Properties

Label 351.2.t.c.64.5
Level $351$
Weight $2$
Character 351.64
Analytic conductor $2.803$
Analytic rank $0$
Dimension $20$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [351,2,Mod(64,351)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(351, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("351.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 351 = 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 351.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.80274911095\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{9} \)
Twist minimal: no (minimal twist has level 117)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 64.5
Root \(0.219737 + 1.71806i\) of defining polynomial
Character \(\chi\) \(=\) 351.64
Dual form 351.2.t.c.181.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.784270 + 0.452798i) q^{2} +(-0.589947 + 1.02182i) q^{4} +(1.94254 + 1.12153i) q^{5} +(2.97576 - 1.71806i) q^{7} -2.87970i q^{8} -2.03130 q^{10} +(3.20133 - 1.84829i) q^{11} +(-3.28340 + 1.48972i) q^{13} +(-1.55587 + 2.69484i) q^{14} +(0.124029 + 0.214825i) q^{16} +4.21120 q^{17} +4.25298i q^{19} +(-2.29200 + 1.32329i) q^{20} +(-1.67380 + 2.89911i) q^{22} +(-1.89162 + 3.27639i) q^{23} +(0.0156524 + 0.0271108i) q^{25} +(1.90053 - 2.65506i) q^{26} +4.05425i q^{28} +(1.18945 + 2.06020i) q^{29} +(6.37163 + 3.67866i) q^{31} +(4.79325 + 2.76738i) q^{32} +(-3.30272 + 1.90682i) q^{34} +7.70739 q^{35} -5.49928i q^{37} +(-1.92574 - 3.33549i) q^{38} +(3.22967 - 5.59395i) q^{40} +(-6.86085 - 3.96111i) q^{41} +(-0.450266 - 0.779883i) q^{43} +4.36157i q^{44} -3.42609i q^{46} +(-4.80060 + 2.77163i) q^{47} +(2.40343 - 4.16287i) q^{49} +(-0.0245514 - 0.0141748i) q^{50} +(0.414812 - 4.23390i) q^{52} -7.59566 q^{53} +8.29163 q^{55} +(-4.94749 - 8.56930i) q^{56} +(-1.86571 - 1.07717i) q^{58} +(4.44379 + 2.56562i) q^{59} +(6.50907 + 11.2740i) q^{61} -6.66277 q^{62} -5.50838 q^{64} +(-8.04892 - 0.788585i) q^{65} +(-11.7002 - 6.75511i) q^{67} +(-2.48439 + 4.30308i) q^{68} +(-6.04468 + 3.48989i) q^{70} -2.65506i q^{71} -5.45741i q^{73} +(2.49006 + 4.31292i) q^{74} +(-4.34578 - 2.50904i) q^{76} +(6.35092 - 11.0001i) q^{77} +(-5.46886 - 9.47234i) q^{79} +0.556410i q^{80} +7.17434 q^{82} +(0.465547 - 0.268784i) q^{83} +(8.18044 + 4.72298i) q^{85} +(0.706259 + 0.407759i) q^{86} +(-5.32252 - 9.21887i) q^{88} -5.75227i q^{89} +(-7.21120 + 10.0741i) q^{91} +(-2.23192 - 3.86579i) q^{92} +(2.50998 - 4.34740i) q^{94} +(-4.76984 + 8.26161i) q^{95} +(5.87585 - 3.39243i) q^{97} +4.35308i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(326\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.784270 + 0.452798i −0.554562 + 0.320177i −0.750960 0.660348i \(-0.770409\pi\)
0.196398 + 0.980524i \(0.437076\pi\)
\(3\) 0 0
\(4\) −0.589947 + 1.02182i −0.294974 + 0.510909i
\(5\) 1.94254 + 1.12153i 0.868732 + 0.501563i 0.866927 0.498436i \(-0.166092\pi\)
0.00180550 + 0.999998i \(0.499425\pi\)
\(6\) 0 0
\(7\) 2.97576 1.71806i 1.12473 0.649364i 0.182127 0.983275i \(-0.441702\pi\)
0.942605 + 0.333911i \(0.108368\pi\)
\(8\) 2.87970i 1.01813i
\(9\) 0 0
\(10\) −2.03130 −0.642355
\(11\) 3.20133 1.84829i 0.965236 0.557279i 0.0674557 0.997722i \(-0.478512\pi\)
0.897781 + 0.440443i \(0.145179\pi\)
\(12\) 0 0
\(13\) −3.28340 + 1.48972i −0.910652 + 0.413174i
\(14\) −1.55587 + 2.69484i −0.415823 + 0.720226i
\(15\) 0 0
\(16\) 0.124029 + 0.214825i 0.0310073 + 0.0537063i
\(17\) 4.21120 1.02137 0.510683 0.859769i \(-0.329393\pi\)
0.510683 + 0.859769i \(0.329393\pi\)
\(18\) 0 0
\(19\) 4.25298i 0.975701i 0.872927 + 0.487851i \(0.162219\pi\)
−0.872927 + 0.487851i \(0.837781\pi\)
\(20\) −2.29200 + 1.32329i −0.512506 + 0.295896i
\(21\) 0 0
\(22\) −1.67380 + 2.89911i −0.356856 + 0.618092i
\(23\) −1.89162 + 3.27639i −0.394431 + 0.683174i −0.993028 0.117876i \(-0.962392\pi\)
0.598598 + 0.801050i \(0.295725\pi\)
\(24\) 0 0
\(25\) 0.0156524 + 0.0271108i 0.00313048 + 0.00542215i
\(26\) 1.90053 2.65506i 0.372725 0.520700i
\(27\) 0 0
\(28\) 4.05425i 0.766181i
\(29\) 1.18945 + 2.06020i 0.220876 + 0.382569i 0.955074 0.296367i \(-0.0957750\pi\)
−0.734198 + 0.678935i \(0.762442\pi\)
\(30\) 0 0
\(31\) 6.37163 + 3.67866i 1.14438 + 0.660707i 0.947511 0.319723i \(-0.103590\pi\)
0.196868 + 0.980430i \(0.436923\pi\)
\(32\) 4.79325 + 2.76738i 0.847334 + 0.489209i
\(33\) 0 0
\(34\) −3.30272 + 1.90682i −0.566411 + 0.327018i
\(35\) 7.70739 1.30279
\(36\) 0 0
\(37\) 5.49928i 0.904076i −0.891999 0.452038i \(-0.850697\pi\)
0.891999 0.452038i \(-0.149303\pi\)
\(38\) −1.92574 3.33549i −0.312397 0.541087i
\(39\) 0 0
\(40\) 3.22967 5.59395i 0.510655 0.884481i
\(41\) −6.86085 3.96111i −1.07148 0.618622i −0.142898 0.989737i \(-0.545642\pi\)
−0.928587 + 0.371116i \(0.878975\pi\)
\(42\) 0 0
\(43\) −0.450266 0.779883i −0.0686649 0.118931i 0.829649 0.558285i \(-0.188541\pi\)
−0.898314 + 0.439354i \(0.855207\pi\)
\(44\) 4.36157i 0.657531i
\(45\) 0 0
\(46\) 3.42609i 0.505150i
\(47\) −4.80060 + 2.77163i −0.700239 + 0.404283i −0.807436 0.589955i \(-0.799146\pi\)
0.107197 + 0.994238i \(0.465812\pi\)
\(48\) 0 0
\(49\) 2.40343 4.16287i 0.343347 0.594695i
\(50\) −0.0245514 0.0141748i −0.00347209 0.00200461i
\(51\) 0 0
\(52\) 0.414812 4.23390i 0.0575241 0.587136i
\(53\) −7.59566 −1.04334 −0.521672 0.853146i \(-0.674692\pi\)
−0.521672 + 0.853146i \(0.674692\pi\)
\(54\) 0 0
\(55\) 8.29163 1.11804
\(56\) −4.94749 8.56930i −0.661136 1.14512i
\(57\) 0 0
\(58\) −1.86571 1.07717i −0.244979 0.141439i
\(59\) 4.44379 + 2.56562i 0.578532 + 0.334016i 0.760550 0.649279i \(-0.224929\pi\)
−0.182018 + 0.983295i \(0.558263\pi\)
\(60\) 0 0
\(61\) 6.50907 + 11.2740i 0.833401 + 1.44349i 0.895326 + 0.445412i \(0.146943\pi\)
−0.0619247 + 0.998081i \(0.519724\pi\)
\(62\) −6.66277 −0.846173
\(63\) 0 0
\(64\) −5.50838 −0.688547
\(65\) −8.04892 0.788585i −0.998346 0.0978120i
\(66\) 0 0
\(67\) −11.7002 6.75511i −1.42941 0.825269i −0.432333 0.901714i \(-0.642310\pi\)
