Properties

Label 1089.2.e.o.364.10
Level $1089$
Weight $2$
Character 1089.364
Analytic conductor $8.696$
Analytic rank $0$
Dimension $36$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1089,2,Mod(364,1089)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1089.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.e (of order \(3\), 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: \(8.69570878012\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 364.10
Character \(\chi\) \(=\) 1089.364
Dual form 1089.2.e.o.727.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.142574 + 0.246946i) q^{2} +(0.0364826 + 1.73167i) q^{3} +(0.959345 - 1.66163i) q^{4} +(-1.35437 + 2.34583i) q^{5} +(-0.422426 + 0.255900i) q^{6} +(-2.03667 - 3.52761i) q^{7} +1.11741 q^{8} +(-2.99734 + 0.126351i) q^{9} -0.772391 q^{10} +(2.91240 + 1.60065i) q^{12} +(1.92548 - 3.33503i) q^{13} +(0.580752 - 1.00589i) q^{14} +(-4.11161 - 2.25973i) q^{15} +(-1.75938 - 3.04733i) q^{16} +4.32020 q^{17} +(-0.458545 - 0.722165i) q^{18} +1.62229 q^{19} +(2.59861 + 4.50093i) q^{20} +(6.03434 - 3.65553i) q^{21} +(0.932117 - 1.61447i) q^{23} +(0.0407660 + 1.93498i) q^{24} +(-1.16862 - 2.02411i) q^{25} +1.09809 q^{26} +(-0.328149 - 5.18578i) q^{27} -7.81547 q^{28} +(1.77667 + 3.07729i) q^{29} +(-0.0281788 - 1.33752i) q^{30} +(2.43230 - 4.21286i) q^{31} +(1.61909 - 2.80435i) q^{32} +(0.615950 + 1.06686i) q^{34} +11.0336 q^{35} +(-2.66553 + 5.10170i) q^{36} +7.74449 q^{37} +(0.231297 + 0.400619i) q^{38} +(5.84540 + 3.21262i) q^{39} +(-1.51338 + 2.62125i) q^{40} +(3.43607 - 5.95145i) q^{41} +(1.76306 + 0.968972i) q^{42} +(0.492496 + 0.853027i) q^{43} +(3.76310 - 7.20238i) q^{45} +0.531584 q^{46} +(-2.93317 - 5.08041i) q^{47} +(5.21277 - 3.15783i) q^{48} +(-4.79603 + 8.30697i) q^{49} +(0.333230 - 0.577171i) q^{50} +(0.157612 + 7.48115i) q^{51} +(-3.69440 - 6.39888i) q^{52} -1.57183 q^{53} +(1.23382 - 0.820393i) q^{54} +(-2.27579 - 3.94178i) q^{56} +(0.0591855 + 2.80927i) q^{57} +(-0.506615 + 0.877483i) q^{58} +(-5.68125 + 9.84021i) q^{59} +(-7.69930 + 4.66413i) q^{60} +(-4.30374 - 7.45430i) q^{61} +1.38713 q^{62} +(6.55030 + 10.3161i) q^{63} -6.11414 q^{64} +(5.21561 + 9.03370i) q^{65} +(0.870282 - 1.50737i) q^{67} +(4.14457 - 7.17860i) q^{68} +(2.82974 + 1.55522i) q^{69} +(1.57310 + 2.72470i) q^{70} -5.74136 q^{71} +(-3.34925 + 0.141186i) q^{72} +4.04662 q^{73} +(1.10416 + 1.91247i) q^{74} +(3.46245 - 2.09750i) q^{75} +(1.55634 - 2.69566i) q^{76} +(0.0400613 + 1.90153i) q^{78} +(-2.14007 - 3.70672i) q^{79} +9.53137 q^{80} +(8.96807 - 0.757436i) q^{81} +1.95958 q^{82} +(-3.25009 - 5.62933i) q^{83} +(-0.285129 - 13.5338i) q^{84} +(-5.85114 + 10.1345i) q^{85} +(-0.140434 + 0.243239i) q^{86} +(-5.26402 + 3.18887i) q^{87} +9.26243 q^{89} +(2.31512 - 0.0975927i) q^{90} -15.6862 q^{91} +(-1.78844 - 3.09768i) q^{92} +(7.38400 + 4.05823i) q^{93} +(0.836390 - 1.44867i) q^{94} +(-2.19718 + 3.80563i) q^{95} +(4.91527 + 2.70142i) q^{96} +(3.70634 + 6.41957i) q^{97} -2.73516 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23}+ \cdots + 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(848\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.142574 + 0.246946i 0.100815 + 0.174617i 0.912021 0.410144i \(-0.134522\pi\)
−0.811206 + 0.584761i \(0.801188\pi\)
\(3\) 0.0364826 + 1.73167i 0.0210632 + 0.999778i
\(4\) 0.959345 1.66163i 0.479673 0.830817i
\(5\) −1.35437 + 2.34583i −0.605691 + 1.04909i 0.386251 + 0.922394i \(0.373770\pi\)
−0.991942 + 0.126694i \(0.959563\pi\)
\(6\) −0.422426 + 0.255900i −0.172455 + 0.104471i
\(7\) −2.03667 3.52761i −0.769788 1.33331i −0.937678 0.347506i \(-0.887029\pi\)
0.167890 0.985806i \(-0.446305\pi\)
\(8\) 1.11741 0.395063
\(9\) −2.99734 + 0.126351i −0.999113 + 0.0421171i
\(10\) −0.772391 −0.244251
\(11\) 0 0
\(12\) 2.91240 + 1.60065i 0.840736 + 0.462066i
\(13\) 1.92548 3.33503i 0.534032 0.924970i −0.465178 0.885217i \(-0.654010\pi\)
0.999210 0.0397526i \(-0.0126570\pi\)
\(14\) 0.580752 1.00589i 0.155213 0.268836i
\(15\) −4.11161 2.25973i −1.06161 0.583460i
\(16\) −1.75938 3.04733i −0.439844 0.761833i
\(17\) 4.32020 1.04780 0.523902 0.851779i \(-0.324476\pi\)
0.523902 + 0.851779i \(0.324476\pi\)
\(18\) −0.458545 0.722165i −0.108080 0.170216i
\(19\) 1.62229 0.372180 0.186090 0.982533i \(-0.440418\pi\)
0.186090 + 0.982533i \(0.440418\pi\)
\(20\) 2.59861 + 4.50093i 0.581067 + 1.00644i
\(21\) 6.03434 3.65553i 1.31680 0.797701i
\(22\) 0 0
\(23\) 0.932117 1.61447i 0.194360 0.336641i −0.752331 0.658786i \(-0.771070\pi\)
0.946691 + 0.322145i \(0.104404\pi\)
\(24\) 0.0407660 + 1.93498i 0.00832132 + 0.394976i
\(25\) −1.16862 2.02411i −0.233724 0.404822i
\(26\) 1.09809 0.215354
\(27\) −0.328149 5.18578i −0.0631523 0.998004i
\(28\) −7.81547 −1.47698
\(29\) 1.77667 + 3.07729i 0.329920 + 0.571438i 0.982496 0.186286i \(-0.0596450\pi\)
−0.652576 + 0.757723i \(0.726312\pi\)
\(30\) −0.0281788 1.33752i −0.00514473 0.244197i
\(31\) 2.43230 4.21286i 0.436853 0.756652i −0.560592 0.828092i \(-0.689426\pi\)
0.997445 + 0.0714406i \(0.0227596\pi\)
\(32\) 1.61909 2.80435i 0.286218 0.495744i
\(33\) 0 0
\(34\) 0.615950 + 1.06686i 0.105634 + 0.182964i
\(35\) 11.0336 1.86502
\(36\) −2.66553 + 5.10170i −0.444255 + 0.850283i
\(37\) 7.74449 1.27319 0.636593 0.771200i \(-0.280343\pi\)
0.636593 + 0.771200i \(0.280343\pi\)
\(38\) 0.231297 + 0.400619i 0.0375214 + 0.0649889i
\(39\) 5.84540 + 3.21262i 0.936013 + 0.514430i
\(40\) −1.51338 + 2.62125i −0.239286 + 0.414456i
\(41\) 3.43607 5.95145i 0.536624 0.929461i −0.462458 0.886641i \(-0.653033\pi\)
0.999083 0.0428197i \(-0.0136341\pi\)
\(42\) 1.76306 + 0.968972i 0.272046 + 0.149516i
\(43\) 0.492496 + 0.853027i 0.0751049 + 0.130085i 0.901132 0.433545i \(-0.142738\pi\)
−0.826027 + 0.563631i \(0.809404\pi\)
\(44\) 0 0
\(45\) 3.76310 7.20238i 0.560969 1.07367i
\(46\) 0.531584 0.0783777
\(47\) −2.93317 5.08041i −0.427847 0.741054i 0.568834 0.822452i \(-0.307395\pi\)
−0.996682 + 0.0813987i \(0.974061\pi\)
\(48\) 5.21277 3.15783i 0.752399 0.455793i
\(49\) −4.79603 + 8.30697i −0.685147 + 1.18671i
\(50\) 0.333230 0.577171i 0.0471258 0.0816243i
\(51\) 0.157612 + 7.48115i 0.0220701 + 1.04757i
\(52\) −3.69440 6.39888i −0.512321 0.887365i
\(53\) −1.57183 −0.215907 −0.107953 0.994156i \(-0.534430\pi\)
−0.107953 + 0.994156i \(0.534430\pi\)
\(54\) 1.23382 0.820393i 0.167902 0.111641i
\(55\) 0 0
\(56\) −2.27579 3.94178i −0.304115 0.526743i
\(57\) 0.0591855 + 2.80927i 0.00783931 + 0.372097i
\(58\) −0.506615 + 0.877483i −0.0665218 + 0.115219i
\(59\) −5.68125 + 9.84021i −0.739635 + 1.28109i 0.213024 + 0.977047i \(0.431669\pi\)
−0.952660 + 0.304039i \(0.901665\pi\)
\(60\) −7.69930 + 4.66413i −0.993975 + 0.602137i
\(61\) −4.30374 7.45430i −0.551037 0.954425i −0.998200 0.0599721i \(-0.980899\pi\)
0.447163 0.894453i \(-0.352434\pi\)
\(62\) 1.38713 0.176166
\(63\) 6.55030 + 10.3161i 0.825260 + 1.29971i
\(64\) −6.11414 −0.764268
\(65\) 5.21561 + 9.03370i 0.646916 + 1.12049i
\(66\) 0 0
\(67\) 0.870282 1.50737i 0.106322 0.184155i −0.807956 0.589243i \(-0.799426\pi\)
0.914277 + 0.405088i \(0.132759\pi\)
\(68\) 4.14457 7.17860i 0.502603 0.870533i
\(69\) 2.82974 + 1.55522i 0.340660 + 0.187226i
