Properties

Label 300.2.x.a.53.5
Level $300$
Weight $2$
Character 300.53
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 53.5
Character \(\chi\) \(=\) 300.53
Dual form 300.2.x.a.17.5

$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\)

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 −0.0763784 + 0.997079i \(0.524336\pi\)
−0.997079 + 0.0763784i \(0.975664\pi\)
\(8\) 0 0
\(9\) −2.75316 1.19169i −0.917719 0.397230i
\(10\) 0 0
\(11\) 4.71560 + 1.53219i 1.42181 + 0.461973i 0.916175 0.400778i \(-0.131260\pi\)
0.505630 + 0.862750i \(0.331260\pi\)
\(12\) 0 0
\(13\) −0.188444 + 0.369843i −0.0522651 + 0.102576i −0.915662 0.401950i \(-0.868333\pi\)
0.863397 + 0.504526i \(0.168333\pi\)
\(14\) 0 0
\(15\) −1.09545 + 3.71483i −0.282844 + 0.959166i
\(16\) 0 0
\(17\) −7.50930 1.18936i −1.82127 0.288461i −0.850062 0.526683i \(-0.823436\pi\)
−0.971211 + 0.238222i \(0.923436\pi\)
\(18\) 0 0
\(19\) 2.68725 + 3.69868i 0.616497 + 0.848536i 0.997092 0.0762063i \(-0.0242808\pi\)
−0.380595 + 0.924742i \(0.624281\pi\)
\(20\) 0 0
\(21\) −3.81918 5.81471i −0.833414 1.26887i
\(22\) 0 0
\(23\) 0.153636 + 0.301528i 0.0320354 + 0.0628730i 0.906469 0.422271i \(-0.138767\pi\)
−0.874434 + 0.485144i \(0.838767\pi\)
\(24\) 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 0.662732 0.748856i \(-0.269397\pi\)
−0.507409 + 0.861705i \(0.669397\pi\)
\(30\) 0 0
\(31\) −2.24457 + 1.63078i −0.403138 + 0.292897i −0.770818 0.637056i \(-0.780152\pi\)
0.367680 + 0.929952i \(0.380152\pi\)
\(32\) 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 0.771372 0.636384i \(-0.219571\pi\)
−0.0614445 + 0.998111i \(0.519571\pi\)
\(38\) 0 0
\(39\) −0.561068 0.449541i −0.0898428 0.0719842i
\(40\) 0 0
\(41\) 5.67438 1.84372i 0.886189 0.287940i 0.169664 0.985502i \(-0.445732\pi\)
0.716525 + 0.697562i \(0.245732\pi\)
\(42\) 0 0
\(43\) 2.46472 + 2.46472i 0.375866 + 0.375866i 0.869608 0.493742i \(-0.164371\pi\)
−0.493742 + 0.869608i \(0.664371\pi\)
\(44\) 0 0
\(45\) −5.91569 3.16301i −0.881859 0.471513i
\(46\) 0 0
\(47\) −1.21046 7.64252i −0.176563 1.11478i −0.903663 0.428245i \(-0.859132\pi\)
0.727100 0.686532i \(-0.240868\pi\)
\(48\) 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 0.436083 0.899906i \(-0.356365\pi\)
0.692826 + 0.721105i \(0.256365\pi\)
\(54\) 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 −0.922115 0.386917i \(-0.873540\pi\)
0.518583 0.855028i \(-0.326460\pi\)
\(60\) 0 0
\(61\) 3.00345 9.24368i 0.384553 1.18353i −0.552251 0.833678i \(-0.686231\pi\)
0.936804 0.349855i \(-0.113769\pi\)
\(62\) 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 −0.810935 0.585136i \(-0.801041\pi\)
0.952062 0.305905i \(-0.0989590\pi\)
\(68\) 0 0
\(69\) −0.565381 + 0.154644i −0.0680639 + 0.0186169i
\(70\) 0 0
\(71\) −1.25910 + 1.73301i −0.149428 + 0.205670i −0.877169 0.480182i \(-0.840570\pi\)
0.727741 + 0.685852i \(0.240570\pi\)
\(72\) 0 0
\(73\) 12.7520 6.49745i 1.49250 0.760469i 0.498201 0.867061i \(-0.333994\pi\)
0.994303 + 0.106592i \(0.0339940\pi\)
\(74\) 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 −0.982573 0.185877i \(-0.940487\pi\)
0.480411 + 0.877043i \(0.340487\pi\)
\(80\) 0 0
\(81\) 6.15976 + 6.56181i 0.684417 + 0.729090i
\(82\) 0 0
\(83\) −1.02557 + 6.47518i −0.112571 + 0.710743i 0.865256 + 0.501329i \(0.167156\pi\)
