Properties

Label 825.2.n.e.301.1
Level $825$
Weight $2$
Character 825.301
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(301,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 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("825.301");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (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: \(6.58765816676\)
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 301.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 825.301
Dual form 825.2.n.e.751.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.30902 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-1.30902 + 0.951057i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(1.30902 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-1.30902 + 0.951057i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.309017 - 3.30220i) q^{11} -0.618034 q^{12} +(-1.50000 - 1.08981i) q^{13} +(1.50000 - 4.61653i) q^{14} +(3.92705 - 2.85317i) q^{16} +(6.04508 - 4.39201i) q^{17} +(-0.500000 - 1.53884i) q^{18} +(-0.854102 + 2.62866i) q^{19} +3.00000 q^{21} +(3.54508 - 4.02874i) q^{22} -7.61803 q^{23} +(1.80902 + 1.31433i) q^{24} +(-0.927051 - 2.85317i) q^{26} +(0.809017 - 0.587785i) q^{27} +(1.50000 - 1.08981i) q^{28} +(1.11803 + 3.44095i) q^{29} +(7.16312 + 5.20431i) q^{31} +3.38197 q^{32} +(3.04508 + 1.31433i) q^{33} +12.0902 q^{34} +(0.190983 - 0.587785i) q^{36} +(-2.73607 - 8.42075i) q^{37} +(-3.61803 + 2.62866i) q^{38} +(1.50000 - 1.08981i) q^{39} +(-0.0729490 + 0.224514i) q^{41} +(3.92705 + 2.85317i) q^{42} -1.76393 q^{43} +(2.00000 - 0.449028i) q^{44} +(-9.97214 - 7.24518i) q^{46} +(-2.89919 + 8.92278i) q^{47} +(1.50000 + 4.61653i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(2.30902 + 7.10642i) q^{51} +(0.354102 - 1.08981i) q^{52} +(-0.381966 - 0.277515i) q^{53} +1.61803 q^{54} -6.70820 q^{56} +(-2.23607 - 1.62460i) q^{57} +(-1.80902 + 5.56758i) q^{58} +(-1.28115 - 3.94298i) q^{59} +(4.66312 - 3.38795i) q^{61} +(4.42705 + 13.6251i) q^{62} +(-0.927051 + 2.85317i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(2.73607 + 4.61653i) q^{66} +8.70820 q^{67} +(3.73607 + 2.71441i) q^{68} +(2.35410 - 7.24518i) q^{69} +(-1.19098 + 0.865300i) q^{71} +(-1.80902 + 1.31433i) q^{72} +(2.11803 + 6.51864i) q^{73} +(4.42705 - 13.6251i) q^{74} -1.70820 q^{76} +(-9.70820 + 2.17963i) q^{77} +3.00000 q^{78} +(6.11803 + 4.44501i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-0.309017 + 0.224514i) q^{82} +(8.39919 - 6.10237i) q^{83} +(0.572949 + 1.76336i) q^{84} +(-2.30902 - 1.67760i) q^{86} -3.61803 q^{87} +(-6.80902 - 2.93893i) q^{88} +2.56231 q^{89} +(-1.71885 + 5.29007i) q^{91} +(-1.45492 - 4.47777i) q^{92} +(-7.16312 + 5.20431i) q^{93} +(-12.2812 + 8.92278i) q^{94} +(-1.04508 + 3.21644i) q^{96} +(-8.42705 - 6.12261i) q^{97} -3.23607 q^{98} +(-2.19098 + 2.48990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - q^{11} + 2 q^{12} - 6 q^{13} + 6 q^{14} + 9 q^{16} + 13 q^{17} - 2 q^{18} + 10 q^{19} + 12 q^{21} + 3 q^{22} - 26 q^{23} + 5 q^{24} + 3 q^{26} + q^{27} + 6 q^{28} + 13 q^{31} + 18 q^{32} + q^{33} + 26 q^{34} + 3 q^{36} - 2 q^{37} - 10 q^{38} + 6 q^{39} - 7 q^{41} + 9 q^{42} - 16 q^{43} + 8 q^{44} - 22 q^{46} + 13 q^{47} + 6 q^{48} - 2 q^{49} + 7 q^{51} - 12 q^{52} - 6 q^{53} + 2 q^{54} - 5 q^{58} + 15 q^{59} + 3 q^{61} + 11 q^{62} + 3 q^{63} - 7 q^{64} + 2 q^{66} + 8 q^{67} + 6 q^{68} - 4 q^{69} - 7 q^{71} - 5 q^{72} + 4 q^{73} + 11 q^{74} + 20 q^{76} - 12 q^{77} + 12 q^{78} + 20 q^{79} - q^{81} + q^{82} + 9 q^{83} + 9 q^{84} - 7 q^{86} - 10 q^{87} - 25 q^{88} - 30 q^{89} - 27 q^{91} - 17 q^{92} - 13 q^{93} - 29 q^{94} + 7 q^{96} - 27 q^{97} - 4 q^{98} - 11 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30902 + 0.951057i 0.925615 + 0.672499i 0.944915 0.327315i \(-0.106144\pi\)
−0.0193004 + 0.999814i \(0.506144\pi\)
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i
\(4\) 0.190983 + 0.587785i 0.0954915 + 0.293893i
\(5\) 0 0
\(6\) −1.30902 + 0.951057i −0.534404 + 0.388267i
\(7\) −0.927051 2.85317i −0.350392 1.07840i −0.958633 0.284644i \(-0.908125\pi\)
0.608241 0.793752i \(-0.291875\pi\)
\(8\) 0.690983 2.12663i 0.244299 0.751876i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 0 0
\(11\) 0.309017 3.30220i 0.0931721 0.995650i
\(12\) −0.618034 −0.178411
\(13\) −1.50000 1.08981i −0.416025 0.302260i 0.360011 0.932948i \(-0.382773\pi\)
−0.776037 + 0.630688i \(0.782773\pi\)
\(14\) 1.50000 4.61653i 0.400892 1.23382i
\(15\) 0 0
\(16\) 3.92705 2.85317i 0.981763 0.713292i
\(17\) 6.04508 4.39201i 1.46615 1.06522i 0.484441 0.874824i \(-0.339023\pi\)
0.981708 0.190395i \(-0.0609770\pi\)
\(18\) −0.500000 1.53884i −0.117851 0.362708i
\(19\) −0.854102 + 2.62866i −0.195944 + 0.603055i 0.804020 + 0.594602i \(0.202691\pi\)
−0.999964 + 0.00845249i \(0.997309\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 3.54508 4.02874i 0.755815 0.858930i
\(23\) −7.61803 −1.58847 −0.794235 0.607611i \(-0.792128\pi\)
−0.794235 + 0.607611i \(0.792128\pi\)
\(24\) 1.80902 + 1.31433i 0.369264 + 0.268286i
\(25\) 0 0
\(26\) −0.927051 2.85317i −0.181810 0.559553i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) 1.50000 1.08981i 0.283473 0.205955i
\(29\) 1.11803 + 3.44095i 0.207614 + 0.638969i 0.999596 + 0.0284251i \(0.00904922\pi\)
−0.791982 + 0.610544i \(0.790951\pi\)
\(30\) 0 0
\(31\) 7.16312 + 5.20431i 1.28653 + 0.934722i 0.999729 0.0232673i \(-0.00740687\pi\)
0.286805 + 0.957989i \(0.407407\pi\)
\(32\) 3.38197 0.597853
\(33\) 3.04508 + 1.31433i 0.530081 + 0.228795i
\(34\) 12.0902 2.07345
\(35\) 0 0
\(36\) 0.190983 0.587785i 0.0318305 0.0979642i
\(37\) −2.73607 8.42075i −0.449807 1.38436i −0.877125 0.480262i \(-0.840542\pi\)
0.427318 0.904101i \(-0.359458\pi\)
\(38\) −3.61803 + 2.62866i −0.586923 + 0.426424i
\(39\) 1.50000 1.08981i 0.240192 0.174510i
\(40\) 0 0
\(41\) −0.0729490 + 0.224514i −0.0113927 + 0.0350632i −0.956591 0.291433i \(-0.905868\pi\)
0.945199 + 0.326496i \(0.105868\pi\)
\(42\) 3.92705 + 2.85317i 0.605957 + 0.440254i
\(43\) −1.76393 −0.268997 −0.134499 0.990914i \(-0.542942\pi\)
−0.134499 + 0.990914i \(0.542942\pi\)
\(44\) 2.00000 0.449028i 0.301511 0.0676935i
\(45\) 0 0
\(46\) −9.97214 7.24518i −1.47031 1.06824i
\(47\) −2.89919 + 8.92278i −0.422890 + 1.30152i 0.482110 + 0.876110i \(0.339870\pi\)
−0.905000 + 0.425411i \(0.860130\pi\)
\(48\) 1.50000 + 4.61653i 0.216506 + 0.666338i
\(49\) −1.61803 + 1.17557i −0.231148 + 0.167939i
\(50\) 0 0
\(51\) 2.30902 + 7.10642i 0.323327 + 0.995098i
\(52\) 0.354102 1.08981i 0.0491051 0.151130i
\(53\) −0.381966 0.277515i −0.0524671 0.0381196i 0.561243 0.827651i \(-0.310323\pi\)
−0.613710 + 0.789532i \(0.710323\pi\)
\(54\) 1.61803 0.220187
\(55\) 0 0
\(56\) −6.70820 −0.896421
\(57\) −2.23607 1.62460i −0.296174 0.215183i
\(58\) −1.80902 + 5.56758i −0.237536 + 0.731059i
