Properties

Label 1638.2.bj.b.1135.1
Level $1638$
Weight $2$
Character 1638.1135
Analytic conductor $13.079$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1135.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1638.1135
Dual form 1638.2.bj.b.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.73205i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.73205i q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-1.36603 + 2.36603i) q^{10} +(-1.50000 - 0.866025i) q^{11} +(-3.59808 - 0.232051i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.133975 - 0.232051i) q^{17} +(-0.866025 + 0.500000i) q^{19} +(2.36603 - 1.36603i) q^{20} +(0.866025 + 1.50000i) q^{22} +(-1.73205 + 3.00000i) q^{23} -2.46410 q^{25} +(3.00000 + 2.00000i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(-0.232051 + 0.401924i) q^{29} +8.19615i q^{31} +(0.866025 - 0.500000i) q^{32} +0.267949i q^{34} +(1.36603 + 2.36603i) q^{35} +(-2.83013 - 1.63397i) q^{37} +1.00000 q^{38} -2.73205 q^{40} +(2.59808 + 1.50000i) q^{41} +(3.36603 + 5.83013i) q^{43} -1.73205i q^{44} +(3.00000 - 1.73205i) q^{46} -4.46410i q^{47} +(0.500000 - 0.866025i) q^{49} +(2.13397 + 1.23205i) q^{50} +(-1.59808 - 3.23205i) q^{52} -7.00000 q^{53} +(-2.36603 + 4.09808i) q^{55} +(0.500000 + 0.866025i) q^{56} +(0.401924 - 0.232051i) q^{58} +(-11.1962 + 6.46410i) q^{59} +(2.59808 + 4.50000i) q^{61} +(4.09808 - 7.09808i) q^{62} -1.00000 q^{64} +(-0.633975 + 9.83013i) q^{65} +(4.26795 + 2.46410i) q^{67} +(0.133975 - 0.232051i) q^{68} -2.73205i q^{70} +(7.09808 - 4.09808i) q^{71} -1.46410i q^{73} +(1.63397 + 2.83013i) q^{74} +(-0.866025 - 0.500000i) q^{76} +1.73205 q^{77} +15.9282 q^{79} +(2.36603 + 1.36603i) q^{80} +(-1.50000 - 2.59808i) q^{82} -10.1962i q^{83} +(-0.633975 + 0.366025i) q^{85} -6.73205i q^{86} +(-0.866025 + 1.50000i) q^{88} +(-3.06218 - 1.76795i) q^{89} +(3.23205 - 1.59808i) q^{91} -3.46410 q^{92} +(-2.23205 + 3.86603i) q^{94} +(1.36603 + 2.36603i) q^{95} +(1.43782 - 0.830127i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 2 q^{10} - 6 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 6 q^{29} + 2 q^{35} + 6 q^{37} + 4 q^{38} - 4 q^{40} + 10 q^{43} + 12 q^{46} + 2 q^{49} + 12 q^{50} + 4 q^{52} - 28 q^{53} - 6 q^{55} + 2 q^{56} + 12 q^{58} - 24 q^{59} + 6 q^{62} - 4 q^{64} - 6 q^{65} + 24 q^{67} + 4 q^{68} + 18 q^{71} + 10 q^{74} + 36 q^{79} + 6 q^{80} - 6 q^{82} - 6 q^{85} + 12 q^{89} + 6 q^{91} - 2 q^{94} + 2 q^{95} + 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 2.73205i 1.22181i −0.791704 0.610905i \(-0.790806\pi\)
0.791704 0.610905i \(-0.209194\pi\)
\(6\) 0 0
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.36603 + 2.36603i −0.431975 + 0.748203i
\(11\) −1.50000 0.866025i −0.452267 0.261116i 0.256520 0.966539i \(-0.417424\pi\)
−0.708787 + 0.705422i \(0.750757\pi\)
\(12\) 0 0
\(13\) −3.59808 0.232051i −0.997927 0.0643593i
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.133975 0.232051i −0.0324936 0.0562806i 0.849321 0.527876i \(-0.177012\pi\)
−0.881815 + 0.471596i \(0.843678\pi\)
\(18\) 0 0
\(19\) −0.866025 + 0.500000i −0.198680 + 0.114708i −0.596040 0.802955i \(-0.703260\pi\)
0.397360 + 0.917663i \(0.369927\pi\)
\(20\) 2.36603 1.36603i 0.529059 0.305453i
\(21\) 0 0
\(22\) 0.866025 + 1.50000i 0.184637 + 0.319801i
\(23\) −1.73205 + 3.00000i −0.361158 + 0.625543i −0.988152 0.153481i \(-0.950952\pi\)
0.626994 + 0.779024i \(0.284285\pi\)
\(24\) 0 0
\(25\) −2.46410 −0.492820
\(26\) 3.00000 + 2.00000i 0.588348 + 0.392232i
\(27\) 0 0
\(28\) −0.866025 0.500000i −0.163663 0.0944911i
\(29\) −0.232051 + 0.401924i −0.0430908 + 0.0746354i −0.886766 0.462218i \(-0.847054\pi\)
0.843676 + 0.536853i \(0.180387\pi\)
\(30\) 0 0
\(31\) 8.19615i 1.47207i 0.676942 + 0.736036i \(0.263305\pi\)
−0.676942 + 0.736036i \(0.736695\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 0.267949i 0.0459529i
\(35\) 1.36603 + 2.36603i 0.230900 + 0.399931i
\(36\) 0 0
\(37\) −2.83013 1.63397i −0.465270 0.268624i 0.248988 0.968507i \(-0.419902\pi\)
−0.714258 + 0.699883i \(0.753235\pi\)
\(38\) 1.00000 0.162221
\(39\) 0 0
\(40\) −2.73205 −0.431975
\(41\) 2.59808 + 1.50000i 0.405751 + 0.234261i 0.688963 0.724797i \(-0.258066\pi\)
−0.283211 + 0.959058i \(0.591400\pi\)
\(42\) 0 0
\(43\) 3.36603 + 5.83013i 0.513314 + 0.889086i 0.999881 + 0.0154426i \(0.00491573\pi\)
−0.486567 + 0.873643i \(0.661751\pi\)
\(44\) 1.73205i 0.261116i
\(45\) 0 0
\(46\) 3.00000 1.73205i 0.442326 0.255377i
\(47\) 4.46410i 0.651156i −0.945515 0.325578i \(-0.894441\pi\)
0.945515 0.325578i \(-0.105559\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 2.13397 + 1.23205i 0.301790 + 0.174238i
\(51\) 0 0
