Properties

Label 260.2.bf.a.93.1
Level $260$
Weight $2$
Character 260.93
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.bf (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 93.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.93
Dual form 260.2.bf.a.137.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 1.86603i) q^{3} +(2.00000 + 1.00000i) q^{5} +(1.86603 - 3.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 1.86603i) q^{3} +(2.00000 + 1.00000i) q^{5} +(1.86603 - 3.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +(-0.598076 + 2.23205i) q^{11} +(2.00000 + 3.00000i) q^{13} +(-2.86603 + 3.23205i) q^{15} +(-4.23205 + 1.13397i) q^{17} +(-0.866025 + 0.232051i) q^{19} +(5.09808 + 5.09808i) q^{21} +(-6.96410 - 1.86603i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-3.09808 + 3.09808i) q^{27} +(7.96410 - 4.59808i) q^{29} +(5.73205 - 5.73205i) q^{31} +(-3.86603 - 2.23205i) q^{33} +(6.96410 - 4.59808i) q^{35} +(-0.133975 - 0.232051i) q^{37} +(-6.59808 + 2.23205i) q^{39} +(-0.133975 - 0.0358984i) q^{41} +(-3.03590 - 11.3301i) q^{43} +(-0.901924 - 1.36603i) q^{45} -0.535898 q^{47} +(-3.46410 - 6.00000i) q^{49} -8.46410i q^{51} +(-1.53590 - 1.53590i) q^{53} +(-3.42820 + 3.86603i) q^{55} -1.73205i q^{57} +(1.79423 + 6.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-2.36603 + 1.36603i) q^{63} +(1.00000 + 8.00000i) q^{65} +(-4.79423 + 2.76795i) q^{67} +(6.96410 - 12.0622i) q^{69} +(1.13397 + 4.23205i) q^{71} -12.9282i q^{73} +(-8.96410 + 3.59808i) q^{75} +(6.09808 + 6.09808i) q^{77} -4.53590i q^{79} +(-5.33013 - 9.23205i) q^{81} +3.46410 q^{83} +(-9.59808 - 1.96410i) q^{85} +(4.59808 + 17.1603i) q^{87} +(-14.7942 - 3.96410i) q^{89} +(13.4282 - 0.866025i) q^{91} +(7.83013 + 13.5622i) q^{93} +(-1.96410 - 0.401924i) q^{95} +(3.86603 + 2.23205i) q^{97} +(1.19615 - 1.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 10 q^{17} + 10 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} + 18 q^{29} + 16 q^{31} - 12 q^{33} + 14 q^{35} - 4 q^{37} - 16 q^{39} - 4 q^{41} - 26 q^{43} - 14 q^{45} - 16 q^{47} - 20 q^{53} + 14 q^{55} - 24 q^{59} + 2 q^{61} - 6 q^{63} + 4 q^{65} + 12 q^{67} + 14 q^{69} + 8 q^{71} - 22 q^{75} + 14 q^{77} - 4 q^{81} - 28 q^{85} + 8 q^{87} - 28 q^{89} + 26 q^{91} + 14 q^{93} + 6 q^{95} + 12 q^{97} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) −0.500000 + 1.86603i −0.288675 + 1.07735i 0.657437 + 0.753510i \(0.271641\pi\)
−0.946112 + 0.323840i \(0.895026\pi\)
\(4\) 0 0
\(5\) 2.00000 + 1.00000i 0.894427 + 0.447214i
\(6\) 0 0
\(7\) 1.86603 3.23205i 0.705291 1.22160i −0.261295 0.965259i \(-0.584150\pi\)
0.966586 0.256341i \(-0.0825171\pi\)
\(8\) 0 0
\(9\) −0.633975 0.366025i −0.211325 0.122008i
\(10\) 0 0
\(11\) −0.598076 + 2.23205i −0.180327 + 0.672989i 0.815256 + 0.579101i \(0.196596\pi\)
−0.995583 + 0.0938879i \(0.970070\pi\)
\(12\) 0 0
\(13\) 2.00000 + 3.00000i 0.554700 + 0.832050i
\(14\) 0 0
\(15\) −2.86603 + 3.23205i −0.740005 + 0.834512i
\(16\) 0 0
\(17\) −4.23205 + 1.13397i −1.02642 + 0.275029i −0.732476 0.680793i \(-0.761636\pi\)
−0.293947 + 0.955822i \(0.594969\pi\)
\(18\) 0 0
\(19\) −0.866025 + 0.232051i −0.198680 + 0.0532361i −0.356787 0.934186i \(-0.616128\pi\)
0.158107 + 0.987422i \(0.449461\pi\)
\(20\) 0 0
\(21\) 5.09808 + 5.09808i 1.11249 + 1.11249i
\(22\) 0 0
\(23\) −6.96410 1.86603i −1.45212 0.389093i −0.555357 0.831612i \(-0.687418\pi\)
−0.896759 + 0.442519i \(0.854085\pi\)
\(24\) 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 \(-0.340934\pi\)
0.999715 + 0.0238745i \(0.00760020\pi\)
\(30\) 0 0
\(31\) 5.73205 5.73205i 1.02951 1.02951i 0.0299555 0.999551i \(-0.490463\pi\)
0.999551 0.0299555i \(-0.00953655\pi\)
\(32\) 0 0
\(33\) −3.86603 2.23205i −0.672989 0.388550i
\(34\) 0 0
\(35\) 6.96410 4.59808i 1.17715 0.777217i
\(36\) 0 0
\(37\) −0.133975 0.232051i −0.0220253 0.0381489i 0.854803 0.518953i \(-0.173678\pi\)
−0.876828 + 0.480804i \(0.840345\pi\)
