Properties

Label 855.2.da.b.199.2
Level $855$
Weight $2$
Character 855.199
Analytic conductor $6.827$
Analytic rank $0$
Dimension $48$
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] = [855,2,Mod(199,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.da (of order \(18\), degree \(6\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.2
Character \(\chi\) \(=\) 855.199
Dual form 855.2.da.b.739.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.45670 + 0.256855i) q^{2} +(0.176607 - 0.0642796i) q^{4} +(-0.658585 + 2.13688i) q^{5} +(2.81448 + 1.62494i) q^{7} +(2.32124 - 1.34017i) q^{8} +O(q^{10})\) \(q+(-1.45670 + 0.256855i) q^{2} +(0.176607 - 0.0642796i) q^{4} +(-0.658585 + 2.13688i) q^{5} +(2.81448 + 1.62494i) q^{7} +(2.32124 - 1.34017i) q^{8} +(0.410490 - 3.28195i) q^{10} +(-2.09200 - 3.62344i) q^{11} +(1.14682 - 1.36673i) q^{13} +(-4.51721 - 1.64413i) q^{14} +(-3.32506 + 2.79006i) q^{16} +(6.23606 - 1.09959i) q^{17} +(4.09399 - 1.49640i) q^{19} +(0.0210474 + 0.419722i) q^{20} +(3.97810 + 4.74092i) q^{22} +(-0.490346 - 1.34721i) q^{23} +(-4.13253 - 2.81464i) q^{25} +(-1.31952 + 2.28547i) q^{26} +(0.601506 + 0.106062i) q^{28} +(-0.0589345 + 0.334234i) q^{29} +(1.38932 - 2.40638i) q^{31} +(0.681187 - 0.811808i) q^{32} +(-8.80161 + 3.20352i) q^{34} +(-5.32587 + 4.94404i) q^{35} -2.70482i q^{37} +(-5.57935 + 3.23137i) q^{38} +(1.33505 + 5.84284i) q^{40} +(5.46819 - 4.58835i) q^{41} +(-3.38403 + 9.29755i) q^{43} +(-0.602374 - 0.505452i) q^{44} +(1.06032 + 1.83654i) q^{46} +(0.438674 + 0.0773501i) q^{47} +(1.78085 + 3.08452i) q^{49} +(6.74280 + 3.03861i) q^{50} +(0.114683 - 0.315090i) q^{52} +(2.47532 + 6.80087i) q^{53} +(9.12062 - 2.08400i) q^{55} +8.71078 q^{56} -0.502015i q^{58} +(0.545712 + 3.09489i) q^{59} +(2.88074 - 1.04850i) q^{61} +(-1.40573 + 3.86222i) q^{62} +(3.55679 - 6.16055i) q^{64} +(2.16526 + 3.35072i) q^{65} +(8.42261 + 1.48513i) q^{67} +(1.03065 - 0.595046i) q^{68} +(6.48828 - 8.56995i) q^{70} +(12.1153 + 4.40959i) q^{71} +(1.17133 + 1.39594i) q^{73} +(0.694747 + 3.94011i) q^{74} +(0.626839 - 0.527435i) q^{76} -13.5974i q^{77} +(-0.535235 + 0.449116i) q^{79} +(-3.77219 - 8.94276i) q^{80} +(-6.78695 + 8.08837i) q^{82} +(0.478899 + 0.276493i) q^{83} +(-1.75729 + 14.0499i) q^{85} +(2.54139 - 14.4129i) q^{86} +(-9.71206 - 5.60726i) q^{88} +(5.23109 + 4.38940i) q^{89} +(5.44854 - 1.98311i) q^{91} +(-0.173197 - 0.206408i) q^{92} -0.658883 q^{94} +(0.501395 + 9.73389i) q^{95} +(13.0001 - 2.29226i) q^{97} +(-3.38643 - 4.03579i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45670 + 0.256855i −1.03004 + 0.181624i −0.663030 0.748593i \(-0.730730\pi\)
−0.367010 + 0.930217i \(0.619619\pi\)
\(3\) 0 0
\(4\) 0.176607 0.0642796i 0.0883034 0.0321398i
\(5\) −0.658585 + 2.13688i −0.294528 + 0.955643i
\(6\) 0 0
\(7\) 2.81448 + 1.62494i 1.06377 + 0.614169i 0.926473 0.376361i \(-0.122825\pi\)
0.137298 + 0.990530i \(0.456158\pi\)
\(8\) 2.32124 1.34017i 0.820684 0.473822i
\(9\) 0 0
\(10\) 0.410490 3.28195i 0.129808 1.03784i
\(11\) −2.09200 3.62344i −0.630760 1.09251i −0.987397 0.158265i \(-0.949410\pi\)
0.356636 0.934243i \(-0.383924\pi\)
\(12\) 0 0
\(13\) 1.14682 1.36673i 0.318070 0.379062i −0.583193 0.812334i \(-0.698197\pi\)
0.901263 + 0.433272i \(0.142641\pi\)
\(14\) −4.51721 1.64413i −1.20728 0.439412i
\(15\) 0 0
\(16\) −3.32506 + 2.79006i −0.831266 + 0.697515i
\(17\) 6.23606 1.09959i 1.51247 0.266689i 0.644999 0.764183i \(-0.276858\pi\)
0.867467 + 0.497495i \(0.165747\pi\)
\(18\) 0 0
\(19\) 4.09399 1.49640i 0.939226 0.343298i
\(20\) 0.0210474 + 0.419722i 0.00470635 + 0.0938526i
\(21\) 0 0
\(22\) 3.97810 + 4.74092i 0.848134 + 1.01077i
\(23\) −0.490346 1.34721i −0.102244 0.280914i 0.878014 0.478635i \(-0.158868\pi\)
−0.980258 + 0.197721i \(0.936646\pi\)
\(24\) 0 0
\(25\) −4.13253 2.81464i −0.826506 0.562927i
\(26\) −1.31952 + 2.28547i −0.258779 + 0.448218i
\(27\) 0 0
\(28\) 0.601506 + 0.106062i 0.113674 + 0.0200438i
\(29\) −0.0589345 + 0.334234i −0.0109439 + 0.0620657i −0.989791 0.142529i \(-0.954477\pi\)
0.978847 + 0.204595i \(0.0655877\pi\)
\(30\) 0 0
\(31\) 1.38932 2.40638i 0.249530 0.432199i −0.713866 0.700283i \(-0.753057\pi\)
0.963395 + 0.268084i \(0.0863906\pi\)
\(32\) 0.681187 0.811808i 0.120418 0.143509i
\(33\) 0 0
\(34\) −8.80161 + 3.20352i −1.50946 + 0.549400i
\(35\) −5.32587 + 4.94404i −0.900237 + 0.835696i
\(36\) 0 0
\(37\) 2.70482i 0.444670i −0.974970 0.222335i \(-0.928632\pi\)
0.974970 0.222335i \(-0.0713679\pi\)
\(38\) −5.57935 + 3.23137i −0.905090 + 0.524197i
\(39\) 0 0
\(40\) 1.33505 + 5.84284i 0.211090 + 0.923834i
\(41\) 5.46819 4.58835i 0.853987 0.716581i −0.106677 0.994294i \(-0.534021\pi\)
0.960664 + 0.277713i \(0.0895765\pi\)
\(42\) 0 0
\(43\) −3.38403 + 9.29755i −0.516060 + 1.41786i 0.358767 + 0.933427i \(0.383197\pi\)
−0.874827 + 0.484436i \(0.839025\pi\)
\(44\) −0.602374 0.505452i −0.0908113 0.0761997i
\(45\) 0 0
\(46\) 1.06032 + 1.83654i 0.156336 + 0.270782i
\(47\) 0.438674 + 0.0773501i 0.0639872 + 0.0112827i 0.205550 0.978647i \(-0.434102\pi\)
−0.141563 + 0.989929i \(0.545213\pi\)
\(48\) 0 0
\(49\) 1.78085 + 3.08452i 0.254407 + 0.440645i
\(50\) 6.74280 + 3.03861i 0.953576 + 0.429725i
\(51\) 0 0
\(52\) 0.114683 0.315090i 0.0159037 0.0436952i
\(53\) 2.47532 + 6.80087i 0.340011 + 0.934172i 0.985391 + 0.170310i \(0.0544769\pi\)
−0.645380 + 0.763862i \(0.723301\pi\)
\(54\) 0 0
\(55\) 9.12062 2.08400i 1.22982 0.281007i
\(56\) 8.71078 1.16403
\(57\) 0 0
\(58\) 0.502015i 0.0659178i
\(59\) 0.545712 + 3.09489i 0.0710457 + 0.402920i 0.999504 + 0.0314842i \(0.0100234\pi\)
−0.928459 + 0.371436i \(0.878866\pi\)
\(60\) 0 0
\(61\) 2.88074 1.04850i 0.368841 0.134247i −0.150948 0.988542i \(-0.548233\pi\)
0.519789 + 0.854295i \(0.326010\pi\)
\(62\) −1.40573 + 3.86222i −0.178528 + 0.490503i
\(63\) 0 0
\(64\) 3.55679 6.16055i 0.444599 0.770068i
\(65\) 2.16526 + 3.35072i 0.268567 + 0.415606i
\(66\) 0 0
\(67\) 8.42261 + 1.48513i 1.02899 + 0.181438i 0.662559 0.749009i \(-0.269470\pi\)
0.366426 + 0.930447i \(0.380581\pi\)
\(68\) 1.03065 0.595046i 0.124985 0.0721599i
\(69\) 0 0
\(70\) 6.48828 8.56995i 0.775498 1.02430i
\(71\) 12.1153 + 4.40959i 1.43782 + 0.523322i 0.939161 0.343478i \(-0.111605\pi\)
0.498656 + 0.866800i \(0.333827\pi\)
\(72\) 0 0
\(73\) 1.17133 + 1.39594i 0.137094 + 0.163382i 0.830223 0.557431i \(-0.188213\pi\)
−0.693129 + 0.720813i \(0.743768\pi\)
\(74\) 0.694747 + 3.94011i 0.0807627 + 0.458028i
