Properties

Label 637.2.i.a.489.10
Level $637$
Weight $2$
Character 637.489
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
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] = [637,2,Mod(489,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.489");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.i (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 489.10
Character \(\chi\) \(=\) 637.489
Dual form 637.2.i.a.538.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.546480 + 0.546480i) q^{2} +0.487133i q^{3} -1.40272i q^{4} +(-1.29040 + 1.29040i) q^{5} +(-0.266208 + 0.266208i) q^{6} +(1.85952 - 1.85952i) q^{8} +2.76270 q^{9} +O(q^{10})\) \(q+(0.546480 + 0.546480i) q^{2} +0.487133i q^{3} -1.40272i q^{4} +(-1.29040 + 1.29040i) q^{5} +(-0.266208 + 0.266208i) q^{6} +(1.85952 - 1.85952i) q^{8} +2.76270 q^{9} -1.41035 q^{10} +(-0.725276 + 0.725276i) q^{11} +0.683311 q^{12} +(0.266208 + 3.59571i) q^{13} +(-0.628596 - 0.628596i) q^{15} -0.773062 q^{16} +5.20058 q^{17} +(1.50976 + 1.50976i) q^{18} +(3.71699 - 3.71699i) q^{19} +(1.81007 + 1.81007i) q^{20} -0.792697 q^{22} -0.843739i q^{23} +(0.905832 + 0.905832i) q^{24} +1.66974i q^{25} +(-1.81951 + 2.11046i) q^{26} +2.80720i q^{27} +10.3454 q^{29} -0.687030i q^{30} +(-4.16994 + 4.16994i) q^{31} +(-4.14150 - 4.14150i) q^{32} +(-0.353306 - 0.353306i) q^{33} +(2.84201 + 2.84201i) q^{34} -3.87530i q^{36} +(4.41711 - 4.41711i) q^{37} +4.06252 q^{38} +(-1.75159 + 0.129679i) q^{39} +4.79904i q^{40} +(0.0927742 - 0.0927742i) q^{41} +7.36681i q^{43} +(1.01736 + 1.01736i) q^{44} +(-3.56499 + 3.56499i) q^{45} +(0.461086 - 0.461086i) q^{46} +(1.59524 + 1.59524i) q^{47} -0.376584i q^{48} +(-0.912480 + 0.912480i) q^{50} +2.53337i q^{51} +(5.04377 - 0.373416i) q^{52} -6.77180 q^{53} +(-1.53408 + 1.53408i) q^{54} -1.87179i q^{55} +(1.81067 + 1.81067i) q^{57} +(5.65353 + 5.65353i) q^{58} +(-7.12895 - 7.12895i) q^{59} +(-0.881744 + 0.881744i) q^{60} +1.30682i q^{61} -4.55758 q^{62} -2.98037i q^{64} +(-4.98342 - 4.29639i) q^{65} -0.386149i q^{66} +(3.04544 + 3.04544i) q^{67} -7.29496i q^{68} +0.411013 q^{69} +(-6.02388 - 6.02388i) q^{71} +(5.13729 - 5.13729i) q^{72} +(-8.02243 - 8.02243i) q^{73} +4.82772 q^{74} -0.813386 q^{75} +(-5.21390 - 5.21390i) q^{76} +(-1.02807 - 0.886341i) q^{78} -10.3248 q^{79} +(0.997558 - 0.997558i) q^{80} +6.92062 q^{81} +0.101398 q^{82} +(4.16974 - 4.16974i) q^{83} +(-6.71082 + 6.71082i) q^{85} +(-4.02581 + 4.02581i) q^{86} +5.03957i q^{87} +2.69733i q^{88} +(-5.48933 - 5.48933i) q^{89} -3.89639 q^{90} -1.18353 q^{92} +(-2.03132 - 2.03132i) q^{93} +1.74353i q^{94} +9.59280i q^{95} +(2.01746 - 2.01746i) q^{96} +(-2.49152 + 2.49152i) q^{97} +(-2.00372 + 2.00372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.546480 + 0.546480i 0.386420 + 0.386420i 0.873408 0.486989i \(-0.161905\pi\)
−0.486989 + 0.873408i \(0.661905\pi\)
\(3\) 0.487133i 0.281246i 0.990063 + 0.140623i \(0.0449106\pi\)
−0.990063 + 0.140623i \(0.955089\pi\)
\(4\) 1.40272i 0.701360i
\(5\) −1.29040 + 1.29040i −0.577084 + 0.577084i −0.934099 0.357015i \(-0.883795\pi\)
0.357015 + 0.934099i \(0.383795\pi\)
\(6\) −0.266208 + 0.266208i −0.108679 + 0.108679i
\(7\) 0 0
\(8\) 1.85952 1.85952i 0.657439 0.657439i
\(9\) 2.76270 0.920901
\(10\) −1.41035 −0.445993
\(11\) −0.725276 + 0.725276i −0.218679 + 0.218679i −0.807942 0.589263i \(-0.799418\pi\)
0.589263 + 0.807942i \(0.299418\pi\)
\(12\) 0.683311 0.197255
\(13\) 0.266208 + 3.59571i 0.0738329 + 0.997271i
\(14\) 0 0
\(15\) −0.628596 0.628596i −0.162303 0.162303i
\(16\) −0.773062 −0.193266
\(17\) 5.20058 1.26133 0.630663 0.776057i \(-0.282783\pi\)
0.630663 + 0.776057i \(0.282783\pi\)
\(18\) 1.50976 + 1.50976i 0.355854 + 0.355854i
\(19\) 3.71699 3.71699i 0.852736 0.852736i −0.137733 0.990469i \(-0.543982\pi\)
0.990469 + 0.137733i \(0.0439816\pi\)
\(20\) 1.81007 + 1.81007i 0.404743 + 0.404743i
\(21\) 0 0
\(22\) −0.792697 −0.169004
\(23\) 0.843739i 0.175932i −0.996123 0.0879659i \(-0.971963\pi\)
0.996123 0.0879659i \(-0.0280366\pi\)
\(24\) 0.905832 + 0.905832i 0.184902 + 0.184902i
\(25\) 1.66974i 0.333948i
\(26\) −1.81951 + 2.11046i −0.356834 + 0.413895i
\(27\) 2.80720i 0.540246i
\(28\) 0 0
\(29\) 10.3454 1.92109 0.960543 0.278130i \(-0.0897147\pi\)
0.960543 + 0.278130i \(0.0897147\pi\)
\(30\) 0.687030i 0.125434i
\(31\) −4.16994 + 4.16994i −0.748943 + 0.748943i −0.974281 0.225337i \(-0.927652\pi\)
0.225337 + 0.974281i \(0.427652\pi\)
\(32\) −4.14150 4.14150i −0.732120 0.732120i
\(33\) −0.353306 0.353306i −0.0615026 0.0615026i
\(34\) 2.84201 + 2.84201i 0.487401 + 0.487401i
\(35\) 0 0
\(36\) 3.87530i 0.645883i
\(37\) 4.41711 4.41711i 0.726168 0.726168i −0.243686 0.969854i \(-0.578357\pi\)
0.969854 + 0.243686i \(0.0783566\pi\)
\(38\) 4.06252 0.659028
\(39\) −1.75159 + 0.129679i −0.280479 + 0.0207652i
\(40\) 4.79904i 0.758795i
\(41\) 0.0927742 0.0927742i 0.0144889 0.0144889i −0.699825 0.714314i \(-0.746739\pi\)
0.714314 + 0.699825i \(0.246739\pi\)
\(42\) 0 0
\(43\) 7.36681i 1.12343i 0.827331 + 0.561714i \(0.189858\pi\)
−0.827331 + 0.561714i \(0.810142\pi\)
\(44\) 1.01736 + 1.01736i 0.153373 + 0.153373i
\(45\) −3.56499 + 3.56499i −0.531437 + 0.531437i
\(46\) 0.461086 0.461086i 0.0679835 0.0679835i
\(47\) 1.59524 + 1.59524i 0.232689 + 0.232689i 0.813814 0.581125i \(-0.197387\pi\)
−0.581125 + 0.813814i \(0.697387\pi\)
\(48\) 0.376584i 0.0543552i
\(49\) 0 0
\(50\) −0.912480 + 0.912480i −0.129044 + 0.129044i
\(51\) 2.53337i 0.354743i
\(52\) 5.04377 0.373416i 0.699446 0.0517834i
\(53\) −6.77180 −0.930178 −0.465089 0.885264i \(-0.653978\pi\)
−0.465089 + 0.885264i \(0.653978\pi\)
\(54\) −1.53408 + 1.53408i −0.208762 + 0.208762i
\(55\) 1.87179i 0.252392i
\(56\) 0 0
\(57\) 1.81067 + 1.81067i 0.239829 + 0.239829i
\(58\) 5.65353 + 5.65353i 0.742345 + 0.742345i
\(59\) −7.12895 7.12895i −0.928110 0.928110i 0.0694735 0.997584i \(-0.477868\pi\)
−0.997584 + 0.0694735i \(0.977868\pi\)
\(60\) −0.881744 + 0.881744i −0.113833 + 0.113833i
\(61\) 1.30682i 0.167321i 0.996494 + 0.0836604i \(0.0266611\pi\)
−0.996494 + 0.0836604i \(0.973339\pi\)
\(62\) −4.55758 −0.578813
\(63\) 0 0
\(64\) 2.98037i 0.372546i
\(65\) −4.98342 4.29639i −0.618117 0.532901i
\(66\) 0.386149i 0.0475316i
\(67\) 3.04544 + 3.04544i 0.372059 + 0.372059i 0.868227 0.496168i \(-0.165260\pi\)
−0.496168 + 0.868227i \(0.665260\pi\)
\(68\) 7.29496i 0.884643i
\(69\) 0.411013 0.0494802