\(38\) 0 0
\(39\) −6.59808 + 2.23205i −1.05654 + 0.357414i
\(40\) 0 0
\(41\) −0.133975 0.0358984i −0.0209233 0.00560639i 0.248342 0.968672i \(-0.420114\pi\)
−0.269266 + 0.963066i \(0.586781\pi\)
\(42\) 0 0
\(43\) −3.03590 11.3301i −0.462970 1.72783i −0.663533 0.748147i \(-0.730944\pi\)
0.200563 0.979681i \(-0.435723\pi\)
\(44\) 0 0
\(45\) −0.901924 1.36603i −0.134451 0.203635i
\(46\) 0 0
\(47\) −0.535898 −0.0781688 −0.0390844 0.999236i \(-0.512444\pi\)
−0.0390844 + 0.999236i \(0.512444\pi\)
\(48\) 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
\(55\) −3.42820 + 3.86603i −0.462259 + 0.521295i
\(56\) 0 0
\(57\) 1.73205i 0.229416i
\(58\) 0 0
\(59\) 1.79423 + 6.69615i 0.233589 + 0.871765i 0.978780 + 0.204914i \(0.0656915\pi\)
−0.745191 + 0.666851i \(0.767642\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) −2.36603 + 1.36603i −0.298091 + 0.172103i
\(64\) 0 0
\(65\) 1.00000 + 8.00000i 0.124035 + 0.992278i
\(66\) 0 0
\(67\) −4.79423 + 2.76795i −0.585708 + 0.338159i −0.763399 0.645928i \(-0.776471\pi\)
0.177690 + 0.984086i \(0.443137\pi\)
\(68\) 0 0
\(69\) 6.96410 12.0622i 0.838379 1.45212i
\(70\) 0 0
\(71\) 1.13397 + 4.23205i 0.134578 + 0.502252i 0.999999 + 0.00120705i \(0.000384217\pi\)
−0.865421 + 0.501045i \(0.832949\pi\)
\(72\) 0 0
\(73\) 12.9282i 1.51313i −0.653917 0.756566i \(-0.726876\pi\)
0.653917 0.756566i \(-0.273124\pi\)
\(74\) 0 0
\(75\) −8.96410 + 3.59808i −1.03509 + 0.415470i
\(76\) 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
\(83\) 3.46410 0.380235 0.190117 0.981761i \(-0.439113\pi\)
0.190117 + 0.981761i \(0.439113\pi\)
\(84\) 0 0
\(85\) −9.59808 1.96410i −1.04106 0.213037i
\(86\) 0 0
\(87\) 4.59808 + 17.1603i 0.492966 + 1.83977i
\(88\) 0 0
\(89\) −14.7942 3.96410i −1.56819 0.420194i −0.632942 0.774199i \(-0.718153\pi\)
−0.935243 + 0.354005i \(0.884819\pi\)
\(90\) 0 0
\(91\) 13.4282 0.866025i 1.40766 0.0907841i
\(92\) 0 0
\(93\) 7.83013 + 13.5622i 0.811946 + 1.40633i
\(94\) 0 0
\(95\) −1.96410 0.401924i −0.201513 0.0412365i
\(96\) 0 0
\(97\) 3.86603 + 2.23205i 0.392535 + 0.226630i 0.683258 0.730177i \(-0.260562\pi\)
−0.290723 + 0.956807i \(0.593896\pi\)
\(98\) 0 0
\(99\) 1.19615 1.19615i 0.120218 0.120218i
\(100\) 0 0
\(101\) 1.50000 0.866025i 0.149256 0.0861727i −0.423512 0.905890i \(-0.639203\pi\)
0.572768 + 0.819718i \(0.305870\pi\)
\(102\) 0 0
\(103\) −6.66025 + 6.66025i −0.656254 + 0.656254i −0.954492 0.298237i \(-0.903601\pi\)
0.298237 + 0.954492i \(0.403601\pi\)
\(104\) 0 0
\(105\) 5.09808 + 15.2942i 0.497521 + 1.49256i
\(106\) 0 0
\(107\) −5.96410 1.59808i −0.576571 0.154492i −0.0412627 0.999148i \(-0.513138\pi\)
−0.535309 + 0.844656i \(0.679805\pi\)
\(108\) 0 0
\(109\) −9.39230 9.39230i −0.899620 0.899620i 0.0957826 0.995402i \(-0.469465\pi\)
−0.995402 + 0.0957826i \(0.969465\pi\)
\(110\) 0 0
\(111\) 0.500000 0.133975i 0.0474579 0.0127163i
\(112\) 0 0
\(113\) 13.1603 3.52628i 1.23801 0.331724i 0.420318 0.907377i \(-0.361919\pi\)
0.817695 + 0.575652i \(0.195252\pi\)
\(114\) 0 0
\(115\) −12.0622 10.6962i −1.12480 0.997421i
\(116\) 0 0
\(117\) −0.169873 2.63397i −0.0157048 0.243511i
\(118\) 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
\(123\) 0.133975 0.232051i 0.0120801 0.0209233i
\(124\) 0 0
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0 0
\(127\) 4.50000 16.7942i 0.399310 1.49025i −0.415002 0.909820i \(-0.636219\pi\)
0.814313 0.580426i \(-0.197114\pi\)
\(128\) 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
\(133\) −0.866025 + 3.23205i −0.0750939 + 0.280254i
\(134\) 0 0
\(135\) −9.29423 + 3.09808i −0.799920 + 0.266640i
\(136\) 0 0
\(137\) −0.401924 + 0.696152i −0.0343387 + 0.0594763i −0.882684 0.469967i \(-0.844266\pi\)
0.848345 + 0.529443i \(0.177599\pi\)
\(138\) 0 0
\(139\) 8.42820 + 4.86603i 0.714871 + 0.412731i 0.812862 0.582456i \(-0.197908\pi\)
−0.0979911 + 0.995187i \(0.531242\pi\)
\(140\) 0 0
\(141\) 0.267949 1.00000i 0.0225654 0.0842152i
\(142\) 0 0
