Properties

Label 1300.2.bn.a.657.1
Level $1300$
Weight $2$
Character 1300.657
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.bn (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 657.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1300.657
Dual form 1300.2.bn.a.93.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.133975 - 0.500000i) q^{3} +(1.23205 + 2.13397i) q^{7} +(2.36603 - 1.36603i) q^{9} +O(q^{10})\) \(q+(-0.133975 - 0.500000i) q^{3} +(1.23205 + 2.13397i) q^{7} +(2.36603 - 1.36603i) q^{9} +(-1.13397 - 4.23205i) q^{11} +(-3.00000 - 2.00000i) q^{13} +(0.866025 + 0.232051i) q^{17} +(2.86603 + 0.767949i) q^{19} +(0.901924 - 0.901924i) q^{21} +(0.133975 - 0.0358984i) q^{23} +(-2.09808 - 2.09808i) q^{27} +(1.50000 + 0.866025i) q^{29} +(-5.19615 - 5.19615i) q^{31} +(-1.96410 + 1.13397i) q^{33} +(0.767949 - 1.33013i) q^{37} +(-0.598076 + 1.76795i) q^{39} +(9.33013 - 2.50000i) q^{41} +(1.59808 - 5.96410i) q^{43} +10.9282 q^{47} +(0.464102 - 0.803848i) q^{49} -0.464102i q^{51} +(-2.46410 + 2.46410i) q^{53} -1.53590i q^{57} +(-2.33013 + 8.69615i) q^{59} +(4.50000 + 7.79423i) q^{61} +(5.83013 + 3.36603i) q^{63} +(-10.6244 - 6.13397i) q^{67} +(-0.0358984 - 0.0621778i) q^{69} +(0.598076 - 2.23205i) q^{71} -14.9282i q^{73} +(7.63397 - 7.63397i) q^{77} +0.535898i q^{79} +(3.33013 - 5.76795i) q^{81} -2.92820 q^{83} +(0.232051 - 0.866025i) q^{87} +(14.7942 - 3.96410i) q^{89} +(0.571797 - 8.86603i) q^{91} +(-1.90192 + 3.29423i) q^{93} +(6.69615 - 3.86603i) q^{97} +(-8.46410 - 8.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 2 q^{7} + 6 q^{9} - 8 q^{11} - 12 q^{13} + 8 q^{19} + 14 q^{21} + 4 q^{23} + 2 q^{27} + 6 q^{29} + 6 q^{33} + 10 q^{37} + 8 q^{39} + 20 q^{41} - 4 q^{43} + 16 q^{47} - 12 q^{49} + 4 q^{53} + 8 q^{59} + 18 q^{61} + 6 q^{63} + 6 q^{67} - 14 q^{69} - 8 q^{71} + 34 q^{77} - 4 q^{81} + 16 q^{83} - 6 q^{87} + 28 q^{89} + 30 q^{91} - 18 q^{93} + 6 q^{97} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) −0.133975 0.500000i −0.0773503 0.288675i 0.916406 0.400251i \(-0.131077\pi\)
−0.993756 + 0.111576i \(0.964410\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.23205 + 2.13397i 0.465671 + 0.806567i 0.999232 0.0391956i \(-0.0124795\pi\)
−0.533560 + 0.845762i \(0.679146\pi\)
\(8\) 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
\(13\) −3.00000 2.00000i −0.832050 0.554700i
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.866025 + 0.232051i 0.210042 + 0.0562806i 0.362306 0.932059i \(-0.381990\pi\)
−0.152264 + 0.988340i \(0.548656\pi\)
\(18\) 0 0
\(19\) 2.86603 + 0.767949i 0.657511 + 0.176180i 0.572123 0.820168i \(-0.306120\pi\)
0.0853887 + 0.996348i \(0.472787\pi\)
\(20\) 0 0
\(21\) 0.901924 0.901924i 0.196816 0.196816i
\(22\) 0 0
\(23\) 0.133975 0.0358984i 0.0279356 0.00748533i −0.244824 0.969567i \(-0.578730\pi\)
0.272760 + 0.962082i \(0.412064\pi\)
\(24\) 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 \(-0.281920\pi\)
−0.354221 + 0.935162i \(0.615254\pi\)
\(30\) 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
\(33\) −1.96410 + 1.13397i −0.341906 + 0.197400i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.767949 1.33013i 0.126250 0.218672i −0.795971 0.605335i \(-0.793039\pi\)
0.922221 + 0.386663i \(0.126372\pi\)
\(38\) 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
\(43\) 1.59808 5.96410i 0.243704 0.909517i −0.730326 0.683099i \(-0.760632\pi\)