−0.977827 + 0.209414i \(0.932844\pi\)
\(84\) 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 −0.452153 0.891941i \(-0.649344\pi\)
0.890069 0.455826i \(-0.150656\pi\)
\(90\) 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 −0.0437632 0.999042i \(-0.513935\pi\)
0.267100 + 0.963669i \(0.413935\pi\)
\(98\) 0 0
\(99\) −11.1569 9.83788i −1.12131 0.988744i
\(100\) 0 0
\(101\) 12.5854i 1.25230i 0.779704 + 0.626149i \(0.215370\pi\)
−0.779704 + 0.626149i \(0.784630\pi\)
\(102\) 0 0
\(103\) 0.211229 + 1.33365i 0.0208130 + 0.131408i 0.995907 0.0903839i \(-0.0288094\pi\)
−0.975094 + 0.221792i \(0.928809\pi\)
\(104\) 0 0
\(105\) −7.43931 13.6617i −0.726002 1.33324i
\(106\) 0 0
\(107\) 2.51075 + 2.51075i 0.242723 + 0.242723i 0.817976 0.575253i \(-0.195096\pi\)
−0.575253 + 0.817976i \(0.695096\pi\)
\(108\) 0 0
\(109\) −10.8158 + 3.51428i −1.03597 + 0.336607i −0.777148 0.629318i \(-0.783334\pi\)
−0.258822 + 0.965925i \(0.583334\pi\)
\(110\) 0 0
\(111\) −5.24889 + 6.55109i −0.498203 + 0.621802i
\(112\) 0 0
\(113\) −6.91215 3.52192i −0.650240 0.331314i 0.0975678 0.995229i \(-0.468894\pi\)
−0.747808 + 0.663915i \(0.768894\pi\)
\(114\) 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 0.845928 + 0.533297i \(0.179047\pi\)
−0.0657772 + 0.997834i \(0.520953\pi\)
\(128\) 0 0
\(129\) −5.04618 + 3.31440i −0.444291 + 0.291816i
\(130\) 0 0
\(131\) −1.96392 2.70310i −0.171588 0.236171i 0.714558 0.699576i \(-0.246628\pi\)
−0.886147 + 0.463405i \(0.846628\pi\)
\(132\) 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 −0.932635 0.360822i \(-0.882496\pi\)
0.840100 + 0.542431i \(0.182496\pi\)
\(138\) 0 0
\(139\) −1.62858 0.529159i −0.138135 0.0448827i 0.239134 0.970987i \(-0.423137\pi\)
−0.377268 + 0.926104i \(0.623137\pi\)
\(140\) 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 −0.837725 0.546092i \(-0.816115\pi\)
0.546092 + 0.837725i \(0.316115\pi\)
\(158\) 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 −0.814300 0.580444i \(-0.802879\pi\)
0.948223 + 0.317606i \(0.102879\pi\)
\(164\) 0 0
\(165\) −10.8575 + 15.8392i −0.845258 + 1.23308i
\(166\) 0 0
\(167\) −3.33491 0.528199i −0.258063 0.0408732i 0.0260621 0.999660i \(-0.491703\pi\)
−0.284126 + 0.958787i \(0.591703\pi\)
\(168\) 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 −1.00000 0.000736755i \(-0.999765\pi\)
0.587189 0.809450i \(-0.300235\pi\)
\(174\) 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 0.520380 0.853935i \(-0.325790\pi\)
−0.651334 + 0.758791i \(0.725790\pi\)
\(180\) 0 0
\(181\) −0.486921 + 0.353769i −0.0361925 + 0.0262954i −0.605734 0.795667i \(-0.707121\pi\)
0.569542 + 0.821962i \(0.307121\pi\)
\(182\) 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 −0.926702 0.375798i \(-0.877369\pi\)
−0.528829 + 0.848728i \(0.677369\pi\)
\(192\) 0 0
\(193\) 0.525247 + 0.525247i 0.0378081 + 0.0378081i 0.725758 0.687950i \(-0.241489\pi\)
−0.687950 + 0.725758i \(0.741489\pi\)
\(194\) 0 0
\(195\) −1.16747 1.10518i −0.0836045 0.0791439i
\(196\) 0 0
\(197\) 0.380297 + 2.40110i 0.0270950 + 0.171071i 0.997525 0.0703111i \(-0.0223992\pi\)
−0.970430 + 0.241382i \(0.922399\pi\)
\(198\) 0 0
\(199\) 26.6540i 1.88945i −0.327865 0.944725i \(-0.606329\pi\)
0.327865 0.944725i \(-0.393671\pi\)
