Properties

Label 630.2.k.e.361.1
Level $630$
Weight $2$
Character 630.361
Analytic conductor $5.031$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(361,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.k (of order \(3\), 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: \(5.03057532734\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 630.361
Dual form 630.2.k.e.541.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} +5.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{19} +1.00000 q^{20} +3.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.50000 + 4.33013i) q^{26} +(2.50000 - 0.866025i) q^{28} +6.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-0.500000 + 2.59808i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(0.500000 + 0.866025i) q^{40} -3.00000 q^{41} -10.0000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(1.50000 + 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} -1.00000 q^{50} +(-2.50000 + 4.33013i) q^{52} +(1.50000 - 2.59808i) q^{53} -3.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(3.00000 + 5.19615i) q^{58} +(2.00000 + 3.46410i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} +(2.00000 - 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-2.50000 + 0.866025i) q^{70} -12.0000 q^{71} +(2.00000 - 3.46410i) q^{73} +(5.50000 - 9.52628i) q^{74} -1.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} +(5.00000 + 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-1.50000 - 2.59808i) q^{82} +12.0000 q^{83} -6.00000 q^{85} +(-5.00000 - 8.66025i) q^{86} +(-1.50000 + 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-10.0000 - 8.66025i) q^{91} -3.00000 q^{92} +(-1.50000 + 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{95} +14.0000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} - q^{5} - 4 q^{7} - 2 q^{8} + q^{10} + 3 q^{11} + 10 q^{13} + q^{14} - q^{16} + 6 q^{17} + q^{19} + 2 q^{20} + 6 q^{22} + 3 q^{23} - q^{25} + 5 q^{26} + 5 q^{28} + 12 q^{29} + 4 q^{31} + q^{32} + 12 q^{34} - q^{35} - 11 q^{37} - q^{38} + q^{40} - 6 q^{41} - 20 q^{43} + 3 q^{44} - 3 q^{46} + 3 q^{47} + 2 q^{49} - 2 q^{50} - 5 q^{52} + 3 q^{53} - 6 q^{55} + 4 q^{56} + 6 q^{58} + 4 q^{61} + 8 q^{62} + 2 q^{64} - 5 q^{65} + 4 q^{67} + 6 q^{68} - 5 q^{70} - 24 q^{71} + 4 q^{73} + 11 q^{74} - 2 q^{76} - 15 q^{77} + 10 q^{79} - q^{80} - 3 q^{82} + 24 q^{83} - 12 q^{85} - 10 q^{86} - 3 q^{88} + 6 q^{89} - 20 q^{91} - 6 q^{92} - 3 q^{94} + q^{95} + 28 q^{97} - 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0.500000 2.59808i 0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) 0 0
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) −0.500000 + 2.59808i −0.0845154 + 0.439155i
\(36\) 0 0
\(37\) −5.50000 9.52628i −0.904194 1.56611i −0.821995 0.569495i \(-0.807139\pi\)
−0.0821995 0.996616i \(-0.526194\pi\)
\(38\) −0.500000 + 0.866025i −0.0811107 + 0.140488i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 0 0
\(46\) −1.50000 + 2.59808i −0.221163 + 0.383065i
\(47\) 1.50000 + 2.59808i 0.218797 + 0.378968i 0.954441 0.298401i \(-0.0964533\pi\)
−0.735643 + 0.677369i \(0.763120\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −2.50000 + 4.33013i −0.346688 + 0.600481i
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) 0 0
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.50000 4.33013i −0.310087 0.537086i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 3.00000 + 5.19615i 0.363803 + 0.630126i
\(69\) 0 0
\(70\) −2.50000 + 0.866025i −0.298807 + 0.103510i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 2.00000 3.46410i 0.234082 0.405442i −0.724923 0.688830i \(-0.758125\pi\)
0.959006 + 0.283387i \(0.0914581\pi\)
\(74\) 5.50000 9.52628i 0.639362 1.10741i
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) −7.50000 + 2.59808i −0.854704 + 0.296078i
\(78\) 0 0
\(79\) 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 0 0
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) −10.0000 8.66025i −1.04828 0.907841i
\(92\) −3.00000 −0.312772
\(93\) 0 0
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 0 0
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0 0
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) −1.50000 2.59808i −0.143019 0.247717i
\(111\) 0 0
\(112\) −0.500000 + 2.59808i −0.0472456 + 0.245495i
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) 0 0
\(118\) 0 0
\(119\) −15.0000 + 5.19615i −1.37505 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −2.00000 + 3.46410i −0.181071 + 0.313625i
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 2.50000 4.33013i 0.219265 0.379777i
\(131\) 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i \(-0.124830\pi\)
−0.793028 + 0.609185i \(0.791497\pi\)
\(132\) 0 0
\(133\) 0.500000 2.59808i 0.0433555 0.225282i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) −3.00000 + 5.19615i −0.257248 + 0.445566i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −2.00000 1.73205i −0.169031 0.146385i