\(143\) −7.89230 + 2.66987i −0.659988 + 0.223266i
\(144\) 0 0
\(145\) 20.5263 1.23205i 1.70461 0.102316i
\(146\) 0 0
\(147\) 12.9282 3.46410i 1.06630 0.285714i
\(148\) 0 0
\(149\) −18.2583 + 4.89230i −1.49578 + 0.400793i −0.911684 0.410891i \(-0.865218\pi\)
−0.584096 + 0.811684i \(0.698551\pi\)
\(150\) 0 0
\(151\) 0.803848 + 0.803848i 0.0654162 + 0.0654162i 0.739058 0.673642i \(-0.235271\pi\)
−0.673642 + 0.739058i \(0.735271\pi\)
\(152\) 0 0
\(153\) 3.09808 + 0.830127i 0.250465 + 0.0671118i
\(154\) 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
\(163\) 1.33013 + 0.767949i 0.104184 + 0.0601504i 0.551186 0.834382i \(-0.314175\pi\)
−0.447003 + 0.894533i \(0.647509\pi\)
\(164\) 0 0
\(165\) −5.50000 8.33013i −0.428174 0.648500i
\(166\) 0 0
\(167\) 3.33013 + 5.76795i 0.257693 + 0.446337i 0.965623 0.259945i \(-0.0837044\pi\)
−0.707931 + 0.706282i \(0.750371\pi\)
\(168\) 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
\(173\) 2.30385 + 8.59808i 0.175158 + 0.653700i 0.996525 + 0.0832986i \(0.0265455\pi\)
−0.821366 + 0.570401i \(0.806788\pi\)
\(174\) 0 0
\(175\) 18.5263 2.23205i 1.40046 0.168727i
\(176\) 0 0
\(177\) −13.3923 −1.00663
\(178\) 0 0
\(179\) −5.96410 10.3301i −0.445778 0.772110i 0.552328 0.833627i \(-0.313740\pi\)
−0.998106 + 0.0615168i \(0.980406\pi\)
\(180\) 0 0
\(181\) 14.9282i 1.10960i −0.831982 0.554802i \(-0.812794\pi\)
0.831982 0.554802i \(-0.187206\pi\)
\(182\) 0 0
\(183\) 1.36603 + 1.36603i 0.100980 + 0.100980i
\(184\) 0 0
\(185\) −0.0358984 0.598076i −0.00263930 0.0439714i
\(186\) 0 0
\(187\) 10.1244i 0.740366i
\(188\) 0 0
\(189\) 4.23205 + 15.7942i 0.307836 + 1.14886i
\(190\) 0 0
\(191\) −11.9641 + 20.7224i −0.865692 + 1.49942i 0.000666402 1.00000i \(0.499788\pi\)
−0.866358 + 0.499423i \(0.833545\pi\)
\(192\) 0 0
\(193\) −21.0622 + 12.1603i −1.51609 + 0.875314i −0.516267 + 0.856428i \(0.672679\pi\)
−0.999822 + 0.0188866i \(0.993988\pi\)
\(194\) 0 0
\(195\) −15.4282 2.13397i −1.10484 0.152817i
\(196\) 0 0
\(197\) −12.4019 + 7.16025i −0.883600 + 0.510147i −0.871844 0.489784i \(-0.837076\pi\)
−0.0117566 + 0.999931i \(0.503742\pi\)
\(198\) 0 0
\(199\) −4.96410 + 8.59808i −0.351896 + 0.609501i −0.986582 0.163269i \(-0.947796\pi\)
0.634686 + 0.772770i \(0.281130\pi\)
\(200\) 0 0
\(201\) −2.76795 10.3301i −0.195236 0.728631i
\(202\) 0 0
\(203\) 34.3205i 2.40883i
\(204\) 0 0
\(205\) −0.232051 0.205771i −0.0162071 0.0143717i
\(206\) 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 0.925679 0.378309i \(-0.123494\pi\)
−0.790465 + 0.612507i \(0.790161\pi\)
\(212\) 0 0
\(213\) −8.46410 −0.579951
\(214\) 0 0
\(215\) 5.25833 25.6962i 0.358615 1.75246i
\(216\) 0 0
\(217\) −7.83013 29.2224i −0.531544 1.98375i
\(218\) 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
\(223\) 8.13397 + 14.0885i 0.544691 + 0.943433i 0.998626 + 0.0523981i \(0.0166865\pi\)
−0.453935 + 0.891035i \(0.649980\pi\)
\(224\) 0 0
\(225\) −0.437822 3.63397i −0.0291881 0.242265i
\(226\) 0 0
\(227\) 5.59808 + 3.23205i 0.371557 + 0.214519i 0.674139 0.738605i \(-0.264515\pi\)
−0.302581 + 0.953124i \(0.597848\pi\)
\(228\) 0 0
\(229\) 16.8564 16.8564i 1.11390 1.11390i 0.121285 0.992618i \(-0.461299\pi\)
0.992618 0.121285i \(-0.0387015\pi\)
\(230\) 0 0
\(231\) −14.4282 + 8.33013i −0.949306 + 0.548082i
\(232\) 0 0
\(233\) 11.0000 11.0000i 0.720634 0.720634i −0.248100 0.968734i \(-0.579806\pi\)
0.968734 + 0.248100i \(0.0798063\pi\)
\(234\) 0 0
\(235\) −1.07180 0.535898i −0.0699163 0.0349582i
\(236\) 0 0
\(237\) 8.46410 + 2.26795i 0.549802 + 0.147319i
\(238\) 0 0
\(239\) −1.19615 1.19615i −0.0773727 0.0773727i 0.667361 0.744734i \(-0.267424\pi\)
−0.744734 + 0.667361i \(0.767424\pi\)
\(240\) 0 0
\(241\) −17.0622 + 4.57180i −1.09907 + 0.294495i −0.762386 0.647122i \(-0.775972\pi\)
−0.336685 + 0.941617i \(0.609306\pi\)
\(242\) 0 0
\(243\) 7.19615 1.92820i 0.461633 0.123694i
\(244\) 0 0
\(245\) −0.928203 15.4641i −0.0593007 0.987965i
\(246\) 0 0
