Properties

Label 1170.2.cu.c.431.2
Level $1170$
Weight $2$
Character 1170.431
Analytic conductor $9.342$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1170,2,Mod(71,1170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1170, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 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("1170.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.cu (of order \(12\), degree \(4\), 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: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 431.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1170.431
Dual form 1170.2.cu.c.1151.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.866025 + 0.232051i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.866025 + 0.232051i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{10} +(-0.965926 - 0.258819i) q^{11} +(-2.59808 + 2.50000i) q^{13} +0.896575i q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.44949 + 4.24264i) q^{17} +(0.232051 + 0.866025i) q^{19} +(-0.258819 - 0.965926i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(2.63896 + 4.57081i) q^{23} +1.00000i q^{25} +(1.74238 + 3.15660i) q^{26} +(0.866025 + 0.232051i) q^{28} +(-2.44949 + 1.41421i) q^{29} +(1.26795 - 1.26795i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.46410 + 3.46410i) q^{34} +(-0.776457 - 0.448288i) q^{35} +(1.59808 - 5.96410i) q^{37} +0.896575 q^{38} -1.00000 q^{40} +(-1.03528 + 3.86370i) q^{41} +(-3.92820 - 2.26795i) q^{43} +(0.707107 + 0.707107i) q^{44} +(5.09808 - 1.36603i) q^{46} +(-7.02030 + 7.02030i) q^{47} +(-5.36603 + 3.09808i) q^{49} +(0.965926 + 0.258819i) q^{50} +(3.50000 - 0.866025i) q^{52} +12.8666i q^{53} +(-0.500000 - 0.866025i) q^{55} +(0.448288 - 0.776457i) q^{56} +(0.732051 + 2.73205i) q^{58} +(1.03528 + 3.86370i) q^{59} +(2.46410 - 4.26795i) q^{61} +(-0.896575 - 1.55291i) q^{62} -1.00000i q^{64} +(-3.60488 - 0.0693504i) q^{65} +(10.1962 + 2.73205i) q^{67} +(4.24264 - 2.44949i) q^{68} +(-0.633975 + 0.633975i) q^{70} +(1.93185 - 0.517638i) q^{71} +(2.53590 + 2.53590i) q^{73} +(-5.34727 - 3.08725i) q^{74} +(0.232051 - 0.866025i) q^{76} +0.896575 q^{77} +2.00000 q^{79} +(-0.258819 + 0.965926i) q^{80} +(3.46410 + 2.00000i) q^{82} +(9.52056 + 9.52056i) q^{83} +(-4.73205 + 1.26795i) q^{85} +(-3.20736 + 3.20736i) q^{86} +(0.866025 - 0.500000i) q^{88} +(-11.7112 - 3.13801i) q^{89} +(1.66987 - 2.76795i) q^{91} -5.27792i q^{92} +(4.96410 + 8.59808i) q^{94} +(-0.448288 + 0.776457i) q^{95} +(-1.66025 - 6.19615i) q^{97} +(1.60368 + 5.98502i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{16} - 12 q^{19} - 4 q^{22} + 24 q^{31} - 8 q^{37} - 8 q^{40} + 24 q^{43} + 20 q^{46} - 36 q^{49} + 28 q^{52} - 4 q^{55} - 8 q^{58} - 8 q^{61} + 40 q^{67} - 12 q^{70} + 48 q^{73} - 12 q^{76} + 16 q^{79} - 24 q^{85} + 48 q^{91} + 12 q^{94} + 56 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 0.965926i 0.183013 0.683013i
\(3\) 0 0
\(4\) −0.866025 0.500000i −0.433013 0.250000i
\(5\) 0.707107 + 0.707107i 0.316228 + 0.316228i
\(6\) 0 0
\(7\) −0.866025 + 0.232051i −0.327327 + 0.0877070i −0.418740 0.908106i \(-0.637528\pi\)
0.0914134 + 0.995813i \(0.470862\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0.866025 0.500000i 0.273861 0.158114i
\(11\) −0.965926 0.258819i −0.291238 0.0780369i 0.110242 0.993905i \(-0.464837\pi\)
−0.401480 + 0.915868i \(0.631504\pi\)
\(12\) 0 0
\(13\) −2.59808 + 2.50000i −0.720577 + 0.693375i
\(14\) 0.896575i 0.239620i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −2.44949 + 4.24264i −0.594089 + 1.02899i 0.399586 + 0.916696i \(0.369154\pi\)
−0.993675 + 0.112296i \(0.964180\pi\)
\(18\) 0 0
\(19\) 0.232051 + 0.866025i 0.0532361 + 0.198680i 0.987422 0.158107i \(-0.0505390\pi\)
−0.934186 + 0.356787i \(0.883872\pi\)
\(20\) −0.258819 0.965926i −0.0578737 0.215988i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) 2.63896 + 4.57081i 0.550261 + 0.953080i 0.998255 + 0.0590435i \(0.0188051\pi\)
−0.447995 + 0.894036i \(0.647862\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) 1.74238 + 3.15660i 0.341709 + 0.619060i
\(27\) 0 0
\(28\) 0.866025 + 0.232051i 0.163663 + 0.0438535i
\(29\) −2.44949 + 1.41421i −0.454859 + 0.262613i −0.709880 0.704323i \(-0.751251\pi\)
0.255021 + 0.966935i \(0.417918\pi\)
\(30\) 0 0
\(31\) 1.26795 1.26795i 0.227730 0.227730i −0.584014 0.811744i \(-0.698519\pi\)
0.811744 + 0.584014i \(0.198519\pi\)
\(32\) 0.965926 0.258819i 0.170753 0.0457532i
\(33\) 0 0
\(34\) 3.46410 + 3.46410i 0.594089 + 0.594089i
\(35\) −0.776457 0.448288i −0.131245 0.0757745i
\(36\) 0 0
\(37\) 1.59808 5.96410i 0.262722 0.980492i −0.700908 0.713252i \(-0.747222\pi\)
0.963630 0.267240i \(-0.0861118\pi\)
\(38\) 0.896575 0.145444
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) −1.03528 + 3.86370i −0.161683 + 0.603409i 0.836757 + 0.547574i \(0.184449\pi\)
−0.998440 + 0.0558348i \(0.982218\pi\)
\(42\) 0 0
\(43\) −3.92820 2.26795i −0.599045 0.345859i 0.169621 0.985509i \(-0.445746\pi\)
−0.768666 + 0.639650i \(0.779079\pi\)
\(44\) 0.707107 + 0.707107i 0.106600 + 0.106600i
\(45\) 0 0
\(46\) 5.09808 1.36603i 0.751670 0.201409i
\(47\) −7.02030 + 7.02030i −1.02402 + 1.02402i −0.0243115 + 0.999704i \(0.507739\pi\)
−0.999704 + 0.0243115i \(0.992261\pi\)
\(48\) 0 0
\(49\) −5.36603 + 3.09808i −0.766575 + 0.442582i
\(50\) 0.965926 + 0.258819i 0.136603 + 0.0366025i
\(51\) 0 0
\(52\) 3.50000 0.866025i 0.485363 0.120096i
\(53\) 12.8666i 1.76737i 0.468085 + 0.883683i \(0.344944\pi\)
−0.468085 + 0.883683i \(0.655056\pi\)
\(54\) 0 0
\(55\) −0.500000 0.866025i −0.0674200 0.116775i
\(56\) 0.448288 0.776457i 0.0599050 0.103758i
\(57\) 0 0
\(58\) 0.732051 + 2.73205i 0.0961230 + 0.358736i
\(59\) 1.03528 + 3.86370i 0.134781 + 0.503011i 0.999999 + 0.00161411i \(0.000513789\pi\)
−0.865217 + 0.501397i \(0.832820\pi\)
\(60\) 0 0
\(61\) 2.46410 4.26795i 0.315496 0.546455i −0.664047 0.747691i \(-0.731162\pi\)
0.979543 + 0.201236i \(0.0644958\pi\)
\(62\) −0.896575 1.55291i −0.113865 0.197220i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −3.60488 0.0693504i −0.447131 0.00860185i
\(66\) 0 0
\(67\) 10.1962 + 2.73205i 1.24566 + 0.333773i 0.820658 0.571420i \(-0.193607\pi\)
