Properties

Label 351.2.t.c.181.6
Level $351$
Weight $2$
Character 351.181
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 181.6
Root \(-0.219737 + 1.71806i\) of defining polynomial
Character \(\chi\) \(=\) 351.181
Dual form 351.2.t.c.64.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.784270 + 0.452798i) q^{2} +(-0.589947 - 1.02182i) q^{4} +(-1.94254 + 1.12153i) q^{5} +(-2.97576 - 1.71806i) q^{7} -2.87970i q^{8} -2.03130 q^{10} +(-3.20133 - 1.84829i) q^{11} +(0.351567 - 3.58837i) q^{13} +(-1.55587 - 2.69484i) q^{14} +(0.124029 - 0.214825i) q^{16} +4.21120 q^{17} +4.25298i q^{19} +(2.29200 + 1.32329i) q^{20} +(-1.67380 - 2.89911i) q^{22} +(-1.89162 - 3.27639i) q^{23} +(0.0156524 - 0.0271108i) q^{25} +(1.90053 - 2.65506i) q^{26} +4.05425i q^{28} +(1.18945 - 2.06020i) q^{29} +(-6.37163 + 3.67866i) q^{31} +(-4.79325 + 2.76738i) q^{32} +(3.30272 + 1.90682i) q^{34} +7.70739 q^{35} -5.49928i q^{37} +(-1.92574 + 3.33549i) q^{38} +(3.22967 + 5.59395i) q^{40} +(6.86085 - 3.96111i) q^{41} +(-0.450266 + 0.779883i) q^{43} +4.36157i q^{44} -3.42609i q^{46} +(4.80060 + 2.77163i) q^{47} +(2.40343 + 4.16287i) q^{49} +(0.0245514 - 0.0141748i) q^{50} +(-3.87407 + 1.75771i) q^{52} -7.59566 q^{53} +8.29163 q^{55} +(-4.94749 + 8.56930i) q^{56} +(1.86571 - 1.07717i) q^{58} +(-4.44379 + 2.56562i) q^{59} +(6.50907 - 11.2740i) q^{61} -6.66277 q^{62} -5.50838 q^{64} +(3.34152 + 7.36486i) q^{65} +(11.7002 - 6.75511i) q^{67} +(-2.48439 - 4.30308i) q^{68} +(6.04468 + 3.48989i) q^{70} -2.65506i q^{71} -5.45741i q^{73} +(2.49006 - 4.31292i) q^{74} +(4.34578 - 2.50904i) q^{76} +(6.35092 + 11.0001i) q^{77} +(-5.46886 + 9.47234i) q^{79} +0.556410i q^{80} +7.17434 q^{82} +(-0.465547 - 0.268784i) q^{83} +(-8.18044 + 4.72298i) q^{85} +(-0.706259 + 0.407759i) q^{86} +(-5.32252 + 9.21887i) q^{88} -5.75227i q^{89} +(-7.21120 + 10.0741i) q^{91} +(-2.23192 + 3.86579i) q^{92} +(2.50998 + 4.34740i) q^{94} +(-4.76984 - 8.26161i) q^{95} +(-5.87585 - 3.39243i) q^{97} +4.35308i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(28\) \(326\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.784270 + 0.452798i 0.554562 + 0.320177i 0.750960 0.660348i \(-0.229591\pi\)
−0.196398 + 0.980524i \(0.562924\pi\)
\(3\) 0 0
\(4\) −0.589947 1.02182i −0.294974 0.510909i
\(5\) −1.94254 + 1.12153i −0.868732 + 0.501563i −0.866927 0.498436i \(-0.833908\pi\)
−0.00180550 + 0.999998i \(0.500575\pi\)
\(6\) 0 0
\(7\) −2.97576 1.71806i −1.12473 0.649364i −0.182127 0.983275i \(-0.558298\pi\)
−0.942605 + 0.333911i \(0.891632\pi\)
\(8\) 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 \(-0.521488\pi\)
−0.897781 + 0.440443i \(0.854821\pi\)
\(12\) 0 0
\(13\) 0.351567 3.58837i 0.0975072 0.995235i
\(14\) −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 0.598598 0.801050i \(-0.295725\pi\)
−0.993028 + 0.117876i \(0.962392\pi\)
\(24\) 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 −0.734198 0.678935i \(-0.762442\pi\)
0.955074 + 0.296367i \(0.0957750\pi\)
\(30\) 0 0
\(31\) −6.37163 + 3.67866i −1.14438 + 0.660707i −0.947511 0.319723i \(-0.896410\pi\)
