Properties

Label 1050.3.l.h.43.5
Level $1050$
Weight $3$
Character 1050.43
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,3,Mod(43,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.43");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + 1093889 x^{8} - 4595248 x^{7} + 18837632 x^{6} + \cdots + 2560000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{10}\cdot 5^{2} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.5
Root \(-0.394902 - 0.394902i\) of defining polynomial
Character \(\chi\) \(=\) 1050.43
Dual form 1050.3.l.h.757.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} -11.5078 q^{11} +(2.44949 - 2.44949i) q^{12} +(7.70521 + 7.70521i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-21.0749 + 21.0749i) q^{17} +(3.00000 + 3.00000i) q^{18} -24.1173i q^{19} -4.58258 q^{21} +(-11.5078 + 11.5078i) q^{22} +(-30.1762 - 30.1762i) q^{23} -4.89898i q^{24} +15.4104 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} -51.1392i q^{29} -46.9852 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-14.0941 - 14.0941i) q^{33} +42.1499i q^{34} +6.00000 q^{36} +(8.50020 - 8.50020i) q^{37} +(-24.1173 - 24.1173i) q^{38} +18.8738i q^{39} +18.6089 q^{41} +(-4.58258 + 4.58258i) q^{42} +(26.1383 + 26.1383i) q^{43} +23.0156i q^{44} -60.3523 q^{46} +(-50.1311 + 50.1311i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} -51.6228 q^{51} +(15.4104 - 15.4104i) q^{52} +(-7.08527 - 7.08527i) q^{53} +7.34847i q^{54} +7.48331 q^{56} +(29.5376 - 29.5376i) q^{57} +(-51.1392 - 51.1392i) q^{58} +94.3487i q^{59} +8.09003 q^{61} +(-46.9852 + 46.9852i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} -28.1883 q^{66} +(20.6469 - 20.6469i) q^{67} +(42.1499 + 42.1499i) q^{68} -73.9162i q^{69} -63.7595 q^{71} +(6.00000 - 6.00000i) q^{72} +(-50.1883 - 50.1883i) q^{73} -17.0004i q^{74} -48.2346 q^{76} +(21.5292 - 21.5292i) q^{77} +(18.8738 + 18.8738i) q^{78} -1.06121i q^{79} -9.00000 q^{81} +(18.6089 - 18.6089i) q^{82} +(-53.6243 - 53.6243i) q^{83} +9.16515i q^{84} +52.2765 q^{86} +(62.6325 - 62.6325i) q^{87} +(23.0156 + 23.0156i) q^{88} +145.154i q^{89} -28.8303 q^{91} +(-60.3523 + 60.3523i) q^{92} +(-57.5449 - 57.5449i) q^{93} +100.262i q^{94} -9.79796 q^{96} +(-23.7872 + 23.7872i) q^{97} +(-7.00000 - 7.00000i) q^{98} -34.5235i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{2} - 32 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{2} - 32 q^{8} + 8 q^{11} + 32 q^{13} - 64 q^{16} - 56 q^{17} + 48 q^{18} + 8 q^{22} - 24 q^{23} + 64 q^{26} - 112 q^{31} - 64 q^{32} - 24 q^{33} + 96 q^{36} + 152 q^{37} - 48 q^{46} - 80 q^{47} - 72 q^{51} + 64 q^{52} - 48 q^{53} - 24 q^{57} - 96 q^{58} + 96 q^{61} - 112 q^{62} - 48 q^{66} + 80 q^{67} + 112 q^{68} + 536 q^{71} + 96 q^{72} + 168 q^{77} + 48 q^{78} - 144 q^{81} + 256 q^{83} + 144 q^{87} - 16 q^{88} - 48 q^{92} - 192 q^{93} - 688 q^{97} - 112 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 0 0
\(6\) 2.44949 0.408248
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −11.5078 −1.04617 −0.523083 0.852282i \(-0.675218\pi\)
−0.523083 + 0.852282i \(0.675218\pi\)
\(12\) 2.44949 2.44949i 0.204124 0.204124i
\(13\) 7.70521 + 7.70521i 0.592708 + 0.592708i 0.938362 0.345654i \(-0.112343\pi\)
−0.345654 + 0.938362i \(0.612343\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 0 0
\(16\) −4.00000 −0.250000
\(17\) −21.0749 + 21.0749i −1.23970 + 1.23970i −0.279579 + 0.960123i \(0.590195\pi\)
−0.960123 + 0.279579i \(0.909805\pi\)
\(18\) 3.00000 + 3.00000i 0.166667 + 0.166667i
\(19\) 24.1173i 1.26933i −0.772786 0.634666i \(-0.781138\pi\)
0.772786 0.634666i \(-0.218862\pi\)
\(20\) 0 0
\(21\) −4.58258 −0.218218
\(22\) −11.5078 + 11.5078i −0.523083 + 0.523083i
\(23\) −30.1762 30.1762i −1.31201 1.31201i −0.919934 0.392073i \(-0.871758\pi\)
−0.392073 0.919934i \(-0.628242\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 0 0
\(26\) 15.4104 0.592708
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 3.74166 + 3.74166i 0.133631 + 0.133631i
\(29\) 51.1392i 1.76342i −0.471790 0.881711i \(-0.656392\pi\)
0.471790 0.881711i \(-0.343608\pi\)
\(30\) 0 0
\(31\) −46.9852 −1.51565 −0.757826 0.652457i \(-0.773738\pi\)
−0.757826 + 0.652457i \(0.773738\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) −14.0941 14.0941i −0.427095 0.427095i
\(34\) 42.1499i 1.23970i
\(35\) 0 0
\(36\) 6.00000 0.166667
\(37\) 8.50020 8.50020i 0.229735 0.229735i −0.582847 0.812582i \(-0.698061\pi\)
0.812582 + 0.582847i \(0.198061\pi\)
\(38\) −24.1173 24.1173i −0.634666 0.634666i
\(39\) 18.8738i 0.483944i
\(40\) 0 0
\(41\) 18.6089 0.453875 0.226937 0.973909i \(-0.427129\pi\)
0.226937 + 0.973909i \(0.427129\pi\)
\(42\) −4.58258 + 4.58258i −0.109109 + 0.109109i
\(43\) 26.1383 + 26.1383i 0.607867 + 0.607867i 0.942388 0.334522i \(-0.108575\pi\)
−0.334522 + 0.942388i \(0.608575\pi\)
\(44\) 23.0156i 0.523083i
\(45\) 0 0
\(46\) −60.3523 −1.31201
\(47\) −50.1311 + 50.1311i −1.06662 + 1.06662i −0.0690016 + 0.997617i \(0.521981\pi\)
−0.997617 + 0.0690016i \(0.978019\pi\)
\(48\) −4.89898 4.89898i −0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) 0 0
\(51\) −51.6228 −1.01221
\(52\) 15.4104 15.4104i 0.296354 0.296354i
\(53\) −7.08527 7.08527i −0.133684 0.133684i 0.637098 0.770783i \(-0.280135\pi\)
−0.770783 + 0.637098i \(0.780135\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0 0
\(56\) 7.48331 0.133631
\(57\) 29.5376 29.5376i 0.518203 0.518203i
\(58\) −51.1392 51.1392i −0.881711 0.881711i
\(59\) 94.3487i 1.59913i 0.600579 + 0.799565i \(0.294937\pi\)
−0.600579 + 0.799565i \(0.705063\pi\)
\(60\) 0 0
\(61\) 8.09003 0.132623 0.0663117 0.997799i \(-0.478877\pi\)
0.0663117 + 0.997799i \(0.478877\pi\)
\(62\) −46.9852 + 46.9852i −0.757826 + 0.757826i
\(63\) −5.61249 5.61249i −0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) 0 0
\(66\) −28.1883 −0.427095
\(67\) 20.6469 20.6469i 0.308163 0.308163i −0.536034 0.844197i \(-0.680078\pi\)
0.844197 + 0.536034i \(0.180078\pi\)
