Properties

Label 950.2.bb.d.243.2
Level $950$
Weight $2$
Character 950.243
Analytic conductor $7.586$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(143,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([27, 34]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bb (of order \(36\), degree \(12\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(8\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 243.2
Character \(\chi\) \(=\) 950.243
Dual form 950.2.bb.d.907.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.422618 - 0.906308i) q^{2} +(-1.05824 - 0.740990i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.224332 + 1.27225i) q^{6} +(1.24089 + 4.63106i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.455247 - 1.25078i) q^{9} +O(q^{10})\) \(q+(-0.422618 - 0.906308i) q^{2} +(-1.05824 - 0.740990i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.224332 + 1.27225i) q^{6} +(1.24089 + 4.63106i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.455247 - 1.25078i) q^{9} +(-0.369087 - 0.639278i) q^{11} +(1.24786 - 0.334362i) q^{12} +(0.909977 + 1.29958i) q^{13} +(3.67274 - 3.08179i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-6.21911 + 2.90002i) q^{17} +(-0.941197 + 0.941197i) q^{18} +(-3.02046 - 3.14274i) q^{19} +(2.11841 - 5.82027i) q^{21} +(-0.423400 + 0.604678i) q^{22} +(-0.682725 - 7.80358i) q^{23} +(-0.830403 - 0.989635i) q^{24} +(0.793248 - 1.37395i) q^{26} +(-1.44814 + 5.40454i) q^{27} +(-4.34522 - 2.02621i) q^{28} +(7.82931 - 2.84963i) q^{29} +(-8.87983 - 5.12677i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(-0.0831144 + 0.950002i) q^{33} +(5.25662 + 4.41082i) q^{34} +(1.25078 + 0.455247i) q^{36} +(-1.67273 - 1.67273i) q^{37} +(-1.57179 + 4.06565i) q^{38} -2.04956i q^{39} +(-3.65748 + 0.644912i) q^{41} +(-6.17023 + 0.539825i) q^{42} +(-8.17682 - 0.715379i) q^{43} +(0.726960 + 0.128183i) q^{44} +(-6.78391 + 3.91669i) q^{46} +(0.795897 - 1.70681i) q^{47} +(-0.545971 + 1.17084i) q^{48} +(-13.8447 + 7.99324i) q^{49} +(8.73021 + 1.53937i) q^{51} +(-1.58046 - 0.138272i) q^{52} +(1.09996 - 0.0962340i) q^{53} +(5.51019 - 0.971594i) q^{54} +4.79442i q^{56} +(0.867643 + 5.56392i) q^{57} +(-5.89145 - 5.89145i) q^{58} +(-6.79262 - 2.47231i) q^{59} +(-0.548135 - 0.459940i) q^{61} +(-0.893656 + 10.2145i) q^{62} +(5.22753 - 3.66035i) q^{63} +(0.866025 + 0.500000i) q^{64} +(0.896120 - 0.326161i) q^{66} +(2.22487 + 1.03748i) q^{67} +(1.77602 - 6.62821i) q^{68} +(-5.05989 + 8.76398i) q^{69} +(5.62222 + 6.70030i) q^{71} +(-0.116009 - 1.32599i) q^{72} +(-1.93495 + 2.76339i) q^{73} +(-0.809081 + 2.22293i) q^{74} +(4.34899 - 0.293692i) q^{76} +(2.50254 - 2.50254i) q^{77} +(-1.85753 + 0.866180i) q^{78} +(2.39694 + 13.5937i) q^{79} +(2.47826 - 2.07950i) q^{81} +(2.13021 + 3.04225i) q^{82} +(-7.25260 + 1.94333i) q^{83} +(3.09690 + 5.36399i) q^{84} +(2.80732 + 7.71305i) q^{86} +(-10.3969 - 2.78583i) q^{87} +(-0.191054 - 0.713022i) q^{88} +(1.32080 - 7.49061i) q^{89} +(-4.88925 + 5.82679i) q^{91} +(6.41674 + 4.49305i) q^{92} +(5.59814 + 12.0052i) q^{93} -1.88325 q^{94} +1.29188 q^{96} +(0.918712 + 1.97018i) q^{97} +(13.0954 + 9.16946i) q^{98} +(-0.631571 + 0.752677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{11}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.422618 0.906308i −0.298836 0.640856i
\(3\) −1.05824 0.740990i −0.610977 0.427811i 0.226709 0.973963i \(-0.427203\pi\)
−0.837686 + 0.546152i \(0.816092\pi\)
\(4\) −0.642788 + 0.766044i −0.321394 + 0.383022i
\(5\) 0 0
\(6\) −0.224332 + 1.27225i −0.0915832 + 0.519394i
\(7\) 1.24089 + 4.63106i 0.469011 + 1.75037i 0.643236 + 0.765668i \(0.277592\pi\)
−0.174224 + 0.984706i \(0.555742\pi\)
\(8\) 0.965926 + 0.258819i 0.341506 + 0.0915064i
\(9\) −0.455247 1.25078i −0.151749 0.416927i
\(10\) 0 0
\(11\) −0.369087 0.639278i −0.111284 0.192750i 0.805004 0.593269i \(-0.202163\pi\)
−0.916288 + 0.400519i \(0.868830\pi\)
\(12\) 1.24786 0.334362i 0.360225 0.0965221i
\(13\) 0.909977 + 1.29958i 0.252382 + 0.360439i 0.925272 0.379303i \(-0.123836\pi\)
−0.672890 + 0.739742i \(0.734947\pi\)
\(14\) 3.67274 3.08179i 0.981581 0.823644i
\(15\) 0 0
\(16\) −0.173648 0.984808i −0.0434120 0.246202i
\(17\) −6.21911 + 2.90002i −1.50835 + 0.703357i −0.988545 0.150925i \(-0.951775\pi\)
−0.519810 + 0.854282i \(0.673997\pi\)
\(18\) −0.941197 + 0.941197i −0.221842 + 0.221842i
\(19\) −3.02046 3.14274i −0.692941 0.720994i
\(20\) 0 0
\(21\) 2.11841 5.82027i 0.462274 1.27009i
\(22\) −0.423400 + 0.604678i −0.0902691 + 0.128918i
\(23\) −0.682725 7.80358i −0.142358 1.62716i −0.646064 0.763284i \(-0.723586\pi\)
0.503706 0.863875i \(-0.331970\pi\)
\(24\) −0.830403 0.989635i −0.169505 0.202008i
\(25\) 0 0
\(26\) 0.793248 1.37395i 0.155569 0.269453i
\(27\) −1.44814 + 5.40454i −0.278695 + 1.04010i
\(28\) −4.34522 2.02621i −0.821170 0.382918i
\(29\) 7.82931 2.84963i 1.45387 0.529164i 0.510197 0.860057i \(-0.329572\pi\)
0.943668 + 0.330894i \(0.107350\pi\)
\(30\) 0 0
\(31\) −8.87983 5.12677i −1.59487 0.920796i −0.992455 0.122609i \(-0.960874\pi\)
−0.602410 0.798187i \(-0.705793\pi\)
\(32\) −0.819152 + 0.573576i −0.144807 + 0.101395i
\(33\) −0.0831144 + 0.950002i −0.0144684 + 0.165374i
\(34\) 5.25662 + 4.41082i 0.901502 + 0.756450i
\(35\) 0 0
\(36\) 1.25078 + 0.455247i 0.208464 + 0.0758745i
\(37\) −1.67273 1.67273i −0.274995 0.274995i 0.556112 0.831107i \(-0.312292\pi\)
−0.831107 + 0.556112i \(0.812292\pi\)
\(38\) −1.57179 + 4.06565i −0.254978 + 0.659535i
\(39\) 2.04956i 0.328192i
\(40\) 0 0
\(41\) −3.65748 + 0.644912i −0.571202 + 0.100718i −0.451787 0.892126i \(-0.649213\pi\)
−0.119416 + 0.992844i \(0.538102\pi\)
\(42\) −6.17023 + 0.539825i −0.952088 + 0.0832969i
\(43\) −8.17682 0.715379i −1.24695 0.109094i −0.555501 0.831516i \(-0.687473\pi\)
−0.691453 + 0.722422i \(0.743029\pi\)
\(44\) 0.726960 + 0.128183i 0.109593 + 0.0193243i
\(45\) 0 0
\(46\) −6.78391 + 3.91669i −1.00023 + 0.577485i
\(47\) 0.795897 1.70681i 0.116094 0.248963i −0.839672 0.543095i \(-0.817252\pi\)
0.955765 + 0.294131i \(0.0950303\pi\)
\(48\) −0.545971 + 1.17084i −0.0788041 + 0.168996i
\(49\) −13.8447 + 7.99324i −1.97781 + 1.14189i
\(50\) 0 0
\(51\) 8.73021 + 1.53937i 1.22247 + 0.215555i
\(52\) −1.58046 0.138272i −0.219170 0.0191749i
\(53\) 1.09996 0.0962340i 0.151091 0.0132188i −0.0113592 0.999935i \(-0.503616\pi\)
0.162450 + 0.986717i \(0.448060\pi\)
\(54\) 5.51019 0.971594i 0.749841 0.132217i
\(55\) 0 0
\(56\) 4.79442i 0.640681i
\(57\) 0.867643 + 5.56392i 0.114922 + 0.736959i
\(58\) −5.89145 5.89145i −0.773586 0.773586i
\(59\) −6.79262 2.47231i −0.884323 0.321867i −0.140370 0.990099i \(-0.544829\pi\)
−0.743953 + 0.668232i \(0.767051\pi\)
\(60\) 0 0
\(61\) −0.548135 0.459940i −0.0701815 0.0588893i 0.607022 0.794685i \(-0.292364\pi\)
−0.677204 + 0.735796i \(0.736808\pi\)
\(62\) −0.893656 + 10.2145i −0.113494 + 1.29725i
\(63\) 5.22753 3.66035i 0.658607 0.461161i
\(64\) 0.866025 + 0.500000i 0.108253 + 0.0625000i
\(65\) 0 0
\(66\) 0.896120 0.326161i 0.110305 0.0401477i
\(67\) 2.22487 + 1.03748i 0.271812 + 0.126748i 0.553745 0.832686i \(-0.313198\pi\)
