Properties

Label 63.3.m.d.19.1
Level $63$
Weight $3$
Character 63.19
Analytic conductor $1.717$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,3,Mod(10,63)]
 
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([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.10");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 63.m (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: \(1.71662566547\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 63.19
Dual form 63.3.m.d.10.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{2} +(-2.50000 - 4.33013i) q^{4} +(-4.50000 - 2.59808i) q^{5} +(6.50000 - 2.59808i) q^{7} -3.00000 q^{8} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{2} +(-2.50000 - 4.33013i) q^{4} +(-4.50000 - 2.59808i) q^{5} +(6.50000 - 2.59808i) q^{7} -3.00000 q^{8} +(-13.5000 + 7.79423i) q^{10} +(7.50000 + 12.9904i) q^{11} +13.8564i q^{13} +(3.00000 - 20.7846i) q^{14} +(5.50000 - 9.52628i) q^{16} +(-9.00000 + 5.19615i) q^{17} +(-9.00000 - 5.19615i) q^{19} +25.9808i q^{20} +45.0000 q^{22} +(1.00000 + 1.73205i) q^{25} +(36.0000 + 20.7846i) q^{26} +(-27.5000 - 21.6506i) q^{28} +9.00000 q^{29} +(-10.5000 + 6.06218i) q^{31} +(-22.5000 - 38.9711i) q^{32} +31.1769i q^{34} +(-36.0000 - 5.19615i) q^{35} +(-5.00000 + 8.66025i) q^{37} +(-27.0000 + 15.5885i) q^{38} +(13.5000 + 7.79423i) q^{40} -10.3923i q^{41} -74.0000 q^{43} +(37.5000 - 64.9519i) q^{44} +(35.5000 - 33.7750i) q^{49} +6.00000 q^{50} +(60.0000 - 34.6410i) q^{52} +(16.5000 + 28.5788i) q^{53} -77.9423i q^{55} +(-19.5000 + 7.79423i) q^{56} +(13.5000 - 23.3827i) q^{58} +(-13.5000 + 7.79423i) q^{59} +(78.0000 + 45.0333i) q^{61} +36.3731i q^{62} -91.0000 q^{64} +(36.0000 - 62.3538i) q^{65} +(38.0000 + 65.8179i) q^{67} +(45.0000 + 25.9808i) q^{68} +(-67.5000 + 85.7365i) q^{70} -84.0000 q^{71} +(-54.0000 + 31.1769i) q^{73} +(15.0000 + 25.9808i) q^{74} +51.9615i q^{76} +(82.5000 + 64.9519i) q^{77} +(21.5000 - 37.2391i) q^{79} +(-49.5000 + 28.5788i) q^{80} +(-27.0000 - 15.5885i) q^{82} -119.512i q^{83} +54.0000 q^{85} +(-111.000 + 192.258i) q^{86} +(-22.5000 - 38.9711i) q^{88} +(63.0000 + 36.3731i) q^{89} +(36.0000 + 90.0666i) q^{91} +(27.0000 + 46.7654i) q^{95} -185.329i q^{97} +(-34.5000 - 142.894i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} - 5 q^{4} - 9 q^{5} + 13 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} - 5 q^{4} - 9 q^{5} + 13 q^{7} - 6 q^{8} - 27 q^{10} + 15 q^{11} + 6 q^{14} + 11 q^{16} - 18 q^{17} - 18 q^{19} + 90 q^{22} + 2 q^{25} + 72 q^{26} - 55 q^{28} + 18 q^{29} - 21 q^{31} - 45 q^{32} - 72 q^{35} - 10 q^{37} - 54 q^{38} + 27 q^{40} - 148 q^{43} + 75 q^{44} + 71 q^{49} + 12 q^{50} + 120 q^{52} + 33 q^{53} - 39 q^{56} + 27 q^{58} - 27 q^{59} + 156 q^{61} - 182 q^{64} + 72 q^{65} + 76 q^{67} + 90 q^{68} - 135 q^{70} - 168 q^{71} - 108 q^{73} + 30 q^{74} + 165 q^{77} + 43 q^{79} - 99 q^{80} - 54 q^{82} + 108 q^{85} - 222 q^{86} - 45 q^{88} + 126 q^{89} + 72 q^{91} + 54 q^{95} - 69 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 2.59808i 0.750000 1.29904i −0.197822 0.980238i \(-0.563387\pi\)
0.947822 0.318800i \(-0.103280\pi\)
\(3\) 0 0
\(4\) −2.50000 4.33013i −0.625000 1.08253i
\(5\) −4.50000 2.59808i −0.900000 0.519615i −0.0227998 0.999740i \(-0.507258\pi\)
−0.877200 + 0.480125i \(0.840591\pi\)
\(6\) 0 0
\(7\) 6.50000 2.59808i 0.928571 0.371154i
\(8\) −3.00000 −0.375000
\(9\) 0 0
\(10\) −13.5000 + 7.79423i −1.35000 + 0.779423i
\(11\) 7.50000 + 12.9904i 0.681818 + 1.18094i 0.974425 + 0.224711i \(0.0721438\pi\)
−0.292607 + 0.956233i \(0.594523\pi\)
\(12\) 0 0
\(13\) 13.8564i 1.06588i 0.846154 + 0.532939i \(0.178912\pi\)
−0.846154 + 0.532939i \(0.821088\pi\)
\(14\) 3.00000 20.7846i 0.214286 1.48461i
\(15\) 0 0
\(16\) 5.50000 9.52628i 0.343750 0.595392i
\(17\) −9.00000 + 5.19615i −0.529412 + 0.305656i −0.740777 0.671751i \(-0.765542\pi\)
0.211365 + 0.977407i \(0.432209\pi\)
\(18\) 0 0
\(19\) −9.00000 5.19615i −0.473684 0.273482i 0.244096 0.969751i \(-0.421509\pi\)
−0.717781 + 0.696269i \(0.754842\pi\)
\(20\) 25.9808i 1.29904i
\(21\) 0 0
\(22\) 45.0000 2.04545
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 1.00000 + 1.73205i 0.0400000 + 0.0692820i
\(26\) 36.0000 + 20.7846i 1.38462 + 0.799408i
\(27\) 0 0
\(28\) −27.5000 21.6506i −0.982143 0.773237i
\(29\) 9.00000 0.310345 0.155172 0.987887i \(-0.450407\pi\)
0.155172 + 0.987887i \(0.450407\pi\)
\(30\) 0 0
\(31\) −10.5000 + 6.06218i −0.338710 + 0.195554i −0.659701 0.751528i \(-0.729317\pi\)
0.320992 + 0.947082i \(0.395984\pi\)
\(32\) −22.5000 38.9711i −0.703125 1.21785i
\(33\) 0 0
\(34\) 31.1769i 0.916968i
\(35\) −36.0000 5.19615i −1.02857 0.148461i
\(36\) 0 0
\(37\) −5.00000 + 8.66025i −0.135135 + 0.234061i −0.925649 0.378383i \(-0.876480\pi\)
0.790514 + 0.612444i \(0.209814\pi\)
\(38\) −27.0000 + 15.5885i −0.710526 + 0.410223i
\(39\) 0 0
\(40\) 13.5000 + 7.79423i 0.337500 + 0.194856i
\(41\) 10.3923i 0.253471i −0.991937 0.126735i \(-0.959550\pi\)
0.991937 0.126735i \(-0.0404499\pi\)
\(42\) 0 0
\(43\) −74.0000 −1.72093 −0.860465 0.509509i \(-0.829827\pi\)
−0.860465 + 0.509509i \(0.829827\pi\)
\(44\) 37.5000 64.9519i 0.852273 1.47618i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 0 0
\(49\) 35.5000 33.7750i 0.724490 0.689286i
\(50\) 6.00000 0.120000
\(51\) 0 0
\(52\) 60.0000 34.6410i 1.15385 0.666173i
\(53\) 16.5000 + 28.5788i 0.311321 + 0.539223i 0.978649 0.205541i \(-0.0658953\pi\)
−0.667328 + 0.744764i \(0.732562\pi\)
\(54\) 0 0
\(55\) 77.9423i 1.41713i
\(56\) −19.5000 + 7.79423i −0.348214 + 0.139183i
\(57\) 0 0
\(58\) 13.5000 23.3827i 0.232759 0.403150i
\(59\) −13.5000 + 7.79423i −0.228814 + 0.132106i −0.610025 0.792382i \(-0.708840\pi\)
0.381211 + 0.924488i \(0.375507\pi\)
\(60\) 0 0
\(61\) 78.0000 + 45.0333i 1.27869 + 0.738251i 0.976607 0.215031i \(-0.0689853\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(62\) 36.3731i 0.586662i
\(63\) 0 0
\(64\) −91.0000 −1.42188
