Properties

Label 144.2.l.a.35.6
Level $144$
Weight $2$
Character 144.35
Analytic conductor $1.150$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 35.6
Root \(1.40927 - 0.118126i\) of defining polynomial
Character \(\chi\) \(=\) 144.35
Dual form 144.2.l.a.107.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.957325 + 1.04093i) q^{2} +(-0.167056 + 1.99301i) q^{4} +(-0.236253 - 0.236253i) q^{5} +3.27830 q^{7} +(-2.23450 + 1.73407i) q^{8} +O(q^{10})\) \(q+(0.957325 + 1.04093i) q^{2} +(-0.167056 + 1.99301i) q^{4} +(-0.236253 - 0.236253i) q^{5} +3.27830 q^{7} +(-2.23450 + 1.73407i) q^{8} +(0.0197510 - 0.472092i) q^{10} +(-2.58229 + 2.58229i) q^{11} +(-1.70773 - 1.70773i) q^{13} +(3.13840 + 3.41247i) q^{14} +(-3.94418 - 0.665888i) q^{16} -7.05130i q^{17} +(3.04184 - 3.04184i) q^{19} +(0.510322 - 0.431387i) q^{20} +(-5.16007 - 0.215882i) q^{22} +1.47338i q^{23} -4.88837i q^{25} +(0.142768 - 3.41247i) q^{26} +(-0.547659 + 6.53368i) q^{28} +(2.98575 - 2.98575i) q^{29} +8.02552i q^{31} +(-3.08273 - 4.74308i) q^{32} +(7.33988 - 6.75039i) q^{34} +(-0.774506 - 0.774506i) q^{35} +(-7.93021 + 7.93021i) q^{37} +(6.07836 + 0.254301i) q^{38} +(0.937586 + 0.118230i) q^{40} -2.22112 q^{41} +(-4.61007 - 4.61007i) q^{43} +(-4.71515 - 5.57792i) q^{44} +(-1.53368 + 1.41050i) q^{46} +7.13023 q^{47} +3.74723 q^{49} +(5.08843 - 4.67976i) q^{50} +(3.68880 - 3.11823i) q^{52} +(5.81417 + 5.81417i) q^{53} +1.22015 q^{55} +(-7.32537 + 5.68479i) q^{56} +(5.96627 + 0.249611i) q^{58} +(-7.46464 + 7.46464i) q^{59} +(-4.04184 - 4.04184i) q^{61} +(-8.35398 + 7.68304i) q^{62} +(1.98602 - 7.74956i) q^{64} +0.806909i q^{65} +(-2.90468 + 2.90468i) q^{67} +(14.0533 + 1.17796i) q^{68} +(0.0647495 - 1.54766i) q^{70} +1.02064i q^{71} +4.08367i q^{73} +(-15.8466 - 0.662973i) q^{74} +(5.55426 + 6.57057i) q^{76} +(-8.46551 + 8.46551i) q^{77} +5.36197i q^{79} +(0.774506 + 1.08914i) q^{80} +(-2.12634 - 2.31203i) q^{82} +(3.93734 + 3.93734i) q^{83} +(-1.66589 + 1.66589i) q^{85} +(0.385407 - 9.21209i) q^{86} +(1.29227 - 10.2480i) q^{88} +2.35922 q^{89} +(-5.59843 - 5.59843i) q^{91} +(-2.93646 - 0.246137i) q^{92} +(6.82596 + 7.42205i) q^{94} -1.43728 q^{95} +9.97204 q^{97} +(3.58732 + 3.90059i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{10} - 16q^{16} + 16q^{19} - 40q^{22} - 24q^{28} + 24q^{34} + 72q^{40} - 32q^{43} + 40q^{46} + 16q^{49} + 24q^{52} - 64q^{55} + 24q^{58} - 32q^{61} - 48q^{64} - 16q^{67} - 72q^{70} + 80q^{82} - 32q^{85} + 48q^{88} + 48q^{91} + 72q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.957325 + 1.04093i 0.676931 + 0.736046i
\(3\) 0 0
\(4\) −0.167056 + 1.99301i −0.0835279 + 0.996505i
\(5\) −0.236253 0.236253i −0.105655 0.105655i 0.652303 0.757958i \(-0.273803\pi\)
−0.757958 + 0.652303i \(0.773803\pi\)
\(6\) 0 0
\(7\) 3.27830 1.23908 0.619540 0.784965i \(-0.287319\pi\)
0.619540 + 0.784965i \(0.287319\pi\)
\(8\) −2.23450 + 1.73407i −0.790017 + 0.613085i
\(9\) 0 0
\(10\) 0.0197510 0.472092i 0.00624580 0.149289i
\(11\) −2.58229 + 2.58229i −0.778590 + 0.778590i −0.979591 0.201001i \(-0.935580\pi\)
0.201001 + 0.979591i \(0.435580\pi\)
\(12\) 0 0
\(13\) −1.70773 1.70773i −0.473638 0.473638i 0.429452 0.903090i \(-0.358707\pi\)
−0.903090 + 0.429452i \(0.858707\pi\)
\(14\) 3.13840 + 3.41247i 0.838772 + 0.912020i
\(15\) 0 0
\(16\) −3.94418 0.665888i −0.986046 0.166472i
\(17\) 7.05130i 1.71019i −0.518470 0.855096i \(-0.673498\pi\)
0.518470 0.855096i \(-0.326502\pi\)
\(18\) 0 0
\(19\) 3.04184 3.04184i 0.697845 0.697845i −0.266100 0.963945i \(-0.585735\pi\)
0.963945 + 0.266100i \(0.0857352\pi\)
\(20\) 0.510322 0.431387i 0.114111 0.0964610i
\(21\) 0 0
\(22\) −5.16007 0.215882i −1.10013 0.0460262i
\(23\) 1.47338i 0.307221i 0.988131 + 0.153610i \(0.0490901\pi\)
−0.988131 + 0.153610i \(0.950910\pi\)
\(24\) 0 0
\(25\) 4.88837i 0.977674i
\(26\) 0.142768 3.41247i 0.0279990 0.669240i
\(27\) 0 0
\(28\) −0.547659 + 6.53368i −0.103498 + 1.23475i
\(29\) 2.98575 2.98575i 0.554439 0.554439i −0.373280 0.927719i \(-0.621767\pi\)
0.927719 + 0.373280i \(0.121767\pi\)
\(30\) 0 0
\(31\) 8.02552i 1.44143i 0.693233 + 0.720713i \(0.256186\pi\)
−0.693233 + 0.720713i \(0.743814\pi\)
\(32\) −3.08273 4.74308i −0.544954 0.838466i
\(33\) 0 0
\(34\) 7.33988 6.75039i 1.25878 1.15768i
\(35\) −0.774506 0.774506i −0.130915 0.130915i
\(36\) 0 0
\(37\) −7.93021 + 7.93021i −1.30372 + 1.30372i −0.377852 + 0.925866i \(0.623337\pi\)
−0.925866 + 0.377852i \(0.876663\pi\)
\(38\) 6.07836 + 0.254301i 0.986040 + 0.0412530i
\(39\) 0 0
\(40\) 0.937586 + 0.118230i 0.148245 + 0.0186938i
\(41\) −2.22112 −0.346881 −0.173441 0.984844i \(-0.555488\pi\)
−0.173441 + 0.984844i \(0.555488\pi\)
\(42\) 0 0
\(43\) −4.61007 4.61007i −0.703030 0.703030i 0.262030 0.965060i \(-0.415608\pi\)
−0.965060 + 0.262030i \(0.915608\pi\)
