Properties

Label 1512.2.j.c.323.2
Level 1512
Weight 2
Character 1512.323
Analytic conductor 12.073
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.2
Character \(\chi\) = 1512.323
Dual form 1512.2.j.c.323.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.40936 + 0.117111i) q^{2} +(1.97257 - 0.330101i) q^{4} +1.17792 q^{5} -1.00000i q^{7} +(-2.74140 + 0.696239i) q^{8} +O(q^{10})\) \(q+(-1.40936 + 0.117111i) q^{2} +(1.97257 - 0.330101i) q^{4} +1.17792 q^{5} -1.00000i q^{7} +(-2.74140 + 0.696239i) q^{8} +(-1.66010 + 0.137947i) q^{10} +2.90595i q^{11} -1.05317i q^{13} +(0.117111 + 1.40936i) q^{14} +(3.78207 - 1.30230i) q^{16} +6.48837i q^{17} -3.11597 q^{19} +(2.32352 - 0.388832i) q^{20} +(-0.340317 - 4.09552i) q^{22} -0.812516 q^{23} -3.61251 q^{25} +(0.123337 + 1.48429i) q^{26} +(-0.330101 - 1.97257i) q^{28} -4.03607 q^{29} -0.108779i q^{31} +(-5.17777 + 2.27832i) q^{32} +(-0.759857 - 9.14442i) q^{34} -1.17792i q^{35} +9.97034i q^{37} +(4.39151 - 0.364913i) q^{38} +(-3.22914 + 0.820111i) q^{40} +9.44298i q^{41} +10.3446 q^{43} +(0.959257 + 5.73219i) q^{44} +(1.14512 - 0.0951542i) q^{46} -4.03126 q^{47} -1.00000 q^{49} +(5.09132 - 0.423064i) q^{50} +(-0.347652 - 2.07745i) q^{52} -2.97772 q^{53} +3.42296i q^{55} +(0.696239 + 2.74140i) q^{56} +(5.68827 - 0.472667i) q^{58} +0.868874i q^{59} -5.33629i q^{61} +(0.0127391 + 0.153308i) q^{62} +(7.03050 - 3.81733i) q^{64} -1.24054i q^{65} -3.97987 q^{67} +(2.14182 + 12.7988i) q^{68} +(0.137947 + 1.66010i) q^{70} +0.844302 q^{71} +3.59513 q^{73} +(-1.16763 - 14.0518i) q^{74} +(-6.14647 + 1.02859i) q^{76} +2.90595 q^{77} -9.48320i q^{79} +(4.45496 - 1.53400i) q^{80} +(-1.10587 - 13.3085i) q^{82} -2.71280i q^{83} +7.64276i q^{85} +(-14.5793 + 1.21146i) q^{86} +(-2.02323 - 7.96636i) q^{88} -2.22575i q^{89} -1.05317 q^{91} +(-1.60275 + 0.268212i) q^{92} +(5.68148 - 0.472103i) q^{94} -3.67035 q^{95} -3.93019 q^{97} +(1.40936 - 0.117111i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 8q^{4} + O(q^{10}) \) \( 32q + 8q^{4} - 8q^{10} - 8q^{16} - 64q^{19} + 24q^{22} - 16q^{25} - 8q^{28} + 8q^{34} - 24q^{40} - 48q^{43} - 8q^{46} - 32q^{49} - 24q^{52} - 96q^{58} - 40q^{64} + 16q^{67} - 16q^{70} - 16q^{73} + 16q^{76} + 24q^{82} + 72q^{88} + 16q^{91} - 56q^{94} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40936 + 0.117111i −0.996565 + 0.0828097i
\(3\) 0 0
\(4\) 1.97257 0.330101i 0.986285 0.165051i
\(5\) 1.17792 0.526780 0.263390 0.964689i \(-0.415159\pi\)
0.263390 + 0.964689i \(0.415159\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) −2.74140 + 0.696239i −0.969230 + 0.246158i
\(9\) 0 0
\(10\) −1.66010 + 0.137947i −0.524971 + 0.0436225i
\(11\) 2.90595i 0.876176i 0.898932 + 0.438088i \(0.144344\pi\)
−0.898932 + 0.438088i \(0.855656\pi\)
\(12\) 0 0
\(13\) 1.05317i 0.292096i −0.989278 0.146048i \(-0.953345\pi\)
0.989278 0.146048i \(-0.0466554\pi\)
\(14\) 0.117111 + 1.40936i 0.0312991 + 0.376666i
\(15\) 0 0
\(16\) 3.78207 1.30230i 0.945517 0.325574i
\(17\) 6.48837i 1.57366i 0.617169 + 0.786830i \(0.288279\pi\)
−0.617169 + 0.786830i \(0.711721\pi\)
\(18\) 0 0
\(19\) −3.11597 −0.714853 −0.357426 0.933941i \(-0.616346\pi\)
−0.357426 + 0.933941i \(0.616346\pi\)
\(20\) 2.32352 0.388832i 0.519556 0.0869454i
\(21\) 0 0
\(22\) −0.340317 4.09552i −0.0725559 0.873167i
\(23\) −0.812516 −0.169421 −0.0847107 0.996406i \(-0.526997\pi\)
−0.0847107 + 0.996406i \(0.526997\pi\)
\(24\) 0 0
\(25\) −3.61251 −0.722503
\(26\) 0.123337 + 1.48429i 0.0241884 + 0.291093i
\(27\) 0 0
\(28\) −0.330101 1.97257i −0.0623832 0.372781i
\(29\) −4.03607 −0.749480 −0.374740 0.927130i \(-0.622268\pi\)
−0.374740 + 0.927130i \(0.622268\pi\)
\(30\) 0 0
\(31\) 0.108779i 0.0195372i −0.999952 0.00976861i \(-0.996891\pi\)
0.999952 0.00976861i \(-0.00310949\pi\)
\(32\) −5.17777 + 2.27832i −0.915308 + 0.402754i
\(33\) 0 0
\(34\) −0.759857 9.14442i −0.130314 1.56826i
\(35\) 1.17792i 0.199104i
\(36\) 0 0
\(37\) 9.97034i 1.63911i 0.572998 + 0.819557i \(0.305780\pi\)
−0.572998 + 0.819557i \(0.694220\pi\)
\(38\) 4.39151 0.364913i 0.712397 0.0591967i
\(39\) 0 0
\(40\) −3.22914 + 0.820111i −0.510571 + 0.129671i
\(41\) 9.44298i 1.47475i 0.675486 + 0.737373i \(0.263934\pi\)
−0.675486 + 0.737373i \(0.736066\pi\)
\(42\) 0 0
\(43\) 10.3446 1.57754 0.788770 0.614688i \(-0.210718\pi\)
0.788770 + 0.614688i \(0.210718\pi\)
\(44\) 0.959257 + 5.73219i 0.144613 + 0.864160i
\(45\) 0 0
