Properties

Label 70.2.i.b.39.2
Level $70$
Weight $2$
Character 70.39
Analytic conductor $0.559$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.558952814149\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 39.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 70.39
Dual form 70.2.i.b.9.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.23205 + 1.86603i) q^{10} +(-1.50000 + 2.59808i) q^{11} +5.00000i q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(-2.50000 - 4.33013i) q^{19} +(2.00000 + 1.00000i) q^{20} +3.00000i q^{22} +(6.06218 - 3.50000i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.59808 + 0.500000i) q^{28} +4.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +(4.23205 - 4.13397i) q^{35} -3.00000 q^{36} +(0.866025 - 0.500000i) q^{37} +(-4.33013 - 2.50000i) q^{38} +(2.23205 - 0.133975i) q^{40} +3.00000 q^{41} -2.00000i q^{43} +(1.50000 + 2.59808i) q^{44} +(5.59808 - 3.69615i) q^{45} +(3.50000 - 6.06218i) q^{46} +(-6.06218 + 3.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(4.33013 + 2.50000i) q^{52} +(7.79423 + 4.50000i) q^{53} +(-6.00000 - 3.00000i) q^{55} +(-2.00000 + 1.73205i) q^{56} +(3.46410 - 2.00000i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} -2.00000i q^{62} +(-2.59808 + 7.50000i) q^{63} -1.00000 q^{64} +(-11.1603 + 0.669873i) q^{65} +(-1.73205 - 1.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} +(1.59808 - 5.69615i) q^{70} -6.00000 q^{71} +(-2.59808 + 1.50000i) q^{72} +(-13.8564 - 8.00000i) q^{73} +(0.500000 - 0.866025i) q^{74} -5.00000 q^{76} +(7.79423 - 1.50000i) q^{77} +(7.00000 + 12.1244i) q^{79} +(1.86603 - 1.23205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(2.59808 - 1.50000i) q^{82} +6.00000i q^{83} +(-2.00000 + 4.00000i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(2.59808 + 1.50000i) q^{88} +(1.00000 + 1.73205i) q^{89} +(3.00000 - 6.00000i) q^{90} +(10.0000 - 8.66025i) q^{91} -7.00000i q^{92} +(-3.50000 + 6.06218i) q^{94} +(9.33013 - 6.16025i) q^{95} -12.0000i q^{97} +(2.59808 + 6.50000i) q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 4 q^{5} - 6 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{4} + 4 q^{5} - 6 q^{9} - 2 q^{10} - 6 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{19} + 8 q^{20} - 6 q^{25} + 10 q^{26} + 16 q^{29} + 4 q^{31} + 8 q^{34} + 10 q^{35} - 12 q^{36} + 2 q^{40} + 12 q^{41} + 6 q^{44} + 12 q^{45} + 14 q^{46} - 4 q^{49} - 16 q^{50} - 24 q^{55} - 8 q^{56} - 8 q^{59} - 12 q^{61} - 4 q^{64} - 10 q^{65} - 4 q^{70} - 24 q^{71} + 2 q^{74} - 20 q^{76} + 28 q^{79} + 4 q^{80} - 18 q^{81} - 8 q^{85} - 4 q^{86} + 4 q^{89} + 12 q^{90} + 40 q^{91} - 14 q^{94} + 20 q^{95} + 36 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.133975 + 2.23205i 0.0599153 + 0.998203i
\(6\) 0 0
\(7\) −1.73205 2.00000i −0.654654 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) 1.23205 + 1.86603i 0.389609 + 0.590089i
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 5.00000i 1.38675i 0.720577 + 0.693375i \(0.243877\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.73205 + 1.00000i 0.420084 + 0.242536i 0.695113 0.718900i \(-0.255354\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) −2.59808 1.50000i −0.612372 0.353553i
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) 2.00000 + 1.00000i 0.447214 + 0.223607i
\(21\) 0 0
\(22\) 3.00000i 0.639602i
\(23\) 6.06218 3.50000i 1.26405 0.729800i 0.290196 0.956967i \(-0.406280\pi\)
0.973856 + 0.227167i \(0.0729463\pi\)
\(24\) 0 0
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) 0 0
\(28\) −2.59808 + 0.500000i −0.490990 + 0.0944911i
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 4.23205 4.13397i 0.715347 0.698769i
\(36\) −3.00000 −0.500000
\(37\) 0.866025 0.500000i 0.142374 0.0821995i −0.427121 0.904194i \(-0.640472\pi\)
0.569495 + 0.821995i \(0.307139\pi\)
\(38\) −4.33013 2.50000i −0.702439 0.405554i
\(39\) 0 0
\(40\) 2.23205 0.133975i 0.352918 0.0211832i
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 5.59808 3.69615i 0.834512 0.550990i
\(46\) 3.50000 6.06218i 0.516047 0.893819i
\(47\) −6.06218 + 3.50000i −0.884260 + 0.510527i −0.872060 0.489398i \(-0.837217\pi\)
−0.0121990 + 0.999926i \(0.503883\pi\)
\(48\) 0 0
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 4.33013 + 2.50000i 0.600481 + 0.346688i
\(53\) 7.79423 + 4.50000i 1.07062 + 0.618123i 0.928351 0.371706i \(-0.121227\pi\)
0.142269 + 0.989828i \(0.454560\pi\)
\(54\) 0 0
\(55\) −6.00000 3.00000i −0.809040 0.404520i
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 0 0
\(58\) 3.46410 2.00000i 0.454859 0.262613i