0.425000 + 0.905193i \(0.360274\pi\)
\(68\) 4.24264 2.44949i 0.514496 0.297044i
\(69\) 0 0
\(70\) −0.633975 + 0.633975i −0.0757745 + 0.0757745i
\(71\) 1.93185 0.517638i 0.229269 0.0614323i −0.142356 0.989816i \(-0.545468\pi\)
0.371624 + 0.928383i \(0.378801\pi\)
\(72\) 0 0
\(73\) 2.53590 + 2.53590i 0.296804 + 0.296804i 0.839761 0.542956i \(-0.182695\pi\)
−0.542956 + 0.839761i \(0.682695\pi\)
\(74\) −5.34727 3.08725i −0.621607 0.358885i
\(75\) 0 0
\(76\) 0.232051 0.866025i 0.0266181 0.0993399i
\(77\) 0.896575 0.102174
\(78\) 0 0
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) −0.258819 + 0.965926i −0.0289368 + 0.107994i
\(81\) 0 0
\(82\) 3.46410 + 2.00000i 0.382546 + 0.220863i
\(83\) 9.52056 + 9.52056i 1.04502 + 1.04502i 0.998938 + 0.0460792i \(0.0146726\pi\)
0.0460792 + 0.998938i \(0.485327\pi\)
\(84\) 0 0
\(85\) −4.73205 + 1.26795i −0.513263 + 0.137528i
\(86\) −3.20736 + 3.20736i −0.345859 + 0.345859i
\(87\) 0 0
\(88\) 0.866025 0.500000i 0.0923186 0.0533002i
\(89\) −11.7112 3.13801i −1.24139 0.332629i −0.422384 0.906417i \(-0.638807\pi\)
−0.819004 + 0.573788i \(0.805473\pi\)
\(90\) 0 0
\(91\) 1.66987 2.76795i 0.175050 0.290160i
\(92\) 5.27792i 0.550261i
\(93\) 0 0
\(94\) 4.96410 + 8.59808i 0.512008 + 0.886824i
\(95\) −0.448288 + 0.776457i −0.0459934 + 0.0796628i
\(96\) 0 0
\(97\) −1.66025 6.19615i −0.168573 0.629124i −0.997557 0.0698518i \(-0.977747\pi\)
0.828984 0.559272i \(-0.188919\pi\)
\(98\) 1.60368 + 5.98502i 0.161996 + 0.604579i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −2.82843 4.89898i −0.281439 0.487467i 0.690300 0.723523i \(-0.257478\pi\)
−0.971739 + 0.236056i \(0.924145\pi\)
\(102\) 0 0
\(103\) 0.660254i 0.0650568i −0.999471 0.0325284i \(-0.989644\pi\)
0.999471 0.0325284i \(-0.0103559\pi\)
\(104\) 0.0693504 3.60488i 0.00680036 0.353488i
\(105\) 0 0
\(106\) 12.4282 + 3.33013i 1.20713 + 0.323451i
\(107\) 10.6945 6.17449i 1.03388 0.596911i 0.115786 0.993274i \(-0.463061\pi\)
0.918094 + 0.396363i \(0.129728\pi\)
\(108\) 0 0
\(109\) 3.26795 3.26795i 0.313013 0.313013i −0.533063 0.846076i \(-0.678959\pi\)
0.846076 + 0.533063i \(0.178959\pi\)
\(110\) −0.965926 + 0.258819i −0.0920974 + 0.0246774i
\(111\) 0 0
\(112\) −0.633975 0.633975i −0.0599050 0.0599050i
\(113\) 1.79315 + 1.03528i 0.168685 + 0.0973906i 0.581966 0.813213i \(-0.302284\pi\)
−0.413280 + 0.910604i \(0.635617\pi\)
\(114\) 0 0
\(115\) −1.36603 + 5.09808i −0.127383 + 0.475398i
\(116\) 2.82843 0.262613
\(117\) 0 0
\(118\) 4.00000 0.368230
\(119\) 1.13681 4.24264i 0.104211 0.388922i
\(120\) 0 0
\(121\) −8.66025 5.00000i −0.787296 0.454545i
\(122\) −3.48477 3.48477i −0.315496 0.315496i
\(123\) 0 0
\(124\) −1.73205 + 0.464102i −0.155543 + 0.0416776i
\(125\) −0.707107 + 0.707107i −0.0632456 + 0.0632456i
\(126\) 0 0
\(127\) 10.9641 6.33013i 0.972907 0.561708i 0.0727855 0.997348i \(-0.476811\pi\)
0.900121 + 0.435640i \(0.143478\pi\)
\(128\) −0.965926 0.258819i −0.0853766 0.0228766i
\(129\) 0 0
\(130\) −1.00000 + 3.46410i −0.0877058 + 0.303822i
\(131\) 4.38134i 0.382800i −0.981512 0.191400i \(-0.938697\pi\)
0.981512 0.191400i \(-0.0613027\pi\)
\(132\) 0 0
\(133\) −0.401924 0.696152i −0.0348512 0.0603641i
\(134\) 5.27792 9.14162i 0.455943 0.789716i
\(135\) 0 0
\(136\) −1.26795 4.73205i −0.108726 0.405770i
\(137\) −2.07055 7.72741i −0.176899 0.660197i −0.996220 0.0868620i \(-0.972316\pi\)
0.819321 0.573335i \(-0.194351\pi\)
\(138\) 0 0
\(139\) −8.33013 + 14.4282i −0.706552 + 1.22378i 0.259576 + 0.965723i \(0.416417\pi\)
−0.966128 + 0.258062i \(0.916916\pi\)
\(140\) 0.448288 + 0.776457i 0.0378872 + 0.0656226i
\(141\) 0 0
\(142\) 2.00000i 0.167836i
\(143\) 3.15660 1.74238i 0.263968 0.145705i
\(144\) 0 0
\(145\) −2.73205 0.732051i −0.226884 0.0607935i
\(146\) 3.10583 1.79315i 0.257040 0.148402i
\(147\) 0 0
\(148\) −4.36603 + 4.36603i −0.358885 + 0.358885i
\(149\) 2.31079 0.619174i 0.189307 0.0507247i −0.162920 0.986639i \(-0.552091\pi\)
0.352227 + 0.935915i \(0.385425\pi\)
\(150\) 0 0
\(151\) 10.1962 + 10.1962i 0.829751 + 0.829751i 0.987482 0.157731i \(-0.0504179\pi\)
−0.157731 + 0.987482i \(0.550418\pi\)
\(152\) −0.776457 0.448288i −0.0629790 0.0363609i
\(153\) 0 0
\(154\) 0.232051 0.866025i 0.0186992 0.0697863i
\(155\) 1.79315 0.144029
\(156\) 0 0
\(157\) −6.80385 −0.543006 −0.271503 0.962438i \(-0.587521\pi\)
−0.271503 + 0.962438i \(0.587521\pi\)
\(158\) 0.517638 1.93185i 0.0411811 0.153690i
\(159\) 0 0
\(160\) 0.866025 + 0.500000i 0.0684653 + 0.0395285i
\(161\) −3.34607 3.34607i −0.263707 0.263707i
\(162\) 0 0
\(163\) −19.6603 + 5.26795i −1.53991 + 0.412618i −0.926237 0.376942i \(-0.876975\pi\)
−0.613673 + 0.789560i \(0.710309\pi\)
\(164\) 2.82843 2.82843i 0.220863 0.220863i
\(165\) 0 0
\(166\) 11.6603 6.73205i 0.905011 0.522508i
\(167\) −7.32989 1.96404i −0.567204 0.151982i −0.0361899 0.999345i \(-0.511522\pi\)
−0.531014 + 0.847363i \(0.678189\pi\)
\(168\) 0 0
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) 4.89898i 0.375735i
\(171\) 0 0
\(172\) 2.26795 + 3.92820i 0.172930 + 0.299523i
\(173\) −5.86491 + 10.1583i −0.445900 + 0.772322i −0.998114 0.0613801i \(-0.980450\pi\)
0.552214 + 0.833702i \(0.313783\pi\)
\(174\) 0 0
\(175\) −0.232051 0.866025i −0.0175414 0.0654654i
\(176\) −0.258819 0.965926i −0.0195092 0.0728094i
\(177\) 0 0
\(178\) −6.06218 + 10.5000i −0.454379 + 0.787008i
\(179\) −0.189469 0.328169i −0.0141616 0.0245285i 0.858858 0.512214i \(-0.171175\pi\)
−0.873019 + 0.487686i \(0.837841\pi\)
\(180\) 0 0
\(181\) 19.8564i 1.47592i −0.674847 0.737958i \(-0.735790\pi\)
0.674847 0.737958i \(-0.264210\pi\)
\(182\) −2.24144 2.32937i −0.166146 0.172664i
\(183\) 0 0
\(184\) −5.09808 1.36603i −0.375835 0.100705i
\(185\) 5.34727 3.08725i 0.393139 0.226979i
\(186\) 0 0
\(187\) 3.46410 3.46410i 0.253320 0.253320i
\(188\) 9.58991 2.56961i 0.699416 0.187408i
\(189\) 0 0
\(190\) 0.633975 + 0.633975i 0.0459934 + 0.0459934i
\(191\) −20.9730 12.1087i −1.51755 0.876158i −0.999787 0.0206345i \(-0.993431\pi\)
−0.517764 0.855524i \(-0.673235\pi\)
\(192\) 0 0
\(193\) −0.339746 + 1.26795i −0.0244554 + 0.0912690i −0.977075 0.212896i \(-0.931711\pi\)
0.952620 + 0.304165i \(0.0983773\pi\)
\(194\) −6.41473 −0.460551
\(195\) 0 0
