Properties

Label 288.2.bf.a.11.9
Level $288$
Weight $2$
Character 288.11
Analytic conductor $2.300$
Analytic rank $0$
Dimension $368$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(11,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([12, 15, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.bf (of order \(24\), degree \(8\), 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: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(368\)
Relative dimension: \(46\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 11.9
Character \(\chi\) \(=\) 288.11
Dual form 288.2.bf.a.131.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.18241 - 0.775832i) q^{2} +(-0.200716 + 1.72038i) q^{3} +(0.796170 + 1.83470i) q^{4} +(-0.263676 - 2.00282i) q^{5} +(1.57205 - 1.87847i) q^{6} +(-0.327090 - 1.22072i) q^{7} +(0.482020 - 2.78705i) q^{8} +(-2.91943 - 0.690617i) q^{9} +O(q^{10})\) \(q+(-1.18241 - 0.775832i) q^{2} +(-0.200716 + 1.72038i) q^{3} +(0.796170 + 1.83470i) q^{4} +(-0.263676 - 2.00282i) q^{5} +(1.57205 - 1.87847i) q^{6} +(-0.327090 - 1.22072i) q^{7} +(0.482020 - 2.78705i) q^{8} +(-2.91943 - 0.690617i) q^{9} +(-1.24208 + 2.57271i) q^{10} +(4.33754 - 3.32831i) q^{11} +(-3.31618 + 1.00146i) q^{12} +(-1.58016 + 2.05931i) q^{13} +(-0.560318 + 1.69715i) q^{14} +(3.49853 - 0.0516253i) q^{15} +(-2.73223 + 2.92146i) q^{16} +4.55567 q^{17} +(2.91615 + 3.08157i) q^{18} +(5.75676 - 2.38453i) q^{19} +(3.46463 - 2.07835i) q^{20} +(2.16575 - 0.317702i) q^{21} +(-7.71094 + 0.570215i) q^{22} +(2.66447 + 0.713943i) q^{23} +(4.69804 + 1.38866i) q^{24} +(0.887885 - 0.237908i) q^{25} +(3.46607 - 1.20900i) q^{26} +(1.77410 - 4.88391i) q^{27} +(1.97923 - 1.57201i) q^{28} +(-9.89471 - 1.30266i) q^{29} +(-4.17674 - 2.65323i) q^{30} +(3.42244 - 1.97595i) q^{31} +(5.49717 - 1.33461i) q^{32} +(4.85535 + 8.13027i) q^{33} +(-5.38665 - 3.53443i) q^{34} +(-2.35863 + 0.976975i) q^{35} +(-1.05729 - 5.90611i) q^{36} +(-2.63059 + 6.35081i) q^{37} +(-8.65682 - 1.64680i) q^{38} +(-3.22563 - 3.13182i) q^{39} +(-5.70905 - 0.230519i) q^{40} +(2.39889 - 8.95279i) q^{41} +(-2.80728 - 1.30461i) q^{42} +(-0.0159977 - 0.0208487i) q^{43} +(9.55986 + 5.30817i) q^{44} +(-0.613396 + 6.02917i) q^{45} +(-2.59659 - 2.91135i) q^{46} +(-0.938219 - 0.541681i) q^{47} +(-4.47763 - 5.28686i) q^{48} +(4.67901 - 2.70143i) q^{49} +(-1.23442 - 0.407545i) q^{50} +(-0.914396 + 7.83749i) q^{51} +(-5.03628 - 1.25956i) q^{52} +(-0.240880 + 0.581535i) q^{53} +(-5.88680 + 4.39836i) q^{54} +(-7.80969 - 7.80969i) q^{55} +(-3.55987 + 0.323207i) q^{56} +(2.94682 + 10.3824i) q^{57} +(10.6889 + 9.21691i) q^{58} +(-10.3062 + 1.35684i) q^{59} +(2.88014 + 6.37764i) q^{60} +(0.259109 - 1.96813i) q^{61} +(-5.57972 - 0.318866i) q^{62} +(0.111868 + 3.78969i) q^{63} +(-7.53531 - 2.68683i) q^{64} +(4.54106 + 2.62178i) q^{65} +(0.566723 - 13.3802i) q^{66} +(-0.569713 + 0.742465i) q^{67} +(3.62709 + 8.35827i) q^{68} +(-1.76306 + 4.44061i) q^{69} +(3.54682 + 0.674716i) q^{70} +(7.83003 + 7.83003i) q^{71} +(-3.33201 + 7.80370i) q^{72} +(-5.95511 + 5.95511i) q^{73} +(8.03759 - 5.46834i) q^{74} +(0.231080 + 1.57525i) q^{75} +(8.95824 + 8.66342i) q^{76} +(-5.48169 - 4.20625i) q^{77} +(1.38424 + 6.20563i) q^{78} +(0.917276 - 1.58877i) q^{79} +(6.57157 + 4.70183i) q^{80} +(8.04610 + 4.03241i) q^{81} +(-9.78233 + 8.72470i) q^{82} +(-2.87282 - 0.378214i) q^{83} +(2.30719 + 3.72055i) q^{84} +(-1.20122 - 9.12416i) q^{85} +(0.00274078 + 0.0370631i) q^{86} +(4.22711 - 16.7612i) q^{87} +(-7.18539 - 13.6933i) q^{88} +(-4.48131 + 4.48131i) q^{89} +(5.40291 - 6.65304i) q^{90} +(3.03069 + 1.25535i) q^{91} +(0.811504 + 5.45692i) q^{92} +(2.71245 + 6.28451i) q^{93} +(0.689103 + 1.36839i) q^{94} +(-6.29368 - 10.9010i) q^{95} +(1.19266 + 9.72510i) q^{96} +(-7.05812 + 12.2250i) q^{97} +(-7.62835 - 0.435940i) q^{98} +(-14.9617 + 6.72118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18241 0.775832i −0.836088 0.548596i
\(3\) −0.200716 + 1.72038i −0.115884 + 0.993263i
\(4\) 0.796170 + 1.83470i 0.398085 + 0.917349i
\(5\) −0.263676 2.00282i −0.117919 0.895686i −0.943493 0.331392i \(-0.892482\pi\)
0.825574 0.564294i \(-0.190852\pi\)
\(6\) 1.57205 1.87847i 0.641789 0.766881i
\(7\) −0.327090 1.22072i −0.123628 0.461388i 0.876159 0.482023i \(-0.160098\pi\)
−0.999787 + 0.0206352i \(0.993431\pi\)
\(8\) 0.482020 2.78705i 0.170420 0.985372i
\(9\) −2.91943 0.690617i −0.973142 0.230206i
\(10\) −1.24208 + 2.57271i −0.392779 + 0.813562i
\(11\) 4.33754 3.32831i 1.30782 1.00352i 0.309197 0.950998i \(-0.399940\pi\)
0.998620 0.0525253i \(-0.0167270\pi\)
\(12\) −3.31618 + 1.00146i −0.957300 + 0.289097i
\(13\) −1.58016 + 2.05931i −0.438258 + 0.571149i −0.959302 0.282381i \(-0.908876\pi\)
0.521044 + 0.853530i \(0.325543\pi\)
\(14\) −0.560318 + 1.69715i −0.149751 + 0.453583i
\(15\) 3.49853 0.0516253i 0.903317 0.0133296i
\(16\) −2.73223 + 2.92146i −0.683057 + 0.730365i
\(17\) 4.55567 1.10491 0.552456 0.833542i \(-0.313691\pi\)
0.552456 + 0.833542i \(0.313691\pi\)
\(18\) 2.91615 + 3.08157i 0.687342 + 0.726334i
\(19\) 5.75676 2.38453i 1.32069 0.547048i 0.392705 0.919664i \(-0.371539\pi\)
0.927985 + 0.372616i \(0.121539\pi\)
\(20\) 3.46463 2.07835i 0.774715 0.464732i
\(21\) 2.16575 0.317702i 0.472606 0.0693283i
\(22\) −7.71094 + 0.570215i −1.64398 + 0.121570i
\(23\) 2.66447 + 0.713943i 0.555581 + 0.148868i 0.525675 0.850685i \(-0.323813\pi\)
0.0299057 + 0.999553i \(0.490479\pi\)
\(24\) 4.69804 + 1.38866i 0.958984 + 0.283460i
\(25\) 0.887885 0.237908i 0.177577 0.0475816i
\(26\) 3.46607 1.20900i 0.679752 0.237104i
\(27\) 1.77410 4.88391i 0.341426 0.939909i
\(28\) 1.97923 1.57201i 0.374039 0.297082i
\(29\) −9.89471 1.30266i −1.83740 0.241899i −0.869626 0.493711i \(-0.835640\pi\)
−0.967776 + 0.251813i \(0.918973\pi\)
\(30\) −4.17674 2.65323i −0.762565 0.484411i
\(31\) 3.42244 1.97595i 0.614689 0.354891i −0.160109 0.987099i \(-0.551185\pi\)
0.774798 + 0.632208i \(0.217851\pi\)
\(32\) 5.49717 1.33461i 0.971771 0.235927i
\(33\) 4.85535 + 8.13027i 0.845208 + 1.41530i
\(34\) −5.38665 3.53443i −0.923803 0.606150i
\(35\) −2.35863 + 0.976975i −0.398681 + 0.165139i
\(36\) −1.05729 5.90611i −0.176214 0.984352i
\(37\) −2.63059 + 6.35081i −0.432467 + 1.04407i 0.546023 + 0.837770i \(0.316141\pi\)
−0.978490 + 0.206297i \(0.933859\pi\)
\(38\) −8.65682 1.64680i −1.40432 0.267145i
\(39\) −3.22563 3.13182i −0.516514 0.501492i
\(40\) −5.70905 0.230519i −0.902680 0.0364483i
\(41\) 2.39889 8.95279i 0.374644 1.39819i −0.479220 0.877695i \(-0.659080\pi\)
0.853864 0.520496i \(-0.174253\pi\)
\(42\) −2.80728 1.30461i −0.433173 0.201305i
\(43\) −0.0159977 0.0208487i −0.00243963 0.00317939i 0.792132 0.610350i \(-0.208971\pi\)
−0.794572 + 0.607171i \(0.792304\pi\)
\(44\) 9.55986 + 5.30817i 1.44120 + 0.800236i
\(45\) −0.613396 + 6.02917i −0.0914397 + 0.898776i
\(46\) −2.59659 2.91135i −0.382846 0.429256i
\(47\) −0.938219 0.541681i −0.136853 0.0790123i 0.430010 0.902824i \(-0.358510\pi\)
−0.566863 + 0.823812i \(0.691843\pi\)
\(48\) −4.47763 5.28686i −0.646290 0.763092i
\(49\) 4.67901 2.70143i 0.668431 0.385919i
\(50\) −1.23442 0.407545i −0.174573 0.0576356i
\(51\) −0.914396 + 7.83749i −0.128041 + 1.09747i
\(52\) −5.03628 1.25956i −0.698407 0.174670i
\(53\) −0.240880 + 0.581535i −0.0330874 + 0.0798800i −0.939559 0.342386i \(-0.888765\pi\)
0.906472 + 0.422266i \(0.138765\pi\)
\(54\) −5.88680 + 4.39836i −0.801092 + 0.598541i
\(55\) −7.80969 7.80969i −1.05306 1.05306i
\(56\) −3.55987 + 0.323207i −0.475707 + 0.0431904i
\(57\) 2.94682 + 10.3824i 0.390316 + 1.37519i
\(58\) 10.6889 + 9.21691i 1.40352 + 1.21024i
\(59\) −10.3062 + 1.35684i −1.34176 + 0.176646i −0.766984 0.641667i \(-0.778243\pi\)
−0.574774 + 0.818312i \(0.694910\pi\)
\(60\) 2.88014 + 6.37764i 0.371825 + 0.823350i
\(61\) 0.259109 1.96813i 0.0331755 0.251993i −0.966819 0.255464i \(-0.917772\pi\)
0.999994 + 0.00347153i \(0.00110502\pi\)
\(62\) −5.57972 0.318866i −0.708626 0.0404960i
\(63\) 0.111868 + 3.78969i 0.0140940 + 0.477456i
\(64\) −7.53531 2.68683i −0.941914 0.335854i