\(75\) 0 0
\(76\) 0.626839 0.527435i 0.0719034 0.0605010i
\(77\) 13.5974i 1.54957i
\(78\) 0 0
\(79\) −0.535235 + 0.449116i −0.0602187 + 0.0505295i −0.672400 0.740188i \(-0.734737\pi\)
0.612182 + 0.790717i \(0.290292\pi\)
\(80\) −3.77219 8.94276i −0.421744 0.999831i
\(81\) 0 0
\(82\) −6.78695 + 8.08837i −0.749493 + 0.893211i
\(83\) 0.478899 + 0.276493i 0.0525660 + 0.0303490i 0.526053 0.850452i \(-0.323671\pi\)
−0.473487 + 0.880801i \(0.657005\pi\)
\(84\) 0 0
\(85\) −1.75729 + 14.0499i −0.190605 + 1.52392i
\(86\) 2.54139 14.4129i 0.274045 1.55419i
\(87\) 0 0
\(88\) −9.71206 5.60726i −1.03531 0.597736i
\(89\) 5.23109 + 4.38940i 0.554494 + 0.465276i 0.876459 0.481476i \(-0.159899\pi\)
−0.321965 + 0.946751i \(0.604343\pi\)
\(90\) 0 0
\(91\) 5.44854 1.98311i 0.571162 0.207886i
\(92\) −0.173197 0.206408i −0.0180570 0.0215195i
\(93\) 0 0
\(94\) −0.658883 −0.0679586
\(95\) 0.501395 + 9.73389i 0.0514420 + 0.998676i
\(96\) 0 0
\(97\) 13.0001 2.29226i 1.31996 0.232744i 0.531094 0.847313i \(-0.321781\pi\)
0.788863 + 0.614569i \(0.210670\pi\)
\(98\) −3.38643 4.03579i −0.342081 0.407676i
\(99\) 0 0
\(100\) −0.910757 0.231446i −0.0910757 0.0231446i
\(101\) −13.2339 11.1046i −1.31683 1.10495i −0.986968 0.160916i \(-0.948555\pi\)
−0.329857 0.944031i \(-0.607001\pi\)
\(102\) 0 0
\(103\) −11.9759 + 6.91430i −1.18002 + 0.681286i −0.956020 0.293302i \(-0.905246\pi\)
−0.224003 + 0.974589i \(0.571912\pi\)
\(104\) 0.830401 4.70944i 0.0814275 0.461798i
\(105\) 0 0
\(106\) −5.35262 9.27101i −0.519893 0.900481i
\(107\) −2.82722 1.63230i −0.273318 0.157800i 0.357077 0.934075i \(-0.383774\pi\)
−0.630394 + 0.776275i \(0.717107\pi\)
\(108\) 0 0
\(109\) −3.02669 1.10163i −0.289905 0.105517i 0.192974 0.981204i \(-0.438187\pi\)
−0.482879 + 0.875687i \(0.660409\pi\)
\(110\) −12.7507 + 5.37844i −1.21573 + 0.512814i
\(111\) 0 0
\(112\) −13.8920 + 2.44953i −1.31267 + 0.231459i
\(113\) 4.71007i 0.443086i 0.975151 + 0.221543i \(0.0711093\pi\)
−0.975151 + 0.221543i \(0.928891\pi\)
\(114\) 0 0
\(115\) 3.20177 0.160557i 0.298567 0.0149720i
\(116\) 0.0110762 + 0.0628163i 0.00102840 + 0.00583234i
\(117\) 0 0
\(118\) −1.58988 4.36815i −0.146360 0.402121i
\(119\) 19.3380 + 7.03845i 1.77271 + 0.645214i
\(120\) 0 0
\(121\) −3.25289 + 5.63416i −0.295717 + 0.512197i
\(122\) −3.92705 + 2.26729i −0.355539 + 0.205270i
\(123\) 0 0
\(124\) 0.0906829 0.514288i 0.00814356 0.0461844i
\(125\) 8.73617 6.97706i 0.781387 0.624047i
\(126\) 0 0
\(127\) −0.380538 + 0.453507i −0.0337673 + 0.0402423i −0.782664 0.622445i \(-0.786140\pi\)
0.748897 + 0.662687i \(0.230584\pi\)
\(128\) −4.32371 + 11.8793i −0.382165 + 1.04999i
\(129\) 0 0
\(130\) −4.01477 4.32483i −0.352119 0.379313i
\(131\) 3.56830 + 20.2369i 0.311764 + 1.76810i 0.589817 + 0.807537i \(0.299200\pi\)
−0.278053 + 0.960566i \(0.589689\pi\)
\(132\) 0 0
\(133\) 13.9540 + 2.44090i 1.20997 + 0.211653i
\(134\) −12.6507 −1.09285
\(135\) 0 0
\(136\) 13.0018 10.9098i 1.11489 0.935506i
\(137\) 2.99407 + 8.22613i 0.255800 + 0.702806i 0.999415 + 0.0341973i \(0.0108875\pi\)
−0.743615 + 0.668608i \(0.766890\pi\)
\(138\) 0 0
\(139\) −5.89041 4.94264i −0.499618 0.419229i 0.357840 0.933783i \(-0.383513\pi\)
−0.857458 + 0.514553i \(0.827958\pi\)
\(140\) −0.622784 + 1.21550i −0.0526349 + 0.102728i
\(141\) 0 0
\(142\) −18.7809 3.31158i −1.57606 0.277901i
\(143\) −7.35139 1.29625i −0.614754 0.108398i
\(144\) 0 0
\(145\) −0.675405 0.346057i −0.0560893 0.0287385i
\(146\) −2.06483 1.73260i −0.170887 0.143391i
\(147\) 0 0
\(148\) −0.173865 0.477690i −0.0142916 0.0392659i
\(149\) −11.4457 + 9.60412i −0.937672 + 0.786800i −0.977179 0.212419i \(-0.931866\pi\)
0.0395067 + 0.999219i \(0.487421\pi\)
\(150\) 0 0
\(151\) 13.1424 1.06951 0.534757 0.845006i \(-0.320403\pi\)
0.534757 + 0.845006i \(0.320403\pi\)
\(152\) 7.49772 8.96017i 0.608145 0.726765i
\(153\) 0 0
\(154\) 3.49257 + 19.8074i 0.281440 + 1.59612i
\(155\) 4.22716 + 4.55363i 0.339534 + 0.365756i
\(156\) 0 0
\(157\) 3.70654 10.1836i 0.295814 0.812742i −0.699374 0.714756i \(-0.746538\pi\)
0.995188 0.0979861i \(-0.0312401\pi\)
\(158\) 0.664318 0.791704i 0.0528503 0.0629846i
\(159\) 0 0
\(160\) 1.28612 + 1.99026i 0.101677 + 0.157344i
\(161\) 0.809073 4.58848i 0.0637639 0.361623i
\(162\) 0 0
\(163\) −7.31405 + 4.22277i −0.572881 + 0.330753i −0.758299 0.651907i \(-0.773969\pi\)
0.185418 + 0.982660i \(0.440636\pi\)
\(164\) 0.670782 1.16183i 0.0523792 0.0907235i
\(165\) 0 0
\(166\) −0.768630 0.279758i −0.0596573 0.0217135i
\(167\) −6.80663 18.7011i −0.526713 1.44713i −0.862919 0.505343i \(-0.831366\pi\)
0.336206 0.941788i \(-0.390856\pi\)
\(168\) 0 0
\(169\) 1.70468 + 9.66772i 0.131129 + 0.743671i
\(170\) −1.04895 20.9178i −0.0804506 1.60432i
\(171\) 0 0
\(172\) 1.85954i 0.141788i
\(173\) −11.5430 + 2.03534i −0.877597 + 0.154744i −0.594257 0.804275i \(-0.702554\pi\)
−0.283340 + 0.959019i \(0.591443\pi\)
\(174\) 0 0
\(175\) −7.05730 14.6368i −0.533482 1.10644i
\(176\) 17.0656 + 6.21138i 1.28637 + 0.468200i
\(177\) 0 0
\(178\) −8.74755 5.05040i −0.655657 0.378544i
\(179\) −3.54189 6.13473i −0.264733 0.458532i 0.702760 0.711427i \(-0.251951\pi\)
−0.967494 + 0.252895i \(0.918617\pi\)
\(180\) 0 0
\(181\) 1.61176 9.14076i 0.119801 0.679427i −0.864459 0.502703i \(-0.832339\pi\)
0.984260 0.176724i \(-0.0565500\pi\)
\(182\) −7.42750 + 4.28827i −0.550563 + 0.317868i
\(183\) 0 0
\(184\) −2.94371 2.47007i −0.217013 0.182096i
\(185\) 5.77989 + 1.78135i 0.424946 + 0.130968i
\(186\) 0 0
\(187\) −17.0301 20.2957i −1.24536 1.48417i
\(188\) 0.0824448 0.0145373i 0.00601291 0.00106024i
\(189\) 0 0
\(190\) −3.23058 14.0505i −0.234371 1.01933i
\(191\) −8.12426 −0.587850 −0.293925 0.955828i \(-0.594962\pi\)
−0.293925 + 0.955828i \(0.594962\pi\)
\(192\) 0 0
\(193\) −4.96452 5.91649i −0.357354 0.425878i 0.557177 0.830394i \(-0.311885\pi\)
−0.914531 + 0.404516i \(0.867440\pi\)
\(194\) −18.3484 + 6.67827i −1.31734 + 0.479472i
\(195\) 0 0
\(196\) 0.512781 + 0.430275i 0.0366272 + 0.0307339i
\(197\) 3.08965 + 1.78381i 0.220129 + 0.127091i 0.606010 0.795457i \(-0.292769\pi\)
−0.385881 + 0.922548i \(0.626103\pi\)
\(198\) 0 0
\(199\) 1.52279 8.63615i 0.107947 0.612201i −0.882055 0.471147i \(-0.843840\pi\)
0.990002 0.141053i \(-0.0450489\pi\)
\(200\) −13.3647 0.995159i −0.945028 0.0703684i
\(201\) 0 0
\(202\) 22.1301 + 12.7768i 1.55707 + 0.898974i
\(203\) −0.708979 + 0.844928i −0.0497606 + 0.0593023i
\(204\) 0 0
