Properties

Label 605.2.g.h.366.2
Level $605$
Weight $2$
Character 605.366
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
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] = [605,2,Mod(81,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.324000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 366.2
Root \(-0.535233 - 1.64728i\) of defining polynomial
Character \(\chi\) \(=\) 605.366
Dual form 605.2.g.h.81.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40126 - 1.01807i) q^{2} +(0.618034 + 1.90211i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.80252 + 2.03615i) q^{6} +(-1.07047 + 3.29456i) q^{7} +(0.535233 + 1.64728i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(1.40126 - 1.01807i) q^{2} +(0.618034 + 1.90211i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.80252 + 2.03615i) q^{6} +(-1.07047 + 3.29456i) q^{7} +(0.535233 + 1.64728i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.73205 q^{10} +2.00000 q^{12} +(1.85410 + 5.70634i) q^{14} +(0.618034 - 1.90211i) q^{15} +(4.04508 + 2.93893i) q^{16} +(-5.60503 - 4.07230i) q^{17} +(-0.535233 + 1.64728i) q^{18} +(2.14093 + 6.58911i) q^{19} +(-0.809017 + 0.587785i) q^{20} -6.92820 q^{21} +6.00000 q^{23} +(-2.80252 + 2.03615i) q^{24} +(0.309017 + 0.951057i) q^{25} +(3.23607 + 2.35114i) q^{27} +(2.80252 + 2.03615i) q^{28} +(-1.07047 - 3.29456i) q^{30} +(-3.23607 + 2.35114i) q^{31} +5.19615 q^{32} -12.0000 q^{34} +(2.80252 - 2.03615i) q^{35} +(0.309017 + 0.951057i) q^{36} +(3.09017 - 9.51057i) q^{37} +(9.70820 + 7.05342i) q^{38} +(0.535233 - 1.64728i) q^{40} +(-2.14093 - 6.58911i) q^{41} +(-9.70820 + 7.05342i) q^{42} +3.46410 q^{43} +1.00000 q^{45} +(8.40755 - 6.10844i) q^{46} +(-1.85410 - 5.70634i) q^{47} +(-3.09017 + 9.51057i) q^{48} +(-4.04508 - 2.93893i) q^{49} +(1.40126 + 1.01807i) q^{50} +(4.28187 - 13.1782i) q^{51} +(4.85410 - 3.52671i) q^{53} +6.92820 q^{54} -6.00000 q^{56} +(-11.2101 + 8.14459i) q^{57} +(-1.61803 - 1.17557i) q^{60} +(5.60503 + 4.07230i) q^{61} +(-2.14093 + 6.58911i) q^{62} +(-1.07047 - 3.29456i) q^{63} +(-0.809017 + 0.587785i) q^{64} +10.0000 q^{67} +(-5.60503 + 4.07230i) q^{68} +(3.70820 + 11.4127i) q^{69} +(1.85410 - 5.70634i) q^{70} +(-1.40126 - 1.01807i) q^{72} +(2.14093 - 6.58911i) q^{73} +(-5.35233 - 16.4728i) q^{74} +(-1.61803 + 1.17557i) q^{75} +6.92820 q^{76} +(-5.60503 + 4.07230i) q^{79} +(-1.54508 - 4.75528i) q^{80} +(-3.39919 + 10.4616i) q^{81} +(-9.70820 - 7.05342i) q^{82} +(-14.0126 - 10.1807i) q^{83} +(-2.14093 + 6.58911i) q^{84} +(2.14093 + 6.58911i) q^{85} +(4.85410 - 3.52671i) q^{86} -6.00000 q^{89} +(1.40126 - 1.01807i) q^{90} +(1.85410 - 5.70634i) q^{92} +(-6.47214 - 4.70228i) q^{93} +(-8.40755 - 6.10844i) q^{94} +(2.14093 - 6.58911i) q^{95} +(3.21140 + 9.88367i) q^{96} +(8.09017 - 5.87785i) q^{97} -8.66025 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{9} + 16 q^{12} - 12 q^{14} - 4 q^{15} + 10 q^{16} - 2 q^{20} + 48 q^{23} - 2 q^{25} + 8 q^{27} - 8 q^{31} - 96 q^{34} - 2 q^{36} - 20 q^{37} + 24 q^{38} - 24 q^{42} + 8 q^{45} + 12 q^{47} + 20 q^{48} - 10 q^{49} + 12 q^{53} - 48 q^{56} - 4 q^{60} - 2 q^{64} + 80 q^{67} - 24 q^{69} - 12 q^{70} - 4 q^{75} + 10 q^{80} + 22 q^{81} - 24 q^{82} + 12 q^{86} - 48 q^{89} - 12 q^{92} - 16 q^{93} + 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40126 1.01807i 0.990839 0.719887i 0.0307347 0.999528i \(-0.490215\pi\)
0.960105 + 0.279641i \(0.0902153\pi\)
\(3\) 0.618034 + 1.90211i 0.356822 + 1.09819i 0.954945 + 0.296781i \(0.0959133\pi\)
−0.598123 + 0.801404i \(0.704087\pi\)
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) −0.809017 0.587785i −0.361803 0.262866i
\(6\) 2.80252 + 2.03615i 1.14412 + 0.831254i
\(7\) −1.07047 + 3.29456i −0.404598 + 1.24523i 0.516632 + 0.856208i \(0.327186\pi\)
−0.921230 + 0.389018i \(0.872814\pi\)
\(8\) 0.535233 + 1.64728i 0.189233 + 0.582401i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) −1.73205 −0.547723
\(11\) 0 0
\(12\) 2.00000 0.577350
\(13\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(14\) 1.85410 + 5.70634i 0.495530 + 1.52508i
\(15\) 0.618034 1.90211i 0.159576 0.491123i
\(16\) 4.04508 + 2.93893i 1.01127 + 0.734732i
\(17\) −5.60503 4.07230i −1.35942 0.987677i −0.998482 0.0550873i \(-0.982456\pi\)
−0.360939 0.932589i \(-0.617544\pi\)
\(18\) −0.535233 + 1.64728i −0.126156 + 0.388267i
\(19\) 2.14093 + 6.58911i 0.491164 + 1.51165i 0.822851 + 0.568257i \(0.192382\pi\)
−0.331688 + 0.943389i \(0.607618\pi\)
\(20\) −0.809017 + 0.587785i −0.180902 + 0.131433i
\(21\) −6.92820 −1.51186
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −2.80252 + 2.03615i −0.572061 + 0.415627i
\(25\) 0.309017 + 0.951057i 0.0618034 + 0.190211i
\(26\) 0 0
\(27\) 3.23607 + 2.35114i 0.622782 + 0.452477i
\(28\) 2.80252 + 2.03615i 0.529626 + 0.384796i
\(29\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(30\) −1.07047 3.29456i −0.195440 0.601501i
\(31\) −3.23607 + 2.35114i −0.581215 + 0.422277i −0.839162 0.543882i \(-0.816954\pi\)
0.257947 + 0.966159i \(0.416954\pi\)
\(32\) 5.19615 0.918559
\(33\) 0 0
\(34\) −12.0000 −2.05798
\(35\) 2.80252 2.03615i 0.473712 0.344172i
\(36\) 0.309017 + 0.951057i 0.0515028 + 0.158509i
\(37\) 3.09017 9.51057i 0.508021 1.56353i −0.287611 0.957747i \(-0.592861\pi\)
0.795632 0.605780i \(-0.207139\pi\)
\(38\) 9.70820 + 7.05342i 1.57488 + 1.14422i
\(39\) 0 0
\(40\) 0.535233 1.64728i 0.0846278 0.260458i
\(41\) −2.14093 6.58911i −0.334357 1.02905i −0.967038 0.254633i \(-0.918045\pi\)
0.632680 0.774413i \(-0.281955\pi\)
\(42\) −9.70820 + 7.05342i −1.49801 + 1.08837i
\(43\) 3.46410 0.528271 0.264135 0.964486i \(-0.414913\pi\)
0.264135 + 0.964486i \(0.414913\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 8.40755 6.10844i 1.23963 0.900641i
\(47\) −1.85410 5.70634i −0.270449 0.832355i −0.990388 0.138318i \(-0.955830\pi\)
0.719939 0.694037i \(-0.244170\pi\)
\(48\) −3.09017 + 9.51057i −0.446028 + 1.37273i
\(49\) −4.04508 2.93893i −0.577869 0.419847i
\(50\) 1.40126 + 1.01807i 0.198168 + 0.143977i
\(51\) 4.28187 13.1782i 0.599581 1.84532i
\(52\) 0 0
\(53\) 4.85410 3.52671i 0.666762 0.484431i −0.202178 0.979349i \(-0.564802\pi\)
0.868940 + 0.494918i \(0.164802\pi\)
\(54\) 6.92820 0.942809
\(55\) 0 0
\(56\) −6.00000 −0.801784
\(57\) −11.2101 + 8.14459i −1.48481 + 1.07878i
\(58\) 0 0
\(59\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(60\) −1.61803 1.17557i −0.208887 0.151765i
\(61\) 5.60503 + 4.07230i 0.717651 + 0.521404i 0.885633 0.464386i \(-0.153725\pi\)
−0.167982 + 0.985790i \(0.553725\pi\)