\(65\) 4.54106 + 2.62178i 0.563249 + 0.325192i
\(66\) 0.566723 13.3802i 0.0697588 1.64699i
\(67\) −0.569713 + 0.742465i −0.0696016 + 0.0907065i −0.826857 0.562413i \(-0.809873\pi\)
0.757255 + 0.653119i \(0.226540\pi\)
\(68\) 3.62709 + 8.35827i 0.439849 + 1.01359i
\(69\) −1.76306 + 4.44061i −0.212247 + 0.534587i
\(70\) 3.54682 + 0.674716i 0.423926 + 0.0806439i
\(71\) 7.83003 + 7.83003i 0.929253 + 0.929253i 0.997658 0.0684044i \(-0.0217908\pi\)
−0.0684044 + 0.997658i \(0.521791\pi\)
\(72\) −3.33201 + 7.80370i −0.392681 + 0.919675i
\(73\) −5.95511 + 5.95511i −0.696993 + 0.696993i −0.963761 0.266768i \(-0.914044\pi\)
0.266768 + 0.963761i \(0.414044\pi\)
\(74\) 8.03759 5.46834i 0.934351 0.635682i
\(75\) 0.231080 + 1.57525i 0.0266828 + 0.181894i
\(76\) 8.95824 + 8.66342i 1.02758 + 0.993762i
\(77\) −5.48169 4.20625i −0.624697 0.479347i
\(78\) 1.38424 + 6.20563i 0.156735 + 0.702649i
\(79\) 0.917276 1.58877i 0.103202 0.178750i −0.809800 0.586705i \(-0.800425\pi\)
0.913002 + 0.407955i \(0.133758\pi\)
\(80\) 6.57157 + 4.70183i 0.734724 + 0.525680i
\(81\) 8.04610 + 4.03241i 0.894011 + 0.448045i
\(82\) −9.78233 + 8.72470i −1.08028 + 0.963482i
\(83\) −2.87282 0.378214i −0.315333 0.0415144i −0.0288013 0.999585i \(-0.509169\pi\)
−0.286532 + 0.958071i \(0.592502\pi\)
\(84\) 2.30719 + 3.72055i 0.251736 + 0.405946i
\(85\) −1.20122 9.12416i −0.130290 0.989654i
\(86\) 0.00274078 + 0.0370631i 0.000295545 + 0.00399662i
\(87\) 4.22711 16.7612i 0.453193 1.79699i
\(88\) −7.18539 13.6933i −0.765965 1.45971i
\(89\) −4.48131 + 4.48131i −0.475018 + 0.475018i −0.903534 0.428516i \(-0.859037\pi\)
0.428516 + 0.903534i \(0.359037\pi\)
\(90\) 5.40291 6.65304i 0.569516 0.701292i
\(91\) 3.03069 + 1.25535i 0.317702 + 0.131597i
\(92\) 0.811504 + 5.45692i 0.0846051 + 0.568923i
\(93\) 2.71245 + 6.28451i 0.281268 + 0.651674i
\(94\) 0.689103 + 1.36839i 0.0710756 + 0.141138i
\(95\) −6.29368 10.9010i −0.645718 1.11842i
\(96\) 1.19266 + 9.72510i 0.121726 + 0.992564i
\(97\) −7.05812 + 12.2250i −0.716644 + 1.24126i 0.245678 + 0.969351i \(0.420989\pi\)
−0.962322 + 0.271912i \(0.912344\pi\)
\(98\) −7.62835 0.435940i −0.770580 0.0440366i
\(99\) −14.9617 + 6.72118i −1.50371 + 0.675504i
\(100\) 1.14340 + 1.43958i 0.114340 + 0.143958i
\(101\) −9.10255 + 6.98463i −0.905737 + 0.694997i −0.952704 0.303900i \(-0.901711\pi\)
0.0469666 + 0.998896i \(0.485045\pi\)
\(102\) 7.16176 8.55768i 0.709120 0.847336i
\(103\) 11.4115 + 3.05769i 1.12441 + 0.301283i 0.772665 0.634814i \(-0.218923\pi\)
0.351740 + 0.936098i \(0.385590\pi\)
\(104\) 4.97773 + 5.39662i 0.488106 + 0.529182i
\(105\) −1.20736 4.25383i −0.117826 0.415131i
\(106\) 0.735991 0.500729i 0.0714858 0.0486351i
\(107\) −4.31674 1.78805i −0.417315 0.172858i 0.164138 0.986437i \(-0.447516\pi\)
−0.581453 + 0.813580i \(0.697516\pi\)
\(108\) 10.3730 0.633485i 0.998140 0.0609571i
\(109\) −1.51965 3.66875i −0.145556 0.351403i 0.834241 0.551401i \(-0.185906\pi\)
−0.979796 + 0.199998i \(0.935906\pi\)
\(110\) 3.17522 + 15.2932i 0.302746 + 1.45815i
\(111\) −10.3978 5.80033i −0.986917 0.550543i
\(112\) 4.45996 + 2.37970i 0.421427 + 0.224860i
\(113\) −5.90161 10.2219i −0.555177 0.961595i −0.997890 0.0649314i \(-0.979317\pi\)
0.442713 0.896664i \(-0.354016\pi\)
\(114\) 4.57068 14.5625i 0.428083 1.36390i
\(115\) 0.727340 5.52470i 0.0678248 0.515181i
\(116\) −5.48788 19.1909i −0.509537 1.78183i
\(117\) 6.03536 4.92071i 0.557969 0.454920i
\(118\) 13.2388 + 6.39156i 1.21873 + 0.588391i
\(119\) −1.49011 5.56118i −0.136599 0.509793i
\(120\) 1.54248 9.77547i 0.140808 0.892374i
\(121\) 4.88958 18.2482i 0.444507 1.65892i
\(122\) −1.83331 + 2.12610i −0.165980 + 0.192488i
\(123\) 14.9207 + 5.92398i 1.34536 + 0.534147i
\(124\) 6.35011 + 4.70596i 0.570257 + 0.422607i
\(125\) −4.57589 11.0472i −0.409280 0.988089i
\(126\) 2.80789 4.56774i 0.250146 0.406927i
\(127\) 5.23044i 0.464126i −0.972701 0.232063i \(-0.925452\pi\)
0.972701 0.232063i \(-0.0745476\pi\)
\(128\) 6.82528 + 9.02306i 0.603275 + 0.797533i
\(129\) 0.0390786 0.0233375i 0.00344068 0.00205476i
\(130\) −3.33532 6.62311i −0.292527 0.580885i
\(131\) −4.01381 3.07990i −0.350688 0.269092i 0.418363 0.908280i \(-0.362604\pi\)
−0.769051 + 0.639188i \(0.779271\pi\)
\(132\) −11.0509 + 15.3812i −0.961857 + 1.33876i
\(133\) −4.79381 6.24742i −0.415676 0.541720i
\(134\) 1.24966 0.435894i 0.107954 0.0376555i
\(135\) −10.2494 2.26543i −0.882124 0.194977i
\(136\) 2.19592 12.6969i 0.188299 1.08875i
\(137\) −4.49163 + 1.20353i −0.383746 + 0.102824i −0.445534 0.895265i \(-0.646986\pi\)
0.0617885 + 0.998089i \(0.480320\pi\)
\(138\) 5.52982 3.88277i 0.470729 0.330523i
\(139\) 0.223667 0.0294464i 0.0189712 0.00249761i −0.121035 0.992648i \(-0.538621\pi\)
0.140006 + 0.990151i \(0.455288\pi\)
\(140\) −3.67032 3.54953i −0.310199 0.299990i
\(141\) 1.12021 1.50537i 0.0943390 0.126775i
\(142\) −3.18349 15.3331i −0.267153 1.28672i
\(143\) 14.1916i 1.18676i
\(144\) 9.99414 6.64207i 0.832845 0.553506i
\(145\) 20.1608i 1.67426i
\(146\) 11.6615 2.42120i 0.965115 0.200380i
\(147\) 3.70834 + 8.59191i 0.305859 + 0.708649i
\(148\) −13.7462 + 0.229986i −1.12993 + 0.0189047i
\(149\) 15.0440 1.98058i 1.23245 0.162256i 0.513975 0.857805i \(-0.328172\pi\)
0.718478 + 0.695549i \(0.244839\pi\)
\(150\) 0.948901 2.04187i 0.0774774 0.166718i
\(151\) 19.5206 5.23053i 1.58857 0.425655i 0.647002 0.762489i \(-0.276023\pi\)
0.941564 + 0.336834i \(0.109356\pi\)
\(152\) −3.87093 17.1938i −0.313974 1.39460i
\(153\) −13.2999 3.14622i −1.07524 0.254357i
\(154\) 3.21825 + 9.22637i 0.259334 + 0.743482i
\(155\) −4.85988 6.33351i −0.390355 0.508720i
\(156\) 3.17779 8.41151i 0.254427 0.673460i
\(157\) 4.83053 + 3.70660i 0.385519 + 0.295819i 0.783279 0.621671i \(-0.213546\pi\)
−0.397760 + 0.917489i \(0.630212\pi\)
\(158\) −2.31721 + 1.16692i −0.184347 + 0.0928350i
\(159\) −0.952114 0.531129i −0.0755075 0.0421212i
\(160\) −4.12244 10.6579i −0.325907 0.842581i
\(161\) 3.48609i 0.274743i
\(162\) −6.38529 11.0104i −0.501675 0.865056i
\(163\) 5.58820 + 13.4911i 0.437702 + 1.05671i 0.976741 + 0.214424i \(0.0687875\pi\)
−0.539039 + 0.842281i \(0.681212\pi\)
\(164\) 18.3356 2.72670i 1.43177 0.212920i
\(165\) 15.0032 11.8681i 1.16800 0.923932i
\(166\) 3.10341 + 2.67603i 0.240871 + 0.207700i
\(167\) −3.85581 + 14.3901i −0.298371 + 1.11354i 0.640131 + 0.768265i \(0.278880\pi\)
−0.938503 + 0.345272i \(0.887787\pi\)
\(168\) 0.158483 6.18920i 0.0122272 0.477507i
\(169\) 1.62081 + 6.04896i 0.124678 + 0.465305i
\(170\) −5.65849 + 11.7204i −0.433986 + 0.898915i
\(171\) −18.4532 + 2.98574i −1.41115 + 0.228325i
\(172\) 0.0255141 0.0459501i 0.00194543 0.00350366i
\(173\) −2.20950 + 16.7828i −0.167985 + 1.27597i 0.674912 + 0.737898i \(0.264182\pi\)
−0.842897 + 0.538075i \(0.819152\pi\)
\(174\) −18.0020 + 16.5390i −1.36473 + 1.25382i
\(175\) −0.580837 1.00604i −0.0439071 0.0760494i
\(176\) −2.12761 + 21.7656i −0.160374 + 1.64065i
\(177\) −0.265657 18.0030i −0.0199680 1.35319i
\(178\) 8.77547 1.82199i 0.657750 0.136564i
\(179\) 7.45450 + 17.9968i 0.557176 + 1.34514i 0.911993 + 0.410206i \(0.134543\pi\)
−0.354817 + 0.934936i \(0.615457\pi\)
\(180\) −11.5501 + 3.67485i −0.860891 + 0.273907i
\(181\) −16.1706 6.69808i −1.20195 0.497865i −0.310322 0.950631i \(-0.600437\pi\)
−0.891629 + 0.452767i \(0.850437\pi\)
\(182\) −2.60956 3.83564i −0.193434 0.284317i
\(183\) 3.33392 + 0.840801i 0.246451 + 0.0621538i
\(184\) 3.27413 7.08189i 0.241372 0.522084i
\(185\) 13.4131 + 3.59404i 0.986152 + 0.264239i
\(186\) 1.66851 9.53525i 0.122341 0.699159i
\(187\) 19.7604 15.1627i 1.44502 1.10880i
\(188\) 0.246839 2.15262i 0.0180026 0.156996i
\(189\) −6.54216 0.568196i −0.475872 0.0413302i
\(190\) −1.01563 + 17.7722i −0.0736819 + 1.28933i
\(191\) −9.08076 + 15.7283i −0.657061 + 1.13806i 0.324312 + 0.945950i \(0.394867\pi\)
−0.981373 + 0.192113i \(0.938466\pi\)
\(192\) 6.13483 12.4243i 0.442743 0.896648i
\(193\) 4.03491 + 6.98867i 0.290439 + 0.503055i 0.973914 0.226919i \(-0.0728653\pi\)
−0.683475 + 0.729974i \(0.739532\pi\)
\(194\) 17.8301 8.97903i 1.28013 0.644657i
