Properties

Label 525.2.i.f.226.2
Level $525$
Weight $2$
Character 525.226
Analytic conductor $4.192$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(151,525)]
 
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([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.i (of order \(3\), 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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 525.226
Dual form 525.2.i.f.151.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.366025 - 0.633975i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.732051 + 1.26795i) q^{4} -0.732051 q^{6} +(0.866025 + 2.50000i) q^{7} +2.53590 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.366025 - 0.633975i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.732051 + 1.26795i) q^{4} -0.732051 q^{6} +(0.866025 + 2.50000i) q^{7} +2.53590 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.36603 + 2.36603i) q^{11} +(0.732051 - 1.26795i) q^{12} -5.73205 q^{13} +(1.90192 + 0.366025i) q^{14} +(-0.535898 + 0.928203i) q^{16} +(3.36603 + 5.83013i) q^{17} +(0.366025 + 0.633975i) q^{18} +(1.23205 - 2.13397i) q^{19} +(1.73205 - 2.00000i) q^{21} +2.00000 q^{22} +(-0.633975 + 1.09808i) q^{23} +(-1.26795 - 2.19615i) q^{24} +(-2.09808 + 3.63397i) q^{26} +1.00000 q^{27} +(-2.53590 + 2.92820i) q^{28} +6.19615 q^{29} +(-3.23205 - 5.59808i) q^{31} +(2.92820 + 5.07180i) q^{32} +(1.36603 - 2.36603i) q^{33} +4.92820 q^{34} -1.46410 q^{36} +(3.59808 - 6.23205i) q^{37} +(-0.901924 - 1.56218i) q^{38} +(2.86603 + 4.96410i) q^{39} +2.73205 q^{41} +(-0.633975 - 1.83013i) q^{42} +7.19615 q^{43} +(-2.00000 + 3.46410i) q^{44} +(0.464102 + 0.803848i) q^{46} +(1.00000 - 1.73205i) q^{47} +1.07180 q^{48} +(-5.50000 + 4.33013i) q^{49} +(3.36603 - 5.83013i) q^{51} +(-4.19615 - 7.26795i) q^{52} +(-4.19615 - 7.26795i) q^{53} +(0.366025 - 0.633975i) q^{54} +(2.19615 + 6.33975i) q^{56} -2.46410 q^{57} +(2.26795 - 3.92820i) q^{58} +(-5.09808 - 8.83013i) q^{59} +(-2.00000 + 3.46410i) q^{61} -4.73205 q^{62} +(-2.59808 - 0.500000i) q^{63} +2.14359 q^{64} +(-1.00000 - 1.73205i) q^{66} +(1.33013 + 2.30385i) q^{67} +(-4.92820 + 8.53590i) q^{68} +1.26795 q^{69} -4.19615 q^{71} +(-1.26795 + 2.19615i) q^{72} +(-2.33013 - 4.03590i) q^{73} +(-2.63397 - 4.56218i) q^{74} +3.60770 q^{76} +(-4.73205 + 5.46410i) q^{77} +4.19615 q^{78} +(-6.69615 + 11.5981i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +9.12436 q^{83} +(3.80385 + 0.732051i) q^{84} +(2.63397 - 4.56218i) q^{86} +(-3.09808 - 5.36603i) q^{87} +(3.46410 + 6.00000i) q^{88} +(4.56218 - 7.90192i) q^{89} +(-4.96410 - 14.3301i) q^{91} -1.85641 q^{92} +(-3.23205 + 5.59808i) q^{93} +(-0.732051 - 1.26795i) q^{94} +(2.92820 - 5.07180i) q^{96} -1.07180 q^{97} +(0.732051 + 5.07180i) q^{98} -2.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 4 q^{4} + 4 q^{6} + 24 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{3} - 4 q^{4} + 4 q^{6} + 24 q^{8} - 2 q^{9} + 2 q^{11} - 4 q^{12} - 16 q^{13} + 18 q^{14} - 16 q^{16} + 10 q^{17} - 2 q^{18} - 2 q^{19} + 8 q^{22} - 6 q^{23} - 12 q^{24} + 2 q^{26} + 4 q^{27} - 24 q^{28} + 4 q^{29} - 6 q^{31} - 16 q^{32} + 2 q^{33} - 8 q^{34} + 8 q^{36} + 4 q^{37} - 14 q^{38} + 8 q^{39} + 4 q^{41} - 6 q^{42} + 8 q^{43} - 8 q^{44} - 12 q^{46} + 4 q^{47} + 32 q^{48} - 22 q^{49} + 10 q^{51} + 4 q^{52} + 4 q^{53} - 2 q^{54} - 12 q^{56} + 4 q^{57} + 16 q^{58} - 10 q^{59} - 8 q^{61} - 12 q^{62} + 64 q^{64} - 4 q^{66} - 12 q^{67} + 8 q^{68} + 12 q^{69} + 4 q^{71} - 12 q^{72} + 8 q^{73} - 14 q^{74} + 56 q^{76} - 12 q^{77} - 4 q^{78} - 6 q^{79} - 2 q^{81} + 4 q^{82} - 12 q^{83} + 36 q^{84} + 14 q^{86} - 2 q^{87} - 6 q^{89} - 6 q^{91} + 48 q^{92} - 6 q^{93} + 4 q^{94} - 16 q^{96} - 32 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 0.633975i 0.258819 0.448288i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.732051 + 1.26795i 0.366025 + 0.633975i
\(5\) 0 0
\(6\) −0.732051 −0.298858
\(7\) 0.866025 + 2.50000i 0.327327 + 0.944911i
\(8\) 2.53590 0.896575
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.36603 + 2.36603i 0.411872 + 0.713384i 0.995094 0.0989291i \(-0.0315417\pi\)
−0.583222 + 0.812313i \(0.698208\pi\)
\(12\) 0.732051 1.26795i 0.211325 0.366025i
\(13\) −5.73205 −1.58978 −0.794892 0.606750i \(-0.792473\pi\)
−0.794892 + 0.606750i \(0.792473\pi\)
\(14\) 1.90192 + 0.366025i 0.508311 + 0.0978244i
\(15\) 0 0
\(16\) −0.535898 + 0.928203i −0.133975 + 0.232051i
\(17\) 3.36603 + 5.83013i 0.816381 + 1.41401i 0.908332 + 0.418250i \(0.137356\pi\)
−0.0919509 + 0.995764i \(0.529310\pi\)
\(18\) 0.366025 + 0.633975i 0.0862730 + 0.149429i
\(19\) 1.23205 2.13397i 0.282652 0.489567i −0.689385 0.724395i \(-0.742119\pi\)
0.972037 + 0.234828i \(0.0754526\pi\)
\(20\) 0 0
\(21\) 1.73205 2.00000i 0.377964 0.436436i
\(22\) 2.00000 0.426401
\(23\) −0.633975 + 1.09808i −0.132193 + 0.228965i −0.924522 0.381130i \(-0.875535\pi\)
0.792329 + 0.610094i \(0.208868\pi\)
\(24\) −1.26795 2.19615i −0.258819 0.448288i
\(25\) 0 0
\(26\) −2.09808 + 3.63397i −0.411467 + 0.712681i
\(27\) 1.00000 0.192450
\(28\) −2.53590 + 2.92820i −0.479240 + 0.553378i
\(29\) 6.19615 1.15060 0.575298 0.817944i \(-0.304886\pi\)
0.575298 + 0.817944i \(0.304886\pi\)
\(30\) 0 0
\(31\) −3.23205 5.59808i −0.580493 1.00544i −0.995421 0.0955896i \(-0.969526\pi\)
0.414927 0.909855i \(-0.363807\pi\)
\(32\) 2.92820 + 5.07180i 0.517638 + 0.896575i
\(33\) 1.36603 2.36603i 0.237795 0.411872i
\(34\) 4.92820 0.845180
\(35\) 0 0
\(36\) −1.46410 −0.244017
\(37\) 3.59808 6.23205i 0.591520 1.02454i −0.402508 0.915417i \(-0.631861\pi\)
0.994028 0.109126i \(-0.0348053\pi\)
\(38\) −0.901924 1.56218i −0.146311 0.253419i
\(39\) 2.86603 + 4.96410i 0.458931 + 0.794892i
\(40\) 0 0
\(41\) 2.73205 0.426675 0.213337 0.976979i \(-0.431567\pi\)
0.213337 + 0.976979i \(0.431567\pi\)
\(42\) −0.633975 1.83013i −0.0978244 0.282395i
\(43\) 7.19615 1.09740 0.548701 0.836018i \(-0.315122\pi\)
0.548701 + 0.836018i \(0.315122\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 0 0
\(46\) 0.464102 + 0.803848i 0.0684280 + 0.118521i
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 1.07180 0.154701
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) 0 0
\(51\) 3.36603 5.83013i 0.471338 0.816381i
\(52\) −4.19615 7.26795i −0.581902 1.00788i
\(53\) −4.19615 7.26795i −0.576386 0.998330i −0.995890 0.0905760i \(-0.971129\pi\)
0.419504 0.907754i \(-0.362204\pi\)
\(54\) 0.366025 0.633975i 0.0498097 0.0862730i
\(55\) 0 0
\(56\) 2.19615 + 6.33975i 0.293473 + 0.847184i
\(57\) −2.46410 −0.326378
\(58\) 2.26795 3.92820i 0.297796 0.515798i
