Properties

Label 260.2.bk.a.197.1
Level $260$
Weight $2$
Character 260.197
Analytic conductor $2.076$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(1\)
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 197.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.197
Dual form 260.2.bk.a.33.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.133975i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-2.13397 - 1.23205i) q^{7} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.133975i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-2.13397 - 1.23205i) q^{7} +(-2.36603 - 1.36603i) q^{9} +(-1.13397 + 4.23205i) q^{11} +(-2.00000 - 3.00000i) q^{13} +(1.13397 - 0.232051i) q^{15} +(-0.232051 - 0.866025i) q^{17} +(-2.86603 + 0.767949i) q^{19} +(0.901924 + 0.901924i) q^{21} +(-0.0358984 + 0.133975i) q^{23} +(3.00000 - 4.00000i) q^{25} +(2.09808 + 2.09808i) q^{27} +(-1.50000 + 0.866025i) q^{29} +(-5.19615 + 5.19615i) q^{31} +(1.13397 - 1.96410i) q^{33} +(5.50000 + 0.330127i) q^{35} +(1.33013 - 0.767949i) q^{37} +(0.598076 + 1.76795i) q^{39} +(9.33013 + 2.50000i) q^{41} +(-5.96410 + 1.59808i) q^{43} +(6.09808 + 0.366025i) q^{45} -10.9282i q^{47} +(-0.464102 - 0.803848i) q^{49} +0.464102i q^{51} +(2.46410 - 2.46410i) q^{53} +(-1.96410 - 9.59808i) q^{55} +1.53590 q^{57} +(2.33013 + 8.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(3.36603 + 5.83013i) q^{63} +(7.00000 + 4.00000i) q^{65} +(6.13397 + 10.6244i) q^{67} +(0.0358984 - 0.0621778i) q^{69} +(0.598076 + 2.23205i) q^{71} -14.9282 q^{73} +(-2.03590 + 1.59808i) q^{75} +(7.63397 - 7.63397i) q^{77} +0.535898i q^{79} +(3.33013 + 5.76795i) q^{81} -2.92820i q^{83} +(1.33013 + 1.50000i) q^{85} +(0.866025 - 0.232051i) q^{87} +(-14.7942 - 3.96410i) q^{89} +(0.571797 + 8.86603i) q^{91} +(3.29423 - 1.90192i) q^{93} +(4.96410 - 4.40192i) q^{95} +(3.86603 - 6.69615i) q^{97} +(8.46410 - 8.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9} - 8 q^{11} - 8 q^{13} + 8 q^{15} + 6 q^{17} - 8 q^{19} + 14 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} - 6 q^{29} + 8 q^{33} + 22 q^{35} - 12 q^{37} - 8 q^{39} + 20 q^{41} - 10 q^{43} + 14 q^{45} + 12 q^{49} - 4 q^{53} + 6 q^{55} + 20 q^{57} - 8 q^{59} + 18 q^{61} + 10 q^{63} + 28 q^{65} + 28 q^{67} + 14 q^{69} - 8 q^{71} - 32 q^{73} - 22 q^{75} + 34 q^{77} - 4 q^{81} - 12 q^{85} - 28 q^{89} + 30 q^{91} - 18 q^{93} + 6 q^{95} + 12 q^{97} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(7\) −2.13397 1.23205i −0.806567 0.465671i 0.0391956 0.999232i \(-0.487520\pi\)
−0.845762 + 0.533560i \(0.820854\pi\)
\(8\) 0 0
\(9\) −2.36603 1.36603i −0.788675 0.455342i
\(10\) 0 0
\(11\) −1.13397 + 4.23205i −0.341906 + 1.27601i 0.554279 + 0.832331i \(0.312994\pi\)
−0.896185 + 0.443680i \(0.853673\pi\)
\(12\) 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
\(17\) −0.232051 0.866025i −0.0562806 0.210042i 0.932059 0.362306i \(-0.118010\pi\)
−0.988340 + 0.152264i \(0.951344\pi\)
\(18\) 0 0
\(19\) −2.86603 + 0.767949i −0.657511 + 0.176180i −0.572123 0.820168i \(-0.693880\pi\)
−0.0853887 + 0.996348i \(0.527213\pi\)
\(20\) 0 0
\(21\) 0.901924 + 0.901924i 0.196816 + 0.196816i
\(22\) 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
\(29\) −1.50000 + 0.866025i −0.278543 + 0.160817i −0.632764 0.774345i \(-0.718080\pi\)
0.354221 + 0.935162i \(0.384746\pi\)
\(30\) 0 0
\(31\) −5.19615 + 5.19615i −0.933257 + 0.933257i −0.997908 0.0646514i \(-0.979406\pi\)
0.0646514 + 0.997908i \(0.479406\pi\)
\(32\) 0 0
\(33\) 1.13397 1.96410i 0.197400 0.341906i
\(34\) 0 0
\(35\) 5.50000 + 0.330127i 0.929670 + 0.0558017i
\(36\) 0 0
\(37\) 1.33013 0.767949i 0.218672 0.126250i −0.386663 0.922221i \(-0.626372\pi\)
0.605335 + 0.795971i \(0.293039\pi\)
\(38\) 0 0
\(39\) 0.598076 + 1.76795i 0.0957688 + 0.283098i
\(40\) 0 0
\(41\) 9.33013 + 2.50000i 1.45712 + 0.390434i 0.898494 0.438985i \(-0.144662\pi\)
0.558627 + 0.829419i \(0.311329\pi\)
\(42\) 0 0
\(43\) −5.96410 + 1.59808i −0.909517 + 0.243704i −0.683099 0.730326i \(-0.739368\pi\)
−0.226418 + 0.974030i \(0.572702\pi\)
\(44\) 0 0
\(45\) 6.09808 + 0.366025i 0.909048 + 0.0545638i
\(46\) 0 0
\(47\) 10.9282i 1.59404i −0.603951 0.797021i \(-0.706408\pi\)
0.603951 0.797021i \(-0.293592\pi\)
\(48\) 0 0
\(49\) −0.464102 0.803848i −0.0663002 0.114835i
\(50\) 0 0
\(51\) 0.464102i 0.0649872i
\(52\) 0 0
