Properties

Label 418.2.f.b.267.1
Level $418$
Weight $2$
Character 418.267
Analytic conductor $3.338$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [418,2,Mod(115,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.115");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.f (of order \(5\), degree \(4\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 267.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 418.267
Dual form 418.2.f.b.191.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(3.11803 + 2.26538i) q^{5} +(0.190983 - 0.587785i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.42705 - 1.76336i) q^{9} +O(q^{10})\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(3.11803 + 2.26538i) q^{5} +(0.190983 - 0.587785i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.42705 - 1.76336i) q^{9} -3.85410 q^{10} +(2.54508 - 2.12663i) q^{11} +(-2.00000 + 1.45309i) q^{13} +(0.190983 + 0.587785i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-3.30902 - 2.40414i) q^{17} +(-0.927051 + 2.85317i) q^{18} +(0.309017 + 0.951057i) q^{19} +(3.11803 - 2.26538i) q^{20} +(-0.809017 + 3.21644i) q^{22} +1.14590 q^{23} +(3.04508 + 9.37181i) q^{25} +(0.763932 - 2.35114i) q^{26} +(-0.500000 - 0.363271i) q^{28} +(0.381966 - 1.17557i) q^{29} +(4.61803 - 3.35520i) q^{31} +1.00000 q^{32} +4.09017 q^{34} +(1.92705 - 1.40008i) q^{35} +(-0.927051 - 2.85317i) q^{36} +(-2.85410 + 8.78402i) q^{37} +(-0.809017 - 0.587785i) q^{38} +(-1.19098 + 3.66547i) q^{40} +(3.23607 + 9.95959i) q^{41} -1.61803 q^{43} +(-1.23607 - 3.07768i) q^{44} +11.5623 q^{45} +(-0.927051 + 0.673542i) q^{46} +(-3.59017 - 11.0494i) q^{47} +(5.35410 + 3.88998i) q^{49} +(-7.97214 - 5.79210i) q^{50} +(0.763932 + 2.35114i) q^{52} +(-1.61803 + 1.17557i) q^{53} +(12.7533 - 0.865300i) q^{55} +0.618034 q^{56} +(0.381966 + 1.17557i) q^{58} +(-3.09017 + 9.51057i) q^{59} +(-8.16312 - 5.93085i) q^{61} +(-1.76393 + 5.42882i) q^{62} +(-0.572949 - 1.76336i) q^{63} +(-0.809017 + 0.587785i) q^{64} -9.52786 q^{65} -8.00000 q^{67} +(-3.30902 + 2.40414i) q^{68} +(-0.736068 + 2.26538i) q^{70} +(-6.85410 - 4.97980i) q^{71} +(2.42705 + 1.76336i) q^{72} +(-2.61803 + 8.05748i) q^{73} +(-2.85410 - 8.78402i) q^{74} +1.00000 q^{76} +(-0.763932 - 1.90211i) q^{77} +(9.70820 - 7.05342i) q^{79} +(-1.19098 - 3.66547i) q^{80} +(2.78115 - 8.55951i) q^{81} +(-8.47214 - 6.15537i) q^{82} +(-3.11803 - 2.26538i) q^{83} +(-4.87132 - 14.9924i) q^{85} +(1.30902 - 0.951057i) q^{86} +(2.80902 + 1.76336i) q^{88} -14.1803 q^{89} +(-9.35410 + 6.79615i) q^{90} +(0.472136 + 1.45309i) q^{91} +(0.354102 - 1.08981i) q^{92} +(9.39919 + 6.82891i) q^{94} +(-1.19098 + 3.66547i) q^{95} +(6.09017 - 4.42477i) q^{97} -6.61803 q^{98} +(2.42705 - 9.64932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9} - 2 q^{10} - q^{11} - 8 q^{13} + 3 q^{14} - q^{16} - 11 q^{17} + 3 q^{18} - q^{19} + 8 q^{20} - q^{22} + 18 q^{23} + q^{25} + 12 q^{26} - 2 q^{28} + 6 q^{29} + 14 q^{31} + 4 q^{32} - 6 q^{34} + q^{35} + 3 q^{36} + 2 q^{37} - q^{38} - 7 q^{40} + 4 q^{41} - 2 q^{43} + 4 q^{44} + 6 q^{45} + 3 q^{46} + 8 q^{47} + 8 q^{49} - 14 q^{50} + 12 q^{52} - 2 q^{53} + 13 q^{55} - 2 q^{56} + 6 q^{58} + 10 q^{59} - 17 q^{61} - 16 q^{62} - 9 q^{63} - q^{64} - 56 q^{65} - 32 q^{67} - 11 q^{68} + 6 q^{70} - 14 q^{71} + 3 q^{72} - 6 q^{73} + 2 q^{74} + 4 q^{76} - 12 q^{77} + 12 q^{79} - 7 q^{80} - 9 q^{81} - 16 q^{82} - 8 q^{83} + 23 q^{85} + 3 q^{86} + 9 q^{88} - 12 q^{89} - 24 q^{90} - 16 q^{91} - 12 q^{92} + 13 q^{94} - 7 q^{95} + 2 q^{97} - 22 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 + 0.587785i −0.572061 + 0.415627i
\(3\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 3.11803 + 2.26538i 1.39443 + 1.01311i 0.995363 + 0.0961876i \(0.0306649\pi\)
0.399064 + 0.916923i \(0.369335\pi\)
\(6\) 0 0
\(7\) 0.190983 0.587785i 0.0721848 0.222162i −0.908455 0.417983i \(-0.862737\pi\)
0.980640 + 0.195821i \(0.0627372\pi\)
\(8\) 0.309017 + 0.951057i 0.109254 + 0.336249i
\(9\) 2.42705 1.76336i 0.809017 0.587785i
\(10\) −3.85410 −1.21877
\(11\) 2.54508 2.12663i 0.767372 0.641202i
\(12\) 0 0
\(13\) −2.00000 + 1.45309i −0.554700 + 0.403013i −0.829515 0.558484i \(-0.811383\pi\)
0.274815 + 0.961497i \(0.411383\pi\)
\(14\) 0.190983 + 0.587785i 0.0510424 + 0.157092i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) −3.30902 2.40414i −0.802555 0.583090i 0.109108 0.994030i \(-0.465201\pi\)
−0.911662 + 0.410940i \(0.865201\pi\)
\(18\) −0.927051 + 2.85317i −0.218508 + 0.672499i
\(19\) 0.309017 + 0.951057i 0.0708934 + 0.218187i
\(20\) 3.11803 2.26538i 0.697214 0.506555i
\(21\) 0 0
\(22\) −0.809017 + 3.21644i −0.172483 + 0.685747i
\(23\) 1.14590 0.238936 0.119468 0.992838i \(-0.461881\pi\)
0.119468 + 0.992838i \(0.461881\pi\)
\(24\) 0 0
\(25\) 3.04508 + 9.37181i 0.609017 + 1.87436i
\(26\) 0.763932 2.35114i 0.149819 0.461097i
\(27\) 0 0
\(28\) −0.500000 0.363271i −0.0944911 0.0686518i
\(29\) 0.381966 1.17557i 0.0709293 0.218298i −0.909308 0.416124i \(-0.863388\pi\)
0.980237 + 0.197826i \(0.0633882\pi\)
\(30\) 0 0
\(31\) 4.61803 3.35520i 0.829423 0.602611i −0.0899727 0.995944i \(-0.528678\pi\)
0.919396 + 0.393333i \(0.128678\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 4.09017 0.701458
\(35\) 1.92705 1.40008i 0.325731 0.236657i
\(36\) −0.927051 2.85317i −0.154508 0.475528i
\(37\) −2.85410 + 8.78402i −0.469211 + 1.44408i 0.384396 + 0.923168i \(0.374410\pi\)
−0.853608 + 0.520916i \(0.825590\pi\)
\(38\) −0.809017 0.587785i −0.131240 0.0953514i
\(39\) 0 0
\(40\) −1.19098 + 3.66547i −0.188311 + 0.579562i
\(41\) 3.23607 + 9.95959i 0.505389 + 1.55543i 0.800116 + 0.599846i \(0.204771\pi\)
−0.294727 + 0.955582i \(0.595229\pi\)
\(42\) 0 0
\(43\) −1.61803 −0.246748 −0.123374 0.992360i \(-0.539371\pi\)
−0.123374 + 0.992360i \(0.539371\pi\)
\(44\) −1.23607 3.07768i −0.186344 0.463978i
\(45\) 11.5623 1.72361
\(46\) −0.927051 + 0.673542i −0.136686 + 0.0993083i
\(47\) −3.59017 11.0494i −0.523680 1.61172i −0.766911 0.641753i \(-0.778207\pi\)
0.243231 0.969968i \(-0.421793\pi\)
\(48\) 0 0
\(49\) 5.35410 + 3.88998i 0.764872 + 0.555712i
\(50\) −7.97214 5.79210i −1.12743 0.819126i
\(51\) 0 0
\(52\) 0.763932 + 2.35114i 0.105938 + 0.326045i
\(53\) −1.61803 + 1.17557i −0.222254 + 0.161477i −0.693341 0.720610i \(-0.743862\pi\)
0.471087 + 0.882087i \(0.343862\pi\)
\(54\) 0 0
\(55\) 12.7533 0.865300i 1.71965 0.116677i
\(56\) 0.618034 0.0825883
\(57\) 0 0
\(58\) 0.381966 + 1.17557i 0.0501546 + 0.154360i
\(59\) −3.09017 + 9.51057i −0.402306 + 1.23817i 0.520818 + 0.853668i \(0.325627\pi\)
