Properties

Label 1148.2.ba.a.113.9
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.9
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.12

$q$-expansion

\(f(q)\) \(=\) \(q+0.216695i q^{3} +(-1.22916 - 3.78295i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.95304 q^{9} +O(q^{10})\) \(q+0.216695i q^{3} +(-1.22916 - 3.78295i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.95304 q^{9} +(0.409185 + 0.132952i) q^{11} +(2.74295 - 3.77534i) q^{13} +(0.819748 - 0.266352i) q^{15} +(-4.29238 - 1.39468i) q^{17} +(1.21601 + 1.67369i) q^{19} +(-0.175310 + 0.127370i) q^{21} +(1.13883 + 0.827411i) q^{23} +(-8.75484 + 6.36076i) q^{25} +1.29000i q^{27} +(-0.472988 + 0.153683i) q^{29} +(1.57517 - 4.84788i) q^{31} +(-0.0288101 + 0.0886683i) q^{33} +(2.33799 - 3.21797i) q^{35} +(-3.01426 - 9.27694i) q^{37} +(0.818098 + 0.594383i) q^{39} +(-6.19055 - 1.63618i) q^{41} +(5.23055 + 3.80022i) q^{43} +(-3.62975 - 11.1712i) q^{45} +(2.13941 - 2.94464i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(0.302220 - 0.930139i) q^{51} +(3.39420 - 1.10284i) q^{53} -1.71135i q^{55} +(-0.362680 + 0.263503i) q^{57} +(-11.4286 - 8.30337i) q^{59} +(5.50434 - 3.99914i) q^{61} +(1.73576 + 2.38906i) q^{63} +(-17.6535 - 5.73596i) q^{65} +(-4.97041 + 1.61498i) q^{67} +(-0.179296 + 0.246780i) q^{69} +(-11.2847 - 3.66663i) q^{71} +3.95893 q^{73} +(-1.37835 - 1.89713i) q^{75} +(0.132952 + 0.409185i) q^{77} +2.17988i q^{79} +8.57959 q^{81} +3.14995 q^{83} +17.9522i q^{85} +(-0.0333024 - 0.102494i) q^{87} +(-6.28917 - 8.65631i) q^{89} +4.66658 q^{91} +(1.05051 + 0.341332i) q^{93} +(4.83683 - 6.65733i) q^{95} +(10.7442 - 3.49101i) q^{97} +(1.20834 + 0.392613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 0.216695i 0.125109i 0.998042 + 0.0625545i \(0.0199247\pi\)
−0.998042 + 0.0625545i \(0.980075\pi\)
\(4\) 0 0
\(5\) −1.22916 3.78295i −0.549696 1.69179i −0.709556 0.704649i \(-0.751104\pi\)
0.159860 0.987140i \(-0.448896\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) 2.95304 0.984348
\(10\) 0 0
\(11\) 0.409185 + 0.132952i 0.123374 + 0.0400866i 0.370053 0.929011i \(-0.379339\pi\)
−0.246679 + 0.969097i \(0.579339\pi\)
\(12\) 0 0
\(13\) 2.74295 3.77534i 0.760757 1.04709i −0.236394 0.971657i \(-0.575966\pi\)
0.997151 0.0754345i \(-0.0240344\pi\)
\(14\) 0 0
\(15\) 0.819748 0.266352i 0.211658 0.0687719i
\(16\) 0 0
\(17\) −4.29238 1.39468i −1.04106 0.338260i −0.261904 0.965094i \(-0.584350\pi\)
−0.779152 + 0.626834i \(0.784350\pi\)
\(18\) 0 0
\(19\) 1.21601 + 1.67369i 0.278971 + 0.383971i 0.925393 0.379010i \(-0.123735\pi\)
−0.646422 + 0.762980i \(0.723735\pi\)
\(20\) 0 0
\(21\) −0.175310 + 0.127370i −0.0382558 + 0.0277945i
\(22\) 0 0
\(23\) 1.13883 + 0.827411i 0.237463 + 0.172527i 0.700152 0.713993i \(-0.253115\pi\)
−0.462689 + 0.886521i \(0.653115\pi\)
\(24\) 0 0
\(25\) −8.75484 + 6.36076i −1.75097 + 1.27215i
\(26\) 0 0
\(27\) 1.29000i 0.248260i
\(28\) 0 0
\(29\) −0.472988 + 0.153683i −0.0878318 + 0.0285383i −0.352603 0.935773i \(-0.614703\pi\)
0.264771 + 0.964311i \(0.414703\pi\)
\(30\) 0 0
\(31\) 1.57517 4.84788i 0.282909 0.870705i −0.704108 0.710093i \(-0.748653\pi\)
0.987018 0.160613i \(-0.0513470\pi\)
\(32\) 0 0
\(33\) −0.0288101 + 0.0886683i −0.00501519 + 0.0154352i
\(34\) 0 0
\(35\) 2.33799 3.21797i 0.395193 0.543937i
\(36\) 0 0
\(37\) −3.01426 9.27694i −0.495542 1.52512i −0.816111 0.577895i \(-0.803874\pi\)
0.320570 0.947225i \(-0.396126\pi\)
\(38\) 0 0
\(39\) 0.818098 + 0.594383i 0.131001 + 0.0951775i
\(40\) 0 0
\(41\) −6.19055 1.63618i −0.966801 0.255529i
\(42\) 0 0
\(43\) 5.23055 + 3.80022i 0.797651 + 0.579527i 0.910224 0.414116i \(-0.135909\pi\)
−0.112573 + 0.993643i \(0.535909\pi\)
\(44\) 0 0
\(45\) −3.62975 11.1712i −0.541092 1.66531i
\(46\) 0 0
\(47\) 2.13941 2.94464i 0.312065 0.429520i −0.623959 0.781457i \(-0.714477\pi\)
0.936024 + 0.351937i \(0.114477\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 0.302220 0.930139i 0.0423193 0.130245i
\(52\) 0 0
\(53\) 3.39420 1.10284i 0.466229 0.151487i −0.0664757 0.997788i \(-0.521175\pi\)
0.532705 + 0.846301i \(0.321175\pi\)
\(54\) 0 0
\(55\) 1.71135i 0.230758i
\(56\) 0 0
\(57\) −0.362680 + 0.263503i −0.0480382 + 0.0349018i
\(58\) 0 0
\(59\) −11.4286 8.30337i −1.48788 1.08101i −0.974910 0.222600i \(-0.928546\pi\)
