Properties

Label 1260.2.c.e.811.9
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.9
Root \(-0.102186 - 1.41052i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.e.811.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.102186 - 1.41052i) q^{2} +(-1.97912 - 0.288270i) q^{4} +1.00000i q^{5} +(0.178143 - 2.63975i) q^{7} +(-0.608847 + 2.76212i) q^{8} +O(q^{10})\) \(q+(0.102186 - 1.41052i) q^{2} +(-1.97912 - 0.288270i) q^{4} +1.00000i q^{5} +(0.178143 - 2.63975i) q^{7} +(-0.608847 + 2.76212i) q^{8} +(1.41052 + 0.102186i) q^{10} +5.22855i q^{11} -4.52534i q^{13} +(-3.70520 - 0.521019i) q^{14} +(3.83380 + 1.14104i) q^{16} -6.70156i q^{17} -2.81981 q^{19} +(0.288270 - 1.97912i) q^{20} +(7.37496 + 0.534284i) q^{22} -0.858617i q^{23} -1.00000 q^{25} +(-6.38308 - 0.462426i) q^{26} +(-1.11353 + 5.17301i) q^{28} -6.47333 q^{29} -2.60723 q^{31} +(2.00121 - 5.29104i) q^{32} +(-9.45266 - 0.684805i) q^{34} +(2.63975 + 0.178143i) q^{35} +2.13976 q^{37} +(-0.288144 + 3.97738i) q^{38} +(-2.76212 - 0.608847i) q^{40} -8.71476i q^{41} -7.42042i q^{43} +(1.50723 - 10.3479i) q^{44} +(-1.21109 - 0.0877385i) q^{46} -9.82671 q^{47} +(-6.93653 - 0.940508i) q^{49} +(-0.102186 + 1.41052i) q^{50} +(-1.30452 + 8.95618i) q^{52} -3.69301 q^{53} -5.22855 q^{55} +(7.18284 + 2.09926i) q^{56} +(-0.661483 + 9.13075i) q^{58} +4.27962 q^{59} +10.7054i q^{61} +(-0.266423 + 3.67755i) q^{62} +(-7.25861 - 3.36342i) q^{64} +4.52534 q^{65} +4.52269i q^{67} +(-1.93186 + 13.2632i) q^{68} +(0.521019 - 3.70520i) q^{70} +7.23513i q^{71} -9.24697i q^{73} +(0.218653 - 3.01816i) q^{74} +(5.58072 + 0.812865i) q^{76} +(13.8020 + 0.931432i) q^{77} +2.68314i q^{79} +(-1.14104 + 3.83380i) q^{80} +(-12.2923 - 0.890525i) q^{82} -16.2812 q^{83} +6.70156 q^{85} +(-10.4666 - 0.758262i) q^{86} +(-14.4419 - 3.18339i) q^{88} -8.53516i q^{89} +(-11.9458 - 0.806161i) q^{91} +(-0.247513 + 1.69930i) q^{92} +(-1.00415 + 13.8607i) q^{94} -2.81981i q^{95} -10.5209i q^{97} +(-2.03542 + 9.68799i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.102186 1.41052i 0.0722563 0.997386i
\(3\) 0 0
\(4\) −1.97912 0.288270i −0.989558 0.144135i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 0.178143 2.63975i 0.0673319 0.997731i
\(8\) −0.608847 + 2.76212i −0.215260 + 0.976557i
\(9\) 0 0
\(10\) 1.41052 + 0.102186i 0.446045 + 0.0323140i
\(11\) 5.22855i 1.57647i 0.615376 + 0.788234i \(0.289004\pi\)
−0.615376 + 0.788234i \(0.710996\pi\)
\(12\) 0 0
\(13\) 4.52534i 1.25510i −0.778574 0.627552i \(-0.784057\pi\)
0.778574 0.627552i \(-0.215943\pi\)
\(14\) −3.70520 0.521019i −0.990258 0.139248i
\(15\) 0 0
\(16\) 3.83380 + 1.14104i 0.958450 + 0.285260i
\(17\) 6.70156i 1.62537i −0.582705 0.812684i \(-0.698006\pi\)
0.582705 0.812684i \(-0.301994\pi\)
\(18\) 0 0
\(19\) −2.81981 −0.646908 −0.323454 0.946244i \(-0.604844\pi\)
−0.323454 + 0.946244i \(0.604844\pi\)
\(20\) 0.288270 1.97912i 0.0644591 0.442544i
\(21\) 0 0
\(22\) 7.37496 + 0.534284i 1.57235 + 0.113910i
\(23\) 0.858617i 0.179034i −0.995985 0.0895170i \(-0.971468\pi\)
0.995985 0.0895170i \(-0.0285323\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −6.38308 0.462426i −1.25182 0.0906893i
\(27\) 0 0
\(28\) −1.11353 + 5.17301i −0.210437 + 0.977607i
\(29\) −6.47333 −1.20207 −0.601034 0.799224i \(-0.705244\pi\)
−0.601034 + 0.799224i \(0.705244\pi\)
\(30\) 0 0
\(31\) −2.60723 −0.468273 −0.234137 0.972204i \(-0.575226\pi\)
−0.234137 + 0.972204i \(0.575226\pi\)
\(32\) 2.00121 5.29104i 0.353768 0.935333i
\(33\) 0 0
\(34\) −9.45266 0.684805i −1.62112 0.117443i
\(35\) 2.63975 + 0.178143i 0.446199 + 0.0301117i
\(36\) 0 0
\(37\) 2.13976 0.351774 0.175887 0.984410i \(-0.443721\pi\)
0.175887 + 0.984410i \(0.443721\pi\)
\(38\) −0.288144 + 3.97738i −0.0467432 + 0.645217i
\(39\) 0 0
\(40\) −2.76212 0.608847i −0.436729 0.0962672i
\(41\) 8.71476i 1.36102i −0.732740 0.680508i \(-0.761759\pi\)
0.732740 0.680508i \(-0.238241\pi\)
\(42\) 0 0
\(43\) 7.42042i 1.13160i −0.824541 0.565802i \(-0.808567\pi\)
0.824541 0.565802i \(-0.191433\pi\)
\(44\) 1.50723 10.3479i 0.227224 1.56001i
\(45\) 0 0
\(46\) −1.21109 0.0877385i −0.178566 0.0129363i
\(47\) −9.82671 −1.43337 −0.716686 0.697396i \(-0.754342\pi\)
−0.716686 + 0.697396i \(0.754342\pi\)
\(48\) 0 0
\(49\) −6.93653 0.940508i −0.990933 0.134358i
\(50\) −0.102186 + 1.41052i −0.0144513 + 0.199477i
\(51\) 0 0
\(52\) −1.30452 + 8.95618i −0.180904 + 1.24200i
\(53\) −3.69301 −0.507274 −0.253637 0.967299i \(-0.581627\pi\)
−0.253637 + 0.967299i \(0.581627\pi\)