−0.281934 + 0.959434i \(0.590976\pi\)
\(68\) 1.77602 6.62821i 0.215374 0.803788i
\(69\) −5.05989 + 8.76398i −0.609139 + 1.05506i
\(70\) 0 0
\(71\) 5.62222 + 6.70030i 0.667234 + 0.795179i 0.988405 0.151842i \(-0.0485206\pi\)
−0.321170 + 0.947021i \(0.604076\pi\)
\(72\) −0.116009 1.32599i −0.0136718 0.156269i
\(73\) −1.93495 + 2.76339i −0.226468 + 0.323430i −0.916265 0.400573i \(-0.868811\pi\)
0.689797 + 0.724003i \(0.257700\pi\)
\(74\) −0.809081 + 2.22293i −0.0940537 + 0.258411i
\(75\) 0 0
\(76\) 4.34899 0.293692i 0.498864 0.0336888i
\(77\) 2.50254 2.50254i 0.285191 0.285191i
\(78\) −1.85753 + 0.866180i −0.210324 + 0.0980756i
\(79\) 2.39694 + 13.5937i 0.269676 + 1.52941i 0.755380 + 0.655287i \(0.227452\pi\)
−0.485704 + 0.874124i \(0.661437\pi\)
\(80\) 0 0
\(81\) 2.47826 2.07950i 0.275362 0.231056i
\(82\) 2.13021 + 3.04225i 0.235242 + 0.335960i
\(83\) −7.25260 + 1.94333i −0.796076 + 0.213308i −0.633861 0.773447i \(-0.718531\pi\)
−0.162216 + 0.986755i \(0.551864\pi\)
\(84\) 3.09690 + 5.36399i 0.337900 + 0.585259i
\(85\) 0 0
\(86\) 2.80732 + 7.71305i 0.302721 + 0.831720i
\(87\) −10.3969 2.78583i −1.11466 0.298672i
\(88\) −0.191054 0.713022i −0.0203664 0.0760084i
\(89\) 1.32080 7.49061i 0.140004 0.794003i −0.831239 0.555915i \(-0.812368\pi\)
0.971243 0.238088i \(-0.0765208\pi\)
\(90\) 0 0
\(91\) −4.88925 + 5.82679i −0.512533 + 0.610813i
\(92\) 6.41674 + 4.49305i 0.668991 + 0.468433i
\(93\) 5.59814 + 12.0052i 0.580500 + 1.24489i
\(94\) −1.88325 −0.194243
\(95\) 0 0
\(96\) 1.29188 0.131852
\(97\) 0.918712 + 1.97018i 0.0932811 + 0.200042i 0.947412 0.320016i \(-0.103688\pi\)
−0.854131 + 0.520058i \(0.825910\pi\)
\(98\) 13.0954 + 9.16946i 1.32283 + 0.926256i
\(99\) −0.631571 + 0.752677i −0.0634753 + 0.0756469i
\(100\) 0 0
\(101\) 0.747923 4.24168i 0.0744211 0.422063i −0.924721 0.380646i \(-0.875702\pi\)
0.999142 0.0414171i \(-0.0131873\pi\)
\(102\) −2.29440 8.56283i −0.227180 0.847846i
\(103\) −12.2405 3.27983i −1.20609 0.323171i −0.400865 0.916137i \(-0.631290\pi\)
−0.805228 + 0.592966i \(0.797957\pi\)
\(104\) 0.542613 + 1.49082i 0.0532076 + 0.146187i
\(105\) 0 0
\(106\) −0.552081 0.956232i −0.0536228 0.0928775i
\(107\) 4.16763 1.11671i 0.402900 0.107957i −0.0516776 0.998664i \(-0.516457\pi\)
0.454578 + 0.890707i \(0.349790\pi\)
\(108\) −3.20927 4.58331i −0.308812 0.441029i
\(109\) −2.13296 + 1.78976i −0.204300 + 0.171428i −0.739197 0.673489i \(-0.764795\pi\)
0.534897 + 0.844917i \(0.320350\pi\)
\(110\) 0 0
\(111\) 0.530679 + 3.00963i 0.0503698 + 0.285661i
\(112\) 4.34522 2.02621i 0.410585 0.191459i
\(113\) 3.54197 3.54197i 0.333200 0.333200i −0.520600 0.853800i \(-0.674292\pi\)
0.853800 + 0.520600i \(0.174292\pi\)
\(114\) 4.67594 3.13776i 0.437942 0.293879i
\(115\) 0 0
\(116\) −2.84963 + 7.82931i −0.264582 + 0.726933i
\(117\) 1.21123 1.72981i 0.111978 0.159921i
\(118\) 0.630010 + 7.20104i 0.0579971 + 0.662910i
\(119\) −21.1474 25.2024i −1.93857 2.31030i
\(120\) 0 0
\(121\) 5.22755 9.05438i 0.475232 0.823125i
\(122\) −0.185195 + 0.691158i −0.0167668 + 0.0625745i
\(123\) 4.34838 + 2.02768i 0.392080 + 0.182830i
\(124\) 9.63518 3.50692i 0.865265 0.314931i
\(125\) 0 0
\(126\) −5.52666 3.19082i −0.492354 0.284261i
\(127\) −12.0101 + 8.40959i −1.06573 + 0.746231i −0.968495 0.249031i \(-0.919888\pi\)
−0.0972323 + 0.995262i \(0.530999\pi\)
\(128\) 0.0871557 0.996195i 0.00770355 0.0880520i
\(129\) 8.12298 + 6.81599i 0.715189 + 0.600115i
\(130\) 0 0
\(131\) −12.8132 4.66362i −1.11949 0.407462i −0.285026 0.958520i \(-0.592002\pi\)
−0.834468 + 0.551057i \(0.814225\pi\)
\(132\) −0.674319 0.674319i −0.0586919 0.0586919i
\(133\) 10.8062 17.8877i 0.937012 1.55106i
\(134\) 2.45488i 0.212069i
\(135\) 0 0
\(136\) −6.75778 + 1.19158i −0.579474 + 0.102177i
\(137\) −4.44500 + 0.388887i −0.379762 + 0.0332249i −0.275439 0.961319i \(-0.588823\pi\)
−0.104323 + 0.994543i \(0.533268\pi\)
\(138\) 10.0813 + 0.881996i 0.858174 + 0.0750805i
\(139\) −8.03402 1.41661i −0.681436 0.120156i −0.177794 0.984068i \(-0.556896\pi\)
−0.503643 + 0.863912i \(0.668007\pi\)
\(140\) 0 0
\(141\) −2.10698 + 1.21647i −0.177440 + 0.102445i
\(142\) 3.69648 7.92713i 0.310202 0.665230i
\(143\) 0.494933 1.06139i 0.0413884 0.0887577i
\(144\) −1.15273 + 0.665527i −0.0960605 + 0.0554606i
\(145\) 0 0
\(146\) 3.32222 + 0.585798i 0.274949 + 0.0484810i
\(147\) 20.5740 + 1.79999i 1.69691 + 0.148461i
\(148\) 2.35659 0.206175i 0.193711 0.0169475i
\(149\) 15.0889 2.66058i 1.23613 0.217964i 0.482875 0.875689i \(-0.339592\pi\)
0.753258 + 0.657726i \(0.228481\pi\)
\(150\) 0 0
\(151\) 3.73791i 0.304187i −0.988366 0.152093i \(-0.951399\pi\)
0.988366 0.152093i \(-0.0486015\pi\)
\(152\) −2.10414 3.81741i −0.170668 0.309633i
\(153\) 6.45852 + 6.45852i 0.522140 + 0.522140i
\(154\) −3.32569 1.21045i −0.267991 0.0975409i
\(155\) 0 0
\(156\) 1.57005 + 1.31743i 0.125705 + 0.105479i
\(157\) 1.74862 19.9868i 0.139555 1.59512i −0.527131 0.849784i \(-0.676732\pi\)
0.666686 0.745338i \(-0.267712\pi\)
\(158\) 11.3071 7.91731i 0.899543 0.629867i
\(159\) −1.23533 0.713221i −0.0979684 0.0565621i
\(160\) 0 0
\(161\) 35.2916 12.8451i 2.78137 1.01234i
\(162\) −2.93203 1.36723i −0.230362 0.107419i
\(163\) −2.86904 + 10.7074i −0.224721 + 0.838669i 0.757796 + 0.652492i \(0.226276\pi\)
−0.982516 + 0.186177i \(0.940390\pi\)
\(164\) 1.85695 3.21633i 0.145003 0.251153i
\(165\) 0 0
\(166\) 4.82633 + 5.75180i 0.374596 + 0.446426i
\(167\) −1.36812 15.6376i −0.105868 1.21008i −0.844345 0.535799i \(-0.820010\pi\)
0.738477 0.674278i \(-0.235545\pi\)
\(168\) 3.55262 5.07367i 0.274091 0.391442i
\(169\) 3.58541 9.85083i 0.275801 0.757756i
\(170\) 0 0
\(171\) −2.55583 + 5.20866i −0.195449 + 0.398316i
\(172\) 5.80397 5.80397i 0.442549 0.442549i
\(173\) −17.6944 + 8.25103i −1.34528 + 0.627314i −0.955881 0.293755i \(-0.905095\pi\)
−0.389399 + 0.921069i \(0.627317\pi\)
\(174\) 1.86908 + 10.6001i 0.141695 + 0.803592i
\(175\) 0 0
\(176\) −0.565475 + 0.474490i −0.0426243 + 0.0357660i
\(177\) 5.35629 + 7.64957i 0.402603 + 0.574977i
\(178\) −7.34699 + 1.96862i −0.550680 + 0.147554i
\(179\) 10.3573 + 17.9393i 0.774139 + 1.34085i 0.935277 + 0.353916i \(0.115150\pi\)
−0.161138 + 0.986932i \(0.551517\pi\)
\(180\) 0 0
\(181\) 5.45026 + 14.9745i 0.405115 + 1.11304i 0.959727 + 0.280934i \(0.0906443\pi\)
−0.554612 + 0.832109i \(0.687133\pi\)
\(182\) 7.34715 + 1.96866i 0.544607 + 0.145927i
\(183\) 0.239250 + 0.892892i 0.0176858 + 0.0660045i
\(184\) 1.36025 7.71438i 0.100279 0.568712i
\(185\) 0 0
\(186\) 8.51457 10.1473i 0.624319 0.744034i
\(187\) 4.14931 + 2.90538i 0.303428 + 0.212462i
\(188\) 0.795897 + 1.70681i 0.0580468 + 0.124482i
\(189\) −26.8257 −1.95128
\(190\) 0 0
\(191\) −16.3996 −1.18663 −0.593317 0.804969i \(-0.702182\pi\)
−0.593317 + 0.804969i \(0.702182\pi\)
\(192\) −0.545971 1.17084i −0.0394020 0.0844980i
\(193\) −7.48324 5.23982i −0.538655 0.377171i 0.272360 0.962195i \(-0.412196\pi\)
−0.811015 + 0.585025i \(0.801085\pi\)
\(194\) 1.39733 1.66527i 0.100322 0.119560i
\(195\) 0 0
\(196\) 2.77602 15.7436i 0.198287 1.12454i