−0.923124 + 0.384502i \(0.874373\pi\)
\(60\) 0 0
\(61\) −8.16312 5.93085i −1.04518 0.759368i −0.0738903 0.997266i \(-0.523541\pi\)
−0.971290 + 0.237898i \(0.923541\pi\)
\(62\) −1.76393 + 5.42882i −0.224020 + 0.689461i
\(63\) −0.572949 1.76336i −0.0721848 0.222162i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −9.52786 −1.18179
\(66\) 0 0
\(67\) −8.00000 −0.977356 −0.488678 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) −3.30902 + 2.40414i −0.401277 + 0.291545i
\(69\) 0 0
\(70\) −0.736068 + 2.26538i −0.0879770 + 0.270765i
\(71\) −6.85410 4.97980i −0.813432 0.590993i 0.101391 0.994847i \(-0.467671\pi\)
−0.914824 + 0.403853i \(0.867671\pi\)
\(72\) 2.42705 + 1.76336i 0.286031 + 0.207813i
\(73\) −2.61803 + 8.05748i −0.306418 + 0.943057i 0.672727 + 0.739891i \(0.265123\pi\)
−0.979144 + 0.203166i \(0.934877\pi\)
\(74\) −2.85410 8.78402i −0.331783 1.02112i
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) −0.763932 1.90211i −0.0870581 0.216766i
\(78\) 0 0
\(79\) 9.70820 7.05342i 1.09226 0.793572i 0.112479 0.993654i \(-0.464121\pi\)
0.979779 + 0.200082i \(0.0641209\pi\)
\(80\) −1.19098 3.66547i −0.133156 0.409812i
\(81\) 2.78115 8.55951i 0.309017 0.951057i
\(82\) −8.47214 6.15537i −0.935591 0.679747i
\(83\) −3.11803 2.26538i −0.342249 0.248658i 0.403361 0.915041i \(-0.367842\pi\)
−0.745610 + 0.666383i \(0.767842\pi\)
\(84\) 0 0
\(85\) −4.87132 14.9924i −0.528369 1.62615i
\(86\) 1.30902 0.951057i 0.141155 0.102555i
\(87\) 0 0
\(88\) 2.80902 + 1.76336i 0.299442 + 0.187974i
\(89\) −14.1803 −1.50311 −0.751557 0.659669i \(-0.770697\pi\)
−0.751557 + 0.659669i \(0.770697\pi\)
\(90\) −9.35410 + 6.79615i −0.986009 + 0.716377i
\(91\) 0.472136 + 1.45309i 0.0494933 + 0.152325i
\(92\) 0.354102 1.08981i 0.0369177 0.113621i
\(93\) 0 0
\(94\) 9.39919 + 6.82891i 0.969452 + 0.704348i
\(95\) −1.19098 + 3.66547i −0.122192 + 0.376069i
\(96\) 0 0
\(97\) 6.09017 4.42477i 0.618363 0.449267i −0.233986 0.972240i \(-0.575177\pi\)
0.852349 + 0.522973i \(0.175177\pi\)
\(98\) −6.61803 −0.668522
\(99\) 2.42705 9.64932i 0.243928 0.969793i
\(100\) 9.85410 0.985410
\(101\) −1.11803 + 0.812299i −0.111249 + 0.0808268i −0.642019 0.766689i \(-0.721903\pi\)
0.530770 + 0.847516i \(0.321903\pi\)
\(102\) 0 0
\(103\) 2.29180 7.05342i 0.225817 0.694994i −0.772390 0.635148i \(-0.780939\pi\)
0.998208 0.0598462i \(-0.0190610\pi\)
\(104\) −2.00000 1.45309i −0.196116 0.142487i
\(105\) 0 0
\(106\) 0.618034 1.90211i 0.0600288 0.184750i
\(107\) −2.85410 8.78402i −0.275916 0.849184i −0.988975 0.148079i \(-0.952691\pi\)
0.713059 0.701104i \(-0.247309\pi\)
\(108\) 0 0
\(109\) 1.70820 0.163616 0.0818081 0.996648i \(-0.473931\pi\)
0.0818081 + 0.996648i \(0.473931\pi\)
\(110\) −9.80902 + 8.19624i −0.935253 + 0.781481i
\(111\) 0 0
\(112\) −0.500000 + 0.363271i −0.0472456 + 0.0343259i
\(113\) −4.23607 13.0373i −0.398496 1.22644i −0.926205 0.377019i \(-0.876949\pi\)
0.527710 0.849425i \(-0.323051\pi\)
\(114\) 0 0
\(115\) 3.57295 + 2.59590i 0.333179 + 0.242069i
\(116\) −1.00000 0.726543i −0.0928477 0.0674578i
\(117\) −2.29180 + 7.05342i −0.211877 + 0.652089i
\(118\) −3.09017 9.51057i −0.284473 0.875518i
\(119\) −2.04508 + 1.48584i −0.187473 + 0.136207i
\(120\) 0 0
\(121\) 1.95492 10.8249i 0.177720 0.984081i
\(122\) 10.0902 0.913521
\(123\) 0 0
\(124\) −1.76393 5.42882i −0.158406 0.487523i
\(125\) −5.78115 + 17.7926i −0.517082 + 1.59141i
\(126\) 1.50000 + 1.08981i 0.133631 + 0.0970883i
\(127\) 4.23607 + 3.07768i 0.375890 + 0.273100i 0.759649 0.650333i \(-0.225371\pi\)
−0.383759 + 0.923433i \(0.625371\pi\)
\(128\) 0.309017 0.951057i 0.0273135 0.0840623i
\(129\) 0 0
\(130\) 7.70820 5.60034i 0.676054 0.491182i
\(131\) −6.32624 −0.552726 −0.276363 0.961053i \(-0.589129\pi\)
−0.276363 + 0.961053i \(0.589129\pi\)
\(132\) 0 0
\(133\) 0.618034 0.0535903
\(134\) 6.47214 4.70228i 0.559107 0.406215i
\(135\) 0 0
\(136\) 1.26393 3.88998i 0.108381 0.333563i
\(137\) 13.4443 + 9.76784i 1.14862 + 0.834522i 0.988297 0.152542i \(-0.0487459\pi\)
0.160325 + 0.987064i \(0.448746\pi\)
\(138\) 0 0
\(139\) −5.97214 + 18.3803i −0.506550 + 1.55900i 0.291599 + 0.956541i \(0.405813\pi\)
−0.798149 + 0.602460i \(0.794187\pi\)
\(140\) −0.736068 2.26538i −0.0622091 0.191460i
\(141\) 0 0
\(142\) 8.47214 0.710966
\(143\) −2.00000 + 7.95148i −0.167248 + 0.664936i
\(144\) −3.00000 −0.250000
\(145\) 3.85410 2.80017i 0.320066 0.232541i
\(146\) −2.61803 8.05748i −0.216670 0.666842i
\(147\) 0 0
\(148\) 7.47214 + 5.42882i 0.614206 + 0.446247i
\(149\) −10.8541 7.88597i −0.889203 0.646044i 0.0464673 0.998920i \(-0.485204\pi\)
−0.935670 + 0.352876i \(0.885204\pi\)
\(150\) 0 0
\(151\) −4.38197 13.4863i −0.356599 1.09750i −0.955076 0.296360i \(-0.904227\pi\)
0.598477 0.801140i \(-0.295773\pi\)
\(152\) −0.809017 + 0.587785i −0.0656199 + 0.0476757i
\(153\) −12.2705 −0.992012
\(154\) 1.73607 + 1.08981i 0.139896 + 0.0878197i
\(155\) 22.0000 1.76708
\(156\) 0 0
\(157\) 0.135255 + 0.416272i 0.0107945 + 0.0332221i 0.956309 0.292359i \(-0.0944401\pi\)
−0.945514 + 0.325581i \(0.894440\pi\)
\(158\) −3.70820 + 11.4127i −0.295009 + 0.907944i
\(159\) 0 0
\(160\) 3.11803 + 2.26538i 0.246502 + 0.179094i
\(161\) 0.218847 0.673542i 0.0172476 0.0530825i
\(162\) 2.78115 + 8.55951i 0.218508 + 0.672499i
\(163\) −20.2984 + 14.7476i −1.58989 + 1.15512i −0.685795 + 0.727795i \(0.740545\pi\)
−0.904096 + 0.427329i \(0.859455\pi\)
\(164\) 10.4721 0.817736
\(165\) 0 0
\(166\) 3.85410 0.299136
\(167\) −6.47214 + 4.70228i −0.500829 + 0.363874i −0.809334 0.587349i \(-0.800171\pi\)
0.308505 + 0.951223i \(0.400171\pi\)
\(168\) 0 0
\(169\) −2.12868 + 6.55139i −0.163744 + 0.503953i
\(170\) 12.7533 + 9.26581i 0.978133 + 0.710655i
\(171\) 2.42705 + 1.76336i 0.185601 + 0.134847i
\(172\) −0.500000 + 1.53884i −0.0381246 + 0.117336i
\(173\) −6.00000 18.4661i −0.456172 1.40395i −0.869754 0.493485i \(-0.835723\pi\)
0.413583 0.910467i \(-0.364277\pi\)
\(174\) 0 0
\(175\) 6.09017 0.460374
\(176\) −3.30902 + 0.224514i −0.249427 + 0.0169234i
\(177\) 0 0
\(178\) 11.4721 8.33499i 0.859873 0.624734i
\(179\) 2.23607 + 6.88191i 0.167132 + 0.514378i 0.999187 0.0403143i \(-0.0128359\pi\)
−0.832055 + 0.554692i \(0.812836\pi\)
\(180\) 3.57295 10.9964i 0.266312 0.819624i
\(181\) 10.2361 + 7.43694i 0.760841 + 0.552783i 0.899168 0.437603i \(-0.144173\pi\)
−0.138327 + 0.990387i \(0.544173\pi\)
\(182\) −1.23607 0.898056i −0.0916235 0.0665683i
\(183\) 0 0
\(184\) 0.354102 + 1.08981i 0.0261047 + 0.0803421i
\(185\) −28.7984 + 20.9232i −2.11730 + 1.53831i
