Properties

Label 260.2.bf.a.37.1
Level $260$
Weight $2$
Character 260.37
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 37.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.37
Dual form 260.2.bf.a.253.1

$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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 0.111576 0.993756i \(-0.464410\pi\)
−0.400251 + 0.916406i \(0.631077\pi\)
\(4\) 0 0
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 0 0
\(7\) 0.133975 0.232051i 0.0506376 0.0877070i −0.839596 0.543212i \(-0.817208\pi\)
0.890233 + 0.455505i \(0.150541\pi\)
\(8\) 0 0
\(9\) −2.36603 1.36603i −0.788675 0.455342i
\(10\) 0 0
\(11\) 4.59808 + 1.23205i 1.38637 + 0.371477i 0.873432 0.486947i \(-0.161889\pi\)
0.512941 + 0.858424i \(0.328556\pi\)
\(12\) 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 −0.994358 0.106073i \(-0.966172\pi\)
0.808103 0.589041i \(-0.200494\pi\)
\(18\) 0 0
\(19\) 0.866025 + 3.23205i 0.198680 + 0.741483i 0.991283 + 0.131746i \(0.0420584\pi\)
−0.792604 + 0.609737i \(0.791275\pi\)
\(20\) 0 0
\(21\) −0.0980762 + 0.0980762i −0.0214020 + 0.0214020i
\(22\) 0 0
\(23\) −0.0358984 + 0.133975i −0.00748533 + 0.0279356i −0.969567 0.244824i \(-0.921270\pi\)
0.962082 + 0.272760i \(0.0879364\pi\)
\(24\) 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 −0.400726 0.916198i \(-0.631242\pi\)
0.593088 + 0.805138i \(0.297909\pi\)
\(30\) 0 0
\(31\) 2.26795 + 2.26795i 0.407336 + 0.407336i 0.880808 0.473473i \(-0.157000\pi\)
−0.473473 + 0.880808i \(0.657000\pi\)
\(32\) 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 0.670882 0.741564i \(-0.265916\pi\)
−0.977654 + 0.210218i \(0.932582\pi\)
\(38\) 0 0
\(39\) −1.40192 + 1.23205i −0.224487 + 0.197286i
\(40\) 0 0
\(41\) −1.86603 + 6.96410i −0.291424 + 1.08761i 0.652592 + 0.757710i \(0.273682\pi\)
−0.944016 + 0.329900i \(0.892985\pi\)
\(42\) 0 0
\(43\) −9.96410 + 2.66987i −1.51951 + 0.407152i −0.919581 0.392900i \(-0.871472\pi\)
−0.599930 + 0.800052i \(0.704805\pi\)
\(44\) 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 −0.178737 + 0.983897i \(0.557201\pi\)
−0.983897 + 0.178737i \(0.942799\pi\)
\(54\) 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 −0.993319 0.115404i \(-0.963184\pi\)
−0.802537 + 0.596602i \(0.796517\pi\)
\(60\) 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
\(63\) −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 0.335201 0.942146i \(-0.391196\pi\)
0.983524 + 0.180780i \(0.0578623\pi\)
\(68\) 0 0
\(69\) 0.0358984 0.0621778i 0.00432166 0.00748533i
\(70\) 0 0
\(71\) 2.86603 0.767949i 0.340135 0.0911388i −0.0847085 0.996406i \(-0.526996\pi\)
0.424843 + 0.905267i \(0.360329\pi\)
\(72\) 0 0
\(73\) 0.928203i 0.108638i −0.998524 0.0543190i \(-0.982701\pi\)
0.998524 0.0543190i \(-0.0172988\pi\)
\(74\) 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 \(0.223104\pi\)
−0.764262 + 0.644906i \(0.776896\pi\)
\(80\) 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 −0.910971 0.412470i \(-0.864666\pi\)
0.995159 + 0.0982760i \(0.0313328\pi\)
\(90\) 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 0.604408 0.796675i \(-0.293410\pi\)
−0.387736 + 0.921770i \(0.626743\pi\)
\(98\) 0 0
