Properties

Label 63.4.p.a.17.1
Level $63$
Weight $4$
Character 63.17
Analytic conductor $3.717$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,4,Mod(17,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.17");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.1
Root \(-4.21355 + 2.43270i\) of defining polynomial
Character \(\chi\) \(=\) 63.17
Dual form 63.4.p.a.26.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.21355 + 2.43270i) q^{2} +(7.83601 - 13.5724i) q^{4} +(6.38217 + 11.0542i) q^{5} +(2.53897 + 18.3454i) q^{7} +37.3274i q^{8} +O(q^{10})\) \(q+(-4.21355 + 2.43270i) q^{2} +(7.83601 - 13.5724i) q^{4} +(6.38217 + 11.0542i) q^{5} +(2.53897 + 18.3454i) q^{7} +37.3274i q^{8} +(-53.7832 - 31.0517i) q^{10} +(-46.8633 - 27.0565i) q^{11} +8.85528i q^{13} +(-55.3268 - 71.1228i) q^{14} +(-28.1181 - 48.7020i) q^{16} +(-34.4587 + 59.6841i) q^{17} +(-141.898 + 81.9246i) q^{19} +200.043 q^{20} +263.281 q^{22} +(81.3807 - 46.9852i) q^{23} +(-18.9642 + 32.8469i) q^{25} +(-21.5422 - 37.3122i) q^{26} +(268.886 + 109.295i) q^{28} +119.620i q^{29} +(85.6311 + 49.4391i) q^{31} +(-21.6577 - 12.5041i) q^{32} -335.310i q^{34} +(-186.590 + 145.150i) q^{35} +(-47.0949 - 81.5708i) q^{37} +(398.595 - 690.387i) q^{38} +(-412.626 + 238.230i) q^{40} +259.347 q^{41} +5.01418 q^{43} +(-734.443 + 424.031i) q^{44} +(-228.601 + 395.949i) q^{46} +(28.6747 + 49.6660i) q^{47} +(-330.107 + 93.1568i) q^{49} -184.536i q^{50} +(120.187 + 69.3901i) q^{52} +(407.058 + 235.015i) q^{53} -690.718i q^{55} +(-684.786 + 94.7731i) q^{56} +(-290.999 - 504.025i) q^{58} +(-112.979 + 195.685i) q^{59} +(370.650 - 213.995i) q^{61} -481.082 q^{62} +571.564 q^{64} +(-97.8884 + 56.5159i) q^{65} +(-81.9267 + 141.901i) q^{67} +(540.037 + 935.372i) q^{68} +(433.103 - 1065.51i) q^{70} +79.8529i q^{71} +(666.447 + 384.774i) q^{73} +(396.874 + 229.135i) q^{74} +2567.85i q^{76} +(377.379 - 928.422i) q^{77} +(-267.408 - 463.165i) q^{79} +(358.909 - 621.648i) q^{80} +(-1092.77 + 630.912i) q^{82} +438.520 q^{83} -879.684 q^{85} +(-21.1275 + 12.1980i) q^{86} +(1009.95 - 1749.29i) q^{88} +(12.8242 + 22.2121i) q^{89} +(-162.454 + 22.4833i) q^{91} -1472.71i q^{92} +(-241.644 - 139.513i) q^{94} +(-1811.23 - 1045.71i) q^{95} +1381.00i q^{97} +(1164.30 - 1195.57i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} + 56 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} + 56 q^{7} - 72 q^{10} - 188 q^{16} - 612 q^{19} + 528 q^{22} - 20 q^{25} + 1036 q^{28} + 1128 q^{31} - 1196 q^{37} - 3204 q^{40} + 328 q^{43} - 1392 q^{46} + 784 q^{49} + 4452 q^{52} - 3372 q^{58} - 1632 q^{61} + 5432 q^{64} + 308 q^{67} + 3612 q^{70} + 4068 q^{73} - 2176 q^{79} - 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 924 q^{91} - 2916 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.21355 + 2.43270i −1.48972 + 0.860088i −0.999931 0.0117558i \(-0.996258\pi\)
−0.489785 + 0.871843i \(0.662925\pi\)
\(3\) 0 0
\(4\) 7.83601 13.5724i 0.979502 1.69655i
\(5\) 6.38217 + 11.0542i 0.570839 + 0.988721i 0.996480 + 0.0838295i \(0.0267151\pi\)
−0.425642 + 0.904892i \(0.639952\pi\)
\(6\) 0 0
\(7\) 2.53897 + 18.3454i 0.137091 + 0.990558i
\(8\) 37.3274i 1.64965i
\(9\) 0 0
\(10\) −53.7832 31.0517i −1.70077 0.981942i
\(11\) −46.8633 27.0565i −1.28453 0.741623i −0.306856 0.951756i \(-0.599277\pi\)
−0.977673 + 0.210133i \(0.932610\pi\)
\(12\) 0 0
\(13\) 8.85528i 0.188924i 0.995528 + 0.0944620i \(0.0301131\pi\)
−0.995528 + 0.0944620i \(0.969887\pi\)
\(14\) −55.3268 71.1228i −1.05619 1.35774i
\(15\) 0 0
\(16\) −28.1181 48.7020i −0.439345 0.760968i
\(17\) −34.4587 + 59.6841i −0.491615 + 0.851502i −0.999953 0.00965543i \(-0.996927\pi\)
0.508339 + 0.861157i \(0.330260\pi\)
\(18\) 0 0
\(19\) −141.898 + 81.9246i −1.71334 + 0.989199i −0.783383 + 0.621540i \(0.786508\pi\)
−0.929960 + 0.367660i \(0.880159\pi\)
\(20\) 200.043 2.23655
\(21\) 0 0
\(22\) 263.281 2.55144
\(23\) 81.3807 46.9852i 0.737785 0.425960i −0.0834783 0.996510i \(-0.526603\pi\)
0.821263 + 0.570549i \(0.193270\pi\)
\(24\) 0 0
\(25\) −18.9642 + 32.8469i −0.151713 + 0.262775i
\(26\) −21.5422 37.3122i −0.162491 0.281443i
\(27\) 0 0
\(28\) 268.886 + 109.295i 1.81481 + 0.737672i
\(29\) 119.620i 0.765961i 0.923756 + 0.382981i \(0.125102\pi\)
−0.923756 + 0.382981i \(0.874898\pi\)
\(30\) 0 0
\(31\) 85.6311 + 49.4391i 0.496123 + 0.286437i 0.727111 0.686520i \(-0.240863\pi\)
−0.230988 + 0.972957i \(0.574196\pi\)
\(32\) −21.6577 12.5041i −0.119643 0.0690760i
\(33\) 0 0
\(34\) 335.310i 1.69133i
\(35\) −186.590 + 145.150i −0.901129 + 0.700994i
\(36\) 0 0
\(37\) −47.0949 81.5708i −0.209253 0.362437i 0.742227 0.670149i \(-0.233770\pi\)
−0.951479 + 0.307712i \(0.900437\pi\)
\(38\) 398.595 690.387i 1.70160 2.94725i
\(39\) 0 0
\(40\) −412.626 + 238.230i −1.63105 + 0.941686i
\(41\) 259.347 0.987883 0.493941 0.869495i \(-0.335556\pi\)
0.493941 + 0.869495i \(0.335556\pi\)
\(42\) 0 0
\(43\) 5.01418 0.0177827 0.00889133 0.999960i \(-0.497170\pi\)
0.00889133 + 0.999960i \(0.497170\pi\)
\(44\) −734.443 + 424.031i −2.51640 + 1.45284i
\(45\) 0 0
\(46\) −228.601 + 395.949i −0.732727 + 1.26912i
\(47\) 28.6747 + 49.6660i 0.0889921 + 0.154139i 0.907085 0.420947i \(-0.138302\pi\)
−0.818093 + 0.575086i \(0.804969\pi\)
\(48\) 0 0
\(49\) −330.107 + 93.1568i −0.962412 + 0.271594i
\(50\) 184.536i 0.521947i
\(51\) 0 0
\(52\) 120.187 + 69.3901i 0.320518 + 0.185051i
\(53\) 407.058 + 235.015i 1.05497 + 0.609090i 0.924038 0.382301i \(-0.124868\pi\)
0.130937 + 0.991391i \(0.458202\pi\)
\(54\) 0 0
\(55\) 690.718i 1.69339i
\(56\) −684.786 + 94.7731i −1.63408 + 0.226153i
\(57\) 0 0
\(58\) −290.999 504.025i −0.658794 1.14106i
\(59\) −112.979 + 195.685i −0.249299 + 0.431798i −0.963331 0.268314i \(-0.913533\pi\)
0.714033 + 0.700112i \(0.246867\pi\)
\(60\) 0 0
\(61\) 370.650 213.995i 0.777982 0.449168i −0.0577325 0.998332i \(-0.518387\pi\)
0.835715 + 0.549164i \(0.185054\pi\)
\(62\) −481.082 −0.985442
\(63\) 0 0
\(64\) 571.564 1.11634
\(65\) −97.8884 + 56.5159i −0.186793 + 0.107845i
