Properties

Label 576.2.bb.b.529.1
Level $576$
Weight $2$
Character 576.529
Analytic conductor $4.599$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 529.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.529
Dual form 576.2.bb.b.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205i q^{3} +(0.500000 + 0.133975i) q^{5} +(2.13397 + 1.23205i) q^{7} -3.00000 q^{9} +O(q^{10})\) \(q+1.73205i q^{3} +(0.500000 + 0.133975i) q^{5} +(2.13397 + 1.23205i) q^{7} -3.00000 q^{9} +(-0.133975 - 0.500000i) q^{11} +(-1.23205 + 4.59808i) q^{13} +(-0.232051 + 0.866025i) q^{15} +4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(-2.13397 + 3.69615i) q^{21} +(-0.401924 + 0.232051i) q^{23} +(-4.09808 - 2.36603i) q^{25} -5.19615i q^{27} +(-3.23205 + 0.866025i) q^{29} +(-0.598076 - 1.03590i) q^{31} +(0.866025 - 0.232051i) q^{33} +(0.901924 + 0.901924i) q^{35} +(-7.73205 + 7.73205i) q^{37} +(-7.96410 - 2.13397i) q^{39} +(9.69615 - 5.59808i) q^{41} +(2.33013 + 8.69615i) q^{43} +(-1.50000 - 0.401924i) q^{45} +(-4.59808 + 7.96410i) q^{47} +(-0.464102 - 0.803848i) q^{49} +6.92820i q^{51} +(2.26795 - 2.26795i) q^{53} -0.267949i q^{55} +(-5.19615 + 5.19615i) q^{57} +(-5.59808 - 1.50000i) q^{59} +(14.4282 - 3.86603i) q^{61} +(-6.40192 - 3.69615i) q^{63} +(-1.23205 + 2.13397i) q^{65} +(0.330127 - 1.23205i) q^{67} +(-0.401924 - 0.696152i) q^{69} -10.9282i q^{71} +0.535898i q^{73} +(4.09808 - 7.09808i) q^{75} +(0.330127 - 1.23205i) q^{77} +(-0.866025 + 1.50000i) q^{79} +9.00000 q^{81} +(11.7942 - 3.16025i) q^{83} +(2.00000 + 0.535898i) q^{85} +(-1.50000 - 5.59808i) q^{87} -11.8564i q^{89} +(-8.29423 + 8.29423i) q^{91} +(1.79423 - 1.03590i) q^{93} +(1.09808 + 1.90192i) q^{95} +(-0.500000 + 0.866025i) q^{97} +(0.401924 + 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{5} + 12 q^{7} - 12 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{5} + 12 q^{7} - 12 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{15} + 16 q^{17} + 12 q^{19} - 12 q^{21} - 12 q^{23} - 6 q^{25} - 6 q^{29} + 8 q^{31} + 14 q^{35} - 24 q^{37} - 18 q^{39} + 18 q^{41} - 8 q^{43} - 6 q^{45} - 8 q^{47} + 12 q^{49} + 16 q^{53} - 12 q^{59} + 30 q^{61} - 36 q^{63} + 2 q^{65} - 16 q^{67} - 12 q^{69} + 6 q^{75} - 16 q^{77} + 36 q^{81} + 16 q^{83} + 8 q^{85} - 6 q^{87} - 2 q^{91} - 24 q^{93} - 6 q^{95} - 2 q^{97} + 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 1.73205i 1.00000i
\(4\) 0 0
\(5\) 0.500000 + 0.133975i 0.223607 + 0.0599153i 0.368883 0.929476i \(-0.379740\pi\)
−0.145276 + 0.989391i \(0.546407\pi\)
\(6\) 0 0
\(7\) 2.13397 + 1.23205i 0.806567 + 0.465671i 0.845762 0.533560i \(-0.179146\pi\)
−0.0391956 + 0.999232i \(0.512480\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) −0.133975 0.500000i −0.0403949 0.150756i 0.942783 0.333408i \(-0.108199\pi\)
−0.983178 + 0.182652i \(0.941532\pi\)
\(12\) 0 0
\(13\) −1.23205 + 4.59808i −0.341709 + 1.27528i 0.554700 + 0.832050i \(0.312833\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) 0 0
\(15\) −0.232051 + 0.866025i −0.0599153 + 0.223607i
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 3.00000 + 3.00000i 0.688247 + 0.688247i 0.961844 0.273597i \(-0.0882135\pi\)
−0.273597 + 0.961844i \(0.588214\pi\)
\(20\) 0 0
\(21\) −2.13397 + 3.69615i −0.465671 + 0.806567i
\(22\) 0 0
\(23\) −0.401924 + 0.232051i −0.0838069 + 0.0483859i −0.541318 0.840818i \(-0.682074\pi\)
0.457511 + 0.889204i \(0.348741\pi\)
\(24\) 0 0
\(25\) −4.09808 2.36603i −0.819615 0.473205i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −3.23205 + 0.866025i −0.600177 + 0.160817i −0.546100 0.837720i \(-0.683888\pi\)
−0.0540766 + 0.998537i \(0.517222\pi\)
\(30\) 0 0
\(31\) −0.598076 1.03590i −0.107418 0.186053i 0.807306 0.590133i \(-0.200925\pi\)
−0.914723 + 0.404081i \(0.867592\pi\)
\(32\) 0 0
\(33\) 0.866025 0.232051i 0.150756 0.0403949i
\(34\) 0 0
\(35\) 0.901924 + 0.901924i 0.152453 + 0.152453i
\(36\) 0 0
\(37\) −7.73205 + 7.73205i −1.27114 + 1.27114i −0.325651 + 0.945490i \(0.605584\pi\)
−0.945490 + 0.325651i \(0.894416\pi\)
\(38\) 0 0
\(39\) −7.96410 2.13397i −1.27528 0.341709i
\(40\) 0 0
\(41\) 9.69615 5.59808i 1.51428 0.874273i 0.514425 0.857536i \(-0.328006\pi\)
0.999860 0.0167371i \(-0.00532782\pi\)
\(42\) 0 0
\(43\) 2.33013 + 8.69615i 0.355341 + 1.32615i 0.880055 + 0.474872i \(0.157506\pi\)
−0.524714 + 0.851279i \(0.675828\pi\)