\(44\) −4.71515 5.57792i −0.710835 0.840903i
\(45\) 0 0
\(46\) −1.53368 + 1.41050i −0.226129 + 0.207968i
\(47\) 7.13023 1.04005 0.520026 0.854151i \(-0.325922\pi\)
0.520026 + 0.854151i \(0.325922\pi\)
\(48\) 0 0
\(49\) 3.74723 0.535318
\(50\) 5.08843 4.67976i 0.719613 0.661818i
\(51\) 0 0
\(52\) 3.68880 3.11823i 0.511545 0.432421i
\(53\) 5.81417 + 5.81417i 0.798638 + 0.798638i 0.982881 0.184243i \(-0.0589833\pi\)
−0.184243 + 0.982881i \(0.558983\pi\)
\(54\) 0 0
\(55\) 1.22015 0.164524
\(56\) −7.32537 + 5.68479i −0.978894 + 0.759662i
\(57\) 0 0
\(58\) 5.96627 + 0.249611i 0.783410 + 0.0327756i
\(59\) −7.46464 + 7.46464i −0.971813 + 0.971813i −0.999613 0.0278004i \(-0.991150\pi\)
0.0278004 + 0.999613i \(0.491150\pi\)
\(60\) 0 0
\(61\) −4.04184 4.04184i −0.517504 0.517504i 0.399311 0.916815i \(-0.369249\pi\)
−0.916815 + 0.399311i \(0.869249\pi\)
\(62\) −8.35398 + 7.68304i −1.06096 + 0.975747i
\(63\) 0 0
\(64\) 1.98602 7.74956i 0.248253 0.968695i
\(65\) 0.806909i 0.100085i
\(66\) 0 0
\(67\) −2.90468 + 2.90468i −0.354863 + 0.354863i −0.861915 0.507052i \(-0.830735\pi\)
0.507052 + 0.861915i \(0.330735\pi\)
\(68\) 14.0533 + 1.17796i 1.70421 + 0.142849i
\(69\) 0 0
\(70\) 0.0647495 1.54766i 0.00773904 0.184981i
\(71\) 1.02064i 0.121128i 0.998164 + 0.0605640i \(0.0192899\pi\)
−0.998164 + 0.0605640i \(0.980710\pi\)
\(72\) 0 0
\(73\) 4.08367i 0.477958i 0.971025 + 0.238979i \(0.0768127\pi\)
−0.971025 + 0.238979i \(0.923187\pi\)
\(74\) −15.8466 0.662973i −1.84212 0.0770691i
\(75\) 0 0
\(76\) 5.55426 + 6.57057i 0.637117 + 0.753696i
\(77\) −8.46551 + 8.46551i −0.964735 + 0.964735i
\(78\) 0 0
\(79\) 5.36197i 0.603269i 0.953424 + 0.301634i \(0.0975322\pi\)
−0.953424 + 0.301634i \(0.902468\pi\)
\(80\) 0.774506 + 1.08914i 0.0865924 + 0.121770i
\(81\) 0 0
\(82\) −2.12634 2.31203i −0.234815 0.255321i
\(83\) 3.93734 + 3.93734i 0.432179 + 0.432179i 0.889369 0.457190i \(-0.151144\pi\)
−0.457190 + 0.889369i \(0.651144\pi\)
\(84\) 0 0
\(85\) −1.66589 + 1.66589i −0.180691 + 0.180691i
\(86\) 0.385407 9.21209i 0.0415595 0.993365i
\(87\) 0 0
\(88\) 1.29227 10.2480i 0.137757 1.09244i
\(89\) 2.35922 0.250077 0.125039 0.992152i \(-0.460095\pi\)
0.125039 + 0.992152i \(0.460095\pi\)
\(90\) 0 0
\(91\) −5.59843 5.59843i −0.586875 0.586875i
\(92\) −2.93646 0.246137i −0.306147 0.0256615i
\(93\) 0 0
\(94\) 6.82596 + 7.42205i 0.704044 + 0.765526i
\(95\) −1.43728 −0.147462
\(96\) 0 0
\(97\) 9.97204 1.01251 0.506254 0.862385i \(-0.331030\pi\)
0.506254 + 0.862385i \(0.331030\pi\)
\(98\) 3.58732 + 3.90059i 0.362374 + 0.394019i
\(99\) 0 0
\(100\) 9.74257 + 0.816631i 0.974257 + 0.0816631i
\(101\) 2.65134 + 2.65134i 0.263818 + 0.263818i 0.826603 0.562785i \(-0.190270\pi\)
−0.562785 + 0.826603i \(0.690270\pi\)
\(102\) 0 0
\(103\) −0.0255237 −0.00251492 −0.00125746 0.999999i \(-0.500400\pi\)
−0.00125746 + 0.999999i \(0.500400\pi\)
\(104\) 6.77723 + 0.854610i 0.664562 + 0.0838014i
\(105\) 0 0
\(106\) −0.486071 + 11.6182i −0.0472113 + 1.12846i
\(107\) 11.7664 11.7664i 1.13751 1.13751i 0.148609 0.988896i \(-0.452520\pi\)
0.988896 0.148609i \(-0.0474797\pi\)
\(108\) 0 0
\(109\) 6.26432 + 6.26432i 0.600013 + 0.600013i 0.940316 0.340303i \(-0.110530\pi\)
−0.340303 + 0.940316i \(0.610530\pi\)
\(110\) 1.16808 + 1.27008i 0.111372 + 0.121098i
\(111\) 0 0
\(112\) −12.9302 2.18298i −1.22179 0.206272i
\(113\) 4.36097i 0.410246i 0.978736 + 0.205123i \(0.0657594\pi\)
−0.978736 + 0.205123i \(0.934241\pi\)
\(114\) 0 0
\(115\) 0.348090 0.348090i 0.0324596 0.0324596i
\(116\) 5.45184 + 6.44941i 0.506190 + 0.598813i
\(117\) 0 0
\(118\) −14.9162 0.624051i −1.37315 0.0574486i
\(119\) 23.1162i 2.11906i
\(120\) 0 0
\(121\) 2.33645i 0.212404i
\(122\) 0.337902 8.07661i 0.0305922 0.731222i
\(123\) 0 0
\(124\) −15.9950 1.34071i −1.43639 0.120399i
\(125\) −2.33615 + 2.33615i −0.208952 + 0.208952i
\(126\) 0 0
\(127\) 8.66579i 0.768965i −0.923132 0.384482i \(-0.874380\pi\)
0.923132 0.384482i \(-0.125620\pi\)
\(128\) 9.96799 5.35155i 0.881055 0.473015i
\(129\) 0 0
\(130\) −0.839933 + 0.772475i −0.0736670 + 0.0677505i
\(131\) −14.9293 14.9293i −1.30438 1.30438i −0.925410 0.378967i \(-0.876280\pi\)
−0.378967 0.925410i \(1.37628\pi\)
\(132\) 0 0
\(133\) 9.97204 9.97204i 0.864686 0.864686i
\(134\) −5.80429 0.242834i −0.501414 0.0209777i
\(135\) 0 0
\(136\) 12.2274 + 15.7562i 1.04849 + 1.35108i
\(137\) −10.9365 −0.934365 −0.467183 0.884161i \(-0.654731\pi\)
−0.467183 + 0.884161i \(0.654731\pi\)
\(138\) 0 0
\(139\) −1.09532 1.09532i −0.0929036 0.0929036i 0.659128 0.752031i \(-0.270926\pi\)
−0.752031 + 0.659128i \(0.770926\pi\)
\(140\) 1.67299 1.41421i 0.141393 0.119523i
\(141\) 0 0
\(142\) −1.06241 + 0.977088i −0.0891558 + 0.0819954i
\(143\) 8.81969 0.737539
\(144\) 0 0
\(145\) −1.41078 −0.117159
\(146\) −4.25080 + 3.90941i −0.351799 + 0.323545i
