Properties

Label 300.2.m.a.61.2
Level $300$
Weight $2$
Character 300.61
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\Q(\zeta_{15})\)
Defining polynomial: \(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 61.2
Root \(-0.104528 - 0.994522i\) of defining polynomial
Character \(\chi\) \(=\) 300.61
Dual form 300.2.m.a.241.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{3} +(2.18720 - 0.464905i) q^{5} +0.547318 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{3} +(2.18720 - 0.464905i) q^{5} +0.547318 q^{7} +(-0.809017 - 0.587785i) q^{9} +(1.08268 - 0.786610i) q^{11} +(-0.244415 - 0.177578i) q^{13} +(0.233733 - 2.22382i) q^{15} +(1.24898 + 3.84398i) q^{17} +(-1.74064 - 5.35713i) q^{19} +(0.169131 - 0.520530i) q^{21} +(-0.198375 + 0.144128i) q^{23} +(4.56773 - 2.03368i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-0.423273 + 1.30270i) q^{29} +(-1.09336 - 3.36501i) q^{31} +(-0.413545 - 1.27276i) q^{33} +(1.19710 - 0.254451i) q^{35} +(1.76988 + 1.28589i) q^{37} +(-0.244415 + 0.177578i) q^{39} +(7.93066 + 5.76196i) q^{41} -8.35963 q^{43} +(-2.04275 - 0.909491i) q^{45} +(-3.23656 + 9.96110i) q^{47} -6.70044 q^{49} +4.04179 q^{51} +(-2.37819 + 7.31931i) q^{53} +(2.00234 - 2.22382i) q^{55} -5.63282 q^{57} +(-3.35916 - 2.44057i) q^{59} +(-1.67981 + 1.22046i) q^{61} +(-0.442790 - 0.321706i) q^{63} +(-0.617142 - 0.274769i) q^{65} +(2.62230 + 8.07061i) q^{67} +(0.0757724 + 0.233204i) q^{69} +(-2.83777 + 8.73377i) q^{71} +(-8.86356 + 6.43975i) q^{73} +(-0.522642 - 4.97261i) q^{75} +(0.592568 - 0.430526i) q^{77} +(4.69177 - 14.4398i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-2.05626 - 6.32850i) q^{83} +(4.51886 + 7.82690i) q^{85} +(1.10814 + 0.805112i) q^{87} +(-4.02780 + 2.92637i) q^{89} +(-0.133773 - 0.0971915i) q^{91} -3.53818 q^{93} +(-6.29768 - 10.9079i) q^{95} +(1.25499 - 3.86248i) q^{97} -1.33826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} + O(q^{10}) \) \( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} - 2q^{11} - 5q^{15} + 7q^{17} + 5q^{19} - 3q^{21} + 7q^{23} + 5q^{25} - 2q^{27} + 27q^{29} - 3q^{31} + 3q^{33} + 20q^{35} - 9q^{37} + 20q^{41} - 68q^{43} - 5q^{45} - 7q^{47} - 8q^{49} - 8q^{51} - 11q^{53} + 5q^{55} - 10q^{57} + 2q^{59} - 14q^{61} + 7q^{63} - 35q^{65} + 28q^{67} + 2q^{69} - 15q^{71} + 6q^{73} + 5q^{75} + 17q^{77} + 24q^{79} - 2q^{81} + 2q^{83} + 10q^{85} - 23q^{87} + 5q^{91} - 18q^{93} + 5q^{95} + 34q^{97} - 2q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

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
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) 0 0
\(5\) 2.18720 0.464905i 0.978148 0.207912i
\(6\) 0 0
\(7\) 0.547318 0.206867 0.103433 0.994636i \(-0.467017\pi\)
0.103433 + 0.994636i \(0.467017\pi\)
\(8\) 0 0
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 0 0
\(11\) 1.08268 0.786610i 0.326439 0.237172i −0.412479 0.910967i \(-0.635337\pi\)
0.738918 + 0.673795i \(0.235337\pi\)
\(12\) 0 0
\(13\) −0.244415 0.177578i −0.0677885 0.0492512i 0.553375 0.832932i \(-0.313340\pi\)
−0.621163 + 0.783681i \(0.713340\pi\)
\(14\) 0 0
\(15\) 0.233733 2.22382i 0.0603495 0.574187i
\(16\) 0 0
\(17\) 1.24898 + 3.84398i 0.302923 + 0.932301i 0.980444 + 0.196798i \(0.0630542\pi\)
−0.677521 + 0.735503i \(0.736946\pi\)
\(18\) 0 0
\(19\) −1.74064 5.35713i −0.399329 1.22901i −0.925538 0.378654i \(-0.876387\pi\)
0.526209 0.850355i \(-0.323613\pi\)
\(20\) 0 0
\(21\) 0.169131 0.520530i 0.0369073 0.113589i
\(22\) 0 0
\(23\) −0.198375 + 0.144128i −0.0413640 + 0.0300527i −0.608275 0.793726i \(-0.708138\pi\)
0.566911 + 0.823779i \(0.308138\pi\)
\(24\) 0 0
\(25\) 4.56773 2.03368i 0.913545 0.406737i
\(26\) 0 0
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) 0 0
\(29\) −0.423273 + 1.30270i −0.0785997 + 0.241905i −0.982634 0.185555i \(-0.940592\pi\)
0.904034 + 0.427460i \(0.140592\pi\)
\(30\) 0 0
\(31\) −1.09336 3.36501i −0.196373 0.604374i −0.999958 0.00918358i \(-0.997077\pi\)
0.803585 0.595190i \(-0.202923\pi\)
\(32\) 0 0
\(33\) −0.413545 1.27276i −0.0719890 0.221559i
\(34\) 0 0
\(35\) 1.19710 0.254451i 0.202346 0.0430100i
\(36\) 0 0
\(37\) 1.76988 + 1.28589i 0.290967 + 0.211400i 0.723687 0.690129i \(-0.242446\pi\)
−0.432720 + 0.901528i \(0.642446\pi\)
\(38\) 0 0
\(39\) −0.244415 + 0.177578i −0.0391377 + 0.0284352i
\(40\) 0 0
\(41\) 7.93066 + 5.76196i 1.23856 + 0.899868i 0.997502 0.0706425i \(-0.0225049\pi\)
