Properties

Label 375.2.g.e.76.3
Level $375$
Weight $2$
Character 375.76
Analytic conductor $2.994$
Analytic rank $0$
Dimension $16$
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] = [375,2,Mod(76,375)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(375, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("375.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.99439007580\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 76.3
Root \(-1.08982i\) of defining polynomial
Character \(\chi\) \(=\) 375.76
Dual form 375.2.g.e.301.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.881682 + 0.640580i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.251013 - 0.772537i) q^{4} +(-0.336773 + 1.03648i) q^{6} +3.08724 q^{7} +(0.947104 - 2.91489i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(0.881682 + 0.640580i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.251013 - 0.772537i) q^{4} +(-0.336773 + 1.03648i) q^{6} +3.08724 q^{7} +(0.947104 - 2.91489i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.929002 + 0.674959i) q^{11} +(0.657159 - 0.477454i) q^{12} +(3.30042 - 2.39789i) q^{13} +(2.72197 + 1.97763i) q^{14} +(1.38794 - 1.00840i) q^{16} +(-1.43000 + 4.40109i) q^{17} -1.08982 q^{18} +(-1.84452 + 5.67685i) q^{19} +(0.954011 + 2.93614i) q^{21} +(0.386719 + 1.19020i) q^{22} +(-1.88152 - 1.36700i) q^{23} +3.06489 q^{24} +4.44596 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.774937 - 2.38501i) q^{28} +(-1.63290 - 5.02554i) q^{29} +(-0.182097 + 0.560438i) q^{31} -4.26010 q^{32} +(-0.354847 + 1.09211i) q^{33} +(-4.08005 + 2.96433i) q^{34} +(0.657159 + 0.477454i) q^{36} +(9.22252 - 6.70056i) q^{37} +(-5.26275 + 3.82361i) q^{38} +(3.30042 + 2.39789i) q^{39} +(-7.67919 + 5.57926i) q^{41} +(-1.03970 + 3.19987i) q^{42} -2.42954 q^{43} +(0.288240 - 0.887112i) q^{44} +(-0.783227 - 2.41052i) q^{46} +(-1.86955 - 5.75387i) q^{47} +(1.38794 + 1.00840i) q^{48} +2.53108 q^{49} -4.62758 q^{51} +(-2.68091 - 1.94779i) q^{52} +(1.00239 + 3.08503i) q^{53} +(-0.336773 - 1.03648i) q^{54} +(2.92394 - 8.99897i) q^{56} -5.96899 q^{57} +(1.77956 - 5.47693i) q^{58} +(-2.57785 + 1.87292i) q^{59} +(-11.1201 - 8.07922i) q^{61} +(-0.519557 + 0.377480i) q^{62} +(-2.49763 + 1.81464i) q^{63} +(-6.53194 - 4.74573i) q^{64} +(-1.01244 + 0.735584i) q^{66} +(-0.976103 + 3.00414i) q^{67} +3.75895 q^{68} +(0.718676 - 2.21186i) q^{69} +(1.99795 + 6.14907i) q^{71} +(0.947104 + 2.91489i) q^{72} +(5.83300 + 4.23792i) q^{73} +12.4236 q^{74} +4.84857 q^{76} +(2.86806 + 2.08376i) q^{77} +(1.37388 + 4.22836i) q^{78} +(-3.81246 - 11.7336i) q^{79} +(0.309017 - 0.951057i) q^{81} -10.3446 q^{82} +(-3.82999 + 11.7875i) q^{83} +(2.02881 - 1.47402i) q^{84} +(-2.14208 - 1.55631i) q^{86} +(4.27498 - 3.10596i) q^{87} +(2.84729 - 2.06868i) q^{88} +(-0.877003 - 0.637180i) q^{89} +(10.1892 - 7.40289i) q^{91} +(-0.583776 + 1.79668i) q^{92} -0.589279 q^{93} +(2.03747 - 6.27068i) q^{94} +(-1.31644 - 4.05159i) q^{96} +(-1.39717 - 4.30003i) q^{97} +(2.23161 + 1.62136i) q^{98} -1.14831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.881682 + 0.640580i 0.623444 + 0.452958i 0.854123 0.520072i \(-0.174095\pi\)
−0.230679 + 0.973030i \(0.574095\pi\)
\(3\) 0.309017 + 0.951057i 0.178411 + 0.549093i
\(4\) −0.251013 0.772537i −0.125506 0.386269i
\(5\) 0 0
\(6\) −0.336773 + 1.03648i −0.137487 + 0.423141i
\(7\) 3.08724 1.16687 0.583434 0.812160i \(-0.301709\pi\)
0.583434 + 0.812160i \(0.301709\pi\)
\(8\) 0.947104 2.91489i 0.334852 1.03057i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 0 0
\(11\) 0.929002 + 0.674959i 0.280105 + 0.203508i 0.718963 0.695048i \(-0.244617\pi\)
−0.438858 + 0.898556i \(0.644617\pi\)
\(12\) 0.657159 0.477454i 0.189706 0.137829i
\(13\) 3.30042 2.39789i 0.915372 0.665056i −0.0269961 0.999636i \(-0.508594\pi\)
0.942368 + 0.334579i \(0.108594\pi\)
\(14\) 2.72197 + 1.97763i 0.727477 + 0.528543i
\(15\) 0 0
\(16\) 1.38794 1.00840i 0.346986 0.252100i
\(17\) −1.43000 + 4.40109i −0.346826 + 1.06742i 0.613773 + 0.789482i \(0.289651\pi\)
−0.960599 + 0.277938i \(0.910349\pi\)
\(18\) −1.08982 −0.256873
\(19\) −1.84452 + 5.67685i −0.423162 + 1.30236i 0.481582 + 0.876401i \(0.340062\pi\)
−0.904744 + 0.425957i \(0.859938\pi\)
\(20\) 0 0
\(21\) 0.954011 + 2.93614i 0.208182 + 0.640719i
\(22\) 0.386719 + 1.19020i 0.0824488 + 0.253751i
\(23\) −1.88152 1.36700i −0.392324 0.285040i 0.374083 0.927395i \(-0.377957\pi\)
−0.766407 + 0.642355i \(0.777957\pi\)
\(24\) 3.06489 0.625619
\(25\) 0 0
\(26\) 4.44596 0.871925
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) −0.774937 2.38501i −0.146449 0.450725i
\(29\) −1.63290 5.02554i −0.303221 0.933220i −0.980335 0.197341i \(-0.936769\pi\)
0.677113 0.735879i \(-0.263231\pi\)
\(30\) 0 0
\(31\) −0.182097 + 0.560438i −0.0327056 + 0.100658i −0.966077 0.258255i \(-0.916852\pi\)
0.933371 + 0.358913i \(0.116852\pi\)
\(32\) −4.26010 −0.753086
\(33\) −0.354847 + 1.09211i −0.0617709 + 0.190111i
\(34\) −4.08005 + 2.96433i −0.699723 + 0.508379i
\(35\) 0 0
\(36\) 0.657159 + 0.477454i 0.109527 + 0.0795757i
\(37\) 9.22252 6.70056i 1.51617 1.10156i 0.552830 0.833294i \(-0.313548\pi\)
0.963344 0.268271i \(-0.0864521\pi\)
\(38\) −5.26275 + 3.82361i −0.853731 + 0.620272i
\(39\) 3.30042 + 2.39789i 0.528490 + 0.383970i
\(40\) 0 0
\(41\) −7.67919 + 5.57926i −1.19929 + 0.871334i −0.994215 0.107413i \(-0.965743\pi\)
−0.205073 + 0.978747i \(0.565743\pi\)
\(42\) −1.03970 + 3.19987i −0.160429 + 0.493750i
\(43\) −2.42954 −0.370501 −0.185250 0.982691i \(-0.559310\pi\)
−0.185250 + 0.982691i \(0.559310\pi\)
\(44\) 0.288240 0.887112i 0.0434538 0.133737i
\(45\) 0 0
\(46\) −0.783227 2.41052i −0.115481 0.355412i
\(47\) −1.86955 5.75387i −0.272701 0.839289i −0.989818 0.142336i \(-0.954539\pi\)
0.717117 0.696953i \(-0.245461\pi\)
\(48\) 1.38794 + 1.00840i 0.200332 + 0.145550i
\(49\) 2.53108 0.361583
\(50\) 0 0
\(51\) −4.62758 −0.647990
\(52\) −2.68091 1.94779i −0.371775 0.270111i
\(53\) 1.00239 + 3.08503i 0.137689 + 0.423762i 0.995999 0.0893696i \(-0.0284852\pi\)
−0.858310 + 0.513132i \(0.828485\pi\)
\(54\) −0.336773 1.03648i −0.0458290 0.141047i
\(55\) 0 0
\(56\) 2.92394 8.99897i 0.390728 1.20254i
\(57\) −5.96899 −0.790612
\(58\) 1.77956 5.47693i 0.233668 0.719157i
\(59\) −2.57785 + 1.87292i −0.335607 + 0.243833i −0.742806 0.669507i \(-0.766506\pi\)
0.407199 + 0.913340i \(0.366506\pi\)
\(60\) 0 0
\(61\) −11.1201 8.07922i −1.42378 1.03444i −0.991133 0.132876i \(-0.957579\pi\)
−0.432650 0.901562i \(-0.642421\pi\)
\(62\) −0.519557 + 0.377480i −0.0659838 + 0.0479400i
\(63\) −2.49763 + 1.81464i −0.314672 + 0.228623i
\(64\) −6.53194 4.74573i −0.816493 0.593217i
\(65\) 0 0
\(66\) −1.01244 + 0.735584i −0.124623 + 0.0905441i
\(67\) −0.976103 + 3.00414i −0.119250 + 0.367014i −0.992810 0.119703i \(-0.961806\pi\)
