Properties

Label 260.2.bf.a.253.1
Level $260$
Weight $2$
Character 260.253
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 253.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.253
Dual form 260.2.bf.a.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.133975i) q^{3} +(2.00000 + 1.00000i) q^{5} +(0.133975 + 0.232051i) q^{7} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.133975i) q^{3} +(2.00000 + 1.00000i) q^{5} +(0.133975 + 0.232051i) q^{7} +(-2.36603 + 1.36603i) q^{9} +(4.59808 - 1.23205i) q^{11} +(2.00000 + 3.00000i) q^{13} +(-1.13397 - 0.232051i) q^{15} +(-0.767949 + 2.86603i) q^{17} +(0.866025 - 3.23205i) q^{19} +(-0.0980762 - 0.0980762i) q^{21} +(-0.0358984 - 0.133975i) q^{23} +(3.00000 + 4.00000i) q^{25} +(2.09808 - 2.09808i) q^{27} +(1.03590 + 0.598076i) q^{29} +(2.26795 - 2.26795i) q^{31} +(-2.13397 + 1.23205i) q^{33} +(0.0358984 + 0.598076i) q^{35} +(-1.86603 + 3.23205i) q^{37} +(-1.40192 - 1.23205i) q^{39} +(-1.86603 - 6.96410i) q^{41} +(-9.96410 - 2.66987i) q^{43} +(-6.09808 + 0.366025i) q^{45} -7.46410 q^{47} +(3.46410 - 6.00000i) q^{49} -1.53590i q^{51} +(-8.46410 - 8.46410i) q^{53} +(10.4282 + 2.13397i) q^{55} +1.73205i q^{57} +(-13.7942 - 3.69615i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-0.633975 - 0.366025i) q^{63} +(1.00000 + 8.00000i) q^{65} +(10.7942 + 6.23205i) q^{67} +(0.0358984 + 0.0621778i) q^{69} +(2.86603 + 0.767949i) q^{71} +0.928203i q^{73} +(-2.03590 - 1.59808i) q^{75} +(0.901924 + 0.901924i) q^{77} -11.4641i q^{79} +(3.33013 - 5.76795i) q^{81} -3.46410 q^{83} +(-4.40192 + 4.96410i) q^{85} +(-0.598076 - 0.160254i) q^{87} +(0.794229 + 2.96410i) q^{89} +(-0.428203 + 0.866025i) q^{91} +(-0.830127 + 1.43782i) q^{93} +(4.96410 - 5.59808i) q^{95} +(2.13397 - 1.23205i) q^{97} +(-9.19615 + 9.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 + 0.133975i −0.288675 + 0.0773503i −0.400251 0.916406i \(-0.631077\pi\)
0.111576 + 0.993756i \(0.464410\pi\)
\(4\) 0 0
\(5\) 2.00000 + 1.00000i 0.894427 + 0.447214i
\(6\) 0 0
\(7\) 0.133975 + 0.232051i 0.0506376 + 0.0877070i 0.890233 0.455505i \(-0.150541\pi\)
−0.839596 + 0.543212i \(0.817208\pi\)
\(8\) 0 0
\(9\) −2.36603 + 1.36603i −0.788675 + 0.455342i
\(10\) 0 0
\(11\) 4.59808 1.23205i 1.38637 0.371477i 0.512941 0.858424i \(-0.328556\pi\)
0.873432 + 0.486947i \(0.161889\pi\)
\(12\) 0 0
\(13\) 2.00000 + 3.00000i 0.554700 + 0.832050i
\(14\) 0 0
\(15\) −1.13397 0.232051i −0.292791 0.0599153i
\(16\) 0 0
\(17\) −0.767949 + 2.86603i −0.186255 + 0.695113i 0.808103 + 0.589041i \(0.200494\pi\)
−0.994358 + 0.106073i \(0.966172\pi\)
\(18\) 0 0
\(19\) 0.866025 3.23205i 0.198680 0.741483i −0.792604 0.609737i \(-0.791275\pi\)
0.991283 0.131746i \(-0.0420584\pi\)
\(20\) 0 0
\(21\) −0.0980762 0.0980762i −0.0214020 0.0214020i
\(22\) 0 0
\(23\) −0.0358984 0.133975i −0.00748533 0.0279356i 0.962082 0.272760i \(-0.0879364\pi\)
−0.969567 + 0.244824i \(0.921270\pi\)
\(24\) 0 0
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 0 0
\(27\) 2.09808 2.09808i 0.403775 0.403775i
\(28\) 0 0
\(29\) 1.03590 + 0.598076i 0.192362 + 0.111060i 0.593088 0.805138i \(-0.297909\pi\)
−0.400726 + 0.916198i \(0.631242\pi\)
\(30\) 0 0
\(31\) 2.26795 2.26795i 0.407336 0.407336i −0.473473 0.880808i \(-0.657000\pi\)
0.880808 + 0.473473i \(0.157000\pi\)
\(32\) 0 0
\(33\) −2.13397 + 1.23205i −0.371477 + 0.214473i
\(34\) 0 0
\(35\) 0.0358984 + 0.598076i 0.00606793 + 0.101093i
\(36\) 0 0
\(37\) −1.86603 + 3.23205i −0.306773 + 0.531346i −0.977654 0.210218i \(-0.932582\pi\)
0.670882 + 0.741564i \(0.265916\pi\)
\(38\) 0 0
\(39\) −1.40192 1.23205i −0.224487 0.197286i
\(40\) 0 0
\(41\) −1.86603 6.96410i −0.291424 1.08761i −0.944016 0.329900i \(-0.892985\pi\)
0.652592 0.757710i \(-0.273682\pi\)
\(42\) 0 0
\(43\) −9.96410 2.66987i −1.51951 0.407152i −0.599930 0.800052i \(-0.704805\pi\)
−0.919581 + 0.392900i \(0.871472\pi\)
\(44\) 0 0
\(45\) −6.09808 + 0.366025i −0.909048 + 0.0545638i
\(46\) 0 0
\(47\) −7.46410 −1.08875 −0.544376 0.838842i \(-0.683233\pi\)
−0.544376 + 0.838842i \(0.683233\pi\)
\(48\) 0 0
\(49\) 3.46410 6.00000i 0.494872 0.857143i
\(50\) 0 0
\(51\) 1.53590i 0.215069i
\(52\) 0 0
\(53\) −8.46410 8.46410i −1.16263 1.16263i −0.983897 0.178737i \(-0.942799\pi\)
−0.178737 0.983897i \(-0.557201\pi\)
\(54\) 0 0
\(55\) 10.4282 + 2.13397i 1.40614 + 0.287745i
