Properties

Label 260.2.bk.b.33.1
Level $260$
Weight $2$
Character 260.33
Analytic conductor $2.076$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bk (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 33.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.33
Dual form 260.2.bk.b.197.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.86603 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(3.23205 - 1.86603i) q^{7} +(0.633975 - 0.366025i) q^{9} +O(q^{10})\) \(q+(1.86603 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(3.23205 - 1.86603i) q^{7} +(0.633975 - 0.366025i) q^{9} +(-0.598076 - 2.23205i) q^{11} +(3.00000 + 2.00000i) q^{13} +(-0.866025 + 4.23205i) q^{15} +(-1.13397 + 4.23205i) q^{17} +(0.866025 + 0.232051i) q^{19} +(5.09808 - 5.09808i) q^{21} +(-1.86603 - 6.96410i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(-3.09808 + 3.09808i) q^{27} +(-7.96410 - 4.59808i) q^{29} +(5.73205 + 5.73205i) q^{31} +(-2.23205 - 3.86603i) q^{33} +(0.500000 + 8.33013i) q^{35} +(0.232051 + 0.133975i) q^{37} +(6.59808 + 2.23205i) q^{39} +(-0.133975 + 0.0358984i) q^{41} +(-11.3301 - 3.03590i) q^{43} +(0.0980762 + 1.63397i) q^{45} +0.535898i q^{47} +(3.46410 - 6.00000i) q^{49} +8.46410i q^{51} +(-1.53590 - 1.53590i) q^{53} +(5.06218 + 1.03590i) q^{55} +1.73205 q^{57} +(-1.79423 + 6.69615i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.36603 - 2.36603i) q^{63} +(-7.00000 + 4.00000i) q^{65} +(-2.76795 + 4.79423i) q^{67} +(-6.96410 - 12.0622i) q^{69} +(1.13397 - 4.23205i) q^{71} -12.9282 q^{73} +(-7.59808 - 5.96410i) q^{75} +(-6.09808 - 6.09808i) q^{77} -4.53590i q^{79} +(-5.33013 + 9.23205i) q^{81} +3.46410i q^{83} +(-7.33013 - 6.50000i) q^{85} +(-17.1603 - 4.59808i) q^{87} +(14.7942 - 3.96410i) q^{89} +(13.4282 + 0.866025i) q^{91} +(13.5622 + 7.83013i) q^{93} +(-1.33013 + 1.50000i) q^{95} +(-2.23205 - 3.86603i) q^{97} +(-1.19615 - 1.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} - 4 q^{5} + 6 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} - 4 q^{5} + 6 q^{7} + 6 q^{9} + 8 q^{11} + 12 q^{13} - 8 q^{17} + 10 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} - 18 q^{29} + 16 q^{31} - 2 q^{33} + 2 q^{35} - 6 q^{37} + 16 q^{39} - 4 q^{41} - 28 q^{43} - 10 q^{45} - 20 q^{53} - 4 q^{55} + 24 q^{59} + 2 q^{61} + 2 q^{63} - 28 q^{65} - 18 q^{67} - 14 q^{69} + 8 q^{71} - 24 q^{73} - 20 q^{75} - 14 q^{77} - 4 q^{81} - 12 q^{85} - 34 q^{87} + 28 q^{89} + 26 q^{91} + 30 q^{93} + 12 q^{95} - 2 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.86603 0.500000i 1.07735 0.288675i 0.323840 0.946112i \(-0.395026\pi\)
0.753510 + 0.657437i \(0.228359\pi\)
\(4\) 0 0
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) 3.23205 1.86603i 1.22160 0.705291i 0.256341 0.966586i \(-0.417483\pi\)
0.965259 + 0.261295i \(0.0841495\pi\)
\(8\) 0 0
\(9\) 0.633975 0.366025i 0.211325 0.122008i
\(10\) 0 0
\(11\) −0.598076 2.23205i −0.180327 0.672989i −0.995583 0.0938879i \(-0.970070\pi\)
0.815256 0.579101i \(-0.196596\pi\)
\(12\) 0 0
\(13\) 3.00000 + 2.00000i 0.832050 + 0.554700i
\(14\) 0 0
\(15\) −0.866025 + 4.23205i −0.223607 + 1.09271i
\(16\) 0 0
\(17\) −1.13397 + 4.23205i −0.275029 + 1.02642i 0.680793 + 0.732476i \(0.261636\pi\)
−0.955822 + 0.293947i \(0.905031\pi\)
\(18\) 0 0
\(19\) 0.866025 + 0.232051i 0.198680 + 0.0532361i 0.356787 0.934186i \(-0.383872\pi\)
−0.158107 + 0.987422i \(0.550539\pi\)
\(20\) 0 0
\(21\) 5.09808 5.09808i 1.11249 1.11249i
\(22\) 0 0
\(23\) −1.86603 6.96410i −0.389093 1.45212i −0.831612 0.555357i \(-0.812582\pi\)
0.442519 0.896759i \(-0.354085\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) −3.09808 + 3.09808i −0.596225 + 0.596225i
\(28\) 0 0
\(29\) −7.96410 4.59808i −1.47890 0.853841i −0.479182 0.877716i \(-0.659066\pi\)
−0.999715 + 0.0238745i \(0.992400\pi\)
\(30\) 0 0
\(31\) 5.73205 + 5.73205i 1.02951 + 1.02951i 0.999551 + 0.0299555i \(0.00953655\pi\)
0.0299555 + 0.999551i \(0.490463\pi\)
\(32\) 0 0
\(33\) −2.23205 3.86603i −0.388550 0.672989i
\(34\) 0 0
\(35\) 0.500000 + 8.33013i 0.0845154 + 1.40805i
\(36\) 0 0
\(37\) 0.232051 + 0.133975i 0.0381489 + 0.0220253i 0.518953 0.854803i \(-0.326322\pi\)
−0.480804 + 0.876828i \(0.659655\pi\)
\(38\) 0 0
\(39\) 6.59808 + 2.23205i 1.05654 + 0.357414i
\(40\) 0 0
\(41\) −0.133975 + 0.0358984i −0.0209233 + 0.00560639i −0.269266 0.963066i \(-0.586781\pi\)
0.248342 + 0.968672i \(0.420114\pi\)