\(68\) 42.1499 + 42.1499i 0.619851 + 0.619851i
\(69\) 73.9162i 1.07125i
\(70\) 0 0
\(71\) −63.7595 −0.898021 −0.449011 0.893526i \(-0.648223\pi\)
−0.449011 + 0.893526i \(0.648223\pi\)
\(72\) 6.00000 6.00000i 0.0833333 0.0833333i
\(73\) −50.1883 50.1883i −0.687511 0.687511i 0.274170 0.961681i \(-0.411597\pi\)
−0.961681 + 0.274170i \(0.911597\pi\)
\(74\) 17.0004i 0.229735i
\(75\) 0 0
\(76\) −48.2346 −0.634666
\(77\) 21.5292 21.5292i 0.279599 0.279599i
\(78\) 18.8738 + 18.8738i 0.241972 + 0.241972i
\(79\) 1.06121i 0.0134331i −0.999977 0.00671653i \(-0.997862\pi\)
0.999977 0.00671653i \(-0.00213796\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 18.6089 18.6089i 0.226937 0.226937i
\(83\) −53.6243 53.6243i −0.646075 0.646075i 0.305967 0.952042i \(-0.401020\pi\)
−0.952042 + 0.305967i \(0.901020\pi\)
\(84\) 9.16515i 0.109109i
\(85\) 0 0
\(86\) 52.2765 0.607867
\(87\) 62.6325 62.6325i 0.719914 0.719914i
\(88\) 23.0156 + 23.0156i 0.261541 + 0.261541i
\(89\) 145.154i 1.63095i 0.578794 + 0.815473i \(0.303523\pi\)
−0.578794 + 0.815473i \(0.696477\pi\)
\(90\) 0 0
\(91\) −28.8303 −0.316816
\(92\) −60.3523 + 60.3523i −0.656003 + 0.656003i
\(93\) −57.5449 57.5449i −0.618762 0.618762i
\(94\) 100.262i 1.06662i
\(95\) 0 0
\(96\) −9.79796 −0.102062
\(97\) −23.7872 + 23.7872i −0.245229 + 0.245229i −0.819009 0.573780i \(-0.805476\pi\)
0.573780 + 0.819009i \(0.305476\pi\)
\(98\) −7.00000 7.00000i −0.0714286 0.0714286i
\(99\) 34.5235i 0.348722i
\(100\) 0 0
\(101\) 50.1467 0.496502 0.248251 0.968696i \(-0.420144\pi\)
0.248251 + 0.968696i \(0.420144\pi\)
\(102\) −51.6228 + 51.6228i −0.506106 + 0.506106i
\(103\) −56.3876 56.3876i −0.547453 0.547453i 0.378251 0.925703i \(-0.376526\pi\)
−0.925703 + 0.378251i \(0.876526\pi\)
\(104\) 30.8208i 0.296354i
\(105\) 0 0
\(106\) −14.1705 −0.133684
\(107\) 135.365 135.365i 1.26510 1.26510i 0.316506 0.948590i \(-0.397490\pi\)
0.948590 0.316506i \(-0.102510\pi\)
\(108\) 7.34847 + 7.34847i 0.0680414 + 0.0680414i
\(109\) 100.934i 0.926001i 0.886358 + 0.463001i \(0.153227\pi\)
−0.886358 + 0.463001i \(0.846773\pi\)
\(110\) 0 0
\(111\) 20.8211 0.187578
\(112\) 7.48331 7.48331i 0.0668153 0.0668153i
\(113\) −25.3174 25.3174i −0.224048 0.224048i 0.586153 0.810201i \(-0.300642\pi\)
−0.810201 + 0.586153i \(0.800642\pi\)
\(114\) 59.0751i 0.518203i
\(115\) 0 0
\(116\) −102.278 −0.881711
\(117\) −23.1156 + 23.1156i −0.197569 + 0.197569i
\(118\) 94.3487 + 94.3487i 0.799565 + 0.799565i
\(119\) 78.8552i 0.662649i
\(120\) 0 0
\(121\) 11.4299 0.0944623
\(122\) 8.09003 8.09003i 0.0663117 0.0663117i
\(123\) 22.7911 + 22.7911i 0.185294 + 0.185294i
\(124\) 93.9704i 0.757826i
\(125\) 0 0
\(126\) −11.2250 −0.0890871
\(127\) −116.746 + 116.746i −0.919262 + 0.919262i −0.996976 0.0777140i \(-0.975238\pi\)
0.0777140 + 0.996976i \(0.475238\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 64.0254i 0.496321i
\(130\) 0 0
\(131\) 34.8004 0.265652 0.132826 0.991139i \(-0.457595\pi\)
0.132826 + 0.991139i \(0.457595\pi\)
\(132\) −28.1883 + 28.1883i −0.213548 + 0.213548i
\(133\) 45.1194 + 45.1194i 0.339243 + 0.339243i
\(134\) 41.2938i 0.308163i
\(135\) 0 0
\(136\) 84.2997 0.619851
\(137\) −131.552 + 131.552i −0.960235 + 0.960235i −0.999239 0.0390044i \(-0.987581\pi\)
0.0390044 + 0.999239i \(0.487581\pi\)
\(138\) −73.9162 73.9162i −0.535625 0.535625i
\(139\) 89.4407i 0.643458i −0.946832 0.321729i \(-0.895736\pi\)
0.946832 0.321729i \(-0.104264\pi\)
\(140\) 0 0
\(141\) −122.795 −0.870890
\(142\) −63.7595 + 63.7595i −0.449011 + 0.449011i
\(143\) −88.6702 88.6702i −0.620071 0.620071i
\(144\) 12.0000i 0.0833333i
\(145\) 0 0
\(146\) −100.377 −0.687511
\(147\) 8.57321 8.57321i 0.0583212 0.0583212i
\(148\) −17.0004 17.0004i −0.114868 0.114868i
\(149\) 55.7399i 0.374093i 0.982351 + 0.187047i \(0.0598915\pi\)
−0.982351 + 0.187047i \(0.940108\pi\)
\(150\) 0 0
\(151\) 82.9665 0.549447 0.274724 0.961523i \(-0.411414\pi\)
0.274724 + 0.961523i \(0.411414\pi\)
\(152\) −48.2346 + 48.2346i −0.317333 + 0.317333i
\(153\) −63.2248 63.2248i −0.413234 0.413234i
\(154\) 43.0583i 0.279599i
\(155\) 0 0
\(156\) 37.7477 0.241972
\(157\) 99.7950 99.7950i 0.635637 0.635637i −0.313839 0.949476i \(-0.601615\pi\)
0.949476 + 0.313839i \(0.101615\pi\)
\(158\) −1.06121 1.06121i −0.00671653 0.00671653i
\(159\) 17.3553i 0.109153i
\(160\) 0 0
\(161\) 112.909 0.701297
\(162\) −9.00000 + 9.00000i −0.0555556 + 0.0555556i
\(163\) 45.3884 + 45.3884i 0.278457 + 0.278457i 0.832493 0.554036i \(-0.186913\pi\)
−0.554036 + 0.832493i \(0.686913\pi\)
\(164\) 37.2177i 0.226937i
\(165\) 0 0
\(166\) −107.249 −0.646075
\(167\) 99.2501 99.2501i 0.594312 0.594312i −0.344481 0.938793i \(-0.611945\pi\)
0.938793 + 0.344481i \(0.111945\pi\)
\(168\) 9.16515 + 9.16515i 0.0545545 + 0.0545545i
\(169\) 50.2595i 0.297393i
\(170\) 0 0
\(171\) 72.3520 0.423111
\(172\) 52.2765 52.2765i 0.303933 0.303933i
\(173\) 80.5404 + 80.5404i 0.465551 + 0.465551i 0.900470 0.434919i \(-0.143223\pi\)
−0.434919 + 0.900470i \(0.643223\pi\)
\(174\) 125.265i 0.719914i
\(175\) 0 0
\(176\) 46.0313 0.261541
\(177\) −115.553 + 115.553i −0.652842 + 0.652842i
\(178\) 145.154 + 145.154i 0.815473 + 0.815473i
\(179\) 154.267i 0.861824i −0.902394 0.430912i \(-0.858192\pi\)
0.902394 0.430912i \(-0.141808\pi\)
\(180\) 0 0
\(181\) 166.548 0.920155 0.460078 0.887879i \(-0.347822\pi\)
0.460078 + 0.887879i \(0.347822\pi\)
\(182\) −28.8303 + 28.8303i −0.158408 + 0.158408i
\(183\) 9.90822 + 9.90822i 0.0541433 + 0.0541433i
\(184\) 120.705i 0.656003i
\(185\) 0 0
\(186\) −115.090 −0.618762
\(187\) 242.527 242.527i 1.29693 1.29693i
\(188\) 100.262 + 100.262i 0.533309 + 0.533309i
\(189\) 13.7477i 0.0727393i
\(190\) 0 0
\(191\) −235.646 −1.23375 −0.616873 0.787063i \(-0.711601\pi\)
−0.616873 + 0.787063i \(0.711601\pi\)
\(192\) −9.79796 + 9.79796i −0.0510310 + 0.0510310i
\(193\) 16.2211 + 16.2211i 0.0840471 + 0.0840471i 0.747880 0.663833i \(-0.231072\pi\)
−0.663833 + 0.747880i \(0.731072\pi\)
\(194\) 47.5744i 0.245229i