\(197\) −0.656151 2.44879i −0.0467488 0.174469i 0.938604 0.344996i \(-0.112120\pi\)
−0.985353 + 0.170527i \(0.945453\pi\)
\(198\) 0.949071 + 0.254303i 0.0674475 + 0.0180725i
\(199\) −3.14532 8.64168i −0.222966 0.612593i 0.776889 0.629637i \(-0.216797\pi\)
−0.999855 + 0.0170446i \(0.994574\pi\)
\(200\) 0 0
\(201\) −1.58570 2.74651i −0.111847 0.193724i
\(202\) −4.16036 + 1.11476i −0.292722 + 0.0784345i
\(203\) 22.9121 + 32.7219i 1.60811 + 2.29663i
\(204\) −6.79090 + 5.69824i −0.475458 + 0.398957i
\(205\) 0 0
\(206\) 2.20052 + 12.4798i 0.153318 + 0.869507i
\(207\) −9.44976 + 4.40650i −0.656804 + 0.306273i
\(208\) 1.12182 1.12182i 0.0777844 0.0777844i
\(209\) −0.894272 + 3.09086i −0.0618581 + 0.213799i
\(210\) 0 0
\(211\) −5.10066 + 14.0139i −0.351144 + 0.964760i 0.630860 + 0.775897i \(0.282702\pi\)
−0.982004 + 0.188863i \(0.939520\pi\)
\(212\) −0.633321 + 0.904476i −0.0434967 + 0.0621197i
\(213\) −0.984821 11.2566i −0.0674788 0.771286i
\(214\) −2.77340 3.30521i −0.189586 0.225940i
\(215\) 0 0
\(216\) −2.79759 + 4.84558i −0.190352 + 0.329700i
\(217\) 12.7235 47.4847i 0.863727 3.22347i
\(218\) 2.52350 + 1.17673i 0.170913 + 0.0796981i
\(219\) 4.09529 1.49056i 0.276734 0.100723i
\(220\) 0 0
\(221\) −9.42805 5.44329i −0.634199 0.366155i
\(222\) 2.50338 1.75288i 0.168016 0.117646i
\(223\) 0.0425390 0.486223i 0.00284862 0.0325599i −0.994637 0.103424i \(-0.967020\pi\)
0.997486 + 0.0708642i \(0.0225757\pi\)
\(224\) −3.67274 3.08179i −0.245395 0.205911i
\(225\) 0 0
\(226\) −4.70701 1.71321i −0.313106 0.113961i
\(227\) 4.99910 + 4.99910i 0.331802 + 0.331802i 0.853271 0.521468i \(-0.174616\pi\)
−0.521468 + 0.853271i \(0.674616\pi\)
\(228\) −4.81992 2.91176i −0.319207 0.192836i
\(229\) 1.37503i 0.0908645i 0.998967 + 0.0454323i \(0.0144665\pi\)
−0.998967 + 0.0454323i \(0.985533\pi\)
\(230\) 0 0
\(231\) −4.50265 + 0.793939i −0.296253 + 0.0522373i
\(232\) 8.30007 0.726162i 0.544926 0.0476749i
\(233\) 3.29263 + 0.288068i 0.215707 + 0.0188719i 0.194497 0.980903i \(-0.437693\pi\)
0.0212102 + 0.999775i \(0.493248\pi\)
\(234\) −2.07963 0.366695i −0.135950 0.0239716i
\(235\) 0 0
\(236\) 6.26011 3.61428i 0.407498 0.235269i
\(237\) 7.53626 16.1616i 0.489532 1.04981i
\(238\) −13.9039 + 29.8170i −0.901256 + 1.93275i
\(239\) 16.2393 9.37579i 1.05044 0.606469i 0.127665 0.991817i \(-0.459252\pi\)
0.922771 + 0.385348i \(0.125919\pi\)
\(240\) 0 0
\(241\) 7.15659 + 1.26190i 0.460997 + 0.0812861i 0.399323 0.916810i \(-0.369245\pi\)
0.0616734 + 0.998096i \(0.480356\pi\)
\(242\) −10.4153 0.911222i −0.669522 0.0585756i
\(243\) 12.5582 1.09870i 0.805609 0.0704817i
\(244\) 0.704669 0.124252i 0.0451118 0.00795443i
\(245\) 0 0
\(246\) 4.79790i 0.305903i
\(247\) 1.33570 6.78515i 0.0849885 0.431729i
\(248\) −7.25035 7.25035i −0.460398 0.460398i
\(249\) 9.11500 + 3.31759i 0.577640 + 0.210244i
\(250\) 0 0
\(251\) −4.00381 3.35960i −0.252718 0.212056i 0.507623 0.861579i \(-0.330524\pi\)
−0.760342 + 0.649523i \(0.774969\pi\)
\(252\) −0.556196 + 6.35735i −0.0350371 + 0.400475i
\(253\) −4.73667 + 3.31665i −0.297792 + 0.208516i
\(254\) 12.6974 + 7.33084i 0.796705 + 0.459978i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) 8.07977 + 3.76766i 0.504002 + 0.235020i 0.657954 0.753058i \(-0.271422\pi\)
−0.153951 + 0.988078i \(0.549200\pi\)
\(258\) 2.74447 10.2425i 0.170863 0.637669i
\(259\) 5.67083 9.82216i 0.352368 0.610319i
\(260\) 0 0
\(261\) −7.12854 8.49546i −0.441245 0.525856i
\(262\) 1.18841 + 13.5836i 0.0734204 + 0.839199i
\(263\) 15.1892 21.6924i 0.936603 1.33761i −0.00467925 0.999989i \(-0.501489\pi\)
0.941283 0.337619i \(-0.109622\pi\)
\(264\) −0.326161 + 0.896120i −0.0200738 + 0.0551524i
\(265\) 0 0
\(266\) −20.7786 2.23403i −1.27402 0.136977i
\(267\) −6.94820 + 6.94820i −0.425223 + 0.425223i
\(268\) −2.22487 + 1.03748i −0.135906 + 0.0633739i
\(269\) 3.78473 + 21.4643i 0.230759 + 1.30870i 0.851364 + 0.524576i \(0.175776\pi\)
−0.620604 + 0.784124i \(0.713113\pi\)
\(270\) 0 0
\(271\) 5.26450 4.41744i 0.319796 0.268340i −0.468731 0.883341i \(-0.655289\pi\)
0.788527 + 0.615001i \(0.210844\pi\)
\(272\) 3.93590 + 5.62104i 0.238649 + 0.340826i
\(273\) 9.49161 2.54327i 0.574459 0.153926i
\(274\) 2.23099 + 3.86419i 0.134779 + 0.233444i
\(275\) 0 0
\(276\) −3.46117 9.50948i −0.208338 0.572403i
\(277\) 24.5430 + 6.57627i 1.47464 + 0.395130i 0.904521 0.426430i \(-0.140229\pi\)
0.570123 + 0.821559i \(0.306896\pi\)
\(278\) 2.11143 + 7.87998i 0.126635 + 0.472610i
\(279\) −2.36995 + 13.4407i −0.141885 + 0.804673i
\(280\) 0 0
\(281\) 4.32831 5.15828i 0.258206 0.307717i −0.621331 0.783548i \(-0.713408\pi\)
0.879537 + 0.475830i \(0.157852\pi\)
\(282\) 1.99294 + 1.39547i 0.118678 + 0.0830992i
\(283\) 9.15872 + 19.6409i 0.544429 + 1.16753i 0.965476 + 0.260493i \(0.0838851\pi\)
−0.421047 + 0.907039i \(0.638337\pi\)
\(284\) −8.74662 −0.519016
\(285\) 0 0
\(286\) −1.17111 −0.0692493
\(287\) −7.52514 16.1377i −0.444195 0.952580i
\(288\) 1.09034 + 0.763461i 0.0642486 + 0.0449874i
\(289\) 19.3398 23.0483i 1.13764 1.35578i
\(290\) 0 0
\(291\) 0.487666 2.76569i 0.0285875 0.162128i
\(292\) −0.873119 3.25853i −0.0510954 0.190691i
\(293\) 7.53940 + 2.02018i 0.440457 + 0.118020i 0.472231 0.881475i \(-0.343449\pi\)
−0.0317738 + 0.999495i \(0.510116\pi\)
\(294\) −7.06359 19.4071i −0.411957 1.13184i
\(295\) 0 0
\(296\) −1.18280 2.04866i −0.0687487 0.119076i
\(297\) 3.98949 1.06898i 0.231494 0.0620286i
\(298\) −8.78816 12.5508i −0.509085 0.727048i
\(299\) 9.52012 7.98833i 0.550563 0.461977i
\(300\) 0 0
\(301\) −6.83356 38.7550i −0.393880 2.23380i
\(302\) −3.38770 + 1.57971i −0.194940 + 0.0909020i
\(303\) −3.93453 + 3.93453i −0.226033 + 0.226033i
\(304\) −2.57050 + 3.52030i −0.147428 + 0.201903i
\(305\) 0 0
\(306\) 3.12392 8.58289i 0.178582 0.490651i
\(307\) 3.06414 4.37604i 0.174879 0.249754i −0.722138 0.691749i \(-0.756840\pi\)
0.897017 + 0.441995i \(0.145729\pi\)
\(308\) 0.308455 + 3.52565i 0.0175758 + 0.200893i
\(309\) 10.5231 + 12.5410i 0.598639 + 0.713430i
\(310\) 0 0
\(311\) −8.01772 + 13.8871i −0.454643 + 0.787465i −0.998668 0.0516042i \(-0.983567\pi\)
0.544024 + 0.839069i \(0.316900\pi\)
\(312\) 0.530464 1.97972i 0.0300316 0.112080i
\(313\) −18.4778 8.61636i −1.04443 0.487025i −0.176805 0.984246i \(-0.556576\pi\)
−0.867624 + 0.497221i \(0.834354\pi\)
\(314\) −18.8532 + 6.86201i −1.06395 + 0.387246i
\(315\) 0 0
\(316\) −11.9541 6.90170i −0.672471 0.388251i
\(317\) −15.6247 + 10.9405i −0.877570 + 0.614481i −0.923133 0.384480i \(-0.874381\pi\)
0.0455628 + 0.998961i \(0.485492\pi\)
\(318\) −0.124323 + 1.42101i −0.00697166 + 0.0796865i
\(319\) −4.71141 3.95334i −0.263788 0.221345i
\(320\) 0 0
\(321\) −5.23784 1.90642i −0.292348 0.106406i
\(322\) −26.5565 26.5565i −1.47994 1.47994i
\(323\) 27.8986 + 10.7857i 1.55232 + 0.600130i
\(324\) 3.23513i 0.179730i
\(325\) 0 0
\(326\) 10.9167 1.92491i 0.604621 0.106611i
\(327\) 3.58338 0.313505i 0.198162 0.0173369i
\(328\) −3.69977 0.323688i −0.204286 0.0178727i
\(329\) 8.89194 + 1.56789i 0.490228 + 0.0864405i
\(330\) 0 0
\(331\) −27.5761 + 15.9211i −1.51572 + 0.875101i −0.515889 + 0.856655i \(0.672538\pi\)
