Properties

Label 99.3.k.b.28.2
Level $99$
Weight $3$
Character 99.28
Analytic conductor $2.698$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,3,Mod(19,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.k (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 21x^{14} + 227x^{12} - 1488x^{10} + 24225x^{8} - 62832x^{6} + 64372x^{4} + 7986x^{2} + 14641 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 28.2
Root \(-0.386583 - 0.532086i\) of defining polynomial
Character \(\chi\) \(=\) 99.28
Dual form 99.3.k.b.46.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.625505 + 0.203239i) q^{2} +(-2.88612 + 2.09689i) q^{4} +(2.50346 - 7.70484i) q^{5} +(-2.40175 - 3.30573i) q^{7} +(2.92545 - 4.02653i) q^{8} +O(q^{10})\) \(q+(-0.625505 + 0.203239i) q^{2} +(-2.88612 + 2.09689i) q^{4} +(2.50346 - 7.70484i) q^{5} +(-2.40175 - 3.30573i) q^{7} +(2.92545 - 4.02653i) q^{8} +5.32822i q^{10} +(6.70179 - 8.72273i) q^{11} +(14.0643 - 4.56975i) q^{13} +(2.17416 + 1.57962i) q^{14} +(3.39806 - 10.4582i) q^{16} +(-28.0003 - 9.09786i) q^{17} +(-7.52161 + 10.3526i) q^{19} +(8.93092 + 27.4865i) q^{20} +(-2.41921 + 6.81818i) q^{22} +12.6293 q^{23} +(-32.8719 - 23.8828i) q^{25} +(-7.86851 + 5.71681i) q^{26} +(13.8635 + 4.50452i) q^{28} +(7.85901 + 10.8170i) q^{29} +(10.9884 + 33.8187i) q^{31} +27.1405i q^{32} +19.3634 q^{34} +(-31.4828 + 10.2294i) q^{35} +(14.5329 - 10.5587i) q^{37} +(2.60075 - 8.00429i) q^{38} +(-23.7001 - 32.6203i) q^{40} +(-9.51144 + 13.0914i) q^{41} +44.2415i q^{43} +(-1.05159 + 39.2277i) q^{44} +(-7.89971 + 2.56677i) q^{46} +(-7.76454 - 5.64127i) q^{47} +(9.98240 - 30.7227i) q^{49} +(25.4155 + 8.25799i) q^{50} +(-31.0088 + 42.6800i) q^{52} +(-17.8438 - 54.9177i) q^{53} +(-50.4296 - 73.4732i) q^{55} -20.3368 q^{56} +(-7.11429 - 5.16883i) q^{58} +(81.1105 - 58.9302i) q^{59} +(79.0445 + 25.6831i) q^{61} +(-13.7466 - 18.9205i) q^{62} +(8.07624 + 24.8561i) q^{64} -119.803i q^{65} +87.5688 q^{67} +(99.8895 - 32.4561i) q^{68} +(17.6136 - 12.7971i) q^{70} +(-21.1594 + 65.1219i) q^{71} +(-15.2790 - 21.0298i) q^{73} +(-6.94443 + 9.55819i) q^{74} -45.6508i q^{76} +(-44.9310 - 1.20448i) q^{77} +(-62.3915 + 20.2722i) q^{79} +(-72.0716 - 52.3631i) q^{80} +(3.28878 - 10.1218i) q^{82} +(83.0198 + 26.9748i) q^{83} +(-140.195 + 192.962i) q^{85} +(-8.99160 - 27.6733i) q^{86} +(-15.5166 - 52.5028i) q^{88} -29.3444 q^{89} +(-48.8852 - 35.5172i) q^{91} +(-36.4497 + 26.4823i) q^{92} +(6.00329 + 1.95059i) q^{94} +(60.9352 + 83.8701i) q^{95} +(-11.3670 - 34.9841i) q^{97} +21.2460i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4} + 30 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} + 30 q^{7} - 30 q^{13} - 176 q^{16} + 90 q^{22} - 74 q^{25} - 50 q^{28} + 130 q^{31} + 328 q^{34} + 90 q^{37} + 450 q^{40} - 370 q^{46} - 54 q^{49} - 790 q^{52} - 476 q^{55} - 630 q^{58} + 210 q^{61} + 1104 q^{64} + 300 q^{67} + 268 q^{70} - 170 q^{73} + 30 q^{79} + 90 q^{82} - 610 q^{85} - 600 q^{88} - 402 q^{91} + 1030 q^{94} + 870 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{9}{10}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.625505 + 0.203239i −0.312753 + 0.101619i −0.461187 0.887303i \(-0.652576\pi\)
0.148435 + 0.988922i \(0.452576\pi\)
\(3\) 0 0
\(4\) −2.88612 + 2.09689i −0.721529 + 0.524222i
\(5\) 2.50346 7.70484i 0.500691 1.54097i −0.307205 0.951643i \(-0.599394\pi\)
0.807896 0.589325i \(-0.200606\pi\)
\(6\) 0 0
\(7\) −2.40175 3.30573i −0.343108 0.472247i 0.602238 0.798316i \(-0.294276\pi\)
−0.945346 + 0.326069i \(0.894276\pi\)
\(8\) 2.92545 4.02653i 0.365681 0.503316i
\(9\) 0 0
\(10\) 5.32822i 0.532822i
\(11\) 6.70179 8.72273i 0.609254 0.792975i
\(12\) 0 0
\(13\) 14.0643 4.56975i 1.08187 0.351520i 0.286768 0.958000i \(-0.407419\pi\)
0.795098 + 0.606481i \(0.207419\pi\)
\(14\) 2.17416 + 1.57962i 0.155297 + 0.112830i
\(15\) 0 0
\(16\) 3.39806 10.4582i 0.212379 0.653635i
\(17\) −28.0003 9.09786i −1.64708 0.535169i −0.668975 0.743285i \(-0.733267\pi\)
−0.978104 + 0.208116i \(0.933267\pi\)
\(18\) 0 0
\(19\) −7.52161 + 10.3526i −0.395874 + 0.544874i −0.959702 0.281018i \(-0.909328\pi\)
0.563828 + 0.825892i \(0.309328\pi\)
\(20\) 8.93092 + 27.4865i 0.446546 + 1.37433i
\(21\) 0 0
\(22\) −2.41921 + 6.81818i −0.109964 + 0.309917i
\(23\) 12.6293 0.549101 0.274551 0.961573i \(-0.411471\pi\)
0.274551 + 0.961573i \(0.411471\pi\)
\(24\) 0 0
\(25\) −32.8719 23.8828i −1.31488 0.955314i
\(26\) −7.86851 + 5.71681i −0.302635 + 0.219877i
\(27\) 0 0
\(28\) 13.8635 + 4.50452i 0.495124 + 0.160876i
\(29\) 7.85901 + 10.8170i 0.271000 + 0.373000i 0.922727 0.385454i \(-0.125955\pi\)
−0.651727 + 0.758454i \(0.725955\pi\)
\(30\) 0 0
\(31\) 10.9884 + 33.8187i 0.354464 + 1.09093i 0.956320 + 0.292322i \(0.0944280\pi\)
−0.601856 + 0.798604i \(0.705572\pi\)
\(32\) 27.1405i 0.848141i
\(33\) 0 0
\(34\) 19.3634 0.569512
\(35\) −31.4828 + 10.2294i −0.899509 + 0.292268i
\(36\) 0 0
\(37\) 14.5329 10.5587i 0.392780 0.285371i −0.373814 0.927504i \(-0.621950\pi\)
0.766594 + 0.642132i \(0.221950\pi\)
\(38\) 2.60075 8.00429i 0.0684408 0.210639i
\(39\) 0 0
\(40\) −23.7001 32.6203i −0.592502 0.815509i
\(41\) −9.51144 + 13.0914i −0.231986 + 0.319302i −0.909101 0.416576i \(-0.863230\pi\)
0.677115 + 0.735877i \(0.263230\pi\)
\(42\) 0 0
\(43\) 44.2415i 1.02887i 0.857529 + 0.514436i \(0.171999\pi\)
−0.857529 + 0.514436i \(0.828001\pi\)
\(44\) −1.05159 + 39.2277i −0.0238998 + 0.891539i
\(45\) 0 0
\(46\) −7.89971 + 2.56677i −0.171733 + 0.0557994i
\(47\) −7.76454 5.64127i −0.165203 0.120027i 0.502112 0.864803i \(-0.332557\pi\)
−0.667315 + 0.744776i \(0.732557\pi\)
\(48\) 0 0
\(49\) 9.98240 30.7227i 0.203723 0.626994i
\(50\) 25.4155 + 8.25799i 0.508309 + 0.165160i
\(51\) 0 0
\(52\) −31.0088 + 42.6800i −0.596324 + 0.820769i
\(53\) −17.8438 54.9177i −0.336676 1.03618i −0.965890 0.258951i \(-0.916623\pi\)
0.629214 0.777232i \(-0.283377\pi\)
\(54\) 0 0
\(55\) −50.4296 73.4732i −0.916902 1.33588i
\(56\) −20.3368 −0.363157
\(57\) 0 0
\(58\) −7.11429 5.16883i −0.122660 0.0891178i
\(59\) 81.1105 58.9302i 1.37475 0.998817i 0.377405 0.926048i \(-0.376817\pi\)
0.997349 0.0727685i \(-0.0231834\pi\)
\(60\) 0 0
\(61\) 79.0445 + 25.6831i 1.29581 + 0.421035i 0.874123 0.485705i \(-0.161437\pi\)