\(70\) 0 0
\(71\) −6.02388 6.02388i −0.714903 0.714903i 0.252654 0.967557i \(-0.418697\pi\)
−0.967557 + 0.252654i \(0.918697\pi\)
\(72\) 5.13729 5.13729i 0.605436 0.605436i
\(73\) −8.02243 8.02243i −0.938954 0.938954i 0.0592870 0.998241i \(-0.481117\pi\)
−0.998241 + 0.0592870i \(0.981117\pi\)
\(74\) 4.82772 0.561211
\(75\) −0.813386 −0.0939218
\(76\) −5.21390 5.21390i −0.598075 0.598075i
\(77\) 0 0
\(78\) −1.02807 0.886341i −0.116407 0.100358i
\(79\) −10.3248 −1.16163 −0.580816 0.814035i \(-0.697266\pi\)
−0.580816 + 0.814035i \(0.697266\pi\)
\(80\) 0.997558 0.997558i 0.111530 0.111530i
\(81\) 6.92062 0.768958
\(82\) 0.101398 0.0111976
\(83\) 4.16974 4.16974i 0.457689 0.457689i −0.440207 0.897896i \(-0.645095\pi\)
0.897896 + 0.440207i \(0.145095\pi\)
\(84\) 0 0
\(85\) −6.71082 + 6.71082i −0.727891 + 0.727891i
\(86\) −4.02581 + 4.02581i −0.434115 + 0.434115i
\(87\) 5.03957i 0.540299i
\(88\) 2.69733i 0.287536i
\(89\) −5.48933 5.48933i −0.581868 0.581868i 0.353548 0.935416i \(-0.384975\pi\)
−0.935416 + 0.353548i \(0.884975\pi\)
\(90\) −3.89639 −0.410715
\(91\) 0 0
\(92\) −1.18353 −0.123391
\(93\) −2.03132 2.03132i −0.210638 0.210638i
\(94\) 1.74353i 0.179831i
\(95\) 9.59280i 0.984201i
\(96\) 2.01746 2.01746i 0.205906 0.205906i
\(97\) −2.49152 + 2.49152i −0.252976 + 0.252976i −0.822189 0.569214i \(-0.807248\pi\)
0.569214 + 0.822189i \(0.307248\pi\)
\(98\) 0 0
\(99\) −2.00372 + 2.00372i −0.201381 + 0.201381i
\(100\) 2.34218 0.234218
\(101\) 2.43372 0.242164 0.121082 0.992642i \(-0.461364\pi\)
0.121082 + 0.992642i \(0.461364\pi\)
\(102\) −1.38444 + 1.38444i −0.137080 + 0.137080i
\(103\) −2.73634 −0.269620 −0.134810 0.990871i \(-0.543042\pi\)
−0.134810 + 0.990871i \(0.543042\pi\)
\(104\) 7.18131 + 6.19127i 0.704185 + 0.607104i
\(105\) 0 0
\(106\) −3.70065 3.70065i −0.359439 0.359439i
\(107\) 2.25627 0.218122 0.109061 0.994035i \(-0.465216\pi\)
0.109061 + 0.994035i \(0.465216\pi\)
\(108\) 3.93772 0.378907
\(109\) 1.15158 + 1.15158i 0.110301 + 0.110301i 0.760103 0.649802i \(-0.225148\pi\)
−0.649802 + 0.760103i \(0.725148\pi\)
\(110\) 1.02290 1.02290i 0.0975292 0.0975292i
\(111\) 2.15172 + 2.15172i 0.204232 + 0.204232i
\(112\) 0 0
\(113\) 2.63227 0.247623 0.123812 0.992306i \(-0.460488\pi\)
0.123812 + 0.992306i \(0.460488\pi\)
\(114\) 1.97899i 0.185349i
\(115\) 1.08876 + 1.08876i 0.101527 + 0.101527i
\(116\) 14.5117i 1.34737i
\(117\) 0.735454 + 9.93387i 0.0679928 + 0.918387i
\(118\) 7.79165i 0.717280i
\(119\) 0 0
\(120\) −2.33777 −0.213408
\(121\) 9.94795i 0.904359i
\(122\) −0.714149 + 0.714149i −0.0646560 + 0.0646560i
\(123\) 0.0451934 + 0.0451934i 0.00407495 + 0.00407495i
\(124\) 5.84926 + 5.84926i 0.525279 + 0.525279i
\(125\) −8.60663 8.60663i −0.769800 0.769800i
\(126\) 0 0
\(127\) 11.8104i 1.04801i 0.851716 + 0.524004i \(0.175562\pi\)
−0.851716 + 0.524004i \(0.824438\pi\)
\(128\) −6.65429 + 6.65429i −0.588161 + 0.588161i
\(129\) −3.58862 −0.315960
\(130\) −0.375448 5.07122i −0.0329290 0.444776i
\(131\) 15.4467i 1.34959i −0.738006 0.674794i \(-0.764232\pi\)
0.738006 0.674794i \(-0.235768\pi\)
\(132\) −0.495589 + 0.495589i −0.0431355 + 0.0431355i
\(133\) 0 0
\(134\) 3.32854i 0.287542i
\(135\) −3.62241 3.62241i −0.311767 0.311767i
\(136\) 9.67057 9.67057i 0.829245 0.829245i
\(137\) −0.724831 + 0.724831i −0.0619265 + 0.0619265i −0.737392 0.675465i \(-0.763943\pi\)
0.675465 + 0.737392i \(0.263943\pi\)
\(138\) 0.224610 + 0.224610i 0.0191201 + 0.0191201i
\(139\) 11.4028i 0.967171i −0.875297 0.483585i \(-0.839334\pi\)
0.875297 0.483585i \(-0.160666\pi\)
\(140\) 0 0
\(141\) −0.777092 + 0.777092i −0.0654429 + 0.0654429i
\(142\) 6.58385i 0.552505i
\(143\) −2.80096 2.41481i −0.234228 0.201936i
\(144\) −2.13574 −0.177978
\(145\) −13.3497 + 13.3497i −1.10863 + 1.10863i
\(146\) 8.76819i 0.725660i
\(147\) 0 0
\(148\) −6.19597 6.19597i −0.509305 0.509305i
\(149\) −5.40106 5.40106i −0.442472 0.442472i 0.450370 0.892842i \(-0.351292\pi\)
−0.892842 + 0.450370i \(0.851292\pi\)
\(150\) −0.444499 0.444499i −0.0362932 0.0362932i
\(151\) 4.84411 4.84411i 0.394208 0.394208i −0.481976 0.876184i \(-0.660081\pi\)
0.876184 + 0.481976i \(0.160081\pi\)
\(152\) 13.8236i 1.12124i
\(153\) 14.3677 1.16156
\(154\) 0 0
\(155\) 10.7618i 0.864406i
\(156\) 0.181903 + 2.45699i 0.0145639 + 0.196717i
\(157\) 12.8475i 1.02534i 0.858586 + 0.512670i \(0.171343\pi\)
−0.858586 + 0.512670i \(0.828657\pi\)
\(158\) −5.64230 5.64230i −0.448877 0.448877i
\(159\) 3.29876i 0.261609i
\(160\) 10.6884 0.844990
\(161\) 0 0
\(162\) 3.78198 + 3.78198i 0.297140 + 0.297140i
\(163\) −0.694096 + 0.694096i −0.0543658 + 0.0543658i −0.733767 0.679401i \(-0.762240\pi\)
0.679401 + 0.733767i \(0.262240\pi\)
\(164\) −0.130136 0.130136i −0.0101619 0.0101619i
\(165\) 0.911811 0.0709844
\(166\) 4.55736 0.353720
\(167\) −9.25126 9.25126i −0.715884 0.715884i 0.251876 0.967760i \(-0.418953\pi\)
−0.967760 + 0.251876i \(0.918953\pi\)
\(168\) 0 0
\(169\) −12.8583 + 1.91442i −0.989097 + 0.147263i
\(170\) −7.33466 −0.562543
\(171\) 10.2689 10.2689i 0.785285 0.785285i
\(172\) 10.3336 0.787927
\(173\) 22.1121 1.68115 0.840576 0.541693i \(-0.182217\pi\)
0.840576 + 0.541693i \(0.182217\pi\)
\(174\) −2.75402 + 2.75402i −0.208782 + 0.208782i
\(175\) 0 0
\(176\) 0.560683 0.560683i 0.0422631 0.0422631i
\(177\) 3.47275 3.47275i 0.261028 0.261028i
\(178\) 5.99962i 0.449690i
\(179\) 8.07047i 0.603216i 0.953432 + 0.301608i \(0.0975233\pi\)
−0.953432 + 0.301608i \(0.902477\pi\)
\(180\) 5.00068 + 5.00068i 0.372728 + 0.372728i
\(181\) −20.5622 −1.52838 −0.764189 0.644993i \(-0.776860\pi\)
−0.764189 + 0.644993i \(0.776860\pi\)
\(182\) 0 0
\(183\) −0.636594 −0.0470584
\(184\) −1.56895 1.56895i −0.115664 0.115664i
\(185\) 11.3997i 0.838120i
\(186\) 2.22015i 0.162789i
\(187\) −3.77186 + 3.77186i −0.275825 + 0.275825i
\(188\) 2.23767 2.23767i 0.163199 0.163199i
\(189\) 0 0
\(190\) −5.24227 + 5.24227i −0.380314 + 0.380314i
\(191\) −13.8382 −1.00129 −0.500647 0.865651i \(-0.666905\pi\)
−0.500647 + 0.865651i \(0.666905\pi\)
\(192\) 1.45183 0.104777
\(193\) 17.2582 17.2582i 1.24227 1.24227i 0.283212 0.959057i \(-0.408600\pi\)
0.959057 0.283212i \(-0.0914000\pi\)
\(194\) −2.72313 −0.195509
\(195\) 2.09291 2.42759i 0.149876 0.173843i
\(196\) 0 0
\(197\) −14.3424 14.3424i −1.02185 1.02185i −0.999756 0.0220979i \(-0.992965\pi\)
−0.0220979 0.999756i \(-0.507035\pi\)
\(198\) −2.18999 −0.155635
