Properties

Label 70.2.i.b.39.1
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 39.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 70.39
Dual form 70.2.i.b.9.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-2.23205 - 0.133975i) 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} +(1.96410 + 4.59808i) 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} +(0.767949 + 5.86603i) q^{35} -3.00000 q^{36} +(-0.866025 + 0.500000i) q^{37} +(4.33013 + 2.50000i) q^{38} +(-1.23205 + 1.86603i) q^{40} +3.00000 q^{41} +2.00000i q^{43} +(1.50000 + 2.59808i) q^{44} +(0.401924 - 6.69615i) 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} +(6.16025 - 9.33013i) q^{65} +(1.73205 + 1.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(-3.59808 - 4.69615i) 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} +(0.133975 - 2.23205i) 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} +(0.669873 - 11.1603i) 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
\(5\) 1.86603 + 1.23205i 0.834512 + 0.550990i
\(6\) 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
\(10\) −2.23205 0.133975i −0.705836 0.0423665i
\(11\) −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 \(-0.756123\pi\)
0.720577 0.693375i \(-0.243877\pi\)
\(14\) −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 0.275029 0.961436i \(-0.411312\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 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 −0.973856 0.227167i \(-0.927054\pi\)
−0.290196 + 0.956967i \(0.593720\pi\)
\(24\) 0 0
\(25\) 1.96410 + 4.59808i 0.392820 + 0.919615i
\(26\) 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
\(35\) 0.767949 + 5.86603i 0.129807 + 0.991539i
\(36\) −3.00000 −0.500000
\(37\) −0.866025 + 0.500000i −0.142374 + 0.0821995i −0.569495 0.821995i \(-0.692861\pi\)
0.427121 + 0.904194i \(0.359528\pi\)
\(38\) 4.33013 + 2.50000i 0.702439 + 0.405554i
\(39\) 0 0
\(40\) −1.23205 + 1.86603i −0.194804 + 0.295045i
\(41\) 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 \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 0.401924 6.69615i 0.0599153 0.998203i
\(46\) 3.50000 6.06218i 0.516047 0.893819i
\(47\) 6.06218 3.50000i 0.884260 0.510527i 0.0121990 0.999926i \(-0.496117\pi\)
0.872060 + 0.489398i \(0.162783\pi\)
\(48\) 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 −0.142269 0.989828i \(-0.545440\pi\)
−0.928351 + 0.371706i \(0.878773\pi\)
\(54\) 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
\(65\) 6.16025 9.33013i 0.764085 1.15726i
\(66\) 0 0
\(67\) 1.73205 + 1.00000i 0.211604 + 0.122169i 0.602056 0.798454i \(-0.294348\pi\)
−0.390453 + 0.920623i \(0.627682\pi\)
\(68\) −1.73205 + 1.00000i −0.210042 + 0.121268i
\(69\) 0 0
\(70\) −3.59808 4.69615i −0.430052 0.561298i
\(71\) −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 \(0.0524664\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(74\) 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 \(0.544677\pi\)
\(80\) 0.133975 2.23205i 0.0149788 0.249551i
\(81\) −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 \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) 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
\(95\) 0.669873 11.1603i 0.0687275 1.14502i
\(96\) 0 0
