Properties

Label 1148.2.ba.a.113.7
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 113.7
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.14

$q$-expansion

\(f(q)\) \(=\) \(q-1.15530i q^{3} +(-1.04872 - 3.22763i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.66528 q^{9} +O(q^{10})\) \(q-1.15530i q^{3} +(-1.04872 - 3.22763i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.66528 q^{9} +(-4.79368 - 1.55756i) q^{11} +(-0.242673 + 0.334011i) q^{13} +(-3.72888 + 1.21159i) q^{15} +(4.09880 + 1.33178i) q^{17} +(-4.03463 - 5.55319i) q^{19} +(-0.934658 + 0.679068i) q^{21} +(2.71308 + 1.97117i) q^{23} +(-5.27268 + 3.83082i) q^{25} -5.38980i q^{27} +(-5.54178 + 1.80063i) q^{29} +(1.17885 - 3.62811i) q^{31} +(-1.79945 + 5.53814i) q^{33} +(-1.99478 + 2.74558i) q^{35} +(1.51545 + 4.66407i) q^{37} +(0.385883 + 0.280360i) q^{39} +(-2.10916 + 6.04578i) q^{41} +(2.08403 + 1.51413i) q^{43} +(-1.74641 - 5.37491i) q^{45} +(-2.14962 + 2.95870i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(1.53861 - 4.73534i) q^{51} +(-4.59927 + 1.49439i) q^{53} +17.1057i q^{55} +(-6.41561 + 4.66121i) q^{57} +(2.76662 + 2.01006i) q^{59} +(9.57199 - 6.95446i) q^{61} +(-0.978828 - 1.34724i) q^{63} +(1.33256 + 0.432974i) q^{65} +(-4.00013 + 1.29972i) q^{67} +(2.27729 - 3.13442i) q^{69} +(-3.48844 - 1.13346i) q^{71} -16.2956 q^{73} +(4.42575 + 6.09152i) q^{75} +(1.55756 + 4.79368i) q^{77} -5.78329i q^{79} -1.23099 q^{81} -8.92404 q^{83} -14.6261i q^{85} +(2.08027 + 6.40242i) q^{87} +(4.55641 + 6.27135i) q^{89} +0.412860 q^{91} +(-4.19156 - 1.36192i) q^{93} +(-13.6924 + 18.8460i) q^{95} +(0.934792 - 0.303732i) q^{97} +(-7.98283 - 2.59378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

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
\(3\) 1.15530i 0.667013i −0.942748 0.333506i \(-0.891768\pi\)
0.942748 0.333506i \(-0.108232\pi\)
\(4\) 0 0
\(5\) −1.04872 3.22763i −0.469002 1.44344i −0.853879 0.520471i \(-0.825756\pi\)
0.384878 0.922968i \(-0.374244\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) 1.66528 0.555094
\(10\) 0 0
\(11\) −4.79368 1.55756i −1.44535 0.469623i −0.521789 0.853074i \(-0.674735\pi\)
−0.923561 + 0.383452i \(0.874735\pi\)
\(12\) 0 0
\(13\) −0.242673 + 0.334011i −0.0673054 + 0.0926379i −0.841343 0.540502i \(-0.818234\pi\)
0.774037 + 0.633140i \(0.218234\pi\)
\(14\) 0 0
\(15\) −3.72888 + 1.21159i −0.962792 + 0.312830i
\(16\) 0 0
\(17\) 4.09880 + 1.33178i 0.994105 + 0.323004i 0.760507 0.649329i \(-0.224950\pi\)
0.233597 + 0.972333i \(0.424950\pi\)
\(18\) 0 0
\(19\) −4.03463 5.55319i −0.925608 1.27399i −0.961548 0.274636i \(-0.911443\pi\)
0.0359405 0.999354i \(-0.488557\pi\)
\(20\) 0 0
\(21\) −0.934658 + 0.679068i −0.203959 + 0.148185i
\(22\) 0 0
\(23\) 2.71308 + 1.97117i 0.565717 + 0.411017i 0.833547 0.552449i \(-0.186307\pi\)
−0.267830 + 0.963466i \(0.586307\pi\)
\(24\) 0 0
\(25\) −5.27268 + 3.83082i −1.05454 + 0.766165i
\(26\) 0 0
\(27\) 5.38980i 1.03727i
\(28\) 0 0
\(29\) −5.54178 + 1.80063i −1.02908 + 0.334369i −0.774427 0.632663i \(-0.781962\pi\)
−0.254655 + 0.967032i \(0.581962\pi\)
\(30\) 0 0
\(31\) 1.17885 3.62811i 0.211727 0.651628i −0.787643 0.616132i \(-0.788699\pi\)
0.999370 0.0354964i \(-0.0113012\pi\)
\(32\) 0 0
\(33\) −1.79945 + 5.53814i −0.313244 + 0.964067i
\(34\) 0 0
\(35\) −1.99478 + 2.74558i −0.337180 + 0.464088i
\(36\) 0 0
\(37\) 1.51545 + 4.66407i 0.249138 + 0.766768i 0.994928 + 0.100587i \(0.0320720\pi\)
−0.745790 + 0.666181i \(0.767928\pi\)
\(38\) 0 0
\(39\) 0.385883 + 0.280360i 0.0617907 + 0.0448936i
\(40\) 0 0
\(41\) −2.10916 + 6.04578i −0.329395 + 0.944192i
\(42\) 0 0
\(43\) 2.08403 + 1.51413i 0.317811 + 0.230903i 0.735241 0.677806i \(-0.237069\pi\)
−0.417430 + 0.908709i \(0.637069\pi\)
\(44\) 0 0
\(45\) −1.74641 5.37491i −0.260340 0.801244i
\(46\) 0 0
\(47\) −2.14962 + 2.95870i −0.313554 + 0.431570i −0.936486 0.350706i \(-0.885942\pi\)
0.622931 + 0.782276i \(0.285942\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 1.53861 4.73534i 0.215448 0.663081i
\(52\) 0 0
\(53\) −4.59927 + 1.49439i −0.631758 + 0.205271i −0.607354 0.794432i \(-0.707769\pi\)
−0.0244041 + 0.999702i \(0.507769\pi\)
\(54\) 0 0
\(55\) 17.1057i 2.30653i
\(56\) 0 0
\(57\) −6.41561 + 4.66121i −0.849768 + 0.617392i
