Properties

Label 300.2.x.a.53.7
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 53.7
Character \(\chi\) \(=\) 300.53
Dual form 300.2.x.a.17.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.858227 + 1.50448i) q^{3} +(-2.22846 - 0.184289i) q^{5} +(-2.84010 + 2.84010i) q^{7} +(-1.52689 + 2.58236i) q^{9} +O(q^{10})\) \(q+(0.858227 + 1.50448i) q^{3} +(-2.22846 - 0.184289i) q^{5} +(-2.84010 + 2.84010i) q^{7} +(-1.52689 + 2.58236i) q^{9} +(-4.71560 - 1.53219i) q^{11} +(-0.188444 + 0.369843i) q^{13} +(-1.63527 - 3.51083i) q^{15} +(7.50930 + 1.18936i) q^{17} +(2.68725 + 3.69868i) q^{19} +(-6.71031 - 1.83541i) q^{21} +(-0.153636 - 0.301528i) q^{23} +(4.93208 + 0.821362i) q^{25} +(-5.19552 - 0.0809244i) q^{27} +(-0.836442 - 0.607711i) q^{29} +(-2.24457 + 1.63078i) q^{31} +(-1.74191 - 8.40946i) q^{33} +(6.85245 - 5.80565i) q^{35} +(4.31832 + 2.20029i) q^{37} +(-0.718148 + 0.0338990i) q^{39} +(-5.67438 + 1.84372i) q^{41} +(2.46472 + 2.46472i) q^{43} +(3.87853 - 5.47330i) q^{45} +(1.21046 + 7.64252i) q^{47} -9.13235i q^{49} +(4.65532 + 12.3183i) q^{51} +(-8.21858 + 1.30170i) q^{53} +(10.2262 + 4.28346i) q^{55} +(-3.25831 + 7.21721i) q^{57} +(3.09959 + 9.53955i) q^{59} +(3.00345 - 9.24368i) q^{61} +(-2.99763 - 11.6707i) q^{63} +(0.488099 - 0.789452i) q^{65} +(1.15518 - 7.29349i) q^{67} +(0.321787 - 0.489922i) q^{69} +(1.25910 - 1.73301i) q^{71} +(12.7520 - 6.49745i) q^{73} +(2.99712 + 8.12510i) q^{75} +(17.7443 - 9.04119i) q^{77} +(-4.46331 + 6.14322i) q^{79} +(-4.33719 - 7.88599i) q^{81} +(1.02557 - 6.47518i) q^{83} +(-16.5150 - 4.03432i) q^{85} +(0.196429 - 1.77996i) q^{87} +(-4.13129 + 12.7148i) q^{89} +(-0.515190 - 1.58559i) q^{91} +(-4.37982 - 1.97733i) q^{93} +(-5.30680 - 8.73760i) q^{95} +(2.19961 - 0.348384i) q^{97} +(11.1569 - 9.83788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

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
\(3\) 0.858227 + 1.50448i 0.495497 + 0.868609i
\(4\) 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
\(9\) −1.52689 + 2.58236i −0.508965 + 0.860787i
\(10\) 0 0
\(11\) −4.71560 1.53219i −1.42181 0.461973i −0.505630 0.862750i \(-0.668740\pi\)
−0.916175 + 0.400778i \(0.868740\pi\)
\(12\) 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
\(15\) −1.63527 3.51083i −0.422224 0.906492i
\(16\) 0 0
\(17\) 7.50930 + 1.18936i 1.82127 + 0.288461i 0.971211 0.238222i \(-0.0765645\pi\)
0.850062 + 0.526683i \(0.176564\pi\)
\(18\) 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
\(21\) −6.71031 1.83541i −1.46431 0.400520i
\(22\) 0 0
\(23\) −0.153636 0.301528i −0.0320354 0.0628730i 0.874434 0.485144i \(-0.161233\pi\)
−0.906469 + 0.422271i \(0.861233\pi\)
\(24\) 0 0
\(25\) 4.93208 + 0.821362i 0.986415 + 0.164272i
\(26\) 0 0
\(27\) −5.19552 0.0809244i −0.999879 0.0155739i
\(28\) 0 0
\(29\) −0.836442 0.607711i −0.155323 0.112849i 0.507409 0.861705i \(-0.330603\pi\)
−0.662732 + 0.748856i \(0.730603\pi\)
\(30\) 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
\(33\) −1.74191 8.40946i −0.303227 1.46390i
\(34\) 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