0.974030 0.226418i \(-0.0727016\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.9282 1.59404 0.797021 0.603951i \(-0.206408\pi\)
0.797021 + 0.603951i \(0.206408\pi\)
\(48\) 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
\(57\) 1.53590i 0.203435i
\(58\) 0 0
\(59\) −2.33013 + 8.69615i −0.303357 + 1.13214i 0.630994 + 0.775788i \(0.282647\pi\)
−0.934351 + 0.356355i \(0.884019\pi\)
\(60\) 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
\(63\) 5.83013 + 3.36603i 0.734527 + 0.424079i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −10.6244 6.13397i −1.29797 0.749384i −0.317918 0.948118i \(-0.602984\pi\)
−0.980053 + 0.198734i \(0.936317\pi\)
\(68\) 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
\(73\) 14.9282i 1.74721i −0.486632 0.873607i \(-0.661775\pi\)
0.486632 0.873607i \(-0.338225\pi\)
\(74\) 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
\(83\) −2.92820 −0.321412 −0.160706 0.987002i \(-0.551377\pi\)
−0.160706 + 0.987002i \(0.551377\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.232051 0.866025i 0.0248785 0.0928477i
\(88\) 0 0
\(89\) 14.7942 3.96410i 1.56819 0.420194i 0.632942 0.774199i \(-0.281847\pi\)
0.935243 + 0.354005i \(0.115181\pi\)
\(90\) 0 0
\(91\) 0.571797 8.86603i 0.0599406 0.929412i
\(92\) 0 0
\(93\) −1.90192 + 3.29423i −0.197220 + 0.341596i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.69615 3.86603i 0.679891 0.392535i −0.119923 0.992783i \(-0.538265\pi\)
0.799814 + 0.600248i \(0.204931\pi\)
\(98\) 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 −0.994024 0.109166i \(-0.965182\pi\)
−0.109166 0.994024i \(-0.534818\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.33013 + 1.96410i −0.708630 + 0.189877i −0.595093 0.803657i \(-0.702885\pi\)
−0.113537 + 0.993534i \(0.536218\pi\)
\(108\) 0 0
\(109\) 3.53590 3.53590i 0.338678 0.338678i −0.517192 0.855869i \(-0.673023\pi\)
0.855869 + 0.517192i \(0.173023\pi\)
\(110\) 0 0
\(111\) −0.767949 0.205771i −0.0728905 0.0195310i
\(112\) 0 0
\(113\) 2.86603 + 0.767949i 0.269613 + 0.0722426i 0.391093 0.920351i \(-0.372097\pi\)
−0.121480 + 0.992594i \(0.538764\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −9.83013 0.633975i −0.908796 0.0586110i
\(118\) 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
\(123\) −2.50000 4.33013i −0.225417 0.390434i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 5.33013 + 19.8923i 0.472972 + 1.76516i 0.629001 + 0.777404i \(0.283464\pi\)
−0.156029 + 0.987752i \(0.549869\pi\)
\(128\) 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
\(133\) 1.89230 + 7.06218i 0.164084 + 0.612368i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.16025 + 12.4019i 0.611742 + 1.05957i 0.990947 + 0.134255i \(0.0428642\pi\)
−0.379205 + 0.925313i \(0.623802\pi\)
\(138\) 0 0
\(139\) 4.50000 2.59808i 0.381685 0.220366i −0.296866 0.954919i \(-0.595942\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) −1.46410 5.46410i −0.123300 0.460160i
\(142\) 0 0
\(143\) −5.06218 + 14.9641i −0.423321 + 1.25136i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.464102 0.124356i −0.0382785 0.0102567i
\(148\) 0 0
\(149\) 3.33013 + 0.892305i 0.272815 + 0.0731005i 0.392633 0.919695i \(-0.371564\pi\)
−0.119818 + 0.992796i \(0.538231\pi\)
\(150\) 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
\(153\) 2.36603 0.633975i 0.191282 0.0512538i
\(154\) 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
\(163\) 2.76795 1.59808i 0.216803 0.125171i −0.387666 0.921800i \(-0.626719\pi\)
