Properties

Label 930.2.n.e.721.1
Level $930$
Weight $2$
Character 930.721
Analytic conductor $7.426$
Analytic rank $0$
Dimension $12$
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] = [930,2,Mod(481,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, 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("930.481");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 16 x^{10} - 6 x^{9} + 161 x^{8} - 180 x^{7} + 1725 x^{6} - 2255 x^{5} + 17635 x^{4} - 18375 x^{3} + 60975 x^{2} + 2000 x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 721.1
Root \(1.05776 + 3.25545i\) of defining polynomial
Character \(\chi\) \(=\) 930.721
Dual form 930.2.n.e.841.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.96024 - 1.42420i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.96024 - 1.42420i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(-1.46024 - 1.06092i) q^{11} +(0.309017 - 0.951057i) q^{12} +(-1.45758 - 4.48597i) q^{13} +(1.96024 - 1.42420i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.05638 - 2.94713i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-0.100180 + 0.308322i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(0.748744 - 2.30440i) q^{21} +(1.46024 - 1.06092i) q^{22} +(-0.902476 + 0.655687i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +4.71683 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.748744 + 2.30440i) q^{28} +(2.50698 - 7.71569i) q^{29} -1.00000 q^{30} +(-3.74736 - 4.11792i) q^{31} -1.00000 q^{32} +(0.557761 - 1.71661i) q^{33} +(1.54940 + 4.76856i) q^{34} +(-1.96024 - 1.42420i) q^{35} +1.00000 q^{36} +8.55247 q^{37} +(-0.262274 - 0.190553i) q^{38} +(3.81600 - 2.77248i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-0.649419 + 1.99870i) q^{41} +(1.96024 + 1.42420i) q^{42} +(-1.66907 + 5.13688i) q^{43} +(0.557761 + 1.71661i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(-0.344715 - 1.06092i) q^{46} +(-1.86006 - 5.72467i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-0.348924 - 1.07388i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(4.05638 + 2.94713i) q^{51} +(-1.45758 + 4.48597i) q^{52} +(-1.13590 + 0.825283i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-1.46024 - 1.06092i) q^{55} -2.42299 q^{56} -0.324189 q^{57} +(6.56336 + 4.76856i) q^{58} +(-2.07310 - 6.38035i) q^{59} +(0.309017 - 0.951057i) q^{60} -15.5525 q^{61} +(5.07438 - 2.29144i) q^{62} +2.42299 q^{63} +(0.309017 - 0.951057i) q^{64} +(-1.45758 - 4.48597i) q^{65} +(1.46024 + 1.06092i) q^{66} +16.3524 q^{67} -5.01396 q^{68} +(-0.902476 - 0.655687i) q^{69} +(1.96024 - 1.42420i) q^{70} +(8.91048 - 6.47384i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(4.87235 + 3.53997i) q^{73} +(-2.64286 + 8.13388i) q^{74} +(0.309017 + 0.951057i) q^{75} +(0.262274 - 0.190553i) q^{76} +(1.35145 + 4.15932i) q^{77} +(1.45758 + 4.48597i) q^{78} +(-3.44939 + 2.50613i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.70020 - 1.23527i) q^{82} +(-2.69898 + 8.30660i) q^{83} +(-1.96024 + 1.42420i) q^{84} +(4.05638 - 2.94713i) q^{85} +(-4.36969 - 3.17477i) q^{86} +8.11276 q^{87} -1.80495 q^{88} +(-7.37667 - 5.35947i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(-3.53170 + 10.8694i) q^{91} +1.11552 q^{92} +(2.75838 - 4.83646i) q^{93} +6.01927 q^{94} +(-0.100180 + 0.308322i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(14.2119 + 10.3256i) q^{97} +1.12914 q^{98} +1.80495 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) 0.309017 + 0.951057i 0.178411 + 0.549093i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) −1.96024 1.42420i −0.740900 0.538295i 0.152093 0.988366i \(-0.451399\pi\)
−0.892993 + 0.450071i \(0.851399\pi\)
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) −0.309017 + 0.951057i −0.0977198 + 0.300750i
\(11\) −1.46024 1.06092i −0.440278 0.319881i 0.345467 0.938431i \(-0.387720\pi\)
−0.785745 + 0.618550i \(0.787720\pi\)
\(12\) 0.309017 0.951057i 0.0892055 0.274546i
\(13\) −1.45758 4.48597i −0.404260 1.24419i −0.921511 0.388351i \(-0.873045\pi\)
0.517251 0.855834i \(-0.326955\pi\)
\(14\) 1.96024 1.42420i 0.523895 0.380632i
\(15\) 0.309017 + 0.951057i 0.0797878 + 0.245562i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 4.05638 2.94713i 0.983816 0.714784i 0.0252579 0.999681i \(-0.491959\pi\)
0.958558 + 0.284897i \(0.0919593\pi\)
\(18\) −0.309017 0.951057i −0.0728360 0.224166i
\(19\) −0.100180 + 0.308322i −0.0229828 + 0.0707339i −0.961890 0.273436i \(-0.911840\pi\)
0.938907 + 0.344170i \(0.111840\pi\)
\(20\) −0.809017 0.587785i −0.180902 0.131433i
\(21\) 0.748744 2.30440i 0.163389 0.502861i
\(22\) 1.46024 1.06092i 0.311323 0.226190i
\(23\) −0.902476 + 0.655687i −0.188179 + 0.136720i −0.677886 0.735167i \(-0.737104\pi\)
0.489707 + 0.871887i \(0.337104\pi\)
\(24\) 0.809017 + 0.587785i 0.165140 + 0.119981i
\(25\) 1.00000 0.200000
\(26\) 4.71683 0.925047
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) 0.748744 + 2.30440i 0.141499 + 0.435490i
\(29\) 2.50698 7.71569i 0.465534 1.43277i −0.392775 0.919635i \(-0.628485\pi\)
0.858309 0.513133i \(-0.171515\pi\)
\(30\) −1.00000 −0.182574
\(31\) −3.74736 4.11792i −0.673046 0.739601i
\(32\) −1.00000 −0.176777
\(33\) 0.557761 1.71661i 0.0970937 0.298824i
\(34\) 1.54940 + 4.76856i 0.265720 + 0.817801i
\(35\) −1.96024 1.42420i −0.331340 0.240733i
\(36\) 1.00000 0.166667
\(37\) 8.55247 1.40602 0.703008 0.711182i \(-0.251840\pi\)
0.703008 + 0.711182i \(0.251840\pi\)
\(38\) −0.262274 0.190553i −0.0425465 0.0309118i
\(39\) 3.81600 2.77248i 0.611048 0.443953i
\(40\) 0.809017 0.587785i 0.127917 0.0929370i
\(41\) −0.649419 + 1.99870i −0.101422 + 0.312145i −0.988874 0.148755i \(-0.952473\pi\)
0.887452 + 0.460900i \(0.152473\pi\)
\(42\) 1.96024 + 1.42420i 0.302471 + 0.219758i
\(43\) −1.66907 + 5.13688i −0.254531 + 0.783367i 0.739390 + 0.673277i \(0.235114\pi\)
−0.993922 + 0.110090i \(0.964886\pi\)
\(44\) 0.557761 + 1.71661i 0.0840856 + 0.258789i
\(45\) −0.809017 + 0.587785i −0.120601 + 0.0876219i
\(46\) −0.344715 1.06092i −0.0508255 0.156425i
\(47\) −1.86006 5.72467i −0.271317 0.835028i −0.990170 0.139866i \(-0.955333\pi\)
0.718853 0.695162i \(-0.244667\pi\)
\(48\) −0.809017 + 0.587785i −0.116772 + 0.0848395i
\(49\) −0.348924 1.07388i −0.0498462 0.153411i
\(50\) −0.309017 + 0.951057i −0.0437016 + 0.134500i
\(51\) 4.05638 + 2.94713i 0.568007 + 0.412681i
\(52\) −1.45758 + 4.48597i −0.202130 + 0.622093i
\(53\) −1.13590 + 0.825283i −0.156029 + 0.113361i −0.663060 0.748566i \(-0.730743\pi\)
0.507032 + 0.861927i \(0.330743\pi\)
\(54\) 0.809017 0.587785i 0.110093 0.0799874i
\(55\) −1.46024 1.06092i −0.196898 0.143055i
\(56\) −2.42299 −0.323785
\(57\) −0.324189 −0.0429398
\(58\) 6.56336 + 4.76856i 0.861811 + 0.626142i
\(59\) −2.07310 6.38035i −0.269895 0.830651i −0.990525 0.137332i \(-0.956147\pi\)
0.720630 0.693320i \(-0.243853\pi\)
\(60\) 0.309017 0.951057i 0.0398939 0.122781i
\(61\) −15.5525 −1.99129 −0.995645 0.0932298i \(-0.970281\pi\)
−0.995645 + 0.0932298i \(0.970281\pi\)
\(62\) 5.07438 2.29144i 0.644446 0.291014i
\(63\) 2.42299 0.305268
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −1.45758 4.48597i −0.180791 0.556416i
\(66\) 1.46024 + 1.06092i 0.179743 + 0.130591i
\(67\) 16.3524 1.99776 0.998881 0.0472865i \(-0.0150574\pi\)
0.998881 + 0.0472865i \(0.0150574\pi\)
\(68\) −5.01396 −0.608032
\(69\) −0.902476 0.655687i −0.108645 0.0789354i
\(70\) 1.96024 1.42420i 0.234293 0.170224i
\(71\) 8.91048 6.47384i 1.05748 0.768304i 0.0838590 0.996478i \(-0.473275\pi\)