\(54\) 0 0
\(55\) −5.22855 −0.705018
\(56\) 7.18284 + 2.09926i 0.959847 + 0.280525i
\(57\) 0 0
\(58\) −0.661483 + 9.13075i −0.0868570 + 1.19893i
\(59\) 4.27962 0.557159 0.278579 0.960413i \(-0.410136\pi\)
0.278579 + 0.960413i \(0.410136\pi\)
\(60\) 0 0
\(61\) 10.7054i 1.37069i 0.728221 + 0.685343i \(0.240347\pi\)
−0.728221 + 0.685343i \(0.759653\pi\)
\(62\) −0.266423 + 3.67755i −0.0338357 + 0.467049i
\(63\) 0 0
\(64\) −7.25861 3.36342i −0.907326 0.420427i
\(65\) 4.52534 0.561300
\(66\) 0 0
\(67\) 4.52269i 0.552534i 0.961081 + 0.276267i \(0.0890975\pi\)
−0.961081 + 0.276267i \(0.910903\pi\)
\(68\) −1.93186 + 13.2632i −0.234272 + 1.60840i
\(69\) 0 0
\(70\) 0.521019 3.70520i 0.0622737 0.442857i
\(71\) 7.23513i 0.858652i 0.903150 + 0.429326i \(0.141249\pi\)
−0.903150 + 0.429326i \(0.858751\pi\)
\(72\) 0 0
\(73\) 9.24697i 1.08228i −0.840934 0.541138i \(-0.817994\pi\)
0.840934 0.541138i \(-0.182006\pi\)
\(74\) 0.218653 3.01816i 0.0254179 0.350854i
\(75\) 0 0
\(76\) 5.58072 + 0.812865i 0.640153 + 0.0932420i
\(77\) 13.8020 + 0.931432i 1.57289 + 0.106147i
\(78\) 0 0
\(79\) 2.68314i 0.301877i 0.988543 + 0.150938i \(0.0482295\pi\)
−0.988543 + 0.150938i \(0.951770\pi\)
\(80\) −1.14104 + 3.83380i −0.127572 + 0.428632i
\(81\) 0 0
\(82\) −12.2923 0.890525i −1.35746 0.0983421i
\(83\) −16.2812 −1.78710 −0.893548 0.448967i \(-0.851792\pi\)
−0.893548 + 0.448967i \(0.851792\pi\)
\(84\) 0 0
\(85\) 6.70156 0.726886
\(86\) −10.4666 0.758262i −1.12865 0.0817655i
\(87\) 0 0
\(88\) −14.4419 3.18339i −1.53951 0.339350i
\(89\) 8.53516i 0.904725i −0.891834 0.452362i \(-0.850581\pi\)
0.891834 0.452362i \(-0.149419\pi\)
\(90\) 0 0
\(91\) −11.9458 0.806161i −1.25226 0.0845086i
\(92\) −0.247513 + 1.69930i −0.0258051 + 0.177165i
\(93\) 0 0
\(94\) −1.00415 + 13.8607i −0.103570 + 1.42963i
\(95\) 2.81981i 0.289306i
\(96\) 0 0
\(97\) 10.5209i 1.06824i −0.845410 0.534118i \(-0.820644\pi\)
0.845410 0.534118i \(-0.179356\pi\)
\(98\) −2.03542 + 9.68799i −0.205608 + 0.978634i
\(99\) 0 0
\(100\) 1.97912 + 0.288270i 0.197912 + 0.0288270i
\(101\) 3.97836i 0.395861i −0.980216 0.197931i \(-0.936578\pi\)
0.980216 0.197931i \(-0.0634221\pi\)
\(102\) 0 0
\(103\) −3.78934 −0.373375 −0.186688 0.982419i \(-0.559775\pi\)
−0.186688 + 0.982419i \(0.559775\pi\)
\(104\) 12.4995 + 2.75524i 1.22568 + 0.270174i
\(105\) 0 0
\(106\) −0.377374 + 5.20906i −0.0366538 + 0.505948i
\(107\) 2.38868i 0.230922i −0.993312 0.115461i \(-0.963165\pi\)
0.993312 0.115461i \(-0.0368346\pi\)
\(108\) 0 0
\(109\) 5.79748 0.555298 0.277649 0.960683i \(-0.410445\pi\)
0.277649 + 0.960683i \(0.410445\pi\)
\(110\) −0.534284 + 7.37496i −0.0509420 + 0.703175i
\(111\) 0 0
\(112\) 3.69502 9.91700i 0.349147 0.937068i
\(113\) 6.86598 0.645897 0.322948 0.946417i \(-0.395326\pi\)
0.322948 + 0.946417i \(0.395326\pi\)
\(114\) 0 0
\(115\) 0.858617 0.0800665
\(116\) 12.8115 + 1.86607i 1.18952 + 0.173260i
\(117\) 0 0
\(118\) 0.437316 6.03647i 0.0402582 0.555702i
\(119\) −17.6904 1.19384i −1.62168 0.109439i
\(120\) 0 0
\(121\) −16.3377 −1.48525
\(122\) 15.1001 + 1.09394i 1.36710 + 0.0990407i
\(123\) 0 0
\(124\) 5.16002 + 0.751587i 0.463384 + 0.0674945i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 10.4834i 0.930250i −0.885245 0.465125i \(-0.846009\pi\)
0.885245 0.465125i \(-0.153991\pi\)
\(128\) −5.48588 + 9.89470i −0.484888 + 0.874576i
\(129\) 0 0
\(130\) 0.462426 6.38308i 0.0405575 0.559833i
\(131\) 19.0936 1.66821 0.834106 0.551604i \(-0.185984\pi\)
0.834106 + 0.551604i \(0.185984\pi\)
\(132\) 0 0
\(133\) −0.502330 + 7.44358i −0.0435576 + 0.645440i
\(134\) 6.37933 + 0.462155i 0.551090 + 0.0399241i
\(135\) 0 0
\(136\) 18.5105 + 4.08023i 1.58726 + 0.349876i
\(137\) −5.47214 −0.467516 −0.233758 0.972295i \(-0.575102\pi\)
−0.233758 + 0.972295i \(0.575102\pi\)
\(138\) 0 0
\(139\) 2.83943 0.240838 0.120419 0.992723i \(-0.461576\pi\)
0.120419 + 0.992723i \(0.461576\pi\)
\(140\) −5.17301 1.11353i −0.437199 0.0941101i
\(141\) 0 0
\(142\) 10.2053 + 0.739328i 0.856407 + 0.0620430i
\(143\) 23.6610 1.97863
\(144\) 0 0
\(145\) 6.47333i 0.537581i
\(146\) −13.0430 0.944910i −1.07945 0.0782013i
\(147\) 0 0
\(148\) −4.23483 0.616827i −0.348101 0.0507029i
\(149\) −1.72856 −0.141609 −0.0708045 0.997490i \(-0.522557\pi\)
−0.0708045 + 0.997490i \(0.522557\pi\)
\(150\) 0 0
\(151\) 14.9532i 1.21687i 0.793603 + 0.608436i \(0.208203\pi\)
−0.793603 + 0.608436i \(0.791797\pi\)
\(152\) 1.71683 7.78864i 0.139253 0.631742i
\(153\) 0 0
