Properties

Label 1300.2.bs.b.457.1
Level $1300$
Weight $2$
Character 1300.457
Analytic conductor $10.381$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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 457.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1300.457
Dual form 1300.2.bs.b.293.1

$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).

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

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 0.400251 0.916406i \(-0.368923\pi\)
−0.111576 + 0.993756i \(0.535590\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.13397 + 1.23205i 0.806567 + 0.465671i 0.845762 0.533560i \(-0.179146\pi\)
−0.0391956 + 0.999232i \(0.512480\pi\)
\(8\) 0 0
\(9\) −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
\(15\) 0 0
\(16\) 0 0
\(17\) 0.232051 + 0.866025i 0.0562806 + 0.210042i 0.988340 0.152264i \(-0.0486563\pi\)
−0.932059 + 0.362306i \(0.881990\pi\)
\(18\) 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 −0.962082 0.272760i \(-0.912064\pi\)
0.969567 + 0.244824i \(0.0787302\pi\)
\(24\) 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 −0.632764 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
\(35\) 0 0
\(36\) 0 0
\(37\) −1.33013 + 0.767949i −0.218672 + 0.126250i −0.605335 0.795971i \(-0.706961\pi\)
0.386663 + 0.922221i \(0.373628\pi\)
\(38\) 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 0.226418 0.974030i \(-0.427298\pi\)
0.683099 + 0.730326i \(0.260632\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.9282i 1.59404i 0.603951 + 0.797021i \(0.293592\pi\)
−0.603951 + 0.797021i \(0.706408\pi\)
\(48\) 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 −0.855791 0.517321i \(-0.826929\pi\)
0.517321 + 0.855791i \(0.326929\pi\)
\(54\) 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 0.934351 + 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
\(65\) 0 0
\(66\) 0 0
\(67\) −6.13397 10.6244i −0.749384 1.29797i −0.948118 0.317918i \(-0.897016\pi\)
0.198734 0.980053i \(-0.436317\pi\)
\(68\) 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 \(-0.161775\pi\)
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 \(0.00959743\pi\)
−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 \(0.0513771\pi\)
−0.987002 + 0.160706i \(0.948623\pi\)
\(84\) 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 −0.632942 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
\(95\) 0 0
\(96\) 0 0
\(97\) −3.86603 + 6.69615i −0.392535 + 0.679891i −0.992783 0.119923i \(-0.961735\pi\)
0.600248 + 0.799814i \(0.295069\pi\)
\(98\) 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 \(0.0348181\pi\)
0.109166 + 0.994024i \(0.465182\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.96410 7.33013i 0.189877 0.708630i −0.803657 0.595093i \(-0.797115\pi\)
0.993534 0.113537i \(-0.0362181\pi\)
\(108\) 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 0.920351 0.391093i \(-0.127903\pi\)
−0.992594 + 0.121480i \(0.961236\pi\)
\(114\) 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 0.987752 0.156029i \(-0.0498694\pi\)
0.777404 + 0.629001i \(0.216536\pi\)
\(128\) 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 0.925313 0.379205i \(-0.123802\pi\)
0.134255 + 0.990947i \(0.457136\pi\)
\(138\) 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
\(145\) 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 −0.392633 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
\(155\) 0 0
\(156\) 0 0
\(157\) −6.46410 6.46410i −0.515891 0.515891i 0.400434 0.916326i \(-0.368859\pi\)
−0.916326 + 0.400434i \(0.868859\pi\)
\(158\) 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 −0.796629 0.604469i \(-0.793385\pi\)
0.921800 + 0.387666i \(0.126719\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.9904 9.23205i 1.23737 0.714398i 0.268816 0.963191i \(-0.413368\pi\)
0.968556 + 0.248794i \(0.0800342\pi\)
\(168\) 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 −0.152057 0.988372i \(-0.548590\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(174\) 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 0.999715 + 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
\(185\) 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 −0.456068 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 \(-0.794082\pi\)
−0.122998 0.992407i \(-0.539251\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.13397 3.69615i −0.152039 0.263340i 0.779938 0.625857i \(-0.215251\pi\)
−0.931977 + 0.362517i \(0.881917\pi\)
\(198\) 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
\(205\) 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 0.745775 0.666198i \(-0.232080\pi\)
−0.949832 + 0.312761i \(0.898746\pi\)
\(212\) 0 0
\(213\) 1.19615i 0.0819590i
\(214\) 0 0
