Properties

Label 525.2.t.j.26.10
Level $525$
Weight $2$
Character 525.26
Analytic conductor $4.192$
Analytic rank $0$
Dimension $24$
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] = [525,2,Mod(26,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.t (of order \(6\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.10
Character \(\chi\) \(=\) 525.26
Dual form 525.2.t.j.101.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.31176 + 0.757344i) q^{2} +(1.20362 - 1.24551i) q^{3} +(0.147140 + 0.254854i) q^{4} +(2.52214 - 0.722254i) q^{6} +(2.64468 + 0.0753638i) q^{7} -2.58363i q^{8} +(-0.102593 - 2.99825i) q^{9} +O(q^{10})\) \(q+(1.31176 + 0.757344i) q^{2} +(1.20362 - 1.24551i) q^{3} +(0.147140 + 0.254854i) q^{4} +(2.52214 - 0.722254i) q^{6} +(2.64468 + 0.0753638i) q^{7} -2.58363i q^{8} +(-0.102593 - 2.99825i) q^{9} +(-1.86048 + 1.07415i) q^{11} +(0.494525 + 0.123483i) q^{12} +3.48097i q^{13} +(3.41210 + 2.10179i) q^{14} +(2.25098 - 3.89881i) q^{16} +(-1.78859 - 3.09793i) q^{17} +(2.13613 - 4.01067i) q^{18} +(1.05858 + 0.611171i) q^{19} +(3.27706 - 3.20326i) q^{21} -3.25401 q^{22} +(1.31176 + 0.757344i) q^{23} +(-3.21794 - 3.10972i) q^{24} +(-2.63629 + 4.56619i) q^{26} +(-3.85783 - 3.48097i) q^{27} +(0.369932 + 0.685096i) q^{28} +5.95645i q^{29} +(2.75098 - 1.58828i) q^{31} +(1.43050 - 0.825899i) q^{32} +(-0.901451 + 3.61012i) q^{33} -5.41832i q^{34} +(0.749020 - 0.467309i) q^{36} +(-3.90175 + 6.75803i) q^{37} +(0.925734 + 1.60342i) q^{38} +(4.33559 + 4.18977i) q^{39} +11.8685 q^{41} +(6.72468 - 1.72005i) q^{42} -2.99294 q^{43} +(-0.547504 - 0.316101i) q^{44} +(1.14714 + 1.98691i) q^{46} +(-3.05084 + 5.28420i) q^{47} +(-2.14668 - 7.49631i) q^{48} +(6.98864 + 0.398626i) q^{49} +(-6.01129 - 1.50103i) q^{51} +(-0.887140 + 0.512191i) q^{52} +(-9.72202 + 5.61301i) q^{53} +(-2.42425 - 7.48790i) q^{54} +(0.194713 - 6.83288i) q^{56} +(2.03535 - 0.582853i) q^{57} +(-4.51108 + 7.81342i) q^{58} +(-1.08467 - 1.87871i) q^{59} +(-2.94338 - 1.69936i) q^{61} +4.81149 q^{62} +(-0.0453652 - 7.93712i) q^{63} -6.50196 q^{64} +(-3.91659 + 4.05290i) q^{66} +(-5.15882 - 8.93534i) q^{67} +(0.526347 - 0.911660i) q^{68} +(2.52214 - 0.722254i) q^{69} +10.3968i q^{71} +(-7.74637 + 0.265062i) q^{72} +(-5.93710 + 3.42779i) q^{73} +(-10.2363 + 5.90993i) q^{74} +0.359711i q^{76} +(-5.00133 + 2.70057i) q^{77} +(2.51414 + 8.77950i) q^{78} +(-0.941421 + 1.63059i) q^{79} +(-8.97895 + 0.615196i) q^{81} +(15.5686 + 8.98853i) q^{82} +9.10486 q^{83} +(1.29855 + 0.363843i) q^{84} +(-3.92601 - 2.26668i) q^{86} +(7.41882 + 7.16930i) q^{87} +(2.77521 + 4.80681i) q^{88} +(0.889962 - 1.54146i) q^{89} +(-0.262339 + 9.20605i) q^{91} +0.445743i q^{92} +(1.33292 - 5.33806i) q^{93} +(-8.00392 + 4.62107i) q^{94} +(0.693113 - 2.77577i) q^{96} +1.32584i q^{97} +(8.86551 + 5.81571i) q^{98} +(3.41144 + 5.46799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84} - 96 q^{91} + 72 q^{94} - 90 q^{96} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31176 + 0.757344i 0.927553 + 0.535523i 0.886037 0.463615i \(-0.153448\pi\)
0.0415164 + 0.999138i \(0.486781\pi\)
\(3\) 1.20362 1.24551i 0.694911 0.719096i
\(4\) 0.147140 + 0.254854i 0.0735701 + 0.127427i
\(5\) 0 0
\(6\) 2.52214 0.722254i 1.02966 0.294859i
\(7\) 2.64468 + 0.0753638i 0.999594 + 0.0284849i
\(8\) 2.58363i 0.913452i
\(9\) −0.102593 2.99825i −0.0341975 0.999415i
\(10\) 0 0
\(11\) −1.86048 + 1.07415i −0.560957 + 0.323869i −0.753529 0.657414i \(-0.771650\pi\)
0.192573 + 0.981283i \(0.438317\pi\)
\(12\) 0.494525 + 0.123483i 0.142757 + 0.0356466i
\(13\) 3.48097i 0.965448i 0.875773 + 0.482724i \(0.160353\pi\)
−0.875773 + 0.482724i \(0.839647\pi\)
\(14\) 3.41210 + 2.10179i 0.911923 + 0.561727i
\(15\) 0 0
\(16\) 2.25098 3.89881i 0.562745 0.974703i
\(17\) −1.78859 3.09793i −0.433797 0.751359i 0.563399 0.826185i \(-0.309493\pi\)
−0.997197 + 0.0748259i \(0.976160\pi\)
\(18\) 2.13613 4.01067i 0.503490 0.945324i
\(19\) 1.05858 + 0.611171i 0.242855 + 0.140212i 0.616488 0.787364i \(-0.288555\pi\)
−0.373633 + 0.927576i \(0.621888\pi\)
\(20\) 0 0
\(21\) 3.27706 3.20326i 0.715112 0.699010i
\(22\) −3.25401 −0.693757
\(23\) 1.31176 + 0.757344i 0.273521 + 0.157917i 0.630486 0.776200i \(-0.282855\pi\)
−0.356966 + 0.934117i \(0.616189\pi\)
\(24\) −3.21794 3.10972i −0.656860 0.634768i
\(25\) 0 0
\(26\) −2.63629 + 4.56619i −0.517020 + 0.895504i
\(27\) −3.85783 3.48097i −0.742439 0.669913i
\(28\) 0.369932 + 0.685096i 0.0699105 + 0.129471i
\(29\) 5.95645i 1.10608i 0.833153 + 0.553042i \(0.186533\pi\)
−0.833153 + 0.553042i \(0.813467\pi\)
\(30\) 0 0
\(31\) 2.75098 1.58828i 0.494091 0.285263i −0.232179 0.972673i \(-0.574586\pi\)
0.726270 + 0.687410i \(0.241252\pi\)
\(32\) 1.43050 0.825899i 0.252879 0.146000i
\(33\) −0.901451 + 3.61012i −0.156923 + 0.628442i
\(34\) 5.41832i 0.929234i
\(35\) 0 0
\(36\) 0.749020 0.467309i 0.124837 0.0778848i
\(37\) −3.90175 + 6.75803i −0.641444 + 1.11101i 0.343667 + 0.939092i \(0.388331\pi\)
−0.985111 + 0.171921i \(0.945002\pi\)
\(38\) 0.925734 + 1.60342i 0.150174 + 0.260109i
\(39\) 4.33559 + 4.18977i 0.694249 + 0.670900i
\(40\) 0 0
\(41\) 11.8685 1.85355 0.926773 0.375622i \(-0.122571\pi\)
0.926773 + 0.375622i \(0.122571\pi\)
\(42\) 6.72468 1.72005i 1.03764 0.265409i
\(43\) −2.99294 −0.456419 −0.228209 0.973612i \(-0.573287\pi\)
−0.228209 + 0.973612i \(0.573287\pi\)
\(44\) −0.547504 0.316101i −0.0825393 0.0476541i
\(45\) 0 0
\(46\) 1.14714 + 1.98691i 0.169137 + 0.292953i
\(47\) −3.05084 + 5.28420i −0.445010 + 0.770780i −0.998053 0.0623727i \(-0.980133\pi\)
0.553043 + 0.833153i \(0.313467\pi\)
\(48\) −2.14668 7.49631i −0.309847 1.08200i
\(49\) 6.98864 + 0.398626i 0.998377 + 0.0569466i
\(50\) 0 0
\(51\) −6.01129 1.50103i −0.841749 0.210186i
\(52\) −0.887140 + 0.512191i −0.123024 + 0.0710281i
\(53\) −9.72202 + 5.61301i −1.33542 + 0.771006i −0.986125 0.166006i \(-0.946913\pi\)
−0.349297 + 0.937012i \(0.613580\pi\)
\(54\) −2.42425 7.48790i −0.329898 1.01897i
\(55\) 0 0
\(56\) 0.194713 6.83288i 0.0260196 0.913082i
\(57\) 2.03535 0.582853i 0.269589 0.0772008i
\(58\) −4.51108 + 7.81342i −0.592334 + 1.02595i
\(59\) −1.08467 1.87871i −0.141213 0.244587i 0.786741 0.617283i \(-0.211767\pi\)
−0.927954 + 0.372696i \(0.878433\pi\)
\(60\) 0 0
\(61\) −2.94338 1.69936i −0.376861 0.217581i 0.299591 0.954068i \(-0.403150\pi\)
−0.676452 + 0.736487i \(0.736483\pi\)
\(62\) 4.81149 0.611060
\(63\) −0.0453652 7.93712i −0.00571548 0.999984i
\(64\) −6.50196 −0.812745
\(65\) 0 0
\(66\) −3.91659 + 4.05290i −0.482099 + 0.498877i
\(67\) −5.15882 8.93534i −0.630250 1.09163i −0.987500 0.157617i \(-0.949619\pi\)
0.357250 0.934009i \(-0.383714\pi\)
\(68\) 0.526347 0.911660i 0.0638290 0.110555i
\(69\) 2.52214 0.722254i 0.303630 0.0869491i
\(70\) 0 0
\(71\) 10.3968i 1.23387i 0.787013 + 0.616936i \(0.211626\pi\)
−0.787013 + 0.616936i \(0.788374\pi\)
\(72\) −7.74637 + 0.265062i −0.912918 + 0.0312378i