\(66\) 0 0
\(67\) −81.9267 + 141.901i −0.149387 + 0.258746i −0.931001 0.365016i \(-0.881063\pi\)
0.781614 + 0.623762i \(0.214397\pi\)
\(68\) 540.037 + 935.372i 0.963075 + 1.66809i
\(69\) 0 0
\(70\) 433.103 1065.51i 0.739510 1.81933i
\(71\) 79.8529i 0.133476i 0.997771 + 0.0667380i \(0.0212592\pi\)
−0.997771 + 0.0667380i \(0.978741\pi\)
\(72\) 0 0
\(73\) 666.447 + 384.774i 1.06852 + 0.616909i 0.927776 0.373138i \(-0.121718\pi\)
0.140741 + 0.990046i \(0.455051\pi\)
\(74\) 396.874 + 229.135i 0.623454 + 0.359952i
\(75\) 0 0
\(76\) 2567.85i 3.87569i
\(77\) 377.379 928.422i 0.558523 1.37407i
\(78\) 0 0
\(79\) −267.408 463.165i −0.380833 0.659622i 0.610349 0.792133i \(-0.291029\pi\)
−0.991182 + 0.132511i \(0.957696\pi\)
\(80\) 358.909 621.648i 0.501590 0.868780i
\(81\) 0 0
\(82\) −1092.77 + 630.912i −1.47166 + 0.849666i
\(83\) 438.520 0.579926 0.289963 0.957038i \(-0.406357\pi\)
0.289963 + 0.957038i \(0.406357\pi\)
\(84\) 0 0
\(85\) −879.684 −1.12253
\(86\) −21.1275 + 12.1980i −0.0264911 + 0.0152947i
\(87\) 0 0
\(88\) 1009.95 1749.29i 1.22342 2.11903i
\(89\) 12.8242 + 22.2121i 0.0152737 + 0.0264548i 0.873561 0.486714i \(-0.161805\pi\)
−0.858288 + 0.513169i \(0.828471\pi\)
\(90\) 0 0
\(91\) −162.454 + 22.4833i −0.187140 + 0.0258999i
\(92\) 1472.71i 1.66892i
\(93\) 0 0
\(94\) −241.644 139.513i −0.265146 0.153082i
\(95\) −1811.23 1045.71i −1.95608 1.12935i
\(96\) 0 0
\(97\) 1381.00i 1.44555i 0.691081 + 0.722777i \(0.257135\pi\)
−0.691081 + 0.722777i \(0.742865\pi\)
\(98\) 1164.30 1195.57i 1.20013 1.23236i
\(99\) 0 0
\(100\) 297.207 + 514.777i 0.297207 + 0.514777i
\(101\) −356.808 + 618.009i −0.351522 + 0.608854i −0.986516 0.163663i \(-0.947669\pi\)
0.634994 + 0.772517i \(0.281002\pi\)
\(102\) 0 0
\(103\) 1552.42 896.288i 1.48509 0.857416i 0.485232 0.874385i \(-0.338735\pi\)
0.999856 + 0.0169695i \(0.00540182\pi\)
\(104\) −330.544 −0.311659
\(105\) 0 0
\(106\) −2286.88 −2.09548
\(107\) −19.5366 + 11.2794i −0.0176511 + 0.0101909i −0.508800 0.860885i \(-0.669911\pi\)
0.491148 + 0.871076i \(0.336577\pi\)
\(108\) 0 0
\(109\) −476.210 + 824.820i −0.418465 + 0.724802i −0.995785 0.0917154i \(-0.970765\pi\)
0.577320 + 0.816518i \(0.304098\pi\)
\(110\) 1680.31 + 2910.37i 1.45646 + 2.52267i
\(111\) 0 0
\(112\) 822.066 639.490i 0.693553 0.539519i
\(113\) 120.145i 0.100020i −0.998749 0.0500102i \(-0.984075\pi\)
0.998749 0.0500102i \(-0.0159254\pi\)
\(114\) 0 0
\(115\) 1038.77 + 599.735i 0.842312 + 0.486309i
\(116\) 1623.53 + 937.344i 1.29949 + 0.750260i
\(117\) 0 0
\(118\) 1099.37i 0.857674i
\(119\) −1182.42 480.622i −0.910859 0.370240i
\(120\) 0 0
\(121\) 798.612 + 1383.24i 0.600009 + 1.03925i
\(122\) −1041.17 + 1803.36i −0.772648 + 1.33827i
\(123\) 0 0
\(124\) 1342.01 774.812i 0.971906 0.561130i
\(125\) 1111.41 0.795262
\(126\) 0 0
\(127\) 884.302 0.617867 0.308934 0.951084i \(-0.400028\pi\)
0.308934 + 0.951084i \(0.400028\pi\)
\(128\) −2235.05 + 1290.41i −1.54338 + 0.891071i
\(129\) 0 0
\(130\) 274.972 476.265i 0.185512 0.321317i
\(131\) −803.439 1391.60i −0.535853 0.928125i −0.999122 0.0419070i \(-0.986657\pi\)
0.463268 0.886218i \(-0.346677\pi\)
\(132\) 0 0
\(133\) −1863.21 2395.16i −1.21474 1.56156i
\(134\) 797.210i 0.513944i
\(135\) 0 0
\(136\) −2227.85 1286.25i −1.40468 0.810994i
\(137\) −615.297 355.242i −0.383711 0.221535i 0.295721 0.955274i \(-0.404440\pi\)
−0.679431 + 0.733739i \(0.737773\pi\)
\(138\) 0 0
\(139\) 1531.91i 0.934782i −0.884051 0.467391i \(-0.845194\pi\)
0.884051 0.467391i \(-0.154806\pi\)
\(140\) 507.903 + 3669.87i 0.306612 + 2.21543i
\(141\) 0 0
\(142\) −194.258 336.464i −0.114801 0.198841i
\(143\) 239.593 414.987i 0.140110 0.242678i
\(144\) 0 0
\(145\) −1322.31 + 763.435i −0.757322 + 0.437240i
\(146\) −3744.15 −2.12238
\(147\) 0 0
\(148\) −1476.15 −0.819854
\(149\) 2079.39 1200.54i 1.14329 0.660079i 0.196046 0.980595i \(-0.437190\pi\)
0.947243 + 0.320516i \(0.103856\pi\)
\(150\) 0 0
\(151\) −1233.99 + 2137.33i −0.665035 + 1.15188i 0.314240 + 0.949343i \(0.398250\pi\)
−0.979276 + 0.202532i \(0.935083\pi\)
\(152\) −3058.03 5296.67i −1.63184 2.82642i
\(153\) 0 0
\(154\) 668.463 + 4830.00i 0.349781 + 2.52735i
\(155\) 1262.12i 0.654036i
\(156\) 0 0
\(157\) 2109.74 + 1218.06i 1.07246 + 0.619184i 0.928852 0.370451i \(-0.120797\pi\)
0.143606 + 0.989635i \(0.454130\pi\)
\(158\) 2253.48 + 1301.05i 1.13466 + 0.655099i
\(159\) 0 0
\(160\) 319.213i 0.157725i
\(161\) 1068.59 + 1373.67i 0.523083 + 0.672424i
\(162\) 0 0
\(163\) −1638.50 2837.97i −0.787347 1.36372i −0.927587 0.373607i \(-0.878121\pi\)
0.140240 0.990118i \(-0.455213\pi\)
\(164\) 2032.25 3519.95i 0.967633 1.67599i
\(165\) 0 0
\(166\) −1847.73 + 1066.79i −0.863924 + 0.498787i
\(167\) −365.585 −0.169400 −0.0847000 0.996406i \(-0.526993\pi\)
−0.0847000 + 0.996406i \(0.526993\pi\)
\(168\) 0 0
\(169\) 2118.58 0.964308
\(170\) 3706.59 2140.00i 1.67225 0.965475i
\(171\) 0 0
\(172\) 39.2912 68.0543i 0.0174182 0.0301691i
\(173\) 1046.47 + 1812.53i 0.459892 + 0.796557i 0.998955 0.0457089i \(-0.0145547\pi\)
−0.539062 + 0.842266i \(0.681221\pi\)
\(174\) 0 0
\(175\) −650.739 264.508i −0.281093 0.114257i
\(176\) 3043.11i 1.30331i
\(177\) 0 0
\(178\) −108.071 62.3946i −0.0455070 0.0262735i
\(179\) −1524.01 879.890i −0.636370 0.367408i 0.146845 0.989160i \(-0.453088\pi\)
−0.783215 + 0.621751i \(0.786422\pi\)
\(180\) 0 0
\(181\) 3197.54i 1.31310i −0.754282 0.656551i \(-0.772015\pi\)
0.754282 0.656551i \(-0.227985\pi\)
\(182\) 629.812 489.934i 0.256510 0.199540i
\(183\) 0 0
\(184\) 1753.84 + 3037.73i 0.702687 + 1.21709i
\(185\) 601.135 1041.20i 0.238899 0.413786i
\(186\) 0 0
\(187\) 3229.69 1864.66i 1.26299 0.729186i
\(188\) 898.780 0.348672
\(189\) 0 0
\(190\) 10175.6 3.88535
\(191\) −475.772 + 274.687i −0.180239 + 0.104061i −0.587405 0.809293i \(-0.699850\pi\)
0.407166 + 0.913354i \(0.366517\pi\)
\(192\) 0 0
\(193\) 352.238 610.094i 0.131371 0.227542i −0.792834 0.609437i \(-0.791395\pi\)
0.924205 + 0.381896i \(0.124729\pi\)
\(194\) −3359.54 5818.90i −1.24330 2.15347i
