Properties

Label 360.2.x.a.53.22
Level $360$
Weight $2$
Character 360.53
Analytic conductor $2.875$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(53,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.x (of order \(4\), 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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 53.22
Character \(\chi\) \(=\) 360.53
Dual form 360.2.x.a.197.22

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.33270 - 0.473189i) q^{2} +(1.55218 - 1.26124i) q^{4} +(-1.45381 - 1.69895i) q^{5} +(1.53029 - 1.53029i) q^{7} +(1.47179 - 2.41533i) q^{8} +O(q^{10})\) \(q+(1.33270 - 0.473189i) q^{2} +(1.55218 - 1.26124i) q^{4} +(-1.45381 - 1.69895i) q^{5} +(1.53029 - 1.53029i) q^{7} +(1.47179 - 2.41533i) q^{8} +(-2.74142 - 1.57626i) q^{10} -2.72480 q^{11} +(-0.857617 + 0.857617i) q^{13} +(1.31530 - 2.76353i) q^{14} +(0.818554 - 3.91535i) q^{16} +(2.55531 + 2.55531i) q^{17} +3.54160 q^{19} +(-4.39937 - 0.803474i) q^{20} +(-3.63135 + 1.28935i) q^{22} +(-0.626051 + 0.626051i) q^{23} +(-0.772849 + 4.93991i) q^{25} +(-0.737133 + 1.54876i) q^{26} +(0.445231 - 4.30535i) q^{28} -5.12260i q^{29} +7.89544 q^{31} +(-0.761813 - 5.60532i) q^{32} +(4.61460 + 2.19632i) q^{34} +(-4.82463 - 0.375125i) q^{35} +(4.21539 + 4.21539i) q^{37} +(4.71990 - 1.67585i) q^{38} +(-6.24324 + 1.01094i) q^{40} +12.4074i q^{41} +(-5.67823 + 5.67823i) q^{43} +(-4.22940 + 3.43663i) q^{44} +(-0.538098 + 1.13058i) q^{46} +(-9.45505 - 9.45505i) q^{47} +2.31644i q^{49} +(1.30753 + 6.94913i) q^{50} +(-0.249520 + 2.41284i) q^{52} +(6.46657 + 6.46657i) q^{53} +(3.96136 + 4.62930i) q^{55} +(-1.44388 - 5.94842i) q^{56} +(-2.42396 - 6.82690i) q^{58} +2.51407i q^{59} +9.49179i q^{61} +(10.5223 - 3.73603i) q^{62} +(-3.66765 - 7.10974i) q^{64} +(2.70386 + 0.210231i) q^{65} +(-9.91318 - 9.91318i) q^{67} +(7.18916 + 0.743456i) q^{68} +(-6.60730 + 1.78303i) q^{70} +2.19671i q^{71} +(-5.71276 - 5.71276i) q^{73} +(7.61252 + 3.62318i) q^{74} +(5.49722 - 4.46681i) q^{76} +(-4.16973 + 4.16973i) q^{77} -12.7576i q^{79} +(-7.84200 + 4.30151i) q^{80} +(5.87103 + 16.5353i) q^{82} +(3.58072 + 3.58072i) q^{83} +(0.626392 - 8.05627i) q^{85} +(-4.88051 + 10.2543i) q^{86} +(-4.01035 + 6.58130i) q^{88} +10.2214 q^{89} +2.62480i q^{91} +(-0.182147 + 1.76135i) q^{92} +(-17.0748 - 8.12673i) q^{94} +(-5.14884 - 6.01700i) q^{95} +(-1.29731 + 1.29731i) q^{97} +(1.09611 + 3.08712i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33270 0.473189i 0.942362 0.334595i
\(3\) 0 0
\(4\) 1.55218 1.26124i 0.776092 0.630619i
\(5\) −1.45381 1.69895i −0.650165 0.759793i
\(6\) 0 0
\(7\) 1.53029 1.53029i 0.578394 0.578394i −0.356066 0.934461i \(-0.615882\pi\)
0.934461 + 0.356066i \(0.115882\pi\)
\(8\) 1.47179 2.41533i 0.520358 0.853948i
\(9\) 0 0
\(10\) −2.74142 1.57626i −0.866914 0.498458i
\(11\) −2.72480 −0.821559 −0.410779 0.911735i \(-0.634743\pi\)
−0.410779 + 0.911735i \(0.634743\pi\)
\(12\) 0 0
\(13\) −0.857617 + 0.857617i −0.237860 + 0.237860i −0.815964 0.578103i \(-0.803793\pi\)
0.578103 + 0.815964i \(0.303793\pi\)
\(14\) 1.31530 2.76353i 0.351529 0.738585i
\(15\) 0 0
\(16\) 0.818554 3.91535i 0.204638 0.978838i
\(17\) 2.55531 + 2.55531i 0.619753 + 0.619753i 0.945468 0.325715i \(-0.105605\pi\)
−0.325715 + 0.945468i \(0.605605\pi\)
\(18\) 0 0
\(19\) 3.54160 0.812500 0.406250 0.913762i \(-0.366836\pi\)
0.406250 + 0.913762i \(0.366836\pi\)
\(20\) −4.39937 0.803474i −0.983728 0.179662i
\(21\) 0 0
\(22\) −3.63135 + 1.28935i −0.774206 + 0.274889i
\(23\) −0.626051 + 0.626051i −0.130541 + 0.130541i −0.769358 0.638818i \(-0.779424\pi\)
0.638818 + 0.769358i \(0.279424\pi\)
\(24\) 0 0
\(25\) −0.772849 + 4.93991i −0.154570 + 0.987982i
\(26\) −0.737133 + 1.54876i −0.144564 + 0.303737i
\(27\) 0 0
\(28\) 0.445231 4.30535i 0.0841407 0.813634i
\(29\) 5.12260i 0.951243i −0.879650 0.475622i \(-0.842223\pi\)
0.879650 0.475622i \(-0.157777\pi\)
\(30\) 0 0
\(31\) 7.89544 1.41806 0.709031 0.705177i \(-0.249132\pi\)
0.709031 + 0.705177i \(0.249132\pi\)
\(32\) −0.761813 5.60532i −0.134671 0.990890i
\(33\) 0 0
\(34\) 4.61460 + 2.19632i 0.791398 + 0.376665i
\(35\) −4.82463 0.375125i −0.815512 0.0634078i
\(36\) 0 0
\(37\) 4.21539 + 4.21539i 0.693005 + 0.693005i 0.962892 0.269887i \(-0.0869863\pi\)
−0.269887 + 0.962892i \(0.586986\pi\)
\(38\) 4.71990 1.67585i 0.765669 0.271858i
\(39\) 0 0
\(40\) −6.24324 + 1.01094i −0.987142 + 0.159844i
\(41\) 12.4074i 1.93771i 0.247638 + 0.968853i \(0.420346\pi\)
−0.247638 + 0.968853i \(0.579654\pi\)
\(42\) 0 0
\(43\) −5.67823 + 5.67823i −0.865922 + 0.865922i −0.992018 0.126096i \(-0.959755\pi\)
0.126096 + 0.992018i \(0.459755\pi\)
\(44\) −4.22940 + 3.43663i −0.637605 + 0.518091i
\(45\) 0 0
\(46\) −0.538098 + 1.13058i −0.0793383 + 0.166695i
\(47\) −9.45505 9.45505i −1.37916 1.37916i −0.846037 0.533124i \(-0.821018\pi\)
−0.533124 0.846037i \(-0.678982\pi\)
\(48\) 0 0
\(49\) 2.31644i 0.330920i
\(50\) 1.30753 + 6.94913i 0.184913 + 0.982755i
\(51\) 0 0
\(52\) −0.249520 + 2.41284i −0.0346022 + 0.334601i
\(53\) 6.46657 + 6.46657i 0.888252 + 0.888252i 0.994355 0.106103i \(-0.0338373\pi\)
−0.106103 + 0.994355i \(0.533837\pi\)
\(54\) 0 0
\(55\) 3.96136 + 4.62930i 0.534149 + 0.624214i
\(56\) −1.44388 5.94842i −0.192947 0.794891i
\(57\) 0 0
\(58\) −2.42396 6.82690i −0.318281 0.896416i
\(59\) 2.51407i 0.327304i 0.986518 + 0.163652i \(0.0523274\pi\)
−0.986518 + 0.163652i \(0.947673\pi\)
\(60\) 0 0
\(61\) 9.49179i 1.21530i 0.794205 + 0.607649i \(0.207887\pi\)
−0.794205 + 0.607649i \(0.792113\pi\)
\(62\) 10.5223 3.73603i 1.33633 0.474477i
\(63\) 0 0
\(64\) −3.66765 7.10974i −0.458456 0.888717i
\(65\) 2.70386 + 0.210231i 0.335373 + 0.0260760i
\(66\) 0 0
\(67\) −9.91318 9.91318i −1.21109 1.21109i −0.970669 0.240418i \(-0.922715\pi\)
−0.240418 0.970669i \(-0.577285\pi\)
\(68\) 7.18916 + 0.743456i 0.871814 + 0.0901573i
\(69\) 0 0
\(70\) −6.60730 + 1.78303i −0.789723 + 0.213113i
\(71\) 2.19671i 0.260702i 0.991468 + 0.130351i \(0.0416104\pi\)
−0.991468 + 0.130351i \(0.958390\pi\)
\(72\) 0 0
\(73\) −5.71276 5.71276i −0.668628 0.668628i 0.288771 0.957398i \(-0.406754\pi\)
−0.957398 + 0.288771i \(0.906754\pi\)
