Properties

Label 420.2.bh.b.101.3
Level $420$
Weight $2$
Character 420.101
Analytic conductor $3.354$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 420.bh (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.35371688489\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.29471584693248.1
Defining polynomial: \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.3
Root \(-1.08831 + 1.34743i\) of defining polynomial
Character \(\chi\) \(=\) 420.101
Dual form 420.2.bh.b.341.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.622752 + 1.61622i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.57325 - 0.615143i) q^{7} +(-2.22436 + 2.01301i) q^{9} +O(q^{10})\) \(q+(0.622752 + 1.61622i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.57325 - 0.615143i) q^{7} +(-2.22436 + 2.01301i) q^{9} +(1.80606 + 1.04273i) q^{11} +0.245770i q^{13} +(-1.08831 + 1.34743i) q^{15} +(0.471640 - 0.816904i) q^{17} +(-0.465563 + 0.268793i) q^{19} +(2.59670 + 3.77586i) q^{21} +(-2.40010 + 1.38570i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.63871 - 2.34145i) q^{27} +0.267475i q^{29} +(0.981097 + 0.566436i) q^{31} +(-0.560556 + 3.56836i) q^{33} +(1.81935 + 1.92093i) q^{35} +(3.08164 + 5.33755i) q^{37} +(-0.397219 + 0.153054i) q^{39} +2.38340 q^{41} -11.4354 q^{43} +(-2.85550 - 0.919845i) q^{45} +(-6.23215 - 10.7944i) q^{47} +(6.24320 - 3.16583i) q^{49} +(1.61401 + 0.253547i) q^{51} +(10.8541 + 6.26660i) q^{53} +2.08546i q^{55} +(-0.724359 - 0.585062i) q^{57} +(6.25478 - 10.8336i) q^{59} +(4.96556 - 2.86687i) q^{61} +(-4.48553 + 6.54828i) q^{63} +(-0.212843 + 0.122885i) q^{65} +(2.78001 - 4.81512i) q^{67} +(-3.73427 - 3.01616i) q^{69} -10.1375i q^{71} +(-11.3758 - 6.56784i) q^{73} +(-1.71107 - 0.268793i) q^{75} +(5.28887 + 1.57221i) q^{77} +(3.17314 + 5.49605i) q^{79} +(0.895549 - 8.95533i) q^{81} -1.06674 q^{83} +0.943279 q^{85} +(-0.432299 + 0.166571i) q^{87} +(0.463787 + 0.803302i) q^{89} +(0.151184 + 0.632426i) q^{91} +(-0.304508 + 1.93842i) q^{93} +(-0.465563 - 0.268793i) q^{95} -3.01245i q^{97} +(-6.11636 + 1.31622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(241\) \(281\) \(337\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\)

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 0
\(3\) 0.622752 + 1.61622i 0.359546 + 0.933127i
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.57325 0.615143i 0.972596 0.232502i
\(8\) 0 0
\(9\) −2.22436 + 2.01301i −0.741453 + 0.671005i
\(10\) 0 0
\(11\) 1.80606 + 1.04273i 0.544548 + 0.314395i 0.746920 0.664914i \(-0.231532\pi\)
−0.202372 + 0.979309i \(0.564865\pi\)
\(12\) 0 0
\(13\) 0.245770i 0.0681643i 0.999419 + 0.0340821i \(0.0108508\pi\)
−0.999419 + 0.0340821i \(0.989149\pi\)
\(14\) 0 0
\(15\) −1.08831 + 1.34743i −0.281002 + 0.347905i
\(16\) 0 0
\(17\) 0.471640 0.816904i 0.114389 0.198128i −0.803146 0.595782i \(-0.796842\pi\)
0.917536 + 0.397654i \(0.130176\pi\)
\(18\) 0 0
\(19\) −0.465563 + 0.268793i −0.106807 + 0.0616653i −0.552452 0.833545i \(-0.686308\pi\)
0.445645 + 0.895210i \(0.352974\pi\)
\(20\) 0 0
\(21\) 2.59670 + 3.77586i 0.566647 + 0.823960i
\(22\) 0 0
\(23\) −2.40010 + 1.38570i −0.500456 + 0.288938i −0.728902 0.684618i \(-0.759969\pi\)
0.228446 + 0.973557i \(0.426636\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −4.63871 2.34145i −0.892719 0.450613i
\(28\) 0 0
\(29\) 0.267475i 0.0496688i 0.999692 + 0.0248344i \(0.00790585\pi\)
−0.999692 + 0.0248344i \(0.992094\pi\)
\(30\) 0 0
\(31\) 0.981097 + 0.566436i 0.176210 + 0.101735i 0.585511 0.810665i \(-0.300894\pi\)
−0.409301 + 0.912400i \(0.634227\pi\)
\(32\) 0 0
\(33\) −0.560556 + 3.56836i −0.0975803 + 0.621172i
\(34\) 0 0
\(35\) 1.81935 + 1.92093i 0.307527 + 0.324696i
\(36\) 0 0
\(37\) 3.08164 + 5.33755i 0.506618 + 0.877488i 0.999971 + 0.00765857i \(0.00243782\pi\)
−0.493353 + 0.869829i \(0.664229\pi\)
\(38\) 0 0
\(39\) −0.397219 + 0.153054i −0.0636059 + 0.0245082i
\(40\) 0 0
\(41\) 2.38340 0.372224 0.186112 0.982529i \(-0.440411\pi\)
0.186112 + 0.982529i \(0.440411\pi\)
\(42\) 0 0
\(43\) −11.4354 −1.74388 −0.871938 0.489616i \(-0.837137\pi\)
−0.871938 + 0.489616i \(0.837137\pi\)
\(44\) 0 0
\(45\) −2.85550 0.919845i −0.425673 0.137122i
\(46\) 0 0
\(47\) −6.23215 10.7944i −0.909052 1.57452i −0.815384 0.578921i \(-0.803474\pi\)
−0.0936683 0.995603i \(-0.529859\pi\)
\(48\) 0 0