\(199\) −14.8160 −1.05028 −0.525140 0.851016i \(-0.675987\pi\)
−0.525140 + 0.851016i \(0.675987\pi\)
\(200\) 3.10491 + 3.10491i 0.219551 + 0.219551i
\(201\) −1.48353 + 1.48353i −0.104640 + 0.104640i
\(202\) 1.32998 + 1.32998i 0.0935770 + 0.0935770i
\(203\) 0 0
\(204\) 3.55361 0.248803
\(205\) 0.239431i 0.0167226i
\(206\) −1.49536 1.49536i −0.104186 0.104186i
\(207\) 2.33100i 0.162016i
\(208\) −0.205796 2.77971i −0.0142694 0.192738i
\(209\) 5.39169i 0.372951i
\(210\) 0 0
\(211\) 6.98585 0.480925 0.240463 0.970658i \(-0.422701\pi\)
0.240463 + 0.970658i \(0.422701\pi\)
\(212\) 9.49893i 0.652389i
\(213\) 2.93443 2.93443i 0.201064 0.201064i
\(214\) 1.23301 + 1.23301i 0.0842866 + 0.0842866i
\(215\) −9.50612 9.50612i −0.648312 0.648312i
\(216\) 5.22004 + 5.22004i 0.355179 + 0.355179i
\(217\) 0 0
\(218\) 1.25863i 0.0852451i
\(219\) 3.90799 3.90799i 0.264077 0.264077i
\(220\) −2.62560 −0.177018
\(221\) 1.38444 + 18.6998i 0.0931274 + 1.25788i
\(222\) 2.35174i 0.157839i
\(223\) −19.4291 + 19.4291i −1.30107 + 1.30107i −0.373403 + 0.927669i \(0.621809\pi\)
−0.927669 + 0.373403i \(0.878191\pi\)
\(224\) 0 0
\(225\) 4.61300i 0.307533i
\(226\) 1.43848 + 1.43848i 0.0956864 + 0.0956864i
\(227\) −0.0497885 + 0.0497885i −0.00330458 + 0.00330458i −0.708757 0.705453i \(-0.750744\pi\)
0.705453 + 0.708757i \(0.250744\pi\)
\(228\) 2.53986 2.53986i 0.168206 0.168206i
\(229\) 3.86548 + 3.86548i 0.255438 + 0.255438i 0.823196 0.567758i \(-0.192189\pi\)
−0.567758 + 0.823196i \(0.692189\pi\)
\(230\) 1.18997i 0.0784643i
\(231\) 0 0
\(232\) 19.2374 19.2374i 1.26300 1.26300i
\(233\) 1.05440i 0.0690762i −0.999403 0.0345381i \(-0.989004\pi\)
0.999403 0.0345381i \(-0.0109960\pi\)
\(234\) −5.02675 + 5.83057i −0.328609 + 0.381156i
\(235\) −4.11698 −0.268562
\(236\) −9.99992 + 9.99992i −0.650939 + 0.650939i
\(237\) 5.02955i 0.326705i
\(238\) 0 0
\(239\) 18.6963 + 18.6963i 1.20936 + 1.20936i 0.971234 + 0.238127i \(0.0765333\pi\)
0.238127 + 0.971234i \(0.423467\pi\)
\(240\) 0.485944 + 0.485944i 0.0313675 + 0.0313675i
\(241\) 6.93020 + 6.93020i 0.446413 + 0.446413i 0.894160 0.447747i \(-0.147773\pi\)
−0.447747 + 0.894160i \(0.647773\pi\)
\(242\) −5.43635 + 5.43635i −0.349462 + 0.349462i
\(243\) 11.7929i 0.756513i
\(244\) 1.83310 0.117352
\(245\) 0 0
\(246\) 0.0493945i 0.00314928i
\(247\) 14.3547 + 12.3757i 0.913369 + 0.787449i
\(248\) 15.5082i 0.984769i
\(249\) 2.03122 + 2.03122i 0.128723 + 0.128723i
\(250\) 9.40669i 0.594932i
\(251\) 24.9249 1.57325 0.786623 0.617434i \(-0.211828\pi\)
0.786623 + 0.617434i \(0.211828\pi\)
\(252\) 0 0
\(253\) 0.611943 + 0.611943i 0.0384726 + 0.0384726i
\(254\) −6.45417 + 6.45417i −0.404971 + 0.404971i
\(255\) −3.26906 3.26906i −0.204717 0.204717i
\(256\) −13.2336 −0.827100
\(257\) −3.96236 −0.247165 −0.123583 0.992334i \(-0.539438\pi\)
−0.123583 + 0.992334i \(0.539438\pi\)
\(258\) −1.96111 1.96111i −0.122093 0.122093i
\(259\) 0 0
\(260\) −6.02662 + 6.99033i −0.373755 + 0.433522i
\(261\) 28.5812 1.76913
\(262\) 8.44133 8.44133i 0.521507 0.521507i
\(263\) −30.9269 −1.90703 −0.953516 0.301343i \(-0.902565\pi\)
−0.953516 + 0.301343i \(0.902565\pi\)
\(264\) −1.31396 −0.0808684
\(265\) 8.73832 8.73832i 0.536791 0.536791i
\(266\) 0 0
\(267\) 2.67403 2.67403i 0.163648 0.163648i
\(268\) 4.27189 4.27189i 0.260947 0.260947i
\(269\) 11.0114i 0.671378i −0.941973 0.335689i \(-0.891031\pi\)
0.941973 0.335689i \(-0.108969\pi\)
\(270\) 3.95915i 0.240946i
\(271\) −3.54185 3.54185i −0.215152 0.215152i 0.591300 0.806452i \(-0.298615\pi\)
−0.806452 + 0.591300i \(0.798615\pi\)
\(272\) −4.02037 −0.243771
\(273\) 0 0
\(274\) −0.792211 −0.0478592
\(275\) −1.21102 1.21102i −0.0730275 0.0730275i
\(276\) 0.576536i 0.0347034i
\(277\) 12.2075i 0.733476i 0.930324 + 0.366738i \(0.119525\pi\)
−0.930324 + 0.366738i \(0.880475\pi\)
\(278\) 6.23139 6.23139i 0.373734 0.373734i
\(279\) −11.5203 + 11.5203i −0.689702 + 0.689702i
\(280\) 0 0
\(281\) −12.8351 + 12.8351i −0.765677 + 0.765677i −0.977342 0.211665i \(-0.932111\pi\)
0.211665 + 0.977342i \(0.432111\pi\)
\(282\) −0.849330 −0.0505768
\(283\) 16.8992 1.00455 0.502277 0.864707i \(-0.332496\pi\)
0.502277 + 0.864707i \(0.332496\pi\)
\(284\) −8.44981 + 8.44981i −0.501404 + 0.501404i
\(285\) −4.67297 −0.276803
\(286\) −0.211023 2.85031i −0.0124780 0.168542i
\(287\) 0 0
\(288\) −11.4417 11.4417i −0.674210 0.674210i
\(289\) 10.0460 0.590943
\(290\) −14.5906 −0.856791
\(291\) −1.21370 1.21370i −0.0711484 0.0711484i
\(292\) −11.2532 + 11.2532i −0.658545 + 0.658545i
\(293\) 11.1183 + 11.1183i 0.649536 + 0.649536i 0.952881 0.303345i \(-0.0981033\pi\)
−0.303345 + 0.952881i \(0.598103\pi\)
\(294\) 0 0
\(295\) 18.3984 1.07120
\(296\) 16.4274i 0.954822i
\(297\) −2.03600 2.03600i −0.118140 0.118140i
\(298\) 5.90314i 0.341960i
\(299\) 3.03384 0.224610i 0.175452 0.0129896i
\(300\) 1.14095i 0.0658730i
\(301\) 0 0
\(302\) 5.29441 0.304659
\(303\) 1.18555i 0.0681078i
\(304\) −2.87347 + 2.87347i −0.164805 + 0.164805i
\(305\) −1.68632 1.68632i −0.0965582 0.0965582i
\(306\) 7.85163 + 7.85163i 0.448848 + 0.448848i
\(307\) 14.6604 + 14.6604i 0.836715 + 0.836715i 0.988425 0.151710i \(-0.0484781\pi\)
−0.151710 + 0.988425i \(0.548478\pi\)
\(308\) 0 0
\(309\) 1.33296i 0.0758296i
\(310\) 5.88109 5.88109i 0.334024 0.334024i
\(311\) −10.7063 −0.607101 −0.303550 0.952815i \(-0.598172\pi\)
−0.303550 + 0.952815i \(0.598172\pi\)
\(312\) −3.01597 + 3.49825i −0.170746 + 0.198049i
\(313\) 10.7494i 0.607590i −0.952737 0.303795i \(-0.901746\pi\)
0.952737 0.303795i \(-0.0982538\pi\)
\(314\) −7.02088 + 7.02088i −0.396211 + 0.396211i
\(315\) 0 0
\(316\) 14.4828i 0.814722i
\(317\) 8.29001 + 8.29001i 0.465613 + 0.465613i 0.900490 0.434877i \(-0.143208\pi\)
−0.434877 + 0.900490i \(0.643208\pi\)
\(318\) 1.80271 1.80271i 0.101091 0.101091i
\(319\) −7.50325 + 7.50325i −0.420101 + 0.420101i
\(320\) 3.84586 + 3.84586i 0.214990 + 0.214990i
\(321\) 1.09910i 0.0613460i
\(322\) 0 0
\(323\) 19.3305 19.3305i 1.07558 1.07558i
\(324\) 9.70770i 0.539316i
\(325\) −6.00391 + 0.444499i −0.333037 + 0.0246564i
\(326\) −0.758619 −0.0420160
\(327\) −0.560972 + 0.560972i −0.0310218 + 0.0310218i
\(328\) 0.345031i 0.0190511i
\(329\) 0 0
\(330\) 0.498286 + 0.498286i 0.0274297 + 0.0274297i
\(331\) −19.1719 19.1719i −1.05378 1.05378i −0.998469 0.0553146i \(-0.982384\pi\)
−0.0553146 0.998469i \(-0.517616\pi\)
\(332\) −5.84898 5.84898i −0.321005 0.321005i