\(62\) −2.14093 + 6.58911i −0.271899 + 0.836818i
\(63\) −1.07047 3.29456i −0.134866 0.415075i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) 0 0
\(66\) 0 0
\(67\) 10.0000 1.22169 0.610847 0.791748i \(-0.290829\pi\)
0.610847 + 0.791748i \(0.290829\pi\)
\(68\) −5.60503 + 4.07230i −0.679710 + 0.493838i
\(69\) 3.70820 + 11.4127i 0.446415 + 1.37393i
\(70\) 1.85410 5.70634i 0.221608 0.682038i
\(71\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(72\) −1.40126 1.01807i −0.165140 0.119981i
\(73\) 2.14093 6.58911i 0.250577 0.771197i −0.744092 0.668077i \(-0.767117\pi\)
0.994669 0.103120i \(-0.0328825\pi\)
\(74\) −5.35233 16.4728i −0.622196 1.91492i
\(75\) −1.61803 + 1.17557i −0.186834 + 0.135743i
\(76\) 6.92820 0.794719
\(77\) 0 0
\(78\) 0 0
\(79\) −5.60503 + 4.07230i −0.630616 + 0.458169i −0.856613 0.515959i \(-0.827436\pi\)
0.225998 + 0.974128i \(0.427436\pi\)
\(80\) −1.54508 4.75528i −0.172746 0.531657i
\(81\) −3.39919 + 10.4616i −0.377687 + 1.16240i
\(82\) −9.70820 7.05342i −1.07209 0.778920i
\(83\) −14.0126 10.1807i −1.53808 1.11748i −0.951524 0.307573i \(-0.900483\pi\)
−0.586557 0.809908i \(-0.699517\pi\)
\(84\) −2.14093 + 6.58911i −0.233595 + 0.718931i
\(85\) 2.14093 + 6.58911i 0.232217 + 0.714690i
\(86\) 4.85410 3.52671i 0.523431 0.380295i
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 1.40126 1.01807i 0.147706 0.107314i
\(91\) 0 0
\(92\) 1.85410 5.70634i 0.193303 0.594927i
\(93\) −6.47214 4.70228i −0.671129 0.487604i
\(94\) −8.40755 6.10844i −0.867173 0.630038i
\(95\) 2.14093 6.58911i 0.219655 0.676029i
\(96\) 3.21140 + 9.88367i 0.327762 + 1.00875i
\(97\) 8.09017 5.87785i 0.821432 0.596806i −0.0956901 0.995411i \(-0.530506\pi\)
0.917122 + 0.398606i \(0.130506\pi\)
\(98\) −8.66025 −0.874818
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 11.2101 8.14459i 1.11544 0.810417i 0.131931 0.991259i \(-0.457882\pi\)
0.983512 + 0.180842i \(0.0578822\pi\)
\(102\) −7.41641 22.8254i −0.734334 2.26005i
\(103\) 0.618034 1.90211i 0.0608967 0.187421i −0.915980 0.401224i \(-0.868585\pi\)
0.976877 + 0.213803i \(0.0685850\pi\)
\(104\) 0 0
\(105\) 5.60503 + 4.07230i 0.546995 + 0.397415i
\(106\) 3.21140 9.88367i 0.311919 0.959987i
\(107\) 1.07047 + 3.29456i 0.103486 + 0.318497i 0.989372 0.145406i \(-0.0464488\pi\)
−0.885886 + 0.463903i \(0.846449\pi\)
\(108\) 3.23607 2.35114i 0.311391 0.226239i
\(109\) −6.92820 −0.663602 −0.331801 0.943349i \(-0.607656\pi\)
−0.331801 + 0.943349i \(0.607656\pi\)
\(110\) 0 0
\(111\) 20.0000 1.89832
\(112\) −14.0126 + 10.1807i −1.32406 + 0.961989i
\(113\) 1.85410 + 5.70634i 0.174419 + 0.536807i 0.999606 0.0280521i \(-0.00893043\pi\)
−0.825187 + 0.564859i \(0.808930\pi\)
\(114\) −7.41641 + 22.8254i −0.694610 + 2.13779i
\(115\) −4.85410 3.52671i −0.452647 0.328868i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 19.4164 14.1068i 1.77990 1.29317i
\(120\) 3.46410 0.316228
\(121\) 0 0
\(122\) 12.0000 1.08643
\(123\) 11.2101 8.14459i 1.01078 0.734373i
\(124\) 1.23607 + 3.80423i 0.111002 + 0.341630i
\(125\) 0.309017 0.951057i 0.0276393 0.0850651i
\(126\) −4.85410 3.52671i −0.432438 0.314184i
\(127\) 8.40755 + 6.10844i 0.746050 + 0.542037i 0.894600 0.446868i \(-0.147461\pi\)
−0.148550 + 0.988905i \(0.547461\pi\)
\(128\) −3.74663 + 11.5309i −0.331159 + 1.01920i
\(129\) 2.14093 + 6.58911i 0.188499 + 0.580139i
\(130\) 0 0
\(131\) −6.92820 −0.605320 −0.302660 0.953099i \(-0.597875\pi\)
−0.302660 + 0.953099i \(0.597875\pi\)
\(132\) 0 0
\(133\) −24.0000 −2.08106
\(134\) 14.0126 10.1807i 1.21050 0.879482i
\(135\) −1.23607 3.80423i −0.106384 0.327416i
\(136\) 3.70820 11.4127i 0.317976 0.978629i
\(137\) −4.85410 3.52671i −0.414714 0.301307i 0.360794 0.932646i \(-0.382506\pi\)
−0.775507 + 0.631338i \(0.782506\pi\)
\(138\) 16.8151 + 12.2169i 1.43140 + 1.03997i
\(139\) −4.28187 + 13.1782i −0.363183 + 1.11776i 0.587928 + 0.808913i \(0.299944\pi\)
−0.951111 + 0.308849i \(0.900056\pi\)
\(140\) −1.07047 3.29456i −0.0904709 0.278441i
\(141\) 9.70820 7.05342i 0.817578 0.594005i
\(142\) 0 0
\(143\) 0 0
\(144\) −5.00000 −0.416667
\(145\) 0 0
\(146\) −3.70820 11.4127i −0.306893 0.944520i
\(147\) 3.09017 9.51057i 0.254873 0.784418i
\(148\) −8.09017 5.87785i −0.665008 0.483157i
\(149\) 5.60503 + 4.07230i 0.459182 + 0.333615i 0.793210 0.608948i \(-0.208408\pi\)
−0.334028 + 0.942563i \(0.608408\pi\)
\(150\) −1.07047 + 3.29456i −0.0874032 + 0.268999i
\(151\) −2.14093 6.58911i −0.174227 0.536214i 0.825371 0.564591i \(-0.190966\pi\)
−0.999597 + 0.0283768i \(0.990966\pi\)
\(152\) −9.70820 + 7.05342i −0.787439 + 0.572108i
\(153\) 6.92820 0.560112
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −0.618034 1.90211i −0.0493245 0.151805i 0.923361 0.383934i \(-0.125431\pi\)
−0.972685 + 0.232129i \(0.925431\pi\)
\(158\) −3.70820 + 11.4127i −0.295009 + 0.907944i
\(159\) 9.70820 + 7.05342i 0.769911 + 0.559373i
\(160\) −4.20378 3.05422i −0.332338 0.241457i
\(161\) −6.42280 + 19.7673i −0.506187 + 1.55788i
\(162\) 5.88756 + 18.1201i 0.462571 + 1.42365i
\(163\) −1.61803 + 1.17557i −0.126734 + 0.0920778i −0.649347 0.760493i \(-0.724958\pi\)
0.522612 + 0.852570i \(0.324958\pi\)
\(164\) −6.92820 −0.541002
\(165\) 0 0
\(166\) −30.0000 −2.32845
\(167\) 8.40755 6.10844i 0.650596 0.472686i −0.212878 0.977079i \(-0.568284\pi\)
0.863474 + 0.504393i \(0.168284\pi\)
\(168\) −3.70820 11.4127i −0.286094 0.880507i
\(169\) −4.01722 + 12.3637i −0.309017 + 0.951057i
\(170\) 9.70820 + 7.05342i 0.744585 + 0.540973i
\(171\) −5.60503 4.07230i −0.428628 0.311416i
\(172\) 1.07047 3.29456i 0.0816223 0.251208i
\(173\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(174\) 0 0
\(175\) −3.46410 −0.261861
\(176\) 0 0
\(177\) 0 0
\(178\) −8.40755 + 6.10844i −0.630173 + 0.457847i
\(179\) −3.70820 11.4127i −0.277164 0.853024i −0.988639 0.150312i \(-0.951972\pi\)
0.711474 0.702712i \(-0.248028\pi\)
\(180\) 0.309017 0.951057i 0.0230328 0.0708876i
\(181\) −11.3262 8.22899i −0.841873 0.611656i 0.0810205 0.996712i \(-0.474182\pi\)
−0.922893 + 0.385056i \(0.874182\pi\)
\(182\) 0 0
\(183\) −4.28187 + 13.1782i −0.316525 + 0.974162i
\(184\) 3.21140 + 9.88367i 0.236747 + 0.728634i
\(185\) −8.09017 + 5.87785i −0.594801 + 0.432148i
\(186\) −13.8564 −1.01600
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) −11.2101 + 8.14459i −0.815412 + 0.592432i
\(190\) −3.70820 11.4127i −0.269021 0.827963i
\(191\) −3.70820 + 11.4127i −0.268316 + 0.825792i 0.722595 + 0.691272i \(0.242949\pi\)
−0.990911 + 0.134520i \(0.957051\pi\)
\(192\) −1.61803 1.17557i −0.116772 0.0848395i
