Properties

Label 756.2.ck.a.5.5
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 5.5
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.61581 - 0.623825i) q^{3} +(-0.221654 + 1.25706i) q^{5} +(2.55927 - 0.670941i) q^{7} +(2.22168 + 2.01597i) q^{9} +O(q^{10})\) \(q+(-1.61581 - 0.623825i) q^{3} +(-0.221654 + 1.25706i) q^{5} +(2.55927 - 0.670941i) q^{7} +(2.22168 + 2.01597i) q^{9} +(-5.67482 + 1.00062i) q^{11} +(3.02767 - 3.60823i) q^{13} +(1.14234 - 1.89290i) q^{15} +0.342095 q^{17} +8.19307i q^{19} +(-4.55384 - 0.512420i) q^{21} +(0.332785 - 0.396598i) q^{23} +(3.16739 + 1.15283i) q^{25} +(-2.33221 - 4.64336i) q^{27} +(0.622374 + 0.741717i) q^{29} +(1.45520 + 3.99812i) q^{31} +(9.79364 + 1.92328i) q^{33} +(0.276144 + 3.36587i) q^{35} +(-1.18931 - 2.05995i) q^{37} +(-7.14304 + 3.94148i) q^{39} +(7.78109 + 6.52911i) q^{41} +(4.17869 + 1.52092i) q^{43} +(-3.02664 + 2.34595i) q^{45} +(2.92248 + 1.06369i) q^{47} +(6.09968 - 3.43423i) q^{49} +(-0.552760 - 0.213407i) q^{51} +(5.32288 - 3.07317i) q^{53} -7.35539i q^{55} +(5.11105 - 13.2385i) q^{57} +(9.66502 + 8.10991i) q^{59} +(-2.33107 + 6.40456i) q^{61} +(7.03847 + 3.66877i) q^{63} +(3.86468 + 4.60575i) q^{65} +(-0.683823 + 3.87815i) q^{67} +(-0.785125 + 0.433227i) q^{69} +(-2.19597 - 1.26784i) q^{71} +(10.4470 + 6.03160i) q^{73} +(-4.39873 - 3.83866i) q^{75} +(-13.8520 + 6.36833i) q^{77} +(-0.898458 - 5.09541i) q^{79} +(0.871763 + 8.95768i) q^{81} +(-0.555623 + 0.466223i) q^{83} +(-0.0758267 + 0.430035i) q^{85} +(-0.542937 - 1.58673i) q^{87} -10.2413 q^{89} +(5.32769 - 11.2658i) q^{91} +(0.142806 - 7.36798i) q^{93} +(-10.2992 - 1.81603i) q^{95} +(-3.14019 + 8.62759i) q^{97} +(-14.6249 - 9.21717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

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
\(3\) −1.61581 0.623825i −0.932888 0.360166i
\(4\) 0 0
\(5\) −0.221654 + 1.25706i −0.0991267 + 0.562176i 0.894278 + 0.447512i \(0.147690\pi\)
−0.993404 + 0.114663i \(0.963421\pi\)
\(6\) 0 0
\(7\) 2.55927 0.670941i 0.967311 0.253592i
\(8\) 0 0
\(9\) 2.22168 + 2.01597i 0.740561 + 0.671989i
\(10\) 0 0
\(11\) −5.67482 + 1.00062i −1.71102 + 0.301699i −0.941523 0.336949i \(-0.890605\pi\)
−0.769499 + 0.638648i \(0.779494\pi\)
\(12\) 0 0
\(13\) 3.02767 3.60823i 0.839724 1.00074i −0.160183 0.987087i \(-0.551208\pi\)
0.999907 0.0136566i \(-0.00434715\pi\)
\(14\) 0 0
\(15\) 1.14234 1.89290i 0.294950 0.488745i
\(16\) 0 0
\(17\) 0.342095 0.0829702 0.0414851 0.999139i \(-0.486791\pi\)
0.0414851 + 0.999139i \(0.486791\pi\)
\(18\) 0 0
\(19\) 8.19307i 1.87962i 0.341697 + 0.939810i \(0.388998\pi\)
−0.341697 + 0.939810i \(0.611002\pi\)
\(20\) 0 0
\(21\) −4.55384 0.512420i −0.993729 0.111819i
\(22\) 0 0
\(23\) 0.332785 0.396598i 0.0693905 0.0826964i −0.730232 0.683199i \(-0.760588\pi\)
0.799623 + 0.600502i \(0.205033\pi\)
\(24\) 0 0
\(25\) 3.16739 + 1.15283i 0.633477 + 0.230567i
\(26\) 0 0
\(27\) −2.33221 4.64336i −0.448834 0.893615i
\(28\) 0 0
\(29\) 0.622374 + 0.741717i 0.115572 + 0.137733i 0.820729 0.571318i \(-0.193568\pi\)
−0.705157 + 0.709052i \(0.749123\pi\)
\(30\) 0 0
\(31\) 1.45520 + 3.99812i 0.261361 + 0.718083i 0.999076 + 0.0429711i \(0.0136823\pi\)
−0.737716 + 0.675112i \(0.764095\pi\)
\(32\) 0 0
\(33\) 9.79364 + 1.92328i 1.70485 + 0.334799i
\(34\) 0 0
\(35\) 0.276144 + 3.36587i 0.0466768 + 0.568936i
\(36\) 0 0
\(37\) −1.18931 2.05995i −0.195522 0.338653i 0.751550 0.659676i \(-0.229307\pi\)
−0.947071 + 0.321023i \(0.895973\pi\)
\(38\) 0 0
\(39\) −7.14304 + 3.94148i −1.14380 + 0.631143i
\(40\) 0 0
\(41\) 7.78109 + 6.52911i 1.21520 + 1.01968i 0.999062 + 0.0433131i \(0.0137913\pi\)
0.216140 + 0.976362i \(0.430653\pi\)
\(42\) 0 0
\(43\) 4.17869 + 1.52092i 0.637245 + 0.231938i 0.640381 0.768057i \(-0.278776\pi\)
−0.00313689 + 0.999995i \(0.500999\pi\)
\(44\) 0 0
\(45\) −3.02664 + 2.34595i −0.451185 + 0.349713i
\(46\) 0 0
\(47\) 2.92248 + 1.06369i 0.426287 + 0.155156i 0.546249 0.837623i \(-0.316055\pi\)
−0.119962 + 0.992778i \(0.538277\pi\)
\(48\) 0 0
\(49\) 6.09968 3.43423i 0.871382 0.490605i
\(50\) 0 0
\(51\) −0.552760 0.213407i −0.0774019 0.0298830i
\(52\) 0 0
\(53\) 5.32288 3.07317i 0.731154 0.422132i −0.0876903 0.996148i \(-0.527949\pi\)
0.818844 + 0.574016i \(0.194615\pi\)
\(54\) 0 0
\(55\) 7.35539i 0.991801i
\(56\) 0 0
\(57\) 5.11105 13.2385i 0.676975 1.75348i