0.973620 + 0.228174i \(0.0732755\pi\)
\(72\) −0.309017 + 0.951057i −0.0364180 + 0.112083i
\(73\) 4.87235 + 3.53997i 0.570265 + 0.414322i 0.835202 0.549944i \(-0.185351\pi\)
−0.264936 + 0.964266i \(0.585351\pi\)
\(74\) −2.64286 + 8.13388i −0.307226 + 0.945544i
\(75\) 0.309017 + 0.951057i 0.0356822 + 0.109819i
\(76\) 0.262274 0.190553i 0.0300849 0.0218580i
\(77\) 1.35145 + 4.15932i 0.154012 + 0.473999i
\(78\) 1.45758 + 4.48597i 0.165039 + 0.507936i
\(79\) −3.44939 + 2.50613i −0.388087 + 0.281961i −0.764671 0.644421i \(-0.777098\pi\)
0.376584 + 0.926382i \(0.377098\pi\)
\(80\) 0.309017 + 0.951057i 0.0345492 + 0.106331i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) −1.70020 1.23527i −0.187756 0.136412i
\(83\) −2.69898 + 8.30660i −0.296251 + 0.911767i 0.686547 + 0.727085i \(0.259126\pi\)
−0.982798 + 0.184682i \(0.940874\pi\)
\(84\) −1.96024 + 1.42420i −0.213879 + 0.155392i
\(85\) 4.05638 2.94713i 0.439976 0.319661i
\(86\) −4.36969 3.17477i −0.471196 0.342344i
\(87\) 8.11276 0.869779
\(88\) −1.80495 −0.192408
\(89\) −7.37667 5.35947i −0.781926 0.568102i 0.123631 0.992328i \(-0.460546\pi\)
−0.905556 + 0.424226i \(0.860546\pi\)
\(90\) −0.309017 0.951057i −0.0325733 0.100250i
\(91\) −3.53170 + 10.8694i −0.370223 + 1.13943i
\(92\) 1.11552 0.116301
\(93\) 2.75838 4.83646i 0.286031 0.501518i
\(94\) 6.01927 0.620840
\(95\) −0.100180 + 0.308322i −0.0102782 + 0.0316331i
\(96\) −0.309017 0.951057i −0.0315389 0.0970668i
\(97\) 14.2119 + 10.3256i 1.44300 + 1.04840i 0.987404 + 0.158219i \(0.0505751\pi\)
0.455600 + 0.890185i \(0.349425\pi\)
\(98\) 1.12914 0.114060
\(99\) 1.80495 0.181404
\(100\) −0.809017 0.587785i −0.0809017 0.0587785i
\(101\) 14.1775 10.3006i 1.41071 1.02494i 0.417495 0.908679i \(-0.362908\pi\)
0.993218 0.116264i \(-0.0370920\pi\)
\(102\) −4.05638 + 2.94713i −0.401641 + 0.291809i
\(103\) −5.45135 + 16.7775i −0.537137 + 1.65314i 0.201848 + 0.979417i \(0.435305\pi\)
−0.738986 + 0.673721i \(0.764695\pi\)
\(104\) −3.81600 2.77248i −0.374189 0.271864i
\(105\) 0.748744 2.30440i 0.0730699 0.224886i
\(106\) −0.433877 1.33534i −0.0421419 0.129699i
\(107\) −2.69184 + 1.95573i −0.260230 + 0.189068i −0.710248 0.703951i \(-0.751417\pi\)
0.450019 + 0.893019i \(0.351417\pi\)
\(108\) 0.309017 + 0.951057i 0.0297352 + 0.0915155i
\(109\) 0.978026 + 3.01005i 0.0936779 + 0.288311i 0.986907 0.161291i \(-0.0515658\pi\)
−0.893229 + 0.449602i \(0.851566\pi\)
\(110\) 1.46024 1.06092i 0.139228 0.101155i
\(111\) 2.64286 + 8.13388i 0.250849 + 0.772034i
\(112\) 0.748744 2.30440i 0.0707496 0.217745i
\(113\) −5.51661 4.00806i −0.518959 0.377046i 0.297252 0.954799i \(-0.403930\pi\)
−0.816212 + 0.577753i \(0.803930\pi\)
\(114\) 0.100180 0.308322i 0.00938270 0.0288770i
\(115\) −0.902476 + 0.655687i −0.0841563 + 0.0611431i
\(116\) −6.56336 + 4.76856i −0.609392 + 0.442750i
\(117\) 3.81600 + 2.77248i 0.352789 + 0.256316i
\(118\) 6.70870 0.617586
\(119\) −12.1488 −1.11367
\(120\) 0.809017 + 0.587785i 0.0738528 + 0.0536572i
\(121\) −2.39246 7.36322i −0.217496 0.669384i
\(122\) 4.80598 14.7913i 0.435113 1.33914i
\(123\) −2.10156 −0.189492
\(124\) 0.611225 + 5.53411i 0.0548896 + 0.496978i
\(125\) 1.00000 0.0894427
\(126\) −0.748744 + 2.30440i −0.0667034 + 0.205292i
\(127\) −3.62388 11.1532i −0.321568 0.989684i −0.972966 0.230948i \(-0.925817\pi\)
0.651398 0.758736i \(-0.274183\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) −5.40124 −0.475552
\(130\) 4.71683 0.413693
\(131\) −7.29944 5.30335i −0.637755 0.463356i 0.221323 0.975201i \(-0.428962\pi\)
−0.859078 + 0.511844i \(0.828962\pi\)
\(132\) −1.46024 + 1.06092i −0.127097 + 0.0923416i
\(133\) 0.635487 0.461708i 0.0551037 0.0400352i
\(134\) −5.05317 + 15.5520i −0.436527 + 1.34349i
\(135\) −0.809017 0.587785i −0.0696291 0.0505885i
\(136\) 1.54940 4.76856i 0.132860 0.408900i
\(137\) −1.21313 3.73364i −0.103645 0.318987i 0.885765 0.464134i \(-0.153634\pi\)
−0.989410 + 0.145147i \(0.953634\pi\)
\(138\) 0.902476 0.655687i 0.0768238 0.0558158i
\(139\) 2.18271 + 6.71769i 0.185135 + 0.569787i 0.999951 0.00993322i \(-0.00316190\pi\)
−0.814816 + 0.579720i \(0.803162\pi\)
\(140\) 0.748744 + 2.30440i 0.0632804 + 0.194757i
\(141\) 4.86969 3.53804i 0.410102 0.297957i
\(142\) 3.40350 + 10.4749i 0.285615 + 0.879034i
\(143\) −2.63086 + 8.09696i −0.220004 + 0.677102i
\(144\) −0.809017 0.587785i −0.0674181 0.0489821i
\(145\) 2.50698 7.71569i 0.208193 0.640753i
\(146\) −4.87235 + 3.53997i −0.403238 + 0.292970i
\(147\) 0.913494 0.663692i 0.0753437 0.0547404i
\(148\) −6.91909 5.02701i −0.568746 0.413218i
\(149\) −12.0385 −0.986236 −0.493118 0.869963i \(-0.664143\pi\)
−0.493118 + 0.869963i \(0.664143\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −3.08961 2.24473i −0.251429 0.182674i 0.454931 0.890527i \(-0.349664\pi\)
−0.706360 + 0.707853i \(0.749664\pi\)
\(152\) 0.100180 + 0.308322i 0.00812566 + 0.0250082i
\(153\) −1.54940 + 4.76856i −0.125261 + 0.385515i
\(154\) −4.37337 −0.352416
\(155\) −3.74736 4.11792i −0.300995 0.330759i
\(156\) −4.71683 −0.377649
\(157\) −5.35410 + 16.4782i −0.427304 + 1.31511i 0.473467 + 0.880812i \(0.343002\pi\)
−0.900771 + 0.434295i \(0.856998\pi\)
\(158\) −1.31755 4.05500i −0.104819 0.322598i
\(159\) −1.13590 0.825283i −0.0900831 0.0654492i
\(160\) −1.00000 −0.0790569
\(161\) 2.70289 0.213018
\(162\) 0.809017 + 0.587785i 0.0635624 + 0.0461808i
\(163\) 3.64244 2.64639i 0.285298 0.207281i −0.435927 0.899982i \(-0.643579\pi\)
0.721225 + 0.692701i \(0.243579\pi\)
\(164\) 1.70020 1.23527i 0.132763 0.0964582i
\(165\) 0.557761 1.71661i 0.0434216 0.133638i
\(166\) −7.06601 5.13376i −0.548429 0.398457i
\(167\) 4.33386 13.3382i 0.335364 1.03214i −0.631179 0.775638i \(-0.717429\pi\)
0.966543 0.256506i \(-0.0825715\pi\)
\(168\) −0.748744 2.30440i −0.0577668 0.177788i
\(169\) −7.48219 + 5.43613i −0.575553 + 0.418164i
\(170\) 1.54940 + 4.76856i 0.118833 + 0.365732i
\(171\) −0.100180 0.308322i −0.00766094 0.0235780i
\(172\) 4.36969 3.17477i 0.333186 0.242074i
\(173\) −4.16908 12.8311i −0.316970 0.975532i −0.974936 0.222485i \(-0.928583\pi\)
0.657967 0.753047i \(-0.271417\pi\)
\(174\) −2.50698 + 7.71569i −0.190054 + 0.584925i
\(175\) −1.96024 1.42420i −0.148180 0.107659i
\(176\) 0.557761 1.71661i 0.0420428 0.129394i
\(177\) 5.42745 3.94328i 0.407952 0.296395i
\(178\) 7.37667 5.35947i 0.552905 0.401709i
\(179\) 0.653457 + 0.474764i 0.0488417 + 0.0354856i 0.611938 0.790906i \(-0.290390\pi\)
−0.563097 + 0.826391i \(0.690390\pi\)
\(180\) 1.00000 0.0745356
\(181\) 13.7986 1.02564 0.512820 0.858496i \(-0.328601\pi\)
0.512820 + 0.858496i \(0.328601\pi\)
\(182\) −9.24610 6.71769i −0.685367 0.497948i
\(183\) −4.80598 14.7913i −0.355268 1.09340i
\(184\) −0.344715 + 1.06092i −0.0254127 + 0.0782124i
\(185\) 8.55247 0.628790
\(186\) 3.74736 + 4.11792i 0.274770 + 0.301941i
\(187\) −9.04995 −0.661798
\(188\) −1.86006 + 5.72467i −0.135659 + 0.417514i
\(189\) 0.748744 + 2.30440i 0.0544631 + 0.167620i
\(190\) −0.262274 0.190553i −0.0190274 0.0138242i
\(191\) 4.61521 0.333945 0.166973 0.985962i \(-0.446601\pi\)
0.166973 + 0.985962i \(0.446601\pi\)
\(192\) 1.00000 0.0721688
\(193\) −14.7913 10.7465i −1.06470 0.773548i −0.0897459 0.995965i \(-0.528605\pi\)
−0.974952 + 0.222417i \(0.928605\pi\)
\(194\) −14.2119 + 10.3256i −1.02036 + 0.741333i
\(195\) 3.81600 2.77248i 0.273269 0.198542i
\(196\) −0.348924 + 1.07388i −0.0249231 + 0.0767055i
\(197\) −1.82112 1.32312i −0.129750 0.0942685i 0.521018 0.853546i \(-0.325553\pi\)
−0.650767 + 0.759277i \(0.725553\pi\)