\(39\) −0.718148 + 0.0338990i −0.114996 + 0.00542818i
\(40\) 0 0
\(41\) −5.67438 + 1.84372i −0.886189 + 0.287940i −0.716525 0.697562i \(-0.754268\pi\)
−0.169664 + 0.985502i \(0.554268\pi\)
\(42\) 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
\(45\) 3.87853 5.47330i 0.578177 0.815912i
\(46\) 0 0
\(47\) 1.21046 + 7.64252i 0.176563 + 1.11478i 0.903663 + 0.428245i \(0.140868\pi\)
−0.727100 + 0.686532i \(0.759132\pi\)
\(48\) 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 \(-0.743635\pi\)
−0.436083 + 0.899906i \(0.643635\pi\)
\(54\) 0 0
\(55\) 10.2262 + 4.28346i 1.37889 + 0.577581i
\(56\) 0 0
\(57\) −3.25831 + 7.21721i −0.431573 + 0.955942i
\(58\) 0 0
\(59\) 3.09959 + 9.53955i 0.403532 + 1.24194i 0.922115 + 0.386917i \(0.126460\pi\)
−0.518583 + 0.855028i \(0.673540\pi\)
\(60\) 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
\(63\) −2.99763 11.6707i −0.377666 1.47037i
\(64\) 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
\(69\) 0.321787 0.489922i 0.0387387 0.0589797i
\(70\) 0 0
\(71\) 1.25910 1.73301i 0.149428 0.205670i −0.727741 0.685852i \(-0.759430\pi\)
0.877169 + 0.480182i \(0.159430\pi\)
\(72\) 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
\(75\) 2.99712 + 8.12510i 0.346077 + 0.938206i
\(76\) 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
\(81\) −4.33719 7.88599i −0.481910 0.876221i
\(82\) 0 0
\(83\) 1.02557 6.47518i 0.112571 0.710743i −0.865256 0.501329i \(-0.832844\pi\)
0.977827 0.209414i \(-0.0671555\pi\)
\(84\) 0 0
\(85\) −16.5150 4.03432i −1.79130 0.437583i
\(86\) 0 0
\(87\) 0.196429 1.77996i 0.0210594 0.190832i
\(88\) 0 0
\(89\) −4.13129 + 12.7148i −0.437916 + 1.34777i 0.452153 + 0.891941i \(0.350656\pi\)
−0.890069 + 0.455826i \(0.849344\pi\)
\(90\) 0 0
\(91\) −0.515190 1.58559i −0.0540066 0.166215i
\(92\) 0 0
\(93\) −4.37982 1.97733i −0.454166 0.205040i
\(94\) 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 \(-0.784630\pi\)
0.779704 0.626149i \(-0.215370\pi\)
\(102\) 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
\(105\) 14.6154 + 5.32678i 1.42632 + 0.519841i
\(106\) 0 0
\(107\) −2.51075 2.51075i −0.242723 0.242723i 0.575253 0.817976i \(-0.304904\pi\)
−0.817976 + 0.575253i \(0.804904\pi\)
\(108\) 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
\(111\) 0.395808 + 8.38516i 0.0375684 + 0.795884i
\(112\) 0 0
\(113\) 6.91215 + 3.52192i 0.650240 + 0.331314i 0.747808 0.663915i \(-0.231106\pi\)
−0.0975678 + 0.995229i \(0.531106\pi\)
\(114\) 0 0
\(115\) 0.286804 + 0.700258i 0.0267446 + 0.0652994i
\(116\) 0 0
\(117\) −0.667333 1.05134i −0.0616950 0.0971967i
\(118\) 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
\(123\) −7.64373 6.95464i −0.689212 0.627079i
\(124\) 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
\(129\) −1.59282 + 5.82340i −0.140240 + 0.512722i
\(130\) 0 0
\(131\) 1.96392 + 2.70310i 0.171588 + 0.236171i 0.886147 0.463405i \(-0.153372\pi\)
−0.714558 + 0.699576i \(0.753372\pi\)
\(132\) 0 0
\(133\) −18.1367 2.87257i −1.57265 0.249083i
\(134\) 0 0
\(135\) 11.5631 + 1.13782i 0.995194 + 0.0979275i
\(136\) 0 0