−0.999830 + 0.0184452i \(0.994128\pi\)
\(332\) 3.17321 6.80496i 0.174152 0.373471i
\(333\) −1.33071 + 2.85372i −0.0729226 + 0.156383i
\(334\) −13.5943 + 7.84869i −0.743849 + 0.429461i
\(335\) 0 0
\(336\) −6.09970 1.07554i −0.332766 0.0586757i
\(337\) −19.2699 1.68590i −1.04970 0.0918366i −0.450770 0.892640i \(-0.648851\pi\)
−0.598927 + 0.800803i \(0.704406\pi\)
\(338\) −10.4431 + 0.913656i −0.568032 + 0.0496964i
\(339\) −6.37283 + 1.12370i −0.346124 + 0.0610311i
\(340\) 0 0
\(341\) 7.56891i 0.409880i
\(342\) 5.80079 + 0.115090i 0.313671 + 0.00622335i
\(343\) −30.4657 30.4657i −1.64499 1.64499i
\(344\) −7.71305 2.80732i −0.415860 0.151361i
\(345\) 0 0
\(346\) 14.9559 + 12.5495i 0.804036 + 0.674667i
\(347\) −1.41010 + 16.1175i −0.0756980 + 0.865233i 0.859507 + 0.511125i \(0.170771\pi\)
−0.935205 + 0.354108i \(0.884785\pi\)
\(348\) 8.81705 6.17376i 0.472643 0.330948i
\(349\) 24.2367 + 13.9931i 1.29736 + 0.749032i 0.979948 0.199254i \(-0.0638520\pi\)
0.317414 + 0.948287i \(0.397185\pi\)
\(350\) 0 0
\(351\) −8.34141 + 3.03602i −0.445232 + 0.162051i
\(352\) 0.669014 + 0.311966i 0.0356586 + 0.0166279i
\(353\) 1.98751 7.41748i 0.105784 0.394792i −0.892649 0.450753i \(-0.851155\pi\)
0.998433 + 0.0559606i \(0.0178221\pi\)
\(354\) 4.66920 8.08729i 0.248165 0.429835i
\(355\) 0 0
\(356\) 4.88915 + 5.82666i 0.259124 + 0.308812i
\(357\) 3.70430 + 42.3403i 0.196052 + 2.24089i
\(358\) 11.8814 16.9684i 0.627950 0.896806i
\(359\) −6.23081 + 17.1190i −0.328849 + 0.903506i 0.659554 + 0.751657i \(0.270745\pi\)
−0.988404 + 0.151849i \(0.951477\pi\)
\(360\) 0 0
\(361\) −0.753638 + 18.9850i −0.0396652 + 0.999213i
\(362\) 11.2681 11.2681i 0.592238 0.592238i
\(363\) −12.2412 + 5.70818i −0.642498 + 0.299602i
\(364\) −1.32083 7.49077i −0.0692300 0.392623i
\(365\) 0 0
\(366\) 0.708123 0.594186i 0.0370142 0.0310586i
\(367\) −1.61068 2.30028i −0.0840766 0.120074i 0.774911 0.632071i \(-0.217795\pi\)
−0.858987 + 0.511997i \(0.828906\pi\)
\(368\) −7.56647 + 2.02743i −0.394430 + 0.105687i
\(369\) 2.47170 + 4.28111i 0.128672 + 0.222866i
\(370\) 0 0
\(371\) 1.81059 + 4.97456i 0.0940012 + 0.258266i
\(372\) −12.7950 3.42840i −0.663388 0.177754i
\(373\) −1.00013 3.73255i −0.0517850 0.193264i 0.935188 0.354153i \(-0.115231\pi\)
−0.986973 + 0.160888i \(0.948564\pi\)
\(374\) 0.879593 4.98842i 0.0454827 0.257945i
\(375\) 0 0
\(376\) 1.21053 1.44266i 0.0624284 0.0743993i
\(377\) 10.8278 + 7.58172i 0.557661 + 0.390478i
\(378\) 11.3370 + 24.3123i 0.583114 + 1.25049i
\(379\) −23.0971 −1.18642 −0.593209 0.805048i \(-0.702139\pi\)
−0.593209 + 0.805048i \(0.702139\pi\)
\(380\) 0 0
\(381\) 18.9411 0.970381
\(382\) 6.93078 + 14.8631i 0.354609 + 0.760462i
\(383\) 3.61586 + 2.53185i 0.184762 + 0.129372i 0.662298 0.749240i \(-0.269581\pi\)
−0.477536 + 0.878612i \(0.658470\pi\)
\(384\) −0.830403 + 0.989635i −0.0423763 + 0.0505021i
\(385\) 0 0
\(386\) −1.58634 + 8.99656i −0.0807424 + 0.457913i
\(387\) 2.82769 + 10.5531i 0.143740 + 0.536444i
\(388\) −2.09979 0.562636i −0.106600 0.0285635i
\(389\) 7.25446 + 19.9315i 0.367816 + 1.01057i 0.976190 + 0.216915i \(0.0695996\pi\)
−0.608375 + 0.793650i \(0.708178\pi\)
\(390\) 0 0
\(391\) 26.8765 + 46.5514i 1.35920 + 2.35420i
\(392\) −15.4417 + 4.13760i −0.779926 + 0.208981i
\(393\) 10.1038 + 14.4297i 0.509668 + 0.727882i
\(394\) −1.94205 + 1.62958i −0.0978393 + 0.0820969i
\(395\) 0 0
\(396\) −0.170618 0.967623i −0.00857388 0.0486249i
\(397\) −27.1965 + 12.6819i −1.36495 + 0.636488i −0.960554 0.278095i \(-0.910297\pi\)
−0.404399 + 0.914583i \(0.632519\pi\)
\(398\) −6.50276 + 6.50276i −0.325954 + 0.325954i
\(399\) −24.6902 + 10.9223i −1.23605 + 0.546799i
\(400\) 0 0
\(401\) −1.67191 + 4.59355i −0.0834914 + 0.229391i −0.974412 0.224768i \(-0.927838\pi\)
0.890921 + 0.454158i \(0.150060\pi\)
\(402\) −1.81904 + 2.59786i −0.0907255 + 0.129569i
\(403\) −1.41778 16.2053i −0.0706247 0.807244i
\(404\) 2.76856 + 3.29944i 0.137741 + 0.164153i
\(405\) 0 0
\(406\) 19.9730 34.5943i 0.991244 1.71688i
\(407\) −0.451956 + 1.68672i −0.0224026 + 0.0836077i
\(408\) 8.03432 + 3.74647i 0.397758 + 0.185478i
\(409\) −0.115696 + 0.0421098i −0.00572079 + 0.00208220i −0.344879 0.938647i \(-0.612080\pi\)
0.339158 + 0.940729i \(0.389858\pi\)
\(410\) 0 0
\(411\) 4.99206 + 2.88217i 0.246240 + 0.142167i
\(412\) 10.3805 7.26853i 0.511412 0.358095i
\(413\) 3.02053 34.5248i 0.148631 1.69886i
\(414\) 7.98729 + 6.70213i 0.392554 + 0.329392i
\(415\) 0 0
\(416\) −1.49082 0.542613i −0.0730934 0.0266038i
\(417\) 7.45225 + 7.45225i 0.364938 + 0.364938i
\(418\) 3.17921 0.495769i 0.155500 0.0242488i
\(419\) 34.8270i 1.70141i −0.525645 0.850704i \(-0.676176\pi\)
0.525645 0.850704i \(-0.323824\pi\)
\(420\) 0 0
\(421\) 25.0090 4.40976i 1.21886 0.214918i 0.473027 0.881048i \(-0.343161\pi\)
0.745836 + 0.666130i \(0.232050\pi\)
\(422\) 14.8566 1.29978i 0.723207 0.0632724i
\(423\) −2.49717 0.218474i −0.121417 0.0106226i
\(424\) 1.08739 + 0.191736i 0.0528082 + 0.00931151i
\(425\) 0 0
\(426\) −9.78570 + 5.64978i −0.474119 + 0.273733i
\(427\) 1.44983 3.10918i 0.0701624 0.150464i
\(428\) −1.82345 + 3.91040i −0.0881398 + 0.189016i
\(429\) −1.31024 + 0.756466i −0.0632589 + 0.0365225i
\(430\) 0 0
\(431\) 20.3683 + 3.59148i 0.981106 + 0.172995i 0.641125 0.767437i \(-0.278468\pi\)
0.339981 + 0.940432i \(0.389579\pi\)
\(432\) 5.57390 + 0.487653i 0.268174 + 0.0234622i
\(433\) 14.9466 1.30765i 0.718286 0.0628419i 0.277848 0.960625i \(-0.410379\pi\)
0.440438 + 0.897783i \(0.354823\pi\)
\(434\) −48.4130 + 8.53651i −2.32390 + 0.409766i
\(435\) 0 0
\(436\) 2.78438i 0.133347i
\(437\) −22.4625 + 25.7160i −1.07453 + 1.23016i
\(438\) −3.08165 3.08165i −0.147247 0.147247i
\(439\) 15.8421 + 5.76604i 0.756101 + 0.275198i 0.691171 0.722692i \(-0.257095\pi\)
0.0649302 + 0.997890i \(0.479318\pi\)
\(440\) 0 0
\(441\) 16.3006 + 13.6778i 0.776217 + 0.651323i
\(442\) −0.948827 + 10.8451i −0.0451311 + 0.515851i
\(443\) −4.94246 + 3.46075i −0.234823 + 0.164425i −0.685066 0.728481i \(-0.740226\pi\)
0.450242 + 0.892906i \(0.351338\pi\)
\(444\) −2.64662 1.52803i −0.125603 0.0725170i
\(445\) 0 0
\(446\) −0.458645 + 0.166933i −0.0217175 + 0.00790451i
\(447\) −17.9392 8.36520i −0.848496 0.395660i
\(448\) −1.24089 + 4.63106i −0.0586264 + 0.218797i
\(449\) 5.86960 10.1664i 0.277003 0.479784i −0.693635 0.720326i \(-0.743992\pi\)
0.970639 + 0.240543i \(0.0773254\pi\)
\(450\) 0 0
\(451\) 1.76221 + 2.10012i 0.0829791 + 0.0988907i
\(452\) 0.436572 + 4.99004i 0.0205346 + 0.234712i
\(453\) −2.76975 + 3.95562i −0.130134 + 0.185851i
\(454\) 2.41801 6.64344i 0.113483 0.311792i
\(455\) 0 0
\(456\) −0.601969 + 5.59889i −0.0281898 + 0.262192i
\(457\) −3.52025 + 3.52025i −0.164670 + 0.164670i −0.784632 0.619962i \(-0.787148\pi\)
0.619962 + 0.784632i \(0.287148\pi\)
\(458\) 1.24620 0.581113i 0.0582311 0.0271536i
\(459\) −6.66710 37.8110i −0.311194 1.76487i
\(460\) 0 0
\(461\) −5.84057 + 4.90082i −0.272022 + 0.228254i −0.768586 0.639746i \(-0.779039\pi\)
0.496564 + 0.868000i \(0.334595\pi\)
\(462\) 2.62245 + 3.74525i 0.122008 + 0.174245i