\(195\) 0 0
\(196\) −14.0000 −0.0714286
\(197\) 6.68134 6.68134i 0.0339154 0.0339154i −0.689946 0.723861i \(-0.742366\pi\)
0.723861 + 0.689946i \(0.242366\pi\)
\(198\) −34.5235 34.5235i −0.174361 0.174361i
\(199\) 32.0712i 0.161162i 0.996748 + 0.0805808i \(0.0256775\pi\)
−0.996748 + 0.0805808i \(0.974322\pi\)
\(200\) 0 0
\(201\) 50.5744 0.251614
\(202\) 50.1467 50.1467i 0.248251 0.248251i
\(203\) 95.6728 + 95.6728i 0.471294 + 0.471294i
\(204\) 103.246i 0.506106i
\(205\) 0 0
\(206\) −112.775 −0.547453
\(207\) 90.5285 90.5285i 0.437336 0.437336i
\(208\) −30.8208 30.8208i −0.148177 0.148177i
\(209\) 277.538i 1.32793i
\(210\) 0 0
\(211\) 123.531 0.585457 0.292728 0.956196i \(-0.405437\pi\)
0.292728 + 0.956196i \(0.405437\pi\)
\(212\) −14.1705 + 14.1705i −0.0668422 + 0.0668422i
\(213\) −78.0891 78.0891i −0.366616 0.366616i
\(214\) 270.731i 1.26510i
\(215\) 0 0
\(216\) 14.6969 0.0680414
\(217\) 87.9013 87.9013i 0.405075 0.405075i
\(218\) 100.934 + 100.934i 0.463001 + 0.463001i
\(219\) 122.936i 0.561350i
\(220\) 0 0
\(221\) −324.774 −1.46956
\(222\) 20.8211 20.8211i 0.0937890 0.0937890i
\(223\) 81.9590 + 81.9590i 0.367529 + 0.367529i 0.866575 0.499046i \(-0.166316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 0 0
\(226\) −50.6348 −0.224048
\(227\) −93.6089 + 93.6089i −0.412374 + 0.412374i −0.882565 0.470191i \(-0.844185\pi\)
0.470191 + 0.882565i \(0.344185\pi\)
\(228\) −59.0751 59.0751i −0.259101 0.259101i
\(229\) 348.973i 1.52390i 0.647635 + 0.761950i \(0.275758\pi\)
−0.647635 + 0.761950i \(0.724242\pi\)
\(230\) 0 0
\(231\) 52.7355 0.228292
\(232\) −102.278 + 102.278i −0.440856 + 0.440856i
\(233\) −208.319 208.319i −0.894074 0.894074i 0.100829 0.994904i \(-0.467850\pi\)
−0.994904 + 0.100829i \(0.967850\pi\)
\(234\) 46.2313i 0.197569i
\(235\) 0 0
\(236\) 188.697 0.799565
\(237\) 1.29971 1.29971i 0.00548403 0.00548403i
\(238\) −78.8552 78.8552i −0.331324 0.331324i
\(239\) 330.793i 1.38407i 0.721864 + 0.692035i \(0.243285\pi\)
−0.721864 + 0.692035i \(0.756715\pi\)
\(240\) 0 0
\(241\) 375.584 1.55844 0.779221 0.626749i \(-0.215615\pi\)
0.779221 + 0.626749i \(0.215615\pi\)
\(242\) 11.4299 11.4299i 0.0472312 0.0472312i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 16.1801i 0.0663117i
\(245\) 0 0
\(246\) 45.5822 0.185294
\(247\) 185.829 185.829i 0.752344 0.752344i
\(248\) 93.9704 + 93.9704i 0.378913 + 0.378913i
\(249\) 131.352i 0.527518i
\(250\) 0 0
\(251\) 41.2876 0.164493 0.0822463 0.996612i \(-0.473791\pi\)
0.0822463 + 0.996612i \(0.473791\pi\)
\(252\) −11.2250 + 11.2250i −0.0445435 + 0.0445435i
\(253\) 347.262 + 347.262i 1.37258 + 1.37258i
\(254\) 233.492i 0.919262i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 101.370 101.370i 0.394437 0.394437i −0.481828 0.876266i \(-0.660027\pi\)
0.876266 + 0.481828i \(0.160027\pi\)
\(258\) 64.0254 + 64.0254i 0.248161 + 0.248161i
\(259\) 31.8048i 0.122799i
\(260\) 0 0
\(261\) 153.418 0.587807
\(262\) 34.8004 34.8004i 0.132826 0.132826i
\(263\) −164.594 164.594i −0.625833 0.625833i 0.321184 0.947017i \(-0.395919\pi\)
−0.947017 + 0.321184i \(0.895919\pi\)
\(264\) 56.3766i 0.213548i
\(265\) 0 0
\(266\) 90.2387 0.339243
\(267\) −177.777 + 177.777i −0.665831 + 0.665831i
\(268\) −41.2938 41.2938i −0.154081 0.154081i
\(269\) 254.148i 0.944788i −0.881387 0.472394i \(-0.843390\pi\)
0.881387 0.472394i \(-0.156610\pi\)
\(270\) 0 0
\(271\) 22.4723 0.0829237 0.0414619 0.999140i \(-0.486798\pi\)
0.0414619 + 0.999140i \(0.486798\pi\)
\(272\) 84.2997 84.2997i 0.309925 0.309925i
\(273\) −35.3097 35.3097i −0.129340 0.129340i
\(274\) 263.104i 0.960235i
\(275\) 0 0
\(276\) −147.832 −0.535625
\(277\) −47.3949 + 47.3949i −0.171101 + 0.171101i −0.787463 0.616362i \(-0.788606\pi\)
0.616362 + 0.787463i \(0.288606\pi\)
\(278\) −89.4407 89.4407i −0.321729 0.321729i
\(279\) 140.956i 0.505217i
\(280\) 0 0
\(281\) −18.8810 −0.0671920 −0.0335960 0.999435i \(-0.510696\pi\)
−0.0335960 + 0.999435i \(0.510696\pi\)
\(282\) −122.795 + 122.795i −0.435445 + 0.435445i
\(283\) 115.825 + 115.825i 0.409277 + 0.409277i 0.881486 0.472209i \(-0.156543\pi\)
−0.472209 + 0.881486i \(0.656543\pi\)
\(284\) 127.519i 0.449011i
\(285\) 0 0
\(286\) −177.340 −0.620071
\(287\) −34.8140 + 34.8140i −0.121303 + 0.121303i
\(288\) −12.0000 12.0000i −0.0416667 0.0416667i
\(289\) 599.306i 2.07372i
\(290\) 0 0
\(291\) −58.2665 −0.200228
\(292\) −100.377 + 100.377i −0.343756 + 0.343756i
\(293\) −224.451 224.451i −0.766043 0.766043i 0.211364 0.977407i \(-0.432209\pi\)
−0.977407 + 0.211364i \(0.932209\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) 0 0
\(296\) −34.0008 −0.114868
\(297\) 42.2824 42.2824i 0.142365 0.142365i
\(298\) 55.7399 + 55.7399i 0.187047 + 0.187047i
\(299\) 465.027i 1.55528i
\(300\) 0 0
\(301\) −97.8004 −0.324918
\(302\) 82.9665 82.9665i 0.274724 0.274724i
\(303\) 61.4169 + 61.4169i 0.202696 + 0.202696i
\(304\) 96.4693i 0.317333i
\(305\) 0 0
\(306\) −126.450 −0.413234
\(307\) 42.5120 42.5120i 0.138476 0.138476i −0.634471 0.772947i \(-0.718782\pi\)
0.772947 + 0.634471i \(0.218782\pi\)
\(308\) −43.0583 43.0583i −0.139800 0.139800i
\(309\) 138.121i 0.446993i
\(310\) 0 0
\(311\) −97.1353 −0.312332 −0.156166 0.987731i \(-0.549914\pi\)
−0.156166 + 0.987731i \(0.549914\pi\)
\(312\) 37.7477 37.7477i 0.120986 0.120986i
\(313\) 94.4913 + 94.4913i 0.301889 + 0.301889i 0.841753 0.539863i \(-0.181524\pi\)
−0.539863 + 0.841753i \(0.681524\pi\)
\(314\) 199.590i 0.635637i
\(315\) 0 0
\(316\) −2.12242 −0.00671653
\(317\) −146.150 + 146.150i −0.461040 + 0.461040i −0.898996 0.437956i \(-0.855703\pi\)
0.437956 + 0.898996i \(0.355703\pi\)
\(318\) −17.3553 17.3553i −0.0545764 0.0545764i
\(319\) 588.501i 1.84483i
\(320\) 0 0
\(321\) 331.576 1.03295
\(322\) 112.909 112.909i 0.350649 0.350649i
\(323\) 508.271 + 508.271i 1.57359 + 1.57359i
\(324\) 18.0000i 0.0555556i
\(325\) 0 0
\(326\) 90.7768 0.278457
\(327\) −123.619 + 123.619i −0.378039 + 0.378039i
\(328\) −37.2177 37.2177i −0.113469 0.113469i