\(42\) 0 0
\(43\) −11.3301 3.03590i −1.72783 0.462970i −0.748147 0.663533i \(-0.769056\pi\)
−0.979681 + 0.200563i \(0.935723\pi\)
\(44\) 0 0
\(45\) 0.0980762 + 1.63397i 0.0146203 + 0.243579i
\(46\) 0 0
\(47\) 0.535898i 0.0781688i 0.999236 + 0.0390844i \(0.0124441\pi\)
−0.999236 + 0.0390844i \(0.987556\pi\)
\(48\) 0 0
\(49\) 3.46410 6.00000i 0.494872 0.857143i
\(50\) 0 0
\(51\) 8.46410i 1.18521i
\(52\) 0 0
\(53\) −1.53590 1.53590i −0.210972 0.210972i 0.593708 0.804680i \(-0.297663\pi\)
−0.804680 + 0.593708i \(0.797663\pi\)
\(54\) 0 0
\(55\) 5.06218 + 1.03590i 0.682584 + 0.139681i
\(56\) 0 0
\(57\) 1.73205 0.229416
\(58\) 0 0
\(59\) −1.79423 + 6.69615i −0.233589 + 0.871765i 0.745191 + 0.666851i \(0.232358\pi\)
−0.978780 + 0.204914i \(0.934309\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) 1.36603 2.36603i 0.172103 0.298091i
\(64\) 0 0
\(65\) −7.00000 + 4.00000i −0.868243 + 0.496139i
\(66\) 0 0
\(67\) −2.76795 + 4.79423i −0.338159 + 0.585708i −0.984086 0.177690i \(-0.943137\pi\)
0.645928 + 0.763399i \(0.276471\pi\)
\(68\) 0 0
\(69\) −6.96410 12.0622i −0.838379 1.45212i
\(70\) 0 0
\(71\) 1.13397 4.23205i 0.134578 0.502252i −0.865421 0.501045i \(-0.832949\pi\)
0.999999 0.00120705i \(-0.000384217\pi\)
\(72\) 0 0
\(73\) −12.9282 −1.51313 −0.756566 0.653917i \(-0.773124\pi\)
−0.756566 + 0.653917i \(0.773124\pi\)
\(74\) 0 0
\(75\) −7.59808 5.96410i −0.877350 0.688675i
\(76\) 0 0
\(77\) −6.09808 6.09808i −0.694940 0.694940i
\(78\) 0 0
\(79\) 4.53590i 0.510328i −0.966898 0.255164i \(-0.917870\pi\)
0.966898 0.255164i \(-0.0821295\pi\)
\(80\) 0 0
\(81\) −5.33013 + 9.23205i −0.592236 + 1.02578i
\(82\) 0 0
\(83\) 3.46410i 0.380235i 0.981761 + 0.190117i \(0.0608868\pi\)
−0.981761 + 0.190117i \(0.939113\pi\)
\(84\) 0 0
\(85\) −7.33013 6.50000i −0.795064 0.705024i
\(86\) 0 0
\(87\) −17.1603 4.59808i −1.83977 0.492966i
\(88\) 0 0
\(89\) 14.7942 3.96410i 1.56819 0.420194i 0.632942 0.774199i \(-0.281847\pi\)
0.935243 + 0.354005i \(0.115181\pi\)
\(90\) 0 0
\(91\) 13.4282 + 0.866025i 1.40766 + 0.0907841i
\(92\) 0 0
\(93\) 13.5622 + 7.83013i 1.40633 + 0.811946i
\(94\) 0 0
\(95\) −1.33013 + 1.50000i −0.136468 + 0.153897i
\(96\) 0 0
\(97\) −2.23205 3.86603i −0.226630 0.392535i 0.730177 0.683258i \(-0.239438\pi\)
−0.956807 + 0.290723i \(0.906104\pi\)
\(98\) 0 0
\(99\) −1.19615 1.19615i −0.120218 0.120218i
\(100\) 0 0
\(101\) 1.50000 + 0.866025i 0.149256 + 0.0861727i 0.572768 0.819718i \(-0.305870\pi\)
−0.423512 + 0.905890i \(0.639203\pi\)
\(102\) 0 0
\(103\) 6.66025 6.66025i 0.656254 0.656254i −0.298237 0.954492i \(-0.596399\pi\)
0.954492 + 0.298237i \(0.0963987\pi\)
\(104\) 0 0
\(105\) 5.09808 + 15.2942i 0.497521 + 1.49256i
\(106\) 0 0
\(107\) 1.59808 + 5.96410i 0.154492 + 0.576571i 0.999148 + 0.0412627i \(0.0131381\pi\)
−0.844656 + 0.535309i \(0.820195\pi\)
\(108\) 0 0
\(109\) 9.39230 9.39230i 0.899620 0.899620i −0.0957826 0.995402i \(-0.530535\pi\)
0.995402 + 0.0957826i \(0.0305354\pi\)
\(110\) 0 0
\(111\) 0.500000 + 0.133975i 0.0474579 + 0.0127163i
\(112\) 0 0
\(113\) −3.52628 + 13.1603i −0.331724 + 1.23801i 0.575652 + 0.817695i \(0.304748\pi\)
−0.907377 + 0.420318i \(0.861919\pi\)
\(114\) 0 0
\(115\) 15.7942 + 3.23205i 1.47282 + 0.301390i
\(116\) 0 0
\(117\) 2.63397 + 0.169873i 0.243511 + 0.0157048i
\(118\) 0 0
\(119\) 4.23205 + 15.7942i 0.387951 + 1.44785i
\(120\) 0 0
\(121\) 4.90192 2.83013i 0.445629 0.257284i
\(122\) 0 0
\(123\) −0.232051 + 0.133975i −0.0209233 + 0.0120801i
\(124\) 0 0
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 16.7942 4.50000i 1.49025 0.399310i 0.580426 0.814313i \(-0.302886\pi\)
0.909820 + 0.415002i \(0.136219\pi\)
\(128\) 0 0
\(129\) −22.6603 −1.99512
\(130\) 0 0
\(131\) 13.8564 1.21064 0.605320 0.795982i \(-0.293045\pi\)
0.605320 + 0.795982i \(0.293045\pi\)
\(132\) 0 0
\(133\) 3.23205 0.866025i 0.280254 0.0750939i
\(134\) 0 0
\(135\) −3.09808 9.29423i −0.266640 0.799920i
\(136\) 0 0
\(137\) −0.696152 + 0.401924i −0.0594763 + 0.0343387i −0.529443 0.848345i \(-0.677599\pi\)
0.469967 + 0.882684i \(0.344266\pi\)
\(138\) 0 0
\(139\) −8.42820 + 4.86603i −0.714871 + 0.412731i −0.812862 0.582456i \(-0.802092\pi\)
0.0979911 + 0.995187i \(0.468758\pi\)
\(140\) 0 0
\(141\) 0.267949 + 1.00000i 0.0225654 + 0.0842152i
\(142\) 0 0
\(143\) 2.66987 7.89230i 0.223266 0.659988i
\(144\) 0 0
\(145\) 17.1603 11.3301i 1.42508 0.940916i
\(146\) 0 0