\(97\) 12.0000i 1.21842i 0.793011 + 0.609208i \(0.208512\pi\)
−0.793011 + 0.609208i \(0.791488\pi\)
\(98\) −2.59808 6.50000i −0.262445 0.656599i
\(99\) 9.00000 0.904534
\(100\) 4.96410 + 0.598076i 0.496410 + 0.0598076i
\(101\) 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 −0.800855 0.598858i \(-0.795621\pi\)
0.118199 + 0.992990i \(0.462288\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) 13.8564 8.00000i 1.33955 0.773389i 0.352809 0.935695i \(-0.385227\pi\)
0.986740 + 0.162306i \(0.0518932\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 3.69615 5.59808i 0.352414 0.533756i
\(111\) 0 0
\(112\) 0.866025 2.50000i 0.0818317 0.236228i
\(113\) 14.0000i 1.31701i 0.752577 + 0.658505i \(0.228811\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) −15.6244 0.937822i −1.45698 0.0874524i
\(116\) 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 \(-0.899478\pi\)
0.950549 0.310575i \(-0.100522\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −0.669873 + 11.1603i −0.0587517 + 0.978819i
\(131\) 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 0.173939 0.984757i \(-0.444351\pi\)
−0.765855 + 0.643013i \(0.777684\pi\)
\(138\) 0 0
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 5.46410 + 2.26795i 0.461801 + 0.191677i
\(141\) 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
\(145\) 7.46410 + 4.92820i 0.619860 + 0.409265i
\(146\) −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 0.155618 0.987817i \(-0.450263\pi\)
−0.777666 + 0.628678i \(0.783596\pi\)
\(158\) −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 −0.848339 0.529454i \(-0.822397\pi\)
0.0343508 + 0.999410i \(0.489064\pi\)
\(164\) 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 \(-0.802909\pi\)
0.814355 0.580367i \(-0.197091\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 3.73205 + 2.46410i 0.286235 + 0.188988i
\(171\) −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 −0.173534 0.984828i \(-0.555519\pi\)
0.766119 + 0.642699i \(0.222185\pi\)
\(174\) 0 0
\(175\) −5.79423 + 11.8923i −0.438003 + 0.898974i
\(176\) 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 \(0.00518305\pi\)
\(180\) −5.59808 3.69615i −0.417256 0.275495i
\(181\) 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
\(185\) −2.23205 0.133975i −0.164104 0.00985001i
\(186\) 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 0.778183 0.628037i \(-0.216141\pi\)
−0.154805 + 0.987945i \(0.549475\pi\)
\(194\) −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 \(0.0570008\pi\)
−0.984009 + 0.178118i \(0.942999\pi\)
\(198\) −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 \(-0.0535685\pi\)
\(200\) −4.59808 + 1.96410i −0.325133 + 0.138883i
\(201\) 0 0
\(202\) 0 0
\(203\) 6.92820 + 8.00000i 0.486265 + 0.561490i
\(204\) 0 0
\(205\) 5.59808 + 3.69615i 0.390987 + 0.258150i
\(206\) 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
\(215\) −2.46410 + 3.73205i −0.168050 + 0.254524i
\(216\) 0 0
\(217\) 5.19615 1.00000i 0.352738 0.0678844i
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) −0.401924 + 6.69615i −0.0270977 + 0.451455i
\(221\) −5.00000 + 8.66025i −0.336336 + 0.582552i
\(222\) 0 0
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 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 0.317547 0.948242i \(-0.397141\pi\)