\(333\) 12.2032 12.2032i 0.668729 0.668729i
\(334\) 10.1113i 0.553263i
\(335\) −7.85966 −0.429419
\(336\) 0 0
\(337\) 20.5911i 1.12167i −0.827927 0.560835i \(-0.810480\pi\)
0.827927 0.560835i \(-0.189520\pi\)
\(338\) −8.07297 5.98059i −0.439112 0.325301i
\(339\) 1.28227i 0.0696431i
\(340\) 9.41340 + 9.41340i 0.510513 + 0.510513i
\(341\) 6.04871i 0.327556i
\(342\) 11.2235 0.606899
\(343\) 0 0
\(344\) 13.6987 + 13.6987i 0.738585 + 0.738585i
\(345\) −0.530371 + 0.530371i −0.0285542 + 0.0285542i
\(346\) 12.0838 + 12.0838i 0.649630 + 0.649630i
\(347\) 14.9791 0.804122 0.402061 0.915613i \(-0.368294\pi\)
0.402061 + 0.915613i \(0.368294\pi\)
\(348\) 7.06910 0.378944
\(349\) 3.25693 + 3.25693i 0.174340 + 0.174340i 0.788883 0.614543i \(-0.210660\pi\)
−0.614543 + 0.788883i \(0.710660\pi\)
\(350\) 0 0
\(351\) −10.0939 + 0.747300i −0.538772 + 0.0398879i
\(352\) 6.00746 0.320198
\(353\) 3.94222 3.94222i 0.209823 0.209823i −0.594369 0.804192i \(-0.702598\pi\)
0.804192 + 0.594369i \(0.202598\pi\)
\(354\) 3.79557 0.201732
\(355\) 15.5464 0.825118
\(356\) −7.70000 + 7.70000i −0.408099 + 0.408099i
\(357\) 0 0
\(358\) −4.41035 + 4.41035i −0.233094 + 0.233094i
\(359\) 3.55021 3.55021i 0.187373 0.187373i −0.607186 0.794559i \(-0.707702\pi\)
0.794559 + 0.607186i \(0.207702\pi\)
\(360\) 13.2583i 0.698774i
\(361\) 8.63206i 0.454319i
\(362\) −11.2368 11.2368i −0.590595 0.590595i
\(363\) −4.84597 −0.254348
\(364\) 0 0
\(365\) 20.7043 1.08371
\(366\) −0.347886 0.347886i −0.0181843 0.0181843i
\(367\) 3.07383i 0.160452i −0.996777 0.0802262i \(-0.974436\pi\)
0.996777 0.0802262i \(-0.0255643\pi\)
\(368\) 0.652263i 0.0340015i
\(369\) 0.256307 0.256307i 0.0133428 0.0133428i
\(370\) −6.22969 + 6.22969i −0.323866 + 0.323866i
\(371\) 0 0
\(372\) −2.84937 + 2.84937i −0.147733 + 0.147733i
\(373\) 23.3509 1.20906 0.604532 0.796581i \(-0.293360\pi\)
0.604532 + 0.796581i \(0.293360\pi\)
\(374\) −4.12248 −0.213169
\(375\) 4.19257 4.19257i 0.216503 0.216503i
\(376\) 5.93273 0.305957
\(377\) 2.75402 + 37.1989i 0.141839 + 1.91584i
\(378\) 0 0
\(379\) −1.97284 1.97284i −0.101338 0.101338i 0.654620 0.755958i \(-0.272829\pi\)
−0.755958 + 0.654620i \(0.772829\pi\)
\(380\) 13.4560 0.690279
\(381\) −5.75326 −0.294748
\(382\) −7.56228 7.56228i −0.386920 0.386920i
\(383\) −2.18952 + 2.18952i −0.111879 + 0.111879i −0.760830 0.648951i \(-0.775208\pi\)
0.648951 + 0.760830i \(0.275208\pi\)
\(384\) −3.24152 3.24152i −0.165418 0.165418i
\(385\) 0 0
\(386\) 18.8625 0.960074
\(387\) 20.3523i 1.03457i
\(388\) 3.49490 + 3.49490i 0.177427 + 0.177427i
\(389\) 11.0113i 0.558295i 0.960248 + 0.279148i \(0.0900519\pi\)
−0.960248 + 0.279148i \(0.909948\pi\)
\(390\) 2.47036 0.182893i 0.125092 0.00926115i
\(391\) 4.38793i 0.221907i
\(392\) 0 0
\(393\) 7.52462 0.379567
\(394\) 15.6757i 0.789729i
\(395\) 13.3231 13.3231i 0.670359 0.670359i
\(396\) 2.81066 + 2.81066i 0.141241 + 0.141241i
\(397\) 27.0816 + 27.0816i 1.35918 + 1.35918i 0.874923 + 0.484262i \(0.160912\pi\)
0.484262 + 0.874923i \(0.339088\pi\)
\(398\) −8.09666 8.09666i −0.405849 0.405849i
\(399\) 0 0
\(400\) 1.29081i 0.0645407i
\(401\) −4.75621 + 4.75621i −0.237514 + 0.237514i −0.815820 0.578306i \(-0.803714\pi\)
0.578306 + 0.815820i \(0.303714\pi\)
\(402\) −1.62144 −0.0808701
\(403\) −16.1040 13.8838i −0.802196 0.691603i
\(404\) 3.41383i 0.169844i
\(405\) −8.93036 + 8.93036i −0.443753 + 0.443753i
\(406\) 0 0
\(407\) 6.40725i 0.317595i
\(408\) 4.71085 + 4.71085i 0.233222 + 0.233222i
\(409\) −24.0696 + 24.0696i −1.19017 + 1.19017i −0.213146 + 0.977020i \(0.568371\pi\)
−0.977020 + 0.213146i \(0.931629\pi\)
\(410\) −0.130844 + 0.130844i −0.00646195 + 0.00646195i
\(411\) −0.353089 0.353089i −0.0174166 0.0174166i
\(412\) 3.83832i 0.189101i
\(413\) 0 0
\(414\) 1.27384 1.27384i 0.0626060 0.0626060i
\(415\) 10.7613i 0.528250i
\(416\) 13.7891 15.9941i 0.676067 0.784177i
\(417\) 5.55467 0.272013
\(418\) −2.94645 + 2.94645i −0.144116 + 0.144116i
\(419\) 35.5515i 1.73680i −0.495862 0.868401i \(-0.665148\pi\)
0.495862 0.868401i \(-0.334852\pi\)
\(420\) 0 0
\(421\) −10.3166 10.3166i −0.502802 0.502802i 0.409505 0.912308i \(-0.365701\pi\)
−0.912308 + 0.409505i \(0.865701\pi\)
\(422\) 3.81762 + 3.81762i 0.185839 + 0.185839i
\(423\) 4.40716 + 4.40716i 0.214283 + 0.214283i
\(424\) −12.5923 + 12.5923i −0.611535 + 0.611535i
\(425\) 8.68363i 0.421218i
\(426\) 3.20721 0.155390
\(427\) 0 0
\(428\) 3.16492i 0.152982i
\(429\) 1.17633 1.36444i 0.0567939 0.0658757i
\(430\) 10.3898i 0.501041i
\(431\) −25.2499 25.2499i −1.21624 1.21624i −0.968937 0.247307i \(-0.920454\pi\)
−0.247307 0.968937i \(-0.579546\pi\)
\(432\) 2.17014i 0.104411i
\(433\) 18.6845 0.897919 0.448959 0.893552i \(-0.351795\pi\)
0.448959 + 0.893552i \(0.351795\pi\)
\(434\) 0 0
\(435\) −6.50305 6.50305i −0.311798 0.311798i
\(436\) 1.61534 1.61534i 0.0773608 0.0773608i
\(437\) −3.13617 3.13617i −0.150023 0.150023i
\(438\) 4.27127 0.204089
\(439\) −23.8317 −1.13742 −0.568712 0.822537i \(-0.692558\pi\)
−0.568712 + 0.822537i \(0.692558\pi\)
\(440\) −3.48063 3.48063i −0.165932 0.165932i
\(441\) 0 0
\(442\) −9.46248 + 10.9756i −0.450084 + 0.522057i
\(443\) −23.3815 −1.11089 −0.555445 0.831553i \(-0.687452\pi\)
−0.555445 + 0.831553i \(0.687452\pi\)
\(444\) 3.01826 3.01826i 0.143240 0.143240i
\(445\) 14.1669 0.671573
\(446\) −21.2353 −1.00552
\(447\) 2.63104 2.63104i 0.124444 0.124444i
\(448\) 0 0
\(449\) −17.6188 + 17.6188i −0.831482 + 0.831482i −0.987720 0.156237i \(-0.950063\pi\)
0.156237 + 0.987720i \(0.450063\pi\)
\(450\) −2.52091 + 2.52091i −0.118837 + 0.118837i
\(451\) 0.134574i 0.00633683i
\(452\) 3.69234i 0.173673i
\(453\) 2.35972 + 2.35972i 0.110869 + 0.110869i
\(454\) −0.0544168 −0.00255391
\(455\) 0 0
\(456\) 6.73394 0.315346
\(457\) 2.86848 + 2.86848i 0.134182 + 0.134182i 0.771008 0.636826i \(-0.219753\pi\)
−0.636826 + 0.771008i \(0.719753\pi\)
\(458\) 4.22481i 0.197412i
\(459\) 14.5991i 0.681427i
\(460\) 1.52722 1.52722i 0.0712072 0.0712072i
\(461\) 7.54874 7.54874i 0.351580 0.351580i −0.509117 0.860697i \(-0.670028\pi\)
0.860697 + 0.509117i \(0.170028\pi\)
\(462\) 0 0
\(463\) 13.5419 13.5419i 0.629344 0.629344i −0.318559 0.947903i \(-0.603199\pi\)
0.947903 + 0.318559i \(0.103199\pi\)
\(464\) −7.99761 −0.371280
\(465\) 5.24241 0.243111
\(466\) 0.576209 0.576209i 0.0266924 0.0266924i
\(467\) −36.1267 −1.67175 −0.835873 0.548923i \(-0.815038\pi\)