\(147\) 3.46410 12.9282i 0.285714 1.06630i
\(148\) 0 0
\(149\) 18.2583 + 4.89230i 1.49578 + 0.400793i 0.911684 0.410891i \(-0.134782\pi\)
0.584096 + 0.811684i \(0.301449\pi\)
\(150\) 0 0
\(151\) 0.803848 0.803848i 0.0654162 0.0654162i −0.673642 0.739058i \(-0.735271\pi\)
0.739058 + 0.673642i \(0.235271\pi\)
\(152\) 0 0
\(153\) 0.830127 + 3.09808i 0.0671118 + 0.250465i
\(154\) 0 0
\(155\) −17.1962 + 5.73205i −1.38123 + 0.460409i
\(156\) 0 0
\(157\) −7.39230 + 7.39230i −0.589970 + 0.589970i −0.937623 0.347653i \(-0.886979\pi\)
0.347653 + 0.937623i \(0.386979\pi\)
\(158\) 0 0
\(159\) −3.63397 2.09808i −0.288193 0.166388i
\(160\) 0 0
\(161\) −19.0263 19.0263i −1.49948 1.49948i
\(162\) 0 0
\(163\) 0.767949 + 1.33013i 0.0601504 + 0.104184i 0.894533 0.447003i \(-0.147509\pi\)
−0.834382 + 0.551186i \(0.814175\pi\)
\(164\) 0 0
\(165\) 9.96410 0.598076i 0.775704 0.0465602i
\(166\) 0 0
\(167\) −5.76795 3.33013i −0.446337 0.257693i 0.259945 0.965623i \(-0.416296\pi\)
−0.706282 + 0.707931i \(0.749629\pi\)
\(168\) 0 0
\(169\) 5.00000 + 12.0000i 0.384615 + 0.923077i
\(170\) 0 0
\(171\) 0.633975 0.169873i 0.0484812 0.0129905i
\(172\) 0 0
\(173\) 8.59808 + 2.30385i 0.653700 + 0.175158i 0.570401 0.821366i \(-0.306788\pi\)
0.0832986 + 0.996525i \(0.473454\pi\)
\(174\) 0 0
\(175\) −17.1603 7.33013i −1.29719 0.554106i
\(176\) 0 0
\(177\) 13.3923i 1.00663i
\(178\) 0 0
\(179\) 5.96410 10.3301i 0.445778 0.772110i −0.552328 0.833627i \(-0.686260\pi\)
0.998106 + 0.0615168i \(0.0195938\pi\)
\(180\) 0 0
\(181\) 14.9282i 1.10960i 0.831982 + 0.554802i \(0.187206\pi\)
−0.831982 + 0.554802i \(0.812794\pi\)
\(182\) 0 0
\(183\) 1.36603 + 1.36603i 0.100980 + 0.100980i
\(184\) 0 0
\(185\) −0.500000 + 0.330127i −0.0367607 + 0.0242714i
\(186\) 0 0
\(187\) 10.1244 0.740366
\(188\) 0 0
\(189\) −4.23205 + 15.7942i −0.307836 + 1.14886i
\(190\) 0 0
\(191\) −11.9641 20.7224i −0.865692 1.49942i −0.866358 0.499423i \(-0.833545\pi\)
0.000666402 1.00000i \(-0.499788\pi\)
\(192\) 0 0
\(193\) 12.1603 21.0622i 0.875314 1.51609i 0.0188866 0.999822i \(-0.493988\pi\)
0.856428 0.516267i \(-0.172679\pi\)
\(194\) 0 0
\(195\) −11.0622 + 10.9641i −0.792179 + 0.785156i
\(196\) 0 0
\(197\) −7.16025 + 12.4019i −0.510147 + 0.883600i 0.489784 + 0.871844i \(0.337076\pi\)
−0.999931 + 0.0117566i \(0.996258\pi\)
\(198\) 0 0
\(199\) 4.96410 + 8.59808i 0.351896 + 0.609501i 0.986582 0.163269i \(-0.0522038\pi\)
−0.634686 + 0.772770i \(0.718870\pi\)
\(200\) 0 0
\(201\) −2.76795 + 10.3301i −0.195236 + 0.728631i
\(202\) 0 0
\(203\) −34.3205 −2.40883
\(204\) 0 0
\(205\) 0.0621778 0.303848i 0.00434269 0.0212216i
\(206\) 0 0
\(207\) −3.73205 3.73205i −0.259395 0.259395i
\(208\) 0 0
\(209\) 2.07180i 0.143309i
\(210\) 0 0
\(211\) 1.96410 3.40192i 0.135214 0.234198i −0.790465 0.612507i \(-0.790161\pi\)
0.925679 + 0.378309i \(0.123494\pi\)
\(212\) 0 0
\(213\) 8.46410i 0.579951i
\(214\) 0 0
\(215\) 17.4019 19.6244i 1.18680 1.33837i
\(216\) 0 0
\(217\) 29.2224 + 7.83013i 1.98375 + 0.531544i
\(218\) 0 0
\(219\) −24.1244 + 6.46410i −1.63017 + 0.436804i
\(220\) 0 0
\(221\) −11.8660 + 10.4282i −0.798195 + 0.701477i
\(222\) 0 0
\(223\) 14.0885 + 8.13397i 0.943433 + 0.544691i 0.891035 0.453935i \(-0.149980\pi\)
0.0523981 + 0.998626i \(0.483314\pi\)
\(224\) 0 0
\(225\) −3.36603 1.43782i −0.224402 0.0958548i
\(226\) 0 0
\(227\) −3.23205 5.59808i −0.214519 0.371557i 0.738605 0.674139i \(-0.235485\pi\)
−0.953124 + 0.302581i \(0.902152\pi\)
\(228\) 0 0
\(229\) −16.8564 16.8564i −1.11390 1.11390i −0.992618 0.121285i \(-0.961299\pi\)
−0.121285 0.992618i \(-0.538701\pi\)
\(230\) 0 0
\(231\) −14.4282 8.33013i −0.949306 0.548082i
\(232\) 0 0
\(233\) −11.0000 + 11.0000i −0.720634 + 0.720634i −0.968734 0.248100i \(-0.920194\pi\)
0.248100 + 0.968734i \(0.420194\pi\)
\(234\) 0 0
\(235\) −1.07180 0.535898i −0.0699163 0.0349582i
\(236\) 0 0
\(237\) −2.26795 8.46410i −0.147319 0.549802i
\(238\) 0 0
\(239\) 1.19615 1.19615i 0.0773727 0.0773727i −0.667361 0.744734i \(-0.732576\pi\)
0.744734 + 0.667361i \(0.232576\pi\)
\(240\) 0 0
\(241\) −17.0622 4.57180i −1.09907 0.294495i −0.336685 0.941617i \(-0.609306\pi\)
−0.762386 + 0.647122i \(0.775972\pi\)
\(242\) 0 0
\(243\) −1.92820 + 7.19615i −0.123694 + 0.461633i
\(244\) 0 0
\(245\) 8.53590 + 12.9282i 0.545339 + 0.825953i
\(246\) 0 0
\(247\) 2.13397 + 2.42820i 0.135782 + 0.154503i
\(248\) 0 0
