Properties

Label 63.4.p.a.26.7
Level $63$
Weight $4$
Character 63.26
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 26.7
Root \(3.91663 + 2.26127i\) of defining polynomial
Character \(\chi\) \(=\) 63.26
Dual form 63.4.p.a.17.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.91663 + 2.26127i) q^{2} +(6.22668 + 10.7849i) q^{4} +(0.632851 - 1.09613i) q^{5} +(13.4032 + 12.7810i) q^{7} +20.1405i q^{8} +O(q^{10})\) \(q+(3.91663 + 2.26127i) q^{2} +(6.22668 + 10.7849i) q^{4} +(0.632851 - 1.09613i) q^{5} +(13.4032 + 12.7810i) q^{7} +20.1405i q^{8} +(4.95730 - 2.86210i) q^{10} +(-36.0248 + 20.7989i) q^{11} -85.7355i q^{13} +(23.5942 + 80.3668i) q^{14} +(4.27028 - 7.39634i) q^{16} +(-38.8929 - 67.3645i) q^{17} +(42.1638 + 24.3433i) q^{19} +15.7623 q^{20} -188.128 q^{22} +(-78.7639 - 45.4743i) q^{23} +(61.6990 + 106.866i) q^{25} +(193.871 - 335.795i) q^{26} +(-54.3848 + 224.136i) q^{28} +151.196i q^{29} +(76.3661 - 44.0900i) q^{31} +(172.988 - 99.8747i) q^{32} -351.790i q^{34} +(22.4919 - 6.60319i) q^{35} +(-45.2914 + 78.4470i) q^{37} +(110.093 + 190.687i) q^{38} +(22.0767 + 12.7460i) q^{40} -383.530 q^{41} -227.894 q^{43} +(-448.630 - 259.017i) q^{44} +(-205.660 - 356.213i) q^{46} +(-69.5529 + 120.469i) q^{47} +(16.2918 + 342.613i) q^{49} +558.072i q^{50} +(924.652 - 533.848i) q^{52} +(289.749 - 167.287i) q^{53} +52.6505i q^{55} +(-257.416 + 269.948i) q^{56} +(-341.895 + 592.179i) q^{58} +(440.050 + 762.189i) q^{59} +(11.3944 + 6.57854i) q^{61} +398.797 q^{62} +835.050 q^{64} +(-93.9774 - 54.2579i) q^{65} +(221.212 + 383.151i) q^{67} +(484.348 - 838.915i) q^{68} +(103.024 + 24.9980i) q^{70} -341.552i q^{71} +(-798.218 + 460.851i) q^{73} +(-354.780 + 204.832i) q^{74} +606.311i q^{76} +(-748.678 - 181.661i) q^{77} +(206.564 - 357.780i) q^{79} +(-5.40490 - 9.36157i) q^{80} +(-1502.15 - 867.265i) q^{82} +954.307 q^{83} -98.4538 q^{85} +(-892.579 - 515.331i) q^{86} +(-418.901 - 725.558i) q^{88} +(14.8490 - 25.7193i) q^{89} +(1095.79 - 1149.13i) q^{91} -1132.62i q^{92} +(-544.826 + 314.556i) q^{94} +(53.3668 - 30.8113i) q^{95} -1199.63i q^{97} +(-710.931 + 1378.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} + 56 q^{7}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.91663 + 2.26127i 1.38474 + 0.799480i 0.992716 0.120476i \(-0.0384420\pi\)
0.392023 + 0.919955i \(0.371775\pi\)
\(3\) 0 0
\(4\) 6.22668 + 10.7849i 0.778336 + 1.34812i
\(5\) 0.632851 1.09613i 0.0566040 0.0980409i −0.836335 0.548219i \(-0.815306\pi\)
0.892939 + 0.450178i \(0.148639\pi\)
\(6\) 0 0
\(7\) 13.4032 + 12.7810i 0.723705 + 0.690109i
\(8\) 20.1405i 0.890094i
\(9\) 0 0
\(10\) 4.95730 2.86210i 0.156763 0.0905074i
\(11\) −36.0248 + 20.7989i −0.987443 + 0.570101i −0.904509 0.426454i \(-0.859763\pi\)
−0.0829344 + 0.996555i \(0.526429\pi\)
\(12\) 0 0
\(13\) 85.7355i 1.82914i −0.404433 0.914568i \(-0.632531\pi\)
0.404433 0.914568i \(-0.367469\pi\)
\(14\) 23.5942 + 80.3668i 0.450415 + 1.53421i
\(15\) 0 0
\(16\) 4.27028 7.39634i 0.0667231 0.115568i
\(17\) −38.8929 67.3645i −0.554878 0.961076i −0.997913 0.0645722i \(-0.979432\pi\)
0.443035 0.896504i \(-0.353902\pi\)
\(18\) 0 0
\(19\) 42.1638 + 24.3433i 0.509107 + 0.293933i 0.732466 0.680803i \(-0.238369\pi\)
−0.223360 + 0.974736i \(0.571702\pi\)
\(20\) 15.7623 0.176227
\(21\) 0 0
\(22\) −188.128 −1.82314
\(23\) −78.7639 45.4743i −0.714061 0.412263i 0.0985019 0.995137i \(-0.468595\pi\)
−0.812563 + 0.582874i \(0.801928\pi\)
\(24\) 0 0
\(25\) 61.6990 + 106.866i 0.493592 + 0.854926i
\(26\) 193.871 335.795i 1.46236 2.53288i
\(27\) 0 0
\(28\) −54.3848 + 224.136i −0.367063 + 1.51278i
\(29\) 151.196i 0.968151i 0.875026 + 0.484075i \(0.160844\pi\)
−0.875026 + 0.484075i \(0.839156\pi\)
\(30\) 0 0
\(31\) 76.3661 44.0900i 0.442444 0.255445i −0.262190 0.965016i \(-0.584445\pi\)
0.704634 + 0.709571i \(0.251111\pi\)
\(32\) 172.988 99.8747i 0.955633 0.551735i
\(33\) 0 0
\(34\) 351.790i 1.77445i
\(35\) 22.4919 6.60319i 0.108624 0.0318898i
\(36\) 0 0
\(37\) −45.2914 + 78.4470i −0.201239 + 0.348557i −0.948928 0.315493i \(-0.897830\pi\)
0.747689 + 0.664050i \(0.231164\pi\)
\(38\) 110.093 + 190.687i 0.469987 + 0.814041i
\(39\) 0 0
\(40\) 22.0767 + 12.7460i 0.0872657 + 0.0503829i
\(41\) −383.530 −1.46091 −0.730455 0.682961i \(-0.760692\pi\)
−0.730455 + 0.682961i \(0.760692\pi\)
\(42\) 0 0
\(43\) −227.894 −0.808222 −0.404111 0.914710i \(-0.632419\pi\)
−0.404111 + 0.914710i \(0.632419\pi\)
\(44\) −448.630 259.017i −1.53712 0.887459i
\(45\) 0 0
\(46\) −205.660 356.213i −0.659192 1.14175i
\(47\) −69.5529 + 120.469i −0.215858 + 0.373877i −0.953538 0.301274i \(-0.902588\pi\)
0.737680 + 0.675151i \(0.235922\pi\)
\(48\) 0 0
\(49\) 16.2918 + 342.613i 0.0474981 + 0.998871i
\(50\) 558.072i 1.57847i
\(51\) 0 0
\(52\) 924.652 533.848i 2.46589 1.42368i
\(53\) 289.749 167.287i 0.750945 0.433558i −0.0750904 0.997177i \(-0.523925\pi\)
0.826035 + 0.563619i \(0.190591\pi\)
\(54\) 0 0
\(55\) 52.6505i 0.129080i
\(56\) −257.416 + 269.948i −0.614263 + 0.644166i
\(57\) 0 0
\(58\) −341.895 + 592.179i −0.774017 + 1.34064i
\(59\) 440.050 + 762.189i 0.971010 + 1.68184i 0.692518 + 0.721401i \(0.256501\pi\)
0.278493 + 0.960438i \(0.410165\pi\)
\(60\) 0 0
\(61\) 11.3944 + 6.57854i 0.0239164 + 0.0138081i 0.511911 0.859039i \(-0.328938\pi\)
−0.487994 + 0.872847i \(0.662271\pi\)
\(62\) 398.797 0.816892
\(63\) 0 0
\(64\) 835.050 1.63096
\(65\) −93.9774 54.2579i −0.179330 0.103536i
\(66\) 0 0
\(67\) 221.212 + 383.151i 0.403364 + 0.698647i 0.994130 0.108197i \(-0.0345076\pi\)
−0.590766 + 0.806843i \(0.701174\pi\)
\(68\) 484.348 838.915i 0.863762 1.49608i
\(69\) 0 0
\(70\) 103.024 + 24.9980i 0.175911 + 0.0426833i
\(71\) 341.552i 0.570912i −0.958392 0.285456i \(-0.907855\pi\)
0.958392 0.285456i \(-0.0921450\pi\)
\(72\) 0 0
\(73\) −798.218 + 460.851i −1.27979 + 0.738885i −0.976809 0.214113i \(-0.931314\pi\)
−0.302977 + 0.952998i \(0.597981\pi\)
\(74\) −354.780 + 204.832i −0.557328 + 0.321774i
\(75\) 0 0
