Properties

Label 1300.2.bs.b.293.1
Level $1300$
Weight $2$
Character 1300.293
Analytic conductor $10.381$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1300.bs (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.3805522628\)
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: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 293.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1300.293
Dual form 1300.2.bs.b.457.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(651\) \(677\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 −0.111576 0.993756i \(-0.535590\pi\)
0.400251 + 0.916406i \(0.368923\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.13397 1.23205i 0.806567 0.465671i −0.0391956 0.999232i \(-0.512480\pi\)
0.845762 + 0.533560i \(0.179146\pi\)
\(8\) 0 0
\(9\) −2.36603 + 1.36603i −0.788675 + 0.455342i
\(10\) 0 0
\(11\) −1.13397 4.23205i −0.341906 1.27601i −0.896185 0.443680i \(-0.853673\pi\)
0.554279 0.832331i \(-0.312994\pi\)
\(12\) 0 0
\(13\) 2.00000 3.00000i 0.554700 0.832050i
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.232051 0.866025i 0.0562806 0.210042i −0.932059 0.362306i \(-0.881990\pi\)
0.988340 + 0.152264i \(0.0486563\pi\)
\(18\) 0 0
\(19\) −2.86603 0.767949i −0.657511 0.176180i −0.0853887 0.996348i \(-0.527213\pi\)
−0.572123 + 0.820168i \(0.693880\pi\)
\(20\) 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 \(-0.0787302\pi\)
−0.962082 + 0.272760i \(0.912064\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.09808 + 2.09808i −0.403775 + 0.403775i
\(28\) 0 0
\(29\) −1.50000 0.866025i −0.278543 0.160817i 0.354221 0.935162i \(-0.384746\pi\)
−0.632764 + 0.774345i \(0.718080\pi\)
\(30\) 0 0
\(31\) −5.19615 5.19615i −0.933257 0.933257i 0.0646514 0.997908i \(-0.479406\pi\)
−0.997908 + 0.0646514i \(0.979406\pi\)
\(32\) 0 0
\(33\) −1.13397 1.96410i −0.197400 0.341906i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.33013 0.767949i −0.218672 0.126250i 0.386663 0.922221i \(-0.373628\pi\)
−0.605335 + 0.795971i \(0.706961\pi\)
\(38\) 0 0
\(39\) 0.598076 1.76795i 0.0957688 0.283098i
\(40\) 0 0
\(41\) 9.33013 2.50000i 1.45712 0.390434i 0.558627 0.829419i \(-0.311329\pi\)
0.898494 + 0.438985i \(0.144662\pi\)
\(42\) 0 0
\(43\) 5.96410 + 1.59808i 0.909517 + 0.243704i 0.683099 0.730326i \(-0.260632\pi\)
0.226418 + 0.974030i \(0.427298\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 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 \(-0.326929\pi\)
−0.855791 + 0.517321i \(0.826929\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.53590 −0.203435
\(58\) 0 0
\(59\) 2.33013 8.69615i 0.303357 1.13214i −0.630994 0.775788i \(-0.717353\pi\)
0.934351 0.356355i \(-0.115981\pi\)
\(60\) 0 0
\(61\) 4.50000 + 7.79423i 0.576166 + 0.997949i 0.995914 + 0.0903080i \(0.0287851\pi\)
−0.419748 + 0.907641i \(0.637882\pi\)
\(62\) 0 0
\(63\) −3.36603 + 5.83013i −0.424079 + 0.734527i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.13397 + 10.6244i −0.749384 + 1.29797i 0.198734 + 0.980053i \(0.436317\pi\)
−0.948118 + 0.317918i \(0.897016\pi\)
\(68\) 0 0
\(69\) 0.0358984 + 0.0621778i 0.00432166 + 0.00748533i
\(70\) 0 0
\(71\) 0.598076 2.23205i 0.0709786 0.264896i −0.921313 0.388822i \(-0.872882\pi\)
0.992291 + 0.123927i \(0.0395487\pi\)
\(72\) 0 0
\(73\) 14.9282 1.74721 0.873607 0.486632i \(-0.161775\pi\)
0.873607 + 0.486632i \(0.161775\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.63397 7.63397i −0.869972 0.869972i
\(78\) 0 0