\(70\) 1.57310 + 2.72470i 0.188022 + 0.325663i
\(71\) −5.74136 −0.681374 −0.340687 0.940177i \(-0.610660\pi\)
−0.340687 + 0.940177i \(0.610660\pi\)
\(72\) −3.34925 + 0.141186i −0.394713 + 0.0166389i
\(73\) 4.04662 0.473622 0.236811 0.971556i \(-0.423898\pi\)
0.236811 + 0.971556i \(0.423898\pi\)
\(74\) 1.10416 + 1.91247i 0.128356 + 0.222320i
\(75\) 3.46245 2.09750i 0.399809 0.242199i
\(76\) 1.55634 2.69566i 0.178524 0.309213i
\(77\) 0 0
\(78\) 0.0400613 + 1.90153i 0.00453605 + 0.215306i
\(79\) −2.14007 3.70672i −0.240777 0.417038i 0.720159 0.693809i \(-0.244069\pi\)
−0.960936 + 0.276771i \(0.910736\pi\)
\(80\) 9.53137 1.06564
\(81\) 8.96807 0.757436i 0.996452 0.0841595i
\(82\) 1.95958 0.216400
\(83\) −3.25009 5.62933i −0.356744 0.617899i 0.630671 0.776050i \(-0.282780\pi\)
−0.987415 + 0.158152i \(0.949446\pi\)
\(84\) −0.285129 13.5338i −0.0311101 1.47666i
\(85\) −5.85114 + 10.1345i −0.634645 + 1.09924i
\(86\) −0.140434 + 0.243239i −0.0151434 + 0.0262292i
\(87\) −5.26402 + 3.18887i −0.564362 + 0.341883i
\(88\) 0 0
\(89\) 9.26243 0.981816 0.490908 0.871211i \(-0.336665\pi\)
0.490908 + 0.871211i \(0.336665\pi\)
\(90\) 2.31512 0.0975927i 0.244035 0.0102872i
\(91\) −15.6862 −1.64436
\(92\) −1.78844 3.09768i −0.186458 0.322955i
\(93\) 7.38400 + 4.05823i 0.765685 + 0.420819i
\(94\) 0.836390 1.44867i 0.0862670 0.149419i
\(95\) −2.19718 + 3.80563i −0.225426 + 0.390449i
\(96\) 4.91527 + 2.70142i 0.501662 + 0.275712i
\(97\) 3.70634 + 6.41957i 0.376322 + 0.651809i 0.990524 0.137340i \(-0.0438553\pi\)
−0.614202 + 0.789149i \(0.710522\pi\)
\(98\) −2.73516 −0.276293
\(99\) 0 0
\(100\) −4.48444 −0.448444
\(101\) −6.85880 11.8798i −0.682476 1.18208i −0.974223 0.225588i \(-0.927570\pi\)
0.291747 0.956496i \(-0.405764\pi\)
\(102\) −1.82497 + 1.10554i −0.180699 + 0.109465i
\(103\) −2.53762 + 4.39529i −0.250039 + 0.433081i −0.963536 0.267577i \(-0.913777\pi\)
0.713497 + 0.700658i \(0.247110\pi\)
\(104\) 2.15154 3.72659i 0.210976 0.365422i
\(105\) 0.402534 + 19.1065i 0.0392833 + 1.86460i
\(106\) −0.224102 0.388156i −0.0217667 0.0377010i
\(107\) 2.77898 0.268654 0.134327 0.990937i \(-0.457113\pi\)
0.134327 + 0.990937i \(0.457113\pi\)
\(108\) −8.93168 4.42969i −0.859451 0.426247i
\(109\) 17.3573 1.66253 0.831263 0.555879i \(-0.187618\pi\)
0.831263 + 0.555879i \(0.187618\pi\)
\(110\) 0 0
\(111\) 0.282539 + 13.4109i 0.0268174 + 1.27290i
\(112\) −7.16653 + 12.4128i −0.677174 + 1.17290i
\(113\) −0.471827 + 0.817228i −0.0443858 + 0.0768784i −0.887365 0.461068i \(-0.847466\pi\)
0.842979 + 0.537946i \(0.180800\pi\)
\(114\) −0.685300 + 0.415145i −0.0641842 + 0.0388819i
\(115\) 2.52486 + 4.37318i 0.235444 + 0.407801i
\(116\) 6.81777 0.633014
\(117\) −5.34992 + 10.2395i −0.494601 + 0.946641i
\(118\) −3.24000 −0.298266
\(119\) −8.79882 15.2400i −0.806587 1.39705i
\(120\) −4.59435 2.52504i −0.419405 0.230504i
\(121\) 0 0
\(122\) 1.22720 2.12558i 0.111106 0.192441i
\(123\) 10.4313 + 5.73301i 0.940558 + 0.516928i
\(124\) −4.66682 8.08317i −0.419093 0.725890i
\(125\) −7.21271 −0.645125
\(126\) −1.61362 + 3.08838i −0.143752 + 0.275135i
\(127\) −2.45040 −0.217438 −0.108719 0.994073i \(-0.534675\pi\)
−0.108719 + 0.994073i \(0.534675\pi\)
\(128\) −4.10990 7.11856i −0.363267 0.629198i
\(129\) −1.45919 + 0.883959i −0.128475 + 0.0778282i
\(130\) −1.48722 + 2.57594i −0.130438 + 0.225925i
\(131\) 1.99869 3.46183i 0.174626 0.302461i −0.765406 0.643548i \(-0.777462\pi\)
0.940032 + 0.341087i \(0.110795\pi\)
\(132\) 0 0
\(133\) −3.30407 5.72282i −0.286500 0.496232i
\(134\) 0.496319 0.0428754
\(135\) 12.6094 + 6.25367i 1.08524 + 0.538230i
\(136\) 4.82743 0.413949
\(137\) −0.544628 0.943324i −0.0465307 0.0805936i 0.841822 0.539755i \(-0.181483\pi\)
−0.888353 + 0.459162i \(0.848150\pi\)
\(138\) 0.0193935 + 0.920525i 0.00165089 + 0.0783603i
\(139\) 1.44246 2.49842i 0.122348 0.211913i −0.798345 0.602200i \(-0.794291\pi\)
0.920693 + 0.390287i \(0.127624\pi\)
\(140\) 10.5850 18.3338i 0.894597 1.54949i
\(141\) 8.69056 5.26463i 0.731877 0.443362i
\(142\) −0.818570 1.41780i −0.0686929 0.118980i
\(143\) 0 0
\(144\) 5.65848 + 8.91158i 0.471540 + 0.742632i
\(145\) −9.62506 −0.799318
\(146\) 0.576944 + 0.999297i 0.0477482 + 0.0827024i
\(147\) −14.5599 8.00206i −1.20088 0.659999i
\(148\) 7.42964 12.8685i 0.610712 1.05778i
\(149\) 10.0874 17.4719i 0.826393 1.43135i −0.0744578 0.997224i \(-0.523723\pi\)
0.900850 0.434130i \(-0.142944\pi\)
\(150\) 1.01163 + 0.555986i 0.0825988 + 0.0453961i
\(151\) −5.53918 9.59414i −0.450772 0.780760i 0.547662 0.836700i \(-0.315518\pi\)
−0.998434 + 0.0559396i \(0.982185\pi\)
\(152\) 1.81276 0.147035
\(153\) −12.9491 + 0.545864i −1.04687 + 0.0441305i
\(154\) 0 0
\(155\) 6.58844 + 11.4115i 0.529196 + 0.916595i
\(156\) 10.9459 6.63091i 0.876377 0.530898i
\(157\) −0.166392 + 0.288200i −0.0132795 + 0.0230008i −0.872589 0.488455i \(-0.837560\pi\)
0.859309 + 0.511456i \(0.170894\pi\)
\(158\) 0.610238 1.05696i 0.0485480 0.0840875i
\(159\) −0.0573443 2.72188i −0.00454770 0.215859i
\(160\) 4.38569 + 7.59623i 0.346719 + 0.600535i
\(161\) −7.59365 −0.598464
\(162\) 1.46566 + 2.10664i 0.115153 + 0.165513i
\(163\) 13.3380 1.04472 0.522358 0.852726i \(-0.325053\pi\)
0.522358 + 0.852726i \(0.325053\pi\)
\(164\) −6.59276 11.4190i −0.514808 0.891674i
\(165\) 0 0
\(166\) 0.926759 1.60519i 0.0719304 0.124587i
\(167\) −9.45758 + 16.3810i −0.731849 + 1.26760i 0.224243 + 0.974533i \(0.428009\pi\)
−0.956092 + 0.293067i \(0.905324\pi\)
\(168\) 6.74283 4.08471i 0.520220 0.315143i
\(169\) −0.914932 1.58471i −0.0703794 0.121901i
\(170\) −3.33689 −0.255928
\(171\) −4.86256 + 0.204979i −0.371850 + 0.0156751i
\(172\) 1.88989 0.144103
\(173\) −0.757044 1.31124i −0.0575570 0.0996916i 0.835811 0.549017i \(-0.184998\pi\)
−0.893368 + 0.449325i \(0.851664\pi\)
\(174\) −1.53799 0.845276i −0.116595 0.0640802i
\(175\) −4.76018 + 8.24487i −0.359836 + 0.623254i
\(176\) 0 0
\(177\) −17.2472 9.47903i −1.29638 0.712487i
\(178\) 1.32058 + 2.28732i 0.0989819 + 0.171442i
\(179\) 13.1892 0.985810 0.492905 0.870083i \(-0.335935\pi\)
0.492905 + 0.870083i \(0.335935\pi\)
\(180\) −8.35761 13.1625i −0.622940 0.981072i
\(181\) 2.79883 0.208035 0.104018 0.994575i \(-0.466830\pi\)
0.104018 + 0.994575i \(0.466830\pi\)
\(182\) −2.23645 3.87365i −0.165777 0.287134i
\(183\) 12.7513 7.72459i 0.942606 0.571018i
\(184\) 1.04156 1.80403i 0.0767845 0.132995i
\(185\) −10.4889 + 18.1673i −0.771158 + 1.33568i
\(186\) 0.0506061 + 2.40205i 0.00371062 + 0.176127i
\(187\) 0 0
\(188\) −11.2557 −0.820907
\(189\) −17.6251 + 11.7193i −1.28204 + 0.852453i
\(190\) −1.25305 −0.0909055
\(191\) 8.37078 + 14.4986i 0.605688 + 1.04908i 0.991942 + 0.126690i \(0.0404354\pi\)
−0.386254 + 0.922392i \(0.626231\pi\)
\(192\) −0.223060 10.5877i −0.0160980 0.764099i
\(193\) −11.0197 + 19.0867i −0.793214 + 1.37389i 0.130752 + 0.991415i \(0.458261\pi\)
−0.923967 + 0.382473i \(0.875073\pi\)
\(194\) −1.05686 + 1.83053i −0.0758779 + 0.131424i
\(195\) −15.4531 + 9.36127i −1.10662 + 0.670374i
\(196\) 9.20210 + 15.9385i 0.657293 + 1.13846i
\(197\) −18.2247 −1.29845 −0.649227 0.760595i \(-0.724907\pi\)
−0.649227 + 0.760595i \(0.724907\pi\)
\(198\) 0 0
\(199\) −25.0958 −1.77899 −0.889497 0.456942i \(-0.848945\pi\)
