Properties

Label 300.2.x.a.17.5
Level $300$
Weight $2$
Character 300.17
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.x (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 17.5
Character \(\chi\) \(=\) 300.17
Dual form 300.2.x.a.53.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.351313 - 1.69605i) q^{3} +(2.22846 - 0.184289i) q^{5} +(-2.84010 - 2.84010i) q^{7} +(-2.75316 + 1.19169i) q^{9} +O(q^{10})\) \(q+(-0.351313 - 1.69605i) q^{3} +(2.22846 - 0.184289i) q^{5} +(-2.84010 - 2.84010i) q^{7} +(-2.75316 + 1.19169i) q^{9} +(4.71560 - 1.53219i) q^{11} +(-0.188444 - 0.369843i) q^{13} +(-1.09545 - 3.71483i) q^{15} +(-7.50930 + 1.18936i) q^{17} +(2.68725 - 3.69868i) q^{19} +(-3.81918 + 5.81471i) q^{21} +(0.153636 - 0.301528i) q^{23} +(4.93208 - 0.821362i) q^{25} +(2.98838 + 4.25083i) q^{27} +(0.836442 - 0.607711i) q^{29} +(-2.24457 - 1.63078i) q^{31} +(-4.25532 - 7.45960i) q^{33} +(-6.85245 - 5.80565i) q^{35} +(4.31832 - 2.20029i) q^{37} +(-0.561068 + 0.449541i) q^{39} +(5.67438 + 1.84372i) q^{41} +(2.46472 - 2.46472i) q^{43} +(-5.91569 + 3.16301i) q^{45} +(-1.21046 + 7.64252i) q^{47} +9.13235i q^{49} +(4.65532 + 12.3183i) q^{51} +(8.21858 + 1.30170i) q^{53} +(10.2262 - 4.28346i) q^{55} +(-7.21721 - 3.25831i) q^{57} +(-3.09959 + 9.53955i) q^{59} +(3.00345 + 9.24368i) q^{61} +(11.2038 + 4.43473i) q^{63} +(-0.488099 - 0.789452i) q^{65} +(1.15518 + 7.29349i) q^{67} +(-0.565381 - 0.154644i) q^{69} +(-1.25910 - 1.73301i) q^{71} +(12.7520 + 6.49745i) q^{73} +(-3.12577 - 8.07648i) q^{75} +(-17.7443 - 9.04119i) q^{77} +(-4.46331 - 6.14322i) q^{79} +(6.15976 - 6.56181i) q^{81} +(-1.02557 - 6.47518i) q^{83} +(-16.5150 + 4.03432i) q^{85} +(-1.32456 - 1.20515i) q^{87} +(4.13129 + 12.7148i) q^{89} +(-0.515190 + 1.58559i) q^{91} +(-1.97733 + 4.37982i) q^{93} +(5.30680 - 8.73760i) q^{95} +(2.19961 + 0.348384i) q^{97} +(-11.1569 + 9.83788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\)

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
\(3\) −0.351313 1.69605i −0.202831 0.979214i
\(4\) 0 0
\(5\) 2.22846 0.184289i 0.996598 0.0824166i
\(6\) 0 0
\(7\) −2.84010 2.84010i −1.07346 1.07346i −0.997079 0.0763784i \(-0.975664\pi\)
−0.0763784 0.997079i \(-0.524336\pi\)
\(8\) 0 0
\(9\) −2.75316 + 1.19169i −0.917719 + 0.397230i
\(10\) 0 0
\(11\) 4.71560 1.53219i 1.42181 0.461973i 0.505630 0.862750i \(-0.331260\pi\)
0.916175 + 0.400778i \(0.131260\pi\)
\(12\) 0 0
\(13\) −0.188444 0.369843i −0.0522651 0.102576i 0.863397 0.504526i \(-0.168333\pi\)
−0.915662 + 0.401950i \(0.868333\pi\)
\(14\) 0 0
\(15\) −1.09545 3.71483i −0.282844 0.959166i
\(16\) 0 0
\(17\) −7.50930 + 1.18936i −1.82127 + 0.288461i −0.971211 0.238222i \(-0.923436\pi\)
−0.850062 + 0.526683i \(0.823436\pi\)
\(18\) 0 0
\(19\) 2.68725 3.69868i 0.616497 0.848536i −0.380595 0.924742i \(-0.624281\pi\)
0.997092 + 0.0762063i \(0.0242808\pi\)
\(20\) 0 0
\(21\) −3.81918 + 5.81471i −0.833414 + 1.26887i
\(22\) 0 0
\(23\) 0.153636 0.301528i 0.0320354 0.0628730i −0.874434 0.485144i \(-0.838767\pi\)
0.906469 + 0.422271i \(0.138767\pi\)
\(24\) 0 0
\(25\) 4.93208 0.821362i 0.986415 0.164272i
\(26\) 0 0
\(27\) 2.98838 + 4.25083i 0.575114 + 0.818073i
\(28\) 0 0
\(29\) 0.836442 0.607711i 0.155323 0.112849i −0.507409 0.861705i \(-0.669397\pi\)
0.662732 + 0.748856i \(0.269397\pi\)
\(30\) 0 0
\(31\) −2.24457 1.63078i −0.403138 0.292897i 0.367680 0.929952i \(-0.380152\pi\)
−0.770818 + 0.637056i \(0.780152\pi\)
\(32\) 0 0
\(33\) −4.25532 7.45960i −0.740756 1.29855i
\(34\) 0 0
\(35\) −6.85245 5.80565i −1.15828 0.981335i
\(36\) 0 0
\(37\) 4.31832 2.20029i 0.709928 0.361726i −0.0614445 0.998111i \(-0.519571\pi\)
0.771372 + 0.636384i \(0.219571\pi\)
\(38\) 0 0
\(39\) −0.561068 + 0.449541i −0.0898428 + 0.0719842i
\(40\) 0 0
\(41\) 5.67438 + 1.84372i 0.886189 + 0.287940i 0.716525 0.697562i \(-0.245732\pi\)
0.169664 + 0.985502i \(0.445732\pi\)
\(42\) 0 0
\(43\) 2.46472 2.46472i 0.375866 0.375866i −0.493742 0.869608i \(-0.664371\pi\)
0.869608 + 0.493742i \(0.164371\pi\)
\(44\) 0 0
\(45\) −5.91569 + 3.16301i −0.881859 + 0.471513i
\(46\) 0 0
\(47\) −1.21046 + 7.64252i −0.176563 + 1.11478i 0.727100 + 0.686532i \(0.240868\pi\)
−0.903663 + 0.428245i \(0.859132\pi\)
\(48\) 0 0
\(49\) 9.13235i 1.30462i
\(50\) 0 0
\(51\) 4.65532 + 12.3183i 0.651875 + 1.72491i
\(52\) 0 0
\(53\) 8.21858 + 1.30170i 1.12891 + 0.178802i 0.692826 0.721105i \(-0.256365\pi\)
0.436083 + 0.899906i \(0.356365\pi\)