\(52\) −1.59808 3.23205i −0.221613 0.448205i
\(53\) −7.00000 −0.961524 −0.480762 0.876851i \(-0.659640\pi\)
−0.480762 + 0.876851i \(0.659640\pi\)
\(54\) 0 0
\(55\) −2.36603 + 4.09808i −0.319035 + 0.552584i
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 0 0
\(58\) 0.401924 0.232051i 0.0527752 0.0304698i
\(59\) −11.1962 + 6.46410i −1.45761 + 0.841554i −0.998894 0.0470259i \(-0.985026\pi\)
−0.458721 + 0.888580i \(0.651692\pi\)
\(60\) 0 0
\(61\) 2.59808 + 4.50000i 0.332650 + 0.576166i 0.983030 0.183442i \(-0.0587240\pi\)
−0.650381 + 0.759608i \(0.725391\pi\)
\(62\) 4.09808 7.09808i 0.520456 0.901457i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −0.633975 + 9.83013i −0.0786349 + 1.21928i
\(66\) 0 0
\(67\) 4.26795 + 2.46410i 0.521413 + 0.301038i 0.737513 0.675333i \(-0.236000\pi\)
−0.216100 + 0.976371i \(0.569334\pi\)
\(68\) 0.133975 0.232051i 0.0162468 0.0281403i
\(69\) 0 0
\(70\) 2.73205i 0.326543i
\(71\) 7.09808 4.09808i 0.842387 0.486352i −0.0156881 0.999877i \(-0.504994\pi\)
0.858075 + 0.513525i \(0.171661\pi\)
\(72\) 0 0
\(73\) 1.46410i 0.171360i −0.996323 0.0856801i \(-0.972694\pi\)
0.996323 0.0856801i \(-0.0273063\pi\)
\(74\) 1.63397 + 2.83013i 0.189946 + 0.328996i
\(75\) 0 0
\(76\) −0.866025 0.500000i −0.0993399 0.0573539i
\(77\) 1.73205 0.197386
\(78\) 0 0
\(79\) 15.9282 1.79206 0.896031 0.443991i \(-0.146438\pi\)
0.896031 + 0.443991i \(0.146438\pi\)
\(80\) 2.36603 + 1.36603i 0.264530 + 0.152726i
\(81\) 0 0
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) 10.1962i 1.11917i −0.828772 0.559587i \(-0.810960\pi\)
0.828772 0.559587i \(-0.189040\pi\)
\(84\) 0 0
\(85\) −0.633975 + 0.366025i −0.0687642 + 0.0397010i
\(86\) 6.73205i 0.725936i
\(87\) 0 0
\(88\) −0.866025 + 1.50000i −0.0923186 + 0.159901i
\(89\) −3.06218 1.76795i −0.324590 0.187402i 0.328847 0.944383i \(-0.393340\pi\)
−0.653437 + 0.756981i \(0.726673\pi\)
\(90\) 0 0
\(91\) 3.23205 1.59808i 0.338811 0.167524i
\(92\) −3.46410 −0.361158
\(93\) 0 0
\(94\) −2.23205 + 3.86603i −0.230218 + 0.398750i
\(95\) 1.36603 + 2.36603i 0.140151 + 0.242749i
\(96\) 0 0
\(97\) 1.43782 0.830127i 0.145989 0.0842866i −0.425226 0.905087i \(-0.639806\pi\)
0.571215 + 0.820800i \(0.306472\pi\)
\(98\) −0.866025 + 0.500000i −0.0874818 + 0.0505076i
\(99\) 0 0
\(100\) −1.23205 2.13397i −0.123205 0.213397i
\(101\) −8.46410 + 14.6603i −0.842210 + 1.45875i 0.0458130 + 0.998950i \(0.485412\pi\)
−0.888023 + 0.459800i \(0.847921\pi\)
\(102\) 0 0
\(103\) −11.2679 −1.11026 −0.555132 0.831762i \(-0.687332\pi\)
−0.555132 + 0.831762i \(0.687332\pi\)
\(104\) −0.232051 + 3.59808i −0.0227545 + 0.352820i
\(105\) 0 0
\(106\) 6.06218 + 3.50000i 0.588811 + 0.339950i
\(107\) −8.42820 + 14.5981i −0.814785 + 1.41125i 0.0946969 + 0.995506i \(0.469812\pi\)
−0.909482 + 0.415743i \(0.863522\pi\)
\(108\) 0 0
\(109\) 1.26795i 0.121448i −0.998155 0.0607238i \(-0.980659\pi\)
0.998155 0.0607238i \(-0.0193409\pi\)
\(110\) 4.09808 2.36603i 0.390736 0.225592i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 9.36603 + 16.2224i 0.881082 + 1.52608i 0.850140 + 0.526557i \(0.176517\pi\)
0.0309416 + 0.999521i \(0.490149\pi\)
\(114\) 0 0
\(115\) 8.19615 + 4.73205i 0.764295 + 0.441266i
\(116\) −0.464102 −0.0430908
\(117\) 0 0
\(118\) 12.9282 1.19014
\(119\) 0.232051 + 0.133975i 0.0212721 + 0.0122814i
\(120\) 0 0
\(121\) −4.00000 6.92820i −0.363636 0.629837i
\(122\) 5.19615i 0.470438i
\(123\) 0 0
\(124\) −7.09808 + 4.09808i −0.637426 + 0.368018i
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) −4.26795 + 7.39230i −0.378719 + 0.655961i −0.990876 0.134775i \(-0.956969\pi\)
0.612157 + 0.790736i \(0.290302\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 5.46410 8.19615i 0.479233 0.718850i
\(131\) −13.8564 −1.21064 −0.605320 0.795982i \(-0.706955\pi\)
−0.605320 + 0.795982i \(0.706955\pi\)
\(132\) 0 0
\(133\) 0.500000 0.866025i 0.0433555 0.0750939i
\(134\) −2.46410 4.26795i −0.212866 0.368695i
\(135\) 0 0
\(136\) −0.232051 + 0.133975i −0.0198982 + 0.0114882i
\(137\) −5.53590 + 3.19615i −0.472964 + 0.273066i −0.717480 0.696580i \(-0.754704\pi\)
0.244516 + 0.969645i \(0.421371\pi\)
\(138\) 0 0
\(139\) 9.79423 + 16.9641i 0.830736 + 1.43888i 0.897456 + 0.441105i \(0.145413\pi\)
−0.0667201 + 0.997772i \(0.521253\pi\)
\(140\) −1.36603 + 2.36603i −0.115450 + 0.199966i
\(141\) 0 0
\(142\) −8.19615 −0.687806
\(143\) 5.19615 + 3.46410i 0.434524 + 0.289683i
\(144\) 0 0
\(145\) 1.09808 + 0.633975i 0.0911903 + 0.0526487i
\(146\) −0.732051 + 1.26795i −0.0605850 + 0.104936i
\(147\) 0 0
\(148\) 3.26795i 0.268624i
\(149\) −12.0000 + 6.92820i −0.983078 + 0.567581i −0.903198 0.429224i \(-0.858787\pi\)
−0.0798802 + 0.996804i \(0.525454\pi\)