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 2.00000i 0.254000i
\(63\) −2.59808 + 7.50000i −0.327327 + 0.944911i
\(64\) −1.00000 −0.125000
\(65\) −11.1603 + 0.669873i −1.38426 + 0.0830875i
\(66\) 0 0
\(67\) −1.73205 1.00000i −0.211604 0.122169i 0.390453 0.920623i \(-0.372318\pi\)
−0.602056 + 0.798454i \(0.705652\pi\)
\(68\) 1.73205 1.00000i 0.210042 0.121268i
\(69\) 0 0
\(70\) 1.59808 5.69615i 0.191007 0.680820i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −2.59808 + 1.50000i −0.306186 + 0.176777i
\(73\) −13.8564 8.00000i −1.62177 0.936329i −0.986447 0.164083i \(-0.947534\pi\)
−0.635323 0.772246i \(-0.719133\pi\)
\(74\) 0.500000 0.866025i 0.0581238 0.100673i
\(75\) 0 0
\(76\) −5.00000 −0.573539
\(77\) 7.79423 1.50000i 0.888235 0.170941i
\(78\) 0 0
\(79\) 7.00000 + 12.1244i 0.787562 + 1.36410i 0.927457 + 0.373930i \(0.121990\pi\)
−0.139895 + 0.990166i \(0.544677\pi\)
\(80\) 1.86603 1.23205i 0.208628 0.137747i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 2.59808 1.50000i 0.286910 0.165647i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 0 0
\(85\) −2.00000 + 4.00000i −0.216930 + 0.433861i
\(86\) −1.00000 1.73205i −0.107833 0.186772i
\(87\) 0 0
\(88\) 2.59808 + 1.50000i 0.276956 + 0.159901i
\(89\) 1.00000 + 1.73205i 0.106000 + 0.183597i 0.914146 0.405385i \(-0.132862\pi\)
−0.808146 + 0.588982i \(0.799529\pi\)
\(90\) 3.00000 6.00000i 0.316228 0.632456i
\(91\) 10.0000 8.66025i 1.04828 0.907841i
\(92\) 7.00000i 0.729800i
\(93\) 0 0
\(94\) −3.50000 + 6.06218i −0.360997 + 0.625266i
\(95\) 9.33013 6.16025i 0.957251 0.632029i
\(96\) 0 0
\(97\) 12.0000i 1.21842i −0.793011 0.609208i \(-0.791488\pi\)
0.793011 0.609208i \(-0.208512\pi\)
\(98\) 2.59808 + 6.50000i 0.262445 + 0.656599i
\(99\) 9.00000 0.904534
\(100\) −1.96410 + 4.59808i −0.196410 + 0.459808i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 6.92820 4.00000i 0.682656 0.394132i −0.118199 0.992990i \(-0.537712\pi\)
0.800855 + 0.598858i \(0.204379\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) −13.8564 + 8.00000i −1.33955 + 0.773389i −0.986740 0.162306i \(-0.948107\pi\)
−0.352809 + 0.935695i \(0.614773\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) −6.69615 + 0.401924i −0.638453 + 0.0383219i
\(111\) 0 0
\(112\) −0.866025 + 2.50000i −0.0818317 + 0.236228i
\(113\) 14.0000i 1.31701i −0.752577 0.658505i \(-0.771189\pi\)
0.752577 0.658505i \(-0.228811\pi\)
\(114\) 0 0
\(115\) 8.62436 + 13.0622i 0.804225 + 1.21805i
\(116\) 2.00000 3.46410i 0.185695 0.321634i
\(117\) 12.9904 7.50000i 1.20096 0.693375i
\(118\) 4.00000i 0.368230i
\(119\) −1.00000 5.19615i −0.0916698 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −5.19615 3.00000i −0.470438 0.271607i
\(123\) 0 0
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 1.50000 + 7.79423i 0.133631 + 0.694365i
\(127\) 7.00000i 0.621150i 0.950549 + 0.310575i \(0.100522\pi\)
−0.950549 + 0.310575i \(0.899478\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −9.33013 + 6.16025i −0.818306 + 0.540290i
\(131\) 0.500000 + 0.866025i 0.0436852 + 0.0756650i 0.887041 0.461690i \(-0.152757\pi\)
−0.843356 + 0.537355i \(0.819423\pi\)
\(132\) 0 0
\(133\) −4.33013 + 12.5000i −0.375470 + 1.08389i
\(134\) −2.00000 −0.172774
\(135\) 0 0
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) 6.92820 + 4.00000i 0.591916 + 0.341743i 0.765855 0.643013i \(-0.222316\pi\)
−0.173939 + 0.984757i \(0.555649\pi\)
\(138\) 0 0
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −1.46410 5.73205i −0.123739 0.484447i
\(141\) 0 0
\(142\) −5.19615 + 3.00000i −0.436051 + 0.251754i
\(143\) −12.9904 7.50000i −1.08631 0.627182i
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) 0.535898 + 8.92820i 0.0445039 + 0.741447i
\(146\) −16.0000 −1.32417
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 0 0
\(151\) 3.00000 5.19615i 0.244137 0.422857i −0.717752 0.696299i \(-0.754829\pi\)
0.961888 + 0.273442i \(0.0881622\pi\)
\(152\) −4.33013 + 2.50000i −0.351220 + 0.202777i
\(153\) 6.00000i 0.485071i
\(154\) 6.00000 5.19615i 0.483494 0.418718i
\(155\) 4.00000 + 2.00000i 0.321288 + 0.160644i
\(156\) 0 0
\(157\) 7.79423 + 4.50000i 0.622047 + 0.359139i 0.777666 0.628678i \(-0.216404\pi\)
−0.155618 + 0.987817i \(0.549737\pi\)
\(158\) 12.1244 + 7.00000i 0.964562 + 0.556890i
\(159\) 0 0
\(160\) 1.00000 2.00000i 0.0790569 0.158114i
\(161\) −17.5000 6.06218i −1.37919 0.477767i
\(162\) 9.00000i 0.707107i
\(163\) 10.3923 6.00000i 0.813988 0.469956i −0.0343508 0.999410i \(-0.510936\pi\)
0.848339 + 0.529454i \(0.177603\pi\)
\(164\) 1.50000 2.59808i 0.117130 0.202876i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 15.0000i 1.16073i 0.814355 + 0.580367i \(0.197091\pi\)