\(154\) 2.72418 19.3728i 0.219520 1.56111i
\(155\) 2.60723i 0.209418i
\(156\) 0 0
\(157\) 11.0383i 0.880953i 0.897764 + 0.440476i \(0.145190\pi\)
−0.897764 + 0.440476i \(0.854810\pi\)
\(158\) 3.78461 + 0.274179i 0.301088 + 0.0218125i
\(159\) 0 0
\(160\) 5.29104 + 2.00121i 0.418294 + 0.158210i
\(161\) −2.26653 0.152957i −0.178628 0.0120547i
\(162\) 0 0
\(163\) 18.7969i 1.47229i 0.676826 + 0.736143i \(0.263355\pi\)
−0.676826 + 0.736143i \(0.736645\pi\)
\(164\) −2.51220 + 17.2475i −0.196170 + 1.34681i
\(165\) 0 0
\(166\) −1.66371 + 22.9649i −0.129129 + 1.78243i
\(167\) −1.89315 −0.146496 −0.0732481 0.997314i \(-0.523337\pi\)
−0.0732481 + 0.997314i \(0.523337\pi\)
\(168\) 0 0
\(169\) −7.47874 −0.575288
\(170\) 0.684805 9.45266i 0.0525221 0.724986i
\(171\) 0 0
\(172\) −2.13908 + 14.6859i −0.163104 + 1.11979i
\(173\) 9.43306i 0.717182i 0.933495 + 0.358591i \(0.116743\pi\)
−0.933495 + 0.358591i \(0.883257\pi\)
\(174\) 0 0
\(175\) −0.178143 + 2.63975i −0.0134664 + 0.199546i
\(176\) −5.96598 + 20.0452i −0.449703 + 1.51097i
\(177\) 0 0
\(178\) −12.0390 0.872173i −0.902360 0.0653721i
\(179\) 21.4618i 1.60413i −0.597239 0.802063i \(-0.703736\pi\)
0.597239 0.802063i \(-0.296264\pi\)
\(180\) 0 0
\(181\) 24.1736i 1.79681i −0.439171 0.898403i \(-0.644728\pi\)
0.439171 0.898403i \(-0.355272\pi\)
\(182\) −2.35779 + 16.7673i −0.174771 + 1.24288i
\(183\) 0 0
\(184\) 2.37160 + 0.522767i 0.174837 + 0.0385389i
\(185\) 2.13976i 0.157318i
\(186\) 0 0
\(187\) 35.0394 2.56234
\(188\) 19.4482 + 2.83274i 1.41841 + 0.206599i
\(189\) 0 0
\(190\) −3.97738 0.288144i −0.288550 0.0209042i
\(191\) 18.9822i 1.37350i −0.726892 0.686751i \(-0.759036\pi\)
0.726892 0.686751i \(-0.240964\pi\)
\(192\) 0 0
\(193\) 26.5854 1.91366 0.956828 0.290654i \(-0.0938728\pi\)
0.956828 + 0.290654i \(0.0938728\pi\)
\(194\) −14.8399 1.07509i −1.06544 0.0771868i
\(195\) 0 0
\(196\) 13.4571 + 3.86097i 0.961220 + 0.275783i
\(197\) −23.2008 −1.65299 −0.826494 0.562945i \(-0.809668\pi\)
−0.826494 + 0.562945i \(0.809668\pi\)
\(198\) 0 0
\(199\) 19.8867 1.40973 0.704866 0.709341i \(-0.251007\pi\)
0.704866 + 0.709341i \(0.251007\pi\)
\(200\) 0.608847 2.76212i 0.0430520 0.195311i
\(201\) 0 0
\(202\) −5.61154 0.406532i −0.394827 0.0286035i
\(203\) −1.15318 + 17.0880i −0.0809375 + 1.19934i
\(204\) 0 0
\(205\) 8.71476 0.608665
\(206\) −0.387217 + 5.34493i −0.0269787 + 0.372399i
\(207\) 0 0
\(208\) 5.16359 17.3493i 0.358031 1.20296i
\(209\) 14.7435i 1.01983i
\(210\) 0 0
\(211\) 2.51318i 0.173014i 0.996251 + 0.0865072i \(0.0275706\pi\)
−0.996251 + 0.0865072i \(0.972429\pi\)
\(212\) 7.30890 + 1.06458i 0.501977 + 0.0731159i
\(213\) 0 0
\(214\) −3.36927 0.244089i −0.230319 0.0166856i
\(215\) 7.42042 0.506068
\(216\) 0 0
\(217\) −0.464462 + 6.88244i −0.0315297 + 0.467211i
\(218\) 0.592420 8.17744i 0.0401238 0.553846i
\(219\) 0 0
\(220\) 10.3479 + 1.50723i 0.697656 + 0.101618i
\(221\) −30.3269 −2.04001
\(222\) 0 0
\(223\) 1.23567 0.0827463 0.0413732 0.999144i \(-0.486827\pi\)
0.0413732 + 0.999144i \(0.486827\pi\)
\(224\) −13.6105 6.22527i −0.909391 0.415943i
\(225\) 0 0
\(226\) 0.701606 9.68458i 0.0466701 0.644208i
\(227\) 1.76552 0.117182 0.0585909 0.998282i \(-0.481339\pi\)
0.0585909 + 0.998282i \(0.481339\pi\)
\(228\) 0 0
\(229\) 8.94803i 0.591302i −0.955296 0.295651i \(-0.904463\pi\)
0.955296 0.295651i \(-0.0955366\pi\)
\(230\) 0.0877385 1.21109i 0.00578531 0.0798572i
\(231\) 0 0
\(232\) 3.94127 17.8801i 0.258757 1.17389i
\(233\) 21.8087 1.42874 0.714368 0.699770i \(-0.246714\pi\)
0.714368 + 0.699770i \(0.246714\pi\)
\(234\) 0 0
\(235\) 9.82671i 0.641024i
\(236\) −8.46986 1.23368i −0.551341 0.0803060i
\(237\) 0 0
\(238\) −3.49164 + 24.8306i −0.226330 + 1.60953i
\(239\) 14.7558i 0.954471i −0.878776 0.477235i \(-0.841639\pi\)
0.878776 0.477235i \(-0.158361\pi\)
\(240\) 0 0
\(241\) 15.3302i 0.987503i 0.869603 + 0.493751i \(0.164375\pi\)
−0.869603 + 0.493751i \(0.835625\pi\)
\(242\) −1.66949 + 23.0447i −0.107319 + 1.48137i
\(243\) 0 0
\(244\) 3.08604 21.1872i 0.197564 1.35637i
\(245\) 0.940508 6.93653i 0.0600868 0.443159i
\(246\) 0 0
\(247\) 12.7606i 0.811937i
\(248\) 1.58741 7.20149i 0.100800 0.457295i
\(249\) 0 0
\(250\) −1.41052 0.102186i −0.0892089 0.00646280i
\(251\) 15.4063 0.972435 0.486218 0.873838i \(-0.338376\pi\)
0.486218 + 0.873838i \(0.338376\pi\)
\(252\) 0 0
\(253\) 4.48932 0.282241
\(254\) −14.7870 1.07125i −0.927818 0.0672164i
\(255\) 0 0
\(256\) 13.3961 + 8.74903i 0.837254 + 0.546814i