\(74\) 7.61252 + 3.62318i 0.884938 + 0.421186i
\(75\) 0 0
\(76\) 5.49722 4.46681i 0.630575 0.512378i
\(77\) −4.16973 + 4.16973i −0.475185 + 0.475185i
\(78\) 0 0
\(79\) 12.7576i 1.43534i −0.696384 0.717670i \(-0.745209\pi\)
0.696384 0.717670i \(-0.254791\pi\)
\(80\) −7.84200 + 4.30151i −0.876763 + 0.480924i
\(81\) 0 0
\(82\) 5.87103 + 16.5353i 0.648347 + 1.82602i
\(83\) 3.58072 + 3.58072i 0.393035 + 0.393035i 0.875768 0.482733i \(-0.160356\pi\)
−0.482733 + 0.875768i \(0.660356\pi\)
\(84\) 0 0
\(85\) 0.626392 8.05627i 0.0679418 0.873826i
\(86\) −4.88051 + 10.2543i −0.526279 + 1.10575i
\(87\) 0 0
\(88\) −4.01035 + 6.58130i −0.427504 + 0.701569i
\(89\) 10.2214 1.08347 0.541734 0.840550i \(-0.317768\pi\)
0.541734 + 0.840550i \(0.317768\pi\)
\(90\) 0 0
\(91\) 2.62480i 0.275154i
\(92\) −0.182147 + 1.76135i −0.0189901 + 0.183633i
\(93\) 0 0
\(94\) −17.0748 8.12673i −1.76113 0.838208i
\(95\) −5.14884 6.01700i −0.528259 0.617331i
\(96\) 0 0
\(97\) −1.29731 + 1.29731i −0.131722 + 0.131722i −0.769894 0.638172i \(-0.779691\pi\)
0.638172 + 0.769894i \(0.279691\pi\)
\(98\) 1.09611 + 3.08712i 0.110724 + 0.311846i
\(99\) 0 0
\(100\) 5.03080 + 8.64240i 0.503080 + 0.864240i
\(101\) 5.82360 0.579470 0.289735 0.957107i \(-0.406433\pi\)
0.289735 + 0.957107i \(0.406433\pi\)
\(102\) 0 0
\(103\) −3.08360 3.08360i −0.303836 0.303836i 0.538677 0.842513i \(-0.318924\pi\)
−0.842513 + 0.538677i \(0.818924\pi\)
\(104\) 0.809193 + 3.33367i 0.0793479 + 0.326893i
\(105\) 0 0
\(106\) 11.6779 + 5.55810i 1.13426 + 0.539850i
\(107\) −6.49670 + 6.49670i −0.628060 + 0.628060i −0.947580 0.319520i \(-0.896478\pi\)
0.319520 + 0.947580i \(0.396478\pi\)
\(108\) 0 0
\(109\) −5.41031 −0.518213 −0.259107 0.965849i \(-0.583428\pi\)
−0.259107 + 0.965849i \(0.583428\pi\)
\(110\) 7.46984 + 4.29500i 0.712221 + 0.409512i
\(111\) 0 0
\(112\) −4.73899 7.24424i −0.447793 0.684516i
\(113\) −0.358788 + 0.358788i −0.0337519 + 0.0337519i −0.723781 0.690029i \(-0.757598\pi\)
0.690029 + 0.723781i \(0.257598\pi\)
\(114\) 0 0
\(115\) 1.97379 + 0.153466i 0.184057 + 0.0143108i
\(116\) −6.46082 7.95122i −0.599873 0.738253i
\(117\) 0 0
\(118\) 1.18963 + 3.35050i 0.109514 + 0.308439i
\(119\) 7.82071 0.716923
\(120\) 0 0
\(121\) −3.57545 −0.325041
\(122\) 4.49141 + 12.6497i 0.406633 + 1.14525i
\(123\) 0 0
\(124\) 12.2552 9.95803i 1.10055 0.894258i
\(125\) 9.51623 5.86868i 0.851157 0.524911i
\(126\) 0 0
\(127\) −0.916401 + 0.916401i −0.0813174 + 0.0813174i −0.746596 0.665278i \(-0.768313\pi\)
0.665278 + 0.746596i \(0.268313\pi\)
\(128\) −8.25212 7.73967i −0.729392 0.684096i
\(129\) 0 0
\(130\) 3.70292 0.999263i 0.324768 0.0876412i
\(131\) 19.5355 1.70683 0.853413 0.521235i \(-0.174529\pi\)
0.853413 + 0.521235i \(0.174529\pi\)
\(132\) 0 0
\(133\) 5.41968 5.41968i 0.469945 0.469945i
\(134\) −17.9021 8.52050i −1.54651 0.736059i
\(135\) 0 0
\(136\) 9.93280 2.41103i 0.851730 0.206744i
\(137\) −7.66611 7.66611i −0.654960 0.654960i 0.299223 0.954183i \(-0.403273\pi\)
−0.954183 + 0.299223i \(0.903273\pi\)
\(138\) 0 0
\(139\) 14.7210 1.24862 0.624308 0.781178i \(-0.285381\pi\)
0.624308 + 0.781178i \(0.285381\pi\)
\(140\) −7.96185 + 5.50275i −0.672899 + 0.465067i
\(141\) 0 0
\(142\) 1.03946 + 2.92756i 0.0872296 + 0.245676i
\(143\) 2.33684 2.33684i 0.195416 0.195416i
\(144\) 0 0
\(145\) −8.70304 + 7.44731i −0.722748 + 0.618466i
\(146\) −10.3166 4.91019i −0.853809 0.406370i
\(147\) 0 0
\(148\) 11.8597 + 1.22645i 0.974859 + 0.100813i
\(149\) 15.6300i 1.28046i −0.768182 0.640231i \(-0.778838\pi\)
0.768182 0.640231i \(-0.221162\pi\)
\(150\) 0 0
\(151\) −17.5889 −1.43136 −0.715682 0.698426i \(-0.753884\pi\)
−0.715682 + 0.698426i \(0.753884\pi\)
\(152\) 5.21251 8.55415i 0.422791 0.693833i
\(153\) 0 0
\(154\) −3.58394 + 7.53008i −0.288802 + 0.606791i
\(155\) −11.4785 13.4139i −0.921975 1.07743i
\(156\) 0 0
\(157\) −7.60352 7.60352i −0.606827 0.606827i 0.335288 0.942116i \(-0.391166\pi\)
−0.942116 + 0.335288i \(0.891166\pi\)
\(158\) −6.03674 17.0020i −0.480257 1.35261i
\(159\) 0 0
\(160\) −8.41562 + 9.44338i −0.665313 + 0.746565i
\(161\) 1.91608i 0.151008i
\(162\) 0 0
\(163\) 8.53586 8.53586i 0.668580 0.668580i −0.288807 0.957387i \(-0.593259\pi\)
0.957387 + 0.288807i \(0.0932586\pi\)
\(164\) 15.6487 + 19.2585i 1.22195 + 1.50384i
\(165\) 0 0
\(166\) 6.46639 + 3.07767i 0.501889 + 0.238874i
\(167\) −6.11022 6.11022i −0.472823 0.472823i 0.430004 0.902827i \(-0.358512\pi\)
−0.902827 + 0.430004i \(0.858512\pi\)
\(168\) 0 0
\(169\) 11.5290i 0.886845i
\(170\) −2.97735 11.0330i −0.228352 0.846193i
\(171\) 0 0
\(172\) −1.65206 + 15.9753i −0.125968 + 1.21810i
\(173\) −0.593720 0.593720i −0.0451397 0.0451397i 0.684177 0.729316i \(-0.260162\pi\)
−0.729316 + 0.684177i \(0.760162\pi\)
\(174\) 0 0
\(175\) 6.37680 + 8.74217i 0.482041 + 0.660846i
\(176\) −2.23040 + 10.6686i −0.168123 + 0.804173i
\(177\) 0 0
\(178\) 13.6221 4.83666i 1.02102 0.362523i
\(179\) 11.3935i 0.851593i 0.904819 + 0.425796i \(0.140006\pi\)
−0.904819 + 0.425796i \(0.859994\pi\)
\(180\) 0 0
\(181\) 7.31410i 0.543653i 0.962346 + 0.271827i \(0.0876277\pi\)
−0.962346 + 0.271827i \(0.912372\pi\)
\(182\) 1.24203 + 3.49808i 0.0920652 + 0.259295i
\(183\) 0 0
\(184\) 0.590702 + 2.43354i 0.0435471 + 0.179403i
\(185\) 1.03333 13.2901i 0.0759722 0.977108i
\(186\) 0 0
\(187\) −6.96270 6.96270i −0.509163 0.509163i
\(188\) −26.6011 2.75091i −1.94008 0.200631i
\(189\) 0 0
\(190\) −9.70904 5.58249i −0.704368 0.404997i
\(191\) 1.32855i 0.0961302i −0.998844 0.0480651i \(-0.984695\pi\)
0.998844 0.0480651i \(-0.0153055\pi\)
\(192\) 0 0
\(193\) −11.5366 11.5366i −0.830423 0.830423i 0.157152 0.987574i \(-0.449769\pi\)
−0.987574 + 0.157152i \(0.949769\pi\)
\(194\) −1.11506 + 2.34280i −0.0800563 + 0.168203i
\(195\) 0 0
\(196\) 2.92158 + 3.59554i 0.208684 + 0.256824i
\(197\) −16.1999 + 16.1999i −1.15420 + 1.15420i −0.168494 + 0.985703i \(0.553890\pi\)
−0.985703 + 0.168494i \(0.946110\pi\)
\(198\) 0 0
\(199\) 6.09388i 0.431984i 0.976395 + 0.215992i \(0.0692985\pi\)
−0.976395 + 0.215992i \(0.930702\pi\)
\(200\) 10.7940 + 9.13721i 0.763254 + 0.646099i
\(201\) 0 0
\(202\) 7.76112 2.75566i 0.546071 0.193888i
