Properties

Label 260.2.bf.b.93.1
Level $260$
Weight $2$
Character 260.93
Analytic conductor $2.076$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 93.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.93
Dual form 260.2.bf.b.137.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-1.23205 + 2.13397i) q^{7} +(2.36603 + 1.36603i) q^{9} +O(q^{10})\) \(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-1.23205 + 2.13397i) q^{7} +(2.36603 + 1.36603i) q^{9} +(-1.13397 + 4.23205i) q^{11} +(3.00000 - 2.00000i) q^{13} +(0.866025 + 0.767949i) q^{15} +(-0.866025 + 0.232051i) q^{17} +(2.86603 - 0.767949i) q^{19} +(0.901924 + 0.901924i) q^{21} +(-0.133975 - 0.0358984i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(2.09808 - 2.09808i) q^{27} +(1.50000 - 0.866025i) q^{29} +(-5.19615 + 5.19615i) q^{31} +(1.96410 + 1.13397i) q^{33} +(-3.03590 - 4.59808i) q^{35} +(-0.767949 - 1.33013i) q^{37} +(-0.598076 - 1.76795i) q^{39} +(9.33013 + 2.50000i) q^{41} +(-1.59808 - 5.96410i) q^{43} +(-5.09808 + 3.36603i) q^{45} -10.9282 q^{47} +(0.464102 + 0.803848i) q^{49} +0.464102i q^{51} +(2.46410 + 2.46410i) q^{53} +(-7.33013 - 6.50000i) q^{55} -1.53590i q^{57} +(-2.33013 - 8.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(-5.83013 + 3.36603i) q^{63} +(1.00000 + 8.00000i) q^{65} +(10.6244 - 6.13397i) q^{67} +(-0.0358984 + 0.0621778i) q^{69} +(0.598076 + 2.23205i) q^{71} -14.9282i q^{73} +(-2.40192 + 0.964102i) q^{75} +(-7.63397 - 7.63397i) q^{77} -0.535898i q^{79} +(3.33013 + 5.76795i) q^{81} +2.92820 q^{83} +(0.401924 - 1.96410i) q^{85} +(-0.232051 - 0.866025i) q^{87} +(14.7942 + 3.96410i) q^{89} +(0.571797 + 8.86603i) q^{91} +(1.90192 + 3.29423i) q^{93} +(-1.33013 + 6.50000i) q^{95} +(-6.69615 - 3.86603i) q^{97} +(-8.46410 + 8.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9} - 8 q^{11} + 12 q^{13} + 8 q^{19} + 14 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} + 6 q^{29} - 6 q^{33} - 26 q^{35} - 10 q^{37} + 8 q^{39} + 20 q^{41} + 4 q^{43} - 10 q^{45} - 16 q^{47} - 12 q^{49} - 4 q^{53} - 12 q^{55} + 8 q^{59} + 18 q^{61} - 6 q^{63} + 4 q^{65} - 6 q^{67} - 14 q^{69} - 8 q^{71} - 20 q^{75} - 34 q^{77} - 4 q^{81} - 16 q^{83} + 12 q^{85} + 6 q^{87} + 28 q^{89} + 30 q^{91} + 18 q^{93} + 12 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 0.133975 0.500000i 0.0773503 0.288675i −0.916406 0.400251i \(-0.868923\pi\)
0.993756 + 0.111576i \(0.0355897\pi\)
\(4\) 0 0
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) −1.23205 + 2.13397i −0.465671 + 0.806567i −0.999232 0.0391956i \(-0.987520\pi\)
0.533560 + 0.845762i \(0.320854\pi\)
\(8\) 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
\(13\) 3.00000 2.00000i 0.832050 0.554700i
\(14\) 0 0
\(15\) 0.866025 + 0.767949i 0.223607 + 0.198284i
\(16\) 0 0
\(17\) −0.866025 + 0.232051i −0.210042 + 0.0562806i −0.362306 0.932059i \(-0.618010\pi\)
0.152264 + 0.988340i \(0.451344\pi\)
\(18\) 0 0
\(19\) 2.86603 0.767949i 0.657511 0.176180i 0.0853887 0.996348i \(-0.472787\pi\)
0.572123 + 0.820168i \(0.306120\pi\)
\(20\) 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 \(-0.421270\pi\)
−0.272760 + 0.962082i \(0.587936\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) 2.09808 2.09808i 0.403775 0.403775i