\(186\) 0 0
\(187\) −13.5344 + 0.918300i −0.989736 + 0.0671528i
\(188\) −11.6180 −0.847332
\(189\) 0 0
\(190\) −1.19098 3.66547i −0.0864030 0.265921i
\(191\) 2.95492 9.09429i 0.213810 0.658040i −0.785426 0.618956i \(-0.787556\pi\)
0.999236 0.0390841i \(-0.0124440\pi\)
\(192\) 0 0
\(193\) −1.61803 1.17557i −0.116469 0.0846194i 0.528026 0.849228i \(-0.322932\pi\)
−0.644495 + 0.764609i \(0.722932\pi\)
\(194\) −2.32624 + 7.15942i −0.167014 + 0.514017i
\(195\) 0 0
\(196\) 5.35410 3.88998i 0.382436 0.277856i
\(197\) 7.52786 0.536338 0.268169 0.963372i \(-0.413581\pi\)
0.268169 + 0.963372i \(0.413581\pi\)
\(198\) 3.70820 + 9.23305i 0.263531 + 0.656164i
\(199\) 4.61803 0.327364 0.163682 0.986513i \(-0.447663\pi\)
0.163682 + 0.986513i \(0.447663\pi\)
\(200\) −7.97214 + 5.79210i −0.563715 + 0.409563i
\(201\) 0 0
\(202\) 0.427051 1.31433i 0.0300472 0.0924758i
\(203\) −0.618034 0.449028i −0.0433775 0.0315156i
\(204\) 0 0
\(205\) −12.4721 + 38.3853i −0.871092 + 2.68094i
\(206\) 2.29180 + 7.05342i 0.159677 + 0.491435i
\(207\) 2.78115 2.02063i 0.193303 0.140443i
\(208\) 2.47214 0.171412
\(209\) 2.80902 + 1.76336i 0.194304 + 0.121974i
\(210\) 0 0
\(211\) 13.8541 10.0656i 0.953756 0.692944i 0.00206355 0.999998i \(-0.499343\pi\)
0.951692 + 0.307054i \(0.0993432\pi\)
\(212\) 0.618034 + 1.90211i 0.0424467 + 0.130638i
\(213\) 0 0
\(214\) 7.47214 + 5.42882i 0.510785 + 0.371107i
\(215\) −5.04508 3.66547i −0.344072 0.249983i
\(216\) 0 0
\(217\) −1.09017 3.35520i −0.0740056 0.227766i
\(218\) −1.38197 + 1.00406i −0.0935985 + 0.0680033i
\(219\) 0 0
\(220\) 3.11803 12.3965i 0.210218 0.835771i
\(221\) 10.1115 0.680170
\(222\) 0 0
\(223\) 1.38197 + 4.25325i 0.0925433 + 0.284819i 0.986606 0.163124i \(-0.0521569\pi\)
−0.894062 + 0.447943i \(0.852157\pi\)
\(224\) 0.190983 0.587785i 0.0127606 0.0392731i
\(225\) 23.9164 + 17.3763i 1.59443 + 1.15842i
\(226\) 11.0902 + 8.05748i 0.737707 + 0.535976i
\(227\) 3.56231 10.9637i 0.236439 0.727683i −0.760489 0.649351i \(-0.775041\pi\)
0.996927 0.0783320i \(-0.0249594\pi\)
\(228\) 0 0
\(229\) 0.454915 0.330515i 0.0300616 0.0218411i −0.572653 0.819798i \(-0.694086\pi\)
0.602715 + 0.797957i \(0.294086\pi\)
\(230\) −4.41641 −0.291209
\(231\) 0 0
\(232\) 1.23607 0.0811518
\(233\) 7.20820 5.23707i 0.472225 0.343092i −0.326083 0.945341i \(-0.605729\pi\)
0.798308 + 0.602250i \(0.205729\pi\)
\(234\) −2.29180 7.05342i −0.149819 0.461097i
\(235\) 13.8369 42.5855i 0.902619 2.77797i
\(236\) 8.09017 + 5.87785i 0.526625 + 0.382616i
\(237\) 0 0
\(238\) 0.781153 2.40414i 0.0506346 0.155837i
\(239\) 4.88197 + 15.0251i 0.315788 + 0.971896i 0.975429 + 0.220315i \(0.0707085\pi\)
−0.659641 + 0.751581i \(0.729292\pi\)
\(240\) 0 0
\(241\) 9.05573 0.583331 0.291665 0.956520i \(-0.405791\pi\)
0.291665 + 0.956520i \(0.405791\pi\)
\(242\) 4.78115 + 9.90659i 0.307344 + 0.636820i
\(243\) 0 0
\(244\) −8.16312 + 5.93085i −0.522590 + 0.379684i
\(245\) 7.88197 + 24.2582i 0.503560 + 1.54980i
\(246\) 0 0
\(247\) −2.00000 1.45309i −0.127257 0.0924576i
\(248\) 4.61803 + 3.35520i 0.293245 + 0.213055i
\(249\) 0 0
\(250\) −5.78115 17.7926i −0.365632 1.12530i
\(251\) 18.8713 13.7108i 1.19115 0.865419i 0.197762 0.980250i \(-0.436633\pi\)
0.993385 + 0.114831i \(0.0366326\pi\)
\(252\) −1.85410 −0.116797
\(253\) 2.91641 2.43690i 0.183353 0.153206i
\(254\) −5.23607 −0.328540
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −1.76393 + 5.42882i −0.110031 + 0.338641i −0.990878 0.134760i \(-0.956974\pi\)
0.880847 + 0.473401i \(0.156974\pi\)
\(258\) 0 0
\(259\) 4.61803 + 3.35520i 0.286951 + 0.208482i
\(260\) −2.94427 + 9.06154i −0.182596 + 0.561973i
\(261\) −1.14590 3.52671i −0.0709293 0.218298i
\(262\) 5.11803 3.71847i 0.316193 0.229728i
\(263\) −1.52786 −0.0942121 −0.0471061 0.998890i \(-0.515000\pi\)
−0.0471061 + 0.998890i \(0.515000\pi\)
\(264\) 0 0
\(265\) −7.70820 −0.473511
\(266\) −0.500000 + 0.363271i −0.0306570 + 0.0222736i
\(267\) 0 0
\(268\) −2.47214 + 7.60845i −0.151010 + 0.464760i
\(269\) −13.2361 9.61657i −0.807017 0.586332i 0.105947 0.994372i \(-0.466213\pi\)
−0.912964 + 0.408039i \(0.866213\pi\)
\(270\) 0 0
\(271\) −4.35410 + 13.4005i −0.264493 + 0.814025i 0.727317 + 0.686302i \(0.240767\pi\)
−0.991810 + 0.127724i \(0.959233\pi\)
\(272\) 1.26393 + 3.88998i 0.0766371 + 0.235865i
\(273\) 0 0
\(274\) −16.6180 −1.00393
\(275\) 27.6803 + 17.3763i 1.66919 + 1.04783i
\(276\) 0 0
\(277\) 17.7984 12.9313i 1.06940 0.776965i 0.0935962 0.995610i \(-0.470164\pi\)
0.975804 + 0.218645i \(0.0701637\pi\)
\(278\) −5.97214 18.3803i −0.358185 1.10238i
\(279\) 5.29180 16.2865i 0.316812 0.975046i
\(280\) 1.92705 + 1.40008i 0.115163 + 0.0836711i
\(281\) −17.0902 12.4167i −1.01951 0.740720i −0.0533309 0.998577i \(-0.516984\pi\)
−0.966183 + 0.257857i \(0.916984\pi\)
\(282\) 0 0
\(283\) 8.42705 + 25.9358i 0.500936 + 1.54172i 0.807497 + 0.589872i \(0.200822\pi\)
−0.306561 + 0.951851i \(0.599178\pi\)
\(284\) −6.85410 + 4.97980i −0.406716 + 0.295497i
\(285\) 0 0
\(286\) −3.05573 7.60845i −0.180689 0.449897i
\(287\) 6.47214 0.382038
\(288\) 2.42705 1.76336i 0.143015 0.103907i
\(289\) −0.0835921 0.257270i −0.00491718 0.0151335i
\(290\) −1.47214 + 4.53077i −0.0864468 + 0.266056i
\(291\) 0 0
\(292\) 6.85410 + 4.97980i 0.401106 + 0.291421i
\(293\) −0.527864 + 1.62460i −0.0308381 + 0.0949101i −0.965291 0.261177i \(-0.915889\pi\)
0.934453 + 0.356087i \(0.115889\pi\)
\(294\) 0 0
\(295\) −31.1803 + 22.6538i −1.81539 + 1.31896i
\(296\) −9.23607 −0.536836
\(297\) 0 0
\(298\) 13.4164 0.777192
\(299\) −2.29180 + 1.66509i −0.132538 + 0.0962945i
\(300\) 0 0
\(301\) −0.309017 + 0.951057i −0.0178114 + 0.0548180i
\(302\) 11.4721 + 8.33499i 0.660147 + 0.479625i
\(303\) 0 0
\(304\) 0.309017 0.951057i 0.0177233 0.0545468i
\(305\) −12.0172 36.9852i −0.688104 2.11777i
\(306\) 9.92705 7.21242i 0.567492 0.412307i
\(307\) −19.4164 −1.10815 −0.554076 0.832466i \(-0.686928\pi\)
−0.554076 + 0.832466i \(0.686928\pi\)
\(308\) −2.04508 + 0.138757i −0.116530 + 0.00790643i
\(309\) 0 0
\(310\) −17.7984 + 12.9313i −1.01088 + 0.734447i
\(311\) −10.2984 31.6951i −0.583967 1.79727i −0.603379 0.797455i \(-0.706179\pi\)
0.0194116 0.999812i \(-0.493821\pi\)
\(312\) 0 0
\(313\) 0.836881 + 0.608030i 0.0473033 + 0.0343679i 0.611186 0.791487i \(-0.290693\pi\)
−0.563882 + 0.825855i \(0.690693\pi\)
\(314\) −0.354102 0.257270i −0.0199831 0.0145186i
\(315\) 2.20820 6.79615i 0.124418 0.382920i
\(316\) −3.70820 11.4127i −0.208603 0.642013i
\(317\) −12.4721 + 9.06154i −0.700505 + 0.508947i −0.880097 0.474795i \(-0.842522\pi\)