\(58\) 0 0
\(59\) 2.76662 + 2.01006i 0.360183 + 0.261688i 0.753128 0.657874i \(-0.228544\pi\)
−0.392946 + 0.919562i \(0.628544\pi\)
\(60\) 0 0
\(61\) 9.57199 6.95446i 1.22557 0.890427i 0.229018 0.973422i \(-0.426449\pi\)
0.996550 + 0.0829951i \(0.0264486\pi\)
\(62\) 0 0
\(63\) −0.978828 1.34724i −0.123321 0.169736i
\(64\) 0 0
\(65\) 1.33256 + 0.432974i 0.165283 + 0.0537038i
\(66\) 0 0
\(67\) −4.00013 + 1.29972i −0.488693 + 0.158786i −0.542991 0.839739i \(-0.682708\pi\)
0.0542973 + 0.998525i \(0.482708\pi\)
\(68\) 0 0
\(69\) 2.27729 3.13442i 0.274154 0.377340i
\(70\) 0 0
\(71\) −3.48844 1.13346i −0.414002 0.134517i 0.0946077 0.995515i \(-0.469840\pi\)
−0.508610 + 0.860997i \(0.669840\pi\)
\(72\) 0 0
\(73\) −16.2956 −1.90725 −0.953627 0.300991i \(-0.902682\pi\)
−0.953627 + 0.300991i \(0.902682\pi\)
\(74\) 0 0
\(75\) 4.42575 + 6.09152i 0.511042 + 0.703389i
\(76\) 0 0
\(77\) 1.55756 + 4.79368i 0.177501 + 0.546291i
\(78\) 0 0
\(79\) 5.78329i 0.650671i −0.945599 0.325336i \(-0.894523\pi\)
0.945599 0.325336i \(-0.105477\pi\)
\(80\) 0 0
\(81\) −1.23099 −0.136777
\(82\) 0 0
\(83\) −8.92404 −0.979541 −0.489770 0.871851i \(-0.662919\pi\)
−0.489770 + 0.871851i \(0.662919\pi\)
\(84\) 0 0
\(85\) 14.6261i 1.58642i
\(86\) 0 0
\(87\) 2.08027 + 6.40242i 0.223029 + 0.686411i
\(88\) 0 0
\(89\) 4.55641 + 6.27135i 0.482978 + 0.664762i 0.979074 0.203506i \(-0.0652335\pi\)
−0.496096 + 0.868268i \(0.665234\pi\)
\(90\) 0 0
\(91\) 0.412860 0.0432795
\(92\) 0 0
\(93\) −4.19156 1.36192i −0.434645 0.141225i
\(94\) 0 0
\(95\) −13.6924 + 18.8460i −1.40481 + 1.93356i
\(96\) 0 0
\(97\) 0.934792 0.303732i 0.0949138 0.0308394i −0.261175 0.965291i \(-0.584110\pi\)
0.356089 + 0.934452i \(0.384110\pi\)
\(98\) 0 0
\(99\) −7.98283 2.59378i −0.802305 0.260685i
\(100\) 0 0
\(101\) −0.0408997 0.0562936i −0.00406967 0.00560142i 0.806977 0.590582i \(-0.201102\pi\)
−0.811047 + 0.584981i \(0.801102\pi\)
\(102\) 0 0
\(103\) 14.9785 10.8825i 1.47588 1.07229i 0.497018 0.867740i \(-0.334428\pi\)
0.978857 0.204546i \(-0.0655717\pi\)
\(104\) 0 0
\(105\) 3.17197 + 2.30457i 0.309553 + 0.224903i
\(106\) 0 0
\(107\) −7.04598 + 5.11920i −0.681160 + 0.494892i −0.873742 0.486389i \(-0.838314\pi\)
0.192582 + 0.981281i \(0.438314\pi\)
\(108\) 0 0
\(109\) 12.2495i 1.17329i −0.809844 0.586645i \(-0.800448\pi\)
0.809844 0.586645i \(-0.199552\pi\)
\(110\) 0 0
\(111\) 5.38840 1.75080i 0.511444 0.166178i
\(112\) 0 0
\(113\) 1.01600 3.12691i 0.0955768 0.294155i −0.891827 0.452377i \(-0.850576\pi\)
0.987404 + 0.158222i \(0.0505761\pi\)
\(114\) 0 0
\(115\) 3.51694 10.8240i 0.327956 1.00934i
\(116\) 0 0
\(117\) −0.404119 + 0.556222i −0.0373608 + 0.0514227i
\(118\) 0 0
\(119\) −1.33178 4.09880i −0.122084 0.375736i
\(120\) 0 0
\(121\) 11.6542 + 8.46729i 1.05947 + 0.769753i
\(122\) 0 0
\(123\) 6.98469 + 2.43671i 0.629788 + 0.219711i
\(124\) 0 0
\(125\) 4.16611 + 3.02685i 0.372628 + 0.270730i
\(126\) 0 0
\(127\) −5.85134 18.0086i −0.519222 1.59800i −0.775466 0.631390i \(-0.782485\pi\)
0.256244 0.966612i \(-0.417515\pi\)
\(128\) 0 0
\(129\) 1.74928 2.40768i 0.154016 0.211984i
\(130\) 0 0
\(131\) 1.90333 5.85786i 0.166295 0.511803i −0.832834 0.553522i \(-0.813283\pi\)
0.999129 + 0.0417190i \(0.0132834\pi\)
\(132\) 0 0
\(133\) −2.12113 + 6.52817i −0.183925 + 0.566064i
\(134\) 0 0
\(135\) −17.3963 + 5.65239i −1.49723 + 0.486480i
\(136\) 0 0
\(137\) 8.52526i 0.728362i −0.931328 0.364181i \(-0.881349\pi\)
0.931328 0.364181i \(-0.118651\pi\)
\(138\) 0 0
\(139\) 13.6500 9.91729i 1.15778 0.841174i 0.168281 0.985739i \(-0.446178\pi\)
0.989495 + 0.144565i \(0.0461783\pi\)
\(140\) 0 0
\(141\) 3.41818 + 2.48345i 0.287863 + 0.209145i
\(142\) 0 0
\(143\) 1.68354 1.22316i 0.140785 0.102286i
\(144\) 0 0
\(145\) 11.6235 + 15.9984i 0.965283 + 1.32860i
\(146\) 0 0
\(147\) 1.09876 + 0.357007i 0.0906239 + 0.0294455i
\(148\) 0 0
\(149\) −11.5183 + 3.74252i −0.943615 + 0.306599i −0.740118 0.672477i \(-0.765231\pi\)
−0.203497 + 0.979076i \(0.565231\pi\)
\(150\) 0 0
\(151\) 5.96279 8.20708i 0.485245 0.667882i −0.494257 0.869316i \(-0.664560\pi\)
0.979502 + 0.201433i \(0.0645599\pi\)
\(152\) 0 0
\(153\) 6.82565 + 2.21779i 0.551821 + 0.179298i
\(154\) 0 0
\(155\) −12.9465 −1.03989
\(156\) 0 0