\(76\) 606.311i 0.915114i
\(77\) −748.678 181.661i −1.10805 0.268859i
\(78\) 0 0
\(79\) 206.564 357.780i 0.294181 0.509537i −0.680613 0.732643i \(-0.738286\pi\)
0.974794 + 0.223107i \(0.0716198\pi\)
\(80\) −5.40490 9.36157i −0.00755358 0.0130832i
\(81\) 0 0
\(82\) −1502.15 867.265i −2.02298 1.16797i
\(83\) 954.307 1.26203 0.631017 0.775769i \(-0.282638\pi\)
0.631017 + 0.775769i \(0.282638\pi\)
\(84\) 0 0
\(85\) −98.4538 −0.125633
\(86\) −892.579 515.331i −1.11918 0.646157i
\(87\) 0 0
\(88\) −418.901 725.558i −0.507444 0.878918i
\(89\) 14.8490 25.7193i 0.0176853 0.0306319i −0.857047 0.515238i \(-0.827704\pi\)
0.874733 + 0.484606i \(0.161037\pi\)
\(90\) 0 0
\(91\) 1095.79 1149.13i 1.26230 1.32375i
\(92\) 1132.62i 1.28352i
\(93\) 0 0
\(94\) −544.826 + 314.556i −0.597814 + 0.345148i
\(95\) 53.3668 30.8113i 0.0576349 0.0332755i
\(96\) 0 0
\(97\) 1199.63i 1.25572i −0.778328 0.627858i \(-0.783932\pi\)
0.778328 0.627858i \(-0.216068\pi\)
\(98\) −710.931 + 1378.73i −0.732805 + 1.42115i
\(99\) 0 0
\(100\) −768.360 + 1330.84i −0.768360 + 1.33084i
\(101\) −327.422 567.111i −0.322571 0.558710i 0.658447 0.752628i \(-0.271214\pi\)
−0.981018 + 0.193918i \(0.937881\pi\)
\(102\) 0 0
\(103\) −1186.01 684.744i −1.13457 0.655047i −0.189493 0.981882i \(-0.560684\pi\)
−0.945081 + 0.326836i \(0.894018\pi\)
\(104\) 1726.76 1.62810
\(105\) 0 0
\(106\) 1513.12 1.38648
\(107\) 371.311 + 214.377i 0.335477 + 0.193688i 0.658270 0.752782i \(-0.271289\pi\)
−0.322793 + 0.946470i \(0.604622\pi\)
\(108\) 0 0
\(109\) 334.261 + 578.957i 0.293728 + 0.508752i 0.974688 0.223568i \(-0.0717706\pi\)
−0.680960 + 0.732321i \(0.738437\pi\)
\(110\) −119.057 + 206.213i −0.103197 + 0.178742i
\(111\) 0 0
\(112\) 151.768 44.5562i 0.128042 0.0375908i
\(113\) 914.837i 0.761598i −0.924658 0.380799i \(-0.875649\pi\)
0.924658 0.380799i \(-0.124351\pi\)
\(114\) 0 0
\(115\) −99.6917 + 57.5570i −0.0808374 + 0.0466715i
\(116\) −1630.64 + 941.449i −1.30518 + 0.753546i
\(117\) 0 0
\(118\) 3980.29i 3.10521i
\(119\) 339.696 1399.99i 0.261680 1.07846i
\(120\) 0 0
\(121\) 199.690 345.873i 0.150030 0.259859i
\(122\) 29.7517 + 51.5314i 0.0220786 + 0.0382413i
\(123\) 0 0
\(124\) 951.015 + 549.069i 0.688739 + 0.397644i
\(125\) 314.398 0.224965
\(126\) 0 0
\(127\) 1260.95 0.881034 0.440517 0.897744i \(-0.354795\pi\)
0.440517 + 0.897744i \(0.354795\pi\)
\(128\) 1886.68 + 1089.28i 1.30282 + 0.752182i
\(129\) 0 0
\(130\) −245.383 425.016i −0.165550 0.286742i
\(131\) −683.600 + 1184.03i −0.455926 + 0.789688i −0.998741 0.0501648i \(-0.984025\pi\)
0.542814 + 0.839853i \(0.317359\pi\)
\(132\) 0 0
\(133\) 253.998 + 865.173i 0.165597 + 0.564060i
\(134\) 2000.88i 1.28992i
\(135\) 0 0
\(136\) 1356.76 783.325i 0.855449 0.493894i
\(137\) 953.631 550.579i 0.594702 0.343351i −0.172252 0.985053i \(-0.555104\pi\)
0.766955 + 0.641701i \(0.221771\pi\)
\(138\) 0 0
\(139\) 2306.56i 1.40748i −0.710458 0.703739i \(-0.751512\pi\)
0.710458 0.703739i \(-0.248488\pi\)
\(140\) 211.265 + 201.458i 0.127537 + 0.121616i
\(141\) 0 0
\(142\) 772.341 1337.73i 0.456432 0.790564i
\(143\) 1783.21 + 3088.60i 1.04279 + 1.80617i
\(144\) 0 0
\(145\) 165.730 + 95.6845i 0.0949184 + 0.0548012i
\(146\) −4168.44 −2.36289
\(147\) 0 0
\(148\) −1128.06 −0.626527
\(149\) −1520.57 877.901i −0.836040 0.482688i 0.0198764 0.999802i \(-0.493673\pi\)
−0.855916 + 0.517115i \(0.827006\pi\)
\(150\) 0 0
\(151\) 262.491 + 454.647i 0.141465 + 0.245024i 0.928048 0.372460i \(-0.121485\pi\)
−0.786584 + 0.617484i \(0.788152\pi\)
\(152\) −490.286 + 849.201i −0.261628 + 0.453153i
\(153\) 0 0
\(154\) −2521.52 2404.46i −1.31941 1.25816i
\(155\) 111.610i 0.0578368i
\(156\) 0 0
\(157\) −1141.44 + 659.009i −0.580233 + 0.334998i −0.761226 0.648487i \(-0.775402\pi\)
0.180993 + 0.983484i \(0.442069\pi\)
\(158\) 1618.07 934.195i 0.814728 0.470384i
\(159\) 0 0
\(160\) 252.823i 0.124921i
\(161\) −474.481 1616.18i −0.232263 0.791137i
\(162\) 0 0
\(163\) 223.916 387.834i 0.107598 0.186365i −0.807199 0.590280i \(-0.799017\pi\)
0.914797 + 0.403915i \(0.132351\pi\)
\(164\) −2388.12 4136.35i −1.13708 1.96948i
\(165\) 0 0
\(166\) 3737.67 + 2157.95i 1.74759 + 1.00897i
\(167\) −811.124 −0.375848 −0.187924 0.982184i \(-0.560176\pi\)
−0.187924 + 0.982184i \(0.560176\pi\)
\(168\) 0 0
\(169\) −5153.58 −2.34574
\(170\) −385.608 222.631i −0.173969 0.100441i
\(171\) 0 0
\(172\) −1419.03 2457.82i −0.629068 1.08958i
\(173\) −1121.24 + 1942.04i −0.492751 + 0.853470i −0.999965 0.00834994i \(-0.997342\pi\)
0.507214 + 0.861820i \(0.330675\pi\)
\(174\) 0 0
\(175\) −538.888 + 2220.92i −0.232778 + 0.959347i
\(176\) 355.269i 0.152156i
\(177\) 0 0
\(178\) 116.317 67.1554i 0.0489792 0.0282781i
\(179\) 2531.77 1461.72i 1.05717 0.610357i 0.132521 0.991180i \(-0.457693\pi\)
0.924648 + 0.380824i \(0.124359\pi\)
\(180\) 0 0
\(181\) 282.859i 0.116159i 0.998312 + 0.0580794i \(0.0184977\pi\)
−0.998312 + 0.0580794i \(0.981502\pi\)
\(182\) 6890.29 2022.86i 2.80628 0.823869i
\(183\) 0 0
\(184\) 915.878 1586.35i 0.366953 0.635582i
\(185\) 57.3255 + 99.2906i 0.0227819 + 0.0394594i
\(186\) 0 0
\(187\) 2802.22 + 1617.86i 1.09582 + 0.632672i
\(188\) −1732.34 −0.672040
\(189\) 0 0
\(190\) 278.691 0.106412
\(191\) 3998.63 + 2308.61i 1.51482 + 0.874582i 0.999849 + 0.0173741i \(0.00553064\pi\)
0.514971 + 0.857208i \(0.327803\pi\)
\(192\) 0 0
\(193\) 2077.73 + 3598.73i 0.774912 + 1.34219i 0.934844 + 0.355058i \(0.115539\pi\)
−0.159933 + 0.987128i \(0.551128\pi\)
\(194\) 2712.70 4698.53i 1.00392 1.73884i
\(195\) 0 0
\(196\) −3593.61 + 2309.05i −1.30963 + 0.841490i
\(197\) 1626.36i 0.588190i −0.955776 0.294095i \(-0.904982\pi\)
0.955776 0.294095i \(-0.0950183\pi\)
\(198\) 0 0
\(199\) 150.861 87.0995i 0.0537399 0.0310267i −0.472889 0.881122i \(-0.656789\pi\)
0.526629 + 0.850095i \(0.323456\pi\)
\(200\) −2152.33 + 1242.65i −0.760965 + 0.439344i
\(201\) 0 0
\(202\) 2961.56i 1.03156i
\(203\) −1932.44 + 2026.51i −0.668130 + 0.700656i
\(204\) 0 0