\(79\) 0.535898i 0.0602933i −0.999545 0.0301466i \(-0.990403\pi\)
0.999545 0.0301466i \(-0.00959743\pi\)
\(80\) 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
\(85\) 0 0
\(86\) 0 0
\(87\) −0.866025 0.232051i −0.0928477 0.0248785i
\(88\) 0 0
\(89\) −14.7942 + 3.96410i −1.56819 + 0.420194i −0.935243 0.354005i \(-0.884819\pi\)
−0.632942 + 0.774199i \(0.718153\pi\)
\(90\) 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
\(95\) 0 0
\(96\) 0 0
\(97\) −3.86603 6.69615i −0.392535 0.679891i 0.600248 0.799814i \(-0.295069\pi\)
−0.992783 + 0.119923i \(0.961735\pi\)
\(98\) 0 0
\(99\) 8.46410 + 8.46410i 0.850674 + 0.850674i
\(100\) 0 0
\(101\) −14.8923 8.59808i −1.48184 0.855541i −0.482052 0.876143i \(-0.660108\pi\)
−0.999788 + 0.0206021i \(0.993442\pi\)
\(102\) 0 0
\(103\) 11.1962 11.1962i 1.10319 1.10319i 0.109166 0.994024i \(-0.465182\pi\)
0.994024 0.109166i \(-0.0348181\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.96410 + 7.33013i 0.189877 + 0.708630i 0.993534 + 0.113537i \(0.0362181\pi\)
−0.803657 + 0.595093i \(0.797115\pi\)
\(108\) 0 0
\(109\) −3.53590 + 3.53590i −0.338678 + 0.338678i −0.855869 0.517192i \(-0.826977\pi\)
0.517192 + 0.855869i \(0.326977\pi\)
\(110\) 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 \(-0.961236\pi\)
0.920351 + 0.391093i \(0.127903\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 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
\(125\) 0 0
\(126\) 0 0
\(127\) 19.8923 5.33013i 1.76516 0.472972i 0.777404 0.629001i \(-0.216536\pi\)
0.987752 + 0.156029i \(0.0498694\pi\)
\(128\) 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
\(135\) 0 0
\(136\) 0 0
\(137\) 12.4019 7.16025i 1.05957 0.611742i 0.134255 0.990947i \(-0.457136\pi\)
0.925313 + 0.379205i \(0.123802\pi\)
\(138\) 0 0
\(139\) −4.50000 + 2.59808i −0.381685 + 0.220366i −0.678551 0.734553i \(-0.737392\pi\)
0.296866 + 0.954919i \(0.404058\pi\)
\(140\) 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
\(145\) 0 0
\(146\) 0 0
\(147\) −0.124356 + 0.464102i −0.0102567 + 0.0382785i
\(148\) 0 0
\(149\) −3.33013 0.892305i −0.272815 0.0731005i 0.119818 0.992796i \(-0.461769\pi\)
−0.392633 + 0.919695i \(0.628436\pi\)
\(150\) 0 0
\(151\) −0.267949 + 0.267949i −0.0218054 + 0.0218054i −0.717925 0.696120i \(-0.754908\pi\)
0.696120 + 0.717925i \(0.254908\pi\)
\(152\) 0 0
\(153\) 0.633975 + 2.36603i 0.0512538 + 0.191282i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −6.46410 + 6.46410i −0.515891 + 0.515891i −0.916326 0.400434i \(-0.868859\pi\)
0.400434 + 0.916326i \(0.368859\pi\)
\(158\) 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 \(-0.126719\pi\)
−0.796629 + 0.604469i \(0.793385\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.9904 + 9.23205i 1.23737 + 0.714398i 0.968556 0.248794i \(-0.0800342\pi\)
0.268816 + 0.963191i \(0.413368\pi\)
\(168\) 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 \(-0.381923\pi\)
−0.152057 + 0.988372i \(0.548590\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.66025i 0.350286i
\(178\) 0 0
\(179\) 6.96410 12.0622i 0.520521 0.901570i −0.479194 0.877709i \(-0.659071\pi\)
0.999715 0.0238604i \(-0.00759573\pi\)
\(180\) 0 0
\(181\) 22.9282i 1.70424i 0.523347 + 0.852120i \(0.324683\pi\)
−0.523347 + 0.852120i \(0.675317\pi\)
\(182\) 0 0
\(183\) 3.29423 + 3.29423i 0.243516 + 0.243516i
\(184\) 0 0
\(185\) 0 0
\(186\) 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 0.998749 + 0.0500060i \(0.0159241\pi\)
−0.456068 + 0.889945i \(0.650743\pi\)