\(200\) 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 −0.999679 0.0253480i \(-0.991931\pi\)
0.823656 + 0.567089i \(0.191931\pi\)
\(212\) 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 −0.791513 0.611153i \(-0.790706\pi\)
0.0291937 + 0.999574i \(0.490706\pi\)
\(224\) 0 0
\(225\) −12.6000 8.13884i −0.839998 0.542589i
\(226\) 0 0
\(227\) 21.6298 11.0209i 1.43562 0.731484i 0.448848 0.893608i \(-0.351835\pi\)
0.986770 + 0.162124i \(0.0518346\pi\)
\(228\) 0 0
\(229\) 4.36425 6.00687i 0.288398 0.396945i −0.640095 0.768296i \(-0.721105\pi\)
0.928493 + 0.371350i \(0.121105\pi\)
\(230\) 0 0
\(231\) −9.10047 33.2715i −0.598767 2.18911i
\(232\) 0 0
\(233\) 2.77715 17.5342i 0.181937 1.14871i −0.712553 0.701618i \(-0.752461\pi\)
0.894490 0.447087i \(-0.147539\pi\)
\(234\) 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 −0.958058 0.286573i \(-0.907484\pi\)
0.943529 + 0.331290i \(0.107484\pi\)
\(240\) 0 0
\(241\) −4.44165 13.6700i −0.286112 0.880561i −0.986063 0.166371i \(-0.946795\pi\)
0.699951 0.714190i \(-0.253205\pi\)
\(242\) 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 \(0.109406\pi\)
−0.941512 + 0.336981i \(0.890594\pi\)
\(252\) 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 0.354822 0.934934i \(-0.384541\pi\)
−0.934934 + 0.354822i \(0.884541\pi\)
\(258\) 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 −0.441055 0.897480i \(-0.645396\pi\)
−0.985322 + 0.170704i \(0.945396\pi\)
\(264\) 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 −0.920452 0.390855i \(-0.872179\pi\)
0.0872901 + 0.996183i \(0.472179\pi\)
\(270\) 0 0
\(271\) 12.7884 + 9.29128i 0.776837 + 0.564405i 0.904028 0.427473i \(-0.140596\pi\)
−0.127191 + 0.991878i \(0.540596\pi\)
\(272\) 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 0.997631 + 0.0687889i \(0.0219135\pi\)
−0.530742 + 0.847534i \(0.678087\pi\)
\(278\) 0 0
\(279\) 8.12305 1.81496i 0.486314 0.108659i
\(280\) 0 0
\(281\) 16.0338 + 22.0687i 0.956499 + 1.31651i 0.948580 + 0.316539i \(0.102521\pi\)
0.00791912 + 0.999969i \(0.497479\pi\)
\(282\) 0 0
\(283\) −3.01460 0.477465i −0.179199 0.0283824i 0.0661898 0.997807i \(-0.478916\pi\)
−0.245389 + 0.969425i \(0.578916\pi\)
\(284\) 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 −0.327918 0.944706i \(-0.606347\pi\)
0.944706 + 0.327918i \(0.106347\pi\)
\(294\) 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 −0.0109073 0.999941i \(-0.503472\pi\)
0.999941 + 0.0109073i \(0.00347197\pi\)
\(308\) 0 0
\(309\) −2.33614 0.110273i −0.132898 0.00627324i
\(310\) 0 0
\(311\) −4.35394 1.41468i −0.246889 0.0802191i 0.182958 0.983121i \(-0.441433\pi\)
−0.429847 + 0.902902i \(0.641433\pi\)
\(312\) 0 0
\(313\) −4.00451 + 7.85929i −0.226348 + 0.444233i −0.976051 0.217541i \(-0.930196\pi\)
0.749703 + 0.661774i \(0.230196\pi\)
\(314\) 0 0
\(315\) 25.7844 7.81789i 1.45279 0.440488i
\(316\) 0 0
\(317\) −17.3151 2.74245i −0.972515 0.154031i −0.350095 0.936714i \(-0.613851\pi\)
−0.622420 + 0.782683i \(0.713851\pi\)
\(318\) 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 −0.179918 0.983682i \(-0.557583\pi\)
0.879939 + 0.475087i \(0.157583\pi\)
\(332\) 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 0.546203 0.837653i \(-0.316073\pi\)
−0.356626 + 0.934247i \(0.616073\pi\)