\(73\) −5.93710 + 3.42779i −0.694885 + 0.401192i −0.805439 0.592678i \(-0.798071\pi\)
0.110555 + 0.993870i \(0.464737\pi\)
\(74\) −10.2363 + 5.90993i −1.18995 + 0.687016i
\(75\) 0 0
\(76\) 0.359711i 0.0412617i
\(77\) −5.00133 + 2.70057i −0.569955 + 0.307758i
\(78\) 2.51414 + 8.77950i 0.284671 + 0.994082i
\(79\) −0.941421 + 1.63059i −0.105918 + 0.183456i −0.914113 0.405460i \(-0.867111\pi\)
0.808195 + 0.588915i \(0.200445\pi\)
\(80\) 0 0
\(81\) −8.97895 + 0.615196i −0.997661 + 0.0683551i
\(82\) 15.5686 + 8.98853i 1.71926 + 0.992617i
\(83\) 9.10486 0.999388 0.499694 0.866202i \(-0.333446\pi\)
0.499694 + 0.866202i \(0.333446\pi\)
\(84\) 1.29855 + 0.363843i 0.141684 + 0.0396985i
\(85\) 0 0
\(86\) −3.92601 2.26668i −0.423353 0.244423i
\(87\) 7.41882 + 7.16930i 0.795380 + 0.768630i
\(88\) 2.77521 + 4.80681i 0.295839 + 0.512407i
\(89\) 0.889962 1.54146i 0.0943358 0.163394i −0.814995 0.579467i \(-0.803261\pi\)
0.909331 + 0.416073i \(0.136594\pi\)
\(90\) 0 0
\(91\) −0.262339 + 9.20605i −0.0275006 + 0.965056i
\(92\) 0.445743i 0.0464719i
\(93\) 1.33292 5.33806i 0.138217 0.553531i
\(94\) −8.00392 + 4.62107i −0.825541 + 0.476626i
\(95\) 0 0
\(96\) 0.693113 2.77577i 0.0707406 0.283301i
\(97\) 1.32584i 0.134618i 0.997732 + 0.0673092i \(0.0214414\pi\)
−0.997732 + 0.0673092i \(0.978559\pi\)
\(98\) 8.86551 + 5.81571i 0.895552 + 0.587475i
\(99\) 3.41144 + 5.46799i 0.342863 + 0.549553i
\(100\) 0 0
\(101\) −6.71005 11.6221i −0.667675 1.15645i −0.978553 0.205997i \(-0.933956\pi\)
0.310878 0.950450i \(-0.399377\pi\)
\(102\) −6.74857 6.52160i −0.668208 0.645735i
\(103\) 5.01154 + 2.89342i 0.493802 + 0.285097i 0.726150 0.687536i \(-0.241308\pi\)
−0.232348 + 0.972633i \(0.574641\pi\)
\(104\) 8.99355 0.881890
\(105\) 0 0
\(106\) −17.0039 −1.65157
\(107\) −3.36576 1.94323i −0.325381 0.187859i 0.328408 0.944536i \(-0.393488\pi\)
−0.653788 + 0.756677i \(0.726821\pi\)
\(108\) 0.319499 1.49537i 0.0307438 0.143893i
\(109\) 2.60384 + 4.50998i 0.249403 + 0.431978i 0.963360 0.268211i \(-0.0864324\pi\)
−0.713958 + 0.700189i \(0.753099\pi\)
\(110\) 0 0
\(111\) 3.72097 + 12.9938i 0.353179 + 1.23331i
\(112\) 6.24695 10.1415i 0.590281 0.958278i
\(113\) 9.36235i 0.880736i −0.897817 0.440368i \(-0.854848\pi\)
0.897817 0.440368i \(-0.145152\pi\)
\(114\) 3.11131 + 0.776896i 0.291401 + 0.0727630i
\(115\) 0 0
\(116\) −1.51803 + 0.876432i −0.140945 + 0.0813747i
\(117\) 10.4368 0.357122i 0.964883 0.0330159i
\(118\) 3.28589i 0.302490i
\(119\) −4.49678 8.32783i −0.412219 0.763411i
\(120\) 0 0
\(121\) −3.19240 + 5.52940i −0.290218 + 0.502673i
\(122\) −2.57400 4.45830i −0.233039 0.403636i
\(123\) 14.2852 14.7823i 1.28805 1.33288i
\(124\) 0.809559 + 0.467399i 0.0727006 + 0.0419737i
\(125\) 0 0
\(126\) 5.95163 10.4459i 0.530213 0.930599i
\(127\) −9.57778 −0.849891 −0.424945 0.905219i \(-0.639707\pi\)
−0.424945 + 0.905219i \(0.639707\pi\)
\(128\) −11.3900 6.57602i −1.00674 0.581243i
\(129\) −3.60236 + 3.72774i −0.317170 + 0.328209i
\(130\) 0 0
\(131\) 4.72508 8.18408i 0.412832 0.715047i −0.582366 0.812927i \(-0.697873\pi\)
0.995198 + 0.0978802i \(0.0312062\pi\)
\(132\) −1.05269 + 0.301455i −0.0916253 + 0.0262383i
\(133\) 2.75354 + 1.69613i 0.238762 + 0.147073i
\(134\) 15.6280i 1.35005i
\(135\) 0 0
\(136\) −8.00392 + 4.62107i −0.686330 + 0.396253i
\(137\) 9.27125 5.35276i 0.792096 0.457317i −0.0486038 0.998818i \(-0.515477\pi\)
0.840700 + 0.541501i \(0.182144\pi\)
\(138\) 3.85543 + 0.962706i 0.328196 + 0.0819510i
\(139\) 4.11136i 0.348721i 0.984682 + 0.174360i \(0.0557858\pi\)
−0.984682 + 0.174360i \(0.944214\pi\)
\(140\) 0 0
\(141\) 2.90948 + 10.1600i 0.245022 + 0.855629i
\(142\) −7.87395 + 13.6381i −0.660767 + 1.14448i
\(143\) −3.73909 6.47629i −0.312678 0.541575i
\(144\) −11.9205 6.34900i −0.993377 0.529083i
\(145\) 0 0
\(146\) −10.3841 −0.859390
\(147\) 8.90817 8.22463i 0.734733 0.678356i
\(148\) −2.29642 −0.188764
\(149\) −2.20294 1.27187i −0.180472 0.104196i 0.407042 0.913409i \(-0.366560\pi\)
−0.587514 + 0.809214i \(0.699893\pi\)
\(150\) 0 0
\(151\) 2.80956 + 4.86630i 0.228639 + 0.396014i 0.957405 0.288749i \(-0.0932392\pi\)
−0.728766 + 0.684763i \(0.759906\pi\)
\(152\) 1.57904 2.73498i 0.128077 0.221836i
\(153\) −9.10486 + 5.68046i −0.736084 + 0.459238i
\(154\) −8.60580 0.245234i −0.693475 0.0197616i
\(155\) 0 0
\(156\) −0.429842 + 1.72143i −0.0344149 + 0.137824i
\(157\) −12.0584 + 6.96194i −0.962368 + 0.555623i −0.896901 0.442231i \(-0.854187\pi\)
−0.0654670 + 0.997855i \(0.520854\pi\)
\(158\) −2.46983 + 1.42596i −0.196489 + 0.113443i
\(159\) −4.71056 + 18.8648i −0.373572 + 1.49608i
\(160\) 0 0
\(161\) 3.41210 + 2.10179i 0.268911 + 0.165644i
\(162\) −12.2441 5.99317i −0.961990 0.470868i
\(163\) −2.03535 + 3.52533i −0.159421 + 0.276125i −0.934660 0.355543i \(-0.884296\pi\)
0.775239 + 0.631668i \(0.217629\pi\)
\(164\) 1.74633 + 3.02473i 0.136366 + 0.236192i
\(165\) 0 0
\(166\) 11.9434 + 6.89551i 0.926986 + 0.535196i
\(167\) 13.9722 1.08120 0.540602 0.841279i \(-0.318197\pi\)
0.540602 + 0.841279i \(0.318197\pi\)
\(168\) −8.27606 8.46671i −0.638512 0.653221i
\(169\) 0.882841 0.0679109
\(170\) 0 0
\(171\) 1.72384 3.23658i 0.131825 0.247508i
\(172\) −0.440382 0.762763i −0.0335788 0.0581602i
\(173\) 5.00133 8.66256i 0.380244 0.658602i −0.610853 0.791744i \(-0.709173\pi\)
0.991097 + 0.133142i \(0.0425066\pi\)
\(174\) 4.30206 + 15.0230i 0.326139 + 1.13889i
\(175\) 0 0
\(176\) 9.67157i 0.729022i
\(177\) −3.64549 0.910283i −0.274012 0.0684211i
\(178\) 2.33483 1.34801i 0.175003 0.101038i
\(179\) 14.0378 8.10475i 1.04924 0.605777i 0.126801 0.991928i \(-0.459529\pi\)
0.922436 + 0.386151i \(0.126196\pi\)
\(180\) 0 0
\(181\) 19.4123i 1.44290i −0.692465 0.721451i \(-0.743475\pi\)
0.692465 0.721451i \(-0.256525\pi\)
\(182\) −7.31627 + 11.8774i −0.542318 + 0.880414i
\(183\) −5.65929 + 1.62062i −0.418347 + 0.119800i
\(184\) 1.95670 3.38910i 0.144250 0.249848i
\(185\) 0 0
\(186\) 5.79122 5.99277i 0.424633 0.439411i
\(187\) 6.65529 + 3.84243i 0.486683 + 0.280987i
\(188\) −1.79560 −0.130958
\(189\) −9.94037 9.49679i −0.723056 0.690790i
\(190\) 0 0
\(191\) −11.0018 6.35188i −0.796061 0.459606i 0.0460309 0.998940i \(-0.485343\pi\)
−0.842092 + 0.539334i \(0.818676\pi\)
\(192\) −7.82590 + 8.09826i −0.564785 + 0.584441i
\(193\) −10.4098 18.0302i −0.749311 1.29785i −0.948153 0.317813i \(-0.897051\pi\)
0.198842 0.980032i \(-0.436282\pi\)
\(194\) −1.00411 + 1.73918i −0.0720912 + 0.124866i
\(195\) 0 0
\(196\) 0.926718 + 1.83974i 0.0661942 + 0.131410i
\(197\) 2.23465i 0.159212i −0.996826 0.0796062i \(-0.974634\pi\)
0.996826 0.0796062i \(-0.0253663\pi\)
\(198\) 0.333837 + 9.75631i 0.0237248 + 0.693351i
\(199\) 21.5831 12.4610i 1.52998 0.883337i 0.530622 0.847608i \(-0.321958\pi\)
0.999362 0.0357284i \(-0.0113751\pi\)
\(200\) 0 0
\(201\) −17.3383 4.32940i −1.22295 0.305372i
\(202\) 20.3273i 1.43022i
\(203\) −0.448901 + 15.7529i −0.0315066 + 1.10564i
\(204\) −0.501960 1.75286i −0.0351442 0.122725i