\(195\) −5.42193 + 7.28612i −0.388273 + 0.521770i
\(196\) 8.68160 + 6.43378i 0.620114 + 0.459555i
\(197\) 10.2940 + 4.26391i 0.733417 + 0.303791i 0.717955 0.696089i \(-0.245078\pi\)
0.0154617 + 0.999880i \(0.495078\pi\)
\(198\) 22.9053 + 3.66060i 1.62781 + 0.260148i
\(199\) 3.30532 3.30532i 0.234308 0.234308i −0.580180 0.814488i \(-0.697018\pi\)
0.814488 + 0.580180i \(0.197018\pi\)
\(200\) −0.235084 2.58926i −0.0166229 0.183088i
\(201\) −1.16297 1.12915i −0.0820297 0.0796440i
\(202\) 16.1818 1.19663i 1.13855 0.0841943i
\(203\) 1.64628 + 12.5047i 0.115546 + 0.877660i
\(204\) −15.1074 + 4.56233i −1.05773 + 0.319427i
\(205\) −18.5633 2.44391i −1.29652 0.170690i
\(206\) −11.1207 12.4688i −0.774818 0.868743i
\(207\) −7.28567 3.92444i −0.506389 0.272767i
\(208\) −1.69883 10.2429i −0.117792 0.710216i
\(209\) 17.0337 29.5032i 1.17825 2.04078i
\(210\) −1.87267 + 5.96646i −0.129227 + 0.411725i
\(211\) 6.31725 + 4.84739i 0.434897 + 0.333708i 0.802897 0.596117i \(-0.203291\pi\)
−0.368000 + 0.929826i \(0.619957\pi\)
\(212\) −1.25872 + 0.0210595i −0.0864494 + 0.00144637i
\(213\) −15.0422 + 11.8990i −1.03068 + 0.815308i
\(214\) 3.71692 + 5.46327i 0.254083 + 0.373462i
\(215\) −0.0375378 + 0.0375378i −0.00256006 + 0.00256006i
\(216\) −12.7566 7.29865i −0.867974 0.496610i
\(217\) −3.53152 3.53152i −0.239735 0.239735i
\(218\) −1.04949 + 5.51695i −0.0710807 + 0.373655i
\(219\) −9.04977 11.4403i −0.611527 0.773067i
\(220\) 8.11058 20.5463i 0.546815 1.38523i
\(221\) −7.19869 + 9.38152i −0.484236 + 0.631069i
\(222\) 7.79436 + 14.9253i 0.523123 + 1.00172i
\(223\) −18.0899 10.4442i −1.21139 0.699398i −0.248330 0.968676i \(-0.579882\pi\)
−0.963063 + 0.269278i \(0.913215\pi\)
\(224\) −3.42725 6.27395i −0.228993 0.419196i
\(225\) −2.75642 + 0.0813667i −0.183761 + 0.00542444i
\(226\) −0.952365 + 16.6651i −0.0633504 + 1.10855i
\(227\) −2.47554 + 18.8036i −0.164307 + 1.24804i 0.688278 + 0.725447i \(0.258367\pi\)
−0.852585 + 0.522589i \(0.824966\pi\)
\(228\) −16.7024 + 13.6727i −1.10615 + 0.905497i
\(229\) −0.759987 + 0.100054i −0.0502214 + 0.00661177i −0.155595 0.987821i \(-0.549729\pi\)
0.105374 + 0.994433i \(0.466396\pi\)
\(230\) −5.14625 + 5.96814i −0.339334 + 0.393528i
\(231\) 8.33662 8.58634i 0.548509 0.564940i
\(232\) −8.40004 + 26.9492i −0.551490 + 1.76930i
\(233\) 0.724953 + 0.724953i 0.0474933 + 0.0474933i 0.730455 0.682961i \(-0.239308\pi\)
−0.682961 + 0.730455i \(0.739308\pi\)
\(234\) −10.9539 + 1.13585i −0.716078 + 0.0742531i
\(235\) −0.837502 + 2.02191i −0.0546326 + 0.131895i
\(236\) −10.6949 17.8285i −0.696179 1.16054i
\(237\) 2.54918 + 1.89696i 0.165587 + 0.123221i
\(238\) −2.55262 + 7.73166i −0.165462 + 0.501169i
\(239\) 25.5871 14.7727i 1.65509 0.955567i 0.680159 0.733065i \(-0.261911\pi\)
0.974932 0.222503i \(-0.0714226\pi\)
\(240\) −9.40796 + 10.3619i −0.607281 + 0.668856i
\(241\) 12.3171 + 7.11131i 0.793417 + 0.458080i 0.841164 0.540780i \(-0.181871\pi\)
−0.0477470 + 0.998859i \(0.515204\pi\)
\(242\) −19.9390 + 17.7832i −1.28173 + 1.14315i
\(243\) −8.55226 + 13.0330i −0.548628 + 0.836067i
\(244\) 3.81721 1.09158i 0.244372 0.0698811i
\(245\) −6.64421 8.65890i −0.424483 0.553197i
\(246\) −13.0463 18.5805i −0.831804 1.18465i
\(247\) −4.18613 + 15.6229i −0.266357 + 0.994059i
\(248\) −3.85739 10.4910i −0.244944 0.666178i
\(249\) 1.22729 4.86643i 0.0777766 0.308398i
\(250\) −3.16019 + 16.6124i −0.199868 + 1.05066i
\(251\) 4.38515 10.5867i 0.276788 0.668226i −0.722955 0.690896i \(-0.757216\pi\)
0.999743 + 0.0226692i \(0.00721646\pi\)
\(252\) −6.86386 + 3.22248i −0.432383 + 0.202997i
\(253\) 13.9335 5.77144i 0.875990 0.362847i
\(254\) −4.05794 + 6.18450i −0.254618 + 0.388050i
\(255\) 15.9381 0.235188i 0.998085 0.0147280i
\(256\) −1.06987 15.9642i −0.0668672 0.997762i
\(257\) 1.50445 0.868593i 0.0938448 0.0541813i −0.452343 0.891844i \(-0.649412\pi\)
0.546188 + 0.837663i \(0.316078\pi\)
\(258\) −0.0643129 0.00272399i −0.00400394 0.000169588i
\(259\) 8.61299 + 1.13392i 0.535185 + 0.0704584i
\(260\) −1.19472 + 10.4189i −0.0740934 + 0.646150i
\(261\) 27.9872 + 10.6365i 1.73237 + 0.658382i
\(262\) 2.35647 + 6.75574i 0.145583 + 0.417371i
\(263\) 6.25459 1.67591i 0.385674 0.103341i −0.0607717 0.998152i \(-0.519356\pi\)
0.446446 + 0.894811i \(0.352689\pi\)
\(264\) 24.9998 9.61316i 1.53863 0.591649i
\(265\) 1.22822 + 0.329101i 0.0754490 + 0.0202165i
\(266\) 0.821289 + 11.1062i 0.0503565 + 0.680964i
\(267\) −6.81009 8.60904i −0.416771 0.526864i
\(268\) −1.81579 0.454123i −0.110917 0.0277400i
\(269\) −15.5138 + 6.42603i −0.945894 + 0.391802i −0.801686 0.597745i \(-0.796063\pi\)
−0.144208 + 0.989547i \(0.546063\pi\)
\(270\) 10.3613 + 10.6304i 0.630569 + 0.646948i
\(271\) −13.3512 −0.811026 −0.405513 0.914089i \(-0.632907\pi\)
−0.405513 + 0.914089i \(0.632907\pi\)
\(272\) −12.4471 + 13.3092i −0.754717 + 0.806989i
\(273\) −2.76799 + 4.96197i −0.167526 + 0.300312i
\(274\) 6.24466 + 2.06169i 0.377254 + 0.124551i
\(275\) 3.05940 3.98709i 0.184489 0.240431i
\(276\) −9.55087 + 0.300804i −0.574895 + 0.0181063i
\(277\) 18.3468 14.0780i 1.10235 0.845864i 0.113318 0.993559i \(-0.463852\pi\)
0.989033 + 0.147695i \(0.0471853\pi\)
\(278\) −0.287311 0.138711i −0.0172318 0.00831931i
\(279\) −11.3562 + 3.40504i −0.679878 + 0.203854i
\(280\) 1.58597 + 7.04453i 0.0947801 + 0.420991i
\(281\) 0.251777 + 0.939646i 0.0150198 + 0.0560546i 0.973029 0.230683i \(-0.0740960\pi\)
−0.958009 + 0.286737i \(0.907429\pi\)
\(282\) −2.49246 + 0.910863i −0.148424 + 0.0542411i
\(283\) 2.47527 + 18.8016i 0.147140 + 1.11764i 0.892523 + 0.451001i \(0.148933\pi\)
−0.745384 + 0.666635i \(0.767734\pi\)
\(284\) −8.13169 + 20.5998i −0.482527 + 1.22237i
\(285\) 20.0171 8.63953i 1.18571 0.511762i
\(286\) 11.0103 16.7802i 0.651052 0.992236i
\(287\) −11.7135 −0.691425
\(288\) −16.9703 + 0.0998504i −0.999983 + 0.00588374i
\(289\) 3.75411 0.220830
\(290\) 15.6414 23.8382i 0.918492 1.39983i
\(291\) −19.6150 14.5964i −1.14985 0.855657i
\(292\) −15.6671 6.18454i −0.916848 0.361923i
\(293\) −3.58108 27.2010i −0.209209 1.58910i −0.697609 0.716479i \(-0.745753\pi\)
0.488400 0.872620i \(-0.337581\pi\)
\(294\) 2.28112 13.0362i 0.133037 0.760285i
\(295\) 5.43500 + 20.2837i 0.316438 + 1.18096i
\(296\) 16.4320 + 10.3928i 0.955093 + 0.604070i
\(297\) −8.55993 27.0889i −0.496698 1.57186i
\(298\) −19.3247 9.32977i −1.11945 0.540459i
\(299\) −5.68053 + 4.35882i −0.328513 + 0.252077i
\(300\) −2.70613 + 1.67813i −0.156239 + 0.0968869i
\(301\) −0.0202176 + 0.0263481i −0.00116532 + 0.00151868i
\(302\) −27.1393 8.96010i −1.56169 0.515596i
\(303\) −10.1892 17.0618i −0.585354 0.980174i
\(304\) −8.76246 + 23.3332i −0.502562 + 1.33825i
\(305\) −4.01011 −0.229618
\(306\) 13.2850 + 14.0386i 0.759452 + 0.802535i
\(307\) 3.72231 1.54183i 0.212443 0.0879969i −0.273924 0.961751i \(-0.588322\pi\)
0.486367 + 0.873754i \(0.338322\pi\)
\(308\) 3.35284 13.4061i 0.191046 0.763885i
\(309\) −7.55086 + 19.0183i −0.429554 + 1.08192i
\(310\) 0.832607 + 11.2592i 0.0472889 + 0.639481i
\(311\) 19.3019 + 5.17192i 1.09451 + 0.293273i 0.760527 0.649306i \(-0.224941\pi\)
0.333982 + 0.942579i \(0.391607\pi\)
\(312\) −10.2834 + 7.48040i −0.582180 + 0.423494i
\(313\) −11.3791 + 3.04903i −0.643186 + 0.172341i −0.565646 0.824648i \(-0.691373\pi\)
−0.0775400 + 0.996989i \(0.524707\pi\)
\(314\) −2.83596 8.13039i −0.160042 0.458824i
\(315\) 7.56055 1.22330i 0.425989 0.0689251i
\(316\) 3.64522 + 0.417994i 0.205059 + 0.0235140i
\(317\) 2.87683 + 0.378742i 0.161579 + 0.0212722i 0.210881 0.977512i \(-0.432367\pi\)
−0.0493027 + 0.998784i \(0.515700\pi\)
\(318\) 0.713719 + 1.36669i 0.0400234 + 0.0766402i
\(319\) −47.2544 + 27.2823i −2.64574 + 1.52752i
\(320\) −3.39434 + 15.8003i −0.189749 + 0.883263i
\(321\) 3.94257 7.06755i 0.220053 0.394472i
\(322\) −2.70462 + 4.12198i −0.150723 + 0.229709i
\(323\) 26.2259 10.8631i 1.45925 0.604440i
\(324\) −0.992189 + 17.9726i −0.0551216 + 0.998480i
\(325\) −0.913076 + 2.20436i −0.0506483 + 0.122276i
\(326\) 3.85931 20.2875i 0.213747 1.12362i
\(327\) 6.61667 1.87800i 0.365903 0.103853i