\(157\) 2.29599 + 3.16016i 0.183240 + 0.252209i 0.890749 0.454496i \(-0.150181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(158\) 0 0
\(159\) 1.72647 + 5.31353i 0.136918 + 0.421391i
\(160\) 0 0
\(161\) 3.35355i 0.264297i
\(162\) 0 0
\(163\) 5.83646 0.457147 0.228573 0.973527i \(-0.426594\pi\)
0.228573 + 0.973527i \(0.426594\pi\)
\(164\) 0 0
\(165\) 19.7622 1.53848
\(166\) 0 0
\(167\) 13.5723i 1.05026i −0.851023 0.525128i \(-0.824017\pi\)
0.851023 0.525128i \(-0.175983\pi\)
\(168\) 0 0
\(169\) 3.96455 + 12.2016i 0.304965 + 0.938586i
\(170\) 0 0
\(171\) −6.71880 9.24763i −0.513799 0.707184i
\(172\) 0 0
\(173\) 18.5650 1.41147 0.705734 0.708477i \(-0.250617\pi\)
0.705734 + 0.708477i \(0.250617\pi\)
\(174\) 0 0
\(175\) 6.19840 + 2.01398i 0.468555 + 0.152243i
\(176\) 0 0
\(177\) 2.32223 3.19627i 0.174549 0.240247i
\(178\) 0 0
\(179\) −20.6874 + 6.72174i −1.54625 + 0.502406i −0.953092 0.302682i \(-0.902118\pi\)
−0.593155 + 0.805088i \(0.702118\pi\)
\(180\) 0 0
\(181\) −17.1455 5.57091i −1.27441 0.414082i −0.407805 0.913069i \(-0.633706\pi\)
−0.866609 + 0.498987i \(0.833706\pi\)
\(182\) 0 0
\(183\) −8.03449 11.0585i −0.593926 0.817470i
\(184\) 0 0
\(185\) 13.4646 9.78259i 0.989936 0.719230i
\(186\) 0 0
\(187\) −17.5740 12.7683i −1.28514 0.933708i
\(188\) 0 0
\(189\) −4.36044 + 3.16805i −0.317175 + 0.230441i
\(190\) 0 0
\(191\) 5.75897i 0.416704i −0.978054 0.208352i \(-0.933190\pi\)
0.978054 0.208352i \(-0.0668100\pi\)
\(192\) 0 0
\(193\) −9.59712 + 3.11829i −0.690816 + 0.224460i −0.633325 0.773886i \(-0.718310\pi\)
−0.0574914 + 0.998346i \(0.518310\pi\)
\(194\) 0 0
\(195\) 0.500215 1.53950i 0.0358212 0.110246i
\(196\) 0 0
\(197\) 4.66718 14.3641i 0.332523 1.02340i −0.635406 0.772178i \(-0.719167\pi\)
0.967929 0.251223i \(-0.0808327\pi\)
\(198\) 0 0
\(199\) 2.12212 2.92085i 0.150433 0.207054i −0.727149 0.686480i \(-0.759155\pi\)
0.877582 + 0.479426i \(0.159155\pi\)
\(200\) 0 0
\(201\) 1.50157 + 4.62135i 0.105912 + 0.325965i
\(202\) 0 0
\(203\) 4.71412 + 3.42501i 0.330866 + 0.240388i
\(204\) 0 0
\(205\) 21.7254 + 0.467247i 1.51737 + 0.0326339i
\(206\) 0 0
\(207\) 4.51804 + 3.28255i 0.314026 + 0.228153i
\(208\) 0 0
\(209\) 10.6913 + 32.9044i 0.739533 + 2.27605i
\(210\) 0 0
\(211\) −10.6477 + 14.6553i −0.733017 + 1.00891i 0.265973 + 0.963981i \(0.414307\pi\)
−0.998990 + 0.0449311i \(0.985693\pi\)
\(212\) 0 0
\(213\) −1.30949 + 4.03020i −0.0897248 + 0.276145i
\(214\) 0 0
\(215\) 2.70150 8.31436i 0.184241 0.567035i
\(216\) 0 0
\(217\) −3.62811 + 1.17885i −0.246292 + 0.0800253i
\(218\) 0 0
\(219\) 18.8263i 1.27216i
\(220\) 0 0
\(221\) −1.43950 + 1.04586i −0.0968310 + 0.0703518i
\(222\) 0 0
\(223\) −1.11339 0.808922i −0.0745579 0.0541695i 0.549882 0.835242i \(-0.314673\pi\)
−0.624440 + 0.781073i \(0.714673\pi\)
\(224\) 0 0
\(225\) −8.78049 + 6.37940i −0.585366 + 0.425293i
\(226\) 0 0
\(227\) 5.87373 + 8.08449i 0.389853 + 0.536587i 0.958161 0.286229i \(-0.0924019\pi\)
−0.568308 + 0.822816i \(0.692402\pi\)
\(228\) 0 0
\(229\) 19.2691 + 6.26092i 1.27334 + 0.413733i 0.866230 0.499646i \(-0.166536\pi\)
0.407110 + 0.913379i \(0.366536\pi\)
\(230\) 0 0
\(231\) 5.53814 1.79945i 0.364383 0.118395i
\(232\) 0 0
\(233\) 7.03542 9.68342i 0.460905 0.634382i −0.513791 0.857916i \(-0.671759\pi\)
0.974696 + 0.223534i \(0.0717592\pi\)
\(234\) 0 0
\(235\) 11.8039 + 3.83532i 0.770002 + 0.250189i
\(236\) 0 0
\(237\) −6.68144 −0.434006
\(238\) 0 0
\(239\) −4.02745 5.54331i −0.260514 0.358567i 0.658645 0.752454i \(-0.271130\pi\)
−0.919159 + 0.393887i \(0.871130\pi\)
\(240\) 0 0
\(241\) 0.114728 + 0.353096i 0.00739028 + 0.0227449i 0.954684 0.297622i \(-0.0961936\pi\)
−0.947293 + 0.320367i \(0.896194\pi\)
\(242\) 0 0
\(243\) 14.7472i 0.946036i
\(244\) 0 0
\(245\) 3.39373 0.216817
\(246\) 0 0
\(247\) 2.83392 0.180318
\(248\) 0 0
\(249\) 10.3099i 0.653366i
\(250\) 0 0
\(251\) 0.428825 + 1.31979i 0.0270672 + 0.0833043i 0.963678 0.267068i \(-0.0860550\pi\)
−0.936610 + 0.350373i \(0.886055\pi\)
\(252\) 0 0
\(253\) −9.93544 13.6750i −0.624636 0.859737i
\(254\) 0 0
\(255\) −16.8975 −1.05816
\(256\) 0 0
\(257\) 5.36241 + 1.74235i 0.334498 + 0.108685i 0.471450 0.881893i \(-0.343731\pi\)
−0.136952 + 0.990578i \(0.543731\pi\)
\(258\) 0 0
\(259\) 2.88255 3.96749i 0.179113 0.246528i
\(260\) 0 0