\(99\) −9.19615 9.19615i −0.924248 0.924248i
\(100\) 0 0
\(101\) 1.50000 0.866025i 0.149256 0.0861727i −0.423512 0.905890i \(-0.639203\pi\)
0.572768 + 0.819718i \(0.305870\pi\)
\(102\) 0 0
\(103\) 10.6603 + 10.6603i 1.05039 + 1.05039i 0.998661 + 0.0517247i \(0.0164718\pi\)
0.0517247 + 0.998661i \(0.483528\pi\)
\(104\) 0 0
\(105\) −0.0980762 + 0.294229i −0.00957126 + 0.0287138i
\(106\) 0 0
\(107\) 0.964102 3.59808i 0.0932032 0.347839i −0.903538 0.428509i \(-0.859039\pi\)
0.996741 + 0.0806695i \(0.0257058\pi\)
\(108\) 0 0
\(109\) 11.3923 11.3923i 1.09118 1.09118i 0.0957826 0.995402i \(-0.469465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) 0 0
\(111\) 0.500000 + 1.86603i 0.0474579 + 0.177115i
\(112\) 0 0
\(113\) −4.16025 15.5263i −0.391364 1.46059i −0.827886 0.560896i \(-0.810457\pi\)
0.436522 0.899693i \(-0.356210\pi\)
\(114\) 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 0.452885 0.891569i \(-0.350395\pi\)
−0.0535746 + 0.998564i \(0.517061\pi\)
\(128\) 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 −0.999690 0.0249057i \(-0.992071\pi\)
0.521414 + 0.853304i \(0.325405\pi\)
\(138\) 0 0
\(139\) −5.42820 3.13397i −0.460414 0.265820i 0.251804 0.967778i \(-0.418976\pi\)
−0.712218 + 0.701958i \(0.752309\pi\)
\(140\) 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 0.888042 + 0.459762i \(0.152065\pi\)
−0.539186 + 0.842187i \(0.681268\pi\)
\(150\) 0 0
\(151\) 11.1962 11.1962i 0.911130 0.911130i −0.0852312 0.996361i \(-0.527163\pi\)
0.996361 + 0.0852312i \(0.0271629\pi\)
\(152\) 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 0.997450 + 0.0713726i \(0.0227379\pi\)
0.0713726 + 0.997450i \(0.477262\pi\)
\(158\) 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 0.184661 0.982802i \(-0.440881\pi\)
−0.758801 + 0.651322i \(0.774215\pi\)
\(164\) 0 0
\(165\) −5.50000 0.330127i −0.428174 0.0257004i
\(166\) 0 0
\(167\) −5.33013 9.23205i −0.412458 0.714398i 0.582700 0.812687i \(-0.301996\pi\)
−0.995158 + 0.0982896i \(0.968663\pi\)
\(168\) 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 0.258441 0.966027i \(-0.416791\pi\)
0.706830 + 0.707384i \(0.250125\pi\)
\(174\) 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 0.899804 0.436294i \(-0.143709\pi\)
−0.827744 + 0.561106i \(0.810376\pi\)
\(180\) 0 0
\(181\) 1.07180i 0.0796660i 0.999206 + 0.0398330i \(0.0126826\pi\)
−0.999206 + 0.0398330i \(0.987317\pi\)
\(182\) 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 −0.988677 0.150058i \(-0.952054\pi\)
0.624292 + 0.781191i \(0.285387\pi\)
\(192\) 0 0
\(193\) −8.93782 + 5.16025i −0.643359 + 0.371443i −0.785907 0.618345i \(-0.787804\pi\)
0.142549 + 0.989788i \(0.454470\pi\)
\(194\) 0 0
\(195\) −1.57180 + 3.86603i −0.112559 + 0.276852i
\(196\) 0 0
\(197\) −17.5981 + 10.1603i −1.25381 + 0.723888i −0.971864 0.235542i \(-0.924314\pi\)
−0.281947 + 0.959430i \(0.590980\pi\)
\(198\) 0 0
\(199\) 1.96410 3.40192i 0.139231 0.241156i −0.787974 0.615708i \(-0.788870\pi\)
0.927206 + 0.374552i \(0.122203\pi\)
\(200\) 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 0.643014 0.765855i \(-0.277684\pi\)
−0.984756 + 0.173939i \(0.944351\pi\)
\(212\) 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 0.980438 + 0.196829i \(0.0630644\pi\)