\(150\) 0 0
\(151\) 5.19615i 0.422857i 0.977393 + 0.211428i \(0.0678115\pi\)
−0.977393 + 0.211428i \(0.932188\pi\)
\(152\) 0.500000 + 0.866025i 0.0405554 + 0.0702439i
\(153\) 0 0
\(154\) −1.50000 0.866025i −0.120873 0.0697863i
\(155\) 22.3923 1.79859
\(156\) 0 0
\(157\) −7.46410 −0.595700 −0.297850 0.954613i \(-0.596270\pi\)
−0.297850 + 0.954613i \(0.596270\pi\)
\(158\) −13.7942 7.96410i −1.09741 0.633590i
\(159\) 0 0
\(160\) −1.36603 2.36603i −0.107994 0.187051i
\(161\) 3.46410i 0.273009i
\(162\) 0 0
\(163\) 0.633975 0.366025i 0.0496567 0.0286693i −0.474966 0.880004i \(-0.657540\pi\)
0.524623 + 0.851335i \(0.324206\pi\)
\(164\) 3.00000i 0.234261i
\(165\) 0 0
\(166\) −5.09808 + 8.83013i −0.395687 + 0.685351i
\(167\) 12.0000 + 6.92820i 0.928588 + 0.536120i 0.886365 0.462988i \(-0.153223\pi\)
0.0422232 + 0.999108i \(0.486556\pi\)
\(168\) 0 0
\(169\) 12.8923 + 1.66987i 0.991716 + 0.128452i
\(170\) 0.732051 0.0561457
\(171\) 0 0
\(172\) −3.36603 + 5.83013i −0.256657 + 0.444543i
\(173\) −7.56218 13.0981i −0.574942 0.995828i −0.996048 0.0888170i \(-0.971691\pi\)
0.421106 0.907011i \(-0.361642\pi\)
\(174\) 0 0
\(175\) 2.13397 1.23205i 0.161313 0.0931343i
\(176\) 1.50000 0.866025i 0.113067 0.0652791i
\(177\) 0 0
\(178\) 1.76795 + 3.06218i 0.132513 + 0.229520i
\(179\) −2.26795 + 3.92820i −0.169514 + 0.293608i −0.938249 0.345960i \(-0.887553\pi\)
0.768735 + 0.639568i \(0.220887\pi\)
\(180\) 0 0
\(181\) −14.6603 −1.08969 −0.544844 0.838537i \(-0.683411\pi\)
−0.544844 + 0.838537i \(0.683411\pi\)
\(182\) −3.59808 0.232051i −0.266707 0.0172008i
\(183\) 0 0
\(184\) 3.00000 + 1.73205i 0.221163 + 0.127688i
\(185\) −4.46410 + 7.73205i −0.328207 + 0.568472i
\(186\) 0 0
\(187\) 0.464102i 0.0339385i
\(188\) 3.86603 2.23205i 0.281959 0.162789i
\(189\) 0 0
\(190\) 2.73205i 0.198204i
\(191\) −0.562178 0.973721i −0.0406778 0.0704559i 0.844970 0.534814i \(-0.179618\pi\)
−0.885647 + 0.464358i \(0.846285\pi\)
\(192\) 0 0
\(193\) −7.96410 4.59808i −0.573269 0.330977i 0.185185 0.982704i \(-0.440712\pi\)
−0.758454 + 0.651727i \(0.774045\pi\)
\(194\) −1.66025 −0.119199
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 8.08846 + 4.66987i 0.576279 + 0.332715i 0.759653 0.650328i \(-0.225369\pi\)
−0.183374 + 0.983043i \(0.558702\pi\)
\(198\) 0 0
\(199\) −2.90192 5.02628i −0.205712 0.356304i 0.744647 0.667458i \(-0.232618\pi\)
−0.950359 + 0.311155i \(0.899284\pi\)
\(200\) 2.46410i 0.174238i
\(201\) 0 0
\(202\) 14.6603 8.46410i 1.03149 0.595532i
\(203\) 0.464102i 0.0325735i
\(204\) 0 0
\(205\) 4.09808 7.09808i 0.286222 0.495751i
\(206\) 9.75833 + 5.63397i 0.679895 + 0.392538i
\(207\) 0 0
\(208\) 2.00000 3.00000i 0.138675 0.208013i
\(209\) 1.73205 0.119808
\(210\) 0 0
\(211\) −13.0000 + 22.5167i −0.894957 + 1.55011i −0.0610990 + 0.998132i \(0.519461\pi\)
−0.833858 + 0.551979i \(0.813873\pi\)
\(212\) −3.50000 6.06218i −0.240381 0.416352i
\(213\) 0 0
\(214\) 14.5981 8.42820i 0.997904 0.576140i
\(215\) 15.9282 9.19615i 1.08629 0.627172i
\(216\) 0 0
\(217\) −4.09808 7.09808i −0.278196 0.481849i
\(218\) −0.633975 + 1.09808i −0.0429382 + 0.0743711i
\(219\) 0 0
\(220\) −4.73205 −0.319035
\(221\) 0.428203 + 0.866025i 0.0288041 + 0.0582552i
\(222\) 0 0
\(223\) −3.12436 1.80385i −0.209222 0.120795i 0.391728 0.920081i \(-0.371878\pi\)
−0.600950 + 0.799287i \(0.705211\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 18.7321i 1.24604i
\(227\) −2.07180 + 1.19615i −0.137510 + 0.0793914i −0.567177 0.823596i \(-0.691964\pi\)
0.429667 + 0.902988i \(0.358631\pi\)
\(228\) 0 0
\(229\) 6.07180i 0.401236i 0.979670 + 0.200618i \(0.0642949\pi\)
−0.979670 + 0.200618i \(0.935705\pi\)
\(230\) −4.73205 8.19615i −0.312022 0.540438i
\(231\) 0 0
\(232\) 0.401924 + 0.232051i 0.0263876 + 0.0152349i
\(233\) 15.1244 0.990829 0.495415 0.868657i \(-0.335016\pi\)
0.495415 + 0.868657i \(0.335016\pi\)
\(234\) 0 0
\(235\) −12.1962 −0.795589
\(236\) −11.1962 6.46410i −0.728807 0.420777i
\(237\) 0 0
\(238\) −0.133975 0.232051i −0.00868428 0.0150416i
\(239\) 2.73205i 0.176722i −0.996089 0.0883608i \(-0.971837\pi\)
0.996089 0.0883608i \(-0.0281629\pi\)
\(240\) 0 0
\(241\) 6.92820 4.00000i 0.446285 0.257663i −0.259975 0.965615i \(-0.583714\pi\)
0.706260 + 0.707953i \(0.250381\pi\)
\(242\) 8.00000i 0.514259i
\(243\) 0 0
\(244\) −2.59808 + 4.50000i −0.166325 + 0.288083i
\(245\) −2.36603 1.36603i −0.151160 0.0872722i
\(246\) 0 0
\(247\) 3.23205 1.59808i 0.205650 0.101683i
\(248\) 8.19615 0.520456
\(249\) 0 0
\(250\) −3.46410 + 6.00000i −0.219089 + 0.379473i
\(251\) 5.56218 + 9.63397i 0.351082 + 0.608091i 0.986439 0.164127i \(-0.0524807\pi\)
−0.635358 + 0.772218i \(0.719147\pi\)