−0.814355 + 0.580367i \(0.802909\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0.267949 + 4.46410i 0.0205508 + 0.342381i
\(171\) −7.50000 + 12.9904i −0.573539 + 0.993399i
\(172\) −1.73205 1.00000i −0.132068 0.0762493i
\(173\) −7.79423 + 4.50000i −0.592584 + 0.342129i −0.766119 0.642699i \(-0.777815\pi\)
0.173534 + 0.984828i \(0.444481\pi\)
\(174\) 0 0
\(175\) 9.79423 + 8.89230i 0.740374 + 0.672195i
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) 1.73205 + 1.00000i 0.129823 + 0.0749532i
\(179\) 6.50000 11.2583i 0.485833 0.841487i −0.514035 0.857769i \(-0.671850\pi\)
0.999867 + 0.0162823i \(0.00518305\pi\)
\(180\) −0.401924 6.69615i −0.0299576 0.499102i
\(181\) 26.0000 1.93256 0.966282 0.257485i \(-0.0828937\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 4.33013 12.5000i 0.320970 0.926562i
\(183\) 0 0
\(184\) −3.50000 6.06218i −0.258023 0.446910i
\(185\) 1.23205 + 1.86603i 0.0905822 + 0.137193i
\(186\) 0 0
\(187\) −5.19615 + 3.00000i −0.379980 + 0.219382i
\(188\) 7.00000i 0.510527i
\(189\) 0 0
\(190\) 5.00000 10.0000i 0.362738 0.725476i
\(191\) 10.0000 + 17.3205i 0.723575 + 1.25327i 0.959558 + 0.281511i \(0.0908356\pi\)
−0.235983 + 0.971757i \(0.575831\pi\)
\(192\) 0 0
\(193\) −8.66025 5.00000i −0.623379 0.359908i 0.154805 0.987945i \(-0.450525\pi\)
−0.778183 + 0.628037i \(0.783859\pi\)
\(194\) −6.00000 10.3923i −0.430775 0.746124i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 5.00000i 0.356235i −0.984009 0.178118i \(-0.942999\pi\)
0.984009 0.178118i \(-0.0570008\pi\)
\(198\) 7.79423 4.50000i 0.553912 0.319801i
\(199\) 9.00000 15.5885i 0.637993 1.10504i −0.347879 0.937539i \(-0.613098\pi\)
0.985873 0.167497i \(-0.0535685\pi\)
\(200\) 0.598076 + 4.96410i 0.0422904 + 0.351015i
\(201\) 0 0
\(202\) 0 0
\(203\) −6.92820 8.00000i −0.486265 0.561490i
\(204\) 0 0
\(205\) 0.401924 + 6.69615i 0.0280716 + 0.467680i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) −18.1865 10.5000i −1.26405 0.729800i
\(208\) 4.33013 2.50000i 0.300240 0.173344i
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) −9.00000 −0.619586 −0.309793 0.950804i \(-0.600260\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(212\) 7.79423 4.50000i 0.535310 0.309061i
\(213\) 0 0
\(214\) −8.00000 + 13.8564i −0.546869 + 0.947204i
\(215\) 4.46410 0.267949i 0.304449 0.0182740i
\(216\) 0 0
\(217\) −5.19615 + 1.00000i −0.352738 + 0.0678844i
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) −5.59808 + 3.69615i −0.377422 + 0.249195i
\(221\) −5.00000 + 8.66025i −0.336336 + 0.582552i
\(222\) 0 0
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) 0.500000 + 2.59808i 0.0334077 + 0.173591i
\(225\) 9.00000 + 12.0000i 0.600000 + 0.800000i
\(226\) −7.00000 12.1244i −0.465633 0.806500i
\(227\) 5.19615 + 3.00000i 0.344881 + 0.199117i 0.662428 0.749125i \(-0.269526\pi\)
−0.317547 + 0.948242i \(0.602859\pi\)
\(228\) 0 0
\(229\) 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i \(0.0106368\pi\)
−0.470787 + 0.882247i \(0.656030\pi\)
\(230\) 14.0000 + 7.00000i 0.923133 + 0.461566i
\(231\) 0 0
\(232\) 4.00000i 0.262613i
\(233\) 6.92820 4.00000i 0.453882 0.262049i −0.255586 0.966786i \(-0.582269\pi\)
0.709468 + 0.704737i \(0.248935\pi\)
\(234\) 7.50000 12.9904i 0.490290 0.849208i
\(235\) −8.62436 13.0622i −0.562591 0.852083i
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) 0 0
\(238\) −3.46410 4.00000i −0.224544 0.259281i
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 0 0
\(241\) 4.50000 7.79423i 0.289870 0.502070i −0.683908 0.729568i \(-0.739721\pi\)
0.973779 + 0.227498i \(0.0730544\pi\)
\(242\) 1.73205 + 1.00000i 0.111340 + 0.0642824i
\(243\) 0 0
\(244\) −6.00000 −0.384111
\(245\) −15.5981 1.30385i −0.996525 0.0832998i
\(246\) 0 0
\(247\) 21.6506 12.5000i 1.37760 0.795356i
\(248\) −1.73205 1.00000i −0.109985 0.0635001i
\(249\) 0 0
\(250\) −7.23205 8.52628i −0.457395 0.539249i
\(251\) 5.00000 0.315597 0.157799 0.987471i \(-0.449560\pi\)
0.157799 + 0.987471i \(0.449560\pi\)
\(252\) 5.19615 + 6.00000i 0.327327 + 0.377964i
\(253\) 21.0000i 1.32026i
\(254\) 3.50000 + 6.06218i 0.219610 + 0.380375i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.19615 + 3.00000i −0.324127 + 0.187135i −0.653231 0.757159i \(-0.726587\pi\)
0.329104 + 0.944294i \(0.393253\pi\)
\(258\) 0 0
\(259\) −2.50000 0.866025i −0.155342 0.0538122i
\(260\) −5.00000 + 10.0000i −0.310087 + 0.620174i
\(261\) −6.00000 10.3923i −0.371391 0.643268i
\(262\) 0.866025 + 0.500000i 0.0535032 + 0.0308901i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) −9.00000 + 18.0000i −0.552866 + 1.10573i