\(247\) −2.42820 2.13397i −0.154503 0.135782i
\(248\) 0 0
\(249\) −1.73205 + 6.46410i −0.109764 + 0.409646i
\(250\) 0 0
\(251\) −3.10770 1.79423i −0.196156 0.113251i 0.398705 0.917079i \(-0.369460\pi\)
−0.594861 + 0.803828i \(0.702793\pi\)
\(252\) 0 0
\(253\) 8.33013 14.4282i 0.523711 0.907093i
\(254\) 0 0
\(255\) 8.46410 16.9282i 0.530043 1.06009i
\(256\) 0 0
\(257\) 4.16025 15.5263i 0.259510 0.968503i −0.706016 0.708196i \(-0.749510\pi\)
0.965526 0.260307i \(-0.0838238\pi\)
\(258\) 0 0
\(259\) −1.00000 −0.0621370
\(260\) 0 0
\(261\) −6.73205 −0.416703
\(262\) 0 0
\(263\) −2.89230 + 10.7942i −0.178347 + 0.665601i 0.817610 + 0.575772i \(0.195299\pi\)
−0.995957 + 0.0898284i \(0.971368\pi\)
\(264\) 0 0
\(265\) −1.53590 4.60770i −0.0943495 0.283048i
\(266\) 0 0
\(267\) 14.7942 25.6244i 0.905392 1.56819i
\(268\) 0 0
\(269\) 9.57180 + 5.52628i 0.583603 + 0.336943i 0.762564 0.646913i \(-0.223940\pi\)
−0.178961 + 0.983856i \(0.557274\pi\)
\(270\) 0 0
\(271\) −4.20577 + 15.6962i −0.255482 + 0.953473i 0.712339 + 0.701836i \(0.247636\pi\)
−0.967821 + 0.251638i \(0.919031\pi\)
\(272\) 0 0
\(273\) −5.09808 + 25.4904i −0.308550 + 1.54275i
\(274\) 0 0
\(275\) −10.7224 + 4.30385i −0.646587 + 0.259532i
\(276\) 0 0
\(277\) −11.1603 + 2.99038i −0.670555 + 0.179675i −0.578005 0.816033i \(-0.696168\pi\)
−0.0925500 + 0.995708i \(0.529502\pi\)
\(278\) 0 0
\(279\) −5.73205 + 1.53590i −0.343169 + 0.0919518i
\(280\) 0 0
\(281\) 13.3923 + 13.3923i 0.798918 + 0.798918i 0.982925 0.184007i \(-0.0589069\pi\)
−0.184007 + 0.982925i \(0.558907\pi\)
\(282\) 0 0
\(283\) 24.3564 + 6.52628i 1.44784 + 0.387947i 0.895271 0.445522i \(-0.146982\pi\)
0.552567 + 0.833469i \(0.313648\pi\)
\(284\) 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
\(293\) 13.4545 + 7.76795i 0.786019 + 0.453808i 0.838559 0.544810i \(-0.183398\pi\)
−0.0525400 + 0.998619i \(0.516732\pi\)
\(294\) 0 0
\(295\) −3.10770 + 15.1865i −0.180937 + 0.884194i
\(296\) 0 0
\(297\) −5.06218 8.76795i −0.293737 0.508768i
\(298\) 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
\(303\) 0.866025 + 3.23205i 0.0497519 + 0.185676i
\(304\) 0 0
\(305\) 1.86603 1.23205i 0.106848 0.0705470i
\(306\) 0 0
\(307\) −9.60770 −0.548340 −0.274170 0.961681i \(-0.588403\pi\)
−0.274170 + 0.961681i \(0.588403\pi\)
\(308\) 0 0
\(309\) −9.09808 15.7583i −0.517571 0.896460i
\(310\) 0 0
\(311\) 32.2487i 1.82866i −0.404974 0.914328i \(-0.632719\pi\)
0.404974 0.914328i \(-0.367281\pi\)
\(312\) 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
\(315\) −6.09808 + 0.366025i −0.343588 + 0.0206232i
\(316\) 0 0
\(317\) 16.9282i 0.950783i 0.879774 + 0.475391i \(0.157694\pi\)
−0.879774 + 0.475391i \(0.842306\pi\)
\(318\) 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
\(323\) 3.40192 1.96410i 0.189288 0.109286i
\(324\) 0 0
\(325\) −6.00000 + 17.0000i −0.332820 + 0.942990i
\(326\) 0 0
\(327\) 22.2224 12.8301i 1.22890 0.709508i
\(328\) 0 0
\(329\) −1.00000 + 1.73205i −0.0551318 + 0.0954911i
\(330\) 0 0
\(331\) 1.66987 + 6.23205i 0.0917845 + 0.342544i 0.996512 0.0834456i \(-0.0265925\pi\)
−0.904728 + 0.425990i \(0.859926\pi\)
\(332\) 0 0
\(333\) 0.196152i 0.0107491i
\(334\) 0 0
\(335\) −12.3564 + 0.741670i −0.675103 + 0.0405217i
\(336\) 0 0
\(337\) 13.9282 + 13.9282i 0.758718 + 0.758718i 0.976089 0.217371i \(-0.0697483\pi\)
−0.217371 + 0.976089i \(0.569748\pi\)
\(338\) 0 0
\(339\) 26.3205i 1.42953i
\(340\) 0 0
\(341\) 9.36603 + 16.2224i 0.507199 + 0.878494i
\(342\) 0 0
\(343\) 0.267949 0.0144679
\(344\) 0 0
\(345\) 25.9904 17.1603i 1.39928 0.923877i
\(346\) 0 0
\(347\) 4.10770 + 15.3301i 0.220513 + 0.822964i 0.984153 + 0.177322i \(0.0567435\pi\)
−0.763640 + 0.645642i \(0.776590\pi\)
\(348\) 0 0
\(349\) 24.5263 + 6.57180i 1.31286 + 0.351780i 0.846299 0.532708i \(-0.178826\pi\)
0.466563 + 0.884488i \(0.345492\pi\)
\(350\) 0 0
\(351\) −15.4904 3.09808i −0.826815 0.165363i
\(352\) 0 0