\(44\) 0 0
\(45\) −1.50000 0.401924i −0.223607 0.0599153i
\(46\) 0 0
\(47\) −4.59808 + 7.96410i −0.670698 + 1.16168i 0.307008 + 0.951707i \(0.400672\pi\)
−0.977706 + 0.209977i \(0.932661\pi\)
\(48\) 0 0
\(49\) −0.464102 0.803848i −0.0663002 0.114835i
\(50\) 0 0
\(51\) 6.92820i 0.970143i
\(52\) 0 0
\(53\) 2.26795 2.26795i 0.311527 0.311527i −0.533974 0.845501i \(-0.679302\pi\)
0.845501 + 0.533974i \(0.179302\pi\)
\(54\) 0 0
\(55\) 0.267949i 0.0361303i
\(56\) 0 0
\(57\) −5.19615 + 5.19615i −0.688247 + 0.688247i
\(58\) 0 0
\(59\) −5.59808 1.50000i −0.728807 0.195283i −0.124709 0.992193i \(-0.539800\pi\)
−0.604098 + 0.796910i \(0.706467\pi\)
\(60\) 0 0
\(61\) 14.4282 3.86603i 1.84734 0.494994i 0.847957 0.530065i \(-0.177832\pi\)
0.999385 + 0.0350707i \(0.0111656\pi\)
\(62\) 0 0
\(63\) −6.40192 3.69615i −0.806567 0.465671i
\(64\) 0 0
\(65\) −1.23205 + 2.13397i −0.152817 + 0.264687i
\(66\) 0 0
\(67\) 0.330127 1.23205i 0.0403314 0.150519i −0.942824 0.333292i \(-0.891841\pi\)
0.983155 + 0.182773i \(0.0585073\pi\)
\(68\) 0 0
\(69\) −0.401924 0.696152i −0.0483859 0.0838069i
\(70\) 0 0
\(71\) 10.9282i 1.29694i −0.761241 0.648470i \(-0.775409\pi\)
0.761241 0.648470i \(-0.224591\pi\)
\(72\) 0 0
\(73\) 0.535898i 0.0627222i 0.999508 + 0.0313611i \(0.00998418\pi\)
−0.999508 + 0.0313611i \(0.990016\pi\)
\(74\) 0 0
\(75\) 4.09808 7.09808i 0.473205 0.819615i
\(76\) 0 0
\(77\) 0.330127 1.23205i 0.0376215 0.140405i
\(78\) 0 0
\(79\) −0.866025 + 1.50000i −0.0974355 + 0.168763i −0.910622 0.413239i \(-0.864397\pi\)
0.813187 + 0.582003i \(0.197731\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 11.7942 3.16025i 1.29458 0.346883i 0.455185 0.890397i \(-0.349573\pi\)
0.839400 + 0.543514i \(0.182907\pi\)
\(84\) 0 0
\(85\) 2.00000 + 0.535898i 0.216930 + 0.0581263i
\(86\) 0 0
\(87\) −1.50000 5.59808i −0.160817 0.600177i
\(88\) 0 0
\(89\) 11.8564i 1.25678i −0.777900 0.628388i \(-0.783715\pi\)
0.777900 0.628388i \(-0.216285\pi\)
\(90\) 0 0
\(91\) −8.29423 + 8.29423i −0.869471 + 0.869471i
\(92\) 0 0
\(93\) 1.79423 1.03590i 0.186053 0.107418i
\(94\) 0 0
\(95\) 1.09808 + 1.90192i 0.112660 + 0.195133i
\(96\) 0 0
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 0 0
\(99\) 0.401924 + 1.50000i 0.0403949 + 0.150756i
\(100\) 0 0
\(101\) 0.500000 + 1.86603i 0.0497519 + 0.185676i 0.986330 0.164783i \(-0.0526922\pi\)
−0.936578 + 0.350459i \(0.886026\pi\)
\(102\) 0 0
\(103\) −1.79423 + 1.03590i −0.176791 + 0.102070i −0.585784 0.810467i \(-0.699213\pi\)
0.408993 + 0.912537i \(0.365880\pi\)
\(104\) 0 0
\(105\) −1.56218 + 1.56218i −0.152453 + 0.152453i
\(106\) 0 0
\(107\) 11.3923 11.3923i 1.10134 1.10134i 0.107086 0.994250i \(-0.465848\pi\)
0.994250 0.107086i \(-0.0341520\pi\)
\(108\) 0 0
\(109\) 1.73205 + 1.73205i 0.165900 + 0.165900i 0.785175 0.619274i \(-0.212573\pi\)
−0.619274 + 0.785175i \(0.712573\pi\)
\(110\) 0 0
\(111\) −13.3923 13.3923i −1.27114 1.27114i
\(112\) 0 0
\(113\) −2.76795 4.79423i −0.260387 0.451003i 0.705958 0.708254i \(-0.250517\pi\)
−0.966345 + 0.257251i \(0.917183\pi\)
\(114\) 0 0
\(115\) −0.232051 + 0.0621778i −0.0216388 + 0.00579811i
\(116\) 0 0
\(117\) 3.69615 13.7942i 0.341709 1.27528i
\(118\) 0 0
\(119\) 8.53590 + 4.92820i 0.782485 + 0.451768i
\(120\) 0 0
\(121\) 9.29423 5.36603i 0.844930 0.487820i
\(122\) 0 0
\(123\) 9.69615 + 16.7942i 0.874273 + 1.51428i
\(124\) 0 0
\(125\) −3.56218 3.56218i −0.318611 0.318611i
\(126\) 0 0
\(127\) 20.3923 1.80952 0.904762 0.425917i \(-0.140048\pi\)
0.904762 + 0.425917i \(0.140048\pi\)
\(128\) 0 0
\(129\) −15.0622 + 4.03590i −1.32615 + 0.355341i
\(130\) 0 0
\(131\) 3.13397 11.6962i 0.273817 1.02190i −0.682814 0.730593i \(-0.739244\pi\)
0.956630 0.291305i \(-0.0940894\pi\)
\(132\) 0 0
\(133\) 2.70577 + 10.0981i 0.234620 + 0.875614i
\(134\) 0 0
\(135\) 0.696152 2.59808i 0.0599153 0.223607i
\(136\) 0 0
\(137\) 14.4282 + 8.33013i 1.23268 + 0.711691i 0.967589 0.252531i \(-0.0812631\pi\)
0.265096 + 0.964222i \(0.414596\pi\)
\(138\) 0 0
\(139\) −4.33013 1.16025i −0.367277 0.0984115i 0.0704603 0.997515i \(-0.477553\pi\)
−0.437737 + 0.899103i \(0.644220\pi\)
\(140\) 0 0
\(141\) −13.7942 7.96410i −1.16168 0.670698i
\(142\) 0 0
\(143\) 2.46410 0.206059
\(144\) 0 0
\(145\) −1.73205 −0.143839
\(146\) 0 0
\(147\) 1.39230 0.803848i 0.114835 0.0663002i
\(148\) 0 0