\(266\) 2.50000 + 12.9904i 0.153285 + 0.796491i
\(267\) 0 0
\(268\) −1.73205 + 1.00000i −0.105802 + 0.0610847i
\(269\) −5.00000 + 8.66025i −0.304855 + 0.528025i −0.977229 0.212187i \(-0.931941\pi\)
0.672374 + 0.740212i \(0.265275\pi\)
\(270\) 0 0
\(271\) −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i \(-0.906676\pi\)
0.228380 0.973572i \(-0.426657\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) 8.00000 0.483298
\(275\) 5.89230 13.7942i 0.355319 0.831823i
\(276\) 0 0
\(277\) 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i \(-0.314196\pi\)
−0.447062 + 0.894503i \(0.647530\pi\)
\(278\) −13.8564 + 8.00000i −0.831052 + 0.479808i
\(279\) −6.00000 −0.359211
\(280\) −4.13397 4.23205i −0.247052 0.252913i
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 0 0
\(283\) 12.1244 + 7.00000i 0.720718 + 0.416107i 0.815017 0.579437i \(-0.196728\pi\)
−0.0942988 + 0.995544i \(0.530061\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) −15.0000 −0.886969
\(287\) −5.19615 6.00000i −0.306719 0.354169i
\(288\) 3.00000i 0.176777i
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 4.92820 + 7.46410i 0.289394 + 0.438307i
\(291\) 0 0
\(292\) −13.8564 + 8.00000i −0.810885 + 0.468165i
\(293\) 9.00000i 0.525786i 0.964825 + 0.262893i \(0.0846766\pi\)
−0.964825 + 0.262893i \(0.915323\pi\)
\(294\) 0 0
\(295\) −8.00000 4.00000i −0.465778 0.232889i
\(296\) −0.500000 0.866025i −0.0290619 0.0503367i
\(297\) 0 0
\(298\) −15.5885 9.00000i −0.903015 0.521356i
\(299\) 17.5000 + 30.3109i 1.01205 + 1.75292i
\(300\) 0 0
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) 6.00000i 0.345261i
\(303\) 0 0
\(304\) −2.50000 + 4.33013i −0.143385 + 0.248350i
\(305\) 11.1962 7.39230i 0.641090 0.423282i
\(306\) −3.00000 5.19615i −0.171499 0.297044i
\(307\) 22.0000i 1.25561i −0.778372 0.627803i \(-0.783954\pi\)
0.778372 0.627803i \(-0.216046\pi\)
\(308\) 2.59808 7.50000i 0.148039 0.427352i
\(309\) 0 0
\(310\) 4.46410 0.267949i 0.253544 0.0152185i
\(311\) −3.00000 + 5.19615i −0.170114 + 0.294647i −0.938460 0.345389i \(-0.887747\pi\)
0.768345 + 0.640036i \(0.221080\pi\)
\(312\) 0 0
\(313\) 19.0526 11.0000i 1.07691 0.621757i 0.146852 0.989158i \(-0.453086\pi\)
0.930062 + 0.367402i \(0.119753\pi\)
\(314\) 9.00000 0.507899
\(315\) −17.0885 4.79423i −0.962825 0.270124i
\(316\) 14.0000 0.787562
\(317\) −1.73205 + 1.00000i −0.0972817 + 0.0561656i −0.547852 0.836576i \(-0.684554\pi\)
0.450570 + 0.892741i \(0.351221\pi\)
\(318\) 0 0
\(319\) −6.00000 + 10.3923i −0.335936 + 0.581857i
\(320\) −0.133975 2.23205i −0.00748941 0.124775i
\(321\) 0 0
\(322\) −18.1865 + 3.50000i −1.01350 + 0.195047i
\(323\) 10.0000i 0.556415i
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) −2.99038 24.8205i −0.165876 1.37679i
\(326\) 6.00000 10.3923i 0.332309 0.575577i
\(327\) 0 0
\(328\) 3.00000i 0.165647i
\(329\) 17.5000 + 6.06218i 0.964806 + 0.334219i
\(330\) 0 0
\(331\) −2.50000 4.33013i −0.137412 0.238005i 0.789104 0.614260i \(-0.210545\pi\)
−0.926516 + 0.376254i \(0.877212\pi\)
\(332\) 5.19615 + 3.00000i 0.285176 + 0.164646i
\(333\) −2.59808 1.50000i −0.142374 0.0821995i
\(334\) 7.50000 + 12.9904i 0.410382 + 0.710802i
\(335\) 2.00000 4.00000i 0.109272 0.218543i
\(336\) 0 0
\(337\) 10.0000i 0.544735i 0.962193 + 0.272367i \(0.0878066\pi\)
−0.962193 + 0.272367i \(0.912193\pi\)
\(338\) −10.3923 + 6.00000i −0.565267 + 0.326357i
\(339\) 0 0
\(340\) 2.46410 + 3.73205i 0.133635 + 0.202399i
\(341\) 3.00000 + 5.19615i 0.162459 + 0.281387i
\(342\) 15.0000i 0.811107i
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) −2.00000 −0.107833
\(345\) 0 0
\(346\) −4.50000 + 7.79423i −0.241921 + 0.419020i
\(347\) 10.3923 + 6.00000i 0.557888 + 0.322097i 0.752297 0.658824i \(-0.228946\pi\)
−0.194409 + 0.980921i \(0.562279\pi\)
\(348\) 0 0
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 12.9282 + 2.80385i 0.691042 + 0.149872i
\(351\) 0 0
\(352\) 2.59808 1.50000i 0.138478 0.0799503i
\(353\) 20.7846 + 12.0000i 1.10625 + 0.638696i 0.937856 0.347024i \(-0.112808\pi\)
0.168397 + 0.985719i \(0.446141\pi\)
\(354\) 0 0
\(355\) −0.803848 13.3923i −0.0426638 0.710790i
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) 13.0000i 0.687071i
\(359\) 8.00000 + 13.8564i 0.422224 + 0.731313i 0.996157 0.0875892i \(-0.0279163\pi\)
−0.573933 + 0.818902i \(0.694583\pi\)
\(360\) −3.69615 5.59808i −0.194804 0.295045i
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 22.5167 13.0000i 1.18345 0.683265i
\(363\) 0 0
\(364\) −2.50000 12.9904i −0.131036 0.680881i
\(365\) 16.0000 32.0000i 0.837478 1.67496i
\(366\) 0 0