\(205\) 6.20351 + 14.7067i 0.433272 + 1.02716i
\(206\) 15.6693 13.1481i 1.09173 0.916073i
\(207\) 0 0
\(208\) 7.74414i 0.536960i
\(209\) −13.9867 11.7039i −0.967483 0.809574i
\(210\) 0 0
\(211\) 2.05203 + 11.6376i 0.141267 + 0.801167i 0.970289 + 0.241950i \(0.0777870\pi\)
−0.829021 + 0.559217i \(0.811102\pi\)
\(212\) 0.874315 + 1.04197i 0.0600482 + 0.0715627i
\(213\) 0 0
\(214\) 4.53767 + 1.65158i 0.310189 + 0.112899i
\(215\) −17.6391 13.3545i −1.20298 0.910770i
\(216\) 0 0
\(217\) 7.82043 4.51513i 0.530886 0.306507i
\(218\) 4.69193 + 0.827314i 0.317778 + 0.0560328i
\(219\) 0 0
\(220\) 1.47681 0.954320i 0.0995662 0.0643402i
\(221\) 5.64880 9.78401i 0.379979 0.658144i
\(222\) 0 0
\(223\) −3.04316 + 8.36101i −0.203785 + 0.559895i −0.998916 0.0465426i \(-0.985180\pi\)
0.795131 + 0.606437i \(0.207402\pi\)
\(224\) 3.23632 1.17792i 0.216236 0.0787034i
\(225\) 0 0
\(226\) −1.20980 6.86114i −0.0804750 0.456396i
\(227\) 26.4080i 1.75276i 0.481620 + 0.876380i \(0.340049\pi\)
−0.481620 + 0.876380i \(0.659951\pi\)
\(228\) 0 0
\(229\) −21.7852 −1.43961 −0.719804 0.694177i \(-0.755768\pi\)
−0.719804 + 0.694177i \(0.755768\pi\)
\(230\) −4.62277 + 1.05627i −0.304817 + 0.0696486i
\(231\) 0 0
\(232\) 0.311129 + 0.854821i 0.0204266 + 0.0561217i
\(233\) 3.42052 9.39780i 0.224086 0.615670i −0.775797 0.630982i \(-0.782652\pi\)
0.999883 + 0.0153122i \(0.00487421\pi\)
\(234\) 0 0
\(235\) −0.454192 + 0.886453i −0.0296282 + 0.0578258i
\(236\) 0.295315 + 0.511500i 0.0192234 + 0.0332958i
\(237\) 0 0
\(238\) −29.9774 5.28583i −1.94315 0.342630i
\(239\) −8.91823 15.4468i −0.576872 0.999172i −0.995835 0.0911689i \(-0.970940\pi\)
0.418963 0.908003i \(-0.362394\pi\)
\(240\) 0 0
\(241\) −13.1332 11.0201i −0.845984 0.709864i 0.112918 0.993604i \(-0.463980\pi\)
−0.958901 + 0.283740i \(0.908425\pi\)
\(242\) 3.29131 9.04279i 0.211573 0.581293i
\(243\) 0 0
\(244\) 0.441361 0.370346i 0.0282552 0.0237090i
\(245\) −7.76409 + 1.77404i −0.496029 + 0.113339i
\(246\) 0 0
\(247\) 2.64990 7.31147i 0.168609 0.465218i
\(248\) 7.44772i 0.472931i
\(249\) 0 0
\(250\) −10.9339 + 12.4074i −0.691518 + 0.784712i
\(251\) 9.11112 3.31618i 0.575089 0.209315i −0.0380697 0.999275i \(-0.512121\pi\)
0.613159 + 0.789960i \(0.289899\pi\)
\(252\) 0 0
\(253\) −3.85575 + 4.59511i −0.242409 + 0.288892i
\(254\) 0.437843 0.758366i 0.0274727 0.0475841i
\(255\) 0 0
\(256\) 0.776555 4.40406i 0.0485347 0.275254i
\(257\) 9.89795 + 1.74528i 0.617417 + 0.108867i 0.473605 0.880738i \(-0.342953\pi\)
0.143813 + 0.989605i \(0.454064\pi\)
\(258\) 0 0
\(259\) 4.39517 7.61265i 0.273102 0.473027i
\(260\) 0.597782 + 0.452579i 0.0370729 + 0.0280677i
\(261\) 0 0
\(262\) −10.3959 28.5624i −0.642259 1.76459i
\(263\) −14.0324 16.7232i −0.865276 1.03120i −0.999192 0.0402026i \(-0.987200\pi\)
0.133916 0.990993i \(-0.457245\pi\)
\(264\) 0 0
\(265\) −16.1629 + 0.810506i −0.992877 + 0.0497890i
\(266\) −20.9537 + 0.0285081i −1.28475 + 0.00174794i
\(267\) 0 0
\(268\) 1.58295 0.279117i 0.0966943 0.0170498i
\(269\) 11.8393 9.93433i 0.721853 0.605707i −0.206044 0.978543i \(-0.566059\pi\)
0.927897 + 0.372836i \(0.121615\pi\)
\(270\) 0 0
\(271\) −4.85182 1.76592i −0.294727 0.107272i 0.190425 0.981702i \(-0.439013\pi\)
−0.485152 + 0.874430i \(0.661236\pi\)
\(272\) −17.6674 + 21.0552i −1.07124 + 1.27666i
\(273\) 0 0
\(274\) −6.47437 11.2139i −0.391131 0.677459i
\(275\) −1.55343 + 20.8622i −0.0936756 + 1.25804i
\(276\) 0 0
\(277\) −4.82402 + 2.78515i −0.289847 + 0.167343i −0.637873 0.770142i \(-0.720186\pi\)
0.348026 + 0.937485i \(0.386852\pi\)
\(278\) 9.85009 + 5.68695i 0.590769 + 0.341081i
\(279\) 0 0
\(280\) −5.73679 + 18.6139i −0.342839 + 1.11239i
\(281\) 25.6282 9.32789i 1.52885 0.556455i 0.565509 0.824742i \(-0.308680\pi\)
0.963339 + 0.268287i \(0.0864576\pi\)
\(282\) 0 0
\(283\) 14.8172 2.61267i 0.880792 0.155307i 0.285078 0.958504i \(-0.407980\pi\)
0.595714 + 0.803197i \(0.296869\pi\)
\(284\) 2.42308 0.143784
\(285\) 0 0
\(286\) 11.0417 0.652910
\(287\) 22.8459 4.02834i 1.34855 0.237786i
\(288\) 0 0
\(289\) 21.7045 7.89981i 1.27674 0.464694i
\(290\) 1.07275 + 0.330620i 0.0629939 + 0.0194147i
\(291\) 0 0
\(292\) 0.296596 + 0.171240i 0.0173570 + 0.0100210i
\(293\) 6.77995 3.91441i 0.396089 0.228682i −0.288706 0.957418i \(-0.593225\pi\)
0.684795 + 0.728736i \(0.259892\pi\)
\(294\) 0 0
\(295\) −6.97281 0.872124i −0.405973 0.0507770i
\(296\) −3.62492 6.27855i −0.210694 0.364933i
\(297\) 0 0
\(298\) 14.2061 16.9302i 0.822938 0.980740i
\(299\) −2.40361 0.874843i −0.139004 0.0505935i
\(300\) 0 0
\(301\) −24.6322 + 20.6689i −1.41978 + 1.19133i
\(302\) −19.1445 + 3.37569i −1.10164 + 0.194249i
\(303\) 0 0
\(304\) −9.43773 + 16.3981i −0.541291 + 0.940496i
\(305\) 0.343317 + 6.84633i 0.0196583 + 0.392020i
\(306\) 0 0
\(307\) 10.1011 + 12.0381i 0.576503 + 0.687049i 0.972952 0.231008i \(-0.0742022\pi\)
−0.396449 + 0.918057i \(0.629758\pi\)
\(308\) −0.874039 2.40140i −0.0498030 0.136833i
\(309\) 0 0
\(310\) −7.32732 5.54749i −0.416164 0.315076i
\(311\) 8.99061 15.5722i 0.509810 0.883018i −0.490125 0.871652i \(-0.663049\pi\)
0.999935 0.0113654i \(-0.00361781\pi\)
\(312\) 0 0
\(313\) 20.8784 + 3.68143i 1.18012 + 0.208087i 0.729087 0.684422i \(-0.239945\pi\)
0.451031 + 0.892508i \(0.351056\pi\)
\(314\) −2.78359 + 15.7865i −0.157087 + 0.890884i
\(315\) 0 0
\(316\) −0.0656572 + 0.113722i −0.00369351 + 0.00639734i
\(317\) −1.96977 + 2.34748i −0.110633 + 0.131848i −0.818519 0.574479i \(-0.805205\pi\)
0.707886 + 0.706327i \(0.249649\pi\)
\(318\) 0 0
\(319\) 1.33437 0.485670i 0.0747102 0.0271923i
\(320\) 10.8219 + 11.6577i 0.604963 + 0.651685i
\(321\) 0 0
\(322\) 6.89184i 0.384067i
\(323\) 23.8850 13.8333i 1.32899 0.769708i
\(324\) 0 0
\(325\) −8.58611 + 2.42016i −0.476271 + 0.134246i
\(326\) 9.56972 8.02995i 0.530018 0.444738i
\(327\) 0 0
\(328\) 6.54382 17.9790i 0.361322 0.992724i
\(329\) 1.10895 + 0.930518i 0.0611383 + 0.0513011i
\(330\) 0 0
\(331\) 12.9754 + 22.4741i 0.713195 + 1.23529i 0.963652 + 0.267162i \(0.0860858\pi\)
−0.250457 + 0.968128i \(0.580581\pi\)
\(332\) 0.102350 + 0.0180470i 0.00561717 + 0.000990459i
\(333\) 0 0
\(334\) 14.7187 + 25.4935i 0.805369 + 1.39494i
\(335\) −8.72056 + 17.0200i −0.476455 + 0.929904i
\(336\) 0 0
\(337\) −3.43986 + 9.45093i −0.187381 + 0.514825i −0.997439 0.0715252i \(-0.977213\pi\)
0.810058 + 0.586350i \(0.199436\pi\)
\(338\) −4.96641 13.6451i −0.270137 0.742195i
\(339\) 0 0