\(198\) −0.557761 + 1.71661i −0.0396383 + 0.121994i
\(199\) 2.20376 + 6.78247i 0.156220 + 0.480796i 0.998282 0.0585839i \(-0.0186585\pi\)
−0.842062 + 0.539380i \(0.818659\pi\)
\(200\) 0.809017 0.587785i 0.0572061 0.0415627i
\(201\) 5.05317 + 15.5520i 0.356423 + 1.09696i
\(202\) 5.41532 + 16.6666i 0.381021 + 1.17266i
\(203\) −15.9029 + 11.5541i −1.11617 + 0.810942i
\(204\) −1.54940 4.76856i −0.108480 0.333866i
\(205\) −0.649419 + 1.99870i −0.0453574 + 0.139596i
\(206\) −14.2718 10.3691i −0.994364 0.722448i
\(207\) 0.344715 1.06092i 0.0239594 0.0737393i
\(208\) 3.81600 2.77248i 0.264592 0.192237i
\(209\) 0.473392 0.343940i 0.0327452 0.0237908i
\(210\) 1.96024 + 1.42420i 0.135269 + 0.0982788i
\(211\) −25.7779 −1.77463 −0.887313 0.461167i \(-0.847431\pi\)
−0.887313 + 0.461167i \(0.847431\pi\)
\(212\) 1.40406 0.0964309
\(213\) 8.91048 + 6.47384i 0.610536 + 0.443580i
\(214\) −1.02819 3.16444i −0.0702857 0.216317i
\(215\) −1.66907 + 5.13688i −0.113830 + 0.350332i
\(216\) −1.00000 −0.0680414
\(217\) 1.48099 + 13.4091i 0.100536 + 0.910267i
\(218\) −3.16496 −0.214358
\(219\) −1.86107 + 5.72779i −0.125760 + 0.387048i
\(220\) 0.557761 + 1.71661i 0.0376042 + 0.115734i
\(221\) −19.1332 13.9011i −1.28704 0.935090i
\(222\) −8.55247 −0.574004
\(223\) −4.09935 −0.274513 −0.137256 0.990536i \(-0.543828\pi\)
−0.137256 + 0.990536i \(0.543828\pi\)
\(224\) 1.96024 + 1.42420i 0.130974 + 0.0951580i
\(225\) −0.809017 + 0.587785i −0.0539345 + 0.0391857i
\(226\) 5.51661 4.00806i 0.366960 0.266612i
\(227\) −4.57067 + 14.0671i −0.303366 + 0.933664i 0.676916 + 0.736060i \(0.263316\pi\)
−0.980282 + 0.197604i \(0.936684\pi\)
\(228\) 0.262274 + 0.190553i 0.0173695 + 0.0126197i
\(229\) −0.501543 + 1.54359i −0.0331429 + 0.102003i −0.966259 0.257571i \(-0.917078\pi\)
0.933117 + 0.359574i \(0.117078\pi\)
\(230\) −0.344715 1.06092i −0.0227298 0.0699553i
\(231\) −3.53813 + 2.57060i −0.232792 + 0.169133i
\(232\) −2.50698 7.71569i −0.164591 0.506560i
\(233\) 7.62781 + 23.4760i 0.499715 + 1.53796i 0.809478 + 0.587150i \(0.199750\pi\)
−0.309764 + 0.950814i \(0.600250\pi\)
\(234\) −3.81600 + 2.77248i −0.249459 + 0.181243i
\(235\) −1.86006 5.72467i −0.121337 0.373436i
\(236\) −2.07310 + 6.38035i −0.134947 + 0.415326i
\(237\) −3.44939 2.50613i −0.224062 0.162790i
\(238\) 3.75417 11.5541i 0.243347 0.748944i
\(239\) −4.92480 + 3.57807i −0.318559 + 0.231446i −0.735560 0.677459i \(-0.763081\pi\)
0.417002 + 0.908906i \(0.363081\pi\)
\(240\) −0.809017 + 0.587785i −0.0522218 + 0.0379414i
\(241\) −4.21977 3.06584i −0.271819 0.197488i 0.443522 0.896263i \(-0.353729\pi\)
−0.715341 + 0.698775i \(0.753729\pi\)
\(242\) 7.74215 0.497684
\(243\) 1.00000 0.0641500
\(244\) 12.5822 + 9.14151i 0.805493 + 0.585225i
\(245\) −0.348924 1.07388i −0.0222919 0.0686074i
\(246\) 0.649419 1.99870i 0.0414054 0.127433i
\(247\) 1.52914 0.0972971
\(248\) −5.45213 1.12883i −0.346211 0.0716805i
\(249\) −8.73407 −0.553499
\(250\) −0.309017 + 0.951057i −0.0195440 + 0.0601501i
\(251\) −0.776676 2.39036i −0.0490233 0.150878i 0.923548 0.383482i \(-0.125275\pi\)
−0.972571 + 0.232604i \(0.925275\pi\)
\(252\) −1.96024 1.42420i −0.123483 0.0897159i
\(253\) 2.01346 0.126585
\(254\) 11.7271 0.735826
\(255\) 4.05638 + 2.94713i 0.254020 + 0.184557i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 22.5899 16.4126i 1.40912 1.02379i 0.415672 0.909515i \(-0.363546\pi\)
0.993449 0.114272i \(-0.0364536\pi\)
\(258\) 1.66907 5.13688i 0.103912 0.319808i
\(259\) −16.7649 12.1804i −1.04172 0.756852i
\(260\) −1.45758 + 4.48597i −0.0903953 + 0.278208i
\(261\) 2.50698 + 7.71569i 0.155178 + 0.477589i
\(262\) 7.29944 5.30335i 0.450961 0.327642i
\(263\) −0.720991 2.21898i −0.0444582 0.136828i 0.926364 0.376631i \(-0.122917\pi\)
−0.970822 + 0.239802i \(0.922917\pi\)
\(264\) −0.557761 1.71661i −0.0343278 0.105650i
\(265\) −1.13590 + 0.825283i −0.0697781 + 0.0506967i
\(266\) 0.242734 + 0.747059i 0.0148830 + 0.0458051i
\(267\) 2.81764 8.67180i 0.172437 0.530705i
\(268\) −13.2294 9.61170i −0.808112 0.587128i
\(269\) 5.61719 17.2879i 0.342486 1.05406i −0.620430 0.784262i \(-0.713042\pi\)
0.962916 0.269802i \(-0.0869582\pi\)
\(270\) 0.809017 0.587785i 0.0492352 0.0357715i
\(271\) −16.1899 + 11.7626i −0.983465 + 0.714529i −0.958480 0.285159i \(-0.907954\pi\)
−0.0249846 + 0.999688i \(0.507954\pi\)
\(272\) 4.05638 + 2.94713i 0.245954 + 0.178696i
\(273\) −11.4288 −0.691703
\(274\) 3.92578 0.237165
\(275\) −1.46024 1.06092i −0.0880556 0.0639761i
\(276\) 0.344715 + 1.06092i 0.0207494 + 0.0638601i
\(277\) 8.75742 26.9526i 0.526182 1.61942i −0.235784 0.971806i \(-0.575766\pi\)
0.761966 0.647617i \(-0.224234\pi\)
\(278\) −7.06340 −0.423634
\(279\) 5.45213 + 1.12883i 0.326411 + 0.0675810i
\(280\) −2.42299 −0.144801
\(281\) −5.80800 + 17.8752i −0.346476 + 1.06634i 0.614312 + 0.789063i \(0.289434\pi\)
−0.960789 + 0.277282i \(0.910566\pi\)
\(282\) 1.86006 + 5.72467i 0.110765 + 0.340899i
\(283\) −9.00698 6.54395i −0.535409 0.388998i 0.286968 0.957940i \(-0.407353\pi\)
−0.822377 + 0.568943i \(0.807353\pi\)
\(284\) −11.0140 −0.653558
\(285\) −0.324189 −0.0192033
\(286\) −6.88769 5.00420i −0.407278 0.295904i
\(287\) 4.11956 2.99304i 0.243170 0.176673i
\(288\) 0.809017 0.587785i 0.0476718 0.0346356i
\(289\) 2.51533 7.74139i 0.147961 0.455376i
\(290\) 6.56336 + 4.76856i 0.385414 + 0.280019i
\(291\) −5.42848 + 16.7071i −0.318223 + 0.979390i
\(292\) −1.86107 5.72779i −0.108911 0.335193i
\(293\) −6.04511 + 4.39203i −0.353159 + 0.256585i −0.750193 0.661219i \(-0.770040\pi\)
0.397034 + 0.917804i \(0.370040\pi\)
\(294\) 0.348924 + 1.07388i 0.0203496 + 0.0626297i
\(295\) −2.07310 6.38035i −0.120701 0.371479i
\(296\) 6.91909 5.02701i 0.402164 0.292189i
\(297\) 0.557761 + 1.71661i 0.0323646 + 0.0996079i
\(298\) 3.72011 11.4493i 0.215500 0.663242i
\(299\) 4.25683 + 3.09277i 0.246179 + 0.178859i
\(300\) 0.309017 0.951057i 0.0178411 0.0549093i
\(301\) 10.5877 7.69241i 0.610265 0.443383i
\(302\) 3.08961 2.24473i 0.177787 0.129170i
\(303\) 14.1775 + 10.3006i 0.814476 + 0.591751i
\(304\) −0.324189 −0.0185935
\(305\) −15.5525 −0.890532
\(306\) −4.05638 2.94713i −0.231888 0.168476i
\(307\) −1.63840 5.04248i −0.0935085 0.287789i 0.893354 0.449354i \(-0.148346\pi\)
−0.986862 + 0.161565i \(0.948346\pi\)
\(308\) 1.35145 4.15932i 0.0770058 0.236999i
\(309\) −17.6409 −1.00356
\(310\) 5.07438 2.29144i 0.288205 0.130145i
\(311\) 23.9381 1.35740 0.678702 0.734414i \(-0.262543\pi\)
0.678702 + 0.734414i \(0.262543\pi\)
\(312\) 1.45758 4.48597i 0.0825193 0.253968i
\(313\) 1.06712 + 3.28426i 0.0603172 + 0.185637i 0.976675 0.214723i \(-0.0688849\pi\)
−0.916358 + 0.400360i \(0.868885\pi\)
\(314\) −14.0172 10.1841i −0.791038 0.574722i
\(315\) 2.42299 0.136520
\(316\) 4.26368 0.239851
\(317\) 11.3941 + 8.27831i 0.639957 + 0.464956i 0.859835 0.510571i \(-0.170566\pi\)
−0.219878 + 0.975527i \(0.570566\pi\)
\(318\) 1.13590 0.825283i 0.0636984 0.0462796i
\(319\) −11.8465 + 8.60702i −0.663279 + 0.481900i
\(320\) 0.309017 0.951057i 0.0172746 0.0531657i
\(321\) −2.69184 1.95573i −0.150244 0.109158i
\(322\) −0.835240 + 2.57060i −0.0465461 + 0.143254i
\(323\) 0.502297 + 1.54591i 0.0279486 + 0.0860169i
\(324\) −0.809017 + 0.587785i −0.0449454 + 0.0326547i
\(325\) −1.45758 4.48597i −0.0808520 0.248837i
\(326\) 1.39129 + 4.28194i 0.0770563 + 0.237155i
\(327\) −2.56050 + 1.86032i −0.141596 + 0.102876i
\(328\) 0.649419 + 1.99870i 0.0358581 + 0.110360i
\(329\) −4.50689 + 13.8708i −0.248473 + 0.764721i
\(330\) 1.46024 + 1.06092i 0.0803834 + 0.0584019i