−0.835873 + 0.548923i \(0.815038\pi\)
\(468\) 13.9344 1.03164i 0.644120 0.0476874i
\(469\) 0 0
\(470\) −2.24985 2.24985i −0.103778 0.103778i
\(471\) −6.25842 −0.288373
\(472\) −26.5128 −1.22035
\(473\) −5.34297 5.34297i −0.245670 0.245670i
\(474\) 2.74855 2.74855i 0.126245 0.126245i
\(475\) 6.20642 + 6.20642i 0.284770 + 0.284770i
\(476\) 0 0
\(477\) −18.7085 −0.856601
\(478\) 20.4343i 0.934641i
\(479\) 23.3427 + 23.3427i 1.06656 + 1.06656i 0.997621 + 0.0689350i \(0.0219601\pi\)
0.0689350 + 0.997621i \(0.478040\pi\)
\(480\) 5.20666i 0.237650i
\(481\) 17.0585 + 14.7068i 0.777802 + 0.670571i
\(482\) 7.57443i 0.345006i
\(483\) 0 0
\(484\) 13.9542 0.634281
\(485\) 6.43011i 0.291976i
\(486\) −6.44456 + 6.44456i −0.292331 + 0.292331i
\(487\) −4.37289 4.37289i −0.198155 0.198155i 0.601054 0.799209i \(-0.294748\pi\)
−0.799209 + 0.601054i \(0.794748\pi\)
\(488\) 2.43005 + 2.43005i 0.110003 + 0.110003i
\(489\) −0.338117 0.338117i −0.0152902 0.0152902i
\(490\) 0 0
\(491\) 33.4149i 1.50799i −0.656879 0.753996i \(-0.728124\pi\)
0.656879 0.753996i \(-0.271876\pi\)
\(492\) 0.0633936 0.0633936i 0.00285801 0.00285801i
\(493\) 53.8019 2.42312
\(494\) 1.08148 + 14.6077i 0.0486580 + 0.657229i
\(495\) 5.17120i 0.232428i
\(496\) 3.22362 3.22362i 0.144745 0.144745i
\(497\) 0 0
\(498\) 2.22004i 0.0994824i
\(499\) −10.5085 10.5085i −0.470427 0.470427i 0.431626 0.902053i \(-0.357940\pi\)
−0.902053 + 0.431626i \(0.857940\pi\)
\(500\) −12.0727 + 12.0727i −0.539907 + 0.539907i
\(501\) 4.50659 4.50659i 0.201340 0.201340i
\(502\) 13.6210 + 13.6210i 0.607933 + 0.607933i
\(503\) 24.9299i 1.11157i −0.831327 0.555784i \(-0.812418\pi\)
0.831327 0.555784i \(-0.187582\pi\)
\(504\) 0 0
\(505\) −3.14047 + 3.14047i −0.139749 + 0.139749i
\(506\) 0.668829i 0.0297331i
\(507\) −0.932575 6.26369i −0.0414171 0.278180i
\(508\) 16.5667 0.735030
\(509\) −1.34716 + 1.34716i −0.0597116 + 0.0597116i −0.736332 0.676620i \(-0.763444\pi\)
0.676620 + 0.736332i \(0.263444\pi\)
\(510\) 3.57295i 0.158213i
\(511\) 0 0
\(512\) 6.07668 + 6.07668i 0.268554 + 0.268554i
\(513\) 10.4343 + 10.4343i 0.460688 + 0.460688i
\(514\) −2.16535 2.16535i −0.0955094 0.0955094i
\(515\) 3.53098 3.53098i 0.155593 0.155593i
\(516\) 5.03382i 0.221602i
\(517\) −2.31397 −0.101768
\(518\) 0 0
\(519\) 10.7715i 0.472818i
\(520\) −17.2560 + 1.27754i −0.756724 + 0.0560240i
\(521\) 10.8700i 0.476222i −0.971238 0.238111i \(-0.923472\pi\)
0.971238 0.238111i \(-0.0765283\pi\)
\(522\) 15.6190 + 15.6190i 0.683626 + 0.683626i
\(523\) 23.3792i 1.02230i −0.859491 0.511151i \(-0.829219\pi\)
0.859491 0.511151i \(-0.170781\pi\)
\(524\) −21.6675 −0.946547
\(525\) 0 0
\(526\) −16.9009 16.9009i −0.736914 0.736914i
\(527\) −21.6861 + 21.6861i −0.944662 + 0.944662i
\(528\) 0.273127 + 0.273127i 0.0118863 + 0.0118863i
\(529\) 22.2881 0.969048
\(530\) 9.55063 0.414853
\(531\) −19.6952 19.6952i −0.854697 0.854697i
\(532\) 0 0
\(533\) 0.358286 + 0.308892i 0.0155191 + 0.0133796i
\(534\) 2.92261 0.126474
\(535\) −2.91149 + 2.91149i −0.125875 + 0.125875i
\(536\) 11.3261 0.489212
\(537\) −3.93139 −0.169652
\(538\) 6.01752 6.01752i 0.259434 0.259434i
\(539\) 0 0
\(540\) −5.08123 + 5.08123i −0.218661 + 0.218661i
\(541\) −4.80784 + 4.80784i −0.206705 + 0.206705i −0.802865 0.596160i \(-0.796692\pi\)
0.596160 + 0.802865i \(0.296692\pi\)
\(542\) 3.87110i 0.166278i
\(543\) 10.0165i 0.429850i
\(544\) −21.5382 21.5382i −0.923442 0.923442i
\(545\) −2.97199 −0.127306
\(546\) 0 0
\(547\) −14.2303 −0.608446 −0.304223 0.952601i \(-0.598397\pi\)
−0.304223 + 0.952601i \(0.598397\pi\)
\(548\) 1.01673 + 1.01673i 0.0434328 + 0.0434328i
\(549\) 3.61035i 0.154086i
\(550\) 1.32360i 0.0564385i
\(551\) 38.4537 38.4537i 1.63818 1.63818i
\(552\) 0.764286 0.764286i 0.0325302 0.0325302i
\(553\) 0 0
\(554\) −6.67114 + 6.67114i −0.283429 + 0.283429i
\(555\) −5.55315 −0.235718
\(556\) −15.9949 −0.678335
\(557\) 5.73436 5.73436i 0.242973 0.242973i −0.575106 0.818079i \(-0.695039\pi\)
0.818079 + 0.575106i \(0.195039\pi\)
\(558\) −12.5912 −0.533029
\(559\) −26.4889 + 1.96111i −1.12036 + 0.0829459i
\(560\) 0 0
\(561\) −1.83739 1.83739i −0.0775749 0.0775749i
\(562\) −14.0282 −0.591745
\(563\) 35.5046 1.49634 0.748170 0.663507i \(-0.230933\pi\)
0.748170 + 0.663507i \(0.230933\pi\)
\(564\) 1.09004 + 1.09004i 0.0458990 + 0.0458990i
\(565\) −3.39668 + 3.39668i −0.142899 + 0.142899i
\(566\) 9.23508 + 9.23508i 0.388179 + 0.388179i
\(567\) 0 0
\(568\) −22.4030 −0.940009
\(569\) 31.7463i 1.33087i −0.746454 0.665437i \(-0.768245\pi\)
0.746454 0.665437i \(-0.231755\pi\)
\(570\) −2.55368 2.55368i −0.106962 0.106962i
\(571\) 8.26604i 0.345923i 0.984929 + 0.172961i \(0.0553336\pi\)
−0.984929 + 0.172961i \(0.944666\pi\)
\(572\) −3.38730 + 3.92896i −0.141630 + 0.164278i
\(573\) 6.74103i 0.281611i
\(574\) 0 0
\(575\) 1.40883 0.0587521
\(576\) 8.23386i 0.343077i
\(577\) −2.38091 + 2.38091i −0.0991186 + 0.0991186i −0.754927 0.655809i \(-0.772328\pi\)
0.655809 + 0.754927i \(0.272328\pi\)
\(578\) 5.48996 + 5.48996i 0.228352 + 0.228352i
\(579\) 8.40702 + 8.40702i 0.349384 + 0.349384i
\(580\) 18.7258 + 18.7258i 0.777547 + 0.777547i
\(581\) 0 0
\(582\) 1.32653i 0.0549863i
\(583\) 4.91142 4.91142i 0.203410 0.203410i
\(584\) −29.8357 −1.23461
\(585\) −13.7677 11.8696i −0.569224 0.490749i
\(586\) 12.1518i 0.501987i
\(587\) 3.33097 3.33097i 0.137484 0.137484i −0.635016 0.772499i \(-0.719006\pi\)
0.772499 + 0.635016i \(0.219006\pi\)
\(588\) 0 0
\(589\) 30.9993i 1.27730i
\(590\) 10.0543 + 10.0543i 0.413931 + 0.413931i
\(591\) 6.98666 6.98666i 0.287393 0.287393i
\(592\) −3.41470 + 3.41470i −0.140343 + 0.140343i
\(593\) 10.6290 + 10.6290i 0.436480 + 0.436480i 0.890826 0.454345i \(-0.150127\pi\)
−0.454345 + 0.890826i \(0.650127\pi\)
\(594\) 2.22526i 0.0913035i
\(595\) 0 0
\(596\) −7.57618 + 7.57618i −0.310332 + 0.310332i
\(597\) 7.21737i 0.295387i
\(598\) 1.78068 + 1.53519i 0.0728173 + 0.0627785i
\(599\) 7.27545 0.297267 0.148633 0.988892i \(-0.452513\pi\)
0.148633 + 0.988892i \(0.452513\pi\)
\(600\) −1.51251 + 1.51251i −0.0617478 + 0.0617478i
\(601\) 2.83288i 0.115555i 0.998329 + 0.0577777i \(0.0184015\pi\)
−0.998329 + 0.0577777i \(0.981599\pi\)
\(602\) 0 0
\(603\) 8.41363 + 8.41363i 0.342630 + 0.342630i
\(604\) −6.79492 6.79492i −0.276481 0.276481i
\(605\) −12.8368 12.8368i −0.521891 0.521891i
\(606\) −0.647877 + 0.647877i −0.0263182 + 0.0263182i
