Properties

Label 189.3.j.b.116.6
Level $189$
Weight $3$
Character 189.116
Analytic conductor $5.150$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,3,Mod(44,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.44");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 189.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.14987699641\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 116.6
Character \(\chi\) \(=\) 189.116
Dual form 189.3.j.b.44.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.513687i q^{2} +3.73613 q^{4} +(6.08350 + 3.51231i) q^{5} +(1.23968 - 6.88935i) q^{7} +3.97395i q^{8} +O(q^{10})\) \(q+0.513687i q^{2} +3.73613 q^{4} +(6.08350 + 3.51231i) q^{5} +(1.23968 - 6.88935i) q^{7} +3.97395i q^{8} +(-1.80423 + 3.12502i) q^{10} +(-3.15993 + 1.82439i) q^{11} +(-3.79085 - 6.56594i) q^{13} +(3.53897 + 0.636806i) q^{14} +12.9031 q^{16} +(-17.5124 - 10.1108i) q^{17} +(13.6978 + 23.7253i) q^{19} +(22.7287 + 13.1224i) q^{20} +(-0.937164 - 1.62322i) q^{22} +(-3.42024 - 1.97468i) q^{23} +(12.1726 + 21.0836i) q^{25} +(3.37284 - 1.94731i) q^{26} +(4.63159 - 25.7395i) q^{28} +(23.7260 + 13.6982i) q^{29} +4.85004 q^{31} +22.5240i q^{32} +(5.19377 - 8.99588i) q^{34} +(31.7391 - 37.5572i) q^{35} +(-18.7209 - 32.4256i) q^{37} +(-12.1874 + 7.03639i) q^{38} +(-13.9577 + 24.1755i) q^{40} +(-61.1213 + 35.2884i) q^{41} +(-9.41887 + 16.3140i) q^{43} +(-11.8059 + 6.81613i) q^{44} +(1.01437 - 1.75694i) q^{46} -23.9730i q^{47} +(-45.9264 - 17.0811i) q^{49} +(-10.8304 + 6.25292i) q^{50} +(-14.1631 - 24.5312i) q^{52} +(-23.1126 - 13.3441i) q^{53} -25.6312 q^{55} +(27.3779 + 4.92641i) q^{56} +(-7.03661 + 12.1878i) q^{58} -52.8103i q^{59} -106.944 q^{61} +2.49140i q^{62} +40.0422 q^{64} -53.2585i q^{65} +102.155 q^{67} +(-65.4284 - 37.7751i) q^{68} +(19.2927 + 16.3040i) q^{70} -138.410i q^{71} +(-34.7679 + 60.2198i) q^{73} +(16.6566 - 9.61670i) q^{74} +(51.1767 + 88.6406i) q^{76} +(8.65155 + 24.0315i) q^{77} +23.2155 q^{79} +(78.4962 + 45.3198i) q^{80} +(-18.1272 - 31.3973i) q^{82} +(25.9282 + 14.9697i) q^{83} +(-71.0243 - 123.018i) q^{85} +(-8.38027 - 4.83835i) q^{86} +(-7.25002 - 12.5574i) q^{88} +(-135.658 + 78.3225i) q^{89} +(-49.9345 + 17.9769i) q^{91} +(-12.7785 - 7.37765i) q^{92} +12.3146 q^{94} +192.444i q^{95} +(2.93155 - 5.07760i) q^{97} +(8.77437 - 23.5918i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.513687i 0.256844i 0.991720 + 0.128422i \(0.0409911\pi\)
−0.991720 + 0.128422i \(0.959009\pi\)
\(3\) 0 0
\(4\) 3.73613 0.934031
\(5\) 6.08350 + 3.51231i 1.21670 + 0.702462i 0.964210 0.265138i \(-0.0854176\pi\)
0.252489 + 0.967600i \(0.418751\pi\)
\(6\) 0 0
\(7\) 1.23968 6.88935i 0.177097 0.984193i
\(8\) 3.97395i 0.496744i
\(9\) 0 0
\(10\) −1.80423 + 3.12502i −0.180423 + 0.312502i
\(11\) −3.15993 + 1.82439i −0.287266 + 0.165853i −0.636708 0.771105i \(-0.719704\pi\)
0.349442 + 0.936958i \(0.386371\pi\)
\(12\) 0 0
\(13\) −3.79085 6.56594i −0.291604 0.505073i 0.682585 0.730806i \(-0.260856\pi\)
−0.974189 + 0.225733i \(0.927522\pi\)
\(14\) 3.53897 + 0.636806i 0.252784 + 0.0454862i
\(15\) 0 0
\(16\) 12.9031 0.806446
\(17\) −17.5124 10.1108i −1.03014 0.594751i −0.113114 0.993582i \(-0.536083\pi\)
−0.917024 + 0.398831i \(0.869416\pi\)
\(18\) 0 0
\(19\) 13.6978 + 23.7253i 0.720937 + 1.24870i 0.960625 + 0.277849i \(0.0896216\pi\)
−0.239688 + 0.970850i \(0.577045\pi\)
\(20\) 22.7287 + 13.1224i 1.13644 + 0.656121i
\(21\) 0 0
\(22\) −0.937164 1.62322i −0.0425984 0.0737825i
\(23\) −3.42024 1.97468i −0.148706 0.0858556i 0.423801 0.905755i \(-0.360696\pi\)
−0.572507 + 0.819900i \(0.694029\pi\)
\(24\) 0 0
\(25\) 12.1726 + 21.0836i 0.486905 + 0.843344i
\(26\) 3.37284 1.94731i 0.129725 0.0748966i
\(27\) 0 0
\(28\) 4.63159 25.7395i 0.165414 0.919268i
\(29\) 23.7260 + 13.6982i 0.818139 + 0.472353i 0.849774 0.527147i \(-0.176738\pi\)
−0.0316352 + 0.999499i \(0.510071\pi\)
\(30\) 0 0
\(31\) 4.85004 0.156453 0.0782264 0.996936i \(-0.475074\pi\)
0.0782264 + 0.996936i \(0.475074\pi\)
\(32\) 22.5240i 0.703874i
\(33\) 0 0
\(34\) 5.19377 8.99588i 0.152758 0.264585i
\(35\) 31.7391 37.5572i 0.906832 1.07306i
\(36\) 0 0
\(37\) −18.7209 32.4256i −0.505971 0.876367i −0.999976 0.00690796i \(-0.997801\pi\)
0.494006 0.869459i \(-0.335532\pi\)
\(38\) −12.1874 + 7.03639i −0.320721 + 0.185168i
\(39\) 0 0
\(40\) −13.9577 + 24.1755i −0.348943 + 0.604388i
\(41\) −61.1213 + 35.2884i −1.49076 + 0.860693i −0.999944 0.0105682i \(-0.996636\pi\)
−0.490820 + 0.871261i \(0.663303\pi\)
\(42\) 0 0
\(43\) −9.41887 + 16.3140i −0.219043 + 0.379394i −0.954516 0.298160i \(-0.903627\pi\)
0.735472 + 0.677555i \(0.236960\pi\)
\(44\) −11.8059 + 6.81613i −0.268316 + 0.154912i
\(45\) 0 0
\(46\) 1.01437 1.75694i 0.0220515 0.0381943i
\(47\) 23.9730i 0.510063i −0.966933 0.255031i \(-0.917914\pi\)
0.966933 0.255031i \(-0.0820858\pi\)
\(48\) 0 0
\(49\) −45.9264 17.0811i −0.937274 0.348595i
\(50\) −10.8304 + 6.25292i −0.216608 + 0.125058i
\(51\) 0 0
\(52\) −14.1631 24.5312i −0.272367 0.471754i
\(53\) −23.1126 13.3441i −0.436087 0.251775i 0.265850 0.964015i \(-0.414348\pi\)
−0.701936 + 0.712240i \(0.747681\pi\)
\(54\) 0 0
\(55\) −25.6312 −0.466022
\(56\) 27.3779 + 4.92641i 0.488892 + 0.0879717i
\(57\) 0 0
\(58\) −7.03661 + 12.1878i −0.121321 + 0.210134i
\(59\) 52.8103i 0.895089i −0.894262 0.447545i \(-0.852299\pi\)
0.894262 0.447545i \(-0.147701\pi\)
\(60\) 0 0
\(61\) −106.944 −1.75318 −0.876588 0.481242i \(-0.840186\pi\)
−0.876588 + 0.481242i \(0.840186\pi\)
\(62\) 2.49140i 0.0401839i
\(63\) 0 0
\(64\) 40.0422 0.625660
\(65\) 53.2585i 0.819362i
\(66\) 0 0
\(67\) 102.155 1.52471 0.762354 0.647161i \(-0.224044\pi\)
0.762354 + 0.647161i \(0.224044\pi\)
\(68\) −65.4284 37.7751i −0.962182 0.555516i
\(69\) 0 0
\(70\) 19.2927 + 16.3040i 0.275610 + 0.232914i
\(71\) 138.410i 1.94944i −0.223427 0.974721i \(-0.571725\pi\)
0.223427 0.974721i \(-0.428275\pi\)
\(72\) 0 0
\(73\) −34.7679 + 60.2198i −0.476273 + 0.824929i −0.999630 0.0271843i \(-0.991346\pi\)