\(137\) 1.08309 2.12568i 0.0925343 0.181609i −0.840100 0.542431i \(-0.817504\pi\)
0.932635 + 0.360822i \(0.117504\pi\)
\(138\) 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
\(141\) −10.4591 + 8.38012i −0.880819 + 0.705733i
\(142\) 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
\(147\) 13.7394 7.83762i 1.13321 0.646436i
\(148\) 0 0
\(149\) 7.67808 0.629012 0.314506 0.949255i \(-0.398161\pi\)
0.314506 + 0.949255i \(0.398161\pi\)
\(150\) 0 0
\(151\) −18.9987 −1.54609 −0.773045 0.634352i \(-0.781267\pi\)
−0.773045 + 0.634352i \(0.781267\pi\)
\(152\) 0 0
\(153\) −14.5373 + 17.5757i −1.17527 + 1.42091i
\(154\) 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
\(159\) −9.01178 11.2475i −0.714680 0.891985i
\(160\) 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
\(165\) 2.33200 + 19.0612i 0.181546 + 1.48391i
\(166\) 0 0
\(167\) 3.33491 + 0.528199i 0.258063 + 0.0408732i 0.284126 0.958787i \(-0.408297\pi\)
−0.0260621 + 0.999660i \(0.508297\pi\)
\(168\) 0 0
\(169\) 7.53994 + 10.3778i 0.579995 + 0.798295i
\(170\) 0 0
\(171\) −13.6545 + 1.29195i −1.04418 + 0.0987982i
\(172\) 0 0
\(173\) 5.42968 + 10.6563i 0.412811 + 0.810187i 1.00000 0.000736755i \(0.000234516\pi\)
−0.587189 + 0.809450i \(0.699765\pi\)
\(174\) 0 0
\(175\) −16.3403 + 11.6748i −1.23521 + 0.882535i
\(176\) 0 0
\(177\) −11.6919 + 12.8504i −0.878815 + 0.965892i
\(178\) 0 0
\(179\) 1.75204 + 1.27293i 0.130954 + 0.0951434i 0.651334 0.758791i \(-0.274210\pi\)
−0.520380 + 0.853935i \(0.674210\pi\)
\(180\) 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
\(183\) 16.4845 3.41455i 1.21857 0.252411i
\(184\) 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
\(189\) 14.9856 14.5260i 1.09005 1.05661i
\(190\) 0 0
\(191\) 20.1158 6.53603i 1.45553 0.472931i 0.528829 0.848728i \(-0.322631\pi\)
0.926702 + 0.375798i \(0.122631\pi\)
\(192\) 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
\(195\) 1.60661 + 0.0568042i 0.115052 + 0.00406784i
\(196\) 0 0
\(197\) −0.380297 2.40110i −0.0270950 0.171071i 0.970430 0.241382i \(-0.0776008\pi\)
−0.997525 + 0.0703111i \(0.977601\pi\)
\(198\) 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
\(207\) 1.01324 + 0.0636573i 0.0704252 + 0.00442449i
\(208\) 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
\(213\) 3.68786 + 0.406978i 0.252688 + 0.0278856i
\(214\) 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
\(219\) 20.7193 + 13.6087i 1.40008 + 0.919593i
\(220\) 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
\(225\) −9.65181 + 11.4823i −0.643454 + 0.765485i
\(226\) 0 0
\(227\) −21.6298 + 11.0209i −1.43562 + 0.731484i −0.986770 0.162124i \(-0.948165\pi\)
−0.448848 + 0.893608i \(0.648165\pi\)
\(228\) 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
\(231\) 28.8309 + 18.9365i 1.89694 + 1.24593i
\(232\) 0 0
\(233\) −2.77715 + 17.5342i −0.181937 + 1.14871i 0.712553 + 0.701618i \(0.247539\pi\)
−0.894490 + 0.447087i \(0.852461\pi\)
\(234\) 0 0
\(235\) −1.28902 17.2541i −0.0840865 1.12554i
\(236\) 0 0
\(237\) −13.0729 1.44267i −0.849173 0.0937114i
\(238\) 0 0