\(607\) 27.5502i 1.11823i −0.829091 0.559114i \(-0.811141\pi\)
0.829091 0.559114i \(-0.188859\pi\)
\(608\) −30.7878 −1.24861
\(609\) 0 0
\(610\) 1.84308i 0.0746239i
\(611\) −5.31134 + 6.16067i −0.214874 + 0.249234i
\(612\) 20.1538i 0.814669i
\(613\) −17.3792 17.3792i −0.701941 0.701941i 0.262886 0.964827i \(-0.415326\pi\)
−0.964827 + 0.262886i \(0.915326\pi\)
\(614\) 16.0233i 0.646646i
\(615\) −0.116635 −0.00470318
\(616\) 0 0
\(617\) −10.3106 10.3106i −0.415090 0.415090i 0.468417 0.883507i \(-0.344824\pi\)
−0.883507 + 0.468417i \(0.844824\pi\)
\(618\) 0.728438 0.728438i 0.0293021 0.0293021i
\(619\) −21.4347 21.4347i −0.861532 0.861532i 0.129984 0.991516i \(-0.458508\pi\)
−0.991516 + 0.129984i \(0.958508\pi\)
\(620\) −15.0958 −0.606260
\(621\) 2.36855 0.0950465
\(622\) −5.85080 5.85080i −0.234596 0.234596i
\(623\) 0 0
\(624\) 1.35409 0.100250i 0.0542069 0.00401320i
\(625\) 13.8633 0.554530
\(626\) 5.87431 5.87431i 0.234785 0.234785i
\(627\) −2.62647 −0.104891
\(628\) 18.0214 0.719132
\(629\) 22.9715 22.9715i 0.915935 0.915935i
\(630\) 0 0
\(631\) −9.56348 + 9.56348i −0.380716 + 0.380716i −0.871360 0.490644i \(-0.836762\pi\)
0.490644 + 0.871360i \(0.336762\pi\)
\(632\) −19.1992 + 19.1992i −0.763701 + 0.763701i
\(633\) 3.40304i 0.135259i
\(634\) 9.06065i 0.359844i
\(635\) −15.2402 15.2402i −0.604788 0.604788i
\(636\) −4.62724 −0.183482
\(637\) 0 0
\(638\) −8.20074 −0.324671
\(639\) −16.6422 16.6422i −0.658354 0.658354i
\(640\) 17.1734i 0.678837i
\(641\) 27.3055i 1.07850i −0.842145 0.539251i \(-0.818708\pi\)
0.842145 0.539251i \(-0.181292\pi\)
\(642\) −0.600638 + 0.600638i −0.0237053 + 0.0237053i
\(643\) 17.4331 17.4331i 0.687495 0.687495i −0.274183 0.961678i \(-0.588407\pi\)
0.961678 + 0.274183i \(0.0884073\pi\)
\(644\) 0 0
\(645\) 4.63075 4.63075i 0.182335 0.182335i
\(646\) 21.1275 0.831249
\(647\) −19.2142 −0.755386 −0.377693 0.925931i \(-0.623283\pi\)
−0.377693 + 0.925931i \(0.623283\pi\)
\(648\) 12.8690 12.8690i 0.505543 0.505543i
\(649\) 10.3409 0.405916
\(650\) −3.52392 3.03810i −0.138220 0.119164i
\(651\) 0 0
\(652\) 0.973622 + 0.973622i 0.0381300 + 0.0381300i
\(653\) −18.1628 −0.710765 −0.355383 0.934721i \(-0.615649\pi\)
−0.355383 + 0.934721i \(0.615649\pi\)
\(654\) −0.613119 −0.0239749
\(655\) 19.9325 + 19.9325i 0.778826 + 0.778826i
\(656\) −0.0717202 + 0.0717202i −0.00280020 + 0.00280020i
\(657\) −22.1636 22.1636i −0.864683 0.864683i
\(658\) 0 0
\(659\) −36.6851 −1.42905 −0.714525 0.699610i \(-0.753357\pi\)
−0.714525 + 0.699610i \(0.753357\pi\)
\(660\) 1.27901i 0.0497856i
\(661\) 1.78106 + 1.78106i 0.0692752 + 0.0692752i 0.740895 0.671620i \(-0.234401\pi\)
−0.671620 + 0.740895i \(0.734401\pi\)
\(662\) 20.9541i 0.814405i
\(663\) −9.10928 + 0.674405i −0.353775 + 0.0261917i
\(664\) 15.5074i 0.601805i
\(665\) 0 0
\(666\) 13.3376 0.516820
\(667\) 8.72879i 0.337980i
\(668\) −12.9769 + 12.9769i −0.502092 + 0.502092i
\(669\) −9.46458 9.46458i −0.365922 0.365922i
\(670\) −4.29514 4.29514i −0.165936 0.165936i
\(671\) −0.947803 0.947803i −0.0365895 0.0365895i
\(672\) 0 0
\(673\) 3.52257i 0.135785i −0.997693 0.0678925i \(-0.978373\pi\)
0.997693 0.0678925i \(-0.0216275\pi\)
\(674\) 11.2526 11.2526i 0.433436 0.433436i
\(675\) −4.68730 −0.180414
\(676\) 2.68539 + 18.0365i 0.103284 + 0.693713i
\(677\) 21.2972i 0.818518i 0.912418 + 0.409259i \(0.134213\pi\)
−0.912418 + 0.409259i \(0.865787\pi\)
\(678\) −0.700732 + 0.700732i −0.0269115 + 0.0269115i
\(679\) 0 0
\(680\) 24.9578i 0.957087i
\(681\) −0.0242536 0.0242536i −0.000929400 0.000929400i
\(682\) 3.30550 3.30550i 0.126574 0.126574i
\(683\) 1.42970 1.42970i 0.0547060 0.0547060i −0.679225 0.733931i \(-0.737684\pi\)
0.733931 + 0.679225i \(0.237684\pi\)
\(684\) −14.4044 14.4044i −0.550768 0.550768i
\(685\) 1.87064i 0.0714736i
\(686\) 0 0
\(687\) −1.88300 + 1.88300i −0.0718410 + 0.0718410i
\(688\) 5.69500i 0.217120i
\(689\) −1.80271 24.3494i −0.0686777 0.927639i
\(690\) −0.579674 −0.0220678
\(691\) 0.899585 0.899585i 0.0342218 0.0342218i −0.689789 0.724011i \(-0.742297\pi\)
0.724011 + 0.689789i \(0.242297\pi\)
\(692\) 31.0171i 1.17909i
\(693\) 0 0
\(694\) 8.18579 + 8.18579i 0.310728 + 0.310728i
\(695\) 14.7141 + 14.7141i 0.558139 + 0.558139i
\(696\) 9.37117 + 9.37117i 0.355213 + 0.355213i
\(697\) 0.482480 0.482480i 0.0182752 0.0182752i
\(698\) 3.55970i 0.134737i
\(699\) 0.513634 0.0194274
\(700\) 0 0
\(701\) 2.12113i 0.0801138i −0.999197 0.0400569i \(-0.987246\pi\)
0.999197 0.0400569i \(-0.0127539\pi\)
\(702\) −5.92449 5.10772i −0.223605 0.192778i
\(703\) 32.8367i 1.23846i
\(704\) 2.16159 + 2.16159i 0.0814679 + 0.0814679i
\(705\) 2.00552i 0.0755321i
\(706\) 4.30869 0.162160
\(707\) 0 0
\(708\) −4.87129 4.87129i −0.183074 0.183074i
\(709\) −0.990630 + 0.990630i −0.0372039 + 0.0372039i −0.725464 0.688260i \(-0.758375\pi\)
0.688260 + 0.725464i \(0.258375\pi\)
\(710\) 8.49580 + 8.49580i 0.318842 + 0.318842i
\(711\) −28.5244 −1.06975
\(712\) −20.4150 −0.765085
\(713\) 3.51834 + 3.51834i 0.131763 + 0.131763i
\(714\) 0 0
\(715\) 6.73041 0.498286i 0.251703 0.0186348i
\(716\) 11.3206 0.423071
\(717\) −9.10757 + 9.10757i −0.340128 + 0.340128i
\(718\) 3.88024 0.144809
\(719\) 33.0502 1.23256 0.616281 0.787526i \(-0.288638\pi\)
0.616281 + 0.787526i \(0.288638\pi\)
\(720\) 2.75596 2.75596i 0.102708 0.102708i
\(721\) 0 0
\(722\) 4.71725 4.71725i 0.175558 0.175558i
\(723\) −3.37593 + 3.37593i −0.125552 + 0.125552i
\(724\) 28.8430i 1.07194i
\(725\) 17.2741i 0.641544i
\(726\) −2.64823 2.64823i −0.0982849 0.0982849i
\(727\) 33.8896 1.25689 0.628447 0.777852i \(-0.283691\pi\)
0.628447 + 0.777852i \(0.283691\pi\)
\(728\) 0 0
\(729\) 15.0172 0.556192
\(730\) 11.3145 + 11.3145i 0.418767 + 0.418767i
\(731\) 38.3117i 1.41701i
\(732\) 0.892963i 0.0330049i
\(733\) −27.8480 + 27.8480i −1.02859 + 1.02859i −0.0290099 + 0.999579i \(0.509235\pi\)
−0.999579 + 0.0290099i \(0.990765\pi\)
\(734\) 1.67978 1.67978i 0.0620020 0.0620020i
\(735\) 0 0
\(736\) −3.49434 + 3.49434i −0.128803 + 0.128803i
\(737\) −4.41756 −0.162723
\(738\) 0.280134 0.0103119
\(739\) −26.6484 + 26.6484i −0.980277 + 0.980277i −0.999809 0.0195327i \(-0.993782\pi\)
0.0195327 + 0.999809i \(0.493782\pi\)
\(740\) 15.9905 0.587824
\(741\) −6.02863 + 6.99266i −0.221467 + 0.256882i
\(742\) 0 0
\(743\) −31.2340 31.2340i −1.14587 1.14587i −0.987358 0.158508i \(-0.949332\pi\)
−0.158508 0.987358i \(-0.550668\pi\)