0.179592 + 0.983741i \(0.442522\pi\)
\(318\) 0 0
\(319\) −1.52786 3.80423i −0.0855440 0.212996i
\(320\) −3.85410 −0.215451
\(321\) 0 0
\(322\) 0.218847 + 0.673542i 0.0121959 + 0.0375350i
\(323\) 1.26393 3.88998i 0.0703271 0.216444i
\(324\) −7.28115 5.29007i −0.404508 0.293893i
\(325\) −19.7082 14.3188i −1.09321 0.794267i
\(326\) 7.75329 23.8622i 0.429415 1.32160i
\(327\) 0 0
\(328\) −8.47214 + 6.15537i −0.467795 + 0.339873i
\(329\) −7.18034 −0.395865
\(330\) 0 0
\(331\) −16.4721 −0.905390 −0.452695 0.891665i \(-0.649537\pi\)
−0.452695 + 0.891665i \(0.649537\pi\)
\(332\) −3.11803 + 2.26538i −0.171124 + 0.124329i
\(333\) 8.56231 + 26.3521i 0.469211 + 1.44408i
\(334\) 2.47214 7.60845i 0.135269 0.416316i
\(335\) −24.9443 18.1231i −1.36285 0.990169i
\(336\) 0 0
\(337\) −4.52786 + 13.9353i −0.246648 + 0.759106i 0.748712 + 0.662895i \(0.230672\pi\)
−0.995361 + 0.0962111i \(0.969328\pi\)
\(338\) −2.12868 6.55139i −0.115785 0.356349i
\(339\) 0 0
\(340\) −15.7639 −0.854919
\(341\) 4.61803 18.3601i 0.250081 0.994255i
\(342\) −3.00000 −0.162221
\(343\) 6.80902 4.94704i 0.367652 0.267115i
\(344\) −0.500000 1.53884i −0.0269582 0.0829688i
\(345\) 0 0
\(346\) 15.7082 + 11.4127i 0.844478 + 0.613549i
\(347\) −13.9271 10.1186i −0.747643 0.543195i 0.147452 0.989069i \(-0.452893\pi\)
−0.895095 + 0.445875i \(0.852893\pi\)
\(348\) 0 0
\(349\) 9.66312 + 29.7400i 0.517255 + 1.59195i 0.779141 + 0.626848i \(0.215655\pi\)
−0.261887 + 0.965099i \(0.584345\pi\)
\(350\) −4.92705 + 3.57971i −0.263362 + 0.191344i
\(351\) 0 0
\(352\) 2.54508 2.12663i 0.135653 0.113350i
\(353\) 8.32624 0.443161 0.221580 0.975142i \(-0.428878\pi\)
0.221580 + 0.975142i \(0.428878\pi\)
\(354\) 0 0
\(355\) −10.0902 31.0543i −0.535531 1.64819i
\(356\) −4.38197 + 13.4863i −0.232244 + 0.714773i
\(357\) 0 0
\(358\) −5.85410 4.25325i −0.309399 0.224791i
\(359\) 0.534442 1.64484i 0.0282068 0.0868115i −0.935962 0.352101i \(-0.885467\pi\)
0.964169 + 0.265289i \(0.0854674\pi\)
\(360\) 3.57295 + 10.9964i 0.188311 + 0.579562i
\(361\) −0.809017 + 0.587785i −0.0425798 + 0.0309361i
\(362\) −12.6525 −0.664999
\(363\) 0 0
\(364\) 1.52786 0.0800818
\(365\) −26.4164 + 19.1926i −1.38270 + 1.00459i
\(366\) 0 0
\(367\) 0.371323 1.14281i 0.0193829 0.0596544i −0.940897 0.338692i \(-0.890015\pi\)
0.960280 + 0.279038i \(0.0900155\pi\)
\(368\) −0.927051 0.673542i −0.0483259 0.0351108i
\(369\) 25.4164 + 18.4661i 1.32313 + 0.961307i
\(370\) 11.0000 33.8545i 0.571863 1.76001i
\(371\) 0.381966 + 1.17557i 0.0198307 + 0.0610326i
\(372\) 0 0
\(373\) 25.5967 1.32535 0.662675 0.748907i \(-0.269421\pi\)
0.662675 + 0.748907i \(0.269421\pi\)
\(374\) 10.4098 8.69827i 0.538279 0.449777i
\(375\) 0 0
\(376\) 9.39919 6.82891i 0.484726 0.352174i
\(377\) 0.944272 + 2.90617i 0.0486325 + 0.149675i
\(378\) 0 0
\(379\) −1.23607 0.898056i −0.0634925 0.0461300i 0.555586 0.831459i \(-0.312494\pi\)
−0.619079 + 0.785329i \(0.712494\pi\)
\(380\) 3.11803 + 2.26538i 0.159952 + 0.116212i
\(381\) 0 0
\(382\) 2.95492 + 9.09429i 0.151187 + 0.465305i
\(383\) −14.9443 + 10.8576i −0.763617 + 0.554800i −0.900017 0.435854i \(-0.856446\pi\)
0.136401 + 0.990654i \(0.456446\pi\)
\(384\) 0 0
\(385\) 1.92705 7.66145i 0.0982116 0.390464i
\(386\) 2.00000 0.101797
\(387\) −3.92705 + 2.85317i −0.199623 + 0.145035i
\(388\) −2.32624 7.15942i −0.118097 0.363465i
\(389\) 2.35410 7.24518i 0.119358 0.367345i −0.873473 0.486872i \(-0.838138\pi\)
0.992831 + 0.119527i \(0.0381378\pi\)
\(390\) 0 0
\(391\) −3.79180 2.75490i −0.191759 0.139321i
\(392\) −2.04508 + 6.29412i −0.103292 + 0.317901i
\(393\) 0 0
\(394\) −6.09017 + 4.42477i −0.306818 + 0.222917i
\(395\) 46.2492 2.32705
\(396\) −8.42705 5.29007i −0.423475 0.265836i
\(397\) 7.79837 0.391389 0.195695 0.980665i \(-0.437304\pi\)
0.195695 + 0.980665i \(0.437304\pi\)
\(398\) −3.73607 + 2.71441i −0.187272 + 0.136061i
\(399\) 0 0
\(400\) 3.04508 9.37181i 0.152254 0.468590i
\(401\) 2.76393 + 2.00811i 0.138024 + 0.100280i 0.654655 0.755928i \(-0.272814\pi\)
−0.516631 + 0.856208i \(0.672814\pi\)
\(402\) 0 0
\(403\) −4.36068 + 13.4208i −0.217221 + 0.668537i
\(404\) 0.427051 + 1.31433i 0.0212466 + 0.0653903i
\(405\) 28.0623 20.3885i 1.39443 1.01311i
\(406\) 0.763932 0.0379133
\(407\) 11.4164 + 28.4257i 0.565890 + 1.40901i
\(408\) 0 0
\(409\) −19.1803 + 13.9353i −0.948407 + 0.689058i −0.950430 0.310940i \(-0.899356\pi\)
0.00202274 + 0.999998i \(0.499356\pi\)
\(410\) −12.4721 38.3853i −0.615955 1.89571i
\(411\) 0 0
\(412\) −6.00000 4.35926i −0.295599 0.214765i
\(413\) 5.00000 + 3.63271i 0.246034 + 0.178754i
\(414\) −1.06231 + 3.26944i −0.0522095 + 0.160684i
\(415\) −4.59017 14.1271i −0.225323 0.693472i
\(416\) −2.00000 + 1.45309i −0.0980581 + 0.0712434i
\(417\) 0 0
\(418\) −3.30902 + 0.224514i −0.161849 + 0.0109813i
\(419\) 12.6738 0.619154 0.309577 0.950874i \(-0.399813\pi\)
0.309577 + 0.950874i \(0.399813\pi\)
\(420\) 0 0
\(421\) −7.65248 23.5519i −0.372959 1.14785i −0.944845 0.327517i \(-0.893788\pi\)
0.571887 0.820333i \(-0.306212\pi\)
\(422\) −5.29180 + 16.2865i −0.257601 + 0.792813i
\(423\) −28.1976 20.4867i −1.37101 0.996099i
\(424\) −1.61803 1.17557i −0.0785787 0.0570908i
\(425\) 12.4549 38.3323i 0.604152 1.85939i
\(426\) 0 0
\(427\) −5.04508 + 3.66547i −0.244149 + 0.177384i
\(428\) −9.23607 −0.446442
\(429\) 0 0
\(430\) 6.23607 0.300730
\(431\) 22.5623 16.3925i 1.08679 0.789598i 0.107934 0.994158i \(-0.465576\pi\)
0.978854 + 0.204560i \(0.0655765\pi\)
\(432\) 0 0
\(433\) −11.2918 + 34.7526i −0.542649 + 1.67010i 0.183866 + 0.982951i \(0.441139\pi\)
−0.726515 + 0.687151i \(0.758861\pi\)
\(434\) 2.85410 + 2.07363i 0.137001 + 0.0995373i
\(435\) 0 0
\(436\) 0.527864 1.62460i 0.0252801 0.0778042i
\(437\) 0.354102 + 1.08981i 0.0169390 + 0.0521329i
\(438\) 0 0
\(439\) −36.3607 −1.73540 −0.867700 0.497088i \(-0.834403\pi\)
−0.867700 + 0.497088i \(0.834403\pi\)
\(440\) 4.76393 + 11.8617i 0.227112 + 0.565485i
\(441\) 19.8541 0.945433
\(442\) −8.18034 + 5.94336i −0.389099 + 0.282697i
\(443\) −0.809017 2.48990i −0.0384376 0.118299i 0.929997 0.367568i \(-0.119810\pi\)
−0.968434 + 0.249269i \(0.919810\pi\)
\(444\) 0 0
\(445\) −44.2148 32.1239i −2.09598 1.52282i
\(446\) −3.61803 2.62866i −0.171319 0.124470i
\(447\) 0 0
\(448\) 0.190983 + 0.587785i 0.00902310 + 0.0277702i
\(449\) 26.6525 19.3642i 1.25781 0.913851i 0.259160 0.965834i \(-0.416554\pi\)
0.998648 + 0.0519833i \(0.0165543\pi\)
\(450\) −29.5623 −1.39358
\(451\) 29.4164 + 18.4661i 1.38516 + 0.869535i
\(452\) −13.7082 −0.644780
\(453\) 0 0