0.523358 + 0.852113i \(0.324679\pi\)
\(74\) 16.6566 9.61670i 0.225089 0.129955i
\(75\) 0 0
\(76\) 51.1767 + 88.6406i 0.673378 + 1.16632i
\(77\) 8.65155 + 24.0315i 0.112358 + 0.312098i
\(78\) 0 0
\(79\) 23.2155 0.293867 0.146933 0.989146i \(-0.453060\pi\)
0.146933 + 0.989146i \(0.453060\pi\)
\(80\) 78.4962 + 45.3198i 0.981202 + 0.566497i
\(81\) 0 0
\(82\) −18.1272 31.3973i −0.221064 0.382893i
\(83\) 25.9282 + 14.9697i 0.312388 + 0.180357i 0.647995 0.761645i \(-0.275608\pi\)
−0.335606 + 0.942002i \(0.608941\pi\)
\(84\) 0 0
\(85\) −71.0243 123.018i −0.835579 1.44727i
\(86\) −8.38027 4.83835i −0.0974450 0.0562599i
\(87\) 0 0
\(88\) −7.25002 12.5574i −0.0823866 0.142698i
\(89\) −135.658 + 78.3225i −1.52425 + 0.880028i −0.524665 + 0.851309i \(0.675809\pi\)
−0.999588 + 0.0287188i \(0.990857\pi\)
\(90\) 0 0
\(91\) −49.9345 + 17.9769i −0.548731 + 0.197548i
\(92\) −12.7785 7.37765i −0.138896 0.0801918i
\(93\) 0 0
\(94\) 12.3146 0.131006
\(95\) 192.444i 2.02572i
\(96\) 0 0
\(97\) 2.93155 5.07760i 0.0302222 0.0523464i −0.850519 0.525945i \(-0.823712\pi\)
0.880741 + 0.473598i \(0.157045\pi\)
\(98\) 8.77437 23.5918i 0.0895344 0.240733i
\(99\) 0 0
\(100\) 45.4784 + 78.7710i 0.454784 + 0.787710i
\(101\) 16.8659 9.73752i 0.166989 0.0964111i −0.414176 0.910197i \(-0.635930\pi\)
0.581165 + 0.813786i \(0.302597\pi\)
\(102\) 0 0
\(103\) −13.0458 + 22.5961i −0.126659 + 0.219379i −0.922380 0.386284i \(-0.873759\pi\)
0.795721 + 0.605663i \(0.207092\pi\)
\(104\) 26.0927 15.0646i 0.250892 0.144852i
\(105\) 0 0
\(106\) 6.85468 11.8727i 0.0646668 0.112006i
\(107\) −25.2215 + 14.5616i −0.235715 + 0.136090i −0.613206 0.789923i \(-0.710120\pi\)
0.377491 + 0.926013i \(0.376787\pi\)
\(108\) 0 0
\(109\) 50.9986 88.3322i 0.467877 0.810387i −0.531449 0.847090i \(-0.678352\pi\)
0.999326 + 0.0367034i \(0.0116857\pi\)
\(110\) 13.1664i 0.119695i
\(111\) 0 0
\(112\) 15.9957 88.8943i 0.142819 0.793699i
\(113\) 122.755 70.8728i 1.08633 0.627193i 0.153734 0.988112i \(-0.450870\pi\)
0.932597 + 0.360919i \(0.117537\pi\)
\(114\) 0 0
\(115\) −13.8714 24.0259i −0.120621 0.208921i
\(116\) 88.6434 + 51.1783i 0.764168 + 0.441192i
\(117\) 0 0
\(118\) 27.1280 0.229898
\(119\) −91.3663 + 108.115i −0.767784 + 0.908527i
\(120\) 0 0
\(121\) −53.8432 + 93.2592i −0.444985 + 0.770737i
\(122\) 54.9356i 0.450292i
\(123\) 0 0
\(124\) 18.1204 0.146132
\(125\) 4.59944i 0.0367955i
\(126\) 0 0
\(127\) −39.8045 −0.313421 −0.156711 0.987645i \(-0.550089\pi\)
−0.156711 + 0.987645i \(0.550089\pi\)
\(128\) 110.665i 0.864571i
\(129\) 0 0
\(130\) 27.3582 0.210448
\(131\) 60.2047 + 34.7592i 0.459578 + 0.265337i 0.711867 0.702315i \(-0.247850\pi\)
−0.252289 + 0.967652i \(0.581183\pi\)
\(132\) 0 0
\(133\) 180.433 64.9573i 1.35664 0.488401i
\(134\) 52.4759i 0.391611i
\(135\) 0 0
\(136\) 40.1797 69.5932i 0.295439 0.511715i
\(137\) 65.6043 37.8766i 0.478863 0.276472i −0.241079 0.970505i \(-0.577501\pi\)
0.719943 + 0.694034i \(0.244168\pi\)
\(138\) 0 0
\(139\) 37.4261 + 64.8239i 0.269253 + 0.466359i 0.968669 0.248355i \(-0.0798900\pi\)
−0.699416 + 0.714714i \(0.746557\pi\)
\(140\) 118.581 140.319i 0.847009 1.00228i
\(141\) 0 0
\(142\) 71.0996 0.500702
\(143\) 23.9576 + 13.8319i 0.167536 + 0.0967269i
\(144\) 0 0
\(145\) 96.2248 + 166.666i 0.663620 + 1.14942i
\(146\) −30.9342 17.8598i −0.211878 0.122328i
\(147\) 0 0
\(148\) −69.9437 121.146i −0.472592 0.818554i
\(149\) 18.7773 + 10.8411i 0.126022 + 0.0727591i 0.561686 0.827351i \(-0.310153\pi\)
−0.435664 + 0.900110i \(0.643486\pi\)
\(150\) 0 0
\(151\) 85.7533 + 148.529i 0.567902 + 0.983636i 0.996773 + 0.0802700i \(0.0255783\pi\)
−0.428871 + 0.903366i \(0.641088\pi\)
\(152\) −94.2831 + 54.4344i −0.620284 + 0.358121i
\(153\) 0 0
\(154\) −12.3447 + 4.44419i −0.0801603 + 0.0288584i
\(155\) 29.5052 + 17.0348i 0.190356 + 0.109902i
\(156\) 0 0
\(157\) −80.4532 −0.512441 −0.256220 0.966618i \(-0.582477\pi\)
−0.256220 + 0.966618i \(0.582477\pi\)
\(158\) 11.9255i 0.0754778i
\(159\) 0 0
\(160\) −79.1112 + 137.025i −0.494445 + 0.856403i
\(161\) −17.8443 + 21.1153i −0.110834 + 0.131151i
\(162\) 0 0
\(163\) −67.6792 117.224i −0.415210 0.719165i 0.580240 0.814445i \(-0.302959\pi\)
−0.995450 + 0.0952804i \(0.969625\pi\)
\(164\) −228.357 + 131.842i −1.39242 + 0.803914i
\(165\) 0 0
\(166\) −7.68973 + 13.3190i −0.0463237 + 0.0802349i
\(167\) −97.2491 + 56.1468i −0.582330 + 0.336208i −0.762059 0.647508i \(-0.775811\pi\)
0.179729 + 0.983716i \(0.442478\pi\)
\(168\) 0 0
\(169\) 55.7589 96.5773i 0.329934 0.571463i
\(170\) 63.1926 36.4843i 0.371721 0.214613i
\(171\) 0 0
\(172\) −35.1901 + 60.9510i −0.204593 + 0.354366i
\(173\) 182.045i 1.05229i −0.850396 0.526143i \(-0.823638\pi\)
0.850396 0.526143i \(-0.176362\pi\)
\(174\) 0 0
\(175\) 160.342 57.7246i 0.916243 0.329855i
\(176\) −40.7730 + 23.5403i −0.231665 + 0.133752i
\(177\) 0 0
\(178\) −40.2333 69.6860i −0.226030 0.391495i
\(179\) 182.206 + 105.197i 1.01791 + 0.587691i 0.913498 0.406843i \(-0.133370\pi\)
0.104413 + 0.994534i \(0.466704\pi\)
\(180\) 0 0
\(181\) 104.037 0.574791 0.287396 0.957812i \(-0.407211\pi\)
0.287396 + 0.957812i \(0.407211\pi\)
\(182\) −9.23449 25.6507i −0.0507389 0.140938i
\(183\) 0 0
\(184\) 7.84728 13.5919i 0.0426482 0.0738689i
\(185\) 263.014i 1.42170i
\(186\) 0 0
\(187\) 73.7838 0.394566
\(188\) 89.5660i 0.476415i
\(189\) 0 0
\(190\) −98.8559 −0.520294
\(191\) 89.7823i 0.470065i −0.971988 0.235032i \(-0.924480\pi\)
0.971988 0.235032i \(-0.0755196\pi\)
\(192\) 0 0
\(193\) −80.1195 −0.415127 −0.207564 0.978222i \(-0.566553\pi\)
−0.207564 + 0.978222i \(0.566553\pi\)
\(194\) 2.60830 + 1.50590i 0.0134448 + 0.00776238i
\(195\) 0 0
\(196\) −171.587 63.8173i −0.875443 0.325598i
\(197\) 49.3712i 0.250615i 0.992118 + 0.125308i \(0.0399918\pi\)
−0.992118 + 0.125308i \(0.960008\pi\)
\(198\) 0 0
\(199\) 1.01765 1.76262i 0.00511381 0.00885737i −0.863457 0.504422i \(-0.831706\pi\)
0.868571 + 0.495565i \(0.165039\pi\)
\(200\) −83.7852 + 48.3734i −0.418926 + 0.241867i
\(201\) 0 0
