Properties

Label 1148.2.ba.a.113.15
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 113.15
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.6

$q$-expansion

\(f(q)\) \(=\) \(q+1.49455i q^{3} +(-0.331199 - 1.01933i) q^{5} +(-0.587785 - 0.809017i) q^{7} +0.766322 q^{9} +O(q^{10})\) \(q+1.49455i q^{3} +(-0.331199 - 1.01933i) q^{5} +(-0.587785 - 0.809017i) q^{7} +0.766322 q^{9} +(2.51743 + 0.817962i) q^{11} +(2.13014 - 2.93189i) q^{13} +(1.52343 - 0.494994i) q^{15} +(-4.41518 - 1.43458i) q^{17} +(-4.70970 - 6.48235i) q^{19} +(1.20912 - 0.878474i) q^{21} +(1.02450 + 0.744340i) q^{23} +(3.11575 - 2.26373i) q^{25} +5.62895i q^{27} +(5.56167 - 1.80710i) q^{29} +(-0.118298 + 0.364085i) q^{31} +(-1.22248 + 3.76242i) q^{33} +(-0.629979 + 0.867091i) q^{35} +(0.591352 + 1.82000i) q^{37} +(4.38186 + 3.18361i) q^{39} +(2.68889 - 5.81118i) q^{41} +(-1.78623 - 1.29777i) q^{43} +(-0.253805 - 0.781133i) q^{45} +(4.11743 - 5.66715i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(2.14405 - 6.59870i) q^{51} +(-0.335641 + 0.109056i) q^{53} -2.83699i q^{55} +(9.68819 - 7.03888i) q^{57} +(11.8101 + 8.58057i) q^{59} +(10.6461 - 7.73483i) q^{61} +(-0.450433 - 0.619967i) q^{63} +(-3.69406 - 1.20027i) q^{65} +(-4.13585 + 1.34382i) q^{67} +(-1.11245 + 1.53116i) q^{69} +(5.05236 + 1.64161i) q^{71} -3.35273 q^{73} +(3.38325 + 4.65664i) q^{75} +(-0.817962 - 2.51743i) q^{77} +10.3297i q^{79} -6.11379 q^{81} -1.94220 q^{83} +4.97564i q^{85} +(2.70080 + 8.31219i) q^{87} +(1.27320 + 1.75241i) q^{89} -3.62402 q^{91} +(-0.544142 - 0.176803i) q^{93} +(-5.04778 + 6.94768i) q^{95} +(4.24196 - 1.37830i) q^{97} +(1.92916 + 0.626822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

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
\(3\) 1.49455i 0.862879i 0.902142 + 0.431439i \(0.141994\pi\)
−0.902142 + 0.431439i \(0.858006\pi\)
\(4\) 0 0
\(5\) −0.331199 1.01933i −0.148117 0.455857i 0.849282 0.527940i \(-0.177035\pi\)
−0.997399 + 0.0720829i \(0.977035\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) 0.766322 0.255441
\(10\) 0 0
\(11\) 2.51743 + 0.817962i 0.759033 + 0.246625i 0.662864 0.748740i \(-0.269341\pi\)
0.0961695 + 0.995365i \(0.469341\pi\)
\(12\) 0 0
\(13\) 2.13014 2.93189i 0.590796 0.813161i −0.404031 0.914745i \(-0.632391\pi\)
0.994827 + 0.101585i \(0.0323913\pi\)
\(14\) 0 0
\(15\) 1.52343 0.494994i 0.393349 0.127807i
\(16\) 0 0
\(17\) −4.41518 1.43458i −1.07084 0.347936i −0.280024 0.959993i \(-0.590342\pi\)
−0.790814 + 0.612057i \(0.790342\pi\)
\(18\) 0 0
\(19\) −4.70970 6.48235i −1.08048 1.48715i −0.858992 0.511989i \(-0.828909\pi\)
−0.221488 0.975163i \(-0.571091\pi\)
\(20\) 0 0
\(21\) 1.20912 0.878474i 0.263851 0.191699i
\(22\) 0 0
\(23\) 1.02450 + 0.744340i 0.213622 + 0.155206i 0.689451 0.724332i \(-0.257852\pi\)
−0.475829 + 0.879538i \(0.657852\pi\)
\(24\) 0 0
\(25\) 3.11575 2.26373i 0.623150 0.452745i
\(26\) 0 0
\(27\) 5.62895i 1.08329i
\(28\) 0 0
\(29\) 5.56167 1.80710i 1.03278 0.335569i 0.256889 0.966441i \(-0.417303\pi\)
0.775887 + 0.630872i \(0.217303\pi\)
\(30\) 0 0
\(31\) −0.118298 + 0.364085i −0.0212470 + 0.0653915i −0.961118 0.276139i \(-0.910945\pi\)
0.939871 + 0.341530i \(0.110945\pi\)
\(32\) 0 0
\(33\) −1.22248 + 3.76242i −0.212807 + 0.654953i
\(34\) 0 0
\(35\) −0.629979 + 0.867091i −0.106486 + 0.146565i
\(36\) 0 0
\(37\) 0.591352 + 1.82000i 0.0972177 + 0.299205i 0.987825 0.155567i \(-0.0497205\pi\)
−0.890608 + 0.454773i \(0.849721\pi\)
\(38\) 0 0
\(39\) 4.38186 + 3.18361i 0.701659 + 0.509785i
\(40\) 0 0
\(41\) 2.68889 5.81118i 0.419934 0.907555i
\(42\) 0 0
\(43\) −1.78623 1.29777i −0.272397 0.197908i 0.443198 0.896424i \(-0.353844\pi\)
−0.715594 + 0.698516i \(0.753844\pi\)
\(44\) 0 0
\(45\) −0.253805 0.781133i −0.0378351 0.116444i
\(46\) 0 0
\(47\) 4.11743 5.66715i 0.600589 0.826639i −0.395173 0.918607i \(-0.629315\pi\)
0.995762 + 0.0919671i \(0.0293155\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 2.14405 6.59870i 0.300227 0.924003i
\(52\) 0 0
\(53\) −0.335641 + 0.109056i −0.0461039 + 0.0149801i −0.331978 0.943287i \(-0.607716\pi\)
0.285874 + 0.958267i \(0.407716\pi\)
\(54\) 0 0
\(55\) 2.83699i 0.382540i
\(56\) 0 0
\(57\) 9.68819 7.03888i 1.28323 0.932323i
\(58\) 0 0
\(59\) 11.8101 + 8.58057i 1.53755 + 1.11709i 0.951849 + 0.306566i \(0.0991801\pi\)