\(59\) −1.28115 3.94298i −0.166792 0.513333i 0.832372 0.554217i \(-0.186982\pi\)
−0.999164 + 0.0408847i \(0.986982\pi\)
\(60\) 0 0
\(61\) 4.66312 3.38795i 0.597051 0.433783i −0.247780 0.968816i \(-0.579701\pi\)
0.844831 + 0.535033i \(0.179701\pi\)
\(62\) 4.42705 + 13.6251i 0.562236 + 1.73038i
\(63\) −0.927051 + 2.85317i −0.116797 + 0.359466i
\(64\) −3.42705 2.48990i −0.428381 0.311237i
\(65\) 0 0
\(66\) 2.73607 + 4.61653i 0.336787 + 0.568255i
\(67\) 8.70820 1.06388 0.531938 0.846783i \(-0.321464\pi\)
0.531938 + 0.846783i \(0.321464\pi\)
\(68\) 3.73607 + 2.71441i 0.453065 + 0.329171i
\(69\) 2.35410 7.24518i 0.283401 0.872217i
\(70\) 0 0
\(71\) −1.19098 + 0.865300i −0.141344 + 0.102692i −0.656210 0.754578i \(-0.727842\pi\)
0.514866 + 0.857270i \(0.327842\pi\)
\(72\) −1.80902 + 1.31433i −0.213195 + 0.154895i
\(73\) 2.11803 + 6.51864i 0.247897 + 0.762949i 0.995146 + 0.0984051i \(0.0313741\pi\)
−0.747249 + 0.664544i \(0.768626\pi\)
\(74\) 4.42705 13.6251i 0.514634 1.58388i
\(75\) 0 0
\(76\) −1.70820 −0.195944
\(77\) −9.70820 + 2.17963i −1.10635 + 0.248392i
\(78\) 3.00000 0.339683
\(79\) 6.11803 + 4.44501i 0.688333 + 0.500103i 0.876112 0.482108i \(-0.160129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −0.309017 + 0.224514i −0.0341252 + 0.0247934i
\(83\) 8.39919 6.10237i 0.921931 0.669822i −0.0220732 0.999756i \(-0.507027\pi\)
0.944004 + 0.329935i \(0.107027\pi\)
\(84\) 0.572949 + 1.76336i 0.0625139 + 0.192398i
\(85\) 0 0
\(86\) −2.30902 1.67760i −0.248988 0.180900i
\(87\) −3.61803 −0.387894
\(88\) −6.80902 2.93893i −0.725844 0.313291i
\(89\) 2.56231 0.271604 0.135802 0.990736i \(-0.456639\pi\)
0.135802 + 0.990736i \(0.456639\pi\)
\(90\) 0 0
\(91\) −1.71885 + 5.29007i −0.180184 + 0.554550i
\(92\) −1.45492 4.47777i −0.151685 0.466840i
\(93\) −7.16312 + 5.20431i −0.742781 + 0.539662i
\(94\) −12.2812 + 8.92278i −1.26670 + 0.920314i
\(95\) 0 0
\(96\) −1.04508 + 3.21644i −0.106664 + 0.328277i
\(97\) −8.42705 6.12261i −0.855637 0.621657i 0.0710572 0.997472i \(-0.477363\pi\)
−0.926695 + 0.375815i \(0.877363\pi\)
\(98\) −3.23607 −0.326892
\(99\) −2.19098 + 2.48990i −0.220202 + 0.250244i
\(100\) 0 0
\(101\) 0.881966 + 0.640786i 0.0877589 + 0.0637606i 0.630800 0.775946i \(-0.282727\pi\)
−0.543041 + 0.839706i \(0.682727\pi\)
\(102\) −3.73607 + 11.4984i −0.369926 + 1.13851i
\(103\) −4.69098 14.4374i −0.462216 1.42256i −0.862450 0.506142i \(-0.831071\pi\)
0.400234 0.916413i \(-0.368929\pi\)
\(104\) −3.35410 + 2.43690i −0.328897 + 0.238957i
\(105\) 0 0
\(106\) −0.236068 0.726543i −0.0229289 0.0705680i
\(107\) −5.07295 + 15.6129i −0.490420 + 1.50936i 0.333553 + 0.942731i \(0.391752\pi\)
−0.823974 + 0.566628i \(0.808248\pi\)
\(108\) 0.500000 + 0.363271i 0.0481125 + 0.0349558i
\(109\) 15.0000 1.43674 0.718370 0.695662i \(-0.244889\pi\)
0.718370 + 0.695662i \(0.244889\pi\)
\(110\) 0 0
\(111\) 8.85410 0.840394
\(112\) −11.7812 8.55951i −1.11321 0.808798i
\(113\) −2.61803 + 8.05748i −0.246284 + 0.757984i 0.749139 + 0.662413i \(0.230468\pi\)
−0.995423 + 0.0955708i \(0.969532\pi\)
\(114\) −1.38197 4.25325i −0.129433 0.398354i
\(115\) 0 0
\(116\) −1.80902 + 1.31433i −0.167963 + 0.122032i
\(117\) 0.572949 + 1.76336i 0.0529692 + 0.163022i
\(118\) 2.07295 6.37988i 0.190830 0.587316i
\(119\) −18.1353 13.1760i −1.66246 1.20785i
\(120\) 0 0
\(121\) −10.8090 2.04087i −0.982638 0.185534i
\(122\) 9.32624 0.844358
\(123\) −0.190983 0.138757i −0.0172204 0.0125113i
\(124\) −1.69098 + 5.20431i −0.151855 + 0.467361i
\(125\) 0 0
\(126\) −3.92705 + 2.85317i −0.349850 + 0.254181i
\(127\) 5.35410 3.88998i 0.475100 0.345180i −0.324326 0.945945i \(-0.605137\pi\)
0.799425 + 0.600765i \(0.205137\pi\)
\(128\) −4.20820 12.9515i −0.371956 1.14476i
\(129\) 0.545085 1.67760i 0.0479921 0.147704i
\(130\) 0 0
\(131\) 7.32624 0.640096 0.320048 0.947401i \(-0.396301\pi\)
0.320048 + 0.947401i \(0.396301\pi\)
\(132\) −0.190983 + 2.04087i −0.0166229 + 0.177635i
\(133\) 8.29180 0.718990
\(134\) 11.3992 + 8.28199i 0.984740 + 0.715455i
\(135\) 0 0
\(136\) −5.16312 15.8904i −0.442734 1.36259i
\(137\) 10.3541 7.52270i 0.884611 0.642707i −0.0498566 0.998756i \(-0.515876\pi\)
0.934467 + 0.356049i \(0.115876\pi\)
\(138\) 9.97214 7.24518i 0.848885 0.616751i
\(139\) 1.80902 + 5.56758i 0.153439 + 0.472236i 0.997999 0.0632239i \(-0.0201382\pi\)
−0.844561 + 0.535460i \(0.820138\pi\)
\(140\) 0 0
\(141\) −7.59017 5.51458i −0.639208 0.464412i
\(142\) −2.38197 −0.199890
\(143\) −4.06231 + 4.61653i −0.339707 + 0.386053i
\(144\) −4.85410 −0.404508
\(145\) 0 0
\(146\) −3.42705 + 10.5474i −0.283625 + 0.872907i
\(147\) −0.618034 1.90211i −0.0509746 0.156884i
\(148\) 4.42705 3.21644i 0.363901 0.264390i
\(149\) −13.0902 + 9.51057i −1.07239 + 0.779136i −0.976340 0.216241i \(-0.930620\pi\)
−0.0960484 + 0.995377i \(0.530620\pi\)
\(150\) 0 0
\(151\) −2.83688 + 8.73102i −0.230862 + 0.710520i 0.766781 + 0.641908i \(0.221857\pi\)
−0.997643 + 0.0686121i \(0.978143\pi\)
\(152\) 5.00000 + 3.63271i 0.405554 + 0.294652i
\(153\) −7.47214 −0.604086
\(154\) −14.7812 6.37988i −1.19110 0.514105i
\(155\) 0 0
\(156\) 0.927051 + 0.673542i 0.0742235 + 0.0539265i
\(157\) −5.50000 + 16.9273i −0.438948 + 1.35094i 0.450039 + 0.893009i \(0.351410\pi\)
−0.888987 + 0.457933i \(0.848590\pi\)
\(158\) 3.78115 + 11.6372i 0.300812 + 0.925805i
\(159\) 0.381966 0.277515i 0.0302919 0.0220083i
\(160\) 0 0
\(161\) 7.06231 + 21.7355i 0.556588 + 1.71300i
\(162\) −0.500000 + 1.53884i −0.0392837 + 0.120903i
\(163\) 13.8262 + 10.0453i 1.08295 + 0.786813i 0.978196 0.207685i \(-0.0665929\pi\)
0.104759 + 0.994498i \(0.466593\pi\)
\(164\) −0.145898 −0.0113927
\(165\) 0 0
\(166\) 16.7984 1.30381
\(167\) −16.9443 12.3107i −1.31119 0.952633i −0.999997 0.00228541i \(-0.999273\pi\)
−0.311190 0.950348i \(-0.600727\pi\)
\(168\) 2.07295 6.37988i 0.159931 0.492219i
\(169\) −2.95492 9.09429i −0.227301 0.699561i
\(170\) 0 0
\(171\) 2.23607 1.62460i 0.170996 0.124236i
\(172\) −0.336881 1.03681i −0.0256869 0.0790563i
\(173\) 1.69098 5.20431i 0.128563 0.395676i −0.865970 0.500095i \(-0.833298\pi\)
0.994533 + 0.104419i \(0.0332983\pi\)
\(174\) −4.73607 3.44095i −0.359040 0.260858i
\(175\) 0 0
\(176\) −8.20820 13.8496i −0.618717 1.04395i
\(177\) 4.14590 0.311625
\(178\) 3.35410 + 2.43690i 0.251401 + 0.182653i
\(179\) −6.21885 + 19.1396i −0.464818 + 1.43056i 0.394392 + 0.918942i \(0.370955\pi\)
−0.859211 + 0.511622i \(0.829045\pi\)
\(180\) 0 0
\(181\) 10.3541 7.52270i 0.769614 0.559158i −0.132230 0.991219i \(-0.542214\pi\)
0.901844 + 0.432062i \(0.142214\pi\)
\(182\) −7.28115 + 5.29007i −0.539715 + 0.392126i
\(183\) 1.78115 + 5.48183i 0.131667 + 0.405228i
\(184\) −5.26393 + 16.2007i −0.388062 + 1.19433i
\(185\) 0 0
\(186\) −14.3262 −1.05045
\(187\) −12.6353 21.3193i −0.923981 1.55902i
\(188\) −5.79837 −0.422890
\(189\) −2.42705 1.76336i −0.176542 0.128265i