\(202\) 5.00204 + 8.66379i 0.0247626 + 0.0428900i
\(203\) 123.785 146.476i 0.609776 0.721555i
\(204\) 0 0
\(205\) −495.775 −2.41842
\(206\) −11.6073 6.70148i −0.0563462 0.0325315i
\(207\) 0 0
\(208\) −48.9138 84.7213i −0.235163 0.407314i
\(209\) −86.5682 49.9802i −0.414202 0.239139i
\(210\) 0 0
\(211\) 144.840 + 250.871i 0.686446 + 1.18896i 0.972980 + 0.230890i \(0.0741637\pi\)
−0.286534 + 0.958070i \(0.592503\pi\)
\(212\) −86.3516 49.8551i −0.407319 0.235166i
\(213\) 0 0
\(214\) −7.48013 12.9560i −0.0349539 0.0605419i
\(215\) −114.599 + 66.1639i −0.533020 + 0.307739i
\(216\) 0 0
\(217\) 6.01248 33.4136i 0.0277073 0.153980i
\(218\) 45.3751 + 26.1973i 0.208143 + 0.120171i
\(219\) 0 0
\(220\) −95.7615 −0.435279
\(221\) 153.314i 0.693727i
\(222\) 0 0
\(223\) 67.9693 117.726i 0.304795 0.527921i −0.672421 0.740169i \(-0.734745\pi\)
0.977216 + 0.212249i \(0.0680787\pi\)
\(224\) 155.176 + 27.9225i 0.692748 + 0.124654i
\(225\) 0 0
\(226\) 36.4065 + 63.0579i 0.161091 + 0.279017i
\(227\) 43.1303 24.9013i 0.190001 0.109697i −0.401982 0.915648i \(-0.631678\pi\)
0.591983 + 0.805950i \(0.298345\pi\)
\(228\) 0 0
\(229\) −71.2489 + 123.407i −0.311131 + 0.538894i −0.978607 0.205737i \(-0.934041\pi\)
0.667477 + 0.744631i \(0.267374\pi\)
\(230\) 12.3418 7.12555i 0.0536600 0.0309806i
\(231\) 0 0
\(232\) −54.4361 + 94.2861i −0.234638 + 0.406405i
\(233\) −72.6863 + 41.9654i −0.311958 + 0.180109i −0.647802 0.761808i \(-0.724312\pi\)
0.335844 + 0.941918i \(0.390978\pi\)
\(234\) 0 0
\(235\) 84.2004 145.839i 0.358300 0.620593i
\(236\) 197.306i 0.836041i
\(237\) 0 0
\(238\) −55.5372 46.9337i −0.233350 0.197201i
\(239\) −222.986 + 128.741i −0.932995 + 0.538665i −0.887758 0.460311i \(-0.847738\pi\)
−0.0452374 + 0.998976i \(0.514404\pi\)
\(240\) 0 0
\(241\) 63.9892 + 110.832i 0.265515 + 0.459886i 0.967698 0.252110i \(-0.0811246\pi\)
−0.702183 + 0.711996i \(0.747791\pi\)
\(242\) −47.9061 27.6586i −0.197959 0.114292i
\(243\) 0 0
\(244\) −399.555 −1.63752
\(245\) −219.399 265.221i −0.895506 1.08253i
\(246\) 0 0
\(247\) 103.853 179.878i 0.420456 0.728251i
\(248\) 19.2738i 0.0777170i
\(249\) 0 0
\(250\) 2.36267 0.00945069
\(251\) 277.115i 1.10404i 0.833830 + 0.552022i \(0.186144\pi\)
−0.833830 + 0.552022i \(0.813856\pi\)
\(252\) 0 0
\(253\) 14.4103 0.0569577
\(254\) 20.4471i 0.0805003i
\(255\) 0 0
\(256\) 103.322 0.403600
\(257\) 164.899 + 95.2045i 0.641630 + 0.370445i 0.785242 0.619189i \(-0.212538\pi\)
−0.143612 + 0.989634i \(0.545872\pi\)
\(258\) 0 0
\(259\) −246.599 + 88.7778i −0.952120 + 0.342771i
\(260\) 198.981i 0.765310i
\(261\) 0 0
\(262\) −17.8554 + 30.9264i −0.0681502 + 0.118040i
\(263\) 44.0020 25.4046i 0.167308 0.0965954i −0.414008 0.910273i \(-0.635871\pi\)
0.581316 + 0.813678i \(0.302538\pi\)
\(264\) 0 0
\(265\) −93.7369 162.357i −0.353724 0.612669i
\(266\) 33.3678 + 92.6860i 0.125443 + 0.348444i
\(267\) 0 0
\(268\) 381.665 1.42412
\(269\) 15.6224 + 9.01962i 0.0580760 + 0.0335302i 0.528757 0.848773i \(-0.322658\pi\)
−0.470681 + 0.882304i \(0.655992\pi\)
\(270\) 0 0
\(271\) −85.9218 148.821i −0.317055 0.549155i 0.662818 0.748781i \(-0.269361\pi\)
−0.979872 + 0.199626i \(0.936027\pi\)
\(272\) −225.964 130.461i −0.830751 0.479634i
\(273\) 0 0
\(274\) 19.4568 + 33.7001i 0.0710101 + 0.122993i
\(275\) −76.9292 44.4151i −0.279743 0.161510i
\(276\) 0 0
\(277\) 113.295 + 196.232i 0.409006 + 0.708419i 0.994779 0.102057i \(-0.0325423\pi\)
−0.585773 + 0.810475i \(0.699209\pi\)
\(278\) −33.2992 + 19.2253i −0.119781 + 0.0691558i
\(279\) 0 0
\(280\) 149.251 + 126.130i 0.533038 + 0.450463i
\(281\) 360.913 + 208.373i 1.28439 + 0.741541i 0.977647 0.210252i \(-0.0674286\pi\)
0.306740 + 0.951793i \(0.400762\pi\)
\(282\) 0 0
\(283\) −124.309 −0.439255 −0.219627 0.975584i \(-0.570484\pi\)
−0.219627 + 0.975584i \(0.570484\pi\)
\(284\) 517.118i 1.82084i
\(285\) 0 0
\(286\) −7.10530 + 12.3067i −0.0248437 + 0.0430305i
\(287\) 167.344 + 464.833i 0.583079 + 1.61963i
\(288\) 0 0
\(289\) 59.9552 + 103.845i 0.207457 + 0.359327i
\(290\) −85.6144 + 49.4295i −0.295222 + 0.170446i
\(291\) 0 0
\(292\) −129.897 + 224.989i −0.444854 + 0.770509i
\(293\) 362.584 209.338i 1.23749 0.714464i 0.268908 0.963166i \(-0.413337\pi\)
0.968580 + 0.248702i \(0.0800039\pi\)
\(294\) 0 0
\(295\) 185.486 321.271i 0.628766 1.08905i
\(296\) 128.858 74.3960i 0.435330 0.251338i
\(297\) 0 0
\(298\) −5.56894 + 9.64568i −0.0186877 + 0.0323681i
\(299\) 29.9429i 0.100143i
\(300\) 0 0
\(301\) 100.716 + 85.1139i 0.334605 + 0.282771i
\(302\) −76.2975 + 44.0504i −0.252641 + 0.145862i
\(303\) 0 0
\(304\) 176.745 + 306.131i 0.581397 + 1.00701i
\(305\) −650.592 375.619i −2.13309 1.23154i
\(306\) 0 0
\(307\) 457.334 1.48969 0.744843 0.667239i \(-0.232524\pi\)
0.744843 + 0.667239i \(0.232524\pi\)
\(308\) 32.3233 + 89.7848i 0.104946 + 0.291509i
\(309\) 0 0
\(310\) −8.75058 + 15.1564i −0.0282277 + 0.0488918i
\(311\) 348.141i 1.11942i 0.828687 + 0.559712i \(0.189088\pi\)
−0.828687 + 0.559712i \(0.810912\pi\)
\(312\) 0 0
\(313\) −135.708 −0.433571 −0.216785 0.976219i \(-0.569557\pi\)
−0.216785 + 0.976219i \(0.569557\pi\)
\(314\) 41.3278i 0.131617i
\(315\) 0 0
\(316\) 86.7359 0.274481
\(317\) 407.641i 1.28593i 0.765894 + 0.642967i \(0.222297\pi\)
−0.765894 + 0.642967i \(0.777703\pi\)
\(318\) 0 0
\(319\) −99.9634 −0.313365
\(320\) 243.597 + 140.641i 0.761240 + 0.439502i
\(321\) 0 0
\(322\) −10.8467 9.16637i −0.0336853 0.0284670i
\(323\) 553.981i 1.71511i
\(324\) 0 0
\(325\) 92.2892 159.850i 0.283967 0.491845i
\(326\) 60.2164 34.7660i 0.184713 0.106644i
\(327\) 0 0
\(328\) −140.234 242.893i −0.427544 0.740528i
\(329\) −165.158 29.7187i −0.502001 0.0903304i
\(330\) 0 0
\(331\) 184.399 0.557098 0.278549 0.960422i \(-0.410147\pi\)
0.278549 + 0.960422i \(0.410147\pi\)
\(332\) 96.8711 + 55.9285i 0.291780 + 0.168459i
\(333\) 0 0
\(334\) −28.8419 49.9557i −0.0863530 0.149568i
\(335\) 621.462 + 358.801i 1.85511 + 1.07105i
\(336\) 0 0
\(337\) 121.608 + 210.631i 0.360855 + 0.625019i 0.988102 0.153802i \(-0.0491516\pi\)