−0.319760 + 0.947499i \(0.603602\pi\)
\(224\) 0 0
\(225\) −12.5622 + 5.36603i −0.837479 + 0.357735i
\(226\) 0 0
\(227\) 0.401924 + 0.232051i 0.0266766 + 0.0154018i 0.513279 0.858222i \(-0.328431\pi\)
−0.486602 + 0.873624i \(0.661764\pi\)
\(228\) 0 0
\(229\) −10.8564 10.8564i −0.717412 0.717412i 0.250663 0.968074i \(-0.419351\pi\)
−0.968074 + 0.250663i \(0.919351\pi\)
\(230\) 0 0
\(231\) −0.571797 + 0.330127i −0.0376215 + 0.0217208i
\(232\) 0 0
\(233\) 11.0000 + 11.0000i 0.720634 + 0.720634i 0.968734 0.248100i \(-0.0798063\pi\)
−0.248100 + 0.968734i \(0.579806\pi\)
\(234\) 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 −0.344088 0.938937i \(-0.611812\pi\)
0.938937 + 0.344088i \(0.111812\pi\)
\(240\) 0 0
\(241\) −4.93782 18.4282i −0.318073 1.18706i −0.921094 0.389340i \(-0.872703\pi\)
0.603021 0.797725i \(-0.293963\pi\)
\(242\) 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 −0.999956 0.00939359i \(-0.997010\pi\)
−0.508113 0.861290i \(-0.669657\pi\)
\(252\) 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 −0.176168 0.984360i \(-0.556370\pi\)
−0.644746 + 0.764397i \(0.723037\pi\)
\(258\) 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 0.764102 0.645095i \(-0.223182\pi\)
0.339184 + 0.940720i \(0.389849\pi\)
\(264\) 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 0.996998 0.0774275i \(-0.0246706\pi\)
0.431445 + 0.902139i \(0.358004\pi\)
\(270\) 0 0
\(271\) −19.7942 5.30385i −1.20241 0.322186i −0.398633 0.917111i \(-0.630515\pi\)
−0.803781 + 0.594925i \(0.797182\pi\)
\(272\) 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 0.860326 + 0.509744i \(0.170260\pi\)
−0.490192 + 0.871614i \(0.663073\pi\)
\(278\) 0 0
\(279\) −2.26795 8.46410i −0.135779 0.506733i
\(280\) 0 0
\(281\) −7.39230 + 7.39230i −0.440988 + 0.440988i −0.892344 0.451356i \(-0.850940\pi\)
0.451356 + 0.892344i \(0.350940\pi\)
\(282\) 0 0
\(283\) −3.35641 + 12.5263i −0.199518 + 0.744610i 0.791533 + 0.611126i \(0.209283\pi\)
−0.991051 + 0.133484i \(0.957384\pi\)
\(284\) 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 −0.190971 0.981596i \(-0.561164\pi\)
−0.945572 + 0.325412i \(0.894497\pi\)
\(294\) 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 \(-0.847602\pi\)
0.887561 0.460690i \(-0.152398\pi\)
\(312\) 0 0
\(313\) 20.3205 20.3205i 1.14858 1.14858i 0.161752 0.986832i \(-0.448286\pi\)
0.986832 0.161752i \(-0.0517143\pi\)
\(314\) 0 0
\(315\) −0.901924 + 1.36603i −0.0508176 + 0.0769668i
\(316\) 0 0
\(317\) 3.07180i 0.172529i −0.996272 0.0862646i \(-0.972507\pi\)
0.996272 0.0862646i \(-0.0274931\pi\)
\(318\) 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 0.0365099 0.999333i \(-0.488376\pi\)
0.531285 + 0.847193i \(0.321709\pi\)
\(332\) 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 −0.705149 0.709060i \(-0.749120\pi\)
0.709060 + 0.705149i \(0.249120\pi\)
\(338\) 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 0.481233 0.876593i \(-0.340189\pi\)
0.855056 + 0.518535i \(0.173523\pi\)
\(348\) 0 0
\(349\) 5.47372 20.4282i 0.293002 1.09350i −0.649790 0.760114i \(-0.725143\pi\)
0.942792 0.333383i \(-0.108190\pi\)
\(350\) 0 0
\(351\) 10.4904 2.09808i 0.559935 0.111987i