\(147\) 0 0
\(148\) −14.4802 17.1298i −1.19027 1.40806i
\(149\) −5.42060 5.42060i −0.444073 0.444073i 0.449305 0.893378i \(-0.351672\pi\)
−0.893378 + 0.449305i \(0.851672\pi\)
\(150\) 0 0
\(151\) −14.5821 −1.18668 −0.593338 0.804953i \(-0.702190\pi\)
−0.593338 + 0.804953i \(0.702190\pi\)
\(152\) −1.52225 + 12.0717i −0.123471 + 0.979148i
\(153\) 0 0
\(154\) −16.9162 0.707725i −1.36315 0.0570301i
\(155\) 1.89605 1.89605i 0.152295 0.152295i
\(156\) 0 0
\(157\) 6.04184 + 6.04184i 0.482191 + 0.482191i 0.905831 0.423640i \(-0.139248\pi\)
−0.423640 + 0.905831i \(0.639248\pi\)
\(158\) −5.58142 + 5.13315i −0.444034 + 0.408372i
\(159\) 0 0
\(160\) −0.392262 + 1.84887i −0.0310110 + 0.146166i
\(161\) 4.83018i 0.380671i
\(162\) 0 0
\(163\) 3.16667 3.16667i 0.248032 0.248032i −0.572130 0.820163i \(-0.693883\pi\)
0.820163 + 0.572130i \(0.193883\pi\)
\(164\) 0.371052 4.42672i 0.0289743 0.345669i
\(165\) 0 0
\(166\) −0.329165 + 7.86779i −0.0255482 + 0.610659i
\(167\) 15.5333i 1.20200i 0.799249 + 0.601001i \(0.205231\pi\)
−0.799249 + 0.601001i \(0.794769\pi\)
\(168\) 0 0
\(169\) 7.16735i 0.551334i
\(170\) −3.32886 0.139270i −0.255312 0.0106815i
\(171\) 0 0
\(172\) 9.95807 8.41779i 0.759295 0.641850i
\(173\) 11.0577 11.0577i 0.840700 0.840700i −0.148250 0.988950i \(-0.547364\pi\)
0.988950 + 0.148250i \(0.0473639\pi\)
\(174\) 0 0
\(175\) 16.0255i 1.21142i
\(176\) 11.9045 8.46551i 0.897339 0.638112i
\(177\) 0 0
\(178\) 2.25855 + 2.45578i 0.169285 + 0.184068i
\(179\) 3.84907 + 3.84907i 0.287693 + 0.287693i 0.836167 0.548474i \(-0.184791\pi\)
−0.548474 + 0.836167i \(0.684791\pi\)
\(180\) 0 0
\(181\) 4.29227 4.29227i 0.319042 0.319042i −0.529357 0.848399i \(-0.677567\pi\)
0.848399 + 0.529357i \(0.177567\pi\)
\(182\) 0.468034 11.1871i 0.0346930 0.829241i
\(183\) 0 0
\(184\) −2.55494 3.29227i −0.188353 0.242710i
\(185\) 3.74706 0.275490
\(186\) 0 0
\(187\) 18.2085 + 18.2085i 1.33154 + 1.33154i
\(188\) −1.19115 + 14.2106i −0.0868734 + 1.03642i
\(189\) 0 0
\(190\) −1.37595 1.49611i −0.0998218 0.108539i
\(191\) −24.8057 −1.79488 −0.897439 0.441139i \(-0.854575\pi\)
−0.897439 + 0.441139i \(0.854575\pi\)
\(192\) 0 0
\(193\) −8.08367 −0.581876 −0.290938 0.956742i \(-0.593967\pi\)
−0.290938 + 0.956742i \(0.593967\pi\)
\(194\) 9.54649 + 10.3802i 0.685398 + 0.745252i
\(195\) 0 0
\(196\) −0.625996 + 7.46826i −0.0447140 + 0.533447i
\(197\) −7.34342 7.34342i −0.523197 0.523197i 0.395339 0.918535i \(-0.370627\pi\)
−0.918535 + 0.395339i \(0.870627\pi\)
\(198\) 0 0
\(199\) 11.5526 0.818942 0.409471 0.912323i \(-0.365713\pi\)
0.409471 + 0.912323i \(0.365713\pi\)
\(200\) 8.47676 + 10.9231i 0.599398 + 0.772379i
\(201\) 0 0
\(202\) −0.221655 + 5.29805i −0.0155956 + 0.372769i
\(203\) 9.78816 9.78816i 0.686994 0.686994i
\(204\) 0 0
\(205\) 0.524746 + 0.524746i 0.0366499 + 0.0366499i
\(206\) −0.0244345 0.0265683i −0.00170243 0.00185110i
\(207\) 0 0
\(208\) 5.59843 + 7.87274i 0.388181 + 0.545876i
\(209\) 15.7098i 1.08667i
\(210\) 0 0
\(211\) 0.821009 0.821009i 0.0565206 0.0565206i −0.678282 0.734802i \(-0.737275\pi\)
0.734802 + 0.678282i \(0.237275\pi\)
\(212\) −12.5590 + 10.6164i −0.862556 + 0.729138i
\(213\) 0 0
\(214\) 23.5123 + 0.983687i 1.60727 + 0.0672434i
\(215\) 2.17828i 0.148558i
\(216\) 0 0
\(217\) 26.3100i 1.78604i
\(218\) −0.523703 + 12.5177i −0.0354697 + 0.847805i
\(219\) 0 0
\(220\) −0.203833 + 2.43176i −0.0137424 + 0.163950i
\(221\) −12.0417 + 12.0417i −0.810011 + 0.810011i
\(222\) 0 0
\(223\) 9.83489i 0.658593i 0.944227 + 0.329296i \(0.106812\pi\)
−0.944227 + 0.329296i \(0.893188\pi\)
\(224\) −10.1061 15.5492i −0.675242 1.03893i
\(225\) 0 0
\(226\) −4.53945 + 4.17487i −0.301960 + 0.277708i
\(227\) 15.6642 + 15.6642i 1.03967 + 1.03967i 0.999180 + 0.0404927i \(0.0128928\pi\)
0.0404927 + 0.999180i \(0.487107\pi\)
\(228\) 0 0
\(229\) 11.4845 11.4845i 0.758915 0.758915i −0.217210 0.976125i \(-0.569696\pi\)
0.976125 + 0.217210i \(0.0696957\pi\)
\(230\) 0.695571 + 0.0291007i 0.0458646 + 0.00191884i
\(231\) 0 0
\(232\) −1.49418 + 11.8491i −0.0980976 + 0.777934i
\(233\) 22.8992 1.50018 0.750089 0.661337i \(-0.230011\pi\)
0.750089 + 0.661337i \(0.230011\pi\)
\(234\) 0 0
\(235\) −1.68454 1.68454i −0.109887 0.109887i
\(236\) −13.6301 16.1241i −0.887244 1.04959i
\(237\) 0 0
\(238\) 24.0623 22.1298i 1.55973 1.43446i
\(239\) −1.50948 −0.0976399 −0.0488199 0.998808i \(-0.515546\pi\)
−0.0488199 + 0.998808i \(0.515546\pi\)
\(240\) 0 0
\(241\) −19.3922 −1.24916 −0.624580 0.780961i \(-0.714730\pi\)
−0.624580 + 0.780961i \(0.714730\pi\)
\(242\) 2.43207 2.23674i 0.156339 0.143783i
\(243\) 0 0
\(244\) 8.73064 7.38021i 0.558922 0.472470i
\(245\) −0.885292 0.885292i −0.0565593 0.0565593i
\(246\) 0 0
\(247\) −10.3892 −0.661052
\(248\) −13.9168 17.9331i −0.883718 1.13875i
\(249\) 0 0
\(250\) −4.66822 0.195305i −0.295244 0.0123522i