0.241060 + 0.970510i \(0.422505\pi\)
\(42\) 0 0
\(43\) −8.35963 −1.27483 −0.637415 0.770520i \(-0.719996\pi\)
−0.637415 + 0.770520i \(0.719996\pi\)
\(44\) 0 0
\(45\) −2.04275 0.909491i −0.304515 0.135579i
\(46\) 0 0
\(47\) −3.23656 + 9.96110i −0.472100 + 1.45298i 0.377729 + 0.925916i \(0.376705\pi\)
−0.849829 + 0.527059i \(0.823295\pi\)
\(48\) 0 0
\(49\) −6.70044 −0.957206
\(50\) 0 0
\(51\) 4.04179 0.565964
\(52\) 0 0
\(53\) −2.37819 + 7.31931i −0.326669 + 1.00538i 0.644012 + 0.765015i \(0.277269\pi\)
−0.970682 + 0.240369i \(0.922731\pi\)
\(54\) 0 0
\(55\) 2.00234 2.22382i 0.269995 0.299860i
\(56\) 0 0
\(57\) −5.63282 −0.746085
\(58\) 0 0
\(59\) −3.35916 2.44057i −0.437325 0.317735i 0.347246 0.937774i \(-0.387117\pi\)
−0.784571 + 0.620039i \(0.787117\pi\)
\(60\) 0 0
\(61\) −1.67981 + 1.22046i −0.215078 + 0.156263i −0.690108 0.723706i \(-0.742437\pi\)
0.475030 + 0.879969i \(0.342437\pi\)
\(62\) 0 0
\(63\) −0.442790 0.321706i −0.0557863 0.0405311i
\(64\) 0 0
\(65\) −0.617142 0.274769i −0.0765470 0.0340809i
\(66\) 0 0
\(67\) 2.62230 + 8.07061i 0.320365 + 0.985982i 0.973490 + 0.228732i \(0.0734578\pi\)
−0.653125 + 0.757251i \(0.726542\pi\)
\(68\) 0 0
\(69\) 0.0757724 + 0.233204i 0.00912193 + 0.0280744i
\(70\) 0 0
\(71\) −2.83777 + 8.73377i −0.336782 + 1.03651i 0.629056 + 0.777360i \(0.283442\pi\)
−0.965838 + 0.259148i \(0.916558\pi\)
\(72\) 0 0
\(73\) −8.86356 + 6.43975i −1.03740 + 0.753716i −0.969777 0.243995i \(-0.921542\pi\)
−0.0676248 + 0.997711i \(0.521542\pi\)
\(74\) 0 0
\(75\) −0.522642 4.97261i −0.0603495 0.574187i
\(76\) 0 0
\(77\) 0.592568 0.430526i 0.0675294 0.0490630i
\(78\) 0 0
\(79\) 4.69177 14.4398i 0.527866 1.62460i −0.230713 0.973022i \(-0.574106\pi\)
0.758578 0.651582i \(-0.225894\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 0 0
\(83\) −2.05626 6.32850i −0.225703 0.694643i −0.998219 0.0596483i \(-0.981002\pi\)
0.772516 0.634995i \(-0.218998\pi\)
\(84\) 0 0
\(85\) 4.51886 + 7.82690i 0.490140 + 0.848947i
\(86\) 0 0
\(87\) 1.10814 + 0.805112i 0.118805 + 0.0863171i
\(88\) 0 0
\(89\) −4.02780 + 2.92637i −0.426946 + 0.310194i −0.780427 0.625247i \(-0.784998\pi\)
0.353481 + 0.935442i \(0.384998\pi\)
\(90\) 0 0
\(91\) −0.133773 0.0971915i −0.0140232 0.0101884i
\(92\) 0 0
\(93\) −3.53818 −0.366892
\(94\) 0 0
\(95\) −6.29768 10.9079i −0.646128 1.11913i
\(96\) 0 0
\(97\) 1.25499 3.86248i 0.127425 0.392175i −0.866910 0.498465i \(-0.833897\pi\)
0.994335 + 0.106290i \(0.0338972\pi\)
\(98\) 0 0
\(99\) −1.33826 −0.134500
\(100\) 0 0
\(101\) 18.4489 1.83573 0.917865 0.396892i \(-0.129911\pi\)
0.917865 + 0.396892i \(0.129911\pi\)
\(102\) 0 0
\(103\) −4.54762 + 13.9961i −0.448090 + 1.37908i 0.430969 + 0.902367i \(0.358172\pi\)
−0.879059 + 0.476713i \(0.841828\pi\)
\(104\) 0 0
\(105\) 0.127926 1.21714i 0.0124843 0.118780i
\(106\) 0 0
\(107\) −5.10528 −0.493546 −0.246773 0.969073i \(-0.579370\pi\)
−0.246773 + 0.969073i \(0.579370\pi\)
\(108\) 0 0
\(109\) −3.82331 2.77780i −0.366207 0.266065i 0.389429 0.921056i \(-0.372672\pi\)
−0.755636 + 0.654991i \(0.772672\pi\)
\(110\) 0 0
\(111\) 1.76988 1.28589i 0.167990 0.122052i
\(112\) 0 0
\(113\) −3.34799 2.43246i −0.314952 0.228826i 0.419066 0.907956i \(-0.362357\pi\)
−0.734019 + 0.679129i \(0.762357\pi\)
\(114\) 0 0
\(115\) −0.366881 + 0.407462i −0.0342118 + 0.0379961i
\(116\) 0 0
\(117\) 0.0933582 + 0.287327i 0.00863097 + 0.0265634i
\(118\) 0 0
\(119\) 0.683591 + 2.10388i 0.0626647 + 0.192862i
\(120\) 0 0
\(121\) −2.84576 + 8.75833i −0.258705 + 0.796212i
\(122\) 0 0
\(123\) 7.93066 5.76196i 0.715084 0.519539i
\(124\) 0 0
\(125\) 9.04508 6.57164i 0.809017 0.587785i
\(126\) 0 0
\(127\) 10.2568 7.45200i 0.910144 0.661258i −0.0309074 0.999522i \(-0.509840\pi\)
0.941051 + 0.338264i \(0.109840\pi\)
\(128\) 0 0
\(129\) −2.58327 + 7.95048i −0.227444 + 0.700000i
\(130\) 0 0
\(131\) −3.81046 11.7274i −0.332921 1.02463i −0.967737 0.251963i \(-0.918924\pi\)
0.634815 0.772664i \(-0.281076\pi\)
\(132\) 0 0
\(133\) −0.952682 2.93205i −0.0826080 0.254241i
\(134\) 0 0
\(135\) −1.49622 + 1.66172i −0.128774 + 0.143018i
\(136\) 0 0
\(137\) −8.67508 6.30281i −0.741162 0.538486i 0.151913 0.988394i \(-0.451457\pi\)
−0.893075 + 0.449908i \(0.851457\pi\)
\(138\) 0 0
\(139\) 11.0632 8.03786i 0.938365 0.681762i −0.00966163 0.999953i \(-0.503075\pi\)
0.948027 + 0.318191i \(0.103075\pi\)
\(140\) 0 0
\(141\) 8.47341 + 6.15630i 0.713590 + 0.518454i
\(142\) 0 0
\(143\) −0.404307 −0.0338098