\(59\) −5.09808 8.83013i −0.663713 1.14958i −0.979633 0.200799i \(-0.935646\pi\)
0.315920 0.948786i \(-0.397687\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) −4.73205 −0.600971
\(63\) −2.59808 0.500000i −0.327327 0.0629941i
\(64\) 2.14359 0.267949
\(65\) 0 0
\(66\) −1.00000 1.73205i −0.123091 0.213201i
\(67\) 1.33013 + 2.30385i 0.162501 + 0.281460i 0.935765 0.352624i \(-0.114711\pi\)
−0.773264 + 0.634084i \(0.781377\pi\)
\(68\) −4.92820 + 8.53590i −0.597632 + 1.03513i
\(69\) 1.26795 0.152643
\(70\) 0 0
\(71\) −4.19615 −0.497992 −0.248996 0.968505i \(-0.580101\pi\)
−0.248996 + 0.968505i \(0.580101\pi\)
\(72\) −1.26795 + 2.19615i −0.149429 + 0.258819i
\(73\) −2.33013 4.03590i −0.272721 0.472366i 0.696837 0.717230i \(-0.254590\pi\)
−0.969558 + 0.244864i \(0.921257\pi\)
\(74\) −2.63397 4.56218i −0.306193 0.530342i
\(75\) 0 0
\(76\) 3.60770 0.413831
\(77\) −4.73205 + 5.46410i −0.539267 + 0.622692i
\(78\) 4.19615 0.475121
\(79\) −6.69615 + 11.5981i −0.753376 + 1.30489i 0.192802 + 0.981238i \(0.438243\pi\)
−0.946178 + 0.323648i \(0.895091\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) 9.12436 1.00153 0.500764 0.865584i \(-0.333052\pi\)
0.500764 + 0.865584i \(0.333052\pi\)
\(84\) 3.80385 + 0.732051i 0.415034 + 0.0798733i
\(85\) 0 0
\(86\) 2.63397 4.56218i 0.284029 0.491952i
\(87\) −3.09808 5.36603i −0.332149 0.575298i
\(88\) 3.46410 + 6.00000i 0.369274 + 0.639602i
\(89\) 4.56218 7.90192i 0.483590 0.837602i −0.516233 0.856448i \(-0.672666\pi\)
0.999822 + 0.0188462i \(0.00599930\pi\)
\(90\) 0 0
\(91\) −4.96410 14.3301i −0.520379 1.50221i
\(92\) −1.85641 −0.193544
\(93\) −3.23205 + 5.59808i −0.335148 + 0.580493i
\(94\) −0.732051 1.26795i −0.0755053 0.130779i
\(95\) 0 0
\(96\) 2.92820 5.07180i 0.298858 0.517638i
\(97\) −1.07180 −0.108824 −0.0544122 0.998519i \(-0.517329\pi\)
−0.0544122 + 0.998519i \(0.517329\pi\)
\(98\) 0.732051 + 5.07180i 0.0739483 + 0.512329i
\(99\) −2.73205 −0.274581
\(100\) 0 0
\(101\) 5.36603 + 9.29423i 0.533939 + 0.924810i 0.999214 + 0.0396438i \(0.0126223\pi\)
−0.465274 + 0.885167i \(0.654044\pi\)
\(102\) −2.46410 4.26795i −0.243982 0.422590i
\(103\) 0.598076 1.03590i 0.0589302 0.102070i −0.835055 0.550166i \(-0.814564\pi\)
0.893985 + 0.448096i \(0.147898\pi\)
\(104\) −14.5359 −1.42536
\(105\) 0 0
\(106\) −6.14359 −0.596719
\(107\) −4.09808 + 7.09808i −0.396176 + 0.686197i −0.993251 0.115989i \(-0.962996\pi\)
0.597075 + 0.802186i \(0.296330\pi\)
\(108\) 0.732051 + 1.26795i 0.0704416 + 0.122008i
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 0 0
\(111\) −7.19615 −0.683029
\(112\) −2.78461 0.535898i −0.263121 0.0506376i
\(113\) 4.92820 0.463606 0.231803 0.972763i \(-0.425537\pi\)
0.231803 + 0.972763i \(0.425537\pi\)
\(114\) −0.901924 + 1.56218i −0.0844729 + 0.146311i
\(115\) 0 0
\(116\) 4.53590 + 7.85641i 0.421148 + 0.729449i
\(117\) 2.86603 4.96410i 0.264964 0.458931i
\(118\) −7.46410 −0.687126
\(119\) −11.6603 + 13.4641i −1.06889 + 1.23425i
\(120\) 0 0
\(121\) 1.76795 3.06218i 0.160723 0.278380i
\(122\) 1.46410 + 2.53590i 0.132554 + 0.229589i
\(123\) −1.36603 2.36603i −0.123170 0.213337i
\(124\) 4.73205 8.19615i 0.424951 0.736036i
\(125\) 0 0
\(126\) −1.26795 + 1.46410i −0.112958 + 0.130433i
\(127\) −15.1962 −1.34844 −0.674220 0.738530i \(-0.735520\pi\)
−0.674220 + 0.738530i \(0.735520\pi\)
\(128\) −5.07180 + 8.78461i −0.448288 + 0.776457i
\(129\) −3.59808 6.23205i −0.316793 0.548701i
\(130\) 0 0
\(131\) −4.26795 + 7.39230i −0.372892 + 0.645869i −0.990009 0.141003i \(-0.954967\pi\)
0.617117 + 0.786872i \(0.288301\pi\)
\(132\) 4.00000 0.348155
\(133\) 6.40192 + 1.23205i 0.555117 + 0.106832i
\(134\) 1.94744 0.168233
\(135\) 0 0
\(136\) 8.53590 + 14.7846i 0.731947 + 1.26777i
\(137\) −4.09808 7.09808i −0.350122 0.606430i 0.636148 0.771567i \(-0.280527\pi\)
−0.986271 + 0.165137i \(0.947193\pi\)
\(138\) 0.464102 0.803848i 0.0395070 0.0684280i
\(139\) −7.92820 −0.672461 −0.336231 0.941780i \(-0.609152\pi\)
−0.336231 + 0.941780i \(0.609152\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) −1.53590 + 2.66025i −0.128890 + 0.223244i
\(143\) −7.83013 13.5622i −0.654788 1.13413i
\(144\) −0.535898 0.928203i −0.0446582 0.0773503i
\(145\) 0 0
\(146\) −3.41154 −0.282341
\(147\) 6.50000 + 2.59808i 0.536111 + 0.214286i
\(148\) 10.5359 0.866046
\(149\) 10.9282 18.9282i 0.895273 1.55066i 0.0618073 0.998088i \(-0.480314\pi\)
0.833466 0.552571i \(-0.186353\pi\)
\(150\) 0 0
\(151\) −2.46410 4.26795i −0.200526 0.347321i 0.748172 0.663505i \(-0.230932\pi\)
−0.948698 + 0.316184i \(0.897598\pi\)
\(152\) 3.12436 5.41154i 0.253419 0.438934i
\(153\) −6.73205 −0.544254
\(154\) 1.73205 + 5.00000i 0.139573 + 0.402911i
\(155\) 0 0
\(156\) −4.19615 + 7.26795i −0.335961 + 0.581902i
\(157\) −7.19615 12.4641i −0.574315 0.994744i −0.996116 0.0880548i \(-0.971935\pi\)
0.421800 0.906689i \(-0.361398\pi\)
\(158\) 4.90192 + 8.49038i 0.389976 + 0.675458i
\(159\) −4.19615 + 7.26795i −0.332777 + 0.576386i
\(160\) 0 0
\(161\) −3.29423 0.633975i −0.259622 0.0499642i
\(162\) −0.732051 −0.0575153
\(163\) −2.92820 + 5.07180i −0.229355 + 0.397254i −0.957617 0.288045i \(-0.906995\pi\)
0.728262 + 0.685298i \(0.240328\pi\)
\(164\) 2.00000 + 3.46410i 0.156174 + 0.270501i
\(165\) 0 0
\(166\) 3.33975 5.78461i 0.259215 0.448973i
\(167\) 0.339746 0.0262903 0.0131452 0.999914i \(-0.495816\pi\)
0.0131452 + 0.999914i \(0.495816\pi\)
\(168\) 4.39230 5.07180i 0.338874 0.391298i
\(169\) 19.8564 1.52742
\(170\) 0 0
\(171\) 1.23205 + 2.13397i 0.0942173 + 0.163189i
\(172\) 5.26795 + 9.12436i 0.401677 + 0.695726i
\(173\) 10.7321 18.5885i 0.815943 1.41325i −0.0927063 0.995693i \(-0.529552\pi\)
0.908649 0.417561i \(-0.137115\pi\)
\(174\) −4.53590 −0.343866
\(175\) 0 0
\(176\) −2.92820 −0.220722
\(177\) −5.09808 + 8.83013i −0.383195 + 0.663713i
\(178\) −3.33975 5.78461i −0.250325 0.433575i
\(179\) 5.00000 + 8.66025i 0.373718 + 0.647298i 0.990134 0.140122i \(-0.0447496\pi\)
−0.616417 + 0.787420i \(0.711416\pi\)
\(180\) 0 0
\(181\) 10.3205 0.767117 0.383559 0.923517i \(-0.374698\pi\)
0.383559 + 0.923517i \(0.374698\pi\)
\(182\) −10.9019 2.09808i −0.808104 0.155520i
\(183\) 4.00000 0.295689
\(184\) −1.60770 + 2.78461i −0.118521 + 0.205284i
\(185\) 0 0
\(186\) 2.36603 + 4.09808i 0.173485 + 0.300486i
\(187\) −9.19615 + 15.9282i −0.672489 + 1.16479i
\(188\) 2.92820 0.213561
\(189\) 0.866025 + 2.50000i 0.0629941 + 0.181848i
\(190\) 0 0
\(191\) −2.46410 + 4.26795i −0.178296 + 0.308818i −0.941297 0.337579i \(-0.890392\pi\)
0.763001 + 0.646397i \(0.223725\pi\)
\(192\) −1.07180 1.85641i −0.0773503 0.133975i
\(193\) −4.59808 7.96410i −0.330977 0.573269i 0.651727 0.758454i \(-0.274045\pi\)