\(53\) 2.46410 2.46410i 0.338470 0.338470i −0.517321 0.855791i \(-0.673071\pi\)
0.855791 + 0.517321i \(0.173071\pi\)
\(54\) 0 0
\(55\) −1.96410 9.59808i −0.264839 1.29420i
\(56\) 0 0
\(57\) 1.53590 0.203435
\(58\) 0 0
\(59\) 2.33013 + 8.69615i 0.303357 + 1.13214i 0.934351 + 0.356355i \(0.115981\pi\)
−0.630994 + 0.775788i \(0.717353\pi\)
\(60\) 0 0
\(61\) 4.50000 7.79423i 0.576166 0.997949i −0.419748 0.907641i \(-0.637882\pi\)
0.995914 0.0903080i \(-0.0287851\pi\)
\(62\) 0 0
\(63\) 3.36603 + 5.83013i 0.424079 + 0.734527i
\(64\) 0 0
\(65\) 7.00000 + 4.00000i 0.868243 + 0.496139i
\(66\) 0 0
\(67\) 6.13397 + 10.6244i 0.749384 + 1.29797i 0.948118 + 0.317918i \(0.102984\pi\)
−0.198734 + 0.980053i \(0.563683\pi\)
\(68\) 0 0
\(69\) 0.0358984 0.0621778i 0.00432166 0.00748533i
\(70\) 0 0
\(71\) 0.598076 + 2.23205i 0.0709786 + 0.264896i 0.992291 0.123927i \(-0.0395487\pi\)
−0.921313 + 0.388822i \(0.872882\pi\)
\(72\) 0 0
\(73\) −14.9282 −1.74721 −0.873607 0.486632i \(-0.838225\pi\)
−0.873607 + 0.486632i \(0.838225\pi\)
\(74\) 0 0
\(75\) −2.03590 + 1.59808i −0.235085 + 0.184530i
\(76\) 0 0
\(77\) 7.63397 7.63397i 0.869972 0.869972i
\(78\) 0 0
\(79\) 0.535898i 0.0602933i 0.999545 + 0.0301466i \(0.00959743\pi\)
−0.999545 + 0.0301466i \(0.990403\pi\)
\(80\) 0 0
\(81\) 3.33013 + 5.76795i 0.370014 + 0.640883i
\(82\) 0 0
\(83\) 2.92820i 0.321412i −0.987002 0.160706i \(-0.948623\pi\)
0.987002 0.160706i \(-0.0513771\pi\)
\(84\) 0 0
\(85\) 1.33013 + 1.50000i 0.144273 + 0.162698i
\(86\) 0 0
\(87\) 0.866025 0.232051i 0.0928477 0.0248785i
\(88\) 0 0
\(89\) −14.7942 3.96410i −1.56819 0.420194i −0.632942 0.774199i \(-0.718153\pi\)
−0.935243 + 0.354005i \(0.884819\pi\)
\(90\) 0 0
\(91\) 0.571797 + 8.86603i 0.0599406 + 0.929412i
\(92\) 0 0
\(93\) 3.29423 1.90192i 0.341596 0.197220i
\(94\) 0 0
\(95\) 4.96410 4.40192i 0.509306 0.451628i
\(96\) 0 0
\(97\) 3.86603 6.69615i 0.392535 0.679891i −0.600248 0.799814i \(-0.704931\pi\)
0.992783 + 0.119923i \(0.0382647\pi\)
\(98\) 0 0
\(99\) 8.46410 8.46410i 0.850674 0.850674i
\(100\) 0 0
\(101\) −14.8923 + 8.59808i −1.48184 + 0.855541i −0.999788 0.0206021i \(-0.993442\pi\)
−0.482052 + 0.876143i \(0.660108\pi\)
\(102\) 0 0
\(103\) −11.1962 11.1962i −1.10319 1.10319i −0.994024 0.109166i \(-0.965182\pi\)
−0.109166 0.994024i \(-0.534818\pi\)
\(104\) 0 0
\(105\) −2.70577 0.901924i −0.264056 0.0880187i
\(106\) 0 0
\(107\) −1.96410 + 7.33013i −0.189877 + 0.708630i 0.803657 + 0.595093i \(0.202885\pi\)
−0.993534 + 0.113537i \(0.963782\pi\)
\(108\) 0 0
\(109\) −3.53590 3.53590i −0.338678 0.338678i 0.517192 0.855869i \(-0.326977\pi\)
−0.855869 + 0.517192i \(0.826977\pi\)
\(110\) 0 0
\(111\) −0.767949 + 0.205771i −0.0728905 + 0.0195310i
\(112\) 0 0
\(113\) 0.767949 + 2.86603i 0.0722426 + 0.269613i 0.992594 0.121480i \(-0.0387639\pi\)
−0.920351 + 0.391093i \(0.872097\pi\)
\(114\) 0 0
\(115\) −0.0621778 0.303848i −0.00579811 0.0283339i
\(116\) 0 0
\(117\) 0.633975 + 9.83013i 0.0586110 + 0.908796i
\(118\) 0 0
\(119\) −0.571797 + 2.13397i −0.0524165 + 0.195621i
\(120\) 0 0
\(121\) −7.09808 4.09808i −0.645280 0.372552i
\(122\) 0 0
\(123\) −4.33013 2.50000i −0.390434 0.225417i
\(124\) 0 0
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) −19.8923 5.33013i −1.76516 0.472972i −0.777404 0.629001i \(-0.783464\pi\)
−0.987752 + 0.156029i \(0.950131\pi\)
\(128\) 0 0
\(129\) 3.19615 0.281406
\(130\) 0 0
\(131\) 5.85641 0.511677 0.255838 0.966720i \(-0.417649\pi\)
0.255838 + 0.966720i \(0.417649\pi\)
\(132\) 0 0
\(133\) 7.06218 + 1.89230i 0.612368 + 0.164084i
\(134\) 0 0
\(135\) −6.29423 2.09808i −0.541721 0.180574i
\(136\) 0 0
\(137\) −12.4019 7.16025i −1.05957 0.611742i −0.134255 0.990947i \(-0.542864\pi\)
−0.925313 + 0.379205i \(0.876198\pi\)
\(138\) 0 0
\(139\) −4.50000 2.59808i −0.381685 0.220366i 0.296866 0.954919i \(-0.404058\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) −1.46410 + 5.46410i −0.123300 + 0.460160i
\(142\) 0 0
\(143\) 14.9641 5.06218i 1.25136 0.423321i
\(144\) 0 0
\(145\) 2.13397 3.23205i 0.177217 0.268407i
\(146\) 0 0
\(147\) 0.124356 + 0.464102i 0.0102567 + 0.0382785i
\(148\) 0 0
\(149\) −3.33013 + 0.892305i −0.272815 + 0.0731005i −0.392633 0.919695i \(-0.628436\pi\)
0.119818 + 0.992796i \(0.461769\pi\)
\(150\) 0 0
\(151\) −0.267949 0.267949i −0.0218054 0.0218054i 0.696120 0.717925i \(-0.254908\pi\)