0.585699 + 0.810528i \(0.300820\pi\)
\(60\) 0 0
\(61\) 10.6461 7.73483i 1.36309 0.990343i 0.364849 0.931067i \(-0.381121\pi\)
0.998242 0.0592763i \(-0.0188793\pi\)
\(62\) 0 0
\(63\) −0.450433 0.619967i −0.0567492 0.0781085i
\(64\) 0 0
\(65\) −3.69406 1.20027i −0.458192 0.148876i
\(66\) 0 0
\(67\) −4.13585 + 1.34382i −0.505275 + 0.164174i −0.550552 0.834801i \(-0.685583\pi\)
0.0452775 + 0.998974i \(0.485583\pi\)
\(68\) 0 0
\(69\) −1.11245 + 1.53116i −0.133924 + 0.184330i
\(70\) 0 0
\(71\) 5.05236 + 1.64161i 0.599605 + 0.194824i 0.593064 0.805155i \(-0.297918\pi\)
0.00654094 + 0.999979i \(0.497918\pi\)
\(72\) 0 0
\(73\) −3.35273 −0.392407 −0.196204 0.980563i \(-0.562861\pi\)
−0.196204 + 0.980563i \(0.562861\pi\)
\(74\) 0 0
\(75\) 3.38325 + 4.65664i 0.390664 + 0.537703i
\(76\) 0 0
\(77\) −0.817962 2.51743i −0.0932154 0.286888i
\(78\) 0 0
\(79\) 10.3297i 1.16218i 0.813838 + 0.581092i \(0.197374\pi\)
−0.813838 + 0.581092i \(0.802626\pi\)
\(80\) 0 0
\(81\) −6.11379 −0.679309
\(82\) 0 0
\(83\) −1.94220 −0.213185 −0.106592 0.994303i \(-0.533994\pi\)
−0.106592 + 0.994303i \(0.533994\pi\)
\(84\) 0 0
\(85\) 4.97564i 0.539684i
\(86\) 0 0
\(87\) 2.70080 + 8.31219i 0.289556 + 0.891161i
\(88\) 0 0
\(89\) 1.27320 + 1.75241i 0.134959 + 0.185755i 0.871147 0.491022i \(-0.163376\pi\)
−0.736189 + 0.676776i \(0.763376\pi\)
\(90\) 0 0
\(91\) −3.62402 −0.379900
\(92\) 0 0
\(93\) −0.544142 0.176803i −0.0564249 0.0183336i
\(94\) 0 0
\(95\) −5.04778 + 6.94768i −0.517891 + 0.712816i
\(96\) 0 0
\(97\) 4.24196 1.37830i 0.430706 0.139945i −0.0856377 0.996326i \(-0.527293\pi\)
0.516344 + 0.856382i \(0.327293\pi\)
\(98\) 0 0
\(99\) 1.92916 + 0.626822i 0.193888 + 0.0629980i
\(100\) 0 0
\(101\) −2.16400 2.97849i −0.215326 0.296371i 0.687667 0.726026i \(-0.258635\pi\)
−0.902993 + 0.429655i \(0.858635\pi\)
\(102\) 0 0
\(103\) −3.73549 + 2.71399i −0.368069 + 0.267418i −0.756410 0.654098i \(-0.773048\pi\)
0.388341 + 0.921516i \(0.373048\pi\)
\(104\) 0 0
\(105\) −1.29591 0.941535i −0.126468 0.0918844i
\(106\) 0 0
\(107\) −1.10062 + 0.799649i −0.106401 + 0.0773050i −0.639714 0.768613i \(-0.720947\pi\)
0.533312 + 0.845918i \(0.320947\pi\)
\(108\) 0 0
\(109\) 10.0640i 0.963956i 0.876183 + 0.481978i \(0.160081\pi\)
−0.876183 + 0.481978i \(0.839919\pi\)
\(110\) 0 0
\(111\) −2.72007 + 0.883805i −0.258178 + 0.0838871i
\(112\) 0 0
\(113\) 0.254840 0.784317i 0.0239733 0.0737823i −0.938354 0.345676i \(-0.887650\pi\)
0.962327 + 0.271893i \(0.0876498\pi\)
\(114\) 0 0
\(115\) 0.419413 1.29082i 0.0391105 0.120370i
\(116\) 0 0
\(117\) 1.63238 2.24677i 0.150913 0.207714i
\(118\) 0 0
\(119\) 1.43458 + 4.41518i 0.131508 + 0.404739i
\(120\) 0 0
\(121\) −3.23081 2.34732i −0.293710 0.213392i
\(122\) 0 0
\(123\) 8.68510 + 4.01868i 0.783109 + 0.362352i
\(124\) 0 0
\(125\) −7.67487 5.57612i −0.686461 0.498743i
\(126\) 0 0
\(127\) 4.02156 + 12.3771i 0.356856 + 1.09829i 0.954926 + 0.296845i \(0.0959345\pi\)
−0.598070 + 0.801444i \(0.704066\pi\)
\(128\) 0 0
\(129\) 1.93958 2.66960i 0.170770 0.235045i
\(130\) 0 0
\(131\) 4.55842 14.0294i 0.398271 1.22575i −0.528114 0.849174i \(-0.677101\pi\)
0.926385 0.376578i \(-0.122899\pi\)
\(132\) 0 0
\(133\) −2.47604 + 7.62046i −0.214700 + 0.660777i
\(134\) 0 0
\(135\) 5.73775 1.86431i 0.493827 0.160454i
\(136\) 0 0
\(137\) 17.2129i 1.47060i −0.677743 0.735298i \(-0.737042\pi\)
0.677743 0.735298i \(-0.262958\pi\)
\(138\) 0 0
\(139\) 6.36351 4.62336i 0.539746 0.392148i −0.284245 0.958752i \(-0.591743\pi\)
0.823991 + 0.566603i \(0.191743\pi\)
\(140\) 0 0
\(141\) 8.46984 + 6.15370i 0.713289 + 0.518235i
\(142\) 0 0
\(143\) 7.76066 5.63845i 0.648979 0.471511i
\(144\) 0 0
\(145\) −3.68404 5.07065i −0.305943 0.421095i
\(146\) 0 0
\(147\) −1.42140 0.461841i −0.117235 0.0380920i
\(148\) 0 0
\(149\) −8.05944 + 2.61867i −0.660255 + 0.214530i −0.619930 0.784657i \(-0.712839\pi\)
−0.0403246 + 0.999187i \(0.512839\pi\)
\(150\) 0 0
\(151\) 3.14927 4.33459i 0.256284 0.352744i −0.661416 0.750019i \(-0.730044\pi\)
0.917700 + 0.397275i \(0.130044\pi\)
\(152\) 0 0
\(153\) −3.38345 1.09935i −0.273536 0.0888771i
\(154\) 0 0
\(155\) 0.410302 0.0329562
\(156\) 0 0
\(157\) 5.33909 + 7.34863i 0.426106 + 0.586485i 0.967054 0.254571i \(-0.0819344\pi\)