\(149\) −14.6962 3.93782i −1.20396 0.322599i −0.399568 0.916704i \(-0.630840\pi\)
−0.804388 + 0.594105i \(0.797507\pi\)
\(150\) 0 0
\(151\) 6.06218 + 3.50000i 0.493333 + 0.284826i 0.725956 0.687741i \(-0.241398\pi\)
−0.232623 + 0.972567i \(0.574731\pi\)
\(152\) 0 0
\(153\) −12.0000 −0.970143
\(154\) 0 0
\(155\) −0.160254 0.598076i −0.0128719 0.0480386i
\(156\) 0 0
\(157\) −0.232051 + 0.866025i −0.0185197 + 0.0691164i −0.974567 0.224095i \(-0.928057\pi\)
0.956048 + 0.293212i \(0.0947240\pi\)
\(158\) 0 0
\(159\) 3.92820 + 3.92820i 0.311527 + 0.311527i
\(160\) 0 0
\(161\) −1.14359 −0.0901278
\(162\) 0 0
\(163\) −11.9282 11.9282i −0.934289 0.934289i 0.0636813 0.997970i \(-0.479716\pi\)
−0.997970 + 0.0636813i \(0.979716\pi\)
\(164\) 0 0
\(165\) 0.464102 0.0361303
\(166\) 0 0
\(167\) 8.25833 4.76795i 0.639049 0.368955i −0.145199 0.989402i \(-0.546382\pi\)
0.784248 + 0.620447i \(0.213049\pi\)
\(168\) 0 0
\(169\) −8.36603 4.83013i −0.643540 0.371548i
\(170\) 0 0
\(171\) −9.00000 9.00000i −0.688247 0.688247i
\(172\) 0 0
\(173\) −8.96410 + 2.40192i −0.681528 + 0.182615i −0.582942 0.812514i \(-0.698099\pi\)
−0.0985859 + 0.995129i \(0.531432\pi\)
\(174\) 0 0
\(175\) −5.83013 10.0981i −0.440716 0.763343i
\(176\) 0 0
\(177\) 2.59808 9.69615i 0.195283 0.728807i
\(178\) 0 0
\(179\) −7.92820 7.92820i −0.592582 0.592582i 0.345746 0.938328i \(-0.387626\pi\)
−0.938328 + 0.345746i \(0.887626\pi\)
\(180\) 0 0
\(181\) −4.26795 + 4.26795i −0.317234 + 0.317234i −0.847704 0.530470i \(-0.822016\pi\)
0.530470 + 0.847704i \(0.322016\pi\)
\(182\) 0 0
\(183\) 6.69615 + 24.9904i 0.494994 + 1.84734i
\(184\) 0 0
\(185\) −4.90192 + 2.83013i −0.360397 + 0.208075i
\(186\) 0 0
\(187\) −0.535898 2.00000i −0.0391888 0.146254i
\(188\) 0 0
\(189\) 6.40192 11.0885i 0.465671 0.806567i
\(190\) 0 0
\(191\) −6.59808 + 11.4282i −0.477420 + 0.826916i −0.999665 0.0258797i \(-0.991761\pi\)
0.522245 + 0.852795i \(0.325095\pi\)
\(192\) 0 0
\(193\) −1.23205 2.13397i −0.0886850 0.153607i 0.818271 0.574833i \(-0.194933\pi\)
−0.906956 + 0.421226i \(0.861600\pi\)
\(194\) 0 0
\(195\) −3.69615 2.13397i −0.264687 0.152817i
\(196\) 0 0
\(197\) 10.4641 10.4641i 0.745536 0.745536i −0.228101 0.973637i \(-0.573252\pi\)
0.973637 + 0.228101i \(0.0732517\pi\)
\(198\) 0 0
\(199\) 5.85641i 0.415150i −0.978219 0.207575i \(-0.933443\pi\)
0.978219 0.207575i \(-0.0665570\pi\)
\(200\) 0 0
\(201\) 2.13397 + 0.571797i 0.150519 + 0.0403314i
\(202\) 0 0
\(203\) −7.96410 2.13397i −0.558970 0.149776i
\(204\) 0 0
\(205\) 5.59808 1.50000i 0.390987 0.104765i
\(206\) 0 0
\(207\) 1.20577 0.696152i 0.0838069 0.0483859i
\(208\) 0 0
\(209\) 1.09808 1.90192i 0.0759555 0.131559i
\(210\) 0 0
\(211\) 0.526279 1.96410i 0.0362306 0.135214i −0.945442 0.325791i \(-0.894369\pi\)
0.981672 + 0.190577i \(0.0610359\pi\)
\(212\) 0 0
\(213\) 18.9282 1.29694
\(214\) 0 0
\(215\) 4.66025i 0.317827i
\(216\) 0 0
\(217\) 2.94744i 0.200085i
\(218\) 0 0
\(219\) −0.928203 −0.0627222
\(220\) 0 0
\(221\) −4.92820 + 18.3923i −0.331507 + 1.23720i
\(222\) 0 0
\(223\) 7.79423 13.5000i 0.521940 0.904027i −0.477734 0.878504i \(-0.658542\pi\)
0.999674 0.0255224i \(-0.00812491\pi\)
\(224\) 0 0
\(225\) 12.2942 + 7.09808i 0.819615 + 0.473205i
\(226\) 0 0
\(227\) −17.2583 + 4.62436i −1.14548 + 0.306929i −0.781151 0.624343i \(-0.785367\pi\)
−0.364325 + 0.931272i \(0.618700\pi\)
\(228\) 0 0
\(229\) 9.42820 + 2.52628i 0.623033 + 0.166941i 0.556506 0.830843i \(-0.312142\pi\)
0.0665269 + 0.997785i \(0.478808\pi\)
\(230\) 0 0
\(231\) 2.13397 + 0.571797i 0.140405 + 0.0376215i
\(232\) 0 0
\(233\) 22.9282i 1.50208i 0.660259 + 0.751038i \(0.270447\pi\)
−0.660259 + 0.751038i \(0.729553\pi\)
\(234\) 0 0
\(235\) −3.36603 + 3.36603i −0.219575 + 0.219575i
\(236\) 0 0
\(237\) −2.59808 1.50000i −0.168763 0.0974355i
\(238\) 0 0
\(239\) 5.59808 + 9.69615i 0.362109 + 0.627192i 0.988308 0.152472i \(-0.0487233\pi\)
−0.626198 + 0.779664i \(0.715390\pi\)
\(240\) 0 0
\(241\) −6.23205 + 10.7942i −0.401442 + 0.695317i −0.993900 0.110284i \(-0.964824\pi\)
0.592458 + 0.805601i \(0.298157\pi\)
\(242\) 0 0
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) −0.124356 0.464102i −0.00794479 0.0296504i
\(246\) 0 0
\(247\) −17.4904 + 10.0981i −1.11289 + 0.642525i
\(248\) 0 0
\(249\) 5.47372 + 20.4282i 0.346883 + 1.29458i
\(250\) 0 0
\(251\) −7.39230 + 7.39230i −0.466598 + 0.466598i −0.900811 0.434212i \(-0.857027\pi\)
