Properties

Label 1148.2.ba.a.113.8
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 113.8
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.13

$q$-expansion

\(f(q)\) \(=\) \(q-0.904348i q^{3} +(0.129544 + 0.398696i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.18215 q^{9} +O(q^{10})\) \(q-0.904348i q^{3} +(0.129544 + 0.398696i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.18215 q^{9} +(1.99111 + 0.646951i) q^{11} +(-1.84603 + 2.54084i) q^{13} +(0.360560 - 0.117153i) q^{15} +(0.218991 + 0.0711543i) q^{17} +(1.62945 + 2.24275i) q^{19} +(-0.731633 + 0.531562i) q^{21} +(6.51499 + 4.73342i) q^{23} +(3.90291 - 2.83563i) q^{25} -4.68647i q^{27} +(-6.06473 + 1.97055i) q^{29} +(1.52993 - 4.70863i) q^{31} +(0.585069 - 1.80066i) q^{33} +(0.246408 - 0.339151i) q^{35} +(-1.51532 - 4.66367i) q^{37} +(2.29780 + 1.66945i) q^{39} +(2.22688 - 6.00342i) q^{41} +(8.75738 + 6.36261i) q^{43} +(0.282685 + 0.870016i) q^{45} +(0.514310 - 0.707887i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(0.0643483 - 0.198044i) q^{51} +(-1.28343 + 0.417011i) q^{53} +0.877657i q^{55} +(2.02823 - 1.47359i) q^{57} +(1.10026 + 0.799383i) q^{59} +(-2.01068 + 1.46085i) q^{61} +(-1.28264 - 1.76540i) q^{63} +(-1.25216 - 0.406853i) q^{65} +(3.04069 - 0.987979i) q^{67} +(4.28066 - 5.89182i) q^{69} +(9.37008 + 3.04452i) q^{71} +12.9116 q^{73} +(-2.56440 - 3.52959i) q^{75} +(-0.646951 - 1.99111i) q^{77} -9.73942i q^{79} +2.30826 q^{81} +4.97099 q^{83} +0.0965282i q^{85} +(1.78206 + 5.48463i) q^{87} +(-3.59722 - 4.95116i) q^{89} +3.14065 q^{91} +(-4.25824 - 1.38359i) q^{93} +(-0.683089 + 0.940192i) q^{95} +(-13.7927 + 4.48154i) q^{97} +(4.34491 + 1.41175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

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
\(3\) 0.904348i 0.522126i −0.965322 0.261063i \(-0.915927\pi\)
0.965322 0.261063i \(-0.0840730\pi\)
\(4\) 0 0
\(5\) 0.129544 + 0.398696i 0.0579339 + 0.178302i 0.975836 0.218505i \(-0.0701181\pi\)
−0.917902 + 0.396807i \(0.870118\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) 2.18215 0.727385
\(10\) 0 0
\(11\) 1.99111 + 0.646951i 0.600343 + 0.195063i 0.593393 0.804913i \(-0.297788\pi\)
0.00694948 + 0.999976i \(0.497788\pi\)
\(12\) 0 0
\(13\) −1.84603 + 2.54084i −0.511996 + 0.704702i −0.984254 0.176758i \(-0.943439\pi\)
0.472258 + 0.881460i \(0.343439\pi\)
\(14\) 0 0
\(15\) 0.360560 0.117153i 0.0930961 0.0302488i
\(16\) 0 0
\(17\) 0.218991 + 0.0711543i 0.0531130 + 0.0172575i 0.335453 0.942057i \(-0.391111\pi\)
−0.282340 + 0.959314i \(0.591111\pi\)
\(18\) 0 0
\(19\) 1.62945 + 2.24275i 0.373822 + 0.514522i 0.953935 0.300014i \(-0.0969914\pi\)
−0.580112 + 0.814536i \(0.696991\pi\)
\(20\) 0 0
\(21\) −0.731633 + 0.531562i −0.159655 + 0.115996i
\(22\) 0 0
\(23\) 6.51499 + 4.73342i 1.35847 + 0.986986i 0.998541 + 0.0540065i \(0.0171992\pi\)
0.359929 + 0.932980i \(0.382801\pi\)
\(24\) 0 0
\(25\) 3.90291 2.83563i 0.780582 0.567126i
\(26\) 0 0
\(27\) 4.68647i 0.901912i
\(28\) 0 0
\(29\) −6.06473 + 1.97055i −1.12619 + 0.365922i −0.812128 0.583480i \(-0.801691\pi\)
−0.314064 + 0.949402i \(0.601691\pi\)
\(30\) 0 0
\(31\) 1.52993 4.70863i 0.274783 0.845695i −0.714494 0.699642i \(-0.753343\pi\)
0.989277 0.146053i \(-0.0466571\pi\)
\(32\) 0 0
\(33\) 0.585069 1.80066i 0.101847 0.313454i
\(34\) 0 0
\(35\) 0.246408 0.339151i 0.0416505 0.0573270i
\(36\) 0 0
\(37\) −1.51532 4.66367i −0.249117 0.766703i −0.994932 0.100550i \(-0.967940\pi\)
0.745815 0.666153i \(-0.232060\pi\)
\(38\) 0 0
\(39\) 2.29780 + 1.66945i 0.367943 + 0.267326i
\(40\) 0 0
\(41\) 2.22688 6.00342i 0.347780 0.937576i
\(42\) 0 0
\(43\) 8.75738 + 6.36261i 1.33549 + 0.970289i 0.999597 + 0.0283886i \(0.00903760\pi\)
0.335892 + 0.941901i \(0.390962\pi\)
\(44\) 0 0
\(45\) 0.282685 + 0.870016i 0.0421402 + 0.129694i
\(46\) 0 0
\(47\) 0.514310 0.707887i 0.0750199 0.103256i −0.769858 0.638215i \(-0.779673\pi\)
0.844878 + 0.534959i \(0.179673\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 0.0643483 0.198044i 0.00901056 0.0277317i
\(52\) 0 0
\(53\) −1.28343 + 0.417011i −0.176292 + 0.0572809i −0.395833 0.918322i \(-0.629544\pi\)
0.219541 + 0.975603i \(0.429544\pi\)
\(54\) 0 0
\(55\) 0.877657i 0.118343i
\(56\) 0 0
\(57\) 2.02823 1.47359i 0.268645 0.195182i
\(58\) 0 0