\(331\) −4.50567 + 13.8670i −0.247654 + 0.762200i 0.747535 + 0.664223i \(0.231237\pi\)
−0.995189 + 0.0979777i \(0.968763\pi\)
\(332\) 7.06601 5.13376i 0.387798 0.281752i
\(333\) −6.91909 + 5.02701i −0.379164 + 0.275479i
\(334\) 11.3462 + 8.24349i 0.620836 + 0.451063i
\(335\) 16.3524 0.893427
\(336\) 2.42299 0.132185
\(337\) 21.3796 + 15.5332i 1.16462 + 0.846147i 0.990355 0.138552i \(-0.0442448\pi\)
0.174266 + 0.984699i \(0.444245\pi\)
\(338\) −2.85794 8.79584i −0.155452 0.478431i
\(339\) 2.10716 6.48517i 0.114445 0.352226i
\(340\) −5.01396 −0.271920
\(341\) 1.10323 + 9.98881i 0.0597433 + 0.540924i
\(342\) 0.324189 0.0175301
\(343\) −6.08664 + 18.7328i −0.328648 + 1.01147i
\(344\) 1.66907 + 5.13688i 0.0899904 + 0.276962i
\(345\) −0.902476 0.655687i −0.0485877 0.0353010i
\(346\) 13.4914 0.725304
\(347\) 13.9275 0.747668 0.373834 0.927496i \(-0.378043\pi\)
0.373834 + 0.927496i \(0.378043\pi\)
\(348\) −6.56336 4.76856i −0.351833 0.255622i
\(349\) −10.6818 + 7.76080i −0.571785 + 0.415426i −0.835753 0.549105i \(-0.814969\pi\)
0.263968 + 0.964531i \(0.414969\pi\)
\(350\) 1.96024 1.42420i 0.104779 0.0761264i
\(351\) −1.45758 + 4.48597i −0.0777999 + 0.239444i
\(352\) 1.46024 + 1.06092i 0.0778309 + 0.0565474i
\(353\) 3.78675 11.6544i 0.201549 0.620303i −0.798289 0.602275i \(-0.794261\pi\)
0.999837 0.0180281i \(-0.00573883\pi\)
\(354\) 2.07310 + 6.38035i 0.110184 + 0.339112i
\(355\) 8.91048 6.47384i 0.472919 0.343596i
\(356\) 2.81764 + 8.67180i 0.149335 + 0.459604i
\(357\) −3.75417 11.5541i −0.198692 0.611510i
\(358\) −0.653457 + 0.474764i −0.0345363 + 0.0250921i
\(359\) 3.23374 + 9.95242i 0.170670 + 0.525268i 0.999409 0.0343665i \(-0.0109414\pi\)
−0.828739 + 0.559635i \(0.810941\pi\)
\(360\) −0.309017 + 0.951057i −0.0162866 + 0.0501251i
\(361\) 15.2863 + 11.1061i 0.804542 + 0.584534i
\(362\) −4.26400 + 13.1232i −0.224111 + 0.689742i
\(363\) 6.26353 4.55072i 0.328750 0.238851i
\(364\) 9.24610 6.71769i 0.484628 0.352103i
\(365\) 4.87235 + 3.53997i 0.255030 + 0.185290i
\(366\) 15.5525 0.812940
\(367\) −30.1192 −1.57221 −0.786104 0.618094i \(-0.787905\pi\)
−0.786104 + 0.618094i \(0.787905\pi\)
\(368\) −0.902476 0.655687i −0.0470448 0.0341801i
\(369\) −0.649419 1.99870i −0.0338074 0.104048i
\(370\) −2.64286 + 8.13388i −0.137396 + 0.422860i
\(371\) 3.40201 0.176623
\(372\) −5.07438 + 2.29144i −0.263094 + 0.118806i
\(373\) 20.2901 1.05058 0.525290 0.850923i \(-0.323957\pi\)
0.525290 + 0.850923i \(0.323957\pi\)
\(374\) 2.79659 8.60702i 0.144608 0.445058i
\(375\) 0.309017 + 0.951057i 0.0159576 + 0.0491123i
\(376\) −4.86969 3.53804i −0.251135 0.182460i
\(377\) −38.2665 −1.97082
\(378\) −2.42299 −0.124625
\(379\) 13.5373 + 9.83542i 0.695364 + 0.505212i 0.878419 0.477891i \(-0.158599\pi\)
−0.183055 + 0.983103i \(0.558599\pi\)
\(380\) 0.262274 0.190553i 0.0134544 0.00977518i
\(381\) 9.48745 6.89304i 0.486057 0.353141i
\(382\) −1.42618 + 4.38933i −0.0729697 + 0.224578i
\(383\) 5.96204 + 4.33168i 0.304646 + 0.221338i 0.729596 0.683879i \(-0.239708\pi\)
−0.424950 + 0.905217i \(0.639708\pi\)
\(384\) −0.309017 + 0.951057i −0.0157695 + 0.0485334i
\(385\) 1.35145 + 4.15932i 0.0688761 + 0.211979i
\(386\) 14.7913 10.7465i 0.752855 0.546981i
\(387\) −1.66907 5.13688i −0.0848438 0.261122i
\(388\) −5.42848 16.7071i −0.275589 0.848176i
\(389\) 22.1971 16.1271i 1.12544 0.817677i 0.140411 0.990093i \(-0.455158\pi\)
0.985024 + 0.172417i \(0.0551576\pi\)
\(390\) 1.45758 + 4.48597i 0.0738075 + 0.227156i
\(391\) −1.72839 + 5.31943i −0.0874083 + 0.269015i
\(392\) −0.913494 0.663692i −0.0461384 0.0335215i
\(393\) 2.78814 8.58101i 0.140643 0.432855i
\(394\) 1.82112 1.32312i 0.0917468 0.0666579i
\(395\) −3.44939 + 2.50613i −0.173558 + 0.126097i
\(396\) −1.46024 1.06092i −0.0733796 0.0533134i
\(397\) −9.17272 −0.460365 −0.230183 0.973147i \(-0.573932\pi\)
−0.230183 + 0.973147i \(0.573932\pi\)
\(398\) −7.13151 −0.357470
\(399\) 0.635487 + 0.461708i 0.0318141 + 0.0231143i
\(400\) 0.309017 + 0.951057i 0.0154508 + 0.0475528i
\(401\) −5.54794 + 17.0748i −0.277051 + 0.852676i 0.711618 + 0.702566i \(0.247963\pi\)
−0.988669 + 0.150109i \(0.952037\pi\)
\(402\) −16.3524 −0.815583
\(403\) −13.0108 + 22.8128i −0.648114 + 1.13638i
\(404\) −17.5243 −0.871869
\(405\) 0.309017 0.951057i 0.0153552 0.0472584i
\(406\) −6.07438 18.6950i −0.301466 0.927818i
\(407\) −12.4886 9.07352i −0.619038 0.449758i
\(408\) 5.01396 0.248228
\(409\) 32.8063 1.62217 0.811083 0.584931i \(-0.198878\pi\)
0.811083 + 0.584931i \(0.198878\pi\)
\(410\) −1.70020 1.23527i −0.0839669 0.0610055i
\(411\) 3.17603 2.30752i 0.156662 0.113821i
\(412\) 14.2718 10.3691i 0.703122 0.510848i
\(413\) −5.02310 + 15.4595i −0.247170 + 0.760712i
\(414\) 0.902476 + 0.655687i 0.0443543 + 0.0322253i
\(415\) −2.69898 + 8.30660i −0.132488 + 0.407755i
\(416\) 1.45758 + 4.48597i 0.0714638 + 0.219943i
\(417\) −5.71441 + 4.15176i −0.279836 + 0.203313i
\(418\) 0.180820 + 0.556506i 0.00884418 + 0.0272196i
\(419\) 4.58941 + 14.1248i 0.224207 + 0.690039i 0.998371 + 0.0570539i \(0.0181707\pi\)
−0.774164 + 0.632985i \(0.781829\pi\)
\(420\) −1.96024 + 1.42420i −0.0956498 + 0.0694936i
\(421\) −2.71404 8.35295i −0.132274 0.407098i 0.862882 0.505406i \(-0.168657\pi\)
−0.995156 + 0.0983076i \(0.968657\pi\)
\(422\) 7.96582 24.5163i 0.387770 1.19343i
\(423\) 4.86969 + 3.53804i 0.236773 + 0.172025i
\(424\) −0.433877 + 1.33534i −0.0210709 + 0.0648497i
\(425\) 4.05638 2.94713i 0.196763 0.142957i
\(426\) −8.91048 + 6.47384i −0.431714 + 0.313659i
\(427\) 30.4865 + 22.1497i 1.47535 + 1.07190i
\(428\) 3.32729 0.160831
\(429\) −8.51365 −0.411043
\(430\) −4.36969 3.17477i −0.210725 0.153101i
\(431\) 7.34746 + 22.6132i 0.353915 + 1.08924i 0.956636 + 0.291286i \(0.0940831\pi\)
−0.602721 + 0.797952i \(0.705917\pi\)
\(432\) 0.309017 0.951057i 0.0148676 0.0457577i
\(433\) 10.1903 0.489714 0.244857 0.969559i \(-0.421259\pi\)
0.244857 + 0.969559i \(0.421259\pi\)
\(434\) −13.2104 2.73513i −0.634121 0.131290i
\(435\) 8.11276 0.388977
\(436\) 0.978026 3.01005i 0.0468389 0.144155i
\(437\) −0.111753 0.343940i −0.00534586 0.0164529i
\(438\) −4.87235 3.53997i −0.232810 0.169146i
\(439\) 11.7134 0.559050 0.279525 0.960138i \(-0.409823\pi\)
0.279525 + 0.960138i \(0.409823\pi\)
\(440\) −1.80495 −0.0860477
\(441\) 0.913494 + 0.663692i 0.0434997 + 0.0316044i
\(442\) 19.1332 13.9011i 0.910076 0.661209i
\(443\) 29.9228 21.7402i 1.42168 1.03291i 0.430185 0.902741i \(-0.358448\pi\)
0.991492 0.130168i \(-0.0415516\pi\)
\(444\) 2.64286 8.13388i 0.125424 0.386017i
\(445\) −7.37667 5.35947i −0.349688 0.254063i
\(446\) 1.26677 3.89871i 0.0599832 0.184609i
\(447\) −3.72011 11.4493i −0.175955 0.541535i
\(448\) −1.96024 + 1.42420i −0.0926125 + 0.0672869i
\(449\) 6.03928 + 18.5870i 0.285011 + 0.877174i 0.986395 + 0.164391i \(0.0525658\pi\)
−0.701384 + 0.712784i \(0.747434\pi\)
\(450\) −0.309017 0.951057i −0.0145672 0.0448332i
\(451\) 3.06878 2.22960i 0.144503 0.104988i
\(452\) 2.10716 + 6.48517i 0.0991124 + 0.305037i
\(453\) 1.18012 3.63205i 0.0554471 0.170649i
\(454\) −11.9662 8.69393i −0.561600 0.408026i
\(455\) −3.53170 + 10.8694i −0.165569 + 0.509568i
\(456\) −0.262274 + 0.190553i −0.0122821 + 0.00892348i
\(457\) 26.8230 19.4881i 1.25473 0.911613i 0.256242 0.966613i \(-0.417516\pi\)
0.998486 + 0.0549996i \(0.0175158\pi\)
\(458\) −1.31306 0.953991i −0.0613551 0.0445771i
\(459\) −5.01396 −0.234032
\(460\) 1.11552 0.0520115
\(461\) 3.43399 + 2.49494i 0.159937 + 0.116201i 0.664875 0.746955i \(-0.268485\pi\)