\(329\) 187.573i 0.570131i
\(330\) 0 0
\(331\) 223.981 0.676679 0.338339 0.941024i \(-0.390135\pi\)
0.338339 + 0.941024i \(0.390135\pi\)
\(332\) −107.249 + 107.249i −0.323038 + 0.323038i
\(333\) 25.5006 + 25.5006i 0.0765784 + 0.0765784i
\(334\) 198.500i 0.594312i
\(335\) 0 0
\(336\) 18.3303 0.0545545
\(337\) 41.7444 41.7444i 0.123871 0.123871i −0.642454 0.766324i \(-0.722084\pi\)
0.766324 + 0.642454i \(0.222084\pi\)
\(338\) −50.2595 50.2595i −0.148697 0.148697i
\(339\) 62.0147i 0.182934i
\(340\) 0 0
\(341\) 540.697 1.58562
\(342\) 72.3520 72.3520i 0.211555 0.211555i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 104.553i 0.303933i
\(345\) 0 0
\(346\) 161.081 0.465551
\(347\) −283.163 + 283.163i −0.816031 + 0.816031i −0.985530 0.169500i \(-0.945785\pi\)
0.169500 + 0.985530i \(0.445785\pi\)
\(348\) −125.265 125.265i −0.359957 0.359957i
\(349\) 73.8529i 0.211613i −0.994387 0.105807i \(-0.966258\pi\)
0.994387 0.105807i \(-0.0337424\pi\)
\(350\) 0 0
\(351\) −56.6215 −0.161315
\(352\) 46.0313 46.0313i 0.130771 0.130771i
\(353\) 221.700 + 221.700i 0.628047 + 0.628047i 0.947576 0.319530i \(-0.103525\pi\)
−0.319530 + 0.947576i \(0.603525\pi\)
\(354\) 231.106i 0.652842i
\(355\) 0 0
\(356\) 290.309 0.815473
\(357\) 96.5775 96.5775i 0.270525 0.270525i
\(358\) −154.267 154.267i −0.430912 0.430912i
\(359\) 351.735i 0.979764i −0.871789 0.489882i \(-0.837040\pi\)
0.871789 0.489882i \(-0.162960\pi\)
\(360\) 0 0
\(361\) −220.645 −0.611205
\(362\) 166.548 166.548i 0.460078 0.460078i
\(363\) 13.9988 + 13.9988i 0.0385641 + 0.0385641i
\(364\) 57.6605i 0.158408i
\(365\) 0 0
\(366\) 19.8164 0.0541433
\(367\) −9.03767 + 9.03767i −0.0246258 + 0.0246258i −0.719312 0.694687i \(-0.755543\pi\)
0.694687 + 0.719312i \(0.255543\pi\)
\(368\) 120.705 + 120.705i 0.328002 + 0.328002i
\(369\) 55.8266i 0.151292i
\(370\) 0 0
\(371\) 26.5107 0.0714573
\(372\) −115.090 + 115.090i −0.309381 + 0.309381i
\(373\) 151.095 + 151.095i 0.405079 + 0.405079i 0.880019 0.474939i \(-0.157530\pi\)
−0.474939 + 0.880019i \(0.657530\pi\)
\(374\) 485.053i 1.29693i
\(375\) 0 0
\(376\) 200.524 0.533309
\(377\) 394.039 394.039i 1.04520 1.04520i
\(378\) −13.7477 13.7477i −0.0363696 0.0363696i
\(379\) 268.787i 0.709201i −0.935018 0.354601i \(-0.884617\pi\)
0.935018 0.354601i \(-0.115383\pi\)
\(380\) 0 0
\(381\) −285.969 −0.750574
\(382\) −235.646 + 235.646i −0.616873 + 0.616873i
\(383\) −304.341 304.341i −0.794625 0.794625i 0.187618 0.982242i \(-0.439923\pi\)
−0.982242 + 0.187618i \(0.939923\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 32.4422 0.0840471
\(387\) −78.4148 + 78.4148i −0.202622 + 0.202622i
\(388\) 47.5744 + 47.5744i 0.122614 + 0.122614i
\(389\) 50.0127i 0.128567i 0.997932 + 0.0642837i \(0.0204763\pi\)
−0.997932 + 0.0642837i \(0.979524\pi\)
\(390\) 0 0
\(391\) 1271.92 3.25299
\(392\) −14.0000 + 14.0000i −0.0357143 + 0.0357143i
\(393\) 42.6216 + 42.6216i 0.108452 + 0.108452i
\(394\) 13.3627i 0.0339154i
\(395\) 0 0
\(396\) −69.0469 −0.174361
\(397\) 325.002 325.002i 0.818644 0.818644i −0.167268 0.985912i \(-0.553494\pi\)
0.985912 + 0.167268i \(0.0534944\pi\)
\(398\) 32.0712 + 32.0712i 0.0805808 + 0.0805808i
\(399\) 110.519i 0.276991i
\(400\) 0 0
\(401\) −462.981 −1.15457 −0.577283 0.816544i \(-0.695887\pi\)
−0.577283 + 0.816544i \(0.695887\pi\)
\(402\) 50.5744 50.5744i 0.125807 0.125807i
\(403\) −362.031 362.031i −0.898340 0.898340i
\(404\) 100.293i 0.248251i
\(405\) 0 0
\(406\) 191.346 0.471294
\(407\) −97.8188 + 97.8188i −0.240341 + 0.240341i
\(408\) 103.246 + 103.246i 0.253053 + 0.253053i
\(409\) 131.630i 0.321834i −0.986968 0.160917i \(-0.948555\pi\)
0.986968 0.160917i \(-0.0514451\pi\)
\(410\) 0 0
\(411\) −322.236 −0.784028
\(412\) −112.775 + 112.775i −0.273726 + 0.273726i
\(413\) −176.510 176.510i −0.427386 0.427386i
\(414\) 181.057i 0.437336i
\(415\) 0 0
\(416\) −61.6417 −0.148177
\(417\) 109.542 109.542i 0.262691 0.262691i
\(418\) 277.538 + 277.538i 0.663966 + 0.663966i
\(419\) 536.418i 1.28023i −0.768277 0.640117i \(-0.778886\pi\)
0.768277 0.640117i \(-0.221114\pi\)
\(420\) 0 0
\(421\) −508.770 −1.20848 −0.604240 0.796803i \(-0.706523\pi\)
−0.604240 + 0.796803i \(0.706523\pi\)
\(422\) 123.531 123.531i 0.292728 0.292728i
\(423\) −150.393 150.393i −0.355539 0.355539i
\(424\) 28.3411i 0.0668422i
\(425\) 0 0
\(426\) −156.178 −0.366616
\(427\) −15.1351 + 15.1351i −0.0354451 + 0.0354451i
\(428\) −270.731 270.731i −0.632548 0.632548i
\(429\) 217.197i 0.506286i
\(430\) 0 0
\(431\) 467.561 1.08483 0.542414 0.840111i \(-0.317510\pi\)
0.542414 + 0.840111i \(0.317510\pi\)
\(432\) 14.6969 14.6969i 0.0340207 0.0340207i
\(433\) 129.391 + 129.391i 0.298825 + 0.298825i 0.840554 0.541729i \(-0.182230\pi\)
−0.541729 + 0.840554i \(0.682230\pi\)
\(434\) 175.803i 0.405075i
\(435\) 0 0
\(436\) 201.868 0.463001
\(437\) −727.768 + 727.768i −1.66537 + 1.66537i
\(438\) −122.936 122.936i −0.280675 0.280675i
\(439\) 51.7818i 0.117954i 0.998259 + 0.0589770i \(0.0187839\pi\)
−0.998259 + 0.0589770i \(0.981216\pi\)
\(440\) 0 0
\(441\) 21.0000 0.0476190
\(442\) −324.774 + 324.774i −0.734782 + 0.734782i
\(443\) −357.514 357.514i −0.807029 0.807029i 0.177154 0.984183i \(-0.443311\pi\)
−0.984183 + 0.177154i \(0.943311\pi\)
\(444\) 41.6423i 0.0937890i
\(445\) 0 0
\(446\) 163.918 0.367529
\(447\) −68.2671 + 68.2671i −0.152723 + 0.152723i
\(448\) −14.9666 14.9666i −0.0334077 0.0334077i
\(449\) 615.742i 1.37136i 0.727902 + 0.685681i \(0.240496\pi\)
−0.727902 + 0.685681i \(0.759504\pi\)
\(450\) 0 0
\(451\) −214.148 −0.474828
\(452\) −50.6348 + 50.6348i −0.112024 + 0.112024i
\(453\) 101.613 + 101.613i 0.224311 + 0.224311i
\(454\) 187.218i 0.412374i
\(455\) 0 0
\(456\) −118.150 −0.259101
\(457\) 502.144 502.144i 1.09878 1.09878i 0.104230 0.994553i \(-0.466762\pi\)
0.994553 0.104230i \(-0.0332379\pi\)
\(458\) 348.973 + 348.973i 0.761950 + 0.761950i
\(459\) 154.868i 0.337404i
\(460\) 0 0
\(461\) 100.965 0.219012 0.109506 0.993986i \(-0.465073\pi\)
0.109506 + 0.993986i \(0.465073\pi\)