0.873560 + 0.486717i \(0.161806\pi\)
\(68\) 3.75895 0.455840
\(69\) 0.718676 2.21186i 0.0865184 0.266276i
\(70\) 0 0
\(71\) 1.99795 + 6.14907i 0.237113 + 0.729760i 0.996834 + 0.0795103i \(0.0253357\pi\)
−0.759721 + 0.650250i \(0.774664\pi\)
\(72\) 0.947104 + 2.91489i 0.111617 + 0.343523i
\(73\) 5.83300 + 4.23792i 0.682701 + 0.496011i 0.874252 0.485472i \(-0.161352\pi\)
−0.191552 + 0.981482i \(0.561352\pi\)
\(74\) 12.4236 1.44421
\(75\) 0 0
\(76\) 4.84857 0.556169
\(77\) 2.86806 + 2.08376i 0.326845 + 0.237467i
\(78\) 1.37388 + 4.22836i 0.155561 + 0.478768i
\(79\) −3.81246 11.7336i −0.428936 1.32013i −0.899175 0.437590i \(-0.855832\pi\)
0.470239 0.882539i \(-0.344168\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) −10.3446 −1.14237
\(83\) −3.82999 + 11.7875i −0.420396 + 1.29384i 0.486939 + 0.873436i \(0.338113\pi\)
−0.907335 + 0.420409i \(0.861887\pi\)
\(84\) 2.02881 1.47402i 0.221361 0.160829i
\(85\) 0 0
\(86\) −2.14208 1.55631i −0.230986 0.167821i
\(87\) 4.27498 3.10596i 0.458326 0.332993i
\(88\) 2.84729 2.06868i 0.303522 0.220522i
\(89\) −0.877003 0.637180i −0.0929621 0.0675409i 0.540333 0.841451i \(-0.318298\pi\)
−0.633295 + 0.773910i \(0.718298\pi\)
\(90\) 0 0
\(91\) 10.1892 7.40289i 1.06812 0.776034i
\(92\) −0.583776 + 1.79668i −0.0608628 + 0.187317i
\(93\) −0.589279 −0.0611054
\(94\) 2.03747 6.27068i 0.210149 0.646772i
\(95\) 0 0
\(96\) −1.31644 4.05159i −0.134359 0.413514i
\(97\) −1.39717 4.30003i −0.141861 0.436602i 0.854733 0.519067i \(-0.173721\pi\)
−0.996594 + 0.0824653i \(0.973721\pi\)
\(98\) 2.23161 + 1.62136i 0.225426 + 0.163782i
\(99\) −1.14831 −0.115409
\(100\) 0 0
\(101\) −6.61332 −0.658050 −0.329025 0.944321i \(-0.606720\pi\)
−0.329025 + 0.944321i \(0.606720\pi\)
\(102\) −4.08005 2.96433i −0.403985 0.293513i
\(103\) −1.29983 4.00047i −0.128076 0.394178i 0.866373 0.499398i \(-0.166445\pi\)
−0.994449 + 0.105220i \(0.966445\pi\)
\(104\) −3.86375 11.8914i −0.378872 1.16605i
\(105\) 0 0
\(106\) −1.09242 + 3.36213i −0.106105 + 0.326559i
\(107\) 4.01195 0.387849 0.193925 0.981016i \(-0.437878\pi\)
0.193925 + 0.981016i \(0.437878\pi\)
\(108\) −0.251013 + 0.772537i −0.0241537 + 0.0743374i
\(109\) −7.35691 + 5.34511i −0.704664 + 0.511969i −0.881448 0.472281i \(-0.843431\pi\)
0.176784 + 0.984250i \(0.443431\pi\)
\(110\) 0 0
\(111\) 9.22252 + 6.70056i 0.875363 + 0.635989i
\(112\) 4.28492 3.11318i 0.404887 0.294168i
\(113\) 3.03758 2.20693i 0.285751 0.207610i −0.435671 0.900106i \(-0.643489\pi\)
0.721422 + 0.692496i \(0.243489\pi\)
\(114\) −5.26275 3.82361i −0.492902 0.358114i
\(115\) 0 0
\(116\) −3.47254 + 2.52295i −0.322417 + 0.234250i
\(117\) −1.26065 + 3.87988i −0.116547 + 0.358695i
\(118\) −3.47260 −0.319678
\(119\) −4.41476 + 13.5872i −0.404700 + 1.24554i
\(120\) 0 0
\(121\) −2.99171 9.20755i −0.271974 0.837050i
\(122\) −4.62901 14.2466i −0.419091 1.28983i
\(123\) −7.67919 5.57926i −0.692409 0.503065i
\(124\) 0.478668 0.0429856
\(125\) 0 0
\(126\) −3.36454 −0.299737
\(127\) 9.18904 + 6.67623i 0.815395 + 0.592419i 0.915390 0.402569i \(-0.131883\pi\)
−0.0999946 + 0.994988i \(0.531883\pi\)
\(128\) −0.0861909 0.265268i −0.00761827 0.0234466i
\(129\) −0.750768 2.31063i −0.0661014 0.203439i
\(130\) 0 0
\(131\) −0.642289 + 1.97676i −0.0561170 + 0.172711i −0.975186 0.221385i \(-0.928942\pi\)
0.919069 + 0.394096i \(0.128942\pi\)
\(132\) 0.932764 0.0811867
\(133\) −5.69448 + 17.5258i −0.493774 + 1.51968i
\(134\) −2.78500 + 2.02342i −0.240587 + 0.174797i
\(135\) 0 0
\(136\) 11.4743 + 8.33657i 0.983914 + 0.714855i
\(137\) −15.6975 + 11.4049i −1.34113 + 0.974387i −0.341726 + 0.939800i \(0.611012\pi\)
−0.999402 + 0.0345870i \(0.988988\pi\)
\(138\) 2.05051 1.48979i 0.174551 0.126819i
\(139\) 13.8830 + 10.0866i 1.17754 + 0.855531i 0.991892 0.127086i \(-0.0405624\pi\)
0.185646 + 0.982617i \(0.440562\pi\)
\(140\) 0 0
\(141\) 4.89454 3.55609i 0.412194 0.299477i
\(142\) −2.17741 + 6.70137i −0.182724 + 0.562367i
\(143\) 4.68458 0.391744
\(144\) −0.530147 + 1.63162i −0.0441789 + 0.135969i
\(145\) 0 0
\(146\) 2.42812 + 7.47300i 0.200953 + 0.618470i
\(147\) 0.782147 + 2.40720i 0.0645104 + 0.198542i
\(148\) −7.49140 5.44282i −0.615789 0.447397i
\(149\) 0.210127 0.0172143 0.00860714 0.999963i \(-0.497260\pi\)
0.00860714 + 0.999963i \(0.497260\pi\)
\(150\) 0 0
\(151\) −4.05924 −0.330336 −0.165168 0.986265i \(-0.552817\pi\)
−0.165168 + 0.986265i \(0.552817\pi\)
\(152\) 14.8004 + 10.7531i 1.20047 + 0.872194i
\(153\) −1.43000 4.40109i −0.115609 0.355807i
\(154\) 1.19390 + 3.67444i 0.0962070 + 0.296095i
\(155\) 0 0
\(156\) 1.02402 3.15160i 0.0819869 0.252330i
\(157\) −0.440336 −0.0351426 −0.0175713 0.999846i \(-0.505593\pi\)
−0.0175713 + 0.999846i \(0.505593\pi\)
\(158\) 4.15490 12.7875i 0.330546 1.01732i
\(159\) −2.62429 + 1.90666i −0.208119 + 0.151208i
\(160\) 0 0
\(161\) −5.80871 4.22027i −0.457790 0.332604i
\(162\) 0.881682 0.640580i 0.0692715 0.0503287i
\(163\) 2.62210 1.90506i 0.205378 0.149216i −0.480342 0.877081i \(-0.659487\pi\)
0.685720 + 0.727865i \(0.259487\pi\)
\(164\) 6.23776 + 4.53200i 0.487087 + 0.353889i
\(165\) 0 0
\(166\) −10.9277 + 7.93941i −0.848151 + 0.616218i
\(167\) 4.93207 15.1793i 0.381655 1.17461i −0.557223 0.830363i \(-0.688133\pi\)
0.938878 0.344250i \(-0.111867\pi\)
\(168\) 9.46207 0.730015
\(169\) 1.12565 3.46438i 0.0865882 0.266491i
\(170\) 0 0
\(171\) −1.84452 5.67685i −0.141054 0.434119i
\(172\) 0.609844 + 1.87691i 0.0465002 + 0.143113i
\(173\) 0.454497 + 0.330212i 0.0345548 + 0.0251055i 0.604929 0.796280i \(-0.293202\pi\)
−0.570374 + 0.821385i \(0.693202\pi\)
\(174\) 5.75879 0.436573
\(175\) 0 0
\(176\) 1.97003 0.148497
\(177\) −2.57785 1.87292i −0.193763 0.140777i
\(178\) −0.365073 1.12358i −0.0273634 0.0842159i
\(179\) 4.92532 + 15.1586i 0.368136 + 1.13301i 0.947994 + 0.318288i \(0.103108\pi\)
−0.579858 + 0.814718i \(0.696892\pi\)
\(180\) 0 0
\(181\) −6.64001 + 20.4358i −0.493548 + 1.51898i 0.325660 + 0.945487i \(0.394414\pi\)
−0.819208 + 0.573497i \(0.805586\pi\)
\(182\) 13.7258 1.01742
\(183\) 4.24750 13.0725i 0.313984 0.966344i
\(184\) −5.76665 + 4.18972i −0.425123 + 0.308870i
\(185\) 0 0
\(186\) −0.519557 0.377480i −0.0380958 0.0276782i
\(187\) −4.29903 + 3.12343i −0.314376 + 0.228408i
\(188\) −3.97580 + 2.88859i −0.289965 + 0.210672i
\(189\) −2.49763 1.81464i −0.181676 0.131995i
\(190\) 0 0
\(191\) 14.8810 10.8117i 1.07675 0.782304i 0.0996355 0.995024i \(-0.468232\pi\)
0.977113 + 0.212720i \(0.0682323\pi\)
\(192\) 2.49498 7.67876i 0.180060 0.554167i
\(193\) 2.02523 0.145780 0.0728898 0.997340i \(-0.476778\pi\)
0.0728898 + 0.997340i \(0.476778\pi\)
\(194\) 1.52266 4.68626i 0.109320 0.336454i
\(195\) 0 0
\(196\) −0.635333 1.95535i −0.0453809 0.139668i
