Properties

Label 684.2.ce.a.359.3
Level $684$
Weight $2$
Character 684.359
Analytic conductor $5.462$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [684,2,Mod(35,684)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(684, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("684.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 684.ce (of order \(18\), degree \(6\), 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: \(5.46176749826\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(40\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 359.3
Character \(\chi\) \(=\) 684.359
Dual form 684.2.ce.a.503.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39232 + 0.247874i) q^{2} +(1.87712 - 0.690240i) q^{4} +(0.294744 + 0.809802i) q^{5} +(-2.07545 + 1.19826i) q^{7} +(-2.44246 + 1.42632i) q^{8} +O(q^{10})\) \(q+(-1.39232 + 0.247874i) q^{2} +(1.87712 - 0.690240i) q^{4} +(0.294744 + 0.809802i) q^{5} +(-2.07545 + 1.19826i) q^{7} +(-2.44246 + 1.42632i) q^{8} +(-0.611107 - 1.05445i) q^{10} +(-1.68767 + 2.92312i) q^{11} +(1.65614 - 1.38967i) q^{13} +(2.59267 - 2.18281i) q^{14} +(3.04714 - 2.59132i) q^{16} +(-7.72199 - 1.36160i) q^{17} +(-0.789602 - 4.28679i) q^{19} +(1.11223 + 1.31665i) q^{20} +(1.62521 - 4.48825i) q^{22} +(-2.80559 - 1.02115i) q^{23} +(3.26132 - 2.73657i) q^{25} +(-1.96142 + 2.34538i) q^{26} +(-3.06877 + 3.68183i) q^{28} +(4.45240 - 0.785078i) q^{29} +(-7.62096 + 4.39996i) q^{31} +(-3.60028 + 4.36326i) q^{32} +(11.0890 - 0.0182998i) q^{34} +(-1.58208 - 1.32752i) q^{35} -7.33783 q^{37} +(2.16196 + 5.77286i) q^{38} +(-1.87494 - 1.55751i) q^{40} +(4.47507 - 5.33318i) q^{41} +(1.61673 + 4.44193i) q^{43} +(-1.15029 + 6.65194i) q^{44} +(4.15941 + 0.726340i) q^{46} +(-1.49426 - 8.47439i) q^{47} +(-0.628347 + 1.08833i) q^{49} +(-3.86248 + 4.61858i) q^{50} +(2.14957 - 3.75171i) q^{52} +(0.0611610 - 0.168038i) q^{53} +(-2.86458 - 0.505103i) q^{55} +(3.36009 - 5.88696i) q^{56} +(-6.00457 + 2.19671i) q^{58} +(-0.802194 + 4.54947i) q^{59} +(-2.65253 - 0.965440i) q^{61} +(9.52019 - 8.01520i) q^{62} +(3.93120 - 6.96747i) q^{64} +(1.61349 + 0.931551i) q^{65} +(-11.8747 + 2.09382i) q^{67} +(-15.4349 + 2.77415i) q^{68} +(2.53182 + 1.45618i) q^{70} +(-9.81994 + 3.57417i) q^{71} +(-5.28753 - 4.43677i) q^{73} +(10.2166 - 1.81886i) q^{74} +(-4.44108 - 7.50178i) q^{76} -8.08905i q^{77} +(-3.94292 + 4.69899i) q^{79} +(2.99658 + 1.70380i) q^{80} +(-4.90878 + 8.53475i) q^{82} +(-7.58820 - 13.1432i) q^{83} +(-1.17339 - 6.65461i) q^{85} +(-3.35205 - 5.78385i) q^{86} +(-0.0472644 - 9.54676i) q^{88} +(-2.98845 - 3.56150i) q^{89} +(-1.77205 + 4.86867i) q^{91} +(-5.97127 + 0.0197084i) q^{92} +(4.18107 + 11.4287i) q^{94} +(3.23872 - 1.90292i) q^{95} +(0.117541 - 0.666610i) q^{97} +(0.605092 - 1.67105i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39232 + 0.247874i −0.984520 + 0.175273i
\(3\) 0 0
\(4\) 1.87712 0.690240i 0.938559 0.345120i
\(5\) 0.294744 + 0.809802i 0.131813 + 0.362154i 0.987988 0.154533i \(-0.0493872\pi\)
−0.856174 + 0.516687i \(0.827165\pi\)
\(6\) 0 0
\(7\) −2.07545 + 1.19826i −0.784445 + 0.452900i −0.838003 0.545665i \(-0.816277\pi\)
0.0535581 + 0.998565i \(0.482944\pi\)
\(8\) −2.44246 + 1.42632i −0.863539 + 0.504281i
\(9\) 0 0
\(10\) −0.611107 1.05445i −0.193249 0.333445i
\(11\) −1.68767 + 2.92312i −0.508850 + 0.881355i 0.491097 + 0.871105i \(0.336596\pi\)
−0.999947 + 0.0102500i \(0.996737\pi\)
\(12\) 0 0
\(13\) 1.65614 1.38967i 0.459331 0.385425i −0.383554 0.923519i \(-0.625300\pi\)
0.842885 + 0.538094i \(0.180855\pi\)
\(14\) 2.59267 2.18281i 0.692921 0.583381i
\(15\) 0 0
\(16\) 3.04714 2.59132i 0.761785 0.647830i
\(17\) −7.72199 1.36160i −1.87286 0.330235i −0.882672 0.469989i \(-0.844258\pi\)
−0.990186 + 0.139754i \(0.955369\pi\)
\(18\) 0 0
\(19\) −0.789602 4.28679i −0.181147 0.983456i
\(20\) 1.11223 + 1.31665i 0.248701 + 0.294412i
\(21\) 0 0
\(22\) 1.62521 4.48825i 0.346496 0.956899i
\(23\) −2.80559 1.02115i −0.585007 0.212925i 0.0325250 0.999471i \(-0.489645\pi\)
−0.617532 + 0.786546i \(0.711867\pi\)
\(24\) 0 0
\(25\) 3.26132 2.73657i 0.652263 0.547314i
\(26\) −1.96142 + 2.34538i −0.384666 + 0.459967i
\(27\) 0 0
\(28\) −3.06877 + 3.68183i −0.579943 + 0.695800i
\(29\) 4.45240 0.785078i 0.826789 0.145785i 0.255786 0.966733i \(-0.417666\pi\)
0.571003 + 0.820948i \(0.306555\pi\)
\(30\) 0 0
\(31\) −7.62096 + 4.39996i −1.36876 + 0.790257i −0.990770 0.135551i \(-0.956719\pi\)
−0.377994 + 0.925808i \(0.623386\pi\)
\(32\) −3.60028 + 4.36326i −0.636445 + 0.771322i
\(33\) 0 0
\(34\) 11.0890 0.0182998i 1.90175 0.00313839i
\(35\) −1.58208 1.32752i −0.267420 0.224392i
\(36\) 0 0
\(37\) −7.33783 −1.20633 −0.603166 0.797615i \(-0.706094\pi\)
−0.603166 + 0.797615i \(0.706094\pi\)
\(38\) 2.16196 + 5.77286i 0.350716 + 0.936482i
\(39\) 0 0
\(40\) −1.87494 1.55751i −0.296454 0.246264i
\(41\) 4.47507 5.33318i 0.698888 0.832903i −0.293512 0.955955i \(-0.594824\pi\)
0.992400 + 0.123053i \(0.0392685\pi\)
\(42\) 0 0
\(43\) 1.61673 + 4.44193i 0.246549 + 0.677388i 0.999807 + 0.0196624i \(0.00625914\pi\)
−0.753258 + 0.657726i \(0.771519\pi\)
\(44\) −1.15029 + 6.65194i −0.173413 + 1.00282i
\(45\) 0 0
\(46\) 4.15941 + 0.726340i 0.613271 + 0.107093i
\(47\) −1.49426 8.47439i −0.217961 1.23612i −0.875694 0.482866i \(-0.839596\pi\)
0.657734 0.753251i \(-0.271515\pi\)
\(48\) 0 0
\(49\) −0.628347 + 1.08833i −0.0897638 + 0.155475i
\(50\) −3.86248 + 4.61858i −0.546237 + 0.653166i
\(51\) 0 0
\(52\) 2.14957 3.75171i 0.298092 0.520268i
\(53\) 0.0611610 0.168038i 0.00840111 0.0230819i −0.935421 0.353535i \(-0.884979\pi\)
0.943822 + 0.330453i \(0.107202\pi\)
\(54\) 0 0
\(55\) −2.86458 0.505103i −0.386260 0.0681080i
\(56\) 3.36009 5.88696i 0.449011 0.786678i
\(57\) 0 0
\(58\) −6.00457 + 2.19671i −0.788438 + 0.288442i
\(59\) −0.802194 + 4.54947i −0.104437 + 0.592291i 0.887007 + 0.461756i \(0.152780\pi\)
−0.991444 + 0.130534i \(0.958331\pi\)
\(60\) 0 0
\(61\) −2.65253 0.965440i −0.339621 0.123612i 0.166579 0.986028i \(-0.446728\pi\)
−0.506200 + 0.862416i \(0.668950\pi\)
\(62\) 9.52019 8.01520i 1.20907 1.01793i
\(63\) 0 0
\(64\) 3.93120 6.96747i 0.491401 0.870934i
\(65\) 1.61349 + 0.931551i 0.200129 + 0.115545i
\(66\) 0 0
\(67\) −11.8747 + 2.09382i −1.45072 + 0.255801i −0.842813 0.538207i \(-0.819102\pi\)
−0.607907 + 0.794008i \(0.707991\pi\)
\(68\) −15.4349 + 2.77415i −1.87176 + 0.336415i
\(69\) 0 0