\(462\) 52.7355 52.7355i 0.114146 0.114146i
\(463\) −312.235 312.235i −0.674374 0.674374i 0.284347 0.958721i \(-0.408223\pi\)
−0.958721 + 0.284347i \(0.908223\pi\)
\(464\) 204.557i 0.440856i
\(465\) 0 0
\(466\) −416.639 −0.894074
\(467\) −502.571 + 502.571i −1.07617 + 1.07617i −0.0793198 + 0.996849i \(0.525275\pi\)
−0.996849 + 0.0793198i \(0.974725\pi\)
\(468\) 46.2313 + 46.2313i 0.0987847 + 0.0987847i
\(469\) 77.2537i 0.164720i
\(470\) 0 0
\(471\) 244.447 0.518995
\(472\) 188.697 188.697i 0.399783 0.399783i
\(473\) −300.794 300.794i −0.635929 0.635929i
\(474\) 2.59943i 0.00548403i
\(475\) 0 0
\(476\) −157.710 −0.331324
\(477\) 21.2558 21.2558i 0.0445614 0.0445614i
\(478\) 330.793 + 330.793i 0.692035 + 0.692035i
\(479\) 270.133i 0.563952i −0.959421 0.281976i \(-0.909010\pi\)
0.959421 0.281976i \(-0.0909899\pi\)
\(480\) 0 0
\(481\) 130.992 0.272332
\(482\) 375.584 375.584i 0.779221 0.779221i
\(483\) 138.285 + 138.285i 0.286303 + 0.286303i
\(484\) 22.8599i 0.0472312i
\(485\) 0 0
\(486\) −22.0454 −0.0453609
\(487\) 227.632 227.632i 0.467417 0.467417i −0.433660 0.901077i \(-0.642778\pi\)
0.901077 + 0.433660i \(0.142778\pi\)
\(488\) −16.1801 16.1801i −0.0331559 0.0331559i
\(489\) 111.178i 0.227359i
\(490\) 0 0
\(491\) −23.2563 −0.0473652 −0.0236826 0.999720i \(-0.507539\pi\)
−0.0236826 + 0.999720i \(0.507539\pi\)
\(492\) 45.5822 45.5822i 0.0926468 0.0926468i
\(493\) 1077.76 + 1077.76i 2.18612 + 2.18612i
\(494\) 371.658i 0.752344i
\(495\) 0 0
\(496\) 187.941 0.378913
\(497\) 119.283 119.283i 0.240006 0.240006i
\(498\) −131.352 131.352i −0.263759 0.263759i
\(499\) 319.077i 0.639433i −0.947513 0.319717i \(-0.896412\pi\)
0.947513 0.319717i \(-0.103588\pi\)
\(500\) 0 0
\(501\) 243.112 0.485254
\(502\) 41.2876 41.2876i 0.0822463 0.0822463i
\(503\) −585.731 585.731i −1.16448 1.16448i −0.983485 0.180990i \(-0.942070\pi\)
−0.180990 0.983485i \(-0.557930\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) 0 0
\(506\) 694.524 1.37258
\(507\) 61.5551 61.5551i 0.121410 0.121410i
\(508\) 233.492 + 233.492i 0.459631 + 0.459631i
\(509\) 266.157i 0.522902i −0.965217 0.261451i \(-0.915799\pi\)
0.965217 0.261451i \(-0.0842009\pi\)
\(510\) 0 0
\(511\) 187.787 0.367490
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 88.6127 + 88.6127i 0.172734 + 0.172734i
\(514\) 202.741i 0.394437i
\(515\) 0 0
\(516\) 128.051 0.248161
\(517\) 576.899 576.899i 1.11586 1.11586i
\(518\) 31.8048 + 31.8048i 0.0613993 + 0.0613993i
\(519\) 197.283i 0.380121i
\(520\) 0 0
\(521\) −1.52542 −0.00292786 −0.00146393 0.999999i \(-0.500466\pi\)
−0.00146393 + 0.999999i \(0.500466\pi\)
\(522\) 153.418 153.418i 0.293904 0.293904i
\(523\) −260.120 260.120i −0.497362 0.497362i 0.413254 0.910616i \(-0.364392\pi\)
−0.910616 + 0.413254i \(0.864392\pi\)
\(524\) 69.6007i 0.132826i
\(525\) 0 0
\(526\) −329.188 −0.625833
\(527\) 990.210 990.210i 1.87896 1.87896i
\(528\) 56.3766 + 56.3766i 0.106774 + 0.106774i
\(529\) 1292.20i 2.44272i
\(530\) 0 0
\(531\) −283.046 −0.533044
\(532\) 90.2387 90.2387i 0.169622 0.169622i
\(533\) 143.385 + 143.385i 0.269015 + 0.269015i
\(534\) 355.554i 0.665831i
\(535\) 0 0
\(536\) −82.5877 −0.154081
\(537\) 188.937 188.937i 0.351838 0.351838i
\(538\) −254.148 254.148i −0.472394 0.472394i
\(539\) 80.5547i 0.149452i
\(540\) 0 0
\(541\) −273.648 −0.505820 −0.252910 0.967490i \(-0.581388\pi\)
−0.252910 + 0.967490i \(0.581388\pi\)
\(542\) 22.4723 22.4723i 0.0414619 0.0414619i
\(543\) 203.979 + 203.979i 0.375652 + 0.375652i
\(544\) 168.599i 0.309925i
\(545\) 0 0
\(546\) −70.6194 −0.129340
\(547\) −355.490 + 355.490i −0.649890 + 0.649890i −0.952966 0.303077i \(-0.901986\pi\)
0.303077 + 0.952966i \(0.401986\pi\)
\(548\) 263.104 + 263.104i 0.480117 + 0.480117i
\(549\) 24.2701i 0.0442078i
\(550\) 0 0
\(551\) −1233.34 −2.23837
\(552\) −147.832 + 147.832i −0.267812 + 0.267812i
\(553\) 1.98535 + 1.98535i 0.00359014 + 0.00359014i
\(554\) 94.7898i 0.171101i
\(555\) 0 0
\(556\) −178.881 −0.321729
\(557\) 270.897 270.897i 0.486350 0.486350i −0.420802 0.907152i \(-0.638251\pi\)
0.907152 + 0.420802i \(0.138251\pi\)
\(558\) −140.956 140.956i −0.252609 0.252609i
\(559\) 402.802i 0.720575i
\(560\) 0 0
\(561\) 594.066 1.05894
\(562\) −18.8810 + 18.8810i −0.0335960 + 0.0335960i
\(563\) −73.1143 73.1143i −0.129866 0.129866i 0.639186 0.769052i \(-0.279271\pi\)
−0.769052 + 0.639186i \(0.779271\pi\)
\(564\) 245.591i 0.435445i
\(565\) 0 0
\(566\) 231.651 0.409277
\(567\) 16.8375 16.8375i 0.0296957 0.0296957i
\(568\) 127.519 + 127.519i 0.224505 + 0.224505i
\(569\) 1018.55i 1.79007i 0.445992 + 0.895037i \(0.352851\pi\)
−0.445992 + 0.895037i \(0.647149\pi\)
\(570\) 0 0
\(571\) −621.517 −1.08847 −0.544236 0.838932i \(-0.683180\pi\)
−0.544236 + 0.838932i \(0.683180\pi\)
\(572\) −177.340 + 177.340i −0.310036 + 0.310036i
\(573\) −288.606 288.606i −0.503675 0.503675i
\(574\) 69.6280i 0.121303i
\(575\) 0 0
\(576\) −24.0000 −0.0416667
\(577\) −760.301 + 760.301i −1.31768 + 1.31768i −0.402071 + 0.915608i \(0.631710\pi\)
−0.915608 + 0.402071i \(0.868290\pi\)
\(578\) −599.306 599.306i −1.03686 1.03686i
\(579\) 39.7334i 0.0686242i
\(580\) 0 0
\(581\) 200.644 0.345342
\(582\) −58.2665 + 58.2665i −0.100114 + 0.100114i
\(583\) 81.5360 + 81.5360i 0.139856 + 0.139856i
\(584\) 200.753i 0.343756i
\(585\) 0 0
\(586\) −448.901 −0.766043
\(587\) −5.94607 + 5.94607i −0.0101296 + 0.0101296i −0.712153 0.702024i \(-0.752280\pi\)
0.702024 + 0.712153i \(0.252280\pi\)
\(588\) −17.1464 17.1464i −0.0291606 0.0291606i
\(589\) 1133.16i 1.92387i
\(590\) 0 0
\(591\) 16.3659 0.0276918
\(592\) −34.0008 + 34.0008i −0.0574338 + 0.0574338i
\(593\) 463.916 + 463.916i 0.782320 + 0.782320i 0.980222 0.197902i \(-0.0634127\pi\)
−0.197902 + 0.980222i \(0.563413\pi\)
\(594\) 84.5649i 0.142365i
\(595\) 0 0
\(596\) 111.480 0.187047
\(597\) −39.2790 + 39.2790i −0.0657940 + 0.0657940i
\(598\) −465.027 465.027i −0.777638 0.777638i
\(599\) 660.745i 1.10308i −0.834148 0.551540i \(-0.814040\pi\)