\(203\) −7.83906 7.83906i −0.550194 0.550194i
\(204\) 0 0
\(205\) 21.0795 18.0380i 1.47225 1.25983i
\(206\) −5.56864 2.65039i −0.387986 0.184662i
\(207\) 0 0
\(208\) 2.65587 + 4.05988i 0.184151 + 0.281502i
\(209\) −9.65017 −0.667516
\(210\) 0 0
\(211\) 24.9318i 1.71637i −0.513338 0.858186i \(-0.671591\pi\)
0.513338 0.858186i \(-0.328409\pi\)
\(212\) 18.1932 + 1.88142i 1.24951 + 0.129217i
\(213\) 0 0
\(214\) −5.58399 + 11.7323i −0.381714 + 0.802005i
\(215\) 17.9021 + 1.39193i 1.22091 + 0.0949286i
\(216\) 0 0
\(217\) 12.0823 12.0823i 0.820200 0.820200i
\(218\) −7.21032 + 2.56010i −0.488345 + 0.173392i
\(219\) 0 0
\(220\) 11.9874 + 2.18931i 0.808191 + 0.147603i
\(221\) −4.38295 −0.294829
\(222\) 0 0
\(223\) −5.42573 5.42573i −0.363334 0.363334i 0.501705 0.865039i \(-0.332706\pi\)
−0.865039 + 0.501705i \(0.832706\pi\)
\(224\) −9.74355 7.41196i −0.651018 0.495233i
\(225\) 0 0
\(226\) −0.308383 + 0.647931i −0.0205133 + 0.0430998i
\(227\) 8.15485 8.15485i 0.541256 0.541256i −0.382641 0.923897i \(-0.624985\pi\)
0.923897 + 0.382641i \(0.124985\pi\)
\(228\) 0 0
\(229\) −14.5344 −0.960462 −0.480231 0.877142i \(-0.659447\pi\)
−0.480231 + 0.877142i \(0.659447\pi\)
\(230\) 2.70309 0.729451i 0.178237 0.0480986i
\(231\) 0 0
\(232\) −12.3728 7.53942i −0.812313 0.494987i
\(233\) 2.40471 2.40471i 0.157538 0.157538i −0.623937 0.781475i \(-0.714468\pi\)
0.781475 + 0.623937i \(0.214468\pi\)
\(234\) 0 0
\(235\) −2.31775 + 29.8095i −0.151194 + 1.94456i
\(236\) 3.17084 + 3.90230i 0.206404 + 0.254018i
\(237\) 0 0
\(238\) 10.4227 3.70067i 0.675601 0.239879i
\(239\) 6.79965 0.439833 0.219917 0.975519i \(-0.429422\pi\)
0.219917 + 0.975519i \(0.429422\pi\)
\(240\) 0 0
\(241\) 16.2108 1.04423 0.522114 0.852876i \(-0.325143\pi\)
0.522114 + 0.852876i \(0.325143\pi\)
\(242\) −4.76501 + 1.69187i −0.306307 + 0.108757i
\(243\) 0 0
\(244\) 11.9714 + 14.7330i 0.766391 + 0.943184i
\(245\) 3.93551 3.36767i 0.251430 0.215153i
\(246\) 0 0
\(247\) −3.03734 + 3.03734i −0.193261 + 0.193261i
\(248\) 11.6205 19.0701i 0.737900 1.21095i
\(249\) 0 0
\(250\) 9.90529 12.3242i 0.626466 0.779449i
\(251\) 9.56946 0.604019 0.302009 0.953305i \(-0.402343\pi\)
0.302009 + 0.953305i \(0.402343\pi\)
\(252\) 0 0
\(253\) 1.70587 1.70587i 0.107247 0.107247i
\(254\) −0.787658 + 1.65492i −0.0494220 + 0.103839i
\(255\) 0 0
\(256\) −14.6599 6.40985i −0.916246 0.400616i
\(257\) −5.61999 5.61999i −0.350566 0.350566i 0.509754 0.860320i \(-0.329736\pi\)
−0.860320 + 0.509754i \(0.829736\pi\)
\(258\) 0 0
\(259\) 12.9015 0.801661
\(260\) 4.46205 3.08390i 0.276724 0.191255i
\(261\) 0 0
\(262\) 26.0350 9.24399i 1.60845 0.571096i
\(263\) −16.0240 + 16.0240i −0.988080 + 0.988080i −0.999930 0.0118502i \(-0.996228\pi\)
0.0118502 + 0.999930i \(0.496228\pi\)
\(264\) 0 0
\(265\) 1.58518 20.3876i 0.0973766 1.25240i
\(266\) 4.65828 9.78734i 0.285617 0.600100i
\(267\) 0 0
\(268\) −27.8900 2.88420i −1.70365 0.176180i
\(269\) 8.90392i 0.542882i 0.962455 + 0.271441i \(0.0875001\pi\)
−0.962455 + 0.271441i \(0.912500\pi\)
\(270\) 0 0
\(271\) −14.0162 −0.851422 −0.425711 0.904859i \(-0.639976\pi\)
−0.425711 + 0.904859i \(0.639976\pi\)
\(272\) 12.0966 7.91326i 0.733463 0.479812i
\(273\) 0 0
\(274\) −13.8442 6.58912i −0.836356 0.398063i
\(275\) 2.10586 13.4603i 0.126988 0.811685i
\(276\) 0 0
\(277\) 2.00404 + 2.00404i 0.120411 + 0.120411i 0.764745 0.644333i \(-0.222865\pi\)
−0.644333 + 0.764745i \(0.722865\pi\)
\(278\) 19.6186 6.96580i 1.17665 0.417781i
\(279\) 0 0
\(280\) −8.00692 + 11.1010i −0.478505 + 0.663410i
\(281\) 9.33618i 0.556950i −0.960444 0.278475i \(-0.910171\pi\)
0.960444 0.278475i \(-0.0898289\pi\)
\(282\) 0 0
\(283\) −22.3583 + 22.3583i −1.32906 + 1.32906i −0.422877 + 0.906187i \(0.638980\pi\)
−0.906187 + 0.422877i \(0.861020\pi\)
\(284\) 2.77058 + 3.40971i 0.164404 + 0.202329i
\(285\) 0 0
\(286\) 2.00854 4.22007i 0.118767 0.249538i
\(287\) 18.9868 + 18.9868i 1.12076 + 1.12076i
\(288\) 0 0
\(289\) 3.94082i 0.231813i
\(290\) −8.07456 + 14.0432i −0.474154 + 0.824646i
\(291\) 0 0
\(292\) −16.0724 1.66210i −0.940566 0.0972672i
\(293\) 5.84966 + 5.84966i 0.341741 + 0.341741i 0.857021 0.515281i \(-0.172312\pi\)
−0.515281 + 0.857021i \(0.672312\pi\)
\(294\) 0 0
\(295\) 4.27127 3.65499i 0.248683 0.212802i
\(296\) 16.3857 3.97737i 0.952401 0.231180i
\(297\) 0 0
\(298\) −7.39596 20.8302i −0.428437 1.20666i
\(299\) 1.07382i 0.0621009i
\(300\) 0 0
\(301\) 17.3787i 1.00169i
\(302\) −23.4407 + 8.32287i −1.34886 + 0.478927i
\(303\) 0 0
\(304\) 2.89899 13.8666i 0.166269 0.795305i
\(305\) 16.1261 13.7993i 0.923375 0.790145i
\(306\) 0 0
\(307\) −6.13875 6.13875i −0.350357 0.350357i 0.509886 0.860242i \(-0.329688\pi\)
−0.860242 + 0.509886i \(0.829688\pi\)
\(308\) −1.21317 + 11.7312i −0.0691266 + 0.668448i
\(309\) 0 0
\(310\) −21.6447 12.4453i −1.22934 0.706844i
\(311\) 13.0614i 0.740642i 0.928904 + 0.370321i \(0.120752\pi\)
−0.928904 + 0.370321i \(0.879248\pi\)
\(312\) 0 0
\(313\) 22.0110 + 22.0110i 1.24414 + 1.24414i 0.958269 + 0.285869i \(0.0922822\pi\)
0.285869 + 0.958269i \(0.407718\pi\)
\(314\) −13.7311 6.53532i −0.774892 0.368810i
\(315\) 0 0
\(316\) −16.0903 19.8021i −0.905153 1.11396i
\(317\) −6.28577 + 6.28577i −0.353044 + 0.353044i −0.861241 0.508197i \(-0.830312\pi\)
0.508197 + 0.861241i \(0.330312\pi\)
\(318\) 0 0
\(319\) 13.9581i 0.781502i
\(320\) −6.74700 + 16.5674i −0.377169 + 0.926145i
\(321\) 0 0
\(322\) 0.906666 + 2.55356i 0.0505265 + 0.142304i
\(323\) 9.04989 + 9.04989i 0.503549 + 0.503549i
\(324\) 0 0
\(325\) −3.57374 4.89936i −0.198236 0.271768i
\(326\) 7.33668 15.4148i 0.406341 0.853748i
\(327\) 0 0
\(328\) 29.9679 + 18.2611i 1.65470 + 1.00830i
\(329\) −28.9379 −1.59540
\(330\) 0 0
\(331\) 26.2733i 1.44411i 0.691836 + 0.722055i \(0.256802\pi\)
−0.691836 + 0.722055i \(0.743198\pi\)
\(332\) 10.0741 + 1.04180i 0.552887 + 0.0571760i
\(333\) 0 0
\(334\) −11.0344 5.25181i −0.603775 0.287366i
\(335\) −2.43006 + 31.2539i −0.132768 + 1.70758i
\(336\) 0 0
\(337\) 16.4860 16.4860i 0.898047 0.898047i −0.0972161 0.995263i \(-0.530994\pi\)
0.995263 + 0.0972161i \(0.0309938\pi\)
\(338\) 5.45539 + 15.3647i 0.296734 + 0.835729i