−0.717925 + 0.696120i \(0.754908\pi\)
\(152\) 0 0
\(153\) −0.633975 + 2.36603i −0.0512538 + 0.191282i
\(154\) 0 0
\(155\) 5.19615 15.5885i 0.417365 1.25210i
\(156\) 0 0
\(157\) 6.46410 + 6.46410i 0.515891 + 0.515891i 0.916326 0.400434i \(-0.131141\pi\)
−0.400434 + 0.916326i \(0.631141\pi\)
\(158\) 0 0
\(159\) −1.56218 + 0.901924i −0.123889 + 0.0715272i
\(160\) 0 0
\(161\) 0.241670 0.241670i 0.0190462 0.0190462i
\(162\) 0 0
\(163\) −1.59808 + 2.76795i −0.125171 + 0.216803i −0.921800 0.387666i \(-0.873281\pi\)
0.796629 + 0.604469i \(0.206615\pi\)
\(164\) 0 0
\(165\) −0.303848 + 5.06218i −0.0236545 + 0.394090i
\(166\) 0 0
\(167\) −15.9904 + 9.23205i −1.23737 + 0.714398i −0.968556 0.248794i \(-0.919966\pi\)
−0.268816 + 0.963191i \(0.586632\pi\)
\(168\) 0 0
\(169\) −5.00000 + 12.0000i −0.384615 + 0.923077i
\(170\) 0 0
\(171\) 7.83013 + 2.09808i 0.598785 + 0.160444i
\(172\) 0 0
\(173\) −2.76795 + 0.741670i −0.210443 + 0.0563881i −0.362500 0.931984i \(-0.618077\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(174\) 0 0
\(175\) −11.3301 + 4.83975i −0.856477 + 0.365850i
\(176\) 0 0
\(177\) 4.66025i 0.350286i
\(178\) 0 0
\(179\) 6.96410 + 12.0622i 0.520521 + 0.901570i 0.999715 + 0.0238604i \(0.00759573\pi\)
−0.479194 + 0.877709i \(0.659071\pi\)
\(180\) 0 0
\(181\) 22.9282i 1.70424i −0.523347 0.852120i \(-0.675317\pi\)
0.523347 0.852120i \(-0.324683\pi\)
\(182\) 0 0
\(183\) −3.29423 + 3.29423i −0.243516 + 0.243516i
\(184\) 0 0
\(185\) −1.89230 + 2.86603i −0.139125 + 0.210714i
\(186\) 0 0
\(187\) 3.92820 0.287259
\(188\) 0 0
\(189\) −1.89230 7.06218i −0.137645 0.513698i
\(190\) 0 0
\(191\) 7.50000 12.9904i 0.542681 0.939951i −0.456068 0.889945i \(-0.650743\pi\)
0.998749 0.0500060i \(-0.0159241\pi\)
\(192\) 0 0
\(193\) 12.7942 + 22.1603i 0.920949 + 1.59513i 0.797950 + 0.602723i \(0.205918\pi\)
0.122998 + 0.992407i \(0.460749\pi\)
\(194\) 0 0
\(195\) −2.96410 2.93782i −0.212264 0.210382i
\(196\) 0 0
\(197\) 2.13397 + 3.69615i 0.152039 + 0.263340i 0.931977 0.362517i \(-0.118083\pi\)
−0.779938 + 0.625857i \(0.784749\pi\)
\(198\) 0 0
\(199\) 9.42820 16.3301i 0.668348 1.15761i −0.310018 0.950731i \(-0.600335\pi\)
0.978366 0.206881i \(-0.0663314\pi\)
\(200\) 0 0
\(201\) −1.64359 6.13397i −0.115930 0.432657i
\(202\) 0 0
\(203\) 4.26795 0.299551
\(204\) 0 0
\(205\) −21.1603 + 4.33013i −1.47790 + 0.302429i
\(206\) 0 0
\(207\) 0.267949 0.267949i 0.0186238 0.0186238i
\(208\) 0 0
\(209\) 13.0000i 0.899229i
\(210\) 0 0
\(211\) −2.96410 5.13397i −0.204057 0.353437i 0.745775 0.666198i \(-0.232080\pi\)
−0.949832 + 0.312761i \(0.898746\pi\)
\(212\) 0 0
\(213\) 1.19615i 0.0819590i
\(214\) 0 0
\(215\) 10.3301 9.16025i 0.704509 0.624724i
\(216\) 0 0
\(217\) 17.4904 4.68653i 1.18732 0.318143i
\(218\) 0 0
\(219\) 7.46410 + 2.00000i 0.504377 + 0.135147i
\(220\) 0 0
\(221\) −2.13397 + 2.42820i −0.143547 + 0.163339i
\(222\) 0 0
\(223\) −1.33013 + 0.767949i −0.0890719 + 0.0514257i −0.543874 0.839167i \(-0.683043\pi\)
0.454802 + 0.890592i \(0.349710\pi\)
\(224\) 0 0
\(225\) −12.5622 + 5.36603i −0.837479 + 0.357735i
\(226\) 0 0
\(227\) 1.59808 2.76795i 0.106068 0.183715i −0.808106 0.589037i \(-0.799507\pi\)
0.914174 + 0.405322i \(0.132841\pi\)
\(228\) 0 0
\(229\) 0.0717968 0.0717968i 0.00474446 0.00474446i −0.704731 0.709475i \(-0.748932\pi\)
0.709475 + 0.704731i \(0.248932\pi\)
\(230\) 0 0
\(231\) −4.83975 + 2.79423i −0.318432 + 0.183847i
\(232\) 0 0
\(233\) 12.8564 + 12.8564i 0.842251 + 0.842251i 0.989151 0.146900i \(-0.0469296\pi\)
−0.146900 + 0.989151i \(0.546930\pi\)
\(234\) 0 0
\(235\) 10.9282 + 21.8564i 0.712877 + 1.42575i
\(236\) 0 0
\(237\) 0.0717968 0.267949i 0.00466370 0.0174052i
\(238\) 0 0
\(239\) 16.6603 + 16.6603i 1.07766 + 1.07766i 0.996719 + 0.0809436i \(0.0257934\pi\)
0.0809436 + 0.996719i \(0.474207\pi\)
\(240\) 0 0
\(241\) 11.3301 3.03590i 0.729838 0.195559i 0.125281 0.992121i \(-0.460017\pi\)
0.604557 + 0.796562i \(0.293350\pi\)
\(242\) 0 0
\(243\) −3.19615 11.9282i −0.205033 0.765195i
\(244\) 0 0
\(245\) 1.73205 + 1.14359i 0.110657 + 0.0730615i
\(246\) 0 0
\(247\) 8.03590 + 7.06218i 0.511312 + 0.449356i
\(248\) 0 0
\(249\) −0.392305 + 1.46410i −0.0248613 + 0.0927837i
\(250\) 0 0
\(251\) −15.3564 8.86603i −0.969288 0.559619i −0.0702687 0.997528i \(-0.522386\pi\)
−0.899019 + 0.437910i \(0.855719\pi\)
\(252\) 0 0
\(253\) −0.526279 0.303848i −0.0330869 0.0191027i