\(352\) 0 0
\(353\) 7.86603 + 13.6244i 0.418666 + 0.725151i 0.995806 0.0914944i \(-0.0291644\pi\)
−0.577139 + 0.816646i \(0.695831\pi\)
\(354\) 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 0.878410 0.477907i \(-0.158604\pi\)
−0.477907 + 0.878410i \(0.658604\pi\)
\(360\) 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 0.848439 + 0.529293i \(0.177543\pi\)
−0.999416 + 0.0341614i \(0.989124\pi\)
\(368\) 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 −0.854130 0.520059i \(-0.825910\pi\)
0.479669 0.877450i \(-0.340757\pi\)
\(374\) 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 −0.402305 0.915506i \(-0.631791\pi\)
−0.806159 + 0.591699i \(0.798457\pi\)
\(380\) 0 0
\(381\) −2.08846 1.20577i −0.106995 0.0617735i
\(382\) 0 0
\(383\) 0.401924 0.696152i 0.0205373 0.0355717i −0.855574 0.517680i \(-0.826796\pi\)
0.876111 + 0.482109i \(0.160129\pi\)
\(384\) 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 −0.739156 0.673534i \(-0.764775\pi\)
0.952876 + 0.303361i \(0.0981088\pi\)
\(398\) 0 0
\(399\) −0.401924 0.232051i −0.0201214 0.0116171i
\(400\) 0 0
\(401\) 5.86603 + 1.57180i 0.292935 + 0.0784918i 0.402294 0.915511i \(-0.368213\pi\)
−0.109359 + 0.994002i \(0.534880\pi\)
\(402\) 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 −0.999386 0.0350453i \(-0.988842\pi\)
0.847971 0.530043i \(-0.177824\pi\)
\(410\) 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 −0.986279 0.165088i \(-0.947209\pi\)
−0.350169 + 0.936687i \(0.613876\pi\)
\(420\) 0 0
\(421\) 14.0718 + 14.0718i 0.685817 + 0.685817i 0.961305 0.275487i \(-0.0888392\pi\)
−0.275487 + 0.961305i \(0.588839\pi\)
\(422\) 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 −0.389979 0.920824i \(-0.627518\pi\)
0.798143 0.602468i \(-0.205816\pi\)
\(432\) 0 0
\(433\) 10.1603 2.72243i 0.488271 0.130832i −0.00628046 0.999980i \(-0.501999\pi\)
0.494551 + 0.869149i \(0.335332\pi\)
\(434\) 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 0.687873 0.725831i \(-0.258544\pi\)
−0.972524 + 0.232801i \(0.925211\pi\)
\(440\) 0 0
\(441\) 18.9282i 0.901343i
\(442\) 0 0
\(443\) 27.0526 27.0526i 1.28531 1.28531i 0.347700 0.937606i \(-0.386963\pi\)
0.937606 0.347700i \(-0.113037\pi\)
\(444\) 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 0.356375 0.934343i \(-0.384013\pi\)
0.775801 + 0.630977i \(0.217346\pi\)
\(450\) 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 −0.958468 0.285201i \(-0.907940\pi\)
−0.232243 + 0.972658i \(0.574606\pi\)
\(458\) 0 0
\(459\) 4.40192 7.62436i 0.205464 0.355874i
\(460\) 0 0
\(461\) −23.9904 + 6.42820i −1.11734 + 0.299391i −0.769808 0.638276i \(-0.779648\pi\)
−0.347535 + 0.937667i \(0.612981\pi\)
\(462\) 0 0
\(463\) 29.8564i 1.38754i 0.720194 + 0.693772i \(0.244053\pi\)
−0.720194 + 0.693772i \(0.755947\pi\)
\(464\) 0 0
\(465\) −3.09808 2.04552i −0.143670 0.0948586i
\(466\) 0 0
\(467\) −20.1244 + 20.1244i −0.931244 + 0.931244i −0.997784 0.0665397i \(-0.978804\pi\)
0.0665397 + 0.997784i \(0.478804\pi\)
\(468\) 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 −0.985148 0.171708i \(-0.945071\pi\)
0.939017 + 0.343870i \(0.111738\pi\)
\(480\) 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 0.987802 0.155713i \(-0.0497675\pi\)