\(353\) 6.13397 + 10.6244i 0.326479 + 0.565477i 0.981810 0.189864i \(-0.0608046\pi\)
−0.655332 + 0.755341i \(0.727471\pi\)
\(354\) 0 0
\(355\) −1.96410 + 9.59808i −0.104244 + 0.509413i
\(356\) 0 0
\(357\) −27.3564 15.7942i −1.44785 0.835919i
\(358\) 0 0
\(359\) −23.5885 + 23.5885i −1.24495 + 1.24495i −0.287029 + 0.957922i \(0.592668\pi\)
−0.957922 + 0.287029i \(0.907332\pi\)
\(360\) 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
\(367\) 17.8923 + 4.79423i 0.933971 + 0.250257i 0.693547 0.720411i \(-0.256047\pi\)
0.240424 + 0.970668i \(0.422714\pi\)
\(368\) 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
\(373\) −3.76795 + 1.00962i −0.195097 + 0.0522761i −0.355044 0.934849i \(-0.615534\pi\)
0.159947 + 0.987126i \(0.448868\pi\)
\(374\) 0 0
\(375\) −21.5263 1.76795i −1.11161 0.0912965i
\(376\) 0 0
\(377\) 29.7224 + 14.6962i 1.53078 + 0.756890i
\(378\) 0 0
\(379\) −4.47372 + 16.6962i −0.229800 + 0.857624i 0.750625 + 0.660729i \(0.229753\pi\)
−0.980425 + 0.196895i \(0.936914\pi\)
\(380\) 0 0
\(381\) 29.0885 + 16.7942i 1.49025 + 0.860394i
\(382\) 0 0
\(383\) 5.59808 9.69615i 0.286048 0.495450i −0.686815 0.726833i \(-0.740992\pi\)
0.972863 + 0.231382i \(0.0743249\pi\)
\(384\) 0 0
\(385\) 6.09808 + 18.2942i 0.310787 + 0.932360i
\(386\) 0 0
\(387\) −2.22243 + 8.29423i −0.112973 + 0.421619i
\(388\) 0 0
\(389\) −23.8564 −1.20957 −0.604784 0.796390i \(-0.706741\pi\)
−0.604784 + 0.796390i \(0.706741\pi\)
\(390\) 0 0
\(391\) 31.5885 1.59750
\(392\) 0 0
\(393\) −6.92820 + 25.8564i −0.349482 + 1.30428i
\(394\) 0 0
\(395\) 4.53590 9.07180i 0.228226 0.456452i
\(396\) 0 0
\(397\) −18.2583 + 31.6244i −0.916359 + 1.58718i −0.111460 + 0.993769i \(0.535553\pi\)
−0.804899 + 0.593412i \(0.797780\pi\)
\(398\) 0 0
\(399\) −5.59808 3.23205i −0.280254 0.161805i
\(400\) 0 0
\(401\) 4.13397 15.4282i 0.206441 0.770448i −0.782565 0.622569i \(-0.786089\pi\)
0.989006 0.147878i \(-0.0472444\pi\)
\(402\) 0 0
\(403\) 28.6603 + 5.73205i 1.42767 + 0.285534i
\(404\) 0 0
\(405\) −1.42820 23.7942i −0.0709680 1.18234i
\(406\) 0 0
\(407\) 0.598076 0.160254i 0.0296455 0.00794350i
\(408\) 0 0
\(409\) 9.06218 2.42820i 0.448096 0.120067i −0.0277124 0.999616i \(-0.508822\pi\)
0.475808 + 0.879549i \(0.342156\pi\)
\(410\) 0 0
\(411\) −1.09808 1.09808i −0.0541641 0.0541641i
\(412\) 0 0
\(413\) 24.9904 + 6.69615i 1.22970 + 0.329496i
\(414\) 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 \(-0.663467\pi\)
0.508681 + 0.860955i \(0.330133\pi\)
\(420\) 0 0
\(421\) 27.9282 27.9282i 1.36114 1.36114i 0.488667 0.872470i \(-0.337483\pi\)
0.872470 0.488667i \(-0.162517\pi\)
\(422\) 0 0
\(423\) 0.339746 + 0.196152i 0.0165190 + 0.00953726i
\(424\) 0 0
\(425\) −17.2321 13.5263i −0.835877 0.656121i
\(426\) 0 0
\(427\) −1.86603 3.23205i −0.0903033 0.156410i
\(428\) 0 0
\(429\) −1.03590 16.0622i −0.0500136 0.775489i
\(430\) 0 0
\(431\) 27.5263 + 7.37564i 1.32589 + 0.355272i 0.851183 0.524869i \(-0.175886\pi\)
0.474711 + 0.880142i \(0.342552\pi\)
\(432\) 0 0
\(433\) −7.16025 26.7224i −0.344100 1.28420i −0.893660 0.448744i \(-0.851871\pi\)
0.549560 0.835454i \(-0.314795\pi\)
\(434\) 0 0
\(435\) −7.96410 + 38.9186i −0.381849 + 1.86600i
\(436\) 0 0
\(437\) 6.46410 0.309220
\(438\) 0 0
\(439\) 0.964102 + 1.66987i 0.0460141 + 0.0796987i 0.888115 0.459621i \(-0.152015\pi\)
−0.842101 + 0.539320i \(0.818681\pi\)
\(440\) 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
\(445\) −25.6244 22.7224i −1.21471 1.07715i
\(446\) 0 0
\(447\) 36.5167i 1.72718i
\(448\) 0 0
\(449\) −1.99038 7.42820i −0.0939319 0.350559i 0.902923 0.429801i \(-0.141416\pi\)
−0.996855 + 0.0792428i \(0.974750\pi\)
\(450\) 0 0
\(451\) 0.160254 0.277568i 0.00754607 0.0130702i
\(452\) 0 0
\(453\) −1.90192 + 1.09808i −0.0893602 + 0.0515921i
\(454\) 0 0
\(455\) 27.7224 + 11.6962i 1.29965 + 0.548324i
\(456\) 0 0
\(457\) 7.45448 4.30385i 0.348706 0.201325i −0.315409 0.948956i \(-0.602142\pi\)
0.664115 + 0.747630i \(0.268808\pi\)
\(458\) 0 0
