\)
0.416255 + 0.909248i \(0.363342\pi\)
\(422\) 0 0
\(423\) −0.0960924 0.259791i −0.00467217 0.0126315i
\(424\) 0 0
\(425\) 22.7813 + 8.29172i 1.10506 + 0.402208i
\(426\) 0 0
\(427\) 28.7838 4.16486i 1.39294 0.201552i
\(428\) 0 0
\(429\) 20.7751 + 29.5060i 1.00303 + 1.42456i
\(430\) 0 0
\(431\) 30.0524 17.3507i 1.44757 0.835756i 0.449236 0.893413i \(-0.351696\pi\)
0.998336 + 0.0576573i \(0.0183631\pi\)
\(432\) 0 0
\(433\) 22.3944i 1.07620i 0.842880 + 0.538102i \(0.180859\pi\)
−0.842880 + 0.538102i \(0.819141\pi\)
\(434\) 0 0
\(435\) −4.53529 50.3279i −0.217451 2.41304i
\(436\) 0 0
\(437\) −28.6728 24.0594i −1.37161 1.15092i
\(438\) 0 0
\(439\) −9.41439 + 25.8658i −0.449324 + 1.23451i 0.483871 + 0.875139i \(0.339230\pi\)
−0.933195 + 0.359369i \(0.882992\pi\)
\(440\) 0 0
\(441\) 20.8538 2.47378i 0.993037 0.117799i
\(442\) 0 0
\(443\) −3.01473 3.59281i −0.143234 0.170700i 0.689658 0.724135i \(-0.257761\pi\)
−0.832892 + 0.553436i \(0.813316\pi\)
\(444\) 0 0
\(445\) −0.930321 + 5.27611i −0.0441014 + 0.250112i
\(446\) 0 0
\(447\) −29.9852 2.54465i −1.41825 0.120358i
\(448\) 0 0
\(449\) 1.49280 + 0.861866i 0.0704494 + 0.0406740i 0.534811 0.844972i \(-0.320383\pi\)
−0.464362 + 0.885646i \(0.653716\pi\)
\(450\) 0 0
\(451\) −19.4039 11.2029i −0.913694 0.527522i
\(452\) 0 0
\(453\) −29.3316 7.77752i −1.37812 0.365420i
\(454\) 0 0
\(455\) 13.3455 33.4225i 0.625649 1.56687i
\(456\) 0 0
\(457\) 1.98772 + 11.2729i 0.0929815 + 0.527324i 0.995347 + 0.0963531i \(0.0307178\pi\)
−0.902366 + 0.430971i \(0.858171\pi\)
\(458\) 0 0
\(459\) 18.4204 5.09038i 0.859790 0.237599i
\(460\) 0 0
\(461\) 0.965463 0.810120i 0.0449661 0.0377310i −0.620028 0.784580i \(-0.712879\pi\)
0.664994 + 0.746849i \(0.268434\pi\)
\(462\) 0 0
\(463\) −6.39773 + 36.2833i −0.297328 + 1.68623i 0.360261 + 0.932851i \(0.382687\pi\)
−0.657589 + 0.753377i \(0.728424\pi\)
\(464\) 0 0
\(465\) 6.04561 22.8000i 0.280358 1.05732i
\(466\) 0 0
\(467\) −20.3672 −0.942483 −0.471242 0.882004i \(-0.656194\pi\)
−0.471242 + 0.882004i \(0.656194\pi\)
\(468\) 0 0
\(469\) −1.65849 + 0.546351i −0.0765821 + 0.0252282i
\(470\) 0 0
\(471\) 13.0817 + 27.8641i 0.602775 + 1.28391i
\(472\) 0 0
\(473\) −46.2748 8.15950i −2.12772 0.375174i
\(474\) 0 0
\(475\) −17.0815 + 46.9309i −0.783751 + 2.15334i
\(476\) 0 0
\(477\) 2.68365 + 0.960960i 0.122876 + 0.0439993i
\(478\) 0 0
\(479\) 21.7978 18.2905i 0.995968 0.835716i 0.00954704 0.999954i \(-0.496961\pi\)
