Properties

Label 1148.2.ba.a.113.13
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.13
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.8

$q$-expansion

\(f(q)\) \(=\) \(q+1.06924i q^{3} +(0.727989 + 2.24052i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.85672 q^{9} +O(q^{10})\) \(q+1.06924i q^{3} +(0.727989 + 2.24052i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.85672 q^{9} +(-5.06104 - 1.64443i) q^{11} +(-3.77521 + 5.19613i) q^{13} +(-2.39565 + 0.778395i) q^{15} +(-6.88228 - 2.23619i) q^{17} +(-2.95505 - 4.06728i) q^{19} +(0.865034 - 0.628484i) q^{21} +(-0.323552 - 0.235074i) q^{23} +(-0.444870 + 0.323217i) q^{25} +5.19301i q^{27} +(1.59102 - 0.516955i) q^{29} +(0.969786 - 2.98469i) q^{31} +(1.75829 - 5.41147i) q^{33} +(1.38472 - 1.90590i) q^{35} +(1.22037 + 3.75592i) q^{37} +(-5.55591 - 4.03661i) q^{39} +(1.37748 + 6.25320i) q^{41} +(2.21734 + 1.61099i) q^{43} +(1.35167 + 4.16002i) q^{45} +(-4.48048 + 6.16686i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(2.39102 - 7.35882i) q^{51} +(7.71403 - 2.50644i) q^{53} -12.5365i q^{55} +(4.34890 - 3.15966i) q^{57} +(-8.99273 - 6.53360i) q^{59} +(-10.7395 + 7.80272i) q^{61} +(-1.09135 - 1.50212i) q^{63} +(-14.3903 - 4.67570i) q^{65} +(12.1237 - 3.93924i) q^{67} +(0.251351 - 0.345955i) q^{69} +(-10.8704 - 3.53199i) q^{71} -13.1398 q^{73} +(-0.345597 - 0.475674i) q^{75} +(1.64443 + 5.06104i) q^{77} +11.9532i q^{79} +0.0175922 q^{81} +14.5368 q^{83} -17.0478i q^{85} +(0.552750 + 1.70119i) q^{87} +(-8.48226 - 11.6748i) q^{89} +6.42276 q^{91} +(3.19136 + 1.03693i) q^{93} +(6.96156 - 9.58177i) q^{95} +(-5.79801 + 1.88389i) q^{97} +(-9.39695 - 3.05325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 1.06924i 0.617327i 0.951171 + 0.308663i \(0.0998816\pi\)
−0.951171 + 0.308663i \(0.900118\pi\)
\(4\) 0 0
\(5\) 0.727989 + 2.24052i 0.325566 + 1.00199i 0.971184 + 0.238330i \(0.0765999\pi\)
−0.645618 + 0.763661i \(0.723400\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) 1.85672 0.618908
\(10\) 0 0
\(11\) −5.06104 1.64443i −1.52596 0.495815i −0.578498 0.815684i \(-0.696361\pi\)
−0.947462 + 0.319869i \(0.896361\pi\)
\(12\) 0 0
\(13\) −3.77521 + 5.19613i −1.04705 + 1.44115i −0.155718 + 0.987802i \(0.549769\pi\)
−0.891336 + 0.453344i \(0.850231\pi\)
\(14\) 0 0
\(15\) −2.39565 + 0.778395i −0.618555 + 0.200981i
\(16\) 0 0
\(17\) −6.88228 2.23619i −1.66920 0.542355i −0.686430 0.727196i \(-0.740823\pi\)
−0.982768 + 0.184841i \(0.940823\pi\)
\(18\) 0 0
\(19\) −2.95505 4.06728i −0.677935 0.933097i 0.321972 0.946749i \(-0.395654\pi\)
−0.999907 + 0.0136521i \(0.995654\pi\)
\(20\) 0 0
\(21\) 0.865034 0.628484i 0.188766 0.137146i
\(22\) 0 0
\(23\) −0.323552 0.235074i −0.0674653 0.0490164i 0.553541 0.832822i \(-0.313276\pi\)
−0.621007 + 0.783805i \(0.713276\pi\)
\(24\) 0 0
\(25\) −0.444870 + 0.323217i −0.0889741 + 0.0646434i
\(26\) 0 0
\(27\) 5.19301i 0.999395i
\(28\) 0 0
\(29\) 1.59102 0.516955i 0.295446 0.0959962i −0.157544 0.987512i \(-0.550357\pi\)
0.452990 + 0.891516i \(0.350357\pi\)
\(30\) 0 0
\(31\) 0.969786 2.98469i 0.174179 0.536067i −0.825416 0.564524i \(-0.809060\pi\)
0.999595 + 0.0284577i \(0.00905958\pi\)
\(32\) 0 0
\(33\) 1.75829 5.41147i 0.306080 0.942016i
\(34\) 0 0
\(35\) 1.38472 1.90590i 0.234060 0.322156i
\(36\) 0 0
\(37\) 1.22037 + 3.75592i 0.200628 + 0.617470i 0.999865 + 0.0164533i \(0.00523748\pi\)
−0.799236 + 0.601017i \(0.794763\pi\)
\(38\) 0 0
\(39\) −5.55591 4.03661i −0.889658 0.646374i
\(40\) 0 0
\(41\) 1.37748 + 6.25320i 0.215126 + 0.976586i
\(42\) 0 0
\(43\) 2.21734 + 1.61099i 0.338141 + 0.245674i 0.743877 0.668316i \(-0.232985\pi\)
−0.405736 + 0.913990i \(0.632985\pi\)
\(44\) 0 0
\(45\) 1.35167 + 4.16002i 0.201496 + 0.620140i
\(46\) 0 0
\(47\) −4.48048 + 6.16686i −0.653546 + 0.899529i −0.999246 0.0388163i \(-0.987641\pi\)
0.345701 + 0.938345i \(0.387641\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 2.39102 7.35882i 0.334810 1.03044i
\(52\) 0 0
\(53\) 7.71403 2.50644i 1.05960 0.344286i 0.273173 0.961965i \(-0.411927\pi\)
0.786431 + 0.617679i \(0.211927\pi\)
\(54\) 0 0
\(55\) 12.5365i 1.69042i
\(56\) 0 0
\(57\) 4.34890 3.15966i 0.576026 0.418507i
\(58\) 0 0
\(59\) −8.99273 6.53360i −1.17075 0.850602i −0.179655 0.983730i \(-0.557498\pi\)