\(254\) 0 0
\(255\) −0.464102 0.928203i −0.0290632 0.0581263i
\(256\) 0 0
\(257\) 21.6244 + 5.79423i 1.34889 + 0.361434i 0.859725 0.510757i \(-0.170635\pi\)
0.489165 + 0.872191i \(0.337302\pi\)
\(258\) 0 0
\(259\) −3.78461 −0.235164
\(260\) 0 0
\(261\) 4.73205 0.292907
\(262\) 0 0
\(263\) 13.8923 + 3.72243i 0.856636 + 0.229535i 0.660300 0.751002i \(-0.270429\pi\)
0.196336 + 0.980537i \(0.437096\pi\)
\(264\) 0 0
\(265\) −2.46410 + 7.39230i −0.151369 + 0.454106i
\(266\) 0 0
\(267\) 6.86603 + 3.96410i 0.420194 + 0.242599i
\(268\) 0 0
\(269\) 15.8205 + 9.13397i 0.964593 + 0.556908i 0.897584 0.440844i \(-0.145321\pi\)
0.0670097 + 0.997752i \(0.478654\pi\)
\(270\) 0 0
\(271\) 4.33013 16.1603i 0.263036 0.981666i −0.700405 0.713746i \(-0.746997\pi\)
0.963441 0.267920i \(-0.0863362\pi\)
\(272\) 0 0
\(273\) 0.901924 4.50962i 0.0545869 0.272935i
\(274\) 0 0
\(275\) 13.5263 + 17.2321i 0.815665 + 1.03913i
\(276\) 0 0
\(277\) −2.76795 10.3301i −0.166310 0.620677i −0.997869 0.0652416i \(-0.979218\pi\)
0.831560 0.555436i \(-0.187448\pi\)
\(278\) 0 0
\(279\) 19.3923 5.19615i 1.16099 0.311086i
\(280\) 0 0
\(281\) −16.4641 16.4641i −0.982166 0.982166i 0.0176778 0.999844i \(-0.494373\pi\)
−0.999844 + 0.0176778i \(0.994373\pi\)
\(282\) 0 0
\(283\) 7.96410 29.7224i 0.473417 1.76682i −0.153937 0.988081i \(-0.549195\pi\)
0.627354 0.778735i \(-0.284138\pi\)
\(284\) 0 0
\(285\) −3.07180 + 1.53590i −0.181958 + 0.0909788i
\(286\) 0 0
\(287\) −16.8301 16.8301i −0.993451 0.993451i
\(288\) 0 0
\(289\) 14.0263 8.09808i 0.825075 0.476357i
\(290\) 0 0
\(291\) −2.83013 + 2.83013i −0.165905 + 0.165905i
\(292\) 0 0
\(293\) −10.2583 + 17.7679i −0.599298 + 1.03801i 0.393627 + 0.919270i \(0.371220\pi\)
−0.992925 + 0.118744i \(0.962113\pi\)
\(294\) 0 0
\(295\) −13.3564 15.0622i −0.777640 0.876954i
\(296\) 0 0
\(297\) −11.2583 + 6.50000i −0.653275 + 0.377168i
\(298\) 0 0
\(299\) 0.473721 0.160254i 0.0273960 0.00926773i
\(300\) 0 0
\(301\) 14.6962 + 3.93782i 0.847072 + 0.226972i
\(302\) 0 0
\(303\) 8.59808 2.30385i 0.493947 0.132353i
\(304\) 0 0
\(305\) −1.20577 + 20.0885i −0.0690423 + 1.15026i
\(306\) 0 0
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 0 0
\(309\) 4.09808 + 7.09808i 0.233131 + 0.403795i
\(310\) 0 0
\(311\) 3.46410i 0.196431i 0.995165 + 0.0982156i \(0.0313135\pi\)
−0.995165 + 0.0982156i \(0.968687\pi\)
\(312\) 0 0
\(313\) −5.53590 + 5.53590i −0.312907 + 0.312907i −0.846035 0.533127i \(-0.821017\pi\)
0.533127 + 0.846035i \(0.321017\pi\)
\(314\) 0 0
\(315\) −12.5622 8.29423i −0.707799 0.467327i
\(316\) 0 0
\(317\) −18.9282 −1.06311 −0.531557 0.847023i \(-0.678393\pi\)
−0.531557 + 0.847023i \(0.678393\pi\)
\(318\) 0 0
\(319\) −1.96410 7.33013i −0.109969 0.410408i
\(320\) 0 0
\(321\) 1.96410 3.40192i 0.109625 0.189877i
\(322\) 0 0
\(323\) 1.33013 + 2.30385i 0.0740102 + 0.128190i
\(324\) 0 0
\(325\) −18.0000 1.00000i −0.998460 0.0554700i
\(326\) 0 0
\(327\) 1.29423 + 2.24167i 0.0715710 + 0.123965i
\(328\) 0 0
\(329\) −13.4641 + 23.3205i −0.742300 + 1.28570i
\(330\) 0 0
\(331\) 4.45448 + 16.6244i 0.244841 + 0.913757i 0.973464 + 0.228842i \(0.0734940\pi\)
−0.728623 + 0.684915i \(0.759839\pi\)
\(332\) 0 0
\(333\) −4.19615 −0.229948
\(334\) 0 0
\(335\) −22.8923 15.1147i −1.25074 0.825806i
\(336\) 0 0
\(337\) −15.9282 + 15.9282i −0.867665 + 0.867665i −0.992213 0.124549i \(-0.960252\pi\)
0.124549 + 0.992213i \(0.460252\pi\)
\(338\) 0 0
\(339\) 1.53590i 0.0834185i
\(340\) 0 0
\(341\) −16.0981 27.8827i −0.871760 1.50993i
\(342\) 0 0
\(343\) 19.5359i 1.05484i
\(344\) 0 0
\(345\) −0.00961894 + 0.160254i −0.000517866 + 0.00862779i
\(346\) 0 0
\(347\) −10.4282 + 2.79423i −0.559815 + 0.150002i −0.527621 0.849480i \(-0.676916\pi\)
−0.0321938 + 0.999482i \(0.510249\pi\)
\(348\) 0 0
\(349\) −7.86603 2.10770i −0.421059 0.112822i 0.0420673 0.999115i \(-0.486606\pi\)
−0.463126 + 0.886292i \(0.653272\pi\)
\(350\) 0 0
\(351\) 2.09808 10.4904i 0.111987 0.559935i
\(352\) 0 0
\(353\) 9.06218 5.23205i 0.482331 0.278474i −0.239056 0.971006i \(-0.576838\pi\)
0.721387 + 0.692532i \(0.243505\pi\)
\(354\) 0 0
\(355\) −3.42820 3.86603i −0.181950 0.205187i
\(356\) 0 0
\(357\) 0.571797 0.990381i 0.0302627 0.0524165i
\(358\) 0 0
\(359\) 13.1962 13.1962i 0.696466 0.696466i −0.267180 0.963647i \(-0.586092\pi\)
0.963647 + 0.267180i \(0.0860919\pi\)
\(360\) 0 0