\(205\) −242.718 + 420.399i −0.0826933 + 0.143229i
\(206\) −3096.78 5363.78i −1.04739 1.81414i
\(207\) 0 0
\(208\) −634.129 366.115i −0.211389 0.122046i
\(209\) −2025.25 −0.670286
\(210\) 0 0
\(211\) −2942.35 −0.959999 −0.479999 0.877269i \(-0.659363\pi\)
−0.479999 + 0.877269i \(0.659363\pi\)
\(212\) 3608.35 + 2083.28i 1.16897 + 0.674907i
\(213\) 0 0
\(214\) 969.527 + 1679.27i 0.309699 + 0.536414i
\(215\) −144.223 + 249.802i −0.0457486 + 0.0792389i
\(216\) 0 0
\(217\) 1587.06 + 385.088i 0.496484 + 0.120468i
\(218\) 3023.42i 0.939319i
\(219\) 0 0
\(220\) −567.832 + 327.838i −0.174015 + 0.100467i
\(221\) −5775.53 + 3334.51i −1.75794 + 1.01495i
\(222\) 0 0
\(223\) 3374.75i 1.01341i −0.862120 0.506704i \(-0.830864\pi\)
0.862120 0.506704i \(-0.169136\pi\)
\(224\) 3595.09 + 872.320i 1.07235 + 0.260198i
\(225\) 0 0
\(226\) 2068.69 3583.08i 0.608882 1.05461i
\(227\) −1515.43 2624.79i −0.443094 0.767461i 0.554823 0.831968i \(-0.312786\pi\)
−0.997917 + 0.0645069i \(0.979453\pi\)
\(228\) 0 0
\(229\) 960.030 + 554.274i 0.277033 + 0.159945i 0.632080 0.774904i \(-0.282202\pi\)
−0.355046 + 0.934849i \(0.615535\pi\)
\(230\) −520.608 −0.149252
\(231\) 0 0
\(232\) −3045.17 −0.861746
\(233\) −2684.57 1549.94i −0.754815 0.435793i 0.0726160 0.997360i \(-0.476865\pi\)
−0.827431 + 0.561567i \(0.810199\pi\)
\(234\) 0 0
\(235\) 88.0333 + 152.478i 0.0244368 + 0.0423259i
\(236\) −5480.10 + 9491.82i −1.51154 + 2.61807i
\(237\) 0 0
\(238\) 4496.23 4715.11i 1.22457 1.28418i
\(239\) 1735.25i 0.469640i 0.972039 + 0.234820i \(0.0754501\pi\)
−0.972039 + 0.234820i \(0.924550\pi\)
\(240\) 0 0
\(241\) −1039.26 + 600.019i −0.277779 + 0.160376i −0.632418 0.774628i \(-0.717937\pi\)
0.354638 + 0.935004i \(0.384604\pi\)
\(242\) 1564.22 903.104i 0.415504 0.239892i
\(243\) 0 0
\(244\) 163.850i 0.0429894i
\(245\) 385.859 + 198.965i 0.100619 + 0.0518833i
\(246\) 0 0
\(247\) 2087.08 3614.93i 0.537643 0.931225i
\(248\) 887.996 + 1538.05i 0.227370 + 0.393817i
\(249\) 0 0
\(250\) 1231.38 + 710.939i 0.311518 + 0.179855i
\(251\) 3712.56 0.933603 0.466802 0.884362i \(-0.345406\pi\)
0.466802 + 0.884362i \(0.345406\pi\)
\(252\) 0 0
\(253\) 3783.27 0.940126
\(254\) 4938.69 + 2851.35i 1.22000 + 0.704369i
\(255\) 0 0
\(256\) 1586.09 + 2747.20i 0.387230 + 0.670702i
\(257\) 389.574 674.762i 0.0945563 0.163776i −0.814867 0.579648i \(-0.803190\pi\)
0.909423 + 0.415872i \(0.136523\pi\)
\(258\) 0 0
\(259\) −1609.68 + 472.572i −0.386180 + 0.113375i
\(260\) 1351.39i 0.322344i
\(261\) 0 0
\(262\) −5354.82 + 3091.61i −1.26268 + 0.729008i
\(263\) −1702.07 + 982.690i −0.399065 + 0.230400i −0.686080 0.727526i \(-0.740670\pi\)
0.287015 + 0.957926i \(0.407337\pi\)
\(264\) 0 0
\(265\) 423.470i 0.0981644i
\(266\) −961.571 + 3962.92i −0.221646 + 0.913468i
\(267\) 0 0
\(268\) −2754.84 + 4771.52i −0.627905 + 1.08756i
\(269\) 1236.41 + 2141.53i 0.280243 + 0.485395i 0.971444 0.237267i \(-0.0762516\pi\)
−0.691201 + 0.722662i \(0.742918\pi\)
\(270\) 0 0
\(271\) 4095.79 + 2364.71i 0.918088 + 0.530058i 0.883025 0.469327i \(-0.155503\pi\)
0.0350633 + 0.999385i \(0.488837\pi\)
\(272\) −664.334 −0.148093
\(273\) 0 0
\(274\) 4980.03 1.09801
\(275\) −4445.39 2566.54i −0.974788 0.562794i
\(276\) 0 0
\(277\) −586.579 1015.98i −0.127235 0.220378i 0.795369 0.606125i \(-0.207277\pi\)
−0.922604 + 0.385747i \(0.873944\pi\)
\(278\) 5215.74 9033.93i 1.12525 1.94899i
\(279\) 0 0
\(280\) 132.992 + 452.999i 0.0283849 + 0.0966852i
\(281\) 8195.18i 1.73980i −0.493229 0.869899i \(-0.664184\pi\)
0.493229 0.869899i \(-0.335816\pi\)
\(282\) 0 0
\(283\) 2242.44 1294.67i 0.471021 0.271944i −0.245646 0.969360i \(-0.579000\pi\)
0.716667 + 0.697415i \(0.245667\pi\)
\(284\) 3683.61 2126.74i 0.769656 0.444361i
\(285\) 0 0
\(286\) 16129.2i 3.33476i
\(287\) −5140.53 4901.90i −1.05727 1.00819i
\(288\) 0 0
\(289\) −568.820 + 985.225i −0.115779 + 0.200534i
\(290\) 432.737 + 749.523i 0.0876248 + 0.151771i
\(291\) 0 0
\(292\) −9940.50 5739.15i −1.99221 1.15020i
\(293\) 8871.16 1.76880 0.884400 0.466729i \(-0.154568\pi\)
0.884400 + 0.466729i \(0.154568\pi\)
\(294\) 0 0
\(295\) 1113.94 0.219852
\(296\) −1579.96 912.193i −0.310249 0.179122i
\(297\) 0 0
\(298\) −3970.34 6876.84i −0.771798 1.33679i
\(299\) −3898.77 + 6752.86i −0.754085 + 1.30611i
\(300\) 0 0
\(301\) −3054.51 2912.72i −0.584915 0.557762i
\(302\) 2374.25i 0.452393i
\(303\) 0 0
\(304\) 360.102 207.905i 0.0679383 0.0392242i
\(305\) 14.4219 8.32647i 0.00270752 0.00156319i
\(306\) 0 0
\(307\) 2707.52i 0.503344i 0.967813 + 0.251672i \(0.0809804\pi\)
−0.967813 + 0.251672i \(0.919020\pi\)
\(308\) −2702.59 9205.59i −0.499981 1.70304i
\(309\) 0 0
\(310\) 252.379 437.134i 0.0462393 0.0800889i
\(311\) 1080.55 + 1871.56i 0.197017 + 0.341243i 0.947560 0.319579i \(-0.103541\pi\)
−0.750543 + 0.660822i \(0.770208\pi\)
\(312\) 0 0
\(313\) −7300.25 4214.80i −1.31832 0.761133i −0.334863 0.942267i \(-0.608690\pi\)
−0.983459 + 0.181133i \(0.942023\pi\)
\(314\) −5960.79 −1.07130
\(315\) 0 0
\(316\) 5144.84 0.915886
\(317\) 8310.07 + 4797.82i 1.47237 + 0.850071i 0.999517 0.0310734i \(-0.00989256\pi\)
0.472848 + 0.881144i \(0.343226\pi\)
\(318\) 0 0
\(319\) −3144.71 5446.80i −0.551943 0.955994i
\(320\) 528.463 915.324i 0.0923186 0.159901i
\(321\) 0 0
\(322\) 1796.26 7402.93i 0.310875 1.28121i
\(323\) 3787.12i 0.652387i
\(324\) 0 0
\(325\) 9162.20 5289.80i 1.56378 0.902847i
\(326\) 1753.99 1012.67i 0.297990 0.172045i
\(327\) 0 0
\(328\) 7724.50i 1.30035i
\(329\) −2471.95 + 725.717i −0.414234 + 0.121611i
\(330\) 0 0
\(331\) −4271.96 + 7399.25i −0.709390 + 1.22870i 0.255694 + 0.966758i \(0.417696\pi\)
−0.965084 + 0.261941i \(0.915637\pi\)
\(332\) 5942.17 + 10292.1i 0.982286 + 1.70137i
\(333\) 0 0
\(334\) −3176.88 1834.17i −0.520452 0.300483i
\(335\) 559.978 0.0913280
\(336\) 0 0
\(337\) 598.875 0.0968036 0.0484018 0.998828i \(-0.484587\pi\)
0.0484018 + 0.998828i \(0.484587\pi\)
\(338\) −20184.7 11653.6i −3.24823 1.87537i
\(339\) 0 0