0.834148 0.551540i \(-0.185960\pi\)
\(600\) 0 0
\(601\) −905.439 −1.50655 −0.753277 0.657704i \(-0.771528\pi\)
−0.753277 + 0.657704i \(0.771528\pi\)
\(602\) −97.8004 + 97.8004i −0.162459 + 0.162459i
\(603\) 61.9407 + 61.9407i 0.102721 + 0.102721i
\(604\) 165.933i 0.274724i
\(605\) 0 0
\(606\) 122.834 0.202696
\(607\) −518.514 + 518.514i −0.854224 + 0.854224i −0.990650 0.136426i \(-0.956438\pi\)
0.136426 + 0.990650i \(0.456438\pi\)
\(608\) 96.4693 + 96.4693i 0.158667 + 0.158667i
\(609\) 234.349i 0.384810i
\(610\) 0 0
\(611\) −772.541 −1.26439
\(612\) −126.450 + 126.450i −0.206617 + 0.206617i
\(613\) 500.739 + 500.739i 0.816867 + 0.816867i 0.985653 0.168786i \(-0.0539847\pi\)
−0.168786 + 0.985653i \(0.553985\pi\)
\(614\) 85.0240i 0.138476i
\(615\) 0 0
\(616\) −86.1166 −0.139800
\(617\) −122.242 + 122.242i −0.198123 + 0.198123i −0.799195 0.601072i \(-0.794740\pi\)
0.601072 + 0.799195i \(0.294740\pi\)
\(618\) −138.121 138.121i −0.223497 0.223497i
\(619\) 320.914i 0.518440i 0.965818 + 0.259220i \(0.0834655\pi\)
−0.965818 + 0.259220i \(0.916534\pi\)
\(620\) 0 0
\(621\) 221.749 0.357083
\(622\) −97.1353 + 97.1353i −0.156166 + 0.156166i
\(623\) −271.559 271.559i −0.435889 0.435889i
\(624\) 75.4953i 0.120986i
\(625\) 0 0
\(626\) 188.983 0.301889
\(627\) −339.913 + 339.913i −0.542126 + 0.542126i
\(628\) −199.590 199.590i −0.317818 0.317818i
\(629\) 358.282i 0.569606i
\(630\) 0 0
\(631\) −636.141 −1.00815 −0.504074 0.863661i \(-0.668166\pi\)
−0.504074 + 0.863661i \(0.668166\pi\)
\(632\) −2.12242 + 2.12242i −0.00335827 + 0.00335827i
\(633\) 151.294 + 151.294i 0.239012 + 0.239012i
\(634\) 292.300i 0.461040i
\(635\) 0 0
\(636\) −34.7106 −0.0545764
\(637\) 53.9365 53.9365i 0.0846726 0.0846726i
\(638\) 588.501 + 588.501i 0.922416 + 0.922416i
\(639\) 191.278i 0.299340i
\(640\) 0 0
\(641\) −682.051 −1.06404 −0.532021 0.846731i \(-0.678567\pi\)
−0.532021 + 0.846731i \(0.678567\pi\)
\(642\) 331.576 331.576i 0.516474 0.516474i
\(643\) 5.33298 + 5.33298i 0.00829390 + 0.00829390i 0.711242 0.702948i \(-0.248133\pi\)
−0.702948 + 0.711242i \(0.748133\pi\)
\(644\) 225.818i 0.350649i
\(645\) 0 0
\(646\) 1016.54 1.57359
\(647\) −285.931 + 285.931i −0.441933 + 0.441933i −0.892661 0.450728i \(-0.851164\pi\)
0.450728 + 0.892661i \(0.351164\pi\)
\(648\) 18.0000 + 18.0000i 0.0277778 + 0.0277778i
\(649\) 1085.75i 1.67296i
\(650\) 0 0
\(651\) 215.313 0.330742
\(652\) 90.7768 90.7768i 0.139228 0.139228i
\(653\) −199.462 199.462i −0.305455 0.305455i 0.537689 0.843144i \(-0.319298\pi\)
−0.843144 + 0.537689i \(0.819298\pi\)
\(654\) 247.237i 0.378039i
\(655\) 0 0
\(656\) −74.4355 −0.113469
\(657\) 150.565 150.565i 0.229170 0.229170i
\(658\) −187.573 187.573i −0.285066 0.285066i
\(659\) 204.685i 0.310599i 0.987867 + 0.155300i \(0.0496343\pi\)
−0.987867 + 0.155300i \(0.950366\pi\)
\(660\) 0 0
\(661\) 143.044 0.216406 0.108203 0.994129i \(-0.465490\pi\)
0.108203 + 0.994129i \(0.465490\pi\)
\(662\) 223.981 223.981i 0.338339 0.338339i
\(663\) −397.765 397.765i −0.599947 0.599947i
\(664\) 214.497i 0.323038i
\(665\) 0 0
\(666\) 51.0012 0.0765784
\(667\) −1543.19 + 1543.19i −2.31362 + 2.31362i
\(668\) −198.500 198.500i −0.297156 0.297156i
\(669\) 200.758i 0.300086i
\(670\) 0 0
\(671\) −93.0986 −0.138746
\(672\) 18.3303 18.3303i 0.0272772 0.0272772i
\(673\) 317.527 + 317.527i 0.471808 + 0.471808i 0.902499 0.430691i \(-0.141730\pi\)
−0.430691 + 0.902499i \(0.641730\pi\)
\(674\) 83.4888i 0.123871i
\(675\) 0 0
\(676\) −100.519 −0.148697
\(677\) 272.663 272.663i 0.402752 0.402752i −0.476450 0.879202i \(-0.658077\pi\)
0.879202 + 0.476450i \(0.158077\pi\)
\(678\) −62.0147 62.0147i −0.0914671 0.0914671i
\(679\) 89.0035i 0.131080i
\(680\) 0 0
\(681\) −229.294 −0.336702
\(682\) 540.697 540.697i 0.792812 0.792812i
\(683\) 449.231 + 449.231i 0.657732 + 0.657732i 0.954843 0.297111i \(-0.0960232\pi\)
−0.297111 + 0.954843i \(0.596023\pi\)
\(684\) 144.704i 0.211555i
\(685\) 0 0
\(686\) 26.1916 0.0381802
\(687\) −427.403 + 427.403i −0.622130 + 0.622130i
\(688\) −104.553 104.553i −0.151967 0.151967i
\(689\) 109.187i 0.158472i
\(690\) 0 0
\(691\) 1004.13 1.45316 0.726578 0.687084i \(-0.241109\pi\)
0.726578 + 0.687084i \(0.241109\pi\)
\(692\) 161.081 161.081i 0.232776 0.232776i
\(693\) 64.5875 + 64.5875i 0.0931998 + 0.0931998i
\(694\) 566.325i 0.816031i
\(695\) 0 0
\(696\) −250.530 −0.359957
\(697\) −392.181 + 392.181i −0.562669 + 0.562669i
\(698\) −73.8529 73.8529i −0.105807 0.105807i
\(699\) 510.276i 0.730009i
\(700\) 0 0
\(701\) −869.248 −1.24001 −0.620006 0.784597i \(-0.712870\pi\)
−0.620006 + 0.784597i \(0.712870\pi\)
\(702\) −56.6215 + 56.6215i −0.0806574 + 0.0806574i
\(703\) −205.002 205.002i −0.291610 0.291610i
\(704\) 92.0626i 0.130771i
\(705\) 0 0
\(706\) 443.401 0.628047
\(707\) −93.8159 + 93.8159i −0.132696 + 0.132696i
\(708\) 231.106 + 231.106i 0.326421 + 0.326421i
\(709\) 79.6980i 0.112409i 0.998419 + 0.0562045i \(0.0178999\pi\)
−0.998419 + 0.0562045i \(0.982100\pi\)
\(710\) 0 0
\(711\) 3.18364 0.00447769
\(712\) 290.309 290.309i 0.407737 0.407737i
\(713\) 1417.83 + 1417.83i 1.98855 + 1.98855i
\(714\) 193.155i 0.270525i
\(715\) 0 0
\(716\) −308.533 −0.430912
\(717\) −405.136 + 405.136i −0.565044 + 0.565044i
\(718\) −351.735 351.735i −0.489882 0.489882i
\(719\) 1081.03i 1.50351i 0.659440 + 0.751757i \(0.270793\pi\)
−0.659440 + 0.751757i \(0.729207\pi\)
\(720\) 0 0
\(721\) 210.983 0.292626
\(722\) −220.645 + 220.645i −0.305603 + 0.305603i
\(723\) 459.995 + 459.995i 0.636231 + 0.636231i
\(724\) 333.096i 0.460078i
\(725\) 0 0
\(726\) 27.9975 0.0385641
\(727\) −281.701 + 281.701i −0.387484 + 0.387484i −0.873789 0.486305i \(-0.838344\pi\)
0.486305 + 0.873789i \(0.338344\pi\)
\(728\) 57.6605 + 57.6605i 0.0792040 + 0.0792040i
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) −1101.72 −1.50715
\(732\) 19.8164 19.8164i 0.0270716 0.0270716i
\(733\) −1016.28 1016.28i −1.38647 1.38647i −0.832611 0.553858i \(-0.813155\pi\)
−0.553858 0.832611i \(-0.686845\pi\)