0.421690 + 0.906740i \(0.361437\pi\)
\(62\) −13.7466 18.9205i −0.221719 0.305170i
\(63\) 0 0
\(64\) 8.07624 + 24.8561i 0.126191 + 0.388377i
\(65\) 119.803i 1.84312i
\(66\) 0 0
\(67\) 87.5688 1.30700 0.653499 0.756928i \(-0.273301\pi\)
0.653499 + 0.756928i \(0.273301\pi\)
\(68\) 99.8895 32.4561i 1.46896 0.477295i
\(69\) 0 0
\(70\) 17.6136 12.7971i 0.251624 0.182815i
\(71\) −21.1594 + 65.1219i −0.298019 + 0.917210i 0.684171 + 0.729322i \(0.260164\pi\)
−0.982190 + 0.187888i \(0.939836\pi\)
\(72\) 0 0
\(73\) −15.2790 21.0298i −0.209302 0.288079i 0.691440 0.722434i \(-0.256977\pi\)
−0.900742 + 0.434355i \(0.856977\pi\)
\(74\) −6.94443 + 9.55819i −0.0938436 + 0.129165i
\(75\) 0 0
\(76\) 45.6508i 0.600668i
\(77\) −44.9310 1.20448i −0.583520 0.0156426i
\(78\) 0 0
\(79\) −62.3915 + 20.2722i −0.789766 + 0.256611i −0.676004 0.736898i \(-0.736290\pi\)
−0.113762 + 0.993508i \(0.536290\pi\)
\(80\) −72.0716 52.3631i −0.900895 0.654538i
\(81\) 0 0
\(82\) 3.28878 10.1218i 0.0401070 0.123437i
\(83\) 83.0198 + 26.9748i 1.00024 + 0.324997i 0.762961 0.646444i \(-0.223745\pi\)
0.237278 + 0.971442i \(0.423745\pi\)
\(84\) 0 0
\(85\) −140.195 + 192.962i −1.64936 + 2.27014i
\(86\) −8.99160 27.6733i −0.104554 0.321783i
\(87\) 0 0
\(88\) −15.5166 52.5028i −0.176325 0.596623i
\(89\) −29.3444 −0.329713 −0.164856 0.986318i \(-0.552716\pi\)
−0.164856 + 0.986318i \(0.552716\pi\)
\(90\) 0 0
\(91\) −48.8852 35.5172i −0.537200 0.390299i
\(92\) −36.4497 + 26.4823i −0.396193 + 0.287851i
\(93\) 0 0
\(94\) 6.00329 + 1.95059i 0.0638647 + 0.0207509i
\(95\) 60.9352 + 83.8701i 0.641423 + 0.882843i
\(96\) 0 0
\(97\) −11.3670 34.9841i −0.117186 0.360661i 0.875211 0.483741i \(-0.160723\pi\)
−0.992397 + 0.123081i \(0.960723\pi\)
\(98\) 21.2460i 0.216796i
\(99\) 0 0
\(100\) 144.952 1.44952
\(101\) −86.1862 + 28.0036i −0.853329 + 0.277263i −0.702840 0.711348i \(-0.748085\pi\)
−0.150489 + 0.988612i \(0.548085\pi\)
\(102\) 0 0
\(103\) 124.184 90.2248i 1.20567 0.875969i 0.210838 0.977521i \(-0.432381\pi\)
0.994830 + 0.101552i \(0.0323809\pi\)
\(104\) 22.7440 69.9987i 0.218692 0.673065i
\(105\) 0 0
\(106\) 22.3228 + 30.7247i 0.210593 + 0.289856i
\(107\) −39.6735 + 54.6059i −0.370780 + 0.510336i −0.953113 0.302615i \(-0.902140\pi\)
0.582332 + 0.812951i \(0.302140\pi\)
\(108\) 0 0
\(109\) 150.536i 1.38106i 0.723304 + 0.690530i \(0.242623\pi\)
−0.723304 + 0.690530i \(0.757377\pi\)
\(110\) 46.4766 + 35.7086i 0.422515 + 0.324624i
\(111\) 0 0
\(112\) −42.7331 + 13.8848i −0.381546 + 0.123972i
\(113\) 118.763 + 86.2867i 1.05100 + 0.763599i 0.972403 0.233307i \(-0.0749547\pi\)
0.0786011 + 0.996906i \(0.474955\pi\)
\(114\) 0 0
\(115\) 31.6170 97.3070i 0.274930 0.846148i
\(116\) −45.3641 14.7397i −0.391070 0.127066i
\(117\) 0 0
\(118\) −38.7581 + 53.3459i −0.328458 + 0.452084i
\(119\) 37.1748 + 114.412i 0.312394 + 0.961449i
\(120\) 0 0
\(121\) −31.1719 116.916i −0.257619 0.966247i
\(122\) −54.6626 −0.448054
\(123\) 0 0
\(124\) −102.628 74.5634i −0.827643 0.601318i
\(125\) −102.454 + 74.4369i −0.819629 + 0.595496i
\(126\) 0 0
\(127\) 61.3816 + 19.9441i 0.483320 + 0.157040i 0.540535 0.841322i \(-0.318222\pi\)
−0.0572147 + 0.998362i \(0.518222\pi\)
\(128\) −73.9146 101.735i −0.577458 0.794803i
\(129\) 0 0
\(130\) 24.3486 + 74.9374i 0.187297 + 0.576442i
\(131\) 222.809i 1.70083i 0.526110 + 0.850416i \(0.323650\pi\)
−0.526110 + 0.850416i \(0.676350\pi\)
\(132\) 0 0
\(133\) 52.2879 0.393142
\(134\) −54.7747 + 17.7974i −0.408767 + 0.132816i
\(135\) 0 0
\(136\) −118.546 + 86.1289i −0.871664 + 0.633301i
\(137\) −15.7350 + 48.4274i −0.114854 + 0.353485i −0.991917 0.126892i \(-0.959500\pi\)
0.877062 + 0.480376i \(0.159500\pi\)
\(138\) 0 0
\(139\) −78.0268 107.395i −0.561344 0.772623i 0.430153 0.902756i \(-0.358460\pi\)
−0.991497 + 0.130133i \(0.958460\pi\)
\(140\) 69.4132 95.5391i 0.495809 0.682422i
\(141\) 0 0
\(142\) 45.0345i 0.317144i
\(143\) 54.3950 153.304i 0.380385 1.07206i
\(144\) 0 0
\(145\) 103.018 33.4726i 0.710469 0.230845i
\(146\) 13.8312 + 10.0489i 0.0947341 + 0.0688283i
\(147\) 0 0
\(148\) −19.8030 + 60.9475i −0.133804 + 0.411808i
\(149\) −250.465 81.3809i −1.68097 0.546181i −0.695872 0.718166i \(-0.744982\pi\)
−0.985100 + 0.171985i \(0.944982\pi\)
\(150\) 0 0
\(151\) −29.6709 + 40.8385i −0.196496 + 0.270453i −0.895883 0.444289i \(-0.853456\pi\)
0.699387 + 0.714743i \(0.253456\pi\)
\(152\) 19.6810 + 60.5720i 0.129480 + 0.398500i
\(153\) 0 0
\(154\) 28.3494 8.37832i 0.184087 0.0544047i
\(155\) 288.077 1.85856
\(156\) 0 0
\(157\) −24.3706 17.7063i −0.155227 0.112779i 0.507461 0.861675i \(-0.330584\pi\)
−0.662688 + 0.748896i \(0.730584\pi\)
\(158\) 34.9061 25.3608i 0.220925 0.160511i
\(159\) 0 0
\(160\) 209.113 + 67.9451i 1.30696 + 0.424657i
\(161\) −30.3325 41.7491i −0.188401 0.259311i
\(162\) 0 0
\(163\) 31.7613 + 97.7512i 0.194855 + 0.599701i 0.999978 + 0.00659367i \(0.00209884\pi\)
−0.805124 + 0.593107i \(0.797901\pi\)
\(164\) 57.7276i 0.351998i
\(165\) 0 0
\(166\) −57.4117 −0.345853
\(167\) 126.936 41.2441i 0.760098 0.246971i 0.0967772 0.995306i \(-0.469147\pi\)
0.663321 + 0.748335i \(0.269147\pi\)
\(168\) 0 0
\(169\) 40.1968 29.2047i 0.237851 0.172809i
\(170\) 48.4754 149.192i 0.285150 0.877600i
\(171\) 0 0
\(172\) −92.7695 127.686i −0.539358 0.742362i
\(173\) 144.968 199.531i 0.837963 1.15336i −0.148426 0.988924i \(-0.547421\pi\)
0.986388 0.164433i \(-0.0525794\pi\)
\(174\) 0 0
\(175\) 166.026i 0.948722i
\(176\) −68.4505 99.7288i −0.388924 0.566641i
\(177\) 0 0
\(178\) 18.3551 5.96393i 0.103119 0.0335052i
\(179\) −53.5634 38.9161i −0.299237 0.217408i 0.428028 0.903766i \(-0.359209\pi\)
−0.727264 + 0.686357i \(0.759209\pi\)
\(180\) 0 0
\(181\) 48.9480 150.646i 0.270431 0.832301i −0.719961 0.694014i \(-0.755840\pi\)
0.990392 0.138287i \(-0.0441595\pi\)
\(182\) 37.7964 + 12.2808i 0.207673 + 0.0674770i
\(183\) 0 0
\(184\) 36.9464 50.8524i 0.200796 0.276372i
\(185\) −44.9711 138.407i −0.243087 0.748144i
\(186\) 0 0
\(187\) −267.011 + 183.267i −1.42786 + 0.980039i
\(188\) 34.2385 0.182120
\(189\) 0 0
\(190\) −55.1609 40.0768i −0.290321 0.210930i
\(191\) −120.402 + 87.4774i −0.630378 + 0.457997i −0.856531 0.516095i \(-0.827385\pi\)
