Properties

Label 925.2.f.f.43.8
Level $925$
Weight $2$
Character 925.43
Analytic conductor $7.386$
Analytic rank $0$
Dimension $48$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [925,2,Mod(43,925)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(925, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("925.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 925.f (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: \(7.38616218697\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.8
Character \(\chi\) \(=\) 925.43
Dual form 925.2.f.f.882.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.892090i q^{2} +(0.959592 - 0.959592i) q^{3} +1.20418 q^{4} +(-0.856042 - 0.856042i) q^{6} +(2.14902 - 2.14902i) q^{7} -2.85841i q^{8} +1.15837i q^{9} +2.59867i q^{11} +(1.15552 - 1.15552i) q^{12} -1.09555i q^{13} +(-1.91712 - 1.91712i) q^{14} -0.141611 q^{16} -1.12847 q^{17} +1.03337 q^{18} +(4.94052 - 4.94052i) q^{19} -4.12437i q^{21} +2.31825 q^{22} +2.95255i q^{23} +(-2.74291 - 2.74291i) q^{24} -0.977325 q^{26} +(3.99034 + 3.99034i) q^{27} +(2.58780 - 2.58780i) q^{28} +(-5.98850 - 5.98850i) q^{29} +(-5.48087 + 5.48087i) q^{31} -5.59050i q^{32} +(2.49366 + 2.49366i) q^{33} +1.00670i q^{34} +1.39488i q^{36} +(0.815717 - 6.02782i) q^{37} +(-4.40739 - 4.40739i) q^{38} +(-1.05128 - 1.05128i) q^{39} +8.76245i q^{41} -3.67931 q^{42} +8.11756i q^{43} +3.12925i q^{44} +2.63394 q^{46} +(3.21193 - 3.21193i) q^{47} +(-0.135889 + 0.135889i) q^{48} -2.23660i q^{49} +(-1.08287 + 1.08287i) q^{51} -1.31923i q^{52} +(-0.974225 - 0.974225i) q^{53} +(3.55974 - 3.55974i) q^{54} +(-6.14280 - 6.14280i) q^{56} -9.48176i q^{57} +(-5.34228 + 5.34228i) q^{58} +(1.29273 - 1.29273i) q^{59} +(1.92641 - 1.92641i) q^{61} +(4.88943 + 4.88943i) q^{62} +(2.48936 + 2.48936i) q^{63} -5.27045 q^{64} +(2.22457 - 2.22457i) q^{66} +(0.150889 + 0.150889i) q^{67} -1.35887 q^{68} +(2.83324 + 2.83324i) q^{69} -14.3040 q^{71} +3.31109 q^{72} +(3.28425 - 3.28425i) q^{73} +(-5.37736 - 0.727693i) q^{74} +(5.94925 - 5.94925i) q^{76} +(5.58460 + 5.58460i) q^{77} +(-0.937833 + 0.937833i) q^{78} +(1.03590 - 1.03590i) q^{79} +4.18309 q^{81} +7.81689 q^{82} +(-1.76539 - 1.76539i) q^{83} -4.96647i q^{84} +7.24159 q^{86} -11.4930 q^{87} +7.42807 q^{88} +(7.17852 + 7.17852i) q^{89} +(-2.35435 - 2.35435i) q^{91} +3.55539i q^{92} +10.5188i q^{93} +(-2.86533 - 2.86533i) q^{94} +(-5.36460 - 5.36460i) q^{96} -16.2227 q^{97} -1.99525 q^{98} -3.01021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 40 q^{4} + 8 q^{14} + 64 q^{16} + 12 q^{19} - 52 q^{24} - 16 q^{26} + 20 q^{31} + 32 q^{39} - 24 q^{46} - 36 q^{51} - 116 q^{54} - 28 q^{56} + 28 q^{59} - 20 q^{61} - 24 q^{64} - 76 q^{66} + 68 q^{69}+ \cdots - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/925\mathbb{Z}\right)^\times\).

\(n\) \(76\) \(852\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.892090i 0.630803i −0.948958 0.315401i \(-0.897861\pi\)
0.948958 0.315401i \(-0.102139\pi\)
\(3\) 0.959592 0.959592i 0.554021 0.554021i −0.373578 0.927599i \(-0.621869\pi\)
0.927599 + 0.373578i \(0.121869\pi\)
\(4\) 1.20418 0.602088
\(5\) 0 0
\(6\) −0.856042 0.856042i −0.349478 0.349478i
\(7\) 2.14902 2.14902i 0.812254 0.812254i −0.172717 0.984971i \(-0.555255\pi\)
0.984971 + 0.172717i \(0.0552546\pi\)
\(8\) 2.85841i 1.01060i
\(9\) 1.15837i 0.386122i
\(10\) 0 0
\(11\) 2.59867i 0.783528i 0.920066 + 0.391764i \(0.128135\pi\)
−0.920066 + 0.391764i \(0.871865\pi\)
\(12\) 1.15552 1.15552i 0.333569 0.333569i
\(13\) 1.09555i 0.303850i −0.988392 0.151925i \(-0.951453\pi\)
0.988392 0.151925i \(-0.0485472\pi\)
\(14\) −1.91712 1.91712i −0.512372 0.512372i
\(15\) 0 0
\(16\) −0.141611 −0.0354027
\(17\) −1.12847 −0.273694 −0.136847 0.990592i \(-0.543697\pi\)
−0.136847 + 0.990592i \(0.543697\pi\)
\(18\) 1.03337 0.243567
\(19\) 4.94052 4.94052i 1.13343 1.13343i 0.143830 0.989602i \(-0.454058\pi\)
0.989602 0.143830i \(-0.0459420\pi\)
\(20\) 0 0
\(21\) 4.12437i 0.900012i
\(22\) 2.31825 0.494252
\(23\) 2.95255i 0.615649i 0.951443 + 0.307825i \(0.0996010\pi\)
−0.951443 + 0.307825i \(0.900399\pi\)
\(24\) −2.74291 2.74291i −0.559894 0.559894i
\(25\) 0 0
\(26\) −0.977325 −0.191669
\(27\) 3.99034 + 3.99034i 0.767940 + 0.767940i
\(28\) 2.58780 2.58780i 0.489048 0.489048i
\(29\) −5.98850 5.98850i −1.11204 1.11204i −0.992875 0.119161i \(-0.961980\pi\)
−0.119161 0.992875i \(-0.538020\pi\)
\(30\) 0 0
\(31\) −5.48087 + 5.48087i −0.984393 + 0.984393i −0.999880 0.0154869i \(-0.995070\pi\)
0.0154869 + 0.999880i \(0.495070\pi\)
\(32\) 5.59050i 0.988269i
\(33\) 2.49366 + 2.49366i 0.434091 + 0.434091i
\(34\) 1.00670i 0.172647i
\(35\) 0 0
\(36\) 1.39488i 0.232479i
\(37\) 0.815717 6.02782i 0.134103 0.990967i
\(38\) −4.40739 4.40739i −0.714973 0.714973i
\(39\) −1.05128 1.05128i −0.168339 0.168339i
\(40\) 0 0
\(41\) 8.76245i 1.36846i 0.729264 + 0.684232i \(0.239862\pi\)
−0.729264 + 0.684232i \(0.760138\pi\)
\(42\) −3.67931 −0.567730
\(43\) 8.11756i 1.23792i 0.785424 + 0.618958i \(0.212445\pi\)
−0.785424 + 0.618958i \(0.787555\pi\)
\(44\) 3.12925i 0.471753i
\(45\) 0 0
\(46\) 2.63394 0.388353
\(47\) 3.21193 3.21193i 0.468509 0.468509i −0.432923 0.901431i \(-0.642518\pi\)
0.901431 + 0.432923i \(0.142518\pi\)
\(48\) −0.135889 + 0.135889i −0.0196138 + 0.0196138i
\(49\) 2.23660i 0.319515i
\(50\) 0 0
\(51\) −1.08287 + 1.08287i −0.151632 + 0.151632i
\(52\) 1.31923i 0.182944i
\(53\) −0.974225 0.974225i −0.133820 0.133820i 0.637024 0.770844i \(-0.280165\pi\)
−0.770844 + 0.637024i \(0.780165\pi\)
\(54\) 3.55974 3.55974i 0.484419 0.484419i
\(55\) 0 0
\(56\) −6.14280 6.14280i −0.820866 0.820866i
\(57\) 9.48176i 1.25589i
\(58\) −5.34228 + 5.34228i −0.701475 + 0.701475i
\(59\) 1.29273 1.29273i 0.168300 0.168300i −0.617932 0.786232i \(-0.712029\pi\)
0.786232 + 0.617932i \(0.212029\pi\)
\(60\) 0 0
\(61\) 1.92641 1.92641i 0.246651 0.246651i −0.572944 0.819595i \(-0.694199\pi\)
0.819595 + 0.572944i \(0.194199\pi\)
\(62\) 4.88943 + 4.88943i 0.620958 + 0.620958i
\(63\) 2.48936 + 2.48936i 0.313629 + 0.313629i
\(64\) −5.27045 −0.658806