\(205\) 0 0
\(206\) 4.38262 + 7.59093i 0.305352 + 0.528885i
\(207\) 2.13613 4.01067i 0.148471 0.278761i
\(208\) 13.5716 + 7.83560i 0.941025 + 0.543301i
\(209\) −2.62596 −0.181641
\(210\) 0 0
\(211\) −6.61520 −0.455409 −0.227705 0.973730i \(-0.573122\pi\)
−0.227705 + 0.973730i \(0.573122\pi\)
\(212\) −2.86100 1.65180i −0.196494 0.113446i
\(213\) 12.9493 + 12.5138i 0.887272 + 0.857431i
\(214\) −2.94338 5.09808i −0.201205 0.348498i
\(215\) 0 0
\(216\) −8.99355 + 9.96721i −0.611934 + 0.678183i
\(217\) 7.39515 3.99316i 0.502016 0.271073i
\(218\) 7.88801i 0.534243i
\(219\) −2.87667 + 11.5205i −0.194388 + 0.778481i
\(220\) 0 0
\(221\) 10.7838 6.22604i 0.725398 0.418808i
\(222\) −4.95975 + 19.8627i −0.332877 + 1.33310i
\(223\) 4.31027i 0.288637i 0.989531 + 0.144318i \(0.0460990\pi\)
−0.989531 + 0.144318i \(0.953901\pi\)
\(224\) 3.84545 2.07643i 0.256935 0.138737i
\(225\) 0 0
\(226\) 7.09052 12.2811i 0.471654 0.816929i
\(227\) −5.55561 9.62260i −0.368739 0.638675i 0.620630 0.784104i \(-0.286877\pi\)
−0.989369 + 0.145429i \(0.953544\pi\)
\(228\) 0.448024 + 0.432956i 0.0296711 + 0.0286732i
\(229\) −8.63774 4.98700i −0.570798 0.329550i 0.186670 0.982423i \(-0.440230\pi\)
−0.757468 + 0.652872i \(0.773564\pi\)
\(230\) 0 0
\(231\) −2.65612 + 9.47967i −0.174760 + 0.623717i
\(232\) 15.3893 1.01036
\(233\) 17.8650 + 10.3144i 1.17037 + 0.675716i 0.953768 0.300543i \(-0.0971678\pi\)
0.216606 + 0.976259i \(0.430501\pi\)
\(234\) 13.9610 + 7.43579i 0.912661 + 0.486093i
\(235\) 0 0
\(236\) 0.319198 0.552868i 0.0207780 0.0359886i
\(237\) 0.897801 + 3.13516i 0.0583184 + 0.203650i
\(238\) 0.408345 14.3297i 0.0264691 0.928857i
\(239\) 2.87353i 0.185873i 0.995672 + 0.0929365i \(0.0296254\pi\)
−0.995672 + 0.0929365i \(0.970375\pi\)
\(240\) 0 0
\(241\) 22.5792 13.0361i 1.45445 0.839728i 0.455722 0.890122i \(-0.349381\pi\)
0.998729 + 0.0503940i \(0.0160477\pi\)
\(242\) −8.37532 + 4.83549i −0.538386 + 0.310837i
\(243\) −10.0410 + 11.9238i −0.644132 + 0.764915i
\(244\) 1.00018i 0.0640298i
\(245\) 0 0
\(246\) 29.9340 8.57206i 1.90852 0.546534i
\(247\) −2.12747 + 3.68488i −0.135368 + 0.234464i
\(248\) −4.10353 7.10752i −0.260574 0.451328i
\(249\) 10.9588 11.3402i 0.694486 0.718656i
\(250\) 0 0
\(251\) −0.161120 −0.0101698 −0.00508489 0.999987i \(-0.501619\pi\)
−0.00508489 + 0.999987i \(0.501619\pi\)
\(252\) 2.01613 1.17943i 0.127005 0.0742972i
\(253\) −3.25401 −0.204578
\(254\) −12.5637 7.25368i −0.788319 0.455136i
\(255\) 0 0
\(256\) −3.45866 5.99057i −0.216166 0.374411i
\(257\) −6.56514 + 11.3712i −0.409522 + 0.709314i −0.994836 0.101493i \(-0.967638\pi\)
0.585314 + 0.810807i \(0.300971\pi\)
\(258\) −7.54861 + 2.16166i −0.469956 + 0.134579i
\(259\) −10.8282 + 17.5788i −0.672830 + 1.09229i
\(260\) 0 0
\(261\) 17.8589 0.611087i 1.10544 0.0378254i
\(262\) 12.3963 7.15703i 0.765848 0.442163i
\(263\) −15.3551 + 8.86526i −0.946835 + 0.546655i −0.892096 0.451846i \(-0.850766\pi\)
−0.0547384 + 0.998501i \(0.517432\pi\)
\(264\) 9.32723 + 2.32902i 0.574051 + 0.143341i
\(265\) 0 0
\(266\) 2.32743 + 4.31029i 0.142704 + 0.264281i
\(267\) −0.848727 2.96379i −0.0519412 0.181381i
\(268\) 1.51814 2.62950i 0.0927352 0.160622i
\(269\) 2.20294 + 3.81561i 0.134316 + 0.232642i 0.925336 0.379148i \(-0.123783\pi\)
−0.791020 + 0.611790i \(0.790450\pi\)
\(270\) 0 0
\(271\) 20.4287 + 11.7945i 1.24095 + 0.716465i 0.969288 0.245927i \(-0.0790923\pi\)
0.271665 + 0.962392i \(0.412426\pi\)
\(272\) −16.1043 −0.976469
\(273\) 11.1505 + 11.4073i 0.674857 + 0.690403i
\(274\) 16.2155 0.979615
\(275\) 0 0
\(276\) 0.555178 + 0.536506i 0.0334178 + 0.0322938i
\(277\) −6.41589 11.1127i −0.385494 0.667695i 0.606344 0.795203i \(-0.292636\pi\)
−0.991838 + 0.127508i \(0.959302\pi\)
\(278\) −3.11371 + 5.39311i −0.186748 + 0.323457i
\(279\) −5.04428 8.08517i −0.301993 0.484046i
\(280\) 0 0
\(281\) 21.2397i 1.26706i −0.773719 0.633528i \(-0.781606\pi\)
0.773719 0.633528i \(-0.218394\pi\)
\(282\) −3.87810 + 15.5310i −0.230938 + 0.924856i
\(283\) 5.67603 3.27706i 0.337405 0.194801i −0.321719 0.946835i \(-0.604261\pi\)
0.659124 + 0.752034i \(0.270927\pi\)
\(284\) −2.64967 + 1.52979i −0.157229 + 0.0907761i
\(285\) 0 0
\(286\) 11.3271i 0.669786i
\(287\) 31.3883 + 0.894454i 1.85279 + 0.0527980i
\(288\) −2.62301 4.20426i −0.154562 0.247738i
\(289\) 2.10188 3.64056i 0.123640 0.214151i
\(290\) 0 0
\(291\) 1.65134 + 1.59581i 0.0968035 + 0.0935477i
\(292\) −1.74717 1.00873i −0.102245 0.0590315i
\(293\) 3.71937 0.217288 0.108644 0.994081i \(-0.465349\pi\)
0.108644 + 0.994081i \(0.465349\pi\)
\(294\) 17.9142 4.04218i 1.04478 0.235745i
\(295\) 0 0
\(296\) 17.4603 + 10.0807i 1.01486 + 0.585928i
\(297\) 10.9165 + 2.33240i 0.633440 + 0.135340i
\(298\) −1.92648 3.33677i −0.111598 0.193294i
\(299\) −2.63629 + 4.56619i −0.152461 + 0.264070i
\(300\) 0 0
\(301\) −7.91536 0.225559i −0.456234 0.0130010i
\(302\) 8.51121i 0.489765i
\(303\) −22.5519 5.63123i −1.29557 0.323505i
\(304\) 4.76568 2.75147i 0.273331 0.157808i
\(305\) 0 0
\(306\) −16.2454 + 0.555880i −0.928690 + 0.0317775i
\(307\) 11.2102i 0.639800i 0.947451 + 0.319900i \(0.103649\pi\)
−0.947451 + 0.319900i \(0.896351\pi\)
\(308\) −1.42415 0.877248i −0.0811484 0.0499859i
\(309\) 9.63578 2.75935i 0.548160 0.156974i
\(310\) 0 0
\(311\) 9.46050 + 16.3861i 0.536456 + 0.929168i 0.999091 + 0.0426199i \(0.0135704\pi\)
−0.462636 + 0.886548i \(0.653096\pi\)
\(312\) 10.8248 11.2016i 0.612835 0.634164i
\(313\) −14.1859 8.19024i −0.801835 0.462940i 0.0422775 0.999106i \(-0.486539\pi\)
−0.844112 + 0.536166i \(0.819872\pi\)
\(314\) −21.0903 −1.19020
\(315\) 0 0
\(316\) −0.554083 −0.0311696
\(317\) 8.76134 + 5.05836i 0.492086 + 0.284106i 0.725439 0.688286i \(-0.241637\pi\)
−0.233353 + 0.972392i \(0.574970\pi\)
\(318\) −20.4663 + 21.1786i −1.14769 + 1.18763i
\(319\) −6.39812 11.0819i −0.358226 0.620466i
\(320\) 0 0
\(321\) −6.47141 + 1.85319i −0.361199 + 0.103435i
\(322\) 2.88408 + 5.34118i 0.160723 + 0.297652i
\(323\) 4.37254i 0.243295i
\(324\) −1.47795 2.19780i −0.0821083 0.122100i
\(325\) 0 0
\(326\) −5.33977 + 3.08292i −0.295743 + 0.170747i
\(327\) 8.75127 + 2.18520i 0.483946 + 0.120842i
\(328\) 30.6638i 1.69313i
\(329\) −8.46672 + 13.7451i −0.466785 + 0.757791i
\(330\) 0 0
\(331\) −9.63774 + 16.6931i −0.529738 + 0.917533i 0.469660 + 0.882847i \(0.344376\pi\)
−0.999398 + 0.0346861i \(0.988957\pi\)
\(332\) 1.33969 + 2.32041i 0.0735251 + 0.127349i
\(333\) 20.6625 + 11.0051i 1.13230 + 0.603075i
\(334\) 18.3282 + 10.5818i 1.00287 + 0.579009i
\(335\) 0 0
\(336\) −5.11234 19.9871i −0.278901 1.09039i
\(337\) −23.6381 −1.28765 −0.643824 0.765174i \(-0.722653\pi\)
−0.643824 + 0.765174i \(0.722653\pi\)
\(338\) 1.15807 + 0.668614i 0.0629909 + 0.0363678i
\(339\) −11.6609 11.2687i −0.633333 0.612033i
\(340\) 0 0
\(341\) −3.41210 + 5.90993i −0.184776 + 0.320041i
\(342\) 4.71247 2.94008i 0.254821 0.158981i
\(343\) 18.4527 + 1.58093i 0.996350 + 0.0853621i