\(49\) 6.24320 3.16583i 0.891885 0.452261i
\(50\) 0 0
\(51\) 1.61401 + 0.253547i 0.226007 + 0.0355036i
\(52\) 0 0
\(53\) 10.8541 + 6.26660i 1.49092 + 0.860784i 0.999946 0.0103892i \(-0.00330704\pi\)
0.490976 + 0.871173i \(0.336640\pi\)
\(54\) 0 0
\(55\) 2.08546i 0.281203i
\(56\) 0 0
\(57\) −0.724359 0.585062i −0.0959437 0.0774934i
\(58\) 0 0
\(59\) 6.25478 10.8336i 0.814303 1.41041i −0.0955244 0.995427i \(-0.530453\pi\)
0.909827 0.414987i \(-0.136214\pi\)
\(60\) 0 0
\(61\) 4.96556 2.86687i 0.635775 0.367065i −0.147210 0.989105i \(-0.547029\pi\)
0.782985 + 0.622040i \(0.213696\pi\)
\(62\) 0 0
\(63\) −4.48553 + 6.54828i −0.565124 + 0.825006i
\(64\) 0 0
\(65\) −0.212843 + 0.122885i −0.0263999 + 0.0152420i
\(66\) 0 0
\(67\) 2.78001 4.81512i 0.339633 0.588261i −0.644731 0.764410i \(-0.723031\pi\)
0.984364 + 0.176149i \(0.0563639\pi\)
\(68\) 0 0
\(69\) −3.73427 3.01616i −0.449553 0.363103i
\(70\) 0 0
\(71\) 10.1375i 1.20310i −0.798835 0.601551i \(-0.794550\pi\)
0.798835 0.601551i \(-0.205450\pi\)
\(72\) 0 0
\(73\) −11.3758 6.56784i −1.33144 0.768707i −0.345919 0.938264i \(-0.612433\pi\)
−0.985520 + 0.169557i \(0.945766\pi\)
\(74\) 0 0
\(75\) −1.71107 0.268793i −0.197577 0.0310375i
\(76\) 0 0
\(77\) 5.28887 + 1.57221i 0.602722 + 0.179170i
\(78\) 0 0
\(79\) 3.17314 + 5.49605i 0.357007 + 0.618353i 0.987459 0.157874i \(-0.0504641\pi\)
−0.630453 + 0.776228i \(0.717131\pi\)
\(80\) 0 0
\(81\) 0.895549 8.95533i 0.0995055 0.995037i
\(82\) 0 0
\(83\) −1.06674 −0.117090 −0.0585449 0.998285i \(-0.518646\pi\)
−0.0585449 + 0.998285i \(0.518646\pi\)
\(84\) 0 0
\(85\) 0.943279 0.102313
\(86\) 0 0
\(87\) −0.432299 + 0.166571i −0.0463473 + 0.0178582i
\(88\) 0 0
\(89\) 0.463787 + 0.803302i 0.0491613 + 0.0851499i 0.889559 0.456820i \(-0.151012\pi\)
−0.840398 + 0.541970i \(0.817678\pi\)
\(90\) 0 0
\(91\) 0.151184 + 0.632426i 0.0158483 + 0.0662963i
\(92\) 0 0
\(93\) −0.304508 + 1.93842i −0.0315760 + 0.201005i
\(94\) 0 0
\(95\) −0.465563 0.268793i −0.0477657 0.0275776i
\(96\) 0 0
\(97\) 3.01245i 0.305868i −0.988236 0.152934i \(-0.951128\pi\)
0.988236 0.152934i \(-0.0488722\pi\)
\(98\) 0 0
\(99\) −6.11636 + 1.31622i −0.614717 + 0.132285i
\(100\) 0 0
\(101\) 6.19049 10.7223i 0.615977 1.06690i −0.374235 0.927334i \(-0.622095\pi\)
0.990212 0.139570i \(-0.0445720\pi\)
\(102\) 0 0
\(103\) −14.5787 + 8.41703i −1.43648 + 0.829355i −0.997603 0.0691903i \(-0.977958\pi\)
−0.438881 + 0.898545i \(0.644625\pi\)
\(104\) 0 0
\(105\) −1.97164 + 4.13674i −0.192412 + 0.403705i
\(106\) 0 0
\(107\) 11.1031 6.41036i 1.07337 0.619713i 0.144273 0.989538i \(-0.453916\pi\)
0.929101 + 0.369825i \(0.120582\pi\)
\(108\) 0 0
\(109\) 1.79448 3.10813i 0.171880 0.297705i −0.767197 0.641411i \(-0.778349\pi\)
0.939077 + 0.343707i \(0.111683\pi\)
\(110\) 0 0
\(111\) −6.70758 + 8.30459i −0.636655 + 0.788236i
\(112\) 0 0
\(113\) 1.00353i 0.0944041i 0.998885 + 0.0472020i \(0.0150305\pi\)
−0.998885 + 0.0472020i \(0.984970\pi\)
\(114\) 0 0
\(115\) −2.40010 1.38570i −0.223811 0.129217i
\(116\) 0 0
\(117\) −0.494738 0.546680i −0.0457385 0.0505406i
\(118\) 0 0
\(119\) 0.711132 2.39222i 0.0651894 0.219295i
\(120\) 0 0
\(121\) −3.32543 5.75981i −0.302312 0.523619i
\(122\) 0 0
\(123\) 1.48426 + 3.85210i 0.133832 + 0.347332i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −7.76096 −0.688674 −0.344337 0.938846i \(-0.611896\pi\)
−0.344337 + 0.938846i \(0.611896\pi\)
\(128\) 0 0
\(129\) −7.12140 18.4821i −0.627004 1.62726i
\(130\) 0 0
\(131\) −8.58199 14.8644i −0.749812 1.29871i −0.947913 0.318530i \(-0.896811\pi\)
0.198101 0.980182i \(-0.436523\pi\)
\(132\) 0 0
\(133\) −1.03266 + 0.978058i −0.0895431 + 0.0848084i
\(134\) 0 0
\(135\) −0.291594 5.18796i −0.0250965 0.446509i
\(136\) 0 0
\(137\) 13.0137 + 7.51345i 1.11183 + 0.641918i 0.939304 0.343087i \(-0.111472\pi\)
0.172530 + 0.985004i \(0.444806\pi\)
\(138\) 0 0
\(139\) 9.83141i 0.833889i 0.908932 + 0.416945i \(0.136899\pi\)
−0.908932 + 0.416945i \(0.863101\pi\)
\(140\) 0 0
\(141\) 13.5651 16.7948i 1.14239 1.41438i
\(142\) 0 0
\(143\) −0.256271 + 0.443875i −0.0214305 + 0.0371187i
\(144\) 0 0
\(145\) −0.231640 + 0.133737i −0.0192367 + 0.0111063i
\(146\) 0 0
\(147\) 9.00466 + 8.11888i 0.742692 + 0.669634i
\(148\) 0 0
\(149\) −19.9895 + 11.5409i −1.63760 + 0.945469i −0.655943 + 0.754810i \(0.727729\pi\)
−0.981656 + 0.190658i \(0.938938\pi\)