\(65\) 0 0
\(66\) 2.22457 2.22457i 0.273826 0.273826i
\(67\) 0.150889 + 0.150889i 0.0184341 + 0.0184341i 0.716264 0.697830i \(-0.245851\pi\)
−0.697830 + 0.716264i \(0.745851\pi\)
\(68\) −1.35887 −0.164788
\(69\) 2.83324 + 2.83324i 0.341083 + 0.341083i
\(70\) 0 0
\(71\) −14.3040 −1.69757 −0.848784 0.528740i \(-0.822665\pi\)
−0.848784 + 0.528740i \(0.822665\pi\)
\(72\) 3.31109 0.390216
\(73\) 3.28425 3.28425i 0.384393 0.384393i −0.488289 0.872682i \(-0.662379\pi\)
0.872682 + 0.488289i \(0.162379\pi\)
\(74\) −5.37736 0.727693i −0.625105 0.0845926i
\(75\) 0 0
\(76\) 5.94925 5.94925i 0.682426 0.682426i
\(77\) 5.58460 + 5.58460i 0.636424 + 0.636424i
\(78\) −0.937833 + 0.937833i −0.106189 + 0.106189i
\(79\) 1.03590 1.03590i 0.116548 0.116548i −0.646427 0.762975i \(-0.723738\pi\)
0.762975 + 0.646427i \(0.223738\pi\)
\(80\) 0 0
\(81\) 4.18309 0.464788
\(82\) 7.81689 0.863231
\(83\) −1.76539 1.76539i −0.193776 0.193776i 0.603549 0.797326i \(-0.293753\pi\)
−0.797326 + 0.603549i \(0.793753\pi\)
\(84\) 4.96647i 0.541886i
\(85\) 0 0
\(86\) 7.24159 0.780881
\(87\) −11.4930 −1.23218
\(88\) 7.42807 0.791835
\(89\) 7.17852 + 7.17852i 0.760921 + 0.760921i 0.976489 0.215567i \(-0.0691601\pi\)
−0.215567 + 0.976489i \(0.569160\pi\)
\(90\) 0 0
\(91\) −2.35435 2.35435i −0.246803 0.246803i
\(92\) 3.55539i 0.370675i
\(93\) 10.5188i 1.09075i
\(94\) −2.86533 2.86533i −0.295537 0.295537i
\(95\) 0 0
\(96\) −5.36460 5.36460i −0.547522 0.547522i
\(97\) −16.2227 −1.64716 −0.823582 0.567197i \(-0.808028\pi\)
−0.823582 + 0.567197i \(0.808028\pi\)
\(98\) −1.99525 −0.201551
\(99\) −3.01021 −0.302538
\(100\) 0 0
\(101\) 13.5881i 1.35207i 0.736871 + 0.676033i \(0.236302\pi\)
−0.736871 + 0.676033i \(0.763698\pi\)
\(102\) 0.966017 + 0.966017i 0.0956500 + 0.0956500i
\(103\) −13.2201 −1.30261 −0.651307 0.758815i \(-0.725779\pi\)
−0.651307 + 0.758815i \(0.725779\pi\)
\(104\) −3.13152 −0.307071
\(105\) 0 0
\(106\) −0.869097 + 0.869097i −0.0844141 + 0.0844141i
\(107\) −4.98363 + 4.98363i −0.481786 + 0.481786i −0.905702 0.423916i \(-0.860655\pi\)
0.423916 + 0.905702i \(0.360655\pi\)
\(108\) 4.80506 + 4.80506i 0.462367 + 0.462367i
\(109\) 7.85185 7.85185i 0.752071 0.752071i −0.222795 0.974865i \(-0.571518\pi\)
0.974865 + 0.222795i \(0.0715179\pi\)
\(110\) 0 0
\(111\) −5.00149 6.56700i −0.474721 0.623312i
\(112\) −0.304325 + 0.304325i −0.0287560 + 0.0287560i
\(113\) 0.445171 0.0418782 0.0209391 0.999781i \(-0.493334\pi\)
0.0209391 + 0.999781i \(0.493334\pi\)
\(114\) −8.45859 −0.792219
\(115\) 0 0
\(116\) −7.21120 7.21120i −0.669543 0.669543i
\(117\) 1.26904 0.117323
\(118\) −1.15324 1.15324i −0.106164 0.106164i
\(119\) −2.42511 + 2.42511i −0.222309 + 0.222309i
\(120\) 0 0
\(121\) 4.24692 0.386083
\(122\) −1.71853 1.71853i −0.155588 0.155588i
\(123\) 8.40837 + 8.40837i 0.758157 + 0.758157i
\(124\) −6.59993 + 6.59993i −0.592691 + 0.592691i
\(125\) 0 0
\(126\) 2.22073 2.22073i 0.197838 0.197838i
\(127\) −0.190451 + 0.190451i −0.0168998 + 0.0168998i −0.715506 0.698606i \(-0.753804\pi\)
0.698606 + 0.715506i \(0.253804\pi\)
\(128\) 6.47928i 0.572693i
\(129\) 7.78955 + 7.78955i 0.685831 + 0.685831i
\(130\) 0 0
\(131\) −0.166208 + 0.166208i −0.0145217 + 0.0145217i −0.714330 0.699809i \(-0.753269\pi\)
0.699809 + 0.714330i \(0.253269\pi\)
\(132\) 3.00281 + 3.00281i 0.261361 + 0.261361i
\(133\) 21.2346i 1.84127i
\(134\) 0.134607 0.134607i 0.0116283 0.0116283i
\(135\) 0 0
\(136\) 3.22563i 0.276596i
\(137\) −7.79134 + 7.79134i −0.665659 + 0.665659i −0.956708 0.291049i \(-0.905996\pi\)
0.291049 + 0.956708i \(0.405996\pi\)
\(138\) 2.52751 2.52751i 0.215156 0.215156i
\(139\) −0.387836 −0.0328958 −0.0164479 0.999865i \(-0.505236\pi\)
−0.0164479 + 0.999865i \(0.505236\pi\)
\(140\) 0 0
\(141\) 6.16429i 0.519127i
\(142\) 12.7604i 1.07083i
\(143\) 2.84696 0.238075
\(144\) 0.164037i 0.0136698i
\(145\) 0 0
\(146\) −2.92985 2.92985i −0.242476 0.242476i
\(147\) −2.14623 2.14623i −0.177018 0.177018i
\(148\) 0.982266 7.25855i 0.0807418 0.596649i
\(149\) 3.52323i 0.288634i 0.989531 + 0.144317i \(0.0460986\pi\)
−0.989531 + 0.144317i \(0.953901\pi\)
\(150\) 0 0
\(151\) 3.58653i 0.291867i 0.989294 + 0.145934i \(0.0466186\pi\)
−0.989294 + 0.145934i \(0.953381\pi\)
\(152\) −14.1220 14.1220i −1.14545 1.14545i
\(153\) 1.30718i 0.105679i
\(154\) 4.98197 4.98197i 0.401458 0.401458i
\(155\) 0 0
\(156\) −1.26592 1.26592i −0.101355 0.101355i
\(157\) −5.74290 + 5.74290i −0.458334 + 0.458334i −0.898108 0.439775i \(-0.855058\pi\)
0.439775 + 0.898108i \(0.355058\pi\)
\(158\) −0.924117 0.924117i −0.0735188 0.0735188i
\(159\) −1.86972 −0.148278
\(160\) 0 0
\(161\) 6.34510 + 6.34510i 0.500064 + 0.500064i
\(162\) 3.73169i 0.293189i
\(163\) 23.5513 1.84468 0.922342 0.386375i \(-0.126273\pi\)
0.922342 + 0.386375i \(0.126273\pi\)
\(164\) 10.5515i 0.823935i
\(165\) 0 0
\(166\) −1.57488 + 1.57488i −0.122235 + 0.122235i
\(167\) 1.42360 0.110161 0.0550806 0.998482i \(-0.482458\pi\)
0.0550806 + 0.998482i \(0.482458\pi\)
\(168\) −11.7892 −0.909553
\(169\) 11.7998 0.907675
\(170\) 0 0
\(171\) 5.72293 + 5.72293i 0.437643 + 0.437643i
\(172\) 9.77497i 0.745334i
\(173\) −11.1240 + 11.1240i −0.845745 + 0.845745i −0.989599 0.143854i \(-0.954050\pi\)
0.143854 + 0.989599i \(0.454050\pi\)
\(174\) 10.2528i 0.777264i
\(175\) 0 0
\(176\) 0.368000i 0.0277390i
\(177\) 2.48100i 0.186483i
\(178\) 6.40388 6.40388i 0.479991 0.479991i
\(179\) 13.3089 + 13.3089i 0.994756 + 0.994756i 0.999986 0.00523000i \(-0.00166477\pi\)
−0.00523000 + 0.999986i \(0.501665\pi\)
\(180\) 0 0
\(181\) 8.71060 0.647453 0.323727 0.946151i \(-0.395064\pi\)
0.323727 + 0.946151i \(0.395064\pi\)
\(182\) −2.10029 + 2.10029i −0.155684 + 0.155684i
\(183\) 3.69713i 0.273300i
\(184\) 8.43961 0.622176
\(185\) 0 0
\(186\) 9.38371 0.688047
\(187\) 2.93252i 0.214447i
\(188\) 3.86773 3.86773i 0.282083 0.282083i
\(189\) 17.1506 1.24753
\(190\) 0 0
\(191\) 4.14532 + 4.14532i 0.299945 + 0.299945i 0.840992 0.541047i \(-0.181972\pi\)
−0.541047 + 0.840992i \(0.681972\pi\)
\(192\) −5.05748 + 5.05748i −0.364992 + 0.364992i
\(193\) 1.89550i 0.136441i −0.997670 0.0682204i \(-0.978268\pi\)