\(197\) −3.56774 10.9804i −0.254191 0.782319i −0.993988 0.109489i \(-0.965079\pi\)
0.739797 0.672830i \(-0.234921\pi\)
\(198\) −1.01244 0.735584i −0.0719513 0.0522757i
\(199\) 22.9779 1.62886 0.814431 0.580260i \(-0.197049\pi\)
0.814431 + 0.580260i \(0.197049\pi\)
\(200\) 0 0
\(201\) −3.15873 −0.222800
\(202\) −5.83085 4.23636i −0.410257 0.298069i
\(203\) −5.04115 15.5151i −0.353820 1.08894i
\(204\) 1.16158 + 3.57497i 0.0813268 + 0.250298i
\(205\) 0 0
\(206\) 1.41658 4.35979i 0.0986978 0.303761i
\(207\) 2.32568 0.161646
\(208\) 2.16276 6.65628i 0.149960 0.461530i
\(209\) −5.54520 + 4.02882i −0.383570 + 0.278680i
\(210\) 0 0
\(211\) 5.56717 + 4.04479i 0.383260 + 0.278455i 0.762688 0.646767i \(-0.223879\pi\)
−0.379428 + 0.925221i \(0.623879\pi\)
\(212\) 2.13169 1.54876i 0.146405 0.106370i
\(213\) −5.23071 + 3.80033i −0.358402 + 0.260394i
\(214\) 3.53726 + 2.56997i 0.241802 + 0.175680i
\(215\) 0 0
\(216\) −2.47955 + 1.80150i −0.168712 + 0.122576i
\(217\) −0.562179 + 1.73021i −0.0381632 + 0.117454i
\(218\) −9.91043 −0.671219
\(219\) −2.22801 + 6.85710i −0.150555 + 0.463360i
\(220\) 0 0
\(221\) 5.83375 + 17.9544i 0.392420 + 1.20775i
\(222\) 3.83910 + 11.8155i 0.257663 + 0.793006i
\(223\) 6.57432 + 4.77652i 0.440249 + 0.319860i 0.785734 0.618565i \(-0.212286\pi\)
−0.345485 + 0.938424i \(0.612286\pi\)
\(224\) −13.1520 −0.878753
\(225\) 0 0
\(226\) 4.09189 0.272188
\(227\) 20.7351 + 15.0649i 1.37624 + 0.999895i 0.997221 + 0.0745050i \(0.0237377\pi\)
0.379017 + 0.925390i \(0.376262\pi\)
\(228\) 1.49829 + 4.61127i 0.0992268 + 0.305389i
\(229\) 0.381062 + 1.17279i 0.0251813 + 0.0775001i 0.962857 0.270010i \(-0.0870271\pi\)
−0.937676 + 0.347510i \(0.887027\pi\)
\(230\) 0 0
\(231\) −1.09550 + 3.37160i −0.0720786 + 0.221835i
\(232\) −16.1954 −1.06328
\(233\) 0.927012 2.85305i 0.0607306 0.186909i −0.916088 0.400976i \(-0.868671\pi\)
0.976819 + 0.214067i \(0.0686710\pi\)
\(234\) −3.59686 + 2.61327i −0.235134 + 0.170835i
\(235\) 0 0
\(236\) 2.09397 + 1.52136i 0.136306 + 0.0990320i
\(237\) 9.98116 7.25174i 0.648346 0.471051i
\(238\) −12.5961 + 9.15162i −0.816485 + 0.593211i
\(239\) −17.9069 13.0101i −1.15830 0.841554i −0.168738 0.985661i \(-0.553969\pi\)
−0.989562 + 0.144107i \(0.953969\pi\)
\(240\) 0 0
\(241\) 10.8734 7.89999i 0.700418 0.508883i −0.179651 0.983730i \(-0.557497\pi\)
0.880068 + 0.474847i \(0.157497\pi\)
\(242\) 3.26043 10.0346i 0.209588 0.645046i
\(243\) 1.00000 0.0641500
\(244\) −3.45022 + 10.6187i −0.220877 + 0.679791i
\(245\) 0 0
\(246\) −3.19665 9.83827i −0.203811 0.627265i
\(247\) 7.52479 + 23.1589i 0.478791 + 1.47357i
\(248\) 1.46115 + 1.06159i 0.0927829 + 0.0674107i
\(249\) −12.3941 −0.785444
\(250\) 0 0
\(251\) 18.8799 1.19169 0.595843 0.803101i \(-0.296818\pi\)
0.595843 + 0.803101i \(0.296818\pi\)
\(252\) 2.02881 + 1.47402i 0.127803 + 0.0928544i
\(253\) −0.825262 2.53990i −0.0518838 0.159682i
\(254\) 3.82516 + 11.7726i 0.240012 + 0.738680i
\(255\) 0 0
\(256\) −4.89603 + 15.0684i −0.306002 + 0.941776i
\(257\) −7.06320 −0.440590 −0.220295 0.975433i \(-0.570702\pi\)
−0.220295 + 0.975433i \(0.570702\pi\)
\(258\) 0.818201 2.51816i 0.0509390 0.156774i
\(259\) 28.4722 20.6863i 1.76918 1.28538i
\(260\) 0 0
\(261\) 4.27498 + 3.10596i 0.264615 + 0.192254i
\(262\) −1.83257 + 1.33144i −0.113216 + 0.0822566i
\(263\) 16.5328 12.0118i 1.01945 0.740677i 0.0532829 0.998579i \(-0.483031\pi\)
0.966171 + 0.257903i \(0.0830315\pi\)
\(264\) 2.84729 + 2.06868i 0.175239 + 0.127318i
\(265\) 0 0
\(266\) −16.2474 + 11.8044i −0.996192 + 0.723776i
\(267\) 0.334985 1.03098i 0.0205008 0.0630949i
\(268\) 2.56582 0.156732
\(269\) 6.54880 20.1551i 0.399287 1.22888i −0.526285 0.850308i \(-0.676416\pi\)
0.925572 0.378571i \(-0.123584\pi\)
\(270\) 0 0
\(271\) 3.07570 + 9.46603i 0.186835 + 0.575020i 0.999975 0.00704817i \(-0.00224352\pi\)
−0.813140 + 0.582069i \(0.802244\pi\)
\(272\) 2.45330 + 7.55047i 0.148753 + 0.457814i
\(273\) 10.1892 + 7.40289i 0.616679 + 0.448043i
\(274\) −21.1460 −1.27747
\(275\) 0 0
\(276\) −1.88914 −0.113713
\(277\) −15.1569 11.0121i −0.910689 0.661654i 0.0304998 0.999535i \(-0.490290\pi\)
−0.941189 + 0.337880i \(0.890290\pi\)
\(278\) 5.77912 + 17.7863i 0.346608 + 1.06675i
\(279\) −0.182097 0.560438i −0.0109019 0.0335525i
\(280\) 0 0
\(281\) 8.98981 27.6678i 0.536287 1.65052i −0.204565 0.978853i \(-0.565578\pi\)
0.740852 0.671668i \(-0.234422\pi\)
\(282\) 6.59339 0.392630
\(283\) −2.21876 + 6.82865i −0.131892 + 0.405921i −0.995094 0.0989379i \(-0.968455\pi\)
0.863202 + 0.504859i \(0.168455\pi\)
\(284\) 4.24887 3.08699i 0.252124 0.183179i
\(285\) 0 0
\(286\) 4.13031 + 3.00084i 0.244230 + 0.177444i
\(287\) −23.7075 + 17.2245i −1.39941 + 1.01673i
\(288\) 3.44649 2.50402i 0.203087 0.147551i
\(289\) −3.57138 2.59476i −0.210081 0.152633i
\(290\) 0 0
\(291\) 3.65783 2.65757i 0.214426 0.155789i
\(292\) 1.80980 5.56998i 0.105910 0.325958i
\(293\) 1.79825 0.105055 0.0525276 0.998619i \(-0.483272\pi\)
0.0525276 + 0.998619i \(0.483272\pi\)
\(294\) −0.852398 + 2.62341i −0.0497129 + 0.153001i
\(295\) 0 0
\(296\) −10.7967 33.2287i −0.627544 1.93138i
\(297\) −0.354847 1.09211i −0.0205903 0.0633705i
\(298\) 0.185265 + 0.134603i 0.0107321 + 0.00779735i
\(299\) −9.48773 −0.548689
\(300\) 0 0
\(301\) −7.50057 −0.432326
\(302\) −3.57896 2.60027i −0.205946 0.149629i
\(303\) −2.04363 6.28965i −0.117403 0.361331i
\(304\) 3.16444 + 9.73915i 0.181493 + 0.558579i
\(305\) 0 0
\(306\) 1.55844 4.79639i 0.0890902 0.274191i
\(307\) 5.98864 0.341790 0.170895 0.985289i \(-0.445334\pi\)
0.170895 + 0.985289i \(0.445334\pi\)
\(308\) 0.889867 2.73873i 0.0507049 0.156054i
\(309\) 3.40300 2.47242i 0.193590 0.140651i
\(310\) 0 0
\(311\) −19.3099 14.0295i −1.09497 0.795539i −0.114735 0.993396i \(-0.536602\pi\)
−0.980231 + 0.197857i \(0.936602\pi\)
\(312\) 10.1154 7.34929i 0.572673 0.416072i
\(313\) −4.65924 + 3.38513i −0.263356 + 0.191339i −0.711625 0.702559i \(-0.752041\pi\)
0.448269 + 0.893898i \(0.352041\pi\)
\(314\) −0.388236 0.282070i −0.0219094 0.0159181i
\(315\) 0 0
\(316\) −8.10763 + 5.89054i −0.456090 + 0.331369i
\(317\) −3.78487 + 11.6486i −0.212580 + 0.654253i 0.786737 + 0.617288i \(0.211769\pi\)
−0.999317 + 0.0369645i \(0.988231\pi\)
\(318\) −3.53515 −0.198242
\(319\) 1.87507 5.77088i 0.104984 0.323107i
\(320\) 0 0
\(321\) 1.23976 + 3.81559i 0.0691966 + 0.212965i
\(322\) −2.41801 7.44188i −0.134751 0.414720i
\(323\) −22.3466 16.2358i −1.24340 0.903383i
\(324\) −0.812294 −0.0451274
\(325\) 0 0
\(326\) 3.53220 0.195631
\(327\) −7.35691 5.34511i −0.406838 0.295585i
\(328\) 8.98991 + 27.6681i 0.496385 + 1.52772i
\(329\) −5.77175 17.7636i −0.318207 0.979340i
\(330\) 0 0
\(331\) −1.86306 + 5.73391i −0.102403 + 0.315164i −0.989112 0.147163i \(-0.952986\pi\)
0.886709 + 0.462328i \(0.152986\pi\)
\(332\) 10.0676 0.552534