\(328\) −23.7956 11.0013i −1.31389 0.607443i
\(329\) −0.354357 + 1.32248i −0.0195363 + 0.0729106i
\(330\) −26.9475 + 2.39300i −1.48341 + 0.131730i
\(331\) −14.9631 19.5003i −0.822446 1.07183i −0.996204 0.0870444i \(-0.972258\pi\)
0.173758 0.984788i \(-0.444409\pi\)
\(332\) −1.59335 5.57188i −0.0874462 0.305796i
\(333\) 12.0658 16.7240i 0.661201 0.916469i
\(334\) 15.7234 14.0235i 0.860347 0.767329i
\(335\) 1.63724 + 0.945261i 0.0894520 + 0.0516451i
\(336\) −4.98917 + 7.19520i −0.272182 + 0.392530i
\(337\) −23.5217 + 13.5803i −1.28131 + 0.739765i −0.977088 0.212835i \(-0.931730\pi\)
−0.304223 + 0.952601i \(0.598397\pi\)
\(338\) 2.77651 8.40981i 0.151023 0.457433i
\(339\) 18.7701 8.10133i 1.01945 0.440004i
\(340\) 15.7837 9.46826i 0.855991 0.513488i
\(341\) 8.26841 19.9617i 0.447759 1.08099i
\(342\) 24.1356 + 10.7862i 1.30511 + 0.583253i
\(343\) −11.0835 11.0835i −0.598455 0.598455i
\(344\) −0.0658175 + 0.0345371i −0.00354864 + 0.00186211i
\(345\) 9.35860 + 2.36020i 0.503850 + 0.127069i
\(346\) 15.6332 18.1299i 0.840444 0.974669i
\(347\) −29.3045 + 3.85801i −1.57315 + 0.207109i −0.866033 0.499988i \(-0.833338\pi\)
−0.707117 + 0.707097i \(0.750005\pi\)
\(348\) 34.1172 5.58932i 1.82888 0.299619i
\(349\) −2.15904 + 16.3995i −0.115571 + 0.877847i 0.831208 + 0.555962i \(0.187650\pi\)
−0.946779 + 0.321885i \(0.895683\pi\)
\(350\) −0.0937318 + 1.64018i −0.00501017 + 0.0876712i
\(351\) 7.25410 + 11.3708i 0.387195 + 0.606928i
\(352\) 19.4022 24.0852i 1.03414 1.28374i
\(353\) 1.37659 + 0.794772i 0.0732682 + 0.0423014i 0.536187 0.844099i \(-0.319864\pi\)
−0.462918 + 0.886401i \(0.653198\pi\)
\(354\) −13.6532 + 21.4930i −0.725658 + 1.14234i
\(355\) 13.6175 17.7467i 0.722742 0.941896i
\(356\) −11.7897 4.65396i −0.624855 0.246660i
\(357\) 9.86645 1.44735i 0.522188 0.0766017i
\(358\) 5.14821 27.0629i 0.272091 1.43032i
\(359\) 6.51734 + 6.51734i 0.343972 + 0.343972i 0.857858 0.513886i \(-0.171795\pi\)
−0.513886 + 0.857858i \(0.671795\pi\)
\(360\) 16.5079 + 4.61575i 0.870045 + 0.243271i
\(361\) 14.0193 14.0193i 0.737855 0.737855i
\(362\) 13.9236 + 20.4655i 0.731810 + 1.07564i
\(363\) 30.4124 + 12.0746i 1.59624 + 0.633754i
\(364\) 0.109752 + 6.55987i 0.00575257 + 0.343830i
\(365\) 13.4972 + 10.3568i 0.706476 + 0.542098i
\(366\) −3.28973 3.58073i −0.171957 0.187168i
\(367\) −6.35270 + 11.0032i −0.331608 + 0.574362i −0.982827 0.184527i \(-0.940925\pi\)
0.651219 + 0.758890i \(0.274258\pi\)
\(368\) −9.36570 + 5.83350i −0.488221 + 0.304092i
\(369\) −13.1863 + 24.4803i −0.686453 + 1.27439i
\(370\) −13.0714 14.6559i −0.679550 0.761926i
\(371\) 0.788679 + 0.103832i 0.0409462 + 0.00539067i
\(372\) −9.37061 + 9.98006i −0.485844 + 0.517442i
\(373\) −2.74555 20.8545i −0.142159 1.07981i −0.902625 0.430428i \(-0.858363\pi\)
0.760466 0.649378i \(-0.224971\pi\)
\(374\) −35.1285 + 2.59771i −1.81645 + 0.134324i
\(375\) 19.9238 5.65493i 1.02886 0.292019i
\(376\) −1.96193 + 2.35376i −0.101179 + 0.121386i
\(377\) 18.3178 18.3178i 0.943416 0.943416i
\(378\) 7.29467 + 5.74746i 0.375197 + 0.295617i
\(379\) 13.5241 + 5.60185i 0.694685 + 0.287748i 0.701950 0.712226i \(-0.252313\pi\)
−0.00726571 + 0.999974i \(0.502313\pi\)
\(380\) 14.9892 20.2260i 0.768927 1.03757i
\(381\) 8.99835 + 1.04983i 0.460999 + 0.0537846i
\(382\) 22.9397 11.5521i 1.17370 0.591059i
\(383\) 2.34591 + 4.06324i 0.119870 + 0.207622i 0.919716 0.392584i \(-0.128419\pi\)
−0.799846 + 0.600206i \(0.795085\pi\)
\(384\) −16.8930 + 9.93101i −0.862070 + 0.506790i
\(385\) −6.97895 + 12.0879i −0.355680 + 0.616057i
\(386\) 0.651128 11.3939i 0.0331415 0.579932i
\(387\) 0.0323058 + 0.0719144i 0.00164219 + 0.00365562i
\(388\) −28.0487 3.21632i −1.42396 0.163284i
\(389\) −14.9116 + 11.4421i −0.756048 + 0.580136i −0.913235 0.407433i \(-0.866424\pi\)
0.157187 + 0.987569i \(0.449757\pi\)
\(390\) 12.0637 4.40865i 0.610871 0.223241i
\(391\) 12.1385 + 3.25249i 0.613868 + 0.164485i
\(392\) −5.27365 14.3428i −0.266359 0.724421i
\(393\) 6.10425 6.28710i 0.307918 0.317142i
\(394\) −8.86361 13.0281i −0.446542 0.656346i
\(395\) −3.42387 1.41821i −0.172274 0.0713581i
\(396\) −24.2434 22.0990i −1.21828 1.11052i
\(397\) 10.0842 + 24.3455i 0.506113 + 1.22186i 0.946104 + 0.323863i \(0.104982\pi\)
−0.439991 + 0.898002i \(0.645018\pi\)
\(398\) −6.47261 + 1.34386i −0.324443 + 0.0673617i
\(399\) 11.7101 6.99323i 0.586240 0.350099i
\(400\) −1.73086 + 3.24394i −0.0865432 + 0.162197i
\(401\) 2.77190 + 4.80107i 0.138422 + 0.239754i 0.926900 0.375310i \(-0.122464\pi\)
−0.788477 + 0.615064i \(0.789130\pi\)
\(402\) 0.499076 + 2.23738i 0.0248917 + 0.111591i
\(403\) −1.33893 + 10.1702i −0.0666968 + 0.506613i
\(404\) −20.0619 11.1395i −0.998115 0.554209i
\(405\) 5.95461 17.1781i 0.295887 0.853586i
\(406\) 7.75500 16.0629i 0.384874 0.797189i
\(407\) 9.72717 + 36.3023i 0.482158 + 1.79944i
\(408\) 21.4027 + 6.32629i 1.05959 + 0.313198i
\(409\) 0.597440 2.22968i 0.0295415 0.110250i −0.949581 0.313522i \(-0.898491\pi\)
0.979122 + 0.203272i \(0.0651576\pi\)
\(410\) 20.0533 + 17.2917i 0.990363 + 0.853976i
\(411\) −1.16899 7.96888i −0.0576618 0.393076i
\(412\) 3.47553 + 23.3710i 0.171227 + 1.15141i
\(413\) 5.02739 + 12.1372i 0.247382 + 0.597232i
\(414\) 5.56992 + 10.2927i 0.273747 + 0.505860i
\(415\) 5.85345i 0.287335i
\(416\) −5.93805 + 13.4292i −0.291137 + 0.658423i
\(417\) 0.00576533 + 0.390704i 0.000282330 + 0.0191328i
\(418\) −43.0303 + 21.6695i −2.10468 + 1.05989i
\(419\) 1.83478 + 1.40788i 0.0896351 + 0.0687794i 0.652607 0.757697i \(-0.273675\pi\)
−0.562972 + 0.826476i \(0.690342\pi\)
\(420\) 6.84323 5.60190i 0.333916 0.273345i
\(421\) −19.2506 25.0879i −0.938219 1.22271i −0.974732 0.223378i \(-0.928292\pi\)
0.0365128 0.999333i \(-0.488375\pi\)
\(422\) −3.70879 10.6327i −0.180541 0.517592i
\(423\) 2.36497 + 2.22935i 0.114989 + 0.108395i
\(424\) 1.50466 + 0.951656i 0.0730727 + 0.0462165i
\(425\) 4.04491 1.08383i 0.196207 0.0525735i
\(426\) 27.0177 2.39923i 1.30901 0.116243i
\(427\) −2.48728 + 0.327456i −0.120368 + 0.0158467i
\(428\) −0.156325 9.34351i −0.00755624 0.451636i
\(429\) −24.4150 2.84848i −1.17876 0.137526i
\(430\) 0.0735079 0.0152619i 0.00354487 0.000735995i
\(431\) 15.4999i 0.746605i 0.927710 + 0.373303i \(0.121775\pi\)
−0.927710 + 0.373303i \(0.878225\pi\)
\(432\) 9.42091 + 18.5269i 0.453264 + 0.891377i
\(433\) 3.24904i 0.156139i 0.996948 + 0.0780694i \(0.0248756\pi\)
−0.996948 + 0.0780694i \(0.975124\pi\)
\(434\) 1.43583 + 6.91556i 0.0689219 + 0.331958i
\(435\) −34.6842 4.04659i −1.66298 0.194019i
\(436\) 5.52115 5.70904i 0.264415 0.273414i
\(437\) 17.0411 2.24351i 0.815188 0.107322i
\(438\) 1.82473 + 20.5482i 0.0871888 + 0.981833i
\(439\) −31.1586 + 8.34893i −1.48712 + 0.398473i −0.908764 0.417311i \(-0.862973\pi\)
−0.578357 + 0.815784i \(0.696306\pi\)
\(440\) −25.5304 + 18.0016i −1.21712 + 0.858192i
\(441\) −15.5257 + 4.65522i −0.739319 + 0.221677i
\(442\) 15.7903 5.50779i 0.751066 0.261979i
\(443\) −15.7597 20.5384i −0.748764 0.975809i −0.999969 0.00787460i \(-0.997493\pi\)
0.251205 0.967934i \(-0.419173\pi\)
\(444\) 2.36342 23.6949i 0.112163 1.12451i
\(445\) 10.1569 + 7.79363i 0.481481 + 0.369453i
\(446\) 13.2867 + 26.3841i 0.629143 + 1.24932i
\(447\) 0.387780 + 26.2790i 0.0183414 + 1.24295i
\(448\) −0.815130 + 10.0773i −0.0385113 + 0.476109i
\(449\) 22.0262i 1.03948i 0.854324 + 0.519741i \(0.173972\pi\)
−0.854324 + 0.519741i \(0.826028\pi\)
\(450\) 3.32233 + 2.04231i 0.156616 + 0.0962753i
\(451\) −19.3924 46.8173i −0.913151 2.20454i
\(452\) 14.0554 18.9660i 0.661110 0.892087i
\(453\) 5.08041 + 34.6328i 0.238699 + 1.62719i
\(454\) 17.5155 20.3128i 0.822042 0.953329i
\(455\) 1.71512 6.40091i 0.0804060 0.300079i
\(456\) 30.3568 3.20841i 1.42159 0.150247i
\(457\) 4.79296 + 17.8876i 0.224205 + 0.836745i 0.982721 + 0.185091i \(0.0592580\pi\)
−0.758516 + 0.651654i \(0.774075\pi\)
\(458\) 0.976239 + 0.471317i 0.0456166 + 0.0220232i
\(459\) 8.08221 22.2495i 0.377245 1.03852i
\(460\) 10.7152 3.06415i 0.499600 0.142867i
\(461\) −0.469815 + 3.56860i −0.0218815 + 0.166206i −0.998897 0.0469637i \(-0.985045\pi\)