\(252\) 0 0
\(253\) 5.19615 3.00000i 0.326679 0.188608i
\(254\) 7.39230 4.26795i 0.463834 0.267795i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.66987 + 2.89230i −0.104164 + 0.180417i −0.913396 0.407072i \(-0.866550\pi\)
0.809232 + 0.587489i \(0.199883\pi\)
\(258\) 0 0
\(259\) 3.26795 0.203060
\(260\) −8.83013 + 4.36603i −0.547621 + 0.270769i
\(261\) 0 0
\(262\) 12.0000 + 6.92820i 0.741362 + 0.428026i
\(263\) 4.56218 7.90192i 0.281316 0.487253i −0.690393 0.723434i \(-0.742562\pi\)
0.971709 + 0.236181i \(0.0758958\pi\)
\(264\) 0 0
\(265\) 19.1244i 1.17480i
\(266\) −0.866025 + 0.500000i −0.0530994 + 0.0306570i
\(267\) 0 0
\(268\) 4.92820i 0.301038i
\(269\) 8.92820 + 15.4641i 0.544362 + 0.942863i 0.998647 + 0.0520063i \(0.0165616\pi\)
−0.454285 + 0.890857i \(0.650105\pi\)
\(270\) 0 0
\(271\) −8.70577 5.02628i −0.528838 0.305325i 0.211705 0.977334i \(-0.432098\pi\)
−0.740543 + 0.672009i \(0.765432\pi\)
\(272\) 0.267949 0.0162468
\(273\) 0 0
\(274\) 6.39230 0.386173
\(275\) 3.69615 + 2.13397i 0.222886 + 0.128684i
\(276\) 0 0
\(277\) −12.6603 21.9282i −0.760681 1.31754i −0.942500 0.334206i \(-0.891532\pi\)
0.181819 0.983332i \(-0.441801\pi\)
\(278\) 19.5885i 1.17484i
\(279\) 0 0
\(280\) 2.36603 1.36603i 0.141397 0.0816356i
\(281\) 17.6603i 1.05352i −0.850013 0.526761i \(-0.823406\pi\)
0.850013 0.526761i \(-0.176594\pi\)
\(282\) 0 0
\(283\) 8.92820 15.4641i 0.530727 0.919245i −0.468631 0.883394i \(-0.655252\pi\)
0.999357 0.0358512i \(-0.0114142\pi\)
\(284\) 7.09808 + 4.09808i 0.421193 + 0.243176i
\(285\) 0 0
\(286\) −2.76795 5.59808i −0.163672 0.331021i
\(287\) −3.00000 −0.177084
\(288\) 0 0
\(289\) 8.46410 14.6603i 0.497888 0.862368i
\(290\) −0.633975 1.09808i −0.0372283 0.0644813i
\(291\) 0 0
\(292\) 1.26795 0.732051i 0.0742011 0.0428400i
\(293\) −26.7846 + 15.4641i −1.56477 + 0.903422i −0.568011 + 0.823021i \(0.692287\pi\)
−0.996763 + 0.0804015i \(0.974380\pi\)
\(294\) 0 0
\(295\) 17.6603 + 30.5885i 1.02822 + 1.78093i
\(296\) −1.63397 + 2.83013i −0.0949728 + 0.164498i
\(297\) 0 0
\(298\) 13.8564 0.802680
\(299\) 6.92820 10.3923i 0.400668 0.601003i
\(300\) 0 0
\(301\) −5.83013 3.36603i −0.336043 0.194014i
\(302\) 2.59808 4.50000i 0.149502 0.258946i
\(303\) 0 0
\(304\) 1.00000i 0.0573539i
\(305\) 12.2942 7.09808i 0.703965 0.406435i
\(306\) 0 0
\(307\) 29.3923i 1.67751i −0.544511 0.838754i \(-0.683285\pi\)
0.544511 0.838754i \(-0.316715\pi\)
\(308\) 0.866025 + 1.50000i 0.0493464 + 0.0854704i
\(309\) 0 0
\(310\) −19.3923 11.1962i −1.10141 0.635899i
\(311\) 7.73205 0.438444 0.219222 0.975675i \(-0.429648\pi\)
0.219222 + 0.975675i \(0.429648\pi\)
\(312\) 0 0
\(313\) −31.5167 −1.78143 −0.890713 0.454565i \(-0.849795\pi\)
−0.890713 + 0.454565i \(0.849795\pi\)
\(314\) 6.46410 + 3.73205i 0.364790 + 0.210612i
\(315\) 0 0
\(316\) 7.96410 + 13.7942i 0.448016 + 0.775986i
\(317\) 15.8564i 0.890585i −0.895385 0.445292i \(-0.853100\pi\)
0.895385 0.445292i \(-0.146900\pi\)
\(318\) 0 0
\(319\) 0.696152 0.401924i 0.0389771 0.0225034i
\(320\) 2.73205i 0.152726i
\(321\) 0 0
\(322\) −1.73205 + 3.00000i −0.0965234 + 0.167183i
\(323\) 0.232051 + 0.133975i 0.0129117 + 0.00745455i
\(324\) 0 0
\(325\) 8.86603 + 0.571797i 0.491799 + 0.0317176i
\(326\) −0.732051 −0.0405445
\(327\) 0 0
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) 2.23205 + 3.86603i 0.123057 + 0.213141i
\(330\) 0 0
\(331\) −0.124356 + 0.0717968i −0.00683520 + 0.00394631i −0.503414 0.864046i \(-0.667923\pi\)
0.496579 + 0.867992i \(0.334589\pi\)
\(332\) 8.83013 5.09808i 0.484616 0.279793i
\(333\) 0 0
\(334\) −6.92820 12.0000i −0.379094 0.656611i
\(335\) 6.73205 11.6603i 0.367811 0.637068i
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) −10.3301 7.89230i −0.561885 0.429285i
\(339\) 0 0
\(340\) −0.633975 0.366025i −0.0343821 0.0198505i
\(341\) 7.09808 12.2942i 0.384382 0.665770i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 5.83013 3.36603i 0.314339 0.181484i
\(345\) 0 0
\(346\) 15.1244i 0.813090i
\(347\) −7.69615 13.3301i −0.413151 0.715599i 0.582081 0.813131i \(-0.302239\pi\)
−0.995232 + 0.0975319i \(0.968905\pi\)
\(348\) 0 0
\(349\) −27.4641 15.8564i −1.47012 0.848774i −0.470682 0.882303i \(-0.655992\pi\)
−0.999438 + 0.0335290i \(0.989325\pi\)
\(350\) −2.46410 −0.131712
\(351\) 0 0
\(352\) −1.73205 −0.0923186
\(353\) −2.19615 1.26795i −0.116889 0.0674861i 0.440415 0.897794i \(-0.354831\pi\)
−0.557305 + 0.830308i \(0.688165\pi\)
\(354\) 0 0
\(355\) −11.1962 19.3923i −0.594230 1.02924i
\(356\) 3.53590i 0.187402i
\(357\) 0 0
\(358\) 3.92820 2.26795i 0.207612 0.119865i
\(359\) 14.1962i 0.749244i −0.927178 0.374622i \(-0.877772\pi\)
0.927178 0.374622i \(-0.122228\pi\)