\(56\) 0 0
\(57\) 1.73205i 0.229416i
\(58\) 0 0
\(59\) −13.7942 3.69615i −1.79586 0.481198i −0.802537 0.596602i \(-0.796517\pi\)
−0.993319 + 0.115404i \(0.963184\pi\)
\(60\) 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
\(63\) −0.633975 0.366025i −0.0798733 0.0461149i
\(64\) 0 0
\(65\) 1.00000 + 8.00000i 0.124035 + 0.992278i
\(66\) 0 0
\(67\) 10.7942 + 6.23205i 1.31872 + 0.761366i 0.983524 0.180780i \(-0.0578623\pi\)
0.335201 + 0.942146i \(0.391196\pi\)
\(68\) 0 0
\(69\) 0.0358984 + 0.0621778i 0.00432166 + 0.00748533i
\(70\) 0 0
\(71\) 2.86603 + 0.767949i 0.340135 + 0.0911388i 0.424843 0.905267i \(-0.360329\pi\)
−0.0847085 + 0.996406i \(0.526996\pi\)
\(72\) 0 0
\(73\) 0.928203i 0.108638i 0.998524 + 0.0543190i \(0.0172988\pi\)
−0.998524 + 0.0543190i \(0.982701\pi\)
\(74\) 0 0
\(75\) −2.03590 1.59808i −0.235085 0.184530i
\(76\) 0 0
\(77\) 0.901924 + 0.901924i 0.102784 + 0.102784i
\(78\) 0 0
\(79\) 11.4641i 1.28981i −0.764262 0.644906i \(-0.776896\pi\)
0.764262 0.644906i \(-0.223104\pi\)
\(80\) 0 0
\(81\) 3.33013 5.76795i 0.370014 0.640883i
\(82\) 0 0
\(83\) −3.46410 −0.380235 −0.190117 0.981761i \(-0.560887\pi\)
−0.190117 + 0.981761i \(0.560887\pi\)
\(84\) 0 0
\(85\) −4.40192 + 4.96410i −0.477456 + 0.538432i
\(86\) 0 0
\(87\) −0.598076 0.160254i −0.0641205 0.0171810i
\(88\) 0 0
\(89\) 0.794229 + 2.96410i 0.0841881 + 0.314194i 0.995159 0.0982760i \(-0.0313328\pi\)
−0.910971 + 0.412470i \(0.864666\pi\)
\(90\) 0 0
\(91\) −0.428203 + 0.866025i −0.0448879 + 0.0907841i
\(92\) 0 0
\(93\) −0.830127 + 1.43782i −0.0860802 + 0.149095i
\(94\) 0 0
\(95\) 4.96410 5.59808i 0.509306 0.574351i
\(96\) 0 0
\(97\) 2.13397 1.23205i 0.216672 0.125096i −0.387736 0.921770i \(-0.626743\pi\)
0.604408 + 0.796675i \(0.293410\pi\)
\(98\) 0 0
\(99\) −9.19615 + 9.19615i −0.924248 + 0.924248i
\(100\) 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
\(103\) 10.6603 10.6603i 1.05039 1.05039i 0.0517247 0.998661i \(-0.483528\pi\)
0.998661 0.0517247i \(-0.0164718\pi\)
\(104\) 0 0
\(105\) −0.0980762 0.294229i −0.00957126 0.0287138i
\(106\) 0 0
\(107\) 0.964102 + 3.59808i 0.0932032 + 0.347839i 0.996741 0.0806695i \(-0.0257058\pi\)
−0.903538 + 0.428509i \(0.859039\pi\)
\(108\) 0 0
\(109\) 11.3923 + 11.3923i 1.09118 + 1.09118i 0.995402 + 0.0957826i \(0.0305354\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 0.500000 1.86603i 0.0474579 0.177115i
\(112\) 0 0
\(113\) −4.16025 + 15.5263i −0.391364 + 1.46059i 0.436522 + 0.899693i \(0.356210\pi\)
−0.827886 + 0.560896i \(0.810457\pi\)
\(114\) 0 0
\(115\) 0.0621778 0.303848i 0.00579811 0.0283339i
\(116\) 0 0
\(117\) −8.83013 4.36603i −0.816346 0.403639i
\(118\) 0 0
\(119\) −0.767949 + 0.205771i −0.0703978 + 0.0188630i
\(120\) 0 0
\(121\) 10.0981 5.83013i 0.918007 0.530012i
\(122\) 0 0
\(123\) 1.86603 + 3.23205i 0.168254 + 0.291424i
\(124\) 0 0
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0 0
\(127\) 4.50000 1.20577i 0.399310 0.106995i −0.0535746 0.998564i \(-0.517061\pi\)
0.452885 + 0.891569i \(0.350395\pi\)
\(128\) 0 0
\(129\) 5.33975 0.470138
\(130\) 0 0
\(131\) −13.8564 −1.21064 −0.605320 0.795982i \(-0.706955\pi\)
−0.605320 + 0.795982i \(0.706955\pi\)
\(132\) 0 0
\(133\) 0.866025 0.232051i 0.0750939 0.0201214i
\(134\) 0 0
\(135\) 6.29423 2.09808i 0.541721 0.180574i
\(136\) 0 0
\(137\) −5.59808 9.69615i −0.478276 0.828398i 0.521414 0.853304i \(-0.325405\pi\)
−0.999690 + 0.0249057i \(0.992071\pi\)
\(138\) 0 0
\(139\) −5.42820 + 3.13397i −0.460414 + 0.265820i −0.712218 0.701958i \(-0.752309\pi\)
0.251804 + 0.967778i \(0.418976\pi\)
\(140\) 0 0
\(141\) 3.73205 1.00000i 0.314295 0.0842152i
\(142\) 0 0
\(143\) 12.8923 + 11.3301i 1.07811 + 0.947473i
\(144\) 0 0
\(145\) 1.47372 + 2.23205i 0.122386 + 0.185362i
\(146\) 0 0
\(147\) −0.928203 + 3.46410i −0.0765569 + 0.285714i
\(148\) 0 0
\(149\) 4.25833 15.8923i 0.348856 1.30195i −0.539186 0.842187i \(-0.681268\pi\)
0.888042 0.459762i \(-0.152065\pi\)
\(150\) 0 0
\(151\) 11.1962 + 11.1962i 0.911130 + 0.911130i 0.996361 0.0852312i \(-0.0271629\pi\)
−0.0852312 + 0.996361i \(0.527163\pi\)
\(152\) 0 0
\(153\) −2.09808 7.83013i −0.169619 0.633028i
\(154\) 0 0
\(155\) 6.80385 2.26795i 0.546498 0.182166i
\(156\) 0 0
\(157\) 13.3923 13.3923i 1.06882 1.06882i 0.0713726 0.997450i \(-0.477262\pi\)