\(257\) 11.6114i 0.724298i −0.932120 0.362149i \(-0.882043\pi\)
0.932120 0.362149i \(-0.117957\pi\)
\(258\) 0 0
\(259\) 0.381184 5.64842i 0.0236856 0.350976i
\(260\) −8.95618 1.30452i −0.555439 0.0809029i
\(261\) 0 0
\(262\) 1.95109 26.9318i 0.120539 1.66385i
\(263\) 14.4160i 0.888927i 0.895797 + 0.444463i \(0.146606\pi\)
−0.895797 + 0.444463i \(0.853394\pi\)
\(264\) 0 0
\(265\) 3.69301i 0.226860i
\(266\) 10.4480 + 1.46917i 0.640605 + 0.0900808i
\(267\) 0 0
\(268\) 1.30375 8.95093i 0.0796395 0.546765i
\(269\) 10.8482i 0.661425i 0.943732 + 0.330712i \(0.107289\pi\)
−0.943732 + 0.330712i \(0.892711\pi\)
\(270\) 0 0
\(271\) −18.9758 −1.15270 −0.576349 0.817204i \(-0.695523\pi\)
−0.576349 + 0.817204i \(0.695523\pi\)
\(272\) 7.64674 25.6924i 0.463652 1.55783i
\(273\) 0 0
\(274\) −0.559175 + 7.71854i −0.0337810 + 0.466294i
\(275\) 5.22855i 0.315293i
\(276\) 0 0
\(277\) 11.0960 0.666692 0.333346 0.942804i \(-0.391822\pi\)
0.333346 + 0.942804i \(0.391822\pi\)
\(278\) 0.290150 4.00507i 0.0174020 0.240208i
\(279\) 0 0
\(280\) −2.09926 + 7.18284i −0.125455 + 0.429257i
\(281\) 26.1397 1.55937 0.779683 0.626175i \(-0.215380\pi\)
0.779683 + 0.626175i \(0.215380\pi\)
\(282\) 0 0
\(283\) 15.0023 0.891793 0.445897 0.895084i \(-0.352885\pi\)
0.445897 + 0.895084i \(0.352885\pi\)
\(284\) 2.08567 14.3192i 0.123762 0.849686i
\(285\) 0 0
\(286\) 2.41782 33.3742i 0.142969 1.97346i
\(287\) −23.0048 1.55248i −1.35793 0.0916399i
\(288\) 0 0
\(289\) −27.9109 −1.64182
\(290\) −9.13075 0.661483i −0.536176 0.0388436i
\(291\) 0 0
\(292\) −2.66562 + 18.3008i −0.155994 + 1.07097i
\(293\) 30.1766i 1.76293i −0.472245 0.881467i \(-0.656556\pi\)
0.472245 0.881467i \(-0.343444\pi\)
\(294\) 0 0
\(295\) 4.27962i 0.249169i
\(296\) −1.30278 + 5.91026i −0.0757228 + 0.343527i
\(297\) 0 0
\(298\) −0.176634 + 2.43816i −0.0102321 + 0.141239i
\(299\) −3.88554 −0.224706
\(300\) 0 0
\(301\) −19.5880 1.32190i −1.12904 0.0761930i
\(302\) 21.0917 + 1.52800i 1.21369 + 0.0879267i
\(303\) 0 0
\(304\) −10.8106 3.21751i −0.620029 0.184537i
\(305\) −10.7054 −0.612989
\(306\) 0 0
\(307\) −6.17458 −0.352402 −0.176201 0.984354i \(-0.556381\pi\)
−0.176201 + 0.984354i \(0.556381\pi\)
\(308\) −27.0474 5.82213i −1.54117 0.331746i
\(309\) 0 0
\(310\) −3.67755 0.266423i −0.208871 0.0151318i
\(311\) −3.80564 −0.215798 −0.107899 0.994162i \(-0.534412\pi\)
−0.107899 + 0.994162i \(0.534412\pi\)
\(312\) 0 0
\(313\) 16.5774i 0.937011i −0.883461 0.468506i \(-0.844793\pi\)
0.883461 0.468506i \(-0.155207\pi\)
\(314\) 15.5697 + 1.12796i 0.878650 + 0.0636544i
\(315\) 0 0
\(316\) 0.773468 5.31025i 0.0435110 0.298725i
\(317\) 11.1118 0.624098 0.312049 0.950066i \(-0.398985\pi\)
0.312049 + 0.950066i \(0.398985\pi\)
\(318\) 0 0
\(319\) 33.8461i 1.89502i
\(320\) 3.36342 7.25861i 0.188021 0.405769i
\(321\) 0 0
\(322\) −0.447356 + 3.18135i −0.0249302 + 0.177290i
\(323\) 18.8971i 1.05146i
\(324\) 0 0
\(325\) 4.52534i 0.251021i
\(326\) 26.5133 + 1.92078i 1.46844 + 0.106382i
\(327\) 0 0
\(328\) 24.0712 + 5.30596i 1.32911 + 0.292972i
\(329\) −1.75056 + 25.9400i −0.0965117 + 1.43012i
\(330\) 0 0
\(331\) 22.4709i 1.23511i −0.786526 0.617557i \(-0.788123\pi\)
0.786526 0.617557i \(-0.211877\pi\)
\(332\) 32.2224 + 4.69339i 1.76844 + 0.257583i
\(333\) 0 0
\(334\) −0.193453 + 2.67032i −0.0105853 + 0.146113i
\(335\) −4.52269 −0.247101
\(336\) 0 0
\(337\) −6.02729 −0.328328 −0.164164 0.986433i \(-0.552493\pi\)
−0.164164 + 0.986433i \(0.552493\pi\)
\(338\) −0.764222 + 10.5489i −0.0415682 + 0.573784i
\(339\) 0 0
\(340\) −13.2632 1.93186i −0.719296 0.104770i
\(341\) 13.6321i 0.738217i
\(342\) 0 0
\(343\) −3.71840 + 18.1431i −0.200775 + 0.979637i
\(344\) 20.4961 + 4.51790i 1.10508 + 0.243589i
\(345\) 0 0
\(346\) 13.3055 + 0.963925i 0.715307 + 0.0518209i
\(347\) 9.57093i 0.513794i 0.966439 + 0.256897i \(0.0827001\pi\)
−0.966439 + 0.256897i \(0.917300\pi\)
\(348\) 0 0
\(349\) 12.9442i 0.692884i 0.938071 + 0.346442i \(0.112610\pi\)
−0.938071 + 0.346442i \(0.887390\pi\)
\(350\) 3.70520 + 0.521019i 0.198052 + 0.0278497i
\(351\) 0 0
\(352\) 27.6645 + 10.4635i 1.47452 + 0.557704i
\(353\) 11.6209i 0.618520i 0.950978 + 0.309260i \(0.100081\pi\)
−0.950978 + 0.309260i \(0.899919\pi\)
\(354\) 0 0
\(355\) −7.23513 −0.384001
\(356\) −2.46043 + 16.8921i −0.130402 + 0.895278i
\(357\) 0 0
\(358\) −30.2722 2.19309i −1.59993 0.115908i
\(359\) 5.42483i 0.286312i 0.989700 + 0.143156i \(0.0457250\pi\)
−0.989700 + 0.143156i \(0.954275\pi\)
\(360\) 0 0
\(361\) −11.0487 −0.581510