\(339\) 0 0
\(340\) −9.18861 13.2949i −0.498322 0.721015i
\(341\) −21.5135 −1.16502
\(342\) 0 0
\(343\) 14.2568 + 14.2568i 0.769797 + 0.769797i
\(344\) 5.35762 + 22.0720i 0.288863 + 1.19004i
\(345\) 0 0
\(346\) −1.07219 0.510310i −0.0576415 0.0274344i
\(347\) −2.85611 + 2.85611i −0.153324 + 0.153324i −0.779601 0.626277i \(-0.784578\pi\)
0.626277 + 0.779601i \(0.284578\pi\)
\(348\) 0 0
\(349\) −19.3216 −1.03426 −0.517130 0.855907i \(-0.673000\pi\)
−0.517130 + 0.855907i \(0.673000\pi\)
\(350\) 12.6351 + 8.63326i 0.675373 + 0.461467i
\(351\) 0 0
\(352\) 2.07579 + 15.2734i 0.110640 + 0.814075i
\(353\) −17.0194 + 17.0194i −0.905850 + 0.905850i −0.995934 0.0900845i \(-0.971286\pi\)
0.0900845 + 0.995934i \(0.471286\pi\)
\(354\) 0 0
\(355\) 3.73210 3.19361i 0.198079 0.169499i
\(356\) 15.8655 12.8917i 0.840872 0.683256i
\(357\) 0 0
\(358\) 5.39129 + 15.1842i 0.284939 + 0.802509i
\(359\) 14.6210 0.771665 0.385832 0.922569i \(-0.373914\pi\)
0.385832 + 0.922569i \(0.373914\pi\)
\(360\) 0 0
\(361\) −6.45703 −0.339844
\(362\) 3.46095 + 9.74751i 0.181904 + 0.512318i
\(363\) 0 0
\(364\) 3.31050 + 4.07418i 0.173517 + 0.213545i
\(365\) −1.40039 + 18.0110i −0.0732998 + 0.942737i
\(366\) 0 0
\(367\) −8.21722 + 8.21722i −0.428935 + 0.428935i −0.888266 0.459330i \(-0.848089\pi\)
0.459330 + 0.888266i \(0.348089\pi\)
\(368\) 1.93875 + 2.96367i 0.101064 + 0.154492i
\(369\) 0 0
\(370\) −4.91161 18.2007i −0.255342 0.946210i
\(371\) 19.7914 1.02752
\(372\) 0 0
\(373\) −9.54965 + 9.54965i −0.494462 + 0.494462i −0.909709 0.415247i \(-0.863695\pi\)
0.415247 + 0.909709i \(0.363695\pi\)
\(374\) −12.5739 5.98453i −0.650180 0.309453i
\(375\) 0 0
\(376\) −36.7530 + 8.92119i −1.89539 + 0.460075i
\(377\) 4.39323 + 4.39323i 0.226263 + 0.226263i
\(378\) 0 0
\(379\) 9.71237 0.498891 0.249445 0.968389i \(-0.419752\pi\)
0.249445 + 0.968389i \(0.419752\pi\)
\(380\) −15.5808 2.84559i −0.799279 0.145976i
\(381\) 0 0
\(382\) −0.628653 1.77056i −0.0321647 0.0905895i
\(383\) −3.97088 + 3.97088i −0.202903 + 0.202903i −0.801242 0.598340i \(-0.795827\pi\)
0.598340 + 0.801242i \(0.295827\pi\)
\(384\) 0 0
\(385\) 13.1462 + 1.02214i 0.669991 + 0.0520932i
\(386\) −20.8338 9.91585i −1.06041 0.504703i
\(387\) 0 0
\(388\) −0.377447 + 3.64989i −0.0191620 + 0.185295i
\(389\) 15.9006i 0.806194i −0.915157 0.403097i \(-0.867934\pi\)
0.915157 0.403097i \(-0.132066\pi\)
\(390\) 0 0
\(391\) −3.19950 −0.161806
\(392\) 5.59496 + 3.40932i 0.282588 + 0.172197i
\(393\) 0 0
\(394\) −13.9240 + 29.2553i −0.701483 + 1.47386i
\(395\) −21.6745 + 18.5471i −1.09056 + 0.933208i
\(396\) 0 0
\(397\) 17.2354 + 17.2354i 0.865019 + 0.865019i 0.991916 0.126897i \(-0.0405017\pi\)
−0.126897 + 0.991916i \(0.540502\pi\)
\(398\) 2.88356 + 8.12132i 0.144540 + 0.407085i
\(399\) 0 0
\(400\) 18.7089 + 7.06956i 0.935443 + 0.353478i
\(401\) 13.1249i 0.655428i −0.944777 0.327714i \(-0.893722\pi\)
0.944777 0.327714i \(-0.106278\pi\)
\(402\) 0 0
\(403\) −6.77127 + 6.77127i −0.337301 + 0.337301i
\(404\) 9.03931 7.34495i 0.449722 0.365425i
\(405\) 0 0
\(406\) −14.1565 6.73777i −0.702574 0.334390i
\(407\) −11.4861 11.4861i −0.569345 0.569345i
\(408\) 0 0
\(409\) 11.2852i 0.558017i 0.960289 + 0.279008i \(0.0900058\pi\)
−0.960289 + 0.279008i \(0.909994\pi\)
\(410\) 19.5573 34.0138i 0.965864 1.67982i
\(411\) 0 0
\(412\) −8.67547 0.897160i −0.427410 0.0441999i
\(413\) 3.84725 + 3.84725i 0.189311 + 0.189311i
\(414\) 0 0
\(415\) 0.877757 11.2892i 0.0430874 0.554163i
\(416\) 5.46057 + 4.15388i 0.267726 + 0.203661i
\(417\) 0 0
\(418\) −12.8608 + 4.56635i −0.629042 + 0.223348i
\(419\) 4.75266i 0.232183i 0.993239 + 0.116091i \(0.0370365\pi\)
−0.993239 + 0.116091i \(0.962963\pi\)
\(420\) 0 0
\(421\) 0.283341i 0.0138092i −0.999976 0.00690460i \(-0.997802\pi\)
0.999976 0.00690460i \(-0.00219782\pi\)
\(422\) −11.7974 33.2266i −0.574290 1.61744i
\(423\) 0 0
\(424\) 25.1364 6.10145i 1.22073 0.296313i
\(425\) −14.5978 + 10.6481i −0.708100 + 0.516510i
\(426\) 0 0
\(427\) 14.5252 + 14.5252i 0.702922 + 0.702922i
\(428\) −1.89019 + 18.2780i −0.0913657 + 0.883499i
\(429\) 0 0
\(430\) 24.5168 6.61606i 1.18231 0.319055i
\(431\) 10.1002i 0.486508i −0.969963 0.243254i \(-0.921785\pi\)
0.969963 0.243254i \(-0.0782149\pi\)
\(432\) 0 0
\(433\) 5.65232 + 5.65232i 0.271633 + 0.271633i 0.829757 0.558124i \(-0.188479\pi\)
−0.558124 + 0.829757i \(0.688479\pi\)
\(434\) 10.3849 21.8193i 0.498490 1.04736i
\(435\) 0 0
\(436\) −8.39779 + 6.82369i −0.402181 + 0.326795i
\(437\) −2.21723 + 2.21723i −0.106064 + 0.106064i
\(438\) 0 0
\(439\) 17.0307i 0.812831i −0.913688 0.406415i \(-0.866779\pi\)
0.913688 0.406415i \(-0.133221\pi\)
\(440\) 17.0116 2.75461i 0.810995 0.131321i
\(441\) 0 0
\(442\) −5.84116 + 2.07396i −0.277836 + 0.0986484i
\(443\) −10.8863 10.8863i −0.517226 0.517226i 0.399505 0.916731i \(-0.369182\pi\)
−0.916731 + 0.399505i \(0.869182\pi\)
\(444\) 0 0
\(445\) −14.8600 17.3657i −0.704434 0.823211i
\(446\) −9.79827 4.66348i −0.463961 0.220822i
\(447\) 0 0
\(448\) −16.4925 5.26739i −0.779197 0.248861i
\(449\) −10.3509 −0.488488 −0.244244 0.969714i \(-0.578540\pi\)
−0.244244 + 0.969714i \(0.578540\pi\)
\(450\) 0 0
\(451\) 33.8076i 1.59194i
\(452\) −0.104388 + 1.00942i −0.00490999 + 0.0474792i
\(453\) 0 0
\(454\) 7.00919 14.7268i 0.328958 0.691161i
\(455\) 4.45940 3.81598i 0.209060 0.178896i
\(456\) 0 0
\(457\) 6.38449 6.38449i 0.298654 0.298654i −0.541833 0.840486i \(-0.682269\pi\)
0.840486 + 0.541833i \(0.182269\pi\)
\(458\) −19.3700 + 6.87753i −0.905103 + 0.321366i
\(459\) 0 0
\(460\) 3.25724 2.25121i 0.151870 0.104963i
\(461\) −6.07751 −0.283058 −0.141529 0.989934i \(-0.545202\pi\)
−0.141529 + 0.989934i \(0.545202\pi\)
\(462\) 0 0
\(463\) 22.2374 + 22.2374i 1.03346 + 1.03346i 0.999421 + 0.0340371i \(0.0108364\pi\)
0.0340371 + 0.999421i \(0.489164\pi\)
\(464\) −20.0568 4.19313i −0.931113 0.194661i
\(465\) 0 0
\(466\) 2.06688 4.34265i 0.0957464 0.201169i
\(467\) 17.6001 17.6001i 0.814434 0.814434i −0.170861 0.985295i \(-0.554655\pi\)
0.985295 + 0.170861i \(0.0546549\pi\)
\(468\) 0 0
\(469\) −30.3400 −1.40097
\(470\) 11.0167 + 40.8239i 0.508161 + 1.88307i