\(141\) 0 0
\(142\) −6.00000 10.3923i −0.503509 0.872103i
\(143\) 7.50000 12.9904i 0.627182 1.08631i
\(144\) 0 0
\(145\) −3.00000 5.19615i −0.249136 0.431517i
\(146\) 4.00000 0.331042
\(147\) 0 0
\(148\) 11.0000 0.904194
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) −7.00000 + 12.1244i −0.569652 + 0.986666i 0.426948 + 0.904276i \(0.359589\pi\)
−0.996600 + 0.0823900i \(0.973745\pi\)
\(152\) −0.500000 0.866025i −0.0405554 0.0702439i
\(153\) 0 0
\(154\) −6.00000 5.19615i −0.483494 0.418718i
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −2.50000 + 4.33013i −0.199522 + 0.345582i −0.948373 0.317156i \(-0.897272\pi\)
0.748852 + 0.662738i \(0.230606\pi\)
\(158\) −5.00000 + 8.66025i −0.397779 + 0.688973i
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) 1.50000 7.79423i 0.118217 0.614271i
\(162\) 0 0
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) 1.50000 2.59808i 0.117130 0.202876i
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) −9.00000 −0.696441 −0.348220 0.937413i \(-0.613214\pi\)
−0.348220 + 0.937413i \(0.613214\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) −3.00000 5.19615i −0.230089 0.398527i
\(171\) 0 0
\(172\) 5.00000 8.66025i 0.381246 0.660338i
\(173\) 1.50000 + 2.59808i 0.114043 + 0.197528i 0.917397 0.397974i \(-0.130287\pi\)
−0.803354 + 0.595502i \(0.796953\pi\)
\(174\) 0 0
\(175\) 2.50000 0.866025i 0.188982 0.0654654i
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −1.50000 + 2.59808i −0.112115 + 0.194189i −0.916623 0.399753i \(-0.869096\pi\)
0.804508 + 0.593942i \(0.202429\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 2.50000 12.9904i 0.185312 0.962911i
\(183\) 0 0
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) −5.50000 + 9.52628i −0.404368 + 0.700386i
\(186\) 0 0
\(187\) −9.00000 15.5885i −0.658145 1.13994i
\(188\) −3.00000 −0.218797
\(189\) 0 0
\(190\) 1.00000 0.0725476
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i \(-0.787349\pi\)
0.928986 + 0.370116i \(0.120682\pi\)
\(194\) 7.00000 + 12.1244i 0.502571 + 0.870478i
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 0 0
\(202\) −12.0000 −0.844317
\(203\) −12.0000 10.3923i −0.842235 0.729397i
\(204\) 0 0
\(205\) 1.50000 + 2.59808i 0.104765 + 0.181458i
\(206\) −2.00000 + 3.46410i −0.139347 + 0.241355i
\(207\) 0 0
\(208\) −2.50000 4.33013i −0.173344 0.300240i
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) −1.00000 −0.0688428 −0.0344214 0.999407i \(-0.510959\pi\)
−0.0344214 + 0.999407i \(0.510959\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) 0 0
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) 5.00000 + 8.66025i 0.340997 + 0.590624i
\(216\) 0 0
\(217\) −10.0000 + 3.46410i −0.678844 + 0.235159i
\(218\) 4.00000 0.270914
\(219\) 0 0
\(220\) 1.50000 2.59808i 0.101130 0.175162i
\(221\) 15.0000 25.9808i 1.00901 1.74766i
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) 0 0
\(226\) −6.00000 10.3923i −0.399114 0.691286i
\(227\) −12.0000 + 20.7846i −0.796468 + 1.37952i 0.125435 + 0.992102i \(0.459967\pi\)
−0.921903 + 0.387421i \(0.873366\pi\)
\(228\) 0 0
\(229\) 14.0000 + 24.2487i 0.925146 + 1.60240i 0.791326 + 0.611394i \(0.209391\pi\)
0.133820 + 0.991006i \(0.457276\pi\)
\(230\) 3.00000 0.197814
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) 0 0
\(235\) 1.50000 2.59808i 0.0978492 0.169480i
\(236\) 0 0
\(237\) 0 0
\(238\) −12.0000 10.3923i −0.777844 0.673633i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i \(-0.535394\pi\)
0.916159 0.400815i \(-0.131273\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) 0 0
\(244\) −4.00000 −0.256074
\(245\) 5.50000 4.33013i 0.351382 0.276642i
\(246\) 0 0
\(247\) 2.50000 + 4.33013i 0.159071 + 0.275519i
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 15.0000 0.946792 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) −9.50000 16.4545i −0.596083 1.03245i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.00000 10.3923i −0.374270 0.648254i 0.615948 0.787787i \(-0.288773\pi\)
−0.990217 + 0.139533i \(0.955440\pi\)
\(258\) 0 0
\(259\) −5.50000 + 28.5788i −0.341753 + 1.77580i
\(260\) 5.00000 0.310087
\(261\) 0 0
\(262\) −1.50000 + 2.59808i −0.0926703 + 0.160510i
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) −3.00000 −0.184289
\(266\) 2.50000 0.866025i 0.153285 0.0530994i
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −6.00000 + 10.3923i −0.365826 + 0.633630i −0.988908 0.148527i \(-0.952547\pi\)
0.623082 + 0.782157i \(0.285880\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 0 0
\(277\) −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) −2.00000 3.46410i −0.119952 0.207763i
\(279\) 0 0
\(280\) 0.500000 2.59808i 0.0298807 0.155265i
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) 0 0
