Properties

Label 144.2.l.a.35.3
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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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [144,2,Mod(35,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) Copy content Toggle raw display
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 35.3
Root \(-1.40927 + 0.118126i\) of defining polynomial
Character \(\chi\) \(=\) 144.35
Dual form 144.2.l.a.107.3

$q$-expansion

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

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 0.757958 0.652303i \(-0.226197\pi\)
−0.652303 + 0.757958i \(0.726197\pi\)
\(6\) 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 −0.201001 0.979591i \(-0.564420\pi\)
0.979591 + 0.201001i \(0.0644195\pi\)
\(12\) 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 \(0.326502\pi\)
−0.518470 + 0.855096i \(0.673498\pi\)
\(18\) 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 \(-0.950910\pi\)
0.988131 0.153610i \(-0.0490901\pi\)
\(24\) 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 −0.927719 0.373280i \(-0.878233\pi\)
0.373280 + 0.927719i \(0.378233\pi\)
\(30\) 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 \(-0.444512\pi\)
0.173441 + 0.984844i \(0.444512\pi\)
\(42\) 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 \(-0.674078\pi\)
−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 0.184243 0.982881i \(-0.441017\pi\)
−0.982881 + 0.184243i \(0.941017\pi\)
\(54\) 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 −0.0278004 0.999613i \(-0.508850\pi\)
0.999613 + 0.0278004i \(0.00885027\pi\)
\(60\) 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 \(-0.980710\pi\)
0.998164 0.0605640i \(-0.0192899\pi\)
\(72\) 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 0.457190 0.889369i \(-0.348856\pi\)
−0.889369 + 0.457190i \(0.848856\pi\)
\(84\) 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 0.562785 0.826603i \(-0.309730\pi\)
−0.826603 + 0.562785i \(0.809730\pi\)
\(102\) 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 \(0.547480\pi\)
−0.988896 + 0.148609i \(0.952520\pi\)
\(108\) 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 \(-0.934241\pi\)
0.978736 0.205123i \(-0.0657594\pi\)
\(114\) 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 \(0.123720\pi\)
0.378967 + 0.925410i \(0.376280\pi\)
\(132\) 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 0.659128 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 0.893378 0.449305i \(-0.148328\pi\)
−0.449305 + 0.893378i \(0.648328\pi\)
\(150\) 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 \(-0.794769\pi\)
0.799249 0.601001i \(-0.205231\pi\)
\(168\) 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 −0.988950 0.148250i \(-0.952636\pi\)
0.148250 + 0.988950i \(0.452636\pi\)
\(174\) 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 0.548474 0.836167i \(-0.315209\pi\)
−0.836167 + 0.548474i \(0.815209\pi\)
\(180\) 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 \(-0.145425\pi\)
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 0.918535 0.395339i \(-0.129373\pi\)