\(28\) 0 0
\(29\) 1.50000 0.866025i 0.278543 0.160817i −0.354221 0.935162i \(-0.615254\pi\)
0.632764 + 0.774345i \(0.281920\pi\)
\(30\) 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
\(33\) 1.96410 + 1.13397i 0.341906 + 0.197400i
\(34\) 0 0
\(35\) −3.03590 4.59808i −0.513160 0.777217i
\(36\) 0 0
\(37\) −0.767949 1.33013i −0.126250 0.218672i 0.795971 0.605335i \(-0.206961\pi\)
−0.922221 + 0.386663i \(0.873628\pi\)
\(38\) 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
\(43\) −1.59808 5.96410i −0.243704 0.909517i −0.974030 0.226418i \(-0.927298\pi\)
0.730326 0.683099i \(-0.239368\pi\)
\(44\) 0 0
\(45\) −5.09808 + 3.36603i −0.759976 + 0.501777i
\(46\) 0 0
\(47\) −10.9282 −1.59404 −0.797021 0.603951i \(-0.793592\pi\)
−0.797021 + 0.603951i \(0.793592\pi\)
\(48\) 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 \(-0.173071\pi\)
−0.517321 + 0.855791i \(0.673071\pi\)
\(54\) 0 0
\(55\) −7.33013 6.50000i −0.988394 0.876460i
\(56\) 0 0
\(57\) 1.53590i 0.203435i
\(58\) 0 0
\(59\) −2.33013 8.69615i −0.303357 1.13214i −0.934351 0.356355i \(-0.884019\pi\)
0.630994 0.775788i \(-0.282647\pi\)
\(60\) 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
\(63\) −5.83013 + 3.36603i −0.734527 + 0.424079i
\(64\) 0 0
\(65\) 1.00000 + 8.00000i 0.124035 + 0.992278i
\(66\) 0 0
\(67\) 10.6244 6.13397i 1.29797 0.749384i 0.317918 0.948118i \(-0.397016\pi\)
0.980053 + 0.198734i \(0.0636829\pi\)
\(68\) 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
\(73\) 14.9282i 1.74721i −0.486632 0.873607i \(-0.661775\pi\)
0.486632 0.873607i \(-0.338225\pi\)
\(74\) 0 0
\(75\) −2.40192 + 0.964102i −0.277350 + 0.111325i
\(76\) 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
\(83\) 2.92820 0.321412 0.160706 0.987002i \(-0.448623\pi\)
0.160706 + 0.987002i \(0.448623\pi\)
\(84\) 0 0
\(85\) 0.401924 1.96410i 0.0435948 0.213037i
\(86\) 0 0
\(87\) −0.232051 0.866025i −0.0248785 0.0928477i
\(88\) 0 0
\(89\) 14.7942 + 3.96410i 1.56819 + 0.420194i 0.935243 0.354005i \(-0.115181\pi\)
0.632942 + 0.774199i \(0.281847\pi\)
\(90\) 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
\(95\) −1.33013 + 6.50000i −0.136468 + 0.666886i
\(96\) 0 0
\(97\) −6.69615 3.86603i −0.679891 0.392535i 0.119923 0.992783i \(-0.461735\pi\)
−0.799814 + 0.600248i \(0.795069\pi\)
\(98\) 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 0.109166 0.994024i \(-0.465182\pi\)
0.994024 0.109166i \(-0.0348181\pi\)
\(104\) 0 0
\(105\) −2.70577 + 0.901924i −0.264056 + 0.0880187i
\(106\) 0 0
\(107\) 7.33013 + 1.96410i 0.708630 + 0.189877i 0.595093 0.803657i \(-0.297115\pi\)
0.113537 + 0.993534i \(0.463782\pi\)
\(108\) 0 0
\(109\) 3.53590 + 3.53590i 0.338678 + 0.338678i 0.855869 0.517192i \(-0.173023\pi\)
−0.517192 + 0.855869i \(0.673023\pi\)
\(110\) 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 \(-0.627903\pi\)
0.121480 + 0.992594i \(0.461236\pi\)
\(114\) 0 0
\(115\) 0.205771 0.232051i 0.0191883 0.0216388i
\(116\) 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
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) −5.33013 + 19.8923i −0.472972 + 1.76516i 0.156029 + 0.987752i \(0.450131\pi\)
−0.629001 + 0.777404i \(0.716536\pi\)