\(344\) 7.73266i 0.416917i
\(345\) 0 0
\(346\) 13.1211 7.57546i 0.705394 0.407259i
\(347\) −13.7760 + 7.95360i −0.739536 + 0.426971i −0.821901 0.569631i \(-0.807086\pi\)
0.0823644 + 0.996602i \(0.473753\pi\)
\(348\) −0.735522 + 2.94561i −0.0394281 + 0.157901i
\(349\) 0.0192397i 0.00102988i 1.00000 0.000514938i \(0.000163910\pi\)
−1.00000 0.000514938i \(0.999836\pi\)
\(350\) 0 0
\(351\) 12.1172 13.4290i 0.646766 0.716786i
\(352\) −1.77428 + 3.07314i −0.0945695 + 0.163799i
\(353\) −12.7100 22.0143i −0.676484 1.17170i −0.976033 0.217624i \(-0.930170\pi\)
0.299549 0.954081i \(-0.403164\pi\)
\(354\) −4.09261 3.95496i −0.217520 0.210204i
\(355\) 0 0
\(356\) 0.523797 0.0277612
\(357\) −15.7848 4.42276i −0.835421 0.234078i
\(358\) 24.5523 1.29763
\(359\) 20.9396 + 12.0895i 1.10515 + 0.638057i 0.937568 0.347801i \(-0.113072\pi\)
0.167579 + 0.985859i \(0.446405\pi\)
\(360\) 0 0
\(361\) −8.75294 15.1605i −0.460681 0.797923i
\(362\) 14.7018 25.4642i 0.772708 1.33837i
\(363\) 3.04448 + 10.6315i 0.159794 + 0.558007i
\(364\) −2.38480 + 1.28772i −0.124998 + 0.0674949i
\(365\) 0 0
\(366\) −8.65099 2.16016i −0.452194 0.112913i
\(367\) 7.85721 4.53636i 0.410143 0.236796i −0.280708 0.959793i \(-0.590569\pi\)
0.690851 + 0.722997i \(0.257236\pi\)
\(368\) 5.90548 3.40953i 0.307845 0.177734i
\(369\) −1.21762 35.5846i −0.0633867 1.85246i
\(370\) 0 0
\(371\) −26.1346 + 14.1119i −1.35684 + 0.732654i
\(372\) 1.55655 0.445743i 0.0807035 0.0231107i
\(373\) 7.78183 13.4785i 0.402928 0.697891i −0.591150 0.806562i \(-0.701326\pi\)
0.994078 + 0.108670i \(0.0346592\pi\)
\(374\) 5.82009 + 10.0807i 0.300950 + 0.521260i
\(375\) 0 0
\(376\) 13.6524 + 7.88224i 0.704071 + 0.406496i
\(377\) −20.7342 −1.06787
\(378\) −5.84703 19.9858i −0.300739 1.02796i
\(379\) −34.0984 −1.75152 −0.875758 0.482751i \(-0.839638\pi\)
−0.875758 + 0.482751i \(0.839638\pi\)
\(380\) 0 0
\(381\) −11.5280 + 11.9292i −0.590598 + 0.611153i
\(382\) −9.62112 16.6643i −0.492259 0.852618i
\(383\) 5.28833 9.15965i 0.270221 0.468036i −0.698697 0.715417i \(-0.746237\pi\)
0.968918 + 0.247381i \(0.0795699\pi\)
\(384\) −21.8997 + 6.27133i −1.11757 + 0.320032i
\(385\) 0 0
\(386\) 31.5351i 1.60509i
\(387\) 0.307054 + 8.97356i 0.0156084 + 0.456152i
\(388\) −0.337895 + 0.195084i −0.0171540 + 0.00990388i
\(389\) 14.6659 8.46736i 0.743590 0.429312i −0.0797828 0.996812i \(-0.525423\pi\)
0.823373 + 0.567500i \(0.192089\pi\)
\(390\) 0 0
\(391\) 5.41832i 0.274016i
\(392\) 1.02990 18.0561i 0.0520180 0.911970i
\(393\) −4.50615 15.7357i −0.227305 0.793760i
\(394\) 1.69240 2.93132i 0.0852619 0.147678i
\(395\) 0 0
\(396\) −0.891580 + 1.67398i −0.0448036 + 0.0841207i
\(397\) 0.353188 + 0.203913i 0.0177260 + 0.0102341i 0.508837 0.860863i \(-0.330076\pi\)
−0.491111 + 0.871097i \(0.663409\pi\)
\(398\) 37.7491 1.89219
\(399\) 5.42677 1.38807i 0.271678 0.0694903i
\(400\) 0 0
\(401\) 24.2302 + 13.9893i 1.21000 + 0.698593i 0.962759 0.270361i \(-0.0871430\pi\)
0.247240 + 0.968954i \(0.420476\pi\)
\(402\) −19.4649 18.8102i −0.970819 0.938168i
\(403\) 5.52875 + 9.57608i 0.275407 + 0.477019i
\(404\) 1.97464 3.42017i 0.0982418 0.170160i
\(405\) 0 0
\(406\) −12.5192 + 20.3240i −0.621317 + 1.00866i
\(407\) 16.7643i 0.830974i
\(408\) −3.87810 + 15.5310i −0.191995 + 0.768898i
\(409\) −2.26960 + 1.31036i −0.112225 + 0.0647929i −0.555062 0.831809i \(-0.687305\pi\)
0.442837 + 0.896602i \(0.353972\pi\)
\(410\) 0 0
\(411\) 4.49215 17.9901i 0.221582 0.887388i
\(412\) 1.70295i 0.0838984i
\(413\) −2.72703 5.05033i −0.134188 0.248511i
\(414\) 5.83954 3.64325i 0.286998 0.179056i
\(415\) 0 0
\(416\) 2.87493 + 4.97953i 0.140955 + 0.244141i
\(417\) 5.12074 + 4.94852i 0.250764 + 0.242330i
\(418\) −3.44462 1.98876i −0.168482 0.0972732i
\(419\) −8.39649 −0.410195 −0.205098 0.978742i \(-0.565751\pi\)
−0.205098 + 0.978742i \(0.565751\pi\)
\(420\) 0 0
\(421\) −7.84952 −0.382562 −0.191281 0.981535i \(-0.561264\pi\)
−0.191281 + 0.981535i \(0.561264\pi\)
\(422\) −8.67754 5.00998i −0.422416 0.243882i
\(423\) 16.1563 + 8.60503i 0.785548 + 0.418391i
\(424\) 14.5020 + 25.1181i 0.704277 + 1.21984i
\(425\) 0 0
\(426\) 7.50912 + 26.2222i 0.363818 + 1.27047i
\(427\) −7.65622 4.71609i −0.370511 0.228227i
\(428\) 1.14371i 0.0552831i
\(429\) −12.5667 3.13793i −0.606727 0.151500i
\(430\) 0 0
\(431\) 10.6154 6.12880i 0.511326 0.295214i −0.222053 0.975035i \(-0.571276\pi\)
0.733378 + 0.679821i \(0.237942\pi\)
\(432\) −22.2555 + 7.20535i −1.07077 + 0.346668i
\(433\) 5.13957i 0.246992i 0.992345 + 0.123496i \(0.0394106\pi\)
−0.992345 + 0.123496i \(0.960589\pi\)
\(434\) 12.7249 + 0.362613i 0.610813 + 0.0174060i
\(435\) 0 0
\(436\) −0.766259 + 1.32720i −0.0366971 + 0.0635613i
\(437\) 0.925734 + 1.60342i 0.0442838 + 0.0767019i
\(438\) −12.4985 + 12.9334i −0.597200 + 0.617984i
\(439\) 14.4620 + 8.34964i 0.690234 + 0.398507i 0.803700 0.595035i \(-0.202862\pi\)
−0.113466 + 0.993542i \(0.536195\pi\)
\(440\) 0 0
\(441\) 0.478196 20.9946i 0.0227712 0.999741i
\(442\) 18.8610 0.897127
\(443\) −0.218429 0.126110i −0.0103779 0.00599167i 0.494802 0.869006i \(-0.335241\pi\)
−0.505180 + 0.863014i \(0.668574\pi\)
\(444\) −2.76402 + 2.86021i −0.131174 + 0.135740i
\(445\) 0 0
\(446\) −3.26436 + 5.65403i −0.154572 + 0.267726i
\(447\) −4.23563 + 1.21294i −0.200339 + 0.0573700i
\(448\) −17.1956 0.490013i −0.812415 0.0231509i
\(449\) 28.8710i 1.36250i 0.732049 + 0.681252i \(0.238564\pi\)
−0.732049 + 0.681252i \(0.761436\pi\)
\(450\) 0 0
\(451\) −22.0811 + 12.7485i −1.03976 + 0.600305i
\(452\) 2.38603 1.37758i 0.112230 0.0647958i
\(453\) 9.44267 + 2.35785i 0.443655 + 0.110781i
\(454\) 16.8300i 0.789873i
\(455\) 0 0
\(456\) −1.50588 5.25859i −0.0705193 0.246256i
\(457\) 12.0368 20.8483i 0.563056 0.975242i −0.434171 0.900830i \(-0.642959\pi\)
0.997228 0.0744117i \(-0.0237079\pi\)
\(458\) −7.55375 13.0835i −0.352964 0.611351i
\(459\) −3.88373 + 18.1773i −0.181277 + 0.848445i
\(460\) 0 0
\(461\) −39.8709 −1.85697 −0.928486 0.371367i \(-0.878889\pi\)
−0.928486 + 0.371367i \(0.878889\pi\)
\(462\) −10.6636 + 10.4234i −0.496114 + 0.484943i
\(463\) −29.8417 −1.38686 −0.693430 0.720524i \(-0.743901\pi\)
−0.693430 + 0.720524i \(0.743901\pi\)
\(464\) 23.2231 + 13.4078i 1.07810 + 0.622443i
\(465\) 0 0
\(466\) 15.6230 + 27.0599i 0.723723 + 1.25353i
\(467\) −2.09082 + 3.62140i −0.0967515 + 0.167579i −0.910338 0.413865i \(-0.864179\pi\)
0.813587 + 0.581444i \(0.197512\pi\)
\(468\) 1.62669 + 2.60732i 0.0751937 + 0.120523i
\(469\) −12.9700 24.0199i −0.598900 1.10914i
\(470\) 0 0
\(471\) −5.84262 + 23.3984i −0.269214 + 1.07814i
\(472\) −4.85390 + 2.80240i −0.223419 + 0.128991i
\(473\) 5.56831 3.21487i 0.256031 0.147820i
\(474\) −1.19670 + 4.79252i −0.0549661 + 0.220128i
\(475\) 0 0
\(476\) 1.46073 2.37138i 0.0669522 0.108692i
\(477\) 17.8266 + 28.5731i 0.816223 + 1.30827i
\(478\) −2.17625 + 3.76937i −0.0995393 + 0.172407i
\(479\) −13.9676 24.1926i −0.638196 1.10539i −0.985828 0.167757i \(-0.946348\pi\)