\(744\) −7.55453 −0.276963
\(745\) 13.9390 0.510687
\(746\) 12.7608 + 12.7608i 0.467206 + 0.467206i
\(747\) 11.5198 11.5198i 0.421486 0.421486i
\(748\) 5.29086 + 5.29086i 0.193453 + 0.193453i
\(749\) 0 0
\(750\) 4.58231 0.167322
\(751\) 18.0891i 0.660080i 0.943967 + 0.330040i \(0.107062\pi\)
−0.943967 + 0.330040i \(0.892938\pi\)
\(752\) −1.23322 1.23322i −0.0449708 0.0449708i
\(753\) 12.1417i 0.442470i
\(754\) −18.8235 + 21.8335i −0.685510 + 0.795129i
\(755\) 12.5017i 0.454982i
\(756\) 0 0
\(757\) 4.04733 0.147103 0.0735514 0.997291i \(-0.476567\pi\)
0.0735514 + 0.997291i \(0.476567\pi\)
\(758\) 2.15623i 0.0783180i
\(759\) −0.298098 + 0.298098i −0.0108203 + 0.0108203i
\(760\) 17.8380 + 17.8380i 0.647052 + 0.647052i
\(761\) −27.1193 27.1193i −0.983073 0.983073i 0.0167862 0.999859i \(-0.494657\pi\)
−0.999859 + 0.0167862i \(0.994657\pi\)
\(762\) −3.14404 3.14404i −0.113897 0.113897i
\(763\) 0 0
\(764\) 19.4111i 0.702268i
\(765\) −18.5400 + 18.5400i −0.670315 + 0.670315i
\(766\) −2.39305 −0.0864645
\(767\) 23.7359 27.5314i 0.857052 0.994102i
\(768\) 6.44652i 0.232619i
\(769\) −24.8051 + 24.8051i −0.894496 + 0.894496i −0.994942 0.100446i \(-0.967973\pi\)
0.100446 + 0.994942i \(0.467973\pi\)
\(770\) 0 0
\(771\) 1.93020i 0.0695143i
\(772\) −24.2084 24.2084i −0.871278 0.871278i
\(773\) 21.3049 21.3049i 0.766284 0.766284i −0.211166 0.977450i \(-0.567726\pi\)
0.977450 + 0.211166i \(0.0677262\pi\)
\(774\) −11.1221 + 11.1221i −0.399776 + 0.399776i
\(775\) −6.96273 6.96273i −0.250108 0.250108i
\(776\) 9.26605i 0.332632i
\(777\) 0 0
\(778\) −6.01745 + 6.01745i −0.215736 + 0.215736i
\(779\) 0.689682i 0.0247104i
\(780\) −3.40522 2.93577i −0.121927 0.105117i
\(781\) 8.73794 0.312668
\(782\) 2.39792 2.39792i 0.0857493 0.0857493i
\(783\) 29.0415i 1.03786i
\(784\) 0 0
\(785\) −16.5784 16.5784i −0.591707 0.591707i
\(786\) 4.11205 + 4.11205i 0.146672 + 0.146672i
\(787\) 6.86137 + 6.86137i 0.244581 + 0.244581i 0.818742 0.574161i \(-0.194672\pi\)
−0.574161 + 0.818742i \(0.694672\pi\)
\(788\) −20.1184 + 20.1184i −0.716687 + 0.716687i
\(789\) 15.0655i 0.536346i
\(790\) 14.5616 0.518079
\(791\) 0 0
\(792\) 7.45191i 0.264792i
\(793\) −4.69894 + 0.347886i −0.166864 + 0.0123538i
\(794\) 29.5991i 1.05043i
\(795\) 4.25672 + 4.25672i 0.150970 + 0.150970i
\(796\) 20.7827i 0.736624i
\(797\) −9.46979 −0.335437 −0.167719 0.985835i \(-0.553640\pi\)
−0.167719 + 0.985835i \(0.553640\pi\)
\(798\) 0 0
\(799\) 8.29615 + 8.29615i 0.293497 + 0.293497i
\(800\) 6.91523 6.91523i 0.244490 0.244490i
\(801\) −15.1654 15.1654i −0.535843 0.535843i
\(802\) −5.19835 −0.183560
\(803\) 11.6369 0.410659
\(804\) 2.08098 + 2.08098i 0.0733905 + 0.0733905i
\(805\) 0 0
\(806\) −1.21326 16.3877i −0.0427354 0.577233i
\(807\) 5.36402 0.188823
\(808\) 4.52555 4.52555i 0.159208 0.159208i
\(809\) 23.7060 0.833458 0.416729 0.909031i \(-0.363176\pi\)
0.416729 + 0.909031i \(0.363176\pi\)
\(810\) −9.76053 −0.342950
\(811\) −29.4470 + 29.4470i −1.03403 + 1.03403i −0.0346248 + 0.999400i \(0.511024\pi\)
−0.999400 + 0.0346248i \(0.988976\pi\)
\(812\) 0 0
\(813\) 1.72535 1.72535i 0.0605108 0.0605108i
\(814\) −3.50143 + 3.50143i −0.122725 + 0.122725i
\(815\) 1.79132i 0.0627473i
\(816\) 1.95846i 0.0685597i
\(817\) 27.3824 + 27.3824i 0.957988 + 0.957988i
\(818\) −26.3071 −0.919807
\(819\) 0 0
\(820\) 0.335855 0.0117286
\(821\) 15.1774 + 15.1774i 0.529696 + 0.529696i 0.920482 0.390786i \(-0.127797\pi\)
−0.390786 + 0.920482i \(0.627797\pi\)
\(822\) 0.385912i 0.0134602i
\(823\) 18.9392i 0.660178i −0.943950 0.330089i \(-0.892921\pi\)
0.943950 0.330089i \(-0.107079\pi\)
\(824\) −5.08828 + 5.08828i −0.177259 + 0.177259i
\(825\) 0.589929 0.589929i 0.0205387 0.0205387i
\(826\) 0 0
\(827\) 0.174463 0.174463i 0.00606667 0.00606667i −0.704067 0.710134i \(-0.748635\pi\)
0.710134 + 0.704067i \(0.248635\pi\)
\(828\) −3.26974 −0.113631
\(829\) −17.0844 −0.593365 −0.296682 0.954976i \(-0.595880\pi\)
−0.296682 + 0.954976i \(0.595880\pi\)
\(830\) −5.88081 + 5.88081i −0.204126 + 0.204126i
\(831\) −5.94666 −0.206287
\(832\) 10.7165 0.793398i 0.371529 0.0275061i
\(833\) 0 0
\(834\) 3.03551 + 3.03551i 0.105111 + 0.105111i
\(835\) 23.8756 0.826250
\(836\) 7.56303 0.261573
\(837\) −11.7059 11.7059i −0.404614 0.404614i
\(838\) 19.4282 19.4282i 0.671134 0.671134i
\(839\) 22.4787 + 22.4787i 0.776052 + 0.776052i 0.979157 0.203105i \(-0.0651032\pi\)
−0.203105 + 0.979157i \(0.565103\pi\)
\(840\) 0 0
\(841\) 78.0266 2.69057
\(842\) 11.2757i 0.388585i
\(843\) −6.25240 6.25240i −0.215344 0.215344i
\(844\) 9.79918i 0.337302i
\(845\) 14.1219 19.0627i 0.485809 0.655775i
\(846\) 4.81685i 0.165607i
\(847\) 0 0
\(848\) 5.23502 0.179771
\(849\) 8.23216i 0.282527i
\(850\) −4.74543 + 4.74543i −0.162767 + 0.162767i
\(851\) −3.72689 3.72689i −0.127756 0.127756i
\(852\) −4.11618 4.11618i −0.141018 0.141018i
\(853\) 3.63231 + 3.63231i 0.124368 + 0.124368i 0.766551 0.642183i \(-0.221971\pi\)
−0.642183 + 0.766551i \(0.721971\pi\)
\(854\) 0 0
\(855\) 26.5021i 0.906351i
\(856\) 4.19558 4.19558i 0.143402 0.143402i
\(857\) 48.1799 1.64579 0.822897 0.568190i \(-0.192356\pi\)
0.822897 + 0.568190i \(0.192356\pi\)
\(858\) 1.38848 0.102796i 0.0474019 0.00350940i
\(859\) 3.08901i 0.105396i −0.998611 0.0526978i \(-0.983218\pi\)
0.998611 0.0526978i \(-0.0167820\pi\)
\(860\) −13.3344 + 13.3344i −0.454700 + 0.454700i
\(861\) 0 0
\(862\) 27.5971i 0.939961i
\(863\) 18.1969 + 18.1969i 0.619430 + 0.619430i 0.945385 0.325955i \(-0.105686\pi\)
−0.325955 + 0.945385i \(0.605686\pi\)
\(864\) 11.6260 11.6260i 0.395525 0.395525i
\(865\) −28.5334 + 28.5334i −0.970166 + 0.970166i
\(866\) 10.2107 + 10.2107i 0.346973 + 0.346973i
\(867\) 4.89375i 0.166201i
\(868\) 0 0
\(869\) 7.48833 7.48833i 0.254024 0.254024i
\(870\) 7.10758i 0.240969i
\(871\) −10.1398 + 11.7612i −0.343574 + 0.398514i
\(872\) 4.28276 0.145033
\(873\) −6.88333 + 6.88333i −0.232965 + 0.232965i
\(874\) 3.42771i 0.115944i
\(875\) 0 0
\(876\) −5.48181 5.48181i −0.185213 0.185213i
\(877\) 0.845403 + 0.845403i 0.0285472 + 0.0285472i 0.721236 0.692689i \(-0.243574\pi\)
−0.692689 + 0.721236i \(0.743574\pi\)
\(878\) −13.0235 13.0235i −0.439523 0.439523i
\(879\) −5.41608 + 5.41608i −0.182680 + 0.182680i
\(880\) 1.44701i 0.0487787i
\(881\) 20.3067 0.684151 0.342075 0.939672i \(-0.388870\pi\)
0.342075 + 0.939672i \(0.388870\pi\)
\(882\) 0 0
\(883\) 28.8309i 0.970238i −0.874448 0.485119i \(-0.838776\pi\)