\(59\) 1.10026 + 0.799383i 0.143241 + 0.104071i 0.657098 0.753805i \(-0.271784\pi\)
−0.513857 + 0.857876i \(0.671784\pi\)
\(60\) 0 0
\(61\) −2.01068 + 1.46085i −0.257442 + 0.187042i −0.709018 0.705190i \(-0.750862\pi\)
0.451577 + 0.892232i \(0.350862\pi\)
\(62\) 0 0
\(63\) −1.28264 1.76540i −0.161597 0.222420i
\(64\) 0 0
\(65\) −1.25216 0.406853i −0.155312 0.0504639i
\(66\) 0 0
\(67\) 3.04069 0.987979i 0.371479 0.120701i −0.117327 0.993093i \(-0.537433\pi\)
0.488806 + 0.872392i \(0.337433\pi\)
\(68\) 0 0
\(69\) 4.28066 5.89182i 0.515331 0.709292i
\(70\) 0 0
\(71\) 9.37008 + 3.04452i 1.11202 + 0.361318i 0.806718 0.590936i \(-0.201241\pi\)
0.305305 + 0.952254i \(0.401241\pi\)
\(72\) 0 0
\(73\) 12.9116 1.51119 0.755593 0.655042i \(-0.227349\pi\)
0.755593 + 0.655042i \(0.227349\pi\)
\(74\) 0 0
\(75\) −2.56440 3.52959i −0.296111 0.407562i
\(76\) 0 0
\(77\) −0.646951 1.99111i −0.0737270 0.226908i
\(78\) 0 0
\(79\) 9.73942i 1.09577i −0.836553 0.547885i \(-0.815433\pi\)
0.836553 0.547885i \(-0.184567\pi\)
\(80\) 0 0
\(81\) 2.30826 0.256474
\(82\) 0 0
\(83\) 4.97099 0.545637 0.272819 0.962066i \(-0.412044\pi\)
0.272819 + 0.962066i \(0.412044\pi\)
\(84\) 0 0
\(85\) 0.0965282i 0.0104700i
\(86\) 0 0
\(87\) 1.78206 + 5.48463i 0.191057 + 0.588014i
\(88\) 0 0
\(89\) −3.59722 4.95116i −0.381305 0.524821i 0.574625 0.818417i \(-0.305148\pi\)
−0.955930 + 0.293596i \(0.905148\pi\)
\(90\) 0 0
\(91\) 3.14065 0.329230
\(92\) 0 0
\(93\) −4.25824 1.38359i −0.441559 0.143471i
\(94\) 0 0
\(95\) −0.683089 + 0.940192i −0.0700835 + 0.0964616i
\(96\) 0 0
\(97\) −13.7927 + 4.48154i −1.40044 + 0.455031i −0.909334 0.416068i \(-0.863408\pi\)
−0.491108 + 0.871099i \(0.663408\pi\)
\(98\) 0 0
\(99\) 4.34491 + 1.41175i 0.436680 + 0.141886i
\(100\) 0 0
\(101\) −1.37232 1.88884i −0.136551 0.187946i 0.735265 0.677780i \(-0.237058\pi\)
−0.871816 + 0.489833i \(0.837058\pi\)
\(102\) 0 0
\(103\) −11.0964 + 8.06201i −1.09336 + 0.794373i −0.979964 0.199176i \(-0.936173\pi\)
−0.113397 + 0.993550i \(0.536173\pi\)
\(104\) 0 0
\(105\) −0.306710 0.222838i −0.0299319 0.0217468i
\(106\) 0 0
\(107\) 2.42990 1.76543i 0.234908 0.170670i −0.464104 0.885781i \(-0.653624\pi\)
0.699012 + 0.715110i \(0.253624\pi\)
\(108\) 0 0
\(109\) 2.03889i 0.195290i 0.995221 + 0.0976452i \(0.0311310\pi\)
−0.995221 + 0.0976452i \(0.968869\pi\)
\(110\) 0 0
\(111\) −4.21758 + 1.37038i −0.400315 + 0.130070i
\(112\) 0 0
\(113\) 1.05355 3.24251i 0.0991101 0.305029i −0.889193 0.457532i \(-0.848733\pi\)
0.988303 + 0.152503i \(0.0487334\pi\)
\(114\) 0 0
\(115\) −1.04322 + 3.21069i −0.0972804 + 0.299398i
\(116\) 0 0
\(117\) −4.02832 + 5.54451i −0.372418 + 0.512590i
\(118\) 0 0
\(119\) −0.0711543 0.218991i −0.00652271 0.0200748i
\(120\) 0 0
\(121\) −5.35321 3.88933i −0.486655 0.353576i
\(122\) 0 0
\(123\) −5.42918 2.01387i −0.489532 0.181585i
\(124\) 0 0
\(125\) 3.33191 + 2.42077i 0.298015 + 0.216520i
\(126\) 0 0
\(127\) 0.959438 + 2.95285i 0.0851364 + 0.262023i 0.984558 0.175060i \(-0.0560118\pi\)
−0.899421 + 0.437082i \(0.856012\pi\)
\(128\) 0 0
\(129\) 5.75402 7.91972i 0.506613 0.697293i
\(130\) 0 0
\(131\) 2.24384 6.90582i 0.196045 0.603364i −0.803918 0.594740i \(-0.797255\pi\)
0.999963 0.00862407i \(-0.00274516\pi\)
\(132\) 0 0
\(133\) 0.856654 2.63651i 0.0742814 0.228615i
\(134\) 0 0
\(135\) 1.86848 0.607105i 0.160813 0.0522513i
\(136\) 0 0
\(137\) 2.72152i 0.232515i 0.993219 + 0.116258i \(0.0370898\pi\)
−0.993219 + 0.116258i \(0.962910\pi\)
\(138\) 0 0
\(139\) −4.70343 + 3.41724i −0.398940 + 0.289847i −0.769109 0.639118i \(-0.779300\pi\)
0.370169 + 0.928964i \(0.379300\pi\)
\(140\) 0 0
\(141\) −0.640177 0.465116i −0.0539126 0.0391698i
\(142\) 0 0
\(143\) −5.31945 + 3.86481i −0.444835 + 0.323191i
\(144\) 0 0
\(145\) −1.57130 2.16271i −0.130489 0.179603i
\(146\) 0 0
\(147\) 0.860086 + 0.279459i 0.0709387 + 0.0230494i
\(148\) 0 0
\(149\) 7.41892 2.41055i 0.607782 0.197480i 0.0110736 0.999939i \(-0.496475\pi\)
0.596708 + 0.802458i \(0.296475\pi\)
\(150\) 0 0
\(151\) 7.26959 10.0057i 0.591591 0.814255i −0.403315 0.915061i \(-0.632142\pi\)
0.994906 + 0.100806i \(0.0321422\pi\)
\(152\) 0 0
\(153\) 0.477871 + 0.155270i 0.0386336 + 0.0125528i
\(154\) 0 0
\(155\) 2.07551 0.166709
\(156\) 0 0
\(157\) 0.609904 + 0.839460i 0.0486756 + 0.0669962i 0.832661 0.553783i \(-0.186816\pi\)