−0.540948 + 0.841056i \(0.681934\pi\)
\(158\) 0 0
\(159\) −0.162990 0.501632i −0.0129260 0.0397820i
\(160\) 0 0
\(161\) 1.26635i 0.0998021i
\(162\) 0 0
\(163\) −24.5690 −1.92439 −0.962197 0.272355i \(-0.912197\pi\)
−0.962197 + 0.272355i \(0.912197\pi\)
\(164\) 0 0
\(165\) 4.24002 0.330085
\(166\) 0 0
\(167\) 9.31857i 0.721093i −0.932741 0.360546i \(-0.882590\pi\)
0.932741 0.360546i \(-0.117410\pi\)
\(168\) 0 0
\(169\) −0.0412563 0.126974i −0.00317356 0.00976721i
\(170\) 0 0
\(171\) −3.60915 4.96756i −0.275998 0.379879i
\(172\) 0 0
\(173\) −7.25967 −0.551942 −0.275971 0.961166i \(-0.588999\pi\)
−0.275971 + 0.961166i \(0.588999\pi\)
\(174\) 0 0
\(175\) −3.66278 1.19011i −0.276880 0.0899639i
\(176\) 0 0
\(177\) −12.8241 + 17.6508i −0.963917 + 1.32672i
\(178\) 0 0
\(179\) −15.2904 + 4.96816i −1.14286 + 0.371338i −0.818449 0.574579i \(-0.805166\pi\)
−0.324411 + 0.945916i \(0.605166\pi\)
\(180\) 0 0
\(181\) −22.6258 7.35156i −1.68176 0.546438i −0.696510 0.717547i \(-0.745265\pi\)
−0.985252 + 0.171110i \(0.945265\pi\)
\(182\) 0 0
\(183\) 11.5601 + 15.9111i 0.854546 + 1.17618i
\(184\) 0 0
\(185\) 1.65932 1.20556i 0.121995 0.0886348i
\(186\) 0 0
\(187\) −9.94146 7.22290i −0.726992 0.528190i
\(188\) 0 0
\(189\) 4.55392 3.30862i 0.331249 0.240666i
\(190\) 0 0
\(191\) 1.43742i 0.104008i 0.998647 + 0.0520039i \(0.0165608\pi\)
−0.998647 + 0.0520039i \(0.983439\pi\)
\(192\) 0 0
\(193\) 14.3423 4.66009i 1.03238 0.335440i 0.256649 0.966505i \(-0.417382\pi\)
0.775730 + 0.631064i \(0.217382\pi\)
\(194\) 0 0
\(195\) 1.79387 5.52096i 0.128461 0.395364i
\(196\) 0 0
\(197\) 1.23566 3.80297i 0.0880371 0.270950i −0.897339 0.441341i \(-0.854503\pi\)
0.985377 + 0.170391i \(0.0545029\pi\)
\(198\) 0 0
\(199\) −15.1894 + 20.9064i −1.07675 + 1.48202i −0.213697 + 0.976900i \(0.568551\pi\)
−0.863051 + 0.505117i \(0.831449\pi\)
\(200\) 0 0
\(201\) −2.00841 6.18124i −0.141662 0.435991i
\(202\) 0 0
\(203\) −4.73104 3.43730i −0.332054 0.241251i
\(204\) 0 0
\(205\) −6.81406 0.816197i −0.475914 0.0570057i
\(206\) 0 0
\(207\) 0.785093 + 0.570404i 0.0545678 + 0.0396458i
\(208\) 0 0
\(209\) −6.55402 20.1712i −0.453351 1.39527i
\(210\) 0 0
\(211\) 7.18518 9.88955i 0.494648 0.680825i −0.486589 0.873631i \(-0.661759\pi\)
0.981237 + 0.192807i \(0.0617590\pi\)
\(212\) 0 0
\(213\) −2.45347 + 7.55101i −0.168109 + 0.517387i
\(214\) 0 0
\(215\) −0.731254 + 2.25057i −0.0498711 + 0.153487i
\(216\) 0 0
\(217\) 0.364085 0.118298i 0.0247157 0.00803061i
\(218\) 0 0
\(219\) 5.01082i 0.338600i
\(220\) 0 0
\(221\) −13.6110 + 9.88897i −0.915575 + 0.665204i
\(222\) 0 0
\(223\) 9.94843 + 7.22796i 0.666196 + 0.484020i 0.868750 0.495251i \(-0.164924\pi\)
−0.202554 + 0.979271i \(0.564924\pi\)
\(224\) 0 0
\(225\) 2.38767 1.73474i 0.159178 0.115649i
\(226\) 0 0
\(227\) 4.20407 + 5.78640i 0.279034 + 0.384057i 0.925414 0.378959i \(-0.123718\pi\)
−0.646380 + 0.763016i \(0.723718\pi\)
\(228\) 0 0
\(229\) −24.3949 7.92638i −1.61206 0.523790i −0.642009 0.766697i \(-0.721899\pi\)
−0.970050 + 0.242907i \(0.921899\pi\)
\(230\) 0 0
\(231\) 3.76242 1.22248i 0.247549 0.0804336i
\(232\) 0 0
\(233\) 11.3959 15.6851i 0.746570 1.02757i −0.251644 0.967820i \(-0.580971\pi\)
0.998214 0.0597454i \(-0.0190289\pi\)
\(234\) 0 0
\(235\) −7.14037 2.32005i −0.465787 0.151343i
\(236\) 0 0
\(237\) −15.4383 −1.00282
\(238\) 0 0
\(239\) 1.52483 + 2.09875i 0.0986331 + 0.135757i 0.855481 0.517834i \(-0.173262\pi\)
−0.756848 + 0.653591i \(0.773262\pi\)
\(240\) 0 0
\(241\) −2.30328 7.08875i −0.148367 0.456627i 0.849062 0.528294i \(-0.177168\pi\)
−0.997429 + 0.0716672i \(0.977168\pi\)
\(242\) 0 0
\(243\) 7.74951i 0.497131i
\(244\) 0 0
\(245\) 1.07178 0.0684738
\(246\) 0 0
\(247\) −29.0379 −1.84764
\(248\) 0 0
\(249\) 2.90272i 0.183952i
\(250\) 0 0
\(251\) 5.86948 + 18.0644i 0.370478 + 1.14021i 0.946479 + 0.322766i \(0.104613\pi\)
−0.576001 + 0.817449i \(0.695387\pi\)
\(252\) 0 0
\(253\) 1.97025 + 2.71182i 0.123869 + 0.170491i
\(254\) 0 0
\(255\) −7.43634 −0.465682
\(256\) 0 0
\(257\) −8.20644 2.66644i −0.511904 0.166328i 0.0416640 0.999132i \(-0.486734\pi\)
−0.553568 + 0.832804i \(0.686734\pi\)
\(258\) 0 0
\(259\) 1.12482 1.54818i 0.0698929 0.0961993i
\(260\) 0 0
\(261\) 4.26203 1.38482i 0.263813 0.0857180i
\(262\) 0 0