−0.627247 + 0.778820i \(0.715818\pi\)
\(338\) 49.6105 + 28.6426i 0.146777 + 0.0847416i
\(339\) 0 0
\(340\) −265.356 459.609i −0.780457 1.35179i
\(341\) −15.3258 + 8.84834i −0.0449436 + 0.0259482i
\(342\) 0 0
\(343\) −174.612 + 295.228i −0.509073 + 0.860723i
\(344\) −64.8308 37.4301i −0.188462 0.108808i
\(345\) 0 0
\(346\) 93.5145 0.270273
\(347\) 336.800i 0.970604i 0.874347 + 0.485302i \(0.161290\pi\)
−0.874347 + 0.485302i \(0.838710\pi\)
\(348\) 0 0
\(349\) 239.411 414.673i 0.685992 1.18817i −0.287132 0.957891i \(-0.592702\pi\)
0.973124 0.230282i \(-0.0739650\pi\)
\(350\) 29.6524 + 82.3659i 0.0847212 + 0.235331i
\(351\) 0 0
\(352\) −41.0924 71.1742i −0.116740 0.202199i
\(353\) 184.488 106.514i 0.522630 0.301740i −0.215380 0.976530i \(-0.569099\pi\)
0.738010 + 0.674790i \(0.235766\pi\)
\(354\) 0 0
\(355\) 486.140 842.019i 1.36941 2.37188i
\(356\) −506.837 + 292.623i −1.42370 + 0.821973i
\(357\) 0 0
\(358\) −54.0382 + 93.5970i −0.150945 + 0.261444i
\(359\) 439.984 254.025i 1.22558 0.707590i 0.259479 0.965749i \(-0.416449\pi\)
0.966103 + 0.258159i \(0.0831157\pi\)
\(360\) 0 0
\(361\) −194.760 + 337.333i −0.539500 + 0.934441i
\(362\) 53.4426i 0.147631i
\(363\) 0 0
\(364\) −186.562 + 67.1638i −0.512532 + 0.184516i
\(365\) −423.021 + 244.231i −1.15896 + 0.669127i
\(366\) 0 0
\(367\) −19.9885 34.6211i −0.0544646 0.0943355i 0.837508 0.546426i \(-0.184012\pi\)
−0.891972 + 0.452090i \(0.850679\pi\)
\(368\) −44.1319 25.4795i −0.119924 0.0692379i
\(369\) 0 0
\(370\) 135.107 0.365155
\(371\) −120.584 + 142.689i −0.325025 + 0.384605i
\(372\) 0 0
\(373\) −34.6838 + 60.0741i −0.0929860 + 0.161056i −0.908766 0.417305i \(-0.862975\pi\)
0.815780 + 0.578362i \(0.196308\pi\)
\(374\) 37.9018i 0.101342i
\(375\) 0 0
\(376\) 95.2673 0.253371
\(377\) 207.712i 0.550960i
\(378\) 0 0
\(379\) −140.172 −0.369847 −0.184924 0.982753i \(-0.559204\pi\)
−0.184924 + 0.982753i \(0.559204\pi\)
\(380\) 718.993i 1.89209i
\(381\) 0 0
\(382\) 46.1201 0.120733
\(383\) 453.525 + 261.843i 1.18414 + 0.683663i 0.956968 0.290192i \(-0.0937193\pi\)
0.227170 + 0.973855i \(0.427053\pi\)
\(384\) 0 0
\(385\) −31.7744 + 176.583i −0.0825310 + 0.458656i
\(386\) 41.1564i 0.106623i
\(387\) 0 0
\(388\) 10.9526 18.9705i 0.0282285 0.0488931i
\(389\) 127.462 73.5902i 0.327666 0.189178i −0.327139 0.944976i \(-0.606084\pi\)
0.654804 + 0.755798i \(0.272751\pi\)
\(390\) 0 0
\(391\) 39.9310 + 69.1626i 0.102125 + 0.176886i
\(392\) 67.8796 182.509i 0.173162 0.465585i
\(393\) 0 0
\(394\) −25.3614 −0.0643690
\(395\) 141.231 + 81.5399i 0.357547 + 0.206430i
\(396\) 0 0
\(397\) 91.5634 + 158.592i 0.230638 + 0.399477i 0.957996 0.286781i \(-0.0925853\pi\)
−0.727358 + 0.686258i \(0.759252\pi\)
\(398\) 0.905434 + 0.522753i 0.00227496 + 0.00131345i
\(399\) 0 0
\(400\) 157.065 + 272.044i 0.392662 + 0.680111i
\(401\) −531.766 307.015i −1.32610 0.765624i −0.341406 0.939916i \(-0.610903\pi\)
−0.984694 + 0.174291i \(0.944237\pi\)
\(402\) 0 0
\(403\) −18.3858 31.8451i −0.0456223 0.0790201i
\(404\) 63.0130 36.3806i 0.155973 0.0900510i
\(405\) 0 0
\(406\) 75.2427 + 63.5866i 0.185327 + 0.156617i
\(407\) 118.313 + 68.3083i 0.290697 + 0.167834i
\(408\) 0 0
\(409\) 477.066 1.16642 0.583210 0.812321i \(-0.301796\pi\)
0.583210 + 0.812321i \(0.301796\pi\)
\(410\) 254.673i 0.621155i
\(411\) 0 0
\(412\) −48.7409 + 84.4217i −0.118303 + 0.204907i
\(413\) −363.829 65.4677i −0.880941 0.158517i
\(414\) 0 0
\(415\) 105.156 + 182.136i 0.253388 + 0.438881i
\(416\) 147.891 85.3850i 0.355508 0.205252i
\(417\) 0 0
\(418\) 25.6742 44.4690i 0.0614215 0.106385i
\(419\) 212.402 122.630i 0.506926 0.292674i −0.224643 0.974441i \(-0.572122\pi\)
0.731569 + 0.681767i \(0.238788\pi\)
\(420\) 0 0
\(421\) −247.132 + 428.045i −0.587012 + 1.01673i 0.407609 + 0.913156i \(0.366363\pi\)
−0.994621 + 0.103578i \(0.966971\pi\)
\(422\) −128.869 + 74.4026i −0.305377 + 0.176309i
\(423\) 0 0
\(424\) 53.0287 91.8483i 0.125068 0.216623i
\(425\) 492.298i 1.15835i
\(426\) 0 0
\(427\) −132.576 + 736.773i −0.310482 + 1.72546i
\(428\) −94.2307 + 54.4041i −0.220165 + 0.127112i
\(429\) 0 0
\(430\) −33.9876 58.8682i −0.0790409 0.136903i
\(431\) −274.768 158.637i −0.637513 0.368068i 0.146143 0.989263i \(-0.453314\pi\)
−0.783656 + 0.621195i \(0.786647\pi\)
\(432\) 0 0
\(433\) −671.335 −1.55043 −0.775213 0.631699i \(-0.782358\pi\)
−0.775213 + 0.631699i \(0.782358\pi\)
\(434\) 17.1642 + 3.08854i 0.0395488 + 0.00711644i
\(435\) 0 0
\(436\) 190.537 330.020i 0.437012 0.756927i
\(437\) 108.195i 0.247586i
\(438\) 0 0
\(439\) 297.955 0.678713 0.339356 0.940658i \(-0.389791\pi\)
0.339356 + 0.940658i \(0.389791\pi\)
\(440\) 101.857i 0.231494i
\(441\) 0 0
\(442\) −78.7553 −0.178179
\(443\) 829.378i 1.87218i −0.351754 0.936092i \(-0.614415\pi\)
0.351754 0.936092i \(-0.385585\pi\)
\(444\) 0 0
\(445\) −1100.37 −2.47274
\(446\) 60.4745 + 34.9150i 0.135593 + 0.0782847i
\(447\) 0 0
\(448\) 49.6395 275.865i 0.110802 0.615771i
\(449\) 190.382i 0.424012i 0.977268 + 0.212006i \(0.0679997\pi\)
−0.977268 + 0.212006i \(0.932000\pi\)
\(450\) 0 0
\(451\) 128.759 223.018i 0.285497 0.494496i
\(452\) 458.629 264.790i 1.01467 0.585818i
\(453\) 0 0
\(454\) 12.7915 + 22.1555i 0.0281751 + 0.0488007i
\(455\) −366.917 66.0234i −0.806411 0.145106i
\(456\) 0 0
\(457\) −279.974 −0.612635 −0.306318 0.951929i \(-0.599097\pi\)
−0.306318 + 0.951929i \(0.599097\pi\)
\(458\) −63.3925 36.5997i −0.138411 0.0799119i
\(459\) 0 0
\(460\) −51.8252 89.7638i −0.112663 0.195139i
\(461\) −132.923 76.7433i −0.288337 0.166471i 0.348855 0.937177i \(-0.386571\pi\)
−0.637192 + 0.770705i \(0.719904\pi\)
\(462\) 0 0
\(463\) −251.599 435.782i −0.543410 0.941215i −0.998705 0.0508737i \(-0.983799\pi\)
0.455295 0.890341i \(-0.349534\pi\)
\(464\) 306.140 + 176.750i 0.659785 + 0.380927i
\(465\) 0 0
\(466\) −21.5571 37.3380i −0.0462599 0.0801245i
\(467\) 153.150 88.4210i 0.327943 0.189338i −0.326984 0.945030i \(-0.606032\pi\)
0.654928 + 0.755692i \(0.272699\pi\)
\(468\) 0 0