−0.982704 + 0.185185i \(0.940712\pi\)
\(194\) −0.392305 + 0.679492i −0.0281658 + 0.0487847i
\(195\) 0 0
\(196\) −9.51666 3.80385i −0.679761 0.271703i
\(197\) 17.6603 1.25824 0.629121 0.777308i \(-0.283415\pi\)
0.629121 + 0.777308i \(0.283415\pi\)
\(198\) −1.00000 + 1.73205i −0.0710669 + 0.123091i
\(199\) −11.0000 19.0526i −0.779769 1.35060i −0.932075 0.362267i \(-0.882003\pi\)
0.152305 0.988334i \(-0.451330\pi\)
\(200\) 0 0
\(201\) 1.33013 2.30385i 0.0938199 0.162501i
\(202\) 7.85641 0.552775
\(203\) 5.36603 + 15.4904i 0.376621 + 1.08721i
\(204\) 9.85641 0.690086
\(205\) 0 0
\(206\) −0.437822 0.758330i −0.0305045 0.0528354i
\(207\) −0.633975 1.09808i −0.0440643 0.0763216i
\(208\) 3.07180 5.32051i 0.212991 0.368911i
\(209\) 6.73205 0.465666
\(210\) 0 0
\(211\) 20.9282 1.44076 0.720378 0.693581i \(-0.243968\pi\)
0.720378 + 0.693581i \(0.243968\pi\)
\(212\) 6.14359 10.6410i 0.421944 0.730828i
\(213\) 2.09808 + 3.63397i 0.143758 + 0.248996i
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 0 0
\(216\) 2.53590 0.172546
\(217\) 11.1962 12.9282i 0.760044 0.877624i
\(218\) −8.05256 −0.545388
\(219\) −2.33013 + 4.03590i −0.157455 + 0.272721i
\(220\) 0 0
\(221\) −19.2942 33.4186i −1.29787 2.24798i
\(222\) −2.63397 + 4.56218i −0.176781 + 0.306193i
\(223\) −0.392305 −0.0262707 −0.0131353 0.999914i \(-0.504181\pi\)
−0.0131353 + 0.999914i \(0.504181\pi\)
\(224\) −10.1436 + 11.7128i −0.677747 + 0.782595i
\(225\) 0 0
\(226\) 1.80385 3.12436i 0.119990 0.207829i
\(227\) 7.83013 + 13.5622i 0.519704 + 0.900153i 0.999738 + 0.0229034i \(0.00729102\pi\)
−0.480034 + 0.877250i \(0.659376\pi\)
\(228\) −1.80385 3.12436i −0.119463 0.206916i
\(229\) 1.50000 2.59808i 0.0991228 0.171686i −0.812199 0.583380i \(-0.801730\pi\)
0.911322 + 0.411695i \(0.135063\pi\)
\(230\) 0 0
\(231\) 7.09808 + 1.36603i 0.467019 + 0.0898779i
\(232\) 15.7128 1.03160
\(233\) −8.66025 + 15.0000i −0.567352 + 0.982683i 0.429474 + 0.903079i \(0.358699\pi\)
−0.996827 + 0.0796037i \(0.974635\pi\)
\(234\) −2.09808 3.63397i −0.137156 0.237560i
\(235\) 0 0
\(236\) 7.46410 12.9282i 0.485872 0.841554i
\(237\) 13.3923 0.869924
\(238\) 4.26795 + 12.3205i 0.276650 + 0.798620i
\(239\) 20.9282 1.35373 0.676866 0.736106i \(-0.263337\pi\)
0.676866 + 0.736106i \(0.263337\pi\)
\(240\) 0 0
\(241\) −3.26795 5.66025i −0.210507 0.364609i 0.741366 0.671101i \(-0.234178\pi\)
−0.951873 + 0.306492i \(0.900845\pi\)
\(242\) −1.29423 2.24167i −0.0831962 0.144100i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −5.85641 −0.374918
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) −7.06218 + 12.2321i −0.449356 + 0.778307i
\(248\) −8.19615 14.1962i −0.520456 0.901457i
\(249\) −4.56218 7.90192i −0.289116 0.500764i
\(250\) 0 0
\(251\) 6.58846 0.415860 0.207930 0.978144i \(-0.433327\pi\)
0.207930 + 0.978144i \(0.433327\pi\)
\(252\) −1.26795 3.66025i −0.0798733 0.230574i
\(253\) −3.46410 −0.217786
\(254\) −5.56218 + 9.63397i −0.349002 + 0.604489i
\(255\) 0 0
\(256\) 5.85641 + 10.1436i 0.366025 + 0.633975i
\(257\) 5.83013 10.0981i 0.363673 0.629901i −0.624889 0.780714i \(-0.714856\pi\)
0.988562 + 0.150813i \(0.0481891\pi\)
\(258\) −5.26795 −0.327968
\(259\) 18.6962 + 3.59808i 1.16172 + 0.223574i
\(260\) 0 0
\(261\) −3.09808 + 5.36603i −0.191766 + 0.332149i
\(262\) 3.12436 + 5.41154i 0.193023 + 0.334326i
\(263\) −6.19615 10.7321i −0.382071 0.661767i 0.609287 0.792950i \(-0.291456\pi\)
−0.991358 + 0.131183i \(0.958122\pi\)
\(264\) 3.46410 6.00000i 0.213201 0.369274i
\(265\) 0 0
\(266\) 3.12436 3.60770i 0.191567 0.221202i
\(267\) −9.12436 −0.558401
\(268\) −1.94744 + 3.37307i −0.118959 + 0.206043i
\(269\) 9.73205 + 16.8564i 0.593374 + 1.02775i 0.993774 + 0.111413i \(0.0355377\pi\)
−0.400401 + 0.916340i \(0.631129\pi\)
\(270\) 0 0
\(271\) −8.46410 + 14.6603i −0.514158 + 0.890547i 0.485708 + 0.874121i \(0.338562\pi\)
−0.999865 + 0.0164256i \(0.994771\pi\)
\(272\) −7.21539 −0.437497
\(273\) −9.92820 + 11.4641i −0.600882 + 0.693839i
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) 0.928203 + 1.60770i 0.0558713 + 0.0967719i
\(277\) 1.33013 + 2.30385i 0.0799196 + 0.138425i 0.903215 0.429188i \(-0.141200\pi\)
−0.823295 + 0.567613i \(0.807867\pi\)
\(278\) −2.90192 + 5.02628i −0.174046 + 0.301456i
\(279\) 6.46410 0.386996
\(280\) 0 0
\(281\) −13.8564 −0.826604 −0.413302 0.910594i \(-0.635625\pi\)
−0.413302 + 0.910594i \(0.635625\pi\)
\(282\) −0.732051 + 1.26795i −0.0435930 + 0.0755053i
\(283\) 0.0621778 + 0.107695i 0.00369609 + 0.00640181i 0.867868 0.496796i \(-0.165490\pi\)
−0.864171 + 0.503197i \(0.832157\pi\)
\(284\) −3.07180 5.32051i −0.182278 0.315714i
\(285\) 0 0
\(286\) −11.4641 −0.677887
\(287\) 2.36603 + 6.83013i 0.139662 + 0.403170i
\(288\) −5.85641 −0.345092
\(289\) −14.1603 + 24.5263i −0.832956 + 1.44272i
\(290\) 0 0
\(291\) 0.535898 + 0.928203i 0.0314149 + 0.0544122i
\(292\) 3.41154 5.90897i 0.199645 0.345796i
\(293\) −5.07180 −0.296298 −0.148149 0.988965i \(-0.547331\pi\)
−0.148149 + 0.988965i \(0.547331\pi\)
\(294\) 4.02628 3.16987i 0.234817 0.184871i
\(295\) 0 0
\(296\) 9.12436 15.8038i 0.530342 0.918580i
\(297\) 1.36603 + 2.36603i 0.0792648 + 0.137291i
\(298\) −8.00000 13.8564i −0.463428 0.802680i
\(299\) 3.63397 6.29423i 0.210158 0.364005i
\(300\) 0 0
\(301\) 6.23205 + 17.9904i 0.359209 + 1.03695i
\(302\) −3.60770 −0.207600
\(303\) 5.36603 9.29423i 0.308270 0.533939i
\(304\) 1.32051 + 2.28719i 0.0757363 + 0.131179i
\(305\) 0 0
\(306\) −2.46410 + 4.26795i −0.140863 + 0.243982i
\(307\) 7.87564 0.449487 0.224743 0.974418i \(-0.427846\pi\)
0.224743 + 0.974418i \(0.427846\pi\)
\(308\) −10.3923 2.00000i −0.592157 0.113961i
\(309\) −1.19615 −0.0680467
\(310\) 0 0
\(311\) 7.56218 + 13.0981i 0.428812 + 0.742724i 0.996768 0.0803351i \(-0.0255990\pi\)
−0.567956 + 0.823059i \(0.692266\pi\)
\(312\) 7.26795 + 12.5885i 0.411467 + 0.712681i
\(313\) 2.33013 4.03590i 0.131707 0.228122i −0.792628 0.609706i \(-0.791288\pi\)
0.924335 + 0.381583i \(0.124621\pi\)
\(314\) −10.5359 −0.594575
\(315\) 0 0
\(316\) −19.6077 −1.10302
\(317\) 15.2224 26.3660i 0.854977 1.48086i −0.0216894 0.999765i \(-0.506905\pi\)
0.876666 0.481099i \(-0.159762\pi\)
\(318\) 3.07180 + 5.32051i 0.172258 + 0.298359i
\(319\) 8.46410 + 14.6603i 0.473899 + 0.820817i
\(320\) 0 0
\(321\) 8.19615 0.457465
\(322\) −1.60770 + 1.85641i −0.0895933 + 0.103453i
\(323\) 16.5885 0.923006
\(324\) 0.732051 1.26795i 0.0406695 0.0704416i
\(325\) 0 0
\(326\) 2.14359 + 3.71281i 0.118723 + 0.205634i
\(327\) −5.50000 + 9.52628i −0.304151 + 0.526804i
\(328\) 6.92820 0.382546
\(329\) 5.19615 + 1.00000i 0.286473 + 0.0551318i
