Properties

Label 432.2.y.e.37.12
Level $432$
Weight $2$
Character 432.37
Analytic conductor $3.450$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(37,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.y (of order \(12\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.12
Character \(\chi\) \(=\) 432.37
Dual form 432.2.y.e.397.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.751042 - 1.19831i) q^{2} +(-0.871873 - 1.79995i) q^{4} +(1.60558 - 0.430214i) q^{5} +(3.62762 - 2.09441i) q^{7} +(-2.81171 - 0.307071i) q^{8} +O(q^{10})\) \(q+(0.751042 - 1.19831i) q^{2} +(-0.871873 - 1.79995i) q^{4} +(1.60558 - 0.430214i) q^{5} +(3.62762 - 2.09441i) q^{7} +(-2.81171 - 0.307071i) q^{8} +(0.690330 - 2.24708i) q^{10} +(-1.24125 + 4.63241i) q^{11} +(-0.879738 - 3.28323i) q^{13} +(0.214754 - 5.91998i) q^{14} +(-2.47968 + 3.13866i) q^{16} +2.14142 q^{17} +(1.03156 - 1.03156i) q^{19} +(-2.17423 - 2.51488i) q^{20} +(4.61882 + 4.96653i) q^{22} +(0.405884 + 0.234337i) q^{23} +(-1.93733 + 1.11852i) q^{25} +(-4.59503 - 1.41164i) q^{26} +(-6.93266 - 4.70349i) q^{28} +(-6.55186 - 1.75557i) q^{29} +(3.18054 - 5.50886i) q^{31} +(1.89874 + 5.32868i) q^{32} +(1.60829 - 2.56607i) q^{34} +(4.92339 - 4.92339i) q^{35} +(-0.728237 - 0.728237i) q^{37} +(-0.461380 - 2.01087i) q^{38} +(-4.64653 + 0.716609i) q^{40} +(-2.52351 - 1.45695i) q^{41} +(-2.84802 + 10.6289i) q^{43} +(9.42035 - 1.80468i) q^{44} +(0.585644 - 0.310376i) q^{46} +(4.61716 + 7.99715i) q^{47} +(5.27308 - 9.13324i) q^{49} +(-0.114689 + 3.16156i) q^{50} +(-5.14264 + 4.44604i) q^{52} +(-1.17892 - 1.17892i) q^{53} +7.97171i q^{55} +(-10.8429 + 4.77492i) q^{56} +(-7.02443 + 6.53263i) q^{58} +(1.48185 - 0.397061i) q^{59} +(7.53224 + 2.01826i) q^{61} +(-4.21258 - 7.94865i) q^{62} +(7.81141 + 1.72679i) q^{64} +(-2.82498 - 4.89300i) q^{65} +(2.63252 + 9.82470i) q^{67} +(-1.86704 - 3.85445i) q^{68} +(-2.20205 - 9.59739i) q^{70} +8.27863i q^{71} +8.16641i q^{73} +(-1.41959 + 0.325714i) q^{74} +(-2.75615 - 0.957372i) q^{76} +(5.19937 + 19.4043i) q^{77} +(3.63065 + 6.28847i) q^{79} +(-2.63102 + 6.10616i) q^{80} +(-3.64113 + 1.92970i) q^{82} +(7.59149 + 2.03413i) q^{83} +(3.43821 - 0.921267i) q^{85} +(10.5977 + 11.3956i) q^{86} +(4.91252 - 12.6438i) q^{88} -11.1968i q^{89} +(-10.0678 - 10.0678i) q^{91} +(0.0679173 - 0.934886i) q^{92} +(13.0507 + 0.473428i) q^{94} +(1.21246 - 2.10004i) q^{95} +(-5.67759 - 9.83387i) q^{97} +(-6.98411 - 13.1782i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.751042 1.19831i 0.531067 0.847330i
\(3\) 0 0
\(4\) −0.871873 1.79995i −0.435936 0.899977i
\(5\) 1.60558 0.430214i 0.718037 0.192397i 0.118741 0.992925i \(-0.462114\pi\)
0.599296 + 0.800528i \(0.295447\pi\)
\(6\) 0 0
\(7\) 3.62762 2.09441i 1.37111 0.791611i 0.380043 0.924969i \(-0.375909\pi\)
0.991068 + 0.133358i \(0.0425759\pi\)
\(8\) −2.81171 0.307071i −0.994089 0.108566i
\(9\) 0 0
\(10\) 0.690330 2.24708i 0.218301 0.710590i
\(11\) −1.24125 + 4.63241i −0.374251 + 1.39673i 0.480184 + 0.877168i \(0.340570\pi\)
−0.854436 + 0.519557i \(0.826097\pi\)
\(12\) 0 0
\(13\) −0.879738 3.28323i −0.243995 0.910603i −0.973886 0.227039i \(-0.927096\pi\)
0.729890 0.683564i \(-0.239571\pi\)
\(14\) 0.214754 5.91998i 0.0573953 1.58218i
\(15\) 0 0
\(16\) −2.47968 + 3.13866i −0.619919 + 0.784666i
\(17\) 2.14142 0.519370 0.259685 0.965693i \(-0.416381\pi\)
0.259685 + 0.965693i \(0.416381\pi\)
\(18\) 0 0
\(19\) 1.03156 1.03156i 0.236656 0.236656i −0.578808 0.815464i \(-0.696482\pi\)
0.815464 + 0.578808i \(0.196482\pi\)
\(20\) −2.17423 2.51488i −0.486172 0.562344i
\(21\) 0 0
\(22\) 4.61882 + 4.96653i 0.984735 + 1.05887i
\(23\) 0.405884 + 0.234337i 0.0846327 + 0.0488627i 0.541719 0.840560i \(-0.317774\pi\)
−0.457086 + 0.889422i \(0.651107\pi\)
\(24\) 0 0
\(25\) −1.93733 + 1.11852i −0.387465 + 0.223703i
\(26\) −4.59503 1.41164i −0.901159 0.276846i
\(27\) 0 0
\(28\) −6.93266 4.70349i −1.31015 0.888877i
\(29\) −6.55186 1.75557i −1.21665 0.326000i −0.407282 0.913302i \(-0.633523\pi\)
−0.809368 + 0.587302i \(0.800190\pi\)
\(30\) 0 0
\(31\) 3.18054 5.50886i 0.571242 0.989421i −0.425196 0.905101i \(-0.639795\pi\)
0.996439 0.0843198i \(-0.0268717\pi\)
\(32\) 1.89874 + 5.32868i 0.335653 + 0.941986i
\(33\) 0 0
\(34\) 1.60829 2.56607i 0.275820 0.440078i
\(35\) 4.92339 4.92339i 0.832204 0.832204i
\(36\) 0 0
\(37\) −0.728237 0.728237i −0.119721 0.119721i 0.644708 0.764429i \(-0.276979\pi\)
−0.764429 + 0.644708i \(0.776979\pi\)
\(38\) −0.461380 2.01087i −0.0748456 0.326206i
\(39\) 0 0
\(40\) −4.64653 + 0.716609i −0.734681 + 0.113306i
\(41\) −2.52351 1.45695i −0.394105 0.227537i 0.289832 0.957078i \(-0.406401\pi\)
−0.683937 + 0.729541i \(0.739734\pi\)
\(42\) 0 0
\(43\) −2.84802 + 10.6289i −0.434318 + 1.62090i 0.308374 + 0.951265i \(0.400215\pi\)
−0.742692 + 0.669633i \(0.766451\pi\)
\(44\) 9.42035 1.80468i 1.42017 0.272066i
\(45\) 0 0
\(46\) 0.585644 0.310376i 0.0863485 0.0457625i
\(47\) 4.61716 + 7.99715i 0.673482 + 1.16650i 0.976910 + 0.213650i \(0.0685352\pi\)
−0.303429 + 0.952854i \(0.598131\pi\)
\(48\) 0 0
\(49\) 5.27308 9.13324i 0.753297 1.30475i
\(50\) −0.114689 + 3.16156i −0.0162195 + 0.447112i
\(51\) 0 0
\(52\) −5.14264 + 4.44604i −0.713156 + 0.616555i
\(53\) −1.17892 1.17892i −0.161937 0.161937i 0.621487 0.783424i \(-0.286529\pi\)
−0.783424 + 0.621487i \(0.786529\pi\)
\(54\) 0 0
\(55\) 7.97171i 1.07491i
\(56\) −10.8429 + 4.77492i −1.44895 + 0.638076i
\(57\) 0 0
\(58\) −7.02443 + 6.53263i −0.922352 + 0.857776i
\(59\) 1.48185 0.397061i 0.192921 0.0516930i −0.161065 0.986944i \(-0.551493\pi\)
0.353986 + 0.935251i \(0.384826\pi\)
\(60\) 0 0
\(61\) 7.53224 + 2.01826i 0.964404 + 0.258411i 0.706464 0.707749i \(-0.250289\pi\)
0.257941 + 0.966161i \(0.416956\pi\)
\(62\) −4.21258 7.94865i −0.534998 1.00948i
\(63\) 0 0
\(64\) 7.81141 + 1.72679i 0.976427 + 0.215849i
\(65\) −2.82498 4.89300i −0.350395 0.606902i
\(66\) 0 0
\(67\) 2.63252 + 9.82470i 0.321614 + 1.20028i 0.917673 + 0.397338i \(0.130066\pi\)
−0.596059 + 0.802941i \(0.703268\pi\)
\(68\) −1.86704 3.85445i −0.226412 0.467421i
\(69\) 0 0
\(70\) −2.20205 9.59739i −0.263196 1.14711i
\(71\) 8.27863i 0.982493i 0.871021 + 0.491246i \(0.163458\pi\)
−0.871021 + 0.491246i \(0.836542\pi\)
\(72\) 0 0
\(73\) 8.16641i 0.955806i 0.878413 + 0.477903i \(0.158603\pi\)
−0.878413 + 0.477903i \(0.841397\pi\)
\(74\) −1.41959 + 0.325714i −0.165024 + 0.0378635i