\(150\) 0 0
\(151\) 7.20527 12.4799i 0.586357 1.01560i −0.408348 0.912826i \(-0.633895\pi\)
0.994705 0.102774i \(-0.0327717\pi\)
\(152\) 0 0
\(153\) 0.595343 + 2.76650i 0.0481306 + 0.223659i
\(154\) 0 0
\(155\) 1.13287i 0.0909945i
\(156\) 0 0
\(157\) −1.90441 1.09951i −0.151988 0.0877506i 0.422077 0.906560i \(-0.361301\pi\)
−0.574065 + 0.818809i \(0.694635\pi\)
\(158\) 0 0
\(159\) −3.36883 + 21.4452i −0.267166 + 1.70071i
\(160\) 0 0
\(161\) −5.32365 + 5.04216i −0.419563 + 0.397378i
\(162\) 0 0
\(163\) −4.92757 8.53481i −0.385957 0.668498i 0.605944 0.795507i \(-0.292795\pi\)
−0.991902 + 0.127009i \(0.959462\pi\)
\(164\) 0 0
\(165\) −3.37057 + 1.29872i −0.262398 + 0.101106i
\(166\) 0 0
\(167\) −22.8349 −1.76702 −0.883509 0.468415i \(-0.844825\pi\)
−0.883509 + 0.468415i \(0.844825\pi\)
\(168\) 0 0
\(169\) 12.9396 0.995354
\(170\) 0 0
\(171\) 0.494495 1.53508i 0.0378150 0.117390i
\(172\) 0 0
\(173\) 4.87085 + 8.43656i 0.370324 + 0.641420i 0.989615 0.143741i \(-0.0459133\pi\)
−0.619291 + 0.785161i \(0.712580\pi\)
\(174\) 0 0
\(175\) −0.753894 + 2.53607i −0.0569890 + 0.191709i
\(176\) 0 0
\(177\) 21.4047 + 3.36248i 1.60888 + 0.252739i
\(178\) 0 0
\(179\) 15.6543 + 9.03800i 1.17006 + 0.675532i 0.953693 0.300781i \(-0.0972473\pi\)
0.216363 + 0.976313i \(0.430581\pi\)
\(180\) 0 0
\(181\) 17.7230i 1.31734i 0.752433 + 0.658669i \(0.228880\pi\)
−0.752433 + 0.658669i \(0.771120\pi\)
\(182\) 0 0
\(183\) 7.72582 + 6.24011i 0.571109 + 0.461282i
\(184\) 0 0
\(185\) −3.08164 + 5.33755i −0.226566 + 0.392425i
\(186\) 0 0
\(187\) 1.70362 0.983585i 0.124581 0.0719269i
\(188\) 0 0
\(189\) −13.3769 3.17167i −0.973024 0.230705i
\(190\) 0 0
\(191\) −19.0353 + 10.9901i −1.37735 + 0.795212i −0.991840 0.127492i \(-0.959307\pi\)
−0.385508 + 0.922704i \(0.625974\pi\)
\(192\) 0 0
\(193\) 4.48820 7.77378i 0.323067 0.559569i −0.658052 0.752973i \(-0.728619\pi\)
0.981119 + 0.193403i \(0.0619526\pi\)
\(194\) 0 0
\(195\) −0.331158 0.267475i −0.0237147 0.0191543i
\(196\) 0 0
\(197\) 22.3002i 1.58882i 0.607382 + 0.794410i \(0.292220\pi\)
−0.607382 + 0.794410i \(0.707780\pi\)
\(198\) 0 0
\(199\) 16.3807 + 9.45740i 1.16120 + 0.670417i 0.951591 0.307368i \(-0.0994484\pi\)
0.209606 + 0.977786i \(0.432782\pi\)
\(200\) 0 0
\(201\) 9.51358 + 1.49449i 0.671036 + 0.105414i
\(202\) 0 0
\(203\) 0.164535 + 0.688279i 0.0115481 + 0.0483077i
\(204\) 0 0
\(205\) 1.19170 + 2.06408i 0.0832318 + 0.144162i
\(206\) 0 0
\(207\) 2.54926 7.91374i 0.177186 0.550043i
\(208\) 0 0
\(209\) −1.12111 −0.0775490
\(210\) 0 0
\(211\) 20.4152 1.40544 0.702722 0.711465i \(-0.251968\pi\)
0.702722 + 0.711465i \(0.251968\pi\)
\(212\) 0 0
\(213\) 16.3845 6.31316i 1.12265 0.432571i
\(214\) 0 0
\(215\) −5.71768 9.90331i −0.389943 0.675400i
\(216\) 0 0
\(217\) 2.87304 + 0.854066i 0.195035 + 0.0579778i
\(218\) 0 0
\(219\) 3.53077 22.4760i 0.238588 1.51879i
\(220\) 0 0
\(221\) 0.200770 + 0.115915i 0.0135053 + 0.00779727i
\(222\) 0 0
\(223\) 13.5949i 0.910379i 0.890395 + 0.455189i \(0.150428\pi\)
−0.890395 + 0.455189i \(0.849572\pi\)
\(224\) 0 0
\(225\) −0.631142 2.93286i −0.0420761 0.195524i
\(226\) 0 0
\(227\) −5.03260 + 8.71671i −0.334025 + 0.578549i −0.983297 0.182008i \(-0.941740\pi\)
0.649272 + 0.760556i \(0.275074\pi\)
\(228\) 0 0
\(229\) 12.3651 7.13897i 0.817106 0.471756i −0.0323114 0.999478i \(-0.510287\pi\)
0.849418 + 0.527721i \(0.176953\pi\)
\(230\) 0 0
\(231\) 0.752603 + 9.52709i 0.0495176 + 0.626837i
\(232\) 0 0
\(233\) −17.9716 + 10.3759i −1.17736 + 0.679750i −0.955403 0.295306i \(-0.904578\pi\)
−0.221958 + 0.975056i \(0.571245\pi\)
\(234\) 0 0
\(235\) 6.23215 10.7944i 0.406540 0.704149i
\(236\) 0 0
\(237\) −6.90676 + 8.55118i −0.448642 + 0.555459i
\(238\) 0 0
\(239\) 4.86422i 0.314640i 0.987548 + 0.157320i \(0.0502854\pi\)
−0.987548 + 0.157320i \(0.949715\pi\)
\(240\) 0 0
\(241\) −14.9239 8.61634i −0.961336 0.555028i −0.0647520 0.997901i \(-0.520626\pi\)
−0.896584 + 0.442874i \(0.853959\pi\)
\(242\) 0 0
\(243\) 15.0315 4.12954i 0.964273 0.264910i
\(244\) 0 0
\(245\) 5.86329 + 3.82385i 0.374592 + 0.244297i
\(246\) 0 0
\(247\) −0.0660611 0.114421i −0.00420337 0.00728045i
\(248\) 0 0
\(249\) −0.664314 1.72409i −0.0420992 0.109260i
\(250\) 0 0
\(251\) 15.8276 0.999031 0.499516 0.866305i \(-0.333511\pi\)
0.499516 + 0.866305i \(0.333511\pi\)
\(252\) 0 0