−0.196868 + 0.980430i \(0.563077\pi\)
\(32\) −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 \(-0.454358\pi\)
0.928587 + 0.371116i \(0.121025\pi\)
\(42\) 0 0
\(43\) −0.450266 + 0.779883i −0.0686649 + 0.118931i −0.898314 0.439354i \(-0.855207\pi\)
0.829649 + 0.558285i \(0.188541\pi\)
\(44\) 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 \(-0.200854\pi\)
−0.107197 + 0.994238i \(0.534188\pi\)
\(48\) 0 0
\(49\) 2.40343 + 4.16287i 0.343347 + 0.594695i
\(50\) 0.0245514 0.0141748i 0.00347209 0.00200461i
\(51\) 0 0
\(52\) −3.87407 + 1.75771i −0.537237 + 0.243751i
\(53\) −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 \(-0.775071\pi\)
0.182018 + 0.983295i \(0.441737\pi\)
\(60\) 0 0
\(61\) 6.50907 11.2740i 0.833401 1.44349i −0.0619247 0.998081i \(-0.519724\pi\)
0.895326 0.445412i \(-0.146943\pi\)
\(62\) −6.66277 −0.846173
\(63\) 0 0
\(64\) −5.50838 −0.688547
\(65\) 3.34152 + 7.36486i 0.414465 + 0.913499i
\(66\) 0 0
\(67\) 11.7002 6.75511i 1.42941 0.825269i 0.432333 0.901714i \(-0.357690\pi\)
0.997074 + 0.0764454i \(0.0243571\pi\)
\(68\) −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 0.375038 + 0.927009i \(0.377630\pi\)
−0.990333 + 0.138712i \(0.955704\pi\)
\(80\) 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 \(-0.342726\pi\)
−0.525333 + 0.850897i \(0.676059\pi\)
\(84\) 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 \(-0.445267\pi\)
−0.767704 + 0.640805i \(0.778601\pi\)
\(98\) 4.35308i 0.439727i
\(99\) 0 0
\(100\) −0.0369364 −0.00369364
\(101\) −2.48116 + 4.29749i −0.246884 + 0.427616i −0.962660 0.270715i \(-0.912740\pi\)
0.715776 + 0.698330i \(0.246073\pi\)
\(102\) 0 0
\(103\) −1.05587 1.82881i −0.104038 0.180198i 0.809307 0.587386i \(-0.199843\pi\)
−0.913345 + 0.407188i \(0.866510\pi\)
\(104\) −10.3334 1.01241i −1.01328 0.0992748i
\(105\) 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 0.808171 + 0.588948i \(0.200458\pi\)
0.105959 + 0.994371i \(0.466209\pi\)
\(114\) 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
\(130\) −0.714140 + 7.28907i −0.0626342 + 0.639294i
\(131\) −3.56490 6.17458i −0.311466 0.539476i 0.667214 0.744866i \(-0.267487\pi\)
−0.978680 + 0.205391i \(0.934153\pi\)
\(132\) 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 \(-0.395191\pi\)
−0.657826 + 0.753170i \(0.728524\pi\)
\(138\) 0 0
\(139\) −7.05496 12.2195i −0.598394 1.03645i −0.993058 0.117623i \(-0.962472\pi\)
0.394664 0.918825i \(-0.370861\pi\)
\(140\) −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 \(-0.590282\pi\)
0.691504 + 0.722372i \(0.256948\pi\)
\(150\) 0 0
\(151\) 8.44018 + 4.87294i 0.686852 + 0.396554i 0.802432 0.596744i \(-0.203539\pi\)
−0.115580 + 0.993298i \(0.536873\pi\)
\(152\) 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 0.886762 0.462227i \(-0.152949\pi\)
−0.843681 + 0.536845i \(0.819616\pi\)
\(158\) −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 \(-0.494057\pi\)
0.875210 + 0.483744i \(0.160723\pi\)
\(168\) 0 0
\(169\) −12.7528 2.52311i −0.980985 0.194085i
\(170\) −8.55423 −0.656079