0.997670 0.0682204i \(-0.0217321\pi\)
\(194\) 14.4721i 1.03904i
\(195\) 0 0
\(196\) 2.69326i 0.192376i
\(197\) 17.7999 17.7999i 1.26819 1.26819i 0.321170 0.947022i \(-0.395924\pi\)
0.947022 0.321170i \(-0.104076\pi\)
\(198\) 2.68538i 0.190842i
\(199\) −15.6296 15.6296i −1.10796 1.10796i −0.993419 0.114536i \(-0.963462\pi\)
−0.114536 0.993419i \(-0.536538\pi\)
\(200\) 0 0
\(201\) 0.289584 0.0204257
\(202\) 12.1218 0.852888
\(203\) −25.7388 −1.80651
\(204\) −1.30397 + 1.30397i −0.0912958 + 0.0912958i
\(205\) 0 0
\(206\) 11.7935i 0.821692i
\(207\) −3.42014 −0.237716
\(208\) 0.155141i 0.0107571i
\(209\) 12.8388 + 12.8388i 0.888077 + 0.888077i
\(210\) 0 0
\(211\) 27.6028 1.90026 0.950128 0.311860i \(-0.100952\pi\)
0.950128 + 0.311860i \(0.100952\pi\)
\(212\) −1.17314 1.17314i −0.0805715 0.0805715i
\(213\) −13.7260 + 13.7260i −0.940488 + 0.940488i
\(214\) 4.44585 + 4.44585i 0.303912 + 0.303912i
\(215\) 0 0
\(216\) 11.4060 11.4060i 0.776082 0.776082i
\(217\) 23.5570i 1.59916i
\(218\) −7.00456 7.00456i −0.474409 0.474409i
\(219\) 6.30309i 0.425923i
\(220\) 0 0
\(221\) 1.23629i 0.0831618i
\(222\) −5.85836 + 4.46178i −0.393187 + 0.299455i
\(223\) 2.24971 + 2.24971i 0.150652 + 0.150652i 0.778409 0.627757i \(-0.216027\pi\)
−0.627757 + 0.778409i \(0.716027\pi\)
\(224\) −12.0141 12.0141i −0.802726 0.802726i
\(225\) 0 0
\(226\) 0.397133i 0.0264169i
\(227\) 20.5079 1.36116 0.680579 0.732675i \(-0.261728\pi\)
0.680579 + 0.732675i \(0.261728\pi\)
\(228\) 11.4177i 0.756156i
\(229\) 25.4327i 1.68064i 0.542090 + 0.840321i \(0.317633\pi\)
−0.542090 + 0.840321i \(0.682367\pi\)
\(230\) 0 0
\(231\) 10.7179 0.705185
\(232\) −17.1176 + 17.1176i −1.12383 + 1.12383i
\(233\) 14.3258 14.3258i 0.938516 0.938516i −0.0596999 0.998216i \(-0.519014\pi\)
0.998216 + 0.0596999i \(0.0190144\pi\)
\(234\) 1.13210i 0.0740077i
\(235\) 0 0
\(236\) 1.55668 1.55668i 0.101331 0.101331i
\(237\) 1.98808i 0.129140i
\(238\) 2.16341 + 2.16341i 0.140233 + 0.140233i
\(239\) −15.3785 + 15.3785i −0.994755 + 0.994755i −0.999986 0.00523162i \(-0.998335\pi\)
0.00523162 + 0.999986i \(0.498335\pi\)
\(240\) 0 0
\(241\) 8.65711 + 8.65711i 0.557653 + 0.557653i 0.928639 0.370985i \(-0.120980\pi\)
−0.370985 + 0.928639i \(0.620980\pi\)
\(242\) 3.78863i 0.243542i
\(243\) −7.95695 + 7.95695i −0.510438 + 0.510438i
\(244\) 2.31973 2.31973i 0.148506 0.148506i
\(245\) 0 0
\(246\) 7.50103 7.50103i 0.478248 0.478248i
\(247\) −5.41256 5.41256i −0.344393 0.344393i
\(248\) 15.6666 + 15.6666i 0.994829 + 0.994829i
\(249\) −3.38810 −0.214712
\(250\) 0 0
\(251\) −5.04737 + 5.04737i −0.318587 + 0.318587i −0.848224 0.529637i \(-0.822328\pi\)
0.529637 + 0.848224i \(0.322328\pi\)
\(252\) 2.99762 + 2.99762i 0.188832 + 0.188832i
\(253\) −7.67271 −0.482379
\(254\) 0.169899 + 0.169899i 0.0106604 + 0.0106604i
\(255\) 0 0
\(256\) −16.3210 −1.02006
\(257\) −12.0006 −0.748579 −0.374290 0.927312i \(-0.622113\pi\)
−0.374290 + 0.927312i \(0.622113\pi\)
\(258\) 6.94898 6.94898i 0.432624 0.432624i
\(259\) −11.2009 14.7069i −0.695992 0.913843i
\(260\) 0 0
\(261\) 6.93687 6.93687i 0.429382 0.429382i
\(262\) 0.148272 + 0.148272i 0.00916030 + 0.00916030i
\(263\) −8.73538 + 8.73538i −0.538646 + 0.538646i −0.923131 0.384485i \(-0.874379\pi\)
0.384485 + 0.923131i \(0.374379\pi\)
\(264\) 7.12792 7.12792i 0.438693 0.438693i
\(265\) 0 0
\(266\) −18.9432 −1.16148
\(267\) 13.7769 0.843132
\(268\) 0.181697 + 0.181697i 0.0110989 + 0.0110989i
\(269\) 15.4726i 0.943383i 0.881764 + 0.471691i \(0.156356\pi\)
−0.881764 + 0.471691i \(0.843644\pi\)
\(270\) 0 0
\(271\) 6.32651 0.384308 0.192154 0.981365i \(-0.438453\pi\)
0.192154 + 0.981365i \(0.438453\pi\)
\(272\) 0.159803 0.00968951
\(273\) −4.51844 −0.273468
\(274\) 6.95057 + 6.95057i 0.419899 + 0.419899i
\(275\) 0 0
\(276\) 3.41172 + 3.41172i 0.205362 + 0.205362i
\(277\) 18.4438i 1.10818i 0.832457 + 0.554090i \(0.186934\pi\)
−0.832457 + 0.554090i \(0.813066\pi\)
\(278\) 0.345984i 0.0207508i
\(279\) −6.34885 6.34885i −0.380096 0.380096i
\(280\) 0 0
\(281\) −6.99108 6.99108i −0.417053 0.417053i 0.467134 0.884187i \(-0.345287\pi\)
−0.884187 + 0.467134i \(0.845287\pi\)
\(282\) −5.49910 −0.327467
\(283\) −30.5458 −1.81576 −0.907878 0.419234i \(-0.862299\pi\)
−0.907878 + 0.419234i \(0.862299\pi\)
\(284\) −17.2245 −1.02208
\(285\) 0 0
\(286\) 2.53975i 0.150178i
\(287\) 18.8307 + 18.8307i 1.11154 + 1.11154i
\(288\) 6.47584 0.381593
\(289\) −15.7266 −0.925092
\(290\) 0 0
\(291\) −15.5672 + 15.5672i −0.912563 + 0.912563i
\(292\) 3.95482 3.95482i 0.231438 0.231438i
\(293\) −18.9163 18.9163i −1.10510 1.10510i −0.993785 0.111314i \(-0.964494\pi\)
−0.111314 0.993785i \(-0.535506\pi\)
\(294\) −1.91463 + 1.91463i −0.111663 + 0.111663i
\(295\) 0 0
\(296\) −17.2300 2.33166i −1.00147 0.135525i
\(297\) −10.3696 + 10.3696i −0.601703 + 0.601703i
\(298\) 3.14304 0.182071
\(299\) 3.23465 0.187065
\(300\) 0 0
\(301\) 17.4448 + 17.4448i 1.00550 + 1.00550i
\(302\) 3.19950 0.184111
\(303\) 13.0390 + 13.0390i 0.749073 + 0.749073i
\(304\) −0.699631 + 0.699631i −0.0401266 + 0.0401266i
\(305\) 0 0
\(306\) −1.16612 −0.0666628
\(307\) −3.76916 3.76916i −0.215117 0.215117i 0.591320 0.806437i \(-0.298607\pi\)
−0.806437 + 0.591320i \(0.798607\pi\)
\(308\) 6.72484 + 6.72484i 0.383183 + 0.383183i
\(309\) −12.6859 + 12.6859i −0.721675 + 0.721675i
\(310\) 0 0
\(311\) −0.698586 + 0.698586i −0.0396132 + 0.0396132i −0.726636 0.687023i \(-0.758917\pi\)
0.687023 + 0.726636i \(0.258917\pi\)
\(312\) −3.00498 + 3.00498i −0.170124 + 0.170124i
\(313\) 11.4225i 0.645637i 0.946461 + 0.322818i \(0.104630\pi\)
−0.946461 + 0.322818i \(0.895370\pi\)
\(314\) 5.12319 + 5.12319i 0.289118 + 0.289118i
\(315\) 0 0
\(316\) 1.24741 1.24741i 0.0701721 0.0701721i
\(317\) 3.41961 + 3.41961i 0.192064 + 0.192064i 0.796588 0.604523i \(-0.206636\pi\)
−0.604523 + 0.796588i \(0.706636\pi\)
\(318\) 1.66796i 0.0935344i
\(319\) 15.5621 15.5621i 0.871312 0.871312i
\(320\) 0 0
\(321\) 9.56451i 0.533839i
\(322\) 5.66040 5.66040i 0.315442 0.315442i
\(323\) −5.57522 + 5.57522i −0.310214 + 0.310214i