\(144\) 0 0
\(145\) −0.320153 + 3.04605i −0.0265872 + 0.252961i
\(146\) 0 0
\(147\) −2.07055 + 6.37250i −0.170776 + 0.525595i
\(148\) 0 0
\(149\) 8.88176 0.727622 0.363811 0.931473i \(-0.381475\pi\)
0.363811 + 0.931473i \(0.381475\pi\)
\(150\) 0 0
\(151\) 2.68310 0.218348 0.109174 0.994023i \(-0.465179\pi\)
0.109174 + 0.994023i \(0.465179\pi\)
\(152\) 0 0
\(153\) 1.24898 3.84398i 0.100974 0.310767i
\(154\) 0 0
\(155\) −3.95581 6.85166i −0.317738 0.550338i
\(156\) 0 0
\(157\) 11.7576 0.938355 0.469178 0.883104i \(-0.344550\pi\)
0.469178 + 0.883104i \(0.344550\pi\)
\(158\) 0 0
\(159\) 6.22618 + 4.52358i 0.493768 + 0.358743i
\(160\) 0 0
\(161\) −0.108574 + 0.0788837i −0.00855684 + 0.00621691i
\(162\) 0 0
\(163\) 14.8153 + 10.7639i 1.16042 + 0.843097i 0.989831 0.142245i \(-0.0454322\pi\)
0.170592 + 0.985342i \(0.445432\pi\)
\(164\) 0 0
\(165\) −1.49622 2.59153i −0.116481 0.201750i
\(166\) 0 0
\(167\) 1.36097 + 4.18862i 0.105315 + 0.324125i 0.989804 0.142435i \(-0.0454931\pi\)
−0.884489 + 0.466560i \(0.845493\pi\)
\(168\) 0 0
\(169\) −3.98902 12.2769i −0.306847 0.944379i
\(170\) 0 0
\(171\) −1.74064 + 5.35713i −0.133110 + 0.409670i
\(172\) 0 0
\(173\) 12.8882 9.36385i 0.979875 0.711921i 0.0221940 0.999754i \(-0.492935\pi\)
0.957681 + 0.287833i \(0.0929349\pi\)
\(174\) 0 0
\(175\) 2.50000 1.11307i 0.188982 0.0841403i
\(176\) 0 0
\(177\) −3.35916 + 2.44057i −0.252490 + 0.183445i
\(178\) 0 0
\(179\) 1.16493 3.58528i 0.0870707 0.267976i −0.898035 0.439923i \(-0.855006\pi\)
0.985106 + 0.171947i \(0.0550057\pi\)
\(180\) 0 0
\(181\) −8.24669 25.3807i −0.612971 1.88653i −0.427967 0.903794i \(-0.640770\pi\)
−0.185004 0.982738i \(-0.559230\pi\)
\(182\) 0 0
\(183\) 0.641631 + 1.97474i 0.0474308 + 0.145977i
\(184\) 0 0
\(185\) 4.46891 + 1.98969i 0.328561 + 0.146285i
\(186\) 0 0
\(187\) 4.37595 + 3.17932i 0.320001 + 0.232495i
\(188\) 0 0
\(189\) −0.442790 + 0.321706i −0.0322082 + 0.0234006i
\(190\) 0 0
\(191\) −3.74803 2.72310i −0.271198 0.197037i 0.443871 0.896091i \(-0.353605\pi\)
−0.715069 + 0.699054i \(0.753605\pi\)
\(192\) 0 0
\(193\) −20.7440 −1.49319 −0.746594 0.665280i \(-0.768312\pi\)
−0.746594 + 0.665280i \(0.768312\pi\)
\(194\) 0 0
\(195\) −0.452029 + 0.502029i −0.0323704 + 0.0359510i
\(196\) 0 0
\(197\) 6.34529 19.5288i 0.452083 1.39137i −0.422443 0.906390i \(-0.638827\pi\)
0.874526 0.484979i \(-0.161173\pi\)
\(198\) 0 0
\(199\) 5.91437 0.419259 0.209629 0.977781i \(-0.432774\pi\)
0.209629 + 0.977781i \(0.432774\pi\)
\(200\) 0 0
\(201\) 8.48594 0.598552
\(202\) 0 0
\(203\) −0.231665 + 0.712991i −0.0162597 + 0.0500421i
\(204\) 0 0
\(205\) 20.0247 + 8.91559i 1.39859 + 0.622692i
\(206\) 0 0
\(207\) 0.245205 0.0170429
\(208\) 0 0
\(209\) −6.09852 4.43083i −0.421843 0.306487i
\(210\) 0 0
\(211\) −18.5512 + 13.4782i −1.27712 + 0.927880i −0.999462 0.0328013i \(-0.989557\pi\)
−0.277655 + 0.960681i \(0.589557\pi\)
\(212\) 0 0
\(213\) 7.42939 + 5.39777i 0.509053 + 0.369849i
\(214\) 0 0
\(215\) −18.2842 + 3.88643i −1.24697 + 0.265052i
\(216\) 0 0
\(217\) −0.598415 1.84173i −0.0406230 0.125025i
\(218\) 0 0
\(219\) 3.38558 + 10.4197i 0.228776 + 0.704101i
\(220\) 0 0
\(221\) 0.377335 1.16132i 0.0253823 0.0781186i
\(222\) 0 0
\(223\) 10.3148 7.49414i 0.690730 0.501845i −0.186170 0.982518i \(-0.559607\pi\)
0.876900 + 0.480673i \(0.159607\pi\)
\(224\) 0 0
\(225\) −4.89074 1.03956i −0.326049 0.0693039i
\(226\) 0 0
\(227\) −8.92301 + 6.48294i −0.592241 + 0.430288i −0.843116 0.537731i \(-0.819281\pi\)
0.250876 + 0.968019i \(0.419281\pi\)
\(228\) 0 0
\(229\) −7.13214 + 21.9505i −0.471305 + 1.45053i 0.379571 + 0.925163i \(0.376072\pi\)
−0.850876 + 0.525366i \(0.823928\pi\)
\(230\) 0 0
\(231\) −0.226341 0.696606i −0.0148921 0.0458333i
\(232\) 0 0
\(233\) −9.05055 27.8547i −0.592921 1.82482i −0.564814 0.825218i \(-0.691052\pi\)
−0.0281067 0.999605i \(-0.508948\pi\)
\(234\) 0 0
\(235\) −2.44805 + 23.2916i −0.159693 + 1.51938i
\(236\) 0 0
\(237\) −12.2832 8.92428i −0.797881 0.579694i
\(238\) 0 0
\(239\) −8.57443 + 6.22969i −0.554634 + 0.402965i −0.829491 0.558520i \(-0.811369\pi\)
0.274857 + 0.961485i \(0.411369\pi\)
\(240\) 0 0
\(241\) −15.3888 11.1806i −0.991282 0.720208i −0.0310802 0.999517i \(-0.509895\pi\)
−0.960201 + 0.279309i \(0.909895\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −14.6552 + 3.11507i −0.936289 + 0.199014i
\(246\) 0 0
\(247\) −0.525870 + 1.61846i −0.0334603 + 0.102980i
\(248\) 0 0