\(249\) 1.73205 + 6.46410i 0.109764 + 0.409646i
\(250\) 0 0
\(251\) −3.10770 + 1.79423i −0.196156 + 0.113251i −0.594861 0.803828i \(-0.702793\pi\)
0.398705 + 0.917079i \(0.369460\pi\)
\(252\) 0 0
\(253\) −14.4282 + 8.33013i −0.907093 + 0.523711i
\(254\) 0 0
\(255\) −16.9282 8.46410i −1.06009 0.530043i
\(256\) 0 0
\(257\) 15.5263 4.16025i 0.968503 0.259510i 0.260307 0.965526i \(-0.416176\pi\)
0.708196 + 0.706016i \(0.249510\pi\)
\(258\) 0 0
\(259\) 1.00000 0.0621370
\(260\) 0 0
\(261\) −6.73205 −0.416703
\(262\) 0 0
\(263\) 10.7942 2.89230i 0.665601 0.178347i 0.0898284 0.995957i \(-0.471368\pi\)
0.575772 + 0.817610i \(0.304701\pi\)
\(264\) 0 0
\(265\) 4.60770 1.53590i 0.283048 0.0943495i
\(266\) 0 0
\(267\) 25.6244 14.7942i 1.56819 0.905392i
\(268\) 0 0
\(269\) −9.57180 + 5.52628i −0.583603 + 0.336943i −0.762564 0.646913i \(-0.776060\pi\)
0.178961 + 0.983856i \(0.442726\pi\)
\(270\) 0 0
\(271\) −4.20577 15.6962i −0.255482 0.953473i −0.967821 0.251638i \(-0.919031\pi\)
0.712339 0.701836i \(-0.247636\pi\)
\(272\) 0 0
\(273\) 25.4904 5.09808i 1.54275 0.308550i
\(274\) 0 0
\(275\) −7.13397 + 9.08846i −0.430195 + 0.548055i
\(276\) 0 0
\(277\) −2.99038 + 11.1603i −0.179675 + 0.670555i 0.816033 + 0.578005i \(0.196168\pi\)
−0.995708 + 0.0925500i \(0.970498\pi\)
\(278\) 0 0
\(279\) 5.73205 + 1.53590i 0.343169 + 0.0919518i
\(280\) 0 0
\(281\) 13.3923 13.3923i 0.798918 0.798918i −0.184007 0.982925i \(-0.558907\pi\)
0.982925 + 0.184007i \(0.0589069\pi\)
\(282\) 0 0
\(283\) 6.52628 + 24.3564i 0.387947 + 1.44784i 0.833469 + 0.552567i \(0.186352\pi\)
−0.445522 + 0.895271i \(0.646982\pi\)
\(284\) 0 0
\(285\) −1.73205 + 3.46410i −0.102598 + 0.205196i
\(286\) 0 0
\(287\) −0.366025 + 0.366025i −0.0216058 + 0.0216058i
\(288\) 0 0
\(289\) −1.90192 1.09808i −0.111878 0.0645927i
\(290\) 0 0
\(291\) −6.09808 6.09808i −0.357476 0.357476i
\(292\) 0 0
\(293\) 7.76795 + 13.4545i 0.453808 + 0.786019i 0.998619 0.0525400i \(-0.0167317\pi\)
−0.544810 + 0.838559i \(0.683398\pi\)
\(294\) 0 0
\(295\) −11.5981 10.2846i −0.675266 0.598793i
\(296\) 0 0
\(297\) 8.76795 + 5.06218i 0.508768 + 0.293737i
\(298\) 0 0
\(299\) 8.33013 24.6244i 0.481744 1.42406i
\(300\) 0 0
\(301\) −42.2846 + 11.3301i −2.43724 + 0.653058i
\(302\) 0 0
\(303\) 3.23205 + 0.866025i 0.185676 + 0.0497519i
\(304\) 0 0
\(305\) −2.23205 + 0.133975i −0.127807 + 0.00767136i
\(306\) 0 0
\(307\) 9.60770i 0.548340i 0.961681 + 0.274170i \(0.0884031\pi\)
−0.961681 + 0.274170i \(0.911597\pi\)
\(308\) 0 0
\(309\) 9.09808 15.7583i 0.517571 0.896460i
\(310\) 0 0
\(311\) 32.2487i 1.82866i 0.404974 + 0.914328i \(0.367281\pi\)
−0.404974 + 0.914328i \(0.632719\pi\)
\(312\) 0 0
\(313\) −14.3205 14.3205i −0.809443 0.809443i 0.175107 0.984549i \(-0.443973\pi\)
−0.984549 + 0.175107i \(0.943973\pi\)
\(314\) 0 0
\(315\) 3.36603 + 5.09808i 0.189654 + 0.287244i
\(316\) 0 0
\(317\) −16.9282 −0.950783 −0.475391 0.879774i \(-0.657694\pi\)
−0.475391 + 0.879774i \(0.657694\pi\)
\(318\) 0 0
\(319\) −5.50000 + 20.5263i −0.307941 + 1.14925i
\(320\) 0 0
\(321\) 5.96410 + 10.3301i 0.332884 + 0.576571i
\(322\) 0 0
\(323\) −1.96410 + 3.40192i −0.109286 + 0.189288i
\(324\) 0 0
\(325\) −1.00000 18.0000i −0.0554700 0.998460i
\(326\) 0 0
\(327\) 12.8301 22.2224i 0.709508 1.22890i
\(328\) 0 0
\(329\) 1.00000 + 1.73205i 0.0551318 + 0.0954911i
\(330\) 0 0
\(331\) 1.66987 6.23205i 0.0917845 0.342544i −0.904728 0.425990i \(-0.859926\pi\)
0.996512 + 0.0834456i \(0.0265925\pi\)
\(332\) 0 0
\(333\) 0.196152 0.0107491
\(334\) 0 0
\(335\) −6.82051 10.3301i −0.372644 0.564395i
\(336\) 0 0
\(337\) −13.9282 13.9282i −0.758718 0.758718i 0.217371 0.976089i \(-0.430252\pi\)
−0.976089 + 0.217371i \(0.930252\pi\)
\(338\) 0 0
\(339\) 26.3205i 1.42953i
\(340\) 0 0
\(341\) 9.36603 16.2224i 0.507199 0.878494i
\(342\) 0 0
\(343\) 0.267949i 0.0144679i
\(344\) 0 0
\(345\) 31.0885 1.86603i 1.67375 0.100463i
\(346\) 0 0
\(347\) −15.3301 4.10770i −0.822964 0.220513i −0.177322 0.984153i \(-0.556744\pi\)
−0.645642 + 0.763640i \(0.723410\pi\)
\(348\) 0 0
\(349\) −24.5263 + 6.57180i −1.31286 + 0.351780i −0.846299 0.532708i \(-0.821174\pi\)
−0.466563 + 0.884488i \(0.654508\pi\)
\(350\) 0 0
\(351\) −15.4904 + 3.09808i −0.826815 + 0.165363i
\(352\) 0 0
\(353\) 10.6244 + 6.13397i 0.565477 + 0.326479i 0.755341 0.655332i \(-0.227471\pi\)
−0.189864 + 0.981810i \(0.560805\pi\)
\(354\) 0 0
\(355\) 7.33013 + 6.50000i 0.389043 + 0.344984i