\(196\) 6.19615 0.442582
\(197\) −1.96404 + 7.32989i −0.139932 + 0.522233i 0.859997 + 0.510299i \(0.170465\pi\)
−0.999929 + 0.0119336i \(0.996201\pi\)
\(198\) 0 0
\(199\) −3.92820 2.26795i −0.278463 0.160771i 0.354264 0.935145i \(-0.384731\pi\)
−0.632727 + 0.774375i \(0.718065\pi\)
\(200\) −0.707107 0.707107i −0.0500000 0.0500000i
\(201\) 0 0
\(202\) −5.46410 + 1.46410i −0.384453 + 0.103014i
\(203\) 1.79315 1.79315i 0.125855 0.125855i
\(204\) 0 0
\(205\) −3.46410 + 2.00000i −0.241943 + 0.139686i
\(206\) −0.637756 0.170886i −0.0444346 0.0119062i
\(207\) 0 0
\(208\) −3.46410 1.00000i −0.240192 0.0693375i
\(209\) 0.896575i 0.0620174i
\(210\) 0 0
\(211\) 4.96410 + 8.59808i 0.341743 + 0.591916i 0.984756 0.173939i \(-0.0556495\pi\)
−0.643014 + 0.765855i \(0.722316\pi\)
\(212\) 6.43331 11.1428i 0.441842 0.765292i
\(213\) 0 0
\(214\) −3.19615 11.9282i −0.218484 0.815395i
\(215\) −1.17398 4.38134i −0.0800646 0.298805i
\(216\) 0 0
\(217\) −0.803848 + 1.39230i −0.0545687 + 0.0945158i
\(218\) −2.31079 4.00240i −0.156506 0.271077i
\(219\) 0 0
\(220\) 1.00000i 0.0674200i
\(221\) −4.24264 17.1464i −0.285391 1.15339i
\(222\) 0 0
\(223\) −2.33013 0.624356i −0.156037 0.0418099i 0.179955 0.983675i \(-0.442405\pi\)
−0.335992 + 0.941865i \(0.609071\pi\)
\(224\) −0.776457 + 0.448288i −0.0518792 + 0.0299525i
\(225\) 0 0
\(226\) 1.46410 1.46410i 0.0973906 0.0973906i
\(227\) 10.9348 2.92996i 0.725766 0.194468i 0.123023 0.992404i \(-0.460741\pi\)
0.602743 + 0.797935i \(0.294074\pi\)
\(228\) 0 0
\(229\) −0.339746 0.339746i −0.0224510 0.0224510i 0.695792 0.718243i \(-0.255053\pi\)
−0.718243 + 0.695792i \(0.755053\pi\)
\(230\) 4.57081 + 2.63896i 0.301390 + 0.174008i
\(231\) 0 0
\(232\) 0.732051 2.73205i 0.0480615 0.179368i
\(233\) 8.76268 0.574062 0.287031 0.957921i \(-0.407332\pi\)
0.287031 + 0.957921i \(0.407332\pi\)
\(234\) 0 0
\(235\) −9.92820 −0.647645
\(236\) 1.03528 3.86370i 0.0673907 0.251506i
\(237\) 0 0
\(238\) −3.80385 2.19615i −0.246567 0.142355i
\(239\) 10.4543 + 10.4543i 0.676232 + 0.676232i 0.959146 0.282913i \(-0.0913008\pi\)
−0.282913 + 0.959146i \(0.591301\pi\)
\(240\) 0 0
\(241\) −5.96410 + 1.59808i −0.384182 + 0.102941i −0.445740 0.895162i \(-0.647060\pi\)
0.0615587 + 0.998103i \(0.480393\pi\)
\(242\) −7.07107 + 7.07107i −0.454545 + 0.454545i
\(243\) 0 0
\(244\) −4.26795 + 2.46410i −0.273227 + 0.157748i
\(245\) −5.98502 1.60368i −0.382369 0.102456i
\(246\) 0 0
\(247\) −2.76795 1.66987i −0.176120 0.106251i
\(248\) 1.79315i 0.113865i
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 11.4710 19.8683i 0.724043 1.25408i −0.235324 0.971917i \(-0.575615\pi\)
0.959367 0.282162i \(-0.0910514\pi\)
\(252\) 0 0
\(253\) −1.36603 5.09808i −0.0858813 0.320513i
\(254\) −3.27671 12.2289i −0.205599 0.767307i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 13.6617 + 23.6627i 0.852191 + 1.47604i 0.879227 + 0.476404i \(0.158060\pi\)
−0.0270355 + 0.999634i \(0.508607\pi\)
\(258\) 0 0
\(259\) 5.53590i 0.343984i
\(260\) 3.08725 + 1.86250i 0.191463 + 0.115507i
\(261\) 0 0
\(262\) −4.23205 1.13397i −0.261457 0.0700572i
\(263\) 14.0728 8.12493i 0.867765 0.501004i 0.00116020 0.999999i \(-0.499631\pi\)
0.866605 + 0.498995i \(0.166297\pi\)
\(264\) 0 0
\(265\) −9.09808 + 9.09808i −0.558890 + 0.558890i
\(266\) −0.776457 + 0.208051i −0.0476076 + 0.0127564i
\(267\) 0 0
\(268\) −7.46410 7.46410i −0.455943 0.455943i
\(269\) −17.6269 10.1769i −1.07473 0.620496i −0.145261 0.989393i \(-0.546402\pi\)
−0.929470 + 0.368897i \(0.879735\pi\)
\(270\) 0 0
\(271\) 5.07180 18.9282i 0.308090 1.14981i −0.622163 0.782888i \(-0.713746\pi\)
0.930253 0.366919i \(-0.119587\pi\)
\(272\) −4.89898 −0.297044
\(273\) 0 0
\(274\) −8.00000 −0.483298
\(275\) 0.258819 0.965926i 0.0156074 0.0582475i
\(276\) 0 0
\(277\) −18.0622 10.4282i −1.08525 0.626570i −0.152943 0.988235i \(-0.548875\pi\)
−0.932308 + 0.361665i \(0.882208\pi\)
\(278\) 11.7806 + 11.7806i 0.706552 + 0.706552i
\(279\) 0 0
\(280\) 0.866025 0.232051i 0.0517549 0.0138677i
\(281\) 5.55532 5.55532i 0.331403 0.331403i −0.521716 0.853119i \(-0.674708\pi\)
0.853119 + 0.521716i \(0.174708\pi\)
\(282\) 0 0
\(283\) −25.3923 + 14.6603i −1.50942 + 0.871462i −0.509476 + 0.860485i \(0.670161\pi\)
−0.999940 + 0.0109768i \(0.996506\pi\)
\(284\) −1.93185 0.517638i −0.114634 0.0307162i
\(285\) 0 0
\(286\) −0.866025 3.50000i −0.0512092 0.206959i
\(287\) 3.58630i 0.211693i
\(288\) 0 0
\(289\) −3.50000 6.06218i −0.205882 0.356599i
\(290\) −1.41421 + 2.44949i −0.0830455 + 0.143839i
\(291\) 0 0
\(292\) −0.928203 3.46410i −0.0543190 0.202721i
\(293\) 3.60488 + 13.4536i 0.210600 + 0.785968i 0.987669 + 0.156554i \(0.0500385\pi\)
−0.777070 + 0.629414i \(0.783295\pi\)
\(294\) 0 0
\(295\) −2.00000 + 3.46410i −0.116445 + 0.201688i
\(296\) 3.08725 + 5.34727i 0.179443 + 0.310804i
\(297\) 0 0
\(298\) 2.39230i 0.138582i
\(299\) −18.2832 5.27792i −1.05735 0.305230i
\(300\) 0 0
\(301\) 3.92820 + 1.05256i 0.226418 + 0.0606685i
\(302\) 12.4877 7.20977i 0.718586 0.414876i
\(303\) 0 0
\(304\) −0.633975 + 0.633975i −0.0363609 + 0.0363609i
\(305\) 4.76028 1.27551i 0.272573 0.0730357i
\(306\) 0 0
\(307\) 16.1962 + 16.1962i 0.924363 + 0.924363i 0.997334 0.0729708i \(-0.0232480\pi\)
−0.0729708 + 0.997334i \(0.523248\pi\)
\(308\) −0.776457 0.448288i −0.0442428 0.0255436i
\(309\) 0 0
\(310\) 0.464102 1.73205i 0.0263592 0.0983739i
\(311\) 0.554803 0.0314600 0.0157300 0.999876i \(-0.494993\pi\)
0.0157300 + 0.999876i \(0.494993\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −1.76097 + 6.57201i −0.0993770 + 0.370880i
\(315\) 0 0
\(316\) −1.73205 1.00000i −0.0974355 0.0562544i
\(317\) −11.3645 11.3645i −0.638293 0.638293i 0.311842 0.950134i \(-0.399054\pi\)
−0.950134 + 0.311842i \(0.899054\pi\)
\(318\) 0 0
\(319\) 2.73205 0.732051i 0.152965 0.0409870i
\(320\) 0.707107 0.707107i 0.0395285 0.0395285i
\(321\) 0 0
\(322\) −4.09808 + 2.36603i −0.228377 + 0.131853i
\(323\) −4.24264 1.13681i −0.236067 0.0632539i
\(324\) 0 0
\(325\) −2.50000 2.59808i −0.138675 0.144115i
\(326\) 20.3538i 1.12729i
\(327\) 0 0
\(328\) −2.00000 3.46410i −0.110432 0.191273i
\(329\) 4.45069 7.70882i 0.245375 0.425001i
\(330\) 0 0
\(331\) 0.294229 + 1.09808i 0.0161723 + 0.0603557i 0.973540 0.228515i \(-0.0733869\pi\)