\(58\) 0 0
\(59\) 9.66502 + 8.10991i 1.25828 + 1.05582i 0.995863 + 0.0908657i \(0.0289634\pi\)
0.262415 + 0.964955i \(0.415481\pi\)
\(60\) 0 0
\(61\) −2.33107 + 6.40456i −0.298463 + 0.820020i 0.696294 + 0.717756i \(0.254831\pi\)
−0.994757 + 0.102264i \(0.967391\pi\)
\(62\) 0 0
\(63\) 7.03847 + 3.66877i 0.886764 + 0.462222i
\(64\) 0 0
\(65\) 3.86468 + 4.60575i 0.479355 + 0.571273i
\(66\) 0 0
\(67\) −0.683823 + 3.87815i −0.0835423 + 0.473792i 0.914119 + 0.405445i \(0.132883\pi\)
−0.997662 + 0.0683466i \(0.978228\pi\)
\(68\) 0 0
\(69\) −0.785125 + 0.433227i −0.0945180 + 0.0521544i
\(70\) 0 0
\(71\) −2.19597 1.26784i −0.260614 0.150465i 0.364001 0.931399i \(-0.381411\pi\)
−0.624614 + 0.780933i \(0.714744\pi\)
\(72\) 0 0
\(73\) 10.4470 + 6.03160i 1.22273 + 0.705945i 0.965500 0.260404i \(-0.0838559\pi\)
0.257233 + 0.966349i \(0.417189\pi\)
\(74\) 0 0
\(75\) −4.39873 3.83866i −0.507921 0.443250i
\(76\) 0 0
\(77\) −13.8520 + 6.36833i −1.57858 + 0.725738i
\(78\) 0 0
\(79\) −0.898458 5.09541i −0.101084 0.573278i −0.992712 0.120509i \(-0.961547\pi\)
0.891628 0.452769i \(-0.149564\pi\)
\(80\) 0 0
\(81\) 0.871763 + 8.95768i 0.0968626 + 0.995298i
\(82\) 0 0
\(83\) −0.555623 + 0.466223i −0.0609875 + 0.0511746i −0.672772 0.739850i \(-0.734896\pi\)
0.611784 + 0.791025i \(0.290452\pi\)
\(84\) 0 0
\(85\) −0.0758267 + 0.430035i −0.00822456 + 0.0466438i
\(86\) 0 0
\(87\) −0.542937 1.58673i −0.0582090 0.170115i
\(88\) 0 0
\(89\) −10.2413 −1.08558 −0.542790 0.839868i \(-0.682632\pi\)
−0.542790 + 0.839868i \(0.682632\pi\)
\(90\) 0 0
\(91\) 5.32769 11.2658i 0.558494 1.18098i
\(92\) 0 0
\(93\) 0.142806 7.36798i 0.0148083 0.764024i
\(94\) 0 0
\(95\) −10.2992 1.81603i −1.05668 0.186321i
\(96\) 0 0
\(97\) −3.14019 + 8.62759i −0.318838 + 0.875999i 0.671953 + 0.740594i \(0.265456\pi\)
−0.990790 + 0.135405i \(0.956766\pi\)
\(98\) 0 0
\(99\) −14.6249 9.21717i −1.46985 0.926360i
\(100\) 0 0
\(101\) 1.23150 1.03335i 0.122539 0.102822i −0.579459 0.815001i \(-0.696736\pi\)
0.701998 + 0.712179i \(0.252292\pi\)
\(102\) 0 0
\(103\) −3.07793 0.542722i −0.303277 0.0534759i 0.0199387 0.999801i \(-0.493653\pi\)
−0.323216 + 0.946325i \(0.604764\pi\)
\(104\) 0 0
\(105\) 1.65352 5.61088i 0.161367 0.547566i
\(106\) 0 0
\(107\) −15.1503 8.74701i −1.46463 0.845605i −0.465411 0.885095i \(-0.654093\pi\)
−0.999220 + 0.0394897i \(0.987427\pi\)
\(108\) 0 0
\(109\) −8.26215 14.3105i −0.791371 1.37069i −0.925118 0.379679i \(-0.876034\pi\)
0.133748 0.991015i \(-0.457299\pi\)
\(110\) 0 0
\(111\) 0.636654 + 4.07041i 0.0604286 + 0.386346i
\(112\) 0 0
\(113\) −0.603550 1.65824i −0.0567772 0.155994i 0.908061 0.418837i \(-0.137562\pi\)
−0.964839 + 0.262843i \(0.915340\pi\)
\(114\) 0 0
\(115\) 0.424785 + 0.506239i 0.0396114 + 0.0472070i
\(116\) 0 0
\(117\) 14.0006 1.91268i 1.29436 0.176827i
\(118\) 0 0
\(119\) 0.875511 0.229526i 0.0802580 0.0210406i
\(120\) 0 0
\(121\) 20.8657 7.59448i 1.89688 0.690408i
\(122\) 0 0
\(123\) −8.49974 15.4038i −0.766396 1.38892i
\(124\) 0 0
\(125\) −5.34239 + 9.25329i −0.477838 + 0.827639i
\(126\) 0 0
\(127\) −7.47580 12.9485i −0.663370 1.14899i −0.979725 0.200349i \(-0.935792\pi\)
0.316355 0.948641i \(-0.397541\pi\)
\(128\) 0 0
\(129\) −5.80318 5.06429i −0.510942 0.445886i
\(130\) 0 0
\(131\) −9.41368 7.89901i −0.822477 0.690140i 0.131074 0.991373i \(-0.458158\pi\)
−0.953551 + 0.301232i \(0.902602\pi\)
\(132\) 0 0
\(133\) 5.49707 + 20.9683i 0.476657 + 1.81818i
\(134\) 0 0
\(135\) 6.35394 1.90251i 0.546860 0.163742i
\(136\) 0 0
\(137\) −0.439344 + 1.20709i −0.0375357 + 0.103128i −0.957045 0.289941i \(-0.906364\pi\)
0.919509 + 0.393069i \(0.128587\pi\)
\(138\) 0 0
\(139\) −0.844510 0.148910i −0.0716304 0.0126304i 0.137718 0.990471i \(-0.456023\pi\)
−0.209349 + 0.977841i \(0.567134\pi\)
\(140\) 0 0
\(141\) −4.05861 3.54184i −0.341796 0.298277i
\(142\) 0 0
\(143\) −13.5710 + 23.5056i −1.13486 + 1.96564i
\(144\) 0 0
\(145\) −1.07034 + 0.617959i −0.0888866 + 0.0513187i
\(146\) 0 0
\(147\) −11.9983 + 1.74394i −0.989601 + 0.143838i
\(148\) 0 0
\(149\) 6.43770 + 17.6874i 0.527397 + 1.44901i 0.862125 + 0.506696i \(0.169133\pi\)
−0.334728 + 0.942315i \(0.608644\pi\)
\(150\) 0 0
\(151\) −0.178851 1.01431i −0.0145547 0.0825435i 0.976665 0.214767i \(-0.0688993\pi\)
−0.991220 + 0.132224i \(0.957788\pi\)
\(152\) 0 0