0.997450 0.0713726i \(-0.0227379\pi\)
\(158\) 0 0
\(159\) 5.36603 + 3.09808i 0.425553 + 0.245693i
\(160\) 0 0
\(161\) 0.0262794 0.0262794i 0.00207111 0.00207111i
\(162\) 0 0
\(163\) −7.33013 + 4.23205i −0.574140 + 0.331480i −0.758801 0.651322i \(-0.774215\pi\)
0.184661 + 0.982802i \(0.440881\pi\)
\(164\) 0 0
\(165\) −5.50000 + 0.330127i −0.428174 + 0.0257004i
\(166\) 0 0
\(167\) −5.33013 + 9.23205i −0.412458 + 0.714398i −0.995158 0.0982896i \(-0.968663\pi\)
0.582700 + 0.812687i \(0.301996\pi\)
\(168\) 0 0
\(169\) −5.00000 + 12.0000i −0.384615 + 0.923077i
\(170\) 0 0
\(171\) 2.36603 + 8.83013i 0.180934 + 0.675257i
\(172\) 0 0
\(173\) 12.6962 + 3.40192i 0.965271 + 0.258643i 0.706830 0.707384i \(-0.250125\pi\)
0.258441 + 0.966027i \(0.416791\pi\)
\(174\) 0 0
\(175\) −0.526279 + 1.23205i −0.0397830 + 0.0931343i
\(176\) 0 0
\(177\) 7.39230 0.555640
\(178\) 0 0
\(179\) 0.964102 1.66987i 0.0720603 0.124812i −0.827744 0.561106i \(-0.810376\pi\)
0.899804 + 0.436294i \(0.143709\pi\)
\(180\) 0 0
\(181\) 1.07180i 0.0796660i −0.999206 0.0398330i \(-0.987317\pi\)
0.999206 0.0398330i \(-0.0126826\pi\)
\(182\) 0 0
\(183\) −0.366025 0.366025i −0.0270574 0.0270574i
\(184\) 0 0
\(185\) −6.96410 + 4.59808i −0.512011 + 0.338057i
\(186\) 0 0
\(187\) 14.1244i 1.03288i
\(188\) 0 0
\(189\) 0.767949 + 0.205771i 0.0558601 + 0.0149677i
\(190\) 0 0
\(191\) −5.03590 8.72243i −0.364385 0.631133i 0.624292 0.781191i \(-0.285387\pi\)
−0.988677 + 0.150058i \(0.952054\pi\)
\(192\) 0 0
\(193\) −8.93782 5.16025i −0.643359 0.371443i 0.142549 0.989788i \(-0.454470\pi\)
−0.785907 + 0.618345i \(0.787804\pi\)
\(194\) 0 0
\(195\) −1.57180 3.86603i −0.112559 0.276852i
\(196\) 0 0
\(197\) −17.5981 10.1603i −1.25381 0.723888i −0.281947 0.959430i \(-0.590980\pi\)
−0.971864 + 0.235542i \(0.924314\pi\)
\(198\) 0 0
\(199\) 1.96410 + 3.40192i 0.139231 + 0.241156i 0.927206 0.374552i \(-0.122203\pi\)
−0.787974 + 0.615708i \(0.788870\pi\)
\(200\) 0 0
\(201\) −6.23205 1.66987i −0.439575 0.117784i
\(202\) 0 0
\(203\) 0.320508i 0.0224953i
\(204\) 0 0
\(205\) 3.23205 15.7942i 0.225736 1.10312i
\(206\) 0 0
\(207\) 0.267949 + 0.267949i 0.0186238 + 0.0186238i
\(208\) 0 0
\(209\) 15.9282i 1.10178i
\(210\) 0 0
\(211\) −4.96410 + 8.59808i −0.341743 + 0.591916i −0.984756 0.173939i \(-0.944351\pi\)
0.643014 + 0.765855i \(0.277684\pi\)
\(212\) 0 0
\(213\) −1.53590 −0.105238
\(214\) 0 0
\(215\) −17.2583 15.3038i −1.17701 1.04371i
\(216\) 0 0
\(217\) 0.830127 + 0.222432i 0.0563527 + 0.0150997i
\(218\) 0 0
\(219\) −0.124356 0.464102i −0.00840318 0.0313611i
\(220\) 0 0
\(221\) −10.1340 + 3.42820i −0.681685 + 0.230606i
\(222\) 0 0
\(223\) 9.86603 17.0885i 0.660678 1.14433i −0.319760 0.947499i \(-0.603602\pi\)
0.980438 0.196829i \(-0.0630644\pi\)
\(224\) 0 0
\(225\) −12.5622 5.36603i −0.837479 0.357735i
\(226\) 0 0
\(227\) 0.401924 0.232051i 0.0266766 0.0154018i −0.486602 0.873624i \(-0.661764\pi\)
0.513279 + 0.858222i \(0.328431\pi\)
\(228\) 0 0
\(229\) −10.8564 + 10.8564i −0.717412 + 0.717412i −0.968074 0.250663i \(-0.919351\pi\)
0.250663 + 0.968074i \(0.419351\pi\)
\(230\) 0 0
\(231\) −0.571797 0.330127i −0.0376215 0.0217208i
\(232\) 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
\(235\) −14.9282 7.46410i −0.973809 0.486904i
\(236\) 0 0
\(237\) 1.53590 + 5.73205i 0.0997673 + 0.372337i
\(238\) 0 0
\(239\) 9.19615 + 9.19615i 0.594850 + 0.594850i 0.938937 0.344088i \(-0.111812\pi\)
−0.344088 + 0.938937i \(0.611812\pi\)
\(240\) 0 0
\(241\) −4.93782 + 18.4282i −0.318073 + 1.18706i 0.603021 + 0.797725i \(0.293963\pi\)
−0.921094 + 0.389340i \(0.872703\pi\)
\(242\) 0 0
\(243\) −3.19615 + 11.9282i −0.205033 + 0.765195i
\(244\) 0 0
\(245\) 12.9282 8.53590i 0.825953 0.545339i
\(246\) 0 0
\(247\) 11.4282 3.86603i 0.727159 0.245989i
\(248\) 0 0
\(249\) 1.73205 0.464102i 0.109764 0.0294112i
\(250\) 0 0
\(251\) −23.8923 + 13.7942i −1.50807 + 0.870684i −0.508113 + 0.861290i \(0.669657\pi\)
−0.999956 + 0.00939359i \(0.997010\pi\)
\(252\) 0 0
\(253\) −0.330127 0.571797i −0.0207549 0.0359486i
\(254\) 0 0
\(255\) 1.53590 3.07180i 0.0961817 0.192363i
\(256\) 0 0
\(257\) −13.1603 + 3.52628i −0.820914 + 0.219963i −0.644746 0.764397i \(-0.723037\pi\)
−0.176168 + 0.984360i \(0.556370\pi\)
\(258\) 0 0
\(259\) −1.00000 −0.0621370
\(260\) 0 0
\(261\) −3.26795 −0.202281
\(262\) 0 0