\(340\) 0.592773 + 2.59426i 0.0321476 + 0.140694i
\(341\) −11.6258 −0.629574
\(342\) 0 0
\(343\) 11.1741i 0.603343i
\(344\) 4.60514 + 26.1171i 0.248293 + 1.40814i
\(345\) 0 0
\(346\) 16.2918 5.92975i 0.875855 0.318785i
\(347\) 2.33190 6.40683i 0.125183 0.343937i −0.861232 0.508213i \(-0.830306\pi\)
0.986414 + 0.164276i \(0.0525287\pi\)
\(348\) 0 0
\(349\) 15.7983 27.3634i 0.845663 1.46473i −0.0393817 0.999224i \(-0.512539\pi\)
0.885044 0.465507i \(-0.154128\pi\)
\(350\) 14.0399 + 19.5087i 0.750464 + 1.04279i
\(351\) 0 0
\(352\) −4.36658 0.769945i −0.232739 0.0410382i
\(353\) 5.46165 3.15328i 0.290694 0.167832i −0.347561 0.937658i \(-0.612990\pi\)
0.638255 + 0.769825i \(0.279657\pi\)
\(354\) 0 0
\(355\) −17.4017 + 22.9848i −0.923587 + 1.21991i
\(356\) 1.20600 + 0.438946i 0.0639176 + 0.0232641i
\(357\) 0 0
\(358\) 6.73520 + 8.02670i 0.355966 + 0.424224i
\(359\) 0.725269 + 4.11321i 0.0382782 + 0.217087i 0.997947 0.0640469i \(-0.0204007\pi\)
−0.959669 + 0.281134i \(0.909290\pi\)
\(360\) 0 0
\(361\) 14.5216 12.2525i 0.764293 0.644870i
\(362\) 13.7293i 0.721596i
\(363\) 0 0
\(364\) 0.834776 0.700460i 0.0437542 0.0367141i
\(365\) −3.75438 + 1.58365i −0.196513 + 0.0828923i
\(366\) 0 0
\(367\) −10.6516 + 12.6941i −0.556010 + 0.662627i −0.968697 0.248246i \(-0.920146\pi\)
0.412687 + 0.910873i \(0.364590\pi\)
\(368\) 5.38924 + 3.11148i 0.280933 + 0.162197i
\(369\) 0 0
\(370\) −8.87709 1.11030i −0.461498 0.0577218i
\(371\) −4.08428 + 23.1631i −0.212045 + 1.20257i
\(372\) 0 0
\(373\) 32.0433 + 18.5002i 1.65914 + 0.957905i 0.973113 + 0.230330i \(0.0739804\pi\)
0.686028 + 0.727576i \(0.259353\pi\)
\(374\) 30.0207 + 25.1904i 1.55233 + 1.30256i
\(375\) 0 0
\(376\) 1.12193 0.408350i 0.0578592 0.0210590i
\(377\) 0.389219 + 0.463853i 0.0200458 + 0.0238897i
\(378\) 0 0
\(379\) −31.5147 −1.61880 −0.809400 0.587257i \(-0.800208\pi\)
−0.809400 + 0.587257i \(0.800208\pi\)
\(380\) 0.714241 + 1.68684i 0.0366398 + 0.0865332i
\(381\) 0 0
\(382\) 11.8346 2.08676i 0.605510 0.106768i
\(383\) 1.99144 + 2.37331i 0.101758 + 0.121270i 0.814520 0.580136i \(-0.197000\pi\)
−0.712762 + 0.701406i \(0.752556\pi\)
\(384\) 0 0
\(385\) 29.0561 + 8.95507i 1.48084 + 0.456393i
\(386\) 8.75148 + 7.34337i 0.445439 + 0.373768i
\(387\) 0 0
\(388\) 2.14856 1.24047i 0.109076 0.0629753i
\(389\) 4.52037 25.6363i 0.229192 1.29981i −0.625316 0.780372i \(-0.715030\pi\)
0.854507 0.519439i \(-0.173859\pi\)
\(390\) 0 0
\(391\) −4.53920 7.86213i −0.229557 0.397605i
\(392\) 8.26756 + 4.77328i 0.417575 + 0.241087i
\(393\) 0 0
\(394\) −4.95887 1.80488i −0.249824 0.0909285i
\(395\) −0.607210 1.43952i −0.0305520 0.0724299i
\(396\) 0 0
\(397\) 12.4684 2.19851i 0.625770 0.110340i 0.148234 0.988952i \(-0.452641\pi\)
0.477536 + 0.878612i \(0.341530\pi\)
\(398\) 12.9714i 0.650197i
\(399\) 0 0
\(400\) 21.5939 2.17116i 1.07970 0.108558i
\(401\) 1.60135 + 9.08170i 0.0799675 + 0.453518i 0.998330 + 0.0577770i \(0.0184012\pi\)
−0.918362 + 0.395741i \(0.870488\pi\)
\(402\) 0 0
\(403\) −1.69556 4.65851i −0.0844618 0.232057i
\(404\) −3.05100 1.11047i −0.151793 0.0552481i
\(405\) 0 0
\(406\) 0.815744 1.41291i 0.0404847 0.0701215i
\(407\) −9.80076 + 5.65847i −0.485806 + 0.280480i
\(408\) 0 0
\(409\) −5.98343 + 33.9337i −0.295861 + 1.67791i 0.367819 + 0.929897i \(0.380105\pi\)
−0.663680 + 0.748016i \(0.731007\pi\)
\(410\) −12.8141 19.8298i −0.632844 0.979324i
\(411\) 0 0
\(412\) −1.67058 + 1.99092i −0.0823036 + 0.0980856i
\(413\) −3.49311 + 9.59724i −0.171885 + 0.472249i
\(414\) 0 0
\(415\) −0.906228 + 0.841258i −0.0444850 + 0.0412957i
\(416\) −0.328320 1.86199i −0.0160972 0.0912917i
\(417\) 0 0
\(418\) 23.3806 + 13.4564i 1.14358 + 0.658176i
\(419\) −7.86047 −0.384009 −0.192005 0.981394i \(-0.561499\pi\)
−0.192005 + 0.981394i \(0.561499\pi\)
\(420\) 0 0
\(421\) 8.03752 6.74428i 0.391725 0.328696i −0.425560 0.904930i \(-0.639923\pi\)
0.817285 + 0.576234i \(0.195478\pi\)
\(422\) −5.97836 16.4254i −0.291022 0.799577i
\(423\) 0 0
\(424\) 14.8601 + 12.4691i 0.721672 + 0.605555i
\(425\) −28.8656 13.0082i −1.40019 0.630989i
\(426\) 0 0
\(427\) 9.81153 + 1.73004i 0.474813 + 0.0837223i
\(428\) −0.604230 0.106542i −0.0292066 0.00514991i
\(429\) 0 0
\(430\) 29.1250 + 14.9228i 1.40453 + 0.719640i
\(431\) −22.8988 19.2144i −1.10300 0.925525i −0.105375 0.994433i \(-0.533604\pi\)
−0.997623 + 0.0689073i \(0.978049\pi\)
\(432\) 0 0
\(433\) −2.32566 6.38969i −0.111764 0.307069i 0.871183 0.490959i \(-0.163353\pi\)
−0.982947 + 0.183890i \(0.941131\pi\)
\(434\) −10.2323 + 8.58589i −0.491165 + 0.412136i
\(435\) 0 0
\(436\) −0.605347 −0.0289908
\(437\) −4.02345 4.78173i −0.192468 0.228741i
\(438\) 0 0
\(439\) −1.38329 7.84504i −0.0660209 0.374423i −0.999860 0.0167300i \(-0.994674\pi\)
0.933839 0.357693i \(-0.116437\pi\)
\(440\) 18.3783 17.0607i 0.876150 0.813336i
\(441\) 0 0
\(442\) −5.71552 + 15.7033i −0.271859 + 0.746928i
\(443\) −14.0059 + 16.6916i −0.665440 + 0.793041i −0.988156 0.153455i \(-0.950960\pi\)
0.322715 + 0.946496i \(0.395404\pi\)
\(444\) 0 0
\(445\) −12.8248 + 8.28742i −0.607952 + 0.392862i
\(446\) 2.28539 12.9611i 0.108217 0.613726i
\(447\) 0 0
\(448\) 20.0210 11.5591i 0.945904 0.546118i
\(449\) −9.39185 + 16.2672i −0.443229 + 0.767695i −0.997927 0.0643569i \(-0.979500\pi\)
0.554698 + 0.832052i \(0.312834\pi\)
\(450\) 0 0
\(451\) −28.0651 10.2148i −1.32153 0.480998i
\(452\) 0.302761 + 0.831830i 0.0142407 + 0.0391260i
\(453\) 0 0
\(454\) −6.78303 38.4685i −0.318343 1.80541i
\(455\) 0.649339 + 12.9489i 0.0304415 + 0.607055i
\(456\) 0 0
\(457\) 28.2368i 1.32086i −0.750887 0.660431i \(-0.770373\pi\)
0.750887 0.660431i \(-0.229627\pi\)
\(458\) 31.7345 5.59564i 1.48285 0.261467i
\(459\) 0 0
\(460\) 0.555134 0.234164i 0.0258833 0.0109180i
\(461\) −0.184187 0.0670386i −0.00857845 0.00312230i 0.337727 0.941244i \(-0.390342\pi\)
−0.346306 + 0.938122i \(0.612564\pi\)
\(462\) 0 0
\(463\) −12.0933 6.98206i −0.562022 0.324484i 0.191935 0.981408i \(-0.438524\pi\)
−0.753957 + 0.656924i \(0.771857\pi\)
\(464\) −0.736571 1.27578i −0.0341945 0.0592266i
\(465\) 0 0
\(466\) −2.56879 + 14.5683i −0.118997 + 0.674865i
\(467\) −27.8016 + 16.0512i −1.28650 + 0.742763i −0.978029 0.208470i \(-0.933152\pi\)
−0.308474 + 0.951233i \(0.599818\pi\)
\(468\) 0 0
\(469\) 21.2920 + 17.8661i 0.983172 + 0.824979i
\(470\) 0.433930 1.40796i 0.0200157 0.0649441i
\(471\) 0 0
\(472\) 5.41441 + 6.45264i 0.249218 + 0.297007i