0.347632 0.937631i \(-0.386986\pi\)
\(480\) 0 0
\(481\) −23.5245 13.5819i −1.07262 0.619280i
\(482\) 39.4912 1.79878
\(483\) 6.72468 1.72005i 0.305984 0.0782650i
\(484\) −1.87892 −0.0854055
\(485\) 0 0
\(486\) −22.2018 + 8.03669i −1.00710 + 0.364552i
\(487\) 18.6216 + 32.2536i 0.843826 + 1.46155i 0.886637 + 0.462466i \(0.153035\pi\)
−0.0428116 + 0.999083i \(0.513632\pi\)
\(488\) −4.39053 + 7.60462i −0.198750 + 0.344245i
\(489\) 1.94104 + 6.77821i 0.0877770 + 0.306521i
\(490\) 0 0
\(491\) 5.90572i 0.266522i −0.991081 0.133261i \(-0.957455\pi\)
0.991081 0.133261i \(-0.0425448\pi\)
\(492\) 5.86926 + 1.46556i 0.264607 + 0.0660725i
\(493\) 18.4527 10.6536i 0.831066 0.479816i
\(494\) −5.58145 + 3.22245i −0.251121 + 0.144985i
\(495\) 0 0
\(496\) 14.3007i 0.642122i
\(497\) −0.783542 + 27.4962i −0.0351467 + 1.23337i
\(498\) 22.9637 6.57602i 1.02903 0.294678i
\(499\) −9.37010 + 16.2295i −0.419463 + 0.726532i −0.995886 0.0906204i \(-0.971115\pi\)
0.576422 + 0.817152i \(0.304448\pi\)
\(500\) 0 0
\(501\) 16.8173 17.4025i 0.751340 0.777489i
\(502\) −0.211350 0.122023i −0.00943301 0.00544615i
\(503\) −32.0398 −1.42858 −0.714291 0.699849i \(-0.753251\pi\)
−0.714291 + 0.699849i \(0.753251\pi\)
\(504\) −20.5066 + 0.117207i −0.913437 + 0.00522082i
\(505\) 0 0
\(506\) −4.26847 2.46440i −0.189757 0.109556i
\(507\) 1.06261 1.09959i 0.0471920 0.0488344i
\(508\) −1.40928 2.44094i −0.0625265 0.108299i
\(509\) 9.57465 16.5838i 0.424389 0.735063i −0.571974 0.820272i \(-0.693822\pi\)
0.996363 + 0.0852085i \(0.0271556\pi\)
\(510\) 0 0
\(511\) −15.9600 + 8.61794i −0.706031 + 0.381235i
\(512\) 15.8265i 0.699439i
\(513\) −1.95635 6.04268i −0.0863749 0.266791i
\(514\) −17.2238 + 9.94415i −0.759708 + 0.438617i
\(515\) 0 0
\(516\) −1.48008 0.369578i −0.0651570 0.0162698i
\(517\) 13.1082i 0.576499i
\(518\) −27.5171 + 14.8584i −1.20903 + 0.652842i
\(519\) −4.76960 16.6557i −0.209362 0.731102i
\(520\) 0 0
\(521\) −1.94104 3.36199i −0.0850387 0.147291i 0.820369 0.571834i \(-0.193768\pi\)
−0.905408 + 0.424543i \(0.860435\pi\)
\(522\) 23.8893 + 12.7237i 1.04561 + 0.556902i
\(523\) 1.83929 + 1.06192i 0.0804266 + 0.0464343i 0.539674 0.841874i \(-0.318548\pi\)
−0.459247 + 0.888308i \(0.651881\pi\)
\(524\) 2.78100 0.121488
\(525\) 0 0
\(526\) −26.8562 −1.17099
\(527\) −9.84076 5.68157i −0.428670 0.247493i
\(528\) 12.0460 + 11.6409i 0.524236 + 0.506605i
\(529\) −10.3529 17.9317i −0.450124 0.779638i
\(530\) 0 0
\(531\) −5.52156 + 3.44486i −0.239615 + 0.149494i
\(532\) −0.0271092 + 0.951321i −0.00117533 + 0.0412450i
\(533\) 41.3138i 1.78950i
\(534\) 1.13128 4.53055i 0.0489555 0.196056i
\(535\) 0 0
\(536\) −23.0856 + 13.3285i −0.997148 + 0.575704i
\(537\) 6.80168 27.2393i 0.293514 1.17546i
\(538\) 6.67354i 0.287717i
\(539\) −13.4304 + 6.76522i −0.578490 + 0.291398i
\(540\) 0 0
\(541\) 7.59052 13.1472i 0.326342 0.565241i −0.655441 0.755246i \(-0.727517\pi\)
0.981783 + 0.190005i \(0.0608506\pi\)
\(542\) 17.8650 + 30.9431i 0.767367 + 1.32912i
\(543\) −24.1782 23.3650i −1.03759 1.00269i
\(544\) −5.11716 2.95439i −0.219396 0.126669i
\(545\) 0 0
\(546\) 5.98744 + 23.4084i 0.256239 + 1.00179i
\(547\) −11.7540 −0.502566 −0.251283 0.967914i \(-0.580852\pi\)
−0.251283 + 0.967914i \(0.580852\pi\)
\(548\) 2.72835 + 1.57521i 0.116549 + 0.0672897i
\(549\) −4.79313 + 8.99932i −0.204566 + 0.384082i
\(550\) 0 0
\(551\) −3.64041 + 6.30537i −0.155087 + 0.268618i
\(552\) −1.86604 6.51629i −0.0794239 0.277352i
\(553\) −2.61264 + 4.24143i −0.111101 + 0.180364i
\(554\) 19.4362i 0.825763i
\(555\) 0 0
\(556\) −1.04780 + 0.604946i −0.0444365 + 0.0256554i
\(557\) −8.14298 + 4.70135i −0.345029 + 0.199203i −0.662494 0.749068i \(-0.730502\pi\)
0.317465 + 0.948270i \(0.397169\pi\)
\(558\) −0.493624 14.4260i −0.0208968 0.610703i
\(559\) 10.4183i 0.440649i
\(560\) 0 0
\(561\) 12.7962 3.66440i 0.540258 0.154711i
\(562\) 16.0858 27.8614i 0.678538 1.17526i
\(563\) 9.76331 + 16.9106i 0.411475 + 0.712695i 0.995051 0.0993632i \(-0.0316806\pi\)
−0.583577 + 0.812058i \(0.698347\pi\)
\(564\) −2.16122 + 2.23644i −0.0910040 + 0.0941712i
\(565\) 0 0
\(566\) 9.92744 0.417281
\(567\) −23.7928 + 0.950307i −0.999203 + 0.0399091i
\(568\) 26.8615 1.12708
\(569\) −11.1702 6.44911i −0.468279 0.270361i 0.247240 0.968954i \(-0.420476\pi\)
−0.715519 + 0.698593i \(0.753810\pi\)
\(570\) 0 0
\(571\) 20.8321 + 36.0823i 0.871796 + 1.51000i 0.860137 + 0.510063i \(0.170378\pi\)
0.0116595 + 0.999932i \(0.496289\pi\)
\(572\) 1.10034 1.90584i 0.0460075 0.0796874i
\(573\) −21.1533 + 6.05758i −0.883692 + 0.253059i
\(574\) 40.4965 + 24.9451i 1.69029 + 1.04119i
\(575\) 0 0
\(576\) 0.667053 + 19.4945i 0.0277939 + 0.812270i
\(577\) −6.48634 + 3.74489i −0.270030 + 0.155902i −0.628901 0.777485i \(-0.716495\pi\)
0.358871 + 0.933387i \(0.383162\pi\)
\(578\) 5.51432 3.18369i 0.229365 0.132424i
\(579\) −34.9863 8.73611i −1.45398 0.363060i
\(580\) 0 0
\(581\) 24.0794 + 0.686177i 0.998983 + 0.0284674i
\(582\) 0.957590 + 3.34395i 0.0396934 + 0.138611i
\(583\) 12.0584 20.8858i 0.499409 0.865003i
\(584\) 8.85614 + 15.3393i 0.366470 + 0.634744i
\(585\) 0 0
\(586\) 4.87892 + 2.81685i 0.201546 + 0.116363i
\(587\) −22.1920 −0.915961 −0.457981 0.888962i \(-0.651427\pi\)
−0.457981 + 0.888962i \(0.651427\pi\)
\(588\) 3.40683 + 1.06011i 0.140495 + 0.0437182i
\(589\) 3.88284 0.159990
\(590\) 0 0
\(591\) −2.78328 2.68967i −0.114489 0.110638i
\(592\) 17.5655 + 30.4244i 0.721938 + 1.25043i
\(593\) −3.15687 + 5.46787i −0.129637 + 0.224538i −0.923536 0.383512i \(-0.874715\pi\)
0.793899 + 0.608050i \(0.208048\pi\)
\(594\) 12.5534 + 11.3271i 0.515072 + 0.464757i
\(595\) 0 0
\(596\) 0.748572i 0.0306627i
\(597\) 10.4575 41.8803i 0.427999 1.71405i
\(598\) −6.91636 + 3.99316i −0.282831 + 0.163293i
\(599\) −17.8962 + 10.3324i −0.731219 + 0.422170i −0.818868 0.573982i \(-0.805398\pi\)
0.0876487 + 0.996151i \(0.472065\pi\)
\(600\) 0 0
\(601\) 12.5956i 0.513785i −0.966440 0.256892i \(-0.917301\pi\)
0.966440 0.256892i \(-0.0826986\pi\)
\(602\) −10.2122 6.29053i −0.416219 0.256383i
\(603\) −26.2611 + 16.3841i −1.06943 + 0.667213i
\(604\) −0.826798 + 1.43206i −0.0336419 + 0.0582695i
\(605\) 0 0
\(606\) −25.3178 24.4663i −1.02847 0.993877i
\(607\) −36.9590 21.3383i −1.50012 0.866095i −1.00000 0.000139312i \(-0.999956\pi\)
−0.500121 0.865956i \(-0.666711\pi\)
\(608\) 2.01906 0.0818838
\(609\) 19.0801 + 19.5196i 0.773163 + 0.790974i
\(610\) 0 0
\(611\) −18.3942 10.6199i −0.744148 0.429634i
\(612\) −2.78738 1.48459i −0.112673 0.0600110i
\(613\) −2.66142 4.60972i −0.107494 0.186185i 0.807261 0.590195i \(-0.200949\pi\)
−0.914754 + 0.404011i \(0.867616\pi\)
\(614\) −8.48998 + 14.7051i −0.342628 + 0.593448i
\(615\) 0 0
\(616\) 6.97728 + 12.9216i 0.281123 + 0.520626i
\(617\) 30.1002i 1.21179i −0.795545 0.605895i \(-0.792815\pi\)
0.795545 0.605895i \(-0.207185\pi\)
\(618\) 14.7296 + 3.67800i 0.592511 + 0.147951i