−0.662428 + 0.749125i \(0.730474\pi\)
\(228\) 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 −0.709468 0.704737i \(-0.751065\pi\)
0.255586 + 0.966786i \(0.417731\pi\)
\(234\) 7.50000 12.9904i 0.490290 0.849208i
\(235\) 15.6244 + 0.937822i 1.01922 + 0.0611768i
\(236\) 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
\(245\) −10.4019 + 11.6962i −0.664555 + 0.747240i
\(246\) 0 0
\(247\) −21.6506 + 12.5000i −1.37760 + 0.795356i
\(248\) 1.73205 + 1.00000i 0.109985 + 0.0635001i
\(249\) 0 0
\(250\) −3.76795 10.5263i −0.238306 0.665740i
\(251\) 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 −0.329104 0.944294i \(-0.606747\pi\)
0.653231 + 0.757159i \(0.273413\pi\)
\(258\) 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
\(275\) −14.8923 1.79423i −0.898040 0.108196i
\(276\) 0 0
\(277\) −1.73205 1.00000i −0.104069 0.0600842i 0.447062 0.894503i \(-0.352470\pi\)
−0.551131 + 0.834419i \(0.685804\pi\)
\(278\) 13.8564 8.00000i 0.831052 0.479808i
\(279\) −6.00000 −0.359211
\(280\) −5.86603 + 0.767949i −0.350562 + 0.0458937i
\(281\) 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 0.0942988 0.995544i \(-0.469939\pi\)
−0.815017 + 0.579437i \(0.803272\pi\)
\(284\) −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
\(290\) −8.92820 0.535898i −0.524282 0.0314690i
\(291\) 0 0
\(292\) 13.8564 8.00000i 0.810885 0.468165i
\(293\) 9.00000i 0.525786i −0.964825 0.262893i \(-0.915323\pi\)
0.964825 0.262893i \(-0.0846766\pi\)
\(294\) 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
\(305\) 0.803848 13.3923i 0.0460282 0.766841i
\(306\) −3.00000 5.19615i −0.171499 0.297044i
\(307\) 22.0000i 1.25561i 0.778372 + 0.627803i \(0.216046\pi\)
−0.778372 + 0.627803i \(0.783954\pi\)
\(308\) −2.59808 + 7.50000i −0.148039 + 0.427352i
\(309\) 0 0
\(310\) −2.46410 + 3.73205i −0.139952 + 0.211966i
\(311\) −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 −0.930062 0.367402i \(-0.880247\pi\)
−0.146852 + 0.989158i \(0.546914\pi\)
\(314\) 9.00000 0.507899
\(315\) 14.0885 10.7942i 0.793795 0.608186i
\(316\) 14.0000 0.787562
\(317\) 1.73205 1.00000i 0.0972817 0.0561656i −0.450570 0.892741i \(-0.648779\pi\)
0.547852 + 0.836576i \(0.315446\pi\)
\(318\) 0 0
\(319\) −6.00000 + 10.3923i −0.335936 + 0.581857i
\(320\) −1.86603 1.23205i −0.104314 0.0688737i
\(321\) 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
\(325\) 22.9904 9.82051i 1.27528 0.544744i
\(326\) 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 \(-0.912193\pi\)
0.962193 0.272367i \(-0.0878066\pi\)
\(338\) 10.3923 6.00000i 0.565267 0.326357i
\(339\) 0 0
\(340\) −4.46410 0.267949i −0.242100 0.0145316i
\(341\) 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 0.194409 0.980921i \(-0.437721\pi\)
−0.752297 + 0.658824i \(0.771054\pi\)
\(348\) 0 0
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) −0.928203 13.1962i −0.0496145 0.705364i
\(351\) 0 0
\(352\) −2.59808 + 1.50000i −0.138478 + 0.0799503i
\(353\) −20.7846 12.0000i −1.10625 0.638696i −0.168397 0.985719i \(-0.553859\pi\)
−0.937856 + 0.347024i \(0.887192\pi\)
\(354\) 0 0
\(355\) −11.1962 7.39230i −0.594230 0.392343i
\(356\) 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 \(0.694583\pi\)
\(360\) 6.69615 + 0.401924i 0.352918 + 0.0211832i