\(473\) 40.7685 7.18859i 1.87454 0.330532i
\(474\) 0 0
\(475\) −21.1304 5.33917i −0.969529 0.244978i
\(476\) 3.86765 0.177273
\(477\) 0 0
\(478\) 16.9588 + 20.2107i 0.775675 + 0.924414i
\(479\) 1.86271 0.677972i 0.0851095 0.0309773i −0.299114 0.954217i \(-0.596691\pi\)
0.384224 + 0.923240i \(0.374469\pi\)
\(480\) 0 0
\(481\) −3.69675 3.10194i −0.168557 0.141436i
\(482\) 21.9616 + 12.6796i 1.00033 + 0.577538i
\(483\) 0 0
\(484\) −0.212320 + 1.20413i −0.00965091 + 0.0547330i
\(485\) −3.66335 + 29.2893i −0.166344 + 1.32996i
\(486\) 0 0
\(487\) 7.43843 + 4.29458i 0.337068 + 0.194606i 0.658975 0.752165i \(-0.270990\pi\)
−0.321907 + 0.946771i \(0.604324\pi\)
\(488\) 5.28173 6.29452i 0.239093 0.284939i
\(489\) 0 0
\(490\) 10.8543 4.57849i 0.490345 0.206835i
\(491\) −19.8407 + 16.6483i −0.895398 + 0.751328i −0.969285 0.245938i \(-0.920904\pi\)
0.0738874 + 0.997267i \(0.476459\pi\)
\(492\) 0 0
\(493\) 2.14910i 0.0967908i
\(494\) −1.98211 + 11.3312i −0.0891794 + 0.509817i
\(495\) 0 0
\(496\) 2.09435 + 11.8777i 0.0940391 + 0.533322i
\(497\) 26.9328 + 32.0972i 1.20810 + 1.43976i
\(498\) 0 0
\(499\) −19.9251 7.25214i −0.891970 0.324650i −0.144939 0.989441i \(-0.546299\pi\)
−0.747030 + 0.664790i \(0.768521\pi\)
\(500\) 1.09438 1.79375i 0.0489424 0.0802191i
\(501\) 0 0
\(502\) −12.4204 + 7.17090i −0.554348 + 0.320053i
\(503\) −25.1285 4.43084i −1.12043 0.197561i −0.417398 0.908724i \(-0.637058\pi\)
−0.703028 + 0.711162i \(0.748169\pi\)
\(504\) 0 0
\(505\) 32.4449 20.9660i 1.44378 0.932976i
\(506\) 4.43639 7.68405i 0.197221 0.341597i
\(507\) 0 0
\(508\) −0.0380543 + 0.104553i −0.00168839 + 0.00463880i
\(509\) 16.0130 5.82825i 0.709763 0.258333i 0.0381894 0.999271i \(-0.487841\pi\)
0.671574 + 0.740938i \(0.265619\pi\)
\(510\) 0 0
\(511\) 1.02837 + 5.83218i 0.0454924 + 0.258000i
\(512\) 18.6685i 0.825039i
\(513\) 0 0
\(514\) −14.8666 −0.655738
\(515\) −6.88789 30.1448i −0.303517 1.32834i
\(516\) 0 0
\(517\) −0.637430 1.75133i −0.0280342 0.0770232i
\(518\) −4.44708 + 12.2183i −0.195393 + 0.536839i
\(519\) 0 0
\(520\) 9.51663 + 4.87603i 0.417332 + 0.213828i
\(521\) 10.8909 + 18.8635i 0.477137 + 0.826426i 0.999657 0.0262016i \(-0.00834118\pi\)
−0.522520 + 0.852627i \(0.675008\pi\)
\(522\) 0 0
\(523\) −17.2199 3.03633i −0.752973 0.132769i −0.216028 0.976387i \(-0.569310\pi\)
−0.536944 + 0.843618i \(0.680422\pi\)
\(524\) 1.93100 + 3.34460i 0.0843563 + 0.146109i
\(525\) 0 0
\(526\) 24.7364 + 20.7563i 1.07856 + 0.905018i
\(527\) 6.01788 16.5340i 0.262143 0.720232i
\(528\) 0 0
\(529\) 16.0445 13.4629i 0.697586 0.585344i
\(530\) 23.3362 5.33218i 1.01366 0.231615i
\(531\) 0 0
\(532\) 2.62127 0.465879i 0.113647 0.0201984i
\(533\) 12.7355i 0.551637i
\(534\) 0 0
\(535\) 5.34999 4.96644i 0.231300 0.214718i
\(536\) 21.5413 7.84038i 0.930441 0.338653i
\(537\) 0 0
\(538\) −14.6945 + 17.5123i −0.633527 + 0.755008i
\(539\) 7.45104 12.9056i 0.320939 0.555883i
\(540\) 0 0
\(541\) 2.57157 14.5841i 0.110560 0.627018i −0.878293 0.478123i \(-0.841317\pi\)
0.988853 0.148895i \(-0.0475717\pi\)
\(542\) 7.52121 + 1.32619i 0.323064 + 0.0569648i
\(543\) 0 0
\(544\) 3.35527 5.81150i 0.143856 0.249166i
\(545\) 4.34738 5.74217i 0.186221 0.245968i
\(546\) 0 0
\(547\) −9.08867 24.9709i −0.388603 1.06768i −0.967631 0.252371i \(-0.918790\pi\)
0.579027 0.815308i \(-0.303433\pi\)
\(548\) 1.05754 + 1.26033i 0.0451761 + 0.0538388i
\(549\) 0 0
\(550\) −3.09568 30.7889i −0.132000 1.31284i
\(551\) 0.258871 + 1.45654i 0.0110283 + 0.0620507i
\(552\) 0 0
\(553\) −2.23619 + 0.394301i −0.0950926 + 0.0167674i
\(554\) 6.31176 5.29619i 0.268161 0.225014i
\(555\) 0 0
\(556\) −1.35800 0.494271i −0.0575919 0.0209618i
\(557\) 10.3330 12.3143i 0.437821 0.521775i −0.501340 0.865250i \(-0.667160\pi\)
0.939162 + 0.343475i \(0.111604\pi\)
\(558\) 0 0
\(559\) 8.82633 + 15.2877i 0.373314 + 0.646599i
\(560\) 3.91469 31.2987i 0.165426 1.32261i
\(561\) 0 0
\(562\) −34.9365 + 20.1706i −1.47371 + 0.850847i
\(563\) −1.75929 1.01573i −0.0741452 0.0428078i 0.462469 0.886635i \(-0.346964\pi\)
−0.536614 + 0.843828i \(0.680297\pi\)
\(564\) 0 0
\(565\) −10.0649 3.10198i −0.423432 0.130501i
\(566\) −20.9131 + 7.61175i −0.879044 + 0.319946i
\(567\) 0 0
\(568\) 34.0321 6.00077i 1.42795 0.251787i
\(569\) −12.8224 −0.537543 −0.268772 0.963204i \(-0.586618\pi\)
−0.268772 + 0.963204i \(0.586618\pi\)
\(570\) 0 0
\(571\) 12.9168 0.540551 0.270276 0.962783i \(-0.412885\pi\)
0.270276 + 0.962783i \(0.412885\pi\)
\(572\) −1.38163 + 0.243618i −0.0577688 + 0.0101862i
\(573\) 0 0
\(574\) −32.2448 + 11.7362i −1.34587 + 0.489858i
\(575\) −1.76555 + 6.94755i −0.0736285 + 0.289733i
\(576\) 0 0
\(577\) −7.02658 4.05680i −0.292520 0.168887i 0.346558 0.938029i \(-0.387351\pi\)
−0.639078 + 0.769142i \(0.720684\pi\)
\(578\) −29.5878 + 17.0825i −1.23069 + 0.710540i
\(579\) 0 0
\(580\) −0.141526 0.0177013i −0.00587653 0.000735007i
\(581\) 0.898567 + 1.55636i 0.0372788 + 0.0645689i
\(582\) 0 0
\(583\) 19.4642 23.1966i 0.806126 0.960703i
\(584\) 4.58975 + 1.67053i 0.189925 + 0.0691271i
\(585\) 0 0
\(586\) −8.87090 + 7.44357i −0.366454 + 0.307491i
\(587\) −32.0670 + 5.65427i −1.32355 + 0.233377i −0.790371 0.612629i \(-0.790112\pi\)
−0.533174 + 0.846005i \(0.679001\pi\)
\(588\) 0 0
\(589\) 2.08697 11.9307i 0.0859921 0.491595i
\(590\) 10.3813 0.520581i 0.427391 0.0214320i
\(591\) 0 0
\(592\) 7.54661 + 8.99370i 0.310164 + 0.369639i
\(593\) 3.92476 + 10.7832i 0.161171 + 0.442812i 0.993822 0.110985i \(-0.0354005\pi\)
−0.832652 + 0.553797i \(0.813178\pi\)
\(594\) 0 0
\(595\) −27.7760 + 36.6876i −1.13871 + 1.50404i
\(596\) −1.40405 + 2.43188i −0.0575120 + 0.0996138i
\(597\) 0 0
\(598\) 3.72604 + 0.657002i 0.152369 + 0.0268668i
\(599\) 5.76684 32.7054i 0.235627 1.33631i −0.605663 0.795721i \(-0.707092\pi\)
0.841290 0.540584i \(-0.181797\pi\)
\(600\) 0 0
\(601\) −13.6590 + 23.6581i −0.557163 + 0.965034i 0.440569 + 0.897719i \(0.354777\pi\)
−0.997732 + 0.0673154i \(0.978557\pi\)
\(602\) 30.5728 36.4352i 1.24605 1.48499i
\(603\) 0 0
\(604\) 2.32104 0.844789i 0.0944417 0.0343740i
\(605\) −9.89725 10.6616i −0.402380 0.433456i
\(606\) 0 0
\(607\) 25.7405i 1.04478i 0.852708 + 0.522388i \(0.174959\pi\)
−0.852708 + 0.522388i \(0.825041\pi\)
\(608\) 1.57399 4.34286i 0.0638335 0.176126i
\(609\) 0 0
\(610\) −2.25862 9.88485i −0.0914490 0.400226i
\(611\) 0.608796 0.510841i 0.0246293 0.0206664i
\(612\) 0 0
\(613\) −13.8873 + 38.1551i −0.560904 + 1.54107i 0.257411 + 0.966302i \(0.417131\pi\)