\(195\) 0 0
\(196\) −1322.37 + 5210.32i −0.481912 + 1.89880i
\(197\) 5317.81i 1.92324i 0.274384 + 0.961620i \(0.411526\pi\)
−0.274384 + 0.961620i \(0.588474\pi\)
\(198\) 0 0
\(199\) −2155.80 1244.65i −0.767942 0.443371i 0.0641982 0.997937i \(-0.479551\pi\)
−0.832140 + 0.554566i \(0.812884\pi\)
\(200\) −1226.09 707.883i −0.433488 0.250274i
\(201\) 0 0
\(202\) 3472.02i 1.20936i
\(203\) −2194.48 + 303.711i −0.758729 + 0.105007i
\(204\) 0 0
\(205\) 1655.20 + 2866.88i 0.563922 + 0.976741i
\(206\) −4360.79 + 7553.11i −1.47491 + 2.55461i
\(207\) 0 0
\(208\) 431.269 248.993i 0.143765 0.0830029i
\(209\) 8866.38 2.93445
\(210\) 0 0
\(211\) −3454.31 −1.12704 −0.563519 0.826103i \(-0.690553\pi\)
−0.563519 + 0.826103i \(0.690553\pi\)
\(212\) 6379.42 3683.16i 2.06670 1.19321i
\(213\) 0 0
\(214\) 54.8789 95.0530i 0.0175301 0.0303630i
\(215\) 32.0013 + 55.4279i 0.0101510 + 0.0175821i
\(216\) 0 0
\(217\) −689.566 + 1696.46i −0.215718 + 0.530706i
\(218\) 4633.90i 1.43967i
\(219\) 0 0
\(220\) −9374.68 5412.47i −2.87291 1.65868i
\(221\) −528.520 305.141i −0.160869 0.0928778i
\(222\) 0 0
\(223\) 3896.38i 1.17005i 0.811016 + 0.585024i \(0.198915\pi\)
−0.811016 + 0.585024i \(0.801085\pi\)
\(224\) 174.404 429.067i 0.0520218 0.127983i
\(225\) 0 0
\(226\) 292.277 + 506.238i 0.0860263 + 0.149002i
\(227\) −302.747 + 524.374i −0.0885201 + 0.153321i −0.906886 0.421377i \(-0.861547\pi\)
0.818366 + 0.574698i \(0.194880\pi\)
\(228\) 0 0
\(229\) −1912.98 + 1104.46i −0.552023 + 0.318711i −0.749938 0.661509i \(-0.769917\pi\)
0.197914 + 0.980219i \(0.436583\pi\)
\(230\) −5835.89 −1.67307
\(231\) 0 0
\(232\) −4465.10 −1.26357
\(233\) −2065.77 + 1192.67i −0.580829 + 0.335342i −0.761463 0.648209i \(-0.775518\pi\)
0.180634 + 0.983550i \(0.442185\pi\)
\(234\) 0 0
\(235\) −366.013 + 633.953i −0.101600 + 0.175977i
\(236\) 1770.61 + 3066.79i 0.488377 + 0.845893i
\(237\) 0 0
\(238\) 6151.39 851.341i 1.67536 0.231866i
\(239\) 3017.95i 0.816798i 0.912803 + 0.408399i \(0.133913\pi\)
−0.912803 + 0.408399i \(0.866087\pi\)
\(240\) 0 0
\(241\) −2178.48 1257.75i −0.582275 0.336176i 0.179762 0.983710i \(-0.442467\pi\)
−0.762037 + 0.647534i \(0.775800\pi\)
\(242\) −6729.99 3885.56i −1.78769 1.03212i
\(243\) 0 0
\(244\) 6707.47i 1.75984i
\(245\) −3136.58 3054.54i −0.817913 0.796521i
\(246\) 0 0
\(247\) −725.465 1256.54i −0.186883 0.323692i
\(248\) −1845.44 + 3196.39i −0.472521 + 0.818431i
\(249\) 0 0
\(250\) −4682.99 + 2703.73i −1.18471 + 0.683995i
\(251\) −1306.11 −0.328451 −0.164226 0.986423i \(-0.552512\pi\)
−0.164226 + 0.986423i \(0.552512\pi\)
\(252\) 0 0
\(253\) −5085.03 −1.26361
\(254\) −3726.05 + 2151.24i −0.920447 + 0.531420i
\(255\) 0 0
\(256\) 3992.09 6914.50i 0.974630 1.68811i
\(257\) −3735.91 6470.79i −0.906770 1.57057i −0.818524 0.574473i \(-0.805207\pi\)
−0.0882460 0.996099i \(-0.528126\pi\)
\(258\) 0 0
\(259\) 1376.88 1071.08i 0.330328 0.256964i
\(260\) 1771.44i 0.422538i
\(261\) 0 0
\(262\) 6770.66 + 3909.04i 1.59654 + 0.921762i
\(263\) 1330.77 + 768.318i 0.312010 + 0.180139i 0.647825 0.761789i \(-0.275679\pi\)
−0.335816 + 0.941928i \(0.609012\pi\)
\(264\) 0 0
\(265\) 5999.62i 1.39077i
\(266\) 13677.4 + 5559.51i 3.15270 + 1.28149i
\(267\) 0 0
\(268\) 1283.96 + 2223.88i 0.292650 + 0.506884i
\(269\) −1958.09 + 3391.52i −0.443818 + 0.768715i −0.997969 0.0637010i \(-0.979710\pi\)
0.554151 + 0.832416i \(0.313043\pi\)
\(270\) 0 0
\(271\) 3117.42 1799.84i 0.698780 0.403441i −0.108113 0.994139i \(-0.534481\pi\)
0.806893 + 0.590698i \(0.201147\pi\)
\(272\) 3875.65 0.863955
\(273\) 0 0
\(274\) 3456.78 0.762159
\(275\) 1777.45 1026.21i 0.389760 0.225028i
\(276\) 0 0
\(277\) −142.040 + 246.021i −0.0308100 + 0.0533645i −0.881019 0.473080i \(-0.843142\pi\)
0.850209 + 0.526445i \(0.176475\pi\)
\(278\) 3726.67 + 6454.77i 0.803995 + 1.39256i
\(279\) 0 0
\(280\) −5418.07 6964.93i −1.15640 1.48655i
\(281\) 321.256i 0.0682011i −0.999418 0.0341006i \(-0.989143\pi\)
0.999418 0.0341006i \(-0.0108566\pi\)
\(282\) 0 0
\(283\) 5891.40 + 3401.40i 1.23748 + 0.714460i 0.968579 0.248707i \(-0.0800057\pi\)
0.268903 + 0.963167i \(0.413339\pi\)
\(284\) 1083.79 + 625.728i 0.226448 + 0.130740i
\(285\) 0 0
\(286\) 2331.43i 0.482029i
\(287\) 658.474 + 4757.82i 0.135430 + 0.978556i
\(288\) 0 0
\(289\) 81.7017 + 141.511i 0.0166297 + 0.0288035i
\(290\) 3714.41 6433.55i 0.752130 1.30273i
\(291\) 0 0
\(292\) 10444.6 6030.18i 2.09323 1.20853i
\(293\) −3180.05 −0.634063 −0.317031 0.948415i \(-0.602686\pi\)
−0.317031 + 0.948415i \(0.602686\pi\)
\(294\) 0 0
\(295\) −2884.20 −0.569237
\(296\) 3044.83 1757.93i 0.597895 0.345195i
\(297\) 0 0
\(298\) −5841.07 + 10117.0i −1.13545 + 1.96666i
\(299\) 416.067 + 720.649i 0.0804741 + 0.139385i
\(300\) 0 0
\(301\) 12.7308 + 91.9871i 0.00243785 + 0.0176148i
\(302\) 12007.6i 2.28795i
\(303\) 0 0
\(304\) 7979.78 + 4607.13i 1.50550 + 0.869200i
\(305\) 4731.11 + 2731.51i 0.888204 + 0.512805i
\(306\) 0 0
\(307\) 2976.39i 0.553328i 0.960967 + 0.276664i \(0.0892289\pi\)
−0.960967 + 0.276664i \(0.910771\pi\)
\(308\) −9643.74 12397.0i −1.78410 2.29346i
\(309\) 0 0
\(310\) −3070.34 5317.99i −0.562528 0.974328i
\(311\) 2340.89 4054.55i 0.426817 0.739268i −0.569772 0.821803i \(-0.692968\pi\)
0.996588 + 0.0825352i \(0.0263017\pi\)
\(312\) 0 0
\(313\) −850.477 + 491.023i −0.153584 + 0.0886718i −0.574823 0.818278i \(-0.694929\pi\)
0.421238 + 0.906950i \(0.361596\pi\)
\(314\) −11852.7 −2.13021
\(315\) 0 0
\(316\) −8381.66 −1.49211
\(317\) −4269.80 + 2465.17i −0.756516 + 0.436775i −0.828044 0.560664i \(-0.810546\pi\)
0.0715272 + 0.997439i \(0.477213\pi\)
\(318\) 0 0
\(319\) 3236.50 5605.79i 0.568055 0.983899i
\(320\) 3647.82 + 6318.21i 0.637248 + 1.10375i
\(321\) 0 0
\(322\) −7844.26 3188.48i −1.35759 0.551823i
\(323\) 11292.0i 1.94522i
\(324\) 0 0
\(325\) −290.868 167.933i −0.0496445 0.0286623i
\(326\) 13807.8 + 7971.96i 2.34585 + 1.35437i
\(327\) 0 0
\(328\) 9680.75i 1.62966i
\(329\) −838.338 + 652.148i −0.140483 + 0.109283i
\(330\) 0 0