\(463\) −30.4522 + 8.15964i −1.41523 + 0.379211i −0.883790 0.467884i \(-0.845017\pi\)
−0.531443 + 0.847094i \(0.678350\pi\)
\(464\) −4.16589 7.21553i −0.193396 0.334972i
\(465\) 0 0
\(466\) −1.13045 3.10588i −0.0523669 0.143877i
\(467\) −13.8839 3.72017i −0.642469 0.172149i −0.0771474 0.997020i \(-0.524581\pi\)
−0.565321 + 0.824871i \(0.691248\pi\)
\(468\) 0.546551 + 2.03976i 0.0252643 + 0.0942878i
\(469\) −2.04379 + 11.5909i −0.0943735 + 0.535218i
\(470\) 0 0
\(471\) −16.6605 + 19.8552i −0.767676 + 0.914880i
\(472\) −5.92128 4.14613i −0.272549 0.190841i
\(473\) 2.56064 + 5.49130i 0.117738 + 0.252490i
\(474\) −17.8323 −0.819065
\(475\) 0 0
\(476\) 32.8994 1.50794
\(477\) −0.621122 1.33200i −0.0284392 0.0609881i
\(478\) −15.3604 10.7555i −0.702568 0.491943i
\(479\) 19.8540 23.6611i 0.907152 1.08110i −0.0892218 0.996012i \(-0.528438\pi\)
0.996373 0.0850893i \(-0.0271176\pi\)
\(480\) 0 0
\(481\) 0.651703 3.69599i 0.0297151 0.168523i
\(482\) −1.88084 7.01938i −0.0856697 0.319724i
\(483\) −46.8652 12.5575i −2.13244 0.571386i
\(484\) 3.57585 + 9.82458i 0.162539 + 0.446572i
\(485\) 0 0
\(486\) −6.30309 10.9173i −0.285914 0.495217i
\(487\) 2.51254 0.673233i 0.113854 0.0305071i −0.201442 0.979500i \(-0.564563\pi\)
0.315296 + 0.948993i \(0.397896\pi\)
\(488\) −0.410417 0.586136i −0.0185787 0.0265331i
\(489\) 10.9702 9.20511i 0.496091 0.416270i
\(490\) 0 0
\(491\) −4.94664 28.0538i −0.223239 1.26605i −0.866024 0.500002i \(-0.833332\pi\)
0.642785 0.766046i \(-0.277779\pi\)
\(492\) −4.34838 + 2.02768i −0.196040 + 0.0914150i
\(493\) −40.4273 + 40.4273i −1.82075 + 1.82075i
\(494\) −6.71393 + 1.65698i −0.302074 + 0.0745509i
\(495\) 0 0
\(496\) −3.50692 + 9.63518i −0.157465 + 0.432633i
\(497\) −24.0529 + 34.3511i −1.07892 + 1.54086i
\(498\) −0.845409 9.66307i −0.0378837 0.433013i
\(499\) 16.3278 + 19.4587i 0.730932 + 0.871091i 0.995644 0.0932369i \(-0.0297214\pi\)
−0.264712 + 0.964327i \(0.585277\pi\)
\(500\) 0 0
\(501\) −10.1395 + 17.5622i −0.453001 + 0.784621i
\(502\) −1.35274 + 5.04851i −0.0603760 + 0.225326i
\(503\) −6.58283 3.06962i −0.293514 0.136868i 0.270284 0.962781i \(-0.412882\pi\)
−0.563798 + 0.825913i \(0.690660\pi\)
\(504\) 5.99677 2.18265i 0.267118 0.0972228i
\(505\) 0 0
\(506\) 5.00772 + 2.89121i 0.222620 + 0.128530i
\(507\) −11.0936 + 7.76782i −0.492684 + 0.344981i
\(508\) 1.27785 14.6059i 0.0566954 0.648031i
\(509\) −7.30974 6.13360i −0.323998 0.271867i 0.466251 0.884653i \(-0.345604\pi\)
−0.790249 + 0.612786i \(0.790049\pi\)
\(510\) 0 0
\(511\) −15.1985 5.53178i −0.672340 0.244712i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 21.3591 11.7731i 0.943028 0.519793i
\(514\) 8.91504i 0.393226i
\(515\) 0 0
\(516\) −10.4427 + 1.84133i −0.459714 + 0.0810601i
\(517\) −1.38488 + 0.121161i −0.0609070 + 0.00532867i
\(518\) −11.2985 0.988490i −0.496427 0.0434318i
\(519\) 24.8389 + 4.37977i 1.09031 + 0.192250i
\(520\) 0 0
\(521\) 31.0768 17.9422i 1.36150 0.786063i 0.371677 0.928362i \(-0.378783\pi\)
0.989824 + 0.142299i \(0.0454495\pi\)
\(522\) −4.68685 + 10.0510i −0.205138 + 0.439920i
\(523\) 12.7791 27.4049i 0.558791 1.19833i −0.400601 0.916253i \(-0.631198\pi\)
0.959391 0.282078i \(-0.0910237\pi\)
\(524\) 11.8087 6.81776i 0.515866 0.297835i
\(525\) 0 0
\(526\) −26.0792 4.59846i −1.13711 0.200502i
\(527\) 70.0924 + 6.13229i 3.05327 + 0.267127i
\(528\) 0.950002 0.0831144i 0.0413435 0.00361709i
\(529\) −37.7792 + 6.66149i −1.64257 + 0.289630i
\(530\) 0 0
\(531\) 9.62159i 0.417541i
\(532\) 6.75672 + 19.7760i 0.292941 + 0.857398i
\(533\) −4.16634 4.16634i −0.180464 0.180464i
\(534\) 9.23364 + 3.36077i 0.399579 + 0.145435i
\(535\) 0 0
\(536\) 1.88055 + 1.57797i 0.0812272 + 0.0681577i
\(537\) 2.33234 26.6588i 0.100648 1.15041i
\(538\) 17.8537 12.5013i 0.769729 0.538970i
\(539\) 10.2198 + 5.90041i 0.440198 + 0.254149i
\(540\) 0 0
\(541\) −26.3330 + 9.58444i −1.13215 + 0.412067i −0.839071 0.544023i \(-0.816901\pi\)
−0.293074 + 0.956090i \(0.594678\pi\)
\(542\) −6.22843 2.90437i −0.267534 0.124753i
\(543\) 5.32823 19.8852i 0.228656 0.853357i
\(544\) 3.43101 5.94269i 0.147103 0.254791i
\(545\) 0 0
\(546\) −6.31631 7.52749i −0.270313 0.322147i
\(547\) −2.16345 24.7283i −0.0925023 1.05731i −0.890603 0.454782i \(-0.849717\pi\)
0.798101 0.602524i \(-0.205838\pi\)
\(548\) 2.55929 3.65504i 0.109327 0.156136i
\(549\) −0.325748 + 0.894984i −0.0139026 + 0.0381970i
\(550\) 0 0
\(551\) −32.6038 15.9983i −1.38897 0.681549i
\(552\) −7.15576 + 7.15576i −0.304569 + 0.304569i
\(553\) −59.9788 + 27.9686i −2.55056 + 1.18935i
\(554\) −4.41218 25.0227i −0.187456 1.06311i
\(555\) 0 0
\(556\) 6.24935 5.24383i 0.265032 0.222388i
\(557\) 1.14685 + 1.63787i 0.0485936 + 0.0693989i 0.842714 0.538362i \(-0.180957\pi\)
−0.794120 + 0.607761i \(0.792068\pi\)
\(558\) 13.1830 3.53237i 0.558080 0.149537i
\(559\) −6.51102 11.2774i −0.275387 0.476984i
\(560\) 0 0
\(561\) −2.23813 6.14920i −0.0944937 0.259619i
\(562\) −6.50422 1.74280i −0.274364 0.0735156i
\(563\) 6.09059 + 22.7304i 0.256688 + 0.957972i 0.967144 + 0.254230i \(0.0818221\pi\)
−0.710456 + 0.703742i \(0.751511\pi\)
\(564\) 0.422474 2.39597i 0.0177894 0.100889i
\(565\) 0 0
\(566\) 13.9301 16.6012i 0.585525 0.697802i
\(567\) 12.7055 + 8.89651i 0.533582 + 0.373618i
\(568\) 3.69648 + 7.92713i 0.155101 + 0.332615i
\(569\) 16.9592 0.710967 0.355484 0.934683i \(-0.384316\pi\)
0.355484 + 0.934683i \(0.384316\pi\)
\(570\) 0 0
\(571\) 23.5925 0.987316 0.493658 0.869656i \(-0.335659\pi\)
0.493658 + 0.869656i \(0.335659\pi\)
\(572\) 0.494933 + 1.06139i 0.0206942 + 0.0443788i
\(573\) 17.3548 + 12.1520i 0.725007 + 0.507655i
\(574\) −11.4455 + 13.6402i −0.477725 + 0.569331i
\(575\) 0 0
\(576\) 0.231135 1.31083i 0.00963063 0.0546180i
\(577\) −6.55121 24.4495i −0.272731 1.01784i −0.957347 0.288941i \(-0.906697\pi\)
0.684616 0.728904i \(-0.259970\pi\)
\(578\) −29.0622 7.78719i −1.20883 0.323904i
\(579\) 4.03644 + 11.0900i 0.167749 + 0.460885i
\(580\) 0 0
\(581\) −17.9993 31.1757i −0.746738 1.29339i
\(582\) −2.71267 + 0.726856i −0.112444 + 0.0301292i
\(583\) −0.467502 0.667662i −0.0193619 0.0276517i
\(584\) −2.58423 + 2.16843i −0.106936 + 0.0897302i
\(585\) 0 0
\(586\) −1.35539 7.68679i −0.0559905 0.317538i
\(587\) −30.9536 + 14.4339i −1.27759 + 0.595750i −0.938589 0.345036i \(-0.887867\pi\)
−0.339000 + 0.940786i \(0.610089\pi\)
\(588\) −14.6036 + 14.6036i −0.602241 + 0.602241i
\(589\) 10.7091 + 43.3922i 0.441259 + 1.78795i
\(590\) 0 0
\(591\) −1.12016 + 3.07762i −0.0460772 + 0.126596i
\(592\) −1.35685 + 1.93778i −0.0557662 + 0.0796423i
\(593\) −1.31637 15.0461i −0.0540567 0.617871i −0.974110 0.226076i \(-0.927410\pi\)
0.920053 0.391794i \(-0.128145\pi\)
\(594\) −2.65486 3.16394i −0.108930 0.129818i
\(595\) 0 0
\(596\) −7.66085 + 13.2690i −0.313801 + 0.543518i
\(597\) −3.07489 + 11.4757i −0.125847 + 0.469667i
\(598\) −11.2633 5.25215i −0.460589 0.214776i
\(599\) 0.135258 0.0492298i 0.00552648 0.00201148i −0.339255 0.940694i \(-0.610175\pi\)
0.344782 + 0.938683i \(0.387953\pi\)
\(600\) 0 0
\(601\) 27.3869 + 15.8118i 1.11713 + 0.644978i 0.940668 0.339328i \(-0.110200\pi\)