\(75\) 0 0
\(76\) −2.75615 0.957372i −0.316152 0.109818i
\(77\) 5.19937 + 19.4043i 0.592523 + 2.21133i
\(78\) 0 0
\(79\) 3.63065 + 6.28847i 0.408480 + 0.707508i 0.994720 0.102630i \(-0.0327257\pi\)
−0.586240 + 0.810138i \(0.699392\pi\)
\(80\) −2.63102 + 6.10616i −0.294157 + 0.682690i
\(81\) 0 0
\(82\) −3.64113 + 1.92970i −0.402095 + 0.213100i
\(83\) 7.59149 + 2.03413i 0.833274 + 0.223275i 0.650142 0.759813i \(-0.274710\pi\)
0.183133 + 0.983088i \(0.441376\pi\)
\(84\) 0 0
\(85\) 3.43821 0.921267i 0.372927 0.0999254i
\(86\) 10.5977 + 11.3956i 1.14278 + 1.22882i
\(87\) 0 0
\(88\) 4.91252 12.6438i 0.523676 1.34784i
\(89\) 11.1968i 1.18686i −0.804886 0.593429i \(-0.797774\pi\)
0.804886 0.593429i \(-0.202226\pi\)
\(90\) 0 0
\(91\) −10.0678 10.0678i −1.05539 1.05539i
\(92\) 0.0679173 0.934886i 0.00708087 0.0974686i
\(93\) 0 0
\(94\) 13.0507 + 0.473428i 1.34608 + 0.0488304i
\(95\) 1.21246 2.10004i 0.124396 0.215460i
\(96\) 0 0
\(97\) −5.67759 9.83387i −0.576472 0.998479i −0.995880 0.0906808i \(-0.971096\pi\)
0.419408 0.907798i \(-0.362238\pi\)
\(98\) −6.98411 13.1782i −0.705501 1.33120i
\(99\) 0 0
\(100\) 3.70238 + 2.51190i 0.370238 + 0.251190i
\(101\) −0.777558 + 2.90189i −0.0773699 + 0.288749i −0.993760 0.111537i \(-0.964423\pi\)
0.916390 + 0.400286i \(0.131089\pi\)
\(102\) 0 0
\(103\) −1.24824 0.720669i −0.122992 0.0710096i 0.437242 0.899344i \(-0.355955\pi\)
−0.560234 + 0.828334i \(0.689289\pi\)
\(104\) 1.46538 + 9.50162i 0.143693 + 0.931710i
\(105\) 0 0
\(106\) −2.29812 + 0.527287i −0.223213 + 0.0512146i
\(107\) −5.85602 5.85602i −0.566123 0.566123i 0.364917 0.931040i \(-0.381097\pi\)
−0.931040 + 0.364917i \(0.881097\pi\)
\(108\) 0 0
\(109\) −2.05249 + 2.05249i −0.196593 + 0.196593i −0.798538 0.601945i \(-0.794393\pi\)
0.601945 + 0.798538i \(0.294393\pi\)
\(110\) 9.55255 + 5.98709i 0.910799 + 0.570846i
\(111\) 0 0
\(112\) −2.42168 + 16.5793i −0.228827 + 1.56660i
\(113\) 4.12726 7.14862i 0.388260 0.672486i −0.603956 0.797018i \(-0.706410\pi\)
0.992216 + 0.124532i \(0.0397430\pi\)
\(114\) 0 0
\(115\) 0.752495 + 0.201630i 0.0701705 + 0.0188021i
\(116\) 2.55245 + 13.3237i 0.236989 + 1.23707i
\(117\) 0 0
\(118\) 0.637132 2.07392i 0.0586528 0.190920i
\(119\) 7.76824 4.48500i 0.712114 0.411139i
\(120\) 0 0
\(121\) −10.3923 5.99998i −0.944752 0.545453i
\(122\) 8.07551 7.51013i 0.731123 0.679935i
\(123\) 0 0
\(124\) −12.6887 0.921808i −1.13948 0.0827808i
\(125\) −8.50616 + 8.50616i −0.760814 + 0.760814i
\(126\) 0 0
\(127\) −1.68483 −0.149504 −0.0747521 0.997202i \(-0.523817\pi\)
−0.0747521 + 0.997202i \(0.523817\pi\)
\(128\) 7.93592 8.06357i 0.701443 0.712726i
\(129\) 0 0
\(130\) −7.98499 0.289664i −0.700330 0.0254052i
\(131\) −1.97334 7.36461i −0.172412 0.643449i −0.996978 0.0776838i \(-0.975248\pi\)
0.824566 0.565765i \(-0.191419\pi\)
\(132\) 0 0
\(133\) 1.58160 5.90261i 0.137142 0.511821i
\(134\) 13.7501 + 4.22420i 1.18783 + 0.364915i
\(135\) 0 0
\(136\) −6.02104 0.657567i −0.516300 0.0563859i
\(137\) −8.26806 + 4.77357i −0.706388 + 0.407833i −0.809722 0.586813i \(-0.800382\pi\)
0.103334 + 0.994647i \(0.467049\pi\)
\(138\) 0 0
\(139\) −13.9684 + 3.74281i −1.18478 + 0.317461i −0.796821 0.604215i \(-0.793487\pi\)
−0.387960 + 0.921676i \(0.626820\pi\)
\(140\) −13.1544 4.56931i −1.11175 0.386177i
\(141\) 0 0
\(142\) 9.92033 + 6.21760i 0.832495 + 0.521769i
\(143\) 16.3012 1.36318
\(144\) 0 0
\(145\) −11.2748 −0.936321
\(146\) 9.78586 + 6.13331i 0.809883 + 0.507597i
\(147\) 0 0
\(148\) −0.675864 + 1.94572i −0.0555557 + 0.159938i
\(149\) 1.66249 0.445462i 0.136196 0.0364937i −0.190077 0.981769i \(-0.560874\pi\)
0.326273 + 0.945276i \(0.394207\pi\)
\(150\) 0 0
\(151\) 18.5071 10.6851i 1.50609 0.869542i 0.506115 0.862466i \(-0.331081\pi\)
0.999975 0.00707596i \(-0.00225237\pi\)
\(152\) −3.21721 + 2.58368i −0.260950 + 0.209564i
\(153\) 0 0
\(154\) 27.1572 + 8.34301i 2.18839 + 0.672299i
\(155\) 2.73663 10.2132i 0.219811 0.820346i
\(156\) 0 0
\(157\) 2.74550 + 10.2463i 0.219114 + 0.817746i 0.984677 + 0.174385i \(0.0557938\pi\)
−0.765563 + 0.643361i \(0.777539\pi\)
\(158\) 10.2623 + 0.372275i 0.816422 + 0.0296166i
\(159\) 0 0
\(160\) 5.34104 + 7.73875i 0.422247 + 0.611802i
\(161\) 1.96319 0.154721
\(162\) 0 0
\(163\) −3.47621 + 3.47621i −0.272278 + 0.272278i −0.830017 0.557739i \(-0.811669\pi\)
0.557739 + 0.830017i \(0.311669\pi\)
\(164\) −0.422263 + 5.81247i −0.0329732 + 0.453878i
\(165\) 0 0
\(166\) 8.13904 7.56920i 0.631712 0.587484i
\(167\) −0.277442 0.160181i −0.0214691 0.0123952i 0.489227 0.872156i \(-0.337279\pi\)
−0.510696 + 0.859761i \(0.670612\pi\)
\(168\) 0 0
\(169\) 1.25270 0.723245i 0.0963613 0.0556342i
\(170\) 1.47828 4.81194i 0.113379 0.369059i
\(171\) 0 0
\(172\) 21.6147 4.14078i 1.64811 0.315732i
\(173\) −11.6901 3.13236i −0.888784 0.238149i −0.214591 0.976704i \(-0.568842\pi\)
−0.674193 + 0.738555i \(0.735509\pi\)
\(174\) 0 0
\(175\) −4.68525 + 8.11510i −0.354172 + 0.613444i
\(176\) −11.4617 15.3828i −0.863957 1.15952i
\(177\) 0 0
\(178\) −13.4172 8.40926i −1.00566 0.630301i
\(179\) −18.6780 + 18.6780i −1.39606 + 1.39606i −0.585104 + 0.810958i \(0.698946\pi\)
−0.810958 + 0.585104i \(0.801054\pi\)
\(180\) 0 0
\(181\) 4.10527 + 4.10527i 0.305143 + 0.305143i 0.843022 0.537879i \(-0.180774\pi\)
−0.537879 + 0.843022i \(0.680774\pi\)
\(182\) −19.6256 + 4.50295i −1.45474 + 0.333781i
\(183\) 0 0
\(184\) −1.06927 0.783524i −0.0788277 0.0577622i
\(185\) −1.48254 0.855945i −0.108998 0.0629303i
\(186\) 0 0
\(187\) −2.65804 + 9.91993i −0.194375 + 0.725417i
\(188\) 10.3689 15.2832i 0.756232 1.11464i
\(189\) 0 0
\(190\) −1.60588 3.03012i −0.116503 0.219828i
\(191\) −8.60099 14.8974i −0.622346 1.07793i −0.989048 0.147596i \(-0.952846\pi\)
0.366702 0.930338i \(-0.380487\pi\)
\(192\) 0 0
\(193\) 9.17459 15.8909i 0.660402 1.14385i −0.320108 0.947381i \(-0.603719\pi\)
0.980510 0.196468i \(-0.0629473\pi\)
\(194\) −16.0481 0.582162i −1.15219 0.0417968i
\(195\) 0 0
\(196\) −21.0369 1.52828i −1.50263 0.109163i
\(197\) −8.80431 8.80431i −0.627281 0.627281i 0.320102 0.947383i \(-0.396283\pi\)
−0.947383 + 0.320102i \(0.896283\pi\)
\(198\) 0 0
\(199\) 10.0277i 0.710847i 0.934705 + 0.355423i \(0.115663\pi\)
−0.934705 + 0.355423i \(0.884337\pi\)
\(200\) 5.79066 2.55004i 0.409462 0.180315i
\(201\) 0 0
\(202\) 2.89337 + 3.11119i 0.203577 + 0.218903i