\(171\) 0 0
\(172\) 1.06253 0.0810173
\(173\) 3.72080 6.44461i 0.282887 0.489975i −0.689208 0.724564i \(-0.742041\pi\)
0.972095 + 0.234589i \(0.0753745\pi\)
\(174\) 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 \(0.438283\pi\)
\(182\) −10.2171 + 4.63560i −0.757339 + 0.343614i
\(183\) 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 −0.411037 0.911619i \(-0.634833\pi\)
0.995003 0.0998406i \(-0.0318333\pi\)
\(192\) 0 0
\(193\) −2.83991 + 1.63962i −0.204421 + 0.118023i −0.598716 0.800961i \(-0.704322\pi\)
0.394295 + 0.918984i \(0.370989\pi\)
\(194\) −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 0.503158 0.864195i \(-0.332171\pi\)
−0.999993 + 0.00365007i \(0.998838\pi\)
\(212\) 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
\(221\) 1.48052 15.1113i 0.0995905 1.01650i
\(222\) 0 0
\(223\) −9.52959 5.50191i −0.638149 0.368435i 0.145752 0.989321i \(-0.453440\pi\)
−0.783901 + 0.620886i \(0.786773\pi\)
\(224\) 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 \(-0.420162\pi\)
−0.714830 + 0.699299i \(0.753496\pi\)
\(228\) 0 0
\(229\) 4.65740 2.68895i 0.307769 0.177691i −0.338158 0.941089i \(-0.609804\pi\)
0.645928 + 0.763398i \(0.276471\pi\)
\(230\) 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 \(-0.818097\pi\)
0.0478485 + 0.998855i \(0.484764\pi\)
\(240\) 0 0
\(241\) 26.2041 + 15.1289i 1.68795 + 0.974539i 0.956084 + 0.293092i \(0.0946842\pi\)
0.731867 + 0.681447i \(0.238649\pi\)
\(242\) 2.41310i 0.155120i
\(243\) 0 0
\(244\) −15.3600 −0.983326
\(245\) −9.33754 5.39103i −0.596554 0.344421i
\(246\) 0 0
\(247\) 15.2613 + 1.49521i 0.971052 + 0.0951379i
\(248\) 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 0.996475 + 0.0838952i \(0.0267361\pi\)
−0.425582 + 0.904920i \(0.639931\pi\)
\(258\) 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 −0.965914 0.258864i \(-0.916652\pi\)
0.707140 + 0.707074i \(0.249985\pi\)
\(264\) 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 −0.706830 0.707383i \(-0.749875\pi\)
0.966027 + 0.258441i \(0.0832087\pi\)
\(278\) 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 \(-0.300283\pi\)
−0.407548 + 0.913184i \(0.633616\pi\)
\(282\) 0 0
\(283\) 6.89178 + 11.9369i 0.409674 + 0.709576i 0.994853 0.101328i \(-0.0323091\pi\)
−0.585179 + 0.810904i \(0.698976\pi\)
\(284\) −2.71299 + 1.56635i −0.160986 + 0.0929456i
\(285\) 0 0
\(286\) −10.9915 + 4.98699i −0.649943 + 0.294887i
\(287\) −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 \(-0.353397\pi\)
0.998014 + 0.0629917i \(0.0200642\pi\)
\(294\) 0 0
\(295\) 5.75484 9.96768i 0.335060 0.580341i
\(296\) −15.8363 −0.920465
\(297\) 0 0
\(298\) 5.25460 0.304391
\(299\) −12.4219 + 5.63597i −0.718378 + 0.325937i
\(300\) 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 0.750268 0.661133i \(-0.229924\pi\)
−0.947692 + 0.319185i \(0.896591\pi\)
\(312\) 0 0
\(313\) −11.2253 + 19.4428i −0.634491 + 1.09897i 0.352131 + 0.935951i \(0.385457\pi\)
−0.986623 + 0.163020i \(0.947876\pi\)
\(314\) 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 \(-0.425957\pi\)