\(65\) 36.0000 62.3538i 0.553846 0.959290i
\(66\) 0 0
\(67\) 38.0000 + 65.8179i 0.567164 + 0.982357i 0.996845 + 0.0793762i \(0.0252928\pi\)
−0.429681 + 0.902981i \(0.641374\pi\)
\(68\) 45.0000 + 25.9808i 0.661765 + 0.382070i
\(69\) 0 0
\(70\) −67.5000 + 85.7365i −0.964286 + 1.22481i
\(71\) −84.0000 −1.18310 −0.591549 0.806269i \(-0.701483\pi\)
−0.591549 + 0.806269i \(0.701483\pi\)
\(72\) 0 0
\(73\) −54.0000 + 31.1769i −0.739726 + 0.427081i −0.821970 0.569531i \(-0.807125\pi\)
0.0822437 + 0.996612i \(0.473791\pi\)
\(74\) 15.0000 + 25.9808i 0.202703 + 0.351091i
\(75\) 0 0
\(76\) 51.9615i 0.683704i
\(77\) 82.5000 + 64.9519i 1.07143 + 0.843531i
\(78\) 0 0
\(79\) 21.5000 37.2391i 0.272152 0.471381i −0.697261 0.716818i \(-0.745598\pi\)
0.969413 + 0.245437i \(0.0789313\pi\)
\(80\) −49.5000 + 28.5788i −0.618750 + 0.357235i
\(81\) 0 0
\(82\) −27.0000 15.5885i −0.329268 0.190103i
\(83\) 119.512i 1.43990i −0.694027 0.719949i \(-0.744165\pi\)
0.694027 0.719949i \(-0.255835\pi\)
\(84\) 0 0
\(85\) 54.0000 0.635294
\(86\) −111.000 + 192.258i −1.29070 + 2.23555i
\(87\) 0 0
\(88\) −22.5000 38.9711i −0.255682 0.442854i
\(89\) 63.0000 + 36.3731i 0.707865 + 0.408686i 0.810270 0.586057i \(-0.199320\pi\)
−0.102405 + 0.994743i \(0.532654\pi\)
\(90\) 0 0
\(91\) 36.0000 + 90.0666i 0.395604 + 0.989743i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 27.0000 + 46.7654i 0.284211 + 0.492267i
\(96\) 0 0
\(97\) 185.329i 1.91061i −0.295618 0.955306i \(-0.595525\pi\)
0.295618 0.955306i \(-0.404475\pi\)
\(98\) −34.5000 142.894i −0.352041 1.45810i
\(99\) 0 0
\(100\) 5.00000 8.66025i 0.0500000 0.0866025i
\(101\) 126.000 72.7461i 1.24752 0.720259i 0.276910 0.960896i \(-0.410690\pi\)
0.970615 + 0.240637i \(0.0773564\pi\)
\(102\) 0 0
\(103\) −60.0000 34.6410i −0.582524 0.336321i 0.179612 0.983738i \(-0.442516\pi\)
−0.762136 + 0.647417i \(0.775849\pi\)
\(104\) 41.5692i 0.399704i
\(105\) 0 0
\(106\) 99.0000 0.933962
\(107\) 46.5000 80.5404i 0.434579 0.752714i −0.562682 0.826674i \(-0.690230\pi\)
0.997261 + 0.0739599i \(0.0235637\pi\)
\(108\) 0 0
\(109\) 4.00000 + 6.92820i 0.0366972 + 0.0635615i 0.883791 0.467882i \(-0.154983\pi\)
−0.847093 + 0.531444i \(0.821650\pi\)
\(110\) −202.500 116.913i −1.84091 1.06285i
\(111\) 0 0
\(112\) 11.0000 76.2102i 0.0982143 0.680449i
\(113\) −42.0000 −0.371681 −0.185841 0.982580i \(-0.559501\pi\)
−0.185841 + 0.982580i \(0.559501\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −22.5000 38.9711i −0.193966 0.335958i
\(117\) 0 0
\(118\) 46.7654i 0.396317i
\(119\) −45.0000 + 57.1577i −0.378151 + 0.480317i
\(120\) 0 0
\(121\) −52.0000 + 90.0666i −0.429752 + 0.744352i
\(122\) 234.000 135.100i 1.91803 1.10738i
\(123\) 0 0
\(124\) 52.5000 + 30.3109i 0.423387 + 0.244443i
\(125\) 119.512i 0.956092i
\(126\) 0 0
\(127\) 35.0000 0.275591 0.137795 0.990461i \(-0.455998\pi\)
0.137795 + 0.990461i \(0.455998\pi\)
\(128\) −46.5000 + 80.5404i −0.363281 + 0.629222i
\(129\) 0 0
\(130\) −108.000 187.061i −0.830769 1.43893i
\(131\) −148.500 85.7365i −1.13359 0.654477i −0.188753 0.982025i \(-0.560445\pi\)
−0.944835 + 0.327547i \(0.893778\pi\)
\(132\) 0 0
\(133\) −72.0000 10.3923i −0.541353 0.0781376i
\(134\) 228.000 1.70149
\(135\) 0 0
\(136\) 27.0000 15.5885i 0.198529 0.114621i
\(137\) −48.0000 83.1384i −0.350365 0.606850i 0.635948 0.771732i \(-0.280609\pi\)
−0.986313 + 0.164882i \(0.947276\pi\)
\(138\) 0 0
\(139\) 183.597i 1.32084i 0.750894 + 0.660422i \(0.229623\pi\)
−0.750894 + 0.660422i \(0.770377\pi\)
\(140\) 67.5000 + 168.875i 0.482143 + 1.20625i
\(141\) 0 0
\(142\) −126.000 + 218.238i −0.887324 + 1.53689i
\(143\) −180.000 + 103.923i −1.25874 + 0.726735i
\(144\) 0 0
\(145\) −40.5000 23.3827i −0.279310 0.161260i
\(146\) 187.061i 1.28124i
\(147\) 0 0
\(148\) 50.0000 0.337838
\(149\) −93.0000 + 161.081i −0.624161 + 1.08108i 0.364541 + 0.931187i \(0.381226\pi\)
−0.988702 + 0.149892i \(0.952108\pi\)
\(150\) 0 0
\(151\) −39.5000 68.4160i −0.261589 0.453086i 0.705075 0.709133i \(-0.250913\pi\)
−0.966664 + 0.256047i \(0.917580\pi\)
\(152\) 27.0000 + 15.5885i 0.177632 + 0.102556i
\(153\) 0 0
\(154\) 292.500 116.913i 1.89935 0.759178i
\(155\) 63.0000 0.406452
\(156\) 0 0
\(157\) −18.0000 + 10.3923i −0.114650 + 0.0661930i −0.556228 0.831030i \(-0.687752\pi\)
0.441579 + 0.897223i \(0.354419\pi\)
\(158\) −64.5000 111.717i −0.408228 0.707071i
\(159\) 0 0
\(160\) 233.827i 1.46142i
\(161\) 0 0
\(162\) 0 0
\(163\) 104.000 180.133i 0.638037 1.10511i −0.347826 0.937559i \(-0.613080\pi\)
0.985863 0.167553i \(-0.0535866\pi\)
\(164\) −45.0000 + 25.9808i −0.274390 + 0.158419i
\(165\) 0 0
\(166\) −310.500 179.267i −1.87048 1.07992i
\(167\) 249.415i 1.49350i −0.665102 0.746752i \(-0.731612\pi\)
0.665102 0.746752i \(-0.268388\pi\)
\(168\) 0 0
\(169\) −23.0000 −0.136095
\(170\) 81.0000 140.296i 0.476471 0.825271i
\(171\) 0 0
\(172\) 185.000 + 320.429i 1.07558 + 1.86296i
\(173\) 198.000 + 114.315i 1.14451 + 0.660782i 0.947543 0.319628i \(-0.103558\pi\)
0.196966 + 0.980410i \(0.436891\pi\)
\(174\) 0 0
\(175\) 11.0000 + 8.66025i 0.0628571 + 0.0494872i
\(176\) 165.000 0.937500
\(177\) 0 0
\(178\) 189.000 109.119i 1.06180 0.613029i
\(179\) 45.0000 + 77.9423i 0.251397 + 0.435432i 0.963911 0.266226i \(-0.0857768\pi\)
−0.712514 + 0.701658i \(0.752443\pi\)
\(180\) 0 0
\(181\) 10.3923i 0.0574160i 0.999588 + 0.0287080i \(0.00913930\pi\)
−0.999588 + 0.0287080i \(0.990861\pi\)
\(182\) 288.000 + 41.5692i 1.58242 + 0.228402i
\(183\) 0 0
\(184\) 0 0
\(185\) 45.0000 25.9808i 0.243243 0.140437i
\(186\) 0 0
\(187\) −135.000 77.9423i −0.721925 0.416804i
\(188\) 0 0
\(189\) 0 0
\(190\) 162.000 0.852632
\(191\) −156.000 + 270.200i −0.816754 + 1.41466i 0.0913077 + 0.995823i \(0.470895\pi\)
−0.908062 + 0.418837i \(0.862438\pi\)
\(192\) 0 0
\(193\) 92.5000 + 160.215i 0.479275 + 0.830128i 0.999717 0.0237685i \(-0.00756646\pi\)
−0.520443 + 0.853896i \(0.674233\pi\)
\(194\) −481.500 277.994i −2.48196 1.43296i
\(195\) 0 0