−0.889497 + 0.456942i \(0.848945\pi\)
\(200\) −1.30582 2.26176i −0.0923358 0.159930i
\(201\) 2.64202 + 1.45204i 0.186353 + 0.102419i
\(202\) 1.95578 3.38750i 0.137608 0.238344i
\(203\) 7.23698 12.5348i 0.507937 0.879772i
\(204\) 12.5821 + 6.91512i 0.880927 + 0.484155i
\(205\) 9.30741 + 16.1209i 0.650057 + 1.12593i
\(206\) −1.44720 −0.100831
\(207\) −2.58988 + 4.95690i −0.180009 + 0.344528i
\(208\) −13.5506 −0.939563
\(209\) 0 0
\(210\) −4.66087 + 2.82350i −0.321631 + 0.194840i
\(211\) 4.13501 7.16205i 0.284666 0.493056i −0.687862 0.725841i \(-0.741451\pi\)
0.972528 + 0.232785i \(0.0747840\pi\)
\(212\) −1.50792 + 2.61180i −0.103565 + 0.179379i
\(213\) −0.209460 9.94213i −0.0143520 0.681223i
\(214\) 0.396210 + 0.686257i 0.0270844 + 0.0469115i
\(215\) −2.66808 −0.181961
\(216\) −0.366677 5.79463i −0.0249492 0.394275i
\(217\) −19.8151 −1.34514
\(218\) 2.47470 + 4.28631i 0.167608 + 0.290305i
\(219\) 0.147631 + 7.00740i 0.00997600 + 0.473516i
\(220\) 0 0
\(221\) 8.31846 14.4080i 0.559560 0.969187i
\(222\) −3.27147 + 1.98182i −0.219567 + 0.133011i
\(223\) 3.67604 + 6.36709i 0.246166 + 0.426372i 0.962459 0.271428i \(-0.0874959\pi\)
−0.716293 + 0.697800i \(0.754163\pi\)
\(224\) −13.1902 −0.881308
\(225\) 3.75850 + 5.91928i 0.250566 + 0.394619i
\(226\) −0.269081 −0.0178990
\(227\) −9.47060 16.4036i −0.628586 1.08874i −0.987836 0.155501i \(-0.950301\pi\)
0.359250 0.933241i \(-0.383032\pi\)
\(228\) 4.72476 + 2.59672i 0.312905 + 0.171972i
\(229\) 3.92972 6.80648i 0.259683 0.449785i −0.706474 0.707739i \(-0.749715\pi\)
0.966157 + 0.257954i \(0.0830485\pi\)
\(230\) −0.719959 + 1.24701i −0.0474727 + 0.0822251i
\(231\) 0 0
\(232\) 1.98527 + 3.43859i 0.130339 + 0.225754i
\(233\) 6.56942 0.430377 0.215188 0.976573i \(-0.430963\pi\)
0.215188 + 0.976573i \(0.430963\pi\)
\(234\) −3.29136 + 0.138746i −0.215163 + 0.00907009i
\(235\) 15.8904 1.03657
\(236\) 10.9006 + 18.8803i 0.709566 + 1.22900i
\(237\) 6.34072 3.84112i 0.411874 0.249508i
\(238\) 2.50897 4.34566i 0.162632 0.281687i
\(239\) −12.7731 + 22.1237i −0.826226 + 1.43107i 0.0747530 + 0.997202i \(0.476183\pi\)
−0.900979 + 0.433863i \(0.857150\pi\)
\(240\) 0.347729 + 16.5051i 0.0224458 + 1.06540i
\(241\) −1.49099 2.58247i −0.0960432 0.166352i 0.814000 0.580864i \(-0.197285\pi\)
−0.910044 + 0.414513i \(0.863952\pi\)
\(242\) 0 0
\(243\) 1.63880 + 15.5021i 0.105129 + 0.994459i
\(244\) −16.5151 −1.05727
\(245\) −12.9912 22.5014i −0.829975 1.43756i
\(246\) 0.0714906 + 3.39334i 0.00455807 + 0.216352i
\(247\) 3.12369 5.41039i 0.198756 0.344255i
\(248\) 2.71787 4.70748i 0.172585 0.298925i
\(249\) 9.62954 5.83345i 0.610248 0.369680i
\(250\) −1.02835 1.78115i −0.0650383 0.112650i
\(251\) 11.6685 0.736510 0.368255 0.929725i \(-0.379955\pi\)
0.368255 + 0.929725i \(0.379955\pi\)
\(252\) 23.4256 0.987495i 1.47567 0.0622064i
\(253\) 0 0
\(254\) −0.349364 0.605116i −0.0219211 0.0379684i
\(255\) −17.7630 9.76250i −1.11236 0.611351i
\(256\) −4.94221 + 8.56016i −0.308888 + 0.535010i
\(257\) −10.3622 + 17.9479i −0.646378 + 1.11956i 0.337604 + 0.941288i \(0.390384\pi\)
−0.983981 + 0.178271i \(0.942950\pi\)
\(258\) −0.426333 0.234311i −0.0265423 0.0145876i
\(259\) −15.7729 27.3195i −0.980083 1.69755i
\(260\) 20.0143 1.24123
\(261\) −5.71411 8.99918i −0.353694 0.557035i
\(262\) 1.13984 0.0704198
\(263\) 4.54273 + 7.86823i 0.280117 + 0.485176i 0.971413 0.237395i \(-0.0762936\pi\)
−0.691297 + 0.722571i \(0.742960\pi\)
\(264\) 0 0
\(265\) 2.12883 3.68724i 0.130773 0.226505i
\(266\) 0.942151 1.63185i 0.0577670 0.100055i
\(267\) 0.337918 + 16.0394i 0.0206802 + 0.981598i
\(268\) −1.66980 2.89218i −0.101999 0.176668i
\(269\) 7.94129 0.484189 0.242094 0.970253i \(-0.422166\pi\)
0.242094 + 0.970253i \(0.422166\pi\)
\(270\) 0.253459 + 4.00545i 0.0154251 + 0.243764i
\(271\) −3.72364 −0.226195 −0.113097 0.993584i \(-0.536077\pi\)
−0.113097 + 0.993584i \(0.536077\pi\)
\(272\) −7.60087 13.1651i −0.460870 0.798251i
\(273\) −0.572275 27.1633i −0.0346356 1.64400i
\(274\) 0.155300 0.268987i 0.00938201 0.0162501i
\(275\) 0 0
\(276\) 5.29890 3.21000i 0.318956 0.193219i
\(277\) −1.95032 3.37805i −0.117183 0.202967i 0.801467 0.598039i \(-0.204053\pi\)
−0.918650 + 0.395071i \(0.870720\pi\)
\(278\) 0.822632 0.0493382
\(279\) −6.75811 + 12.9347i −0.404597 + 0.774379i
\(280\) 12.3290 0.736799
\(281\) 0.0198115 + 0.0343146i 0.00118186 + 0.00204704i 0.866616 0.498976i \(-0.166290\pi\)
−0.865434 + 0.501023i \(0.832957\pi\)
\(282\) 2.53913 + 1.39550i 0.151203 + 0.0831006i
\(283\) 3.19694 5.53725i 0.190038 0.329156i −0.755225 0.655466i \(-0.772472\pi\)
0.945263 + 0.326311i \(0.105806\pi\)
\(284\) −5.50795 + 9.54005i −0.326837 + 0.566098i
\(285\) −6.67024 3.66595i −0.395111 0.217152i
\(286\) 0 0
\(287\) −27.9925 −1.65235
\(288\) −4.49863 + 8.61016i −0.265084 + 0.507358i
\(289\) 1.66417 0.0978923
\(290\) −1.37229 2.37687i −0.0805834 0.139575i
\(291\) −10.9813 + 6.65235i −0.643738 + 0.389968i
\(292\) 3.88211 6.72401i 0.227183 0.393493i
\(293\) −11.7037 + 20.2714i −0.683738 + 1.18427i 0.290094 + 0.956998i \(0.406314\pi\)
−0.973832 + 0.227271i \(0.927020\pi\)
\(294\) −0.0997857 4.73638i −0.00581962 0.276232i
\(295\) −15.3890 26.6545i −0.895981 1.55189i
\(296\) 8.65375 0.502989
\(297\) 0 0
\(298\) 5.75282 0.333252
\(299\) −3.58954 6.21727i −0.207589 0.359554i
\(300\) −0.163604 7.76555i −0.00944568 0.448344i
\(301\) 2.00610 3.47467i 0.115630 0.200276i
\(302\) 1.57949 2.73575i 0.0908893 0.157425i
\(303\) 20.3216 12.3106i 1.16745 0.707223i
\(304\) −2.85423 4.94367i −0.163701 0.283539i
\(305\) 23.3154 1.33503
\(306\) −1.98101 3.11990i −0.113247 0.178353i
\(307\) −29.1494 −1.66365 −0.831823 0.555042i \(-0.812702\pi\)
−0.831823 + 0.555042i \(0.812702\pi\)
\(308\) 0 0
\(309\) −7.70376 4.23397i −0.438252 0.240862i
\(310\) −1.87868 + 3.25397i −0.106702 + 0.184813i
\(311\) 9.85287 17.0657i 0.558705 0.967705i −0.438900 0.898536i \(-0.644632\pi\)
0.997605 0.0691692i \(-0.0220348\pi\)
\(312\) 6.53170 + 3.58980i 0.369785 + 0.203233i
\(313\) −0.669188 1.15907i −0.0378248 0.0655144i 0.846493 0.532399i \(-0.178710\pi\)
−0.884318 + 0.466885i \(0.845376\pi\)
\(314\) −0.0948929 −0.00535511
\(315\) −33.0714 + 1.39411i −1.86336 + 0.0785491i
\(316\) −8.21228 −0.461977
\(317\) −2.00045 3.46487i −0.112356 0.194607i 0.804364 0.594137i \(-0.202506\pi\)
−0.916720 + 0.399531i \(0.869173\pi\)
\(318\) 0.663980 0.402230i 0.0372342 0.0225560i
\(319\) 0 0
\(320\) 8.28080 14.3428i 0.462911 0.801785i
\(321\) 0.101384 + 4.81226i 0.00565872 + 0.268594i
\(322\) −1.08266 1.87522i −0.0603342 0.104502i
\(323\) 7.00864 0.389971
\(324\) 7.34489 15.6283i 0.408050 0.868239i
\(325\) −9.00060 −0.499264
\(326\) 1.90166 + 3.29377i 0.105323 + 0.182425i
\(327\) 0.633239 + 30.0570i 0.0350182 + 1.66216i
\(328\) 3.83950 6.65020i 0.212001 0.367196i
\(329\) −11.9478 + 20.6942i −0.658704 + 1.14091i
\(330\) 0 0
\(331\) −1.59017 2.75425i −0.0874034 0.151387i 0.819009 0.573780i \(-0.194524\pi\)
−0.906413 + 0.422393i \(0.861190\pi\)
\(332\) −12.4718 −0.684481
\(333\) −23.2128 + 0.978527i −1.27206 + 0.0536229i
\(334\) −5.39362 −0.295126
\(335\) 2.35736 + 4.08307i 0.128796 + 0.223082i
\(336\) −21.7563 11.9572i −1.18690 0.652318i