\(190\) 0 0
\(191\) 4.86475 + 14.9721i 0.352001 + 1.08335i 0.957728 + 0.287674i \(0.0928821\pi\)
−0.605728 + 0.795672i \(0.707118\pi\)
\(192\) 3.42705 2.48990i 0.247326 0.179693i
\(193\) 14.9443 10.8576i 1.07571 0.781551i 0.0987819 0.995109i \(-0.468505\pi\)
0.976930 + 0.213558i \(0.0685054\pi\)
\(194\) −5.20820 16.0292i −0.373927 1.15083i
\(195\) 0 0
\(196\) −1.00000 0.726543i −0.0714286 0.0518959i
\(197\) −9.70820 −0.691681 −0.345840 0.938293i \(-0.612406\pi\)
−0.345840 + 0.938293i \(0.612406\pi\)
\(198\) −5.23607 + 1.17557i −0.372111 + 0.0835442i
\(199\) −8.29180 −0.587790 −0.293895 0.955838i \(-0.594952\pi\)
−0.293895 + 0.955838i \(0.594952\pi\)
\(200\) 0 0
\(201\) −2.69098 + 8.28199i −0.189807 + 0.584167i
\(202\) 0.545085 + 1.67760i 0.0383520 + 0.118035i
\(203\) 8.78115 6.37988i 0.616316 0.447780i
\(204\) −3.73607 + 2.71441i −0.261577 + 0.190047i
\(205\) 0 0
\(206\) 7.59017 23.3601i 0.528832 1.62758i
\(207\) 6.16312 + 4.47777i 0.428366 + 0.311226i
\(208\) −9.00000 −0.624038
\(209\) 8.41641 + 3.63271i 0.582175 + 0.251280i
\(210\) 0 0
\(211\) −10.6631 7.74721i −0.734079 0.533340i 0.156772 0.987635i \(-0.449891\pi\)
−0.890851 + 0.454295i \(0.849891\pi\)
\(212\) 0.0901699 0.277515i 0.00619290 0.0190598i
\(213\) −0.454915 1.40008i −0.0311703 0.0959322i
\(214\) −21.4894 + 15.6129i −1.46898 + 1.06728i
\(215\) 0 0
\(216\) −0.690983 2.12663i −0.0470154 0.144699i
\(217\) 8.20820 25.2623i 0.557209 1.71491i
\(218\) 19.6353 + 14.2658i 1.32987 + 0.966205i
\(219\) −6.85410 −0.463157
\(220\) 0 0
\(221\) −13.8541 −0.931928
\(222\) 11.5902 + 8.42075i 0.777881 + 0.565164i
\(223\) 3.92705 12.0862i 0.262975 0.809353i −0.729178 0.684324i \(-0.760097\pi\)
0.992153 0.125029i \(-0.0399025\pi\)
\(224\) −3.13525 9.64932i −0.209483 0.644722i
\(225\) 0 0
\(226\) −11.0902 + 8.05748i −0.737707 + 0.535976i
\(227\) 4.50000 + 13.8496i 0.298675 + 0.919229i 0.981962 + 0.189078i \(0.0605500\pi\)
−0.683287 + 0.730150i \(0.739450\pi\)
\(228\) 0.527864 1.62460i 0.0349587 0.107592i
\(229\) 8.09017 + 5.87785i 0.534613 + 0.388419i 0.822081 0.569371i \(-0.192813\pi\)
−0.287467 + 0.957790i \(0.592813\pi\)
\(230\) 0 0
\(231\) 0.927051 9.90659i 0.0609955 0.651806i
\(232\) 8.09017 0.531146
\(233\) −5.11803 3.71847i −0.335294 0.243605i 0.407380 0.913259i \(-0.366443\pi\)
−0.742673 + 0.669654i \(0.766443\pi\)
\(234\) −0.927051 + 2.85317i −0.0606032 + 0.186518i
\(235\) 0 0
\(236\) 2.07295 1.50609i 0.134937 0.0980378i
\(237\) −6.11803 + 4.44501i −0.397409 + 0.288735i
\(238\) −11.2082 34.4953i −0.726520 2.23600i
\(239\) −6.38197 + 19.6417i −0.412815 + 1.27051i 0.501376 + 0.865230i \(0.332827\pi\)
−0.914191 + 0.405284i \(0.867173\pi\)
\(240\) 0 0
\(241\) 7.85410 0.505927 0.252964 0.967476i \(-0.418595\pi\)
0.252964 + 0.967476i \(0.418595\pi\)
\(242\) −12.2082 12.9515i −0.784773 0.832555i
\(243\) −1.00000 −0.0641500
\(244\) 2.88197 + 2.09387i 0.184499 + 0.134046i
\(245\) 0 0
\(246\) −0.118034 0.363271i −0.00752557 0.0231613i
\(247\) 4.14590 3.01217i 0.263797 0.191660i
\(248\) 16.0172 11.6372i 1.01709 0.738962i
\(249\) 3.20820 + 9.87384i 0.203312 + 0.625729i
\(250\) 0 0
\(251\) 16.6353 + 12.0862i 1.05001 + 0.762875i 0.972214 0.234094i \(-0.0752124\pi\)
0.0777940 + 0.996969i \(0.475212\pi\)
\(252\) −1.85410 −0.116797
\(253\) −2.35410 + 25.1563i −0.148001 + 1.58156i
\(254\) 10.7082 0.671892
\(255\) 0 0
\(256\) 4.19098 12.8985i 0.261936 0.806157i
\(257\) −3.10081 9.54332i −0.193423 0.595296i −0.999991 0.00415466i \(-0.998678\pi\)
0.806568 0.591141i \(-0.201322\pi\)
\(258\) 2.30902 1.67760i 0.143753 0.104443i
\(259\) −21.4894 + 15.6129i −1.33528 + 0.970140i
\(260\) 0 0
\(261\) 1.11803 3.44095i 0.0692046 0.212990i
\(262\) 9.59017 + 6.96767i 0.592483 + 0.430464i
\(263\) 11.1246 0.685973 0.342986 0.939340i \(-0.388561\pi\)
0.342986 + 0.939340i \(0.388561\pi\)
\(264\) 4.89919 5.56758i 0.301524 0.342661i
\(265\) 0 0
\(266\) 10.8541 + 7.88597i 0.665508 + 0.483520i
\(267\) −0.791796 + 2.43690i −0.0484571 + 0.149136i
\(268\) 1.66312 + 5.11855i 0.101591 + 0.312665i
\(269\) 0.427051 0.310271i 0.0260378 0.0189175i −0.574690 0.818371i \(-0.694877\pi\)
0.600728 + 0.799453i \(0.294877\pi\)
\(270\) 0 0
\(271\) −6.88197 21.1805i −0.418050 1.28662i −0.909495 0.415716i \(-0.863531\pi\)
0.491445 0.870909i \(-0.336469\pi\)
\(272\) 11.2082 34.4953i 0.679597 2.09159i
\(273\) −4.50000 3.26944i −0.272352 0.197876i
\(274\) 20.7082 1.25103
\(275\) 0 0
\(276\) 4.70820 0.283401
\(277\) 19.3992 + 14.0943i 1.16558 + 0.846846i 0.990474 0.137702i \(-0.0439717\pi\)
0.175111 + 0.984549i \(0.443972\pi\)
\(278\) −2.92705 + 9.00854i −0.175553 + 0.540296i
\(279\) −2.73607 8.42075i −0.163804 0.504137i
\(280\) 0 0
\(281\) 2.69098 1.95511i 0.160531 0.116632i −0.504620 0.863342i \(-0.668367\pi\)
0.665151 + 0.746709i \(0.268367\pi\)
\(282\) −4.69098 14.4374i −0.279344 0.859732i
\(283\) −8.37132 + 25.7643i −0.497623 + 1.53153i 0.315204 + 0.949024i \(0.397927\pi\)
−0.812828 + 0.582504i \(0.802073\pi\)
\(284\) −0.736068 0.534785i −0.0436776 0.0317336i
\(285\) 0 0
\(286\) −9.70820 + 2.17963i −0.574058 + 0.128884i
\(287\) 0.708204 0.0418040
\(288\) −2.73607 1.98787i −0.161224 0.117136i
\(289\) 12.0000 36.9322i 0.705882 2.17248i
\(290\) 0 0
\(291\) 8.42705 6.12261i 0.494002 0.358914i
\(292\) −3.42705 + 2.48990i −0.200553 + 0.145710i
\(293\) 6.00000 + 18.4661i 0.350524 + 1.07880i 0.958560 + 0.284892i \(0.0919576\pi\)
−0.608036 + 0.793909i \(0.708042\pi\)
\(294\) 1.00000 3.07768i 0.0583212 0.179494i
\(295\) 0 0
\(296\) −19.7984 −1.15076
\(297\) −1.69098 2.85317i −0.0981208 0.165558i
\(298\) −26.1803 −1.51659
\(299\) 11.4271 + 8.30224i 0.660843 + 0.480131i
\(300\) 0 0
\(301\) 1.63525 + 5.03280i 0.0942545 + 0.290086i
\(302\) −12.0172 + 8.73102i −0.691513 + 0.502414i
\(303\) −0.881966 + 0.640786i −0.0506676 + 0.0368122i
\(304\) 4.14590 + 12.7598i 0.237784 + 0.731823i
\(305\) 0 0
\(306\) −9.78115 7.10642i −0.559151 0.406247i
\(307\) −15.8885 −0.906807 −0.453404 0.891305i \(-0.649790\pi\)
−0.453404 + 0.891305i \(0.649790\pi\)
\(308\) −3.13525 5.29007i −0.178648 0.301430i
\(309\) 15.1803 0.863579
\(310\) 0 0
\(311\) −5.72542 + 17.6210i −0.324659 + 0.999198i 0.646935 + 0.762545i \(0.276050\pi\)
−0.971594 + 0.236653i \(0.923950\pi\)
\(312\) −1.28115 3.94298i −0.0725310 0.223227i
\(313\) 24.8435 18.0498i 1.40424 1.02024i 0.410106 0.912038i \(-0.365492\pi\)
0.994129 0.108199i \(-0.0345083\pi\)
\(314\) −23.2984 + 16.9273i −1.31480 + 0.955261i
\(315\) 0 0
\(316\) −1.44427 + 4.44501i −0.0812466 + 0.250051i
\(317\) 7.42705 + 5.39607i 0.417145 + 0.303073i 0.776488 0.630132i \(-0.216999\pi\)
−0.359343 + 0.933205i \(0.616999\pi\)
\(318\) 0.763932 0.0428392
\(319\) 11.7082 2.62866i 0.655534 0.147176i
\(320\) 0 0
\(321\) −13.2812 9.64932i −0.741282 0.538573i
\(322\) −11.4271 + 35.1688i −0.636805 + 1.95988i