\(128\) 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
\(135\) 2.09808 + 6.29423i 0.180574 + 0.541721i
\(136\) 0 0
\(137\) −7.16025 + 12.4019i −0.611742 + 1.05957i 0.379205 + 0.925313i \(0.376198\pi\)
−0.990947 + 0.134255i \(0.957136\pi\)
\(138\) 0 0
\(139\) 4.50000 + 2.59808i 0.381685 + 0.220366i 0.678551 0.734553i \(-0.262608\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 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
\(145\) 0.232051 + 3.86603i 0.0192708 + 0.321056i
\(146\) 0 0
\(147\) 0.464102 0.124356i 0.0382785 0.0102567i
\(148\) 0 0
\(149\) 3.33013 0.892305i 0.272815 0.0731005i −0.119818 0.992796i \(-0.538231\pi\)
0.392633 + 0.919695i \(0.371564\pi\)
\(150\) 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
\(153\) −2.36603 0.633975i −0.191282 0.0512538i
\(154\) 0 0
\(155\) −5.19615 15.5885i −0.417365 1.25210i
\(156\) 0 0
\(157\) 6.46410 6.46410i 0.515891 0.515891i −0.400434 0.916326i \(-0.631141\pi\)
0.916326 + 0.400434i \(0.131141\pi\)
\(158\) 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 \(-0.373281\pi\)
−0.604469 + 0.796629i \(0.706615\pi\)
\(164\) 0 0
\(165\) −4.23205 + 2.79423i −0.329465 + 0.217530i
\(166\) 0 0
\(167\) 9.23205 + 15.9904i 0.714398 + 1.23737i 0.963191 + 0.268816i \(0.0866325\pi\)
−0.248794 + 0.968556i \(0.580034\pi\)
\(168\) 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 \(-0.118077\pi\)
−0.988372 + 0.152057i \(0.951410\pi\)
\(174\) 0 0
\(175\) 12.2321 1.47372i 0.924656 0.111403i
\(176\) 0 0
\(177\) −4.66025 −0.350286
\(178\) 0 0
\(179\) −6.96410 12.0622i −0.520521 0.901570i −0.999715 0.0238604i \(-0.992404\pi\)
0.479194 0.877709i \(-0.340929\pi\)
\(180\) 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
\(185\) 3.42820 0.205771i 0.252047 0.0151286i
\(186\) 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 −0.456068 0.889945i \(-0.650743\pi\)
0.998749 0.0500060i \(-0.0159241\pi\)
\(192\) 0 0
\(193\) −22.1603 + 12.7942i −1.59513 + 0.920949i −0.602723 + 0.797950i \(0.705918\pi\)
−0.992407 + 0.122998i \(0.960749\pi\)
\(194\) 0 0
\(195\) 4.13397 + 0.571797i 0.296040 + 0.0409472i
\(196\) 0 0
\(197\) 3.69615 2.13397i 0.263340 0.152039i −0.362517 0.931977i \(-0.618083\pi\)
0.625857 + 0.779938i \(0.284749\pi\)
\(198\) 0 0
\(199\) −9.42820 + 16.3301i −0.668348 + 1.15761i 0.310018 + 0.950731i \(0.399665\pi\)
−0.978366 + 0.206881i \(0.933669\pi\)
\(200\) 0 0
\(201\) −1.64359 6.13397i −0.115930 0.432657i
\(202\) 0 0
\(203\) 4.26795i 0.299551i
\(204\) 0 0
\(205\) −14.3301 + 16.1603i −1.00086 + 1.12868i
\(206\) 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
\(213\) 1.19615 0.0819590
\(214\) 0 0
\(215\) 13.5263 + 2.76795i 0.922485 + 0.188773i
\(216\) 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 \(-0.183043\pi\)
−0.890592 + 0.454802i \(0.849710\pi\)
\(224\) 0 0
\(225\) −1.63397 13.5622i −0.108932 0.904145i
\(226\) 0 0
\(227\) −2.76795 1.59808i −0.183715 0.106068i 0.405322 0.914174i \(-0.367159\pi\)
−0.589037 + 0.808106i \(0.700493\pi\)
\(228\) 0 0
\(229\) −0.0717968 + 0.0717968i −0.00474446 + 0.00474446i −0.709475 0.704731i \(-0.751068\pi\)
0.704731 + 0.709475i \(0.251068\pi\)
\(230\) 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
\(235\) 10.9282 21.8564i 0.712877 1.42575i