−0.395339 + 0.918535i \(0.629373\pi\)
\(198\) 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 \(-0.987107\pi\)
−0.0404927 0.999180i \(-0.512893\pi\)
\(228\) 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 \(-0.769989\pi\)
−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 −0.200383 0.979718i \(-0.564219\pi\)
0.979718 + 0.200383i \(0.0642186\pi\)
\(252\) 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 \(0.106504\pi\)
−0.944545 + 0.328383i \(0.893496\pi\)
\(258\) 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 \(-0.859321\pi\)
0.903917 0.427709i \(-0.140679\pi\)
\(264\) 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 −0.959230 0.282628i \(-0.908794\pi\)
0.282628 + 0.959230i \(0.408794\pi\)
\(270\) 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 \(-0.384486\pi\)
0.354984 + 0.934872i \(0.384486\pi\)
\(282\) 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 0.841247 0.540651i \(-0.181822\pi\)
−0.540651 + 0.841247i \(0.681822\pi\)
\(294\) 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 \(-0.841030\pi\)
0.877862 0.478914i \(-0.158970\pi\)
\(312\) 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 \(0.627889\pi\)
−0.920368 + 0.391054i \(0.872111\pi\)
\(318\) 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 −0.785811 0.618467i \(-0.787754\pi\)
0.618467 + 0.785811i \(0.287754\pi\)
\(348\) 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 \(0.0450975\pi\)
−0.989980 + 0.141205i \(0.954902\pi\)
\(354\) 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 \(-0.843973\pi\)
0.882252 0.470778i \(-0.156027\pi\)
\(360\) 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 \(-0.438776\pi\)
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 −0.998658 0.0517883i \(-0.983508\pi\)
−0.0517883 0.998658i \(-0.516492\pi\)
\(390\) 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 \(0.0926514\pi\)
−0.957937 + 0.286980i \(0.907349\pi\)
\(402\) 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 \(0.0106789\pi\)
0.0335424 + 0.999437i \(0.489321\pi\)
\(420\) 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 \(-0.645109\pi\)
−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 −0.127265 0.991869i \(-0.540620\pi\)
0.991869 + 0.127265i \(0.0406198\pi\)
\(444\) 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 \(-0.932688\pi\)
0.977724 0.209895i \(-0.0673121\pi\)
\(450\) 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 −0.407389 0.913255i \(-0.633561\pi\)
0.913255 + 0.407389i \(0.133561\pi\)
\(462\) 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 0.610115 0.792313i \(-0.291123\pi\)
−0.792313 + 0.610115i \(0.791123\pi\)
\(468\) 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 −0.999896 0.0144135i \(-0.995412\pi\)
0.0144135 + 0.999896i \(0.495412\pi\)
\(492\) 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 \(0.164187\pi\)
−0.869895 + 0.493237i \(0.835813\pi\)
\(504\) 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 −0.942401 0.334485i \(-0.891438\pi\)
0.334485 + 0.942401i \(0.391438\pi\)