\(471\) 0 0
\(472\) 6.07231 + 3.70019i 0.279501 + 0.170315i
\(473\) 15.4721 15.4721i 0.711406 0.711406i
\(474\) 0 0
\(475\) −2.73713 + 17.4952i −0.125588 + 0.802735i
\(476\) 12.1392 9.86378i 0.556399 0.452106i
\(477\) 0 0
\(478\) 9.06191 3.21752i 0.414482 0.147166i
\(479\) 2.47636 0.113148 0.0565740 0.998398i \(-0.481982\pi\)
0.0565740 + 0.998398i \(0.481982\pi\)
\(480\) 0 0
\(481\) −7.23038 −0.329677
\(482\) 21.6041 7.67076i 0.984041 0.349394i
\(483\) 0 0
\(484\) −5.54976 + 4.50950i −0.252262 + 0.204977i
\(485\) 4.09012 + 0.318015i 0.185723 + 0.0144403i
\(486\) 0 0
\(487\) 12.3734 12.3734i 0.560694 0.560694i −0.368811 0.929505i \(-0.620235\pi\)
0.929505 + 0.368811i \(0.120235\pi\)
\(488\) 22.9258 + 13.9700i 1.03780 + 0.632390i
\(489\) 0 0
\(490\) 3.65131 6.35034i 0.164949 0.286879i
\(491\) −37.1551 −1.67679 −0.838394 0.545064i \(-0.816505\pi\)
−0.838394 + 0.545064i \(0.816505\pi\)
\(492\) 0 0
\(493\) 13.0898 13.0898i 0.589536 0.589536i
\(494\) −2.61063 + 5.48510i −0.117458 + 0.246787i
\(495\) 0 0
\(496\) 6.46284 30.9134i 0.290190 1.38805i
\(497\) 3.36160 + 3.36160i 0.150789 + 0.150789i
\(498\) 0 0
\(499\) 34.8644 1.56075 0.780373 0.625315i \(-0.215029\pi\)
0.780373 + 0.625315i \(0.215029\pi\)
\(500\) 7.36914 21.1115i 0.329558 0.944135i
\(501\) 0 0
\(502\) 12.7532 4.52816i 0.569204 0.202102i
\(503\) 1.25041 1.25041i 0.0557529 0.0557529i −0.678681 0.734434i \(-0.737448\pi\)
0.734434 + 0.678681i \(0.237448\pi\)
\(504\) 0 0
\(505\) −8.46644 9.89400i −0.376752 0.440277i
\(506\) 1.46621 3.08060i 0.0651811 0.136950i
\(507\) 0 0
\(508\) −0.266623 + 2.57822i −0.0118295 + 0.114390i
\(509\) 38.4393i 1.70379i −0.523711 0.851896i \(-0.675453\pi\)
0.523711 0.851896i \(-0.324547\pi\)
\(510\) 0 0
\(511\) −17.4843 −0.773461
\(512\) −22.5704 1.60549i −0.997480 0.0709535i
\(513\) 0 0
\(514\) −10.1491 4.83045i −0.447657 0.213062i
\(515\) −0.755895 + 9.72185i −0.0333087 + 0.428396i
\(516\) 0 0
\(517\) 25.7631 + 25.7631i 1.13306 + 1.13306i
\(518\) 17.1939 6.10485i 0.755455 0.268232i
\(519\) 0 0
\(520\) 4.48731 6.22131i 0.196781 0.272822i
\(521\) 19.1329i 0.838226i 0.907934 + 0.419113i \(0.137659\pi\)
−0.907934 + 0.419113i \(0.862341\pi\)
\(522\) 0 0
\(523\) −0.870444 + 0.870444i −0.0380619 + 0.0380619i −0.725882 0.687820i \(-0.758568\pi\)
0.687820 + 0.725882i \(0.258568\pi\)
\(524\) 30.3227 24.6389i 1.32465 1.07636i
\(525\) 0 0
\(526\) −13.7728 + 28.9375i −0.600522 + 1.26174i
\(527\) 20.1753 + 20.1753i 0.878849 + 0.878849i
\(528\) 0 0
\(529\) 22.2161i 0.965918i
\(530\) −7.53460 27.9206i −0.327282 1.21279i
\(531\) 0 0
\(532\) 1.57683 15.2478i 0.0683643 0.661078i
\(533\) −10.6408 10.6408i −0.460903 0.460903i
\(534\) 0 0
\(535\) 20.4825 + 1.59256i 0.885538 + 0.0688524i
\(536\) −38.5338 + 9.35345i −1.66441 + 0.404007i
\(537\) 0 0
\(538\) 4.21324 + 11.8663i 0.181646 + 0.511591i
\(539\) 6.31183i 0.271870i
\(540\) 0 0
\(541\) 18.7259i 0.805089i −0.915400 0.402544i \(-0.868126\pi\)
0.915400 0.402544i \(-0.131874\pi\)
\(542\) −18.6794 + 6.63230i −0.802347 + 0.284881i
\(543\) 0 0
\(544\) 12.3767 16.2700i 0.530645 0.697570i
\(545\) 7.86558 + 9.19183i 0.336924 + 0.393735i
\(546\) 0 0
\(547\) −25.7085 25.7085i −1.09922 1.09922i −0.994502 0.104713i \(-0.966608\pi\)
−0.104713 0.994502i \(-0.533392\pi\)
\(548\) −21.5680 2.23042i −0.921340 0.0952790i
\(549\) 0 0
\(550\) −3.56277 18.9350i −0.151917 0.807391i
\(551\) 18.1422i 0.772885i
\(552\) 0 0
\(553\) −19.5228 19.5228i −0.830192 0.830192i
\(554\) 3.61908 + 1.72250i 0.153760 + 0.0731819i
\(555\) 0 0
\(556\) 22.8497 18.5667i 0.969041 0.787401i
\(557\) 4.85098 4.85098i 0.205543 0.205543i −0.596827 0.802370i \(-0.703572\pi\)
0.802370 + 0.596827i \(0.203572\pi\)
\(558\) 0 0
\(559\) 9.73950i 0.411937i
\(560\) −5.41797 + 18.5831i −0.228951 + 0.785278i
\(561\) 0 0
\(562\) −4.41778 12.4423i −0.186353 0.524848i
\(563\) −5.13320 5.13320i −0.216339 0.216339i 0.590615 0.806954i \(-0.298885\pi\)
−0.806954 + 0.590615i \(0.798885\pi\)
\(564\) 0 0
\(565\) 1.13117 + 0.0879511i 0.0475888 + 0.00370013i
\(566\) −19.2172 + 40.3767i −0.807761 + 1.69716i
\(567\) 0 0
\(568\) 5.30579 + 3.23311i 0.222626 + 0.135658i
\(569\) 27.4425 1.15045 0.575224 0.817996i \(-0.304915\pi\)
0.575224 + 0.817996i \(0.304915\pi\)
\(570\) 0 0
\(571\) 7.73020i 0.323499i 0.986832 + 0.161749i \(0.0517136\pi\)
−0.986832 + 0.161749i \(0.948286\pi\)
\(572\) 0.679893 6.57451i 0.0284278 0.274894i
\(573\) 0 0
\(574\) 34.2882 + 16.3194i 1.43116 + 0.681160i
\(575\) −2.60879 3.57648i −0.108794 0.149149i
\(576\) 0 0
\(577\) −9.33858 + 9.33858i −0.388770 + 0.388770i −0.874249 0.485478i \(-0.838645\pi\)
0.485478 + 0.874249i \(0.338645\pi\)
\(578\) −1.86475 5.25193i −0.0775634 0.218452i
\(579\) 0 0
\(580\) −4.11588 + 22.5362i −0.170903 + 0.935765i
\(581\) 10.9591 0.454659
\(582\) 0 0
\(583\) −17.6201 17.6201i −0.729751 0.729751i
\(584\) −22.2062 + 5.39020i −0.918899 + 0.223048i
\(585\) 0 0
\(586\) 10.5638 + 5.02785i 0.436388 + 0.207699i
\(587\) 20.5419 20.5419i 0.847856 0.847856i −0.142010 0.989865i \(-0.545356\pi\)
0.989865 + 0.142010i \(0.0453564\pi\)
\(588\) 0 0
\(589\) 27.9625 1.15218
\(590\) 3.96283 6.89213i 0.163147 0.283744i
\(591\) 0 0
\(592\) 19.9552 13.0542i 0.820155 0.536524i
\(593\) 15.8708 15.8708i 0.651734 0.651734i −0.301676 0.953410i \(-0.597546\pi\)
0.953410 + 0.301676i \(0.0975462\pi\)
\(594\) 0 0
\(595\) −11.3699 13.2870i −0.466119 0.544713i
\(596\) −19.7132 24.2607i −0.807485 0.993757i
\(597\) 0 0
\(598\) −0.508122 1.43109i −0.0207786 0.0585215i
\(599\) −31.5111 −1.28751 −0.643754 0.765232i \(-0.722624\pi\)
−0.643754 + 0.765232i \(0.722624\pi\)
\(600\) 0 0
\(601\) 7.28520 0.297169 0.148585 0.988900i \(-0.452528\pi\)
0.148585 + 0.988900i \(0.452528\pi\)
\(602\) 8.22339 + 23.1606i 0.335160 + 0.943954i
\(603\) 0 0
\(604\) −27.3012 + 22.1838i −1.11087 + 0.902646i
\(605\) 5.19805 + 6.07451i 0.211331 + 0.246964i
\(606\) 0 0
\(607\) −28.1836 + 28.1836i −1.14394 + 1.14394i −0.156213 + 0.987723i \(0.549929\pi\)
−0.987723 + 0.156213i \(0.950071\pi\)
\(608\) −2.69804 19.8518i −0.109420 0.805098i
\(609\) 0 0
\(610\) 14.9615 26.0210i 0.605775 1.05356i
\(611\) 16.2176 0.656095