\(337\) −9.09890 + 15.7598i −0.495649 + 0.858489i −0.999987 0.00501702i \(-0.998403\pi\)
0.504339 + 0.863506i \(0.331736\pi\)
\(338\) 0.260891 0.451877i 0.0141906 0.0245789i
\(339\) −1.43238 0.787232i −0.0777962 0.0427566i
\(340\) 11.2265 + 19.4449i 0.608844 + 1.05455i
\(341\) 0 0
\(342\) −0.743895 1.17156i −0.0402252 0.0633510i
\(343\) 10.5583 0.570096
\(344\) 0.550319 + 0.953180i 0.0296712 + 0.0513920i
\(345\) −7.48078 + 4.53176i −0.402752 + 0.243982i
\(346\) 0.215870 0.373898i 0.0116052 0.0201009i
\(347\) −13.7071 + 23.7413i −0.735833 + 1.27450i 0.218524 + 0.975832i \(0.429876\pi\)
−0.954357 + 0.298669i \(0.903457\pi\)
\(348\) 0.248730 + 11.8061i 0.0133333 + 0.632873i
\(349\) 11.4528 + 19.8368i 0.613052 + 1.06184i 0.990723 + 0.135898i \(0.0433919\pi\)
−0.377671 + 0.925940i \(0.623275\pi\)
\(350\) −2.71471 −0.145108
\(351\) −17.9266 8.89072i −0.956849 0.474552i
\(352\) 0 0
\(353\) 14.8524 + 25.7250i 0.790511 + 1.36921i 0.925651 + 0.378379i \(0.123518\pi\)
−0.135140 + 0.990827i \(0.543148\pi\)
\(354\) −0.118204 5.61059i −0.00628245 0.298200i
\(355\) 7.77591 13.4683i 0.412703 0.714822i
\(356\) 8.88587 15.3908i 0.470950 0.815710i
\(357\) 26.0696 15.7926i 1.37975 0.835834i
\(358\) 1.88045 + 3.25703i 0.0993846 + 0.172139i
\(359\) 36.8574 1.94526 0.972631 0.232356i \(-0.0746436\pi\)
0.972631 + 0.232356i \(0.0746436\pi\)
\(360\) 4.20491 8.04800i 0.221618 0.424167i
\(361\) −16.3682 −0.861482
\(362\) 0.399041 + 0.691159i 0.0209731 + 0.0363265i
\(363\) 0 0
\(364\) −15.0485 + 26.0648i −0.788756 + 1.36617i
\(365\) −5.48061 + 9.49270i −0.286868 + 0.496871i
\(366\) 3.72557 + 2.04756i 0.194739 + 0.107028i
\(367\) 12.4303 + 21.5299i 0.648857 + 1.12385i 0.983396 + 0.181472i \(0.0580860\pi\)
−0.334539 + 0.942382i \(0.608581\pi\)
\(368\) −6.55978 −0.341952
\(369\) −9.54710 + 18.2727i −0.497002 + 0.951237i
\(370\) −5.98177 −0.310978
\(371\) 3.20129 + 5.54479i 0.166202 + 0.287871i
\(372\) 13.8271 8.37627i 0.716902 0.434290i
\(373\) 9.13952 15.8301i 0.473227 0.819653i −0.526304 0.850297i \(-0.676422\pi\)
0.999530 + 0.0306440i \(0.00975583\pi\)
\(374\) 0 0
\(375\) −0.263138 12.4900i −0.0135884 0.644981i
\(376\) −3.27755 5.67689i −0.169027 0.292763i
\(377\) 13.6838 0.704750
\(378\) −5.40691 2.68157i −0.278102 0.137925i
\(379\) −31.4593 −1.61595 −0.807977 0.589213i \(-0.799438\pi\)
−0.807977 + 0.589213i \(0.799438\pi\)
\(380\) 4.21571 + 7.30183i 0.216261 + 0.374576i
\(381\) −0.0893970 4.24328i −0.00457995 0.217390i
\(382\) −2.38691 + 4.13425i −0.122125 + 0.211527i
\(383\) 6.21588 10.7662i 0.317617 0.550129i −0.662373 0.749174i \(-0.730451\pi\)
0.979990 + 0.199045i \(0.0637841\pi\)
\(384\) 12.1770 7.37668i 0.621407 0.376440i
\(385\) 0 0
\(386\) −6.28449 −0.319872
\(387\) −1.58396 2.49458i −0.0805170 0.126807i
\(388\) 14.2226 0.722045
\(389\) −3.65984 6.33903i −0.185561 0.321402i 0.758204 0.652017i \(-0.226077\pi\)
−0.943766 + 0.330616i \(0.892744\pi\)
\(390\) −4.51493 2.48140i −0.228623 0.125650i
\(391\) 4.02694 6.97486i 0.203651 0.352734i
\(392\) −5.35912 + 9.28227i −0.270677 + 0.468826i
\(393\) 6.06765 + 3.33476i 0.306072 + 0.168217i
\(394\) −2.59837 4.50050i −0.130904 0.226732i
\(395\) 11.5938 0.583346
\(396\) 0 0
\(397\) 34.2087 1.71688 0.858442 0.512911i \(-0.171433\pi\)
0.858442 + 0.512911i \(0.171433\pi\)
\(398\) −3.57801 6.19730i −0.179350 0.310642i
\(399\) 9.78948 5.93034i 0.490087 0.296888i
\(400\) −4.11208 + 7.12234i −0.205604 + 0.356117i
\(401\) −3.73789 + 6.47421i −0.186661 + 0.323307i −0.944135 0.329559i \(-0.893100\pi\)
0.757474 + 0.652865i \(0.226433\pi\)
\(402\) 0.0181070 + 0.859459i 0.000903095 + 0.0428659i
\(403\) −9.36666 16.2235i −0.466587 0.808152i
\(404\) −26.3198 −1.30946
\(405\) −10.3692 + 22.0634i −0.515252 + 1.09634i
\(406\) 4.12723 0.204831
\(407\) 0 0
\(408\) 0.176117 + 8.35950i 0.00871910 + 0.413857i
\(409\) 1.20510 2.08729i 0.0595883 0.103210i −0.834692 0.550717i \(-0.814355\pi\)
0.894281 + 0.447507i \(0.147688\pi\)
\(410\) −2.65399 + 4.59685i −0.131071 + 0.227022i
\(411\) 1.61365 0.977529i 0.0795956 0.0482180i
\(412\) 4.86891 + 8.43321i 0.239874 + 0.415474i
\(413\) 46.2832 2.27745
\(414\) −1.59334 + 0.0671663i −0.0783082 + 0.00330104i
\(415\) 17.6073 0.864307
\(416\) −6.23505 10.7994i −0.305699 0.529485i
\(417\) 4.37905 + 2.40672i 0.214443 + 0.117857i
\(418\) 0 0
\(419\) 5.60088 9.70101i 0.273621 0.473925i −0.696165 0.717881i \(-0.745112\pi\)
0.969786 + 0.243956i \(0.0784453\pi\)
\(420\) 32.1342 + 17.6608i 1.56799 + 0.861761i
\(421\) 3.45243 + 5.97979i 0.168261 + 0.291437i 0.937809 0.347153i \(-0.112851\pi\)
−0.769547 + 0.638590i \(0.779518\pi\)
\(422\) 2.35818 0.114795
\(423\) 9.43363 + 14.8571i 0.458679 + 0.722376i
\(424\) −1.75637 −0.0852969
\(425\) −5.04868 8.74456i −0.244897 0.424174i
\(426\) 2.42530 1.46922i 0.117506 0.0711837i
\(427\) −17.5306 + 30.3638i −0.848364 + 1.46941i
\(428\) 2.66600 4.61765i 0.128866 0.223202i
\(429\) 0 0
\(430\) −0.380399 0.658871i −0.0183445 0.0317736i
\(431\) 29.1806 1.40558 0.702789 0.711398i \(-0.251938\pi\)
0.702789 + 0.711398i \(0.251938\pi\)
\(432\) −15.2254 + 10.1237i −0.732535 + 0.487078i
\(433\) −36.5360 −1.75581 −0.877903 0.478838i \(-0.841058\pi\)
−0.877903 + 0.478838i \(0.841058\pi\)
\(434\) −2.82512 4.89326i −0.135610 0.234884i
\(435\) −0.351147 16.6674i −0.0168362 0.799141i
\(436\) 16.6516 28.8415i 0.797468 1.38126i
\(437\) 1.51217 2.61915i 0.0723368 0.125291i
\(438\) −1.70940 + 1.03553i −0.0816783 + 0.0494796i
\(439\) −10.7487 18.6173i −0.513009 0.888557i −0.999886 0.0150869i \(-0.995197\pi\)
0.486877 0.873470i \(-0.338136\pi\)
\(440\) 0 0
\(441\) 13.3257 25.5048i 0.634558 1.21451i
\(442\) 4.74399 0.225649
\(443\) 16.7225 + 28.9642i 0.794510 + 1.37613i 0.923150 + 0.384440i \(0.125605\pi\)
−0.128640 + 0.991691i \(0.541061\pi\)
\(444\) 22.5550 + 12.3962i 1.07041 + 0.588297i
\(445\) −12.5447 + 21.7281i −0.594677 + 1.03001i
\(446\) −1.04822 + 1.81557i −0.0496345 + 0.0859695i
\(447\) 30.6235 + 16.8306i 1.44844 + 0.796060i
\(448\) 12.4525 + 21.5683i 0.588324 + 1.01901i
\(449\) 39.5333 1.86569 0.932846 0.360276i \(-0.117318\pi\)
0.932846 + 0.360276i \(0.117318\pi\)
\(450\) −0.925876 + 1.77208i −0.0436462 + 0.0835367i
\(451\) 0 0
\(452\) 0.905290 + 1.56801i 0.0425813 + 0.0737529i
\(453\) 16.4118 9.94203i 0.771092 0.467117i
\(454\) 2.70053 4.67745i 0.126742 0.219523i
\(455\) 21.2449 36.7973i 0.995977 1.72508i
\(456\) 0.0661344 + 3.13910i 0.00309703 + 0.147002i
\(457\) 18.7562 + 32.4866i 0.877376 + 1.51966i 0.854210 + 0.519929i \(0.174041\pi\)
0.0231665 + 0.999732i \(0.492625\pi\)
\(458\) 2.24111 0.104720
\(459\) −1.41767 22.4036i −0.0661712 1.04571i
\(460\) 9.68884 0.451745
\(461\) 9.68265 + 16.7708i 0.450966 + 0.781096i 0.998446 0.0557228i \(-0.0177463\pi\)
−0.547480 + 0.836818i \(0.684413\pi\)
\(462\) 0 0
\(463\) 7.17464 12.4268i 0.333434 0.577524i −0.649749 0.760149i \(-0.725126\pi\)
0.983183 + 0.182625i \(0.0584594\pi\)
\(464\) 6.25167 10.8282i 0.290227 0.502687i
\(465\) −19.5206 + 11.8253i −0.905245 + 0.548385i
\(466\) 0.936629 + 1.62229i 0.0433885 + 0.0751511i
\(467\) −22.3209 −1.03289 −0.516445 0.856320i \(-0.672745\pi\)
−0.516445 + 0.856320i \(0.672745\pi\)
\(468\) 11.8819 + 18.7128i 0.549239 + 0.865000i