\(249\) −6.65418 −0.421692
\(250\) 0 0
\(251\) 0.0370816 0.00234057 0.00117028 0.999999i \(-0.499627\pi\)
0.00117028 + 0.999999i \(0.499627\pi\)
\(252\) 0 0
\(253\) −0.101403 + 0.312087i −0.00637517 + 0.0196208i
\(254\) 0 0
\(255\) 8.84023 1.87905i 0.553597 0.117671i
\(256\) 0 0
\(257\) −10.0237 −0.625262 −0.312631 0.949875i \(-0.601210\pi\)
−0.312631 + 0.949875i \(0.601210\pi\)
\(258\) 0 0
\(259\) 0.968688 + 0.703793i 0.0601913 + 0.0437316i
\(260\) 0 0
\(261\) 1.10814 0.805112i 0.0685923 0.0498352i
\(262\) 0 0
\(263\) 10.3407 + 7.51296i 0.637635 + 0.463269i 0.859037 0.511914i \(-0.171063\pi\)
−0.221402 + 0.975183i \(0.571063\pi\)
\(264\) 0 0
\(265\) −1.79880 + 17.1145i −0.110500 + 1.05133i
\(266\) 0 0
\(267\) 1.53848 + 4.73496i 0.0941536 + 0.289775i
\(268\) 0 0
\(269\) 6.58562 + 20.2685i 0.401533 + 1.23579i 0.923756 + 0.382981i \(0.125103\pi\)
−0.522224 + 0.852809i \(0.674897\pi\)
\(270\) 0 0
\(271\) −4.14194 + 12.7476i −0.251605 + 0.774361i 0.742875 + 0.669431i \(0.233462\pi\)
−0.994480 + 0.104930i \(0.966538\pi\)
\(272\) 0 0
\(273\) −0.133773 + 0.0971915i −0.00809629 + 0.00588230i
\(274\) 0 0
\(275\) 3.34565 5.79484i 0.201750 0.349442i
\(276\) 0 0
\(277\) 15.2678 11.0927i 0.917354 0.666496i −0.0255104 0.999675i \(-0.508121\pi\)
0.942864 + 0.333178i \(0.108121\pi\)
\(278\) 0 0
\(279\) −1.09336 + 3.36501i −0.0654576 + 0.201458i
\(280\) 0 0
\(281\) −5.37674 16.5479i −0.320750 0.987166i −0.973323 0.229440i \(-0.926310\pi\)
0.652573 0.757726i \(-0.273690\pi\)
\(282\) 0 0
\(283\) 7.31371 + 22.5093i 0.434755 + 1.33804i 0.893338 + 0.449386i \(0.148357\pi\)
−0.458583 + 0.888652i \(0.651643\pi\)
\(284\) 0 0
\(285\) −12.3201 + 2.61872i −0.729781 + 0.155120i
\(286\) 0 0
\(287\) 4.34060 + 3.15363i 0.256217 + 0.186153i
\(288\) 0 0
\(289\) 0.537103 0.390228i 0.0315943 0.0229546i
\(290\) 0 0
\(291\) −3.28562 2.38714i −0.192606 0.139937i
\(292\) 0 0
\(293\) 19.0317 1.11184 0.555921 0.831235i \(-0.312366\pi\)
0.555921 + 0.831235i \(0.312366\pi\)
\(294\) 0 0
\(295\) −8.48180 3.77634i −0.493829 0.219867i
\(296\) 0 0
\(297\) −0.413545 + 1.27276i −0.0239963 + 0.0738531i
\(298\) 0 0
\(299\) 0.0740796 0.00428414
\(300\) 0 0
\(301\) −4.57537 −0.263720
\(302\) 0 0
\(303\) 5.70101 17.5459i 0.327515 1.00799i
\(304\) 0 0
\(305\) −3.10670 + 3.45034i −0.177889 + 0.197566i
\(306\) 0 0
\(307\) −0.669899 −0.0382332 −0.0191166 0.999817i \(-0.506085\pi\)
−0.0191166 + 0.999817i \(0.506085\pi\)
\(308\) 0 0
\(309\) 11.9058 + 8.65009i 0.677299 + 0.492086i
\(310\) 0 0
\(311\) −25.5534 + 18.5656i −1.44900 + 1.05276i −0.462934 + 0.886393i \(0.653203\pi\)
−0.986064 + 0.166366i \(0.946797\pi\)
\(312\) 0 0
\(313\) 1.17726 + 0.855327i 0.0665425 + 0.0483459i 0.620559 0.784160i \(-0.286906\pi\)
−0.554017 + 0.832506i \(0.686906\pi\)
\(314\) 0 0
\(315\) −1.11803 0.497781i −0.0629941 0.0280468i
\(316\) 0 0
\(317\) −4.95857 15.2609i −0.278501 0.857138i −0.988272 0.152705i \(-0.951202\pi\)
0.709771 0.704433i \(-0.248798\pi\)
\(318\) 0 0
\(319\) 0.566449 + 1.74335i 0.0317151 + 0.0976089i
\(320\) 0 0
\(321\) −1.57762 + 4.85541i −0.0880541 + 0.271003i
\(322\) 0 0
\(323\) 18.4186 13.3819i 1.02484 0.744590i
\(324\) 0 0
\(325\) −1.47756 0.314065i −0.0819601 0.0174212i
\(326\) 0 0
\(327\) −3.82331 + 2.77780i −0.211430 + 0.153613i
\(328\) 0 0
\(329\) −1.77143 + 5.45189i −0.0976619 + 0.300572i
\(330\) 0 0
\(331\) −8.31262 25.5836i −0.456903 1.40620i −0.868887 0.495011i \(-0.835164\pi\)
0.411984 0.911191i \(-0.364836\pi\)
\(332\) 0 0
\(333\) −0.676034 2.08062i −0.0370464 0.114017i
\(334\) 0 0
\(335\) 9.48757 + 16.4330i 0.518361 + 0.897828i
\(336\) 0 0
\(337\) −1.10171 0.800436i −0.0600137 0.0436025i 0.557374 0.830262i \(-0.311809\pi\)
−0.617388 + 0.786659i \(0.711809\pi\)
\(338\) 0 0
\(339\) −3.34799 + 2.43246i −0.181838 + 0.132113i
\(340\) 0 0
\(341\) −3.83070 2.78317i −0.207444 0.150717i
\(342\) 0 0
\(343\) −7.49850 −0.404881
\(344\) 0 0
\(345\) 0.274147 + 0.474837i 0.0147596 + 0.0255644i
\(346\) 0 0
\(347\) −0.712835 + 2.19388i −0.0382670 + 0.117774i −0.968365 0.249537i \(-0.919722\pi\)
0.930098 + 0.367311i \(0.119722\pi\)
\(348\) 0 0
\(349\) 2.35292 0.125949 0.0629744 0.998015i \(-0.479941\pi\)
0.0629744 + 0.998015i \(0.479941\pi\)
\(350\) 0 0
\(351\) 0.302113 0.0161256
\(352\) 0 0
\(353\) −9.55559 + 29.4091i −0.508593 + 1.56529i 0.286053 + 0.958214i \(0.407657\pi\)
−0.794646 + 0.607073i \(0.792343\pi\)
\(354\) 0 0
