Properties

Label 144.2.l.a.107.3
Level $144$
Weight $2$
Character 144.107
Analytic conductor $1.150$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

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 107.3
Root \(-1.40927 - 0.118126i\) of defining polynomial
Character \(\chi\) \(=\) 144.107
Dual form 144.2.l.a.35.3

$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

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

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 \(-0.726197\pi\)
0.757958 + 0.652303i \(0.226197\pi\)
\(6\) 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 \(-0.0644195\pi\)
−0.201001 + 0.979591i \(0.564420\pi\)
\(12\) 0 0
\(13\) −1.70773 + 1.70773i −0.473638 + 0.473638i −0.903090 0.429452i \(-0.858707\pi\)
0.429452 + 0.903090i \(0.358707\pi\)
\(14\) −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 0.963945 0.266100i \(-0.0857352\pi\)
−0.266100 + 0.963945i \(0.585735\pi\)
\(20\) −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 \(-0.378233\pi\)
−0.927719 + 0.373280i \(0.878233\pi\)
\(30\) 0 0
\(31\) 8.02552i 1.44143i −0.693233 0.720713i \(-0.743814\pi\)
0.693233 0.720713i \(-0.256186\pi\)
\(32\) 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 −0.925866 0.377852i \(-0.876663\pi\)
−0.377852 0.925866i \(-0.623337\pi\)
\(38\) −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 \(-0.444512\pi\)
0.173441 + 0.984844i \(0.444512\pi\)
\(42\) 0 0
\(43\) −4.61007 + 4.61007i −0.703030 + 0.703030i −0.965060 0.262030i \(-0.915608\pi\)
0.262030 + 0.965060i \(0.415608\pi\)
\(44\) 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 \(-0.674078\pi\)
−0.520026 + 0.854151i \(0.674078\pi\)
\(48\) 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 \(-0.941017\pi\)
0.184243 + 0.982881i \(0.441017\pi\)
\(54\) 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 \(-0.00885027\pi\)
−0.0278004 + 0.999613i \(0.508850\pi\)
\(60\) 0 0
\(61\) −4.04184 + 4.04184i −0.517504 + 0.517504i −0.916815 0.399311i \(-0.869249\pi\)
0.399311 + 0.916815i \(0.369249\pi\)
\(62\) 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 0.507052 0.861915i \(-0.330735\pi\)
−0.861915 + 0.507052i \(0.830735\pi\)
\(68\) −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 \(-0.923187\pi\)
0.971025 0.238979i \(-0.0768127\pi\)
\(74\) 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 \(-0.902468\pi\)
0.953424 0.301634i \(-0.0975322\pi\)
\(80\) −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 \(-0.848856\pi\)
0.457190 + 0.889369i \(0.348856\pi\)
\(84\) 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 \(-0.539905\pi\)
−0.125039 + 0.992152i \(0.539905\pi\)
\(90\) 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 \(-0.809730\pi\)
0.562785 + 0.826603i \(0.309730\pi\)
\(102\) 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 −0.988896 0.148609i \(-0.952520\pi\)
−0.148609 0.988896i \(1.45252\pi\)
\(108\) 0 0
\(109\) 6.26432 6.26432i 0.600013 0.600013i −0.340303 0.940316i \(-0.610530\pi\)
0.940316 + 0.340303i \(0.110530\pi\)
\(110\) −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 \(0.125620\pi\)
−0.923132 + 0.384482i \(0.874380\pi\)
\(128\) −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 0.378967 0.925410i \(-0.376280\pi\)
0.925410 0.378967i \(-0.123720\pi\)
\(132\) 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 \(-0.345269\pi\)
0.467183 + 0.884161i \(0.345269\pi\)
\(138\) 0 0
\(139\) −1.09532 + 1.09532i −0.0929036 + 0.0929036i −0.752031 0.659128i \(-0.770926\pi\)
0.659128 + 0.752031i \(0.270926\pi\)
\(140\) −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 \(-0.648328\pi\)
0.893378 + 0.449305i \(0.148328\pi\)
\(150\) 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 −0.423640 0.905831i \(-0.639248\pi\)
0.905831 + 0.423640i \(0.139248\pi\)
\(158\) 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 0.820163 0.572130i \(-0.193883\pi\)
−0.572130 + 0.820163i \(0.693883\pi\)
\(164\) −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 \(-0.452636\pi\)
−0.988950 + 0.148250i \(0.952636\pi\)
\(174\) 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 \(-0.815209\pi\)
0.548474 + 0.836167i \(0.315209\pi\)
\(180\) 0 0
\(181\) 4.29227 + 4.29227i 0.319042 + 0.319042i 0.848399 0.529357i \(-0.177567\pi\)
−0.529357 + 0.848399i \(0.677567\pi\)
\(182\) −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 \(-0.145425\pi\)
0.897439 + 0.441139i \(0.145425\pi\)