\(469\) −7.08990 −0.327381
\(470\) 2.26556 + 3.92406i 0.104502 + 0.181003i
\(471\) −0.505136 0.277621i −0.0232754 0.0127921i
\(472\) −6.34827 + 10.9955i −0.292203 + 0.506110i
\(473\) 0 0
\(474\) 1.85257 + 1.01817i 0.0850915 + 0.0467660i
\(475\) −1.89584 3.28370i −0.0869873 0.150666i
\(476\) −33.7644 −1.54759
\(477\) 4.71129 0.198602i 0.215715 0.00909338i
\(478\) −7.28448 −0.333184
\(479\) −11.6308 20.1452i −0.531426 0.920456i −0.999327 0.0366756i \(-0.988323\pi\)
0.467902 0.883781i \(-0.345010\pi\)
\(480\) −12.9941 + 7.87168i −0.593099 + 0.359291i
\(481\) 14.9118 25.8281i 0.679921 1.17766i
\(482\) 0.425154 0.736388i 0.0193652 0.0335416i
\(483\) −0.277036 13.1497i −0.0126056 0.598331i
\(484\) 0 0
\(485\) −20.0790 −0.911740
\(486\) −3.59452 + 2.61489i −0.163051 + 0.118614i
\(487\) 0.270802 0.0122712 0.00613559 0.999981i \(-0.498047\pi\)
0.00613559 + 0.999981i \(0.498047\pi\)
\(488\) −4.80903 8.32949i −0.217695 0.377058i
\(489\) 0.486606 + 23.0970i 0.0220051 + 1.04448i
\(490\) 3.70441 6.41623i 0.167348 0.289856i
\(491\) −2.10328 + 3.64298i −0.0949196 + 0.164406i −0.909575 0.415540i \(-0.863593\pi\)
0.814655 + 0.579945i \(0.196926\pi\)
\(492\) 19.5334 11.8331i 0.880632 0.533475i
\(493\) 7.67559 + 13.2945i 0.345691 + 0.598755i
\(494\) 1.78143 0.0801504
\(495\) 0 0
\(496\) −17.1173 −0.768589
\(497\) 11.6932 + 20.2533i 0.524514 + 0.908485i
\(498\) 2.81347 + 1.54628i 0.126075 + 0.0692903i
\(499\) 7.68212 13.3058i 0.343899 0.595650i −0.641254 0.767328i \(-0.721586\pi\)
0.985153 + 0.171678i \(0.0549189\pi\)
\(500\) −6.91948 + 11.9849i −0.309449 + 0.535981i
\(501\) −28.7115 15.7797i −1.28273 0.704987i
\(502\) 1.66363 + 2.88149i 0.0742514 + 0.128607i
\(503\) −3.91570 −0.174592 −0.0872961 0.996182i \(-0.527823\pi\)
−0.0872961 + 0.996182i \(0.527823\pi\)
\(504\) 7.31936 + 11.5273i 0.326030 + 0.513467i
\(505\) 37.1573 1.65348
\(506\) 0 0
\(507\) 2.71081 1.64217i 0.120391 0.0729314i
\(508\) −2.35078 + 4.07167i −0.104299 + 0.180651i
\(509\) −14.2747 + 24.7245i −0.632715 + 1.09589i 0.354280 + 0.935139i \(0.384726\pi\)
−0.986994 + 0.160754i \(0.948607\pi\)
\(510\) −0.121738 5.77838i −0.00539066 0.255871i
\(511\) −8.24163 14.2749i −0.364588 0.631485i
\(512\) −19.2581 −0.851097
\(513\) −0.532354 8.41286i −0.0235040 0.371437i
\(514\) −5.90954 −0.260659
\(515\) −6.87375 11.9057i −0.302893 0.524627i
\(516\) 0.0689482 + 3.27266i 0.00303528 + 0.144071i
\(517\) 0 0
\(518\) 4.49763 7.79012i 0.197615 0.342278i
\(519\) 2.24301 1.35878i 0.0984572 0.0596440i
\(520\) 5.82796 + 10.0943i 0.255573 + 0.442666i
\(521\) −14.2748 −0.625388 −0.312694 0.949854i \(-0.601232\pi\)
−0.312694 + 0.949854i \(0.601232\pi\)
\(522\) 1.40763 2.69413i 0.0616101 0.117919i
\(523\) 33.1573 1.44987 0.724934 0.688818i \(-0.241870\pi\)
0.724934 + 0.688818i \(0.241870\pi\)
\(524\) −3.83486 6.64217i −0.167527 0.290165i
\(525\) −14.4510 7.94225i −0.630695 0.346628i
\(526\) −1.29535 + 2.24361i −0.0564800 + 0.0978262i
\(527\) 10.5080 18.2004i 0.457736 0.792822i
\(528\) 0 0
\(529\) 9.76231 + 16.9088i 0.424448 + 0.735166i
\(530\) 1.21406 0.0527356
\(531\) 15.7853 30.2123i 0.685023 1.31110i
\(532\) −12.6790 −0.549704
\(533\) −13.2322 22.9188i −0.573149 0.992723i
\(534\) −3.91269 + 2.37026i −0.169319 + 0.102571i
\(535\) −3.76376 + 6.51902i −0.162721 + 0.281842i
\(536\) 0.972460 1.68435i 0.0420039 0.0727528i
\(537\) 0.481178 + 22.8394i 0.0207644 + 0.985591i
\(538\) 1.13222 + 1.96107i 0.0488136 + 0.0845476i
\(539\) 0 0
\(540\) 22.4881 14.9528i 0.967733 0.643466i
\(541\) 28.4609 1.22363 0.611815 0.791001i \(-0.290440\pi\)
0.611815 + 0.791001i \(0.290440\pi\)
\(542\) −0.530894 0.919536i −0.0228039 0.0394975i
\(543\) 0.102109 + 4.84664i 0.00438190 + 0.207989i
\(544\) 6.99481 12.1154i 0.299900 0.519442i
\(545\) −23.5081 + 40.7173i −1.00698 + 1.74414i
\(546\) 6.62628 4.01411i 0.283578 0.171788i
\(547\) −15.3733 26.6274i −0.657316 1.13850i −0.981308 0.192444i \(-0.938359\pi\)
0.323992 0.946060i \(-0.394975\pi\)
\(548\) −2.08995 −0.0892781
\(549\) 13.8416 + 21.7993i 0.590746 + 0.930370i
\(550\) 0 0
\(551\) 2.88228 + 4.99226i 0.122789 + 0.212678i
\(552\) 3.16197 + 1.73781i 0.134582 + 0.0739662i
\(553\) −8.71724 + 15.0987i −0.370695 + 0.642062i
\(554\) 0.556130 0.963246i 0.0236277 0.0409244i
\(555\) −31.8423 17.5004i −1.35163 0.742853i
\(556\) −2.76764 4.79369i −0.117374 0.203298i
\(557\) 7.29459 0.309082 0.154541 0.987986i \(-0.450610\pi\)
0.154541 + 0.987986i \(0.450610\pi\)
\(558\) −4.15770 + 0.175266i −0.176009 + 0.00741959i
\(559\) 3.79316 0.160433
\(560\) −19.4122 33.6230i −0.820316 1.42083i
\(561\) 0 0
\(562\) −0.00564923 + 0.00978475i −0.000238298 + 0.000412745i
\(563\) −18.2867 + 31.6735i −0.770693 + 1.33488i 0.166490 + 0.986043i \(0.446757\pi\)
−0.937183 + 0.348837i \(0.886577\pi\)
\(564\) −0.410637 19.4911i −0.0172910 0.820725i
\(565\) −1.27805 2.21365i −0.0537681 0.0931291i
\(566\) 1.82320 0.0766349
\(567\) −20.9369 30.0932i −0.879268 1.26380i
\(568\) −6.41545 −0.269186
\(569\) 0.0757419 + 0.131189i 0.00317527 + 0.00549972i 0.867609 0.497248i \(-0.165656\pi\)
−0.864433 + 0.502747i \(0.832323\pi\)
\(570\) −0.0457144 2.16986i −0.00191476 0.0908853i
\(571\) 21.6127 37.4343i 0.904463 1.56658i 0.0828262 0.996564i \(-0.473605\pi\)
0.821637 0.570012i \(-0.193061\pi\)
\(572\) 0 0
\(573\) −24.8014 + 15.0243i −1.03609 + 0.627651i
\(574\) −3.99101 6.91264i −0.166582 0.288528i
\(575\) −4.35716 −0.181706
\(576\) 18.3262 0.772531i 0.763590 0.0321888i
\(577\) 29.1251 1.21250 0.606248 0.795276i \(-0.292674\pi\)
0.606248 + 0.795276i \(0.292674\pi\)
\(578\) 0.237268 + 0.410959i 0.00986903 + 0.0170937i
\(579\) −33.4538 18.3861i −1.39029 0.764100i
\(580\) −9.23376 + 15.9933i −0.383411 + 0.664087i
\(581\) −13.2387 + 22.9301i −0.549235 + 0.951302i
\(582\) −3.20842 1.76334i −0.132993 0.0730929i
\(583\) 0 0
\(584\) 4.52173 0.187111
\(585\) −16.7744 26.4180i −0.693534 1.09225i
\(586\) −6.67459 −0.275725
\(587\) 11.3474 + 19.6543i 0.468359 + 0.811221i 0.999346 0.0361584i \(-0.0115121\pi\)
−0.530987 + 0.847380i \(0.678179\pi\)
\(588\) −27.2644 + 16.5164i −1.12437 + 0.681126i
\(589\) 3.94590 6.83450i 0.162588 0.281610i
\(590\) 4.38814 7.60049i 0.180657 0.312907i
\(591\) −0.664883 31.5590i −0.0273496 1.29817i
\(592\) −13.6255 23.6000i −0.560003 0.969954i
\(593\) 22.9308 0.941656 0.470828 0.882225i \(-0.343955\pi\)
0.470828 + 0.882225i \(0.343955\pi\)
\(594\) 0 0
\(595\) 47.6673 1.95417
\(596\) −19.3546 33.5232i −0.792796 1.37316i
\(597\) −0.915560 43.4575i −0.0374714 1.77860i
\(598\) 1.02355 1.77284i 0.0418562 0.0724970i
\(599\) 6.25035 10.8259i 0.255382 0.442335i −0.709617 0.704588i \(-0.751132\pi\)
0.964999 + 0.262253i \(0.0844654\pi\)
\(600\) 3.86897 2.34377i 0.157950 0.0956839i
\(601\) 11.2394 + 19.4672i 0.458465 + 0.794085i 0.998880 0.0473137i \(-0.0150660\pi\)
−0.540415 + 0.841399i \(0.681733\pi\)
\(602\) 1.14407 0.0466289
\(603\) −2.41807 + 4.62806i −0.0984714 + 0.188469i
\(604\) −21.2559 −0.864892
\(605\) 0 0
\(606\) 5.93738 + 3.26317i 0.241190 + 0.132557i
\(607\) 13.3524 23.1270i 0.541956 0.938695i −0.456836 0.889551i \(-0.651017\pi\)
0.998792 0.0491443i \(-0.0156494\pi\)
\(608\) 2.62664 4.54948i 0.106524 0.184506i
\(609\) 21.9702 + 12.0747i 0.890275 + 0.489293i