\(261\) −9.22862 + 2.99856i −0.571237 + 0.185606i
\(262\) 0 0
\(263\) 25.0333 + 8.13381i 1.54362 + 0.501552i 0.952372 0.304938i \(-0.0986359\pi\)
0.591247 + 0.806491i \(0.298636\pi\)
\(264\) 0 0
\(265\) 9.64668 + 13.2775i 0.592591 + 0.815631i
\(266\) 0 0
\(267\) 7.24530 5.26402i 0.443405 0.322153i
\(268\) 0 0
\(269\) −4.14563 3.01197i −0.252763 0.183643i 0.454187 0.890906i \(-0.349930\pi\)
−0.706951 + 0.707263i \(0.749930\pi\)
\(270\) 0 0
\(271\) −23.7992 + 17.2911i −1.44570 + 1.05036i −0.458885 + 0.888496i \(0.651751\pi\)
−0.986813 + 0.161865i \(0.948249\pi\)
\(272\) 0 0
\(273\) 0.476977i 0.0288680i
\(274\) 0 0
\(275\) 31.2423 10.1512i 1.88398 0.612142i
\(276\) 0 0
\(277\) 9.91362 30.5110i 0.595652 1.83323i 0.0441978 0.999023i \(-0.485927\pi\)
0.551454 0.834205i \(-0.314073\pi\)
\(278\) 0 0
\(279\) 1.96311 6.04183i 0.117528 0.361715i
\(280\) 0 0
\(281\) 18.4782 25.4330i 1.10232 1.51721i 0.270036 0.962850i \(-0.412965\pi\)
0.832280 0.554356i \(-0.187035\pi\)
\(282\) 0 0
\(283\) −0.429565 1.32207i −0.0255350 0.0785886i 0.937477 0.348047i \(-0.113155\pi\)
−0.963012 + 0.269459i \(0.913155\pi\)
\(284\) 0 0
\(285\) 21.7728 + 15.8189i 1.28971 + 0.937029i
\(286\) 0 0
\(287\) 6.13087 1.84728i 0.361894 0.109041i
\(288\) 0 0
\(289\) 1.27322 + 0.925049i 0.0748954 + 0.0544147i
\(290\) 0 0
\(291\) −0.350902 1.07997i −0.0205702 0.0633087i
\(292\) 0 0
\(293\) 7.54333 10.3825i 0.440686 0.606552i −0.529678 0.848199i \(-0.677687\pi\)
0.970364 + 0.241646i \(0.0776874\pi\)
\(294\) 0 0
\(295\) 3.58633 11.0376i 0.208804 0.642634i
\(296\) 0 0
\(297\) −8.39495 + 25.8370i −0.487124 + 1.49922i
\(298\) 0 0
\(299\) −1.31678 + 0.427849i −0.0761515 + 0.0247431i
\(300\) 0 0
\(301\) 2.57600i 0.148478i
\(302\) 0 0
\(303\) −0.0650360 + 0.0472514i −0.00373622 + 0.00271452i
\(304\) 0 0
\(305\) −32.4847 23.6015i −1.86007 1.35142i
\(306\) 0 0
\(307\) 18.9952 13.8008i 1.08411 0.787653i 0.105716 0.994396i \(-0.466287\pi\)
0.978395 + 0.206744i \(0.0662867\pi\)
\(308\) 0 0
\(309\) −12.5726 17.3047i −0.715229 0.984428i
\(310\) 0 0
\(311\) −11.5910 3.76614i −0.657265 0.213558i −0.0386503 0.999253i \(-0.512306\pi\)
−0.618615 + 0.785694i \(0.712306\pi\)
\(312\) 0 0
\(313\) 25.4243 8.26086i 1.43707 0.466931i 0.516085 0.856537i \(-0.327389\pi\)
0.920982 + 0.389606i \(0.127389\pi\)
\(314\) 0 0
\(315\) −3.32187 + 4.57217i −0.187166 + 0.257612i
\(316\) 0 0
\(317\) −7.65607 2.48761i −0.430008 0.139718i 0.0860130 0.996294i \(-0.472587\pi\)
−0.516021 + 0.856576i \(0.672587\pi\)
\(318\) 0 0
\(319\) 29.3701 1.64441
\(320\) 0 0
\(321\) 5.91422 + 8.14022i 0.330099 + 0.454343i
\(322\) 0 0
\(323\) −9.14151 28.1347i −0.508647 1.56545i
\(324\) 0 0
\(325\) 2.69077i 0.149257i
\(326\) 0 0
\(327\) −14.1519 −0.782600
\(328\) 0 0
\(329\) 3.65715 0.201625
\(330\) 0 0
\(331\) 16.3613i 0.899300i 0.893205 + 0.449650i \(0.148451\pi\)
−0.893205 + 0.449650i \(0.851549\pi\)
\(332\) 0 0
\(333\) 2.52364 + 7.76698i 0.138295 + 0.425628i
\(334\) 0 0
\(335\) 8.39002 + 11.5479i 0.458396 + 0.630928i
\(336\) 0 0
\(337\) 21.1433 1.15175 0.575875 0.817538i \(-0.304662\pi\)
0.575875 + 0.817538i \(0.304662\pi\)
\(338\) 0 0
\(339\) −3.61252 1.17378i −0.196205 0.0637510i
\(340\) 0 0
\(341\) −11.3020 + 15.5559i −0.612039 + 0.842400i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) −12.5050 4.06312i −0.673246 0.218751i
\(346\) 0 0
\(347\) −9.89619 13.6209i −0.531255 0.731210i 0.456066 0.889946i \(-0.349258\pi\)
−0.987321 + 0.158736i \(0.949258\pi\)
\(348\) 0 0
\(349\) 18.1720 13.2028i 0.972727 0.706727i 0.0166552 0.999861i \(-0.494698\pi\)
0.956071 + 0.293134i \(0.0946982\pi\)
\(350\) 0 0
\(351\) 1.80025 + 1.30796i 0.0960903 + 0.0698137i
\(352\) 0 0
\(353\) −18.0279 + 13.0981i −0.959530 + 0.697139i −0.953041 0.302840i \(-0.902065\pi\)
−0.00648827 + 0.999979i \(0.502065\pi\)
\(354\) 0 0
\(355\) 12.4481i 0.660675i
\(356\) 0 0
\(357\) −4.73534 + 1.53861i −0.250621 + 0.0814317i
\(358\) 0 0
\(359\) 1.87799 5.77986i 0.0991166 0.305049i −0.889188 0.457542i \(-0.848730\pi\)
0.988305 + 0.152492i \(0.0487300\pi\)
\(360\) 0 0
\(361\) −8.68838 + 26.7401i −0.457283 + 1.40737i
\(362\) 0 0
\(363\) 9.78226 13.4641i 0.513435 0.706683i
\(364\) 0 0
\(365\) 17.0895 + 52.5961i 0.894505 + 2.75300i
\(366\) 0 0
\(367\) −17.6647 12.8342i −0.922089 0.669937i 0.0219537 0.999759i \(-0.493011\pi\)