\(153\) 0.760027 + 0.689651i 0.0614445 + 0.0557550i
\(154\) 0 0
\(155\) −5.34843 + 0.943073i −0.429596 + 0.0757494i
\(156\) 0 0
\(157\) −4.27157 + 5.09066i −0.340909 + 0.406279i −0.909074 0.416636i \(-0.863209\pi\)
0.568165 + 0.822915i \(0.307654\pi\)
\(158\) 0 0
\(159\) −10.5179 + 1.64511i −0.834122 + 0.130465i
\(160\) 0 0
\(161\) 0.585591 1.23828i 0.0461511 0.0975900i
\(162\) 0 0
\(163\) 1.59932 2.77011i 0.125269 0.216972i −0.796569 0.604547i \(-0.793354\pi\)
0.921838 + 0.387576i \(0.126687\pi\)
\(164\) 0 0
\(165\) −4.58848 + 11.8849i −0.357213 + 0.925239i
\(166\) 0 0
\(167\) 19.3814 7.05424i 1.49977 0.545873i 0.543773 0.839233i \(-0.316995\pi\)
0.956002 + 0.293359i \(0.0947732\pi\)
\(168\) 0 0
\(169\) −1.59515 9.04656i −0.122704 0.695889i
\(170\) 0 0
\(171\) −16.5170 + 18.2024i −1.26308 + 1.39197i
\(172\) 0 0
\(173\) 16.1747 13.5722i 1.22974 1.03187i 0.231484 0.972839i \(-0.425642\pi\)
0.998256 0.0590352i \(-0.0188024\pi\)
\(174\) 0 0
\(175\) 8.87967 + 0.825279i 0.671240 + 0.0623852i
\(176\) 0 0
\(177\) −10.5577 19.1334i −0.793563 1.43815i
\(178\) 0 0
\(179\) 11.6254i 0.868924i 0.900690 + 0.434462i \(0.143061\pi\)
−0.900690 + 0.434462i \(0.856939\pi\)
\(180\) 0 0
\(181\) −7.09964 + 4.09898i −0.527712 + 0.304675i −0.740084 0.672514i \(-0.765214\pi\)
0.212372 + 0.977189i \(0.431881\pi\)
\(182\) 0 0
\(183\) 7.76189 8.89437i 0.573776 0.657491i
\(184\) 0 0
\(185\) 2.85310 1.03844i 0.209764 0.0763479i
\(186\) 0 0
\(187\) −1.94133 + 0.342308i −0.141964 + 0.0250320i
\(188\) 0 0
\(189\) −9.08417 10.3188i −0.660776 0.750583i
\(190\) 0 0
\(191\) −18.3214 + 3.23055i −1.32569 + 0.233754i −0.791270 0.611467i \(-0.790580\pi\)
−0.534417 + 0.845221i \(0.679469\pi\)
\(192\) 0 0
\(193\) −16.1705 + 5.88558i −1.16398 + 0.423654i −0.850517 0.525947i \(-0.823711\pi\)
−0.313461 + 0.949601i \(0.601489\pi\)
\(194\) 0 0
\(195\) −3.37141 9.85290i −0.241432 0.705581i
\(196\) 0 0
\(197\) 8.64136 4.98909i 0.615671 0.355458i −0.159510 0.987196i \(-0.550992\pi\)
0.775182 + 0.631738i \(0.217658\pi\)
\(198\) 0 0
\(199\) 17.1342i 1.21461i −0.794467 0.607307i \(-0.792250\pi\)
0.794467 0.607307i \(-0.207750\pi\)
\(200\) 0 0
\(201\) 3.52422 5.83977i 0.248579 0.411906i
\(202\) 0 0
\(203\) 2.09047 + 1.48067i 0.146722 + 0.103923i
\(204\) 0 0
\(205\) −9.93221 + 8.33411i −0.693696 + 0.582080i
\(206\) 0 0
\(207\) 1.53887 0.210232i 0.106959 0.0146121i
\(208\) 0 0
\(209\) −8.19818 46.4942i −0.567080 3.21607i
\(210\) 0 0
\(211\) 18.9938 6.91319i 1.30759 0.475923i 0.408128 0.912925i \(-0.366182\pi\)
0.899461 + 0.437001i \(0.143960\pi\)
\(212\) 0 0
\(213\) 2.75736 + 3.41849i 0.188931 + 0.234231i
\(214\) 0 0
\(215\) −2.83812 + 4.91576i −0.193558 + 0.335252i
\(216\) 0 0
\(217\) 6.40673 + 9.25589i 0.434917 + 0.628331i
\(218\) 0 0
\(219\) −13.1178 16.2630i −0.886416 1.09895i
\(220\) 0 0
\(221\) 1.03575 1.23436i 0.0696720 0.0830319i
\(222\) 0 0
\(223\) 6.90013 1.21668i 0.462067 0.0814749i 0.0622313 0.998062i \(-0.480178\pi\)
0.399836 + 0.916587i \(0.369067\pi\)
\(224\) 0 0
\(225\) 4.71286 + 8.94658i 0.314191 + 0.596439i
\(226\) 0 0
\(227\) 2.38774 + 13.5416i 0.158480 + 0.898784i 0.955535 + 0.294878i \(0.0952789\pi\)
−0.797055 + 0.603907i \(0.793610\pi\)
\(228\) 0 0
\(229\) −7.05870 19.3936i −0.466452 1.28157i −0.920553 0.390617i \(-0.872262\pi\)
0.454101 0.890950i \(-0.349960\pi\)
\(230\) 0 0
\(231\) 26.3549 1.64878i 1.73403 0.108482i
\(232\) 0 0
\(233\) −24.1468 + 13.9412i −1.58191 + 0.913317i −0.587331 + 0.809347i \(0.699821\pi\)
−0.994580 + 0.103970i \(0.966846\pi\)
\(234\) 0 0
\(235\) −1.98491 + 3.43796i −0.129481 + 0.224268i
\(236\) 0 0
\(237\) −1.72691 + 8.79369i −0.112175 + 0.571212i
\(238\) 0 0
\(239\) 23.7274 + 4.18378i 1.53480 + 0.270626i 0.876229 0.481894i \(-0.160051\pi\)
0.658569 + 0.752520i \(0.271162\pi\)
\(240\) 0 0
\(241\) 0.589073 1.61847i 0.0379455 0.104255i −0.919273 0.393621i \(-0.871222\pi\)
0.957218 + 0.289366i \(0.0934445\pi\)
\(242\) 0 0
\(243\) 4.17942 15.0177i 0.268110 0.963388i
\(244\) 0 0
\(245\) 2.96503 + 8.42889i 0.189429 + 0.538502i
\(246\) 0 0
\(247\) 29.5625 + 24.8059i 1.88102 + 1.57836i
\(248\) 0 0
\(249\) 1.18862 0.406716i 0.0753259 0.0257746i
\(250\) 0 0
\(251\) 1.34720 + 2.33342i 0.0850344 + 0.147284i 0.905406 0.424547i \(-0.139567\pi\)
−0.820371 + 0.571831i \(0.806233\pi\)
\(252\) 0 0