\(367\) −11.2583 6.50000i −0.587680 0.339297i 0.176500 0.984301i \(-0.443523\pi\)
−0.764180 + 0.645003i \(0.776856\pi\)
\(368\) −6.06218 3.50000i −0.316013 0.182450i
\(369\) −4.50000 7.79423i −0.234261 0.405751i
\(370\) 2.00000 + 1.00000i 0.103975 + 0.0519875i
\(371\) −4.50000 23.3827i −0.233628 1.21397i
\(372\) 0 0
\(373\) −22.5167 + 13.0000i −1.16587 + 0.673114i −0.952703 0.303902i \(-0.901711\pi\)
−0.213165 + 0.977016i \(0.568377\pi\)
\(374\) −3.00000 + 5.19615i −0.155126 + 0.268687i
\(375\) 0 0
\(376\) 3.50000 + 6.06218i 0.180499 + 0.312633i
\(377\) 20.0000i 1.03005i
\(378\) 0 0
\(379\) 29.0000 1.48963 0.744815 0.667271i \(-0.232538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(380\) −0.669873 11.1603i −0.0343638 0.572509i
\(381\) 0 0
\(382\) 17.3205 + 10.0000i 0.886194 + 0.511645i
\(383\) −18.1865 + 10.5000i −0.929288 + 0.536525i −0.886586 0.462563i \(-0.846930\pi\)
−0.0427020 + 0.999088i \(0.513597\pi\)
\(384\) 0 0
\(385\) 4.39230 + 17.1962i 0.223853 + 0.876397i
\(386\) −10.0000 −0.508987
\(387\) −5.19615 + 3.00000i −0.264135 + 0.152499i
\(388\) −10.3923 6.00000i −0.527589 0.304604i
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) 14.0000 0.708010
\(392\) 6.92820 + 1.00000i 0.349927 + 0.0505076i
\(393\) 0 0
\(394\) −2.50000 4.33013i −0.125948 0.218149i
\(395\) −26.1244 + 17.2487i −1.31446 + 0.867877i
\(396\) 4.50000 7.79423i 0.226134 0.391675i
\(397\) −12.1244 + 7.00000i −0.608504 + 0.351320i −0.772380 0.635161i \(-0.780934\pi\)
0.163876 + 0.986481i \(0.447600\pi\)
\(398\) 18.0000i 0.902258i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i \(-0.0444700\pi\)
−0.615725 + 0.787961i \(0.711137\pi\)
\(402\) 0 0
\(403\) 8.66025 + 5.00000i 0.431398 + 0.249068i
\(404\) 0 0
\(405\) −18.0000 9.00000i −0.894427 0.447214i
\(406\) −10.0000 3.46410i −0.496292 0.171920i
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) 3.69615 + 5.59808i 0.182540 + 0.276469i
\(411\) 0 0
\(412\) 8.00000i 0.394132i
\(413\) 10.3923 2.00000i 0.511372 0.0984136i
\(414\) −21.0000 −1.03209
\(415\) −13.3923 + 0.803848i −0.657402 + 0.0394593i
\(416\) 2.50000 4.33013i 0.122573 0.212302i
\(417\) 0 0
\(418\) 12.9904 7.50000i 0.635380 0.366837i
\(419\) −35.0000 −1.70986 −0.854931 0.518742i \(-0.826401\pi\)
−0.854931 + 0.518742i \(0.826401\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −7.79423 + 4.50000i −0.379417 + 0.219057i
\(423\) 18.1865 + 10.5000i 0.884260 + 0.510527i
\(424\) 4.50000 7.79423i 0.218539 0.378521i
\(425\) −9.19615 3.92820i −0.446079 0.190546i
\(426\) 0 0
\(427\) −5.19615 + 15.0000i −0.251459 + 0.725901i
\(428\) 16.0000i 0.773389i
\(429\) 0 0
\(430\) 3.73205 2.46410i 0.179975 0.118830i
\(431\) −1.00000 + 1.73205i −0.0481683 + 0.0834300i −0.889104 0.457705i \(-0.848672\pi\)
0.840936 + 0.541135i \(0.182005\pi\)
\(432\) 0 0
\(433\) 28.0000i 1.34559i −0.739827 0.672797i \(-0.765093\pi\)
0.739827 0.672797i \(-0.234907\pi\)
\(434\) −4.00000 + 3.46410i −0.192006 + 0.166282i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) −30.3109 17.5000i −1.44997 0.837139i
\(438\) 0 0
\(439\) −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) −3.00000 + 6.00000i −0.143019 + 0.286039i
\(441\) 19.5000 7.79423i 0.928571 0.371154i
\(442\) 10.0000i 0.475651i
\(443\) −25.9808 + 15.0000i −1.23438 + 0.712672i −0.967941 0.251179i \(-0.919182\pi\)
−0.266443 + 0.963851i \(0.585848\pi\)
\(444\) 0 0
\(445\) −3.73205 + 2.46410i −0.176916 + 0.116810i
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) 0 0
\(448\) 1.73205 + 2.00000i 0.0818317 + 0.0944911i
\(449\) −5.00000 −0.235965 −0.117982 0.993016i \(-0.537643\pi\)
−0.117982 + 0.993016i \(0.537643\pi\)
\(450\) 13.7942 + 5.89230i 0.650266 + 0.277766i
\(451\) −4.50000 + 7.79423i −0.211897 + 0.367016i
\(452\) −12.1244 7.00000i −0.570282 0.329252i
\(453\) 0 0
\(454\) 6.00000 0.281594
\(455\) 20.6699 + 21.1603i 0.969019 + 0.992008i
\(456\) 0 0
\(457\) −8.66025 + 5.00000i −0.405110 + 0.233890i −0.688686 0.725059i \(-0.741812\pi\)
0.283577 + 0.958950i \(0.408479\pi\)
\(458\) 13.8564 + 8.00000i 0.647467 + 0.373815i
\(459\) 0 0
\(460\) 15.6244 0.937822i 0.728489 0.0437262i
\(461\) −32.0000 −1.49039 −0.745194 0.666847i \(-0.767643\pi\)
−0.745194 + 0.666847i \(0.767643\pi\)
\(462\) 0 0
\(463\) 17.0000i 0.790057i 0.918669 + 0.395029i \(0.129265\pi\)
−0.918669 + 0.395029i \(0.870735\pi\)
\(464\) −2.00000 3.46410i −0.0928477 0.160817i
\(465\) 0 0
\(466\) 4.00000 6.92820i 0.185296 0.320943i
\(467\) 29.4449 17.0000i 1.36255 0.786666i 0.372584 0.927999i \(-0.378472\pi\)
0.989962 + 0.141332i \(0.0451386\pi\)
\(468\) 15.0000i 0.693375i
\(469\) 1.00000 + 5.19615i 0.0461757 + 0.239936i