\(355\) −2.14642 + 20.4218i −0.113920 + 1.08388i
\(356\) 0 0
\(357\) 2.21215 0.117079
\(358\) 0 0
\(359\) 15.8812 + 11.5383i 0.838176 + 0.608971i 0.921861 0.387522i \(-0.126669\pi\)
−0.0836845 + 0.996492i \(0.526669\pi\)
\(360\) 0 0
\(361\) −10.2977 + 7.48170i −0.541983 + 0.393774i
\(362\) 0 0
\(363\) 7.45028 + 5.41295i 0.391038 + 0.284106i
\(364\) 0 0
\(365\) −16.3926 + 18.2058i −0.858025 + 0.952934i
\(366\) 0 0
\(367\) −9.94076 30.5945i −0.518903 1.59702i −0.776066 0.630652i \(-0.782788\pi\)
0.257163 0.966368i \(-0.417212\pi\)
\(368\) 0 0
\(369\) −3.02924 9.32306i −0.157696 0.485339i
\(370\) 0 0
\(371\) −1.30163 + 4.00599i −0.0675770 + 0.207981i
\(372\) 0 0
\(373\) 11.0291 8.01309i 0.571064 0.414902i −0.264428 0.964406i \(-0.585183\pi\)
0.835492 + 0.549503i \(0.185183\pi\)
\(374\) 0 0
\(375\) −3.45492 10.6331i −0.178411 0.549093i
\(376\) 0 0
\(377\) 0.334784 0.243235i 0.0172423 0.0125272i
\(378\) 0 0
\(379\) 7.62106 23.4552i 0.391467 1.20481i −0.540211 0.841529i \(-0.681656\pi\)
0.931679 0.363283i \(-0.118344\pi\)
\(380\) 0 0
\(381\) −3.91775 12.0576i −0.200712 0.617729i
\(382\) 0 0
\(383\) −3.79232 11.6716i −0.193779 0.596389i −0.999989 0.00475994i \(-0.998485\pi\)
0.806210 0.591629i \(-0.201515\pi\)
\(384\) 0 0
\(385\) 1.09591 1.21714i 0.0558530 0.0620310i
\(386\) 0 0
\(387\) 6.76308 + 4.91366i 0.343787 + 0.249776i
\(388\) 0 0
\(389\) −9.39823 + 6.82822i −0.476509 + 0.346204i −0.799973 0.600036i \(-0.795153\pi\)
0.323463 + 0.946241i \(0.395153\pi\)
\(390\) 0 0
\(391\) −0.801790 0.582535i −0.0405483 0.0294600i
\(392\) 0 0
\(393\) −12.3309 −0.622012
\(394\) 0 0
\(395\) 3.54874 33.7640i 0.178556 1.69885i
\(396\) 0 0
\(397\) 5.26383 16.2004i 0.264184 0.813075i −0.727696 0.685900i \(-0.759409\pi\)
0.991880 0.127175i \(-0.0405911\pi\)
\(398\) 0 0
\(399\) −3.08294 −0.154340
\(400\) 0 0
\(401\) 32.2134 1.60866 0.804330 0.594183i \(-0.202524\pi\)
0.804330 + 0.594183i \(0.202524\pi\)
\(402\) 0 0
\(403\) −0.330318 + 1.01661i −0.0164543 + 0.0506412i
\(404\) 0 0
\(405\) 1.11803 + 1.93649i 0.0555556 + 0.0962250i
\(406\) 0 0
\(407\) 2.92770 0.145121
\(408\) 0 0
\(409\) 5.64632 + 4.10229i 0.279193 + 0.202845i 0.718565 0.695460i \(-0.244799\pi\)
−0.439373 + 0.898305i \(0.644799\pi\)
\(410\) 0 0
\(411\) −8.67508 + 6.30281i −0.427910 + 0.310895i
\(412\) 0 0
\(413\) −1.83853 1.33577i −0.0904681 0.0657289i
\(414\) 0 0
\(415\) −7.43960 12.8858i −0.365196 0.632537i
\(416\) 0 0
\(417\) −4.22575 13.0055i −0.206936 0.636883i
\(418\) 0 0
\(419\) 8.60796 + 26.4926i 0.420526 + 1.29425i 0.907214 + 0.420670i \(0.138205\pi\)
−0.486687 + 0.873576i \(0.661795\pi\)
\(420\) 0 0
\(421\) 2.65766 8.17943i 0.129526 0.398641i −0.865172 0.501475i \(-0.832791\pi\)
0.994699 + 0.102834i \(0.0327910\pi\)
\(422\) 0 0
\(423\) 8.47341 6.15630i 0.411991 0.299329i
\(424\) 0 0
\(425\) 13.5224 + 15.0182i 0.655935 + 0.728489i
\(426\) 0 0
\(427\) −0.919392 + 0.667977i −0.0444925 + 0.0323257i
\(428\) 0 0
\(429\) −0.124938 + 0.384518i −0.00603204 + 0.0185647i
\(430\) 0 0
\(431\) 0.0559037 + 0.172054i 0.00269278 + 0.00828754i 0.952394 0.304870i \(-0.0986131\pi\)
−0.949701 + 0.313158i \(0.898613\pi\)
\(432\) 0 0
\(433\) −9.71549 29.9012i −0.466897 1.43696i −0.856581 0.516012i \(-0.827416\pi\)
0.389684 0.920948i \(-0.372584\pi\)
\(434\) 0 0
\(435\) 2.79803 + 1.24576i 0.134155 + 0.0597298i
\(436\) 0 0
\(437\) 1.11741 + 0.811845i 0.0534529 + 0.0388358i
\(438\) 0 0
\(439\) 13.6019 9.88233i 0.649181 0.471658i −0.213811 0.976875i \(-0.568588\pi\)
0.862992 + 0.505217i \(0.168588\pi\)
\(440\) 0 0
\(441\) 5.42077 + 3.93842i 0.258132 + 0.187544i
\(442\) 0 0
\(443\) 36.1952 1.71969 0.859843 0.510559i \(-0.170561\pi\)
0.859843 + 0.510559i \(0.170561\pi\)
\(444\) 0 0
\(445\) −7.44914 + 8.27311i −0.353123 + 0.392183i
\(446\) 0 0
\(447\) 2.74461 8.44705i 0.129816 0.399532i
\(448\) 0 0
\(449\) 28.3299 1.33697 0.668486 0.743725i \(-0.266943\pi\)
0.668486 + 0.743725i \(0.266943\pi\)
\(450\) 0 0
\(451\) 13.1188 0.617738
\(452\) 0 0
\(453\) 0.829124 2.55178i 0.0389557 0.119893i
\(454\) 0 0
\(455\) −0.337773 0.150386i −0.0158350 0.00705022i
\(456\) 0 0
\(457\) 16.5396 0.773691 0.386846 0.922144i \(-0.373565\pi\)
0.386846 + 0.922144i \(0.373565\pi\)
\(458\) 0 0
\(459\) −3.26988 2.37571i −0.152625 0.110889i
\(460\) 0 0
\(461\) −0.351142 + 0.255120i −0.0163543 + 0.0118821i −0.595932 0.803035i \(-0.703217\pi\)
0.579578 + 0.814917i \(0.303217\pi\)
\(462\) 0 0