−0.997074 + 0.0764454i \(0.975643\pi\)
\(68\) −2.48439 + 4.30308i −0.301276 + 0.521825i
\(69\) 0 0
\(70\) −6.04468 + 3.48989i −0.722477 + 0.417122i
\(71\) 2.65506i 0.315098i −0.987511 0.157549i \(-0.949641\pi\)
0.987511 0.157549i \(-0.0503592\pi\)
\(72\) 0 0
\(73\) 5.45741i 0.638741i −0.947630 0.319371i \(-0.896528\pi\)
0.947630 0.319371i \(-0.103472\pi\)
\(74\) 2.49006 + 4.31292i 0.289464 + 0.501366i
\(75\) 0 0
\(76\) −4.34578 2.50904i −0.498495 0.287806i
\(77\) 6.35092 11.0001i 0.723755 1.25358i
\(78\) 0 0
\(79\) −5.46886 9.47234i −0.615294 1.06572i −0.990333 0.138712i \(-0.955704\pi\)
0.375038 0.927009i \(-0.377630\pi\)
\(80\) 0.556410i 0.0622085i
\(81\) 0 0
\(82\) 7.17434 0.792273
\(83\) 0.465547 0.268784i 0.0511004 0.0295029i −0.474232 0.880400i \(-0.657274\pi\)
0.525333 + 0.850897i \(0.323941\pi\)
\(84\) 0 0
\(85\) 8.18044 + 4.72298i 0.887294 + 0.512279i
\(86\) 0.706259 + 0.407759i 0.0761579 + 0.0439698i
\(87\) 0 0
\(88\) −5.32252 9.21887i −0.567382 0.982735i
\(89\) 5.75227i 0.609739i −0.952394 0.304870i \(-0.901387\pi\)
0.952394 0.304870i \(-0.0986129\pi\)
\(90\) 0 0
\(91\) −7.21120 + 10.0741i −0.755939 + 1.05605i
\(92\) −2.23192 3.86579i −0.232693 0.403037i
\(93\) 0 0
\(94\) 2.50998 4.34740i 0.258884 0.448401i
\(95\) −4.76984 + 8.26161i −0.489375 + 0.847623i
\(96\) 0 0
\(97\) 5.87585 3.39243i 0.596603 0.344449i −0.171101 0.985253i \(-0.554733\pi\)
0.767704 + 0.640805i \(0.221399\pi\)
\(98\) 4.35308i 0.439727i
\(99\) 0 0
\(100\) −0.0369364 −0.00369364
\(101\) −2.48116 4.29749i −0.246884 0.427616i 0.715776 0.698330i \(-0.246073\pi\)
−0.962660 + 0.270715i \(0.912740\pi\)
\(102\) 0 0
\(103\) −1.05587 + 1.82881i −0.104038 + 0.180198i −0.913345 0.407188i \(-0.866510\pi\)
0.809307 + 0.587386i \(0.199843\pi\)
\(104\) 4.28995 + 9.45522i 0.420664 + 0.927161i
\(105\) 0 0
\(106\) 5.95705 3.43930i 0.578600 0.334055i
\(107\) 8.07404 0.780547 0.390274 0.920699i \(-0.372380\pi\)
0.390274 + 0.920699i \(0.372380\pi\)
\(108\) 0 0
\(109\) 10.0020i 0.958021i −0.877809 0.479011i \(-0.840996\pi\)
0.877809 0.479011i \(-0.159004\pi\)
\(110\) −6.50287 + 3.75443i −0.620024 + 0.357971i
\(111\) 0 0
\(112\) 0.738163 + 0.426179i 0.0697498 + 0.0402701i
\(113\) 9.71733 16.8309i 0.914130 1.58332i 0.105959 0.994371i \(-0.466209\pi\)
0.808171 0.588948i \(-0.200458\pi\)
\(114\) 0 0
\(115\) −7.34912 + 4.24302i −0.685309 + 0.395664i
\(116\) −2.80686 −0.260611
\(117\) 0 0
\(118\) −4.64684 −0.427776
\(119\) 12.5315 7.23508i 1.14876 0.663238i
\(120\) 0 0
\(121\) 1.33233 2.30766i 0.121121 0.209787i
\(122\) −10.2097 5.89459i −0.924346 0.533671i
\(123\) 0 0
\(124\) −7.51786 + 4.34044i −0.675123 + 0.389783i
\(125\) 11.1451i 0.996845i
\(126\) 0 0
\(127\) −1.76413 −0.156541 −0.0782704 0.996932i \(-0.524940\pi\)
−0.0782704 + 0.996932i \(0.524940\pi\)
\(128\) −5.26644 + 3.04058i −0.465492 + 0.268752i
\(129\) 0 0
\(130\) 6.66959 3.02607i 0.584962 0.265404i
\(131\) −3.56490 + 6.17458i −0.311466 + 0.539476i −0.978680 0.205391i \(-0.934153\pi\)
0.667214 + 0.744866i \(0.267487\pi\)
\(132\) 0 0
\(133\) 7.30686 + 12.6559i 0.633585 + 1.09740i
\(134\) 12.2348 1.05693
\(135\) 0 0
\(136\) 12.1270i 1.03988i
\(137\) 3.91494 2.26029i 0.334476 0.193110i −0.323351 0.946279i \(-0.604809\pi\)
0.657826 + 0.753170i \(0.271476\pi\)
\(138\) 0 0
\(139\) −7.05496 + 12.2195i −0.598394 + 1.03645i 0.394664 + 0.918825i \(0.370861\pi\)
−0.993058 + 0.117623i \(0.962472\pi\)
\(140\) −4.54696 + 7.87556i −0.384288 + 0.665606i
\(141\) 0 0
\(142\) 1.20221 + 2.08228i 0.100887 + 0.174741i
\(143\) −7.75782 + 10.8377i −0.648741 + 0.906298i
\(144\) 0 0
\(145\) 5.33603i 0.443133i
\(146\) 2.47111 + 4.28008i 0.204510 + 0.354222i
\(147\) 0 0
\(148\) 5.61927 + 3.24428i 0.461901 + 0.266679i
\(149\) −5.02499 2.90118i −0.411663 0.237674i 0.279841 0.960046i \(-0.409718\pi\)
−0.691504 + 0.722372i \(0.743052\pi\)
\(150\) 0 0
\(151\) −8.44018 + 4.87294i −0.686852 + 0.396554i −0.802432 0.596744i \(-0.796461\pi\)
0.115580 + 0.993298i \(0.463127\pi\)
\(152\) 12.2473 0.993389
\(153\) 0 0
\(154\) 11.5027i 0.926917i
\(155\) 8.25145 + 14.2919i 0.662773 + 1.14796i
\(156\) 0 0
\(157\) 0.539798 0.934957i 0.0430806 0.0746177i −0.843681 0.536845i \(-0.819616\pi\)
0.886762 + 0.462227i \(0.152949\pi\)
\(158\) 8.57812 + 4.95258i 0.682438 + 0.394006i
\(159\) 0 0
\(160\) 6.20739 + 10.7515i 0.490738 + 0.849982i
\(161\) 12.9997i 1.02452i
\(162\) 0 0
\(163\) 5.54857i 0.434598i 0.976105 + 0.217299i \(0.0697247\pi\)
−0.976105 + 0.217299i \(0.930275\pi\)
\(164\) 8.09508 4.67370i 0.632120 0.364954i
\(165\) 0 0
\(166\) −0.243410 + 0.421598i −0.0188923 + 0.0327223i
\(167\) −11.5515 6.66925i −0.893880 0.516082i −0.0186702 0.999826i \(-0.505943\pi\)
−0.875210 + 0.483744i \(0.839277\pi\)
\(168\) 0 0
\(169\) 8.56147 9.78270i 0.658575 0.752515i
\(170\) −8.55423 −0.656079
\(171\) 0 0
\(172\) 1.06253 0.0810173
\(173\) 3.72080 + 6.44461i 0.282887 + 0.489975i 0.972095 0.234589i \(-0.0753745\pi\)
−0.689208 + 0.724564i \(0.742041\pi\)
\(174\) 0 0
\(175\) 0.0931556 + 0.0537834i 0.00704190 + 0.00406564i
\(176\) 0.794117 + 0.458484i 0.0598588 + 0.0345595i
\(177\) 0 0
\(178\) 2.60462 + 4.51133i 0.195224 + 0.338138i
\(179\) −23.2047 −1.73440 −0.867202 0.497957i \(-0.834084\pi\)
−0.867202 + 0.497957i \(0.834084\pi\)
\(180\) 0 0
\(181\) 5.18439 0.385353 0.192676 0.981262i \(-0.438283\pi\)
0.192676 + 0.981262i \(0.438283\pi\)
\(182\) 1.09398 11.1660i 0.0810914 0.827682i
\(183\) 0 0
\(184\) 9.43502 + 5.44731i 0.695559 + 0.401581i
\(185\) 6.16760 10.6826i 0.453451 0.785400i
\(186\) 0 0
\(187\) 13.4814 7.78351i 0.985860 0.569186i
\(188\) 6.54045i 0.477012i
\(189\) 0 0
\(190\) 8.63911i 0.626747i
\(191\) 8.07057 + 13.9786i 0.583966 + 1.01146i 0.995003 + 0.0998406i \(0.0318333\pi\)
−0.411037 + 0.911619i \(0.634833\pi\)
\(192\) 0 0
\(193\) 2.83991 + 1.63962i 0.204421 + 0.118023i 0.598716 0.800961i \(-0.295678\pi\)
−0.394295 + 0.918984i \(0.629011\pi\)
\(194\) −3.07217 + 5.32115i −0.220569 + 0.382037i
\(195\) 0 0