−0.727440 + 0.686171i \(0.759290\pi\)
\(318\) 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 \(-0.285905\pi\)
−0.365898 + 0.930655i \(0.619238\pi\)
\(332\) 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 0.831625 + 0.555338i \(0.187411\pi\)
0.0651239 + 0.997877i \(0.479256\pi\)
\(338\) −8.85918 7.75324i −0.481876 0.421721i
\(339\) 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 0.988902 0.148566i \(-0.0474658\pi\)
−0.623113 + 0.782132i \(0.714132\pi\)
\(348\) 0 0
\(349\) 9.76413 + 5.63732i 0.522662 + 0.301759i 0.738023 0.674776i \(-0.235760\pi\)
−0.215361 + 0.976534i \(0.569093\pi\)
\(350\) −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 \(-0.0826126\pi\)
0.261005 + 0.965337i \(0.415946\pi\)
\(354\) 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
\(364\) 14.5482 + 1.42534i 0.762530 + 0.0747082i
\(365\) 6.12064 + 10.6013i 0.320369 + 0.554895i
\(366\) 0 0
\(367\) 1.35716 2.35068i 0.0708434 0.122704i −0.828428 0.560096i \(-0.810764\pi\)
0.899271 + 0.437392i \(0.144098\pi\)
\(368\) −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 0.887800 0.460229i \(-0.152233\pi\)
−0.842470 + 0.538744i \(0.818899\pi\)
\(374\) −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 \(-0.841616\pi\)
−0.0260185 + 0.999661i \(0.508283\pi\)
\(384\) 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 −0.653610 0.756832i \(-0.726746\pi\)
0.982240 + 0.187627i \(0.0600795\pi\)
\(390\) 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 \(-0.853420\pi\)
−0.0630612 + 0.998010i \(0.520086\pi\)
\(402\) 0 0
\(403\) 10.9603 + 24.1571i 0.545974 + 1.20335i
\(404\) 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 \(-0.683190\pi\)
0.454392 + 0.890802i \(0.349857\pi\)
\(410\) −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
\(416\) 8.24524 + 18.1729i 0.404256 + 0.890998i
\(417\) 0 0
\(418\) 12.3299 7.11865i 0.603074 0.348185i
\(419\) 0.195699 + 0.338961i 0.00956053 + 0.0165593i 0.870766 0.491697i \(-0.163623\pi\)
−0.861206 + 0.508257i \(0.830290\pi\)
\(420\) 0 0
\(421\) 9.59987 + 5.54249i 0.467869 + 0.270124i 0.715347 0.698769i \(-0.246269\pi\)
−0.247478 + 0.968893i \(0.579602\pi\)
\(422\) 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 −0.0527626 0.998607i \(-0.516803\pi\)
0.891200 0.453610i \(-0.149864\pi\)
\(440\) 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 −0.428890 0.903357i \(-0.641095\pi\)
0.996775 0.0802490i \(-0.0255715\pi\)
\(444\) 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
\(455\) 2.70967 27.6570i 0.127031 1.29658i
\(456\) 0 0
\(457\) 15.0872 + 8.71058i 0.705748 + 0.407464i 0.809485 0.587141i \(-0.199747\pi\)
−0.103737 + 0.994605i \(0.533080\pi\)
\(458\) 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 \(-0.520918\pi\)
−0.896990 + 0.442051i \(0.854251\pi\)
\(462\) 0 0
\(463\) −9.12555 + 5.26864i −0.424100 + 0.244854i −0.696830 0.717236i \(-0.745407\pi\)
0.272730 + 0.962091i \(0.412074\pi\)
\(464\) −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 \(-0.216509\pi\)
−0.155945 + 0.987766i \(0.549842\pi\)
\(480\) 0 0