\(253\) −1.49165 + 2.58361i −0.0937792 + 0.162430i
\(254\) 0 0
\(255\) 0.390788 0.647552i 0.0244721 0.0405513i
\(256\) 0 0
\(257\) 17.8813 6.50824i 1.11540 0.405973i 0.282430 0.959288i \(-0.408860\pi\)
0.832972 + 0.553315i \(0.186637\pi\)
\(258\) 0 0
\(259\) −4.42587 4.47400i −0.275010 0.278001i
\(260\) 0 0
\(261\) −0.112557 + 2.90255i −0.00696707 + 0.179663i
\(262\) 0 0
\(263\) −18.5166 22.0672i −1.14178 1.36072i −0.922931 0.384966i \(-0.874213\pi\)
−0.218853 0.975758i \(-0.570231\pi\)
\(264\) 0 0
\(265\) 2.68332 + 7.37237i 0.164835 + 0.452881i
\(266\) 0 0
\(267\) 16.5481 + 6.38881i 1.01272 + 0.390989i
\(268\) 0 0
\(269\) −8.04832 13.9401i −0.490715 0.849943i 0.509228 0.860632i \(-0.329931\pi\)
−0.999943 + 0.0106885i \(0.996598\pi\)
\(270\) 0 0
\(271\) 16.2246 + 9.36726i 0.985572 + 0.569020i 0.903948 0.427643i \(-0.140656\pi\)
0.0816245 + 0.996663i \(0.473989\pi\)
\(272\) 0 0
\(273\) −15.6364 + 14.8799i −0.946360 + 0.900571i
\(274\) 0 0
\(275\) −19.1279 3.37276i −1.15346 0.203385i
\(276\) 0 0
\(277\) −9.44806 + 7.92786i −0.567679 + 0.476339i −0.880875 0.473349i \(-0.843045\pi\)
0.313196 + 0.949689i \(0.398600\pi\)
\(278\) 0 0
\(279\) −4.82708 + 11.8162i −0.288990 + 0.707416i
\(280\) 0 0
\(281\) 3.46150 9.51038i 0.206496 0.567342i −0.792606 0.609735i \(-0.791276\pi\)
0.999101 + 0.0423930i \(0.0134982\pi\)
\(282\) 0 0
\(283\) 9.58146 + 1.68947i 0.569559 + 0.100429i 0.451009 0.892520i \(-0.351064\pi\)
0.118550 + 0.992948i \(0.462175\pi\)
\(284\) 0 0
\(285\) 15.5087 + 9.35926i 0.918655 + 0.554395i
\(286\) 0 0
\(287\) 24.2945 + 11.4891i 1.43406 + 0.678178i
\(288\) 0 0
\(289\) −16.8830 −0.993116
\(290\) 0 0
\(291\) 10.4561 11.9816i 0.612945 0.702375i
\(292\) 0 0
\(293\) −0.111390 + 0.631726i −0.00650749 + 0.0369058i −0.987889 0.155165i \(-0.950409\pi\)
0.981381 + 0.192071i \(0.0615203\pi\)
\(294\) 0 0
\(295\) −12.3370 + 10.3519i −0.718286 + 0.602713i
\(296\) 0 0
\(297\) 17.8811 + 24.0166i 1.03757 + 1.39358i
\(298\) 0 0
\(299\) −0.423455 2.40153i −0.0244890 0.138884i
\(300\) 0 0
\(301\) 11.7148 + 1.08878i 0.675231 + 0.0627562i
\(302\) 0 0
\(303\) −2.63450 + 0.901457i −0.151348 + 0.0517874i
\(304\) 0 0
\(305\) −7.53424 4.34990i −0.431410 0.249074i
\(306\) 0 0
\(307\) −7.14240 4.12367i −0.407638 0.235350i 0.282136 0.959374i \(-0.408957\pi\)
−0.689774 + 0.724024i \(0.742290\pi\)
\(308\) 0 0
\(309\) 4.63478 + 2.79702i 0.263664 + 0.159117i
\(310\) 0 0
\(311\) −3.05631 + 17.3332i −0.173308 + 0.982876i 0.766772 + 0.641920i \(0.221862\pi\)
−0.940079 + 0.340956i \(0.889249\pi\)
\(312\) 0 0
\(313\) −12.9360 15.4166i −0.731188 0.871396i 0.264478 0.964392i \(-0.414800\pi\)
−0.995667 + 0.0929954i \(0.970356\pi\)
\(314\) 0 0
\(315\) −6.17198 + 8.03460i −0.347752 + 0.452699i
\(316\) 0 0
\(317\) 5.39446 14.8212i 0.302983 0.832440i −0.690995 0.722860i \(-0.742827\pi\)
0.993978 0.109580i \(-0.0349505\pi\)
\(318\) 0 0
\(319\) −4.27404 3.58634i −0.239300 0.200797i
\(320\) 0 0
\(321\) 19.0233 + 23.5846i 1.06178 + 1.31636i
\(322\) 0 0
\(323\) 2.80281i 0.155952i
\(324\) 0 0
\(325\) 13.7495 7.93827i 0.762685 0.440336i
\(326\) 0 0
\(327\) 4.42284 + 28.2771i 0.244584 + 1.56373i
\(328\) 0 0
\(329\) 8.19306 + 0.761466i 0.451698 + 0.0419810i
\(330\) 0 0
\(331\) −4.42503 1.61058i −0.243222 0.0885255i 0.217533 0.976053i \(-0.430199\pi\)
−0.460755 + 0.887527i \(0.652421\pi\)
\(332\) 0 0
\(333\) 1.51051 6.97417i 0.0827755 0.382182i
\(334\) 0 0
\(335\) −4.72351 1.71922i −0.258073 0.0939308i
\(336\) 0 0
\(337\) 2.80872 + 2.35680i 0.153001 + 0.128383i 0.716075 0.698024i \(-0.245937\pi\)
−0.563074 + 0.826407i \(0.690381\pi\)
\(338\) 0 0
\(339\) −0.0592296 + 3.05591i −0.00321691 + 0.165974i
\(340\) 0 0
\(341\) −12.2586 21.2325i −0.663839 1.14980i
\(342\) 0 0
\(343\) 13.3065 12.8816i 0.718484 0.695543i
\(344\) 0 0
\(345\) −0.370567 1.08298i −0.0199507 0.0583056i
\(346\) 0 0
\(347\) 10.3261 + 28.3708i 0.554335 + 1.52302i 0.827734 + 0.561121i \(0.189630\pi\)
−0.273399 + 0.961901i \(0.588148\pi\)
\(348\) 0 0
\(349\) −18.5777 22.1400i −0.994441 1.18513i −0.982701 0.185198i \(-0.940707\pi\)
−0.0117402 0.999931i \(-0.503737\pi\)
\(350\) 0 0
\(351\) −23.8155 5.64339i −1.27118 0.301222i
\(352\) 0 0
\(353\) 19.7762 + 7.19796i 1.05258 + 0.383109i 0.809637 0.586931i \(-0.199664\pi\)
0.242946 + 0.970040i \(0.421886\pi\)
\(354\) 0 0
\(355\) 2.08050 2.47945i 0.110422 0.131595i