\(70\) 2.53182 + 1.45618i 0.302610 + 0.174047i
\(71\) −9.81994 + 3.57417i −1.16541 + 0.424176i −0.851028 0.525120i \(-0.824020\pi\)
−0.314385 + 0.949296i \(0.601798\pi\)
\(72\) 0 0
\(73\) −5.28753 4.43677i −0.618859 0.519284i 0.278586 0.960411i \(-0.410134\pi\)
−0.897445 + 0.441127i \(0.854579\pi\)
\(74\) 10.2166 1.81886i 1.18766 0.211438i
\(75\) 0 0
\(76\) −4.44108 7.50178i −0.509427 0.860514i
\(77\) 8.08905i 0.921833i
\(78\) 0 0
\(79\) −3.94292 + 4.69899i −0.443613 + 0.528677i −0.940798 0.338967i \(-0.889922\pi\)
0.497185 + 0.867644i \(0.334367\pi\)
\(80\) 2.99658 + 1.70380i 0.335028 + 0.190491i
\(81\) 0 0
\(82\) −4.90878 + 8.53475i −0.542084 + 0.942505i
\(83\) −7.58820 13.1432i −0.832914 1.44265i −0.895718 0.444623i \(-0.853338\pi\)
0.0628044 0.998026i \(-0.479996\pi\)
\(84\) 0 0
\(85\) −1.17339 6.65461i −0.127272 0.721793i
\(86\) −3.35205 5.78385i −0.361460 0.623689i
\(87\) 0 0
\(88\) −0.0472644 9.54676i −0.00503841 1.01769i
\(89\) −2.98845 3.56150i −0.316775 0.377518i 0.584037 0.811727i \(-0.301472\pi\)
−0.900812 + 0.434209i \(0.857028\pi\)
\(90\) 0 0
\(91\) −1.77205 + 4.86867i −0.185762 + 0.510376i
\(92\) −5.97127 + 0.0197084i −0.622548 + 0.00205474i
\(93\) 0 0
\(94\) 4.18107 + 11.4287i 0.431245 + 1.17878i
\(95\) 3.23872 1.90292i 0.332285 0.195236i
\(96\) 0 0
\(97\) 0.117541 0.666610i 0.0119345 0.0676840i −0.978259 0.207388i \(-0.933504\pi\)
0.990193 + 0.139704i \(0.0446150\pi\)
\(98\) 0.605092 1.67105i 0.0611236 0.168802i
\(99\) 0 0
\(100\) 4.23299 7.38795i 0.423299 0.738795i
\(101\) 1.47271 + 1.75510i 0.146540 + 0.174639i 0.834321 0.551278i \(-0.185860\pi\)
−0.687782 + 0.725918i \(0.741415\pi\)
\(102\) 0 0
\(103\) 15.5341 + 8.96861i 1.53062 + 0.883704i 0.999333 + 0.0365116i \(0.0116246\pi\)
0.531287 + 0.847192i \(0.321709\pi\)
\(104\) −2.06294 + 5.75640i −0.202288 + 0.564462i
\(105\) 0 0
\(106\) −0.0435034 + 0.249124i −0.00422543 + 0.0241970i
\(107\) 1.32317 + 2.29180i 0.127916 + 0.221557i 0.922869 0.385114i \(-0.125838\pi\)
−0.794953 + 0.606671i \(0.792505\pi\)
\(108\) 0 0
\(109\) 4.06044 1.47788i 0.388920 0.141555i −0.140157 0.990129i \(-0.544761\pi\)
0.529077 + 0.848574i \(0.322538\pi\)
\(110\) 4.11362 0.00678856i 0.392218 0.000647264i
\(111\) 0 0
\(112\) −3.21910 + 9.02941i −0.304176 + 0.853199i
\(113\) 13.1332i 1.23546i 0.786389 + 0.617732i \(0.211948\pi\)
−0.786389 + 0.617732i \(0.788052\pi\)
\(114\) 0 0
\(115\) 2.57295i 0.239929i
\(116\) 7.81578 4.54690i 0.725677 0.422169i
\(117\) 0 0
\(118\) −0.0107815 6.53317i −0.000992514 0.601427i
\(119\) 17.6581 6.42703i 1.61872 0.589165i
\(120\) 0 0
\(121\) −0.196433 0.340233i −0.0178576 0.0309302i
\(122\) 3.93247 + 0.686712i 0.356030 + 0.0621720i
\(123\) 0 0
\(124\) −11.2684 + 13.5195i −1.01193 + 1.21409i
\(125\) 6.90892 + 3.98887i 0.617953 + 0.356775i
\(126\) 0 0
\(127\) 4.91926 + 5.86255i 0.436514 + 0.520217i 0.938790 0.344490i \(-0.111948\pi\)
−0.502276 + 0.864707i \(0.667504\pi\)
\(128\) −3.74645 + 10.6754i −0.331142 + 0.943581i
\(129\) 0 0
\(130\) −2.47741 0.897076i −0.217283 0.0786788i
\(131\) 1.44419 8.19039i 0.126179 0.715598i −0.854421 0.519581i \(-0.826088\pi\)
0.980600 0.196017i \(-0.0628008\pi\)
\(132\) 0 0
\(133\) 6.77546 + 7.95085i 0.587507 + 0.689426i
\(134\) 16.0143 5.85869i 1.38343 0.506114i
\(135\) 0 0
\(136\) 20.8027 7.68842i 1.78382 0.659276i
\(137\) −2.75030 + 7.55638i −0.234974 + 0.645585i 0.765025 + 0.644001i \(0.222727\pi\)
−0.999999 + 0.00158449i \(0.999496\pi\)
\(138\) 0 0
\(139\) −5.11738 6.09866i −0.434051 0.517282i 0.504036 0.863683i \(-0.331848\pi\)
−0.938086 + 0.346401i \(0.887404\pi\)
\(140\) −3.88605 1.39990i −0.328432 0.118313i
\(141\) 0 0
\(142\) 12.7866 7.41049i 1.07303 0.621875i
\(143\) 1.26716 + 7.18641i 0.105965 + 0.600958i
\(144\) 0 0
\(145\) 1.94807 + 3.37416i 0.161779 + 0.280209i
\(146\) 8.46170 + 4.86677i 0.700296 + 0.402776i
\(147\) 0 0
\(148\) −13.7740 + 5.06486i −1.13221 + 0.416329i
\(149\) 1.57760 1.88011i 0.129242 0.154025i −0.697542 0.716543i \(-0.745723\pi\)
0.826785 + 0.562519i \(0.190168\pi\)
\(150\) 0 0
\(151\) 1.55905i 0.126874i −0.997986 0.0634370i \(-0.979794\pi\)
0.997986 0.0634370i \(-0.0202062\pi\)
\(152\) 8.04291 + 9.34407i 0.652366 + 0.757904i
\(153\) 0 0
\(154\) 2.00506 + 11.2626i 0.161573 + 0.907563i
\(155\) −5.80933 4.87461i −0.466617 0.391538i
\(156\) 0 0
\(157\) −11.7845 + 4.28921i −0.940506 + 0.342316i −0.766366 0.642405i \(-0.777937\pi\)
−0.174140 + 0.984721i \(0.555715\pi\)
\(158\) 4.32505 7.51984i 0.344083 0.598247i
\(159\) 0 0
\(160\) −4.59453 1.62947i −0.363230 0.128821i
\(161\) 7.04647 1.24248i 0.555340 0.0979214i
\(162\) 0 0
\(163\) −10.5297 6.07933i −0.824750 0.476170i 0.0273018 0.999627i \(-0.491308\pi\)
−0.852052 + 0.523458i \(0.824642\pi\)
\(164\) 4.71906 13.0999i 0.368496 1.02293i
\(165\) 0 0
\(166\) 13.8231 + 16.4186i 1.07288 + 1.27433i
\(167\) 9.20385 + 3.34993i 0.712215 + 0.259225i 0.672617 0.739991i \(-0.265170\pi\)
0.0395978 + 0.999216i \(0.487392\pi\)
\(168\) 0 0
\(169\) −1.44580 + 8.19952i −0.111215 + 0.630732i
\(170\) 3.28323 + 8.97450i 0.251812 + 0.688313i
\(171\) 0 0
\(172\) 6.10079 + 7.22209i 0.465181 + 0.550679i
\(173\) 14.7175 + 2.59509i 1.11895 + 0.197301i 0.702380 0.711802i \(-0.252121\pi\)
0.416571 + 0.909103i \(0.363232\pi\)
\(174\) 0 0
\(175\) −3.48957 + 9.58751i −0.263787 + 0.724748i
\(176\) 2.43220 + 13.2804i 0.183334 + 1.00105i
\(177\) 0 0
\(178\) 5.04368 + 4.21799i 0.378040 + 0.316152i
\(179\) −4.64063 + 8.03781i −0.346857 + 0.600774i −0.985689 0.168572i \(-0.946084\pi\)
0.638832 + 0.769346i \(0.279418\pi\)
\(180\) 0 0
\(181\) 4.37903 + 24.8347i 0.325491 + 1.84595i 0.506203 + 0.862414i \(0.331049\pi\)
−0.180712 + 0.983536i \(0.557840\pi\)
\(182\) 1.26045 7.21800i 0.0934308 0.535034i
\(183\) 0 0
\(184\) 8.30904 1.50756i 0.612551 0.111139i
\(185\) −2.16278 5.94219i −0.159011 0.436879i
\(186\) 0 0
\(187\) 17.0123 20.2744i 1.24406 1.48261i
\(188\) −8.65426 14.8760i −0.631177 1.08495i
\(189\) 0 0
\(190\) −4.03765 + 3.45228i −0.292922 + 0.250454i
\(191\) 24.9747 1.80710 0.903551 0.428480i \(-0.140951\pi\)
0.903551 + 0.428480i \(0.140951\pi\)
\(192\) 0 0
\(193\) −9.61468 8.06768i −0.692080 0.580724i 0.227428 0.973795i \(-0.426968\pi\)
−0.919508 + 0.393071i \(0.871413\pi\)
\(194\) 0.00157975 + 0.957270i 0.000113419 + 0.0687280i
\(195\) 0 0
\(196\) −0.428273 + 2.47663i −0.0305909 + 0.176902i
\(197\) −17.3740 + 10.0309i −1.23785 + 0.714672i −0.968654 0.248414i \(-0.920091\pi\)