\(340\) −613.041 1061.82i −0.0977847 0.169368i
\(341\) −1834.05 + 3176.66i −0.291259 + 0.504475i
\(342\) 0 0
\(343\) −4160.57 + 4800.34i −0.654956 + 0.755667i
\(344\) 4589.91i 0.719394i
\(345\) 0 0
\(346\) −8782.94 + 5070.83i −1.36466 + 0.787889i
\(347\) 6149.62 3550.49i 0.951381 0.549280i 0.0578712 0.998324i \(-0.481569\pi\)
0.893510 + 0.449044i \(0.148235\pi\)
\(348\) 0 0
\(349\) 3620.71i 0.555336i 0.960677 + 0.277668i \(0.0895616\pi\)
−0.960677 + 0.277668i \(0.910438\pi\)
\(350\) −7132.73 + 7479.96i −1.08931 + 1.14234i
\(351\) 0 0
\(352\) −4154.57 + 7195.92i −0.629089 + 1.08961i
\(353\) −1164.89 2017.64i −0.175639 0.304216i 0.764743 0.644335i \(-0.222866\pi\)
−0.940382 + 0.340119i \(0.889533\pi\)
\(354\) 0 0
\(355\) −374.386 216.152i −0.0559727 0.0323159i
\(356\) 369.841 0.0550605
\(357\) 0 0
\(358\) 13221.3 1.95187
\(359\) 1522.43 + 878.975i 0.223818 + 0.129222i 0.607717 0.794154i \(-0.292086\pi\)
−0.383899 + 0.923375i \(0.625419\pi\)
\(360\) 0 0
\(361\) −2244.31 3887.26i −0.327207 0.566739i
\(362\) −639.621 + 1107.86i −0.0928667 + 0.160850i
\(363\) 0 0
\(364\) 19216.4 + 4662.71i 2.76707 + 0.671407i
\(365\) 1166.60i 0.167295i
\(366\) 0 0
\(367\) 1458.89 842.290i 0.207503 0.119802i −0.392648 0.919689i \(-0.628441\pi\)
0.600150 + 0.799887i \(0.295107\pi\)
\(368\) −672.687 + 388.376i −0.0952887 + 0.0550150i
\(369\) 0 0
\(370\) 518.513i 0.0728547i
\(371\) 6021.65 + 1461.11i 0.842665 + 0.204466i
\(372\) 0 0
\(373\) 148.646 257.462i 0.0206343 0.0357397i −0.855524 0.517763i \(-0.826765\pi\)
0.876158 + 0.482024i \(0.160098\pi\)
\(374\) 7316.84 + 12673.1i 1.01162 + 1.75217i
\(375\) 0 0
\(376\) −2426.31 1400.83i −0.332786 0.192134i
\(377\) 12962.9 1.77088
\(378\) 0 0
\(379\) −7402.78 −1.00331 −0.501656 0.865067i \(-0.667276\pi\)
−0.501656 + 0.865067i \(0.667276\pi\)
\(380\) 664.596 + 383.705i 0.0897186 + 0.0517991i
\(381\) 0 0
\(382\) 10440.8 + 18084.0i 1.39842 + 2.42214i
\(383\) 6263.77 10849.2i 0.835676 1.44743i −0.0578031 0.998328i \(-0.518410\pi\)
0.893479 0.449105i \(-0.148257\pi\)
\(384\) 0 0
\(385\) −672.926 + 705.685i −0.0890792 + 0.0934157i
\(386\) 18793.2i 2.47810i
\(387\) 0 0
\(388\) 12938.0 7469.75i 1.69285 0.977368i
\(389\) −6904.14 + 3986.11i −0.899881 + 0.519547i −0.877162 0.480195i \(-0.840566\pi\)
−0.0227196 + 0.999742i \(0.507233\pi\)
\(390\) 0 0
\(391\) 7074.52i 0.915023i
\(392\) −6900.41 + 328.126i −0.889090 + 0.0422778i
\(393\) 0 0
\(394\) 3677.64 6369.87i 0.470246 0.814491i
\(395\) −261.449 452.843i −0.0333036 0.0576836i
\(396\) 0 0
\(397\) 10832.5 + 6254.16i 1.36944 + 0.790648i 0.990857 0.134918i \(-0.0430770\pi\)
0.378586 + 0.925566i \(0.376410\pi\)
\(398\) 787.822 0.0992210
\(399\) 0 0
\(400\) 1053.89 0.131736
\(401\) 6943.55 + 4008.86i 0.864699 + 0.499234i 0.865583 0.500765i \(-0.166948\pi\)
−0.000883860 1.00000i \(0.500281\pi\)
\(402\) 0 0
\(403\) −3780.08 6547.29i −0.467243 0.809289i
\(404\) 4077.51 7062.45i 0.502137 0.869728i
\(405\) 0 0
\(406\) −12151.1 + 3567.34i −1.48535 + 0.436069i
\(407\) 3768.05i 0.458907i
\(408\) 0 0
\(409\) −7566.04 + 4368.26i −0.914711 + 0.528109i −0.881944 0.471354i \(-0.843765\pi\)
−0.0327670 + 0.999463i \(0.510432\pi\)
\(410\) −1901.27 + 1097.70i −0.229017 + 0.132223i
\(411\) 0 0
\(412\) 17054.7i 2.03938i
\(413\) −3843.46 + 15840.1i −0.457928 + 1.88726i
\(414\) 0 0
\(415\) 603.935 1046.05i 0.0714361 0.123731i
\(416\) −8562.81 14831.2i −1.00920 1.74798i
\(417\) 0 0
\(418\) −7932.18 4579.64i −0.928171 0.535880i
\(419\) −3926.67 −0.457829 −0.228914 0.973447i \(-0.573518\pi\)
−0.228914 + 0.973447i \(0.573518\pi\)
\(420\) 0 0
\(421\) 1443.44 0.167100 0.0835499 0.996504i \(-0.473374\pi\)
0.0835499 + 0.996504i \(0.473374\pi\)
\(422\) −11524.1 6653.45i −1.32935 0.767500i
\(423\) 0 0
\(424\) 3369.24 + 5835.70i 0.385908 + 0.668412i
\(425\) 4799.31 8312.65i 0.547766 0.948759i
\(426\) 0 0
\(427\) 68.6406 + 233.805i 0.00777928 + 0.0264979i
\(428\) 5339.42i 0.603016i
\(429\) 0 0
\(430\) −1129.74 + 652.255i −0.126700 + 0.0731501i
\(431\) −12820.5 + 7401.92i −1.43281 + 0.827234i −0.997334 0.0729655i \(-0.976754\pi\)
−0.435477 + 0.900200i \(0.643420\pi\)
\(432\) 0 0
\(433\) 15872.1i 1.76158i −0.473508 0.880790i \(-0.657012\pi\)
0.473508 0.880790i \(-0.342988\pi\)
\(434\) 5345.16 + 5097.03i 0.591189 + 0.563745i
\(435\) 0 0
\(436\) −4162.67 + 7209.96i −0.457238 + 0.791960i
\(437\) −2213.99 3834.74i −0.242356 0.419772i
\(438\) 0 0
\(439\) −2626.58 1516.45i −0.285557 0.164867i 0.350379 0.936608i \(-0.386053\pi\)
−0.635937 + 0.771741i \(0.719386\pi\)
\(440\) −1060.41 −0.114893
\(441\) 0 0
\(442\) −30160.9 −3.24572
\(443\) −11126.8 6424.08i −1.19334 0.688978i −0.234281 0.972169i \(-0.575274\pi\)
−0.959064 + 0.283191i \(0.908607\pi\)
\(444\) 0 0
\(445\) −18.7945 32.5530i −0.00200212 0.00346777i
\(446\) 7631.22 13217.7i 0.810199 1.40331i
\(447\) 0 0
\(448\) 11192.3 + 10672.8i 1.18033 + 1.12554i
\(449\) 107.668i 0.0113166i −0.999984 0.00565831i \(-0.998199\pi\)
0.999984 0.00565831i \(-0.00180111\pi\)
\(450\) 0 0
\(451\) 13816.6 7977.01i 1.44257 0.832866i
\(452\) 9866.45 5696.40i 1.02672 0.592779i
\(453\) 0 0
\(454\) 13707.1i 1.41698i
\(455\) −566.128 1928.35i −0.0583308 0.198687i
\(456\) 0 0
\(457\) 4888.53 8467.18i 0.500385 0.866691i −0.499615 0.866247i \(-0.666525\pi\)
1.00000 0.000444115i \(-0.000141366\pi\)
\(458\) 2506.72 + 4341.77i 0.255746 + 0.442965i
\(459\) 0 0
\(460\) −1241.50 716.779i −0.125837 0.0726521i
\(461\) 638.874 0.0645452 0.0322726 0.999479i \(-0.489726\pi\)
0.0322726 + 0.999479i \(0.489726\pi\)
\(462\) 0 0
\(463\) −5602.26 −0.562331 −0.281165 0.959659i \(-0.590721\pi\)
−0.281165 + 0.959659i \(0.590721\pi\)
\(464\) 1118.30 + 645.648i 0.111887 + 0.0645980i
\(465\) 0 0
\(466\) −7009.65 12141.1i −0.696815 1.20692i
\(467\) −2759.44 + 4779.49i −0.273430 + 0.473594i −0.969738 0.244149i \(-0.921491\pi\)
0.696308 + 0.717743i \(0.254825\pi\)
\(468\) 0 0
\(469\) −1932.10 + 7962.76i −0.190226 + 0.783979i
\(470\) 796.268i 0.0781470i