0.226153 + 0.974092i \(0.427385\pi\)
\(192\) 0 0
\(193\) −204.065 66.3048i −1.05733 0.343548i −0.271790 0.962357i \(-0.587616\pi\)
−0.785542 + 0.618809i \(0.787616\pi\)
\(194\) 14.2202 + 19.5725i 0.0733003 + 0.100889i
\(195\) 0 0
\(196\) 35.6116 + 109.601i 0.181692 + 0.559190i
\(197\) 54.8802i 0.278580i −0.990252 0.139290i \(-0.955518\pi\)
0.990252 0.139290i \(-0.0444820\pi\)
\(198\) 0 0
\(199\) −58.1547 −0.292235 −0.146117 0.989267i \(-0.546678\pi\)
−0.146117 + 0.989267i \(0.546678\pi\)
\(200\) −192.330 + 62.4918i −0.961650 + 0.312459i
\(201\) 0 0
\(202\) 48.2185 35.0328i 0.238705 0.173430i
\(203\) 16.8827 51.9595i 0.0831659 0.255958i
\(204\) 0 0
\(205\) 77.0555 + 106.058i 0.375880 + 0.517355i
\(206\) −59.3404 + 81.6750i −0.288060 + 0.396481i
\(207\) 0 0
\(208\) 162.615i 0.781801i
\(209\) 39.8947 + 134.990i 0.190884 + 0.645885i
\(210\) 0 0
\(211\) 215.270 69.9454i 1.02024 0.331495i 0.249313 0.968423i \(-0.419795\pi\)
0.770923 + 0.636928i \(0.219795\pi\)
\(212\) 166.656 + 121.082i 0.786112 + 0.571144i
\(213\) 0 0
\(214\) 13.7179 42.2195i 0.0641025 0.197287i
\(215\) 340.874 + 110.757i 1.58546 + 0.515148i
\(216\) 0 0
\(217\) 85.4042 117.549i 0.393568 0.541700i
\(218\) −30.5947 94.1607i −0.140343 0.431930i
\(219\) 0 0
\(220\) 299.611 + 106.307i 1.36187 + 0.483215i
\(221\) −435.379 −1.97004
\(222\) 0 0
\(223\) 66.7089 + 48.4669i 0.299143 + 0.217340i 0.727224 0.686400i \(-0.240810\pi\)
−0.428081 + 0.903740i \(0.640810\pi\)
\(224\) 89.7192 65.1848i 0.400532 0.291004i
\(225\) 0 0
\(226\) −91.8240 29.8354i −0.406301 0.132015i
\(227\) −103.962 143.092i −0.457984 0.630361i 0.516105 0.856525i \(-0.327381\pi\)
−0.974089 + 0.226164i \(0.927381\pi\)
\(228\) 0 0
\(229\) −0.902758 2.77840i −0.00394217 0.0121328i 0.949066 0.315077i \(-0.102030\pi\)
−0.953008 + 0.302944i \(0.902030\pi\)
\(230\) 67.2918i 0.292573i
\(231\) 0 0
\(232\) 66.5461 0.286837
\(233\) 280.090 91.0066i 1.20210 0.390586i 0.361568 0.932346i \(-0.382242\pi\)
0.840533 + 0.541760i \(0.182242\pi\)
\(234\) 0 0
\(235\) −62.9033 + 45.7019i −0.267674 + 0.194476i
\(236\) −110.524 + 340.159i −0.468323 + 1.44135i
\(237\) 0 0
\(238\) −46.5061 64.0102i −0.195404 0.268950i
\(239\) −201.543 + 277.400i −0.843275 + 1.16067i 0.142029 + 0.989862i \(0.454637\pi\)
−0.985305 + 0.170806i \(0.945363\pi\)
\(240\) 0 0
\(241\) 43.2741i 0.179561i −0.995962 0.0897804i \(-0.971383\pi\)
0.995962 0.0897804i \(-0.0286165\pi\)
\(242\) 43.2600 + 66.7961i 0.178760 + 0.276017i
\(243\) 0 0
\(244\) −281.986 + 91.6230i −1.15568 + 0.375504i
\(245\) −211.723 153.826i −0.864175 0.627860i
\(246\) 0 0
\(247\) −58.4770 + 179.974i −0.236749 + 0.728638i
\(248\) 168.318 + 54.6898i 0.678702 + 0.220524i
\(249\) 0 0
\(250\) 48.9568 67.3833i 0.195827 0.269533i
\(251\) 36.1563 + 111.278i 0.144049 + 0.443337i 0.996887 0.0788375i \(-0.0251208\pi\)
−0.852838 + 0.522175i \(0.825121\pi\)
\(252\) 0 0
\(253\) 84.6391 110.162i 0.334542 0.435423i
\(254\) −42.4479 −0.167118
\(255\) 0 0
\(256\) −17.6650 12.8344i −0.0690040 0.0501344i
\(257\) 22.8578 16.6072i 0.0889409 0.0646193i −0.542426 0.840104i \(-0.682494\pi\)
0.631367 + 0.775484i \(0.282494\pi\)
\(258\) 0 0
\(259\) −69.8087 22.6822i −0.269531 0.0875761i
\(260\) 251.214 + 345.766i 0.966206 + 1.32987i
\(261\) 0 0
\(262\) −45.2835 139.368i −0.172838 0.531940i
\(263\) 247.683i 0.941759i −0.882198 0.470879i \(-0.843937\pi\)
0.882198 0.470879i \(-0.156063\pi\)
\(264\) 0 0
\(265\) −467.804 −1.76530
\(266\) −32.7064 + 10.6269i −0.122956 + 0.0399509i
\(267\) 0 0
\(268\) −252.734 + 183.622i −0.943037 + 0.685156i
\(269\) −85.7617 + 263.947i −0.318817 + 0.981217i 0.655338 + 0.755336i \(0.272526\pi\)
−0.974155 + 0.225882i \(0.927474\pi\)
\(270\) 0 0
\(271\) 232.311 + 319.749i 0.857238 + 1.17989i 0.982221 + 0.187727i \(0.0601122\pi\)
−0.124984 + 0.992159i \(0.539888\pi\)
\(272\) −190.294 + 261.917i −0.699610 + 0.962930i
\(273\) 0 0
\(274\) 33.4896i 0.122225i
\(275\) −428.624 + 126.675i −1.55863 + 0.460636i
\(276\) 0 0
\(277\) 199.908 64.9542i 0.721691 0.234492i 0.0749347 0.997188i \(-0.476125\pi\)
0.646756 + 0.762697i \(0.276125\pi\)
\(278\) 70.6329 + 51.3178i 0.254075 + 0.184596i
\(279\) 0 0
\(280\) −50.9123 + 156.692i −0.181830 + 0.559614i
\(281\) 24.8709 + 8.08106i 0.0885087 + 0.0287582i 0.352937 0.935647i \(-0.385183\pi\)
−0.264428 + 0.964405i \(0.585183\pi\)
\(282\) 0 0
\(283\) 173.462 238.750i 0.612941 0.843641i −0.383874 0.923385i \(-0.625410\pi\)
0.996815 + 0.0797445i \(0.0254105\pi\)
\(284\) −75.4848 232.318i −0.265791 0.818022i
\(285\) 0 0
\(286\) −2.86699 + 106.948i −0.0100244 + 0.373943i
\(287\) 66.1206 0.230385
\(288\) 0 0
\(289\) 467.442 + 339.617i 1.61745 + 1.17514i
\(290\) −57.6354 + 41.8745i −0.198743 + 0.144395i
\(291\) 0 0
\(292\) 88.1941 + 28.6560i 0.302035 + 0.0981370i
\(293\) −36.5499 50.3066i −0.124744 0.171695i 0.742078 0.670314i \(-0.233841\pi\)
−0.866821 + 0.498619i \(0.833841\pi\)
\(294\) 0 0
\(295\) −250.992 772.473i −0.850819 2.61855i
\(296\) 89.4060i 0.302047i
\(297\) 0 0
\(298\) 173.207 0.581231
\(299\) 177.622 57.7129i 0.594054 0.193020i
\(300\) 0 0
\(301\) 146.251 106.257i 0.485882 0.353014i
\(302\) 10.2593 31.5749i 0.0339713 0.104553i
\(303\) 0 0
\(304\) 82.7103 + 113.841i 0.272073 + 0.374477i
\(305\) 395.769 544.729i 1.29760 1.78600i
\(306\) 0 0
\(307\) 119.712i 0.389941i 0.980809 + 0.194970i \(0.0624610\pi\)
−0.980809 + 0.194970i \(0.937539\pi\)
\(308\) 132.202 90.7390i 0.429227 0.294607i
\(309\) 0 0
\(310\) −180.194 + 58.5484i −0.581270 + 0.188866i
\(311\) −253.352 184.071i −0.814638 0.591869i 0.100534 0.994934i \(-0.467945\pi\)
−0.915172 + 0.403065i \(0.867945\pi\)
\(312\) 0 0
\(313\) −121.315 + 373.369i −0.387588 + 1.19287i 0.546998 + 0.837134i \(0.315770\pi\)
−0.934586 + 0.355738i \(0.884230\pi\)
\(314\) 18.8426 + 6.12232i 0.0600082 + 0.0194978i
\(315\) 0 0
\(316\) 137.561 189.336i 0.435319 0.599165i
\(317\) 10.9585 + 33.7267i 0.0345693 + 0.106393i 0.966852 0.255337i \(-0.0821863\pi\)
−0.932283 + 0.361730i \(0.882186\pi\)
\(318\) 0 0
\(319\) 147.023 + 3.94131i 0.460888 + 0.0123552i
\(320\) 211.731 0.661659
\(321\) 0 0
\(322\) 27.4582 + 19.9495i 0.0852739 + 0.0619551i
\(323\) 304.794 221.446i 0.943635 0.685591i
\(324\) 0 0