\(192\) 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 \(-0.629373\pi\)
0.918535 + 0.395339i \(0.129373\pi\)
\(198\) 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 0.734802 0.678282i \(-0.237275\pi\)
−0.678282 + 0.734802i \(0.737275\pi\)
\(212\) 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 \(-0.893188\pi\)
0.944227 0.329296i \(-0.106812\pi\)
\(224\) 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 −0.0404927 + 0.999180i \(0.512893\pi\)
−0.999180 + 0.0404927i \(0.987107\pi\)
\(228\) 0 0
\(229\) 11.4845 + 11.4845i 0.758915 + 0.758915i 0.976125 0.217210i \(-0.0696957\pi\)
−0.217210 + 0.976125i \(0.569696\pi\)
\(230\) −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 \(-0.769989\pi\)
−0.750089 + 0.661337i \(0.769989\pi\)
\(234\) 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 \(-0.484454\pi\)
0.0488199 + 0.998808i \(0.484454\pi\)
\(240\) 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 \(-0.0642186\pi\)
−0.200383 + 0.979718i \(0.564219\pi\)
\(252\) 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 \(-0.408794\pi\)
−0.959230 + 0.282628i \(0.908794\pi\)
\(270\) 0 0
\(271\) 30.0022i 1.82251i 0.411847 + 0.911253i \(0.364884\pi\)
−0.411847 + 0.911253i \(0.635116\pi\)
\(272\) 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 0.517491 0.855688i \(-0.326866\pi\)
−0.855688 + 0.517491i \(0.826866\pi\)
\(278\) −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 \(-0.384486\pi\)
0.354984 + 0.934872i \(0.384486\pi\)
\(282\) 0 0
\(283\) 17.3875 17.3875i 1.03358 1.03358i 0.0341630 0.999416i \(-0.489123\pi\)
0.999416 0.0341630i \(-0.0108765\pi\)
\(284\) 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 \(-0.681822\pi\)
0.841247 + 0.540651i \(0.181822\pi\)
\(294\) 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 0.990571 0.137002i \(-0.0437467\pi\)
−0.137002 + 0.990571i \(0.543747\pi\)
\(308\) 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 \(0.0127788\pi\)
−0.999194 + 0.0401350i \(0.987221\pi\)
\(314\) 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 −0.920368 0.391054i \(-0.872111\pi\)
−0.391054 0.920368i \(1.37211\pi\)
\(318\) 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 −0.621195 0.783656i \(-0.713352\pi\)
0.783656 + 0.621195i \(0.213352\pi\)
\(332\) 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 \(-0.287754\pi\)
−0.785811 + 0.618467i \(0.787754\pi\)
\(348\) 0 0
\(349\) 11.8465 11.8465i 0.634130 0.634130i −0.314971 0.949101i \(-0.601995\pi\)
0.949101 + 0.314971i \(0.101995\pi\)
\(350\) −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 \(0.0171070\pi\)
−0.998556 + 0.0537173i \(0.982893\pi\)
\(368\) −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 0.955896 0.293704i \(-0.0948879\pi\)
−0.293704 + 0.955896i \(0.594888\pi\)
\(374\) 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 −0.511599 0.859224i \(-0.670947\pi\)
0.859224 + 0.511599i \(0.170947\pi\)
\(380\) −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 \(-0.438776\pi\)
0.191158 + 0.981559i \(0.438776\pi\)
\(384\) 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 −0.0517883 + 0.998658i \(0.516492\pi\)
−0.998658 + 0.0517883i \(0.983508\pi\)
\(390\) 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 −0.319316 0.947648i \(-0.603453\pi\)
0.947648 + 0.319316i \(0.103453\pi\)
\(398\) −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 \(0.194863\pi\)
−0.818398 + 0.574652i \(0.805137\pi\)
\(410\) 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 0.0335424 0.999437i \(-0.489321\pi\)
0.999437 0.0335424i \(-0.0106789\pi\)
\(420\) 0 0
\(421\) 9.60077 + 9.60077i 0.467913 + 0.467913i 0.901238 0.433325i \(-0.142660\pi\)
−0.433325 + 0.901238i \(0.642660\pi\)
\(422\) −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 \(-0.645109\pi\)
−0.440246 + 0.897877i \(0.645109\pi\)
\(432\) 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 \(-0.0406198\pi\)
−0.127265 + 0.991869i \(0.540620\pi\)
\(444\) 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 \(-0.914795\pi\)
0.964387 0.264494i \(-0.0852051\pi\)
\(458\) −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 \(-0.133561\pi\)
−0.407389 + 0.913255i \(0.633561\pi\)
\(462\) 0 0
\(463\) 3.05504i 0.141980i −0.997477 0.0709898i \(-0.977384\pi\)
0.997477 0.0709898i \(-0.0226158\pi\)
\(464\) 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 \(-0.791123\pi\)
0.610115 + 0.792313i \(0.291123\pi\)
\(468\) 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 \(-0.282678\pi\)