−0.783985 + 0.620779i \(0.786816\pi\)
\(158\) 0 0
\(159\) 0.377123 + 1.16067i 0.0299078 + 0.0920468i
\(160\) 0 0
\(161\) 8.05297i 0.634663i
\(162\) 0 0
\(163\) −16.4606 −1.28930 −0.644648 0.764480i \(-0.722996\pi\)
−0.644648 + 0.764480i \(0.722996\pi\)
\(164\) 0 0
\(165\) 0.793707 0.0617900
\(166\) 0 0
\(167\) 16.2288i 1.25583i 0.778284 + 0.627913i \(0.216091\pi\)
−0.778284 + 0.627913i \(0.783909\pi\)
\(168\) 0 0
\(169\) 0.969174 + 2.98281i 0.0745518 + 0.229447i
\(170\) 0 0
\(171\) 3.55572 + 4.89403i 0.271913 + 0.374256i
\(172\) 0 0
\(173\) 1.36678 0.103915 0.0519573 0.998649i \(-0.483454\pi\)
0.0519573 + 0.998649i \(0.483454\pi\)
\(174\) 0 0
\(175\) −4.58814 1.49078i −0.346831 0.112692i
\(176\) 0 0
\(177\) 0.722921 0.995015i 0.0543380 0.0747899i
\(178\) 0 0
\(179\) 8.96777 2.91380i 0.670282 0.217788i 0.0459464 0.998944i \(-0.485370\pi\)
0.624336 + 0.781156i \(0.285370\pi\)
\(180\) 0 0
\(181\) −15.7972 5.13283i −1.17420 0.381520i −0.343990 0.938973i \(-0.611779\pi\)
−0.830208 + 0.557453i \(0.811779\pi\)
\(182\) 0 0
\(183\) 1.32111 + 1.81836i 0.0976596 + 0.134417i
\(184\) 0 0
\(185\) 1.66309 1.20830i 0.122273 0.0888362i
\(186\) 0 0
\(187\) 0.390001 + 0.283352i 0.0285197 + 0.0207208i
\(188\) 0 0
\(189\) −3.79143 + 2.75464i −0.275786 + 0.200370i
\(190\) 0 0
\(191\) 0.0658133i 0.00476208i 0.999997 + 0.00238104i \(0.000757910\pi\)
−0.999997 + 0.00238104i \(0.999242\pi\)
\(192\) 0 0
\(193\) −13.8948 + 4.51469i −1.00017 + 0.324974i −0.762933 0.646478i \(-0.776241\pi\)
−0.237235 + 0.971452i \(0.576241\pi\)
\(194\) 0 0
\(195\) −0.367937 + 1.13239i −0.0263485 + 0.0810923i
\(196\) 0 0
\(197\) −5.32298 + 16.3825i −0.379247 + 1.16720i 0.561322 + 0.827598i \(0.310293\pi\)
−0.940569 + 0.339604i \(0.889707\pi\)
\(198\) 0 0
\(199\) −5.30008 + 7.29493i −0.375713 + 0.517124i −0.954442 0.298395i \(-0.903549\pi\)
0.578730 + 0.815519i \(0.303549\pi\)
\(200\) 0 0
\(201\) −0.893477 2.74984i −0.0630210 0.193959i
\(202\) 0 0
\(203\) 5.15897 + 3.74821i 0.362088 + 0.263073i
\(204\) 0 0
\(205\) 2.68202 + 0.110140i 0.187320 + 0.00769252i
\(206\) 0 0
\(207\) 14.2167 + 10.3291i 0.988130 + 0.717919i
\(208\) 0 0
\(209\) 1.79347 + 5.51974i 0.124057 + 0.381809i
\(210\) 0 0
\(211\) −13.0346 + 17.9406i −0.897341 + 1.23508i 0.0739671 + 0.997261i \(0.476434\pi\)
−0.971308 + 0.237824i \(0.923566\pi\)
\(212\) 0 0
\(213\) 2.75331 8.47381i 0.188654 0.580616i
\(214\) 0 0
\(215\) −1.40228 + 4.31577i −0.0956347 + 0.294333i
\(216\) 0 0
\(217\) −4.70863 + 1.52993i −0.319643 + 0.103858i
\(218\) 0 0
\(219\) 11.6766i 0.789028i
\(220\) 0 0
\(221\) −0.585054 + 0.425067i −0.0393550 + 0.0285931i
\(222\) 0 0
\(223\) −17.6106 12.7948i −1.17929 0.856805i −0.187199 0.982322i \(-0.559941\pi\)
−0.992091 + 0.125517i \(0.959941\pi\)
\(224\) 0 0
\(225\) 8.51675 6.18778i 0.567783 0.412519i
\(226\) 0 0
\(227\) 15.4912 + 21.3218i 1.02818 + 1.41517i 0.906302 + 0.422630i \(0.138893\pi\)
0.121882 + 0.992545i \(0.461107\pi\)
\(228\) 0 0
\(229\) −15.7367 5.11315i −1.03991 0.337887i −0.261208 0.965283i \(-0.584121\pi\)
−0.778700 + 0.627396i \(0.784121\pi\)
\(230\) 0 0
\(231\) −1.80066 + 0.585069i −0.118475 + 0.0384947i
\(232\) 0 0
\(233\) −12.5681 + 17.2985i −0.823361 + 1.13326i 0.165761 + 0.986166i \(0.446992\pi\)
−0.989123 + 0.147094i \(0.953008\pi\)
\(234\) 0 0
\(235\) 0.348858 + 0.113351i 0.0227570 + 0.00739419i
\(236\) 0 0
\(237\) −8.80783 −0.572130
\(238\) 0 0
\(239\) 15.5801 + 21.4442i 1.00779 + 1.38711i 0.920419 + 0.390933i \(0.127848\pi\)
0.0873746 + 0.996176i \(0.472152\pi\)
\(240\) 0 0
\(241\) 1.10831 + 3.41103i 0.0713927 + 0.219724i 0.980386 0.197086i \(-0.0631479\pi\)
−0.908993 + 0.416810i \(0.863148\pi\)
\(242\) 0 0
\(243\) 16.1469i 1.03582i
\(244\) 0 0
\(245\) −0.419214 −0.0267826
\(246\) 0 0
\(247\) −8.70649 −0.553981
\(248\) 0 0
\(249\) 4.49551i 0.284891i
\(250\) 0 0
\(251\) −5.97814 18.3988i −0.377337 1.16132i −0.941889 0.335925i \(-0.890951\pi\)
0.564552 0.825398i \(-0.309049\pi\)
\(252\) 0 0
\(253\) 9.90979 + 13.6397i 0.623023 + 0.857517i
\(254\) 0 0
\(255\) 0.0872951 0.00546663
\(256\) 0 0
\(257\) −18.9898 6.17015i −1.18455 0.384883i −0.350494 0.936565i \(-0.613986\pi\)
−0.834055 + 0.551682i \(0.813986\pi\)
\(258\) 0 0
\(259\) −2.88231 + 3.96716i −0.179098 + 0.246507i
\(260\) 0 0