\(196\) −235.000 69.2820i −1.19898 0.353480i
\(197\) −330.000 −1.67513 −0.837563 0.546340i \(-0.816021\pi\)
−0.837563 + 0.546340i \(0.816021\pi\)
\(198\) 0 0
\(199\) 6.00000 3.46410i 0.0301508 0.0174075i −0.484849 0.874598i \(-0.661125\pi\)
0.515000 + 0.857190i \(0.327792\pi\)
\(200\) −3.00000 5.19615i −0.0150000 0.0259808i
\(201\) 0 0
\(202\) 436.477i 2.16078i
\(203\) 58.5000 23.3827i 0.288177 0.115186i
\(204\) 0 0
\(205\) −27.0000 + 46.7654i −0.131707 + 0.228124i
\(206\) −180.000 + 103.923i −0.873786 + 0.504481i
\(207\) 0 0
\(208\) 132.000 + 76.2102i 0.634615 + 0.366395i
\(209\) 155.885i 0.745859i
\(210\) 0 0
\(211\) −248.000 −1.17536 −0.587678 0.809095i \(-0.699958\pi\)
−0.587678 + 0.809095i \(0.699958\pi\)
\(212\) 82.5000 142.894i 0.389151 0.674029i
\(213\) 0 0
\(214\) −139.500 241.621i −0.651869 1.12907i
\(215\) 333.000 + 192.258i 1.54884 + 0.894222i
\(216\) 0 0
\(217\) −52.5000 + 66.6840i −0.241935 + 0.307299i
\(218\) 24.0000 0.110092
\(219\) 0 0
\(220\) −337.500 + 194.856i −1.53409 + 0.885708i
\(221\) −72.0000 124.708i −0.325792 0.564288i
\(222\) 0 0
\(223\) 192.258i 0.862142i 0.902318 + 0.431071i \(0.141864\pi\)
−0.902318 + 0.431071i \(0.858136\pi\)
\(224\) −247.500 194.856i −1.10491 0.869892i
\(225\) 0 0
\(226\) −63.0000 + 109.119i −0.278761 + 0.482828i
\(227\) 76.5000 44.1673i 0.337004 0.194570i −0.321942 0.946759i \(-0.604336\pi\)
0.658947 + 0.752190i \(0.271002\pi\)
\(228\) 0 0
\(229\) 285.000 + 164.545i 1.24454 + 0.718536i 0.970015 0.243043i \(-0.0781457\pi\)
0.274526 + 0.961580i \(0.411479\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −27.0000 −0.116379
\(233\) 135.000 233.827i 0.579399 1.00355i −0.416149 0.909296i \(-0.636621\pi\)
0.995548 0.0942524i \(-0.0300461\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 67.5000 + 38.9711i 0.286017 + 0.165132i
\(237\) 0 0
\(238\) 81.0000 + 202.650i 0.340336 + 0.851470i
\(239\) 228.000 0.953975 0.476987 0.878910i \(-0.341729\pi\)
0.476987 + 0.878910i \(0.341729\pi\)
\(240\) 0 0
\(241\) 385.500 222.569i 1.59959 0.923521i 0.608018 0.793923i \(-0.291965\pi\)
0.991567 0.129598i \(-0.0413687\pi\)
\(242\) 156.000 + 270.200i 0.644628 + 1.11653i
\(243\) 0 0
\(244\) 450.333i 1.84563i
\(245\) −247.500 + 59.7558i −1.01020 + 0.243901i
\(246\) 0 0
\(247\) 72.0000 124.708i 0.291498 0.504889i
\(248\) 31.5000 18.1865i 0.127016 0.0733328i
\(249\) 0 0
\(250\) 310.500 + 179.267i 1.24200 + 0.717069i
\(251\) 5.19615i 0.0207018i −0.999946 0.0103509i \(-0.996705\pi\)
0.999946 0.0103509i \(-0.00329485\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 52.5000 90.9327i 0.206693 0.358003i
\(255\) 0 0
\(256\) −42.5000 73.6122i −0.166016 0.287547i
\(257\) −99.0000 57.1577i −0.385214 0.222403i 0.294870 0.955537i \(-0.404724\pi\)
−0.680084 + 0.733134i \(0.738057\pi\)
\(258\) 0 0
\(259\) −10.0000 + 69.2820i −0.0386100 + 0.267498i
\(260\) −360.000 −1.38462
\(261\) 0 0
\(262\) −445.500 + 257.210i −1.70038 + 0.981716i
\(263\) 93.0000 + 161.081i 0.353612 + 0.612474i 0.986879 0.161459i \(-0.0516199\pi\)
−0.633267 + 0.773933i \(0.718287\pi\)
\(264\) 0 0
\(265\) 171.473i 0.647068i
\(266\) −135.000 + 171.473i −0.507519 + 0.644635i
\(267\) 0 0
\(268\) 190.000 329.090i 0.708955 1.22795i
\(269\) 292.500 168.875i 1.08736 0.627788i 0.154488 0.987995i \(-0.450627\pi\)
0.932873 + 0.360207i \(0.117294\pi\)
\(270\) 0 0
\(271\) 79.5000 + 45.8993i 0.293358 + 0.169370i 0.639455 0.768828i \(-0.279160\pi\)
−0.346097 + 0.938199i \(0.612493\pi\)
\(272\) 114.315i 0.420277i
\(273\) 0 0
\(274\) −288.000 −1.05109
\(275\) −15.0000 + 25.9808i −0.0545455 + 0.0944755i
\(276\) 0 0
\(277\) −190.000 329.090i −0.685921 1.18805i −0.973147 0.230186i \(-0.926066\pi\)
0.287226 0.957863i \(-0.407267\pi\)
\(278\) 477.000 + 275.396i 1.71583 + 0.990633i
\(279\) 0 0
\(280\) 108.000 + 15.5885i 0.385714 + 0.0556731i
\(281\) −300.000 −1.06762 −0.533808 0.845606i \(-0.679239\pi\)
−0.533808 + 0.845606i \(0.679239\pi\)
\(282\) 0 0
\(283\) 177.000 102.191i 0.625442 0.361099i −0.153543 0.988142i \(-0.549068\pi\)
0.778985 + 0.627043i \(0.215735\pi\)
\(284\) 210.000 + 363.731i 0.739437 + 1.28074i
\(285\) 0 0
\(286\) 623.538i 2.18020i
\(287\) −27.0000 67.5500i −0.0940767 0.235366i
\(288\) 0 0
\(289\) −90.5000 + 156.751i −0.313149 + 0.542390i
\(290\) −121.500 + 70.1481i −0.418966 + 0.241890i
\(291\) 0 0
\(292\) 270.000 + 155.885i 0.924658 + 0.533851i
\(293\) 545.596i 1.86210i 0.364889 + 0.931051i \(0.381107\pi\)
−0.364889 + 0.931051i \(0.618893\pi\)
\(294\) 0 0
\(295\) 81.0000 0.274576
\(296\) 15.0000 25.9808i 0.0506757 0.0877728i
\(297\) 0 0
\(298\) 279.000 + 483.242i 0.936242 + 1.62162i
\(299\) 0 0
\(300\) 0 0
\(301\) −481.000 + 192.258i −1.59801 + 0.638730i
\(302\) −237.000 −0.784768
\(303\) 0 0
\(304\) −99.0000 + 57.1577i −0.325658 + 0.188019i
\(305\) −234.000 405.300i −0.767213 1.32885i
\(306\) 0 0
\(307\) 173.205i 0.564186i −0.959387 0.282093i \(-0.908971\pi\)
0.959387 0.282093i \(-0.0910287\pi\)
\(308\) 75.0000 519.615i 0.243506 1.68706i
\(309\) 0 0
\(310\) 94.5000 163.679i 0.304839 0.527996i
\(311\) 153.000 88.3346i 0.491961 0.284034i −0.233426 0.972374i \(-0.574994\pi\)
0.725388 + 0.688340i \(0.241660\pi\)
\(312\) 0 0
\(313\) −184.500 106.521i −0.589457 0.340323i 0.175426 0.984493i \(-0.443870\pi\)
−0.764883 + 0.644170i \(0.777203\pi\)
\(314\) 62.3538i 0.198579i
\(315\) 0 0
\(316\) −215.000 −0.680380
\(317\) 58.5000 101.325i 0.184543 0.319637i −0.758880 0.651231i \(-0.774253\pi\)
0.943422 + 0.331594i \(0.107586\pi\)
\(318\) 0 0
\(319\) 67.5000 + 116.913i 0.211599 + 0.366500i
\(320\) 409.500 + 236.425i 1.27969 + 0.738828i
\(321\) 0 0
\(322\) 0 0
\(323\) 108.000 0.334365
\(324\) 0 0
\(325\) −24.0000 + 13.8564i −0.0738462 + 0.0426351i
\(326\) −312.000 540.400i −0.957055 1.65767i
\(327\) 0 0
\(328\) 31.1769i 0.0950516i
\(329\) 0 0
\(330\) 0 0
\(331\) −20.0000 + 34.6410i −0.0604230 + 0.104656i −0.894655 0.446759i \(-0.852578\pi\)
0.834232 + 0.551414i \(0.185912\pi\)