\(333\) −3.52269 + 10.8417i −0.193042 + 0.594123i
\(334\) 14.0721 10.2240i 0.769991 0.559431i
\(335\) 0 0
\(336\) 4.28492 + 3.11318i 0.233762 + 0.169838i
\(337\) −4.47454 + 3.25094i −0.243744 + 0.177090i −0.702949 0.711240i \(-0.748134\pi\)
0.459206 + 0.888330i \(0.348134\pi\)
\(338\) 3.21168 2.33342i 0.174692 0.126921i
\(339\) 3.03758 + 2.20693i 0.164978 + 0.119864i
\(340\) 0 0
\(341\) −0.547441 + 0.397739i −0.0296456 + 0.0215388i
\(342\) 2.01019 6.18674i 0.108699 0.334540i
\(343\) −13.7967 −0.744949
\(344\) −2.30102 + 7.08182i −0.124063 + 0.381826i
\(345\) 0 0
\(346\) 0.189195 + 0.582283i 0.0101712 + 0.0313038i
\(347\) −8.01729 24.6747i −0.430391 1.32461i −0.897737 0.440532i \(-0.854790\pi\)
0.467346 0.884075i \(-0.345210\pi\)
\(348\) −3.47254 2.52295i −0.186148 0.135244i
\(349\) −19.0025 −1.01718 −0.508591 0.861008i \(-0.669833\pi\)
−0.508591 + 0.861008i \(0.669833\pi\)
\(350\) 0 0
\(351\) −4.07954 −0.217750
\(352\) −3.95764 2.87539i −0.210943 0.153259i
\(353\) 2.53126 + 7.79043i 0.134726 + 0.414642i 0.995547 0.0942642i \(-0.0300498\pi\)
−0.860822 + 0.508907i \(0.830050\pi\)
\(354\) −1.07309 3.30263i −0.0570341 0.175533i
\(355\) 0 0
\(356\) −0.272106 + 0.837457i −0.0144216 + 0.0443852i
\(357\) −14.2865 −0.756120
\(358\) −5.36771 + 16.5201i −0.283692 + 0.873116i
\(359\) 21.6701 15.7442i 1.14370 0.830948i 0.156071 0.987746i \(-0.450117\pi\)
0.987631 + 0.156797i \(0.0501170\pi\)
\(360\) 0 0
\(361\) −13.4530 9.77419i −0.708053 0.514431i
\(362\) −18.9452 + 13.7645i −0.995736 + 0.723444i
\(363\) 7.83241 5.69058i 0.411095 0.298678i
\(364\) −8.27662 6.01332i −0.433813 0.315184i
\(365\) 0 0
\(366\) 12.1189 8.80489i 0.633465 0.460239i
\(367\) 5.82600 17.9306i 0.304114 0.935968i −0.675892 0.737001i \(-0.736241\pi\)
0.980006 0.198967i \(-0.0637587\pi\)
\(368\) −3.98992 −0.207989
\(369\) 2.93319 9.02743i 0.152696 0.469949i
\(370\) 0 0
\(371\) 3.09462 + 9.52426i 0.160665 + 0.494475i
\(372\) 0.147916 + 0.455240i 0.00766911 + 0.0236031i
\(373\) 14.4391 + 10.4906i 0.747627 + 0.543183i 0.895090 0.445885i \(-0.147111\pi\)
−0.147464 + 0.989067i \(0.547111\pi\)
\(374\) −5.79118 −0.299455
\(375\) 0 0
\(376\) −18.5425 −0.956259
\(377\) −17.4400 12.6709i −0.898204 0.652583i
\(378\) −1.03970 3.19987i −0.0534764 0.164583i
\(379\) 3.88290 + 11.9503i 0.199451 + 0.613848i 0.999896 + 0.0144408i \(0.00459680\pi\)
−0.800445 + 0.599407i \(0.795403\pi\)
\(380\) 0 0
\(381\) −3.50990 + 10.8024i −0.179818 + 0.553422i
\(382\) 20.0460 1.02564
\(383\) 2.32918 7.16849i 0.119016 0.366292i −0.873748 0.486379i \(-0.838317\pi\)
0.992763 + 0.120087i \(0.0383173\pi\)
\(384\) 0.225651 0.163945i 0.0115152 0.00836628i
\(385\) 0 0
\(386\) 1.78561 + 1.29732i 0.0908854 + 0.0660321i
\(387\) 1.96554 1.42805i 0.0999138 0.0725916i
\(388\) −2.97123 + 2.15872i −0.150841 + 0.109593i
\(389\) 11.1103 + 8.07211i 0.563315 + 0.409272i 0.832671 0.553768i \(-0.186811\pi\)
−0.269356 + 0.963041i \(0.586811\pi\)
\(390\) 0 0
\(391\) 8.70687 6.32591i 0.440325 0.319915i
\(392\) 2.39719 7.37781i 0.121077 0.372636i
\(393\) −2.07849 −0.104846
\(394\) 3.88819 11.9666i 0.195884 0.602869i
\(395\) 0 0
\(396\) 0.288240 + 0.887112i 0.0144846 + 0.0445790i
\(397\) 4.01790 + 12.3658i 0.201653 + 0.620623i 0.999834 + 0.0182061i \(0.00579551\pi\)
−0.798182 + 0.602417i \(0.794204\pi\)
\(398\) 20.2592 + 14.7192i 1.01550 + 0.737807i
\(399\) −18.4277 −0.922540
\(400\) 0 0
\(401\) −6.47047 −0.323120 −0.161560 0.986863i \(-0.551653\pi\)
−0.161560 + 0.986863i \(0.551653\pi\)
\(402\) −2.78500 2.02342i −0.138903 0.100919i
\(403\) 0.742874 + 2.28633i 0.0370052 + 0.113890i
\(404\) 1.66003 + 5.10904i 0.0825894 + 0.254184i
\(405\) 0 0
\(406\) 5.49395 16.9086i 0.272660 0.839161i
\(407\) 13.0903 0.648864
\(408\) −4.38280 + 13.4889i −0.216981 + 0.667798i
\(409\) 0.899629 0.653619i 0.0444838 0.0323194i −0.565321 0.824871i \(-0.691248\pi\)
0.609805 + 0.792552i \(0.291248\pi\)
\(410\) 0 0
\(411\) −15.6975 11.4049i −0.774301 0.562562i
\(412\) −2.76424 + 2.00833i −0.136184 + 0.0989435i
\(413\) −7.95845 + 5.78215i −0.391610 + 0.284521i
\(414\) 2.05051 + 1.48979i 0.100777 + 0.0732190i
\(415\) 0 0
\(416\) −14.0601 + 10.2153i −0.689354 + 0.500845i
\(417\) −5.30282 + 16.3204i −0.259680 + 0.799213i
\(418\) −7.46989 −0.365364
\(419\) 3.64430 11.2160i 0.178036 0.547938i −0.821723 0.569887i \(-0.806987\pi\)
0.999759 + 0.0219489i \(0.00698712\pi\)
\(420\) 0 0
\(421\) −3.12900 9.63007i −0.152498 0.469341i 0.845401 0.534133i \(-0.179362\pi\)
−0.997899 + 0.0647918i \(0.979362\pi\)
\(422\) 2.31747 + 7.13244i 0.112813 + 0.347202i
\(423\) 4.89454 + 3.55609i 0.237981 + 0.172903i
\(424\) 9.94189 0.482821
\(425\) 0 0
\(426\) −7.04624 −0.341391
\(427\) −34.3305 24.9425i −1.66137 1.20705i
\(428\) −1.00705 3.09938i −0.0486775 0.149814i
\(429\) 1.44761 + 4.45530i 0.0698914 + 0.215104i
\(430\) 0 0
\(431\) −1.75911 + 5.41397i −0.0847332 + 0.260782i −0.984442 0.175708i \(-0.943779\pi\)
0.899709 + 0.436490i \(0.143779\pi\)
\(432\) −1.71559 −0.0825415
\(433\) 10.2126 31.4313i 0.490788 1.51049i −0.332631 0.943057i \(-0.607936\pi\)
0.823419 0.567434i \(-0.192064\pi\)
\(434\) −1.60400 + 1.16537i −0.0769945 + 0.0559397i
\(435\) 0 0
\(436\) 5.97597 + 4.34180i 0.286197 + 0.207934i
\(437\) 11.2308 8.15963i 0.537240 0.390328i
\(438\) −6.35691 + 4.61857i −0.303745 + 0.220684i
\(439\) −9.27430 6.73818i −0.442638 0.321596i 0.344044 0.938954i \(-0.388203\pi\)
−0.786682 + 0.617358i \(0.788203\pi\)
\(440\) 0 0
\(441\) −2.04769 + 1.48773i −0.0975089 + 0.0708443i
\(442\) −6.35773 + 19.5671i −0.302406 + 0.930711i
\(443\) −17.8993 −0.850422 −0.425211 0.905094i \(-0.639800\pi\)
−0.425211 + 0.905094i \(0.639800\pi\)
\(444\) 2.86146 8.80667i 0.135799 0.417946i
\(445\) 0 0
\(446\) 2.73672 + 8.42275i 0.129587 + 0.398829i
\(447\) 0.0649328 + 0.199843i 0.00307122 + 0.00945223i
\(448\) −20.1657 14.6512i −0.952740 0.692206i
\(449\) −6.82040 −0.321874 −0.160937 0.986965i \(-0.551452\pi\)
−0.160937 + 0.986965i \(0.551452\pi\)
\(450\) 0 0
\(451\) −10.8998 −0.513249
\(452\) −2.46740 1.79267i −0.116057 0.0843203i
\(453\) −1.25437 3.86057i −0.0589356 0.181385i
\(454\) 8.63148 + 26.5650i 0.405096 + 1.24676i
\(455\) 0 0
\(456\) −5.65325 + 17.3989i −0.264738 + 0.814779i
\(457\) −2.76381 −0.129286 −0.0646429 0.997908i \(-0.520591\pi\)
−0.0646429 + 0.997908i \(0.520591\pi\)
\(458\) −0.415289 + 1.27813i −0.0194052 + 0.0597230i
\(459\) 3.74379 2.72002i 0.174745 0.126960i
\(460\) 0 0
\(461\) 7.25254 + 5.26928i 0.337784 + 0.245415i 0.743726 0.668484i \(-0.233057\pi\)
−0.405942 + 0.913899i \(0.633057\pi\)
\(462\) −3.12566 + 2.27093i −0.145419 + 0.105653i
\(463\) 10.6480 7.73623i 0.494855 0.359533i −0.312193 0.950019i \(-0.601064\pi\)
0.807048 + 0.590485i \(0.201064\pi\)
\(464\) −7.33412 5.32855i −0.340478 0.247372i
\(465\) 0 0