\(470\) −14.0000 7.00000i −0.645772 0.322886i
\(471\) 0 0
\(472\) 3.46410 + 2.00000i 0.159448 + 0.0920575i
\(473\) 5.19615 + 3.00000i 0.238919 + 0.137940i
\(474\) 0 0
\(475\) 15.0000 + 20.0000i 0.688247 + 0.917663i
\(476\) −5.00000 1.73205i −0.229175 0.0793884i
\(477\) 27.0000i 1.23625i
\(478\) −17.3205 + 10.0000i −0.792222 + 0.457389i
\(479\) 18.0000 31.1769i 0.822441 1.42451i −0.0814184 0.996680i \(-0.525945\pi\)
0.903859 0.427830i \(-0.140722\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 9.00000i 0.409939i
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) 26.7846 1.60770i 1.21623 0.0730017i
\(486\) 0 0
\(487\) 27.7128 + 16.0000i 1.25579 + 0.725029i 0.972253 0.233933i \(-0.0751596\pi\)
0.283535 + 0.958962i \(0.408493\pi\)
\(488\) −5.19615 + 3.00000i −0.235219 + 0.135804i
\(489\) 0 0
\(490\) −14.1603 + 6.66987i −0.639695 + 0.301314i
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) 6.92820 + 4.00000i 0.312031 + 0.180151i
\(494\) 12.5000 21.6506i 0.562402 0.974108i
\(495\) 1.20577 + 20.0885i 0.0541954 + 0.902909i
\(496\) −2.00000 −0.0898027
\(497\) 10.3923 + 12.0000i 0.466159 + 0.538274i
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) −10.5263 3.76795i −0.470750 0.168508i
\(501\) 0 0
\(502\) 4.33013 2.50000i 0.193263 0.111580i
\(503\) 40.0000i 1.78351i −0.452517 0.891756i \(-0.649474\pi\)
0.452517 0.891756i \(-0.350526\pi\)
\(504\) 7.50000 + 2.59808i 0.334077 + 0.115728i
\(505\) 0 0
\(506\) 10.5000 + 18.1865i 0.466782 + 0.808490i
\(507\) 0 0
\(508\) 6.06218 + 3.50000i 0.268966 + 0.155287i
\(509\) −17.0000 29.4449i −0.753512 1.30512i −0.946111 0.323843i \(-0.895025\pi\)
0.192599 0.981278i \(-0.438308\pi\)
\(510\) 0 0
\(511\) 8.00000 + 41.5692i 0.353899 + 1.83891i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −3.00000 + 5.19615i −0.132324 + 0.229192i
\(515\) 9.85641 + 14.9282i 0.434325 + 0.657815i
\(516\) 0 0
\(517\) 21.0000i 0.923579i
\(518\) −2.59808 + 0.500000i −0.114153 + 0.0219687i
\(519\) 0 0
\(520\) 0.669873 + 11.1603i 0.0293759 + 0.489410i
\(521\) 13.5000 23.3827i 0.591446 1.02441i −0.402592 0.915379i \(-0.631891\pi\)
0.994038 0.109035i \(-0.0347759\pi\)
\(522\) −10.3923 6.00000i −0.454859 0.262613i
\(523\) −13.8564 + 8.00000i −0.605898 + 0.349816i −0.771358 0.636401i \(-0.780422\pi\)
0.165460 + 0.986216i \(0.447089\pi\)
\(524\) 1.00000 0.0436852
\(525\) 0 0
\(526\) 0 0
\(527\) 3.46410 2.00000i 0.150899 0.0871214i
\(528\) 0 0
\(529\) 13.0000 22.5167i 0.565217 0.978985i
\(530\) 1.20577 + 20.0885i 0.0523754 + 0.872587i
\(531\) 12.0000 0.520756
\(532\) 8.66025 + 10.0000i 0.375470 + 0.433555i
\(533\) 15.0000i 0.649722i
\(534\) 0 0
\(535\) −19.7128 29.8564i −0.852259 1.29081i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 0 0
\(538\) 10.0000i 0.431131i
\(539\) −16.5000 12.9904i −0.710705 0.559535i
\(540\) 0 0
\(541\) 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i \(-0.0549027\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(542\) −20.7846 12.0000i −0.892775 0.515444i
\(543\) 0 0
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) 4.00000 + 2.00000i 0.171341 + 0.0856706i
\(546\) 0 0
\(547\) 26.0000i 1.11168i −0.831289 0.555840i \(-0.812397\pi\)
0.831289 0.555840i \(-0.187603\pi\)
\(548\) 6.92820 4.00000i 0.295958 0.170872i
\(549\) −9.00000 + 15.5885i −0.384111 + 0.665299i
\(550\) −1.79423 14.8923i −0.0765062 0.635010i
\(551\) −10.0000 17.3205i −0.426014 0.737878i
\(552\) 0 0
\(553\) 12.1244 35.0000i 0.515580 1.48835i
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) −8.00000 + 13.8564i −0.339276 + 0.587643i
\(557\) −19.9186 11.5000i −0.843978 0.487271i 0.0146368 0.999893i \(-0.495341\pi\)
−0.858614 + 0.512622i \(0.828674\pi\)
\(558\) −5.19615 + 3.00000i −0.219971 + 0.127000i
\(559\) 10.0000 0.422955
\(560\) −5.69615 1.59808i −0.240706 0.0675310i
\(561\) 0 0
\(562\) 7.79423 4.50000i 0.328780 0.189821i
\(563\) 1.73205 + 1.00000i 0.0729972 + 0.0421450i 0.536054 0.844183i \(-0.319914\pi\)
−0.463057 + 0.886328i \(0.653248\pi\)
\(564\) 0 0
\(565\) 31.2487 1.87564i 1.31464 0.0789090i
\(566\) 14.0000 0.588464
\(567\) 23.3827 4.50000i 0.981981 0.188982i
\(568\) 6.00000i 0.251754i
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −12.9904 + 7.50000i −0.543155 + 0.313591i
\(573\) 0 0
\(574\) −7.50000 2.59808i −0.313044 0.108442i
\(575\) −28.0000 + 21.0000i −1.16768 + 0.875761i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) 3.46410 + 2.00000i 0.144212 + 0.0832611i 0.570370 0.821388i \(-0.306800\pi\)
−0.426158 + 0.904649i \(0.640133\pi\)
\(578\) −11.2583 6.50000i −0.468285 0.270364i
\(579\) 0 0