\(356\) 0 0
\(357\) −1.55784 0.175296i −0.0824498 0.00927766i
\(358\) 0 0
\(359\) 12.7571i 0.673296i −0.941631 0.336648i \(-0.890707\pi\)
0.941631 0.336648i \(-0.109293\pi\)
\(360\) 0 0
\(361\) −48.1265 −2.53297
\(362\) 0 0
\(363\) −38.4526 0.745288i −2.01824 0.0391175i
\(364\) 0 0
\(365\) −9.89772 + 11.7956i −0.518070 + 0.617412i
\(366\) 0 0
\(367\) −31.3571 + 5.52911i −1.63683 + 0.288617i −0.915000 0.403454i \(-0.867809\pi\)
−0.721829 + 0.692071i \(0.756698\pi\)
\(368\) 0 0
\(369\) 4.12466 + 30.1920i 0.214721 + 1.57173i
\(370\) 0 0
\(371\) 11.5607 11.4364i 0.600204 0.593748i
\(372\) 0 0
\(373\) −1.05676 + 5.99316i −0.0547167 + 0.310314i −0.999867 0.0163225i \(-0.994804\pi\)
0.945150 + 0.326636i \(0.105915\pi\)
\(374\) 0 0
\(375\) 14.4047 11.6188i 0.743856 0.599994i
\(376\) 0 0
\(377\) 4.56063 0.234884
\(378\) 0 0
\(379\) −2.73209 −0.140338 −0.0701690 0.997535i \(-0.522354\pi\)
−0.0701690 + 0.997535i \(0.522354\pi\)
\(380\) 0 0
\(381\) 4.00189 + 25.5858i 0.205023 + 1.31080i
\(382\) 0 0
\(383\) 0.927013 5.25735i 0.0473681 0.268638i −0.951921 0.306344i \(-0.900894\pi\)
0.999289 + 0.0377064i \(0.0120052\pi\)
\(384\) 0 0
\(385\) −4.93504 18.8244i −0.251513 0.959380i
\(386\) 0 0
\(387\) 6.21761 + 11.8031i 0.316059 + 0.599985i
\(388\) 0 0
\(389\) 24.3024 4.28518i 1.23218 0.217267i 0.480620 0.876929i \(-0.340412\pi\)
0.751563 + 0.659662i \(0.229300\pi\)
\(390\) 0 0
\(391\) 0.113844 0.135674i 0.00575734 0.00686133i
\(392\) 0 0
\(393\) 10.2831 + 18.6358i 0.518714 + 0.940052i
\(394\) 0 0
\(395\) 6.60439 0.332303
\(396\) 0 0
\(397\) 9.61693i 0.482660i 0.970443 + 0.241330i \(0.0775836\pi\)
−0.970443 + 0.241330i \(0.922416\pi\)
\(398\) 0 0
\(399\) 4.19830 37.3099i 0.210178 1.86783i
\(400\) 0 0
\(401\) 20.9612 24.9806i 1.04675 1.24747i 0.0786520 0.996902i \(-0.474938\pi\)
0.968099 0.250567i \(-0.0806172\pi\)
\(402\) 0 0
\(403\) 18.8320 + 6.85428i 0.938088 + 0.341436i
\(404\) 0 0
\(405\) −11.4536 0.889645i −0.569134 0.0442068i
\(406\) 0 0
\(407\) 8.81036 + 10.4998i 0.436713 + 0.520455i
\(408\) 0 0
\(409\) −0.279129 0.766899i −0.0138020 0.0379207i 0.932600 0.360911i \(-0.117534\pi\)
−0.946402 + 0.322990i \(0.895312\pi\)
\(410\) 0 0
\(411\) 1.46291 1.67635i 0.0721600 0.0826883i
\(412\) 0 0
\(413\) 30.1766 + 14.2708i 1.48489 + 0.702218i
\(414\) 0 0
\(415\) −0.462915 0.801793i −0.0227236 0.0393585i
\(416\) 0 0
\(417\) 1.27167 + 0.767437i 0.0622741 + 0.0375815i
\(418\) 0 0
\(419\) 0.632382 + 0.530632i 0.0308939 + 0.0259231i 0.658104 0.752927i \(-0.271359\pi\)
−0.627210 + 0.778850i \(0.715803\pi\)
\(420\) 0 0
\(421\) 32.9353 + 11.9875i 1.60517 + 0.584233i 0.980476 0.196640i \(-0.0630030\pi\)
0.624690 + 0.780873i \(0.285225\pi\)
\(422\) 0 0
\(423\) 4.34845 + 8.25480i 0.211429 + 0.401362i
\(424\) 0 0
\(425\) 1.08355 + 0.394379i 0.0525597 + 0.0191302i
\(426\) 0 0
\(427\) −1.66874 + 17.9550i −0.0807560 + 0.868902i
\(428\) 0 0
\(429\) 36.5915 29.5147i 1.76665 1.42498i
\(430\) 0 0
\(431\) −1.84508 + 1.06526i −0.0888745 + 0.0513117i −0.543779 0.839229i \(-0.683007\pi\)
0.454904 + 0.890540i \(0.349674\pi\)
\(432\) 0 0
\(433\) 24.2310i 1.16447i 0.813022 + 0.582233i \(0.197821\pi\)
−0.813022 + 0.582233i \(0.802179\pi\)
\(434\) 0 0
\(435\) 2.11496 0.330802i 0.101404 0.0158607i
\(436\) 0 0
\(437\) 3.24936 + 2.72653i 0.155438 + 0.130428i
\(438\) 0 0
\(439\) −10.0841 + 27.7057i −0.481286 + 1.32232i 0.427106 + 0.904202i \(0.359533\pi\)
−0.908392 + 0.418120i \(0.862689\pi\)
\(440\) 0 0
\(441\) 20.4749 + 4.66696i 0.974993 + 0.222236i
\(442\) 0 0
\(443\) −5.29303 6.30799i −0.251480 0.299702i 0.625505 0.780220i \(-0.284893\pi\)
−0.876985 + 0.480518i \(0.840449\pi\)
\(444\) 0 0
\(445\) 2.27003 12.8740i 0.107610 0.610286i
\(446\) 0 0
\(447\) 0.631766 32.5955i 0.0298815 1.54172i
\(448\) 0 0
\(449\) −31.8671 18.3985i −1.50390 0.868278i −0.999990 0.00452223i \(-0.998561\pi\)
−0.503911 0.863755i \(-0.668106\pi\)
\(450\) 0 0
\(451\) −50.6894 29.2656i −2.38687 1.37806i
\(452\) 0 0
\(453\) −0.343765 + 1.75051i −0.0161515 + 0.0822460i
\(454\) 0 0
\(455\) 12.9809 + 9.19435i 0.608555 + 0.431038i
\(456\) 0 0
\(457\) 5.68848 + 32.2609i 0.266096 + 1.50910i 0.765897 + 0.642963i \(0.222295\pi\)
−0.499801 + 0.866140i \(0.666594\pi\)
\(458\) 0 0
\(459\) −0.797837 1.58847i −0.0372398 0.0741434i
\(460\) 0 0