\(332\) −517.500 + 298.779i −1.55873 + 0.899936i
\(333\) 0 0
\(334\) −648.000 374.123i −1.94012 1.12013i
\(335\) 394.908i 1.17883i
\(336\) 0 0
\(337\) 91.0000 0.270030 0.135015 0.990844i \(-0.456892\pi\)
0.135015 + 0.990844i \(0.456892\pi\)
\(338\) −34.5000 + 59.7558i −0.102071 + 0.176792i
\(339\) 0 0
\(340\) −135.000 233.827i −0.397059 0.687726i
\(341\) −157.500 90.9327i −0.461877 0.266665i
\(342\) 0 0
\(343\) 143.000 311.769i 0.416910 0.908948i
\(344\) 222.000 0.645349
\(345\) 0 0
\(346\) 594.000 342.946i 1.71676 0.991174i
\(347\) 105.000 + 181.865i 0.302594 + 0.524108i 0.976723 0.214506i \(-0.0688142\pi\)
−0.674129 + 0.738614i \(0.735481\pi\)
\(348\) 0 0
\(349\) 304.841i 0.873470i 0.899590 + 0.436735i \(0.143865\pi\)
−0.899590 + 0.436735i \(0.856135\pi\)
\(350\) 39.0000 15.5885i 0.111429 0.0445384i
\(351\) 0 0
\(352\) 337.500 584.567i 0.958807 1.66070i
\(353\) −342.000 + 197.454i −0.968839 + 0.559359i −0.898882 0.438191i \(-0.855619\pi\)
−0.0699566 + 0.997550i \(0.522286\pi\)
\(354\) 0 0
\(355\) 378.000 + 218.238i 1.06479 + 0.614756i
\(356\) 363.731i 1.02172i
\(357\) 0 0
\(358\) 270.000 0.754190
\(359\) 246.000 426.084i 0.685237 1.18686i −0.288126 0.957593i \(-0.593032\pi\)
0.973362 0.229272i \(-0.0736346\pi\)
\(360\) 0 0
\(361\) −126.500 219.104i −0.350416 0.606937i
\(362\) 27.0000 + 15.5885i 0.0745856 + 0.0430620i
\(363\) 0 0
\(364\) 300.000 381.051i 0.824176 1.04684i
\(365\) 324.000 0.887671
\(366\) 0 0
\(367\) −283.500 + 163.679i −0.772480 + 0.445991i −0.833758 0.552129i \(-0.813815\pi\)
0.0612789 + 0.998121i \(0.480482\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 155.885i 0.421310i
\(371\) 181.500 + 142.894i 0.489218 + 0.385160i
\(372\) 0 0
\(373\) −85.0000 + 147.224i −0.227882 + 0.394703i −0.957180 0.289493i \(-0.906513\pi\)
0.729298 + 0.684196i \(0.239847\pi\)
\(374\) −405.000 + 233.827i −1.08289 + 0.625206i
\(375\) 0 0
\(376\) 0 0
\(377\) 124.708i 0.330790i
\(378\) 0 0
\(379\) 82.0000 0.216359 0.108179 0.994131i \(-0.465498\pi\)
0.108179 + 0.994131i \(0.465498\pi\)
\(380\) 135.000 233.827i 0.355263 0.615334i
\(381\) 0 0
\(382\) 468.000 + 810.600i 1.22513 + 2.12199i
\(383\) −189.000 109.119i −0.493473 0.284907i 0.232541 0.972587i \(-0.425296\pi\)
−0.726014 + 0.687680i \(0.758629\pi\)
\(384\) 0 0
\(385\) −202.500 506.625i −0.525974 1.31591i
\(386\) 555.000 1.43782
\(387\) 0 0
\(388\) −802.500 + 463.324i −2.06830 + 1.19413i
\(389\) 153.000 + 265.004i 0.393316 + 0.681244i 0.992885 0.119080i \(-0.0379944\pi\)
−0.599568 + 0.800323i \(0.704661\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −106.500 + 101.325i −0.271684 + 0.258482i
\(393\) 0 0
\(394\) −495.000 + 857.365i −1.25635 + 2.17605i
\(395\) −193.500 + 111.717i −0.489873 + 0.282829i
\(396\) 0 0
\(397\) −222.000 128.172i −0.559194 0.322851i 0.193628 0.981075i \(-0.437975\pi\)
−0.752822 + 0.658224i \(0.771308\pi\)
\(398\) 20.7846i 0.0522226i
\(399\) 0 0
\(400\) 22.0000 0.0550000
\(401\) 66.0000 114.315i 0.164589 0.285076i −0.771921 0.635719i \(-0.780704\pi\)
0.936509 + 0.350643i \(0.114037\pi\)
\(402\) 0 0
\(403\) −84.0000 145.492i −0.208437 0.361023i
\(404\) −630.000 363.731i −1.55941 0.900323i
\(405\) 0 0
\(406\) 27.0000 187.061i 0.0665025 0.460743i
\(407\) −150.000 −0.368550
\(408\) 0 0
\(409\) −313.500 + 180.999i −0.766504 + 0.442541i −0.831626 0.555336i \(-0.812590\pi\)
0.0651223 + 0.997877i \(0.479256\pi\)
\(410\) 81.0000 + 140.296i 0.197561 + 0.342186i
\(411\) 0 0
\(412\) 346.410i 0.840801i
\(413\) −67.5000 + 85.7365i −0.163438 + 0.207594i
\(414\) 0 0
\(415\) −310.500 + 537.802i −0.748193 + 1.29591i
\(416\) 540.000 311.769i 1.29808 0.749445i
\(417\) 0 0
\(418\) −405.000 233.827i −0.968900 0.559394i
\(419\) 644.323i 1.53776i 0.639391 + 0.768882i \(0.279187\pi\)
−0.639391 + 0.768882i \(0.720813\pi\)
\(420\) 0 0
\(421\) 752.000 1.78622 0.893112 0.449835i \(-0.148517\pi\)
0.893112 + 0.449835i \(0.148517\pi\)
\(422\) −372.000 + 644.323i −0.881517 + 1.52683i
\(423\) 0 0
\(424\) −49.5000 85.7365i −0.116745 0.202209i
\(425\) −18.0000 10.3923i −0.0423529 0.0244525i
\(426\) 0 0
\(427\) 624.000 + 90.0666i 1.46136 + 0.210929i
\(428\) −465.000 −1.08645
\(429\) 0 0
\(430\) 999.000 576.773i 2.32326 1.34133i
\(431\) 81.0000 + 140.296i 0.187935 + 0.325513i 0.944562 0.328334i \(-0.106487\pi\)
−0.756627 + 0.653847i \(0.773154\pi\)
\(432\) 0 0
\(433\) 339.482i 0.784023i 0.919960 + 0.392011i \(0.128221\pi\)
−0.919960 + 0.392011i \(0.871779\pi\)
\(434\) 94.5000 + 236.425i 0.217742 + 0.544758i
\(435\) 0 0
\(436\) 20.0000 34.6410i 0.0458716 0.0794519i
\(437\) 0 0
\(438\) 0 0
\(439\) 337.500 + 194.856i 0.768793 + 0.443863i 0.832444 0.554110i \(-0.186941\pi\)
−0.0636511 + 0.997972i \(0.520274\pi\)
\(440\) 233.827i 0.531425i
\(441\) 0 0
\(442\) −432.000 −0.977376
\(443\) −148.500 + 257.210i −0.335214 + 0.580608i −0.983526 0.180767i \(-0.942142\pi\)
0.648312 + 0.761375i \(0.275475\pi\)
\(444\) 0 0
\(445\) −189.000 327.358i −0.424719 0.735635i
\(446\) 499.500 + 288.386i 1.11996 + 0.646606i
\(447\) 0 0
\(448\) −591.500 + 236.425i −1.32031 + 0.527734i
\(449\) 492.000 1.09577 0.547884 0.836554i \(-0.315433\pi\)
0.547884 + 0.836554i \(0.315433\pi\)
\(450\) 0 0
\(451\) 135.000 77.9423i 0.299335 0.172821i
\(452\) 105.000 + 181.865i 0.232301 + 0.402357i
\(453\) 0 0
\(454\) 265.004i 0.583709i
\(455\) 72.0000 498.831i 0.158242 1.09633i
\(456\) 0 0
\(457\) 221.500 383.649i 0.484683 0.839495i −0.515162 0.857093i \(-0.672268\pi\)
0.999845 + 0.0175975i \(0.00560174\pi\)
\(458\) 855.000 493.634i 1.86681 1.07780i
\(459\) 0 0
\(460\) 0 0
\(461\) 415.692i 0.901718i 0.892595 + 0.450859i \(0.148882\pi\)
−0.892595 + 0.450859i \(0.851118\pi\)
\(462\) 0 0
\(463\) −82.0000 −0.177106 −0.0885529 0.996071i \(-0.528224\pi\)
−0.0885529 + 0.996071i \(0.528224\pi\)
\(464\) 49.5000 85.7365i 0.106681 0.184777i
\(465\) 0 0
\(466\) −405.000 701.481i −0.869099 1.50532i
\(467\) −234.000 135.100i −0.501071 0.289293i 0.228085 0.973641i \(-0.426754\pi\)