\(192\) 0 0
\(193\) −12.7942 + 22.1603i −0.920949 + 1.59513i −0.122998 + 0.992407i \(0.539251\pi\)
−0.797950 + 0.602723i \(0.794082\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.13397 + 3.69615i −0.152039 + 0.263340i −0.931977 0.362517i \(-0.881917\pi\)
0.779938 + 0.625857i \(0.215251\pi\)
\(198\) 0 0
\(199\) 9.42820 + 16.3301i 0.668348 + 1.15761i 0.978366 + 0.206881i \(0.0663314\pi\)
−0.310018 + 0.950731i \(0.600335\pi\)
\(200\) 0 0
\(201\) −1.64359 + 6.13397i −0.115930 + 0.432657i
\(202\) 0 0
\(203\) −4.26795 −0.299551
\(204\) 0 0
\(205\) 0 0
\(206\) 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 −0.949832 0.312761i \(-0.898746\pi\)
0.745775 + 0.666198i \(0.232080\pi\)
\(212\) 0 0
\(213\) 1.19615i 0.0819590i
\(214\) 0 0
\(215\) 0 0
\(216\) 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 \(-0.316957\pi\)
−0.454802 + 0.890592i \(0.650290\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.59808 2.76795i −0.106068 0.183715i 0.808106 0.589037i \(-0.200493\pi\)
−0.914174 + 0.405322i \(0.867159\pi\)
\(228\) 0 0
\(229\) 0.0717968 + 0.0717968i 0.00474446 + 0.00474446i 0.709475 0.704731i \(-0.248932\pi\)
−0.704731 + 0.709475i \(0.748932\pi\)
\(230\) 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 \(-0.953070\pi\)
0.146900 + 0.989151i \(0.453070\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −0.0717968 0.267949i −0.00466370 0.0174052i
\(238\) 0 0
\(239\) 16.6603 16.6603i 1.07766 1.07766i 0.0809436 0.996719i \(-0.474207\pi\)
0.996719 0.0809436i \(-0.0257934\pi\)
\(240\) 0 0
\(241\) 11.3301 + 3.03590i 0.729838 + 0.195559i 0.604557 0.796562i \(-0.293350\pi\)
0.125281 + 0.992121i \(0.460017\pi\)
\(242\) 0 0
\(243\) 3.19615 11.9282i 0.205033 0.765195i
\(244\) 0 0
\(245\) 0 0
\(246\) 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 −0.899019 0.437910i \(-0.855719\pi\)
−0.0702687 + 0.997528i \(0.522386\pi\)
\(252\) 0 0
\(253\) 0.526279 0.303848i 0.0330869 0.0191027i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −21.6244 + 5.79423i −1.34889 + 0.361434i −0.859725 0.510757i \(-0.829365\pi\)
−0.489165 + 0.872191i \(0.662698\pi\)
\(258\) 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 \(-0.729571\pi\)
−0.196336 + 0.980537i \(0.562904\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −6.86603 + 3.96410i −0.420194 + 0.242599i
\(268\) 0 0
\(269\) 15.8205 9.13397i 0.964593 0.556908i 0.0670097 0.997752i \(-0.478654\pi\)
0.897584 + 0.440844i \(0.145321\pi\)
\(270\) 0 0
\(271\) 4.33013 + 16.1603i 0.263036 + 0.981666i 0.963441 + 0.267920i \(0.0863362\pi\)
−0.700405 + 0.713746i \(0.746997\pi\)
\(272\) 0 0
\(273\) −0.901924 4.50962i −0.0545869 0.272935i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.76795 10.3301i 0.166310 0.620677i −0.831560 0.555436i \(-0.812552\pi\)
0.997869 0.0652416i \(-0.0207818\pi\)
\(278\) 0 0
\(279\) 19.3923 + 5.19615i 1.16099 + 0.311086i
\(280\) 0 0
\(281\) −16.4641 + 16.4641i −0.982166 + 0.982166i −0.999844 0.0176778i \(-0.994373\pi\)
0.0176778 + 0.999844i \(0.494373\pi\)
\(282\) 0 0
\(283\) −7.96410 29.7224i −0.473417 1.76682i −0.627354 0.778735i \(-0.715862\pi\)
0.153937 0.988081i \(-0.450805\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 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 0.992925 + 0.118744i \(0.0378869\pi\)
−0.393627 + 0.919270i \(0.628780\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 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
\(305\) 0 0