\(362\) −34.0972 2.47020i −1.79211 0.129831i
\(363\) 0 0
\(364\) 23.4097 + 5.03909i 1.22700 + 0.264120i
\(365\) 9.24697 0.484009
\(366\) 0 0
\(367\) −28.4203 −1.48353 −0.741763 0.670662i \(-0.766010\pi\)
−0.741763 + 0.670662i \(0.766010\pi\)
\(368\) 0.979715 3.29177i 0.0510712 0.171595i
\(369\) 0 0
\(370\) 3.01816 + 0.218653i 0.156907 + 0.0113672i
\(371\) −0.657886 + 9.74862i −0.0341557 + 0.506123i
\(372\) 0 0
\(373\) 23.0923 1.19568 0.597838 0.801617i \(-0.296027\pi\)
0.597838 + 0.801617i \(0.296027\pi\)
\(374\) 3.58054 49.4237i 0.185145 2.55564i
\(375\) 0 0
\(376\) 5.98296 27.1425i 0.308548 1.39977i
\(377\) 29.2941i 1.50872i
\(378\) 0 0
\(379\) 12.0804i 0.620527i 0.950651 + 0.310263i \(0.100417\pi\)
−0.950651 + 0.310263i \(0.899583\pi\)
\(380\) −0.812865 + 5.58072i −0.0416991 + 0.286285i
\(381\) 0 0
\(382\) −26.7747 1.93971i −1.36991 0.0992443i
\(383\) 4.05602 0.207253 0.103626 0.994616i \(-0.466955\pi\)
0.103626 + 0.994616i \(0.466955\pi\)
\(384\) 0 0
\(385\) −0.931432 + 13.8020i −0.0474702 + 0.703418i
\(386\) 2.71665 37.4991i 0.138274 1.90865i
\(387\) 0 0
\(388\) −3.03286 + 20.8221i −0.153970 + 1.05708i
\(389\) −5.28804 −0.268114 −0.134057 0.990974i \(-0.542801\pi\)
−0.134057 + 0.990974i \(0.542801\pi\)
\(390\) 0 0
\(391\) −5.75407 −0.290996
\(392\) 6.82108 18.5869i 0.344517 0.938780i
\(393\) 0 0
\(394\) −2.37079 + 32.7251i −0.119439 + 1.64867i
\(395\) −2.68314 −0.135003
\(396\) 0 0
\(397\) 15.0058i 0.753121i −0.926392 0.376561i \(-0.877107\pi\)
0.926392 0.376561i \(-0.122893\pi\)
\(398\) 2.03214 28.0505i 0.101862 1.40605i
\(399\) 0 0
\(400\) −3.83380 1.14104i −0.191690 0.0570519i
\(401\) −19.3630 −0.966942 −0.483471 0.875360i \(-0.660624\pi\)
−0.483471 + 0.875360i \(0.660624\pi\)
\(402\) 0 0
\(403\) 11.7986i 0.587732i
\(404\) −1.14684 + 7.87363i −0.0570574 + 0.391728i
\(405\) 0 0
\(406\) 23.9850 + 3.37273i 1.19036 + 0.167386i
\(407\) 11.1878i 0.554560i
\(408\) 0 0
\(409\) 0.432474i 0.0213845i −0.999943 0.0106922i \(-0.996596\pi\)
0.999943 0.0106922i \(-0.00340351\pi\)
\(410\) 0.890525 12.2923i 0.0439799 0.607074i
\(411\) 0 0
\(412\) 7.49955 + 1.09235i 0.369476 + 0.0538164i
\(413\) 0.762386 11.2971i 0.0375146 0.555894i
\(414\) 0 0
\(415\) 16.2812i 0.799214i
\(416\) −23.9438 9.05619i −1.17394 0.444016i
\(417\) 0 0
\(418\) −20.7960 1.50658i −1.01716 0.0736891i
\(419\) −5.56216 −0.271729 −0.135865 0.990727i \(-0.543381\pi\)
−0.135865 + 0.990727i \(0.543381\pi\)
\(420\) 0 0
\(421\) −1.97874 −0.0964379 −0.0482190 0.998837i \(-0.515355\pi\)
−0.0482190 + 0.998837i \(0.515355\pi\)
\(422\) 3.54488 + 0.256811i 0.172562 + 0.0125014i
\(423\) 0 0
\(424\) 2.24848 10.2005i 0.109196 0.495382i
\(425\) 6.70156i 0.325073i
\(426\) 0 0
\(427\) 28.2595 + 1.90710i 1.36757 + 0.0922908i
\(428\) −0.688584 + 4.72747i −0.0332840 + 0.228511i
\(429\) 0 0
\(430\) 0.758262 10.4666i 0.0365666 0.504746i
\(431\) 14.0974i 0.679048i 0.940597 + 0.339524i \(0.110266\pi\)
−0.940597 + 0.339524i \(0.889734\pi\)
\(432\) 0 0
\(433\) 18.3496i 0.881826i 0.897550 + 0.440913i \(0.145345\pi\)
−0.897550 + 0.440913i \(0.854655\pi\)
\(434\) 9.66034 + 1.35842i 0.463711 + 0.0652062i
\(435\) 0 0
\(436\) −11.4739 1.67124i −0.549499 0.0800378i
\(437\) 2.42113i 0.115819i
\(438\) 0 0
\(439\) 8.36492 0.399236 0.199618 0.979874i \(-0.436030\pi\)
0.199618 + 0.979874i \(0.436030\pi\)
\(440\) 3.18339 14.4419i 0.151762 0.688490i
\(441\) 0 0
\(442\) −3.09898 + 42.7766i −0.147403 + 2.03467i
\(443\) 1.47488i 0.0700737i 0.999386 + 0.0350368i \(0.0111549\pi\)
−0.999386 + 0.0350368i \(0.988845\pi\)
\(444\) 0 0
\(445\) 8.53516 0.404605
\(446\) 0.126268 1.74293i 0.00597895 0.0825300i
\(447\) 0 0
\(448\) −10.1716 + 18.5617i −0.480565 + 0.876959i
\(449\) 16.1871 0.763918 0.381959 0.924179i \(-0.375250\pi\)
0.381959 + 0.924179i \(0.375250\pi\)
\(450\) 0 0
\(451\) 45.5656 2.14560
\(452\) −13.5886 1.97925i −0.639152 0.0930963i
\(453\) 0 0
\(454\) 0.180411 2.49030i 0.00846713 0.116876i
\(455\) 0.806161 11.9458i 0.0377934 0.560026i
\(456\) 0 0
\(457\) −26.6551 −1.24687 −0.623435 0.781875i \(-0.714264\pi\)
−0.623435 + 0.781875i \(0.714264\pi\)
\(458\) −12.6213 0.914362i −0.589757 0.0427253i
\(459\) 0 0
\(460\) −1.69930 0.247513i −0.0792304 0.0115404i
\(461\) 34.3308i 1.59895i 0.600703 + 0.799473i \(0.294888\pi\)
−0.600703 + 0.799473i \(0.705112\pi\)
\(462\) 0 0
\(463\) 16.8787i 0.784421i −0.919875 0.392210i \(-0.871710\pi\)
0.919875 0.392210i \(-0.128290\pi\)
\(464\) −24.8175 7.38632i −1.15212 0.342902i
\(465\) 0 0