\(46\) 1.14512 0.0951542i 0.168839 0.0140297i
\(47\) −4.03126 −0.588019 −0.294010 0.955802i \(-0.594990\pi\)
−0.294010 + 0.955802i \(0.594990\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 5.09132 0.423064i 0.720021 0.0598302i
\(51\) 0 0
\(52\) −0.347652 2.07745i −0.0482106 0.288090i
\(53\) −2.97772 −0.409022 −0.204511 0.978864i \(-0.565560\pi\)
−0.204511 + 0.978864i \(0.565560\pi\)
\(54\) 0 0
\(55\) 3.42296i 0.461552i
\(56\) 0.696239 + 2.74140i 0.0930388 + 0.366334i
\(57\) 0 0
\(58\) 5.68827 0.472667i 0.746906 0.0620642i
\(59\) 0.868874i 0.113118i 0.998399 + 0.0565589i \(0.0180129\pi\)
−0.998399 + 0.0565589i \(0.981987\pi\)
\(60\) 0 0
\(61\) 5.33629i 0.683242i −0.939838 0.341621i \(-0.889024\pi\)
0.939838 0.341621i \(-0.110976\pi\)
\(62\) 0.0127391 + 0.153308i 0.00161787 + 0.0194701i
\(63\) 0 0
\(64\) 7.03050 3.81733i 0.878813 0.477167i
\(65\) 1.24054i 0.153870i
\(66\) 0 0
\(67\) −3.97987 −0.486218 −0.243109 0.969999i \(-0.578167\pi\)
−0.243109 + 0.969999i \(0.578167\pi\)
\(68\) 2.14182 + 12.7988i 0.259734 + 1.55208i
\(69\) 0 0
\(70\) 0.137947 + 1.66010i 0.0164878 + 0.198420i
\(71\) 0.844302 0.100200 0.0501001 0.998744i \(-0.484046\pi\)
0.0501001 + 0.998744i \(0.484046\pi\)
\(72\) 0 0
\(73\) 3.59513 0.420778 0.210389 0.977618i \(-0.432527\pi\)
0.210389 + 0.977618i \(0.432527\pi\)
\(74\) −1.16763 14.0518i −0.135734 1.63348i
\(75\) 0 0
\(76\) −6.14647 + 1.02859i −0.705048 + 0.117987i
\(77\) 2.90595 0.331164
\(78\) 0 0
\(79\) 9.48320i 1.06694i −0.845818 0.533472i \(-0.820887\pi\)
0.845818 0.533472i \(-0.179113\pi\)
\(80\) 4.45496 1.53400i 0.498080 0.171506i
\(81\) 0 0
\(82\) −1.10587 13.3085i −0.122123 1.46968i
\(83\) 2.71280i 0.297769i −0.988855 0.148884i \(-0.952432\pi\)
0.988855 0.148884i \(-0.0475682\pi\)
\(84\) 0 0
\(85\) 7.64276i 0.828973i
\(86\) −14.5793 + 1.21146i −1.57212 + 0.130636i
\(87\) 0 0
\(88\) −2.02323 7.96636i −0.215678 0.849216i
\(89\) 2.22575i 0.235930i −0.993018 0.117965i \(-0.962363\pi\)
0.993018 0.117965i \(-0.0376370\pi\)
\(90\) 0 0
\(91\) −1.05317 −0.110402
\(92\) −1.60275 + 0.268212i −0.167098 + 0.0279631i
\(93\) 0 0
\(94\) 5.68148 0.472103i 0.586000 0.0486937i
\(95\) −3.67035 −0.376570
\(96\) 0 0
\(97\) −3.93019 −0.399050 −0.199525 0.979893i \(-0.563940\pi\)
−0.199525 + 0.979893i \(0.563940\pi\)
\(98\) 1.40936 0.117111i 0.142366 0.0118300i
\(99\) 0 0
\(100\) −7.12593 + 1.19249i −0.712593 + 0.119249i
\(101\) 18.0700 1.79803 0.899016 0.437915i \(-0.144283\pi\)
0.899016 + 0.437915i \(0.144283\pi\)
\(102\) 0 0
\(103\) 17.8616i 1.75995i 0.475017 + 0.879977i \(0.342442\pi\)
−0.475017 + 0.879977i \(0.657558\pi\)
\(104\) 0.733256 + 2.88715i 0.0719016 + 0.283108i
\(105\) 0 0
\(106\) 4.19667 0.348723i 0.407617 0.0338709i
\(107\) 7.67720i 0.742183i −0.928596 0.371091i \(-0.878984\pi\)
0.928596 0.371091i \(-0.121016\pi\)
\(108\) 0 0
\(109\) 12.6991i 1.21635i 0.793801 + 0.608177i \(0.208099\pi\)
−0.793801 + 0.608177i \(0.791901\pi\)
\(110\) −0.400865 4.82418i −0.0382210 0.459967i
\(111\) 0 0
\(112\) −1.30230 3.78207i −0.123055 0.357372i
\(113\) 15.4017i 1.44887i 0.689342 + 0.724437i \(0.257900\pi\)
−0.689342 + 0.724437i \(0.742100\pi\)
\(114\) 0 0
\(115\) −0.957076 −0.0892478
\(116\) −7.96144 + 1.33231i −0.739201 + 0.123702i
\(117\) 0 0
\(118\) −0.101754 1.22455i −0.00936725 0.112729i
\(119\) 6.48837 0.594788
\(120\) 0 0
\(121\) 2.55546 0.232315
\(122\) 0.624936 + 7.52074i 0.0565791 + 0.680896i
\(123\) 0 0
\(124\) −0.0359079 0.214573i −0.00322463 0.0192693i
\(125\) −10.1448 −0.907380
\(126\) 0 0
\(127\) 17.1514i 1.52194i 0.648787 + 0.760970i \(0.275276\pi\)
−0.648787 + 0.760970i \(0.724724\pi\)
\(128\) −9.46143 + 6.20333i −0.836280 + 0.548302i
\(129\) 0 0
\(130\) 0.145281 + 1.74837i 0.0127420 + 0.153342i
\(131\) 10.5118i 0.918421i −0.888328 0.459210i \(-0.848132\pi\)
0.888328 0.459210i \(-0.151868\pi\)
\(132\) 0 0
\(133\) 3.11597i 0.270189i
\(134\) 5.60905 0.466084i 0.484548 0.0402636i
\(135\) 0 0
\(136\) −4.51745 17.7872i −0.387369 1.52524i
\(137\) 13.6268i 1.16422i 0.813110 + 0.582110i \(0.197773\pi\)
−0.813110 + 0.582110i \(0.802227\pi\)
\(138\) 0 0
\(139\) −5.37620 −0.456003 −0.228002 0.973661i \(-0.573219\pi\)
−0.228002 + 0.973661i \(0.573219\pi\)
\(140\) −0.388832 2.32352i −0.0328623 0.196374i
\(141\) 0 0
\(142\) −1.18992 + 0.0988767i −0.0998560 + 0.00829755i
\(143\) 3.06045 0.255928
\(144\) 0 0
\(145\) −4.75416 −0.394811