\(331\) 2017.25 + 3493.99i 0.334980 + 0.580202i 0.983481 0.181012i \(-0.0579372\pi\)
−0.648501 + 0.761214i \(0.724604\pi\)
\(332\) 3436.25 5951.76i 0.568038 0.983871i
\(333\) 0 0
\(334\) 1540.41 889.356i 0.252358 0.145699i
\(335\) −2091.48 −0.341104
\(336\) 0 0
\(337\) 2771.62 0.448011 0.224006 0.974588i \(-0.428087\pi\)
0.224006 + 0.974588i \(0.428087\pi\)
\(338\) −8926.76 + 5153.87i −1.43654 + 0.829389i
\(339\) 0 0
\(340\) −6893.21 + 11939.4i −1.09952 + 1.90443i
\(341\) −2675.30 4633.76i −0.424856 0.735872i
\(342\) 0 0
\(343\) −2547.13 5819.43i −0.400968 0.916092i
\(344\) 187.166i 0.0293352i
\(345\) 0 0
\(346\) −8818.68 5091.47i −1.37022 0.791095i
\(347\) 3743.15 + 2161.11i 0.579085 + 0.334335i 0.760770 0.649022i \(-0.224822\pi\)
−0.181685 + 0.983357i \(0.558155\pi\)
\(348\) 0 0
\(349\) 1331.65i 0.204245i −0.994772 0.102122i \(-0.967437\pi\)
0.994772 0.102122i \(-0.0325634\pi\)
\(350\) 3385.39 468.531i 0.517019 0.0715545i
\(351\) 0 0
\(352\) 676.635 + 1171.97i 0.102457 + 0.177460i
\(353\) 5674.26 9828.10i 0.855553 1.48186i −0.0205782 0.999788i \(-0.506551\pi\)
0.876131 0.482073i \(-0.160116\pi\)
\(354\) 0 0
\(355\) −882.713 + 509.634i −0.131970 + 0.0761932i
\(356\) 401.962 0.0598425
\(357\) 0 0
\(358\) 8562.02 1.26401
\(359\) 7247.49 4184.34i 1.06548 0.615156i 0.138538 0.990357i \(-0.455760\pi\)
0.926943 + 0.375201i \(0.122426\pi\)
\(360\) 0 0
\(361\) 9993.77 17309.7i 1.45703 2.52365i
\(362\) 7778.64 + 13473.0i 1.12938 + 1.95615i
\(363\) 0 0
\(364\) −967.837 + 2381.06i −0.139364 + 0.342861i
\(365\) 9822.76i 1.40862i
\(366\) 0 0
\(367\) 2351.31 + 1357.53i 0.334434 + 0.193086i 0.657808 0.753186i \(-0.271484\pi\)
−0.323374 + 0.946271i \(0.604817\pi\)
\(368\) −4576.54 2642.27i −0.648285 0.374287i
\(369\) 0 0
\(370\) 5849.52i 0.821897i
\(371\) −3277.93 + 8064.33i −0.458711 + 1.12851i
\(372\) 0 0
\(373\) −3048.56 5280.25i −0.423186 0.732979i 0.573063 0.819511i \(-0.305755\pi\)
−0.996249 + 0.0865320i \(0.972422\pi\)
\(374\) −9072.32 + 15713.7i −1.25433 + 2.17256i
\(375\) 0 0
\(376\) −1853.90 + 1070.35i −0.254276 + 0.146806i
\(377\) −1059.27 −0.144708
\(378\) 0 0
\(379\) −9922.24 −1.34478 −0.672389 0.740198i \(-0.734732\pi\)
−0.672389 + 0.740198i \(0.734732\pi\)
\(380\) −28385.6 + 16388.4i −3.83198 + 2.21239i
\(381\) 0 0
\(382\) 1336.46 2314.82i 0.179003 0.310043i
\(383\) 609.532 + 1055.74i 0.0813202 + 0.140851i 0.903817 0.427919i \(-0.140753\pi\)
−0.822497 + 0.568769i \(0.807420\pi\)
\(384\) 0 0
\(385\) 12671.5 1753.71i 1.67740 0.232149i
\(386\) 3427.55i 0.451963i
\(387\) 0 0
\(388\) 18743.4 + 10821.5i 2.45245 + 1.41592i
\(389\) −11374.6 6567.15i −1.48256 0.855958i −0.482759 0.875753i \(-0.660365\pi\)
−0.999804 + 0.0197949i \(0.993699\pi\)
\(390\) 0 0
\(391\) 6476.19i 0.837634i
\(392\) −3477.30 12322.0i −0.448036 1.58765i
\(393\) 0 0
\(394\) −12936.6 22406.9i −1.65416 2.86508i
\(395\) 3413.29 5911.99i 0.434788 0.753075i
\(396\) 0 0
\(397\) 2697.68 1557.51i 0.341040 0.196900i −0.319692 0.947522i \(-0.603579\pi\)
0.660732 + 0.750622i \(0.270246\pi\)
\(398\) 12111.4 1.52535
\(399\) 0 0
\(400\) 2132.94 0.266618
\(401\) 9724.47 5614.42i 1.21101 0.699179i 0.248034 0.968751i \(-0.420216\pi\)
0.962980 + 0.269572i \(0.0868822\pi\)
\(402\) 0 0
\(403\) −437.797 + 758.287i −0.0541147 + 0.0937295i
\(404\) 5591.90 + 9685.46i 0.688633 + 1.19275i
\(405\) 0 0
\(406\) 8507.70 6618.20i 1.03998 0.809004i
\(407\) 5096.90i 0.620747i
\(408\) 0 0
\(409\) −10739.4 6200.41i −1.29836 0.749610i −0.318242 0.948010i \(-0.603092\pi\)
−0.980121 + 0.198399i \(0.936426\pi\)
\(410\) −13948.5 8053.18i −1.68017 0.970044i
\(411\) 0 0
\(412\) 28093.3i 3.35936i
\(413\) −3876.78 1575.81i −0.461898 0.187749i
\(414\) 0 0
\(415\) 2798.71 + 4847.51i 0.331044 + 0.573385i
\(416\) 110.727 191.785i 0.0130501 0.0226035i
\(417\) 0 0
\(418\) −37359.0 + 21569.2i −4.37150 + 2.52389i
\(419\) 8260.19 0.963095 0.481547 0.876420i \(-0.340075\pi\)
0.481547 + 0.876420i \(0.340075\pi\)
\(420\) 0 0
\(421\) 5571.81 0.645020 0.322510 0.946566i \(-0.395473\pi\)
0.322510 + 0.946566i \(0.395473\pi\)
\(422\) 14554.9 8403.30i 1.67896 0.969351i
\(423\) 0 0
\(424\) −8772.49 + 15194.4i −1.00479 + 1.74034i
\(425\) −1306.96 2263.72i −0.149169 0.258368i
\(426\) 0 0
\(427\) 4866.89 + 6256.40i 0.551582 + 0.709060i
\(428\) 353.543i 0.0399279i
\(429\) 0 0
\(430\) −269.678 155.699i −0.0302443 0.0174616i
\(431\) 6094.88 + 3518.88i 0.681160 + 0.393268i 0.800292 0.599611i \(-0.204678\pi\)
−0.119132 + 0.992878i \(0.538011\pi\)
\(432\) 0 0
\(433\) 9212.26i 1.02243i 0.859452 + 0.511216i \(0.170805\pi\)
−0.859452 + 0.511216i \(0.829195\pi\)
\(434\) −1221.45 8825.63i −0.135096 0.976138i
\(435\) 0 0
\(436\) 7463.18 + 12926.6i 0.819774 + 1.41989i
\(437\) −7698.48 + 13334.2i −0.842719 + 1.45963i
\(438\) 0 0
\(439\) −7345.30 + 4240.81i −0.798570 + 0.461054i −0.842971 0.537959i \(-0.819195\pi\)
0.0444012 + 0.999014i \(0.485862\pi\)
\(440\) 25782.7 2.79350
\(441\) 0 0
\(442\) 2969.26 0.319532
\(443\) −11305.9 + 6527.49i −1.21255 + 0.700068i −0.963315 0.268374i \(-0.913514\pi\)
−0.249239 + 0.968442i \(0.580180\pi\)
\(444\) 0 0
\(445\) −163.692 + 283.523i −0.0174376 + 0.0302029i
\(446\) −9478.70 16417.6i −1.00634 1.74304i
\(447\) 0 0
\(448\) 1451.18 + 10485.6i 0.153040 + 1.10580i
\(449\) 14114.0i 1.48348i −0.670689 0.741738i \(-0.734002\pi\)
0.670689 0.741738i \(-0.265998\pi\)
\(450\) 0 0
\(451\) −12153.9 7017.03i −1.26896 0.732637i
\(452\) −1630.66 941.459i −0.169689 0.0979702i
\(453\) 0 0
\(454\) 2945.97i 0.304540i
\(455\) −1285.34 1652.31i −0.132435 0.170245i
\(456\) 0 0
\(457\) 4486.87 + 7771.49i 0.459271 + 0.795481i 0.998923 0.0464073i \(-0.0147772\pi\)
−0.539651 + 0.841889i \(0.681444\pi\)
\(458\) 5373.63 9307.40i 0.548238 0.949577i
\(459\) 0 0
\(460\) 16279.7 9399.06i 1.65009 0.952682i
\(461\) −955.010 −0.0964842 −0.0482421 0.998836i \(-0.515362\pi\)
−0.0482421 + 0.998836i \(0.515362\pi\)
\(462\) 0 0
\(463\) 12004.5 1.20496 0.602479 0.798135i \(-0.294180\pi\)
0.602479 + 0.798135i \(0.294180\pi\)