\(263\) 27.7928 + 9.03043i 1.71378 + 0.556840i 0.990955 0.134193i \(-0.0428442\pi\)
0.722823 + 0.691033i \(0.242844\pi\)
\(264\) 0 0
\(265\) 0.222328 + 0.306009i 0.0136575 + 0.0187980i
\(266\) 0 0
\(267\) −2.61906 + 1.90286i −0.160284 + 0.116453i
\(268\) 0 0
\(269\) 10.9080 + 7.92512i 0.665072 + 0.483203i 0.868372 0.495913i \(-0.165167\pi\)
−0.203300 + 0.979117i \(0.565167\pi\)
\(270\) 0 0
\(271\) 5.80370 4.21663i 0.352550 0.256142i −0.397388 0.917651i \(-0.630083\pi\)
0.749938 + 0.661508i \(0.230083\pi\)
\(272\) 0 0
\(273\) 5.41627i 0.327808i
\(274\) 0 0
\(275\) 9.69532 3.15020i 0.584650 0.189964i
\(276\) 0 0
\(277\) −8.00344 + 24.6321i −0.480880 + 1.48000i 0.356980 + 0.934112i \(0.383807\pi\)
−0.837860 + 0.545885i \(0.816193\pi\)
\(278\) 0 0
\(279\) −0.0906545 + 0.279006i −0.00542735 + 0.0167037i
\(280\) 0 0
\(281\) −1.19229 + 1.64104i −0.0711259 + 0.0978964i −0.843098 0.537760i \(-0.819271\pi\)
0.771972 + 0.635657i \(0.219271\pi\)
\(282\) 0 0
\(283\) −0.273225 0.840902i −0.0162416 0.0499864i 0.942607 0.333903i \(-0.108366\pi\)
−0.958849 + 0.283917i \(0.908366\pi\)
\(284\) 0 0
\(285\) −10.3836 7.54416i −0.615074 0.446877i
\(286\) 0 0
\(287\) −6.28184 + 1.24037i −0.370805 + 0.0732168i
\(288\) 0 0
\(289\) 3.68249 + 2.67549i 0.216617 + 0.157382i
\(290\) 0 0
\(291\) 2.05993 + 6.33982i 0.120755 + 0.371647i
\(292\) 0 0
\(293\) −17.0897 + 23.5219i −0.998390 + 1.37417i −0.0720823 + 0.997399i \(0.522964\pi\)
−0.926308 + 0.376767i \(0.877036\pi\)
\(294\) 0 0
\(295\) 4.83489 14.8803i 0.281498 0.866363i
\(296\) 0 0
\(297\) −4.60427 + 14.1705i −0.267167 + 0.822255i
\(298\) 0 0
\(299\) 4.36465 1.41816i 0.252414 0.0820143i
\(300\) 0 0
\(301\) 2.20790i 0.127261i
\(302\) 0 0
\(303\) 4.45150 3.23421i 0.255732 0.185800i
\(304\) 0 0
\(305\) −11.4103 8.29006i −0.653351 0.474688i
\(306\) 0 0
\(307\) −21.9244 + 15.9290i −1.25129 + 0.909119i −0.998296 0.0583482i \(-0.981417\pi\)
−0.252998 + 0.967467i \(0.581417\pi\)
\(308\) 0 0
\(309\) −4.05619 5.58287i −0.230749 0.317599i
\(310\) 0 0
\(311\) 9.43566 + 3.06583i 0.535047 + 0.173847i 0.564063 0.825732i \(-0.309237\pi\)
−0.0290161 + 0.999579i \(0.509237\pi\)
\(312\) 0 0
\(313\) −24.0323 + 7.80856i −1.35839 + 0.441366i −0.895504 0.445054i \(-0.853184\pi\)
−0.462881 + 0.886420i \(0.653184\pi\)
\(314\) 0 0
\(315\) −0.482767 + 0.664471i −0.0272008 + 0.0374387i
\(316\) 0 0
\(317\) 13.5051 + 4.38808i 0.758523 + 0.246459i 0.662644 0.748934i \(-0.269434\pi\)
0.0958782 + 0.995393i \(0.469434\pi\)
\(318\) 0 0
\(319\) 15.4792 0.866671
\(320\) 0 0
\(321\) −1.19511 1.64493i −0.0667048 0.0918113i
\(322\) 0 0
\(323\) 11.4947 + 35.3772i 0.639584 + 1.96844i
\(324\) 0 0
\(325\) 13.9571i 0.774201i
\(326\) 0 0
\(327\) −15.0411 −0.831777
\(328\) 0 0
\(329\) −7.00499 −0.386197
\(330\) 0 0
\(331\) 19.5106i 1.07240i −0.844090 0.536201i \(-0.819859\pi\)
0.844090 0.536201i \(-0.180141\pi\)
\(332\) 0 0
\(333\) 0.453166 + 1.39470i 0.0248334 + 0.0764292i
\(334\) 0 0
\(335\) 2.73958 + 3.77071i 0.149679 + 0.206016i
\(336\) 0 0
\(337\) −9.25542 −0.504175 −0.252088 0.967704i \(-0.581117\pi\)
−0.252088 + 0.967704i \(0.581117\pi\)
\(338\) 0 0
\(339\) 1.17220 + 0.380871i 0.0636652 + 0.0206861i
\(340\) 0 0
\(341\) −0.595615 + 0.819793i −0.0322543 + 0.0443943i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) 1.92920 + 0.626834i 0.103864 + 0.0337476i
\(346\) 0 0
\(347\) −19.0582 26.2313i −1.02310 1.40817i −0.910010 0.414586i \(-0.863926\pi\)
−0.113086 0.993585i \(-0.536074\pi\)
\(348\) 0 0
\(349\) −9.23809 + 6.71186i −0.494504 + 0.359278i −0.806914 0.590669i \(-0.798864\pi\)
0.312410 + 0.949947i \(0.398864\pi\)
\(350\) 0 0
\(351\) 16.5035 + 11.9905i 0.880891 + 0.640005i
\(352\) 0 0
\(353\) 25.8668 18.7933i 1.37675 1.00027i 0.379576 0.925161i \(-0.376070\pi\)
0.997175 0.0751078i \(-0.0239301\pi\)
\(354\) 0 0
\(355\) 5.69371i 0.302191i
\(356\) 0 0
\(357\) −6.59870 + 2.14405i −0.349240 + 0.113475i
\(358\) 0 0
\(359\) 6.53482 20.1121i 0.344895 1.06148i −0.616745 0.787163i \(-0.711549\pi\)
0.961640 0.274314i \(-0.0884508\pi\)
\(360\) 0 0
\(361\) −13.9682 + 42.9898i −0.735169 + 2.26262i
\(362\) 0 0
\(363\) 3.50818 4.82860i 0.184132 0.253436i
\(364\) 0 0
\(365\) 1.11042 + 3.41753i 0.0581222 + 0.178882i
\(366\) 0 0
\(367\) 19.5162 + 14.1794i 1.01874 + 0.740157i 0.966024 0.258452i \(-0.0832125\pi\)