0.604469 + 0.796629i \(0.293385\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.23205 + 15.9904i −0.714398 + 1.23737i 0.248794 + 0.968556i \(0.419966\pi\)
−0.963191 + 0.268816i \(0.913368\pi\)
\(168\) 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
\(173\) 0.741670 2.76795i 0.0563881 0.210443i −0.931984 0.362500i \(-0.881923\pi\)
0.988372 + 0.152057i \(0.0485898\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.66025 0.350286
\(178\) 0 0
\(179\) −6.96410 + 12.0622i −0.520521 + 0.901570i 0.479194 + 0.877709i \(0.340929\pi\)
−0.999715 + 0.0238604i \(0.992404\pi\)
\(180\) 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
\(187\) 3.92820i 0.287259i
\(188\) 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
\(193\) 22.1603 + 12.7942i 1.59513 + 0.920949i 0.992407 + 0.122998i \(0.0392510\pi\)
0.602723 + 0.797950i \(0.294082\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.69615 2.13397i −0.263340 0.152039i 0.362517 0.931977i \(-0.381917\pi\)
−0.625857 + 0.779938i \(0.715251\pi\)
\(198\) 0 0
\(199\) −9.42820 16.3301i −0.668348 1.15761i −0.978366 0.206881i \(-0.933669\pi\)
0.310018 0.950731i \(-0.399665\pi\)
\(200\) 0 0
\(201\) −1.64359 + 6.13397i −0.115930 + 0.432657i
\(202\) 0 0
\(203\) 4.26795i 0.299551i
\(204\) 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
\(213\) −1.19615 −0.0819590
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 4.68653 17.4904i 0.318143 1.18732i
\(218\) 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
\(223\) 0.767949 1.33013i 0.0514257 0.0890719i −0.839167 0.543874i \(-0.816957\pi\)
0.890592 + 0.454802i \(0.150290\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.76795 1.59808i 0.183715 0.106068i −0.405322 0.914174i \(-0.632841\pi\)
0.589037 + 0.808106i \(0.299507\pi\)
\(228\) 0 0
\(229\) −0.0717968 0.0717968i −0.00474446 0.00474446i 0.704731 0.709475i \(-0.251068\pi\)
−0.709475 + 0.704731i \(0.751068\pi\)
\(230\) 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
\(235\) 0 0
\(236\) 0 0
\(237\) 0.267949 0.0717968i 0.0174052 0.00466370i
\(238\) 0 0
\(239\) −16.6603 + 16.6603i −1.07766 + 1.07766i −0.0809436 + 0.996719i \(0.525793\pi\)
−0.996719 + 0.0809436i \(0.974207\pi\)
\(240\) 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
\(243\) −11.9282 3.19615i −0.765195 0.205033i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.06218 8.03590i −0.449356 0.511312i
\(248\) 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
\(253\) −0.303848 0.526279i −0.0191027 0.0330869i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.79423 21.6244i −0.361434 1.34889i −0.872191 0.489165i \(-0.837302\pi\)
0.510757 0.859725i \(-0.329365\pi\)
\(258\) 0 0
\(259\) 3.78461 0.235164
\(260\) 0 0
\(261\) 4.73205 0.292907
\(262\) 0 0
\(263\) 3.72243 + 13.8923i 0.229535 + 0.856636i 0.980537 + 0.196336i \(0.0629043\pi\)
−0.751002 + 0.660300i \(0.770429\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −3.96410 6.86603i −0.242599 0.420194i
\(268\) 0 0
\(269\) −15.8205 + 9.13397i −0.964593 + 0.556908i −0.897584 0.440844i \(-0.854679\pi\)
−0.0670097 + 0.997752i \(0.521346\pi\)
\(270\) 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
\(273\) −4.50962 + 0.901924i −0.272935 + 0.0545869i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 10.3301 + 2.76795i 0.620677 + 0.166310i 0.555436 0.831560i \(-0.312552\pi\)
0.0652416 + 0.997869i \(0.479218\pi\)
\(278\) 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