−0.944043 + 0.329822i \(0.893011\pi\)
\(368\) 0 0
\(369\) −3.51234 + 10.0679i −0.182845 + 0.524115i
\(370\) 0 0
\(371\) 3.91237 + 2.84250i 0.203120 + 0.147575i
\(372\) 0 0
\(373\) 1.12547 + 3.46385i 0.0582748 + 0.179351i 0.975957 0.217964i \(-0.0699417\pi\)
−0.917682 + 0.397316i \(0.869942\pi\)
\(374\) 0 0
\(375\) 3.49693 4.81310i 0.180580 0.248548i
\(376\) 0 0
\(377\) 0.743409 2.28798i 0.0382875 0.117837i
\(378\) 0 0
\(379\) −5.02114 + 15.4535i −0.257918 + 0.793791i 0.735322 + 0.677718i \(0.237031\pi\)
−0.993241 + 0.116074i \(0.962969\pi\)
\(380\) 0 0
\(381\) −20.8053 + 6.76005i −1.06589 + 0.346328i
\(382\) 0 0
\(383\) 27.9579i 1.42858i −0.699848 0.714292i \(-0.746749\pi\)
0.699848 0.714292i \(-0.253251\pi\)
\(384\) 0 0
\(385\) 13.8388 10.0545i 0.705289 0.512423i
\(386\) 0 0
\(387\) 3.47049 + 2.52146i 0.176415 + 0.128173i
\(388\) 0 0
\(389\) 14.8202 10.7675i 0.751416 0.545935i −0.144850 0.989454i \(-0.546270\pi\)
0.896265 + 0.443518i \(0.146270\pi\)
\(390\) 0 0
\(391\) 8.49521 + 11.6927i 0.429621 + 0.591323i
\(392\) 0 0
\(393\) −6.76758 2.19892i −0.341379 0.110921i
\(394\) 0 0
\(395\) −18.6663 + 6.06505i −0.939204 + 0.305166i
\(396\) 0 0
\(397\) −11.3115 + 15.5689i −0.567706 + 0.781381i −0.992281 0.124012i \(-0.960424\pi\)
0.424574 + 0.905393i \(0.360424\pi\)
\(398\) 0 0
\(399\) 7.54200 + 2.45054i 0.377572 + 0.122681i
\(400\) 0 0
\(401\) 17.2859 0.863215 0.431607 0.902062i \(-0.357947\pi\)
0.431607 + 0.902062i \(0.357947\pi\)
\(402\) 0 0
\(403\) 0.925755 + 1.27419i 0.0461151 + 0.0634720i
\(404\) 0 0
\(405\) 1.29097 + 3.97319i 0.0641487 + 0.197429i
\(406\) 0 0
\(407\) 24.7185i 1.22525i
\(408\) 0 0
\(409\) −27.4513 −1.35738 −0.678689 0.734426i \(-0.737452\pi\)
−0.678689 + 0.734426i \(0.737452\pi\)
\(410\) 0 0
\(411\) −9.84923 −0.485827
\(412\) 0 0
\(413\) 3.41973i 0.168274i
\(414\) 0 0
\(415\) 9.35881 + 28.8035i 0.459406 + 1.41391i
\(416\) 0 0
\(417\) −11.4575 15.7698i −0.561074 0.772252i
\(418\) 0 0
\(419\) −14.7604 −0.721091 −0.360546 0.932742i \(-0.617409\pi\)
−0.360546 + 0.932742i \(0.617409\pi\)
\(420\) 0 0
\(421\) −13.3618 4.34150i −0.651212 0.211592i −0.0352636 0.999378i \(-0.511227\pi\)
−0.615949 + 0.787786i \(0.711227\pi\)
\(422\) 0 0
\(423\) −3.57972 + 4.92706i −0.174052 + 0.239562i
\(424\) 0 0
\(425\) −26.7134 + 8.67973i −1.29579 + 0.421029i
\(426\) 0 0
\(427\) −11.2525 3.65618i −0.544549 0.176935i
\(428\) 0 0
\(429\) −1.41312 1.94499i −0.0682261 0.0939052i
\(430\) 0 0
\(431\) −3.96353 + 2.87968i −0.190917 + 0.138709i −0.679138 0.734011i \(-0.737646\pi\)
0.488221 + 0.872720i \(0.337646\pi\)
\(432\) 0 0
\(433\) 1.96971 + 1.43108i 0.0946583 + 0.0687733i 0.634108 0.773245i \(-0.281368\pi\)
−0.539449 + 0.842018i \(0.681368\pi\)
\(434\) 0 0
\(435\) 18.4830 13.4287i 0.886192 0.643856i
\(436\) 0 0
\(437\) 23.0192i 1.10116i
\(438\) 0 0
\(439\) 34.3307 11.1547i 1.63852 0.532386i 0.662310 0.749230i \(-0.269576\pi\)
0.976206 + 0.216844i \(0.0695763\pi\)
\(440\) 0 0
\(441\) −0.514600 + 1.58378i −0.0245048 + 0.0754179i
\(442\) 0 0
\(443\) −12.3084 + 37.8815i −0.584792 + 1.79980i 0.0153139 + 0.999883i \(0.495125\pi\)
−0.600106 + 0.799921i \(0.704875\pi\)
\(444\) 0 0
\(445\) 15.4632 21.2833i 0.733026 1.00892i
\(446\) 0 0
\(447\) 4.32373 + 13.3071i 0.204506 + 0.629403i
\(448\) 0 0
\(449\) 4.10203 + 2.98030i 0.193587 + 0.140649i 0.680357 0.732881i \(-0.261825\pi\)
−0.486770 + 0.873530i \(0.661825\pi\)
\(450\) 0 0
\(451\) 19.5273 25.6964i 0.919505 1.21000i
\(452\) 0 0
\(453\) −9.48164 6.88881i −0.445486 0.323665i
\(454\) 0 0
\(455\) −0.432974 1.33256i −0.0202981 0.0624713i
\(456\) 0 0
\(457\) 2.68451 3.69492i 0.125576 0.172841i −0.741600 0.670843i \(-0.765933\pi\)
0.867176 + 0.498002i \(0.165933\pi\)
\(458\) 0 0
\(459\) 7.17803 22.0917i 0.335042 1.03115i
\(460\) 0 0
\(461\) −12.6223 + 38.8475i −0.587880 + 1.80931i −0.000494251 1.00000i \(0.500157\pi\)
−0.587385 + 0.809307i \(0.699843\pi\)
\(462\) 0 0
\(463\) −5.48043 + 1.78070i −0.254697 + 0.0827562i −0.433583 0.901114i \(-0.642751\pi\)
0.178886 + 0.983870i \(0.442751\pi\)
\(464\) 0 0
\(465\) 14.9571i 0.693617i
\(466\) 0 0
\(467\) −17.1600 + 12.4675i −0.794072 + 0.576927i −0.909169 0.416427i \(-0.863282\pi\)
0.115097 + 0.993354i \(0.463282\pi\)
\(468\) 0 0