\(466\) 2.64494 1.92166i 0.122524 0.0890191i
\(467\) 6.73671 20.7335i 0.311738 0.959430i −0.665339 0.746542i \(-0.731713\pi\)
0.977076 0.212889i \(-0.0682872\pi\)
\(468\) 3.31379 0.153180
\(469\) −3.01347 + 9.27450i −0.139149 + 0.428257i
\(470\) 0 0
\(471\) −0.136071 0.418784i −0.00626983 0.0192966i
\(472\) 3.01785 + 9.28798i 0.138908 + 0.427514i
\(473\) −2.25704 1.63984i −0.103779 0.0753998i
\(474\) 13.4455 0.617574
\(475\) 0 0
\(476\) 11.6048 0.531905
\(477\) −2.62429 1.90666i −0.120158 0.0872998i
\(478\) −7.45417 22.9416i −0.340946 1.04932i
\(479\) 13.2102 + 40.6567i 0.603588 + 1.85765i 0.506221 + 0.862404i \(0.331042\pi\)
0.0973673 + 0.995249i \(0.468958\pi\)
\(480\) 0 0
\(481\) 14.3710 44.2293i 0.655260 2.01668i
\(482\) 14.6475 0.667174
\(483\) 2.21873 6.82854i 0.100956 0.310709i
\(484\) −6.36221 + 4.62242i −0.289192 + 0.210110i
\(485\) 0 0
\(486\) 0.881682 + 0.640580i 0.0399939 + 0.0290573i
\(487\) 9.18213 6.67121i 0.416082 0.302301i −0.359978 0.932961i \(-0.617216\pi\)
0.776059 + 0.630660i \(0.217216\pi\)
\(488\) −34.0819 + 24.7619i −1.54281 + 1.12092i
\(489\) 2.62210 + 1.90506i 0.118575 + 0.0861500i
\(490\) 0 0
\(491\) −13.4739 + 9.78936i −0.608068 + 0.441788i −0.848734 0.528821i \(-0.822634\pi\)
0.240665 + 0.970608i \(0.422634\pi\)
\(492\) −2.38261 + 7.33292i −0.107416 + 0.330594i
\(493\) 24.4529 1.10130
\(494\) −8.20067 + 25.2391i −0.368965 + 1.13556i
\(495\) 0 0
\(496\) 0.312405 + 0.961483i 0.0140274 + 0.0431718i
\(497\) 6.16817 + 18.9837i 0.276680 + 0.851534i
\(498\) −10.9277 7.93941i −0.489680 0.355773i
\(499\) −12.2321 −0.547584 −0.273792 0.961789i \(-0.588278\pi\)
−0.273792 + 0.961789i \(0.588278\pi\)
\(500\) 0 0
\(501\) 15.9605 0.713063
\(502\) 16.6460 + 12.0941i 0.742949 + 0.539784i
\(503\) −0.404709 1.24557i −0.0180451 0.0555371i 0.941629 0.336654i \(-0.109295\pi\)
−0.959674 + 0.281117i \(0.909295\pi\)
\(504\) 2.92394 + 8.99897i 0.130243 + 0.400846i
\(505\) 0 0
\(506\) 0.899387 2.76803i 0.0399826 0.123054i
\(507\) 3.64267 0.161777
\(508\) 2.85107 8.77469i 0.126496 0.389314i
\(509\) −14.3453 + 10.4225i −0.635844 + 0.461968i −0.858420 0.512948i \(-0.828553\pi\)
0.222576 + 0.974915i \(0.428553\pi\)
\(510\) 0 0
\(511\) 18.0079 + 13.0835i 0.796622 + 0.578780i
\(512\) −14.4206 + 10.4772i −0.637305 + 0.463029i
\(513\) 4.82901 3.50848i 0.213206 0.154903i
\(514\) −6.22750 4.52454i −0.274683 0.199569i
\(515\) 0 0
\(516\) −1.59659 + 1.15999i −0.0702860 + 0.0510658i
\(517\) 2.14682 6.60723i 0.0944170 0.290586i
\(518\) 38.3546 1.68521
\(519\) −0.173602 + 0.534294i −0.00762030 + 0.0234529i
\(520\) 0 0
\(521\) 8.11527 + 24.9762i 0.355536 + 1.09423i 0.955698 + 0.294349i \(0.0951030\pi\)
−0.600162 + 0.799879i \(0.704897\pi\)
\(522\) 1.77956 + 5.47693i 0.0778894 + 0.239719i
\(523\) 2.06844 + 1.50281i 0.0904467 + 0.0657134i 0.632090 0.774895i \(-0.282197\pi\)
−0.541643 + 0.840609i \(0.682197\pi\)
\(524\) 1.68834 0.0737557
\(525\) 0 0
\(526\) 22.2711 0.971068
\(527\) −2.20614 1.60285i −0.0961008 0.0698213i
\(528\) 0.608773 + 1.87361i 0.0264934 + 0.0815384i
\(529\) −5.43598 16.7302i −0.236347 0.727401i
\(530\) 0 0
\(531\) 0.984650 3.03044i 0.0427302 0.131510i
\(532\) 14.9687 0.648977
\(533\) −11.9661 + 36.8278i −0.518308 + 1.59519i
\(534\) 0.955775 0.694411i 0.0413604 0.0300501i
\(535\) 0 0
\(536\) 7.83224 + 5.69046i 0.338301 + 0.245790i
\(537\) −12.8947 + 9.36852i −0.556446 + 0.404282i
\(538\) 18.6849 13.5754i 0.805564 0.585277i
\(539\) 2.35138 + 1.70838i 0.101281 + 0.0735849i
\(540\) 0 0
\(541\) −7.59599 + 5.51881i −0.326577 + 0.237272i −0.738977 0.673731i \(-0.764691\pi\)
0.412400 + 0.911003i \(0.364691\pi\)
\(542\) −3.35196 + 10.3163i −0.143979 + 0.443121i
\(543\) −21.4875 −0.922118
\(544\) 6.09194 18.7491i 0.261190 0.803860i
\(545\) 0 0
\(546\) 4.24150 + 13.0540i 0.181519 + 0.558659i
\(547\) 10.7708 + 33.1490i 0.460524 + 1.41735i 0.864525 + 0.502590i \(0.167619\pi\)
−0.404000 + 0.914759i \(0.632381\pi\)
\(548\) 12.7510 + 9.26413i 0.544695 + 0.395744i
\(549\) 13.7452 0.586631
\(550\) 0 0
\(551\) 31.5411 1.34370
\(552\) −5.76665 4.18972i −0.245445 0.178326i
\(553\) −11.7700 36.2244i −0.500512 1.54042i
\(554\) −6.30942 19.4184i −0.268062 0.825009i
\(555\) 0 0
\(556\) 4.30745 13.2570i 0.182676 0.562220i
\(557\) 14.1466 0.599411 0.299705 0.954032i \(-0.403112\pi\)
0.299705 + 0.954032i \(0.403112\pi\)
\(558\) 0.198453 0.610776i 0.00840119 0.0258562i
\(559\) −8.01849 + 5.82577i −0.339146 + 0.246404i
\(560\) 0 0
\(561\) −4.29903 3.12343i −0.181505 0.131871i
\(562\) 25.6496 18.6355i 1.08196 0.786091i
\(563\) 30.8926 22.4448i 1.30197 0.945936i 0.301996 0.953309i \(-0.402347\pi\)
0.999973 + 0.00737325i \(0.00234700\pi\)
\(564\) −3.97580 2.88859i −0.167411 0.121632i
\(565\) 0 0
\(566\) −6.33054 + 4.59941i −0.266092 + 0.193327i
\(567\) 0.954011 2.93614i 0.0400647 0.123306i
\(568\) 19.8161 0.831465
\(569\) 9.15622 28.1799i 0.383849 1.18136i −0.553463 0.832873i \(-0.686694\pi\)
0.937312 0.348491i \(-0.113306\pi\)
\(570\) 0 0
\(571\) 10.0895 + 31.0524i 0.422234 + 1.29950i 0.905618 + 0.424093i \(0.139407\pi\)
−0.483385 + 0.875408i \(0.660593\pi\)
\(572\) −1.17589 3.61901i −0.0491663 0.151318i
\(573\) 14.8810 + 10.8117i 0.621661 + 0.451663i
\(574\) −31.9362 −1.33299
\(575\) 0 0
\(576\) 8.07392 0.336413
\(577\) 18.3188 + 13.3094i 0.762622 + 0.554077i 0.899713 0.436481i \(-0.143775\pi\)
−0.137091 + 0.990558i \(0.543775\pi\)
\(578\) −1.48667 4.57551i −0.0618374 0.190316i
\(579\) 0.625832 + 1.92611i 0.0260087 + 0.0800465i
\(580\) 0 0
\(581\) −11.8241 + 36.3909i −0.490547 + 1.50975i
\(582\) 4.92742 0.204248
\(583\) −1.15105 + 3.54257i −0.0476717 + 0.146718i
\(584\) 17.8775 12.9888i 0.739776 0.537479i
\(585\) 0 0
\(586\) 1.58549 + 1.15193i 0.0654960 + 0.0475856i
\(587\) 33.6281 24.4323i 1.38798 1.00843i 0.391899 0.920008i \(-0.371818\pi\)
0.996083 0.0884196i \(-0.0281816\pi\)
\(588\) 1.66332 1.20847i 0.0685943 0.0498366i
\(589\) −2.84564 2.06748i −0.117252 0.0851889i
\(590\) 0 0
\(591\) 9.34046 6.78624i 0.384215 0.279149i
\(592\) 6.04350 18.6000i 0.248386 0.764454i
\(593\) −2.09050 −0.0858465 −0.0429233 0.999078i \(-0.513667\pi\)
−0.0429233 + 0.999078i \(0.513667\pi\)
\(594\) 0.386719 1.19020i 0.0158673 0.0488345i
\(595\) 0 0
\(596\) −0.0527445 0.162331i −0.00216050 0.00664933i
\(597\) 7.10057 + 21.8533i 0.290607 + 0.894397i
\(598\) −8.36516 6.07765i −0.342077 0.248533i
\(599\) 17.9768 0.734511 0.367255 0.930120i \(-0.380298\pi\)
0.367255 + 0.930120i \(0.380298\pi\)
\(600\) 0 0
\(601\) −1.11000 −0.0452778 −0.0226389 0.999744i \(-0.507207\pi\)
−0.0226389 + 0.999744i \(0.507207\pi\)
\(602\) −6.61312 4.80471i −0.269531 0.195826i
\(603\) −0.976103 3.00414i −0.0397500 0.122338i
\(604\) 1.01892 + 3.13591i 0.0414593 + 0.127599i
\(605\) 0 0
\(606\) 2.22719 6.85458i 0.0904733 0.278448i