0.630920 + 0.775848i \(0.282678\pi\)
\(480\) 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 \(-0.495412\pi\)
−0.999896 + 0.0144135i \(0.995412\pi\)
\(492\) 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 0.236665 0.971591i \(-0.423946\pi\)
−0.971591 + 0.236665i \(0.923946\pi\)
\(500\) 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 \(-0.391438\pi\)
−0.942401 + 0.334485i \(0.891438\pi\)
\(510\) 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 \(-0.493807\pi\)
0.0194560 + 0.999811i \(0.493807\pi\)
\(522\) 0 0
\(523\) −14.8186 + 14.8186i −0.647971 + 0.647971i −0.952502 0.304531i \(-0.901500\pi\)
0.304531 + 0.952502i \(0.401500\pi\)
\(524\) −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 −0.792808 0.609471i \(-0.791382\pi\)
0.609471 + 0.792808i \(0.291382\pi\)
\(542\) −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 0.695055 0.718957i \(-0.255380\pi\)
−0.718957 + 0.695055i \(0.755380\pi\)
\(548\) −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 \(-0.0403390\pi\)
−0.126390 + 0.991981i \(0.540339\pi\)
\(558\) 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 \(-0.613339\pi\)
0.937276 + 0.348587i \(0.113339\pi\)
\(564\) 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 \(-0.352642\pi\)
0.446579 + 0.894744i \(0.352642\pi\)
\(570\) 0 0
\(571\) −18.3333 + 18.3333i −0.767226 + 0.767226i −0.977617 0.210391i \(-0.932526\pi\)
0.210391 + 0.977617i \(0.432526\pi\)
\(572\) 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 \(-0.275601\pi\)
−0.761631 + 0.648011i \(0.775601\pi\)
\(588\) 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 \(0.105642\pi\)
−0.945430 + 0.325824i \(0.894358\pi\)
\(602\) −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 \(-0.894908\pi\)
0.945991 0.324192i \(-0.105092\pi\)
\(608\) 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 0.169206 0.985581i \(-0.445880\pi\)
−0.985581 + 0.169206i \(0.945880\pi\)
\(614\) −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 \(-0.474052\pi\)
0.0814275 + 0.996679i \(0.474052\pi\)
\(618\) 0 0
\(619\) −20.7472 + 20.7472i −0.833901 + 0.833901i −0.988048 0.154147i \(-0.950737\pi\)
0.154147 + 0.988048i \(0.450737\pi\)
\(620\) −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 0.860246 0.509880i \(-0.170310\pi\)
−0.509880 + 0.860246i \(0.670310\pi\)
\(644\) 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 \(-0.0406062\pi\)
−0.127222 + 0.991874i \(0.540606\pi\)
\(654\) 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 \(-0.879772\pi\)
0.368790 + 0.929513i \(0.379772\pi\)
\(660\) 0 0
\(661\) −27.1550 27.1550i −1.05621 1.05621i −0.998323 0.0578847i \(-0.981564\pi\)
−0.0578847 0.998323i \(-0.518436\pi\)
\(662\) 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 \(-0.574722\pi\)
0.972573 + 0.232597i \(0.0747223\pi\)
\(678\) 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 \(-0.214496\pi\)
−0.624006 + 0.781419i \(0.714496\pi\)
\(684\) 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 0.999252 0.0386833i \(-0.0123164\pi\)
−0.0386833 + 0.999252i \(0.512316\pi\)
\(692\) −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 \(-0.297092\pi\)
−0.803613 + 0.595152i \(0.797092\pi\)
\(702\) 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 0.601842 0.798615i \(-0.294434\pi\)
−0.798615 + 0.601842i \(0.794434\pi\)
\(710\) −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 \(-0.262063\pi\)
0.679808 + 0.733390i \(0.262063\pi\)
\(720\) 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 −0.878784 0.477219i \(-0.841645\pi\)
0.477219 + 0.878784i \(0.341645\pi\)
\(734\) −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 −0.950650 0.310265i \(-0.899582\pi\)
−0.310265 0.950650i \(-0.600418\pi\)
\(740\) 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 \(0.0870660\pi\)
−0.962824 + 0.270128i \(0.912934\pi\)
\(752\) 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 0.976250 + 0.216646i \(0.0695118\pi\)
0.216646 + 0.976250i \(0.430488\pi\)
\(758\) 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 \(-0.780086\pi\)
−0.770685 + 0.637217i \(0.780086\pi\)
\(762\) 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 \(-0.618234\pi\)
0.931805 + 0.362960i \(0.118234\pi\)
\(774\) 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 0.958398 0.285436i \(-0.0921382\pi\)
−0.285436 + 0.958398i \(0.592138\pi\)
\(788\) −15.8623 13.4087i −0.565070 0.477667i
\(789\) 0 0
\(790\)