0.986421 + 0.164238i \(0.0525166\pi\)
\(480\) 0 0
\(481\) 24.4940 + 4.31895i 1.11683 + 0.196927i
\(482\) 0 0
\(483\) −13.5032 + 18.1705i −0.614418 + 0.826788i
\(484\) 0 0
\(485\) −10.7965 6.23337i −0.490245 0.283043i
\(486\) 0 0
\(487\) 0.199066 + 0.344792i 0.00902053 + 0.0156240i 0.870500 0.492168i \(-0.163795\pi\)
−0.861480 + 0.507792i \(0.830462\pi\)
\(488\) 0 0
\(489\) −2.52961 3.59270i −0.114393 0.162468i
\(490\) 0 0
\(491\) 5.68427 + 15.6174i 0.256528 + 0.704804i 0.999375 + 0.0353434i \(0.0112525\pi\)
−0.742848 + 0.669461i \(0.766525\pi\)
\(492\) 0 0
\(493\) 20.2580 + 24.1425i 0.912373 + 1.08732i
\(494\) 0 0
\(495\) −40.6236 + 34.4496i −1.82590 + 1.54839i
\(496\) 0 0
\(497\) −0.436273 + 14.1439i −0.0195695 + 0.634441i
\(498\) 0 0
\(499\) −12.1474 + 4.42128i −0.543791 + 0.197924i −0.599286 0.800535i \(-0.704549\pi\)
0.0554945 + 0.998459i \(0.482326\pi\)
\(500\) 0 0
\(501\) −1.50386 + 17.7209i −0.0671876 + 0.791712i
\(502\) 0 0
\(503\) −13.1104 + 22.7079i −0.584565 + 1.01250i 0.410365 + 0.911921i \(0.365401\pi\)
−0.994930 + 0.100574i \(0.967932\pi\)
\(504\) 0 0
\(505\) 3.22474 + 5.58542i 0.143499 + 0.248548i
\(506\) 0 0
\(507\) −4.95858 1.31481i −0.220218 0.0583928i
\(508\) 0 0
\(509\) 8.78538 + 7.37181i 0.389405 + 0.326750i 0.816381 0.577513i \(-0.195977\pi\)
−0.426976 + 0.904263i \(0.640421\pi\)
\(510\) 0 0
\(511\) −0.786511 + 25.4985i −0.0347932 + 1.12799i
\(512\) 0 0
\(513\) 10.4865 + 37.9471i 0.462990 + 1.67541i
\(514\) 0 0
\(515\) 5.92948 16.2911i 0.261284 0.717872i
\(516\) 0 0
\(517\) −0.474175 0.0836099i −0.0208542 0.00367716i
\(518\) 0 0
\(519\) −10.2939 38.0207i −0.451851 1.66892i
\(520\) 0 0
\(521\) −3.75886 + 6.51053i −0.164679 + 0.285232i −0.936541 0.350558i \(-0.885992\pi\)
0.771863 + 0.635789i \(0.219325\pi\)
\(522\) 0 0
\(523\) 30.3709 17.5346i 1.32803 0.766736i 0.343031 0.939324i \(-0.388546\pi\)
0.984994 + 0.172588i \(0.0552129\pi\)
\(524\) 0 0
\(525\) 28.9453 + 8.63858i 1.26328 + 0.377018i
\(526\) 0 0
\(527\) 5.03157 + 13.8241i 0.219179 + 0.602189i
\(528\) 0 0
\(529\) −0.243980 1.38368i −0.0106078 0.0601600i
\(530\) 0 0
\(531\) −0.00322136 0.618158i −0.000139795 0.0268258i
\(532\) 0 0
\(533\) 16.9049 2.98078i 0.732231 0.129112i
\(534\) 0 0
\(535\) −14.0890 + 16.7906i −0.609121 + 0.725922i
\(536\) 0 0
\(537\) −12.8900 5.96986i −0.556244 0.257618i
\(538\) 0 0
\(539\) 14.5754 33.4676i 0.627807 1.44155i
\(540\) 0 0