\(466\) 2.22854 30.7615i 0.103235 1.42500i
\(467\) 33.4884 1.54966 0.774829 0.632171i \(-0.217836\pi\)
0.774829 + 0.632171i \(0.217836\pi\)
\(468\) 0 0
\(469\) 11.9388 + 0.805688i 0.551280 + 0.0372032i
\(470\) −13.8607 1.00415i −0.639348 0.0463180i
\(471\) 0 0
\(472\) −2.60563 + 11.8208i −0.119934 + 0.544097i
\(473\) 38.7980 1.78394
\(474\) 0 0
\(475\) 2.81981 0.129382
\(476\) 34.6673 + 7.46236i 1.58897 + 0.342037i
\(477\) 0 0
\(478\) −20.8132 1.50783i −0.951976 0.0689665i
\(479\) 21.1342 0.965644 0.482822 0.875718i \(-0.339612\pi\)
0.482822 + 0.875718i \(0.339612\pi\)
\(480\) 0 0
\(481\) 9.68314i 0.441513i
\(482\) 21.6235 + 1.56653i 0.984921 + 0.0713533i
\(483\) 0 0
\(484\) 32.3343 + 4.70968i 1.46974 + 0.214076i
\(485\) 10.5209 0.477730
\(486\) 0 0
\(487\) 13.3600i 0.605399i −0.953086 0.302699i \(-0.902112\pi\)
0.953086 0.302699i \(-0.0978878\pi\)
\(488\) −29.5696 6.51795i −1.33855 0.295054i
\(489\) 0 0
\(490\) −9.68799 2.03542i −0.437659 0.0919508i
\(491\) 10.6077i 0.478717i −0.970931 0.239359i \(-0.923063\pi\)
0.970931 0.239359i \(-0.0769372\pi\)
\(492\) 0 0
\(493\) 43.3814i 1.95380i
\(494\) 17.9990 + 1.30395i 0.809815 + 0.0586676i
\(495\) 0 0
\(496\) −9.99562 2.97496i −0.448817 0.133579i
\(497\) 19.0989 + 1.28889i 0.856703 + 0.0578147i
\(498\) 0 0
\(499\) 22.9131i 1.02573i −0.858470 0.512865i \(-0.828584\pi\)
0.858470 0.512865i \(-0.171416\pi\)
\(500\) −0.288270 + 1.97912i −0.0128918 + 0.0885088i
\(501\) 0 0
\(502\) 1.57430 21.7308i 0.0702646 0.969893i
\(503\) −15.2517 −0.680040 −0.340020 0.940418i \(-0.610434\pi\)
−0.340020 + 0.940418i \(0.610434\pi\)
\(504\) 0 0
\(505\) 3.97836 0.177035
\(506\) 0.458745 6.33227i 0.0203937 0.281504i
\(507\) 0 0
\(508\) −3.02204 + 20.7478i −0.134081 + 0.920536i
\(509\) 6.06153i 0.268673i 0.990936 + 0.134336i \(0.0428902\pi\)
−0.990936 + 0.134336i \(0.957110\pi\)
\(510\) 0 0
\(511\) −24.4097 1.64729i −1.07982 0.0728717i
\(512\) 13.7095 18.0013i 0.605882 0.795555i
\(513\) 0 0
\(514\) −16.3781 1.18652i −0.722405 0.0523351i
\(515\) 3.78934i 0.166978i
\(516\) 0 0
\(517\) 51.3794i 2.25967i
\(518\) −7.92824 1.11485i −0.348347 0.0489839i
\(519\) 0 0
\(520\) −2.75524 + 12.4995i −0.120825 + 0.548141i
\(521\) 33.7238i 1.47747i 0.673998 + 0.738733i \(0.264576\pi\)
−0.673998 + 0.738733i \(0.735424\pi\)
\(522\) 0 0
\(523\) 17.5830 0.768852 0.384426 0.923156i \(-0.374399\pi\)
0.384426 + 0.923156i \(0.374399\pi\)
\(524\) −37.7884 5.50410i −1.65079 0.240448i
\(525\) 0 0
\(526\) 20.3340 + 1.47311i 0.886603 + 0.0642306i
\(527\) 17.4725i 0.761116i
\(528\) 0 0
\(529\) 22.2628 0.967947
\(530\) −5.20906 0.377374i −0.226267 0.0163921i
\(531\) 0 0
\(532\) 3.13993 14.5869i 0.136133 0.632422i
\(533\) −39.4373 −1.70822
\(534\) 0 0
\(535\) 2.38868 0.103272
\(536\) −12.4922 2.75363i −0.539581 0.118939i
\(537\) 0 0
\(538\) 15.3015 + 1.10853i 0.659696 + 0.0477921i
\(539\) 4.91749 36.2680i 0.211811 1.56217i
\(540\) 0 0
\(541\) −22.7960 −0.980079 −0.490039 0.871700i \(-0.663018\pi\)
−0.490039 + 0.871700i \(0.663018\pi\)
\(542\) −1.93906 + 26.7657i −0.0832897 + 1.14968i
\(543\) 0 0
\(544\) −35.4582 13.4113i −1.52026 0.575003i
\(545\) 5.79748i 0.248337i
\(546\) 0 0
\(547\) 14.4784i 0.619053i 0.950891 + 0.309527i \(0.100171\pi\)
−0.950891 + 0.309527i \(0.899829\pi\)
\(548\) 10.8300 + 1.57745i 0.462635 + 0.0673854i
\(549\) 0 0
\(550\) −7.37496 0.534284i −0.314469 0.0227819i
\(551\) 18.2535 0.777627
\(552\) 0 0
\(553\) 7.08281 + 0.477984i 0.301192 + 0.0203259i
\(554\) 1.13385 15.6511i 0.0481727 0.664950i
\(555\) 0 0
\(556\) −5.61957 0.818523i −0.238323 0.0347131i
\(557\) −14.9697 −0.634288 −0.317144 0.948377i \(-0.602724\pi\)
−0.317144 + 0.948377i \(0.602724\pi\)
\(558\) 0 0
\(559\) −33.5800 −1.42028
\(560\) 9.91700 + 3.69502i 0.419070 + 0.156143i
\(561\) 0 0
\(562\) 2.67111 36.8705i 0.112674 1.55529i
\(563\) −6.81282 −0.287126 −0.143563 0.989641i \(-0.545856\pi\)
−0.143563 + 0.989641i \(0.545856\pi\)
\(564\) 0 0
\(565\) 6.86598i 0.288854i
\(566\) 1.53302 21.1610i 0.0644377 0.889462i
\(567\) 0 0
\(568\) −19.9843 4.40509i −0.838522 0.184833i
\(569\) −15.3819 −0.644841 −0.322421 0.946597i \(-0.604497\pi\)
−0.322421 + 0.946597i \(0.604497\pi\)
\(570\) 0 0
\(571\) 33.9875i 1.42233i 0.703024 + 0.711167i \(0.251833\pi\)
−0.703024 + 0.711167i \(0.748167\pi\)
\(572\) −46.8278 6.82075i −1.95797 0.285190i
\(573\) 0 0
\(574\) −4.54056 + 32.2900i −0.189519 + 1.34776i
\(575\) 0.858617i 0.0358068i
\(576\) 0 0
\(577\) 41.9819i 1.74773i 0.486170 + 0.873864i \(0.338394\pi\)