\(306\) 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 \(-0.968687\pi\)
0.995165 0.0982156i \(-0.0313135\pi\)
\(312\) 0 0
\(313\) 5.53590 + 5.53590i 0.312907 + 0.312907i 0.846035 0.533127i \(-0.178983\pi\)
−0.533127 + 0.846035i \(0.678983\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 18.9282 1.06311 0.531557 0.847023i \(-0.321607\pi\)
0.531557 + 0.847023i \(0.321607\pi\)
\(318\) 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
\(325\) 0 0
\(326\) 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 −0.728623 0.684915i \(-0.759839\pi\)
0.973464 0.228842i \(-0.0734940\pi\)
\(332\) 0 0
\(333\) 4.19615 0.229948
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 15.9282 + 15.9282i 0.867665 + 0.867665i 0.992213 0.124549i \(-0.0397484\pi\)
−0.124549 + 0.992213i \(0.539748\pi\)
\(338\) 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 0
\(346\) 0 0
\(347\) 10.4282 + 2.79423i 0.559815 + 0.150002i 0.527621 0.849480i \(-0.323084\pi\)
0.0321938 + 0.999482i \(0.489751\pi\)
\(348\) 0 0
\(349\) −7.86603 + 2.10770i −0.421059 + 0.112822i −0.463126 0.886292i \(-0.653272\pi\)
0.0420673 + 0.999115i \(0.486606\pi\)
\(350\) 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 \(-0.423162\pi\)
−0.721387 + 0.692532i \(0.756495\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −0.571797 0.990381i −0.0302627 0.0524165i
\(358\) 0 0
\(359\) 13.1962 + 13.1962i 0.696466 + 0.696466i 0.963647 0.267180i \(-0.0860919\pi\)
−0.267180 + 0.963647i \(0.586092\pi\)
\(360\) 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
\(365\) 0 0
\(366\) 0 0
\(367\) 3.96410 + 14.7942i 0.206924 + 0.772252i 0.988854 + 0.148886i \(0.0475688\pi\)
−0.781930 + 0.623366i \(0.785765\pi\)
\(368\) 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 0.681471 + 0.731845i \(0.261341\pi\)
−0.956094 + 0.293061i \(0.905326\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.59808 + 2.76795i −0.288316 + 0.142557i
\(378\) 0 0
\(379\) 2.59808 + 9.69615i 0.133454 + 0.498058i 0.999999 0.00104063i \(-0.000331242\pi\)
−0.866545 + 0.499099i \(0.833665\pi\)
\(380\) 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 \(-0.440424\pi\)
0.943937 + 0.330124i \(0.107091\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 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 0
\(396\) 0 0
\(397\) 9.86603 5.69615i 0.495162 0.285882i −0.231552 0.972823i \(-0.574380\pi\)
0.726713 + 0.686941i \(0.241047\pi\)
\(398\) 0 0
\(399\) −3.27757 + 1.89230i −0.164084 + 0.0947337i
\(400\) 0 0
\(401\) 2.66987 + 9.96410i 0.133327 + 0.497583i 0.999999 0.00129478i \(-0.000412141\pi\)
−0.866672 + 0.498878i \(0.833745\pi\)
\(402\) 0 0
\(403\) −25.9808 + 5.19615i −1.29419 + 0.258839i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.74167 + 6.50000i −0.0863314 + 0.322193i
\(408\) 0 0
\(409\) 18.5263 + 4.96410i 0.916066 + 0.245459i 0.685903 0.727693i \(-0.259407\pi\)
0.230163 + 0.973152i \(0.426074\pi\)
\(410\) 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
\(415\) 0 0
\(416\) 0 0
\(417\) −1.90192 + 1.90192i −0.0931376 + 0.0931376i
\(418\) 0 0
\(419\) −31.5000 18.1865i −1.53888 0.888470i −0.998905 0.0467865i \(-0.985102\pi\)
−0.539971 0.841684i \(-0.681565\pi\)
\(420\) 0 0
\(421\) 6.85641 + 6.85641i 0.334161 + 0.334161i 0.854164 0.520003i \(-0.174069\pi\)
−0.520003 + 0.854164i \(0.674069\pi\)
\(422\) 0 0
\(423\) 14.9282 + 25.8564i 0.725834 + 1.25718i
\(424\) 0 0
\(425\) 0 0
\(426\) 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 −0.771011 0.636822i \(-0.780249\pi\)