\(203\) −27.4445 + 7.35374i −1.92623 + 0.516131i
\(204\) 0 0
\(205\) −4.67849 1.25360i −0.326760 0.0875550i
\(206\) −1.80106 + 0.954515i −0.125486 + 0.0665042i
\(207\) 0 0
\(208\) 12.4864 + 5.38014i 0.865776 + 0.373045i
\(209\) 3.49819 + 6.05904i 0.241975 + 0.419112i
\(210\) 0 0
\(211\) −5.14678 19.2080i −0.354319 1.32234i −0.881340 0.472483i \(-0.843358\pi\)
0.527021 0.849852i \(-0.323309\pi\)
\(212\) −1.09413 + 3.14986i −0.0751452 + 0.216333i
\(213\) 0 0
\(214\) −11.4154 + 2.61919i −0.780342 + 0.179044i
\(215\) 18.2909i 1.24743i
\(216\) 0 0
\(217\) 26.6454i 1.80881i
\(218\) 0.918005 + 4.00102i 0.0621751 + 0.270983i
\(219\) 0 0
\(220\) 14.3487 6.95032i 0.967390 0.468590i
\(221\) −1.88389 7.03076i −0.126724 0.472940i
\(222\) 0 0
\(223\) −6.96587 12.0652i −0.466469 0.807948i 0.532797 0.846243i \(-0.321141\pi\)
−0.999266 + 0.0382947i \(0.987807\pi\)
\(224\) 18.0483 + 15.3537i 1.20590 + 1.02586i
\(225\) 0 0
\(226\) −5.46649 10.3146i −0.363625 0.686119i
\(227\) 7.32092 + 1.96164i 0.485907 + 0.130198i 0.493452 0.869773i \(-0.335735\pi\)
−0.00754492 + 0.999972i \(0.502402\pi\)
\(228\) 0 0
\(229\) −18.4637 + 4.94734i −1.22012 + 0.326930i −0.810724 0.585428i \(-0.800926\pi\)
−0.409394 + 0.912358i \(0.634260\pi\)
\(230\) 0.806770 0.750286i 0.0531968 0.0494724i
\(231\) 0 0
\(232\) 17.8828 + 6.94803i 1.17407 + 0.456160i
\(233\) 10.7647i 0.705216i −0.935771 0.352608i \(-0.885295\pi\)
0.935771 0.352608i \(-0.114705\pi\)
\(234\) 0 0
\(235\) 10.8537 + 10.8537i 0.708017 + 0.708017i
\(236\) −2.00668 2.32108i −0.130624 0.151089i
\(237\) 0 0
\(238\) 0.459877 12.6771i 0.0298094 0.821738i
\(239\) 11.1429 19.3001i 0.720774 1.24842i −0.239916 0.970794i \(-0.577120\pi\)
0.960690 0.277624i \(-0.0895469\pi\)
\(240\) 0 0
\(241\) 13.7285 + 23.7785i 0.884332 + 1.53171i 0.846478 + 0.532424i \(0.178719\pi\)
0.0378540 + 0.999283i \(0.487948\pi\)
\(242\) −14.9948 + 7.94688i −0.963905 + 0.510845i
\(243\) 0 0
\(244\) −2.93438 15.3174i −0.187855 0.980593i
\(245\) 4.53710 16.9327i 0.289865 1.08179i
\(246\) 0 0
\(247\) −4.29435 2.47934i −0.273243 0.157757i
\(248\) −10.6344 + 14.5127i −0.675284 + 0.921555i
\(249\) 0 0
\(250\) 3.80450 + 16.5815i 0.240618 + 1.04870i
\(251\) −11.4125 11.4125i −0.720350 0.720350i 0.248326 0.968676i \(-0.420119\pi\)
−0.968676 + 0.248326i \(0.920119\pi\)
\(252\) 0 0
\(253\) −1.58935 + 1.58935i −0.0999217 + 0.0999217i
\(254\) −1.26538 + 2.01894i −0.0793967 + 0.126679i
\(255\) 0 0
\(256\) −3.70242 15.5657i −0.231401 0.972858i
\(257\) 0.930384 1.61147i 0.0580357 0.100521i −0.835548 0.549418i \(-0.814850\pi\)
0.893584 + 0.448897i \(0.148183\pi\)
\(258\) 0 0
\(259\) −4.16699 1.11654i −0.258924 0.0693785i
\(260\) −6.34417 + 9.35091i −0.393449 + 0.579919i
\(261\) 0 0
\(262\) −10.3071 3.16646i −0.636776 0.195625i
\(263\) −0.0414842 + 0.0239509i −0.00255802 + 0.00147687i −0.501278 0.865286i \(-0.667137\pi\)
0.498720 + 0.866763i \(0.333803\pi\)
\(264\) 0 0
\(265\) −2.40003 1.38566i −0.147433 0.0851203i
\(266\) −5.88528 6.32835i −0.360850 0.388016i
\(267\) 0 0
\(268\) 15.3888 13.3043i 0.940020 0.812690i
\(269\) 14.5681 14.5681i 0.888235 0.888235i −0.106118 0.994354i \(-0.533842\pi\)
0.994354 + 0.106118i \(0.0338421\pi\)
\(270\) 0 0
\(271\) −15.7807 −0.958607 −0.479304 0.877649i \(-0.659111\pi\)
−0.479304 + 0.877649i \(0.659111\pi\)
\(272\) −5.31002 + 6.72119i −0.321967 + 0.407532i
\(273\) 0 0
\(274\) −0.489466 + 13.4928i −0.0295697 + 0.815131i
\(275\) −2.77672 10.3629i −0.167442 0.624904i
\(276\) 0 0
\(277\) −1.93294 + 7.21383i −0.116139 + 0.433437i −0.999370 0.0355022i \(-0.988697\pi\)
0.883231 + 0.468939i \(0.155364\pi\)
\(278\) −6.00579 + 19.5494i −0.360203 + 1.17249i
\(279\) 0 0
\(280\) −15.3550 + 12.3313i −0.917634 + 0.736936i
\(281\) 5.84440 3.37427i 0.348648 0.201292i −0.315442 0.948945i \(-0.602153\pi\)
0.664089 + 0.747653i \(0.268819\pi\)
\(282\) 0 0
\(283\) 12.4414 3.33366i 0.739563 0.198165i 0.130679 0.991425i \(-0.458284\pi\)
0.608884 + 0.793259i \(0.291617\pi\)
\(284\) 14.9012 7.21791i 0.884221 0.428304i
\(285\) 0 0
\(286\) 12.2429 19.5339i 0.723938 1.15506i
\(287\) −12.2058 −0.720483
\(288\) 0 0
\(289\) −12.4143 −0.730255
\(290\) −8.46785 + 13.5107i −0.497249 + 0.793373i
\(291\) 0 0
\(292\) 14.6992 7.12007i 0.860204 0.416671i
\(293\) −13.8785 + 3.71874i −0.810792 + 0.217251i −0.640317 0.768111i \(-0.721197\pi\)
−0.170475 + 0.985362i \(0.554530\pi\)
\(294\) 0 0
\(295\) 2.20841 1.27503i 0.128579 0.0742349i
\(296\) 1.82397 + 2.27121i 0.106016 + 0.132011i
\(297\) 0 0
\(298\) 0.714797 2.32673i 0.0414071 0.134784i
\(299\) 0.412311 1.53877i 0.0238446 0.0889891i
\(300\) 0 0
\(301\) 11.9298 + 44.5226i 0.687622 + 2.56624i
\(302\) 1.09562 30.2022i 0.0630456 1.73794i
\(303\) 0 0
\(304\) 0.679785 + 5.79565i 0.0389884 + 0.332404i
\(305\) 12.9619 0.742196
\(306\) 0 0
\(307\) 12.2394 12.2394i 0.698539 0.698539i −0.265556 0.964095i \(-0.585556\pi\)
0.964095 + 0.265556i \(0.0855556\pi\)
\(308\) 30.3937 26.2767i 1.73184 1.49726i
\(309\) 0 0
\(310\) −10.1832 10.9499i −0.578370 0.621911i
\(311\) 0.742777 + 0.428842i 0.0421190 + 0.0243174i 0.520912 0.853611i \(-0.325592\pi\)
−0.478793 + 0.877928i \(0.658925\pi\)
\(312\) 0 0
\(313\) −15.8984 + 9.17895i −0.898631 + 0.518825i −0.876756 0.480936i \(-0.840297\pi\)
−0.0218755 + 0.999761i \(0.506964\pi\)
\(314\) 14.3402 + 4.40548i 0.809265 + 0.248616i
\(315\) 0 0
\(316\) 8.15349 12.0177i 0.458670 0.676051i
\(317\) 4.02641 + 1.07887i 0.226146 + 0.0605956i 0.370112 0.928987i \(-0.379319\pi\)
−0.143967 + 0.989583i \(0.545986\pi\)
\(318\) 0 0
\(319\) 16.2650 28.1718i 0.910666 1.57732i
\(320\) 13.2847 0.588080i 0.742639 0.0328747i
\(321\) 0 0
\(322\) 1.47444 2.35250i 0.0821673 0.131100i
\(323\) 2.20900 2.20900i 0.122912 0.122912i
\(324\) 0 0
\(325\) 5.37668 + 5.37668i 0.298244 + 0.298244i
\(326\) 1.55478 + 6.77634i 0.0861115 + 0.375307i
\(327\) 0 0
\(328\) 6.64798 + 4.87141i 0.367073 + 0.268978i
\(329\) 33.4986 + 19.3404i 1.84684 + 1.06627i
\(330\) 0 0
\(331\) 1.33734 4.99103i 0.0735070 0.274332i −0.919384 0.393362i \(-0.871312\pi\)
0.992891 + 0.119030i \(0.0379785\pi\)
\(332\) −2.95746 15.4378i −0.162312 0.847262i
\(333\) 0 0
\(334\) −0.400317 + 0.212158i −0.0219044 + 0.0116088i
\(335\) 8.45344 + 14.6418i 0.461861 + 0.799966i
\(336\) 0 0
\(337\) 1.94762 3.37338i 0.106094 0.183760i −0.808091 0.589058i \(-0.799499\pi\)
0.914185 + 0.405298i \(0.132832\pi\)