−0.504938 + 0.863155i \(0.668485\pi\)
\(462\) −1.35145 4.15932i −0.0628750 0.193509i
\(463\) −0.925426 + 2.84817i −0.0430082 + 0.132366i −0.970255 0.242085i \(-0.922169\pi\)
0.927247 + 0.374451i \(0.122169\pi\)
\(464\) 8.11276 0.376625
\(465\) 2.75838 4.83646i 0.127917 0.224285i
\(466\) −24.6841 −1.14347
\(467\) −1.42206 + 4.37664i −0.0658049 + 0.202527i −0.978553 0.205997i \(-0.933956\pi\)
0.912748 + 0.408524i \(0.133956\pi\)
\(468\) −1.45758 4.48597i −0.0673767 0.207364i
\(469\) −32.0546 23.2890i −1.48014 1.07539i
\(470\) 6.01927 0.277648
\(471\) −17.3262 −0.798351
\(472\) −5.42745 3.94328i −0.249819 0.181504i
\(473\) 7.88708 5.73030i 0.362648 0.263480i
\(474\) 3.44939 2.50613i 0.158436 0.115110i
\(475\) −0.100180 + 0.308322i −0.00459657 + 0.0141468i
\(476\) 9.82855 + 7.14086i 0.450491 + 0.327301i
\(477\) 0.433877 1.33534i 0.0198659 0.0611408i
\(478\) −1.88111 5.78945i −0.0860397 0.264803i
\(479\) 6.58800 4.78646i 0.301014 0.218699i −0.427017 0.904243i \(-0.640436\pi\)
0.728031 + 0.685544i \(0.240436\pi\)
\(480\) −0.309017 0.951057i −0.0141046 0.0434096i
\(481\) −12.4659 38.3661i −0.568397 1.74934i
\(482\) 4.21977 3.06584i 0.192205 0.139645i
\(483\) 0.835240 + 2.57060i 0.0380047 + 0.116967i
\(484\) −2.39246 + 7.36322i −0.108748 + 0.334692i
\(485\) 14.2119 + 10.3256i 0.645331 + 0.468860i
\(486\) −0.309017 + 0.951057i −0.0140173 + 0.0431408i
\(487\) 28.0537 20.3822i 1.27124 0.923607i 0.271984 0.962302i \(-0.412320\pi\)
0.999251 + 0.0386950i \(0.0123201\pi\)
\(488\) −12.5822 + 9.14151i −0.569570 + 0.413817i
\(489\) 3.64244 + 2.64639i 0.164717 + 0.119674i
\(490\) 1.12914 0.0510094
\(491\) 21.1104 0.952698 0.476349 0.879256i \(-0.341960\pi\)
0.476349 + 0.879256i \(0.341960\pi\)
\(492\) 1.70020 + 1.23527i 0.0766509 + 0.0556902i
\(493\) −12.5699 38.6861i −0.566119 1.74234i
\(494\) −0.472531 + 1.45430i −0.0212602 + 0.0654321i
\(495\) 1.80495 0.0811265
\(496\) 2.75838 4.83646i 0.123855 0.217163i
\(497\) −26.6867 −1.19706
\(498\) 2.69898 8.30660i 0.120944 0.372227i
\(499\) −7.66259 23.5830i −0.343024 1.05572i −0.962633 0.270810i \(-0.912709\pi\)
0.619608 0.784911i \(-0.287291\pi\)
\(500\) −0.809017 0.587785i −0.0361803 0.0262866i
\(501\) 14.0247 0.626575
\(502\) 2.51338 0.112177
\(503\) 25.1874 + 18.2997i 1.12305 + 0.815943i 0.984669 0.174436i \(-0.0558101\pi\)
0.138381 + 0.990379i \(0.455810\pi\)
\(504\) 1.96024 1.42420i 0.0873159 0.0634387i
\(505\) 14.1775 10.3006i 0.630890 0.458369i
\(506\) −0.622194 + 1.91492i −0.0276599 + 0.0851284i
\(507\) −7.48219 5.43613i −0.332296 0.241427i
\(508\) −3.62388 + 11.1532i −0.160784 + 0.494842i
\(509\) −7.38814 22.7383i −0.327473 1.00786i −0.970312 0.241858i \(-0.922243\pi\)
0.642838 0.766002i \(-0.277757\pi\)
\(510\) −4.05638 + 2.94713i −0.179619 + 0.130501i
\(511\) −4.50935 13.8783i −0.199482 0.613942i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) 0.262274 0.190553i 0.0115797 0.00841313i
\(514\) 8.62859 + 26.5561i 0.380591 + 1.17134i
\(515\) −5.45135 + 16.7775i −0.240215 + 0.739306i
\(516\) 4.36969 + 3.17477i 0.192365 + 0.139761i
\(517\) −3.35731 + 10.3327i −0.147654 + 0.454434i
\(518\) 16.7649 12.1804i 0.736606 0.535175i
\(519\) 10.9148 7.93007i 0.479107 0.348091i
\(520\) −3.81600 2.77248i −0.167343 0.121581i
\(521\) 28.0331 1.22815 0.614075 0.789248i \(-0.289529\pi\)
0.614075 + 0.789248i \(0.289529\pi\)
\(522\) −8.11276 −0.355086
\(523\) 13.1521 + 9.55557i 0.575102 + 0.417836i 0.836955 0.547272i \(-0.184334\pi\)
−0.261853 + 0.965108i \(0.584334\pi\)
\(524\) 2.78814 + 8.58101i 0.121800 + 0.374863i
\(525\) 0.748744 2.30440i 0.0326779 0.100572i
\(526\) 2.33318 0.101731
\(527\) −27.3368 5.65989i −1.19081 0.246549i
\(528\) 1.80495 0.0785504
\(529\) −6.72285 + 20.6908i −0.292298 + 0.899601i
\(530\) −0.433877 1.33534i −0.0188464 0.0580033i
\(531\) 5.42745 + 3.94328i 0.235531 + 0.171124i
\(532\) −0.785505 −0.0340559
\(533\) 9.91272 0.429367
\(534\) 7.37667 + 5.35947i 0.319220 + 0.231927i
\(535\) −2.69184 + 1.95573i −0.116378 + 0.0845538i
\(536\) 13.2294 9.61170i 0.571421 0.415162i
\(537\) −0.249598 + 0.768185i −0.0107710 + 0.0331496i
\(538\) 14.7060 + 10.6845i 0.634020 + 0.460643i
\(539\) −0.629790 + 1.93829i −0.0271270 + 0.0834883i
\(540\) 0.309017 + 0.951057i 0.0132980 + 0.0409270i
\(541\) −4.25960 + 3.09478i −0.183135 + 0.133055i −0.675576 0.737291i \(-0.736105\pi\)
0.492441 + 0.870346i \(0.336105\pi\)
\(542\) −6.18398 19.0323i −0.265625 0.817509i
\(543\) 4.26400 + 13.1232i 0.182986 + 0.563172i
\(544\) −4.05638 + 2.94713i −0.173916 + 0.126357i
\(545\) 0.978026 + 3.01005i 0.0418940 + 0.128937i
\(546\) 3.53170 10.8694i 0.151143 0.465169i
\(547\) 8.74771 + 6.35558i 0.374025 + 0.271745i 0.758878 0.651233i \(-0.225748\pi\)
−0.384853 + 0.922978i \(0.625748\pi\)
\(548\) −1.21313 + 3.73364i −0.0518225 + 0.159493i
\(549\) 12.5822 9.14151i 0.536996 0.390150i
\(550\) 1.46024 1.06092i 0.0622647 0.0452380i
\(551\) 2.12777 + 1.54591i 0.0906459 + 0.0658581i
\(552\) −1.11552 −0.0474797
\(553\) 10.3308 0.439312
\(554\) 22.9272 + 16.6576i 0.974084 + 0.707714i
\(555\) 2.64286 + 8.13388i 0.112183 + 0.345264i
\(556\) 2.18271 6.71769i 0.0925675 0.284893i
\(557\) 15.2354 0.645543 0.322771 0.946477i \(-0.395385\pi\)
0.322771 + 0.946477i \(0.395385\pi\)
\(558\) −2.75838 + 4.83646i −0.116771 + 0.204744i
\(559\) 25.4767 1.07755
\(560\) 0.748744 2.30440i 0.0316402 0.0973785i
\(561\) −2.79659 8.60702i −0.118072 0.363389i
\(562\) −15.2055 11.0475i −0.641407 0.466010i
\(563\) 6.07239 0.255921 0.127960 0.991779i \(-0.459157\pi\)
0.127960 + 0.991779i \(0.459157\pi\)
\(564\) −6.01927 −0.253457
\(565\) −5.51661 4.00806i −0.232086 0.168620i
\(566\) 9.00698 6.54395i 0.378592 0.275063i
\(567\) −1.96024 + 1.42420i −0.0823222 + 0.0598106i
\(568\) 3.40350 10.4749i 0.142808 0.439517i
\(569\) −19.7611 14.3573i −0.828429 0.601889i 0.0906852 0.995880i \(-0.471094\pi\)
−0.919115 + 0.393990i \(0.871094\pi\)
\(570\) 0.100180 0.308322i 0.00419607 0.0129142i
\(571\) 5.41561 + 16.6675i 0.226636 + 0.697515i 0.998121 + 0.0612673i \(0.0195142\pi\)
−0.771485 + 0.636247i \(0.780486\pi\)
\(572\) 6.88769 5.00420i 0.287989 0.209236i
\(573\) 1.42618 + 4.38933i 0.0595795 + 0.183367i
\(574\) 1.57353 + 4.84283i 0.0656780 + 0.202136i
\(575\) −0.902476 + 0.655687i −0.0376358 + 0.0273440i
\(576\) 0.309017 + 0.951057i 0.0128757 + 0.0396274i
\(577\) −10.4038 + 32.0197i −0.433117 + 1.33300i 0.461886 + 0.886939i \(0.347173\pi\)
−0.895004 + 0.446059i \(0.852827\pi\)
\(578\) 6.58522 + 4.78444i 0.273909 + 0.199007i
\(579\) 5.64976 17.3882i 0.234796 0.722627i
\(580\) −6.56336 + 4.76856i −0.272529 + 0.198004i
\(581\) 17.1208 12.4390i 0.710292 0.516058i
\(582\) −14.2119 10.3256i −0.589104 0.428009i
\(583\) 2.53425 0.104958
\(584\) 6.02255 0.249215
\(585\) 3.81600 + 2.77248i 0.157772 + 0.114628i
\(586\) −2.30903 7.10646i −0.0953850 0.293565i
\(587\) 2.86701 8.82375i 0.118334 0.364195i −0.874294 0.485397i \(-0.838675\pi\)
0.992628 + 0.121202i \(0.0386750\pi\)
\(588\) −1.12914 −0.0465650
\(589\) 1.64506 0.742860i 0.0677833 0.0306090i
\(590\) 6.70870 0.276193
\(591\) 0.695606 2.14086i 0.0286134 0.0880631i
\(592\) 2.64286 + 8.13388i 0.108621 + 0.334300i
\(593\) −3.35825 2.43991i −0.137907 0.100195i 0.516693 0.856171i \(-0.327163\pi\)
−0.654600 + 0.755976i \(0.727163\pi\)
\(594\) −1.80495 −0.0740581
\(595\) −12.1488 −0.498050
\(596\) 9.73938 + 7.07608i 0.398941 + 0.289847i
\(597\) −5.76951 + 4.19180i −0.236130 + 0.171559i
\(598\) −4.25683 + 3.09277i −0.174075 + 0.126473i