\(463\) 16.1500 + 11.7337i 0.750556 + 0.545311i 0.895999 0.444056i \(-0.146461\pi\)
−0.145443 + 0.989367i \(0.546461\pi\)
\(464\) 0 0
\(465\) −7.73873 + 1.64492i −0.358875 + 0.0762812i
\(466\) 0 0
\(467\) −1.91815 5.90347i −0.0887615 0.273180i 0.896816 0.442403i \(-0.145874\pi\)
−0.985578 + 0.169223i \(0.945874\pi\)
\(468\) 0 0
\(469\) 1.43523 + 4.41719i 0.0662729 + 0.203967i
\(470\) 0 0
\(471\) 3.63328 11.1821i 0.167413 0.515244i
\(472\) 0 0
\(473\) −9.05077 + 6.57577i −0.416155 + 0.302354i
\(474\) 0 0
\(475\) −18.8455 20.9300i −0.864689 0.960334i
\(476\) 0 0
\(477\) 6.22618 4.52358i 0.285077 0.207121i
\(478\) 0 0
\(479\) 7.25191 22.3191i 0.331348 1.01978i −0.637145 0.770744i \(-0.719885\pi\)
0.968493 0.249041i \(-0.0801153\pi\)
\(480\) 0 0
\(481\) −0.204239 0.628583i −0.00931250 0.0286609i
\(482\) 0 0
\(483\) 0.0414716 + 0.127637i 0.00188702 + 0.00580766i
\(484\) 0 0
\(485\) 0.949247 9.03148i 0.0431031 0.410098i
\(486\) 0 0
\(487\) 2.70709 + 1.96682i 0.122670 + 0.0891250i 0.647429 0.762126i \(-0.275844\pi\)
−0.524759 + 0.851251i \(0.675844\pi\)
\(488\) 0 0
\(489\) 14.8153 10.7639i 0.669971 0.486762i
\(490\) 0 0
\(491\) 0.442522 + 0.321511i 0.0199708 + 0.0145096i 0.597726 0.801701i \(-0.296071\pi\)
−0.577755 + 0.816210i \(0.696071\pi\)
\(492\) 0 0
\(493\) −5.53620 −0.249338
\(494\) 0 0
\(495\) −2.92705 + 0.622164i −0.131561 + 0.0279642i
\(496\) 0 0
\(497\) −1.55316 + 4.78015i −0.0696690 + 0.214419i
\(498\) 0 0
\(499\) −8.08164 −0.361784 −0.180892 0.983503i \(-0.557898\pi\)
−0.180892 + 0.983503i \(0.557898\pi\)
\(500\) 0 0
\(501\) 4.40418 0.196764
\(502\) 0 0
\(503\) −8.74922 + 26.9273i −0.390109 + 1.20063i 0.542597 + 0.839993i \(0.317441\pi\)
−0.932706 + 0.360638i \(0.882559\pi\)
\(504\) 0 0
\(505\) 40.3514 8.57696i 1.79562 0.381670i
\(506\) 0 0
\(507\) −12.9087 −0.573297
\(508\) 0 0
\(509\) −4.61968 3.35639i −0.204764 0.148770i 0.480678 0.876897i \(-0.340391\pi\)
−0.685441 + 0.728128i \(0.740391\pi\)
\(510\) 0 0
\(511\) −4.85119 + 3.52459i −0.214604 + 0.155919i
\(512\) 0 0
\(513\) 4.55705 + 3.31089i 0.201198 + 0.146179i
\(514\) 0 0
\(515\) −3.43971 + 32.7266i −0.151572 + 1.44211i
\(516\) 0 0
\(517\) 4.33136 + 13.3305i 0.190493 + 0.586277i
\(518\) 0 0
\(519\) −4.92287 15.1510i −0.216090 0.665056i
\(520\) 0 0
\(521\) −7.87683 + 24.2424i −0.345090 + 1.06208i 0.616445 + 0.787398i \(0.288572\pi\)
−0.961536 + 0.274681i \(0.911428\pi\)
\(522\) 0 0
\(523\) −2.29098 + 1.66449i −0.100177 + 0.0727832i −0.636746 0.771073i \(-0.719720\pi\)
0.536569 + 0.843857i \(0.319720\pi\)
\(524\) 0 0
\(525\) −0.286052 2.72160i −0.0124843 0.118780i
\(526\) 0 0
\(527\) 11.5694 8.40568i 0.503972 0.366157i
\(528\) 0 0
\(529\) −7.08881 + 21.8171i −0.308209 + 0.948570i
\(530\) 0 0
\(531\) 1.28308 + 3.94893i 0.0556811 + 0.171369i
\(532\) 0 0
\(533\) −0.915175 2.81662i −0.0396406 0.122001i
\(534\) 0 0
\(535\) −11.1663 + 2.37347i −0.482761 + 0.102614i
\(536\) 0 0
\(537\) −3.04982 2.21582i −0.131609 0.0956198i
\(538\) 0 0
\(539\) −7.25441 + 5.27064i −0.312470 + 0.227022i
\(540\) 0 0
\(541\) −3.64130 2.64556i −0.156552 0.113742i 0.506752 0.862092i \(-0.330846\pi\)
−0.663303 + 0.748351i \(0.730846\pi\)
\(542\) 0 0
\(543\) −26.6868 −1.14524
\(544\) 0 0
\(545\) −9.65378 4.29814i −0.413522 0.184112i
\(546\) 0 0
\(547\) 2.94045 9.04979i 0.125725 0.386941i −0.868308 0.496026i \(-0.834792\pi\)
0.994032 + 0.109085i \(0.0347921\pi\)
\(548\) 0 0
\(549\) 2.07636 0.0886170
\(550\) 0 0
\(551\) 7.71549 0.328691
\(552\) 0 0
\(553\) 2.56789 7.90316i 0.109198 0.336077i
\(554\) 0 0
\(555\) 3.27327 3.63534i 0.138943 0.154311i
\(556\) 0 0
\(557\) 25.5173 1.08120 0.540601 0.841279i \(-0.318197\pi\)
0.540601 + 0.841279i \(0.318197\pi\)
\(558\) 0 0
\(559\) 2.04322 + 1.48448i 0.0864189 + 0.0627870i
\(560\) 0 0
\(561\) 4.37595 3.17932i 0.184753 0.134231i
\(562\) 0 0
\(563\) −11.1180 8.07772i −0.468569 0.340435i 0.328314 0.944569i \(-0.393520\pi\)
−0.796883 + 0.604133i \(0.793520\pi\)
\(564\) 0 0
\(565\) −8.45360 3.76378i −0.355645 0.158344i
\(566\) 0 0
\(567\) 0.169131 + 0.520530i 0.00710282 + 0.0218602i
\(568\) 0 0
\(569\) −8.75873 26.9566i −0.367185 1.13008i −0.948601 0.316473i \(-0.897501\pi\)
0.581416 0.813606i \(-0.302499\pi\)
\(570\) 0 0
\(571\) −0.603552 + 1.85754i −0.0252579 + 0.0777357i −0.962891 0.269891i \(-0.913012\pi\)
0.937633 + 0.347627i \(0.113012\pi\)
\(572\) 0 0
\(573\) −3.74803 + 2.72310i −0.156576 + 0.113759i
\(574\) 0 0
\(575\) −0.613012 + 1.06177i −0.0255644 + 0.0442788i