\(481\) −19.7334 1.93337i −0.899768 0.0881539i
\(482\) 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 0.820474 0.571684i \(-0.193709\pi\)
−0.905330 + 0.424710i \(0.860376\pi\)
\(492\) 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 \(-0.725868\pi\)
0.331234 + 0.943549i \(0.392535\pi\)
\(500\) −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 \(-0.869722\pi\)
−0.114070 + 0.993473i \(0.536389\pi\)
\(510\) 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
\(520\) 21.2086 9.62260i 0.930059 0.421979i
\(521\) −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
\(533\) −11.8019 26.0119i −0.511197 1.12670i
\(534\) 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 −0.295823 0.955243i \(-0.595594\pi\)
0.975176 0.221431i \(-0.0710729\pi\)
\(548\) 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 −0.965184 0.261571i \(-0.915760\pi\)
0.256065 0.966659i \(-0.417574\pi\)
\(564\) 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 −0.960029 0.279902i \(-0.909698\pi\)
0.722416 + 0.691458i \(0.243031\pi\)
\(570\) 0 0
\(571\) 0.127260 + 0.220421i 0.00532568 + 0.00922435i 0.868676 0.495381i \(-0.164971\pi\)
−0.863350 + 0.504605i \(0.831638\pi\)
\(572\) 15.6509 + 1.53338i 0.654398 + 0.0641140i
\(573\) 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 \(-0.274639\pi\)
−0.332739 + 0.943019i \(0.607973\pi\)
\(588\) 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
\(598\) −12.2941 1.20450i −0.502743 0.0492558i
\(599\) −5.59868 9.69720i −0.228756 0.396217i 0.728684 0.684850i \(-0.240132\pi\)
−0.957440 + 0.288634i \(0.906799\pi\)
\(600\) 0 0
\(601\) −2.96273 + 5.13159i −0.120852 + 0.209322i −0.920104 0.391674i \(-0.871896\pi\)
0.799252 + 0.600996i \(0.205229\pi\)
\(602\) 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 0.809990 0.586444i \(-0.199472\pi\)
−0.912870 + 0.408250i \(0.866139\pi\)
\(608\) −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 0.534387 0.845240i \(-0.320543\pi\)
0.999193 0.0401727i \(-0.0127908\pi\)
\(618\) 0 0
\(619\) −17.7979 10.2756i −0.715358 0.413012i 0.0976839 0.995217i \(-0.468857\pi\)
−0.813042 + 0.582206i \(0.802190\pi\)
\(620\) −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
\(637\) 15.7829 7.16088i 0.625340 0.283724i
\(638\) −7.96365 −0.315284
\(639\) 0 0
\(640\) −13.6404 −0.539183
\(641\) −16.6711 + 28.8751i −0.658467 + 1.14050i 0.322545 + 0.946554i \(0.395462\pi\)
−0.981012 + 0.193945i \(0.937872\pi\)
\(642\) 0 0
\(643\) 27.1759 15.6900i 1.07171 0.618754i 0.143065 0.989713i \(-0.454304\pi\)
0.928649 + 0.370959i \(0.120971\pi\)
\(644\) 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
\(650\) −0.0422328 0.0930829i −0.00165651 0.00365101i
\(651\) 0 0
\(652\) 5.66964 3.27337i 0.222040 0.128195i
\(653\) −13.8728 24.0284i −0.542884 0.940302i −0.998737 0.0502473i \(-0.983999\pi\)
0.455853 0.890055i \(-0.349334\pi\)
\(654\) 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 −0.672874 0.739757i \(-0.734940\pi\)
0.977085 + 0.212848i \(0.0682738\pi\)
\(660\) 0 0
\(661\) −15.5161 + 8.95822i −0.603506 + 0.348434i −0.770420 0.637537i \(-0.779953\pi\)