\(599\) 8.65424 26.6350i 0.353603 1.08828i −0.603213 0.797580i \(-0.706113\pi\)
0.956815 0.290697i \(-0.0938870\pi\)
\(600\) 0.809017 + 0.587785i 0.0330280 + 0.0239962i
\(601\) 6.74578 20.7614i 0.275166 0.846874i −0.714009 0.700136i \(-0.753123\pi\)
0.989175 0.146738i \(-0.0468774\pi\)
\(602\) 4.04414 + 12.4466i 0.164827 + 0.507285i
\(603\) −13.2294 + 9.61170i −0.538741 + 0.391418i
\(604\) 1.18012 + 3.63205i 0.0480186 + 0.147786i
\(605\) −2.39246 7.36322i −0.0972672 0.299358i
\(606\) −14.1775 + 10.3006i −0.575921 + 0.418431i
\(607\) 0.844896 + 2.60032i 0.0342933 + 0.105544i 0.966738 0.255769i \(-0.0823286\pi\)
−0.932445 + 0.361313i \(0.882329\pi\)
\(608\) 0.100180 0.308322i 0.00406283 0.0125041i
\(609\) −15.9029 11.5541i −0.644419 0.468198i
\(610\) 4.80598 14.7913i 0.194588 0.598881i
\(611\) −22.9695 + 16.6883i −0.929247 + 0.675138i
\(612\) 4.05638 2.94713i 0.163969 0.119131i
\(613\) −23.5616 17.1185i −0.951645 0.691410i −0.000449259 1.00000i \(-0.500143\pi\)
−0.951195 + 0.308590i \(0.900143\pi\)
\(614\) 5.30198 0.213970
\(615\) −2.10156 −0.0847432
\(616\) 3.53813 + 2.57060i 0.142555 + 0.103573i
\(617\) 2.54647 + 7.83723i 0.102517 + 0.315515i 0.989140 0.146978i \(-0.0469548\pi\)
−0.886623 + 0.462494i \(0.846955\pi\)
\(618\) 5.45135 16.7775i 0.219285 0.674891i
\(619\) −41.0774 −1.65104 −0.825520 0.564373i \(-0.809118\pi\)
−0.825520 + 0.564373i \(0.809118\pi\)
\(620\) 0.611225 + 5.53411i 0.0245474 + 0.222255i
\(621\) 1.11552 0.0447643
\(622\) −7.39728 + 22.7665i −0.296604 + 0.912852i
\(623\) 6.82710 + 21.0116i 0.273522 + 0.841814i
\(624\) 3.81600 + 2.77248i 0.152762 + 0.110988i
\(625\) 1.00000 0.0400000
\(626\) −3.45328 −0.138021
\(627\) 0.473392 + 0.343940i 0.0189055 + 0.0137356i
\(628\) 14.0172 10.1841i 0.559348 0.406390i
\(629\) 34.6920 25.2052i 1.38326 1.00500i
\(630\) −0.748744 + 2.30440i −0.0298307 + 0.0918093i
\(631\) 17.3436 + 12.6009i 0.690438 + 0.501633i 0.876804 0.480848i \(-0.159671\pi\)
−0.186366 + 0.982480i \(0.559671\pi\)
\(632\) −1.31755 + 4.05500i −0.0524093 + 0.161299i
\(633\) −7.96582 24.5163i −0.316613 0.974435i
\(634\) −11.3941 + 8.27831i −0.452518 + 0.328774i
\(635\) −3.62388 11.1532i −0.143809 0.442600i
\(636\) 0.433877 + 1.33534i 0.0172043 + 0.0529495i
\(637\) −4.30880 + 3.13052i −0.170721 + 0.124036i
\(638\) −4.52498 13.9264i −0.179146 0.551353i
\(639\) −3.40350 + 10.4749i −0.134640 + 0.414381i
\(640\) 0.809017 + 0.587785i 0.0319792 + 0.0232343i
\(641\) 7.95563 24.4849i 0.314228 0.967095i −0.661843 0.749643i \(-0.730225\pi\)
0.976071 0.217453i \(-0.0697747\pi\)
\(642\) 2.69184 1.95573i 0.106238 0.0771867i
\(643\) −10.3053 + 7.48725i −0.406402 + 0.295268i −0.772144 0.635448i \(-0.780815\pi\)
0.365742 + 0.930716i \(0.380815\pi\)
\(644\) −2.18669 1.58872i −0.0861675 0.0626044i
\(645\) −5.40124 −0.212673
\(646\) −1.62547 −0.0639532
\(647\) 36.9577 + 26.8513i 1.45296 + 1.05563i 0.985129 + 0.171814i \(0.0549628\pi\)
0.467826 + 0.883820i \(0.345037\pi\)
\(648\) −0.309017 0.951057i −0.0121393 0.0373610i
\(649\) −3.74185 + 11.5162i −0.146880 + 0.452052i
\(650\) 4.71683 0.185009
\(651\) −12.2951 + 5.55214i −0.481884 + 0.217605i
\(652\) −4.50230 −0.176324
\(653\) −14.9951 + 46.1503i −0.586805 + 1.80600i 0.00509251 + 0.999987i \(0.498379\pi\)
−0.591898 + 0.806013i \(0.701621\pi\)
\(654\) −0.978026 3.01005i −0.0382438 0.117702i
\(655\) −7.29944 5.30335i −0.285213 0.207219i
\(656\) −2.10156 −0.0820522
\(657\) −6.02255 −0.234962
\(658\) −11.7992 8.57262i −0.459980 0.334195i
\(659\) −2.98330 + 2.16749i −0.116213 + 0.0844335i −0.644374 0.764711i \(-0.722882\pi\)
0.528161 + 0.849144i \(0.322882\pi\)
\(660\) −1.46024 + 1.06092i −0.0568396 + 0.0412964i
\(661\) −6.82942 + 21.0188i −0.265634 + 0.817537i 0.725913 + 0.687787i \(0.241417\pi\)
−0.991547 + 0.129750i \(0.958583\pi\)
\(662\) −11.7960 8.57029i −0.458464 0.333094i
\(663\) 7.30825 22.4925i 0.283829 0.873536i
\(664\) 2.69898 + 8.30660i 0.104741 + 0.322358i
\(665\) 0.635487 0.461708i 0.0246431 0.0179043i
\(666\) −2.64286 8.13388i −0.102409 0.315181i
\(667\) 2.79659 + 8.60702i 0.108284 + 0.333265i
\(668\) −11.3462 + 8.24349i −0.438997 + 0.318950i
\(669\) −1.26677 3.89871i −0.0489761 0.150733i
\(670\) −5.05317 + 15.5520i −0.195221 + 0.600828i
\(671\) 22.7103 + 16.5000i 0.876721 + 0.636975i
\(672\) −0.748744 + 2.30440i −0.0288834 + 0.0888940i
\(673\) −20.2474 + 14.7106i −0.780480 + 0.567052i −0.905123 0.425149i \(-0.860222\pi\)
0.124643 + 0.992202i \(0.460222\pi\)
\(674\) −21.3796 + 15.5332i −0.823512 + 0.598316i
\(675\) −0.809017 0.587785i −0.0311391 0.0226239i
\(676\) 9.24849 0.355711
\(677\) 8.10371 0.311451 0.155726 0.987800i \(-0.450228\pi\)
0.155726 + 0.987800i \(0.450228\pi\)
\(678\) 5.51661 + 4.00806i 0.211864 + 0.153928i
\(679\) −13.1531 40.4811i −0.504771 1.55352i
\(680\) 1.54940 4.76856i 0.0594167 0.182866i
\(681\) −14.7910 −0.566792
\(682\) −9.84084 2.03748i −0.376825 0.0780190i
\(683\) −30.4097 −1.16359 −0.581797 0.813334i \(-0.697650\pi\)
−0.581797 + 0.813334i \(0.697650\pi\)
\(684\) −0.100180 + 0.308322i −0.00383047 + 0.0117890i
\(685\) −1.21313 3.73364i −0.0463515 0.142655i
\(686\) −15.9350 11.5775i −0.608403 0.442030i
\(687\) −1.62303 −0.0619223
\(688\) −5.40124 −0.205920
\(689\) 5.35787 + 3.89272i 0.204119 + 0.148301i
\(690\) 0.902476 0.655687i 0.0343567 0.0249616i
\(691\) −19.9287 + 14.4790i −0.758122 + 0.550808i −0.898334 0.439314i \(-0.855222\pi\)
0.140212 + 0.990122i \(0.455222\pi\)
\(692\) −4.16908 + 12.8311i −0.158485 + 0.487766i
\(693\) −3.53813 2.57060i −0.134403 0.0976492i
\(694\) −4.30384 + 13.2459i −0.163371 + 0.502806i
\(695\) 2.18271 + 6.71769i 0.0827949 + 0.254816i
\(696\) 6.56336 4.76856i 0.248783 0.180752i
\(697\) 3.25616 + 10.0214i 0.123336 + 0.379588i
\(698\) −4.08009 12.5572i −0.154434 0.475298i
\(699\) −19.9699 + 14.5090i −0.755330 + 0.548779i
\(700\) 0.748744 + 2.30440i 0.0282999 + 0.0870980i
\(701\) 8.26991 25.4522i 0.312350 0.961315i −0.664481 0.747305i \(-0.731347\pi\)
0.976831 0.214010i \(-0.0686526\pi\)
\(702\) −3.81600 2.77248i −0.144026 0.104641i
\(703\) −0.856784 + 2.63691i −0.0323142 + 0.0994530i
\(704\) −1.46024 + 1.06092i −0.0550347 + 0.0399851i
\(705\) 4.86969 3.53804i 0.183403 0.133250i
\(706\) 9.91385 + 7.20284i 0.373113 + 0.271082i
\(707\) −42.4612 −1.59692
\(708\) −6.70870 −0.252128
\(709\) 23.6152 + 17.1574i 0.886886 + 0.644361i 0.935064 0.354478i \(-0.115341\pi\)
−0.0481779 + 0.998839i \(0.515341\pi\)
\(710\) 3.40350 + 10.4749i 0.127731 + 0.393116i
\(711\) 1.31755 4.05500i 0.0494120 0.152074i
\(712\) −9.11807 −0.341714
\(713\) 6.08197 + 1.25923i 0.227772 + 0.0471585i
\(714\) 12.1488 0.454656
\(715\) −2.63086 + 8.09696i −0.0983887 + 0.302809i
\(716\) −0.249598 0.768185i −0.00932793 0.0287084i
\(717\) −4.92480 3.57807i −0.183920 0.133626i
\(718\) −10.4646 −0.390535
\(719\) 24.5029 0.913804 0.456902 0.889517i \(-0.348959\pi\)
0.456902 + 0.889517i \(0.348959\pi\)
\(720\) −0.809017 0.587785i −0.0301503 0.0219055i
\(721\) 34.5804 25.1241i 1.28784 0.935671i
\(722\) −15.2863 + 11.1061i −0.568897 + 0.413328i
\(723\) 1.61181 4.96064i 0.0599438 0.184488i
\(724\) −11.1633 8.11060i −0.414880 0.301428i
\(725\) 2.50698 7.71569i 0.0931069 0.286554i
\(726\) 2.39246 + 7.36322i 0.0887924 + 0.273275i
\(727\) −19.2013 + 13.9505i −0.712136 + 0.517397i −0.883862 0.467748i \(-0.845066\pi\)
0.171726 + 0.985145i \(0.445066\pi\)
\(728\) 3.53170 + 10.8694i 0.130893 + 0.402849i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −4.87235 + 3.53997i −0.180334 + 0.131020i
\(731\) 8.36867 + 25.7561i 0.309526 + 0.952624i