\(360\) 0 0
\(361\) −9.00000 + 15.5885i −0.473684 + 0.820445i
\(362\) 12.6962 + 7.33013i 0.667295 + 0.385263i
\(363\) 0 0
\(364\) 3.00000 + 2.00000i 0.157243 + 0.104828i
\(365\) −4.00000 −0.209370
\(366\) 0 0
\(367\) 4.66025 8.07180i 0.243263 0.421344i −0.718379 0.695652i \(-0.755115\pi\)
0.961642 + 0.274308i \(0.0884488\pi\)
\(368\) −1.73205 3.00000i −0.0902894 0.156386i
\(369\) 0 0
\(370\) 7.73205 4.46410i 0.401970 0.232078i
\(371\) 6.06218 3.50000i 0.314733 0.181711i
\(372\) 0 0
\(373\) 3.83013 + 6.63397i 0.198316 + 0.343494i 0.947983 0.318322i \(-0.103119\pi\)
−0.749666 + 0.661816i \(0.769786\pi\)
\(374\) 0.232051 0.401924i 0.0119991 0.0207830i
\(375\) 0 0
\(376\) −4.46410 −0.230218
\(377\) 0.928203 1.39230i 0.0478049 0.0717073i
\(378\) 0 0
\(379\) 26.3660 + 15.2224i 1.35433 + 0.781924i 0.988853 0.148896i \(-0.0475719\pi\)
0.365479 + 0.930820i \(0.380905\pi\)
\(380\) −1.36603 + 2.36603i −0.0700756 + 0.121375i
\(381\) 0 0
\(382\) 1.12436i 0.0575270i
\(383\) −10.7942 + 6.23205i −0.551559 + 0.318443i −0.749751 0.661720i \(-0.769827\pi\)
0.198191 + 0.980163i \(0.436493\pi\)
\(384\) 0 0
\(385\) 4.73205i 0.241168i
\(386\) 4.59808 + 7.96410i 0.234036 + 0.405362i
\(387\) 0 0
\(388\) 1.43782 + 0.830127i 0.0729944 + 0.0421433i
\(389\) −12.3923 −0.628315 −0.314157 0.949371i \(-0.601722\pi\)
−0.314157 + 0.949371i \(0.601722\pi\)
\(390\) 0 0
\(391\) 0.928203 0.0469413
\(392\) −0.866025 0.500000i −0.0437409 0.0252538i
\(393\) 0 0
\(394\) −4.66987 8.08846i −0.235265 0.407491i
\(395\) 43.5167i 2.18956i
\(396\) 0 0
\(397\) −18.9904 + 10.9641i −0.953100 + 0.550272i −0.894043 0.447982i \(-0.852143\pi\)
−0.0590574 + 0.998255i \(0.518809\pi\)
\(398\) 5.80385i 0.290921i
\(399\) 0 0
\(400\) 1.23205 2.13397i 0.0616025 0.106699i
\(401\) 2.41154 + 1.39230i 0.120427 + 0.0695284i 0.559003 0.829165i \(-0.311184\pi\)
−0.438577 + 0.898694i \(0.644517\pi\)
\(402\) 0 0
\(403\) 1.90192 29.4904i 0.0947416 1.46902i
\(404\) −16.9282 −0.842210
\(405\) 0 0
\(406\) −0.232051 + 0.401924i −0.0115165 + 0.0199471i
\(407\) 2.83013 + 4.90192i 0.140284 + 0.242979i
\(408\) 0 0
\(409\) 30.5429 17.6340i 1.51025 0.871944i 0.510323 0.859983i \(-0.329526\pi\)
0.999928 0.0119609i \(-0.00380738\pi\)
\(410\) −7.09808 + 4.09808i −0.350549 + 0.202390i
\(411\) 0 0
\(412\) −5.63397 9.75833i −0.277566 0.480758i
\(413\) 6.46410 11.1962i 0.318078 0.550927i
\(414\) 0 0
\(415\) −27.8564 −1.36742
\(416\) −3.23205 + 1.59808i −0.158464 + 0.0783521i
\(417\) 0 0
\(418\) −1.50000 0.866025i −0.0733674 0.0423587i
\(419\) −1.36603 + 2.36603i −0.0667347 + 0.115588i −0.897462 0.441091i \(-0.854591\pi\)
0.830727 + 0.556679i \(0.187925\pi\)
\(420\) 0 0
\(421\) 1.60770i 0.0783543i −0.999232 0.0391771i \(-0.987526\pi\)
0.999232 0.0391771i \(-0.0124737\pi\)
\(422\) 22.5167 13.0000i 1.09609 0.632830i
\(423\) 0 0
\(424\) 7.00000i 0.339950i
\(425\) 0.330127 + 0.571797i 0.0160135 + 0.0277362i
\(426\) 0 0
\(427\) −4.50000 2.59808i −0.217770 0.125730i
\(428\) −16.8564 −0.814785
\(429\) 0 0
\(430\) −18.3923 −0.886956
\(431\) −3.29423 1.90192i −0.158677 0.0916124i 0.418559 0.908190i \(-0.362535\pi\)
−0.577236 + 0.816577i \(0.695869\pi\)
\(432\) 0 0
\(433\) −20.4641 35.4449i −0.983442 1.70337i −0.648665 0.761074i \(-0.724672\pi\)
−0.334777 0.942297i \(-0.608661\pi\)
\(434\) 8.19615i 0.393428i
\(435\) 0 0
\(436\) 1.09808 0.633975i 0.0525883 0.0303619i
\(437\) 3.46410i 0.165710i
\(438\) 0 0
\(439\) 18.5885 32.1962i 0.887179 1.53664i 0.0439826 0.999032i \(-0.485995\pi\)
0.843196 0.537606i \(-0.180671\pi\)
\(440\) 4.09808 + 2.36603i 0.195368 + 0.112796i
\(441\) 0 0
\(442\) 0.0621778 0.964102i 0.00295750 0.0458576i
\(443\) −35.6410 −1.69336 −0.846678 0.532106i \(-0.821401\pi\)
−0.846678 + 0.532106i \(0.821401\pi\)
\(444\) 0 0
\(445\) −4.83013 + 8.36603i −0.228970 + 0.396588i
\(446\) 1.80385 + 3.12436i 0.0854147 + 0.147943i
\(447\) 0 0
\(448\) 0.866025 0.500000i 0.0409159 0.0236228i
\(449\) −9.16987 + 5.29423i −0.432753 + 0.249850i −0.700519 0.713634i \(-0.747048\pi\)
0.267766 + 0.963484i \(0.413715\pi\)
\(450\) 0 0
\(451\) −2.59808 4.50000i −0.122339 0.211897i
\(452\) −9.36603 + 16.2224i −0.440541 + 0.763039i
\(453\) 0 0
\(454\) 2.39230 0.112276
\(455\) −4.36603 8.83013i −0.204682 0.413963i
\(456\) 0 0
\(457\) 13.7321 + 7.92820i 0.642358 + 0.370866i 0.785522 0.618833i \(-0.212394\pi\)
−0.143164 + 0.989699i \(0.545728\pi\)
\(458\) 3.03590 5.25833i 0.141858 0.245706i
\(459\) 0 0
\(460\) 9.46410i 0.441266i
\(461\) −11.3205 + 6.53590i −0.527249 + 0.304407i −0.739895 0.672722i \(-0.765125\pi\)
0.212647 + 0.977129i \(0.431792\pi\)
\(462\) 0 0
\(463\) 9.73205i 0.452287i 0.974094 + 0.226143i \(0.0726118\pi\)