\(361\) −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 0.764180 0.645003i \(-0.223144\pi\)
−0.176500 + 0.984301i \(0.556477\pi\)
\(368\) 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 0.213165 0.977016i \(-0.431623\pi\)
0.952703 + 0.303902i \(0.0982894\pi\)
\(374\) −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 \(0.232538\pi\)
\(380\) −9.33013 6.16025i −0.478625 0.316014i
\(381\) 0 0
\(382\) −17.3205 10.0000i −0.886194 0.511645i
\(383\) 18.1865 10.5000i 0.929288 0.536525i 0.0427020 0.999088i \(-0.486403\pi\)
0.886586 + 0.462563i \(0.153070\pi\)
\(384\) 0 0
\(385\) −16.3923 6.80385i −0.835429 0.346756i
\(386\) −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
\(395\) −1.87564 + 31.2487i −0.0943739 + 1.57229i
\(396\) 4.50000 7.79423i 0.226134 0.391675i
\(397\) 12.1244 7.00000i 0.608504 0.351320i −0.163876 0.986481i \(-0.552400\pi\)
0.772380 + 0.635161i \(0.219066\pi\)
\(398\) 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 \(0.279170\pi\)
\(410\) −6.69615 0.401924i −0.330699 0.0198496i
\(411\) 0 0
\(412\) 8.00000i 0.394132i
\(413\) −10.3923 + 2.00000i −0.511372 + 0.0984136i
\(414\) −21.0000 −1.03209
\(415\) 7.39230 11.1962i 0.362874 0.549598i
\(416\) 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
\(425\) 1.19615 9.92820i 0.0580219 0.481589i
\(426\) 0 0
\(427\) 5.19615 15.0000i 0.251459 0.725901i
\(428\) 16.0000i 0.773389i
\(429\) 0 0
\(430\) 0.267949 4.46410i 0.0129217 0.215278i
\(431\) −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 \(0.234907\pi\)
−0.739827 + 0.672797i \(0.765093\pi\)
\(434\) −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 0.266443 0.963851i \(-0.414152\pi\)
0.967941 + 0.251179i \(0.0808184\pi\)
\(444\) 0 0
\(445\) −0.267949 + 4.46410i −0.0127020 + 0.211619i
\(446\) 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 \(0.537643\pi\)
\(450\) −1.79423 + 14.8923i −0.0845807 + 0.702030i
\(451\) −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
\(455\) 29.3301 3.83975i 1.37502 0.180010i
\(456\) 0 0
\(457\) 8.66025 5.00000i 0.405110 0.233890i −0.283577 0.958950i \(-0.591521\pi\)
0.688686 + 0.725059i \(0.258188\pi\)
\(458\) −13.8564 8.00000i −0.647467 0.373815i
\(459\) 0 0
\(460\) −8.62436 + 13.0622i −0.402113 + 0.609027i
\(461\) −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 \(-0.870735\pi\)
0.918669 0.395029i \(-0.129265\pi\)
\(464\) −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 −0.989962 0.141332i \(-0.954861\pi\)
−0.372584 + 0.927999i \(0.621528\pi\)
\(468\) 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
\(485\) −14.7846 + 22.3923i −0.671335 + 1.01678i
\(486\) 0 0
\(487\) −27.7128 16.0000i −1.25579 0.725029i −0.283535 0.958962i \(-0.591507\pi\)
−0.972253 + 0.233933i \(0.924840\pi\)
\(488\) 5.19615 3.00000i 0.235219 0.135804i
\(489\) 0 0
\(490\) 3.16025 15.3301i 0.142766 0.692545i
\(491\) 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
\(495\) 16.7942 + 11.0885i 0.754844 + 0.498389i
\(496\) −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 \(0.804796\pi\)
\(500\) 8.52628 + 7.23205i 0.381307 + 0.323427i
\(501\) 0 0
\(502\) −4.33013 + 2.50000i −0.193263 + 0.111580i
\(503\) 40.0000i 1.78351i 0.452517 + 0.891756i \(0.350526\pi\)
−0.452517 + 0.891756i \(0.649474\pi\)