\(338\) 0.0741592 2.04430i 0.00403373 0.111195i
\(339\) 0 0
\(340\) −4.65592 5.38540i −0.252503 0.292065i
\(341\) 21.5715 + 21.5715i 1.16816 + 1.16816i
\(342\) 0 0
\(343\) 14.8542i 0.802049i
\(344\) 11.2716 29.0109i 0.607726 1.56417i
\(345\) 0 0
\(346\) −12.5333 + 11.6558i −0.673795 + 0.626621i
\(347\) 3.04812 0.816741i 0.163632 0.0438449i −0.176073 0.984377i \(-0.556340\pi\)
0.339705 + 0.940532i \(0.389673\pi\)
\(348\) 0 0
\(349\) 1.39893 + 0.374843i 0.0748831 + 0.0200649i 0.296066 0.955167i \(-0.404325\pi\)
−0.221183 + 0.975232i \(0.570992\pi\)
\(350\) 6.20554 + 11.7091i 0.331700 + 0.625880i
\(351\) 0 0
\(352\) −27.0414 + 2.18151i −1.44131 + 0.116275i
\(353\) −7.73892 13.4042i −0.411901 0.713434i 0.583196 0.812331i \(-0.301802\pi\)
−0.995098 + 0.0988971i \(0.968469\pi\)
\(354\) 0 0
\(355\) 3.56158 + 13.2920i 0.189029 + 0.705466i
\(356\) −20.1537 + 9.76218i −1.06815 + 0.517395i
\(357\) 0 0
\(358\) 8.35401 + 36.4100i 0.441523 + 1.92433i
\(359\) 4.78775i 0.252688i −0.991987 0.126344i \(-0.959676\pi\)
0.991987 0.126344i \(-0.0403242\pi\)
\(360\) 0 0
\(361\) 16.8718i 0.887988i
\(362\) 8.00261 1.83614i 0.420608 0.0965054i
\(363\) 0 0
\(364\) −9.34371 + 26.8993i −0.489743 + 1.40991i
\(365\) 3.51330 + 13.1118i 0.183895 + 0.686304i
\(366\) 0 0
\(367\) −9.93807 17.2133i −0.518763 0.898524i −0.999762 0.0218032i \(-0.993059\pi\)
0.480999 0.876721i \(-0.340274\pi\)
\(368\) −1.74197 + 0.692854i −0.0908064 + 0.0361175i
\(369\) 0 0
\(370\) −2.13913 + 1.13369i −0.111208 + 0.0589375i
\(371\) −6.74579 1.80753i −0.350224 0.0938422i
\(372\) 0 0
\(373\) −0.427591 + 0.114573i −0.0221398 + 0.00593235i −0.269872 0.962896i \(-0.586981\pi\)
0.247732 + 0.968829i \(0.420315\pi\)
\(374\) 9.89081 + 10.6354i 0.511442 + 0.549944i
\(375\) 0 0
\(376\) −10.5264 23.9035i −0.542858 1.23273i
\(377\) 23.0557i 1.18743i
\(378\) 0 0
\(379\) −6.18132 6.18132i −0.317513 0.317513i 0.530298 0.847811i \(-0.322080\pi\)
−0.847811 + 0.530298i \(0.822080\pi\)
\(380\) −4.83709 0.351404i −0.248138 0.0180266i
\(381\) 0 0
\(382\) −24.3113 0.881917i −1.24387 0.0451228i
\(383\) −6.46708 + 11.2013i −0.330452 + 0.572360i −0.982601 0.185731i \(-0.940535\pi\)
0.652148 + 0.758091i \(0.273868\pi\)
\(384\) 0 0
\(385\) 16.6960 + 28.9183i 0.850907 + 1.47381i
\(386\) −12.1516 22.9287i −0.618501 1.16704i
\(387\) 0 0
\(388\) −12.7504 + 18.7933i −0.647303 + 0.954085i
\(389\) −7.08096 + 26.4265i −0.359019 + 1.33988i 0.516331 + 0.856389i \(0.327297\pi\)
−0.875351 + 0.483489i \(0.839369\pi\)
\(390\) 0 0
\(391\) 0.869168 + 0.501814i 0.0439557 + 0.0253778i
\(392\) −17.6309 + 24.0608i −0.890495 + 1.21525i
\(393\) 0 0
\(394\) −17.1627 + 3.93785i −0.864642 + 0.198386i
\(395\) 8.53468 + 8.53468i 0.429426 + 0.429426i
\(396\) 0 0
\(397\) 21.9741 21.9741i 1.10285 1.10285i 0.108781 0.994066i \(-0.465305\pi\)
0.994066 0.108781i \(-0.0346948\pi\)
\(398\) 12.0163 + 7.53124i 0.602322 + 0.377507i
\(399\) 0 0
\(400\) 1.29330 8.85417i 0.0646648 0.442709i
\(401\) −13.4970 + 23.3775i −0.674009 + 1.16742i 0.302749 + 0.953070i \(0.402096\pi\)
−0.976758 + 0.214347i \(0.931238\pi\)
\(402\) 0 0
\(403\) −20.8849 5.59609i −1.04035 0.278761i
\(404\) 5.90120 1.13051i 0.293596 0.0562448i
\(405\) 0 0
\(406\) −11.8000 + 38.4099i −0.585622 + 1.90625i
\(407\) 4.27742 2.46957i 0.212024 0.122412i
\(408\) 0 0
\(409\) 11.1537 + 6.43957i 0.551513 + 0.318416i 0.749732 0.661741i \(-0.230182\pi\)
−0.198219 + 0.980158i \(0.563516\pi\)
\(410\) −5.01593 + 4.66475i −0.247719 + 0.230376i
\(411\) 0 0
\(412\) −0.208869 + 2.87510i −0.0102903 + 0.141646i
\(413\) 4.54399 4.54399i 0.223595 0.223595i
\(414\) 0 0
\(415\) 13.0638 0.641279
\(416\) 15.8249 10.9218i 0.775877 0.535486i
\(417\) 0 0
\(418\) 9.88786 + 0.358693i 0.483631 + 0.0175442i
\(419\) 0.0545100 + 0.203434i 0.00266299 + 0.00993841i 0.967245 0.253846i \(-0.0816958\pi\)
−0.964582 + 0.263785i \(0.915029\pi\)
\(420\) 0 0
\(421\) 9.17194 34.2301i 0.447013 1.66827i −0.263554 0.964645i \(-0.584895\pi\)
0.710567 0.703630i \(-0.248439\pi\)
\(422\) −26.8825 8.25862i −1.30862 0.402023i
\(423\) 0 0
\(424\) 2.95276 + 3.67678i 0.143399 + 0.178560i
\(425\) −4.14862 + 2.39521i −0.201238 + 0.116185i
\(426\) 0 0
\(427\) 31.5511 8.45410i 1.52687 0.409123i
\(428\) −5.43487 + 15.6463i −0.262704 + 0.756292i
\(429\) 0 0
\(430\) 21.9180 + 13.7372i 1.05698 + 0.662467i
\(431\) −33.5339 −1.61527 −0.807635 0.589683i \(-0.799253\pi\)
−0.807635 + 0.589683i \(0.799253\pi\)
\(432\) 0 0
\(433\) −28.9691 −1.39217 −0.696083 0.717962i \(-0.745075\pi\)
−0.696083 + 0.717962i \(0.745075\pi\)
\(434\) −31.9293 20.0118i −1.53266 0.960597i
\(435\) 0 0
\(436\) 5.48390 + 1.90488i 0.262631 + 0.0912272i
\(437\) 0.660427 0.176961i 0.0315925 0.00846519i
\(438\) 0 0
\(439\) −14.6656 + 8.46718i −0.699950 + 0.404116i −0.807329 0.590102i \(-0.799088\pi\)
0.107379 + 0.994218i \(0.465754\pi\)
\(440\) 2.44788 22.4141i 0.116698 1.06855i
\(441\) 0 0
\(442\) −9.83987 3.02292i −0.468035 0.143786i
\(443\) −0.826654 + 3.08511i −0.0392755 + 0.146578i −0.982779 0.184784i \(-0.940841\pi\)
0.943504 + 0.331362i \(0.107508\pi\)
\(444\) 0 0
\(445\) −4.81702 17.9773i −0.228348 0.852208i
\(446\) −19.6895 0.714257i −0.932325 0.0338211i
\(447\) 0 0
\(448\) 31.9534 10.0961i 1.50966 0.476998i
\(449\) 41.9192 1.97829 0.989145 0.146944i \(-0.0469436\pi\)
0.989145 + 0.146944i \(0.0469436\pi\)
\(450\) 0 0
\(451\) 9.88149 9.88149i 0.465301 0.465301i
\(452\) −16.4656 1.19619i −0.774478 0.0562641i
\(453\) 0 0
\(454\) 7.84896 7.29943i 0.368370 0.342579i
\(455\) −20.4959 11.8333i −0.960862 0.554754i
\(456\) 0 0
\(457\) 4.93980 2.85199i 0.231074 0.133411i −0.379993 0.924989i \(-0.624074\pi\)
0.611067 + 0.791579i \(0.290740\pi\)
\(458\) −7.93860 + 25.8409i −0.370947 + 1.20746i
\(459\) 0 0
\(460\) −0.293154 1.53025i −0.0136684 0.0713484i
\(461\) 38.3338 + 10.2715i 1.78538 + 0.478392i 0.991548 0.129743i \(-0.0414153\pi\)
0.793834 + 0.608135i \(0.208082\pi\)
\(462\) 0 0
\(463\) −6.28293 + 10.8824i −0.291992 + 0.505746i −0.974281 0.225337i \(-0.927652\pi\)
0.682288 + 0.731083i \(0.260985\pi\)
\(464\) 21.7566 16.2109i 1.01003 0.752570i
\(465\) 0 0
\(466\) −12.8993 8.08471i −0.597551 0.374517i
\(467\) −12.1784 + 12.1784i −0.563550 + 0.563550i −0.930314 0.366764i \(-0.880466\pi\)
0.366764 + 0.930314i \(0.380466\pi\)
\(468\) 0 0
\(469\) 30.1267 + 30.1267i 1.39112 + 1.39112i
\(470\) 21.1576 4.85447i 0.975928 0.223920i
