Properties

Label 162.3.f.a.89.2
Level $162$
Weight $3$
Character 162.89
Analytic conductor $4.414$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,3,Mod(17,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.f (of order \(18\), degree \(6\), 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: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 89.2
Character \(\chi\) \(=\) 162.89
Dual form 162.3.f.a.71.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(-0.379008 - 0.451684i) q^{5} +(2.96297 - 1.07843i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})\) \(q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(-0.379008 - 0.451684i) q^{5} +(2.96297 - 1.07843i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(0.416932 + 0.722148i) q^{10} +(6.03341 - 7.19034i) q^{11} +(2.11998 + 12.0230i) q^{13} +(-4.39145 + 0.774332i) q^{14} +(3.06418 + 2.57115i) q^{16} +(24.5140 - 14.1532i) q^{17} +(11.2011 - 19.4008i) q^{19} +(-0.403332 - 1.10814i) q^{20} +(-10.1687 + 8.53254i) q^{22} +(-3.44380 + 9.46175i) q^{23} +(4.28083 - 24.2778i) q^{25} -17.2654i q^{26} +6.30626 q^{28} +(23.6767 + 4.17484i) q^{29} +(42.7251 + 15.5506i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(-37.6170 + 13.6915i) q^{34} +(-1.61010 - 0.929592i) q^{35} +(-15.7500 - 27.2799i) q^{37} +(-20.3644 + 24.2694i) q^{38} +(0.289598 + 1.64239i) q^{40} +(-69.7771 + 12.3036i) q^{41} +(-11.1607 - 9.36490i) q^{43} +(16.2576 - 9.38633i) q^{44} +(7.11985 - 12.3319i) q^{46} +(18.9216 + 51.9868i) q^{47} +(-29.9200 + 25.1059i) q^{49} +(-11.9241 + 32.7611i) q^{50} +(-4.23996 + 24.0460i) q^{52} +25.4089i q^{53} -5.53447 q^{55} +(-8.78291 - 1.54866i) q^{56} +(-31.9499 - 11.6288i) q^{58} +(-18.4282 - 21.9619i) q^{59} +(-106.265 + 38.6772i) q^{61} +(-55.6855 - 32.1501i) q^{62} +(4.00000 + 6.92820i) q^{64} +(4.62711 - 5.51438i) q^{65} +(8.68700 + 49.2664i) q^{67} +(55.7526 - 9.83069i) q^{68} +(2.01415 + 1.69007i) q^{70} +(7.59817 - 4.38680i) q^{71} +(-11.7358 + 20.3271i) q^{73} +(15.2363 + 41.8613i) q^{74} +(34.3221 - 28.7997i) q^{76} +(10.1225 - 27.8114i) q^{77} +(23.0535 - 130.743i) q^{79} -2.35853i q^{80} +100.202 q^{82} +(66.1377 + 11.6619i) q^{83} +(-15.6838 - 5.70842i) q^{85} +(13.2440 + 15.7835i) q^{86} +(-24.9475 + 9.08013i) q^{88} +(-62.9935 - 36.3693i) q^{89} +(19.2475 + 33.3376i) q^{91} +(-12.9444 + 15.4266i) q^{92} +(-13.5860 - 77.0502i) q^{94} +(-13.0083 + 2.29372i) q^{95} +(120.419 + 101.043i) q^{97} +(47.8358 - 27.6180i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39273 0.245576i −0.696364 0.122788i
\(3\) 0 0
\(4\) 1.87939 + 0.684040i 0.469846 + 0.171010i
\(5\) −0.379008 0.451684i −0.0758015 0.0903368i 0.726811 0.686838i \(-0.241002\pi\)
−0.802612 + 0.596501i \(0.796557\pi\)
\(6\) 0 0
\(7\) 2.96297 1.07843i 0.423282 0.154062i −0.121592 0.992580i \(-0.538800\pi\)
0.544874 + 0.838518i \(0.316578\pi\)
\(8\) −2.44949 1.41421i −0.306186 0.176777i
\(9\) 0 0
\(10\) 0.416932 + 0.722148i 0.0416932 + 0.0722148i
\(11\) 6.03341 7.19034i 0.548492 0.653667i −0.418577 0.908181i \(-0.637471\pi\)
0.967069 + 0.254514i \(0.0819154\pi\)
\(12\) 0 0
\(13\) 2.11998 + 12.0230i 0.163076 + 0.924847i 0.951027 + 0.309109i \(0.100031\pi\)
−0.787951 + 0.615738i \(0.788858\pi\)
\(14\) −4.39145 + 0.774332i −0.313675 + 0.0553094i
\(15\) 0 0
\(16\) 3.06418 + 2.57115i 0.191511 + 0.160697i
\(17\) 24.5140 14.1532i 1.44200 0.832539i 0.444017 0.896018i \(-0.353553\pi\)
0.997983 + 0.0634789i \(0.0202195\pi\)
\(18\) 0 0
\(19\) 11.2011 19.4008i 0.589530 1.02110i −0.404764 0.914421i \(-0.632646\pi\)
0.994294 0.106675i \(-0.0340205\pi\)
\(20\) −0.403332 1.10814i −0.0201666 0.0554072i
\(21\) 0 0
\(22\) −10.1687 + 8.53254i −0.462213 + 0.387843i
\(23\) −3.44380 + 9.46175i −0.149730 + 0.411381i −0.991770 0.128036i \(-0.959133\pi\)
0.842039 + 0.539416i \(0.181355\pi\)
\(24\) 0 0
\(25\) 4.28083 24.2778i 0.171233 0.971112i
\(26\) 17.2654i 0.664054i
\(27\) 0 0
\(28\) 6.30626 0.225224
\(29\) 23.6767 + 4.17484i 0.816437 + 0.143960i 0.566246 0.824237i \(-0.308395\pi\)
0.250191 + 0.968196i \(0.419506\pi\)
\(30\) 0 0
\(31\) 42.7251 + 15.5506i 1.37823 + 0.501634i 0.921640 0.388045i \(-0.126849\pi\)
0.456587 + 0.889679i \(0.349072\pi\)
\(32\) −3.63616 4.33340i −0.113630 0.135419i
\(33\) 0 0
\(34\) −37.6170 + 13.6915i −1.10638 + 0.402691i
\(35\) −1.61010 0.929592i −0.0460029 0.0265598i
\(36\) 0 0
\(37\) −15.7500 27.2799i −0.425677 0.737293i 0.570807 0.821084i \(-0.306631\pi\)
−0.996483 + 0.0837909i \(0.973297\pi\)
\(38\) −20.3644 + 24.2694i −0.535906 + 0.638668i
\(39\) 0 0
\(40\) 0.289598 + 1.64239i 0.00723995 + 0.0410598i
\(41\) −69.7771 + 12.3036i −1.70188 + 0.300087i −0.938351 0.345685i \(-0.887646\pi\)
−0.763530 + 0.645773i \(0.776535\pi\)
\(42\) 0 0
\(43\) −11.1607 9.36490i −0.259550 0.217788i 0.503722 0.863866i \(-0.331964\pi\)
−0.763272 + 0.646078i \(0.776408\pi\)
\(44\) 16.2576 9.38633i 0.369491 0.213326i
\(45\) 0 0
\(46\) 7.11985 12.3319i 0.154779 0.268086i
\(47\) 18.9216 + 51.9868i 0.402588 + 1.10610i 0.961002 + 0.276540i \(0.0891878\pi\)
−0.558414 + 0.829562i \(0.688590\pi\)
\(48\) 0 0
\(49\) −29.9200 + 25.1059i −0.610612 + 0.512364i
\(50\) −11.9241 + 32.7611i −0.238482 + 0.655223i
\(51\) 0 0
\(52\) −4.23996 + 24.0460i −0.0815378 + 0.462424i
\(53\) 25.4089i 0.479412i 0.970845 + 0.239706i \(0.0770511\pi\)
−0.970845 + 0.239706i \(0.922949\pi\)
\(54\) 0 0
\(55\) −5.53447 −0.100627
\(56\) −8.78291 1.54866i −0.156838 0.0276547i
\(57\) 0 0
\(58\) −31.9499 11.6288i −0.550861 0.200497i
\(59\) −18.4282 21.9619i −0.312343 0.372236i 0.586919 0.809645i \(-0.300341\pi\)
−0.899263 + 0.437409i \(0.855896\pi\)
\(60\) 0 0
\(61\) −106.265 + 38.6772i −1.74205 + 0.634053i −0.999366 0.0355933i \(-0.988668\pi\)
−0.742680 + 0.669646i \(0.766446\pi\)
\(62\) −55.6855 32.1501i −0.898154 0.518549i
\(63\) 0 0
\(64\) 4.00000 + 6.92820i 0.0625000 + 0.108253i
\(65\) 4.62711 5.51438i 0.0711863 0.0848365i
\(66\) 0 0
\(67\) 8.68700 + 49.2664i 0.129657 + 0.735320i 0.978432 + 0.206567i \(0.0662291\pi\)
−0.848776 + 0.528753i \(0.822660\pi\)
\(68\) 55.7526 9.83069i 0.819891 0.144569i
\(69\) 0 0
\(70\) 2.01415 + 1.69007i 0.0287735 + 0.0241439i
\(71\) 7.59817 4.38680i 0.107016 0.0617860i −0.445536 0.895264i \(-0.646987\pi\)
0.552553 + 0.833478i \(0.313654\pi\)
\(72\) 0 0