−0.991099 + 0.133127i \(0.957498\pi\)
\(60\) 0 0
\(61\) −10.7395 + 7.80272i −1.37505 + 0.999035i −0.377731 + 0.925915i \(0.623296\pi\)
−0.997323 + 0.0731200i \(0.976704\pi\)
\(62\) 0 0
\(63\) −1.09135 1.50212i −0.137498 0.189249i
\(64\) 0 0
\(65\) −14.3903 4.67570i −1.78490 0.579949i
\(66\) 0 0
\(67\) 12.1237 3.93924i 1.48115 0.481255i 0.546693 0.837333i \(-0.315886\pi\)
0.934456 + 0.356078i \(0.115886\pi\)
\(68\) 0 0
\(69\) 0.251351 0.345955i 0.0302591 0.0416481i
\(70\) 0 0
\(71\) −10.8704 3.53199i −1.29007 0.419170i −0.417956 0.908467i \(-0.637254\pi\)
−0.872117 + 0.489297i \(0.837254\pi\)
\(72\) 0 0
\(73\) −13.1398 −1.53790 −0.768949 0.639310i \(-0.779220\pi\)
−0.768949 + 0.639310i \(0.779220\pi\)
\(74\) 0 0
\(75\) −0.345597 0.475674i −0.0399061 0.0549261i
\(76\) 0 0
\(77\) 1.64443 + 5.06104i 0.187400 + 0.576759i
\(78\) 0 0
\(79\) 11.9532i 1.34484i 0.740168 + 0.672422i \(0.234746\pi\)
−0.740168 + 0.672422i \(0.765254\pi\)
\(80\) 0 0
\(81\) 0.0175922 0.00195469
\(82\) 0 0
\(83\) 14.5368 1.59562 0.797810 0.602909i \(-0.205992\pi\)
0.797810 + 0.602909i \(0.205992\pi\)
\(84\) 0 0
\(85\) 17.0478i 1.84909i
\(86\) 0 0
\(87\) 0.552750 + 1.70119i 0.0592610 + 0.182387i
\(88\) 0 0
\(89\) −8.48226 11.6748i −0.899118 1.23753i −0.970749 0.240099i \(-0.922820\pi\)
0.0716305 0.997431i \(-0.477180\pi\)
\(90\) 0 0
\(91\) 6.42276 0.673289
\(92\) 0 0
\(93\) 3.19136 + 1.03693i 0.330928 + 0.107525i
\(94\) 0 0
\(95\) 6.96156 9.58177i 0.714241 0.983069i
\(96\) 0 0
\(97\) −5.79801 + 1.88389i −0.588698 + 0.191280i −0.588194 0.808720i \(-0.700161\pi\)
−0.000504716 1.00000i \(0.500161\pi\)
\(98\) 0 0
\(99\) −9.39695 3.05325i −0.944429 0.306863i
\(100\) 0 0
\(101\) −3.71789 5.11724i −0.369944 0.509184i 0.582942 0.812514i \(-0.301902\pi\)
−0.952886 + 0.303330i \(0.901902\pi\)
\(102\) 0 0
\(103\) 1.34492 0.977139i 0.132519 0.0962803i −0.519551 0.854439i \(-0.673901\pi\)
0.652070 + 0.758159i \(0.273901\pi\)
\(104\) 0 0
\(105\) 2.03787 + 1.48060i 0.198875 + 0.144491i
\(106\) 0 0
\(107\) 0.620276 0.450657i 0.0599643 0.0435666i −0.557399 0.830245i \(-0.688201\pi\)
0.617364 + 0.786678i \(0.288201\pi\)
\(108\) 0 0
\(109\) 6.85277i 0.656376i 0.944612 + 0.328188i \(0.106438\pi\)
−0.944612 + 0.328188i \(0.893562\pi\)
\(110\) 0 0
\(111\) −4.01599 + 1.30487i −0.381181 + 0.123853i
\(112\) 0 0
\(113\) 0.983477 3.02683i 0.0925178 0.284740i −0.894081 0.447905i \(-0.852170\pi\)
0.986599 + 0.163165i \(0.0521702\pi\)
\(114\) 0 0
\(115\) 0.291146 0.896056i 0.0271495 0.0835576i
\(116\) 0 0
\(117\) −7.00951 + 9.64777i −0.648030 + 0.891936i
\(118\) 0 0
\(119\) 2.23619 + 6.88228i 0.204991 + 0.630898i
\(120\) 0 0
\(121\) 14.0108 + 10.1794i 1.27371 + 0.925401i
\(122\) 0 0
\(123\) −6.68618 + 1.47285i −0.602873 + 0.132803i
\(124\) 0 0
\(125\) 8.48146 + 6.16214i 0.758605 + 0.551159i
\(126\) 0 0
\(127\) 5.15073 + 15.8523i 0.457054 + 1.40667i 0.868707 + 0.495326i \(0.164951\pi\)
−0.411654 + 0.911340i \(0.635049\pi\)
\(128\) 0 0
\(129\) −1.72254 + 2.37087i −0.151661 + 0.208744i
\(130\) 0 0
\(131\) −3.93063 + 12.0972i −0.343421 + 1.05694i 0.619003 + 0.785388i \(0.287537\pi\)
−0.962424 + 0.271552i \(0.912463\pi\)
\(132\) 0 0
\(133\) −1.55356 + 4.78137i −0.134711 + 0.414597i
\(134\) 0 0
\(135\) −11.6350 + 3.78045i −1.00138 + 0.325369i
\(136\) 0 0
\(137\) 12.4445i 1.06321i 0.846993 + 0.531604i \(0.178411\pi\)
−0.846993 + 0.531604i \(0.821589\pi\)
\(138\) 0 0
\(139\) −5.64370 + 4.10039i −0.478692 + 0.347790i −0.800819 0.598906i \(-0.795602\pi\)
0.322127 + 0.946696i \(0.395602\pi\)
\(140\) 0 0
\(141\) −6.59386 4.79072i −0.555303 0.403451i
\(142\) 0 0
\(143\) 27.6511 20.0897i 2.31230 1.67999i
\(144\) 0 0
\(145\) 2.31650 + 3.18838i 0.192375 + 0.264781i
\(146\) 0 0
\(147\) −1.01691 0.330414i −0.0838732 0.0272521i
\(148\) 0 0
\(149\) −0.139122 + 0.0452035i −0.0113973 + 0.00370322i −0.314710 0.949188i \(-0.601907\pi\)
0.303313 + 0.952891i \(0.401907\pi\)
\(150\) 0 0
\(151\) −0.697695 + 0.960295i −0.0567776 + 0.0781477i −0.836462 0.548025i \(-0.815380\pi\)
0.779684 + 0.626173i \(0.215380\pi\)
\(152\) 0 0
\(153\) −12.7785 4.15198i −1.03308 0.335668i
\(154\) 0 0
\(155\) 7.39325 0.593840
\(156\) 0 0
\(157\) 7.82229 + 10.7665i 0.624287 + 0.859257i 0.997656 0.0684258i \(-0.0217977\pi\)