\(324\) 5.03717 0.279843
\(325\) 0 0
\(326\) 21.0099i 1.16363i
\(327\) 15.0691i 0.833326i
\(328\) 25.0467 1.38297
\(329\) 13.8050i 0.761096i
\(330\) 0 0
\(331\) −10.5201 10.5201i −0.578235 0.578235i 0.356181 0.934417i \(-0.384079\pi\)
−0.934417 + 0.356181i \(0.884079\pi\)
\(332\) −2.12584 2.12584i −0.116670 0.116670i
\(333\) 6.98242 + 0.944899i 0.382634 + 0.0517801i
\(334\) 1.26998i 0.0694900i
\(335\) 0 0
\(336\) 0.584056i 0.0318629i
\(337\) −11.3114 11.3114i −0.616172 0.616172i 0.328375 0.944547i \(-0.393499\pi\)
−0.944547 + 0.328375i \(0.893499\pi\)
\(338\) 10.5265i 0.572564i
\(339\) 0.427183 0.427183i 0.0232014 0.0232014i
\(340\) 0 0
\(341\) −14.2430 14.2430i −0.771300 0.771300i
\(342\) 5.10537 5.10537i 0.276067 0.276067i
\(343\) 10.2367 + 10.2367i 0.552727 + 0.552727i
\(344\) 23.2033 1.25104
\(345\) 0 0
\(346\) 9.92364 + 9.92364i 0.533498 + 0.533498i
\(347\) 21.4215i 1.14997i −0.818164 0.574984i \(-0.805008\pi\)
0.818164 0.574984i \(-0.194992\pi\)
\(348\) −13.8396 −0.741881
\(349\) 11.7476i 0.628836i −0.949285 0.314418i \(-0.898191\pi\)
0.949285 0.314418i \(-0.101809\pi\)
\(350\) 0 0
\(351\) 4.37159 4.37159i 0.233338 0.233338i
\(352\) 14.5279 0.774337
\(353\) 22.8991 1.21879 0.609397 0.792865i \(-0.291412\pi\)
0.609397 + 0.792865i \(0.291412\pi\)
\(354\) −2.21327 −0.117634
\(355\) 0 0
\(356\) 8.64420 + 8.64420i 0.458141 + 0.458141i
\(357\) 4.65423i 0.246328i
\(358\) 11.8728 11.8728i 0.627495 0.627495i
\(359\) 24.3443i 1.28485i 0.766350 + 0.642423i \(0.222071\pi\)
−0.766350 + 0.642423i \(0.777929\pi\)
\(360\) 0 0
\(361\) 29.8175i 1.56934i
\(362\) 7.77064i 0.408416i
\(363\) 4.07531 4.07531i 0.213898 0.213898i
\(364\) −2.83505 2.83505i −0.148597 0.148597i
\(365\) 0 0
\(366\) −3.29817 −0.172398
\(367\) 21.2016 21.2016i 1.10671 1.10671i 0.113135 0.993580i \(-0.463911\pi\)
0.993580 0.113135i \(-0.0360892\pi\)
\(368\) 0.418113i 0.0217957i
\(369\) −10.1501 −0.528394
\(370\) 0 0
\(371\) −4.18727 −0.217392
\(372\) 12.6665i 0.656726i
\(373\) −2.91002 + 2.91002i −0.150675 + 0.150675i −0.778419 0.627745i \(-0.783978\pi\)
0.627745 + 0.778419i \(0.283978\pi\)
\(374\) −2.61607 −0.135274
\(375\) 0 0
\(376\) −9.18103 9.18103i −0.473476 0.473476i
\(377\) −6.56067 + 6.56067i −0.337892 + 0.337892i
\(378\) 15.2999i 0.786943i
\(379\) 24.9909i 1.28370i −0.766832 0.641848i \(-0.778168\pi\)
0.766832 0.641848i \(-0.221832\pi\)
\(380\) 0 0
\(381\) 0.365510i 0.0187257i
\(382\) 3.69800 3.69800i 0.189206 0.189206i
\(383\) 22.2292i 1.13586i −0.823076 0.567931i \(-0.807744\pi\)
0.823076 0.567931i \(-0.192256\pi\)
\(384\) −6.21746 6.21746i −0.317284 0.317284i
\(385\) 0 0
\(386\) −1.69095 −0.0860672
\(387\) −9.40311 −0.477987
\(388\) −19.5350 −0.991737
\(389\) 2.65112 2.65112i 0.134417 0.134417i −0.636697 0.771114i \(-0.719700\pi\)
0.771114 + 0.636697i \(0.219700\pi\)
\(390\) 0 0
\(391\) 3.33186i 0.168500i
\(392\) −6.39313 −0.322902
\(393\) 0.318984i 0.0160906i
\(394\) −15.8791 15.8791i −0.799979 0.799979i
\(395\) 0 0
\(396\) −3.62482 −0.182154
\(397\) −21.0355 21.0355i −1.05574 1.05574i −0.998352 0.0573876i \(-0.981723\pi\)
−0.0573876 0.998352i \(-0.518277\pi\)
\(398\) −13.9430 + 13.9430i −0.698902 + 0.698902i
\(399\) −20.3765 20.3765i −1.02010 1.02010i
\(400\) 0 0
\(401\) −3.82616 + 3.82616i −0.191070 + 0.191070i −0.796158 0.605089i \(-0.793138\pi\)
0.605089 + 0.796158i \(0.293138\pi\)
\(402\) 0.258335i 0.0128846i
\(403\) 6.00454 + 6.00454i 0.299107 + 0.299107i
\(404\) 16.3625i 0.814063i
\(405\) 0 0
\(406\) 22.9614i 1.13955i
\(407\) 15.6643 + 2.11978i 0.776451 + 0.105074i
\(408\) 3.09529 + 3.09529i 0.153240 + 0.153240i
\(409\) 4.11099 + 4.11099i 0.203275 + 0.203275i 0.801402 0.598126i \(-0.204088\pi\)
−0.598126 + 0.801402i \(0.704088\pi\)
\(410\) 0 0
\(411\) 14.9530i 0.737577i
\(412\) −15.9193 −0.784287
\(413\) 5.55623i 0.273404i
\(414\) 3.05107i 0.149952i
\(415\) 0 0
\(416\) −6.12464 −0.300285
\(417\) −0.372164 + 0.372164i −0.0182249 + 0.0182249i
\(418\) 11.4533 11.4533i 0.560201 0.560201i
\(419\) 1.73190i 0.0846091i −0.999105 0.0423045i \(-0.986530\pi\)
0.999105 0.0423045i \(-0.0134700\pi\)
\(420\) 0 0
\(421\) −5.03215 + 5.03215i −0.245252 + 0.245252i −0.819019 0.573767i \(-0.805482\pi\)
0.573767 + 0.819019i \(0.305482\pi\)
\(422\) 24.6242i 1.19869i
\(423\) 3.72060 + 3.72060i 0.180902 + 0.180902i
\(424\) −2.78474 + 2.78474i −0.135239 + 0.135239i
\(425\) 0 0
\(426\) 12.2448 + 12.2448i 0.593262 + 0.593262i
\(427\) 8.27978i 0.400687i
\(428\) −6.00117 + 6.00117i −0.290077 + 0.290077i
\(429\) 2.73192 2.73192i 0.131898 0.131898i
\(430\) 0 0
\(431\) 10.2156 10.2156i 0.492070 0.492070i −0.416888 0.908958i \(-0.636879\pi\)
0.908958 + 0.416888i \(0.136879\pi\)
\(432\) −0.565075 0.565075i −0.0271872 0.0271872i
\(433\) 1.65985 + 1.65985i 0.0797675 + 0.0797675i 0.745865 0.666097i \(-0.232036\pi\)
−0.666097 + 0.745865i \(0.732036\pi\)
\(434\) 21.0150 1.00875
\(435\) 0 0
\(436\) 9.45501 9.45501i 0.452813 0.452813i
\(437\) 14.5871 + 14.5871i 0.697797 + 0.697797i
\(438\) −5.62292 −0.268674
\(439\) 5.34625 + 5.34625i 0.255163 + 0.255163i 0.823083 0.567921i \(-0.192252\pi\)
−0.567921 + 0.823083i \(0.692252\pi\)
\(440\) 0 0
\(441\) 2.59080 0.123372
\(442\) 1.10288 0.0524587
\(443\) −21.4151 + 21.4151i −1.01746 + 1.01746i −0.0176178 + 0.999845i \(0.505608\pi\)
−0.999845 + 0.0176178i \(0.994392\pi\)
\(444\) −6.02267 7.90782i −0.285823 0.375289i
\(445\) 0 0
\(446\) 2.00694 2.00694i 0.0950315 0.0950315i
\(447\) 3.38087 + 3.38087i 0.159909 + 0.159909i
\(448\) −11.3263 + 11.3263i −0.535118 + 0.535118i
\(449\) 28.0426 28.0426i 1.32341 1.32341i 0.412416 0.910996i \(-0.364685\pi\)
0.910996 0.412416i \(-0.135315\pi\)
\(450\) 0 0
\(451\) −22.7707 −1.07223
\(452\) 0.536064 0.0252143
\(453\) 3.44160 + 3.44160i 0.161701 + 0.161701i
\(454\) 18.2949i 0.858622i
\(455\) 0 0
\(456\) −27.1028 −1.26920
\(457\) 9.93504 0.464742 0.232371 0.972627i \(-0.425352\pi\)
0.232371 + 0.972627i \(0.425352\pi\)
\(458\) 22.6883 1.06015
\(459\) −4.50297 4.50297i −0.210181 0.210181i
\(460\) 0 0
\(461\) −14.2559 14.2559i −0.663965 0.663965i 0.292347 0.956312i \(-0.405564\pi\)