−0.269195 + 0.963086i \(0.586757\pi\)
\(198\) 0 0
\(199\) 18.6219 3.28354i 1.32007 0.232764i 0.531161 0.847271i \(-0.321756\pi\)
0.788911 + 0.614507i \(0.210645\pi\)
\(200\) −4.06240 + 11.3356i −0.287255 + 0.801551i
\(201\) 0 0
\(202\) −2.48553 2.07862i −0.174881 0.146251i
\(203\) −8.29999 + 6.96451i −0.582545 + 0.488813i
\(204\) 0 0
\(205\) 5.63782 + 2.05200i 0.393762 + 0.143318i
\(206\) −23.8515 8.63670i −1.66182 0.601747i
\(207\) 0 0
\(208\) 1.44542 8.52611i 0.100222 0.591179i
\(209\) 13.8634 + 4.92656i 0.958951 + 0.340777i
\(210\) 0 0
\(211\) 15.5643 + 2.74440i 1.07149 + 0.188933i 0.681450 0.731865i \(-0.261350\pi\)
0.390041 + 0.920798i \(0.372461\pi\)
\(212\) −0.00118042 0.357644i −8.10714e−5 0.0245631i
\(213\) 0 0
\(214\) −2.41036 2.86295i −0.164769 0.195707i
\(215\) −3.12056 + 2.61846i −0.212821 + 0.178578i
\(216\) 0 0
\(217\) 10.5446 18.2638i 0.715814 1.23983i
\(218\) −5.28711 + 3.06416i −0.358089 + 0.207531i
\(219\) 0 0
\(220\) −5.72579 + 1.02911i −0.386033 + 0.0693825i
\(221\) −14.6809 + 8.47602i −0.987544 + 0.570159i
\(222\) 0 0
\(223\) −0.278472 0.765095i −0.0186479 0.0512346i 0.930019 0.367510i \(-0.119790\pi\)
−0.948667 + 0.316276i \(0.897568\pi\)
\(224\) 2.24387 13.3698i 0.149925 0.893306i
\(225\) 0 0
\(226\) −3.25537 18.2856i −0.216544 1.21634i
\(227\) 4.39878 0.291958 0.145979 0.989288i \(-0.453367\pi\)
0.145979 + 0.989288i \(0.453367\pi\)
\(228\) 0 0
\(229\) 4.48158 0.296151 0.148076 0.988976i \(-0.452692\pi\)
0.148076 + 0.988976i \(0.452692\pi\)
\(230\) 0.637768 + 3.58238i 0.0420531 + 0.236215i
\(231\) 0 0
\(232\) −9.75502 + 8.26807i −0.640448 + 0.542826i
\(233\) −5.42325 14.9003i −0.355289 0.976148i −0.980643 0.195807i \(-0.937268\pi\)
0.625354 0.780341i \(-0.284955\pi\)
\(234\) 0 0
\(235\) 6.42215 3.70783i 0.418935 0.241872i
\(236\) 1.63441 + 9.09359i 0.106391 + 0.591943i
\(237\) 0 0
\(238\) −22.9927 + 13.3255i −1.49040 + 0.863763i
\(239\) 8.37012 14.4975i 0.541418 0.937764i −0.457405 0.889259i \(-0.651221\pi\)
0.998823 0.0485054i \(-0.0154458\pi\)
\(240\) 0 0
\(241\) −18.8812 + 15.8432i −1.21624 + 1.02055i −0.217231 + 0.976120i \(0.569703\pi\)
−0.999013 + 0.0444297i \(0.985853\pi\)
\(242\) 0.357833 + 0.425022i 0.0230024 + 0.0273215i
\(243\) 0 0
\(244\) −5.64549 + 0.0186332i −0.361415 + 0.00119287i
\(245\) −1.06653 0.188058i −0.0681382 0.0120146i
\(246\) 0 0
\(247\) −7.26491 6.00224i −0.462255 0.381914i
\(248\) 12.3381 21.6167i 0.783471 1.37266i
\(249\) 0 0
\(250\) −10.6082 3.84125i −0.670920 0.242942i
\(251\) −15.4669 5.62948i −0.976261 0.355330i −0.195875 0.980629i \(-0.562755\pi\)
−0.780385 + 0.625299i \(0.784977\pi\)
\(252\) 0 0
\(253\) 7.71986 6.47773i 0.485344 0.407252i
\(254\) −8.30236 6.94320i −0.520937 0.435655i
\(255\) 0 0
\(256\) 2.57011 15.7922i 0.160632 0.987014i
\(257\) −8.62199 + 1.52029i −0.537825 + 0.0948331i −0.435962 0.899965i \(-0.643592\pi\)
−0.101864 + 0.994798i \(0.532481\pi\)
\(258\) 0 0
\(259\) 15.2293 8.79263i 0.946302 0.546348i
\(260\) 3.67171 + 0.634934i 0.227710 + 0.0393769i
\(261\) 0 0
\(262\) 0.0194098 + 11.7616i 0.00119914 + 0.726636i
\(263\) 15.4391 + 12.9549i 0.952016 + 0.798836i 0.979636 0.200782i \(-0.0643483\pi\)
−0.0276198 + 0.999618i \(0.508793\pi\)
\(264\) 0 0
\(265\) 0.154105 0.00946657
\(266\) −11.4044 9.39068i −0.699250 0.575779i
\(267\) 0 0
\(268\) −20.8449 + 12.1267i −1.27330 + 0.740757i
\(269\) −4.82085 + 5.74526i −0.293932 + 0.350295i −0.892719 0.450614i \(-0.851205\pi\)
0.598787 + 0.800908i \(0.295650\pi\)
\(270\) 0 0
\(271\) 0.169153 + 0.464745i 0.0102753 + 0.0282313i 0.944724 0.327866i \(-0.106329\pi\)
−0.934449 + 0.356097i \(0.884107\pi\)
\(272\) −27.0583 + 15.8612i −1.64065 + 0.961726i
\(273\) 0 0
\(274\) 1.95627 11.2026i 0.118183 0.676776i
\(275\) 2.49532 + 14.1516i 0.150473 + 0.853376i
\(276\) 0 0
\(277\) 12.0558 20.8812i 0.724361 1.25463i −0.234875 0.972026i \(-0.575468\pi\)
0.959236 0.282605i \(-0.0911986\pi\)
\(278\) 8.63674 + 7.22283i 0.517997 + 0.433197i
\(279\) 0 0
\(280\) 5.75763 + 0.985861i 0.344084 + 0.0589164i
\(281\) 3.69312 10.1468i 0.220313 0.605305i −0.779464 0.626448i \(-0.784508\pi\)
0.999776 + 0.0211428i \(0.00673047\pi\)
\(282\) 0 0
\(283\) −13.1383 2.31664i −0.780990 0.137710i −0.231082 0.972934i \(-0.574226\pi\)
−0.549909 + 0.835225i \(0.685338\pi\)
\(284\) −15.9662 + 13.4872i −0.947417 + 0.800321i
\(285\) 0 0
\(286\) −3.54561 9.69169i −0.209656 0.573082i
\(287\) −2.89723 + 16.4310i −0.171018 + 0.969893i
\(288\) 0 0
\(289\) 41.8005 + 15.2141i 2.45885 + 0.894948i
\(290\) −3.54871 4.21504i −0.208387 0.247516i
\(291\) 0 0
\(292\) −12.9878 4.67867i −0.760051 0.273798i
\(293\) −22.8738 13.2062i −1.33630 0.771513i −0.350043 0.936733i \(-0.613833\pi\)
−0.986257 + 0.165220i \(0.947167\pi\)
\(294\) 0 0
\(295\) −3.92061 + 0.691310i −0.228267 + 0.0402496i
\(296\) 17.9224 10.4661i 1.04172 0.608331i
\(297\) 0 0
\(298\) −1.73050 + 3.00877i −0.100245 + 0.174293i
\(299\) −6.06553 + 2.20767i −0.350779 + 0.127673i
\(300\) 0 0
\(301\) −8.67803 7.28173i −0.500193 0.419712i
\(302\) 0.386448 + 2.17070i 0.0222376 + 0.124910i
\(303\) 0 0
\(304\) −13.5145 11.0163i −0.775108 0.631829i
\(305\) 2.43258i 0.139289i
\(306\) 0 0
\(307\) 11.2323 13.3861i 0.641059 0.763985i −0.343478 0.939161i \(-0.611605\pi\)
0.984537 + 0.175176i \(0.0560495\pi\)
\(308\) −5.58338 15.1841i −0.318143 0.865194i
\(309\) 0 0
\(310\) 9.29674 + 5.34704i 0.528019 + 0.303691i
\(311\) −8.24491 14.2806i −0.467526 0.809779i 0.531786 0.846879i \(-0.321521\pi\)
−0.999312 + 0.0371003i \(0.988188\pi\)
\(312\) 0 0
\(313\) −0.926830 5.25632i −0.0523875 0.297105i 0.947345 0.320213i \(-0.103755\pi\)
−0.999733 + 0.0231090i \(0.992644\pi\)
\(314\) 15.3446 8.89303i 0.865948 0.501863i
\(315\) 0 0
\(316\) −4.15789 + 11.5421i −0.233900 + 0.649294i
\(317\) 14.4777 + 17.2539i 0.813149 + 0.969073i 0.999911 0.0133319i \(-0.00424380\pi\)
−0.186762 + 0.982405i \(0.559799\pi\)
\(318\) 0 0
\(319\) −5.21928 + 14.3399i −0.292224 + 0.802878i
\(320\) 6.80097 + 1.12988i 0.380186 + 0.0631621i
\(321\) 0 0
\(322\) −9.50297 + 3.47657i −0.529580 + 0.193742i
\(323\) 0.260433 + 34.1776i 0.0144909 + 1.90170i
\(324\) 0 0
\(325\) 1.59828 9.06430i 0.0886567 0.502797i
\(326\) 16.1676 + 5.85434i 0.895442 + 0.324242i
\(327\) 0 0
\(328\) −3.32333 + 19.4090i −0.183500 + 1.07168i
\(329\) 13.2558 + 15.7976i 0.730815 + 0.870951i
\(330\) 0 0
\(331\) −4.85664 2.80398i −0.266945 0.154121i 0.360553 0.932739i \(-0.382588\pi\)