\(454\) 3.56231 + 10.9637i 0.167187 + 0.514550i
\(455\) −1.81966 + 5.60034i −0.0853070 + 0.262548i
\(456\) 0 0
\(457\) 24.9164 + 18.1028i 1.16554 + 0.846815i 0.990468 0.137741i \(-0.0439841\pi\)
0.175072 + 0.984556i \(0.443984\pi\)
\(458\) −0.173762 + 0.534785i −0.00811937 + 0.0249888i
\(459\) 0 0
\(460\) 3.57295 2.59590i 0.166590 0.121034i
\(461\) 25.3820 1.18216 0.591078 0.806614i \(-0.298703\pi\)
0.591078 + 0.806614i \(0.298703\pi\)
\(462\) 0 0
\(463\) −17.8541 −0.829750 −0.414875 0.909878i \(-0.636175\pi\)
−0.414875 + 0.909878i \(0.636175\pi\)
\(464\) −1.00000 + 0.726543i −0.0464238 + 0.0337289i
\(465\) 0 0
\(466\) −2.75329 + 8.47375i −0.127544 + 0.392539i
\(467\) −3.35410 2.43690i −0.155209 0.112766i 0.507470 0.861669i \(-0.330581\pi\)
−0.662679 + 0.748903i \(0.730581\pi\)
\(468\) 6.00000 + 4.35926i 0.277350 + 0.201507i
\(469\) −1.52786 + 4.70228i −0.0705502 + 0.217131i
\(470\) 13.8369 + 42.5855i 0.638248 + 1.96432i
\(471\) 0 0
\(472\) −10.0000 −0.460287
\(473\) −4.11803 + 3.44095i −0.189347 + 0.158215i
\(474\) 0 0
\(475\) −7.97214 + 5.79210i −0.365787 + 0.265760i
\(476\) 0.781153 + 2.40414i 0.0358041 + 0.110194i
\(477\) −1.85410 + 5.70634i −0.0848935 + 0.261275i
\(478\) −12.7812 9.28605i −0.584596 0.424734i
\(479\) −13.3992 9.73508i −0.612224 0.444807i 0.237972 0.971272i \(-0.423517\pi\)
−0.850197 + 0.526465i \(0.823517\pi\)
\(480\) 0 0
\(481\) −7.05573 21.7153i −0.321714 0.990132i
\(482\) −7.32624 + 5.32282i −0.333701 + 0.242448i
\(483\) 0 0
\(484\) −9.69098 5.20431i −0.440499 0.236560i
\(485\) 29.0132 1.31742
\(486\) 0 0
\(487\) 7.85410 + 24.1724i 0.355903 + 1.09536i 0.955484 + 0.295043i \(0.0953341\pi\)
−0.599581 + 0.800314i \(0.704666\pi\)
\(488\) 3.11803 9.59632i 0.141147 0.434405i
\(489\) 0 0
\(490\) −20.6353 14.9924i −0.932206 0.677287i
\(491\) −10.9894 + 33.8218i −0.495943 + 1.52635i 0.319540 + 0.947573i \(0.396472\pi\)
−0.815482 + 0.578782i \(0.803528\pi\)
\(492\) 0 0
\(493\) −4.09017 + 2.97168i −0.184212 + 0.133838i
\(494\) 2.47214 0.111227
\(495\) 29.4271 24.5887i 1.32265 1.10518i
\(496\) −5.70820 −0.256306
\(497\) −4.23607 + 3.07768i −0.190014 + 0.138053i
\(498\) 0 0
\(499\) −7.19098 + 22.1316i −0.321913 + 0.990745i 0.650902 + 0.759161i \(0.274391\pi\)
−0.972815 + 0.231584i \(0.925609\pi\)
\(500\) 15.1353 + 10.9964i 0.676869 + 0.491774i
\(501\) 0 0
\(502\) −7.20820 + 22.1846i −0.321718 + 0.990146i
\(503\) 8.47214 + 26.0746i 0.377754 + 1.16261i 0.941602 + 0.336728i \(0.109320\pi\)
−0.563848 + 0.825879i \(0.690680\pi\)
\(504\) 1.50000 1.08981i 0.0668153 0.0485442i
\(505\) −5.32624 −0.237014
\(506\) −0.927051 + 3.68571i −0.0412124 + 0.163850i
\(507\) 0 0
\(508\) 4.23607 3.07768i 0.187945 0.136550i
\(509\) 7.09017 + 21.8213i 0.314266 + 0.967212i 0.976055 + 0.217522i \(0.0697974\pi\)
−0.661789 + 0.749690i \(0.730203\pi\)
\(510\) 0 0
\(511\) 4.23607 + 3.07768i 0.187393 + 0.136149i
\(512\) −0.809017 0.587785i −0.0357538 0.0259767i
\(513\) 0 0
\(514\) −1.76393 5.42882i −0.0778037 0.239455i
\(515\) 23.1246 16.8010i 1.01899 0.740341i
\(516\) 0 0
\(517\) −32.6353 20.4867i −1.43530 0.901005i
\(518\) −5.70820 −0.250804
\(519\) 0 0
\(520\) −2.94427 9.06154i −0.129115 0.397375i
\(521\) −1.76393 + 5.42882i −0.0772793 + 0.237841i −0.982232 0.187671i \(-0.939906\pi\)
0.904953 + 0.425512i \(0.139906\pi\)
\(522\) 3.00000 + 2.17963i 0.131306 + 0.0953997i
\(523\) 19.1803 + 13.9353i 0.838698 + 0.609350i 0.922007 0.387174i \(-0.126549\pi\)
−0.0833089 + 0.996524i \(0.526549\pi\)
\(524\) −1.95492 + 6.01661i −0.0854009 + 0.262837i
\(525\) 0 0
\(526\) 1.23607 0.898056i 0.0538951 0.0391571i
\(527\) −23.3475 −1.01703
\(528\) 0 0
\(529\) −21.6869 −0.942909
\(530\) 6.23607 4.53077i 0.270877 0.196804i
\(531\) 9.27051 + 28.5317i 0.402306 + 1.23817i
\(532\) 0.190983 0.587785i 0.00828016 0.0254837i
\(533\) −20.9443 15.2169i −0.907197 0.659117i
\(534\) 0 0
\(535\) 11.0000 33.8545i 0.475571 1.46366i
\(536\) −2.47214 7.60845i −0.106780 0.328635i
\(537\) 0 0
\(538\) 16.3607 0.705359
\(539\) 21.8992 1.48584i 0.943265 0.0639997i
\(540\) 0 0
\(541\) 25.2533 18.3476i 1.08572 0.788824i 0.107052 0.994253i \(-0.465859\pi\)
0.978672 + 0.205429i \(0.0658590\pi\)
\(542\) −4.35410 13.4005i −0.187025 0.575603i
\(543\) 0 0
\(544\) −3.30902 2.40414i −0.141873 0.103077i
\(545\) 5.32624 + 3.86974i 0.228151 + 0.165761i
\(546\) 0 0
\(547\) 8.27051 + 25.4540i 0.353621 + 1.08833i 0.956804 + 0.290732i \(0.0938989\pi\)
−0.603183 + 0.797603i \(0.706101\pi\)
\(548\) 13.4443 9.76784i 0.574311 0.417261i
\(549\) −30.2705 −1.29191
\(550\) −32.6074 + 2.21238i −1.39038 + 0.0943364i
\(551\) 1.23607 0.0526583
\(552\) 0 0
\(553\) −2.29180 7.05342i −0.0974571 0.299942i
\(554\) −6.79837 + 20.9232i −0.288835 + 0.888943i
\(555\) 0 0
\(556\) 15.6353 + 11.3597i 0.663083 + 0.481758i
\(557\) −9.93363 + 30.5726i −0.420901 + 1.29540i 0.485963 + 0.873979i \(0.338469\pi\)
−0.906865 + 0.421422i \(0.861531\pi\)
\(558\) 5.29180 + 16.2865i 0.224020 + 0.689461i
\(559\) 3.23607 2.35114i 0.136871 0.0994427i
\(560\) −2.38197 −0.100656
\(561\) 0 0
\(562\) 21.1246 0.891088
\(563\) 8.85410 6.43288i 0.373156 0.271114i −0.385362 0.922765i \(-0.625924\pi\)
0.758518 + 0.651652i \(0.225924\pi\)
\(564\) 0 0
\(565\) 16.3262 50.2470i 0.686850 2.11391i
\(566\) −22.0623 16.0292i −0.927348 0.673758i
\(567\) −4.50000 3.26944i −0.188982 0.137304i
\(568\) 2.61803 8.05748i 0.109850 0.338084i
\(569\) 1.90983 + 5.87785i 0.0800642 + 0.246412i 0.983074 0.183207i \(-0.0586478\pi\)
−0.903010 + 0.429619i \(0.858648\pi\)
\(570\) 0 0
\(571\) 24.5066 1.02557 0.512784 0.858518i \(-0.328614\pi\)
0.512784 + 0.858518i \(0.328614\pi\)
\(572\) 6.94427 + 4.35926i 0.290355 + 0.182270i
\(573\) 0 0
\(574\) −5.23607 + 3.80423i −0.218549 + 0.158785i
\(575\) 3.48936 + 10.7391i 0.145516 + 0.447853i
\(576\) −0.927051 + 2.85317i −0.0386271 + 0.118882i
\(577\) −26.2705 19.0866i −1.09366 0.794587i −0.113643 0.993522i \(-0.536252\pi\)
−0.980013 + 0.198934i \(0.936252\pi\)
\(578\) 0.218847 + 0.159002i 0.00910284 + 0.00661360i
\(579\) 0 0
\(580\) −1.47214 4.53077i −0.0611271 0.188130i
\(581\) −1.92705 + 1.40008i −0.0799475 + 0.0580853i
\(582\) 0 0
\(583\) −1.61803 + 6.43288i −0.0670121 + 0.266423i
\(584\) −8.47214 −0.350579
\(585\) −23.1246 + 16.8010i −0.956085 + 0.694636i
\(586\) −0.527864 1.62460i −0.0218059 0.0671115i
\(587\) 0.583592 1.79611i 0.0240874 0.0741335i −0.938290 0.345849i \(-0.887591\pi\)
0.962378 + 0.271715i \(0.0875910\pi\)
\(588\) 0 0
\(589\) 4.61803 + 3.35520i 0.190283 + 0.138249i
\(590\) 11.9098 36.6547i 0.490320 1.50905i
\(591\) 0 0