\(261\) −13.2342 + 4.30004i −0.819175 + 0.266166i
\(262\) 0 0
\(263\) −22.5399 7.32366i −1.38987 0.451596i −0.483969 0.875085i \(-0.660805\pi\)
−0.905901 + 0.423489i \(0.860805\pi\)
\(264\) 0 0
\(265\) −0.332521 0.457676i −0.0204266 0.0281148i
\(266\) 0 0
\(267\) −4.47757 + 3.25314i −0.274023 + 0.199089i
\(268\) 0 0
\(269\) −16.7376 12.1606i −1.02051 0.741443i −0.0541217 0.998534i \(-0.517236\pi\)
−0.966387 + 0.257091i \(0.917236\pi\)
\(270\) 0 0
\(271\) −5.53287 + 4.01986i −0.336098 + 0.244189i −0.743014 0.669276i \(-0.766604\pi\)
0.406916 + 0.913466i \(0.366604\pi\)
\(272\) 0 0
\(273\) 2.84024i 0.171899i
\(274\) 0 0
\(275\) 9.60564 3.12106i 0.579242 0.188207i
\(276\) 0 0
\(277\) −3.48978 + 10.7404i −0.209681 + 0.645331i 0.789808 + 0.613354i \(0.210180\pi\)
−0.999489 + 0.0319765i \(0.989820\pi\)
\(278\) 0 0
\(279\) 3.33854 10.2750i 0.199873 0.615146i
\(280\) 0 0
\(281\) 15.9780 21.9919i 0.953170 1.31193i 0.00306492 0.999995i \(-0.499024\pi\)
0.950105 0.311930i \(-0.100976\pi\)
\(282\) 0 0
\(283\) 8.99516 + 27.6843i 0.534707 + 1.64566i 0.744282 + 0.667866i \(0.232792\pi\)
−0.209575 + 0.977793i \(0.567208\pi\)
\(284\) 0 0
\(285\) 0.850260 + 0.617750i 0.0503651 + 0.0365924i
\(286\) 0 0
\(287\) −6.16579 + 1.72714i −0.363955 + 0.101950i
\(288\) 0 0
\(289\) −13.7104 9.96119i −0.806494 0.585952i
\(290\) 0 0
\(291\) 4.05287 + 12.4734i 0.237583 + 0.731206i
\(292\) 0 0
\(293\) 8.83366 12.1585i 0.516068 0.710307i −0.468860 0.883273i \(-0.655335\pi\)
0.984928 + 0.172966i \(0.0553351\pi\)
\(294\) 0 0
\(295\) −0.176179 + 0.542223i −0.0102575 + 0.0315695i
\(296\) 0 0
\(297\) 3.03192 9.33129i 0.175930 0.541456i
\(298\) 0 0
\(299\) −24.0537 + 7.81553i −1.39106 + 0.451984i
\(300\) 0 0
\(301\) 10.8247i 0.623927i
\(302\) 0 0
\(303\) −1.70817 + 1.24106i −0.0981316 + 0.0712968i
\(304\) 0 0
\(305\) −0.842906 0.612407i −0.0482647 0.0350663i
\(306\) 0 0
\(307\) −8.54457 + 6.20799i −0.487664 + 0.354309i −0.804285 0.594243i \(-0.797452\pi\)
0.316621 + 0.948552i \(0.397452\pi\)
\(308\) 0 0
\(309\) 7.29086 + 10.0350i 0.414763 + 0.570872i
\(310\) 0 0
\(311\) 8.81263 + 2.86340i 0.499719 + 0.162368i 0.548021 0.836464i \(-0.315381\pi\)
−0.0483028 + 0.998833i \(0.515381\pi\)
\(312\) 0 0
\(313\) −14.4665 + 4.70046i −0.817697 + 0.265686i −0.687854 0.725849i \(-0.741447\pi\)
−0.129843 + 0.991535i \(0.541447\pi\)
\(314\) 0 0
\(315\) 0.537700 0.740080i 0.0302959 0.0416988i
\(316\) 0 0
\(317\) −17.0786 5.54919i −0.959232 0.311673i −0.212771 0.977102i \(-0.568249\pi\)
−0.746461 + 0.665429i \(0.768249\pi\)
\(318\) 0 0
\(319\) −13.3504 −0.747479
\(320\) 0 0
\(321\) −1.59656 2.19748i −0.0891114 0.122651i
\(322\) 0 0
\(323\) 0.197253 + 0.607084i 0.0109755 + 0.0337790i
\(324\) 0 0
\(325\) 15.1513i 0.840444i
\(326\) 0 0
\(327\) 1.84387 0.101966
\(328\) 0 0
\(329\) −0.874997 −0.0482401
\(330\) 0 0
\(331\) 6.86868i 0.377537i 0.982022 + 0.188768i \(0.0604496\pi\)
−0.982022 + 0.188768i \(0.939550\pi\)
\(332\) 0 0
\(333\) −3.30666 10.1769i −0.181204 0.557688i
\(334\) 0 0
\(335\) 0.787807 + 1.08432i 0.0430425 + 0.0592429i
\(336\) 0 0
\(337\) 32.9405 1.79438 0.897192 0.441640i \(-0.145603\pi\)
0.897192 + 0.441640i \(0.145603\pi\)
\(338\) 0 0
\(339\) −2.93235 0.952780i −0.159264 0.0517479i
\(340\) 0 0
\(341\) 6.09251 8.38562i 0.329928 0.454107i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) 2.90358 + 0.943430i 0.156323 + 0.0507926i
\(346\) 0 0
\(347\) 2.00308 + 2.75700i 0.107531 + 0.148004i 0.859391 0.511319i \(-0.170843\pi\)
−0.751860 + 0.659323i \(0.770843\pi\)
\(348\) 0 0
\(349\) 16.9999 12.3512i 0.909986 0.661143i −0.0310254 0.999519i \(-0.509877\pi\)
0.941011 + 0.338375i \(0.109877\pi\)
\(350\) 0 0
\(351\) 11.9076 + 8.65136i 0.635579 + 0.461775i
\(352\) 0 0
\(353\) 17.7763 12.9152i 0.946135 0.687407i −0.00375494 0.999993i \(-0.501195\pi\)
0.949889 + 0.312586i \(0.101195\pi\)
\(354\) 0 0
\(355\) 4.13021i 0.219209i
\(356\) 0 0
\(357\) −0.198044 + 0.0643483i −0.0104816 + 0.00340567i
\(358\) 0 0
\(359\) 7.34445 22.6039i 0.387625 1.19299i −0.546932 0.837177i \(-0.684205\pi\)
0.934558 0.355811i \(-0.115795\pi\)
\(360\) 0 0
\(361\) 3.49651 10.7612i 0.184027 0.566377i
\(362\) 0 0
\(363\) −3.51731 + 4.84116i −0.184611 + 0.254095i
\(364\) 0 0
\(365\) 1.67262 + 5.14779i 0.0875489 + 0.269448i
\(366\) 0 0