−0.957368 + 0.288871i \(0.906720\pi\)
\(332\) −3.48477 13.0053i −0.191251 0.713760i
\(333\) 0 0
\(334\) −3.79423 + 6.57180i −0.207611 + 0.359593i
\(335\) 5.27792 + 9.14162i 0.288363 + 0.499460i
\(336\) 0 0
\(337\) 4.53590i 0.247086i 0.992339 + 0.123543i \(0.0394257\pi\)
−0.992339 + 0.123543i \(0.960574\pi\)
\(338\) −12.4183 3.84512i −0.675468 0.209147i
\(339\) 0 0
\(340\) 4.73205 + 1.26795i 0.256631 + 0.0687642i
\(341\) −1.55291 + 0.896575i −0.0840950 + 0.0485523i
\(342\) 0 0
\(343\) 8.36603 8.36603i 0.451723 0.451723i
\(344\) 4.38134 1.17398i 0.236226 0.0632966i
\(345\) 0 0
\(346\) 8.29423 + 8.29423i 0.445900 + 0.445900i
\(347\) 3.76217 + 2.17209i 0.201964 + 0.116604i 0.597571 0.801816i \(-0.296133\pi\)
−0.395607 + 0.918420i \(0.629466\pi\)
\(348\) 0 0
\(349\) −0.679492 + 2.53590i −0.0363724 + 0.135744i −0.981725 0.190308i \(-0.939051\pi\)
0.945352 + 0.326051i \(0.105718\pi\)
\(350\) −0.896575 −0.0479240
\(351\) 0 0
\(352\) −1.00000 −0.0533002
\(353\) −6.86800 + 25.6317i −0.365547 + 1.36424i 0.501132 + 0.865371i \(0.332917\pi\)
−0.866678 + 0.498867i \(0.833750\pi\)
\(354\) 0 0
\(355\) 1.73205 + 1.00000i 0.0919277 + 0.0530745i
\(356\) 8.57321 + 8.57321i 0.454379 + 0.454379i
\(357\) 0 0
\(358\) −0.366025 + 0.0980762i −0.0193450 + 0.00518349i
\(359\) 3.76217 3.76217i 0.198560 0.198560i −0.600823 0.799382i \(-0.705160\pi\)
0.799382 + 0.600823i \(0.205160\pi\)
\(360\) 0 0
\(361\) 15.7583 9.09808i 0.829386 0.478846i
\(362\) −19.1798 5.13922i −1.00807 0.270111i
\(363\) 0 0
\(364\) −2.83013 + 1.56218i −0.148339 + 0.0818804i
\(365\) 3.58630i 0.187716i
\(366\) 0 0
\(367\) −4.66025 8.07180i −0.243263 0.421344i 0.718379 0.695652i \(-0.244885\pi\)
−0.961642 + 0.274308i \(0.911551\pi\)
\(368\) −2.63896 + 4.57081i −0.137565 + 0.238270i
\(369\) 0 0
\(370\) −1.59808 5.96410i −0.0830800 0.310059i
\(371\) −2.98571 11.1428i −0.155010 0.578507i
\(372\) 0 0
\(373\) −18.3923 + 31.8564i −0.952317 + 1.64946i −0.211927 + 0.977286i \(0.567974\pi\)
−0.740391 + 0.672177i \(0.765360\pi\)
\(374\) −2.44949 4.24264i −0.126660 0.219382i
\(375\) 0 0
\(376\) 9.92820i 0.512008i
\(377\) 2.82843 9.79796i 0.145671 0.504621i
\(378\) 0 0
\(379\) 36.5526 + 9.79423i 1.87758 + 0.503096i 0.999707 + 0.0241998i \(0.00770379\pi\)
0.877872 + 0.478896i \(0.158963\pi\)
\(380\) 0.776457 0.448288i 0.0398314 0.0229967i
\(381\) 0 0
\(382\) −17.1244 + 17.1244i −0.876158 + 0.876158i
\(383\) 30.1146 8.06918i 1.53878 0.412316i 0.612911 0.790152i \(-0.289998\pi\)
0.925872 + 0.377836i \(0.123332\pi\)
\(384\) 0 0
\(385\) 0.633975 + 0.633975i 0.0323103 + 0.0323103i
\(386\) 1.13681 + 0.656339i 0.0578622 + 0.0334068i
\(387\) 0 0
\(388\) −1.66025 + 6.19615i −0.0842866 + 0.314562i
\(389\) 26.0106 1.31879 0.659396 0.751796i \(-0.270812\pi\)
0.659396 + 0.751796i \(0.270812\pi\)
\(390\) 0 0
\(391\) −25.8564 −1.30761
\(392\) 1.60368 5.98502i 0.0809982 0.302289i
\(393\) 0 0
\(394\) 6.57180 + 3.79423i 0.331082 + 0.191150i
\(395\) 1.41421 + 1.41421i 0.0711568 + 0.0711568i
\(396\) 0 0
\(397\) 30.3564 8.13397i 1.52354 0.408232i 0.602637 0.798015i \(-0.294117\pi\)
0.920907 + 0.389783i \(0.127450\pi\)
\(398\) −3.20736 + 3.20736i −0.160771 + 0.160771i
\(399\) 0 0
\(400\) −0.866025 + 0.500000i −0.0433013 + 0.0250000i
\(401\) −32.7721 8.78127i −1.63656 0.438515i −0.680755 0.732511i \(-0.738348\pi\)
−0.955807 + 0.293996i \(0.905015\pi\)
\(402\) 0 0
\(403\) −0.124356 + 6.46410i −0.00619460 + 0.322000i
\(404\) 5.65685i 0.281439i
\(405\) 0 0
\(406\) −1.26795 2.19615i −0.0629273 0.108993i
\(407\) −3.08725 + 5.34727i −0.153029 + 0.265054i
\(408\) 0 0
\(409\) −5.64359 21.0622i −0.279058 1.04146i −0.953073 0.302740i \(-0.902099\pi\)
0.674015 0.738717i \(-0.264568\pi\)
\(410\) 1.03528 + 3.86370i 0.0511286 + 0.190815i
\(411\) 0 0
\(412\) −0.330127 + 0.571797i −0.0162642 + 0.0281704i
\(413\) −1.79315 3.10583i −0.0882352 0.152828i
\(414\) 0 0
\(415\) 13.4641i 0.660927i
\(416\) −1.86250 + 3.08725i −0.0913166 + 0.151365i
\(417\) 0 0
\(418\) −0.866025 0.232051i −0.0423587 0.0113500i
\(419\) −6.53983 + 3.77577i −0.319491 + 0.184458i −0.651166 0.758935i \(-0.725720\pi\)
0.331674 + 0.943394i \(0.392386\pi\)
\(420\) 0 0
\(421\) 2.53590 2.53590i 0.123592 0.123592i −0.642605 0.766197i \(-0.722146\pi\)
0.766197 + 0.642605i \(0.222146\pi\)
\(422\) 9.58991 2.56961i 0.466829 0.125087i
\(423\) 0 0
\(424\) −9.09808 9.09808i −0.441842 0.441842i
\(425\) −4.24264 2.44949i −0.205798 0.118818i
\(426\) 0 0
\(427\) −1.14359 + 4.26795i −0.0553424 + 0.206541i
\(428\) −12.3490 −0.596911
\(429\) 0 0
\(430\) −4.53590 −0.218740
\(431\) 2.44949 9.14162i 0.117988 0.440336i −0.881505 0.472174i \(-0.843469\pi\)
0.999493 + 0.0318378i \(0.0101360\pi\)
\(432\) 0 0
\(433\) −23.6603 13.6603i −1.13704 0.656470i −0.191344 0.981523i \(-0.561284\pi\)
−0.945696 + 0.325053i \(0.894618\pi\)
\(434\) 1.13681 + 1.13681i 0.0545687 + 0.0545687i
\(435\) 0 0
\(436\) −4.46410 + 1.19615i −0.213792 + 0.0572853i
\(437\) −3.34607 + 3.34607i −0.160064 + 0.160064i
\(438\) 0 0
\(439\) 12.8038 7.39230i 0.611094 0.352815i −0.162299 0.986742i \(-0.551891\pi\)
0.773394 + 0.633926i \(0.218558\pi\)
\(440\) 0.965926 + 0.258819i 0.0460487 + 0.0123387i
\(441\) 0 0
\(442\) −17.6603 0.339746i −0.840013 0.0161601i
\(443\) 10.2784i 0.488343i −0.969732 0.244172i \(-0.921484\pi\)
0.969732 0.244172i \(-0.0785160\pi\)
\(444\) 0 0
\(445\) −6.06218 10.5000i −0.287375 0.497748i
\(446\) −1.20616 + 2.08913i −0.0571134 + 0.0989234i
\(447\) 0 0
\(448\) 0.232051 + 0.866025i 0.0109634 + 0.0409159i
\(449\) 0.448288 + 1.67303i 0.0211560 + 0.0789553i 0.975697 0.219125i \(-0.0703203\pi\)
−0.954541 + 0.298080i \(0.903654\pi\)
\(450\) 0 0
\(451\) 2.00000 3.46410i 0.0941763 0.163118i
\(452\) −1.03528 1.79315i −0.0486953 0.0843427i
\(453\) 0 0
\(454\) 11.3205i 0.531298i
\(455\) 3.13801 0.776457i 0.147112 0.0364009i
\(456\) 0 0
\(457\) 37.0526 + 9.92820i 1.73325 + 0.464422i 0.980927 0.194377i \(-0.0622687\pi\)
0.752319 + 0.658799i \(0.228935\pi\)
\(458\) −0.416102 + 0.240237i −0.0194432 + 0.0112255i
\(459\) 0 0
\(460\) 3.73205 3.73205i 0.174008 0.174008i
\(461\) 13.0053 3.48477i 0.605718 0.162302i 0.0570913 0.998369i \(-0.481817\pi\)