\(592\) 7.47214 5.42882i 0.307103 0.223123i
\(593\) 31.9098 1.31038 0.655190 0.755464i \(-0.272589\pi\)
0.655190 + 0.755464i \(0.272589\pi\)
\(594\) 0 0
\(595\) −9.74265 −0.399410
\(596\) −10.8541 + 7.88597i −0.444601 + 0.323022i
\(597\) 0 0
\(598\) 0.875388 2.69417i 0.0357973 0.110173i
\(599\) −12.2361 8.89002i −0.499952 0.363237i 0.309047 0.951047i \(-0.399990\pi\)
−0.808999 + 0.587810i \(0.799990\pi\)
\(600\) 0 0
\(601\) 6.81966 20.9888i 0.278180 0.856149i −0.710181 0.704019i \(-0.751387\pi\)
0.988361 0.152130i \(-0.0486132\pi\)
\(602\) −0.309017 0.951057i −0.0125946 0.0387622i
\(603\) −19.4164 + 14.1068i −0.790697 + 0.574475i
\(604\) −14.1803 −0.576990
\(605\) 30.6180 29.3238i 1.24480 1.19218i
\(606\) 0 0
\(607\) 15.0344 10.9232i 0.610229 0.443357i −0.239266 0.970954i \(-0.576907\pi\)
0.849495 + 0.527597i \(0.176907\pi\)
\(608\) 0.309017 + 0.951057i 0.0125323 + 0.0385704i
\(609\) 0 0
\(610\) 31.4615 + 22.8581i 1.27384 + 0.925498i
\(611\) 23.2361 + 16.8820i 0.940031 + 0.682972i
\(612\) −3.79180 + 11.6699i −0.153274 + 0.471730i
\(613\) −3.70163 11.3924i −0.149507 0.460136i 0.848056 0.529907i \(-0.177773\pi\)
−0.997563 + 0.0697709i \(0.977773\pi\)
\(614\) 15.7082 11.4127i 0.633932 0.460578i
\(615\) 0 0
\(616\) 1.57295 1.31433i 0.0633759 0.0529558i
\(617\) 30.9443 1.24577 0.622885 0.782314i \(-0.285961\pi\)
0.622885 + 0.782314i \(0.285961\pi\)
\(618\) 0 0
\(619\) 14.5557 + 44.7979i 0.585044 + 1.80058i 0.599093 + 0.800679i \(0.295528\pi\)
−0.0140491 + 0.999901i \(0.504472\pi\)
\(620\) 6.79837 20.9232i 0.273029 0.840298i
\(621\) 0 0
\(622\) 26.9615 + 19.5887i 1.08106 + 0.785434i
\(623\) −2.70820 + 8.33499i −0.108502 + 0.333935i
\(624\) 0 0
\(625\) −18.4721 + 13.4208i −0.738885 + 0.536832i
\(626\) −1.03444 −0.0413446
\(627\) 0 0
\(628\) 0.437694 0.0174659
\(629\) 30.5623 22.2048i 1.21860 0.885364i
\(630\) 2.20820 + 6.79615i 0.0879770 + 0.270765i
\(631\) 5.41641 16.6700i 0.215624 0.663622i −0.783485 0.621411i \(-0.786560\pi\)
0.999109 0.0422110i \(-0.0134402\pi\)
\(632\) 9.70820 + 7.05342i 0.386172 + 0.280570i
\(633\) 0 0
\(634\) 4.76393 14.6619i 0.189200 0.582297i
\(635\) 6.23607 + 19.1926i 0.247471 + 0.761637i
\(636\) 0 0
\(637\) −16.3607 −0.648234
\(638\) 3.47214 + 2.17963i 0.137463 + 0.0862923i
\(639\) −25.4164 −1.00546
\(640\) 3.11803 2.26538i 0.123251 0.0895472i
\(641\) −10.6525 32.7849i −0.420747 1.29493i −0.907008 0.421114i \(-0.861639\pi\)
0.486260 0.873814i \(-0.338361\pi\)
\(642\) 0 0
\(643\) 26.4336 + 19.2052i 1.04244 + 0.757377i 0.970760 0.240050i \(-0.0771639\pi\)
0.0716801 + 0.997428i \(0.477164\pi\)
\(644\) −0.572949 0.416272i −0.0225774 0.0164034i
\(645\) 0 0
\(646\) 1.26393 + 3.88998i 0.0497287 + 0.153049i
\(647\) −16.4721 + 11.9677i −0.647586 + 0.470499i −0.862448 0.506145i \(-0.831070\pi\)
0.214862 + 0.976644i \(0.431070\pi\)
\(648\) 9.00000 0.353553
\(649\) 12.3607 + 30.7768i 0.485199 + 1.20810i
\(650\) 24.3607 0.955504
\(651\) 0 0
\(652\) 7.75329 + 23.8622i 0.303642 + 0.934515i
\(653\) −3.59017 + 11.0494i −0.140494 + 0.432397i −0.996404 0.0847283i \(-0.972998\pi\)
0.855910 + 0.517125i \(0.172998\pi\)
\(654\) 0 0
\(655\) −19.7254 14.3314i −0.770736 0.559973i
\(656\) 3.23607 9.95959i 0.126347 0.388857i
\(657\) 7.85410 + 24.1724i 0.306418 + 0.943057i
\(658\) 5.80902 4.22050i 0.226459 0.164532i
\(659\) 41.3050 1.60901 0.804506 0.593944i \(-0.202430\pi\)
0.804506 + 0.593944i \(0.202430\pi\)
\(660\) 0 0
\(661\) −6.94427 −0.270101 −0.135050 0.990839i \(-0.543120\pi\)
−0.135050 + 0.990839i \(0.543120\pi\)
\(662\) 13.3262 9.68208i 0.517939 0.376305i
\(663\) 0 0
\(664\) 1.19098 3.66547i 0.0462191 0.142248i
\(665\) 1.92705 + 1.40008i 0.0747278 + 0.0542929i
\(666\) −22.4164 16.2865i −0.868618 0.631088i
\(667\) 0.437694 1.34708i 0.0169476 0.0521593i
\(668\) 2.47214 + 7.60845i 0.0956498 + 0.294380i
\(669\) 0 0
\(670\) 30.8328 1.19118
\(671\) −33.3885 + 2.26538i −1.28895 + 0.0874542i
\(672\) 0 0
\(673\) −3.76393 + 2.73466i −0.145089 + 0.105413i −0.657962 0.753051i \(-0.728581\pi\)
0.512873 + 0.858465i \(0.328581\pi\)
\(674\) −4.52786 13.9353i −0.174407 0.536769i
\(675\) 0 0
\(676\) 5.57295 + 4.04898i 0.214344 + 0.155730i
\(677\) −35.6525 25.9030i −1.37024 0.995535i −0.997719 0.0675095i \(-0.978495\pi\)
−0.372517 0.928025i \(-0.621505\pi\)
\(678\) 0 0
\(679\) −1.43769 4.42477i −0.0551736 0.169807i
\(680\) 12.7533 9.26581i 0.489066 0.355327i
\(681\) 0 0
\(682\) 7.05573 + 17.5680i 0.270178 + 0.672715i
\(683\) 16.8328 0.644090 0.322045 0.946724i \(-0.395630\pi\)
0.322045 + 0.946724i \(0.395630\pi\)
\(684\) 2.42705 1.76336i 0.0928006 0.0674236i
\(685\) 19.7918 + 60.9129i 0.756206 + 2.32736i
\(686\) −2.60081 + 8.00448i −0.0992995 + 0.305612i
\(687\) 0 0
\(688\) 1.30902 + 0.951057i 0.0499058 + 0.0362587i
\(689\) 1.52786 4.70228i 0.0582070 0.179143i
\(690\) 0 0
\(691\) −22.2984 + 16.2007i −0.848270 + 0.616304i −0.924669 0.380773i \(-0.875658\pi\)
0.0763984 + 0.997077i \(0.475658\pi\)
\(692\) −19.4164 −0.738101
\(693\) −5.20820 3.26944i −0.197843 0.124196i
\(694\) 17.2148 0.653464
\(695\) −60.2599 + 43.7814i −2.28579 + 1.66072i
\(696\) 0 0
\(697\) 13.2361 40.7364i 0.501352 1.54300i
\(698\) −25.2984 18.3803i −0.957558 0.695706i
\(699\) 0 0
\(700\) 1.88197 5.79210i 0.0711316 0.218921i
\(701\) 2.29837 + 7.07367i 0.0868084 + 0.267169i 0.985032 0.172369i \(-0.0551422\pi\)
−0.898224 + 0.439538i \(0.855142\pi\)
\(702\) 0 0
\(703\) −9.23607 −0.348345
\(704\) −0.809017 + 3.21644i −0.0304910 + 0.121224i
\(705\) 0 0
\(706\) −6.73607 + 4.89404i −0.253515 + 0.184190i
\(707\) 0.263932 + 0.812299i 0.00992619 + 0.0305497i
\(708\) 0 0
\(709\) 12.1180 + 8.80427i 0.455102 + 0.330651i 0.791607 0.611031i \(-0.209245\pi\)
−0.336505 + 0.941682i \(0.609245\pi\)
\(710\) 26.4164 + 19.1926i 0.991390 + 0.720287i
\(711\) 11.1246 34.2380i 0.417206 1.28403i
\(712\) −4.38197 13.4863i −0.164221 0.505421i
\(713\) 5.29180 3.84471i 0.198179 0.143986i
\(714\) 0 0
\(715\) −24.2492 + 20.2622i −0.906870 + 0.757764i
\(716\) 7.23607 0.270425
\(717\) 0 0
\(718\) 0.534442 + 1.64484i 0.0199452 + 0.0613850i
\(719\) −16.0106 + 49.2757i −0.597096 + 1.83767i −0.0530939 + 0.998590i \(0.516908\pi\)
−0.544002 + 0.839084i \(0.683092\pi\)
\(720\) −9.35410 6.79615i −0.348607 0.253278i
\(721\) −3.70820 2.69417i −0.138101 0.100336i
\(722\) 0.309017 0.951057i 0.0115004 0.0353947i
\(723\) 0 0
\(724\) 10.2361 7.43694i 0.380420 0.276392i
\(725\) 12.1803 0.452366
\(726\) 0 0
\(727\) −25.9098 −0.960942 −0.480471 0.877011i \(-0.659534\pi\)
−0.480471 + 0.877011i \(0.659534\pi\)