\(504\) 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
\(515\) −17.8564 1.07180i −0.786847 0.0472290i
\(516\) 0 0
\(517\) 21.0000i 0.923579i
\(518\) 2.59808 0.500000i 0.114153 0.0219687i
\(519\) 0 0
\(520\) 9.33013 + 6.16025i 0.409153 + 0.270145i
\(521\) 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 −0.165460 0.986216i \(-0.552911\pi\)
0.771358 + 0.636401i \(0.219578\pi\)
\(524\) 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
\(530\) 16.7942 + 11.0885i 0.729495 + 0.481652i
\(531\) 12.0000 0.520756
\(532\) −8.66025 10.0000i −0.375470 0.433555i
\(533\) 15.0000i 0.649722i
\(534\) 0 0
\(535\) 35.7128 + 2.14359i 1.54400 + 0.0926756i
\(536\) −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 \(0.187603\pi\)
−0.831289 + 0.555840i \(0.812397\pi\)
\(548\) −6.92820 + 4.00000i −0.295958 + 0.170872i
\(549\) −9.00000 + 15.5885i −0.384111 + 0.665299i
\(550\) 13.7942 5.89230i 0.588188 0.251249i
\(551\) −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 0.858614 0.512622i \(-0.171326\pi\)
−0.0146368 + 0.999893i \(0.504659\pi\)
\(558\) 5.19615 3.00000i 0.219971 0.127000i
\(559\) 10.0000 0.422955
\(560\) 4.69615 3.59808i 0.198449 0.152046i
\(561\) 0 0
\(562\) −7.79423 + 4.50000i −0.328780 + 0.189821i
\(563\) −1.73205 1.00000i −0.0729972 0.0421450i 0.463057 0.886328i \(-0.346752\pi\)
−0.536054 + 0.844183i \(0.680086\pi\)
\(564\) 0 0
\(565\) −17.2487 + 26.1244i −0.725659 + 1.09906i
\(566\) 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 0.426158 0.904649i \(-0.359867\pi\)
−0.570370 + 0.821388i \(0.693200\pi\)
\(578\) 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
\(585\) −33.4808 2.00962i −1.38426 0.0830875i
\(586\) 4.50000 + 7.79423i 0.185893 + 0.321977i
\(587\) 34.0000i 1.40333i −0.712507 0.701665i \(-0.752440\pi\)
0.712507 0.701665i \(-0.247560\pi\)
\(588\) 0 0
\(589\) −10.0000 −0.412043
\(590\) 4.92820 7.46410i 0.202891 0.307292i
\(591\) 0 0
\(592\) 0.866025 + 0.500000i 0.0355934 + 0.0205499i
\(593\) −5.19615 + 3.00000i −0.213380 + 0.123195i −0.602881 0.797831i \(-0.705981\pi\)
0.389501 + 0.921026i \(0.372647\pi\)
\(594\) 0 0
\(595\) 4.53590 10.9282i 0.185954 0.448013i
\(596\) −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
\(605\) −0.267949 + 4.46410i −0.0108937 + 0.181492i
\(606\) 0 0
\(607\) 11.2583 6.50000i 0.456962 0.263827i −0.253804 0.967256i \(-0.581682\pi\)
0.710766 + 0.703429i \(0.248349\pi\)
\(608\) 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 0.738846 0.673874i \(-0.235371\pi\)
−0.214169 + 0.976797i \(0.568704\pi\)
\(614\) −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 \(-0.909065\pi\)
0.959470 0.281809i \(-0.0909346\pi\)
\(618\) 0 0
\(619\) 9.50000 16.4545i 0.381837 0.661361i −0.609488 0.792796i \(-0.708625\pi\)
0.991325 + 0.131434i \(0.0419582\pi\)
\(620\) 0.267949 4.46410i 0.0107611 0.179283i
\(621\) 0 0
\(622\) 6.00000i 0.240578i
\(623\) −1.73205 + 5.00000i −0.0693932 + 0.200321i
\(624\) 0 0
\(625\) −17.2846 + 18.0622i −0.691384 + 0.722487i
\(626\) 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
\(630\) −6.80385 + 16.3923i −0.271072 + 0.653085i
\(631\) −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
\(635\) 8.62436 13.0622i 0.342247 0.518357i
\(636\) 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