\(469\) 126.640 703.785i 0.270021 1.50061i
\(470\) 74.9159 + 43.2527i 0.159395 + 0.0920270i
\(471\) 0 0
\(472\) 209.865 0.444630
\(473\) 68.7346i 0.145316i
\(474\) 0 0
\(475\) −333.476 + 577.598i −0.702055 + 1.21600i
\(476\) −341.356 + 403.930i −0.717134 + 0.848593i
\(477\) 0 0
\(478\) −66.1326 114.545i −0.138353 0.239634i
\(479\) −409.511 + 236.431i −0.854928 + 0.493593i −0.862311 0.506380i \(-0.830983\pi\)
0.00738248 + 0.999973i \(0.497650\pi\)
\(480\) 0 0
\(481\) −141.936 + 245.841i −0.295086 + 0.511104i
\(482\) −56.9332 + 32.8704i −0.118119 + 0.0681959i
\(483\) 0 0
\(484\) −201.165 + 348.428i −0.415630 + 0.719893i
\(485\) 35.6682 20.5930i 0.0735426 0.0424599i
\(486\) 0 0
\(487\) −49.3289 + 85.4401i −0.101291 + 0.175442i −0.912217 0.409708i \(-0.865631\pi\)
0.810926 + 0.585149i \(0.198964\pi\)
\(488\) 424.989i 0.870879i
\(489\) 0 0
\(490\) 136.241 112.702i 0.278042 0.230005i
\(491\) −807.412 + 466.160i −1.64442 + 0.949409i −0.665190 + 0.746674i \(0.731650\pi\)
−0.979234 + 0.202735i \(0.935017\pi\)
\(492\) 0 0
\(493\) −276.999 479.777i −0.561865 0.973178i
\(494\) 92.4011 + 53.3478i 0.187047 + 0.107991i
\(495\) 0 0
\(496\) 62.5807 0.126171
\(497\) −953.558 171.584i −1.91863 0.345240i
\(498\) 0 0
\(499\) −237.862 + 411.989i −0.476677 + 0.825629i −0.999643 0.0267249i \(-0.991492\pi\)
0.522966 + 0.852354i \(0.324826\pi\)
\(500\) 17.1841i 0.0343681i
\(501\) 0 0
\(502\) −142.351 −0.283567
\(503\) 779.244i 1.54919i −0.632456 0.774596i \(-0.717953\pi\)
0.632456 0.774596i \(-0.282047\pi\)
\(504\) 0 0
\(505\) 136.805 0.270900
\(506\) 7.40239i 0.0146292i
\(507\) 0 0
\(508\) −148.715 −0.292745
\(509\) 368.995 + 213.040i 0.724942 + 0.418545i 0.816569 0.577248i \(-0.195873\pi\)
−0.0916270 + 0.995793i \(0.529207\pi\)
\(510\) 0 0
\(511\) 371.775 + 314.182i 0.727543 + 0.614837i
\(512\) 495.735i 0.968233i
\(513\) 0 0
\(514\) −48.9053 + 84.7065i −0.0951466 + 0.164799i
\(515\) −158.729 + 91.6420i −0.308211 + 0.177946i
\(516\) 0 0
\(517\) 43.7359 + 75.7528i 0.0845956 + 0.146524i
\(518\) −45.6040 126.675i −0.0880386 0.244546i
\(519\) 0 0
\(520\) 211.647 0.407013
\(521\) 418.449 + 241.592i 0.803166 + 0.463708i 0.844577 0.535434i \(-0.179852\pi\)
−0.0414112 + 0.999142i \(0.513185\pi\)
\(522\) 0 0
\(523\) −107.843 186.789i −0.206200 0.357149i 0.744314 0.667829i \(-0.232776\pi\)
−0.950514 + 0.310680i \(0.899443\pi\)
\(524\) 224.932 + 129.865i 0.429260 + 0.247833i
\(525\) 0 0
\(526\) 13.0500 + 22.6033i 0.0248099 + 0.0429720i
\(527\) −84.9356 49.0376i −0.161168 0.0930505i
\(528\) 0 0
\(529\) −256.701 444.620i −0.485258 0.840491i
\(530\) 83.4008 48.1515i 0.157360 0.0908519i
\(531\) 0 0
\(532\) 674.119 242.689i 1.26714 0.456182i
\(533\) 463.404 + 267.546i 0.869425 + 0.501963i
\(534\) 0 0
\(535\) −204.580 −0.382392
\(536\) 405.960i 0.757389i
\(537\) 0 0
\(538\) −4.63327 + 8.02505i −0.00861202 + 0.0149165i
\(539\) 176.287 29.8123i 0.327063 0.0553103i
\(540\) 0 0
\(541\) −436.156 755.444i −0.806203 1.39638i −0.915476 0.402372i \(-0.868186\pi\)
0.109273 0.994012i \(-0.465148\pi\)
\(542\) 76.4474 44.1369i 0.141047 0.0814335i
\(543\) 0 0
\(544\) 227.735 394.448i 0.418630 0.725088i
\(545\) 620.500 358.246i 1.13853 0.657331i
\(546\) 0 0
\(547\) −151.008 + 261.554i −0.276067 + 0.478161i −0.970404 0.241489i \(-0.922364\pi\)
0.694337 + 0.719650i \(0.255698\pi\)
\(548\) 245.106 141.512i 0.447273 0.258233i
\(549\) 0 0
\(550\) 22.8155 39.5176i 0.0414827 0.0718501i
\(551\) 750.543i 1.36215i
\(552\) 0 0
\(553\) 28.7797 159.940i 0.0520428 0.289222i
\(554\) −100.802 + 58.1980i −0.181953 + 0.105051i
\(555\) 0 0
\(556\) 139.829 + 242.190i 0.251490 + 0.435594i
\(557\) −35.2462 20.3494i −0.0632787 0.0365340i 0.468027 0.883714i \(-0.344965\pi\)
−0.531306 + 0.847180i \(0.678298\pi\)
\(558\) 0 0
\(559\) 142.822 0.255496
\(560\) 409.534 484.606i 0.731311 0.865368i
\(561\) 0 0
\(562\) −107.039 + 185.396i −0.190460 + 0.329887i
\(563\) 557.671i 0.990534i −0.868741 0.495267i \(-0.835070\pi\)
0.868741 0.495267i \(-0.164930\pi\)
\(564\) 0 0
\(565\) 995.709 1.76232
\(566\) 63.8560i 0.112820i
\(567\) 0 0
\(568\) 550.036 0.968373
\(569\) 371.333i 0.652606i −0.945265 0.326303i \(-0.894197\pi\)
0.945265 0.326303i \(-0.105803\pi\)
\(570\) 0 0
\(571\) 404.280 0.708021 0.354011 0.935241i \(-0.384818\pi\)
0.354011 + 0.935241i \(0.384818\pi\)
\(572\) 89.5087 + 51.6779i 0.156484 + 0.0903460i
\(573\) 0 0
\(574\) −238.779 + 85.9623i −0.415991 + 0.149760i
\(575\) 96.1481i 0.167214i
\(576\) 0 0
\(577\) −416.462 + 721.333i −0.721770 + 1.25014i 0.238519 + 0.971138i \(0.423338\pi\)
−0.960290 + 0.279005i \(0.909995\pi\)
\(578\) −53.3441 + 30.7982i −0.0922908 + 0.0532841i
\(579\) 0 0
\(580\) 359.508 + 622.686i 0.619841 + 1.07360i
\(581\) 135.274 160.071i 0.232830 0.275510i
\(582\) 0 0
\(583\) 97.3789 0.167031
\(584\) −239.311 138.166i −0.409778 0.236586i
\(585\) 0 0
\(586\) 107.534 + 186.255i 0.183506 + 0.317841i
\(587\) −464.128 267.964i −0.790677 0.456498i 0.0495236 0.998773i \(-0.484230\pi\)
−0.840201 + 0.542275i \(0.817563\pi\)
\(588\) 0 0
\(589\) 66.4349 + 115.069i 0.112793 + 0.195363i
\(590\) 165.033 + 95.2818i 0.279717 + 0.161495i
\(591\) 0 0
\(592\) −241.558 418.391i −0.408038 0.706742i
\(593\) −522.472 + 301.649i −0.881065 + 0.508683i −0.871010 0.491266i \(-0.836534\pi\)
−0.0100559 + 0.999949i \(0.503201\pi\)
\(594\) 0 0
\(595\) −935.559 + 336.809i −1.57237 + 0.566066i
\(596\) 70.1545 + 40.5037i 0.117709 + 0.0679592i
\(597\) 0 0
\(598\) −15.3813 −0.0257212
\(599\) 795.128i 1.32742i −0.747988 0.663712i \(-0.768980\pi\)
0.747988 0.663712i \(-0.231020\pi\)
\(600\) 0 0
\(601\) 284.164 492.186i 0.472818 0.818945i −0.526698 0.850053i \(-0.676570\pi\)
0.999516 + 0.0311074i \(0.00990340\pi\)
\(602\) −43.7220 + 51.7367i −0.0726278 + 0.0859413i
\(603\) 0 0
\(604\) 320.385 + 554.923i 0.530439 + 0.918747i
\(605\) −655.110 + 378.228i −1.08283 + 0.625170i
\(606\) 0 0
\(607\) 119.087 206.265i 0.196190 0.339811i −0.751100 0.660188i \(-0.770476\pi\)
0.947290 + 0.320378i \(0.103810\pi\)