0.434212 + 0.900811i \(0.357027\pi\)
\(252\) 0 0
\(253\) 0.169873 + 0.169873i 0.0106798 + 0.0106798i
\(254\) 0 0
\(255\) −0.928203 + 3.46410i −0.0581263 + 0.216930i
\(256\) 0 0
\(257\) −5.16025 8.93782i −0.321888 0.557526i 0.658990 0.752152i \(-0.270984\pi\)
−0.980878 + 0.194626i \(0.937651\pi\)
\(258\) 0 0
\(259\) −26.0263 + 6.97372i −1.61719 + 0.433326i
\(260\) 0 0
\(261\) 9.69615 2.59808i 0.600177 0.160817i
\(262\) 0 0
\(263\) −3.40192 1.96410i −0.209772 0.121112i 0.391434 0.920206i \(-0.371979\pi\)
−0.601205 + 0.799095i \(0.705313\pi\)
\(264\) 0 0
\(265\) 1.43782 0.830127i 0.0883247 0.0509943i
\(266\) 0 0
\(267\) 20.5359 1.25678
\(268\) 0 0
\(269\) 7.73205 + 7.73205i 0.471431 + 0.471431i 0.902378 0.430946i \(-0.141820\pi\)
−0.430946 + 0.902378i \(0.641820\pi\)
\(270\) 0 0
\(271\) 14.9282 0.906824 0.453412 0.891301i \(-0.350207\pi\)
0.453412 + 0.891301i \(0.350207\pi\)
\(272\) 0 0
\(273\) −14.3660 14.3660i −0.869471 0.869471i
\(274\) 0 0
\(275\) −0.633975 + 2.36603i −0.0382301 + 0.142677i
\(276\) 0 0
\(277\) −3.69615 13.7942i −0.222080 0.828815i −0.983553 0.180618i \(-0.942190\pi\)
0.761473 0.648197i \(-0.224477\pi\)
\(278\) 0 0
\(279\) 1.79423 + 3.10770i 0.107418 + 0.186053i
\(280\) 0 0
\(281\) 16.9641 + 9.79423i 1.01199 + 0.584275i 0.911775 0.410691i \(-0.134712\pi\)
0.100219 + 0.994965i \(0.468046\pi\)
\(282\) 0 0
\(283\) 15.5263 + 4.16025i 0.922942 + 0.247301i 0.688842 0.724911i \(-0.258119\pi\)
0.234099 + 0.972213i \(0.424786\pi\)
\(284\) 0 0
\(285\) −3.29423 + 1.90192i −0.195133 + 0.112660i
\(286\) 0 0
\(287\) 27.5885 1.62850
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −1.50000 0.866025i −0.0879316 0.0507673i
\(292\) 0 0
\(293\) −14.4282 3.86603i −0.842905 0.225856i −0.188569 0.982060i \(-0.560385\pi\)
−0.654336 + 0.756204i \(0.727052\pi\)
\(294\) 0 0
\(295\) −2.59808 1.50000i −0.151266 0.0873334i
\(296\) 0 0
\(297\) −2.59808 + 0.696152i −0.150756 + 0.0403949i
\(298\) 0 0
\(299\) −0.571797 2.13397i −0.0330679 0.123411i
\(300\) 0 0
\(301\) −5.74167 + 21.4282i −0.330944 + 1.23510i
\(302\) 0 0
\(303\) −3.23205 + 0.866025i −0.185676 + 0.0497519i
\(304\) 0 0
\(305\) 7.73205 0.442736
\(306\) 0 0
\(307\) 5.92820 + 5.92820i 0.338340 + 0.338340i 0.855742 0.517402i \(-0.173101\pi\)
−0.517402 + 0.855742i \(0.673101\pi\)
\(308\) 0 0
\(309\) −1.79423 3.10770i −0.102070 0.176791i
\(310\) 0 0
\(311\) −27.1865 + 15.6962i −1.54161 + 0.890047i −0.542869 + 0.839817i \(0.682662\pi\)
−0.998738 + 0.0502299i \(0.984005\pi\)
\(312\) 0 0
\(313\) −7.83975 4.52628i −0.443129 0.255840i 0.261795 0.965123i \(-0.415686\pi\)
−0.704924 + 0.709283i \(0.749019\pi\)
\(314\) 0 0
\(315\) −2.70577 2.70577i −0.152453 0.152453i
\(316\) 0 0
\(317\) 2.03590 0.545517i 0.114347 0.0306393i −0.201192 0.979552i \(-0.564481\pi\)
0.315539 + 0.948913i \(0.397815\pi\)
\(318\) 0 0
\(319\) 0.866025 + 1.50000i 0.0484881 + 0.0839839i
\(320\) 0 0
\(321\) 19.7321 + 19.7321i 1.10134 + 1.10134i
\(322\) 0 0
\(323\) 12.0000 + 12.0000i 0.667698 + 0.667698i
\(324\) 0 0
\(325\) 15.9282 15.9282i 0.883538 0.883538i
\(326\) 0 0
\(327\) −3.00000 + 3.00000i −0.165900 + 0.165900i
\(328\) 0 0
\(329\) −19.6244 + 11.3301i −1.08193 + 0.624650i
\(330\) 0 0
\(331\) −7.06218 26.3564i −0.388172 1.44868i −0.833105 0.553115i \(-0.813439\pi\)
0.444933 0.895564i \(-0.353228\pi\)
\(332\) 0 0
\(333\) 23.1962 23.1962i 1.27114 1.27114i
\(334\) 0 0
\(335\) 0.330127 0.571797i 0.0180368 0.0312406i
\(336\) 0 0
\(337\) 0.696152 + 1.20577i 0.0379218 + 0.0656826i 0.884363 0.466799i \(-0.154593\pi\)
−0.846442 + 0.532482i \(0.821260\pi\)
\(338\) 0 0
\(339\) 8.30385 4.79423i 0.451003 0.260387i
\(340\) 0 0
\(341\) −0.437822 + 0.437822i −0.0237094 + 0.0237094i
\(342\) 0 0
\(343\) 19.5359i 1.05484i
\(344\) 0 0
\(345\) −0.107695 0.401924i −0.00579811 0.0216388i
\(346\) 0 0
\(347\) −19.5263 5.23205i −1.04823 0.280871i −0.306707 0.951804i \(-0.599227\pi\)
−0.741518 + 0.670933i \(0.765894\pi\)
\(348\) 0 0
\(349\) 7.96410 2.13397i 0.426309 0.114229i −0.0392843 0.999228i \(-0.512508\pi\)
0.465593 + 0.884999i \(0.345841\pi\)
\(350\) 0 0
\(351\) 23.8923 + 6.40192i 1.27528 + 0.341709i
\(352\) 0 0
\(353\) −15.2321 + 26.3827i −0.810720 + 1.40421i 0.101640 + 0.994821i \(0.467591\pi\)
−0.912361 + 0.409387i \(0.865742\pi\)
\(354\) 0 0
\(355\) 1.46410 5.46410i 0.0777064 0.290004i