0.166914 + 0.985972i \(0.446620\pi\)
\(662\) 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 −0.803560 0.595224i \(-0.797064\pi\)
0.917259 + 0.398292i \(0.130397\pi\)
\(674\) 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 −0.472809 0.881165i \(-0.656760\pi\)
0.999516 0.0311180i \(-0.00990678\pi\)
\(678\) 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
\(689\) −2.67039 + 27.2561i −0.101734 + 1.03837i
\(690\) 0 0
\(691\) −23.9736 13.8412i −0.912000 0.526543i −0.0309256 0.999522i \(-0.509845\pi\)
−0.881074 + 0.472979i \(0.843179\pi\)
\(692\) −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 \(-0.352635\pi\)
−0.551562 + 0.834134i \(0.685968\pi\)
\(710\) 5.39324i 0.202405i
\(711\) 0 0
\(712\) −16.5648 −0.620793
\(713\) 24.1055 + 13.9173i 0.902756 + 0.521207i
\(714\) 0 0
\(715\) 2.91506 29.7534i 0.109017 1.11271i
\(716\) 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 −0.628519 0.777794i \(-0.716339\pi\)
0.987849 + 0.155416i \(0.0496719\pi\)
\(728\) 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 \(-0.815940\pi\)
0.0546155 + 0.998507i \(0.482607\pi\)
\(734\) 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 \(-0.562760\pi\)
0.751302 + 0.659959i \(0.229426\pi\)
\(744\) 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 0.999686 + 0.0250400i \(0.00797130\pi\)
−0.478158 + 0.878274i \(0.658695\pi\)
\(752\) 1.19083 0.687526i 0.0434251 0.0250715i
\(753\) 0 0
\(754\) −3.20935 7.07354i −0.116878 0.257603i
\(755\) −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 \(-0.654384\pi\)
0.533037 + 0.846092i \(0.321051\pi\)
\(762\) 0 0
\(763\) −17.1841 + 29.7637i −0.622105 + 1.07752i
\(764\) −19.0449 −0.689019
\(765\) 0 0
\(766\) −18.5156 −0.668994
\(767\) 7.64412 + 16.8480i 0.276013 + 0.608345i
\(768\) 0 0
\(769\) 6.62584 3.82543i 0.238934 0.137949i −0.375753 0.926720i \(-0.622616\pi\)
0.614687 + 0.788771i \(0.289282\pi\)
\(770\) −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 \(-0.398536\pi\)
0.979093 + 0.203411i \(0.0652027\pi\)
\(788\) 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 −0.952702 0.303906i \(-0.901709\pi\)
0.213161 0.977017i \(-0.431624\pi\)
\(798\) 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
\(806\) −2.34241 + 23.9085i −0.0825079 + 0.842140i
\(807\) 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 \(-0.538433\pi\)
−0.919945 + 0.392048i \(0.871767\pi\)
\(822\) 0 0
\(823\) 5.99853 + 10.3898i 0.209096 + 0.362164i 0.951430 0.307866i \(-0.0996147\pi\)
−0.742334 + 0.670030i \(0.766281\pi\)
\(824\) −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
\(832\) −1.93657 + 19.7661i −0.0671383 + 0.685266i
\(833\) 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 \(-0.193323\pi\)
−0.0836466 + 0.996495i \(0.526657\pi\)
\(840\) 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 \(-0.483340\pi\)
−0.838683 + 0.544620i \(0.816674\pi\)
\(854\) −40.5089 −1.38619
\(855\) 0 0
\(856\) 23.2508i 0.794697i
\(857\) −3.20474 + 5.55077i −0.109472 + 0.189611i −0.915556 0.402190i \(-0.868249\pi\)