\(338\) 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 0.998423 0.0561397i \(-0.0178792\pi\)
−0.966905 + 0.255138i \(0.917879\pi\)
\(348\) 0 0
\(349\) 12.9374i 0.692525i −0.938138 0.346262i \(-0.887451\pi\)
0.938138 0.346262i \(-0.112549\pi\)
\(350\) 0 0
\(351\) 1.00900 + 1.90628i 0.0538562 + 0.101750i
\(352\) 0 0
\(353\) −26.1583 + 4.14307i −1.39227 + 0.220513i −0.807107 0.590405i \(-0.798968\pi\)
−0.585159 + 0.810919i \(0.698968\pi\)
\(354\) 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 0.904242 0.427021i \(-0.140437\pi\)
−0.982543 + 0.186033i \(0.940437\pi\)
\(360\) 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 −0.595782 0.803146i \(-0.703158\pi\)
0.814808 0.579731i \(-0.196842\pi\)
\(368\) 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 −0.375170 0.926956i \(-0.622416\pi\)
0.529404 + 0.848370i \(0.322416\pi\)
\(374\) 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 −0.845260 0.534355i \(-0.820555\pi\)
0.769401 + 0.638766i \(0.220555\pi\)
\(380\) 0 0
\(381\) −32.3540 + 8.84950i −1.65754 + 0.453373i
\(382\) 0 0
\(383\) 1.45004 9.15521i 0.0740938 0.467810i −0.922545 0.385889i \(-0.873895\pi\)
0.996639 0.0819203i \(-0.0261053\pi\)
\(384\) 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 −0.999793 0.0203282i \(-0.993529\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(390\) 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 −0.394468 0.918910i \(-0.629071\pi\)
−0.0912023 + 0.995832i \(0.529071\pi\)
\(398\) 0 0
\(399\) 11.2437 29.7515i 0.562888 1.48944i
\(400\) 0 0
\(401\) 27.1537i 1.35599i −0.735066 0.677996i \(-0.762849\pi\)
0.735066 0.677996i \(-0.237151\pi\)
\(402\) 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 −0.936250 0.351335i \(-0.885728\pi\)
−0.550932 + 0.834550i \(0.685728\pi\)
\(410\) 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 −0.863251 0.504775i \(-0.831576\pi\)
0.213310 + 0.976985i \(0.431576\pi\)
\(420\) 0 0
\(421\) 11.1129 + 8.07400i 0.541610 + 0.393503i 0.824683 0.565596i \(-0.191354\pi\)
−0.283073 + 0.959098i \(0.591354\pi\)
\(422\) 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 0.868626 0.495468i \(-0.165003\pi\)
−0.739638 + 0.673005i \(0.765003\pi\)
\(432\) 0 0
\(433\) 21.2003 + 3.35781i 1.01882 + 0.161366i 0.643434 0.765501i \(-0.277509\pi\)
0.375389 + 0.926867i \(0.377509\pi\)
\(434\) 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 0.549071 0.835776i \(-0.314982\pi\)
−0.0470490 + 0.998893i \(0.514982\pi\)
\(440\) 0 0
\(441\) −10.8829 + 25.1428i −0.518234 + 1.19728i
\(442\) 0 0
\(443\) 11.3624 11.3624i 0.539846 0.539846i −0.383638 0.923484i \(-0.625329\pi\)
0.923484 + 0.383638i \(0.125329\pi\)
\(444\) 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 −0.978943 0.204136i \(-0.934562\pi\)
0.204136 + 0.978943i \(0.434562\pi\)
\(458\) 0 0
\(459\) −27.4964 + 28.3665i −1.28342 + 1.32404i
\(460\) 0 0
\(461\) −14.5158 4.71648i −0.676070 0.219669i −0.0491963 0.998789i \(-0.515666\pi\)
−0.626874 + 0.779121i \(0.715666\pi\)
\(462\) 0 0
\(463\) −1.93184 + 3.79146i −0.0897804 + 0.176204i −0.931530 0.363664i \(-0.881526\pi\)
0.841750 + 0.539868i \(0.181526\pi\)
\(464\) 0 0
\(465\) −3.59925 10.1247i −0.166911 0.469520i
\(466\) 0 0
\(467\) 30.6114 + 4.84837i 1.41653 + 0.224356i 0.817295 0.576219i \(-0.195472\pi\)