−0.373370 + 0.927683i \(0.621798\pi\)
\(158\) 0 0
\(159\) 2.67999 + 8.24816i 0.212537 + 0.654122i
\(160\) 0 0
\(161\) 0.399932i 0.0315191i
\(162\) 0 0
\(163\) −5.36696 −0.420373 −0.210186 0.977661i \(-0.567407\pi\)
−0.210186 + 0.977661i \(0.567407\pi\)
\(164\) 0 0
\(165\) 13.4045 1.04354
\(166\) 0 0
\(167\) 19.9599i 1.54454i −0.635291 0.772272i \(-0.719120\pi\)
0.635291 0.772272i \(-0.280880\pi\)
\(168\) 0 0
\(169\) −8.73032 26.8691i −0.671563 2.06686i
\(170\) 0 0
\(171\) −5.48671 7.55181i −0.419579 0.577501i
\(172\) 0 0
\(173\) 2.84802 0.216531 0.108265 0.994122i \(-0.465470\pi\)
0.108265 + 0.994122i \(0.465470\pi\)
\(174\) 0 0
\(175\) 0.522976 + 0.169925i 0.0395333 + 0.0128451i
\(176\) 0 0
\(177\) 6.98599 9.61540i 0.525099 0.722737i
\(178\) 0 0
\(179\) −2.71707 + 0.882831i −0.203084 + 0.0659859i −0.408792 0.912627i \(-0.634050\pi\)
0.205709 + 0.978613i \(0.434050\pi\)
\(180\) 0 0
\(181\) 14.2444 + 4.62830i 1.05878 + 0.344018i 0.786108 0.618089i \(-0.212093\pi\)
0.272672 + 0.962107i \(0.412093\pi\)
\(182\) 0 0
\(183\) −8.34298 11.4831i −0.616731 0.848858i
\(184\) 0 0
\(185\) −7.52680 + 5.46854i −0.553381 + 0.402055i
\(186\) 0 0
\(187\) 31.1542 + 22.6349i 2.27822 + 1.65523i
\(188\) 0 0
\(189\) 4.20123 3.05237i 0.305595 0.222028i
\(190\) 0 0
\(191\) 5.05513i 0.365777i −0.983134 0.182888i \(-0.941455\pi\)
0.983134 0.182888i \(-0.0585447\pi\)
\(192\) 0 0
\(193\) 0.121457 0.0394638i 0.00874268 0.00284067i −0.304642 0.952467i \(-0.598537\pi\)
0.313385 + 0.949626i \(0.398537\pi\)
\(194\) 0 0
\(195\) 4.99945 15.3867i 0.358018 1.10187i
\(196\) 0 0
\(197\) −4.48175 + 13.7934i −0.319312 + 0.982740i 0.654631 + 0.755948i \(0.272824\pi\)
−0.973943 + 0.226792i \(0.927176\pi\)
\(198\) 0 0
\(199\) −1.96010 + 2.69784i −0.138948 + 0.191245i −0.872820 0.488043i \(-0.837711\pi\)
0.733872 + 0.679288i \(0.237711\pi\)
\(200\) 0 0
\(201\) 4.21200 + 12.9632i 0.297091 + 0.914353i
\(202\) 0 0
\(203\) −1.35341 0.983307i −0.0949905 0.0690147i
\(204\) 0 0
\(205\) −13.0076 + 7.63852i −0.908492 + 0.533497i
\(206\) 0 0
\(207\) −0.600747 0.436468i −0.0417548 0.0303366i
\(208\) 0 0
\(209\) 8.26726 + 25.4440i 0.571858 + 1.76000i
\(210\) 0 0
\(211\) 1.68113 2.31388i 0.115734 0.159294i −0.747220 0.664577i \(-0.768612\pi\)
0.862954 + 0.505283i \(0.168612\pi\)
\(212\) 0 0
\(213\) 3.77655 11.6230i 0.258765 0.796397i
\(214\) 0 0
\(215\) −1.99526 + 6.14078i −0.136076 + 0.418797i
\(216\) 0 0
\(217\) −2.98469 + 0.969786i −0.202614 + 0.0658333i
\(218\) 0 0
\(219\) 14.0496i 0.949386i
\(220\) 0 0
\(221\) 37.6015 27.3191i 2.52935 1.83768i
\(222\) 0 0
\(223\) −4.40673 3.20168i −0.295097 0.214400i 0.430379 0.902648i \(-0.358380\pi\)
−0.725475 + 0.688248i \(0.758380\pi\)
\(224\) 0 0
\(225\) −0.826001 + 0.600125i −0.0550667 + 0.0400083i
\(226\) 0 0
\(227\) 6.61776 + 9.10857i 0.439236 + 0.604557i 0.970042 0.242936i \(-0.0781106\pi\)
−0.530806 + 0.847494i \(0.678111\pi\)
\(228\) 0 0
\(229\) 14.9488 + 4.85716i 0.987844 + 0.320970i 0.757998 0.652257i \(-0.226178\pi\)
0.229846 + 0.973227i \(0.426178\pi\)
\(230\) 0 0
\(231\) −5.41147 + 1.75829i −0.356049 + 0.115687i
\(232\) 0 0
\(233\) −5.07160 + 6.98046i −0.332252 + 0.457305i −0.942158 0.335168i \(-0.891207\pi\)
0.609907 + 0.792473i \(0.291207\pi\)
\(234\) 0 0
\(235\) −17.0787 5.54921i −1.11409 0.361990i
\(236\) 0 0
\(237\) −12.7809 −0.830208
\(238\) 0 0
\(239\) −15.3779 21.1659i −0.994713 1.36911i −0.928513 0.371299i \(-0.878912\pi\)
−0.0662000 0.997806i \(-0.521088\pi\)
\(240\) 0 0
\(241\) 4.37637 + 13.4691i 0.281907 + 0.867620i 0.987309 + 0.158812i \(0.0507665\pi\)
−0.705402 + 0.708808i \(0.749233\pi\)
\(242\) 0 0
\(243\) 15.5978i 1.00060i
\(244\) 0 0
\(245\) −2.35582 −0.150508
\(246\) 0 0
\(247\) 32.2900 2.05456
\(248\) 0 0
\(249\) 15.5433i 0.985018i
\(250\) 0 0
\(251\) 7.15199 + 22.0116i 0.451430 + 1.38936i 0.875276 + 0.483624i \(0.160680\pi\)
−0.423846 + 0.905734i \(0.639320\pi\)
\(252\) 0 0
\(253\) 1.25095 + 1.72178i 0.0786463 + 0.108247i
\(254\) 0 0
\(255\) 18.2282 1.14149
\(256\) 0 0
\(257\) −27.6362 8.97954i −1.72390 0.560129i −0.731352 0.682000i \(-0.761110\pi\)
−0.992546 + 0.121871i \(0.961110\pi\)
\(258\) 0 0
\(259\) 2.32129 3.19498i 0.144238 0.198526i
\(260\) 0 0
\(261\) 2.95409 0.959843i 0.182854 0.0594128i