\(576\) 0 0
\(577\) −34.6572 + 25.1799i −1.44280 + 1.04825i −0.455350 + 0.890313i \(0.650486\pi\)
−0.987448 + 0.157942i \(0.949514\pi\)
\(578\) 0 0
\(579\) −6.41026 + 19.7287i −0.266401 + 0.819898i
\(580\) 0 0
\(581\) −1.12543 3.46370i −0.0466905 0.143699i
\(582\) 0 0
\(583\) 3.18264 + 9.79515i 0.131811 + 0.405674i
\(584\) 0 0
\(585\) 0.337773 + 0.585040i 0.0139652 + 0.0241884i
\(586\) 0 0
\(587\) 1.59845 + 1.16134i 0.0659751 + 0.0479337i 0.620284 0.784377i \(-0.287017\pi\)
−0.554309 + 0.832311i \(0.687017\pi\)
\(588\) 0 0
\(589\) −16.1237 + 11.7145i −0.664364 + 0.482688i
\(590\) 0 0
\(591\) −16.6122 12.0695i −0.683334 0.496471i
\(592\) 0 0
\(593\) −17.3986 −0.714475 −0.357237 0.934014i \(-0.616281\pi\)
−0.357237 + 0.934014i \(0.616281\pi\)
\(594\) 0 0
\(595\) 2.47326 + 4.28381i 0.101394 + 0.175619i
\(596\) 0 0
\(597\) 1.82764 5.62490i 0.0748004 0.230212i
\(598\) 0 0
\(599\) −3.17298 −0.129644 −0.0648222 0.997897i \(-0.520648\pi\)
−0.0648222 + 0.997897i \(0.520648\pi\)
\(600\) 0 0
\(601\) 32.1659 1.31207 0.656037 0.754729i \(-0.272232\pi\)
0.656037 + 0.754729i \(0.272232\pi\)
\(602\) 0 0
\(603\) 2.62230 8.07061i 0.106788 0.328661i
\(604\) 0 0
\(605\) −2.15246 + 20.4793i −0.0875099 + 0.832601i
\(606\) 0 0
\(607\) −28.4215 −1.15359 −0.576797 0.816888i \(-0.695698\pi\)
−0.576797 + 0.816888i \(0.695698\pi\)
\(608\) 0 0
\(609\) 0.606506 + 0.440652i 0.0245769 + 0.0178561i
\(610\) 0 0
\(611\) 2.55993 1.85990i 0.103564 0.0752435i
\(612\) 0 0
\(613\) 2.00920 + 1.45977i 0.0811510 + 0.0589597i 0.627621 0.778519i \(-0.284029\pi\)
−0.546470 + 0.837479i \(0.684029\pi\)
\(614\) 0 0
\(615\) 14.6672 16.2896i 0.591439 0.656860i
\(616\) 0 0
\(617\) 3.03970 + 9.35524i 0.122374 + 0.376628i 0.993413 0.114585i \(-0.0365538\pi\)
−0.871040 + 0.491213i \(0.836554\pi\)
\(618\) 0 0
\(619\) −4.22997 13.0185i −0.170017 0.523258i 0.829354 0.558723i \(-0.188709\pi\)
−0.999371 + 0.0354655i \(0.988709\pi\)
\(620\) 0 0
\(621\) 0.0757724 0.233204i 0.00304064 0.00935814i
\(622\) 0 0
\(623\) −2.20449 + 1.60165i −0.0883210 + 0.0641689i
\(624\) 0 0
\(625\) 16.7283 18.5786i 0.669131 0.743145i
\(626\) 0 0
\(627\) −6.09852 + 4.43083i −0.243551 + 0.176950i
\(628\) 0 0
\(629\) −2.73239 + 8.40944i −0.108948 + 0.335306i
\(630\) 0 0
\(631\) 6.15441 + 18.9413i 0.245003 + 0.754042i 0.995636 + 0.0933224i \(0.0297487\pi\)
−0.750633 + 0.660720i \(0.770251\pi\)
\(632\) 0 0
\(633\) 7.08592 + 21.8082i 0.281640 + 0.866799i
\(634\) 0 0
\(635\) 18.9692 21.0675i 0.752772 0.836038i
\(636\) 0 0
\(637\) 1.63769 + 1.18985i 0.0648876 + 0.0471436i
\(638\) 0 0
\(639\) 7.42939 5.39777i 0.293902 0.213532i
\(640\) 0 0
\(641\) 10.6407 + 7.73090i 0.420281 + 0.305352i 0.777751 0.628572i \(-0.216360\pi\)
−0.357470 + 0.933925i \(0.616360\pi\)
\(642\) 0 0
\(643\) −34.4841 −1.35992 −0.679960 0.733249i \(-0.738003\pi\)
−0.679960 + 0.733249i \(0.738003\pi\)
\(644\) 0 0
\(645\) −1.95392 + 18.5903i −0.0769355 + 0.731992i
\(646\) 0 0
\(647\) −11.7895 + 36.2842i −0.463492 + 1.42648i 0.397378 + 0.917655i \(0.369920\pi\)
−0.860870 + 0.508825i \(0.830080\pi\)
\(648\) 0 0
\(649\) −5.55666 −0.218118
\(650\) 0 0
\(651\) −1.93651 −0.0758978
\(652\) 0 0
\(653\) −10.7056 + 32.9484i −0.418942 + 1.28937i 0.489736 + 0.871871i \(0.337093\pi\)
−0.908677 + 0.417499i \(0.862907\pi\)
\(654\) 0 0
\(655\) −13.7864 23.8787i −0.538678 0.933018i
\(656\) 0 0
\(657\) 10.9560 0.427433
\(658\) 0 0
\(659\) −40.6525 29.5358i −1.58360 1.15055i −0.912420 0.409254i \(-0.865789\pi\)
−0.671178 0.741297i \(-0.734211\pi\)
\(660\) 0 0
\(661\) −8.72436 + 6.33862i −0.339338 + 0.246544i −0.744383 0.667753i \(-0.767256\pi\)
0.405044 + 0.914297i \(0.367256\pi\)
\(662\) 0 0
\(663\) −0.987875 0.717733i −0.0383659 0.0278744i
\(664\) 0 0
\(665\) −3.44684 5.97009i −0.133663 0.231510i
\(666\) 0 0
\(667\) −0.103788 0.319428i −0.00401870 0.0123683i
\(668\) 0 0
\(669\) −3.93990 12.1258i −0.152325 0.468810i
\(670\) 0 0
\(671\) −0.858670 + 2.64272i −0.0331486 + 0.102021i
\(672\) 0 0
\(673\) 13.6011 9.88179i 0.524285 0.380915i −0.293931 0.955827i \(-0.594964\pi\)
0.818216 + 0.574912i \(0.194964\pi\)
\(674\) 0 0
\(675\) −2.50000 + 4.33013i −0.0962250 + 0.166667i
\(676\) 0 0
\(677\) −30.1258 + 21.8877i −1.15783 + 0.841211i −0.989502 0.144521i \(-0.953836\pi\)
−0.168325 + 0.985731i \(0.553836\pi\)
\(678\) 0 0
\(679\) 0.686881 2.11400i 0.0263601 0.0811280i
\(680\) 0 0
\(681\) 3.40828 + 10.4896i 0.130606 + 0.401963i