−0.627499 + 0.778618i \(0.715921\pi\)
\(332\) −23.3159 19.4336i −1.27962 1.06656i
\(333\) 0 0
\(334\) −13.6451 2.38278i −0.746625 0.130380i
\(335\) −5.19556 8.99898i −0.283864 0.491667i
\(336\) 0 0
\(337\) −23.1701 + 8.43324i −1.26216 + 0.459388i −0.884493 0.466554i \(-0.845495\pi\)
−0.377665 + 0.925942i \(0.623273\pi\)
\(338\) −0.0194315 11.7747i −0.00105693 0.640462i
\(339\) 0 0
\(340\) −6.79586 11.6816i −0.368557 0.633521i
\(341\) 29.7027i 1.60849i
\(342\) 0 0
\(343\) 19.7873i 1.06842i
\(344\) −10.2844 8.54325i −0.554499 0.460621i
\(345\) 0 0
\(346\) −21.1347 + 0.0348779i −1.13621 + 0.00187505i
\(347\) −15.8250 + 5.75983i −0.849531 + 0.309204i −0.729849 0.683608i \(-0.760410\pi\)
−0.119682 + 0.992812i \(0.538187\pi\)
\(348\) 0 0
\(349\) −1.63536 2.83252i −0.0875387 0.151621i 0.818932 0.573891i \(-0.194567\pi\)
−0.906470 + 0.422270i \(0.861233\pi\)
\(350\) 2.48211 14.2139i 0.132674 0.759763i
\(351\) 0 0
\(352\) −6.67827 17.8878i −0.355953 0.953421i
\(353\) −9.30139 5.37016i −0.495063 0.285825i 0.231609 0.972809i \(-0.425601\pi\)
−0.726673 + 0.686984i \(0.758934\pi\)
\(354\) 0 0
\(355\) −5.78873 6.89874i −0.307234 0.366147i
\(356\) −8.06795 4.62260i −0.427601 0.244997i
\(357\) 0 0
\(358\) 4.46889 12.3415i 0.236188 0.652269i
\(359\) −1.27735 + 7.24418i −0.0674157 + 0.382333i 0.932368 + 0.361512i \(0.117739\pi\)
−0.999783 + 0.0208216i \(0.993372\pi\)
\(360\) 0 0
\(361\) −17.7531 + 6.76971i −0.934371 + 0.356300i
\(362\) −12.2529 33.4925i −0.643998 1.76032i
\(363\) 0 0
\(364\) 0.0342009 + 10.3622i 0.00179261 + 0.543127i
\(365\) 2.03443 5.58956i 0.106487 0.292571i
\(366\) 0 0
\(367\) 7.86751 + 9.37613i 0.410680 + 0.489430i 0.931246 0.364392i \(-0.118723\pi\)
−0.520565 + 0.853822i \(0.674279\pi\)
\(368\) −11.1952 + 4.15860i −0.583589 + 0.216782i
\(369\) 0 0
\(370\) 4.48420 + 7.73735i 0.233122 + 0.402245i
\(371\) 0.0744173 + 0.422042i 0.00386356 + 0.0219113i
\(372\) 0 0
\(373\) −7.64556 13.2425i −0.395872 0.685671i 0.597340 0.801988i \(-0.296224\pi\)
−0.993212 + 0.116317i \(0.962891\pi\)
\(374\) −18.6610 + 32.4454i −0.964939 + 1.67771i
\(375\) 0 0
\(376\) 15.7369 + 18.5670i 0.811568 + 0.957522i
\(377\) 6.28281 7.48756i 0.323581 0.385629i
\(378\) 0 0
\(379\) 35.8226i 1.84008i −0.391820 0.920042i \(-0.628155\pi\)
0.391820 0.920042i \(-0.371845\pi\)
\(380\) 4.76598 5.80750i 0.244489 0.297919i
\(381\) 0 0
\(382\) −34.7727 + 6.19056i −1.77913 + 0.316737i
\(383\) 25.6781 + 21.5465i 1.31209 + 1.10097i 0.987918 + 0.154976i \(0.0495299\pi\)
0.324171 + 0.945998i \(0.394915\pi\)
\(384\) 0 0
\(385\) 6.55053 2.38420i 0.333846 0.121510i
\(386\) 15.3865 + 8.84957i 0.783152 + 0.450431i
\(387\) 0 0
\(388\) −0.239482 1.33244i −0.0121578 0.0676442i
\(389\) −16.6303 + 2.93236i −0.843187 + 0.148677i −0.578525 0.815665i \(-0.696372\pi\)
−0.264662 + 0.964341i \(0.585260\pi\)
\(390\) 0 0
\(391\) 20.2744 + 11.7054i 1.02532 + 0.591969i
\(392\) −0.0175973 3.55442i −0.000888800 0.179525i
\(393\) 0 0
\(394\) 21.7038 18.2728i 1.09342 0.920571i
\(395\) −4.96740 1.80799i −0.249937 0.0909696i
\(396\) 0 0
\(397\) −6.52241 + 36.9904i −0.327350 + 1.85650i 0.165266 + 0.986249i \(0.447152\pi\)
−0.492616 + 0.870247i \(0.663959\pi\)
\(398\) −25.1138 + 9.18763i −1.25884 + 0.460534i
\(399\) 0 0
\(400\) 2.84635 16.7898i 0.142318 0.839491i
\(401\) 30.9269 + 5.45325i 1.54442 + 0.272322i 0.879976 0.475018i \(-0.157559\pi\)
0.664441 + 0.747341i \(0.268670\pi\)
\(402\) 0 0
\(403\) −6.50691 + 17.8776i −0.324132 + 0.890546i
\(404\) 3.97589 + 2.27802i 0.197808 + 0.113335i
\(405\) 0 0
\(406\) 9.82993 11.7542i 0.487851 0.583351i
\(407\) 12.3838 21.4494i 0.613843 1.06321i
\(408\) 0 0
\(409\) −1.46956 8.33427i −0.0726649 0.412103i −0.999343 0.0362469i \(-0.988460\pi\)
0.926678 0.375856i \(-0.122651\pi\)
\(410\) −8.35829 1.45957i −0.412786 0.0720832i
\(411\) 0 0
\(412\) 35.3498 + 6.11289i 1.74156 + 0.301161i
\(413\) −3.78654 10.4034i −0.186323 0.511919i
\(414\) 0 0
\(415\) 8.40678 10.0188i 0.412672 0.491804i
\(416\) 0.100911 + 12.2294i 0.00494756 + 0.599594i
\(417\) 0 0
\(418\) −20.5235 3.42298i −1.00383 0.167424i
\(419\) 16.7413 0.817867 0.408933 0.912564i \(-0.365901\pi\)
0.408933 + 0.912564i \(0.365901\pi\)
\(420\) 0 0
\(421\) 1.74700 + 1.46590i 0.0851434 + 0.0714438i 0.684366 0.729139i \(-0.260079\pi\)
−0.599223 + 0.800583i \(0.704524\pi\)
\(422\) −22.3508 + 0.0368847i −1.08802 + 0.00179552i
\(423\) 0 0
\(424\) 0.0902939 + 0.497662i 0.00438506 + 0.0241686i
\(425\) −28.9100 + 16.6912i −1.40234 + 0.809641i
\(426\) 0 0
\(427\) 6.66202 1.17469i 0.322398 0.0568475i
\(428\) 4.06565 + 3.38868i 0.196520 + 0.163798i
\(429\) 0 0
\(430\) 3.69578 4.41925i 0.178226 0.213115i
\(431\) −6.09376 + 5.11327i −0.293526 + 0.246298i −0.777644 0.628705i \(-0.783585\pi\)
0.484118 + 0.875003i \(0.339141\pi\)
\(432\) 0 0
\(433\) 9.28136 + 3.37814i 0.446034 + 0.162343i 0.555265 0.831673i \(-0.312617\pi\)
−0.109231 + 0.994016i \(0.534839\pi\)
\(434\) −10.1544 + 28.0428i −0.487425 + 1.34610i
\(435\) 0 0
\(436\) 6.60184 5.57683i 0.316171 0.267082i
\(437\) −2.16216 + 12.8333i −0.103430 + 0.613899i
\(438\) 0 0
\(439\) −21.4928 3.78976i −1.02579 0.180875i −0.364658 0.931141i \(-0.618814\pi\)
−0.661136 + 0.750266i \(0.729925\pi\)
\(440\) 7.71706 2.85212i 0.367896 0.135970i
\(441\) 0 0
\(442\) 18.3395 15.4403i 0.872323 0.734422i
\(443\) −14.9033 + 12.5054i −0.708078 + 0.594148i −0.924059 0.382250i \(-0.875149\pi\)
0.215981 + 0.976397i \(0.430705\pi\)
\(444\) 0 0
\(445\) 2.00328 3.46978i 0.0949645 0.164483i
\(446\) 0.577369 + 0.996232i 0.0273392 + 0.0471730i
\(447\) 0 0
\(448\) 0.189832 + 19.1712i 0.00896870 + 0.905755i
\(449\) −15.9971 + 9.23594i −0.754951 + 0.435871i −0.827480 0.561495i \(-0.810226\pi\)
0.0725292 + 0.997366i \(0.476893\pi\)
\(450\) 0 0
\(451\) 8.03712 + 22.0818i 0.378453 + 1.03979i
\(452\) 9.06503 + 24.6525i 0.426383 + 1.15956i
\(453\) 0 0
\(454\) −6.12452 + 1.09034i −0.287438 + 0.0511723i
\(455\) −4.46496 −0.209321
\(456\) 0 0
\(457\) 39.9109 1.86695 0.933477 0.358637i \(-0.116758\pi\)
0.933477 + 0.358637i \(0.116758\pi\)
\(458\) −6.23980 + 1.11087i −0.291567 + 0.0519073i
\(459\) 0 0
\(460\) −1.77595 4.82974i −0.0828043 0.225188i
\(461\) −5.09196 13.9900i −0.237156 0.651581i −0.999988 0.00498392i \(-0.998414\pi\)
0.762831 0.646598i \(-0.223809\pi\)
\(462\) 0 0
\(463\) −11.1531 + 6.43926i −0.518329 + 0.299258i −0.736251 0.676709i \(-0.763406\pi\)
0.217922 + 0.975966i \(0.430072\pi\)