−0.486170 + 0.873864i \(0.661606\pi\)
\(578\) −2.85210 + 39.3688i −0.118632 + 1.63753i
\(579\) 0 0
\(580\) −1.86607 + 12.8115i −0.0774842 + 0.531968i
\(581\) −2.90039 + 42.9783i −0.120329 + 1.78304i
\(582\) 0 0
\(583\) 19.3091i 0.799701i
\(584\) 25.5412 + 5.62999i 1.05690 + 0.232971i
\(585\) 0 0
\(586\) −42.5646 3.08362i −1.75833 0.127383i
\(587\) −12.5442 −0.517756 −0.258878 0.965910i \(-0.583353\pi\)
−0.258878 + 0.965910i \(0.583353\pi\)
\(588\) 0 0
\(589\) 7.35190 0.302930
\(590\) 6.03647 + 0.437316i 0.248518 + 0.0180040i
\(591\) 0 0
\(592\) 8.20340 + 2.44155i 0.337158 + 0.100347i
\(593\) 9.26081i 0.380296i 0.981755 + 0.190148i \(0.0608968\pi\)
−0.981755 + 0.190148i \(0.939103\pi\)
\(594\) 0 0
\(595\) 1.19384 17.6904i 0.0489426 0.725237i
\(596\) 3.42102 + 0.498291i 0.140130 + 0.0204108i
\(597\) 0 0
\(598\) −0.397047 + 5.48062i −0.0162365 + 0.224119i
\(599\) 15.8991i 0.649618i 0.945780 + 0.324809i \(0.105300\pi\)
−0.945780 + 0.324809i \(0.894700\pi\)
\(600\) 0 0
\(601\) 31.4061i 1.28108i 0.767925 + 0.640540i \(0.221289\pi\)
−0.767925 + 0.640540i \(0.778711\pi\)
\(602\) −3.86618 + 27.4942i −0.157574 + 1.12058i
\(603\) 0 0
\(604\) 4.31055 29.5941i 0.175394 1.20417i
\(605\) 16.3377i 0.664223i
\(606\) 0 0
\(607\) −14.6628 −0.595147 −0.297573 0.954699i \(-0.596177\pi\)
−0.297573 + 0.954699i \(0.596177\pi\)
\(608\) −5.64304 + 14.9197i −0.228855 + 0.605074i
\(609\) 0 0
\(610\) −1.09394 + 15.1001i −0.0442923 + 0.611387i
\(611\) 44.4692i 1.79903i
\(612\) 0 0
\(613\) 35.6120 1.43836 0.719178 0.694826i \(-0.244519\pi\)
0.719178 + 0.694826i \(0.244519\pi\)
\(614\) −0.630955 + 8.70935i −0.0254633 + 0.351481i
\(615\) 0 0
\(616\) −10.9761 + 37.5558i −0.442238 + 1.51317i
\(617\) −22.0702 −0.888513 −0.444256 0.895900i \(-0.646532\pi\)
−0.444256 + 0.895900i \(0.646532\pi\)
\(618\) 0 0
\(619\) −29.1671 −1.17232 −0.586162 0.810194i \(-0.699362\pi\)
−0.586162 + 0.810194i \(0.699362\pi\)
\(620\) −0.751587 + 5.16002i −0.0301845 + 0.207231i
\(621\) 0 0
\(622\) −0.388882 + 5.36792i −0.0155928 + 0.215234i
\(623\) −22.5307 1.52048i −0.902672 0.0609169i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −23.3827 1.69398i −0.934562 0.0677050i
\(627\) 0 0
\(628\) 3.18201 21.8461i 0.126976 0.871754i
\(629\) 14.3397i 0.571762i
\(630\) 0 0
\(631\) 0.162149i 0.00645504i −0.999995 0.00322752i \(-0.998973\pi\)
0.999995 0.00322752i \(-0.00102735\pi\)
\(632\) −7.41115 1.63362i −0.294800 0.0649820i
\(633\) 0 0
\(634\) 1.13546 15.6733i 0.0450950 0.622467i
\(635\) 10.4834 0.416020
\(636\) 0 0
\(637\) −4.25612 + 31.3902i −0.168634 + 1.24372i
\(638\) −47.7406 3.45860i −1.89007 0.136927i
\(639\) 0 0
\(640\) −9.89470 5.48588i −0.391122 0.216849i
\(641\) −12.4758 −0.492766 −0.246383 0.969173i \(-0.579242\pi\)
−0.246383 + 0.969173i \(0.579242\pi\)
\(642\) 0 0
\(643\) −28.4881 −1.12346 −0.561731 0.827320i \(-0.689864\pi\)
−0.561731 + 0.827320i \(0.689864\pi\)
\(644\) 4.44164 + 0.956093i 0.175025 + 0.0376753i
\(645\) 0 0
\(646\) 26.6547 + 1.93102i 1.04871 + 0.0759748i
\(647\) 24.4328 0.960554 0.480277 0.877117i \(-0.340536\pi\)
0.480277 + 0.877117i \(0.340536\pi\)
\(648\) 0 0
\(649\) 22.3762i 0.878342i
\(650\) 6.38308 + 0.462426i 0.250365 + 0.0181379i
\(651\) 0 0
\(652\) 5.41858 37.2012i 0.212208 1.45691i
\(653\) 39.9022 1.56149 0.780746 0.624848i \(-0.214839\pi\)
0.780746 + 0.624848i \(0.214839\pi\)
\(654\) 0 0
\(655\) 19.0936i 0.746047i
\(656\) 9.94388 33.4107i 0.388243 1.30447i
\(657\) 0 0
\(658\) 36.4100 + 5.11990i 1.41941 + 0.199595i
\(659\) 2.24981i 0.0876403i −0.999039 0.0438202i \(-0.986047\pi\)
0.999039 0.0438202i \(-0.0139529\pi\)
\(660\) 0 0
\(661\) 26.0267i 1.01232i −0.862439 0.506162i \(-0.831064\pi\)
0.862439 0.506162i \(-0.168936\pi\)
\(662\) −31.6956 2.29621i −1.23188 0.0892447i
\(663\) 0 0
\(664\) 9.91278 44.9707i 0.384690 1.74520i
\(665\) −7.44358 0.502330i −0.288650 0.0194795i
\(666\) 0 0
\(667\) 5.55812i 0.215211i
\(668\) 3.74676 + 0.545738i 0.144967 + 0.0211152i
\(669\) 0 0
\(670\) −0.462155 + 6.37933i −0.0178546 + 0.246455i
\(671\) −55.9737 −2.16084
\(672\) 0 0
\(673\) 34.4184 1.32673 0.663365 0.748296i \(-0.269127\pi\)
0.663365 + 0.748296i \(0.269127\pi\)
\(674\) −0.615904 + 8.50160i −0.0237237 + 0.327469i
\(675\) 0 0
\(676\) 14.8013 + 2.15590i 0.569281 + 0.0829191i
\(677\) 37.6392i 1.44659i 0.690538 + 0.723296i \(0.257374\pi\)
−0.690538 + 0.723296i \(0.742626\pi\)
\(678\) 0 0
\(679\) −27.7725 1.87423i −1.06581 0.0719264i
\(680\) −4.08023 + 18.5105i −0.156470 + 0.709846i