\(461\) −28.7198 + 24.0988i −1.33762 + 1.12239i −0.355385 + 0.934720i \(0.615650\pi\)
−0.982231 + 0.187674i \(0.939905\pi\)
\(462\) 0 0
\(463\) 4.27116 24.2230i 0.198498 1.12574i −0.708851 0.705358i \(-0.750786\pi\)
0.907349 0.420379i \(-0.138103\pi\)
\(464\) 0 0
\(465\) 9.23036 + 1.81266i 0.428048 + 0.0840601i
\(466\) 0 0
\(467\) 20.7729 0.961257 0.480628 0.876924i \(-0.340409\pi\)
0.480628 + 0.876924i \(0.340409\pi\)
\(468\) 0 0
\(469\) 0.851928 + 10.3840i 0.0393384 + 0.479490i
\(470\) 0 0
\(471\) 10.0777 5.56083i 0.464358 0.256230i
\(472\) 0 0
\(473\) −25.2352 4.44964i −1.16031 0.204595i
\(474\) 0 0
\(475\) −9.44526 + 25.9506i −0.433378 + 1.19070i
\(476\) 0 0
\(477\) 18.0212 + 3.90314i 0.825132 + 0.178712i
\(478\) 0 0
\(479\) 30.0139 25.1847i 1.37137 1.15072i 0.399088 0.916912i \(-0.369327\pi\)
0.972283 0.233805i \(-0.0751178\pi\)
\(480\) 0 0
\(481\) −11.0336 1.94552i −0.503090 0.0887083i
\(482\) 0 0
\(483\) −1.71867 + 1.63552i −0.0782024 + 0.0744185i
\(484\) 0 0
\(485\) −10.1494 5.85975i −0.460860 0.266078i
\(486\) 0 0
\(487\) 0.541148 + 0.937296i 0.0245218 + 0.0424729i 0.878026 0.478613i \(-0.158860\pi\)
−0.853504 + 0.521086i \(0.825527\pi\)
\(488\) 0 0
\(489\) −4.31227 + 3.47827i −0.195007 + 0.157293i
\(490\) 0 0
\(491\) 9.76500 + 26.8291i 0.440688 + 1.21078i 0.939041 + 0.343806i \(0.111716\pi\)
−0.498353 + 0.866974i \(0.666061\pi\)
\(492\) 0 0
\(493\) 0.212911 + 0.253737i 0.00958903 + 0.0114278i
\(494\) 0 0
\(495\) 14.8282 16.3414i 0.666479 0.734489i
\(496\) 0 0
\(497\) −6.47071 1.77138i −0.290251 0.0794573i
\(498\) 0 0
\(499\) 2.15959 0.786028i 0.0966767 0.0351874i −0.293229 0.956042i \(-0.594730\pi\)
0.389906 + 0.920855i \(0.372508\pi\)
\(500\) 0 0
\(501\) −35.7172 0.692271i −1.59573 0.0309284i
\(502\) 0 0
\(503\) −7.80677 + 13.5217i −0.348087 + 0.602904i −0.985910 0.167279i \(-0.946502\pi\)
0.637823 + 0.770183i \(0.279835\pi\)
\(504\) 0 0
\(505\) 1.02602 + 1.77712i 0.0456572 + 0.0790807i
\(506\) 0 0
\(507\) −3.06601 + 15.6126i −0.136166 + 0.693381i
\(508\) 0 0
\(509\) −32.9005 27.6068i −1.45829 1.22365i −0.926240 0.376935i \(-0.876978\pi\)
−0.532049 0.846714i \(-0.678578\pi\)
\(510\) 0 0
\(511\) 30.7836 + 8.42711i 1.36178 + 0.372793i
\(512\) 0 0
\(513\) 38.0434 19.1080i 1.67966 0.843637i
\(514\) 0 0
\(515\) 1.36447 3.74885i 0.0601257 0.165194i
\(516\) 0 0
\(517\) −17.6489 3.11197i −0.776196 0.136864i
\(518\) 0 0
\(519\) −34.6019 + 11.8399i −1.51886 + 0.519713i
\(520\) 0 0
\(521\) 13.7637 23.8394i 0.602997 1.04442i −0.389367 0.921083i \(-0.627306\pi\)
0.992365 0.123339i \(-0.0393604\pi\)
\(522\) 0 0
\(523\) −8.10797 + 4.68114i −0.354537 + 0.204692i −0.666682 0.745343i \(-0.732286\pi\)
0.312145 + 0.950035i \(0.398953\pi\)
\(524\) 0 0
\(525\) −13.8330 6.87285i −0.603723 0.299956i
\(526\) 0 0
\(527\) 0.497815 + 1.36773i 0.0216851 + 0.0595795i
\(528\) 0 0
\(529\) 3.94736 + 22.3866i 0.171625 + 0.973331i
\(530\) 0 0
\(531\) 5.12331 + 37.5020i 0.222333 + 1.62745i
\(532\) 0 0
\(533\) 47.1171 8.30802i 2.04087 0.359860i
\(534\) 0 0
\(535\) 14.3537 17.1060i 0.620562 0.739558i
\(536\) 0 0
\(537\) 7.25222 18.7844i 0.312956 0.810609i
\(538\) 0 0
\(539\) −31.1782 + 25.5921i −1.34294 + 1.10233i
\(540\) 0 0
\(541\) 6.19661 10.7328i 0.266413 0.461441i −0.701520 0.712650i \(-0.747495\pi\)
0.967933 + 0.251209i \(0.0808281\pi\)
\(542\) 0 0
\(543\) 14.0287 2.19424i 0.602030 0.0941638i
\(544\) 0 0
\(545\) 19.8205 7.21407i 0.849017 0.309017i
\(546\) 0 0
\(547\) −4.56791 25.9059i −0.195310 1.10766i −0.911977 0.410241i \(-0.865444\pi\)
0.716667 0.697415i \(-0.245667\pi\)
\(548\) 0 0
\(549\) −18.0903 + 9.52956i −0.772074 + 0.406712i
\(550\) 0 0
\(551\) −6.07694 + 5.09916i −0.258886 + 0.217231i
\(552\) 0 0
\(553\) −5.71811 12.4377i −0.243159 0.528904i
\(554\) 0 0
\(555\) −5.25788 0.101908i −0.223184 0.00432576i
\(556\) 0 0
\(557\) 8.39463i 0.355692i 0.984058 + 0.177846i \(0.0569129\pi\)
−0.984058 + 0.177846i \(0.943087\pi\)
\(558\) 0 0
\(559\) 18.1395 10.4729i 0.767220 0.442955i
\(560\) 0 0
\(561\) 3.35035 + 0.657943i 0.141452 + 0.0277784i
\(562\) 0 0
\(563\) 4.96933 1.80869i 0.209432 0.0762271i −0.235174 0.971953i \(-0.575566\pi\)
0.444606 + 0.895726i \(0.353344\pi\)
\(564\) 0 0
\(565\) 2.21829 0.391144i 0.0933241 0.0164556i
\(566\) 0 0
\(567\) 8.24115 + 22.3402i 0.346096 + 0.938199i
\(568\) 0 0