\(471\) 0 0
\(472\) −4.28846 + 0.661386i −0.197393 + 0.0304428i
\(473\) −45.7025 26.3864i −2.10140 1.21325i
\(474\) 0 0
\(475\) −0.844652 + 3.15228i −0.0387553 + 0.144637i
\(476\) −14.8457 10.0721i −0.680452 0.461656i
\(477\) 0 0
\(478\) −14.7586 27.8478i −0.675043 1.27373i
\(479\) 10.6864 + 18.5094i 0.488275 + 0.845717i 0.999909 0.0134862i \(-0.00429292\pi\)
−0.511634 + 0.859204i \(0.670960\pi\)
\(480\) 0 0
\(481\) −1.75031 + 3.03162i −0.0798072 + 0.138230i
\(482\) 38.8046 + 1.40768i 1.76750 + 0.0641180i
\(483\) 0 0
\(484\) −1.73896 + 23.9368i −0.0790435 + 1.08804i
\(485\) −13.3465 13.3465i −0.606033 0.606033i
\(486\) 0 0
\(487\) 39.3716i 1.78410i 0.451939 + 0.892049i \(0.350732\pi\)
−0.451939 + 0.892049i \(0.649268\pi\)
\(488\) −20.5587 7.98769i −0.930649 0.361586i
\(489\) 0 0
\(490\) −16.8830 18.1540i −0.762695 0.820113i
\(491\) 33.8903 9.08087i 1.52945 0.409814i 0.606608 0.795001i \(-0.292530\pi\)
0.922839 + 0.385187i \(0.125863\pi\)
\(492\) 0 0
\(493\) −14.0303 3.75940i −0.631891 0.169315i
\(494\) −6.19624 + 3.28385i −0.278782 + 0.147747i
\(495\) 0 0
\(496\) 9.40375 + 23.6428i 0.422241 + 1.06160i
\(497\) 17.3388 + 30.0317i 0.777752 + 1.34711i
\(498\) 0 0
\(499\) 3.38889 + 12.6475i 0.151708 + 0.566181i 0.999365 + 0.0356364i \(0.0113458\pi\)
−0.847657 + 0.530544i \(0.821988\pi\)
\(500\) 22.7270 + 7.89441i 1.01638 + 0.353049i
\(501\) 0 0
\(502\) −22.2469 + 5.10440i −0.992928 + 0.227820i
\(503\) 2.93881i 0.131035i 0.997851 + 0.0655175i \(0.0208698\pi\)
−0.997851 + 0.0655175i \(0.979130\pi\)
\(504\) 0 0
\(505\) 4.99373i 0.222218i
\(506\) 0.710860 + 3.09820i 0.0316016 + 0.137732i
\(507\) 0 0
\(508\) 1.46896 + 3.03261i 0.0651744 + 0.134550i
\(509\) −4.11461 15.3559i −0.182377 0.680640i −0.995177 0.0980972i \(-0.968724\pi\)
0.812800 0.582543i \(-0.197942\pi\)
\(510\) 0 0
\(511\) 17.1038 + 29.6246i 0.756627 + 1.31052i
\(512\) −21.4332 7.25389i −0.947222 0.320580i
\(513\) 0 0
\(514\) −1.23228 2.32517i −0.0543535 0.102559i
\(515\) −2.31418 0.620083i −0.101975 0.0273241i
\(516\) 0 0
\(517\) −42.7772 + 11.4621i −1.88134 + 0.504103i
\(518\) −4.46754 + 4.15476i −0.196293 + 0.182550i
\(519\) 0 0
\(520\) 6.44051 + 14.6252i 0.282435 + 0.641356i
\(521\) 19.2119i 0.841689i −0.907133 0.420844i \(-0.861734\pi\)
0.907133 0.420844i \(-0.138266\pi\)
\(522\) 0 0
\(523\) −10.0495 10.0495i −0.439436 0.439436i 0.452386 0.891822i \(-0.350573\pi\)
−0.891822 + 0.452386i \(0.850573\pi\)
\(524\) −11.5355 + 9.97293i −0.503929 + 0.435669i
\(525\) 0 0
\(526\) −0.00245585 + 0.0676988i −0.000107080 + 0.00295181i
\(527\) 6.81087 11.7968i 0.296686 0.513875i
\(528\) 0 0
\(529\) −11.3902 19.7284i −0.495225 0.857755i
\(530\) −3.46296 + 1.83528i −0.150422 + 0.0797196i
\(531\) 0 0
\(532\) −12.0034 + 2.29952i −0.520413 + 0.0996967i
\(533\) −2.56346 + 9.56697i −0.111036 + 0.414392i
\(534\) 0 0
\(535\) −11.9217 6.88297i −0.515418 0.297577i
\(536\) −4.38500 28.4326i −0.189403 1.22810i
\(537\) 0 0
\(538\) −6.51581 28.3984i −0.280916 1.22434i
\(539\) 35.7637 + 35.7637i 1.54045 + 1.54045i
\(540\) 0 0
\(541\) 15.3802 15.3802i 0.661246 0.661246i −0.294428 0.955674i \(-0.595129\pi\)
0.955674 + 0.294428i \(0.0951290\pi\)
\(542\) −11.8519 + 18.9101i −0.509084 + 0.812257i
\(543\) 0 0
\(544\) 4.06599 + 11.4109i 0.174328 + 0.489239i
\(545\) −2.41243 + 4.17844i −0.103337 + 0.178985i
\(546\) 0 0
\(547\) −23.1362 6.19933i −0.989233 0.265064i −0.272304 0.962211i \(-0.587786\pi\)
−0.716928 + 0.697147i \(0.754452\pi\)
\(548\) 15.8009 + 10.7202i 0.674981 + 0.457944i
\(549\) 0 0
\(550\) −14.5033 4.45558i −0.618423 0.189986i
\(551\) −8.56961 + 4.94767i −0.365078 + 0.210778i
\(552\) 0 0
\(553\) 26.3412 + 15.2081i 1.12014 + 0.646714i
\(554\) 7.19265 + 7.73414i 0.305587 + 0.328592i
\(555\) 0 0
\(556\) 18.9155 + 21.8792i 0.802197 + 0.927883i
\(557\) −0.932077 + 0.932077i −0.0394934 + 0.0394934i −0.726578 0.687084i \(-0.758890\pi\)
0.687084 + 0.726578i \(0.258890\pi\)
\(558\) 0 0
\(559\) 37.4027 1.58197
\(560\) 3.24445 + 27.6613i 0.137103 + 1.16890i
\(561\) 0 0
\(562\) 0.345986 9.53759i 0.0145945 0.402319i
\(563\) 1.71390 + 6.39635i 0.0722321 + 0.269574i 0.992591 0.121500i \(-0.0387704\pi\)
−0.920359 + 0.391074i \(0.872104\pi\)
\(564\) 0 0
\(565\) 3.55121 13.2533i 0.149400 0.557570i
\(566\) 5.34926 17.4123i 0.224846 0.731893i
\(567\) 0 0
\(568\) 2.54213 23.2771i 0.106665 0.976685i
\(569\) −7.84553 + 4.52962i −0.328902 + 0.189892i −0.655353 0.755322i \(-0.727480\pi\)
0.326452 + 0.945214i \(0.394147\pi\)
\(570\) 0 0
\(571\) −17.9078 + 4.79838i −0.749417 + 0.200806i −0.613260 0.789881i \(-0.710142\pi\)
−0.136158 + 0.990687i \(0.543475\pi\)
\(572\) −14.2126 29.3415i −0.594259 1.22683i
\(573\) 0 0
\(574\) −9.16703 + 14.6262i −0.382625 + 0.610487i
\(575\) −1.04844 −0.0437230
\(576\) 0 0
\(577\) 43.3455 1.80450 0.902248 0.431217i \(-0.141916\pi\)
0.902248 + 0.431217i \(0.141916\pi\)
\(578\) −9.32368 + 14.8762i −0.387814 + 0.618767i
\(579\) 0 0
\(580\) 9.83019 + 20.2941i 0.408177 + 0.842668i
\(581\) 31.7993 8.52060i 1.31926 0.353494i
\(582\) 0 0
\(583\) 6.92456 3.99790i 0.286786 0.165576i
\(584\) 2.50767 22.9616i 0.103768 0.950156i
\(585\) 0 0
\(586\) −5.96717 + 19.4236i −0.246501 + 0.802383i
\(587\) 6.81553 25.4359i 0.281307 1.04985i −0.670189 0.742191i \(-0.733787\pi\)
0.951496 0.307662i \(-0.0995465\pi\)
\(588\) 0 0
\(589\) −2.40180 8.96364i −0.0989645 0.369341i
\(590\) 0.130737 3.60395i 0.00538236 0.148372i
\(591\) 0 0
\(592\) 4.09148 0.479899i 0.168159 0.0197237i
\(593\) −41.9274 −1.72175 −0.860876 0.508814i \(-0.830084\pi\)
−0.860876 + 0.508814i \(0.830084\pi\)
\(594\) 0 0
\(595\) 10.5430 10.5430i 0.432222 0.432222i
\(596\) −2.25129 2.60402i −0.0922164 0.106665i
\(597\) 0 0
\(598\) −1.53425 1.64975i −0.0627401 0.0674634i
\(599\) 21.1742 + 12.2249i 0.865154 + 0.499497i 0.865735 0.500503i \(-0.166852\pi\)
−0.000580933 1.00000i \(0.500185\pi\)
\(600\) 0 0
\(601\) 24.7521 14.2906i 1.00966 0.582928i 0.0985682 0.995130i \(-0.468574\pi\)
0.911092 + 0.412203i \(0.135240\pi\)
\(602\) 62.3115 + 19.1428i 2.53963 + 0.780202i
\(603\) 0 0
\(604\) −35.3686 23.9960i −1.43913 0.976383i
\(605\) −19.2669 5.16255i −0.783310 0.209887i
\(606\) 0 0
\(607\) −9.32245 + 16.1470i −0.378387 + 0.655385i −0.990828 0.135131i \(-0.956854\pi\)
0.612441 + 0.790516i \(0.290188\pi\)
\(608\) 7.45551 + 3.53819i 0.302361 + 0.143492i
\(609\) 0 0