\(236\) 0 0
\(237\) −0.267949 0.0717968i −0.0174052 0.00466370i
\(238\) 0 0
\(239\) −16.6603 16.6603i −1.07766 1.07766i −0.996719 0.0809436i \(-0.974207\pi\)
−0.0809436 0.996719i \(-0.525793\pi\)
\(240\) 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
\(243\) 11.9282 3.19615i 0.765195 0.205033i
\(244\) 0 0
\(245\) −2.07180 + 0.124356i −0.132362 + 0.00794479i
\(246\) 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 −0.0702687 0.997528i \(-0.522386\pi\)
−0.899019 + 0.437910i \(0.855719\pi\)
\(252\) 0 0
\(253\) 0.303848 0.526279i 0.0191027 0.0330869i
\(254\) 0 0
\(255\) −0.928203 0.464102i −0.0581263 0.0290632i
\(256\) 0 0
\(257\) 5.79423 21.6244i 0.361434 1.34889i −0.510757 0.859725i \(-0.670635\pi\)
0.872191 0.489165i \(-0.162698\pi\)
\(258\) 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 0.751002 + 0.660300i \(0.229571\pi\)
−0.980537 + 0.196336i \(0.937096\pi\)
\(264\) 0 0
\(265\) −7.39230 + 2.46410i −0.454106 + 0.151369i
\(266\) 0 0
\(267\) 3.96410 6.86603i 0.242599 0.420194i
\(268\) 0 0
\(269\) −15.8205 9.13397i −0.964593 0.556908i −0.0670097 0.997752i \(-0.521346\pi\)
−0.897584 + 0.440844i \(0.854679\pi\)
\(270\) 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
\(273\) 4.50962 + 0.901924i 0.272935 + 0.0545869i
\(274\) 0 0
\(275\) 20.3301 8.16025i 1.22595 0.492082i
\(276\) 0 0
\(277\) −10.3301 + 2.76795i −0.620677 + 0.166310i −0.555436 0.831560i \(-0.687448\pi\)
−0.0652416 + 0.997869i \(0.520782\pi\)
\(278\) 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
\(283\) 29.7224 + 7.96410i 1.76682 + 0.473417i 0.988081 0.153937i \(-0.0491953\pi\)
0.778735 + 0.627354i \(0.215862\pi\)
\(284\) 0 0
\(285\) 3.07180 + 1.53590i 0.181958 + 0.0909788i
\(286\) 0 0
\(287\) −16.8301 + 16.8301i −0.993451 + 0.993451i
\(288\) 0 0
\(289\) −14.0263 + 8.09808i −0.825075 + 0.476357i
\(290\) 0 0
\(291\) −2.83013 + 2.83013i −0.165905 + 0.165905i
\(292\) 0 0
\(293\) −17.7679 10.2583i −1.03801 0.599298i −0.118744 0.992925i \(-0.537887\pi\)
−0.919270 + 0.393627i \(0.871220\pi\)
\(294\) 0 0
\(295\) 19.7224 + 4.03590i 1.14828 + 0.234979i
\(296\) 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
\(305\) 11.0885 + 16.7942i 0.634923 + 0.961635i
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 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 \(-0.321017\pi\)
−0.846035 + 0.533127i \(0.821017\pi\)
\(314\) 0 0
\(315\) −0.901924 15.0263i −0.0508176 0.846635i
\(316\) 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
\(325\) −17.0000 6.00000i −0.942990 0.332820i
\(326\) 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 0.973464 + 0.228842i \(0.0734940\pi\)
−0.728623 + 0.684915i \(0.759839\pi\)
\(332\) 0 0
\(333\) 4.19615i 0.229948i
\(334\) 0 0
\(335\) 1.64359 + 27.3827i 0.0897991 + 1.49608i
\(336\) 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
\(343\) −19.5359 −1.05484
\(344\) 0 0
\(345\) −0.0884573 0.133975i −0.00476238 0.00721295i
\(346\) 0 0
\(347\) 2.79423 + 10.4282i 0.150002 + 0.559815i 0.999482 + 0.0321938i \(0.0102494\pi\)
−0.849480 + 0.527621i \(0.823084\pi\)
\(348\) 0 0
\(349\) 7.86603 + 2.10770i 0.421059 + 0.112822i 0.463126 0.886292i \(-0.346728\pi\)
−0.0420673 + 0.999115i \(0.513394\pi\)