\(728\) −1.23607 + 0.898056i −0.0458117 + 0.0332842i
\(729\) −8.34346 25.6785i −0.309017 0.951057i
\(730\) 10.0902 31.0543i 0.373454 1.14937i
\(731\) 5.35410 + 3.88998i 0.198029 + 0.143876i
\(732\) 0 0
\(733\) 11.5729 35.6179i 0.427457 1.31558i −0.473166 0.880973i \(-0.656889\pi\)
0.900622 0.434603i \(-0.143111\pi\)
\(734\) 0.371323 + 1.14281i 0.0137058 + 0.0421820i
\(735\) 0 0
\(736\) 1.14590 0.0422384
\(737\) −20.3607 + 17.0130i −0.749995 + 0.626683i
\(738\) −31.4164 −1.15645
\(739\) 17.8262 12.9515i 0.655749 0.476429i −0.209476 0.977814i \(-0.567176\pi\)
0.865225 + 0.501384i \(0.167176\pi\)
\(740\) 11.0000 + 33.8545i 0.404368 + 1.24452i
\(741\) 0 0
\(742\) −1.00000 0.726543i −0.0367112 0.0266722i
\(743\) −24.0344 17.4620i −0.881738 0.640620i 0.0519726 0.998649i \(-0.483449\pi\)
−0.933711 + 0.358028i \(0.883449\pi\)
\(744\) 0 0
\(745\) −15.9787 49.1774i −0.585415 1.80172i
\(746\) −20.7082 + 15.0454i −0.758181 + 0.550851i
\(747\) −11.5623 −0.423043
\(748\) −3.30902 + 13.1558i −0.120990 + 0.481023i
\(749\) −5.70820 −0.208573
\(750\) 0 0
\(751\) −10.2705 31.6094i −0.374776 1.15344i −0.943629 0.331004i \(-0.892613\pi\)
0.568853 0.822439i \(-0.307387\pi\)
\(752\) −3.59017 + 11.0494i −0.130920 + 0.402930i
\(753\) 0 0
\(754\) −2.47214 1.79611i −0.0900299 0.0654105i
\(755\) 16.8885 51.9776i 0.614637 1.89166i
\(756\) 0 0
\(757\) 38.2705 27.8052i 1.39097 1.01060i 0.395207 0.918592i \(-0.370673\pi\)
0.995759 0.0920032i \(-0.0293270\pi\)
\(758\) 1.52786 0.0554945
\(759\) 0 0
\(760\) −3.85410 −0.139803
\(761\) −4.38197 + 3.18368i −0.158846 + 0.115408i −0.664369 0.747405i \(-0.731300\pi\)
0.505523 + 0.862813i \(0.331300\pi\)
\(762\) 0 0
\(763\) 0.326238 1.00406i 0.0118106 0.0363493i
\(764\) −7.73607 5.62058i −0.279881 0.203346i
\(765\) −38.2599 27.7974i −1.38329 1.00502i
\(766\) 5.70820 17.5680i 0.206246 0.634759i
\(767\) −7.63932 23.5114i −0.275840 0.848948i
\(768\) 0 0
\(769\) −31.7426 −1.14467 −0.572335 0.820020i \(-0.693962\pi\)
−0.572335 + 0.820020i \(0.693962\pi\)
\(770\) 2.94427 + 7.33094i 0.106104 + 0.264189i
\(771\) 0 0
\(772\) −1.61803 + 1.17557i −0.0582343 + 0.0423097i
\(773\) 13.7082 + 42.1895i 0.493050 + 1.51745i 0.819974 + 0.572401i \(0.193988\pi\)
−0.326924 + 0.945051i \(0.606012\pi\)
\(774\) 1.50000 4.61653i 0.0539164 0.165938i
\(775\) 45.5066 + 33.0625i 1.63464 + 1.18764i
\(776\) 6.09017 + 4.42477i 0.218624 + 0.158840i
\(777\) 0 0
\(778\) 2.35410 + 7.24518i 0.0843986 + 0.259752i
\(779\) −8.47214 + 6.15537i −0.303546 + 0.220539i
\(780\) 0 0
\(781\) −28.0344 + 1.90211i −1.00315 + 0.0680630i
\(782\) 4.68692 0.167604
\(783\) 0 0
\(784\) −2.04508 6.29412i −0.0730387 0.224790i
\(785\) −0.521286 + 1.60435i −0.0186055 + 0.0572619i
\(786\) 0 0
\(787\) 31.5066 + 22.8909i 1.12309 + 0.815971i 0.984674 0.174403i \(-0.0557996\pi\)
0.138414 + 0.990374i \(0.455800\pi\)
\(788\) 2.32624 7.15942i 0.0828688 0.255044i
\(789\) 0 0
\(790\) −37.4164 + 27.1846i −1.33122 + 0.967185i
\(791\) −8.47214 −0.301234
\(792\) 9.92705 0.673542i 0.352742 0.0239333i
\(793\) 24.9443 0.885797
\(794\) −6.30902 + 4.58377i −0.223899 + 0.162672i
\(795\) 0 0
\(796\) 1.42705 4.39201i 0.0505805 0.155671i
\(797\) 10.8541 + 7.88597i 0.384472 + 0.279335i 0.763186 0.646178i \(-0.223634\pi\)
−0.378714 + 0.925514i \(0.623634\pi\)
\(798\) 0 0
\(799\) −14.6844 + 45.1940i −0.519497 + 1.59885i
\(800\) 3.04508 + 9.37181i 0.107660 + 0.331343i
\(801\) −34.4164 + 25.0050i −1.21604 + 0.883508i
\(802\) −3.41641 −0.120638
\(803\) 10.4721 + 26.0746i 0.369554 + 0.920151i
\(804\) 0 0
\(805\) 2.20820 1.60435i 0.0778290 0.0565461i
\(806\) −4.36068 13.4208i −0.153598 0.472727i
\(807\) 0 0
\(808\) −1.11803 0.812299i −0.0393323 0.0285766i
\(809\) 37.3885 + 27.1644i 1.31451 + 0.955048i 0.999983 + 0.00580010i \(0.00184624\pi\)
0.314528 + 0.949248i \(0.398154\pi\)
\(810\) −10.7188 + 32.9892i −0.376622 + 1.15912i
\(811\) 17.2361 + 53.0472i 0.605240 + 1.86274i 0.495131 + 0.868818i \(0.335120\pi\)
0.110109 + 0.993919i \(0.464880\pi\)
\(812\) −0.618034 + 0.449028i −0.0216887 + 0.0157578i
\(813\) 0 0
\(814\) −25.9443 16.2865i −0.909346 0.570841i
\(815\) −96.7001 −3.38726
\(816\) 0 0
\(817\) −0.500000 1.53884i −0.0174928 0.0538373i
\(818\) 7.32624 22.5478i 0.256156 0.788367i
\(819\) 3.70820 + 2.69417i 0.129575 + 0.0941418i
\(820\) 32.6525 + 23.7234i 1.14027 + 0.828457i
\(821\) −2.46556 + 7.58821i −0.0860486 + 0.264830i −0.984818 0.173592i \(-0.944463\pi\)
0.898769 + 0.438422i \(0.144463\pi\)
\(822\) 0 0
\(823\) 7.97214 5.79210i 0.277891 0.201900i −0.440106 0.897946i \(-0.645059\pi\)
0.717997 + 0.696046i \(0.245059\pi\)
\(824\) 7.41641 0.258363
\(825\) 0 0
\(826\) −6.18034 −0.215042
\(827\) 30.0344 21.8213i 1.04440 0.758801i 0.0732603 0.997313i \(-0.476660\pi\)
0.971140 + 0.238512i \(0.0766596\pi\)
\(828\) −1.06231 3.26944i −0.0369177 0.113621i
\(829\) 4.34752 13.3803i 0.150996 0.464717i −0.846737 0.532011i \(-0.821436\pi\)
0.997733 + 0.0672938i \(0.0214365\pi\)
\(830\) 12.0172 + 8.73102i 0.417124 + 0.303058i
\(831\) 0 0
\(832\) 0.763932 2.35114i 0.0264846 0.0815111i
\(833\) −8.36475 25.7440i −0.289821 0.891978i
\(834\) 0 0
\(835\) −30.8328 −1.06701
\(836\) 2.54508 2.12663i 0.0880236 0.0735509i
\(837\) 0 0
\(838\) −10.2533 + 7.44945i −0.354194 + 0.257337i
\(839\) 7.76393 + 23.8949i 0.268041 + 0.824944i 0.990977 + 0.134030i \(0.0427919\pi\)
−0.722937 + 0.690914i \(0.757208\pi\)
\(840\) 0 0
\(841\) 22.2254 + 16.1477i 0.766394 + 0.556818i
\(842\) 20.0344 + 14.5559i 0.690432 + 0.501629i
\(843\) 0 0
\(844\) −5.29180 16.2865i −0.182151 0.560604i
\(845\) −21.4787 + 15.6052i −0.738890 + 0.536835i
\(846\) 34.8541 1.19831
\(847\) −5.98936 3.21644i −0.205797 0.110518i
\(848\) 2.00000 0.0686803
\(849\) 0 0
\(850\) 12.4549 + 38.3323i 0.427200 + 1.31479i
\(851\) −3.27051 + 10.0656i −0.112112 + 0.345044i
\(852\) 0 0
\(853\) 13.2533 + 9.62908i 0.453784 + 0.329693i 0.791088 0.611702i \(-0.209515\pi\)
−0.337304 + 0.941396i \(0.609515\pi\)
\(854\) 1.92705 5.93085i 0.0659423 0.202950i
\(855\) 3.57295 + 10.9964i 0.122192 + 0.376069i
\(856\) 7.47214 5.42882i 0.255392 0.185553i
\(857\) 32.8328 1.12155 0.560774 0.827969i \(-0.310504\pi\)
0.560774 + 0.827969i \(0.310504\pi\)
\(858\) 0 0
\(859\) −19.6869 −0.671709 −0.335854 0.941914i \(-0.609025\pi\)
−0.335854 + 0.941914i \(0.609025\pi\)
\(860\) −5.04508 + 3.66547i −0.172036 + 0.124991i
\(861\) 0 0
\(862\) −8.61803 + 26.5236i −0.293531 + 0.903397i
\(863\) −6.76393 4.91428i −0.230247 0.167284i 0.466680 0.884426i \(-0.345450\pi\)
−0.696927 + 0.717142i \(0.745450\pi\)
\(864\) 0 0