−0.956312 + 0.292347i \(0.905564\pi\)
\(462\) 9.56131i 0.444832i
\(463\) 9.70800i 0.451169i −0.974224 0.225585i \(-0.927571\pi\)
0.974224 0.225585i \(-0.0724292\pi\)
\(464\) 0.848036 + 0.848036i 0.0393691 + 0.0393691i
\(465\) 0 0
\(466\) −12.7799 12.7799i −0.592019 0.592019i
\(467\) −14.9222 −0.690516 −0.345258 0.938508i \(-0.612209\pi\)
−0.345258 + 0.938508i \(0.612209\pi\)
\(468\) 1.52815 0.0706388
\(469\) 0.648529 0.0299463
\(470\) 0 0
\(471\) 11.0217i 0.507853i
\(472\) −3.69517 3.69517i −0.170084 0.170084i
\(473\) −21.0949 −0.969943
\(474\) −1.77355 −0.0814619
\(475\) 0 0
\(476\) −2.92025 + 2.92025i −0.133850 + 0.133850i
\(477\) 1.12851 1.12851i 0.0516709 0.0516709i
\(478\) 13.7190 + 13.7190i 0.627494 + 0.627494i
\(479\) 22.4295 22.4295i 1.02483 1.02483i 0.0251450 0.999684i \(-0.491995\pi\)
0.999684 0.0251450i \(-0.00800475\pi\)
\(480\) 0 0
\(481\) −6.60375 0.893655i −0.301105 0.0407472i
\(482\) 7.72292 7.72292i 0.351769 0.351769i
\(483\) 12.1774 0.554092
\(484\) 5.11403 0.232456
\(485\) 0 0
\(486\) 7.09831 + 7.09831i 0.321986 + 0.321986i
\(487\) −33.2652 −1.50739 −0.753694 0.657226i \(-0.771730\pi\)
−0.753694 + 0.657226i \(0.771730\pi\)
\(488\) −5.50647 5.50647i −0.249266 0.249266i
\(489\) 22.5997 22.5997i 1.02199 1.02199i
\(490\) 0 0
\(491\) −39.0405 −1.76187 −0.880936 0.473235i \(-0.843086\pi\)
−0.880936 + 0.473235i \(0.843086\pi\)
\(492\) 10.1252 + 10.1252i 0.456477 + 0.456477i
\(493\) 6.75783 + 6.75783i 0.304357 + 0.304357i
\(494\) −4.82849 + 4.82849i −0.217244 + 0.217244i
\(495\) 0 0
\(496\) 0.776151 0.776151i 0.0348502 0.0348502i
\(497\) −30.7395 + 30.7395i −1.37886 + 1.37886i
\(498\) 3.02249i 0.135441i
\(499\) −18.5427 18.5427i −0.830084 0.830084i 0.157444 0.987528i \(-0.449675\pi\)
−0.987528 + 0.157444i \(0.949675\pi\)
\(500\) 0 0
\(501\) 1.36607 1.36607i 0.0610315 0.0610315i
\(502\) 4.50271 + 4.50271i 0.200966 + 0.200966i
\(503\) 19.1958i 0.855898i −0.903803 0.427949i \(-0.859236\pi\)
0.903803 0.427949i \(-0.140764\pi\)
\(504\) 7.11561 7.11561i 0.316954 0.316954i
\(505\) 0 0
\(506\) 6.84474i 0.304286i
\(507\) 11.3230 11.3230i 0.502871 0.502871i
\(508\) −0.229336 + 0.229336i −0.0101752 + 0.0101752i
\(509\) −39.3284 −1.74320 −0.871601 0.490217i \(-0.836918\pi\)
−0.871601 + 0.490217i \(0.836918\pi\)
\(510\) 0 0
\(511\) 14.1159i 0.624449i
\(512\) 1.60124i 0.0707655i
\(513\) 39.4287 1.74082
\(514\) 10.7057i 0.472206i
\(515\) 0 0
\(516\) 9.37998 + 9.37998i 0.412931 + 0.412931i
\(517\) 8.34675 + 8.34675i 0.367090 + 0.367090i
\(518\) −13.1199 + 9.99224i −0.576455 + 0.439034i
\(519\) 21.3491i 0.937120i
\(520\) 0 0
\(521\) 5.80271i 0.254221i 0.991889 + 0.127111i \(0.0405704\pi\)
−0.991889 + 0.127111i \(0.959430\pi\)
\(522\) −6.18831 6.18831i −0.270855 0.270855i
\(523\) 6.44208i 0.281692i 0.990031 + 0.140846i \(0.0449823\pi\)
−0.990031 + 0.140846i \(0.955018\pi\)
\(524\) −0.200144 + 0.200144i −0.00874331 + 0.00874331i
\(525\) 0 0
\(526\) 7.79274 + 7.79274i 0.339780 + 0.339780i
\(527\) 6.18499 6.18499i 0.269422 0.269422i
\(528\) −0.353130 0.353130i −0.0153680 0.0153680i
\(529\) 14.2824 0.620976
\(530\) 0 0
\(531\) 1.49746 + 1.49746i 0.0649842 + 0.0649842i
\(532\) 25.5702i 1.10861i
\(533\) 9.59966 0.415807
\(534\) 12.2902i 0.531850i
\(535\) 0 0
\(536\) 0.431304 0.431304i 0.0186295 0.0186295i
\(537\) 25.5423 1.10223
\(538\) 13.8030 0.595089
\(539\) 5.81219 0.250349
\(540\) 0 0
\(541\) 21.6880 + 21.6880i 0.932438 + 0.932438i 0.997858 0.0654197i \(-0.0208386\pi\)
−0.0654197 + 0.997858i \(0.520839\pi\)
\(542\) 5.64382i 0.242423i
\(543\) 8.35862 8.35862i 0.358703 0.358703i
\(544\) 6.30870i 0.270483i
\(545\) 0 0
\(546\) 4.03085i 0.172505i
\(547\) 8.75873i 0.374496i −0.982313 0.187248i \(-0.940043\pi\)
0.982313 0.187248i \(-0.0599568\pi\)
\(548\) −9.38214 + 9.38214i −0.400785 + 0.400785i
\(549\) 2.23148 + 2.23148i 0.0952374 + 0.0952374i
\(550\) 0 0
\(551\) −59.1726 −2.52084
\(552\) 8.09858 8.09858i 0.344699 0.344699i
\(553\) 4.45235i 0.189333i
\(554\) 16.4535 0.699043
\(555\) 0 0
\(556\) −0.467022 −0.0198061
\(557\) 1.38959i 0.0588788i 0.999567 + 0.0294394i \(0.00937221\pi\)
−0.999567 + 0.0294394i \(0.990628\pi\)
\(558\) −5.66375 + 5.66375i −0.239766 + 0.239766i
\(559\) 8.89316 0.376140
\(560\) 0 0
\(561\) −2.81402 2.81402i −0.118808 0.118808i
\(562\) −6.23667 + 6.23667i −0.263078 + 0.263078i
\(563\) 31.5747i 1.33072i −0.746525 0.665358i \(-0.768279\pi\)
0.746525 0.665358i \(-0.231721\pi\)
\(564\) 7.42289i 0.312560i
\(565\) 0 0
\(566\) 27.2496i 1.14538i
\(567\) 8.98955 8.98955i 0.377526 0.377526i
\(568\) 40.8866i 1.71557i
\(569\) −22.5618 22.5618i −0.945839 0.945839i 0.0527679 0.998607i \(-0.483196\pi\)
−0.998607 + 0.0527679i \(0.983196\pi\)
\(570\) 0 0
\(571\) 44.2620 1.85231 0.926154 0.377146i \(-0.123095\pi\)
0.926154 + 0.377146i \(0.123095\pi\)
\(572\) 3.42824 0.143342
\(573\) 7.95564 0.332352
\(574\) 16.7987 16.7987i 0.701163 0.701163i
\(575\) 0 0
\(576\) 6.10511i 0.254380i
\(577\) −17.3465 −0.722145 −0.361073 0.932538i \(-0.617589\pi\)
−0.361073 + 0.932538i \(0.617589\pi\)
\(578\) 14.0295i 0.583550i
\(579\) −1.81890 1.81890i −0.0755910 0.0755910i
\(580\) 0 0
\(581\) −7.58772 −0.314792
\(582\) 13.8873 + 13.8873i 0.575647 + 0.575647i
\(583\) 2.53169 2.53169i 0.104852 0.104852i
\(584\) −9.38775 9.38775i −0.388468 0.388468i
\(585\) 0 0
\(586\) −16.8750 + 16.8750i −0.697100 + 0.697100i
\(587\) 31.2853i 1.29128i −0.763640 0.645642i \(-0.776590\pi\)
0.763640 0.645642i \(-0.223410\pi\)
\(588\) −2.58443 2.58443i −0.106580 0.106580i
\(589\) 54.1567i 2.23149i
\(590\) 0 0
\(591\) 34.1613i 1.40521i
\(592\) −0.115514 + 0.853605i −0.00474761 + 0.0350829i
\(593\) −27.3952 27.3952i −1.12499 1.12499i −0.990981 0.134005i \(-0.957216\pi\)
−0.134005 0.990981i \(-0.542784\pi\)
\(594\) 9.25058 + 9.25058i 0.379556 + 0.379556i
\(595\) 0 0
\(596\) 4.24259i 0.173783i
\(597\) −29.9961 −1.22766
\(598\) 2.88560i 0.118001i
\(599\) 36.7857i 1.50302i −0.659720 0.751511i \(-0.729325\pi\)
0.659720 0.751511i \(-0.270675\pi\)
\(600\) 0 0
\(601\) −28.3683 −1.15717 −0.578584 0.815623i \(-0.696394\pi\)