\(608\) −534.388 + 308.529i −0.878927 + 0.507449i
\(609\) 0 0
\(610\) 192.951 334.201i 0.316313 0.547870i
\(611\) −157.405 + 90.8779i −0.257619 + 0.148736i
\(612\) 0 0
\(613\) −352.492 + 610.534i −0.575028 + 0.995977i 0.421011 + 0.907056i \(0.361675\pi\)
−0.996039 + 0.0889215i \(0.971658\pi\)
\(614\) 234.927i 0.382617i
\(615\) 0 0
\(616\) −95.5001 + 34.3808i −0.155033 + 0.0558130i
\(617\) 722.505 417.138i 1.17100 0.676075i 0.217082 0.976153i \(-0.430346\pi\)
0.953915 + 0.300078i \(0.0970128\pi\)
\(618\) 0 0
\(619\) −67.3116 116.587i −0.108743 0.188348i 0.806519 0.591209i \(-0.201349\pi\)
−0.915261 + 0.402861i \(0.868016\pi\)
\(620\) 110.235 + 63.6443i 0.177799 + 0.102652i
\(621\) 0 0
\(622\) −178.835 −0.287517
\(623\) 371.418 + 1031.69i 0.596177 + 1.65601i
\(624\) 0 0
\(625\) 320.470 555.071i 0.512752 0.888113i
\(626\) 69.7113i 0.111360i
\(627\) 0 0
\(628\) −300.583 −0.478636
\(629\) 757.131i 1.20371i
\(630\) 0 0
\(631\) 951.730 1.50829 0.754144 0.656709i \(-0.228052\pi\)
0.754144 + 0.656709i \(0.228052\pi\)
\(632\) 92.2571i 0.145976i
\(633\) 0 0
\(634\) −209.400 −0.330284
\(635\) −242.151 139.806i −0.381340 0.220166i
\(636\) 0 0
\(637\) 61.9462 + 366.302i 0.0972468 + 0.575043i
\(638\) 51.3500i 0.0804858i
\(639\) 0 0
\(640\) −388.690 + 673.231i −0.607328 + 1.05192i
\(641\) 30.1499 17.4071i 0.0470358 0.0271561i −0.476298 0.879284i \(-0.658022\pi\)
0.523333 + 0.852128i \(0.324688\pi\)
\(642\) 0 0
\(643\) −504.419 873.680i −0.784478 1.35876i −0.929311 0.369299i \(-0.879598\pi\)
0.144833 0.989456i \(-0.453736\pi\)
\(644\) −66.6684 + 78.8895i −0.103522 + 0.122499i
\(645\) 0 0
\(646\) 284.573 0.440516
\(647\) 762.764 + 440.382i 1.17892 + 0.680653i 0.955766 0.294129i \(-0.0950297\pi\)
0.223159 + 0.974782i \(0.428363\pi\)
\(648\) 0 0
\(649\) 96.3463 + 166.877i 0.148453 + 0.257129i
\(650\) 82.1127 + 47.4078i 0.126327 + 0.0729350i
\(651\) 0 0
\(652\) −252.858 437.963i −0.387819 0.671722i
\(653\) 680.639 + 392.967i 1.04233 + 0.601788i 0.920491 0.390763i \(-0.127789\pi\)
0.121835 + 0.992550i \(0.461122\pi\)
\(654\) 0 0
\(655\) 244.170 + 422.915i 0.372778 + 0.645671i
\(656\) −788.657 + 455.331i −1.20222 + 0.694102i
\(657\) 0 0
\(658\) 15.2661 84.8397i 0.0232008 0.128936i
\(659\) −692.308 399.704i −1.05054 0.606531i −0.127741 0.991808i \(-0.540773\pi\)
−0.922801 + 0.385276i \(0.874106\pi\)
\(660\) 0 0
\(661\) 327.723 0.495798 0.247899 0.968786i \(-0.420260\pi\)
0.247899 + 0.968786i \(0.420260\pi\)
\(662\) 94.7237i 0.143087i
\(663\) 0 0
\(664\) −59.4887 + 103.037i −0.0895914 + 0.155177i
\(665\) 1325.81 + 238.568i 1.99370 + 0.358749i
\(666\) 0 0
\(667\) −54.0992 93.7026i −0.0811083 0.140484i
\(668\) −363.335 + 209.772i −0.543915 + 0.314029i
\(669\) 0 0
\(670\) −184.312 + 319.237i −0.275092 + 0.476473i
\(671\) 337.935 195.107i 0.503628 0.290770i
\(672\) 0 0
\(673\) 287.229 497.495i 0.426789 0.739221i −0.569796 0.821786i \(-0.692978\pi\)
0.996586 + 0.0825652i \(0.0263113\pi\)
\(674\) −108.199 + 62.4685i −0.160532 + 0.0926833i
\(675\) 0 0
\(676\) 208.322 360.825i 0.308169 0.533764i
\(677\) 224.951i 0.332276i −0.986102 0.166138i \(-0.946870\pi\)
0.986102 0.166138i \(-0.0531298\pi\)
\(678\) 0 0
\(679\) −31.3472 26.4911i −0.0461667 0.0390148i
\(680\) 488.866 282.247i 0.718920 0.415069i
\(681\) 0 0
\(682\) −4.54528 7.87266i −0.00666464 0.0115435i
\(683\) −322.171 186.006i −0.471700 0.272336i 0.245251 0.969460i \(-0.421130\pi\)
−0.716951 + 0.697123i \(0.754463\pi\)
\(684\) 0 0
\(685\) 532.138 0.776844
\(686\) −151.655 89.6960i −0.221071 0.130752i
\(687\) 0 0
\(688\) −121.533 + 210.501i −0.176647 + 0.305961i
\(689\) 202.341i 0.293674i
\(690\) 0 0
\(691\) −973.332 −1.40858 −0.704292 0.709910i \(-0.748735\pi\)
−0.704292 + 0.709910i \(0.748735\pi\)
\(692\) 680.145i 0.982868i
\(693\) 0 0
\(694\) −173.010 −0.249294
\(695\) 525.808i 0.756558i
\(696\) 0 0
\(697\) 1427.17 2.04759
\(698\) 213.012 + 122.983i 0.305175 + 0.176193i
\(699\) 0 0
\(700\) 599.060 215.666i 0.855799 0.308095i
\(701\) 495.876i 0.707384i 0.935362 + 0.353692i \(0.115074\pi\)
−0.935362 + 0.353692i \(0.884926\pi\)
\(702\) 0 0
\(703\) 512.871 888.318i 0.729546 1.26361i
\(704\) −126.531 + 73.0525i −0.179731 + 0.103768i
\(705\) 0 0
\(706\) 54.7151 + 94.7693i 0.0775001 + 0.134234i
\(707\) −46.1770 128.266i −0.0653140 0.181423i
\(708\) 0 0
\(709\) 98.0951 0.138357 0.0691785 0.997604i \(-0.477962\pi\)
0.0691785 + 0.997604i \(0.477962\pi\)
\(710\) 432.534 + 249.724i 0.609203 + 0.351724i
\(711\) 0 0
\(712\) −311.250 539.100i −0.437148 0.757163i
\(713\) −16.5883 9.57727i −0.0232655 0.0134324i
\(714\) 0 0
\(715\) 97.1641 + 168.293i 0.135894 + 0.235375i
\(716\) 680.745 + 393.028i 0.950761 + 0.548922i
\(717\) 0 0
\(718\) 130.489 + 226.014i 0.181740 + 0.314783i
\(719\) 256.458 148.066i 0.356687 0.205933i −0.310939 0.950430i \(-0.600644\pi\)
0.667627 + 0.744496i \(0.267310\pi\)
\(720\) 0 0
\(721\) 139.500 + 117.889i 0.193481 + 0.163508i
\(722\) −173.284 100.046i −0.240005 0.138567i
\(723\) 0 0
\(724\) 388.696 0.536873
\(725\) 666.973i 0.919963i
\(726\) 0 0
\(727\) 12.9897 22.4988i 0.0178675 0.0309475i −0.856953 0.515394i \(-0.827646\pi\)
0.874821 + 0.484446i \(0.160979\pi\)
\(728\) −71.4391 198.437i −0.0981307 0.272579i
\(729\) 0 0
\(730\) −125.459 217.301i −0.171861 0.297672i
\(731\) 329.893 190.464i 0.451290 0.260553i
\(732\) 0 0
\(733\) −337.765 + 585.026i −0.460798 + 0.798125i −0.999001 0.0446898i \(-0.985770\pi\)
0.538203 + 0.842815i \(0.319103\pi\)
\(734\) 17.7844 10.2678i 0.0242295 0.0139889i
\(735\) 0 0
\(736\) 44.4776 77.0375i 0.0604316 0.104671i
\(737\) −322.804 + 186.371i −0.437997 + 0.252878i
\(738\) 0 0
\(739\) 8.89120 15.4000i 0.0120314 0.0208390i −0.859947 0.510383i \(-0.829504\pi\)
0.871978 + 0.489544i \(0.162837\pi\)
\(740\) 982.655i 1.32791i
\(741\) 0 0
\(742\) −73.2973 61.9426i −0.0987834 0.0834805i
\(743\) 748.369 432.071i 1.00723 0.581522i 0.0968479 0.995299i \(-0.469124\pi\)
0.910378 + 0.413777i \(0.135791\pi\)
\(744\) 0 0