\(283\) −29.7224 + 7.96410i −1.76682 + 0.473417i −0.988081 0.153937i \(-0.950805\pi\)
−0.778735 + 0.627354i \(0.784138\pi\)
\(284\) 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
\(293\) 17.7679 10.2583i 1.03801 0.599298i 0.118744 0.992925i \(-0.462113\pi\)
0.919270 + 0.393627i \(0.128780\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −6.50000 + 11.2583i −0.377168 + 0.653275i
\(298\) 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
\(303\) −2.30385 + 8.59808i −0.132353 + 0.493947i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 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 −0.533127 0.846035i \(-0.678983\pi\)
0.846035 + 0.533127i \(0.178983\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 18.9282i 1.06311i 0.847023 + 0.531557i \(0.178393\pi\)
−0.847023 + 0.531557i \(0.821607\pi\)
\(318\) 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
\(323\) 2.30385 + 1.33013i 0.128190 + 0.0740102i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.24167 1.29423i −0.123965 0.0715710i
\(328\) 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
\(333\) 4.19615i 0.229948i
\(334\) 0 0
\(335\) 0 0
\(336\) 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
\(343\) 19.5359 1.05484
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.79423 + 10.4282i −0.150002 + 0.559815i 0.849480 + 0.527621i \(0.176916\pi\)
−0.999482 + 0.0321938i \(0.989751\pi\)
\(348\) 0 0
\(349\) 7.86603 2.10770i 0.421059 0.112822i −0.0420673 0.999115i \(-0.513394\pi\)
0.463126 + 0.886292i \(0.346728\pi\)
\(350\) 0 0
\(351\) 2.09808 + 10.4904i 0.111987 + 0.559935i
\(352\) 0 0
\(353\) −5.23205 + 9.06218i −0.278474 + 0.482331i −0.971006 0.239056i \(-0.923162\pi\)
0.692532 + 0.721387i \(0.256495\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0.990381 0.571797i 0.0524165 0.0302627i
\(358\) 0 0
\(359\) −13.1962 13.1962i −0.696466 0.696466i 0.267180 0.963647i \(-0.413908\pi\)
−0.963647 + 0.267180i \(0.913908\pi\)
\(360\) 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
\(367\) −14.7942 + 3.96410i −0.772252 + 0.206924i −0.623366 0.781930i \(-0.714235\pi\)
−0.148886 + 0.988854i \(0.547569\pi\)
\(368\) 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
\(373\) 19.7942 + 5.30385i 1.02491 + 0.274623i 0.731845 0.681471i \(-0.238659\pi\)
0.293061 + 0.956094i \(0.405326\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.76795 5.59808i −0.142557 0.288316i
\(378\) 0 0
\(379\) −2.59808 9.69615i −0.133454 0.498058i 0.866545 0.499099i \(-0.166335\pi\)
−0.999999 + 0.00104063i \(0.999669\pi\)
\(380\) 0 0
\(381\) 9.23205 5.33013i 0.472972 0.273071i
\(382\) 0 0
\(383\) −12.7679 22.1147i −0.652412 1.13001i −0.982536 0.186073i \(-0.940424\pi\)
0.330124 0.943937i \(-0.392909\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.36603 16.2942i −0.221938 0.828282i
\(388\) 0 0
\(389\) 15.0718 0.764170 0.382085 0.924127i \(-0.375206\pi\)
0.382085 + 0.924127i \(0.375206\pi\)
\(390\) 0 0
\(391\) 0.124356 0.00628894
\(392\) 0 0
\(393\) −0.784610 2.92820i −0.0395783 0.147708i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5.69615 + 9.86603i 0.285882 + 0.495162i 0.972823 0.231552i \(-0.0743802\pi\)
−0.686941 + 0.726713i \(0.741047\pi\)
\(398\) 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
\(403\) 5.19615 + 25.9808i 0.258839 + 1.29419i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6.50000 1.74167i −0.322193 0.0863314i
\(408\) 0 0