\(619\) −11.0265 + 6.36613i −0.443191 + 0.255876i −0.704950 0.709257i \(-0.749031\pi\)
0.261759 + 0.965133i \(0.415697\pi\)
\(620\) 0 0
\(621\) −2.42425 7.48790i −0.0972817 0.300479i
\(622\) 28.6594i 1.14914i
\(623\) 2.46983 4.00959i 0.0989518 0.160641i
\(624\) 26.0944 7.47254i 1.04461 0.299141i
\(625\) 0 0
\(626\) −12.4057 21.4872i −0.495830 0.858802i
\(627\) −3.16066 + 3.27066i −0.126225 + 0.130618i
\(628\) −3.54856 2.04876i −0.141603 0.0817545i
\(629\) 27.9145 1.11303
\(630\) 0 0
\(631\) −17.4114 −0.693138 −0.346569 0.938024i \(-0.612653\pi\)
−0.346569 + 0.938024i \(0.612653\pi\)
\(632\) 4.21284 + 2.43229i 0.167578 + 0.0967511i
\(633\) −7.96219 + 8.23930i −0.316469 + 0.327483i
\(634\) 7.66184 + 13.2707i 0.304291 + 0.527047i
\(635\) 0 0
\(636\) −5.50089 + 1.57526i −0.218125 + 0.0624633i
\(637\) −1.38761 + 24.3273i −0.0549789 + 0.963881i
\(638\) 19.3823i 0.767353i
\(639\) 31.1721 1.06663i 1.23315 0.0421954i
\(640\) 0 0
\(641\) 1.13893 0.657564i 0.0449852 0.0259722i −0.477339 0.878719i \(-0.658399\pi\)
0.522324 + 0.852747i \(0.325065\pi\)
\(642\) −9.89243 2.47015i −0.390423 0.0974891i
\(643\) 39.2223i 1.54678i 0.633932 + 0.773389i \(0.281440\pi\)
−0.633932 + 0.773389i \(0.718560\pi\)
\(644\) −0.0335929 + 1.17885i −0.00132375 + 0.0464531i
\(645\) 0 0
\(646\) 3.31152 5.73572i 0.130290 0.225669i
\(647\) −3.11558 5.39634i −0.122486 0.212152i 0.798261 0.602311i \(-0.205753\pi\)
−0.920747 + 0.390159i \(0.872420\pi\)
\(648\) 1.58944 + 23.1983i 0.0624391 + 0.911316i
\(649\) 4.03604 + 2.33021i 0.158428 + 0.0914687i
\(650\) 0 0
\(651\) 3.92744 14.0170i 0.153928 0.549369i
\(652\) −1.19793 −0.0469144
\(653\) 16.3348 + 9.43091i 0.639230 + 0.369060i 0.784318 0.620359i \(-0.213013\pi\)
−0.145088 + 0.989419i \(0.546346\pi\)
\(654\) 9.82460 + 9.49418i 0.384172 + 0.371252i
\(655\) 0 0
\(656\) 26.7157 46.2730i 1.04307 1.80666i
\(657\) 10.8864 + 17.4492i 0.424721 + 0.680759i
\(658\) −21.5160 + 11.6180i −0.838783 + 0.452918i
\(659\) 41.6170i 1.62117i −0.585622 0.810584i \(-0.699150\pi\)
0.585622 0.810584i \(-0.300850\pi\)
\(660\) 0 0
\(661\) 3.27232 1.88927i 0.127278 0.0734842i −0.435009 0.900426i \(-0.643255\pi\)
0.562287 + 0.826942i \(0.309921\pi\)
\(662\) −25.2848 + 14.5982i −0.982721 + 0.567374i
\(663\) 5.22503 20.9251i 0.202923 0.812665i
\(664\) 23.5236i 0.912894i
\(665\) 0 0
\(666\) 18.7696 + 30.0846i 0.727307 + 1.16576i
\(667\) −4.51108 + 7.81342i −0.174670 + 0.302537i
\(668\) 2.05588 + 3.56088i 0.0795442 + 0.137775i
\(669\) 5.36848 + 5.18793i 0.207558 + 0.200577i
\(670\) 0 0
\(671\) 7.30148 0.281871
\(672\) 2.04225 7.28879i 0.0787816 0.281171i
\(673\) −31.2573 −1.20488 −0.602441 0.798163i \(-0.705805\pi\)
−0.602441 + 0.798163i \(0.705805\pi\)
\(674\) −31.0075 17.9022i −1.19436 0.689565i
\(675\) 0 0
\(676\) 0.129901 + 0.224996i 0.00499621 + 0.00865369i
\(677\) 4.36895 7.56724i 0.167912 0.290832i −0.769773 0.638317i \(-0.779631\pi\)
0.937686 + 0.347485i \(0.112964\pi\)
\(678\) −6.76199 23.6132i −0.259693 0.906858i
\(679\) −0.0999201 + 3.50641i −0.00383458 + 0.134564i
\(680\) 0 0
\(681\) −18.6719 4.66239i −0.715509 0.178663i
\(682\) −8.95171 + 5.16827i −0.342779 + 0.197903i
\(683\) 18.9393 10.9346i 0.724691 0.418401i −0.0917858 0.995779i \(-0.529257\pi\)
0.816477 + 0.577378i \(0.195924\pi\)
\(684\) 1.07850 0.0369037i 0.0412376 0.00141105i
\(685\) 0 0
\(686\) 23.0081 + 16.0488i 0.878454 + 0.612746i
\(687\) −16.6079 + 4.75594i −0.633632 + 0.181450i
\(688\) −6.73705 + 11.6689i −0.256847 + 0.444873i
\(689\) −19.5387 33.8421i −0.744366 1.28928i
\(690\) 0 0
\(691\) 19.5167 + 11.2680i 0.742449 + 0.428653i 0.822959 0.568101i \(-0.192322\pi\)
−0.0805102 + 0.996754i \(0.525655\pi\)
\(692\) 2.94359 0.111898
\(693\) 8.61007 + 14.7182i 0.327069 + 0.559097i
\(694\) −24.0944 −0.914612
\(695\) 0 0
\(696\) 18.5229 19.1675i 0.702107 0.726542i
\(697\) −21.2279 36.7678i −0.804063 1.39268i
\(698\) −0.0145711 + 0.0252378i −0.000551523 + 0.000955266i
\(699\) 34.3493 9.83646i 1.29921 0.372049i
\(700\) 0 0
\(701\) 35.5019i 1.34089i 0.741960 + 0.670444i \(0.233896\pi\)
−0.741960 + 0.670444i \(0.766104\pi\)
\(702\) 26.0652 8.43873i 0.983766 0.318499i
\(703\) −8.26062 + 4.76927i −0.311555 + 0.179877i
\(704\) 12.0968 6.98408i 0.455915 0.263223i
\(705\) 0 0
\(706\) 38.5033i 1.44909i
\(707\) −16.8700 31.2425i −0.634463 1.17500i
\(708\) −0.304409 1.06301i −0.0114404 0.0399503i
\(709\) 2.03390 3.52282i 0.0763847 0.132302i −0.825303 0.564690i \(-0.808996\pi\)
0.901688 + 0.432388i \(0.142329\pi\)
\(710\) 0 0
\(711\) 4.98549 + 2.65532i 0.186970 + 0.0995824i
\(712\) −3.98257 2.29934i −0.149253 0.0861712i
\(713\) 4.81149 0.180192
\(714\) −17.3563 17.7561i −0.649543 0.664506i
\(715\) 0 0
\(716\) 4.13106 + 2.38507i 0.154385 + 0.0891342i
\(717\) 3.57901 + 3.45864i 0.133660 + 0.129165i
\(718\) 18.3118 + 31.7169i 0.683389 + 1.18366i
\(719\) −15.2703 + 26.4489i −0.569484 + 0.986376i 0.427133 + 0.904189i \(0.359524\pi\)
−0.996617 + 0.0821868i \(0.973810\pi\)
\(720\) 0 0
\(721\) 13.0359 + 8.02984i 0.485481 + 0.299047i
\(722\) 26.5159i 0.986821i
\(723\) 10.9402 43.8131i 0.406869 1.62943i
\(724\) 4.94730 2.85632i 0.183865 0.106154i
\(725\) 0 0
\(726\) −4.05805 + 16.2516i −0.150608 + 0.603155i
\(727\) 23.4181i 0.868528i 0.900786 + 0.434264i \(0.142992\pi\)
−0.900786 + 0.434264i \(0.857008\pi\)
\(728\) 23.7850 + 0.677789i 0.881533 + 0.0251205i
\(729\) 2.76568 + 26.8580i 0.102433 + 0.994740i
\(730\) 0 0
\(731\) 5.35315 + 9.27192i 0.197993 + 0.342934i
\(732\) −1.24573 1.20383i −0.0460436 0.0444950i
\(733\) −14.6277 8.44533i −0.540288 0.311935i 0.204908 0.978781i \(-0.434311\pi\)
−0.745196 + 0.666846i \(0.767644\pi\)
\(734\) 13.7423 0.507239
\(735\) 0 0
\(736\) 2.50196 0.0922235
\(737\) 19.1958 + 11.0827i 0.707087 + 0.408237i
\(738\) 25.3526 47.6006i 0.933242 1.75220i
\(739\) 13.8321 + 23.9579i 0.508822 + 0.881306i 0.999948 + 0.0102170i \(0.00325222\pi\)
−0.491126 + 0.871089i \(0.663414\pi\)
\(740\) 0 0
\(741\) 2.02890 + 7.08499i 0.0745333 + 0.260274i
\(742\) −44.9699 1.28148i −1.65090 0.0470446i
\(743\) 40.1701i 1.47370i −0.676056 0.736850i \(-0.736312\pi\)
0.676056 0.736850i \(-0.263688\pi\)
\(744\) −13.7916 3.44377i −0.505624 0.126255i
\(745\) 0 0
\(746\) 20.4158 11.7870i 0.747474 0.431554i
\(747\) −0.934092 27.2986i −0.0341766 0.998804i
\(748\) 2.26151i 0.0826888i
\(749\) −8.75491 5.39286i −0.319898 0.197051i
\(750\) 0 0
\(751\) 24.8188 42.9874i 0.905650 1.56863i 0.0856082 0.996329i \(-0.472717\pi\)
0.820042 0.572303i \(-0.193950\pi\)
\(752\) 13.7347 + 23.7893i 0.500854 + 0.867505i
\(753\) −0.193927 + 0.200676i −0.00706709 + 0.00731305i
\(754\) −27.1983 15.7029i −0.990503 0.571867i
\(755\) 0 0
\(756\) 0.957668 3.93071i 0.0348301 0.142958i
\(757\) 47.7116 1.73411 0.867054 0.498214i \(-0.166011\pi\)
0.867054 + 0.498214i \(0.166011\pi\)
\(758\) −44.7288 25.8242i −1.62462 0.937977i
\(759\) −3.91659 + 4.05290i −0.142163 + 0.147111i
\(760\) 0 0