\(146\) −5.06681 + 0.421027i −0.419332 + 0.0348445i
\(147\) 0 0
\(148\) 3.29122 + 19.6672i 0.270537 + 1.61663i
\(149\) −17.3187 −1.41880 −0.709401 0.704805i \(-0.751035\pi\)
−0.709401 + 0.704805i \(0.751035\pi\)
\(150\) 0 0
\(151\) 4.50773i 0.366834i 0.983035 + 0.183417i \(0.0587158\pi\)
−0.983035 + 0.183417i \(0.941284\pi\)
\(152\) 8.54211 2.16946i 0.692856 0.175966i
\(153\) 0 0
\(154\) −4.09552 + 0.340317i −0.330026 + 0.0274236i
\(155\) 0.128132i 0.0102918i
\(156\) 0 0
\(157\) 8.84696i 0.706064i 0.935611 + 0.353032i \(0.114849\pi\)
−0.935611 + 0.353032i \(0.885151\pi\)
\(158\) 1.11058 + 13.3652i 0.0883533 + 1.06328i
\(159\) 0 0
\(160\) −6.09898 + 2.68367i −0.482166 + 0.212163i
\(161\) 0.812516i 0.0640352i
\(162\) 0 0
\(163\) −8.38238 −0.656558 −0.328279 0.944581i \(-0.606469\pi\)
−0.328279 + 0.944581i \(0.606469\pi\)
\(164\) 3.11714 + 18.6269i 0.243408 + 1.45452i
\(165\) 0 0
\(166\) 0.317698 + 3.82331i 0.0246582 + 0.296746i
\(167\) 8.93563 0.691460 0.345730 0.938334i \(-0.387631\pi\)
0.345730 + 0.938334i \(0.387631\pi\)
\(168\) 0 0
\(169\) 11.8908 0.914680
\(170\) −0.895048 10.7714i −0.0686470 0.826126i
\(171\) 0 0
\(172\) 20.4055 3.41477i 1.55590 0.260374i
\(173\) −14.1612 −1.07666 −0.538328 0.842736i \(-0.680944\pi\)
−0.538328 + 0.842736i \(0.680944\pi\)
\(174\) 0 0
\(175\) 3.61251i 0.273080i
\(176\) 3.78440 + 10.9905i 0.285260 + 0.828439i
\(177\) 0 0
\(178\) 0.260659 + 3.13688i 0.0195373 + 0.235119i
\(179\) 20.3695i 1.52249i −0.648467 0.761243i \(-0.724589\pi\)
0.648467 0.761243i \(-0.275411\pi\)
\(180\) 0 0
\(181\) 18.2659i 1.35770i 0.734279 + 0.678848i \(0.237520\pi\)
−0.734279 + 0.678848i \(0.762480\pi\)
\(182\) 1.48429 0.123337i 0.110023 0.00914235i
\(183\) 0 0
\(184\) 2.22743 0.565705i 0.164208 0.0417044i
\(185\) 11.7442i 0.863453i
\(186\) 0 0
\(187\) −18.8549 −1.37880
\(188\) −7.95194 + 1.33072i −0.579955 + 0.0970529i
\(189\) 0 0
\(190\) 5.17283 0.429837i 0.375277 0.0311837i
\(191\) −7.83849 −0.567173 −0.283587 0.958947i \(-0.591524\pi\)
−0.283587 + 0.958947i \(0.591524\pi\)
\(192\) 0 0
\(193\) −13.0241 −0.937498 −0.468749 0.883331i \(-0.655295\pi\)
−0.468749 + 0.883331i \(0.655295\pi\)
\(194\) 5.53903 0.460266i 0.397679 0.0330452i
\(195\) 0 0
\(196\) −1.97257 + 0.330101i −0.140898 + 0.0235786i
\(197\) 14.9576 1.06568 0.532842 0.846215i \(-0.321124\pi\)
0.532842 + 0.846215i \(0.321124\pi\)
\(198\) 0 0
\(199\) 16.9147i 1.19905i 0.800356 + 0.599525i \(0.204644\pi\)
−0.800356 + 0.599525i \(0.795356\pi\)
\(200\) 9.90333 2.51517i 0.700271 0.177850i
\(201\) 0 0
\(202\) −25.4671 + 2.11619i −1.79186 + 0.148895i
\(203\) 4.03607i 0.283277i
\(204\) 0 0
\(205\) 11.1230i 0.776867i
\(206\) −2.09178 25.1733i −0.145741 1.75391i
\(207\) 0 0
\(208\) −1.37153 3.98315i −0.0950988 0.276182i
\(209\) 9.05485i 0.626337i
\(210\) 0 0
\(211\) 5.68386 0.391293 0.195647 0.980674i \(-0.437319\pi\)
0.195647 + 0.980674i \(0.437319\pi\)
\(212\) −5.87376 + 0.982949i −0.403412 + 0.0675092i
\(213\) 0 0
\(214\) 0.899081 + 10.8199i 0.0614599 + 0.739633i
\(215\) 12.1851 0.831017
\(216\) 0 0
\(217\) −0.108779 −0.00738437
\(218\) −1.48720 17.8976i −0.100726 1.21218i
\(219\) 0 0
\(220\) 1.12992 + 6.75204i 0.0761795 + 0.455222i
\(221\) 6.83333 0.459660
\(222\) 0 0
\(223\) 3.43963i 0.230335i −0.993346 0.115167i \(-0.963260\pi\)
0.993346 0.115167i \(-0.0367404\pi\)
\(224\) 2.27832 + 5.17777i 0.152227 + 0.345954i
\(225\) 0 0
\(226\) −1.80371 21.7065i −0.119981 1.44390i
\(227\) 8.86522i 0.588406i −0.955743 0.294203i \(-0.904946\pi\)
0.955743 0.294203i \(-0.0950541\pi\)
\(228\) 0 0
\(229\) 17.3653i 1.14753i −0.819019 0.573767i \(-0.805482\pi\)
0.819019 0.573767i \(-0.194518\pi\)
\(230\) 1.34886 0.112084i 0.0889413 0.00739058i
\(231\) 0 0
\(232\) 11.0645 2.81007i 0.726418 0.184490i
\(233\) 9.99149i 0.654564i 0.944927 + 0.327282i \(0.106133\pi\)
−0.944927 + 0.327282i \(0.893867\pi\)
\(234\) 0 0
\(235\) −4.74848 −0.309757
\(236\) 0.286816 + 1.71392i 0.0186702 + 0.111566i
\(237\) 0 0
\(238\) −9.14442 + 0.759857i −0.592745 + 0.0492542i
\(239\) −24.5708 −1.58935 −0.794677 0.607032i \(-0.792360\pi\)
−0.794677 + 0.607032i \(0.792360\pi\)
\(240\) 0 0
\(241\) 23.1786 1.49306 0.746532 0.665349i \(-0.231717\pi\)
0.746532 + 0.665349i \(0.231717\pi\)
\(242\) −3.60156 + 0.299272i −0.231517 + 0.0192379i
\(243\) 0 0
\(244\) −1.76152 10.5262i −0.112769 0.673872i
\(245\) −1.17792 −0.0752543
\(246\) 0 0
\(247\) 3.28164i 0.208806i