\(193\) −5.60503 4.07230i −0.403459 0.293130i 0.367489 0.930028i \(-0.380217\pi\)
−0.770949 + 0.636897i \(0.780217\pi\)
\(194\) 5.35233 16.4728i 0.384275 1.18268i
\(195\) 0 0
\(196\) −4.04508 + 2.93893i −0.288935 + 0.209923i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) −1.40126 + 1.01807i −0.0990839 + 0.0719887i
\(201\) 6.18034 + 19.0211i 0.435928 + 1.34165i
\(202\) 7.41641 22.8254i 0.521817 1.60599i
\(203\) 0 0
\(204\) −11.2101 8.14459i −0.784862 0.570235i
\(205\) −2.14093 + 6.58911i −0.149529 + 0.460204i
\(206\) −1.07047 3.29456i −0.0745829 0.229543i
\(207\) −4.85410 + 3.52671i −0.337383 + 0.245123i
\(208\) 0 0
\(209\) 0 0
\(210\) 12.0000 0.828079
\(211\) −16.8151 + 12.2169i −1.15760 + 0.841045i −0.989473 0.144720i \(-0.953772\pi\)
−0.168127 + 0.985765i \(0.553772\pi\)
\(212\) −1.85410 5.70634i −0.127340 0.391913i
\(213\) 0 0
\(214\) 4.85410 + 3.52671i 0.331820 + 0.241081i
\(215\) −2.80252 2.03615i −0.191130 0.138864i
\(216\) −2.14093 + 6.58911i −0.145672 + 0.448332i
\(217\) −4.28187 13.1782i −0.290672 0.894596i
\(218\) −9.70820 + 7.05342i −0.657523 + 0.477718i
\(219\) 13.8564 0.936329
\(220\) 0 0
\(221\) 0 0
\(222\) 28.0252 20.3615i 1.88093 1.36657i
\(223\) 4.32624 + 13.3148i 0.289706 + 0.891624i 0.984948 + 0.172849i \(0.0552972\pi\)
−0.695242 + 0.718776i \(0.744703\pi\)
\(224\) −5.56231 + 17.1190i −0.371647 + 1.14381i
\(225\) −0.809017 0.587785i −0.0539345 0.0391857i
\(226\) 8.40755 + 6.10844i 0.559262 + 0.406328i
\(227\) −1.07047 + 3.29456i −0.0710493 + 0.218667i −0.980276 0.197635i \(-0.936674\pi\)
0.909226 + 0.416302i \(0.136674\pi\)
\(228\) 4.28187 + 13.1782i 0.283573 + 0.872749i
\(229\) 1.61803 1.17557i 0.106923 0.0776839i −0.533039 0.846091i \(-0.678950\pi\)
0.639962 + 0.768407i \(0.278950\pi\)
\(230\) −10.3923 −0.685248
\(231\) 0 0
\(232\) 0 0
\(233\) 5.60503 4.07230i 0.367198 0.266785i −0.388850 0.921301i \(-0.627128\pi\)
0.756048 + 0.654516i \(0.227128\pi\)
\(234\) 0 0
\(235\) −1.85410 + 5.70634i −0.120948 + 0.372241i
\(236\) 0 0
\(237\) −11.2101 8.14459i −0.728172 0.529048i
\(238\) 12.8456 39.5347i 0.832656 2.56265i
\(239\) 2.14093 + 6.58911i 0.138485 + 0.426214i 0.996116 0.0880522i \(-0.0280642\pi\)
−0.857630 + 0.514266i \(0.828064\pi\)
\(240\) 8.09017 5.87785i 0.522218 0.379414i
\(241\) 20.7846 1.33885 0.669427 0.742878i \(-0.266540\pi\)
0.669427 + 0.742878i \(0.266540\pi\)
\(242\) 0 0
\(243\) −10.0000 −0.641500
\(244\) 5.60503 4.07230i 0.358826 0.260702i
\(245\) 1.54508 + 4.75528i 0.0987119 + 0.303804i
\(246\) 7.41641 22.8254i 0.472853 1.45529i
\(247\) 0 0
\(248\) −5.60503 4.07230i −0.355920 0.258591i
\(249\) 10.7047 32.9456i 0.678380 2.08784i
\(250\) −0.535233 1.64728i −0.0338511 0.104183i
\(251\) −9.70820 + 7.05342i −0.612776 + 0.445208i −0.850391 0.526151i \(-0.823635\pi\)
0.237614 + 0.971360i \(0.423635\pi\)
\(252\) −3.46410 −0.218218
\(253\) 0 0
\(254\) 18.0000 1.12942
\(255\) −11.2101 + 8.14459i −0.702002 + 0.510034i
\(256\) 5.87132 + 18.0701i 0.366958 + 1.12938i
\(257\) −1.85410 + 5.70634i −0.115656 + 0.355952i −0.992083 0.125582i \(-0.959920\pi\)
0.876428 + 0.481534i \(0.159920\pi\)
\(258\) 9.70820 + 7.05342i 0.604406 + 0.439127i
\(259\) 28.0252 + 20.3615i 1.74140 + 1.26520i
\(260\) 0 0
\(261\) 0 0
\(262\) −9.70820 + 7.05342i −0.599775 + 0.435762i
\(263\) −3.46410 −0.213606 −0.106803 0.994280i \(-0.534061\pi\)
−0.106803 + 0.994280i \(0.534061\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) −33.6302 + 24.4338i −2.06200 + 1.49813i
\(267\) −3.70820 11.4127i −0.226938 0.698445i
\(268\) 3.09017 9.51057i 0.188762 0.580950i
\(269\) 24.2705 + 17.6336i 1.47980 + 1.07514i 0.977621 + 0.210373i \(0.0674677\pi\)
0.502178 + 0.864764i \(0.332532\pi\)
\(270\) −5.60503 4.07230i −0.341112 0.247832i
\(271\) −2.14093 + 6.58911i −0.130052 + 0.400260i −0.994788 0.101968i \(-0.967486\pi\)
0.864735 + 0.502228i \(0.167486\pi\)
\(272\) −10.7047 32.9456i −0.649066 1.99762i
\(273\) 0 0
\(274\) −10.3923 −0.627822
\(275\) 0 0
\(276\) 12.0000 0.722315
\(277\) 22.4201 16.2892i 1.34710 0.978722i 0.347945 0.937515i \(-0.386880\pi\)
0.999151 0.0412071i \(-0.0131203\pi\)
\(278\) 7.41641 + 22.8254i 0.444807 + 1.36897i
\(279\) 1.23607 3.80423i 0.0740015 0.227753i
\(280\) 4.85410 + 3.52671i 0.290088 + 0.210761i
\(281\) −5.60503 4.07230i −0.334368 0.242933i 0.407914 0.913021i \(-0.366256\pi\)
−0.742282 + 0.670088i \(0.766256\pi\)
\(282\) 6.42280 19.7673i 0.382472 1.17713i
\(283\) −7.49326 23.0619i −0.445428 1.37089i −0.882013 0.471224i \(-0.843812\pi\)
0.436585 0.899663i \(-0.356188\pi\)
\(284\) 0 0
\(285\) 13.8564 0.820783
\(286\) 0 0
\(287\) 24.0000 1.41668
\(288\) −4.20378 + 3.05422i −0.247710 + 0.179972i
\(289\) 9.57953 + 29.4828i 0.563502 + 1.73428i
\(290\) 0 0
\(291\) 16.1803 + 11.7557i 0.948508 + 0.689132i
\(292\) −5.60503 4.07230i −0.328010 0.238313i
\(293\) −4.28187 + 13.1782i −0.250149 + 0.769880i 0.744598 + 0.667514i \(0.232641\pi\)
−0.994747 + 0.102366i \(0.967359\pi\)
\(294\) −5.35233 16.4728i −0.312154 0.960712i
\(295\) 0 0
\(296\) 17.3205 1.00673
\(297\) 0 0
\(298\) 12.0000 0.695141
\(299\) 0 0
\(300\) 0.618034 + 1.90211i 0.0356822 + 0.109819i
\(301\) −3.70820 + 11.4127i −0.213737 + 0.657816i
\(302\) −9.70820 7.05342i −0.558644 0.405879i
\(303\) 22.4201 + 16.2892i 1.28800 + 0.935789i
\(304\) −10.7047 + 32.9456i −0.613955 + 1.88956i
\(305\) −2.14093 6.58911i −0.122589 0.377292i
\(306\) 9.70820 7.05342i 0.554981 0.403217i
\(307\) 3.46410 0.197707 0.0988534 0.995102i \(-0.468483\pi\)
0.0988534 + 0.995102i \(0.468483\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 5.60503 4.07230i 0.318345 0.231291i
\(311\) −7.41641 22.8254i −0.420546 1.29431i −0.907195 0.420710i \(-0.861781\pi\)
0.486649 0.873597i \(-0.338219\pi\)
\(312\) 0 0
\(313\) −27.5066 19.9847i −1.55476 1.12960i −0.940144 0.340779i \(-0.889309\pi\)
−0.614620 0.788823i \(-0.710691\pi\)
\(314\) −2.80252 2.03615i −0.158155 0.114906i
\(315\) −1.07047 + 3.29456i −0.0603139 + 0.185627i
\(316\) 2.14093 + 6.58911i 0.120437 + 0.370667i
\(317\) 14.5623 10.5801i 0.817901 0.594240i −0.0982098 0.995166i \(-0.531312\pi\)
0.916110 + 0.400926i \(0.131312\pi\)
\(318\) 20.7846 1.16554
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) −5.60503 + 4.07230i −0.312842 + 0.227293i
\(322\) 11.1246 + 34.2380i 0.619950 + 1.90801i
\(323\) 14.8328 45.6507i 0.825320 2.54007i
\(324\) 8.89919 + 6.46564i 0.494399 + 0.359202i
\(325\) 0 0
\(326\) −1.07047 + 3.29456i −0.0592876 + 0.182469i
\(327\) −4.28187 13.1782i −0.236788 0.728758i
\(328\) 9.70820 7.05342i 0.536046 0.389460i
\(329\) 20.7846 1.14589