\(459\) 9.59808 16.6244i 0.448000 0.775958i
\(460\) 0 0
\(461\) 1.99038 + 7.42820i 0.0927013 + 0.345966i 0.996661 0.0816519i \(-0.0260196\pi\)
−0.903960 + 0.427618i \(0.859353\pi\)
\(462\) 0 0
\(463\) 2.14359i 0.0996212i −0.998759 0.0498106i \(-0.984138\pi\)
0.998759 0.0498106i \(-0.0158618\pi\)
\(464\) 0 0
\(465\) 2.09808 + 34.9545i 0.0972960 + 1.62098i
\(466\) 0 0
\(467\) 4.12436 + 4.12436i 0.190852 + 0.190852i 0.796064 0.605212i \(-0.206912\pi\)
−0.605212 + 0.796064i \(0.706912\pi\)
\(468\) 0 0
\(469\) 20.6603i 0.954002i
\(470\) 0 0
\(471\) −10.0981 17.4904i −0.465295 0.805914i
\(472\) 0 0
\(473\) 27.1051 1.24629
\(474\) 0 0
\(475\) −3.52628 2.76795i −0.161797 0.127002i
\(476\) 0 0
\(477\) 0.411543 + 1.53590i 0.0188432 + 0.0703240i
\(478\) 0 0
\(479\) −26.9904 7.23205i −1.23322 0.330441i −0.417389 0.908728i \(-0.637055\pi\)
−0.815833 + 0.578287i \(0.803721\pi\)
\(480\) 0 0
\(481\) 0.428203 0.866025i 0.0195244 0.0394874i
\(482\) 0 0
\(483\) −25.9904 45.0167i −1.18260 2.04833i
\(484\) 0 0
\(485\) 5.50000 + 8.33013i 0.249742 + 0.378252i
\(486\) 0 0
\(487\) 0.277568 + 0.160254i 0.0125778 + 0.00726180i 0.506276 0.862372i \(-0.331022\pi\)
−0.493698 + 0.869633i \(0.664355\pi\)
\(488\) 0 0
\(489\) −2.09808 + 2.09808i −0.0948783 + 0.0948783i
\(490\) 0 0
\(491\) −7.03590 + 4.06218i −0.317526 + 0.183324i −0.650289 0.759687i \(-0.725352\pi\)
0.332763 + 0.943010i \(0.392019\pi\)
\(492\) 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
\(497\) 15.7942 + 4.23205i 0.708468 + 0.189833i
\(498\) 0 0
\(499\) 7.19615 + 7.19615i 0.322144 + 0.322144i 0.849589 0.527445i \(-0.176850\pi\)
−0.527445 + 0.849589i \(0.676850\pi\)
\(500\) 0 0
\(501\) −12.4282 + 3.33013i −0.555251 + 0.148779i
\(502\) 0 0
\(503\) −10.9641 + 2.93782i −0.488865 + 0.130991i −0.494828 0.868991i \(-0.664769\pi\)
0.00596240 + 0.999982i \(0.498102\pi\)
\(504\) 0 0
\(505\) 3.86603 0.232051i 0.172036 0.0103261i
\(506\) 0 0
\(507\) −19.8923 15.3301i −0.883448 0.680835i
\(508\) 0 0
\(509\) 6.79423 25.3564i 0.301149 1.12390i −0.635061 0.772462i \(-0.719025\pi\)
0.936210 0.351441i \(-0.114308\pi\)
\(510\) 0 0
\(511\) −41.7846 24.1244i −1.84844 1.06720i
\(512\) 0 0
\(513\) 1.96410 3.40192i 0.0867172 0.150199i
\(514\) 0 0
\(515\) −19.9808 + 6.66025i −0.880458 + 0.293486i
\(516\) 0 0
\(517\) 0.320508 1.19615i 0.0140959 0.0526067i
\(518\) 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
\(523\) 0.820508 3.06218i 0.0358783 0.133900i −0.945664 0.325146i \(-0.894586\pi\)
0.981542 + 0.191247i \(0.0612531\pi\)
\(524\) 0 0
\(525\) −5.09808 + 35.6865i −0.222498 + 1.55749i
\(526\) 0 0
\(527\) −17.7583 + 30.7583i −0.773565 + 1.33985i
\(528\) 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
\(533\) −0.160254 0.473721i −0.00694137 0.0205191i
\(534\) 0 0
\(535\) −10.3301 9.16025i −0.446610 0.396032i
\(536\) 0 0
\(537\) 22.2583 5.96410i 0.960518 0.257370i
\(538\) 0 0
\(539\) 15.4641 4.14359i 0.666086 0.178477i
\(540\) 0 0
\(541\) 27.9282 + 27.9282i 1.20073 + 1.20073i 0.973946 + 0.226782i \(0.0728204\pi\)
0.226782 + 0.973946i \(0.427180\pi\)
\(542\) 0 0
\(543\) 27.8564 + 7.46410i 1.19543 + 0.320315i
\(544\) 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
\(553\) −14.6603 8.46410i −0.623417 0.359930i
\(554\) 0 0
\(555\) 1.13397 + 0.232051i 0.0481345 + 0.00985001i
\(556\) 0 0
\(557\) 12.2583 + 21.2321i 0.519402 + 0.899631i 0.999746 + 0.0225505i \(0.00717864\pi\)
−0.480344 + 0.877080i \(0.659488\pi\)
\(558\) 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
\(563\) 2.82051 + 10.5263i 0.118870 + 0.443630i 0.999547 0.0300874i \(-0.00957856\pi\)
−0.880677 + 0.473717i \(0.842912\pi\)
\(564\) 0 0
\(565\) 29.8468 + 6.10770i 1.25566 + 0.256953i
\(566\) 0 0
\(567\) −39.7846 −1.67080
\(568\) 0 0
\(569\) −15.4282 26.7224i −0.646784 1.12026i −0.983886 0.178795i \(-0.942780\pi\)
0.337102 0.941468i \(-0.390553\pi\)
\(570\) 0 0
\(571\) 34.1051i 1.42725i 0.700525 + 0.713627i \(0.252949\pi\)