0.548627 + 0.836067i \(0.315151\pi\)
\(462\) 0 0
\(463\) 16.1244 + 16.1244i 0.749362 + 0.749362i 0.974359 0.224997i \(-0.0722373\pi\)
−0.224997 + 0.974359i \(0.572237\pi\)
\(464\) −2.44949 1.41421i −0.113715 0.0656532i
\(465\) 0 0
\(466\) 2.26795 8.46410i 0.105061 0.392092i
\(467\) 4.14110 0.191627 0.0958137 0.995399i \(-0.469455\pi\)
0.0958137 + 0.995399i \(0.469455\pi\)
\(468\) 0 0
\(469\) −9.46410 −0.437012
\(470\) −2.56961 + 9.58991i −0.118527 + 0.442349i
\(471\) 0 0
\(472\) −3.46410 2.00000i −0.159448 0.0920575i
\(473\) 3.20736 + 3.20736i 0.147475 + 0.147475i
\(474\) 0 0
\(475\) −0.866025 + 0.232051i −0.0397360 + 0.0106472i
\(476\) −3.10583 + 3.10583i −0.142355 + 0.142355i
\(477\) 0 0
\(478\) 12.8038 7.39230i 0.585634 0.338116i
\(479\) 9.89949 + 2.65256i 0.452319 + 0.121199i 0.477784 0.878477i \(-0.341440\pi\)
−0.0254650 + 0.999676i \(0.508107\pi\)
\(480\) 0 0
\(481\) 10.7583 + 19.4904i 0.490538 + 0.888685i
\(482\) 6.17449i 0.281240i
\(483\) 0 0
\(484\) 5.00000 + 8.66025i 0.227273 + 0.393648i
\(485\) 3.20736 5.55532i 0.145639 0.252254i
\(486\) 0 0
\(487\) 4.20577 + 15.6962i 0.190582 + 0.711261i 0.993366 + 0.114992i \(0.0366841\pi\)
−0.802785 + 0.596269i \(0.796649\pi\)
\(488\) 1.27551 + 4.76028i 0.0577398 + 0.215488i
\(489\) 0 0
\(490\) −3.09808 + 5.36603i −0.139957 + 0.242412i
\(491\) −0.877993 1.52073i −0.0396233 0.0686295i 0.845534 0.533922i \(-0.179282\pi\)
−0.885157 + 0.465293i \(0.845949\pi\)
\(492\) 0 0
\(493\) 13.8564i 0.624061i
\(494\) −2.32937 + 2.24144i −0.104803 + 0.100847i
\(495\) 0 0
\(496\) 1.73205 + 0.464102i 0.0777714 + 0.0208388i
\(497\) −1.55291 + 0.896575i −0.0696577 + 0.0402169i
\(498\) 0 0
\(499\) 23.1962 23.1962i 1.03840 1.03840i 0.0391698 0.999233i \(-0.487529\pi\)
0.999233 0.0391698i \(-0.0124713\pi\)
\(500\) 0.965926 0.258819i 0.0431975 0.0115747i
\(501\) 0 0
\(502\) −16.2224 16.2224i −0.724043 0.724043i
\(503\) −30.5629 17.6455i −1.36273 0.786773i −0.372745 0.927934i \(-0.621583\pi\)
−0.989987 + 0.141161i \(0.954917\pi\)
\(504\) 0 0
\(505\) 1.46410 5.46410i 0.0651517 0.243149i
\(506\) −5.27792 −0.234632
\(507\) 0 0
\(508\) −12.6603 −0.561708
\(509\) −1.17398 + 4.38134i −0.0520356 + 0.194200i −0.987051 0.160408i \(-0.948719\pi\)
0.935015 + 0.354608i \(0.115386\pi\)
\(510\) 0 0
\(511\) −2.78461 1.60770i −0.123184 0.0711202i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 26.3923 7.07180i 1.16411 0.311924i
\(515\) 0.466870 0.466870i 0.0205728 0.0205728i
\(516\) 0 0
\(517\) 8.59808 4.96410i 0.378143 0.218321i
\(518\) 5.34727 + 1.43280i 0.234945 + 0.0629534i
\(519\) 0 0
\(520\) 2.59808 2.50000i 0.113933 0.109632i
\(521\) 3.72500i 0.163195i −0.996665 0.0815977i \(-0.973998\pi\)
0.996665 0.0815977i \(-0.0260023\pi\)
\(522\) 0 0
\(523\) 19.7846 + 34.2679i 0.865121 + 1.49843i 0.866927 + 0.498434i \(0.166092\pi\)
−0.00180682 + 0.999998i \(0.500575\pi\)
\(524\) −2.19067 + 3.79435i −0.0956999 + 0.165757i
\(525\) 0 0
\(526\) −4.20577 15.6962i −0.183380 0.684385i
\(527\) 2.27362 + 8.48528i 0.0990406 + 0.369625i
\(528\) 0 0
\(529\) −2.42820 + 4.20577i −0.105574 + 0.182860i
\(530\) 6.43331 + 11.1428i 0.279445 + 0.484013i
\(531\) 0 0
\(532\) 0.803848i 0.0348512i
\(533\) −6.96953 12.6264i −0.301884 0.546909i
\(534\) 0 0
\(535\) 11.9282 + 3.19615i 0.515701 + 0.138182i
\(536\) −9.14162 + 5.27792i −0.394858 + 0.227971i
\(537\) 0 0
\(538\) −14.3923 + 14.3923i −0.620496 + 0.620496i
\(539\) 5.98502 1.60368i 0.257793 0.0690755i
\(540\) 0 0
\(541\) 7.80385 + 7.80385i 0.335514 + 0.335514i 0.854676 0.519162i \(-0.173756\pi\)
−0.519162 + 0.854676i \(0.673756\pi\)
\(542\) −16.9706 9.79796i −0.728948 0.420858i
\(543\) 0 0
\(544\) −1.26795 + 4.73205i −0.0543629 + 0.202885i
\(545\) 4.62158 0.197967
\(546\) 0 0
\(547\) 33.7128 1.44146 0.720728 0.693218i \(-0.243808\pi\)
0.720728 + 0.693218i \(0.243808\pi\)
\(548\) −2.07055 + 7.72741i −0.0884496 + 0.330098i
\(549\) 0 0
\(550\) −0.866025 0.500000i −0.0369274 0.0213201i
\(551\) −1.79315 1.79315i −0.0763908 0.0763908i
\(552\) 0 0
\(553\) −1.73205 + 0.464102i −0.0736543 + 0.0197356i
\(554\) −14.7477 + 14.7477i −0.626570 + 0.626570i
\(555\) 0 0
\(556\) 14.4282 8.33013i 0.611892 0.353276i
\(557\) −2.19067 0.586988i −0.0928217 0.0248715i 0.212109 0.977246i \(-0.431967\pi\)
−0.304931 + 0.952374i \(0.598633\pi\)
\(558\) 0 0
\(559\) 15.8756 3.92820i 0.671468 0.166145i
\(560\) 0.896575i 0.0378872i
\(561\) 0 0
\(562\) −3.92820 6.80385i −0.165701 0.287003i
\(563\) −0.757875 + 1.31268i −0.0319406 + 0.0553228i −0.881554 0.472084i \(-0.843502\pi\)
0.849613 + 0.527406i \(0.176835\pi\)
\(564\) 0 0
\(565\) 0.535898 + 2.00000i 0.0225454 + 0.0841406i
\(566\) 7.58871 + 28.3214i 0.318977 + 1.19044i
\(567\) 0 0
\(568\) −1.00000 + 1.73205i −0.0419591 + 0.0726752i
\(569\) 18.3018 + 31.6997i 0.767252 + 1.32892i 0.939048 + 0.343787i \(0.111710\pi\)
−0.171795 + 0.985133i \(0.554957\pi\)
\(570\) 0 0
\(571\) 32.6603i 1.36679i 0.730049 + 0.683395i \(0.239497\pi\)
−0.730049 + 0.683395i \(0.760503\pi\)
\(572\) −3.60488 0.0693504i −0.150728 0.00289968i
\(573\) 0 0
\(574\) −3.46410 0.928203i −0.144589 0.0387425i
\(575\) −4.57081 + 2.63896i −0.190616 + 0.110052i
\(576\) 0 0
\(577\) 7.66025 7.66025i 0.318901 0.318901i −0.529444 0.848345i \(-0.677600\pi\)
0.848345 + 0.529444i \(0.177600\pi\)
\(578\) −6.76148 + 1.81173i −0.281241 + 0.0753582i
\(579\) 0 0
\(580\) 2.00000 + 2.00000i 0.0830455 + 0.0830455i
\(581\) −10.4543 6.03579i −0.433717 0.250407i
\(582\) 0 0
\(583\) 3.33013 12.4282i 0.137920 0.514724i
\(584\) −3.58630 −0.148402
\(585\) 0 0
\(586\) 13.9282 0.575369
\(587\) −10.5930 + 39.5336i −0.437220 + 1.63173i 0.298478 + 0.954417i \(0.403521\pi\)
−0.735698 + 0.677310i \(0.763146\pi\)
\(588\) 0 0
\(589\) 1.39230 + 0.803848i 0.0573689 + 0.0331220i
\(590\) 2.82843 + 2.82843i 0.116445 + 0.116445i
\(591\) 0 0
\(592\) 5.96410 1.59808i 0.245123 0.0656805i
\(593\) −28.0812 + 28.0812i −1.15316 + 1.15316i −0.167241 + 0.985916i \(0.553486\pi\)
−0.985916 + 0.167241i \(0.946514\pi\)
\(594\) 0 0
\(595\) 3.80385 2.19615i 0.155943 0.0900335i
\(596\) −2.31079 0.619174i −0.0946536 0.0253624i
\(597\) 0 0
\(598\) −9.83013 + 16.2942i −0.401984 + 0.666321i
\(599\) 26.4911i 1.08240i 0.840895 + 0.541199i \(0.182029\pi\)