\(323\) 6.38197 + 19.6417i 0.355102 + 1.09289i
\(324\) −0.500000 + 0.363271i −0.0277778 + 0.0201817i
\(325\) 0 0
\(326\) 8.54508 + 26.2991i 0.473268 + 1.45657i
\(327\) −4.63525 + 14.2658i −0.256330 + 0.788903i
\(328\) 0.427051 + 0.310271i 0.0235799 + 0.0171318i
\(329\) 28.1459 1.55173
\(330\) 0 0
\(331\) −16.4164 −0.902327 −0.451164 0.892441i \(-0.648991\pi\)
−0.451164 + 0.892441i \(0.648991\pi\)
\(332\) 5.19098 + 3.77147i 0.284892 + 0.206986i
\(333\) −2.73607 + 8.42075i −0.149936 + 0.461454i
\(334\) −10.4721 32.2299i −0.573010 1.76354i
\(335\) 0 0
\(336\) 11.7812 8.55951i 0.642715 0.466959i
\(337\) 7.32624 + 22.5478i 0.399086 + 1.22826i 0.925734 + 0.378176i \(0.123449\pi\)
−0.526648 + 0.850083i \(0.676551\pi\)
\(338\) 4.78115 14.7149i 0.260060 0.800384i
\(339\) −6.85410 4.97980i −0.372264 0.270465i
\(340\) 0 0
\(341\) 19.3992 22.0458i 1.05052 1.19385i
\(342\) 4.47214 0.241825
\(343\) −12.1353 8.81678i −0.655242 0.476061i
\(344\) −1.21885 + 3.75123i −0.0657158 + 0.202253i
\(345\) 0 0
\(346\) 7.16312 5.20431i 0.385092 0.279785i
\(347\) −9.97214 + 7.24518i −0.535332 + 0.388942i −0.822349 0.568984i \(-0.807337\pi\)
0.287016 + 0.957926i \(0.407337\pi\)
\(348\) −0.690983 2.12663i −0.0370406 0.113999i
\(349\) 8.94427 27.5276i 0.478776 1.47352i −0.362021 0.932170i \(-0.617913\pi\)
0.840797 0.541351i \(-0.182087\pi\)
\(350\) 0 0
\(351\) −1.85410 −0.0989646
\(352\) 1.04508 11.1679i 0.0557032 0.595252i
\(353\) 8.88854 0.473089 0.236545 0.971621i \(-0.423985\pi\)
0.236545 + 0.971621i \(0.423985\pi\)
\(354\) 5.42705 + 3.94298i 0.288445 + 0.209567i
\(355\) 0 0
\(356\) 0.489357 + 1.50609i 0.0259359 + 0.0798224i
\(357\) 18.1353 13.1760i 0.959819 0.697350i
\(358\) −26.3435 + 19.1396i −1.39230 + 1.01156i
\(359\) 5.62868 + 17.3233i 0.297070 + 0.914288i 0.982518 + 0.186167i \(0.0596064\pi\)
−0.685448 + 0.728122i \(0.740394\pi\)
\(360\) 0 0
\(361\) 9.19098 + 6.67764i 0.483736 + 0.351455i
\(362\) 20.7082 1.08840
\(363\) 5.28115 9.64932i 0.277189 0.506458i
\(364\) −3.43769 −0.180184
\(365\) 0 0
\(366\) −2.88197 + 8.86978i −0.150643 + 0.463631i
\(367\) 5.81966 + 17.9111i 0.303784 + 0.934950i 0.980128 + 0.198365i \(0.0635631\pi\)
−0.676344 + 0.736585i \(0.736437\pi\)
\(368\) −29.9164 + 21.7355i −1.55950 + 1.13304i
\(369\) 0.190983 0.138757i 0.00994218 0.00722342i
\(370\) 0 0
\(371\) −0.437694 + 1.34708i −0.0227239 + 0.0699371i
\(372\) −4.42705 3.21644i −0.229532 0.166765i
\(373\) −17.4164 −0.901787 −0.450894 0.892578i \(-0.648895\pi\)
−0.450894 + 0.892578i \(0.648895\pi\)
\(374\) 3.73607 39.9241i 0.193187 2.06443i
\(375\) 0 0
\(376\) 16.9721 + 12.3310i 0.875271 + 0.635922i
\(377\) 2.07295 6.37988i 0.106762 0.328581i
\(378\) −1.50000 4.61653i −0.0771517 0.237448i
\(379\) 18.7812 13.6453i 0.964723 0.700912i 0.0104802 0.999945i \(-0.496664\pi\)
0.954243 + 0.299033i \(0.0966640\pi\)
\(380\) 0 0
\(381\) 2.04508 + 6.29412i 0.104773 + 0.322458i
\(382\) −7.87132 + 24.2254i −0.402732 + 1.23948i
\(383\) −17.4164 12.6538i −0.889937 0.646577i 0.0459247 0.998945i \(-0.485377\pi\)
−0.935862 + 0.352368i \(0.885377\pi\)
\(384\) 13.6180 0.694942
\(385\) 0 0
\(386\) 29.8885 1.52129
\(387\) 1.42705 + 1.03681i 0.0725411 + 0.0527042i
\(388\) 1.98936 6.12261i 0.100994 0.310828i
\(389\) −5.59017 17.2048i −0.283433 0.872317i −0.986864 0.161553i \(-0.948350\pi\)
0.703431 0.710763i \(-0.251650\pi\)
\(390\) 0 0
\(391\) −46.0517 + 33.4585i −2.32893 + 1.69207i
\(392\) 1.38197 + 4.25325i 0.0697998 + 0.214822i
\(393\) −2.26393 + 6.96767i −0.114200 + 0.351472i
\(394\) −12.7082 9.23305i −0.640230 0.465154i
\(395\) 0 0
\(396\) −1.88197 0.812299i −0.0945724 0.0408196i
\(397\) 19.5623 0.981804 0.490902 0.871215i \(-0.336667\pi\)
0.490902 + 0.871215i \(0.336667\pi\)
\(398\) −10.8541 7.88597i −0.544067 0.395288i
\(399\) −2.56231 + 7.88597i −0.128276 + 0.394792i
\(400\) 0 0
\(401\) −0.663119 + 0.481784i −0.0331146 + 0.0240592i −0.604219 0.796818i \(-0.706515\pi\)
0.571105 + 0.820877i \(0.306515\pi\)
\(402\) −11.3992 + 8.28199i −0.568540 + 0.413068i
\(403\) −5.07295 15.6129i −0.252702 0.777736i
\(404\) −0.208204 + 0.640786i −0.0103585 + 0.0318803i
\(405\) 0 0
\(406\) 17.5623 0.871603
\(407\) −28.6525 + 6.43288i −1.42025 + 0.318866i
\(408\) 16.7082 0.827179
\(409\) 8.19098 + 5.95110i 0.405018 + 0.294263i 0.771582 0.636130i \(-0.219466\pi\)
−0.366564 + 0.930393i \(0.619466\pi\)
\(410\) 0 0
\(411\) 3.95492 + 12.1720i 0.195082 + 0.600399i
\(412\) 7.59017 5.51458i 0.373941 0.271684i
\(413\) −10.0623 + 7.31069i −0.495134 + 0.359736i
\(414\) 3.80902 + 11.7229i 0.187203 + 0.576152i
\(415\) 0 0
\(416\) −5.07295 3.68571i −0.248722 0.180707i
\(417\) −5.85410 −0.286677
\(418\) 7.56231 + 12.7598i 0.369884 + 0.624100i
\(419\) 18.9443 0.925488 0.462744 0.886492i \(-0.346865\pi\)
0.462744 + 0.886492i \(0.346865\pi\)
\(420\) 0 0
\(421\) −2.24671 + 6.91467i −0.109498 + 0.337000i −0.990760 0.135628i \(-0.956695\pi\)
0.881262 + 0.472628i \(0.156695\pi\)
\(422\) −6.59017 20.2825i −0.320804 0.987335i
\(423\) 7.59017 5.51458i 0.369047 0.268128i
\(424\) −0.854102 + 0.620541i −0.0414789 + 0.0301362i
\(425\) 0 0
\(426\) 0.736068 2.26538i 0.0356626 0.109758i
\(427\) −13.9894 10.1639i −0.676992 0.491864i
\(428\) −10.1459 −0.490420
\(429\) −3.13525 5.29007i −0.151372 0.255407i
\(430\) 0 0
\(431\) −13.0623 9.49032i −0.629189 0.457133i 0.226930 0.973911i \(-0.427131\pi\)
−0.856119 + 0.516778i \(0.827131\pi\)
\(432\) 1.50000 4.61653i 0.0721688 0.222113i
\(433\) 8.39919 + 25.8500i 0.403639 + 1.24227i 0.922026 + 0.387127i \(0.126533\pi\)
−0.518387 + 0.855146i \(0.673467\pi\)
\(434\) 34.7705 25.2623i 1.66904 1.21263i
\(435\) 0 0
\(436\) 2.86475 + 8.81678i 0.137196 + 0.422247i
\(437\) 6.50658 20.0252i 0.311252 0.957935i
\(438\) −8.97214 6.51864i −0.428705 0.311473i
\(439\) 7.43769 0.354982 0.177491 0.984122i \(-0.443202\pi\)
0.177491 + 0.984122i \(0.443202\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) −18.1353 13.1760i −0.862606 0.626720i
\(443\) 8.50000 26.1603i 0.403847 1.24291i −0.518007 0.855376i \(-0.673326\pi\)
0.921854 0.387537i \(-0.126674\pi\)
\(444\) 1.69098 + 5.20431i 0.0802505 + 0.246986i
\(445\) 0 0
\(446\) 16.6353 12.0862i 0.787702 0.572299i
\(447\) −5.00000 15.3884i −0.236492 0.727847i
\(448\) −3.92705 + 12.0862i −0.185536 + 0.571020i
\(449\) −11.7082 8.50651i −0.552544 0.401447i 0.276178 0.961106i \(-0.410932\pi\)
−0.828723 + 0.559659i \(0.810932\pi\)
\(450\) 0 0
\(451\) 0.718847 + 0.310271i 0.0338492 + 0.0146101i
\(452\) −5.23607 −0.246284
\(453\) −7.42705 5.39607i −0.348953 0.253529i
\(454\) −7.28115 + 22.4091i −0.341721 + 1.05171i
\(455\) 0 0
\(456\) −5.00000 + 3.63271i −0.234146 + 0.170117i
\(457\) 19.0344 13.8293i 0.890394 0.646909i −0.0455870 0.998960i \(-0.514516\pi\)
0.935981 + 0.352052i \(0.114516\pi\)
\(458\) 5.00000 + 15.3884i 0.233635 + 0.719054i
\(459\) 2.30902 7.10642i 0.107776 0.331699i