\(367\) −20.6653 15.0142i −1.07872 0.783734i −0.101259 0.994860i \(-0.532287\pi\)
−0.977459 + 0.211126i \(0.932287\pi\)
\(368\) 0 0
\(369\) 4.85940 13.1004i 0.252970 0.681979i
\(370\) 0 0
\(371\) 1.09175 + 0.793202i 0.0566808 + 0.0411810i
\(372\) 0 0
\(373\) 1.79347 + 5.51973i 0.0928623 + 0.285801i 0.986691 0.162609i \(-0.0519908\pi\)
−0.893828 + 0.448409i \(0.851991\pi\)
\(374\) 0 0
\(375\) 2.18922 3.01320i 0.113051 0.155601i
\(376\) 0 0
\(377\) 6.18881 19.0472i 0.318740 0.980981i
\(378\) 0 0
\(379\) −3.77756 + 11.6261i −0.194040 + 0.597195i 0.805946 + 0.591989i \(0.201657\pi\)
−0.999986 + 0.00520598i \(0.998343\pi\)
\(380\) 0 0
\(381\) 2.67040 0.867666i 0.136809 0.0444519i
\(382\) 0 0
\(383\) 17.3466i 0.886367i −0.896431 0.443184i \(-0.853849\pi\)
0.896431 0.443184i \(-0.146151\pi\)
\(384\) 0 0
\(385\) 0.710039 0.515874i 0.0361870 0.0262914i
\(386\) 0 0
\(387\) 19.1100 + 13.8842i 0.971414 + 0.705774i
\(388\) 0 0
\(389\) −7.28912 + 5.29586i −0.369573 + 0.268511i −0.757034 0.653376i \(-0.773352\pi\)
0.387461 + 0.921886i \(0.373352\pi\)
\(390\) 0 0
\(391\) 1.08992 + 1.50014i 0.0551195 + 0.0758655i
\(392\) 0 0
\(393\) −6.24527 2.02921i −0.315032 0.102360i
\(394\) 0 0
\(395\) 3.88307 1.26169i 0.195378 0.0634823i
\(396\) 0 0
\(397\) −13.0340 + 17.9398i −0.654160 + 0.900374i −0.999271 0.0381879i \(-0.987841\pi\)
0.345110 + 0.938562i \(0.387841\pi\)
\(398\) 0 0
\(399\) −2.38432 0.774714i −0.119365 0.0387842i
\(400\) 0 0
\(401\) −6.47571 −0.323382 −0.161691 0.986841i \(-0.551695\pi\)
−0.161691 + 0.986841i \(0.551695\pi\)
\(402\) 0 0
\(403\) 9.13959 + 12.5796i 0.455275 + 0.626633i
\(404\) 0 0
\(405\) 0.299022 + 0.920295i 0.0148585 + 0.0457298i
\(406\) 0 0
\(407\) 10.2662i 0.508878i
\(408\) 0 0
\(409\) −36.8721 −1.82321 −0.911603 0.411072i \(-0.865155\pi\)
−0.911603 + 0.411072i \(0.865155\pi\)
\(410\) 0 0
\(411\) 2.46120 0.121402
\(412\) 0 0
\(413\) 1.35999i 0.0669208i
\(414\) 0 0
\(415\) 0.643963 + 1.98191i 0.0316109 + 0.0972883i
\(416\) 0 0
\(417\) 3.09038 + 4.25354i 0.151336 + 0.208297i
\(418\) 0 0
\(419\) −28.0131 −1.36853 −0.684264 0.729234i \(-0.739876\pi\)
−0.684264 + 0.729234i \(0.739876\pi\)
\(420\) 0 0
\(421\) −25.8734 8.40679i −1.26099 0.409722i −0.399145 0.916888i \(-0.630693\pi\)
−0.861848 + 0.507166i \(0.830693\pi\)
\(422\) 0 0
\(423\) 1.12230 1.54472i 0.0545683 0.0751069i
\(424\) 0 0
\(425\) 1.05647 0.343267i 0.0512462 0.0166509i
\(426\) 0 0
\(427\) 2.36370 + 0.768013i 0.114387 + 0.0371667i
\(428\) 0 0
\(429\) 3.49513 + 4.81063i 0.168746 + 0.232260i
\(430\) 0 0
\(431\) 25.7348 18.6974i 1.23960 0.900623i 0.242029 0.970269i \(-0.422187\pi\)
0.997572 + 0.0696460i \(0.0221870\pi\)
\(432\) 0 0
\(433\) −6.94748 5.04764i −0.333874 0.242574i 0.408198 0.912893i \(-0.366157\pi\)
−0.742073 + 0.670319i \(0.766157\pi\)
\(434\) 0 0
\(435\) −1.95584 + 1.42100i −0.0937754 + 0.0681318i
\(436\) 0 0
\(437\) 22.3244i 1.06792i
\(438\) 0 0
\(439\) 7.89212 2.56430i 0.376670 0.122388i −0.114562 0.993416i \(-0.536547\pi\)
0.491232 + 0.871029i \(0.336547\pi\)
\(440\) 0 0
\(441\) −0.674323 + 2.07535i −0.0321106 + 0.0988263i
\(442\) 0 0
\(443\) −4.54535 + 13.9891i −0.215956 + 0.664644i 0.783128 + 0.621860i \(0.213623\pi\)
−0.999084 + 0.0427839i \(0.986377\pi\)
\(444\) 0 0
\(445\) 1.50801 2.07559i 0.0714863 0.0983925i
\(446\) 0 0
\(447\) −2.17998 6.70928i −0.103109 0.317338i
\(448\) 0 0
\(449\) 9.71423 + 7.05780i 0.458443 + 0.333078i 0.792920 0.609326i \(-0.208560\pi\)
−0.334477 + 0.942404i \(0.608560\pi\)
\(450\) 0 0
\(451\) 8.31788 10.5128i 0.391674 0.495028i
\(452\) 0 0
\(453\) −9.04866 6.57424i −0.425143 0.308885i
\(454\) 0 0
\(455\) 0.406853 + 1.25216i 0.0190736 + 0.0587024i
\(456\) 0 0
\(457\) −0.599903 + 0.825696i −0.0280623 + 0.0386244i −0.822818 0.568306i \(-0.807599\pi\)
0.794755 + 0.606930i \(0.207599\pi\)
\(458\) 0 0
\(459\) 0.333463 1.02629i 0.0155647 0.0479032i
\(460\) 0 0
\(461\) −0.546117 + 1.68078i −0.0254352 + 0.0782815i −0.962968 0.269614i \(-0.913104\pi\)
0.937533 + 0.347896i \(0.113104\pi\)
\(462\) 0 0
\(463\) 21.9651 7.13690i 1.02081 0.331680i 0.249657 0.968334i \(-0.419682\pi\)
0.771149 + 0.636654i \(0.219682\pi\)
\(464\) 0 0
\(465\) 1.87698i 0.0870428i
\(466\) 0 0
\(467\) 20.9101 15.1921i 0.967603 0.703005i 0.0126990 0.999919i \(-0.495958\pi\)
0.954904 + 0.296915i \(0.0959577\pi\)