\(734\) 18.0753i 0.0246258i
\(735\) 0 0
\(736\) 241.409 0.328002
\(737\) −237.601 + 237.601i −0.322389 + 0.322389i
\(738\) 55.8266 + 55.8266i 0.0756458 + 0.0756458i
\(739\) 289.140i 0.391258i 0.980678 + 0.195629i \(0.0626749\pi\)
−0.980678 + 0.195629i \(0.937325\pi\)
\(740\) 0 0
\(741\) 455.186 0.614286
\(742\) 26.5107 26.5107i 0.0357286 0.0357286i
\(743\) −290.501 290.501i −0.390984 0.390984i 0.484054 0.875038i \(-0.339164\pi\)
−0.875038 + 0.484054i \(0.839164\pi\)
\(744\) 230.180i 0.309381i
\(745\) 0 0
\(746\) 302.189 0.405079
\(747\) 160.873 160.873i 0.215358 0.215358i
\(748\) −485.053 485.053i −0.648467 0.648467i
\(749\) 506.491i 0.676223i
\(750\) 0 0
\(751\) 688.089 0.916231 0.458115 0.888893i \(-0.348525\pi\)
0.458115 + 0.888893i \(0.348525\pi\)
\(752\) 200.524 200.524i 0.266655 0.266655i
\(753\) 50.5668 + 50.5668i 0.0671538 + 0.0671538i
\(754\) 788.077i 1.04520i
\(755\) 0 0
\(756\) −27.4955 −0.0363696
\(757\) −180.960 + 180.960i −0.239049 + 0.239049i −0.816456 0.577408i \(-0.804064\pi\)
0.577408 + 0.816456i \(0.304064\pi\)
\(758\) −268.787 268.787i −0.354601 0.354601i
\(759\) 850.614i 1.12070i
\(760\) 0 0
\(761\) 1096.09 1.44033 0.720163 0.693805i \(-0.244067\pi\)
0.720163 + 0.693805i \(0.244067\pi\)
\(762\) −285.969 + 285.969i −0.375287 + 0.375287i
\(763\) −188.831 188.831i −0.247484 0.247484i
\(764\) 471.291i 0.616873i
\(765\) 0 0
\(766\) −608.682 −0.794625
\(767\) −726.977 + 726.977i −0.947818 + 0.947818i
\(768\) 19.5959 + 19.5959i 0.0255155 + 0.0255155i
\(769\) 892.540i 1.16065i −0.814385 0.580325i \(-0.802925\pi\)
0.814385 0.580325i \(-0.197075\pi\)
\(770\) 0 0
\(771\) 248.306 0.322057
\(772\) 32.4422 32.4422i 0.0420235 0.0420235i
\(773\) −836.773 836.773i −1.08250 1.08250i −0.996276 0.0862244i \(-0.972520\pi\)
−0.0862244 0.996276i \(-0.527480\pi\)
\(774\) 156.830i 0.202622i
\(775\) 0 0
\(776\) 95.1487 0.122614
\(777\) −38.9528 + 38.9528i −0.0501323 + 0.0501323i
\(778\) 50.0127 + 50.0127i 0.0642837 + 0.0642837i
\(779\) 448.796i 0.576118i
\(780\) 0 0
\(781\) 733.733 0.939479
\(782\) 1271.92 1271.92i 1.62650 1.62650i
\(783\) 187.898 + 187.898i 0.239971 + 0.239971i
\(784\) 28.0000i 0.0357143i
\(785\) 0 0
\(786\) 85.2431 0.108452
\(787\) 226.485 226.485i 0.287782 0.287782i −0.548420 0.836203i \(-0.684771\pi\)
0.836203 + 0.548420i \(0.184771\pi\)
\(788\) −13.3627 13.3627i −0.0169577 0.0169577i
\(789\) 403.171i 0.510990i
\(790\) 0 0
\(791\) 94.7290 0.119759
\(792\) −69.0469 + 69.0469i −0.0871805 + 0.0871805i
\(793\) 62.3354 + 62.3354i 0.0786070 + 0.0786070i
\(794\) 650.003i 0.818644i
\(795\) 0 0
\(796\) 64.1423 0.0805808
\(797\) 728.914 728.914i 0.914572 0.914572i −0.0820555 0.996628i \(-0.526148\pi\)
0.996628 + 0.0820555i \(0.0261485\pi\)
\(798\) 110.519 + 110.519i 0.138496 + 0.138496i
\(799\) 2113.02i 2.64458i
\(800\) 0 0
\(801\) −435.463 −0.543649
\(802\) −462.981 + 462.981i −0.577283 + 0.577283i
\(803\) 577.558 + 577.558i 0.719250 + 0.719250i
\(804\) 101.149i 0.125807i
\(805\) 0 0
\(806\) −724.062 −0.898340
\(807\) 311.267 311.267i 0.385708 0.385708i
\(808\) −100.293 100.293i −0.124126 0.124126i
\(809\) 1196.38i 1.47884i 0.673247 + 0.739418i \(0.264899\pi\)
−0.673247 + 0.739418i \(0.735101\pi\)
\(810\) 0 0
\(811\) −1180.03 −1.45503 −0.727513 0.686094i \(-0.759324\pi\)
−0.727513 + 0.686094i \(0.759324\pi\)
\(812\) 191.346 191.346i 0.235647 0.235647i
\(813\) 27.5229 + 27.5229i 0.0338535 + 0.0338535i
\(814\) 195.638i 0.240341i
\(815\) 0 0
\(816\) 206.491 0.253053
\(817\) 630.385 630.385i 0.771585 0.771585i
\(818\) −131.630 131.630i −0.160917 0.160917i
\(819\) 86.4908i 0.105605i
\(820\) 0 0
\(821\) 35.8305 0.0436425 0.0218212 0.999762i \(-0.493054\pi\)
0.0218212 + 0.999762i \(0.493054\pi\)
\(822\) −322.236 + 322.236i −0.392014 + 0.392014i
\(823\) −448.829 448.829i −0.545357 0.545357i 0.379737 0.925094i \(-0.376014\pi\)
−0.925094 + 0.379737i \(0.876014\pi\)
\(824\) 225.550i 0.273726i
\(825\) 0 0
\(826\) −353.021 −0.427386
\(827\) −874.926 + 874.926i −1.05795 + 1.05795i −0.0597373 + 0.998214i \(0.519026\pi\)
−0.998214 + 0.0597373i \(0.980974\pi\)
\(828\) −181.057 181.057i −0.218668 0.218668i
\(829\) 934.022i 1.12669i −0.826223 0.563343i \(-0.809515\pi\)
0.826223 0.563343i \(-0.190485\pi\)
\(830\) 0 0
\(831\) −116.093 −0.139703
\(832\) −61.6417 + 61.6417i −0.0740886 + 0.0740886i
\(833\) 147.525 + 147.525i 0.177100 + 0.177100i
\(834\) 219.084i 0.262691i
\(835\) 0 0
\(836\) 555.076 0.663966
\(837\) 172.635 172.635i 0.206254 0.206254i
\(838\) −536.418 536.418i −0.640117 0.640117i
\(839\) 10.5147i 0.0125324i 0.999980 + 0.00626621i \(0.00199461\pi\)
−0.999980 + 0.00626621i \(0.998005\pi\)
\(840\) 0 0
\(841\) −1774.22 −2.10966
\(842\) −508.770 + 508.770i −0.604240 + 0.604240i
\(843\) −23.1244 23.1244i −0.0274310 0.0274310i
\(844\) 247.063i 0.292728i
\(845\) 0 0
\(846\) −300.786 −0.355539
\(847\) −21.3835 + 21.3835i −0.0252461 + 0.0252461i
\(848\) 28.3411 + 28.3411i 0.0334211 + 0.0334211i
\(849\) 283.713i 0.334173i
\(850\) 0 0
\(851\) −513.007 −0.602828
\(852\) −156.178 + 156.178i −0.183308 + 0.183308i
\(853\) −1082.57 1082.57i −1.26914 1.26914i −0.946534 0.322603i \(-0.895442\pi\)
−0.322603 0.946534i \(-0.604558\pi\)
\(854\) 30.2701i 0.0354451i
\(855\) 0 0
\(856\) −541.461 −0.632548
\(857\) −506.843 + 506.843i −0.591416 + 0.591416i −0.938014 0.346598i \(-0.887337\pi\)
0.346598 + 0.938014i \(0.387337\pi\)
\(858\) −217.197 217.197i −0.253143 0.253143i
\(859\) 471.172i 0.548512i 0.961657 + 0.274256i \(0.0884315\pi\)
−0.961657 + 0.274256i \(0.911568\pi\)
\(860\) 0 0
\(861\) −85.2765 −0.0990436
\(862\) 467.561 467.561i 0.542414 0.542414i
\(863\) −352.570 352.570i −0.408540 0.408540i 0.472689 0.881229i \(-0.343283\pi\)
−0.881229 + 0.472689i \(0.843283\pi\)
\(864\) 29.3939i 0.0340207i
\(865\) 0 0
\(866\) 258.782 0.298825
\(867\) 733.996 733.996i 0.846593 0.846593i
\(868\) −175.803 175.803i −0.202538 0.202538i
\(869\) 12.2122i 0.0140532i
\(870\) 0 0
\(871\) 318.178 0.365301