\(745\) 76.1546 + 131.904i 0.102221 + 0.177052i
\(746\) −30.8593 17.8166i −0.0413663 0.0238829i
\(747\) 0 0
\(748\) 275.665 0.368537
\(749\) 69.0538 + 191.812i 0.0921947 + 0.256090i
\(750\) 0 0
\(751\) −258.812 + 448.276i −0.344623 + 0.596905i −0.985285 0.170918i \(-0.945327\pi\)
0.640662 + 0.767823i \(0.278660\pi\)
\(752\) 309.326i 0.411338i
\(753\) 0 0
\(754\) 106.699 0.141511
\(755\) 1204.77i 1.59572i
\(756\) 0 0
\(757\) −314.752 −0.415789 −0.207895 0.978151i \(-0.566661\pi\)
−0.207895 + 0.978151i \(0.566661\pi\)
\(758\) 72.0046i 0.0949929i
\(759\) 0 0
\(760\) −764.761 −1.00626
\(761\) −511.702 295.431i −0.672408 0.388215i 0.124581 0.992209i \(-0.460241\pi\)
−0.796988 + 0.603995i \(0.793575\pi\)
\(762\) 0 0
\(763\) −545.330 460.851i −0.714718 0.603998i
\(764\) 335.438i 0.439055i
\(765\) 0 0
\(766\) −134.505 + 232.970i −0.175594 + 0.304139i
\(767\) −346.749 + 200.196i −0.452085 + 0.261011i
\(768\) 0 0
\(769\) −292.620 506.833i −0.380521 0.659081i 0.610616 0.791927i \(-0.290922\pi\)
−0.991137 + 0.132846i \(0.957589\pi\)
\(770\) −90.7082 16.3221i −0.117803 0.0211976i
\(771\) 0 0
\(772\) −299.337 −0.387742
\(773\) −856.704 494.618i −1.10828 0.639869i −0.169900 0.985461i \(-0.554345\pi\)
−0.938385 + 0.345593i \(0.887678\pi\)
\(774\) 0 0
\(775\) 59.0377 + 102.256i 0.0761777 + 0.131944i
\(776\) 20.1781 + 11.6498i 0.0260027 + 0.0150127i
\(777\) 0 0
\(778\) 37.8024 + 65.4756i 0.0485892 + 0.0841589i
\(779\) −1674.46 966.747i −2.14949 1.24101i
\(780\) 0 0
\(781\) 252.514 + 437.367i 0.323321 + 0.560009i
\(782\) −35.5279 + 20.5121i −0.0454322 + 0.0262303i
\(783\) 0 0
\(784\) −592.594 220.400i −0.755860 0.281123i
\(785\) −489.437 282.576i −0.623486 0.359970i
\(786\) 0 0
\(787\) −1228.57 −1.56109 −0.780543 0.625102i \(-0.785057\pi\)
−0.780543 + 0.625102i \(0.785057\pi\)
\(788\) 184.457i 0.234083i
\(789\) 0 0
\(790\) −41.8860 + 72.5487i −0.0530203 + 0.0918338i
\(791\) −336.091 933.565i −0.424894 1.18023i
\(792\) 0 0
\(793\) 405.408 + 702.187i 0.511233 + 0.885481i
\(794\) −81.4669 + 47.0349i −0.102603 + 0.0592380i
\(795\) 0 0
\(796\) 3.80206 6.58536i 0.00477645 0.00827306i
\(797\) −631.278 + 364.468i −0.792068 + 0.457300i −0.840690 0.541517i \(-0.817850\pi\)
0.0486223 + 0.998817i \(0.484517\pi\)
\(798\) 0 0
\(799\) −242.385 + 419.823i −0.303360 + 0.525436i
\(800\) −474.886 + 274.176i −0.593608 + 0.342720i
\(801\) 0 0
\(802\) 157.710 273.162i 0.196646 0.340601i
\(803\) 253.720i 0.315966i
\(804\) 0 0
\(805\) −182.719 + 65.7804i −0.226980 + 0.0817148i
\(806\) 16.3584 9.44454i 0.0202958 0.0117178i
\(807\) 0 0
\(808\) 38.6964 + 67.0241i 0.0478916 + 0.0829507i
\(809\) 1007.55 + 581.707i 1.24542 + 0.719044i 0.970193 0.242335i \(-0.0779131\pi\)
0.275229 + 0.961379i \(0.411246\pi\)
\(810\) 0 0
\(811\) −224.013 −0.276219 −0.138109 0.990417i \(-0.544103\pi\)
−0.138109 + 0.990417i \(0.544103\pi\)
\(812\) 462.475 547.251i 0.569550 0.673955i
\(813\) 0 0
\(814\) −35.0891 + 60.7762i −0.0431070 + 0.0746636i
\(815\) 950.841i 1.16668i
\(816\) 0 0
\(817\) −516.071 −0.631666
\(818\) 245.063i 0.299588i
\(819\) 0 0
\(820\) −1852.28 −2.25888
\(821\) 1342.79i 1.63556i −0.575534 0.817778i \(-0.695206\pi\)
0.575534 0.817778i \(-0.304794\pi\)
\(822\) 0 0
\(823\) 1330.16 1.61623 0.808115 0.589024i \(-0.200488\pi\)
0.808115 + 0.589024i \(0.200488\pi\)
\(824\) −89.7956 51.8435i −0.108975 0.0629169i
\(825\) 0 0
\(826\) 33.6299 186.894i 0.0407142 0.226264i
\(827\) 863.204i 1.04378i −0.853014 0.521889i \(-0.825228\pi\)
0.853014 0.521889i \(-0.174772\pi\)
\(828\) 0 0
\(829\) 288.804 500.224i 0.348377 0.603406i −0.637585 0.770380i \(-0.720066\pi\)
0.985961 + 0.166974i \(0.0533997\pi\)
\(830\) −93.5609 + 54.0174i −0.112724 + 0.0650812i
\(831\) 0 0
\(832\) −151.794 262.915i −0.182445 0.316004i
\(833\) 631.576 + 763.482i 0.758195 + 0.916545i
\(834\) 0 0
\(835\) −788.820 −0.944694
\(836\) −323.429 186.732i −0.386877 0.223364i
\(837\) 0 0
\(838\) 62.9937 + 109.108i 0.0751715 + 0.130201i
\(839\) 264.845 + 152.908i 0.315667 + 0.182251i 0.649460 0.760396i \(-0.274995\pi\)
−0.333792 + 0.942647i \(0.608328\pi\)
\(840\) 0 0
\(841\) −45.2169 78.3179i −0.0537656 0.0931248i
\(842\) −219.881 126.949i −0.261142 0.150770i
\(843\) 0 0
\(844\) 541.141 + 937.284i 0.641162 + 1.11053i
\(845\) 678.418 391.685i 0.802862 0.463533i
\(846\) 0 0
\(847\) 575.748 + 486.556i 0.679749 + 0.574447i
\(848\) −298.225 172.180i −0.351680 0.203043i
\(849\) 0 0
\(850\) 252.887 0.297514
\(851\) 147.871i 0.173762i
\(852\) 0 0
\(853\) −42.0979 + 72.9157i −0.0493528 + 0.0854815i −0.889646 0.456650i \(-0.849049\pi\)
0.840294 + 0.542131i \(0.182383\pi\)
\(854\) −378.471 68.1025i −0.443175 0.0797453i
\(855\) 0 0
\(856\) −57.8672 100.229i −0.0676019 0.117090i
\(857\) 205.440 118.611i 0.239720 0.138402i −0.375328 0.926892i \(-0.622470\pi\)
0.615048 + 0.788490i \(0.289137\pi\)
\(858\) 0 0
\(859\) −581.096 + 1006.49i −0.676479 + 1.17170i 0.299555 + 0.954079i \(0.403162\pi\)
−0.976034 + 0.217617i \(0.930172\pi\)
\(860\) −428.157 + 247.197i −0.497857 + 0.287438i
\(861\) 0 0
\(862\) 81.4900 141.145i 0.0945360 0.163741i
\(863\) −582.552 + 336.337i −0.675032 + 0.389730i −0.797980 0.602683i \(-0.794098\pi\)
0.122949 + 0.992413i \(0.460765\pi\)
\(864\) 0 0
\(865\) 639.400 1107.47i 0.739191 1.28032i
\(866\) 344.856i 0.398217i
\(867\) 0 0
\(868\) 22.4634 124.838i 0.0258795 0.143822i
\(869\) −73.3592 + 42.3540i −0.0844180 + 0.0487387i
\(870\) 0 0
\(871\) −387.256 670.747i −0.444611 0.770088i
\(872\) 351.028 + 202.666i 0.402555 + 0.232415i
\(873\) 0 0
\(874\) 55.5784 0.0635909
\(875\) −31.6872 5.70182i −0.0362139 0.00651636i
\(876\) 0 0
\(877\) 375.664 650.670i 0.428352 0.741927i −0.568375 0.822769i \(-0.692428\pi\)
0.996727 + 0.0808428i \(0.0257612\pi\)
\(878\) 153.056i 0.174323i
\(879\) 0 0
\(880\) −330.723 −0.375822
\(881\) 696.005i 0.790017i 0.918677 + 0.395009i \(0.129258\pi\)
−0.918677 + 0.395009i \(0.870742\pi\)
\(882\) 0 0
\(883\) −1217.46 −1.37878 −0.689390 0.724390i \(-0.742121\pi\)
−0.689390 + 0.724390i \(0.742121\pi\)