\(409\) −18.5263 4.96410i −0.916066 0.245459i −0.230163 0.973152i \(-0.573926\pi\)
−0.685903 + 0.727693i \(0.740593\pi\)
\(410\) 0 0
\(411\) 5.24167 5.24167i 0.258553 0.258553i
\(412\) 0 0
\(413\) −21.4282 + 5.74167i −1.05441 + 0.282529i
\(414\) 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 \(0.0148981\pi\)
0.539971 + 0.841684i \(0.318435\pi\)
\(420\) 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
\(423\) 25.8564 14.9282i 1.25718 0.725834i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −11.0885 + 19.2058i −0.536608 + 0.929432i
\(428\) 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
\(433\) −8.72243 + 32.5526i −0.419173 + 1.56438i 0.357154 + 0.934046i \(0.383747\pi\)
−0.776327 + 0.630330i \(0.782919\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.411543 0.0196868
\(438\) 0 0
\(439\) −0.0358984 + 0.0621778i −0.00171334 + 0.00296759i −0.866881 0.498515i \(-0.833879\pi\)
0.865167 + 0.501483i \(0.167212\pi\)
\(440\) 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
\(447\) 1.78461i 0.0844091i
\(448\) 0 0
\(449\) 5.20577 19.4282i 0.245676 0.916874i −0.727367 0.686249i \(-0.759256\pi\)
0.973043 0.230625i \(-0.0740771\pi\)
\(450\) 0 0
\(451\) −21.1603 36.6506i −0.996397 1.72581i
\(452\) 0 0
\(453\) 0.169873 + 0.0980762i 0.00798133 + 0.00460802i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.7679 + 6.79423i 0.550481 + 0.317821i 0.749316 0.662212i \(-0.230382\pi\)
−0.198835 + 0.980033i \(0.563716\pi\)
\(458\) 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
\(463\) 21.6077i 1.00419i −0.864811 0.502097i \(-0.832562\pi\)
0.864811 0.502097i \(-0.167438\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 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
\(473\) −27.0526 −1.24388
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −2.46410 + 9.19615i −0.112823 + 0.421063i
\(478\) 0 0
\(479\) 3.13397 0.839746i 0.143195 0.0383690i −0.186510 0.982453i \(-0.559718\pi\)
0.329705 + 0.944084i \(0.393051\pi\)
\(480\) 0 0
\(481\) −4.96410 + 2.45448i −0.226344 + 0.111915i
\(482\) 0 0
\(483\) 0.0884573 0.153212i 0.00402495 0.00697141i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.37564 + 0.794229i −0.0623364 + 0.0359899i −0.530844 0.847469i \(-0.678125\pi\)
0.468508 + 0.883459i \(0.344792\pi\)
\(488\) 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
\(497\) 5.50000 1.47372i 0.246709 0.0661054i
\(498\) 0 0
\(499\) −20.2679 + 20.2679i −0.907318 + 0.907318i −0.996055 0.0887371i \(-0.971717\pi\)
0.0887371 + 0.996055i \(0.471717\pi\)
\(500\) 0 0
\(501\) 9.23205 + 2.47372i 0.412458 + 0.110518i
\(502\) 0 0
\(503\) −12.5263 3.35641i −0.558519 0.149655i −0.0314933 0.999504i \(-0.510026\pi\)
−0.527026 + 0.849849i \(0.676693\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 5.33013 4.10770i 0.236719 0.182429i
\(508\) 0 0
\(509\) 7.45448 + 27.8205i 0.330414 + 1.23312i 0.908756 + 0.417328i \(0.137033\pi\)
−0.578342 + 0.815795i \(0.696300\pi\)
\(510\) 0 0
\(511\) 31.8564 18.3923i 1.40924 0.813628i
\(512\) 0 0
\(513\) −4.40192 7.62436i −0.194350 0.336624i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −12.3923 46.2487i −0.545013 2.03402i
\(518\) 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
\(523\) 2.93782 + 10.9641i 0.128462 + 0.479427i 0.999939 0.0110090i \(-0.00350433\pi\)
−0.871477 + 0.490436i \(0.836838\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.29423 5.70577i −0.143499 0.248547i
\(528\) 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