−0.512969 0.858407i \(-0.671454\pi\)
\(60\) 0 0
\(61\) 5.50434 3.99914i 0.704759 0.512037i −0.176720 0.984261i \(-0.556549\pi\)
0.881479 + 0.472224i \(0.156549\pi\)
\(62\) 0 0
\(63\) 1.73576 + 2.38906i 0.218685 + 0.300994i
\(64\) 0 0
\(65\) −17.6535 5.73596i −2.18964 0.711458i
\(66\) 0 0
\(67\) −4.97041 + 1.61498i −0.607233 + 0.197302i −0.596464 0.802640i \(-0.703428\pi\)
−0.0107690 + 0.999942i \(0.503428\pi\)
\(68\) 0 0
\(69\) −0.179296 + 0.246780i −0.0215847 + 0.0297088i
\(70\) 0 0
\(71\) −11.2847 3.66663i −1.33925 0.435149i −0.450189 0.892933i \(-0.648643\pi\)
−0.889064 + 0.457784i \(0.848643\pi\)
\(72\) 0 0
\(73\) 3.95893 0.463358 0.231679 0.972792i \(-0.425578\pi\)
0.231679 + 0.972792i \(0.425578\pi\)
\(74\) 0 0
\(75\) −1.37835 1.89713i −0.159158 0.219062i
\(76\) 0 0
\(77\) 0.132952 + 0.409185i 0.0151513 + 0.0466309i
\(78\) 0 0
\(79\) 2.17988i 0.245256i 0.992453 + 0.122628i \(0.0391322\pi\)
−0.992453 + 0.122628i \(0.960868\pi\)
\(80\) 0 0
\(81\) 8.57959 0.953288
\(82\) 0 0
\(83\) 3.14995 0.345751 0.172876 0.984944i \(-0.444694\pi\)
0.172876 + 0.984944i \(0.444694\pi\)
\(84\) 0 0
\(85\) 17.9522i 1.94719i
\(86\) 0 0
\(87\) −0.0333024 0.102494i −0.00357039 0.0109885i
\(88\) 0 0
\(89\) −6.28917 8.65631i −0.666651 0.917567i 0.333027 0.942917i \(-0.391930\pi\)
−0.999679 + 0.0253506i \(0.991930\pi\)
\(90\) 0 0
\(91\) 4.66658 0.489191
\(92\) 0 0
\(93\) 1.05051 + 0.341332i 0.108933 + 0.0353945i
\(94\) 0 0
\(95\) 4.83683 6.65733i 0.496248 0.683027i
\(96\) 0 0
\(97\) 10.7442 3.49101i 1.09091 0.354458i 0.292312 0.956323i \(-0.405576\pi\)
0.798598 + 0.601865i \(0.205576\pi\)
\(98\) 0 0
\(99\) 1.20834 + 0.392613i 0.121443 + 0.0394591i
\(100\) 0 0
\(101\) 1.43053 + 1.96895i 0.142343 + 0.195918i 0.874236 0.485502i \(-0.161363\pi\)
−0.731893 + 0.681419i \(0.761363\pi\)
\(102\) 0 0
\(103\) −1.89414 + 1.37618i −0.186636 + 0.135599i −0.677180 0.735818i \(-0.736798\pi\)
0.490544 + 0.871416i \(0.336798\pi\)
\(104\) 0 0
\(105\) 0.697319 + 0.506632i 0.0680514 + 0.0494422i
\(106\) 0 0
\(107\) 14.4690 10.5123i 1.39877 1.01626i 0.403928 0.914791i \(-0.367645\pi\)
0.994838 0.101473i \(-0.0323554\pi\)
\(108\) 0 0
\(109\) 12.3115i 1.17923i 0.807685 + 0.589614i \(0.200720\pi\)
−0.807685 + 0.589614i \(0.799280\pi\)
\(110\) 0 0
\(111\) 2.01027 0.653176i 0.190806 0.0619967i
\(112\) 0 0
\(113\) −3.14514 + 9.67974i −0.295870 + 0.910594i 0.687058 + 0.726602i \(0.258902\pi\)
−0.982928 + 0.183991i \(0.941098\pi\)
\(114\) 0 0
\(115\) 1.73025 5.32518i 0.161347 0.496575i
\(116\) 0 0
\(117\) 8.10004 11.1488i 0.748849 1.03070i
\(118\) 0 0
\(119\) −1.39468 4.29238i −0.127850 0.393482i
\(120\) 0 0
\(121\) −8.74943 6.35683i −0.795403 0.577894i
\(122\) 0 0
\(123\) 0.354553 1.34146i 0.0319689 0.120956i
\(124\) 0 0
\(125\) 18.7337 + 13.6108i 1.67559 + 1.21739i
\(126\) 0 0
\(127\) 5.14230 + 15.8264i 0.456305 + 1.40436i 0.869596 + 0.493764i \(0.164379\pi\)
−0.413291 + 0.910599i \(0.635621\pi\)
\(128\) 0 0
\(129\) −0.823488 + 1.13343i −0.0725041 + 0.0997933i
\(130\) 0 0
\(131\) −5.66436 + 17.4331i −0.494897 + 1.52314i 0.322220 + 0.946665i \(0.395571\pi\)
−0.817117 + 0.576472i \(0.804429\pi\)
\(132\) 0 0
\(133\) −0.639293 + 1.96754i −0.0554337 + 0.170607i
\(134\) 0 0
\(135\) 4.87999 1.58561i 0.420003 0.136467i
\(136\) 0 0
\(137\) 4.55542i 0.389196i 0.980883 + 0.194598i \(0.0623403\pi\)
−0.980883 + 0.194598i \(0.937660\pi\)
\(138\) 0 0
\(139\) 7.78156 5.65363i 0.660023 0.479535i −0.206648 0.978415i \(-0.566255\pi\)
0.866671 + 0.498880i \(0.166255\pi\)
\(140\) 0 0
\(141\) 0.638090 + 0.463599i 0.0537368 + 0.0390421i
\(142\) 0 0
\(143\) 1.62431 1.18013i 0.135832 0.0986876i
\(144\) 0 0
\(145\) 1.16275 + 1.60039i 0.0965614 + 0.132905i
\(146\) 0 0
\(147\) −0.206089 0.0669625i −0.0169980 0.00552297i
\(148\) 0 0
\(149\) −3.19195 + 1.03713i −0.261495 + 0.0849649i −0.436830 0.899544i \(-0.643899\pi\)
0.175335 + 0.984509i \(0.443899\pi\)
\(150\) 0 0
\(151\) 7.21015 9.92393i 0.586754 0.807598i −0.407661 0.913133i \(-0.633656\pi\)
0.994416 + 0.105535i \(0.0336556\pi\)
\(152\) 0 0
\(153\) −12.6756 4.11855i −1.02476 0.332965i
\(154\) 0 0
\(155\) −20.2755 −1.62856
\(156\) 0 0
\(157\) −1.49501 2.05771i −0.119315 0.164223i 0.745182 0.666861i \(-0.232363\pi\)