\(262\) 0 0
\(263\) −11.3121 3.67554i −0.697537 0.226643i −0.0612798 0.998121i \(-0.519518\pi\)
−0.636257 + 0.771477i \(0.719518\pi\)
\(264\) 0 0
\(265\) 11.2315 + 15.4588i 0.689943 + 0.949625i
\(266\) 0 0
\(267\) 12.4832 9.06958i 0.763960 0.555050i
\(268\) 0 0
\(269\) 2.05046 + 1.48975i 0.125019 + 0.0908314i 0.648537 0.761183i \(-0.275381\pi\)
−0.523519 + 0.852014i \(0.675381\pi\)
\(270\) 0 0
\(271\) 18.7397 13.6152i 1.13836 0.827064i 0.151466 0.988462i \(-0.451600\pi\)
0.986889 + 0.161399i \(0.0516005\pi\)
\(272\) 0 0
\(273\) 6.86748i 0.415639i
\(274\) 0 0
\(275\) 2.78301 0.904256i 0.167822 0.0545287i
\(276\) 0 0
\(277\) −6.21766 + 19.1360i −0.373583 + 1.14977i 0.570846 + 0.821057i \(0.306615\pi\)
−0.944429 + 0.328714i \(0.893385\pi\)
\(278\) 0 0
\(279\) 1.80062 5.54175i 0.107801 0.331776i
\(280\) 0 0
\(281\) −9.99171 + 13.7524i −0.596055 + 0.820400i −0.995340 0.0964271i \(-0.969259\pi\)
0.399285 + 0.916827i \(0.369259\pi\)
\(282\) 0 0
\(283\) −4.45478 13.7104i −0.264809 0.814999i −0.991737 0.128286i \(-0.959053\pi\)
0.726928 0.686714i \(-0.240947\pi\)
\(284\) 0 0
\(285\) 10.2452 + 7.44359i 0.606875 + 0.440920i
\(286\) 0 0
\(287\) 4.24929 4.78994i 0.250828 0.282741i
\(288\) 0 0
\(289\) 28.6120 + 20.7878i 1.68306 + 1.22281i
\(290\) 0 0
\(291\) −2.01433 6.19947i −0.118082 0.363419i
\(292\) 0 0
\(293\) −1.37079 + 1.88673i −0.0800825 + 0.110224i −0.847179 0.531308i \(-0.821701\pi\)
0.767096 + 0.641532i \(0.221701\pi\)
\(294\) 0 0
\(295\) 8.09205 24.9048i 0.471137 1.45001i
\(296\) 0 0
\(297\) 8.53954 26.2820i 0.495515 1.52504i
\(298\) 0 0
\(299\) 2.44295 0.793763i 0.141279 0.0459045i
\(300\) 0 0
\(301\) 2.74078i 0.157976i
\(302\) 0 0
\(303\) 5.47156 3.97532i 0.314333 0.228376i
\(304\) 0 0
\(305\) −25.3004 18.3818i −1.44870 1.05254i
\(306\) 0 0
\(307\) −17.2615 + 12.5412i −0.985168 + 0.715766i −0.958858 0.283888i \(-0.908376\pi\)
−0.0263101 + 0.999654i \(0.508376\pi\)
\(308\) 0 0
\(309\) 1.04480 + 1.43804i 0.0594364 + 0.0818072i
\(310\) 0 0
\(311\) −2.83654 0.921649i −0.160846 0.0522619i 0.227487 0.973781i \(-0.426949\pi\)
−0.388333 + 0.921519i \(0.626949\pi\)
\(312\) 0 0
\(313\) 19.6248 6.37648i 1.10926 0.360420i 0.303599 0.952800i \(-0.401812\pi\)
0.805659 + 0.592380i \(0.201812\pi\)
\(314\) 0 0
\(315\) 2.57104 3.53873i 0.144861 0.199385i
\(316\) 0 0
\(317\) 17.2415 + 5.60210i 0.968379 + 0.314646i 0.750162 0.661255i \(-0.229976\pi\)
0.218218 + 0.975900i \(0.429976\pi\)
\(318\) 0 0
\(319\) −8.90233 −0.498435
\(320\) 0 0
\(321\) 0.481861 + 0.663224i 0.0268948 + 0.0370176i
\(322\) 0 0
\(323\) 11.2423 + 34.6002i 0.625537 + 1.92521i
\(324\) 0 0
\(325\) 3.53181i 0.195910i
\(326\) 0 0
\(327\) −7.32726 −0.405198
\(328\) 0 0
\(329\) 7.62265 0.420251
\(330\) 0 0
\(331\) 21.8420i 1.20054i 0.799796 + 0.600272i \(0.204941\pi\)
−0.799796 + 0.600272i \(0.795059\pi\)
\(332\) 0 0
\(333\) 2.26590 + 6.97371i 0.124170 + 0.382157i
\(334\) 0 0
\(335\) 17.6519 + 24.2957i 0.964425 + 1.32742i
\(336\) 0 0
\(337\) 24.1267 1.31427 0.657133 0.753775i \(-0.271769\pi\)
0.657133 + 0.753775i \(0.271769\pi\)
\(338\) 0 0
\(339\) 3.23641 + 1.05157i 0.175778 + 0.0571137i
\(340\) 0 0
\(341\) −9.81624 + 13.5109i −0.531579 + 0.731656i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) 0.958099 + 0.311305i 0.0515823 + 0.0167601i
\(346\) 0 0
\(347\) −6.69024 9.20832i −0.359151 0.494328i 0.590761 0.806846i \(-0.298828\pi\)
−0.949912 + 0.312518i \(0.898828\pi\)
\(348\) 0 0
\(349\) 4.02434 2.92385i 0.215418 0.156510i −0.474844 0.880070i \(-0.657495\pi\)
0.690262 + 0.723560i \(0.257495\pi\)
\(350\) 0 0
\(351\) −26.9835 19.6047i −1.44027 1.04642i
\(352\) 0 0
\(353\) 14.9641 10.8721i 0.796459 0.578661i −0.113414 0.993548i \(-0.536179\pi\)
0.909873 + 0.414887i \(0.136179\pi\)
\(354\) 0 0
\(355\) 26.9265i 1.42911i
\(356\) 0 0
\(357\) −7.35882 + 2.39102i −0.389470 + 0.126546i
\(358\) 0 0
\(359\) 4.74933 14.6169i 0.250660 0.771452i −0.743994 0.668187i \(-0.767071\pi\)
0.994654 0.103266i \(-0.0329292\pi\)
\(360\) 0 0
\(361\) −1.93910 + 5.96793i −0.102058 + 0.314101i
\(362\) 0 0
\(363\) −10.8842 + 14.9809i −0.571275 + 0.786292i
\(364\) 0 0
\(365\) −9.56563 29.4400i −0.500688 1.54096i
\(366\) 0 0
\(367\) −20.1325 14.6272i −1.05091 0.763531i −0.0785250 0.996912i \(-0.525021\pi\)