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −14.0126 + 10.1807i −0.769041 + 0.558741i
\(333\) 3.09017 + 9.51057i 0.169340 + 0.521176i
\(334\) 5.56231 17.1190i 0.304356 0.936711i
\(335\) −8.09017 5.87785i −0.442013 0.321141i
\(336\) −28.0252 20.3615i −1.52890 1.11081i
\(337\) 6.42280 19.7673i 0.349872 1.07680i −0.609051 0.793131i \(-0.708450\pi\)
0.958924 0.283665i \(-0.0915503\pi\)
\(338\) 6.95803 + 21.4146i 0.378467 + 1.16480i
\(339\) −9.70820 + 7.05342i −0.527277 + 0.383089i
\(340\) 6.92820 0.375735
\(341\) 0 0
\(342\) −12.0000 −0.648886
\(343\) −5.60503 + 4.07230i −0.302643 + 0.219883i
\(344\) 1.85410 + 5.70634i 0.0999665 + 0.307665i
\(345\) 3.70820 11.4127i 0.199643 0.614438i
\(346\) 0 0
\(347\) 19.6176 + 14.2530i 1.05313 + 0.765143i 0.972805 0.231626i \(-0.0744045\pi\)
0.0803240 + 0.996769i \(0.474404\pi\)
\(348\) 0 0
\(349\) 4.28187 + 13.1782i 0.229203 + 0.705414i 0.997838 + 0.0657263i \(0.0209364\pi\)
−0.768635 + 0.639688i \(0.779064\pi\)
\(350\) −4.85410 + 3.52671i −0.259463 + 0.188511i
\(351\) 0 0
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.85410 + 5.70634i −0.0982672 + 0.302435i
\(357\) 38.8328 + 28.2137i 2.05525 + 1.49323i
\(358\) −16.8151 12.2169i −0.888706 0.645683i
\(359\) 10.7047 32.9456i 0.564970 1.73880i −0.103069 0.994674i \(-0.532866\pi\)
0.668039 0.744126i \(-0.267134\pi\)
\(360\) 0.535233 + 1.64728i 0.0282093 + 0.0868192i
\(361\) −23.4615 + 17.0458i −1.23482 + 0.897146i
\(362\) −24.2487 −1.27448
\(363\) 0 0
\(364\) 0 0
\(365\) −5.60503 + 4.07230i −0.293381 + 0.213154i
\(366\) 7.41641 + 22.8254i 0.387662 + 1.19310i
\(367\) 0.618034 1.90211i 0.0322611 0.0992895i −0.933629 0.358240i \(-0.883377\pi\)
0.965890 + 0.258951i \(0.0833768\pi\)
\(368\) 24.2705 + 17.6336i 1.26519 + 0.919213i
\(369\) 5.60503 + 4.07230i 0.291786 + 0.211995i
\(370\) −5.35233 + 16.4728i −0.278254 + 0.856379i
\(371\) 6.42280 + 19.7673i 0.333455 + 1.02627i
\(372\) −6.47214 + 4.70228i −0.335565 + 0.243802i
\(373\) −27.7128 −1.43492 −0.717458 0.696602i \(-0.754694\pi\)
−0.717458 + 0.696602i \(0.754694\pi\)
\(374\) 0 0
\(375\) 2.00000 0.103280
\(376\) 8.40755 6.10844i 0.433586 0.315019i
\(377\) 0 0
\(378\) −7.41641 + 22.8254i −0.381459 + 1.17401i
\(379\) −25.8885 18.8091i −1.32981 0.966160i −0.999754 0.0221971i \(-0.992934\pi\)
−0.330052 0.943963i \(-0.607066\pi\)
\(380\) −5.60503 4.07230i −0.287532 0.208904i
\(381\) −6.42280 + 19.7673i −0.329050 + 1.01271i
\(382\) 6.42280 + 19.7673i 0.328619 + 1.01139i
\(383\) −14.5623 + 10.5801i −0.744099 + 0.540620i −0.893992 0.448083i \(-0.852107\pi\)
0.149893 + 0.988702i \(0.452107\pi\)
\(384\) −24.2487 −1.23744
\(385\) 0 0
\(386\) −12.0000 −0.610784
\(387\) −2.80252 + 2.03615i −0.142460 + 0.103503i
\(388\) −3.09017 9.51057i −0.156880 0.482826i
\(389\) 1.85410 5.70634i 0.0940067 0.289323i −0.892987 0.450083i \(-0.851394\pi\)
0.986994 + 0.160760i \(0.0513945\pi\)
\(390\) 0 0
\(391\) −33.6302 24.4338i −1.70075 1.23567i
\(392\) 2.67617 8.23639i 0.135167 0.416001i
\(393\) −4.28187 13.1782i −0.215992 0.664754i
\(394\) 0 0
\(395\) 6.92820 0.348596
\(396\) 0 0
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) 5.60503 4.07230i 0.280955 0.204126i
\(399\) −14.8328 45.6507i −0.742570 2.28539i
\(400\) −1.54508 + 4.75528i −0.0772542 + 0.237764i
\(401\) 14.5623 + 10.5801i 0.727207 + 0.528347i 0.888679 0.458531i \(-0.151624\pi\)
−0.161472 + 0.986877i \(0.551624\pi\)
\(402\) 28.0252 + 20.3615i 1.39777 + 1.01554i
\(403\) 0 0
\(404\) −4.28187 13.1782i −0.213031 0.655641i
\(405\) 8.89919 6.46564i 0.442204 0.321280i
\(406\) 0 0
\(407\) 0 0
\(408\) 24.0000 1.18818
\(409\) 16.8151 12.2169i 0.831453 0.604086i −0.0885168 0.996075i \(-0.528213\pi\)
0.919970 + 0.391988i \(0.128213\pi\)
\(410\) 3.70820 + 11.4127i 0.183135 + 0.563632i
\(411\) 3.70820 11.4127i 0.182912 0.562946i
\(412\) −1.61803 1.17557i −0.0797148 0.0579162i
\(413\) 0 0
\(414\) −3.21140 + 9.88367i −0.157832 + 0.485756i
\(415\) 5.35233 + 16.4728i 0.262736 + 0.808617i
\(416\) 0 0
\(417\) −27.7128 −1.35710
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 5.60503 4.07230i 0.273498 0.198708i
\(421\) −8.03444 24.7275i −0.391575 1.20514i −0.931597 0.363492i \(-0.881584\pi\)
0.540022 0.841651i \(-0.318416\pi\)
\(422\) −11.1246 + 34.2380i −0.541538 + 1.66668i
\(423\) 4.85410 + 3.52671i 0.236015 + 0.171475i
\(424\) 8.40755 + 6.10844i 0.408307 + 0.296652i
\(425\) 2.14093 6.58911i 0.103850 0.319619i
\(426\) 0 0
\(427\) −19.4164 + 14.1068i −0.939626 + 0.682678i
\(428\) 3.46410 0.167444
\(429\) 0 0
\(430\) −6.00000 −0.289346
\(431\) 22.4201 16.2892i 1.07994 0.784622i 0.102268 0.994757i \(-0.467390\pi\)
0.977672 + 0.210135i \(0.0673902\pi\)
\(432\) 6.18034 + 19.0211i 0.297352 + 0.915155i
\(433\) −10.5066 + 32.3359i −0.504914 + 1.55397i 0.296001 + 0.955188i \(0.404347\pi\)
−0.800915 + 0.598778i \(0.795653\pi\)
\(434\) −19.4164 14.1068i −0.932017 0.677150i
\(435\) 0 0
\(436\) −2.14093 + 6.58911i −0.102532 + 0.315561i
\(437\) 12.8456 + 39.5347i 0.614488 + 1.89120i
\(438\) 19.4164 14.1068i 0.927752 0.674051i
\(439\) −13.8564 −0.661330 −0.330665 0.943748i \(-0.607273\pi\)
−0.330665 + 0.943748i \(0.607273\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) 0 0
\(443\) −1.85410 5.70634i −0.0880910 0.271116i 0.897301 0.441420i \(-0.145525\pi\)
−0.985392 + 0.170304i \(0.945525\pi\)
\(444\) 6.18034 19.0211i 0.293306 0.902703i
\(445\) 4.85410 + 3.52671i 0.230107 + 0.167182i
\(446\) 19.6176 + 14.2530i 0.928921 + 0.674901i
\(447\) −4.28187 + 13.1782i −0.202525 + 0.623309i
\(448\) −1.07047 3.29456i −0.0505748 0.155653i
\(449\) −24.2705 + 17.6336i −1.14540 + 0.832179i −0.987862 0.155334i \(-0.950354\pi\)
−0.157534 + 0.987514i \(0.550354\pi\)
\(450\) −1.73205 −0.0816497
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) 11.2101 8.14459i 0.526695 0.382666i
\(454\) 1.85410 + 5.70634i 0.0870173 + 0.267812i
\(455\) 0 0
\(456\) −19.4164 14.1068i −0.909257 0.660614i
\(457\) 16.8151 + 12.2169i 0.786577 + 0.571482i 0.906946 0.421247i \(-0.138408\pi\)
−0.120368 + 0.992729i \(0.538408\pi\)
\(458\) 1.07047 3.29456i 0.0500196 0.153945i
\(459\) −8.56373 26.3565i −0.399721 1.23021i
\(460\) −4.85410 + 3.52671i −0.226324 + 0.164434i
\(461\) 27.7128 1.29071 0.645357 0.763881i \(-0.276709\pi\)
0.645357 + 0.763881i \(0.276709\pi\)
\(462\) 0 0
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) 0 0
\(465\) 2.47214 + 7.60845i 0.114643 + 0.352834i
\(466\) 3.70820 11.4127i 0.171779 0.528682i
\(467\) −14.5623 10.5801i −0.673863 0.489590i 0.197453 0.980312i \(-0.436733\pi\)