0.176467 + 0.984307i \(0.443533\pi\)
\(602\) −32.2360 + 22.5719i −1.31384 + 0.919961i
\(603\) 0.284788 3.25514i 0.0115975 0.132560i
\(604\) 2.86341 + 2.40268i 0.116510 + 0.0977638i
\(605\) 0 0
\(606\) 5.22870 + 1.90309i 0.212401 + 0.0773078i
\(607\) −7.56254 7.56254i −0.306954 0.306954i 0.536773 0.843727i \(-0.319643\pi\)
−0.843727 + 0.536773i \(0.819643\pi\)
\(608\) 4.27682 + 0.841918i 0.173448 + 0.0341443i
\(609\) 51.6054i 2.09115i
\(610\) 0 0
\(611\) 2.94238 0.518821i 0.119036 0.0209893i
\(612\) −9.09897 + 0.796057i −0.367804 + 0.0321787i
\(613\) 25.2752 + 2.21129i 1.02086 + 0.0893133i 0.585274 0.810836i \(-0.300987\pi\)
0.435582 + 0.900149i \(0.356543\pi\)
\(614\) −5.26100 0.927656i −0.212317 0.0374371i
\(615\) 0 0
\(616\) 3.06497 1.76956i 0.123491 0.0712976i
\(617\) −20.3172 + 43.5704i −0.817941 + 1.75408i −0.180509 + 0.983573i \(0.557775\pi\)
−0.637432 + 0.770507i \(0.720003\pi\)
\(618\) 6.91870 14.8372i 0.278311 0.596840i
\(619\) −31.7586 + 18.3359i −1.27649 + 0.736980i −0.976201 0.216869i \(-0.930416\pi\)
−0.300286 + 0.953849i \(0.597082\pi\)
\(620\) 0 0
\(621\) 43.1634 + 7.61088i 1.73209 + 0.305414i
\(622\) 15.9744 + 1.39758i 0.640516 + 0.0560379i
\(623\) 36.3284 3.17832i 1.45547 0.127337i
\(624\) −2.01842 + 0.355902i −0.0808015 + 0.0142475i
\(625\) 0 0
\(626\) 20.3880i 0.814870i
\(627\) 3.23666 2.60824i 0.129260 0.104163i
\(628\) 14.1868 + 14.1868i 0.566115 + 0.566115i
\(629\) 15.2538 + 5.55193i 0.608209 + 0.221370i
\(630\) 0 0
\(631\) −23.0108 19.3084i −0.916047 0.768655i 0.0572124 0.998362i \(-0.481779\pi\)
−0.973260 + 0.229707i \(0.926223\pi\)
\(632\) −1.20305 + 13.7509i −0.0478546 + 0.546981i
\(633\) 15.7819 11.0506i 0.627276 0.439223i
\(634\) 16.5188 + 9.53712i 0.656044 + 0.378767i
\(635\) 0 0
\(636\) 1.34042 0.487872i 0.0531510 0.0193454i
\(637\) −22.9862 10.7186i −0.910747 0.424688i
\(638\) −1.59182 + 5.94074i −0.0630206 + 0.235196i
\(639\) 5.82111 10.0825i 0.230280 0.398856i
\(640\) 0 0
\(641\) −0.320822 0.382341i −0.0126717 0.0151016i 0.759671 0.650307i \(-0.225360\pi\)
−0.772343 + 0.635206i \(0.780915\pi\)
\(642\) 0.485806 + 5.55279i 0.0191732 + 0.219151i
\(643\) 17.7191 25.3055i 0.698774 0.997952i −0.300254 0.953859i \(-0.597071\pi\)
0.999027 0.0440930i \(-0.0140398\pi\)
\(644\) −12.8451 + 35.2916i −0.506168 + 1.39068i
\(645\) 0 0
\(646\) −2.01532 29.8429i −0.0792918 1.17415i
\(647\) 17.8899 17.8899i 0.703326 0.703326i −0.261797 0.965123i \(-0.584315\pi\)
0.965123 + 0.261797i \(0.0843151\pi\)
\(648\) 2.93203 1.36723i 0.115181 0.0537097i
\(649\) 0.926575 + 5.25487i 0.0363713 + 0.206272i
\(650\) 0 0
\(651\) −48.6503 + 40.8224i −1.90676 + 1.59996i
\(652\) −6.35817 9.08040i −0.249005 0.355616i
\(653\) −12.4688 + 3.34100i −0.487941 + 0.130743i −0.494398 0.869236i \(-0.664611\pi\)
0.00645686 + 0.999979i \(0.497945\pi\)
\(654\) −1.79854 3.11516i −0.0703283 0.121812i
\(655\) 0 0
\(656\) 1.27023 + 3.48993i 0.0495941 + 0.136259i
\(657\) 4.33727 + 1.16217i 0.169213 + 0.0453405i
\(658\) −2.33691 8.72145i −0.0911021 0.339997i
\(659\) −3.86696 + 21.9306i −0.150636 + 0.854296i 0.812033 + 0.583612i \(0.198361\pi\)
−0.962668 + 0.270684i \(0.912750\pi\)
\(660\) 0 0
\(661\) −12.1703 + 14.5040i −0.473369 + 0.564139i −0.948907 0.315556i \(-0.897809\pi\)
0.475538 + 0.879695i \(0.342253\pi\)
\(662\) 26.0835 + 18.2639i 1.01377 + 0.709846i
\(663\) 5.94375 + 12.7464i 0.230836 + 0.495030i
\(664\) −7.50844 −0.291384
\(665\) 0 0
\(666\) 3.14873 0.122011
\(667\) −27.5826 59.1511i −1.06800 2.29034i
\(668\) 12.8585 + 9.00365i 0.497512 + 0.348362i
\(669\) −0.405303 + 0.483021i −0.0156699 + 0.0186747i
\(670\) 0 0
\(671\) −0.0917199 + 0.520169i −0.00354081 + 0.0200809i
\(672\) 1.60307 + 5.98275i 0.0618399 + 0.230790i
\(673\) −32.1752 8.62132i −1.24026 0.332328i −0.421695 0.906738i \(-0.638565\pi\)
−0.818568 + 0.574410i \(0.805232\pi\)
\(674\) 6.61586 + 18.1769i 0.254833 + 0.700149i
\(675\) 0 0
\(676\) 5.24152 + 9.07857i 0.201597 + 0.349176i
\(677\) 19.8750 5.32548i 0.763857 0.204675i 0.144201 0.989548i \(-0.453939\pi\)
0.619656 + 0.784874i \(0.287272\pi\)
\(678\) 3.71169 + 5.30084i 0.142547 + 0.203578i
\(679\) −7.98402 + 6.69939i −0.306398 + 0.257099i
\(680\) 0 0
\(681\) −1.58598 8.99456i −0.0607750 0.344672i
\(682\) 6.85976 3.19876i 0.262674 0.122487i
\(683\) 7.01971 7.01971i 0.268602 0.268602i −0.559935 0.828537i \(-0.689174\pi\)
0.828537 + 0.559935i \(0.189174\pi\)
\(684\) −2.34721 5.30594i −0.0897479 0.202878i
\(685\) 0 0
\(686\) −14.7359 + 40.4866i −0.562620 + 1.54579i
\(687\) 1.01888 1.45512i 0.0388728 0.0555161i
\(688\) 0.715379 + 8.17682i 0.0272736 + 0.311738i
\(689\) 1.12600 + 1.34192i 0.0428973 + 0.0511230i
\(690\) 0 0
\(691\) −0.232096 + 0.402003i −0.00882936 + 0.0152929i −0.870406 0.492334i \(-0.836144\pi\)
0.861577 + 0.507627i \(0.169477\pi\)
\(692\) 5.05308 18.8583i 0.192089 0.716887i
\(693\) −4.26940 1.99085i −0.162181 0.0756263i
\(694\) 15.2033 5.53357i 0.577111 0.210051i
\(695\) 0 0
\(696\) −9.32157 5.38181i −0.353333 0.203997i
\(697\) 20.8760 14.6175i 0.790735 0.553678i
\(698\) 2.43915 27.8797i 0.0923234 1.05526i
\(699\) −3.27095 2.74465i −0.123719 0.103812i
\(700\) 0 0
\(701\) −11.8560 4.31523i −0.447795 0.162984i 0.108272 0.994121i \(-0.465468\pi\)
−0.556067 + 0.831137i \(0.687690\pi\)
\(702\) 6.27681 + 6.27681i 0.236903 + 0.236903i
\(703\) −0.204542 + 10.3094i −0.00771444 + 0.388825i
\(704\) 0.738175i 0.0278210i
\(705\) 0 0
\(706\) −7.56247 + 1.33347i −0.284617 + 0.0501857i
\(707\) 20.5716 1.79978i 0.773673 0.0676876i
\(708\) −9.30286 0.813895i −0.349623 0.0305880i
\(709\) 15.5736 + 2.74604i 0.584878 + 0.103130i 0.458254 0.888821i \(-0.348475\pi\)
0.126624 + 0.991951i \(0.459586\pi\)
\(710\) 0 0
\(711\) 15.9115 9.18654i 0.596730 0.344522i
\(712\) 3.21451 6.89353i 0.120469 0.258346i
\(713\) −33.9447 + 72.7947i −1.27124 + 2.72618i
\(714\) 36.8078 21.2510i 1.37750 0.795299i
\(715\) 0 0
\(716\) −20.3998 3.59704i −0.762378 0.134428i
\(717\) −24.1326 2.11132i −0.901247 0.0788489i
\(718\) 18.1483 1.58777i 0.677290 0.0592552i
\(719\) −26.9388 + 4.75004i −1.00465 + 0.177147i −0.651685 0.758490i \(-0.725937\pi\)
−0.352964 + 0.935637i \(0.614826\pi\)
\(720\) 0 0
\(721\) 60.7563i 2.26268i
\(722\) 17.5248 7.34040i 0.652205 0.273181i
\(723\) −6.63836 6.63836i −0.246883 0.246883i
\(724\) −14.9745 5.45026i −0.556522 0.202557i
\(725\) 0 0
\(726\) 10.3467 + 8.68194i 0.384003 + 0.322217i
\(727\) −3.85906 + 44.1092i −0.143125 + 1.63592i 0.497071 + 0.867710i \(0.334409\pi\)
−0.640196 + 0.768212i \(0.721147\pi\)
\(728\) −6.23074 + 4.36281i −0.230927 + 0.161697i
\(729\) −22.5089 12.9955i −0.833663 0.481315i
\(730\) 0 0
\(731\) 52.9271 19.2639i 1.95758 0.712501i
\(732\) −0.837781 0.390664i −0.0309653 0.0144394i
\(733\) 6.99577 26.1086i 0.258395 0.964342i −0.707776 0.706437i \(-0.750301\pi\)
0.966170 0.257905i \(-0.0830320\pi\)
\(734\) −1.40406 + 2.43191i −0.0518250 + 0.0897635i
\(735\) 0 0
\(736\) 5.03521 + 6.00072i 0.185600 + 0.221190i
\(737\) −0.157937 1.80523i −0.00581770 0.0664966i
\(738\) 2.83542 4.04940i 0.104373 0.149060i