\(54\) 0 0
\(55\) 10.2262 4.28346i 1.37889 0.577581i
\(56\) 0 0
\(57\) −7.21721 3.25831i −0.955942 0.431573i
\(58\) 0 0
\(59\) −3.09959 + 9.53955i −0.403532 + 1.24194i 0.518583 + 0.855028i \(0.326460\pi\)
−0.922115 + 0.386917i \(0.873540\pi\)
\(60\) 0 0
\(61\) 3.00345 + 9.24368i 0.384553 + 1.18353i 0.936804 + 0.349855i \(0.113769\pi\)
−0.552251 + 0.833678i \(0.686231\pi\)
\(62\) 0 0
\(63\) 11.2038 + 4.43473i 1.41154 + 0.558724i
\(64\) 0 0
\(65\) −0.488099 0.789452i −0.0605412 0.0979195i
\(66\) 0 0
\(67\) 1.15518 + 7.29349i 0.141127 + 0.891041i 0.952062 + 0.305905i \(0.0989590\pi\)
−0.810935 + 0.585136i \(0.801041\pi\)
\(68\) 0 0
\(69\) −0.565381 0.154644i −0.0680639 0.0186169i
\(70\) 0 0
\(71\) −1.25910 1.73301i −0.149428 0.205670i 0.727741 0.685852i \(-0.240570\pi\)
−0.877169 + 0.480182i \(0.840570\pi\)
\(72\) 0 0
\(73\) 12.7520 + 6.49745i 1.49250 + 0.760469i 0.994303 0.106592i \(-0.0339940\pi\)
0.498201 + 0.867061i \(0.333994\pi\)
\(74\) 0 0
\(75\) −3.12577 8.07648i −0.360933 0.932592i
\(76\) 0 0
\(77\) −17.7443 9.04119i −2.02216 1.03034i
\(78\) 0 0
\(79\) −4.46331 6.14322i −0.502162 0.691166i 0.480411 0.877043i \(-0.340487\pi\)
−0.982573 + 0.185877i \(0.940487\pi\)
\(80\) 0 0
\(81\) 6.15976 6.56181i 0.684417 0.729090i
\(82\) 0 0
\(83\) −1.02557 6.47518i −0.112571 0.710743i −0.977827 0.209414i \(-0.932844\pi\)
0.865256 0.501329i \(-0.167156\pi\)
\(84\) 0 0
\(85\) −16.5150 + 4.03432i −1.79130 + 0.437583i
\(86\) 0 0
\(87\) −1.32456 1.20515i −0.142008 0.129206i
\(88\) 0 0
\(89\) 4.13129 + 12.7148i 0.437916 + 1.34777i 0.890069 + 0.455826i \(0.150656\pi\)
−0.452153 + 0.891941i \(0.649344\pi\)
\(90\) 0 0
\(91\) −0.515190 + 1.58559i −0.0540066 + 0.166215i
\(92\) 0 0
\(93\) −1.97733 + 4.37982i −0.205040 + 0.454166i
\(94\) 0 0
\(95\) 5.30680 8.73760i 0.544466 0.896458i
\(96\) 0 0
\(97\) 2.19961 + 0.348384i 0.223337 + 0.0353730i 0.267100 0.963669i \(-0.413935\pi\)
−0.0437632 + 0.999042i \(0.513935\pi\)
\(98\) 0 0
\(99\) −11.1569 + 9.83788i −1.12131 + 0.988744i
\(100\) 0 0
\(101\) 12.5854i 1.25230i −0.779704 0.626149i \(-0.784630\pi\)
0.779704 0.626149i \(-0.215370\pi\)
\(102\) 0 0
\(103\) 0.211229 1.33365i 0.0208130 0.131408i −0.975094 0.221792i \(-0.928809\pi\)
0.995907 + 0.0903839i \(0.0288094\pi\)
\(104\) 0 0
\(105\) −7.43931 + 13.6617i −0.726002 + 1.33324i
\(106\) 0 0
\(107\) 2.51075 2.51075i 0.242723 0.242723i −0.575253 0.817976i \(-0.695096\pi\)
0.817976 + 0.575253i \(0.195096\pi\)
\(108\) 0 0
\(109\) −10.8158 3.51428i −1.03597 0.336607i −0.258822 0.965925i \(-0.583334\pi\)
−0.777148 + 0.629318i \(0.783334\pi\)
\(110\) 0 0
\(111\) −5.24889 6.55109i −0.498203 0.621802i
\(112\) 0 0
\(113\) −6.91215 + 3.52192i −0.650240 + 0.331314i −0.747808 0.663915i \(-0.768894\pi\)
0.0975678 + 0.995229i \(0.468894\pi\)
\(114\) 0 0
\(115\) 0.286804 0.700258i 0.0267446 0.0652994i
\(116\) 0 0
\(117\) 0.959555 + 0.793669i 0.0887108 + 0.0733747i
\(118\) 0 0
\(119\) 24.7051 + 17.9493i 2.26471 + 1.64541i
\(120\) 0 0
\(121\) 10.9900 7.98474i 0.999095 0.725885i
\(122\) 0 0
\(123\) 1.13355 10.2717i 0.102209 0.926172i
\(124\) 0 0
\(125\) 10.8396 2.73930i 0.969520 0.245011i
\(126\) 0 0
\(127\) 8.79185 17.2550i 0.780151 1.53113i −0.0657772 0.997834i \(-0.520953\pi\)
0.845928 0.533297i \(-0.179047\pi\)
\(128\) 0 0
\(129\) −5.04618 3.31440i −0.444291 0.291816i
\(130\) 0 0
\(131\) −1.96392 + 2.70310i −0.171588 + 0.236171i −0.886147 0.463405i \(-0.846628\pi\)
0.714558 + 0.699576i \(0.246628\pi\)
\(132\) 0 0
\(133\) −18.1367 + 2.87257i −1.57265 + 0.249083i
\(134\) 0 0
\(135\) 7.44287 + 8.92209i 0.640581 + 0.767891i
\(136\) 0 0
\(137\) −1.08309 2.12568i −0.0925343 0.181609i 0.840100 0.542431i \(-0.182496\pi\)
−0.932635 + 0.360822i \(0.882496\pi\)
\(138\) 0 0
\(139\) −1.62858 + 0.529159i −0.138135 + 0.0448827i −0.377268 0.926104i \(-0.623137\pi\)
0.239134 + 0.970987i \(0.423137\pi\)
\(140\) 0 0
\(141\) 13.3873 0.631928i 1.12742 0.0532179i
\(142\) 0 0
\(143\) −1.45530 1.45530i −0.121698 0.121698i
\(144\) 0 0
\(145\) 1.75198 1.50841i 0.145494 0.125266i
\(146\) 0 0
\(147\) 15.4889 3.20832i 1.27750 0.264617i
\(148\) 0 0
\(149\) −7.67808 −0.629012 −0.314506 0.949255i \(-0.601839\pi\)
−0.314506 + 0.949255i \(0.601839\pi\)
\(150\) 0 0
\(151\) −18.9987 −1.54609 −0.773045 0.634352i \(-0.781267\pi\)
−0.773045 + 0.634352i \(0.781267\pi\)
\(152\) 0 0
\(153\) 19.2569 12.2232i 1.55683 0.988190i
\(154\) 0 0
\(155\) −5.30248 3.22048i −0.425906 0.258675i