\(350\) 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 \(-0.0768381\pi\)
−0.692532 + 0.721387i \(0.743505\pi\)
\(354\) 0 0
\(355\) −5.06218 1.03590i −0.268673 0.0549798i
\(356\) 0 0
\(357\) −0.990381 0.571797i −0.0524165 0.0302627i
\(358\) 0 0
\(359\) −13.1962 + 13.1962i −0.696466 + 0.696466i −0.963647 0.267180i \(-0.913908\pi\)
0.267180 + 0.963647i \(0.413908\pi\)
\(360\) 0 0
\(361\) −8.83013 + 5.09808i −0.464744 + 0.268320i
\(362\) 0 0
\(363\) −3.00000 + 3.00000i −0.157459 + 0.157459i
\(364\) 0 0
\(365\) 29.8564 + 14.9282i 1.56276 + 0.781378i
\(366\) 0 0
\(367\) 14.7942 + 3.96410i 0.772252 + 0.206924i 0.623366 0.781930i \(-0.285765\pi\)
0.148886 + 0.988854i \(0.452431\pi\)
\(368\) 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 \(-0.761341\pi\)
−0.293061 + 0.956094i \(0.594674\pi\)
\(374\) 0 0
\(375\) 0.473721 5.76795i 0.0244628 0.297856i
\(376\) 0 0
\(377\) 2.76795 5.59808i 0.142557 0.288316i
\(378\) 0 0
\(379\) −2.59808 + 9.69615i −0.133454 + 0.498058i −0.999999 0.00104063i \(-0.999669\pi\)
0.866545 + 0.499099i \(0.166335\pi\)
\(380\) 0 0
\(381\) 9.23205 + 5.33013i 0.472972 + 0.273071i
\(382\) 0 0
\(383\) 12.7679 22.1147i 0.652412 1.13001i −0.330124 0.943937i \(-0.607091\pi\)
0.982536 0.186073i \(-0.0595760\pi\)
\(384\) 0 0
\(385\) 22.9019 7.63397i 1.16719 0.389063i
\(386\) 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
\(395\) 1.07180 + 0.535898i 0.0539279 + 0.0269640i
\(396\) 0 0
\(397\) −5.69615 + 9.86603i −0.285882 + 0.495162i −0.972823 0.231552i \(-0.925620\pi\)
0.686941 + 0.726713i \(0.258953\pi\)
\(398\) 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
\(403\) −5.19615 + 25.9808i −0.258839 + 1.29419i
\(404\) 0 0
\(405\) −14.8660 + 0.892305i −0.738699 + 0.0443390i
\(406\) 0 0
\(407\) 6.50000 1.74167i 0.322193 0.0863314i
\(408\) 0 0
\(409\) −18.5263 + 4.96410i −0.916066 + 0.245459i −0.685903 0.727693i \(-0.740593\pi\)
−0.230163 + 0.973152i \(0.573926\pi\)
\(410\) 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
\(415\) −2.92820 + 5.85641i −0.143740 + 0.287480i
\(416\) 0 0
\(417\) 1.90192 1.90192i 0.0931376 0.0931376i
\(418\) 0 0
\(419\) 31.5000 18.1865i 1.53888 0.888470i 0.539971 0.841684i \(-0.318435\pi\)
0.998905 0.0467865i \(-0.0148981\pi\)
\(420\) 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
\(423\) −25.8564 14.9282i −1.25718 0.725834i
\(424\) 0 0
\(425\) 3.52628 + 2.76795i 0.171050 + 0.134265i
\(426\) 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 −0.349304 0.937010i \(-0.613582\pi\)
−0.771011 + 0.636822i \(0.780249\pi\)
\(432\) 0 0
\(433\) 8.72243 + 32.5526i 0.419173 + 1.56438i 0.776327 + 0.630330i \(0.217081\pi\)
−0.357154 + 0.934046i \(0.616253\pi\)
\(434\) 0 0
\(435\) 1.96410 + 0.401924i 0.0941715 + 0.0192708i
\(436\) 0 0
\(437\) −0.411543 −0.0196868
\(438\) 0 0
\(439\) −0.0358984 0.0621778i −0.00171334 0.00296759i 0.865167 0.501483i \(-0.167212\pi\)
−0.866881 + 0.498515i \(0.833879\pi\)
\(440\) 0 0
\(441\) 2.53590i 0.120757i
\(442\) 0 0
\(443\) −15.5885 15.5885i −0.740630 0.740630i 0.232069 0.972699i \(-0.425450\pi\)
−0.972699 + 0.232069i \(0.925450\pi\)
\(444\) 0 0
\(445\) −22.7224 + 25.6244i −1.07715 + 1.21471i
\(446\) 0 0
\(447\) 1.78461i 0.0844091i
\(448\) 0 0