−0.349304 + 0.937010i \(0.613582\pi\)
\(432\) 0 0
\(433\) −32.5526 8.72243i −1.56438 0.419173i −0.630330 0.776327i \(-0.717081\pi\)
−0.934046 + 0.357154i \(0.883747\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.411543i 0.0196868i
\(438\) 0 0
\(439\) 0.0358984 0.0621778i 0.00171334 0.00296759i −0.865167 0.501483i \(-0.832788\pi\)
0.866881 + 0.498515i \(0.166121\pi\)
\(440\) 0 0
\(441\) 2.53590i 0.120757i
\(442\) 0 0
\(443\) 15.5885 + 15.5885i 0.740630 + 0.740630i 0.972699 0.232069i \(-0.0745496\pi\)
−0.232069 + 0.972699i \(0.574550\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1.78461 −0.0844091
\(448\) 0 0
\(449\) −5.20577 + 19.4282i −0.245676 + 0.916874i 0.727367 + 0.686249i \(0.240744\pi\)
−0.973043 + 0.230625i \(0.925923\pi\)
\(450\) 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
\(455\) 0 0
\(456\) 0 0
\(457\) 6.79423 11.7679i 0.317821 0.550481i −0.662212 0.749316i \(-0.730382\pi\)
0.980033 + 0.198835i \(0.0637157\pi\)
\(458\) 0 0
\(459\) 1.33013 + 2.30385i 0.0620850 + 0.107534i
\(460\) 0 0
\(461\) 0.813467 3.03590i 0.0378869 0.141396i −0.944392 0.328823i \(-0.893348\pi\)
0.982279 + 0.187427i \(0.0600148\pi\)
\(462\) 0 0
\(463\) 21.6077 1.00419 0.502097 0.864811i \(-0.332562\pi\)
0.502097 + 0.864811i \(0.332562\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16.6603 16.6603i −0.770945 0.770945i 0.207327 0.978272i \(-0.433524\pi\)
−0.978272 + 0.207327i \(0.933524\pi\)
\(468\) 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
\(475\) 0 0
\(476\) 0 0
\(477\) 9.19615 + 2.46410i 0.421063 + 0.112823i
\(478\) 0 0
\(479\) −3.13397 + 0.839746i −0.143195 + 0.0383690i −0.329705 0.944084i \(-0.606949\pi\)
0.186510 + 0.982453i \(0.440282\pi\)
\(480\) 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
\(485\) 0 0
\(486\) 0 0
\(487\) 0.794229 + 1.37564i 0.0359899 + 0.0623364i 0.883459 0.468508i \(-0.155208\pi\)
−0.847469 + 0.530844i \(0.821875\pi\)
\(488\) 0 0
\(489\) 1.16987 + 1.16987i 0.0529035 + 0.0529035i
\(490\) 0 0
\(491\) 5.89230 + 3.40192i 0.265916 + 0.153527i 0.627030 0.778995i \(-0.284270\pi\)
−0.361114 + 0.932522i \(0.617604\pi\)
\(492\) 0 0
\(493\) −1.09808 + 1.09808i −0.0494549 + 0.0494549i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.47372 5.50000i −0.0661054 0.246709i
\(498\) 0 0
\(499\) 20.2679 20.2679i 0.907318 0.907318i −0.0887371 0.996055i \(-0.528283\pi\)
0.996055 + 0.0887371i \(0.0282831\pi\)
\(500\) 0 0
\(501\) 9.23205 + 2.47372i 0.412458 + 0.110518i
\(502\) 0 0
\(503\) 3.35641 12.5263i 0.149655 0.558519i −0.849849 0.527026i \(-0.823307\pi\)
0.999504 0.0314933i \(-0.0100263\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −4.10770 5.33013i −0.182429 0.236719i
\(508\) 0 0
\(509\) −7.45448 27.8205i −0.330414 1.23312i −0.908756 0.417328i \(-0.862967\pi\)
0.578342 0.815795i \(-0.303700\pi\)
\(510\) 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
\(515\) 0 0
\(516\) 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 \(-0.663162\pi\)
0.0110090 + 0.999939i \(0.496496\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 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
\(535\) 0 0
\(536\) 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 −0.0615128 0.998106i \(-0.519592\pi\)
0.998106 + 0.0615128i \(0.0195925\pi\)
\(542\) 0 0
\(543\) 3.07180 + 11.4641i 0.131823 + 0.491972i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.124356 0.124356i 0.00531706 0.00531706i −0.704443 0.709760i \(-0.748803\pi\)