0.0527151 + 0.998610i \(0.483212\pi\)
\(368\) 0 0
\(369\) 2.06056 4.45324i 0.107268 0.231826i
\(370\) 0 0
\(371\) 0.285514 + 0.207438i 0.0148231 + 0.0107696i
\(372\) 0 0
\(373\) −2.04184 6.28415i −0.105723 0.325381i 0.884177 0.467153i \(-0.154720\pi\)
−0.989899 + 0.141772i \(0.954720\pi\)
\(374\) 0 0
\(375\) 8.33378 11.4705i 0.430355 0.592333i
\(376\) 0 0
\(377\) 6.54895 20.1556i 0.337288 1.03807i
\(378\) 0 0
\(379\) −11.5492 + 35.5449i −0.593245 + 1.82582i −0.0299690 + 0.999551i \(0.509541\pi\)
−0.563276 + 0.826269i \(0.690459\pi\)
\(380\) 0 0
\(381\) −18.4982 + 6.01042i −0.947690 + 0.307923i
\(382\) 0 0
\(383\) 6.44871i 0.329514i 0.986334 + 0.164757i \(0.0526839\pi\)
−0.986334 + 0.164757i \(0.947316\pi\)
\(384\) 0 0
\(385\) −2.29517 + 1.66754i −0.116973 + 0.0849858i
\(386\) 0 0
\(387\) −1.36882 0.994508i −0.0695812 0.0505537i
\(388\) 0 0
\(389\) −12.2445 + 8.89612i −0.620819 + 0.451051i −0.853207 0.521572i \(-0.825346\pi\)
0.232389 + 0.972623i \(0.425346\pi\)
\(390\) 0 0
\(391\) −3.45552 4.75611i −0.174753 0.240527i
\(392\) 0 0
\(393\) 20.9676 + 6.81278i 1.05768 + 0.343659i
\(394\) 0 0
\(395\) 10.5294 3.42119i 0.529789 0.172139i
\(396\) 0 0
\(397\) 6.47932 8.91801i 0.325188 0.447582i −0.614855 0.788640i \(-0.710785\pi\)
0.940042 + 0.341058i \(0.110785\pi\)
\(398\) 0 0
\(399\) −11.3891 3.70056i −0.570171 0.185260i
\(400\) 0 0
\(401\) −8.93915 −0.446400 −0.223200 0.974773i \(-0.571650\pi\)
−0.223200 + 0.974773i \(0.571650\pi\)
\(402\) 0 0
\(403\) 0.815464 + 1.12239i 0.0406212 + 0.0559103i
\(404\) 0 0
\(405\) 2.02488 + 6.23195i 0.100617 + 0.309668i
\(406\) 0 0
\(407\) 5.06541i 0.251083i
\(408\) 0 0
\(409\) 25.6774 1.26967 0.634834 0.772649i \(-0.281069\pi\)
0.634834 + 0.772649i \(0.281069\pi\)
\(410\) 0 0
\(411\) 25.7255 1.26895
\(412\) 0 0
\(413\) 14.5981i 0.718327i
\(414\) 0 0
\(415\) 0.643257 + 1.97974i 0.0315763 + 0.0971817i
\(416\) 0 0
\(417\) 6.90984 + 9.51058i 0.338376 + 0.465735i
\(418\) 0 0
\(419\) 25.5619 1.24878 0.624389 0.781113i \(-0.285348\pi\)
0.624389 + 0.781113i \(0.285348\pi\)
\(420\) 0 0
\(421\) 11.7297 + 3.81120i 0.571669 + 0.185747i 0.580565 0.814214i \(-0.302832\pi\)
−0.00889582 + 0.999960i \(0.502832\pi\)
\(422\) 0 0
\(423\) 3.15528 4.34286i 0.153415 0.211157i
\(424\) 0 0
\(425\) −17.0041 + 5.52496i −0.824819 + 0.268000i
\(426\) 0 0
\(427\) −12.5152 4.06644i −0.605654 0.196789i
\(428\) 0 0
\(429\) 8.42694 + 11.5987i 0.406857 + 0.559990i
\(430\) 0 0
\(431\) 5.35102 3.88774i 0.257750 0.187266i −0.451405 0.892319i \(-0.649077\pi\)
0.709154 + 0.705053i \(0.249077\pi\)
\(432\) 0 0
\(433\) −19.1414 13.9070i −0.919877 0.668330i 0.0236163 0.999721i \(-0.492482\pi\)
−0.943493 + 0.331391i \(0.892482\pi\)
\(434\) 0 0
\(435\) 7.57834 5.50599i 0.363354 0.263992i
\(436\) 0 0
\(437\) 10.1468i 0.485385i
\(438\) 0 0
\(439\) 5.75343 1.86940i 0.274596 0.0892217i −0.168482 0.985705i \(-0.553886\pi\)
0.443078 + 0.896483i \(0.353886\pi\)
\(440\) 0 0
\(441\) −0.236806 + 0.728815i −0.0112765 + 0.0347055i
\(442\) 0 0
\(443\) −2.20782 + 6.79497i −0.104897 + 0.322839i −0.989706 0.143114i \(-0.954288\pi\)
0.884809 + 0.465953i \(0.154288\pi\)
\(444\) 0 0
\(445\) 1.36459 1.87820i 0.0646880 0.0890353i
\(446\) 0 0
\(447\) −3.91373 12.0452i −0.185113 0.569720i
\(448\) 0 0
\(449\) 26.2350 + 19.0608i 1.23810 + 0.899536i 0.997471 0.0710801i \(-0.0226446\pi\)
0.240634 + 0.970616i \(0.422645\pi\)
\(450\) 0 0
\(451\) 11.5224 12.4298i 0.542569 0.585298i
\(452\) 0 0
\(453\) 6.47826 + 4.70673i 0.304375 + 0.221142i
\(454\) 0 0
\(455\) 1.20027 + 3.69406i 0.0562697 + 0.173180i
\(456\) 0 0
\(457\) −7.74914 + 10.6658i −0.362489 + 0.498924i −0.950840 0.309682i \(-0.899777\pi\)
0.588351 + 0.808606i \(0.299777\pi\)
\(458\) 0 0
\(459\) 8.07518 24.8528i 0.376917 1.16003i
\(460\) 0 0
\(461\) −8.90930 + 27.4200i −0.414948 + 1.27708i 0.497350 + 0.867550i \(0.334306\pi\)
−0.912298 + 0.409527i \(0.865694\pi\)
\(462\) 0 0
\(463\) −22.4730 + 7.30193i −1.04441 + 0.339349i −0.780472 0.625190i \(-0.785021\pi\)
−0.263938 + 0.964540i \(0.585021\pi\)
\(464\) 0 0
\(465\) 0.613216i 0.0284372i
\(466\) 0 0
\(467\) −27.6492 + 20.0883i −1.27945 + 0.929577i −0.999536 0.0304473i \(-0.990307\pi\)
−0.279917 + 0.960024i \(0.590307\pi\)
\(468\) 0 0