−0.974094 + 0.226143i \(0.927388\pi\)
\(464\) −0.232051 0.401924i −0.0107727 0.0186588i
\(465\) 0 0
\(466\) −13.0981 7.56218i −0.606757 0.350311i
\(467\) 13.8564 0.641198 0.320599 0.947215i \(-0.396116\pi\)
0.320599 + 0.947215i \(0.396116\pi\)
\(468\) 0 0
\(469\) −4.92820 −0.227563
\(470\) 10.5622 + 6.09808i 0.487197 + 0.281283i
\(471\) 0 0
\(472\) 6.46410 + 11.1962i 0.297534 + 0.515345i
\(473\) 11.6603i 0.536139i
\(474\) 0 0
\(475\) 2.13397 1.23205i 0.0979135 0.0565304i
\(476\) 0.267949i 0.0122814i
\(477\) 0 0
\(478\) −1.36603 + 2.36603i −0.0624805 + 0.108219i
\(479\) −22.1147 12.7679i −1.01045 0.583382i −0.0991253 0.995075i \(-0.531604\pi\)
−0.911323 + 0.411692i \(0.864938\pi\)
\(480\) 0 0
\(481\) 9.80385 + 6.53590i 0.447017 + 0.298011i
\(482\) −8.00000 −0.364390
\(483\) 0 0
\(484\) 4.00000 6.92820i 0.181818 0.314918i
\(485\) −2.26795 3.92820i −0.102982 0.178371i
\(486\) 0 0
\(487\) −0.571797 + 0.330127i −0.0259106 + 0.0149595i −0.512899 0.858449i \(-0.671429\pi\)
0.486989 + 0.873408i \(0.338095\pi\)
\(488\) 4.50000 2.59808i 0.203705 0.117609i
\(489\) 0 0
\(490\) 1.36603 + 2.36603i 0.0617107 + 0.106886i
\(491\) −14.2679 + 24.7128i −0.643904 + 1.11527i 0.340650 + 0.940190i \(0.389353\pi\)
−0.984554 + 0.175083i \(0.943980\pi\)
\(492\) 0 0
\(493\) 0.124356 0.00560070
\(494\) −3.59808 0.232051i −0.161885 0.0104405i
\(495\) 0 0
\(496\) −7.09808 4.09808i −0.318713 0.184009i
\(497\) −4.09808 + 7.09808i −0.183824 + 0.318392i
\(498\) 0 0
\(499\) 33.5167i 1.50041i −0.661204 0.750206i \(-0.729954\pi\)
0.661204 0.750206i \(-0.270046\pi\)
\(500\) 6.00000 3.46410i 0.268328 0.154919i
\(501\) 0 0
\(502\) 11.1244i 0.496504i
\(503\) −3.46410 6.00000i −0.154457 0.267527i 0.778404 0.627763i \(-0.216029\pi\)
−0.932861 + 0.360236i \(0.882696\pi\)
\(504\) 0 0
\(505\) 40.0526 + 23.1244i 1.78232 + 1.02902i
\(506\) −6.00000 −0.266733
\(507\) 0 0
\(508\) −8.53590 −0.378719
\(509\) −34.3468 19.8301i −1.52239 0.878955i −0.999650 0.0264657i \(-0.991575\pi\)
−0.522745 0.852489i \(-0.675092\pi\)
\(510\) 0 0
\(511\) 0.732051 + 1.26795i 0.0323840 + 0.0560908i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 2.89230 1.66987i 0.127574 0.0736549i
\(515\) 30.7846i 1.35653i
\(516\) 0 0
\(517\) −3.86603 + 6.69615i −0.170028 + 0.294496i
\(518\) −2.83013 1.63397i −0.124349 0.0717927i
\(519\) 0 0
\(520\) 9.83013 + 0.633975i 0.431080 + 0.0278016i
\(521\) 31.0526 1.36044 0.680219 0.733009i \(-0.261885\pi\)
0.680219 + 0.733009i \(0.261885\pi\)
\(522\) 0 0
\(523\) 19.0622 33.0167i 0.833531 1.44372i −0.0616902 0.998095i \(-0.519649\pi\)
0.895221 0.445622i \(-0.147018\pi\)
\(524\) −6.92820 12.0000i −0.302660 0.524222i
\(525\) 0 0
\(526\) −7.90192 + 4.56218i −0.344540 + 0.198920i
\(527\) 1.90192 1.09808i 0.0828491 0.0478330i
\(528\) 0 0
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) 9.56218 16.5622i 0.415354 0.719415i
\(531\) 0 0
\(532\) 1.00000 0.0433555
\(533\) −9.00000 6.00000i −0.389833 0.259889i
\(534\) 0 0
\(535\) 39.8827 + 23.0263i 1.72428 + 0.995513i
\(536\) 2.46410 4.26795i 0.106433 0.184347i
\(537\) 0 0
\(538\) 17.8564i 0.769844i
\(539\) −1.50000 + 0.866025i −0.0646096 + 0.0373024i
\(540\) 0 0
\(541\) 41.6603i 1.79111i 0.444947 + 0.895557i \(0.353223\pi\)
−0.444947 + 0.895557i \(0.646777\pi\)
\(542\) 5.02628 + 8.70577i 0.215897 + 0.373945i
\(543\) 0 0
\(544\) −0.232051 0.133975i −0.00994910 0.00574411i
\(545\) −3.46410 −0.148386
\(546\) 0 0
\(547\) −4.73205 −0.202328 −0.101164 0.994870i \(-0.532257\pi\)
−0.101164 + 0.994870i \(0.532257\pi\)
\(548\) −5.53590 3.19615i −0.236482 0.136533i
\(549\) 0 0
\(550\) −2.13397 3.69615i −0.0909930 0.157604i
\(551\) 0.464102i 0.0197714i
\(552\) 0 0
\(553\) −13.7942 + 7.96410i −0.586590 + 0.338668i
\(554\) 25.3205i 1.07577i
\(555\) 0 0
\(556\) −9.79423 + 16.9641i −0.415368 + 0.719438i
\(557\) −21.6962 12.5263i −0.919295 0.530755i −0.0358852 0.999356i \(-0.511425\pi\)
−0.883410 + 0.468600i \(0.844758\pi\)
\(558\) 0 0
\(559\) −10.7583 21.7583i −0.455029 0.920279i
\(560\) −2.73205 −0.115450
\(561\) 0 0
\(562\) −8.83013 + 15.2942i −0.372476 + 0.645148i
\(563\) 12.9019 + 22.3468i 0.543751 + 0.941805i 0.998684 + 0.0512792i \(0.0163298\pi\)
−0.454933 + 0.890526i \(0.650337\pi\)
\(564\) 0 0
\(565\) 44.3205 25.5885i 1.86458 1.07651i
\(566\) −15.4641 + 8.92820i −0.650005 + 0.375280i
\(567\) 0 0
\(568\) −4.09808 7.09808i −0.171951 0.297829i
\(569\) −10.2224 + 17.7058i −0.428547 + 0.742265i −0.996744 0.0806276i \(-0.974308\pi\)
0.568198 + 0.822892i \(0.307641\pi\)
\(570\) 0 0
\(571\) 34.9808 1.46390 0.731950 0.681359i \(-0.238611\pi\)
0.731950 + 0.681359i \(0.238611\pi\)
\(572\) −0.401924 + 6.23205i −0.0168053 + 0.260575i
\(573\) 0 0