\(361\) −8.83013 + 5.09808i −0.464744 + 0.268320i
\(362\) 0 0
\(363\) 3.00000 + 3.00000i 0.157459 + 0.157459i
\(364\) 0 0
\(365\) 29.8564 14.9282i 1.56276 0.781378i
\(366\) 0 0
\(367\) −3.96410 + 14.7942i −0.206924 + 0.772252i 0.781930 + 0.623366i \(0.214235\pi\)
−0.988854 + 0.148886i \(0.952431\pi\)
\(368\) 0 0
\(369\) −18.6603 18.6603i −0.971414 0.971414i
\(370\) 0 0
\(371\) −8.29423 + 2.22243i −0.430615 + 0.115383i
\(372\) 0 0
\(373\) 5.30385 + 19.7942i 0.274623 + 1.02491i 0.956094 + 0.293061i \(0.0946739\pi\)
−0.681471 + 0.731845i \(0.738659\pi\)
\(374\) 0 0
\(375\) 2.47372 5.23205i 0.127742 0.270182i
\(376\) 0 0
\(377\) 5.59808 + 2.76795i 0.288316 + 0.142557i
\(378\) 0 0
\(379\) 2.59808 9.69615i 0.133454 0.498058i −0.866545 0.499099i \(-0.833665\pi\)
0.999999 + 0.00104063i \(0.000331242\pi\)
\(380\) 0 0
\(381\) 9.23205 + 5.33013i 0.472972 + 0.273071i
\(382\) 0 0
\(383\) −22.1147 12.7679i −1.13001 0.652412i −0.186073 0.982536i \(-0.559576\pi\)
−0.943937 + 0.330124i \(0.892909\pi\)
\(384\) 0 0
\(385\) −7.63397 + 22.9019i −0.389063 + 1.16719i
\(386\) 0 0
\(387\) 16.2942 + 4.36603i 0.828282 + 0.221938i
\(388\) 0 0
\(389\) −15.0718 −0.764170 −0.382085 0.924127i \(-0.624794\pi\)
−0.382085 + 0.924127i \(0.624794\pi\)
\(390\) 0 0
\(391\) 0.124356 0.00628894
\(392\) 0 0
\(393\) −2.92820 0.784610i −0.147708 0.0395783i
\(394\) 0 0
\(395\) −0.535898 1.07180i −0.0269640 0.0539279i
\(396\) 0 0
\(397\) −9.86603 5.69615i −0.495162 0.285882i 0.231552 0.972823i \(-0.425620\pi\)
−0.726713 + 0.686941i \(0.758953\pi\)
\(398\) 0 0
\(399\) −3.27757 1.89230i −0.164084 0.0947337i
\(400\) 0 0
\(401\) 2.66987 9.96410i 0.133327 0.497583i −0.866672 0.498878i \(-0.833745\pi\)
0.999999 + 0.00129478i \(0.000412141\pi\)
\(402\) 0 0
\(403\) 25.9808 + 5.19615i 1.29419 + 0.258839i
\(404\) 0 0
\(405\) −12.4282 8.20577i −0.617562 0.407748i
\(406\) 0 0
\(407\) 1.74167 + 6.50000i 0.0863314 + 0.322193i
\(408\) 0 0
\(409\) 18.5263 4.96410i 0.916066 0.245459i 0.230163 0.973152i \(-0.426074\pi\)
0.685903 + 0.727693i \(0.259407\pi\)
\(410\) 0 0
\(411\) 5.24167 + 5.24167i 0.258553 + 0.258553i
\(412\) 0 0
\(413\) 5.74167 21.4282i 0.282529 1.05441i
\(414\) 0 0
\(415\) 2.92820 + 5.85641i 0.143740 + 0.287480i
\(416\) 0 0
\(417\) 1.90192 + 1.90192i 0.0931376 + 0.0931376i
\(418\) 0 0
\(419\) −31.5000 + 18.1865i −1.53888 + 0.888470i −0.539971 + 0.841684i \(0.681565\pi\)
−0.998905 + 0.0467865i \(0.985102\pi\)
\(420\) 0 0
\(421\) 6.85641 6.85641i 0.334161 0.334161i −0.520003 0.854164i \(-0.674069\pi\)
0.854164 + 0.520003i \(0.174069\pi\)
\(422\) 0 0
\(423\) −14.9282 + 25.8564i −0.725834 + 1.25718i
\(424\) 0 0
\(425\) −4.16025 1.66987i −0.201802 0.0810007i
\(426\) 0 0
\(427\) −19.2058 + 11.0885i −0.929432 + 0.536608i
\(428\) 0 0
\(429\) −8.16025 + 0.526279i −0.393981 + 0.0254090i
\(430\) 0 0
\(431\) −23.2583 6.23205i −1.12031 0.300187i −0.349304 0.937010i \(-0.613582\pi\)
−0.771011 + 0.636822i \(0.780249\pi\)
\(432\) 0 0
\(433\) 32.5526 8.72243i 1.56438 0.419173i 0.630330 0.776327i \(-0.282919\pi\)
0.934046 + 0.357154i \(0.116253\pi\)
\(434\) 0 0
\(435\) −1.50000 + 1.33013i −0.0719195 + 0.0637747i
\(436\) 0 0
\(437\) 0.411543i 0.0196868i
\(438\) 0 0
\(439\) 0.0358984 + 0.0621778i 0.00171334 + 0.00296759i 0.866881 0.498515i \(-0.166121\pi\)
−0.865167 + 0.501483i \(0.832788\pi\)
\(440\) 0 0
\(441\) 2.53590i 0.120757i
\(442\) 0 0
\(443\) −15.5885 + 15.5885i −0.740630 + 0.740630i −0.972699 0.232069i \(-0.925450\pi\)
0.232069 + 0.972699i \(0.425450\pi\)
\(444\) 0 0
\(445\) 33.5526 6.86603i 1.59054 0.325481i
\(446\) 0 0
\(447\) 1.78461 0.0844091
\(448\) 0 0
\(449\) −5.20577 19.4282i −0.245676 0.916874i −0.973043 0.230625i \(-0.925923\pi\)
0.727367 0.686249i \(-0.240744\pi\)
\(450\) 0 0
\(451\) −21.1603 + 36.6506i −0.996397 + 1.72581i
\(452\) 0 0
\(453\) 0.0980762 + 0.169873i 0.00460802 + 0.00798133i
\(454\) 0 0
\(455\) −10.0096 17.1603i −0.469258 0.804485i
\(456\) 0 0
\(457\) −6.79423 11.7679i −0.317821 0.550481i 0.662212 0.749316i \(-0.269618\pi\)
−0.980033 + 0.198835i \(0.936284\pi\)
\(458\) 0 0
\(459\) 1.33013 2.30385i 0.0620850 0.107534i
\(460\) 0 0
\(461\) 0.813467 + 3.03590i 0.0378869 + 0.141396i 0.982279 0.187427i \(-0.0600148\pi\)
−0.944392 + 0.328823i \(0.893348\pi\)
\(462\) 0 0
\(463\) −21.6077 −1.00419 −0.502097 0.864811i \(-0.667438\pi\)
−0.502097 + 0.864811i \(0.667438\pi\)