\(610\) 3.32417 + 5.75763i 0.134592 + 0.233120i
\(611\) −22.5911 −0.913936
\(612\) −11.5156 + 22.0404i −0.465492 + 0.890929i
\(613\) 43.4844 1.75632 0.878160 0.478367i \(-0.158771\pi\)
0.878160 + 0.478367i \(0.158771\pi\)
\(614\) −4.15595 7.19832i −0.167721 0.290501i
\(615\) −27.5765 + 16.7055i −1.11199 + 0.673629i
\(616\) 0 0
\(617\) −20.7128 + 35.8756i −0.833864 + 1.44430i 0.0610871 + 0.998132i \(0.480543\pi\)
−0.894952 + 0.446163i \(0.852790\pi\)
\(618\) −0.0527976 2.50606i −0.00212383 0.100809i
\(619\) −4.45588 7.71780i −0.179097 0.310205i 0.762475 0.647018i \(-0.223984\pi\)
−0.941571 + 0.336813i \(0.890651\pi\)
\(620\) 25.2824 1.01536
\(621\) −8.67818 4.30397i −0.348244 0.172712i
\(622\) 5.61906 0.225304
\(623\) −18.8645 32.6743i −0.755790 1.30907i
\(624\) −0.494360 23.4651i −0.0197902 0.939354i
\(625\) 15.6118 27.0404i 0.624470 1.08161i
\(626\) 0.190818 0.330506i 0.00762662 0.0132097i
\(627\) 0 0
\(628\) 0.319255 + 0.552966i 0.0127397 + 0.0220657i
\(629\) 33.4578 1.33405
\(630\) −5.05939 7.96807i −0.201571 0.317456i
\(631\) −5.67049 −0.225739 −0.112869 0.993610i \(-0.536004\pi\)
−0.112869 + 0.993610i \(0.536004\pi\)
\(632\) −2.39134 4.14192i −0.0951222 0.164757i
\(633\) 12.5531 + 6.89917i 0.498942 + 0.274217i
\(634\) 0.570424 0.988003i 0.0226544 0.0392386i
\(635\) 3.31874 5.74823i 0.131700 0.228112i
\(636\) −4.57778 2.51594i −0.181521 0.0997633i
\(637\) 18.4693 + 31.9898i 0.731780 + 1.26748i
\(638\) 0 0
\(639\) 17.2088 0.725429i 0.680770 0.0286975i
\(640\) 22.2653 0.880112
\(641\) −13.4091 23.2252i −0.529628 0.917342i −0.999403 0.0345558i \(-0.988998\pi\)
0.469775 0.882786i \(-0.344335\pi\)
\(642\) −1.17391 + 0.711141i −0.0463306 + 0.0280665i
\(643\) −7.06923 + 12.2443i −0.278783 + 0.482866i −0.971083 0.238744i \(-0.923264\pi\)
0.692299 + 0.721610i \(0.256598\pi\)
\(644\) −7.28493 + 12.6179i −0.287067 + 0.497214i
\(645\) −0.0973384 4.62022i −0.00383270 0.181921i
\(646\) 0.999252 + 1.73075i 0.0393150 + 0.0680956i
\(647\) −1.27403 −0.0500875 −0.0250437 0.999686i \(-0.507973\pi\)
−0.0250437 + 0.999686i \(0.507973\pi\)
\(648\) 10.0210 0.846365i 0.393662 0.0332484i
\(649\) 0 0
\(650\) −1.28325 2.22266i −0.0503334 0.0871799i
\(651\) −0.722907 34.3132i −0.0283329 1.34484i
\(652\) 12.7958 22.1629i 0.501121 0.867968i
\(653\) 2.41417 4.18146i 0.0944736 0.163633i −0.814915 0.579580i \(-0.803217\pi\)
0.909389 + 0.415947i \(0.136550\pi\)
\(654\) −7.33217 + 4.44173i −0.286711 + 0.173685i
\(655\) 5.41391 + 9.37717i 0.211539 + 0.366396i
\(656\) −24.1814 −0.944124
\(657\) −12.1291 + 0.511297i −0.473201 + 0.0199476i
\(658\) −6.81379 −0.265629
\(659\) −11.0889 19.2065i −0.431961 0.748178i 0.565082 0.825035i \(-0.308845\pi\)
−0.997042 + 0.0768574i \(0.975511\pi\)
\(660\) 0 0
\(661\) 13.6987 23.7269i 0.532820 0.922871i −0.466446 0.884550i \(-0.654466\pi\)
0.999265 0.0383209i \(-0.0122009\pi\)
\(662\) 0.453433 0.785369i 0.0176232 0.0305242i
\(663\) 25.2533 + 13.8792i 0.980758 + 0.539022i
\(664\) −3.63168 6.29025i −0.140937 0.244109i
\(665\) 17.8997 0.694121
\(666\) −3.55120 5.59280i −0.137606 0.216717i
\(667\) 6.62427 0.256493
\(668\) 18.1462 + 31.4301i 0.702096 + 1.21607i
\(669\) −10.8916 + 6.59797i −0.421092 + 0.255092i
\(670\) −0.672198 + 1.16428i −0.0259693 + 0.0449801i
\(671\) 0 0
\(672\) −0.481213 22.8410i −0.0185632 0.881112i
\(673\) 17.6218 + 30.5218i 0.679269 + 1.17653i 0.975201 + 0.221320i \(0.0710365\pi\)
−0.295932 + 0.955209i \(0.595630\pi\)
\(674\) −5.18907 −0.199876
\(675\) −10.1131 + 6.72441i −0.389253 + 0.258823i
\(676\) −3.51094 −0.135036
\(677\) −22.0250 38.1484i −0.846489 1.46616i −0.884322 0.466878i \(-0.845379\pi\)
0.0378328 0.999284i \(-0.487955\pi\)
\(678\) −0.00981679 0.465959i −0.000377012 0.0178951i
\(679\) 15.0972 26.1491i 0.579376 1.00351i
\(680\) −6.53811 + 11.3243i −0.250725 + 0.434269i
\(681\) 28.0600 16.9984i 1.07526 0.651379i
\(682\) 0 0
\(683\) 42.2845 1.61797 0.808985 0.587829i \(-0.200017\pi\)
0.808985 + 0.587829i \(0.200017\pi\)
\(684\) −4.32428 + 8.27645i −0.165343 + 0.316458i
\(685\) 2.95051 0.112733
\(686\) 1.50534 + 2.60733i 0.0574743 + 0.0995484i
\(687\) 11.9299 + 6.55665i 0.455155 + 0.250152i
\(688\) 1.73297 3.00159i 0.0660689 0.114435i
\(689\) −3.02652 + 5.24208i −0.115301 + 0.199707i
\(690\) −2.18566 1.20124i −0.0832068 0.0457302i
\(691\) 4.23344 + 7.33253i 0.161048 + 0.278943i 0.935245 0.354002i \(-0.115179\pi\)
−0.774197 + 0.632945i \(0.781846\pi\)
\(692\) −2.90507 −0.110434
\(693\) 0 0
\(694\) −7.81709 −0.296733
\(695\) 3.90725 + 6.76755i 0.148210 + 0.256708i
\(696\) −5.88206 + 3.56327i −0.222959 + 0.135065i
\(697\) 14.8445 25.7115i 0.562277 0.973892i
\(698\) −3.26574 + 5.65642i −0.123610 + 0.214099i
\(699\) 0.239669 + 11.3760i 0.00906513 + 0.430281i
\(700\) 9.13331 + 15.8194i 0.345207 + 0.597915i
\(701\) −43.5518 −1.64493 −0.822465 0.568816i \(-0.807401\pi\)
−0.822465 + 0.568816i \(0.807401\pi\)
\(702\) −0.360339 5.69447i −0.0136001 0.214924i
\(703\) 12.5638 0.473854
\(704\) 0 0
\(705\) 0.579722 + 27.5168i 0.0218336 + 1.03634i
\(706\) −4.23512 + 7.33545i −0.159391 + 0.276073i
\(707\) −27.9382 + 48.3904i −1.05072 + 1.81991i
\(708\) −32.2967 + 19.5649i −1.21379 + 0.735295i
\(709\) 3.01364 + 5.21978i 0.113180 + 0.196033i 0.917051 0.398771i \(-0.130563\pi\)
−0.803871 + 0.594804i \(0.797230\pi\)
\(710\) 4.43458 0.166427
\(711\) 6.88287 + 10.8399i 0.258128 + 0.406527i
\(712\) 10.3499 0.387880
\(713\) −4.53437 7.85376i −0.169813 0.294126i
\(714\) 7.61677 + 4.18616i 0.285051 + 0.156663i
\(715\) 0 0
\(716\) 12.6530 21.9157i 0.472866 0.819028i
\(717\) −38.7769 21.3117i −1.44815 0.795900i
\(718\) 5.25492 + 9.10179i 0.196112 + 0.339676i
\(719\) 40.4066 1.50691 0.753457 0.657498i \(-0.228385\pi\)
0.753457 + 0.657498i \(0.228385\pi\)
\(720\) −28.5687 + 1.20430i −1.06469 + 0.0448817i
\(721\) 20.6732 0.769909
\(722\) −2.33368 4.04205i −0.0868505 0.150429i
\(723\) 4.41759 2.67612i 0.164292 0.0995258i
\(724\) 2.68504 4.65063i 0.0997889 0.172839i
\(725\) 4.15251 7.19235i 0.154220 0.267117i
\(726\) 0 0
\(727\) −9.36031 16.2125i −0.347155 0.601290i 0.638588 0.769549i \(-0.279519\pi\)
−0.985743 + 0.168259i \(0.946185\pi\)
\(728\) −17.5279 −0.649628
\(729\) −26.7846 + 3.40342i −0.992024 + 0.126053i
\(730\) −3.12558 −0.115683
\(731\) 2.12768 + 3.68525i 0.0786951 + 0.136304i
\(732\) −0.602513 28.5986i −0.0222695 1.05704i
\(733\) 0.282096 0.488604i 0.0104194 0.0180470i −0.860769 0.508996i \(-0.830017\pi\)
0.871188 + 0.490949i \(0.163350\pi\)
\(734\) −3.54448 + 6.13923i −0.130829 + 0.226603i
\(735\) 38.4909 23.3173i 1.41976 0.860071i
\(736\) −3.01837 5.22796i −0.111258 0.192705i
\(737\) 0 0
\(738\) −5.87353 + 0.247596i −0.216208 + 0.00911413i
\(739\) −1.94812 −0.0716629 −0.0358315 0.999358i \(-0.511408\pi\)
−0.0358315 + 0.999358i \(0.511408\pi\)
\(740\) 20.1249 + 34.8574i 0.739806 + 1.28138i
\(741\) 9.48296 + 5.21181i 0.348365 + 0.191461i
\(742\) −0.912842 + 1.58109i −0.0335115 + 0.0580436i
\(743\) −13.6313 + 23.6102i −0.500086 + 0.866174i 0.499914 + 0.866075i \(0.333365\pi\)
−1.00000 9.89898e-5i \(0.999968\pi\)
\(744\) 8.25095 + 4.53470i 0.302494 + 0.166250i
\(745\) 27.3241 + 47.3267i 1.00108 + 1.73392i
\(746\) 5.21224 0.190834