\(283\) −13.0000 + 22.5167i −0.772770 + 1.33848i 0.163270 + 0.986581i \(0.447796\pi\)
−0.936039 + 0.351895i \(0.885537\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) 0 0
\(286\) 15.0000 0.886969
\(287\) 6.00000 + 5.19615i 0.354169 + 0.306719i
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 3.00000 5.19615i 0.176166 0.305129i
\(291\) 0 0
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) 27.0000 1.57736 0.788678 0.614806i \(-0.210766\pi\)
0.788678 + 0.614806i \(0.210766\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 5.50000 + 9.52628i 0.319681 + 0.553704i
\(297\) 0 0
\(298\) −9.00000 + 15.5885i −0.521356 + 0.903015i
\(299\) 7.50000 + 12.9904i 0.433736 + 0.751253i
\(300\) 0 0
\(301\) 20.0000 + 17.3205i 1.15278 + 0.998337i
\(302\) −14.0000 −0.805609
\(303\) 0 0
\(304\) 0.500000 0.866025i 0.0286770 0.0496700i
\(305\) 2.00000 3.46410i 0.114520 0.198354i
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 1.50000 7.79423i 0.0854704 0.444117i
\(309\) 0 0
\(310\) −2.00000 3.46410i −0.113592 0.196748i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 0 0
\(313\) −4.00000 6.92820i −0.226093 0.391605i 0.730554 0.682855i \(-0.239262\pi\)
−0.956647 + 0.291250i \(0.905929\pi\)
\(314\) −5.00000 −0.282166
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 0 0
\(322\) 7.50000 2.59808i 0.417959 0.144785i
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) −2.50000 + 4.33013i −0.138675 + 0.240192i
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) 0 0
\(328\) 3.00000 0.165647
\(329\) 1.50000 7.79423i 0.0826977 0.429710i
\(330\) 0 0
\(331\) 3.50000 + 6.06218i 0.192377 + 0.333207i 0.946038 0.324057i \(-0.105047\pi\)
−0.753660 + 0.657264i \(0.771714\pi\)
\(332\) −6.00000 + 10.3923i −0.329293 + 0.570352i
\(333\) 0 0
\(334\) −4.50000 7.79423i −0.246229 0.426481i
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 6.00000 + 10.3923i 0.326357 + 0.565267i
\(339\) 0 0
\(340\) 3.00000 5.19615i 0.162698 0.281801i
\(341\) −6.00000 10.3923i −0.324918 0.562775i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 10.0000 0.539164
\(345\) 0 0
\(346\) −1.50000 + 2.59808i −0.0806405 + 0.139673i
\(347\) 12.0000 20.7846i 0.644194 1.11578i −0.340293 0.940319i \(-0.610526\pi\)
0.984487 0.175457i \(-0.0561403\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 2.00000 + 1.73205i 0.106904 + 0.0925820i
\(351\) 0 0
\(352\) −1.50000 2.59808i −0.0799503 0.138478i
\(353\) 6.00000 10.3923i 0.319348 0.553127i −0.661004 0.750382i \(-0.729870\pi\)
0.980352 + 0.197256i \(0.0632029\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −3.00000 −0.158555
\(359\) 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i \(-0.116054\pi\)
−0.775934 + 0.630814i \(0.782721\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 1.00000 + 1.73205i 0.0525588 + 0.0910346i
\(363\) 0 0
\(364\) 12.5000 4.33013i 0.655178 0.226960i
\(365\) −4.00000 −0.209370
\(366\) 0 0
\(367\) 0.500000 0.866025i 0.0260998 0.0452062i −0.852680 0.522433i \(-0.825025\pi\)
0.878780 + 0.477227i \(0.158358\pi\)
\(368\) 1.50000 2.59808i 0.0781929 0.135434i
\(369\) 0 0
\(370\) −11.0000 −0.571863
\(371\) −7.50000 + 2.59808i −0.389381 + 0.134885i
\(372\) 0 0
\(373\) 17.0000 + 29.4449i 0.880227 + 1.52460i 0.851089 + 0.525022i \(0.175943\pi\)
0.0291379 + 0.999575i \(0.490724\pi\)
\(374\) 9.00000 15.5885i 0.465379 0.806060i
\(375\) 0 0
\(376\) −1.50000 2.59808i −0.0773566 0.133986i
\(377\) 30.0000 1.54508
\(378\) 0 0
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) 0.500000 + 0.866025i 0.0256495 + 0.0444262i
\(381\) 0 0
\(382\) −6.00000 + 10.3923i −0.306987 + 0.531717i
\(383\) 7.50000 + 12.9904i 0.383232 + 0.663777i 0.991522 0.129937i \(-0.0414776\pi\)
−0.608290 + 0.793715i \(0.708144\pi\)
\(384\) 0 0
\(385\) 6.00000 + 5.19615i 0.305788 + 0.264820i
\(386\) 4.00000 0.203595
\(387\) 0 0
\(388\) −7.00000 + 12.1244i −0.355371 + 0.615521i
\(389\) −12.0000 + 20.7846i −0.608424 + 1.05382i 0.383076 + 0.923717i \(0.374865\pi\)
−0.991500 + 0.130105i \(0.958469\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) −1.00000 6.92820i −0.0505076 0.349927i
\(393\) 0 0
\(394\) 1.50000 + 2.59808i 0.0755689 + 0.130889i
\(395\) 5.00000 8.66025i 0.251577 0.435745i
\(396\) 0 0
\(397\) −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i \(-0.182649\pi\)
−0.890028 + 0.455905i \(0.849316\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 10.5000 + 18.1865i 0.524345 + 0.908192i 0.999598 + 0.0283431i \(0.00902310\pi\)
−0.475253 + 0.879849i \(0.657644\pi\)
\(402\) 0 0
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) −6.00000 10.3923i −0.298511 0.517036i
\(405\) 0 0
\(406\) 3.00000 15.5885i 0.148888 0.773642i
\(407\) −33.0000 −1.63575
\(408\) 0 0
\(409\) 11.0000 19.0526i 0.543915 0.942088i −0.454759 0.890614i \(-0.650275\pi\)
0.998674 0.0514740i \(-0.0163919\pi\)