\(541\) 9.21190 15.9555i 0.396050 0.685979i −0.597184 0.802104i \(-0.703714\pi\)
0.993235 + 0.116125i \(0.0370472\pi\)
\(542\) 0 0
\(543\) −3.31301 36.7643i −0.142175 1.57771i
\(544\) 0 0
\(545\) 8.51688 3.09989i 0.364823 0.132785i
\(546\) 0 0
\(547\) −2.17800 12.3520i −0.0931245 0.528135i −0.995306 0.0967786i \(-0.969146\pi\)
0.902181 0.431357i \(-0.141965\pi\)
\(548\) 0 0
\(549\) 30.9296 11.4403i 1.32004 0.488262i
\(550\) 0 0
\(551\) −49.7350 + 41.7326i −2.11878 + 1.77787i
\(552\) 0 0
\(553\) −4.80348 + 3.78448i −0.204265 + 0.160932i
\(554\) 0 0
\(555\) −3.10431 + 36.5800i −0.131771 + 1.55273i
\(556\) 0 0
\(557\) 12.2848i 0.520524i 0.965538 + 0.260262i \(0.0838089\pi\)
−0.965538 + 0.260262i \(0.916191\pi\)
\(558\) 0 0
\(559\) 31.1763 17.9997i 1.31862 0.761305i
\(560\) 0 0
\(561\) 8.51427 32.1101i 0.359473 1.35569i
\(562\) 0 0
\(563\) −27.3440 + 9.95240i −1.15241 + 0.419444i −0.846381 0.532578i \(-0.821223\pi\)
−0.306031 + 0.952022i \(0.599001\pi\)
\(564\) 0 0
\(565\) 13.9952 2.46773i 0.588781 0.103818i
\(566\) 0 0
\(567\) 22.5373 7.68568i 0.946478 0.322768i
\(568\) 0 0
\(569\) 13.2725 2.34030i 0.556412 0.0981104i 0.111631 0.993750i \(-0.464393\pi\)
0.444781 + 0.895639i \(0.353282\pi\)
\(570\) 0 0
\(571\) 12.8860 4.69011i 0.539261 0.196275i −0.0580075 0.998316i \(-0.518475\pi\)
0.597269 + 0.802041i \(0.296253\pi\)
\(572\) 0 0
\(573\) 10.1220 38.1735i 0.422854 1.59472i
\(574\) 0 0
\(575\) −28.2011 + 16.2819i −1.17607 + 0.679004i
\(576\) 0 0
\(577\) 32.2107i 1.34095i −0.741932 0.670476i \(-0.766090\pi\)
0.741932 0.670476i \(-0.233910\pi\)
\(578\) 0 0
\(579\) 2.82848 33.3297i 0.117548 1.38514i
\(580\) 0 0
\(581\) 16.5219 + 6.59715i 0.685442 + 0.273696i
\(582\) 0 0
\(583\) 3.79572 3.18499i 0.157203 0.131909i
\(584\) 0 0
\(585\) 6.87655 40.2235i 0.284310 1.66304i
\(586\) 0 0
\(587\) −4.81253 27.2932i −0.198634 1.12651i −0.907147 0.420813i \(-0.861745\pi\)
0.708513 0.705698i \(-0.249366\pi\)
\(588\) 0 0
\(589\) −28.4786 + 10.3653i −1.17344 + 0.427097i
\(590\) 0 0
\(591\) 0.235827 + 2.61697i 0.00970064 + 0.107648i
\(592\) 0 0
\(593\) −9.73131 + 16.8551i −0.399617 + 0.692157i −0.993679 0.112262i \(-0.964190\pi\)
0.594061 + 0.804420i \(0.297524\pi\)
\(594\) 0 0
\(595\) −31.4664 + 10.3659i −1.29000 + 0.424959i
\(596\) 0 0
\(597\) 16.6084 + 7.69201i 0.679737 + 0.314813i
\(598\) 0 0
\(599\) −14.9010 + 17.7583i −0.608839 + 0.725586i −0.979108 0.203339i \(-0.934821\pi\)