\(471\) 0 0
\(472\) −15350.9 + 8862.84i −1.49700 + 0.864291i
\(473\) 8209.84 4739.95i 0.798074 0.460768i
\(474\) 0 0
\(475\) 6007.82i 0.580332i
\(476\) 17214.0 5053.70i 1.65757 0.486630i
\(477\) 0 0
\(478\) −3923.87 + 6796.34i −0.375468 + 0.650329i
\(479\) −2734.40 4736.11i −0.260830 0.451771i 0.705632 0.708578i \(-0.250663\pi\)
−0.966463 + 0.256807i \(0.917330\pi\)
\(480\) 0 0
\(481\) 6725.70 + 3883.08i 0.637558 + 0.368094i
\(482\) −5427.22 −0.512869
\(483\) 0 0
\(484\) 4973.62 0.467094
\(485\) −1314.96 759.190i −0.123112 0.0710785i
\(486\) 0 0
\(487\) 5866.72 + 10161.5i 0.545886 + 0.945502i 0.998551 + 0.0538213i \(0.0171401\pi\)
−0.452665 + 0.891681i \(0.649527\pi\)
\(488\) −132.495 + 229.489i −0.0122905 + 0.0212878i
\(489\) 0 0
\(490\) 1061.35 + 1651.80i 0.0978512 + 0.152288i
\(491\) 3514.92i 0.323068i −0.986867 0.161534i \(-0.948356\pi\)
0.986867 0.161534i \(-0.0516441\pi\)
\(492\) 0 0
\(493\) 10185.2 5880.45i 0.930467 0.537205i
\(494\) 16348.7 9438.91i 1.48899 0.859670i
\(495\) 0 0
\(496\) 753.106i 0.0681763i
\(497\) 4365.38 4577.89i 0.393992 0.413172i
\(498\) 0 0
\(499\) −4944.49 + 8564.11i −0.443579 + 0.768301i −0.997952 0.0639672i \(-0.979625\pi\)
0.554373 + 0.832268i \(0.312958\pi\)
\(500\) 1957.66 + 3390.76i 0.175098 + 0.303279i
\(501\) 0 0
\(502\) 14540.7 + 8395.09i 1.29280 + 0.746397i
\(503\) −10172.2 −0.901698 −0.450849 0.892600i \(-0.648879\pi\)
−0.450849 + 0.892600i \(0.648879\pi\)
\(504\) 0 0
\(505\) −828.838 −0.0730353
\(506\) 14817.7 + 8554.99i 1.30183 + 0.751612i
\(507\) 0 0
\(508\) 7851.55 + 13599.3i 0.685740 + 1.18774i
\(509\) −2149.56 + 3723.15i −0.187186 + 0.324216i −0.944311 0.329054i \(-0.893270\pi\)
0.757125 + 0.653270i \(0.226603\pi\)
\(510\) 0 0
\(511\) −16588.8 4025.14i −1.43610 0.348458i
\(512\) 3082.06i 0.266033i
\(513\) 0 0
\(514\) 3051.64 1761.86i 0.261872 0.151192i
\(515\) −1501.14 + 866.682i −0.128443 + 0.0741565i
\(516\) 0 0
\(517\) 5786.50i 0.492243i
\(518\) −7373.15 1789.03i −0.625400 0.151748i
\(519\) 0 0
\(520\) 1092.78 1892.76i 0.0921571 0.159621i
\(521\) −5496.48 9520.18i −0.462198 0.800550i 0.536872 0.843664i \(-0.319606\pi\)
−0.999070 + 0.0431133i \(0.986272\pi\)
\(522\) 0 0
\(523\) 7386.80 + 4264.77i 0.617595 + 0.356569i 0.775932 0.630817i \(-0.217280\pi\)
−0.158337 + 0.987385i \(0.550613\pi\)
\(524\) −17026.2 −1.41946
\(525\) 0 0
\(526\) −8888.51 −0.736801
\(527\) −5940.20 3429.58i −0.491004 0.283481i
\(528\) 0 0
\(529\) −1947.67 3373.46i −0.160078 0.277263i
\(530\) 957.581 1658.58i 0.0784805 0.135932i
\(531\) 0 0
\(532\) −7749.26 + 8126.51i −0.631529 + 0.662272i
\(533\) 32882.2i 2.67220i
\(534\) 0 0
\(535\) 469.970 271.337i 0.0379786 0.0219270i
\(536\) −7716.86 + 4455.33i −0.621862 + 0.359032i
\(537\) 0 0
\(538\) 11183.4i 0.896195i
\(539\) −7712.89 12003.7i −0.616359 0.959250i
\(540\) 0 0
\(541\) 4352.93 7539.49i 0.345928 0.599165i −0.639594 0.768713i \(-0.720897\pi\)
0.985522 + 0.169548i \(0.0542308\pi\)
\(542\) 10694.5 + 18523.4i 0.847542 + 1.46799i
\(543\) 0 0
\(544\) −13456.0 7768.84i −1.06052 0.612291i
\(545\) 846.150 0.0665047
\(546\) 0 0
\(547\) 17183.8 1.34319 0.671596 0.740917i \(-0.265609\pi\)
0.671596 + 0.740917i \(0.265609\pi\)
\(548\) 11875.9 + 6856.56i 0.925756 + 0.534485i
\(549\) 0 0
\(550\) −11607.3 20104.4i −0.899885 1.55865i
\(551\) −3680.60 + 6374.99i −0.284571 + 0.492892i
\(552\) 0 0
\(553\) 7341.41 2155.30i 0.564536 0.165737i
\(554\) 5305.66i 0.406888i
\(555\) 0 0
\(556\) 24876.0 14362.2i 1.89744 1.09549i
\(557\) −8989.79 + 5190.26i −0.683859 + 0.394826i −0.801307 0.598253i \(-0.795862\pi\)
0.117448 + 0.993079i \(0.462529\pi\)
\(558\) 0 0
\(559\) 19538.6i 1.47835i
\(560\) 47.2072 194.555i 0.00356226 0.0146812i
\(561\) 0 0
\(562\) 18531.5 32097.5i 1.39093 2.40917i
\(563\) 9248.22 + 16018.4i 0.692302 + 1.19910i 0.971082 + 0.238747i \(0.0767366\pi\)
−0.278780 + 0.960355i \(0.589930\pi\)
\(564\) 0 0
\(565\) −1002.78 578.956i −0.0746678 0.0431095i
\(566\) 11710.4 0.869656
\(567\) 0 0
\(568\) 6879.04 0.508166
\(569\) −3493.45 2016.94i −0.257386 0.148602i 0.365755 0.930711i \(-0.380811\pi\)
−0.623142 + 0.782109i \(0.714144\pi\)
\(570\) 0 0
\(571\) −6430.01 11137.1i −0.471257 0.816241i 0.528203 0.849118i \(-0.322866\pi\)
−0.999459 + 0.0328777i \(0.989533\pi\)
\(572\) −22206.9 + 38463.5i −1.62328 + 2.81161i
\(573\) 0 0
\(574\) −9049.07 30823.1i −0.658015 2.24134i
\(575\) 11222.9i 0.813959i
\(576\) 0 0
\(577\) −17669.2 + 10201.3i −1.27483 + 0.736026i −0.975894 0.218246i \(-0.929967\pi\)
−0.298940 + 0.954272i \(0.596633\pi\)
\(578\) −4455.72 + 2572.51i −0.320646 + 0.185125i
\(579\) 0 0
\(580\) 2383.19i 0.170615i
\(581\) 12790.8 + 12197.0i 0.913340 + 0.870941i
\(582\) 0 0
\(583\) −6958.76 + 12052.9i −0.494344 + 0.856228i
\(584\) −9281.80 16076.5i −0.657677 1.13913i
\(585\) 0 0
\(586\) 34745.1 + 20060.1i 2.44933 + 1.41412i
\(587\) −16279.7 −1.14470 −0.572348 0.820011i \(-0.693967\pi\)
−0.572348 + 0.820011i \(0.693967\pi\)
\(588\) 0 0
\(589\) 4293.17 0.300335
\(590\) 4362.91 + 2518.93i 0.304438 + 0.175767i
\(591\) 0 0
\(592\) 386.814 + 669.981i 0.0268546 + 0.0465136i
\(593\) 1342.16 2324.68i 0.0929440 0.160984i −0.815805 0.578328i \(-0.803706\pi\)
0.908749 + 0.417344i \(0.137039\pi\)
\(594\) 0 0
\(595\) −1319.60 1258.34i −0.0909213 0.0867006i
\(596\) 21865.7i 1.50277i
\(597\) 0 0
\(598\) −30540.1 + 17632.3i −2.08842 + 1.20575i
\(599\) 12224.6 7057.90i 0.833865 0.481432i −0.0213091 0.999773i \(-0.506783\pi\)
0.855174 + 0.518341i \(0.173450\pi\)
\(600\) 0 0
\(601\) 11096.1i 0.753109i 0.926394 + 0.376555i \(0.122891\pi\)
−0.926394 + 0.376555i \(0.877109\pi\)
\(602\) −5376.97 18315.1i −0.364035 1.23998i
\(603\) 0 0
\(604\) −3268.89 + 5661.89i −0.220214 + 0.381422i
\(605\) −252.748 437.772i −0.0169846 0.0294181i
\(606\) 0 0
\(607\) −9592.70 5538.35i −0.641442 0.370337i 0.143728 0.989617i \(-0.454091\pi\)
−0.785170 + 0.619280i \(0.787424\pi\)
\(608\) 9725.10 0.648692
\(609\) 0 0
\(610\) 75.3136 0.00499895