0.709760 + 0.704443i \(0.248803\pi\)
\(548\) 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
\(555\) 0 0
\(556\) 0 0
\(557\) −13.3301 7.69615i −0.564816 0.326096i 0.190260 0.981734i \(-0.439067\pi\)
−0.755076 + 0.655637i \(0.772400\pi\)
\(558\) 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 \(-0.233937\pi\)
0.307212 + 0.951641i \(0.400604\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 16.4115i 0.689220i
\(568\) 0 0
\(569\) 18.8205 32.5981i 0.788997 1.36658i −0.137585 0.990490i \(-0.543934\pi\)
0.926582 0.376093i \(-0.122733\pi\)
\(570\) 0 0
\(571\) 21.6077i 0.904254i −0.891954 0.452127i \(-0.850665\pi\)
0.891954 0.452127i \(-0.149335\pi\)
\(572\) 0 0
\(573\) 5.49038 + 5.49038i 0.229364 + 0.229364i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −20.7846 −0.865275 −0.432637 0.901568i \(-0.642417\pi\)
−0.432637 + 0.901568i \(0.642417\pi\)
\(578\) 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
\(585\) 0 0
\(586\) 0 0
\(587\) 23.7224 41.0885i 0.979130 1.69590i 0.313556 0.949570i \(-0.398480\pi\)
0.665573 0.746333i \(-0.268187\pi\)
\(588\) 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 \(-0.280986\pi\)
0.635035 + 0.772484i \(0.280986\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.90192 + 6.90192i 0.282477 + 0.282477i
\(598\) 0 0
\(599\) 36.2487i 1.48108i −0.672011 0.740541i \(-0.734569\pi\)
0.672011 0.740541i \(-0.265431\pi\)
\(600\) 0 0
\(601\) 7.42820 12.8660i 0.303003 0.524816i −0.673812 0.738903i \(-0.735344\pi\)
0.976815 + 0.214087i \(0.0686775\pi\)
\(602\) 0 0
\(603\) 33.5167i 1.36490i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −3.03590 0.813467i −0.123223 0.0330176i 0.196680 0.980468i \(-0.436984\pi\)
−0.319904 + 0.947450i \(0.603651\pi\)
\(608\) 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 \(-0.168850\pi\)
−0.00685934 + 0.999976i \(0.502183\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.79423 15.2321i −0.354042 0.613219i 0.632911 0.774224i \(-0.281860\pi\)
−0.986954 + 0.161005i \(0.948526\pi\)
\(618\) 0 0
\(619\) 14.6603 + 14.6603i 0.589245 + 0.589245i 0.937427 0.348182i \(-0.113201\pi\)
−0.348182 + 0.937427i \(0.613201\pi\)
\(620\) 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
\(625\) 0 0
\(626\) 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 0.961860 0.273541i \(-0.0881948\pi\)
0.696225 + 0.717823i \(0.254862\pi\)
\(632\) 0 0
\(633\) −0.794229 + 2.96410i −0.0315678 + 0.117812i
\(634\) 0 0
\(635\) 0 0
\(636\) 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 −0.384388 0.923172i \(-0.625587\pi\)
0.607296 + 0.794475i \(0.292254\pi\)
\(642\) 0 0
\(643\) 31.3301 18.0885i 1.23554 0.713339i 0.267360 0.963597i \(-0.413849\pi\)
0.968179 + 0.250258i \(0.0805153\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.50000 + 0.669873i −0.0982851 + 0.0263354i −0.307626 0.951507i \(-0.599535\pi\)
0.209341 + 0.977843i \(0.432868\pi\)
\(648\) 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 −0.876453 + 0.481487i \(0.840097\pi\)
−0.999774 + 0.0212467i \(0.993236\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −35.3205 + 20.3923i −1.37798 + 0.795580i
\(658\) 0 0
\(659\) −35.4282 + 20.4545i −1.38009 + 0.796794i −0.992169 0.124901i \(-0.960139\pi\)
−0.387918 + 0.921694i \(0.626805\pi\)
\(660\) 0 0
\(661\) −0.794229 2.96410i −0.0308919 0.115290i 0.948758 0.316003i \(-0.102341\pi\)
−0.979650 + 0.200713i \(0.935674\pi\)
\(662\) 0 0
\(663\) −1.39230 0.928203i −0.0540726 0.0360484i
\(664\) 0 0
\(665\) 0 0