\(640\) 2.23205 + 0.133975i 0.0882296 + 0.00529581i
\(641\) 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 \(-0.910973\pi\)
0.961142 0.276053i \(-0.0890266\pi\)
\(644\) −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 −0.0358667 0.999357i \(-0.511419\pi\)
−0.883402 + 0.468617i \(0.844753\pi\)
\(648\) −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 −0.448303 0.893882i \(-0.647971\pi\)
0.549973 + 0.835182i \(0.314638\pi\)
\(654\) 0 0
\(655\) −0.133975 + 2.23205i −0.00523482 + 0.0872134i
\(656\) −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
\(665\) 23.4808 17.9904i 0.910545 0.697637i
\(666\) −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
\(670\) −3.73205 2.46410i −0.144182 0.0951966i
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 32.0000i 1.23351i 0.787155 + 0.616755i \(0.211553\pi\)
−0.787155 + 0.616755i \(0.788447\pi\)
\(674\) 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 −0.189653 0.981851i \(-0.560736\pi\)
0.755482 + 0.655170i \(0.227403\pi\)
\(678\) 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 0.998916 0.0465592i \(-0.0148256\pi\)
0.459136 + 0.888366i \(0.348159\pi\)
\(684\) 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
\(695\) −29.8564 19.7128i −1.13252 0.747750i
\(696\) 0 0
\(697\) −5.19615 3.00000i −0.196818 0.113633i
\(698\) −10.3923 + 6.00000i −0.393355 + 0.227103i
\(699\) 0 0
\(700\) 7.40192 + 10.9641i 0.279766 + 0.414404i
\(701\) 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 \(0.760986\pi\)
\(710\) 13.3923 + 0.803848i 0.502604 + 0.0301679i
\(711\) 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
\(725\) 7.85641 + 18.3923i 0.291780 + 0.683073i
\(726\) 0 0
\(727\) 29.0000i 1.07555i 0.843088 + 0.537775i \(0.180735\pi\)
−0.843088 + 0.537775i \(0.819265\pi\)
\(728\) 8.66025 + 10.0000i 0.320970 + 0.370625i
\(729\) 27.0000 1.00000
\(730\) −29.8564 19.7128i −1.10504 0.729604i
\(731\) 2.00000 3.46410i 0.0739727 0.128124i
\(732\) 0 0
\(733\) 35.5070 20.5000i 1.31148 0.757185i 0.329141 0.944281i \(-0.393241\pi\)
0.982342 + 0.187096i \(0.0599076\pi\)
\(734\) −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 \(0.987584\pi\)
\(740\) −1.23205 + 1.86603i −0.0452911 + 0.0685965i
\(741\) 0 0
\(742\) 15.5885 + 18.0000i 0.572270 + 0.660801i
\(743\) 21.0000i 0.770415i −0.922830 0.385208i \(-0.874130\pi\)
0.922830 0.385208i \(-0.125870\pi\)
\(744\) 0 0
\(745\) 2.41154 40.1769i 0.0883521 1.47197i
\(746\) −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 \(-0.723599\pi\)
0.646094 0.763258i \(-0.276401\pi\)
\(758\) −25.1147 + 14.5000i −0.912208 + 0.526664i
\(759\) 0 0
\(760\) 11.1603 + 0.669873i 0.404825 + 0.0242988i
\(761\) −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
\(765\) −7.39230 + 11.1962i −0.267269 + 0.404798i
\(766\) −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 \(0.324856\pi\)
\(770\) 17.5981 2.30385i 0.634191 0.0830249i
\(771\) 0 0
\(772\) 8.66025 5.00000i 0.311689 0.179954i
\(773\) −38.9711 22.5000i −1.40169 0.809269i −0.407128 0.913371i \(-0.633470\pi\)
−0.994567 + 0.104102i \(0.966803\pi\)
\(774\) −3.00000 + 5.19615i −0.107833 + 0.186772i
\(775\) 9.92820 + 1.19615i 0.356632 + 0.0429671i
\(776\) −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