\(239\) 0.224620 0.691308i 0.0145294 0.0447170i −0.943529 0.331290i \(-0.892516\pi\)
0.958058 + 0.286573i \(0.0925161\pi\)
\(240\) 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
\(243\) 8.14199 13.2932i 0.522309 0.852756i
\(244\) 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
\(255\) −8.10407 28.3088i −0.507497 1.77276i
\(256\) 0 0
\(257\) 9.29989 + 9.29989i 0.580111 + 0.580111i 0.934934 0.354822i \(-0.115459\pi\)
−0.354822 + 0.934934i \(0.615459\pi\)
\(258\) 0 0
\(259\) −18.5135 + 6.01541i −1.15037 + 0.373779i
\(260\) 0 0
\(261\) 2.84649 1.23209i 0.176193 0.0762642i
\(262\) 0 0
\(263\) 23.1320 + 11.7863i 1.42638 + 0.726776i 0.985322 0.170704i \(-0.0546042\pi\)
0.441055 + 0.897480i \(0.354604\pi\)
\(264\) 0 0
\(265\) 18.5547 1.38618i 1.13980 0.0851525i
\(266\) 0 0
\(267\) −22.6747 + 4.69676i −1.38767 + 0.287437i
\(268\) 0 0
\(269\) 13.6649 9.92811i 0.833162 0.605328i −0.0872901 0.996183i \(-0.527821\pi\)
0.920452 + 0.390855i \(0.127821\pi\)
\(270\) 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
\(273\) 1.94334 2.13589i 0.117616 0.129270i
\(274\) 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
\(279\) −0.784033 8.28633i −0.0469388 0.496090i
\(280\) 0 0
\(281\) −16.0338 22.0687i −0.956499 1.31651i −0.948580 0.316539i \(-0.897479\pi\)
−0.00791912 0.999969i \(-0.502521\pi\)
\(282\) 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
\(285\) 8.59106 15.4828i 0.508891 0.917121i
\(286\) 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
\(291\) 2.41190 + 3.01027i 0.141388 + 0.176465i
\(292\) 0 0
\(293\) −10.5577 + 10.5577i −0.616788 + 0.616788i −0.944706 0.327918i \(-0.893653\pi\)
0.327918 + 0.944706i \(0.393653\pi\)
\(294\) 0 0
\(295\) −5.14928 21.8297i −0.299802 1.27098i
\(296\) 0 0
\(297\) 24.3760 + 8.34213i 1.41444 + 0.484060i
\(298\) 0 0
\(299\) 0.140470 0.00812359
\(300\) 0 0
\(301\) −14.0001 −0.806953
\(302\) 0 0
\(303\) 18.9345 10.8012i 1.08776 0.620510i
\(304\) 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
\(309\) −1.82516 + 1.46236i −0.103830 + 0.0831907i
\(310\) 0 0
\(311\) 4.35394 + 1.41468i 0.246889 + 0.0802191i 0.429847 0.902902i \(-0.358567\pi\)
−0.182958 + 0.983121i \(0.558567\pi\)
\(312\) 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
\(315\) 4.52933 + 26.5601i 0.255199 + 1.49649i
\(316\) 0 0
\(317\) 17.3151 + 2.74245i 0.972515 + 0.154031i 0.622420 0.782683i \(-0.286149\pi\)
0.350095 + 0.936714i \(0.386149\pi\)
\(318\) 0 0
\(319\) 3.01319 + 4.14731i 0.168707 + 0.232205i
\(320\) 0 0
\(321\) 1.62257 5.93215i 0.0905630 0.331100i
\(322\) 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
\(327\) −14.5696 13.2561i −0.805700 0.733065i
\(328\) 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
\(333\) −12.2756 + 7.79185i −0.672698 + 0.426991i
\(334\) 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
\(339\) 0.633553 + 13.4218i 0.0344098 + 0.728970i
\(340\) 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
\(345\) −0.807378 + 1.03247i −0.0434678 + 0.0555863i
\(346\) 0 0
\(347\) −0.587119 3.70692i −0.0315182 0.198998i 0.966905 0.255138i \(-0.0821208\pi\)