\(747\) 10.4529 + 16.4623i 0.382452 + 0.602325i
\(748\) 0 0
\(749\) −5.65985 9.80315i −0.206807 0.358199i
\(750\) 3.04684 1.84573i 0.111255 0.0673967i
\(751\) −15.1531 + 26.2460i −0.552946 + 0.957730i 0.445115 + 0.895474i \(0.353163\pi\)
−0.998060 + 0.0622562i \(0.980170\pi\)
\(752\) −10.3211 + 17.8767i −0.376372 + 0.651896i
\(753\) 0.425698 + 20.2060i 0.0155133 + 0.736347i
\(754\) 1.95095 + 3.37915i 0.0710495 + 0.123061i
\(755\) 30.0083 1.09211
\(756\) 2.56464 + 40.5293i 0.0932750 + 1.47404i
\(757\) 11.1070 0.403689 0.201845 0.979418i \(-0.435306\pi\)
0.201845 + 0.979418i \(0.435306\pi\)
\(758\) −4.48528 7.76874i −0.162913 0.282173i
\(759\) 0 0
\(760\) −2.45515 + 4.25244i −0.0890576 + 0.154252i
\(761\) −16.6705 + 28.8741i −0.604304 + 1.04669i 0.387857 + 0.921720i \(0.373216\pi\)
−0.992161 + 0.124966i \(0.960118\pi\)
\(762\) 1.03511 0.627058i 0.0374982 0.0227159i
\(763\) −35.3510 61.2298i −1.27979 2.21667i
\(764\) 32.1219 1.16213
\(765\) 16.2573 31.1157i 0.587786 1.12499i
\(766\) 3.54490 0.128082
\(767\) 21.8782 + 37.8942i 0.789977 + 1.36828i
\(768\) −15.0037 8.24597i −0.541398 0.297551i
\(769\) −25.9701 + 44.9815i −0.936504 + 1.62207i −0.164575 + 0.986364i \(0.552625\pi\)
−0.771929 + 0.635709i \(0.780708\pi\)
\(770\) 0 0
\(771\) −31.4578 17.2891i −1.13293 0.622653i
\(772\) 21.1434 + 36.6214i 0.760966 + 1.31803i
\(773\) −7.72276 −0.277768 −0.138884 0.990309i \(-0.544352\pi\)
−0.138884 + 0.990309i \(0.544352\pi\)
\(774\) 0.390195 0.746815i 0.0140253 0.0268437i
\(775\) −11.3697 −0.408412
\(776\) 4.14150 + 7.17328i 0.148671 + 0.257506i
\(777\) 46.7329 28.3102i 1.67653 1.01562i
\(778\) 1.04360 1.80756i 0.0374148 0.0648043i
\(779\) 5.57432 9.65501i 0.199721 0.345926i
\(780\) 0.730173 + 34.6580i 0.0261444 + 1.24096i
\(781\) 0 0
\(782\) 2.29655 0.0821244
\(783\) 15.3751 10.2232i 0.549462 0.365349i
\(784\) 33.7521 1.20543
\(785\) −0.450712 0.780656i −0.0160866 0.0278628i
\(786\) 0.0415845 + 1.97383i 0.00148327 + 0.0704042i
\(787\) −9.85316 + 17.0662i −0.351227 + 0.608343i −0.986465 0.163973i \(-0.947569\pi\)
0.635238 + 0.772317i \(0.280902\pi\)
\(788\) −17.4837 + 30.2827i −0.622833 + 1.07878i
\(789\) −13.4594 + 8.15354i −0.479168 + 0.290274i
\(790\) 1.65297 + 2.86303i 0.0588102 + 0.101862i
\(791\) 3.84382 0.136670
\(792\) 0 0
\(793\) −33.1470 −1.17709
\(794\) 4.87727 + 8.44768i 0.173088 + 0.299797i
\(795\) 6.46273 + 3.55190i 0.229210 + 0.125973i
\(796\) −24.0755 + 41.7000i −0.853334 + 1.47802i
\(797\) −7.01288 + 12.1467i −0.248409 + 0.430257i −0.963085 0.269199i \(-0.913241\pi\)
0.714676 + 0.699456i \(0.246574\pi\)
\(798\) 2.86020 + 1.57196i 0.101250 + 0.0556467i
\(799\) −12.6719 21.9484i −0.448300 0.776479i
\(800\) −7.56841 −0.267584
\(801\) −27.7626 + 1.17032i −0.980945 + 0.0413513i
\(802\) −2.13170 −0.0752731
\(803\) 0 0
\(804\) 4.94737 2.99705i 0.174480 0.105698i
\(805\) 10.2846 17.8134i 0.362484 0.627841i
\(806\) 2.67089 4.62611i 0.0940780 0.162948i
\(807\) 0.289719 + 13.7517i 0.0101986 + 0.484081i
\(808\) −7.66408 13.2746i −0.269621 0.466998i
\(809\) 20.9298 0.735854 0.367927 0.929855i \(-0.380068\pi\)
0.367927 + 0.929855i \(0.380068\pi\)
\(810\) −6.92686 + 0.585037i −0.243385 + 0.0205561i
\(811\) −1.94293 −0.0682255 −0.0341127 0.999418i \(-0.510861\pi\)
−0.0341127 + 0.999418i \(0.510861\pi\)
\(812\) −13.8855 24.0504i −0.487286 0.844005i
\(813\) −0.135848 6.44810i −0.00476440 0.226145i
\(814\) 0 0
\(815\) −18.0646 + 31.2888i −0.632775 + 1.09600i
\(816\) 22.5202 13.6425i 0.788366 0.477582i
\(817\) 0.798973 + 1.38386i 0.0279525 + 0.0484152i
\(818\) 0.687264 0.0240296
\(819\) 47.0169 1.98198i 1.64291 0.0692559i
\(820\) 35.7161 1.24726
\(821\) 5.42088 + 9.38924i 0.189190 + 0.327687i 0.944980 0.327127i \(-0.106080\pi\)
−0.755790 + 0.654814i \(0.772747\pi\)
\(822\) 0.471462 + 0.259114i 0.0164441 + 0.00903765i
\(823\) −23.8339 + 41.2815i −0.830798 + 1.43898i 0.0666091 + 0.997779i \(0.478782\pi\)
−0.897407 + 0.441204i \(0.854551\pi\)
\(824\) −2.83556 + 4.91134i −0.0987815 + 0.171094i
\(825\) 0 0
\(826\) 6.59880 + 11.4295i 0.229601 + 0.397681i
\(827\) −37.4150 −1.30105 −0.650524 0.759486i \(-0.725451\pi\)
−0.650524 + 0.759486i \(0.725451\pi\)
\(828\) 5.75197 + 9.05881i 0.199895 + 0.314816i
\(829\) 10.7069 0.371866 0.185933 0.982562i \(-0.440469\pi\)
0.185933 + 0.982562i \(0.440469\pi\)
\(830\) 2.51034 + 4.34804i 0.0871353 + 0.150923i
\(831\) 5.77850 3.50054i 0.200454 0.121432i
\(832\) −11.7727 + 20.3908i −0.408143 + 0.706925i
\(833\) −20.7198 + 35.8878i −0.717900 + 1.24344i
\(834\) 0.0300117 + 1.42452i 0.00103922 + 0.0493272i
\(835\) −25.6181 44.3718i −0.886549 1.53555i
\(836\) 0 0
\(837\) −22.6451 11.2309i −0.782730 0.388197i
\(838\) 3.19416 0.110341
\(839\) −7.68075 13.3035i −0.265169 0.459286i 0.702439 0.711744i \(-0.252094\pi\)
−0.967608 + 0.252458i \(0.918761\pi\)
\(840\) 0.449794 + 21.3497i 0.0155194 + 0.736636i
\(841\) 8.18687 14.1801i 0.282306 0.488968i
\(842\) −0.984455 + 1.70513i −0.0339266 + 0.0587625i
\(843\) −0.0586987 + 0.0355589i −0.00202169 + 0.00122471i
\(844\) −7.93381 13.7418i −0.273093 0.473011i
\(845\) 4.95661 0.170513
\(846\) −2.32390 + 4.44783i −0.0798974 + 0.152920i
\(847\) 0 0
\(848\) 2.76543 + 4.78987i 0.0949654 + 0.164485i
\(849\) 9.70531 + 5.33401i 0.333085 + 0.183063i
\(850\) 1.43962 2.49350i 0.0493786 0.0855263i
\(851\) 7.21877 12.5033i 0.247456 0.428607i
\(852\) −16.7211 9.18988i −0.572856 0.314840i
\(853\) 20.7321 + 35.9091i 0.709854 + 1.22950i 0.964911 + 0.262578i \(0.0845726\pi\)
−0.255057 + 0.966926i \(0.582094\pi\)
\(854\) −9.99763 −0.342112
\(855\) 6.10485 11.6844i 0.208781 0.399597i
\(856\) 3.10525 0.106135
\(857\) 9.20273 + 15.9396i 0.314359 + 0.544486i 0.979301 0.202409i \(-0.0648770\pi\)
−0.664942 + 0.746895i \(0.731544\pi\)
\(858\) 0 0
\(859\) 7.52426 13.0324i 0.256725 0.444660i −0.708638 0.705572i \(-0.750690\pi\)
0.965363 + 0.260912i \(0.0840233\pi\)
\(860\) −2.55961 + 4.43337i −0.0872819 + 0.151177i
\(861\) −1.02124 48.4738i −0.0348038 1.65198i
\(862\) 4.16040 + 7.20602i 0.141704 + 0.245438i
\(863\) −14.4298 −0.491196 −0.245598 0.969372i \(-0.578984\pi\)
−0.245598 + 0.969372i \(0.578984\pi\)
\(864\) −15.0740 7.47601i −0.512829 0.254339i
\(865\) 4.10126 0.139447
\(866\) −5.20909 9.02240i −0.177012 0.306594i
\(867\) 0.0607132 + 2.88179i 0.00206193 + 0.0978706i
\(868\) −19.0095 + 32.9255i −0.645225 + 1.11756i
\(869\) 0 0
\(870\) 4.06588 2.46306i 0.137846 0.0835054i
\(871\) −3.35142 5.80482i −0.113558 0.196689i
\(872\) 19.3952 0.656803
\(873\) −11.9203 18.7733i −0.403440 0.635381i
\(874\) 0.862385 0.0291706
\(875\) 14.6899 + 25.4436i 0.496609 + 0.860152i
\(876\) 11.7854 + 6.47721i 0.398191 + 0.218845i
\(877\) −12.0377 + 20.8499i −0.406484 + 0.704050i −0.994493 0.104804i \(-0.966579\pi\)
0.588009 + 0.808854i \(0.299912\pi\)
\(878\) 3.06498 5.30870i 0.103438 0.179160i
\(879\) −35.5303 19.5274i −1.19841 0.658642i
\(880\) 0 0
\(881\) −10.0956 −0.340129 −0.170064 0.985433i \(-0.554398\pi\)
−0.170064 + 0.985433i \(0.554398\pi\)
\(882\) 8.19820 0.345591i 0.276048 0.0116367i
\(883\) 50.7198 1.70686 0.853429 0.521209i \(-0.174519\pi\)
0.853429 + 0.521209i \(0.174519\pi\)
\(884\) −15.9605 27.6445i −0.536811 0.929785i
\(885\) 45.5953 27.6210i 1.53267 0.928470i