−0.578584 + 0.815623i \(0.696394\pi\)
\(602\) 15.5624 15.5624i 0.634274 0.634274i
\(603\) −0.174785 + 0.174785i −0.00711780 + 0.00711780i
\(604\) 4.31881i 0.175730i
\(605\) 0 0
\(606\) 11.6320 11.6320i 0.472517 0.472517i
\(607\) 30.1108i 1.22216i −0.791568 0.611081i \(-0.790735\pi\)
0.791568 0.611081i \(-0.209265\pi\)
\(608\) −27.6200 27.6200i −1.12014 1.12014i
\(609\) −24.6988 + 24.6988i −1.00085 + 1.00085i
\(610\) 0 0
\(611\) −3.51882 3.51882i −0.142356 0.142356i
\(612\) 1.57407i 0.0636282i
\(613\) −27.3339 + 27.3339i −1.10400 + 1.10400i −0.110081 + 0.993923i \(0.535111\pi\)
−0.993923 + 0.110081i \(0.964889\pi\)
\(614\) −3.36243 + 3.36243i −0.135696 + 0.135696i
\(615\) 0 0
\(616\) 15.9631 15.9631i 0.643172 0.643172i
\(617\) 25.5809 + 25.5809i 1.02985 + 1.02985i 0.999541 + 0.0303084i \(0.00964896\pi\)
0.0303084 + 0.999541i \(0.490351\pi\)
\(618\) 11.3170 + 11.3170i 0.455235 + 0.455235i
\(619\) −45.1664 −1.81539 −0.907695 0.419631i \(-0.862160\pi\)
−0.907695 + 0.419631i \(0.862160\pi\)
\(620\) 0 0
\(621\) −11.7817 + 11.7817i −0.472782 + 0.472782i
\(622\) 0.623201 + 0.623201i 0.0249881 + 0.0249881i
\(623\) 30.8536 1.23612
\(624\) 0.148872 + 0.148872i 0.00595966 + 0.00595966i
\(625\) 0 0
\(626\) 10.1899 0.407270
\(627\) 24.6400 0.984026
\(628\) −6.91546 + 6.91546i −0.275957 + 0.275957i
\(629\) −0.920511 + 6.80221i −0.0367032 + 0.271222i
\(630\) 0 0
\(631\) 2.54603 2.54603i 0.101356 0.101356i −0.654611 0.755966i \(-0.727167\pi\)
0.755966 + 0.654611i \(0.227167\pi\)
\(632\) −2.96103 2.96103i −0.117784 0.117784i
\(633\) 26.4874 26.4874i 1.05278 1.05278i
\(634\) 3.05060 3.05060i 0.121155 0.121155i
\(635\) 0 0
\(636\) −2.25147 −0.0892765
\(637\) −2.45030 −0.0970844
\(638\) −13.8828 13.8828i −0.549626 0.549626i
\(639\) 16.5692i 0.655469i
\(640\) 0 0
\(641\) 20.0382 0.791461 0.395730 0.918367i \(-0.370491\pi\)
0.395730 + 0.918367i \(0.370491\pi\)
\(642\) 8.53240 0.336747
\(643\) 3.45693 0.136328 0.0681639 0.997674i \(-0.478286\pi\)
0.0681639 + 0.997674i \(0.478286\pi\)
\(644\) 7.64061 + 7.64061i 0.301082 + 0.301082i
\(645\) 0 0
\(646\) 4.97360 + 4.97360i 0.195684 + 0.195684i
\(647\) 3.01463i 0.118517i −0.998243 0.0592587i \(-0.981126\pi\)
0.998243 0.0592587i \(-0.0188737\pi\)
\(648\) 11.9570i 0.469715i
\(649\) 3.35939 + 3.35939i 0.131868 + 0.131868i
\(650\) 0 0
\(651\) 22.6051 + 22.6051i 0.885965 + 0.885965i
\(652\) 28.3599 1.11066
\(653\) −2.89842 −0.113424 −0.0567120 0.998391i \(-0.518062\pi\)
−0.0567120 + 0.998391i \(0.518062\pi\)
\(654\) −13.4430 −0.525664
\(655\) 0 0
\(656\) 1.24086i 0.0484473i
\(657\) 3.80437 + 3.80437i 0.148423 + 0.148423i
\(658\) −12.3153 −0.480102
\(659\) −6.13236 −0.238883 −0.119441 0.992841i \(-0.538110\pi\)
−0.119441 + 0.992841i \(0.538110\pi\)
\(660\) 0 0
\(661\) 31.8731 31.8731i 1.23972 1.23972i 0.279602 0.960116i \(-0.409797\pi\)
0.960116 0.279602i \(-0.0902026\pi\)
\(662\) −9.38485 + 9.38485i −0.364753 + 0.364753i
\(663\) 1.18633 + 1.18633i 0.0460734 + 0.0460734i
\(664\) −5.04621 + 5.04621i −0.195831 + 0.195831i
\(665\) 0 0
\(666\) 0.842935 6.22895i 0.0326631 0.241367i
\(667\) 17.6813 17.6813i 0.684624 0.684624i
\(668\) 1.71426 0.0663267
\(669\) 4.31760 0.166928
\(670\) 0 0
\(671\) 5.00609 + 5.00609i 0.193258 + 0.193258i
\(672\) −23.0573 −0.889454
\(673\) 14.4161 + 14.4161i 0.555701 + 0.555701i 0.928081 0.372379i \(-0.121458\pi\)
−0.372379 + 0.928081i \(0.621458\pi\)
\(674\) −10.0908 + 10.0908i −0.388683 + 0.388683i
\(675\) 0 0
\(676\) 14.2090 0.546500
\(677\) 0.125657 + 0.125657i 0.00482938 + 0.00482938i 0.709517 0.704688i \(-0.248913\pi\)
−0.704688 + 0.709517i \(0.748913\pi\)
\(678\) −0.381085 0.381085i −0.0146355 0.0146355i
\(679\) −34.8629 + 34.8629i −1.33792 + 1.33792i
\(680\) 0 0
\(681\) 19.6792 19.6792i 0.754110 0.754110i
\(682\) −12.7060 + 12.7060i −0.486538 + 0.486538i
\(683\) 38.9395i 1.48998i 0.667077 + 0.744989i \(0.267545\pi\)
−0.667077 + 0.744989i \(0.732455\pi\)
\(684\) 6.89141 + 6.89141i 0.263500 + 0.263500i
\(685\) 0 0
\(686\) 9.13202 9.13202i 0.348662 0.348662i
\(687\) 24.4050 + 24.4050i 0.931110 + 0.931110i
\(688\) 1.14953i 0.0438256i
\(689\) −1.06731 + 1.06731i −0.0406612 + 0.0406612i
\(690\) 0 0
\(691\) 1.66595i 0.0633759i −0.999498 0.0316879i \(-0.989912\pi\)
0.999498 0.0316879i \(-0.0100883\pi\)
\(692\) −13.3953 + 13.3953i −0.509213 + 0.509213i
\(693\) −6.46901 + 6.46901i −0.245738 + 0.245738i
\(694\) −19.1099 −0.725404
\(695\) 0 0
\(696\) 32.8518i 1.24524i
\(697\) 9.88815i 0.374540i
\(698\) −10.4799 −0.396671
\(699\) 27.4939i 1.03992i
\(700\) 0 0
\(701\) −4.18163 4.18163i −0.157938 0.157938i 0.623714 0.781652i \(-0.285623\pi\)
−0.781652 + 0.623714i \(0.785623\pi\)
\(702\) −3.89985 3.89985i −0.147191 0.147191i
\(703\) −25.7505 33.8106i −0.971198 1.27519i
\(704\) 13.6962i 0.516193i
\(705\) 0 0
\(706\) 20.4280i 0.768819i
\(707\) 29.2011 + 29.2011i 1.09822 + 1.09822i
\(708\) 2.98755i 0.112279i
\(709\) −21.5633 + 21.5633i −0.809828 + 0.809828i −0.984608 0.174780i \(-0.944079\pi\)
0.174780 + 0.984608i \(0.444079\pi\)
\(710\) 0 0
\(711\) 1.19995 + 1.19995i 0.0450017 + 0.0450017i
\(712\) 20.5192 20.5192i 0.768988 0.768988i
\(713\) −16.1825 16.1825i −0.606041 0.606041i
\(714\) 4.15199 0.155384
\(715\) 0 0
\(716\) 16.0263 + 16.0263i 0.598931 + 0.598931i
\(717\) 29.5142i 1.10223i
\(718\) 21.7174 0.810484
\(719\) 40.8427i 1.52318i −0.648061 0.761589i \(-0.724420\pi\)
0.648061 0.761589i \(-0.275580\pi\)
\(720\) 0 0
\(721\) −28.4103 + 28.4103i −1.05805 + 1.05805i
\(722\) −26.5999 −0.989944
\(723\) 16.6146 0.617903
\(724\) 10.4891 0.389824
\(725\) 0 0
\(726\) −3.63554 3.63554i −0.134928 0.134928i
\(727\) 44.4056i 1.64691i 0.567379 + 0.823457i \(0.307957\pi\)
−0.567379 + 0.823457i \(0.692043\pi\)
\(728\) −6.72971 + 6.72971i −0.249420 + 0.249420i
\(729\) 27.8201i 1.03037i
\(730\) 0 0
\(731\) 9.16042i 0.338810i
\(732\) 4.45199i 0.164550i
\(733\) −10.8447 + 10.8447i −0.400558 + 0.400558i −0.878430 0.477871i \(-0.841408\pi\)
0.477871 + 0.878430i \(0.341408\pi\)
\(734\) −18.9137 18.9137i −0.698119 0.698119i
\(735\) 0 0
\(736\) 16.5062 0.608428