\(510\) 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 0.304531 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 −0.126390 0.991981i \(-0.540339\pi\)
0.991981 + 0.126390i \(0.0403390\pi\)
\(558\) 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 0.937276 0.348587i \(-0.113339\pi\)
−0.348587 + 0.937276i \(0.613339\pi\)
\(564\) 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 0.210391 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 −0.761631 0.648011i \(-0.775601\pi\)
0.648011 + 0.761631i \(0.275601\pi\)
\(588\) 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 \(0.0749053\pi\)
−0.972439 + 0.233156i \(0.925095\pi\)
\(594\) 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 \(0.177468\pi\)
−0.848564 + 0.529093i \(0.822532\pi\)
\(600\) 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 \(-0.474052\pi\)
0.0814275 + 0.996679i \(0.474052\pi\)
\(618\) 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 \(-0.818242\pi\)
0.841355 0.540482i \(-0.181758\pi\)
\(642\) 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 \(-0.701743\pi\)
0.592206 0.805787i \(-0.298257\pi\)
\(648\) 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 −0.127222 0.991874i \(-0.540606\pi\)
0.991874 + 0.127222i \(0.0406062\pi\)
\(654\) 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 0.368790 0.929513i \(-0.379772\pi\)
−0.929513 + 0.368790i \(0.879772\pi\)
\(660\) 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 0.972573 0.232597i \(-0.0747223\pi\)
−0.232597 + 0.972573i \(0.574722\pi\)
\(678\) 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 −0.624006 0.781419i \(-0.714496\pi\)
0.781419 + 0.624006i \(0.214496\pi\)
\(684\) 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 −0.803613 0.595152i \(-0.797092\pi\)
0.595152 + 0.803613i \(0.297092\pi\)
\(702\) 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 \(-0.262063\pi\)
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 0.477219 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 \(-0.901573\pi\)
0.952572 0.304314i \(-0.0984273\pi\)
\(744\) 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 \(-0.780086\pi\)
−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 0.931805 0.362960i \(-0.118234\pi\)
−0.362960 + 0.931805i \(0.618234\pi\)
\(774\) 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
\(790\) 2.53135 + 0.105904i 0.0900612 + 0.00376790i
\(791\) 14.2966i 0.508327i
\(792\) 0 0
\(793\) 13.8047i 0.490219i
\(794\) 1.04664 25.0170i 0.0371437 0.887819i
\(795\) 0 0
\(796\) −1.92993 + 23.0245i −0.0684046 + 0.816081i
\(797\) 15.5930 15.5930i 0.552332 0.552332i −0.374781 0.927113i \(-0.622282\pi\)
0.927113 + 0.374781i \(0.122282\pi\)
\(798\) 0 0
\(799\) 50.2774i 1.77869i
\(800\) 23.1859 15.0695i 0.819746 0.532788i
\(801\) 0 0
\(802\) 11.9639 11.0031i 0.422461 0.388532i
\(803\) 10.5452 + 10.5452i 0.372133 + 0.372133i
\(804\) 0 0
\(805\) 1.14114 1.14114i 0.0402200 0.0402200i
\(806\) −27.3868 1.14578i −0.964660 0.0403585i
\(807\) 0 0
\(808\) −10.5220 1.32683i −0.370164 0.0466777i
\(809\) 14.7494 0.518563 0.259281 0.965802i \(-0.416514\pi\)
0.259281 + 0.965802i \(0.416514\pi\)
\(810\) 0 0
\(811\) 9.71473 + 9.71473i 0.341130 + 0.341130i 0.856792 0.515662i \(-0.172454\pi\)