\(156\) 0 0
\(157\) −3.65415 3.65415i −0.291633 0.291633i 0.546092 0.837725i \(-0.316115\pi\)
−0.837725 + 0.546092i \(0.816115\pi\)
\(158\) 0 0
\(159\) −0.679559 14.3964i −0.0538926 1.14171i
\(160\) 0 0
\(161\) −1.29271 + 0.420028i −0.101880 + 0.0331029i
\(162\) 0 0
\(163\) 1.70981 + 3.35569i 0.133923 + 0.262838i 0.948223 0.317606i \(-0.102879\pi\)
−0.814300 + 0.580444i \(0.802879\pi\)
\(164\) 0 0
\(165\) −10.8575 15.8392i −0.845258 1.23308i
\(166\) 0 0
\(167\) −3.33491 + 0.528199i −0.258063 + 0.0408732i −0.284126 0.958787i \(-0.591703\pi\)
0.0260621 + 0.999660i \(0.491703\pi\)
\(168\) 0 0
\(169\) 7.53994 10.3778i 0.579995 0.798295i
\(170\) 0 0
\(171\) −2.99074 + 13.3854i −0.228708 + 1.02361i
\(172\) 0 0
\(173\) −5.42968 + 10.6563i −0.412811 + 0.810187i 0.587189 + 0.809450i \(0.300235\pi\)
−1.00000 0.000736755i \(0.999765\pi\)
\(174\) 0 0
\(175\) −16.3403 11.6748i −1.23521 0.882535i
\(176\) 0 0
\(177\) 17.2685 + 1.90568i 1.29798 + 0.143240i
\(178\) 0 0
\(179\) −1.75204 + 1.27293i −0.130954 + 0.0951434i −0.651334 0.758791i \(-0.725790\pi\)
0.520380 + 0.853935i \(0.325790\pi\)
\(180\) 0 0
\(181\) −0.486921 0.353769i −0.0361925 0.0262954i 0.569542 0.821962i \(-0.307121\pi\)
−0.605734 + 0.795667i \(0.707121\pi\)
\(182\) 0 0
\(183\) 14.6226 8.34143i 1.08093 0.616616i
\(184\) 0 0
\(185\) 9.21772 5.69909i 0.677700 0.419005i
\(186\) 0 0
\(187\) −33.5885 + 17.1142i −2.45623 + 1.25151i
\(188\) 0 0
\(189\) 3.58549 20.5601i 0.260806 1.49553i
\(190\) 0 0
\(191\) −20.1158 6.53603i −1.45553 0.472931i −0.528829 0.848728i \(-0.677369\pi\)
−0.926702 + 0.375798i \(0.877369\pi\)
\(192\) 0 0
\(193\) 0.525247 0.525247i 0.0378081 0.0378081i −0.687950 0.725758i \(-0.741489\pi\)
0.725758 + 0.687950i \(0.241489\pi\)
\(194\) 0 0
\(195\) −1.16747 + 1.10518i −0.0836045 + 0.0791439i
\(196\) 0 0
\(197\) 0.380297 2.40110i 0.0270950 0.171071i −0.970430 0.241382i \(-0.922399\pi\)
0.997525 + 0.0703111i \(0.0223992\pi\)
\(198\) 0 0
\(199\) 26.6540i 1.88945i 0.327865 + 0.944725i \(0.393671\pi\)
−0.327865 + 0.944725i \(0.606329\pi\)
\(200\) 0 0
\(201\) 11.9643 4.52153i 0.843895 0.318924i
\(202\) 0 0
\(203\) −4.10154 0.649620i −0.287872 0.0455944i
\(204\) 0 0
\(205\) 12.9849 + 3.06293i 0.906905 + 0.213924i
\(206\) 0 0
\(207\) −0.0636573 + 1.01324i −0.00442449 + 0.0704252i
\(208\) 0 0
\(209\) 7.00490 21.5589i 0.484539 1.49126i
\(210\) 0 0
\(211\) −2.55687 7.86925i −0.176022 0.541741i 0.823656 0.567089i \(-0.191931\pi\)
−0.999679 + 0.0253480i \(0.991931\pi\)
\(212\) 0 0
\(213\) −2.49692 + 2.74433i −0.171086 + 0.188038i
\(214\) 0 0
\(215\) 5.03831 5.94676i 0.343610 0.405565i
\(216\) 0 0
\(217\) 1.74324 + 11.0064i 0.118339 + 0.747163i
\(218\) 0 0
\(219\) 6.54005 23.9106i 0.441936 1.61573i
\(220\) 0 0
\(221\) 1.85496 + 2.55313i 0.124778 + 0.171742i
\(222\) 0 0
\(223\) −11.3838 5.80036i −0.762319 0.388421i 0.0291937 0.999574i \(-0.490706\pi\)
−0.791513 + 0.611153i \(0.790706\pi\)
\(224\) 0 0
\(225\) −12.6000 + 8.13884i −0.839998 + 0.542589i
\(226\) 0 0
\(227\) 21.6298 + 11.0209i 1.43562 + 0.731484i 0.986770 0.162124i \(-0.0518346\pi\)
0.448848 + 0.893608i \(0.351835\pi\)
\(228\) 0 0
\(229\) 4.36425 + 6.00687i 0.288398 + 0.396945i 0.928493 0.371350i \(-0.121105\pi\)
−0.640095 + 0.768296i \(0.721105\pi\)
\(230\) 0 0
\(231\) −9.10047 + 33.2715i −0.598767 + 2.18911i
\(232\) 0 0
\(233\) 2.77715 + 17.5342i 0.181937 + 1.14871i 0.894490 + 0.447087i \(0.147539\pi\)
−0.712553 + 0.701618i \(0.752461\pi\)
\(234\) 0 0
\(235\) −1.28902 + 17.2541i −0.0840865 + 1.12554i
\(236\) 0 0
\(237\) −8.85118 + 9.72819i −0.574946 + 0.631914i
\(238\) 0 0
\(239\) −0.224620 0.691308i −0.0145294 0.0447170i 0.943529 0.331290i \(-0.107484\pi\)
−0.958058 + 0.286573i \(0.907484\pi\)
\(240\) 0 0
\(241\) −4.44165 + 13.6700i −0.286112 + 0.880561i 0.699951 + 0.714190i \(0.253205\pi\)
−0.986063 + 0.166371i \(0.946795\pi\)
\(242\) 0 0
\(243\) −13.2932 8.14199i −0.852756 0.522309i
\(244\) 0 0
\(245\) 1.68299 + 20.3511i 0.107522 + 1.30018i
\(246\) 0 0
\(247\) −1.87433 0.296864i −0.119261 0.0188890i
\(248\) 0 0
\(249\) −10.6219 + 4.01423i −0.673137 + 0.254391i
\(250\) 0 0
\(251\) 10.6776i 0.673961i −0.941512 0.336981i \(-0.890594\pi\)
0.941512 0.336981i \(-0.109406\pi\)
\(252\) 0 0
\(253\) 0.262488 1.65729i 0.0165025 0.104193i
\(254\) 0 0
\(255\) 12.6443 + 26.5929i 0.791819 + 1.66531i
\(256\) 0 0
\(257\) −9.29989 + 9.29989i −0.580111 + 0.580111i −0.934934 0.354822i \(-0.884541\pi\)