\(569\) −13.1074 + 2.31119i −0.549492 + 0.0968902i −0.441500 0.897261i \(-0.645553\pi\)
−0.107992 + 0.994152i \(0.534442\pi\)
\(570\) 0 0
\(571\) 19.0745 6.94253i 0.798241 0.290536i 0.0894837 0.995988i \(-0.471478\pi\)
0.708757 + 0.705452i \(0.249256\pi\)
\(572\) 0 0
\(573\) 31.6191 + 6.20937i 1.32091 + 0.259400i
\(574\) 0 0
\(575\) 1.51127 0.872533i 0.0630244 0.0363871i
\(576\) 0 0
\(577\) 10.4169i 0.433663i −0.976209 0.216832i \(-0.930428\pi\)
0.976209 0.216832i \(-0.0695723\pi\)
\(578\) 0 0
\(579\) 29.8000 + 0.577584i 1.23845 + 0.0240036i
\(580\) 0 0
\(581\) −1.10918 + 1.56598i −0.0460165 + 0.0649677i
\(582\) 0 0
\(583\) −27.1313 + 22.7658i −1.12366 + 0.942865i
\(584\) 0 0
\(585\) −0.698928 + 18.0236i −0.0288971 + 0.745183i
\(586\) 0 0
\(587\) −0.0514158 0.291593i −0.00212216 0.0120354i 0.983728 0.179663i \(-0.0575006\pi\)
−0.985850 + 0.167627i \(0.946389\pi\)
\(588\) 0 0
\(589\) −32.7569 + 11.9225i −1.34972 + 0.491259i
\(590\) 0 0
\(591\) −17.0751 + 2.67073i −0.702376 + 0.109859i
\(592\) 0 0
\(593\) 15.3529 26.5920i 0.630467 1.09200i −0.356989 0.934109i \(-0.616197\pi\)
0.987456 0.157893i \(-0.0504701\pi\)
\(594\) 0 0
\(595\) 0.0944673 + 1.15145i 0.00387278 + 0.0472048i
\(596\) 0 0
\(597\) −10.6888 + 27.6857i −0.437462 + 1.13310i
\(598\) 0 0
\(599\) 19.2095 22.8930i 0.784879 0.935382i −0.214264 0.976776i \(-0.568735\pi\)
0.999143 + 0.0413935i \(0.0131797\pi\)
\(600\) 0 0
\(601\) 7.31717 1.29022i 0.298474 0.0526290i −0.0224059 0.999749i \(-0.507133\pi\)
0.320880 + 0.947120i \(0.396021\pi\)
\(602\) 0 0
\(603\) −9.33746 + 7.23747i −0.380251 + 0.294732i
\(604\) 0 0
\(605\) 4.92178 + 27.9128i 0.200099 + 1.13482i
\(606\) 0 0
\(607\) 12.1959 + 33.5078i 0.495014 + 1.36004i 0.896040 + 0.443974i \(0.146432\pi\)
−0.401025 + 0.916067i \(0.631346\pi\)
\(608\) 0 0
\(609\) −2.45412 3.69657i −0.0994460 0.149793i
\(610\) 0 0
\(611\) 12.6863 7.32446i 0.513234 0.296316i
\(612\) 0 0
\(613\) 7.49646 12.9843i 0.302779 0.524429i −0.673985 0.738745i \(-0.735419\pi\)
0.976764 + 0.214316i \(0.0687522\pi\)
\(614\) 0 0
\(615\) 21.2476 7.27038i 0.856786 0.293170i
\(616\) 0 0
\(617\) −14.8177 2.61276i −0.596537 0.105186i −0.132776 0.991146i \(-0.542389\pi\)
−0.463761 + 0.885960i \(0.653500\pi\)
\(618\) 0 0
\(619\) −7.13530 + 19.6041i −0.286792 + 0.787954i 0.709719 + 0.704485i \(0.248822\pi\)
−0.996510 + 0.0834686i \(0.973400\pi\)
\(620\) 0 0
\(621\) −2.61767 0.620292i −0.105044 0.0248915i
\(622\) 0 0
\(623\) −26.2103 + 6.87134i −1.05009 + 0.275294i
\(624\) 0 0
\(625\) 2.46259 + 2.06636i 0.0985036 + 0.0826544i
\(626\) 0 0
\(627\) −15.7575 + 80.2400i −0.629296 + 3.20448i
\(628\) 0 0
\(629\) −0.406857 0.704698i −0.0162225 0.0280981i
\(630\) 0 0
\(631\) 6.15238 10.6562i 0.244923 0.424218i −0.717187 0.696880i \(-0.754571\pi\)
0.962110 + 0.272662i \(0.0879041\pi\)
\(632\) 0 0
\(633\) −35.0030 0.678428i −1.39125 0.0269651i
\(634\) 0 0
\(635\) 17.9341 6.52747i 0.711692 0.259035i
\(636\) 0 0
\(637\) 6.07627 32.4068i 0.240751 1.28400i
\(638\) 0 0
\(639\) −2.32282 7.24374i −0.0918894 0.286558i
\(640\) 0 0
\(641\) −3.33066 3.96933i −0.131553 0.156779i 0.696246 0.717803i \(-0.254852\pi\)
−0.827800 + 0.561024i \(0.810408\pi\)
\(642\) 0 0
\(643\) −15.2007 41.7635i −0.599457 1.64699i −0.752360 0.658752i \(-0.771085\pi\)
0.152903 0.988241i \(-0.451138\pi\)
\(644\) 0 0
\(645\) 7.65243 6.17245i 0.301314 0.243040i
\(646\) 0 0
\(647\) −0.558967 0.968159i −0.0219753 0.0380623i 0.854829 0.518910i \(-0.173662\pi\)
−0.876804 + 0.480848i \(0.840329\pi\)
\(648\) 0 0
\(649\) −62.9622 36.3512i −2.47148 1.42691i
\(650\) 0 0
\(651\) −4.57801 18.9524i −0.179426 0.742805i
\(652\) 0 0
\(653\) −30.4355 5.36660i −1.19103 0.210011i −0.457215 0.889356i \(-0.651153\pi\)
−0.733819 + 0.679345i \(0.762264\pi\)
\(654\) 0 0
\(655\) 12.0161 10.0827i 0.469509 0.393965i
\(656\) 0 0
\(657\) 11.0505 + 34.4612i 0.431122 + 1.34446i
\(658\) 0 0
\(659\) 12.4980 34.3381i 0.486855 1.33762i −0.416659 0.909063i \(-0.636799\pi\)
0.903514 0.428559i \(-0.140979\pi\)
\(660\) 0 0
\(661\) −24.1321 4.25514i −0.938631 0.165506i −0.316654 0.948541i \(-0.602559\pi\)
−0.621977 + 0.783035i \(0.713670\pi\)
\(662\) 0 0
\(663\) −2.44360 + 1.34836i −0.0949015 + 0.0523660i
\(664\) 0 0
\(665\) −27.5769 + 2.26247i −1.06938 + 0.0877347i
\(666\) 0 0
\(667\) 0.501280 0.0194096
\(668\) 0 0
\(669\) −11.9083 2.33855i −0.460401 0.0904136i