\(356\) 0 0
\(357\) −8.53590 + 14.7846i −0.451768 + 0.782485i
\(358\) 0 0
\(359\) 15.0718i 0.795459i 0.917503 + 0.397730i \(0.130202\pi\)
−0.917503 + 0.397730i \(0.869798\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 0 0
\(363\) 9.29423 + 16.0981i 0.487820 + 0.844930i
\(364\) 0 0
\(365\) −0.0717968 + 0.267949i −0.00375801 + 0.0140251i
\(366\) 0 0
\(367\) −15.4545 + 26.7679i −0.806717 + 1.39728i 0.108408 + 0.994106i \(0.465425\pi\)
−0.915125 + 0.403169i \(0.867909\pi\)
\(368\) 0 0
\(369\) −29.0885 + 16.7942i −1.51428 + 0.874273i
\(370\) 0 0
\(371\) 7.63397 2.04552i 0.396336 0.106198i
\(372\) 0 0
\(373\) −13.4282 3.59808i −0.695286 0.186301i −0.106168 0.994348i \(-0.533858\pi\)
−0.589118 + 0.808047i \(0.700525\pi\)
\(374\) 0 0
\(375\) 6.16987 6.16987i 0.318611 0.318611i
\(376\) 0 0
\(377\) 15.9282i 0.820344i
\(378\) 0 0
\(379\) −15.5885 + 15.5885i −0.800725 + 0.800725i −0.983209 0.182484i \(-0.941586\pi\)
0.182484 + 0.983209i \(0.441586\pi\)
\(380\) 0 0
\(381\) 35.3205i 1.80952i
\(382\) 0 0
\(383\) −12.3301 21.3564i −0.630040 1.09126i −0.987543 0.157349i \(-0.949705\pi\)
0.357503 0.933912i \(-0.383628\pi\)
\(384\) 0 0
\(385\) 0.330127 0.571797i 0.0168248 0.0291415i
\(386\) 0 0
\(387\) −6.99038 26.0885i −0.355341 1.32615i
\(388\) 0 0
\(389\) −2.03590 7.59808i −0.103224 0.385238i 0.894914 0.446240i \(-0.147237\pi\)
−0.998138 + 0.0610019i \(0.980570\pi\)
\(390\) 0 0
\(391\) −1.60770 + 0.928203i −0.0813046 + 0.0469413i
\(392\) 0 0
\(393\) 20.2583 + 5.42820i 1.02190 + 0.273817i
\(394\) 0 0
\(395\) −0.633975 + 0.633975i −0.0318987 + 0.0318987i
\(396\) 0 0
\(397\) −21.0526 21.0526i −1.05660 1.05660i −0.998299 0.0582984i \(-0.981433\pi\)
−0.0582984 0.998299i \(-0.518567\pi\)
\(398\) 0 0
\(399\) −17.4904 + 4.68653i −0.875614 + 0.234620i
\(400\) 0 0
\(401\) 1.16025 + 2.00962i 0.0579403 + 0.100356i 0.893541 0.448982i \(-0.148213\pi\)
−0.835600 + 0.549338i \(0.814880\pi\)
\(402\) 0 0
\(403\) 5.50000 1.47372i 0.273975 0.0734112i
\(404\) 0 0
\(405\) 4.50000 + 1.20577i 0.223607 + 0.0599153i
\(406\) 0 0
\(407\) 4.90192 + 2.83013i 0.242979 + 0.140284i
\(408\) 0 0
\(409\) −4.62436 + 2.66987i −0.228660 + 0.132017i −0.609954 0.792437i \(-0.708812\pi\)
0.381294 + 0.924454i \(0.375479\pi\)
\(410\) 0 0
\(411\) −14.4282 + 24.9904i −0.711691 + 1.23268i
\(412\) 0 0
\(413\) −10.0981 10.0981i −0.496894 0.496894i
\(414\) 0 0
\(415\) 6.32051 0.310262
\(416\) 0 0
\(417\) 2.00962 7.50000i 0.0984115 0.367277i
\(418\) 0 0
\(419\) 0.526279 1.96410i 0.0257104 0.0959526i −0.951878 0.306476i \(-0.900850\pi\)
0.977589 + 0.210523i \(0.0675168\pi\)
\(420\) 0 0
\(421\) −2.89230 10.7942i −0.140962 0.526079i −0.999902 0.0140017i \(-0.995543\pi\)
0.858940 0.512077i \(-0.171124\pi\)
\(422\) 0 0
\(423\) 13.7942 23.8923i 0.670698 1.16168i
\(424\) 0 0
\(425\) −16.3923 9.46410i −0.795144 0.459076i
\(426\) 0 0
\(427\) 35.5526 + 9.52628i 1.72051 + 0.461009i
\(428\) 0 0
\(429\) 4.26795i 0.206059i
\(430\) 0 0
\(431\) −31.3205 −1.50866 −0.754328 0.656498i \(-0.772037\pi\)
−0.754328 + 0.656498i \(0.772037\pi\)
\(432\) 0 0
\(433\) 24.3923 1.17222 0.586110 0.810232i \(-0.300659\pi\)
0.586110 + 0.810232i \(0.300659\pi\)
\(434\) 0 0
\(435\) 3.00000i 0.143839i
\(436\) 0 0
\(437\) −1.90192 0.509619i −0.0909814 0.0243784i
\(438\) 0 0
\(439\) 18.0622 + 10.4282i 0.862061 + 0.497711i 0.864702 0.502286i \(-0.167507\pi\)
−0.00264111 + 0.999997i \(0.500841\pi\)
\(440\) 0 0
\(441\) 1.39230 + 2.41154i 0.0663002 + 0.114835i
\(442\) 0 0
\(443\) 4.33013 + 16.1603i 0.205731 + 0.767797i 0.989226 + 0.146399i \(0.0467683\pi\)
−0.783495 + 0.621398i \(0.786565\pi\)
\(444\) 0 0
\(445\) 1.58846 5.92820i 0.0753001 0.281024i
\(446\) 0 0
\(447\) 6.82051 25.4545i 0.322599 1.20396i
\(448\) 0 0
\(449\) 0.679492 0.0320672 0.0160336 0.999871i \(-0.494896\pi\)
0.0160336 + 0.999871i \(0.494896\pi\)
\(450\) 0 0
\(451\) −4.09808 4.09808i −0.192971 0.192971i
\(452\) 0 0
\(453\) −6.06218 + 10.5000i −0.284826 + 0.493333i
\(454\) 0 0
\(455\) −5.25833 + 3.03590i −0.246514 + 0.142325i
\(456\) 0 0
\(457\) −19.0359 10.9904i −0.890462 0.514108i −0.0163683 0.999866i \(-0.505210\pi\)
−0.874094 + 0.485758i \(0.838544\pi\)
\(458\) 0 0
\(459\) 20.7846i 0.970143i
\(460\) 0 0
\(461\) 2.23205 0.598076i 0.103957 0.0278552i −0.206466 0.978454i \(-0.566196\pi\)
0.310423 + 0.950599i \(0.399529\pi\)
\(462\) 0 0