−0.998423 + 0.0561397i \(0.982121\pi\)
\(348\) 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 0.585159 0.810919i \(-0.301032\pi\)
0.807107 + 0.590405i \(0.201032\pi\)
\(354\) 0 0
\(355\) −3.12523 + 3.62990i −0.165870 + 0.192655i
\(356\) 0 0
\(357\) −48.2068 21.7636i −2.55137 1.15185i
\(358\) 0 0
\(359\) 1.48360 + 4.56607i 0.0783016 + 0.240988i 0.982543 0.186033i \(-0.0595631\pi\)
−0.904242 + 0.427021i \(0.859563\pi\)
\(360\) 0 0
\(361\) −0.587610 + 1.80848i −0.0309269 + 0.0951831i
\(362\) 0 0
\(363\) −2.58089 + 23.3870i −0.135462 + 1.22750i
\(364\) 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
\(369\) 3.90303 17.4685i 0.203184 0.909372i
\(370\) 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
\(375\) −5.18159 18.6588i −0.267576 0.963537i
\(376\) 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
\(381\) −18.4143 + 28.0358i −0.943393 + 1.43632i
\(382\) 0 0
\(383\) −1.45004 + 9.15521i −0.0740938 + 0.467810i 0.922545 + 0.385889i \(0.126105\pi\)
−0.996639 + 0.0819203i \(0.973895\pi\)
\(384\) 0 0
\(385\) −41.2088 + 16.8779i −2.10019 + 0.860175i
\(386\) 0 0
\(387\) −10.1282 + 2.60143i −0.514844 + 0.132238i
\(388\) 0 0
\(389\) 3.53033 10.8652i 0.178995 0.550890i −0.820798 0.571218i \(-0.806471\pi\)
0.999793 + 0.0203282i \(0.00647113\pi\)
\(390\) 0 0
\(391\) −0.795077 2.44700i −0.0402088 0.123750i
\(392\) 0 0
\(393\) −2.38127 + 5.27454i −0.120119 + 0.266066i
\(394\) 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 \(0.237151\pi\)
−0.735066 + 0.677996i \(0.762849\pi\)
\(402\) 0 0
\(403\) −0.180155 1.13745i −0.00897414 0.0566605i
\(404\) 0 0
\(405\) 8.21195 + 18.3729i 0.408055 + 0.912957i
\(406\) 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
\(411\) 4.12756 0.194835i 0.203598 0.00961050i
\(412\) 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
\(417\) −0.601587 2.90430i −0.0294598 0.142224i
\(418\) 0 0
\(419\) 13.3040 9.66590i 0.649941 0.472210i −0.213310 0.976985i \(-0.568424\pi\)
0.863251 + 0.504775i \(0.168424\pi\)
\(420\) 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
\(423\) −21.5840 8.54349i −1.04945 0.415399i
\(424\) 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
\(429\) 3.43843 + 0.940484i 0.166009 + 0.0454070i
\(430\) 0 0
\(431\) −2.67787 3.68577i −0.128989 0.177537i 0.739638 0.673005i \(-0.234997\pi\)
−0.868626 + 0.495468i \(0.834997\pi\)
\(432\) 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
\(435\) −0.765763 + 3.93037i −0.0367155 + 0.188447i
\(436\) 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
\(441\) 23.5830 + 13.9441i 1.12300 + 0.664006i
\(442\) 0 0
\(443\) −11.3624 + 11.3624i −0.539846 + 0.539846i −0.923484 0.383638i \(-0.874671\pi\)
0.383638 + 0.923484i \(0.374671\pi\)
\(444\) 0 0
\(445\) 11.5496 27.5731i 0.547505 1.30709i
\(446\) 0 0
\(447\) 6.58953 + 11.5515i 0.311674 + 0.546366i
\(448\) 0 0
\(449\) −16.5317 −0.780178 −0.390089 0.920777i \(-0.627556\pi\)
−0.390089 + 0.920777i \(0.627556\pi\)
\(450\) 0 0
\(451\) 29.5830 1.39301
\(452\) 0 0
\(453\) −16.3052 28.5830i −0.766083 1.34295i
\(454\) 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