\(469\) 3.40271 + 2.47222i 0.157123 + 0.114156i
\(470\) 0 0
\(471\) 3.65094 2.65256i 0.168226 0.122224i
\(472\) 0 0
\(473\) −7.63181 10.5043i −0.350911 0.482988i
\(474\) 0 0
\(475\) 42.5466 + 13.8242i 1.95217 + 0.634299i
\(476\) 0 0
\(477\) −7.65907 + 2.48858i −0.350685 + 0.113944i
\(478\) 0 0
\(479\) −12.5858 + 17.3228i −0.575058 + 0.791500i −0.993143 0.116909i \(-0.962702\pi\)
0.418085 + 0.908408i \(0.362702\pi\)
\(480\) 0 0
\(481\) −1.92561 0.625667i −0.0878001 0.0285280i
\(482\) 0 0
\(483\) −3.87436 −0.176290
\(484\) 0 0
\(485\) −1.96067 2.69863i −0.0890294 0.122538i
\(486\) 0 0
\(487\) 5.50329 + 16.9374i 0.249378 + 0.767506i 0.994886 + 0.101009i \(0.0322071\pi\)
−0.745508 + 0.666497i \(0.767793\pi\)
\(488\) 0 0
\(489\) 6.74286i 0.304923i
\(490\) 0 0
\(491\) −43.1063 −1.94536 −0.972681 0.232147i \(-0.925425\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(492\) 0 0
\(493\) −25.1127 −1.13102
\(494\) 0 0
\(495\) 28.4858i 1.28034i
\(496\) 0 0
\(497\) 1.13346 + 3.48844i 0.0508428 + 0.156478i
\(498\) 0 0
\(499\) −1.83093 2.52006i −0.0819636 0.112813i 0.766066 0.642761i \(-0.222211\pi\)
−0.848030 + 0.529948i \(0.822211\pi\)
\(500\) 0 0
\(501\) −15.6801 −0.700535
\(502\) 0 0
\(503\) 9.34227 + 3.03549i 0.416551 + 0.135346i 0.509792 0.860298i \(-0.329723\pi\)
−0.0932404 + 0.995644i \(0.529723\pi\)
\(504\) 0 0
\(505\) −0.138802 + 0.191045i −0.00617662 + 0.00850139i
\(506\) 0 0
\(507\) 14.0965 4.58024i 0.626049 0.203416i
\(508\) 0 0
\(509\) 23.3169 + 7.57613i 1.03351 + 0.335806i 0.776175 0.630517i \(-0.217157\pi\)
0.257330 + 0.966324i \(0.417157\pi\)
\(510\) 0 0
\(511\) 9.57830 + 13.1834i 0.423719 + 0.583199i
\(512\) 0 0
\(513\) −29.9306 + 21.7459i −1.32147 + 0.960103i
\(514\) 0 0
\(515\) −50.8329 36.9323i −2.23997 1.62743i
\(516\) 0 0
\(517\) 14.9129 10.8349i 0.655871 0.476518i
\(518\) 0 0
\(519\) 21.4481i 0.941468i
\(520\) 0 0
\(521\) −27.4453 + 8.91750i −1.20240 + 0.390683i −0.840643 0.541590i \(-0.817823\pi\)
−0.361756 + 0.932273i \(0.617823\pi\)
\(522\) 0 0
\(523\) −1.20554 + 3.71028i −0.0527147 + 0.162239i −0.973948 0.226771i \(-0.927183\pi\)
0.921233 + 0.389010i \(0.127183\pi\)
\(524\) 0 0
\(525\) 2.32675 7.16102i 0.101548 0.312532i
\(526\) 0 0
\(527\) 9.66370 13.3009i 0.420957 0.579398i
\(528\) 0 0
\(529\) −3.63209 11.1784i −0.157917 0.486018i
\(530\) 0 0
\(531\) 4.60719 + 3.34732i 0.199935 + 0.145261i
\(532\) 0 0
\(533\) −1.50752 2.17163i −0.0652979 0.0940637i
\(534\) 0 0
\(535\) 23.9121 + 17.3732i 1.03381 + 0.751108i
\(536\) 0 0
\(537\) 7.76562 + 23.9001i 0.335111 + 1.03137i
\(538\) 0 0
\(539\) 2.96266 4.07775i 0.127611 0.175641i
\(540\) 0 0
\(541\) 7.35324 22.6310i 0.316141 0.972981i −0.659142 0.752019i \(-0.729080\pi\)
0.975282 0.220962i \(-0.0709197\pi\)
\(542\) 0 0
\(543\) −6.43607 + 19.8082i −0.276198 + 0.850051i
\(544\) 0 0
\(545\) −39.5368 + 12.8463i −1.69357 + 0.550275i
\(546\) 0 0
\(547\) 17.4613i 0.746590i −0.927713 0.373295i \(-0.878228\pi\)
0.927713 0.373295i \(-0.121772\pi\)
\(548\) 0 0
\(549\) 15.9401 11.5811i 0.680305 0.494271i
\(550\) 0 0
\(551\) 32.3583 + 23.5097i 1.37851 + 1.00155i
\(552\) 0 0
\(553\) −4.67878 + 3.39933i −0.198962 + 0.144554i
\(554\) 0 0
\(555\) −11.3018 15.5556i −0.479736 0.660300i
\(556\) 0 0
\(557\) −1.91316 0.621625i −0.0810634 0.0263391i 0.268205 0.963362i \(-0.413570\pi\)
−0.349268 + 0.937023i \(0.613570\pi\)
\(558\) 0 0
\(559\) −1.01147 + 0.328648i −0.0427808 + 0.0139003i
\(560\) 0 0
\(561\) −14.7512 + 20.3033i −0.622796 + 0.857204i
\(562\) 0 0
\(563\) 13.0919 + 4.25381i 0.551757 + 0.179277i 0.571609 0.820526i \(-0.306319\pi\)
−0.0198518 + 0.999803i \(0.506319\pi\)
\(564\) 0 0
\(565\) −11.1580 −0.469421
\(566\) 0 0
\(567\) 0.723560 + 0.995895i 0.0303867 + 0.0418237i
\(568\) 0 0
\(569\) 4.33035 + 13.3274i 0.181538 + 0.558715i 0.999872 0.0160279i \(-0.00510204\pi\)
−0.818334 + 0.574743i \(0.805102\pi\)
\(570\) 0 0
\(571\) 12.1249i 0.507412i 0.967281 + 0.253706i \(0.0816495\pi\)
−0.967281 + 0.253706i \(0.918351\pi\)
\(572\) 0 0
\(573\) −6.65334 −0.277947
\(574\) 0 0
\(575\) −21.8564 −0.911475
\(576\) 0 0
\(577\) 45.6732i 1.90140i −0.310109 0.950701i \(-0.600365\pi\)
0.310109 0.950701i \(-0.399635\pi\)
\(578\) 0 0
\(579\) 3.60257 + 11.0876i 0.149718 + 0.460783i
\(580\) 0 0