−0.972385 + 0.233381i \(0.925021\pi\)
\(368\) 0 0
\(369\) 2.55759 + 11.6105i 0.133143 + 0.604417i
\(370\) 0 0
\(371\) −6.56195 4.76754i −0.340679 0.247518i
\(372\) 0 0
\(373\) −7.67868 23.6326i −0.397587 1.22365i −0.926928 0.375238i \(-0.877561\pi\)
0.529341 0.848409i \(-0.322439\pi\)
\(374\) 0 0
\(375\) −6.58881 + 9.06872i −0.340245 + 0.468307i
\(376\) 0 0
\(377\) −3.32028 + 10.2188i −0.171003 + 0.526294i
\(378\) 0 0
\(379\) 3.39876 10.4603i 0.174583 0.537310i −0.825032 0.565087i \(-0.808843\pi\)
0.999614 + 0.0277768i \(0.00884276\pi\)
\(380\) 0 0
\(381\) −16.9500 + 5.50737i −0.868373 + 0.282151i
\(382\) 0 0
\(383\) 3.65639i 0.186833i 0.995627 + 0.0934164i \(0.0297788\pi\)
−0.995627 + 0.0934164i \(0.970221\pi\)
\(384\) 0 0
\(385\) −10.1422 + 7.36875i −0.516895 + 0.375547i
\(386\) 0 0
\(387\) 4.11699 + 2.99117i 0.209278 + 0.152050i
\(388\) 0 0
\(389\) −12.1519 + 8.82884i −0.616123 + 0.447640i −0.851565 0.524249i \(-0.824346\pi\)
0.235442 + 0.971888i \(0.424346\pi\)
\(390\) 0 0
\(391\) 1.70111 + 2.34137i 0.0860286 + 0.118408i
\(392\) 0 0
\(393\) −12.9349 4.20279i −0.652477 0.212003i
\(394\) 0 0
\(395\) −26.7814 + 8.70181i −1.34752 + 0.437836i
\(396\) 0 0
\(397\) 19.1158 26.3107i 0.959397 1.32050i 0.0121718 0.999926i \(-0.496125\pi\)
0.947225 0.320570i \(-0.103875\pi\)
\(398\) 0 0
\(399\) −5.11244 1.66113i −0.255942 0.0831606i
\(400\) 0 0
\(401\) −35.0510 −1.75036 −0.875181 0.483795i \(-0.839258\pi\)
−0.875181 + 0.483795i \(0.839258\pi\)
\(402\) 0 0
\(403\) 11.8477 + 16.3070i 0.590176 + 0.812308i
\(404\) 0 0
\(405\) 0.0128069 + 0.0394157i 0.000636381 + 0.00195858i
\(406\) 0 0
\(407\) 21.0157i 1.04171i
\(408\) 0 0
\(409\) 29.9150 1.47920 0.739600 0.673047i \(-0.235015\pi\)
0.739600 + 0.673047i \(0.235015\pi\)
\(410\) 0 0
\(411\) −13.3062 −0.656347
\(412\) 0 0
\(413\) 11.1156i 0.546964i
\(414\) 0 0
\(415\) 10.5826 + 32.5699i 0.519480 + 1.59880i
\(416\) 0 0
\(417\) −4.38430 6.03447i −0.214700 0.295509i
\(418\) 0 0
\(419\) −10.8450 −0.529811 −0.264905 0.964274i \(-0.585341\pi\)
−0.264905 + 0.964274i \(0.585341\pi\)
\(420\) 0 0
\(421\) −15.2006 4.93899i −0.740834 0.240711i −0.0858012 0.996312i \(-0.527345\pi\)
−0.655032 + 0.755601i \(0.727345\pi\)
\(422\) 0 0
\(423\) −8.31902 + 11.4501i −0.404485 + 0.556725i
\(424\) 0 0
\(425\) 3.78450 1.22966i 0.183575 0.0596472i
\(426\) 0 0
\(427\) 12.6251 + 4.10213i 0.610969 + 0.198516i
\(428\) 0 0
\(429\) 21.4808 + 29.5657i 1.03710 + 1.42745i
\(430\) 0 0
\(431\) −21.6374 + 15.7205i −1.04224 + 0.757231i −0.970721 0.240208i \(-0.922784\pi\)
−0.0715179 + 0.997439i \(0.522784\pi\)
\(432\) 0 0
\(433\) 11.6473 + 8.46224i 0.559732 + 0.406669i 0.831361 0.555733i \(-0.187562\pi\)
−0.271629 + 0.962402i \(0.587562\pi\)
\(434\) 0 0
\(435\) −3.40915 + 2.47689i −0.163456 + 0.118758i
\(436\) 0 0
\(437\) 2.01063i 0.0961815i
\(438\) 0 0
\(439\) 19.3755 6.29548i 0.924742 0.300467i 0.192331 0.981330i \(-0.438395\pi\)
0.732411 + 0.680863i \(0.238395\pi\)
\(440\) 0 0
\(441\) −0.573759 + 1.76585i −0.0273219 + 0.0840880i
\(442\) 0 0
\(443\) −1.65971 + 5.10806i −0.0788552 + 0.242691i −0.982711 0.185146i \(-0.940724\pi\)
0.903856 + 0.427837i \(0.140724\pi\)
\(444\) 0 0
\(445\) 19.9827 27.5038i 0.947270 1.30381i
\(446\) 0 0
\(447\) −0.0483335 0.148755i −0.00228609 0.00703588i
\(448\) 0 0
\(449\) −18.4335 13.3927i −0.869931 0.632042i 0.0606371 0.998160i \(-0.480687\pi\)
−0.930569 + 0.366118i \(0.880687\pi\)
\(450\) 0 0
\(451\) 3.31151 33.9129i 0.155933 1.59689i
\(452\) 0 0
\(453\) −1.02679 0.746005i −0.0482427 0.0350504i
\(454\) 0 0
\(455\) 4.67570 + 14.3903i 0.219200 + 0.674629i
\(456\) 0 0
\(457\) −0.176619 + 0.243096i −0.00826190 + 0.0113715i −0.813128 0.582085i \(-0.802237\pi\)
0.804866 + 0.593457i \(0.202237\pi\)
\(458\) 0 0
\(459\) 11.6125 35.7397i 0.542027 1.66819i
\(460\) 0 0
\(461\) −1.40869 + 4.33551i −0.0656094 + 0.201925i −0.978487 0.206308i \(-0.933855\pi\)
0.912878 + 0.408233i \(0.133855\pi\)
\(462\) 0 0
\(463\) 11.8962 3.86530i 0.552862 0.179636i −0.0192448 0.999815i \(-0.506126\pi\)
0.572107 + 0.820179i \(0.306126\pi\)
\(464\) 0 0
\(465\) 7.90517i 0.366594i
\(466\) 0 0
\(467\) −26.1594 + 19.0059i −1.21051 + 0.879490i −0.995277 0.0970720i \(-0.969052\pi\)
−0.215237 + 0.976562i \(0.569052\pi\)
\(468\) 0 0