\(739\) 7.58340 20.8352i 0.278960 0.766436i −0.718521 0.695505i \(-0.755181\pi\)
0.997481 0.0709311i \(-0.0225970\pi\)
\(740\) 0 0
\(741\) −6.44123 + 6.19061i −0.236624 + 0.227418i
\(742\) 3.74329 3.74329i 0.137421 0.137421i
\(743\) 15.0430 7.01468i 0.551875 0.257344i −0.126616 0.991952i \(-0.540412\pi\)
0.678492 + 0.734608i \(0.262634\pi\)
\(744\) 2.30020 + 13.0451i 0.0843294 + 0.478256i
\(745\) 0 0
\(746\) −2.96017 + 2.48388i −0.108379 + 0.0909411i
\(747\) 5.73240 + 8.18672i 0.209738 + 0.299537i
\(748\) −4.89278 + 1.31102i −0.178898 + 0.0479355i
\(749\) 10.3431 + 17.9148i 0.377930 + 0.654593i
\(750\) 0 0
\(751\) 0.794919 + 2.18402i 0.0290070 + 0.0796961i 0.953351 0.301864i \(-0.0976090\pi\)
−0.924344 + 0.381561i \(0.875387\pi\)
\(752\) −1.81908 0.487422i −0.0663351 0.0177744i
\(753\) 1.74758 + 6.52206i 0.0636854 + 0.237677i
\(754\) 2.29534 13.0175i 0.0835913 0.474070i
\(755\) 0 0
\(756\) 17.2432 20.5497i 0.627130 0.747384i
\(757\) 41.1902 + 28.8417i 1.49708 + 1.04827i 0.981508 + 0.191423i \(0.0613104\pi\)
0.515575 + 0.856845i \(0.327579\pi\)
\(758\) 9.76126 + 20.9331i 0.354545 + 0.760324i
\(759\) 7.47016 0.271150
\(760\) 0 0
\(761\) −35.4721 −1.28586 −0.642932 0.765923i \(-0.722282\pi\)
−0.642932 + 0.765923i \(0.722282\pi\)
\(762\) −8.00485 17.1664i −0.289985 0.621875i
\(763\) −10.9352 7.65694i −0.395883 0.277200i
\(764\) 10.5415 12.5628i 0.381377 0.454507i
\(765\) 0 0
\(766\) 0.766510 4.34709i 0.0276951 0.157067i
\(767\) −2.96815 11.0773i −0.107174 0.399978i
\(768\) 1.24786 + 0.334362i 0.0450282 + 0.0120653i
\(769\) 0.814447 + 2.23767i 0.0293697 + 0.0806926i 0.953511 0.301358i \(-0.0974401\pi\)
−0.924141 + 0.382051i \(0.875218\pi\)
\(770\) 0 0
\(771\) −5.75857 9.97414i −0.207390 0.359210i
\(772\) 8.82407 2.36440i 0.317585 0.0850967i
\(773\) 14.8747 + 21.2432i 0.535004 + 0.764065i 0.992113 0.125346i \(-0.0400040\pi\)
−0.457109 + 0.889411i \(0.651115\pi\)
\(774\) 8.36932 7.02269i 0.300829 0.252425i
\(775\) 0 0
\(776\) 0.377487 + 2.14083i 0.0135510 + 0.0768514i
\(777\) −13.2792 + 6.19221i −0.476390 + 0.222144i
\(778\) 14.9982 14.9982i 0.537711 0.537711i
\(779\) 13.0741 + 9.54658i 0.468427 + 0.342042i
\(780\) 0 0
\(781\) 2.20826 6.06716i 0.0790179 0.217100i
\(782\) 30.8314 44.0318i 1.10253 1.57457i
\(783\) 4.06301 + 46.4404i 0.145200 + 1.65965i
\(784\) 10.2759 + 12.2463i 0.366997 + 0.437370i
\(785\) 0 0
\(786\) 8.80771 15.2554i 0.314160 0.544142i
\(787\) −2.45608 + 9.16620i −0.0875497 + 0.326740i −0.995785 0.0917204i \(-0.970763\pi\)
0.908235 + 0.418460i \(0.137430\pi\)
\(788\) 2.29765 + 1.07141i 0.0818502 + 0.0381674i
\(789\) −32.1477 + 11.7008i −1.14449 + 0.416559i
\(790\) 0 0
\(791\) 20.7982 + 12.0079i 0.739500 + 0.426950i
\(792\) −0.804858 + 0.563568i −0.0285994 + 0.0200255i
\(793\) 0.0989393 1.13088i 0.00351344 0.0401588i
\(794\) 22.9875 + 19.2888i 0.815794 + 0.684533i
\(795\) 0 0
\(796\) 8.64168 + 3.14532i 0.306296 + 0.111483i
\(797\) −17.6005 17.6005i −0.623441 0.623441i 0.322969 0.946410i \(-0.395319\pi\)
−0.946410 + 0.322969i \(0.895319\pi\)
\(798\) 20.3335 + 17.7609i 0.719797 + 0.628730i
\(799\) 12.9229i 0.457180i
\(800\) 0 0
\(801\) −9.97041 + 1.75805i −0.352287 + 0.0621177i
\(802\) 4.86975 0.426048i 0.171957 0.0150443i
\(803\) 2.48074 + 0.217036i 0.0875433 + 0.00765905i
\(804\) 3.12322 + 0.550708i 0.110147 + 0.0194220i
\(805\) 0 0
\(806\) −14.0878 + 8.13361i −0.496222 + 0.286494i
\(807\) 11.8996 25.5189i 0.418887 0.898307i
\(808\) 1.82027 3.90357i 0.0640368 0.137327i
\(809\) 14.4694 8.35391i 0.508717 0.293708i −0.223589 0.974683i \(-0.571777\pi\)
0.732306 + 0.680976i \(0.238444\pi\)
\(810\) 0 0
\(811\) −36.8771 6.50244i −1.29493 0.228331i −0.516623 0.856213i \(-0.672811\pi\)
−0.778309 + 0.627882i \(0.783922\pi\)
\(812\) −39.7940 3.48153i −1.39650 0.122178i
\(813\) −8.84440 + 0.773785i −0.310187 + 0.0271378i
\(814\) 1.71969 0.303228i 0.0602752 0.0106281i
\(815\) 0 0
\(816\) 8.86489i 0.310333i
\(817\) 22.4495 + 27.8584i 0.785409 + 0.974642i
\(818\) 0.0870596 + 0.0870596i 0.00304397 + 0.00304397i
\(819\) 9.51385 + 3.46276i 0.332441 + 0.120999i
\(820\) 0 0
\(821\) −21.1352 17.7346i −0.737624 0.618940i 0.194574 0.980888i \(-0.437667\pi\)
−0.932198 + 0.361948i \(0.882112\pi\)
\(822\) 0.502395 5.74240i 0.0175230 0.200289i
\(823\) 30.1865 21.1368i 1.05224 0.736783i 0.0864840 0.996253i \(-0.472437\pi\)
0.965751 + 0.259470i \(0.0835480\pi\)
\(824\) −10.9745 6.33615i −0.382316 0.220730i
\(825\) 0 0
\(826\) −32.5667 + 11.8533i −1.13314 + 0.412429i
\(827\) −18.1633 8.46967i −0.631598 0.294519i 0.0803331 0.996768i \(-0.474402\pi\)
−0.711932 + 0.702249i \(0.752179\pi\)
\(828\) 2.69862 10.0714i 0.0937835 0.350005i
\(829\) 4.05649 7.02605i 0.140888 0.244025i −0.786943 0.617025i \(-0.788338\pi\)
0.927831 + 0.373000i \(0.121671\pi\)
\(830\) 0 0
\(831\) −21.0995 25.1454i −0.731933 0.872284i
\(832\) 0.138272 + 1.58046i 0.00479373 + 0.0547925i
\(833\) 62.9211 89.8606i 2.18009 3.11349i
\(834\) 3.60457 9.90349i 0.124816 0.342930i
\(835\) 0 0
\(836\) −1.79291 2.67182i −0.0620091 0.0924068i
\(837\) 40.5671 40.5671i 1.40220 1.40220i
\(838\) −31.5640 + 14.7185i −1.09036 + 0.508443i
\(839\) −0.902243 5.11688i −0.0311489 0.176654i 0.965264 0.261275i \(-0.0841431\pi\)
−0.996413 + 0.0846213i \(0.973032\pi\)
\(840\) 0 0
\(841\) 30.9623 25.9805i 1.06767 0.895878i
\(842\) −14.5658 20.8022i −0.501972 0.716890i
\(843\) −8.40265 + 2.25148i −0.289403 + 0.0775452i
\(844\) −7.45666 12.9153i −0.256669 0.444564i
\(845\) 0 0
\(846\) 0.857346 + 2.35554i 0.0294762 + 0.0809851i
\(847\) 48.4181 + 12.9736i 1.66367 + 0.445778i
\(848\) −0.285778 1.06654i −0.00981366 0.0366251i
\(849\) 4.86158 27.5714i 0.166849 0.946248i
\(850\) 0 0
\(851\) −11.9113 + 14.1953i −0.408312 + 0.486608i
\(852\) 9.25605 + 6.48116i 0.317107 + 0.222041i
\(853\) 15.2484 + 32.7004i 0.522096 + 1.11964i 0.973786 + 0.227464i \(0.0730436\pi\)
−0.451690 + 0.892175i \(0.649179\pi\)
\(854\) −3.43060 −0.117393
\(855\) 0 0
\(856\) 4.31465 0.147472
\(857\) 5.42815 + 11.6407i 0.185422 + 0.397639i 0.976942 0.213504i \(-0.0684877\pi\)
−0.791520 + 0.611143i \(0.790710\pi\)
\(858\) 1.23932 + 0.867782i 0.0423097 + 0.0296256i
\(859\) 19.9671 23.7958i 0.681268 0.811904i −0.309002 0.951061i \(-0.599995\pi\)
0.990270 + 0.139158i \(0.0444395\pi\)
\(860\) 0 0
\(861\) −3.99446 + 22.6537i −0.136131 + 0.772036i
\(862\) −5.35303 19.9778i −0.182325 0.680445i
\(863\) −30.1712 8.08435i −1.02704 0.275194i −0.294307 0.955711i \(-0.595089\pi\)
−0.732733 + 0.680517i \(0.761755\pi\)
\(864\) −1.91367 5.25776i −0.0651043 0.178873i
\(865\) 0 0
\(866\) −7.50183 12.9935i −0.254922 0.441539i
\(867\) −37.5448 + 10.0601i −1.27509 + 0.341659i
\(868\) 28.1969 + 40.2694i 0.957066 + 1.36683i
\(869\) 7.80548 6.54957i 0.264783 0.222179i
\(870\) 0 0
\(871\) 0.676299 + 3.83548i 0.0229155 + 0.129960i
\(872\) −2.52350 + 1.17673i −0.0854566 + 0.0398491i
\(873\) 2.04603 2.04603i 0.0692476 0.0692476i
\(874\) 32.7997 + 9.48986i 1.10947 + 0.320999i
\(875\) 0 0
\(876\) −1.49056 + 4.09529i −0.0503614 + 0.138367i