−0.864497 + 0.502638i \(0.832363\pi\)
\(158\) 0 0
\(159\) 0.238981 + 0.735507i 0.0189524 + 0.0583295i
\(160\) 0 0
\(161\) 1.40768i 0.110940i
\(162\) 0 0
\(163\) 21.5148 1.68517 0.842585 0.538563i \(-0.181033\pi\)
0.842585 + 0.538563i \(0.181033\pi\)
\(164\) 0 0
\(165\) 0.370840 0.0288699
\(166\) 0 0
\(167\) 10.5967i 0.820000i 0.912085 + 0.410000i \(0.134471\pi\)
−0.912085 + 0.410000i \(0.865529\pi\)
\(168\) 0 0
\(169\) −2.71224 8.34740i −0.208633 0.642108i
\(170\) 0 0
\(171\) 3.59092 + 4.94248i 0.274605 + 0.377961i
\(172\) 0 0
\(173\) 3.44807 0.262152 0.131076 0.991372i \(-0.458157\pi\)
0.131076 + 0.991372i \(0.458157\pi\)
\(174\) 0 0
\(175\) −10.2919 3.34405i −0.777997 0.252786i
\(176\) 0 0
\(177\) 1.79930 2.47652i 0.135244 0.186147i
\(178\) 0 0
\(179\) 14.8273 4.81770i 1.10825 0.360092i 0.302977 0.952998i \(-0.402020\pi\)
0.805271 + 0.592906i \(0.202020\pi\)
\(180\) 0 0
\(181\) 5.09614 + 1.65584i 0.378793 + 0.123077i 0.492224 0.870469i \(-0.336184\pi\)
−0.113431 + 0.993546i \(0.536184\pi\)
\(182\) 0 0
\(183\) 0.866594 + 1.19276i 0.0640605 + 0.0881717i
\(184\) 0 0
\(185\) −31.3893 + 22.8056i −2.30778 + 1.67670i
\(186\) 0 0
\(187\) −1.57095 1.14136i −0.114879 0.0834647i
\(188\) 0 0
\(189\) −1.04363 + 0.758240i −0.0759128 + 0.0551539i
\(190\) 0 0
\(191\) 18.6695i 1.35088i −0.737416 0.675439i \(-0.763954\pi\)
0.737416 0.675439i \(-0.236046\pi\)
\(192\) 0 0
\(193\) −22.1479 + 7.19628i −1.59424 + 0.517999i −0.965674 0.259758i \(-0.916357\pi\)
−0.628565 + 0.777757i \(0.716357\pi\)
\(194\) 0 0
\(195\) 1.24295 3.82542i 0.0890098 0.273944i
\(196\) 0 0
\(197\) 0.451696 1.39018i 0.0321820 0.0990460i −0.933675 0.358121i \(-0.883418\pi\)
0.965857 + 0.259075i \(0.0834176\pi\)
\(198\) 0 0
\(199\) −16.1204 + 22.1879i −1.14275 + 1.57286i −0.381532 + 0.924356i \(0.624603\pi\)
−0.761215 + 0.648500i \(0.775397\pi\)
\(200\) 0 0
\(201\) −0.349959 1.07706i −0.0246842 0.0759703i
\(202\) 0 0
\(203\) −0.402348 0.292323i −0.0282393 0.0205170i
\(204\) 0 0
\(205\) 1.41955 + 25.4297i 0.0991459 + 1.77609i
\(206\) 0 0
\(207\) 3.36303 + 2.44338i 0.233746 + 0.169827i
\(208\) 0 0
\(209\) 0.275051 + 0.846519i 0.0190257 + 0.0585549i
\(210\) 0 0
\(211\) −1.60589 + 2.21031i −0.110554 + 0.152164i −0.860708 0.509098i \(-0.829979\pi\)
0.750155 + 0.661262i \(0.229979\pi\)
\(212\) 0 0
\(213\) 0.794542 2.44535i 0.0544411 0.167553i
\(214\) 0 0
\(215\) 7.94688 24.4580i 0.541973 1.66802i
\(216\) 0 0
\(217\) 4.84788 1.57517i 0.329096 0.106930i
\(218\) 0 0
\(219\) 0.857881i 0.0579703i
\(220\) 0 0
\(221\) −17.0392 + 12.3797i −1.14618 + 0.832748i
\(222\) 0 0
\(223\) −1.96039 1.42431i −0.131277 0.0953787i 0.520209 0.854039i \(-0.325854\pi\)
−0.651486 + 0.758661i \(0.725854\pi\)
\(224\) 0 0
\(225\) −25.8534 + 18.7836i −1.72356 + 1.25224i
\(226\) 0 0
\(227\) 6.10875 + 8.40797i 0.405452 + 0.558056i 0.962102 0.272691i \(-0.0879135\pi\)
−0.556650 + 0.830747i \(0.687914\pi\)
\(228\) 0 0
\(229\) 22.6120 + 7.34710i 1.49425 + 0.485510i 0.938334 0.345731i \(-0.112369\pi\)
0.555912 + 0.831241i \(0.312369\pi\)
\(230\) 0 0
\(231\) −0.0886683 + 0.0288101i −0.00583395 + 0.00189556i
\(232\) 0 0
\(233\) −14.7786 + 20.3410i −0.968179 + 1.33258i −0.0252174 + 0.999682i \(0.508028\pi\)
−0.942961 + 0.332902i \(0.891972\pi\)
\(234\) 0 0
\(235\) −13.7691 4.47386i −0.898198 0.291842i
\(236\) 0 0
\(237\) −0.472370 −0.0306837
\(238\) 0 0
\(239\) −4.74998 6.53779i −0.307251 0.422894i 0.627271 0.778801i \(-0.284172\pi\)
−0.934521 + 0.355907i \(0.884172\pi\)
\(240\) 0 0
\(241\) 2.45473 + 7.55489i 0.158123 + 0.486653i 0.998464 0.0554053i \(-0.0176451\pi\)
−0.840341 + 0.542059i \(0.817645\pi\)
\(242\) 0 0
\(243\) 5.72914i 0.367525i
\(244\) 0 0
\(245\) 3.97763 0.254122
\(246\) 0 0
\(247\) 9.65420 0.614282
\(248\) 0 0
\(249\) 0.682578i 0.0432566i
\(250\) 0 0
\(251\) −8.43428 25.9580i −0.532367 1.63846i −0.749271 0.662264i \(-0.769596\pi\)
0.216904 0.976193i \(-0.430404\pi\)
\(252\) 0 0
\(253\) 0.355987 + 0.489974i 0.0223807 + 0.0308044i
\(254\) 0 0
\(255\) −3.89015 −0.243611
\(256\) 0 0
\(257\) −1.97795 0.642673i −0.123381 0.0400889i 0.246676 0.969098i \(-0.420662\pi\)
−0.370057 + 0.929009i \(0.620662\pi\)
\(258\) 0 0
\(259\) 5.73347 7.89144i 0.356260 0.490350i
\(260\) 0 0
\(261\) −1.39676 + 0.453833i −0.0864570 + 0.0280916i