\(469\) −10.3131 7.49288i −0.476213 0.345989i
\(470\) 0 0
\(471\) −11.5119 + 8.36391i −0.530442 + 0.385389i
\(472\) 0 0
\(473\) −8.57288 11.7996i −0.394181 0.542544i
\(474\) 0 0
\(475\) 2.62923 + 0.854288i 0.120637 + 0.0391974i
\(476\) 0 0
\(477\) 14.3228 4.65377i 0.655797 0.213081i
\(478\) 0 0
\(479\) −2.21588 + 3.04990i −0.101246 + 0.139354i −0.856634 0.515924i \(-0.827449\pi\)
0.755388 + 0.655278i \(0.227449\pi\)
\(480\) 0 0
\(481\) −24.1234 7.83817i −1.09993 0.357390i
\(482\) 0 0
\(483\) −0.427624 −0.0194576
\(484\) 0 0
\(485\) −8.44176 11.6191i −0.383321 0.527596i
\(486\) 0 0
\(487\) −5.99724 18.4576i −0.271761 0.836395i −0.990058 0.140658i \(-0.955078\pi\)
0.718297 0.695736i \(-0.244922\pi\)
\(488\) 0 0
\(489\) 5.73857i 0.259507i
\(490\) 0 0
\(491\) 11.8973 0.536918 0.268459 0.963291i \(-0.413486\pi\)
0.268459 + 0.963291i \(0.413486\pi\)
\(492\) 0 0
\(493\) −12.1059 −0.545222
\(494\) 0 0
\(495\) 23.2768i 1.04621i
\(496\) 0 0
\(497\) 3.53199 + 10.8704i 0.158432 + 0.487602i
\(498\) 0 0
\(499\) 8.68246 + 11.9504i 0.388681 + 0.534973i 0.957858 0.287242i \(-0.0927383\pi\)
−0.569178 + 0.822215i \(0.692738\pi\)
\(500\) 0 0
\(501\) 21.3420 0.953489
\(502\) 0 0
\(503\) 11.7726 + 3.82514i 0.524912 + 0.170554i 0.559474 0.828848i \(-0.311003\pi\)
−0.0345612 + 0.999403i \(0.511003\pi\)
\(504\) 0 0
\(505\) 8.75868 12.0553i 0.389756 0.536454i
\(506\) 0 0
\(507\) 28.7296 9.33481i 1.27593 0.414574i
\(508\) 0 0
\(509\) 36.8310 + 11.9671i 1.63250 + 0.530433i 0.974845 0.222884i \(-0.0715470\pi\)
0.657659 + 0.753316i \(0.271547\pi\)
\(510\) 0 0
\(511\) 7.72339 + 10.6303i 0.341662 + 0.470258i
\(512\) 0 0
\(513\) 21.1214 15.3456i 0.932533 0.677525i
\(514\) 0 0
\(515\) 3.16838 + 2.30196i 0.139616 + 0.101437i
\(516\) 0 0
\(517\) 32.8169 23.8428i 1.44328 1.04861i
\(518\) 0 0
\(519\) 3.04522i 0.133670i
\(520\) 0 0
\(521\) 16.5051 5.36282i 0.723100 0.234950i 0.0757335 0.997128i \(-0.475870\pi\)
0.647367 + 0.762179i \(0.275870\pi\)
\(522\) 0 0
\(523\) −8.85198 + 27.2436i −0.387070 + 1.19128i 0.547897 + 0.836546i \(0.315428\pi\)
−0.934967 + 0.354734i \(0.884572\pi\)
\(524\) 0 0
\(525\) −0.181691 + 0.559188i −0.00792965 + 0.0244050i
\(526\) 0 0
\(527\) −13.3487 + 18.3729i −0.581477 + 0.800335i
\(528\) 0 0
\(529\) −7.05796 21.7222i −0.306868 0.944443i
\(530\) 0 0
\(531\) −16.6970 12.1311i −0.724589 0.526444i
\(532\) 0 0
\(533\) −37.6927 16.4496i −1.63265 0.712511i
\(534\) 0 0
\(535\) 1.46126 + 1.06167i 0.0631757 + 0.0458998i
\(536\) 0 0
\(537\) −0.943959 2.90521i −0.0407348 0.125369i
\(538\) 0 0
\(539\) 3.12789 4.30518i 0.134728 0.185437i
\(540\) 0 0
\(541\) −1.36494 + 4.20086i −0.0586834 + 0.180609i −0.976101 0.217316i \(-0.930270\pi\)
0.917418 + 0.397925i \(0.130270\pi\)
\(542\) 0 0
\(543\) −4.94876 + 15.2307i −0.212372 + 0.653613i
\(544\) 0 0
\(545\) −15.3538 + 4.98874i −0.657683 + 0.213694i
\(546\) 0 0
\(547\) 27.7416i 1.18614i −0.805150 0.593072i \(-0.797915\pi\)
0.805150 0.593072i \(-0.202085\pi\)
\(548\) 0 0
\(549\) −19.9403 + 14.4875i −0.851032 + 0.618311i
\(550\) 0 0
\(551\) −6.80416 4.94351i −0.289867 0.210601i
\(552\) 0 0
\(553\) 9.67037 7.02593i 0.411226 0.298773i
\(554\) 0 0
\(555\) −5.84719 8.04796i −0.248199 0.341617i
\(556\) 0 0
\(557\) −13.3970 4.35296i −0.567651 0.184441i 0.0111099 0.999938i \(-0.496464\pi\)
−0.578761 + 0.815497i \(0.696464\pi\)
\(558\) 0 0
\(559\) −16.7418 + 5.43975i −0.708104 + 0.230077i
\(560\) 0 0
\(561\) −24.2021 + 33.3114i −1.02181 + 1.40641i
\(562\) 0 0
\(563\) −37.7423 12.2632i −1.59065 0.516833i −0.625876 0.779922i \(-0.715258\pi\)
−0.964771 + 0.263090i \(0.915258\pi\)
\(564\) 0 0
\(565\) 7.49763 0.315428
\(566\) 0 0
\(567\) −0.0103404 0.0142324i −0.000434258 0.000597704i
\(568\) 0 0
\(569\) 4.14492 + 12.7568i 0.173764 + 0.534791i 0.999575 0.0291562i \(-0.00928201\pi\)
−0.825811 + 0.563948i \(0.809282\pi\)
\(570\) 0 0
\(571\) 36.6178i 1.53241i 0.642597 + 0.766205i \(0.277857\pi\)
−0.642597 + 0.766205i \(0.722143\pi\)
\(572\) 0 0
\(573\) 5.40516 0.225804
\(574\) 0 0
\(575\) 0.219919 0.00917125
\(576\) 0 0
\(577\) 8.07091i 0.335996i −0.985787 0.167998i \(-0.946270\pi\)
0.985787 0.167998i \(-0.0537303\pi\)
\(578\) 0 0
\(579\) 0.0421964 + 0.129867i 0.00175362 + 0.00539709i
\(580\) 0 0
\(581\) −8.54451 11.7605i −0.354486 0.487908i