\(73\) −11.7358 + 20.3271i −0.160765 + 0.278453i −0.935143 0.354270i \(-0.884729\pi\)
0.774378 + 0.632723i \(0.218063\pi\)
\(74\) 15.2363 + 41.8613i 0.205895 + 0.565693i
\(75\) 0 0
\(76\) 34.3221 28.7997i 0.451606 0.378943i
\(77\) 10.1225 27.8114i 0.131461 0.361187i
\(78\) 0 0
\(79\) 23.0535 130.743i 0.291816 1.65497i −0.388053 0.921637i \(-0.626852\pi\)
0.679869 0.733334i \(-0.262037\pi\)
\(80\) 2.35853i 0.0294816i
\(81\) 0 0
\(82\) 100.202 1.22198
\(83\) 66.1377 + 11.6619i 0.796839 + 0.140504i 0.557223 0.830363i \(-0.311867\pi\)
0.239617 + 0.970868i \(0.422978\pi\)
\(84\) 0 0
\(85\) −15.6838 5.70842i −0.184515 0.0671579i
\(86\) 13.2440 + 15.7835i 0.154000 + 0.183530i
\(87\) 0 0
\(88\) −24.9475 + 9.08013i −0.283494 + 0.103183i
\(89\) −62.9935 36.3693i −0.707792 0.408644i 0.102451 0.994738i \(-0.467332\pi\)
−0.810243 + 0.586094i \(0.800665\pi\)
\(90\) 0 0
\(91\) 19.2475 + 33.3376i 0.211511 + 0.366347i
\(92\) −12.9444 + 15.4266i −0.140700 + 0.167680i
\(93\) 0 0
\(94\) −13.5860 77.0502i −0.144532 0.819683i
\(95\) −13.0083 + 2.29372i −0.136930 + 0.0241444i
\(96\) 0 0
\(97\) 120.419 + 101.043i 1.24143 + 1.04168i 0.997411 + 0.0719147i \(0.0229109\pi\)
0.244021 + 0.969770i \(0.421534\pi\)
\(98\) 47.8358 27.6180i 0.488120 0.281816i
\(99\) 0 0
\(100\) 24.6523 42.6991i 0.246523 0.426991i
\(101\) −42.9450 117.991i −0.425198 1.16822i −0.948694 0.316195i \(-0.897595\pi\)
0.523496 0.852028i \(-0.324628\pi\)
\(102\) 0 0
\(103\) 72.1665 60.5548i 0.700645 0.587911i −0.221312 0.975203i \(-0.571034\pi\)
0.921957 + 0.387292i \(0.126589\pi\)
\(104\) 11.8102 32.4484i 0.113560 0.312003i
\(105\) 0 0
\(106\) 6.23979 35.3876i 0.0588660 0.333846i
\(107\) 107.896i 1.00838i 0.863594 + 0.504188i \(0.168208\pi\)
−0.863594 + 0.504188i \(0.831792\pi\)
\(108\) 0 0
\(109\) −42.9667 −0.394190 −0.197095 0.980384i \(-0.563151\pi\)
−0.197095 + 0.980384i \(0.563151\pi\)
\(110\) 7.70802 + 1.35913i 0.0700729 + 0.0123557i
\(111\) 0 0
\(112\) 11.8519 + 4.31374i 0.105820 + 0.0385155i
\(113\) −6.89768 8.22034i −0.0610414 0.0727463i 0.734660 0.678436i \(-0.237342\pi\)
−0.795701 + 0.605689i \(0.792897\pi\)
\(114\) 0 0
\(115\) 5.57895 2.03057i 0.0485126 0.0176571i
\(116\) 41.6418 + 24.0419i 0.358981 + 0.207258i
\(117\) 0 0
\(118\) 20.2722 + 35.1125i 0.171799 + 0.297564i
\(119\) 57.3711 68.3722i 0.482110 0.574556i
\(120\) 0 0
\(121\) 5.71249 + 32.3971i 0.0472106 + 0.267745i
\(122\) 157.496 27.7708i 1.29095 0.227630i
\(123\) 0 0
\(124\) 69.6596 + 58.4513i 0.561771 + 0.471382i
\(125\) −25.3543 + 14.6383i −0.202834 + 0.117106i
\(126\) 0 0
\(127\) −49.1507 + 85.1315i −0.387013 + 0.670327i −0.992046 0.125874i \(-0.959827\pi\)
0.605033 + 0.796200i \(0.293160\pi\)
\(128\) −3.86952 10.6314i −0.0302306 0.0830579i
\(129\) 0 0
\(130\) −7.79850 + 6.54372i −0.0599885 + 0.0503363i
\(131\) 46.8665 128.765i 0.357760 0.982937i −0.622045 0.782981i \(-0.713698\pi\)
0.979805 0.199956i \(-0.0640799\pi\)
\(132\) 0 0
\(133\) 12.2660 69.5638i 0.0922253 0.523036i
\(134\) 70.7481i 0.527971i
\(135\) 0 0
\(136\) −80.0624 −0.588694
\(137\) −197.146 34.7622i −1.43902 0.253739i −0.600947 0.799289i \(-0.705210\pi\)
−0.838078 + 0.545550i \(0.816321\pi\)
\(138\) 0 0
\(139\) −6.69802 2.43788i −0.0481872 0.0175387i 0.317814 0.948153i \(-0.397051\pi\)
−0.366001 + 0.930614i \(0.619273\pi\)
\(140\) −2.39012 2.84844i −0.0170723 0.0203460i
\(141\) 0 0
\(142\) −11.6595 + 4.24370i −0.0821090 + 0.0298852i
\(143\) 99.2403 + 57.2964i 0.693988 + 0.400674i
\(144\) 0 0
\(145\) −7.08794 12.2767i −0.0488823 0.0846666i
\(146\) 21.3367 25.4281i 0.146142 0.174165i
\(147\) 0 0
\(148\) −10.9399 62.0430i −0.0739180 0.419210i
\(149\) −92.3284 + 16.2800i −0.619654 + 0.109262i −0.474658 0.880171i \(-0.657428\pi\)
−0.144996 + 0.989432i \(0.546317\pi\)
\(150\) 0 0
\(151\) 154.567 + 129.697i 1.02362 + 0.858921i 0.990078 0.140516i \(-0.0448762\pi\)
0.0335439 + 0.999437i \(0.489321\pi\)
\(152\) −54.8738 + 31.6814i −0.361012 + 0.208430i
\(153\) 0 0
\(154\) −20.9277 + 36.2479i −0.135894 + 0.235376i
\(155\) −9.16915 25.1920i −0.0591558 0.162529i
\(156\) 0 0
\(157\) −56.2262 + 47.1794i −0.358128 + 0.300505i −0.804044 0.594569i \(-0.797323\pi\)
0.445916 + 0.895075i \(0.352878\pi\)
\(158\) −64.2144 + 176.428i −0.406420 + 1.11663i
\(159\) 0 0
\(160\) −0.579196 + 3.28479i −0.00361998 + 0.0205299i
\(161\) 31.7488i 0.197198i
\(162\) 0 0
\(163\) −217.128 −1.33208 −0.666038 0.745918i \(-0.732011\pi\)
−0.666038 + 0.745918i \(0.732011\pi\)
\(164\) −139.554 24.6072i −0.850940 0.150044i
\(165\) 0 0
\(166\) −89.2480 32.4836i −0.537638 0.195684i
\(167\) 138.533 + 165.098i 0.829541 + 0.988609i 0.999995 + 0.00324290i \(0.00103225\pi\)
−0.170454 + 0.985366i \(0.554523\pi\)
\(168\) 0 0
\(169\) 18.7495 6.82427i 0.110944 0.0403803i
\(170\) 20.4414 + 11.8018i 0.120243 + 0.0694225i
\(171\) 0 0
\(172\) −14.5692 25.2346i −0.0847046 0.146713i
\(173\) −40.5261 + 48.2971i −0.234255 + 0.279174i −0.870347 0.492439i \(-0.836105\pi\)
0.636092 + 0.771613i \(0.280550\pi\)
\(174\) 0 0
\(175\) −13.4980 76.5511i −0.0771316 0.437435i
\(176\) 36.9749 6.51967i 0.210085 0.0370436i
\(177\) 0 0
\(178\) 78.8015 + 66.1223i 0.442705 + 0.371473i
\(179\) −172.225 + 99.4340i −0.962150 + 0.555497i −0.896834 0.442367i \(-0.854139\pi\)
−0.0653157 + 0.997865i \(0.520805\pi\)
\(180\) 0 0
\(181\) −35.6490 + 61.7458i −0.196956 + 0.341137i −0.947540 0.319638i \(-0.896439\pi\)
0.750584 + 0.660775i \(0.229772\pi\)
\(182\) −18.6196 51.1569i −0.102306 0.281082i
\(183\) 0 0
\(184\) 21.8165 18.3062i 0.118568 0.0994902i
\(185\) −6.35249 + 17.4533i −0.0343378 + 0.0943422i
\(186\) 0 0
\(187\) 46.1370 261.656i 0.246722 1.39923i
\(188\) 110.646i 0.588545i
\(189\) 0 0
\(190\) 18.6804 0.0983177
\(191\) 98.1741 + 17.3107i 0.514000 + 0.0906322i 0.424631 0.905366i \(-0.360404\pi\)
0.0893693 + 0.995999i \(0.471515\pi\)
\(192\) 0 0
\(193\) −178.750 65.0595i −0.926164 0.337096i −0.165476 0.986214i \(-0.552916\pi\)
−0.760688 + 0.649118i \(0.775138\pi\)
\(194\) −142.897 170.298i −0.736582 0.877825i
\(195\) 0 0
\(196\) −73.4046 + 26.7171i −0.374513 + 0.136312i
\(197\) 159.929 + 92.3348i 0.811820 + 0.468705i 0.847588 0.530656i \(-0.178054\pi\)
−0.0357675 + 0.999360i \(0.511388\pi\)
\(198\) 0 0
\(199\) −31.0944 53.8571i −0.156253 0.270639i 0.777261 0.629178i \(-0.216608\pi\)