\(253\) −5.77964 −0.363363
\(254\) 0 0
\(255\) 0.587429 + 1.52455i 0.0367862 + 0.0954710i
\(256\) 0 0
\(257\) −9.10800 15.7755i −0.568141 0.984050i −0.996750 0.0805593i \(-0.974329\pi\)
0.428609 0.903490i \(-0.359004\pi\)
\(258\) 0 0
\(259\) 11.2132 + 11.8392i 0.696752 + 0.735651i
\(260\) 0 0
\(261\) −0.538431 0.594960i −0.0333280 0.0368271i
\(262\) 0 0
\(263\) 4.55971 + 2.63255i 0.281164 + 0.162330i 0.633950 0.773374i \(-0.281432\pi\)
−0.352786 + 0.935704i \(0.614766\pi\)
\(264\) 0 0
\(265\) 12.5332i 0.769909i
\(266\) 0 0
\(267\) −1.00949 + 1.24984i −0.0617799 + 0.0764891i
\(268\) 0 0
\(269\) −0.775418 + 1.34306i −0.0472780 + 0.0818880i −0.888696 0.458497i \(-0.848388\pi\)
0.841418 + 0.540385i \(0.181721\pi\)
\(270\) 0 0
\(271\) −9.77676 + 5.64461i −0.593896 + 0.342886i −0.766636 0.642082i \(-0.778071\pi\)
0.172741 + 0.984967i \(0.444738\pi\)
\(272\) 0 0
\(273\) −0.927992 + 0.638191i −0.0561647 + 0.0386251i
\(274\) 0 0
\(275\) −1.80606 + 1.04273i −0.108910 + 0.0628790i
\(276\) 0 0
\(277\) −8.54371 + 14.7981i −0.513342 + 0.889134i 0.486538 + 0.873659i \(0.338259\pi\)
−0.999880 + 0.0154751i \(0.995074\pi\)
\(278\) 0 0
\(279\) −3.32256 + 0.715003i −0.198916 + 0.0428061i
\(280\) 0 0
\(281\) 15.2188i 0.907880i 0.891032 + 0.453940i \(0.149982\pi\)
−0.891032 + 0.453940i \(0.850018\pi\)
\(282\) 0 0
\(283\) −14.2634 8.23500i −0.847874 0.489520i 0.0120590 0.999927i \(-0.496161\pi\)
−0.859933 + 0.510407i \(0.829495\pi\)
\(284\) 0 0
\(285\) 0.144499 0.919845i 0.00855939 0.0544869i
\(286\) 0 0
\(287\) 6.13307 1.46613i 0.362023 0.0865429i
\(288\) 0 0
\(289\) 8.05511 + 13.9519i 0.473830 + 0.820698i
\(290\) 0 0
\(291\) 4.86879 1.87601i 0.285414 0.109974i
\(292\) 0 0
\(293\) −18.1748 −1.06179 −0.530893 0.847439i \(-0.678143\pi\)
−0.530893 + 0.847439i \(0.678143\pi\)
\(294\) 0 0
\(295\) 12.5096 0.728335
\(296\) 0 0
\(297\) −5.93628 9.06572i −0.344458 0.526047i
\(298\) 0 0
\(299\) −0.340563 0.589873i −0.0196953 0.0341132i
\(300\) 0 0
\(301\) −29.4260 + 7.03438i −1.69609 + 0.405455i
\(302\) 0 0
\(303\) 21.1847 + 3.32792i 1.21703 + 0.191184i
\(304\) 0 0
\(305\) 4.96556 + 2.86687i 0.284327 + 0.164156i
\(306\) 0 0
\(307\) 24.6960i 1.40948i −0.709468 0.704738i \(-0.751065\pi\)
0.709468 0.704738i \(-0.248935\pi\)
\(308\) 0 0
\(309\) −22.6827 18.3208i −1.29038 1.04223i
\(310\) 0 0
\(311\) −11.5061 + 19.9291i −0.652448 + 1.13007i 0.330079 + 0.943953i \(0.392925\pi\)
−0.982527 + 0.186120i \(0.940409\pi\)
\(312\) 0 0
\(313\) 2.73490 1.57900i 0.154586 0.0892502i −0.420712 0.907194i \(-0.638220\pi\)
0.575298 + 0.817944i \(0.304886\pi\)
\(314\) 0 0
\(315\) −7.91374 0.610446i −0.445889 0.0343947i
\(316\) 0 0
\(317\) 2.78696 1.60905i 0.156531 0.0903734i −0.419688 0.907668i \(-0.637861\pi\)
0.576220 + 0.817295i \(0.304527\pi\)
\(318\) 0 0
\(319\) −0.278904 + 0.483076i −0.0156156 + 0.0270471i
\(320\) 0 0
\(321\) 17.2750 + 13.9530i 0.964199 + 0.778780i
\(322\) 0 0
\(323\) 0.507093i 0.0282154i
\(324\) 0 0
\(325\) −0.212843 0.122885i −0.0118064 0.00681643i
\(326\) 0 0
\(327\) 6.14095 + 0.964686i 0.339595 + 0.0533472i
\(328\) 0 0
\(329\) −22.6770 23.9430i −1.25022 1.32002i
\(330\) 0 0
\(331\) −14.0918 24.4077i −0.774554 1.34157i −0.935045 0.354529i \(-0.884641\pi\)
0.160491 0.987037i \(-0.448692\pi\)
\(332\) 0 0
\(333\) −17.5992 5.66925i −0.964432 0.310673i
\(334\) 0 0
\(335\) 5.56003 0.303777
\(336\) 0 0
\(337\) −18.4497 −1.00502 −0.502510 0.864571i \(-0.667590\pi\)
−0.502510 + 0.864571i \(0.667590\pi\)
\(338\) 0 0
\(339\) −1.62193 + 0.624950i −0.0880910 + 0.0339426i
\(340\) 0 0
\(341\) 1.18128 + 2.04604i 0.0639699 + 0.110799i
\(342\) 0 0
\(343\) 14.1178 11.9869i 0.762292 0.647233i
\(344\) 0 0
\(345\) 0.744932 4.74205i 0.0401058 0.255304i
\(346\) 0 0
\(347\) −13.3367 7.69997i −0.715953 0.413356i 0.0973081 0.995254i \(-0.468977\pi\)
−0.813261 + 0.581898i \(0.802310\pi\)
\(348\) 0 0
\(349\) 21.9727i 1.17617i −0.808799 0.588086i \(-0.799882\pi\)
0.808799 0.588086i \(-0.200118\pi\)
\(350\) 0 0
\(351\) 0.575458 1.14005i 0.0307157 0.0608516i
\(352\) 0 0
\(353\) 8.66505 15.0083i 0.461194 0.798811i −0.537827 0.843055i \(-0.680755\pi\)
0.999021 + 0.0442440i \(0.0140879\pi\)
\(354\) 0 0
\(355\) 8.77935 5.06876i 0.465959 0.269022i
\(356\) 0 0
\(357\) 4.30922 0.340412i 0.228068 0.0180165i
\(358\) 0 0
\(359\) −0.270990 + 0.156456i −0.0143023 + 0.00825745i −0.507134 0.861867i \(-0.669295\pi\)