\(356\) 0 0
\(357\) 15.7942 + 27.3564i 0.835919 + 1.44785i
\(358\) 0 0
\(359\) 23.5885 + 23.5885i 1.24495 + 1.24495i 0.957922 + 0.287029i \(0.0926677\pi\)
0.287029 + 0.957922i \(0.407332\pi\)
\(360\) 0 0
\(361\) −15.7583 9.09808i −0.829386 0.478846i
\(362\) 0 0
\(363\) 7.73205 7.73205i 0.405827 0.405827i
\(364\) 0 0
\(365\) 12.9282 25.8564i 0.676693 1.35339i
\(366\) 0 0
\(367\) −4.79423 17.8923i −0.250257 0.933971i −0.970668 0.240424i \(-0.922714\pi\)
0.720411 0.693547i \(-0.243953\pi\)
\(368\) 0 0
\(369\) −0.0717968 + 0.0717968i −0.00373759 + 0.00373759i
\(370\) 0 0
\(371\) −7.83013 2.09808i −0.406520 0.108927i
\(372\) 0 0
\(373\) 1.00962 3.76795i 0.0522761 0.195097i −0.934849 0.355044i \(-0.884466\pi\)
0.987126 + 0.159947i \(0.0511324\pi\)
\(374\) 0 0
\(375\) 19.5263 9.23205i 1.00833 0.476741i
\(376\) 0 0
\(377\) −14.6962 29.7224i −0.756890 1.53078i
\(378\) 0 0
\(379\) 4.47372 + 16.6962i 0.229800 + 0.857624i 0.980425 + 0.196895i \(0.0630859\pi\)
−0.750625 + 0.660729i \(0.770247\pi\)
\(380\) 0 0
\(381\) 29.0885 16.7942i 1.49025 0.860394i
\(382\) 0 0
\(383\) −9.69615 + 5.59808i −0.495450 + 0.286048i −0.726833 0.686815i \(-0.759008\pi\)
0.231382 + 0.972863i \(0.425675\pi\)
\(384\) 0 0
\(385\) 18.2942 6.09808i 0.932360 0.310787i
\(386\) 0 0
\(387\) −8.29423 + 2.22243i −0.421619 + 0.112973i
\(388\) 0 0
\(389\) 23.8564 1.20957 0.604784 0.796390i \(-0.293259\pi\)
0.604784 + 0.796390i \(0.293259\pi\)
\(390\) 0 0
\(391\) 31.5885 1.59750
\(392\) 0 0
\(393\) 25.8564 6.92820i 1.30428 0.349482i
\(394\) 0 0
\(395\) 9.07180 + 4.53590i 0.456452 + 0.228226i
\(396\) 0 0
\(397\) −31.6244 + 18.2583i −1.58718 + 0.916359i −0.593412 + 0.804899i \(0.702220\pi\)
−0.993769 + 0.111460i \(0.964447\pi\)
\(398\) 0 0
\(399\) 5.59808 3.23205i 0.280254 0.161805i
\(400\) 0 0
\(401\) 4.13397 + 15.4282i 0.206441 + 0.770448i 0.989006 + 0.147878i \(0.0472444\pi\)
−0.782565 + 0.622569i \(0.786089\pi\)
\(402\) 0 0
\(403\) 5.73205 + 28.6603i 0.285534 + 1.42767i
\(404\) 0 0
\(405\) −13.1340 19.8923i −0.652632 0.988457i
\(406\) 0 0
\(407\) 0.160254 0.598076i 0.00794350 0.0296455i
\(408\) 0 0
\(409\) −9.06218 2.42820i −0.448096 0.120067i 0.0277124 0.999616i \(-0.491178\pi\)
−0.475808 + 0.879549i \(0.657844\pi\)
\(410\) 0 0
\(411\) −1.09808 + 1.09808i −0.0541641 + 0.0541641i
\(412\) 0 0
\(413\) 6.69615 + 24.9904i 0.329496 + 1.22970i
\(414\) 0 0
\(415\) −6.92820 3.46410i −0.340092 0.170046i
\(416\) 0 0
\(417\) −13.2942 + 13.2942i −0.651021 + 0.651021i
\(418\) 0 0
\(419\) −0.356406 0.205771i −0.0174116 0.0100526i 0.491269 0.871008i \(-0.336533\pi\)
−0.508681 + 0.860955i \(0.669867\pi\)
\(420\) 0 0
\(421\) 27.9282 + 27.9282i 1.36114 + 1.36114i 0.872470 + 0.488667i \(0.162517\pi\)
0.488667 + 0.872470i \(0.337483\pi\)
\(422\) 0 0
\(423\) 0.196152 + 0.339746i 0.00953726 + 0.0165190i
\(424\) 0 0
\(425\) 20.3301 8.16025i 0.986156 0.395830i
\(426\) 0 0
\(427\) 3.23205 + 1.86603i 0.156410 + 0.0903033i
\(428\) 0 0
\(429\) 1.03590 16.0622i 0.0500136 0.775489i
\(430\) 0 0
\(431\) 27.5263 7.37564i 1.32589 0.355272i 0.474711 0.880142i \(-0.342552\pi\)
0.851183 + 0.524869i \(0.175886\pi\)
\(432\) 0 0
\(433\) −26.7224 7.16025i −1.28420 0.344100i −0.448744 0.893660i \(-0.648129\pi\)
−0.835454 + 0.549560i \(0.814795\pi\)
\(434\) 0 0
\(435\) 26.3564 29.7224i 1.26369 1.42508i
\(436\) 0 0
\(437\) 6.46410i 0.309220i
\(438\) 0 0
\(439\) −0.964102 + 1.66987i −0.0460141 + 0.0796987i −0.888115 0.459621i \(-0.847985\pi\)
0.842101 + 0.539320i \(0.181319\pi\)
\(440\) 0 0
\(441\) 5.07180i 0.241514i
\(442\) 0 0
\(443\) −11.0526 11.0526i −0.525123 0.525123i 0.393991 0.919114i \(-0.371094\pi\)
−0.919114 + 0.393991i \(0.871094\pi\)
\(444\) 0 0
\(445\) −6.86603 + 33.5526i −0.325481 + 1.59054i
\(446\) 0 0
\(447\) 36.5167 1.72718
\(448\) 0 0
\(449\) 1.99038 7.42820i 0.0939319 0.350559i −0.902923 0.429801i \(-0.858584\pi\)
0.996855 + 0.0792428i \(0.0252502\pi\)
\(450\) 0 0
\(451\) 0.160254 + 0.277568i 0.00754607 + 0.0130702i
\(452\) 0 0
\(453\) 1.09808 1.90192i 0.0515921 0.0893602i
\(454\) 0 0
\(455\) −15.1603 + 25.9904i −0.710724 + 1.21845i
\(456\) 0 0
\(457\) 4.30385 7.45448i 0.201325 0.348706i −0.747630 0.664115i \(-0.768808\pi\)
0.948956 + 0.315409i \(0.102142\pi\)
\(458\) 0 0
\(459\) −9.59808 16.6244i −0.448000 0.775958i
\(460\) 0 0
\(461\) 1.99038 7.42820i 0.0927013 0.345966i −0.903960 0.427618i \(-0.859353\pi\)