0.599233 + 0.800575i \(0.295472\pi\)
\(468\) 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 −0.105039 0.994468i \(-0.533497\pi\)
−0.978254 + 0.207409i \(0.933497\pi\)
\(480\) 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 0.821128 0.570744i \(-0.193345\pi\)
0.0209053 + 0.999781i \(0.493345\pi\)
\(488\) 0 0
\(489\) 5.09073 + 4.07882i 0.230211 + 0.184451i
\(490\) 0 0
\(491\) 8.67143 2.81752i 0.391336 0.127153i −0.106738 0.994287i \(-0.534041\pi\)
0.498074 + 0.867134i \(0.334041\pi\)
\(492\) 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 \(0.0696729\pi\)
−0.976140 + 0.217140i \(0.930327\pi\)
\(500\) 0 0
\(501\) 2.06745 5.47061i 0.0923669 0.244409i
\(502\) 0 0
\(503\) 8.01914 1.27011i 0.357556 0.0566313i 0.0249274 0.999689i \(-0.492065\pi\)
0.332628 + 0.943058i \(0.392065\pi\)
\(504\) 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 0.815863 + 0.578245i \(0.196262\pi\)
−0.320163 + 0.947362i \(0.603738\pi\)
\(510\) 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 −0.965836 0.259155i \(-0.916556\pi\)
0.544930 + 0.838481i \(0.316556\pi\)
\(522\) 0 0
\(523\) −9.11004 + 4.64180i −0.398354 + 0.202972i −0.641679 0.766973i \(-0.721762\pi\)
0.243325 + 0.969945i \(0.421762\pi\)
\(524\) 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 0.997383 + 0.0723059i \(0.0230358\pi\)
−0.764399 + 0.644743i \(0.776964\pi\)
\(542\) 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 0.195395 0.980725i \(-0.437401\pi\)
0.488893 + 0.872344i \(0.337401\pi\)
\(548\) 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 0.699623 0.714512i \(-0.253351\pi\)
−0.714512 + 0.699623i \(0.753351\pi\)
\(558\) 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 0.240525 0.970643i \(-0.422680\pi\)
−0.643890 + 0.765118i \(0.722680\pi\)
\(564\) 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 0.462484 0.886628i \(-0.346958\pi\)
0.986148 0.165865i \(-0.0530417\pi\)
\(570\) 0 0
\(571\) −37.4429 27.2039i −1.56694 1.13845i −0.930017 0.367517i \(-0.880208\pi\)
−0.636920 0.770930i \(-0.719792\pi\)
\(572\) 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 0.800042 0.599944i \(-0.204811\pi\)
−0.955618 + 0.294609i \(0.904811\pi\)
\(578\) 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 −0.908562 0.417750i \(-0.862819\pi\)
0.872006 + 0.489495i \(0.162819\pi\)
\(588\) 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 −0.0863319 + 0.996266i \(0.527515\pi\)
−0.996266 + 0.0863319i \(0.972485\pi\)
\(594\) 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 −0.950412 0.310994i \(-0.899338\pi\)
0.310994 + 0.950412i \(0.399338\pi\)
\(608\) 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 −0.988405 0.151843i \(-0.951479\pi\)
0.703813 + 0.710385i \(0.251479\pi\)
\(614\) 0 0
\(615\) 0.633098 + 23.0991i 0.0255290 + 0.931445i
\(616\) 0 0
\(617\) −30.2739 4.79492i −1.21878 0.193036i −0.486282 0.873802i \(-0.661647\pi\)
−0.732501 + 0.680766i \(0.761647\pi\)
\(618\) 0 0
\(619\) −24.7268 34.0335i −0.993852 1.36792i −0.929022 0.370024i \(-0.879350\pi\)
−0.0648299 0.997896i \(-0.520650\pi\)
\(620\) 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 0.414834 0.909897i \(-0.363840\pi\)
0.993554 0.113357i \(-0.0361603\pi\)
\(632\) 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 0.676924 0.736053i \(-0.263313\pi\)