\(449\) 5.20577 + 19.4282i 0.245676 + 0.916874i 0.973043 + 0.230625i \(0.0740771\pi\)
−0.727367 + 0.686249i \(0.759256\pi\)
\(450\) 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
\(455\) −18.3038 7.72243i −0.858098 0.362033i
\(456\) 0 0
\(457\) −11.7679 + 6.79423i −0.550481 + 0.317821i −0.749316 0.662212i \(-0.769618\pi\)
0.198835 + 0.980033i \(0.436284\pi\)
\(458\) 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
\(463\) 21.6077i 1.00419i −0.864811 0.502097i \(-0.832562\pi\)
0.864811 0.502097i \(-0.167438\pi\)
\(464\) 0 0
\(465\) −8.49038 + 0.509619i −0.393732 + 0.0236330i
\(466\) 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
\(473\) 27.0526 1.24388
\(474\) 0 0
\(475\) −11.6699 9.16025i −0.535450 0.420301i
\(476\) 0 0
\(477\) 2.46410 + 9.19615i 0.112823 + 0.421063i
\(478\) 0 0
\(479\) 3.13397 + 0.839746i 0.143195 + 0.0383690i 0.329705 0.944084i \(-0.393051\pi\)
−0.186510 + 0.982453i \(0.559718\pi\)
\(480\) 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
\(485\) 14.4282 9.52628i 0.655151 0.432566i
\(486\) 0 0
\(487\) 1.37564 + 0.794229i 0.0623364 + 0.0359899i 0.530844 0.847469i \(-0.321875\pi\)
−0.468508 + 0.883459i \(0.655208\pi\)
\(488\) 0 0
\(489\) −1.16987 + 1.16987i −0.0529035 + 0.0529035i
\(490\) 0 0
\(491\) 5.89230 3.40192i 0.265916 0.153527i −0.361114 0.932522i \(-0.617604\pi\)
0.627030 + 0.778995i \(0.284270\pi\)
\(492\) 0 0
\(493\) −1.09808 + 1.09808i −0.0494549 + 0.0494549i
\(494\) 0 0
\(495\) −8.46410 25.3923i −0.380433 1.14130i
\(496\) 0 0
\(497\) −5.50000 1.47372i −0.246709 0.0661054i
\(498\) 0 0
\(499\) −20.2679 20.2679i −0.907318 0.907318i 0.0887371 0.996055i \(-0.471717\pi\)
−0.996055 + 0.0887371i \(0.971717\pi\)
\(500\) 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 \(-0.489974\pi\)
0.527026 + 0.849849i \(0.323307\pi\)
\(504\) 0 0
\(505\) −2.30385 38.3827i −0.102520 1.70801i
\(506\) 0 0
\(507\) −5.33013 4.10770i −0.236719 0.182429i
\(508\) 0 0
\(509\) 7.45448 27.8205i 0.330414 1.23312i −0.578342 0.815795i \(-0.696300\pi\)
0.908756 0.417328i \(-0.137033\pi\)
\(510\) 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
\(515\) 11.1962 + 33.5885i 0.493361 + 1.48008i
\(516\) 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 \(-0.996496\pi\)
0.871477 + 0.490436i \(0.163162\pi\)
\(524\) 0 0
\(525\) 0.901924 6.31347i 0.0393632 0.275542i
\(526\) 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
\(535\) −11.2583 + 12.6962i −0.486740 + 0.548903i
\(536\) 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 0.998106 0.0615128i \(-0.0195925\pi\)
−0.0615128 + 0.998106i \(0.519592\pi\)
\(542\) 0 0
\(543\) −11.4641 3.07180i −0.491972 0.131823i
\(544\) 0 0
\(545\) −10.6077 + 3.53590i −0.454384 + 0.151461i
\(546\) 0 0
\(547\) −0.124356 + 0.124356i −0.00531706 + 0.00531706i −0.709760 0.704443i \(-0.751197\pi\)
0.704443 + 0.709760i \(0.251197\pi\)
\(548\) 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
\(555\) 0.356406 1.74167i 0.0151286 0.0739298i
\(556\) 0 0
\(557\) −7.69615 13.3301i −0.326096 0.564816i 0.655637 0.755076i \(-0.272400\pi\)
−0.981734 + 0.190260i \(0.939067\pi\)
\(558\) 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 −0.951641 0.307212i \(-0.900604\pi\)
0.670540 0.741874i \(-0.266063\pi\)
\(564\) 0 0