0.996661 + 0.0816519i \(0.0260196\pi\)
\(462\) 0 0
\(463\) −2.14359 −0.0996212 −0.0498106 0.998759i \(-0.515862\pi\)
−0.0498106 + 0.998759i \(0.515862\pi\)
\(464\) 0 0
\(465\) −29.2224 + 19.2942i −1.35516 + 0.894748i
\(466\) 0 0
\(467\) −4.12436 4.12436i −0.190852 0.190852i 0.605212 0.796064i \(-0.293088\pi\)
−0.796064 + 0.605212i \(0.793088\pi\)
\(468\) 0 0
\(469\) 20.6603i 0.954002i
\(470\) 0 0
\(471\) −10.0981 + 17.4904i −0.465295 + 0.805914i
\(472\) 0 0
\(473\) 27.1051i 1.24629i
\(474\) 0 0
\(475\) −1.66987 4.16025i −0.0766190 0.190886i
\(476\) 0 0
\(477\) −1.53590 0.411543i −0.0703240 0.0188432i
\(478\) 0 0
\(479\) 26.9904 7.23205i 1.23322 0.330441i 0.417389 0.908728i \(-0.362945\pi\)
0.815833 + 0.578287i \(0.196279\pi\)
\(480\) 0 0
\(481\) 0.428203 + 0.866025i 0.0195244 + 0.0394874i
\(482\) 0 0
\(483\) −45.0167 25.9904i −2.04833 1.18260i
\(484\) 0 0
\(485\) 9.96410 0.598076i 0.452447 0.0271572i
\(486\) 0 0
\(487\) −0.160254 0.277568i −0.00726180 0.0125778i 0.862372 0.506276i \(-0.168978\pi\)
−0.869633 + 0.493698i \(0.835645\pi\)
\(488\) 0 0
\(489\) 2.09808 + 2.09808i 0.0948783 + 0.0948783i
\(490\) 0 0
\(491\) −7.03590 4.06218i −0.317526 0.183324i 0.332763 0.943010i \(-0.392019\pi\)
−0.650289 + 0.759687i \(0.725352\pi\)
\(492\) 0 0
\(493\) 28.4904 28.4904i 1.28314 1.28314i
\(494\) 0 0
\(495\) 3.58846 1.19615i 0.161289 0.0537631i
\(496\) 0 0
\(497\) −4.23205 15.7942i −0.189833 0.708468i
\(498\) 0 0
\(499\) −7.19615 + 7.19615i −0.322144 + 0.322144i −0.849589 0.527445i \(-0.823150\pi\)
0.527445 + 0.849589i \(0.323150\pi\)
\(500\) 0 0
\(501\) −12.4282 3.33013i −0.555251 0.148779i
\(502\) 0 0
\(503\) 2.93782 10.9641i 0.130991 0.488865i −0.868991 0.494828i \(-0.835231\pi\)
0.999982 + 0.00596240i \(0.00189790\pi\)
\(504\) 0 0
\(505\) −3.23205 + 2.13397i −0.143824 + 0.0949606i
\(506\) 0 0
\(507\) 15.3301 + 19.8923i 0.680835 + 0.883448i
\(508\) 0 0
\(509\) −6.79423 25.3564i −0.301149 1.12390i −0.936210 0.351441i \(-0.885692\pi\)
0.635061 0.772462i \(-0.280975\pi\)
\(510\) 0 0
\(511\) −41.7846 + 24.1244i −1.84844 + 1.06720i
\(512\) 0 0
\(513\) −3.40192 + 1.96410i −0.150199 + 0.0867172i
\(514\) 0 0
\(515\) 6.66025 + 19.9808i 0.293486 + 0.880458i
\(516\) 0 0
\(517\) 1.19615 0.320508i 0.0526067 0.0140959i
\(518\) 0 0
\(519\) 17.1962 0.754827
\(520\) 0 0
\(521\) −23.8564 −1.04517 −0.522584 0.852588i \(-0.675032\pi\)
−0.522584 + 0.852588i \(0.675032\pi\)
\(522\) 0 0
\(523\) −3.06218 + 0.820508i −0.133900 + 0.0358783i −0.325146 0.945664i \(-0.605414\pi\)
0.191247 + 0.981542i \(0.438747\pi\)
\(524\) 0 0
\(525\) −35.6865 5.09808i −1.55749 0.222498i
\(526\) 0 0
\(527\) −30.7583 + 17.7583i −1.33985 + 0.773565i
\(528\) 0 0
\(529\) −25.0981 + 14.4904i −1.09122 + 0.630017i
\(530\) 0 0
\(531\) 1.31347 + 4.90192i 0.0569996 + 0.212725i
\(532\) 0 0
\(533\) −0.473721 0.160254i −0.0205191 0.00694137i
\(534\) 0 0
\(535\) −13.5263 2.76795i −0.584792 0.119669i
\(536\) 0 0
\(537\) 5.96410 22.2583i 0.257370 0.960518i
\(538\) 0 0
\(539\) −15.4641 4.14359i −0.666086 0.178477i
\(540\) 0 0
\(541\) 27.9282 27.9282i 1.20073 1.20073i 0.226782 0.973946i \(-0.427180\pi\)
0.973946 0.226782i \(-0.0728204\pi\)
\(542\) 0 0
\(543\) 7.46410 + 27.8564i 0.320315 + 1.19543i
\(544\) 0 0
\(545\) 9.39230 + 28.1769i 0.402322 + 1.20697i
\(546\) 0 0
\(547\) 1.19615 1.19615i 0.0511438 0.0511438i −0.681072 0.732216i \(-0.738486\pi\)
0.732216 + 0.681072i \(0.238486\pi\)
\(548\) 0 0
\(549\) 0.633975 + 0.366025i 0.0270574 + 0.0156216i
\(550\) 0 0
\(551\) −5.83013 5.83013i −0.248372 0.248372i
\(552\) 0 0
\(553\) −8.46410 14.6603i −0.359930 0.623417i
\(554\) 0 0
\(555\) −0.767949 + 0.866025i −0.0325976 + 0.0367607i
\(556\) 0 0
\(557\) −21.2321 12.2583i −0.899631 0.519402i −0.0225505 0.999746i \(-0.507179\pi\)
−0.877080 + 0.480344i \(0.840512\pi\)
\(558\) 0 0
\(559\) −27.9186 31.7679i −1.18083 1.34364i
\(560\) 0 0
\(561\) 18.8923 5.06218i 0.797634 0.213725i
\(562\) 0 0
\(563\) 10.5263 + 2.82051i 0.443630 + 0.118870i 0.473717 0.880677i \(-0.342912\pi\)
−0.0300874 + 0.999547i \(0.509579\pi\)
\(564\) 0 0
\(565\) −22.7942 20.2128i −0.958960 0.850359i
\(566\) 0 0
\(567\) 39.7846i 1.67080i
\(568\) 0 0
\(569\) 15.4282 26.7224i 0.646784 1.12026i −0.337102 0.941468i \(-0.609447\pi\)
0.983886 0.178795i \(-0.0572198\pi\)
\(570\) 0 0
\(571\) 34.1051i 1.42725i −0.700525 0.713627i \(-0.747051\pi\)
0.700525 0.713627i \(-0.252949\pi\)