\(196\) 2.83580 + 4.91174i 0.202557 + 0.350839i
\(197\) 7.11249i 0.506744i 0.967369 + 0.253372i \(0.0815396\pi\)
−0.967369 + 0.253372i \(0.918460\pi\)
\(198\) 0 0
\(199\) −13.8449 −0.981437 −0.490719 0.871318i \(-0.663266\pi\)
−0.490719 + 0.871318i \(0.663266\pi\)
\(200\) 0.0780709 0.0450743i 0.00552045 0.00318723i
\(201\) 0 0
\(202\) 3.89179 + 2.24693i 0.273825 + 0.158093i
\(203\) 7.07906 + 4.08710i 0.496853 + 0.286858i
\(204\) 0 0
\(205\) −8.88500 15.3893i −0.620555 1.07483i
\(206\) 1.91238i 0.133242i
\(207\) 0 0
\(208\) −0.727267 0.520589i −0.0504269 0.0360963i
\(209\) 7.86073 + 13.6152i 0.543738 + 0.941782i
\(210\) 0 0
\(211\) −7.21695 + 12.5001i −0.496836 + 0.860545i −0.999993 0.00365007i \(-0.998838\pi\)
0.503158 + 0.864195i \(0.332171\pi\)
\(212\) 4.48104 7.76139i 0.307759 0.533055i
\(213\) 0 0
\(214\) −6.33223 + 3.65591i −0.432862 + 0.249913i
\(215\) 2.01994i 0.137759i
\(216\) 0 0
\(217\) 25.2806 1.71616
\(218\) 4.52890 + 7.84429i 0.306736 + 0.531283i
\(219\) 0 0
\(220\) −4.89162 + 8.47254i −0.329793 + 0.571219i
\(221\) −13.8271 + 6.27350i −0.930109 + 0.422002i
\(222\) 0 0
\(223\) 9.52959 5.50191i 0.638149 0.368435i −0.145752 0.989321i \(-0.546560\pi\)
0.783901 + 0.620886i \(0.213227\pi\)
\(224\) 19.0181 1.27070
\(225\) 0 0
\(226\) 17.6000i 1.17073i
\(227\) 7.03055 4.05909i 0.466634 0.269411i −0.248196 0.968710i \(-0.579838\pi\)
0.714830 + 0.699299i \(0.246504\pi\)
\(228\) 0 0
\(229\) −4.65740 2.68895i −0.307769 0.177691i 0.338158 0.941089i \(-0.390196\pi\)
−0.645928 + 0.763398i \(0.723529\pi\)
\(230\) 3.84246 6.65534i 0.253365 0.438840i
\(231\) 0 0
\(232\) 5.93275 3.42528i 0.389504 0.224880i
\(233\) −20.0992 −1.31675 −0.658373 0.752692i \(-0.728755\pi\)
−0.658373 + 0.752692i \(0.728755\pi\)
\(234\) 0 0
\(235\) −12.4338 −0.811094
\(236\) −5.24321 + 3.02717i −0.341304 + 0.197052i
\(237\) 0 0
\(238\) −6.55206 + 11.3485i −0.424707 + 0.735614i
\(239\) 12.2635 + 7.08034i 0.793261 + 0.457989i 0.841109 0.540865i \(-0.181903\pi\)
−0.0478485 + 0.998855i \(0.515236\pi\)
\(240\) 0 0
\(241\) −26.2041 + 15.1289i −1.68795 + 0.974539i −0.731867 + 0.681447i \(0.761351\pi\)
−0.956084 + 0.293092i \(0.905316\pi\)
\(242\) 2.41310i 0.155120i
\(243\) 0 0
\(244\) −15.3600 −0.983326
\(245\) 9.33754 5.39103i 0.596554 0.344421i
\(246\) 0 0
\(247\) −6.33575 13.9643i −0.403134 0.888525i
\(248\) 10.5935 18.3484i 0.672685 1.16512i
\(249\) 0 0
\(250\) 5.04647 + 8.74074i 0.319167 + 0.552813i
\(251\) 17.5085 1.10512 0.552562 0.833472i \(-0.313650\pi\)
0.552562 + 0.833472i \(0.313650\pi\)
\(252\) 0 0
\(253\) 13.9850i 0.879232i
\(254\) 1.38355 0.798793i 0.0868117 0.0501208i
\(255\) 0 0
\(256\) 8.26192 14.3101i 0.516370 0.894379i
\(257\) 9.15211 15.8519i 0.570893 0.988815i −0.425582 0.904920i \(-0.639931\pi\)
0.996475 0.0838952i \(-0.0267361\pi\)
\(258\) 0 0
\(259\) −9.44807 16.3645i −0.587074 1.01684i
\(260\) 5.55423 7.75931i 0.344459 0.481212i
\(261\) 0 0
\(262\) 6.45672i 0.398897i
\(263\) −4.19661 7.26875i −0.258774 0.448210i 0.707140 0.707074i \(-0.249985\pi\)
−0.965914 + 0.258864i \(0.916652\pi\)
\(264\) 0 0
\(265\) −14.7549 8.51875i −0.906387 0.523303i
\(266\) −11.4611 6.61707i −0.702725 0.405719i
\(267\) 0 0
\(268\) 13.8050 7.97032i 0.843275 0.486865i
\(269\) −21.3238 −1.30014 −0.650069 0.759875i \(-0.725260\pi\)
−0.650069 + 0.759875i \(0.725260\pi\)
\(270\) 0 0
\(271\) 18.4587i 1.12129i −0.828057 0.560643i \(-0.810554\pi\)
0.828057 0.560643i \(-0.189446\pi\)
\(272\) 0.522312 + 0.904671i 0.0316698 + 0.0548538i
\(273\) 0 0
\(274\) −2.04691 + 3.54535i −0.123658 + 0.214183i
\(275\) 0.100217 + 0.0578603i 0.00604331 + 0.00348911i
\(276\) 0 0
\(277\) 4.31390 + 7.47189i 0.259197 + 0.448943i 0.966027 0.258441i \(-0.0832087\pi\)
−0.706830 + 0.707383i \(0.749875\pi\)
\(278\) 12.7779i 0.766367i
\(279\) 0 0
\(280\) 22.1950i 1.32640i
\(281\) −3.00928 + 1.73741i −0.179518 + 0.103645i −0.587066 0.809539i \(-0.699717\pi\)
0.407548 + 0.913184i \(0.366384\pi\)
\(282\) 0 0
\(283\) 6.89178 11.9369i 0.409674 0.709576i −0.585179 0.810904i \(-0.698976\pi\)
0.994853 + 0.101328i \(0.0323091\pi\)
\(284\) 2.71299 + 1.56635i 0.160986 + 0.0929456i
\(285\) 0 0
\(286\) 1.17691 12.0124i 0.0695920 0.710311i
\(287\) −27.2217 −1.60684
\(288\) 0 0
\(289\) 0.734202 0.0431884
\(290\) −2.41615 4.18489i −0.141881 0.245745i
\(291\) 0 0
\(292\) 5.57648 + 3.21958i 0.326339 + 0.188412i
\(293\) −24.6911 14.2554i −1.44247 0.832810i −0.444455 0.895801i \(-0.646603\pi\)
−0.998014 + 0.0629917i \(0.979936\pi\)
\(294\) 0 0
\(295\) 5.75484 + 9.96768i 0.335060 + 0.580341i
\(296\) −15.8363 −0.920465
\(297\) 0 0
\(298\) 5.25460 0.304391
\(299\) 1.33007 13.5757i 0.0769196 0.785102i
\(300\) 0 0
\(301\) −2.67977 1.54716i −0.154459 0.0891770i
\(302\) 4.41292 7.64340i 0.253935 0.439828i
\(303\) 0 0
\(304\) −0.913648 + 0.527495i −0.0524013 + 0.0302539i
\(305\) 29.2004i 1.67201i
\(306\) 0 0
\(307\) 21.8137i 1.24497i 0.782631 + 0.622486i \(0.213877\pi\)
−0.782631 + 0.622486i \(0.786123\pi\)
\(308\) 7.49342 + 12.9790i 0.426977 + 0.739546i
\(309\) 0 0
\(310\) −12.9427 7.47249i −0.735097 0.424409i
\(311\) −3.48161 + 6.03032i −0.197424 + 0.341948i −0.947692 0.319185i \(-0.896591\pi\)
0.750268 + 0.661133i \(0.229924\pi\)
\(312\) 0 0
\(313\) −11.2253 19.4428i −0.634491 1.09897i −0.986623 0.163020i \(-0.947876\pi\)
0.352131 0.935951i \(-0.385457\pi\)
\(314\) 0.977678i 0.0551736i
\(315\) 0 0
\(316\) 12.9054 0.725983
\(317\) 8.84739 5.10804i 0.496919 0.286896i −0.230522 0.973067i \(-0.574043\pi\)
0.727440 + 0.686171i \(0.240710\pi\)
\(318\) 0 0
\(319\) 7.61567 + 4.39691i 0.426395 + 0.246180i
\(320\) −10.7003 6.17780i −0.598163 0.345350i
\(321\) 0 0
\(322\) −5.88622 10.1952i −0.328026 0.568158i
\(323\) 17.9102i 0.996548i
\(324\) 0 0
\(325\) −0.0917806 0.0656979i −0.00509107 0.00364426i
\(326\) −2.51239 4.35158i −0.139148 0.241012i
\(327\) 0 0
\(328\) −11.4068 + 19.7572i −0.629836 + 1.09091i
\(329\) −9.52362 + 16.4954i −0.525054 + 0.909420i
\(330\) 0 0