\(580\) 8.00000 + 4.00000i 0.332182 + 0.166091i
\(581\) 12.0000 10.3923i 0.497844 0.431145i
\(582\) 0 0
\(583\) −23.3827 + 13.5000i −0.968412 + 0.559113i
\(584\) −8.00000 + 13.8564i −0.331042 + 0.573382i
\(585\) 18.4808 + 27.9904i 0.764085 + 1.15726i
\(586\) 4.50000 + 7.79423i 0.185893 + 0.321977i
\(587\) 34.0000i 1.40333i 0.712507 + 0.701665i \(0.247560\pi\)
−0.712507 + 0.701665i \(0.752440\pi\)
\(588\) 0 0
\(589\) −10.0000 −0.412043
\(590\) −8.92820 + 0.535898i −0.367568 + 0.0220626i
\(591\) 0 0
\(592\) −0.866025 0.500000i −0.0355934 0.0205499i
\(593\) 5.19615 3.00000i 0.213380 0.123195i −0.389501 0.921026i \(-0.627353\pi\)
0.602881 + 0.797831i \(0.294019\pi\)
\(594\) 0 0
\(595\) 11.4641 2.92820i 0.469982 0.120045i
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) 30.3109 + 17.5000i 1.23950 + 0.715628i
\(599\) −6.00000 + 10.3923i −0.245153 + 0.424618i −0.962175 0.272433i \(-0.912172\pi\)
0.717021 + 0.697051i \(0.245505\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) −1.73205 + 5.00000i −0.0705931 + 0.203785i
\(603\) 6.00000i 0.244339i
\(604\) −3.00000 5.19615i −0.122068 0.211428i
\(605\) −3.73205 + 2.46410i −0.151729 + 0.100180i
\(606\) 0 0
\(607\) −11.2583 + 6.50000i −0.456962 + 0.263827i −0.710766 0.703429i \(-0.751651\pi\)
0.253804 + 0.967256i \(0.418318\pi\)
\(608\) 5.00000i 0.202777i
\(609\) 0 0
\(610\) 6.00000 12.0000i 0.242933 0.485866i
\(611\) −17.5000 30.3109i −0.707974 1.22625i
\(612\) −5.19615 3.00000i −0.210042 0.121268i
\(613\) −12.9904 7.50000i −0.524677 0.302922i 0.214169 0.976797i \(-0.431296\pi\)
−0.738846 + 0.673874i \(0.764629\pi\)
\(614\) −11.0000 19.0526i −0.443924 0.768899i
\(615\) 0 0
\(616\) −1.50000 7.79423i −0.0604367 0.314038i
\(617\) 14.0000i 0.563619i 0.959470 + 0.281809i \(0.0909346\pi\)
−0.959470 + 0.281809i \(0.909065\pi\)
\(618\) 0 0
\(619\) 9.50000 16.4545i 0.381837 0.661361i −0.609488 0.792796i \(-0.708625\pi\)
0.991325 + 0.131434i \(0.0419582\pi\)
\(620\) 3.73205 2.46410i 0.149883 0.0989607i
\(621\) 0 0
\(622\) 6.00000i 0.240578i
\(623\) 1.73205 5.00000i 0.0693932 0.200321i
\(624\) 0 0
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) 11.0000 19.0526i 0.439648 0.761493i
\(627\) 0 0
\(628\) 7.79423 4.50000i 0.311024 0.179570i
\(629\) 2.00000 0.0797452
\(630\) −17.1962 + 4.39230i −0.685111 + 0.174994i
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) 12.1244 7.00000i 0.482281 0.278445i
\(633\) 0 0
\(634\) −1.00000 + 1.73205i −0.0397151 + 0.0687885i
\(635\) −15.6244 + 0.937822i −0.620034 + 0.0372163i
\(636\) 0 0
\(637\) −34.6410 5.00000i −1.37253 0.198107i
\(638\) 12.0000i 0.475085i
\(639\) 9.00000 + 15.5885i 0.356034 + 0.616670i
\(640\) −1.23205 1.86603i −0.0487011 0.0737611i
\(641\) 2.50000 4.33013i 0.0987441 0.171030i −0.812421 0.583071i \(-0.801851\pi\)
0.911165 + 0.412042i \(0.135184\pi\)
\(642\) 0 0
\(643\) 14.0000i 0.552106i 0.961142 + 0.276053i \(0.0890266\pi\)
−0.961142 + 0.276053i \(0.910973\pi\)
\(644\) −14.0000 + 12.1244i −0.551677 + 0.477767i
\(645\) 0 0
\(646\) −5.00000 8.66025i −0.196722 0.340733i
\(647\) 23.3827 + 13.5000i 0.919268 + 0.530740i 0.883402 0.468617i \(-0.155247\pi\)
0.0358667 + 0.999357i \(0.488581\pi\)
\(648\) 7.79423 + 4.50000i 0.306186 + 0.176777i
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) −15.0000 20.0000i −0.588348 0.784465i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) −2.59808 + 1.50000i −0.101671 + 0.0586995i −0.549973 0.835182i \(-0.685362\pi\)
0.448303 + 0.893882i \(0.352029\pi\)
\(654\) 0 0
\(655\) −1.86603 + 1.23205i −0.0729116 + 0.0481402i
\(656\) −1.50000 2.59808i −0.0585652 0.101438i
\(657\) 48.0000i 1.87266i
\(658\) 18.1865 3.50000i 0.708985 0.136444i
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −8.00000 + 13.8564i −0.311164 + 0.538952i −0.978615 0.205702i \(-0.934052\pi\)
0.667451 + 0.744654i \(0.267385\pi\)
\(662\) −4.33013 2.50000i −0.168295 0.0971653i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) −28.4808 7.99038i −1.10444 0.309854i
\(666\) −3.00000 −0.116248
\(667\) 24.2487 14.0000i 0.938914 0.542082i
\(668\) 12.9904 + 7.50000i 0.502613 + 0.290184i
\(669\) 0 0
\(670\) −0.267949 4.46410i −0.0103518 0.172463i
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 32.0000i 1.23351i −0.787155 0.616755i \(-0.788447\pi\)
0.787155 0.616755i \(-0.211553\pi\)
\(674\) 5.00000 + 8.66025i 0.192593 + 0.333581i
\(675\) 0 0
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) −14.7224 + 8.50000i −0.565829 + 0.326682i −0.755482 0.655170i \(-0.772597\pi\)
0.189653 + 0.981851i \(0.439264\pi\)
\(678\) 0 0
\(679\) −24.0000 + 20.7846i −0.921035 + 0.797640i