\(325\) −571.458 185.678i −1.75833 0.571317i
\(326\) −39.7337 54.6887i −0.121882 0.167757i
\(327\) 0 0
\(328\) 24.8876 + 76.5962i 0.0758768 + 0.233525i
\(329\) 39.2164i 0.119199i
\(330\) 0 0
\(331\) −437.250 −1.32100 −0.660498 0.750828i \(-0.729655\pi\)
−0.660498 + 0.750828i \(0.729655\pi\)
\(332\) −296.168 + 96.2308i −0.892072 + 0.289852i
\(333\) 0 0
\(334\) −71.0169 + 51.5968i −0.212625 + 0.154481i
\(335\) 219.225 674.704i 0.654402 2.01404i
\(336\) 0 0
\(337\) 96.3092 + 132.558i 0.285784 + 0.393348i 0.927639 0.373478i \(-0.121835\pi\)
−0.641855 + 0.766826i \(0.721835\pi\)
\(338\) −19.2078 + 26.4372i −0.0568277 + 0.0782166i
\(339\) 0 0
\(340\) 850.885i 2.50260i
\(341\) 368.633 + 130.798i 1.08104 + 0.383571i
\(342\) 0 0
\(343\) −315.956 + 102.660i −0.921154 + 0.299301i
\(344\) 178.140 + 129.426i 0.517849 + 0.376239i
\(345\) 0 0
\(346\) −50.1255 + 154.271i −0.144871 + 0.445868i
\(347\) −475.145 154.384i −1.36929 0.444910i −0.470158 0.882582i \(-0.655803\pi\)
−0.899135 + 0.437672i \(0.855803\pi\)
\(348\) 0 0
\(349\) 172.838 237.892i 0.495239 0.681638i −0.486104 0.873901i \(-0.661583\pi\)
0.981344 + 0.192263i \(0.0615825\pi\)
\(350\) −33.7430 103.850i −0.0964086 0.296715i
\(351\) 0 0
\(352\) 236.739 + 181.890i 0.672555 + 0.516733i
\(353\) 36.8161 0.104295 0.0521474 0.998639i \(-0.483393\pi\)
0.0521474 + 0.998639i \(0.483393\pi\)
\(354\) 0 0
\(355\) 448.782 + 326.059i 1.26418 + 0.918477i
\(356\) 84.6915 61.5320i 0.237897 0.172843i
\(357\) 0 0
\(358\) 41.4134 + 13.4560i 0.115680 + 0.0375867i
\(359\) −219.070 301.524i −0.610224 0.839901i 0.386372 0.922343i \(-0.373728\pi\)
−0.996596 + 0.0824421i \(0.973728\pi\)
\(360\) 0 0
\(361\) 60.9533 + 187.595i 0.168846 + 0.519654i
\(362\) 104.178i 0.287785i
\(363\) 0 0
\(364\) 215.564 0.592209
\(365\) −200.281 + 65.0754i −0.548716 + 0.178289i
\(366\) 0 0
\(367\) 172.545 125.361i 0.470150 0.341584i −0.327350 0.944903i \(-0.606156\pi\)
0.797500 + 0.603319i \(0.206156\pi\)
\(368\) 42.9152 132.079i 0.116617 0.358912i
\(369\) 0 0
\(370\) 56.2593 + 77.4342i 0.152052 + 0.209282i
\(371\) −138.687 + 190.886i −0.373818 + 0.514517i
\(372\) 0 0
\(373\) 32.7478i 0.0877957i −0.999036 0.0438978i \(-0.986022\pi\)
0.999036 0.0438978i \(-0.0139776\pi\)
\(374\) 129.770 168.902i 0.346977 0.451609i
\(375\) 0 0
\(376\) −45.4295 + 14.7609i −0.120823 + 0.0392578i
\(377\) 159.962 + 116.219i 0.424303 + 0.308274i
\(378\) 0 0
\(379\) 167.782 516.378i 0.442695 1.36248i −0.442296 0.896869i \(-0.645836\pi\)
0.884992 0.465607i \(-0.154164\pi\)
\(380\) −351.732 114.285i −0.925611 0.300749i
\(381\) 0 0
\(382\) 57.5334 79.1880i 0.150611 0.207298i
\(383\) 184.991 + 569.343i 0.483005 + 1.48654i 0.834850 + 0.550477i \(0.185554\pi\)
−0.351845 + 0.936058i \(0.614446\pi\)
\(384\) 0 0
\(385\) −121.763 + 343.171i −0.316268 + 0.891354i
\(386\) 141.119 0.365594
\(387\) 0 0
\(388\) 106.164 + 77.1328i 0.273619 + 0.198796i
\(389\) −178.494 + 129.684i −0.458854 + 0.333377i −0.793082 0.609115i \(-0.791525\pi\)
0.334228 + 0.942492i \(0.391525\pi\)
\(390\) 0 0
\(391\) −353.625 114.900i −0.904413 0.293862i
\(392\) −94.5028 130.072i −0.241079 0.331816i
\(393\) 0 0
\(394\) 11.1538 + 34.3278i 0.0283091 + 0.0871265i
\(395\) 531.468i 1.34549i
\(396\) 0 0
\(397\) −734.263 −1.84953 −0.924764 0.380541i \(-0.875738\pi\)
−0.924764 + 0.380541i \(0.875738\pi\)
\(398\) 36.3760 11.8193i 0.0913971 0.0296967i
\(399\) 0 0
\(400\) −361.471 + 262.624i −0.903678 + 0.656561i
\(401\) −28.1108 + 86.5163i −0.0701019 + 0.215751i −0.979970 0.199147i \(-0.936183\pi\)
0.909868 + 0.414898i \(0.136183\pi\)
\(402\) 0 0
\(403\) 309.087 + 425.421i 0.766964 + 1.05564i
\(404\) 190.023 261.544i 0.470354 0.647387i
\(405\) 0 0
\(406\) 35.9322i 0.0885029i
\(407\) 5.29522 197.529i 0.0130104 0.485328i
\(408\) 0 0
\(409\) 165.356 53.7274i 0.404293 0.131363i −0.0998094 0.995007i \(-0.531823\pi\)
0.504103 + 0.863644i \(0.331823\pi\)
\(410\) −69.7537 50.6790i −0.170131 0.123607i
\(411\) 0 0
\(412\) −169.218 + 520.799i −0.410723 + 1.26407i
\(413\) −389.615 126.593i −0.943377 0.306522i
\(414\) 0 0
\(415\) 415.673 572.125i 1.00162 1.37861i
\(416\) 124.025 + 381.711i 0.298138 + 0.917575i
\(417\) 0 0
\(418\) −52.3895 76.3287i −0.125334 0.182605i
\(419\) 374.418 0.893599 0.446800 0.894634i \(-0.352564\pi\)
0.446800 + 0.894634i \(0.352564\pi\)
\(420\) 0 0
\(421\) 0.0922850 + 0.0670490i 0.000219204 + 0.000159261i 0.587895 0.808937i \(-0.299957\pi\)
−0.587676 + 0.809097i \(0.699957\pi\)
\(422\) −120.437 + 87.5024i −0.285395 + 0.207352i
\(423\) 0 0
\(424\) −273.329 88.8100i −0.644644 0.209458i
\(425\) 703.142 + 967.792i 1.65445 + 2.27716i
\(426\) 0 0
\(427\) −104.944 322.984i −0.245770 0.756404i
\(428\) 240.790i 0.562593i
\(429\) 0 0
\(430\) −235.729 −0.548206
\(431\) −252.091 + 81.9092i −0.584897 + 0.190045i −0.586493 0.809954i \(-0.699492\pi\)
0.00159618 + 0.999999i \(0.499492\pi\)
\(432\) 0 0
\(433\) 145.782 105.917i 0.336679 0.244612i −0.406580 0.913615i \(-0.633279\pi\)
0.743259 + 0.669003i \(0.233279\pi\)
\(434\) −29.5303 + 90.8848i −0.0680421 + 0.209412i
\(435\) 0 0
\(436\) −315.656 434.463i −0.723982 0.996475i
\(437\) −94.9928 + 130.746i −0.217375 + 0.299191i
\(438\) 0 0
\(439\) 410.931i 0.936062i 0.883712 + 0.468031i \(0.155037\pi\)
−0.883712 + 0.468031i \(0.844963\pi\)
\(440\) −443.371 11.8856i −1.00766 0.0270128i
\(441\) 0 0
\(442\) 272.332 88.4860i 0.616135 0.200195i
\(443\) −17.7973 12.9305i −0.0401744 0.0291884i 0.567517 0.823362i \(-0.307904\pi\)
−0.607691 + 0.794173i \(0.707904\pi\)
\(444\) 0 0
\(445\) −73.4625 + 226.094i −0.165084 + 0.508077i
\(446\) −51.5771 16.7584i −0.115644 0.0375749i
\(447\) 0 0
\(448\) 62.7704 86.3961i 0.140113 0.192848i
\(449\) 44.5645 + 137.155i 0.0992528 + 0.305469i 0.988339 0.152272i \(-0.0486589\pi\)
−0.889086 + 0.457740i \(0.848659\pi\)
\(450\) 0 0
\(451\) 50.4487 + 170.701i 0.111860 + 0.378495i
\(452\) −523.699 −1.15863
\(453\) 0 0
\(454\) 94.1109 + 68.3756i 0.207293 + 0.150607i
\(455\) −396.037 + 287.737i −0.870410 + 0.632390i
\(456\) 0 0
\(457\) 699.008 + 227.122i 1.52956 + 0.496984i 0.948473 0.316859i \(-0.102628\pi\)
0.581086 + 0.813842i \(0.302628\pi\)
\(458\) 1.12936 + 1.55443i 0.00246585 + 0.00339395i