−0.840895 + 0.541199i \(0.817971\pi\)
\(600\) 0 0
\(601\) −9.42820 16.3301i −0.384584 0.666120i 0.607127 0.794605i \(-0.292322\pi\)
−0.991711 + 0.128485i \(0.958989\pi\)
\(602\) 2.03339 3.52193i 0.0828747 0.143543i
\(603\) 0 0
\(604\) −3.73205 13.9282i −0.151855 0.566731i
\(605\) −2.58819 9.65926i −0.105225 0.392705i
\(606\) 0 0
\(607\) −5.93782 + 10.2846i −0.241009 + 0.417439i −0.961002 0.276542i \(-0.910812\pi\)
0.719993 + 0.693981i \(0.244145\pi\)
\(608\) 0.448288 + 0.776457i 0.0181805 + 0.0314895i
\(609\) 0 0
\(610\) 4.92820i 0.199537i
\(611\) 0.688524 35.7900i 0.0278547 1.44791i
\(612\) 0 0
\(613\) 8.89230 + 2.38269i 0.359157 + 0.0962358i 0.433885 0.900968i \(-0.357142\pi\)
−0.0747284 + 0.997204i \(0.523809\pi\)
\(614\) 19.8362 11.4524i 0.800522 0.462182i
\(615\) 0 0
\(616\) −0.633975 + 0.633975i −0.0255436 + 0.0255436i
\(617\) 12.8666 3.44760i 0.517991 0.138795i 0.00965369 0.999953i \(-0.496927\pi\)
0.508337 + 0.861158i \(0.330260\pi\)
\(618\) 0 0
\(619\) 26.8827 + 26.8827i 1.08051 + 1.08051i 0.996462 + 0.0840444i \(0.0267837\pi\)
0.0840444 + 0.996462i \(0.473216\pi\)
\(620\) −1.55291 0.896575i −0.0623665 0.0360073i
\(621\) 0 0
\(622\) 0.143594 0.535898i 0.00575758 0.0214876i
\(623\) 10.8704 0.435513
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) −2.58819 + 9.65926i −0.103445 + 0.386062i
\(627\) 0 0
\(628\) 5.89230 + 3.40192i 0.235129 + 0.135752i
\(629\) 21.3891 + 21.3891i 0.852838 + 0.852838i
\(630\) 0 0
\(631\) 14.1962 3.80385i 0.565140 0.151429i 0.0350732 0.999385i \(-0.488834\pi\)
0.530067 + 0.847956i \(0.322167\pi\)
\(632\) −1.41421 + 1.41421i −0.0562544 + 0.0562544i
\(633\) 0 0
\(634\) −13.9186 + 8.03590i −0.552778 + 0.319146i
\(635\) 12.2289 + 3.27671i 0.485288 + 0.130032i
\(636\) 0 0
\(637\) 6.19615 21.4641i 0.245500 0.850439i
\(638\) 2.82843i 0.111979i
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 2.62038 4.53862i 0.103499 0.179265i −0.809625 0.586947i \(-0.800330\pi\)
0.913124 + 0.407682i \(0.133663\pi\)
\(642\) 0 0
\(643\) 5.66025 + 21.1244i 0.223219 + 0.833063i 0.983110 + 0.183014i \(0.0585852\pi\)
−0.759892 + 0.650050i \(0.774748\pi\)
\(644\) 1.22474 + 4.57081i 0.0482617 + 0.180115i
\(645\) 0 0
\(646\) −2.19615 + 3.80385i −0.0864065 + 0.149660i
\(647\) 4.17329 + 7.22835i 0.164069 + 0.284176i 0.936324 0.351137i \(-0.114205\pi\)
−0.772255 + 0.635312i \(0.780871\pi\)
\(648\) 0 0
\(649\) 4.00000i 0.157014i
\(650\) −3.15660 + 1.74238i −0.123812 + 0.0683419i
\(651\) 0 0
\(652\) 19.6603 + 5.26795i 0.769955 + 0.206309i
\(653\) −4.29839 + 2.48168i −0.168209 + 0.0971155i −0.581741 0.813374i \(-0.697628\pi\)
0.413532 + 0.910490i \(0.364295\pi\)
\(654\) 0 0
\(655\) 3.09808 3.09808i 0.121052 0.121052i
\(656\) −3.86370 + 1.03528i −0.150852 + 0.0404207i
\(657\) 0 0
\(658\) −6.29423 6.29423i −0.245375 0.245375i
\(659\) 34.2693 + 19.7854i 1.33494 + 0.770729i 0.986053 0.166435i \(-0.0532255\pi\)
0.348890 + 0.937164i \(0.386559\pi\)
\(660\) 0 0
\(661\) −6.41154 + 23.9282i −0.249380 + 0.930699i 0.721751 + 0.692153i \(0.243338\pi\)
−0.971131 + 0.238546i \(0.923329\pi\)
\(662\) 1.13681 0.0441835
\(663\) 0 0
\(664\) −13.4641 −0.522508
\(665\) 0.208051 0.776457i 0.00806787 0.0301097i
\(666\) 0 0
\(667\) −12.9282 7.46410i −0.500582 0.289011i
\(668\) 5.36585 + 5.36585i 0.207611 + 0.207611i
\(669\) 0 0
\(670\) 10.1962 2.73205i 0.393912 0.105548i
\(671\) −3.48477 + 3.48477i −0.134528 + 0.134528i
\(672\) 0 0
\(673\) 37.1769 21.4641i 1.43306 0.827380i 0.435711 0.900086i \(-0.356497\pi\)
0.997353 + 0.0727061i \(0.0231635\pi\)
\(674\) 4.38134 + 1.17398i 0.168763 + 0.0452199i
\(675\) 0 0
\(676\) −6.92820 + 11.0000i −0.266469 + 0.423077i
\(677\) 30.8081i 1.18405i 0.805919 + 0.592026i \(0.201672\pi\)
−0.805919 + 0.592026i \(0.798328\pi\)
\(678\) 0 0
\(679\) 2.87564 + 4.98076i 0.110357 + 0.191144i
\(680\) 2.44949 4.24264i 0.0939336 0.162698i
\(681\) 0 0
\(682\) 0.464102 + 1.73205i 0.0177714 + 0.0663237i
\(683\) −2.20925 8.24504i −0.0845347 0.315488i 0.910691 0.413088i \(-0.135550\pi\)
−0.995226 + 0.0976005i \(0.968883\pi\)
\(684\) 0 0
\(685\) 4.00000 6.92820i 0.152832 0.264713i
\(686\) −5.91567 10.2462i −0.225861 0.391204i
\(687\) 0 0
\(688\) 4.53590i 0.172930i
\(689\) −32.1666 33.4285i −1.22545 1.27352i
\(690\) 0 0
\(691\) 12.1603 + 3.25833i 0.462598 + 0.123953i 0.482588 0.875847i \(-0.339697\pi\)
−0.0199902 + 0.999800i \(0.506364\pi\)
\(692\) 10.1583 5.86491i 0.386161 0.222950i
\(693\) 0 0
\(694\) 3.07180 3.07180i 0.116604 0.116604i
\(695\) −16.0926 + 4.31199i −0.610426 + 0.163563i
\(696\) 0 0
\(697\) −13.8564 13.8564i −0.524849 0.524849i
\(698\) 2.27362 + 1.31268i 0.0860579 + 0.0496856i
\(699\) 0 0
\(700\) −0.232051 + 0.866025i −0.00877070 + 0.0327327i
\(701\) −34.4959 −1.30289 −0.651447 0.758694i \(-0.725838\pi\)
−0.651447 + 0.758694i \(0.725838\pi\)
\(702\) 0 0
\(703\) 5.53590 0.208790
\(704\) −0.258819 + 0.965926i −0.00975461 + 0.0364047i
\(705\) 0 0
\(706\) 22.9808 + 13.2679i 0.864892 + 0.499346i
\(707\) 3.58630 + 3.58630i 0.134877 + 0.134877i
\(708\) 0 0
\(709\) 23.6603 6.33975i 0.888579 0.238094i 0.214474 0.976730i \(-0.431196\pi\)
0.674105 + 0.738635i \(0.264529\pi\)
\(710\) 1.41421 1.41421i 0.0530745 0.0530745i
\(711\) 0 0
\(712\) 10.5000 6.06218i 0.393504 0.227190i
\(713\) 9.14162 + 2.44949i 0.342356 + 0.0917341i
\(714\) 0 0
\(715\) 3.46410 + 1.00000i 0.129550 + 0.0373979i
\(716\) 0.378937i 0.0141616i
\(717\) 0 0
\(718\) −2.66025 4.60770i −0.0992798 0.171958i
\(719\) 4.79744 8.30942i 0.178914 0.309889i −0.762595 0.646877i \(-0.776075\pi\)
0.941509 + 0.336988i \(0.109408\pi\)
\(720\) 0 0
\(721\) 0.153212 + 0.571797i 0.00570593 + 0.0212948i
\(722\) −4.70951 17.5761i −0.175270 0.654116i
\(723\) 0 0
\(724\) −9.92820 + 17.1962i −0.368979 + 0.639090i
\(725\) −1.41421 2.44949i −0.0525226 0.0909718i
\(726\) 0 0
\(727\) 7.92820i 0.294041i 0.989133 + 0.147020i \(0.0469683\pi\)
−0.989133 + 0.147020i \(0.953032\pi\)
\(728\) 0.776457 + 3.13801i 0.0287774 + 0.116303i
\(729\) 0 0
\(730\) 3.46410 + 0.928203i 0.128212 + 0.0343543i
\(731\) 19.2442 11.1106i 0.711772 0.410942i
\(732\) 0 0
\(733\) 14.8301 14.8301i 0.547763 0.547763i −0.378030 0.925793i \(-0.623398\pi\)
0.925793 + 0.378030i \(0.123398\pi\)