0.874448 0.485119i \(-0.161224\pi\)
\(884\) 26.2306 1.94198i 0.882229 0.0653158i
\(885\) 8.96246i 0.301270i
\(886\) −12.7775 12.7775i −0.429270 0.429270i
\(887\) 1.59150i 0.0534373i 0.999643 + 0.0267186i \(0.00850582\pi\)
−0.999643 + 0.0267186i \(0.991494\pi\)
\(888\) 8.00232 0.268540
\(889\) 0 0
\(890\) 7.74190 + 7.74190i 0.259509 + 0.259509i
\(891\) −5.01936 + 5.01936i −0.168155 + 0.168155i
\(892\) 27.2537 + 27.2537i 0.912520 + 0.912520i
\(893\) 11.8590 0.396845
\(894\) 2.87562 0.0961750
\(895\) −10.4141 10.4141i −0.348106 0.348106i
\(896\) 0 0
\(897\) 0.109415 + 1.47788i 0.00365326 + 0.0493451i
\(898\) −19.2566 −0.642602
\(899\) −43.1396 + 43.1396i −1.43879 + 1.43879i
\(900\) 6.47074 0.215691
\(901\) −35.2173 −1.17326
\(902\) −0.0735418 + 0.0735418i −0.00244868 + 0.00244868i
\(903\) 0 0
\(904\) 4.89475 4.89475i 0.162797 0.162797i
\(905\) 26.5335 26.5335i 0.882002 0.882002i
\(906\) 2.57908i 0.0856843i
\(907\) 0.116742i 0.00387636i 0.999998 + 0.00193818i \(0.000616942\pi\)
−0.999998 + 0.00193818i \(0.999383\pi\)
\(908\) 0.0698392 + 0.0698392i 0.00231770 + 0.00231770i
\(909\) 6.72364 0.223009
\(910\) 0 0
\(911\) 19.0003 0.629507 0.314753 0.949173i \(-0.398078\pi\)
0.314753 + 0.949173i \(0.398078\pi\)
\(912\) −1.39976 1.39976i −0.0463507 0.0463507i
\(913\) 6.04843i 0.200174i
\(914\) 3.13513i 0.103701i
\(915\) 0.821460 0.821460i 0.0271566 0.0271566i
\(916\) 5.42218 5.42218i 0.179154 0.179154i
\(917\) 0 0
\(918\) −7.97810 + 7.97810i −0.263317 + 0.263317i
\(919\) −11.6437 −0.384089 −0.192045 0.981386i \(-0.561512\pi\)
−0.192045 + 0.981386i \(0.561512\pi\)
\(920\) 4.04914 0.133496
\(921\) −7.14158 + 7.14158i −0.235323 + 0.235323i
\(922\) 8.25047 0.271715
\(923\) 20.0565 23.2637i 0.660168 0.765735i
\(924\) 0 0
\(925\) 7.37543 + 7.37543i 0.242503 + 0.242503i
\(926\) 14.8007 0.486382
\(927\) −7.55970 −0.248293
\(928\) −42.8453 42.8453i −1.40647 1.40647i
\(929\) −36.5980 + 36.5980i −1.20074 + 1.20074i −0.226802 + 0.973941i \(0.572827\pi\)
−0.973941 + 0.226802i \(0.927173\pi\)
\(930\) 2.86487 + 2.86487i 0.0939429 + 0.0939429i
\(931\) 0 0
\(932\) −1.47903 −0.0484473
\(933\) 5.21541i 0.170745i
\(934\) −19.7425 19.7425i −0.645995 0.645995i
\(935\) 9.73439i 0.318349i
\(936\) 19.8398 + 17.1046i 0.648484 + 0.559082i
\(937\) 47.9005i 1.56484i −0.622751 0.782420i \(-0.713985\pi\)
0.622751 0.782420i \(-0.286015\pi\)
\(938\) 0 0
\(939\) 5.23637 0.170882
\(940\) 5.77497i 0.188359i
\(941\) 22.2959 22.2959i 0.726825 0.726825i −0.243161 0.969986i \(-0.578184\pi\)
0.969986 + 0.243161i \(0.0781844\pi\)
\(942\) −3.42010 3.42010i −0.111433 0.111433i
\(943\) −0.0782772 0.0782772i −0.00254906 0.00254906i
\(944\) 5.51112 + 5.51112i 0.179372 + 0.179372i
\(945\) 0 0
\(946\) 5.83965i 0.189863i
\(947\) 19.4568 19.4568i 0.632261 0.632261i −0.316374 0.948635i \(-0.602465\pi\)
0.948635 + 0.316374i \(0.102465\pi\)
\(948\) −7.05505 −0.229137
\(949\) 26.7107 30.9820i 0.867066 1.00572i
\(950\) 6.78336i 0.220081i
\(951\) −4.03834 + 4.03834i −0.130952 + 0.130952i
\(952\) 0 0
\(953\) 16.2238i 0.525541i −0.964858 0.262771i \(-0.915364\pi\)
0.964858 0.262771i \(-0.0846362\pi\)
\(954\) −10.2238 10.2238i −0.331007 0.331007i
\(955\) 17.8568 17.8568i 0.577831 0.577831i
\(956\) 26.2256 26.2256i 0.848197 0.848197i
\(957\) −3.65508 3.65508i −0.118152 0.118152i
\(958\) 25.5127i 0.824276i
\(959\) 0 0
\(960\) −1.87344 + 1.87344i −0.0604652 + 0.0604652i
\(961\) 3.77681i 0.121833i
\(962\) 1.28518 + 17.3591i 0.0414359 + 0.559680i
\(963\) 6.23341 0.200869
\(964\) 9.72113 9.72113i 0.313097 0.313097i
\(965\) 44.5398i 1.43379i
\(966\) 0 0
\(967\) 18.2029 + 18.2029i 0.585366 + 0.585366i 0.936373 0.351007i \(-0.114161\pi\)
−0.351007 + 0.936373i \(0.614161\pi\)
\(968\) 18.4984 + 18.4984i 0.594561 + 0.594561i
\(969\) 9.41653 + 9.41653i 0.302503 + 0.302503i
\(970\) 3.51392 3.51392i 0.112825 0.112825i
\(971\) 41.8891i 1.34428i 0.740422 + 0.672142i \(0.234626\pi\)
−0.740422 + 0.672142i \(0.765374\pi\)
\(972\) 16.5421 0.530588
\(973\) 0 0
\(974\) 4.77939i 0.153142i
\(975\) −0.216530 2.92470i −0.00693452 0.0936654i
\(976\) 1.01025i 0.0323374i
\(977\) −10.4217 10.4217i −0.333420 0.333420i 0.520464 0.853884i \(-0.325759\pi\)
−0.853884 + 0.520464i \(0.825759\pi\)
\(978\) 0.369548i 0.0118169i
\(979\) 7.96256 0.254485
\(980\) 0 0
\(981\) 3.18147 + 3.18147i 0.101576 + 0.101576i
\(982\) 18.2605 18.2605i 0.582717 0.582717i
\(983\) 14.2126 + 14.2126i 0.453312 + 0.453312i 0.896452 0.443140i \(-0.146136\pi\)
−0.443140 + 0.896452i \(0.646136\pi\)
\(984\) 0.168076 0.00535806
\(985\) 37.0148 1.17939
\(986\) 29.4017 + 29.4017i 0.936340 + 0.936340i
\(987\) 0 0
\(988\) 17.3597 20.1357i 0.552285 0.640600i
\(989\) 6.21566 0.197647
\(990\) 2.82595 2.82595i 0.0898147 0.0898147i
\(991\) −27.0650 −0.859747 −0.429873 0.902889i \(-0.641442\pi\)
−0.429873 + 0.902889i \(0.641442\pi\)
\(992\) 34.5396 1.09663
\(993\) 9.33927 9.33927i 0.296373 0.296373i
\(994\) 0 0
\(995\) 19.1186 19.1186i 0.606100 0.606100i
\(996\) 2.84923 2.84923i 0.0902814 0.0902814i
\(997\) 28.3372i 0.897449i 0.893670 + 0.448725i \(0.148122\pi\)
−0.893670 + 0.448725i \(0.851878\pi\)
\(998\) 11.4854i 0.363564i
\(999\) 12.3997 + 12.3997i 0.392310 + 0.392310i
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 637.2.i.a.489.10 32
7.2 even 3 91.2.bb.a.73.5 yes 32
7.3 odd 6 91.2.bb.a.47.4 yes 32
7.4 even 3 637.2.bc.b.411.4 32
7.5 odd 6 637.2.bc.b.619.5 32
7.6 odd 2 inner 637.2.i.a.489.9 32
13.5 odd 4 inner 637.2.i.a.538.10 32
21.2 odd 6 819.2.fn.e.73.4 32
21.17 even 6 819.2.fn.e.775.5 32
91.5 even 12 637.2.bc.b.31.4 32
91.18 odd 12 637.2.bc.b.460.5 32
91.31 even 12 91.2.bb.a.5.5 32
91.44 odd 12 91.2.bb.a.31.4 yes 32
91.83 even 4 inner 637.2.i.a.538.9 32
273.44 even 12 819.2.fn.e.577.5 32
273.122 odd 12 819.2.fn.e.460.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.bb.a.5.5 32 91.31 even 12
91.2.bb.a.31.4 yes 32 91.44 odd 12
91.2.bb.a.47.4 yes 32 7.3 odd 6
91.2.bb.a.73.5 yes 32 7.2 even 3
637.2.i.a.489.9 32 7.6 odd 2 inner
637.2.i.a.489.10 32 1.1 even 1 trivial
637.2.i.a.538.9 32 91.83 even 4 inner
637.2.i.a.538.10 32 13.5 odd 4 inner
637.2.bc.b.31.4 32 91.5 even 12
637.2.bc.b.411.4 32 7.4 even 3
637.2.bc.b.460.5 32 91.18 odd 12
637.2.bc.b.619.5 32 7.5 odd 6
819.2.fn.e.73.4 32 21.2 odd 6
819.2.fn.e.460.4 32 273.122 odd 12
819.2.fn.e.577.5 32 273.44 even 12
819.2.fn.e.775.5 32 21.17 even 6