−0.818315 + 0.574770i \(0.805092\pi\)
\(614\) −17.8063 14.9413i −0.718606 0.602982i
\(615\) 0 0
\(616\) −18.2229 31.5630i −0.734222 1.27171i
\(617\) −13.9954 2.46776i −0.563433 0.0993485i −0.115325 0.993328i \(-0.536791\pi\)
−0.448108 + 0.893979i \(0.647902\pi\)
\(618\) 0 0
\(619\) −14.7818 25.6028i −0.594129 1.02906i −0.993669 0.112346i \(-0.964164\pi\)
0.399540 0.916716i \(-0.369170\pi\)
\(620\) 1.03925 + 0.532481i 0.0417373 + 0.0213850i
\(621\) 0 0
\(622\) −9.09680 + 24.9932i −0.364748 + 1.00214i
\(623\) 7.59026 + 20.8541i 0.304097 + 0.835500i
\(624\) 0 0
\(625\) 9.15564 + 23.2632i 0.366226 + 0.930526i
\(626\) −31.3591 −1.25336
\(627\) 0 0
\(628\) 2.03675i 0.0812753i
\(629\) −2.97418 16.8674i −0.118588 0.672548i
\(630\) 0 0
\(631\) 1.60465 0.584045i 0.0638801 0.0232505i −0.309882 0.950775i \(-0.600290\pi\)
0.373763 + 0.927524i \(0.378067\pi\)
\(632\) −0.640520 + 1.75981i −0.0254785 + 0.0700017i
\(633\) 0 0
\(634\) 2.26640 3.92552i 0.0900102 0.155902i
\(635\) −0.718475 1.11184i −0.0285118 0.0441219i
\(636\) 0 0
\(637\) 6.25800 + 1.10345i 0.247951 + 0.0437204i
\(638\) −1.81902 + 1.05021i −0.0720158 + 0.0415783i
\(639\) 0 0
\(640\) −22.5371 17.0628i −0.890858 0.674465i
\(641\) 2.59543 + 0.944659i 0.102513 + 0.0373118i 0.392768 0.919638i \(-0.371518\pi\)
−0.290254 + 0.956950i \(0.593740\pi\)
\(642\) 0 0
\(643\) −13.9466 16.6209i −0.550000 0.655465i 0.417398 0.908724i \(-0.362942\pi\)
−0.967398 + 0.253259i \(0.918497\pi\)
\(644\) −0.152058 0.862364i −0.00599193 0.0339819i
\(645\) 0 0
\(646\) −31.2400 + 26.2860i −1.22912 + 1.03421i
\(647\) 28.0268i 1.10185i 0.834556 + 0.550923i \(0.185724\pi\)
−0.834556 + 0.550923i \(0.814276\pi\)
\(648\) 0 0
\(649\) 10.0725 8.45185i 0.395381 0.331764i
\(650\) 11.8857 5.73082i 0.466196 0.224781i
\(651\) 0 0
\(652\) −1.02027 + 1.21591i −0.0399570 + 0.0476189i
\(653\) −6.57580 3.79654i −0.257331 0.148570i 0.365785 0.930699i \(-0.380800\pi\)
−0.623116 + 0.782129i \(0.714134\pi\)
\(654\) 0 0
\(655\) −45.5938 5.70264i −1.78150 0.222821i
\(656\) −5.38029 + 30.5131i −0.210065 + 1.19134i
\(657\) 0 0
\(658\) −1.85441 1.07064i −0.0722924 0.0417380i
\(659\) 5.50322 + 4.61775i 0.214375 + 0.179882i 0.743652 0.668567i \(-0.233092\pi\)
−0.529277 + 0.848449i \(0.677537\pi\)
\(660\) 0 0
\(661\) 27.1268 9.87335i 1.05511 0.384029i 0.244521 0.969644i \(-0.421369\pi\)
0.810589 + 0.585615i \(0.199147\pi\)
\(662\) −24.6739 29.4052i −0.958978 1.14287i
\(663\) 0 0
\(664\) 1.48219 0.0575201
\(665\) −14.4058 + 28.2105i −0.558633 + 1.09396i
\(666\) 0 0
\(667\) 0.479183 0.0844929i 0.0185540 0.00327158i
\(668\) −2.40419 2.86521i −0.0930210 0.110858i
\(669\) 0 0
\(670\) 8.33153 27.0330i 0.321875 1.04437i
\(671\) −9.82569 8.24473i −0.379316 0.318284i
\(672\) 0 0
\(673\) 20.1949 11.6595i 0.778457 0.449442i −0.0574263 0.998350i \(-0.518289\pi\)
0.835883 + 0.548907i \(0.184956\pi\)
\(674\) 2.58331 14.6507i 0.0995054 0.564323i
\(675\) 0 0
\(676\) 0.922496 + 1.59781i 0.0354806 + 0.0614542i
\(677\) 15.1640 + 8.75493i 0.582799 + 0.336479i 0.762245 0.647289i \(-0.224097\pi\)
−0.179446 + 0.983768i \(0.557430\pi\)
\(678\) 0 0
\(679\) 40.3132 + 14.6728i 1.54708 + 0.563090i
\(680\) 14.7502 + 34.9683i 0.565643 + 1.34097i
\(681\) 0 0
\(682\) 16.9353 2.98615i 0.648487 0.114346i
\(683\) 22.0114i 0.842243i −0.907004 0.421122i \(-0.861637\pi\)
0.907004 0.421122i \(-0.138363\pi\)
\(684\) 0 0
\(685\) −19.5501 + 0.980363i −0.746971 + 0.0374577i
\(686\) 2.87012 + 16.2772i 0.109582 + 0.621468i
\(687\) 0 0
\(688\) −14.6886 40.3566i −0.559997 1.53858i
\(689\) 12.1337 + 4.41629i 0.462256 + 0.168247i
\(690\) 0 0
\(691\) 1.32811 2.30036i 0.0505238 0.0875098i −0.839657 0.543116i \(-0.817244\pi\)
0.890181 + 0.455607i \(0.150578\pi\)
\(692\) −1.90774 + 1.10143i −0.0725214 + 0.0418702i
\(693\) 0 0
\(694\) −1.75124 + 9.93178i −0.0664762 + 0.377005i
\(695\) 14.4412 9.33197i 0.547785 0.353982i
\(696\) 0 0
\(697\) 29.0546 34.6260i 1.10052 1.31155i
\(698\) −15.9849 + 43.9181i −0.605037 + 1.66232i
\(699\) 0 0
\(700\) −2.18722 2.13132i −0.0826690 0.0805565i
\(701\) 1.27931 + 7.25535i 0.0483190 + 0.274031i 0.999389 0.0349439i \(-0.0111253\pi\)
−0.951070 + 0.308975i \(0.900014\pi\)
\(702\) 0 0
\(703\) −4.04750 11.0735i −0.152654 0.417646i
\(704\) −29.7632 −1.12174
\(705\) 0 0
\(706\) −7.14603 + 5.99623i −0.268944 + 0.225671i
\(707\) −19.2023 52.7579i −0.722177 1.98416i
\(708\) 0 0
\(709\) 4.58997 + 3.85144i 0.172380 + 0.144644i 0.724896 0.688858i \(-0.241888\pi\)
−0.552516 + 0.833502i \(0.686332\pi\)
\(710\) 19.4453 37.9516i 0.729768 1.42430i
\(711\) 0 0
\(712\) 18.0252 + 3.17833i 0.675522 + 0.119113i
\(713\) −3.92316 0.691759i −0.146923 0.0259066i
\(714\) 0 0
\(715\) 7.61145 14.8554i 0.284652 0.555559i
\(716\) −1.01986 0.855765i −0.0381140 0.0319814i
\(717\) 0 0
\(718\) −2.11300 5.80541i −0.0788563 0.216656i
\(719\) 10.4040 8.73002i 0.388005 0.325575i −0.427831 0.903859i \(-0.640722\pi\)
0.815835 + 0.578284i \(0.196278\pi\)
\(720\) 0 0
\(721\) −44.9412 −1.67370
\(722\) −18.0064 + 21.5782i −0.670128 + 0.803056i
\(723\) 0 0
\(724\) −0.302916 1.71792i −0.0112578 0.0638461i
\(725\) 1.18430 1.21535i 0.0439836 0.0451371i
\(726\) 0 0
\(727\) −14.1065 + 38.7574i −0.523183 + 1.43743i 0.343776 + 0.939052i \(0.388294\pi\)
−0.866958 + 0.498381i \(0.833928\pi\)
\(728\) 9.98969 11.9052i 0.370242 0.441238i
\(729\) 0 0
\(730\) 5.06223 3.27124i 0.187361 0.121074i
\(731\) −10.8796 + 61.7011i −0.402395 + 2.28210i
\(732\) 0 0
\(733\) 0.107256 0.0619240i 0.00396158 0.00228722i −0.498018 0.867167i \(-0.665939\pi\)
0.501979 + 0.864880i \(0.332605\pi\)
\(734\) 12.2556 21.2274i 0.452364 0.783517i
\(735\) 0 0
\(736\) −1.42770 0.519639i −0.0526256 0.0191541i
\(737\) −12.2388 33.6257i −0.450821 1.23862i
\(738\) 0 0
\(739\) 6.34049 + 35.9587i 0.233239 + 1.32276i 0.846291 + 0.532720i \(0.178830\pi\)
−0.613053 + 0.790042i \(0.710059\pi\)
\(740\) 1.13527 0.0569295i 0.0417334 0.00209277i
\(741\) 0 0
\(742\) 34.7907i 1.27721i
\(743\) −8.92430 + 1.57359i −0.327401 + 0.0577296i −0.334933 0.942242i \(-0.608714\pi\)
0.00753195 + 0.999972i \(0.497602\pi\)
\(744\) 0 0
\(745\) −12.9849 30.7833i −0.475729 1.12781i
\(746\) −51.4293 18.7187i −1.88296 0.685341i
\(747\) 0 0
\(748\) −4.31223 2.48967i −0.157671 0.0910312i
\(749\) −5.30476 9.18812i −0.193832 0.335727i
\(750\) 0 0
\(751\) −0.709544 + 4.02402i −0.0258916 + 0.146839i −0.995013 0.0997456i \(-0.968197\pi\)