\(607\) 12.2310 0.496441 0.248220 0.968704i \(-0.420154\pi\)
0.248220 + 0.968704i \(0.420154\pi\)
\(608\) 7.85783 24.1839i 0.318677 0.980788i
\(609\) 13.1979 9.58884i 0.534806 0.388560i
\(610\) 0 0
\(611\) −19.9675 14.5072i −0.807798 0.586899i
\(612\) −3.04106 + 2.20946i −0.122927 + 0.0893120i
\(613\) −10.4991 + 7.62804i −0.424055 + 0.308094i −0.779267 0.626692i \(-0.784409\pi\)
0.355213 + 0.934786i \(0.384409\pi\)
\(614\) 5.28008 + 3.83620i 0.213087 + 0.154817i
\(615\) 0 0
\(616\) 8.79028 6.38651i 0.354171 0.257320i
\(617\) −6.33241 + 19.4891i −0.254933 + 0.784603i 0.738910 + 0.673804i \(0.235341\pi\)
−0.993843 + 0.110799i \(0.964659\pi\)
\(618\) 4.58415 0.184402
\(619\) −12.6838 + 39.0367i −0.509804 + 1.56902i 0.282737 + 0.959198i \(0.408758\pi\)
−0.792541 + 0.609819i \(0.791242\pi\)
\(620\) 0 0
\(621\) 0.718676 + 2.21186i 0.0288395 + 0.0887588i
\(622\) −8.03822 24.7391i −0.322303 0.991948i
\(623\) −2.70752 1.96713i −0.108475 0.0788114i
\(624\) 6.99883 0.280177
\(625\) 0 0
\(626\) −6.27641 −0.250856
\(627\) −5.54520 4.02882i −0.221454 0.160896i
\(628\) 0.110530 + 0.340176i 0.00441062 + 0.0135745i
\(629\) 16.3015 + 50.1709i 0.649984 + 2.00045i
\(630\) 0 0
\(631\) 4.35319 13.3977i 0.173298 0.533356i −0.826254 0.563298i \(-0.809532\pi\)
0.999552 + 0.0299421i \(0.00953228\pi\)
\(632\) −37.8128 −1.50411
\(633\) −2.12647 + 6.54460i −0.0845196 + 0.260125i
\(634\) −10.7989 + 7.84589i −0.428881 + 0.311600i
\(635\) 0 0
\(636\) 2.13169 + 1.54876i 0.0845271 + 0.0614125i
\(637\) 8.35362 6.06926i 0.330983 0.240473i
\(638\) 5.34992 3.88695i 0.211806 0.153886i
\(639\) −5.23071 3.80033i −0.206924 0.150339i
\(640\) 0 0
\(641\) 23.0050 16.7141i 0.908644 0.660168i −0.0320278 0.999487i \(-0.510197\pi\)
0.940671 + 0.339319i \(0.110197\pi\)
\(642\) −1.35111 + 4.15830i −0.0533242 + 0.164115i
\(643\) 10.8408 0.427521 0.213761 0.976886i \(-0.431429\pi\)
0.213761 + 0.976886i \(0.431429\pi\)
\(644\) −1.80226 + 5.54678i −0.0710189 + 0.218574i
\(645\) 0 0
\(646\) −9.30232 28.6296i −0.365995 1.12642i
\(647\) 10.7040 + 32.9435i 0.420817 + 1.29514i 0.906943 + 0.421253i \(0.138410\pi\)
−0.486126 + 0.873889i \(0.661590\pi\)
\(648\) −2.47955 1.80150i −0.0974059 0.0707695i
\(649\) −3.65897 −0.143627
\(650\) 0 0
\(651\) −1.81925 −0.0713020
\(652\) −2.12991 1.54747i −0.0834138 0.0606037i
\(653\) 1.28398 + 3.95170i 0.0502462 + 0.154642i 0.973031 0.230673i \(-0.0740928\pi\)
−0.922785 + 0.385315i \(0.874093\pi\)
\(654\) −3.06249 9.42538i −0.119753 0.368561i
\(655\) 0 0
\(656\) −5.03216 + 15.4874i −0.196473 + 0.604681i
\(657\) −7.20998 −0.281288
\(658\) 6.29016 19.3591i 0.245216 0.754698i
\(659\) 3.24759 2.35951i 0.126508 0.0919135i −0.522732 0.852497i \(-0.675087\pi\)
0.649240 + 0.760584i \(0.275087\pi\)
\(660\) 0 0
\(661\) −15.9107 11.5598i −0.618853 0.449623i 0.233668 0.972316i \(-0.424927\pi\)
−0.852521 + 0.522694i \(0.824927\pi\)
\(662\) −5.31566 + 3.86205i −0.206599 + 0.150103i
\(663\) −15.2729 + 11.0964i −0.593152 + 0.430950i
\(664\) 30.7318 + 22.3279i 1.19262 + 0.866492i
\(665\) 0 0
\(666\) −10.0509 + 7.30240i −0.389464 + 0.282962i
\(667\) −3.79760 + 11.6878i −0.147044 + 0.452554i
\(668\) −12.9646 −0.501616
\(669\) −2.51117 + 7.72858i −0.0970873 + 0.298804i
\(670\) 0 0
\(671\) −4.87744 15.0112i −0.188292 0.579502i
\(672\) −4.06418 12.5083i −0.156779 0.482517i
\(673\) −33.5308 24.3615i −1.29252 0.939068i −0.292663 0.956215i \(-0.594542\pi\)
−0.999853 + 0.0171473i \(0.994542\pi\)
\(674\) −6.02761 −0.232175
\(675\) 0 0
\(676\) −2.95892 −0.113804
\(677\) 14.7109 + 10.6881i 0.565386 + 0.410777i 0.833426 0.552631i \(-0.186376\pi\)
−0.268040 + 0.963408i \(0.586376\pi\)
\(678\) 1.26446 + 3.89162i 0.0485614 + 0.149457i
\(679\) −4.31339 13.2753i −0.165533 0.509457i
\(680\) 0 0
\(681\) −7.92011 + 24.3756i −0.303499 + 0.934074i
\(682\) −0.737453 −0.0282385
\(683\) −8.79224 + 27.0597i −0.336426 + 1.03541i 0.629590 + 0.776928i \(0.283223\pi\)
−0.966015 + 0.258484i \(0.916777\pi\)
\(684\) −3.92258 + 2.84992i −0.149983 + 0.108969i
\(685\) 0 0
\(686\) −12.1643 8.83786i −0.464434 0.337431i
\(687\) −0.997634 + 0.724824i −0.0380621 + 0.0276537i
\(688\) −3.37206 + 2.44994i −0.128558 + 0.0934032i
\(689\) 10.7059 + 7.77828i 0.407862 + 0.296329i
\(690\) 0 0
\(691\) −19.7541 + 14.3522i −0.751483 + 0.545984i −0.896286 0.443476i \(-0.853745\pi\)
0.144803 + 0.989460i \(0.453745\pi\)
\(692\) 0.141016 0.434003i 0.00536063 0.0164983i
\(693\) −3.54511 −0.134668
\(694\) 8.73740 26.8910i 0.331667 1.02077i
\(695\) 0 0
\(696\) −5.00465 15.4027i −0.189701 0.583840i
\(697\) −13.5736 41.7751i −0.514135 1.58235i
\(698\) −16.7542 12.1726i −0.634155 0.460741i
\(699\) 2.99987 0.113466
\(700\) 0 0
\(701\) −25.0371 −0.945638 −0.472819 0.881159i \(-0.656764\pi\)
−0.472819 + 0.881159i \(0.656764\pi\)
\(702\) −3.59686 2.61327i −0.135755 0.0986316i
\(703\) 21.0269 + 64.7142i 0.793045 + 2.44074i
\(704\) −2.86501 8.81759i −0.107979 0.332325i
\(705\) 0 0
\(706\) −2.75862 + 8.49016i −0.103822 + 0.319531i
\(707\) −20.4170 −0.767858
\(708\) −0.799825 + 2.46161i −0.0300593 + 0.0925129i
\(709\) −29.5804 + 21.4914i −1.11091 + 0.807126i −0.982807 0.184634i \(-0.940890\pi\)
−0.128107 + 0.991760i \(0.540890\pi\)
\(710\) 0 0
\(711\) 9.98116 + 7.25174i 0.374323 + 0.271961i
\(712\) −2.68792 + 1.95289i −0.100734 + 0.0731876i
\(713\) 1.10874 0.805546i 0.0415226 0.0301679i
\(714\) −12.5961 9.15162i −0.471398 0.342491i
\(715\) 0 0
\(716\) 10.4743 7.60999i 0.391441 0.284399i
\(717\) 6.83982 21.0508i 0.255438 0.786157i
\(718\) 29.1915 1.08942
\(719\) −2.23596 + 6.88157i −0.0833872 + 0.256639i −0.984054 0.177872i \(-0.943079\pi\)
0.900667 + 0.434511i \(0.143079\pi\)
\(720\) 0 0
\(721\) −4.01289 12.3504i −0.149448 0.459954i
\(722\) −5.60014 17.2355i −0.208416 0.641437i
\(723\) 10.8734 + 7.89999i 0.404386 + 0.293804i
\(724\) 17.4542 0.648679
\(725\) 0 0
\(726\) 10.5510 0.391583
\(727\) 10.7680 + 7.82337i 0.399361 + 0.290153i 0.769281 0.638911i \(-0.220615\pi\)
−0.369920 + 0.929064i \(0.620615\pi\)
\(728\) −11.9283 36.7117i −0.442094 1.36062i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) 3.47424 10.6926i 0.128499 0.395480i
\(732\) −11.1651 −0.412675
\(733\) 8.89333 27.3709i 0.328483 1.01097i −0.641361 0.767239i \(-0.721630\pi\)
0.969844 0.243727i \(-0.0783700\pi\)
\(734\) 16.6226 12.0771i 0.613553 0.445772i
\(735\) 0 0
\(736\) 8.01545 + 5.82357i 0.295454 + 0.214660i
\(737\) −2.93447 + 2.13202i −0.108093 + 0.0785339i
\(738\) 8.36893 6.08038i 0.308065 0.223822i
\(739\) −32.6202 23.7000i −1.19995 0.871818i −0.205674 0.978621i \(-0.565939\pi\)
−0.994280 + 0.106803i \(0.965939\pi\)
\(740\) 0 0
\(741\) −19.7002 + 14.3130i −0.723704 + 0.525802i
\(742\) −3.37258 + 10.3797i −0.123811 + 0.381051i
\(743\) −27.8114 −1.02030 −0.510151 0.860085i \(-0.670411\pi\)