\(680\) 4.00000 + 2.00000i 0.153393 + 0.0766965i
\(681\) 0 0
\(682\) 5.19615 + 3.00000i 0.198971 + 0.114876i
\(683\) −38.1051 22.0000i −1.45805 0.841807i −0.459136 0.888366i \(-0.651841\pi\)
−0.998916 + 0.0465592i \(0.985174\pi\)
\(684\) 7.50000 + 12.9904i 0.286770 + 0.496700i
\(685\) −8.00000 + 16.0000i −0.305664 + 0.611329i
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 0 0
\(688\) −1.73205 + 1.00000i −0.0660338 + 0.0381246i
\(689\) −22.5000 + 38.9711i −0.857182 + 1.48468i
\(690\) 0 0
\(691\) 22.0000 + 38.1051i 0.836919 + 1.44959i 0.892458 + 0.451130i \(0.148979\pi\)
−0.0555386 + 0.998457i \(0.517688\pi\)
\(692\) 9.00000i 0.342129i
\(693\) −15.5885 18.0000i −0.592157 0.683763i
\(694\) 12.0000 0.455514
\(695\) −2.14359 35.7128i −0.0813111 1.35466i
\(696\) 0 0
\(697\) 5.19615 + 3.00000i 0.196818 + 0.113633i
\(698\) 10.3923 6.00000i 0.393355 0.227103i
\(699\) 0 0
\(700\) 12.5981 4.03590i 0.476163 0.152543i
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) −4.33013 2.50000i −0.163314 0.0942893i
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) 0 0
\(709\) 6.00000 + 10.3923i 0.225335 + 0.390291i 0.956420 0.291995i \(-0.0943191\pi\)
−0.731085 + 0.682286i \(0.760986\pi\)
\(710\) −7.39230 11.1962i −0.277428 0.420184i
\(711\) 21.0000 36.3731i 0.787562 1.36410i
\(712\) 1.73205 1.00000i 0.0649113 0.0374766i
\(713\) 14.0000i 0.524304i
\(714\) 0 0
\(715\) 15.0000 30.0000i 0.560968 1.12194i
\(716\) −6.50000 11.2583i −0.242916 0.420744i
\(717\) 0 0
\(718\) 13.8564 + 8.00000i 0.517116 + 0.298557i
\(719\) 13.0000 + 22.5167i 0.484818 + 0.839730i 0.999848 0.0174426i \(-0.00555244\pi\)
−0.515030 + 0.857172i \(0.672219\pi\)
\(720\) −6.00000 3.00000i −0.223607 0.111803i
\(721\) −20.0000 6.92820i −0.744839 0.258020i
\(722\) 6.00000i 0.223297i
\(723\) 0 0
\(724\) 13.0000 22.5167i 0.483141 0.836825i
\(725\) −19.8564 + 2.39230i −0.737448 + 0.0888480i
\(726\) 0 0
\(727\) 29.0000i 1.07555i −0.843088 0.537775i \(-0.819265\pi\)
0.843088 0.537775i \(-0.180735\pi\)
\(728\) −8.66025 10.0000i −0.320970 0.370625i
\(729\) 27.0000 1.00000
\(730\) −2.14359 35.7128i −0.0793380 1.32179i
\(731\) 2.00000 3.46410i 0.0739727 0.128124i
\(732\) 0 0
\(733\) −35.5070 + 20.5000i −1.31148 + 0.757185i −0.982342 0.187096i \(-0.940092\pi\)
−0.329141 + 0.944281i \(0.606759\pi\)
\(734\) −13.0000 −0.479839
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) 5.19615 3.00000i 0.191403 0.110506i
\(738\) −7.79423 4.50000i −0.286910 0.165647i
\(739\) −14.5000 + 25.1147i −0.533391 + 0.923861i 0.465848 + 0.884865i \(0.345749\pi\)
−0.999239 + 0.0389959i \(0.987584\pi\)
\(740\) 2.23205 0.133975i 0.0820518 0.00492500i
\(741\) 0 0
\(742\) −15.5885 18.0000i −0.572270 0.660801i
\(743\) 21.0000i 0.770415i 0.922830 + 0.385208i \(0.125870\pi\)
−0.922830 + 0.385208i \(0.874130\pi\)
\(744\) 0 0
\(745\) 33.5885 22.1769i 1.23059 0.812499i
\(746\) −13.0000 + 22.5167i −0.475964 + 0.824394i
\(747\) 15.5885 9.00000i 0.570352 0.329293i
\(748\) 6.00000i 0.219382i
\(749\) 40.0000 + 13.8564i 1.46157 + 0.506302i
\(750\) 0 0
\(751\) −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i \(-0.995991\pi\)
0.489053 0.872254i \(-0.337342\pi\)
\(752\) 6.06218 + 3.50000i 0.221065 + 0.127632i
\(753\) 0 0
\(754\) 10.0000 + 17.3205i 0.364179 + 0.630776i
\(755\) 12.0000 + 6.00000i 0.436725 + 0.218362i
\(756\) 0 0
\(757\) 42.0000i 1.52652i 0.646094 + 0.763258i \(0.276401\pi\)
−0.646094 + 0.763258i \(0.723599\pi\)
\(758\) 25.1147 14.5000i 0.912208 0.526664i
\(759\) 0 0
\(760\) −6.16025 9.33013i −0.223456 0.338439i
\(761\) −0.500000 0.866025i −0.0181250 0.0313934i 0.856821 0.515615i \(-0.172436\pi\)
−0.874946 + 0.484221i \(0.839103\pi\)
\(762\) 0 0
\(763\) −5.19615 + 1.00000i −0.188113 + 0.0362024i
\(764\) 20.0000 0.723575
\(765\) 13.3923 0.803848i 0.484200 0.0290632i
\(766\) −10.5000 + 18.1865i −0.379380 + 0.657106i
\(767\) −17.3205 10.0000i −0.625407 0.361079i
\(768\) 0 0
\(769\) 29.0000 1.04577 0.522883 0.852404i \(-0.324856\pi\)
0.522883 + 0.852404i \(0.324856\pi\)
\(770\) 12.4019 + 12.6962i 0.446934 + 0.457538i
\(771\) 0 0
\(772\) −8.66025 + 5.00000i −0.311689 + 0.179954i
\(773\) 38.9711 + 22.5000i 1.40169 + 0.809269i 0.994567 0.104102i \(-0.0331970\pi\)
0.407128 + 0.913371i \(0.366530\pi\)
\(774\) −3.00000 + 5.19615i −0.107833 + 0.186772i
\(775\) −3.92820 + 9.19615i −0.141105 + 0.330336i
\(776\) −12.0000 −0.430775
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) −7.50000 12.9904i −0.268715 0.465429i
\(780\) 0 0
\(781\) 9.00000 15.5885i 0.322045 0.557799i
\(782\) 12.1244 7.00000i 0.433566 0.250319i
\(783\) 0 0
\(784\) 6.50000 2.59808i 0.232143 0.0927884i