0.359050 + 0.933318i \(0.383101\pi\)
\(488\) 0 0
\(489\) 3.09808 + 3.09808i 0.140100 + 0.140100i
\(490\) 0 0
\(491\) −13.9641 + 8.06218i −0.630191 + 0.363841i −0.780826 0.624748i \(-0.785202\pi\)
0.150635 + 0.988589i \(0.451868\pi\)
\(492\) 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 −0.775018 0.631939i \(-0.782259\pi\)
0.631939 + 0.775018i \(0.282259\pi\)
\(500\) 0 0
\(501\) 1.42820 + 5.33013i 0.0638074 + 0.238133i
\(502\) 0 0
\(503\) −4.03590 15.0622i −0.179952 0.671589i −0.995655 0.0931187i \(-0.970316\pi\)
0.815703 0.578471i \(-0.196350\pi\)
\(504\) 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 0.0585970 0.998282i \(-0.481337\pi\)
−0.448394 + 0.893836i \(0.648004\pi\)
\(510\) 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 −0.572906 0.819621i \(-0.694184\pi\)
−0.905962 + 0.423360i \(0.860851\pi\)
\(524\) 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 −0.336640 0.941634i \(-0.609290\pi\)
0.941634 + 0.336640i \(0.109290\pi\)
\(542\) 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 0.482627 0.875826i \(-0.339683\pi\)
−0.875826 + 0.482627i \(0.839683\pi\)
\(548\) 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 0.562608 0.826724i \(-0.309798\pi\)
−0.997268 + 0.0738714i \(0.976465\pi\)
\(558\) 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 −0.856833 0.515594i \(-0.827571\pi\)
−0.484242 + 0.874934i \(0.660904\pi\)
\(564\) 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 0.831197 0.555978i \(-0.187656\pi\)
−0.897090 + 0.441848i \(0.854323\pi\)
\(570\) 0 0
\(571\) 42.1051i 1.76204i 0.473075 + 0.881022i \(0.343144\pi\)
−0.473075 + 0.881022i \(0.656856\pi\)
\(572\) 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 \(-0.794312\pi\)
0.798384 0.602148i \(-0.205688\pi\)
\(578\) 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 0.0506017 0.998719i \(-0.483886\pi\)
0.890217 + 0.455537i \(0.150553\pi\)
\(588\) 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 \(0.0463832\pi\)
−0.989402 + 0.145202i \(0.953617\pi\)
\(594\) 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 \(0.0365465\pi\)
−0.993416 + 0.114562i \(0.963454\pi\)
\(600\) 0 0
\(601\) −4.57180 7.91858i −0.186487 0.323006i 0.757589 0.652732i \(-0.226377\pi\)
−0.944077 + 0.329726i \(0.893044\pi\)
\(602\) 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 −0.861571 0.507637i \(-0.830519\pi\)
−0.492324 + 0.870412i \(0.663852\pi\)
\(608\) 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 0.953360 0.301836i \(-0.0975997\pi\)
−0.738078 + 0.674715i \(0.764266\pi\)
\(614\) 0 0
\(615\) 0.500000 8.33013i 0.0201619 0.335903i
\(616\) 0 0
\(617\) −27.8660 16.0885i −1.12184 0.647697i −0.179973 0.983672i \(-0.557601\pi\)
−0.941871 + 0.335975i \(0.890934\pi\)
\(618\) 0 0
\(619\) −5.87564 5.87564i −0.236162 0.236162i 0.579097 0.815259i \(-0.303405\pi\)
−0.815259 + 0.579097i \(0.803405\pi\)
\(620\) 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 0.972343 + 0.233557i \(0.0750366\pi\)
−0.725295 + 0.688438i \(0.758297\pi\)
\(632\) 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 0.993111 + 0.117179i \(0.0373852\pi\)
0.598036 + 0.801470i \(0.295948\pi\)
\(642\) 0 0