\(330\) 0 0
\(331\) −10.9641 + 18.9904i −0.602642 + 1.04381i 0.389778 + 0.920909i \(0.372552\pi\)
−0.992419 + 0.122897i \(0.960782\pi\)
\(332\) 6.67949 + 11.5692i 0.366585 + 0.634943i
\(333\) 3.59808 + 6.23205i 0.197173 + 0.341514i
\(334\) 0.124356 0.215390i 0.00680444 0.0117856i
\(335\) 0 0
\(336\) 0.928203 + 2.67949i 0.0506376 + 0.146178i
\(337\) 33.9808 1.85105 0.925525 0.378686i \(-0.123624\pi\)
0.925525 + 0.378686i \(0.123624\pi\)
\(338\) 7.26795 12.5885i 0.395324 0.684722i
\(339\) −2.46410 4.26795i −0.133832 0.231803i
\(340\) 0 0
\(341\) 8.83013 15.2942i 0.478178 0.828229i
\(342\) 1.80385 0.0975409
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 18.2487 0.983905
\(345\) 0 0
\(346\) −7.85641 13.6077i −0.422363 0.731554i
\(347\) −17.4641 30.2487i −0.937522 1.62384i −0.770074 0.637955i \(-0.779781\pi\)
−0.167449 0.985881i \(-0.553553\pi\)
\(348\) 4.53590 7.85641i 0.243150 0.421148i
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 0 0
\(351\) −5.73205 −0.305954
\(352\) −8.00000 + 13.8564i −0.426401 + 0.738549i
\(353\) 10.5622 + 18.2942i 0.562168 + 0.973704i 0.997307 + 0.0733402i \(0.0233659\pi\)
−0.435139 + 0.900363i \(0.643301\pi\)
\(354\) 3.73205 + 6.46410i 0.198356 + 0.343563i
\(355\) 0 0
\(356\) 13.3590 0.708025
\(357\) 17.4904 + 3.36603i 0.925689 + 0.178149i
\(358\) 7.32051 0.386901
\(359\) 2.36603 4.09808i 0.124874 0.216288i −0.796810 0.604230i \(-0.793481\pi\)
0.921684 + 0.387942i \(0.126814\pi\)
\(360\) 0 0
\(361\) 6.46410 + 11.1962i 0.340216 + 0.589271i
\(362\) 3.77757 6.54294i 0.198545 0.343889i
\(363\) −3.53590 −0.185587
\(364\) 14.5359 16.7846i 0.761888 0.879753i
\(365\) 0 0
\(366\) 1.46410 2.53590i 0.0765298 0.132554i
\(367\) 0.401924 + 0.696152i 0.0209803 + 0.0363389i 0.876325 0.481721i \(-0.159988\pi\)
−0.855345 + 0.518059i \(0.826655\pi\)
\(368\) −0.679492 1.17691i −0.0354210 0.0613509i
\(369\) −1.36603 + 2.36603i −0.0711124 + 0.123170i
\(370\) 0 0
\(371\) 14.5359 16.7846i 0.754666 0.871414i
\(372\) −9.46410 −0.490691
\(373\) −9.25833 + 16.0359i −0.479378 + 0.830307i −0.999720 0.0236505i \(-0.992471\pi\)
0.520342 + 0.853958i \(0.325804\pi\)
\(374\) 6.73205 + 11.6603i 0.348106 + 0.602937i
\(375\) 0 0
\(376\) 2.53590 4.39230i 0.130779 0.226516i
\(377\) −35.5167 −1.82920
\(378\) 1.90192 + 0.366025i 0.0978244 + 0.0188263i
\(379\) −28.3205 −1.45473 −0.727363 0.686253i \(-0.759255\pi\)
−0.727363 + 0.686253i \(0.759255\pi\)
\(380\) 0 0
\(381\) 7.59808 + 13.1603i 0.389261 + 0.674220i
\(382\) 1.80385 + 3.12436i 0.0922929 + 0.159856i
\(383\) 5.66025 9.80385i 0.289225 0.500953i −0.684400 0.729107i \(-0.739936\pi\)
0.973625 + 0.228154i \(0.0732689\pi\)
\(384\) 10.1436 0.517638
\(385\) 0 0
\(386\) −6.73205 −0.342652
\(387\) −3.59808 + 6.23205i −0.182900 + 0.316793i
\(388\) −0.784610 1.35898i −0.0398325 0.0689920i
\(389\) −18.2942 31.6865i −0.927554 1.60657i −0.787401 0.616441i \(-0.788574\pi\)
−0.140153 0.990130i \(-0.544760\pi\)
\(390\) 0 0
\(391\) −8.53590 −0.431679
\(392\) −13.9474 + 10.9808i −0.704452 + 0.554612i
\(393\) 8.53590 0.430579
\(394\) 6.46410 11.1962i 0.325657 0.564054i
\(395\) 0 0
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) −10.4019 + 18.0167i −0.522058 + 0.904230i 0.477613 + 0.878570i \(0.341502\pi\)
−0.999671 + 0.0256600i \(0.991831\pi\)
\(398\) −16.1051 −0.807277
\(399\) −2.13397 6.16025i −0.106832 0.308398i
\(400\) 0 0
\(401\) −2.19615 + 3.80385i −0.109671 + 0.189955i −0.915637 0.402006i \(-0.868313\pi\)
0.805966 + 0.591962i \(0.201646\pi\)
\(402\) −0.973721 1.68653i −0.0485648 0.0841166i
\(403\) 18.5263 + 32.0885i 0.922860 + 1.59844i
\(404\) −7.85641 + 13.6077i −0.390871 + 0.677008i
\(405\) 0 0
\(406\) 11.7846 + 2.26795i 0.584860 + 0.112556i
\(407\) 19.6603 0.974523
\(408\) 8.53590 14.7846i 0.422590 0.731947i
\(409\) −15.4282 26.7224i −0.762876 1.32134i −0.941362 0.337397i \(-0.890454\pi\)
0.178487 0.983942i \(-0.442880\pi\)
\(410\) 0 0
\(411\) −4.09808 + 7.09808i −0.202143 + 0.350122i
\(412\) 1.75129 0.0862798
\(413\) 17.6603 20.3923i 0.869004 1.00344i
\(414\) −0.928203 −0.0456187
\(415\) 0 0
\(416\) −16.7846 29.0718i −0.822933 1.42536i
\(417\) 3.96410 + 6.86603i 0.194123 + 0.336231i
\(418\) 2.46410 4.26795i 0.120523 0.208752i
\(419\) −28.5359 −1.39407 −0.697035 0.717037i \(-0.745498\pi\)
−0.697035 + 0.717037i \(0.745498\pi\)
\(420\) 0 0
\(421\) 13.9282 0.678819 0.339410 0.940639i \(-0.389773\pi\)
0.339410 + 0.940639i \(0.389773\pi\)
\(422\) 7.66025 13.2679i 0.372895 0.645874i
\(423\) 1.00000 + 1.73205i 0.0486217 + 0.0842152i
\(424\) −10.6410 18.4308i −0.516773 0.895078i
\(425\) 0 0
\(426\) 3.07180 0.148829
\(427\) −10.3923 2.00000i −0.502919 0.0967868i
\(428\) −12.0000 −0.580042
\(429\) −7.83013 + 13.5622i −0.378042 + 0.654788i
\(430\) 0 0
\(431\) 8.66025 + 15.0000i 0.417150 + 0.722525i 0.995651 0.0931566i \(-0.0296957\pi\)
−0.578502 + 0.815681i \(0.696362\pi\)
\(432\) −0.535898 + 0.928203i −0.0257834 + 0.0446582i
\(433\) −4.80385 −0.230858 −0.115429 0.993316i \(-0.536824\pi\)
−0.115429 + 0.993316i \(0.536824\pi\)
\(434\) −4.09808 11.8301i −0.196714 0.567864i
\(435\) 0 0
\(436\) 8.05256 13.9474i 0.385648 0.667961i
\(437\) 1.56218 + 2.70577i 0.0747291 + 0.129435i
\(438\) 1.70577 + 2.95448i 0.0815049 + 0.141171i
\(439\) −3.73205 + 6.46410i −0.178121 + 0.308515i −0.941237 0.337747i \(-0.890335\pi\)
0.763116 + 0.646262i \(0.223669\pi\)
\(440\) 0 0
\(441\) −1.00000 6.92820i −0.0476190 0.329914i
\(442\) −28.2487 −1.34365
\(443\) 1.26795 2.19615i 0.0602421 0.104342i −0.834331 0.551263i \(-0.814146\pi\)
0.894574 + 0.446921i \(0.147479\pi\)
\(444\) −5.26795 9.12436i −0.250006 0.433023i
\(445\) 0 0
\(446\) −0.143594 + 0.248711i −0.00679935 + 0.0117768i
\(447\) −21.8564 −1.03377
\(448\) 1.85641 + 5.35898i 0.0877070 + 0.253188i
\(449\) −8.14359 −0.384320 −0.192160 0.981364i \(-0.561549\pi\)
−0.192160 + 0.981364i \(0.561549\pi\)
\(450\) 0 0
\(451\) 3.73205 + 6.46410i 0.175735 + 0.304383i
\(452\) 3.60770 + 6.24871i 0.169692 + 0.293915i
\(453\) −2.46410 + 4.26795i −0.115774 + 0.200526i
\(454\) 11.4641 0.538037
\(455\) 0 0
\(456\) −6.24871 −0.292623
\(457\) 0.330127 0.571797i 0.0154427 0.0267475i −0.858201 0.513314i \(-0.828418\pi\)
0.873643 + 0.486567i \(0.161751\pi\)
\(458\) −1.09808 1.90192i −0.0513097 0.0888711i
\(459\) 3.36603 + 5.83013i 0.157113 + 0.272127i
\(460\) 0 0
\(461\) −34.9808 −1.62922 −0.814608 0.580012i \(-0.803048\pi\)
−0.814608 + 0.580012i \(0.803048\pi\)
\(462\) 3.46410 4.00000i 0.161165 0.186097i
\(463\) −22.2679 −1.03488 −0.517440 0.855720i \(-0.673115\pi\)
−0.517440 + 0.855720i \(0.673115\pi\)
\(464\) −3.32051 + 5.75129i −0.154151 + 0.266997i