\(410\) −1.50000 + 2.59808i −0.0740797 + 0.128310i
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) 0 0
\(415\) −6.00000 10.3923i −0.294528 0.510138i
\(416\) 2.50000 4.33013i 0.122573 0.212302i
\(417\) 0 0
\(418\) 1.50000 + 2.59808i 0.0733674 + 0.127076i
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) −0.500000 0.866025i −0.0243396 0.0421575i
\(423\) 0 0
\(424\) −1.50000 + 2.59808i −0.0728464 + 0.126174i
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) 0 0
\(427\) 2.00000 10.3923i 0.0967868 0.502919i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −5.00000 + 8.66025i −0.241121 + 0.417635i
\(431\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 0 0
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −8.00000 6.92820i −0.384012 0.332564i
\(435\) 0 0
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) −1.50000 + 2.59808i −0.0717547 + 0.124283i
\(438\) 0 0
\(439\) 5.00000 + 8.66025i 0.238637 + 0.413331i 0.960323 0.278889i \(-0.0899661\pi\)
−0.721686 + 0.692220i \(0.756633\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) 30.0000 1.42695
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) 0 0
\(445\) 3.00000 5.19615i 0.142214 0.246321i
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) 0 0
\(448\) −2.00000 1.73205i −0.0944911 0.0818317i
\(449\) 3.00000 0.141579 0.0707894 0.997491i \(-0.477448\pi\)
0.0707894 + 0.997491i \(0.477448\pi\)
\(450\) 0 0
\(451\) −4.50000 + 7.79423i −0.211897 + 0.367016i
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) 0 0
\(454\) −24.0000 −1.12638
\(455\) −2.50000 + 12.9904i −0.117202 + 0.608998i
\(456\) 0 0
\(457\) 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i \(0.00537742\pi\)
−0.485299 + 0.874348i \(0.661289\pi\)
\(458\) −14.0000 + 24.2487i −0.654177 + 1.13307i
\(459\) 0 0
\(460\) 1.50000 + 2.59808i 0.0699379 + 0.121136i
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) −19.0000 −0.883005 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 0 0
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −9.00000 15.5885i −0.416470 0.721348i 0.579111 0.815249i \(-0.303400\pi\)
−0.995582 + 0.0939008i \(0.970066\pi\)
\(468\) 0 0
\(469\) −10.0000 + 3.46410i −0.461757 + 0.159957i
\(470\) 3.00000 0.138380
\(471\) 0 0
\(472\) 0 0
\(473\) −15.0000 + 25.9808i −0.689701 + 1.19460i
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 3.00000 15.5885i 0.137505 0.714496i
\(477\) 0 0
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 0 0
\(481\) −27.5000 47.6314i −1.25389 2.17180i
\(482\) 25.0000 1.13872
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −7.00000 12.1244i −0.317854 0.550539i
\(486\) 0 0
\(487\) 8.00000 13.8564i 0.362515 0.627894i −0.625859 0.779936i \(-0.715252\pi\)
0.988374 + 0.152042i \(0.0485850\pi\)
\(488\) −2.00000 3.46410i −0.0905357 0.156813i
\(489\) 0 0
\(490\) 6.50000 + 2.59808i 0.293640 + 0.117369i
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) 18.0000 31.1769i 0.810679 1.40414i
\(494\) −2.50000 + 4.33013i −0.112480 + 0.194822i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 24.0000 + 20.7846i 1.07655 + 0.932317i
\(498\) 0 0
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 7.50000 + 12.9904i 0.334741 + 0.579789i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 4.50000 + 7.79423i 0.200049 + 0.346496i
\(507\) 0 0
\(508\) 9.50000 16.4545i 0.421494 0.730050i
\(509\) 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) 0 0
\(511\) −10.0000 + 3.46410i −0.442374 + 0.153243i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.00000 10.3923i 0.264649 0.458385i
\(515\) 2.00000 3.46410i 0.0881305 0.152647i
\(516\) 0 0
\(517\) 9.00000 0.395820
\(518\) −27.5000 + 9.52628i −1.20828 + 0.418561i
\(519\) 0 0
\(520\) 2.50000 + 4.33013i 0.109632 + 0.189889i
\(521\) 16.5000 28.5788i 0.722878 1.25206i −0.236963 0.971519i \(-0.576152\pi\)
0.959841 0.280543i \(-0.0905145\pi\)
\(522\) 0 0
\(523\) −10.0000 17.3205i −0.437269 0.757373i 0.560208 0.828352i \(-0.310721\pi\)
−0.997478 + 0.0709788i \(0.977388\pi\)
\(524\) −3.00000 −0.131056
\(525\) 0 0
\(526\) 0 0
\(527\) −12.0000 20.7846i −0.522728 0.905392i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) −1.50000 2.59808i −0.0651558 0.112853i
\(531\) 0 0
\(532\) 2.00000 + 1.73205i 0.0867110 + 0.0750939i
\(533\) −15.0000 −0.649722
\(534\) 0 0
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) 0 0
\(538\) −12.0000 −0.517357
\(539\) 19.5000 + 7.79423i 0.839924 + 0.335721i
\(540\) 0 0
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 0 0
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) −4.00000 −0.171341
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) 0 0
\(550\) −1.50000 + 2.59808i −0.0639602 + 0.110782i
\(551\) 3.00000 + 5.19615i 0.127804 + 0.221364i
\(552\) 0 0
\(553\) 5.00000 25.9808i 0.212622 1.10481i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −13.5000 + 23.3827i −0.572013 + 0.990756i 0.424346 + 0.905500i \(0.360504\pi\)