0.370270 + 0.928924i \(0.379265\pi\)
\(600\) 0 0
\(601\) 37.4177 6.59776i 1.52630 0.269128i 0.653395 0.757017i \(-0.273344\pi\)
0.872906 + 0.487889i \(0.162233\pi\)
\(602\) 0 0
\(603\) −1.70952 + 0.998906i −0.0696170 + 0.0406786i
\(604\) 0 0
\(605\) 9.57428 + 54.2985i 0.389250 + 2.20755i
\(606\) 0 0
\(607\) −12.4714 34.2648i −0.506197 1.39077i −0.885131 0.465342i \(-0.845931\pi\)
0.378933 0.925424i \(-0.376291\pi\)
\(608\) 0 0
\(609\) 26.9720 + 28.5395i 1.09296 + 1.15648i
\(610\) 0 0
\(611\) 0.319462 0.184442i 0.0129241 0.00746171i
\(612\) 0 0
\(613\) 5.58435 9.67238i 0.225550 0.390664i −0.730934 0.682448i \(-0.760915\pi\)
0.956484 + 0.291784i \(0.0942488\pi\)
\(614\) 0 0
\(615\) 6.62142 + 24.4564i 0.267001 + 0.986177i
\(616\) 0 0
\(617\) 21.5546 + 3.80066i 0.867756 + 0.153009i 0.589765 0.807575i \(-0.299220\pi\)
0.277991 + 0.960584i \(0.410332\pi\)
\(618\) 0 0
\(619\) 9.62741 26.4511i 0.386958 1.06316i −0.581405 0.813614i \(-0.697497\pi\)
0.968363 0.249545i \(-0.0802810\pi\)
\(620\) 0 0
\(621\) −10.6663 + 23.3488i −0.428025 + 0.936954i
\(622\) 0 0
\(623\) −1.96950 3.66799i −0.0789064 0.146955i
\(624\) 0 0
\(625\) −11.1139 9.32564i −0.444555 0.373026i
\(626\) 0 0
\(627\) 66.1488 + 17.5399i 2.64173 + 0.700477i
\(628\) 0 0
\(629\) −11.4481 19.8287i −0.456467 0.790624i
\(630\) 0 0
\(631\) 14.2798 24.7334i 0.568472 0.984622i −0.428246 0.903662i \(-0.640868\pi\)
0.996717 0.0809596i \(-0.0257985\pi\)
\(632\) 0 0
\(633\) 1.83859 21.6652i 0.0730775 0.861116i
\(634\) 0 0
\(635\) 7.33978 2.67146i 0.291270 0.106014i
\(636\) 0 0
\(637\) 7.92725 + 26.8195i 0.314089 + 1.06263i
\(638\) 0 0
\(639\) 2.86854 + 15.7868i 0.113478 + 0.624516i
\(640\) 0 0
\(641\) −5.54412 6.60722i −0.218979 0.260969i 0.645360 0.763879i \(-0.276707\pi\)
−0.864339 + 0.502909i \(0.832263\pi\)
\(642\) 0 0
\(643\) 9.28376 + 25.5069i 0.366116 + 1.00589i 0.976825 + 0.214040i \(0.0686623\pi\)
−0.610709 + 0.791855i \(0.709116\pi\)
\(644\) 0 0
\(645\) 30.5908 + 43.4468i 1.20451 + 1.71072i
\(646\) 0 0
\(647\) −19.4819 33.7436i −0.765912 1.32660i −0.939763 0.341827i \(-0.888954\pi\)
0.173850 0.984772i \(-0.444379\pi\)
\(648\) 0 0
\(649\) −0.930580 0.537271i −0.0365285 0.0210897i
\(650\) 0 0
\(651\) 7.27464 + 16.8248i 0.285116 + 0.659414i
\(652\) 0 0
\(653\) 8.30041 + 1.46359i 0.324820 + 0.0572745i 0.333681 0.942686i \(-0.391709\pi\)
−0.00886048 + 0.999961i \(0.502820\pi\)
\(654\) 0 0
\(655\) −49.3319 + 41.3944i −1.92756 + 1.61741i