\(465\) 0 0
\(466\) 6.33975 + 10.9808i 0.293683 + 0.508674i
\(467\) −13.9282 + 24.1244i −0.644520 + 1.11634i 0.339892 + 0.940465i \(0.389610\pi\)
−0.984412 + 0.175877i \(0.943724\pi\)
\(468\) 8.39230 0.387934
\(469\) −4.60770 + 5.32051i −0.212764 + 0.245678i
\(470\) 0 0
\(471\) −7.19615 + 12.4641i −0.331581 + 0.574315i
\(472\) −12.9282 22.3923i −0.595069 1.03069i
\(473\) 9.83013 + 17.0263i 0.451990 + 0.782869i
\(474\) 4.90192 8.49038i 0.225153 0.389976i
\(475\) 0 0
\(476\) −25.6077 4.92820i −1.17373 0.225884i
\(477\) 8.39230 0.384257
\(478\) 7.66025 13.2679i 0.350372 0.606862i
\(479\) 16.3923 + 28.3923i 0.748984 + 1.29728i 0.948310 + 0.317344i \(0.102791\pi\)
−0.199327 + 0.979933i \(0.563876\pi\)
\(480\) 0 0
\(481\) −20.6244 + 35.7224i −0.940390 + 1.62880i
\(482\) −4.78461 −0.217933
\(483\) 1.09808 + 3.16987i 0.0499642 + 0.144234i
\(484\) 5.17691 0.235314
\(485\) 0 0
\(486\) 0.366025 + 0.633975i 0.0166032 + 0.0287577i
\(487\) −15.7942 27.3564i −0.715705 1.23964i −0.962687 0.270617i \(-0.912772\pi\)
0.246982 0.969020i \(-0.420561\pi\)
\(488\) −5.07180 + 8.78461i −0.229589 + 0.397661i
\(489\) 5.85641 0.264836
\(490\) 0 0
\(491\) 10.2487 0.462518 0.231259 0.972892i \(-0.425716\pi\)
0.231259 + 0.972892i \(0.425716\pi\)
\(492\) 2.00000 3.46410i 0.0901670 0.156174i
\(493\) 20.8564 + 36.1244i 0.939325 + 1.62696i
\(494\) 5.16987 + 8.95448i 0.232604 + 0.402881i
\(495\) 0 0
\(496\) 6.92820 0.311086
\(497\) −3.63397 10.4904i −0.163006 0.470558i
\(498\) −6.67949 −0.299315
\(499\) 10.2321 17.7224i 0.458050 0.793365i −0.540808 0.841146i \(-0.681882\pi\)
0.998858 + 0.0477808i \(0.0152149\pi\)
\(500\) 0 0
\(501\) −0.169873 0.294229i −0.00758937 0.0131452i
\(502\) 2.41154 4.17691i 0.107632 0.186425i
\(503\) 6.39230 0.285019 0.142509 0.989793i \(-0.454483\pi\)
0.142509 + 0.989793i \(0.454483\pi\)
\(504\) −6.58846 1.26795i −0.293473 0.0564789i
\(505\) 0 0
\(506\) −1.26795 + 2.19615i −0.0563672 + 0.0976309i
\(507\) −9.92820 17.1962i −0.440927 0.763708i
\(508\) −11.1244 19.2679i −0.493563 0.854877i
\(509\) −5.73205 + 9.92820i −0.254069 + 0.440060i −0.964642 0.263563i \(-0.915102\pi\)
0.710573 + 0.703623i \(0.248436\pi\)
\(510\) 0 0
\(511\) 8.07180 9.32051i 0.357075 0.412315i
\(512\) −11.7128 −0.517638
\(513\) 1.23205 2.13397i 0.0543964 0.0942173i
\(514\) −4.26795 7.39230i −0.188251 0.326061i
\(515\) 0 0
\(516\) 5.26795 9.12436i 0.231909 0.401677i
\(517\) 5.46410 0.240311
\(518\) 9.12436 10.5359i 0.400901 0.462921i
\(519\) −21.4641 −0.942169
\(520\) 0 0
\(521\) −0.732051 1.26795i −0.0320717 0.0555499i 0.849544 0.527518i \(-0.176877\pi\)
−0.881616 + 0.471968i \(0.843544\pi\)
\(522\) 2.26795 + 3.92820i 0.0992654 + 0.171933i
\(523\) −12.1340 + 21.0167i −0.530582 + 0.918994i 0.468782 + 0.883314i \(0.344693\pi\)
−0.999363 + 0.0356803i \(0.988640\pi\)
\(524\) −12.4974 −0.545952
\(525\) 0 0
\(526\) −9.07180 −0.395549
\(527\) 21.7583 37.6865i 0.947808 1.64165i
\(528\) 1.46410 + 2.53590i 0.0637168 + 0.110361i
\(529\) 10.6962 + 18.5263i 0.465050 + 0.805490i
\(530\) 0 0
\(531\) 10.1962 0.442475
\(532\) 3.12436 + 9.01924i 0.135458 + 0.391034i
\(533\) −15.6603 −0.678321
\(534\) −3.33975 + 5.78461i −0.144525 + 0.250325i
\(535\) 0 0
\(536\) 3.37307 + 5.84232i 0.145694 + 0.252350i
\(537\) 5.00000 8.66025i 0.215766 0.373718i
\(538\) 14.2487 0.614306
\(539\) −17.7583 7.09808i −0.764905 0.305736i
\(540\) 0 0
\(541\) 17.8923 30.9904i 0.769250 1.33238i −0.168720 0.985664i \(-0.553963\pi\)
0.937970 0.346716i \(-0.112703\pi\)
\(542\) 6.19615 + 10.7321i 0.266148 + 0.460981i
\(543\) −5.16025 8.93782i −0.221448 0.383559i
\(544\) −19.7128 + 34.1436i −0.845180 + 1.46389i
\(545\) 0 0
\(546\) 3.63397 + 10.4904i 0.155520 + 0.448947i
\(547\) −22.2487 −0.951286 −0.475643 0.879638i \(-0.657785\pi\)
−0.475643 + 0.879638i \(0.657785\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) −2.00000 3.46410i −0.0853579 0.147844i
\(550\) 0 0
\(551\) 7.63397 13.2224i 0.325218 0.563295i
\(552\) 3.21539 0.136856
\(553\) −34.7942 6.69615i −1.47960 0.284749i
\(554\) 1.94744 0.0827388
\(555\) 0 0
\(556\) −5.80385 10.0526i −0.246138 0.426323i
\(557\) −13.3923 23.1962i −0.567450 0.982853i −0.996817 0.0797224i \(-0.974597\pi\)
0.429367 0.903130i \(-0.358737\pi\)
\(558\) 2.36603 4.09808i 0.100162 0.173485i
\(559\) −41.2487 −1.74463
\(560\) 0 0
\(561\) 18.3923 0.776524
\(562\) −5.07180 + 8.78461i −0.213941 + 0.370556i
\(563\) −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i \(-0.290503\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(564\) −1.46410 2.53590i −0.0616498 0.106781i
\(565\) 0 0
\(566\) 0.0910347 0.00382647
\(567\) 1.73205 2.00000i 0.0727393 0.0839921i
\(568\) −10.6410 −0.446487
\(569\) 13.2224 22.9019i 0.554313 0.960099i −0.443643 0.896203i \(-0.646314\pi\)
0.997957 0.0638952i \(-0.0203523\pi\)
\(570\) 0 0
\(571\) −19.6962 34.1147i −0.824258 1.42766i −0.902485 0.430722i \(-0.858259\pi\)
0.0782265 0.996936i \(-0.475074\pi\)
\(572\) 11.4641 19.8564i 0.479338 0.830238i
\(573\) 4.92820 0.205879
\(574\) 5.19615 + 1.00000i 0.216883 + 0.0417392i
\(575\) 0 0
\(576\) −1.07180 + 1.85641i −0.0446582 + 0.0773503i
\(577\) 5.66987 + 9.82051i 0.236040 + 0.408833i 0.959574 0.281455i \(-0.0908171\pi\)
−0.723534 + 0.690288i \(0.757484\pi\)
\(578\) 10.3660 + 17.9545i 0.431170 + 0.746808i
\(579\) −4.59808 + 7.96410i −0.191090 + 0.330977i
\(580\) 0 0
\(581\) 7.90192 + 22.8109i 0.327827 + 0.946355i
\(582\) 0.784610 0.0325231
\(583\) 11.4641 19.8564i 0.474795 0.822368i
\(584\) −5.90897 10.2346i −0.244515 0.423512i
\(585\) 0 0
\(586\) −1.85641 + 3.21539i −0.0766874 + 0.132827i
\(587\) −37.2679 −1.53821 −0.769106 0.639121i \(-0.779298\pi\)
−0.769106 + 0.639121i \(0.779298\pi\)
\(588\) 1.46410 + 10.1436i 0.0603785 + 0.418315i
\(589\) −15.9282 −0.656310
\(590\) 0 0
\(591\) −8.83013 15.2942i −0.363223 0.629121i
\(592\) 3.85641 + 6.67949i 0.158497 + 0.274525i
\(593\) −18.9545 + 32.8301i −0.778367 + 1.34817i 0.154515 + 0.987990i \(0.450619\pi\)
−0.932882 + 0.360181i \(0.882715\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) 32.0000 1.31077
\(597\) −11.0000 + 19.0526i −0.450200 + 0.779769i
\(598\) −2.66025 4.60770i −0.108786 0.188423i
\(599\) −5.12436 8.87564i −0.209375 0.362649i 0.742142 0.670242i \(-0.233810\pi\)
−0.951518 + 0.307593i \(0.900476\pi\)
\(600\) 0 0
\(601\) −13.9282 −0.568143 −0.284072 0.958803i \(-0.591685\pi\)
−0.284072 + 0.958803i \(0.591685\pi\)
\(602\) 13.6865 + 2.63397i 0.557821 + 0.107353i
\(603\) −2.66025 −0.108334
\(604\) 3.60770 6.24871i 0.146795 0.254256i
\(605\) 0 0
\(606\) −3.92820 6.80385i −0.159572 0.276387i