\(610\) 9.73492 15.5323i 0.394155 0.628885i
\(611\) 22.1946 22.1946i 0.897896 0.897896i
\(612\) 0 0
\(613\) −13.3177 13.3177i −0.537896 0.537896i 0.385014 0.922911i \(-0.374196\pi\)
−0.922911 + 0.385014i \(0.874196\pi\)
\(614\) −5.47424 23.8588i −0.220922 0.962864i
\(615\) 0 0
\(616\) −8.66061 56.1559i −0.348946 2.26258i
\(617\) 15.1035 + 8.72003i 0.608045 + 0.351055i 0.772200 0.635379i \(-0.219156\pi\)
−0.164155 + 0.986435i \(0.552490\pi\)
\(618\) 0 0
\(619\) 5.84959 21.8310i 0.235115 0.877461i −0.742982 0.669311i \(-0.766589\pi\)
0.978097 0.208150i \(-0.0667441\pi\)
\(620\) −20.7693 + 3.97883i −0.834117 + 0.159794i
\(621\) 0 0
\(622\) 1.07174 0.567995i 0.0429729 0.0227745i
\(623\) −23.4506 40.6177i −0.939530 1.62731i
\(624\) 0 0
\(625\) −4.40527 + 7.63015i −0.176211 + 0.305206i
\(626\) −0.941180 + 25.9449i −0.0376171 + 1.03697i
\(627\) 0 0
\(628\) 16.0492 13.8753i 0.640433 0.553683i
\(629\) −1.55946 1.55946i −0.0621797 0.0621797i
\(630\) 0 0
\(631\) 19.8510i 0.790254i −0.918627 0.395127i \(-0.870701\pi\)
0.918627 0.395127i \(-0.129299\pi\)
\(632\) −8.27732 18.7962i −0.329254 0.747673i
\(633\) 0 0
\(634\) 4.31682 4.01459i 0.171443 0.159440i
\(635\) −2.70512 + 0.724836i −0.107350 + 0.0287642i
\(636\) 0 0
\(637\) −34.6254 9.27785i −1.37191 0.367602i
\(638\) −21.5428 40.6487i −0.852886 1.60930i
\(639\) 0 0
\(640\) 9.27269 16.3608i 0.366535 0.646719i
\(641\) −20.5842 35.6529i −0.813026 1.40820i −0.910736 0.412988i \(-0.864485\pi\)
0.0977099 0.995215i \(-0.468848\pi\)
\(642\) 0 0
\(643\) 6.73128 + 25.1215i 0.265456 + 0.990694i 0.961971 + 0.273152i \(0.0880662\pi\)
−0.696515 + 0.717542i \(0.745267\pi\)
\(644\) −1.71165 3.53366i −0.0674486 0.139246i
\(645\) 0 0
\(646\) −0.988006 4.30611i −0.0388726 0.169422i
\(647\) 40.3426i 1.58603i −0.609201 0.793016i \(-0.708510\pi\)
0.609201 0.793016i \(-0.291490\pi\)
\(648\) 0 0
\(649\) 7.35741i 0.288803i
\(650\) 10.4810 2.40479i 0.411099 0.0943238i
\(651\) 0 0
\(652\) 9.28783 + 3.22621i 0.363740 + 0.126348i
\(653\) −1.68547 6.29024i −0.0659574 0.246156i 0.925074 0.379787i \(-0.124003\pi\)
−0.991031 + 0.133631i \(0.957336\pi\)
\(654\) 0 0
\(655\) −6.33671 10.9755i −0.247596 0.428849i
\(656\) 10.8303 4.30768i 0.422854 0.168187i
\(657\) 0 0
\(658\) 48.3345 25.6161i 1.88428 0.998618i
\(659\) −0.0887093 0.0237696i −0.00345562 0.000925932i 0.257091 0.966387i \(-0.417236\pi\)
−0.260546 + 0.965461i \(0.583903\pi\)
\(660\) 0 0
\(661\) 27.0157 7.23883i 1.05079 0.281558i 0.308211 0.951318i \(-0.400270\pi\)
0.742578 + 0.669760i \(0.233603\pi\)
\(662\) −4.97638 5.35102i −0.193413 0.207973i
\(663\) 0 0
\(664\) −20.7204 8.05052i −0.804109 0.312421i
\(665\) 10.1575i 0.393892i
\(666\) 0 0
\(667\) −2.24790 2.24790i −0.0870392 0.0870392i
\(668\) −0.0464249 + 0.639041i −0.00179623 + 0.0247253i
\(669\) 0 0
\(670\) 23.8942 + 0.866788i 0.923114 + 0.0334870i
\(671\) −18.6988 + 32.3873i −0.721859 + 1.25030i
\(672\) 0 0
\(673\) 2.48158 + 4.29822i 0.0956578 + 0.165684i 0.909883 0.414865i \(-0.136171\pi\)
−0.814225 + 0.580549i \(0.802838\pi\)
\(674\) −2.57959 4.86739i −0.0993622 0.187485i
\(675\) 0 0
\(676\) −2.39400 1.62422i −0.0920769 0.0624700i
\(677\) −1.77876 + 6.63841i −0.0683632 + 0.255135i −0.991647 0.128985i \(-0.958828\pi\)
0.923283 + 0.384119i \(0.125495\pi\)
\(678\) 0 0
\(679\) −41.1923 23.7824i −1.58081 0.912683i
\(680\) −9.95015 + 1.53456i −0.381571 + 0.0588476i
\(681\) 0 0
\(682\) 42.0503 9.64814i 1.61019 0.369447i
\(683\) −20.7192 20.7192i −0.792797 0.792797i 0.189151 0.981948i \(-0.439426\pi\)
−0.981948 + 0.189151i \(0.939426\pi\)
\(684\) 0 0
\(685\) −11.2214 + 11.2214i −0.428747 + 0.428747i
\(686\) −17.7998 11.1561i −0.679601 0.425942i
\(687\) 0 0
\(688\) −26.2985 35.2953i −1.00262 1.34562i
\(689\) −2.83351 + 4.90779i −0.107948 + 0.186972i
\(690\) 0 0
\(691\) −5.31450 1.42402i −0.202173 0.0541721i 0.156311 0.987708i \(-0.450040\pi\)
−0.358484 + 0.933536i \(0.616706\pi\)
\(692\) 4.55420 + 23.7727i 0.173125 + 0.903704i
\(693\) 0 0
\(694\) 1.31056 4.26598i 0.0497481 0.161934i
\(695\) −20.8171 + 12.0188i −0.789638 + 0.455898i
\(696\) 0 0
\(697\) −5.40388 3.11993i −0.204687 0.118176i
\(698\) 1.49983 1.39483i 0.0567695 0.0527949i
\(699\) 0 0
\(700\) 18.6918 + 1.35791i 0.706482 + 0.0513243i
\(701\) 1.06232 1.06232i 0.0401233 0.0401233i −0.686760 0.726884i \(-0.740968\pi\)
0.726884 + 0.686760i \(0.240968\pi\)
\(702\) 0 0
\(703\) −1.50244 −0.0566656
\(704\) −17.6951 + 34.0423i −0.666910 + 1.28302i
\(705\) 0 0
\(706\) −21.8746 0.793524i −0.823261 0.0298647i
\(707\) 3.25705 + 12.1555i 0.122494 + 0.457153i
\(708\) 0 0
\(709\) −9.50159 + 35.4604i −0.356840 + 1.33174i 0.521314 + 0.853365i \(0.325442\pi\)
−0.878153 + 0.478379i \(0.841224\pi\)
\(710\) 18.6028 + 5.71498i 0.698149 + 0.214479i
\(711\) 0 0
\(712\) −3.43821 + 31.4821i −0.128853 + 1.17984i
\(713\) 2.58187 1.49064i 0.0966916 0.0558249i
\(714\) 0 0
\(715\) 26.1729 7.01301i 0.978812 0.262272i
\(716\) 49.9045 + 17.3348i 1.86502 + 0.647830i
\(717\) 0 0
\(718\) −5.73718 3.59580i −0.214110 0.134194i
\(719\) 7.37513 0.275046 0.137523 0.990499i \(-0.456086\pi\)
0.137523 + 0.990499i \(0.456086\pi\)
\(720\) 0 0
\(721\) −6.03749 −0.224848
\(722\) 20.2175 + 12.6714i 0.752419 + 0.471581i
\(723\) 0 0
\(724\) 3.81003 10.9686i 0.141599 0.407644i
\(725\) 14.6567 3.92726i 0.544337 0.145855i
\(726\) 0 0
\(727\) 5.80127 3.34936i 0.215157 0.124221i −0.388549 0.921428i \(-0.627023\pi\)
0.603706 + 0.797207i \(0.293690\pi\)
\(728\) 25.2161 + 31.3991i 0.934571 + 1.16373i
\(729\) 0 0
\(730\) 18.3506 + 5.63751i 0.679186 + 0.208654i
\(731\) −6.09879 + 22.7610i −0.225572 + 0.841846i
\(732\) 0 0
\(733\) −9.28281 34.6439i −0.342868 1.27960i −0.895083 0.445900i \(-0.852884\pi\)
0.552214 0.833702i \(-0.313783\pi\)
\(734\) −28.0906 1.01902i −1.03684 0.0376126i
\(735\) 0 0
\(736\) −0.478040 + 2.60777i −0.0176208 + 0.0961238i
\(737\) −48.7797 −1.79682
\(738\) 0 0
\(739\) 4.01107 4.01107i 0.147549 0.147549i −0.629473 0.777022i \(-0.716729\pi\)
0.777022 + 0.629473i \(0.216729\pi\)
\(740\) −0.248076 + 3.41478i −0.00911945 + 0.125530i
\(741\) 0 0
\(742\) −7.23234 + 6.72599i −0.265508 + 0.246919i
\(743\) −19.1551 11.0592i −0.702734 0.405724i 0.105631 0.994405i \(-0.466314\pi\)
−0.808365 + 0.588682i \(0.799647\pi\)
\(744\) 0 0
\(745\) 2.47761 1.43045i 0.0907726 0.0524076i
\(746\) −0.183846 + 0.598434i −0.00673107 + 0.0219102i
\(747\) 0 0