\(464\) 0 0
\(465\) −4.68653 + 7.09808i −0.217333 + 0.329165i
\(466\) 0 0
\(467\) 16.6603 16.6603i 0.770945 0.770945i −0.207327 0.978272i \(-0.566476\pi\)
0.978272 + 0.207327i \(0.0664764\pi\)
\(468\) 0 0
\(469\) 30.2295i 1.39587i
\(470\) 0 0
\(471\) −2.36603 4.09808i −0.109021 0.188829i
\(472\) 0 0
\(473\) 27.0526i 1.24388i
\(474\) 0 0
\(475\) −5.52628 + 13.7679i −0.253563 + 0.631717i
\(476\) 0 0
\(477\) −9.19615 + 2.46410i −0.421063 + 0.112823i
\(478\) 0 0
\(479\) −3.13397 0.839746i −0.143195 0.0383690i 0.186510 0.982453i \(-0.440282\pi\)
−0.329705 + 0.944084i \(0.606949\pi\)
\(480\) 0 0
\(481\) −4.96410 2.45448i −0.226344 0.111915i
\(482\) 0 0
\(483\) −0.153212 + 0.0884573i −0.00697141 + 0.00402495i
\(484\) 0 0
\(485\) −1.03590 + 17.2583i −0.0470377 + 0.783660i
\(486\) 0 0
\(487\) −0.794229 + 1.37564i −0.0359899 + 0.0623364i −0.883459 0.468508i \(-0.844792\pi\)
0.847469 + 0.530844i \(0.178125\pi\)
\(488\) 0 0
\(489\) 1.16987 1.16987i 0.0529035 0.0529035i
\(490\) 0 0
\(491\) 5.89230 3.40192i 0.265916 0.153527i −0.361114 0.932522i \(-0.617604\pi\)
0.627030 + 0.778995i \(0.284270\pi\)
\(492\) 0 0
\(493\) 1.09808 + 1.09808i 0.0494549 + 0.0494549i
\(494\) 0 0
\(495\) −8.46410 + 25.3923i −0.380433 + 1.14130i
\(496\) 0 0
\(497\) 1.47372 5.50000i 0.0661054 0.246709i
\(498\) 0 0
\(499\) 20.2679 + 20.2679i 0.907318 + 0.907318i 0.996055 0.0887371i \(-0.0282831\pi\)
−0.0887371 + 0.996055i \(0.528283\pi\)
\(500\) 0 0
\(501\) 9.23205 2.47372i 0.412458 0.110518i
\(502\) 0 0
\(503\) −3.35641 12.5263i −0.149655 0.558519i −0.999504 0.0314933i \(-0.989974\pi\)
0.849849 0.527026i \(-0.176693\pi\)
\(504\) 0 0
\(505\) 21.1865 32.0885i 0.942788 1.42792i
\(506\) 0 0
\(507\) 4.10770 5.33013i 0.182429 0.236719i
\(508\) 0 0
\(509\) −7.45448 + 27.8205i −0.330414 + 1.23312i 0.578342 + 0.815795i \(0.303700\pi\)
−0.908756 + 0.417328i \(0.862967\pi\)
\(510\) 0 0
\(511\) 31.8564 + 18.3923i 1.40924 + 0.813628i
\(512\) 0 0
\(513\) −7.62436 4.40192i −0.336624 0.194350i
\(514\) 0 0
\(515\) 33.5885 + 11.1962i 1.48008 + 0.493361i
\(516\) 0 0
\(517\) 46.2487 + 12.3923i 2.03402 + 0.545013i
\(518\) 0 0
\(519\) 1.48334 0.0651114
\(520\) 0 0
\(521\) −7.85641 −0.344195 −0.172098 0.985080i \(-0.555054\pi\)
−0.172098 + 0.985080i \(0.555054\pi\)
\(522\) 0 0
\(523\) 10.9641 + 2.93782i 0.479427 + 0.128462i 0.490436 0.871477i \(-0.336838\pi\)
−0.0110090 + 0.999939i \(0.503504\pi\)
\(524\) 0 0
\(525\) 6.31347 0.901924i 0.275542 0.0393632i
\(526\) 0 0
\(527\) 5.70577 + 3.29423i 0.248547 + 0.143499i
\(528\) 0 0
\(529\) 19.9019 + 11.4904i 0.865301 + 0.499582i
\(530\) 0 0
\(531\) 6.36603 23.7583i 0.276262 1.03102i
\(532\) 0 0
\(533\) −11.1603 32.9904i −0.483404 1.42897i
\(534\) 0 0
\(535\) −3.40192 16.6244i −0.147078 0.718734i
\(536\) 0 0
\(537\) −1.86603 6.96410i −0.0805249 0.300523i
\(538\) 0 0
\(539\) 3.92820 1.05256i 0.169200 0.0453369i
\(540\) 0 0
\(541\) 21.7846 + 21.7846i 0.936594 + 0.936594i 0.998106 0.0615128i \(-0.0195925\pi\)
−0.0615128 + 0.998106i \(0.519592\pi\)
\(542\) 0 0
\(543\) −3.07180 + 11.4641i −0.131823 + 0.491972i
\(544\) 0 0
\(545\) 10.6077 + 3.53590i 0.454384 + 0.151461i
\(546\) 0 0
\(547\) −0.124356 0.124356i −0.00531706 0.00531706i 0.704443 0.709760i \(-0.251197\pi\)
−0.709760 + 0.704443i \(0.751197\pi\)
\(548\) 0 0
\(549\) −21.2942 + 12.2942i −0.908816 + 0.524705i
\(550\) 0 0
\(551\) 3.63397 3.63397i 0.154813 0.154813i
\(552\) 0 0
\(553\) 0.660254 1.14359i 0.0280769 0.0486305i
\(554\) 0 0
\(555\) 1.33013 1.17949i 0.0564607 0.0500666i
\(556\) 0 0
\(557\) 13.3301 7.69615i 0.564816 0.326096i −0.190260 0.981734i \(-0.560933\pi\)
0.755076 + 0.655637i \(0.227600\pi\)
\(558\) 0 0
\(559\) 16.7224 + 14.6962i 0.707284 + 0.621581i
\(560\) 0 0
\(561\) −1.96410 0.526279i −0.0829244 0.0222195i
\(562\) 0 0
\(563\) −24.8923 + 6.66987i −1.04909 + 0.281102i −0.741874 0.670540i \(-0.766063\pi\)
−0.307212 + 0.951641i \(0.599396\pi\)
\(564\) 0 0
\(565\) −4.40192 4.96410i −0.185190 0.208841i
\(566\) 0 0
\(567\) 16.4115i 0.689220i
\(568\) 0 0
\(569\) 18.8205 + 32.5981i 0.788997 + 1.36658i 0.926582 + 0.376093i \(0.122733\pi\)
−0.137585 + 0.990490i \(0.543934\pi\)
\(570\) 0 0
\(571\) 21.6077i 0.904254i 0.891954 + 0.452127i \(0.149335\pi\)
−0.891954 + 0.452127i \(0.850665\pi\)
\(572\) 0 0
\(573\) −5.49038 + 5.49038i −0.229364 + 0.229364i
\(574\) 0 0