\(565\) 1.33013 6.50000i 0.0559589 0.273457i
\(566\) 0 0
\(567\) −16.4115 −0.689220
\(568\) 0 0
\(569\) −18.8205 32.5981i −0.788997 1.36658i −0.926582 0.376093i \(-0.877267\pi\)
0.137585 0.990490i \(-0.456066\pi\)
\(570\) 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
\(575\) 0.258330 + 0.643594i 0.0107731 + 0.0268397i
\(576\) 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
\(585\) −8.56218 + 20.2942i −0.354002 + 0.839063i
\(586\) 0 0
\(587\) −41.0885 + 23.7224i −1.69590 + 0.979130i −0.746333 + 0.665573i \(0.768187\pi\)
−0.949570 + 0.313556i \(0.898480\pi\)
\(588\) 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
\(595\) 3.69615 + 3.27757i 0.151527 + 0.134367i
\(596\) 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 0.976815 0.214087i \(-0.0686775\pi\)
−0.673812 + 0.738903i \(0.735344\pi\)
\(602\) 0 0
\(603\) 33.5167 1.36490
\(604\) 0 0
\(605\) 15.2942 10.0981i 0.621799 0.410545i
\(606\) 0 0
\(607\) −0.813467 3.03590i −0.0330176 0.123223i 0.947450 0.319904i \(-0.103651\pi\)
−0.980468 + 0.196680i \(0.936984\pi\)
\(608\) 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 \(-0.331150\pi\)
−0.999976 + 0.00685934i \(0.997817\pi\)
\(614\) 0 0
\(615\) 6.16025 + 9.33013i 0.248405 + 0.376227i
\(616\) 0 0
\(617\) −15.2321 8.79423i −0.613219 0.354042i 0.161005 0.986954i \(-0.448526\pi\)
−0.774224 + 0.632911i \(0.781860\pi\)
\(618\) 0 0
\(619\) −14.6603 + 14.6603i −0.589245 + 0.589245i −0.937427 0.348182i \(-0.886799\pi\)
0.348182 + 0.937427i \(0.386799\pi\)
\(620\) 0 0
\(621\) −0.356406 + 0.205771i −0.0143021 + 0.00825732i
\(622\) 0 0
\(623\) −26.6865 + 26.6865i −1.06917 + 1.06917i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) 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 0.696225 0.717823i \(-0.254862\pi\)
0.961860 + 0.273541i \(0.0881948\pi\)
\(632\) 0 0
\(633\) −2.96410 + 0.794229i −0.117812 + 0.0315678i
\(634\) 0 0
\(635\) −34.4545 30.5526i −1.36728 1.21244i
\(636\) 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 0.607296 0.794475i \(-0.292254\pi\)
−0.384388 + 0.923172i \(0.625587\pi\)
\(642\) 0 0
\(643\) 18.0885 31.3301i 0.713339 1.23554i −0.250258 0.968179i \(-0.580515\pi\)
0.963597 0.267360i \(-0.0861514\pi\)
\(644\) 0 0
\(645\) 3.19615 6.39230i 0.125848 0.251697i
\(646\) 0 0
\(647\) 0.669873 2.50000i 0.0263354 0.0982851i −0.951507 0.307626i \(-0.900465\pi\)
0.977843 + 0.209341i \(0.0671320\pi\)
\(648\) 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 −0.0212467 + 0.999774i \(0.506764\pi\)
−0.481487 + 0.876453i \(0.659903\pi\)
\(654\) 0 0
\(655\) −5.85641 + 11.7128i −0.228829 + 0.457657i
\(656\) 0 0
\(657\) 20.3923 35.3205i 0.795580 1.37798i
\(658\) 0 0
\(659\) 35.4282 + 20.4545i 1.38009 + 0.796794i 0.992169 0.124901i \(-0.0398612\pi\)
0.387918 + 0.921694i \(0.373195\pi\)
\(660\) 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
\(663\) 0.928203 + 1.39230i 0.0360484 + 0.0540726i
\(664\) 0 0
\(665\) −12.2321 10.8468i −0.474339 0.420620i
\(666\) 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 \(-0.162318\pi\)
0.511784 + 0.859114i \(0.328985\pi\)
\(674\) 0 0
\(675\) −14.6865 2.09808i −0.565285 0.0807550i
\(676\) 0 0
\(677\) −28.1769 + 28.1769i −1.08293 + 1.08293i −0.0866916 + 0.996235i \(0.527629\pi\)