−0.871316 + 0.490722i \(0.836733\pi\)
\(468\) 0 0
\(469\) −10.7047 + 32.9456i −0.494295 + 1.52128i
\(470\) 3.21140 + 9.88367i 0.148131 + 0.455900i
\(471\) 3.23607 2.35114i 0.149110 0.108335i
\(472\) 0 0
\(473\) 0 0
\(474\) −24.0000 −1.10236
\(475\) −5.60503 + 4.07230i −0.257177 + 0.186850i
\(476\) −7.41641 22.8254i −0.339930 1.04620i
\(477\) −1.85410 + 5.70634i −0.0848935 + 0.261275i
\(478\) 9.70820 + 7.05342i 0.444043 + 0.322616i
\(479\) −16.8151 12.2169i −0.768302 0.558204i 0.133144 0.991097i \(-0.457493\pi\)
−0.901445 + 0.432893i \(0.857493\pi\)
\(480\) 3.21140 9.88367i 0.146580 0.451126i
\(481\) 0 0
\(482\) 29.1246 21.1603i 1.32659 0.963824i
\(483\) −41.5692 −1.89146
\(484\) 0 0
\(485\) −10.0000 −0.454077
\(486\) −14.0126 + 10.1807i −0.635624 + 0.461808i
\(487\) −4.32624 13.3148i −0.196041 0.603351i −0.999963 0.00861648i \(-0.997257\pi\)
0.803922 0.594734i \(-0.202743\pi\)
\(488\) −3.70820 + 11.4127i −0.167863 + 0.516628i
\(489\) −3.23607 2.35114i −0.146340 0.106322i
\(490\) 7.00629 + 5.09037i 0.316512 + 0.229959i
\(491\) −4.28187 + 13.1782i −0.193238 + 0.594725i 0.806755 + 0.590886i \(0.201222\pi\)
−0.999993 + 0.00383859i \(0.998778\pi\)
\(492\) −4.28187 13.1782i −0.193041 0.594120i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −20.0000 −0.898027
\(497\) 0 0
\(498\) −18.5410 57.0634i −0.830843 2.55707i
\(499\) 4.94427 15.2169i 0.221336 0.681202i −0.777307 0.629122i \(-0.783415\pi\)
0.998643 0.0520806i \(-0.0165853\pi\)
\(500\) −0.809017 0.587785i −0.0361803 0.0262866i
\(501\) 16.8151 + 12.2169i 0.751243 + 0.545810i
\(502\) −6.42280 + 19.7673i −0.286663 + 0.882259i
\(503\) 5.35233 + 16.4728i 0.238649 + 0.734485i 0.996616 + 0.0821930i \(0.0261924\pi\)
−0.757968 + 0.652292i \(0.773808\pi\)
\(504\) 4.85410 3.52671i 0.216219 0.157092i
\(505\) −13.8564 −0.616602
\(506\) 0 0
\(507\) −26.0000 −1.15470
\(508\) 8.40755 6.10844i 0.373025 0.271018i
\(509\) 1.85410 + 5.70634i 0.0821816 + 0.252929i 0.983702 0.179808i \(-0.0575477\pi\)
−0.901520 + 0.432737i \(0.857548\pi\)
\(510\) −7.41641 + 22.8254i −0.328404 + 1.01072i
\(511\) 19.4164 + 14.1068i 0.858931 + 0.624050i
\(512\) 7.00629 + 5.09037i 0.309637 + 0.224965i
\(513\) −8.56373 + 26.3565i −0.378098 + 1.16367i
\(514\) 3.21140 + 9.88367i 0.141649 + 0.435950i
\(515\) −1.61803 + 1.17557i −0.0712991 + 0.0518018i
\(516\) 6.92820 0.304997
\(517\) 0 0
\(518\) 60.0000 2.63625
\(519\) 0 0
\(520\) 0 0
\(521\) −12.9787 + 39.9444i −0.568608 + 1.74999i 0.0883730 + 0.996087i \(0.471833\pi\)
−0.656981 + 0.753907i \(0.728167\pi\)
\(522\) 0 0
\(523\) −19.6176 14.2530i −0.857819 0.623242i 0.0694720 0.997584i \(-0.477869\pi\)
−0.927291 + 0.374342i \(0.877869\pi\)
\(524\) −2.14093 + 6.58911i −0.0935271 + 0.287847i
\(525\) −2.14093 6.58911i −0.0934380 0.287572i
\(526\) −4.85410 + 3.52671i −0.211649 + 0.153772i
\(527\) 27.7128 1.20719
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) −8.40755 + 6.10844i −0.365201 + 0.265334i
\(531\) 0 0
\(532\) −7.41641 + 22.8254i −0.321542 + 0.989605i
\(533\) 0 0
\(534\) −16.8151 12.2169i −0.727661 0.528676i
\(535\) 1.07047 3.29456i 0.0462803 0.142436i
\(536\) 5.35233 + 16.4728i 0.231186 + 0.711516i
\(537\) 19.4164 14.1068i 0.837880 0.608755i
\(538\) 51.9615 2.24022
\(539\) 0 0
\(540\) −4.00000 −0.172133
\(541\) −11.2101 + 8.14459i −0.481958 + 0.350163i −0.802083 0.597212i \(-0.796275\pi\)
0.320125 + 0.947375i \(0.396275\pi\)
\(542\) 3.70820 + 11.4127i 0.159281 + 0.490217i
\(543\) 8.65248 26.6296i 0.371313 1.14278i
\(544\) −29.1246 21.1603i −1.24871 0.907239i
\(545\) 5.60503 + 4.07230i 0.240093 + 0.174438i
\(546\) 0 0
\(547\) −5.35233 16.4728i −0.228849 0.704325i −0.997878 0.0651112i \(-0.979260\pi\)
0.769029 0.639214i \(-0.220740\pi\)
\(548\) −4.85410 + 3.52671i −0.207357 + 0.150654i
\(549\) −6.92820 −0.295689
\(550\) 0 0
\(551\) 0 0
\(552\) −16.8151 + 12.2169i −0.715698 + 0.519985i
\(553\) −7.41641 22.8254i −0.315378 0.970633i
\(554\) 14.8328 45.6507i 0.630186 1.93951i
\(555\) −16.1803 11.7557i −0.686817 0.499002i
\(556\) 11.2101 + 8.14459i 0.475413 + 0.345408i
\(557\) 8.56373 26.3565i 0.362857 1.11676i −0.588455 0.808530i \(-0.700264\pi\)
0.951312 0.308229i \(-0.0997363\pi\)
\(558\) −2.14093 6.58911i −0.0906329 0.278939i
\(559\) 0 0
\(560\) 17.3205 0.731925
\(561\) 0 0
\(562\) −12.0000 −0.506189
\(563\) −8.40755 + 6.10844i −0.354336 + 0.257440i −0.750686 0.660659i \(-0.770277\pi\)
0.396350 + 0.918100i \(0.370277\pi\)
\(564\) −3.70820 11.4127i −0.156144 0.480560i
\(565\) 1.85410 5.70634i 0.0780027 0.240067i
\(566\) −33.9787 24.6870i −1.42823 1.03767i
\(567\) −30.8277 22.3976i −1.29464 0.940612i
\(568\) 0 0
\(569\) 2.14093 + 6.58911i 0.0897526 + 0.276230i 0.985851 0.167626i \(-0.0536101\pi\)
−0.896098 + 0.443856i \(0.853610\pi\)
\(570\) 19.4164 14.1068i 0.813264 0.590871i
\(571\) −27.7128 −1.15975 −0.579873 0.814707i \(-0.696898\pi\)
−0.579873 + 0.814707i \(0.696898\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) 33.6302 24.4338i 1.40370 1.01985i
\(575\) 1.85410 + 5.70634i 0.0773214 + 0.237971i
\(576\) 0.309017 0.951057i 0.0128757 0.0396274i
\(577\) 1.61803 + 1.17557i 0.0673596 + 0.0489396i 0.620956 0.783846i \(-0.286745\pi\)
−0.553596 + 0.832785i \(0.686745\pi\)
\(578\) 43.4390 + 31.5603i 1.80682 + 1.31274i
\(579\) 4.28187 13.1782i 0.177948 0.547668i
\(580\) 0 0
\(581\) 48.5410 35.2671i 2.01382 1.46313i
\(582\) 34.6410 1.43592
\(583\) 0 0
\(584\) 12.0000 0.496564
\(585\) 0 0
\(586\) 7.41641 + 22.8254i 0.306369 + 0.942907i
\(587\) −9.27051 + 28.5317i −0.382635 + 1.17763i 0.555547 + 0.831485i \(0.312509\pi\)
−0.938182 + 0.346144i \(0.887491\pi\)
\(588\) −8.09017 5.87785i −0.333633 0.242399i
\(589\) −22.4201 16.2892i −0.923806 0.671184i
\(590\) 0 0
\(591\) 0 0
\(592\) 40.4508 29.3893i 1.66252 1.20789i
\(593\) 6.92820 0.284507 0.142254 0.989830i \(-0.454565\pi\)
0.142254 + 0.989830i \(0.454565\pi\)
\(594\) 0 0
\(595\) −24.0000 −0.983904
\(596\) 5.60503 4.07230i 0.229591 0.166808i
\(597\) 2.47214 + 7.60845i 0.101178 + 0.311393i
\(598\) 0 0
\(599\) −19.4164 14.1068i −0.793333 0.576390i 0.115618 0.993294i \(-0.463115\pi\)
−0.908951 + 0.416904i \(0.863115\pi\)
\(600\) −2.80252 2.03615i −0.114412 0.0831254i
\(601\) 14.9865 46.1238i 0.611313 1.88143i 0.165781 0.986163i \(-0.446985\pi\)
0.445532 0.895266i \(-0.353015\pi\)
\(602\) 6.42280 + 19.7673i 0.261774 + 0.805657i
\(603\) −8.09017 + 5.87785i −0.329457 + 0.239365i
\(604\) −6.92820 −0.281905
\(605\) 0 0
\(606\) 48.0000 1.94987
\(607\) −2.80252 + 2.03615i −0.113751 + 0.0826447i −0.643206 0.765693i \(-0.722396\pi\)