−0.933515 + 0.358539i \(0.883275\pi\)
\(200\) −44.8199 + 53.4142i −0.224099 + 0.267071i
\(201\) 0 0
\(202\) 30.8352 + 174.875i 0.152649 + 0.865718i
\(203\) 74.6556 13.1638i 0.367762 0.0648463i
\(204\) 0 0
\(205\) 32.0034 + 26.8540i 0.156114 + 0.130995i
\(206\) −115.379 + 66.6141i −0.560093 + 0.323370i
\(207\) 0 0
\(208\) −24.4170 + 42.2914i −0.117389 + 0.203324i
\(209\) −71.9179 197.593i −0.344105 0.945420i
\(210\) 0 0
\(211\) 5.60018 4.69911i 0.0265411 0.0222706i −0.629421 0.777065i \(-0.716708\pi\)
0.655962 + 0.754794i \(0.272263\pi\)
\(212\) −17.3807 + 47.7530i −0.0819843 + 0.225250i
\(213\) 0 0
\(214\) 26.4967 150.270i 0.123816 0.702197i
\(215\) 8.59045i 0.0399556i
\(216\) 0 0
\(217\) 143.364 0.660661
\(218\) 59.8410 + 10.5516i 0.274500 + 0.0484017i
\(219\) 0 0
\(220\) −10.4014 3.78580i −0.0472791 0.0172082i
\(221\) 222.133 + 264.728i 1.00513 + 1.19786i
\(222\) 0 0
\(223\) −80.8775 + 29.4370i −0.362679 + 0.132004i −0.516931 0.856027i \(-0.672926\pi\)
0.154252 + 0.988032i \(0.450703\pi\)
\(224\) −15.4471 8.91840i −0.0689604 0.0398143i
\(225\) 0 0
\(226\) 7.58788 + 13.1426i 0.0335747 + 0.0581531i
\(227\) −42.0709 + 50.1382i −0.185335 + 0.220873i −0.850709 0.525636i \(-0.823827\pi\)
0.665375 + 0.746509i \(0.268272\pi\)
\(228\) 0 0
\(229\) −57.3799 325.418i −0.250567 1.42104i −0.807199 0.590279i \(-0.799018\pi\)
0.556632 0.830759i \(-0.312093\pi\)
\(230\) −8.26862 + 1.45798i −0.0359505 + 0.00633904i
\(231\) 0 0
\(232\) −52.0917 43.7101i −0.224533 0.188406i
\(233\) 123.820 71.4877i 0.531418 0.306814i −0.210176 0.977664i \(-0.567404\pi\)
0.741594 + 0.670849i \(0.234070\pi\)
\(234\) 0 0
\(235\) 16.3101 28.2500i 0.0694049 0.120213i
\(236\) −19.6109 53.8806i −0.0830971 0.228308i
\(237\) 0 0
\(238\) −96.6929 + 81.1350i −0.406273 + 0.340903i
\(239\) 103.746 285.040i 0.434084 1.19264i −0.509200 0.860649i \(-0.670058\pi\)
0.943284 0.331988i \(-0.107719\pi\)
\(240\) 0 0
\(241\) −54.3108 + 308.012i −0.225356 + 1.27806i 0.636647 + 0.771155i \(0.280321\pi\)
−0.862003 + 0.506903i \(0.830790\pi\)
\(242\) 46.5232i 0.192245i
\(243\) 0 0
\(244\) −226.169 −0.926924
\(245\) 22.6798 + 3.99906i 0.0925707 + 0.0163227i
\(246\) 0 0
\(247\) 257.003 + 93.5413i 1.04050 + 0.378710i
\(248\) −82.6626 98.5135i −0.333317 0.397232i
\(249\) 0 0
\(250\) 38.9064 14.1608i 0.155626 0.0566431i
\(251\) −116.446 67.2298i −0.463926 0.267848i 0.249767 0.968306i \(-0.419646\pi\)
−0.713694 + 0.700458i \(0.752979\pi\)
\(252\) 0 0
\(253\) 47.2554 + 81.8488i 0.186780 + 0.323513i
\(254\) 89.3598 106.495i 0.351810 0.419271i
\(255\) 0 0
\(256\) 2.77837 + 15.7569i 0.0108530 + 0.0615505i
\(257\) −46.8542 + 8.26166i −0.182312 + 0.0321465i −0.264059 0.964507i \(-0.585061\pi\)
0.0817466 + 0.996653i \(0.473950\pi\)
\(258\) 0 0
\(259\) −76.0865 63.8441i −0.293770 0.246502i
\(260\) 12.4682 7.19851i 0.0479545 0.0276866i
\(261\) 0 0
\(262\) −96.8939 + 167.825i −0.369824 + 0.640554i
\(263\) 162.251 + 445.781i 0.616924 + 1.69498i 0.714392 + 0.699745i \(0.246703\pi\)
−0.0974685 + 0.995239i \(0.531075\pi\)
\(264\) 0 0
\(265\) 11.4768 9.63015i 0.0433085 0.0363402i
\(266\) −34.1663 + 93.8712i −0.128445 + 0.352899i
\(267\) 0 0
\(268\) −17.3740 + 98.5329i −0.0648284 + 0.367660i
\(269\) 455.081i 1.69175i −0.533380 0.845876i \(-0.679078\pi\)
0.533380 0.845876i \(-0.320922\pi\)
\(270\) 0 0
\(271\) 440.939 1.62708 0.813541 0.581508i \(-0.197537\pi\)
0.813541 + 0.581508i \(0.197537\pi\)
\(272\) 111.505 + 19.6614i 0.409946 + 0.0722845i
\(273\) 0 0
\(274\) 266.035 + 96.8287i 0.970929 + 0.353389i
\(275\) −148.738 177.259i −0.540864 0.644577i
\(276\) 0 0
\(277\) −70.8393 + 25.7834i −0.255738 + 0.0930808i −0.466708 0.884412i \(-0.654560\pi\)
0.210970 + 0.977493i \(0.432338\pi\)
\(278\) 8.72984 + 5.04017i 0.0314023 + 0.0181301i
\(279\) 0 0
\(280\) 2.62928 + 4.55405i 0.00939030 + 0.0162645i
\(281\) −4.98848 + 5.94504i −0.0177526 + 0.0211567i −0.774848 0.632148i \(-0.782173\pi\)
0.757095 + 0.653305i \(0.226618\pi\)
\(282\) 0 0
\(283\) 28.3852 + 160.981i 0.100301 + 0.568836i 0.992993 + 0.118169i \(0.0377026\pi\)
−0.892692 + 0.450667i \(0.851186\pi\)
\(284\) 17.2806 3.04704i 0.0608473 0.0107290i
\(285\) 0 0
\(286\) −124.144 104.169i −0.434071 0.364229i
\(287\) −193.479 + 111.705i −0.674143 + 0.389217i
\(288\) 0 0
\(289\) 256.124 443.620i 0.886244 1.53502i
\(290\) 6.85672 + 18.8387i 0.0236439 + 0.0649610i
\(291\) 0 0
\(292\) −35.9607 + 30.1746i −0.123153 + 0.103338i
\(293\) −18.4986 + 50.8246i −0.0631353 + 0.173463i −0.967249 0.253829i \(-0.918310\pi\)
0.904114 + 0.427292i \(0.140532\pi\)
\(294\) 0 0
\(295\) −2.93540 + 16.6475i −0.00995051 + 0.0564321i
\(296\) 89.0956i 0.300999i
\(297\) 0 0
\(298\) 132.586 0.444921
\(299\) −121.060 21.3461i −0.404882 0.0713915i
\(300\) 0 0
\(301\) −43.1681 15.7119i −0.143416 0.0521991i
\(302\) −183.419 218.591i −0.607349 0.723810i
\(303\) 0 0
\(304\) 84.2046 30.6480i 0.276989 0.100816i
\(305\) 57.7451 + 33.3391i 0.189328 + 0.109309i
\(306\) 0 0
\(307\) 73.1993 + 126.785i 0.238434 + 0.412980i 0.960265 0.279089i \(-0.0900325\pi\)
−0.721831 + 0.692069i \(0.756699\pi\)
\(308\) 38.0483 45.3442i 0.123533 0.147221i
\(309\) 0 0
\(310\) 6.58359 + 37.3374i 0.0212374 + 0.120443i
\(311\) −272.335 + 48.0200i −0.875676 + 0.154405i −0.593380 0.804922i \(-0.702207\pi\)
−0.282295 + 0.959328i \(0.591096\pi\)
\(312\) 0 0
\(313\) −22.9780 19.2809i −0.0734123 0.0616002i 0.605343 0.795965i \(-0.293036\pi\)
−0.678755 + 0.734364i \(0.737480\pi\)
\(314\) 89.8939 51.9003i 0.286286 0.165287i
\(315\) 0 0
\(316\) 132.760 229.946i 0.420125 0.727678i
\(317\) 91.5339 + 251.487i 0.288750 + 0.793335i 0.996242 + 0.0866133i \(0.0276045\pi\)
−0.707492 + 0.706722i \(0.750173\pi\)
\(318\) 0 0
\(319\) 172.870 145.055i 0.541911 0.454717i
\(320\) 1.61333 4.43258i 0.00504164 0.0138518i
\(321\) 0 0
\(322\) 7.79674 44.2175i 0.0242135 0.137321i
\(323\) 634.123i 1.96323i
\(324\) 0 0
\(325\) 300.968 0.926055
\(326\) 302.401 + 53.3214i 0.927610 + 0.163563i
\(327\) 0 0
\(328\) 188.318 + 68.5422i 0.574141 + 0.208970i
\(329\) 112.129 + 133.630i 0.340817 + 0.406169i
\(330\) 0 0
\(331\) −358.351 + 130.429i −1.08263 + 0.394045i −0.820886 0.571092i \(-0.806520\pi\)
−0.261744 + 0.965137i \(0.584298\pi\)
\(332\) 116.321 + 67.1580i 0.350364 + 0.202283i