\(666\) 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 −0.859114 0.511784i \(-0.828985\pi\)
0.488122 0.872775i \(-0.337682\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 28.1769 28.1769i 1.08293 1.08293i 0.0866916 0.996235i \(-0.472371\pi\)
0.996235 0.0866916i \(-0.0276295\pi\)
\(678\) 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 \(-0.257160\pi\)
−0.971503 + 0.237028i \(0.923827\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 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 −0.889829 0.456293i \(-0.849177\pi\)
−0.542468 + 0.840076i \(0.682510\pi\)
\(692\) 0 0
\(693\) 28.4904 + 7.63397i 1.08226 + 0.289991i
\(694\) 0 0
\(695\) 0 0
\(696\) 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 \(-0.869727\pi\)
0.917413 0.397935i \(-0.130273\pi\)
\(702\) 0 0
\(703\) 3.22243 + 3.22243i 0.121536 + 0.121536i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −42.3731 −1.59360
\(708\) 0 0
\(709\) −4.27757 + 15.9641i −0.160647 + 0.599544i 0.837908 + 0.545812i \(0.183779\pi\)
−0.998555 + 0.0537328i \(0.982888\pi\)
\(710\) 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
\(715\) 0 0
\(716\) 0 0
\(717\) 6.09808 10.5622i 0.227737 0.394452i
\(718\) 0 0
\(719\) −20.9641 36.3109i −0.781829 1.35417i −0.930875 0.365337i \(-0.880954\pi\)
0.149046 0.988830i \(-0.452380\pi\)
\(720\) 0 0
\(721\) 10.0981 37.6865i 0.376072 1.40352i
\(722\) 0 0
\(723\) 6.07180 0.225813
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 33.5885 + 33.5885i 1.24573 + 1.24573i 0.957589 + 0.288138i \(0.0930362\pi\)
0.288138 + 0.957589i \(0.406964\pi\)
\(728\) 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 0
\(736\) 0 0
\(737\) 51.9186 + 13.9115i 1.91245 + 0.512438i
\(738\) 0 0
\(739\) −37.9186 + 10.1603i −1.39486 + 0.373751i −0.876495 0.481410i \(-0.840125\pi\)
−0.518362 + 0.855161i \(0.673458\pi\)
\(740\) 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 \(-0.199061\pi\)
−0.101594 + 0.994826i \(0.532394\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 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 0.786086 0.618117i \(-0.212104\pi\)
−0.142262 + 0.989829i \(0.545438\pi\)
\(752\) 0 0
\(753\) −6.49038 + 6.49038i −0.236523 + 0.236523i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 4.83975 + 18.0622i 0.175904 + 0.656481i 0.996396 + 0.0848236i \(0.0270327\pi\)
−0.820492 + 0.571657i \(0.806301\pi\)
\(758\) 0 0
\(759\) 0.222432 0.222432i 0.00807377 0.00807377i
\(760\) 0 0
\(761\) −0.669873 0.179492i −0.0242829 0.00650658i 0.246657 0.969103i \(-0.420668\pi\)
−0.270940 + 0.962596i \(0.587335\pi\)
\(762\) 0 0
\(763\) −3.18911 + 11.9019i −0.115454 + 0.430879i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −21.4282 24.3827i −0.773728 0.880408i
\(768\) 0 0
\(769\) 5.47372 + 20.4282i 0.197387 + 0.736660i 0.991636 + 0.129067i \(0.0411982\pi\)
−0.794248 + 0.607593i \(0.792135\pi\)
\(770\) 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 \(-0.781815\pi\)
0.161144 + 0.986931i \(0.448482\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 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
\(785\) 0 0
\(786\) 0 0
\(787\) 37.4545 21.6244i 1.33511 0.770825i 0.349031 0.937111i \(-0.386511\pi\)
0.986078 + 0.166286i \(0.0531776\pi\)
\(788\) 0 0
\(789\) −6.44744 + 3.72243i −0.229535 + 0.132522i
\(790\) 0 0
\(791\) 1.89230 + 7.06218i 0.0672826 + 0.251102i
\(792\) 0 0
\(793\) 32.3827 + 2.08846i 1.14994 + 0.0741633i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0