\(734\) −9.00292 + 2.41233i −0.332304 + 0.0890405i
\(735\) 0 0
\(736\) 3.73205 + 3.73205i 0.137565 + 0.137565i
\(737\) −9.14162 5.27792i −0.336736 0.194415i
\(738\) 0 0
\(739\) −10.3301 + 38.5526i −0.380000 + 1.41818i 0.465900 + 0.884837i \(0.345731\pi\)
−0.845900 + 0.533342i \(0.820936\pi\)
\(740\) −6.17449 −0.226979
\(741\) 0 0
\(742\) −11.5359 −0.423496
\(743\) −2.13492 + 7.96764i −0.0783228 + 0.292304i −0.993966 0.109687i \(-0.965015\pi\)
0.915643 + 0.401991i \(0.131682\pi\)
\(744\) 0 0
\(745\) 2.07180 + 1.19615i 0.0759048 + 0.0438236i
\(746\) 26.0106 + 26.0106i 0.952317 + 0.952317i
\(747\) 0 0
\(748\) −4.73205 + 1.26795i −0.173021 + 0.0463608i
\(749\) −7.82894 + 7.82894i −0.286063 + 0.286063i
\(750\) 0 0
\(751\) −12.9282 + 7.46410i −0.471757 + 0.272369i −0.716975 0.697099i \(-0.754474\pi\)
0.245218 + 0.969468i \(0.421140\pi\)
\(752\) −9.58991 2.56961i −0.349708 0.0937040i
\(753\) 0 0
\(754\) −8.73205 5.26795i −0.318003 0.191847i
\(755\) 14.4195i 0.524781i
\(756\) 0 0
\(757\) −7.50000 12.9904i −0.272592 0.472143i 0.696933 0.717137i \(-0.254548\pi\)
−0.969525 + 0.244993i \(0.921214\pi\)
\(758\) 18.9210 32.7721i 0.687242 1.19034i
\(759\) 0 0
\(760\) −0.232051 0.866025i −0.00841737 0.0314140i
\(761\) 7.89829 + 29.4768i 0.286313 + 1.06853i 0.947875 + 0.318644i \(0.103227\pi\)
−0.661562 + 0.749891i \(0.730106\pi\)
\(762\) 0 0
\(763\) −2.07180 + 3.58846i −0.0750041 + 0.129911i
\(764\) 12.1087 + 20.9730i 0.438079 + 0.758775i
\(765\) 0 0
\(766\) 31.1769i 1.12647i
\(767\) −12.3490 7.45001i −0.445896 0.269004i
\(768\) 0 0
\(769\) −7.56218 2.02628i −0.272699 0.0730695i 0.119878 0.992789i \(-0.461750\pi\)
−0.392577 + 0.919719i \(0.628416\pi\)
\(770\) 0.776457 0.448288i 0.0279816 0.0161552i
\(771\) 0 0
\(772\) 0.928203 0.928203i 0.0334068 0.0334068i
\(773\) 7.79676 2.08913i 0.280430 0.0751410i −0.115863 0.993265i \(-0.536963\pi\)
0.396293 + 0.918124i \(0.370297\pi\)
\(774\) 0 0
\(775\) 1.26795 + 1.26795i 0.0455461 + 0.0455461i
\(776\) 5.55532 + 3.20736i 0.199424 + 0.115138i
\(777\) 0 0
\(778\) 6.73205 25.1244i 0.241356 0.900752i
\(779\) −3.58630 −0.128493
\(780\) 0 0
\(781\) −2.00000 −0.0715656
\(782\) −6.69213 + 24.9754i −0.239310 + 0.893117i
\(783\) 0 0
\(784\) −5.36603 3.09808i −0.191644 0.110646i
\(785\) −4.81105 4.81105i −0.171714 0.171714i
\(786\) 0 0
\(787\) −29.6603 + 7.94744i −1.05727 + 0.283296i −0.745255 0.666780i \(-0.767672\pi\)
−0.312019 + 0.950076i \(0.601005\pi\)
\(788\) 5.36585 5.36585i 0.191150 0.191150i
\(789\) 0 0
\(790\) 1.73205 1.00000i 0.0616236 0.0355784i
\(791\) −1.79315 0.480473i −0.0637571 0.0170837i
\(792\) 0 0
\(793\) 4.26795 + 17.2487i 0.151559 + 0.612520i
\(794\) 31.4273i 1.11531i
\(795\) 0 0
\(796\) 2.26795 + 3.92820i 0.0803853 + 0.139231i
\(797\) −5.50455 + 9.53416i −0.194981 + 0.337717i −0.946894 0.321545i \(-0.895798\pi\)
0.751913 + 0.659262i \(0.229131\pi\)
\(798\) 0 0
\(799\) −12.5885 46.9808i −0.445348 1.66206i
\(800\) 0.258819 + 0.965926i 0.00915064 + 0.0341506i
\(801\) 0 0
\(802\) −16.9641 + 29.3827i −0.599023 + 1.03754i
\(803\) −1.79315 3.10583i −0.0632789 0.109602i
\(804\) 0 0
\(805\) 4.73205i 0.166783i
\(806\) 6.21166 + 1.79315i 0.218796 + 0.0631610i
\(807\) 0 0
\(808\) 5.46410 + 1.46410i 0.192226 + 0.0515069i
\(809\) −23.7506 + 13.7124i −0.835028 + 0.482103i −0.855571 0.517686i \(-0.826794\pi\)
0.0205434 + 0.999789i \(0.493460\pi\)
\(810\) 0 0
\(811\) −8.16987 + 8.16987i −0.286883 + 0.286883i −0.835846 0.548963i \(-0.815023\pi\)
0.548963 + 0.835846i \(0.315023\pi\)
\(812\) −2.44949 + 0.656339i −0.0859602 + 0.0230330i
\(813\) 0 0
\(814\) 4.36603 + 4.36603i 0.153029 + 0.153029i
\(815\) −17.6269 10.1769i −0.617443 0.356481i
\(816\) 0 0
\(817\) 1.05256 3.92820i 0.0368244 0.137430i
\(818\) −21.8052 −0.762400
\(819\) 0 0
\(820\) 4.00000 0.139686
\(821\) −12.4877 + 46.6047i −0.435823 + 1.62651i 0.303265 + 0.952906i \(0.401923\pi\)
−0.739089 + 0.673608i \(0.764744\pi\)
\(822\) 0 0
\(823\) −33.8205 19.5263i −1.17891 0.680643i −0.223147 0.974785i \(-0.571633\pi\)
−0.955762 + 0.294142i \(0.904966\pi\)
\(824\) 0.466870 + 0.466870i 0.0162642 + 0.0162642i
\(825\) 0 0
\(826\) −3.46410 + 0.928203i −0.120532 + 0.0322963i
\(827\) 24.1160 24.1160i 0.838594 0.838594i −0.150080 0.988674i \(-0.547953\pi\)
0.988674 + 0.150080i \(0.0479531\pi\)
\(828\) 0 0
\(829\) −35.9090 + 20.7321i −1.24717 + 0.720054i −0.970544 0.240924i \(-0.922550\pi\)
−0.276626 + 0.960978i \(0.589216\pi\)
\(830\) 13.0053 + 3.48477i 0.451421 + 0.120958i
\(831\) 0 0
\(832\) 2.50000 + 2.59808i 0.0866719 + 0.0900721i
\(833\) 30.3548i 1.05173i
\(834\) 0 0
\(835\) −3.79423 6.57180i −0.131305 0.227426i
\(836\) −0.448288 + 0.776457i −0.0155044 + 0.0268543i
\(837\) 0 0
\(838\) 1.95448 + 7.29423i 0.0675165 + 0.251975i
\(839\) 11.4524 + 42.7410i 0.395381 + 1.47558i 0.821130 + 0.570741i \(0.193344\pi\)
−0.425749 + 0.904841i \(0.639989\pi\)
\(840\) 0 0
\(841\) −10.5000 + 18.1865i −0.362069 + 0.627122i
\(842\) −1.79315 3.10583i −0.0617961 0.107034i
\(843\) 0 0
\(844\) 9.92820i 0.341743i
\(845\) 9.53914 8.83203i 0.328156 0.303831i
\(846\) 0 0
\(847\) 8.66025 + 2.32051i 0.297570 + 0.0797336i
\(848\) −11.1428 + 6.43331i −0.382646 + 0.220921i
\(849\) 0 0
\(850\) −3.46410 + 3.46410i −0.118818 + 0.118818i
\(851\) 31.4780 8.43451i 1.07905 0.289131i
\(852\) 0 0
\(853\) 15.0000 + 15.0000i 0.513590 + 0.513590i 0.915625 0.402034i \(-0.131697\pi\)
−0.402034 + 0.915625i \(0.631697\pi\)
\(854\) 3.82654 + 2.20925i 0.130941 + 0.0755991i
\(855\) 0 0
\(856\) −3.19615 + 11.9282i −0.109242 + 0.407698i
\(857\) −28.7647 −0.982585 −0.491292 0.870995i \(-0.663475\pi\)
−0.491292 + 0.870995i \(0.663475\pi\)
\(858\) 0 0
\(859\) −3.00000 −0.102359 −0.0511793 0.998689i \(-0.516298\pi\)
−0.0511793 + 0.998689i \(0.516298\pi\)
\(860\) −1.17398 + 4.38134i −0.0400323 + 0.149403i
\(861\) 0 0
\(862\) −8.19615 4.73205i −0.279162 0.161174i
\(863\) −25.6317 25.6317i −0.872514 0.872514i 0.120232 0.992746i \(-0.461636\pi\)
−0.992746 + 0.120232i \(0.961636\pi\)
\(864\) 0 0
\(865\) −11.3301 + 3.03590i −0.385236 + 0.103224i
\(866\) −19.3185 + 19.3185i −0.656470 + 0.656470i
\(867\) 0 0
\(868\) 1.39230 0.803848i 0.0472579 0.0272844i
\(869\) −1.93185 0.517638i −0.0655336 0.0175597i