\(262\) 0 0
\(263\) 22.2119 + 7.21709i 1.36965 + 0.445025i 0.899252 0.437431i \(-0.144112\pi\)
0.470394 + 0.882456i \(0.344112\pi\)
\(264\) 0 0
\(265\) −8.34401 11.4845i −0.512569 0.705490i
\(266\) 0 0
\(267\) 1.87578 1.36283i 0.114796 0.0834041i
\(268\) 0 0
\(269\) 24.2208 + 17.5975i 1.47677 + 1.07294i 0.978579 + 0.205870i \(0.0660024\pi\)
0.498192 + 0.867067i \(0.333998\pi\)
\(270\) 0 0
\(271\) 15.9323 11.5755i 0.967819 0.703162i 0.0128656 0.999917i \(-0.495905\pi\)
0.954953 + 0.296755i \(0.0959046\pi\)
\(272\) 0 0
\(273\) 1.01123i 0.0612021i
\(274\) 0 0
\(275\) −4.42802 + 1.43875i −0.267020 + 0.0867600i
\(276\) 0 0
\(277\) −0.667329 + 2.05383i −0.0400959 + 0.123402i −0.969101 0.246665i \(-0.920665\pi\)
0.929005 + 0.370067i \(0.120665\pi\)
\(278\) 0 0
\(279\) 4.65155 14.3160i 0.278481 0.857077i
\(280\) 0 0
\(281\) 0.975261 1.34233i 0.0581792 0.0800768i −0.778936 0.627103i \(-0.784240\pi\)
0.837115 + 0.547027i \(0.184240\pi\)
\(282\) 0 0
\(283\) 1.44905 + 4.45972i 0.0861371 + 0.265103i 0.984843 0.173450i \(-0.0554914\pi\)
−0.898706 + 0.438552i \(0.855491\pi\)
\(284\) 0 0
\(285\) 1.44261 + 1.04812i 0.0854529 + 0.0620851i
\(286\) 0 0
\(287\) −2.31502 5.96998i −0.136651 0.352397i
\(288\) 0 0
\(289\) 2.72614 + 1.98066i 0.160361 + 0.116509i
\(290\) 0 0
\(291\) 0.756484 + 2.32822i 0.0443459 + 0.136483i
\(292\) 0 0
\(293\) −7.95949 + 10.9553i −0.464999 + 0.640016i −0.975536 0.219840i \(-0.929446\pi\)
0.510537 + 0.859856i \(0.329446\pi\)
\(294\) 0 0
\(295\) −17.3637 + 53.4401i −1.01096 + 3.11140i
\(296\) 0 0
\(297\) −0.171508 + 0.527846i −0.00995188 + 0.0306287i
\(298\) 0 0
\(299\) 6.24752 2.02994i 0.361304 0.117395i
\(300\) 0 0
\(301\) 6.46531i 0.372654i
\(302\) 0 0
\(303\) −0.426662 + 0.309988i −0.0245111 + 0.0178084i
\(304\) 0 0
\(305\) −21.8943 15.9071i −1.25366 0.910839i
\(306\) 0 0
\(307\) −12.2669 + 8.91242i −0.700109 + 0.508659i −0.879968 0.475034i \(-0.842436\pi\)
0.179859 + 0.983692i \(0.442436\pi\)
\(308\) 0 0
\(309\) −0.298211 0.410452i −0.0169646 0.0233498i
\(310\) 0 0
\(311\) 20.5959 + 6.69200i 1.16788 + 0.379469i 0.827853 0.560945i \(-0.189562\pi\)
0.340032 + 0.940414i \(0.389562\pi\)
\(312\) 0 0
\(313\) 32.4813 10.5538i 1.83595 0.596537i 0.837183 0.546923i \(-0.184201\pi\)
0.998768 0.0496141i \(-0.0157991\pi\)
\(314\) 0 0
\(315\) 6.90420 9.50282i 0.389008 0.535423i
\(316\) 0 0
\(317\) 24.2007 + 7.86329i 1.35925 + 0.441646i 0.895792 0.444474i \(-0.146609\pi\)
0.463455 + 0.886120i \(0.346609\pi\)
\(318\) 0 0
\(319\) −0.213972 −0.0119801
\(320\) 0 0
\(321\) 2.27797 + 3.13535i 0.127144 + 0.174998i
\(322\) 0 0
\(323\) −2.88531 8.88006i −0.160543 0.494100i
\(324\) 0 0
\(325\) 50.4997i 2.80122i
\(326\) 0 0
\(327\) −2.66784 −0.147532
\(328\) 0 0
\(329\) 3.63978 0.200667
\(330\) 0 0
\(331\) 12.8792i 0.707904i 0.935264 + 0.353952i \(0.115162\pi\)
−0.935264 + 0.353952i \(0.884838\pi\)
\(332\) 0 0
\(333\) −8.90124 27.3952i −0.487785 1.50125i
\(334\) 0 0
\(335\) 12.2188 + 16.8178i 0.667586 + 0.918853i
\(336\) 0 0
\(337\) −1.96009 −0.106773 −0.0533864 0.998574i \(-0.517002\pi\)
−0.0533864 + 0.998574i \(0.517002\pi\)
\(338\) 0 0
\(339\) −2.09755 0.681536i −0.113923 0.0370160i
\(340\) 0 0
\(341\) 1.28907 1.77426i 0.0698072 0.0960814i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) 1.15394 + 0.374938i 0.0621260 + 0.0201860i
\(346\) 0 0
\(347\) 10.6877 + 14.7104i 0.573748 + 0.789696i 0.992993 0.118177i \(-0.0377051\pi\)
−0.419245 + 0.907873i \(0.637705\pi\)
\(348\) 0 0
\(349\) 17.0025 12.3531i 0.910125 0.661245i −0.0309213 0.999522i \(-0.509844\pi\)
0.941047 + 0.338277i \(0.109844\pi\)
\(350\) 0 0
\(351\) 4.87018 + 3.53839i 0.259951 + 0.188865i
\(352\) 0 0
\(353\) 8.32859 6.05107i 0.443286 0.322066i −0.343653 0.939097i \(-0.611664\pi\)
0.786939 + 0.617030i \(0.211664\pi\)
\(354\) 0 0
\(355\) 47.1965i 2.50493i
\(356\) 0 0
\(357\) 0.930139 0.302220i 0.0492282 0.0159952i
\(358\) 0 0
\(359\) 3.99606 12.2986i 0.210904 0.649096i −0.788515 0.615015i \(-0.789150\pi\)
0.999419 0.0340804i \(-0.0108502\pi\)
\(360\) 0 0
\(361\) 4.54876 13.9996i 0.239408 0.736823i
\(362\) 0 0
\(363\) 1.37749 1.89596i 0.0722997 0.0995120i
\(364\) 0 0
\(365\) −4.86615 14.9765i −0.254706 0.783904i
\(366\) 0 0
\(367\) 1.48814 + 1.08120i 0.0776803 + 0.0564381i 0.625948 0.779865i \(-0.284712\pi\)