\(607\) −3.59808 + 6.23205i −0.146041 + 0.252951i −0.929761 0.368164i \(-0.879987\pi\)
0.783720 + 0.621115i \(0.213320\pi\)
\(608\) 14.4308 0.585245
\(609\) 10.7321 12.3923i 0.434885 0.502162i
\(610\) 0 0
\(611\) −5.73205 + 9.92820i −0.231894 + 0.401652i
\(612\) −4.92820 8.53590i −0.199211 0.345043i
\(613\) −6.53590 11.3205i −0.263982 0.457231i 0.703314 0.710879i \(-0.251703\pi\)
−0.967297 + 0.253648i \(0.918369\pi\)
\(614\) 2.88269 4.99296i 0.116336 0.201499i
\(615\) 0 0
\(616\) −12.0000 + 13.8564i −0.483494 + 0.558291i
\(617\) −12.2487 −0.493115 −0.246557 0.969128i \(-0.579299\pi\)
−0.246557 + 0.969128i \(0.579299\pi\)
\(618\) −0.437822 + 0.758330i −0.0176118 + 0.0305045i
\(619\) 21.9641 + 38.0429i 0.882812 + 1.52907i 0.848201 + 0.529674i \(0.177686\pi\)
0.0346105 + 0.999401i \(0.488981\pi\)
\(620\) 0 0
\(621\) −0.633975 + 1.09808i −0.0254405 + 0.0440643i
\(622\) 11.0718 0.443939
\(623\) 23.7058 + 4.56218i 0.949752 + 0.182780i
\(624\) −6.14359 −0.245941
\(625\) 0 0
\(626\) −1.70577 2.95448i −0.0681763 0.118085i
\(627\) −3.36603 5.83013i −0.134426 0.232833i
\(628\) 10.5359 18.2487i 0.420428 0.728203i
\(629\) 48.4449 1.93162
\(630\) 0 0
\(631\) 7.21539 0.287240 0.143620 0.989633i \(-0.454126\pi\)
0.143620 + 0.989633i \(0.454126\pi\)
\(632\) −16.9808 + 29.4115i −0.675458 + 1.16993i
\(633\) −10.4641 18.1244i −0.415911 0.720378i
\(634\) −11.1436 19.3013i −0.442569 0.766551i
\(635\) 0 0
\(636\) −12.2872 −0.487219
\(637\) 31.5263 24.8205i 1.24912 0.983424i
\(638\) 12.3923 0.490616
\(639\) 2.09808 3.63397i 0.0829986 0.143758i
\(640\) 0 0
\(641\) −7.09808 12.2942i −0.280357 0.485593i 0.691116 0.722744i \(-0.257120\pi\)
−0.971473 + 0.237151i \(0.923786\pi\)
\(642\) 3.00000 5.19615i 0.118401 0.205076i
\(643\) 40.5167 1.59782 0.798911 0.601450i \(-0.205410\pi\)
0.798911 + 0.601450i \(0.205410\pi\)
\(644\) −1.60770 4.64102i −0.0633521 0.182882i
\(645\) 0 0
\(646\) 6.07180 10.5167i 0.238892 0.413772i
\(647\) 18.9545 + 32.8301i 0.745178 + 1.29069i 0.950112 + 0.311910i \(0.100969\pi\)
−0.204934 + 0.978776i \(0.565698\pi\)
\(648\) −1.26795 2.19615i −0.0498097 0.0862730i
\(649\) 13.9282 24.1244i 0.546730 0.946964i
\(650\) 0 0
\(651\) −16.7942 3.23205i −0.658218 0.126674i
\(652\) −8.57437 −0.335798
\(653\) −6.70577 + 11.6147i −0.262417 + 0.454520i −0.966884 0.255217i \(-0.917853\pi\)
0.704467 + 0.709737i \(0.251186\pi\)
\(654\) 4.02628 + 6.97372i 0.157440 + 0.272694i
\(655\) 0 0
\(656\) −1.46410 + 2.53590i −0.0571636 + 0.0990102i
\(657\) 4.66025 0.181814
\(658\) 2.53590 2.92820i 0.0988596 0.114153i
\(659\) −10.9282 −0.425702 −0.212851 0.977085i \(-0.568275\pi\)
−0.212851 + 0.977085i \(0.568275\pi\)
\(660\) 0 0
\(661\) −1.76795 3.06218i −0.0687653 0.119105i 0.829593 0.558369i \(-0.188573\pi\)
−0.898358 + 0.439264i \(0.855239\pi\)
\(662\) 8.02628 + 13.9019i 0.311950 + 0.540314i
\(663\) −19.2942 + 33.4186i −0.749326 + 1.29787i
\(664\) 23.1384 0.897946
\(665\) 0 0
\(666\) 5.26795 0.204129
\(667\) −3.92820 + 6.80385i −0.152101 + 0.263446i
\(668\) 0.248711 + 0.430781i 0.00962293 + 0.0166674i
\(669\) 0.196152 + 0.339746i 0.00758369 + 0.0131353i
\(670\) 0 0
\(671\) −10.9282 −0.421879
\(672\) 15.2154 + 2.92820i 0.586946 + 0.112958i
\(673\) 44.6603 1.72153 0.860763 0.509006i \(-0.169987\pi\)
0.860763 + 0.509006i \(0.169987\pi\)
\(674\) 12.4378 21.5429i 0.479087 0.829803i
\(675\) 0 0
\(676\) 14.5359 + 25.1769i 0.559073 + 0.968343i
\(677\) −4.43782 + 7.68653i −0.170559 + 0.295417i −0.938616 0.344965i \(-0.887891\pi\)
0.768056 + 0.640382i \(0.221224\pi\)
\(678\) −3.60770 −0.138553
\(679\) −0.928203 2.67949i −0.0356212 0.102829i
\(680\) 0 0
\(681\) 7.83013 13.5622i 0.300051 0.519704i
\(682\) −6.46410 11.1962i −0.247523 0.428723i
\(683\) 5.02628 + 8.70577i 0.192325 + 0.333117i 0.946020 0.324107i \(-0.105064\pi\)
−0.753695 + 0.657224i \(0.771730\pi\)
\(684\) −1.80385 + 3.12436i −0.0689718 + 0.119463i
\(685\) 0 0
\(686\) −12.0455 + 6.22243i −0.459900 + 0.237574i
\(687\) −3.00000 −0.114457
\(688\) −3.85641 + 6.67949i −0.147024 + 0.254653i
\(689\) 24.0526 + 41.6603i 0.916330 + 1.58713i
\(690\) 0 0
\(691\) 9.42820 16.3301i 0.358666 0.621227i −0.629072 0.777347i \(-0.716565\pi\)
0.987738 + 0.156119i \(0.0498985\pi\)
\(692\) 31.4256 1.19462
\(693\) −2.36603 6.83013i −0.0898779 0.259455i
\(694\) −25.5692 −0.970594
\(695\) 0 0
\(696\) −7.85641 13.6077i −0.297796 0.515798i
\(697\) 9.19615 + 15.9282i 0.348329 + 0.603324i
\(698\) 8.05256 13.9474i 0.304794 0.527918i
\(699\) 17.3205 0.655122
\(700\) 0 0
\(701\) 22.5885 0.853154 0.426577 0.904451i \(-0.359719\pi\)
0.426577 + 0.904451i \(0.359719\pi\)
\(702\) −2.09808 + 3.63397i −0.0791868 + 0.137156i
\(703\) −8.86603 15.3564i −0.334388 0.579178i
\(704\) 2.92820 + 5.07180i 0.110361 + 0.191151i
\(705\) 0 0
\(706\) 15.4641 0.581999
\(707\) −18.5885 + 21.4641i −0.699091 + 0.807241i
\(708\) −14.9282 −0.561036
\(709\) 7.46410 12.9282i 0.280320 0.485529i −0.691143 0.722718i \(-0.742893\pi\)
0.971464 + 0.237189i \(0.0762260\pi\)
\(710\) 0 0
\(711\) −6.69615 11.5981i −0.251125 0.434962i
\(712\) 11.5692 20.0385i 0.433575 0.750974i
\(713\) 8.19615 0.306948
\(714\) 8.53590 9.85641i 0.319448 0.368867i
\(715\) 0 0
\(716\) −7.32051 + 12.6795i −0.273580 + 0.473855i
\(717\) −10.4641 18.1244i −0.390789 0.676866i
\(718\) −1.73205 3.00000i −0.0646396 0.111959i
\(719\) 13.7321 23.7846i 0.512119 0.887016i −0.487782 0.872965i \(-0.662194\pi\)
0.999901 0.0140509i \(-0.00447269\pi\)
\(720\) 0 0
\(721\) 3.10770 + 0.598076i 0.115737 + 0.0222735i
\(722\) 9.46410 0.352217
\(723\) −3.26795 + 5.66025i −0.121536 + 0.210507i
\(724\) 7.55514 + 13.0859i 0.280784 + 0.486333i
\(725\) 0 0
\(726\) −1.29423 + 2.24167i −0.0480333 + 0.0831962i
\(727\) 30.6603 1.13713 0.568563 0.822640i \(-0.307500\pi\)
0.568563 + 0.822640i \(0.307500\pi\)
\(728\) −12.5885 36.3397i −0.466559 1.34684i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 24.2224 + 41.9545i 0.895899 + 1.55174i
\(732\) 2.92820 + 5.07180i 0.108230 + 0.187459i
\(733\) −9.33013 + 16.1603i −0.344616 + 0.596893i −0.985284 0.170926i \(-0.945324\pi\)
0.640668 + 0.767818i \(0.278658\pi\)
\(734\) 0.588457 0.0217204
\(735\) 0 0
\(736\) −7.42563 −0.273712
\(737\) −3.63397 + 6.29423i −0.133859 + 0.231851i
\(738\) 1.00000 + 1.73205i 0.0368105 + 0.0637577i
\(739\) 6.89230 + 11.9378i 0.253538 + 0.439140i 0.964497 0.264093i \(-0.0850725\pi\)
−0.710960 + 0.703233i \(0.751739\pi\)
\(740\) 0 0
\(741\) 14.1244 0.518871
\(742\) −5.32051 15.3590i −0.195322 0.563846i
\(743\) −49.9090 −1.83098 −0.915491 0.402338i \(-0.868198\pi\)
−0.915491 + 0.402338i \(0.868198\pi\)
\(744\) −8.19615 + 14.1962i −0.300486 + 0.520456i
\(745\) 0 0