\(681\) 0 0
\(682\) −19.2282 1.39300i −0.736288 0.0533409i
\(683\) 25.5973i 0.979454i −0.871876 0.489727i \(-0.837096\pi\)
0.871876 0.489727i \(-0.162904\pi\)
\(684\) 0 0
\(685\) 5.47214i 0.209080i
\(686\) 25.2112 + 7.09884i 0.962570 + 0.271035i
\(687\) 0 0
\(688\) 8.46699 28.4484i 0.322801 1.08459i
\(689\) 16.7122i 0.636682i
\(690\) 0 0
\(691\) 20.4140 0.776585 0.388293 0.921536i \(-0.373065\pi\)
0.388293 + 0.921536i \(0.373065\pi\)
\(692\) 2.71927 18.6691i 0.103371 0.709693i
\(693\) 0 0
\(694\) 13.5000 + 0.978013i 0.512451 + 0.0371249i
\(695\) 2.83943i 0.107706i
\(696\) 0 0
\(697\) −58.4025 −2.21215
\(698\) 18.2579 + 1.32271i 0.691073 + 0.0500653i
\(699\) 0 0
\(700\) 1.11353 5.17301i 0.0420873 0.195521i
\(701\) 7.73141 0.292011 0.146006 0.989284i \(-0.453358\pi\)
0.146006 + 0.989284i \(0.453358\pi\)
\(702\) 0 0
\(703\) −6.03370 −0.227565
\(704\) 17.5858 37.9520i 0.662790 1.43037i
\(705\) 0 0
\(706\) 16.3915 + 1.18750i 0.616903 + 0.0446920i
\(707\) −10.5019 0.708718i −0.394963 0.0266541i
\(708\) 0 0
\(709\) 29.7793 1.11839 0.559193 0.829038i \(-0.311111\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(710\) −0.739328 + 10.2053i −0.0277465 + 0.382997i
\(711\) 0 0
\(712\) 23.5751 + 5.19661i 0.883515 + 0.194751i
\(713\) 2.23862i 0.0838369i
\(714\) 0 0
\(715\) 23.6610i 0.884871i
\(716\) −6.18677 + 42.4753i −0.231211 + 1.58738i
\(717\) 0 0
\(718\) 7.65182 + 0.554341i 0.285563 + 0.0206878i
\(719\) 18.4203 0.686963 0.343481 0.939160i \(-0.388394\pi\)
0.343481 + 0.939160i \(0.388394\pi\)
\(720\) 0 0
\(721\) −0.675047 + 10.0029i −0.0251401 + 0.372528i
\(722\) −1.12902 + 15.5844i −0.0420178 + 0.579990i
\(723\) 0 0
\(724\) −6.96851 + 47.8423i −0.258983 + 1.77804i
\(725\) 6.47333 0.240414
\(726\) 0 0
\(727\) −30.7292 −1.13968 −0.569842 0.821754i \(-0.692996\pi\)
−0.569842 + 0.821754i \(0.692996\pi\)
\(728\) 9.49986 32.5048i 0.352088 1.20471i
\(729\) 0 0
\(730\) 0.944910 13.0430i 0.0349727 0.482743i
\(731\) −49.7284 −1.83927
\(732\) 0 0
\(733\) 5.09061i 0.188026i −0.995571 0.0940130i \(-0.970030\pi\)
0.995571 0.0940130i \(-0.0299695\pi\)
\(734\) −2.90415 + 40.0873i −0.107194 + 1.47965i
\(735\) 0 0
\(736\) −4.54298 1.71828i −0.167456 0.0633365i
\(737\) −23.6471 −0.871052
\(738\) 0 0
\(739\) 15.1154i 0.556030i −0.960577 0.278015i \(-0.910323\pi\)
0.960577 0.278015i \(-0.0896765\pi\)
\(740\) 0.616827 4.23483i 0.0226750 0.155675i
\(741\) 0 0
\(742\) 13.6834 + 1.92413i 0.502332 + 0.0706370i
\(743\) 42.0496i 1.54265i −0.636440 0.771326i \(-0.719594\pi\)
0.636440 0.771326i \(-0.280406\pi\)
\(744\) 0 0
\(745\) 1.72856i 0.0633295i
\(746\) 2.35971 32.5721i 0.0863951 1.19255i
\(747\) 0 0
\(748\) −69.3471 10.1008i −2.53558 0.369322i
\(749\) −6.30551 0.425527i −0.230398 0.0155484i
\(750\) 0 0
\(751\) 24.8965i 0.908487i 0.890877 + 0.454244i \(0.150090\pi\)
−0.890877 + 0.454244i \(0.849910\pi\)
\(752\) −37.6736 11.2127i −1.37382 0.408884i
\(753\) 0 0
\(754\) 41.3198 + 2.99344i 1.50478 + 0.109015i
\(755\) −14.9532 −0.544202
\(756\) 0 0
\(757\) −39.7946 −1.44636 −0.723179 0.690661i \(-0.757320\pi\)
−0.723179 + 0.690661i \(0.757320\pi\)
\(758\) 17.0396 + 1.23444i 0.618905 + 0.0448370i
\(759\) 0 0
\(760\) 7.78864 + 1.71683i 0.282524 + 0.0622760i
\(761\) 27.5663i 0.999279i −0.866234 0.499639i \(-0.833466\pi\)
0.866234 0.499639i \(-0.166534\pi\)
\(762\) 0 0
\(763\) 1.03278 15.3039i 0.0373893 0.554038i
\(764\) −5.47199 + 37.5680i −0.197970 + 1.35916i
\(765\) 0 0
\(766\) 0.414468 5.72108i 0.0149753 0.206711i
\(767\) 19.3667i 0.699292i
\(768\) 0 0
\(769\) 5.38100i 0.194044i −0.995282 0.0970219i \(-0.969068\pi\)
0.995282 0.0970219i \(-0.0309317\pi\)
\(770\) 19.3728 + 2.72418i 0.698149 + 0.0981725i
\(771\) 0 0
\(772\) −52.6155 7.66376i −1.89367 0.275825i
\(773\) 18.8696i 0.678693i 0.940661 + 0.339347i \(0.110206\pi\)
−0.940661 + 0.339347i \(0.889794\pi\)
\(774\) 0 0
\(775\) 2.60723 0.0936546
\(776\) 29.0600 + 6.40563i 1.04319 + 0.229949i
\(777\) 0 0
\(778\) −0.540363 + 7.45887i −0.0193730 + 0.267413i
\(779\) 24.5739i 0.880453i
\(780\) 0 0
\(781\) −37.8292 −1.35364
\(782\) −0.587985 + 8.11622i −0.0210263 + 0.290235i
\(783\) 0 0
\(784\) −25.5201 11.5206i −0.911433 0.411449i
\(785\) −11.0383 −0.393974
\(786\) 0 0
\(787\) −36.8177 −1.31241 −0.656204 0.754583i \(-0.727839\pi\)
−0.656204 + 0.754583i \(0.727839\pi\)
\(788\) 45.9171 + 6.68809i 1.63573 + 0.238253i
\(789\) 0 0
\(790\) −0.274179 + 3.78461i −0.00975485 + 0.134651i
\(791\) 1.22313 18.1244i 0.0434895 0.644431i
\(792\)