\(251\) −12.3470 + 12.3470i −0.779335 + 0.779335i −0.979718 0.200383i \(-0.935781\pi\)
0.200383 + 0.979718i \(0.435781\pi\)
\(252\) 0 0
\(253\) −3.80470 3.80470i −0.239199 0.239199i
\(254\) 9.02045 8.29598i 0.565993 0.520536i
\(255\) 0 0
\(256\) 15.1132 + 5.25277i 0.944574 + 0.328298i
\(257\) 10.5288i 0.656766i −0.944545 0.328383i \(-0.893496\pi\)
0.944545 0.328383i \(-0.106504\pi\)
\(258\) 0 0
\(259\) −25.9976 + 25.9976i −1.61541 + 1.61541i
\(260\) −1.60818 0.134799i −0.0997350 0.00835987i
\(261\) 0 0
\(262\) 1.24810 29.8325i 0.0771080 1.84306i
\(263\) 13.8725i 0.855417i 0.903917 + 0.427709i \(0.140679\pi\)
−0.903917 + 0.427709i \(0.859321\pi\)
\(264\) 0 0
\(265\) 2.74723i 0.168761i
\(266\) 19.9267 + 0.833673i 1.22178 + 0.0511158i
\(267\) 0 0
\(268\) −5.30382 6.27431i −0.323982 0.383264i
\(269\) 11.0971 11.0971i 0.676601 0.676601i −0.282628 0.959230i \(-0.591206\pi\)
0.959230 + 0.282628i \(0.0912063\pi\)
\(270\) 0 0
\(271\) 30.0022i 1.82251i −0.411847 0.911253i \(-0.635116\pi\)
0.411847 0.911253i \(-0.364884\pi\)
\(272\) −4.69538 + 27.8116i −0.284699 + 1.68633i
\(273\) 0 0
\(274\) −10.4698 11.3841i −0.632501 0.687736i
\(275\) 12.6232 + 12.6232i 0.761207 + 0.761207i
\(276\) 0 0
\(277\) −5.62872 + 5.62872i −0.338197 + 0.338197i −0.855688 0.517491i \(-0.826866\pi\)
0.517491 + 0.855688i \(0.326866\pi\)
\(278\) 0.0915696 2.18872i 0.00549198 0.131271i
\(279\) 0 0
\(280\) 3.07368 + 0.387592i 0.183688 + 0.0231630i
\(281\) −11.9012 −0.709969 −0.354984 0.934872i \(-0.615514\pi\)
−0.354984 + 0.934872i \(0.615514\pi\)
\(282\) 0 0
\(283\) 17.3875 + 17.3875i 1.03358 + 1.03358i 0.999416 + 0.0341630i \(0.0108765\pi\)
0.0341630 + 0.999416i \(0.489123\pi\)
\(284\) −2.03415 0.170504i −0.120705 0.0101176i
\(285\) 0 0
\(286\) 8.44331 + 9.18064i 0.499263 + 0.542863i
\(287\) −7.28150 −0.429813
\(288\) 0 0
\(289\) −32.7208 −1.92475
\(290\) −1.35058 1.46852i −0.0793086 0.0862344i
\(291\) 0 0
\(292\) −8.13881 0.682202i −0.476288 0.0399228i
\(293\) −5.14536 5.14536i −0.300595 0.300595i 0.540651 0.841247i \(-0.318178\pi\)
−0.841247 + 0.540651i \(0.818178\pi\)
\(294\) 0 0
\(295\) 3.52708 0.205355
\(296\) 3.96857 31.4716i 0.230669 1.82925i
\(297\) 0 0
\(298\) 0.453168 10.8317i 0.0262513 0.627465i
\(299\) 2.51613 2.51613i 0.145511 0.145511i
\(300\) 0 0
\(301\) −15.1132 15.1132i −0.871110 0.871110i
\(302\) −13.9598 15.1789i −0.803298 0.873448i
\(303\) 0 0
\(304\) −14.0231 + 9.97204i −0.804279 + 0.571936i
\(305\) 1.90979i 0.109354i
\(306\) 0 0
\(307\) 14.9557 14.9557i 0.853569 0.853569i −0.137002 0.990571i \(-0.543747\pi\)
0.990571 + 0.137002i \(0.0437467\pi\)
\(308\) −15.4576 18.2861i −0.880781 1.04195i
\(309\) 0 0
\(310\) 3.78879 + 0.158512i 0.215189 + 0.00900286i
\(311\) 16.8915i 0.957829i 0.877862 + 0.478914i \(0.158970\pi\)
−0.877862 + 0.478914i \(0.841030\pi\)
\(312\) 0 0
\(313\) 1.42012i 0.0802700i −0.999194 0.0401350i \(-0.987221\pi\)
0.999194 0.0401350i \(-0.0127788\pi\)
\(314\) −0.505104 + 12.0731i −0.0285046 + 0.681325i
\(315\) 0 0
\(316\) −10.6865 0.895749i −0.601161 0.0503898i
\(317\) 23.3492 23.3492i 1.31142 1.31142i 0.391054 0.920368i \(-0.372111\pi\)
0.920368 0.391054i \(-0.127889\pi\)
\(318\) 0 0
\(319\) 15.4201i 0.863361i
\(320\) −2.30006 + 1.36165i −0.128577 + 0.0761187i
\(321\) 0 0
\(322\) −5.02786 + 4.62405i −0.280192 + 0.257688i
\(323\) −21.4489 21.4489i −1.19345 1.19345i
\(324\) 0 0
\(325\) −8.34799 + 8.34799i −0.463063 + 0.463063i
\(326\) 6.32780 + 0.264736i 0.350464 + 0.0146624i
\(327\) 0 0
\(328\) 4.96311 3.85158i 0.274042 0.212668i
\(329\) 23.3750 1.28871
\(330\) 0 0
\(331\) 2.95573 + 2.95573i 0.162462 + 0.162462i 0.783656 0.621195i \(-0.213352\pi\)
−0.621195 + 0.783656i \(0.713352\pi\)
\(332\) −8.50491 + 7.18940i −0.466768 + 0.394570i
\(333\) 0 0
\(334\) −16.1690 + 14.8704i −0.884728 + 0.813672i
\(335\) 1.37248 0.0749865
\(336\) 0 0
\(337\) −1.41078 −0.0768501 −0.0384251 0.999261i \(-0.512234\pi\)
−0.0384251 + 0.999261i \(0.512234\pi\)
\(338\) 7.46068 6.86149i 0.405808 0.373216i
\(339\) 0 0
\(340\) −3.04184 3.59843i −0.164967 0.195152i
\(341\) −20.7242 20.7242i −1.12228 1.12228i
\(342\) 0 0
\(343\) −10.6636 −0.575778
\(344\) 18.2954 + 2.30705i 0.986422 + 0.124388i
\(345\) 0 0
\(346\) 22.0960 + 0.924434i 1.18789 + 0.0496979i
\(347\) 3.11726 3.11726i 0.167344 0.167344i −0.618467 0.785811i \(-0.712246\pi\)
0.785811 + 0.618467i \(0.212246\pi\)
\(348\) 0 0
\(349\) 11.8465 + 11.8465i 0.634130 + 0.634130i 0.949101 0.314971i \(-0.101995\pi\)
−0.314971 + 0.949101i \(0.601995\pi\)
\(350\) 16.6814 15.3416i 0.891658 0.820045i
\(351\) 0 0
\(352\) 20.2085 + 4.28751i 1.07712 + 0.228525i
\(353\) 5.30598i 0.282409i −0.989980 0.141205i \(-0.954902\pi\)
0.989980 0.141205i \(-0.0450975\pi\)
\(354\) 0 0
\(355\) 0.241130 0.241130i 0.0127978 0.0127978i