\(248\) 0.0757359 + 0.298205i 0.00480924 + 0.0189361i
\(249\) 0 0
\(250\) 14.2977 1.18807i 0.904264 0.0751399i
\(251\) 21.3670i 1.34868i −0.738423 0.674338i \(-0.764429\pi\)
0.738423 0.674338i \(-0.235571\pi\)
\(252\) 0 0
\(253\) 2.36113i 0.148443i
\(254\) −2.00861 24.1724i −0.126031 1.51671i
\(255\) 0 0
\(256\) 12.6081 9.85073i 0.788003 0.615671i
\(257\) 29.5594i 1.84386i 0.387352 + 0.921932i \(0.373390\pi\)
−0.387352 + 0.921932i \(0.626610\pi\)
\(258\) 0 0
\(259\) 9.97034 0.619527
\(260\) −0.409504 2.44706i −0.0253964 0.151760i
\(261\) 0 0
\(262\) 1.23104 + 14.8149i 0.0760542 + 0.915266i
\(263\) 15.8001 0.974277 0.487139 0.873325i \(-0.338041\pi\)
0.487139 + 0.873325i \(0.338041\pi\)
\(264\) 0 0
\(265\) −3.50751 −0.215464
\(266\) −0.364913 4.39151i −0.0223743 0.269261i
\(267\) 0 0
\(268\) −7.85056 + 1.31376i −0.479550 + 0.0802505i
\(269\) 6.41502 0.391131 0.195565 0.980691i \(-0.437346\pi\)
0.195565 + 0.980691i \(0.437346\pi\)
\(270\) 0 0
\(271\) 0.0927686i 0.00563529i −0.999996 0.00281765i \(-0.999103\pi\)
0.999996 0.00281765i \(-0.000896886\pi\)
\(272\) 8.44977 + 24.5394i 0.512343 + 1.48792i
\(273\) 0 0
\(274\) −1.59585 19.2051i −0.0964087 1.16022i
\(275\) 10.4978i 0.633040i
\(276\) 0 0
\(277\) 19.7900i 1.18907i −0.804071 0.594534i \(-0.797337\pi\)
0.804071 0.594534i \(-0.202663\pi\)
\(278\) 7.57698 0.629610i 0.454437 0.0377615i
\(279\) 0 0
\(280\) 0.820111 + 3.22914i 0.0490110 + 0.192978i
\(281\) 14.4404i 0.861443i −0.902485 0.430721i \(-0.858259\pi\)
0.902485 0.430721i \(-0.141741\pi\)
\(282\) 0 0
\(283\) 20.3759 1.21122 0.605612 0.795760i \(-0.292929\pi\)
0.605612 + 0.795760i \(0.292929\pi\)
\(284\) 1.66544 0.278705i 0.0988259 0.0165381i
\(285\) 0 0
\(286\) −4.31326 + 0.358411i −0.255049 + 0.0211933i
\(287\) 9.44298 0.557402
\(288\) 0 0
\(289\) −25.0989 −1.47641
\(290\) 6.70030 0.556762i 0.393455 0.0326942i
\(291\) 0 0
\(292\) 7.09164 1.18675i 0.415007 0.0694496i
\(293\) −10.2919 −0.601262 −0.300631 0.953741i \(-0.597197\pi\)
−0.300631 + 0.953741i \(0.597197\pi\)
\(294\) 0 0
\(295\) 1.02346i 0.0595882i
\(296\) −6.94174 27.3326i −0.403480 1.58868i
\(297\) 0 0
\(298\) 24.4082 2.02820i 1.41393 0.117491i
\(299\) 0.855715i 0.0494873i
\(300\) 0 0
\(301\) 10.3446i 0.596254i
\(302\) −0.527903 6.35300i −0.0303774 0.365574i
\(303\) 0 0
\(304\) −11.7848 + 4.05791i −0.675905 + 0.232737i
\(305\) 6.28571i 0.359919i
\(306\) 0 0
\(307\) 19.8799 1.13461 0.567304 0.823508i \(-0.307986\pi\)
0.567304 + 0.823508i \(0.307986\pi\)
\(308\) 5.73219 0.959257i 0.326622 0.0546587i
\(309\) 0 0
\(310\) 0.0150056 + 0.180584i 0.000852263 + 0.0102565i
\(311\) 7.94464 0.450499 0.225250 0.974301i \(-0.427680\pi\)
0.225250 + 0.974301i \(0.427680\pi\)
\(312\) 0 0
\(313\) −28.2451 −1.59651 −0.798254 0.602321i \(-0.794243\pi\)
−0.798254 + 0.602321i \(0.794243\pi\)
\(314\) −1.03607 12.4685i −0.0584689 0.703639i
\(315\) 0 0
\(316\) −3.13042 18.7063i −0.176100 1.05231i
\(317\) −13.8609 −0.778506 −0.389253 0.921131i \(-0.627267\pi\)
−0.389253 + 0.921131i \(0.627267\pi\)
\(318\) 0 0
\(319\) 11.7286i 0.656677i
\(320\) 8.28135 4.49650i 0.462941 0.251362i
\(321\) 0 0
\(322\) −0.0951542 1.14512i −0.00530274 0.0638153i
\(323\) 20.2176i 1.12494i
\(324\) 0 0
\(325\) 3.80458i 0.211040i
\(326\) 11.8138 0.981665i 0.654303 0.0543694i
\(327\) 0 0
\(328\) −6.57457 25.8869i −0.363020 1.42937i
\(329\) 4.03126i 0.222250i
\(330\) 0 0
\(331\) −14.5450 −0.799468 −0.399734 0.916631i \(-0.630897\pi\)
−0.399734 + 0.916631i \(0.630897\pi\)
\(332\) −0.895500 5.35120i −0.0491469 0.293685i
\(333\) 0 0
\(334\) −12.5935 + 1.04646i −0.689085 + 0.0572596i
\(335\) −4.68795 −0.256130
\(336\) 0 0
\(337\) 5.26170 0.286623 0.143312 0.989678i \(-0.454225\pi\)
0.143312 + 0.989678i \(0.454225\pi\)
\(338\) −16.7584 + 1.39254i −0.911538 + 0.0757444i
\(339\) 0 0
\(340\) 2.52288 + 15.0759i 0.136823 + 0.817604i
\(341\) 0.316105 0.0171181
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −28.3587 + 7.20233i −1.52900 + 0.388324i
\(345\) 0 0
\(346\) 19.9582 1.65843i 1.07296 0.0891575i
\(347\) 15.5549i 0.835029i −0.908670 0.417514i \(-0.862901\pi\)
0.908670 0.417514i \(-0.137099\pi\)
\(348\) 0 0
\(349\) 17.1607i 0.918594i −0.888283 0.459297i \(-0.848101\pi\)
0.888283 0.459297i \(-0.151899\pi\)
\(350\) −0.423064 5.09132i −0.0226137 0.272142i
\(351\) 0 0
\(352\) −6.62067 15.0463i −0.352883 0.801972i
\(353\) 15.5438i 0.827314i −0.910433 0.413657i \(-0.864251\pi\)