−0.729156 + 0.684348i \(0.760087\pi\)
\(468\) 0 0
\(469\) 418.000 + 329.090i 0.891258 + 0.701684i
\(470\) 0 0
\(471\) 0 0
\(472\) 40.5000 23.3827i 0.0858051 0.0495396i
\(473\) −555.000 961.288i −1.17336 2.03232i
\(474\) 0 0
\(475\) 20.7846i 0.0437571i
\(476\) 360.000 + 51.9615i 0.756303 + 0.109163i
\(477\) 0 0
\(478\) 342.000 592.361i 0.715481 1.23925i
\(479\) −297.000 + 171.473i −0.620042 + 0.357981i −0.776885 0.629642i \(-0.783202\pi\)
0.156844 + 0.987623i \(0.449868\pi\)
\(480\) 0 0
\(481\) −120.000 69.2820i −0.249480 0.144037i
\(482\) 1335.41i 2.77056i
\(483\) 0 0
\(484\) 520.000 1.07438
\(485\) −481.500 + 833.982i −0.992784 + 1.71955i
\(486\) 0 0
\(487\) 158.500 + 274.530i 0.325462 + 0.563717i 0.981606 0.190919i \(-0.0611468\pi\)
−0.656144 + 0.754636i \(0.727814\pi\)
\(488\) −234.000 135.100i −0.479508 0.276844i
\(489\) 0 0
\(490\) −216.000 + 732.657i −0.440816 + 1.49522i
\(491\) −27.0000 −0.0549898 −0.0274949 0.999622i \(-0.508753\pi\)
−0.0274949 + 0.999622i \(0.508753\pi\)
\(492\) 0 0
\(493\) −81.0000 + 46.7654i −0.164300 + 0.0948588i
\(494\) −216.000 374.123i −0.437247 0.757334i
\(495\) 0 0
\(496\) 133.368i 0.268887i
\(497\) −546.000 + 218.238i −1.09859 + 0.439111i
\(498\) 0 0
\(499\) 223.000 386.247i 0.446894 0.774043i −0.551288 0.834315i \(-0.685864\pi\)
0.998182 + 0.0602721i \(0.0191969\pi\)
\(500\) 517.500 298.779i 1.03500 0.597558i
\(501\) 0 0
\(502\) −13.5000 7.79423i −0.0268924 0.0155264i
\(503\) 488.438i 0.971050i −0.874223 0.485525i \(-0.838628\pi\)
0.874223 0.485525i \(-0.161372\pi\)
\(504\) 0 0
\(505\) −756.000 −1.49703
\(506\) 0 0
\(507\) 0 0
\(508\) −87.5000 151.554i −0.172244 0.298336i
\(509\) −85.5000 49.3634i −0.167976 0.0969812i 0.413655 0.910434i \(-0.364252\pi\)
−0.581631 + 0.813453i \(0.697585\pi\)
\(510\) 0 0
\(511\) −270.000 + 342.946i −0.528376 + 0.671127i
\(512\) −627.000 −1.22461
\(513\) 0 0
\(514\) −297.000 + 171.473i −0.577821 + 0.333605i
\(515\) 180.000 + 311.769i 0.349515 + 0.605377i
\(516\) 0 0
\(517\) 0 0
\(518\) 165.000 + 129.904i 0.318533 + 0.250780i
\(519\) 0 0
\(520\) −108.000 + 187.061i −0.207692 + 0.359734i
\(521\) 783.000 452.065i 1.50288 0.867688i 0.502885 0.864354i \(-0.332272\pi\)
0.999994 0.00333410i \(-0.00106128\pi\)
\(522\) 0 0
\(523\) −606.000 349.874i −1.15870 0.668976i −0.207708 0.978191i \(-0.566600\pi\)
−0.950992 + 0.309215i \(0.899934\pi\)
\(524\) 857.365i 1.63619i
\(525\) 0 0
\(526\) 558.000 1.06084
\(527\) 63.0000 109.119i 0.119545 0.207057i
\(528\) 0 0
\(529\) 264.500 + 458.127i 0.500000 + 0.866025i
\(530\) −445.500 257.210i −0.840566 0.485301i
\(531\) 0 0
\(532\) 135.000 + 337.750i 0.253759 + 0.634868i
\(533\) 144.000 0.270169
\(534\) 0 0
\(535\) −418.500 + 241.621i −0.782243 + 0.451628i
\(536\) −114.000 197.454i −0.212687 0.368384i
\(537\) 0 0
\(538\) 1013.25i 1.88336i
\(539\) 705.000 + 207.846i 1.30798 + 0.385614i
\(540\) 0 0
\(541\) −37.0000 + 64.0859i −0.0683919 + 0.118458i −0.898194 0.439600i \(-0.855120\pi\)
0.829802 + 0.558058i \(0.188453\pi\)
\(542\) 238.500 137.698i 0.440037 0.254055i
\(543\) 0 0
\(544\) 405.000 + 233.827i 0.744485 + 0.429829i
\(545\) 41.5692i 0.0762738i
\(546\) 0 0
\(547\) −934.000 −1.70750 −0.853748 0.520687i \(-0.825676\pi\)
−0.853748 + 0.520687i \(0.825676\pi\)
\(548\) −240.000 + 415.692i −0.437956 + 0.758562i
\(549\) 0 0
\(550\) 45.0000 + 77.9423i 0.0818182 + 0.141713i
\(551\) −81.0000 46.7654i −0.147005 0.0848736i
\(552\) 0 0
\(553\) 43.0000 297.913i 0.0777577 0.538721i
\(554\) −1140.00 −2.05776
\(555\) 0 0
\(556\) 795.000 458.993i 1.42986 0.825528i
\(557\) 421.500 + 730.059i 0.756732 + 1.31070i 0.944508 + 0.328487i \(0.106539\pi\)
−0.187776 + 0.982212i \(0.560128\pi\)
\(558\) 0 0
\(559\) 1025.37i 1.83430i
\(560\) −247.500 + 314.367i −0.441964 + 0.561370i
\(561\) 0 0
\(562\) −450.000 + 779.423i −0.800712 + 1.38687i
\(563\) −823.500 + 475.448i −1.46270 + 0.844490i −0.999135 0.0415731i \(-0.986763\pi\)
−0.463564 + 0.886063i \(0.653430\pi\)
\(564\) 0 0
\(565\) 189.000 + 109.119i 0.334513 + 0.193131i
\(566\) 613.146i 1.08330i
\(567\) 0 0
\(568\) 252.000 0.443662
\(569\) 111.000 192.258i 0.195079 0.337887i −0.751847 0.659337i \(-0.770837\pi\)
0.946926 + 0.321450i \(0.104170\pi\)
\(570\) 0 0
\(571\) −220.000 381.051i −0.385289 0.667340i 0.606520 0.795068i \(-0.292565\pi\)
−0.991809 + 0.127728i \(0.959232\pi\)
\(572\) 900.000 + 519.615i 1.57343 + 0.908418i
\(573\) 0 0
\(574\) −216.000 31.1769i −0.376307 0.0543152i
\(575\) 0 0
\(576\) 0 0
\(577\) 568.500 328.224i 0.985269 0.568845i 0.0814120 0.996681i \(-0.474057\pi\)
0.903857 + 0.427835i \(0.140724\pi\)
\(578\) 271.500 + 470.252i 0.469723 + 0.813584i
\(579\) 0 0
\(580\) 233.827i 0.403150i
\(581\) −310.500 776.825i −0.534423 1.33705i
\(582\) 0 0
\(583\) −247.500 + 428.683i −0.424528 + 0.735305i
\(584\) 162.000 93.5307i 0.277397 0.160155i
\(585\) 0 0
\(586\) 1417.50 + 818.394i 2.41894 + 1.39658i
\(587\) 1054.82i 1.79697i −0.439008 0.898483i \(-0.644670\pi\)
0.439008 0.898483i \(-0.355330\pi\)
\(588\) 0 0
\(589\) 126.000 0.213922
\(590\) 121.500 210.444i 0.205932 0.356685i
\(591\) 0 0
\(592\) 55.0000 + 95.2628i 0.0929054 + 0.160917i
\(593\) −612.000 353.338i −1.03204 0.595849i −0.114472 0.993426i \(-0.536518\pi\)
−0.917569 + 0.397578i \(0.869851\pi\)
\(594\) 0 0
\(595\) 351.000 140.296i 0.589916 0.235792i
\(596\) 930.000 1.56040
\(597\) 0 0
\(598\) 0 0
\(599\) 258.000 + 446.869i 0.430718 + 0.746025i 0.996935 0.0782307i \(-0.0249271\pi\)
−0.566217 + 0.824256i \(0.691594\pi\)
\(600\) 0 0
\(601\) 247.683i 0.412119i 0.978540 + 0.206059i \(0.0660640\pi\)
−0.978540 + 0.206059i \(0.933936\pi\)
\(602\) −222.000 + 1538.06i −0.368771 + 2.55492i
\(603\) 0 0
\(604\) −197.500 + 342.080i −0.326987 + 0.566358i
\(605\) 468.000 270.200i 0.773554 0.446611i
\(606\) 0 0
\(607\) −562.500 324.760i −0.926689 0.535024i −0.0409259 0.999162i \(-0.513031\pi\)
−0.885763 + 0.464138i \(0.846364\pi\)
\(608\) 467.654i 0.769167i