\(737\) −0.392111 + 0.392111i −0.0144436 + 0.0144436i
\(738\) 9.05482i 0.333313i
\(739\) 41.4582 1.52506 0.762532 0.646950i \(-0.223956\pi\)
0.762532 + 0.646950i \(0.223956\pi\)
\(740\) 0 0
\(741\) −10.3877 −0.381602
\(742\) 3.73542i 0.137132i
\(743\) −17.6037 + 17.6037i −0.645818 + 0.645818i −0.951980 0.306162i \(-0.900955\pi\)
0.306162 + 0.951980i \(0.400955\pi\)
\(744\) 30.0671 1.10231
\(745\) 0 0
\(746\) 2.59600 + 2.59600i 0.0950462 + 0.0950462i
\(747\) 2.04497 2.04497i 0.0748214 0.0748214i
\(748\) 3.53127i 0.129116i
\(749\) 21.4199i 0.782665i
\(750\) 0 0
\(751\) 48.2958i 1.76234i −0.472802 0.881169i \(-0.656757\pi\)
0.472802 0.881169i \(-0.343243\pi\)
\(752\) −0.454845 + 0.454845i −0.0165865 + 0.0165865i
\(753\) 9.68683i 0.353008i
\(754\) 5.85271 + 5.85271i 0.213143 + 0.213143i
\(755\) 0 0
\(756\) 20.6524 0.751120
\(757\) 8.07302 0.293419 0.146710 0.989180i \(-0.453132\pi\)
0.146710 + 0.989180i \(0.453132\pi\)
\(758\) −22.2941 −0.809759
\(759\) −7.36267 + 7.36267i −0.267248 + 0.267248i
\(760\) 0 0
\(761\) 18.8298i 0.682580i −0.939958 0.341290i \(-0.889136\pi\)
0.939958 0.341290i \(-0.110864\pi\)
\(762\) 0.326068 0.0118122
\(763\) 33.7476i 1.22175i
\(764\) 4.99170 + 4.99170i 0.180593 + 0.180593i
\(765\) 0 0
\(766\) −19.8305 −0.716505
\(767\) −1.41625 1.41625i −0.0511378 0.0511378i
\(768\) −15.6615 + 15.6615i −0.565136 + 0.565136i
\(769\) 16.9982 + 16.9982i 0.612971 + 0.612971i 0.943719 0.330748i \(-0.107301\pi\)
−0.330748 + 0.943719i \(0.607301\pi\)
\(770\) 0 0
\(771\) −11.5157 + 11.5157i −0.414729 + 0.414729i
\(772\) 2.28251i 0.0821493i
\(773\) −10.8225 10.8225i −0.389260 0.389260i 0.485164 0.874423i \(-0.338760\pi\)
−0.874423 + 0.485164i \(0.838760\pi\)
\(774\) 8.38842i 0.301515i
\(775\) 0 0
\(776\) 46.3711i 1.66463i
\(777\) −24.8610 3.36432i −0.891882 0.120694i
\(778\) −2.36504 2.36504i −0.0847906 0.0847906i
\(779\) 43.2910 + 43.2910i 1.55106 + 1.55106i
\(780\) 0 0
\(781\) 37.1713i 1.33009i
\(782\) −2.97232 −0.106290
\(783\) 47.7922i 1.70795i
\(784\) 0.316727i 0.0113117i
\(785\) 0 0
\(786\) 0.284562 0.0101500
\(787\) −15.2905 + 15.2905i −0.545048 + 0.545048i −0.925004 0.379956i \(-0.875939\pi\)
0.379956 + 0.925004i \(0.375939\pi\)
\(788\) 21.4342 21.4342i 0.763562 0.763562i
\(789\) 16.7648i 0.596843i
\(790\) 0 0
\(791\) 0.956683 0.956683i 0.0340157 0.0340157i
\(792\) 8.60443i 0.305745i
\(793\) −2.11047 2.11047i −0.0749448 0.0749448i
\(794\) −18.7655 + 18.7655i −0.665964 + 0.665964i
\(795\) 0 0
\(796\) −18.8208 18.8208i −0.667086 0.667086i
\(797\) 10.3032i 0.364957i −0.983210 0.182478i \(-0.941588\pi\)
0.983210 0.182478i \(-0.0584120\pi\)
\(798\) −18.1777 + 18.1777i −0.643484 + 0.643484i
\(799\) −3.62457 + 3.62457i −0.128228 + 0.128228i
\(800\) 0 0
\(801\) −8.31535 + 8.31535i −0.293809 + 0.293809i
\(802\) 3.41328 + 3.41328i 0.120527 + 0.120527i
\(803\) 8.53469 + 8.53469i 0.301183 + 0.301183i
\(804\) 0.348710 0.0122981
\(805\) 0 0
\(806\) 5.35659 5.35659i 0.188678 0.188678i
\(807\) 14.8474 + 14.8474i 0.522654 + 0.522654i
\(808\) 38.8404 1.36640
\(809\) 11.8785 + 11.8785i 0.417626 + 0.417626i 0.884385 0.466759i \(-0.154578\pi\)
−0.466759 + 0.884385i \(0.654578\pi\)
\(810\) 0 0
\(811\) −31.7833 −1.11606 −0.558031 0.829820i \(-0.688443\pi\)
−0.558031 + 0.829820i \(0.688443\pi\)
\(812\) −30.9941 −1.08768
\(813\) 6.07087 6.07087i 0.212915 0.212915i
\(814\) 1.89103 13.9740i 0.0662807 0.489788i
\(815\) 0 0
\(816\) 0.153346 0.153346i 0.00536819 0.00536819i
\(817\) 40.1050 + 40.1050i 1.40309 + 1.40309i
\(818\) 3.66737 3.66737i 0.128227 0.128227i
\(819\) 2.72720 2.72720i 0.0952962 0.0952962i
\(820\) 0 0
\(821\) 21.2903 0.743036 0.371518 0.928426i \(-0.378837\pi\)
0.371518 + 0.928426i \(0.378837\pi\)
\(822\) 13.3394 0.465266
\(823\) 14.8922 + 14.8922i 0.519110 + 0.519110i 0.917302 0.398192i \(-0.130362\pi\)
−0.398192 + 0.917302i \(0.630362\pi\)
\(824\) 37.7885i 1.31642i
\(825\) 0 0
\(826\) −4.95666 −0.172464
\(827\) 3.17504 0.110407 0.0552035 0.998475i \(-0.482419\pi\)
0.0552035 + 0.998475i \(0.482419\pi\)
\(828\) −4.11844 −0.143126
\(829\) −12.8952 12.8952i −0.447867 0.447867i 0.446778 0.894645i \(-0.352571\pi\)
−0.894645 + 0.446778i \(0.852571\pi\)
\(830\) 0 0
\(831\) 17.6985 + 17.6985i 0.613954 + 0.613954i
\(832\) 5.77401i 0.200178i
\(833\) 2.52394i 0.0874492i
\(834\) 0.332004 + 0.332004i 0.0114963 + 0.0114963i
\(835\) 0 0
\(836\) 15.4601 + 15.4601i 0.534700 + 0.534700i
\(837\) −43.7410 −1.51191
\(838\) −1.54501 −0.0533716
\(839\) −4.30116 −0.148493 −0.0742463 0.997240i \(-0.523655\pi\)
−0.0742463 + 0.997240i \(0.523655\pi\)
\(840\) 0 0
\(841\) 42.7242i 1.47325i
\(842\) 4.48913 + 4.48913i 0.154706 + 0.154706i
\(843\) −13.4172 −0.462112
\(844\) 33.2386 1.14412
\(845\) 0 0
\(846\) 3.31911 3.31911i 0.114113 0.114113i
\(847\) 9.12672 9.12672i 0.313598 0.313598i
\(848\) 0.137961 + 0.137961i 0.00473760 + 0.00473760i
\(849\) −29.3115 + 29.3115i −1.00597 + 1.00597i
\(850\) 0 0
\(851\) 17.7974 + 2.40845i 0.610089 + 0.0825604i
\(852\) −16.5285 + 16.5285i −0.566256 + 0.566256i
\(853\) 9.61922 0.329356 0.164678 0.986347i \(-0.447342\pi\)
0.164678 + 0.986347i \(0.447342\pi\)
\(854\) −7.38631 −0.252754
\(855\) 0 0
\(856\) 14.2453 + 14.2453i 0.486894 + 0.486894i
\(857\) −45.8605 −1.56657 −0.783283 0.621665i \(-0.786456\pi\)
−0.783283 + 0.621665i \(0.786456\pi\)
\(858\) −2.43712 2.43712i −0.0832019 0.0832019i
\(859\) 10.0804 10.0804i 0.343939 0.343939i −0.513907 0.857846i \(-0.671802\pi\)
0.857846 + 0.513907i \(0.171802\pi\)
\(860\) 0 0
\(861\) 36.1396 1.23163
\(862\) −9.11326 9.11326i −0.310399 0.310399i
\(863\) 26.1964 + 26.1964i 0.891737 + 0.891737i 0.994687 0.102950i \(-0.0328281\pi\)
−0.102950 + 0.994687i \(0.532828\pi\)
\(864\) 22.3080 22.3080i 0.758932 0.758932i
\(865\) 0 0
\(866\) 1.48074 1.48074i 0.0503176 0.0503176i
\(867\) −15.0911 + 15.0911i −0.512520 + 0.512520i
\(868\) 28.3668i 0.962832i
\(869\) 2.69196 + 2.69196i 0.0913186 + 0.0913186i
\(870\) 0 0
\(871\) 0.165306 0.165306i 0.00560118 0.00560118i
\(872\) −22.4438 22.4438i −0.760044 0.760044i
\(873\) 18.7918i 0.636007i
\(874\) 13.0130 13.0130i 0.440173 0.440173i