\(656\) 0 0
\(657\) 5.17140 + 28.4604i 0.201755 + 1.11034i
\(658\) 0 0
\(659\) −7.86933 + 21.6208i −0.306546 + 0.842227i 0.686778 + 0.726867i \(0.259024\pi\)
−0.993324 + 0.115360i \(0.963198\pi\)
\(660\) 0 0
\(661\) −9.02230 1.59088i −0.350927 0.0618779i −0.00459369 0.999989i \(-0.501462\pi\)
−0.346333 + 0.938112i \(0.612573\pi\)
\(662\) 0 0
\(663\) 10.8160 + 23.0380i 0.420057 + 0.894721i
\(664\) 0 0
\(665\) −21.3543 64.8227i −0.828085 2.51372i
\(666\) 0 0
\(667\) −42.3322 −1.63911
\(668\) 0 0
\(669\) −8.01980 + 30.2453i −0.310063 + 1.16935i
\(670\) 0 0
\(671\) 9.95422 56.4532i 0.384278 2.17935i
\(672\) 0 0
\(673\) −36.6890 + 30.7857i −1.41426 + 1.18670i −0.459923 + 0.887959i \(0.652123\pi\)
−0.954333 + 0.298743i \(0.903433\pi\)
\(674\) 0 0
\(675\) 34.1434 + 2.71840i 1.31418 + 0.104631i
\(676\) 0 0
\(677\) −1.43912 8.16168i −0.0553101 0.313679i 0.944583 0.328271i \(-0.106466\pi\)
−0.999894 + 0.0145924i \(0.995355\pi\)
\(678\) 0 0
\(679\) 9.58803 1.38734i 0.367955 0.0532411i
\(680\) 0 0
\(681\) −40.7649 10.8092i −1.56212 0.414208i
\(682\) 0 0
\(683\) 20.7981 + 12.0078i 0.795818 + 0.459466i 0.842007 0.539467i \(-0.181374\pi\)
−0.0461886 + 0.998933i \(0.514708\pi\)
\(684\) 0 0
\(685\) 59.3556 + 34.2690i 2.26786 + 1.30935i
\(686\) 0 0
\(687\) 15.3427 + 1.30203i 0.585359 + 0.0496757i
\(688\) 0 0
\(689\) −0.659192 + 3.73847i −0.0251132 + 0.142424i
\(690\) 0 0
\(691\) −7.68069 9.15348i −0.292187 0.348215i 0.599903 0.800073i \(-0.295206\pi\)
−0.892090 + 0.451858i \(0.850761\pi\)
\(692\) 0 0
\(693\) 8.22957 40.5650i 0.312615 1.54094i
\(694\) 0 0
\(695\) −10.5076 + 28.8694i −0.398577 + 1.09508i
\(696\) 0 0
\(697\) −12.1052 10.1574i −0.458515 0.384740i
\(698\) 0 0
\(699\) 0.597034 + 6.62526i 0.0225819 + 0.250590i
\(700\) 0 0
\(701\) 23.0672i 0.871236i 0.900132 + 0.435618i \(0.143470\pi\)
−0.900132 + 0.435618i \(0.856530\pi\)
\(702\) 0 0
\(703\) 40.8484 23.5838i 1.54063 0.889482i
\(704\) 0 0
\(705\) 0.313462 + 0.445197i 0.0118057 + 0.0167671i
\(706\) 0 0
\(707\) −4.65454 1.85855i −0.175052 0.0698980i
\(708\) 0 0
\(709\) 33.8202 + 12.3095i 1.27014 + 0.462295i 0.887161 0.461461i \(-0.152674\pi\)
0.382983 + 0.923755i \(0.374897\pi\)
\(710\) 0 0
\(711\) −4.42934 + 5.33489i −0.166113 + 0.200074i
\(712\) 0 0
\(713\) −18.5687 6.75844i −0.695402 0.253106i
\(714\) 0 0
\(715\) −54.3384 45.5953i −2.03214 1.70517i
\(716\) 0 0
\(717\) 3.16903 4.55103i 0.118349 0.169961i
\(718\) 0 0