\(464\) 5825.73 3363.49i 0.582872 0.336521i
\(465\) 0 0
\(466\) 5802.82 10050.8i 0.576846 0.999127i
\(467\) −2532.46 4386.34i −0.250938 0.434638i 0.712846 0.701320i \(-0.247406\pi\)
−0.963784 + 0.266683i \(0.914072\pi\)
\(468\) 0 0
\(469\) −2811.24 1142.69i −0.276783 0.112505i
\(470\) 3561.59i 0.349540i
\(471\) 0 0
\(472\) −7304.43 4217.21i −0.712317 0.411256i
\(473\) −234.981 135.666i −0.0228423 0.0131880i
\(474\) 0 0
\(475\) 6214.52i 0.600299i
\(476\) −15788.6 + 12282.1i −1.52032 + 1.18266i
\(477\) 0 0
\(478\) −7341.75 12716.3i −0.702518 1.21680i
\(479\) 7606.85 13175.5i 0.725607 1.25679i −0.233116 0.972449i \(-0.574892\pi\)
0.958724 0.284340i \(-0.0917744\pi\)
\(480\) 0 0
\(481\) 722.332 417.038i 0.0684730 0.0395329i
\(482\) 12238.8 1.15656
\(483\) 0 0
\(484\) 25031.7 2.35084
\(485\) −15265.9 + 8813.75i −1.42925 + 0.825179i
\(486\) 0 0
\(487\) −7905.92 + 13693.5i −0.735629 + 1.27415i 0.218817 + 0.975766i \(0.429780\pi\)
−0.954447 + 0.298382i \(0.903553\pi\)
\(488\) 7987.88 + 13835.4i 0.740972 + 1.28340i
\(489\) 0 0
\(490\) 20646.9 + 5240.14i 1.90354 + 0.483113i
\(491\) 18064.2i 1.66034i 0.557512 + 0.830169i \(0.311756\pi\)
−0.557512 + 0.830169i \(0.688244\pi\)
\(492\) 0 0
\(493\) −7139.42 4121.94i −0.652217 0.376558i
\(494\) 6113.57 + 3529.67i 0.556806 + 0.321472i
\(495\) 0 0
\(496\) 5560.54i 0.503378i
\(497\) −1464.93 + 202.744i −0.132216 + 0.0182984i
\(498\) 0 0
\(499\) 5262.33 + 9114.62i 0.472092 + 0.817688i 0.999490 0.0319305i \(-0.0101655\pi\)
−0.527398 + 0.849619i \(0.676832\pi\)
\(500\) 8709.04 15084.5i 0.778960 1.34920i
\(501\) 0 0
\(502\) 5503.38 3177.38i 0.489299 0.282497i
\(503\) −7790.82 −0.690607 −0.345304 0.938491i \(-0.612224\pi\)
−0.345304 + 0.938491i \(0.612224\pi\)
\(504\) 0 0
\(505\) −9108.83 −0.802649
\(506\) 21426.0 12370.3i 1.88242 1.08681i
\(507\) 0 0
\(508\) 6929.41 12002.1i 0.605202 1.04824i
\(509\) 5098.24 + 8830.41i 0.443960 + 0.768961i 0.997979 0.0635430i \(-0.0202400\pi\)
−0.554019 + 0.832504i \(0.686907\pi\)
\(510\) 0 0
\(511\) −5366.74 + 13203.2i −0.464600 + 1.14300i
\(512\) 18199.6i 1.57093i
\(513\) 0 0
\(514\) 31482.9 + 18176.7i 2.70166 + 1.55980i
\(515\) 19815.6 + 11440.5i 1.69549 + 0.978892i
\(516\) 0 0
\(517\) 3103.35i 0.263994i
\(518\) −3195.93 + 7862.57i −0.271083 + 0.666914i
\(519\) 0 0
\(520\) −2109.59 3653.92i −0.177907 0.308144i
\(521\) 963.789 1669.33i 0.0810449 0.140374i −0.822654 0.568542i \(-0.807508\pi\)
0.903699 + 0.428168i \(0.140841\pi\)
\(522\) 0 0
\(523\) −6716.70 + 3877.89i −0.561569 + 0.324222i −0.753775 0.657133i \(-0.771769\pi\)
0.192206 + 0.981355i \(0.438436\pi\)
\(524\) −25183.0 −2.09948
\(525\) 0 0
\(526\) −7476.33 −0.619741
\(527\) −5901.47 + 3407.21i −0.487803 + 0.281633i
\(528\) 0 0
\(529\) −1668.28 + 2889.55i −0.137115 + 0.237491i
\(530\) −14595.2 25279.7i −1.19618 2.07185i
\(531\) 0 0
\(532\) −47108.2 + 6519.68i −3.83910 + 0.531324i
\(533\) 2296.59i 0.186635i
\(534\) 0 0
\(535\) −249.371 143.975i −0.0201519 0.0116347i
\(536\) −5296.80 3058.11i −0.426841 0.246437i
\(537\) 0 0
\(538\) 19053.8i 1.52689i
\(539\) 17990.4 + 4565.93i 1.43767 + 0.364876i
\(540\) 0 0
\(541\) −8380.42 14515.3i −0.665993 1.15353i −0.979015 0.203788i \(-0.934675\pi\)
0.313022 0.949746i \(-0.398659\pi\)
\(542\) −8756.93 + 15167.4i −0.693989 + 1.20202i
\(543\) 0 0
\(544\) 1492.59 861.748i 0.117637 0.0679176i
\(545\) −12157.0 −0.955503
\(546\) 0 0
\(547\) 5869.79 0.458819 0.229410 0.973330i \(-0.426320\pi\)
0.229410 + 0.973330i \(0.426320\pi\)
\(548\) −9642.95 + 5567.36i −0.751690 + 0.433989i
\(549\) 0 0
\(550\) −4992.91 + 8647.97i −0.387088 + 0.670456i
\(551\) −9799.82 16973.8i −0.757688 1.31235i
\(552\) 0 0
\(553\) 7818.00 6081.67i 0.601185 0.467666i
\(554\) 1382.16i 0.105997i
\(555\) 0 0
\(556\) −20791.6 12004.1i −1.58590 0.915621i
\(557\) −18756.5 10829.1i −1.42682 0.823774i −0.429951 0.902852i \(-0.641469\pi\)
−0.996868 + 0.0790779i \(0.974802\pi\)
\(558\) 0 0
\(559\) 44.4019i 0.00335957i
\(560\) 12315.6 + 5005.98i 0.929341 + 0.377752i
\(561\) 0 0
\(562\) 781.517 + 1353.63i 0.0586589 + 0.101600i
\(563\) 4795.36 8305.80i 0.358970 0.621755i −0.628819 0.777552i \(-0.716461\pi\)
0.987789 + 0.155797i \(0.0497946\pi\)
\(564\) 0 0
\(565\) 1328.11 766.787i 0.0988923 0.0570955i
\(566\) −33098.3 −2.45799
\(567\) 0 0
\(568\) −2980.70 −0.220189
\(569\) 14405.5 8317.01i 1.06135 0.612772i 0.135546 0.990771i \(-0.456721\pi\)
0.925806 + 0.377999i \(0.123388\pi\)
\(570\) 0 0
\(571\) −3165.51 + 5482.83i −0.232001 + 0.401838i −0.958397 0.285439i \(-0.907861\pi\)
0.726396 + 0.687277i \(0.241194\pi\)
\(572\) −3754.91 6503.69i −0.274477 0.475408i
\(573\) 0 0
\(574\) −14348.8 18445.5i −1.04340 1.34129i
\(575\) 3564.14i 0.258495i
\(576\) 0 0
\(577\) 8431.94 + 4868.18i 0.608364 + 0.351239i 0.772325 0.635228i \(-0.219094\pi\)
−0.163961 + 0.986467i \(0.552427\pi\)
\(578\) −688.509 397.511i −0.0495470 0.0286060i
\(579\) 0 0
\(580\) 23929.1i 1.71311i
\(581\) 1113.39 + 8044.83i 0.0795028 + 0.574450i
\(582\) 0 0
\(583\) −12717.4 22027.1i −0.903430 1.56479i
\(584\) −14362.6 + 24876.8i −1.01769 + 1.76268i
\(585\) 0 0
\(586\) 13399.3 7736.09i 0.944573 0.545350i
\(587\) 10940.3 0.769255 0.384628 0.923072i \(-0.374330\pi\)
0.384628 + 0.923072i \(0.374330\pi\)
\(588\) 0 0
\(589\) −16201.1 −1.13337
\(590\) 12152.7 7016.39i 0.848001 0.489594i
\(591\) 0 0
\(592\) −2648.44 + 4587.23i −0.183869 + 0.318470i
\(593\) 12430.4 + 21530.0i 0.860799 + 1.49095i 0.871159 + 0.491000i \(0.163369\pi\)
−0.0103608 + 0.999946i \(0.503298\pi\)
\(594\) 0 0
\(595\) −2233.49 16138.2i −0.153889 1.11193i
\(596\) 37629.6i 2.58619i
\(597\) 0 0
\(598\) −3506.24 2024.33i −0.239767 0.138430i
\(599\) 20207.8 + 11667.0i 1.37841 + 0.795825i 0.991968 0.126488i \(-0.0403706\pi\)
0.386442 + 0.922314i \(0.373704\pi\)
\(600\) 0 0
\(601\) 13012.4i 0.883175i 0.897218 + 0.441587i \(0.145584\pi\)
−0.897218 + 0.441587i \(0.854416\pi\)
\(602\) −277.419 356.622i −0.0187820 0.0241442i
\(603\) 0 0
\(604\) 19339.1 + 33496.2i 1.30281 + 2.25653i