\(333\) 0 0
\(334\) −152.395 263.957i −0.456274 0.790289i
\(335\) 18.9604 22.5961i 0.0565982 0.0674511i
\(336\) 0 0
\(337\) 20.7953 + 117.936i 0.0617071 + 0.349958i 0.999992 + 0.00409401i \(0.00130317\pi\)
−0.938285 + 0.345864i \(0.887586\pi\)
\(338\) −27.7889 + 4.89993i −0.0822156 + 0.0144968i
\(339\) 0 0
\(340\) −25.5710 21.4566i −0.0752089 0.0631078i
\(341\) 369.592 213.384i 1.08385 0.625760i
\(342\) 0 0
\(343\) −138.829 + 240.459i −0.404749 + 0.701045i
\(344\) 14.0939 + 38.7228i 0.0409707 + 0.112566i
\(345\) 0 0
\(346\) 68.3024 57.3125i 0.197406 0.165643i
\(347\) 85.0851 233.769i 0.245202 0.673687i −0.754644 0.656135i \(-0.772190\pi\)
0.999846 0.0175526i \(-0.00558746\pi\)
\(348\) 0 0
\(349\) −55.5583 + 315.087i −0.159193 + 0.902827i 0.795659 + 0.605745i \(0.207125\pi\)
−0.954852 + 0.297082i \(0.903986\pi\)
\(350\) 109.930i 0.314085i
\(351\) 0 0
\(352\) −53.0971 −0.150844
\(353\) 326.236 + 57.5243i 0.924182 + 0.162958i 0.615437 0.788186i \(-0.288980\pi\)
0.308746 + 0.951145i \(0.400091\pi\)
\(354\) 0 0
\(355\) −4.86121 1.76934i −0.0136936 0.00498405i
\(356\) −93.5110 111.442i −0.262671 0.313040i
\(357\) 0 0
\(358\) 264.281 96.1904i 0.738215 0.268688i
\(359\) −277.930 160.463i −0.774178 0.446972i 0.0601853 0.998187i \(-0.480831\pi\)
−0.834363 + 0.551216i \(0.814164\pi\)
\(360\) 0 0
\(361\) −70.4283 121.985i −0.195092 0.337910i
\(362\) 64.8126 77.2407i 0.179040 0.213372i
\(363\) 0 0
\(364\) 13.3692 + 75.8202i 0.0367284 + 0.208297i
\(365\) 13.6294 2.40323i 0.0373408 0.00658419i
\(366\) 0 0
\(367\) −558.217 468.400i −1.52103 1.27629i −0.837617 0.546258i \(-0.816052\pi\)
−0.683410 0.730035i \(-0.739504\pi\)
\(368\) −34.8800 + 20.1380i −0.0947826 + 0.0547228i
\(369\) 0 0
\(370\) 13.1334 22.7477i 0.0354957 0.0614803i
\(371\) 27.4018 + 75.2857i 0.0738592 + 0.202927i
\(372\) 0 0
\(373\) −262.562 + 220.316i −0.703920 + 0.590659i −0.922886 0.385073i \(-0.874176\pi\)
0.218966 + 0.975733i \(0.429732\pi\)
\(374\) −128.513 + 353.086i −0.343617 + 0.944079i
\(375\) 0 0
\(376\) 27.1721 154.100i 0.0722661 0.409841i
\(377\) 293.516i 0.778556i
\(378\) 0 0
\(379\) −607.166 −1.60202 −0.801011 0.598650i \(-0.795704\pi\)
−0.801011 + 0.598650i \(0.795704\pi\)
\(380\) −26.0167 4.58744i −0.0684649 0.0120722i
\(381\) 0 0
\(382\) −132.479 48.2183i −0.346803 0.126226i
\(383\) 97.3839 + 116.058i 0.254266 + 0.303023i 0.878045 0.478578i \(-0.158848\pi\)
−0.623779 + 0.781601i \(0.714403\pi\)
\(384\) 0 0
\(385\) −16.3985 + 5.96856i −0.0425935 + 0.0155028i
\(386\) 232.973 + 134.507i 0.603556 + 0.348463i
\(387\) 0 0
\(388\) 157.196 + 272.271i 0.405143 + 0.701729i
\(389\) −389.211 + 463.844i −1.00054 + 1.19240i −0.0192633 + 0.999814i \(0.506132\pi\)
−0.981280 + 0.192587i \(0.938312\pi\)
\(390\) 0 0
\(391\) 49.4925 + 280.686i 0.126579 + 0.717867i
\(392\) 108.794 19.1833i 0.277535 0.0489369i
\(393\) 0 0
\(394\) −200.062 167.872i −0.507771 0.426071i
\(395\) −67.7918 + 39.1396i −0.171625 + 0.0990876i
\(396\) 0 0
\(397\) 301.433 522.097i 0.759277 1.31511i −0.183942 0.982937i \(-0.558886\pi\)
0.943220 0.332170i \(-0.107781\pi\)
\(398\) 30.0801 + 82.6444i 0.0755782 + 0.207649i
\(399\) 0 0
\(400\) 75.5391 63.3849i 0.188848 0.158462i
\(401\) −151.840 + 417.177i −0.378653 + 1.04034i 0.593262 + 0.805010i \(0.297840\pi\)
−0.971915 + 0.235332i \(0.924382\pi\)
\(402\) 0 0
\(403\) −96.3893 + 546.651i −0.239179 + 1.35645i
\(404\) 251.126i 0.621599i
\(405\) 0 0
\(406\) −107.208 −0.264058
\(407\) −291.178 51.3425i −0.715425 0.126149i
\(408\) 0 0
\(409\) −388.673 141.465i −0.950300 0.345881i −0.180075 0.983653i \(-0.557634\pi\)
−0.770225 + 0.637772i \(0.779856\pi\)
\(410\) −37.9773 45.2596i −0.0926276 0.110389i
\(411\) 0 0
\(412\) 177.051 64.4411i 0.429734 0.156410i
\(413\) −78.2869 45.1989i −0.189557 0.109441i
\(414\) 0 0
\(415\) −19.7992 34.2932i −0.0477090 0.0826343i
\(416\) 44.3920 52.9043i 0.106711 0.127174i
\(417\) 0 0
\(418\) 51.6381 + 292.854i 0.123536 + 0.700609i
\(419\) −606.886 + 107.010i −1.44842 + 0.255395i −0.841881 0.539662i \(-0.818552\pi\)
−0.606534 + 0.795057i \(0.707441\pi\)
\(420\) 0 0
\(421\) 2.88941 + 2.42451i 0.00686322 + 0.00575892i 0.646213 0.763157i \(-0.276352\pi\)
−0.639350 + 0.768916i \(0.720796\pi\)
\(422\) −8.95351 + 5.16931i −0.0212169 + 0.0122496i
\(423\) 0 0
\(424\) 35.9335 62.2387i 0.0847489 0.146789i
\(425\) −238.668 655.734i −0.561571 1.54290i
\(426\) 0 0
\(427\) −273.149 + 229.199i −0.639693 + 0.536766i
\(428\) −73.8054 + 202.779i −0.172442 + 0.473782i
\(429\) 0 0
\(430\) 2.10961 11.9642i 0.00490606 0.0278237i
\(431\) 658.872i 1.52871i 0.644798 + 0.764353i \(0.276941\pi\)
−0.644798 + 0.764353i \(0.723059\pi\)
\(432\) 0 0
\(433\) 170.484 0.393728 0.196864 0.980431i \(-0.436924\pi\)
0.196864 + 0.980431i \(0.436924\pi\)
\(434\) −199.666 35.2066i −0.460061 0.0811212i
\(435\) 0 0
\(436\) −80.7510 29.3910i −0.185209 0.0674105i
\(437\) 144.992 + 172.794i 0.331789 + 0.395410i
\(438\) 0 0
\(439\) 805.882 293.317i 1.83572 0.668148i 0.844566 0.535452i \(-0.179859\pi\)
0.991157 0.132697i \(-0.0423636\pi\)
\(440\) 13.5566 + 7.82692i 0.0308105 + 0.0177885i
\(441\) 0 0
\(442\) −244.360 423.244i −0.552851 0.957566i
\(443\) 160.598 191.394i 0.362524 0.432040i −0.553693 0.832721i \(-0.686782\pi\)
0.916218 + 0.400681i \(0.131226\pi\)
\(444\) 0 0
\(445\) 7.44759 + 42.2374i 0.0167362 + 0.0949155i
\(446\) 119.869 21.1362i 0.268765 0.0473906i
\(447\) 0 0
\(448\) 19.3235 + 16.2143i 0.0431328 + 0.0361927i
\(449\) 208.642 120.460i 0.464682 0.268284i −0.249329 0.968419i \(-0.580210\pi\)
0.714011 + 0.700135i \(0.246877\pi\)
\(450\) 0 0
\(451\) −332.527 + 575.954i −0.737311 + 1.27706i
\(452\) −7.34036 20.1675i −0.0162397 0.0446183i
\(453\) 0 0
\(454\) 70.9061 59.4973i 0.156181 0.131051i
\(455\) 7.76311 21.3290i 0.0170618 0.0468769i
\(456\) 0 0
\(457\) −33.0420 + 187.391i −0.0723020 + 0.410045i 0.927079 + 0.374866i \(0.122311\pi\)
−0.999381 + 0.0351791i \(0.988800\pi\)
\(458\) 467.310i 1.02033i
\(459\) 0 0
\(460\) 11.8740 0.0258130
\(461\) −282.999 49.9003i −0.613880 0.108244i −0.141941 0.989875i \(-0.545334\pi\)
−0.471938 + 0.881632i \(0.656446\pi\)
\(462\) 0 0
\(463\) 15.8899 + 5.78346i 0.0343195 + 0.0124913i 0.359123 0.933290i \(-0.383076\pi\)
−0.324803 + 0.945782i \(0.605298\pi\)