\(761\) −9.91711 + 17.1769i −0.359495 + 0.622663i −0.987876 0.155242i \(-0.950384\pi\)
0.628382 + 0.777905i \(0.283718\pi\)
\(762\) −24.1565 + 6.91759i −0.875098 + 0.250598i
\(763\) 6.54643 + 12.1237i 0.236997 + 0.438907i
\(764\) 3.73847i 0.135253i
\(765\) 0 0
\(766\) 13.8740 8.01017i 0.501289 0.289419i
\(767\) 6.53974 3.77572i 0.236136 0.136333i
\(768\) −11.6242 2.90258i −0.419454 0.104738i
\(769\) 10.6337i 0.383461i 0.981448 + 0.191731i \(0.0614100\pi\)
−0.981448 + 0.191731i \(0.938590\pi\)
\(770\) 0 0
\(771\) 6.26096 + 21.8635i 0.225483 + 0.787396i
\(772\) 3.06339 5.30595i 0.110254 0.190965i
\(773\) −7.16138 12.4039i −0.257577 0.446136i 0.708015 0.706197i \(-0.249591\pi\)
−0.965592 + 0.260061i \(0.916257\pi\)
\(774\) −6.39330 + 12.0037i −0.229802 + 0.431464i
\(775\) 0 0
\(776\) 3.42548 0.122967
\(777\) 8.86150 + 34.6448i 0.317904 + 1.24287i
\(778\) 25.6508 0.919626
\(779\) 12.5637 + 7.25368i 0.450142 + 0.259890i
\(780\) 0 0
\(781\) −11.1677 19.3431i −0.399613 0.692149i
\(782\) 4.10353 7.10752i 0.146742 0.254165i
\(783\) 20.7342 22.9789i 0.740980 0.821200i
\(784\) 17.2855 26.3501i 0.617338 0.941075i
\(785\) 0 0
\(786\) 6.00634 24.0541i 0.214239 0.857982i
\(787\) 31.9859 18.4671i 1.14017 0.658280i 0.193700 0.981061i \(-0.437951\pi\)
0.946474 + 0.322781i \(0.104618\pi\)
\(788\) 0.569511 0.328807i 0.0202880 0.0117133i
\(789\) −7.43992 + 29.7953i −0.264868 + 1.06074i
\(790\) 0 0
\(791\) 0.705583 24.7604i 0.0250876 0.880378i
\(792\) 14.1273 8.81391i 0.501991 0.313189i
\(793\) 5.91543 10.2458i 0.210063 0.363840i
\(794\) 0.308865 + 0.534970i 0.0109612 + 0.0189854i
\(795\) 0 0
\(796\) 6.35148 + 3.66703i 0.225122 + 0.129974i
\(797\) 37.4862 1.32783 0.663914 0.747809i \(-0.268894\pi\)
0.663914 + 0.747809i \(0.268894\pi\)
\(798\) 8.16985 + 2.28912i 0.289210 + 0.0810340i
\(799\) 21.8268 0.772177
\(800\) 0 0
\(801\) −4.71298 2.51018i −0.166525 0.0886929i
\(802\) 21.1895 + 36.7012i 0.748226 + 1.29597i
\(803\) 7.36392 12.7547i 0.259867 0.450103i
\(804\) −1.44780 5.05578i −0.0510599 0.178303i
\(805\) 0 0
\(806\) 16.7487i 0.589947i
\(807\) 7.40389 + 1.84876i 0.260629 + 0.0650794i
\(808\) −30.0274 + 17.3363i −1.05636 + 0.609889i
\(809\) −22.1518 + 12.7893i −0.778814 + 0.449649i −0.836010 0.548714i \(-0.815117\pi\)
0.0571956 + 0.998363i \(0.481784\pi\)
\(810\) 0 0
\(811\) 7.28791i 0.255913i 0.991780 + 0.127957i \(0.0408418\pi\)
−0.991780 + 0.127957i \(0.959158\pi\)
\(812\) −4.08074 + 2.20348i −0.143206 + 0.0773269i
\(813\) 39.2786 11.2480i 1.37756 0.394485i
\(814\) 12.6963 21.9907i 0.445006 0.770773i
\(815\) 0 0
\(816\) −19.3835 + 20.0581i −0.678559 + 0.702175i
\(817\) −3.16826 1.82920i −0.110844 0.0639955i
\(818\) −3.96956 −0.138792
\(819\) 27.6289 0.157915i 0.965432 0.00551800i
\(820\) 0 0
\(821\) 0.00729231 + 0.00421022i 0.000254504 + 0.000146938i 0.500127 0.865952i \(-0.333287\pi\)
−0.499873 + 0.866099i \(0.666620\pi\)
\(822\) 19.5173 20.1966i 0.680745 0.704437i
\(823\) 15.6119 + 27.0406i 0.544198 + 0.942578i 0.998657 + 0.0518103i \(0.0164991\pi\)
−0.454459 + 0.890767i \(0.650168\pi\)
\(824\) 7.47553 12.9480i 0.260422 0.451065i
\(825\) 0 0
\(826\) 0.247637 8.69011i 0.00861639 0.302368i
\(827\) 38.3189i 1.33248i 0.745738 + 0.666239i \(0.232097\pi\)
−0.745738 + 0.666239i \(0.767903\pi\)
\(828\) 1.33645 0.0457300i 0.0464447 0.00158923i
\(829\) 1.94142 1.12088i 0.0674283 0.0389298i −0.465907 0.884834i \(-0.654272\pi\)
0.533335 + 0.845904i \(0.320938\pi\)
\(830\) 0 0
\(831\) −21.5632 5.38436i −0.748020 0.186781i
\(832\) 22.6331i 0.784663i
\(833\) −11.2649 22.3633i −0.390306 0.774843i
\(834\) 2.96944 + 10.3694i 0.102823 + 0.359064i
\(835\) 0 0
\(836\) −0.386384 0.669237i −0.0133634 0.0231460i
\(837\) −16.1416 3.44877i −0.557934 0.119207i
\(838\) −11.0142 6.35903i −0.380478 0.219669i
\(839\) 20.6544 0.713069 0.356535 0.934282i \(-0.383958\pi\)
0.356535 + 0.934282i \(0.383958\pi\)
\(840\) 0 0
\(841\) −6.47924 −0.223422
\(842\) −10.2967 5.94479i −0.354847 0.204871i
\(843\) −26.4543 25.5646i −0.911135 0.880492i
\(844\) −0.973362 1.68591i −0.0335045 0.0580315i
\(845\) 0 0
\(846\) 14.6762 + 23.5236i 0.504579 + 0.808759i
\(847\) −8.85959 + 14.3829i −0.304419 + 0.494202i
\(848\) 50.5391i 1.73552i
\(849\) 2.75018 11.0139i 0.0943859 0.377996i
\(850\) 0 0
\(851\) −10.2363 + 5.90993i −0.350896 + 0.202590i
\(852\) −1.28383 + 5.14147i −0.0439833 + 0.176144i
\(853\) 7.06831i 0.242014i −0.992652 0.121007i \(-0.961388\pi\)
0.992652 0.121007i \(-0.0386124\pi\)
\(854\) −6.47141 11.9848i −0.221447 0.410110i
\(855\) 0 0
\(856\) −5.02058 + 8.69590i −0.171600 + 0.297220i
\(857\) −8.41661 14.5780i −0.287506 0.497975i 0.685708 0.727877i \(-0.259493\pi\)
−0.973214 + 0.229902i \(0.926159\pi\)
\(858\) −14.1080 13.6335i −0.481640 0.465441i
\(859\) 30.4698 + 17.5918i 1.03962 + 0.600223i 0.919725 0.392563i \(-0.128412\pi\)
0.119893 + 0.992787i \(0.461745\pi\)
\(860\) 0 0
\(861\) 38.8937 38.0179i 1.32549 1.29565i
\(862\) 18.5665 0.632376
\(863\) 32.8880 + 18.9879i 1.11952 + 0.646356i 0.941279 0.337630i \(-0.109625\pi\)
0.178243 + 0.983986i \(0.442959\pi\)
\(864\) −8.39355 1.79335i −0.285554 0.0610110i
\(865\) 0 0
\(866\) −3.89242 + 6.74187i −0.132270 + 0.229098i
\(867\) −2.00449 6.99977i −0.0680761 0.237725i
\(868\) 2.10580 + 1.29713i 0.0714755 + 0.0440275i
\(869\) 4.04491i 0.137214i
\(870\) 0 0
\(871\) 31.1037 17.9577i 1.05391 0.608474i
\(872\) 11.6521 6.72737i 0.394591 0.227817i
\(873\) 3.97518 0.136021i 0.134540 0.00460362i
\(874\) 2.80440i 0.0948601i
\(875\) 0 0
\(876\) −3.35932 + 0.961992i −0.113501 + 0.0325027i
\(877\) 5.72481 9.91566i 0.193313 0.334828i −0.753033 0.657983i \(-0.771410\pi\)
0.946346 + 0.323155i \(0.104743\pi\)
\(878\) 12.6471 + 21.9054i 0.426819 + 0.739272i
\(879\) 4.47672 4.63252i 0.150996 0.156251i
\(880\) 0 0
\(881\) 23.6698 0.797455 0.398728 0.917069i \(-0.369452\pi\)
0.398728 + 0.917069i \(0.369452\pi\)
\(882\) 16.5274 27.1776i 0.556506 0.915118i
\(883\) 16.8355 0.566560 0.283280 0.959037i \(-0.408577\pi\)
0.283280 + 0.959037i \(0.408577\pi\)
\(884\) 3.17346 + 1.83220i 0.106735 + 0.0616236i
\(885\) 0 0
\(886\) −0.191017 0.330852i −0.00641735 0.0111152i
\(887\) −26.2917 + 45.5385i −0.882789 + 1.52903i −0.0345613 + 0.999403i \(0.511003\pi\)
−0.848227 + 0.529632i \(0.822330\pi\)
\(888\) 33.5712 9.61362i 1.12657 0.322612i
\(889\) −25.3301 0.721818i −0.849546 0.0242090i
\(890\) 0 0
\(891\) 16.0444 10.7893i 0.537507 0.361455i
\(892\) −1.09849 + 0.634214i −0.0367802 + 0.0212350i
\(893\) −6.45910 + 3.72917i −0.216146 + 0.124792i
\(894\) −6.47474 1.61675i −0.216548 0.0540722i
\(895\) 0 0
\(896\) −29.6273 18.2498i −0.989778 0.609685i
\(897\) 2.51414 + 8.77950i 0.0839448 + 0.293139i
\(898\) −21.8652 + 37.8717i −0.729653 + 1.26380i
\(899\) 9.46050 + 16.3861i 0.315525 + 0.546506i
\(900\) 0 0
\(901\) 34.7774 + 20.0788i 1.15860 + 0.668921i
\(902\) −38.6201 −1.28591
\(903\) −9.80803 + 9.58717i −0.326391 + 0.319041i
\(904\) −24.1889 −0.804510
\(905\) 0 0