\(459\) −38.9185 6.78701i −1.81656 0.316791i
\(460\) 0 0
\(461\) 14.5158 + 4.71648i 0.676070 + 0.219669i 0.626874 0.779121i \(-0.284334\pi\)
0.0491963 + 0.998789i \(0.484334\pi\)
\(462\) 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
\(465\) 9.39586 + 5.21356i 0.435723 + 0.241773i
\(466\) 0 0
\(467\) −30.6114 4.84837i −1.41653 0.224356i −0.599233 0.800575i \(-0.704528\pi\)
−0.817295 + 0.576219i \(0.804528\pi\)
\(468\) 0 0
\(469\) 17.4334 + 23.9951i 0.805001 + 1.10799i
\(470\) 0 0
\(471\) −8.63368 2.36149i −0.397819 0.108812i
\(472\) 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
\(477\) 9.18746 23.2109i 0.420665 1.06275i
\(478\) 0 0
\(479\) 23.7090 + 17.2256i 1.08329 + 0.787059i 0.978254 0.207409i \(-0.0665032\pi\)
0.105039 + 0.994468i \(0.466503\pi\)
\(480\) 0 0
\(481\) −1.62753 + 1.18247i −0.0742088 + 0.0539159i
\(482\) 0 0
\(483\) 0.477519 + 2.30534i 0.0217279 + 0.104896i
\(484\) 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
\(489\) 6.51596 0.307575i 0.294662 0.0139090i
\(490\) 0 0
\(491\) −8.67143 + 2.81752i −0.391336 + 0.127153i −0.498074 0.867134i \(-0.665959\pi\)
0.106738 + 0.994287i \(0.465959\pi\)
\(492\) 0 0
\(493\) −5.55831 5.55831i −0.250334 0.250334i
\(494\) 0 0
\(495\) −26.6757 + 19.8672i −1.19898 + 0.892966i
\(496\) 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 −0.332628 0.943058i \(-0.607935\pi\)
−0.0249274 + 0.999689i \(0.507935\pi\)
\(504\) 0 0
\(505\) −2.31936 + 28.0461i −0.103210 + 1.24804i
\(506\) 0 0
\(507\) −9.14222 + 20.2502i −0.406020 + 0.899342i
\(508\) 0 0
\(509\) −11.1835 34.4193i −0.495700 1.52561i −0.815863 0.578245i \(-0.803738\pi\)
0.320163 0.947362i \(-0.396262\pi\)
\(510\) 0 0
\(511\) −17.7634 + 54.6703i −0.785809 + 2.41847i
\(512\) 0 0
\(513\) −13.6623 19.4340i −0.603207 0.858034i
\(514\) 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
\(519\) −11.3723 + 17.3144i −0.499189 + 0.760017i
\(520\) 0 0
\(521\) 9.60734 13.2234i 0.420905 0.579326i −0.544930 0.838481i \(-0.683444\pi\)
0.965836 + 0.259155i \(0.0834440\pi\)
\(522\) 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
\(525\) −31.5882 14.5640i −1.37862 0.635625i
\(526\) 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
\(531\) −29.3673 6.56163i −1.27443 0.284751i
\(532\) 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
\(537\) −0.411448 + 3.72837i −0.0177553 + 0.160891i
\(538\) 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
\(543\) −0.950125 0.428947i −0.0407738 0.0184079i
\(544\) 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
\(555\) 0.663252 18.7589i 0.0281535 0.796273i
\(556\) 0 0
\(557\) 0.351406 + 0.351406i 0.0148895 + 0.0148895i 0.714512 0.699623i \(-0.246649\pi\)
−0.699623 + 0.714512i \(0.746649\pi\)
\(558\) 0 0
\(559\) −1.37602 + 0.447097i −0.0581995 + 0.0189102i
\(560\) 0 0
\(561\) −3.07865 65.2209i −0.129981 2.75363i
\(562\) 0 0
\(563\) 9.57089 + 4.87661i 0.403365 + 0.205525i 0.643890 0.765118i \(-0.277320\pi\)
−0.240525 + 0.970643i \(0.577320\pi\)
\(564\) 0 0
\(565\) −14.7544 9.12229i −0.620722 0.383777i
\(566\) 0 0