0.969121 + 0.246584i \(0.0793082\pi\)
\(752\) −1.67443 + 0.966732i −0.0610602 + 0.0352531i
\(753\) 0 0
\(754\) −0.686117 0.575721i −0.0249869 0.0209665i
\(755\) −8.65539 + 28.0838i −0.315002 + 1.02207i
\(756\) 0 0
\(757\) −22.1503 26.3977i −0.805066 0.959441i 0.194704 0.980862i \(-0.437625\pi\)
−0.999771 + 0.0214214i \(0.993181\pi\)
\(758\) 45.9073 8.09470i 1.66743 0.294013i
\(759\) 0 0
\(760\) 14.2089 + 21.9228i 0.515412 + 0.795223i
\(761\) −20.5813 −0.746072 −0.373036 0.927817i \(-0.621683\pi\)
−0.373036 + 0.927817i \(0.621683\pi\)
\(762\) 0 0
\(763\) −6.72848 8.01868i −0.243587 0.290296i
\(764\) −1.43480 + 0.522224i −0.0519092 + 0.0188934i
\(765\) 0 0
\(766\) −3.51052 2.94568i −0.126840 0.106432i
\(767\) 4.85570 + 2.80344i 0.175329 + 0.101226i
\(768\) 0 0
\(769\) 5.27109 29.8939i 0.190081 1.07800i −0.729172 0.684331i \(-0.760094\pi\)
0.919252 0.393669i \(-0.128794\pi\)
\(770\) −44.6262 5.58161i −1.60822 0.201147i
\(771\) 0 0
\(772\) −1.25708 0.725774i −0.0452432 0.0261212i
\(773\) −12.5488 + 14.9551i −0.451350 + 0.537898i −0.942955 0.332921i \(-0.891966\pi\)
0.491605 + 0.870818i \(0.336410\pi\)
\(774\) 0 0
\(775\) −12.5145 + 6.03400i −0.449534 + 0.216748i
\(776\) 27.1043 22.7432i 0.972988 0.816434i
\(777\) 0 0
\(778\) 38.5054i 1.38048i
\(779\) 15.5207 26.9673i 0.556087 0.966204i
\(780\) 0 0
\(781\) −9.36716 53.1238i −0.335183 1.90092i
\(782\) 8.63167 + 10.2868i 0.308668 + 0.367856i
\(783\) 0 0
\(784\) −14.5274 5.28754i −0.518836 0.188841i
\(785\) 19.3201 + 14.6272i 0.689566 + 0.522068i
\(786\) 0 0
\(787\) −30.5046 + 17.6118i −1.08737 + 0.627793i −0.932875 0.360200i \(-0.882708\pi\)
−0.154495 + 0.987994i \(0.549375\pi\)
\(788\) 0.660316 + 0.116432i 0.0235228 + 0.00414770i
\(789\) 0 0
\(790\) 1.25427 + 1.94097i 0.0446248 + 0.0690568i
\(791\) −7.65357 + 13.2564i −0.272129 + 0.471342i
\(792\) 0 0
\(793\) 1.87067 5.13963i 0.0664295 0.182514i
\(794\) −17.5979 + 6.40513i −0.624528 + 0.227309i
\(795\) 0 0
\(796\) −0.286194 1.62309i −0.0101439 0.0575288i
\(797\) 28.7940i 1.01994i −0.860193 0.509969i \(-0.829657\pi\)
0.860193 0.509969i \(-0.170343\pi\)
\(798\) 0 0
\(799\) 2.82065 0.0997874
\(800\) −5.09997 + 1.43753i −0.180311 + 0.0508242i
\(801\) 0 0
\(802\) −4.66536 12.8180i −0.164740 0.452618i
\(803\) 2.60768 7.16455i 0.0920232 0.252832i
\(804\) 0 0
\(805\) 9.27220 + 4.75080i 0.326802 + 0.167444i
\(806\) 3.66648 + 6.35052i 0.129146 + 0.223688i
\(807\) 0 0
\(808\) −45.6012 8.04072i −1.60425 0.282872i
\(809\) 24.0034 + 41.5751i 0.843915 + 1.46170i 0.886560 + 0.462613i \(0.153088\pi\)
−0.0426458 + 0.999090i \(0.513579\pi\)
\(810\) 0 0
\(811\) −7.37613 6.18931i −0.259011 0.217336i 0.504030 0.863686i \(-0.331850\pi\)
−0.763041 + 0.646350i \(0.776295\pi\)
\(812\) −0.0708988 + 0.194793i −0.00248806 + 0.00683589i
\(813\) 0 0
\(814\) 12.8233 10.7601i 0.449458 0.377140i
\(815\) −4.20664 18.4103i −0.147352 0.644885i
\(816\) 0 0
\(817\) 0.0586768 + 43.1280i 0.00205284 + 1.50886i
\(818\) 50.9680i 1.78205i
\(819\) 0 0
\(820\) 2.04092 + 2.19854i 0.0712721 + 0.0767765i
\(821\) −24.1743 + 8.79872i −0.843688 + 0.307077i −0.727464 0.686146i \(-0.759301\pi\)
−0.116224 + 0.993223i \(0.537079\pi\)
\(822\) 0 0
\(823\) −8.65091 + 10.3098i −0.301552 + 0.359376i −0.895448 0.445166i \(-0.853145\pi\)
0.593896 + 0.804542i \(0.297589\pi\)
\(824\) −18.5327 + 32.0996i −0.645617 + 1.11824i
\(825\) 0 0
\(826\) 2.62330 14.8775i 0.0912764 0.517654i
\(827\) −0.169788 0.0299383i −0.00590412 0.00104106i 0.170695 0.985324i \(-0.445399\pi\)
−0.176599 + 0.984283i \(0.556510\pi\)
\(828\) 0 0
\(829\) −21.1895 + 36.7014i −0.735943 + 1.27469i 0.218365 + 0.975867i \(0.429928\pi\)
−0.954308 + 0.298824i \(0.903406\pi\)
\(830\) 1.10402 1.45823i 0.0383211 0.0506158i
\(831\) 0 0
\(832\) −4.34078 11.9262i −0.150490 0.413467i
\(833\) 14.4971 + 17.2770i 0.502296 + 0.598614i
\(834\) 0 0
\(835\) 44.4447 2.22873i 1.53807 0.0771284i
\(836\) −3.22247 1.16792i −0.111452 0.0403934i
\(837\) 0 0
\(838\) 11.4503 2.01900i 0.395545 0.0697452i
\(839\) 34.5791 29.0153i 1.19380 1.00172i 0.194019 0.980998i \(-0.437848\pi\)
0.999785 0.0207231i \(-0.00659684\pi\)
\(840\) 0 0
\(841\) 27.1428 + 9.87919i 0.935960 + 0.340662i
\(842\) −9.97593 + 11.8888i −0.343793 + 0.409717i
\(843\) 0 0
\(844\) 1.11046 + 1.92338i 0.0382237 + 0.0662055i
\(845\) −21.7815 2.72431i −0.749305 0.0937193i
\(846\) 0 0
\(847\) −18.3103 + 10.5715i −0.629151 + 0.363240i
\(848\) −27.2054 15.7070i −0.934238 0.539382i
\(849\) 0 0
\(850\) 45.3897 + 11.5347i 1.55685 + 0.395636i
\(851\) −3.64397 + 1.32630i −0.124914 + 0.0454649i
\(852\) 0 0
\(853\) −45.6364 + 8.04694i −1.56256 + 0.275522i −0.886996 0.461778i \(-0.847212\pi\)
−0.675566 + 0.737299i \(0.736101\pi\)
\(854\) −14.7368 −0.504283
\(855\) 0 0
\(856\) −8.75023 −0.299077
\(857\) 21.5607 3.80174i 0.736501 0.129865i 0.207199 0.978299i \(-0.433565\pi\)
0.529302 + 0.848434i \(0.322454\pi\)
\(858\) 0 0
\(859\) 31.3876 11.4242i 1.07093 0.389787i 0.254406 0.967097i \(-0.418120\pi\)
0.816525 + 0.577310i \(0.195898\pi\)
\(860\) −3.97361 1.22466i −0.135499 0.0417606i
\(861\) 0 0
\(862\) 38.2920 + 22.1079i 1.30423 + 0.752998i
\(863\) −23.4913 + 13.5627i −0.799653 + 0.461680i −0.843350 0.537365i \(-0.819420\pi\)
0.0436971 + 0.999045i \(0.486086\pi\)
\(864\) 0 0
\(865\) 3.25275 26.0064i 0.110597 0.884246i
\(866\) 5.02900 + 8.71049i 0.170892 + 0.295994i
\(867\) 0 0
\(868\) 1.09091 1.30010i 0.0370279 0.0441282i
\(869\) 2.74705 + 0.999846i 0.0931875 + 0.0339175i
\(870\) 0 0
\(871\) 11.6890 9.80822i 0.396066 0.332339i
\(872\) −8.50206 + 1.49914i −0.287916 + 0.0507674i
\(873\) 0 0
\(874\) 7.08916 + 5.93209i 0.239794 + 0.200656i
\(875\) 35.9250 5.44102i 1.21449 0.183940i
\(876\) 0 0
\(877\) −31.5495 37.5992i −1.06535 1.26963i −0.961430 0.275049i \(-0.911306\pi\)
−0.103920 0.994586i \(-0.533139\pi\)
\(878\) 4.03008 + 11.0725i 0.136008 + 0.373680i
\(879\) 0 0
\(880\) −24.5122 + 32.3765i −0.826304 + 1.09141i
\(881\) 18.9889 32.8898i 0.639753 1.10808i −0.345734 0.938332i \(-0.612370\pi\)
0.985487 0.169751i \(-0.0542965\pi\)
\(882\) 0 0
\(883\) −32.7055 5.76686i −1.10063 0.194070i −0.406307 0.913737i \(-0.633184\pi\)
−0.694320 + 0.719666i \(0.744295\pi\)
\(884\) 0.368704 2.09103i 0.0124009 0.0703288i
\(885\) 0 0
\(886\) 16.1150 27.9121i 0.541395 0.937724i
\(887\) 16.8748 20.1106i 0.566601 0.675248i −0.404329 0.914614i \(-0.632495\pi\)
0.970930 + 0.239365i \(0.0769393\pi\)
\(888\) 0 0