\(356\) −0.394122 + 4.70196i −0.0208884 + 0.249203i
\(357\) 0 0
\(358\) −0.321786 + 7.69141i −0.0170069 + 0.406504i
\(359\) 17.8399i 0.941556i 0.882252 + 0.470778i \(0.156027\pi\)
−0.882252 + 0.470778i \(0.843973\pi\)
\(360\) 0 0
\(361\) 0.494455i 0.0260239i
\(362\) 8.57705 + 0.358838i 0.450800 + 0.0188601i
\(363\) 0 0
\(364\) 12.0930 10.2225i 0.633844 0.535804i
\(365\) 0.964779 0.964779i 0.0504988 0.0504988i
\(366\) 0 0
\(367\) 2.05815i 0.107435i −0.998556 0.0537173i \(-0.982893\pi\)
0.998556 0.0537173i \(-0.0171070\pi\)
\(368\) 0.981107 5.81128i 0.0511437 0.302934i
\(369\) 0 0
\(370\) 3.58716 + 3.90042i 0.186488 + 0.202773i
\(371\) 19.0606 + 19.0606i 0.989576 + 0.989576i
\(372\) 0 0
\(373\) 12.7891 12.7891i 0.662193 0.662193i −0.293704 0.955896i \(-0.594888\pi\)
0.955896 + 0.293704i \(0.0948879\pi\)
\(374\) −1.52225 + 36.3852i −0.0787136 + 1.88143i
\(375\) 0 0
\(376\) −15.9325 + 12.3643i −0.821658 + 0.637640i
\(377\) −10.1977 −0.525206
\(378\) 0 0
\(379\) 6.76753 + 6.76753i 0.347625 + 0.347625i 0.859224 0.511599i \(-0.170947\pi\)
−0.511599 + 0.859224i \(0.670947\pi\)
\(380\) 0.240107 2.86452i 0.0123172 0.146947i
\(381\) 0 0
\(382\) −23.7471 25.8209i −1.21501 1.32111i
\(383\) −7.48207 −0.382316 −0.191158 0.981559i \(-0.561224\pi\)
−0.191158 + 0.981559i \(0.561224\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) −7.73871 8.41451i −0.393890 0.428287i
\(387\) 0 0
\(388\) −1.66589 + 19.8744i −0.0845727 + 1.00897i
\(389\) 20.7180 + 20.7180i 1.05045 + 1.05045i 0.998658 + 0.0517883i \(0.0164921\pi\)
0.0517883 + 0.998658i \(0.483508\pi\)
\(390\) 0 0
\(391\) 10.3892 0.525407
\(392\) −8.37320 + 6.49794i −0.422910 + 0.328196i
\(393\) 0 0
\(394\) 0.613917 14.6740i 0.0309287 0.739265i
\(395\) 1.26678 1.26678i 0.0637386 0.0637386i
\(396\) 0 0
\(397\) 12.5194 + 12.5194i 0.628332 + 0.628332i 0.947648 0.319316i \(-0.103453\pi\)
−0.319316 + 0.947648i \(0.603453\pi\)
\(398\) 11.0596 + 12.0254i 0.554368 + 0.602779i
\(399\) 0 0
\(400\) −3.25511 + 19.2806i −0.162755 + 0.964032i
\(401\) 11.4935i 0.573960i −0.957937 0.286980i \(-0.907349\pi\)
0.957937 0.286980i \(-0.0926514\pi\)
\(402\) 0 0
\(403\) 13.7054 13.7054i 0.682714 0.682714i
\(404\) −5.72707 + 4.84123i −0.284933 + 0.240860i
\(405\) 0 0
\(406\) 19.5592 + 0.818300i 0.970707 + 0.0406115i
\(407\) 40.9562i 2.03012i
\(408\) 0 0
\(409\) 23.2432i 1.14930i −0.818398 0.574652i \(-0.805137\pi\)
0.818398 0.574652i \(-0.194863\pi\)
\(410\) −0.0438693 + 1.04858i −0.00216655 + 0.0517854i
\(411\) 0 0
\(412\) 0.00426388 0.0508689i 0.000210066 0.00250613i
\(413\) −24.4713 + 24.4713i −1.20415 + 1.20415i
\(414\) 0 0
\(415\) 1.86041i 0.0913241i
\(416\) −2.83542 + 13.3643i −0.139018 + 0.655240i
\(417\) 0 0
\(418\) −16.3528 + 15.0394i −0.799840 + 0.735601i
\(419\) −21.1446 21.1446i −1.03298 1.03298i −0.999437 0.0335424i \(-0.989321\pi\)
−0.0335424 0.999437i \(1.48932\pi\)
\(420\) 0 0
\(421\) 9.60077 9.60077i 0.467913 0.467913i −0.433325 0.901238i \(-0.642660\pi\)
0.901238 + 0.433325i \(0.142660\pi\)
\(422\) 1.64058 + 0.0686371i 0.0798623 + 0.00334120i
\(423\) 0 0
\(424\) −23.0740 2.90963i −1.12057 0.141304i
\(425\) −34.4694 −1.67201
\(426\) 0 0
\(427\) −13.2503 13.2503i −0.641229 0.641229i
\(428\) 21.4850 + 25.4163i 1.03852 + 1.22854i
\(429\) 0 0
\(430\) −2.26743 + 2.08533i −0.109345 + 0.100563i
\(431\) 18.2795 0.880491 0.440246 0.897877i \(-0.354891\pi\)
0.440246 + 0.897877i \(0.354891\pi\)
\(432\) 0 0
\(433\) 34.3844 1.65241 0.826204 0.563371i \(-0.190496\pi\)
0.826204 + 0.563371i \(0.190496\pi\)
\(434\) −27.3868 + 25.1873i −1.31461 + 1.20903i
\(435\) 0 0
\(436\) −13.5313 + 11.4384i −0.648034 + 0.547798i
\(437\) 4.48178 + 4.48178i 0.214393 + 0.214393i
\(438\) 0 0
\(439\) 15.1713 0.724088 0.362044 0.932161i \(-0.382079\pi\)
0.362044 + 0.932161i \(0.382079\pi\)
\(440\) −2.72642 + 2.11582i −0.129977 + 0.100868i
\(441\) 0 0
\(442\) −24.0623 1.00670i −1.14453 0.0478837i
\(443\) −18.1978 + 18.1978i −0.864604 + 0.864604i −0.991869 0.127265i \(-0.959380\pi\)
0.127265 + 0.991869i \(0.459380\pi\)
\(444\) 0 0
\(445\) −0.557373 0.557373i −0.0264220 0.0264220i
\(446\) −10.2374 + 9.41519i −0.484755 + 0.445822i
\(447\) 0 0
\(448\) 6.51077 25.4054i 0.307605 1.20029i
\(449\) 8.89518i 0.419789i 0.977724 + 0.209895i \(0.0673121\pi\)
−0.977724 + 0.209895i \(0.932688\pi\)
\(450\) 0 0
\(451\) 5.73558 5.73558i 0.270078 0.270078i
\(452\) −8.69147 0.728526i −0.408812 0.0342670i
\(453\) 0 0
\(454\) −1.30955 + 31.3011i −0.0614601 + 1.46903i
\(455\) 2.64529i 0.124013i
\(456\) 0 0
\(457\) 11.3085i 0.528989i 0.964387 + 0.264494i \(0.0852051\pi\)
−0.964387 + 0.264494i \(0.914795\pi\)
\(458\) 22.9489 + 0.960113i 1.07233 + 0.0448631i
\(459\) 0 0
\(460\) 0.635597 + 0.751898i 0.0296348 + 0.0350574i
\(461\) −10.8614 + 10.8614i −0.505865 + 0.505865i −0.913255 0.407389i \(-0.866439\pi\)