0.354822 + 0.934934i \(0.384541\pi\)
\(258\) 0 0
\(259\) −18.5135 6.01541i −1.15037 0.373779i
\(260\) 0 0
\(261\) −1.57866 + 2.66990i −0.0977163 + 0.165263i
\(262\) 0 0
\(263\) −23.1320 + 11.7863i −1.42638 + 0.726776i −0.985322 0.170704i \(-0.945396\pi\)
−0.441055 + 0.897480i \(0.645396\pi\)
\(264\) 0 0
\(265\) 18.5547 + 1.38618i 1.13980 + 0.0851525i
\(266\) 0 0
\(267\) 20.1135 11.4738i 1.23093 0.702182i
\(268\) 0 0
\(269\) −13.6649 9.92811i −0.833162 0.605328i 0.0872901 0.996183i \(-0.472179\pi\)
−0.920452 + 0.390855i \(0.872179\pi\)
\(270\) 0 0
\(271\) 12.7884 9.29128i 0.776837 0.564405i −0.127191 0.991878i \(-0.540596\pi\)
0.904028 + 0.427473i \(0.140596\pi\)
\(272\) 0 0
\(273\) 2.87023 + 0.316748i 0.173714 + 0.0191704i
\(274\) 0 0
\(275\) 21.9992 11.4301i 1.32660 0.689260i
\(276\) 0 0
\(277\) 7.77059 15.2506i 0.466890 0.916323i −0.530742 0.847534i \(-0.678087\pi\)
0.997631 0.0687889i \(-0.0219135\pi\)
\(278\) 0 0
\(279\) 8.12305 + 1.81496i 0.486314 + 0.108659i
\(280\) 0 0
\(281\) 16.0338 22.0687i 0.956499 1.31651i 0.00791912 0.999969i \(-0.497479\pi\)
0.948580 0.316539i \(-0.102521\pi\)
\(282\) 0 0
\(283\) −3.01460 + 0.477465i −0.179199 + 0.0283824i −0.245389 0.969425i \(-0.578916\pi\)
0.0661898 + 0.997807i \(0.478916\pi\)
\(284\) 0 0
\(285\) −16.6837 5.93096i −0.988259 0.351320i
\(286\) 0 0
\(287\) −10.8795 21.3522i −0.642195 1.26038i
\(288\) 0 0
\(289\) 38.8070 12.6092i 2.28277 0.741716i
\(290\) 0 0
\(291\) −0.181876 3.85304i −0.0106618 0.225869i
\(292\) 0 0
\(293\) 10.5577 + 10.5577i 0.616788 + 0.616788i 0.944706 0.327918i \(-0.106347\pi\)
−0.327918 + 0.944706i \(0.606347\pi\)
\(294\) 0 0
\(295\) −5.14928 + 21.8297i −0.299802 + 1.27098i
\(296\) 0 0
\(297\) 20.6051 + 15.4664i 1.19563 + 0.897454i
\(298\) 0 0
\(299\) −0.140470 −0.00812359
\(300\) 0 0
\(301\) −14.0001 −0.806953
\(302\) 0 0
\(303\) −21.3455 + 4.42143i −1.22627 + 0.254005i
\(304\) 0 0
\(305\) 8.39659 + 20.0457i 0.480787 + 1.14781i
\(306\) 0 0
\(307\) 17.3293 + 17.3293i 0.989033 + 0.989033i 0.999941 0.0109073i \(-0.00347197\pi\)
−0.0109073 + 0.999941i \(0.503472\pi\)
\(308\) 0 0
\(309\) −2.33614 + 0.110273i −0.132898 + 0.00627324i
\(310\) 0 0
\(311\) −4.35394 + 1.41468i −0.246889 + 0.0802191i −0.429847 0.902902i \(-0.641433\pi\)
0.182958 + 0.983121i \(0.441433\pi\)
\(312\) 0 0
\(313\) −4.00451 7.85929i −0.226348 0.444233i 0.749703 0.661774i \(-0.230196\pi\)
−0.976051 + 0.217541i \(0.930196\pi\)
\(314\) 0 0
\(315\) 25.7844 + 7.81789i 1.45279 + 0.440488i
\(316\) 0 0
\(317\) −17.3151 + 2.74245i −0.972515 + 0.154031i −0.622420 0.782683i \(-0.713851\pi\)
−0.350095 + 0.936714i \(0.613851\pi\)
\(318\) 0 0
\(319\) 3.01319 4.14731i 0.168707 0.232205i
\(320\) 0 0
\(321\) −5.14041 3.37629i −0.286910 0.188446i
\(322\) 0 0
\(323\) −15.7803 + 30.9706i −0.878040 + 1.72325i
\(324\) 0 0
\(325\) −1.23320 1.66931i −0.0684054 0.0925967i
\(326\) 0 0
\(327\) −2.16064 + 19.5788i −0.119484 + 1.08271i
\(328\) 0 0
\(329\) 25.1434 18.2677i 1.38620 1.00713i
\(330\) 0 0
\(331\) 12.7358 + 9.25307i 0.700020 + 0.508595i 0.879939 0.475087i \(-0.157583\pi\)
−0.179918 + 0.983682i \(0.557583\pi\)
\(332\) 0 0
\(333\) −9.26696 + 11.2039i −0.507826 + 0.613967i
\(334\) 0 0
\(335\) 3.91837 + 16.0404i 0.214084 + 0.876379i
\(336\) 0 0
\(337\) 3.48017 1.77323i 0.189577 0.0965942i −0.356626 0.934247i \(-0.616073\pi\)
0.546203 + 0.837653i \(0.316073\pi\)
\(338\) 0 0
\(339\) 8.40167 + 10.4860i 0.456316 + 0.569524i
\(340\) 0 0
\(341\) −13.0832 4.25098i −0.708493 0.230203i
\(342\) 0 0
\(343\) 6.05609 6.05609i 0.326998 0.326998i
\(344\) 0 0
\(345\) −1.28843 0.240424i −0.0693667 0.0129440i
\(346\) 0 0
\(347\) 0.587119 3.70692i 0.0315182 0.198998i −0.966905 0.255138i \(-0.917879\pi\)
0.998423 + 0.0561397i \(0.0178792\pi\)
\(348\) 0 0
\(349\) 12.9374i 0.692525i 0.938138 + 0.346262i \(0.112549\pi\)
−0.938138 + 0.346262i \(0.887451\pi\)
\(350\) 0 0
\(351\) 1.00900 1.90628i 0.0538562 0.101750i
\(352\) 0 0
\(353\) −26.1583 4.14307i −1.39227 0.220513i −0.585159 0.810919i \(-0.698968\pi\)
−0.807107 + 0.590405i \(0.798968\pi\)
\(354\) 0 0
\(355\) −3.12523 3.62990i −0.165870 0.192655i
\(356\) 0 0
\(357\) 21.7636 48.2068i 1.15185 2.55137i
\(358\) 0 0
\(359\) −1.48360 + 4.56607i −0.0783016 + 0.240988i −0.982543 0.186033i \(-0.940437\pi\)
0.904242 + 0.427021i \(0.140437\pi\)
\(360\) 0 0
\(361\) −0.587610 1.80848i −0.0309269 0.0951831i
\(362\) 0 0
\(363\) −17.4034 15.8345i −0.913444 0.831096i