0.492832 + 0.870125i \(0.335962\pi\)
\(360\) 0 0
\(361\) −9.35550 + 16.2042i −0.492395 + 0.852853i
\(362\) 0 0
\(363\) 7.23823 8.96158i 0.379909 0.470361i
\(364\) 0 0
\(365\) 13.1357i 0.687553i
\(366\) 0 0
\(367\) 3.20094 + 1.84807i 0.167088 + 0.0964682i 0.581212 0.813752i \(-0.302579\pi\)
−0.414124 + 0.910220i \(0.635912\pi\)
\(368\) 0 0
\(369\) −5.30153 + 4.79781i −0.275987 + 0.249764i
\(370\) 0 0
\(371\) 31.7851 + 9.44871i 1.65020 + 0.490552i
\(372\) 0 0
\(373\) 0.351666 + 0.609103i 0.0182086 + 0.0315381i 0.874986 0.484148i \(-0.160870\pi\)
−0.856778 + 0.515686i \(0.827537\pi\)
\(374\) 0 0
\(375\) −0.622752 1.61622i −0.0321588 0.0834614i
\(376\) 0 0
\(377\) −0.0657372 −0.00338564
\(378\) 0 0
\(379\) −10.3929 −0.533849 −0.266924 0.963717i \(-0.586007\pi\)
−0.266924 + 0.963717i \(0.586007\pi\)
\(380\) 0 0
\(381\) −4.83316 12.5435i −0.247610 0.642621i
\(382\) 0 0
\(383\) −14.7524 25.5519i −0.753813 1.30564i −0.945963 0.324276i \(-0.894879\pi\)
0.192150 0.981366i \(-0.438454\pi\)
\(384\) 0 0
\(385\) 1.28286 + 5.36640i 0.0653804 + 0.273497i
\(386\) 0 0
\(387\) 25.4364 23.0195i 1.29300 1.17015i
\(388\) 0 0
\(389\) 11.5224 + 6.65245i 0.584208 + 0.337293i 0.762804 0.646630i \(-0.223822\pi\)
−0.178596 + 0.983923i \(0.557155\pi\)
\(390\) 0 0
\(391\) 2.61420i 0.132206i
\(392\) 0 0
\(393\) 18.6798 23.1273i 0.942271 1.16662i
\(394\) 0 0
\(395\) −3.17314 + 5.49605i −0.159658 + 0.276536i
\(396\) 0 0
\(397\) −3.82832 + 2.21028i −0.192138 + 0.110931i −0.592983 0.805215i \(-0.702050\pi\)
0.400845 + 0.916146i \(0.368717\pi\)
\(398\) 0 0
\(399\) −2.22385 1.05992i −0.111332 0.0530626i
\(400\) 0 0
\(401\) −25.4507 + 14.6940i −1.27095 + 0.733781i −0.975166 0.221475i \(-0.928913\pi\)
−0.295780 + 0.955256i \(0.595580\pi\)
\(402\) 0 0
\(403\) −0.139213 + 0.241124i −0.00693469 + 0.0120112i
\(404\) 0 0
\(405\) 8.20332 3.70210i 0.407626 0.183959i
\(406\) 0 0
\(407\) 12.8533i 0.637112i
\(408\) 0 0
\(409\) 6.67308 + 3.85270i 0.329962 + 0.190504i 0.655824 0.754913i \(-0.272321\pi\)
−0.325862 + 0.945417i \(0.605654\pi\)
\(410\) 0 0
\(411\) −4.03912 + 25.7120i −0.199235 + 1.26828i
\(412\) 0 0
\(413\) 9.43088 31.7251i 0.464063 1.56109i
\(414\) 0 0
\(415\) −0.533370 0.923823i −0.0261821 0.0453487i
\(416\) 0 0
\(417\) −15.8898 + 6.12253i −0.778125 + 0.299822i
\(418\) 0 0
\(419\) 1.40692 0.0687327 0.0343663 0.999409i \(-0.489059\pi\)
0.0343663 + 0.999409i \(0.489059\pi\)
\(420\) 0 0
\(421\) −7.23785 −0.352751 −0.176375 0.984323i \(-0.556437\pi\)
−0.176375 + 0.984323i \(0.556437\pi\)
\(422\) 0 0
\(423\) 35.5918 + 11.4652i 1.73053 + 0.557458i
\(424\) 0 0
\(425\) 0.471640 + 0.816904i 0.0228779 + 0.0396256i
\(426\) 0 0
\(427\) 11.0141 10.4317i 0.533009 0.504825i
\(428\) 0 0
\(429\) −0.876995 0.137768i −0.0423417 0.00665149i
\(430\) 0 0
\(431\) 9.16199 + 5.28968i 0.441317 + 0.254795i 0.704156 0.710045i \(-0.251325\pi\)
−0.262839 + 0.964840i \(0.584659\pi\)
\(432\) 0 0
\(433\) 23.7164i 1.13974i −0.821735 0.569869i \(-0.806994\pi\)
0.821735 0.569869i \(-0.193006\pi\)
\(434\) 0 0
\(435\) −0.360404 0.291097i −0.0172800 0.0139570i
\(436\) 0 0
\(437\) 0.744932 1.29026i 0.0356349 0.0617215i
\(438\) 0 0
\(439\) −17.6684 + 10.2009i −0.843268 + 0.486861i −0.858374 0.513025i \(-0.828525\pi\)
0.0151058 + 0.999886i \(0.495191\pi\)
\(440\) 0 0
\(441\) −7.51425 + 19.6096i −0.357822 + 0.933790i
\(442\) 0 0
\(443\) 0.475830 0.274720i 0.0226074 0.0130524i −0.488654 0.872478i \(-0.662512\pi\)
0.511261 + 0.859425i \(0.329179\pi\)
\(444\) 0 0
\(445\) −0.463787 + 0.803302i −0.0219856 + 0.0380802i
\(446\) 0 0
\(447\) −31.1012 25.1203i −1.47104 1.18815i
\(448\) 0 0
\(449\) 1.12469i 0.0530772i 0.999648 + 0.0265386i \(0.00844850\pi\)
−0.999648 + 0.0265386i \(0.991552\pi\)
\(450\) 0 0
\(451\) 4.30456 + 2.48524i 0.202694 + 0.117025i
\(452\) 0 0
\(453\) 24.6574 + 3.87345i 1.15851 + 0.181991i
\(454\) 0 0
\(455\) −0.472105 + 0.447142i −0.0221326 + 0.0209623i
\(456\) 0 0
\(457\) 14.6946 + 25.4518i 0.687385 + 1.19059i 0.972681 + 0.232146i \(0.0745748\pi\)
−0.285296 + 0.958439i \(0.592092\pi\)
\(458\) 0 0
\(459\) −4.10054 + 2.68505i −0.191397 + 0.125328i
\(460\) 0 0
\(461\) 29.9734 1.39600 0.697999 0.716098i \(-0.254074\pi\)
0.697999 + 0.716098i \(0.254074\pi\)
\(462\) 0 0
\(463\) 13.0355 0.605809 0.302905 0.953021i \(-0.402044\pi\)