−0.510151 + 0.860085i \(0.670411\pi\)
\(744\) −0.558109 + 1.71768i −0.0204613 + 0.0629733i
\(745\) 0 0
\(746\) 6.01061 + 18.4988i 0.220064 + 0.677288i
\(747\) −3.82999 11.7875i −0.140132 0.431282i
\(748\) 3.49207 + 2.53714i 0.127683 + 0.0927670i
\(749\) 12.3859 0.452569
\(750\) 0 0
\(751\) −11.4124 −0.416443 −0.208221 0.978082i \(-0.566767\pi\)
−0.208221 + 0.978082i \(0.566767\pi\)
\(752\) −8.39703 6.10080i −0.306208 0.222473i
\(753\) 5.83420 + 17.9558i 0.212610 + 0.654346i
\(754\) −7.25980 22.3434i −0.264386 0.813698i
\(755\) 0 0
\(756\) −0.774937 + 2.38501i −0.0281842 + 0.0867420i
\(757\) −13.7637 −0.500251 −0.250126 0.968213i \(-0.580472\pi\)
−0.250126 + 0.968213i \(0.580472\pi\)
\(758\) −4.23166 + 13.0237i −0.153701 + 0.473042i
\(759\) 2.16056 1.56974i 0.0784235 0.0569780i
\(760\) 0 0
\(761\) 11.9257 + 8.66451i 0.432305 + 0.314088i 0.782570 0.622562i \(-0.213908\pi\)
−0.350265 + 0.936651i \(0.613908\pi\)
\(762\) −10.0144 + 7.27588i −0.362783 + 0.263577i
\(763\) −22.7126 + 16.5017i −0.822251 + 0.597400i
\(764\) −12.0877 8.78224i −0.437318 0.317730i
\(765\) 0 0
\(766\) 6.64559 4.82830i 0.240115 0.174454i
\(767\) −4.01692 + 12.3628i −0.145043 + 0.446395i
\(768\) −15.8439 −0.571717
\(769\) −0.753239 + 2.31823i −0.0271625 + 0.0835976i −0.963719 0.266920i \(-0.913994\pi\)
0.936556 + 0.350517i \(0.113994\pi\)
\(770\) 0 0
\(771\) −2.18265 6.71750i −0.0786061 0.241925i
\(772\) −0.508359 1.56457i −0.0182963 0.0563101i
\(773\) 20.4957 + 14.8910i 0.737180 + 0.535592i 0.891827 0.452377i \(-0.149424\pi\)
−0.154647 + 0.987970i \(0.549424\pi\)
\(774\) 2.64776 0.0951716
\(775\) 0 0
\(776\) −13.8574 −0.497450
\(777\) 28.4722 + 20.6863i 1.02143 + 0.742115i
\(778\) 4.62493 + 14.2341i 0.165812 + 0.510317i
\(779\) −17.5082 53.8846i −0.627296 1.93062i
\(780\) 0 0
\(781\) −2.29427 + 7.06103i −0.0820953 + 0.252664i
\(782\) 11.7289 0.419426
\(783\) −1.63290 + 5.02554i −0.0583550 + 0.179598i
\(784\) 3.51299 2.55234i 0.125464 0.0911550i
\(785\) 0 0
\(786\) −1.83257 1.33144i −0.0653656 0.0474909i
\(787\) −31.2669 + 22.7167i −1.11454 + 0.809763i −0.983373 0.181597i \(-0.941873\pi\)
−0.131170 + 0.991360i \(0.541873\pi\)
\(788\) −7.58719 + 5.51242i −0.270283 + 0.196372i
\(789\) 16.5328 + 12.0118i 0.588582 + 0.427630i
\(790\) 0 0
\(791\) 9.37774 6.81333i 0.333434 0.242254i
\(792\) −1.08757 + 3.34719i −0.0386450 + 0.118937i
\(793\) −56.0741 −1.99125
\(794\) −4.37879 + 13.4765i −0.155397 + 0.478264i
\(795\) 0 0
\(796\) −5.76775 17.7513i −0.204432 0.629178i
\(797\) −16.1004 49.5519i −0.570306 1.75522i −0.651635 0.758533i \(-0.725917\pi\)
0.0813294 0.996687i \(-0.474083\pi\)
\(798\) −16.2474 11.8044i −0.575152 0.417872i
\(799\) 27.9968 0.990454
\(800\) 0 0
\(801\) 1.08404 0.0383025
\(802\) −5.70490 4.14485i −0.201447 0.146360i
\(803\) 2.55844 + 7.87407i 0.0902854 + 0.277870i
\(804\) 0.792882 + 2.44024i 0.0279628 + 0.0860606i
\(805\) 0 0
\(806\) −0.809598 + 2.49169i −0.0285169 + 0.0877659i
\(807\) 21.1923 0.746006
\(808\) −6.26350 + 19.2771i −0.220349 + 0.678166i
\(809\) −25.7217 + 18.6879i −0.904328 + 0.657033i −0.939574 0.342346i \(-0.888778\pi\)
0.0352461 + 0.999379i \(0.488778\pi\)
\(810\) 0 0
\(811\) 25.1777 + 18.2927i 0.884108 + 0.642342i 0.934335 0.356395i \(-0.115994\pi\)
−0.0502268 + 0.998738i \(0.515994\pi\)
\(812\) −10.7206 + 7.78896i −0.376219 + 0.273339i
\(813\) −8.05229 + 5.85033i −0.282406 + 0.205180i
\(814\) 11.5415 + 8.38541i 0.404530 + 0.293908i
\(815\) 0 0
\(816\) −6.42281 + 4.66645i −0.224843 + 0.163358i
\(817\) 4.48133 13.7921i 0.156782 0.482525i
\(818\) 1.21188 0.0423725
\(819\) −3.89193 + 11.9781i −0.135995 + 0.418550i
\(820\) 0 0
\(821\) −14.5319 44.7247i −0.507168 1.56090i −0.797095 0.603854i \(-0.793631\pi\)
0.289927 0.957049i \(-0.406369\pi\)
\(822\) −6.53446 20.1110i −0.227916 0.701452i
\(823\) 22.9296 + 16.6593i 0.799276 + 0.580708i 0.910702 0.413065i \(-0.135542\pi\)
−0.111426 + 0.993773i \(0.535542\pi\)
\(824\) −12.8920 −0.449113
\(825\) 0 0
\(826\) −10.7208 −0.373023
\(827\) −11.4622 8.32775i −0.398579 0.289584i 0.370383 0.928879i \(-0.379226\pi\)
−0.768962 + 0.639295i \(0.779226\pi\)
\(828\) −0.583776 1.79668i −0.0202876 0.0624389i
\(829\) 0.468647 + 1.44235i 0.0162768 + 0.0500948i 0.958865 0.283862i \(-0.0916159\pi\)
−0.942588 + 0.333957i \(0.891616\pi\)
\(830\) 0 0
\(831\) 5.78942 17.8180i 0.200833 0.618099i
\(832\) −32.9379 −1.14192
\(833\) −3.61944 + 11.1395i −0.125406 + 0.385961i
\(834\) −15.1299 + 10.9925i −0.523906 + 0.380640i
\(835\) 0 0
\(836\) 4.50433 + 3.27259i 0.155786 + 0.113185i
\(837\) 0.476737 0.346370i 0.0164784 0.0119723i
\(838\) 10.3979 7.55449i 0.359188 0.260965i
\(839\) −8.48811 6.16697i −0.293042 0.212908i 0.431544 0.902092i \(-0.357969\pi\)
−0.724586 + 0.689184i \(0.757969\pi\)
\(840\) 0 0
\(841\) 0.871777 0.633383i 0.0300613 0.0218408i
\(842\) 3.41004 10.4950i 0.117518 0.361683i
\(843\) 29.0916 1.00197
\(844\) 1.72732 5.31614i 0.0594568 0.182989i
\(845\) 0 0
\(846\) 2.03747 + 6.27068i 0.0700496 + 0.215591i
\(847\) −9.23615 28.4259i −0.317358 0.976727i
\(848\) 4.50221 + 3.27104i 0.154606 + 0.112328i
\(849\) −7.18007 −0.246419
\(850\) 0 0
\(851\) −26.5120 −0.908820
\(852\) 4.24887 + 3.08699i 0.145564 + 0.105758i
\(853\) −4.59110 14.1300i −0.157196 0.483801i 0.841180 0.540755i \(-0.181861\pi\)
−0.998377 + 0.0569538i \(0.981861\pi\)
\(854\) −14.2909 43.9828i −0.489024 1.50506i
\(855\) 0 0
\(856\) 3.79973 11.6944i 0.129872 0.399705i
\(857\) −26.4088 −0.902109 −0.451054 0.892496i \(-0.648952\pi\)
−0.451054 + 0.892496i \(0.648952\pi\)
\(858\) −1.57764 + 4.85547i −0.0538597 + 0.165763i
\(859\) 7.38643 5.36656i 0.252022 0.183105i −0.454601 0.890695i \(-0.650218\pi\)
0.706622 + 0.707591i \(0.250218\pi\)
\(860\) 0 0
\(861\) −23.7075 17.2245i −0.807951 0.587011i
\(862\) −5.01906 + 3.64656i −0.170950 + 0.124202i
\(863\) −10.0962 + 7.33532i −0.343679 + 0.249697i −0.746212 0.665708i \(-0.768130\pi\)
0.402534 + 0.915405i \(0.368130\pi\)
\(864\) 3.44649 + 2.50402i 0.117252 + 0.0851886i
\(865\) 0 0
\(866\) 29.1386 21.1704i 0.990168 0.719399i
\(867\) 1.36415 4.19841i 0.0463288 0.142585i
\(868\) 1.47776 0.0501586
\(869\) 4.37789 13.4738i 0.148510 0.457066i
\(870\) 0 0
\(871\) 3.98205 + 12.2555i 0.134927 + 0.415262i
\(872\) 8.61262 + 26.5069i 0.291660 + 0.897638i
\(873\) 3.65783 + 2.65757i 0.123799 + 0.0899450i
\(874\) 15.1289 0.511741
\(875\) 0 0
\(876\) 5.85662 0.197877
\(877\) 33.0177 + 23.9888i 1.11493 + 0.810043i 0.983433 0.181273i \(-0.0580219\pi\)
0.131496 + 0.991317i \(0.458022\pi\)
\(878\) −3.86065 11.8819i −0.130291 0.400993i
\(879\) 0.555691 + 1.71024i 0.0187430 + 0.0576850i
\(880\) 0 0
\(881\) −1.12544 + 3.46374i −0.0379170 + 0.116696i −0.968223 0.250087i \(-0.919541\pi\)
0.930306 + 0.366783i \(0.119541\pi\)