−0.996235 + 0.0866916i \(0.972371\pi\)
\(678\) 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 \(-0.242840\pi\)
−0.237028 + 0.971503i \(0.576173\pi\)
\(684\) 0 0
\(685\) −17.6436 26.7224i −0.674127 1.02101i
\(686\) 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 −0.542468 0.840076i \(-0.682510\pi\)
−0.889829 + 0.456293i \(0.849177\pi\)
\(692\) 0 0
\(693\) −7.63397 28.4904i −0.289991 1.08226i
\(694\) 0 0
\(695\) −9.69615 + 6.40192i −0.367796 + 0.242839i
\(696\) 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 \(0.130273\pi\)
−0.917413 + 0.397935i \(0.869727\pi\)
\(702\) 0 0
\(703\) −3.22243 3.22243i −0.121536 0.121536i
\(704\) 0 0
\(705\) −9.46410 8.39230i −0.356439 0.316072i
\(706\) 0 0
\(707\) 42.3731i 1.59360i
\(708\) 0 0
\(709\) 4.27757 + 15.9641i 0.160647 + 0.599544i 0.998555 + 0.0537328i \(0.0171119\pi\)
−0.837908 + 0.545812i \(0.816221\pi\)
\(710\) 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
\(715\) −34.9904 4.83975i −1.30857 0.180996i
\(716\) 0 0
\(717\) −10.5622 + 6.09808i −0.394452 + 0.227737i
\(718\) 0 0
\(719\) 20.9641 36.3109i 0.781829 1.35417i −0.149046 0.988830i \(-0.547620\pi\)
0.930875 0.365337i \(-0.119046\pi\)
\(720\) 0 0
\(721\) 10.0981 + 37.6865i 0.376072 + 1.40352i
\(722\) 0 0
\(723\) 6.07180i 0.225813i
\(724\) 0 0
\(725\) −7.96410 3.40192i −0.295779 0.126344i
\(726\) 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
\(733\) 26.7846 0.989312 0.494656 0.869089i \(-0.335294\pi\)
0.494656 + 0.869089i \(0.335294\pi\)
\(734\) 0 0
\(735\) −0.215390 + 1.05256i −0.00794479 + 0.0388242i
\(736\) 0 0
\(737\) 13.9115 + 51.9186i 0.512438 + 1.91245i
\(738\) 0 0
\(739\) 37.9186 + 10.1603i 1.39486 + 0.373751i 0.876495 0.481410i \(-0.159875\pi\)
0.518362 + 0.855161i \(0.326542\pi\)
\(740\) 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 \(-0.300939\pi\)
−0.994826 + 0.101594i \(0.967606\pi\)
\(744\) 0 0
\(745\) −1.54552 + 7.55256i −0.0566234 + 0.276704i
\(746\) 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 −0.142262 0.989829i \(-0.545438\pi\)
0.786086 + 0.618117i \(0.212104\pi\)
\(752\) 0 0
\(753\) −6.49038 + 6.49038i −0.236523 + 0.236523i
\(754\) 0 0
\(755\) 0.803848 0.267949i 0.0292550 0.00975167i
\(756\) 0 0
\(757\) 18.0622 + 4.83975i 0.656481 + 0.175904i 0.571657 0.820492i \(-0.306301\pi\)
0.0848236 + 0.996396i \(0.472967\pi\)
\(758\) 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
\(763\) −11.9019 + 3.18911i −0.430879 + 0.115454i
\(764\) 0 0
\(765\) 3.63397 4.09808i 0.131387 0.148166i
\(766\) 0 0
\(767\) −24.3827 21.4282i −0.880408 0.773728i
\(768\) 0 0
\(769\) −5.47372 + 20.4282i −0.197387 + 0.736660i 0.794248 + 0.607593i \(0.207865\pi\)
−0.991636 + 0.129067i \(0.958802\pi\)
\(770\) 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 \(-0.948482\pi\)
0.633020 + 0.774136i \(0.281815\pi\)
\(774\) 0 0
\(775\) 36.3731 + 5.19615i 1.30656 + 0.186651i
\(776\) 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
\(785\) 6.46410 + 19.3923i 0.230714 + 0.692141i
\(786\) 0 0
\(787\) −21.6244 + 37.4545i −0.770825 + 1.33511i 0.166286 + 0.986078i \(0.446822\pi\)
−0.937111 + 0.349031i \(0.886511\pi\)
\(788\) 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