\(263\) 17.8923 4.79423i 1.10329 0.295625i 0.339184 0.940720i \(-0.389849\pi\)
0.764102 + 0.645095i \(0.223182\pi\)
\(264\) 0 0
\(265\) −8.46410 25.3923i −0.519946 1.55984i
\(266\) 0 0
\(267\) −0.794229 1.37564i −0.0486060 0.0841881i
\(268\) 0 0
\(269\) 23.4282 13.5263i 1.42844 0.824712i 0.431445 0.902139i \(-0.358004\pi\)
0.996998 + 0.0774275i \(0.0246706\pi\)
\(270\) 0 0
\(271\) −19.7942 + 5.30385i −1.20241 + 0.322186i −0.803781 0.594925i \(-0.797182\pi\)
−0.398633 + 0.917111i \(0.630515\pi\)
\(272\) 0 0
\(273\) 0.0980762 0.490381i 0.00593584 0.0296792i
\(274\) 0 0
\(275\) 18.7224 + 14.6962i 1.12901 + 0.886211i
\(276\) 0 0
\(277\) 6.16025 22.9904i 0.370134 1.38136i −0.490192 0.871614i \(-0.663073\pi\)
0.860326 0.509744i \(-0.170260\pi\)
\(278\) 0 0
\(279\) −2.26795 + 8.46410i −0.135779 + 0.506733i
\(280\) 0 0
\(281\) −7.39230 7.39230i −0.440988 0.440988i 0.451356 0.892344i \(-0.350940\pi\)
−0.892344 + 0.451356i \(0.850940\pi\)
\(282\) 0 0
\(283\) −3.35641 12.5263i −0.199518 0.744610i −0.991051 0.133484i \(-0.957384\pi\)
0.791533 0.611126i \(-0.209283\pi\)
\(284\) 0 0
\(285\) −1.73205 + 3.46410i −0.102598 + 0.205196i
\(286\) 0 0
\(287\) 1.36603 1.36603i 0.0806339 0.0806339i
\(288\) 0 0
\(289\) 7.09808 + 4.09808i 0.417534 + 0.241063i
\(290\) 0 0
\(291\) −0.901924 + 0.901924i −0.0528717 + 0.0528717i
\(292\) 0 0
\(293\) −19.4545 + 11.2321i −1.13654 + 0.656183i −0.945572 0.325412i \(-0.894497\pi\)
−0.190971 + 0.981596i \(0.561164\pi\)
\(294\) 0 0
\(295\) −23.8923 21.1865i −1.39106 1.23353i
\(296\) 0 0
\(297\) 7.06218 12.2321i 0.409789 0.709776i
\(298\) 0 0
\(299\) 0.330127 0.375644i 0.0190917 0.0217241i
\(300\) 0 0
\(301\) −0.715390 2.66987i −0.0412344 0.153889i
\(302\) 0 0
\(303\) −0.866025 0.232051i −0.0497519 0.0133310i
\(304\) 0 0
\(305\) 0.133975 + 2.23205i 0.00767136 + 0.127807i
\(306\) 0 0
\(307\) −30.3923 −1.73458 −0.867290 0.497803i \(-0.834140\pi\)
−0.867290 + 0.497803i \(0.834140\pi\)
\(308\) 0 0
\(309\) −3.90192 + 6.75833i −0.221973 + 0.384468i
\(310\) 0 0
\(311\) 16.2487i 0.921380i 0.887561 + 0.460690i \(0.152398\pi\)
−0.887561 + 0.460690i \(0.847602\pi\)
\(312\) 0 0
\(313\) 20.3205 + 20.3205i 1.14858 + 1.14858i 0.986832 + 0.161752i \(0.0517143\pi\)
0.161752 + 0.986832i \(0.448286\pi\)
\(314\) 0 0
\(315\) −0.901924 1.36603i −0.0508176 0.0769668i
\(316\) 0 0
\(317\) 3.07180i 0.172529i 0.996272 + 0.0862646i \(0.0274931\pi\)
−0.996272 + 0.0862646i \(0.972507\pi\)
\(318\) 0 0
\(319\) 5.50000 + 1.47372i 0.307941 + 0.0825125i
\(320\) 0 0
\(321\) −0.964102 1.66987i −0.0538109 0.0932032i
\(322\) 0 0
\(323\) 8.59808 + 4.96410i 0.478410 + 0.276210i
\(324\) 0 0
\(325\) −6.00000 + 17.0000i −0.332820 + 0.942990i
\(326\) 0 0
\(327\) −7.22243 4.16987i −0.399401 0.230595i
\(328\) 0 0
\(329\) −1.00000 1.73205i −0.0551318 0.0954911i
\(330\) 0 0
\(331\) 10.3301 + 2.76795i 0.567795 + 0.152140i 0.531285 0.847193i \(-0.321709\pi\)
0.0365099 + 0.999333i \(0.488376\pi\)
\(332\) 0 0
\(333\) 10.1962i 0.558746i
\(334\) 0 0
\(335\) 15.3564 + 23.2583i 0.839010 + 1.27074i
\(336\) 0 0
\(337\) 0.0717968 + 0.0717968i 0.00391102 + 0.00391102i 0.709060 0.705149i \(-0.249120\pi\)
−0.705149 + 0.709060i \(0.749120\pi\)
\(338\) 0 0
\(339\) 8.32051i 0.451908i
\(340\) 0 0
\(341\) 7.63397 13.2224i 0.413403 0.716035i
\(342\) 0 0
\(343\) 3.73205 0.201512
\(344\) 0 0
\(345\) 0.00961894 + 0.160254i 0.000517866 + 0.00862779i
\(346\) 0 0
\(347\) 24.8923 + 6.66987i 1.33629 + 0.358058i 0.855056 0.518535i \(-0.173523\pi\)
0.481233 + 0.876593i \(0.340189\pi\)
\(348\) 0 0
\(349\) 5.47372 + 20.4282i 0.293002 + 1.09350i 0.942792 + 0.333383i \(0.108190\pi\)
−0.649790 + 0.760114i \(0.725143\pi\)
\(350\) 0 0
\(351\) 10.4904 + 2.09808i 0.559935 + 0.111987i
\(352\) 0 0
\(353\) 7.86603 13.6244i 0.418666 0.725151i −0.577139 0.816646i \(-0.695831\pi\)
0.995806 + 0.0914944i \(0.0291644\pi\)
\(354\) 0 0
\(355\) 4.96410 + 4.40192i 0.263467 + 0.233630i
\(356\) 0 0
\(357\) 0.356406 0.205771i 0.0188630 0.0108906i
\(358\) 0 0
\(359\) 7.58846 7.58846i 0.400503 0.400503i −0.477907 0.878410i \(-0.658604\pi\)
0.878410 + 0.477907i \(0.158604\pi\)
\(360\) 0 0
\(361\) 6.75833 + 3.90192i 0.355702 + 0.205364i
\(362\) 0 0
\(363\) −4.26795 + 4.26795i −0.224009 + 0.224009i
\(364\) 0 0
\(365\) −0.928203 + 1.85641i −0.0485844 + 0.0971688i
\(366\) 0 0