\(460\) 0 0
\(461\) −9.18034 −0.427571 −0.213786 0.976881i \(-0.568579\pi\)
−0.213786 + 0.976881i \(0.568579\pi\)
\(462\) 10.6353 12.0862i 0.494797 0.562302i
\(463\) 9.29180 0.431826 0.215913 0.976413i \(-0.430727\pi\)
0.215913 + 0.976413i \(0.430727\pi\)
\(464\) 14.2082 + 10.3229i 0.659599 + 0.479227i
\(465\) 0 0
\(466\) −3.16312 9.73508i −0.146529 0.450969i
\(467\) −4.01722 + 2.91868i −0.185895 + 0.135060i −0.676841 0.736130i \(-0.736651\pi\)
0.490946 + 0.871190i \(0.336651\pi\)
\(468\) −0.927051 + 0.673542i −0.0428529 + 0.0311345i
\(469\) −8.07295 24.8460i −0.372774 1.14728i
\(470\) 0 0
\(471\) −14.3992 10.4616i −0.663480 0.482046i
\(472\) −9.27051 −0.426710
\(473\) −0.545085 + 5.82485i −0.0250630 + 0.267827i
\(474\) −12.2361 −0.562021
\(475\) 0 0
\(476\) 4.28115 13.1760i 0.196226 0.603923i
\(477\) 0.145898 + 0.449028i 0.00668021 + 0.0205596i
\(478\) −27.0344 + 19.6417i −1.23653 + 0.898389i
\(479\) −5.95492 + 4.32650i −0.272087 + 0.197683i −0.715459 0.698655i \(-0.753782\pi\)
0.443372 + 0.896338i \(0.353782\pi\)
\(480\) 0 0
\(481\) −5.07295 + 15.6129i −0.231307 + 0.711888i
\(482\) 10.2812 + 7.46969i 0.468294 + 0.340235i
\(483\) −22.8541 −1.03990
\(484\) −0.864745 6.74315i −0.0393066 0.306507i
\(485\) 0 0
\(486\) −1.30902 0.951057i −0.0593782 0.0431408i
\(487\) 0.392609 1.20833i 0.0177908 0.0547545i −0.941767 0.336266i \(-0.890836\pi\)
0.959558 + 0.281512i \(0.0908358\pi\)
\(488\) −3.98278 12.2577i −0.180292 0.554882i
\(489\) −13.8262 + 10.0453i −0.625244 + 0.454266i
\(490\) 0 0
\(491\) −4.28115 13.1760i −0.193206 0.594626i −0.999993 0.00378385i \(-0.998796\pi\)
0.806787 0.590842i \(-0.201204\pi\)
\(492\) 0.0450850 0.138757i 0.00203259 0.00625566i
\(493\) 21.8713 + 15.8904i 0.985035 + 0.715670i
\(494\) 8.29180 0.373066
\(495\) 0 0
\(496\) 42.9787 1.92980
\(497\) 3.57295 + 2.59590i 0.160269 + 0.116442i
\(498\) −5.19098 + 15.9762i −0.232614 + 0.715911i
\(499\) 3.65654 + 11.2537i 0.163689 + 0.503784i 0.998937 0.0460896i \(-0.0146760\pi\)
−0.835248 + 0.549873i \(0.814676\pi\)
\(500\) 0 0
\(501\) 16.9443 12.3107i 0.757014 0.550003i
\(502\) 10.2812 + 31.6421i 0.458870 + 1.41226i
\(503\) 1.06231 3.26944i 0.0473659 0.145777i −0.924576 0.380997i \(-0.875581\pi\)
0.971942 + 0.235220i \(0.0755809\pi\)
\(504\) 5.42705 + 3.94298i 0.241740 + 0.175634i
\(505\) 0 0
\(506\) −27.0066 + 30.6911i −1.20059 + 1.36438i
\(507\) 9.56231 0.424677
\(508\) 3.30902 + 2.40414i 0.146814 + 0.106667i
\(509\) −4.57295 + 14.0741i −0.202692 + 0.623823i 0.797108 + 0.603837i \(0.206362\pi\)
−0.999800 + 0.0199861i \(0.993638\pi\)
\(510\) 0 0
\(511\) 16.6353 12.0862i 0.735900 0.534663i
\(512\) −4.28115 + 3.11044i −0.189202 + 0.137463i
\(513\) 0.854102 + 2.62866i 0.0377095 + 0.116058i
\(514\) 5.01722 15.4414i 0.221300 0.681092i
\(515\) 0 0
\(516\) 1.09017 0.0479921
\(517\) 28.5689 + 12.3310i 1.25646 + 0.542316i
\(518\) −42.9787 −1.88838
\(519\) 4.42705 + 3.21644i 0.194326 + 0.141186i
\(520\) 0 0
\(521\) −13.3647 41.1325i −0.585520 1.80205i −0.597172 0.802113i \(-0.703709\pi\)
0.0116515 0.999932i \(-0.496291\pi\)
\(522\) 4.73607 3.44095i 0.207292 0.150607i
\(523\) 31.3885 22.8051i 1.37253 0.997198i 0.374990 0.927029i \(-0.377646\pi\)
0.997535 0.0701691i \(-0.0223539\pi\)
\(524\) 1.39919 + 4.30625i 0.0611238 + 0.188120i
\(525\) 0 0
\(526\) 14.5623 + 10.5801i 0.634947 + 0.461316i
\(527\) 66.1591 2.88193
\(528\) 15.7082 3.52671i 0.683612 0.153480i
\(529\) 35.0344 1.52324
\(530\) 0 0
\(531\) −1.28115 + 3.94298i −0.0555973 + 0.171111i
\(532\) 1.58359 + 4.87380i 0.0686574 + 0.211306i
\(533\) 0.354102 0.257270i 0.0153379 0.0111436i
\(534\) −3.35410 + 2.43690i −0.145146 + 0.105455i
\(535\) 0 0
\(536\) 6.01722 18.5191i 0.259904 0.799903i
\(537\) −16.2812 11.8290i −0.702584 0.510457i
\(538\) 0.854102 0.0368230
\(539\) 3.38197 + 5.70634i 0.145672 + 0.245789i
\(540\) 0 0
\(541\) 20.0902 + 14.5964i 0.863744 + 0.627547i 0.928901 0.370328i \(-0.120755\pi\)
−0.0651570 + 0.997875i \(0.520755\pi\)
\(542\) 11.1353 34.2708i 0.478300 1.47206i
\(543\) 3.95492 + 12.1720i 0.169722 + 0.522350i
\(544\) 20.4443 14.8536i 0.876541 0.636844i
\(545\) 0 0
\(546\) −2.78115 8.55951i −0.119022 0.366313i
\(547\) −6.57953 + 20.2497i −0.281320 + 0.865815i 0.706157 + 0.708055i \(0.250427\pi\)
−0.987478 + 0.157760i \(0.949573\pi\)
\(548\) 6.39919 + 4.64928i 0.273360 + 0.198607i
\(549\) −5.76393 −0.245999
\(550\) 0 0
\(551\) −10.0000 −0.426014
\(552\) −13.7812 10.0126i −0.586565 0.426164i
\(553\) 7.01064 21.5765i 0.298123 0.917528i
\(554\) 11.9894 + 36.8994i 0.509379 + 1.56771i
\(555\) 0 0
\(556\) −2.92705 + 2.12663i −0.124135 + 0.0901891i
\(557\) 9.43769 + 29.0462i 0.399888 + 1.23073i 0.925089 + 0.379750i \(0.123990\pi\)
−0.525201 + 0.850978i \(0.676010\pi\)
\(558\) 4.42705 13.6251i 0.187412 0.576795i
\(559\) 2.64590 + 1.92236i 0.111910 + 0.0813071i
\(560\) 0 0
\(561\) 24.1803 5.42882i 1.02089 0.229205i
\(562\) 5.38197 0.227025
\(563\) −14.4271 10.4819i −0.608028 0.441758i 0.240692 0.970602i \(-0.422626\pi\)
−0.848719 + 0.528844i \(0.822626\pi\)
\(564\) 1.79180 5.51458i 0.0754482 0.232206i
\(565\) 0 0
\(566\) −35.4615 + 25.7643i −1.49056 + 1.08295i
\(567\) 2.42705 1.76336i 0.101927 0.0740540i
\(568\) 1.01722 + 3.13068i 0.0426816 + 0.131361i
\(569\) 4.79837 14.7679i 0.201158 0.619102i −0.798691 0.601741i \(-0.794474\pi\)
0.999849 0.0173602i \(-0.00552620\pi\)
\(570\) 0 0
\(571\) 13.5836 0.568456 0.284228 0.958757i \(-0.408263\pi\)
0.284228 + 0.958757i \(0.408263\pi\)
\(572\) −3.48936 1.50609i −0.145897 0.0629726i
\(573\) −15.7426 −0.657658
\(574\) 0.927051 + 0.673542i 0.0386944 + 0.0281131i
\(575\) 0 0
\(576\) 1.30902 + 4.02874i 0.0545424 + 0.167864i
\(577\) −16.3541 + 11.8820i −0.680830 + 0.494652i −0.873633 0.486585i \(-0.838242\pi\)
0.192803 + 0.981238i \(0.438242\pi\)
\(578\) 50.8328 36.9322i 2.11437 1.53618i
\(579\) 5.70820 + 17.5680i 0.237225 + 0.730103i
\(580\) 0 0
\(581\) −25.1976 18.3071i −1.04537 0.759506i
\(582\) 16.8541 0.698625
\(583\) −1.03444 + 1.17557i −0.0428422 + 0.0486872i
\(584\) 15.3262 0.634204
\(585\) 0 0
\(586\) −9.70820 + 29.8788i −0.401042 + 1.23428i
\(587\) −10.6008 32.6259i −0.437542 1.34662i −0.890459 0.455064i \(-0.849616\pi\)
0.452916 0.891553i \(-0.350384\pi\)
\(588\) 1.00000 0.726543i 0.0412393 0.0299621i
\(589\) −19.7984 + 14.3844i −0.815778 + 0.592697i
\(590\) 0 0
\(591\) 3.00000 9.23305i 0.123404 0.379797i
\(592\) −34.7705 25.2623i −1.42906 1.03827i
\(593\) −25.5066 −1.04743 −0.523715 0.851894i \(-0.675454\pi\)
−0.523715 + 0.851894i \(0.675454\pi\)
\(594\) 0.500000 5.34307i 0.0205152 0.219229i
\(595\) 0 0
\(596\) −8.09017 5.87785i −0.331386 0.240766i
\(597\) 2.56231 7.88597i 0.104868 0.322751i
\(598\) 7.06231 + 21.7355i 0.288799 + 0.888832i
\(599\) −27.8885 + 20.2622i −1.13950 + 0.827892i −0.987049 0.160420i \(-0.948715\pi\)
−0.152446 + 0.988312i \(0.548715\pi\)