\(572\) 0 0
\(573\) −32.6865 32.6865i −1.36550 1.36550i
\(574\) 0 0
\(575\) −22.2583 + 28.3564i −0.928237 + 1.18254i
\(576\) 0 0
\(577\) −15.0718 −0.627447 −0.313724 0.949514i \(-0.601577\pi\)
−0.313724 + 0.949514i \(0.601577\pi\)
\(578\) 0 0
\(579\) 12.1603 45.3827i 0.505363 1.88604i
\(580\) 0 0
\(581\) 6.46410 + 11.1962i 0.268176 + 0.464495i
\(582\) 0 0
\(583\) −2.50962 + 4.34679i −0.103938 + 0.180026i
\(584\) 0 0
\(585\) −2.97372 + 5.09808i −0.122948 + 0.210780i
\(586\) 0 0
\(587\) 4.16025 7.20577i 0.171712 0.297414i −0.767306 0.641281i \(-0.778403\pi\)
0.939019 + 0.343867i \(0.111737\pi\)
\(588\) 0 0
\(589\) 3.63397 + 6.29423i 0.149735 + 0.259349i
\(590\) 0 0
\(591\) −7.16025 + 26.7224i −0.294533 + 1.09921i
\(592\) 0 0
\(593\) −20.9282 −0.859418 −0.429709 0.902967i \(-0.641384\pi\)
−0.429709 + 0.902967i \(0.641384\pi\)
\(594\) 0 0
\(595\) −35.8205 7.33013i −1.46850 0.300506i
\(596\) 0 0
\(597\) 13.5622 + 13.5622i 0.555063 + 0.555063i
\(598\) 0 0
\(599\) 26.3923i 1.07836i −0.842190 0.539180i \(-0.818734\pi\)
0.842190 0.539180i \(-0.181266\pi\)
\(600\) 0 0
\(601\) −18.4282 + 31.9186i −0.751702 + 1.30199i 0.195295 + 0.980745i \(0.437434\pi\)
−0.946997 + 0.321242i \(0.895900\pi\)
\(602\) 0 0
\(603\) 4.05256i 0.165033i
\(604\) 0 0
\(605\) 0.758330 + 12.6340i 0.0308305 + 0.513644i
\(606\) 0 0
\(607\) 21.0622 + 5.64359i 0.854887 + 0.229066i 0.659542 0.751668i \(-0.270750\pi\)
0.195346 + 0.980734i \(0.437417\pi\)
\(608\) 0 0
\(609\) −64.0429 + 17.1603i −2.59515 + 0.695369i
\(610\) 0 0
\(611\) −1.07180 + 1.60770i −0.0433603 + 0.0650404i
\(612\) 0 0
\(613\) −5.76795 3.33013i −0.232965 0.134503i 0.378974 0.925407i \(-0.376277\pi\)
−0.611939 + 0.790905i \(0.709610\pi\)
\(614\) 0 0
\(615\) −0.0358984 0.598076i −0.00144756 0.0241168i
\(616\) 0 0
\(617\) 15.0885 + 26.1340i 0.607438 + 1.05211i 0.991661 + 0.128874i \(0.0411362\pi\)
−0.384223 + 0.923240i \(0.625530\pi\)
\(618\) 0 0
\(619\) 30.1244 + 30.1244i 1.21080 + 1.21080i 0.970764 + 0.240036i \(0.0771593\pi\)
0.240036 + 0.970764i \(0.422841\pi\)
\(620\) 0 0
\(621\) 27.3564 + 15.7942i 1.09777 + 0.633801i
\(622\) 0 0
\(623\) 40.4186 40.4186i 1.61934 1.61934i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) −1.03590 3.86603i −0.0413698 0.154394i
\(628\) 0 0
\(629\) −0.830127 + 0.830127i −0.0330993 + 0.0330993i
\(630\) 0 0
\(631\) 21.7942 + 5.83975i 0.867615 + 0.232477i 0.665056 0.746794i \(-0.268408\pi\)
0.202559 + 0.979270i \(0.435074\pi\)
\(632\) 0 0
\(633\) 1.96410 7.33013i 0.0780660 0.291346i
\(634\) 0 0
\(635\) −7.79423 + 38.0885i −0.309305 + 1.51149i
\(636\) 0 0
\(637\) 22.3923 11.0718i 0.887215 0.438681i
\(638\) 0 0
\(639\) −0.830127 3.09808i −0.0328393 0.122558i
\(640\) 0 0
\(641\) −1.28461 + 0.741670i −0.0507390 + 0.0292942i −0.525155 0.851007i \(-0.675993\pi\)
0.474416 + 0.880301i \(0.342659\pi\)
\(642\) 0 0
\(643\) 39.2321 22.6506i 1.54716 0.893254i 0.548804 0.835951i \(-0.315083\pi\)
0.998357 0.0573029i \(-0.0182501\pi\)
\(644\) 0 0
\(645\) 22.6603 45.3205i 0.892247 1.78449i
\(646\) 0 0
\(647\) 14.7942 3.96410i 0.581621 0.155845i 0.0440001 0.999032i \(-0.485990\pi\)
0.537621 + 0.843187i \(0.319323\pi\)
\(648\) 0 0
\(649\) 16.0192 0.628810
\(650\) 0 0
\(651\) 58.4449 2.29063
\(652\) 0 0
\(653\) −36.1865 + 9.69615i −1.41609 + 0.379440i −0.884094 0.467308i \(-0.845224\pi\)
−0.531994 + 0.846748i \(0.678557\pi\)
\(654\) 0 0
\(655\) −13.8564 + 27.7128i −0.541415 + 1.08283i
\(656\) 0 0
\(657\) −8.19615 + 4.73205i −0.319762 + 0.184615i
\(658\) 0 0
\(659\) 26.2128 15.1340i 1.02111 0.589536i 0.106682 0.994293i \(-0.465977\pi\)
0.914424 + 0.404757i \(0.132644\pi\)
\(660\) 0 0
\(661\) 3.59808 + 13.4282i 0.139949 + 0.522297i 0.999928 + 0.0119679i \(0.00380959\pi\)
−0.859979 + 0.510329i \(0.829524\pi\)
\(662\) 0 0
\(663\) −16.9282 + 25.3923i −0.657437 + 0.986155i
\(664\) 0 0
\(665\) −1.50000 + 7.33013i −0.0581675 + 0.284250i
\(666\) 0 0
\(667\) −17.1603 + 64.0429i −0.664448 + 2.47975i
\(668\) 0 0
\(669\) 30.3564 + 8.13397i 1.17365 + 0.314478i
\(670\) 0 0
\(671\) 1.63397 1.63397i 0.0630789 0.0630789i
\(672\) 0 0
\(673\) 1.00962 + 3.76795i 0.0389180 + 0.145244i 0.982651 0.185465i \(-0.0593790\pi\)
−0.943733 + 0.330708i \(0.892712\pi\)
\(674\) 0 0
\(675\) 21.6865 + 3.09808i 0.834715 + 0.119245i
\(676\) 0 0
\(677\) 24.3205 24.3205i 0.934713 0.934713i −0.0632826 0.997996i \(-0.520157\pi\)
0.997996 + 0.0632826i \(0.0201569\pi\)