0.910433 0.413657i \(-0.135749\pi\)
\(354\) 0 0
\(355\) 0.994517 0.0527835
\(356\) −0.734724 4.39046i −0.0389403 0.232694i
\(357\) 0 0
\(358\) 2.38548 + 28.7078i 0.126077 + 1.51726i
\(359\) −14.9471 −0.788876 −0.394438 0.918923i \(-0.629061\pi\)
−0.394438 + 0.918923i \(0.629061\pi\)
\(360\) 0 0
\(361\) −9.29073 −0.488986
\(362\) −2.13913 25.7432i −0.112430 1.35303i
\(363\) 0 0
\(364\) −2.07745 + 0.347652i −0.108888 + 0.0182219i
\(365\) 4.23476 0.221657
\(366\) 0 0
\(367\) 2.86184i 0.149387i 0.997207 + 0.0746934i \(0.0237978\pi\)
−0.997207 + 0.0746934i \(0.976202\pi\)
\(368\) −3.07299 + 1.05814i −0.160191 + 0.0551591i
\(369\) 0 0
\(370\) −1.37537 16.5518i −0.0715023 0.860487i
\(371\) 2.97772i 0.154596i
\(372\) 0 0
\(373\) 20.7327i 1.07350i −0.843743 0.536748i \(-0.819653\pi\)
0.843743 0.536748i \(-0.180347\pi\)
\(374\) 26.5732 2.20810i 1.37407 0.114178i
\(375\) 0 0
\(376\) 11.0513 2.80672i 0.569926 0.144745i
\(377\) 4.25066i 0.218920i
\(378\) 0 0
\(379\) 28.1561 1.44628 0.723141 0.690700i \(-0.242698\pi\)
0.723141 + 0.690700i \(0.242698\pi\)
\(380\) −7.24003 + 1.21159i −0.371406 + 0.0621531i
\(381\) 0 0
\(382\) 11.0472 0.917970i 0.565225 0.0469675i
\(383\) 29.9733 1.53156 0.765781 0.643101i \(-0.222352\pi\)
0.765781 + 0.643101i \(0.222352\pi\)
\(384\) 0 0
\(385\) 3.42296 0.174450
\(386\) 18.3556 1.52526i 0.934278 0.0776339i
\(387\) 0 0
\(388\) −7.75257 + 1.29736i −0.393577 + 0.0658634i
\(389\) 29.4931 1.49536 0.747679 0.664060i \(-0.231168\pi\)
0.747679 + 0.664060i \(0.231168\pi\)
\(390\) 0 0
\(391\) 5.27190i 0.266612i
\(392\) 2.74140 0.696239i 0.138461 0.0351654i
\(393\) 0 0
\(394\) −21.0806 + 1.75169i −1.06202 + 0.0882489i
\(395\) 11.1704i 0.562045i
\(396\) 0 0
\(397\) 22.0845i 1.10839i 0.832386 + 0.554196i \(0.186974\pi\)
−0.832386 + 0.554196i \(0.813026\pi\)
\(398\) −1.98089 23.8388i −0.0992930 1.19493i
\(399\) 0 0
\(400\) −13.6628 + 4.70456i −0.683138 + 0.235228i
\(401\) 7.42054i 0.370564i 0.982685 + 0.185282i \(0.0593198\pi\)
−0.982685 + 0.185282i \(0.940680\pi\)
\(402\) 0 0
\(403\) −0.114562 −0.00570674
\(404\) 35.6443 5.96493i 1.77337 0.296766i
\(405\) 0 0
\(406\) −0.472667 5.68827i −0.0234581 0.282304i
\(407\) −28.9733 −1.43615
\(408\) 0 0
\(409\) 37.3983 1.84923 0.924615 0.380904i \(-0.124387\pi\)
0.924615 + 0.380904i \(0.124387\pi\)
\(410\) −1.30263 15.6763i −0.0643321 0.774199i
\(411\) 0 0
\(412\) 5.89612 + 35.2332i 0.290481 + 1.73582i
\(413\) 0.868874 0.0427545
\(414\) 0 0
\(415\) 3.19546i 0.156859i
\(416\) 2.39945 + 5.45305i 0.117643 + 0.267358i
\(417\) 0 0
\(418\) 1.06042 + 12.7615i 0.0518668 + 0.624186i
\(419\) 8.55960i 0.418164i −0.977898 0.209082i \(-0.932952\pi\)
0.977898 0.209082i \(-0.0670475\pi\)
\(420\) 0 0
\(421\) 6.56688i 0.320050i 0.987113 + 0.160025i \(0.0511575\pi\)
−0.987113 + 0.160025i \(0.948842\pi\)
\(422\) −8.01059 + 0.665640i −0.389949 + 0.0324029i
\(423\) 0 0
\(424\) 8.16311 2.07321i 0.396436 0.100684i
\(425\) 23.4393i 1.13697i
\(426\) 0 0
\(427\) −5.33629 −0.258241
\(428\) −2.53425 15.1438i −0.122498 0.732004i
\(429\) 0 0
\(430\) −17.1731 + 1.42700i −0.828163 + 0.0688163i
\(431\) 5.61014 0.270231 0.135116 0.990830i \(-0.456859\pi\)
0.135116 + 0.990830i \(0.456859\pi\)
\(432\) 0 0
\(433\) 7.96675 0.382857 0.191429 0.981507i \(-0.438688\pi\)
0.191429 + 0.981507i \(0.438688\pi\)
\(434\) 0.153308 0.0127391i 0.00735901 0.000611498i
\(435\) 0 0
\(436\) 4.19199 + 25.0499i 0.200760 + 1.19967i
\(437\) 2.53178 0.121111
\(438\) 0 0
\(439\) 33.9176i 1.61880i −0.587258 0.809400i \(-0.699792\pi\)
0.587258 0.809400i \(-0.300208\pi\)
\(440\) −2.38320 9.38370i −0.113615 0.447350i
\(441\) 0 0
\(442\) −9.63060 + 0.800256i −0.458081 + 0.0380643i
\(443\) 6.31862i 0.300207i −0.988670 0.150103i \(-0.952039\pi\)
0.988670 0.150103i \(-0.0479606\pi\)
\(444\) 0 0
\(445\) 2.62175i 0.124283i
\(446\) 0.402817 + 4.84767i 0.0190740 + 0.229544i
\(447\) 0 0
\(448\) −3.81733 7.03050i −0.180352 0.332160i
\(449\) 11.9562i 0.564246i 0.959378 + 0.282123i \(0.0910387\pi\)
−0.959378 + 0.282123i \(0.908961\pi\)
\(450\) 0 0
\(451\) −27.4408 −1.29214
\(452\) 5.08413 + 30.3810i 0.239137 + 1.42900i
\(453\) 0 0
\(454\) 1.03821 + 12.4943i 0.0487257 + 0.586385i
\(455\) −1.24054 −0.0581575
\(456\) 0 0
\(457\) 10.7774 0.504144 0.252072 0.967708i \(-0.418888\pi\)
0.252072 + 0.967708i \(0.418888\pi\)
\(458\) 2.03366 + 24.4739i 0.0950269 + 1.14359i
\(459\) 0 0