\(364\) 0 0
\(365\) 29.6147 + 12.1293i 1.55010 + 0.634875i
\(366\) 0 0
\(367\) 4.19594 + 26.4921i 0.219026 + 1.38288i 0.814808 + 0.579731i \(0.196842\pi\)
−0.595782 + 0.803146i \(0.703158\pi\)
\(368\) 0 0
\(369\) −17.8196 + 1.68605i −0.927651 + 0.0877721i
\(370\) 0 0
\(371\) −19.6447 27.0386i −1.01990 1.40377i
\(372\) 0 0
\(373\) 2.97876 + 1.51776i 0.154234 + 0.0785864i 0.529404 0.848370i \(-0.322416\pi\)
−0.375170 + 0.926956i \(0.622416\pi\)
\(374\) 0 0
\(375\) −8.45407 17.4221i −0.436566 0.899672i
\(376\) 0 0
\(377\) −0.382380 0.194832i −0.0196936 0.0100344i
\(378\) 0 0
\(379\) −1.47681 2.03266i −0.0758588 0.104411i 0.769401 0.638766i \(-0.220555\pi\)
−0.845260 + 0.534355i \(0.820555\pi\)
\(380\) 0 0
\(381\) −32.3540 8.84950i −1.65754 0.453373i
\(382\) 0 0
\(383\) 1.45004 + 9.15521i 0.0740938 + 0.467810i 0.996639 + 0.0819203i \(0.0261053\pi\)
−0.922545 + 0.385889i \(0.873895\pi\)
\(384\) 0 0
\(385\) −41.2088 16.8779i −2.10019 0.860175i
\(386\) 0 0
\(387\) −3.84859 + 9.72295i −0.195635 + 0.494245i
\(388\) 0 0
\(389\) −3.53033 10.8652i −0.178995 0.550890i 0.820798 0.571218i \(-0.193529\pi\)
−0.999793 + 0.0203282i \(0.993529\pi\)
\(390\) 0 0
\(391\) −0.795077 + 2.44700i −0.0402088 + 0.123750i
\(392\) 0 0
\(393\) 5.27454 + 2.38127i 0.266066 + 0.120119i
\(394\) 0 0
\(395\) −11.0784 12.8674i −0.557417 0.647429i
\(396\) 0 0
\(397\) −9.67691 1.53267i −0.485670 0.0769226i −0.0912023 0.995832i \(-0.529071\pi\)
−0.394468 + 0.918910i \(0.629071\pi\)
\(398\) 0 0
\(399\) 11.2437 + 29.7515i 0.562888 + 1.48944i
\(400\) 0 0
\(401\) 27.1537i 1.35599i 0.735066 + 0.677996i \(0.237151\pi\)
−0.735066 + 0.677996i \(0.762849\pi\)
\(402\) 0 0
\(403\) −0.180155 + 1.13745i −0.00897414 + 0.0566605i
\(404\) 0 0
\(405\) 12.5175 15.7579i 0.622000 0.783017i
\(406\) 0 0
\(407\) 16.9922 16.9922i 0.842271 0.842271i
\(408\) 0 0
\(409\) −30.0764 9.77241i −1.48718 0.483215i −0.550932 0.834550i \(-0.685728\pi\)
−0.936250 + 0.351335i \(0.885728\pi\)
\(410\) 0 0
\(411\) −3.22475 + 2.58374i −0.159065 + 0.127447i
\(412\) 0 0
\(413\) 35.8964 18.2902i 1.76635 0.900000i
\(414\) 0 0
\(415\) −3.47874 14.2407i −0.170765 0.699047i
\(416\) 0 0
\(417\) 1.46962 + 2.57626i 0.0719677 + 0.126160i
\(418\) 0 0
\(419\) −13.3040 9.66590i −0.649941 0.472210i 0.213310 0.976985i \(-0.431576\pi\)
−0.863251 + 0.504775i \(0.831576\pi\)
\(420\) 0 0
\(421\) 11.1129 8.07400i 0.541610 0.393503i −0.283073 0.959098i \(-0.591354\pi\)
0.824683 + 0.565596i \(0.191354\pi\)
\(422\) 0 0
\(423\) −5.77493 22.4836i −0.280787 1.09319i
\(424\) 0 0
\(425\) −36.0595 + 12.0338i −1.74914 + 0.583727i
\(426\) 0 0
\(427\) 17.7229 34.7831i 0.857670 1.68327i
\(428\) 0 0
\(429\) −1.95699 + 2.97952i −0.0944843 + 0.143852i
\(430\) 0 0
\(431\) 2.67787 3.68577i 0.128989 0.177537i −0.739638 0.673005i \(-0.765003\pi\)
0.868626 + 0.495468i \(0.165003\pi\)
\(432\) 0 0
\(433\) 21.2003 3.35781i 1.01882 0.161366i 0.375389 0.926867i \(-0.377509\pi\)
0.643434 + 0.765501i \(0.277509\pi\)
\(434\) 0 0
\(435\) −3.17383 2.44153i −0.152173 0.117062i
\(436\) 0 0
\(437\) −0.702398 1.37853i −0.0336003 0.0659442i
\(438\) 0 0
\(439\) 10.5185 3.41768i 0.502022 0.163117i −0.0470490 0.998893i \(-0.514982\pi\)
0.549071 + 0.835776i \(0.314982\pi\)
\(440\) 0 0
\(441\) −10.8829 25.1428i −0.518234 1.19728i
\(442\) 0 0
\(443\) 11.3624 + 11.3624i 0.539846 + 0.539846i 0.923484 0.383638i \(-0.125329\pi\)
−0.383638 + 0.923484i \(0.625329\pi\)
\(444\) 0 0
\(445\) 11.5496 + 27.5731i 0.547505 + 1.30709i
\(446\) 0 0
\(447\) 2.69741 + 13.0224i 0.127583 + 0.615938i
\(448\) 0 0
\(449\) 16.5317 0.780178 0.390089 0.920777i \(-0.372444\pi\)
0.390089 + 0.920777i \(0.372444\pi\)
\(450\) 0 0
\(451\) 29.5830 1.39301
\(452\) 0 0
\(453\) 6.67448 + 32.2226i 0.313595 + 1.51395i
\(454\) 0 0
\(455\) −0.855873 + 3.62837i −0.0401240 + 0.170101i
\(456\) 0 0
\(457\) −16.5635 16.5635i −0.774807 0.774807i 0.204136 0.978943i \(-0.434562\pi\)
−0.978943 + 0.204136i \(0.934562\pi\)
\(458\) 0 0
\(459\) −27.4964 28.3665i −1.28342 1.32404i
\(460\) 0 0
\(461\) −14.5158 + 4.71648i −0.676070 + 0.219669i −0.626874 0.779121i \(-0.715666\pi\)
−0.0491963 + 0.998789i \(0.515666\pi\)
\(462\) 0 0
\(463\) −1.93184 3.79146i −0.0897804 0.176204i 0.841750 0.539868i \(-0.181526\pi\)
−0.931530 + 0.363664i \(0.881526\pi\)
\(464\) 0 0
\(465\) −3.59925 + 10.1247i −0.166911 + 0.469520i
\(466\) 0 0
\(467\) 30.6114 4.84837i 1.41653 0.224356i 0.599233 0.800575i \(-0.295472\pi\)