\(331\) −4.67794 + 2.70081i −0.257123 + 0.148450i −0.623021 0.782205i \(-0.714095\pi\)
0.365898 + 0.930655i \(0.380762\pi\)
\(332\) 0.634273i 0.0348103i
\(333\) 0 0
\(334\) 12.0793 0.660949
\(335\) −15.1521 26.2442i −0.827848 1.43387i
\(336\) 0 0
\(337\) 16.4621 28.5132i 0.896749 1.55321i 0.0651239 0.997877i \(-0.479256\pi\)
0.831625 0.555338i \(-0.187411\pi\)
\(338\) −2.28492 + 11.5489i −0.124283 + 0.628177i
\(339\) 0 0
\(340\) −9.65206 + 5.57262i −0.523457 + 0.302218i
\(341\) 27.1969 1.47279
\(342\) 0 0
\(343\) 7.53586i 0.406898i
\(344\) −2.24583 + 1.29663i −0.121087 + 0.0699097i
\(345\) 0 0
\(346\) −5.83622 3.36954i −0.313757 0.181148i
\(347\) 6.81390 11.8020i 0.365789 0.633566i −0.623113 0.782132i \(-0.714132\pi\)
0.988902 + 0.148566i \(0.0474658\pi\)
\(348\) 0 0
\(349\) −9.76413 + 5.63732i −0.522662 + 0.301759i −0.738023 0.674776i \(-0.764240\pi\)
0.215361 + 0.976534i \(0.430907\pi\)
\(350\) −0.0974121 −0.00520690
\(351\) 0 0
\(352\) 20.4597 1.09050
\(353\) −23.0629 + 13.3154i −1.22751 + 0.708706i −0.966509 0.256631i \(-0.917387\pi\)
−0.261005 + 0.965337i \(0.584054\pi\)
\(354\) 0 0
\(355\) 2.97773 5.15757i 0.158041 0.273736i
\(356\) 5.87778 + 3.39354i 0.311522 + 0.179857i
\(357\) 0 0
\(358\) 18.1988 10.5071i 0.961835 0.555316i
\(359\) 34.9036i 1.84214i 0.389396 + 0.921071i \(0.372684\pi\)
−0.389396 + 0.921071i \(0.627316\pi\)
\(360\) 0 0
\(361\) 0.912132 0.0480069
\(362\) −4.06596 + 2.34748i −0.213702 + 0.123381i
\(363\) 0 0
\(364\) −6.03969 13.3117i −0.316566 0.697725i
\(365\) 6.12064 10.6013i 0.320369 0.554895i
\(366\) 0 0
\(367\) 1.35716 + 2.35068i 0.0708434 + 0.122704i 0.899271 0.437392i \(-0.144098\pi\)
−0.828428 + 0.560096i \(0.810764\pi\)
\(368\) −0.938467 −0.0489210
\(369\) 0 0
\(370\) 11.1707i 0.580737i
\(371\) −22.6029 + 13.0498i −1.17348 + 0.677510i
\(372\) 0 0
\(373\) 0.875481 1.51638i 0.0453307 0.0785150i −0.842470 0.538744i \(-0.818899\pi\)
0.887800 + 0.460229i \(0.152233\pi\)
\(374\) −7.04872 + 12.2087i −0.364480 + 0.631299i
\(375\) 0 0
\(376\) 7.98146 + 13.8243i 0.411612 + 0.712933i
\(377\) −6.97457 4.99250i −0.359209 0.257127i
\(378\) 0 0
\(379\) 2.90941i 0.149446i 0.997204 + 0.0747231i \(0.0238073\pi\)
−0.997204 + 0.0747231i \(0.976193\pi\)
\(380\) −5.62791 9.74783i −0.288706 0.500053i
\(381\) 0 0
\(382\) −12.6590 7.30868i −0.647691 0.373945i
\(383\) 17.7065 + 10.2229i 0.904760 + 0.522363i 0.878741 0.477298i \(-0.158384\pi\)
0.0260185 + 0.999661i \(0.491717\pi\)
\(384\) 0 0
\(385\) 24.6739 14.2455i 1.25750 0.726017i
\(386\) −2.96968 −0.151152
\(387\) 0 0
\(388\) 8.00541i 0.406413i
\(389\) 6.48161 + 11.2265i 0.328631 + 0.569205i 0.982240 0.187627i \(-0.0600795\pi\)
−0.653610 + 0.756832i \(0.726746\pi\)
\(390\) 0 0
\(391\) −7.96600 + 13.7975i −0.402858 + 0.697771i
\(392\) −11.9878 6.92117i −0.605476 0.349572i
\(393\) 0 0
\(394\) −3.22052 5.57811i −0.162248 0.281021i
\(395\) 24.5339i 1.23444i
\(396\) 0 0
\(397\) 29.1809i 1.46455i −0.681010 0.732274i \(-0.738459\pi\)
0.681010 0.732274i \(-0.261541\pi\)
\(398\) 10.8581 6.26894i 0.544268 0.314233i
\(399\) 0 0
\(400\) −0.00388271 + 0.00672506i −0.000194136 + 0.000336253i
\(401\) 19.2018 + 11.0862i 0.958894 + 0.553617i 0.895832 0.444392i \(-0.146580\pi\)
0.0630612 + 0.998010i \(0.479914\pi\)
\(402\) 0 0
\(403\) −26.4008 2.58659i −1.31512 0.128847i
\(404\) 5.85500 0.291297
\(405\) 0 0
\(406\) −7.40253 −0.367381
\(407\) −10.1642 17.6050i −0.503823 0.872647i
\(408\) 0 0
\(409\) 1.81749 + 1.04933i 0.0898689 + 0.0518858i 0.544261 0.838916i \(-0.316810\pi\)
−0.454392 + 0.890802i \(0.650143\pi\)
\(410\) 13.9365 + 8.04623i 0.688273 + 0.397375i
\(411\) 0 0
\(412\) −1.24581 2.15781i −0.0613767 0.106307i
\(413\) 17.6315 0.867591
\(414\) 0 0
\(415\) 1.20579 0.0591901
\(416\) −19.8608 1.94584i −0.973755 0.0954027i
\(417\) 0 0
\(418\) −12.3299 7.11865i −0.603074 0.348185i
\(419\) 0.195699 0.338961i 0.00956053 0.0165593i −0.861206 0.508257i \(-0.830290\pi\)
0.870766 + 0.491697i \(0.163623\pi\)
\(420\) 0 0
\(421\) −9.59987 + 5.54249i −0.467869 + 0.270124i −0.715347 0.698769i \(-0.753731\pi\)
0.247478 + 0.968893i \(0.420398\pi\)
\(422\) 13.0713i 0.636301i
\(423\) 0 0
\(424\) 21.8732i 1.06226i
\(425\) 0.0659154 + 0.114169i 0.00319737 + 0.00553800i
\(426\) 0 0
\(427\) 38.7389 + 22.3659i 1.87470 + 1.08236i
\(428\) −4.76326 + 8.25021i −0.230241 + 0.398789i
\(429\) 0 0
\(430\) 0.914627 + 1.58418i 0.0441072 + 0.0763960i
\(431\) 36.4573i 1.75609i −0.478580 0.878044i \(-0.658848\pi\)
0.478580 0.878044i \(-0.341152\pi\)
\(432\) 0 0
\(433\) 8.82757 0.424226 0.212113 0.977245i \(-0.431966\pi\)
0.212113 + 0.977245i \(0.431966\pi\)
\(434\) −19.8268 + 11.4470i −0.951717 + 0.549474i
\(435\) 0 0
\(436\) 10.2203 + 5.90067i 0.489462 + 0.282591i
\(437\) −13.9344 8.04504i −0.666574 0.384847i
\(438\) 0 0
\(439\) 17.5672 + 30.4273i 0.838438 + 1.45222i 0.891200 + 0.453610i \(0.149864\pi\)
−0.0527626 + 0.998607i \(0.516803\pi\)
\(440\) 23.8774i 1.13831i
\(441\) 0 0
\(442\) 8.00352 11.1810i 0.380688 0.531826i
\(443\) 11.9526 + 20.7025i 0.567885 + 0.983606i 0.996775 + 0.0802490i \(0.0255715\pi\)
−0.428890 + 0.903357i \(0.641095\pi\)
\(444\) 0 0
\(445\) 6.45133 11.1740i 0.305822 0.529700i
\(446\) −4.98251 + 8.62997i −0.235929 + 0.408641i
\(447\) 0 0
\(448\) −16.3916 + 9.46370i −0.774431 + 0.447118i
\(449\) 13.9683i 0.659206i −0.944120 0.329603i \(-0.893085\pi\)
0.944120 0.329603i \(-0.106915\pi\)
\(450\) 0 0
\(451\) −29.2851 −1.37898
\(452\) 11.4654 + 19.8587i 0.539288 + 0.934075i
\(453\) 0 0
\(454\) −3.67590 + 6.36684i −0.172518 + 0.298811i
\(455\) −25.3065 + 11.4819i −1.18639 + 0.538278i
\(456\) 0 0
\(457\) −15.0872 + 8.71058i −0.705748 + 0.407464i −0.809485 0.587141i \(-0.800253\pi\)
0.103737 + 0.994605i \(0.466920\pi\)
\(458\) 4.87021 0.227570
\(459\) 0 0
\(460\) 10.0126i 0.466841i
\(461\) 20.6691 11.9333i 0.962658 0.555791i 0.0656678 0.997842i \(-0.479082\pi\)
0.896990 + 0.442051i \(0.145749\pi\)
\(462\) 0 0
\(463\) 9.12555 + 5.26864i 0.424100 + 0.244854i 0.696830 0.717236i \(-0.254593\pi\)