\(600\) 0 0
\(601\) −9.07953 27.9439i −0.370362 1.13986i −0.946555 0.322542i \(-0.895462\pi\)
0.576193 0.817313i \(-0.304538\pi\)
\(602\) −2.64590 + 8.14324i −0.107839 + 0.331894i
\(603\) −7.04508 5.11855i −0.286898 0.208444i
\(604\) −5.67376 −0.230862
\(605\) 0 0
\(606\) −1.76393 −0.0716548
\(607\) 23.3435 + 16.9600i 0.947482 + 0.688386i 0.950210 0.311610i \(-0.100868\pi\)
−0.00272816 + 0.999996i \(0.500868\pi\)
\(608\) −2.88854 + 8.89002i −0.117146 + 0.360538i
\(609\) 3.35410 + 10.3229i 0.135915 + 0.418304i
\(610\) 0 0
\(611\) 14.0729 10.2246i 0.569331 0.413643i
\(612\) −1.42705 4.39201i −0.0576851 0.177537i
\(613\) −7.71885 + 23.7562i −0.311761 + 0.959503i 0.665306 + 0.746571i \(0.268301\pi\)
−0.977067 + 0.212932i \(0.931699\pi\)
\(614\) −20.7984 15.1109i −0.839354 0.609826i
\(615\) 0 0
\(616\) −2.07295 + 22.1518i −0.0835215 + 0.892522i
\(617\) −9.05573 −0.364570 −0.182285 0.983246i \(-0.558349\pi\)
−0.182285 + 0.983246i \(0.558349\pi\)
\(618\) 19.8713 + 14.4374i 0.799342 + 0.580756i
\(619\) 0.815595 2.51014i 0.0327815 0.100891i −0.933327 0.359028i \(-0.883108\pi\)
0.966108 + 0.258136i \(0.0831084\pi\)
\(620\) 0 0
\(621\) −6.16312 + 4.47777i −0.247317 + 0.179687i
\(622\) −24.2533 + 17.6210i −0.972468 + 0.706540i
\(623\) −2.37539 7.31069i −0.0951679 0.292897i
\(624\) 2.78115 8.55951i 0.111335 0.342655i
\(625\) 0 0
\(626\) 49.6869 1.98589
\(627\) −6.05573 + 6.88191i −0.241842 + 0.274837i
\(628\) −11.0000 −0.438948
\(629\) −53.5238 38.8873i −2.13413 1.55054i
\(630\) 0 0
\(631\) −15.1976 46.7733i −0.605005 1.86201i −0.496754 0.867891i \(-0.665475\pi\)
−0.108251 0.994124i \(-0.534525\pi\)
\(632\) 13.6803 9.93935i 0.544175 0.395366i
\(633\) 10.6631 7.74721i 0.423821 0.307924i
\(634\) 4.59017 + 14.1271i 0.182299 + 0.561058i
\(635\) 0 0
\(636\) 0.236068 + 0.171513i 0.00936070 + 0.00680095i
\(637\) 3.70820 0.146924
\(638\) 17.8262 + 7.69421i 0.705748 + 0.304617i
\(639\) 1.47214 0.0582368
\(640\) 0 0
\(641\) 12.1008 37.2425i 0.477953 1.47099i −0.363979 0.931407i \(-0.618582\pi\)
0.841933 0.539582i \(-0.181418\pi\)
\(642\) −8.20820 25.2623i −0.323952 0.997022i
\(643\) 16.4894 11.9802i 0.650277 0.472454i −0.213089 0.977033i \(-0.568352\pi\)
0.863365 + 0.504579i \(0.168352\pi\)
\(644\) −11.4271 + 8.30224i −0.450289 + 0.327154i
\(645\) 0 0
\(646\) −10.3262 + 31.7809i −0.406280 + 1.25040i
\(647\) 10.6803 + 7.75972i 0.419887 + 0.305066i 0.777593 0.628768i \(-0.216441\pi\)
−0.357705 + 0.933835i \(0.616441\pi\)
\(648\) 2.23607 0.0878410
\(649\) −13.4164 + 3.01217i −0.526640 + 0.118238i
\(650\) 0 0
\(651\) 21.4894 + 15.6129i 0.842234 + 0.611919i
\(652\) −3.26393 + 10.0453i −0.127825 + 0.393406i
\(653\) 1.52786 + 4.70228i 0.0597899 + 0.184015i 0.976491 0.215560i \(-0.0691578\pi\)
−0.916701 + 0.399575i \(0.869158\pi\)
\(654\) −19.6353 + 14.2658i −0.767799 + 0.557839i
\(655\) 0 0
\(656\) 0.354102 + 1.08981i 0.0138254 + 0.0425501i
\(657\) 2.11803 6.51864i 0.0826324 0.254316i
\(658\) 36.8435 + 26.7683i 1.43631 + 1.04354i
\(659\) −44.0689 −1.71668 −0.858340 0.513081i \(-0.828504\pi\)
−0.858340 + 0.513081i \(0.828504\pi\)
\(660\) 0 0
\(661\) −3.00000 −0.116686 −0.0583432 0.998297i \(-0.518582\pi\)
−0.0583432 + 0.998297i \(0.518582\pi\)
\(662\) −21.4894 15.6129i −0.835208 0.606814i
\(663\) 4.28115 13.1760i 0.166266 0.511715i
\(664\) −7.17376 22.0786i −0.278396 0.856815i
\(665\) 0 0
\(666\) −11.5902 + 8.42075i −0.449110 + 0.326297i
\(667\) −8.51722 26.2133i −0.329788 1.01498i
\(668\) 4.00000 12.3107i 0.154765 0.476317i
\(669\) 10.2812 + 7.46969i 0.397492 + 0.288795i
\(670\) 0 0
\(671\) −9.74671 16.4455i −0.376268 0.634871i
\(672\) 10.1459 0.391387
\(673\) −18.2082 13.2290i −0.701875 0.509942i 0.178668 0.983910i \(-0.442821\pi\)
−0.880542 + 0.473968i \(0.842821\pi\)
\(674\) −11.8541 + 36.4832i −0.456603 + 1.40528i
\(675\) 0 0
\(676\) 4.78115 3.47371i 0.183890 0.133604i
\(677\) −6.09017 + 4.42477i −0.234064 + 0.170058i −0.698635 0.715479i \(-0.746209\pi\)
0.464570 + 0.885536i \(0.346209\pi\)
\(678\) −4.23607 13.0373i −0.162685 0.500694i
\(679\) −9.65654 + 29.7198i −0.370584 + 1.14054i
\(680\) 0 0
\(681\) −14.5623 −0.558029
\(682\) 46.3607 10.4086i 1.77524 0.398567i
\(683\) 12.7082 0.486266 0.243133 0.969993i \(-0.421825\pi\)
0.243133 + 0.969993i \(0.421825\pi\)
\(684\) 1.38197 + 1.00406i 0.0528408 + 0.0383911i
\(685\) 0 0
\(686\) −7.50000 23.0826i −0.286351 0.881299i
\(687\) −8.09017 + 5.87785i −0.308659 + 0.224254i
\(688\) −6.92705 + 5.03280i −0.264091 + 0.191874i
\(689\) 0.270510 + 0.832544i 0.0103056 + 0.0317174i
\(690\) 0 0
\(691\) 19.9894 + 14.5231i 0.760431 + 0.552485i 0.899042 0.437861i \(-0.144264\pi\)
−0.138612 + 0.990347i \(0.544264\pi\)
\(692\) 3.38197 0.128563
\(693\) 9.13525 + 3.94298i 0.347020 + 0.149782i
\(694\) −19.9443 −0.757074
\(695\) 0 0
\(696\) −2.50000 + 7.69421i −0.0947623 + 0.291648i
\(697\) 0.545085 + 1.67760i 0.0206466 + 0.0635436i
\(698\) 37.8885 27.5276i 1.43410 1.04194i
\(699\) 5.11803 3.71847i 0.193582 0.140645i
\(700\) 0 0
\(701\) 4.39919 13.5393i 0.166155 0.511373i −0.832965 0.553326i \(-0.813358\pi\)
0.999120 + 0.0419539i \(0.0133582\pi\)
\(702\) −2.42705 1.76336i −0.0916031 0.0665536i
\(703\) 24.4721 0.922984
\(704\) −9.28115 + 10.5474i −0.349797 + 0.397519i
\(705\) 0 0
\(706\) 11.6353 + 8.45351i 0.437899 + 0.318152i
\(707\) 1.01064 3.11044i 0.0380091 0.116980i
\(708\) 0.791796 + 2.43690i 0.0297575 + 0.0915842i
\(709\) 7.66312 5.56758i 0.287794 0.209095i −0.434516 0.900664i \(-0.643080\pi\)
0.722310 + 0.691569i \(0.243080\pi\)
\(710\) 0 0
\(711\) −2.33688 7.19218i −0.0876399 0.269728i
\(712\) 1.77051 5.44907i 0.0663527 0.204212i
\(713\) −54.5689 39.6466i −2.04362 1.48478i
\(714\) 36.2705 1.35739
\(715\) 0 0
\(716\) −12.4377 −0.464818
\(717\) −16.7082 12.1392i −0.623979 0.453348i
\(718\) −9.10739 + 28.0297i −0.339885 + 1.04606i
\(719\) −8.05166 24.7805i −0.300276 0.924156i −0.981398 0.191985i \(-0.938507\pi\)
0.681121 0.732170i \(-0.261493\pi\)
\(720\) 0 0
\(721\) −36.8435 + 26.7683i −1.37212 + 0.996905i
\(722\) 5.68034 + 17.4823i 0.211400 + 0.650623i
\(723\) −2.42705 + 7.46969i −0.0902630 + 0.277801i
\(724\) 6.39919 + 4.64928i 0.237824 + 0.172789i
\(725\) 0 0
\(726\) 16.0902 7.60845i 0.597162 0.282376i
\(727\) −0.236068 −0.00875528 −0.00437764 0.999990i \(-0.501393\pi\)
−0.00437764 + 0.999990i \(0.501393\pi\)
\(728\) 10.0623 + 7.31069i 0.372934 + 0.270952i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 0 0
\(731\) −10.6631 + 7.74721i −0.394390 + 0.286541i
\(732\) −2.88197 + 2.09387i −0.106521 + 0.0773917i
\(733\) −1.98936 6.12261i −0.0734786 0.226144i 0.907572 0.419897i \(-0.137934\pi\)
−0.981050 + 0.193753i \(0.937934\pi\)
\(734\) −9.41641 + 28.9807i −0.347566 + 1.06970i
\(735\) 0 0
\(736\) −25.7639 −0.949671
\(737\) 2.69098 28.7562i 0.0991236 1.05925i
\(738\) 0.381966 0.0140604