\(575\) 0.428203 + 0.545517i 0.0178573 + 0.0227496i
\(576\) 0 0
\(577\) 20.7846 0.865275 0.432637 0.901568i \(-0.357583\pi\)
0.432637 + 0.901568i \(0.357583\pi\)
\(578\) 0 0
\(579\) −3.42820 12.7942i −0.142471 0.531710i
\(580\) 0 0
\(581\) −3.60770 + 6.24871i −0.149672 + 0.259240i
\(582\) 0 0
\(583\) 7.63397 + 13.2224i 0.316167 + 0.547617i
\(584\) 0 0
\(585\) −11.0981 19.0263i −0.458849 0.786640i
\(586\) 0 0
\(587\) −23.7224 41.0885i −0.979130 1.69590i −0.665573 0.746333i \(-0.731813\pi\)
−0.313556 0.949570i \(-0.601520\pi\)
\(588\) 0 0
\(589\) 10.9019 18.8827i 0.449206 0.778048i
\(590\) 0 0
\(591\) −0.571797 2.13397i −0.0235206 0.0877800i
\(592\) 0 0
\(593\) −30.9282 −1.27007 −0.635035 0.772484i \(-0.719014\pi\)
−0.635035 + 0.772484i \(0.719014\pi\)
\(594\) 0 0
\(595\) −0.990381 4.83975i −0.0406017 0.198410i
\(596\) 0 0
\(597\) −6.90192 + 6.90192i −0.282477 + 0.282477i
\(598\) 0 0
\(599\) 36.2487i 1.48108i 0.672011 + 0.740541i \(0.265431\pi\)
−0.672011 + 0.740541i \(0.734569\pi\)
\(600\) 0 0
\(601\) 7.42820 + 12.8660i 0.303003 + 0.524816i 0.976815 0.214087i \(-0.0686775\pi\)
−0.673812 + 0.738903i \(0.735344\pi\)
\(602\) 0 0
\(603\) 33.5167i 1.36490i
\(604\) 0 0
\(605\) 18.2942 + 1.09808i 0.743766 + 0.0446431i
\(606\) 0 0
\(607\) 3.03590 0.813467i 0.123223 0.0330176i −0.196680 0.980468i \(-0.563016\pi\)
0.319904 + 0.947450i \(0.396349\pi\)
\(608\) 0 0
\(609\) −2.13397 0.571797i −0.0864730 0.0231704i
\(610\) 0 0
\(611\) −32.7846 + 21.8564i −1.32632 + 0.884216i
\(612\) 0 0
\(613\) −21.1865 + 12.2321i −0.855716 + 0.494048i −0.862575 0.505929i \(-0.831150\pi\)
0.00685934 + 0.999976i \(0.497817\pi\)
\(614\) 0 0
\(615\) 11.1603 + 0.669873i 0.450025 + 0.0270119i
\(616\) 0 0
\(617\) 8.79423 15.2321i 0.354042 0.613219i −0.632911 0.774224i \(-0.718140\pi\)
0.986954 + 0.161005i \(0.0514735\pi\)
\(618\) 0 0
\(619\) 14.6603 14.6603i 0.589245 0.589245i −0.348182 0.937427i \(-0.613201\pi\)
0.937427 + 0.348182i \(0.113201\pi\)
\(620\) 0 0
\(621\) −0.356406 + 0.205771i −0.0143021 + 0.00825732i
\(622\) 0 0
\(623\) 26.6865 + 26.6865i 1.06917 + 1.06917i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 0 0
\(627\) −1.74167 + 6.50000i −0.0695556 + 0.259585i
\(628\) 0 0
\(629\) −0.973721 0.973721i −0.0388248 0.0388248i
\(630\) 0 0
\(631\) 41.6506 11.1603i 1.65809 0.444283i 0.696225 0.717823i \(-0.254862\pi\)
0.961860 + 0.273541i \(0.0881948\pi\)
\(632\) 0 0
\(633\) 0.794229 + 2.96410i 0.0315678 + 0.117812i
\(634\) 0 0
\(635\) 45.1147 9.23205i 1.79032 0.366363i
\(636\) 0 0
\(637\) −1.48334 + 3.00000i −0.0587721 + 0.118864i
\(638\) 0 0
\(639\) 1.63397 6.09808i 0.0646390 0.241236i
\(640\) 0 0
\(641\) 5.64359 + 3.25833i 0.222909 + 0.128696i 0.607296 0.794475i \(-0.292254\pi\)
−0.384388 + 0.923172i \(0.625587\pi\)
\(642\) 0 0
\(643\) −31.3301 18.0885i −1.23554 0.713339i −0.267360 0.963597i \(-0.586151\pi\)
−0.968179 + 0.250258i \(0.919485\pi\)
\(644\) 0 0
\(645\) −6.39230 + 3.19615i −0.251697 + 0.125848i
\(646\) 0 0
\(647\) 2.50000 + 0.669873i 0.0982851 + 0.0263354i 0.307626 0.951507i \(-0.400465\pi\)
−0.209341 + 0.977843i \(0.567132\pi\)
\(648\) 0 0
\(649\) −39.4449 −1.54835
\(650\) 0 0
\(651\) −9.37307 −0.367359
\(652\) 0 0
\(653\) 47.9449 + 12.8468i 1.87623 + 0.502734i 0.999774 + 0.0212467i \(0.00676353\pi\)
0.876453 + 0.481487i \(0.159903\pi\)
\(654\) 0 0
\(655\) −11.7128 + 5.85641i −0.457657 + 0.228829i
\(656\) 0 0
\(657\) 35.3205 + 20.3923i 1.37798 + 0.795580i
\(658\) 0 0
\(659\) −35.4282 20.4545i −1.38009 0.796794i −0.387918 0.921694i \(-0.626805\pi\)
−0.992169 + 0.124901i \(0.960139\pi\)
\(660\) 0 0
\(661\) −0.794229 + 2.96410i −0.0308919 + 0.115290i −0.979650 0.200713i \(-0.935674\pi\)
0.948758 + 0.316003i \(0.102341\pi\)
\(662\) 0 0
\(663\) 1.39230 0.928203i 0.0540726 0.0360484i
\(664\) 0 0
\(665\) −16.0167 + 3.27757i −0.621099 + 0.127099i
\(666\) 0 0
\(667\) −0.0621778 0.232051i −0.00240754 0.00898504i
\(668\) 0 0
\(669\) 0.767949 0.205771i 0.0296906 0.00795558i
\(670\) 0 0
\(671\) 27.8827 + 27.8827i 1.07640 + 1.07640i
\(672\) 0 0
\(673\) 9.62436 35.9186i 0.370992 1.38456i −0.488122 0.872775i \(-0.662318\pi\)
0.859114 0.511784i \(-0.171015\pi\)
\(674\) 0 0
\(675\) 14.6865 2.09808i 0.565285 0.0807550i
\(676\) 0 0
\(677\) −28.1769 28.1769i −1.08293 1.08293i −0.996235 0.0866916i \(-0.972371\pi\)
−0.0866916 0.996235i \(-0.527629\pi\)
\(678\) 0 0