\(459\) 0 0
\(460\) 112.792 + 347.137i 0.245199 + 0.754645i
\(461\) 128.454i 0.278643i 0.990247 + 0.139321i \(0.0444921\pi\)
−0.990247 + 0.139321i \(0.955508\pi\)
\(462\) 0 0
\(463\) 7.10283 0.0153409 0.00767044 0.999971i \(-0.497558\pi\)
0.00767044 + 0.999971i \(0.497558\pi\)
\(464\) 139.831 45.4340i 0.301361 0.0979180i
\(465\) 0 0
\(466\) −156.701 + 113.850i −0.336269 + 0.244314i
\(467\) −88.2695 + 271.666i −0.189014 + 0.581725i −0.999994 0.00334813i \(-0.998934\pi\)
0.810980 + 0.585073i \(0.198934\pi\)
\(468\) 0 0
\(469\) −210.319 289.479i −0.448441 0.617225i
\(470\) 30.0579 41.3712i 0.0639530 0.0880238i
\(471\) 0 0
\(472\) 498.991i 1.05718i
\(473\) 385.907 + 296.498i 0.815871 + 0.626845i
\(474\) 0 0
\(475\) 494.499 160.673i 1.04105 0.338258i
\(476\) −347.201 252.256i −0.729413 0.529950i
\(477\) 0 0
\(478\) 69.6876 214.476i 0.145790 0.448695i
\(479\) 373.411 + 121.329i 0.779564 + 0.253296i 0.671654 0.740865i \(-0.265584\pi\)
0.107910 + 0.994161i \(0.465584\pi\)
\(480\) 0 0
\(481\) 156.143 214.912i 0.324622 0.446803i
\(482\) 8.79499 + 27.0682i 0.0182469 + 0.0561581i
\(483\) 0 0
\(484\) 335.125 + 272.069i 0.692407 + 0.562126i
\(485\) −298.004 −0.614440
\(486\) 0 0
\(487\) −417.281 303.173i −0.856841 0.622531i 0.0701830 0.997534i \(-0.477642\pi\)
−0.927024 + 0.375003i \(0.877642\pi\)
\(488\) 334.654 243.141i 0.685767 0.498239i
\(489\) 0 0
\(490\) 163.697 + 53.1884i 0.334076 + 0.108548i
\(491\) −181.495 249.807i −0.369644 0.508771i 0.583160 0.812357i \(-0.301816\pi\)
−0.952804 + 0.303586i \(0.901816\pi\)
\(492\) 0 0
\(493\) −121.643 374.380i −0.246741 0.759392i
\(494\) 124.459i 0.251942i
\(495\) 0 0
\(496\) 391.021 0.788348
\(497\) 266.095 86.4595i 0.535402 0.173963i
\(498\) 0 0
\(499\) −469.197 + 340.892i −0.940275 + 0.683149i −0.948487 0.316817i \(-0.897386\pi\)
0.00821221 + 0.999966i \(0.497386\pi\)
\(500\) 139.607 429.668i 0.279215 0.859335i
\(501\) 0 0
\(502\) −45.2319 62.2564i −0.0901034 0.124017i
\(503\) −458.978 + 631.728i −0.912480 + 1.25592i 0.0538322 + 0.998550i \(0.482856\pi\)
−0.966313 + 0.257371i \(0.917144\pi\)
\(504\) 0 0
\(505\) 734.157i 1.45378i
\(506\) −30.5530 + 86.1089i −0.0603814 + 0.170176i
\(507\) 0 0
\(508\) −218.975 + 71.1493i −0.431053 + 0.140058i
\(509\) 547.788 + 397.992i 1.07621 + 0.781909i 0.977017 0.213160i \(-0.0683756\pi\)
0.0991877 + 0.995069i \(0.468376\pi\)
\(510\) 0 0
\(511\) −32.8223 + 101.017i −0.0642315 + 0.197684i
\(512\) 492.044 + 159.875i 0.961023 + 0.312255i
\(513\) 0 0
\(514\) −10.9225 + 15.0335i −0.0212499 + 0.0292480i
\(515\) −384.279 1182.69i −0.746174 2.29649i
\(516\) 0 0
\(517\) −101.244 + 29.9213i −0.195829 + 0.0578750i
\(518\) 48.2756 0.0931961
\(519\) 0 0
\(520\) −482.391 350.477i −0.927675 0.673995i
\(521\) 538.428 391.191i 1.03345 0.750846i 0.0644546 0.997921i \(-0.479469\pi\)
0.968997 + 0.247074i \(0.0794692\pi\)
\(522\) 0 0
\(523\) −856.820 278.398i −1.63828 0.532309i −0.662127 0.749392i \(-0.730346\pi\)
−0.976153 + 0.217083i \(0.930346\pi\)
\(524\) −467.205 643.053i −0.891613 1.22720i
\(525\) 0 0
\(526\) 50.3387 + 154.927i 0.0957010 + 0.294537i
\(527\) 1046.91i 1.98654i
\(528\) 0 0
\(529\) −369.500 −0.698488
\(530\) 292.614 95.0759i 0.552101 0.179389i
\(531\) 0 0
\(532\) −150.909 + 109.642i −0.283664 + 0.206094i
\(533\) −73.9469 + 227.585i −0.138737 + 0.426989i
\(534\) 0 0
\(535\) 321.409 + 442.382i 0.600765 + 0.826882i
\(536\) 256.178 352.598i 0.477944 0.657833i
\(537\) 0 0
\(538\) 182.531i 0.339276i
\(539\) −201.086 292.971i −0.373072 0.543545i
\(540\) 0 0
\(541\) 370.362 120.338i 0.684587 0.222436i 0.0539846 0.998542i \(-0.482808\pi\)
0.630603 + 0.776106i \(0.282808\pi\)
\(542\) −210.297 152.790i −0.388003 0.281900i
\(543\) 0 0
\(544\) 246.921 759.944i 0.453898 1.39696i
\(545\) 1159.85 + 376.859i 2.12817 + 0.691485i
\(546\) 0 0
\(547\) −414.894 + 571.053i −0.758490 + 1.04397i 0.238848 + 0.971057i \(0.423230\pi\)
−0.997338 + 0.0729151i \(0.976770\pi\)
\(548\) −56.1337 172.762i −0.102434 0.315259i
\(549\) 0 0
\(550\) 242.361 166.349i 0.440657 0.302453i
\(551\) −171.097 −0.310520
\(552\) 0 0
\(553\) 216.863 + 157.561i 0.392158 + 0.284920i
\(554\) −111.842 + 81.2583i −0.201882 + 0.146676i
\(555\) 0 0
\(556\) 450.389 + 146.340i 0.810052 + 0.263202i
\(557\) −97.3073 133.932i −0.174699 0.240452i 0.712684 0.701485i \(-0.247479\pi\)
−0.887383 + 0.461032i \(0.847479\pi\)
\(558\) 0 0
\(559\) 202.173 + 622.224i 0.361669 + 1.11310i
\(560\) 364.012i 0.650022i
\(561\) 0 0
\(562\) −17.1993 −0.0306037
\(563\) −345.683 + 112.319i −0.614002 + 0.199501i −0.599475 0.800393i \(-0.704624\pi\)
−0.0145265 + 0.999894i \(0.504624\pi\)
\(564\) 0 0
\(565\) 962.145 699.039i 1.70291 1.23724i
\(566\) −59.9782 + 184.594i −0.105968 + 0.326138i
\(567\) 0 0
\(568\) 200.315 + 275.709i 0.352667 + 0.485404i
\(569\) 136.330 187.642i 0.239596 0.329775i −0.672238 0.740335i \(-0.734667\pi\)
0.911834 + 0.410560i \(0.134667\pi\)
\(570\) 0 0
\(571\) 306.665i 0.537067i 0.963270 + 0.268533i \(0.0865390\pi\)
−0.963270 + 0.268533i \(0.913461\pi\)
\(572\) 164.471 + 556.514i 0.287537 + 0.972927i
\(573\) 0 0
\(574\) −41.3588 + 13.4383i −0.0720536 + 0.0234116i
\(575\) −415.150 301.624i −0.722000 0.524564i
\(576\) 0 0
\(577\) 26.3161 80.9927i 0.0456085 0.140369i −0.925659 0.378359i \(-0.876489\pi\)
0.971268 + 0.237990i \(0.0764886\pi\)
\(578\) −361.411 117.430i −0.625279 0.203165i
\(579\) 0 0
\(580\) −227.134 + 312.623i −0.391610 + 0.539005i
\(581\) −110.222 339.228i −0.189711 0.583869i
\(582\) 0 0
\(583\) −598.618 212.400i −1.02679 0.364323i
\(584\) −129.375 −0.221532
\(585\) 0 0
\(586\) 33.0864 + 24.0387i 0.0564614 + 0.0410216i
\(587\) 497.688 361.591i 0.847849 0.615999i −0.0767029 0.997054i \(-0.524439\pi\)
0.924552 + 0.381055i \(0.124439\pi\)
\(588\) 0 0
\(589\) −432.762 140.613i −0.734740 0.238732i
\(590\) 313.993 + 432.174i 0.532192 + 0.732499i
\(591\) 0 0
\(592\) −61.0414 187.866i −0.103110 0.317341i
\(593\) 74.4809i 0.125600i −0.998026 0.0628001i \(-0.979997\pi\)
0.998026 0.0628001i \(-0.0200030\pi\)
\(594\) 0 0
\(595\) 974.595 1.63798
\(596\) 893.517 290.321i 1.49919 0.487116i
\(597\) 0 0
\(598\) −99.3740 + 72.1994i −0.166177 + 0.120735i
\(599\) −229.210 + 705.436i −0.382654 + 1.17769i 0.555513 + 0.831508i \(0.312522\pi\)