\(870\) 0 0
\(871\) −33.3205 + 18.3923i −1.12902 + 0.623199i
\(872\) 4.62158i 0.156506i
\(873\) 0 0
\(874\) 2.36603 + 4.09808i 0.0800320 + 0.138619i
\(875\) 0.448288 0.776457i 0.0151549 0.0262490i
\(876\) 0 0
\(877\) 3.63397 + 13.5622i 0.122711 + 0.457962i 0.999748 0.0224604i \(-0.00714997\pi\)
−0.877037 + 0.480423i \(0.840483\pi\)
\(878\) −3.82654 14.2808i −0.129139 0.481955i
\(879\) 0 0
\(880\) 0.500000 0.866025i 0.0168550 0.0291937i
\(881\) −3.51695 6.09154i −0.118489 0.205229i 0.800680 0.599092i \(-0.204472\pi\)
−0.919169 + 0.393863i \(0.871138\pi\)
\(882\) 0 0
\(883\) 25.3205i 0.852103i −0.904699 0.426051i \(-0.859904\pi\)
0.904699 0.426051i \(-0.140096\pi\)
\(884\) −4.89898 + 16.9706i −0.164771 + 0.570782i
\(885\) 0 0
\(886\) −9.92820 2.66025i −0.333545 0.0893730i
\(887\) 45.5880 26.3202i 1.53069 0.883747i 0.531365 0.847143i \(-0.321679\pi\)
0.999330 0.0366039i \(-0.0116540\pi\)
\(888\) 0 0
\(889\) −8.02628 + 8.02628i −0.269193 + 0.269193i
\(890\) −11.7112 + 3.13801i −0.392561 + 0.105186i
\(891\) 0 0
\(892\) 1.70577 + 1.70577i 0.0571134 + 0.0571134i
\(893\) −7.70882 4.45069i −0.257966 0.148937i
\(894\) 0 0
\(895\) 0.0980762 0.366025i 0.00327833 0.0122349i
\(896\) 0.896575 0.0299525
\(897\) 0 0
\(898\) 1.73205 0.0577993
\(899\) −1.31268 + 4.89898i −0.0437802 + 0.163390i
\(900\) 0 0
\(901\) −54.5885 31.5167i −1.81861 1.04997i
\(902\) −2.82843 2.82843i −0.0941763 0.0941763i
\(903\) 0 0
\(904\) −2.00000 + 0.535898i −0.0665190 + 0.0178237i
\(905\) 14.0406 14.0406i 0.466725 0.466725i
\(906\) 0 0
\(907\) −8.32051 + 4.80385i −0.276278 + 0.159509i −0.631737 0.775183i \(-0.717658\pi\)
0.355459 + 0.934692i \(0.384324\pi\)
\(908\) −10.9348 2.92996i −0.362883 0.0972342i
\(909\) 0 0
\(910\) 0.0621778 3.23205i 0.00206117 0.107141i
\(911\) 12.8295i 0.425059i −0.977155 0.212529i \(-0.931830\pi\)
0.977155 0.212529i \(-0.0681701\pi\)
\(912\) 0 0
\(913\) −6.73205 11.6603i −0.222798 0.385898i
\(914\) 19.1798 33.2204i 0.634412 1.09883i
\(915\) 0 0
\(916\) 0.124356 + 0.464102i 0.00410883 + 0.0153343i
\(917\) 1.01669 + 3.79435i 0.0335742 + 0.125301i
\(918\) 0 0
\(919\) 9.58846 16.6077i 0.316294 0.547837i −0.663418 0.748249i \(-0.730895\pi\)
0.979712 + 0.200412i \(0.0642281\pi\)
\(920\) −2.63896 4.57081i −0.0870039 0.150695i
\(921\) 0 0
\(922\) 13.4641i 0.443417i
\(923\) −3.72500 + 6.17449i −0.122610 + 0.203236i
\(924\) 0 0
\(925\) 5.96410 + 1.59808i 0.196098 + 0.0525444i
\(926\) 19.7482 11.4016i 0.648967 0.374681i
\(927\) 0 0
\(928\) −2.00000 + 2.00000i −0.0656532 + 0.0656532i
\(929\) 50.8473 13.6245i 1.66825 0.447005i 0.703609 0.710587i \(-0.251571\pi\)
0.964637 + 0.263582i \(0.0849039\pi\)
\(930\) 0 0
\(931\) −3.92820 3.92820i −0.128742 0.128742i
\(932\) −7.58871 4.38134i −0.248576 0.143516i
\(933\) 0 0
\(934\) 1.07180 4.00000i 0.0350703 0.130884i
\(935\) 4.89898 0.160214
\(936\) 0 0
\(937\) −4.92820 −0.160997 −0.0804987 0.996755i \(-0.525651\pi\)
−0.0804987 + 0.996755i \(0.525651\pi\)
\(938\) −2.44949 + 9.14162i −0.0799787 + 0.298484i
\(939\) 0 0
\(940\) 8.59808 + 4.96410i 0.280438 + 0.161911i
\(941\) −0.277401 0.277401i −0.00904303 0.00904303i 0.702571 0.711614i \(-0.252035\pi\)
−0.711614 + 0.702571i \(0.752035\pi\)
\(942\) 0 0
\(943\) −20.3923 + 5.46410i −0.664065 + 0.177936i
\(944\) −2.82843 + 2.82843i −0.0920575 + 0.0920575i
\(945\) 0 0
\(946\) 3.92820 2.26795i 0.127717 0.0737374i
\(947\) −1.65445 0.443309i −0.0537624 0.0144056i 0.231838 0.972755i \(-0.425526\pi\)
−0.285600 + 0.958349i \(0.592193\pi\)
\(948\) 0 0
\(949\) −12.9282 0.248711i −0.419667 0.00807351i
\(950\) 0.896575i 0.0290887i
\(951\) 0 0
\(952\) 2.19615 + 3.80385i 0.0711777 + 0.123283i
\(953\) −0.896575 + 1.55291i −0.0290429 + 0.0503038i −0.880182 0.474637i \(-0.842579\pi\)
0.851139 + 0.524941i \(0.175913\pi\)
\(954\) 0 0
\(955\) −6.26795 23.3923i −0.202826 0.756957i
\(956\) −3.82654 14.2808i −0.123759 0.461875i
\(957\) 0 0
\(958\) 5.12436 8.87564i 0.165560 0.286759i
\(959\) 3.58630 + 6.21166i 0.115808 + 0.200585i
\(960\) 0 0
\(961\) 27.7846i 0.896278i
\(962\) 21.6107 5.34727i 0.696758 0.172403i
\(963\) 0 0
\(964\) 5.96410 + 1.59808i 0.192091 + 0.0514706i
\(965\) −1.13681 + 0.656339i −0.0365953 + 0.0211283i
\(966\) 0 0
\(967\) 31.5429 31.5429i 1.01435 1.01435i 0.0144571 0.999895i \(-0.495398\pi\)
0.999895 0.0144571i \(-0.00460199\pi\)
\(968\) 9.65926 2.58819i 0.310460 0.0831876i
\(969\) 0 0
\(970\) −4.53590 4.53590i −0.145639 0.145639i
\(971\) −26.0800 15.0573i −0.836947 0.483212i 0.0192783 0.999814i \(-0.493863\pi\)
−0.856225 + 0.516603i \(0.827196\pi\)
\(972\) 0 0
\(973\) 3.86603 14.4282i 0.123939 0.462547i
\(974\) 16.2499 0.520679
\(975\) 0 0
\(976\) 4.92820 0.157748
\(977\) −3.66063 + 13.6617i −0.117114 + 0.437075i −0.999436 0.0335702i \(-0.989312\pi\)
0.882322 + 0.470646i \(0.155979\pi\)
\(978\) 0 0
\(979\) 10.5000 + 6.06218i 0.335581 + 0.193748i
\(980\) 4.38134 + 4.38134i 0.139957 + 0.139957i
\(981\) 0 0
\(982\) −1.69615 + 0.454483i −0.0541264 + 0.0145031i
\(983\) 10.0890 10.0890i 0.321788 0.321788i −0.527665 0.849453i \(-0.676932\pi\)
0.849453 + 0.527665i \(0.176932\pi\)
\(984\) 0 0
\(985\) −6.57180 + 3.79423i −0.209395 + 0.120894i
\(986\) −13.3843 3.58630i −0.426242 0.114211i
\(987\) 0 0
\(988\) 1.56218 + 2.83013i 0.0496995 + 0.0900383i
\(989\) 23.9401i 0.761251i
\(990\) 0 0
\(991\) −25.1962 43.6410i −0.800382 1.38630i −0.919365 0.393406i \(-0.871297\pi\)
0.118983 0.992896i \(-0.462037\pi\)
\(992\) 0.896575 1.55291i 0.0284663 0.0493051i
\(993\) 0 0
\(994\) 0.464102 + 1.73205i 0.0147204 + 0.0549373i
\(995\) −1.17398 4.38134i −0.0372176 0.138898i
\(996\) 0 0
\(997\) −17.3564 + 30.0622i −0.549683 + 0.952079i 0.448613 + 0.893726i \(0.351918\pi\)
−0.998296 + 0.0583527i \(0.981415\pi\)
\(998\) −16.4022 28.4094i −0.519201 0.899283i
\(999\) 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 1170.2.cu.c.431.2 yes 8
3.2 odd 2 inner 1170.2.cu.c.431.1 8
13.7 odd 12 inner 1170.2.cu.c.1151.1 yes 8
39.20 even 12 inner 1170.2.cu.c.1151.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1170.2.cu.c.431.1 8 3.2 odd 2 inner
1170.2.cu.c.431.2 yes 8 1.1 even 1 trivial
1170.2.cu.c.1151.1 yes 8 13.7 odd 12 inner
1170.2.cu.c.1151.2 yes 8 39.20 even 12 inner