\(884\) 572.799i 0.647962i
\(885\) 0 0
\(886\) 426.041 0.480859
\(887\) −504.732 291.407i −0.569033 0.328531i 0.187730 0.982221i \(-0.439887\pi\)
−0.756763 + 0.653689i \(0.773220\pi\)
\(888\) 0 0
\(889\) −49.3447 + 274.227i −0.0555059 + 0.308467i
\(890\) 565.246i 0.635108i
\(891\) 0 0
\(892\) 253.942 439.840i 0.284688 0.493094i
\(893\) 568.765 328.377i 0.636915 0.367723i
\(894\) 0 0
\(895\) 738.967 + 1279.93i 0.825661 + 1.43009i
\(896\) 762.411 + 137.189i 0.850905 + 0.153113i
\(897\) 0 0
\(898\) −97.7966 −0.108905
\(899\) 115.072 + 66.4370i 0.128000 + 0.0739010i
\(900\) 0 0
\(901\) 269.837 + 467.372i 0.299487 + 0.518726i
\(902\) 114.561 + 66.1421i 0.127008 + 0.0733282i
\(903\) 0 0
\(904\) 281.645 + 487.824i 0.311554 + 0.539628i
\(905\) 632.910 + 365.411i 0.699348 + 0.403769i
\(906\) 0 0
\(907\) −99.5801 172.478i −0.109791 0.190163i 0.805895 0.592059i \(-0.201685\pi\)
−0.915685 + 0.401896i \(0.868351\pi\)
\(908\) 161.140 93.0344i 0.177467 0.102461i
\(909\) 0 0
\(910\) 33.9154 188.481i 0.0372696 0.207122i
\(911\) 351.011 + 202.656i 0.385303 + 0.222455i 0.680123 0.733098i \(-0.261926\pi\)
−0.294820 + 0.955553i \(0.595260\pi\)
\(912\) 0 0
\(913\) −109.242 −0.119651
\(914\) 143.819i 0.157351i
\(915\) 0 0
\(916\) −266.195 + 461.063i −0.290606 + 0.503344i
\(917\) 314.103 371.681i 0.342533 0.405323i
\(918\) 0 0
\(919\) 471.303 + 816.321i 0.512843 + 0.888271i 0.999889 + 0.0148944i \(0.00474119\pi\)
−0.487046 + 0.873377i \(0.661925\pi\)
\(920\) 95.4778 55.1241i 0.103780 0.0599175i
\(921\) 0 0
\(922\) 39.4221 68.2811i 0.0427571 0.0740576i
\(923\) −908.795 + 524.693i −0.984609 + 0.568465i
\(924\) 0 0
\(925\) 455.765 789.408i 0.492719 0.853414i
\(926\) 223.856 129.243i 0.241745 0.139572i
\(927\) 0 0
\(928\) −308.539 + 534.405i −0.332477 + 0.575867i
\(929\) 1385.69i 1.49160i 0.666171 + 0.745799i \(0.267932\pi\)
−0.666171 + 0.745799i \(0.732068\pi\)
\(930\) 0 0
\(931\) −223.836 1323.59i −0.240425 1.42169i
\(932\) −271.565 + 156.788i −0.291379 + 0.168228i
\(933\) 0 0
\(934\) 45.4207 + 78.6710i 0.0486303 + 0.0842302i
\(935\) 448.863 + 259.151i 0.480068 + 0.277167i
\(936\) 0 0
\(937\) −93.8449 −0.100155 −0.0500773 0.998745i \(-0.515947\pi\)
−0.0500773 + 0.998745i \(0.515947\pi\)
\(938\) 361.525 + 65.0532i 0.385421 + 0.0693531i
\(939\) 0 0
\(940\) 314.583 544.874i 0.334663 0.579653i
\(941\) 533.954i 0.567433i 0.958908 + 0.283716i \(0.0915674\pi\)
−0.958908 + 0.283716i \(0.908433\pi\)
\(942\) 0 0
\(943\) 278.733 0.295581
\(944\) 681.418i 0.721841i
\(945\) 0 0
\(946\) 35.3081 0.0373236
\(947\) 1539.94i 1.62612i 0.582180 + 0.813060i \(0.302200\pi\)
−0.582180 + 0.813060i \(0.697800\pi\)
\(948\) 0 0
\(949\) 527.200 0.555532
\(950\) −296.705 171.303i −0.312321 0.180318i
\(951\) 0 0
\(952\) −429.643 363.085i −0.451305 0.381392i
\(953\) 923.067i 0.968591i 0.874905 + 0.484295i \(0.160924\pi\)
−0.874905 + 0.484295i \(0.839076\pi\)
\(954\) 0 0
\(955\) 315.343 546.191i 0.330202 0.571927i
\(956\) −833.103 + 480.992i −0.871446 + 0.503130i
\(957\) 0 0
\(958\) −121.452 210.360i −0.126776 0.219583i
\(959\) −179.618 498.926i −0.187297 0.520256i
\(960\) 0 0
\(961\) −937.477 −0.975522
\(962\) −126.285 72.9109i −0.131274 0.0757910i
\(963\) 0 0
\(964\) 239.072 + 414.084i 0.248000 + 0.429548i
\(965\) −487.407 281.404i −0.505085 0.291611i
\(966\) 0 0
\(967\) −580.540 1005.53i −0.600352 1.03984i −0.992768 0.120052i \(-0.961694\pi\)
0.392416 0.919788i \(-0.371639\pi\)
\(968\) −370.607 213.970i −0.382859 0.221044i
\(969\) 0 0
\(970\) 10.5784 + 18.3223i 0.0109055 + 0.0188890i
\(971\) 751.650 433.966i 0.774099 0.446926i −0.0602357 0.998184i \(-0.519185\pi\)
0.834335 + 0.551258i \(0.185852\pi\)
\(972\) 0 0
\(973\) 492.991 177.481i 0.506671 0.182406i
\(974\) −43.8895 25.3396i −0.0450611 0.0260160i
\(975\) 0 0
\(976\) −1379.91 −1.41384
\(977\) 1600.75i 1.63844i 0.573483 + 0.819218i \(0.305592\pi\)
−0.573483 + 0.819218i \(0.694408\pi\)
\(978\) 0 0
\(979\) 285.781 494.987i 0.291911 0.505605i
\(980\) −819.702 990.898i −0.836430 1.01112i
\(981\) 0 0
\(982\) −239.460 414.757i −0.243850 0.422360i
\(983\) 1180.61 681.625i 1.20103 0.693413i 0.240243 0.970713i \(-0.422773\pi\)
0.960783 + 0.277300i \(0.0894397\pi\)
\(984\) 0 0
\(985\) −173.407 + 300.350i −0.176048 + 0.304924i
\(986\) 246.455 142.291i 0.249955 0.144311i
\(987\) 0 0
\(988\) 388.006 672.047i 0.392719 0.680209i
\(989\) 64.4296 37.1985i 0.0651463 0.0376122i
\(990\) 0 0
\(991\) −470.682 + 815.244i −0.474956 + 0.822648i −0.999589 0.0286806i \(-0.990869\pi\)
0.524632 + 0.851329i \(0.324203\pi\)
\(992\) 109.242i 0.110123i
\(993\) 0 0
\(994\) 88.1406 489.831i 0.0886726 0.492787i
\(995\) 12.3817 7.14858i 0.0124439 0.00718450i
\(996\) 0 0
\(997\) 673.246 + 1166.10i 0.675272 + 1.16961i 0.976389 + 0.216019i \(0.0693072\pi\)
−0.301117 + 0.953587i \(0.597359\pi\)
\(998\) −211.633 122.187i −0.212058 0.122431i
\(999\) 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 189.3.j.b.116.6 22
3.2 odd 2 63.3.j.b.11.6 22
7.2 even 3 189.3.n.b.170.6 22
9.4 even 3 63.3.n.b.32.6 yes 22
9.5 odd 6 189.3.n.b.179.6 22
21.2 odd 6 63.3.n.b.2.6 yes 22
21.5 even 6 441.3.n.f.128.6 22
21.11 odd 6 441.3.r.g.344.6 22
21.17 even 6 441.3.r.f.344.6 22
21.20 even 2 441.3.j.f.263.6 22
63.4 even 3 441.3.r.g.50.6 22
63.13 odd 6 441.3.n.f.410.6 22
63.23 odd 6 inner 189.3.j.b.44.6 22
63.31 odd 6 441.3.r.f.50.6 22
63.40 odd 6 441.3.j.f.275.6 22
63.58 even 3 63.3.j.b.23.6 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.3.j.b.11.6 22 3.2 odd 2
63.3.j.b.23.6 yes 22 63.58 even 3
63.3.n.b.2.6 yes 22 21.2 odd 6
63.3.n.b.32.6 yes 22 9.4 even 3
189.3.j.b.44.6 22 63.23 odd 6 inner
189.3.j.b.116.6 22 1.1 even 1 trivial
189.3.n.b.170.6 22 7.2 even 3
189.3.n.b.179.6 22 9.5 odd 6
441.3.j.f.263.6 22 21.20 even 2
441.3.j.f.275.6 22 63.40 odd 6
441.3.n.f.128.6 22 21.5 even 6
441.3.n.f.410.6 22 63.13 odd 6
441.3.r.f.50.6 22 63.31 odd 6
441.3.r.f.344.6 22 21.17 even 6
441.3.r.g.50.6 22 63.4 even 3
441.3.r.g.344.6 22 21.11 odd 6