−0.938168 + 0.346181i \(0.887478\pi\)
\(600\) 0 0
\(601\) −659.404 907.591i −1.09718 1.51014i −0.839073 0.544018i \(-0.816902\pi\)
−0.258104 0.966117i \(-0.583098\pi\)
\(602\) −69.8848 + 96.1882i −0.116088 + 0.159781i
\(603\) 0 0
\(604\) 180.081i 0.298147i
\(605\) −978.856 52.5188i −1.61794 0.0868080i
\(606\) 0 0
\(607\) 10.5343 3.42282i 0.0173548 0.00563891i −0.300327 0.953836i \(-0.597096\pi\)
0.317682 + 0.948197i \(0.397096\pi\)
\(608\) −280.975 204.140i −0.462130 0.335757i
\(609\) 0 0
\(610\) −136.845 + 421.167i −0.224337 + 0.690437i
\(611\) −134.982 43.8582i −0.220919 0.0717811i
\(612\) 0 0
\(613\) −439.604 + 605.064i −0.717136 + 0.987053i 0.282478 + 0.959274i \(0.408844\pi\)
−0.999614 + 0.0277794i \(0.991156\pi\)
\(614\) −24.3301 74.8803i −0.0396255 0.121955i
\(615\) 0 0
\(616\) −136.293 + 177.392i −0.221255 + 0.287975i
\(617\) 771.423 1.25028 0.625140 0.780513i \(-0.285042\pi\)
0.625140 + 0.780513i \(0.285042\pi\)
\(618\) 0 0
\(619\) −141.847 103.058i −0.229156 0.166491i 0.467283 0.884108i \(-0.345233\pi\)
−0.696438 + 0.717617i \(0.745233\pi\)
\(620\) −831.424 + 604.065i −1.34101 + 0.974298i
\(621\) 0 0
\(622\) 195.884 + 63.6465i 0.314925 + 0.102325i
\(623\) 70.4781 + 97.0048i 0.113127 + 0.155706i
\(624\) 0 0
\(625\) 3.13803 + 9.65786i 0.00502085 + 0.0154526i
\(626\) 258.200i 0.412460i
\(627\) 0 0
\(628\) 107.465 0.171122
\(629\) −502.987 + 163.430i −0.799661 + 0.259826i
\(630\) 0 0
\(631\) −214.772 + 156.041i −0.340367 + 0.247291i −0.744817 0.667269i \(-0.767463\pi\)
0.404450 + 0.914560i \(0.367463\pi\)
\(632\) −100.896 + 310.527i −0.159646 + 0.491340i
\(633\) 0 0
\(634\) −13.7092 18.8690i −0.0216233 0.0297619i
\(635\) 307.332 423.007i 0.483988 0.666152i
\(636\) 0 0
\(637\) 477.709i 0.749935i
\(638\) −92.7648 + 27.4155i −0.145399 + 0.0429711i
\(639\) 0 0
\(640\) −968.892 + 314.812i −1.51389 + 0.491894i
\(641\) 925.226 + 672.216i 1.44341 + 1.04870i 0.987316 + 0.158768i \(0.0507522\pi\)
0.456095 + 0.889931i \(0.349248\pi\)
\(642\) 0 0
\(643\) 174.074 535.744i 0.270721 0.833195i −0.719599 0.694390i \(-0.755674\pi\)
0.990320 0.138804i \(-0.0443259\pi\)
\(644\) 175.086 + 56.8890i 0.271873 + 0.0883370i
\(645\) 0 0
\(646\) −145.644 + 200.462i −0.225455 + 0.310312i
\(647\) 17.5246 + 53.9352i 0.0270859 + 0.0833620i 0.963686 0.267039i \(-0.0860453\pi\)
−0.936600 + 0.350401i \(0.886045\pi\)
\(648\) 0 0
\(649\) 29.5536 1102.44i 0.0455371 1.69868i
\(650\) 395.187 0.607980
\(651\) 0 0
\(652\) −296.640 215.522i −0.454969 0.330555i
\(653\) −616.756 + 448.100i −0.944496 + 0.686217i −0.949499 0.313771i \(-0.898408\pi\)
0.00500247 + 0.999987i \(0.498408\pi\)
\(654\) 0 0
\(655\) 1716.71 + 557.793i 2.62093 + 0.851592i
\(656\) 104.591 + 143.957i 0.159438 + 0.219447i
\(657\) 0 0
\(658\) −7.97030 24.5301i −0.0121129 0.0372797i
\(659\) 1137.55i 1.72617i 0.505056 + 0.863086i \(0.331472\pi\)
−0.505056 + 0.863086i \(0.668528\pi\)
\(660\) 0 0
\(661\) 814.127 1.23166 0.615829 0.787879i \(-0.288821\pi\)
0.615829 + 0.787879i \(0.288821\pi\)
\(662\) 273.502 88.8661i 0.413145 0.134239i
\(663\) 0 0
\(664\) 351.485 255.369i 0.529345 0.384591i
\(665\) 130.901 402.870i 0.196843 0.605820i
\(666\) 0 0
\(667\) 99.2540 + 136.611i 0.148807 + 0.204815i
\(668\) −279.869 + 385.207i −0.418965 + 0.576656i
\(669\) 0 0
\(670\) 466.586i 0.696397i
\(671\) 753.767 517.361i 1.12335 0.771030i
\(672\) 0 0
\(673\) −301.768 + 98.0504i −0.448393 + 0.145692i −0.524504 0.851408i \(-0.675749\pi\)
0.0761119 + 0.997099i \(0.475749\pi\)
\(674\) −87.1829 63.3421i −0.129352 0.0939794i
\(675\) 0 0
\(676\) −54.7737 + 168.576i −0.0810262 + 0.249373i
\(677\) −467.770 151.988i −0.690946 0.224502i −0.0575647 0.998342i \(-0.518334\pi\)
−0.633381 + 0.773840i \(0.718334\pi\)
\(678\) 0 0
\(679\) −88.3471 + 121.599i −0.130114 + 0.179086i
\(680\) 366.835 + 1129.00i 0.539463 + 1.66030i
\(681\) 0 0
\(682\) −257.165 6.89392i −0.377075 0.0101084i
\(683\) −1267.89 −1.85635 −0.928176 0.372142i \(-0.878624\pi\)
−0.928176 + 0.372142i \(0.878624\pi\)
\(684\) 0 0
\(685\) 333.734 + 242.472i 0.487203 + 0.353973i
\(686\) 176.767 128.429i 0.257678 0.187214i
\(687\) 0 0
\(688\) 462.685 + 150.335i 0.672507 + 0.218511i
\(689\) −501.921 690.835i −0.728477 1.00266i
\(690\) 0 0
\(691\) −71.8167 221.029i −0.103932 0.319868i 0.885547 0.464550i \(-0.153784\pi\)
−0.989478 + 0.144682i \(0.953784\pi\)
\(692\) 879.850i 1.27146i
\(693\) 0 0
\(694\) 328.582 0.473461
\(695\) −1022.80 + 332.326i −1.47165 + 0.478167i
\(696\) 0 0
\(697\) 385.427 280.029i 0.552980 0.401763i
\(698\) −59.7625 + 183.930i −0.0856196 + 0.263510i
\(699\) 0 0
\(700\) −348.138 479.171i −0.497341 0.684531i
\(701\) −260.786 + 358.941i −0.372020 + 0.512041i −0.953448 0.301556i \(-0.902494\pi\)
0.581429 + 0.813597i \(0.302494\pi\)
\(702\) 0 0
\(703\) 229.872i 0.326987i
\(704\) 270.938 + 96.1337i 0.384856 + 0.136554i
\(705\) 0 0
\(706\) −23.0286 + 7.48246i −0.0326185 + 0.0105984i
\(707\) 299.570 + 217.650i 0.423720 + 0.307851i
\(708\) 0 0
\(709\) −126.852 + 390.411i −0.178917 + 0.550650i −0.999791 0.0204599i \(-0.993487\pi\)
0.820874 + 0.571110i \(0.193487\pi\)
\(710\) −346.984 112.742i −0.488709 0.158791i
\(711\) 0 0
\(712\) −85.8456 + 118.156i −0.120570 + 0.165950i
\(713\) 138.776 + 427.108i 0.194636 + 0.599029i
\(714\) 0 0
\(715\) −1045.01 802.896i −1.46155 1.12293i
\(716\) 236.193 0.329878
\(717\) 0 0
\(718\) 198.311 + 144.081i 0.276199 + 0.200671i
\(719\) −187.845 + 136.477i −0.261259 + 0.189815i −0.710702 0.703493i \(-0.751622\pi\)
0.449443 + 0.893309i \(0.351622\pi\)
\(720\) 0 0
\(721\) −596.517 193.820i −0.827347 0.268821i
\(722\) −76.2532 104.954i −0.105614 0.145365i
\(723\) 0 0
\(724\) 174.619 + 537.422i 0.241186 + 0.742295i
\(725\) 543.271i 0.749339i
\(726\) 0 0
\(727\) −523.474 −0.720047 −0.360024 0.932943i \(-0.617231\pi\)
−0.360024 + 0.932943i \(0.617231\pi\)
\(728\) −286.022 + 92.9342i −0.392888 + 0.127657i
\(729\) 0 0
\(730\) 112.051 81.4100i 0.153495 0.111521i
\(731\) 402.504 1238.78i 0.550620 1.69464i
\(732\) 0 0
\(733\) 186.056 + 256.084i 0.253828 + 0.349365i 0.916847 0.399238i \(-0.130725\pi\)
−0.663019 + 0.748602i \(0.730725\pi\)
\(734\) −82.4495 + 113.482i −0.112329 + 0.154608i