−0.996359 + 0.0852559i \(0.972829\pi\)
\(558\) 0 0
\(559\) −50.0000 −2.11477
\(560\) 2.50000 0.866025i 0.105644 0.0365963i
\(561\) 0 0
\(562\) 1.50000 + 2.59808i 0.0632737 + 0.109593i
\(563\) −9.00000 + 15.5885i −0.379305 + 0.656975i −0.990961 0.134148i \(-0.957170\pi\)
0.611656 + 0.791123i \(0.290503\pi\)
\(564\) 0 0
\(565\) 6.00000 + 10.3923i 0.252422 + 0.437208i
\(566\) −26.0000 −1.09286
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) −1.50000 2.59808i −0.0628833 0.108917i 0.832870 0.553469i \(-0.186696\pi\)
−0.895753 + 0.444552i \(0.853363\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 7.50000 + 12.9904i 0.313591 + 0.543155i
\(573\) 0 0
\(574\) −1.50000 + 7.79423i −0.0626088 + 0.325325i
\(575\) −3.00000 −0.125109
\(576\) 0 0
\(577\) −10.0000 + 17.3205i −0.416305 + 0.721062i −0.995565 0.0940813i \(-0.970009\pi\)
0.579259 + 0.815144i \(0.303342\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) 0 0
\(580\) 6.00000 0.249136
\(581\) −24.0000 20.7846i −0.995688 0.862291i
\(582\) 0 0
\(583\) −4.50000 7.79423i −0.186371 0.322804i
\(584\) −2.00000 + 3.46410i −0.0827606 + 0.143346i
\(585\) 0 0
\(586\) 13.5000 + 23.3827i 0.557680 + 0.965930i
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) 0 0
\(592\) −5.50000 + 9.52628i −0.226049 + 0.391528i
\(593\) −18.0000 31.1769i −0.739171 1.28028i −0.952869 0.303383i \(-0.901884\pi\)
0.213697 0.976900i \(-0.431449\pi\)
\(594\) 0 0
\(595\) 12.0000 + 10.3923i 0.491952 + 0.426043i
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) −7.50000 + 12.9904i −0.306698 + 0.531216i
\(599\) 21.0000 36.3731i 0.858037 1.48616i −0.0157622 0.999876i \(-0.505017\pi\)
0.873799 0.486287i \(-0.161649\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −5.00000 + 25.9808i −0.203785 + 1.05890i
\(603\) 0 0
\(604\) −7.00000 12.1244i −0.284826 0.493333i
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) 9.50000 + 16.4545i 0.385593 + 0.667867i 0.991851 0.127401i \(-0.0406635\pi\)
−0.606258 + 0.795268i \(0.707330\pi\)
\(608\) 1.00000 0.0405554
\(609\) 0 0
\(610\) 4.00000 0.161955
\(611\) 7.50000 + 12.9904i 0.303418 + 0.525535i
\(612\) 0 0
\(613\) −23.5000 + 40.7032i −0.949156 + 1.64399i −0.201948 + 0.979396i \(0.564727\pi\)
−0.747208 + 0.664590i \(0.768606\pi\)
\(614\) 1.00000 + 1.73205i 0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) 7.50000 2.59808i 0.302184 0.104679i
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 0.500000 0.866025i 0.0200967 0.0348085i −0.855802 0.517303i \(-0.826936\pi\)
0.875899 + 0.482495i \(0.160269\pi\)
\(620\) 2.00000 3.46410i 0.0803219 0.139122i
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 3.00000 15.5885i 0.120192 0.624538i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 4.00000 6.92820i 0.159872 0.276907i
\(627\) 0 0
\(628\) −2.50000 4.33013i −0.0997609 0.172791i
\(629\) −66.0000 −2.63159
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) −5.00000 8.66025i −0.198889 0.344486i
\(633\) 0 0
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 9.50000 + 16.4545i 0.376996 + 0.652976i
\(636\) 0 0
\(637\) 5.00000 + 34.6410i 0.198107 + 1.37253i
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −22.5000 + 38.9711i −0.888697 + 1.53927i −0.0472793 + 0.998882i \(0.515055\pi\)
−0.841417 + 0.540386i \(0.818278\pi\)
\(642\) 0 0
\(643\) 38.0000 1.49857 0.749287 0.662246i \(-0.230396\pi\)
0.749287 + 0.662246i \(0.230396\pi\)
\(644\) 6.00000 + 5.19615i 0.236433 + 0.204757i
\(645\) 0 0
\(646\) 3.00000 + 5.19615i 0.118033 + 0.204440i
\(647\) −10.5000 + 18.1865i −0.412798 + 0.714986i −0.995194 0.0979182i \(-0.968782\pi\)
0.582397 + 0.812905i \(0.302115\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −5.00000 −0.196116
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 10.5000 + 18.1865i 0.410897 + 0.711694i 0.994988 0.0999939i \(-0.0318823\pi\)
−0.584091 + 0.811688i \(0.698549\pi\)
\(654\) 0 0
\(655\) 1.50000 2.59808i 0.0586098 0.101515i
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) 0 0
\(658\) 7.50000 2.59808i 0.292380 0.101284i
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 0 0
\(661\) −22.0000 + 38.1051i −0.855701 + 1.48212i 0.0202925 + 0.999794i \(0.493540\pi\)
−0.875993 + 0.482323i \(0.839793\pi\)
\(662\) −3.50000 + 6.06218i −0.136031 + 0.235613i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) −2.50000 + 0.866025i −0.0969458 + 0.0335830i
\(666\) 0 0
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 4.50000 7.79423i 0.174110 0.301568i
\(669\) 0 0
\(670\) −2.00000 3.46410i −0.0772667 0.133830i
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 7.00000 + 12.1244i 0.269630 + 0.467013i
\(675\) 0 0
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) −1.50000 2.59808i −0.0576497 0.0998522i 0.835760 0.549095i \(-0.185027\pi\)