\(609\) 0 0
\(610\) −1404.00 −2.30164
\(611\) 0 0
\(612\) 0 0
\(613\) 446.000 + 772.495i 0.727569 + 1.26019i 0.957908 + 0.287076i \(0.0926834\pi\)
−0.230338 + 0.973111i \(0.573983\pi\)
\(614\) −450.000 259.808i −0.732899 0.423139i
\(615\) 0 0
\(616\) −247.500 194.856i −0.401786 0.316324i
\(617\) 1224.00 1.98379 0.991896 0.127050i \(-0.0405510\pi\)
0.991896 + 0.127050i \(0.0405510\pi\)
\(618\) 0 0
\(619\) −348.000 + 200.918i −0.562197 + 0.324585i −0.754027 0.656844i \(-0.771891\pi\)
0.191830 + 0.981428i \(0.438558\pi\)
\(620\) −157.500 272.798i −0.254032 0.439997i
\(621\) 0 0
\(622\) 530.008i 0.852102i
\(623\) 504.000 + 72.7461i 0.808989 + 0.116767i
\(624\) 0 0
\(625\) 335.500 581.103i 0.536800 0.929765i
\(626\) −553.500 + 319.563i −0.884185 + 0.510485i
\(627\) 0 0
\(628\) 90.0000 + 51.9615i 0.143312 + 0.0827413i
\(629\) 103.923i 0.165219i
\(630\) 0 0
\(631\) 1115.00 1.76704 0.883518 0.468397i \(-0.155168\pi\)
0.883518 + 0.468397i \(0.155168\pi\)
\(632\) −64.5000 + 111.717i −0.102057 + 0.176768i
\(633\) 0 0
\(634\) −175.500 303.975i −0.276814 0.479456i
\(635\) −157.500 90.9327i −0.248031 0.143201i
\(636\) 0 0
\(637\) 468.000 + 491.902i 0.734694 + 0.772217i
\(638\) 405.000 0.634796
\(639\) 0 0
\(640\) 418.500 241.621i 0.653906 0.377533i
\(641\) −192.000 332.554i −0.299532 0.518805i 0.676497 0.736445i \(-0.263497\pi\)
−0.976029 + 0.217641i \(0.930164\pi\)
\(642\) 0 0
\(643\) 6.92820i 0.0107748i 0.999985 + 0.00538741i \(0.00171487\pi\)
−0.999985 + 0.00538741i \(0.998285\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 162.000 280.592i 0.250774 0.434353i
\(647\) −774.000 + 446.869i −1.19629 + 0.690679i −0.959726 0.280937i \(-0.909355\pi\)
−0.236564 + 0.971616i \(0.576021\pi\)
\(648\) 0 0
\(649\) −202.500 116.913i −0.312018 0.180144i
\(650\) 83.1384i 0.127905i
\(651\) 0 0
\(652\) −1040.00 −1.59509
\(653\) 37.5000 64.9519i 0.0574273 0.0994669i −0.835883 0.548908i \(-0.815044\pi\)
0.893310 + 0.449441i \(0.148377\pi\)
\(654\) 0 0
\(655\) 445.500 + 771.629i 0.680153 + 1.17806i
\(656\) −99.0000 57.1577i −0.150915 0.0871306i
\(657\) 0 0
\(658\) 0 0
\(659\) −642.000 −0.974203 −0.487102 0.873345i \(-0.661946\pi\)
−0.487102 + 0.873345i \(0.661946\pi\)
\(660\) 0 0
\(661\) −243.000 + 140.296i −0.367625 + 0.212248i −0.672420 0.740170i \(-0.734745\pi\)
0.304795 + 0.952418i \(0.401412\pi\)
\(662\) 60.0000 + 103.923i 0.0906344 + 0.156983i
\(663\) 0 0
\(664\) 358.535i 0.539962i
\(665\) 297.000 + 233.827i 0.446617 + 0.351619i
\(666\) 0 0
\(667\) 0 0
\(668\) −1080.00 + 623.538i −1.61677 + 0.933441i
\(669\) 0 0
\(670\) −1026.00 592.361i −1.53134 0.884121i
\(671\) 1351.00i 2.01341i
\(672\) 0 0
\(673\) 13.0000 0.0193165 0.00965825 0.999953i \(-0.496926\pi\)
0.00965825 + 0.999953i \(0.496926\pi\)
\(674\) 136.500 236.425i 0.202522 0.350779i
\(675\) 0 0
\(676\) 57.5000 + 99.5929i 0.0850592 + 0.147327i
\(677\) 1093.50 + 631.333i 1.61521 + 0.932544i 0.988135 + 0.153589i \(0.0490832\pi\)
0.627079 + 0.778955i \(0.284250\pi\)
\(678\) 0 0
\(679\) −481.500 1204.64i −0.709131 1.77414i
\(680\) −162.000 −0.238235
\(681\) 0 0
\(682\) −472.500 + 272.798i −0.692815 + 0.399997i
\(683\) −484.500 839.179i −0.709370 1.22867i −0.965091 0.261915i \(-0.915646\pi\)
0.255721 0.966751i \(-0.417687\pi\)
\(684\) 0 0
\(685\) 498.831i 0.728220i
\(686\) −595.500 839.179i −0.868076 1.22329i
\(687\) 0 0
\(688\) −407.000 + 704.945i −0.591570 + 1.02463i
\(689\) −396.000 + 228.631i −0.574746 + 0.331830i
\(690\) 0 0
\(691\) −87.0000 50.2295i −0.125904 0.0726910i 0.435725 0.900080i \(-0.356492\pi\)
−0.561629 + 0.827389i \(0.689825\pi\)
\(692\) 1143.15i 1.65196i
\(693\) 0 0
\(694\) 630.000 0.907781
\(695\) 477.000 826.188i 0.686331 1.18876i
\(696\) 0 0
\(697\) 54.0000 + 93.5307i 0.0774749 + 0.134190i
\(698\) 792.000 + 457.261i 1.13467 + 0.655102i
\(699\) 0 0
\(700\) 10.0000 69.2820i 0.0142857 0.0989743i
\(701\) −597.000 −0.851641 −0.425820 0.904808i \(-0.640014\pi\)
−0.425820 + 0.904808i \(0.640014\pi\)
\(702\) 0 0
\(703\) 90.0000 51.9615i 0.128023 0.0739140i
\(704\) −682.500 1182.12i −0.969460 1.67915i
\(705\) 0 0
\(706\) 1184.72i 1.67808i
\(707\) 630.000 800.207i 0.891089 1.13184i
\(708\) 0 0
\(709\) 415.000 718.801i 0.585331 1.01382i −0.409503 0.912309i \(-0.634298\pi\)
0.994834 0.101515i \(-0.0323689\pi\)
\(710\) 1134.00 654.715i 1.59718 0.922134i
\(711\) 0 0
\(712\) −189.000 109.119i −0.265449 0.153257i
\(713\) 0 0
\(714\) 0 0
\(715\) 1080.00 1.51049
\(716\) 225.000 389.711i 0.314246 0.544290i
\(717\) 0 0
\(718\) −738.000 1278.25i −1.02786 1.78030i
\(719\) −297.000 171.473i −0.413074 0.238488i 0.279036 0.960281i \(-0.409985\pi\)
−0.692110 + 0.721792i \(0.743319\pi\)
\(720\) 0 0
\(721\) −480.000 69.2820i −0.665742 0.0960916i
\(722\) −759.000 −1.05125
\(723\) 0 0
\(724\) 45.0000 25.9808i 0.0621547 0.0358850i
\(725\) 9.00000 + 15.5885i 0.0124138 + 0.0215013i
\(726\) 0 0
\(727\) 50.2295i 0.0690914i −0.999403 0.0345457i \(-0.989002\pi\)
0.999403 0.0345457i \(-0.0109984\pi\)
\(728\) −108.000 270.200i −0.148352 0.371154i
\(729\) 0 0
\(730\) 486.000 841.777i 0.665753 1.15312i
\(731\) 666.000 384.515i 0.911081 0.526013i
\(732\) 0 0
\(733\) −159.000 91.7987i −0.216917 0.125237i 0.387605 0.921826i \(-0.373302\pi\)
−0.604522 + 0.796589i \(0.706636\pi\)
\(734\) 982.073i 1.33797i
\(735\) 0 0
\(736\) 0 0
\(737\) −570.000 + 987.269i −0.773406 + 1.33958i
\(738\) 0 0
\(739\) 167.000 + 289.252i 0.225981 + 0.391411i 0.956613 0.291361i \(-0.0941079\pi\)
−0.730632 + 0.682771i \(0.760775\pi\)
\(740\) −225.000 129.904i −0.304054 0.175546i
\(741\) 0 0
\(742\) 643.500 257.210i 0.867251 0.346644i
\(743\) −84.0000 −0.113055 −0.0565276 0.998401i \(-0.518003\pi\)
−0.0565276 + 0.998401i \(0.518003\pi\)
\(744\) 0 0
\(745\) 837.000 483.242i 1.12349 0.648647i
\(746\) 255.000 + 441.673i 0.341823 + 0.592055i
\(747\) 0 0
\(748\) 779.423i 1.04201i
\(749\) 93.0000 644.323i 0.124166 0.860244i
\(750\) 0 0