\(872\) 201.868 201.868i 0.231500 0.231500i
\(873\) −71.3616 71.3616i −0.0817429 0.0817429i
\(874\) 1455.54i 1.66537i
\(875\) 0 0
\(876\) −245.872 −0.280675
\(877\) 1223.94 1223.94i 1.39560 1.39560i 0.583467 0.812137i \(-0.301696\pi\)
0.812137 0.583467i \(-0.198304\pi\)
\(878\) 51.7818 + 51.7818i 0.0589770 + 0.0589770i
\(879\) 549.790i 0.625472i
\(880\) 0 0
\(881\) −635.103 −0.720889 −0.360444 0.932781i \(-0.617375\pi\)
−0.360444 + 0.932781i \(0.617375\pi\)
\(882\) 21.0000 21.0000i 0.0238095 0.0238095i
\(883\) 230.546 + 230.546i 0.261094 + 0.261094i 0.825498 0.564405i \(-0.190894\pi\)
−0.564405 + 0.825498i \(0.690894\pi\)
\(884\) 649.547i 0.734782i
\(885\) 0 0
\(886\) −715.028 −0.807029
\(887\) 1224.61 1224.61i 1.38062 1.38062i 0.537101 0.843518i \(-0.319520\pi\)
0.843518 0.537101i \(-0.180480\pi\)
\(888\) −41.6423 41.6423i −0.0468945 0.0468945i
\(889\) 436.824i 0.491366i
\(890\) 0 0
\(891\) 103.570 0.116241
\(892\) 163.918 163.918i 0.183765 0.183765i
\(893\) 1209.03 + 1209.03i 1.35389 + 1.35389i
\(894\) 136.534i 0.152723i
\(895\) 0 0
\(896\) −29.9333 −0.0334077
\(897\) 569.540 569.540i 0.634938 0.634938i
\(898\) 615.742 + 615.742i 0.685681 + 0.685681i
\(899\) 2402.79i 2.67273i
\(900\) 0 0
\(901\) 298.643 0.331457
\(902\) −214.148 + 214.148i −0.237414 + 0.237414i
\(903\) −119.781 119.781i −0.132647 0.132647i
\(904\) 101.270i 0.112024i
\(905\) 0 0
\(906\) 203.226 0.224311
\(907\) −766.713 + 766.713i −0.845329 + 0.845329i −0.989546 0.144217i \(-0.953934\pi\)
0.144217 + 0.989546i \(0.453934\pi\)
\(908\) 187.218 + 187.218i 0.206187 + 0.206187i
\(909\) 150.440i 0.165501i
\(910\) 0 0
\(911\) −754.441 −0.828146 −0.414073 0.910244i \(-0.635894\pi\)
−0.414073 + 0.910244i \(0.635894\pi\)
\(912\) −118.150 + 118.150i −0.129551 + 0.129551i
\(913\) 617.098 + 617.098i 0.675902 + 0.675902i
\(914\) 1004.29i 1.09878i
\(915\) 0 0
\(916\) 697.947 0.761950
\(917\) −65.1055 + 65.1055i −0.0709984 + 0.0709984i
\(918\) −154.868 154.868i −0.168702 0.168702i
\(919\) 858.117i 0.933750i 0.884323 + 0.466875i \(0.154620\pi\)
−0.884323 + 0.466875i \(0.845380\pi\)
\(920\) 0 0
\(921\) 104.133 0.113065
\(922\) 100.965 100.965i 0.109506 0.109506i
\(923\) −491.280 491.280i −0.532265 0.532265i
\(924\) 105.471i 0.114146i
\(925\) 0 0
\(926\) −624.471 −0.674374
\(927\) 169.163 169.163i 0.182484 0.182484i
\(928\) 204.557 + 204.557i 0.220428 + 0.220428i
\(929\) 631.542i 0.679809i 0.940460 + 0.339904i \(0.110395\pi\)
−0.940460 + 0.339904i \(0.889605\pi\)
\(930\) 0 0
\(931\) −168.821 −0.181333
\(932\) −416.639 + 416.639i −0.447037 + 0.447037i
\(933\) −118.966 118.966i −0.127509 0.127509i
\(934\) 1005.14i 1.07617i
\(935\) 0 0
\(936\) 92.4625 0.0987847
\(937\) −1167.50 + 1167.50i −1.24599 + 1.24599i −0.288519 + 0.957474i \(0.593163\pi\)
−0.957474 + 0.288519i \(0.906837\pi\)
\(938\) 77.2537 + 77.2537i 0.0823600 + 0.0823600i
\(939\) 231.455i 0.246491i
\(940\) 0 0
\(941\) −614.550 −0.653082 −0.326541 0.945183i \(-0.605883\pi\)
−0.326541 + 0.945183i \(0.605883\pi\)
\(942\) 244.447 244.447i 0.259498 0.259498i
\(943\) −561.544 561.544i −0.595487 0.595487i
\(944\) 377.395i 0.399783i
\(945\) 0 0
\(946\) −601.589 −0.635929
\(947\) 635.282 635.282i 0.670837 0.670837i −0.287072 0.957909i \(-0.592682\pi\)
0.957909 + 0.287072i \(0.0926820\pi\)
\(948\) −2.59943 2.59943i −0.00274201 0.00274201i
\(949\) 773.423i 0.814987i
\(950\) 0 0
\(951\) −357.992 −0.376438
\(952\) −157.710 + 157.710i −0.165662 + 0.165662i
\(953\) −350.517 350.517i −0.367803 0.367803i 0.498872 0.866676i \(-0.333748\pi\)
−0.866676 + 0.498872i \(0.833748\pi\)
\(954\) 42.5116i 0.0445614i
\(955\) 0 0
\(956\) 661.585 0.692035
\(957\) −720.764 + 720.764i −0.753149 + 0.753149i
\(958\) −270.133 270.133i −0.281976 0.281976i
\(959\) 492.223i 0.513267i
\(960\) 0 0
\(961\) 1246.61 1.29720
\(962\) 130.992 130.992i 0.136166 0.136166i
\(963\) 406.096 + 406.096i 0.421699 + 0.421699i
\(964\) 751.169i 0.779221i
\(965\) 0 0
\(966\) 276.569 0.286303
\(967\) −435.204 + 435.204i −0.450056 + 0.450056i −0.895373 0.445317i \(-0.853091\pi\)
0.445317 + 0.895373i \(0.353091\pi\)
\(968\) −22.8599 22.8599i −0.0236156 0.0236156i
\(969\) 1245.00i 1.28483i
\(970\) 0 0
\(971\) 218.866 0.225403 0.112701 0.993629i \(-0.464050\pi\)
0.112701 + 0.993629i \(0.464050\pi\)
\(972\) −22.0454 + 22.0454i −0.0226805 + 0.0226805i
\(973\) 167.328 + 167.328i 0.171971 + 0.171971i
\(974\) 455.264i 0.467417i
\(975\) 0 0
\(976\) −32.3601 −0.0331559
\(977\) −1000.73 + 1000.73i −1.02429 + 1.02429i −0.0245886 + 0.999698i \(0.507828\pi\)
−0.999698 + 0.0245886i \(0.992172\pi\)
\(978\) 111.178 + 111.178i 0.113679 + 0.113679i
\(979\) 1670.41i 1.70624i
\(980\) 0 0
\(981\) −302.802 −0.308667
\(982\) −23.2563 + 23.2563i −0.0236826 + 0.0236826i
\(983\) −915.596 915.596i −0.931431 0.931431i 0.0663648 0.997795i \(-0.478860\pi\)
−0.997795 + 0.0663648i \(0.978860\pi\)
\(984\) 91.1645i 0.0926468i
\(985\) 0 0
\(986\) 2155.51 2.18612
\(987\) 229.729 229.729i 0.232755 0.232755i
\(988\) −371.658 371.658i −0.376172 0.376172i
\(989\) 1577.50i 1.59505i
\(990\) 0 0
\(991\) −437.633 −0.441608 −0.220804 0.975318i \(-0.570868\pi\)
−0.220804 + 0.975318i \(0.570868\pi\)
\(992\) 187.941 187.941i 0.189457 0.189457i
\(993\) 274.319 + 274.319i 0.276253 + 0.276253i
\(994\) 238.566i 0.240006i
\(995\) 0 0
\(996\) −262.704 −0.263759
\(997\) −180.748 + 180.748i −0.181292 + 0.181292i −0.791919 0.610627i \(-0.790918\pi\)
0.610627 + 0.791919i \(0.290918\pi\)
\(998\) −319.077 319.077i −0.319717 0.319717i
\(999\) 62.4634i 0.0625260i
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 1050.3.l.h.43.5 16
5.2 odd 4 inner 1050.3.l.h.757.5 16
5.3 odd 4 210.3.l.b.127.4 yes 16
5.4 even 2 210.3.l.b.43.4 16
15.8 even 4 630.3.o.f.127.1 16
15.14 odd 2 630.3.o.f.253.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.l.b.43.4 16 5.4 even 2
210.3.l.b.127.4 yes 16 5.3 odd 4
630.3.o.f.127.1 16 15.8 even 4
630.3.o.f.253.1 16 15.14 odd 2
1050.3.l.h.43.5 16 1.1 even 1 trivial
1050.3.l.h.757.5 16 5.2 odd 4 inner