\(367\) −2.89230 10.7942i −0.150977 0.563454i −0.999416 0.0341614i \(-0.989124\pi\)
0.848439 0.529293i \(-0.177543\pi\)
\(368\) 0 0
\(369\) 13.9282 + 13.9282i 0.725073 + 0.725073i
\(370\) 0 0
\(371\) 0.830127 3.09808i 0.0430980 0.160844i
\(372\) 0 0
\(373\) −7.23205 + 26.9904i −0.374461 + 1.39751i 0.479669 + 0.877450i \(0.340757\pi\)
−0.854130 + 0.520059i \(0.825910\pi\)
\(374\) 0 0
\(375\) −2.47372 5.23205i −0.127742 0.270182i
\(376\) 0 0
\(377\) 0.277568 + 4.30385i 0.0142955 + 0.221659i
\(378\) 0 0
\(379\) −23.5263 + 6.30385i −1.20846 + 0.323807i −0.806159 0.591699i \(-0.798457\pi\)
−0.402305 + 0.915506i \(0.631791\pi\)
\(380\) 0 0
\(381\) −2.08846 + 1.20577i −0.106995 + 0.0617735i
\(382\) 0 0
\(383\) 0.401924 + 0.696152i 0.0205373 + 0.0355717i 0.876111 0.482109i \(-0.160129\pi\)
−0.855574 + 0.517680i \(0.826796\pi\)
\(384\) 0 0
\(385\) 0.901924 + 2.70577i 0.0459663 + 0.137899i
\(386\) 0 0
\(387\) 27.2224 7.29423i 1.38379 0.370786i
\(388\) 0 0
\(389\) 3.85641 0.195528 0.0977638 0.995210i \(-0.468831\pi\)
0.0977638 + 0.995210i \(0.468831\pi\)
\(390\) 0 0
\(391\) 0.411543 0.0208126
\(392\) 0 0
\(393\) 6.92820 1.85641i 0.349482 0.0936433i
\(394\) 0 0
\(395\) 11.4641 22.9282i 0.576822 1.15364i
\(396\) 0 0
\(397\) 4.25833 + 7.37564i 0.213719 + 0.370173i 0.952876 0.303361i \(-0.0981088\pi\)
−0.739156 + 0.673534i \(0.764775\pi\)
\(398\) 0 0
\(399\) −0.401924 + 0.232051i −0.0201214 + 0.0116171i
\(400\) 0 0
\(401\) 5.86603 1.57180i 0.292935 0.0784918i −0.109359 0.994002i \(-0.534880\pi\)
0.402294 + 0.915511i \(0.368213\pi\)
\(402\) 0 0
\(403\) 11.3397 + 2.26795i 0.564873 + 0.112975i
\(404\) 0 0
\(405\) 12.4282 8.20577i 0.617562 0.407748i
\(406\) 0 0
\(407\) −4.59808 + 17.1603i −0.227918 + 0.850602i
\(408\) 0 0
\(409\) −3.06218 + 11.4282i −0.151415 + 0.565088i 0.847971 + 0.530043i \(0.177824\pi\)
−0.999386 + 0.0350453i \(0.988842\pi\)
\(410\) 0 0
\(411\) 4.09808 + 4.09808i 0.202143 + 0.202143i
\(412\) 0 0
\(413\) −0.990381 3.69615i −0.0487335 0.181876i
\(414\) 0 0
\(415\) −6.92820 3.46410i −0.340092 0.170046i
\(416\) 0 0
\(417\) 2.29423 2.29423i 0.112349 0.112349i
\(418\) 0 0
\(419\) −27.3564 15.7942i −1.33645 0.771599i −0.350169 0.936687i \(-0.613876\pi\)
−0.986279 + 0.165088i \(0.947209\pi\)
\(420\) 0 0
\(421\) 14.0718 14.0718i 0.685817 0.685817i −0.275487 0.961305i \(-0.588839\pi\)
0.961305 + 0.275487i \(0.0888392\pi\)
\(422\) 0 0
\(423\) 17.6603 10.1962i 0.858671 0.495754i
\(424\) 0 0
\(425\) −13.7679 + 5.52628i −0.667844 + 0.268064i
\(426\) 0 0
\(427\) −0.133975 + 0.232051i −0.00648349 + 0.0112297i
\(428\) 0 0
\(429\) −7.96410 3.93782i −0.384510 0.190120i
\(430\) 0 0
\(431\) 8.47372 + 31.6244i 0.408165 + 1.52329i 0.798143 + 0.602468i \(0.205816\pi\)
−0.389979 + 0.920824i \(0.627518\pi\)
\(432\) 0 0
\(433\) 10.1603 + 2.72243i 0.488271 + 0.130832i 0.494551 0.869149i \(-0.335332\pi\)
−0.00628046 + 0.999980i \(0.501999\pi\)
\(434\) 0 0
\(435\) −1.03590 0.918584i −0.0496675 0.0440427i
\(436\) 0 0
\(437\) −0.464102 −0.0222010
\(438\) 0 0
\(439\) −5.96410 + 10.3301i −0.284651 + 0.493030i −0.972524 0.232801i \(-0.925211\pi\)
0.687873 + 0.725831i \(0.258544\pi\)
\(440\) 0 0
\(441\) 18.9282i 0.901343i
\(442\) 0 0
\(443\) 27.0526 + 27.0526i 1.28531 + 1.28531i 0.937606 + 0.347700i \(0.113037\pi\)
0.347700 + 0.937606i \(0.386963\pi\)
\(444\) 0 0
\(445\) −1.37564 + 6.72243i −0.0652118 + 0.318674i
\(446\) 0 0
\(447\) 8.51666i 0.402824i
\(448\) 0 0
\(449\) 23.9904 + 6.42820i 1.13218 + 0.303366i 0.775801 0.630977i \(-0.217346\pi\)
0.356375 + 0.934343i \(0.384013\pi\)
\(450\) 0 0
\(451\) −17.1603 29.7224i −0.808045 1.39957i
\(452\) 0 0
\(453\) −7.09808 4.09808i −0.333497 0.192544i
\(454\) 0 0
\(455\) −1.72243 + 1.30385i −0.0807489 + 0.0611253i
\(456\) 0 0
\(457\) −25.4545 14.6962i −1.19071 0.687457i −0.232243 0.972658i \(-0.574606\pi\)
−0.958468 + 0.285201i \(0.907940\pi\)
\(458\) 0 0
\(459\) 4.40192 + 7.62436i 0.205464 + 0.355874i
\(460\) 0 0
\(461\) −23.9904 6.42820i −1.11734 0.299391i −0.347535 0.937667i \(-0.612981\pi\)
−0.769808 + 0.638276i \(0.779648\pi\)
\(462\) 0 0
\(463\) 29.8564i 1.38754i −0.720194 0.693772i \(-0.755947\pi\)
0.720194 0.693772i \(-0.244053\pi\)
\(464\) 0 0
\(465\) −3.09808 + 2.04552i −0.143670 + 0.0948586i
\(466\) 0 0
\(467\) −20.1244 20.1244i −0.931244 0.931244i 0.0665397 0.997784i \(-0.478804\pi\)