0.817295 + 0.576219i \(0.195472\pi\)
\(468\) 0 0
\(469\) 17.4334 23.9951i 0.805001 1.10799i
\(470\) 0 0
\(471\) −4.91387 + 7.48137i −0.226419 + 0.344723i
\(472\) 0 0
\(473\) 7.84621 15.3990i 0.360769 0.708049i
\(474\) 0 0
\(475\) 10.2158 20.4494i 0.468731 0.938282i
\(476\) 0 0
\(477\) −24.1783 + 6.21022i −1.10705 + 0.284346i
\(478\) 0 0
\(479\) −23.7090 + 17.2256i −1.08329 + 0.787059i −0.978254 0.207409i \(-0.933497\pi\)
−0.105039 + 0.994468i \(0.533497\pi\)
\(480\) 0 0
\(481\) −1.62753 1.18247i −0.0742088 0.0539159i
\(482\) 0 0
\(483\) 1.16654 + 2.04494i 0.0530792 + 0.0930482i
\(484\) 0 0
\(485\) 4.96595 + 0.370996i 0.225492 + 0.0168460i
\(486\) 0 0
\(487\) 18.5821 9.46803i 0.842033 0.429037i 0.0209053 0.999781i \(-0.493345\pi\)
0.821128 + 0.570744i \(0.193345\pi\)
\(488\) 0 0
\(489\) 5.09073 4.07882i 0.230211 0.184451i
\(490\) 0 0
\(491\) 8.67143 + 2.81752i 0.391336 + 0.127153i 0.498074 0.867134i \(-0.334041\pi\)
−0.106738 + 0.994287i \(0.534041\pi\)
\(492\) 0 0
\(493\) −5.55831 + 5.55831i −0.250334 + 0.250334i
\(494\) 0 0
\(495\) −23.0497 + 23.9794i −1.03601 + 1.07780i
\(496\) 0 0
\(497\) −1.34593 + 8.49789i −0.0603734 + 0.381183i
\(498\) 0 0
\(499\) 9.70109i 0.434280i −0.976140 0.217140i \(-0.930327\pi\)
0.976140 0.217140i \(-0.0696729\pi\)
\(500\) 0 0
\(501\) 2.06745 + 5.47061i 0.0923669 + 0.244409i
\(502\) 0 0
\(503\) 8.01914 + 1.27011i 0.357556 + 0.0566313i 0.332628 0.943058i \(-0.392065\pi\)
0.0249274 + 0.999689i \(0.492065\pi\)
\(504\) 0 0
\(505\) −2.31936 28.0461i −0.103210 1.24804i
\(506\) 0 0
\(507\) −20.2502 9.14222i −0.899342 0.406020i
\(508\) 0 0
\(509\) 11.1835 34.4193i 0.495700 1.52561i −0.320163 0.947362i \(-0.603738\pi\)
0.815863 0.578245i \(-0.196262\pi\)
\(510\) 0 0
\(511\) −17.7634 54.6703i −0.785809 2.41847i
\(512\) 0 0
\(513\) 23.7530 + 0.369972i 1.04872 + 0.0163347i
\(514\) 0 0
\(515\) 0.224939 3.01091i 0.00991198 0.132676i
\(516\) 0 0
\(517\) 6.00177 + 37.8937i 0.263958 + 1.66656i
\(518\) 0 0
\(519\) 19.9812 + 5.46528i 0.877077 + 0.239899i
\(520\) 0 0
\(521\) −9.60734 13.2234i −0.420905 0.579326i 0.544930 0.838481i \(-0.316556\pi\)
−0.965836 + 0.259155i \(0.916556\pi\)
\(522\) 0 0
\(523\) −9.11004 4.64180i −0.398354 0.202972i 0.243325 0.969945i \(-0.421762\pi\)
−0.641679 + 0.766973i \(0.721762\pi\)
\(524\) 0 0
\(525\) −14.0605 + 31.8155i −0.613651 + 1.38854i
\(526\) 0 0
\(527\) 18.7948 + 9.57641i 0.818713 + 0.417155i
\(528\) 0 0
\(529\) 13.4517 + 18.5147i 0.584859 + 0.804989i
\(530\) 0 0
\(531\) −2.83452 29.9576i −0.123008 1.30005i
\(532\) 0 0
\(533\) −0.387419 2.44607i −0.0167810 0.105951i
\(534\) 0 0
\(535\) 5.13240 6.05781i 0.221893 0.261902i
\(536\) 0 0
\(537\) 2.77447 + 2.52435i 0.119727 + 0.108934i
\(538\) 0 0
\(539\) 13.9925 + 43.0645i 0.602699 + 1.85492i
\(540\) 0 0
\(541\) 5.41906 16.6781i 0.232983 0.717049i −0.764399 0.644743i \(-0.776964\pi\)
0.997383 0.0723059i \(-0.0230358\pi\)
\(542\) 0 0
\(543\) −0.428947 + 0.950125i −0.0184079 + 0.0407738i
\(544\) 0 0
\(545\) −24.7503 5.83819i −1.06019 0.250081i
\(546\) 0 0
\(547\) 16.0041 + 2.53481i 0.684288 + 0.108381i 0.488893 0.872344i \(-0.337401\pi\)
0.195395 + 0.980725i \(0.437401\pi\)
\(548\) 0 0
\(549\) −19.2846 21.8701i −0.823046 0.933395i
\(550\) 0 0
\(551\) 4.72680i 0.201369i
\(552\) 0 0
\(553\) −4.77111 + 30.1236i −0.202888 + 1.28099i
\(554\) 0 0
\(555\) −12.9042 13.6315i −0.547754 0.578626i
\(556\) 0 0
\(557\) −0.351406 + 0.351406i −0.0148895 + 0.0148895i −0.714512 0.699623i \(-0.753351\pi\)
0.699623 + 0.714512i \(0.253351\pi\)
\(558\) 0 0
\(559\) −1.37602 0.447097i −0.0581995 0.0189102i
\(560\) 0 0
\(561\) 40.8266 + 50.9553i 1.72370 + 2.15133i
\(562\) 0 0
\(563\) −9.57089 + 4.87661i −0.403365 + 0.205525i −0.643890 0.765118i \(-0.722680\pi\)
0.240525 + 0.970643i \(0.422680\pi\)
\(564\) 0 0
\(565\) −14.7544 + 9.12229i −0.620722 + 0.383777i
\(566\) 0 0
\(567\) −36.1305 + 1.14188i −1.51734 + 0.0479546i
\(568\) 0 0
\(569\) 34.5553 + 25.1059i 1.44863 + 1.05249i 0.986148 + 0.165865i \(0.0530417\pi\)
0.462484 + 0.886628i \(0.346958\pi\)
\(570\) 0 0
\(571\) −37.4429 + 27.2039i −1.56694 + 1.13845i −0.636920 + 0.770930i \(0.719792\pi\)
−0.930017 + 0.367517i \(0.880208\pi\)
\(572\) 0 0
\(573\) −4.01846 + 36.4136i −0.167874 + 1.52120i
\(574\) 0 0
\(575\) 0.510082 1.61335i 0.0212719 0.0672814i
\(576\) 0 0
\(577\) −3.73707 + 7.33441i −0.155576 + 0.305335i −0.955618 0.294609i \(-0.904811\pi\)