\(469\) 3.51817 + 2.55610i 0.162454 + 0.118030i
\(470\) 0 0
\(471\) −10.9829 + 7.97954i −0.506065 + 0.367678i
\(472\) 0 0
\(473\) −3.43517 4.72810i −0.157949 0.217398i
\(474\) 0 0
\(475\) −29.3485 9.53591i −1.34660 0.437537i
\(476\) 0 0
\(477\) −0.257209 + 0.0835723i −0.0117768 + 0.00382651i
\(478\) 0 0
\(479\) 3.62426 4.98836i 0.165597 0.227924i −0.718152 0.695886i \(-0.755012\pi\)
0.883748 + 0.467962i \(0.155012\pi\)
\(480\) 0 0
\(481\) 6.59570 + 2.14307i 0.300738 + 0.0977157i
\(482\) 0 0
\(483\) 1.89262 0.0861171
\(484\) 0 0
\(485\) −2.80987 3.86746i −0.127590 0.175612i
\(486\) 0 0
\(487\) −0.0479182 0.147477i −0.00217138 0.00668282i 0.949965 0.312356i \(-0.101118\pi\)
−0.952136 + 0.305674i \(0.901118\pi\)
\(488\) 0 0
\(489\) 36.7196i 1.66052i
\(490\) 0 0
\(491\) 11.0131 0.497012 0.248506 0.968630i \(-0.420060\pi\)
0.248506 + 0.968630i \(0.420060\pi\)
\(492\) 0 0
\(493\) −27.1482 −1.22269
\(494\) 0 0
\(495\) 2.17405i 0.0977162i
\(496\) 0 0
\(497\) −1.64161 5.05236i −0.0736364 0.226630i
\(498\) 0 0
\(499\) 0.354823 + 0.488372i 0.0158841 + 0.0218625i 0.816885 0.576800i \(-0.195699\pi\)
−0.801001 + 0.598663i \(0.795699\pi\)
\(500\) 0 0
\(501\) 13.9271 0.622216
\(502\) 0 0
\(503\) 13.0882 + 4.25263i 0.583576 + 0.189615i 0.585902 0.810382i \(-0.300740\pi\)
−0.00232615 + 0.999997i \(0.500740\pi\)
\(504\) 0 0
\(505\) −2.31934 + 3.19230i −0.103209 + 0.142055i
\(506\) 0 0
\(507\) 0.189769 0.0616595i 0.00842792 0.00273840i
\(508\) 0 0
\(509\) 18.9828 + 6.16788i 0.841398 + 0.273387i 0.697839 0.716255i \(-0.254145\pi\)
0.143559 + 0.989642i \(0.454145\pi\)
\(510\) 0 0
\(511\) 1.97069 + 2.71242i 0.0871780 + 0.119990i
\(512\) 0 0
\(513\) 36.4888 26.5107i 1.61102 1.17048i
\(514\) 0 0
\(515\) 4.00364 + 2.90881i 0.176421 + 0.128178i
\(516\) 0 0
\(517\) 15.0008 10.8988i 0.659736 0.479327i
\(518\) 0 0
\(519\) 10.8499i 0.476259i
\(520\) 0 0
\(521\) 29.1020 9.45580i 1.27498 0.414266i 0.408170 0.912906i \(-0.366167\pi\)
0.866809 + 0.498640i \(0.166167\pi\)
\(522\) 0 0
\(523\) −6.49194 + 19.9801i −0.283873 + 0.873670i 0.702862 + 0.711327i \(0.251905\pi\)
−0.986734 + 0.162344i \(0.948095\pi\)
\(524\) 0 0
\(525\) 1.77868 5.47421i 0.0776279 0.238914i
\(526\) 0 0
\(527\) 1.04462 1.43779i 0.0455042 0.0626311i
\(528\) 0 0
\(529\) −6.61184 20.3492i −0.287471 0.884746i
\(530\) 0 0
\(531\) 9.05036 + 6.57547i 0.392752 + 0.285351i
\(532\) 0 0
\(533\) −11.3100 20.2622i −0.489892 0.877653i
\(534\) 0 0
\(535\) 1.17963 + 0.857051i 0.0509998 + 0.0370535i
\(536\) 0 0
\(537\) −7.42516 22.8523i −0.320419 0.986149i
\(538\) 0 0
\(539\) −1.55586 + 2.14145i −0.0670155 + 0.0922389i
\(540\) 0 0
\(541\) 9.28748 28.5839i 0.399300 1.22892i −0.526262 0.850323i \(-0.676407\pi\)
0.925562 0.378596i \(-0.123593\pi\)
\(542\) 0 0
\(543\) 10.9873 33.8154i 0.471509 1.45116i
\(544\) 0 0
\(545\) 10.2585 3.33319i 0.439426 0.142778i
\(546\) 0 0
\(547\) 9.93488i 0.424785i 0.977184 + 0.212392i \(0.0681255\pi\)
−0.977184 + 0.212392i \(0.931875\pi\)
\(548\) 0 0
\(549\) 8.15832 5.92737i 0.348189 0.252974i
\(550\) 0 0
\(551\) −37.9080 27.5418i −1.61494 1.17332i
\(552\) 0 0
\(553\) 8.35691 6.07165i 0.355372 0.258193i
\(554\) 0 0
\(555\) 1.80177 + 2.47993i 0.0764810 + 0.105267i
\(556\) 0 0
\(557\) 38.0995 + 12.3793i 1.61433 + 0.524527i 0.970594 0.240722i \(-0.0773841\pi\)
0.643735 + 0.765249i \(0.277384\pi\)
\(558\) 0 0
\(559\) −7.60984 + 2.47259i −0.321862 + 0.104579i
\(560\) 0 0
\(561\) 10.7950 14.8580i 0.455764 0.627306i
\(562\) 0 0
\(563\) −36.4224 11.8343i −1.53502 0.498758i −0.585023 0.811017i \(-0.698914\pi\)
−0.949997 + 0.312259i \(0.898914\pi\)
\(564\) 0 0
\(565\) −0.883878 −0.0371850
\(566\) 0 0
\(567\) 3.59359 + 4.94616i 0.150917 + 0.207719i
\(568\) 0 0
\(569\) 13.6926 + 42.1416i 0.574025 + 1.76667i 0.639474 + 0.768813i \(0.279152\pi\)
−0.0654484 + 0.997856i \(0.520848\pi\)
\(570\) 0 0
\(571\) 26.7725i 1.12039i −0.828360 0.560196i \(-0.810726\pi\)
0.828360 0.560196i \(-0.189274\pi\)
\(572\) 0 0
\(573\) −2.14829 −0.0897462
\(574\) 0 0
\(575\) 4.87705 0.203387
\(576\) 0 0
\(577\) 15.8434i 0.659569i −0.944056 0.329784i \(-0.893024\pi\)
0.944056 0.329784i \(-0.106976\pi\)
\(578\) 0 0
\(579\) 6.96473 + 21.4352i 0.289444 + 0.890818i
\(580\) 0 0
\(581\) 1.14160 + 1.57128i 0.0473615 + 0.0651875i
\(582\) 0 0