\(574\) 2.59808 + 1.50000i 0.108442 + 0.0626088i
\(575\) 4.26795 7.39230i 0.177986 0.308280i
\(576\) 0 0
\(577\) 27.6603i 1.15151i 0.817622 + 0.575756i \(0.195292\pi\)
−0.817622 + 0.575756i \(0.804708\pi\)
\(578\) −14.6603 + 8.46410i −0.609786 + 0.352060i
\(579\) 0 0
\(580\) 1.26795i 0.0526487i
\(581\) 5.09808 + 8.83013i 0.211504 + 0.366335i
\(582\) 0 0
\(583\) 10.5000 + 6.06218i 0.434866 + 0.251070i
\(584\) −1.46410 −0.0605850
\(585\) 0 0
\(586\) 30.9282 1.27763
\(587\) 25.6865 + 14.8301i 1.06020 + 0.612105i 0.925487 0.378780i \(-0.123656\pi\)
0.134710 + 0.990885i \(0.456990\pi\)
\(588\) 0 0
\(589\) −4.09808 7.09808i −0.168858 0.292471i
\(590\) 35.3205i 1.45412i
\(591\) 0 0
\(592\) 2.83013 1.63397i 0.116318 0.0671559i
\(593\) 6.46410i 0.265449i −0.991153 0.132724i \(-0.957627\pi\)
0.991153 0.132724i \(-0.0423725\pi\)
\(594\) 0 0
\(595\) 0.366025 0.633975i 0.0150056 0.0259904i
\(596\) −12.0000 6.92820i −0.491539 0.283790i
\(597\) 0 0
\(598\) −11.1962 + 5.53590i −0.457845 + 0.226380i
\(599\) −40.6410 −1.66055 −0.830273 0.557356i \(-0.811816\pi\)
−0.830273 + 0.557356i \(0.811816\pi\)
\(600\) 0 0
\(601\) 9.63397 16.6865i 0.392978 0.680658i −0.599863 0.800103i \(-0.704778\pi\)
0.992841 + 0.119445i \(0.0381115\pi\)
\(602\) 3.36603 + 5.83013i 0.137189 + 0.237618i
\(603\) 0 0
\(604\) −4.50000 + 2.59808i −0.183102 + 0.105714i
\(605\) −18.9282 + 10.9282i −0.769541 + 0.444295i
\(606\) 0 0
\(607\) −6.75833 11.7058i −0.274312 0.475123i 0.695649 0.718382i \(-0.255117\pi\)
−0.969961 + 0.243259i \(0.921783\pi\)
\(608\) −0.500000 + 0.866025i −0.0202777 + 0.0351220i
\(609\) 0 0
\(610\) −14.1962 −0.574785
\(611\) −1.03590 + 16.0622i −0.0419080 + 0.649806i
\(612\) 0 0
\(613\) −3.46410 2.00000i −0.139914 0.0807792i 0.428409 0.903585i \(-0.359074\pi\)
−0.568323 + 0.822806i \(0.692408\pi\)
\(614\) −14.6962 + 25.4545i −0.593088 + 1.02726i
\(615\) 0 0
\(616\) 1.73205i 0.0697863i
\(617\) −7.09808 + 4.09808i −0.285758 + 0.164982i −0.636027 0.771667i \(-0.719423\pi\)
0.350269 + 0.936649i \(0.386090\pi\)
\(618\) 0 0
\(619\) 35.9282i 1.44408i −0.691853 0.722038i \(-0.743205\pi\)
0.691853 0.722038i \(-0.256795\pi\)
\(620\) 11.1962 + 19.3923i 0.449648 + 0.778814i
\(621\) 0 0
\(622\) −6.69615 3.86603i −0.268491 0.155013i
\(623\) 3.53590 0.141663
\(624\) 0 0
\(625\) −31.2487 −1.24995
\(626\) 27.2942 + 15.7583i 1.09090 + 0.629830i
\(627\) 0 0
\(628\) −3.73205 6.46410i −0.148925 0.257946i
\(629\) 0.875644i 0.0349142i
\(630\) 0 0
\(631\) −23.5526 + 13.5981i −0.937613 + 0.541331i −0.889211 0.457497i \(-0.848746\pi\)
−0.0484014 + 0.998828i \(0.515413\pi\)
\(632\) 15.9282i 0.633590i
\(633\) 0 0
\(634\) −7.92820 + 13.7321i −0.314869 + 0.545369i
\(635\) 20.1962 + 11.6603i 0.801460 + 0.462723i
\(636\) 0 0
\(637\) −2.00000 + 3.00000i −0.0792429 + 0.118864i
\(638\) −0.803848 −0.0318246
\(639\) 0 0
\(640\) 1.36603 2.36603i 0.0539969 0.0935254i
\(641\) 15.5885 + 27.0000i 0.615707 + 1.06644i 0.990260 + 0.139230i \(0.0444629\pi\)
−0.374553 + 0.927206i \(0.622204\pi\)
\(642\) 0 0
\(643\) −4.45448 + 2.57180i −0.175668 + 0.101422i −0.585256 0.810849i \(-0.699006\pi\)
0.409588 + 0.912271i \(0.365672\pi\)
\(644\) 3.00000 1.73205i 0.118217 0.0682524i
\(645\) 0 0
\(646\) −0.133975 0.232051i −0.00527116 0.00912992i
\(647\) 21.9186 37.9641i 0.861708 1.49252i −0.00857027 0.999963i \(-0.502728\pi\)
0.870279 0.492560i \(-0.163939\pi\)
\(648\) 0 0
\(649\) 22.3923 0.878975
\(650\) −7.39230 4.92820i −0.289950 0.193300i
\(651\) 0 0
\(652\) 0.633975 + 0.366025i 0.0248284 + 0.0143347i
\(653\) −4.35641 + 7.54552i −0.170479 + 0.295279i −0.938588 0.345041i \(-0.887865\pi\)
0.768108 + 0.640320i \(0.221198\pi\)
\(654\) 0 0
\(655\) 37.8564i 1.47917i
\(656\) −2.59808 + 1.50000i −0.101438 + 0.0585652i
\(657\) 0 0
\(658\) 4.46410i 0.174029i
\(659\) 19.6962 + 34.1147i 0.767253 + 1.32892i 0.939047 + 0.343789i \(0.111710\pi\)
−0.171794 + 0.985133i \(0.554956\pi\)
\(660\) 0 0
\(661\) 7.26795 + 4.19615i 0.282690 + 0.163211i 0.634641 0.772807i \(-0.281148\pi\)
−0.351950 + 0.936019i \(0.614481\pi\)
\(662\) 0.143594 0.00558092
\(663\) 0 0
\(664\) −10.1962 −0.395687
\(665\) −2.36603 1.36603i −0.0917505 0.0529722i
\(666\) 0 0
\(667\) −0.803848 1.39230i −0.0311251 0.0539103i
\(668\) 13.8564i 0.536120i
\(669\) 0 0
\(670\) −11.6603 + 6.73205i −0.450475 + 0.260082i
\(671\) 9.00000i 0.347441i
\(672\) 0 0
\(673\) 11.3564 19.6699i 0.437757 0.758218i −0.559759 0.828656i \(-0.689106\pi\)
0.997516 + 0.0704376i \(0.0224396\pi\)
\(674\) 16.4545 + 9.50000i 0.633803 + 0.365926i
\(675\) 0 0
\(676\) 5.00000 + 12.0000i 0.192308 + 0.461538i
\(677\) −33.2679 −1.27859 −0.639296 0.768961i \(-0.720774\pi\)
−0.639296 + 0.768961i \(0.720774\pi\)