0.529456 + 0.848338i \(0.322396\pi\)
\(608\) 11.1246 + 34.2380i 0.451163 + 1.38854i
\(609\) 0 0
\(610\) −9.70820 7.05342i −0.393074 0.285585i
\(611\) 0 0
\(612\) 2.14093 6.58911i 0.0865421 0.266349i
\(613\) −8.56373 26.3565i −0.345886 1.06453i −0.961108 0.276173i \(-0.910934\pi\)
0.615222 0.788354i \(-0.289066\pi\)
\(614\) 4.85410 3.52671i 0.195896 0.142326i
\(615\) −13.8564 −0.558744
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 5.60503 4.07230i 0.225468 0.163812i
\(619\) −8.65248 26.6296i −0.347772 1.07033i −0.960083 0.279716i \(-0.909760\pi\)
0.612310 0.790617i \(-0.290240\pi\)
\(620\) 1.23607 3.80423i 0.0496417 0.152781i
\(621\) 19.4164 + 14.1068i 0.779154 + 0.566088i
\(622\) −33.6302 24.4338i −1.34845 0.979705i
\(623\) 6.42280 19.7673i 0.257324 0.791962i
\(624\) 0 0
\(625\) −0.809017 + 0.587785i −0.0323607 + 0.0235114i
\(626\) −58.8897 −2.35371
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) −56.0503 + 40.7230i −2.23487 + 1.62373i
\(630\) 1.85410 + 5.70634i 0.0738692 + 0.227346i
\(631\) 4.94427 15.2169i 0.196828 0.605775i −0.803122 0.595815i \(-0.796829\pi\)
0.999950 0.00996082i \(-0.00317068\pi\)
\(632\) −9.70820 7.05342i −0.386172 0.280570i
\(633\) −33.6302 24.4338i −1.33668 0.971155i
\(634\) 9.63420 29.6510i 0.382623 1.17759i
\(635\) −3.21140 9.88367i −0.127440 0.392221i
\(636\) 9.70820 7.05342i 0.384955 0.279686i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 9.80881 7.12652i 0.387727 0.281700i
\(641\) −12.9787 39.9444i −0.512628 1.57771i −0.787556 0.616243i \(-0.788654\pi\)
0.274928 0.961465i \(-0.411346\pi\)
\(642\) −3.70820 + 11.4127i −0.146351 + 0.450422i
\(643\) −21.0344 15.2824i −0.829517 0.602680i 0.0899053 0.995950i \(-0.471344\pi\)
−0.919423 + 0.393271i \(0.871344\pi\)
\(644\) 16.8151 + 12.2169i 0.662608 + 0.481413i
\(645\) 2.14093 6.58911i 0.0842991 0.259446i
\(646\) −25.6912 79.0694i −1.01081 3.11094i
\(647\) −4.85410 + 3.52671i −0.190834 + 0.138649i −0.679100 0.734046i \(-0.737630\pi\)
0.488266 + 0.872695i \(0.337630\pi\)
\(648\) −19.0526 −0.748455
\(649\) 0 0
\(650\) 0 0
\(651\) 22.4201 16.2892i 0.878714 0.638423i
\(652\) 0.618034 + 1.90211i 0.0242041 + 0.0744925i
\(653\) −1.85410 + 5.70634i −0.0725566 + 0.223306i −0.980758 0.195227i \(-0.937456\pi\)
0.908201 + 0.418533i \(0.137456\pi\)
\(654\) −19.4164 14.1068i −0.759242 0.551621i
\(655\) 5.60503 + 4.07230i 0.219007 + 0.159118i
\(656\) 10.7047 32.9456i 0.417947 1.28631i
\(657\) 2.14093 + 6.58911i 0.0835257 + 0.257066i
\(658\) 29.1246 21.1603i 1.13540 0.824913i
\(659\) 27.7128 1.07954 0.539769 0.841813i \(-0.318512\pi\)
0.539769 + 0.841813i \(0.318512\pi\)
\(660\) 0 0
\(661\) 22.0000 0.855701 0.427850 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) 11.2101 8.14459i 0.435692 0.316549i
\(663\) 0 0
\(664\) 9.27051 28.5317i 0.359766 1.10724i
\(665\) 19.4164 + 14.1068i 0.752936 + 0.547040i
\(666\) 14.0126 + 10.1807i 0.542977 + 0.394496i
\(667\) 0 0
\(668\) −3.21140 9.88367i −0.124253 0.382411i
\(669\) −22.6525 + 16.4580i −0.875795 + 0.636303i
\(670\) −17.3205 −0.669150
\(671\) 0 0
\(672\) −36.0000 −1.38873
\(673\) −28.0252 + 20.3615i −1.08029 + 0.784877i −0.977734 0.209850i \(-0.932703\pi\)
−0.102557 + 0.994727i \(0.532703\pi\)
\(674\) −11.1246 34.2380i −0.428504 1.31880i
\(675\) −1.23607 + 3.80423i −0.0475763 + 0.146425i
\(676\) 10.5172 + 7.64121i 0.404508 + 0.293893i
\(677\) −11.2101 8.14459i −0.430838 0.313022i 0.351146 0.936321i \(-0.385792\pi\)
−0.781984 + 0.623299i \(0.785792\pi\)
\(678\) −6.42280 + 19.7673i −0.246666 + 0.759160i
\(679\) 10.7047 + 32.9456i 0.410807 + 1.26433i
\(680\) −9.70820 + 7.05342i −0.372293 + 0.270486i
\(681\) −6.92820 −0.265489
\(682\) 0 0
\(683\) −42.0000 −1.60709 −0.803543 0.595247i \(-0.797054\pi\)
−0.803543 + 0.595247i \(0.797054\pi\)
\(684\) −5.60503 + 4.07230i −0.214314 + 0.155708i
\(685\) 1.85410 + 5.70634i 0.0708416 + 0.218028i
\(686\) −3.70820 + 11.4127i −0.141580 + 0.435738i
\(687\) 3.23607 + 2.35114i 0.123464 + 0.0897016i
\(688\) 14.0126 + 10.1807i 0.534225 + 0.388137i
\(689\) 0 0
\(690\) −6.42280 19.7673i −0.244512 0.752530i
\(691\) −16.1803 + 11.7557i −0.615529 + 0.447208i −0.851357 0.524587i \(-0.824220\pi\)
0.235828 + 0.971795i \(0.424220\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 42.0000 1.59430
\(695\) 11.2101 8.14459i 0.425222 0.308942i
\(696\) 0 0
\(697\) −14.8328 + 45.6507i −0.561833 + 1.72914i
\(698\) 19.4164 + 14.1068i 0.734922 + 0.533952i
\(699\) 11.2101 + 8.14459i 0.424004 + 0.308057i
\(700\) −1.07047 + 3.29456i −0.0404598 + 0.124523i
\(701\) −6.42280 19.7673i −0.242586 0.746602i −0.996024 0.0890836i \(-0.971606\pi\)
0.753438 0.657518i \(-0.228394\pi\)
\(702\) 0 0
\(703\) 69.2820 2.61302
\(704\) 0 0
\(705\) −12.0000 −0.451946
\(706\) −8.40755 + 6.10844i −0.316422 + 0.229894i
\(707\) 14.8328 + 45.6507i 0.557845 + 1.71687i
\(708\) 0 0
\(709\) 21.0344 + 15.2824i 0.789965 + 0.573943i 0.907953 0.419072i \(-0.137644\pi\)
−0.117988 + 0.993015i \(0.537644\pi\)
\(710\) 0 0
\(711\) 2.14093 6.58911i 0.0802912 0.247111i
\(712\) −3.21140 9.88367i −0.120352 0.370406i
\(713\) −19.4164 + 14.1068i −0.727150 + 0.528306i
\(714\) 83.1384 3.11138
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) −11.2101 + 8.14459i −0.418648 + 0.304165i
\(718\) −18.5410 57.0634i −0.691945 2.12959i
\(719\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(720\) 4.04508 + 2.93893i 0.150751 + 0.109527i
\(721\) 5.60503 + 4.07230i 0.208742 + 0.151660i
\(722\) −15.5218 + 47.7711i −0.577660 + 1.77786i
\(723\) 12.8456 + 39.5347i 0.477733 + 1.47031i
\(724\) −11.3262 + 8.22899i −0.420936 + 0.305828i
\(725\) 0 0
\(726\) 0 0
\(727\) 46.0000 1.70605 0.853023 0.521874i \(-0.174767\pi\)
0.853023 + 0.521874i \(0.174767\pi\)
\(728\) 0 0
\(729\) 4.01722 + 12.3637i 0.148786 + 0.457916i
\(730\) −3.70820 + 11.4127i −0.137247 + 0.422402i
\(731\) −19.4164 14.1068i −0.718142 0.521761i
\(732\) 11.2101 + 8.14459i 0.414336 + 0.301033i
\(733\) 12.8456 39.5347i 0.474463 1.46025i −0.372218 0.928145i \(-0.621403\pi\)
0.846681 0.532101i \(-0.178597\pi\)
\(734\) −1.07047 3.29456i −0.0395116 0.121604i
\(735\) −8.09017 + 5.87785i −0.298410 + 0.216808i
\(736\) 31.1769 1.14920
\(737\) 0 0
\(738\) 12.0000 0.441726
\(739\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(740\) 3.09017 + 9.51057i 0.113597 + 0.349615i
\(741\) 0 0
\(742\) 29.1246 + 21.1603i 1.06920 + 0.776818i
\(743\) 25.2227 + 18.3253i 0.925329 + 0.672291i 0.944845 0.327518i \(-0.106212\pi\)
−0.0195154 + 0.999810i \(0.506212\pi\)
\(744\) 4.28187 13.1782i 0.156981 0.483137i