\(583\) −0.934157 −0.0386888
\(584\) 0 0
\(585\) −2.83084 0.919795i −0.117041 0.0380289i
\(586\) 0 0
\(587\) −3.19870 + 4.40263i −0.132024 + 0.181716i −0.869911 0.493209i \(-0.835824\pi\)
0.737887 + 0.674925i \(0.235824\pi\)
\(588\) 0 0
\(589\) 2.91727 0.947879i 0.120204 0.0390567i
\(590\) 0 0
\(591\) 5.68373 + 1.84675i 0.233797 + 0.0759653i
\(592\) 0 0
\(593\) 2.98305 + 4.10582i 0.122499 + 0.168606i 0.865862 0.500282i \(-0.166770\pi\)
−0.743363 + 0.668888i \(0.766770\pi\)
\(594\) 0 0
\(595\) 4.02538 2.92461i 0.165024 0.119897i
\(596\) 0 0
\(597\) −31.2457 22.7013i −1.27880 0.929103i
\(598\) 0 0
\(599\) 5.09991 3.70530i 0.208377 0.151395i −0.478702 0.877977i \(-0.658893\pi\)
0.687079 + 0.726583i \(0.258893\pi\)
\(600\) 0 0
\(601\) 11.2134i 0.457405i −0.973496 0.228703i \(-0.926552\pi\)
0.973496 0.228703i \(-0.0734484\pi\)
\(602\) 0 0
\(603\) −3.16939 + 1.02980i −0.129068 + 0.0419366i
\(604\) 0 0
\(605\) −1.32264 + 4.07068i −0.0537731 + 0.165497i
\(606\) 0 0
\(607\) −8.16809 + 25.1388i −0.331532 + 1.02035i 0.636873 + 0.770969i \(0.280228\pi\)
−0.968405 + 0.249383i \(0.919772\pi\)
\(608\) 0 0
\(609\) 5.13722 7.07077i 0.208171 0.286522i
\(610\) 0 0
\(611\) −7.84477 24.1437i −0.317365 0.976750i
\(612\) 0 0
\(613\) 18.0075 + 13.0832i 0.727318 + 0.528427i 0.888714 0.458463i \(-0.151600\pi\)
−0.161396 + 0.986890i \(0.551600\pi\)
\(614\) 0 0
\(615\) 1.21985 10.1839i 0.0491890 0.410656i
\(616\) 0 0
\(617\) 12.6834 + 9.21502i 0.510614 + 0.370983i 0.813056 0.582185i \(-0.197802\pi\)
−0.302442 + 0.953168i \(0.597802\pi\)
\(618\) 0 0
\(619\) 10.9348 + 33.6538i 0.439506 + 1.35266i 0.888397 + 0.459075i \(0.151819\pi\)
−0.448891 + 0.893587i \(0.648181\pi\)
\(620\) 0 0
\(621\) −4.18985 + 5.76684i −0.168133 + 0.231415i
\(622\) 0 0
\(623\) 0.669360 2.06008i 0.0268173 0.0825353i
\(624\) 0 0
\(625\) 2.80858 8.64391i 0.112343 0.345756i
\(626\) 0 0
\(627\) 30.1469 9.79531i 1.20395 0.391187i
\(628\) 0 0
\(629\) 8.88395i 0.354226i
\(630\) 0 0
\(631\) 25.8383 18.7726i 1.02861 0.747327i 0.0605778 0.998163i \(-0.480706\pi\)
0.968029 + 0.250837i \(0.0807057\pi\)
\(632\) 0 0
\(633\) 14.7804 + 10.7386i 0.587469 + 0.426821i
\(634\) 0 0
\(635\) 11.2844 8.19857i 0.447806 0.325350i
\(636\) 0 0
\(637\) 2.13014 + 2.93189i 0.0843994 + 0.116166i
\(638\) 0 0
\(639\) 3.87174 + 1.25800i 0.153164 + 0.0497659i
\(640\) 0 0
\(641\) 11.5720 3.75996i 0.457065 0.148509i −0.0714305 0.997446i \(-0.522756\pi\)
0.528495 + 0.848936i \(0.322756\pi\)
\(642\) 0 0
\(643\) −18.4099 + 25.3391i −0.726017 + 0.999277i 0.273286 + 0.961933i \(0.411890\pi\)
−0.999302 + 0.0373436i \(0.988110\pi\)
\(644\) 0 0
\(645\) −3.36359 1.09290i −0.132441 0.0430327i
\(646\) 0 0
\(647\) −39.1174 −1.53787 −0.768933 0.639330i \(-0.779212\pi\)
−0.768933 + 0.639330i \(0.779212\pi\)
\(648\) 0 0
\(649\) 22.7126 + 31.2612i 0.891547 + 1.22711i
\(650\) 0 0
\(651\) 0.176803 + 0.544142i 0.00692944 + 0.0213266i
\(652\) 0 0
\(653\) 0.201913i 0.00790149i 0.999992 + 0.00395074i \(0.00125756\pi\)
−0.999992 + 0.00395074i \(0.998742\pi\)
\(654\) 0 0
\(655\) −15.8103 −0.617758
\(656\) 0 0
\(657\) −2.56927 −0.100237
\(658\) 0 0
\(659\) 7.55689i 0.294375i 0.989109 + 0.147187i \(0.0470220\pi\)
−0.989109 + 0.147187i \(0.952978\pi\)
\(660\) 0 0
\(661\) 2.23852 + 6.88947i 0.0870685 + 0.267969i 0.985106 0.171950i \(-0.0550069\pi\)
−0.898037 + 0.439920i \(0.855007\pi\)
\(662\) 0 0
\(663\) −14.7796 20.3423i −0.573990 0.790030i
\(664\) 0 0
\(665\) 8.58780 0.333021
\(666\) 0 0
\(667\) 7.04300 + 2.28841i 0.272706 + 0.0886076i
\(668\) 0 0
\(669\) −10.8025 + 14.8684i −0.417650 + 0.574846i
\(670\) 0 0
\(671\) 33.1275 10.7638i 1.27887 0.415531i
\(672\) 0 0
\(673\) 16.7791 + 5.45187i 0.646787 + 0.210154i 0.613997 0.789308i \(-0.289561\pi\)
0.0327903 + 0.999462i \(0.489561\pi\)
\(674\) 0 0
\(675\) 12.7424 + 17.5384i 0.490455 + 0.675054i
\(676\) 0 0
\(677\) −22.0606 + 16.0279i −0.847856 + 0.616004i −0.924554 0.381051i \(-0.875562\pi\)
0.0766977 + 0.997054i \(0.475562\pi\)
\(678\) 0 0
\(679\) −3.60843 2.62168i −0.138479 0.100611i
\(680\) 0 0
\(681\) −8.64806 + 6.28319i −0.331395 + 0.240772i
\(682\) 0 0
\(683\) 14.8951i 0.569946i −0.958536 0.284973i \(-0.908015\pi\)
0.958536 0.284973i \(-0.0919846\pi\)
\(684\) 0 0
\(685\) −17.5456 + 5.70090i −0.670382 + 0.217820i