\(682\) 0 0
\(683\) −9.83629 30.2730i −0.376375 1.15836i −0.942546 0.334076i \(-0.891576\pi\)
0.566171 0.824288i \(-0.308424\pi\)
\(684\) 0 0
\(685\) −21.9044 9.75246i −0.836923 0.372622i
\(686\) 0 0
\(687\) 18.6722 + 13.5661i 0.712389 + 0.517581i
\(688\) 0 0
\(689\) 1.88101 1.36663i 0.0716608 0.0520646i
\(690\) 0 0
\(691\) 15.3436 + 11.1478i 0.583699 + 0.424082i 0.840056 0.542500i \(-0.182522\pi\)
−0.256357 + 0.966582i \(0.582522\pi\)
\(692\) 0 0
\(693\) −0.732455 −0.0278237
\(694\) 0 0
\(695\) 20.4606 22.7237i 0.776113 0.861961i
\(696\) 0 0
\(697\) −12.2436 + 37.6819i −0.463759 + 1.42730i
\(698\) 0 0
\(699\) −29.2882 −1.10778
\(700\) 0 0
\(701\) −19.2027 −0.725275 −0.362638 0.931930i \(-0.618124\pi\)
−0.362638 + 0.931930i \(0.618124\pi\)
\(702\) 0 0
\(703\) 3.80798 11.7197i 0.143621 0.442019i
\(704\) 0 0
\(705\) 21.3952 + 9.52575i 0.805789 + 0.358760i
\(706\) 0 0
\(707\) 10.0974 0.379752
\(708\) 0 0
\(709\) 8.91896 + 6.48000i 0.334959 + 0.243362i 0.742532 0.669811i \(-0.233625\pi\)
−0.407573 + 0.913173i \(0.633625\pi\)
\(710\) 0 0
\(711\) −12.2832 + 8.92428i −0.460657 + 0.334687i
\(712\) 0 0
\(713\) 0.701886 + 0.509950i 0.0262858 + 0.0190978i
\(714\) 0 0
\(715\) −0.884301 + 0.187964i −0.0330710 + 0.00702946i
\(716\) 0 0
\(717\) 3.27514 + 10.0798i 0.122312 + 0.376439i
\(718\) 0 0
\(719\) 8.20996 + 25.2676i 0.306180 + 0.942324i 0.979234 + 0.202732i \(0.0649819\pi\)
−0.673055 + 0.739593i \(0.735018\pi\)
\(720\) 0 0
\(721\) −2.48899 + 7.66034i −0.0926950 + 0.285286i
\(722\) 0 0
\(723\) −15.3888 + 11.1806i −0.572317 + 0.415812i
\(724\) 0 0
\(725\) 0.715883 + 6.81118i 0.0265872 + 0.252961i
\(726\) 0 0
\(727\) −22.1224 + 16.0729i −0.820474 + 0.596109i −0.916848 0.399236i \(-0.869275\pi\)
0.0963741 + 0.995345i \(0.469275\pi\)
\(728\) 0 0
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 0 0
\(731\) −10.4410 32.1342i −0.386176 1.18853i
\(732\) 0 0
\(733\) 2.56626 + 7.89814i 0.0947871 + 0.291725i 0.987198 0.159499i \(-0.0509878\pi\)
−0.892411 + 0.451223i \(0.850988\pi\)
\(734\) 0 0
\(735\) −1.56611 + 14.9006i −0.0577669 + 0.549616i
\(736\) 0 0
\(737\) 9.18753 + 6.67513i 0.338427 + 0.245882i
\(738\) 0 0
\(739\) −1.30623 + 0.949030i −0.0480504 + 0.0349106i −0.611551 0.791205i \(-0.709454\pi\)
0.563501 + 0.826116i \(0.309454\pi\)
\(740\) 0 0
\(741\) 1.37674 + 1.00026i 0.0505760 + 0.0367456i
\(742\) 0 0
\(743\) −3.77367 −0.138443 −0.0692213 0.997601i \(-0.522051\pi\)
−0.0692213 + 0.997601i \(0.522051\pi\)
\(744\) 0 0
\(745\) 19.4262 4.12917i 0.711722 0.151281i
\(746\) 0 0
\(747\) −2.05626 + 6.32850i −0.0752344 + 0.231548i
\(748\) 0 0
\(749\) −2.79421 −0.102098
\(750\) 0 0
\(751\) 53.4032 1.94871 0.974355 0.225016i \(-0.0722435\pi\)
0.974355 + 0.225016i \(0.0722435\pi\)
\(752\) 0 0
\(753\) 0.0114588 0.0352667i 0.000417583 0.00128519i
\(754\) 0 0
\(755\) 5.86850 1.24739i 0.213576 0.0453971i
\(756\) 0 0
\(757\) 11.6322 0.422781 0.211390 0.977402i \(-0.432201\pi\)
0.211390 + 0.977402i \(0.432201\pi\)
\(758\) 0 0
\(759\) 0.265477 + 0.192881i 0.00963622 + 0.00700112i
\(760\) 0 0
\(761\) −3.77626 + 2.74361i −0.136889 + 0.0994560i −0.654123 0.756389i \(-0.726962\pi\)
0.517233 + 0.855844i \(0.326962\pi\)
\(762\) 0 0
\(763\) −2.09257 1.52034i −0.0757561 0.0550400i
\(764\) 0 0
\(765\) 0.944700 8.98822i 0.0341557 0.324970i
\(766\) 0 0
\(767\) 0.387637 + 1.19302i 0.0139968 + 0.0430776i
\(768\) 0 0
\(769\) −6.98515 21.4981i −0.251891 0.775241i −0.994426 0.105434i \(-0.966377\pi\)
0.742535 0.669807i \(-0.233623\pi\)
\(770\) 0 0
\(771\) −3.09750 + 9.53312i −0.111554 + 0.343327i
\(772\) 0 0
\(773\) −32.1006 + 23.3225i −1.15458 + 0.838851i −0.989083 0.147359i \(-0.952923\pi\)
−0.165497 + 0.986210i \(0.552923\pi\)
\(774\) 0 0
\(775\) −11.8375 13.1469i −0.425217 0.472251i
\(776\) 0 0
\(777\) 0.968688 0.703793i 0.0347515 0.0252484i
\(778\) 0 0
\(779\) 17.0632 52.5151i 0.611352 1.88155i
\(780\) 0 0
\(781\) 3.79768 + 11.6881i 0.135892 + 0.418232i
\(782\) 0 0
\(783\) −0.423273 1.30270i −0.0151265 0.0465547i
\(784\) 0 0
\(785\) 25.7162 5.46614i 0.917850 0.195095i
\(786\) 0 0
\(787\) −3.83261 2.78456i −0.136618 0.0992587i 0.517377 0.855757i \(-0.326908\pi\)
−0.653995 + 0.756499i \(0.726908\pi\)
\(788\) 0 0
\(789\) 10.3407 7.51296i 0.368139 0.267468i
\(790\) 0 0
\(791\) −1.83241 1.33133i −0.0651532 0.0473365i
\(792\) 0 0
\(793\) 0.627297 0.0222760
\(794\) 0 0
\(795\) 15.7210 + 6.99942i 0.557565 + 0.248244i