−0.700525 + 0.713627i \(0.747051\pi\)
\(572\) 0 0
\(573\) −32.6865 32.6865i −1.36550 1.36550i
\(574\) 0 0
\(575\) −13.4282 33.4545i −0.559995 1.39515i
\(576\) 0 0
\(577\) 15.0718i 0.627447i 0.949514 + 0.313724i \(0.101577\pi\)
−0.949514 + 0.313724i \(0.898423\pi\)
\(578\) 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
\(583\) 4.34679 2.50962i 0.180026 0.103938i
\(584\) 0 0
\(585\) 2.29423 5.43782i 0.0948547 0.224826i
\(586\) 0 0
\(587\) 7.20577 4.16025i 0.297414 0.171712i −0.343867 0.939019i \(-0.611737\pi\)
0.641281 + 0.767306i \(0.278403\pi\)
\(588\) 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
\(593\) 20.9282i 0.859418i −0.902967 0.429709i \(-0.858616\pi\)
0.902967 0.429709i \(-0.141384\pi\)
\(594\) 0 0
\(595\) −24.2583 + 27.3564i −0.994495 + 1.12150i
\(596\) 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 −0.946997 0.321242i \(-0.895900\pi\)
0.195295 0.980745i \(-0.437434\pi\)
\(602\) 0 0
\(603\) 4.05256 0.165033
\(604\) 0 0
\(605\) 6.97372 + 10.5622i 0.283522 + 0.429414i
\(606\) 0 0
\(607\) −5.64359 21.0622i −0.229066 0.854887i −0.980734 0.195346i \(-0.937417\pi\)
0.751668 0.659542i \(-0.229250\pi\)
\(608\) 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
\(613\) −3.33013 5.76795i −0.134503 0.232965i 0.790905 0.611939i \(-0.209610\pi\)
−0.925407 + 0.378974i \(0.876277\pi\)
\(614\) 0 0
\(615\) 0.500000 0.330127i 0.0201619 0.0133120i
\(616\) 0 0
\(617\) −26.1340 15.0885i −1.05211 0.607438i −0.128874 0.991661i \(-0.541136\pi\)
−0.923240 + 0.384223i \(0.874470\pi\)
\(618\) 0 0
\(619\) −30.1244 + 30.1244i −1.21080 + 1.21080i −0.240036 + 0.970764i \(0.577159\pi\)
−0.970764 + 0.240036i \(0.922841\pi\)
\(620\) 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
\(627\) 3.86603 + 1.03590i 0.154394 + 0.0413698i
\(628\) 0 0
\(629\) 0.830127 + 0.830127i 0.0330993 + 0.0330993i
\(630\) 0 0
\(631\) 21.7942 5.83975i 0.867615 0.232477i 0.202559 0.979270i \(-0.435074\pi\)
0.665056 + 0.746794i \(0.268408\pi\)
\(632\) 0 0
\(633\) −7.33013 + 1.96410i −0.291346 + 0.0780660i
\(634\) 0 0
\(635\) 25.7942 29.0885i 1.02361 1.15434i
\(636\) 0 0
\(637\) 11.0718 22.3923i 0.438681 0.887215i
\(638\) 0 0
\(639\) 0.830127 3.09808i 0.0328393 0.122558i
\(640\) 0 0
\(641\) −1.28461 0.741670i −0.0507390 0.0292942i 0.474416 0.880301i \(-0.342659\pi\)
−0.525155 + 0.851007i \(0.675993\pi\)
\(642\) 0 0
\(643\) −22.6506 + 39.2321i −0.893254 + 1.54716i −0.0573029 + 0.998357i \(0.518250\pi\)
−0.835951 + 0.548804i \(0.815083\pi\)
\(644\) 0 0
\(645\) 45.3205 + 22.6603i 1.78449 + 0.892247i
\(646\) 0 0
\(647\) 3.96410 14.7942i 0.155845 0.581621i −0.843187 0.537621i \(-0.819323\pi\)
0.999032 0.0440001i \(-0.0140102\pi\)
\(648\) 0 0
\(649\) −16.0192 −0.628810
\(650\) 0 0
\(651\) 58.4449 2.29063
\(652\) 0 0
\(653\) 9.69615 36.1865i 0.379440 1.41609i −0.467308 0.884094i \(-0.654776\pi\)
0.846748 0.531994i \(-0.178557\pi\)
\(654\) 0 0
\(655\) 27.7128 + 13.8564i 1.08283 + 0.541415i
\(656\) 0 0
\(657\) −4.73205 + 8.19615i −0.184615 + 0.319762i
\(658\) 0 0
\(659\) −26.2128 15.1340i −1.02111 0.589536i −0.106682 0.994293i \(-0.534023\pi\)
−0.914424 + 0.404757i \(0.867356\pi\)
\(660\) 0 0
\(661\) 3.59808 13.4282i 0.139949 0.522297i −0.859979 0.510329i \(-0.829524\pi\)
0.999928 0.0119679i \(-0.00380959\pi\)
\(662\) 0 0
\(663\) 25.3923 16.9282i 0.986155 0.657437i
\(664\) 0 0
\(665\) −4.96410 + 5.59808i −0.192500 + 0.217084i
\(666\) 0 0
\(667\) −64.0429 + 17.1603i −2.47975 + 0.664448i
\(668\) 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
\(673\) 3.76795 + 1.00962i 0.145244 + 0.0389180i 0.330708 0.943733i \(-0.392712\pi\)
−0.185465 + 0.982651i \(0.559379\pi\)
\(674\) 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
\(683\) −20.3827 11.7679i −0.779922 0.450288i 0.0564808 0.998404i \(-0.482012\pi\)
−0.836403 + 0.548116i \(0.815345\pi\)
\(684\) 0 0
\(685\) −1.50000 + 0.990381i −0.0573121 + 0.0378405i
\(686\) 0 0
\(687\) 23.0263 + 39.8827i 0.878507 + 1.52162i