−0.893410 + 0.449242i \(0.851694\pi\)
\(678\) 0 0
\(679\) −28.0000 24.2487i −1.07454 0.930580i
\(680\) 6.00000 0.230089
\(681\) 0 0
\(682\) 6.00000 10.3923i 0.229752 0.397942i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 18.5000 + 0.866025i 0.706333 + 0.0330650i
\(687\) 0 0
\(688\) 5.00000 + 8.66025i 0.190623 + 0.330169i
\(689\) 7.50000 12.9904i 0.285727 0.494894i
\(690\) 0 0
\(691\) −16.0000 27.7128i −0.608669 1.05425i −0.991460 0.130410i \(-0.958371\pi\)
0.382791 0.923835i \(-0.374963\pi\)
\(692\) −3.00000 −0.114043
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 2.00000 + 3.46410i 0.0758643 + 0.131401i
\(696\) 0 0
\(697\) −9.00000 + 15.5885i −0.340899 + 0.590455i
\(698\) −5.00000 8.66025i −0.189253 0.327795i
\(699\) 0 0
\(700\) −0.500000 + 2.59808i −0.0188982 + 0.0981981i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 5.50000 9.52628i 0.207436 0.359290i
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 0 0
\(706\) 12.0000 0.451626
\(707\) 30.0000 10.3923i 1.12827 0.390843i
\(708\) 0 0
\(709\) −7.00000 12.1244i −0.262891 0.455340i 0.704118 0.710083i \(-0.251342\pi\)
−0.967009 + 0.254743i \(0.918009\pi\)
\(710\) −6.00000 + 10.3923i −0.225176 + 0.390016i
\(711\) 0 0
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) 12.0000 0.449404
\(714\) 0 0
\(715\) −15.0000 −0.560968
\(716\) −1.50000 2.59808i −0.0560576 0.0970947i
\(717\) 0 0
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) −18.0000 31.1769i −0.671287 1.16270i −0.977539 0.210752i \(-0.932409\pi\)
0.306253 0.951950i \(-0.400925\pi\)
\(720\) 0 0
\(721\) 2.00000 10.3923i 0.0744839 0.387030i
\(722\) 18.0000 0.669891
\(723\) 0 0
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 0 0
\(727\) 29.0000 1.07555 0.537775 0.843088i \(-0.319265\pi\)
0.537775 + 0.843088i \(0.319265\pi\)
\(728\) 10.0000 + 8.66025i 0.370625 + 0.320970i
\(729\) 0 0
\(730\) −2.00000 3.46410i −0.0740233 0.128212i
\(731\) −30.0000 + 51.9615i −1.10959 + 1.92187i
\(732\) 0 0
\(733\) −23.5000 40.7032i −0.867992 1.50341i −0.864045 0.503415i \(-0.832077\pi\)
−0.00394730 0.999992i \(-0.501256\pi\)
\(734\) 1.00000 0.0369107
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −6.00000 10.3923i −0.221013 0.382805i
\(738\) 0 0
\(739\) 18.5000 32.0429i 0.680534 1.17872i −0.294285 0.955718i \(-0.595081\pi\)
0.974818 0.223001i \(-0.0715853\pi\)
\(740\) −5.50000 9.52628i −0.202184 0.350193i
\(741\) 0 0
\(742\) −6.00000 5.19615i −0.220267 0.190757i
\(743\) −9.00000 −0.330178 −0.165089 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) −17.0000 + 29.4449i −0.622414 + 1.07805i
\(747\) 0 0
\(748\) 18.0000 0.658145
\(749\) −6.00000 + 31.1769i −0.219235 + 1.13918i
\(750\) 0 0
\(751\) −13.0000 22.5167i −0.474377 0.821645i 0.525193 0.850983i \(-0.323993\pi\)
−0.999570 + 0.0293387i \(0.990660\pi\)
\(752\) 1.50000 2.59808i 0.0546994 0.0947421i
\(753\) 0 0
\(754\) 15.0000 + 25.9808i 0.546268 + 0.946164i
\(755\) 14.0000 0.509512
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) −12.5000 21.6506i −0.454020 0.786386i
\(759\) 0 0
\(760\) −0.500000 + 0.866025i −0.0181369 + 0.0314140i
\(761\) −25.5000 44.1673i −0.924374 1.60106i −0.792564 0.609788i \(-0.791255\pi\)
−0.131810 0.991275i \(-0.542079\pi\)
\(762\) 0 0
\(763\) −10.0000 + 3.46410i −0.362024 + 0.125409i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) −7.50000 + 12.9904i −0.270986 + 0.469362i
\(767\) 0 0
\(768\) 0 0
\(769\) −49.0000 −1.76699 −0.883493 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) −1.50000 + 7.79423i −0.0540562 + 0.280885i
\(771\) 0 0
\(772\) 2.00000 + 3.46410i 0.0719816 + 0.124676i
\(773\) 19.5000 33.7750i 0.701366 1.21480i −0.266621 0.963802i \(-0.585907\pi\)
0.967987 0.251000i \(-0.0807596\pi\)
\(774\) 0 0
\(775\) 2.00000 + 3.46410i 0.0718421 + 0.124434i
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) −24.0000 −0.860442
\(779\) −1.50000 2.59808i −0.0537431 0.0930857i
\(780\) 0 0
\(781\) −18.0000 + 31.1769i −0.644091 + 1.11560i
\(782\) 9.00000 + 15.5885i 0.321839 + 0.557442i
\(783\) 0 0
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 5.00000 0.178458
\(786\) 0 0
\(787\) 17.0000 29.4449i 0.605985 1.04960i −0.385911 0.922536i \(-0.626113\pi\)
0.991895 0.127060i \(-0.0405540\pi\)
\(788\) −1.50000 + 2.59808i −0.0534353 + 0.0925526i
\(789\) 0 0
\(790\) 10.0000 0.355784
\(791\) 24.0000 + 20.7846i 0.853342 + 0.739016i
\(792\) 0 0
\(793\) 10.0000 + 17.3205i 0.355110 + 0.615069i
\(794\) 1.00000 1.73205i 0.0354887 0.0614682i
\(795\) 0 0
\(796\) 2.00000 + 3.46410i 0.0708881 + 0.122782i
\(797\) 30.0000 1.06265 0.531327 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) 0 0
\(799\) 18.0000 0.636794
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) 0 0
\(802\) −10.5000 + 18.1865i −0.370768 + 0.642189i
\(803\) −6.00000 10.3923i −0.211735 0.366736i
\(804\) 0 0
\(805\) −7.50000 + 2.59808i −0.264340 + 0.0915702i