\(460\) −1.88790 + 0.315932i −0.0880238 + 0.0147304i
\(461\) −2.36887 −0.110329 −0.0551647 0.998477i \(-0.517568\pi\)
−0.0551647 + 0.998477i \(0.517568\pi\)
\(462\) 0 0
\(463\) 38.4537i 1.78709i −0.448969 0.893547i \(-0.648209\pi\)
0.448969 0.893547i \(-0.351791\pi\)
\(464\) −15.2647 + 5.25616i −0.708646 + 0.244011i
\(465\) 0 0
\(466\) −1.17011 14.0816i −0.0542043 0.652316i
\(467\) 5.09381i 0.235713i −0.993031 0.117857i \(-0.962398\pi\)
0.993031 0.117857i \(-0.0376023\pi\)
\(468\) 0 0
\(469\) 3.97987i 0.183773i
\(470\) 6.69231 0.556098i 0.308693 0.0256509i
\(471\) 0 0
\(472\) −0.604944 2.38193i −0.0278448 0.109637i
\(473\) 30.0609i 1.38220i
\(474\) 0 0
\(475\) 11.2565 0.516483
\(476\) 12.7988 2.14182i 0.586630 0.0981701i
\(477\) 0 0
\(478\) 34.6291 2.87750i 1.58390 0.131614i
\(479\) 20.8166 0.951137 0.475568 0.879679i \(-0.342242\pi\)
0.475568 + 0.879679i \(0.342242\pi\)
\(480\) 0 0
\(481\) 10.5004 0.478778
\(482\) −32.6669 + 2.71446i −1.48794 + 0.123640i
\(483\) 0 0
\(484\) 5.04083 0.843561i 0.229129 0.0383437i
\(485\) −4.62943 −0.210212
\(486\) 0 0
\(487\) 26.1716i 1.18595i 0.805222 + 0.592973i \(0.202046\pi\)
−0.805222 + 0.592973i \(0.797954\pi\)
\(488\) 3.71533 + 14.6289i 0.168185 + 0.662219i
\(489\) 0 0
\(490\) 1.66010 0.137947i 0.0749959 0.00623179i
\(491\) 27.7686i 1.25318i −0.779349 0.626590i \(-0.784450\pi\)
0.779349 0.626590i \(-0.215550\pi\)
\(492\) 0 0
\(493\) 26.1875i 1.17943i
\(494\) −0.384314 4.62499i −0.0172911 0.208088i
\(495\) 0 0
\(496\) −0.141662 0.411408i −0.00636081 0.0184728i
\(497\) 0.844302i 0.0378721i
\(498\) 0 0
\(499\) −13.7781 −0.616791 −0.308395 0.951258i \(-0.599792\pi\)
−0.308395 + 0.951258i \(0.599792\pi\)
\(500\) −20.0114 + 3.34882i −0.894936 + 0.149764i
\(501\) 0 0
\(502\) 2.50231 + 30.1138i 0.111683 + 1.34404i
\(503\) −32.5875 −1.45300 −0.726502 0.687165i \(-0.758855\pi\)
−0.726502 + 0.687165i \(0.758855\pi\)
\(504\) 0 0
\(505\) 21.2850 0.947168
\(506\) 0.276513 + 3.32767i 0.0122925 + 0.147933i
\(507\) 0 0
\(508\) 5.66169 + 33.8323i 0.251197 + 1.50107i
\(509\) 17.1161 0.758657 0.379328 0.925262i \(-0.376155\pi\)
0.379328 + 0.925262i \(0.376155\pi\)
\(510\) 0 0
\(511\) 3.59513i 0.159039i
\(512\) −16.6156 + 15.3597i −0.734313 + 0.678811i
\(513\) 0 0
\(514\) −3.46172 41.6597i −0.152690 1.83753i
\(515\) 21.0394i 0.927109i
\(516\) 0 0
\(517\) 11.7146i 0.515209i
\(518\) −14.0518 + 1.16763i −0.617399 + 0.0513028i
\(519\) 0 0
\(520\) 0.863714 + 3.40082i 0.0378764 + 0.149136i
\(521\) 22.6308i 0.991471i 0.868473 + 0.495736i \(0.165102\pi\)
−0.868473 + 0.495736i \(0.834898\pi\)
\(522\) 0 0
\(523\) −19.0252 −0.831914 −0.415957 0.909384i \(-0.636553\pi\)
−0.415957 + 0.909384i \(0.636553\pi\)
\(524\) −3.46996 20.7353i −0.151586 0.905825i
\(525\) 0 0
\(526\) −22.2680 + 1.85036i −0.970931 + 0.0806796i
\(527\) 0.705796 0.0307450
\(528\) 0 0
\(529\) −22.3398 −0.971296
\(530\) 4.94333 0.410766i 0.214724 0.0178425i
\(531\) 0 0
\(532\) 1.02859 + 6.14647i 0.0445948 + 0.266483i
\(533\) 9.94503 0.430767
\(534\) 0 0
\(535\) 9.04310i 0.390967i
\(536\) 10.9104 2.77094i 0.471257 0.119686i
\(537\) 0 0
\(538\) −9.04105 + 0.751267i −0.389787 + 0.0323894i
\(539\) 2.90595i 0.125168i
\(540\) 0 0
\(541\) 17.3996i 0.748066i −0.927415 0.374033i \(-0.877975\pi\)
0.927415 0.374033i \(-0.122025\pi\)
\(542\) 0.0108642 + 0.130744i 0.000466657 + 0.00561594i
\(543\) 0 0
\(544\) −14.7826 33.5953i −0.633797 1.44038i
\(545\) 14.9585i 0.640751i
\(546\) 0 0
\(547\) 4.96571 0.212318 0.106159 0.994349i \(-0.466145\pi\)
0.106159 + 0.994349i \(0.466145\pi\)
\(548\) 4.49824 + 26.8799i 0.192155 + 1.14825i
\(549\) 0 0
\(550\) 1.22940 + 14.7951i 0.0524218 + 0.630865i
\(551\) 12.5763 0.535768
\(552\) 0 0
\(553\) −9.48320 −0.403267
\(554\) 2.31762 + 27.8912i 0.0984663 + 1.18498i
\(555\) 0 0
\(556\) −10.6049 + 1.77469i −0.449749 + 0.0752635i
\(557\) 5.67400 0.240415 0.120208 0.992749i \(-0.461644\pi\)
0.120208 + 0.992749i \(0.461644\pi\)
\(558\) 0 0
\(559\) 10.8946i 0.460793i
\(560\) −1.53400 4.45496i −0.0648231 0.188256i
\(561\) 0 0
\(562\) 1.69113 + 20.3517i 0.0713358 + 0.858484i
\(563\) 25.4752i 1.07365i −0.843693 0.536826i \(-0.819623\pi\)
0.843693 0.536826i \(-0.180377\pi\)
\(564\) 0 0
\(565\) 18.1420i 0.763238i
\(566\) −28.7169 + 2.38624i −1.20706 + 0.100301i
\(567\) 0 0
\(568\) −2.31457 + 0.587836i −0.0971170 + 0.0246650i
\(569\) 19.5120i 0.817986i −0.912537 0.408993i \(-0.865880\pi\)