\(463\) −3.33013 5.76795i −0.154764 0.268059i 0.778209 0.628005i \(-0.216128\pi\)
−0.932973 + 0.359946i \(0.882795\pi\)
\(464\) 0 0
\(465\) 1.03590 0.277568i 0.0480386 0.0128719i
\(466\) 0 0
\(467\) 19.7846 + 19.7846i 0.915523 + 0.915523i 0.996700 0.0811771i \(-0.0258679\pi\)
−0.0811771 + 0.996700i \(0.525868\pi\)
\(468\) 0 0
\(469\) 2.22243 2.22243i 0.102622 0.102622i
\(470\) 0 0
\(471\) −1.50000 0.401924i −0.0691164 0.0185197i
\(472\) 0 0
\(473\) 4.03590 2.33013i 0.185571 0.107139i
\(474\) 0 0
\(475\) −5.19615 19.3923i −0.238416 0.889780i
\(476\) 0 0
\(477\) −6.80385 + 6.80385i −0.311527 + 0.311527i
\(478\) 0 0
\(479\) −0.669873 + 1.16025i −0.0306073 + 0.0530134i −0.880923 0.473259i \(-0.843077\pi\)
0.850316 + 0.526272i \(0.176411\pi\)
\(480\) 0 0
\(481\) −26.0263 45.0788i −1.18670 2.05542i
\(482\) 0 0
\(483\) 1.98076i 0.0901278i
\(484\) 0 0
\(485\) −0.366025 + 0.366025i −0.0166204 + 0.0166204i
\(486\) 0 0
\(487\) 34.7846i 1.57624i −0.615521 0.788121i \(-0.711054\pi\)
0.615521 0.788121i \(-0.288946\pi\)
\(488\) 0 0
\(489\) 20.6603 20.6603i 0.934289 0.934289i
\(490\) 0 0
\(491\) 1.86603 + 0.500000i 0.0842125 + 0.0225647i 0.300679 0.953725i \(-0.402787\pi\)
−0.216467 + 0.976290i \(0.569453\pi\)
\(492\) 0 0
\(493\) −12.9282 + 3.46410i −0.582257 + 0.156015i
\(494\) 0 0
\(495\) 0.803848i 0.0361303i
\(496\) 0 0
\(497\) 13.4641 23.3205i 0.603947 1.04607i
\(498\) 0 0
\(499\) −0.669873 + 2.50000i −0.0299876 + 0.111915i −0.979297 0.202427i \(-0.935117\pi\)
0.949310 + 0.314342i \(0.101784\pi\)
\(500\) 0 0
\(501\) 8.25833 + 14.3038i 0.368955 + 0.639049i
\(502\) 0 0
\(503\) 13.8564i 0.617827i 0.951090 + 0.308913i \(0.0999653\pi\)
−0.951090 + 0.308913i \(0.900035\pi\)
\(504\) 0 0
\(505\) 1.00000i 0.0444994i
\(506\) 0 0
\(507\) 8.36603 14.4904i 0.371548 0.643540i
\(508\) 0 0
\(509\) 5.69615 21.2583i 0.252478 0.942259i −0.716999 0.697074i \(-0.754485\pi\)
0.969476 0.245185i \(-0.0788486\pi\)
\(510\) 0 0
\(511\) −0.660254 + 1.14359i −0.0292079 + 0.0505896i
\(512\) 0 0
\(513\) 15.5885 15.5885i 0.688247 0.688247i
\(514\) 0 0
\(515\) −1.03590 + 0.277568i −0.0456471 + 0.0122311i
\(516\) 0 0
\(517\) 4.59808 + 1.23205i 0.202223 + 0.0541855i
\(518\) 0 0
\(519\) −4.16025 15.5263i −0.182615 0.681528i
\(520\) 0 0
\(521\) 14.1436i 0.619642i −0.950795 0.309821i \(-0.899731\pi\)
0.950795 0.309821i \(-0.100269\pi\)
\(522\) 0 0
\(523\) 2.12436 2.12436i 0.0928916 0.0928916i −0.659134 0.752026i \(-0.729077\pi\)
0.752026 + 0.659134i \(0.229077\pi\)
\(524\) 0 0
\(525\) 17.4904 10.0981i 0.763343 0.440716i
\(526\) 0 0
\(527\) −2.39230 4.14359i −0.104210 0.180498i
\(528\) 0 0
\(529\) −11.3923 + 19.7321i −0.495318 + 0.857915i
\(530\) 0 0
\(531\) 16.7942 + 4.50000i 0.728807 + 0.195283i
\(532\) 0 0
\(533\) 13.7942 + 51.4808i 0.597494 + 2.22988i
\(534\) 0 0
\(535\) 7.22243 4.16987i 0.312253 0.180279i
\(536\) 0 0
\(537\) 13.7321 13.7321i 0.592582 0.592582i
\(538\) 0 0
\(539\) −0.339746 + 0.339746i −0.0146339 + 0.0146339i
\(540\) 0 0
\(541\) −15.0000 15.0000i −0.644900 0.644900i 0.306856 0.951756i \(-0.400723\pi\)
−0.951756 + 0.306856i \(0.900723\pi\)
\(542\) 0 0
\(543\) −7.39230 7.39230i −0.317234 0.317234i
\(544\) 0 0
\(545\) 0.633975 + 1.09808i 0.0271565 + 0.0470364i
\(546\) 0 0
\(547\) 28.2583 7.57180i 1.20824 0.323747i 0.402168 0.915566i \(-0.368257\pi\)
0.806071 + 0.591819i \(0.201590\pi\)
\(548\) 0 0
\(549\) −43.2846 + 11.5981i −1.84734 + 0.494994i
\(550\) 0 0
\(551\) −12.2942 7.09808i −0.523752 0.302388i
\(552\) 0 0
\(553\) −3.69615 + 2.13397i −0.157176 + 0.0907458i
\(554\) 0 0
\(555\) −4.90192 8.49038i −0.208075 0.360397i
\(556\) 0 0
\(557\) 27.9808 + 27.9808i 1.18558 + 1.18558i 0.978276 + 0.207307i \(0.0664699\pi\)
0.207307 + 0.978276i \(0.433530\pi\)
\(558\) 0 0
\(559\) −42.8564 −1.81263
\(560\) 0 0
\(561\) 3.46410 0.928203i 0.146254 0.0391888i
\(562\) 0 0
\(563\) −7.86603 + 29.3564i −0.331513 + 1.23723i 0.576086 + 0.817389i \(0.304579\pi\)
−0.907600 + 0.419836i \(0.862088\pi\)
\(564\) 0 0
\(565\) −0.741670 2.76795i −0.0312023 0.116448i
\(566\) 0 0
\(567\) 19.2058 + 11.0885i 0.806567 + 0.465671i
\(568\) 0 0
\(569\) −24.4808 14.1340i −1.02629 0.592527i −0.110368 0.993891i \(-0.535203\pi\)
−0.915919 + 0.401364i \(0.868536\pi\)
\(570\) 0 0
\(571\) 5.40192 + 1.44744i 0.226063 + 0.0605735i 0.370073 0.929003i \(-0.379333\pi\)