0.302905 + 0.953021i \(0.402044\pi\)
\(464\) 0 0
\(465\) −1.83098 + 0.705499i −0.0849095 + 0.0327167i
\(466\) 0 0
\(467\) −1.21626 2.10662i −0.0562817 0.0974828i 0.836512 0.547949i \(-0.184591\pi\)
−0.892794 + 0.450466i \(0.851258\pi\)
\(468\) 0 0
\(469\) 4.19167 14.1006i 0.193553 0.651105i
\(470\) 0 0
\(471\) 0.591082 3.76268i 0.0272356 0.173375i
\(472\) 0 0
\(473\) −20.6530 11.9240i −0.949624 0.548266i
\(474\) 0 0
\(475\) 0.537585i 0.0246661i
\(476\) 0 0
\(477\) −36.7581 + 7.91023i −1.68304 + 0.362184i
\(478\) 0 0
\(479\) −5.49101 + 9.51071i −0.250891 + 0.434555i −0.963771 0.266730i \(-0.914057\pi\)
0.712881 + 0.701285i \(0.247390\pi\)
\(480\) 0 0
\(481\) −1.31181 + 0.757373i −0.0598133 + 0.0345332i
\(482\) 0 0
\(483\) −11.4646 5.46420i −0.521656 0.248630i
\(484\) 0 0
\(485\) 2.60886 1.50622i 0.118462 0.0683941i
\(486\) 0 0
\(487\) −13.4393 + 23.2776i −0.608993 + 1.05481i 0.382414 + 0.923991i \(0.375093\pi\)
−0.991407 + 0.130816i \(0.958240\pi\)
\(488\) 0 0
\(489\) 10.7255 13.2791i 0.485024 0.600503i
\(490\) 0 0
\(491\) 25.1295i 1.13408i −0.823692 0.567038i \(-0.808089\pi\)
0.823692 0.567038i \(-0.191911\pi\)
\(492\) 0 0
\(493\) 0.218501 + 0.126152i 0.00984080 + 0.00568159i
\(494\) 0 0
\(495\) −4.19806 4.63881i −0.188689 0.208499i
\(496\) 0 0
\(497\) −6.23602 26.0863i −0.279724 1.17013i
\(498\) 0 0
\(499\) −2.58341 4.47460i −0.115649 0.200311i 0.802390 0.596800i \(-0.203562\pi\)
−0.918039 + 0.396490i \(0.870228\pi\)
\(500\) 0 0
\(501\) −14.2205 36.9063i −0.635324 1.64885i
\(502\) 0 0
\(503\) 42.2496 1.88382 0.941908 0.335872i \(-0.109031\pi\)
0.941908 + 0.335872i \(0.109031\pi\)
\(504\) 0 0
\(505\) 12.3810 0.550947
\(506\) 0 0
\(507\) 8.05816 + 20.9133i 0.357876 + 0.928792i
\(508\) 0 0
\(509\) 3.76320 + 6.51806i 0.166801 + 0.288908i 0.937293 0.348541i \(-0.113323\pi\)
−0.770492 + 0.637449i \(0.779990\pi\)
\(510\) 0 0
\(511\) −33.3130 9.90290i −1.47368 0.438079i
\(512\) 0 0
\(513\) 2.78897 0.156757i 0.123136 0.00692099i
\(514\) 0 0
\(515\) −14.5787 8.41703i −0.642415 0.370899i
\(516\) 0 0
\(517\) 25.9938i 1.14320i
\(518\) 0 0
\(519\) −10.6020 + 13.1263i −0.465378 + 0.576180i
\(520\) 0 0
\(521\) −10.1668 + 17.6095i −0.445417 + 0.771484i −0.998081 0.0619196i \(-0.980278\pi\)
0.552665 + 0.833404i \(0.313611\pi\)
\(522\) 0 0
\(523\) 3.14832 1.81768i 0.137666 0.0794818i −0.429585 0.903026i \(-0.641340\pi\)
0.567251 + 0.823545i \(0.308007\pi\)
\(524\) 0 0
\(525\) −4.56834 + 0.360881i −0.199379 + 0.0157501i
\(526\) 0 0
\(527\) 0.925448 0.534308i 0.0403131 0.0232748i
\(528\) 0 0
\(529\) −7.65967 + 13.2669i −0.333029 + 0.576823i
\(530\) 0 0
\(531\) 7.89530 + 36.6888i 0.342627 + 1.59216i
\(532\) 0 0
\(533\) 0.585766i 0.0253724i
\(534\) 0 0
\(535\) 11.1031 + 6.41036i 0.480028 + 0.277144i
\(536\) 0 0
\(537\) −4.85870 + 30.9293i −0.209668 + 1.33470i
\(538\) 0 0
\(539\) 14.5767 + 0.792285i 0.627863 + 0.0341261i
\(540\) 0 0
\(541\) −9.20758 15.9480i −0.395865 0.685658i 0.597346 0.801983i \(-0.296222\pi\)
−0.993211 + 0.116325i \(0.962888\pi\)
\(542\) 0 0
\(543\) −28.6443 + 11.0370i −1.22924 + 0.473644i
\(544\) 0 0
\(545\) 3.58896 0.153734
\(546\) 0 0
\(547\) −22.6376 −0.967915 −0.483957 0.875092i \(-0.660801\pi\)
−0.483957 + 0.875092i \(0.660801\pi\)
\(548\) 0 0
\(549\) −5.27415 + 16.3727i −0.225095 + 0.698770i
\(550\) 0 0
\(551\) −0.0718953 0.124526i −0.00306284 0.00530500i
\(552\) 0 0
\(553\) 11.5461 + 12.1907i 0.490992 + 0.518403i
\(554\) 0 0
\(555\) −10.5458 1.65664i −0.447643 0.0703206i
\(556\) 0 0
\(557\) 33.9272 + 19.5879i 1.43754 + 0.829965i 0.997679 0.0680994i \(-0.0216935\pi\)
0.439863 + 0.898065i \(0.355027\pi\)
\(558\) 0 0
\(559\) 2.81047i 0.118870i
\(560\) 0 0
\(561\) 2.65063 + 2.14090i 0.111910 + 0.0903889i
\(562\) 0 0
\(563\) −1.82483 + 3.16069i −0.0769073 + 0.133207i −0.901914 0.431915i \(-0.857838\pi\)
0.825007 + 0.565123i \(0.191171\pi\)
\(564\) 0 0
\(565\) −0.869081 + 0.501764i −0.0365625 + 0.0211094i
\(566\) 0 0
\(567\) −3.20434 23.5952i −0.134570 0.990904i
\(568\) 0 0
\(569\) 17.1456 9.89902i 0.718781 0.414988i −0.0955229 0.995427i \(-0.530452\pi\)
0.814304 + 0.580439i \(0.197119\pi\)
\(570\) 0 0
\(571\) −18.7342 + 32.4487i −0.784004 + 1.35793i 0.145589 + 0.989345i \(0.453492\pi\)
−0.929592 + 0.368589i \(0.879841\pi\)
\(572\) 0 0
\(573\) −29.6167 23.9213i −1.23725 0.999326i
\(574\) 0 0