−0.548267 + 0.836303i \(0.684712\pi\)
\(368\) 0 0
\(369\) −18.2810 4.83172i −0.951669 0.251529i
\(370\) 0 0
\(371\) 2.88728 + 2.09773i 0.149900 + 0.108909i
\(372\) 0 0
\(373\) −0.723809 2.22765i −0.0374774 0.115344i 0.930568 0.366120i \(-0.119314\pi\)
−0.968045 + 0.250777i \(0.919314\pi\)
\(374\) 0 0
\(375\) −2.94940 + 4.05950i −0.152306 + 0.209631i
\(376\) 0 0
\(377\) −0.717175 + 2.20724i −0.0369364 + 0.113679i
\(378\) 0 0
\(379\) 1.88762 5.80949i 0.0969605 0.298414i −0.890799 0.454397i \(-0.849855\pi\)
0.987760 + 0.155984i \(0.0498547\pi\)
\(380\) 0 0
\(381\) −3.42950 + 1.11431i −0.175698 + 0.0570879i
\(382\) 0 0
\(383\) 29.0345i 1.48360i −0.670624 0.741798i \(-0.733973\pi\)
0.670624 0.741798i \(-0.266027\pi\)
\(384\) 0 0
\(385\) 1.38451 1.00590i 0.0705611 0.0512656i
\(386\) 0 0
\(387\) 15.4460 + 11.2222i 0.785166 + 0.570457i
\(388\) 0 0
\(389\) 2.41673 1.75585i 0.122533 0.0890253i −0.524831 0.851206i \(-0.675871\pi\)
0.647364 + 0.762181i \(0.275871\pi\)
\(390\) 0 0
\(391\) −3.73434 5.13988i −0.188854 0.259935i
\(392\) 0 0
\(393\) −3.77767 1.22744i −0.190558 0.0619161i
\(394\) 0 0
\(395\) 8.24639 2.67942i 0.414921 0.134816i
\(396\) 0 0
\(397\) −9.04581 + 12.4505i −0.453996 + 0.624872i −0.973250 0.229748i \(-0.926210\pi\)
0.519254 + 0.854620i \(0.326210\pi\)
\(398\) 0 0
\(399\) −0.426356 0.138532i −0.0213445 0.00693526i
\(400\) 0 0
\(401\) 24.1478 1.20588 0.602942 0.797785i \(-0.293995\pi\)
0.602942 + 0.797785i \(0.293995\pi\)
\(402\) 0 0
\(403\) −13.9818 19.2443i −0.696483 0.958627i
\(404\) 0 0
\(405\) −10.5457 32.4562i −0.524018 1.61276i
\(406\) 0 0
\(407\) 4.19673i 0.208024i
\(408\) 0 0
\(409\) −15.2044 −0.751810 −0.375905 0.926658i \(-0.622668\pi\)
−0.375905 + 0.926658i \(0.622668\pi\)
\(410\) 0 0
\(411\) −0.987138 −0.0486919
\(412\) 0 0
\(413\) 14.1265i 0.695122i
\(414\) 0 0
\(415\) −3.87178 11.9161i −0.190058 0.584938i
\(416\) 0 0
\(417\) 1.22511 + 1.68623i 0.0599941 + 0.0825748i
\(418\) 0 0
\(419\) 8.21864 0.401507 0.200754 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(420\) 0 0
\(421\) −22.1900 7.20998i −1.08148 0.351393i −0.286529 0.958072i \(-0.592501\pi\)
−0.794947 + 0.606679i \(0.792501\pi\)
\(422\) 0 0
\(423\) 6.31776 8.69565i 0.307180 0.422797i
\(424\) 0 0
\(425\) 46.4503 15.0926i 2.25317 0.732100i
\(426\) 0 0
\(427\) 6.47074 + 2.10247i 0.313141 + 0.101746i
\(428\) 0 0
\(429\) 0.255729 + 0.351980i 0.0123467 + 0.0169938i
\(430\) 0 0
\(431\) −16.9722 + 12.3310i −0.817521 + 0.593964i −0.916001 0.401175i \(-0.868602\pi\)
0.0984805 + 0.995139i \(0.468602\pi\)
\(432\) 0 0
\(433\) 1.17329 + 0.852444i 0.0563846 + 0.0409658i 0.615621 0.788043i \(-0.288905\pi\)
−0.559236 + 0.829009i \(0.688905\pi\)
\(434\) 0 0
\(435\) −0.346797 + 0.251963i −0.0166277 + 0.0120807i
\(436\) 0 0
\(437\) 2.91219i 0.139309i
\(438\) 0 0
\(439\) 2.70574 0.879149i 0.129138 0.0419595i −0.243735 0.969842i \(-0.578373\pi\)
0.372873 + 0.927882i \(0.378373\pi\)
\(440\) 0 0
\(441\) −0.912541 + 2.80851i −0.0434543 + 0.133739i
\(442\) 0 0
\(443\) 8.70423 26.7889i 0.413550 1.27278i −0.499991 0.866031i \(-0.666663\pi\)
0.913541 0.406746i \(-0.133337\pi\)
\(444\) 0 0
\(445\) −25.0160 + 34.4316i −1.18587 + 1.63222i
\(446\) 0 0
\(447\) −0.224741 0.691681i −0.0106299 0.0327154i
\(448\) 0 0
\(449\) 11.2150 + 8.14820i 0.529270 + 0.384537i 0.820085 0.572242i \(-0.193926\pi\)
−0.290815 + 0.956779i \(0.593926\pi\)
\(450\) 0 0
\(451\) −2.31554 1.49255i −0.109035 0.0702813i
\(452\) 0 0
\(453\) 2.15047 + 1.56241i 0.101038 + 0.0734082i
\(454\) 0 0
\(455\) −5.73596 17.6535i −0.268906 0.827607i
\(456\) 0 0
\(457\) −8.48268 + 11.6754i −0.396803 + 0.546152i −0.959938 0.280213i \(-0.909595\pi\)
0.563135 + 0.826365i \(0.309595\pi\)
\(458\) 0 0
\(459\) 1.79913 5.53716i 0.0839762 0.258452i
\(460\) 0 0
\(461\) 8.32203 25.6126i 0.387596 1.19290i −0.546984 0.837143i \(-0.684224\pi\)
0.934580 0.355754i \(-0.115776\pi\)
\(462\) 0 0
\(463\) −32.3641 + 10.5157i −1.50409 + 0.488707i −0.941207 0.337831i \(-0.890307\pi\)
−0.562880 + 0.826539i \(0.690307\pi\)
\(464\) 0 0
\(465\) 4.39359i 0.203748i
\(466\) 0 0
\(467\) −21.5943 + 15.6892i −0.999267 + 0.726010i −0.961931 0.273293i \(-0.911887\pi\)
−0.0373362 + 0.999303i \(0.511887\pi\)
\(468\) 0 0