\(686\) 0 0
\(687\) 11.8464 36.4594i 0.451967 1.39101i
\(688\) 0 0
\(689\) −0.395223 + 1.21637i −0.0150568 + 0.0463400i
\(690\) 0 0
\(691\) 18.4323 25.3699i 0.701199 0.965117i −0.298743 0.954334i \(-0.596567\pi\)
0.999942 0.0107838i \(-0.00343264\pi\)
\(692\) 0 0
\(693\) −0.626822 1.92916i −0.0238110 0.0732827i
\(694\) 0 0
\(695\) −6.82031 4.95524i −0.258709 0.187963i
\(696\) 0 0
\(697\) −20.2085 + 21.8000i −0.765453 + 0.825734i
\(698\) 0 0
\(699\) 23.4422 + 17.0317i 0.886664 + 0.644199i
\(700\) 0 0
\(701\) 15.8600 + 48.8120i 0.599024 + 1.84361i 0.533581 + 0.845749i \(0.320846\pi\)
0.0654431 + 0.997856i \(0.479154\pi\)
\(702\) 0 0
\(703\) 9.01275 12.4050i 0.339922 0.467863i
\(704\) 0 0
\(705\) 3.46743 10.6716i 0.130591 0.401917i
\(706\) 0 0
\(707\) −1.13768 + 3.50143i −0.0427870 + 0.131685i
\(708\) 0 0
\(709\) 4.69926 1.52688i 0.176484 0.0573432i −0.219442 0.975626i \(-0.570424\pi\)
0.395926 + 0.918282i \(0.370424\pi\)
\(710\) 0 0
\(711\) 7.91588i 0.296869i
\(712\) 0 0
\(713\) −0.392199 + 0.284949i −0.0146880 + 0.0106714i
\(714\) 0 0
\(715\) −8.31775 6.04320i −0.311066 0.226003i
\(716\) 0 0
\(717\) −3.13669 + 2.27894i −0.117142 + 0.0851084i
\(718\) 0 0
\(719\) −12.7738 17.5816i −0.476381 0.655682i 0.501423 0.865202i \(-0.332810\pi\)
−0.977804 + 0.209520i \(0.932810\pi\)
\(720\) 0 0
\(721\) 4.39133 + 1.42683i 0.163542 + 0.0531379i
\(722\) 0 0
\(723\) 10.5945 3.44236i 0.394013 0.128023i
\(724\) 0 0
\(725\) 13.2380 18.2206i 0.491647 0.676694i
\(726\) 0 0
\(727\) −35.8157 11.6372i −1.32833 0.431601i −0.442983 0.896530i \(-0.646080\pi\)
−0.885348 + 0.464929i \(0.846080\pi\)
\(728\) 0 0
\(729\) −29.9234 −1.10827
\(730\) 0 0
\(731\) 6.02475 + 8.29236i 0.222834 + 0.306704i
\(732\) 0 0
\(733\) 2.68677 + 8.26904i 0.0992383 + 0.305424i 0.988335 0.152295i \(-0.0486665\pi\)
−0.889097 + 0.457719i \(0.848666\pi\)
\(734\) 0 0
\(735\) 1.60183i 0.0590845i
\(736\) 0 0
\(737\) −11.5109 −0.424010
\(738\) 0 0
\(739\) 20.8067 0.765386 0.382693 0.923875i \(-0.374997\pi\)
0.382693 + 0.923875i \(0.374997\pi\)
\(740\) 0 0
\(741\) 43.3986i 1.59429i
\(742\) 0 0
\(743\) 8.59140 + 26.4416i 0.315188 + 0.970048i 0.975677 + 0.219213i \(0.0703489\pi\)
−0.660489 + 0.750835i \(0.729651\pi\)
\(744\) 0 0
\(745\) 5.33856 + 7.34790i 0.195590 + 0.269206i
\(746\) 0 0
\(747\) −1.48835 −0.0544560
\(748\) 0 0
\(749\) 1.29386 + 0.420400i 0.0472766 + 0.0153611i
\(750\) 0 0
\(751\) 4.78137 6.58100i 0.174475 0.240144i −0.712820 0.701347i \(-0.752582\pi\)
0.887294 + 0.461203i \(0.152582\pi\)
\(752\) 0 0
\(753\) −26.9981 + 8.77223i −0.983867 + 0.319678i
\(754\) 0 0
\(755\) −5.46140 1.77452i −0.198761 0.0645813i
\(756\) 0 0
\(757\) 17.2372 + 23.7250i 0.626497 + 0.862299i 0.997806 0.0662108i \(-0.0210910\pi\)
−0.371309 + 0.928509i \(0.621091\pi\)
\(758\) 0 0
\(759\) −4.05295 + 2.94464i −0.147113 + 0.106884i
\(760\) 0 0
\(761\) −6.42303 4.66661i −0.232835 0.169164i 0.465250 0.885179i \(-0.345964\pi\)
−0.698085 + 0.716015i \(0.745964\pi\)
\(762\) 0 0
\(763\) 8.14194 5.91547i 0.294758 0.214154i
\(764\) 0 0
\(765\) 3.81294i 0.137857i
\(766\) 0 0
\(767\) 50.3146 16.3482i 1.81675 0.590299i
\(768\) 0 0
\(769\) 6.37070 19.6070i 0.229733 0.707047i −0.768043 0.640398i \(-0.778769\pi\)
0.997777 0.0666486i \(-0.0212306\pi\)
\(770\) 0 0
\(771\) 3.98512 12.2649i 0.143521 0.441711i
\(772\) 0 0
\(773\) 21.3090 29.3293i 0.766430 1.05490i −0.230222 0.973138i \(-0.573945\pi\)
0.996652 0.0817620i \(-0.0260547\pi\)
\(774\) 0 0
\(775\) 0.455600 + 1.40219i 0.0163656 + 0.0503682i
\(776\) 0 0
\(777\) 2.31383 + 1.68110i 0.0830083 + 0.0603090i
\(778\) 0 0
\(779\) −50.3340 + 9.93862i −1.80340 + 0.356088i
\(780\) 0 0
\(781\) 11.3762 + 8.26528i 0.407072 + 0.295755i
\(782\) 0 0
\(783\) 10.1721 + 31.3064i 0.363520 + 1.11880i
\(784\) 0 0
\(785\) 5.72235 7.87614i 0.204240 0.281112i
\(786\) 0 0
\(787\) 7.50785 23.1068i 0.267626 0.823668i −0.723451 0.690376i \(-0.757445\pi\)
0.991077 0.133292i \(-0.0425548\pi\)
\(788\) 0 0
\(789\) −13.4964 + 41.5377i −0.480486 + 1.47878i
\(790\) 0 0
\(791\) −0.784317 + 0.254840i −0.0278871 + 0.00906106i
\(792\) 0 0
\(793\) 47.6894i 1.69350i
\(794\) 0 0
\(795\) −0.457345 + 0.332281i −0.0162204 + 0.0117848i
\(796\) 0 0
\(797\) −1.59441 1.15841i −0.0564768 0.0410328i 0.559189