\(748\) 20.1729 3.86457i 0.737594 0.141303i
\(749\) −33.5083 8.97853i −1.22437 0.328068i
\(750\) 0 0
\(751\) −6.05672 + 10.4905i −0.221013 + 0.382805i −0.955116 0.296233i \(-0.904270\pi\)
0.734103 + 0.679038i \(0.237603\pi\)
\(752\) −36.5494 5.33864i −1.33282 0.194680i
\(753\) 0 0
\(754\) 27.6278 + 17.3158i 1.00614 + 0.630603i
\(755\) 25.1178 25.1178i 0.914131 0.914131i
\(756\) 0 0
\(757\) −19.9365 19.9365i −0.724604 0.724604i 0.244935 0.969539i \(-0.421233\pi\)
−0.969539 + 0.244935i \(0.921233\pi\)
\(758\) −12.0495 + 2.76468i −0.437659 + 0.100418i
\(759\) 0 0
\(760\) −4.05395 + 5.53240i −0.147052 + 0.200681i
\(761\) 37.1681 + 21.4590i 1.34734 + 0.777889i 0.987873 0.155267i \(-0.0496237\pi\)
0.359471 + 0.933156i \(0.382957\pi\)
\(762\) 0 0
\(763\) −3.14690 + 11.7444i −0.113925 + 0.425176i
\(764\) −19.3156 + 28.4700i −0.698814 + 1.03001i
\(765\) 0 0
\(766\) 8.56555 + 16.1622i 0.309486 + 0.583964i
\(767\) −2.60728 4.51595i −0.0941435 0.163061i
\(768\) 0 0
\(769\) −13.7618 + 23.8361i −0.496263 + 0.859553i −0.999991 0.00430961i \(-0.998628\pi\)
0.503728 + 0.863863i \(0.331962\pi\)
\(770\) 47.1924 + 1.71195i 1.70070 + 0.0616945i
\(771\) 0 0
\(772\) −36.6019 2.65905i −1.31733 0.0957011i
\(773\) 11.4688 + 11.4688i 0.412504 + 0.412504i 0.882610 0.470106i \(-0.155784\pi\)
−0.470106 + 0.882610i \(0.655784\pi\)
\(774\) 0 0
\(775\) 14.2300i 0.511155i
\(776\) 12.9440 + 29.3934i 0.464664 + 1.05516i
\(777\) 0 0
\(778\) 26.3489 + 28.3326i 0.944655 + 1.01577i
\(779\) −4.10608 + 1.10022i −0.147115 + 0.0394195i
\(780\) 0 0
\(781\) −38.3500 10.2759i −1.37227 0.367699i
\(782\) 1.25411 0.664645i 0.0448468 0.0237677i
\(783\) 0 0
\(784\) 15.5906 + 39.1979i 0.556808 + 1.39992i
\(785\) 8.81622 + 15.2701i 0.314664 + 0.545015i
\(786\) 0 0
\(787\) 11.4753 + 42.8263i 0.409049 + 1.52659i 0.796463 + 0.604687i \(0.206702\pi\)
−0.387414 + 0.921906i \(0.626632\pi\)
\(788\) −8.17112 + 23.5236i −0.291084 + 0.837993i
\(789\) 0 0
\(790\) 16.6370 3.81725i 0.591920 0.135812i
\(791\) 34.5766i 1.22940i
\(792\) 0 0
\(793\) 26.5056i 0.941241i
\(794\) −9.82821 42.8351i −0.348790 1.52016i
\(795\) 0 0
\(796\) 18.0495 8.74290i 0.639746 0.309884i
\(797\) −7.68647 28.6863i −0.272269 1.01612i −0.957650 0.287936i \(-0.907031\pi\)
0.685381 0.728185i \(-0.259636\pi\)
\(798\) 0 0
\(799\) 9.88726 + 17.1252i 0.349786 + 0.605847i
\(800\) −9.63868 8.19961i −0.340779 0.289900i
\(801\) 0 0
\(802\) 17.8766 + 33.7310i 0.631244 + 1.19108i
\(803\) −37.8302 10.1366i −1.33500 0.357712i
\(804\) 0 0
\(805\) 3.15206 0.844592i 0.111096 0.0297679i
\(806\) −22.3912 + 20.8236i −0.788698 + 0.733479i
\(807\) 0 0
\(808\) 3.07735 7.92049i 0.108261 0.278642i
\(809\) 16.7474i 0.588806i 0.955681 + 0.294403i \(0.0951209\pi\)
−0.955681 + 0.294403i \(0.904879\pi\)
\(810\) 0 0
\(811\) −7.60619 7.60619i −0.267090 0.267090i 0.560837 0.827926i \(-0.310480\pi\)
−0.827926 + 0.560837i \(0.810480\pi\)
\(812\) 37.1645 + 42.9874i 1.30422 + 1.50856i
\(813\) 0 0
\(814\) 0.253222 6.98041i 0.00887541 0.244663i
\(815\) −4.08582 + 7.07684i −0.143120 + 0.247891i
\(816\) 0 0
\(817\) 8.02649 + 13.9023i 0.280811 + 0.486379i
\(818\) 16.0934 8.52912i 0.562694 0.298214i
\(819\) 0 0
\(820\) 1.82263 + 9.51404i 0.0636489 + 0.332245i
\(821\) 9.99074 37.2860i 0.348679 1.30129i −0.539575 0.841937i \(-0.681415\pi\)
0.888255 0.459351i \(-0.151918\pi\)
\(822\) 0 0
\(823\) −23.9783 13.8439i −0.835831 0.482567i 0.0200141 0.999800i \(-0.493629\pi\)
−0.855845 + 0.517233i \(0.826962\pi\)
\(824\) 3.28838 + 2.40961i 0.114556 + 0.0839427i
\(825\) 0 0
\(826\) −2.03236 8.85781i −0.0707149 0.308203i
\(827\) 27.6025 + 27.6025i 0.959833 + 0.959833i 0.999224 0.0393907i \(-0.0125417\pi\)
−0.0393907 + 0.999224i \(0.512542\pi\)
\(828\) 0 0
\(829\) 14.8542 14.8542i 0.515908 0.515908i −0.400423 0.916330i \(-0.631137\pi\)
0.916330 + 0.400423i \(0.131137\pi\)
\(830\) 9.81150 15.6545i 0.340562 0.543375i
\(831\) 0 0
\(832\) −1.20256 27.1658i −0.0416911 0.941803i
\(833\) 11.2919 19.5581i 0.391240 0.677647i
\(834\) 0 0
\(835\) −0.514368 0.137824i −0.0178004 0.00476961i
\(836\) 7.85602 11.5793i 0.271706 0.400478i
\(837\) 0 0
\(838\) 0.284716 + 0.0874679i 0.00983534 + 0.00302153i
\(839\) 44.0413 25.4272i 1.52047 0.877846i 0.520766 0.853700i \(-0.325647\pi\)
0.999708 0.0241463i \(-0.00768676\pi\)
\(840\) 0 0
\(841\) 14.7301 + 8.50445i 0.507936 + 0.293257i
\(842\) −34.1297 36.6990i −1.17619 1.26473i
\(843\) 0 0
\(844\) −30.0863 + 26.0109i −1.03561 + 0.895333i
\(845\) 1.70015 1.70015i 0.0584871 0.0584871i
\(846\) 0 0
\(847\) −50.2656 −1.72715
\(848\) 6.62355 0.776891i 0.227454 0.0266786i
\(849\) 0 0
\(850\) −0.245597 + 6.77022i −0.00842390 + 0.232217i
\(851\) −0.124927 0.466233i −0.00428244 0.0159823i
\(852\) 0 0
\(853\) 3.65390 13.6365i 0.125107 0.466906i −0.874736 0.484599i \(-0.838966\pi\)
0.999843 + 0.0176931i \(0.00563219\pi\)
\(854\) 13.5656 44.1573i 0.464206 1.51103i
\(855\) 0 0
\(856\) 14.6672 + 18.2637i 0.501315 + 0.624239i
\(857\) −14.7618 + 8.52275i −0.504255 + 0.291132i −0.730469 0.682946i \(-0.760698\pi\)
0.226214 + 0.974078i \(0.427365\pi\)
\(858\) 0 0
\(859\) 24.9255 6.67877i 0.850448 0.227877i 0.192833 0.981232i \(-0.438232\pi\)
0.657614 + 0.753355i \(0.271566\pi\)
\(860\) 32.9227 15.9473i 1.12266 0.543798i
\(861\) 0 0
\(862\) −25.1853 + 40.1838i −0.857816 + 1.36867i
\(863\) 18.8217 0.640698 0.320349 0.947300i \(-0.396200\pi\)
0.320349 + 0.947300i \(0.396200\pi\)
\(864\) 0 0
\(865\) −20.1170 −0.683999
\(866\) −21.7570 + 34.7138i −0.739333 + 1.17962i
\(867\) 0 0
\(868\) −47.9605 + 23.2314i −1.62789 + 0.788525i
\(869\) −33.6373 + 9.01309i −1.14107 + 0.305748i
\(870\) 0 0
\(871\) 29.9408 17.2863i 1.01450 0.585725i
\(872\) 6.40126 5.14074i 0.216774 0.174088i
\(873\) 0 0
\(874\) 0.283955 0.924299i 0.00960492 0.0312649i
\(875\) −13.0417 + 48.6724i −0.440891 + 1.64543i
\(876\) 0 0
\(877\) 2.80014 + 10.4503i 0.0945540 + 0.352880i 0.996951 0.0780244i \(-0.0248612\pi\)
−0.902397 + 0.430905i \(0.858195\pi\)
\(878\) −0.868197 + 23.9330i −0.0293002 + 0.807701i
\(879\) 0 0
\(880\) −25.0205 19.7673i −0.843441 0.666354i
\(881\) −40.1658 −1.35322 −0.676610 0.736342i \(-0.736552\pi\)
−0.676610 + 0.736342i \(0.736552\pi\)
\(882\) 0 0
\(883\) −16.5617 + 16.5617i −0.557346 + 0.557346i −0.928551 0.371205i \(-0.878945\pi\)
0.371205 + 0.928551i \(0.378945\pi\)
\(884\) −11.0125 + 9.52083i −0.370392 + 0.320220i