\(611\) 10328.5 + 5963.15i 0.683872 + 0.394834i
\(612\) 0 0
\(613\) 3801.34 + 6584.11i 0.250464 + 0.433817i 0.963654 0.267154i \(-0.0860834\pi\)
−0.713189 + 0.700971i \(0.752750\pi\)
\(614\) −6122.44 + 10604.4i −0.402413 + 0.697000i
\(615\) 0 0
\(616\) 3658.74 15078.8i 0.239310 0.986269i
\(617\) 11325.9i 0.738998i −0.929231 0.369499i \(-0.879529\pi\)
0.929231 0.369499i \(-0.120471\pi\)
\(618\) 0 0
\(619\) −16595.2 + 9581.22i −1.07757 + 0.622136i −0.930240 0.366952i \(-0.880401\pi\)
−0.147330 + 0.989087i \(0.547068\pi\)
\(620\) 1203.70 694.958i 0.0779707 0.0450164i
\(621\) 0 0
\(622\) 9773.64i 0.630044i
\(623\) 527.743 154.935i 0.0339383 0.00996365i
\(624\) 0 0
\(625\) −7513.41 + 13013.6i −0.480858 + 0.832871i
\(626\) −19061.6 33015.7i −1.21702 2.10794i
\(627\) 0 0
\(628\) −14214.7 8206.88i −0.903232 0.521481i
\(629\) 7046.06 0.446653
\(630\) 0 0
\(631\) 10140.7 0.639768 0.319884 0.947457i \(-0.396356\pi\)
0.319884 + 0.947457i \(0.396356\pi\)
\(632\) 7205.88 + 4160.32i 0.453536 + 0.261849i
\(633\) 0 0
\(634\) 21698.3 + 37582.6i 1.35923 + 2.35425i
\(635\) 797.995 1382.17i 0.0498700 0.0863774i
\(636\) 0 0
\(637\) 29374.1 1396.79i 1.82707 0.0868804i
\(638\) 28444.2i 1.76507i
\(639\) 0 0
\(640\) 2387.98 1378.70i 0.147489 0.0851530i
\(641\) −2950.66 + 1703.56i −0.181816 + 0.104972i −0.588146 0.808755i \(-0.700142\pi\)
0.406330 + 0.913727i \(0.366808\pi\)
\(642\) 0 0
\(643\) 659.110i 0.0404242i 0.999796 + 0.0202121i \(0.00643415\pi\)
−0.999796 + 0.0202121i \(0.993566\pi\)
\(644\) 14476.0 15180.7i 0.885767 0.928888i
\(645\) 0 0
\(646\) 8563.71 14832.8i 0.521570 0.903386i
\(647\) 3303.47 + 5721.78i 0.200731 + 0.347676i 0.948764 0.315985i \(-0.102335\pi\)
−0.748033 + 0.663661i \(0.769002\pi\)
\(648\) 0 0
\(649\) −31705.4 18305.1i −1.91764 1.10715i
\(650\) 47846.6 2.88723
\(651\) 0 0
\(652\) 5577.01 0.334989
\(653\) 22417.1 + 12942.5i 1.34342 + 0.775622i 0.987307 0.158823i \(-0.0507698\pi\)
0.356109 + 0.934444i \(0.384103\pi\)
\(654\) 0 0
\(655\) 865.234 + 1498.63i 0.0516145 + 0.0893989i
\(656\) −1637.78 + 2836.72i −0.0974764 + 0.168834i
\(657\) 0 0
\(658\) −11322.8 2747.37i −0.670831 0.162772i
\(659\) 7468.86i 0.441495i 0.975331 + 0.220748i \(0.0708497\pi\)
−0.975331 + 0.220748i \(0.929150\pi\)
\(660\) 0 0
\(661\) −5501.96 + 3176.56i −0.323754 + 0.186919i −0.653065 0.757302i \(-0.726517\pi\)
0.329311 + 0.944222i \(0.393184\pi\)
\(662\) −33463.4 + 19320.1i −1.96464 + 1.13429i
\(663\) 0 0
\(664\) 19220.3i 1.12333i
\(665\) 1109.09 + 269.111i 0.0646744 + 0.0156927i
\(666\) 0 0
\(667\) 6875.53 11908.8i 0.399133 0.691319i
\(668\) −5050.61 8747.92i −0.292536 0.506687i
\(669\) 0 0
\(670\) 2193.23 + 1266.26i 0.126465 + 0.0730148i
\(671\) −547.306 −0.0314881
\(672\) 0 0
\(673\) −20238.2 −1.15918 −0.579589 0.814909i \(-0.696787\pi\)
−0.579589 + 0.814909i \(0.696787\pi\)
\(674\) 2345.58 + 1354.22i 0.134048 + 0.0773925i
\(675\) 0 0
\(676\) −32089.7 55581.1i −1.82577 3.16233i
\(677\) 5658.37 9800.59i 0.321224 0.556377i −0.659516 0.751690i \(-0.729239\pi\)
0.980741 + 0.195313i \(0.0625723\pi\)
\(678\) 0 0
\(679\) 15332.5 16078.9i 0.866581 0.908768i
\(680\) 1982.91i 0.111825i
\(681\) 0 0
\(682\) −14366.6 + 8294.55i −0.806635 + 0.465711i
\(683\) 14869.4 8584.87i 0.833035 0.480953i −0.0218557 0.999761i \(-0.506957\pi\)
0.854891 + 0.518808i \(0.173624\pi\)
\(684\) 0 0
\(685\) 1393.74i 0.0777402i
\(686\) −27150.3 + 9392.98i −1.51108 + 0.522778i
\(687\) 0 0
\(688\) −973.172 + 1685.58i −0.0539271 + 0.0934044i
\(689\) −14342.4 24841.8i −0.793037 1.37358i
\(690\) 0 0
\(691\) −7238.59 4179.20i −0.398508 0.230079i 0.287332 0.957831i \(-0.407232\pi\)
−0.685840 + 0.727752i \(0.740565\pi\)
\(692\) −27926.3 −1.53410
\(693\) 0 0
\(694\) 32114.4 1.75655
\(695\) −2528.29 1459.71i −0.137990 0.0796688i
\(696\) 0 0
\(697\) 14916.6 + 25836.3i 0.810627 + 1.40405i
\(698\) −8187.41 + 14181.0i −0.443980 + 0.768996i
\(699\) 0 0
\(700\) −27308.0 + 8017.09i −1.47449 + 0.432882i
\(701\) 19235.8i 1.03641i −0.855256 0.518206i \(-0.826600\pi\)
0.855256 0.518206i \(-0.173400\pi\)
\(702\) 0 0
\(703\) −3819.31 + 2205.08i −0.204905 + 0.118302i
\(704\) −30082.5 + 17368.1i −1.61048 + 0.929810i
\(705\) 0 0
\(706\) 10536.5i 0.561680i
\(707\) 2859.75 11785.9i 0.152124 0.626951i
\(708\) 0 0
\(709\) 5160.17 8937.67i 0.273334 0.473429i −0.696379 0.717674i \(-0.745207\pi\)
0.969714 + 0.244245i \(0.0785401\pi\)
\(710\) −977.554 1693.17i −0.0516718 0.0894981i
\(711\) 0 0
\(712\) 518.001 + 299.068i 0.0272653 + 0.0157416i
\(713\) −8019.85 −0.421242
\(714\) 0 0
\(715\) 4514.02 0.236105
\(716\) 31529.0 + 18203.3i 1.64566 + 0.950124i
\(717\) 0 0
\(718\) 3975.20 + 6885.25i 0.206620 + 0.357876i
\(719\) −11679.8 + 20229.9i −0.605815 + 1.04930i 0.386107 + 0.922454i \(0.373820\pi\)
−0.991922 + 0.126849i \(0.959514\pi\)
\(720\) 0 0
\(721\) −7144.63 24336.2i −0.369043 1.25704i
\(722\) 20300.0i 1.04638i
\(723\) 0 0
\(724\) −3050.62 + 1761.28i −0.156596 + 0.0904106i
\(725\) −16157.7 + 9328.63i −0.827698 + 0.477871i
\(726\) 0 0
\(727\) 22260.4i 1.13561i −0.823162 0.567807i \(-0.807792\pi\)
0.823162 0.567807i \(-0.192208\pi\)
\(728\) 23144.1 + 22069.7i 1.17827 + 1.12357i
\(729\) 0 0
\(730\) −2638.00 + 4569.15i −0.133749 + 0.231660i
\(731\) 8863.48 + 15352.0i 0.448464 + 0.776763i
\(732\) 0 0
\(733\) 9047.84 + 5223.77i 0.455920 + 0.263226i 0.710327 0.703872i \(-0.248547\pi\)
−0.254407 + 0.967097i \(0.581880\pi\)
\(734\) 7618.58 0.383116
\(735\) 0 0
\(736\) −18166.9 −0.909840
\(737\) −15938.2 9201.95i −0.796598 0.459916i
\(738\) 0 0
\(739\) −6595.44 11423.6i −0.328304 0.568640i 0.653871 0.756606i \(-0.273144\pi\)
−0.982176 + 0.187966i \(0.939811\pi\)
\(740\) −713.895 + 1236.50i −0.0354639 + 0.0614253i
\(741\) 0 0
\(742\) 20280.7 + 19339.2i 1.00341 + 0.956825i
\(743\) 35382.2i 1.74703i 0.486795 + 0.873517i \(0.338166\pi\)
−0.486795 + 0.873517i \(0.661834\pi\)
\(744\) 0 0
\(745\) −1924.59 + 1111.16i −0.0946463 + 0.0546441i
\(746\) 1164.38 672.258i 0.0571463 0.0329934i