\(739\) −35.8156 26.0216i −1.31750 0.957218i −0.999960 0.00897282i \(-0.997144\pi\)
−0.317538 0.948245i \(-0.602856\pi\)
\(740\) 0 0
\(741\) 1.58359 + 4.87380i 0.0581747 + 0.179043i
\(742\) −1.85410 + 1.34708i −0.0680662 + 0.0494530i
\(743\) −30.0795 + 21.8541i −1.10351 + 0.801748i −0.981629 0.190797i \(-0.938893\pi\)
−0.121881 + 0.992545i \(0.538893\pi\)
\(744\) 6.11803 + 18.8294i 0.224298 + 0.690318i
\(745\) 0 0
\(746\) −22.7984 16.5640i −0.834708 0.606451i
\(747\) −10.3820 −0.379856
\(748\) 10.1180 11.4984i 0.369952 0.420424i
\(749\) 49.2492 1.79953
\(750\) 0 0
\(751\) −5.39919 + 16.6170i −0.197019 + 0.606363i 0.802928 + 0.596076i \(0.203274\pi\)
−0.999947 + 0.0102865i \(0.996726\pi\)
\(752\) 14.0729 + 43.3121i 0.513188 + 1.57943i
\(753\) −16.6353 + 12.0862i −0.606222 + 0.440446i
\(754\) 8.78115 6.37988i 0.319791 0.232342i
\(755\) 0 0
\(756\) 0.572949 1.76336i 0.0208380 0.0641326i
\(757\) −31.5795 22.9439i −1.14778 0.833909i −0.159594 0.987183i \(-0.551018\pi\)
−0.988184 + 0.153274i \(0.951018\pi\)
\(758\) 37.5623 1.36432
\(759\) −23.1976 10.0126i −0.842018 0.363434i
\(760\) 0 0
\(761\) 0.0901699 + 0.0655123i 0.00326866 + 0.00237482i 0.589418 0.807828i \(-0.299357\pi\)
−0.586150 + 0.810203i \(0.699357\pi\)
\(762\) −3.30902 + 10.1841i −0.119873 + 0.368931i
\(763\) −13.9058 42.7975i −0.503422 1.54938i
\(764\) −7.87132 + 5.71885i −0.284774 + 0.206901i
\(765\) 0 0
\(766\) −10.7639 33.1280i −0.388917 1.19696i
\(767\) −2.37539 + 7.31069i −0.0857703 + 0.263974i
\(768\) 10.9721 + 7.97172i 0.395923 + 0.287655i
\(769\) −24.1459 −0.870723 −0.435362 0.900256i \(-0.643380\pi\)
−0.435362 + 0.900256i \(0.643380\pi\)
\(770\) 0 0
\(771\) 10.0344 0.361382
\(772\) 9.23607 + 6.71040i 0.332413 + 0.241512i
\(773\) 6.69098 20.5927i 0.240658 0.740669i −0.755662 0.654961i \(-0.772685\pi\)
0.996320 0.0857076i \(-0.0273151\pi\)
\(774\) 0.881966 + 2.71441i 0.0317016 + 0.0975675i
\(775\) 0 0
\(776\) −18.8435 + 13.6906i −0.676441 + 0.491463i
\(777\) −8.20820 25.2623i −0.294468 0.906278i
\(778\) 9.04508 27.8379i 0.324282 0.998037i
\(779\) −0.527864 0.383516i −0.0189127 0.0137409i
\(780\) 0 0
\(781\) 2.48936 + 4.20025i 0.0890762 + 0.150297i
\(782\) −92.1033 −3.29361
\(783\) 2.92705 + 2.12663i 0.104604 + 0.0759994i
\(784\) −3.00000 + 9.23305i −0.107143 + 0.329752i
\(785\) 0 0
\(786\) −9.59017 + 6.96767i −0.342070 + 0.248528i
\(787\) −20.7254 + 15.0579i −0.738782 + 0.536756i −0.892329 0.451385i \(-0.850930\pi\)
0.153548 + 0.988141i \(0.450930\pi\)
\(788\) −1.85410 5.70634i −0.0660496 0.203280i
\(789\) −3.43769 + 10.5801i −0.122385 + 0.376663i
\(790\) 0 0
\(791\) 25.4164 0.903703
\(792\) 3.78115 + 6.37988i 0.134357 + 0.226699i
\(793\) −10.6869 −0.379504
\(794\) 25.6074 + 18.6049i 0.908772 + 0.660262i
\(795\) 0 0
\(796\) −1.58359 4.87380i −0.0561289 0.172747i
\(797\) −33.4894 + 24.3314i −1.18625 + 0.861864i −0.992863 0.119258i \(-0.961948\pi\)
−0.193391 + 0.981122i \(0.561948\pi\)
\(798\) −10.8541 + 7.88597i −0.384231 + 0.279160i
\(799\) 21.6631 + 66.6722i 0.766386 + 2.35869i
\(800\) 0 0
\(801\) −2.07295 1.50609i −0.0732441 0.0532149i
\(802\) −1.32624 −0.0468311
\(803\) 22.1803 4.97980i 0.782727 0.175733i
\(804\) −5.38197 −0.189807
\(805\) 0 0
\(806\) 8.20820 25.2623i 0.289122 0.889825i
\(807\) 0.163119 + 0.502029i 0.00574206 + 0.0176722i
\(808\) 1.97214 1.43284i 0.0693795 0.0504072i
\(809\) −1.80902 + 1.31433i −0.0636017 + 0.0462093i −0.619132 0.785287i \(-0.712515\pi\)
0.555530 + 0.831496i \(0.312515\pi\)
\(810\) 0 0
\(811\) −6.09017 + 18.7436i −0.213855 + 0.658177i 0.785378 + 0.619016i \(0.212469\pi\)
−0.999233 + 0.0391610i \(0.987531\pi\)
\(812\) 5.42705 + 3.94298i 0.190452 + 0.138372i
\(813\) 22.2705 0.781061
\(814\) −43.6246 18.8294i −1.52904 0.659969i
\(815\) 0 0
\(816\) 29.3435 + 21.3193i 1.02723 + 0.746324i
\(817\) 1.50658 4.63677i 0.0527085 0.162220i
\(818\) 5.06231 + 15.5802i 0.176999 + 0.544748i
\(819\) 4.50000 3.26944i 0.157243 0.114244i
\(820\) 0 0
\(821\) 17.4271 + 53.6349i 0.608208 + 1.87187i 0.473018 + 0.881053i \(0.343165\pi\)
0.135191 + 0.990820i \(0.456835\pi\)
\(822\) −6.39919 + 19.6947i −0.223197 + 0.686931i
\(823\) 2.80902 + 2.04087i 0.0979162 + 0.0711403i 0.635666 0.771964i \(-0.280726\pi\)
−0.537750 + 0.843104i \(0.680726\pi\)
\(824\) −33.9443 −1.18250
\(825\) 0 0
\(826\) −20.1246 −0.700225
\(827\) 37.9164 + 27.5479i 1.31848 + 0.957934i 0.999950 + 0.0100219i \(0.00319014\pi\)
0.318533 + 0.947912i \(0.396810\pi\)
\(828\) −1.45492 + 4.47777i −0.0505618 + 0.155613i
\(829\) −7.82624 24.0867i −0.271816 0.836565i −0.990044 0.140757i \(-0.955046\pi\)
0.718228 0.695808i \(-0.244954\pi\)
\(830\) 0 0
\(831\) −19.3992 + 14.0943i −0.672950 + 0.488927i
\(832\) 2.42705 + 7.46969i 0.0841429 + 0.258965i
\(833\) −4.61803 + 14.2128i −0.160005 + 0.492446i
\(834\) −7.66312 5.56758i −0.265352 0.192790i
\(835\) 0 0
\(836\) −0.527864 + 5.64083i −0.0182566 + 0.195092i
\(837\) 8.85410 0.306043
\(838\) 24.7984 + 18.0171i 0.856646 + 0.622389i
\(839\) 7.66312 23.5847i 0.264560 0.814233i −0.727234 0.686389i \(-0.759195\pi\)
0.991794 0.127843i \(-0.0408054\pi\)
\(840\) 0 0
\(841\) 12.8713 9.35156i 0.443839 0.322468i
\(842\) −9.51722 + 6.91467i −0.327985 + 0.238295i
\(843\) 1.02786 + 3.16344i 0.0354015 + 0.108955i
\(844\) 2.51722 7.74721i 0.0866463 0.266670i
\(845\) 0 0
\(846\) 15.1803 0.521911
\(847\) 4.19756 + 32.7319i 0.144230 + 1.12468i
\(848\) −2.29180 −0.0787006
\(849\) −21.9164 15.9232i −0.752169 0.546483i
\(850\) 0 0
\(851\) 20.8435 + 64.1496i 0.714505 + 2.19902i
\(852\) 0.736068 0.534785i 0.0252173 0.0183214i
\(853\) −43.4336 + 31.5564i −1.48714 + 1.08047i −0.511971 + 0.859003i \(0.671085\pi\)
−0.975168 + 0.221467i \(0.928915\pi\)
\(854\) −8.64590 26.6093i −0.295857 0.910553i
\(855\) 0 0
\(856\) 29.6976 + 21.5765i 1.01504 + 0.737471i
\(857\) 10.0902 0.344674 0.172337 0.985038i \(-0.444868\pi\)
0.172337 + 0.985038i \(0.444868\pi\)
\(858\) 0.927051 9.90659i 0.0316490 0.338205i
\(859\) −2.56231 −0.0874247 −0.0437124 0.999044i \(-0.513919\pi\)
−0.0437124 + 0.999044i \(0.513919\pi\)
\(860\) 0 0
\(861\) −0.218847 + 0.673542i −0.00745829 + 0.0229542i
\(862\) −8.07295 24.8460i −0.274966 0.846258i
\(863\) −28.0066 + 20.3480i −0.953355 + 0.692653i −0.951598 0.307346i \(-0.900559\pi\)
−0.00175700 + 0.999998i \(0.500559\pi\)
\(864\) 2.73607 1.98787i 0.0930829 0.0676287i
\(865\) 0 0
\(866\) −13.5902 + 41.8262i −0.461813 + 1.42131i
\(867\) 31.4164 + 22.8254i 1.06696 + 0.775190i
\(868\) 16.4164 0.557209
\(869\) 16.5689 18.8294i 0.562061 0.638743i
\(870\) 0 0
\(871\) −13.0623 9.49032i −0.442599 0.321567i
\(872\) 10.3647 31.8994i 0.350995 1.08025i
\(873\) 3.21885 + 9.90659i 0.108941 + 0.335287i
\(874\) 27.5623 20.0252i 0.932309 0.677362i
\(875\) 0 0
\(876\) −1.30902 4.02874i −0.0442276 0.136119i
\(877\) −9.14183 + 28.1357i −0.308698 + 0.950074i 0.669574 + 0.742746i \(0.266477\pi\)