\(885\) 0 0
\(886\) 3.07606 + 3.30763i 0.103342 + 0.111122i
\(887\) 13.1259 + 7.57822i 0.440723 + 0.254452i 0.703904 0.710295i \(-0.251438\pi\)
−0.263181 + 0.964746i \(0.584772\pi\)
\(888\) 0 0
\(889\) −6.11191 + 3.52871i −0.204987 + 0.118349i
\(890\) −25.1601 7.72948i −0.843370 0.259093i
\(891\) 0 0
\(892\) −15.6435 + 23.0576i −0.523784 + 0.772026i
\(893\) 13.0124 + 3.48667i 0.435444 + 0.116677i
\(894\) 0 0
\(895\) −21.9535 + 38.0246i −0.733826 + 1.27102i
\(896\) 11.9001 45.8726i 0.397554 1.53250i
\(897\) 0 0
\(898\) 31.4831 50.2320i 1.05060 1.67626i
\(899\) −30.5097 + 30.5097i −1.01755 + 1.01755i
\(900\) 0 0
\(901\) −2.52455 2.52455i −0.0841050 0.0841050i
\(902\) −4.41963 19.2624i −0.147158 0.641369i
\(903\) 0 0
\(904\) −13.7998 + 18.8325i −0.458974 + 0.626359i
\(905\) 8.35749 + 4.82520i 0.277812 + 0.160395i
\(906\) 0 0
\(907\) −2.61434 + 9.75684i −0.0868077 + 0.323971i −0.995650 0.0931683i \(-0.970301\pi\)
0.908843 + 0.417139i \(0.136967\pi\)
\(908\) −2.85206 14.8876i −0.0946489 0.494063i
\(909\) 0 0
\(910\) −29.5732 + 15.6730i −0.980341 + 0.519556i
\(911\) 25.2358 + 43.7097i 0.836099 + 1.44817i 0.893132 + 0.449794i \(0.148503\pi\)
−0.0570332 + 0.998372i \(0.518164\pi\)
\(912\) 0 0
\(913\) −18.8459 + 32.6420i −0.623708 + 1.08029i
\(914\) 0.292434 8.06136i 0.00967286 0.266646i
\(915\) 0 0
\(916\) 25.0030 + 28.9204i 0.826123 + 0.955558i
\(917\) −22.5830 22.5830i −0.745757 0.745757i
\(918\) 0 0
\(919\) 16.7422i 0.552274i 0.961118 + 0.276137i \(0.0890544\pi\)
−0.961118 + 0.276137i \(0.910946\pi\)
\(920\) −2.05388 0.797995i −0.0677145 0.0263091i
\(921\) 0 0
\(922\) 41.0987 38.2212i 1.35351 1.25875i
\(923\) 27.1806 7.28302i 0.894661 0.239724i
\(924\) 0 0
\(925\) 2.22538 + 0.596288i 0.0731699 + 0.0196058i
\(926\) 8.32164 + 15.7020i 0.273466 + 0.515999i
\(927\) 0 0
\(928\) −3.08543 38.2461i −0.101284 1.25549i
\(929\) −9.92665 17.1935i −0.325683 0.564099i 0.655967 0.754789i \(-0.272261\pi\)
−0.981650 + 0.190690i \(0.938927\pi\)
\(930\) 0 0
\(931\) −3.98199 14.8610i −0.130504 0.487049i
\(932\) −19.3759 + 9.38541i −0.634679 + 0.307429i
\(933\) 0 0
\(934\) 5.44696 + 23.7400i 0.178230 + 0.776795i
\(935\) 17.0708i 0.558273i
\(936\) 0 0
\(937\) 3.05876i 0.0999253i 0.998751 + 0.0499626i \(0.0159102\pi\)
−0.998751 + 0.0499626i \(0.984090\pi\)
\(938\) 58.7274 13.4746i 1.91752 0.439961i
\(939\) 0 0
\(940\) 10.0731 28.9992i 0.328549 0.945850i
\(941\) −3.07424 11.4732i −0.100217 0.374016i 0.897541 0.440930i \(-0.145351\pi\)
−0.997759 + 0.0669140i \(0.978685\pi\)
\(942\) 0 0
\(943\) −0.682835 1.18270i −0.0222362 0.0385141i
\(944\) −2.42827 + 5.63562i −0.0790335 + 0.183424i
\(945\) 0 0
\(946\) −65.9434 + 34.9483i −2.14401 + 1.13627i
\(947\) 55.6732 + 14.9176i 1.80914 + 0.484757i 0.995343 0.0963965i \(-0.0307317\pi\)
0.813794 + 0.581153i \(0.197398\pi\)
\(948\) 0 0
\(949\) 26.8122 7.18430i 0.870360 0.233212i
\(950\) 3.14303 + 3.37965i 0.101973 + 0.109650i
\(951\) 0 0
\(952\) −23.2193 + 10.2251i −0.752540 + 0.331397i
\(953\) 44.2546i 1.43355i 0.697306 + 0.716774i \(0.254382\pi\)
−0.697306 + 0.716774i \(0.745618\pi\)
\(954\) 0 0
\(955\) −20.2186 20.2186i −0.654259 0.654259i
\(956\) −44.4544 3.22951i −1.43776 0.104450i
\(957\) 0 0
\(958\) 30.2059 + 1.09575i 0.975908 + 0.0354021i
\(959\) −19.9956 + 34.6334i −0.645691 + 1.11837i
\(960\) 0 0
\(961\) −4.73171 8.19557i −0.152636 0.264373i
\(962\) 2.31826 + 4.37428i 0.0747436 + 0.141032i
\(963\) 0 0
\(964\) 30.8307 45.4425i 0.992990 1.46361i
\(965\) 7.89407 29.4611i 0.254119 0.948386i
\(966\) 0 0
\(967\) 36.7930 + 21.2424i 1.18318 + 0.683110i 0.956748 0.290916i \(-0.0939602\pi\)
0.226433 + 0.974027i \(0.427294\pi\)
\(968\) 27.3776 + 20.0614i 0.879950 + 0.644797i
\(969\) 0 0
\(970\) −26.0169 + 5.96940i −0.835354 + 0.191666i
\(971\) −11.1469 11.1469i −0.357720 0.357720i 0.505252 0.862972i \(-0.331400\pi\)
−0.862972 + 0.505252i \(0.831400\pi\)
\(972\) 0 0
\(973\) −42.8329 + 42.8329i −1.37316 + 1.37316i
\(974\) 47.1792 + 29.5697i 1.51172 + 0.947475i
\(975\) 0 0
\(976\) −25.0121 + 18.6365i −0.800619 + 0.596541i
\(977\) 2.47430 4.28561i 0.0791598 0.137109i −0.823728 0.566985i \(-0.808110\pi\)
0.902888 + 0.429877i \(0.141443\pi\)
\(978\) 0 0
\(979\) 51.8682 + 13.8980i 1.65771 + 0.444183i
\(980\) −34.4338 + 6.59657i −1.09995 + 0.210720i
\(981\) 0 0
\(982\) 14.5714 47.4310i 0.464991 1.51359i
\(983\) −41.6831 + 24.0658i −1.32948 + 0.767578i −0.985220 0.171294i \(-0.945205\pi\)
−0.344265 + 0.938873i \(0.611872\pi\)
\(984\) 0 0
\(985\) −17.9237 10.3483i −0.571098 0.329724i
\(986\) −15.0422 + 13.9891i −0.479042 + 0.445503i
\(987\) 0 0
\(988\) −0.718580 + 9.89130i −0.0228611 + 0.314684i
\(989\) −3.64672 + 3.64672i −0.115959 + 0.115959i
\(990\) 0 0
\(991\) −8.90020 −0.282724 −0.141362 0.989958i \(-0.545148\pi\)
−0.141362 + 0.989958i \(0.545148\pi\)
\(992\) 35.3940 + 6.48820i 1.12376 + 0.206001i
\(993\) 0 0
\(994\) 49.0093 + 1.77787i 1.55448 + 0.0563905i
\(995\) 4.31407 + 16.1003i 0.136765 + 0.510414i
\(996\) 0 0
\(997\) 6.66586 24.8773i 0.211110 0.787873i −0.776390 0.630253i \(-0.782951\pi\)
0.987500 0.157620i \(-0.0503822\pi\)
\(998\) 17.7008 + 5.43789i 0.560309 + 0.172133i
\(999\) 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 432.2.y.e.37.12 72
3.2 odd 2 144.2.x.e.85.7 yes 72
4.3 odd 2 1728.2.bc.e.1009.13 72
9.2 odd 6 144.2.x.e.133.18 yes 72
9.7 even 3 inner 432.2.y.e.181.1 72
12.11 even 2 576.2.bb.e.49.16 72
16.3 odd 4 1728.2.bc.e.145.6 72
16.13 even 4 inner 432.2.y.e.253.1 72
36.7 odd 6 1728.2.bc.e.1585.6 72
36.11 even 6 576.2.bb.e.241.8 72
48.29 odd 4 144.2.x.e.13.18 72
48.35 even 4 576.2.bb.e.337.8 72
144.29 odd 12 144.2.x.e.61.7 yes 72
144.61 even 12 inner 432.2.y.e.397.12 72
144.83 even 12 576.2.bb.e.529.16 72
144.115 odd 12 1728.2.bc.e.721.13 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.e.13.18 72 48.29 odd 4
144.2.x.e.61.7 yes 72 144.29 odd 12
144.2.x.e.85.7 yes 72 3.2 odd 2
144.2.x.e.133.18 yes 72 9.2 odd 6
432.2.y.e.37.12 72 1.1 even 1 trivial
432.2.y.e.181.1 72 9.7 even 3 inner
432.2.y.e.253.1 72 16.13 even 4 inner
432.2.y.e.397.12 72 144.61 even 12 inner
576.2.bb.e.49.16 72 12.11 even 2
576.2.bb.e.241.8 72 36.11 even 6
576.2.bb.e.337.8 72 48.35 even 4
576.2.bb.e.529.16 72 144.83 even 12
1728.2.bc.e.145.6 72 16.3 odd 4
1728.2.bc.e.721.13 72 144.115 odd 12
1728.2.bc.e.1009.13 72 4.3 odd 2
1728.2.bc.e.1585.6 72 36.7 odd 6