−0.515662 + 0.856792i \(0.672454\pi\)
\(812\) −17.8727 21.1431i −0.627210 0.741976i
\(813\) 0 0
\(814\) 42.6324 39.2084i 1.49426 1.37425i
\(815\) 1.49627 0.0524119
\(816\) 0 0
\(817\) −28.0462 −0.981212
\(818\) −24.1945 + 22.2513i −0.845941 + 0.778000i
\(819\) 0 0
\(820\) −1.13349 + 0.958163i −0.0395831 + 0.0334605i
\(821\) −10.2311 10.2311i −0.357070 0.357070i 0.505662 0.862732i \(-0.331248\pi\)
−0.862732 + 0.505662i \(0.831248\pi\)
\(822\) 0 0
\(823\) −22.8564 −0.796725 −0.398362 0.917228i \(-0.630421\pi\)
−0.398362 + 0.917228i \(0.630421\pi\)
\(824\) −0.0570327 + 0.0442597i −0.00198683 + 0.00154186i
\(825\) 0 0
\(826\) −48.8998 2.04582i −1.70144 0.0711834i
\(827\) −19.1488 + 19.1488i −0.665871 + 0.665871i −0.956757 0.290887i \(-0.906050\pi\)
0.290887 + 0.956757i \(0.406050\pi\)
\(828\) 0 0
\(829\) −32.8813 32.8813i −1.14201 1.14201i −0.988081 0.153934i \(-0.950806\pi\)
−0.153934 0.988081i \(-0.549194\pi\)
\(830\) −1.93655 + 1.78102i −0.0672187 + 0.0618201i
\(831\) 0 0
\(832\) −16.6257 + 9.84254i −0.576393 + 0.341229i
\(833\) 26.4228i 0.915497i
\(834\) 0 0
\(835\) 3.66978 3.66978i 0.126998 0.126998i
\(836\) 31.3098 + 2.62442i 1.08287 + 0.0907673i
\(837\) 0 0
\(838\) 1.76771 42.2522i 0.0610644 1.45958i
\(839\) 41.2084i 1.42267i 0.702853 + 0.711335i \(0.251909\pi\)
−0.702853 + 0.711335i \(0.748091\pi\)
\(840\) 0 0
\(841\) 11.1707i 0.385195i
\(842\) −19.1847 0.802634i −0.661150 0.0276606i
\(843\) 0 0
\(844\) 1.49912 + 1.77343i 0.0516020 + 0.0610441i
\(845\) 1.69331 1.69331i 0.0582515 0.0582515i
\(846\) 0 0
\(847\) 7.65957i 0.263186i
\(848\) 19.0606 + 26.8038i 0.654543 + 0.920445i
\(849\) 0 0
\(850\) −32.9984 35.8801i −1.13184 1.23068i
\(851\) 11.6842 + 11.6842i 0.400530 + 0.400530i
\(852\) 0 0
\(853\) −16.3985 + 16.3985i −0.561472 + 0.561472i −0.929726 0.368253i \(-0.879956\pi\)
0.368253 + 0.929726i \(0.379956\pi\)
\(854\) −1.10774 + 26.4775i −0.0379061 + 0.906042i
\(855\) 0 0
\(856\) −5.88837 + 46.6960i −0.201260 + 1.59604i
\(857\) −3.15292 −0.107702 −0.0538509 0.998549i \(-0.517150\pi\)
−0.0538509 + 0.998549i \(0.517150\pi\)
\(858\) 0 0
\(859\) 14.6691 + 14.6691i 0.500503 + 0.500503i 0.911594 0.411091i \(-0.134852\pi\)
−0.411091 + 0.911594i \(0.634852\pi\)
\(860\) 4.34134 + 0.363895i 0.148039 + 0.0124087i
\(861\) 0 0
\(862\) 17.4994 + 19.0276i 0.596032 + 0.648082i
\(863\) 42.0851 1.43259 0.716297 0.697795i \(-0.245836\pi\)
0.716297 + 0.697795i \(0.245836\pi\)
\(864\) 0 0
\(865\) −5.22482 −0.177649
\(866\) −32.9170 35.7916i −1.11857 1.21625i
\(867\) 0 0
\(868\) −52.4362 4.39525i −1.77980 0.149184i
\(869\) 13.8462 + 13.8462i 0.469699 + 0.469699i
\(870\) 0 0
\(871\) 9.92080 0.336154
\(872\) 24.8604 + 3.13490i 0.841879 + 0.106161i
\(873\) 0 0
\(874\) −0.374681 + 8.95573i −0.0126738 + 0.302932i
\(875\) 7.65860 7.65860i 0.258908 0.258908i
\(876\) 0 0
\(877\) −2.42641 2.42641i −0.0819341 0.0819341i 0.664952 0.746886i \(-0.268452\pi\)
−0.746886 + 0.664952i \(0.768452\pi\)
\(878\) −14.5239 15.7922i −0.490158 0.532962i
\(879\) 0 0
\(880\) −4.81248 0.812481i −0.162229 0.0273887i