\(678\) 0 0
\(679\) −14.4282 8.33013i −0.553704 0.319681i
\(680\) 0 0
\(681\) −8.83013 8.83013i −0.338371 0.338371i
\(682\) 0 0
\(683\) −11.7679 20.3827i −0.450288 0.779922i 0.548116 0.836403i \(-0.315345\pi\)
−0.998404 + 0.0564808i \(0.982012\pi\)
\(684\) 0 0
\(685\) −0.107695 1.79423i −0.00411482 0.0685540i
\(686\) 0 0
\(687\) −39.8827 23.0263i −1.52162 0.878507i
\(688\) 0 0
\(689\) −1.53590 7.67949i −0.0585131 0.292565i
\(690\) 0 0
\(691\) 12.0622 3.23205i 0.458867 0.122953i −0.0219785 0.999758i \(-0.506997\pi\)
0.480845 + 0.876805i \(0.340330\pi\)
\(692\) 0 0
\(693\) −6.09808 1.63397i −0.231647 0.0620696i
\(694\) 0 0
\(695\) −1.30385 21.7224i −0.0494578 0.823979i
\(696\) 0 0
\(697\) 0.607695i 0.0230181i
\(698\) 0 0
\(699\) −15.0263 + 26.0263i −0.568346 + 0.984404i
\(700\) 0 0
\(701\) 42.9282i 1.62138i −0.585479 0.810688i \(-0.699093\pi\)
0.585479 0.810688i \(-0.300907\pi\)
\(702\) 0 0
\(703\) 0.169873 + 0.169873i 0.00640688 + 0.00640688i
\(704\) 0 0
\(705\) −2.26795 0.464102i −0.0854159 0.0174791i
\(706\) 0 0
\(707\) 6.46410 0.243108
\(708\) 0 0
\(709\) −0.401924 + 1.50000i −0.0150946 + 0.0563337i −0.973062 0.230542i \(-0.925950\pi\)
0.957968 + 0.286876i \(0.0926167\pi\)
\(710\) 0 0
\(711\) −1.66025 2.87564i −0.0622644 0.107845i
\(712\) 0 0
\(713\) 29.2224 50.6147i 1.09439 1.89554i
\(714\) 0 0
\(715\) 13.1147 + 13.2321i 0.490463 + 0.494851i
\(716\) 0 0
\(717\) 1.63397 2.83013i 0.0610219 0.105693i
\(718\) 0 0
\(719\) 5.89230 + 10.2058i 0.219746 + 0.380611i 0.954730 0.297473i \(-0.0961438\pi\)
−0.734984 + 0.678084i \(0.762811\pi\)
\(720\) 0 0
\(721\) 9.09808 33.9545i 0.338830 1.26453i
\(722\) 0 0
\(723\) −34.1244 −1.26910
\(724\) 0 0
\(725\) 5.50000 + 45.6506i 0.204265 + 1.69542i
\(726\) 0 0
\(727\) −17.5885 17.5885i −0.652320 0.652320i 0.301231 0.953551i \(-0.402602\pi\)
−0.953551 + 0.301231i \(0.902602\pi\)
\(728\) 0 0
\(729\) 17.5885i 0.651424i
\(730\) 0 0
\(731\) 25.6962 44.5070i 0.950407 1.64615i
\(732\) 0 0
\(733\) 30.6410i 1.13175i 0.824490 + 0.565876i \(0.191462\pi\)
−0.824490 + 0.565876i \(0.808538\pi\)
\(734\) 0 0
\(735\) 22.3923 + 19.8564i 0.825953 + 0.732415i
\(736\) 0 0
\(737\) 12.3564 + 3.31089i 0.455154 + 0.121958i
\(738\) 0 0
\(739\) −33.2583 + 8.91154i −1.22343 + 0.327816i −0.812017 0.583634i \(-0.801630\pi\)
−0.411410 + 0.911450i \(0.634964\pi\)
\(740\) 0 0
\(741\) 5.19615 + 3.46410i 0.190885 + 0.127257i
\(742\) 0 0
\(743\) −21.4808 12.4019i −0.788053 0.454982i 0.0512238 0.998687i \(-0.483688\pi\)
−0.839277 + 0.543705i \(0.817021\pi\)
\(744\) 0 0
\(745\) −28.0429 + 31.6244i −1.02741 + 1.15863i
\(746\) 0 0
\(747\) 1.26795 + 2.19615i 0.0463918 + 0.0803530i
\(748\) 0 0
\(749\) 16.2942 + 16.2942i 0.595378 + 0.595378i
\(750\) 0 0
\(751\) −16.7487 9.66987i −0.611169 0.352859i 0.162254 0.986749i \(-0.448124\pi\)
−0.773423 + 0.633890i \(0.781457\pi\)
\(752\) 0 0
\(753\) −4.90192 + 4.90192i −0.178636 + 0.178636i
\(754\) 0 0
\(755\) 0.803848 + 2.41154i 0.0292550 + 0.0877650i
\(756\) 0 0
\(757\) 3.93782 + 14.6962i 0.143123 + 0.534141i 0.999832 + 0.0183410i \(0.00583846\pi\)
−0.856709 + 0.515800i \(0.827495\pi\)
\(758\) 0 0
\(759\) −22.7583 + 22.7583i −0.826075 + 0.826075i
\(760\) 0 0
\(761\) 11.3301 + 3.03590i 0.410717 + 0.110051i 0.458261 0.888818i \(-0.348473\pi\)
−0.0475437 + 0.998869i \(0.515139\pi\)
\(762\) 0 0
\(763\) 12.8301 47.8827i 0.464482 1.73347i
\(764\) 0 0
\(765\) −7.02628 1.43782i −0.254036 0.0519846i
\(766\) 0 0
\(767\) −18.7750 + 16.5000i −0.677926 + 0.595780i
\(768\) 0 0
\(769\) −3.33013 12.4282i −0.120087 0.448172i 0.879530 0.475844i \(-0.157857\pi\)
−0.999617 + 0.0276717i \(0.991191\pi\)
\(770\) 0 0
\(771\) 26.8923 15.5263i 0.968503 0.559165i
\(772\) 0 0
\(773\) −15.4808 + 8.93782i −0.556804 + 0.321471i −0.751862 0.659321i \(-0.770844\pi\)
0.195058 + 0.980792i \(0.437511\pi\)
\(774\) 0 0
\(775\) 5.73205 40.1244i 0.205901 1.44131i
\(776\) 0 0
\(777\) 1.86603 0.500000i 0.0669433 0.0179374i
\(778\) 0 0
\(779\) −0.124356 −0.00445550
\(780\) 0 0
\(781\) −10.1244 −0.362278
\(782\) 0 0
\(783\) 38.9186 10.4282i 1.39084 0.372674i
\(784\) 0 0
\(785\) −7.39230 22.1769i −0.263843 0.791528i
\(786\) 0 0
\(787\) −6.91154 + 3.99038i −0.246370 + 0.142242i −0.618101 0.786099i \(-0.712098\pi\)
0.371731 + 0.928340i \(0.378764\pi\)
\(788\) 0 0
\(789\) 18.6962 10.7942i 0.665601 0.384285i
\(790\) 0 0
\(791\) 13.1603 + 49.1147i 0.467925 + 1.74632i