\(567\) 34.7151 + 10.0790i 1.45790 + 0.423276i
\(568\) 0 0
\(569\) −34.5553 + 25.1059i −1.44863 + 1.05249i −0.462484 + 0.886628i \(0.653042\pi\)
−0.986148 + 0.165865i \(0.946958\pi\)
\(570\) 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
\(573\) 27.0972 + 24.6544i 1.13200 + 1.02995i
\(574\) 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
\(579\) −0.339441 + 1.24100i −0.0141067 + 0.0515743i
\(580\) 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
\(585\) 1.29338 + 2.46586i 0.0534745 + 0.101951i
\(586\) 0 0
\(587\) 0.885671 1.73823i 0.0365556 0.0717444i −0.872006 0.489495i \(-0.837181\pi\)
0.908562 + 0.417750i \(0.137181\pi\)
\(588\) 0 0
\(589\) −12.0635 3.91966i −0.497066 0.161507i
\(590\) 0 0
\(591\) 3.28602 2.63284i 0.135169 0.108300i
\(592\) 0 0
\(593\) 26.3630 26.3630i 1.08260 1.08260i 0.0863319 0.996266i \(-0.472485\pi\)
0.996266 0.0863319i \(-0.0275146\pi\)
\(594\) 0 0
\(595\) 58.3621 35.4464i 2.39261 1.45316i
\(596\) 0 0
\(597\) 40.1002 22.8751i 1.64119 0.936217i
\(598\) 0 0
\(599\) 27.2293 1.11256 0.556280 0.830995i \(-0.312228\pi\)
0.556280 + 0.830995i \(0.312228\pi\)
\(600\) 0 0
\(601\) −0.707518 −0.0288602 −0.0144301 0.999896i \(-0.504593\pi\)
−0.0144301 + 0.999896i \(0.504593\pi\)
\(602\) 0 0
\(603\) 17.0706 + 14.1195i 0.695168 + 0.574989i
\(604\) 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
\(609\) 4.49739 + 5.61315i 0.182243 + 0.227456i
\(610\) 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
\(615\) 15.7521 + 16.9068i 0.635186 + 0.681748i
\(616\) 0 0
\(617\) 30.2739 + 4.79492i 1.21878 + 0.193036i 0.732501 0.680766i \(-0.238353\pi\)
0.486282 + 0.873802i \(0.338353\pi\)
\(618\) 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
\(621\) 0.773820 + 1.57903i 0.0310523 + 0.0633643i
\(622\) 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
\(627\) 26.4230 29.0411i 1.05523 1.15979i
\(628\) 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
\(633\) −14.0335 + 2.90684i −0.557780 + 0.115537i
\(634\) 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
\(639\) 2.55273 + 5.89758i 0.100985 + 0.233305i
\(640\) 0 0
\(641\) −41.9572 + 13.6327i −1.65721 + 0.538460i −0.980284 0.197593i \(-0.936687\pi\)
−0.676924 + 0.736053i \(0.736687\pi\)
\(642\) 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
\(645\) 4.62274 12.6837i 0.182020 0.499420i
\(646\) 0 0
\(647\) −4.83284 30.5133i −0.189998 1.19960i −0.879707 0.475516i \(-0.842261\pi\)
0.689709 0.724087i \(-0.257739\pi\)
\(648\) 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 \(-0.350890\pi\)
0.705127 + 0.709081i \(0.250890\pi\)
\(654\) 0 0
\(655\) −3.87836 6.38569i −0.151540 0.249510i
\(656\) 0 0
\(657\) −2.69214 + 42.8511i −0.105030 + 1.67178i
\(658\) 0 0
\(659\) 3.30930 + 10.1850i 0.128912 + 0.396750i 0.994594 0.103845i \(-0.0331145\pi\)
−0.865682 + 0.500595i \(0.833115\pi\)
\(660\) 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
\(663\) −5.43310 0.599576i −0.211004 0.0232856i
\(664\) 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
\(669\) −18.4964 12.1487i −0.715113 0.469696i
\(670\) 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