\(881\) 32.2178i 1.08544i 0.839912 + 0.542722i \(0.182606\pi\)
−0.839912 + 0.542722i \(0.817394\pi\)
\(882\) 0 0
\(883\) 0.924984 0.924984i 0.0311282 0.0311282i −0.691371 0.722500i \(-0.742993\pi\)
0.722500 + 0.691371i \(0.242993\pi\)
\(884\) 21.9876 + 26.0108i 0.739522 + 0.874839i
\(885\) 0 0
\(886\) −36.3638 1.52135i −1.22167 0.0511109i
\(887\) 17.9482i 0.602643i −0.953523 0.301321i \(-0.902572\pi\)
0.953523 0.301321i \(-0.0974277\pi\)
\(888\) 0 0
\(889\) 28.4090i 0.952808i
\(890\) −0.0465969 + 1.11377i −0.00156193 + 0.0373337i
\(891\) 0 0
\(892\) −19.6010 1.64298i −0.656291 0.0550109i
\(893\) −21.6890 + 21.6890i −0.725795 + 0.725795i
\(894\) 0 0
\(895\) 1.81871i 0.0607926i
\(896\) −32.6780 + 17.5440i −1.09170 + 0.586103i
\(897\) 0 0
\(898\) −9.25923 + 8.51558i −0.308984 + 0.284169i
\(899\) −23.9622 23.9622i −0.799183 0.799183i
\(900\) 0 0
\(901\) 40.9975 40.9975i 1.36582 1.36582i
\(902\) −11.4611 0.479501i −0.381614 0.0159656i
\(903\) 0 0
\(904\) −7.56222 9.74462i −0.251516 0.324101i
\(905\) 2.02812 0.0674171
\(906\) 0 0
\(907\) −17.2503 17.2503i −0.572788 0.572788i 0.360118 0.932907i \(-0.382736\pi\)
−0.932907 + 0.360118i \(0.882736\pi\)
\(908\) 33.8358 28.6022i 1.12288 0.949198i
\(909\) 0 0
\(910\) −2.75355 + 2.53240i −0.0912793 + 0.0839483i
\(911\) 19.5368 0.647282 0.323641 0.946180i \(-0.395093\pi\)
0.323641 + 0.946180i \(0.395093\pi\)
\(912\) 0 0
\(913\) −20.3347 −0.672980
\(914\) 11.7713 10.8259i 0.389360 0.358089i
\(915\) 0 0
\(916\) 20.9701 + 24.8072i 0.692872 + 0.819653i
\(917\) 48.9426 + 48.9426i 1.61623 + 1.61623i
\(918\) 0 0
\(919\) 15.9943 0.527602 0.263801 0.964577i \(-0.415024\pi\)
0.263801 + 0.964577i \(0.415024\pi\)
\(920\) 0.174197 1.38142i 0.00574311 0.0455441i
\(921\) 0 0
\(922\) −21.7038 0.908023i −0.714776 0.0299041i
\(923\) −1.74298 + 1.74298i −0.0573708 + 0.0573708i
\(924\) 0 0
\(925\) 38.7658 + 38.7658i 1.27461 + 1.27461i
\(926\) 3.18007 2.92466i 0.104503 0.0961104i
\(927\) 0 0
\(928\) −23.3659 4.95738i −0.767022 0.162734i
\(929\) 1.11164i 0.0364717i −0.999834 0.0182358i \(-0.994195\pi\)
0.999834 0.0182358i \(-0.00580497\pi\)
\(930\) 0 0
\(931\) 11.3985 11.3985i 0.373569 0.373569i
\(932\) 3.82545 45.6384i 0.125307 1.49493i
\(933\) 0 0
\(934\) −0.329165 + 7.86779i −0.0107706 + 0.257442i
\(935\) 8.60361i 0.281368i
\(936\) 0 0
\(937\) 17.7208i 0.578914i −0.957191 0.289457i \(-0.906525\pi\)
0.957191 0.289457i \(-0.0934747\pi\)
\(938\) 19.0282 + 0.796083i 0.621292 + 0.0259930i
\(939\) 0 0
\(940\) 3.63871 3.07589i 0.118682 0.100324i
\(941\) −30.8171 + 30.8171i −1.00461 + 1.00461i −0.00462076 + 0.999989i \(0.501471\pi\)
−0.999989 + 0.00462076i \(0.998529\pi\)
\(942\) 0 0
\(943\) 3.27256i 0.106569i
\(944\) −34.4125 + 24.4713i −1.12003 + 0.796473i
\(945\) 0 0
\(946\) 22.7931 + 24.7835i 0.741066 + 0.805782i
\(947\) −16.6327 16.6327i −0.540491 0.540491i 0.383182 0.923673i \(-0.374828\pi\)
−0.923673 + 0.383182i \(0.874828\pi\)
\(948\) 0 0
\(949\) 6.97379 6.97379i 0.226379 0.226379i
\(950\) −1.24312 + 29.7133i −0.0403320 + 0.964025i
\(951\) 0 0
\(952\) 40.0851 + 51.6534i 1.29917 + 1.67410i
\(953\) −14.5520 −0.471387 −0.235693 0.971827i \(-0.575736\pi\)