\(719\) 11.8984 + 20.6086i 0.443736 + 0.768573i 0.997963 0.0637925i \(-0.0203196\pi\)
−0.554228 + 0.832365i \(0.686986\pi\)
\(720\) 0 0
\(721\) 4.21529 + 12.7958i 0.156985 + 0.476542i
\(722\) 0 0
\(723\) 1.00512 + 0.999896i 0.0373808 + 0.0371865i
\(724\) 0 0
\(725\) 19.3188 + 53.0779i 0.717481 + 1.97126i
\(726\) 0 0
\(727\) −3.48709 4.15575i −0.129329 0.154128i 0.697494 0.716591i \(-0.254298\pi\)
−0.826823 + 0.562463i \(0.809854\pi\)
\(728\) 0 0
\(729\) 23.1688 13.8639i 0.858103 0.513477i
\(730\) 0 0
\(731\) −31.1413 11.3345i −1.15180 0.419222i
\(732\) 0 0
\(733\) 3.72206 4.43578i 0.137478 0.163839i −0.692913 0.721021i \(-0.743673\pi\)
0.830390 + 0.557182i \(0.188117\pi\)
\(734\) 0 0
\(735\) −38.3763 + 15.2065i −1.41553 + 0.560900i
\(736\) 0 0
\(737\) 3.44172i 0.126777i
\(738\) 0 0
\(739\) −16.9316 −0.622838 −0.311419 0.950273i \(-0.600804\pi\)
−0.311419 + 0.950273i \(0.600804\pi\)
\(740\) 0 0
\(741\) −47.4596 + 22.2815i −1.74347 + 0.818532i
\(742\) 0 0
\(743\) 14.8397 17.6852i 0.544415 0.648808i −0.421757 0.906709i \(-0.638586\pi\)
0.966171 + 0.257901i \(0.0830308\pi\)
\(744\) 0 0
\(745\) 58.2544 10.2718i 2.13428 0.376330i
\(746\) 0 0
\(747\) 19.8838 + 3.39931i 0.727510 + 0.124374i
\(748\) 0 0
\(749\) 0.525136 17.0248i 0.0191880 0.622073i
\(750\) 0 0
\(751\) 7.05220 39.9950i 0.257338 1.45944i −0.532660 0.846329i \(-0.678808\pi\)
0.789999 0.613109i \(-0.210081\pi\)
\(752\) 0 0
\(753\) −5.46045 + 0.492067i −0.198990 + 0.0179319i
\(754\) 0 0
\(755\) 59.6490 2.17085
\(756\) 0 0
\(757\) −17.6945 −0.643118 −0.321559 0.946890i \(-0.604207\pi\)
−0.321559 + 0.946890i \(0.604207\pi\)
\(758\) 0 0
\(759\) 25.6887 + 36.4846i 0.932441 + 1.32431i
\(760\) 0 0
\(761\) −1.35890 + 7.70670i −0.0492601 + 0.279368i −0.999481 0.0322086i \(-0.989746\pi\)
0.950221 + 0.311576i \(0.100857\pi\)
\(762\) 0 0
\(763\) −3.70798 + 5.98812i −0.134238 + 0.216785i
\(764\) 0 0
\(765\) −32.4345 + 18.9521i −1.17267 + 0.685215i
\(766\) 0 0
\(767\) 0.810730 0.142954i 0.0292738 0.00516175i
\(768\) 0 0
\(769\) −27.7523 + 33.0738i −1.00077 + 1.19267i −0.0195465 + 0.999809i \(0.506222\pi\)
−0.981225 + 0.192865i \(0.938222\pi\)
\(770\) 0 0
\(771\) −1.10717 + 13.0464i −0.0398737 + 0.469856i
\(772\) 0 0
\(773\) −0.416923 −0.0149957 −0.00749783 0.999972i \(-0.502387\pi\)
−0.00749783 + 0.999972i \(0.502387\pi\)
\(774\) 0 0
\(775\) 26.3665i 0.947111i
\(776\) 0 0
\(777\) −15.6971 23.8217i −0.563130 0.854597i