0.806085 + 0.591800i \(0.201583\pi\)
\(858\) 0 0
\(859\) −12.7998 22.1699i −0.436723 0.756427i 0.560711 0.828011i \(-0.310528\pi\)
−0.997435 + 0.0715846i \(0.977194\pi\)
\(860\) −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
\(871\) −20.1264 44.3595i −0.681959 1.50307i
\(872\) −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 \(-0.843136\pi\)
−0.0307911 + 0.999526i \(0.509803\pi\)
\(878\) 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 \(0.329380\pi\)
\(884\) −16.3145 + 7.40207i −0.548715 + 0.248959i
\(885\) 0 0
\(886\) 18.7481 10.8242i 0.629855 0.363647i
\(887\) 6.42161 + 11.1226i 0.215616 + 0.373459i 0.953463 0.301510i \(-0.0974906\pi\)
−0.737847 + 0.674968i \(0.764157\pi\)
\(888\) 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 −0.642818 0.766019i \(-0.722235\pi\)
0.984801 + 0.173688i \(0.0555683\pi\)
\(908\) 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 −0.265466 0.964120i \(-0.585526\pi\)
0.967686 0.252159i \(-0.0811407\pi\)
\(912\) 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
\(923\) −9.52734 0.933432i −0.313596 0.0307243i
\(924\) 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 \(-0.395372\pi\)
−0.658257 + 0.752794i \(0.728706\pi\)
\(930\) 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 \(-0.793640\pi\)
0.124376 + 0.992235i \(0.460307\pi\)
\(942\) 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 \(-0.626641\pi\)
−0.992104 + 0.125415i \(0.959974\pi\)
\(948\) 0 0
\(949\) −19.5832 1.91865i −0.635698 0.0622819i
\(950\) 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 \(-0.873295\pi\)
−0.125213 + 0.992130i \(0.539961\pi\)
\(968\) 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 \(-0.393139\pi\)
0.982401 + 0.186782i \(0.0598058\pi\)
\(978\) 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 \(-0.416717\pi\)
−0.707219 + 0.706995i \(0.750050\pi\)
\(984\) 0 0
\(985\) −7.97686 13.8163i −0.254164 0.440225i
\(986\) 7.85686 4.53616i 0.250213 0.144461i
\(987\) 0 0
\(988\) −7.47552 16.4764i −0.237828 0.524183i
\(989\) 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 0.190899 + 0.981610i \(0.438860\pi\)
−0.945549 + 0.325481i \(0.894474\pi\)
\(998\) −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.181.6 20
3.2 odd 2 117.2.t.c.25.5 20
9.2 odd 6 1053.2.b.j.649.6 10
9.4 even 3 inner 351.2.t.c.64.5 20
9.5 odd 6 117.2.t.c.103.6 yes 20
9.7 even 3 1053.2.b.i.649.5 10
13.12 even 2 inner 351.2.t.c.181.5 20
39.38 odd 2 117.2.t.c.25.6 yes 20
117.25 even 6 1053.2.b.i.649.6 10
117.38 odd 6 1053.2.b.j.649.5 10
117.77 odd 6 117.2.t.c.103.5 yes 20
117.103 even 6 inner 351.2.t.c.64.6 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.t.c.25.5 20 3.2 odd 2
117.2.t.c.25.6 yes 20 39.38 odd 2
117.2.t.c.103.5 yes 20 117.77 odd 6
117.2.t.c.103.6 yes 20 9.5 odd 6
351.2.t.c.64.5 20 9.4 even 3 inner
351.2.t.c.64.6 20 117.103 even 6 inner
351.2.t.c.181.5 20 13.12 even 2 inner
351.2.t.c.181.6 20 1.1 even 1 trivial
1053.2.b.i.649.5 10 9.7 even 3
1053.2.b.i.649.6 10 117.25 even 6
1053.2.b.j.649.5 10 117.38 odd 6
1053.2.b.j.649.6 10 9.2 odd 6