\(732\) −4.80598 + 14.7913i −0.177634 + 0.546701i
\(733\) 10.1816 + 7.39739i 0.376067 + 0.273229i 0.759722 0.650248i \(-0.225335\pi\)
−0.383655 + 0.923476i \(0.625335\pi\)
\(734\) 9.30734 28.6450i 0.343540 1.05731i
\(735\) 0.913494 0.663692i 0.0336947 0.0244807i
\(736\) 0.902476 0.655687i 0.0332657 0.0241689i
\(737\) −23.8784 17.3486i −0.879571 0.639046i
\(738\) 2.10156 0.0773596
\(739\) −29.7735 −1.09524 −0.547618 0.836728i \(-0.684465\pi\)
−0.547618 + 0.836728i \(0.684465\pi\)
\(740\) −6.91909 5.02701i −0.254351 0.184797i
\(741\) 0.472531 + 1.45430i 0.0173589 + 0.0534251i
\(742\) −1.05128 + 3.23550i −0.0385936 + 0.118779i
\(743\) 1.68416 0.0617859 0.0308930 0.999523i \(-0.490165\pi\)
0.0308930 + 0.999523i \(0.490165\pi\)
\(744\) −0.611225 5.53411i −0.0224086 0.202890i
\(745\) −12.0385 −0.441058
\(746\) −6.26998 + 19.2970i −0.229560 + 0.706514i
\(747\) −2.69898 8.30660i −0.0987504 0.303922i
\(748\) 7.32157 + 5.31943i 0.267703 + 0.194498i
\(749\) 8.06199 0.294579
\(750\) −1.00000 −0.0365148
\(751\) −11.4137 8.29254i −0.416492 0.302599i 0.359733 0.933055i \(-0.382868\pi\)
−0.776225 + 0.630456i \(0.782868\pi\)
\(752\) 4.86969 3.53804i 0.177579 0.129019i
\(753\) 2.03336 1.47733i 0.0740999 0.0538367i
\(754\) 11.8250 36.3936i 0.430641 1.32538i
\(755\) −3.08961 2.24473i −0.112442 0.0816941i
\(756\) 0.748744 2.30440i 0.0272315 0.0838101i
\(757\) −0.493620 1.51921i −0.0179409 0.0552165i 0.941685 0.336495i \(-0.109242\pi\)
−0.959626 + 0.281279i \(0.909242\pi\)
\(758\) −13.5373 + 9.83542i −0.491697 + 0.357239i
\(759\) 0.622194 + 1.91492i 0.0225842 + 0.0695071i
\(760\) 0.100180 + 0.308322i 0.00363390 + 0.0111840i
\(761\) −19.5514 + 14.2049i −0.708738 + 0.514928i −0.882766 0.469812i \(-0.844322\pi\)
0.174028 + 0.984741i \(0.444322\pi\)
\(762\) 3.62388 + 11.1532i 0.131279 + 0.404037i
\(763\) 2.36974 7.29332i 0.0857904 0.264036i
\(764\) −3.73379 2.71276i −0.135084 0.0981440i
\(765\) −1.54940 + 4.76856i −0.0560186 + 0.172408i
\(766\) −5.96204 + 4.33168i −0.215417 + 0.156510i
\(767\) −25.6004 + 18.5998i −0.924376 + 0.671598i
\(768\) −0.809017 0.587785i −0.0291929 0.0212099i
\(769\) 7.98207 0.287841 0.143920 0.989589i \(-0.454029\pi\)
0.143920 + 0.989589i \(0.454029\pi\)
\(770\) −4.37337 −0.157605
\(771\) 22.5899 + 16.4126i 0.813557 + 0.591084i
\(772\) 5.64976 + 17.3882i 0.203339 + 0.625814i
\(773\) −2.81150 + 8.65290i −0.101123 + 0.311223i −0.988801 0.149241i \(-0.952317\pi\)
0.887678 + 0.460464i \(0.152317\pi\)
\(774\) 5.40124 0.194143
\(775\) −3.74736 4.11792i −0.134609 0.147920i
\(776\) 17.5669 0.630616
\(777\) 6.40361 19.7083i 0.229728 0.707030i
\(778\) 8.47852 + 26.0942i 0.303970 + 0.935522i
\(779\) −0.551186 0.400460i −0.0197483 0.0143480i
\(780\) −4.71683 −0.168890
\(781\) −19.8797 −0.711350
\(782\) −4.52498 3.28759i −0.161813 0.117564i
\(783\) −6.56336 + 4.76856i −0.234555 + 0.170414i
\(784\) 0.913494 0.663692i 0.0326248 0.0237033i
\(785\) −5.35410 + 16.4782i −0.191096 + 0.588133i
\(786\) 7.29944 + 5.30335i 0.260362 + 0.189164i
\(787\) 4.85077 14.9291i 0.172911 0.532166i −0.826621 0.562759i \(-0.809740\pi\)
0.999532 + 0.0305936i \(0.00973976\pi\)
\(788\) 0.695606 + 2.14086i 0.0247800 + 0.0762648i
\(789\) 1.88758 1.37141i 0.0671996 0.0488234i
\(790\) −1.31755 4.05500i −0.0468763 0.144270i
\(791\) 5.10562 + 15.7135i 0.181535 + 0.558707i
\(792\) 1.46024 1.06092i 0.0518872 0.0376983i
\(793\) 22.6690 + 69.7679i 0.804999 + 2.47753i
\(794\) 2.83452 8.72377i 0.100594 0.309595i
\(795\) −1.13590 0.825283i −0.0402864 0.0292698i
\(796\) 2.20376 6.78247i 0.0781101 0.240398i
\(797\) −22.3483 + 16.2370i −0.791617 + 0.575143i −0.908443 0.418009i \(-0.862728\pi\)
0.116826 + 0.993152i \(0.462728\pi\)
\(798\) −0.635487 + 0.461708i −0.0224960 + 0.0163443i
\(799\) −24.4164 17.7396i −0.863791 0.627581i
\(800\) −1.00000 −0.0353553
\(801\) 9.11807 0.322171
\(802\) −14.5247 10.5528i −0.512885 0.372633i
\(803\) −3.35914 10.3384i −0.118542 0.364834i
\(804\) 5.05317 15.5520i 0.178211 0.548479i
\(805\) 2.70289 0.0952644
\(806\) −17.6757 19.4235i −0.622599 0.684165i
\(807\) 18.1776 0.639882
\(808\) 5.41532 16.6666i 0.190510 0.586331i
\(809\) −13.2674 40.8328i −0.466456 1.43560i −0.857142 0.515080i \(-0.827762\pi\)
0.390686 0.920524i \(-0.372238\pi\)
\(810\) 0.809017 + 0.587785i 0.0284260 + 0.0206527i
\(811\) −53.0390 −1.86245 −0.931226 0.364442i \(-0.881260\pi\)
−0.931226 + 0.364442i \(0.881260\pi\)
\(812\) 19.6571 0.689829
\(813\) −16.1899 11.7626i −0.567804 0.412534i
\(814\) 12.4886 9.07352i 0.437726 0.318027i
\(815\) 3.64244 2.64639i 0.127589 0.0926989i
\(816\) −1.54940 + 4.76856i −0.0542398 + 0.166933i
\(817\) −1.41660 1.02922i −0.0495607 0.0360080i
\(818\) −10.1377 + 31.2006i −0.354456 + 1.09090i
\(819\) −3.53170 10.8694i −0.123408 0.379809i
\(820\) 1.70020 1.23527i 0.0593736 0.0431374i
\(821\) 2.39687 + 7.37680i 0.0836513 + 0.257452i 0.984130 0.177447i \(-0.0567839\pi\)
−0.900479 + 0.434899i \(0.856784\pi\)
\(822\) 1.21313 + 3.73364i 0.0423129 + 0.130226i
\(823\) 42.3576 30.7746i 1.47649 1.07273i 0.497826 0.867277i \(-0.334132\pi\)
0.978666 0.205458i \(-0.0658683\pi\)
\(824\) 5.45135 + 16.7775i 0.189907 + 0.584473i
\(825\) 0.557761 1.71661i 0.0194187 0.0597647i
\(826\) −13.1506 9.55450i −0.457569 0.332444i
\(827\) 0.408959 1.25865i 0.0142209 0.0437674i −0.943694 0.330819i \(-0.892675\pi\)
0.957915 + 0.287051i \(0.0926751\pi\)
\(828\) −0.902476 + 0.655687i −0.0313632 + 0.0227867i
\(829\) 15.6629 11.3798i 0.543996 0.395236i −0.281571 0.959540i \(-0.590856\pi\)
0.825567 + 0.564304i \(0.190856\pi\)
\(830\) −7.06601 5.13376i −0.245265 0.178195i
\(831\) 28.3396 0.983090
\(832\) −4.71683 −0.163527
\(833\) −4.58022 3.32772i −0.158695 0.115299i
\(834\) −2.18271 6.71769i −0.0755810 0.232615i
\(835\) 4.33386 13.3382i 0.149979 0.461589i
\(836\) −0.585145 −0.0202377
\(837\) 0.611225 + 5.53411i 0.0211270 + 0.191287i
\(838\) −14.8516 −0.513041
\(839\) 10.5086 32.3423i 0.362799 1.11658i −0.588549 0.808461i \(-0.700301\pi\)
0.951348 0.308118i \(-0.0996993\pi\)
\(840\) −0.748744 2.30440i −0.0258341 0.0795092i
\(841\) −29.7854 21.6404i −1.02708 0.746220i
\(842\) 8.78281 0.302676
\(843\) −18.7951 −0.647337
\(844\) 20.8548 + 15.1519i 0.717852 + 0.521550i
\(845\) −7.48219 + 5.43613i −0.257395 + 0.187009i
\(846\) −4.86969 + 3.53804i −0.167423 + 0.121640i
\(847\) −5.79689 + 17.8410i −0.199183 + 0.613023i
\(848\) −1.13590 0.825283i −0.0390071 0.0283403i
\(849\) 3.44036 10.5883i 0.118073 0.363391i
\(850\) 1.54940 + 4.76856i 0.0531439 + 0.163560i
\(851\) −7.71839 + 5.60774i −0.264583 + 0.192231i
\(852\) −3.40350 10.4749i −0.116602 0.358864i
\(853\) 16.0919 + 49.5257i 0.550975 + 1.69573i 0.706342 + 0.707870i \(0.250344\pi\)
−0.155367 + 0.987857i \(0.549656\pi\)
\(854\) −30.4865 + 22.1497i −1.04323 + 0.757949i
\(855\) −0.100180 0.308322i −0.00342608 0.0105444i
\(856\) −1.02819 + 3.16444i −0.0351428 + 0.108159i
\(857\) −43.7750 31.8044i −1.49533 1.08642i −0.972197 0.234165i \(-0.924764\pi\)
−0.523129 0.852253i \(-0.675236\pi\)
\(858\) 2.63086 8.09696i 0.0898162 0.276426i
\(859\) 26.1411 18.9926i 0.891923 0.648020i −0.0444560 0.999011i \(-0.514155\pi\)
0.936379 + 0.350992i \(0.114155\pi\)
\(860\) 4.36969 3.17477i 0.149005 0.108259i
\(861\) 4.11956 + 2.99304i 0.140394 + 0.102002i
\(862\) −23.7769 −0.809844
\(863\) 10.0039 0.340538 0.170269 0.985398i \(-0.445536\pi\)
0.170269 + 0.985398i \(0.445536\pi\)
\(864\) 0.809017 + 0.587785i 0.0275233 + 0.0199969i
\(865\) −4.16908 12.8311i −0.141753 0.436271i