\(678\) 0 0
\(679\) −0.830127 + 1.43782i −0.0318574 + 0.0551786i
\(680\) 0.366025 + 0.633975i 0.0140364 + 0.0243118i
\(681\) 0 0
\(682\) −12.2942 + 7.09808i −0.470770 + 0.271799i
\(683\) 43.6410 25.1962i 1.66988 0.964104i 0.702176 0.712003i \(-0.252212\pi\)
0.967701 0.252101i \(-0.0811214\pi\)
\(684\) 0 0
\(685\) 8.73205 + 15.1244i 0.333635 + 0.577872i
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) 0 0
\(688\) −6.73205 −0.256657
\(689\) 25.1865 + 1.62436i 0.959531 + 0.0618830i
\(690\) 0 0
\(691\) 10.1436 + 5.85641i 0.385880 + 0.222788i 0.680374 0.732865i \(-0.261817\pi\)
−0.294493 + 0.955654i \(0.595151\pi\)
\(692\) 7.56218 13.0981i 0.287471 0.497914i
\(693\) 0 0
\(694\) 15.3923i 0.584284i
\(695\) 46.3468 26.7583i 1.75803 1.01500i
\(696\) 0 0
\(697\) 0.803848i 0.0304479i
\(698\) 15.8564 + 27.4641i 0.600174 + 1.03953i
\(699\) 0 0
\(700\) 2.13397 + 1.23205i 0.0806567 + 0.0465671i
\(701\) 28.8564 1.08989 0.544946 0.838471i \(-0.316550\pi\)
0.544946 + 0.838471i \(0.316550\pi\)
\(702\) 0 0
\(703\) 3.26795 0.123253
\(704\) 1.50000 + 0.866025i 0.0565334 + 0.0326396i
\(705\) 0 0
\(706\) 1.26795 + 2.19615i 0.0477199 + 0.0826533i
\(707\) 16.9282i 0.636651i
\(708\) 0 0
\(709\) −5.24167 + 3.02628i −0.196855 + 0.113654i −0.595188 0.803587i \(-0.702922\pi\)
0.398333 + 0.917241i \(0.369589\pi\)
\(710\) 22.3923i 0.840368i
\(711\) 0 0
\(712\) −1.76795 + 3.06218i −0.0662567 + 0.114760i
\(713\) −24.5885 14.1962i −0.920845 0.531650i
\(714\) 0 0
\(715\) 9.46410 14.1962i 0.353937 0.530906i
\(716\) −4.53590 −0.169514
\(717\) 0 0
\(718\) −7.09808 + 12.2942i −0.264898 + 0.458817i
\(719\) 9.25833 + 16.0359i 0.345277 + 0.598038i 0.985404 0.170231i \(-0.0544515\pi\)
−0.640127 + 0.768269i \(0.721118\pi\)
\(720\) 0 0
\(721\) 9.75833 5.63397i 0.363419 0.209820i
\(722\) 15.5885 9.00000i 0.580142 0.334945i
\(723\) 0 0
\(724\) −7.33013 12.6962i −0.272422 0.471849i
\(725\) 0.571797 0.990381i 0.0212360 0.0367818i
\(726\) 0 0
\(727\) −15.3205 −0.568206 −0.284103 0.958794i \(-0.591696\pi\)
−0.284103 + 0.958794i \(0.591696\pi\)
\(728\) −1.59808 3.23205i −0.0592286 0.119788i
\(729\) 0 0
\(730\) 3.46410 + 2.00000i 0.128212 + 0.0740233i
\(731\) 0.901924 1.56218i 0.0333589 0.0577792i
\(732\) 0 0
\(733\) 14.1769i 0.523636i −0.965117 0.261818i \(-0.915678\pi\)
0.965117 0.261818i \(-0.0843221\pi\)
\(734\) −8.07180 + 4.66025i −0.297935 + 0.172013i
\(735\) 0 0
\(736\) 3.46410i 0.127688i
\(737\) −4.26795 7.39230i −0.157212 0.272299i
\(738\) 0 0
\(739\) 40.8564 + 23.5885i 1.50293 + 0.867715i 0.999994 + 0.00339000i \(0.00107907\pi\)
0.502933 + 0.864325i \(0.332254\pi\)
\(740\) −8.92820 −0.328207
\(741\) 0 0
\(742\) −7.00000 −0.256978
\(743\) 20.8301 + 12.0263i 0.764183 + 0.441201i 0.830796 0.556578i \(-0.187886\pi\)
−0.0666124 + 0.997779i \(0.521219\pi\)
\(744\) 0 0
\(745\) 18.9282 + 32.7846i 0.693476 + 1.20114i
\(746\) 7.66025i 0.280462i
\(747\) 0 0
\(748\) −0.401924 + 0.232051i −0.0146958 + 0.00848462i
\(749\) 16.8564i 0.615920i
\(750\) 0 0
\(751\) −23.4282 + 40.5788i −0.854907 + 1.48074i 0.0218237 + 0.999762i \(0.493053\pi\)
−0.876731 + 0.480981i \(0.840281\pi\)
\(752\) 3.86603 + 2.23205i 0.140979 + 0.0813945i
\(753\) 0 0
\(754\) −1.50000 + 0.741670i −0.0546268 + 0.0270100i
\(755\) 14.1962 0.516651
\(756\) 0 0
\(757\) −15.2942 + 26.4904i −0.555878 + 0.962809i 0.441956 + 0.897037i \(0.354285\pi\)
−0.997835 + 0.0657728i \(0.979049\pi\)
\(758\) −15.2224 26.3660i −0.552904 0.957657i
\(759\) 0 0
\(760\) 2.36603 1.36603i 0.0858248 0.0495509i
\(761\) −16.7321 + 9.66025i −0.606536 + 0.350184i −0.771609 0.636098i \(-0.780548\pi\)
0.165072 + 0.986281i \(0.447214\pi\)
\(762\) 0 0
\(763\) 0.633975 + 1.09808i 0.0229514 + 0.0397530i
\(764\) 0.562178 0.973721i 0.0203389 0.0352280i
\(765\) 0 0
\(766\) 12.4641 0.450346
\(767\) 41.7846 20.6603i 1.50875 0.745999i
\(768\) 0 0
\(769\) 38.3660 + 22.1506i 1.38351 + 0.798772i 0.992574 0.121644i \(-0.0388165\pi\)
0.390940 + 0.920416i \(0.372150\pi\)
\(770\) −2.36603 + 4.09808i −0.0852656 + 0.147684i
\(771\) 0 0
\(772\) 9.19615i 0.330977i
\(773\) 13.1436 7.58846i 0.472742 0.272938i −0.244645 0.969613i \(-0.578671\pi\)
0.717387 + 0.696675i \(0.245338\pi\)
\(774\) 0 0
\(775\) 20.1962i 0.725467i
\(776\) −0.830127 1.43782i −0.0297998 0.0516148i
\(777\) 0 0
\(778\) 10.7321 + 6.19615i 0.384763 + 0.222143i
\(779\) −3.00000 −0.107486
\(780\) 0 0
\(781\) −14.1962 −0.507978
\(782\) −0.803848 0.464102i −0.0287455 0.0165962i
\(783\) 0 0
\(784\) 0.500000 + 0.866025i 0.0178571 + 0.0309295i
\(785\) 20.3923i 0.727833i
\(786\) 0 0
\(787\) −33.1865 + 19.1603i −1.18297 + 0.682989i −0.956700 0.291075i \(-0.905987\pi\)
−0.226272 + 0.974064<