−0.272730 + 0.962091i \(0.587926\pi\)
\(464\) −0.295055 + 0.511049i −0.0136976 + 0.0237249i
\(465\) 0 0
\(466\) 15.7632 9.10090i 0.730217 0.421591i
\(467\) 8.40923 0.389133 0.194566 0.980889i \(-0.437670\pi\)
0.194566 + 0.980889i \(0.437670\pi\)
\(468\) 0 0
\(469\) −46.4227 −2.14360
\(470\) 9.75148 5.63002i 0.449802 0.259693i
\(471\) 0 0
\(472\) 7.38823 12.7968i 0.340071 0.589020i
\(473\) −2.88290 1.66444i −0.132556 0.0765310i
\(474\) 0 0
\(475\) −0.115302 + 0.0665694i −0.00529040 + 0.00305441i
\(476\) 17.0733i 0.782551i
\(477\) 0 0
\(478\) −12.8239 −0.586550
\(479\) −13.6025 + 7.85338i −0.621512 + 0.358830i −0.777457 0.628935i \(-0.783491\pi\)
0.155945 + 0.987766i \(0.450158\pi\)
\(480\) 0 0
\(481\) 8.19238 + 18.0563i 0.373540 + 0.823298i
\(482\) 13.7007 23.7303i 0.624050 1.08089i
\(483\) 0 0
\(484\) 1.57201 + 2.72280i 0.0714549 + 0.123764i
\(485\) 15.2188 0.691051
\(486\) 0 0
\(487\) 37.8948i 1.71718i −0.512666 0.858588i \(-0.671342\pi\)
0.512666 0.858588i \(-0.328658\pi\)
\(488\) 32.4659 18.7442i 1.46966 0.848509i
\(489\) 0 0
\(490\) −4.88210 + 8.45605i −0.220551 + 0.382005i
\(491\) −1.88027 + 3.25672i −0.0848553 + 0.146974i −0.905330 0.424710i \(-0.860376\pi\)
0.820474 + 0.571684i \(0.193709\pi\)
\(492\) 0 0
\(493\) 5.00903 + 8.67590i 0.225595 + 0.390743i
\(494\) 11.2919 + 8.08293i 0.508048 + 0.363668i
\(495\) 0 0
\(496\) 1.82505i 0.0819471i
\(497\) −4.56154 7.90082i −0.204613 0.354400i
\(498\) 0 0
\(499\) 7.15464 + 4.13073i 0.320286 + 0.184917i 0.651520 0.758632i \(-0.274132\pi\)
−0.331234 + 0.943549i \(0.607465\pi\)
\(500\) 11.3882 + 6.57500i 0.509298 + 0.294043i
\(501\) 0 0
\(502\) −13.7314 + 7.92780i −0.612860 + 0.353835i
\(503\) 12.9954 0.579434 0.289717 0.957112i \(-0.406439\pi\)
0.289717 + 0.957112i \(0.406439\pi\)
\(504\) 0 0
\(505\) 11.1307i 0.495312i
\(506\) −6.33241 10.9680i −0.281510 0.487589i
\(507\) 0 0
\(508\) 1.04074 1.80262i 0.0461754 0.0799782i
\(509\) 23.2712 + 13.4356i 1.03148 + 0.595524i 0.917408 0.397949i \(-0.130278\pi\)
0.114070 + 0.993473i \(0.463611\pi\)
\(510\) 0 0
\(511\) −9.37613 16.2399i −0.414776 0.718413i
\(512\) 2.80162i 0.123815i
\(513\) 0 0
\(514\) 16.5762i 0.731146i
\(515\) −4.10213 + 2.36837i −0.180761 + 0.104363i
\(516\) 0 0
\(517\) −10.2455 + 17.7458i −0.450597 + 0.780458i
\(518\) 14.8197 + 8.55614i 0.651139 + 0.375935i
\(519\) 0 0
\(520\) −2.27089 + 23.1785i −0.0995851 + 1.01644i
\(521\) −14.2080 −0.622464 −0.311232 0.950334i \(-0.600742\pi\)
−0.311232 + 0.950334i \(0.600742\pi\)
\(522\) 0 0
\(523\) 7.07846 0.309519 0.154760 0.987952i \(-0.450540\pi\)
0.154760 + 0.987952i \(0.450540\pi\)
\(524\) −4.20620 7.28536i −0.183749 0.318262i
\(525\) 0 0
\(526\) 6.58255 + 3.80044i 0.287013 + 0.165707i
\(527\) 26.8322 + 15.4916i 1.16883 + 0.674824i
\(528\) 0 0
\(529\) 4.34352 + 7.52320i 0.188849 + 0.327096i
\(530\) 15.4291 0.670198
\(531\) 0 0
\(532\) −17.2427 −0.747564
\(533\) 28.4279 + 2.78519i 1.23135 + 0.120640i
\(534\) 0 0
\(535\) 15.6842 + 9.05527i 0.678086 + 0.391493i
\(536\) −19.4527 + 33.6931i −0.840229 + 1.45532i
\(537\) 0 0
\(538\) 16.7236 9.65540i 0.721007 0.416274i
\(539\) 17.7689i 0.765362i
\(540\) 0 0
\(541\) 7.18897i 0.309078i 0.987987 + 0.154539i \(0.0493892\pi\)
−0.987987 + 0.154539i \(0.950611\pi\)
\(542\) 8.35807 + 14.4766i 0.359010 + 0.621823i
\(543\) 0 0
\(544\) 20.1853 + 11.6540i 0.865438 + 0.499661i
\(545\) 11.2176 19.4294i 0.480508 0.832264i
\(546\) 0 0
\(547\) 15.8887 + 27.5201i 0.679353 + 1.17667i 0.975176 + 0.221431i \(0.0710729\pi\)
−0.295823 + 0.955243i \(0.595594\pi\)
\(548\) 5.33381i 0.227849i
\(549\) 0 0
\(550\) −0.104796 −0.00446852
\(551\) −8.76198 + 5.05873i −0.373273 + 0.215509i
\(552\) 0 0
\(553\) −32.5480 18.7916i −1.38408 0.799100i
\(554\) −6.76652 3.90665i −0.287482 0.165978i
\(555\) 0 0
\(556\) −8.32411 14.4178i −0.353021 0.611450i
\(557\) 32.2223i 1.36530i 0.730745 + 0.682650i \(0.239173\pi\)
−0.730745 + 0.682650i \(0.760827\pi\)
\(558\) 0 0
\(559\) 2.64021 + 1.88990i 0.111669 + 0.0799343i
\(560\) 0.955943 + 1.65574i 0.0403960 + 0.0699679i
\(561\) 0 0
\(562\) 1.57339 2.72519i 0.0663694 0.114955i
\(563\) −16.8257 + 29.1430i −0.709119 + 1.22823i 0.256065 + 0.966659i \(0.417574\pi\)
−0.965184 + 0.261571i \(0.915760\pi\)
\(564\) 0 0
\(565\) 37.7527 21.7965i 1.58827 0.916987i
\(566\) 12.4824i 0.524672i
\(567\) 0 0
\(568\) −7.64578 −0.320810
\(569\) −5.66793 9.81715i −0.237612 0.411556i 0.722416 0.691458i \(-0.243031\pi\)
−0.960029 + 0.279902i \(0.909698\pi\)
\(570\) 0 0
\(571\) 0.127260 0.220421i 0.00532568 0.00922435i −0.863350 0.504605i \(-0.831638\pi\)
0.868676 + 0.495381i \(0.164971\pi\)
\(572\) −6.49751 14.3208i −0.271675 0.598782i
\(573\) 0 0
\(574\) 21.3491 12.3259i 0.891095 0.514474i
\(575\) −0.118434 −0.00493903
\(576\) 0 0
\(577\) 1.91400i 0.0796807i −0.999206 0.0398403i \(-0.987315\pi\)
0.999206 0.0398403i \(-0.0126849\pi\)
\(578\) −0.575812 + 0.332445i −0.0239506 + 0.0138279i
\(579\) 0 0
\(580\) −5.45246 3.14798i −0.226401 0.130713i
\(581\) 0.923571 1.59967i 0.0383162 0.0663656i
\(582\) 0 0
\(583\) −24.3162 + 14.0390i −1.00707 + 0.581435i
\(584\) −15.7157 −0.650321
\(585\) 0 0
\(586\) 25.8193 1.06659
\(587\) −7.69412 + 4.44220i −0.317570 + 0.183349i −0.650309 0.759670i \(-0.725361\pi\)
0.332739 + 0.943019i \(0.392027\pi\)
\(588\) 0 0
\(589\) −15.6453 + 27.0984i −0.644653 + 1.11657i
\(590\) −9.02670 5.21156i −0.371623 0.214557i
\(591\) 0 0
\(592\) 1.18138 0.682072i 0.0485545 0.0280330i
\(593\) 43.1136i 1.77046i −0.465152 0.885231i \(-0.654000\pi\)
0.465152 0.885231i \(-0.346000\pi\)
\(594\) 0 0
\(595\) 32.4574 1.33062
\(596\) 5.92896 3.42309i 0.242860 0.140215i
\(597\) 0 0
\(598\) 5.10392 + 11.2493i 0.208715 + 0.460016i
\(599\) −5.59868 + 9.69720i −0.228756 + 0.396217i −0.957440 0.288634i \(-0.906799\pi\)
0.728684 + 0.684850i \(0.240132\pi\)
\(600\) 0 0
\(601\) −2.96273 5.13159i −0.120852 0.209322i 0.799252 0.600996i \(-0.205229\pi\)