\(468\) 0 0
\(469\) −2.58656 1.87925i −0.119436 0.0867756i
\(470\) 0 0
\(471\) 0.759164 0.551565i 0.0349804 0.0254148i
\(472\) 0 0
\(473\) 13.3206 + 18.3343i 0.612483 + 0.843011i
\(474\) 0 0
\(475\) 12.7192 + 4.13272i 0.583598 + 0.189622i
\(476\) 0 0
\(477\) −2.80064 + 0.909983i −0.128232 + 0.0416653i
\(478\) 0 0
\(479\) −15.2401 + 20.9762i −0.696338 + 0.958427i 0.303646 + 0.952785i \(0.401796\pi\)
−0.999984 + 0.00564216i \(0.998204\pi\)
\(480\) 0 0
\(481\) 14.6470 + 4.75909i 0.667844 + 0.216996i
\(482\) 0 0
\(483\) −7.28269 −0.331374
\(484\) 0 0
\(485\) −3.57354 4.91856i −0.162266 0.223340i
\(486\) 0 0
\(487\) −0.0406868 0.125221i −0.00184369 0.00567430i 0.950130 0.311853i \(-0.100950\pi\)
−0.951974 + 0.306178i \(0.900950\pi\)
\(488\) 0 0
\(489\) 14.8861i 0.673174i
\(490\) 0 0
\(491\) 24.8763 1.12265 0.561327 0.827594i \(-0.310291\pi\)
0.561327 + 0.827594i \(0.310291\pi\)
\(492\) 0 0
\(493\) −1.46833 −0.0661303
\(494\) 0 0
\(495\) 1.91518i 0.0860811i
\(496\) 0 0
\(497\) −3.04452 9.37008i −0.136566 0.420306i
\(498\) 0 0
\(499\) 2.57033 + 3.53776i 0.115064 + 0.158372i 0.862664 0.505777i \(-0.168794\pi\)
−0.747600 + 0.664149i \(0.768794\pi\)
\(500\) 0 0
\(501\) 14.6765 0.655699
\(502\) 0 0
\(503\) −4.68339 1.52173i −0.208822 0.0678504i 0.202738 0.979233i \(-0.435016\pi\)
−0.411560 + 0.911383i \(0.635016\pi\)
\(504\) 0 0
\(505\) 0.575296 0.791827i 0.0256003 0.0352358i
\(506\) 0 0
\(507\) 2.69750 0.876470i 0.119800 0.0389254i
\(508\) 0 0
\(509\) 7.74645 + 2.51698i 0.343355 + 0.111563i 0.475618 0.879652i \(-0.342224\pi\)
−0.132263 + 0.991215i \(0.542224\pi\)
\(510\) 0 0
\(511\) −7.58923 10.4457i −0.335728 0.462090i
\(512\) 0 0
\(513\) 10.5106 7.63639i 0.464054 0.337155i
\(514\) 0 0
\(515\) −4.65176 3.37970i −0.204981 0.148928i
\(516\) 0 0
\(517\) 1.48202 1.07675i 0.0651791 0.0473554i
\(518\) 0 0
\(519\) 1.23605i 0.0542565i
\(520\) 0 0
\(521\) 37.4349 12.1633i 1.64005 0.532886i 0.663503 0.748174i \(-0.269069\pi\)
0.976551 + 0.215288i \(0.0690691\pi\)
\(522\) 0 0
\(523\) 11.9880 36.8953i 0.524199 1.61332i −0.241694 0.970352i \(-0.577703\pi\)
0.765894 0.642967i \(-0.222297\pi\)
\(524\) 0 0
\(525\) −1.34818 + 4.14928i −0.0588395 + 0.181089i
\(526\) 0 0
\(527\) 0.670079 0.922285i 0.0291891 0.0401754i
\(528\) 0 0
\(529\) 12.9325 + 39.8021i 0.562282 + 1.73053i
\(530\) 0 0
\(531\) 2.40093 + 1.74438i 0.104192 + 0.0756996i
\(532\) 0 0
\(533\) 11.1428 + 16.7406i 0.482650 + 0.725117i
\(534\) 0 0
\(535\) 1.01865 + 0.740092i 0.0440400 + 0.0319970i
\(536\) 0 0
\(537\) −2.63509 8.10998i −0.113713 0.349971i
\(538\) 0 0
\(539\) −1.23057 + 1.69374i −0.0530046 + 0.0729546i
\(540\) 0 0
\(541\) −2.72788 + 8.39557i −0.117281 + 0.360954i −0.992416 0.122925i \(-0.960772\pi\)
0.875135 + 0.483879i \(0.160772\pi\)
\(542\) 0 0
\(543\) −4.64186 + 14.2862i −0.199201 + 0.613079i
\(544\) 0 0
\(545\) −0.812898 + 0.264127i −0.0348207 + 0.0113139i
\(546\) 0 0
\(547\) 10.3796i 0.443799i −0.975070 0.221899i \(-0.928774\pi\)
0.975070 0.221899i \(-0.0712257\pi\)
\(548\) 0 0
\(549\) −4.38762 + 3.18779i −0.187259 + 0.136052i
\(550\) 0 0
\(551\) −14.3016 10.3908i −0.609271 0.442661i
\(552\) 0 0
\(553\) −7.87936 + 5.72469i −0.335064 + 0.243439i
\(554\) 0 0
\(555\) −1.09273 1.50401i −0.0463837 0.0638416i
\(556\) 0 0
\(557\) 38.9391 + 12.6521i 1.64990 + 0.536086i 0.978719 0.205204i \(-0.0657859\pi\)
0.671184 + 0.741290i \(0.265786\pi\)
\(558\) 0 0
\(559\) −32.3328 + 10.5055i −1.36753 + 0.444337i
\(560\) 0 0
\(561\) 0.256249 0.352697i 0.0108188 0.0148909i
\(562\) 0 0
\(563\) 1.02495 + 0.333025i 0.0431963 + 0.0140353i 0.330535 0.943794i \(-0.392771\pi\)
−0.287339 + 0.957829i \(0.592771\pi\)
\(564\) 0 0
\(565\) 1.42926 0.0601292
\(566\) 0 0
\(567\) −1.35676 1.86742i −0.0569787 0.0784245i
\(568\) 0 0
\(569\) −6.39945 19.6955i −0.268279 0.825677i −0.990920 0.134454i \(-0.957072\pi\)
0.722641 0.691223i \(-0.242928\pi\)
\(570\) 0 0
\(571\) 10.8456i 0.453876i −0.973909 0.226938i \(-0.927129\pi\)
0.973909 0.226938i \(-0.0728715\pi\)
\(572\) 0 0
\(573\) 0.0595181 0.00248641
\(574\) 0 0
\(575\) 38.8496 1.62014
\(576\) 0 0
\(577\) 13.3323i 0.555033i 0.960721 + 0.277516i \(0.0895113\pi\)
−0.960721 + 0.277516i \(0.910489\pi\)
\(578\) 0 0
\(579\) 4.08285 + 12.5657i 0.169677 + 0.522213i
\(580\) 0 0
\(581\) −2.92187 4.02162i −0.121220 0.166845i