−0.978271 + 0.207328i \(0.933523\pi\)
\(878\) 9.73607 + 7.07367i 0.328576 + 0.238725i
\(879\) −19.4164 −0.654899
\(880\) 0 0
\(881\) −34.1803 −1.15156 −0.575782 0.817603i \(-0.695302\pi\)
−0.575782 + 0.817603i \(0.695302\pi\)
\(882\) 2.61803 + 1.90211i 0.0881538 + 0.0640475i
\(883\) −5.15654 + 15.8702i −0.173531 + 0.534075i −0.999563 0.0295485i \(-0.990593\pi\)
0.826032 + 0.563623i \(0.190593\pi\)
\(884\) −2.64590 8.14324i −0.0889912 0.273887i
\(885\) 0 0
\(886\) 36.0066 26.1603i 1.20966 0.878873i
\(887\) 5.61803 + 17.2905i 0.188635 + 0.580559i 0.999992 0.00399187i \(-0.00127066\pi\)
−0.811357 + 0.584551i \(0.801271\pi\)
\(888\) 6.11803 18.8294i 0.205308 0.631872i
\(889\) −16.0623 11.6699i −0.538712 0.391398i
\(890\) 0 0
\(891\) 3.23607 0.726543i 0.108412 0.0243401i
\(892\) 7.85410 0.262975
\(893\) −20.9787 15.2419i −0.702026 0.510052i
\(894\) 8.09017 24.8990i 0.270576 0.832747i
\(895\) 0 0
\(896\) −33.0517 + 24.0134i −1.10418 + 0.802233i
\(897\) −11.4271 + 8.30224i −0.381538 + 0.277204i
\(898\) −7.23607 22.2703i −0.241471 0.743170i
\(899\) −9.89919 + 30.4666i −0.330156 + 1.01612i
\(900\) 0 0
\(901\) −3.52786 −0.117530
\(902\) 0.645898 + 1.08981i 0.0215061 + 0.0362868i
\(903\) −5.29180 −0.176100
\(904\) 15.3262 + 11.1352i 0.509743 + 0.370350i
\(905\) 0 0
\(906\) −4.59017 14.1271i −0.152498 0.469341i
\(907\) −43.5517 + 31.6421i −1.44611 + 1.05066i −0.459388 + 0.888236i \(0.651931\pi\)
−0.986721 + 0.162424i \(0.948069\pi\)
\(908\) −7.28115 + 5.29007i −0.241634 + 0.175557i
\(909\) −0.336881 1.03681i −0.0111736 0.0343889i
\(910\) 0 0
\(911\) −43.7148 31.7606i −1.44834 1.05228i −0.986217 0.165459i \(-0.947089\pi\)
−0.462119 0.886818i \(-0.652911\pi\)
\(912\) −13.4164 −0.444262
\(913\) −17.5557 29.6215i −0.581010 0.980329i
\(914\) 38.0689 1.25921
\(915\) 0 0
\(916\) −1.90983 + 5.87785i −0.0631026 + 0.194210i
\(917\) −6.79180 20.9030i −0.224285 0.690278i
\(918\) 9.78115 7.10642i 0.322826 0.234547i
\(919\) −12.8262 + 9.31881i −0.423099 + 0.307399i −0.778883 0.627169i \(-0.784214\pi\)
0.355785 + 0.934568i \(0.384214\pi\)
\(920\) 0 0
\(921\) 4.90983 15.1109i 0.161784 0.497921i
\(922\) −12.0172 8.73102i −0.395766 0.287541i
\(923\) 2.72949 0.0898423
\(924\) 6.00000 1.34708i 0.197386 0.0443158i
\(925\) 0 0
\(926\) 12.1631 + 8.83702i 0.399705 + 0.290403i
\(927\) −4.69098 + 14.4374i −0.154072 + 0.474185i
\(928\) 3.78115 + 11.6372i 0.124122 + 0.382010i
\(929\) 44.0689 32.0179i 1.44585 1.05047i 0.459075 0.888398i \(-0.348181\pi\)
0.986778 0.162076i \(-0.0518191\pi\)
\(930\) 0 0
\(931\) −1.70820 5.25731i −0.0559841 0.172301i
\(932\) 1.20820 3.71847i 0.0395760 0.121803i
\(933\) −14.9894 10.8904i −0.490730 0.356536i
\(934\) −8.03444 −0.262895
\(935\) 0 0
\(936\) 4.14590 0.135513
\(937\) 29.4615 + 21.4050i 0.962465 + 0.699272i 0.953722 0.300690i \(-0.0972170\pi\)
0.00874309 + 0.999962i \(0.497217\pi\)
\(938\) 13.0623 40.2016i 0.426499 1.31263i
\(939\) 9.48936 + 29.2052i 0.309673 + 0.953077i
\(940\) 0 0
\(941\) 2.42705 1.76336i 0.0791196 0.0574838i −0.547522 0.836791i \(-0.684429\pi\)
0.626642 + 0.779307i \(0.284429\pi\)
\(942\) −8.89919 27.3889i −0.289951 0.892378i
\(943\) 0.555728 1.71036i 0.0180970 0.0556968i
\(944\) −16.2812 11.8290i −0.529906 0.385000i
\(945\) 0 0
\(946\) −6.25329 + 7.10642i −0.203312 + 0.231050i
\(947\) −21.4934 −0.698442 −0.349221 0.937040i \(-0.613554\pi\)
−0.349221 + 0.937040i \(0.613554\pi\)
\(948\) −3.78115 2.74717i −0.122806 0.0892239i
\(949\) 3.92705 12.0862i 0.127477 0.392335i
\(950\) 0 0
\(951\) −7.42705 + 5.39607i −0.240839 + 0.174980i
\(952\) −40.5517 + 29.4625i −1.31429 + 0.954885i
\(953\) 17.2188 + 52.9942i 0.557773 + 1.71665i 0.688505 + 0.725232i \(0.258267\pi\)
−0.130732 + 0.991418i \(0.541733\pi\)
\(954\) −0.236068 + 0.726543i −0.00764298 + 0.0235227i
\(955\) 0 0
\(956\) −12.7639 −0.412815
\(957\) −1.11803 + 11.9475i −0.0361409 + 0.386207i
\(958\) −11.9098 −0.384789
\(959\) −31.0623 22.5681i −1.00305 0.728762i
\(960\) 0 0
\(961\) 14.6459 + 45.0754i 0.472448 + 1.45405i
\(962\) −21.4894 + 15.6129i −0.692845 + 0.503381i
\(963\) 13.2812 9.64932i 0.427979 0.310945i
\(964\) 1.50000 + 4.61653i 0.0483117 + 0.148688i
\(965\) 0 0
\(966\) −29.9164 21.7355i −0.962545 0.699330i
\(967\) 5.21478 0.167696 0.0838480 0.996479i \(-0.473279\pi\)
0.0838480 + 0.996479i \(0.473279\pi\)
\(968\) −11.8090 + 21.5765i −0.379556 + 0.693496i
\(969\) −20.6525 −0.663453
\(970\) 0 0
\(971\) 18.3820 56.5739i 0.589905 1.81554i 0.0112975 0.999936i \(-0.496404\pi\)
0.578608 0.815606i \(-0.303596\pi\)
\(972\) −0.190983 0.587785i −0.00612578 0.0188532i
\(973\) 14.2082 10.3229i 0.455494 0.330936i
\(974\) 1.66312 1.20833i 0.0532898 0.0387173i
\(975\) 0 0
\(976\) 8.64590 26.6093i 0.276748 0.851744i
\(977\) −29.3435 21.3193i −0.938780 0.682064i 0.00934637 0.999956i \(-0.497025\pi\)
−0.948127 + 0.317892i \(0.897025\pi\)
\(978\) −27.6525 −0.884229
\(979\) 0.791796 8.46124i 0.0253059 0.270422i
\(980\) 0 0
\(981\) −12.1353 8.81678i −0.387449 0.281498i
\(982\) 6.92705 21.3193i 0.221051 0.680325i
\(983\) 0.270510 + 0.832544i 0.00862792 + 0.0265540i 0.955278 0.295710i \(-0.0955562\pi\)
−0.946650 + 0.322264i \(0.895556\pi\)
\(984\) −0.427051 + 0.310271i −0.0136139 + 0.00989107i
\(985\) 0 0
\(986\) 13.5172 + 41.6017i 0.430476 + 1.32487i
\(987\) −8.69756 + 26.7683i −0.276846 + 0.852046i
\(988\) 2.56231 + 1.86162i 0.0815178 + 0.0592262i
\(989\) 13.4377 0.427294
\(990\) 0 0
\(991\) −48.4508 −1.53909 −0.769546 0.638591i \(-0.779517\pi\)
−0.769546 + 0.638591i \(0.779517\pi\)
\(992\) 24.2254 + 17.6008i 0.769158 + 0.558826i
\(993\) 5.07295 15.6129i 0.160985 0.495461i
\(994\) 2.20820 + 6.79615i 0.0700400 + 0.215561i
\(995\) 0 0
\(996\) −5.19098 + 3.77147i −0.164483 + 0.119504i
\(997\) −4.54508 13.9883i −0.143944 0.443015i 0.852929 0.522026i \(-0.174824\pi\)
−0.996874 + 0.0790113i \(0.974824\pi\)
\(998\) −5.91641 + 18.2088i −0.187281 + 0.576390i
\(999\) −7.16312 5.20431i −0.226631 0.164657i
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 825.2.n.e.301.1 yes 4
5.2 odd 4 825.2.bx.a.499.1 8
5.3 odd 4 825.2.bx.a.499.2 8
5.4 even 2 825.2.n.a.301.1 4
11.3 even 5 inner 825.2.n.e.751.1 yes 4
11.5 even 5 9075.2.a.y.1.1 2
11.6 odd 10 9075.2.a.bu.1.2 2
55.3 odd 20 825.2.bx.a.124.1 8
55.14 even 10 825.2.n.a.751.1 yes 4
55.39 odd 10 9075.2.a.bb.1.1 2
55.47 odd 20 825.2.bx.a.124.2 8
55.49 even 10 9075.2.a.bz.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
825.2.n.a.301.1 4 5.4 even 2
825.2.n.a.751.1 yes 4 55.14 even 10
825.2.n.e.301.1 yes 4 1.1 even 1 trivial
825.2.n.e.751.1 yes 4 11.3 even 5 inner
825.2.bx.a.124.1 8 55.3 odd 20
825.2.bx.a.124.2 8 55.47 odd 20
825.2.bx.a.499.1 8 5.2 odd 4
825.2.bx.a.499.2 8 5.3 odd 4
9075.2.a.y.1.1 2 11.5 even 5
9075.2.a.bb.1.1 2 55.39 odd 10
9075.2.a.bu.1.2 2 11.6 odd 10
9075.2.a.bz.1.2 2 55.49 even 10