0.980284 + 0.197593i \(0.0633125\pi\)
\(642\) 0 0
\(643\) −21.6567 21.6567i −0.854057 0.854057i 0.136573 0.990630i \(-0.456391\pi\)
−0.990630 + 0.136573i \(0.956391\pi\)
\(644\) 0 0
\(645\) −11.8560 + 6.45605i −0.466830 + 0.254207i
\(646\) 0 0
\(647\) 4.83284 + 30.5133i 0.189998 + 1.19960i 0.879707 + 0.475516i \(0.157739\pi\)
−0.689709 + 0.724087i \(0.742261\pi\)
\(648\) 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 −0.705127 0.709081i \(-0.749110\pi\)
−0.451497 + 0.892272i \(0.649110\pi\)
\(654\) 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 0.865682 0.500595i \(-0.166885\pi\)
−0.994594 + 0.103845i \(0.966885\pi\)
\(660\) 0 0
\(661\) 8.67556 26.7006i 0.337440 1.03853i −0.628067 0.778159i \(-0.716154\pi\)
0.965507 0.260375i \(-0.0838463\pi\)
\(662\) 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 −0.836831 0.547461i \(-0.815594\pi\)
−0.0489715 + 0.998800i \(0.515594\pi\)
\(674\) 0 0
\(675\) 18.2304 18.5109i 0.701688 0.712484i
\(676\) 0 0
\(677\) 3.98966 2.03283i 0.153335 0.0781281i −0.375639 0.926766i \(-0.622577\pi\)
0.528974 + 0.848638i \(0.322577\pi\)
\(678\) 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 −0.731297 0.682059i \(-0.761085\pi\)
0.906273 0.422693i \(-0.138915\pi\)
\(684\) 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 −0.983701 0.179810i \(-0.942452\pi\)
0.690141 0.723674i \(-0.257548\pi\)
\(692\) 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 \(-0.958474\pi\)
0.991503 0.130087i \(-0.0415257\pi\)
\(702\) 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 −0.370607 0.928790i \(-0.620850\pi\)
0.246101 + 0.969244i \(0.420850\pi\)
\(710\) 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 −0.803677 0.595066i \(-0.797126\pi\)
0.317592 + 0.948228i \(0.397126\pi\)
\(720\) 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 0.997754 + 0.0669890i \(0.0213392\pi\)
−0.532270 + 0.846575i \(0.678661\pi\)
\(728\) 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 0.507974 0.861372i \(-0.330395\pi\)
0.216933 + 0.976186i \(0.430395\pi\)
\(734\) 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 0.935048 0.354522i \(-0.115356\pi\)
0.548087 + 0.836421i \(0.315356\pi\)
\(740\) 0 0
\(741\) 0.154980 3.28324i 0.00569334 0.120613i
\(742\) 0 0
\(743\) −27.1592 + 27.1592i −0.996375 + 0.996375i −0.999993 0.00361798i \(-0.998848\pi\)
0.00361798 + 0.999993i \(0.498848\pi\)
\(744\) 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 −0.372230 0.928141i \(-0.621407\pi\)
0.928141 + 0.372230i \(0.121407\pi\)
\(758\) 0 0
\(759\) −2.90305 0.137034i −0.105374 0.00497402i
\(760\) 0 0
\(761\) 10.8598 + 3.52857i 0.393669 + 0.127911i 0.499161 0.866509i \(-0.333642\pi\)
−0.105492 + 0.994420i \(0.533642\pi\)
\(762\) 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 0.980661 0.195714i \(-0.0627025\pi\)
−0.489176 + 0.872185i \(0.662702\pi\)
\(770\) 0 0
\(771\) 19.0402 12.5059i 0.685717 0.450388i
\(772\) 0 0
\(773\) 15.7994 + 31.0081i 0.568265 + 1.11528i 0.979063 + 0.203556i \(0.0652499\pi\)
−0.410799 + 0.911726i \(0.634750\pi\)
\(774\) 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 −0.392718 0.919659i \(-0.628465\pi\)
−0.974854 + 0.222847i \(0.928465\pi\)
\(788\) 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