0.912537 0.408993i \(-0.134120\pi\)
\(570\) 0 0
\(571\) −38.0268 −1.59137 −0.795686 0.605709i \(-0.792889\pi\)
−0.795686 + 0.605709i \(0.792889\pi\)
\(572\) 6.03695 1.01026i 0.252418 0.0422410i
\(573\) 0 0
\(574\) −13.3085 + 1.10587i −0.555487 + 0.0461582i
\(575\) 2.93522 0.122407
\(576\) 0 0
\(577\) 5.32632 0.221738 0.110869 0.993835i \(-0.464637\pi\)
0.110869 + 0.993835i \(0.464637\pi\)
\(578\) 35.3733 2.93935i 1.47134 0.122261i
\(579\) 0 0
\(580\) −9.37791 + 1.56935i −0.389397 + 0.0651638i
\(581\) −2.71280 −0.112546
\(582\) 0 0
\(583\) 8.65311i 0.358375i
\(584\) −9.85566 + 2.50307i −0.407830 + 0.103578i
\(585\) 0 0
\(586\) 14.5050 1.20530i 0.599197 0.0497903i
\(587\) 25.6946i 1.06053i 0.847832 + 0.530265i \(0.177908\pi\)
−0.847832 + 0.530265i \(0.822092\pi\)
\(588\) 0 0
\(589\) 0.338951i 0.0139662i
\(590\) −0.119858 1.44242i −0.00493448 0.0593836i
\(591\) 0 0
\(592\) 12.9843 + 37.7085i 0.533652 + 1.54981i
\(593\) 35.9249i 1.47526i 0.675205 + 0.737630i \(0.264055\pi\)
−0.675205 + 0.737630i \(0.735945\pi\)
\(594\) 0 0
\(595\) 7.64276 0.313322
\(596\) −34.1623 + 5.71692i −1.39934 + 0.234174i
\(597\) 0 0
\(598\) −0.100213 1.20601i −0.00409803 0.0493173i
\(599\) −8.08090 −0.330177 −0.165088 0.986279i \(-0.552791\pi\)
−0.165088 + 0.986279i \(0.552791\pi\)
\(600\) 0 0
\(601\) 39.0492 1.59285 0.796425 0.604738i \(-0.206722\pi\)
0.796425 + 0.604738i \(0.206722\pi\)
\(602\) 1.21146 + 14.5793i 0.0493756 + 0.594206i
\(603\) 0 0
\(604\) 1.48801 + 8.89181i 0.0605461 + 0.361803i
\(605\) 3.01012 0.122379
\(606\) 0 0
\(607\) 39.0636i 1.58554i −0.609519 0.792772i \(-0.708637\pi\)
0.609519 0.792772i \(-0.291363\pi\)
\(608\) 16.1338 7.09917i 0.654311 0.287909i
\(609\) 0 0
\(610\) 0.736123 + 8.85880i 0.0298047 + 0.358682i
\(611\) 4.24559i 0.171758i
\(612\) 0 0
\(613\) 27.0877i 1.09406i −0.837112 0.547031i \(-0.815758\pi\)
0.837112 0.547031i \(-0.184242\pi\)
\(614\) −28.0179 + 2.32815i −1.13071 + 0.0939566i
\(615\) 0 0
\(616\) −7.96636 + 2.02323i −0.320974 + 0.0815184i
\(617\) 10.2143i 0.411213i −0.978635 0.205607i \(-0.934083\pi\)
0.978635 0.205607i \(-0.0659167\pi\)
\(618\) 0 0
\(619\) 28.5400 1.14712 0.573560 0.819164i \(-0.305562\pi\)
0.573560 + 0.819164i \(0.305562\pi\)
\(620\) −0.0422966 0.252750i −0.00169867 0.0101507i
\(621\) 0 0
\(622\) −11.1968 + 0.930401i −0.448952 + 0.0373057i
\(623\) −2.22575 −0.0891730
\(624\) 0 0
\(625\) 6.11281 0.244512
\(626\) 39.8074 3.30780i 1.59102 0.132206i
\(627\) 0 0
\(628\) 2.92039 + 17.4512i 0.116536 + 0.696380i
\(629\) −64.6912 −2.57941
\(630\) 0 0
\(631\) 17.9037i 0.712734i 0.934346 + 0.356367i \(0.115985\pi\)
−0.934346 + 0.356367i \(0.884015\pi\)
\(632\) 6.60258 + 25.9972i 0.262636 + 1.03411i
\(633\) 0 0
\(634\) 19.5350 1.62326i 0.775832 0.0644679i
\(635\) 20.2029i 0.801728i
\(636\) 0 0
\(637\) 1.05317i 0.0417280i
\(638\) 1.37355 + 16.5298i 0.0543792 + 0.654421i
\(639\) 0 0
\(640\) −11.1448 + 7.30700i −0.440536 + 0.288835i
\(641\) 36.5576i 1.44394i −0.691925 0.721969i \(-0.743237\pi\)
0.691925 0.721969i \(-0.256763\pi\)
\(642\) 0 0
\(643\) 28.5306 1.12514 0.562568 0.826751i \(-0.309813\pi\)
0.562568 + 0.826751i \(0.309813\pi\)
\(644\) 0.268212 + 1.60275i 0.0105691 + 0.0631570i
\(645\) 0 0
\(646\) 2.36769 + 28.4938i 0.0931556 + 1.12107i
\(647\) −25.0326 −0.984134 −0.492067 0.870557i \(-0.663758\pi\)
−0.492067 + 0.870557i \(0.663758\pi\)
\(648\) 0 0
\(649\) −2.52490 −0.0991112
\(650\) −0.445556 5.36201i −0.0174762 0.210315i
\(651\) 0 0
\(652\) −16.5348 + 2.76703i −0.647554 + 0.108365i
\(653\) −43.1196 −1.68740 −0.843699 0.536816i \(-0.819627\pi\)
−0.843699 + 0.536816i \(0.819627\pi\)
\(654\) 0 0
\(655\) 12.3820i 0.483806i
\(656\) 12.2975 + 35.7140i 0.480139 + 1.39440i
\(657\) 0 0
\(658\) −0.472103 5.68148i −0.0184045 0.221487i
\(659\) 8.36352i 0.325796i 0.986643 + 0.162898i \(0.0520842\pi\)
−0.986643 + 0.162898i \(0.947916\pi\)
\(660\) 0 0
\(661\) 8.48754i 0.330127i 0.986283 + 0.165064i \(0.0527829\pi\)
−0.986283 + 0.165064i \(0.947217\pi\)
\(662\) 20.4991 1.70338i 0.796722 0.0662037i
\(663\) 0 0
\(664\) 1.88876 + 7.43687i 0.0732981 + 0.288607i
\(665\) 3.67035i 0.142330i
\(666\) 0 0
\(667\) 3.27937 0.126978
\(668\) 17.6262 2.94966i 0.681977 0.114126i
\(669\) 0 0
\(670\) 6.60699 0.549009i 0.255250 0.0212100i
\(671\) 15.5070 0.598641
\(672\) 0 0
\(673\) −25.4287 −0.980206 −0.490103 0.871664i \(-0.663041\pi\)
−0.490103 + 0.871664i \(0.663041\pi\)