\(865\) 23.1246 71.1702i 0.786260 2.41986i
\(866\) −11.2918 34.7526i −0.383711 1.18094i
\(867\) 0 0
\(868\) −3.52786 −0.119744
\(869\) 9.70820 38.5973i 0.329328 1.30932i
\(870\) 0 0
\(871\) 16.0000 11.6247i 0.542139 0.393887i
\(872\) 0.527864 + 1.62460i 0.0178757 + 0.0550158i
\(873\) 6.97871 21.4783i 0.236194 0.726929i
\(874\) −0.927051 0.673542i −0.0313580 0.0227829i
\(875\) 9.35410 + 6.79615i 0.316226 + 0.229752i
\(876\) 0 0
\(877\) −5.36068 16.4985i −0.181017 0.557114i 0.818840 0.574022i \(-0.194618\pi\)
−0.999857 + 0.0169082i \(0.994618\pi\)
\(878\) 29.4164 21.3723i 0.992756 0.721279i
\(879\) 0 0
\(880\) −10.8262 6.79615i −0.364952 0.229098i
\(881\) −10.9443 −0.368722 −0.184361 0.982859i \(-0.559022\pi\)
−0.184361 + 0.982859i \(0.559022\pi\)
\(882\) −16.0623 + 11.6699i −0.540846 + 0.392948i
\(883\) −10.6976 32.9237i −0.360002 1.10797i −0.953052 0.302806i \(-0.902077\pi\)
0.593051 0.805165i \(-0.297923\pi\)
\(884\) 3.12461 9.61657i 0.105092 0.323440i
\(885\) 0 0
\(886\) 2.11803 + 1.53884i 0.0711567 + 0.0516984i
\(887\) 12.0344 37.0382i 0.404077 1.24362i −0.517586 0.855631i \(-0.673169\pi\)
0.921663 0.387990i \(-0.126831\pi\)
\(888\) 0 0
\(889\) 2.61803 1.90211i 0.0878060 0.0637948i
\(890\) 54.6525 1.83196
\(891\) −11.1246 27.6992i −0.372689 0.927957i
\(892\) 4.47214 0.149738
\(893\) 9.39919 6.82891i 0.314532 0.228521i
\(894\) 0 0
\(895\) −8.61803 + 26.5236i −0.288069 + 0.886586i
\(896\) −0.500000 0.363271i −0.0167038 0.0121360i
\(897\) 0 0
\(898\) −10.1803 + 31.3319i −0.339722 + 1.04556i
\(899\) −2.18034 6.71040i −0.0727184 0.223804i
\(900\) 23.9164 17.3763i 0.797214 0.579210i
\(901\) 8.18034 0.272527
\(902\) −34.6525 + 2.35114i −1.15380 + 0.0782844i
\(903\) 0 0
\(904\) 11.0902 8.05748i 0.368854 0.267988i
\(905\) 15.0689 + 46.3773i 0.500907 + 1.54163i
\(906\) 0 0
\(907\) −32.1246 23.3399i −1.06668 0.774989i −0.0913676 0.995817i \(-0.529124\pi\)
−0.975313 + 0.220829i \(0.929124\pi\)
\(908\) −9.32624 6.77591i −0.309502 0.224866i
\(909\) −1.28115 + 3.94298i −0.0424932 + 0.130781i
\(910\) −1.81966 5.60034i −0.0603211 0.185649i
\(911\) 9.70820 7.05342i 0.321647 0.233690i −0.415231 0.909716i \(-0.636299\pi\)
0.736878 + 0.676026i \(0.236299\pi\)
\(912\) 0 0
\(913\) −12.7533 + 0.865300i −0.422072 + 0.0286372i
\(914\) −30.7984 −1.01872
\(915\) 0 0
\(916\) −0.173762 0.534785i −0.00574126 0.0176698i
\(917\) −1.20820 + 3.71847i −0.0398984 + 0.122795i
\(918\) 0 0
\(919\) 7.73607 + 5.62058i 0.255189 + 0.185406i 0.708024 0.706189i \(-0.249587\pi\)
−0.452834 + 0.891595i \(0.649587\pi\)
\(920\) −1.36475 + 4.20025i −0.0449943 + 0.138478i
\(921\) 0 0
\(922\) −20.5344 + 14.9191i −0.676266 + 0.491336i
\(923\) 20.9443 0.689389
\(924\) 0 0
\(925\) −91.0132 −2.99249
\(926\) 14.4443 10.4944i 0.474668 0.344867i
\(927\) −6.87539 21.1603i −0.225817 0.694994i
\(928\) 0.381966 1.17557i 0.0125386 0.0385900i
\(929\) −28.1074 20.4212i −0.922174 0.669998i 0.0218905 0.999760i \(-0.493031\pi\)
−0.944064 + 0.329762i \(0.893031\pi\)
\(930\) 0 0
\(931\) −2.04508 + 6.29412i −0.0670250 + 0.206282i
\(932\) −2.75329 8.47375i −0.0901870 0.277567i
\(933\) 0 0
\(934\) 4.14590 0.135658
\(935\) −44.2812 27.7974i −1.44815 0.909073i
\(936\) −7.41641 −0.242413
\(937\) 17.6353 12.8128i 0.576119 0.418575i −0.261204 0.965284i \(-0.584120\pi\)
0.837323 + 0.546709i \(0.184120\pi\)
\(938\) −1.52786 4.70228i −0.0498865 0.153535i
\(939\) 0 0
\(940\) −36.2254 26.3193i −1.18154 0.858441i
\(941\) 6.52786 + 4.74277i 0.212802 + 0.154610i 0.689081 0.724685i \(-0.258015\pi\)
−0.476278 + 0.879295i \(0.658015\pi\)
\(942\) 0 0
\(943\) 3.70820 + 11.4127i 0.120756 + 0.371648i
\(944\) 8.09017 5.87785i 0.263313 0.191308i
\(945\) 0 0
\(946\) 1.30902 5.20431i 0.0425598 0.169207i
\(947\) −50.0344 −1.62590 −0.812950 0.582333i \(-0.802140\pi\)
−0.812950 + 0.582333i \(0.802140\pi\)
\(948\) 0 0
\(949\) −6.47214 19.9192i −0.210094 0.646604i
\(950\) 3.04508 9.37181i 0.0987956 0.304062i
\(951\) 0 0
\(952\) −2.04508 1.48584i −0.0662816 0.0481564i
\(953\) −6.47214 + 19.9192i −0.209653 + 0.645246i 0.789837 + 0.613317i \(0.210165\pi\)
−0.999490 + 0.0319290i \(0.989835\pi\)
\(954\) −1.85410 5.70634i −0.0600288 0.184750i
\(955\) 29.8156 21.6623i 0.964810 0.700975i
\(956\) 15.7984 0.510956
\(957\) 0 0
\(958\) 16.5623 0.535104
\(959\) 8.30902 6.03685i 0.268312 0.194940i
\(960\) 0 0
\(961\) 0.489357 1.50609i 0.0157857 0.0485834i
\(962\) 18.4721 + 13.4208i 0.595566 + 0.432704i
\(963\) −22.4164 16.2865i −0.722359 0.524824i
\(964\) 2.79837 8.61251i 0.0901296 0.277390i
\(965\) −2.38197 7.33094i −0.0766782 0.235991i
\(966\) 0 0
\(967\) −0.201626 −0.00648386 −0.00324193 0.999995i \(-0.501032\pi\)
−0.00324193 + 0.999995i \(0.501032\pi\)
\(968\) 10.8992 1.48584i 0.350313 0.0477567i
\(969\) 0 0
\(970\) −23.4721 + 17.0535i −0.753645 + 0.547555i
\(971\) −7.90983 24.3440i −0.253839 0.781235i −0.994056 0.108867i \(-0.965278\pi\)
0.740218 0.672367i \(-0.234722\pi\)
\(972\) 0 0
\(973\) 9.66312 + 7.02067i 0.309785 + 0.225072i
\(974\) −20.5623 14.9394i −0.658859 0.478689i
\(975\) 0 0
\(976\) 3.11803 + 9.59632i 0.0998058 + 0.307171i
\(977\) 7.00000 5.08580i 0.223950 0.162709i −0.470153 0.882585i \(-0.655801\pi\)
0.694103 + 0.719876i \(0.255801\pi\)
\(978\) 0 0
\(979\) −36.0902 + 30.1563i −1.15345 + 0.963799i
\(980\) 25.5066 0.814778
\(981\) 4.14590 3.01217i 0.132368 0.0961712i
\(982\) −10.9894 33.8218i −0.350684 1.07930i
\(983\) 5.72949 17.6336i 0.182742 0.562423i −0.817160 0.576411i \(-0.804453\pi\)
0.999902 + 0.0139880i \(0.00445268\pi\)
\(984\) 0 0
\(985\) 23.4721 + 17.0535i 0.747884 + 0.543370i
\(986\) 1.56231 4.80828i 0.0497540 0.153127i
\(987\) 0 0
\(988\) −2.00000 + 1.45309i −0.0636285 + 0.0462288i
\(989\) −1.85410 −0.0589570
\(990\) −9.35410 + 37.1895i −0.297293 + 1.18196i
\(991\) −39.7082 −1.26137 −0.630686 0.776038i \(-0.717227\pi\)
−0.630686 + 0.776038i \(0.717227\pi\)
\(992\) 4.61803 3.35520i 0.146623 0.106528i
\(993\) 0 0
\(994\) 1.61803 4.97980i 0.0513209 0.157950i
\(995\) 14.3992 + 10.4616i 0.456485 + 0.331656i
\(996\) 0 0
\(997\) 1.84346 5.67358i 0.0583829 0.179684i −0.917612 0.397477i \(-0.869886\pi\)
0.975995 + 0.217793i \(0.0698858\pi\)
\(998\) −7.19098 22.1316i −0.227627 0.700563i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 418.2.f.b.267.1 yes 4
11.2 odd 10 4598.2.a.z.1.1 2
11.4 even 5 inner 418.2.f.b.191.1 4
11.9 even 5 4598.2.a.bh.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.b.191.1 4 11.4 even 5 inner
418.2.f.b.267.1 yes 4 1.1 even 1 trivial
4598.2.a.z.1.1 2 11.2 odd 10
4598.2.a.bh.1.1 2 11.9 even 5