0.800042 + 0.599944i \(0.204811\pi\)
\(578\) 0 0
\(579\) −1.07537 0.706318i −0.0446909 0.0293536i
\(580\) 0 0
\(581\) −15.4774 + 21.3029i −0.642113 + 0.883792i
\(582\) 0 0
\(583\) 40.7500 6.45416i 1.68769 0.267304i
\(584\) 0 0
\(585\) 2.28459 + 1.59182i 0.0944563 + 0.0658138i
\(586\) 0 0
\(587\) −0.885671 1.73823i −0.0365556 0.0717444i 0.872006 0.489495i \(-0.162819\pi\)
−0.908562 + 0.417750i \(0.862819\pi\)
\(588\) 0 0
\(589\) −12.0635 + 3.91966i −0.497066 + 0.161507i
\(590\) 0 0
\(591\) −4.20599 + 0.198537i −0.173011 + 0.00816671i
\(592\) 0 0
\(593\) −26.3630 26.3630i −1.08260 1.08260i −0.996266 0.0863319i \(-0.972485\pi\)
−0.0863319 0.996266i \(-0.527515\pi\)
\(594\) 0 0
\(595\) 58.3621 + 35.4464i 2.39261 + 1.45316i
\(596\) 0 0
\(597\) 45.2064 9.36389i 1.85017 0.383239i
\(598\) 0 0
\(599\) −27.2293 −1.11256 −0.556280 0.830995i \(-0.687772\pi\)
−0.556280 + 0.830995i \(0.687772\pi\)
\(600\) 0 0
\(601\) −0.707518 −0.0288602 −0.0144301 0.999896i \(-0.504593\pi\)
−0.0144301 + 0.999896i \(0.504593\pi\)
\(602\) 0 0
\(603\) −11.8719 18.7035i −0.483463 0.761666i
\(604\) 0 0
\(605\) 23.0194 19.8190i 0.935871 0.805758i
\(606\) 0 0
\(607\) −15.7536 15.7536i −0.639418 0.639418i 0.310994 0.950412i \(-0.399338\pi\)
−0.950412 + 0.310994i \(0.899338\pi\)
\(608\) 0 0
\(609\) 0.339139 + 7.18463i 0.0137426 + 0.291136i
\(610\) 0 0
\(611\) 3.05464 0.992512i 0.123577 0.0401527i
\(612\) 0 0
\(613\) −7.04615 13.8288i −0.284591 0.558542i 0.703813 0.710385i \(-0.251479\pi\)
−0.988405 + 0.151843i \(0.951479\pi\)
\(614\) 0 0
\(615\) 0.633098 23.0991i 0.0255290 0.931445i
\(616\) 0 0
\(617\) −30.2739 + 4.79492i −1.21878 + 0.193036i −0.732501 0.680766i \(-0.761647\pi\)
−0.486282 + 0.873802i \(0.661647\pi\)
\(618\) 0 0
\(619\) −24.7268 + 34.0335i −0.993852 + 1.36792i −0.0648299 + 0.997896i \(0.520650\pi\)
−0.929022 + 0.370024i \(0.879350\pi\)
\(620\) 0 0
\(621\) 1.74087 0.248000i 0.0698588 0.00995188i
\(622\) 0 0
\(623\) 24.3781 47.8446i 0.976686 1.91685i
\(624\) 0 0
\(625\) 23.6507 8.10204i 0.946029 0.324082i
\(626\) 0 0
\(627\) −39.0258 4.30673i −1.55854 0.171994i
\(628\) 0 0
\(629\) −29.8106 + 21.6587i −1.18863 + 0.863589i
\(630\) 0 0
\(631\) 35.3783 + 25.7038i 1.40839 + 1.02325i 0.993554 + 0.113357i \(0.0361603\pi\)
0.414834 + 0.909897i \(0.363840\pi\)
\(632\) 0 0
\(633\) −12.4484 + 7.10115i −0.494778 + 0.282246i
\(634\) 0 0
\(635\) 16.4124 40.0723i 0.651306 1.59022i
\(636\) 0 0
\(637\) 3.37753 1.72094i 0.133823 0.0681861i
\(638\) 0 0
\(639\) 5.53171 + 3.27078i 0.218831 + 0.129390i
\(640\) 0 0
\(641\) 41.9572 + 13.6327i 1.65721 + 0.538460i 0.980284 0.197593i \(-0.0633125\pi\)
0.676924 + 0.736053i \(0.263313\pi\)
\(642\) 0 0
\(643\) −21.6567 + 21.6567i −0.854057 + 0.854057i −0.990630 0.136573i \(-0.956391\pi\)
0.136573 + 0.990630i \(0.456391\pi\)
\(644\) 0 0
\(645\) −11.8560 6.45605i −0.466830 0.254207i
\(646\) 0 0
\(647\) 4.83284 30.5133i 0.189998 1.19960i −0.689709 0.724087i \(-0.742261\pi\)
0.879707 0.475516i \(-0.157739\pi\)
\(648\) 0 0
\(649\) 49.7338i 1.95222i
\(650\) 0 0
\(651\) 18.0550 6.82332i 0.707629 0.267427i
\(652\) 0 0
\(653\) −29.5562 4.68124i −1.15662 0.183191i −0.451497 0.892272i \(-0.649110\pi\)
−0.705127 + 0.709081i \(0.749110\pi\)
\(654\) 0 0
\(655\) −3.87836 + 6.38569i −0.151540 + 0.249510i
\(656\) 0 0
\(657\) −42.8511 2.69214i −1.67178 0.105030i
\(658\) 0 0
\(659\) −3.30930 + 10.1850i −0.128912 + 0.396750i −0.994594 0.103845i \(-0.966885\pi\)
0.865682 + 0.500595i \(0.166885\pi\)
\(660\) 0 0
\(661\) 8.67556 + 26.7006i 0.337440 + 1.03853i 0.965507 + 0.260375i \(0.0838463\pi\)
−0.628067 + 0.778159i \(0.716154\pi\)
\(662\) 0 0
\(663\) 3.67856 4.04305i 0.142864 0.157019i
\(664\) 0 0
\(665\) −39.8875 + 9.74380i −1.54677 + 0.377848i
\(666\) 0 0
\(667\) −0.0547341 0.345578i −0.00211931 0.0133808i
\(668\) 0 0
\(669\) −5.83839 + 21.3453i −0.225725 + 0.825257i
\(670\) 0 0
\(671\) 28.3262 + 38.9876i 1.09352 + 1.50510i
\(672\) 0 0
\(673\) −22.9797 11.7087i −0.885803 0.451339i −0.0489715 0.998800i \(-0.515594\pi\)
−0.836831 + 0.547461i \(0.815594\pi\)
\(674\) 0 0
\(675\) 18.2304 + 18.5109i 0.701688 + 0.712484i
\(676\) 0 0
\(677\) 3.98966 + 2.03283i 0.153335 + 0.0781281i 0.528974 0.848638i \(-0.322577\pi\)
−0.375639 + 0.926766i \(0.622577\pi\)
\(678\) 0 0
\(679\) −5.25767 7.23656i −0.201771 0.277714i
\(680\) 0 0
\(681\) 11.0932 40.5569i 0.425092 1.55414i
\(682\) 0 0
\(683\) 4.57286 + 28.8719i 0.174976 + 1.10475i 0.906273 + 0.422693i \(0.138915\pi\)