\(469\) −4.22809 3.07188i −0.195235 0.141846i
\(470\) 0 0
\(471\) 0.445895 0.323962i 0.0205458 0.0149274i
\(472\) 0 0
\(473\) 1.63501 + 2.25040i 0.0751780 + 0.103474i
\(474\) 0 0
\(475\) −21.2919 6.91815i −0.976939 0.317427i
\(476\) 0 0
\(477\) 10.0232 3.25674i 0.458932 0.149116i
\(478\) 0 0
\(479\) −14.4742 + 19.9220i −0.661343 + 0.910260i −0.999525 0.0308203i \(-0.990188\pi\)
0.338182 + 0.941081i \(0.390188\pi\)
\(480\) 0 0
\(481\) −43.2916 14.0663i −1.97393 0.641368i
\(482\) 0 0
\(483\) −0.305037 −0.0138796
\(484\) 0 0
\(485\) −26.4126 36.3539i −1.19934 1.65074i
\(486\) 0 0
\(487\) 10.8022 + 33.2458i 0.489496 + 1.50651i 0.825363 + 0.564603i \(0.190971\pi\)
−0.335867 + 0.941909i \(0.609029\pi\)
\(488\) 0 0
\(489\) 4.66216i 0.210830i
\(490\) 0 0
\(491\) −16.3713 −0.738828 −0.369414 0.929265i \(-0.620442\pi\)
−0.369414 + 0.929265i \(0.620442\pi\)
\(492\) 0 0
\(493\) 2.24459 0.101091
\(494\) 0 0
\(495\) 5.05368i 0.227146i
\(496\) 0 0
\(497\) −3.66663 11.2847i −0.164471 0.506190i
\(498\) 0 0
\(499\) 22.7804 + 31.3545i 1.01979 + 1.40362i 0.912351 + 0.409408i \(0.134265\pi\)
0.107438 + 0.994212i \(0.465735\pi\)
\(500\) 0 0
\(501\) −2.29626 −0.102589
\(502\) 0 0
\(503\) 38.3663 + 12.4660i 1.71067 + 0.555830i 0.990445 0.137910i \(-0.0440386\pi\)
0.720225 + 0.693741i \(0.244039\pi\)
\(504\) 0 0
\(505\) 5.69011 7.83177i 0.253207 0.348509i
\(506\) 0 0
\(507\) 1.80884 0.587728i 0.0803335 0.0261019i
\(508\) 0 0
\(509\) −38.2295 12.4215i −1.69449 0.550574i −0.706858 0.707355i \(-0.749888\pi\)
−0.987633 + 0.156781i \(0.949888\pi\)
\(510\) 0 0
\(511\) 2.32700 + 3.20284i 0.102941 + 0.141685i
\(512\) 0 0
\(513\) −2.15905 + 1.56864i −0.0953245 + 0.0692573i
\(514\) 0 0
\(515\) 7.53421 + 5.47392i 0.331997 + 0.241210i
\(516\) 0 0
\(517\) 1.26691 0.920463i 0.0557186 0.0404819i
\(518\) 0 0
\(519\) 0.747179i 0.0327975i
\(520\) 0 0
\(521\) 12.8706 4.18191i 0.563871 0.183213i −0.0131915 0.999913i \(-0.504199\pi\)
0.577062 + 0.816700i \(0.304199\pi\)
\(522\) 0 0
\(523\) −10.5194 + 32.3753i −0.459980 + 1.41567i 0.405208 + 0.914225i \(0.367199\pi\)
−0.865188 + 0.501448i \(0.832801\pi\)
\(524\) 0 0
\(525\) 0.724639 2.23021i 0.0316259 0.0973344i
\(526\) 0 0
\(527\) −13.5225 + 18.6121i −0.589049 + 0.810756i
\(528\) 0 0
\(529\) −6.49506 19.9897i −0.282394 0.869119i
\(530\) 0 0
\(531\) −33.7492 24.5202i −1.46459 1.06409i
\(532\) 0 0
\(533\) −23.1575 + 18.8835i −1.00306 + 0.817935i
\(534\) 0 0
\(535\) −57.5522 41.8141i −2.48820 1.80778i
\(536\) 0 0
\(537\) 1.04397 + 3.21301i 0.0450507 + 0.138652i
\(538\) 0 0
\(539\) −0.252890 + 0.348073i −0.0108927 + 0.0149926i
\(540\) 0 0
\(541\) 7.97878 24.5562i 0.343035 1.05575i −0.619593 0.784923i \(-0.712702\pi\)
0.962627 0.270829i \(-0.0872978\pi\)
\(542\) 0 0
\(543\) −0.358811 + 1.10431i −0.0153981 + 0.0473904i
\(544\) 0 0
\(545\) 46.5739 15.1328i 1.99501 0.648217i
\(546\) 0 0
\(547\) 15.1067i 0.645916i −0.946413 0.322958i \(-0.895323\pi\)
0.946413 0.322958i \(-0.104677\pi\)
\(548\) 0 0
\(549\) 16.2546 11.8096i 0.693728 0.504023i
\(550\) 0 0
\(551\) −0.832375 0.604756i −0.0354604 0.0257635i
\(552\) 0 0
\(553\) −1.76356 + 1.28130i −0.0749942 + 0.0544865i
\(554\) 0 0
\(555\) −4.94187 6.80190i −0.209771 0.288725i
\(556\) 0 0
\(557\) 2.13139 + 0.692529i 0.0903097 + 0.0293434i 0.353823 0.935312i \(-0.384881\pi\)
−0.263514 + 0.964656i \(0.584881\pi\)
\(558\) 0 0
\(559\) 28.6942 9.32332i 1.21364 0.394335i
\(560\) 0 0
\(561\) 0.247328 0.340418i 0.0104422 0.0143724i
\(562\) 0 0
\(563\) 10.4568 + 3.39762i 0.440701 + 0.143193i 0.520959 0.853582i \(-0.325574\pi\)
−0.0802578 + 0.996774i \(0.525574\pi\)
\(564\) 0 0
\(565\) 40.4839 1.70317
\(566\) 0 0
\(567\) 5.04296 + 6.94104i 0.211784 + 0.291496i
\(568\) 0 0
\(569\) 2.51711 + 7.74688i 0.105523 + 0.324766i 0.989853 0.142096i \(-0.0453843\pi\)
−0.884330 + 0.466863i \(0.845384\pi\)
\(570\) 0 0
\(571\) 12.4554i 0.521244i −0.965441 0.260622i \(-0.916072\pi\)
0.965441 0.260622i \(-0.0839277\pi\)
\(572\) 0 0
\(573\) 4.04559 0.169007
\(574\) 0 0
\(575\) −15.2333 −0.635271
\(576\) 0 0
\(577\) 1.17753i 0.0490213i −0.999700 0.0245106i \(-0.992197\pi\)
0.999700 0.0245106i \(-0.00780276\pi\)
\(578\) 0 0
\(579\) −1.55940 4.79933i −0.0648064 0.199454i
\(580\) 0 0
\(581\) 1.85149 + 2.54836i 0.0768128 + 0.105724i
\(582\) 0 0