\(612\) 0 0
\(613\) 24.9782 24.9782i 1.00886 1.00886i 0.00890069 0.999960i \(-0.497167\pi\)
0.999960 0.00890069i \(-0.00283322\pi\)
\(614\) −11.0859 5.27633i −0.447391 0.212935i
\(615\) 0 0
\(616\) 3.93430 + 16.2083i 0.158517 + 0.653050i
\(617\) 19.7928 + 19.7928i 0.796830 + 0.796830i 0.982594 0.185764i \(-0.0594761\pi\)
−0.185764 + 0.982594i \(0.559476\pi\)
\(618\) 0 0
\(619\) −25.0717 −1.00772 −0.503859 0.863786i \(-0.668087\pi\)
−0.503859 + 0.863786i \(0.668087\pi\)
\(620\) −34.7349 6.34378i −1.39499 0.254772i
\(621\) 0 0
\(622\) 6.18049 + 17.4069i 0.247815 + 0.697953i
\(623\) 15.6417 15.6417i 0.626672 0.626672i
\(624\) 0 0
\(625\) −23.8054 7.63561i −0.952216 0.305424i
\(626\) 39.7495 + 18.9188i 1.58871 + 0.756146i
\(627\) 0 0
\(628\) −21.3919 2.21221i −0.853631 0.0882769i
\(629\) 21.5432i 0.858984i
\(630\) 0 0
\(631\) 6.42730 0.255867 0.127933 0.991783i \(-0.459166\pi\)
0.127933 + 0.991783i \(0.459166\pi\)
\(632\) −30.8138 18.7765i −1.22571 0.746890i
\(633\) 0 0
\(634\) −5.40270 + 11.3514i −0.214569 + 0.450822i
\(635\) 2.88919 + 0.224641i 0.114654 + 0.00891460i
\(636\) 0 0
\(637\) −1.98662 1.98662i −0.0787126 0.0787126i
\(638\) 6.60481 + 18.6019i 0.261487 + 0.736458i
\(639\) 0 0
\(640\) −1.15224 + 25.2720i −0.0455462 + 0.998962i
\(641\) 28.9552i 1.14366i −0.820372 0.571830i \(-0.806234\pi\)
0.820372 0.571830i \(-0.193766\pi\)
\(642\) 0 0
\(643\) 20.0962 20.0962i 0.792517 0.792517i −0.189385 0.981903i \(-0.560650\pi\)
0.981903 + 0.189385i \(0.0606495\pi\)
\(644\) 2.41663 + 2.97410i 0.0952286 + 0.117196i
\(645\) 0 0
\(646\) 16.3431 + 7.77849i 0.643011 + 0.306041i
\(647\) −27.5740 27.5740i −1.08405 1.08405i −0.996128 0.0879193i \(-0.971978\pi\)
−0.0879193 0.996128i \(-0.528022\pi\)
\(648\) 0 0
\(649\) 6.85034i 0.268899i
\(650\) −7.08105 4.83833i −0.277742 0.189775i
\(651\) 0 0
\(652\) 2.48347 24.0150i 0.0972603 0.940500i
\(653\) 17.8261 + 17.8261i 0.697590 + 0.697590i 0.963890 0.266300i \(-0.0858013\pi\)
−0.266300 + 0.963890i \(0.585801\pi\)
\(654\) 0 0
\(655\) −28.4010 33.1898i −1.10972 1.29683i
\(656\) 48.5792 + 10.1561i 1.89670 + 0.396529i
\(657\) 0 0
\(658\) −38.5656 + 13.6931i −1.50344 + 0.533812i
\(659\) 37.7533i 1.47066i 0.677709 + 0.735331i \(0.262973\pi\)
−0.677709 + 0.735331i \(0.737027\pi\)
\(660\) 0 0
\(661\) 6.03049i 0.234559i −0.993099 0.117279i \(-0.962583\pi\)
0.993099 0.117279i \(-0.0374173\pi\)
\(662\) 12.4322 + 35.0144i 0.483192 + 1.36087i
\(663\) 0 0
\(664\) 13.9187 3.37854i 0.540151 0.131113i
\(665\) −17.0869 1.32855i −0.662603 0.0515188i
\(666\) 0 0
\(667\) 3.20701 + 3.20701i 0.124176 + 0.124176i
\(668\) −17.1906 1.77774i −0.665126 0.0687830i
\(669\) 0 0
\(670\) 11.5505 + 42.8020i 0.446233 + 1.65358i
\(671\) 25.8632i 0.998439i
\(672\) 0 0
\(673\) 3.75403 + 3.75403i 0.144707 + 0.144707i 0.775749 0.631042i \(-0.217372\pi\)
−0.631042 + 0.775749i \(0.717372\pi\)
\(674\) 14.1699 29.7718i 0.545803 1.14677i
\(675\) 0 0
\(676\) 14.5408 + 17.8951i 0.559262 + 0.688274i
\(677\) 12.0579 12.0579i 0.463421 0.463421i −0.436354 0.899775i \(-0.643730\pi\)
0.899775 + 0.436354i \(0.143730\pi\)
\(678\) 0 0
\(679\) 3.97052i 0.152375i
\(680\) −18.5366 13.3701i −0.710848 0.512721i
\(681\) 0 0
\(682\) −28.6711 + 10.1800i −1.09787 + 0.389811i
\(683\) −18.0083 18.0083i −0.689068 0.689068i 0.272958 0.962026i \(-0.411998\pi\)
−0.962026 + 0.272958i \(0.911998\pi\)
\(684\) 0 0
\(685\) −1.87922 + 24.1694i −0.0718015 + 0.923467i
\(686\) 25.7463 + 12.2539i 0.982997 + 0.467857i
\(687\) 0 0
\(688\) 17.5843 + 26.8802i 0.670396 + 1.02480i
\(689\) −11.0917 −0.422560
\(690\) 0 0
\(691\) 37.0052i 1.40774i −0.710327 0.703872i \(-0.751453\pi\)
0.710327 0.703872i \(-0.248547\pi\)
\(692\) −1.67039 0.172740i −0.0634985 0.00656660i
\(693\) 0 0
\(694\) −2.45486 + 5.15782i −0.0931853 + 0.195788i
\(695\) −21.4015 25.0102i −0.811807 0.948689i
\(696\) 0 0
\(697\) −31.7046 + 31.7046i −1.20090 + 1.20090i
\(698\) −25.7499 + 9.14276i −0.974648 + 0.346058i
\(699\) 0 0
\(700\) 20.9239 + 5.52678i 0.790850 + 0.208893i
\(701\) −10.8810 −0.410968 −0.205484 0.978660i \(-0.565877\pi\)
−0.205484 + 0.978660i \(0.565877\pi\)
\(702\) 0 0
\(703\) 14.9292 + 14.9292i 0.563067 + 0.563067i
\(704\) 9.99361 + 19.3726i 0.376648 + 0.730133i
\(705\) 0 0
\(706\) −14.6284 + 30.7351i −0.550545 + 1.15673i
\(707\) 8.91179 8.91179i 0.335162 0.335162i
\(708\) 0 0
\(709\) 17.9836 0.675389 0.337695 0.941256i \(-0.390353\pi\)
0.337695 + 0.941256i \(0.390353\pi\)
\(710\) 3.46259 6.02212i 0.129949 0.226006i
\(711\) 0 0
\(712\) 15.0438 24.6881i 0.563791 0.925226i
\(713\) −4.94295 + 4.94295i −0.185115 + 0.185115i
\(714\) 0 0
\(715\) −7.36749 0.572838i −0.275529 0.0214229i
\(716\) 14.3700 + 17.6849i 0.537031 + 0.660915i
\(717\) 0 0
\(718\) 19.4854 6.91848i 0.727188 0.258195i
\(719\) −32.0959 −1.19698 −0.598488 0.801132i \(-0.704231\pi\)
−0.598488 + 0.801132i \(0.704231\pi\)
\(720\) 0 0
\(721\) −9.43759 −0.351474
\(722\) −8.60530 + 3.05540i −0.320256 + 0.113710i
\(723\) 0 0
\(724\) 9.22483 + 11.3528i 0.342838 + 0.421925i
\(725\) 25.3052 + 3.95900i 0.939811 + 0.147033i
\(726\) 0 0
\(727\) 15.2813 15.2813i 0.566754 0.566754i −0.364464 0.931218i \(-0.618748\pi\)
0.931218 + 0.364464i \(0.118748\pi\)
\(728\) 6.33977 + 3.86317i 0.234967 + 0.143179i
\(729\) 0 0
\(730\) 6.65629 + 24.6659i 0.246360 + 0.912925i
\(731\) −29.0192 −1.07332
\(732\) 0 0
\(733\) −25.4494 + 25.4494i −0.939996 + 0.939996i −0.998299 0.0583028i \(-0.981431\pi\)
0.0583028 + 0.998299i \(0.481431\pi\)
\(734\) −7.06280 + 14.8394i −0.260693 + 0.547732i
\(735\) 0 0
\(736\) 3.98615 + 3.03228i 0.146931 + 0.111771i
\(737\) 27.0115 + 27.0115i 0.994980 + 0.994980i
\(738\) 0 0
\(739\) −23.6936 −0.871584 −0.435792 0.900047i \(-0.643532\pi\)
−0.435792 + 0.900047i \(0.643532\pi\)
\(740\) −15.1581 21.9320i −0.557222 0.806236i
\(741\) 0 0
\(742\) 26.3761 9.36509i 0.968296 0.343803i
\(743\) 10.4630 10.4630i 0.383852 0.383852i −0.488636 0.872488i \(-0.662505\pi\)
0.872488 + 0.488636i \(0.162505\pi\)
\(744\) 0 0
\(745\) −26.5546 + 22.7232i −0.972886 + 0.832513i
\(746\) −8.20804 + 17.2456i −0.300518 + 0.631407i
\(747\) 0 0
\(748\) −19.5890 2.02577i −0.716246 0.0740695i