0.977015 + 0.213170i \(0.0683788\pi\)
\(462\) −16.5188 + 3.68473i −0.768526 + 0.171429i
\(463\) −7.93318 13.7407i −0.368686 0.638583i 0.620674 0.784068i \(-0.286859\pi\)
−0.989360 + 0.145485i \(0.953526\pi\)
\(464\) 30.8403 25.3478i 1.43172 1.17674i
\(465\) 11.8715 7.08960i 0.550528 0.328772i
\(466\) −0.294748 1.41963i −0.0136539 0.0657631i
\(467\) −7.72826 18.6577i −0.357621 0.863374i −0.995634 0.0933480i \(-0.970243\pi\)
0.638012 0.770026i \(-0.279757\pi\)
\(468\) 13.8332 + 7.15533i 0.639439 + 0.330755i
\(469\) 1.09269 + 0.452606i 0.0504556 + 0.0208994i
\(470\) 2.55893 1.74096i 0.118035 0.0803043i
\(471\) −7.34633 + 7.56639i −0.338501 + 0.348641i
\(472\) −1.18622 + 29.3780i −0.0546003 + 1.35223i
\(473\) −0.138782 0.0371864i −0.00638118 0.00170983i
\(474\) −1.54244 4.22071i −0.0708468 0.193863i
\(475\) 4.54404 3.48676i 0.208495 0.159984i
\(476\) 9.01670 7.16156i 0.413280 0.328249i
\(477\) 1.10485 1.53139i 0.0505875 0.0701177i
\(478\) −41.7155 2.38393i −1.90802 0.109038i
\(479\) 19.6902 34.1044i 0.899667 1.55827i 0.0717476 0.997423i \(-0.477142\pi\)
0.827920 0.560847i \(-0.189524\pi\)
\(480\) 19.1631 4.95296i 0.874672 0.226070i
\(481\) −8.92151 15.4525i −0.406786 0.704573i
\(482\) −9.04669 17.9645i −0.412066 0.818260i
\(483\) 5.99741 + 0.699715i 0.272892 + 0.0318381i
\(484\) 37.3728 5.55774i 1.69876 0.252625i
\(485\) 26.3455 + 10.9127i 1.19629 + 0.495519i
\(486\) 20.2237 8.77517i 0.917364 0.398050i
\(487\) 15.1909 15.1909i 0.688366 0.688366i −0.273504 0.961871i \(-0.588183\pi\)
0.961871 + 0.273504i \(0.0881828\pi\)
\(488\) −5.36037 1.67083i −0.242653 0.0756347i
\(489\) −24.3315 + 6.90595i −1.10031 + 0.312298i
\(490\) 1.13830 + 15.3931i 0.0514233 + 0.695391i
\(491\) −0.602058 4.57308i −0.0271705 0.206380i 0.972475 0.233007i \(-0.0748566\pi\)
−0.999645 + 0.0266271i \(0.991523\pi\)
\(492\) 1.01072 + 32.0915i 0.0455667 + 1.44680i
\(493\) −45.0770 5.93450i −2.03017 0.267277i
\(494\) 17.0704 15.2248i 0.768035 0.684998i
\(495\) 17.4063 + 28.1933i 0.782356 + 1.26720i
\(496\) −3.57823 + 15.3973i −0.160667 + 0.691358i
\(497\) 6.99712 12.1194i 0.313864 0.543628i
\(498\) −5.22669 + 4.80193i −0.234214 + 0.215180i
\(499\) −33.2610 25.5220i −1.48896 1.14252i −0.954841 0.297116i \(-0.903975\pi\)
−0.534123 0.845407i \(-0.679358\pi\)
\(500\) 16.6250 17.1908i 0.743494 0.768796i
\(501\) −23.9825 9.52178i −1.07146 0.425402i
\(502\) −13.3985 + 9.11564i −0.598006 + 0.406851i
\(503\) −4.57278 + 4.57278i −0.203890 + 0.203890i −0.801665 0.597774i \(-0.796052\pi\)
0.597774 + 0.801665i \(0.296052\pi\)
\(504\) 10.6160 + 1.51492i 0.472873 + 0.0674801i
\(505\) 16.3890 + 16.3890i 0.729303 + 0.729303i
\(506\) −20.9527 3.98585i −0.931461 0.177193i
\(507\) −10.7318 + 1.57429i −0.476618 + 0.0699169i
\(508\) 9.59627 4.16432i 0.425765 0.184762i
\(509\) −23.8501 + 31.0821i −1.05714 + 1.37769i −0.134993 + 0.990847i \(0.543101\pi\)
−0.922146 + 0.386843i \(0.873566\pi\)
\(510\) −19.0278 12.0872i −0.842567 0.535232i
\(511\) 9.21736 + 5.32165i 0.407752 + 0.235416i
\(512\) −11.1205 + 19.7062i −0.491461 + 0.870899i
\(513\) −1.43275 32.3459i −0.0632573 1.42810i
\(514\) −2.45275 0.140168i −0.108186 0.00618255i
\(515\) 3.11507 23.6613i 0.137266 1.04264i
\(516\) 0.0739306 + 0.0531168i 0.00325461 + 0.00233834i
\(517\) −5.87244 + 0.773122i −0.258270 + 0.0340019i
\(518\) −9.30432 8.02298i −0.408808 0.352510i
\(519\) −28.4293 7.16976i −1.24791 0.314718i
\(520\) 9.49593 11.3924i 0.416424 0.499591i
\(521\) −13.1462 13.1462i −0.575945 0.575945i 0.357838 0.933784i \(-0.383514\pi\)
−0.933784 + 0.357838i \(0.883514\pi\)
\(522\) −24.8402 34.2900i −1.08722 1.50083i
\(523\) −5.54810 + 13.3943i −0.242601 + 0.585692i −0.997540 0.0701042i \(-0.977667\pi\)
0.754938 + 0.655796i \(0.227667\pi\)
\(524\) 2.45502 9.81625i 0.107248 0.428825i
\(525\) 1.84735 0.797333i 0.0806251 0.0347985i
\(526\) −8.69569 2.87090i −0.379150 0.125177i
\(527\) 15.5915 9.00177i 0.679177 0.392123i
\(528\) −37.0182 8.02901i −1.61101 0.349418i
\(529\) −13.3289 7.69543i −0.579517 0.334584i
\(530\) −1.19693 1.34202i −0.0519913 0.0582938i
\(531\) 31.0253 + 3.15646i 1.34639 + 0.136979i
\(532\) 7.64543 13.7692i 0.331471 0.596971i
\(533\) 14.6459 + 19.0869i 0.634385 + 0.826746i
\(534\) 1.37313 + 15.4629i 0.0594213 + 0.669144i
\(535\) −2.44292 + 9.11710i −0.105617 + 0.394167i
\(536\) 1.79467 + 1.94570i 0.0775181 + 0.0840416i
\(537\) −32.4575 + 9.21235i −1.40065 + 0.397542i
\(538\) 23.3292 + 4.43793i 1.00579 + 0.191333i
\(539\) 11.3042 27.2908i 0.486907 1.17550i
\(540\) −4.00386 20.6081i −0.172298 0.886833i
\(541\) 35.5371 14.7199i 1.52786 0.632859i 0.548711 0.836012i \(-0.315119\pi\)
0.979147 + 0.203153i \(0.0651188\pi\)
\(542\) 15.7865 + 10.3583i 0.678089 + 0.444926i
\(543\) 14.7690 26.4752i 0.633797 1.13616i
\(544\) 25.0433 6.08002i 1.07372 0.260679i
\(545\) −6.94714 + 4.01093i −0.297583 + 0.171810i
\(546\) 7.12254 3.71957i 0.304817 0.159183i
\(547\) 26.9141 + 3.54330i 1.15076 + 0.151501i 0.681677 0.731653i \(-0.261251\pi\)
0.469084 + 0.883153i \(0.344584\pi\)
\(548\) −5.78421 7.28256i −0.247089 0.311096i
\(549\) −2.11567 + 5.56685i −0.0902946 + 0.237588i
\(550\) −6.71077 + 2.34078i −0.286148 + 0.0998112i
\(551\) −60.0677 + 16.0951i −2.55897 + 0.685674i
\(552\) 11.5264 + 7.05420i 0.490595 + 0.300247i
\(553\) −2.23947 0.600064i −0.0952319 0.0255173i
\(554\) −32.6155 + 2.41188i −1.38570 + 0.102471i
\(555\) −8.87534 + 22.3543i −0.376737 + 0.948888i
\(556\) 0.232102 + 0.386918i 0.00984334 + 0.0164090i
\(557\) 33.4645 13.8614i 1.41794 0.587328i 0.463595 0.886047i \(-0.346559\pi\)
0.954341 + 0.298719i \(0.0965593\pi\)
\(558\) 16.0694 + 4.78436i 0.680271 + 0.202538i
\(559\) 0.0682128 0.00288509
\(560\) 3.59011 9.55995i 0.151710 0.403982i
\(561\) 22.1194 + 37.0388i 0.933880 + 1.56378i
\(562\) 0.431304 1.30638i 0.0181935 0.0551064i
\(563\) 5.69136 7.41712i 0.239862 0.312594i −0.657874 0.753128i \(-0.728544\pi\)
0.897736 + 0.440534i \(0.145211\pi\)
\(564\) 3.65378 + 0.856722i 0.153852 + 0.0360745i
\(565\) −18.9165 + 14.5151i −0.795821 + 0.610655i
\(566\) 11.6601 24.1515i 0.490109 1.01516i
\(567\) 2.29063 11.1410i 0.0961975 0.467877i
\(568\) 25.5969 18.0485i 1.07402 0.757297i
\(569\) 4.66587 + 17.4133i 0.195603 + 0.730002i 0.992110 + 0.125372i \(0.0400124\pi\)
−0.796506 + 0.604630i \(0.793321\pi\)
\(570\) −30.3712 5.31445i −1.27211 0.222598i
\(571\) 4.53485 + 34.4456i 0.189777 + 1.44150i 0.775683 + 0.631123i \(0.217406\pi\)
−0.585905 + 0.810379i \(0.699261\pi\)
\(572\) −26.0373 + 11.2989i −1.08867 + 0.472431i
\(573\) −25.2361 18.7793i −1.05425 0.784517i
\(574\) 13.8501 + 9.08769i 0.578092 + 0.379313i
\(575\) 2.53560 0.105742
\(576\) 20.1432 + 13.0480i 0.839301 + 0.543667i
\(577\) −6.04244 −0.251550 −0.125775 0.992059i \(-0.540142\pi\)
−0.125775 + 0.992059i \(0.540142\pi\)
\(578\) −4.43889 2.91256i −0.184633 0.121147i
\(579\) −12.8330 + 5.53884i −0.533323 + 0.230186i
\(580\) −36.9889 + 16.0514i −1.53588 + 0.666498i
\(581\) 0.477979 + 3.63061i 0.0198299 + 0.150623i
\(582\) 11.8686 + 32.4769i 0.491968 + 1.34621i
\(583\) 0.890704 + 3.32415i 0.0368892 + 0.137672i
\(584\) 13.7267 + 19.4677i 0.568016 + 0.805578i
\(585\) −11.4466 10.7902i −0.473261 0.446121i
\(586\) −16.8691 + 34.9409i −0.696856 + 1.44340i
\(587\) 22.0765 16.9399i 0.911196 0.699185i −0.0427750 0.999085i \(-0.513620\pi\)
0.953971 + 0.299900i \(0.0969532\pi\)
\(588\) −12.8111 + 13.6443i −0.528320 + 0.562681i
\(589\) 14.9905 19.5360i 0.617672 0.804965i
\(590\) 9.31037 28.2002i 0.383302 1.16099i
\(591\) −9.40173 + 16.8538i −0.386736 + 0.693272i
\(592\) −11.3663 25.0370i −0.467151 1.02902i
\(593\) −37.3176 −1.53245 −0.766226 0.642572i \(-0.777868\pi\)
−0.766226 + 0.642572i \(0.777868\pi\)
\(594\) −10.8951 + 38.6712i −0.447032 + 1.58670i
\(595\) −10.7451 + 4.45077i −0.440507 + 0.182464i
\(596\) 15.6114 + 26.0243i 0.639466 + 1.06600i
\(597\) 5.02299 + 6.34985i 0.205577 + 0.259882i
\(598\) 10.0984 0.746765i 0.412954 0.0305375i
\(599\) −9.66704 2.59028i −0.394984 0.105836i 0.0558593 0.998439i \(-0.482210\pi\)
−0.450844 + 0.892603i \(0.648877\pi\)