0.407389 + 0.913255i \(0.366439\pi\)
\(462\) 0 0
\(463\) 3.05504i 0.141980i 0.997477 + 0.0709898i \(0.0226158\pi\)
−0.997477 + 0.0709898i \(0.977384\pi\)
\(464\) −13.7645 + 9.78816i −0.639001 + 0.454404i
\(465\) 0 0
\(466\) 21.9220 + 23.8364i 1.01552 + 1.10420i
\(467\) 3.93734 + 3.93734i 0.182198 + 0.182198i 0.792313 0.610115i \(-0.208877\pi\)
−0.610115 + 0.792313i \(0.708877\pi\)
\(468\) 0 0
\(469\) −9.52241 + 9.52241i −0.439704 + 0.439704i
\(470\) 0.140829 3.36613i 0.00649596 0.155268i
\(471\) 0 0
\(472\) 3.73558 29.6240i 0.171944 1.36355i
\(473\) 23.8091 1.09474
\(474\) 0 0
\(475\) −14.8696 14.8696i −0.682265 0.682265i
\(476\) 46.0709 + 3.86170i 2.11166 + 0.177001i
\(477\) 0 0
\(478\) −1.44506 1.57125i −0.0660955 0.0718675i
\(479\) −27.6167 −1.26184 −0.630920 0.775848i \(-0.717322\pi\)
−0.630920 + 0.775848i \(0.717322\pi\)
\(480\) 0 0
\(481\) 27.0852 1.23498
\(482\) −18.5646 20.1858i −0.845595 0.919439i
\(483\) 0 0
\(484\) 4.65656 + 0.390317i 0.211662 + 0.0177417i
\(485\) −2.35592 2.35592i −0.106977 0.106977i
\(486\) 0 0
\(487\) 13.0783 0.592635 0.296318 0.955089i \(-0.404241\pi\)
0.296318 + 0.955089i \(0.404241\pi\)
\(488\) 16.0403 + 2.02269i 0.726111 + 0.0915627i
\(489\) 0 0
\(490\) 0.0740113 1.76904i 0.00334349 0.0799170i
\(491\) 21.8368 21.8368i 0.985483 0.985483i −0.0144135 0.999896i \(-0.504588\pi\)
0.999896 + 0.0144135i \(0.00458813\pi\)
\(492\) 0 0
\(493\) −21.0534 21.0534i −0.948197 0.948197i
\(494\) −9.94589 10.8144i −0.447487 0.486565i
\(495\) 0 0
\(496\) 5.34410 31.6541i 0.239957 1.42131i
\(497\) 3.34597i 0.150087i
\(498\) 0 0
\(499\) −16.4170 + 16.4170i −0.734926 + 0.734926i −0.971591 0.236665i \(-0.923946\pi\)
0.236665 + 0.971591i \(0.423946\pi\)
\(500\) −4.26571 5.04625i −0.190768 0.225675i
\(501\) 0 0
\(502\) −24.6724 1.03222i −1.10118 0.0460703i
\(503\) 22.1243i 0.986475i −0.869895 0.493237i \(-0.835813\pi\)
0.869895 0.493237i \(-0.164187\pi\)
\(504\) 0 0
\(505\) 1.25277i 0.0557477i
\(506\) 0.318076 7.60274i 0.0141402 0.337983i
\(507\) 0 0
\(508\) 17.2710 + 1.44767i 0.766277 + 0.0642300i
\(509\) 13.7152 13.7152i 0.607916 0.607916i −0.334485 0.942401i \(-0.608562\pi\)
0.942401 + 0.334485i \(0.108562\pi\)
\(510\) 0 0
\(511\) 13.3875i 0.592228i
\(512\) 9.00049 + 20.7603i 0.397769 + 0.917486i
\(513\) 0 0
\(514\) 10.9597 10.0795i 0.483410 0.444586i
\(515\) 0.00603003 + 0.00603003i 0.000265715 + 0.000265715i
\(516\) 0 0
\(517\) −18.4123 + 18.4123i −0.809774 + 0.809774i
\(518\) −51.9497 2.17342i −2.28254 0.0954947i
\(519\) 0 0
\(520\) −1.39923 1.80304i −0.0613605 0.0790686i
\(521\) −0.888181 −0.0389119 −0.0194560 0.999811i \(-0.506193\pi\)
−0.0194560 + 0.999811i \(0.506193\pi\)
\(522\) 0 0
\(523\) −14.8186 14.8186i −0.647971 0.647971i 0.304531 0.952502i \(-0.401500\pi\)
−0.952502 + 0.304531i \(0.901500\pi\)
\(524\) 32.2482 27.2602i 1.40877 1.19087i
\(525\) 0 0
\(526\) −14.4403 + 13.2805i −0.629627 + 0.579059i
\(527\) 56.5904 2.46512
\(528\) 0 0
\(529\) 20.8292 0.905615
\(530\) 2.85966 2.62999i 0.124216 0.114239i
\(531\) 0 0
\(532\) 18.2085 + 21.5403i 0.789439 + 0.933890i
\(533\) 3.79307 + 3.79307i 0.164296 + 0.164296i
\(534\) 0 0
\(535\) −5.55971 −0.240367
\(536\) 1.45361 11.5274i 0.0627865 0.497910i
\(537\) 0 0
\(538\) 22.1748 + 0.927727i 0.956022 + 0.0399972i
\(539\) −9.67643 + 9.67643i −0.416793 + 0.416793i
\(540\) 0 0
\(541\) −4.26432 4.26432i −0.183337 0.183337i 0.609471 0.792808i \(-0.291382\pi\)
−0.792808 + 0.609471i \(0.791382\pi\)
\(542\) 31.2301 28.7219i 1.34145 1.23371i
\(543\) 0 0
\(544\) −33.4449 + 21.7372i −1.43394 + 0.931976i
\(545\) 2.95992i 0.126789i
\(546\) 0 0
\(547\) −0.559026 + 0.559026i −0.0239022 + 0.0239022i −0.718957 0.695055i \(-0.755380\pi\)
0.695055 + 0.718957i \(0.255380\pi\)
\(548\) 1.82700 21.7965i 0.0780456 0.931100i
\(549\) 0 0
\(550\) −1.05531 + 25.2243i −0.0449986 + 1.07557i
\(551\) 18.1643i 0.773825i
\(552\) 0 0
\(553\) 17.5781i 0.747498i
\(554\) −11.2476 0.470567i −0.477865 0.0199925i
\(555\) 0 0
\(556\) 2.36596 2.00000i 0.100339 0.0848189i
\(557\) −20.4287 + 20.4287i −0.865591 + 0.865591i −0.991981 0.126390i \(-0.959661\pi\)
0.126390 + 0.991981i \(0.459661\pi\)
\(558\) 0 0
\(559\) 15.7455i 0.665963i
\(560\) 2.53906 + 3.57053i 0.107295 + 0.150882i
\(561\) 0 0
\(562\) −11.3934 12.3883i −0.480600 0.522570i
\(563\) −13.9682 13.9682i −0.588689 0.588689i 0.348587 0.937276i \(-0.386661\pi\)
−0.937276 + 0.348587i \(0.886661\pi\)
\(564\) 0 0
\(565\) 1.03029 1.03029i 0.0433447 0.0433447i
\(566\) −1.45361 + 34.7446i −0.0610999 + 1.46042i
\(567\) 0 0
\(568\) −1.76986 2.28063i −0.0742618 0.0956932i
\(569\) −21.3052 −0.893159 −0.446579 0.894744i \(-0.647358\pi\)
−0.446579 + 0.894744i \(0.647358\pi\)
\(570\) 0 0
\(571\) −18.3333 18.3333i −0.767226 0.767226i 0.210391 0.977617i \(-0.432526\pi\)
−0.977617 + 0.210391i \(0.932526\pi\)