\(749\) 19.8836i 0.726532i
\(750\) 0 0
\(751\) 51.4858 1.87874 0.939372 0.342899i \(-0.111409\pi\)
0.939372 + 0.342899i \(0.111409\pi\)
\(752\) −44.7593 + 29.2804i −1.63220 + 1.06775i
\(753\) 0 0
\(754\) 7.93369 + 3.77604i 0.288928 + 0.137515i
\(755\) 25.5710 + 29.8826i 0.930623 + 1.08754i
\(756\) 0 0
\(757\) −20.4014 20.4014i −0.741501 0.741501i 0.231366 0.972867i \(-0.425681\pi\)
−0.972867 + 0.231366i \(0.925681\pi\)
\(758\) 12.9437 4.59579i 0.470136 0.166926i
\(759\) 0 0
\(760\) −22.1111 + 3.58035i −0.802053 + 0.129873i
\(761\) 13.3989i 0.485709i 0.970063 + 0.242855i \(0.0780838\pi\)
−0.970063 + 0.242855i \(0.921916\pi\)
\(762\) 0 0
\(763\) −8.27933 + 8.27933i −0.299732 + 0.299732i
\(764\) −1.67561 2.06215i −0.0606216 0.0746059i
\(765\) 0 0
\(766\) −3.41302 + 7.17097i −0.123317 + 0.259098i
\(767\) −2.15611 2.15611i −0.0778526 0.0778526i
\(768\) 0 0
\(769\) 15.5493i 0.560721i −0.959895 0.280361i \(-0.909546\pi\)
0.959895 0.280361i \(-0.0904540\pi\)
\(770\) 18.0036 4.85841i 0.648804 0.175085i
\(771\) 0 0
\(772\) −32.4573 3.35653i −1.16817 0.120804i
\(773\) −4.70360 4.70360i −0.169177 0.169177i 0.617441 0.786617i \(-0.288170\pi\)
−0.786617 + 0.617441i \(0.788170\pi\)
\(774\) 0 0
\(775\) −6.10198 + 39.0028i −0.219190 + 1.40102i
\(776\) 1.22406 + 5.04281i 0.0439412 + 0.181026i
\(777\) 0 0
\(778\) −7.52401 21.1908i −0.269749 0.759727i
\(779\) 43.9420i 1.57439i
\(780\) 0 0
\(781\) 5.98561i 0.214182i
\(782\) −4.26398 + 1.51397i −0.152480 + 0.0541395i
\(783\) 0 0
\(784\) 9.06966 + 1.89613i 0.323917 + 0.0677189i
\(785\) −1.86388 + 23.9721i −0.0665248 + 0.855601i
\(786\) 0 0
\(787\) 7.45088 + 7.45088i 0.265595 + 0.265595i 0.827322 0.561727i \(-0.189863\pi\)
−0.561727 + 0.827322i \(0.689863\pi\)
\(788\) −4.71330 + 45.5772i −0.167904 + 1.62362i
\(789\) 0 0
\(790\) −20.1093 + 34.9739i −0.715456 + 1.24432i
\(791\) 1.09810i 0.0390439i
\(792\) 0 0
\(793\) −8.14032 8.14032i −0.289071 0.289071i
\(794\) 31.1252 + 14.8140i 1.10459 + 0.525730i
\(795\) 0 0
\(796\) 7.68584 + 9.45883i 0.272417 + 0.335259i
\(797\) 27.5898 27.5898i 0.977280 0.977280i −0.0224677 0.999748i \(-0.507152\pi\)
0.999748 + 0.0224677i \(0.00715228\pi\)
\(798\) 0 0
\(799\) 48.3211i 1.70948i
\(800\) 28.2786 + 0.568782i 0.999798 + 0.0201095i
\(801\) 0 0
\(802\) −6.21058 17.4916i −0.219303 0.617651i
\(803\) 15.5661 + 15.5661i 0.549317 + 0.549317i
\(804\) 0 0
\(805\) 3.25531 2.78562i 0.114735 0.0981802i
\(806\) −5.81999 + 12.2282i −0.205000 + 0.430719i
\(807\) 0 0
\(808\) 8.57115 14.0659i 0.301532 0.494838i
\(809\) 9.93002 0.349121 0.174560 0.984646i \(-0.444150\pi\)
0.174560 + 0.984646i \(0.444150\pi\)
\(810\) 0 0
\(811\) 0.144213i 0.00506400i 0.999997 + 0.00253200i \(0.000805962\pi\)
−0.999997 + 0.00253200i \(0.999194\pi\)
\(812\) −22.0546 2.28074i −0.773964 0.0800383i
\(813\) 0 0
\(814\) −20.7426 9.87244i −0.727028 0.346029i
\(815\) −26.9115 2.09243i −0.942670 0.0732946i
\(816\) 0 0
\(817\) −20.1100 + 20.1100i −0.703562 + 0.703562i
\(818\) 5.34003 + 15.0398i 0.186710 + 0.525854i
\(819\) 0 0
\(820\) 9.96900 54.5846i 0.348133 1.90618i
\(821\) 20.3654 0.710757 0.355379 0.934722i \(-0.384352\pi\)
0.355379 + 0.934722i \(0.384352\pi\)
\(822\) 0 0
\(823\) −31.7594 31.7594i −1.10706 1.10706i −0.993535 0.113529i \(-0.963784\pi\)
−0.113529 0.993535i \(-0.536216\pi\)
\(824\) −11.9863 + 2.90949i −0.417564 + 0.101357i
\(825\) 0 0
\(826\) 6.94771 + 3.30676i 0.241742 + 0.115057i
\(827\) −28.5251 + 28.5251i −0.991916 + 0.991916i −0.999968 0.00805118i \(-0.997437\pi\)
0.00805118 + 0.999968i \(0.497437\pi\)
\(828\) 0 0
\(829\) −54.4189 −1.89005 −0.945024 0.327002i \(-0.893962\pi\)
−0.945024 + 0.327002i \(0.893962\pi\)
\(830\) −4.17212 15.4604i −0.144816 0.536639i
\(831\) 0 0
\(832\) 9.24287 + 2.95200i 0.320439 + 0.102342i
\(833\) −5.91921 + 5.91921i −0.205088 + 0.205088i
\(834\) 0 0
\(835\) −1.49782 + 19.2641i −0.0518343 + 0.666661i
\(836\) −14.9788 + 12.1712i −0.518054 + 0.420949i
\(837\) 0 0
\(838\) 2.24891 + 6.33388i 0.0776872 + 0.218800i
\(839\) 47.3060 1.63318 0.816592 0.577215i \(-0.195861\pi\)
0.816592 + 0.577215i \(0.195861\pi\)
\(840\) 0 0
\(841\) 2.75894 0.0951360
\(842\) −0.134074 0.377609i −0.00462049 0.0130133i
\(843\) 0 0
\(844\) −31.4449 38.6987i −1.08238 1.33206i
\(845\) 19.5871 16.7610i 0.673818 0.576596i
\(846\) 0 0
\(847\) −5.47147 + 5.47147i −0.188002 + 0.188002i
\(848\) 30.6121 20.0257i 1.05123 0.687684i
\(849\) 0 0
\(850\) −14.4160 + 21.0983i −0.494465 + 0.723666i
\(851\) −5.27809 −0.180931
\(852\) 0 0
\(853\) 14.9083 14.9083i 0.510449 0.510449i −0.404215 0.914664i \(-0.632455\pi\)
0.914664 + 0.404215i \(0.132455\pi\)
\(854\) 26.2309 + 12.4846i 0.897601 + 0.427213i
\(855\) 0 0
\(856\) 6.12987 + 25.2535i 0.209515 + 0.863146i
\(857\) −6.64085 6.64085i −0.226847 0.226847i 0.584527 0.811374i \(-0.301280\pi\)
−0.811374 + 0.584527i \(0.801280\pi\)
\(858\) 0 0
\(859\) 3.27984 0.111907 0.0559534 0.998433i \(-0.482180\pi\)
0.0559534 + 0.998433i \(0.482180\pi\)
\(860\) 29.5429 20.4183i 1.00741 0.696259i
\(861\) 0 0
\(862\) −4.77929 13.4605i −0.162783 0.458467i
\(863\) 11.7285 11.7285i 0.399243 0.399243i −0.478723 0.877966i \(-0.658900\pi\)
0.877966 + 0.478723i \(0.158900\pi\)
\(864\) 0 0
\(865\) −0.145541 + 1.87186i −0.00494854 + 0.0636451i
\(866\) 10.2075 + 4.85824i 0.346864 + 0.165090i
\(867\) 0 0
\(868\) 3.51529 33.9926i 0.119317 1.15378i
\(869\) 34.7619i 1.17922i
\(870\) 0 0
\(871\) 17.0034 0.576139
\(872\) −7.96286 + 13.0677i −0.269656 + 0.442527i
\(873\) 0 0
\(874\) −1.90573 + 4.00406i −0.0644624 + 0.135440i
\(875\) 5.58180 23.5433i 0.188699 0.795910i
\(876\) 0 0
\(877\) 27.6401 + 27.6401i 0.933339 + 0.933339i 0.997913 0.0645744i \(-0.0205690\pi\)
−0.0645744 + 0.997913i \(0.520569\pi\)
\(878\) −8.05874 22.6968i −0.271969 0.765981i
\(879\) 0 0
\(880\) 21.3679 11.7208i 0.720312 0.395107i
\(881\) 37.9900i 1.27991i 0.768410 + 0.639957i \(0.221048\pi\)
−0.768410 + 0.639957i \(0.778952\pi\)
\(882\) 0 0
\(883\) 33.6777 33.6777i 1.13335 1.13335i 0.143729 0.989617i \(-0.454091\pi\)
0.989617 0.143729i \(-0.0459095\pi\)
\(884\) −6.80315 + 5.52795i −0.228815 + 0.185925i
\(885\) 0 0