\(600\) 4.50169 + 0.115272i 0.183781 + 0.00470595i
\(601\) 13.2200 3.54229i 0.539256 0.144493i 0.0210969 0.999777i \(-0.493284\pi\)
0.518159 + 0.855284i \(0.326617\pi\)
\(602\) 0.0443471 0.0154687i 0.00180745 0.000630457i
\(603\) 2.17599 1.77412i 0.0886134 0.0722477i
\(604\) 25.1382 + 31.6500i 1.02286 + 1.28782i
\(605\) −37.8370 4.98133i −1.53829 0.202520i
\(606\) −1.18930 + 28.0791i −0.0483119 + 1.14063i
\(607\) 8.01566 4.62784i 0.325346 0.187838i −0.328427 0.944529i \(-0.606519\pi\)
0.653773 + 0.756691i \(0.273185\pi\)
\(608\) 28.4634 20.7911i 1.15434 0.843192i
\(609\) −21.8434 + 0.322327i −0.885137 + 0.0130613i
\(610\) 4.74158 + 3.11117i 0.191981 + 0.125968i
\(611\) 2.59803 1.07614i 0.105105 0.0435359i
\(612\) −4.81665 26.9063i −0.194701 1.08762i
\(613\) 9.68206 23.3746i 0.391055 0.944090i −0.598656 0.801006i \(-0.704298\pi\)
0.989711 0.143083i \(-0.0457017\pi\)
\(614\) −5.59748 1.06481i −0.225896 0.0429724i
\(615\) 7.93041 31.4455i 0.319785 1.26800i
\(616\) −14.3653 + 13.2503i −0.578795 + 0.533868i
\(617\) −8.26416 + 30.8423i −0.332703 + 1.24166i 0.573636 + 0.819111i \(0.305533\pi\)
−0.906338 + 0.422553i \(0.861134\pi\)
\(618\) 23.6832 16.6292i 0.952679 0.668925i
\(619\) 21.6463 + 28.2099i 0.870036 + 1.13385i 0.989999 + 0.141075i \(0.0450559\pi\)
−0.119963 + 0.992778i \(0.538277\pi\)
\(620\) 7.75079 13.9590i 0.311279 0.560605i
\(621\) 8.21388 11.7464i 0.329612 0.471368i
\(622\) −18.8101 21.0903i −0.754217 0.845645i
\(623\) 6.93621 + 4.00462i 0.277893 + 0.160442i
\(624\) 17.9626 0.866718i 0.719081 0.0346965i
\(625\) −16.9386 + 9.77952i −0.677545 + 0.391181i
\(626\) 15.8203 + 5.22310i 0.632306 + 0.208757i
\(627\) 47.3379 + 35.2263i 1.89049 + 1.40680i
\(628\) −2.95456 + 11.8136i −0.117900 + 0.471416i
\(629\) −11.9841 + 28.9322i −0.477837 + 1.15360i
\(630\) −9.88872 4.41928i −0.393976 0.176068i
\(631\) −12.6730 12.6730i −0.504505 0.504505i 0.408329 0.912835i \(-0.366112\pi\)
−0.912835 + 0.408329i \(0.866112\pi\)
\(632\) −3.98584 3.32231i −0.158548 0.132155i
\(633\) −9.60734 + 9.89513i −0.381858 + 0.393296i
\(634\) −3.10774 2.67976i −0.123424 0.106427i
\(635\) −10.4756 + 1.37914i −0.415711 + 0.0547295i
\(636\) 0.216415 2.16971i 0.00858143 0.0860346i
\(637\) −1.83053 + 13.9042i −0.0725281 + 0.550905i
\(638\) 77.0403 + 4.40265i 3.05006 + 0.174302i
\(639\) −17.4516 28.2667i −0.690376 1.11821i
\(640\) 16.2719 16.0489i 0.643202 0.634390i
\(641\) −21.2176 12.2500i −0.838044 0.483845i 0.0185552 0.999828i \(-0.494093\pi\)
−0.856599 + 0.515983i \(0.827427\pi\)
\(642\) −10.1450 + 5.29795i −0.400390 + 0.209093i
\(643\) −17.6156 + 22.9571i −0.694692 + 0.905341i −0.998882 0.0472706i \(-0.984948\pi\)
0.304190 + 0.952612i \(0.401614\pi\)
\(644\) 6.39592 2.77552i 0.252035 0.109371i
\(645\) −0.0570449 0.0721138i −0.00224614 0.00283948i
\(646\) −39.4376 7.50225i −1.55165 0.295172i
\(647\) 7.35806 + 7.35806i 0.289275 + 0.289275i 0.836794 0.547519i \(-0.184427\pi\)
−0.547519 + 0.836794i \(0.684427\pi\)
\(648\) 15.1169 20.4812i 0.593848 0.804577i
\(649\) −40.1877 + 40.1877i −1.57750 + 1.57750i
\(650\) 2.78984 1.89806i 0.109426 0.0744479i
\(651\) 6.78440 5.36673i 0.265902 0.210339i
\(652\) −20.3029 + 20.9939i −0.795124 + 0.822183i
\(653\) −27.4633 21.0734i −1.07472 0.824664i −0.0895084 0.995986i \(-0.528530\pi\)
−0.985215 + 0.171322i \(0.945196\pi\)
\(654\) −9.28060 2.91287i −0.362900 0.113902i
\(655\) −5.11013 + 8.85101i −0.199669 + 0.345838i
\(656\) 19.6009 + 31.4693i 0.765287 + 1.22867i
\(657\) 21.4982 13.2728i 0.838725 0.517821i
\(658\) 1.44502 1.28879i 0.0563326 0.0502421i
\(659\) 8.08934 + 1.06498i 0.315116 + 0.0414858i 0.286425 0.958103i \(-0.407533\pi\)
0.0286906 + 0.999588i \(0.490866\pi\)
\(660\) 33.7195 + 18.0773i 1.31253 + 0.703656i
\(661\) 5.26123 + 39.9630i 0.204638 + 1.55438i 0.717899 + 0.696148i \(0.245104\pi\)
−0.513260 + 0.858233i \(0.671563\pi\)
\(662\) 2.56352 + 34.6661i 0.0996340 + 1.34734i
\(663\) −14.6949 14.2675i −0.570703 0.554105i
\(664\) −2.43886 + 7.82439i −0.0946460 + 0.303645i
\(665\) −11.2484 + 11.2484i −0.436195 + 0.436195i
\(666\) −27.2417 + 10.4135i −1.05559 + 0.403516i
\(667\) −25.4342 10.5352i −0.984815 0.407924i
\(668\) −29.4713 + 4.38270i −1.14028 + 0.169572i
\(669\) 21.5990 29.0253i 0.835066 1.12218i
\(670\) −1.20252 2.38790i −0.0464574 0.0922528i
\(671\) −5.42664 9.39922i −0.209493 0.362853i
\(672\) 11.4815 4.63689i 0.442908 0.178872i
\(673\) 14.3618 24.8753i 0.553605 0.958873i −0.444405 0.895826i \(-0.646585\pi\)
0.998011 0.0630468i \(-0.0200817\pi\)
\(674\) 38.3483 + 2.19150i 1.47712 + 0.0844135i
\(675\) 0.413276 4.75842i 0.0159070 0.183152i
\(676\) −9.80757 + 7.78970i −0.377214 + 0.299604i
\(677\) 8.62306 6.61671i 0.331411 0.254301i −0.429629 0.903006i \(-0.641356\pi\)
0.761040 + 0.648705i \(0.224689\pi\)
\(678\) −28.4792 4.98339i −1.09374 0.191386i
\(679\) 17.2319 + 4.61729i 0.661301 + 0.177195i
\(680\) −26.0085 1.05017i −0.997381 0.0402721i
\(681\) −31.8524 8.03304i −1.22059 0.307827i
\(682\) −25.2635 + 17.1880i −0.967391 + 0.658161i
\(683\) 8.11168 + 3.35997i 0.310385 + 0.128566i 0.532438 0.846469i \(-0.321276\pi\)
−0.222053 + 0.975035i \(0.571276\pi\)
\(684\) −20.1698 31.4789i −0.771212 1.20363i
\(685\) 3.59478 + 8.67856i 0.137349 + 0.331591i
\(686\) 4.50628 + 21.7042i 0.172051 + 0.828670i
\(687\) −0.0195897 1.32755i −0.000747394 0.0506492i
\(688\) 0.104618 + 0.0102265i 0.00398852 + 0.000389881i
\(689\) −0.816930 1.41496i −0.0311226 0.0539059i
\(690\) −9.23455 10.0514i −0.351553 0.382651i
\(691\) 2.07623 15.7706i 0.0789836 0.599940i −0.905485 0.424379i \(-0.860493\pi\)
0.984468 0.175561i \(-0.0561741\pi\)
\(692\) −32.5505 + 9.30821i −1.23738 + 0.353845i
\(693\) 13.0985 + 16.0656i 0.497570 + 0.610281i
\(694\) 37.6430 + 18.1736i 1.42891 + 0.689862i
\(695\) −0.117951 0.440200i −0.00447415 0.0166977i
\(696\) −44.6768 19.8604i −1.69347 0.752807i
\(697\) 10.9286 40.7859i 0.413949 1.54488i
\(698\) 15.2761 17.7159i 0.578210 0.670555i
\(699\) −1.39271 + 1.10169i −0.0526770 + 0.0416696i
\(700\) 1.38333 1.86664i 0.0522850 0.0705523i
\(701\) 13.0511 + 31.5082i 0.492935 + 1.19005i 0.953220 + 0.302278i \(0.0977472\pi\)
−0.460285 + 0.887771i \(0.652253\pi\)
\(702\) 0.244519 19.0728i 0.00922877 0.719858i
\(703\) 42.8328i 1.61547i
\(704\) −41.6273 + 13.4256i −1.56889 + 0.505998i
\(705\) −3.31035 1.84665i −0.124675 0.0695490i
\(706\) −1.01107 2.00774i −0.0380523 0.0755624i
\(707\) 11.5036 + 8.82703i 0.432638 + 0.331975i
\(708\) 32.8185 14.8208i 1.23340 0.557001i
\(709\) 19.2471 + 25.0833i 0.722839 + 0.942022i 0.999822 0.0188529i \(-0.00600141\pi\)
−0.276984 + 0.960875i \(0.589335\pi\)
\(710\) −29.8699 + 10.4189i −1.12100 + 0.391014i
\(711\) −3.77515 + 4.00481i −0.141579 + 0.150192i
\(712\) 10.3296 + 14.6497i 0.387117 + 0.549022i
\(713\) 10.5297 2.82143i 0.394341 0.105663i
\(714\) −12.7890 5.94335i −0.478618 0.222424i
\(715\) 28.4231 3.74198i 1.06296 0.139942i
\(716\) −27.0836 + 28.0052i −1.01216 + 1.04661i
\(717\) 20.2790 + 46.9847i 0.757332 + 1.75467i
\(718\) −2.64978 12.7625i −0.0988891 0.476292i
\(719\) 7.72243i 0.287998i −0.989578 0.143999i \(-0.954004\pi\)
0.989578 0.143999i \(-0.0459962\pi\)
\(720\) −15.9381 18.2651i −0.593976 0.680699i
\(721\) 14.9303i 0.556034i
\(722\) −27.4530 + 5.69987i −1.02170 + 0.212127i
\(723\) −14.7064 + 19.7628i −0.546937 + 0.734988i
\(724\) −0.585596 35.0010i −0.0217635 1.30080i
\(725\) −9.09528 + 1.19742i −0.337790 + 0.0444709i
\(726\) −26.5919 37.8720i −0.986918 1.40556i
\(727\) 33.3123 8.92600i 1.23548 0.331047i 0.418772 0.908092i \(-0.362461\pi\)
0.816713 + 0.577044i \(0.195794\pi\)
\(728\) 4.95958 7.84158i 0.183814 0.290628i
\(729\) −20.7051 17.3291i −0.766857 0.641818i
\(730\) −7.92407 22.7175i −0.293283 0.840811i
\(731\) −0.0728804 0.0949796i −0.00269558 0.00351295i
\(732\) 1.11175 + 6.78615i 0.0410916 + 0.250823i
\(733\) −24.4099 18.7303i −0.901599 0.691821i 0.0501363 0.998742i \(-0.484034\pi\)
−0.951735 + 0.306922i \(0.900701\pi\)
\(734\) 16.0481 8.08163i 0.592346 0.298298i
\(735\) 16.2302 9.69259i 0.598661 0.357517i
\(736\) 15.5999 + 0.368642i 0.575019 + 0.0135883i