\(464\) 61.8154 + 73.6687i 0.133223 + 0.158769i
\(465\) 0 0
\(466\) −190.004 + 69.1557i −0.407734 + 0.148403i
\(467\) −590.760 341.075i −1.26501 0.730354i −0.290971 0.956732i \(-0.593978\pi\)
−0.974040 + 0.226378i \(0.927312\pi\)
\(468\) 0 0
\(469\) 78.8699 + 136.607i 0.168166 + 0.291272i
\(470\) −29.6531 + 35.3392i −0.0630917 + 0.0751898i
\(471\) 0 0
\(472\) 14.0809 + 79.8570i 0.0298325 + 0.169189i
\(473\) −134.674 + 23.7466i −0.284722 + 0.0502042i
\(474\) 0 0
\(475\) −423.060 354.989i −0.890652 0.747346i
\(476\) 154.592 89.2536i 0.324772 0.187507i
\(477\) 0 0
\(478\) −214.489 + 371.506i −0.448722 + 0.777209i
\(479\) 191.036 + 524.867i 0.398822 + 1.09576i 0.962859 + 0.270005i \(0.0870255\pi\)
−0.564037 + 0.825750i \(0.690752\pi\)
\(480\) 0 0
\(481\) 294.596 247.196i 0.612466 0.513920i
\(482\) 151.280 415.640i 0.313860 0.862323i
\(483\) 0 0
\(484\) −11.4250 + 64.7942i −0.0236053 + 0.133872i
\(485\) 92.6875i 0.191108i
\(486\) 0 0
\(487\) −115.842 −0.237869 −0.118935 0.992902i \(-0.537948\pi\)
−0.118935 + 0.992902i \(0.537948\pi\)
\(488\) 314.992 + 55.5417i 0.645476 + 0.113815i
\(489\) 0 0
\(490\) −30.6047 11.1392i −0.0624587 0.0227331i
\(491\) −79.5701 94.8280i −0.162057 0.193132i 0.678905 0.734226i \(-0.262455\pi\)
−0.840962 + 0.541094i \(0.818010\pi\)
\(492\) 0 0
\(493\) 639.497 232.758i 1.29715 0.472126i
\(494\) −334.963 193.391i −0.678063 0.391480i
\(495\) 0 0
\(496\) 90.9341 + 157.502i 0.183335 + 0.317545i
\(497\) 17.7823 21.1921i 0.0357793 0.0426401i
\(498\) 0 0
\(499\) −65.4282 371.062i −0.131119 0.743610i −0.977484 0.211008i \(-0.932325\pi\)
0.846366 0.532602i \(-0.178786\pi\)
\(500\) −57.6636 + 10.1676i −0.115327 + 0.0203353i
\(501\) 0 0
\(502\) 145.667 + 122.229i 0.290173 + 0.243484i
\(503\) 363.520 209.878i 0.722704 0.417253i −0.0930432 0.995662i \(-0.529659\pi\)
0.815747 + 0.578409i \(0.196326\pi\)
\(504\) 0 0
\(505\) −37.0179 + 64.1169i −0.0733028 + 0.126964i
\(506\) −45.7139 125.598i −0.0903436 0.248217i
\(507\) 0 0
\(508\) −150.606 + 126.374i −0.296469 + 0.248767i
\(509\) 41.8155 114.887i 0.0821523 0.225712i −0.891815 0.452400i \(-0.850568\pi\)
0.973967 + 0.226689i \(0.0727900\pi\)
\(510\) 0 0
\(511\) −12.8516 + 72.8849i −0.0251498 + 0.142632i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 67.2841 0.130903
\(515\) −54.7033 9.64566i −0.106220 0.0187294i
\(516\) 0 0
\(517\) 487.965 + 177.605i 0.943840 + 0.343530i
\(518\) 90.2892 + 107.602i 0.174303 + 0.207727i
\(519\) 0 0
\(520\) −19.1326 + 6.96368i −0.0367934 + 0.0133917i
\(521\) 891.453 + 514.680i 1.71104 + 0.987870i 0.933161 + 0.359458i \(0.117038\pi\)
0.777880 + 0.628412i \(0.216295\pi\)
\(522\) 0 0
\(523\) −131.269 227.364i −0.250992 0.434731i 0.712807 0.701360i \(-0.247423\pi\)
−0.963799 + 0.266629i \(0.914090\pi\)
\(524\) 176.161 209.940i 0.336184 0.400649i
\(525\) 0 0
\(526\) −116.499 660.697i −0.221480 1.25608i
\(527\) 1267.45 223.486i 2.40503 0.424072i
\(528\) 0 0
\(529\) 327.572 + 274.866i 0.619230 + 0.519595i
\(530\) −18.3489 + 10.5938i −0.0346207 + 0.0199882i
\(531\) 0 0
\(532\) 70.6369 122.347i 0.132776 0.229975i
\(533\) −295.852 812.848i −0.555070 1.52504i
\(534\) 0 0
\(535\) 48.7350 40.8935i 0.0910934 0.0764364i
\(536\) 48.3945 132.963i 0.0902883 0.248065i
\(537\) 0 0
\(538\) −111.757 + 633.804i −0.207726 + 1.17808i
\(539\) 366.609i 0.680165i
\(540\) 0 0
\(541\) 14.7044 0.0271800 0.0135900 0.999908i \(-0.495674\pi\)
0.0135900 + 0.999908i \(0.495674\pi\)
\(542\) −614.109 108.284i −1.13304 0.199786i
\(543\) 0 0
\(544\) −150.468 54.7659i −0.276596 0.100673i
\(545\) 16.2847 + 19.4074i 0.0298802 + 0.0356098i
\(546\) 0 0
\(547\) 353.812 128.777i 0.646823 0.235424i 0.00228579 0.999997i \(-0.499272\pi\)
0.644537 + 0.764573i \(0.277050\pi\)
\(548\) −346.735 200.188i −0.632729 0.365306i
\(549\) 0 0
\(550\) 163.621 + 283.400i 0.297492 + 0.515272i
\(551\) 346.200 412.585i 0.628311 0.748792i
\(552\) 0 0
\(553\) −72.6906 412.249i −0.131448 0.745477i
\(554\) 104.992 18.5129i 0.189516 0.0334167i
\(555\) 0 0
\(556\) −10.9205 9.16343i −0.0196413 0.0164810i
\(557\) −339.531 + 196.028i −0.609571 + 0.351936i −0.772798 0.634653i \(-0.781143\pi\)
0.163226 + 0.986589i \(0.447810\pi\)
\(558\) 0 0
\(559\) 88.9339 154.038i 0.159095 0.275560i
\(560\) −2.54351 6.98825i −0.00454199 0.0124790i
\(561\) 0 0
\(562\) 8.40755 7.05477i 0.0149601 0.0125530i
\(563\) 282.488 776.129i 0.501754 1.37856i −0.387806 0.921741i \(-0.626767\pi\)
0.889560 0.456818i \(-0.151011\pi\)
\(564\) 0 0
\(565\) −1.09872 + 6.23114i −0.00194463 + 0.0110286i
\(566\) 231.173i 0.408433i
\(567\) 0 0
\(568\) −24.8155 −0.0436893
\(569\) 820.292 + 144.640i 1.44164 + 0.254200i 0.839138 0.543919i \(-0.183060\pi\)
0.602501 + 0.798118i \(0.294171\pi\)
\(570\) 0 0
\(571\) −171.024 62.2478i −0.299517 0.109015i 0.187890 0.982190i \(-0.439835\pi\)
−0.487407 + 0.873175i \(0.662057\pi\)
\(572\) 147.318 + 175.566i 0.257548 + 0.306934i
\(573\) 0 0
\(574\) 296.896 108.061i 0.517240 0.188260i
\(575\) 214.968 + 124.112i 0.373858 + 0.215847i
\(576\) 0 0
\(577\) −25.3860 43.9699i −0.0439966 0.0762043i 0.843189 0.537618i \(-0.180676\pi\)
−0.887185 + 0.461414i \(0.847342\pi\)
\(578\) −465.654 + 554.945i −0.805630 + 0.960112i
\(579\) 0 0
\(580\) −4.92323 27.9210i −0.00848832 0.0481397i
\(581\) 208.541 36.7713i 0.358934 0.0632898i
\(582\) 0 0
\(583\) 182.698 + 153.302i 0.313376 + 0.262954i
\(584\) 57.4936 33.1940i 0.0984480 0.0568390i
\(585\) 0 0
\(586\) 38.2449 66.2421i 0.0652643 0.113041i
\(587\) −29.4058 80.7919i −0.0500951 0.137635i 0.912122 0.409919i \(-0.134443\pi\)
−0.962217 + 0.272284i \(0.912221\pi\)
\(588\) 0 0
\(589\) 780.262 654.718i 1.32472 1.11158i
\(590\) 8.17643 22.4646i 0.0138584 0.0380755i
\(591\) 0 0
\(592\) 21.8797 124.086i 0.0369590 0.209605i
\(593\) 333.051i 0.561638i 0.959761 + 0.280819i \(0.0906060\pi\)
−0.959761 + 0.280819i \(0.909394\pi\)
\(594\) 0 0
\(595\) −52.6267 −0.0884482
\(596\) −184.657 32.5600i −0.309827 0.0546308i
\(597\) 0 0
\(598\) 163.361 + 59.4586i 0.273179 + 0.0994290i
\(599\) −376.276 448.428i −0.628173 0.748628i 0.354279 0.935140i \(-0.384726\pi\)
−0.982453 + 0.186512i \(0.940282\pi\)
\(600\) 0 0
\(601\) 684.489 249.134i 1.13892 0.414532i 0.297395 0.954755i \(-0.403882\pi\)
0.841522 + 0.540223i \(0.181660\pi\)
\(602\) 56.2630 + 32.4835i 0.0934602 + 0.0539593i