\(464\) 11.5327 13.9298i 0.535391 0.646676i
\(465\) 0 0
\(466\) 11.2443 + 19.4017i 0.520881 + 0.898765i
\(467\) −7.54976 + 13.0766i −0.349361 + 0.605111i −0.986136 0.165938i \(-0.946935\pi\)
0.636775 + 0.771050i \(0.280268\pi\)
\(468\) 0 0
\(469\) 22.1363 18.5745i 1.02216 0.857693i
\(470\) −8.02262 + 6.75437i −0.370056 + 0.311556i
\(471\) 0 0
\(472\) −4.52969 12.2561i −0.208496 0.564132i
\(473\) −15.7128 2.77059i −0.722476 0.127392i
\(474\) 0 0
\(475\) −14.3062 11.8198i −0.656415 0.542328i
\(476\) 28.7102 24.2526i 1.31593 1.11162i
\(477\) 0 0
\(478\) −8.06036 + 22.2599i −0.368672 + 1.01814i
\(479\) 6.31766 + 2.29944i 0.288661 + 0.105064i 0.482292 0.876010i \(-0.339804\pi\)
−0.193631 + 0.981074i \(0.562026\pi\)
\(480\) 0 0
\(481\) −12.1525 + 10.1972i −0.554106 + 0.464950i
\(482\) 22.3616 26.7390i 1.01854 1.21793i
\(483\) 0 0
\(484\) −0.603570 0.503070i −0.0274350 0.0228668i
\(485\) 0.574466 0.101294i 0.0260852 0.00459952i
\(486\) 0 0
\(487\) 7.89672 4.55917i 0.357834 0.206596i −0.310296 0.950640i \(-0.600428\pi\)
0.668130 + 0.744044i \(0.267095\pi\)
\(488\) 7.85571 1.42531i 0.355611 0.0645208i
\(489\) 0 0
\(490\) 1.53157 0.00252750i 0.0691892 0.000114181i
\(491\) −28.3728 23.8076i −1.28045 1.07442i −0.993182 0.116571i \(-0.962810\pi\)
−0.287264 0.957851i \(-0.592746\pi\)
\(492\) 0 0
\(493\) −35.4503 −1.59660
\(494\) 11.6029 + 6.55627i 0.522038 + 0.294981i
\(495\) 0 0
\(496\) −11.8204 + 33.1557i −0.530752 + 1.48873i
\(497\) 16.0980 19.1848i 0.722093 0.860558i
\(498\) 0 0
\(499\) −7.82010 21.4856i −0.350076 0.961825i −0.982345 0.187077i \(-0.940099\pi\)
0.632269 0.774749i \(-0.282124\pi\)
\(500\) 15.7221 + 2.71876i 0.703115 + 0.121587i
\(501\) 0 0
\(502\) 22.9303 + 4.00422i 1.02343 + 0.178717i
\(503\) 3.18840 + 18.0823i 0.142164 + 0.806250i 0.969601 + 0.244692i \(0.0786868\pi\)
−0.827437 + 0.561558i \(0.810202\pi\)
\(504\) 0 0
\(505\) −0.987215 + 1.70991i −0.0439305 + 0.0760899i
\(506\) −9.14287 + 10.9326i −0.406450 + 0.486015i
\(507\) 0 0
\(508\) 13.2806 + 7.60922i 0.589231 + 0.337605i
\(509\) −1.37680 + 3.78273i −0.0610256 + 0.167666i −0.966458 0.256823i \(-0.917324\pi\)
0.905433 + 0.424490i \(0.139546\pi\)
\(510\) 0 0
\(511\) 16.2904 + 2.87244i 0.720645 + 0.127069i
\(512\) 0.336059 + 22.6249i 0.0148518 + 0.999890i
\(513\) 0 0
\(514\) 11.6277 4.25390i 0.512878 0.187631i
\(515\) −2.68422 + 15.2230i −0.118281 + 0.670805i
\(516\) 0 0
\(517\) 27.2935 + 9.93402i 1.20037 + 0.436898i
\(518\) −19.0246 + 16.0171i −0.835893 + 0.703751i
\(519\) 0 0
\(520\) −5.26959 + 0.0260888i −0.231087 + 0.00114407i
\(521\) −0.605646 0.349670i −0.0265338 0.0153193i 0.486674 0.873583i \(-0.338210\pi\)
−0.513208 + 0.858264i \(0.671543\pi\)
\(522\) 0 0
\(523\) −26.9707 + 4.75567i −1.17935 + 0.207951i −0.728753 0.684777i \(-0.759900\pi\)
−0.450596 + 0.892728i \(0.648788\pi\)
\(524\) −2.94242 16.3712i −0.128540 0.715177i
\(525\) 0 0
\(526\) −24.7074 14.2105i −1.07729 0.619607i
\(527\) 64.8400 23.5998i 2.82447 1.02802i
\(528\) 0 0
\(529\) −10.7904 9.05423i −0.469148 0.393662i
\(530\) −0.214563 + 0.0381985i −0.00932003 + 0.00165924i
\(531\) 0 0
\(532\) 18.2063 + 10.2480i 0.789344 + 0.444306i
\(533\) 15.0514i 0.651947i
\(534\) 0 0
\(535\) −1.46591 + 1.74700i −0.0633768 + 0.0755296i
\(536\) 26.0169 22.0512i 1.12376 0.952466i
\(537\) 0 0
\(538\) 5.28807 9.19421i 0.227985 0.396391i
\(539\) −2.12088 3.67347i −0.0913527 0.158227i
\(540\) 0 0
\(541\) −6.20240 35.1756i −0.266662 1.51232i −0.764260 0.644908i \(-0.776896\pi\)
0.497598 0.867408i \(-0.334215\pi\)
\(542\) −0.350714 0.605146i −0.0150645 0.0259932i
\(543\) 0 0
\(544\) 33.7423 28.7909i 1.44669 1.23440i
\(545\) 2.39358 + 2.85256i 0.102530 + 0.122190i
\(546\) 0 0
\(547\) 7.02410 19.2985i 0.300329 0.825146i −0.694114 0.719865i \(-0.744204\pi\)
0.994443 0.105281i \(-0.0335742\pi\)
\(548\) 0.0530812 + 16.0826i 0.00226752 + 0.687014i
\(549\) 0 0
\(550\) −6.98210 19.0851i −0.297718 0.813792i
\(551\) −6.88108 18.4666i −0.293144 0.786702i
\(552\) 0 0
\(553\) 2.55271 14.4771i 0.108552 0.615630i
\(554\) −11.6096 + 32.0617i −0.493245 + 1.36217i
\(555\) 0 0
\(556\) −13.8155 7.91568i −0.585906 0.335700i
\(557\) 6.07847 + 7.24404i 0.257553 + 0.306940i 0.879290 0.476286i \(-0.158017\pi\)
−0.621737 + 0.783226i \(0.713573\pi\)
\(558\) 0 0
\(559\) 8.85035 + 5.10975i 0.374330 + 0.216119i
\(560\) −8.26085 + 0.0545311i −0.349084 + 0.00230436i
\(561\) 0 0
\(562\) −2.62689 + 15.0430i −0.110809 + 0.634549i
\(563\) −13.3746 23.1654i −0.563671 0.976306i −0.997172 0.0751534i \(-0.976055\pi\)
0.433501 0.901153i \(-0.357278\pi\)
\(564\) 0 0
\(565\) −10.6353 + 3.87092i −0.447429 + 0.162851i
\(566\) 18.8670 0.0311355i 0.793037 0.00130872i
\(567\) 0 0
\(568\) 18.8869 22.7362i 0.792476 0.953988i
\(569\) 30.3341i 1.27167i 0.771825 + 0.635835i \(0.219344\pi\)
−0.771825 + 0.635835i \(0.780656\pi\)
\(570\) 0 0
\(571\) 36.5696i 1.53039i 0.643799 + 0.765195i \(0.277357\pi\)
−0.643799 + 0.765195i \(0.722643\pi\)
\(572\) 7.33894 + 12.6151i 0.306857 + 0.527463i
\(573\) 0 0
\(574\) −0.0389387 23.5954i −0.00162527 0.984854i
\(575\) −11.9444 + 4.34740i −0.498115 + 0.181299i
\(576\) 0 0
\(577\) 5.56387 + 9.63690i 0.231627 + 0.401189i 0.958287 0.285808i \(-0.0922618\pi\)
−0.726660 + 0.686997i \(0.758929\pi\)
\(578\) −61.9708 10.8217i −2.57765 0.450124i
\(579\) 0 0
\(580\) 5.98574 + 4.98906i 0.248544 + 0.207159i
\(581\) 31.4978 + 18.1853i 1.30675 + 0.754453i
\(582\) 0 0
\(583\) 0.387978 + 0.462374i 0.0160684 + 0.0191496i
\(584\) 19.2428 + 3.29489i 0.796275 + 0.136343i
\(585\) 0 0
\(586\) 35.1211 + 12.7174i 1.45084 + 0.525353i
\(587\) 5.71714 32.4235i 0.235971 1.33826i −0.604587 0.796539i \(-0.706662\pi\)
0.840558 0.541721i \(-0.182227\pi\)
\(588\) 0 0
\(589\) 24.8792 + 29.1952i 1.02513 + 1.20297i
\(590\) 5.28739 1.93434i 0.217679 0.0796356i
\(591\) 0 0
\(592\) −22.3594 + 19.0147i −0.918966 + 0.781499i
\(593\) −12.0571 + 33.1267i −0.495126 + 1.36035i 0.400808 + 0.916162i \(0.368729\pi\)
−0.895934 + 0.444187i \(0.853493\pi\)
\(594\) 0 0
\(595\) 10.4092 + 12.4053i 0.426738 + 0.508566i
\(596\) 1.66361 4.61811i 0.0681443 0.189165i
\(597\) 0 0
\(598\) 7.89794 4.57727i 0.322971 0.187179i
\(599\) −5.37209 30.4666i −0.219498 1.24483i −0.872929 0.487847i \(-0.837782\pi\)
0.653432 0.756985i \(-0.273329\pi\)
\(600\) 0 0
\(601\) 15.3151 + 26.5266i 0.624717 + 1.08204i 0.988596 + 0.150595i \(0.0481189\pi\)
−0.363879 + 0.931446i \(0.618548\pi\)