\(747\) 0 0
\(748\) 40295.6i 1.96973i
\(749\) 2236.81 + 7619.07i 0.109121 + 0.371688i
\(750\) 0 0
\(751\) 14692.3 25447.8i 0.713888 1.23649i −0.249498 0.968375i \(-0.580266\pi\)
0.963387 0.268116i \(-0.0864010\pi\)
\(752\) 594.020 + 1028.87i 0.0288054 + 0.0498925i
\(753\) 0 0
\(754\) 50770.8 + 29312.5i 2.45221 + 1.41578i
\(755\) 664.470 0.0320299
\(756\) 0 0
\(757\) 11329.1 0.543939 0.271969 0.962306i \(-0.412325\pi\)
0.271969 + 0.962306i \(0.412325\pi\)
\(758\) −28994.0 16739.7i −1.38932 0.802127i
\(759\) 0 0
\(760\) 620.557 + 1074.84i 0.0296184 + 0.0513005i
\(761\) 12696.5 21990.9i 0.604792 1.04753i −0.387292 0.921957i \(-0.626589\pi\)
0.992084 0.125574i \(-0.0400772\pi\)
\(762\) 0 0
\(763\) −2919.48 + 12032.1i −0.138522 + 0.570891i
\(764\) 57499.9i 2.72287i
\(765\) 0 0
\(766\) 49065.8 28328.2i 2.31439 1.33621i
\(767\) 65346.7 37727.9i 3.07631 1.77611i
\(768\) 0 0
\(769\) 18120.8i 0.849744i −0.905253 0.424872i \(-0.860319\pi\)
0.905253 0.424872i \(-0.139681\pi\)
\(770\) −4231.35 + 1242.24i −0.198035 + 0.0581394i
\(771\) 0 0
\(772\) −25874.7 + 44816.3i −1.20628 + 2.08934i
\(773\) 8673.05 + 15022.2i 0.403555 + 0.698978i 0.994152 0.107989i \(-0.0344410\pi\)
−0.590597 + 0.806967i \(0.701108\pi\)
\(774\) 0 0
\(775\) 9423.42 + 5440.61i 0.436773 + 0.252171i
\(776\) 24161.3 1.11771
\(777\) 0 0
\(778\) −36054.7 −1.66147
\(779\) −16171.1 9336.37i −0.743759 0.429410i
\(780\) 0 0
\(781\) 7103.91 + 12304.3i 0.325477 + 0.563743i
\(782\) −15997.4 + 27708.3i −0.731542 + 1.26707i
\(783\) 0 0
\(784\) 2603.65 + 1342.55i 0.118607 + 0.0611585i
\(785\) 1668.22i 0.0758488i
\(786\) 0 0
\(787\) 1801.52 1040.11i 0.0815977 0.0471104i −0.458646 0.888619i \(-0.651665\pi\)
0.540244 + 0.841509i \(0.318332\pi\)
\(788\) 17540.2 10126.8i 0.792949 0.457810i
\(789\) 0 0
\(790\) 2364.83i 0.106502i
\(791\) 11692.5 12261.7i 0.525586 0.551172i
\(792\) 0 0
\(793\) 564.014 976.901i 0.0252569 0.0437463i
\(794\) 28284.7 + 48990.5i 1.26421 + 2.18968i
\(795\) 0 0
\(796\) 1878.73 + 1084.68i 0.0836554 + 0.0482984i
\(797\) −39737.3 −1.76608 −0.883041 0.469297i \(-0.844507\pi\)
−0.883041 + 0.469297i \(0.844507\pi\)
\(798\) 0 0
\(799\) 10820.5 0.479099
\(800\) 21346.4 + 12324.3i 0.943385 + 0.544664i
\(801\) 0 0
\(802\) 18130.2 + 31402.5i 0.798255 + 1.38262i
\(803\) 19170.4 33204.1i 0.842477 1.45921i
\(804\) 0 0
\(805\) −2071.82 502.711i −0.0907108 0.0220102i
\(806\) 34191.1i 1.49421i
\(807\) 0 0
\(808\) 11421.9 6594.45i 0.497305 0.287119i
\(809\) −9713.37 + 5608.02i −0.422131 + 0.243717i −0.695989 0.718053i \(-0.745034\pi\)
0.273858 + 0.961770i \(0.411700\pi\)
\(810\) 0 0
\(811\) 14792.0i 0.640465i 0.947339 + 0.320232i \(0.103761\pi\)
−0.947339 + 0.320232i \(0.896239\pi\)
\(812\) −33888.4 8222.75i −1.46459 0.355372i
\(813\) 0 0
\(814\) 8520.57 14758.1i 0.366887 0.635467i
\(815\) −283.411 490.882i −0.0121809 0.0210980i
\(816\) 0 0
\(817\) −9608.88 5547.69i −0.411471 0.237563i
\(818\) −39511.2 −1.68885
\(819\) 0 0
\(820\) −6045.30 −0.257453
\(821\) −28632.7 16531.1i −1.21716 0.702726i −0.252849 0.967506i \(-0.581368\pi\)
−0.964309 + 0.264779i \(0.914701\pi\)
\(822\) 0 0
\(823\) −10045.4 17399.1i −0.425467 0.736930i 0.570997 0.820952i \(-0.306557\pi\)
−0.996464 + 0.0840220i \(0.973223\pi\)
\(824\) 13791.1 23886.9i 0.583053 1.00988i
\(825\) 0 0
\(826\) −50872.1 + 53348.6i −2.14294 + 2.24726i
\(827\) 36882.5i 1.55082i 0.631458 + 0.775410i \(0.282457\pi\)
−0.631458 + 0.775410i \(0.717543\pi\)
\(828\) 0 0
\(829\) −32697.0 + 18877.6i −1.36986 + 0.790888i −0.990910 0.134530i \(-0.957048\pi\)
−0.378949 + 0.925418i \(0.623714\pi\)
\(830\) 4730.78 2731.32i 0.197841 0.114223i
\(831\) 0 0
\(832\) 71593.5i 2.98324i
\(833\) 22446.3 14422.7i 0.933636 0.599901i
\(834\) 0 0
\(835\) −513.321 + 889.098i −0.0212745 + 0.0368485i
\(836\) −12610.6 21842.2i −0.521707 0.903623i
\(837\) 0 0
\(838\) −15379.3 8879.25i −0.633973 0.366025i
\(839\) −44250.4 −1.82085 −0.910426 0.413672i \(-0.864246\pi\)
−0.910426 + 0.413672i \(0.864246\pi\)
\(840\) 0 0
\(841\) 1528.81 0.0626844
\(842\) 5653.43 + 3264.01i 0.231390 + 0.133593i
\(843\) 0 0
\(844\) −18321.1 31733.1i −0.747201 1.29419i
\(845\) −3261.45 + 5649.00i −0.132778 + 0.229978i
\(846\) 0 0
\(847\) 7097.08 2083.57i 0.287909 0.0845245i
\(848\) 2857.44i 0.115713i
\(849\) 0 0
\(850\) 37594.3 21705.1i 1.51703 0.875856i
\(851\) 7134.65 4119.19i 0.287394 0.165927i
\(852\) 0 0
\(853\) 14952.2i 0.600179i −0.953911 0.300089i \(-0.902983\pi\)
0.953911 0.300089i \(-0.0970165\pi\)
\(854\) −259.856 + 1070.94i −0.0104123 + 0.0429121i
\(855\) 0 0
\(856\) −4317.66 + 7478.41i −0.172400 + 0.298606i
\(857\) −1224.76 2121.35i −0.0488181 0.0845555i 0.840584 0.541682i \(-0.182212\pi\)
−0.889402 + 0.457126i \(0.848879\pi\)
\(858\) 0 0
\(859\) −5751.97 3320.90i −0.228469 0.131906i 0.381397 0.924411i \(-0.375443\pi\)
−0.609865 + 0.792505i \(0.708777\pi\)
\(860\) −3592.13 −0.142431
\(861\) 0 0
\(862\) −66951.0 −2.64543
\(863\) 16339.2 + 9433.46i 0.644489 + 0.372096i 0.786342 0.617792i \(-0.211973\pi\)
−0.141853 + 0.989888i \(0.545306\pi\)
\(864\) 0 0
\(865\) 1419.15 + 2458.04i 0.0557833 + 0.0966196i
\(866\) 35891.1 62165.2i 1.40835 2.43933i
\(867\) 0 0
\(868\) 5729.00 + 19514.2i 0.224026 + 0.763082i
\(869\) 17185.3i 0.670851i
\(870\) 0 0
\(871\) 32849.6 18965.8i 1.27792 0.737807i
\(872\) −11660.5 + 6732.19i −0.452837 + 0.261446i
\(873\) 0 0
\(874\) 20025.7i 0.775033i
\(875\) 4213.94 + 4018.32i 0.162808 + 0.155250i
\(876\) 0 0
\(877\) −5989.84 + 10374.7i −0.230630 + 0.399463i −0.957994 0.286789i \(-0.907412\pi\)
0.727364 + 0.686252i \(0.240745\pi\)
\(878\) −6858.23 11878.8i −0.263615 0.456594i
\(879\) 0 0
\(880\) 389.421 + 224.832i 0.0149175 + 0.00861261i
\(881\) 34504.0 1.31949 0.659743 0.751491i \(-0.270665\pi\)
0.659743 + 0.751491i \(0.270665\pi\)
\(882\) 0 0
\(883\) −8148.85 −0.310567 −0.155283 0.987870i \(-0.549629\pi\)
−0.155283 + 0.987870i \(0.549629\pi\)
\(884\) −71924.9 41525.8i −2.73653 1.57994i