\(581\) 5.24542 + 7.21970i 0.217617 + 0.299524i
\(582\) 0 0
\(583\) 24.3750 1.00951
\(584\) 0 0
\(585\) 2.21908 + 0.721024i 0.0917478 + 0.0298107i
\(586\) 0 0
\(587\) 3.92364 5.40043i 0.161946 0.222900i −0.720331 0.693631i \(-0.756010\pi\)
0.882277 + 0.470731i \(0.156010\pi\)
\(588\) 0 0
\(589\) −24.9038 + 8.09174i −1.02614 + 0.333414i
\(590\) 0 0
\(591\) −16.5949 5.39200i −0.682622 0.221797i
\(592\) 0 0
\(593\) −12.3908 17.0545i −0.508831 0.700346i 0.474891 0.880045i \(-0.342488\pi\)
−0.983722 + 0.179699i \(0.942488\pi\)
\(594\) 0 0
\(595\) −11.8327 + 8.59698i −0.485094 + 0.352442i
\(596\) 0 0
\(597\) −3.37446 2.45169i −0.138108 0.100341i
\(598\) 0 0
\(599\) −17.6596 + 12.8304i −0.721551 + 0.524238i −0.886879 0.462001i \(-0.847132\pi\)
0.165328 + 0.986239i \(0.447132\pi\)
\(600\) 0 0
\(601\) 0.602524i 0.0245775i −0.999924 0.0122887i \(-0.996088\pi\)
0.999924 0.0122887i \(-0.00391172\pi\)
\(602\) 0 0
\(603\) −6.66134 + 2.16440i −0.271271 + 0.0881412i
\(604\) 0 0
\(605\) 15.1072 46.4953i 0.614196 1.89030i
\(606\) 0 0
\(607\) 1.85120 5.69740i 0.0751377 0.231250i −0.906433 0.422350i \(-0.861205\pi\)
0.981571 + 0.191100i \(0.0612054\pi\)
\(608\) 0 0
\(609\) 3.95691 5.44622i 0.160342 0.220692i
\(610\) 0 0
\(611\) −0.466582 1.43599i −0.0188759 0.0580940i
\(612\) 0 0
\(613\) 1.40076 + 1.01771i 0.0565762 + 0.0411050i 0.615714 0.787970i \(-0.288868\pi\)
−0.559138 + 0.829075i \(0.688868\pi\)
\(614\) 0 0
\(615\) 0.539811 25.0994i 0.0217673 1.01211i
\(616\) 0 0
\(617\) −21.0097 15.2644i −0.845819 0.614524i 0.0781710 0.996940i \(-0.475092\pi\)
−0.923990 + 0.382416i \(0.875092\pi\)
\(618\) 0 0
\(619\) −13.7261 42.2446i −0.551698 1.69795i −0.704507 0.709697i \(-0.748832\pi\)
0.152809 0.988256i \(-0.451168\pi\)
\(620\) 0 0
\(621\) 10.6242 14.6230i 0.426335 0.586799i
\(622\) 0 0
\(623\) 2.39544 7.37242i 0.0959714 0.295370i
\(624\) 0 0
\(625\) −4.66944 + 14.3710i −0.186777 + 0.574842i
\(626\) 0 0
\(627\) 38.0145 12.3517i 1.51815 0.493278i
\(628\) 0 0
\(629\) 21.1353i 0.842720i
\(630\) 0 0
\(631\) −24.0201 + 17.4516i −0.956224 + 0.694737i −0.952271 0.305255i \(-0.901258\pi\)
−0.00395328 + 0.999992i \(0.501258\pi\)
\(632\) 0 0
\(633\) 16.9313 + 12.3013i 0.672957 + 0.488932i
\(634\) 0 0
\(635\) −51.9885 + 37.7719i −2.06310 + 1.49893i
\(636\) 0 0
\(637\) −0.242673 0.334011i −0.00961505 0.0132340i
\(638\) 0 0
\(639\) −5.80924 1.88754i −0.229810 0.0746697i
\(640\) 0 0
\(641\) −22.9307 + 7.45065i −0.905710 + 0.294283i −0.724592 0.689178i \(-0.757972\pi\)
−0.181118 + 0.983461i \(0.557972\pi\)
\(642\) 0 0
\(643\) −10.9189 + 15.0285i −0.430598 + 0.592667i −0.968090 0.250601i \(-0.919372\pi\)
0.537492 + 0.843269i \(0.319372\pi\)
\(644\) 0 0
\(645\) −9.60559 3.12104i −0.378220 0.122891i
\(646\) 0 0
\(647\) 46.6864 1.83543 0.917717 0.397236i \(-0.130031\pi\)
0.917717 + 0.397236i \(0.130031\pi\)
\(648\) 0 0
\(649\) −10.1315 13.9448i −0.397696 0.547381i
\(650\) 0 0
\(651\) 1.36192 + 4.19156i 0.0533779 + 0.164280i
\(652\) 0 0
\(653\) 45.6865i 1.78785i −0.448215 0.893926i \(-0.647940\pi\)
0.448215 0.893926i \(-0.352060\pi\)
\(654\) 0 0
\(655\) −20.9030 −0.816749
\(656\) 0 0
\(657\) −27.1367 −1.05870
\(658\) 0 0
\(659\) 16.5351i 0.644118i −0.946720 0.322059i \(-0.895625\pi\)
0.946720 0.322059i \(-0.104375\pi\)
\(660\) 0 0
\(661\) 10.9357 + 33.6566i 0.425349 + 1.30909i 0.902660 + 0.430355i \(0.141612\pi\)
−0.477311 + 0.878735i \(0.658388\pi\)
\(662\) 0 0
\(663\) 1.20828 + 1.66305i 0.0469256 + 0.0645875i
\(664\) 0 0
\(665\) 23.2950 0.903340
\(666\) 0 0
\(667\) −18.5847 6.03852i −0.719601 0.233812i
\(668\) 0 0
\(669\) −0.934548 + 1.28630i −0.0361317 + 0.0497311i
\(670\) 0 0
\(671\) −56.7171 + 18.4285i −2.18954 + 0.711425i
\(672\) 0 0
\(673\) −34.3566 11.1631i −1.32435 0.430307i −0.440362 0.897820i \(-0.645150\pi\)
−0.883986 + 0.467513i \(0.845150\pi\)
\(674\) 0 0
\(675\) 20.6474 + 28.4187i 0.794718 + 1.09384i
\(676\) 0 0
\(677\) 23.0289 16.7315i 0.885073 0.643043i −0.0495155 0.998773i \(-0.515768\pi\)
0.934589 + 0.355730i \(0.115768\pi\)
\(678\) 0 0
\(679\) −0.795182 0.577733i −0.0305163 0.0221714i
\(680\) 0 0
\(681\) 9.34002 6.78592i 0.357910 0.260037i
\(682\) 0 0
\(683\) 51.6711i 1.97714i 0.150763 + 0.988570i \(0.451827\pi\)
−0.150763 + 0.988570i \(0.548173\pi\)
\(684\) 0 0