\(906\) 10.6008 + 10.2443i 0.352188 + 0.340343i
\(907\) 25.3858 + 43.9694i 0.842920 + 1.45998i 0.887415 + 0.460971i \(0.152499\pi\)
−0.0444946 + 0.999010i \(0.514168\pi\)
\(908\) 1.63491 2.83174i 0.0542563 0.0939747i
\(909\) −34.1577 + 21.3107i −1.13294 + 0.706832i
\(910\) 0 0
\(911\) 16.1165i 0.533963i 0.963702 + 0.266981i \(0.0860262\pi\)
−0.963702 + 0.266981i \(0.913974\pi\)
\(912\) 2.30909 9.24743i 0.0764617 0.306213i
\(913\) −16.9394 + 9.77999i −0.560614 + 0.323671i
\(914\) 31.5787 18.2319i 1.04453 0.603059i
\(915\) 0 0
\(916\) 2.93515i 0.0969802i
\(917\) 13.1131 21.2882i 0.433033 0.702997i
\(918\) −18.8610 + 20.9029i −0.622506 + 0.689900i
\(919\) 19.8721 34.4194i 0.655519 1.13539i −0.326245 0.945285i \(-0.605783\pi\)
0.981763 0.190106i \(-0.0608833\pi\)
\(920\) 0 0
\(921\) 13.9624 + 13.4928i 0.460077 + 0.444604i
\(922\) −52.3010 30.1960i −1.72244 0.994452i
\(923\) −36.1909 −1.19124
\(924\) −2.80676 + 0.717917i −0.0923355 + 0.0236177i
\(925\) 0 0
\(926\) −39.1451 22.6004i −1.28639 0.742696i
\(927\) 8.16102 15.3227i 0.268043 0.503263i
\(928\) 4.91942 + 8.52069i 0.161488 + 0.279705i
\(929\) 18.2593 31.6261i 0.599069 1.03762i −0.393889 0.919158i \(-0.628871\pi\)
0.992959 0.118461i \(-0.0377960\pi\)
\(930\) 0 0
\(931\) 7.15440 + 4.69323i 0.234476 + 0.153814i
\(932\) 6.07063i 0.198850i
\(933\) 31.7959 + 7.93946i 1.04095 + 0.259926i
\(934\) −5.48530 + 3.16694i −0.179484 + 0.103625i
\(935\) 0 0
\(936\) −0.922672 26.9649i −0.0301585 0.881375i
\(937\) 7.60980i 0.248601i 0.992245 + 0.124301i \(0.0396687\pi\)
−0.992245 + 0.124301i \(0.960331\pi\)
\(938\) 1.17779 41.3311i 0.0384561 1.34951i
\(939\) −27.2755 + 7.81075i −0.890102 + 0.254894i
\(940\) 0 0
\(941\) −11.0121 19.0735i −0.358985 0.621780i 0.628807 0.777562i \(-0.283544\pi\)
−0.987791 + 0.155782i \(0.950210\pi\)
\(942\) −25.3848 + 26.2682i −0.827081 + 0.855866i
\(943\) 15.5686 + 8.98853i 0.506983 + 0.292707i
\(944\) −9.76632 −0.317867
\(945\) 0 0
\(946\) 9.73904 0.316644
\(947\) 42.6589 + 24.6291i 1.38623 + 0.800339i 0.992888 0.119053i \(-0.0379860\pi\)
0.393341 + 0.919393i \(0.371319\pi\)
\(948\) −0.666906 + 0.690116i −0.0216601 + 0.0224139i
\(949\) −11.9320 20.6669i −0.387330 0.670875i
\(950\) 0 0
\(951\) 16.8456 4.82399i 0.546255 0.156429i
\(952\) −21.5160 + 11.6180i −0.697339 + 0.376542i
\(953\) 10.2538i 0.332154i 0.986113 + 0.166077i \(0.0531101\pi\)
−0.986113 + 0.166077i \(0.946890\pi\)
\(954\) 1.74448 + 50.9819i 0.0564795 + 1.65060i
\(955\) 0 0
\(956\) −0.732331 + 0.422811i −0.0236853 + 0.0136747i
\(957\) −21.5035 5.36945i −0.695109 0.173570i
\(958\) 42.3131i 1.36708i
\(959\) 24.9229 13.4576i 0.804801 0.434569i
\(960\) 0 0
\(961\) −10.4547 + 18.1081i −0.337250 + 0.584134i
\(962\) −20.5723 35.6323i −0.663278 1.14883i
\(963\) −5.48096 + 10.2907i −0.176622 + 0.331615i
\(964\) 6.64460 + 3.83626i 0.214008 + 0.123558i
\(965\) 0 0
\(966\) 10.1238 + 2.83661i 0.325729 + 0.0912663i
\(967\) 4.62632 0.148772 0.0743862 0.997230i \(-0.476300\pi\)
0.0743862 + 0.997230i \(0.476300\pi\)
\(968\) 14.2859 + 8.24799i 0.459168 + 0.265101i
\(969\) −5.44605 5.26288i −0.174952 0.169068i
\(970\) 0 0
\(971\) −12.6443 + 21.9006i −0.405775 + 0.702822i −0.994411 0.105575i \(-0.966332\pi\)
0.588637 + 0.808398i \(0.299665\pi\)
\(972\) −4.51628 0.804521i −0.144860 0.0258050i
\(973\) −0.309848 + 10.8732i −0.00993326 + 0.348579i
\(974\) 56.4119i 1.80755i
\(975\) 0 0
\(976\) −13.2510 + 7.65046i −0.424154 + 0.244885i
\(977\) 20.8797 12.0549i 0.668000 0.385670i −0.127318 0.991862i \(-0.540637\pi\)
0.795318 + 0.606192i \(0.207304\pi\)
\(978\) −2.58725 + 10.3614i −0.0827313 + 0.331321i
\(979\) 3.82381i 0.122210i
\(980\) 0 0
\(981\) 13.2549 8.26964i 0.423196 0.264029i
\(982\) 4.47267 7.74688i 0.142728 0.247213i
\(983\) 24.0441 + 41.6456i 0.766888 + 1.32829i 0.939243 + 0.343254i \(0.111529\pi\)
−0.172354 + 0.985035i \(0.555137\pi\)
\(984\) −38.1921 36.9076i −1.21752 1.17657i
\(985\) 0 0
\(986\) 32.2739 1.02781
\(987\) 6.92894 + 27.0893i 0.220550 + 0.862261i
\(988\) −1.25214 −0.0398360
\(989\) −3.92601 2.26668i −0.124840 0.0720764i
\(990\) 0 0
\(991\) −14.8587 25.7361i −0.472003 0.817534i 0.527483 0.849565i \(-0.323136\pi\)
−0.999487 + 0.0320314i \(0.989802\pi\)
\(992\) 2.62352 4.54406i 0.0832967 0.144274i
\(993\) 9.19119 + 32.0960i 0.291674 + 1.01854i
\(994\) −21.8519 + 35.4749i −0.693099 + 1.12520i
\(995\) 0 0
\(996\) 4.50258 + 1.12430i 0.142670 + 0.0356248i
\(997\) −23.1647 + 13.3742i −0.733634 + 0.423564i −0.819750 0.572721i \(-0.805888\pi\)
0.0861161 + 0.996285i \(0.472554\pi\)
\(998\) −24.5826 + 14.1928i −0.778149 + 0.449265i
\(999\) 38.5768 12.4894i 1.22052 0.395148i
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 525.2.t.j.26.10 24
3.2 odd 2 inner 525.2.t.j.26.4 24
5.2 odd 4 105.2.p.a.89.3 yes 24
5.3 odd 4 105.2.p.a.89.10 yes 24
5.4 even 2 inner 525.2.t.j.26.3 24
7.3 odd 6 inner 525.2.t.j.101.4 24
15.2 even 4 105.2.p.a.89.9 yes 24
15.8 even 4 105.2.p.a.89.4 yes 24
15.14 odd 2 inner 525.2.t.j.26.9 24
21.17 even 6 inner 525.2.t.j.101.10 24
35.2 odd 12 735.2.g.b.734.19 24
35.3 even 12 105.2.p.a.59.9 yes 24
35.12 even 12 735.2.g.b.734.18 24
35.13 even 4 735.2.p.f.509.9 24
35.17 even 12 105.2.p.a.59.4 yes 24
35.18 odd 12 735.2.p.f.374.10 24
35.23 odd 12 735.2.g.b.734.6 24
35.24 odd 6 inner 525.2.t.j.101.9 24
35.27 even 4 735.2.p.f.509.4 24
35.32 odd 12 735.2.p.f.374.3 24
35.33 even 12 735.2.g.b.734.7 24
105.2 even 12 735.2.g.b.734.8 24
105.17 odd 12 105.2.p.a.59.10 yes 24
105.23 even 12 735.2.g.b.734.17 24
105.32 even 12 735.2.p.f.374.9 24
105.38 odd 12 105.2.p.a.59.3 24
105.47 odd 12 735.2.g.b.734.5 24
105.53 even 12 735.2.p.f.374.4 24
105.59 even 6 inner 525.2.t.j.101.3 24
105.62 odd 4 735.2.p.f.509.10 24
105.68 odd 12 735.2.g.b.734.20 24
105.83 odd 4 735.2.p.f.509.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.p.a.59.3 24 105.38 odd 12
105.2.p.a.59.4 yes 24 35.17 even 12
105.2.p.a.59.9 yes 24 35.3 even 12
105.2.p.a.59.10 yes 24 105.17 odd 12
105.2.p.a.89.3 yes 24 5.2 odd 4
105.2.p.a.89.4 yes 24 15.8 even 4
105.2.p.a.89.9 yes 24 15.2 even 4
105.2.p.a.89.10 yes 24 5.3 odd 4
525.2.t.j.26.3 24 5.4 even 2 inner
525.2.t.j.26.4 24 3.2 odd 2 inner
525.2.t.j.26.9 24 15.14 odd 2 inner
525.2.t.j.26.10 24 1.1 even 1 trivial
525.2.t.j.101.3 24 105.59 even 6 inner
525.2.t.j.101.4 24 7.3 odd 6 inner
525.2.t.j.101.9 24 35.24 odd 6 inner
525.2.t.j.101.10 24 21.17 even 6 inner
735.2.g.b.734.5 24 105.47 odd 12
735.2.g.b.734.6 24 35.23 odd 12
735.2.g.b.734.7 24 35.33 even 12
735.2.g.b.734.8 24 105.2 even 12
735.2.g.b.734.17 24 105.23 even 12
735.2.g.b.734.18 24 35.12 even 12
735.2.g.b.734.19 24 35.2 odd 12
735.2.g.b.734.20 24 105.68 odd 12
735.2.p.f.374.3 24 35.32 odd 12
735.2.p.f.374.4 24 105.53 even 12
735.2.p.f.374.9 24 105.32 even 12
735.2.p.f.374.10 24 35.18 odd 12
735.2.p.f.509.3 24 105.83 odd 4
735.2.p.f.509.4 24 35.27 even 4
735.2.p.f.509.9 24 35.13 even 4
735.2.p.f.509.10 24 105.62 odd 4