\(583\) 1.53548 0.0635931
\(584\) 0 0
\(585\) −52.1314 16.9385i −2.15537 0.700322i
\(586\) 0 0
\(587\) −1.14260 + 1.57265i −0.0471601 + 0.0649103i −0.831946 0.554857i \(-0.812773\pi\)
0.784786 + 0.619767i \(0.212773\pi\)
\(588\) 0 0
\(589\) 10.0293 3.25871i 0.413249 0.134273i
\(590\) 0 0
\(591\) 0.301244 + 0.0978802i 0.0123915 + 0.00402626i
\(592\) 0 0
\(593\) −20.4868 28.1977i −0.841292 1.15794i −0.985715 0.168423i \(-0.946133\pi\)
0.144423 0.989516i \(-0.453867\pi\)
\(594\) 0 0
\(595\) −14.5236 + 10.5520i −0.595410 + 0.432591i
\(596\) 0 0
\(597\) −4.80800 3.49322i −0.196778 0.142968i
\(598\) 0 0
\(599\) 29.2814 21.2742i 1.19641 0.869239i 0.202479 0.979287i \(-0.435100\pi\)
0.993926 + 0.110047i \(0.0351002\pi\)
\(600\) 0 0
\(601\) 31.9839i 1.30465i −0.757939 0.652325i \(-0.773794\pi\)
0.757939 0.652325i \(-0.226206\pi\)
\(602\) 0 0
\(603\) −14.6778 + 4.76912i −0.597728 + 0.194214i
\(604\) 0 0
\(605\) −13.2932 + 40.9122i −0.540445 + 1.66332i
\(606\) 0 0
\(607\) 4.76037 14.6509i 0.193217 0.594662i −0.806775 0.590858i \(-0.798789\pi\)
0.999993 0.00380388i \(-0.00121082\pi\)
\(608\) 0 0
\(609\) 0.0633450 0.0871869i 0.00256687 0.00353299i
\(610\) 0 0
\(611\) −5.24875 16.1540i −0.212342 0.653521i
\(612\) 0 0
\(613\) −8.03801 5.83996i −0.324652 0.235874i 0.413506 0.910501i \(-0.364304\pi\)
−0.738158 + 0.674628i \(0.764304\pi\)
\(614\) 0 0
\(615\) −5.51049 + 0.307610i −0.222204 + 0.0124040i
\(616\) 0 0
\(617\) −8.09555 5.88176i −0.325915 0.236791i 0.412781 0.910831i \(-0.364558\pi\)
−0.738695 + 0.674040i \(0.764558\pi\)
\(618\) 0 0
\(619\) −0.285586 0.878943i −0.0114787 0.0353277i 0.945153 0.326628i \(-0.105912\pi\)
−0.956632 + 0.291300i \(0.905912\pi\)
\(620\) 0 0
\(621\) −1.06736 + 1.46909i −0.0428316 + 0.0589526i
\(622\) 0 0
\(623\) 3.30641 10.1761i 0.132469 0.407697i
\(624\) 0 0
\(625\) 11.7422 36.1388i 0.469688 1.44555i
\(626\) 0 0
\(627\) −0.183437 + 0.0596021i −0.00732575 + 0.00238028i
\(628\) 0 0
\(629\) 44.0241i 1.75536i
\(630\) 0 0
\(631\) 1.13038 0.821273i 0.0449999 0.0326944i −0.565058 0.825051i \(-0.691146\pi\)
0.610058 + 0.792357i \(0.291146\pi\)
\(632\) 0 0
\(633\) −0.478964 0.347988i −0.0190371 0.0138313i
\(634\) 0 0
\(635\) 53.5497 38.9062i 2.12506 1.54394i
\(636\) 0 0
\(637\) 2.74295 + 3.77534i 0.108680 + 0.149585i
\(638\) 0 0
\(639\) −33.3243 10.8277i −1.31829 0.428338i
\(640\) 0 0
\(641\) −12.0262 + 3.90755i −0.475007 + 0.154339i −0.536730 0.843754i \(-0.680340\pi\)
0.0617229 + 0.998093i \(0.480340\pi\)
\(642\) 0 0
\(643\) −7.73287 + 10.6434i −0.304955 + 0.419734i −0.933799 0.357797i \(-0.883528\pi\)
0.628845 + 0.777531i \(0.283528\pi\)
\(644\) 0 0
\(645\) 5.29993 + 1.72205i 0.208684 + 0.0678057i
\(646\) 0 0
\(647\) 22.0631 0.867389 0.433695 0.901060i \(-0.357210\pi\)
0.433695 + 0.901060i \(0.357210\pi\)
\(648\) 0 0
\(649\) −3.57246 4.91707i −0.140231 0.193012i
\(650\) 0 0
\(651\) 0.341332 + 1.05051i 0.0133779 + 0.0411728i
\(652\) 0 0
\(653\) 24.5879i 0.962198i 0.876666 + 0.481099i \(0.159762\pi\)
−0.876666 + 0.481099i \(0.840238\pi\)
\(654\) 0 0
\(655\) 72.9110 2.84887
\(656\) 0 0
\(657\) 11.6909 0.456105
\(658\) 0 0
\(659\) 19.0955i 0.743856i 0.928262 + 0.371928i \(0.121303\pi\)
−0.928262 + 0.371928i \(0.878697\pi\)
\(660\) 0 0
\(661\) −0.958737 2.95069i −0.0372906 0.114769i 0.930678 0.365838i \(-0.119218\pi\)
−0.967969 + 0.251070i \(0.919218\pi\)
\(662\) 0 0
\(663\) −2.68262 3.69231i −0.104184 0.143397i
\(664\) 0 0
\(665\) 8.22891 0.319103
\(666\) 0 0
\(667\) −0.665815 0.216336i −0.0257804 0.00837657i
\(668\) 0 0
\(669\) 0.308640 0.424807i 0.0119327 0.0164240i
\(670\) 0 0
\(671\) 2.78399 0.904572i 0.107475 0.0349206i
\(672\) 0 0
\(673\) 29.7834 + 9.67721i 1.14806 + 0.373029i 0.820414 0.571770i \(-0.193743\pi\)
0.327651 + 0.944799i \(0.393743\pi\)
\(674\) 0 0
\(675\) −8.20535 11.2937i −0.315824 0.434695i
\(676\) 0 0
\(677\) 23.4802 17.0594i 0.902419 0.655646i −0.0366672 0.999328i \(-0.511674\pi\)
0.939086 + 0.343682i \(0.111674\pi\)
\(678\) 0 0
\(679\) 9.13957 + 6.64029i 0.350745 + 0.254831i
\(680\) 0 0
\(681\) −1.82197 + 1.32374i −0.0698179 + 0.0507257i
\(682\) 0 0
\(683\) 12.1143i 0.463542i 0.972770 + 0.231771i \(0.0744520\pi\)
−0.972770 + 0.231771i \(0.925548\pi\)
\(684\) 0 0
\(685\) 17.2330 5.59933i 0.658438 0.213939i