\(685\) −27.5163 + 8.94060i −1.05135 + 0.341603i
\(686\) 0 0
\(687\) 7.23324 22.2616i 0.275965 0.849334i
\(688\) 0 0
\(689\) 0.616975 1.89885i 0.0235049 0.0723405i
\(690\) 0 0
\(691\) −17.1495 + 23.6043i −0.652398 + 0.897949i −0.999200 0.0399893i \(-0.987268\pi\)
0.346802 + 0.937938i \(0.387268\pi\)
\(692\) 0 0
\(693\) 2.59378 + 7.98283i 0.0985295 + 0.303243i
\(694\) 0 0
\(695\) −46.3243 33.6566i −1.75718 1.27667i
\(696\) 0 0
\(697\) −16.6967 + 21.9715i −0.632431 + 0.832230i
\(698\) 0 0
\(699\) −11.1873 8.12802i −0.423141 0.307430i
\(700\) 0 0
\(701\) 12.6497 + 38.9317i 0.477771 + 1.47043i 0.842183 + 0.539191i \(0.181270\pi\)
−0.364412 + 0.931238i \(0.618730\pi\)
\(702\) 0 0
\(703\) 19.7862 27.2333i 0.746250 1.02713i
\(704\) 0 0
\(705\) 4.43095 13.6371i 0.166879 0.513602i
\(706\) 0 0
\(707\) −0.0215022 + 0.0661771i −0.000808675 + 0.00248884i
\(708\) 0 0
\(709\) 39.8172 12.9374i 1.49537 0.485874i 0.556705 0.830710i \(-0.312065\pi\)
0.938663 + 0.344836i \(0.112065\pi\)
\(710\) 0 0
\(711\) 9.63081i 0.361183i
\(712\) 0 0
\(713\) 10.3499 7.51966i 0.387608 0.281614i
\(714\) 0 0
\(715\) −5.71348 4.15108i −0.213672 0.155242i
\(716\) 0 0
\(717\) −6.40419 + 4.65292i −0.239169 + 0.173766i
\(718\) 0 0
\(719\) −9.09406 12.5169i −0.339151 0.466802i 0.605042 0.796194i \(-0.293156\pi\)
−0.944193 + 0.329392i \(0.893156\pi\)
\(720\) 0 0
\(721\) −17.6083 5.72128i −0.655767 0.213071i
\(722\) 0 0
\(723\) 0.407932 0.132545i 0.0151712 0.00492941i
\(724\) 0 0
\(725\) 22.3221 30.7237i 0.829022 1.14105i
\(726\) 0 0
\(727\) −3.96990 1.28990i −0.147235 0.0478397i 0.234472 0.972123i \(-0.424664\pi\)
−0.381708 + 0.924283i \(0.624664\pi\)
\(728\) 0 0
\(729\) −20.7305 −0.767795
\(730\) 0 0
\(731\) 6.52551 + 8.98160i 0.241355 + 0.332196i
\(732\) 0 0
\(733\) 1.30718 + 4.02308i 0.0482817 + 0.148596i 0.972291 0.233775i \(-0.0751078\pi\)
−0.924009 + 0.382370i \(0.875108\pi\)
\(734\) 0 0
\(735\) 3.92077i 0.144620i
\(736\) 0 0
\(737\) 21.1997 0.780903
\(738\) 0 0
\(739\) 36.8473 1.35545 0.677725 0.735315i \(-0.262966\pi\)
0.677725 + 0.735315i \(0.262966\pi\)
\(740\) 0 0
\(741\) 3.27403i 0.120275i
\(742\) 0 0
\(743\) −6.67553 20.5452i −0.244902 0.753730i −0.995653 0.0931444i \(-0.970308\pi\)
0.750751 0.660585i \(-0.229692\pi\)
\(744\) 0 0
\(745\) 24.1589 + 33.2519i 0.885114 + 1.21825i
\(746\) 0 0
\(747\) −14.8610 −0.543737
\(748\) 0 0
\(749\) 8.28304 + 2.69132i 0.302656 + 0.0983389i
\(750\) 0 0
\(751\) −14.1236 + 19.4394i −0.515377 + 0.709355i −0.984814 0.173610i \(-0.944457\pi\)
0.469438 + 0.882966i \(0.344457\pi\)
\(752\) 0 0
\(753\) 1.52475 0.495422i 0.0555650 0.0180542i
\(754\) 0 0
\(755\) −32.7427 10.6387i −1.19163 0.387183i
\(756\) 0 0
\(757\) 16.0107 + 22.0368i 0.581918 + 0.800942i 0.993904 0.110248i \(-0.0351646\pi\)
−0.411986 + 0.911190i \(0.635165\pi\)
\(758\) 0 0
\(759\) −15.7987 + 11.4784i −0.573456 + 0.416640i
\(760\) 0 0
\(761\) −3.60970 2.62260i −0.130852 0.0950693i 0.520434 0.853902i \(-0.325770\pi\)
−0.651286 + 0.758832i \(0.725770\pi\)
\(762\) 0 0
\(763\) −9.91006 + 7.20008i −0.358768 + 0.260660i
\(764\) 0 0
\(765\) 24.3565i 0.880611i
\(766\) 0 0
\(767\) −1.34277 + 0.436291i −0.0484845 + 0.0157536i
\(768\) 0 0
\(769\) 15.4993 47.7021i 0.558920 1.72018i −0.126439 0.991974i \(-0.540355\pi\)
0.685359 0.728205i \(-0.259645\pi\)
\(770\) 0 0
\(771\) 2.01294 6.19520i 0.0724943 0.223115i
\(772\) 0 0
\(773\) −7.75841 + 10.6785i −0.279051 + 0.384080i −0.925419 0.378945i \(-0.876287\pi\)
0.646369 + 0.763025i \(0.276287\pi\)
\(774\) 0 0
\(775\) 7.68299 + 23.6458i 0.275981 + 0.849383i
\(776\) 0 0
\(777\) −4.58364 3.33021i −0.164437 0.119471i
\(778\) 0 0
\(779\) 42.0831 12.6799i 1.50778 0.454306i
\(780\) 0 0
\(781\) 14.9570 + 10.8669i 0.535205 + 0.388849i
\(782\) 0 0
\(783\) 9.70505 + 29.8691i 0.346830 + 1.06743i
\(784\) 0 0
\(785\) 7.79198 10.7247i 0.278108 0.382782i
\(786\) 0 0
\(787\) 4.96943 15.2943i 0.177141 0.545184i −0.822584 0.568644i \(-0.807468\pi\)
0.999725 + 0.0234597i \(0.00746815\pi\)
\(788\) 0 0
\(789\) 9.39699 28.9210i 0.334542 1.02961i
\(790\) 0 0
\(791\) −3.12691 + 1.01600i −0.111180 + 0.0361246i
\(792\) 0 0
\(793\) 4.88481i 0.173465i
\(794\) 0 0
\(795\) 15.3395 11.1448i 0.544037 0.395266i
\(796\) 0 0
\(797\) 5.90392 + 4.28945i 0.209127 + 0.151940i