\(602\) 13.8875 + 7.98745i 0.566014 + 0.325544i
\(603\) 0 0
\(604\) −1.07612 2.92653i −0.0437867 0.119079i
\(605\) 0.217623 0.259354i 0.00884765 0.0105442i
\(606\) 0 0
\(607\) 19.0703i 0.774038i 0.922072 + 0.387019i \(0.126495\pi\)
−0.922072 + 0.387019i \(0.873505\pi\)
\(608\) 21.5471 + 11.9884i 0.873852 + 0.486193i
\(609\) 0 0
\(610\) 0.602972 + 3.38693i 0.0244136 + 0.137133i
\(611\) −14.2513 11.9583i −0.576546 0.483780i
\(612\) 0 0
\(613\) −36.7090 + 13.3610i −1.48266 + 0.539645i −0.951506 0.307629i \(-0.900464\pi\)
−0.531156 + 0.847274i \(0.678242\pi\)
\(614\) −12.3209 + 21.4219i −0.497230 + 0.864518i
\(615\) 0 0
\(616\) 11.5376 + 19.7572i 0.464863 + 0.796039i
\(617\) 13.9514 2.46001i 0.561662 0.0990362i 0.114393 0.993436i \(-0.463508\pi\)
0.447269 + 0.894399i \(0.352397\pi\)
\(618\) 0 0
\(619\) 9.86407 + 5.69503i 0.396471 + 0.228902i 0.684960 0.728581i \(-0.259820\pi\)
−0.288489 + 0.957483i \(0.593153\pi\)
\(620\) −14.2694 5.14038i −0.573074 0.206443i
\(621\) 0 0
\(622\) 15.0193 + 17.8395i 0.602221 + 0.715299i
\(623\) 10.4700 + 3.81076i 0.419470 + 0.152675i
\(624\) 0 0
\(625\) 2.50257 14.1928i 0.100103 0.567712i
\(626\) 2.59335 + 7.08874i 0.103651 + 0.283323i
\(627\) 0 0
\(628\) −19.1603 + 16.1855i −0.764580 + 0.645871i
\(629\) 56.6627 + 9.99116i 2.25929 + 0.398374i
\(630\) 0 0
\(631\) −14.5251 + 39.9073i −0.578234 + 1.58869i 0.212920 + 0.977070i \(0.431703\pi\)
−0.791155 + 0.611616i \(0.790520\pi\)
\(632\) 2.92814 17.1010i 0.116475 0.680239i
\(633\) 0 0
\(634\) −24.4344 20.4343i −0.970414 0.811549i
\(635\) −3.29758 + 5.71158i −0.130861 + 0.226657i
\(636\) 0 0
\(637\) 0.471784 + 2.67562i 0.0186928 + 0.106012i
\(638\) 3.71244 21.2594i 0.146977 0.841668i
\(639\) 0 0
\(640\) −9.74920 + 0.112626i −0.385371 + 0.00445195i
\(641\) −8.79213 24.1562i −0.347268 0.954111i −0.983227 0.182388i \(-0.941617\pi\)
0.635959 0.771723i \(-0.280605\pi\)
\(642\) 0 0
\(643\) −11.1027 + 13.2317i −0.437847 + 0.521806i −0.939169 0.343455i \(-0.888403\pi\)
0.501322 + 0.865261i \(0.332847\pi\)
\(644\) 12.3694 7.19604i 0.487424 0.283564i
\(645\) 0 0
\(646\) −8.83434 47.5217i −0.347583 1.86972i
\(647\) 2.56660 0.100904 0.0504518 0.998726i \(-0.483934\pi\)
0.0504518 + 0.998726i \(0.483934\pi\)
\(648\) 0 0
\(649\) −11.9448 10.0229i −0.468875 0.393433i
\(650\) 0.0214808 + 13.0166i 0.000842548 + 0.510553i
\(651\) 0 0
\(652\) −23.9617 4.14359i −0.938412 0.162276i
\(653\) −1.23323 + 0.712004i −0.0482599 + 0.0278629i −0.523936 0.851758i \(-0.675537\pi\)
0.475676 + 0.879621i \(0.342204\pi\)
\(654\) 0 0
\(655\) 7.05826 1.24456i 0.275789 0.0486290i
\(656\) −0.183824 27.8473i −0.00717713 1.08725i
\(657\) 0 0
\(658\) −22.3721 18.7096i −0.872156 0.729377i
\(659\) 5.23948 4.39644i 0.204101 0.171261i −0.535008 0.844847i \(-0.679691\pi\)
0.739109 + 0.673586i \(0.235247\pi\)
\(660\) 0 0
\(661\) 6.12000 + 2.22750i 0.238040 + 0.0866396i 0.458286 0.888805i \(-0.348464\pi\)
−0.220246 + 0.975444i \(0.570686\pi\)
\(662\) 7.45704 + 2.70021i 0.289826 + 0.104947i
\(663\) 0 0
\(664\) 37.2803 + 21.2784i 1.44675 + 0.825761i
\(665\) −4.44159 + 7.83024i −0.172237 + 0.303644i
\(666\) 0 0
\(667\) −13.2933 2.34397i −0.514719 0.0907588i
\(668\) 19.5889 0.0646541i 0.757919 0.00250154i
\(669\) 0 0
\(670\) 9.46450 + 11.2416i 0.365646 + 0.434302i
\(671\) 7.29868 6.12432i 0.281762 0.236427i
\(672\) 0 0
\(673\) 6.77884 11.7413i 0.261305 0.452594i −0.705284 0.708925i \(-0.749180\pi\)
0.966589 + 0.256331i \(0.0825138\pi\)
\(674\) 30.1699 17.4850i 1.16210 0.673499i
\(675\) 0 0
\(676\) 2.94570 + 16.3894i 0.113296 + 0.630362i
\(677\) 12.1931 7.03971i 0.468620 0.270558i −0.247042 0.969005i \(-0.579458\pi\)
0.715662 + 0.698447i \(0.246125\pi\)
\(678\) 0 0
\(679\) 0.554821 + 1.52436i 0.0212921 + 0.0584995i
\(680\) 12.3576 + 14.5800i 0.473891 + 0.559116i
\(681\) 0 0
\(682\) 7.36251 + 41.3557i 0.281925 + 1.58359i
\(683\) −43.9380 −1.68124 −0.840621 0.541624i \(-0.817810\pi\)
−0.840621 + 0.541624i \(0.817810\pi\)
\(684\) 0 0
\(685\) −6.92980 −0.264774
\(686\) 4.90476 + 27.5503i 0.187264 + 1.05188i
\(687\) 0 0
\(688\) 16.4369 + 9.34571i 0.626650 + 0.356302i
\(689\) −0.132226 0.363289i −0.00503743 0.0138402i
\(690\) 0 0
\(691\) −6.64458 + 3.83625i −0.252772 + 0.145938i −0.621033 0.783785i \(-0.713287\pi\)
0.368261 + 0.929722i \(0.379953\pi\)
\(692\) 29.4177 5.28731i 1.11829 0.200993i
\(693\) 0 0
\(694\) 20.6058 11.9421i 0.782185 0.453317i
\(695\) 3.43039 5.94161i 0.130122 0.225378i
\(696\) 0 0
\(697\) −41.8181 + 35.0895i −1.58397 + 1.32911i
\(698\) 2.97905 + 3.53842i 0.112759 + 0.133931i
\(699\) 0 0
\(700\) 0.0673493 + 20.4055i 0.00254556 + 0.771256i
\(701\) −9.62261 1.69673i −0.363441 0.0640845i −0.0110543 0.999939i \(-0.503519\pi\)
−0.352387 + 0.935854i \(0.614630\pi\)
\(702\) 0 0
\(703\) 5.79397 + 31.4557i 0.218524 + 1.18638i
\(704\) 13.7322 + 23.2502i 0.517552 + 0.876273i
\(705\) 0 0
\(706\) 14.2817 + 5.17142i 0.537497 + 0.194629i
\(707\) −5.15960 1.87794i −0.194047 0.0706272i
\(708\) 0 0
\(709\) −15.8648 + 13.3121i −0.595814 + 0.499947i −0.890097 0.455771i \(-0.849364\pi\)
0.294283 + 0.955718i \(0.404919\pi\)
\(710\) 9.76979 + 8.17039i 0.366654 + 0.306629i
\(711\) 0 0
\(712\) 12.3790 + 4.43631i 0.463923 + 0.166258i
\(713\) 25.8744 4.56235i 0.969002 0.170861i
\(714\) 0 0
\(715\) −5.44608 + 3.14430i −0.203672 + 0.117590i
\(716\) −3.16300 + 18.2911i −0.118207 + 0.683569i
\(717\) 0 0
\(718\) −0.0171675 10.4029i −0.000640684 0.388231i
\(719\) 15.4370 + 12.9532i 0.575704 + 0.483073i 0.883533 0.468368i \(-0.155158\pi\)
−0.307829 + 0.951442i \(0.599602\pi\)
\(720\) 0 0
\(721\) −42.9869 −1.60092
\(722\) 23.0399 13.8261i 0.857457 0.514555i
\(723\) 0 0
\(724\) 25.3619 + 43.5951i 0.942566 + 1.62020i
\(725\) 12.3723 14.7447i 0.459494 0.547604i
\(726\) 0 0
\(727\) −18.3825 50.5056i −0.681771 1.87315i −0.417372 0.908735i \(-0.637049\pi\)
−0.264398 0.964414i \(-0.585173\pi\)
\(728\) −2.61614 14.4191i −0.0969605 0.534406i
\(729\) 0 0
\(730\) −1.44708 + 8.28675i −0.0535589 + 0.306706i
\(731\) −6.43627 36.5019i −0.238054 1.35007i
\(732\) 0 0
\(733\) 11.0451 19.1307i 0.407961 0.706609i −0.586700 0.809804i \(-0.699573\pi\)
0.994661 + 0.103195i \(0.0329067\pi\)
\(734\) −13.2782 11.1044i −0.490107 0.409872i
\(735\) 0 0
\(736\) 14.5565 8.56510i 0.536559 0.315714i
\(737\) 13.9200 38.2448i 0.512748 1.40876i
\(738\) 0 0
\(739\) −44.9753 7.93037i −1.65444 0.291723i −0.732999 0.680230i \(-0.761880\pi\)