\(572\) −1.47338 + 17.5777i −0.0616051 + 0.734962i
\(573\) 0 0
\(574\) −6.97076 7.57951i −0.290954 0.316362i
\(575\) 7.20243 0.300362
\(576\) 0 0
\(577\) 7.57813 0.315482 0.157741 0.987481i \(-0.449579\pi\)
0.157741 + 0.987481i \(0.449579\pi\)
\(578\) −31.3245 34.0600i −1.30293 1.41671i
\(579\) 0 0
\(580\) 0.235679 2.81170i 0.00978604 0.116750i
\(581\) 12.9078 + 12.9078i 0.535504 + 0.535504i
\(582\) 0 0
\(583\) −30.0278 −1.24362
\(584\) −7.08137 9.12499i −0.293029 0.377595i
\(585\) 0 0
\(586\) 0.430158 10.2817i 0.0177696 0.424735i
\(587\) 2.75279 2.75279i 0.113620 0.113620i −0.648011 0.761631i \(-0.724399\pi\)
0.761631 + 0.648011i \(0.224399\pi\)
\(588\) 0 0
\(589\) 24.4123 + 24.4123i 1.00589 + 1.00589i
\(590\) 3.37656 + 3.67143i 0.139011 + 0.151150i
\(591\) 0 0
\(592\) 36.5588 25.9976i 1.50256 1.06849i
\(593\) 11.3554i 0.466312i −0.972439 0.233156i \(-0.925095\pi\)
0.972439 0.233156i \(-0.0749053\pi\)
\(594\) 0 0
\(595\) −5.46128 + 5.46128i −0.223890 + 0.223890i
\(596\) 11.7089 9.89777i 0.479614 0.405429i
\(597\) 0 0
\(598\) 5.02786 + 0.210351i 0.205604 + 0.00860189i
\(599\) 25.8985i 1.05819i −0.848564 0.529093i \(-0.822532\pi\)
0.848564 0.529093i \(-0.177468\pi\)
\(600\) 0 0
\(601\) 15.9753i 0.651648i −0.945430 0.325824i \(-0.894358\pi\)
0.945430 0.325824i \(-0.105642\pi\)
\(602\) 1.26348 30.2000i 0.0514955 1.23086i
\(603\) 0 0
\(604\) 2.43603 29.0623i 0.0991206 1.18253i
\(605\) −0.551992 + 0.551992i −0.0224417 + 0.0224417i
\(606\) 0 0
\(607\) 15.9745i 0.648384i 0.945991 + 0.324192i \(0.105092\pi\)
−0.945991 + 0.324192i \(0.894908\pi\)
\(608\) −23.8048 5.05052i −0.965413 0.204825i
\(609\) 0 0
\(610\) −1.98795 + 1.82829i −0.0804898 + 0.0740253i
\(611\) −12.1765 12.1765i −0.492608 0.492608i
\(612\) 0 0
\(613\) −20.2125 + 20.2125i −0.816375 + 0.816375i −0.985581 0.169206i \(-0.945880\pi\)
0.169206 + 0.985581i \(0.445880\pi\)
\(614\) 29.8853 + 1.25031i 1.20607 + 0.0504586i
\(615\) 0 0
\(616\) 4.23646 33.5960i 0.170692 1.35362i
\(617\) −4.04523 −0.162855 −0.0814275 0.996679i \(-0.525948\pi\)
−0.0814275 + 0.996679i \(0.525948\pi\)
\(618\) 0 0
\(619\) −20.7472 20.7472i −0.833901 0.833901i 0.154147 0.988048i \(-0.450737\pi\)
−0.988048 + 0.154147i \(0.950737\pi\)
\(620\) 3.46210 + 4.09560i 0.139041 + 0.164483i
\(621\) 0 0
\(622\) −17.5828 + 16.1707i −0.705006 + 0.648384i
\(623\) 7.73424 0.309866
\(624\) 0 0
\(625\) −23.3380 −0.933520
\(626\) 1.47824 1.35952i 0.0590824 0.0543373i
\(627\) 0 0
\(628\) −13.0508 + 11.0321i −0.520782 + 0.440230i
\(629\) 55.9183 + 55.9183i 2.22961 + 2.22961i
\(630\) 0 0
\(631\) −38.0533 −1.51488 −0.757439 0.652906i \(-0.773550\pi\)
−0.757439 + 0.652906i \(0.773550\pi\)
\(632\) −9.29802 11.9813i −0.369855 0.476592i
\(633\) 0 0
\(634\) 46.6576 + 1.95202i 1.85301 + 0.0775245i
\(635\) −2.04732 + 2.04732i −0.0812453 + 0.0812453i
\(636\) 0 0
\(637\) −6.39923 6.39923i −0.253547 0.253547i
\(638\) −16.0512 + 14.7621i −0.635474 + 0.584436i
\(639\) 0 0
\(640\) −3.61928 1.09065i −0.143065 0.0431116i
\(641\) 27.3678i 1.08096i 0.841355 + 0.540482i \(0.181758\pi\)
−0.841355 + 0.540482i \(0.818242\pi\)
\(642\) 0 0
\(643\) 8.88438 8.88438i 0.350366 0.350366i −0.509880 0.860246i \(-0.670310\pi\)
0.860246 + 0.509880i \(0.170310\pi\)
\(644\) −9.62659 0.806909i −0.379341 0.0317967i
\(645\) 0 0
\(646\) 1.79315 42.8603i 0.0705505 1.68632i
\(647\) 40.9923i 1.61157i 0.592206 + 0.805787i \(0.298257\pi\)
−0.592206 + 0.805787i \(0.701743\pi\)
\(648\) 0 0
\(649\) 38.5517i 1.51329i
\(650\) −16.6814 0.697900i −0.654298 0.0273739i
\(651\) 0 0
\(652\) 5.78219 + 6.84021i 0.226448 + 0.267883i
\(653\) −22.0952 + 22.0952i −0.864652 + 0.864652i −0.991874 0.127222i \(-0.959394\pi\)
0.127222 + 0.991874i \(0.459394\pi\)
\(654\) 0 0
\(655\) 7.05416i 0.275629i
\(656\) 8.76052 + 1.47902i 0.342041 + 0.0577460i
\(657\) 0 0
\(658\) 22.3775 + 24.3317i 0.872366 + 0.948548i
\(659\) 14.3943 + 14.3943i 0.560722 + 0.560722i 0.929513 0.368790i \(-0.120228\pi\)
−0.368790 + 0.929513i \(0.620228\pi\)
\(660\) 0 0
\(661\) −27.1550 + 27.1550i −1.05621 + 1.05621i −0.0578847 + 0.998323i \(0.518436\pi\)
−0.998323 + 0.0578847i \(0.981564\pi\)
\(662\) −0.247102 + 5.90629i −0.00960389 + 0.229555i
\(663\) 0 0
\(664\) −15.6256 1.97039i −0.606391 0.0764660i
\(665\) −4.71184 −0.182717
\(666\) 0 0
\(667\) 4.39914 + 4.39914i 0.170335 + 0.170335i
\(668\) −30.9580 2.59493i −1.19780 0.100401i
\(669\) 0 0
\(670\) 1.31391 + 1.42865i 0.0507607 + 0.0551935i
\(671\) 20.8744 0.805847
\(672\) 0 0
\(673\) 20.8899 0.805247 0.402624 0.915366i \(-0.368098\pi\)
0.402624 + 0.915366i \(0.368098\pi\)
\(674\) −1.35058 1.46852i −0.0520222 0.0565652i
\(675\) 0 0
\(676\) 14.2846 + 1.19735i 0.549408 + 0.0460518i
\(677\) −19.2536 19.2536i −0.739976 0.739976i 0.232597 0.972573i \(-0.425278\pi\)
−0.972573 + 0.232597i \(0.925278\pi\)