\(737\) 5.11665i 0.188474i
\(738\) 34.5842 18.7153i 1.27306 0.688919i
\(739\) −3.96081 9.56225i −0.145701 0.351753i 0.834134 0.551562i \(-0.185968\pi\)
−0.979835 + 0.199809i \(0.935968\pi\)
\(740\) 4.08516 + 27.4705i 0.150173 + 1.00983i
\(741\) −26.0371 10.3375i −0.956496 0.379758i
\(742\) −0.851984 0.734654i −0.0312773 0.0269700i
\(743\) 4.84432 18.0793i 0.177721 0.663264i −0.818351 0.574718i \(-0.805112\pi\)
0.996072 0.0885452i \(-0.0282218\pi\)
\(744\) 18.8227 4.53047i 0.690074 0.166095i
\(745\) −7.93348 29.6082i −0.290660 1.08476i
\(746\) −12.9332 + 26.7886i −0.473520 + 0.980800i
\(747\) 8.12578 + 3.08819i 0.297307 + 0.112991i
\(748\) 43.5515 + 24.1823i 1.59240 + 0.884191i
\(749\) −0.770743 + 5.85438i −0.0281623 + 0.213914i
\(750\) −27.9453 8.77110i −1.02042 0.320275i
\(751\) −4.93547 8.54848i −0.180098 0.311939i 0.761816 0.647794i \(-0.224308\pi\)
−0.941914 + 0.335855i \(0.890975\pi\)
\(752\) 4.14593 1.26098i 0.151186 0.0459831i
\(753\) 17.3330 + 9.66906i 0.631649 + 0.352360i
\(754\) −35.8707 + 7.44756i −1.30633 + 0.271224i
\(755\) −15.6229 37.7170i −0.568576 1.37266i
\(756\) −4.16621 12.4553i −0.151523 0.452994i
\(757\) 23.5354 + 9.74869i 0.855409 + 0.354322i 0.766910 0.641754i \(-0.221793\pi\)
0.0884987 + 0.996076i \(0.471793\pi\)
\(758\) −11.6449 17.1161i −0.422960 0.621684i
\(759\) 7.13240 + 25.1293i 0.258890 + 0.912137i
\(760\) −33.4153 + 12.2863i −1.21210 + 0.445672i
\(761\) 30.2740 + 8.11189i 1.09743 + 0.294056i 0.761718 0.647909i \(-0.224356\pi\)
0.335713 + 0.941964i \(0.391023\pi\)
\(762\) −9.82521 8.22253i −0.355930 0.297871i
\(763\) −3.98145 + 3.05507i −0.144138 + 0.110601i
\(764\) −36.0866 4.13801i −1.30557 0.149708i
\(765\) −2.79443 + 27.4669i −0.101033 + 0.993068i
\(766\) 0.378568 6.62443i 0.0136782 0.239350i
\(767\) 13.4914 23.3677i 0.487145 0.843760i
\(768\) 27.6792 + 1.36368i 0.998789 + 0.0492075i
\(769\) 4.03859 + 6.99504i 0.145635 + 0.252248i 0.929610 0.368545i \(-0.120144\pi\)
−0.783974 + 0.620793i \(0.786811\pi\)
\(770\) 17.6301 8.87832i 0.635346 0.319952i
\(771\) 1.19234 + 2.76256i 0.0429412 + 0.0994913i
\(772\) −9.60961 + 12.9670i −0.345858 + 0.466693i
\(773\) −33.4583 13.8589i −1.20341 0.498470i −0.311312 0.950308i \(-0.600769\pi\)
−0.892100 + 0.451838i \(0.850769\pi\)
\(774\) 0.0175949 0.110096i 0.000632437 0.00395732i
\(775\) 2.56864 2.56864i 0.0922683 0.0922683i
\(776\) 30.6696 + 25.5641i 1.10098 + 0.917696i
\(777\) −3.67954 + 14.5900i −0.132003 + 0.523414i
\(778\) 26.5087 1.96029i 0.950382 0.0702797i
\(779\) −7.53833 57.2593i −0.270089 2.05153i
\(780\) −17.6846 4.14661i −0.633211 0.148472i
\(781\) 60.0238 + 7.90228i 2.14782 + 0.282766i
\(782\) −11.8292 13.2632i −0.423011 0.474290i
\(783\) −23.9163 + 46.0138i −0.854699 + 1.64440i
\(784\) −4.89200 + 21.0505i −0.174714 + 0.751803i
\(785\) 6.14994 10.6520i 0.219501 0.380186i
\(786\) −12.0954 + 2.69803i −0.431430 + 0.0962357i
\(787\) −34.8624 26.7509i −1.24271 0.953566i −0.242847 0.970065i \(-0.578081\pi\)
−0.999864 + 0.0164990i \(0.994748\pi\)
\(788\) 0.372783 + 22.2812i 0.0132798 + 0.793734i
\(789\) 1.62781 + 11.0967i 0.0579516 + 0.395052i
\(790\) 2.94811 + 4.33326i 0.104889 + 0.154170i
\(791\) −10.5477 + 10.5477i −0.375033 + 0.375033i
\(792\) 11.5204 + 44.9388i 0.409361 + 1.59683i
\(793\) 3.64354 + 3.64354i 0.129386 + 0.129386i
\(794\) 6.96434 36.6099i 0.247155 1.29924i
\(795\) −0.812703 + 2.04695i −0.0288236 + 0.0725980i
\(796\) 8.69587 + 3.43267i 0.308217 + 0.121668i
\(797\) 7.53090 9.81446i 0.266758 0.347646i −0.640698 0.767793i \(-0.721355\pi\)
0.907456 + 0.420147i \(0.138021\pi\)
\(798\) −19.2717 0.816259i −0.682211 0.0288953i
\(799\) −4.27422 2.46772i −0.151211 0.0873016i
\(800\) 4.56333 2.49280i 0.161338 0.0881337i
\(801\) 16.1777 9.98799i 0.571612 0.352908i
\(802\) 0.447312 7.82735i 0.0157951 0.276393i
\(803\) −6.01006 + 45.6510i −0.212091 + 1.61099i
\(804\) 1.14572 3.03270i 0.0404065 0.106955i
\(805\) −6.98200 + 0.919198i −0.246083 + 0.0323975i
\(806\) 9.47351 10.9865i 0.333690 0.386983i
\(807\) −7.94136 27.9795i −0.279549 0.984925i
\(808\) 15.0789 + 28.7360i 0.530475 + 1.01093i
\(809\) 20.1552 + 20.1552i 0.708618 + 0.708618i 0.966244 0.257627i \(-0.0829405\pi\)
−0.257627 + 0.966244i \(0.582941\pi\)
\(810\) −20.3681 + 15.6917i −0.715662 + 0.551351i
\(811\) −0.0879265 + 0.212273i −0.00308752 + 0.00745393i −0.925416 0.378953i \(-0.876284\pi\)
0.922328 + 0.386407i \(0.126284\pi\)
\(812\) −21.6317 + 12.9763i −0.759123 + 0.455380i
\(813\) 2.67980 22.9691i 0.0939846 0.805562i
\(814\) 16.6630 50.4707i 0.584038 1.76900i
\(815\) 25.5467 14.7494i 0.894863 0.516649i
\(816\) −20.3986 24.0852i −0.714093 0.843149i
\(817\) −0.141809 0.0818736i −0.00496128 0.00286440i
\(818\) −2.43627 + 2.17287i −0.0851822 + 0.0759726i
\(819\) −7.98090 5.75795i −0.278875 0.201199i
\(820\) −10.2957 36.0038i −0.359542 1.25731i
\(821\) 29.3115 + 38.1994i 1.02298 + 1.33317i 0.941691 + 0.336479i \(0.109236\pi\)
0.0812861 + 0.996691i \(0.474097\pi\)
\(822\) −4.80030 + 10.3294i −0.167430 + 0.360279i
\(823\) 8.24869 30.7845i 0.287531 1.07308i −0.659439 0.751758i \(-0.729206\pi\)
0.946970 0.321323i \(-0.104127\pi\)
\(824\) 14.0225 30.3305i 0.488497 1.05661i
\(825\) 6.24525 + 6.06361i 0.217432 + 0.211108i
\(826\) 3.47200 18.2515i 0.120806 0.635051i
\(827\) −3.94538 + 9.52499i −0.137194 + 0.331216i −0.977513 0.210877i \(-0.932368\pi\)
0.840318 + 0.542093i \(0.182368\pi\)
\(828\) 1.39952 16.4915i 0.0486366 0.573120i
\(829\) 46.9698 19.4555i 1.63133 0.675718i 0.635948 0.771732i \(-0.280609\pi\)
0.995380 + 0.0960132i \(0.0306091\pi\)
\(830\) 4.54130 6.92116i 0.157631 0.240237i
\(831\) 20.5370 + 34.3892i 0.712421 + 1.19295i
\(832\) 17.4400 11.2719i 0.604624 0.390783i
\(833\) 21.3160 12.3068i 0.738557 0.426406i
\(834\) 0.296303 0.466443i 0.0102601 0.0161516i
\(835\) 29.8373 + 3.92816i 1.03256 + 0.135940i
\(836\) 67.6912 + 7.76209i 2.34115 + 0.268458i
\(837\) −3.57860 20.2204i −0.123694 0.698920i
\(838\) −1.07718 3.08817i −0.0372107 0.106679i
\(839\) −16.9392 + 4.53883i −0.584805 + 0.156698i −0.539078 0.842256i \(-0.681227\pi\)
−0.0457270 + 0.998954i \(0.514560\pi\)
\(840\) −12.4376 + 1.31453i −0.429139 + 0.0453556i
\(841\) 68.1965 + 18.2732i 2.35161 + 0.630111i
\(842\) 3.29807 + 44.5994i 0.113659 + 1.53700i
\(843\) −1.66709 + 0.244551i −0.0574175 + 0.00842279i
\(844\) −3.86390 + 15.4496i −0.133001 + 0.531797i
\(845\) 11.6876 4.84115i 0.402065 0.166541i
\(846\) −1.06675 4.47081i −0.0366758 0.153710i
\(847\) −23.8752 −0.820361
\(848\) −1.04079 2.29261i −0.0357410 0.0787284i
\(849\) −32.8427 + 0.484636i −1.12716 + 0.0166327i
\(850\) −5.62359 1.85664i −0.192888 0.0636823i
\(851\) −11.5433 + 15.0435i −0.395698 + 0.515684i
\(852\) −33.8073 18.1243i −1.15822 0.620929i
\(853\) 22.5258 17.2846i 0.771268 0.591815i −0.146371 0.989230i \(-0.546759\pi\)
0.917639 + 0.397415i \(0.130093\pi\)
\(854\) 3.19502 + 1.54252i 0.109331 + 0.0527840i
\(855\) 10.8455 + 36.1711i 0.370910 + 1.23703i
\(856\) −7.06415 + 11.1691i −0.241448 + 0.381752i
\(857\) −0.543927 2.02996i −0.0185802 0.0693422i 0.956013 0.293323i \(-0.0947613\pi\)
−0.974593 + 0.223981i \(0.928095\pi\)
\(858\) 26.6585 + 22.3100i 0.910105 + 0.761649i
\(859\) 1.94185 + 14.7498i 0.0662550 + 0.503257i 0.992109 + 0.125376i \(0.0400137\pi\)
−0.925854 + 0.377881i \(0.876653\pi\)
\(860\) −0.0987569 0.0389840i −0.00336758 0.00132934i
\(861\) 2.35109 20.1517i 0.0801248 0.686767i
\(862\) 12.0253 18.3272i 0.409585 0.624227i
\(863\) −9.45227 −0.321759 −0.160880 0.986974i \(-0.551433\pi\)
−0.160880 + 0.986974i \(0.551433\pi\)
\(864\) 3.23443 29.2154i 0.110037 0.993927i
\(865\) 34.1955 1.16268
\(866\) 2.52071 3.84168i 0.0856571 0.130546i
\(867\) −0.753511 + 6.45851i −0.0255906 + 0.219342i
\(868\) 3.66758 9.29097i 0.124486 0.315356i
\(869\) −1.30920 9.94432i −0.0444114 0.337338i
\(870\) 37.8714 + 31.6938i 1.28396 + 1.07452i
\(871\) −0.628724 2.34643i −0.0213035 0.0795057i
\(872\) −10.9575 + 2.46692i −0.371068 + 0.0835406i
\(873\) 29.0485 30.8156i 0.983142 1.04295i
\(874\) −21.8901 10.5683i −0.740445 0.357479i