\(605\) −10193.8 + 17656.1i −0.685017 + 1.18648i
\(606\) 0 0
\(607\) 7355.69 4246.81i 0.491859 0.283975i −0.233486 0.972360i \(-0.575013\pi\)
0.725345 + 0.688385i \(0.241680\pi\)
\(608\) 4097.57 0.273320
\(609\) 0 0
\(610\) −26579.7 −1.76423
\(611\) −439.806 + 253.922i −0.0291205 + 0.0168127i
\(612\) 0 0
\(613\) 4569.79 7915.11i 0.301097 0.521514i −0.675288 0.737554i \(-0.735981\pi\)
0.976385 + 0.216040i \(0.0693140\pi\)
\(614\) −7240.66 12541.2i −0.475911 0.824302i
\(615\) 0 0
\(616\) 34655.6 + 14086.6i 2.26674 + 0.921370i
\(617\) 7360.91i 0.480290i −0.970737 0.240145i \(-0.922805\pi\)
0.970737 0.240145i \(-0.0771950\pi\)
\(618\) 0 0
\(619\) 19878.5 + 11476.9i 1.29077 + 0.745225i 0.978790 0.204864i \(-0.0656753\pi\)
0.311978 + 0.950089i \(0.399009\pi\)
\(620\) 17129.9 + 9889.96i 1.10960 + 0.640629i
\(621\) 0 0
\(622\) 22778.7i 1.46840i
\(623\) −374.930 + 291.660i −0.0241112 + 0.0187562i
\(624\) 0 0
\(625\) 9463.74 + 16391.7i 0.605679 + 1.04907i
\(626\) 2389.02 4137.91i 0.152531 0.264192i
\(627\) 0 0
\(628\) 33064.0 19089.5i 2.10095 1.21298i
\(629\) 6491.31 0.411487
\(630\) 0 0
\(631\) 21126.0 1.33282 0.666412 0.745584i \(-0.267829\pi\)
0.666412 + 0.745584i \(0.267829\pi\)
\(632\) 17288.7 9981.66i 1.08815 0.628242i
\(633\) 0 0
\(634\) 11994.0 20774.2i 0.751330 1.30134i
\(635\) 5643.77 + 9775.29i 0.352703 + 0.610899i
\(636\) 0 0
\(637\) −824.929 2923.19i −0.0513106 0.181823i
\(638\) 31493.7i 1.95431i
\(639\) 0 0
\(640\) −28529.0 16471.2i −1.76204 1.01732i
\(641\) −15447.5 8918.61i −0.951855 0.549554i −0.0581985 0.998305i \(-0.518536\pi\)
−0.893657 + 0.448751i \(0.851869\pi\)
\(642\) 0 0
\(643\) 25449.0i 1.56082i −0.625266 0.780412i \(-0.715009\pi\)
0.625266 0.780412i \(-0.284991\pi\)
\(644\) 27017.4 3739.16i 1.65316 0.228794i
\(645\) 0 0
\(646\) 27470.1 + 47579.6i 1.67306 + 2.89782i
\(647\) −13149.2 + 22775.1i −0.798993 + 1.38390i 0.121280 + 0.992618i \(0.461300\pi\)
−0.920273 + 0.391277i \(0.872033\pi\)
\(648\) 0 0
\(649\) 10589.1 6113.64i 0.640462 0.369771i
\(650\) 1634.12 0.0986083
\(651\) 0 0
\(652\) −51357.4 −3.08483
\(653\) 8203.79 4736.46i 0.491637 0.283847i −0.233616 0.972329i \(-0.575056\pi\)
0.725253 + 0.688482i \(0.241723\pi\)
\(654\) 0 0
\(655\) 10255.4 17762.8i 0.611771 1.05962i
\(656\) −7292.34 12630.7i −0.434022 0.751747i
\(657\) 0 0
\(658\) 1945.90 4787.28i 0.115287 0.283629i
\(659\) 22384.5i 1.32318i −0.749865 0.661591i \(-0.769882\pi\)
0.749865 0.661591i \(-0.230118\pi\)
\(660\) 0 0
\(661\) −19857.3 11464.6i −1.16847 0.674618i −0.215153 0.976580i \(-0.569025\pi\)
−0.953320 + 0.301962i \(0.902359\pi\)
\(662\) −16999.6 9814.73i −0.998049 0.576224i
\(663\) 0 0
\(664\) 16368.8i 0.956677i
\(665\) 14585.4 35882.7i 0.850521 2.09244i
\(666\) 0 0
\(667\) 5620.37 + 9734.77i 0.326269 + 0.565115i
\(668\) −2864.73 + 4961.85i −0.165928 + 0.287395i
\(669\) 0 0
\(670\) 8812.56 5087.93i 0.508147 0.293379i
\(671\) −23159.9 −1.33245
\(672\) 0 0
\(673\) −4873.86 −0.279158 −0.139579 0.990211i \(-0.544575\pi\)
−0.139579 + 0.990211i \(0.544575\pi\)
\(674\) −11678.4 + 6742.51i −0.667409 + 0.385329i
\(675\) 0 0
\(676\) 16601.3 28754.2i 0.944541 1.63599i
\(677\) 8123.71 + 14070.7i 0.461181 + 0.798789i 0.999020 0.0442583i \(-0.0140925\pi\)
−0.537839 + 0.843048i \(0.680759\pi\)
\(678\) 0 0
\(679\) −25334.9 + 3506.30i −1.43191 + 0.198173i
\(680\) 32836.3i 1.85179i
\(681\) 0 0
\(682\) 22545.1 + 13016.4i 1.26583 + 0.730827i
\(683\) −18786.2 10846.2i −1.05247 0.607641i −0.129127 0.991628i \(-0.541217\pi\)
−0.923339 + 0.383987i \(0.874551\pi\)
\(684\) 0 0
\(685\) 9068.85i 0.505844i
\(686\) 24889.4 + 18324.1i 1.38525 + 1.01985i
\(687\) 0 0
\(688\) −140.989 244.200i −0.00781273 0.0135320i
\(689\) −2081.12 + 3604.61i −0.115072 + 0.199310i
\(690\) 0 0
\(691\) −19499.9 + 11258.3i −1.07353 + 0.619803i −0.929144 0.369718i \(-0.879454\pi\)
−0.144387 + 0.989521i \(0.546121\pi\)
\(692\) 32800.5 1.80186
\(693\) 0 0
\(694\) −21029.2 −1.15023
\(695\) 16934.1 9776.90i 0.924239 0.533610i
\(696\) 0 0
\(697\) −8936.75 + 15478.9i −0.485658 + 0.841184i
\(698\) 3239.49 + 5610.97i 0.175669 + 0.304267i
\(699\) 0 0
\(700\) −8689.20 + 6759.38i −0.469173 + 0.364972i
\(701\) 33929.0i 1.82807i −0.405631 0.914037i \(-0.632948\pi\)
0.405631 0.914037i \(-0.367052\pi\)
\(702\) 0 0
\(703\) 13365.3 + 7716.46i 0.717044 + 0.413986i
\(704\) −26785.4 15464.5i −1.43397 0.827901i
\(705\) 0 0
\(706\) 55214.9i 2.94340i
\(707\) −12243.6 4976.68i −0.651296 0.264734i
\(708\) 0 0
\(709\) −9593.62 16616.6i −0.508175 0.880185i −0.999955 0.00946553i \(-0.996987\pi\)
0.491780 0.870719i \(-0.336346\pi\)
\(710\) 2479.57 4294.74i 0.131066 0.227012i
\(711\) 0 0
\(712\) −829.121 + 478.693i −0.0436413 + 0.0251963i
\(713\) 9291.63 0.488043
\(714\) 0 0
\(715\) 6116.49 0.319922
\(716\) −23884.4 + 13789.7i −1.24665 + 0.719754i
\(717\) 0 0
\(718\) −20358.4 + 35261.8i −1.05818 + 1.83281i
\(719\) 6883.43 + 11922.4i 0.357036 + 0.618404i 0.987464 0.157844i \(-0.0504542\pi\)
−0.630429 + 0.776247i \(0.717121\pi\)
\(720\) 0 0
\(721\) 20384.3 + 26204.0i 1.05291 + 1.35352i
\(722\) 97247.2i 5.01269i
\(723\) 0 0
\(724\) −43398.2 25056.0i −2.22774 1.28618i
\(725\) −3929.15 2268.49i −0.201276 0.116207i
\(726\) 0 0
\(727\) 12226.1i 0.623717i −0.950129 0.311858i \(-0.899049\pi\)
0.950129 0.311858i \(-0.100951\pi\)
\(728\) −839.242 6063.97i −0.0427258 0.308717i
\(729\) 0 0
\(730\) −23895.8 41388.7i −1.21154 2.09845i
\(731\) −172.782 + 299.267i −0.00874222 + 0.0151420i
\(732\) 0 0
\(733\) 2256.76 1302.94i 0.113718 0.0656553i −0.442062 0.896984i \(-0.645753\pi\)
0.555780 + 0.831329i \(0.312420\pi\)
\(734\) −13209.8 −0.664282
\(735\) 0 0
\(736\) −2350.03 −0.117695
\(737\) 7678.71 4433.30i 0.383784 0.221578i
\(738\) 0 0
\(739\) −16871.7 + 29222.7i −0.839833 + 1.45463i 0.0502016 + 0.998739i \(0.484014\pi\)
−0.890034 + 0.455894i \(0.849320\pi\)
\(740\) −9421.01 16317.7i −0.468004 0.810607i
\(741\) 0 0
\(742\) −5806.31 41953.7i −0.287273 2.07570i
\(743\) 14586.9i 0.720244i −0.932905 0.360122i \(-0.882735\pi\)