−0.920104 + 0.391674i \(0.871896\pi\)
\(602\) 2.80221 0.114210
\(603\) 0 0
\(604\) 11.4991i 0.467892i
\(605\) 5.17622 2.98849i 0.210443 0.121499i
\(606\) 0 0
\(607\) −2.53470 + 4.39022i −0.102880 + 0.178194i −0.912870 0.408250i \(-0.866139\pi\)
0.809990 + 0.586444i \(0.199472\pi\)
\(608\) −11.7696 + 20.3856i −0.477321 + 0.826745i
\(609\) 0 0
\(610\) −13.2219 22.9010i −0.535339 0.927235i
\(611\) 11.6334 16.2519i 0.470635 0.657482i
\(612\) 0 0
\(613\) 24.6393i 0.995173i 0.867414 + 0.497587i \(0.165780\pi\)
−0.867414 + 0.497587i \(0.834220\pi\)
\(614\) −9.87719 17.1078i −0.398611 0.690414i
\(615\) 0 0
\(616\) −31.6771 18.2888i −1.27630 0.736875i
\(617\) −38.0933 21.9932i −1.53358 0.885413i −0.999193 0.0401727i \(-0.987209\pi\)
−0.534387 0.845240i \(-0.679457\pi\)
\(618\) 0 0
\(619\) 17.7979 10.2756i 0.715358 0.413012i −0.0976839 0.995217i \(-0.531143\pi\)
0.813042 + 0.582206i \(0.197810\pi\)
\(620\) −19.4717 −0.782002
\(621\) 0 0
\(622\) 6.30587i 0.252842i
\(623\) −9.88272 17.1174i −0.395943 0.685793i
\(624\) 0 0
\(625\) 12.5778 21.7853i 0.503111 0.871414i
\(626\) 17.6073 + 10.1656i 0.703730 + 0.406299i
\(627\) 0 0
\(628\) 0.636905 + 1.10315i 0.0254153 + 0.0440205i
\(629\) 23.1586i 0.923392i
\(630\) 0 0
\(631\) 25.1460i 1.00105i 0.865723 + 0.500523i \(0.166859\pi\)
−0.865723 + 0.500523i \(0.833141\pi\)
\(632\) −27.2775 + 15.7487i −1.08504 + 0.626449i
\(633\) 0 0
\(634\) −4.62582 + 8.01216i −0.183715 + 0.318204i
\(635\) −3.42689 1.97852i −0.135992 0.0785151i
\(636\) 0 0
\(637\) −1.68994 + 17.2488i −0.0669577 + 0.683422i
\(638\) −7.96365 −0.315284
\(639\) 0 0
\(640\) −13.6404 −0.539183
\(641\) −16.6711 28.8751i −0.658467 1.14050i −0.981012 0.193945i \(-0.937872\pi\)
0.322545 0.946554i \(-0.395462\pi\)
\(642\) 0 0
\(643\) −27.1759 15.6900i −1.07171 0.618754i −0.143065 0.989713i \(-0.545696\pi\)
−0.928649 + 0.370959i \(0.879029\pi\)
\(644\) −13.2833 7.66911i −0.523435 0.302205i
\(645\) 0 0
\(646\) −8.10969 14.0464i −0.319072 0.552648i
\(647\) 47.5495 1.86936 0.934681 0.355486i \(-0.115685\pi\)
0.934681 + 0.355486i \(0.115685\pi\)
\(648\) 0 0
\(649\) 18.9680 0.744561
\(650\) 0.101729 + 0.00996676i 0.00399012 + 0.000390929i
\(651\) 0 0
\(652\) −5.66964 3.27337i −0.222040 0.128195i
\(653\) −13.8728 + 24.0284i −0.542884 + 0.940302i 0.455853 + 0.890055i \(0.349334\pi\)
−0.998737 + 0.0502473i \(0.983999\pi\)
\(654\) 0 0
\(655\) −13.8499 + 7.99627i −0.541162 + 0.312440i
\(656\) 1.96518i 0.0767273i
\(657\) 0 0
\(658\) 17.2491i 0.672440i
\(659\) 7.80940 + 13.5263i 0.304211 + 0.526909i 0.977085 0.212848i \(-0.0682738\pi\)
−0.672874 + 0.739757i \(0.734940\pi\)
\(660\) 0 0
\(661\) 15.5161 + 8.95822i 0.603506 + 0.348434i 0.770420 0.637537i \(-0.220047\pi\)
−0.166914 + 0.985972i \(0.553380\pi\)
\(662\) 2.44585 4.23633i 0.0950605 0.164650i
\(663\) 0 0
\(664\) −0.774017 1.34064i −0.0300377 0.0520268i
\(665\) 32.7794i 1.27113i
\(666\) 0 0
\(667\) −9.00000 −0.348481
\(668\) 13.6295 7.86901i 0.527342 0.304461i
\(669\) 0 0
\(670\) 23.7667 + 13.7217i 0.918187 + 0.530115i
\(671\) 41.6753 + 24.0613i 1.60886 + 0.928875i
\(672\) 0 0
\(673\) 2.94960 + 5.10885i 0.113699 + 0.196932i 0.917259 0.398292i \(-0.130397\pi\)
−0.803560 + 0.595224i \(0.797064\pi\)
\(674\) 29.8161i 1.14847i
\(675\) 0 0
\(676\) 4.94532 + 14.5196i 0.190205 + 0.558444i
\(677\) 13.7045 + 23.7369i 0.526707 + 0.912283i 0.999516 + 0.0311180i \(0.00990678\pi\)
−0.472809 + 0.881165i \(0.656760\pi\)
\(678\) 0 0
\(679\) 11.6568 20.1901i 0.447345 0.774825i
\(680\) 13.6008 23.5572i 0.521566 0.903379i
\(681\) 0 0
\(682\) −21.3297 + 12.3147i −0.816757 + 0.471555i
\(683\) 16.0989i 0.616006i −0.951385 0.308003i \(-0.900339\pi\)
0.951385 0.308003i \(-0.0996607\pi\)
\(684\) 0 0
\(685\) 10.1399 0.387427
\(686\) −3.41223 5.91015i −0.130279 0.225651i
\(687\) 0 0
\(688\) 0.111692 0.193457i 0.00425823 0.00737547i
\(689\) 24.9396 11.3154i 0.950124 0.431083i
\(690\) 0 0
\(691\) 23.9736 13.8412i 0.912000 0.526543i 0.0309256 0.999522i \(-0.490155\pi\)
0.881074 + 0.472979i \(0.156821\pi\)
\(692\) −8.78030 −0.333777
\(693\) 0 0
\(694\) 12.3413i 0.468469i
\(695\) −27.4091 + 15.8247i −1.03969 + 0.600264i
\(696\) 0 0
\(697\) −28.8924 16.6810i −1.09438 0.631839i
\(698\) 5.10514 8.84236i 0.193232 0.334688i
\(699\) 0 0
\(700\) −0.109914 + 0.0634588i −0.00415435 + 0.00239852i
\(701\) 10.0776 0.380624 0.190312 0.981724i \(-0.439050\pi\)
0.190312 + 0.981724i \(0.439050\pi\)
\(702\) 0 0
\(703\) 23.3883 0.882108
\(704\) −17.6341 + 10.1811i −0.664611 + 0.383713i
\(705\) 0 0
\(706\) 12.0584 20.8857i 0.453822 0.786043i
\(707\) −14.7666 8.52553i −0.555357 0.320635i
\(708\) 0 0
\(709\) 2.79484 1.61360i 0.104962 0.0606000i −0.446600 0.894734i \(-0.647365\pi\)
0.551562 + 0.834134i \(0.314032\pi\)
\(710\) 5.39324i 0.202405i
\(711\) 0 0
\(712\) −16.5648 −0.620793
\(713\) −24.1055 + 13.9173i −0.902756 + 0.521207i
\(714\) 0 0
\(715\) −27.2248 + 12.3522i −1.01815 + 0.461946i
\(716\) 13.6896 23.7110i 0.511604 0.886123i
\(717\) 0 0
\(718\) −15.8043 27.3738i −0.589811 1.02158i
\(719\) 30.0712 1.12147 0.560733 0.827996i \(-0.310519\pi\)
0.560733 + 0.827996i \(0.310519\pi\)
\(720\) 0 0
\(721\) 7.25614i 0.270233i
\(722\) −0.715357 + 0.413012i −0.0266228 + 0.0153707i
\(723\) 0 0
\(724\) −3.05852 + 5.29751i −0.113669 + 0.196880i
\(725\) −0.0372356 + 0.0644940i −0.00138290 + 0.00239525i
\(726\) 0 0
\(727\) 9.68860 + 16.7811i 0.359330 + 0.622378i 0.987849 0.155416i \(-0.0496719\pi\)
−0.628519 + 0.777794i \(0.716339\pi\)
\(728\) 29.0105 + 20.7661i 1.07520 + 0.769643i
\(729\) 0 0
\(730\) 11.0857i 0.410299i
\(731\) −1.89616 3.28424i −0.0701320 0.121472i
\(732\) 0 0
\(733\) 21.1938 + 12.2362i 0.782810 + 0.451955i 0.837425 0.546552i \(-0.184060\pi\)
−0.0546155 + 0.998507i \(0.517393\pi\)
\(734\) −2.12877 1.22904i −0.0785742 0.0453648i
\(735\) 0 0
\(736\) −18.1340 + 10.4697i −0.668429 + 0.385918i
\(737\) −49.9416 −1.83962
\(738\) 0 0
\(739\) 3.30687i 0.121645i −0.998149 0.0608226i \(-0.980628\pi\)