\(751\) 179.500 310.903i 0.239015 0.413986i −0.721417 0.692501i \(-0.756509\pi\)
0.960432 + 0.278515i \(0.0898423\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 324.000 + 187.061i 0.429708 + 0.248092i
\(755\) 410.496i 0.543703i
\(756\) 0 0
\(757\) −80.0000 −0.105680 −0.0528402 0.998603i \(-0.516827\pi\)
−0.0528402 + 0.998603i \(0.516827\pi\)
\(758\) 123.000 213.042i 0.162269 0.281058i
\(759\) 0 0
\(760\) −81.0000 140.296i −0.106579 0.184600i
\(761\) 702.000 + 405.300i 0.922470 + 0.532589i 0.884422 0.466687i \(-0.154553\pi\)
0.0380481 + 0.999276i \(0.487886\pi\)
\(762\) 0 0
\(763\) 44.0000 + 34.6410i 0.0576671 + 0.0454011i
\(764\) 1560.00 2.04188
\(765\) 0 0
\(766\) −567.000 + 327.358i −0.740209 + 0.427360i
\(767\) −108.000 187.061i −0.140808 0.243887i
\(768\) 0 0
\(769\) 774.227i 1.00680i 0.864054 + 0.503398i \(0.167917\pi\)
−0.864054 + 0.503398i \(0.832083\pi\)
\(770\) −1620.00 233.827i −2.10390 0.303671i
\(771\) 0 0
\(772\) 462.500 801.073i 0.599093 1.03766i
\(773\) 630.000 363.731i 0.815006 0.470544i −0.0336850 0.999433i \(-0.510724\pi\)
0.848691 + 0.528888i \(0.177391\pi\)
\(774\) 0 0
\(775\) −21.0000 12.1244i −0.0270968 0.0156443i
\(776\) 555.988i 0.716480i
\(777\) 0 0
\(778\) 918.000 1.17995
\(779\) −54.0000 + 93.5307i −0.0693196 + 0.120065i
\(780\) 0 0
\(781\) −630.000 1091.19i −0.806658 1.39717i
\(782\) 0 0
\(783\) 0 0
\(784\) −126.500 523.945i −0.161352 0.668298i
\(785\) 108.000 0.137580
\(786\) 0 0
\(787\) −1236.00 + 713.605i −1.57052 + 0.906741i −0.574416 + 0.818563i \(0.694771\pi\)
−0.996105 + 0.0881773i \(0.971896\pi\)
\(788\) 825.000 + 1428.94i 1.04695 + 1.81338i
\(789\) 0 0
\(790\) 670.304i 0.848486i
\(791\) −273.000 + 109.119i −0.345133 + 0.137951i
\(792\) 0 0
\(793\) −624.000 + 1080.80i −0.786885 + 1.36293i
\(794\) −666.000 + 384.515i −0.838791 + 0.484276i
\(795\) 0 0
\(796\) −30.0000 17.3205i −0.0376884 0.0217594i
\(797\) 607.950i 0.762798i 0.924411 + 0.381399i \(0.124558\pi\)
−0.924411 + 0.381399i \(0.875442\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 45.0000 77.9423i 0.0562500 0.0974279i
\(801\) 0 0
\(802\) −198.000 342.946i −0.246883 0.427614i
\(803\) −810.000 467.654i −1.00872 0.582383i
\(804\) 0 0
\(805\) 0 0
\(806\) −504.000 −0.625310
\(807\) 0 0
\(808\) −378.000 + 218.238i −0.467822 + 0.270097i
\(809\) −84.0000 145.492i −0.103832 0.179842i 0.809428 0.587218i \(-0.199777\pi\)
−0.913260 + 0.407376i \(0.866444\pi\)
\(810\) 0 0
\(811\) 353.338i 0.435682i −0.975984 0.217841i \(-0.930099\pi\)
0.975984 0.217841i \(-0.0699015\pi\)
\(812\) −247.500 194.856i −0.304803 0.239970i
\(813\) 0 0
\(814\) −225.000 + 389.711i −0.276413 + 0.478761i
\(815\) −936.000 + 540.400i −1.14847 + 0.663067i
\(816\) 0 0
\(817\) 666.000 + 384.515i 0.815177 + 0.470643i
\(818\) 1086.00i 1.32762i
\(819\) 0 0
\(820\) 270.000 0.329268
\(821\) 142.500 246.817i 0.173569 0.300630i −0.766096 0.642726i \(-0.777803\pi\)
0.939665 + 0.342096i \(0.111137\pi\)
\(822\) 0 0
\(823\) 137.000 + 237.291i 0.166464 + 0.288324i 0.937174 0.348862i \(-0.113432\pi\)
−0.770710 + 0.637186i \(0.780098\pi\)
\(824\) 180.000 + 103.923i 0.218447 + 0.126120i
\(825\) 0 0
\(826\) 121.500 + 303.975i 0.147094 + 0.368008i
\(827\) −429.000 −0.518742 −0.259371 0.965778i \(-0.583515\pi\)
−0.259371 + 0.965778i \(0.583515\pi\)
\(828\) 0 0
\(829\) −819.000 + 472.850i −0.987937 + 0.570386i −0.904657 0.426140i \(-0.859873\pi\)
−0.0832802 + 0.996526i \(0.526540\pi\)
\(830\) 931.500 + 1613.41i 1.12229 + 1.94386i
\(831\) 0 0
\(832\) 1260.93i 1.51554i
\(833\) −144.000 + 488.438i −0.172869 + 0.586361i
\(834\) 0 0
\(835\) −648.000 + 1122.37i −0.776048 + 1.34415i
\(836\) −675.000 + 389.711i −0.807416 + 0.466162i
\(837\) 0 0
\(838\) 1674.00 + 966.484i 1.99761 + 1.15332i
\(839\) 259.808i 0.309663i 0.987941 + 0.154832i \(0.0494835\pi\)
−0.987941 + 0.154832i \(0.950516\pi\)
\(840\) 0 0
\(841\) −760.000 −0.903686
\(842\) 1128.00 1953.75i 1.33967 2.32037i
\(843\) 0 0
\(844\) 620.000 + 1073.87i 0.734597 + 1.27236i
\(845\) 103.500 + 59.7558i 0.122485 + 0.0707169i
\(846\) 0 0
\(847\) −104.000 + 720.533i −0.122786 + 0.850688i
\(848\) 363.000 0.428066
\(849\) 0 0
\(850\) −54.0000 + 31.1769i −0.0635294 + 0.0366787i
\(851\) 0 0
\(852\) 0 0
\(853\) 997.661i 1.16959i −0.811181 0.584796i \(-0.801175\pi\)
0.811181 0.584796i \(-0.198825\pi\)
\(854\) 1170.00 1486.10i 1.37002 1.74016i
\(855\) 0 0
\(856\) −139.500 + 241.621i −0.162967 + 0.282268i
\(857\) −378.000 + 218.238i −0.441074 + 0.254654i −0.704053 0.710148i \(-0.748628\pi\)
0.262979 + 0.964801i \(0.415295\pi\)
\(858\) 0 0
\(859\) −393.000 226.899i −0.457509 0.264143i 0.253487 0.967339i \(-0.418422\pi\)
−0.710996 + 0.703196i \(0.751756\pi\)
\(860\) 1922.58i 2.23555i
\(861\) 0 0
\(862\) 486.000 0.563805
\(863\) −195.000 + 337.750i −0.225956 + 0.391367i −0.956606 0.291385i \(-0.905884\pi\)
0.730650 + 0.682752i \(0.239217\pi\)
\(864\) 0 0
\(865\) −594.000 1028.84i −0.686705 1.18941i
\(866\) 882.000 + 509.223i 1.01848 + 0.588017i
\(867\) 0 0
\(868\) 420.000 + 60.6218i 0.483871 + 0.0698408i
\(869\) 645.000 0.742232
\(870\) 0 0
\(871\) −912.000 + 526.543i −1.04707 + 0.604527i
\(872\) −12.0000 20.7846i −0.0137615 0.0238356i
\(873\) 0 0
\(874\) 0 0
\(875\) 310.500 + 776.825i 0.354857 + 0.887800i
\(876\) 0 0
\(877\) 272.000 471.118i 0.310148 0.537192i −0.668246 0.743940i \(-0.732955\pi\)
0.978394 + 0.206748i \(0.0662880\pi\)
\(878\) 1012.50 584.567i 1.15319 0.665794i
\(879\) 0 0
\(880\) −742.500 428.683i −0.843750 0.487139i
\(881\) 187.061i 0.212329i −0.994349 0.106164i \(-0.966143\pi\)
0.994349 0.106164i \(-0.0338569\pi\)
\(882\) 0 0
\(883\) 322.000 0.364666 0.182333 0.983237i \(-0.441635\pi\)
0.182333 + 0.983237i \(0.441635\pi\)
\(884\) −360.000 + 623.538i −0.407240 + 0.705360i
\(885\) 0 0
\(886\) 445.500 + 771.629i 0.502822 + 0.870913i
\(887\) −612.000 353.338i −0.689966 0.398352i 0.113633 0.993523i \(-0.463751\pi\)
−0.803599 + 0.595171i \(0.797084\pi\)
\(888\) 0 0
\(889\) 227.500 90.9327i 0.255906 0.102286i