−0.235693 + 0.971827i \(0.575736\pi\)
\(954\) 0 0
\(955\) 5.86041 + 5.86041i 0.189639 + 0.189639i
\(956\) −0.252167 + 3.00840i −0.00815566 + 0.0972987i
\(957\) 0 0
\(958\) −26.4382 28.7470i −0.854178 0.928772i
\(959\) 35.8530 1.15775
\(960\) 0 0
\(961\) −33.4090 −1.07771
\(962\) −25.9294 28.1937i −0.835997 0.909002i
\(963\) 0 0
\(964\) 3.23957 38.6488i 0.104340 1.24479i
\(965\) −1.90979 1.90979i −0.0614783 0.0614783i
\(966\) 0 0
\(967\) −17.3884 −0.559172 −0.279586 0.960121i \(-0.590197\pi\)
−0.279586 + 0.960121i \(0.590197\pi\)
\(968\) −4.05156 5.22080i −0.130222 0.167803i
\(969\) 0 0
\(970\) 0.196957 4.70773i 0.00632392 0.151156i
\(971\) −20.2644 + 20.2644i −0.650314 + 0.650314i −0.953069 0.302754i \(-0.902094\pi\)
0.302754 + 0.953069i \(0.402094\pi\)
\(972\) 0 0
\(973\) −3.59077 3.59077i −0.115115 0.115115i
\(974\) −12.5202 13.6136i −0.401173 0.436207i
\(975\) 0 0
\(976\) 13.2503 + 18.6332i 0.424133 + 0.596433i
\(977\) 35.3026i 1.12943i −0.825285 0.564716i \(-0.808986\pi\)
0.825285 0.564716i \(-0.191014\pi\)
\(978\) 0 0
\(979\) −6.09220 + 6.09220i −0.194708 + 0.194708i
\(980\) −1.91229 + 1.61650i −0.0610859 + 0.0516373i
\(981\) 0 0
\(982\) 43.6355 + 1.82558i 1.39246 + 0.0582566i
\(983\) 51.7381i 1.65019i −0.564995 0.825094i \(-0.691122\pi\)
0.564995 0.825094i \(-0.308878\pi\)
\(984\) 0 0
\(985\) 3.46980i 0.110557i
\(986\) −1.76008 + 42.0700i −0.0560525 + 1.33978i
\(987\) 0 0
\(988\) 1.73558 20.7059i 0.0552163 0.658742i
\(989\) −6.79239 + 6.79239i −0.215985 + 0.215985i
\(990\) 0 0
\(991\) 25.0317i 0.795160i 0.917568 + 0.397580i \(0.130150\pi\)
−0.917568 + 0.397580i \(0.869850\pi\)
\(992\) −38.0657 + 24.7405i −1.20859 + 0.785512i
\(993\) 0 0
\(994\) −3.48291 + 3.20318i −0.110471 + 0.101599i
\(995\) 2.72933 + 2.72933i 0.0865257 + 0.0865257i
\(996\) 0 0
\(997\) −17.3224 + 17.3224i −0.548605 + 0.548605i −0.926037 0.377432i \(-0.876807\pi\)
0.377432 + 0.926037i \(0.376807\pi\)
\(998\) 32.8053 + 1.37248i 1.03843 + 0.0434450i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 144.2.l.a.35.3 16
3.2 odd 2 inner 144.2.l.a.35.6 yes 16
4.3 odd 2 576.2.l.a.431.5 16
8.3 odd 2 1152.2.l.b.863.4 16
8.5 even 2 1152.2.l.a.863.4 16
12.11 even 2 576.2.l.a.431.4 16
16.3 odd 4 1152.2.l.a.287.5 16
16.5 even 4 576.2.l.a.143.4 16
16.11 odd 4 inner 144.2.l.a.107.6 yes 16
16.13 even 4 1152.2.l.b.287.5 16
24.5 odd 2 1152.2.l.a.863.5 16
24.11 even 2 1152.2.l.b.863.5 16
48.5 odd 4 576.2.l.a.143.5 16
48.11 even 4 inner 144.2.l.a.107.3 yes 16
48.29 odd 4 1152.2.l.b.287.4 16
48.35 even 4 1152.2.l.a.287.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.l.a.35.3 16 1.1 even 1 trivial
144.2.l.a.35.6 yes 16 3.2 odd 2 inner
144.2.l.a.107.3 yes 16 48.11 even 4 inner
144.2.l.a.107.6 yes 16 16.11 odd 4 inner
576.2.l.a.143.4 16 16.5 even 4
576.2.l.a.143.5 16 48.5 odd 4
576.2.l.a.431.4 16 12.11 even 2
576.2.l.a.431.5 16 4.3 odd 2
1152.2.l.a.287.4 16 48.35 even 4
1152.2.l.a.287.5 16 16.3 odd 4
1152.2.l.a.863.4 16 8.5 even 2
1152.2.l.a.863.5 16 24.5 odd 2
1152.2.l.b.287.4 16 48.29 odd 4
1152.2.l.b.287.5 16 16.13 even 4
1152.2.l.b.863.4 16 8.3 odd 2
1152.2.l.b.863.5 16 24.11 even 2