\(582\) 0 0
\(583\) −43.1627 −1.78762
\(584\) 0 0
\(585\) −26.7188 8.68148i −1.10469 0.358935i
\(586\) 0 0
\(587\) 2.00612 2.76119i 0.0828016 0.113967i −0.765607 0.643309i \(-0.777561\pi\)
0.848408 + 0.529342i \(0.177561\pi\)
\(588\) 0 0
\(589\) −15.0053 + 4.87553i −0.618284 + 0.200893i
\(590\) 0 0
\(591\) −14.7485 4.79208i −0.606672 0.197120i
\(592\) 0 0
\(593\) −2.11067 2.90508i −0.0866747 0.119297i 0.763478 0.645834i \(-0.223490\pi\)
−0.850152 + 0.526537i \(0.823490\pi\)
\(594\) 0 0
\(595\) −13.7920 + 10.0204i −0.565415 + 0.410798i
\(596\) 0 0
\(597\) −2.88464 2.09582i −0.118061 0.0857761i
\(598\) 0 0
\(599\) 16.0782 11.6815i 0.656937 0.477293i −0.208690 0.977982i \(-0.566920\pi\)
0.865627 + 0.500689i \(0.166920\pi\)
\(600\) 0 0
\(601\) 15.7216i 0.641299i 0.947198 + 0.320650i \(0.103901\pi\)
−0.947198 + 0.320650i \(0.896099\pi\)
\(602\) 0 0
\(603\) 22.5104 7.31408i 0.916695 0.297852i
\(604\) 0 0
\(605\) −12.6075 + 38.8019i −0.512567 + 1.57752i
\(606\) 0 0
\(607\) −1.65147 + 5.08270i −0.0670311 + 0.206300i −0.978962 0.204044i \(-0.934591\pi\)
0.911931 + 0.410344i \(0.134591\pi\)
\(608\) 0 0
\(609\) 1.05139 1.44712i 0.0426046 0.0586402i
\(610\) 0 0
\(611\) −15.1290 46.5623i −0.612054 1.88371i
\(612\) 0 0
\(613\) 18.2599 + 13.2666i 0.737509 + 0.535832i 0.891930 0.452173i \(-0.149351\pi\)
−0.154421 + 0.988005i \(0.549351\pi\)
\(614\) 0 0
\(615\) −8.16742 13.9083i −0.329342 0.560837i
\(616\) 0 0
\(617\) 19.6016 + 14.2414i 0.789129 + 0.573336i 0.907705 0.419609i \(-0.137833\pi\)
−0.118576 + 0.992945i \(0.537833\pi\)
\(618\) 0 0
\(619\) −5.30776 16.3356i −0.213337 0.656584i −0.999267 0.0382688i \(-0.987816\pi\)
0.785931 0.618315i \(-0.212184\pi\)
\(620\) 0 0
\(621\) 1.22074 1.68021i 0.0489867 0.0674244i
\(622\) 0 0
\(623\) −4.45939 + 13.7246i −0.178662 + 0.549864i
\(624\) 0 0
\(625\) −8.48161 + 26.1037i −0.339264 + 1.04415i
\(626\) 0 0
\(627\) −27.2058 + 8.83969i −1.08649 + 0.353023i
\(628\) 0 0
\(629\) 28.5783i 1.13949i
\(630\) 0 0
\(631\) −30.0162 + 21.8081i −1.19493 + 0.868165i −0.993776 0.111395i \(-0.964468\pi\)
−0.201151 + 0.979560i \(0.564468\pi\)
\(632\) 0 0
\(633\) 2.47409 + 1.79753i 0.0983363 + 0.0714455i
\(634\) 0 0
\(635\) −31.7677 + 23.0806i −1.26066 + 0.915926i
\(636\) 0 0
\(637\) −3.77521 5.19613i −0.149579 0.205878i
\(638\) 0 0
\(639\) −20.1832 6.55793i −0.798437 0.259428i
\(640\) 0 0
\(641\) −22.1531 + 7.19799i −0.874997 + 0.284304i −0.711878 0.702303i \(-0.752155\pi\)
−0.163118 + 0.986607i \(0.552155\pi\)
\(642\) 0 0
\(643\) 3.61173 4.97112i 0.142433 0.196042i −0.731841 0.681476i \(-0.761338\pi\)
0.874273 + 0.485434i \(0.161338\pi\)
\(644\) 0 0
\(645\) −6.56597 2.13341i −0.258535 0.0840030i
\(646\) 0 0
\(647\) 21.6649 0.851735 0.425867 0.904786i \(-0.359969\pi\)
0.425867 + 0.904786i \(0.359969\pi\)
\(648\) 0 0
\(649\) 34.7685 + 47.8547i 1.36478 + 1.87846i
\(650\) 0 0
\(651\) −1.03693 3.19136i −0.0406407 0.125079i
\(652\) 0 0
\(653\) 14.7647i 0.577787i 0.957361 + 0.288893i \(0.0932873\pi\)
−0.957361 + 0.288893i \(0.906713\pi\)
\(654\) 0 0
\(655\) −29.9655 −1.17085
\(656\) 0 0
\(657\) −24.3970 −0.951817
\(658\) 0 0
\(659\) 33.7317i 1.31400i −0.753890 0.657001i \(-0.771825\pi\)
0.753890 0.657001i \(-0.228175\pi\)
\(660\) 0 0
\(661\) −3.31046 10.1885i −0.128762 0.396288i 0.865806 0.500380i \(-0.166806\pi\)
−0.994568 + 0.104092i \(0.966806\pi\)
\(662\) 0 0
\(663\) 29.2107 + 40.2051i 1.13445 + 1.56144i
\(664\) 0 0
\(665\) −11.8437 −0.459280
\(666\) 0 0
\(667\) −0.636302 0.206747i −0.0246377 0.00800528i
\(668\) 0 0
\(669\) 3.42337 4.71186i 0.132355 0.182171i
\(670\) 0 0
\(671\) 67.1841 21.8294i 2.59361 0.842716i
\(672\) 0 0
\(673\) −34.9491 11.3556i −1.34719 0.437728i −0.455442 0.890266i \(-0.650519\pi\)
−0.891745 + 0.452538i \(0.850519\pi\)
\(674\) 0 0
\(675\) −1.67847 2.31022i −0.0646043 0.0889202i
\(676\) 0 0
\(677\) 19.8485 14.4208i 0.762839 0.554235i −0.136941 0.990579i \(-0.543727\pi\)
0.899780 + 0.436344i \(0.143727\pi\)
\(678\) 0 0
\(679\) 4.93208 + 3.58336i 0.189276 + 0.137517i
\(680\) 0 0
\(681\) −9.73926 + 7.07599i −0.373209 + 0.271152i
\(682\) 0 0
\(683\) 15.1599i 0.580078i −0.957015 0.290039i \(-0.906332\pi\)
0.957015 0.290039i \(-0.0936683\pi\)
\(684\) 0 0