\(603\) 0 0
\(604\) 201.773 + 349.481i 0.334061 + 0.578611i
\(605\) 12.4682 14.8590i 0.0206086 0.0245603i
\(606\) 0 0
\(607\) 50.2841 + 285.175i 0.0828404 + 0.469811i 0.997802 + 0.0662697i \(0.0211098\pi\)
−0.914961 + 0.403541i \(0.867779\pi\)
\(608\) −124.800 + 22.0057i −0.205264 + 0.0361936i
\(609\) 0 0
\(610\) −72.2359 60.6131i −0.118420 0.0993658i
\(611\) −584.925 + 337.706i −0.957323 + 0.552711i
\(612\) 0 0
\(613\) −431.468 + 747.325i −0.703864 + 1.21913i 0.263236 + 0.964731i \(0.415210\pi\)
−0.967100 + 0.254396i \(0.918123\pi\)
\(614\) −70.8115 194.553i −0.115328 0.316862i
\(615\) 0 0
\(616\) −64.1263 + 53.8084i −0.104101 + 0.0873513i
\(617\) 37.3588 102.642i 0.0605491 0.166357i −0.905729 0.423856i \(-0.860676\pi\)
0.966279 + 0.257499i \(0.0828984\pi\)
\(618\) 0 0
\(619\) 16.5748 94.0001i 0.0267767 0.151858i −0.968488 0.249060i \(-0.919878\pi\)
0.995265 + 0.0972023i \(0.0309894\pi\)
\(620\) 53.6176i 0.0864800i
\(621\) 0 0
\(622\) 391.081 0.628748
\(623\) −225.870 39.8270i −0.362552 0.0639277i
\(624\) 0 0
\(625\) −562.919 204.886i −0.900671 0.327817i
\(626\) 27.2673 + 32.4959i 0.0435579 + 0.0519103i
\(627\) 0 0
\(628\) −137.943 + 50.2072i −0.219655 + 0.0799478i
\(629\) −772.193 445.826i −1.22765 0.708785i
\(630\) 0 0
\(631\) 264.888 + 458.800i 0.419791 + 0.727100i 0.995918 0.0902603i \(-0.0287699\pi\)
−0.576127 + 0.817360i \(0.695437\pi\)
\(632\) −241.367 + 287.650i −0.381910 + 0.455143i
\(633\) 0 0
\(634\) −65.7227 372.732i −0.103664 0.587905i
\(635\) 57.0810 10.0649i 0.0898914 0.0158503i
\(636\) 0 0
\(637\) −365.278 306.504i −0.573435 0.481169i
\(638\) −276.382 + 159.569i −0.433201 + 0.250109i
\(639\) 0 0
\(640\) −3.33546 + 5.77718i −0.00521165 + 0.00902685i
\(641\) 90.7979 + 249.465i 0.141650 + 0.389181i 0.990149 0.140016i \(-0.0447154\pi\)
−0.848499 + 0.529197i \(0.822493\pi\)
\(642\) 0 0
\(643\) 111.106 93.2293i 0.172794 0.144991i −0.552290 0.833652i \(-0.686246\pi\)
0.725083 + 0.688661i \(0.241801\pi\)
\(644\) −21.7175 + 59.6683i −0.0337228 + 0.0926526i
\(645\) 0 0
\(646\) −155.725 + 883.161i −0.241061 + 1.36712i
\(647\) 578.671i 0.894391i 0.894436 + 0.447196i \(0.147577\pi\)
−0.894436 + 0.447196i \(0.852423\pi\)
\(648\) 0 0
\(649\) −269.099 −0.414636
\(650\) −419.166 73.9103i −0.644871 0.113708i
\(651\) 0 0
\(652\) −408.068 148.525i −0.625871 0.227798i
\(653\) 417.061 + 497.034i 0.638684 + 0.761154i 0.984162 0.177273i \(-0.0567275\pi\)
−0.345477 + 0.938427i \(0.612283\pi\)
\(654\) 0 0
\(655\) −75.9237 + 27.6340i −0.115914 + 0.0421893i
\(656\) −245.444 141.707i −0.374152 0.216017i
\(657\) 0 0
\(658\) −123.349 213.646i −0.187460 0.324690i
\(659\) 346.075 412.436i 0.525151 0.625851i −0.436639 0.899637i \(-0.643831\pi\)
0.961791 + 0.273785i \(0.0882758\pi\)
\(660\) 0 0
\(661\) −66.4965 377.120i −0.100600 0.570530i −0.992887 0.119061i \(-0.962011\pi\)
0.892287 0.451468i \(-0.149100\pi\)
\(662\) 531.115 93.6500i 0.802289 0.141465i
\(663\) 0 0
\(664\) −145.511 122.098i −0.219143 0.183883i
\(665\) −36.0697 + 20.8249i −0.0542402 + 0.0313156i
\(666\) 0 0
\(667\) −121.039 + 209.646i −0.181468 + 0.314311i
\(668\) 147.424 + 405.044i 0.220695 + 0.606354i
\(669\) 0 0
\(670\) −31.9558 + 26.8141i −0.0476952 + 0.0400210i
\(671\) −363.037 + 997.436i −0.541039 + 1.48649i
\(672\) 0 0
\(673\) 28.0045 158.821i 0.0416114 0.235990i −0.956908 0.290392i \(-0.906214\pi\)
0.998519 + 0.0544023i \(0.0173253\pi\)
\(674\) 169.360i 0.251275i
\(675\) 0 0
\(676\) 39.9056 0.0590320
\(677\) −126.078 22.2310i −0.186231 0.0328375i 0.0797548 0.996815i \(-0.474586\pi\)
−0.265986 + 0.963977i \(0.585697\pi\)
\(678\) 0 0
\(679\) 465.766 + 169.525i 0.685959 + 0.249669i
\(680\) 30.3443 + 36.1629i 0.0446239 + 0.0531807i
\(681\) 0 0
\(682\) −567.144 + 206.423i −0.831589 + 0.302674i
\(683\) 410.786 + 237.168i 0.601444 + 0.347244i 0.769609 0.638515i \(-0.220451\pi\)
−0.168165 + 0.985759i \(0.553784\pi\)
\(684\) 0 0
\(685\) 59.0185 + 102.223i 0.0861583 + 0.149231i
\(686\) 252.402 300.800i 0.367932 0.438485i
\(687\) 0 0
\(688\) −10.1197 57.3914i −0.0147088 0.0834178i
\(689\) −305.491 + 53.8663i −0.443383 + 0.0781804i
\(690\) 0 0
\(691\) −218.877 183.660i −0.316754 0.265788i 0.470523 0.882388i \(-0.344065\pi\)
−0.787277 + 0.616600i \(0.788510\pi\)
\(692\) −109.201 + 63.0474i −0.157805 + 0.0911089i
\(693\) 0 0
\(694\) −175.909 + 304.683i −0.253471 + 0.439024i
\(695\) 1.43745 + 3.94936i 0.00206827 + 0.00568253i
\(696\) 0 0
\(697\) −1536.38 + 1289.18i −2.20428 + 1.84961i
\(698\) 154.755 425.186i 0.221712 0.609149i
\(699\) 0 0
\(700\) 26.9960 153.102i 0.0385658 0.218717i
\(701\) 320.086i 0.456613i 0.973589 + 0.228307i \(0.0733189\pi\)
−0.973589 + 0.228307i \(0.926681\pi\)
\(702\) 0 0
\(703\) −705.669 −1.00380
\(704\) 73.9498 + 13.0393i 0.105042 + 0.0185218i
\(705\) 0 0
\(706\) −440.232 160.231i −0.623558 0.226957i
\(707\) −254.490 303.289i −0.359958 0.428981i
\(708\) 0 0
\(709\) −796.794 + 290.009i −1.12383 + 0.409040i −0.836048 0.548657i \(-0.815139\pi\)
−0.287780 + 0.957697i \(0.592917\pi\)
\(710\) 6.33584 + 3.65800i 0.00892372 + 0.00515211i
\(711\) 0 0
\(712\) 102.868 + 178.173i 0.144478 + 0.250242i
\(713\) −294.273 + 350.701i −0.412725 + 0.491866i
\(714\) 0 0
\(715\) −11.7330 66.5410i −0.0164098 0.0930644i
\(716\) −391.694 + 69.0662i −0.547058 + 0.0964611i
\(717\) 0 0
\(718\) 347.675 + 291.734i 0.484227 + 0.406315i
\(719\) −143.869 + 83.0628i −0.200096 + 0.115525i −0.596700 0.802464i \(-0.703522\pi\)
0.396604 + 0.917990i \(0.370189\pi\)
\(720\) 0 0
\(721\) 148.523 257.249i 0.205996 0.356795i
\(722\) 68.1308 + 187.188i 0.0943640 + 0.259263i
\(723\) 0 0
\(724\) −109.235 + 91.6589i −0.150877 + 0.126601i
\(725\) 202.712 556.946i 0.279602 0.768201i
\(726\) 0 0
\(727\) 136.863 776.190i 0.188258 1.06766i −0.733440 0.679754i \(-0.762087\pi\)
0.921698 0.387908i \(-0.126802\pi\)
\(728\) 108.880i 0.149561i
\(729\) 0 0
\(730\) −19.5722 −0.0268112
\(731\) −406.135 71.6126i −0.555589 0.0979653i
\(732\) 0 0
\(733\) 650.225 + 236.663i 0.887074 + 0.322869i 0.745061 0.666996i \(-0.232420\pi\)
0.142013 + 0.989865i \(0.454643\pi\)
\(734\) 662.417 + 789.438i 0.902475 + 1.07553i
\(735\) 0 0
\(736\) 53.5238 19.4811i 0.0727225 0.0264688i
\(737\) 406.655 + 234.782i 0.551770 + 0.318565i
\(738\) 0 0