\(882\) −2.75842 −0.0928808
\(883\) −0.102858 + 0.316564i −0.00346144 + 0.0106532i −0.952772 0.303686i \(-0.901783\pi\)
0.949311 + 0.314339i \(0.101783\pi\)
\(884\) 12.4061 9.01357i 0.417263 0.303159i
\(885\) 0 0
\(886\) −15.7815 11.4659i −0.530190 0.385206i
\(887\) −0.924496 + 0.671685i −0.0310415 + 0.0225530i −0.603198 0.797592i \(-0.706107\pi\)
0.572156 + 0.820145i \(0.306107\pi\)
\(888\) 28.2660 20.5365i 0.948546 0.689159i
\(889\) 28.3688 + 20.6111i 0.951459 + 0.691276i
\(890\) 0 0
\(891\) 0.929002 0.674959i 0.0311227 0.0226120i
\(892\) 2.03980 6.27787i 0.0682977 0.210199i
\(893\) 36.1123 1.20845
\(894\) −0.0707650 + 0.217792i −0.00236674 + 0.00728407i
\(895\) 0 0
\(896\) −0.266092 0.818948i −0.00888953 0.0273591i
\(897\) −2.93187 9.02336i −0.0978923 0.301281i
\(898\) −6.01342 4.36901i −0.200671 0.145796i
\(899\) 3.11385 0.103853
\(900\) 0 0
\(901\) −15.0109 −0.500086
\(902\) −9.61012 6.98216i −0.319982 0.232481i
\(903\) −2.31780 7.13347i −0.0771317 0.237387i
\(904\) −3.55604 10.9444i −0.118272 0.364004i
\(905\) 0 0
\(906\) 1.36704 4.20732i 0.0454169 0.139779i
\(907\) 18.4202 0.611632 0.305816 0.952091i \(-0.401071\pi\)
0.305816 + 0.952091i \(0.401071\pi\)
\(908\) 6.43345 19.8001i 0.213502 0.657090i
\(909\) 5.35029 3.88721i 0.177458 0.128931i
\(910\) 0 0
\(911\) −14.7651 10.7274i −0.489188 0.355416i 0.315684 0.948864i \(-0.397766\pi\)
−0.804872 + 0.593449i \(0.797766\pi\)
\(912\) −8.28462 + 6.01913i −0.274331 + 0.199313i
\(913\) −11.5141 + 8.36551i −0.381062 + 0.276858i
\(914\) −2.43681 1.77044i −0.0806024 0.0585611i
\(915\) 0 0
\(916\) 0.810372 0.588770i 0.0267754 0.0194535i
\(917\) −1.98290 + 6.10275i −0.0654812 + 0.201531i
\(918\) 5.04322 0.166451
\(919\) 3.34919 10.3078i 0.110480 0.340022i −0.880498 0.474050i \(-0.842791\pi\)
0.990977 + 0.134029i \(0.0427914\pi\)
\(920\) 0 0
\(921\) 1.85059 + 5.69554i 0.0609791 + 0.187674i
\(922\) 3.01904 + 9.29166i 0.0994269 + 0.306005i
\(923\) 21.3389 + 15.5036i 0.702378 + 0.510308i
\(924\) 2.87967 0.0947342
\(925\) 0 0
\(926\) 14.3438 0.471368
\(927\) 3.40300 + 2.47242i 0.111769 + 0.0812051i
\(928\) 6.95631 + 21.4093i 0.228352 + 0.702795i
\(929\) −16.1768 49.7870i −0.530743 1.63346i −0.752673 0.658395i \(-0.771236\pi\)
0.221930 0.975063i \(-0.428764\pi\)
\(930\) 0 0
\(931\) −4.66862 + 14.3685i −0.153008 + 0.470910i
\(932\) −2.43678 −0.0798193
\(933\) 7.37574 22.7002i 0.241471 0.743171i
\(934\) 19.2211 13.9649i 0.628933 0.456947i
\(935\) 0 0
\(936\) 10.1154 + 7.34929i 0.330633 + 0.240219i
\(937\) −0.00106163 0.000771322i −3.46821e−5 2.51980e-5i −0.587803 0.809004i \(-0.700007\pi\)
0.587768 + 0.809030i \(0.300007\pi\)
\(938\) −8.59798 + 6.24680i −0.280734 + 0.203965i
\(939\) −4.65924 3.38513i −0.152048 0.110470i
\(940\) 0 0
\(941\) 17.5737 12.7680i 0.572885 0.416225i −0.263267 0.964723i \(-0.584800\pi\)
0.836152 + 0.548498i \(0.184800\pi\)
\(942\) 0.148293 0.456399i 0.00483165 0.0148703i
\(943\) 22.0754 0.718874
\(944\) −1.68926 + 5.19900i −0.0549807 + 0.169213i
\(945\) 0 0
\(946\) −0.939548 2.89163i −0.0305473 0.0940151i
\(947\) 10.4839 + 32.2661i 0.340681 + 1.04851i 0.963855 + 0.266426i \(0.0858427\pi\)
−0.623174 + 0.782083i \(0.714157\pi\)
\(948\) −8.10763 5.89054i −0.263324 0.191316i
\(949\) 29.4134 0.954800
\(950\) 0 0
\(951\) −12.2481 −0.397172
\(952\) 35.4240 + 25.7370i 1.14810 + 0.834142i
\(953\) 2.56579 + 7.89670i 0.0831142 + 0.255799i 0.983974 0.178310i \(-0.0570631\pi\)
−0.900860 + 0.434109i \(0.857063\pi\)
\(954\) −1.09242 3.36213i −0.0353685 0.108853i
\(955\) 0 0
\(956\) −5.55594 + 17.0994i −0.179692 + 0.553035i
\(957\) 6.06786 0.196146
\(958\) −14.3967 + 44.3085i −0.465136 + 1.43154i
\(959\) −48.4620 + 35.2097i −1.56492 + 1.13698i
\(960\) 0 0
\(961\) 24.7986 + 18.0172i 0.799955 + 0.581201i
\(962\) 41.0030 29.7904i 1.32199 0.960482i
\(963\) −3.24573 + 2.35816i −0.104592 + 0.0759907i
\(964\) −8.83240 6.41711i −0.284472 0.206681i
\(965\) 0 0
\(966\) 6.33044 4.59933i 0.203679 0.147981i
\(967\) −8.58804 + 26.4313i −0.276173 + 0.849972i 0.712734 + 0.701434i \(0.247457\pi\)
−0.988907 + 0.148538i \(0.952543\pi\)
\(968\) −29.6724 −0.953707
\(969\) 8.53565 26.2700i 0.274205 0.843915i
\(970\) 0 0
\(971\) −9.59377 29.5266i −0.307879 0.947554i −0.978587 0.205833i \(-0.934010\pi\)
0.670708 0.741721i \(-0.265990\pi\)
\(972\) −0.251013 0.772537i −0.00805123 0.0247791i
\(973\) 42.8601 + 31.1397i 1.37403 + 0.998292i
\(974\) 12.3692 0.396333
\(975\) 0 0
\(976\) −23.5811 −0.754814
\(977\) 35.9137 + 26.0928i 1.14898 + 0.834783i 0.988345 0.152231i \(-0.0486457\pi\)
0.160635 + 0.987014i \(0.448646\pi\)
\(978\) 1.09151 + 3.35932i 0.0349027 + 0.107419i
\(979\) −0.384667 1.18388i −0.0122940 0.0378370i
\(980\) 0 0
\(981\) 2.81009 8.64857i 0.0897193 0.276127i
\(982\) −18.1506 −0.579208
\(983\) 13.5305 41.6427i 0.431557 1.32820i −0.465017 0.885302i \(-0.653952\pi\)
0.896574 0.442894i \(-0.146048\pi\)
\(984\) −23.5359 + 17.0998i −0.750297 + 0.545123i
\(985\) 0 0
\(986\) 21.5597 + 15.6640i 0.686600 + 0.498844i
\(987\) 15.1106 10.9785i 0.480977 0.349450i
\(988\) 16.0023 11.6264i 0.509102 0.369884i
\(989\) 4.57121 + 3.32118i 0.145356 + 0.105607i
\(990\) 0 0
\(991\) −27.8586 + 20.2404i −0.884957 + 0.642959i −0.934558 0.355810i \(-0.884205\pi\)
0.0496015 + 0.998769i \(0.484205\pi\)
\(992\) 0.775752 2.38752i 0.0246302 0.0758039i
\(993\) −6.02899 −0.191324
\(994\) −6.72219 + 20.6888i −0.213215 + 0.656208i
\(995\) 0 0
\(996\) 3.11107 + 9.57490i 0.0985781 + 0.303392i
\(997\) −5.99154 18.4401i −0.189754 0.584002i 0.810244 0.586093i \(-0.199335\pi\)
−0.999998 + 0.00209042i \(0.999335\pi\)
\(998\) −10.7848 7.83564i −0.341388 0.248033i
\(999\) −11.3997 −0.360670
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 375.2.g.e.76.3 16
5.2 odd 4 75.2.i.a.34.2 16
5.3 odd 4 375.2.i.c.49.3 16
5.4 even 2 375.2.g.d.76.2 16
15.2 even 4 225.2.m.b.109.3 16
25.2 odd 20 375.2.i.c.199.3 16
25.6 even 5 1875.2.a.m.1.4 8
25.8 odd 20 1875.2.b.h.1249.11 16
25.11 even 5 inner 375.2.g.e.301.3 16
25.14 even 10 375.2.g.d.301.2 16
25.17 odd 20 1875.2.b.h.1249.6 16
25.19 even 10 1875.2.a.p.1.5 8
25.23 odd 20 75.2.i.a.64.2 yes 16
75.23 even 20 225.2.m.b.64.3 16
75.44 odd 10 5625.2.a.t.1.4 8
75.56 odd 10 5625.2.a.bd.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.i.a.34.2 16 5.2 odd 4
75.2.i.a.64.2 yes 16 25.23 odd 20
225.2.m.b.64.3 16 75.23 even 20
225.2.m.b.109.3 16 15.2 even 4
375.2.g.d.76.2 16 5.4 even 2
375.2.g.d.301.2 16 25.14 even 10
375.2.g.e.76.3 16 1.1 even 1 trivial
375.2.g.e.301.3 16 25.11 even 5 inner
375.2.i.c.49.3 16 5.3 odd 4
375.2.i.c.199.3 16 25.2 odd 20
1875.2.a.m.1.4 8 25.6 even 5
1875.2.a.p.1.5 8 25.19 even 10
1875.2.b.h.1249.6 16 25.17 odd 20
1875.2.b.h.1249.11 16 25.8 odd 20
5625.2.a.t.1.4 8 75.44 odd 10
5625.2.a.bd.1.5 8 75.56 odd 10