\(670\) 0 0
\(671\) 6.81984 38.6772i 0.263277 1.49312i
\(672\) 0 0
\(673\) 4.11606 3.45379i 0.158663 0.133134i −0.560000 0.828492i \(-0.689199\pi\)
0.718663 + 0.695359i \(0.244755\pi\)
\(674\) 0 0
\(675\) −2.03398 17.3960i −0.0782881 0.669571i
\(676\) 0 0
\(677\) −2.21240 12.5472i −0.0850295 0.482226i −0.997350 0.0727498i \(-0.976823\pi\)
0.912321 0.409476i \(-0.134289\pi\)
\(678\) 0 0
\(679\) −2.24796 + 24.1872i −0.0862689 + 0.928219i
\(680\) 0 0
\(681\) 4.58942 23.3701i 0.175867 0.895545i
\(682\) 0 0
\(683\) −30.9994 17.8975i −1.18616 0.684830i −0.228729 0.973490i \(-0.573457\pi\)
−0.957432 + 0.288660i \(0.906790\pi\)
\(684\) 0 0
\(685\) −1.42000 0.819839i −0.0542555 0.0313244i
\(686\) 0 0
\(687\) −0.692709 + 35.7398i −0.0264285 + 1.36356i
\(688\) 0 0
\(689\) 5.02721 28.5107i 0.191521 1.08617i
\(690\) 0 0
\(691\) 0.636884 + 0.759009i 0.0242282 + 0.0288740i 0.778022 0.628236i \(-0.216223\pi\)
−0.753794 + 0.657110i \(0.771778\pi\)
\(692\) 0 0
\(693\) −43.6131 13.7767i −1.65672 0.523335i
\(694\) 0 0
\(695\) 0.374378 1.02860i 0.0142010 0.0390169i
\(696\) 0 0
\(697\) 2.66187 + 2.23357i 0.100826 + 0.0846027i
\(698\) 0 0
\(699\) 47.7135 7.46290i 1.80469 0.282273i
\(700\) 0 0
\(701\) 21.7180i 0.820277i 0.912023 + 0.410139i \(0.134520\pi\)
−0.912023 + 0.410139i \(0.865480\pi\)
\(702\) 0 0
\(703\) 16.8773 9.74412i 0.636540 0.367506i
\(704\) 0 0
\(705\) 5.35192 4.31686i 0.201565 0.162582i
\(706\) 0 0
\(707\) 2.45841 3.47088i 0.0924582 0.130536i
\(708\) 0 0
\(709\) 12.7552 + 4.64252i 0.479032 + 0.174354i 0.570240 0.821478i \(-0.306850\pi\)
−0.0912072 + 0.995832i \(0.529073\pi\)
\(710\) 0 0
\(711\) 8.27608 13.1316i 0.310377 0.492475i
\(712\) 0 0
\(713\) 2.06991 + 0.753386i 0.0775188 + 0.0282145i
\(714\) 0 0
\(715\) −26.5400 22.2697i −0.992539 0.832839i
\(716\) 0 0
\(717\) −35.7290 21.5620i −1.33433 0.805246i
\(718\) 0 0
\(719\) −6.02285 10.4319i −0.224614 0.389044i 0.731589 0.681746i \(-0.238779\pi\)
−0.956204 + 0.292702i \(0.905446\pi\)
\(720\) 0 0
\(721\) −8.24137 + 0.676140i −0.306924 + 0.0251808i
\(722\) 0 0
\(723\) −1.96147 + 2.24765i −0.0729479 + 0.0835912i
\(724\) 0 0
\(725\) 1.11622 + 3.06680i 0.0414555 + 0.113898i
\(726\) 0 0
\(727\) −29.9518 35.6951i −1.11085 1.32386i −0.941007 0.338387i \(-0.890119\pi\)
−0.169842 0.985471i \(-0.554326\pi\)
\(728\) 0 0
\(729\) −16.1216 + 21.6586i −0.597096 + 0.802170i
\(730\) 0 0
\(731\) 1.42951 + 0.520299i 0.0528723 + 0.0192439i
\(732\) 0 0
\(733\) −21.7050 + 25.8670i −0.801691 + 0.955418i −0.999693 0.0247835i \(-0.992110\pi\)
0.198002 + 0.980202i \(0.436555\pi\)
\(734\) 0 0
\(735\) 0.467228 15.4691i 0.0172340 0.570588i
\(736\) 0 0
\(737\) 22.6920i 0.835872i
\(738\) 0 0
\(739\) 11.3481 0.417448 0.208724 0.977975i \(-0.433069\pi\)
0.208724 + 0.977975i \(0.433069\pi\)
\(740\) 0 0
\(741\) −32.2929 58.5235i −1.18631 2.14991i
\(742\) 0 0
\(743\) 19.8314 23.6342i 0.727544 0.867053i −0.267796 0.963476i \(-0.586295\pi\)
0.995341 + 0.0964222i \(0.0307399\pi\)
\(744\) 0 0
\(745\) −23.6612 + 4.17210i −0.866878 + 0.152854i
\(746\) 0 0
\(747\) −2.17431 0.0843165i −0.0795538 0.00308498i
\(748\) 0 0
\(749\) −44.6423 12.2210i −1.63119 0.446545i
\(750\) 0 0
\(751\) −4.22235 + 23.9461i −0.154076 + 0.873807i 0.805550 + 0.592528i \(0.201870\pi\)
−0.959626 + 0.281279i \(0.909241\pi\)
\(752\) 0 0
\(753\) −0.721173 4.61077i −0.0262810 0.168026i
\(754\) 0 0
\(755\) 1.31470 0.0478467
\(756\) 0 0
\(757\) −6.10213 −0.221786 −0.110893 0.993832i \(-0.535371\pi\)
−0.110893 + 0.993832i \(0.535371\pi\)
\(758\) 0 0
\(759\) 4.02194 3.24410i 0.145987 0.117753i
\(760\) 0 0
\(761\) −2.51770 + 14.2786i −0.0912667 + 0.517599i 0.904561 + 0.426344i \(0.140199\pi\)
−0.995828 + 0.0912546i \(0.970912\pi\)
\(762\) 0 0
\(763\) −30.7465 31.0809i −1.11310 1.12520i
\(764\) 0 0
\(765\) −1.03540 + 0.802537i −0.0374349 + 0.0290158i
\(766\) 0 0
\(767\) 58.5249 10.3195i 2.11321 0.372616i
\(768\) 0 0
\(769\) −22.5194 + 26.8375i −0.812069 + 0.967786i −0.999896 0.0144157i \(-0.995411\pi\)
0.187827 + 0.982202i \(0.439856\pi\)
\(770\) 0 0
\(771\) −32.9527 0.638689i −1.18676 0.0230018i
\(772\) 0 0
\(773\) 38.8404 1.39699 0.698496 0.715614i \(-0.253853\pi\)
0.698496 + 0.715614i \(0.253853\pi\)
\(774\) 0 0
\(775\) 14.3412i 0.515150i
\(776\) 0 0
\(777\) 4.36037 + 9.99010i 0.156427 + 0.358393i