\(875\) −11.9887 + 9.19929i −0.405294 + 0.310993i
\(876\) 13.7844 25.7121i 0.465732 0.868730i
\(877\) 15.0518 19.6159i 0.508265 0.662383i −0.466785 0.884371i \(-0.654588\pi\)
0.975049 + 0.221988i \(0.0712544\pi\)
\(878\) 43.3196 + 14.3020i 1.46196 + 0.482670i
\(879\) 47.5148 0.701143i 1.60264 0.0236490i
\(880\) 44.1536 1.47787i 1.48842 0.0498189i
\(881\) −38.1147 −1.28412 −0.642059 0.766656i \(-0.721919\pi\)
−0.642059 + 0.766656i \(0.721919\pi\)
\(882\) 21.9693 + 6.54096i 0.739746 + 0.220246i
\(883\) −5.89871 + 2.44333i −0.198507 + 0.0822245i −0.479722 0.877420i \(-0.659263\pi\)
0.281215 + 0.959645i \(0.409263\pi\)
\(884\) −22.9436 5.73814i −0.771678 0.192994i
\(885\) −35.9866 + 5.27901i −1.20968 + 0.177452i
\(886\) 2.69999 + 36.5116i 0.0907079 + 1.22663i
\(887\) 15.1366 + 4.05583i 0.508236 + 0.136182i 0.503820 0.863809i \(-0.331928\pi\)
0.00441648 + 0.999990i \(0.498594\pi\)
\(888\) −21.1778 + 26.1834i −0.710680 + 0.878656i
\(889\) −6.38489 + 1.71082i −0.214142 + 0.0573792i
\(890\) −5.96298 17.0952i −0.199880 0.573034i
\(891\) 48.3214 9.28918i 1.61883 0.311199i
\(892\) 4.75934 41.5050i 0.159354 1.38969i
\(893\) −6.69275 0.881118i −0.223964 0.0294855i
\(894\) 19.9296 31.3733i 0.666544 1.04928i
\(895\) 34.0786 19.6753i 1.13912 0.657673i
\(896\) 8.78212 11.2831i 0.293390 0.376942i
\(897\) −6.35866 10.6476i −0.212310 0.355512i
\(898\) 17.0887 26.0440i 0.570256 0.869099i
\(899\) −36.4381 + 15.0932i −1.21528 + 0.503385i
\(900\) −2.34386 4.99241i −0.0781287 0.166414i
\(901\) −1.09737 + 2.64928i −0.0365586 + 0.0882603i
\(902\) −13.3927 + 70.4023i −0.445928 + 2.34414i
\(903\) −0.0412708 0.0400705i −0.00137341 0.00133346i
\(904\) −31.3336 + 11.5209i −1.04214 + 0.383181i
\(905\) −9.15123 + 34.1529i −0.304197 + 1.13528i
\(906\) 20.8621 44.8916i 0.693097 1.49142i
\(907\) 3.39309 + 4.42196i 0.112666 + 0.146829i 0.846282 0.532735i \(-0.178836\pi\)
−0.733616 + 0.679564i \(0.762169\pi\)
\(908\) −36.4698 + 10.4290i −1.21029 + 0.346098i
\(909\) 31.3979 14.1047i 1.04140 0.467825i
\(910\) −6.99400 + 6.23784i −0.231849 + 0.206782i
\(911\) −12.3305 7.11904i −0.408529 0.235864i 0.281628 0.959524i \(-0.409125\pi\)
−0.690157 + 0.723659i \(0.742459\pi\)
\(912\) −38.3833 19.7581i −1.27100 0.654257i
\(913\) −13.7198 + 7.92112i −0.454058 + 0.262151i
\(914\) 8.21052 24.8689i 0.271580 0.822590i
\(915\) 0.804895 6.89893i 0.0266090 0.228071i
\(916\) −0.788648 1.31469i −0.0260577 0.0434384i
\(917\) −2.44681 + 5.90713i −0.0808009 + 0.195071i
\(918\) −26.8183 + 20.0375i −0.885136 + 0.661335i
\(919\) −31.7164 31.7164i −1.04623 1.04623i −0.998878 0.0473494i \(-0.984923\pi\)
−0.0473494 0.998878i \(-0.515077\pi\)
\(920\) −15.0470 4.69015i −0.496086 0.154630i
\(921\) 1.90541 + 6.71326i 0.0627854 + 0.221209i
\(922\) 3.32415 3.85504i 0.109475 0.126959i
\(923\) −28.4971 + 3.75172i −0.937995 + 0.123489i
\(924\) 22.3907 + 8.45899i 0.736600 + 0.278280i
\(925\) −0.824754 + 6.26463i −0.0271177 + 0.205980i
\(926\) −1.28021 + 22.4019i −0.0420702 + 0.736171i
\(927\) −31.2032 16.8077i −1.02485 0.552036i
\(928\) −56.1314 + 6.04459i −1.84260 + 0.198423i
\(929\) 14.5035 + 8.37358i 0.475843 + 0.274728i 0.718683 0.695338i \(-0.244745\pi\)
−0.242839 + 0.970067i \(0.578079\pi\)
\(930\) −19.5373 0.827508i −0.640653 0.0271351i
\(931\) 20.4943 26.7087i 0.671674 0.875343i
\(932\) −0.752883 + 1.90726i −0.0246615 + 0.0624742i
\(933\) −12.7719 + 32.1685i −0.418133 + 1.05315i
\(934\) −5.33727 + 28.0568i −0.174641 + 0.918046i
\(935\) −35.5784 35.5784i −1.16354 1.16354i
\(936\) −10.8051 19.1927i −0.353176 0.627334i
\(937\) 31.8100 31.8100i 1.03919 1.03919i 0.0399880 0.999200i \(-0.487268\pi\)
0.999200 0.0399880i \(-0.0127320\pi\)
\(938\) −0.940855 1.38291i −0.0307200 0.0451535i
\(939\) −2.96152 20.1884i −0.0966454 0.658824i
\(940\) −4.37638 + 0.0732206i −0.142742 + 0.00238819i
\(941\) −31.1264 23.8842i −1.01469 0.778602i −0.0393344 0.999226i \(-0.512524\pi\)
−0.975359 + 0.220625i \(0.929190\pi\)
\(942\) 14.5566 3.24703i 0.474279 0.105794i
\(943\) 12.7836 22.1418i 0.416290 0.721036i
\(944\) 24.1950 33.8165i 0.787480 1.10063i
\(945\) 0.587017 + 13.2526i 0.0190957 + 0.431106i
\(946\) 0.135246 + 0.151641i 0.00439722 + 0.00493026i
\(947\) 54.9180 + 7.23009i 1.78459 + 0.234946i 0.949193 0.314694i \(-0.101902\pi\)
0.835401 + 0.549641i \(0.185235\pi\)
\(948\) −1.45076 + 6.18727i −0.0471186 + 0.200953i
\(949\) −2.85336 21.6734i −0.0926240 0.703549i
\(950\) −8.07804 + 0.597362i −0.262086 + 0.0193810i
\(951\) −1.22901 + 4.87322i −0.0398532 + 0.158025i
\(952\) −16.2176 + 1.47243i −0.525614 + 0.0477216i
\(953\) −1.73657 + 1.73657i −0.0562531 + 0.0562531i −0.734674 0.678421i \(-0.762665\pi\)
0.678421 + 0.734674i \(0.262665\pi\)
\(954\) −2.49448 + 0.953552i −0.0807619 + 0.0308724i
\(955\) 33.8953 + 14.0399i 1.09683 + 0.454321i
\(956\) 47.4751 + 35.1830i 1.53546 + 1.13790i
\(957\) −37.4513 86.7715i −1.21063 2.80493i
\(958\) −49.7411 + 25.0490i −1.60706 + 0.809296i
\(959\) 2.93834 + 5.08935i 0.0948838 + 0.164344i
\(960\) −26.5012 9.01094i −0.855324 0.290827i
\(961\) −7.69125 + 13.3216i −0.248105 + 0.429730i
\(962\) −1.43970 + 25.1927i −0.0464177 + 0.812246i
\(963\) 11.3675 + 8.20130i 0.366314 + 0.264283i
\(964\) −3.24055 + 28.2600i −0.104371 + 0.910195i
\(965\) 12.9331 9.92392i 0.416331 0.319462i
\(966\) −6.54852 5.48033i −0.210695 0.176327i
\(967\) −10.9299 2.92865i −0.351481 0.0941790i 0.0787589 0.996894i \(-0.474904\pi\)
−0.430240 + 0.902715i \(0.641571\pi\)
\(968\) −48.5017 22.4235i −1.55890 0.720718i
\(969\) 13.4247 + 47.2989i 0.431265 + 1.51946i
\(970\) −22.6847 33.3429i −0.728362 1.07058i
\(971\) −25.6462 10.6230i −0.823027 0.340909i −0.0688884 0.997624i \(-0.521945\pi\)
−0.754138 + 0.656715i \(0.771945\pi\)
\(972\) −30.7206 5.31434i −0.985365 0.170458i
\(973\) −0.109105 0.263403i −0.00349775 0.00844431i
\(974\) −29.7474 + 6.17624i −0.953169 + 0.197900i
\(975\) −3.60907 2.01329i −0.115583 0.0644769i
\(976\) 5.04186 + 6.13434i 0.161386 + 0.196356i
\(977\) 7.94833 + 13.7669i 0.254290 + 0.440443i 0.964702 0.263343i \(-0.0848250\pi\)
−0.710413 + 0.703785i \(0.751492\pi\)
\(978\) 34.1276 + 10.7115i 1.09128 + 0.342516i
\(979\) −4.52266 + 34.3530i −0.144545 + 1.09793i
\(980\) 10.5965 19.0841i 0.338494 0.609618i
\(981\) 1.90280 + 11.7601i 0.0607516 + 0.375473i
\(982\) −2.83607 + 5.87434i −0.0905025 + 0.187458i
\(983\) −7.80698 29.1360i −0.249004 0.929295i −0.971329 0.237741i \(-0.923593\pi\)
0.722325 0.691554i \(-0.243074\pi\)
\(984\) 23.7025 38.7293i 0.755609 1.23465i
\(985\) 5.82556 21.7413i 0.185618 0.692734i
\(986\) 48.6952 + 41.9892i 1.55077 + 1.33721i
\(987\) −2.20404 0.875073i −0.0701555 0.0278539i
\(988\) −31.9961 + 4.75817i −1.01793 + 0.151378i
\(989\) −0.0277408 0.0669722i −0.000882105 0.00212959i
\(990\) 1.29194 46.8403i 0.0410605 1.48868i
\(991\) 8.80828i 0.279804i −0.990165 0.139902i \(-0.955321\pi\)
0.990165 0.139902i \(-0.0446788\pi\)
\(992\) 16.1766 15.4297i 0.513608 0.489895i
\(993\) 36.5513 21.8282i 1.15992 0.692697i
\(994\) −17.6760 + 8.90144i −0.560650 + 0.282336i
\(995\) −7.49149 5.74842i −0.237496 0.182237i
\(996\) 9.90557 1.62280i 0.313870 0.0514203i
\(997\) −19.1310 24.9320i −0.605885 0.789605i 0.385200 0.922833i \(-0.374132\pi\)
−0.991085 + 0.133228i \(0.957466\pi\)
\(998\) 19.5272 + 55.9823i 0.618122 + 1.77209i
\(999\) 26.3498 + 24.1145i 0.833672 + 0.762950i
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 288.2.bf.a.11.9 368
3.2 odd 2 864.2.bn.a.683.38 368
9.4 even 3 864.2.bn.a.395.39 368
9.5 odd 6 inner 288.2.bf.a.203.8 yes 368
32.3 odd 8 inner 288.2.bf.a.227.8 yes 368
96.35 even 8 864.2.bn.a.35.39 368
288.67 odd 24 864.2.bn.a.611.38 368
288.131 even 24 inner 288.2.bf.a.131.9 yes 368
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.bf.a.11.9 368 1.1 even 1 trivial
288.2.bf.a.131.9 yes 368 288.131 even 24 inner
288.2.bf.a.203.8 yes 368 9.5 odd 6 inner
288.2.bf.a.227.8 yes 368 32.3 odd 8 inner
864.2.bn.a.35.39 368 96.35 even 8
864.2.bn.a.395.39 368 9.4 even 3
864.2.bn.a.611.38 368 288.67 odd 24
864.2.bn.a.683.38 368 3.2 odd 2