0.932905 0.360122i \(-0.117265\pi\)
\(744\) 0 0
\(745\) 26542.0 + 15324.0i 1.30527 + 0.753597i
\(746\) 25690.5 + 14832.4i 1.26085 + 0.727953i
\(747\) 0 0
\(748\) 58446.1i 2.85695i
\(749\) −256.528 329.768i −0.0125145 0.0160874i
\(750\) 0 0
\(751\) 3757.62 + 6508.39i 0.182580 + 0.316238i 0.942758 0.333477i \(-0.108222\pi\)
−0.760178 + 0.649714i \(0.774889\pi\)
\(752\) 1612.55 2793.02i 0.0781965 0.135440i
\(753\) 0 0
\(754\) 4463.28 2576.88i 0.215574 0.124462i
\(755\) −31502.0 −1.51851
\(756\) 0 0
\(757\) 23917.4 1.14834 0.574169 0.818737i \(-0.305325\pi\)
0.574169 + 0.818737i \(0.305325\pi\)
\(758\) 41807.9 24137.8i 2.00334 1.15663i
\(759\) 0 0
\(760\) 39033.7 67608.4i 1.86303 3.22686i
\(761\) −6099.27 10564.2i −0.290537 0.503224i 0.683400 0.730044i \(-0.260500\pi\)
−0.973937 + 0.226820i \(0.927167\pi\)
\(762\) 0 0
\(763\) −16340.7 6642.07i −0.775327 0.315150i
\(764\) 8609.80i 0.407712i
\(765\) 0 0
\(766\) −5136.59 2965.61i −0.242288 0.139885i
\(767\) −1732.85 1000.46i −0.0815769 0.0470985i
\(768\) 0 0
\(769\) 2013.08i 0.0943999i −0.998885 0.0471999i \(-0.984970\pi\)
0.998885 0.0471999i \(-0.0150298\pi\)
\(770\) −49125.7 + 38215.2i −2.29918 + 1.78855i
\(771\) 0 0
\(772\) −5520.28 9561.41i −0.257357 0.445755i
\(773\) −15139.1 + 26221.7i −0.704418 + 1.22009i 0.262483 + 0.964937i \(0.415459\pi\)
−0.966901 + 0.255152i \(0.917875\pi\)
\(774\) 0 0
\(775\) −3247.85 + 1875.14i −0.150537 + 0.0869125i
\(776\) −51549.0 −2.38467
\(777\) 0 0
\(778\) 63903.5 2.94480
\(779\) −36800.7 + 21246.9i −1.69258 + 0.977213i
\(780\) 0 0
\(781\) 2160.54 3742.17i 0.0989888 0.171454i
\(782\) −15754.6 27287.8i −0.720439 1.24784i
\(783\) 0 0
\(784\) 13818.9 + 13457.5i 0.629506 + 0.613041i
\(785\) 31095.5i 1.41382i
\(786\) 0 0
\(787\) 24839.3 + 14341.0i 1.12507 + 0.649557i 0.942689 0.333671i \(-0.108288\pi\)
0.182377 + 0.983229i \(0.441621\pi\)
\(788\) 72175.3 + 41670.4i 3.26287 + 1.88382i
\(789\) 0 0
\(790\) 33214.0i 1.49582i
\(791\) 2204.11 305.045i 0.0990761 0.0137119i
\(792\) 0 0
\(793\) 1894.99 + 3282.21i 0.0848586 + 0.146979i
\(794\) −7577.89 + 13125.3i −0.338702 + 0.586649i
\(795\) 0 0
\(796\) −33785.7 + 19506.2i −1.50440 + 0.868566i
\(797\) 27108.9 1.20483 0.602413 0.798184i \(-0.294206\pi\)
0.602413 + 0.798184i \(0.294206\pi\)
\(798\) 0 0
\(799\) −3952.36 −0.174999
\(800\) 821.441 474.259i 0.0363029 0.0209595i
\(801\) 0 0
\(802\) −27316.4 + 47313.3i −1.20271 + 2.08316i
\(803\) −20821.3 36063.5i −0.915028 1.58487i
\(804\) 0 0
\(805\) −8364.97 + 20579.4i −0.366244 + 0.901029i
\(806\) 4260.11i 0.186174i
\(807\) 0 0
\(808\) −23068.7 13318.7i −1.00440 0.579890i
\(809\) 17128.3 + 9889.03i 0.744375 + 0.429765i 0.823658 0.567087i \(-0.191930\pi\)
−0.0792832 + 0.996852i \(0.525263\pi\)
\(810\) 0 0
\(811\) 44456.6i 1.92488i −0.271487 0.962442i \(-0.587516\pi\)
0.271487 0.962442i \(-0.412484\pi\)
\(812\) −13073.9 + 32164.1i −0.565028 + 1.39007i
\(813\) 0 0
\(814\) −12399.2 21476.1i −0.533897 0.924736i
\(815\) 20914.4 36224.8i 0.898896 1.55693i
\(816\) 0 0
\(817\) −711.499 + 410.784i −0.0304678 + 0.0175906i
\(818\) 60334.8 2.57892
\(819\) 0 0
\(820\) 51880.6 2.20945
\(821\) −9958.57 + 5749.58i −0.423333 + 0.244411i −0.696502 0.717555i \(-0.745261\pi\)
0.273169 + 0.961966i \(0.411928\pi\)
\(822\) 0 0
\(823\) −596.549 + 1033.25i −0.0252666 + 0.0437630i −0.878382 0.477959i \(-0.841377\pi\)
0.853116 + 0.521722i \(0.174710\pi\)
\(824\) 33456.1 + 57947.6i 1.41444 + 2.44988i
\(825\) 0 0
\(826\) 20168.5 2791.28i 0.849577 0.117580i
\(827\) 29552.9i 1.24263i −0.783561 0.621315i \(-0.786599\pi\)
0.783561 0.621315i \(-0.213401\pi\)
\(828\) 0 0
\(829\) −11762.7 6791.21i −0.492806 0.284521i 0.232932 0.972493i \(-0.425168\pi\)
−0.725738 + 0.687972i \(0.758501\pi\)
\(830\) −23585.0 13616.8i −0.986323 0.569454i
\(831\) 0 0
\(832\) 5061.36i 0.210903i
\(833\) 5815.07 22912.2i 0.241873 0.953015i
\(834\) 0 0
\(835\) −2333.22 4041.26i −0.0967000 0.167489i
\(836\) 69477.1 120338.i 2.87430 4.97843i
\(837\) 0 0
\(838\) −34804.7 + 20094.5i −1.43474 + 0.828346i
\(839\) −11623.6 −0.478297 −0.239149 0.970983i \(-0.576868\pi\)
−0.239149 + 0.970983i \(0.576868\pi\)
\(840\) 0 0
\(841\) 10080.1 0.413303
\(842\) −23477.1 + 13554.5i −0.960896 + 0.554774i
\(843\) 0 0
\(844\) −27068.1 + 46883.2i −1.10393 + 1.91207i
\(845\) 13521.2 + 23419.3i 0.550464 + 0.953432i
\(846\) 0 0
\(847\) −23348.4 + 18162.9i −0.947178 + 0.736816i
\(848\) 26432.7i 1.07040i
\(849\) 0 0
\(850\) 11013.9 + 6358.87i 0.444439 + 0.256597i
\(851\) −7665.24 4425.53i −0.308767 0.178267i
\(852\) 0 0
\(853\) 1019.82i 0.0409354i 0.999791 + 0.0204677i \(0.00651553\pi\)
−0.999791 + 0.0204677i \(0.993484\pi\)
\(854\) −35726.8 14522.0i −1.43155 0.581888i
\(855\) 0 0
\(856\) −421.032 729.249i −0.0168114 0.0291182i
\(857\) −4299.43 + 7446.83i −0.171372 + 0.296825i −0.938900 0.344191i \(-0.888153\pi\)
0.767528 + 0.641016i \(0.221487\pi\)
\(858\) 0 0
\(859\) 32182.1 18580.4i 1.27828 0.738013i 0.301745 0.953389i \(-0.402431\pi\)
0.976531 + 0.215375i \(0.0690974\pi\)
\(860\) 1003.05 0.0397718
\(861\) 0 0
\(862\) −34241.4 −1.35298
\(863\) −10634.2 + 6139.68i −0.419459 + 0.242175i −0.694846 0.719159i \(-0.744527\pi\)
0.275387 + 0.961334i \(0.411194\pi\)
\(864\) 0 0
\(865\) −13357.5 + 23135.8i −0.525049 + 0.909411i
\(866\) −22410.6 38816.3i −0.879381 1.52313i
\(867\) 0 0
\(868\) 17621.6 + 22652.5i 0.689072 + 0.885803i
\(869\) 28940.6i 1.12974i
\(870\) 0 0
\(871\) −1256.57 725.483i −0.0488833 0.0282228i
\(872\) −30788.4 17775.7i −1.19567 0.690322i
\(873\) 0 0
\(874\) 74912.3i 2.89925i
\(875\) 2821.84 + 20389.3i 0.109024 + 0.787753i
\(876\) 0 0
\(877\) −15935.8 27601.6i −0.613583 1.06276i −0.990631 0.136564i \(-0.956394\pi\)
0.377048 0.926194i \(-0.376939\pi\)
\(878\) 20633.2 35737.8i 0.793094 1.37368i
\(879\) 0 0
\(880\) −33639.3 + 19421.7i −1.28861 + 0.743982i
\(881\) 29427.6 1.12536 0.562679 0.826676i \(-0.309771\pi\)
0.562679 + 0.826676i \(0.309771\pi\)
\(882\) 0 0
\(883\) 846.860 0.0322753 0.0161377 0.999870i \(-0.494863\pi\)