\(575\) 2.77140i 0.115575i
\(576\) 0 0
\(577\) 22.1156 + 12.7684i 0.920685 + 0.531558i 0.883853 0.467764i \(-0.154940\pi\)
0.0368312 + 0.999322i \(0.488274\pi\)
\(578\) 0 0
\(579\) 15.3592 + 2.41279i 0.638307 + 0.100272i
\(580\) 0 0
\(581\) −2.74498 + 0.656198i −0.113881 + 0.0272237i
\(582\) 0 0
\(583\) 13.0687 + 22.6357i 0.541252 + 0.937476i
\(584\) 0 0
\(585\) 0.226070 0.701796i 0.00934684 0.0290157i
\(586\) 0 0
\(587\) 7.57204 0.312531 0.156266 0.987715i \(-0.450054\pi\)
0.156266 + 0.987715i \(0.450054\pi\)
\(588\) 0 0
\(589\) −0.609016 −0.0250941
\(590\) 0 0
\(591\) −36.0420 + 13.8875i −1.48257 + 0.571254i
\(592\) 0 0
\(593\) 1.58920 + 2.75258i 0.0652606 + 0.113035i 0.896810 0.442417i \(-0.145879\pi\)
−0.831549 + 0.555452i \(0.812545\pi\)
\(594\) 0 0
\(595\) 2.42729 0.580252i 0.0995092 0.0237880i
\(596\) 0 0
\(597\) −5.08416 + 32.3645i −0.208081 + 1.32459i
\(598\) 0 0
\(599\) −23.5750 13.6110i −0.963247 0.556131i −0.0660761 0.997815i \(-0.521048\pi\)
−0.897171 + 0.441684i \(0.854381\pi\)
\(600\) 0 0
\(601\) 13.1953i 0.538247i −0.963106 0.269123i \(-0.913266\pi\)
0.963106 0.269123i \(-0.0867340\pi\)
\(602\) 0 0
\(603\) 3.50916 + 16.3068i 0.142904 + 0.664063i
\(604\) 0 0
\(605\) 3.32543 5.75981i 0.135198 0.234170i
\(606\) 0 0
\(607\) −6.66879 + 3.85023i −0.270678 + 0.156276i −0.629196 0.777247i \(-0.716616\pi\)
0.358518 + 0.933523i \(0.383282\pi\)
\(608\) 0 0
\(609\) −1.00995 + 0.694553i −0.0409252 + 0.0281447i
\(610\) 0 0
\(611\) 2.65294 1.53167i 0.107326 0.0619649i
\(612\) 0 0
\(613\) 14.4287 24.9912i 0.582769 1.00939i −0.412381 0.911012i \(-0.635303\pi\)
0.995150 0.0983735i \(-0.0313640\pi\)
\(614\) 0 0
\(615\) −2.59388 + 3.21146i −0.104596 + 0.129499i
\(616\) 0 0
\(617\) 31.5272i 1.26924i 0.772825 + 0.634619i \(0.218843\pi\)
−0.772825 + 0.634619i \(0.781157\pi\)
\(618\) 0 0
\(619\) 25.4695 + 14.7048i 1.02370 + 0.591036i 0.915175 0.403057i \(-0.132052\pi\)
0.108530 + 0.994093i \(0.465386\pi\)
\(620\) 0 0
\(621\) 14.3779 0.808125i 0.576966 0.0324289i
\(622\) 0 0
\(623\) 1.68758 + 1.78180i 0.0676116 + 0.0713863i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −0.698175 1.81197i −0.0278824 0.0723631i
\(628\) 0 0
\(629\) 5.81369 0.231807
\(630\) 0 0
\(631\) 29.9987 1.19423 0.597115 0.802155i \(-0.296313\pi\)
0.597115 + 0.802155i \(0.296313\pi\)
\(632\) 0 0
\(633\) 12.7136 + 32.9956i 0.505322 + 1.31146i
\(634\) 0 0
\(635\) −3.88048 6.72119i −0.153992 0.266722i
\(636\) 0 0
\(637\) 0.778065 + 1.53439i 0.0308281 + 0.0607947i
\(638\) 0 0
\(639\) 20.4070 + 22.5495i 0.807287 + 0.892044i
\(640\) 0 0
\(641\) −27.8245 16.0645i −1.09900 0.634510i −0.163044 0.986619i \(-0.552131\pi\)
−0.935959 + 0.352109i \(0.885465\pi\)
\(642\) 0 0
\(643\) 5.88352i 0.232024i 0.993248 + 0.116012i \(0.0370110\pi\)
−0.993248 + 0.116012i \(0.962989\pi\)
\(644\) 0 0
\(645\) 12.4453 15.4084i 0.490032 0.606704i
\(646\) 0 0
\(647\) −9.99202 + 17.3067i −0.392827 + 0.680396i −0.992821 0.119608i \(-0.961836\pi\)
0.599994 + 0.800004i \(0.295170\pi\)
\(648\) 0 0
\(649\) 22.5930 13.0441i 0.886854 0.512025i
\(650\) 0 0
\(651\) 0.408832 + 5.17535i 0.0160234 + 0.202838i
\(652\) 0 0
\(653\) 2.19720 1.26856i 0.0859832 0.0496424i −0.456392 0.889779i \(-0.650858\pi\)
0.542375 + 0.840136i \(0.317525\pi\)
\(654\) 0 0
\(655\) 8.58199 14.8644i 0.335326 0.580802i
\(656\) 0 0
\(657\) 38.5251 8.29047i 1.50301 0.323442i
\(658\) 0 0
\(659\) 28.5964i 1.11396i 0.830526 + 0.556979i \(0.188040\pi\)
−0.830526 + 0.556979i \(0.811960\pi\)
\(660\) 0 0
\(661\) 25.4569 + 14.6975i 0.990158 + 0.571668i 0.905321 0.424727i \(-0.139630\pi\)
0.0848363 + 0.996395i \(0.472963\pi\)
\(662\) 0 0
\(663\) −0.0623141 + 0.396676i −0.00242008 + 0.0154056i
\(664\) 0 0
\(665\) −1.36335 0.405282i −0.0528686 0.0157162i
\(666\) 0 0
\(667\) −0.370640 0.641967i −0.0143512 0.0248571i
\(668\) 0 0
\(669\) −21.9723 + 8.46623i −0.849499 + 0.327323i
\(670\) 0 0
\(671\) 11.9575 0.461613
\(672\) 0 0
\(673\) −18.1428 −0.699354 −0.349677 0.936870i \(-0.613709\pi\)
−0.349677 + 0.936870i \(0.613709\pi\)
\(674\) 0 0
\(675\) 4.34711 2.84651i 0.167320 0.109562i
\(676\) 0 0
\(677\) 19.2622 + 33.3630i 0.740305 + 1.28225i 0.952356 + 0.304987i \(0.0986523\pi\)
−0.212051 + 0.977259i \(0.568014\pi\)
\(678\) 0 0
\(679\) −1.85309 7.75178i −0.0711150 0.297486i
\(680\) 0 0
\(681\) −17.2222 2.70545i −0.659957 0.103673i