0.998149 0.0608226i \(-0.0193724\pi\)
\(740\) 7.27712 + 12.6043i 0.267512 + 0.463344i
\(741\) 0 0
\(742\) 11.8178 20.4691i 0.433846 0.751444i
\(743\) −15.1394 8.74076i −0.555412 0.320667i 0.195890 0.980626i \(-0.437240\pi\)
−0.751302 + 0.659959i \(0.770574\pi\)
\(744\) 0 0
\(745\) −6.50751 11.2713i −0.238417 0.412950i
\(746\) 1.58566i 0.0580553i
\(747\) 0 0
\(748\) 18.3674i 0.671580i
\(749\) 24.0264 13.8717i 0.877906 0.506859i
\(750\) 0 0
\(751\) 14.2922 24.7548i 0.521528 0.903314i −0.478158 0.878274i \(-0.658695\pi\)
0.999686 0.0250400i \(-0.00797130\pi\)
\(752\) −1.19083 0.687526i −0.0434251 0.0250715i
\(753\) 0 0
\(754\) 7.73054 + 0.757392i 0.281530 + 0.0275826i
\(755\) −21.8606 −0.795587
\(756\) 0 0
\(757\) 11.9611 0.434733 0.217367 0.976090i \(-0.430253\pi\)
0.217367 + 0.976090i \(0.430253\pi\)
\(758\) −1.31737 2.28176i −0.0478492 0.0828772i
\(759\) 0 0
\(760\) 23.7910 + 13.7357i 0.862989 + 0.498247i
\(761\) −1.84327 1.06421i −0.0668185 0.0385777i 0.466219 0.884670i \(-0.345616\pi\)
−0.533037 + 0.846092i \(0.678949\pi\)
\(762\) 0 0
\(763\) −17.1841 29.7637i −0.622105 1.07752i
\(764\) −19.0449 −0.689019
\(765\) 0 0
\(766\) −18.5156 −0.668994
\(767\) −18.4128 1.80398i −0.664848 0.0651379i
\(768\) 0 0
\(769\) −6.62584 3.82543i −0.238934 0.137949i 0.375753 0.926720i \(-0.377384\pi\)
−0.614687 + 0.788771i \(0.710718\pi\)
\(770\) −12.9007 + 22.3446i −0.464907 + 0.805243i
\(771\) 0 0
\(772\) −3.35080 + 1.93458i −0.120598 + 0.0696272i
\(773\) 24.6440i 0.886383i 0.896427 + 0.443191i \(0.146154\pi\)
−0.896427 + 0.443191i \(0.853846\pi\)
\(774\) 0 0
\(775\) 0.230320i 0.00827333i
\(776\) −9.76918 16.9207i −0.350693 0.607418i
\(777\) 0 0
\(778\) −10.1667 5.86972i −0.364492 0.210440i
\(779\) 16.8465 29.1791i 0.603590 1.04545i
\(780\) 0 0
\(781\) −4.90731 8.49972i −0.175598 0.304144i
\(782\) 14.4280i 0.515943i
\(783\) 0 0
\(784\) 1.19238 0.0425851
\(785\) 2.09716 1.21080i 0.0748509 0.0432152i
\(786\) 0 0
\(787\) −36.2586 20.9339i −1.29248 0.746214i −0.313388 0.949625i \(-0.601464\pi\)
−0.979093 + 0.203411i \(0.934797\pi\)
\(788\) −7.26768 4.19599i −0.258900 0.149476i
\(789\) 0 0
\(790\) 11.1089 + 19.2412i 0.395237 + 0.684571i
\(791\) 66.7797i 2.37441i
\(792\) 0 0
\(793\) −38.1671 27.3205i −1.35535 0.970181i
\(794\) 13.2131 + 22.8857i 0.468914 + 0.812183i
\(795\) 0 0
\(796\) 8.16775 14.1470i 0.289498 0.501426i
\(797\) −20.8781 + 36.1620i −0.739541 + 1.28092i 0.213161 + 0.977017i \(0.431624\pi\)
−0.952702 + 0.303906i \(0.901709\pi\)
\(798\) 0 0
\(799\) −20.2163 + 11.6719i −0.715200 + 0.412921i
\(800\) 0.173265i 0.00612583i
\(801\) 0 0
\(802\) −20.0792 −0.709022
\(803\) −10.0869 17.4709i −0.355957 0.616536i
\(804\) 0 0
\(805\) −14.5795 + 25.2524i −0.513859 + 0.890030i
\(806\) 21.8766 9.92565i 0.770569 0.349616i
\(807\) 0 0
\(808\) −12.3755 + 7.14499i −0.435368 + 0.251360i
\(809\) −45.2476 −1.59082 −0.795410 0.606072i \(-0.792744\pi\)
−0.795410 + 0.606072i \(0.792744\pi\)
\(810\) 0 0
\(811\) 52.8820i 1.85694i −0.371410 0.928469i \(-0.621126\pi\)
0.371410 0.928469i \(-0.378874\pi\)
\(812\) −8.35255 + 4.82235i −0.293117 + 0.169231i
\(813\) 0 0
\(814\) 15.9430 + 9.20470i 0.558802 + 0.322625i
\(815\) −6.22288 + 10.7784i −0.217978 + 0.377549i
\(816\) 0 0
\(817\) 3.31683 1.91497i 0.116041 0.0669964i
\(818\) −1.90053 −0.0664505
\(819\) 0 0
\(820\) 20.9667 0.732190
\(821\) 29.8105 17.2111i 1.04039 0.600671i 0.120449 0.992720i \(-0.461567\pi\)
0.919945 + 0.392048i \(0.128233\pi\)
\(822\) 0 0
\(823\) 5.99853 10.3898i 0.209096 0.362164i −0.742334 0.670030i \(-0.766281\pi\)
0.951430 + 0.307866i \(0.0996147\pi\)
\(824\) 5.26644 + 3.04058i 0.183465 + 0.105924i
\(825\) 0 0
\(826\) −13.8279 + 7.98353i −0.481134 + 0.277783i
\(827\) 4.35092i 0.151296i 0.997135 + 0.0756482i \(0.0241026\pi\)
−0.997135 + 0.0756482i \(0.975897\pi\)
\(828\) 0 0
\(829\) 45.6204 1.58446 0.792230 0.610222i \(-0.208920\pi\)
0.792230 + 0.610222i \(0.208920\pi\)
\(830\) −0.945668 + 0.545982i −0.0328246 + 0.0189513i
\(831\) 0 0
\(832\) 18.0862 8.20594i 0.627027 0.284490i
\(833\) 10.1213 17.5307i 0.350683 0.607401i
\(834\) 0 0
\(835\) −14.9595 25.9106i −0.517695 0.896674i
\(836\) −18.5497 −0.641554
\(837\) 0 0
\(838\) 0.354449i 0.0122442i
\(839\) −21.3626 + 12.3337i −0.737520 + 0.425808i −0.821167 0.570688i \(-0.806677\pi\)
0.0836466 + 0.996495i \(0.473343\pi\)
\(840\) 0 0
\(841\) 11.6704 20.2137i 0.402427 0.697025i
\(842\) 5.01926 8.69361i 0.172975 0.299602i
\(843\) 0 0
\(844\) −8.51525 14.7488i −0.293107 0.507676i
\(845\) 27.6026 9.40138i 0.949559 0.323417i
\(846\) 0 0
\(847\) 9.15606i 0.314606i
\(848\) −0.942085 1.63174i −0.0323513 0.0560341i
\(849\) 0 0
\(850\) −0.103391 0.0596928i −0.00354628 0.00204744i
\(851\) 18.0178 + 10.4026i 0.617641 + 0.356595i
\(852\) 0 0
\(853\) 22.9668 13.2599i 0.786369 0.454010i −0.0523138 0.998631i \(-0.516660\pi\)
0.838683 + 0.544620i \(0.183326\pi\)
\(854\) −40.5089 −1.38619
\(855\) 0 0
\(856\) 23.2508i 0.794697i
\(857\) −3.20474 5.55077i −0.109472 0.189611i 0.806085 0.591800i \(-0.201583\pi\)
−0.915556 + 0.402190i \(0.868249\pi\)
\(858\) 0 0
\(859\) −12.7998 + 22.1699i −0.436723 + 0.756427i −0.997435 0.0715846i \(-0.977194\pi\)
0.560711 + 0.828011i \(0.310528\pi\)
\(860\) 2.06402 + 1.19166i 0.0703824 + 0.0406353i
\(861\) 0 0
\(862\) 16.5078 + 28.5924i 0.562258 + 0.973860i
\(863\) 48.4823i 1.65036i 0.564873 + 0.825178i \(0.308925\pi\)
−0.564873 + 0.825178i \(0.691075\pi\)
\(864\) 0 0
\(865\) 16.6919i 0.567542i
\(866\) −6.92319 + 3.99711i −0.235260 + 0.135827i
\(867\) 0 0
\(868\) −14.9142 + 25.8322i −0.506222 + 0.876802i
\(869\) −35.0152 20.2160i −1.18781 0.685782i
\(870\) 0 0
\(871\) 48.4797 + 4.74975i 1.64267 + 0.160939i
\(872\) −28.8029 −0.975389
\(873\) 0 0
\(874\) 14.5711 0.492876
\(875\) −19.1478 33.1650i −0.647315 1.12118i
\(876\) 0 0
\(877\) 27.0023 + 15.5898i 0.911801 + 0.526429i 0.881010 0.473097i \(-0.156864\pi\)
0.0307911 + 0.999526i \(0.490197\pi\)
\(878\) −27.5549 15.9088i −0.929932 0.536897i