\(533\) −32.9904 11.1603i −1.42897 0.483404i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 6.96410 + 1.86603i 0.300523 + 0.0805249i
\(538\) 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
\(543\) 11.4641 3.07180i 0.491972 0.131823i
\(544\) 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
\(553\) −1.14359 + 0.660254i −0.0486305 + 0.0280769i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.69615 13.3301i 0.326096 0.564816i −0.655637 0.755076i \(-0.727600\pi\)
0.981734 + 0.190260i \(0.0609332\pi\)
\(558\) 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
\(563\) 6.66987 24.8923i 0.281102 1.04909i −0.670540 0.741874i \(-0.733937\pi\)
0.951641 0.307212i \(-0.0993960\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 16.4115 0.689220
\(568\) 0 0
\(569\) −18.8205 + 32.5981i −0.788997 + 1.36658i 0.137585 + 0.990490i \(0.456066\pi\)
−0.926582 + 0.376093i \(0.877267\pi\)
\(570\) 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
\(577\) 20.7846i 0.865275i −0.901568 0.432637i \(-0.857583\pi\)
0.901568 0.432637i \(-0.142417\pi\)
\(578\) 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
\(583\) 13.2224 + 7.63397i 0.547617 + 0.316167i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 41.0885 + 23.7224i 1.69590 + 0.979130i 0.949570 + 0.313556i \(0.101520\pi\)
0.746333 + 0.665573i \(0.231813\pi\)
\(588\) 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
\(593\) 30.9282i 1.27007i −0.772484 0.635035i \(-0.780986\pi\)
0.772484 0.635035i \(-0.219014\pi\)
\(594\) 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 −0.673812 0.738903i \(-0.735344\pi\)
0.976815 + 0.214087i \(0.0686775\pi\)
\(602\) 0 0
\(603\) −33.5167 −1.36490
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0.813467 3.03590i 0.0330176 0.123223i −0.947450 0.319904i \(-0.896349\pi\)
0.980468 + 0.196680i \(0.0630161\pi\)
\(608\) 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
\(613\) 12.2321 21.1865i 0.494048 0.855716i −0.505929 0.862575i \(-0.668850\pi\)
0.999976 + 0.00685934i \(0.00218341\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.2321 8.79423i 0.613219 0.354042i −0.161005 0.986954i \(-0.551474\pi\)
0.774224 + 0.632911i \(0.218140\pi\)
\(618\) 0 0
\(619\) −14.6603 14.6603i −0.589245 0.589245i 0.348182 0.937427i \(-0.386799\pi\)
−0.937427 + 0.348182i \(0.886799\pi\)
\(620\) 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
\(627\) −6.50000 + 1.74167i −0.259585 + 0.0695556i
\(628\) 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
\(633\) 2.96410 + 0.794229i 0.117812 + 0.0315678i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −3.00000 + 1.48334i −0.118864 + 0.0587721i
\(638\) 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
\(643\) −18.0885 31.3301i −0.713339 1.23554i −0.963597 0.267360i \(-0.913849\pi\)
0.250258 0.968179i \(-0.419485\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.669873 2.50000i −0.0263354 0.0982851i 0.951507 0.307626i \(-0.0995347\pi\)
−0.977843 + 0.209341i \(0.932868\pi\)
\(648\) 0 0
\(649\) 39.4449 1.54835
\(650\) 0 0
\(651\) −9.37307 −0.367359
\(652\) 0 0
\(653\) 12.8468 + 47.9449i 0.502734 + 1.87623i 0.481487 + 0.876453i \(0.340097\pi\)
0.0212467 + 0.999774i \(0.493236\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −20.3923 35.3205i −0.795580 1.37798i
\(658\) 0 0
\(659\) 35.4282 20.4545i 1.38009 0.796794i 0.387918 0.921694i \(-0.373195\pi\)
0.992169 + 0.124901i \(0.0398612\pi\)