−0.144009 + 0.989576i \(0.545999\pi\)
\(572\) 0 0
\(573\) −19.7942 11.4282i −0.826916 0.477420i
\(574\) 0 0
\(575\) 2.19615 0.0915859
\(576\) 0 0
\(577\) 37.1769 1.54770 0.773848 0.633372i \(-0.218330\pi\)
0.773848 + 0.633372i \(0.218330\pi\)
\(578\) 0 0
\(579\) 3.69615 2.13397i 0.153607 0.0886850i
\(580\) 0 0
\(581\) 29.0622 + 7.78719i 1.20570 + 0.323067i
\(582\) 0 0
\(583\) −1.43782 0.830127i −0.0595485 0.0343803i
\(584\) 0 0
\(585\) 3.69615 6.40192i 0.152817 0.264687i
\(586\) 0 0
\(587\) −0.794229 2.96410i −0.0327813 0.122342i 0.947596 0.319470i \(-0.103505\pi\)
−0.980378 + 0.197129i \(0.936838\pi\)
\(588\) 0 0
\(589\) 1.31347 4.90192i 0.0541204 0.201980i
\(590\) 0 0
\(591\) 18.1244 + 18.1244i 0.745536 + 0.745536i
\(592\) 0 0
\(593\) 1.46410 0.0601234 0.0300617 0.999548i \(-0.490430\pi\)
0.0300617 + 0.999548i \(0.490430\pi\)
\(594\) 0 0
\(595\) 3.60770 + 3.60770i 0.147901 + 0.147901i
\(596\) 0 0
\(597\) 10.1436 0.415150
\(598\) 0 0
\(599\) 30.3109 17.5000i 1.23847 0.715031i 0.269688 0.962948i \(-0.413079\pi\)
0.968781 + 0.247917i \(0.0797461\pi\)
\(600\) 0 0
\(601\) 30.2321 + 17.4545i 1.23319 + 0.711983i 0.967694 0.252128i \(-0.0811305\pi\)
0.265497 + 0.964112i \(0.414464\pi\)
\(602\) 0 0
\(603\) −0.990381 + 3.69615i −0.0403314 + 0.150519i
\(604\) 0 0
\(605\) 5.36603 1.43782i 0.218160 0.0584558i
\(606\) 0 0
\(607\) 4.59808 + 7.96410i 0.186630 + 0.323253i 0.944125 0.329589i \(-0.106910\pi\)
−0.757494 + 0.652842i \(0.773577\pi\)
\(608\) 0 0
\(609\) 3.69615 13.7942i 0.149776 0.558970i
\(610\) 0 0
\(611\) −30.9545 30.9545i −1.25228 1.25228i
\(612\) 0 0
\(613\) −7.58846 + 7.58846i −0.306495 + 0.306495i −0.843548 0.537053i \(-0.819537\pi\)
0.537053 + 0.843548i \(0.319537\pi\)
\(614\) 0 0
\(615\) 2.59808 + 9.69615i 0.104765 + 0.390987i
\(616\) 0 0
\(617\) 8.08846 4.66987i 0.325629 0.188002i −0.328270 0.944584i \(-0.606466\pi\)
0.653899 + 0.756582i \(0.273132\pi\)
\(618\) 0 0
\(619\) −8.86603 33.0885i −0.356356 1.32994i −0.878770 0.477246i \(-0.841635\pi\)
0.522414 0.852692i \(-0.325031\pi\)
\(620\) 0 0
\(621\) 1.20577 + 2.08846i 0.0483859 + 0.0838069i
\(622\) 0 0
\(623\) 14.6077 25.3013i 0.585245 1.01367i
\(624\) 0 0
\(625\) 10.5263 + 18.2321i 0.421051 + 0.729282i
\(626\) 0 0
\(627\) 3.29423 + 1.90192i 0.131559 + 0.0759555i
\(628\) 0 0
\(629\) −30.9282 + 30.9282i −1.23319 + 1.23319i
\(630\) 0 0
\(631\) 32.2487i 1.28380i 0.766788 + 0.641900i \(0.221854\pi\)
−0.766788 + 0.641900i \(0.778146\pi\)
\(632\) 0 0
\(633\) 3.40192 + 0.911543i 0.135214 + 0.0362306i
\(634\) 0 0
\(635\) 10.1962 + 2.73205i 0.404622 + 0.108418i
\(636\) 0 0
\(637\) 4.26795 1.14359i 0.169102 0.0453108i
\(638\) 0 0
\(639\) 32.7846i 1.29694i
\(640\) 0 0
\(641\) 5.76795 9.99038i 0.227820 0.394596i −0.729342 0.684150i \(-0.760173\pi\)
0.957162 + 0.289553i \(0.0935068\pi\)
\(642\) 0 0
\(643\) 0.277568 1.03590i 0.0109462 0.0408518i −0.960237 0.279187i \(-0.909935\pi\)
0.971183 + 0.238335i \(0.0766017\pi\)
\(644\) 0 0
\(645\) −8.07180 −0.317827
\(646\) 0 0
\(647\) 46.3923i 1.82387i −0.410335 0.911935i \(-0.634588\pi\)
0.410335 0.911935i \(-0.365412\pi\)
\(648\) 0 0
\(649\) 3.00000i 0.117760i
\(650\) 0 0
\(651\) 5.10512 0.200085
\(652\) 0 0
\(653\) 5.71539 21.3301i 0.223661 0.834712i −0.759276 0.650768i \(-0.774447\pi\)
0.982937 0.183944i \(-0.0588865\pi\)
\(654\) 0 0
\(655\) 3.13397 5.42820i 0.122455 0.212097i
\(656\) 0 0
\(657\) 1.60770i 0.0627222i
\(658\) 0 0
\(659\) −8.33013 + 2.23205i −0.324496 + 0.0869484i −0.417390 0.908728i \(-0.637055\pi\)
0.0928939 + 0.995676i \(0.470388\pi\)
\(660\) 0 0
\(661\) −15.6962 4.20577i −0.610510 0.163586i −0.0596998 0.998216i \(-0.519014\pi\)
−0.550810 + 0.834631i \(0.685681\pi\)
\(662\) 0 0
\(663\) −31.8564 8.53590i −1.23720 0.331507i
\(664\) 0 0
\(665\) 5.41154i 0.209851i
\(666\) 0 0
\(667\) 1.09808 1.09808i 0.0425177 0.0425177i
\(668\) 0 0
\(669\) 23.3827 + 13.5000i 0.904027 + 0.521940i
\(670\) 0 0
\(671\) −3.86603 6.69615i −0.149246 0.258502i
\(672\) 0 0
\(673\) 3.83975 6.65064i 0.148011 0.256363i −0.782481 0.622674i \(-0.786046\pi\)
0.930492 + 0.366311i \(0.119379\pi\)
\(674\) 0 0
\(675\) −12.2942 + 21.2942i −0.473205 + 0.819615i
\(676\) 0 0
\(677\) −12.2321 45.6506i −0.470116 1.75450i −0.639345 0.768920i \(-0.720795\pi\)
0.169229 0.985577i \(-0.445872\pi\)
\(678\) 0 0
\(679\) −2.13397 + 1.23205i −0.0818944 + 0.0472818i
\(680\) 0 0