\(877\) 13.0297 18.6084i 0.439983 0.628361i −0.536514 0.843891i \(-0.680259\pi\)
0.976497 + 0.215531i \(0.0691481\pi\)
\(878\) −1.46934 16.7946i −0.0495878 0.566791i
\(879\) −6.48160 7.72447i −0.218619 0.260540i
\(880\) 0 0
\(881\) −8.67839 + 15.0314i −0.292382 + 0.506421i −0.974373 0.224940i \(-0.927781\pi\)
0.681990 + 0.731361i \(0.261115\pi\)
\(882\) 5.50737 20.5538i 0.185443 0.692082i
\(883\) 4.54919 + 2.12132i 0.153092 + 0.0713881i 0.497654 0.867375i \(-0.334195\pi\)
−0.344562 + 0.938764i \(0.611973\pi\)
\(884\) 10.2300 3.72343i 0.344073 0.125232i
\(885\) 0 0
\(886\) 5.22528 + 3.01681i 0.175547 + 0.101352i
\(887\) 29.6484 20.7600i 0.995497 0.697054i 0.0422060 0.999109i \(-0.486561\pi\)
0.953291 + 0.302055i \(0.0976725\pi\)
\(888\) −0.266353 + 3.04443i −0.00893822 + 0.102164i
\(889\) −53.8485 45.1843i −1.80602 1.51543i
\(890\) 0 0
\(891\) −2.24408 0.816777i −0.0751793 0.0273630i
\(892\) 0.345125 + 0.345125i 0.0115556 + 0.0115556i
\(893\) −7.76803 + 2.65404i −0.259947 + 0.0888142i
\(894\) 19.7937i 0.662002i
\(895\) 0 0
\(896\) 4.72158 0.832542i 0.157737 0.0278133i
\(897\) −15.9939 + 1.39928i −0.534020 + 0.0467207i
\(898\) −11.6945 1.02314i −0.390251 0.0341426i
\(899\) −84.1324 14.8348i −2.80597 0.494768i
\(900\) 0 0
\(901\) −6.56169 + 3.78839i −0.218602 + 0.126210i
\(902\) 1.15861 2.48465i 0.0385776 0.0827298i
\(903\) −21.4855 + 46.0759i −0.714994 + 1.53331i
\(904\) 4.33800 2.50455i 0.144280 0.0833000i
\(905\) 0 0
\(906\) 4.75556 + 0.838533i 0.157993 + 0.0278584i
\(907\) 26.6373 + 2.33046i 0.884477 + 0.0773817i 0.520336 0.853962i \(-0.325807\pi\)
0.364142 + 0.931344i \(0.381362\pi\)
\(908\) −7.04290 + 0.616174i −0.233727 + 0.0204484i
\(909\) −5.64591 + 0.995526i −0.187263 + 0.0330195i
\(910\) 0 0
\(911\) 34.8134i 1.15342i −0.816949 0.576709i \(-0.804336\pi\)
0.816949 0.576709i \(-0.195664\pi\)
\(912\) 5.32872 1.82063i 0.176452 0.0602869i
\(913\) 3.91917 + 3.91917i 0.129706 + 0.129706i
\(914\) 4.67815 + 1.70271i 0.154740 + 0.0563206i
\(915\) 0 0
\(916\) −1.05333 0.883852i −0.0348031 0.0292033i
\(917\) 5.69776 65.1256i 0.188156 2.15064i
\(918\) −31.4508 + 22.0221i −1.03803 + 0.726837i
\(919\) 0.0710129 + 0.0409993i 0.00234250 + 0.00135244i 0.501171 0.865348i \(-0.332903\pi\)
−0.498828 + 0.866701i \(0.666236\pi\)
\(920\) 0 0
\(921\) −6.48520 + 2.36042i −0.213695 + 0.0777785i
\(922\) 6.90998 + 3.22218i 0.227568 + 0.106117i
\(923\) −3.59149 + 13.4036i −0.118215 + 0.441186i
\(924\) 2.28605 3.95956i 0.0752057 0.130260i
\(925\) 0 0
\(926\) 20.2648 + 24.1506i 0.665942 + 0.793639i
\(927\) 1.47010 + 16.8033i 0.0482844 + 0.551894i
\(928\) −4.77891 + 6.82499i −0.156875 + 0.224041i
\(929\) 0.114920 0.315740i 0.00377040 0.0103591i −0.937793 0.347194i \(-0.887134\pi\)
0.941564 + 0.336835i \(0.109357\pi\)
\(930\) 0 0
\(931\) 66.9380 + 19.3670i 2.19380 + 0.634729i
\(932\) −2.33713 + 2.33713i −0.0765553 + 0.0765553i
\(933\) 18.7749 8.75488i 0.614663 0.286622i
\(934\) 2.49596 + 14.1553i 0.0816702 + 0.463175i
\(935\) 0 0
\(936\) 1.61766 1.35738i 0.0528750 0.0443674i
\(937\) −0.159464 0.227738i −0.00520946 0.00743989i 0.816539 0.577290i \(-0.195890\pi\)
−0.821748 + 0.569851i \(0.807001\pi\)
\(938\) 11.3687 3.04623i 0.371200 0.0994628i
\(939\) 13.1694 + 22.8101i 0.429768 + 0.744380i
\(940\) 0 0
\(941\) −6.89714 18.9497i −0.224840 0.617744i 0.775060 0.631888i \(-0.217720\pi\)
−0.999900 + 0.0141443i \(0.995498\pi\)
\(942\) 25.0360 + 6.70837i 0.815716 + 0.218570i
\(943\) 7.52968 + 28.1011i 0.245200 + 0.915099i
\(944\) −1.25522 + 7.11873i −0.0408541 + 0.231695i
\(945\) 0 0
\(946\) 3.89464 4.64145i 0.126626 0.150907i
\(947\) −36.3195 25.4312i −1.18023 0.826403i −0.192301 0.981336i \(-0.561595\pi\)
−0.987925 + 0.154932i \(0.950484\pi\)
\(948\) 7.53626 + 16.1616i 0.244766 + 0.524903i
\(949\) −5.35200 −0.173733
\(950\) 0 0
\(951\) 24.6416 0.799057
\(952\) −13.9039 29.8170i −0.450628 0.966375i
\(953\) −5.59767 3.91953i −0.181326 0.126966i 0.479389 0.877602i \(-0.340858\pi\)
−0.660716 + 0.750636i \(0.729747\pi\)
\(954\) −0.944704 + 1.12585i −0.0305859 + 0.0364509i
\(955\) 0 0
\(956\) −3.25618 + 18.4667i −0.105312 + 0.597256i
\(957\) 2.05643 + 7.67470i 0.0664750 + 0.248088i
\(958\) −29.8349 7.99422i −0.963920 0.258282i
\(959\) −7.31671 20.1025i −0.236269 0.649143i
\(960\) 0 0
\(961\) 37.0676 + 64.2030i 1.19573 + 2.07107i
\(962\) −3.62512 + 0.971349i −0.116879 + 0.0313176i
\(963\) −3.29407 4.70442i −0.106150 0.151598i
\(964\) −5.56684 + 4.67113i −0.179296 + 0.150447i
\(965\) 0 0
\(966\) 8.42514 + 47.7814i 0.271075 + 1.53734i
\(967\) −20.4405 + 9.53156i −0.657322 + 0.306514i −0.722512 0.691359i \(-0.757012\pi\)
0.0651898 + 0.997873i \(0.479235\pi\)
\(968\) 7.39287 7.39287i 0.237616 0.237616i
\(969\) −21.5314 32.0864i −0.691689 1.03076i
\(970\) 0 0
\(971\) 19.0127 52.2370i 0.610146 1.67636i −0.119749 0.992804i \(-0.538209\pi\)
0.729895 0.683559i \(-0.239569\pi\)
\(972\) −7.23060 + 10.3264i −0.231922 + 0.331218i
\(973\) −3.40889 38.9638i −0.109284 1.24912i
\(974\) −1.67200 1.99262i −0.0535744 0.0638475i
\(975\) 0 0
\(976\) −0.357770 + 0.619676i −0.0114519 + 0.0198353i
\(977\) 12.2621 45.7629i 0.392301 1.46409i −0.434029 0.900899i \(-0.642908\pi\)
0.826330 0.563187i \(-0.190425\pi\)
\(978\) −12.9789 6.05215i −0.415019 0.193527i
\(979\) −5.27608 + 1.92033i −0.168624 + 0.0613742i
\(980\) 0 0
\(981\) 3.20962 + 1.85308i 0.102475 + 0.0591642i
\(982\) −23.3348 + 16.3392i −0.744644 + 0.521405i
\(983\) −0.311680 + 3.56252i −0.00994104 + 0.113627i −0.999544 0.0302006i \(-0.990385\pi\)
0.989603 + 0.143827i \(0.0459409\pi\)
\(984\) 3.67541 + 3.08403i 0.117168 + 0.0983154i
\(985\) 0 0
\(986\) 53.7249 + 19.5543i 1.71095 + 0.622735i
\(987\) −8.24805 8.24805i −0.262538 0.262538i
\(988\) 4.33916 + 5.38462i 0.138047 + 0.171307i
\(989\) 64.2969i 2.04452i
\(990\) 0 0
\(991\) 8.07184 1.42328i 0.256410 0.0452121i −0.0439652 0.999033i \(-0.513999\pi\)
0.300376 + 0.953821i \(0.402888\pi\)
\(992\) 10.2145 0.893656i 0.324312 0.0283736i
\(993\) 40.9796 + 3.58525i 1.30045 + 0.113774i
\(994\) 41.2979 + 7.28193i 1.30989 + 0.230969i
\(995\) 0 0
\(996\) −8.40043 + 4.84999i −0.266178 + 0.153678i
\(997\) 5.35529 11.4845i 0.169604 0.363717i −0.803073 0.595881i \(-0.796803\pi\)
0.972677 + 0.232164i \(0.0745807\pi\)
\(998\) 10.7351 23.0216i 0.339815 0.728736i
\(999\) 11.4627 6.61797i 0.362663 0.209383i
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 950.2.bb.d.243.2 96
5.2 odd 4 inner 950.2.bb.d.357.6 yes 96
5.3 odd 4 inner 950.2.bb.d.357.3 yes 96
5.4 even 2 inner 950.2.bb.d.243.7 yes 96
19.14 odd 18 inner 950.2.bb.d.793.6 yes 96
95.14 odd 18 inner 950.2.bb.d.793.3 yes 96
95.33 even 36 inner 950.2.bb.d.907.7 yes 96
95.52 even 36 inner 950.2.bb.d.907.2 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.bb.d.243.2 96 1.1 even 1 trivial
950.2.bb.d.243.7 yes 96 5.4 even 2 inner
950.2.bb.d.357.3 yes 96 5.3 odd 4 inner
950.2.bb.d.357.6 yes 96 5.2 odd 4 inner
950.2.bb.d.793.3 yes 96 95.14 odd 18 inner
950.2.bb.d.793.6 yes 96 19.14 odd 18 inner
950.2.bb.d.907.2 yes 96 95.52 even 36 inner
950.2.bb.d.907.7 yes 96 95.33 even 36 inner