\(582\) 0 0
\(583\) −2.82524 −0.117009
\(584\) 0 0
\(585\) −2.73242 0.887816i −0.112972 0.0367067i
\(586\) 0 0
\(587\) −18.8332 + 25.9217i −0.777330 + 1.06990i 0.218241 + 0.975895i \(0.429968\pi\)
−0.995571 + 0.0940081i \(0.970032\pi\)
\(588\) 0 0
\(589\) 13.0532 4.24125i 0.537849 0.174758i
\(590\) 0 0
\(591\) 14.8154 + 4.81383i 0.609426 + 0.198014i
\(592\) 0 0
\(593\) −0.396731 0.546054i −0.0162918 0.0224237i 0.800793 0.598941i \(-0.204411\pi\)
−0.817085 + 0.576517i \(0.804411\pi\)
\(594\) 0 0
\(595\) 0.0780930 0.0567379i 0.00320150 0.00232603i
\(596\) 0 0
\(597\) 6.59716 + 4.79311i 0.270004 + 0.196169i
\(598\) 0 0
\(599\) −4.08326 + 2.96667i −0.166838 + 0.121215i −0.668071 0.744097i \(-0.732880\pi\)
0.501233 + 0.865312i \(0.332880\pi\)
\(600\) 0 0
\(601\) 27.6469i 1.12774i −0.825863 0.563871i \(-0.809311\pi\)
0.825863 0.563871i \(-0.190689\pi\)
\(602\) 0 0
\(603\) 6.63525 2.15592i 0.270208 0.0877960i
\(604\) 0 0
\(605\) 0.857184 2.63814i 0.0348495 0.107256i
\(606\) 0 0
\(607\) 4.01401 12.3538i 0.162924 0.501427i −0.835954 0.548800i \(-0.815085\pi\)
0.998877 + 0.0473728i \(0.0150849\pi\)
\(608\) 0 0
\(609\) 3.38968 4.66550i 0.137357 0.189056i
\(610\) 0 0
\(611\) 0.849197 + 2.61356i 0.0343548 + 0.105733i
\(612\) 0 0
\(613\) 5.02586 + 3.65150i 0.202993 + 0.147483i 0.684638 0.728884i \(-0.259960\pi\)
−0.481645 + 0.876366i \(0.659960\pi\)
\(614\) 0 0
\(615\) 0.0996050 2.42548i 0.00401646 0.0978046i
\(616\) 0 0
\(617\) 30.4908 + 22.1528i 1.22751 + 0.891840i 0.996701 0.0811586i \(-0.0258620\pi\)
0.230811 + 0.972999i \(0.425862\pi\)
\(618\) 0 0
\(619\) −3.53321 10.8741i −0.142012 0.437067i 0.854603 0.519282i \(-0.173801\pi\)
−0.996615 + 0.0822150i \(0.973801\pi\)
\(620\) 0 0
\(621\) 22.1830 30.5323i 0.890174 1.22522i
\(622\) 0 0
\(623\) −1.89117 + 5.82043i −0.0757682 + 0.233191i
\(624\) 0 0
\(625\) 6.92037 21.2987i 0.276815 0.851948i
\(626\) 0 0
\(627\) 4.99177 1.62192i 0.199352 0.0647734i
\(628\) 0 0
\(629\) 1.12912i 0.0450210i
\(630\) 0 0
\(631\) −20.2384 + 14.7041i −0.805678 + 0.585359i −0.912574 0.408911i \(-0.865909\pi\)
0.106897 + 0.994270i \(0.465909\pi\)
\(632\) 0 0
\(633\) 16.2246 + 11.7878i 0.644869 + 0.468525i
\(634\) 0 0
\(635\) −1.05300 + 0.765048i −0.0417870 + 0.0303600i
\(636\) 0 0
\(637\) −1.84603 2.54084i −0.0731423 0.100672i
\(638\) 0 0
\(639\) 20.4470 + 6.64362i 0.808869 + 0.262818i
\(640\) 0 0
\(641\) −27.1521 + 8.82226i −1.07244 + 0.348458i −0.791439 0.611248i \(-0.790668\pi\)
−0.281006 + 0.959706i \(0.590668\pi\)
\(642\) 0 0
\(643\) 25.8556 35.5872i 1.01965 1.40342i 0.107195 0.994238i \(-0.465813\pi\)
0.912451 0.409185i \(-0.134187\pi\)
\(644\) 0 0
\(645\) 3.90296 + 1.26815i 0.153679 + 0.0499333i
\(646\) 0 0
\(647\) 36.0356 1.41670 0.708352 0.705859i \(-0.249439\pi\)
0.708352 + 0.705859i \(0.249439\pi\)
\(648\) 0 0
\(649\) 1.67357 + 2.30347i 0.0656934 + 0.0904193i
\(650\) 0 0
\(651\) 1.38359 + 4.25824i 0.0542270 + 0.166894i
\(652\) 0 0
\(653\) 2.51651i 0.0984786i −0.998787 0.0492393i \(-0.984320\pi\)
0.998787 0.0492393i \(-0.0156797\pi\)
\(654\) 0 0
\(655\) 3.04400 0.118939
\(656\) 0 0
\(657\) 28.1750 1.09921
\(658\) 0 0
\(659\) 11.9875i 0.466967i −0.972361 0.233483i \(-0.924988\pi\)
0.972361 0.233483i \(-0.0750125\pi\)
\(660\) 0 0
\(661\) 13.5361 + 41.6598i 0.526493 + 1.62038i 0.761344 + 0.648348i \(0.224540\pi\)
−0.234851 + 0.972031i \(0.575460\pi\)
\(662\) 0 0
\(663\) 0.384408 + 0.529093i 0.0149292 + 0.0205483i
\(664\) 0 0
\(665\) 1.16214 0.0450659
\(666\) 0 0
\(667\) −48.8391 15.8688i −1.89106 0.614442i
\(668\) 0 0
\(669\) −11.5710 + 15.9261i −0.447360 + 0.615738i
\(670\) 0 0
\(671\) −4.94859 + 1.60790i −0.191038 + 0.0620721i
\(672\) 0 0
\(673\) −23.5399 7.64859i −0.907397 0.294831i −0.182111 0.983278i \(-0.558293\pi\)
−0.725287 + 0.688447i \(0.758293\pi\)
\(674\) 0 0
\(675\) −13.2891 18.2909i −0.511497 0.704016i
\(676\) 0 0
\(677\) −7.70855 + 5.60059i −0.296264 + 0.215248i −0.725980 0.687716i \(-0.758614\pi\)
0.429716 + 0.902964i \(0.358614\pi\)
\(678\) 0 0
\(679\) 11.7328 + 8.52439i 0.450264 + 0.327136i
\(680\) 0 0
\(681\) 19.2823 14.0094i 0.738899 0.536841i
\(682\) 0 0
\(683\) 39.8358i 1.52427i −0.647416 0.762137i \(-0.724150\pi\)
0.647416 0.762137i \(-0.275850\pi\)
\(684\) 0 0
\(685\) −1.08506 + 0.352557i −0.0414580 + 0.0134705i