\(806\) 20.0000 0.704470
\(807\) 0 0
\(808\) 6.00000 10.3923i 0.211079 0.365600i
\(809\) 19.5000 33.7750i 0.685583 1.18747i −0.287670 0.957730i \(-0.592880\pi\)
0.973253 0.229736i \(-0.0737862\pi\)
\(810\) 0 0
\(811\) 47.0000 1.65039 0.825197 0.564846i \(-0.191064\pi\)
0.825197 + 0.564846i \(0.191064\pi\)
\(812\) 15.0000 5.19615i 0.526397 0.182349i
\(813\) 0 0
\(814\) −16.5000 28.5788i −0.578325 1.00169i
\(815\) 2.00000 3.46410i 0.0700569 0.121342i
\(816\) 0 0
\(817\) −5.00000 8.66025i −0.174928 0.302984i
\(818\) 22.0000 0.769212
\(819\) 0 0
\(820\) −3.00000 −0.104765
\(821\) −9.00000 15.5885i −0.314102 0.544041i 0.665144 0.746715i \(-0.268370\pi\)
−0.979246 + 0.202674i \(0.935037\pi\)
\(822\) 0 0
\(823\) −22.0000 + 38.1051i −0.766872 + 1.32826i 0.172379 + 0.985031i \(0.444854\pi\)
−0.939251 + 0.343230i \(0.888479\pi\)
\(824\) −2.00000 3.46410i −0.0696733 0.120678i
\(825\) 0 0
\(826\) 0 0
\(827\) 54.0000 1.87776 0.938882 0.344239i \(-0.111863\pi\)
0.938882 + 0.344239i \(0.111863\pi\)
\(828\) 0 0
\(829\) −7.00000 + 12.1244i −0.243120 + 0.421096i −0.961601 0.274450i \(-0.911504\pi\)
0.718481 + 0.695546i \(0.244838\pi\)
\(830\) 6.00000 10.3923i 0.208263 0.360722i
\(831\) 0 0
\(832\) 5.00000 0.173344
\(833\) 39.0000 + 15.5885i 1.35127 + 0.540108i
\(834\) 0 0
\(835\) 4.50000 + 7.79423i 0.155729 + 0.269730i
\(836\) −1.50000 + 2.59808i −0.0518786 + 0.0898563i
\(837\) 0 0
\(838\) −7.50000 12.9904i −0.259083 0.448745i
\(839\) 6.00000 0.207143 0.103572 0.994622i \(-0.466973\pi\)
0.103572 + 0.994622i \(0.466973\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −17.0000 29.4449i −0.585859 1.01474i
\(843\) 0 0
\(844\) 0.500000 0.866025i 0.0172107 0.0298098i
\(845\) −6.00000 10.3923i −0.206406 0.357506i
\(846\) 0 0
\(847\) 1.00000 5.19615i 0.0343604 0.178542i
\(848\) −3.00000 −0.103020
\(849\) 0 0
\(850\) −3.00000 + 5.19615i −0.102899 + 0.178227i
\(851\) 16.5000 28.5788i 0.565613 0.979670i
\(852\) 0 0
\(853\) −1.00000 −0.0342393 −0.0171197 0.999853i \(-0.505450\pi\)
−0.0171197 + 0.999853i \(0.505450\pi\)
\(854\) 10.0000 3.46410i 0.342193 0.118539i
\(855\) 0 0
\(856\) 6.00000 + 10.3923i 0.205076 + 0.355202i
\(857\) −9.00000 + 15.5885i −0.307434 + 0.532492i −0.977800 0.209539i \(-0.932804\pi\)
0.670366 + 0.742030i \(0.266137\pi\)
\(858\) 0 0
\(859\) −16.0000 27.7128i −0.545913 0.945549i −0.998549 0.0538535i \(-0.982850\pi\)
0.452636 0.891695i \(-0.350484\pi\)
\(860\) −10.0000 −0.340997
\(861\) 0 0
\(862\) 0 0
\(863\) 19.5000 + 33.7750i 0.663788 + 1.14971i 0.979612 + 0.200897i \(0.0643855\pi\)
−0.315825 + 0.948818i \(0.602281\pi\)
\(864\) 0 0
\(865\) 1.50000 2.59808i 0.0510015 0.0883372i
\(866\) −8.00000 13.8564i −0.271851 0.470860i
\(867\) 0 0
\(868\) 2.00000 10.3923i 0.0678844 0.352738i
\(869\) 30.0000 1.01768
\(870\) 0 0
\(871\) 10.0000 17.3205i 0.338837 0.586883i
\(872\) −2.00000 + 3.46410i −0.0677285 + 0.117309i
\(873\) 0 0
\(874\) −3.00000 −0.101477
\(875\) −2.00000 1.73205i −0.0676123 0.0585540i
\(876\) 0 0
\(877\) 3.50000 + 6.06218i 0.118187 + 0.204705i 0.919049 0.394143i \(-0.128959\pi\)
−0.800862 + 0.598848i \(0.795625\pi\)
\(878\) −5.00000 + 8.66025i −0.168742 + 0.292269i
\(879\) 0 0
\(880\) 1.50000 + 2.59808i 0.0505650 + 0.0875811i
\(881\) −33.0000 −1.11180 −0.555899 0.831250i \(-0.687626\pi\)
−0.555899 + 0.831250i \(0.687626\pi\)
\(882\) 0 0
\(883\) 8.00000 0.269221 0.134611 0.990899i \(-0.457022\pi\)
0.134611 + 0.990899i \(0.457022\pi\)
\(884\) 15.0000 + 25.9808i 0.504505 + 0.873828i
\(885\) 0 0
\(886\) 12.0000 20.7846i 0.403148 0.698273i
\(887\) 12.0000 + 20.7846i 0.402921 + 0.697879i 0.994077 0.108678i \(-0.0346618\pi\)
−0.591156 + 0.806557i \(0.701328\pi\)
\(888\) 0 0
\(889\) 38.0000 + 32.9090i 1.27448 + 1.10373i
\(890\) 6.00000 0.201120
\(891\) 0 0
\(892\) −4.00000 + 6.92820i −0.133930 + 0.231973i
\(893\) −1.50000 + 2.59808i −0.0501956 + 0.0869413i
\(894\) 0 0
\(895\) 3.00000 0.100279
\(896\) 0.500000 2.59808i 0.0167038 0.0867956i
\(897\) 0 0
\(898\) 1.50000 + 2.59808i 0.0500556 + 0.0866989i
\(899\) 12.0000 20.7846i 0.400222 0.693206i
\(900\) 0 0
\(901\) −9.00000 15.5885i −0.299833 0.519327i
\(902\) −9.00000 −0.299667
\(903\) 0 0
\(904\) 12.0000 0.399114
\(905\) −1.00000 1.73205i −0.0332411 0.0575753i
\(906\) 0 0
\(907\) 5.00000 8.66025i 0.166022 0.287559i −0.770996 0.636841i \(-0.780241\pi\)
0.937018 + 0.349281i \(0.113574\pi\)
\(908\) −12.0000 20.7846i −0.398234 0.689761i
\(909\) 0 0
\(910\) −12.5000 + 4.33013i −0.414371 + 0.143542i
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) 0 0
\(913\) 18.0000 31.1769i 0.595713 1.03181i
\(914\) −11.0000 + 19.0526i −0.363848 + 0.630203i
\(915\) 0 0
\(916\) −28.0000 −0.925146
\(917\) 1.50000 7.79423i 0.0495344 0.257388i
\(918\) 0 0
\(919\) −19.0000 32.9090i −0.626752 1.08557i −0.988199 0.153174i \(-0.951051\pi\)
0.361447 0.932393i \(-0.382283\pi\)