−0.731297 + 0.682059i \(0.761085\pi\)
\(684\) 0 0
\(685\) −2.80535 4.53739i −0.107187 0.173365i
\(686\) 0 0
\(687\) 8.65473 9.51227i 0.330198 0.362916i
\(688\) 0 0
\(689\) −1.06732 3.28488i −0.0406618 0.125144i
\(690\) 0 0
\(691\) −7.71677 + 23.7498i −0.293560 + 0.903484i 0.690141 + 0.723674i \(0.257548\pi\)
−0.983701 + 0.179810i \(0.942452\pi\)
\(692\) 0 0
\(693\) 59.6273 + 3.74610i 2.26505 + 0.142303i
\(694\) 0 0
\(695\) −3.53172 + 1.47934i −0.133966 + 0.0561146i
\(696\) 0 0
\(697\) −44.8035 7.09617i −1.69705 0.268787i
\(698\) 0 0
\(699\) 28.7632 10.8702i 1.08793 0.411148i
\(700\) 0 0
\(701\) 6.88847i 0.260174i 0.991503 + 0.130087i \(0.0415257\pi\)
−0.991503 + 0.130087i \(0.958474\pi\)
\(702\) 0 0
\(703\) 3.46622 21.8848i 0.130731 0.825402i
\(704\) 0 0
\(705\) 29.7167 3.87537i 1.11920 0.145955i
\(706\) 0 0
\(707\) −35.7439 + 35.7439i −1.34429 + 1.34429i
\(708\) 0 0
\(709\) −3.31523 1.07719i −0.124506 0.0404545i 0.246101 0.969244i \(-0.420850\pi\)
−0.370607 + 0.928790i \(0.620850\pi\)
\(710\) 0 0
\(711\) 19.6090 + 11.5944i 0.735395 + 0.434823i
\(712\) 0 0
\(713\) −0.836575 + 0.426256i −0.0313300 + 0.0159634i
\(714\) 0 0
\(715\) −3.51127 2.97488i −0.131314 0.111254i
\(716\) 0 0
\(717\) −1.09358 + 0.623832i −0.0408405 + 0.0232974i
\(718\) 0 0
\(719\) −13.0340 9.46973i −0.486085 0.353161i 0.317592 0.948228i \(-0.397126\pi\)
−0.803677 + 0.595066i \(0.797126\pi\)
\(720\) 0 0
\(721\) −4.38760 + 3.18778i −0.163403 + 0.118719i
\(722\) 0 0
\(723\) 24.7454 + 2.73080i 0.920290 + 0.101560i
\(724\) 0 0
\(725\) 3.62624 3.68430i 0.134675 0.136831i
\(726\) 0 0
\(727\) 12.5508 24.6324i 0.465484 0.913564i −0.532270 0.846575i \(-0.678661\pi\)
0.997754 0.0669890i \(-0.0213392\pi\)
\(728\) 0 0
\(729\) −9.13914 + 25.4062i −0.338487 + 0.940971i
\(730\) 0 0
\(731\) −15.5769 + 21.4398i −0.576132 + 0.792978i
\(732\) 0 0
\(733\) 19.6261 3.10847i 0.724907 0.114814i 0.216933 0.976186i \(-0.430395\pi\)
0.507974 + 0.861372i \(0.330395\pi\)
\(734\) 0 0
\(735\) 33.9252 10.0040i 1.25135 0.369005i
\(736\) 0 0
\(737\) 16.6223 + 32.6232i 0.612292 + 1.20169i
\(738\) 0 0
\(739\) 40.3184 13.1002i 1.48313 0.481900i 0.548087 0.836421i \(-0.315356\pi\)
0.935048 + 0.354522i \(0.115356\pi\)
\(740\) 0 0
\(741\) 0.154980 + 3.28324i 0.00569334 + 0.120613i
\(742\) 0 0
\(743\) −27.1592 27.1592i −0.996375 0.996375i 0.00361798 0.999993i \(-0.498848\pi\)
−0.999993 + 0.00361798i \(0.998848\pi\)
\(744\) 0 0
\(745\) −17.1103 + 1.41499i −0.626873 + 0.0518411i
\(746\) 0 0
\(747\) 10.5399 + 16.6050i 0.385636 + 0.607546i
\(748\) 0 0
\(749\) −14.2616 −0.521106
\(750\) 0 0
\(751\) −7.33413 −0.267626 −0.133813 0.991007i \(-0.542722\pi\)
−0.133813 + 0.991007i \(0.542722\pi\)
\(752\) 0 0
\(753\) −18.1096 + 3.75117i −0.659952 + 0.136700i
\(754\) 0 0
\(755\) −42.3378 + 3.50125i −1.54083 + 0.127423i
\(756\) 0 0
\(757\) 15.2951 + 15.2951i 0.555911 + 0.555911i 0.928141 0.372230i \(-0.121407\pi\)
−0.372230 + 0.928141i \(0.621407\pi\)
\(758\) 0 0
\(759\) −2.90305 + 0.137034i −0.105374 + 0.00497402i
\(760\) 0 0
\(761\) 10.8598 3.52857i 0.393669 0.127911i −0.105492 0.994420i \(-0.533642\pi\)
0.499161 + 0.866509i \(0.333642\pi\)
\(762\) 0 0
\(763\) 20.7372 + 40.6990i 0.750736 + 1.47340i
\(764\) 0 0
\(765\) 40.6607 30.7878i 1.47009 1.11314i
\(766\) 0 0
\(767\) 4.11224 0.651314i 0.148484 0.0235176i
\(768\) 0 0
\(769\) 13.6293 18.7591i 0.491485 0.676471i −0.489176 0.872185i \(-0.662702\pi\)
0.980661 + 0.195714i \(0.0627025\pi\)
\(770\) 0 0
\(771\) 19.0402 + 12.5059i 0.685717 + 0.450388i
\(772\) 0 0
\(773\) 15.7994 31.0081i 0.568265 1.11528i −0.410799 0.911726i \(-0.634750\pi\)
0.979063 0.203556i \(-0.0652499\pi\)
\(774\) 0 0
\(775\) −12.4099 6.19952i −0.445776 0.222693i
\(776\) 0 0
\(777\) −3.69838 + 33.5131i −0.132678 + 1.20228i
\(778\) 0 0
\(779\) 22.0678 16.0332i 0.790661 0.574449i
\(780\) 0 0
\(781\) −8.59271 6.24297i −0.307471 0.223391i
\(782\) 0 0
\(783\) 5.08289 + 1.73950i 0.181648 + 0.0621648i
\(784\) 0 0
\(785\) −8.81656 7.46972i −0.314677 0.266606i
\(786\) 0 0
\(787\) −38.3652 + 19.5480i −1.36757 + 0.696812i −0.974854 0.222847i \(-0.928465\pi\)
−0.392718 + 0.919659i \(0.628465\pi\)
\(788\) 0 0
\(789\) 28.1167 + 35.0922i 1.00098 + 1.24932i
\(790\) 0 0
\(791\) 29.6338 + 9.62861i 1.05366 + 0.342354i
\(792\) 0 0
\(793\) 2.85273 2.85273i 0.101303 0.101303i
\(794\) 0 0
\(795\) −4.16747 31.9566i −0.147805 1.13338i
\(796\) 0 0
\(797\) −5.41838 +