\(660\) 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
\(663\) −0.928203 + 1.39230i −0.0360484 + 0.0540726i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.232051 + 0.0621778i 0.00898504 + 0.00240754i
\(668\) 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
\(673\) −35.9186 + 9.62436i −1.38456 + 0.370992i −0.872775 0.488122i \(-0.837682\pi\)
−0.511784 + 0.859114i \(0.671015\pi\)
\(674\) 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
\(683\) −12.6962 + 7.33013i −0.485805 + 0.280480i −0.722832 0.691023i \(-0.757160\pi\)
0.237028 + 0.971503i \(0.423827\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −0.0262794 + 0.0455173i −0.00100262 + 0.00173659i
\(688\) 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
\(693\) 7.63397 28.4904i 0.289991 1.08226i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 8.66025 0.328031
\(698\) 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
\(707\) 42.3731i 1.59360i
\(708\) 0 0
\(709\) 4.27757 15.9641i 0.160647 0.599544i −0.837908 0.545812i \(-0.816221\pi\)
0.998555 0.0537328i \(-0.0171119\pi\)
\(710\) 0 0
\(711\) 0.732051 + 1.26795i 0.0274541 + 0.0475518i
\(712\) 0 0
\(713\) −0.882686 0.509619i −0.0330568 0.0190854i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.5622 + 6.09808i 0.394452 + 0.227737i
\(718\) 0 0
\(719\) 20.9641 + 36.3109i 0.781829 + 1.35417i 0.930875 + 0.365337i \(0.119046\pi\)
−0.149046 + 0.988830i \(0.547620\pi\)
\(720\) 0 0
\(721\) 10.0981 37.6865i 0.376072 1.40352i
\(722\) 0 0
\(723\) 6.07180i 0.225813i
\(724\) 0 0
\(725\) 0 0
\(726\) 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
\(733\) −26.7846 −0.989312 −0.494656 0.869089i \(-0.664706\pi\)
−0.494656 + 0.869089i \(0.664706\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −13.9115 + 51.9186i −0.512438 + 1.91245i
\(738\) 0 0
\(739\) 37.9186 10.1603i 1.39486 0.373751i 0.518362 0.855161i \(-0.326542\pi\)
0.876495 + 0.481410i \(0.159875\pi\)
\(740\) 0 0
\(741\) −3.07180 + 4.60770i −0.112845 + 0.169268i
\(742\) 0 0
\(743\) 11.1603 19.3301i 0.409430 0.709154i −0.585396 0.810748i \(-0.699061\pi\)
0.994826 + 0.101594i \(0.0323943\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −6.92820 + 4.00000i −0.253490 + 0.146352i
\(748\) 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
\(757\) −18.0622 + 4.83975i −0.656481 + 0.175904i −0.571657 0.820492i \(-0.693699\pi\)
−0.0848236 + 0.996396i \(0.527033\pi\)
\(758\) 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
\(763\) 11.9019 + 3.18911i 0.430879 + 0.115454i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 24.3827 21.4282i 0.880408 0.773728i
\(768\) 0 0
\(769\) −5.47372 20.4282i −0.197387 0.736660i −0.991636 0.129067i \(-0.958802\pi\)
0.794248 0.607593i \(-0.207865\pi\)
\(770\) 0 0
\(771\) −10.0359 + 5.79423i −0.361434 + 0.208674i
\(772\) 0 0
\(773\) 9.83975 + 17.0429i 0.353911 + 0.612992i 0.986931 0.161144i \(-0.0515182\pi\)
−0.633020 + 0.774136i \(0.718185\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −0.507042 1.89230i −0.0181900 0.0678861i
\(778\) 0 0
\(779\) 28.6603 1.02686
\(780\) 0 0
\(781\) −10.1244 −0.362278
\(782\) 0 0
\(783\) −1.33013 4.96410i −0.0475349 0.177403i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 21.6244 + 37.4545i 0.770825 + 1.33511i 0.937111 + 0.349031i \(0.113489\pi\)
−0.166286 + 0.986078i \(0.553178\pi\)
\(788\) 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
\(793\) 2.08846 32.3827i 0.0741633 1.14994i
\(794\) 0 0
\(795\) 0 0