−0.997784 + 0.0665397i \(0.978804\pi\)
\(468\) 0 0
\(469\) 3.33975i 0.154215i
\(470\) 0 0
\(471\) −4.90192 + 8.49038i −0.225869 + 0.391216i
\(472\) 0 0
\(473\) −49.1051 −2.25786
\(474\) 0 0
\(475\) 15.5263 6.23205i 0.712395 0.285946i
\(476\) 0 0
\(477\) 31.5885 + 8.46410i 1.44634 + 0.387545i
\(478\) 0 0
\(479\) −1.00962 3.76795i −0.0461307 0.172162i 0.939017 0.343870i \(-0.111738\pi\)
−0.985148 + 0.171708i \(0.945071\pi\)
\(480\) 0 0
\(481\) −13.4282 + 0.866025i −0.612273 + 0.0394874i
\(482\) 0 0
\(483\) −0.00961894 + 0.0166605i −0.000437677 + 0.000758079i
\(484\) 0 0
\(485\) 5.50000 0.330127i 0.249742 0.0149903i
\(486\) 0 0
\(487\) 29.7224 17.1603i 1.34685 0.777605i 0.359050 0.933318i \(-0.383101\pi\)
0.987802 + 0.155713i \(0.0497675\pi\)
\(488\) 0 0
\(489\) 3.09808 3.09808i 0.140100 0.140100i
\(490\) 0 0
\(491\) −13.9641 8.06218i −0.630191 0.363841i 0.150635 0.988589i \(-0.451868\pi\)
−0.780826 + 0.624748i \(0.785202\pi\)
\(492\) 0 0
\(493\) −2.50962 + 2.50962i −0.113028 + 0.113028i
\(494\) 0 0
\(495\) −27.5885 + 9.19615i −1.24001 + 0.413336i
\(496\) 0 0
\(497\) 0.205771 + 0.767949i 0.00923011 + 0.0344472i
\(498\) 0 0
\(499\) −3.19615 3.19615i −0.143079 0.143079i 0.631939 0.775018i \(-0.282259\pi\)
−0.775018 + 0.631939i \(0.782259\pi\)
\(500\) 0 0
\(501\) 1.42820 5.33013i 0.0638074 0.238133i
\(502\) 0 0
\(503\) −4.03590 + 15.0622i −0.179952 + 0.671589i 0.815703 + 0.578471i \(0.196350\pi\)
−0.995655 + 0.0931187i \(0.970316\pi\)
\(504\) 0 0
\(505\) 2.13397 + 3.23205i 0.0949606 + 0.143824i
\(506\) 0 0
\(507\) 0.892305 6.66987i 0.0396286 0.296219i
\(508\) 0 0
\(509\) −8.79423 + 2.35641i −0.389797 + 0.104446i −0.448394 0.893836i \(-0.648004\pi\)
0.0585970 + 0.998282i \(0.481337\pi\)
\(510\) 0 0
\(511\) −0.215390 + 0.124356i −0.00952831 + 0.00550117i
\(512\) 0 0
\(513\) −4.96410 8.59808i −0.219170 0.379614i
\(514\) 0 0
\(515\) 31.9808 10.6603i 1.40924 0.469747i
\(516\) 0 0
\(517\) −34.3205 + 9.19615i −1.50941 + 0.404446i
\(518\) 0 0
\(519\) −6.80385 −0.298656
\(520\) 0 0
\(521\) 3.85641 0.168952 0.0844761 0.996426i \(-0.473078\pi\)
0.0844761 + 0.996426i \(0.473078\pi\)
\(522\) 0 0
\(523\) −33.8205 + 9.06218i −1.47887 + 0.396261i −0.905962 0.423360i \(-0.860851\pi\)
−0.572906 + 0.819621i \(0.694184\pi\)
\(524\) 0 0
\(525\) 0.0980762 0.686533i 0.00428040 0.0299628i
\(526\) 0 0
\(527\) 4.75833 + 8.24167i 0.207276 + 0.359013i
\(528\) 0 0
\(529\) 19.9019 11.4904i 0.865301 0.499582i
\(530\) 0 0
\(531\) 37.6865 10.0981i 1.63546 0.438219i
\(532\) 0 0
\(533\) 17.1603 19.5263i 0.743293 0.845777i
\(534\) 0 0
\(535\) −1.66987 + 8.16025i −0.0721949 + 0.352799i
\(536\) 0 0
\(537\) −0.258330 + 0.964102i −0.0111478 + 0.0416041i
\(538\) 0 0
\(539\) 8.53590 31.8564i 0.367667 1.37215i
\(540\) 0 0
\(541\) 14.0718 + 14.0718i 0.604994 + 0.604994i 0.941634 0.336640i \(-0.109290\pi\)
−0.336640 + 0.941634i \(0.609290\pi\)
\(542\) 0 0
\(543\) 0.143594 + 0.535898i 0.00616219 + 0.0229976i
\(544\) 0 0
\(545\) 11.3923 + 34.1769i 0.487993 + 1.46398i
\(546\) 0 0
\(547\) −9.19615 + 9.19615i −0.393199 + 0.393199i −0.875826 0.482627i \(-0.839683\pi\)
0.482627 + 0.875826i \(0.339683\pi\)
\(548\) 0 0
\(549\) −2.36603 1.36603i −0.100980 0.0583005i
\(550\) 0 0
\(551\) 2.83013 2.83013i 0.120567 0.120567i
\(552\) 0 0
\(553\) 2.66025 1.53590i 0.113126 0.0653130i
\(554\) 0 0
\(555\) 2.86603 3.23205i 0.121656 0.137193i
\(556\) 0 0
\(557\) −10.2583 + 17.7679i −0.434659 + 0.752852i −0.997268 0.0738714i \(-0.976465\pi\)
0.562608 + 0.826724i \(0.309798\pi\)
\(558\) 0 0
\(559\) −11.9186 35.2321i −0.504102 1.49016i
\(560\) 0 0
\(561\) −1.89230 7.06218i −0.0798932 0.298165i
\(562\) 0 0
\(563\) −31.8205 8.52628i −1.34107 0.359340i −0.484242 0.874934i \(-0.660904\pi\)
−0.856833 + 0.515594i \(0.827571\pi\)
\(564\) 0 0
\(565\) −23.8468 + 26.8923i −1.00324 + 1.13137i
\(566\) 0 0
\(567\) 1.78461 0.0749466
\(568\) 0 0
\(569\) −1.57180 + 2.72243i −0.0658931 + 0.114130i −0.897090 0.441848i \(-0.854323\pi\)
0.831197 + 0.555978i \(0.187656\pi\)
\(570\) 0 0
\(571\) 42.1051i 1.76204i −0.473075 0.881022i \(-0.656856\pi\)
0.473075 0.881022i \(-0.343144\pi\)
\(572\) 0 0
\(573\) 3.68653 + 3.68653i 0.154007 + 0.154007i
\(574\) 0 0
\(575\) 0.428203 0.545517i 0.0178573 0.0227496i
\(576\) 0 0
\(577\) 28.9282i 1.20430i 0.798384 + 0.602148i \(0.205688\pi\)