\(739\) −117.695 203.854i −0.159262 0.275851i 0.775340 0.631543i \(-0.217578\pi\)
−0.934603 + 0.355693i \(0.884245\pi\)
\(740\) −23.8775 + 28.4561i −0.0322669 + 0.0384542i
\(741\) 0 0
\(742\) −19.6749 111.582i −0.0265160 0.150380i
\(743\) −600.536 + 105.891i −0.808259 + 0.142518i −0.562483 0.826809i \(-0.690154\pi\)
−0.245776 + 0.969327i \(0.579043\pi\)
\(744\) 0 0
\(745\) 42.3466 + 35.5330i 0.0568411 + 0.0476953i
\(746\) 419.782 242.361i 0.562711 0.324881i
\(747\) 0 0
\(748\) 265.692 460.193i 0.355204 0.615231i
\(749\) 116.359 + 319.694i 0.155352 + 0.426827i
\(750\) 0 0
\(751\) 163.414 137.121i 0.217596 0.182585i −0.527474 0.849571i \(-0.676861\pi\)
0.745070 + 0.666987i \(0.232416\pi\)
\(752\) −75.6866 + 207.947i −0.100647 + 0.276526i
\(753\) 0 0
\(754\) 72.0803 408.787i 0.0955972 0.542158i
\(755\) 118.972i 0.157578i
\(756\) 0 0
\(757\) −212.260 −0.280397 −0.140198 0.990123i \(-0.544774\pi\)
−0.140198 + 0.990123i \(0.544774\pi\)
\(758\) 845.618 + 149.105i 1.11559 + 0.196709i
\(759\) 0 0
\(760\) 35.1076 + 12.7781i 0.0461942 + 0.0168133i
\(761\) −934.612 1113.83i −1.22814 1.46364i −0.840488 0.541830i \(-0.817732\pi\)
−0.387649 0.921807i \(-0.626713\pi\)
\(762\) 0 0
\(763\) −127.309 + 46.3368i −0.166853 + 0.0607297i
\(764\) 172.666 + 99.6886i 0.226002 + 0.130482i
\(765\) 0 0
\(766\) −107.128 185.552i −0.139854 0.242235i
\(767\) 224.981 268.122i 0.293326 0.349572i
\(768\) 0 0
\(769\) 150.826 + 855.378i 0.196133 + 1.11233i 0.910796 + 0.412856i \(0.135469\pi\)
−0.714663 + 0.699469i \(0.753420\pi\)
\(770\) 24.3044 4.28552i 0.0315641 0.00556561i
\(771\) 0 0
\(772\) −291.436 244.544i −0.377508 0.316767i
\(773\) 14.6924 8.48268i 0.0190070 0.0109737i −0.490466 0.871460i \(-0.663174\pi\)
0.509473 + 0.860486i \(0.329840\pi\)
\(774\) 0 0
\(775\) 560.435 970.701i 0.723141 1.25252i
\(776\) −152.068 417.803i −0.195964 0.538406i
\(777\) 0 0
\(778\) 655.974 550.428i 0.843155 0.707491i
\(779\) −542.879 + 1491.55i −0.696892 + 1.91469i
\(780\) 0 0
\(781\) 14.3003 81.1008i 0.0183102 0.103842i
\(782\) 403.074i 0.515440i
\(783\) 0 0
\(784\) −156.231 −0.199274
\(785\) 42.6203 + 7.51511i 0.0542934 + 0.00957339i
\(786\) 0 0
\(787\) 382.780 + 139.321i 0.486379 + 0.177027i 0.573557 0.819165i \(-0.305563\pi\)
−0.0871788 + 0.996193i \(0.527785\pi\)
\(788\) 237.407 + 282.930i 0.301277 + 0.359048i
\(789\) 0 0
\(790\) 104.027 37.8628i 0.131680 0.0479276i
\(791\) −29.3027 16.9179i −0.0370452 0.0213880i
\(792\) 0 0
\(793\) −690.296 1195.63i −0.870487 1.50773i
\(794\) −548.029 + 653.115i −0.690213 + 0.822563i
\(795\) 0 0
\(796\) −21.5980 122.488i −0.0271331 0.153880i
\(797\) −114.221 + 20.1403i −0.143314 + 0.0252702i −0.244845 0.969562i \(-0.578737\pi\)
0.101531 + 0.994832i \(0.467626\pi\)
\(798\) 0 0
\(799\) 1199.62 + 1006.60i 1.50141 + 1.25983i
\(800\) −120.771 + 69.7273i −0.150964 + 0.0871592i
\(801\) 0 0
\(802\) 313.920 543.726i 0.391422 0.677963i
\(803\) 75.3514 + 207.026i 0.0938374 + 0.257816i
\(804\) 0 0
\(805\) 14.3404 12.0331i 0.0178142 0.0149479i
\(806\) 268.488 737.666i 0.333112 0.915218i
\(807\) 0 0
\(808\) −61.6704 + 349.750i −0.0763247 + 0.432859i
\(809\) 1246.51i 1.54080i −0.637560 0.770401i \(-0.720056\pi\)
0.637560 0.770401i \(-0.279944\pi\)
\(810\) 0 0
\(811\) 593.707 0.732067 0.366034 0.930602i \(-0.380715\pi\)
0.366034 + 0.930602i \(0.380715\pi\)
\(812\) 149.311 + 26.3276i 0.183881 + 0.0324232i
\(813\) 0 0
\(814\) 392.923 + 143.012i 0.482707 + 0.175691i
\(815\) 82.2933 + 98.0734i 0.100973 + 0.120335i
\(816\) 0 0
\(817\) −306.698 + 111.629i −0.375396 + 0.136633i
\(818\) 506.575 + 292.471i 0.619285 + 0.357544i
\(819\) 0 0
\(820\) 41.7774 + 72.3607i 0.0509481 + 0.0882447i
\(821\) −291.743 + 347.685i −0.355350 + 0.423490i −0.913874 0.405999i \(-0.866924\pi\)
0.558523 + 0.829489i \(0.311368\pi\)
\(822\) 0 0
\(823\) 25.9808 + 147.345i 0.0315685 + 0.179034i 0.996515 0.0834125i \(-0.0265819\pi\)
−0.964947 + 0.262446i \(0.915471\pi\)
\(824\) −262.408 + 46.2697i −0.318457 + 0.0561525i
\(825\) 0 0
\(826\) 97.9326 + 82.1752i 0.118562 + 0.0994857i
\(827\) 858.941 495.910i 1.03862 0.599649i 0.119180 0.992873i \(-0.461973\pi\)
0.919443 + 0.393223i \(0.128640\pi\)
\(828\) 0 0
\(829\) −554.523 + 960.463i −0.668906 + 1.15858i 0.309304 + 0.950963i \(0.399904\pi\)
−0.978210 + 0.207617i \(0.933429\pi\)
\(830\) 19.1533 + 52.6234i 0.0230763 + 0.0634017i
\(831\) 0 0
\(832\) −74.8180 + 62.7797i −0.0899254 + 0.0754564i
\(833\) −378.131 + 1038.91i −0.453939 + 1.24719i
\(834\) 0 0
\(835\) 22.0667 125.147i 0.0264272 0.149876i
\(836\) 420.548i 0.503048i
\(837\) 0 0
\(838\) 871.507 1.03998
\(839\) 717.074 + 126.440i 0.854677 + 0.150703i 0.583786 0.811907i \(-0.301571\pi\)
0.270891 + 0.962610i \(0.412682\pi\)
\(840\) 0 0
\(841\) −247.126 89.9465i −0.293848 0.106952i
\(842\) −3.42877 4.08625i −0.00407217 0.00485303i
\(843\) 0 0
\(844\) 13.7393 5.00069i 0.0162788 0.00592498i
\(845\) −10.1886 5.88240i −0.0120575 0.00696142i
\(846\) 0 0
\(847\) 51.8641 + 89.8313i 0.0612327 + 0.106058i
\(848\) −65.3300 + 77.8572i −0.0770401 + 0.0918128i
\(849\) 0 0
\(850\) 171.367 + 971.870i 0.201608 + 1.14338i
\(851\) 312.355 55.0767i 0.367045 0.0647199i
\(852\) 0 0
\(853\) −1035.22 868.650i −1.21362 1.01835i −0.999134 0.0416200i \(-0.986748\pi\)
−0.214485 0.976727i \(-0.568807\pi\)
\(854\) 436.708 252.134i 0.511368 0.295238i
\(855\) 0 0
\(856\) 152.588 264.291i 0.178257 0.308751i
\(857\) −469.442 1289.78i −0.547774 1.50500i −0.836709 0.547647i \(-0.815524\pi\)
0.288936 0.957348i \(-0.406699\pi\)
\(858\) 0 0
\(859\) −49.4325 + 41.4788i −0.0575466 + 0.0482873i −0.671107 0.741360i \(-0.734181\pi\)
0.613561 + 0.789648i \(0.289737\pi\)
\(860\) −5.87622 + 16.1448i −0.00683281 + 0.0187730i
\(861\) 0 0
\(862\) 161.803 917.630i 0.187706 1.06454i
\(863\) 998.597i 1.15712i −0.815639 0.578561i \(-0.803614\pi\)
0.815639 0.578561i \(-0.196386\pi\)
\(864\) 0 0
\(865\) 37.1747 0.0429765
\(866\) −237.438 41.8667i −0.274178 0.0483449i
\(867\) 0 0
\(868\) 269.435 + 98.0664i 0.310409 + 0.112980i
\(869\) −800.994 954.587i −0.921742 1.09849i
\(870\) 0 0
\(871\) −573.915 + 208.888i −0.658915 + 0.239825i
\(872\) 105.247 + 60.7641i 0.120696 + 0.0696836i
\(873\) 0 0
\(874\) −159.500 276.262i −0.182494 0.316089i
\(875\) −59.3375 + 70.7157i −0.0678143 + 0.0808180i