\(746\) 6.77757 + 11.7391i 0.248144 + 0.429799i
\(747\) −4.56218 + 7.90192i −0.166921 + 0.289116i
\(748\) −26.9282 −0.984593
\(749\) −21.2942 4.09808i −0.778074 0.149740i
\(750\) 0 0
\(751\) −15.9641 + 27.6506i −0.582538 + 1.00899i 0.412639 + 0.910895i \(0.364607\pi\)
−0.995177 + 0.0980914i \(0.968726\pi\)
\(752\) 1.07180 + 1.85641i 0.0390844 + 0.0676962i
\(753\) −3.29423 5.70577i −0.120048 0.207930i
\(754\) −13.0000 + 22.5167i −0.473432 + 0.820008i
\(755\) 0 0
\(756\) −2.53590 + 2.92820i −0.0922297 + 0.106498i
\(757\) 0.143594 0.00521900 0.00260950 0.999997i \(-0.499169\pi\)
0.00260950 + 0.999997i \(0.499169\pi\)
\(758\) −10.3660 + 17.9545i −0.376511 + 0.652136i
\(759\) 1.73205 + 3.00000i 0.0628695 + 0.108893i
\(760\) 0 0
\(761\) −21.6340 + 37.4711i −0.784231 + 1.35833i 0.145226 + 0.989398i \(0.453609\pi\)
−0.929457 + 0.368929i \(0.879724\pi\)
\(762\) 11.1244 0.402993
\(763\) 19.0526 22.0000i 0.689749 0.796453i
\(764\) −7.21539 −0.261044
\(765\) 0 0
\(766\) −4.14359 7.17691i −0.149714 0.259312i
\(767\) 29.2224 + 50.6147i 1.05516 + 1.82759i
\(768\) 5.85641 10.1436i 0.211325 0.366025i
\(769\) 17.6795 0.637539 0.318769 0.947832i \(-0.396730\pi\)
0.318769 + 0.947832i \(0.396730\pi\)
\(770\) 0 0
\(771\) −11.6603 −0.419934
\(772\) 6.73205 11.6603i 0.242292 0.419662i
\(773\) −0.758330 1.31347i −0.0272752 0.0472421i 0.852066 0.523435i \(-0.175350\pi\)
−0.879341 + 0.476193i \(0.842016\pi\)
\(774\) 2.63397 + 4.56218i 0.0946763 + 0.163984i
\(775\) 0 0
\(776\) −2.71797 −0.0975694
\(777\) −6.23205 17.9904i −0.223574 0.645401i
\(778\) −26.7846 −0.960275
\(779\) 3.36603 5.83013i 0.120600 0.208886i
\(780\) 0 0
\(781\) −5.73205 9.92820i −0.205109 0.355259i
\(782\) −3.12436 + 5.41154i −0.111727 + 0.193516i
\(783\) 6.19615 0.221432
\(784\) −1.07180 7.42563i −0.0382785 0.265201i
\(785\) 0 0
\(786\) 3.12436 5.41154i 0.111442 0.193023i
\(787\) 3.26795 + 5.66025i 0.116490 + 0.201766i 0.918374 0.395713i \(-0.129502\pi\)
−0.801885 + 0.597479i \(0.796169\pi\)
\(788\) 12.9282 + 22.3923i 0.460548 + 0.797693i
\(789\) −6.19615 + 10.7321i −0.220589 + 0.382071i
\(790\) 0 0
\(791\) 4.26795 + 12.3205i 0.151751 + 0.438067i
\(792\) −6.92820 −0.246183
\(793\) 11.4641 19.8564i 0.407102 0.705122i
\(794\) 7.61474 + 13.1891i 0.270237 + 0.468064i
\(795\) 0 0
\(796\) 16.1051 27.8949i 0.570831 0.988708i
\(797\) 42.0526 1.48958 0.744789 0.667300i \(-0.232550\pi\)
0.744789 + 0.667300i \(0.232550\pi\)
\(798\) −4.68653 0.901924i −0.165901 0.0319278i
\(799\) 13.4641 0.476326
\(800\) 0 0
\(801\) 4.56218 + 7.90192i 0.161197 + 0.279201i
\(802\) 1.60770 + 2.78461i 0.0567697 + 0.0983280i
\(803\) 6.36603 11.0263i 0.224652 0.389109i
\(804\) 3.89488 0.137362
\(805\) 0 0
\(806\) 27.1244 0.955415
\(807\) 9.73205 16.8564i 0.342584 0.593374i
\(808\) 13.6077 + 23.5692i 0.478717 + 0.829162i
\(809\) 14.8564 + 25.7321i 0.522323 + 0.904691i 0.999663 + 0.0259716i \(0.00826796\pi\)
−0.477339 + 0.878719i \(0.658399\pi\)
\(810\) 0 0
\(811\) 3.46410 0.121641 0.0608205 0.998149i \(-0.480628\pi\)
0.0608205 + 0.998149i \(0.480628\pi\)
\(812\) −15.7128 + 18.1436i −0.551412 + 0.636715i
\(813\) 16.9282 0.593698
\(814\) 7.19615 12.4641i 0.252225 0.436867i
\(815\) 0 0
\(816\) 3.60770 + 6.24871i 0.126295 + 0.218749i
\(817\) 8.86603 15.3564i 0.310183 0.537253i
\(818\) −22.5885 −0.789787
\(819\) 14.8923 + 2.86603i 0.520379 + 0.100147i
\(820\) 0 0
\(821\) −9.75833 + 16.9019i −0.340568 + 0.589881i −0.984538 0.175169i \(-0.943953\pi\)
0.643970 + 0.765051i \(0.277286\pi\)
\(822\) 3.00000 + 5.19615i 0.104637 + 0.181237i
\(823\) −11.5885 20.0718i −0.403948 0.699659i 0.590250 0.807220i \(-0.299029\pi\)
−0.994198 + 0.107561i \(0.965696\pi\)
\(824\) 1.51666 2.62693i 0.0528354 0.0915135i
\(825\) 0 0
\(826\) −6.46410 18.6603i −0.224915 0.649273i
\(827\) 52.2487 1.81687 0.908433 0.418031i \(-0.137280\pi\)
0.908433 + 0.418031i \(0.137280\pi\)
\(828\) 0.928203 1.60770i 0.0322573 0.0558713i
\(829\) 12.6962 + 21.9904i 0.440956 + 0.763758i 0.997761 0.0668857i \(-0.0213063\pi\)
−0.556805 + 0.830643i \(0.687973\pi\)
\(830\) 0 0
\(831\) 1.33013 2.30385i 0.0461416 0.0799196i
\(832\) −12.2872 −0.425982
\(833\) −43.7583 17.4904i −1.51614 0.606006i
\(834\) 5.80385 0.200971
\(835\) 0 0
\(836\) 4.92820 + 8.53590i 0.170445 + 0.295220i
\(837\) −3.23205 5.59808i −0.111716 0.193498i
\(838\) −10.4449 + 18.0910i −0.360812 + 0.624944i
\(839\) −40.4449 −1.39631 −0.698156 0.715946i \(-0.745996\pi\)
−0.698156 + 0.715946i \(0.745996\pi\)
\(840\) 0 0
\(841\) 9.39230 0.323873
\(842\) 5.09808 8.83013i 0.175691 0.304306i
\(843\) 6.92820 + 12.0000i 0.238620 + 0.413302i
\(844\) 15.3205 + 26.5359i 0.527354 + 0.913403i
\(845\) 0 0
\(846\) 1.46410 0.0503369
\(847\) 9.18653 + 1.76795i 0.315653 + 0.0607475i
\(848\) 8.99485 0.308884
\(849\) 0.0621778 0.107695i 0.00213394 0.00369609i
\(850\) 0 0
\(851\) 4.56218 + 7.90192i 0.156389 + 0.270874i
\(852\) −3.07180 + 5.32051i −0.105238 + 0.182278i
\(853\) −19.9808 −0.684128 −0.342064 0.939677i \(-0.611126\pi\)
−0.342064 + 0.939677i \(0.611126\pi\)
\(854\) −5.07180 + 5.85641i −0.173553 + 0.200402i
\(855\) 0 0
\(856\) −10.3923 + 18.0000i −0.355202 + 0.615227i
\(857\) 2.43782 + 4.22243i 0.0832744 + 0.144236i 0.904655 0.426146i \(-0.140129\pi\)
−0.821380 + 0.570381i \(0.806796\pi\)
\(858\) 5.73205 + 9.92820i 0.195689 + 0.338943i
\(859\) −0.267949 + 0.464102i −0.00914231 + 0.0158349i −0.870560 0.492062i \(-0.836243\pi\)
0.861418 + 0.507897i \(0.169577\pi\)
\(860\) 0 0
\(861\) 4.73205 5.46410i 0.161268 0.186216i
\(862\) 12.6795 0.431865
\(863\) −3.19615 + 5.53590i −0.108798 + 0.188444i −0.915284 0.402810i \(-0.868034\pi\)
0.806485 + 0.591254i \(0.201367\pi\)
\(864\) 2.92820 + 5.07180i 0.0996195 + 0.172546i
\(865\) 0 0
\(866\) −1.75833 + 3.04552i −0.0597505 + 0.103491i
\(867\) 28.3205 0.961815
\(868\) 24.5885 + 4.73205i 0.834587 + 0.160616i
\(869\) −36.5885 −1.24118
\(870\) 0 0
\(871\) −7.62436 13.2058i −0.258341 0.447460i
\(872\) −13.9474 24.1577i −0.472320 0.818082i
\(873\) 0.535898 0.928203i 0.0181374 0.0314149i
\(874\) 2.28719 0.0773653
\(875\) 0 0
\(876\) −6.82309 −0.230531
\(877\) −15.9282 + 27.5885i −0.537857 + 0.931596i 0.461162 + 0.887316i \(0.347433\pi\)
−0.999019 + 0.0442800i \(0.985901\pi\)
\(878\) 2.73205 + 4.73205i 0.0922022 + 0.159699i
\(879\) 2.53590 + 4.39230i 0.0855337 + 0.148149i
\(880\) 0 0
\(881\) −17.8564 −0.601598 −0.300799 0.953688i \(-0.597253\pi\)
−0.300799 + 0.953688i \(0.597253\pi\)
\(882\) −4.75833 1.90192i −0.160221 0.0640411i
\(883\) −22.4115 −0.754208 −0.377104 0.926171i \(-0.623080\pi\)
−0.377104 + 0.926171i \(0.623080\pi\)
\(884\) 28.2487 48.9282i 0.950107 1.64563i