\(735\) 0 0
\(736\) 342.766i 0.465715i
\(737\) 586.868 763.839i 0.796293 1.03642i
\(738\) 0 0
\(739\) −671.840 + 218.294i −0.909120 + 0.295391i −0.725996 0.687699i \(-0.758621\pi\)
−0.183124 + 0.983090i \(0.558621\pi\)
\(740\) 420.015 + 305.159i 0.567588 + 0.412377i
\(741\) 0 0
\(742\) 47.9538 147.586i 0.0646277 0.198904i
\(743\) −306.573 99.6115i −0.412615 0.134067i 0.0953515 0.995444i \(-0.469602\pi\)
−0.507966 + 0.861377i \(0.669602\pi\)
\(744\) 0 0
\(745\) −1254.05 + 1726.06i −1.68329 + 2.31686i
\(746\) 6.65563 + 20.4839i 0.00892175 + 0.0274583i
\(747\) 0 0
\(748\) 386.333 1088.82i 0.516489 1.45565i
\(749\) 275.798 0.368222
\(750\) 0 0
\(751\) −1067.26 775.408i −1.42112 1.03250i −0.991586 0.129448i \(-0.958679\pi\)
−0.429530 0.903053i \(-0.641321\pi\)
\(752\) −85.3817 + 62.0334i −0.113539 + 0.0824913i
\(753\) 0 0
\(754\) −123.677 40.1852i −0.164028 0.0532961i
\(755\) 240.374 + 330.847i 0.318376 + 0.438208i
\(756\) 0 0
\(757\) 281.697 + 866.976i 0.372123 + 1.14528i 0.945399 + 0.325915i \(0.105672\pi\)
−0.573275 + 0.819363i \(0.694328\pi\)
\(758\) 357.097i 0.471104i
\(759\) 0 0
\(760\) 515.968 0.678905
\(761\) 166.965 54.2501i 0.219402 0.0712879i −0.197254 0.980352i \(-0.563202\pi\)
0.416655 + 0.909065i \(0.363202\pi\)
\(762\) 0 0
\(763\) 497.630 361.549i 0.652201 0.473852i
\(764\) 164.065 504.940i 0.214745 0.660916i
\(765\) 0 0
\(766\) −231.425 318.530i −0.302122 0.415835i
\(767\) 871.462 1199.46i 1.13620 1.56384i
\(768\) 0 0
\(769\) 692.657i 0.900725i 0.892846 + 0.450362i \(0.148705\pi\)
−0.892846 + 0.450362i \(0.851295\pi\)
\(770\) 6.41775 239.402i 0.00833473 0.310912i
\(771\) 0 0
\(772\) 727.989 236.538i 0.942991 0.306396i
\(773\) −339.099 246.370i −0.438679 0.318719i 0.346431 0.938076i \(-0.387394\pi\)
−0.785110 + 0.619357i \(0.787394\pi\)
\(774\) 0 0
\(775\) 446.479 1374.12i 0.576101 1.77306i
\(776\) −174.118 56.5744i −0.224379 0.0729051i
\(777\) 0 0
\(778\) 85.2923 117.395i 0.109630 0.150893i
\(779\) −63.9885 196.936i −0.0821418 0.252806i
\(780\) 0 0
\(781\) 426.235 + 621.001i 0.545755 + 0.795136i
\(782\) 244.547 0.312720
\(783\) 0 0
\(784\) −287.382 208.795i −0.366558 0.266320i
\(785\) −197.435 + 143.445i −0.251510 + 0.182732i
\(786\) 0 0
\(787\) 936.899 + 304.417i 1.19047 + 0.386807i 0.836246 0.548355i \(-0.184746\pi\)
0.354222 + 0.935161i \(0.384746\pi\)
\(788\) 115.078 + 158.391i 0.146038 + 0.201003i
\(789\) 0 0
\(790\) −108.015 332.436i −0.136728 0.420805i
\(791\) 599.839i 0.758330i
\(792\) 0 0
\(793\) 1229.07 1.54990
\(794\) 459.285 149.231i 0.578445 0.187948i
\(795\) 0 0
\(796\) 167.841 121.944i 0.210856 0.153196i
\(797\) 231.830 713.499i 0.290878 0.895230i −0.693697 0.720267i \(-0.744019\pi\)
0.984575 0.174963i \(-0.0559807\pi\)
\(798\) 0 0
\(799\) 166.086 + 228.598i 0.207868 + 0.286105i
\(800\) 648.193 892.161i 0.810241 1.11520i
\(801\) 0 0
\(802\) 59.8296i 0.0746005i
\(803\) −285.834 7.66245i −0.355957 0.00954228i
\(804\) 0 0
\(805\) −397.607 + 129.190i −0.493921 + 0.160485i
\(806\) −279.797 203.285i −0.347143 0.252214i
\(807\) 0 0
\(808\) −139.376 + 428.954i −0.172495 + 0.530884i
\(809\) −694.235 225.571i −0.858140 0.278827i −0.153288 0.988181i \(-0.548986\pi\)
−0.704851 + 0.709355i \(0.748986\pi\)
\(810\) 0 0
\(811\) −14.0885 + 19.3911i −0.0173717 + 0.0239101i −0.817615 0.575766i \(-0.804704\pi\)
0.800243 + 0.599676i \(0.204704\pi\)
\(812\) 60.2279 + 185.362i 0.0741723 + 0.228279i
\(813\) 0 0
\(814\) 36.8333 + 124.631i 0.0452498 + 0.153110i
\(815\) 832.671 1.02168
\(816\) 0 0
\(817\) −458.015 332.767i −0.560606 0.407304i
\(818\) −92.5115 + 67.2135i −0.113095 + 0.0821681i
\(819\) 0 0
\(820\) −444.782 144.519i −0.542418 0.176242i
\(821\) −1.54301 2.12377i −0.00187943 0.00258681i 0.808076 0.589078i \(-0.200509\pi\)
−0.809956 + 0.586491i \(0.800509\pi\)
\(822\) 0 0
\(823\) 10.4352 + 32.1162i 0.0126795 + 0.0390233i 0.957196 0.289440i \(-0.0934692\pi\)
−0.944517 + 0.328464i \(0.893469\pi\)
\(824\) 763.978i 0.927157i
\(825\) 0 0
\(826\) 269.435 0.326192
\(827\) 1132.85 368.086i 1.36984 0.445086i 0.470521 0.882389i \(-0.344066\pi\)
0.899314 + 0.437303i \(0.144066\pi\)
\(828\) 0 0
\(829\) −380.631 + 276.544i −0.459144 + 0.333588i −0.793195 0.608967i \(-0.791584\pi\)
0.334051 + 0.942555i \(0.391584\pi\)
\(830\) −143.728 + 442.348i −0.173166 + 0.532949i
\(831\) 0 0
\(832\) 227.173 + 312.676i 0.273044 + 0.375813i
\(833\) −559.022 + 769.427i −0.671094 + 0.923682i
\(834\) 0 0
\(835\) 1081.28i 1.29494i
\(836\) −398.199 305.942i −0.476315 0.365960i
\(837\) 0 0
\(838\) −234.200 + 76.0963i −0.279475 + 0.0908071i
\(839\) −439.290 319.163i −0.523588 0.380409i 0.294366 0.955693i \(-0.404892\pi\)
−0.817954 + 0.575284i \(0.804892\pi\)
\(840\) 0 0
\(841\) 204.640 629.817i 0.243329 0.748890i
\(842\) −0.0713517 0.0231836i −8.47408e−5 2.75339e-5i
\(843\) 0 0
\(844\) −474.626 + 653.267i −0.562353 + 0.774013i
\(845\) −124.387 382.823i −0.147203 0.453044i
\(846\) 0 0
\(847\) −311.625 + 383.849i −0.367916 + 0.453186i
\(848\) −634.973 −0.748789
\(849\) 0 0
\(850\) −636.512 462.453i −0.748838 0.544062i
\(851\) 183.540 133.350i 0.215676 0.156698i
\(852\) 0 0
\(853\) 411.114 + 133.579i 0.481962 + 0.156599i 0.539914 0.841720i \(-0.318457\pi\)
−0.0579514 + 0.998319i \(0.518457\pi\)
\(854\) 131.286 + 180.700i 0.153731 + 0.211592i
\(855\) 0 0
\(856\) 103.810 + 319.493i 0.121273 + 0.373240i
\(857\) 267.129i 0.311703i 0.987781 + 0.155851i \(0.0498121\pi\)
−0.987781 + 0.155851i \(0.950188\pi\)
\(858\) 0 0
\(859\) 537.909 0.626203 0.313102 0.949720i \(-0.398632\pi\)
0.313102 + 0.949720i \(0.398632\pi\)
\(860\) −1216.05 + 395.118i −1.41401 + 0.459439i
\(861\) 0 0
\(862\) 141.037 102.469i 0.163616 0.118874i
\(863\) −351.588 + 1082.08i −0.407402 + 1.25386i 0.511470 + 0.859301i \(0.329101\pi\)
−0.918872 + 0.394555i \(0.870899\pi\)
\(864\) 0 0
\(865\) −1174.43 1616.47i −1.35773 1.86875i
\(866\) −69.6610 + 95.8802i −0.0804400 + 0.110716i
\(867\) 0 0
\(868\) 518.343i 0.597169i
\(869\) −241.306 + 680.084i −0.277682 + 0.782606i
\(870\) 0 0
\(871\) 1231.59 400.168i 1.41400 0.459435i
\(872\) 606.136 + 440.384i 0.695110 + 0.505027i
\(873\) 0 0
\(874\) 32.8457 101.089i 0.0375809 0.115662i