\(876\) 0 0
\(877\) 263.675 + 1495.37i 0.300656 + 1.70510i 0.643281 + 0.765630i \(0.277573\pi\)
−0.342625 + 0.939472i \(0.611316\pi\)
\(878\) −1194.41 + 210.606i −1.36037 + 0.239870i
\(879\) 0 0
\(880\) −16.9586 14.2300i −0.0192711 0.0161704i
\(881\) −462.122 + 266.806i −0.524543 + 0.302845i −0.738791 0.673934i \(-0.764603\pi\)
0.214249 + 0.976779i \(0.431270\pi\)
\(882\) 0 0
\(883\) 268.778 465.537i 0.304392 0.527222i −0.672734 0.739885i \(-0.734880\pi\)
0.977126 + 0.212662i \(0.0682134\pi\)
\(884\) 236.389 + 649.473i 0.267408 + 0.734698i
\(885\) 0 0
\(886\) −270.671 + 227.120i −0.305498 + 0.256343i
\(887\) 335.258 921.113i 0.377968 1.03846i −0.594229 0.804296i \(-0.702543\pi\)
0.972197 0.234163i \(-0.0752350\pi\)
\(888\) 0 0
\(889\) −53.8235 + 305.248i −0.0605439 + 0.343361i
\(890\) 60.6542i 0.0681508i
\(891\) 0 0
\(892\) −172.136 −0.192978
\(893\) 1220.53 + 215.212i 1.36678 + 0.240999i
\(894\) 0 0
\(895\) 110.187 + 40.1049i 0.123114 + 0.0448099i
\(896\) −22.9305 27.3276i −0.0255921 0.0304995i
\(897\) 0 0
\(898\) −320.164 + 116.530i −0.356530 + 0.129766i
\(899\) 946.666 + 546.558i 1.05302 + 0.607962i
\(900\) 0 0
\(901\) 359.616 + 622.873i 0.399130 + 0.691313i
\(902\) 604.560 720.487i 0.670244 0.798766i
\(903\) 0 0
\(904\) 5.27049 + 29.8904i 0.00583019 + 0.0330646i
\(905\) 41.4008 7.30008i 0.0457468 0.00806639i
\(906\) 0 0
\(907\) 261.282 + 219.241i 0.288072 + 0.241721i 0.775359 0.631521i \(-0.217569\pi\)
−0.487287 + 0.873242i \(0.662013\pi\)
\(908\) −113.364 + 65.4508i −0.124850 + 0.0720823i
\(909\) 0 0
\(910\) −16.0498 + 27.7990i −0.0176371 + 0.0305484i
\(911\) 468.039 + 1285.93i 0.513764 + 1.41156i 0.877285 + 0.479970i \(0.159352\pi\)
−0.363520 + 0.931586i \(0.618425\pi\)
\(912\) 0 0
\(913\) 482.889 405.192i 0.528903 0.443803i
\(914\) 92.0371 252.870i 0.100697 0.276663i
\(915\) 0 0
\(916\) 114.760 650.835i 0.125284 0.710519i
\(917\) 432.069i 0.471177i
\(918\) 0 0
\(919\) 558.729 0.607975 0.303987 0.952676i \(-0.401682\pi\)
0.303987 + 0.952676i \(0.401682\pi\)
\(920\) −16.5372 2.91596i −0.0179753 0.00316952i
\(921\) 0 0
\(922\) 381.886 + 138.995i 0.414193 + 0.150754i
\(923\) 68.8506 + 82.0529i 0.0745944 + 0.0888981i
\(924\) 0 0
\(925\) −729.719 + 265.596i −0.788885 + 0.287131i
\(926\) −20.7101 11.9570i −0.0223651 0.0129125i
\(927\) 0 0
\(928\) −68.0008 117.781i −0.0732768 0.126919i
\(929\) 667.609 795.625i 0.718632 0.856432i −0.275865 0.961196i \(-0.588964\pi\)
0.994497 + 0.104764i \(0.0334088\pi\)
\(930\) 0 0
\(931\) 151.938 + 861.685i 0.163199 + 0.925548i
\(932\) 281.607 49.6549i 0.302153 0.0532778i
\(933\) 0 0
\(934\) 739.008 + 620.102i 0.791230 + 0.663920i
\(935\) −135.672 + 78.3303i −0.145104 + 0.0837757i
\(936\) 0 0
\(937\) 323.576 560.450i 0.345332 0.598132i −0.640082 0.768306i \(-0.721100\pi\)
0.985414 + 0.170174i \(0.0544330\pi\)
\(938\) −76.2971 209.625i −0.0813402 0.223480i
\(939\) 0 0
\(940\) 49.9772 41.9358i 0.0531672 0.0446126i
\(941\) −228.423 + 627.587i −0.242745 + 0.666936i 0.757161 + 0.653228i \(0.226586\pi\)
−0.999906 + 0.0137078i \(0.995637\pi\)
\(942\) 0 0
\(943\) 123.885 702.585i 0.131373 0.745053i
\(944\) 114.677i 0.121480i
\(945\) 0 0
\(946\) 193.395 0.204435
\(947\) −1716.52 302.668i −1.81258 0.319607i −0.838347 0.545136i \(-0.816478\pi\)
−0.974237 + 0.225529i \(0.927589\pi\)
\(948\) 0 0
\(949\) −269.272 98.0071i −0.283743 0.103274i
\(950\) 502.031 + 598.297i 0.528453 + 0.629786i
\(951\) 0 0
\(952\) −237.223 + 86.3420i −0.249184 + 0.0906954i
\(953\) −671.945 387.948i −0.705084 0.407080i 0.104154 0.994561i \(-0.466786\pi\)
−0.809238 + 0.587481i \(0.800120\pi\)
\(954\) 0 0
\(955\) −29.3898 50.9045i −0.0307746 0.0533032i
\(956\) 389.958 464.734i 0.407906 0.486123i
\(957\) 0 0
\(958\) −137.167 777.911i −0.143180 0.812015i
\(959\) −621.628 + 109.610i −0.648205 + 0.114296i
\(960\) 0 0
\(961\) 847.439 + 711.086i 0.881830 + 0.739943i
\(962\) −470.998 + 271.931i −0.489603 + 0.282672i
\(963\) 0 0
\(964\) −312.764 + 541.722i −0.324444 + 0.561953i
\(965\) 38.3611 + 105.396i 0.0397525 + 0.109219i
\(966\) 0 0
\(967\) −149.339 + 125.310i −0.154435 + 0.129586i −0.716731 0.697350i \(-0.754363\pi\)
0.562296 + 0.826936i \(0.309918\pi\)
\(968\) 31.8238 87.4351i 0.0328758 0.0903255i
\(969\) 0 0
\(970\) −22.7618 + 129.088i −0.0234658 + 0.133081i
\(971\) 1753.94i 1.80633i −0.429299 0.903163i \(-0.641239\pi\)
0.429299 0.903163i \(-0.358761\pi\)
\(972\) 0 0
\(973\) −22.4751 −0.0230988
\(974\) 161.337 + 28.4481i 0.165644 + 0.0292075i
\(975\) 0 0
\(976\) −425.059 154.709i −0.435512 0.158513i
\(977\) −88.8872 105.932i −0.0909797 0.108425i 0.718634 0.695389i \(-0.244768\pi\)
−0.809614 + 0.586963i \(0.800323\pi\)
\(978\) 0 0
\(979\) −641.574 + 233.514i −0.655336 + 0.238523i
\(980\) 39.8886 + 23.0297i 0.0407026 + 0.0234997i
\(981\) 0 0
\(982\) 87.5321 + 151.610i 0.0891366 + 0.154389i
\(983\) 123.405 147.069i 0.125540 0.149612i −0.699613 0.714522i \(-0.746644\pi\)
0.825153 + 0.564909i \(0.191089\pi\)
\(984\) 0 0
\(985\) −18.9080 107.233i −0.0191960 0.108866i
\(986\) −947.806 + 167.124i −0.961264 + 0.169497i
\(987\) 0 0
\(988\) 419.021 + 351.600i 0.424110 + 0.355871i
\(989\) 127.043 73.3485i 0.128456 0.0741644i
\(990\) 0 0
\(991\) 193.368 334.923i 0.195124 0.337964i −0.751817 0.659372i \(-0.770822\pi\)
0.946941 + 0.321407i \(0.104156\pi\)
\(992\) −87.9677 241.689i −0.0886772 0.243639i
\(993\) 0 0
\(994\) −29.9702 + 25.1480i −0.0301511 + 0.0252998i
\(995\) −12.5414 + 34.4571i −0.0126044 + 0.0346303i
\(996\) 0 0
\(997\) 212.742 1206.52i 0.213382 1.21015i −0.670310 0.742081i \(-0.733839\pi\)
0.883692 0.468069i \(-0.155050\pi\)
\(998\) 532.856i 0.533923i
\(999\) 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 162.3.f.a.89.2 36
3.2 odd 2 54.3.f.a.29.5 36
12.11 even 2 432.3.bc.c.353.3 36
27.11 odd 18 1458.3.b.c.1457.27 36
27.13 even 9 54.3.f.a.41.5 yes 36
27.14 odd 18 inner 162.3.f.a.71.2 36
27.16 even 9 1458.3.b.c.1457.10 36
108.67 odd 18 432.3.bc.c.257.3 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.f.a.29.5 36 3.2 odd 2
54.3.f.a.41.5 yes 36 27.13 even 9
162.3.f.a.71.2 36 27.14 odd 18 inner
162.3.f.a.89.2 36 1.1 even 1 trivial
432.3.bc.c.257.3 36 108.67 odd 18
432.3.bc.c.353.3 36 12.11 even 2
1458.3.b.c.1457.10 36 27.16 even 9
1458.3.b.c.1457.27 36 27.11 odd 18