−0.921446 + 0.388506i \(0.872991\pi\)
\(740\) −8.16133 9.66136i −0.300016 0.355158i
\(741\) 0 0
\(742\) −0.208226 0.569171i −0.00764421 0.0208949i
\(743\) −1.88482 + 10.6893i −0.0691474 + 0.392154i 0.930517 + 0.366249i \(0.119358\pi\)
−0.999664 + 0.0259055i \(0.991753\pi\)
\(744\) 0 0
\(745\) 1.98751 + 0.723393i 0.0728166 + 0.0265031i
\(746\) 13.9275 + 16.5427i 0.509924 + 0.605671i
\(747\) 0 0
\(748\) 17.9398 49.8000i 0.655944 1.82087i
\(749\) −5.49236 3.17101i −0.200686 0.115866i
\(750\) 0 0
\(751\) 1.46846 0.258930i 0.0535849 0.00944847i −0.146791 0.989167i \(-0.546895\pi\)
0.200376 + 0.979719i \(0.435784\pi\)
\(752\) −26.5131 21.9505i −0.966833 0.800453i
\(753\) 0 0
\(754\) −6.89172 + 11.9824i −0.250982 + 0.436374i
\(755\) 1.26252 0.459521i 0.0459480 0.0167237i
\(756\) 0 0
\(757\) −39.1287 32.8329i −1.42216 1.19333i −0.950173 0.311724i \(-0.899094\pi\)
−0.471984 0.881607i \(-0.656462\pi\)
\(758\) 8.87948 + 49.8766i 0.322517 + 1.81160i
\(759\) 0 0
\(760\) −5.19624 + 9.26727i −0.188488 + 0.336159i
\(761\) 21.3388i 0.773530i −0.922178 0.386765i \(-0.873592\pi\)
0.922178 0.386765i \(-0.126408\pi\)
\(762\) 0 0
\(763\) −6.65635 + 7.93273i −0.240976 + 0.287184i
\(764\) 46.8804 17.2385i 1.69607 0.623667i
\(765\) 0 0
\(766\) −41.0930 23.6347i −1.48475 0.853957i
\(767\) 4.99371 + 8.64936i 0.180312 + 0.312310i
\(768\) 0 0
\(769\) −8.44886 47.9159i −0.304674 1.72789i −0.625036 0.780596i \(-0.714916\pi\)
0.320362 0.947295i \(-0.396195\pi\)
\(770\) −8.52946 + 4.94327i −0.307380 + 0.178143i
\(771\) 0 0
\(772\) −23.6165 8.50754i −0.849977 0.306193i
\(773\) −15.0239 17.9048i −0.540373 0.643992i 0.424898 0.905241i \(-0.360310\pi\)
−0.965271 + 0.261249i \(0.915866\pi\)
\(774\) 0 0
\(775\) −12.8136 + 35.2050i −0.460277 + 1.26460i
\(776\) 0.663711 + 1.79582i 0.0238258 + 0.0644661i
\(777\) 0 0
\(778\) 22.4278 8.20499i 0.804076 0.294163i
\(779\) −26.3957 14.9726i −0.945725 0.536448i
\(780\) 0 0
\(781\) 6.12505 34.7369i 0.219172 1.24298i
\(782\) −31.1299 11.2722i −1.11320 0.403094i
\(783\) 0 0
\(784\) 0.905548 + 4.94453i 0.0323410 + 0.176591i
\(785\) −6.94682 8.27890i −0.247943 0.295487i
\(786\) 0 0
\(787\) 11.9135 + 6.87826i 0.424670 + 0.245184i 0.697074 0.717000i \(-0.254485\pi\)
−0.272403 + 0.962183i \(0.587818\pi\)
\(788\) −25.6894 + 30.8214i −0.915146 + 1.09797i
\(789\) 0 0
\(790\) 7.36437 + 1.28601i 0.262012 + 0.0457542i
\(791\) −15.7369 27.2572i −0.559541 0.969154i
\(792\) 0 0
\(793\) −5.73460 + 2.08722i −0.203642 + 0.0741195i
\(794\) −0.0876609 53.1193i −0.00311097 1.88513i
\(795\) 0 0
\(796\) 32.6891 19.0172i 1.15863 0.674046i
\(797\) 10.8460i 0.384185i 0.981377 + 0.192093i \(0.0615274\pi\)
−0.981377 + 0.192093i \(0.938473\pi\)
\(798\) 0 0
\(799\) 67.4737i 2.38705i
\(800\) 0.198716 + 24.0824i 0.00702567 + 0.851440i
\(801\) 0 0
\(802\) −44.4119 + 0.0732915i −1.56824 + 0.00258801i
\(803\) 21.8928 7.96833i 0.772580 0.281196i
\(804\) 0 0
\(805\) 3.08307 + 5.34003i 0.108664 + 0.188211i
\(806\) 4.62832 26.5042i 0.163026 0.933571i
\(807\) 0 0
\(808\) −6.10037 2.18621i −0.214610 0.0769107i
\(809\) −17.9152 10.3433i −0.629864 0.363652i 0.150835 0.988559i \(-0.451804\pi\)
−0.780700 + 0.624907i \(0.785137\pi\)
\(810\) 0 0
\(811\) −6.57226 7.83251i −0.230783 0.275037i 0.638208 0.769864i \(-0.279676\pi\)
−0.868991 + 0.494827i \(0.835231\pi\)
\(812\) −10.7729 + 18.8022i −0.378053 + 0.659827i
\(813\) 0 0
\(814\) −11.9255 + 32.9341i −0.417989 + 1.15434i
\(815\) 1.81949 10.3188i 0.0637338 0.361452i
\(816\) 0 0
\(817\) 17.7650 10.4379i 0.621520 0.365177i
\(818\) 4.11194 + 11.2397i 0.143771 + 0.392988i
\(819\) 0 0
\(820\) 11.9992 0.0396039i 0.419031 0.00138303i
\(821\) −17.0854 + 46.9419i −0.596286 + 1.63828i 0.162324 + 0.986737i \(0.448101\pi\)
−0.758610 + 0.651545i \(0.774121\pi\)
\(822\) 0 0
\(823\) −10.3566 12.3425i −0.361008 0.430232i 0.554717 0.832039i \(-0.312827\pi\)
−0.915724 + 0.401807i \(0.868382\pi\)
\(824\) −50.7335 + 0.251173i −1.76739 + 0.00875003i
\(825\) 0 0
\(826\) 7.85081 + 13.5463i 0.273165 + 0.471337i
\(827\) 1.54355 + 8.75389i 0.0536744 + 0.304403i 0.999813 0.0193604i \(-0.00616300\pi\)
−0.946138 + 0.323763i \(0.895052\pi\)
\(828\) 0 0
\(829\) 7.48543 + 12.9651i 0.259980 + 0.450298i 0.966236 0.257658i \(-0.0829508\pi\)
−0.706256 + 0.707956i \(0.749617\pi\)
\(830\) −9.22154 + 16.0332i −0.320084 + 0.556521i
\(831\) 0 0
\(832\) −3.17184 17.0022i −0.109964 0.589445i
\(833\) 6.33395 7.54851i 0.219458 0.261540i
\(834\) 0 0
\(835\) 8.44066i 0.292101i
\(836\) 29.4237 0.321330i 1.01764 0.0111134i
\(837\) 0 0
\(838\) −23.3093 + 4.14973i −0.805206 + 0.143350i
\(839\) 19.4852 + 16.3500i 0.672704 + 0.564465i 0.913864 0.406020i \(-0.133084\pi\)
−0.241161 + 0.970485i \(0.577528\pi\)
\(840\) 0 0
\(841\) −8.04360 + 2.92763i −0.277366 + 0.100953i
\(842\) −2.79574 1.60798i −0.0963475 0.0554145i
\(843\) 0 0
\(844\) 31.1103 5.59152i 1.07086 0.192468i
\(845\) −7.06613 + 1.24595i −0.243082 + 0.0428619i
\(846\) 0 0
\(847\) 0.815374 + 0.470756i 0.0280166 + 0.0161754i
\(848\) −0.249076 0.670524i −0.00855329 0.0230259i
\(849\) 0 0
\(850\) 36.1147 30.4055i 1.23872 1.04290i
\(851\) 20.5870 + 7.49305i 0.705713 + 0.256859i
\(852\) 0 0
\(853\) 0.208823 1.18429i 0.00714995 0.0405494i −0.981024 0.193886i \(-0.937891\pi\)
0.988174 + 0.153337i \(0.0490019\pi\)
\(854\) −8.98450 + 3.28689i −0.307443 + 0.112475i
\(855\) 0 0
\(856\) −6.50065 3.71036i −0.222188 0.126818i
\(857\) 24.2624 + 4.27811i 0.828786 + 0.146137i 0.571920 0.820309i \(-0.306199\pi\)
0.256867 + 0.966447i \(0.417310\pi\)
\(858\) 0 0
\(859\) 18.3498 50.4156i 0.626086 1.72016i −0.0654906 0.997853i \(-0.520861\pi\)
0.691576 0.722303i \(-0.256917\pi\)
\(860\) −4.05030 + 7.06910i −0.138114 + 0.241054i
\(861\) 0 0
\(862\) 7.21703 8.62980i 0.245813 0.293932i
\(863\) 15.4850 26.8209i 0.527117 0.912993i −0.472384 0.881393i \(-0.656606\pi\)
0.999501 0.0316000i \(-0.0100603\pi\)
\(864\) 0 0
\(865\) 2.23638 + 12.6831i 0.0760392 + 0.431240i
\(866\) −13.7600 2.40285i −0.467584 0.0816522i
\(867\) 0 0
\(868\) 7.18707 41.5616i 0.243945 1.41069i
\(869\) −7.08139 19.4560i −0.240220 0.659998i
\(870\) 0 0
\(871\) −16.7564 + 19.9695i −0.567769 + 0.676641i
\(872\) −7.80953 + 9.40116i −0.264464 + 0.318364i
\(873\) 0 0
\(874\) −0.170612 18.4040i −0.00577103 0.622525i
\(875\) −19.1188 −0.646333
\(876\) 0 0
\(877\) 41.1372 + 34.5182i 1.38910 + 1.16560i 0.965701 + 0.259655i \(0.0836090\pi\)