\(890\) −1134.00 −1.27416
\(891\) 0 0
\(892\) 832.500 480.644i 0.933296 0.538839i
\(893\) 0 0
\(894\) 0 0
\(895\) 467.654i 0.522518i
\(896\) −93.0000 + 644.323i −0.103795 + 0.719110i
\(897\) 0 0
\(898\) 738.000 1278.25i 0.821826 1.42344i
\(899\) −94.5000 + 54.5596i −0.105117 + 0.0606892i
\(900\) 0 0
\(901\) −297.000 171.473i −0.329634 0.190314i
\(902\) 467.654i 0.518463i
\(903\) 0 0
\(904\) 126.000 0.139381
\(905\) 27.0000 46.7654i 0.0298343 0.0516744i
\(906\) 0 0
\(907\) 550.000 + 952.628i 0.606395 + 1.05031i 0.991829 + 0.127571i \(0.0407182\pi\)
−0.385435 + 0.922735i \(0.625948\pi\)
\(908\) −382.500 220.836i −0.421256 0.243212i
\(909\) 0 0
\(910\) −1188.00 935.307i −1.30549 1.02781i
\(911\) −900.000 −0.987925 −0.493963 0.869483i \(-0.664452\pi\)
−0.493963 + 0.869483i \(0.664452\pi\)
\(912\) 0 0
\(913\) 1552.50 896.336i 1.70044 0.981748i
\(914\) −664.500 1150.95i −0.727024 1.25924i
\(915\) 0 0
\(916\) 1645.45i 1.79634i
\(917\) −1188.00 171.473i −1.29553 0.186993i
\(918\) 0 0
\(919\) 859.000 1487.83i 0.934712 1.61897i 0.159564 0.987188i \(-0.448991\pi\)
0.775147 0.631781i \(-0.217676\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1080.00 + 623.538i 1.17137 + 0.676289i
\(923\) 1163.94i 1.26104i
\(924\) 0 0
\(925\) −20.0000 −0.0216216
\(926\) −123.000 + 213.042i −0.132829 + 0.230067i
\(927\) 0 0
\(928\) −202.500 350.740i −0.218211 0.377953i
\(929\) 1287.00 + 743.050i 1.38536 + 0.799838i 0.992788 0.119883i \(-0.0382519\pi\)
0.392573 + 0.919721i \(0.371585\pi\)
\(930\) 0 0
\(931\) −495.000 + 119.512i −0.531686 + 0.128369i
\(932\) −1350.00 −1.44850
\(933\) 0 0
\(934\) −702.000 + 405.300i −0.751606 + 0.433940i
\(935\) 405.000 + 701.481i 0.433155 + 0.750247i
\(936\) 0 0
\(937\) 957.824i 1.02222i 0.859514 + 0.511112i \(0.170766\pi\)
−0.859514 + 0.511112i \(0.829234\pi\)
\(938\) 1482.00 592.361i 1.57996 0.631515i
\(939\) 0 0
\(940\) 0 0
\(941\) −310.500 + 179.267i −0.329968 + 0.190507i −0.655827 0.754911i \(-0.727680\pi\)
0.325859 + 0.945418i \(0.394347\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 171.473i 0.181645i
\(945\) 0 0
\(946\) −3330.00 −3.52008
\(947\) 81.0000 140.296i 0.0855333 0.148148i −0.820085 0.572242i \(-0.806074\pi\)
0.905618 + 0.424094i \(0.139407\pi\)
\(948\) 0 0
\(949\) −432.000 748.246i −0.455216 0.788457i
\(950\) −54.0000 31.1769i −0.0568421 0.0328178i
\(951\) 0 0
\(952\) 135.000 171.473i 0.141807 0.180119i
\(953\) 954.000 1.00105 0.500525 0.865722i \(-0.333140\pi\)
0.500525 + 0.865722i \(0.333140\pi\)
\(954\) 0 0
\(955\) 1404.00 810.600i 1.47016 0.848796i
\(956\) −570.000 987.269i −0.596234 1.03271i
\(957\) 0 0
\(958\) 1028.84i 1.07394i
\(959\) −528.000 415.692i −0.550574 0.433464i
\(960\) 0 0
\(961\) −407.000 + 704.945i −0.423517 + 0.733553i
\(962\) −360.000 + 207.846i −0.374220 + 0.216056i
\(963\) 0 0
\(964\) −1927.50 1112.84i −1.99948 1.15440i
\(965\) 961.288i 0.996154i
\(966\) 0 0
\(967\) −751.000 −0.776629 −0.388314 0.921527i \(-0.626943\pi\)
−0.388314 + 0.921527i \(0.626943\pi\)
\(968\) 156.000 270.200i 0.161157 0.279132i
\(969\) 0 0
\(970\) 1444.50 + 2501.95i 1.48918 + 2.57933i
\(971\) 247.500 + 142.894i 0.254892 + 0.147162i 0.622002 0.783016i \(-0.286320\pi\)
−0.367110 + 0.930177i \(0.619653\pi\)
\(972\) 0 0
\(973\) 477.000 + 1193.38i 0.490236 + 1.22650i
\(974\) 951.000 0.976386
\(975\) 0 0
\(976\) 858.000 495.367i 0.879098 0.507548i
\(977\) −9.00000 15.5885i −0.00921187 0.0159554i 0.861383 0.507957i \(-0.169599\pi\)
−0.870595 + 0.492001i \(0.836266\pi\)
\(978\) 0 0
\(979\) 1091.19i 1.11460i
\(980\) 877.500 + 922.317i 0.895408 + 0.941140i
\(981\) 0 0
\(982\) −40.5000 + 70.1481i −0.0412424 + 0.0714339i
\(983\) 855.000 493.634i 0.869786 0.502171i 0.00250913 0.999997i \(-0.499201\pi\)
0.867277 + 0.497825i \(0.165868\pi\)
\(984\) 0 0
\(985\) 1485.00 + 857.365i 1.50761 + 0.870421i
\(986\) 280.592i 0.284576i
\(987\) 0 0
\(988\) −720.000 −0.728745
\(989\) 0 0
\(990\) 0 0
\(991\) −351.500 608.816i −0.354692 0.614345i 0.632373 0.774664i \(-0.282081\pi\)
−0.987065 + 0.160319i \(0.948748\pi\)
\(992\) 472.500 + 272.798i 0.476310 + 0.274998i
\(993\) 0 0
\(994\) −252.000 + 1745.91i −0.253521 + 1.75645i
\(995\) −36.0000 −0.0361809
\(996\) 0 0
\(997\) 186.000 107.387i 0.186560 0.107710i −0.403811 0.914842i \(-0.632315\pi\)
0.590371 + 0.807132i \(0.298981\pi\)
\(998\) −669.000 1158.74i −0.670341 1.16106i
\(999\) 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 63.3.m.d.19.1 2
3.2 odd 2 21.3.f.a.19.1 yes 2
4.3 odd 2 1008.3.cg.a.145.1 2
7.2 even 3 441.3.d.a.244.2 2
7.3 odd 6 inner 63.3.m.d.10.1 2
7.4 even 3 441.3.m.g.325.1 2
7.5 odd 6 441.3.d.a.244.1 2
7.6 odd 2 441.3.m.g.19.1 2
12.11 even 2 336.3.bh.d.145.1 2
15.2 even 4 525.3.s.e.124.1 4
15.8 even 4 525.3.s.e.124.2 4
15.14 odd 2 525.3.o.h.376.1 2
21.2 odd 6 147.3.d.c.97.1 2
21.5 even 6 147.3.d.c.97.2 2
21.11 odd 6 147.3.f.a.31.1 2
21.17 even 6 21.3.f.a.10.1 2
21.20 even 2 147.3.f.a.19.1 2
28.3 even 6 1008.3.cg.a.577.1 2
84.23 even 6 2352.3.f.a.97.2 2
84.47 odd 6 2352.3.f.a.97.1 2
84.59 odd 6 336.3.bh.d.241.1 2
105.17 odd 12 525.3.s.e.199.2 4
105.38 odd 12 525.3.s.e.199.1 4
105.59 even 6 525.3.o.h.451.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.3.f.a.10.1 2 21.17 even 6
21.3.f.a.19.1 yes 2 3.2 odd 2
63.3.m.d.10.1 2 7.3 odd 6 inner
63.3.m.d.19.1 2 1.1 even 1 trivial
147.3.d.c.97.1 2 21.2 odd 6
147.3.d.c.97.2 2 21.5 even 6
147.3.f.a.19.1 2 21.20 even 2
147.3.f.a.31.1 2 21.11 odd 6
336.3.bh.d.145.1 2 12.11 even 2
336.3.bh.d.241.1 2 84.59 odd 6
441.3.d.a.244.1 2 7.5 odd 6
441.3.d.a.244.2 2 7.2 even 3
441.3.m.g.19.1 2 7.6 odd 2
441.3.m.g.325.1 2 7.4 even 3
525.3.o.h.376.1 2 15.14 odd 2
525.3.o.h.451.1 2 105.59 even 6
525.3.s.e.124.1 4 15.2 even 4
525.3.s.e.124.2 4 15.8 even 4
525.3.s.e.199.1 4 105.38 odd 12
525.3.s.e.199.2 4 105.17 odd 12
1008.3.cg.a.145.1 2 4.3 odd 2
1008.3.cg.a.577.1 2 28.3 even 6
2352.3.f.a.97.1 2 84.47 odd 6
2352.3.f.a.97.2 2 84.23 even 6