−0.798384 + 0.602148i \(0.794312\pi\)
\(578\) 0 0
\(579\) 5.16025 + 1.38269i 0.214453 + 0.0574625i
\(580\) 0 0
\(581\) −0.464102 0.803848i −0.0192542 0.0333492i
\(582\) 0 0
\(583\) −49.3468 28.4904i −2.04374 1.17995i
\(584\) 0 0
\(585\) −13.2942 17.5622i −0.549649 0.726107i
\(586\) 0 0
\(587\) 22.7942 + 13.1603i 0.940819 + 0.543182i 0.890217 0.455537i \(-0.150553\pi\)
0.0506017 + 0.998719i \(0.483886\pi\)
\(588\) 0 0
\(589\) −5.36603 9.29423i −0.221103 0.382962i
\(590\) 0 0
\(591\) 10.1603 + 2.72243i 0.417937 + 0.111986i
\(592\) 0 0
\(593\) 7.07180i 0.290404i −0.989402 0.145202i \(-0.953617\pi\)
0.989402 0.145202i \(-0.0463832\pi\)
\(594\) 0 0
\(595\) −1.74167 0.356406i −0.0714015 0.0146112i
\(596\) 0 0
\(597\) −1.43782 1.43782i −0.0588461 0.0588461i
\(598\) 0 0
\(599\) 5.60770i 0.229124i −0.993416 0.114562i \(-0.963454\pi\)
0.993416 0.114562i \(-0.0365465\pi\)
\(600\) 0 0
\(601\) −4.57180 + 7.91858i −0.186487 + 0.323006i −0.944077 0.329726i \(-0.893044\pi\)
0.757589 + 0.652732i \(0.226377\pi\)
\(602\) 0 0
\(603\) −34.0526 −1.38673
\(604\) 0 0
\(605\) 26.0263 1.56218i 1.05812 0.0635116i
\(606\) 0 0
\(607\) −33.3564 8.93782i −1.35389 0.362775i −0.492324 0.870412i \(-0.663852\pi\)
−0.861571 + 0.507637i \(0.830519\pi\)
\(608\) 0 0
\(609\) −0.0429399 0.160254i −0.00174001 0.00649382i
\(610\) 0 0
\(611\) −14.9282 22.3923i −0.603930 0.905896i
\(612\) 0 0
\(613\) 5.33013 9.23205i 0.215282 0.372879i −0.738078 0.674715i \(-0.764266\pi\)
0.953360 + 0.301836i \(0.0975997\pi\)
\(614\) 0 0
\(615\) 0.500000 + 8.33013i 0.0201619 + 0.335903i
\(616\) 0 0
\(617\) −27.8660 + 16.0885i −1.12184 + 0.647697i −0.941871 0.335975i \(-0.890934\pi\)
−0.179973 + 0.983672i \(0.557601\pi\)
\(618\) 0 0
\(619\) −5.87564 + 5.87564i −0.236162 + 0.236162i −0.815259 0.579097i \(-0.803405\pi\)
0.579097 + 0.815259i \(0.303405\pi\)
\(620\) 0 0
\(621\) −0.356406 0.205771i −0.0143021 0.00825732i
\(622\) 0 0
\(623\) −0.581416 + 0.581416i −0.0232939 + 0.0232939i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) 2.13397 + 7.96410i 0.0852227 + 0.318056i
\(628\) 0 0
\(629\) −7.83013 7.83013i −0.312208 0.312208i
\(630\) 0 0
\(631\) 6.20577 23.1603i 0.247048 0.921995i −0.725295 0.688438i \(-0.758297\pi\)
0.972343 0.233557i \(-0.0750366\pi\)
\(632\) 0 0
\(633\) 1.33013 4.96410i 0.0528678 0.197305i
\(634\) 0 0
\(635\) 10.2058 + 2.08846i 0.405004 + 0.0828779i
\(636\) 0 0
\(637\) 24.9282 1.60770i 0.987691 0.0636992i
\(638\) 0 0
\(639\) −7.83013 + 2.09808i −0.309755 + 0.0829986i
\(640\) 0 0
\(641\) 40.2846 23.2583i 1.59115 0.918649i 0.598036 0.801470i \(-0.295948\pi\)
0.993111 0.117179i \(-0.0373852\pi\)
\(642\) 0 0
\(643\) 20.6506 + 35.7679i 0.814382 + 1.41055i 0.909771 + 0.415110i \(0.136257\pi\)
−0.0953896 + 0.995440i \(0.530410\pi\)
\(644\) 0 0
\(645\) 10.6795 + 5.33975i 0.420505 + 0.210252i
\(646\) 0 0
\(647\) −2.96410 + 0.794229i −0.116531 + 0.0312243i −0.316613 0.948555i \(-0.602546\pi\)
0.200082 + 0.979779i \(0.435879\pi\)
\(648\) 0 0
\(649\) −67.9808 −2.66848
\(650\) 0 0
\(651\) −0.444864 −0.0174356
\(652\) 0 0
\(653\) −0.696152 + 0.186533i −0.0272425 + 0.00729962i −0.272415 0.962180i \(-0.587822\pi\)
0.245172 + 0.969480i \(0.421156\pi\)
\(654\) 0 0
\(655\) −27.7128 13.8564i −1.08283 0.541415i
\(656\) 0 0
\(657\) −1.26795 2.19615i −0.0494674 0.0856801i
\(658\) 0 0
\(659\) 29.2128 16.8660i 1.13797 0.657007i 0.192043 0.981387i \(-0.438489\pi\)
0.945927 + 0.324380i \(0.105155\pi\)
\(660\) 0 0
\(661\) −1.59808 + 0.428203i −0.0621580 + 0.0166552i −0.289764 0.957098i \(-0.593577\pi\)
0.227606 + 0.973753i \(0.426910\pi\)
\(662\) 0 0
\(663\) 4.60770 3.07180i 0.178948 0.119299i
\(664\) 0 0
\(665\) 1.96410 + 0.401924i 0.0761646 + 0.0155859i
\(666\) 0 0
\(667\) 0.0429399 0.160254i 0.00166264 0.00620506i
\(668\) 0 0
\(669\) −2.64359 + 9.86603i −0.102207 + 0.381443i
\(670\) 0 0
\(671\) 3.36603 + 3.36603i 0.129944 + 0.129944i
\(672\) 0 0
\(673\) 7.23205 + 26.9904i 0.278775 + 1.04040i 0.953269 + 0.302122i \(0.0976952\pi\)
−0.674494 + 0.738280i \(0.735638\pi\)
\(674\) 0 0
\(675\) 14.6865 + 2.09808i 0.565285 + 0.0807550i
\(676\) 0 0
\(677\) −10.3205 + 10.3205i −0.396649 + 0.396649i −0.877049 0.480400i \(-0.840491\pi\)
0.480400 + 0.877049i \(0.340491\pi\)
\(678\) 0 0
\(679\) 0.571797 + 0.330127i 0.0219435 + 0.0126691i