\(686\) 0 0
\(687\) −1.59208 + 4.89992i −0.0607417 + 0.186944i
\(688\) 0 0
\(689\) 5.14651 15.8393i 0.196066 0.603430i
\(690\) 0 0
\(691\) 9.19916 12.6616i 0.349952 0.481668i −0.597363 0.801971i \(-0.703785\pi\)
0.947315 + 0.320303i \(0.103785\pi\)
\(692\) 0 0
\(693\) 0.392613 + 1.20834i 0.0149141 + 0.0459010i
\(694\) 0 0
\(695\) −30.9522 22.4881i −1.17408 0.853022i
\(696\) 0 0
\(697\) 24.2903 + 15.6570i 0.920060 + 0.593050i
\(698\) 0 0
\(699\) −4.40780 3.20245i −0.166718 0.121128i
\(700\) 0 0
\(701\) 3.19278 + 9.82636i 0.120590 + 0.371136i 0.993072 0.117509i \(-0.0374910\pi\)
−0.872482 + 0.488646i \(0.837491\pi\)
\(702\) 0 0
\(703\) 11.8614 16.3258i 0.447360 0.615738i
\(704\) 0 0
\(705\) 0.969463 2.98370i 0.0365121 0.112373i
\(706\) 0 0
\(707\) −0.752072 + 2.31464i −0.0282846 + 0.0870510i
\(708\) 0 0
\(709\) 0.0188840 0.00613579i 0.000709204 0.000230434i −0.308662 0.951172i \(-0.599881\pi\)
0.309372 + 0.950941i \(0.399881\pi\)
\(710\) 0 0
\(711\) 6.43728i 0.241417i
\(712\) 0 0
\(713\) 5.80505 4.21762i 0.217401 0.157951i
\(714\) 0 0
\(715\) −6.46092 4.69413i −0.241625 0.175551i
\(716\) 0 0
\(717\) 1.41671 1.02930i 0.0529079 0.0384398i
\(718\) 0 0
\(719\) 5.82008 + 8.01065i 0.217052 + 0.298747i 0.903634 0.428306i \(-0.140889\pi\)
−0.686581 + 0.727053i \(0.740889\pi\)
\(720\) 0 0
\(721\) −2.22670 0.723499i −0.0829266 0.0269445i
\(722\) 0 0
\(723\) −1.63711 + 0.531928i −0.0608847 + 0.0197826i
\(724\) 0 0
\(725\) 3.16339 4.35404i 0.117486 0.161705i
\(726\) 0 0
\(727\) 14.8932 + 4.83909i 0.552358 + 0.179472i 0.571880 0.820338i \(-0.306214\pi\)
−0.0195219 + 0.999809i \(0.506214\pi\)
\(728\) 0 0
\(729\) 24.4973 0.907308
\(730\) 0 0
\(731\) −17.1514 23.6069i −0.634369 0.873134i
\(732\) 0 0
\(733\) −12.7297 39.1781i −0.470183 1.44707i −0.852345 0.522979i \(-0.824820\pi\)
0.382162 0.924095i \(-0.375180\pi\)
\(734\) 0 0
\(735\) 0.861934i 0.0317929i
\(736\) 0 0
\(737\) −2.24853 −0.0828257
\(738\) 0 0
\(739\) 28.3486 1.04282 0.521410 0.853306i \(-0.325406\pi\)
0.521410 + 0.853306i \(0.325406\pi\)
\(740\) 0 0
\(741\) 2.09202i 0.0768522i
\(742\) 0 0
\(743\) −1.60008 4.92454i −0.0587013 0.180664i 0.917406 0.397952i \(-0.130279\pi\)
−0.976108 + 0.217288i \(0.930279\pi\)
\(744\) 0 0
\(745\) 7.84682 + 10.8002i 0.287485 + 0.395690i
\(746\) 0 0
\(747\) 9.30193 0.340340
\(748\) 0 0
\(749\) 17.0093 + 5.52665i 0.621505 + 0.201939i
\(750\) 0 0
\(751\) −4.88786 + 6.72756i −0.178360 + 0.245492i −0.888831 0.458235i \(-0.848482\pi\)
0.710471 + 0.703727i \(0.248482\pi\)
\(752\) 0 0
\(753\) 5.62498 1.82767i 0.204986 0.0666039i
\(754\) 0 0
\(755\) −46.4042 15.0776i −1.68882 0.548731i
\(756\) 0 0
\(757\) 8.49926 + 11.6982i 0.308911 + 0.425179i 0.935041 0.354539i \(-0.115362\pi\)
−0.626130 + 0.779718i \(0.715362\pi\)
\(758\) 0 0
\(759\) −0.106175 + 0.0771407i −0.00385391 + 0.00280003i
\(760\) 0 0
\(761\) −23.5850 17.1355i −0.854954 0.621161i 0.0715532 0.997437i \(-0.477204\pi\)
−0.926508 + 0.376276i \(0.877204\pi\)
\(762\) 0 0
\(763\) −9.96022 + 7.23652i −0.360584 + 0.261980i
\(764\) 0 0
\(765\) 53.0136i 1.91671i
\(766\) 0 0
\(767\) −62.6962 + 20.3712i −2.26383 + 0.735562i
\(768\) 0 0
\(769\) −15.3565 + 47.2623i −0.553768 + 1.70432i 0.145407 + 0.989372i \(0.453551\pi\)
−0.699175 + 0.714951i \(0.746449\pi\)
\(770\) 0 0
\(771\) 0.139264 0.428611i 0.00501548 0.0154361i
\(772\) 0 0
\(773\) 4.28435 5.89690i 0.154097 0.212097i −0.724988 0.688762i \(-0.758155\pi\)
0.879085 + 0.476665i \(0.158155\pi\)
\(774\) 0 0
\(775\) 17.0458 + 52.4617i 0.612305 + 1.88448i
\(776\) 0 0
\(777\) 1.71004 + 1.24241i 0.0613472 + 0.0445714i
\(778\) 0 0
\(779\) −4.78929 12.3507i −0.171594 0.442509i
\(780\) 0 0
\(781\) −4.13006 3.00066i −0.147785 0.107372i
\(782\) 0 0
\(783\) −0.198251 0.610153i −0.00708490 0.0218051i
\(784\) 0 0
\(785\) −5.94661 + 8.18481i −0.212244 + 0.292128i
\(786\) 0 0
\(787\) −10.9182 + 33.6028i −0.389192 + 1.19781i 0.544201 + 0.838955i \(0.316833\pi\)
−0.933393 + 0.358856i \(0.883167\pi\)
\(788\) 0 0
\(789\) −1.56391 + 4.81322i −0.0556766 + 0.171355i
\(790\) 0 0
\(791\) −9.67974 + 3.14514i −0.344172 + 0.111828i
\(792\) 0 0
\(793\) 31.7502i 1.12748i
\(794\) 0 0
\(795\) 2.48865 1.80811i 0.0882631 0.0641269i
\(796\) 0 0
\(797\) 1.00198 + 0.727979i 0.0354918 + 0.0257863i