\(678\) 0 0
\(679\) 32.6913 1.25458
\(680\) 0.833673 6.61120i 0.0319699 0.253528i
\(681\) 0 0
\(682\) 1.73257 41.4122i 0.0663434 1.58576i
\(683\) −4.11387 + 4.11387i −0.157413 + 0.157413i −0.781419 0.624006i \(-0.785504\pi\)
0.624006 + 0.781419i \(0.285504\pi\)
\(684\) 0 0
\(685\) 2.58377 + 2.58377i 0.0987207 + 0.0987207i
\(686\) −10.2085 11.1000i −0.389762 0.423799i
\(687\) 0 0
\(688\) 15.1132 + 21.2528i 0.576185 + 0.810254i
\(689\) 19.8580i 0.756530i
\(690\) 0 0
\(691\) 25.2503 25.2503i 0.960568 0.960568i −0.0386833 0.999252i \(-0.512316\pi\)
0.999252 + 0.0386833i \(0.0123164\pi\)
\(692\) 20.1908 + 23.8853i 0.767541 + 0.907985i
\(693\) 0 0
\(694\) 6.22908 + 0.260606i 0.236453 + 0.00989248i
\(695\) 0.517543i 0.0196315i
\(696\) 0 0
\(697\) 15.6618i 0.593233i
\(698\) −0.990382 + 23.6724i −0.0374865 + 0.896012i
\(699\) 0 0
\(700\) 31.9390 + 2.67716i 1.20718 + 0.101187i
\(701\) 5.51930 5.51930i 0.208461 0.208461i −0.595152 0.803613i \(-0.702908\pi\)
0.803613 + 0.595152i \(0.202908\pi\)
\(702\) 0 0
\(703\) 48.2448i 1.81959i
\(704\) 14.8831 + 25.1401i 0.560929 + 0.947503i
\(705\) 0 0
\(706\) 5.52314 5.07955i 0.207866 0.191172i
\(707\) 8.69188 + 8.69188i 0.326892 + 0.326892i
\(708\) 0 0
\(709\) −5.23948 + 5.23948i −0.196773 + 0.196773i −0.798615 0.601842i \(-0.794434\pi\)
0.601842 + 0.798615i \(0.294434\pi\)
\(710\) 0.481838 + 0.0201587i 0.0180830 + 0.000756542i
\(711\) 0 0
\(712\) −5.27170 + 4.09105i −0.197565 + 0.153319i
\(713\) −11.8246 −0.442837
\(714\) 0 0
\(715\) −2.08367 2.08367i −0.0779250 0.0779250i
\(716\) −8.31425 + 7.02823i −0.310718 + 0.262657i
\(717\) 0 0
\(718\) −18.5701 + 17.0786i −0.693029 + 0.637369i
\(719\) −36.4570 −1.35962 −0.679808 0.733390i \(-0.737937\pi\)
−0.679808 + 0.733390i \(0.737937\pi\)
\(720\) 0 0
\(721\) −0.0836741 −0.00311619
\(722\) −0.514691 + 0.473354i −0.0191548 + 0.0176164i
\(723\) 0 0
\(724\) 7.83750 + 9.27160i 0.291278 + 0.344576i
\(725\) −14.5954 14.5954i −0.542060 0.542060i
\(726\) 0 0
\(727\) 31.5790 1.17120 0.585600 0.810600i \(-0.300859\pi\)
0.585600 + 0.810600i \(0.300859\pi\)
\(728\) 22.2178 + 2.80166i 0.823445 + 0.103837i
\(729\) 0 0
\(730\) 1.92787 + 0.0806565i 0.0713537 + 0.00298523i
\(731\) −32.5070 + 32.5070i −1.20232 + 1.20232i
\(732\) 0 0
\(733\) −10.8720 10.8720i −0.401565 0.401565i 0.477219 0.878784i \(-0.341645\pi\)
−0.878784 + 0.477219i \(0.841645\pi\)
\(734\) 2.14238 1.97032i 0.0790768 0.0727258i
\(735\) 0 0
\(736\) 6.98836 4.54203i 0.257594 0.167421i
\(737\) 15.0015i 0.552586i
\(738\) 0 0
\(739\) −34.2774 + 34.2774i −1.26092 + 1.26092i −0.310265 + 0.950650i \(0.600418\pi\)
−0.950650 + 0.310265i \(0.899582\pi\)
\(740\) −0.625969 + 7.46794i −0.0230111 + 0.274527i
\(741\) 0 0
\(742\) −1.59348 + 38.0878i −0.0584986 + 1.39825i
\(743\) 16.5900i 0.608629i 0.952572 + 0.304314i \(0.0984273\pi\)
−0.952572 + 0.304314i \(0.901573\pi\)
\(744\) 0 0
\(745\) 2.56126i 0.0938374i
\(746\) 25.5558 + 1.06918i 0.935663 + 0.0391454i
\(747\) 0 0
\(748\) −39.3316 + 33.2479i −1.43811 + 1.21566i
\(749\) 38.5739 38.5739i 1.40946 1.40946i
\(750\) 0 0
\(751\) 14.8054i 0.540256i −0.962824 0.270128i \(-0.912934\pi\)
0.962824 0.270128i \(-0.0870660\pi\)
\(752\) −28.1230 4.74794i −1.02554 0.173140i
\(753\) 0 0
\(754\) −9.76248 10.6150i −0.355529 0.386576i
\(755\) 3.44506 + 3.44506i 0.125379 + 0.125379i
\(756\) 0 0
\(757\) 32.8209 32.8209i 1.19290 1.19290i 0.216646 0.976250i \(-0.430488\pi\)
0.976250 0.216646i \(-0.0695118\pi\)
\(758\) −0.565772 + 13.5232i −0.0205498 + 0.491186i
\(759\) 0 0
\(760\) 3.21162 2.49235i 0.116498 0.0904069i
\(761\) 42.5206 1.54137 0.770685 0.637217i \(-0.219914\pi\)
0.770685 + 0.637217i \(0.219914\pi\)
\(762\) 0 0
\(763\) 20.5363 + 20.5363i 0.743464 + 0.743464i
\(764\) 4.14394 49.4380i 0.149922 1.78861i
\(765\) 0 0
\(766\) −7.16278 7.78828i −0.258802 0.281402i
\(767\) 25.4951 0.920575
\(768\) 0 0
\(769\) 22.9146 0.826321 0.413160 0.910658i \(-0.364425\pi\)
0.413160 + 0.910658i \(0.364425\pi\)
\(770\) 3.82930 + 4.16371i 0.137998 + 0.150050i
\(771\) 0 0
\(772\) 1.35043 16.1109i 0.0486029 0.579842i
\(773\) −15.8155 15.8155i −0.568845 0.568845i 0.362960 0.931805i \(-0.381766\pi\)
−0.931805 + 0.362960i \(0.881766\pi\)
\(774\) 0 0
\(775\) 39.2317 1.40925
\(776\) −22.2826 + 17.2922i −0.799898 + 0.620754i
\(777\) 0 0
\(778\) −1.73205 + 41.3999i −0.0620970 + 1.48426i
\(779\) −6.75629 + 6.75629i −0.242069 + 0.242069i
\(780\) 0 0
\(781\) −2.63560 2.63560i −0.0943091 0.0943091i
\(782\) 9.94589 + 10.8144i 0.355664 + 0.386724i
\(783\) 0 0
\(784\) −14.7798 2.49523i −0.527848 0.0891155i
\(785\) 2.85480i 0.101892i
\(786\) 0 0
\(787\) 18.8790 18.8790i 0.672962 0.672962i −0.285436 0.958398i \(-0.592138\pi\)
0.958398 + 0.285436i \(0.0921382\pi\)
\(788\) 15.8623 13.4087i 0.565070 0.477667i
\(789\) 0 0
\(790\)