\(215\) 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 −0.454802 0.890592i \(-0.650290\pi\)
0.543874 + 0.839167i \(0.316957\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.59808 + 2.76795i −0.106068 + 0.183715i −0.914174 0.405322i \(-0.867159\pi\)
0.808106 + 0.589037i \(0.200493\pi\)
\(228\) 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 0.146900 0.989151i \(-0.453070\pi\)
−0.989151 + 0.146900i \(0.953070\pi\)
\(234\) 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 0.996719 + 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
\(245\) 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 −0.0702687 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 0
\(256\) 0 0
\(257\) −21.6244 5.79423i −1.34889 0.361434i −0.489165 0.872191i \(-0.662698\pi\)
−0.859725 + 0.510757i \(0.829365\pi\)
\(258\) 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 −0.196336 0.980537i \(-0.562904\pi\)
−0.660300 + 0.751002i \(0.729571\pi\)
\(264\) 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 0.897584 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
\(275\) 0 0
\(276\) 0 0
\(277\) 2.76795 + 10.3301i 0.166310 + 0.620677i 0.997869 + 0.0652416i \(0.0207818\pi\)
−0.831560 + 0.555436i \(0.812552\pi\)
\(278\) 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 \(0.450805\pi\)
−0.627354 + 0.778735i \(0.715862\pi\)
\(284\) 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 −0.393627 0.919270i \(-0.628780\pi\)
0.992925 0.118744i \(-0.0378869\pi\)
\(294\) 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 \(-0.963587\pi\)
0.993464 0.114146i \(-0.0364132\pi\)
\(308\) 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 −0.533127 0.846035i \(-0.678983\pi\)
0.846035 + 0.533127i \(0.178983\pi\)
\(314\) 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 0.973464 + 0.228842i \(0.0734940\pi\)
−0.728623 + 0.684915i \(0.759839\pi\)
\(332\) 0 0
\(333\) 4.19615 0.229948
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 15.9282 15.9282i 0.867665 0.867665i −0.124549 0.992213i \(-0.539748\pi\)
0.992213 + 0.124549i \(0.0397484\pi\)
\(338\) 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 0.0321938 0.999482i \(-0.489751\pi\)
0.527621 + 0.849480i \(0.323084\pi\)
\(348\) 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 −0.721387 0.692532i \(-0.756495\pi\)
0.239056 + 0.971006i \(0.423162\pi\)
\(354\) 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 −0.267180 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
\(365\) 0 0
\(366\) 0 0
\(367\) 3.96410 14.7942i 0.206924 0.772252i −0.781930 0.623366i \(-0.785765\pi\)
0.988854 0.148886i \(-0.0475688\pi\)
\(368\) 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 \(-0.905326\pi\)
0.681471 0.731845i \(-0.261341\pi\)
\(374\) 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 −0.866545 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 0.943937 0.330124i \(-0.107091\pi\)
0.186073 + 0.982536i \(0.440424\pi\)
\(384\) 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 0.726713 0.686941i \(-0.241047\pi\)
−0.231552 + 0.972823i \(0.574380\pi\)
\(398\) 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
\(405\) 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 0.230163 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
\(415\) 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 −0.539971 + 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
\(425\) 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 −0.349304 0.937010i \(-0.613582\pi\)
−0.771011 + 0.636822i \(0.780249\pi\)
\(432\) 0 0
\(433\) −32.5526 + 8.72243i −1.56438 + 0.419173i −0.934046 0.357154i \(-0.883747\pi\)
−0.630330 + 0.776327i \(0.717081\pi\)
\(434\) 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 0.866881 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 −0.232069 0.972699i \(-0.574550\pi\)
0.972699 + 0.232069i \(0.0745496\pi\)
\(444\) 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 −0.973043 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
\(455\) 0 0
\(456\) 0 0
\(457\) 6.79423 + 11.7679i 0.317821 + 0.550481i 0.980033 0.198835i \(-0.0637157\pi\)
−0.662212 + 0.749316i \(0.730382\pi\)
\(458\) 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 \(-0.332562\pi\)
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 −0.978272 0.207327i \(-0.933524\pi\)
0.207327 + 0.978272i \(0.433524\pi\)
\(468\) 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 0.186510 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
\(485\) 0 0
\(486\) 0 0
\(487\) 0.794229 1.37564i 0.0359899 0.0623364i −0.847469 0.530844i \(-0.821875\pi\)
0.883459 + 0.468508i \(0.155208\pi\)
\(488\) 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
\(495\) 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 0.996055 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 \(0.0100263\pi\)