\(745\) −2.14093 6.58911i −0.0784377 0.241406i
\(746\) −38.8328 + 28.2137i −1.42177 + 1.03298i
\(747\) 17.3205 0.633724
\(748\) 0 0
\(749\) −12.0000 −0.438470
\(750\) 2.80252 2.03615i 0.102333 0.0743496i
\(751\) 4.94427 + 15.2169i 0.180419 + 0.555273i 0.999839 0.0179203i \(-0.00570452\pi\)
−0.819420 + 0.573193i \(0.805705\pi\)
\(752\) 9.27051 28.5317i 0.338061 1.04044i
\(753\) −19.4164 14.1068i −0.707573 0.514082i
\(754\) 0 0
\(755\) −2.14093 + 6.58911i −0.0779165 + 0.239802i
\(756\) 4.28187 + 13.1782i 0.155730 + 0.479287i
\(757\) 1.61803 1.17557i 0.0588084 0.0427268i −0.557993 0.829846i \(-0.688428\pi\)
0.616801 + 0.787119i \(0.288428\pi\)
\(758\) −55.4256 −2.01315
\(759\) 0 0
\(760\) 12.0000 0.435286
\(761\) 11.2101 8.14459i 0.406365 0.295241i −0.365764 0.930708i \(-0.619192\pi\)
0.772128 + 0.635467i \(0.219192\pi\)
\(762\) 11.1246 + 34.2380i 0.403002 + 1.24031i
\(763\) 7.41641 22.8254i 0.268492 0.826333i
\(764\) 9.70820 + 7.05342i 0.351230 + 0.255184i
\(765\) −5.60503 4.07230i −0.202650 0.147234i
\(766\) −9.63420 + 29.6510i −0.348098 + 1.07133i
\(767\) 0 0
\(768\) −30.7426 + 22.3358i −1.10933 + 0.805975i
\(769\) −41.5692 −1.49902 −0.749512 0.661991i \(-0.769712\pi\)
−0.749512 + 0.661991i \(0.769712\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) −5.60503 + 4.07230i −0.201730 + 0.146565i
\(773\) −1.85410 5.70634i −0.0666874 0.205243i 0.912160 0.409834i \(-0.134413\pi\)
−0.978847 + 0.204591i \(0.934413\pi\)
\(774\) −1.85410 + 5.70634i −0.0666443 + 0.205110i
\(775\) −3.23607 2.35114i −0.116243 0.0844555i
\(776\) 14.0126 + 10.1807i 0.503023 + 0.365467i
\(777\) −21.4093 + 65.8911i −0.768055 + 2.36383i
\(778\) −3.21140 9.88367i −0.115134 0.354347i
\(779\) 38.8328 28.2137i 1.39133 1.01086i
\(780\) 0 0
\(781\) 0 0
\(782\) −72.0000 −2.57471
\(783\) 0 0
\(784\) −7.72542 23.7764i −0.275908 0.849158i
\(785\) −0.618034 + 1.90211i −0.0220586 + 0.0678893i
\(786\) −19.4164 14.1068i −0.692560 0.503175i
\(787\) −36.4327 26.4699i −1.29869 0.943551i −0.298744 0.954333i \(-0.596568\pi\)
−0.999942 + 0.0107823i \(0.996568\pi\)
\(788\) 0 0
\(789\) −2.14093 6.58911i −0.0762192 0.234579i
\(790\) 9.70820 7.05342i 0.345402 0.250950i
\(791\) −20.7846 −0.739016
\(792\) 0 0
\(793\) 0 0
\(794\) −47.6428 + 34.6145i −1.69078 + 1.22842i
\(795\) −3.70820 11.4127i −0.131516 0.404766i
\(796\) 1.23607 3.80423i 0.0438113 0.134837i
\(797\) 14.5623 + 10.5801i 0.515823 + 0.374768i 0.815028 0.579421i \(-0.196721\pi\)
−0.299205 + 0.954189i \(0.596721\pi\)
\(798\) −67.2604 48.8675i −2.38099 1.72989i
\(799\) −12.8456 + 39.5347i −0.454444 + 1.39864i
\(800\) 1.60570 + 4.94183i 0.0567700 + 0.174720i
\(801\) 4.85410 3.52671i 0.171511 0.124610i
\(802\) 31.1769 1.10090
\(803\) 0 0
\(804\) 20.0000 0.705346
\(805\) 16.8151 12.2169i 0.592654 0.430589i
\(806\) 0 0
\(807\) −18.5410 + 57.0634i −0.652675 + 2.00873i
\(808\) 19.4164 + 14.1068i 0.683067 + 0.496277i
\(809\) 11.2101 + 8.14459i 0.394125 + 0.286349i 0.767144 0.641475i \(-0.221677\pi\)
−0.373019 + 0.927824i \(0.621677\pi\)
\(810\) 5.88756 18.1201i 0.206868 0.636674i
\(811\) 4.28187 + 13.1782i 0.150357 + 0.462750i 0.997661 0.0683577i \(-0.0217759\pi\)
−0.847304 + 0.531108i \(0.821776\pi\)
\(812\) 0 0
\(813\) −13.8564 −0.485965
\(814\) 0 0
\(815\) 2.00000 0.0700569
\(816\) 56.0503 40.7230i 1.96215 1.42559i
\(817\) 7.41641 + 22.8254i 0.259467 + 0.798558i
\(818\) 11.1246 34.2380i 0.388963 1.19710i
\(819\) 0 0
\(820\) 5.60503 + 4.07230i 0.195736 + 0.142211i
\(821\) 14.9865 46.1238i 0.523033 1.60973i −0.245139 0.969488i \(-0.578834\pi\)
0.768172 0.640243i \(-0.221166\pi\)
\(822\) −6.42280 19.7673i −0.224021 0.689465i
\(823\) −21.0344 + 15.2824i −0.733215 + 0.532712i −0.890579 0.454829i \(-0.849700\pi\)
0.157364 + 0.987541i \(0.449700\pi\)
\(824\) 3.46410 0.120678
\(825\) 0 0
\(826\) 0 0
\(827\) −14.0126 + 10.1807i −0.487265 + 0.354019i −0.804132 0.594451i \(-0.797369\pi\)
0.316866 + 0.948470i \(0.397369\pi\)
\(828\) 1.85410 + 5.70634i 0.0644345 + 0.198309i
\(829\) −10.5066 + 32.3359i −0.364909 + 1.12307i 0.585130 + 0.810940i \(0.301044\pi\)
−0.950038 + 0.312133i \(0.898956\pi\)
\(830\) 24.2705 + 17.6336i 0.842442 + 0.612070i
\(831\) 44.8403 + 32.5784i 1.55549 + 1.13013i
\(832\) 0 0
\(833\) 10.7047 + 32.9456i 0.370895 + 1.14150i
\(834\) −38.8328 + 28.2137i −1.34467 + 0.976960i
\(835\) −10.3923 −0.359641
\(836\) 0 0
\(837\) −16.0000 −0.553041
\(838\) −16.8151 + 12.2169i −0.580868 + 0.422025i
\(839\) −3.70820 11.4127i −0.128021 0.394009i 0.866418 0.499319i \(-0.166417\pi\)
−0.994439 + 0.105310i \(0.966417\pi\)
\(840\) −3.70820 + 11.4127i −0.127945 + 0.393775i
\(841\) 23.4615 + 17.0458i 0.809017 + 0.587785i
\(842\) −36.4327 26.4699i −1.25555 0.912214i
\(843\) 4.28187 13.1782i 0.147475 0.453882i
\(844\) 6.42280 + 19.7673i 0.221082 + 0.680420i
\(845\) 10.5172 7.64121i 0.361803 0.262866i
\(846\) 10.3923 0.357295
\(847\) 0 0
\(848\) 30.0000 1.03020
\(849\) 39.2352 28.5061i 1.34655 0.978326i
\(850\) −3.70820 11.4127i −0.127190 0.391452i
\(851\) 18.5410 57.0634i 0.635578 1.95611i
\(852\) 0 0
\(853\) 33.6302 + 24.4338i 1.15148 + 0.836596i 0.988676 0.150063i \(-0.0479475\pi\)
0.162800 + 0.986659i \(0.447948\pi\)
\(854\) −12.8456 + 39.5347i −0.439567 + 1.35285i
\(855\) 2.14093 + 6.58911i 0.0732183 + 0.225343i
\(856\) −4.85410 + 3.52671i −0.165910 + 0.120541i
\(857\) −20.7846 −0.709989 −0.354994 0.934868i \(-0.615517\pi\)
−0.354994 + 0.934868i \(0.615517\pi\)
\(858\) 0 0
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) −2.80252 + 2.03615i −0.0955650 + 0.0694321i
\(861\) 14.8328 + 45.6507i 0.505501 + 1.55577i
\(862\) 14.8328 45.6507i 0.505208 1.55487i
\(863\) 43.6869 + 31.7404i 1.48712 + 1.08046i 0.975174 + 0.221438i \(0.0710750\pi\)
0.511946 + 0.859018i \(0.328925\pi\)
\(864\) 16.8151 + 12.2169i 0.572061 + 0.415627i
\(865\) 0 0
\(866\) 18.1979 + 56.0075i 0.618391 + 1.90321i
\(867\) −50.1591 + 36.4427i −1.70349 + 1.23766i
\(868\) −13.8564 −0.470317
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −3.70820 11.4127i −0.125576 0.386482i
\(873\) −3.09017 + 9.51057i −0.104586 + 0.321884i
\(874\) 58.2492 + 42.3205i 1.97031 + 1.43151i
\(875\) 2.80252 + 2.03615i 0.0947424 + 0.0688344i
\(876\) 4.28187 13.1782i 0.144671 0.445251i
\(877\) −8.56373 26.3565i −0.289177 0.889994i −0.985116 0.171893i \(-0.945012\pi\)
0.695939 0.718101i \(-0.254988\pi\)
\(878\) −19.4164 + 14.1068i −0.655272 + 0.476083i
\(879\) −27.7128 −0.934730
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 7.00629 5.09037i 0.235914 0.171402i