\(886\) −4.76839 + 8.25910i −0.160197 + 0.277470i
\(887\) −1.28635 + 2.22803i −0.0431915 + 0.0748099i −0.886813 0.462128i \(-0.847086\pi\)
0.843621 + 0.536938i \(0.180419\pi\)
\(888\) 0.315711 + 14.9854i 0.0105946 + 0.502878i
\(889\) 4.99065 + 8.64407i 0.167381 + 0.289913i
\(890\) −7.15422 −0.239810
\(891\) 0 0
\(892\) 14.1064 0.472316
\(893\) −4.75847 8.24191i −0.159236 0.275805i
\(894\) 0.209878 + 9.96196i 0.00701936 + 0.333178i
\(895\) −17.8631 + 30.9397i −0.597097 + 1.03420i
\(896\) −16.7410 + 28.9963i −0.559278 + 0.968698i
\(897\) 10.6353 6.44271i 0.355102 0.215116i
\(898\) 5.63643 + 9.76258i 0.188090 + 0.325781i
\(899\) 17.2856 0.576506
\(900\) 13.4414 0.566615i 0.448046 0.0188872i
\(901\) −6.79061 −0.226228
\(902\) 0 0
\(903\) 6.09015 + 3.34713i 0.202668 + 0.111386i
\(904\) −0.527223 + 0.913178i −0.0175352 + 0.0303718i
\(905\) −3.79064 + 6.56559i −0.126005 + 0.218247i
\(906\) 4.79504 + 2.63534i 0.159304 + 0.0875533i
\(907\) −5.14743 8.91562i −0.170918 0.296038i 0.767823 0.640662i \(-0.221340\pi\)
−0.938741 + 0.344624i \(0.888007\pi\)
\(908\) −36.3423 −1.20606
\(909\) 22.0592 + 34.7411i 0.731657 + 1.15229i
\(910\) 12.1159 0.401638
\(911\) 7.80127 + 13.5122i 0.258468 + 0.447679i 0.965832 0.259170i \(-0.0834491\pi\)
−0.707364 + 0.706850i \(0.750116\pi\)
\(912\) 8.45665 5.12293i 0.280028 0.169637i
\(913\) 0 0
\(914\) −5.34829 + 9.26351i −0.176906 + 0.306410i
\(915\) 0.850605 + 40.3744i 0.0281201 + 1.33474i
\(916\) −7.53992 13.0595i −0.249126 0.431499i
\(917\) −16.2826 −0.537700
\(918\) 5.33036 3.54427i 0.175928 0.116978i
\(919\) −11.2124 −0.369864 −0.184932 0.982751i \(-0.559206\pi\)
−0.184932 + 0.982751i \(0.559206\pi\)
\(920\) 2.82130 + 4.88663i 0.0930154 + 0.161107i
\(921\) −1.06345 50.4771i −0.0350418 1.66328i
\(922\) −2.76099 + 4.78218i −0.0909284 + 0.157493i
\(923\) −11.0549 + 19.1476i −0.363875 + 0.630251i
\(924\) 0 0
\(925\) −9.05036 15.6757i −0.297574 0.515413i
\(926\) 4.09167 0.134461
\(927\) 7.05076 13.4948i 0.231577 0.443228i
\(928\) 11.5064 0.377715
\(929\) −11.7638 20.3754i −0.385956 0.668496i 0.605945 0.795506i \(-0.292795\pi\)
−0.991901 + 0.127011i \(0.959462\pi\)
\(930\) −5.70334 3.13454i −0.187020 0.102786i
\(931\) −7.78057 + 13.4763i −0.254998 + 0.441669i
\(932\) 6.30234 10.9160i 0.206440 0.357565i
\(933\) 29.9115 + 16.4393i 0.979258 + 0.538198i
\(934\) −3.18239 5.51206i −0.104131 0.180360i
\(935\) 0 0
\(936\) −5.97805 + 11.4417i −0.195399 + 0.373983i
\(937\) −18.6555 −0.609448 −0.304724 0.952441i \(-0.598564\pi\)
−0.304724 + 0.952441i \(0.598564\pi\)
\(938\) −1.01084 1.75082i −0.0330050 0.0571663i
\(939\) 1.98271 1.20110i 0.0647032 0.0391963i
\(940\) 15.2444 26.4040i 0.497216 0.861204i
\(941\) −16.2463 + 28.1394i −0.529615 + 0.917320i 0.469789 + 0.882779i \(0.344330\pi\)
−0.999403 + 0.0345407i \(0.989003\pi\)
\(942\) −0.00346194 0.164323i −0.000112796 0.00535393i
\(943\) −6.40565 11.0949i −0.208597 0.361300i
\(944\) 39.9818 1.30130
\(945\) −3.62066 57.2177i −0.117780 1.86129i
\(946\) 0 0
\(947\) 1.92137 + 3.32790i 0.0624360 + 0.108142i 0.895554 0.444953i \(-0.146780\pi\)
−0.833118 + 0.553096i \(0.813446\pi\)
\(948\) −0.299605 14.2209i −0.00973073 0.461874i
\(949\) 7.79169 13.4956i 0.252929 0.438086i
\(950\) 0.540597 0.936341i 0.0175393 0.0303789i
\(951\) 5.92702 3.59051i 0.192197 0.116430i
\(952\) −9.83187 17.0293i −0.318653 0.551923i
\(953\) −19.0891 −0.618358 −0.309179 0.951004i \(-0.600054\pi\)
−0.309179 + 0.951004i \(0.600054\pi\)
\(954\) 0.720753 + 1.13512i 0.0233352 + 0.0367508i
\(955\) −45.3484 −1.46744
\(956\) 24.5077 + 42.4486i 0.792636 + 1.37289i
\(957\) 0 0
\(958\) 3.31651 5.74436i 0.107152 0.185592i
\(959\) −2.21845 + 3.84247i −0.0716376 + 0.124080i
\(960\) 25.1390 + 13.8163i 0.811357 + 0.445920i
\(961\) 3.66788 + 6.35296i 0.118319 + 0.204934i
\(962\) 8.50417 0.274186
\(963\) −8.32953 + 0.351128i −0.268416 + 0.0113149i
\(964\) −5.72150 −0.184277
\(965\) −29.8494 51.7007i −0.960886 1.66430i
\(966\) 3.20776 1.94322i 0.103208 0.0625220i
\(967\) 13.2813 23.0039i 0.427099 0.739757i −0.569515 0.821981i \(-0.692869\pi\)
0.996614 + 0.0822239i \(0.0262023\pi\)
\(968\) 0 0
\(969\) 0.255693 + 12.1366i 0.00821406 + 0.389885i
\(970\) −2.86274 4.95842i −0.0919172 0.159205i
\(971\) −51.1079 −1.64013 −0.820066 0.572269i \(-0.806063\pi\)
−0.820066 + 0.572269i \(0.806063\pi\)
\(972\) 27.3310 + 12.1487i 0.876641 + 0.389671i
\(973\) −11.7513 −0.376728
\(974\) 0.0386093 + 0.0668733i 0.00123712 + 0.00214276i
\(975\) −0.328365 15.5860i −0.0105161 0.499153i
\(976\) −15.1438 + 26.2298i −0.484741 + 0.839596i
\(977\) 10.5873 18.3377i 0.338717 0.586676i −0.645474 0.763782i \(-0.723340\pi\)
0.984192 + 0.177106i \(0.0566736\pi\)
\(978\) −5.63434 + 3.41321i −0.180166 + 0.109142i
\(979\) 0 0
\(980\) −49.8521 −1.59247
\(981\) −52.0257 + 2.19312i −1.66105 + 0.0700208i
\(982\) −1.19949 −0.0382774
\(983\) −25.4177 44.0248i −0.810699 1.40417i −0.912375 0.409355i \(-0.865754\pi\)
0.101676 0.994818i \(-0.467579\pi\)
\(984\) 11.6560 + 6.40611i 0.371580 + 0.204219i
\(985\) 24.6829 42.7520i 0.786462 1.36219i
\(986\) −2.18868 + 3.79091i −0.0697018 + 0.120727i
\(987\) −36.2713 19.9346i −1.15453 0.634526i
\(988\) −5.99340 10.3809i −0.190675 0.330259i
\(989\) 1.83625 0.0583895
\(990\) 0 0
\(991\) −13.1480 −0.417662 −0.208831 0.977952i \(-0.566966\pi\)
−0.208831 + 0.977952i \(0.566966\pi\)
\(992\) −7.87622 13.6420i −0.250070 0.433134i
\(993\) 4.71142 2.85412i 0.149513 0.0905727i
\(994\) −3.33431 + 5.77519i −0.105758 + 0.183178i
\(995\) 33.9889 58.8705i 1.07752 1.86632i
\(996\) −0.455005 21.5971i −0.0144174 0.684329i
\(997\) −18.6043 32.2237i −0.589205 1.02053i −0.994337 0.106275i \(-0.966108\pi\)
0.405132 0.914258i \(-0.367226\pi\)
\(998\) 4.38109 0.138681
\(999\) −2.54135 40.1612i −0.0804047 1.27064i
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 1089.2.e.o.364.10 36
9.4 even 3 9801.2.a.co.1.9 18
9.5 odd 6 9801.2.a.cn.1.10 18
9.7 even 3 inner 1089.2.e.o.727.10 36
11.7 odd 10 99.2.m.b.49.5 yes 72
11.8 odd 10 99.2.m.b.31.5 yes 72
11.10 odd 2 1089.2.e.p.364.9 36
33.8 even 10 297.2.n.b.64.5 72
33.29 even 10 297.2.n.b.280.5 72
99.7 odd 30 99.2.m.b.16.5 72
99.29 even 30 297.2.n.b.181.5 72
99.32 even 6 9801.2.a.cp.1.9 18
99.40 odd 30 891.2.f.f.82.5 36
99.41 even 30 891.2.f.e.163.5 36
99.43 odd 6 1089.2.e.p.727.9 36
99.52 odd 30 99.2.m.b.97.5 yes 72
99.74 even 30 297.2.n.b.262.5 72
99.76 odd 6 9801.2.a.cm.1.10 18
99.85 odd 30 891.2.f.f.163.5 36
99.95 even 30 891.2.f.e.82.5 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.16.5 72 99.7 odd 30
99.2.m.b.31.5 yes 72 11.8 odd 10
99.2.m.b.49.5 yes 72 11.7 odd 10
99.2.m.b.97.5 yes 72 99.52 odd 30
297.2.n.b.64.5 72 33.8 even 10
297.2.n.b.181.5 72 99.29 even 30
297.2.n.b.262.5 72 99.74 even 30
297.2.n.b.280.5 72 33.29 even 10
891.2.f.e.82.5 36 99.95 even 30
891.2.f.e.163.5 36 99.41 even 30
891.2.f.f.82.5 36 99.40 odd 30
891.2.f.f.163.5 36 99.85 odd 30
1089.2.e.o.364.10 36 1.1 even 1 trivial
1089.2.e.o.727.10 36 9.7 even 3 inner
1089.2.e.p.364.9 36 11.10 odd 2
1089.2.e.p.727.9 36 99.43 odd 6
9801.2.a.cm.1.10 18 99.76 odd 6
9801.2.a.cn.1.10 18 9.5 odd 6
9801.2.a.co.1.9 18 9.4 even 3
9801.2.a.cp.1.9 18 99.32 even 6