\(875\) 0 0
\(876\) 7.59002i 0.256443i
\(877\) −19.8704 + 19.8704i −0.670975 + 0.670975i −0.957941 0.286966i \(-0.907353\pi\)
0.286966 + 0.957941i \(0.407353\pi\)
\(878\) 4.76934 4.76934i 0.160957 0.160957i
\(879\) −36.3038 −1.22450
\(880\) 0 0
\(881\) 28.6663i 0.965791i −0.875678 0.482895i \(-0.839585\pi\)
0.875678 0.482895i \(-0.160415\pi\)
\(882\) 2.31123i 0.0778232i
\(883\) 51.6260 1.73735 0.868677 0.495380i \(-0.164971\pi\)
0.868677 + 0.495380i \(0.164971\pi\)
\(884\) 1.48871i 0.0500707i
\(885\) 0 0
\(886\) 19.1042 + 19.1042i 0.641818 + 0.641818i
\(887\) −28.9624 28.9624i −0.972463 0.972463i 0.0271676 0.999631i \(-0.491351\pi\)
−0.999631 + 0.0271676i \(0.991351\pi\)
\(888\) −18.7712 + 14.2963i −0.629920 + 0.479753i
\(889\) 0.818567i 0.0274538i
\(890\) 0 0
\(891\) 10.8705i 0.364174i
\(892\) 2.70904 + 2.70904i 0.0907055 + 0.0907055i
\(893\) 31.7372i 1.06205i
\(894\) 3.01604 3.01604i 0.100871 0.100871i
\(895\) 0 0
\(896\) −13.9241 13.9241i −0.465172 0.465172i
\(897\) 3.10395 3.10395i 0.103638 0.103638i
\(898\) −25.0165 25.0165i −0.834812 0.834812i
\(899\) 65.6443 2.18936
\(900\) 0 0
\(901\) 1.09938 + 1.09938i 0.0366258 + 0.0366258i
\(902\) 20.3135i 0.676366i
\(903\) 33.4798 1.11414
\(904\) 1.27248i 0.0423221i
\(905\) 0 0
\(906\) 3.07022 3.07022i 0.102001 0.102001i
\(907\) −42.8804 −1.42382 −0.711910 0.702271i \(-0.752170\pi\)
−0.711910 + 0.702271i \(0.752170\pi\)
\(908\) 24.6951 0.819536
\(909\) −15.7400 −0.522063
\(910\) 0 0
\(911\) −25.0706 25.0706i −0.830627 0.830627i 0.156975 0.987603i \(-0.449826\pi\)
−0.987603 + 0.156975i \(0.949826\pi\)
\(912\) 1.34272i 0.0444619i
\(913\) 4.58766 4.58766i 0.151829 0.151829i
\(914\) 8.86295i 0.293160i
\(915\) 0 0
\(916\) 30.6255i 1.01189i
\(917\) 0.714370i 0.0235906i
\(918\) −4.01705 + 4.01705i −0.132583 + 0.132583i
\(919\) −14.7305 14.7305i −0.485915 0.485915i 0.421099 0.907015i \(-0.361644\pi\)
−0.907015 + 0.421099i \(0.861644\pi\)
\(920\) 0 0
\(921\) −7.23370 −0.238359
\(922\) −12.7176 + 12.7176i −0.418831 + 0.418831i
\(923\) 15.6706i 0.515805i
\(924\) 12.9062 0.424583
\(925\) 0 0
\(926\) −8.66041 −0.284599
\(927\) 15.3137i 0.502968i
\(928\) −33.4787 + 33.4787i −1.09899 + 1.09899i
\(929\) 24.7348 0.811524 0.405762 0.913979i \(-0.367006\pi\)
0.405762 + 0.913979i \(0.367006\pi\)
\(930\) 0 0
\(931\) −11.0500 11.0500i −0.362148 0.362148i
\(932\) 17.2508 17.2508i 0.565069 0.565069i
\(933\) 1.34071i 0.0438930i
\(934\) 13.3119i 0.435580i
\(935\) 0 0
\(936\) 3.62745i 0.118567i
\(937\) 34.2202 34.2202i 1.11792 1.11792i 0.125879 0.992046i \(-0.459825\pi\)
0.992046 0.125879i \(-0.0401752\pi\)
\(938\) 0.578546i 0.0188902i
\(939\) 10.9609 + 10.9609i 0.357696 + 0.357696i
\(940\) 0 0
\(941\) 57.6914 1.88069 0.940343 0.340227i \(-0.110504\pi\)
0.940343 + 0.340227i \(0.110504\pi\)
\(942\) 9.83234 0.320355
\(943\) −25.8716 −0.842494
\(944\) −0.183065 + 0.183065i −0.00595827 + 0.00595827i
\(945\) 0 0
\(946\) 18.8185i 0.611843i
\(947\) −23.8260 −0.774242 −0.387121 0.922029i \(-0.626530\pi\)
−0.387121 + 0.922029i \(0.626530\pi\)
\(948\) 2.39400i 0.0777536i
\(949\) −3.59805 3.59805i −0.116798 0.116798i
\(950\) 0 0
\(951\) 6.56286 0.212815
\(952\) 6.93196 + 6.93196i 0.224666 + 0.224666i
\(953\) −22.6117 + 22.6117i −0.732466 + 0.732466i −0.971108 0.238642i \(-0.923298\pi\)
0.238642 + 0.971108i \(0.423298\pi\)
\(954\) −1.00673 1.00673i −0.0325942 0.0325942i
\(955\) 0 0
\(956\) −18.5185 + 18.5185i −0.598930 + 0.598930i
\(957\) 29.8666i 0.965449i
\(958\) −20.0091 20.0091i −0.646465 0.646465i
\(959\) 33.4875i 1.08137i
\(960\) 0 0
\(961\) 29.0799i 0.938060i
\(962\) −0.797221 + 5.89114i −0.0257034 + 0.189938i
\(963\) −5.77287 5.77287i −0.186028 0.186028i
\(964\) 10.4247 + 10.4247i 0.335756 + 0.335756i
\(965\) 0 0
\(966\) 10.8634i 0.349523i
\(967\) −8.87384 −0.285364 −0.142682 0.989769i \(-0.545573\pi\)
−0.142682 + 0.989769i \(0.545573\pi\)
\(968\) 12.1394i 0.390176i
\(969\) 10.6999i 0.343730i
\(970\) 0 0
\(971\) 4.41358 0.141638 0.0708192 0.997489i \(-0.477439\pi\)
0.0708192 + 0.997489i \(0.477439\pi\)
\(972\) −9.58156 + 9.58156i −0.307329 + 0.307329i
\(973\) −0.833468 + 0.833468i −0.0267197 + 0.0267197i
\(974\) 29.6755i 0.950865i
\(975\) 0 0
\(976\) −0.272800 + 0.272800i −0.00873212 + 0.00873212i
\(977\) 36.2447i 1.15957i 0.814769 + 0.579785i \(0.196864\pi\)
−0.814769 + 0.579785i \(0.803136\pi\)
\(978\) −20.1610 20.1610i −0.644676 0.644676i
\(979\) −18.6546 + 18.6546i −0.596204 + 0.596204i
\(980\) 0 0
\(981\) 9.09532 + 9.09532i 0.290391 + 0.290391i
\(982\) 34.8276i 1.11139i
\(983\) 38.8340 38.8340i 1.23861 1.23861i 0.278044 0.960568i \(-0.410314\pi\)
0.960568 0.278044i \(-0.0896860\pi\)
\(984\) 24.0346 24.0346i 0.766195 0.766195i
\(985\) 0 0
\(986\) 6.02859 6.02859i 0.191990 0.191990i
\(987\) −13.2472 13.2472i −0.421663 0.421663i
\(988\) −6.51767 6.51767i −0.207355 0.207355i
\(989\) −23.9675 −0.762122
\(990\) 0 0
\(991\) −9.71202 + 9.71202i −0.308512 + 0.308512i −0.844332 0.535820i \(-0.820003\pi\)
0.535820 + 0.844332i \(0.320003\pi\)
\(992\) 30.6408 + 30.6408i 0.972846 + 0.972846i
\(993\) −20.1900 −0.640709
\(994\) 27.4224 + 27.4224i 0.869787 + 0.869787i
\(995\) 0 0
\(996\) −4.07987 −0.129276
\(997\) −1.35721 −0.0429833 −0.0214917 0.999769i \(-0.506842\pi\)
−0.0214917 + 0.999769i \(0.506842\pi\)
\(998\) −16.5417 + 16.5417i −0.523620 + 0.523620i
\(999\) 27.3080 20.7980i 0.863987 0.658021i
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 925.2.f.f.43.8 48
5.2 odd 4 925.2.k.f.857.17 yes 48
5.3 odd 4 925.2.k.f.857.8 yes 48
5.4 even 2 inner 925.2.f.f.43.17 yes 48
37.31 odd 4 925.2.k.f.68.17 yes 48
185.68 even 4 inner 925.2.f.f.882.8 yes 48
185.142 even 4 inner 925.2.f.f.882.17 yes 48
185.179 odd 4 925.2.k.f.68.8 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
925.2.f.f.43.8 48 1.1 even 1 trivial
925.2.f.f.43.17 yes 48 5.4 even 2 inner
925.2.f.f.882.8 yes 48 185.68 even 4 inner
925.2.f.f.882.17 yes 48 185.142 even 4 inner
925.2.k.f.68.8 yes 48 185.179 odd 4
925.2.k.f.68.17 yes 48 37.31 odd 4
925.2.k.f.857.8 yes 48 5.3 odd 4
925.2.k.f.857.17 yes 48 5.2 odd 4