−0.849849 + 0.527026i \(0.823307\pi\)
\(504\) 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 0.578342 + 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
\(515\) 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 0.0110090 0.999939i \(-0.496496\pi\)
−0.490436 + 0.871477i \(0.663162\pi\)
\(524\) 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 0.998106 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
\(545\) 0 0
\(546\) 0 0
\(547\) 0.124356 + 0.124356i 0.00531706 + 0.00531706i 0.709760 0.704443i \(-0.248803\pi\)
−0.704443 + 0.709760i \(0.748803\pi\)
\(548\) 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 −0.755076 0.655637i \(-0.772400\pi\)
0.190260 + 0.981734i \(0.439067\pi\)
\(558\) 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 0.307212 0.951641i \(-0.400604\pi\)
0.741874 + 0.670540i \(0.233937\pi\)
\(564\) 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 0.926582 + 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 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 0.665573 + 0.746333i \(0.268187\pi\)
0.313556 + 0.949570i \(0.398480\pi\)
\(588\) 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 \(0.265431\pi\)
−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
\(605\) 0 0
\(606\) 0 0
\(607\) −3.03590 + 0.813467i −0.123223 + 0.0330176i −0.319904 0.947450i \(-0.603651\pi\)
0.196680 + 0.980468i \(0.436984\pi\)
\(608\) 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 −0.00685934 0.999976i \(-0.502183\pi\)
0.862575 + 0.505929i \(0.168850\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.79423 + 15.2321i −0.354042 + 0.613219i −0.986954 0.161005i \(-0.948526\pi\)
0.632911 + 0.774224i \(0.281860\pi\)
\(618\) 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
\(625\) 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 0.696225 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
\(635\) 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 0.607296 0.794475i \(-0.292254\pi\)
−0.384388 + 0.923172i \(0.625587\pi\)
\(642\) 0 0
\(643\) 31.3301 + 18.0885i 1.23554 + 0.713339i 0.968179 0.250258i \(-0.0805153\pi\)
0.267360 + 0.963597i \(0.413849\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.50000 0.669873i −0.0982851 0.0263354i 0.209341 0.977843i \(-0.432868\pi\)
−0.307626 + 0.951507i \(0.599535\pi\)
\(648\) 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 \(-0.993236\pi\)
−0.876453 0.481487i \(-0.840097\pi\)
\(654\) 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 −0.387918 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
\(665\) 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 0.488122 + 0.872775i \(0.337682\pi\)
−0.859114 + 0.511784i \(0.828985\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 28.1769 + 28.1769i 1.08293 + 1.08293i 0.996235 + 0.0866916i \(0.0276295\pi\)
0.0866916 + 0.996235i \(0.472371\pi\)
\(678\) 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 −0.971503 0.237028i \(-0.923827\pi\)
0.691023 + 0.722832i \(0.257160\pi\)
\(684\) 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 −0.542468 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
\(695\) 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 \(0.130273\pi\)
−0.917413 + 0.397935i \(0.869727\pi\)
\(702\) 0 0
\(703\) 3.22243 3.22243i 0.121536 0.121536i
\(704\) 0 0
\(705\) 0 0
\(706\) 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
\(715\) 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 0.149046 + 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
\(725\) 0 0
\(726\) 0 0
\(727\) 33.5885 33.5885i 1.24573 1.24573i 0.288138 0.957589i \(-0.406964\pi\)
0.957589 0.288138i \(-0.0930362\pi\)
\(728\) 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 \(0.164706\pi\)
−0.869089 + 0.494656i \(0.835294\pi\)
\(734\) 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 −0.518362 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 −0.101594 0.994826i \(-0.532394\pi\)
0.810748 + 0.585396i \(0.199061\pi\)
\(744\) 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 −0.142262 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 0
\(756\) 0 0
\(757\) 4.83975 18.0622i 0.175904 0.656481i −0.820492 0.571657i \(-0.806301\pi\)
0.996396 0.0848236i \(-0.0270327\pi\)
\(758\) 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
\(765\) 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 −0.794248 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 0.161144 0.986931i \(-0.448482\pi\)
−0.774136 + 0.633020i \(0.781815\pi\)
\(774\) 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 0.986078 0.166286i \(-0.0531776\pi\)
0.349031 + 0.937111i \(0.386511\pi\)
\(788\) 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