\(681\) −8.00962 29.8923i −0.306929 1.14548i
\(682\) 0 0
\(683\) 5.39230 5.39230i 0.206331 0.206331i −0.596375 0.802706i \(-0.703393\pi\)
0.802706 + 0.596375i \(0.203393\pi\)
\(684\) 0 0
\(685\) 6.09808 + 6.09808i 0.232996 + 0.232996i
\(686\) 0 0
\(687\) −4.37564 + 16.3301i −0.166941 + 0.623033i
\(688\) 0 0
\(689\) 7.63397 + 13.2224i 0.290831 + 0.503735i
\(690\) 0 0
\(691\) 18.5263 4.96410i 0.704773 0.188843i 0.111405 0.993775i \(-0.464465\pi\)
0.593367 + 0.804932i \(0.297798\pi\)
\(692\) 0 0
\(693\) −0.990381 + 3.69615i −0.0376215 + 0.140405i
\(694\) 0 0
\(695\) −2.00962 1.16025i −0.0762292 0.0440109i
\(696\) 0 0
\(697\) 38.7846 22.3923i 1.46907 0.848169i
\(698\) 0 0
\(699\) −39.7128 −1.50208
\(700\) 0 0
\(701\) −21.0526 21.0526i −0.795144 0.795144i 0.187181 0.982325i \(-0.440065\pi\)
−0.982325 + 0.187181i \(0.940065\pi\)
\(702\) 0 0
\(703\) −46.3923 −1.74972
\(704\) 0 0
\(705\) −5.83013 5.83013i −0.219575 0.219575i
\(706\) 0 0
\(707\) −1.23205 + 4.59808i −0.0463360 + 0.172928i
\(708\) 0 0
\(709\) 10.7487 + 40.1147i 0.403676 + 1.50654i 0.806484 + 0.591256i \(0.201368\pi\)
−0.402808 + 0.915285i \(0.631966\pi\)
\(710\) 0 0
\(711\) 2.59808 4.50000i 0.0974355 0.168763i
\(712\) 0 0
\(713\) 0.480762 + 0.277568i 0.0180047 + 0.0103950i
\(714\) 0 0
\(715\) 1.23205 + 0.330127i 0.0460761 + 0.0123461i
\(716\) 0 0
\(717\) −16.7942 + 9.69615i −0.627192 + 0.362109i
\(718\) 0 0
\(719\) −23.3205 −0.869708 −0.434854 0.900501i \(-0.643200\pi\)
−0.434854 + 0.900501i \(0.643200\pi\)
\(720\) 0 0
\(721\) −5.10512 −0.190125
\(722\) 0 0
\(723\) −18.6962 10.7942i −0.695317 0.401442i
\(724\) 0 0
\(725\) 15.2942 + 4.09808i 0.568013 + 0.152199i
\(726\) 0 0
\(727\) −9.06218 5.23205i −0.336098 0.194046i 0.322447 0.946587i \(-0.395494\pi\)
−0.658545 + 0.752541i \(0.728828\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 9.32051 + 34.7846i 0.344731 + 1.28656i
\(732\) 0 0
\(733\) −7.37564 + 27.5263i −0.272426 + 1.01671i 0.685121 + 0.728429i \(0.259749\pi\)
−0.957547 + 0.288277i \(0.906917\pi\)
\(734\) 0 0
\(735\) 0.803848 0.215390i 0.0296504 0.00794479i
\(736\) 0 0
\(737\) −0.660254 −0.0243208
\(738\) 0 0
\(739\) 29.7321 + 29.7321i 1.09371 + 1.09371i 0.995129 + 0.0985823i \(0.0314308\pi\)
0.0985823 + 0.995129i \(0.468569\pi\)
\(740\) 0 0
\(741\) −17.4904 30.2942i −0.642525 1.11289i
\(742\) 0 0
\(743\) −25.1147 + 14.5000i −0.921370 + 0.531953i −0.884072 0.467351i \(-0.845209\pi\)
−0.0372984 + 0.999304i \(0.511875\pi\)
\(744\) 0 0
\(745\) −6.82051 3.93782i −0.249884 0.144271i
\(746\) 0 0
\(747\) −35.3827 + 9.48076i −1.29458 + 0.346883i
\(748\) 0 0
\(749\) 38.3468 10.2750i 1.40116 0.375440i
\(750\) 0 0
\(751\) −4.72243 8.17949i −0.172324 0.298474i 0.766908 0.641757i \(-0.221794\pi\)
−0.939232 + 0.343283i \(0.888461\pi\)
\(752\) 0 0
\(753\) −12.8038 12.8038i −0.466598 0.466598i
\(754\) 0 0
\(755\) 2.56218 + 2.56218i 0.0932472 + 0.0932472i
\(756\) 0 0
\(757\) 8.46410 8.46410i 0.307633 0.307633i −0.536358 0.843991i \(-0.680200\pi\)
0.843991 + 0.536358i \(0.180200\pi\)
\(758\) 0 0
\(759\) −0.294229 + 0.294229i −0.0106798 + 0.0106798i
\(760\) 0 0
\(761\) −25.2846 + 14.5981i −0.916566 + 0.529180i −0.882538 0.470241i \(-0.844167\pi\)
−0.0340283 + 0.999421i \(0.510834\pi\)
\(762\) 0 0
\(763\) 1.56218 + 5.83013i 0.0565546 + 0.211065i
\(764\) 0 0
\(765\) −6.00000 1.60770i −0.216930 0.0581263i
\(766\) 0 0
\(767\) 13.7942 23.8923i 0.498081 0.862701i
\(768\) 0 0
\(769\) −3.50000 6.06218i −0.126213 0.218608i 0.795993 0.605305i \(-0.206949\pi\)
−0.922207 + 0.386698i \(0.873616\pi\)
\(770\) 0 0
\(771\) 15.4808 8.93782i 0.557526 0.321888i
\(772\) 0 0
\(773\) 7.58846 7.58846i 0.272938 0.272938i −0.557344 0.830282i \(-0.688179\pi\)
0.830282 + 0.557344i \(0.188179\pi\)
\(774\) 0 0
\(775\) 5.66025i 0.203322i
\(776\) 0 0
\(777\) −12.0788 45.0788i −0.433326 1.61719i
\(778\) 0 0
\(779\) 45.8827 + 12.2942i 1.64392 + 0.440486i
\(780\) 0 0
\(781\) −5.46410 + 1.46410i −0.195521 + 0.0523897i
\(782\) 0 0
\(783\) 4.50000 + 16.7942i 0.160817 + 0.600177i
\(784\) 0 0
\(785\) −0.232051 + 0.401924i −0.00828225 + 0.0143453i
\(786\) 0 0
\(787\) −9.06218 + 33.8205i −0.323032 + 1.20557i 0.593244 + 0.805023i \(0.297847\pi\)
−0.916276 + 0.400548i \(0.868820\pi\)
\(788\) 0 0
\(789\) 3.40192 5.89230i 0.121112 0.209772i
\(790\) 0 0
\(791\) 13.6410i 0.485019i
\(792\) 0 0
\(793\)