\(883\) 10.5066 + 32.3359i 0.353574 + 1.08819i 0.956831 + 0.290643i \(0.0938694\pi\)
−0.603257 + 0.797547i \(0.706131\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −8.40755 6.10844i −0.282457 0.205217i
\(887\) 5.35233 16.4728i 0.179714 0.553102i −0.820104 0.572215i \(-0.806084\pi\)
0.999817 + 0.0191131i \(0.00608427\pi\)
\(888\) 10.7047 + 32.9456i 0.359225 + 1.10558i
\(889\) −29.1246 + 21.1603i −0.976808 + 0.709693i
\(890\) 10.3923 0.348351
\(891\) 0 0
\(892\) 14.0000 0.468755
\(893\) 33.6302 24.4338i 1.12539 0.817645i
\(894\) 7.41641 + 22.8254i 0.248042 + 0.763394i
\(895\) −3.70820 + 11.4127i −0.123952 + 0.381484i
\(896\) −33.9787 24.6870i −1.13515 0.824734i
\(897\) 0 0
\(898\) −16.0570 + 49.4183i −0.535829 + 1.64911i
\(899\) 0 0
\(900\) −0.809017 + 0.587785i −0.0269672 + 0.0195928i
\(901\) −41.5692 −1.38487
\(902\) 0 0
\(903\) −24.0000 −0.798670
\(904\) −8.40755 + 6.10844i −0.279631 + 0.203164i
\(905\) 4.32624 + 13.3148i 0.143809 + 0.442599i
\(906\) 7.41641 22.8254i 0.246394 0.758322i
\(907\) −21.0344 15.2824i −0.698437 0.507444i 0.180986 0.983486i \(-0.442071\pi\)
−0.879423 + 0.476041i \(0.842071\pi\)
\(908\) 2.80252 + 2.03615i 0.0930048 + 0.0675719i
\(909\) −4.28187 + 13.1782i −0.142020 + 0.437094i
\(910\) 0 0
\(911\) 29.1246 21.1603i 0.964941 0.701071i 0.0106483 0.999943i \(-0.496610\pi\)
0.954293 + 0.298872i \(0.0966105\pi\)
\(912\) −69.2820 −2.29416
\(913\) 0 0
\(914\) 36.0000 1.19077
\(915\) 11.2101 8.14459i 0.370593 0.269252i
\(916\) −0.618034 1.90211i −0.0204204 0.0628476i
\(917\) 7.41641 22.8254i 0.244911 0.753760i
\(918\) −38.8328 28.2137i −1.28167 0.931191i
\(919\) −11.2101 8.14459i −0.369786 0.268665i 0.387336 0.921939i \(-0.373395\pi\)
−0.757122 + 0.653273i \(0.773395\pi\)
\(920\) 3.21140 9.88367i 0.105877 0.325855i
\(921\) 2.14093 + 6.58911i 0.0705461 + 0.217119i
\(922\) 38.8328 28.2137i 1.27889 0.929168i
\(923\) 0 0
\(924\) 0 0
\(925\) 10.0000 0.328798
\(926\) 19.6176 14.2530i 0.644675 0.468384i
\(927\) 0.618034 + 1.90211i 0.0202989 + 0.0624736i
\(928\) 0 0
\(929\) 4.85410 + 3.52671i 0.159258 + 0.115708i 0.664560 0.747235i \(-0.268619\pi\)
−0.505302 + 0.862942i \(0.668619\pi\)
\(930\) 11.2101 + 8.14459i 0.367593 + 0.267072i
\(931\) 10.7047 32.9456i 0.350831 1.07975i
\(932\) −2.14093 6.58911i −0.0701286 0.215834i
\(933\) 38.8328 28.2137i 1.27133 0.923675i
\(934\) −31.1769 −1.02014
\(935\) 0 0
\(936\) 0 0
\(937\) −28.0252 + 20.3615i −0.915542 + 0.665181i −0.942410 0.334458i \(-0.891447\pi\)
0.0268681 + 0.999639i \(0.491447\pi\)
\(938\) 18.5410 + 57.0634i 0.605386 + 1.86319i
\(939\) 21.0132 64.6718i 0.685738 2.11049i
\(940\) 4.85410 + 3.52671i 0.158323 + 0.115029i
\(941\) −11.2101 8.14459i −0.365438 0.265506i 0.389879 0.920866i \(-0.372517\pi\)
−0.755317 + 0.655360i \(0.772517\pi\)
\(942\) 2.14093 6.58911i 0.0697554 0.214685i
\(943\) −12.8456 39.5347i −0.418310 1.28743i
\(944\) 0 0
\(945\) 13.8564 0.450749
\(946\) 0 0
\(947\) −6.00000 −0.194974 −0.0974869 0.995237i \(-0.531080\pi\)
−0.0974869 + 0.995237i \(0.531080\pi\)
\(948\) −11.2101 + 8.14459i −0.364086 + 0.264524i
\(949\) 0 0
\(950\) −3.70820 + 11.4127i −0.120310 + 0.370276i
\(951\) 29.1246 + 21.1603i 0.944430 + 0.686169i
\(952\) 33.6302 + 24.4338i 1.08996 + 0.791903i
\(953\) −10.7047 + 32.9456i −0.346758 + 1.06721i 0.613878 + 0.789401i \(0.289609\pi\)
−0.960636 + 0.277810i \(0.910391\pi\)
\(954\) 3.21140 + 9.88367i 0.103973 + 0.319996i
\(955\) 9.70820 7.05342i 0.314150 0.228243i
\(956\) 6.92820 0.224074
\(957\) 0 0
\(958\) −36.0000 −1.16311
\(959\) 16.8151 12.2169i 0.542988 0.394504i
\(960\) 0.618034 + 1.90211i 0.0199470 + 0.0613904i
\(961\) −4.63525 + 14.2658i −0.149524 + 0.460189i
\(962\) 0 0
\(963\) −2.80252 2.03615i −0.0903099 0.0656139i
\(964\) 6.42280 19.7673i 0.206864 0.636663i
\(965\) 2.14093 + 6.58911i 0.0689191 + 0.212111i
\(966\) −58.2492 + 42.3205i −1.87414 + 1.36164i
\(967\) −24.2487 −0.779786 −0.389893 0.920860i \(-0.627488\pi\)
−0.389893 + 0.920860i \(0.627488\pi\)
\(968\) 0 0
\(969\) 96.0000 3.08396
\(970\) −14.0126 + 10.1807i −0.449917 + 0.326884i
\(971\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(972\) −3.09017 + 9.51057i −0.0991172 + 0.305052i
\(973\) −38.8328 28.2137i −1.24492 0.904489i
\(974\) −19.6176 14.2530i −0.628589 0.456697i
\(975\) 0 0
\(976\) 10.7047 + 32.9456i 0.342648 + 1.05456i
\(977\) 33.9787 24.6870i 1.08708 0.789806i 0.108172 0.994132i \(-0.465500\pi\)
0.978903 + 0.204326i \(0.0655002\pi\)
\(978\) −6.92820 −0.221540
\(979\) 0 0
\(980\) 5.00000 0.159719
\(981\) 5.60503 4.07230i 0.178955 0.130018i
\(982\) 7.41641 + 22.8254i 0.236667 + 0.728386i
\(983\) 12.9787 39.9444i 0.413957 1.27403i −0.499224 0.866473i \(-0.666382\pi\)
0.913181 0.407555i \(-0.133618\pi\)
\(984\) 19.4164 + 14.1068i 0.618972 + 0.449710i
\(985\) 0 0
\(986\) 0 0
\(987\) 12.8456 + 39.5347i 0.408880 + 1.25840i
\(988\) 0 0
\(989\) 20.7846 0.660912
\(990\) 0 0
\(991\) 28.0000 0.889449 0.444725 0.895667i \(-0.353302\pi\)
0.444725 + 0.895667i \(0.353302\pi\)
\(992\) −16.8151 + 12.2169i −0.533880 + 0.387887i
\(993\) 4.94427 + 15.2169i 0.156902 + 0.482894i
\(994\) 0 0
\(995\) −3.23607 2.35114i −0.102590 0.0745362i
\(996\) −28.0252 20.3615i −0.888012 0.645178i
\(997\) −12.8456 + 39.5347i −0.406824 + 1.25208i 0.512538 + 0.858664i \(0.328705\pi\)
−0.919362 + 0.393411i \(0.871295\pi\)
\(998\) −8.56373 26.3565i −0.271080 0.834299i
\(999\) 32.3607 23.5114i 1.02385 0.743868i
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 605.2.g.h.366.2 8
11.2 odd 10 605.2.a.f.1.2 yes 2
11.3 even 5 inner 605.2.g.h.511.1 8
11.4 even 5 inner 605.2.g.h.81.2 8
11.5 even 5 inner 605.2.g.h.251.1 8
11.6 odd 10 inner 605.2.g.h.251.2 8
11.7 odd 10 inner 605.2.g.h.81.1 8
11.8 odd 10 inner 605.2.g.h.511.2 8
11.9 even 5 605.2.a.f.1.1 2
11.10 odd 2 inner 605.2.g.h.366.1 8
33.2 even 10 5445.2.a.r.1.1 2
33.20 odd 10 5445.2.a.r.1.2 2
44.31 odd 10 9680.2.a.bg.1.2 2
44.35 even 10 9680.2.a.bg.1.1 2
55.9 even 10 3025.2.a.j.1.2 2
55.24 odd 10 3025.2.a.j.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.a.f.1.1 2 11.9 even 5
605.2.a.f.1.2 yes 2 11.2 odd 10
605.2.g.h.81.1 8 11.7 odd 10 inner
605.2.g.h.81.2 8 11.4 even 5 inner
605.2.g.h.251.1 8 11.5 even 5 inner
605.2.g.h.251.2 8 11.6 odd 10 inner
605.2.g.h.366.1 8 11.10 odd 2 inner
605.2.g.h.366.2 8 1.1 even 1 trivial
605.2.g.h.511.1 8 11.3 even 5 inner
605.2.g.h.511.2 8 11.8 odd 10 inner
3025.2.a.j.1.1 2 55.24 odd 10
3025.2.a.j.1.2 2 55.9 even 10
5445.2.a.r.1.1 2 33.2 even 10
5445.2.a.r.1.2 2 33.20 odd 10
9680.2.a.bg.1.1 2 44.35 even 10
9680.2.a.bg.1.2 2 44.31 odd 10