\(680\) 0 0
\(681\) −0.169873 + 0.169873i −0.00650955 + 0.00650955i
\(682\) 0 0
\(683\) 26.3827 15.2321i 1.00951 0.582838i 0.0984586 0.995141i \(-0.468609\pi\)
0.911047 + 0.412303i \(0.135275\pi\)
\(684\) 0 0
\(685\) −1.50000 24.9904i −0.0573121 0.954833i
\(686\) 0 0
\(687\) 3.97372 6.88269i 0.151607 0.262591i
\(688\) 0 0
\(689\) 8.46410 42.3205i 0.322457 1.61228i
\(690\) 0 0
\(691\) −0.0621778 0.232051i −0.00236536 0.00882763i 0.964733 0.263230i \(-0.0847879\pi\)
−0.967098 + 0.254403i \(0.918121\pi\)
\(692\) 0 0
\(693\) −3.36603 0.901924i −0.127865 0.0342613i
\(694\) 0 0
\(695\) −13.9904 + 0.839746i −0.530685 + 0.0318534i
\(696\) 0 0
\(697\) 21.3923 0.810291
\(698\) 0 0
\(699\) −4.02628 + 6.97372i −0.152288 + 0.263770i
\(700\) 0 0
\(701\) 29.0718i 1.09803i 0.835814 + 0.549013i \(0.184996\pi\)
−0.835814 + 0.549013i \(0.815004\pi\)
\(702\) 0 0
\(703\) 8.83013 + 8.83013i 0.333035 + 0.333035i
\(704\) 0 0
\(705\) 8.46410 + 1.73205i 0.318777 + 0.0652328i
\(706\) 0 0
\(707\) 0.464102i 0.0174543i
\(708\) 0 0
\(709\) 5.59808 + 1.50000i 0.210240 + 0.0563337i 0.362402 0.932022i \(-0.381957\pi\)
−0.152162 + 0.988356i \(0.548623\pi\)
\(710\) 0 0
\(711\) 15.6603 + 27.1244i 0.587305 + 1.01724i
\(712\) 0 0
\(713\) −0.385263 0.222432i −0.0144282 0.00833014i
\(714\) 0 0
\(715\) 14.4545 + 35.5526i 0.540567 + 1.32959i
\(716\) 0 0
\(717\) −5.83013 3.36603i −0.217730 0.125707i
\(718\) 0 0
\(719\) 14.8923 + 25.7942i 0.555389 + 0.961962i 0.997873 + 0.0651859i \(0.0207641\pi\)
−0.442484 + 0.896776i \(0.645903\pi\)
\(720\) 0 0
\(721\) 3.90192 + 1.04552i 0.145315 + 0.0389371i
\(722\) 0 0
\(723\) 9.87564i 0.367279i
\(724\) 0 0
\(725\) 0.715390 + 5.93782i 0.0265689 + 0.220525i
\(726\) 0 0
\(727\) −13.5885 13.5885i −0.503968 0.503968i 0.408701 0.912669i \(-0.365982\pi\)
−0.912669 + 0.408701i \(0.865982\pi\)
\(728\) 0 0
\(729\) 13.5885i 0.503276i
\(730\) 0 0
\(731\) 15.3038 26.5070i 0.566033 0.980398i
\(732\) 0 0
\(733\) −38.6410 −1.42724 −0.713619 0.700534i \(-0.752945\pi\)
−0.713619 + 0.700534i \(0.752945\pi\)
\(734\) 0 0
\(735\) −5.32051 + 6.00000i −0.196250 + 0.221313i
\(736\) 0 0
\(737\) 57.3109 + 15.3564i 2.11107 + 0.565661i
\(738\) 0 0
\(739\) 10.7417 + 40.0885i 0.395139 + 1.47468i 0.821544 + 0.570145i \(0.193113\pi\)
−0.426405 + 0.904532i \(0.640220\pi\)
\(740\) 0 0
\(741\) −5.19615 + 3.46410i −0.190885 + 0.127257i
\(742\) 0 0
\(743\) −17.5981 + 30.4808i −0.645611 + 1.11823i 0.338549 + 0.940949i \(0.390064\pi\)
−0.984160 + 0.177282i \(0.943270\pi\)
\(744\) 0 0
\(745\) 24.4090 27.5263i 0.894275 1.00848i
\(746\) 0 0
\(747\) 8.19615 4.73205i 0.299882 0.173137i
\(748\) 0 0
\(749\) −0.705771 + 0.705771i −0.0257883 + 0.0257883i
\(750\) 0 0
\(751\) 31.7487 + 18.3301i 1.15853 + 0.668876i 0.950951 0.309343i \(-0.100109\pi\)
0.207576 + 0.978219i \(0.433442\pi\)
\(752\) 0 0
\(753\) 10.0981 10.0981i 0.367994 0.367994i
\(754\) 0 0
\(755\) 11.1962 + 33.5885i 0.407470 + 1.22241i
\(756\) 0 0
\(757\) −4.30385 16.0622i −0.156426 0.583790i −0.998979 0.0451764i \(-0.985615\pi\)
0.842553 0.538613i \(-0.181052\pi\)
\(758\) 0 0
\(759\) 0.241670 + 0.241670i 0.00877206 + 0.00877206i
\(760\) 0 0
\(761\) 2.66987 9.96410i 0.0967828 0.361198i −0.900501 0.434854i \(-0.856800\pi\)
0.997284 + 0.0736557i \(0.0234666\pi\)
\(762\) 0 0
\(763\) −1.11731 + 4.16987i −0.0404495 + 0.150960i
\(764\) 0 0
\(765\) 3.63397 17.7583i 0.131387 0.642054i
\(766\) 0 0
\(767\) −16.5000 48.7750i −0.595780 1.76116i
\(768\) 0 0
\(769\) −5.33013 + 1.42820i −0.192209 + 0.0515023i −0.353639 0.935382i \(-0.615056\pi\)
0.161430 + 0.986884i \(0.448389\pi\)
\(770\) 0 0
\(771\) 6.10770 3.52628i 0.219963 0.126996i
\(772\) 0 0
\(773\) 21.0622 + 36.4808i 0.757554 + 1.31212i 0.944095 + 0.329675i \(0.106939\pi\)
−0.186541 + 0.982447i \(0.559728\pi\)
\(774\) 0 0
\(775\) 15.8756 + 2.26795i 0.570270 + 0.0814671i
\(776\) 0 0
\(777\) 0.500000 0.133975i 0.0179374 0.00480631i
\(778\) 0 0
\(779\) −24.1244 −0.864345
\(780\) 0 0
\(781\) 14.1244 0.505409
\(782\) 0 0
\(783\) 3.42820 0.918584i 0.122514 0.0328275i
\(784\) 0 0
\(785\) 40.1769 13.3923i 1.43398 0.477992i
\(786\) 0 0
\(787\) 21.9904 + 38.0885i 0.783872 + 1.35771i 0.929670 + 0.368392i \(0.120092\pi\)
−0.145798 + 0.989314i \(0.546575\pi\)
\(788\) 0 0
\(789\) −8.30385 + 4.79423i −0.295625 + 0.170679i
\(790\) 0 0
\(791\) −4.16025