\(686\) 0 0
\(687\) −4.62407 + 14.2314i −0.176419 + 0.542963i
\(688\) 0 0
\(689\) 1.30969 4.03080i 0.0498951 0.153561i
\(690\) 0 0
\(691\) −4.51589 + 6.21559i −0.171793 + 0.236452i −0.886228 0.463249i \(-0.846684\pi\)
0.714436 + 0.699701i \(0.246684\pi\)
\(692\) 0 0
\(693\) −1.41175 4.34491i −0.0536279 0.165050i
\(694\) 0 0
\(695\) −1.97174 1.43256i −0.0747925 0.0543399i
\(696\) 0 0
\(697\) 0.914834 1.15624i 0.0346518 0.0437957i
\(698\) 0 0
\(699\) 15.6438 + 11.3659i 0.591704 + 0.429898i
\(700\) 0 0
\(701\) −13.5647 41.7478i −0.512331 1.57679i −0.788087 0.615564i \(-0.788928\pi\)
0.275756 0.961228i \(-0.411072\pi\)
\(702\) 0 0
\(703\) 7.99031 10.9977i 0.301360 0.414787i
\(704\) 0 0
\(705\) 0.102509 0.315489i 0.00386069 0.0118820i
\(706\) 0 0
\(707\) −0.721472 + 2.22046i −0.0271337 + 0.0835091i
\(708\) 0 0
\(709\) −41.0018 + 13.3223i −1.53985 + 0.500329i −0.951336 0.308156i \(-0.900288\pi\)
−0.588518 + 0.808484i \(0.700288\pi\)
\(710\) 0 0
\(711\) 21.2529i 0.797047i
\(712\) 0 0
\(713\) 32.2554 23.4349i 1.20797 0.877644i
\(714\) 0 0
\(715\) −2.22999 1.62018i −0.0833967 0.0605913i
\(716\) 0 0
\(717\) 19.3930 14.0898i 0.724245 0.526195i
\(718\) 0 0
\(719\) −9.13692 12.5759i −0.340750 0.469002i 0.603910 0.797052i \(-0.293608\pi\)
−0.944660 + 0.328050i \(0.893608\pi\)
\(720\) 0 0
\(721\) 13.0446 + 4.23845i 0.485806 + 0.157848i
\(722\) 0 0
\(723\) 3.08476 1.00230i 0.114724 0.0372759i
\(724\) 0 0
\(725\) −18.0823 + 24.8882i −0.671561 + 0.924324i
\(726\) 0 0
\(727\) −10.8239 3.51688i −0.401435 0.130434i 0.101339 0.994852i \(-0.467687\pi\)
−0.502774 + 0.864418i \(0.667687\pi\)
\(728\) 0 0
\(729\) −7.67761 −0.284356
\(730\) 0 0
\(731\) 1.46506 + 2.01648i 0.0541871 + 0.0745821i
\(732\) 0 0
\(733\) 5.09849 + 15.6915i 0.188317 + 0.579580i 0.999990 0.00453239i \(-0.00144271\pi\)
−0.811673 + 0.584112i \(0.801443\pi\)
\(734\) 0 0
\(735\) 0.379115i 0.0139839i
\(736\) 0 0
\(737\) 6.69352 0.246559
\(738\) 0 0
\(739\) −10.8437 −0.398892 −0.199446 0.979909i \(-0.563914\pi\)
−0.199446 + 0.979909i \(0.563914\pi\)
\(740\) 0 0
\(741\) 7.87369i 0.289247i
\(742\) 0 0
\(743\) 0.875666 + 2.69502i 0.0321251 + 0.0988708i 0.965833 0.259164i \(-0.0834470\pi\)
−0.933708 + 0.358035i \(0.883447\pi\)
\(744\) 0 0
\(745\) 1.92216 + 2.64562i 0.0704223 + 0.0969280i
\(746\) 0 0
\(747\) 10.8475 0.396888
\(748\) 0 0
\(749\) −2.85652 0.928141i −0.104375 0.0339135i
\(750\) 0 0
\(751\) −0.578661 + 0.796458i −0.0211156 + 0.0290632i −0.819444 0.573159i \(-0.805718\pi\)
0.798329 + 0.602222i \(0.205718\pi\)
\(752\) 0 0
\(753\) −16.6389 + 5.40632i −0.606356 + 0.197017i
\(754\) 0 0
\(755\) 4.93098 + 1.60217i 0.179457 + 0.0583090i
\(756\) 0 0
\(757\) 9.66954 + 13.3090i 0.351445 + 0.483723i 0.947740 0.319042i \(-0.103361\pi\)
−0.596295 + 0.802765i \(0.703361\pi\)
\(758\) 0 0
\(759\) 12.3350 8.96189i 0.447732 0.325296i
\(760\) 0 0
\(761\) 10.0609 + 7.30964i 0.364706 + 0.264974i 0.755012 0.655711i \(-0.227631\pi\)
−0.390306 + 0.920685i \(0.627631\pi\)
\(762\) 0 0
\(763\) 1.64950 1.19843i 0.0597158 0.0433861i
\(764\) 0 0
\(765\) 0.210640i 0.00761569i
\(766\) 0 0
\(767\) −4.06221 + 1.31989i −0.146678 + 0.0476585i
\(768\) 0 0
\(769\) 7.63007 23.4829i 0.275147 0.846816i −0.714033 0.700112i \(-0.753133\pi\)
0.989180 0.146704i \(-0.0468666\pi\)
\(770\) 0 0
\(771\) −5.57996 + 17.1733i −0.200957 + 0.618483i
\(772\) 0 0
\(773\) −31.3381 + 43.1332i −1.12715 + 1.55139i −0.333786 + 0.942649i \(0.608326\pi\)
−0.793367 + 0.608744i \(0.791674\pi\)
\(774\) 0 0
\(775\) −7.38077 22.7157i −0.265125 0.815971i
\(776\) 0 0
\(777\) 3.58769 + 2.60661i 0.128708 + 0.0935116i
\(778\) 0 0
\(779\) 17.0928 4.78795i 0.612412 0.171546i
\(780\) 0 0
\(781\) 16.6872 + 12.1240i 0.597116 + 0.433830i
\(782\) 0 0
\(783\) 9.23493 + 28.4222i 0.330029 + 1.01573i
\(784\) 0 0
\(785\) −0.255680 + 0.351913i −0.00912561 + 0.0125603i
\(786\) 0 0
\(787\) −0.435269 + 1.33962i −0.0155157 + 0.0477523i −0.958515 0.285043i \(-0.907992\pi\)
0.942999 + 0.332796i \(0.107992\pi\)
\(788\) 0 0
\(789\) −6.62313 + 20.3839i −0.235790 + 0.725686i
\(790\) 0 0
\(791\) −3.24251 + 1.05355i −0.115290 + 0.0374601i
\(792\) 0 0
\(793\) 7.80559i 0.277185i
\(794\) 0 0
\(795\) −0.413899 + 0.300715i −0.0146795 + 0.0106653i
\(796\) 0 0
\(797\) −25.8845 18.8062i −0.916878 0.666151i 0.0258673