\(682\) 0 0
\(683\) 8.24278 + 4.75897i 0.315401 + 0.182097i 0.649341 0.760497i \(-0.275045\pi\)
−0.333940 + 0.942594i \(0.608378\pi\)
\(684\) 0 0
\(685\) 15.0269i 0.574149i
\(686\) 0 0
\(687\) 19.2385 + 15.5389i 0.733996 + 0.592846i
\(688\) 0 0
\(689\) −1.54014 + 2.66760i −0.0586747 + 0.101628i
\(690\) 0 0
\(691\) 36.4810 21.0623i 1.38780 0.801248i 0.394734 0.918795i \(-0.370837\pi\)
0.993067 + 0.117548i \(0.0375033\pi\)
\(692\) 0 0
\(693\) −14.9292 + 7.14939i −0.567115 + 0.271583i
\(694\) 0 0
\(695\) −8.51425 + 4.91570i −0.322964 + 0.186463i
\(696\) 0 0
\(697\) 1.12410 1.94700i 0.0425785 0.0737481i
\(698\) 0 0
\(699\) −27.9617 22.5846i −1.05761 0.854226i
\(700\) 0 0
\(701\) 20.1103i 0.759555i −0.925078 0.379778i \(-0.876001\pi\)
0.925078 0.379778i \(-0.123999\pi\)
\(702\) 0 0
\(703\) −2.86939 1.65664i −0.108221 0.0624815i
\(704\) 0 0
\(705\) 21.3272 + 3.35031i 0.803230 + 0.126180i
\(706\) 0 0
\(707\) 9.33395 31.3990i 0.351039 1.18088i
\(708\) 0 0
\(709\) 12.6523 + 21.9145i 0.475168 + 0.823015i 0.999596 0.0284398i \(-0.00905390\pi\)
−0.524427 + 0.851455i \(0.675721\pi\)
\(710\) 0 0
\(711\) −18.1218 5.83760i −0.679622 0.218927i
\(712\) 0 0
\(713\) −3.13964 −0.117581
\(714\) 0 0
\(715\) −0.512543 −0.0191680
\(716\) 0 0
\(717\) −7.86166 + 3.02920i −0.293599 + 0.113128i
\(718\) 0 0
\(719\) −7.70568 13.3466i −0.287373 0.497745i 0.685809 0.727782i \(-0.259449\pi\)
−0.973182 + 0.230037i \(0.926115\pi\)
\(720\) 0 0
\(721\) −32.3370 + 30.6271i −1.20429 + 1.14061i
\(722\) 0 0
\(723\) 4.63202 29.4863i 0.172267 1.09661i
\(724\) 0 0
\(725\) −0.231640 0.133737i −0.00860289 0.00496688i
\(726\) 0 0
\(727\) 17.2053i 0.638109i −0.947736 0.319054i \(-0.896635\pi\)
0.947736 0.319054i \(-0.103365\pi\)
\(728\) 0 0
\(729\) 16.0352 + 21.7226i 0.593896 + 0.804542i
\(730\) 0 0
\(731\) −5.39337 + 9.34159i −0.199481 + 0.345511i
\(732\) 0 0
\(733\) −4.21946 + 2.43611i −0.155849 + 0.0899797i −0.575896 0.817523i \(-0.695347\pi\)
0.420047 + 0.907502i \(0.362014\pi\)
\(734\) 0 0
\(735\) −2.52883 + 11.8577i −0.0932772 + 0.437378i
\(736\) 0 0
\(737\) 10.0417 5.79760i 0.369892 0.213557i
\(738\) 0 0
\(739\) −11.2489 + 19.4836i −0.413796 + 0.716716i −0.995301 0.0968269i \(-0.969131\pi\)
0.581505 + 0.813543i \(0.302464\pi\)
\(740\) 0 0
\(741\) 0.143791 0.178026i 0.00528228 0.00653993i
\(742\) 0 0
\(743\) 5.74923i 0.210919i 0.994424 + 0.105459i \(0.0336313\pi\)
−0.994424 + 0.105459i \(0.966369\pi\)
\(744\) 0 0
\(745\) −19.9895 11.5409i −0.732357 0.422826i
\(746\) 0 0
\(747\) 2.37281 2.14736i 0.0868167 0.0785678i
\(748\) 0 0
\(749\) 24.6277 23.3254i 0.899875 0.852292i
\(750\) 0 0
\(751\) −13.4867 23.3597i −0.492138 0.852409i 0.507821 0.861463i \(-0.330451\pi\)
−0.999959 + 0.00905407i \(0.997118\pi\)
\(752\) 0 0
\(753\) 9.85669 + 25.5810i 0.359198 + 0.932223i
\(754\) 0 0
\(755\) 14.4105 0.524454
\(756\) 0 0
\(757\) −3.74640 −0.136165 −0.0680826 0.997680i \(-0.521688\pi\)
−0.0680826 + 0.997680i \(0.521688\pi\)
\(758\) 0 0
\(759\) −3.59929 9.34120i −0.130646 0.339064i
\(760\) 0 0
\(761\) −9.03998 15.6577i −0.327699 0.567591i 0.654356 0.756187i \(-0.272940\pi\)
−0.982055 + 0.188595i \(0.939607\pi\)
\(762\) 0 0
\(763\) 2.70569 9.10184i 0.0979527 0.329509i
\(764\) 0 0
\(765\) −2.09819 + 1.89883i −0.0758603 + 0.0686525i
\(766\) 0 0
\(767\) 2.66257 + 1.53724i 0.0961398 + 0.0555064i
\(768\) 0 0
\(769\) 25.1297i 0.906199i −0.891460 0.453100i \(-0.850318\pi\)
0.891460 0.453100i \(-0.149682\pi\)
\(770\) 0 0
\(771\) 19.8247 24.5448i 0.713971 0.883959i
\(772\) 0 0
\(773\) −16.3082 + 28.2467i −0.586567 + 1.01596i 0.408112 + 0.912932i \(0.366187\pi\)
−0.994678 + 0.103031i \(0.967146\pi\)
\(774\) 0 0
\(775\) −0.981097 + 0.566436i −0.0352420 + 0.0203470i
\(776\) 0 0
\(777\) −12.1518 + 25.4959i −0.435942 + 0.914659i
\(778\) 0 0
\(779\) −1.10962 + 0.640639i −0.0397563 + 0.0229533i
\(780\) 0 0
\(781\) 10.5707 18.3090i 0.378249 0.655146i
\(782\) 0 0
\(783\) 0.626280 1.24074i 0.0223814 0.0443403i
\(784\) 0 0
\(785\) 2.19902i 0.0784865i
\(786\) 0 0
\(787\) 3.98518 + 2.30085i 0.142056 + 0.0820164i 0.569344 0.822100i \(-0.307197\pi\)
−0.427287 + 0.904116i \(0.640531\pi\)
\(788\) 0 0
\(789\) −1.41522 + 9.00894i −0.0503832 + 0.320727i
\(790\) 0 0
\(791\) 0.617314 + 2.58233i 0.0219492 + 0.0918170i
\(792\) 0 0
\(793\) 0.704590 + 1.22038i 0.0250207 + 0.0433371i