\(889\) −1.80794 + 0.658035i −0.0606362 + 0.0220698i
\(890\) 16.5531 15.3664i 0.554862 0.515082i
\(891\) 0 0
\(892\) 1.67222i 0.0559902i
\(893\) 1.91167 0.339762i 0.0639718 0.0113697i
\(894\) 0 0
\(895\) 15.4418 3.52836i 0.516164 0.117940i
\(896\) −31.4721 + 26.4082i −1.05141 + 0.882236i
\(897\) 0 0
\(898\) 9.50278 26.1087i 0.317112 0.871258i
\(899\) 0.722415 + 0.606178i 0.0240939 + 0.0202172i
\(900\) 0 0
\(901\) 22.9143 + 39.6888i 0.763387 + 1.32223i
\(902\) 43.5060 + 7.67129i 1.44859 + 0.255426i
\(903\) 0 0
\(904\) 6.31229 + 10.9332i 0.209944 + 0.363633i
\(905\) 18.4712 + 9.46411i 0.614005 + 0.314598i
\(906\) 0 0
\(907\) 2.71140 7.44950i 0.0900305 0.247357i −0.886503 0.462723i \(-0.846872\pi\)
0.976533 + 0.215366i \(0.0690946\pi\)
\(908\) 1.69750 + 4.66383i 0.0563334 + 0.154775i
\(909\) 0 0
\(910\) −4.27189 18.6959i −0.141612 0.619763i
\(911\) 0.619746 0.0205331 0.0102665 0.999947i \(-0.496732\pi\)
0.0102665 + 0.999947i \(0.496732\pi\)
\(912\) 0 0
\(913\) 2.31369i 0.0765718i
\(914\) 7.25277 + 41.1325i 0.239900 + 1.36054i
\(915\) 0 0
\(916\) −3.84742 + 1.40035i −0.127122 + 0.0462687i
\(917\) −22.8407 + 62.7544i −0.754268 + 2.07233i
\(918\) 0 0
\(919\) −17.5287 + 30.3606i −0.578219 + 1.00150i 0.417465 + 0.908693i \(0.362919\pi\)
−0.995684 + 0.0928113i \(0.970415\pi\)
\(920\) 7.21692 4.66361i 0.237935 0.153755i
\(921\) 0 0
\(922\) 0.285524 + 0.0503456i 0.00940324 + 0.00165804i
\(923\) 19.9207 11.5012i 0.655699 0.378568i
\(924\) 0 0
\(925\) −7.61309 + 11.1778i −0.250317 + 0.367523i
\(926\) 19.4096 + 7.06452i 0.637840 + 0.232155i
\(927\) 0 0
\(928\) 0.231188 + 0.275519i 0.00758912 + 0.00904437i
\(929\) 2.09132 + 11.8605i 0.0686140 + 0.389129i 0.999704 + 0.0243392i \(0.00774816\pi\)
−0.931090 + 0.364790i \(0.881141\pi\)
\(930\) 0 0
\(931\) 11.9065 + 9.96313i 0.390218 + 0.326528i
\(932\) 1.87959i 0.0615679i
\(933\) 0 0
\(934\) 36.3756 30.5228i 1.19025 0.998735i
\(935\) 54.5852 23.0249i 1.78513 0.752994i
\(936\) 0 0
\(937\) −9.59711 + 11.4374i −0.313524 + 0.373643i −0.899676 0.436558i \(-0.856198\pi\)
0.586152 + 0.810201i \(0.300642\pi\)
\(938\) −35.6049 20.5565i −1.16254 0.671194i
\(939\) 0 0
\(940\) −0.0232325 + 0.185749i −0.000757762 + 0.00605846i
\(941\) −3.37221 + 19.1248i −0.109931 + 0.623450i 0.879205 + 0.476444i \(0.158075\pi\)
−0.989136 + 0.147006i \(0.953036\pi\)
\(942\) 0 0
\(943\) −8.86280 5.11694i −0.288612 0.166630i
\(944\) −10.4494 8.76813i −0.340101 0.285378i
\(945\) 0 0
\(946\) −57.5409 + 20.9432i −1.87082 + 0.680922i
\(947\) −10.7583 12.8212i −0.349598 0.416634i 0.562377 0.826881i \(-0.309887\pi\)
−0.911975 + 0.410247i \(0.865443\pi\)
\(948\) 0 0
\(949\) 3.25117 0.105538
\(950\) 32.1520 + 2.35011i 1.04315 + 0.0762476i
\(951\) 0 0
\(952\) 54.3209 9.57824i 1.76055 0.310433i
\(953\) −34.1817 40.7361i −1.10725 1.31957i −0.942864 0.333177i \(-0.891879\pi\)
−0.164389 0.986396i \(-0.552565\pi\)
\(954\) 0 0
\(955\) 5.35051 17.3606i 0.173138 0.561775i
\(956\) −2.56794 2.15475i −0.0830530 0.0696897i
\(957\) 0 0
\(958\) −2.53927 + 1.46605i −0.0820400 + 0.0473658i
\(959\) −4.94022 + 28.0174i −0.159528 + 0.904729i
\(960\) 0 0
\(961\) 11.6396 + 20.1603i 0.375470 + 0.650332i
\(962\) 6.18179 + 3.56906i 0.199309 + 0.115071i
\(963\) 0 0
\(964\) −3.02778 1.10202i −0.0975181 0.0354937i
\(965\) 15.9124 6.71209i 0.512238 0.216070i
\(966\) 0 0
\(967\) −29.5719 + 5.21432i −0.950967 + 0.167681i −0.627551 0.778576i \(-0.715943\pi\)
−0.323416 + 0.946257i \(0.604831\pi\)
\(968\) 17.4377i 0.560469i
\(969\) 0 0
\(970\) −2.18670 43.6065i −0.0702107 1.40012i
\(971\) −4.19210 23.7746i −0.134531 0.762962i −0.975185 0.221390i \(-0.928940\pi\)
0.840654 0.541572i \(-0.182171\pi\)
\(972\) 0 0
\(973\) −8.54693 23.4825i −0.274002 0.752814i
\(974\) −11.9386 4.34531i −0.382538 0.139233i
\(975\) 0 0
\(976\) −6.65325 + 11.5238i −0.212965 + 0.368867i
\(977\) 8.29375 4.78840i 0.265341 0.153195i −0.361428 0.932400i \(-0.617711\pi\)
0.626768 + 0.779206i \(0.284377\pi\)
\(978\) 0 0
\(979\) 4.96134 28.1372i 0.158565 0.899267i
\(980\) −1.25716 + 0.812381i −0.0401584 + 0.0259506i
\(981\) 0 0
\(982\) 24.6257 29.3477i 0.785837 0.936524i
\(983\) 10.6613 29.2916i 0.340042 0.934257i −0.645340 0.763896i \(-0.723284\pi\)
0.985382 0.170362i \(-0.0544936\pi\)
\(984\) 0 0
\(985\) −5.84659 + 5.42743i −0.186288 + 0.172932i
\(986\) −0.552008 3.13060i −0.0175795 0.0996985i
\(987\) 0 0
\(988\) −0.00198853 1.46159i −6.32636e−5 0.0464994i
\(989\) 14.1851 0.451061
\(990\) 0 0
\(991\) −37.2791 + 31.2808i −1.18421 + 0.993669i −0.184266 + 0.982876i \(0.558991\pi\)
−0.999942 + 0.0107922i \(0.996565\pi\)
\(992\) −1.00713 2.76706i −0.0319763 0.0878542i
\(993\) 0 0
\(994\) −47.4772 39.8381i −1.50589 1.26359i
\(995\) 17.4516 + 8.94165i 0.553252 + 0.283469i
\(996\) 0 0
\(997\) 31.4108 + 5.53857i 0.994790 + 0.175408i 0.647267 0.762263i \(-0.275912\pi\)
0.347523 + 0.937672i \(0.387023\pi\)
\(998\) 30.8876 + 5.44631i 0.977729 + 0.172400i
\(999\) 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 855.2.da.b.199.2 48
3.2 odd 2 95.2.p.a.9.7 yes 48
5.4 even 2 inner 855.2.da.b.199.7 48
15.2 even 4 475.2.l.f.351.7 48
15.8 even 4 475.2.l.f.351.2 48
15.14 odd 2 95.2.p.a.9.2 48
19.17 even 9 inner 855.2.da.b.739.7 48
57.17 odd 18 95.2.p.a.74.2 yes 48
57.32 even 18 1805.2.b.l.1084.18 24
57.44 odd 18 1805.2.b.k.1084.7 24
95.74 even 18 inner 855.2.da.b.739.2 48
285.17 even 36 475.2.l.f.226.7 48
285.32 odd 36 9025.2.a.ct.1.7 24
285.44 odd 18 1805.2.b.k.1084.18 24
285.74 odd 18 95.2.p.a.74.7 yes 48
285.89 even 18 1805.2.b.l.1084.7 24
285.158 even 36 9025.2.a.cu.1.7 24
285.188 even 36 475.2.l.f.226.2 48
285.203 odd 36 9025.2.a.ct.1.18 24
285.272 even 36 9025.2.a.cu.1.18 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.9.2 48 15.14 odd 2
95.2.p.a.9.7 yes 48 3.2 odd 2
95.2.p.a.74.2 yes 48 57.17 odd 18
95.2.p.a.74.7 yes 48 285.74 odd 18
475.2.l.f.226.2 48 285.188 even 36
475.2.l.f.226.7 48 285.17 even 36
475.2.l.f.351.2 48 15.8 even 4
475.2.l.f.351.7 48 15.2 even 4
855.2.da.b.199.2 48 1.1 even 1 trivial
855.2.da.b.199.7 48 5.4 even 2 inner
855.2.da.b.739.2 48 95.74 even 18 inner
855.2.da.b.739.7 48 19.17 even 9 inner
1805.2.b.k.1084.7 24 57.44 odd 18
1805.2.b.k.1084.18 24 285.44 odd 18
1805.2.b.l.1084.7 24 285.89 even 18
1805.2.b.l.1084.18 24 57.32 even 18
9025.2.a.ct.1.7 24 285.32 odd 36
9025.2.a.ct.1.18 24 285.203 odd 36
9025.2.a.cu.1.7 24 285.158 even 36
9025.2.a.cu.1.18 24 285.272 even 36