\(643\) 20.6506 35.7679i 0.814382 1.41055i −0.0953896 0.995440i \(-0.530410\pi\)
0.909771 0.415110i \(-0.136257\pi\)
\(644\) 0 0
\(645\) 10.6795 5.33975i 0.420505 0.210252i
\(646\) 0 0
\(647\) −2.96410 0.794229i −0.116531 0.0312243i 0.200082 0.979779i \(-0.435879\pi\)
−0.316613 + 0.948555i \(0.602546\pi\)
\(648\) 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 0.245172 0.969480i \(-0.421156\pi\)
−0.272415 + 0.962180i \(0.587822\pi\)
\(654\) 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 0.945927 0.324380i \(-0.105155\pi\)
0.192043 + 0.981387i \(0.438489\pi\)
\(660\) 0 0
\(661\) −1.59808 0.428203i −0.0621580 0.0166552i 0.227606 0.973753i \(-0.426910\pi\)
−0.289764 + 0.957098i \(0.593577\pi\)
\(662\) 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 −0.674494 0.738280i \(-0.735638\pi\)
0.953269 0.302122i \(-0.0976952\pi\)
\(674\) 0 0
\(675\) 14.6865 2.09808i 0.565285 0.0807550i
\(676\) 0 0
\(677\) −10.3205 10.3205i −0.396649 0.396649i 0.480400 0.877049i \(-0.340491\pi\)
−0.877049 + 0.480400i \(0.840491\pi\)
\(678\) 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 0.911047 0.412303i \(-0.135275\pi\)
0.0984586 + 0.995141i \(0.468609\pi\)
\(684\) 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 −0.967098 0.254403i \(-0.918121\pi\)
0.964733 + 0.263230i \(0.0847879\pi\)
\(692\) 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 \(-0.815004\pi\)
0.835814 0.549013i \(-0.184996\pi\)
\(702\) 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 −0.152162 0.988356i \(-0.548623\pi\)
0.362402 + 0.932022i \(0.381957\pi\)
\(710\) 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 −0.442484 0.896776i \(-0.645903\pi\)
0.997873 0.0651859i \(-0.0207641\pi\)
\(720\) 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 −0.912669 0.408701i \(-0.865982\pi\)
0.408701 + 0.912669i \(0.365982\pi\)
\(728\) 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 −0.426405 0.904532i \(-0.640220\pi\)
0.821544 0.570145i \(-0.193113\pi\)
\(740\) 0 0
\(741\) −5.19615 3.46410i −0.190885 0.127257i
\(742\) 0 0
\(743\) −17.5981 30.4808i −0.645611 1.11823i −0.984160 0.177282i \(-0.943270\pi\)
0.338549 0.940949i \(-0.390064\pi\)
\(744\) 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 0.207576 0.978219i \(-0.433442\pi\)
0.950951 + 0.309343i \(0.100109\pi\)
\(752\) 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 0.842553 + 0.538613i \(0.181052\pi\)
−0.998979 + 0.0451764i \(0.985615\pi\)
\(758\) 0 0
\(759\) 0.241670 0.241670i 0.00877206 0.00877206i
\(760\) 0 0
\(761\) 2.66987 + 9.96410i 0.0967828 + 0.361198i 0.997284 0.0736557i \(-0.0234666\pi\)
−0.900501 + 0.434854i \(0.856800\pi\)
\(762\) 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 0.161430 0.986884i \(-0.448389\pi\)
−0.353639 + 0.935382i \(0.615056\pi\)
\(770\) 0 0
\(771\) 6.10770 + 3.52628i 0.219963 + 0.126996i
\(772\) 0 0
\(773\) 21.0622 36.4808i 0.757554 1.31212i −0.186541 0.982447i \(-0.559728\pi\)
0.944095 0.329675i \(-0.106939\pi\)
\(774\) 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 −0.145798 0.989314i \(-0.546575\pi\)
0.929670 0.368392i \(-0.120092\pi\)
\(788\) 0 0
\(789\) −8.30385 4.79423i −0.295625 0.170679i
\(790\) 0 0
\(791\)