\(875\) 492.137 + 159.905i 0.562442 + 0.182748i
\(876\) 0 0
\(877\) −399.155 + 549.389i −0.455136 + 0.626442i −0.973491 0.228724i \(-0.926545\pi\)
0.518355 + 0.855166i \(0.326545\pi\)
\(878\) −83.5172 257.040i −0.0951222 0.292756i
\(879\) 0 0
\(880\) −939.758 + 277.734i −1.06791 + 0.315607i
\(881\) 419.212 0.475837 0.237918 0.971285i \(-0.423535\pi\)
0.237918 + 0.971285i \(0.423535\pi\)
\(882\) 0 0
\(883\) 292.750 + 212.695i 0.331540 + 0.240878i 0.741084 0.671413i \(-0.234312\pi\)
−0.409544 + 0.912290i \(0.634312\pi\)
\(884\) 1256.56 912.941i 1.42144 1.03274i
\(885\) 0 0
\(886\) 13.7602 + 4.47097i 0.0155308 + 0.00504625i
\(887\) 24.9623 + 34.3576i 0.0281424 + 0.0387346i 0.822856 0.568249i \(-0.192379\pi\)
−0.794714 + 0.606984i \(0.792379\pi\)
\(888\) 0 0
\(889\) −81.4937 250.812i −0.0916690 0.282128i
\(890\) 156.354i 0.175678i
\(891\) 0 0
\(892\) −294.159 −0.329775
\(893\) 116.804 37.9518i 0.130799 0.0424992i
\(894\) 0 0
\(895\) −433.936 + 315.273i −0.484844 + 0.352260i
\(896\) −158.783 + 488.683i −0.177213 + 0.545406i
\(897\) 0 0
\(898\) −55.7506 76.7342i −0.0620831 0.0854501i
\(899\) −279.460 + 384.643i −0.310856 + 0.427857i
\(900\) 0 0
\(901\) 1700.06i 1.88685i
\(902\) −66.2491 96.5214i −0.0734469 0.107008i
\(903\) 0 0
\(904\) 694.872 225.778i 0.768664 0.249754i
\(905\) −1038.17 754.274i −1.14715 0.833451i
\(906\) 0 0
\(907\) −19.0536 + 58.6409i −0.0210073 + 0.0646537i −0.961011 0.276512i \(-0.910822\pi\)
0.940003 + 0.341165i \(0.110822\pi\)
\(908\) 600.096 + 194.983i 0.660898 + 0.214739i
\(909\) 0 0
\(910\) 189.243 260.471i 0.207960 0.286232i
\(911\) 83.8172 + 257.963i 0.0920057 + 0.283165i 0.986462 0.163991i \(-0.0524369\pi\)
−0.894456 + 0.447156i \(0.852437\pi\)
\(912\) 0 0
\(913\) 791.675 543.380i 0.867114 0.595159i
\(914\) −483.393 −0.528877
\(915\) 0 0
\(916\) 8.43146 + 6.12581i 0.00920465 + 0.00668757i
\(917\) 736.546 535.132i 0.803213 0.583568i
\(918\) 0 0
\(919\) 119.898 + 38.9574i 0.130466 + 0.0423910i 0.373522 0.927621i \(-0.378150\pi\)
−0.243056 + 0.970012i \(0.578150\pi\)
\(920\) −299.316 411.973i −0.325343 0.447797i
\(921\) 0 0
\(922\) −26.1069 80.3488i −0.0283155 0.0871462i
\(923\) 1012.58i 1.09706i
\(924\) 0 0
\(925\) −729.895 −0.789076
\(926\) −4.44286 + 1.44357i −0.00479790 + 0.00155893i
\(927\) 0 0
\(928\) −293.579 + 213.298i −0.316357 + 0.229847i
\(929\) −85.0652 + 261.804i −0.0915664 + 0.281813i −0.986344 0.164700i \(-0.947334\pi\)
0.894777 + 0.446513i \(0.147334\pi\)
\(930\) 0 0
\(931\) 242.976 + 334.428i 0.260984 + 0.359214i
\(932\) −617.541 + 849.972i −0.662597 + 0.911987i
\(933\) 0 0
\(934\) 187.868i 0.201144i
\(935\) 743.597 + 2516.08i 0.795291 + 2.69099i
\(936\) 0 0
\(937\) 1469.07 477.330i 1.56784 0.509424i 0.608955 0.793204i \(-0.291589\pi\)
0.958889 + 0.283781i \(0.0915888\pi\)
\(938\) 190.389 + 138.325i 0.202973 + 0.147469i
\(939\) 0 0
\(940\) 85.7145 263.802i 0.0911857 0.280641i
\(941\) 1018.35 + 330.882i 1.08220 + 0.351628i 0.795228 0.606310i \(-0.207351\pi\)
0.286973 + 0.957939i \(0.407351\pi\)
\(942\) 0 0
\(943\) −120.123 + 165.335i −0.127384 + 0.175329i
\(944\) −340.683 1048.51i −0.360893 1.11071i
\(945\) 0 0
\(946\) −301.647 107.030i −0.318865 0.113139i
\(947\) −1480.48 −1.56333 −0.781667 0.623696i \(-0.785630\pi\)
−0.781667 + 0.623696i \(0.785630\pi\)
\(948\) 0 0
\(949\) −310.989 225.947i −0.327702 0.238089i
\(950\) −276.657 + 201.003i −0.291218 + 0.211582i
\(951\) 0 0
\(952\) 569.438 + 185.022i 0.598149 + 0.194350i
\(953\) −254.489 350.274i −0.267040 0.367549i 0.654348 0.756194i \(-0.272943\pi\)
−0.921388 + 0.388645i \(0.872943\pi\)
\(954\) 0 0
\(955\) 372.578 + 1146.68i 0.390134 + 1.20071i
\(956\) 1223.22i 1.27952i
\(957\) 0 0
\(958\) −258.229 −0.269550
\(959\) 197.880 64.2950i 0.206339 0.0670437i
\(960\) 0 0
\(961\) −245.497 + 178.364i −0.255460 + 0.185602i
\(962\) −53.9897 + 166.163i −0.0561223 + 0.172727i
\(963\) 0 0
\(964\) 90.7410 + 124.894i 0.0941297 + 0.129558i
\(965\) −1021.74 + 1406.30i −1.05879 + 1.45730i
\(966\) 0 0
\(967\) 211.542i 0.218761i −0.994000 0.109381i \(-0.965113\pi\)
0.994000 0.109381i \(-0.0348867\pi\)
\(968\) −561.957 216.516i −0.580534 0.223674i
\(969\) 0 0
\(970\) 186.403 60.5659i 0.192168 0.0624391i
\(971\) 1125.89 + 818.004i 1.15951 + 0.842434i 0.989716 0.143045i \(-0.0456894\pi\)
0.169795 + 0.985479i \(0.445689\pi\)
\(972\) 0 0
\(973\) −167.617 + 515.871i −0.172268 + 0.530186i
\(974\) 322.628 + 104.828i 0.331240 + 0.107627i
\(975\) 0 0
\(976\) 537.196 739.388i 0.550406 0.757569i
\(977\) −10.0534 30.9411i −0.0102900 0.0316695i 0.945780 0.324809i \(-0.105300\pi\)
−0.956070 + 0.293139i \(0.905300\pi\)
\(978\) 0 0
\(979\) −196.660 + 255.964i −0.200879 + 0.261454i
\(980\) 933.613 0.952666
\(981\) 0 0
\(982\) 164.296 + 119.368i 0.167308 + 0.121556i
\(983\) −980.893 + 712.660i −0.997856 + 0.724985i −0.961627 0.274359i \(-0.911534\pi\)
−0.0362286 + 0.999344i \(0.511534\pi\)
\(984\) 0 0
\(985\) −422.843 137.390i −0.429283 0.139482i
\(986\) 152.177 + 209.454i 0.154338 + 0.212428i
\(987\) 0 0
\(988\) −208.613 642.044i −0.211147 0.649843i
\(989\) 558.741i 0.564955i
\(990\) 0 0
\(991\) −106.677 −0.107645 −0.0538227 0.998551i \(-0.517141\pi\)
−0.0538227 + 0.998551i \(0.517141\pi\)
\(992\) −917.858 + 298.230i −0.925260 + 0.300635i
\(993\) 0 0
\(994\) −148.872 + 108.162i −0.149770 + 0.108815i
\(995\) −145.588 + 448.073i −0.146319 + 0.450324i
\(996\) 0 0
\(997\) −759.309 1045.10i −0.761593 1.04824i −0.997080 0.0763658i \(-0.975668\pi\)
0.235486 0.971878i \(-0.424332\pi\)
\(998\) 224.203 308.588i 0.224652 0.309207i
\(999\) 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 99.3.k.b.28.2 16
3.2 odd 2 inner 99.3.k.b.28.3 yes 16
11.2 odd 10 inner 99.3.k.b.46.2 yes 16
11.3 even 5 1089.3.c.l.604.10 16
11.8 odd 10 1089.3.c.l.604.8 16
33.2 even 10 inner 99.3.k.b.46.3 yes 16
33.8 even 10 1089.3.c.l.604.9 16
33.14 odd 10 1089.3.c.l.604.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.3.k.b.28.2 16 1.1 even 1 trivial
99.3.k.b.28.3 yes 16 3.2 odd 2 inner
99.3.k.b.46.2 yes 16 11.2 odd 10 inner
99.3.k.b.46.3 yes 16 33.2 even 10 inner
1089.3.c.l.604.7 16 33.14 odd 10
1089.3.c.l.604.8 16 11.8 odd 10
1089.3.c.l.604.9 16 33.8 even 10
1089.3.c.l.604.10 16 11.3 even 5