\(866\) −3.14897 + 9.69154i −0.107006 + 0.329332i
\(867\) 8.13978 0.276442
\(868\) 6.68351 11.7187i 0.226853 0.397758i
\(869\) 7.69573 0.261060
\(870\) −2.50698 + 7.71569i −0.0849946 + 0.261586i
\(871\) −23.8349 73.3564i −0.807616 2.48559i
\(872\) 2.56050 + 1.86032i 0.0867096 + 0.0629982i
\(873\) −17.5669 −0.594550
\(874\) 0.361639 0.0122326
\(875\) −1.96024 1.42420i −0.0662681 0.0481466i
\(876\) 4.87235 3.53997i 0.164621 0.119604i
\(877\) −2.74491 + 1.99429i −0.0926890 + 0.0673425i −0.633165 0.774017i \(-0.718244\pi\)
0.540476 + 0.841360i \(0.318244\pi\)
\(878\) −3.61964 + 11.1401i −0.122157 + 0.375960i
\(879\) −6.04511 4.39203i −0.203897 0.148140i
\(880\) 0.557761 1.71661i 0.0188021 0.0578669i
\(881\) 10.2312 + 31.4885i 0.344699 + 1.06087i 0.961745 + 0.273946i \(0.0883291\pi\)
−0.617046 + 0.786927i \(0.711671\pi\)
\(882\) −0.913494 + 0.663692i −0.0307589 + 0.0223477i
\(883\) −2.99169 9.20746i −0.100678 0.309856i 0.888014 0.459817i \(-0.152085\pi\)
−0.988692 + 0.149961i \(0.952085\pi\)
\(884\) 7.30825 + 22.4925i 0.245803 + 0.756504i
\(885\) 5.42745 3.94328i 0.182442 0.132552i
\(886\) 11.4295 + 35.1764i 0.383982 + 1.18177i
\(887\) 11.3960 35.0732i 0.382639 1.17764i −0.555540 0.831490i \(-0.687488\pi\)
0.938179 0.346151i \(-0.112512\pi\)
\(888\) 6.91909 + 5.02701i 0.232189 + 0.168696i
\(889\) −8.78062 + 27.0240i −0.294492 + 0.906355i
\(890\) 7.37667 5.35947i 0.247267 0.179650i
\(891\) −1.46024 + 1.06092i −0.0489198 + 0.0355423i
\(892\) 3.31644 + 2.40954i 0.111043 + 0.0806772i
\(893\) 1.95138 0.0653004
\(894\) 12.0385 0.402629
\(895\) 0.653457 + 0.474764i 0.0218427 + 0.0158696i
\(896\) −0.748744 2.30440i −0.0250138 0.0769845i
\(897\) −1.62596 + 5.00420i −0.0542893 + 0.167085i
\(898\) −19.5435 −0.652176
\(899\) −41.1672 + 18.5899i −1.37300 + 0.620009i
\(900\) 1.00000 0.0333333
\(901\) −2.17544 + 6.69532i −0.0724745 + 0.223053i
\(902\) 1.17217 + 3.60757i 0.0390290 + 0.120119i
\(903\) 10.5877 + 7.69241i 0.352337 + 0.255988i
\(904\) −6.81891 −0.226794
\(905\) 13.7986 0.458680
\(906\) 3.08961 + 2.24473i 0.102645 + 0.0745762i
\(907\) −17.2831 + 12.5569i −0.573875 + 0.416945i −0.836511 0.547950i \(-0.815408\pi\)
0.262636 + 0.964895i \(0.415408\pi\)
\(908\) 11.9662 8.69393i 0.397111 0.288518i
\(909\) −5.41532 + 16.6666i −0.179615 + 0.552798i
\(910\) −9.24610 6.71769i −0.306505 0.222689i
\(911\) 7.40895 22.8024i 0.245469 0.755477i −0.750089 0.661336i \(-0.769990\pi\)
0.995559 0.0941408i \(-0.0300104\pi\)
\(912\) −0.100180 0.308322i −0.00331729 0.0102096i
\(913\) 12.7538 9.26619i 0.422090 0.306666i
\(914\) 10.2455 + 31.5324i 0.338890 + 1.04300i
\(915\) −4.80598 14.7913i −0.158881 0.488984i
\(916\) 1.31306 0.953991i 0.0433846 0.0315207i
\(917\) 6.75562 + 20.7917i 0.223090 + 0.686601i
\(918\) 1.54940 4.76856i 0.0511378 0.157386i
\(919\) 30.1080 + 21.8747i 0.993170 + 0.721580i 0.960613 0.277890i \(-0.0896349\pi\)
0.0325570 + 0.999470i \(0.489635\pi\)
\(920\) −0.344715 + 1.06092i −0.0113649 + 0.0349776i
\(921\) 4.28939 3.11642i 0.141340 0.102690i
\(922\) −3.43399 + 2.49494i −0.113092 + 0.0821664i
\(923\) −42.0292 30.5360i −1.38341 1.00511i
\(924\) 4.37337 0.143873
\(925\) 8.55247 0.281203
\(926\) −2.42280 1.76027i −0.0796181 0.0578459i
\(927\) −5.45135 16.7775i −0.179046 0.551046i
\(928\) −2.50698 + 7.71569i −0.0822956 + 0.253280i
\(929\) 5.38273 0.176602 0.0883009 0.996094i \(-0.471856\pi\)
0.0883009 + 0.996094i \(0.471856\pi\)
\(930\) 3.74736 + 4.11792i 0.122881 + 0.135032i
\(931\) 0.366055 0.0119970
\(932\) 7.62781 23.4760i 0.249857 0.768982i
\(933\) 7.39728 + 22.7665i 0.242176 + 0.745341i
\(934\) −3.72299 2.70491i −0.121820 0.0885074i
\(935\) −9.04995 −0.295965
\(936\) 4.71683 0.154174
\(937\) 16.6234 + 12.0776i 0.543063 + 0.394558i 0.825221 0.564810i \(-0.191050\pi\)
−0.282159 + 0.959368i \(0.591050\pi\)
\(938\) 32.0546 23.2890i 1.04662 0.760413i
\(939\) −2.79376 + 2.02978i −0.0911709 + 0.0662395i
\(940\) −1.86006 + 5.72467i −0.0606684 + 0.186718i
\(941\) −39.0622 28.3803i −1.27339 0.925172i −0.274058 0.961713i \(-0.588366\pi\)
−0.999332 + 0.0365408i \(0.988366\pi\)
\(942\) 5.35410 16.4782i 0.174446 0.536890i
\(943\) −0.724440 2.22960i −0.0235910 0.0726057i
\(944\) 5.42745 3.94328i 0.176649 0.128343i
\(945\) 0.748744 + 2.30440i 0.0243566 + 0.0749620i
\(946\) 3.01260 + 9.27182i 0.0979480 + 0.301453i
\(947\) −5.63111 + 4.09124i −0.182986 + 0.132947i −0.675508 0.737353i \(-0.736075\pi\)
0.492521 + 0.870301i \(0.336075\pi\)
\(948\) 1.31755 + 4.05500i 0.0427920 + 0.131700i
\(949\) 8.77836 27.0170i 0.284958 0.877009i
\(950\) −0.262274 0.190553i −0.00850930 0.00618237i
\(951\) −4.35216 + 13.3946i −0.141129 + 0.434349i
\(952\) −9.82855 + 7.14086i −0.318545 + 0.231436i
\(953\) 21.3565 15.5164i 0.691806 0.502627i −0.185447 0.982654i \(-0.559373\pi\)
0.877253 + 0.480028i \(0.159373\pi\)
\(954\) 1.13590 + 0.825283i 0.0367763 + 0.0267195i
\(955\) 4.61521 0.149345
\(956\) 6.08738 0.196880
\(957\) −11.8465 8.60702i −0.382944 0.278225i
\(958\) 2.51639 + 7.74466i 0.0813010 + 0.250219i
\(959\) −2.93941 + 9.04656i −0.0949184 + 0.292129i
\(960\) 1.00000 0.0322749
\(961\) −2.91457 + 30.8627i −0.0940185 + 0.995570i
\(962\) 40.3405 1.30063
\(963\) 1.02819 3.16444i 0.0331330 0.101973i
\(964\) 1.61181 + 4.96064i 0.0519129 + 0.159771i
\(965\) −14.7913 10.7465i −0.476147 0.345941i
\(966\) −2.70289 −0.0869641
\(967\) 24.0701 0.774043 0.387021 0.922071i \(-0.373504\pi\)
0.387021 + 0.922071i \(0.373504\pi\)
\(968\) −6.26353 4.55072i −0.201317 0.146266i
\(969\) −1.31503 + 0.955427i −0.0422449 + 0.0306927i
\(970\) −14.2119 + 10.3256i −0.456318 + 0.331534i
\(971\) −12.9516 + 39.8608i −0.415636 + 1.27920i 0.496045 + 0.868297i \(0.334785\pi\)
−0.911681 + 0.410899i \(0.865215\pi\)
\(972\) −0.809017 0.587785i −0.0259492 0.0188532i
\(973\) 5.28867 16.2769i 0.169547 0.521812i
\(974\) 10.7156 + 32.9791i 0.343349 + 1.05672i
\(975\) 3.81600 2.77248i 0.122210 0.0887905i
\(976\) −4.80598 14.7913i −0.153836 0.473457i
\(977\) 6.07981 + 18.7117i 0.194510 + 0.598641i 0.999982 + 0.00600699i \(0.00191210\pi\)
−0.805472 + 0.592634i \(0.798088\pi\)
\(978\) −3.64244 + 2.64639i −0.116472 + 0.0846221i
\(979\) 5.08570 + 15.6522i 0.162540 + 0.500246i
\(980\) −0.348924 + 1.07388i −0.0111460 + 0.0343037i
\(981\) −2.56050 1.86032i −0.0817506 0.0593953i
\(982\) −6.52347 + 20.0772i −0.208172 + 0.640688i
\(983\) 44.3552 32.2259i 1.41471 1.02785i 0.422094 0.906552i \(-0.361295\pi\)
0.992617 0.121295i \(-0.0387046\pi\)
\(984\) −1.70020 + 1.23527i −0.0542004 + 0.0393789i
\(985\) −1.82112 1.32312i −0.0580257 0.0421582i
\(986\) 40.6770 1.29542
\(987\) −14.5846 −0.464233
\(988\) −1.23710 0.898808i −0.0393575 0.0285949i
\(989\) −1.86189 5.73030i −0.0592046 0.182213i
\(990\) −0.557761 + 1.71661i −0.0177268 + 0.0545575i
\(991\) −5.41290 −0.171947 −0.0859733 0.996297i \(-0.527400\pi\)
−0.0859733 + 0.996297i \(0.527400\pi\)
\(992\) 3.74736 + 4.11792i 0.118979 + 0.130744i
\(993\) −14.5806 −0.462703
\(994\) 8.24663 25.3805i 0.261567 0.805021i
\(995\) 2.20376 + 6.78247i 0.0698638 + 0.215019i
\(996\) 7.06601 + 5.13376i 0.223895 + 0.162669i
\(997\) −31.3340 −0.992356 −0.496178 0.868221i \(-0.665264\pi\)
−0.496178 + 0.868221i \(0.665264\pi\)
\(998\) 24.7967 0.784924
\(999\) −6.91909 5.02701i −0.218910 0.159048i
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 930.2.n.e.721.1 12
31.4 even 5 inner 930.2.n.e.841.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.n.e.721.1 12 1.1 even 1 trivial
930.2.n.e.841.1 yes 12 31.4 even 5 inner