\(685\) −27.8822 + 9.05948i −1.06532 + 0.346145i
\(686\) 0 0
\(687\) −5.19347 + 15.9839i −0.198143 + 0.609822i
\(688\) 0 0
\(689\) −16.0983 + 49.5454i −0.613296 + 1.88753i
\(690\) 0 0
\(691\) −30.3945 + 41.8344i −1.15626 + 1.59145i −0.432093 + 0.901829i \(0.642225\pi\)
−0.724166 + 0.689626i \(0.757775\pi\)
\(692\) 0 0
\(693\) 3.05325 + 9.39695i 0.115983 + 0.356960i
\(694\) 0 0
\(695\) −13.2955 9.65978i −0.504329 0.366416i
\(696\) 0 0
\(697\) 4.50317 46.1166i 0.170570 1.74679i
\(698\) 0 0
\(699\) −7.46379 5.42276i −0.282307 0.205108i
\(700\) 0 0
\(701\) −11.7561 36.1816i −0.444023 1.36656i −0.883552 0.468333i \(-0.844855\pi\)
0.439529 0.898228i \(-0.355145\pi\)
\(702\) 0 0
\(703\) 11.6701 16.0625i 0.440147 0.605810i
\(704\) 0 0
\(705\) 5.93344 18.2612i 0.223466 0.687758i
\(706\) 0 0
\(707\) −1.95461 + 6.01567i −0.0735107 + 0.226243i
\(708\) 0 0
\(709\) 18.1328 5.89169i 0.680990 0.221267i 0.0519611 0.998649i \(-0.483453\pi\)
0.629029 + 0.777382i \(0.283453\pi\)
\(710\) 0 0
\(711\) 22.1938i 0.832334i
\(712\) 0 0
\(713\) −1.01540 + 0.737732i −0.0380271 + 0.0276283i
\(714\) 0 0
\(715\) 65.1411 + 47.3278i 2.43614 + 1.76996i
\(716\) 0 0
\(717\) 22.6314 16.4427i 0.845185 0.614063i
\(718\) 0 0
\(719\) 9.31758 + 12.8245i 0.347487 + 0.478275i 0.946609 0.322382i \(-0.104484\pi\)
−0.599122 + 0.800657i \(0.704484\pi\)
\(720\) 0 0
\(721\) −1.58104 0.513712i −0.0588811 0.0191316i
\(722\) 0 0
\(723\) −14.4017 + 4.67940i −0.535605 + 0.174029i
\(724\) 0 0
\(725\) −0.540711 + 0.744225i −0.0200815 + 0.0276398i
\(726\) 0 0
\(727\) 42.5975 + 13.8408i 1.57985 + 0.513326i 0.962019 0.272982i \(-0.0880099\pi\)
0.617835 + 0.786308i \(0.288010\pi\)
\(728\) 0 0
\(729\) −16.6251 −0.615743
\(730\) 0 0
\(731\) −11.6579 16.0457i −0.431182 0.593471i
\(732\) 0 0
\(733\) −12.2090 37.5753i −0.450948 1.38788i −0.875827 0.482626i \(-0.839683\pi\)
0.424878 0.905250i \(-0.360317\pi\)
\(734\) 0 0
\(735\) 2.51894i 0.0929125i
\(736\) 0 0
\(737\) −67.8365 −2.49879
\(738\) 0 0
\(739\) −21.5720 −0.793541 −0.396770 0.917918i \(-0.629869\pi\)
−0.396770 + 0.917918i \(0.629869\pi\)
\(740\) 0 0
\(741\) 34.5258i 1.26834i
\(742\) 0 0
\(743\) −4.91530 15.1277i −0.180325 0.554983i 0.819512 0.573062i \(-0.194245\pi\)
−0.999837 + 0.0180796i \(0.994245\pi\)
\(744\) 0 0
\(745\) −0.202559 0.278798i −0.00742117 0.0102144i
\(746\) 0 0
\(747\) 26.9908 0.987541
\(748\) 0 0
\(749\) −0.729178 0.236924i −0.0266436 0.00865703i
\(750\) 0 0
\(751\) −27.8026 + 38.2670i −1.01453 + 1.39638i −0.0985617 + 0.995131i \(0.531424\pi\)
−0.915969 + 0.401250i \(0.868576\pi\)
\(752\) 0 0
\(753\) −23.5357 + 7.64720i −0.857688 + 0.278680i
\(754\) 0 0
\(755\) −2.65947 0.864115i −0.0967881 0.0314484i
\(756\) 0 0
\(757\) 22.5860 + 31.0870i 0.820903 + 1.12988i 0.989549 + 0.144199i \(0.0460605\pi\)
−0.168646 + 0.985677i \(0.553939\pi\)
\(758\) 0 0
\(759\) −1.84100 + 1.33756i −0.0668239 + 0.0485504i
\(760\) 0 0
\(761\) −23.9830 17.4246i −0.869382 0.631643i 0.0610390 0.998135i \(-0.480559\pi\)
−0.930421 + 0.366492i \(0.880559\pi\)
\(762\) 0 0
\(763\) 5.54401 4.02796i 0.200706 0.145822i
\(764\) 0 0
\(765\) 31.6530i 1.14442i
\(766\) 0 0
\(767\) 67.8988 22.0617i 2.45168 0.796600i
\(768\) 0 0
\(769\) 13.4537 41.4061i 0.485152 1.49314i −0.346610 0.938009i \(-0.612667\pi\)
0.831761 0.555133i \(-0.187333\pi\)
\(770\) 0 0
\(771\) 9.60130 29.5498i 0.345782 1.06421i
\(772\) 0 0
\(773\) 1.69578 2.33404i 0.0609929 0.0839495i −0.777431 0.628968i \(-0.783478\pi\)
0.838424 + 0.545019i \(0.183478\pi\)
\(774\) 0 0
\(775\) 0.533275 + 1.64125i 0.0191558 + 0.0589556i
\(776\) 0 0
\(777\) 3.41620 + 2.48202i 0.122556 + 0.0890419i
\(778\) 0 0
\(779\) 21.3630 24.0811i 0.765409 0.862795i
\(780\) 0 0
\(781\) 49.2072 + 35.7511i 1.76077 + 1.27927i
\(782\) 0 0
\(783\) 2.68455 + 8.26221i 0.0959381 + 0.295267i
\(784\) 0 0
\(785\) −18.4279 + 25.3638i −0.657720 + 0.905274i
\(786\) 0 0
\(787\) −3.96071 + 12.1898i −0.141184 + 0.434520i −0.996501 0.0835859i \(-0.973363\pi\)
0.855316 + 0.518106i \(0.173363\pi\)
\(788\) 0 0
\(789\) 3.93004 12.0954i 0.139913 0.430608i
\(790\) 0 0
\(791\) −3.02683 + 0.983477i −0.107622 + 0.0349684i
\(792\) 0 0
\(793\) 85.2607i 3.02770i
\(794\) 0 0
\(795\) −16.5292 + 12.0091i −0.586229 + 0.425920i
\(796\) 0 0
\(797\) −16.5539 12.0271i −0.586370