\(675\) −25.5582 4.66653i −0.983737 0.179615i
\(676\) 0 0
\(677\) −3.98966 + 2.03283i −0.153335 + 0.0781281i −0.528974 0.848638i \(-0.677423\pi\)
0.375639 + 0.926766i \(0.377423\pi\)
\(678\) 0 0
\(679\) −5.25767 + 7.23656i −0.201771 + 0.277714i
\(680\) 0 0
\(681\) −35.1439 23.0830i −1.34672 0.884543i
\(682\) 0 0
\(683\) −4.57286 + 28.8719i −0.174976 + 1.10475i 0.731297 + 0.682059i \(0.238915\pi\)
−0.906273 + 0.422693i \(0.861085\pi\)
\(684\) 0 0
\(685\) −2.80535 + 4.53739i −0.107187 + 0.173365i
\(686\) 0 0
\(687\) 12.7827 + 1.41065i 0.487691 + 0.0538196i
\(688\) 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
\(693\) −3.74610 + 59.6273i −0.142303 + 2.26505i
\(694\) 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
\(705\) 24.8522 16.7473i 0.935987 0.630738i
\(706\) 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
\(711\) −9.04901 20.9059i −0.339365 0.784034i
\(712\) 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
\(717\) 1.23283 0.255364i 0.0460409 0.00953675i
\(718\) 0 0
\(719\) 13.0340 9.46973i 0.486085 0.353161i −0.317592 0.948228i \(-0.602874\pi\)
0.803677 + 0.595066i \(0.202874\pi\)
\(720\) 0 0
\(721\) −4.38760 3.18778i −0.163403 0.118719i
\(722\) 0 0
\(723\) 16.7542 18.4143i 0.623096 0.684835i
\(724\) 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
\(729\) 26.9869 + 0.840889i 0.999515 + 0.0311440i
\(730\) 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
\(735\) −32.0621 + 14.9338i −1.18263 + 0.550842i
\(736\) 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
\(741\) −2.05522 2.56510i −0.0755005 0.0942314i
\(742\) 0 0
\(743\) 27.1592 27.1592i 0.996375 0.996375i −0.00361798 0.999993i \(-0.501152\pi\)
0.999993 + 0.00361798i \(0.00115164\pi\)
\(744\) 0 0
\(745\) −17.1103 1.41499i −0.626873 0.0518411i
\(746\) 0 0
\(747\) 15.1553 + 12.5353i 0.554504 + 0.458643i
\(748\) 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
\(753\) 16.0641 9.16376i 0.585409 0.333946i
\(754\) 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
\(759\) −2.26807 + 1.81723i −0.0823258 + 0.0659614i
\(760\) 0 0
\(761\) −10.8598 3.52857i −0.393669 0.127911i 0.105492 0.994420i \(-0.466358\pi\)
−0.499161 + 0.866509i \(0.666358\pi\)
\(762\) 0 0
\(763\) 20.7372 40.6990i 0.750736 1.47340i
\(764\) 0 0
\(765\) 35.6347 36.4877i 1.28838 1.31922i
\(766\) 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
\(771\) −6.01005 + 21.9729i −0.216447 + 0.791334i
\(772\) 0 0
\(773\) −15.7994 31.0081i −0.568265 1.11528i −0.979063 0.203556i \(-0.934750\pi\)
0.410799 0.911726i \(-0.365250\pi\)
\(774\) 0 0
\(775\) −12.4099 + 6.19952i −0.445776 + 0.222693i
\(776\) 0 0
\(777\) −24.9388 22.6906i −0.894676 0.814020i
\(778\) 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
\(783\) 4.29658 + 3.22506i 0.153547 + 0.115254i
\(784\) 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
\(789\) 2.12023 + 44.9168i 0.0754820 + 1.59908i
\(790\) 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
\(795\) 18.0096 + 26.7254i 0.638734 + 0.947852i
\(796\) 0 0
\(797\) 5.41838 + 34.2103i 0.191929