\(920\) −1.50000 + 2.59808i −0.0494535 + 0.0856560i
\(921\) 0 0
\(922\) −3.00000 5.19615i −0.0987997 0.171126i
\(923\) −60.0000 −1.97492
\(924\) 0 0
\(925\) 11.0000 0.361678
\(926\) −9.50000 16.4545i −0.312189 0.540728i
\(927\) 0 0
\(928\) 3.00000 5.19615i 0.0984798 0.170572i
\(929\) 16.5000 + 28.5788i 0.541347 + 0.937641i 0.998827 + 0.0484211i \(0.0154190\pi\)
−0.457480 + 0.889220i \(0.651248\pi\)
\(930\) 0 0
\(931\) −5.50000 + 4.33013i −0.180255 + 0.141914i
\(932\) 6.00000 0.196537
\(933\) 0 0
\(934\) 9.00000 15.5885i 0.294489 0.510070i
\(935\) −9.00000 + 15.5885i −0.294331 + 0.509797i
\(936\) 0 0
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) −8.00000 6.92820i −0.261209 0.226214i
\(939\) 0 0
\(940\) 1.50000 + 2.59808i 0.0489246 + 0.0847399i
\(941\) 12.0000 20.7846i 0.391189 0.677559i −0.601418 0.798935i \(-0.705397\pi\)
0.992607 + 0.121376i \(0.0387306\pi\)
\(942\) 0 0
\(943\) −4.50000 7.79423i −0.146540 0.253815i
\(944\) 0 0
\(945\) 0 0
\(946\) −30.0000 −0.975384
\(947\) 15.0000 + 25.9808i 0.487435 + 0.844261i 0.999896 0.0144491i \(-0.00459946\pi\)
−0.512461 + 0.858710i \(0.671266\pi\)
\(948\) 0 0
\(949\) 10.0000 17.3205i 0.324614 0.562247i
\(950\) −0.500000 0.866025i −0.0162221 0.0280976i
\(951\) 0 0
\(952\) 15.0000 5.19615i 0.486153 0.168408i
\(953\) 12.0000 0.388718 0.194359 0.980930i \(-0.437737\pi\)
0.194359 + 0.980930i \(0.437737\pi\)
\(954\) 0 0
\(955\) 6.00000 10.3923i 0.194155 0.336287i
\(956\) 3.00000 5.19615i 0.0970269 0.168056i
\(957\) 0 0
\(958\) 24.0000 0.775405
\(959\) −30.0000 + 10.3923i −0.968751 + 0.335585i
\(960\) 0 0
\(961\) 7.50000 + 12.9904i 0.241935 + 0.419045i
\(962\) 27.5000 47.6314i 0.886636 1.53570i
\(963\) 0 0
\(964\) 12.5000 + 21.6506i 0.402598 + 0.697320i
\(965\) −4.00000 −0.128765
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) 0 0
\(970\) 7.00000 12.1244i 0.224756 0.389290i
\(971\) 13.5000 + 23.3827i 0.433236 + 0.750386i 0.997150 0.0754473i \(-0.0240385\pi\)
−0.563914 + 0.825833i \(0.690705\pi\)
\(972\) 0 0
\(973\) 8.00000 + 6.92820i 0.256468 + 0.222108i
\(974\) 16.0000 0.512673
\(975\) 0 0
\(976\) 2.00000 3.46410i 0.0640184 0.110883i
\(977\) −15.0000 + 25.9808i −0.479893 + 0.831198i −0.999734 0.0230645i \(-0.992658\pi\)
0.519841 + 0.854263i \(0.325991\pi\)
\(978\) 0 0
\(979\) 18.0000 0.575282
\(980\) 1.00000 + 6.92820i 0.0319438 + 0.221313i
\(981\) 0 0
\(982\) 6.00000 + 10.3923i 0.191468 + 0.331632i
\(983\) 28.5000 49.3634i 0.909009 1.57445i 0.0935651 0.995613i \(-0.470174\pi\)
0.815444 0.578836i \(-0.196493\pi\)
\(984\) 0 0
\(985\) −1.50000 2.59808i −0.0477940 0.0827816i
\(986\) 36.0000 1.14647
\(987\) 0 0
\(988\) −5.00000 −0.159071
\(989\) −15.0000 25.9808i −0.476972 0.826140i
\(990\) 0 0
\(991\) −10.0000 + 17.3205i −0.317660 + 0.550204i −0.979999 0.199000i \(-0.936231\pi\)
0.662339 + 0.749204i \(0.269564\pi\)
\(992\) −2.00000 3.46410i −0.0635001 0.109985i
\(993\) 0 0
\(994\) −6.00000 + 31.1769i −0.190308 + 0.988872i
\(995\) −4.00000 −0.126809
\(996\) 0 0
\(997\) −7.00000 + 12.1244i −0.221692 + 0.383982i −0.955322 0.295567i \(-0.904491\pi\)
0.733630 + 0.679549i \(0.237825\pi\)
\(998\) −14.0000 + 24.2487i −0.443162 + 0.767580i
\(999\) 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 630.2.k.e.361.1 2
3.2 odd 2 70.2.e.b.11.1 2
7.2 even 3 inner 630.2.k.e.541.1 2
7.3 odd 6 4410.2.a.c.1.1 1
7.4 even 3 4410.2.a.m.1.1 1
12.11 even 2 560.2.q.d.81.1 2
15.2 even 4 350.2.j.a.249.2 4
15.8 even 4 350.2.j.a.249.1 4
15.14 odd 2 350.2.e.h.151.1 2
21.2 odd 6 70.2.e.b.51.1 yes 2
21.5 even 6 490.2.e.a.471.1 2
21.11 odd 6 490.2.a.g.1.1 1
21.17 even 6 490.2.a.j.1.1 1
21.20 even 2 490.2.e.a.361.1 2
84.11 even 6 3920.2.a.be.1.1 1
84.23 even 6 560.2.q.d.401.1 2
84.59 odd 6 3920.2.a.g.1.1 1
105.2 even 12 350.2.j.a.149.1 4
105.17 odd 12 2450.2.c.p.99.2 2
105.23 even 12 350.2.j.a.149.2 4
105.32 even 12 2450.2.c.f.99.2 2
105.38 odd 12 2450.2.c.p.99.1 2
105.44 odd 6 350.2.e.h.51.1 2
105.53 even 12 2450.2.c.f.99.1 2
105.59 even 6 2450.2.a.f.1.1 1
105.74 odd 6 2450.2.a.p.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.e.b.11.1 2 3.2 odd 2
70.2.e.b.51.1 yes 2 21.2 odd 6
350.2.e.h.51.1 2 105.44 odd 6
350.2.e.h.151.1 2 15.14 odd 2
350.2.j.a.149.1 4 105.2 even 12
350.2.j.a.149.2 4 105.23 even 12
350.2.j.a.249.1 4 15.8 even 4
350.2.j.a.249.2 4 15.2 even 4
490.2.a.g.1.1 1 21.11 odd 6
490.2.a.j.1.1 1 21.17 even 6
490.2.e.a.361.1 2 21.20 even 2
490.2.e.a.471.1 2 21.5 even 6
560.2.q.d.81.1 2 12.11 even 2
560.2.q.d.401.1 2 84.23 even 6
630.2.k.e.361.1 2 1.1 even 1 trivial
630.2.k.e.541.1 2 7.2 even 3 inner
2450.2.a.f.1.1 1 105.59 even 6
2450.2.a.p.1.1 1 105.74 odd 6
2450.2.c.f.99.1 2 105.53 even 12
2450.2.c.f.99.2 2 105.32 even 12
2450.2.c.p.99.1 2 105.38 odd 12
2450.2.c.p.99.2 2 105.17 odd 12
3920.2.a.g.1.1 1 84.59 odd 6
3920.2.a.be.1.1 1 84.11 even 6
4410.2.a.c.1.1 1 7.3 odd 6
4410.2.a.m.1.1 1 7.4 even 3