0.423403 + 0.905941i \(0.360835\pi\)
\(878\) 30.8642 0.0509342i 1.04162 0.00171895i
\(879\) 0 0
\(880\) −10.0377 + 5.88393i −0.338369 + 0.198347i
\(881\) −10.8128 + 6.24276i −0.364292 + 0.210324i −0.670962 0.741492i \(-0.734119\pi\)
0.306670 + 0.951816i \(0.400785\pi\)
\(882\) 0 0
\(883\) −0.870075 + 0.153418i −0.0292803 + 0.00516291i −0.188269 0.982117i \(-0.560288\pi\)
0.158989 + 0.987280i \(0.449177\pi\)
\(884\) −21.7073 + 26.0438i −0.730095 + 0.875948i
\(885\) 0 0
\(886\) 17.6504 21.1056i 0.592978 0.709057i
\(887\) −20.0221 + 16.8005i −0.672276 + 0.564106i −0.913738 0.406304i \(-0.866817\pi\)
0.241462 + 0.970410i \(0.422373\pi\)
\(888\) 0 0
\(889\) −17.2345 6.27285i −0.578027 0.210385i
\(890\) −1.92914 + 5.32761i −0.0646649 + 0.178582i
\(891\) 0 0
\(892\) −1.05082 1.24396i −0.0351842 0.0416509i
\(893\) −35.1480 + 13.0970i −1.17618 + 0.438274i
\(894\) 0 0
\(895\) −7.87683 1.38890i −0.263293 0.0464257i
\(896\) −5.01635 26.6454i −0.167584 0.890162i
\(897\) 0 0
\(898\) 19.9838 16.8247i 0.666868 0.561446i
\(899\) −30.4772 + 25.5734i −1.01647 + 0.852921i
\(900\) 0 0
\(901\) −0.701085 + 1.21432i −0.0233565 + 0.0404547i
\(902\) −16.6637 28.7528i −0.554842 0.957363i
\(903\) 0 0
\(904\) −18.7321 32.0772i −0.623022 1.06687i
\(905\) −18.8205 + 10.8660i −0.625615 + 0.361199i
\(906\) 0 0
\(907\) −16.9326 46.5219i −0.562238 1.54473i −0.816348 0.577560i \(-0.804005\pi\)
0.254111 0.967175i \(-0.418217\pi\)
\(908\) 8.25703 3.03621i 0.274019 0.100760i
\(909\) 0 0
\(910\) 6.21666 1.10675i 0.206080 0.0366883i
\(911\) −40.7601 −1.35044 −0.675221 0.737615i \(-0.735952\pi\)
−0.675221 + 0.737615i \(0.735952\pi\)
\(912\) 0 0
\(913\) 51.2254 1.69531
\(914\) −55.5688 + 9.89286i −1.83805 + 0.327227i
\(915\) 0 0
\(916\) 8.41245 3.09336i 0.277955 0.102208i
\(917\) 6.81688 + 18.7292i 0.225113 + 0.618494i
\(918\) 0 0
\(919\) 12.4780 7.20419i 0.411612 0.237644i −0.279870 0.960038i \(-0.590291\pi\)
0.691482 + 0.722394i \(0.256958\pi\)
\(920\) 3.66986 + 6.28433i 0.120992 + 0.207188i
\(921\) 0 0
\(922\) 10.5574 + 18.2165i 0.347690 + 0.599928i
\(923\) −11.2963 + 19.5658i −0.371823 + 0.644016i
\(924\) 0 0
\(925\) −23.9310 + 20.0805i −0.786847 + 0.660243i
\(926\) 13.9326 11.7301i 0.457854 0.385474i
\(927\) 0 0
\(928\) −12.6044 + 22.2534i −0.413758 + 0.730505i
\(929\) −23.3111 4.11037i −0.764812 0.134857i −0.222384 0.974959i \(-0.571384\pi\)
−0.542428 + 0.840102i \(0.682495\pi\)
\(930\) 0 0
\(931\) 5.16157 + 1.83424i 0.169164 + 0.0601148i
\(932\) −20.4648 24.2262i −0.670347 0.793555i
\(933\) 0 0
\(934\) 7.27036 20.0782i 0.237893 0.656978i
\(935\) 21.4325 + 7.80080i 0.700918 + 0.255113i
\(936\) 0 0
\(937\) 41.2829 34.6405i 1.34865 1.13166i 0.369344 0.929293i \(-0.379583\pi\)
0.979311 0.202362i \(-0.0648619\pi\)
\(938\) −26.2167 + 31.3487i −0.856005 + 1.02357i
\(939\) 0 0
\(940\) 9.49584 11.3929i 0.309720 0.371594i
\(941\) 35.2664 6.21841i 1.14965 0.202714i 0.433828 0.900996i \(-0.357163\pi\)
0.715823 + 0.698281i \(0.246052\pi\)
\(942\) 0 0
\(943\) −18.0012 + 10.3930i −0.586200 + 0.338443i
\(944\) 9.34474 + 15.9416i 0.304145 + 0.518855i
\(945\) 0 0
\(946\) 22.5640 0.0372367i 0.733620 0.00121067i
\(947\) 7.68149 + 6.44553i 0.249615 + 0.209452i 0.759006 0.651083i \(-0.225685\pi\)
−0.509392 + 0.860535i \(0.670130\pi\)
\(948\) 0 0
\(949\) −14.9225 −0.484406
\(950\) 22.8487 + 12.9108i 0.741309 + 0.418881i
\(951\) 0 0
\(952\) −33.9622 + 40.8840i −1.10072 + 1.32506i
\(953\) −7.01559 + 8.36085i −0.227257 + 0.270835i −0.867609 0.497247i \(-0.834344\pi\)
0.640352 + 0.768082i \(0.278789\pi\)
\(954\) 0 0
\(955\) 7.36113 + 20.2245i 0.238200 + 0.654450i
\(956\) 5.70497 32.9909i 0.184512 1.06700i
\(957\) 0 0
\(958\) −9.36619 1.63558i −0.302608 0.0528432i
\(959\) −3.34641 18.9784i −0.108061 0.612846i
\(960\) 0 0
\(961\) 23.2194 40.2171i 0.749011 1.29733i
\(962\) 14.3926 17.2100i 0.464035 0.554873i
\(963\) 0 0
\(964\) −24.5066 + 42.7721i −0.789304 + 1.37760i
\(965\) 3.69935 10.1639i 0.119086 0.327187i
\(966\) 0 0
\(967\) −4.74891 0.837361i −0.152715 0.0269277i 0.0967681 0.995307i \(-0.469149\pi\)
−0.249483 + 0.968379i \(0.580261\pi\)
\(968\) 0.965062 + 0.550826i 0.0310183 + 0.0177042i
\(969\) 0 0
\(970\) −0.774734 + 0.283429i −0.0248752 + 0.00910035i
\(971\) −8.78529 + 49.8239i −0.281933 + 1.59892i 0.434105 + 0.900862i \(0.357065\pi\)
−0.716038 + 0.698061i \(0.754046\pi\)
\(972\) 0 0
\(973\) 17.9286 + 6.52549i 0.574766 + 0.209198i
\(974\) −9.86467 + 8.30522i −0.316084 + 0.266116i
\(975\) 0 0
\(976\) −10.5844 + 3.93171i −0.338798 + 0.125851i
\(977\) 27.0288 + 15.6051i 0.864728 + 0.499251i 0.865593 0.500749i \(-0.166942\pi\)
−0.000864660 1.00000i \(0.500275\pi\)
\(978\) 0 0
\(979\) 15.4542 2.72499i 0.493918 0.0870911i
\(980\) −2.13181 + 0.383155i −0.0680982 + 0.0122394i
\(981\) 0 0
\(982\) 45.4053 + 26.1150i 1.44894 + 0.833362i
\(983\) −1.24629 + 0.453613i −0.0397505 + 0.0144680i −0.361819 0.932248i \(-0.617844\pi\)
0.322068 + 0.946716i \(0.395622\pi\)
\(984\) 0 0
\(985\) −13.2439 11.1130i −0.421987 0.354089i
\(986\) 49.3583 8.78720i 1.57189 0.279842i
\(987\) 0 0
\(988\) −17.7801 6.25239i −0.565659 0.198915i
\(989\) 14.1132i 0.448773i
\(990\) 0 0
\(991\) 14.0462 16.7396i 0.446192 0.531751i −0.495329 0.868705i \(-0.664953\pi\)
0.941521 + 0.336955i \(0.109397\pi\)
\(992\) 8.23939 49.0933i 0.261601 1.55871i
\(993\) 0 0
\(994\) −17.6582 + 30.7017i −0.560083 + 0.973800i
\(995\) 8.14771 + 14.1123i 0.258300 + 0.447388i
\(996\) 0 0
\(997\) 8.63415 + 48.9667i 0.273446 + 1.55079i 0.743855 + 0.668341i \(0.232995\pi\)
−0.470408 + 0.882449i \(0.655893\pi\)
\(998\) 16.2138 + 27.9764i 0.513239 + 0.885577i
\(999\) 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 684.2.ce.a.359.3 240
3.2 odd 2 inner 684.2.ce.a.359.38 yes 240
4.3 odd 2 inner 684.2.ce.a.359.8 yes 240
12.11 even 2 inner 684.2.ce.a.359.33 yes 240
19.9 even 9 inner 684.2.ce.a.503.33 yes 240
57.47 odd 18 inner 684.2.ce.a.503.8 yes 240
76.47 odd 18 inner 684.2.ce.a.503.38 yes 240
228.47 even 18 inner 684.2.ce.a.503.3 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
684.2.ce.a.359.3 240 1.1 even 1 trivial
684.2.ce.a.359.8 yes 240 4.3 odd 2 inner
684.2.ce.a.359.33 yes 240 12.11 even 2 inner
684.2.ce.a.359.38 yes 240 3.2 odd 2 inner
684.2.ce.a.503.3 yes 240 228.47 even 18 inner
684.2.ce.a.503.8 yes 240 57.47 odd 18 inner
684.2.ce.a.503.33 yes 240 19.9 even 9 inner
684.2.ce.a.503.38 yes 240 76.47 odd 18 inner