\(885\) 0 0
\(886\) −29053.2 50321.6i −1.10165 1.90811i
\(887\) −17477.6 + 30272.1i −0.661602 + 1.14593i 0.318593 + 0.947892i \(0.396790\pi\)
−0.980195 + 0.198036i \(0.936544\pi\)
\(888\) 0 0
\(889\) 16900.8 + 16116.2i 0.637609 + 0.608010i
\(890\) 169.998i 0.00640262i
\(891\) 0 0
\(892\) 36396.4 21013.5i 1.36619 0.788771i
\(893\) −5865.22 + 3386.29i −0.219790 + 0.126896i
\(894\) 0 0
\(895\) 3700.20i 0.138194i
\(896\) 11365.5 + 38713.5i 0.423768 + 1.44344i
\(897\) 0 0
\(898\) 243.466 421.696i 0.00904741 0.0156706i
\(899\) 6666.22 + 11546.2i 0.247309 + 0.428352i
\(900\) 0 0
\(901\) −22538.4 13012.5i −0.833365 0.481144i
\(902\) 72152.7 2.66344
\(903\) 0 0
\(904\) 18425.3 0.677894
\(905\) 310.051 + 179.008i 0.0113883 + 0.00657505i
\(906\) 0 0
\(907\) 12494.5 + 21641.1i 0.457412 + 0.792261i 0.998823 0.0484970i \(-0.0154431\pi\)
−0.541411 + 0.840758i \(0.682110\pi\)
\(908\) 18872.2 32687.5i 0.689752 1.19468i
\(909\) 0 0
\(910\) 2143.21 8832.83i 0.0780735 0.321764i
\(911\) 41609.1i 1.51325i 0.653849 + 0.756625i \(0.273153\pi\)
−0.653849 + 0.756625i \(0.726847\pi\)
\(912\) 0 0
\(913\) −34378.7 + 19848.5i −1.24619 + 0.719486i
\(914\) 38293.2 22108.6i 1.38580 0.800095i
\(915\) 0 0
\(916\) 13805.1i 0.497964i
\(917\) −24295.5 + 7132.70i −0.874927 + 0.256862i
\(918\) 0 0
\(919\) −25496.0 + 44160.4i −0.915164 + 1.58511i −0.108502 + 0.994096i \(0.534605\pi\)
−0.806661 + 0.591014i \(0.798728\pi\)
\(920\) −1159.23 2007.84i −0.0415420 0.0719529i
\(921\) 0 0
\(922\) 2502.24 + 1444.67i 0.0893782 + 0.0516025i
\(923\) −29283.1 −1.04428
\(924\) 0 0
\(925\) −11177.7 −0.397321
\(926\) −21942.0 12668.2i −0.778682 0.449572i
\(927\) 0 0
\(928\) 15100.6 + 26155.1i 0.534162 + 0.925196i
\(929\) 23746.5 41130.2i 0.838642 1.45257i −0.0523888 0.998627i \(-0.516684\pi\)
0.891031 0.453943i \(-0.149983\pi\)
\(930\) 0 0
\(931\) −7653.39 + 14842.4i −0.269420 + 0.522493i
\(932\) 38603.9i 1.35677i
\(933\) 0 0
\(934\) −21615.4 + 12479.7i −0.757258 + 0.437203i
\(935\) 3546.78 2047.73i 0.124056 0.0716235i
\(936\) 0 0
\(937\) 6811.98i 0.237500i 0.992924 + 0.118750i \(0.0378887\pi\)
−0.992924 + 0.118750i \(0.962111\pi\)
\(938\) −25573.3 + 26818.2i −0.890189 + 0.933525i
\(939\) 0 0
\(940\) −1096.31 + 1898.87i −0.0380401 + 0.0658874i
\(941\) −16271.0 28182.2i −0.563677 0.976318i −0.997171 0.0751612i \(-0.976053\pi\)
0.433494 0.901156i \(-0.357280\pi\)
\(942\) 0 0
\(943\) 30208.3 + 17440.8i 1.04318 + 0.602280i
\(944\) 7516.54 0.259155
\(945\) 0 0
\(946\) 42873.3 1.47350
\(947\) 10119.9 + 5842.70i 0.347256 + 0.200488i 0.663476 0.748198i \(-0.269080\pi\)
−0.316220 + 0.948686i \(0.602414\pi\)
\(948\) 0 0
\(949\) 39511.3 + 68435.7i 1.35152 + 2.34090i
\(950\) −13585.3 + 23530.4i −0.463963 + 0.803608i
\(951\) 0 0
\(952\) 28196.6 + 6841.67i 0.959933 + 0.232920i
\(953\) 46457.5i 1.57912i −0.613671 0.789562i \(-0.710308\pi\)
0.613671 0.789562i \(-0.289692\pi\)
\(954\) 0 0
\(955\) 5061.08 2922.01i 0.171490 0.0990096i
\(956\) −18714.6 + 10804.9i −0.633130 + 0.365538i
\(957\) 0 0
\(958\) 24732.8i 0.834114i
\(959\) 19818.7 + 4808.84i 0.667339 + 0.161924i
\(960\) 0 0
\(961\) −11007.6 + 19065.8i −0.369496 + 0.639986i
\(962\) 17561.4 + 30417.2i 0.588568 + 1.01943i
\(963\) 0 0
\(964\) −12942.3 7472.25i −0.432411 0.249653i
\(965\) 5259.57 0.175452
\(966\) 0 0
\(967\) −27949.1 −0.929455 −0.464728 0.885454i \(-0.653848\pi\)
−0.464728 + 0.885454i \(0.653848\pi\)
\(968\) 6966.06 + 4021.86i 0.231299 + 0.133541i
\(969\) 0 0
\(970\) −3433.47 5946.94i −0.113652 0.196850i
\(971\) 1609.85 2788.33i 0.0532053 0.0921544i −0.838196 0.545369i \(-0.816390\pi\)
0.891401 + 0.453215i \(0.149723\pi\)
\(972\) 0 0
\(973\) 29480.1 30915.2i 0.971314 1.01860i
\(974\) 53064.9i 1.74570i
\(975\) 0 0
\(976\) 97.3141 56.1843i 0.00319155 0.00184264i
\(977\) −33258.6 + 19201.9i −1.08909 + 0.628785i −0.933333 0.359011i \(-0.883114\pi\)
−0.155754 + 0.987796i \(0.549781\pi\)
\(978\) 0 0
\(979\) 1235.38i 0.0403297i
\(980\) 256.796 + 5400.36i 0.00837047 + 0.176029i
\(981\) 0 0
\(982\) 7948.19 13766.7i 0.258286 0.447364i
\(983\) 13709.1 + 23744.8i 0.444814 + 0.770440i 0.998039 0.0625917i \(-0.0199366\pi\)
−0.553226 + 0.833031i \(0.686603\pi\)
\(984\) 0 0
\(985\) −1782.71 1029.25i −0.0576667 0.0332939i
\(986\) 53189.1 1.71794
\(987\) 0 0
\(988\) 51982.4 1.67387
\(989\) 17949.8 + 10363.3i 0.577120 + 0.333200i
\(990\) 0 0
\(991\) −21857.9 37859.1i −0.700646 1.21355i −0.968240 0.250023i \(-0.919562\pi\)
0.267594 0.963532i \(-0.413771\pi\)
\(992\) 8806.94 15254.1i 0.281876 0.488223i
\(993\) 0 0
\(994\) 27449.4 8058.63i 0.875898 0.257147i
\(995\) 220.484i 0.00702495i
\(996\) 0 0
\(997\) −21930.8 + 12661.7i −0.696644 + 0.402208i −0.806096 0.591784i \(-0.798424\pi\)
0.109452 + 0.993992i \(0.465090\pi\)
\(998\) −38731.5 + 22361.7i −1.22848 + 0.709264i
\(999\) 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.26.7 yes 16
3.2 odd 2 inner 63.4.p.a.26.2 yes 16
4.3 odd 2 1008.4.bt.a.593.5 16
7.2 even 3 441.4.c.a.440.3 16
7.3 odd 6 inner 63.4.p.a.17.2 16
7.4 even 3 441.4.p.c.80.2 16
7.5 odd 6 441.4.c.a.440.4 16
7.6 odd 2 441.4.p.c.215.7 16
12.11 even 2 1008.4.bt.a.593.4 16
21.2 odd 6 441.4.c.a.440.14 16
21.5 even 6 441.4.c.a.440.13 16
21.11 odd 6 441.4.p.c.80.7 16
21.17 even 6 inner 63.4.p.a.17.7 yes 16
21.20 even 2 441.4.p.c.215.2 16
28.3 even 6 1008.4.bt.a.17.4 16
84.59 odd 6 1008.4.bt.a.17.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.p.a.17.2 16 7.3 odd 6 inner
63.4.p.a.17.7 yes 16 21.17 even 6 inner
63.4.p.a.26.2 yes 16 3.2 odd 2 inner
63.4.p.a.26.7 yes 16 1.1 even 1 trivial
441.4.c.a.440.3 16 7.2 even 3
441.4.c.a.440.4 16 7.5 odd 6
441.4.c.a.440.13 16 21.5 even 6
441.4.c.a.440.14 16 21.2 odd 6
441.4.p.c.80.2 16 7.4 even 3
441.4.p.c.80.7 16 21.11 odd 6
441.4.p.c.215.2 16 21.20 even 2
441.4.p.c.215.7 16 7.6 odd 2
1008.4.bt.a.17.4 16 28.3 even 6
1008.4.bt.a.17.5 16 84.59 odd 6
1008.4.bt.a.593.4 16 12.11 even 2
1008.4.bt.a.593.5 16 4.3 odd 2