\(679\) −16.5000 + 9.52628i −0.633212 + 0.365585i
\(680\) 0 0
\(681\) −1.16987 + 1.16987i −0.0448296 + 0.0448296i
\(682\) 0 0
\(683\) 7.33013 12.6962i 0.280480 0.485805i −0.691023 0.722832i \(-0.742840\pi\)
0.971503 + 0.237028i \(0.0761732\pi\)
\(684\) 0 0
\(685\) 31.9641 + 1.91858i 1.22129 + 0.0733053i
\(686\) 0 0
\(687\) −0.0455173 + 0.0262794i −0.00173659 + 0.00100262i
\(688\) 0 0
\(689\) −12.3205 2.46410i −0.469374 0.0938748i
\(690\) 0 0
\(691\) −37.6506 10.0885i −1.43230 0.383783i −0.542468 0.840076i \(-0.682510\pi\)
−0.889829 + 0.456293i \(0.849177\pi\)
\(692\) 0 0
\(693\) −28.4904 + 7.63397i −1.08226 + 0.289991i
\(694\) 0 0
\(695\) 11.5981 + 0.696152i 0.439940 + 0.0264066i
\(696\) 0 0
\(697\) 8.66025i 0.328031i
\(698\) 0 0
\(699\) −4.70577 8.15064i −0.177989 0.308285i
\(700\) 0 0
\(701\) 21.0718i 0.795871i 0.917413 + 0.397935i \(0.130273\pi\)
−0.917413 + 0.397935i \(0.869727\pi\)
\(702\) 0 0
\(703\) −3.22243 + 3.22243i −0.121536 + 0.121536i
\(704\) 0 0
\(705\) −2.53590 12.3923i −0.0955075 0.466721i
\(706\) 0 0
\(707\) 42.3731 1.59360
\(708\) 0 0
\(709\) −4.27757 15.9641i −0.160647 0.599544i −0.998555 0.0537328i \(-0.982888\pi\)
0.837908 0.545812i \(-0.183779\pi\)
\(710\) 0 0
\(711\) 0.732051 1.26795i 0.0274541 0.0475518i
\(712\) 0 0
\(713\) −0.509619 0.882686i −0.0190854 0.0330568i
\(714\) 0 0
\(715\) −24.8660 + 25.0885i −0.929937 + 0.938255i
\(716\) 0 0
\(717\) −6.09808 10.5622i −0.227737 0.394452i
\(718\) 0 0
\(719\) −20.9641 + 36.3109i −0.781829 + 1.35417i 0.149046 + 0.988830i \(0.452380\pi\)
−0.930875 + 0.365337i \(0.880954\pi\)
\(720\) 0 0
\(721\) 10.0981 + 37.6865i 0.376072 + 1.40352i
\(722\) 0 0
\(723\) −6.07180 −0.225813
\(724\) 0 0
\(725\) −1.03590 + 8.59808i −0.0384723 + 0.319325i
\(726\) 0 0
\(727\) −33.5885 + 33.5885i −1.24573 + 1.24573i −0.288138 + 0.957589i \(0.593036\pi\)
−0.957589 + 0.288138i \(0.906964\pi\)
\(728\) 0 0
\(729\) 13.5885i 0.503276i
\(730\) 0 0
\(731\) 2.76795 + 4.79423i 0.102376 + 0.177321i
\(732\) 0 0
\(733\) 26.7846i 0.989312i −0.869089 0.494656i \(-0.835294\pi\)
0.869089 0.494656i \(-0.164706\pi\)
\(734\) 0 0
\(735\) −0.712813 0.803848i −0.0262925 0.0296504i
\(736\) 0 0
\(737\) −51.9186 + 13.9115i −1.91245 + 0.512438i
\(738\) 0 0
\(739\) −37.9186 10.1603i −1.39486 0.373751i −0.518362 0.855161i \(-0.673458\pi\)
−0.876495 + 0.481410i \(0.840125\pi\)
\(740\) 0 0
\(741\) −3.07180 4.60770i −0.112845 0.169268i
\(742\) 0 0
\(743\) −19.3301 + 11.1603i −0.709154 + 0.409430i −0.810748 0.585396i \(-0.800939\pi\)
0.101594 + 0.994826i \(0.467606\pi\)
\(744\) 0 0
\(745\) 5.76795 5.11474i 0.211321 0.187389i
\(746\) 0 0
\(747\) −4.00000 + 6.92820i −0.146352 + 0.253490i
\(748\) 0 0
\(749\) 13.2224 13.2224i 0.483137 0.483137i
\(750\) 0 0
\(751\) 17.6436 10.1865i 0.643824 0.371712i −0.142262 0.989829i \(-0.545438\pi\)
0.786086 + 0.618117i \(0.212104\pi\)
\(752\) 0 0
\(753\) 6.49038 + 6.49038i 0.236523 + 0.236523i
\(754\) 0 0
\(755\) 0.803848 + 0.267949i 0.0292550 + 0.00975167i
\(756\) 0 0
\(757\) −4.83975 + 18.0622i −0.175904 + 0.656481i 0.820492 + 0.571657i \(0.193699\pi\)
−0.996396 + 0.0848236i \(0.972967\pi\)
\(758\) 0 0
\(759\) 0.222432 + 0.222432i 0.00807377 + 0.00807377i
\(760\) 0 0
\(761\) −0.669873 + 0.179492i −0.0242829 + 0.00650658i −0.270940 0.962596i \(-0.587335\pi\)
0.246657 + 0.969103i \(0.420668\pi\)
\(762\) 0 0
\(763\) 3.18911 + 11.9019i 0.115454 + 0.430879i
\(764\) 0 0
\(765\) −1.09808 5.36603i −0.0397010 0.194009i
\(766\) 0 0
\(767\) 21.4282 24.3827i 0.773728 0.880408i
\(768\) 0 0
\(769\) 5.47372 20.4282i 0.197387 0.736660i −0.794248 0.607593i \(-0.792135\pi\)
0.991636 0.129067i \(-0.0411982\pi\)
\(770\) 0 0
\(771\) −10.0359 5.79423i −0.361434 0.208674i
\(772\) 0 0
\(773\) 17.0429 + 9.83975i 0.612992 + 0.353911i 0.774136 0.633020i \(-0.218185\pi\)
−0.161144 + 0.986931i \(0.551518\pi\)
\(774\) 0 0
\(775\) 5.19615 + 36.3731i 0.186651 + 1.30656i
\(776\) 0 0
\(777\) 1.89230 + 0.507042i 0.0678861 + 0.0181900i
\(778\) 0 0
\(779\) −28.6603 −1.02686
\(780\) 0 0
\(781\) −10.1244 −0.362278
\(782\) 0 0
\(783\) −4.96410 1.33013i −0.177403 0.0475349i
\(784\) 0 0
\(785\) −19.3923 6.46410i −0.692141 0.230714i
\(786\) 0 0
\(787\) −37.4545 21.6244i −1.33511 0.770825i −0.349031 0.937111i \(-0.613489\pi\)
−0.986078 + 0.166286i \(0.946822\pi\)
\(788\) 0 0
\(789\) −6.44744 3.72243i −0.229535 0.132522i
\(790\) 0