\(674\) −7.41562 + 0.616201i −0.285639 + 0.0237352i
\(675\) 0 0
\(676\) 23.4555 3.92518i 0.902135 0.150968i
\(677\) −17.0820 −0.656515 −0.328258 0.944588i \(-0.606461\pi\)
−0.328258 + 0.944588i \(0.606461\pi\)
\(678\) 0 0
\(679\) 3.93019i 0.150827i
\(680\) −5.32118 20.9518i −0.204058 0.803466i
\(681\) 0 0
\(682\) −0.445505 + 0.0370193i −0.0170593 + 0.00141754i
\(683\) 44.0552i 1.68573i 0.538128 + 0.842863i \(0.319132\pi\)
−0.538128 + 0.842863i \(0.680868\pi\)
\(684\) 0 0
\(685\) 16.0513i 0.613288i
\(686\) −0.117111 1.40936i −0.00447130 0.0538095i
\(687\) 0 0
\(688\) 39.1240 13.4718i 1.49159 0.513606i
\(689\) 3.13604i 0.119474i
\(690\) 0 0
\(691\) −18.3483 −0.698002 −0.349001 0.937122i \(-0.613479\pi\)
−0.349001 + 0.937122i \(0.613479\pi\)
\(692\) −27.9339 + 4.67462i −1.06189 + 0.177703i
\(693\) 0 0
\(694\) 1.82164 + 21.9223i 0.0691485 + 0.832161i
\(695\) −6.33271 −0.240213
\(696\) 0 0
\(697\) −61.2695 −2.32075
\(698\) 2.00971 + 24.1856i 0.0760685 + 0.915439i
\(699\) 0 0
\(700\) 1.19249 + 7.12593i 0.0450721 + 0.269335i
\(701\) 33.6724 1.27179 0.635894 0.771777i \(-0.280632\pi\)
0.635894 + 0.771777i \(0.280632\pi\)
\(702\) 0 0
\(703\) 31.0673i 1.17172i
\(704\) 11.0930 + 20.4303i 0.418082 + 0.769995i
\(705\) 0 0
\(706\) 1.82035 + 21.9068i 0.0685096 + 0.824472i
\(707\) 18.0700i 0.679592i
\(708\) 0 0
\(709\) 15.9147i 0.597689i −0.954302 0.298845i \(-0.903399\pi\)
0.954302 0.298845i \(-0.0966013\pi\)
\(710\) −1.40163 + 0.116468i −0.0526022 + 0.00437098i
\(711\) 0 0
\(712\) 1.54966 + 6.10168i 0.0580759 + 0.228670i
\(713\) 0.0883844i 0.00331002i
\(714\) 0 0
\(715\) 3.60495 0.134818
\(716\) −6.72399 40.1802i −0.251287 1.50161i
\(717\) 0 0
\(718\) 21.0657 1.75046i 0.786167 0.0653266i
\(719\) 34.6441 1.29201 0.646004 0.763334i \(-0.276439\pi\)
0.646004 + 0.763334i \(0.276439\pi\)
\(720\) 0 0
\(721\) 17.8616 0.665200
\(722\) 13.0939 1.08804i 0.487306 0.0404928i
\(723\) 0 0
\(724\) 6.02960 + 36.0308i 0.224088 + 1.33907i
\(725\) 14.5804 0.541501
\(726\) 0 0
\(727\) 38.6477i 1.43336i 0.697400 + 0.716682i \(0.254340\pi\)
−0.697400 + 0.716682i \(0.745660\pi\)
\(728\) 2.88715 0.733256i 0.107005 0.0271763i
\(729\) 0 0
\(730\) −5.96828 + 0.495935i −0.220896 + 0.0183554i
\(731\) 67.1197i 2.48251i
\(732\) 0 0
\(733\) 4.45768i 0.164648i 0.996606 + 0.0823240i \(0.0262342\pi\)
−0.996606 + 0.0823240i \(0.973766\pi\)
\(734\) −0.335152 4.03335i −0.0123707 0.148874i
\(735\) 0 0
\(736\) 4.20702 1.85117i 0.155073 0.0682350i
\(737\) 11.5653i 0.426013i
\(738\) 0 0
\(739\) −32.0619 −1.17942 −0.589709 0.807616i \(-0.700757\pi\)
−0.589709 + 0.807616i \(0.700757\pi\)
\(740\) 3.87678 + 23.1663i 0.142513 + 0.851611i
\(741\) 0 0
\(742\) −0.348723 4.19667i −0.0128020 0.154065i
\(743\) −44.9201 −1.64796 −0.823979 0.566620i \(-0.808251\pi\)
−0.823979 + 0.566620i \(0.808251\pi\)
\(744\) 0 0
\(745\) −20.4000 −0.747397
\(746\) 2.42801 + 29.2197i 0.0888959 + 1.06981i
\(747\) 0 0
\(748\) −37.1925 + 6.22401i −1.35989 + 0.227572i
\(749\) −7.67720 −0.280519
\(750\) 0 0
\(751\) 20.4697i 0.746951i 0.927640 + 0.373475i \(0.121834\pi\)
−0.927640 + 0.373475i \(0.878166\pi\)
\(752\) −15.2465 + 5.24989i −0.555982 + 0.191444i
\(753\) 0 0
\(754\) −0.497797 5.99069i −0.0181287 0.218168i
\(755\) 5.30973i 0.193241i
\(756\) 0 0
\(757\) 11.4003i 0.414352i 0.978304 + 0.207176i \(0.0664273\pi\)
−0.978304 + 0.207176i \(0.933573\pi\)
\(758\) −39.6820 + 3.29738i −1.44131 + 0.119766i
\(759\) 0 0
\(760\) 10.0619 2.55544i 0.364983 0.0926956i
\(761\) 32.5142i 1.17864i −0.807901 0.589319i \(-0.799396\pi\)
0.807901 0.589319i \(-0.200604\pi\)
\(762\) 0 0
\(763\) 12.6991 0.459739
\(764\) −15.4620 + 2.58749i −0.559395 + 0.0936123i
\(765\) 0 0
\(766\) −42.2430 + 3.51019i −1.52630 + 0.126828i
\(767\) 0.915070 0.0330413
\(768\) 0 0
\(769\) 25.1134 0.905614 0.452807 0.891609i \(-0.350423\pi\)
0.452807 + 0.891609i \(0.350423\pi\)
\(770\) −4.82418 + 0.400865i −0.173851 + 0.0144462i
\(771\) 0 0
\(772\) −25.6910 + 4.29928i −0.924640 + 0.154735i
\(773\) 42.4890 1.52822 0.764112 0.645083i \(-0.223177\pi\)
0.764112 + 0.645083i \(0.223177\pi\)
\(774\) 0 0
\(775\) 0.392964i 0.0141157i
\(776\) 10.7742 2.73635i 0.386771 0.0982292i
\(777\) 0 0
\(778\) −41.5663 + 3.45395i −1.49022 + 0.123830i
\(779\) 29.4240i 1.05423i
\(780\) 0 0
\(781\) 2.45350i 0.0877930i
\(782\) 0.617396 + 7.42999i 0.0220780 + 0.265696i
\(783\) 0 0
\(784\) −3.78207 + 1.30230i −0.135074 + 0.0465105i