0.0161377 + 0.999870i \(0.494863\pi\)
\(884\) −8282.97 + 4782.18i −0.315143 + 0.181948i
\(885\) 0 0
\(886\) 31758.8 55007.8i 1.20424 2.08580i
\(887\) 3940.07 + 6824.39i 0.149148 + 0.258332i 0.930913 0.365241i \(-0.119014\pi\)
−0.781765 + 0.623574i \(0.785680\pi\)
\(888\) 0 0
\(889\) 2245.22 + 16222.9i 0.0847043 + 0.612034i
\(890\) 1592.85i 0.0599916i
\(891\) 0 0
\(892\) 52883.1 + 30532.1i 1.98504 + 1.14606i
\(893\) −8137.73 4698.32i −0.304948 0.176062i
\(894\) 0 0
\(895\) 22462.4i 0.838923i
\(896\) −29347.8 37726.6i −1.09424 1.40665i
\(897\) 0 0
\(898\) 34335.1 + 59470.1i 1.27592 + 2.20996i
\(899\) −5913.91 + 10243.2i −0.219399 + 0.380011i
\(900\) 0 0
\(901\) −28053.3 + 16196.6i −1.03728 + 0.598875i
\(902\) 68281.2 2.52053
\(903\) 0 0
\(904\) 4484.71 0.164999
\(905\) 35346.4 20407.2i 1.29829 0.749569i
\(906\) 0 0
\(907\) −10646.6 + 18440.4i −0.389762 + 0.675088i −0.992417 0.122914i \(-0.960776\pi\)
0.602655 + 0.798002i \(0.294109\pi\)
\(908\) 4744.67 + 8218.00i 0.173411 + 0.300357i
\(909\) 0 0
\(910\) 9435.42 + 3835.24i 0.343715 + 0.139711i
\(911\) 14634.3i 0.532225i 0.963942 + 0.266112i \(0.0857393\pi\)
−0.963942 + 0.266112i \(0.914261\pi\)
\(912\) 0 0
\(913\) −20550.5 11864.8i −0.744931 0.430086i
\(914\) −37811.3 21830.4i −1.36837 0.790027i
\(915\) 0 0
\(916\) 34618.2i 1.24871i
\(917\) 23489.5 18272.6i 0.845901 0.658032i
\(918\) 0 0
\(919\) −6098.61 10563.1i −0.218906 0.379156i 0.735568 0.677451i \(-0.236915\pi\)
−0.954474 + 0.298295i \(0.903582\pi\)
\(920\) −22386.5 + 38774.6i −0.802242 + 1.38952i
\(921\) 0 0
\(922\) 4023.98 2323.25i 0.143734 0.0829849i
\(923\) −707.119 −0.0252168
\(924\) 0 0
\(925\) 3572.46 0.126986
\(926\) −50581.5 + 29203.2i −1.79504 + 1.03637i
\(927\) 0 0
\(928\) 1495.74 2590.70i 0.0529095 0.0916420i
\(929\) 12348.1 + 21387.5i 0.436091 + 0.755331i 0.997384 0.0722858i \(-0.0230294\pi\)
−0.561293 + 0.827617i \(0.689696\pi\)
\(930\) 0 0
\(931\) 39209.6 40262.6i 1.38028 1.41735i
\(932\) 37383.2i 1.31387i
\(933\) 0 0
\(934\) 21341.3 + 12321.4i 0.747653 + 0.431658i
\(935\) 41224.9 + 23801.2i 1.44192 + 0.832495i
\(936\) 0 0
\(937\) 14448.0i 0.503730i −0.967762 0.251865i \(-0.918956\pi\)
0.967762 0.251865i \(-0.0810439\pi\)
\(938\) 14625.1 2024.09i 0.509092 0.0704573i
\(939\) 0 0
\(940\) 5736.17 + 9935.33i 0.199035 + 0.344739i
\(941\) −15580.4 + 26986.0i −0.539752 + 0.934878i 0.459165 + 0.888351i \(0.348149\pi\)
−0.998917 + 0.0465268i \(0.985185\pi\)
\(942\) 0 0
\(943\) 21105.9 12185.5i 0.728845 0.420799i
\(944\) 12707.0 0.438113
\(945\) 0 0
\(946\) 1320.14 0.0453715
\(947\) 8887.48 5131.19i 0.304968 0.176073i −0.339705 0.940532i \(-0.610327\pi\)
0.644672 + 0.764459i \(0.276994\pi\)
\(948\) 0 0
\(949\) −3407.28 + 5901.58i −0.116549 + 0.201869i
\(950\) 15118.0 + 26185.2i 0.516310 + 0.894274i
\(951\) 0 0
\(952\) 17940.4 44136.6i 0.610767 1.50260i
\(953\) 12686.9i 0.431236i −0.976478 0.215618i \(-0.930823\pi\)
0.976478 0.215618i \(-0.0691766\pi\)
\(954\) 0 0
\(955\) −6072.91 3506.20i −0.205775 0.118804i
\(956\) 40960.7 + 23648.7i 1.38574 + 0.800055i
\(957\) 0 0
\(958\) 74020.6i 2.49634i
\(959\) 4954.83 12189.8i 0.166840 0.410458i
\(960\) 0 0
\(961\) −10007.0 17332.7i −0.335908 0.581810i
\(962\) −2029.05 + 3514.43i −0.0680035 + 0.117785i
\(963\) 0 0
\(964\) −34141.2 + 19711.4i −1.14068 + 0.658571i
\(965\) 8992.17 0.299967
\(966\) 0 0
\(967\) 16129.8 0.536401 0.268200 0.963363i \(-0.413571\pi\)
0.268200 + 0.963363i \(0.413571\pi\)
\(968\) −51632.7 + 29810.1i −1.71440 + 0.989808i
\(969\) 0 0
\(970\) 42882.3 74274.4i 1.41945 2.45856i
\(971\) 26382.4 + 45695.6i 0.871937 + 1.51024i 0.859990 + 0.510311i \(0.170470\pi\)
0.0119472 + 0.999929i \(0.496197\pi\)
\(972\) 0 0
\(973\) 28103.5 3889.47i 0.925956 0.128151i
\(974\) 76930.8i 2.53082i
\(975\) 0 0
\(976\) −20844.0 12034.3i −0.683606 0.394680i
\(977\) −46759.5 26996.6i −1.53118 0.884030i −0.999308 0.0372085i \(-0.988153\pi\)
−0.531877 0.846821i \(-0.678513\pi\)
\(978\) 0 0
\(979\) 1387.91i 0.0453093i
\(980\) −66035.7 + 18635.4i −2.15248 + 0.607434i
\(981\) 0 0
\(982\) −43944.7 76114.4i −1.42804 2.47343i
\(983\) −26119.2 + 45239.8i −0.847480 + 1.46788i 0.0359696 + 0.999353i \(0.488548\pi\)
−0.883450 + 0.468526i \(0.844785\pi\)
\(984\) 0 0
\(985\) −58784.4 + 33939.2i −1.90155 + 1.09786i
\(986\) 40109.7 1.29549
\(987\) 0 0
\(988\) −22739.0 −0.732211
\(989\) 408.057 235.592i 0.0131198 0.00757471i
\(990\) 0 0
\(991\) 4812.21 8334.99i 0.154253 0.267174i −0.778534 0.627603i \(-0.784036\pi\)
0.932787 + 0.360429i \(0.117370\pi\)
\(992\) −1236.38 2141.48i −0.0395718 0.0685403i
\(993\) 0 0
\(994\) 5679.35 4418.01i 0.181226 0.140977i
\(995\) 31774.3i 1.01237i
\(996\) 0 0
\(997\) −25023.0 14447.0i −0.794871 0.458919i 0.0468034 0.998904i \(-0.485097\pi\)
−0.841675 + 0.539985i \(0.818430\pi\)
\(998\) −44346.2 25603.3i −1.40657 0.812082i
\(999\) 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 63.4.p.a.17.1 16
3.2 odd 2 inner 63.4.p.a.17.8 yes 16
4.3 odd 2 1008.4.bt.a.17.7 16
7.2 even 3 441.4.p.c.215.8 16
7.3 odd 6 441.4.c.a.440.2 16
7.4 even 3 441.4.c.a.440.1 16
7.5 odd 6 inner 63.4.p.a.26.8 yes 16
7.6 odd 2 441.4.p.c.80.1 16
12.11 even 2 1008.4.bt.a.17.2 16
21.2 odd 6 441.4.p.c.215.1 16
21.5 even 6 inner 63.4.p.a.26.1 yes 16
21.11 odd 6 441.4.c.a.440.16 16
21.17 even 6 441.4.c.a.440.15 16
21.20 even 2 441.4.p.c.80.8 16
28.19 even 6 1008.4.bt.a.593.2 16
84.47 odd 6 1008.4.bt.a.593.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.p.a.17.1 16 1.1 even 1 trivial
63.4.p.a.17.8 yes 16 3.2 odd 2 inner
63.4.p.a.26.1 yes 16 21.5 even 6 inner
63.4.p.a.26.8 yes 16 7.5 odd 6 inner
441.4.c.a.440.1 16 7.4 even 3
441.4.c.a.440.2 16 7.3 odd 6
441.4.c.a.440.15 16 21.17 even 6
441.4.c.a.440.16 16 21.11 odd 6
441.4.p.c.80.1 16 7.6 odd 2
441.4.p.c.80.8 16 21.20 even 2
441.4.p.c.215.1 16 21.2 odd 6
441.4.p.c.215.8 16 7.2 even 3
1008.4.bt.a.17.2 16 12.11 even 2
1008.4.bt.a.17.7 16 4.3 odd 2
1008.4.bt.a.593.2 16 28.19 even 6
1008.4.bt.a.593.7 16 84.47 odd 6