\(885\) 0 0
\(886\) −0.928203 1.60770i −0.0311836 0.0540116i
\(887\) −14.3660 + 24.8827i −0.482364 + 0.835479i −0.999795 0.0202460i \(-0.993555\pi\)
0.517431 + 0.855725i \(0.326888\pi\)
\(888\) −18.2487 −0.612387
\(889\) −13.1603 37.9904i −0.441381 1.27416i
\(890\) 0 0
\(891\) 1.36603 2.36603i 0.0457636 0.0792648i
\(892\) −0.287187 0.497423i −0.00961573 0.0166549i
\(893\) −2.46410 4.26795i −0.0824580 0.142821i
\(894\) −8.00000 + 13.8564i −0.267560 + 0.463428i
\(895\) 0 0
\(896\) −26.3538 5.07180i −0.880420 0.169437i
\(897\) −7.26795 −0.242670
\(898\) −2.98076 + 5.16283i −0.0994693 + 0.172286i
\(899\) −20.0263 34.6865i −0.667914 1.15686i
\(900\) 0 0
\(901\) 28.2487 48.9282i 0.941101 1.63003i
\(902\) 5.46410 0.181935
\(903\) 12.4641 14.3923i 0.414779 0.478946i
\(904\) 12.4974 0.415658
\(905\) 0 0
\(906\) 1.80385 + 3.12436i 0.0599288 + 0.103800i
\(907\) 1.20577 + 2.08846i 0.0400370 + 0.0693461i 0.885350 0.464926i \(-0.153919\pi\)
−0.845313 + 0.534272i \(0.820586\pi\)
\(908\) −11.4641 + 19.8564i −0.380450 + 0.658958i
\(909\) −10.7321 −0.355960
\(910\) 0 0
\(911\) −11.2679 −0.373324 −0.186662 0.982424i \(-0.559767\pi\)
−0.186662 + 0.982424i \(0.559767\pi\)
\(912\) 1.32051 2.28719i 0.0437264 0.0757363i
\(913\) 12.4641 + 21.5885i 0.412502 + 0.714474i
\(914\) −0.241670 0.418584i −0.00799372 0.0138455i
\(915\) 0 0
\(916\) 4.39230 0.145126
\(917\) −22.1769 4.26795i −0.732346 0.140940i
\(918\) 4.92820 0.162655
\(919\) 1.57180 2.72243i 0.0518488 0.0898047i −0.838936 0.544230i \(-0.816822\pi\)
0.890785 + 0.454425i \(0.150155\pi\)
\(920\) 0 0
\(921\) −3.93782 6.82051i −0.129756 0.224743i
\(922\) −12.8038 + 22.1769i −0.421672 + 0.730358i
\(923\) 24.0526 0.791700
\(924\) 3.46410 + 10.0000i 0.113961 + 0.328976i
\(925\) 0 0
\(926\) −8.15064 + 14.1173i −0.267846 + 0.463924i
\(927\) 0.598076 + 1.03590i 0.0196434 + 0.0340234i
\(928\) 18.1436 + 31.4256i 0.595593 + 1.03160i
\(929\) −3.22243 + 5.58142i −0.105725 + 0.183120i −0.914034 0.405638i \(-0.867050\pi\)
0.808309 + 0.588758i \(0.200383\pi\)
\(930\) 0 0
\(931\) 2.46410 + 17.0718i 0.0807577 + 0.559506i
\(932\) −25.3590 −0.830661
\(933\) 7.56218 13.0981i 0.247575 0.428812i
\(934\) 10.1962 + 17.6603i 0.333628 + 0.577861i
\(935\) 0 0
\(936\) 7.26795 12.5885i 0.237560 0.411467i
\(937\) −28.2679 −0.923474 −0.461737 0.887017i \(-0.652774\pi\)
−0.461737 + 0.887017i \(0.652774\pi\)
\(938\) 1.68653 + 4.86860i 0.0550673 + 0.158966i
\(939\) −4.66025 −0.152082
\(940\) 0 0
\(941\) −4.02628 6.97372i −0.131253 0.227337i 0.792907 0.609343i \(-0.208567\pi\)
−0.924160 + 0.382006i \(0.875233\pi\)
\(942\) 5.26795 + 9.12436i 0.171639 + 0.297288i
\(943\) −1.73205 + 3.00000i −0.0564033 + 0.0976934i
\(944\) 10.9282 0.355683
\(945\) 0 0
\(946\) 14.3923 0.467934
\(947\) 5.83013 10.0981i 0.189454 0.328143i −0.755615 0.655017i \(-0.772662\pi\)
0.945068 + 0.326873i \(0.105995\pi\)
\(948\) 9.80385 + 16.9808i 0.318414 + 0.551510i
\(949\) 13.3564 + 23.1340i 0.433567 + 0.750961i
\(950\) 0 0
\(951\) −30.4449 −0.987242
\(952\) −29.5692 + 34.1436i −0.958344 + 1.10660i
\(953\) −40.1051 −1.29913 −0.649566 0.760305i \(-0.725049\pi\)
−0.649566 + 0.760305i \(0.725049\pi\)
\(954\) 3.07180 5.32051i 0.0994531 0.172258i
\(955\) 0 0
\(956\) 15.3205 + 26.5359i 0.495501 + 0.858232i
\(957\) 8.46410 14.6603i 0.273606 0.473899i
\(958\) 24.0000 0.775405
\(959\) 14.1962 16.3923i 0.458418 0.529335i
\(960\) 0 0
\(961\) −5.39230 + 9.33975i −0.173945 + 0.301282i
\(962\) 15.0981 + 26.1506i 0.486782 + 0.843130i
\(963\) −4.09808 7.09808i −0.132059 0.228732i
\(964\) 4.78461 8.28719i 0.154102 0.266912i
\(965\) 0 0
\(966\) 2.41154 + 0.464102i 0.0775901 + 0.0149322i
\(967\) −14.1244 −0.454209 −0.227104 0.973870i \(-0.572926\pi\)
−0.227104 + 0.973870i \(0.572926\pi\)
\(968\) 4.48334 7.76537i 0.144100 0.249589i
\(969\) −8.29423 14.3660i −0.266449 0.461503i
\(970\) 0 0
\(971\) 12.0000 20.7846i 0.385098 0.667010i −0.606685 0.794943i \(-0.707501\pi\)
0.991783 + 0.127933i \(0.0408342\pi\)
\(972\) −1.46410 −0.0469611
\(973\) −6.86603 19.8205i −0.220115 0.635416i
\(974\) −23.1244 −0.740952
\(975\) 0 0
\(976\) −2.14359 3.71281i −0.0686148 0.118844i
\(977\) 7.29423 + 12.6340i 0.233363 + 0.404197i 0.958796 0.284097i \(-0.0916936\pi\)
−0.725433 + 0.688293i \(0.758360\pi\)
\(978\) 2.14359 3.71281i 0.0685446 0.118723i
\(979\) 24.9282 0.796709
\(980\) 0 0
\(981\) 11.0000 0.351203
\(982\) 3.75129 6.49742i 0.119708 0.207341i
\(983\) 10.0981 + 17.4904i 0.322079 + 0.557857i 0.980917 0.194428i \(-0.0622851\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(984\) −3.46410 6.00000i −0.110432 0.191273i
\(985\) 0 0
\(986\) 30.5359 0.972461
\(987\) −1.73205 5.00000i −0.0551318 0.159152i
\(988\) −20.6795 −0.657902
\(989\) −4.56218 + 7.90192i −0.145069 + 0.251267i
\(990\) 0 0
\(991\) −27.5526 47.7224i −0.875236 1.51595i −0.856511 0.516128i \(-0.827373\pi\)
−0.0187246 0.999825i \(-0.505961\pi\)
\(992\) 18.9282 32.7846i 0.600971 1.04091i
\(993\) 21.9282 0.695870
\(994\) −7.98076 1.53590i −0.253134 0.0487157i
\(995\) 0 0
\(996\) 6.67949 11.5692i 0.211648 0.366585i
\(997\) −2.00962 3.48076i −0.0636453 0.110237i 0.832447 0.554105i \(-0.186939\pi\)
−0.896092 + 0.443868i \(0.853606\pi\)
\(998\) −7.49038 12.9737i −0.237104 0.410676i
\(999\) 3.59808 6.23205i 0.113838 0.197173i
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.i.f.226.2 4
5.2 odd 4 525.2.r.f.499.1 4
5.3 odd 4 525.2.r.a.499.2 4
5.4 even 2 105.2.i.d.16.1 4
7.2 even 3 3675.2.a.bg.1.1 2
7.4 even 3 inner 525.2.i.f.151.2 4
7.5 odd 6 3675.2.a.be.1.1 2
15.14 odd 2 315.2.j.c.226.2 4
20.19 odd 2 1680.2.bg.o.961.2 4
35.4 even 6 105.2.i.d.46.1 yes 4
35.9 even 6 735.2.a.g.1.2 2
35.18 odd 12 525.2.r.f.424.1 4
35.19 odd 6 735.2.a.h.1.2 2
35.24 odd 6 735.2.i.l.361.1 4
35.32 odd 12 525.2.r.a.424.2 4
35.34 odd 2 735.2.i.l.226.1 4
105.44 odd 6 2205.2.a.z.1.1 2
105.74 odd 6 315.2.j.c.46.2 4
105.89 even 6 2205.2.a.ba.1.1 2
140.39 odd 6 1680.2.bg.o.1201.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.i.d.16.1 4 5.4 even 2
105.2.i.d.46.1 yes 4 35.4 even 6
315.2.j.c.46.2 4 105.74 odd 6
315.2.j.c.226.2 4 15.14 odd 2
525.2.i.f.151.2 4 7.4 even 3 inner
525.2.i.f.226.2 4 1.1 even 1 trivial
525.2.r.a.424.2 4 35.32 odd 12
525.2.r.a.499.2 4 5.3 odd 4
525.2.r.f.424.1 4 35.18 odd 12
525.2.r.f.499.1 4 5.2 odd 4
735.2.a.g.1.2 2 35.9 even 6
735.2.a.h.1.2 2 35.19 odd 6
735.2.i.l.226.1 4 35.34 odd 2
735.2.i.l.361.1 4 35.24 odd 6
1680.2.bg.o.961.2 4 20.19 odd 2
1680.2.bg.o.1201.2 4 140.39 odd 6
2205.2.a.z.1.1 2 105.44 odd 6
2205.2.a.ba.1.1 2 105.89 even 6
3675.2.a.be.1.1 2 7.5 odd 6
3675.2.a.bg.1.1 2 7.2 even 3