\(688\) 0 0
\(689\) 1.53590 7.67949i 0.0585131 0.292565i
\(690\) 0 0
\(691\) 12.0622 + 3.23205i 0.458867 + 0.122953i 0.480845 0.876805i \(-0.340330\pi\)
−0.0219785 + 0.999758i \(0.506997\pi\)
\(692\) 0 0
\(693\) −1.63397 6.09808i −0.0620696 0.231647i
\(694\) 0 0
\(695\) 11.9904 + 18.1603i 0.454821 + 0.688858i
\(696\) 0 0
\(697\) 0.607695 0.0230181
\(698\) 0 0
\(699\) 15.0263 + 26.0263i 0.568346 + 0.984404i
\(700\) 0 0
\(701\) 42.9282i 1.62138i 0.585479 + 0.810688i \(0.300907\pi\)
−0.585479 + 0.810688i \(0.699093\pi\)
\(702\) 0 0
\(703\) 0.169873 + 0.169873i 0.00640688 + 0.00640688i
\(704\) 0 0
\(705\) 1.53590 1.73205i 0.0578453 0.0652328i
\(706\) 0 0
\(707\) 6.46410i 0.243108i
\(708\) 0 0
\(709\) 0.401924 + 1.50000i 0.0150946 + 0.0563337i 0.973062 0.230542i \(-0.0740500\pi\)
−0.957968 + 0.286876i \(0.907383\pi\)
\(710\) 0 0
\(711\) −1.66025 + 2.87564i −0.0622644 + 0.107845i
\(712\) 0 0
\(713\) −50.6147 + 29.2224i −1.89554 + 1.09439i
\(714\) 0 0
\(715\) −18.4545 2.55256i −0.690159 0.0954603i
\(716\) 0 0
\(717\) 2.83013 1.63397i 0.105693 0.0610219i
\(718\) 0 0
\(719\) −5.89230 + 10.2058i −0.219746 + 0.380611i −0.954730 0.297473i \(-0.903856\pi\)
0.734984 + 0.678084i \(0.237189\pi\)
\(720\) 0 0
\(721\) 9.09808 + 33.9545i 0.338830 + 1.26453i
\(722\) 0 0
\(723\) 34.1244i 1.26910i
\(724\) 0 0
\(725\) 42.2846 + 18.0622i 1.57041 + 0.670812i
\(726\) 0 0
\(727\) 17.5885 + 17.5885i 0.652320 + 0.652320i 0.953551 0.301231i \(-0.0973976\pi\)
−0.301231 + 0.953551i \(0.597398\pi\)
\(728\) 0 0
\(729\) 17.5885i 0.651424i
\(730\) 0 0
\(731\) 25.6962 + 44.5070i 0.950407 + 1.64615i
\(732\) 0 0
\(733\) 30.6410 1.13175 0.565876 0.824490i \(-0.308538\pi\)
0.565876 + 0.824490i \(0.308538\pi\)
\(734\) 0 0
\(735\) 29.3205 + 6.00000i 1.08150 + 0.221313i
\(736\) 0 0
\(737\) −3.31089 12.3564i −0.121958 0.455154i
\(738\) 0 0
\(739\) 33.2583 + 8.91154i 1.22343 + 0.327816i 0.812017 0.583634i \(-0.198370\pi\)
0.411410 + 0.911450i \(0.365036\pi\)
\(740\) 0 0
\(741\) 5.19615 3.46410i 0.190885 0.127257i
\(742\) 0 0
\(743\) −12.4019 21.4808i −0.454982 0.788053i 0.543705 0.839277i \(-0.317021\pi\)
−0.998687 + 0.0512238i \(0.983688\pi\)
\(744\) 0 0
\(745\) −41.4090 8.47372i −1.51711 0.310453i
\(746\) 0 0
\(747\) −2.19615 1.26795i −0.0803530 0.0463918i
\(748\) 0 0
\(749\) −16.2942 + 16.2942i −0.595378 + 0.595378i
\(750\) 0 0
\(751\) −16.7487 + 9.66987i −0.611169 + 0.352859i −0.773423 0.633890i \(-0.781457\pi\)
0.162254 + 0.986749i \(0.448124\pi\)
\(752\) 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
\(757\) −14.6962 3.93782i −0.534141 0.143123i −0.0183410 0.999832i \(-0.505838\pi\)
−0.515800 + 0.856709i \(0.672505\pi\)
\(758\) 0 0
\(759\) 22.7583 + 22.7583i 0.826075 + 0.826075i
\(760\) 0 0
\(761\) 11.3301 3.03590i 0.410717 0.110051i −0.0475437 0.998869i \(-0.515139\pi\)
0.458261 + 0.888818i \(0.348473\pi\)
\(762\) 0 0
\(763\) −47.8827 + 12.8301i −1.73347 + 0.464482i
\(764\) 0 0
\(765\) 5.36603 + 4.75833i 0.194009 + 0.172038i
\(766\) 0 0
\(767\) −16.5000 + 18.7750i −0.595780 + 0.677926i
\(768\) 0 0
\(769\) 3.33013 12.4282i 0.120087 0.448172i −0.879530 0.475844i \(-0.842143\pi\)
0.999617 + 0.0276717i \(0.00880929\pi\)
\(770\) 0 0
\(771\) 26.8923 + 15.5263i 0.968503 + 0.559165i
\(772\) 0 0
\(773\) 8.93782 15.4808i 0.321471 0.556804i −0.659321 0.751862i \(-0.729156\pi\)
0.980792 + 0.195058i \(0.0624894\pi\)
\(774\) 0 0
\(775\) 40.1244 + 5.73205i 1.44131 + 0.205901i
\(776\) 0 0
\(777\) 0.500000 1.86603i 0.0179374 0.0669433i
\(778\) 0 0
\(779\) 0.124356 0.00445550
\(780\) 0 0
\(781\) −10.1244 −0.362278
\(782\) 0 0
\(783\) −10.4282 + 38.9186i −0.372674 + 1.39084i
\(784\) 0 0
\(785\) −22.1769 + 7.39230i −0.791528 + 0.263843i
\(786\) 0 0
\(787\) −3.99038 + 6.91154i −0.142242 + 0.246370i −0.928340 0.371731i \(-0.878764\pi\)
0.786099 + 0.618101i \(0.212098\pi\)
\(788\) 0 0
\(789\) −18.6962 10.7942i −0.665601 0.384285i
\(790\) 0 0
\(791\) 13.1603 49.1147i