\(879\) 0 0
\(880\) 1.02840 + 1.78125i 0.0346675 + 0.0600459i
\(881\) 49.6614 1.67314 0.836568 0.547863i \(-0.184558\pi\)
0.836568 + 0.547863i \(0.184558\pi\)
\(882\) 0 0
\(883\) 30.3523 1.02144 0.510718 0.859748i \(-0.329380\pi\)
0.510718 + 0.859748i \(0.329380\pi\)
\(884\) 1.74686 17.8298i 0.0587532 0.599681i
\(885\) 0 0
\(886\) −18.7481 10.8242i −0.629855 0.363647i
\(887\) 6.42161 11.1226i 0.215616 0.373459i −0.737847 0.674968i \(-0.764157\pi\)
0.953463 + 0.301510i \(0.0974906\pi\)
\(888\) 0 0
\(889\) −5.24962 + 3.03087i −0.176066 + 0.101652i
\(890\) 11.6846i 0.391669i
\(891\) 0 0
\(892\) 12.9834i 0.434715i
\(893\) −11.7877 20.4169i −0.394460 0.683224i
\(894\) 0 0
\(895\) −45.0762 26.0248i −1.50673 0.869912i
\(896\) −10.4478 + 18.0961i −0.349035 + 0.604547i
\(897\) 0 0
\(898\) 6.32484 + 10.9549i 0.211063 + 0.365571i
\(899\) 17.5024i 0.583738i
\(900\) 0 0
\(901\) −31.9869 −1.06564
\(902\) 22.9674 13.2602i 0.764731 0.441518i
\(903\) 0 0
\(904\) −48.4680 27.9830i −1.61202 0.930701i
\(905\) 10.0709 + 5.81444i 0.334768 + 0.193279i
\(906\) 0 0
\(907\) 10.2993 + 17.8389i 0.341983 + 0.592331i 0.984801 0.173688i \(-0.0555683\pi\)
−0.642818 + 0.766019i \(0.722235\pi\)
\(908\) 9.57860i 0.317877i
\(909\) 0 0
\(910\) 14.6481 20.4636i 0.485581 0.678362i
\(911\) 21.1949 + 36.7107i 0.702219 + 1.21628i 0.967686 + 0.252159i \(0.0811407\pi\)
−0.265466 + 0.964120i \(0.585526\pi\)
\(912\) 0 0
\(913\) 0.993579 1.72093i 0.0328827 0.0569545i
\(914\) 7.88827 13.6629i 0.260921 0.451928i
\(915\) 0 0
\(916\) 5.49524 3.17268i 0.181568 0.104828i
\(917\) 24.4988i 0.809021i
\(918\) 0 0
\(919\) −42.7987 −1.41180 −0.705899 0.708313i \(-0.749457\pi\)
−0.705899 + 0.708313i \(0.749457\pi\)
\(920\) 12.2186 + 21.1633i 0.402836 + 0.697733i
\(921\) 0 0
\(922\) −10.8068 + 18.7179i −0.355903 + 0.616441i
\(923\) 3.95529 + 8.71764i 0.130190 + 0.286944i
\(924\) 0 0
\(925\) 0.149090 0.0860769i 0.00490203 0.00283019i
\(926\) −9.54253 −0.313587
\(927\) 0 0
\(928\) 13.1667i 0.432218i
\(929\) 10.2242 5.90296i 0.335446 0.193670i −0.322810 0.946464i \(-0.604628\pi\)
0.658257 + 0.752794i \(0.271294\pi\)
\(930\) 0 0
\(931\) 17.7046 + 10.2218i 0.580245 + 0.335004i
\(932\) 11.8575 20.5378i 0.388405 0.672738i
\(933\) 0 0
\(934\) −6.59511 + 3.80769i −0.215799 + 0.124591i
\(935\) 34.9177 1.14193
\(936\) 0 0
\(937\) 24.7925 0.809935 0.404967 0.914331i \(-0.367283\pi\)
0.404967 + 0.914331i \(0.367283\pi\)
\(938\) 36.4079 21.0201i 1.18876 0.686331i
\(939\) 0 0
\(940\) 7.33531 12.7051i 0.239251 0.414395i
\(941\) 20.6367 + 11.9146i 0.672737 + 0.388405i 0.797113 0.603830i \(-0.206360\pi\)
−0.124376 + 0.992235i \(0.539693\pi\)
\(942\) 0 0
\(943\) 25.9563 14.9859i 0.845253 0.488007i
\(944\) 1.27285i 0.0414278i
\(945\) 0 0
\(946\) 3.01462 0.0980138
\(947\) 42.4532 24.5104i 1.37954 0.796480i 0.387440 0.921895i \(-0.373359\pi\)
0.992104 + 0.125415i \(0.0400261\pi\)
\(948\) 0 0
\(949\) 8.13001 + 17.9189i 0.263911 + 0.581671i
\(950\) 0.0602850 0.104417i 0.00195590 0.00338773i
\(951\) 0 0
\(952\) −20.8349 36.0870i −0.675262 1.16959i
\(953\) −7.78372 −0.252140 −0.126070 0.992021i \(-0.540236\pi\)
−0.126070 + 0.992021i \(0.540236\pi\)
\(954\) 0 0
\(955\) 36.2055i 1.17158i
\(956\) −14.4697 + 8.35406i −0.467982 + 0.270190i
\(957\) 0 0
\(958\) 7.11200 12.3183i 0.229778 0.397987i
\(959\) 7.76661 13.4522i 0.250797 0.434393i
\(960\) 0 0
\(961\) 11.5651 + 20.0314i 0.373069 + 0.646174i
\(962\) −14.6009 10.4515i −0.470752 0.336971i
\(963\) 0 0
\(964\) 35.7011i 1.14985i
\(965\) 3.67777 + 6.37008i 0.118392 + 0.205060i
\(966\) 0 0
\(967\) 32.5591 + 18.7980i 1.04703 + 0.604502i 0.921816 0.387627i \(-0.126705\pi\)
0.125213 + 0.992130i \(0.460039\pi\)
\(968\) −6.64538 3.83671i −0.213590 0.123317i
\(969\) 0 0
\(970\) −11.9357 + 6.89105i −0.383231 + 0.221258i
\(971\) 9.16512 0.294123 0.147061 0.989127i \(-0.453019\pi\)
0.147061 + 0.989127i \(0.453019\pi\)
\(972\) 0 0
\(973\) 48.4833i 1.55430i
\(974\) 17.1587 + 29.7197i 0.549800 + 0.952281i
\(975\) 0 0
\(976\) −1.61463 + 2.79662i −0.0516831 + 0.0895177i
\(977\) −41.0043 23.6739i −1.31184 0.757394i −0.329443 0.944176i \(-0.606861\pi\)
−0.982401 + 0.186782i \(0.940194\pi\)
\(978\) 0 0
\(979\) −10.6318 18.4149i −0.339795 0.588542i
\(980\) 12.7217i 0.406380i
\(981\) 0 0
\(982\) 3.40553i 0.108675i
\(983\) 14.0634 8.11949i 0.448552 0.258972i −0.258666 0.965967i \(-0.583283\pi\)
0.707219 + 0.706995i \(0.249950\pi\)
\(984\) 0 0
\(985\) −7.97686 + 13.8163i −0.254164 + 0.440225i
\(986\) −7.85686 4.53616i −0.250213 0.144461i
\(987\) 0 0
\(988\) 18.0067 + 1.76419i 0.572870 + 0.0561263i
\(989\) 3.40693 0.108334
\(990\) 0 0
\(991\) −37.7634 −1.19959 −0.599797 0.800152i \(-0.704752\pi\)
−0.599797 + 0.800152i \(0.704752\pi\)
\(992\) 20.3605 + 35.2655i 0.646447 + 1.11968i
\(993\) 0 0
\(994\) 7.15496 + 4.13092i 0.226942 + 0.131025i
\(995\) −26.8943 15.5274i −0.852606 0.492252i
\(996\) 0 0
\(997\) −23.8283 41.2718i −0.754649 1.30709i −0.945549 0.325481i \(-0.894474\pi\)
0.190899 0.981610i \(-0.438860\pi\)
\(998\) −7.48156 −0.236824
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 351.2.t.c.64.5 20
3.2 odd 2 117.2.t.c.103.6 yes 20
9.2 odd 6 117.2.t.c.25.5 20
9.4 even 3 1053.2.b.i.649.5 10
9.5 odd 6 1053.2.b.j.649.6 10
9.7 even 3 inner 351.2.t.c.181.6 20
13.12 even 2 inner 351.2.t.c.64.6 20
39.38 odd 2 117.2.t.c.103.5 yes 20
117.25 even 6 inner 351.2.t.c.181.5 20
117.38 odd 6 117.2.t.c.25.6 yes 20
117.77 odd 6 1053.2.b.j.649.5 10
117.103 even 6 1053.2.b.i.649.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.t.c.25.5 20 9.2 odd 6
117.2.t.c.25.6 yes 20 117.38 odd 6
117.2.t.c.103.5 yes 20 39.38 odd 2
117.2.t.c.103.6 yes 20 3.2 odd 2
351.2.t.c.64.5 20 1.1 even 1 trivial
351.2.t.c.64.6 20 13.12 even 2 inner
351.2.t.c.181.5 20 117.25 even 6 inner
351.2.t.c.181.6 20 9.7 even 3 inner
1053.2.b.i.649.5 10 9.4 even 3
1053.2.b.i.649.6 10 117.103 even 6
1053.2.b.j.649.5 10 117.77 odd 6
1053.2.b.j.649.6 10 9.5 odd 6