\(886\) −19.6595 9.35694i −0.660475 0.314353i
\(887\) 1.17366 + 1.17366i 0.0394078 + 0.0394078i 0.726536 0.687128i \(-0.241129\pi\)
−0.687128 + 0.726536i \(0.741129\pi\)
\(888\) 0 0
\(889\) 2.80471i 0.0940671i
\(890\) −28.0212 16.1116i −0.939274 0.540063i
\(891\) 0 0
\(892\) −15.2649 1.57859i −0.511106 0.0528552i
\(893\) −33.4861 33.4861i −1.12057 1.12057i
\(894\) 0 0
\(895\) 19.3570 16.5641i 0.647034 0.553676i
\(896\) −24.4720 + 0.784206i −0.817554 + 0.0261985i
\(897\) 0 0
\(898\) −13.7946 + 4.89792i −0.460332 + 0.163446i
\(899\) 40.4452i 1.34892i
\(900\) 0 0
\(901\) 33.0482i 1.10099i
\(902\) −15.9974 45.0555i −0.532655 1.50018i
\(903\) 0 0
\(904\) 0.338530 + 1.39465i 0.0112593 + 0.0463855i
\(905\) 12.4263 10.6333i 0.413064 0.353464i
\(906\) 0 0
\(907\) 16.4248 + 16.4248i 0.545377 + 0.545377i 0.925100 0.379723i \(-0.123981\pi\)
−0.379723 + 0.925100i \(0.623981\pi\)
\(908\) 2.37262 22.9430i 0.0787381 0.761391i
\(909\) 0 0
\(910\) 4.13738 7.19569i 0.137153 0.238535i
\(911\) 32.3497i 1.07179i −0.844284 0.535897i \(-0.819974\pi\)
0.844284 0.535897i \(-0.180026\pi\)
\(912\) 0 0
\(913\) −9.75676 9.75676i −0.322902 0.322902i
\(914\) 5.48755 11.5297i 0.181512 0.381368i
\(915\) 0 0
\(916\) −22.5601 + 18.3314i −0.745407 + 0.605686i
\(917\) 29.8950 29.8950i 0.987219 0.987219i
\(918\) 0 0
\(919\) 5.60588i 0.184921i −0.995716 0.0924605i \(-0.970527\pi\)
0.995716 0.0924605i \(-0.0294732\pi\)
\(920\) 3.27568 4.54148i 0.107996 0.149728i
\(921\) 0 0
\(922\) −8.09950 + 2.87581i −0.266743 + 0.0947097i
\(923\) −1.88394 1.88394i −0.0620106 0.0620106i
\(924\) 0 0
\(925\) −24.0815 + 17.5658i −0.791794 + 0.577559i
\(926\) 40.1582 + 19.1133i 1.31968 + 0.628101i
\(927\) 0 0
\(928\) −28.7138 + 3.90246i −0.942578 + 0.128105i
\(929\) 34.7413 1.13983 0.569913 0.821705i \(-0.306977\pi\)
0.569913 + 0.821705i \(0.306977\pi\)
\(930\) 0 0
\(931\) 8.20391i 0.268872i
\(932\) 0.699642 6.76548i 0.0229175 0.221611i
\(933\) 0 0
\(934\) 15.1275 31.7838i 0.494986 1.04000i
\(935\) −1.70680 + 21.9518i −0.0558182 + 0.717899i
\(936\) 0 0
\(937\) 5.80471 5.80471i 0.189632 0.189632i −0.605905 0.795537i \(-0.707189\pi\)
0.795537 + 0.605905i \(0.207189\pi\)
\(938\) −40.4342 + 14.3566i −1.32022 + 0.468759i
\(939\) 0 0
\(940\) 33.9994 + 49.1931i 1.10894 + 1.60450i
\(941\) −23.7893 −0.775510 −0.387755 0.921762i \(-0.626749\pi\)
−0.387755 + 0.921762i \(0.626749\pi\)
\(942\) 0 0
\(943\) −7.76765 7.76765i −0.252949 0.252949i
\(944\) 9.84346 + 2.05790i 0.320377 + 0.0669789i
\(945\) 0 0
\(946\) 13.2984 27.9408i 0.432369 0.908435i
\(947\) −12.4008 + 12.4008i −0.402972 + 0.402972i −0.879279 0.476307i \(-0.841975\pi\)
0.476307 + 0.879279i \(0.341975\pi\)
\(948\) 0 0
\(949\) 9.79872 0.318080
\(950\) 4.63077 + 24.6111i 0.150242 + 0.798488i
\(951\) 0 0
\(952\) 11.5105 18.8896i 0.373057 0.612215i
\(953\) 4.46081 4.46081i 0.144500 0.144500i −0.631156 0.775656i \(-0.717419\pi\)
0.775656 + 0.631156i \(0.217419\pi\)
\(954\) 0 0
\(955\) −2.25713 + 1.93146i −0.0730390 + 0.0625006i
\(956\) 10.5543 8.57599i 0.341351 0.277367i
\(957\) 0 0
\(958\) 3.30025 1.17179i 0.106626 0.0378587i
\(959\) −23.4627 −0.757651
\(960\) 0 0
\(961\) 31.3380 1.01090
\(962\) −9.63593 + 3.42133i −0.310675 + 0.110308i
\(963\) 0 0
\(964\) 25.1621 20.4457i 0.810418 0.658511i
\(965\) −2.82801 + 36.3722i −0.0910369 + 1.17086i
\(966\) 0 0
\(967\) 2.74162 2.74162i 0.0881645 0.0881645i −0.661649 0.749814i \(-0.730143\pi\)
0.749814 + 0.661649i \(0.230143\pi\)
\(968\) −5.26233 + 8.63590i −0.169138 + 0.277568i
\(969\) 0 0
\(970\) 5.60138 1.51158i 0.179850 0.0485338i
\(971\) 10.5455 0.338421 0.169210 0.985580i \(-0.445878\pi\)
0.169210 + 0.985580i \(0.445878\pi\)
\(972\) 0 0
\(973\) 22.5273 22.5273i 0.722193 0.722193i
\(974\) 10.6351 22.3451i 0.340771 0.715982i
\(975\) 0 0
\(976\) 37.1637 + 7.76954i 1.18958 + 0.248697i
\(977\) 13.3372 + 13.3372i 0.426695 + 0.426695i 0.887501 0.460806i \(-0.152440\pi\)
−0.460806 + 0.887501i \(0.652440\pi\)
\(978\) 0 0
\(979\) −27.8513 −0.890133
\(980\) 1.86120 10.1909i 0.0594538 0.325535i
\(981\) 0 0
\(982\) −49.5167 + 17.5814i −1.58014 + 0.561045i
\(983\) −3.84412 + 3.84412i −0.122608 + 0.122608i −0.765749 0.643140i \(-0.777631\pi\)
0.643140 + 0.765749i \(0.277631\pi\)
\(984\) 0 0
\(985\) 51.0745 + 3.97115i 1.62737 + 0.126531i
\(986\) 11.2509 23.6388i 0.358300 0.752812i
\(987\) 0 0
\(988\) −0.883702 + 8.54533i −0.0281143 + 0.271863i
\(989\) 7.10972i 0.226076i
\(990\) 0 0
\(991\) 34.9248 1.10942 0.554711 0.832043i \(-0.312829\pi\)
0.554711 + 0.832043i \(0.312829\pi\)
\(992\) −6.01485 44.2565i −0.190972 1.40514i
\(993\) 0 0
\(994\) 6.07069 + 2.88934i 0.192551 + 0.0916443i
\(995\) 10.3532 8.85937i 0.328218 0.280861i
\(996\) 0 0
\(997\) −11.0217 11.0217i −0.349062 0.349062i 0.510698 0.859760i \(-0.329387\pi\)
−0.859760 + 0.510698i \(0.829387\pi\)
\(998\) 46.4638 16.4975i 1.47079 0.522218i
\(999\) 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 360.2.x.a.53.22 yes 48
3.2 odd 2 inner 360.2.x.a.53.3 48
4.3 odd 2 1440.2.bj.a.593.5 48
5.2 odd 4 inner 360.2.x.a.197.15 yes 48
8.3 odd 2 1440.2.bj.a.593.19 48
8.5 even 2 inner 360.2.x.a.53.10 yes 48
12.11 even 2 1440.2.bj.a.593.20 48
15.2 even 4 inner 360.2.x.a.197.10 yes 48
20.7 even 4 1440.2.bj.a.17.6 48
24.5 odd 2 inner 360.2.x.a.53.15 yes 48
24.11 even 2 1440.2.bj.a.593.6 48
40.27 even 4 1440.2.bj.a.17.20 48
40.37 odd 4 inner 360.2.x.a.197.3 yes 48
60.47 odd 4 1440.2.bj.a.17.19 48
120.77 even 4 inner 360.2.x.a.197.22 yes 48
120.107 odd 4 1440.2.bj.a.17.5 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.x.a.53.3 48 3.2 odd 2 inner
360.2.x.a.53.10 yes 48 8.5 even 2 inner
360.2.x.a.53.15 yes 48 24.5 odd 2 inner
360.2.x.a.53.22 yes 48 1.1 even 1 trivial
360.2.x.a.197.3 yes 48 40.37 odd 4 inner
360.2.x.a.197.10 yes 48 15.2 even 4 inner
360.2.x.a.197.15 yes 48 5.2 odd 4 inner
360.2.x.a.197.22 yes 48 120.77 even 4 inner
1440.2.bj.a.17.5 48 120.107 odd 4
1440.2.bj.a.17.6 48 20.7 even 4
1440.2.bj.a.17.19 48 60.47 odd 4
1440.2.bj.a.17.20 48 40.27 even 4
1440.2.bj.a.593.5 48 4.3 odd 2
1440.2.bj.a.593.6 48 24.11 even 2
1440.2.bj.a.593.19 48 8.3 odd 2
1440.2.bj.a.593.20 48 12.11 even 2