Properties

Label 462.2.w.a.365.10
Level $462$
Weight $2$
Character 462.365
Analytic conductor $3.689$
Analytic rank $0$
Dimension $48$
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] = [462,2,Mod(29,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.w (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 365.10
Character \(\chi\) \(=\) 462.365
Dual form 462.2.w.a.281.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(1.23159 + 1.21786i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.20361 - 0.391077i) q^{5} +(1.53884 - 0.794973i) q^{6} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.0336340 + 2.99981i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(1.23159 + 1.21786i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.20361 - 0.391077i) q^{5} +(1.53884 - 0.794973i) q^{6} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.0336340 + 2.99981i) q^{9} -1.26555i q^{10} +(3.11275 - 1.14489i) q^{11} +(-0.280538 - 1.70918i) q^{12} +(-0.142725 - 0.0463742i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(1.95863 + 0.984183i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.379364 - 1.16756i) q^{17} +(2.86338 + 0.895005i) q^{18} +(2.43237 + 3.34788i) q^{19} +(-1.20361 - 0.391077i) q^{20} +(1.70918 - 0.280538i) q^{21} +(-0.126956 - 3.31419i) q^{22} -7.98930i q^{23} +(-1.71222 - 0.261358i) q^{24} +(-2.74935 + 1.99752i) q^{25} +(-0.0882090 + 0.121409i) q^{26} +(-3.61193 + 3.73550i) q^{27} +(-0.951057 + 0.309017i) q^{28} +(4.28495 + 3.11320i) q^{29} +(1.54126 - 1.55864i) q^{30} +(-1.38692 + 4.26849i) q^{31} +1.00000 q^{32} +(5.22795 + 2.38087i) q^{33} -1.22765 q^{34} +(0.391077 - 1.20361i) q^{35} +(1.73603 - 2.44667i) q^{36} +(-6.04544 - 4.39227i) q^{37} +(3.93566 - 1.27878i) q^{38} +(-0.119302 - 0.230933i) q^{39} +(-0.743872 + 1.02385i) q^{40} +(7.89214 - 5.73398i) q^{41} +(0.261358 - 1.71222i) q^{42} +4.38794i q^{43} +(-3.19122 - 0.903399i) q^{44} +(1.21364 + 3.59745i) q^{45} +(-7.59828 - 2.46883i) q^{46} +(-1.64278 - 2.26109i) q^{47} +(-0.777671 + 1.54765i) q^{48} +(-0.309017 - 0.951057i) q^{49} +(1.05016 + 3.23205i) q^{50} +(0.954706 - 1.89997i) q^{51} +(0.0882090 + 0.121409i) q^{52} +(-5.52399 - 1.79485i) q^{53} +(2.43653 + 4.58948i) q^{54} +(3.29881 - 2.59532i) q^{55} +1.00000i q^{56} +(-1.08155 + 7.08551i) q^{57} +(4.28495 - 3.11320i) q^{58} +(-8.64390 + 11.8973i) q^{59} +(-1.00608 - 1.94748i) q^{60} +(-2.40987 + 0.783013i) q^{61} +(3.63099 + 2.63807i) q^{62} +(2.44667 + 1.73603i) q^{63} +(0.309017 - 0.951057i) q^{64} -0.189921 q^{65} +(3.87987 - 4.23635i) q^{66} -12.1494 q^{67} +(-0.379364 + 1.16756i) q^{68} +(9.72985 - 9.83955i) q^{69} +(-1.02385 - 0.743872i) q^{70} +(-5.97482 + 1.94134i) q^{71} +(-1.79046 - 2.40713i) q^{72} +(6.32399 - 8.70422i) q^{73} +(-6.04544 + 4.39227i) q^{74} +(-5.81877 - 0.888195i) q^{75} -4.13820i q^{76} +(0.903399 - 3.19122i) q^{77} +(-0.256497 + 0.0421004i) q^{78} +(-10.3548 - 3.36448i) q^{79} +(0.743872 + 1.02385i) q^{80} +(-8.99774 + 0.201791i) q^{81} +(-3.01453 - 9.27777i) q^{82} +(-3.01551 - 9.28079i) q^{83} +(-1.54765 - 0.777671i) q^{84} +(-0.913213 - 1.25693i) q^{85} +(4.17318 + 1.35595i) q^{86} +(1.48587 + 9.05266i) q^{87} +(-1.84532 + 2.75586i) q^{88} -1.07013i q^{89} +(3.79642 - 0.0425656i) q^{90} +(-0.121409 + 0.0882090i) q^{91} +(-4.69599 + 6.46348i) q^{92} +(-6.90654 + 3.56796i) q^{93} +(-2.65807 + 0.863658i) q^{94} +(4.23691 + 3.07830i) q^{95} +(1.23159 + 1.21786i) q^{96} +(-3.06249 + 9.42539i) q^{97} -1.00000 q^{98} +(3.53913 + 9.29917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{11} + 6 q^{12} + 36 q^{15} - 12 q^{16} - 24 q^{17} + 30 q^{19} - 8 q^{22} - 4 q^{24} + 18 q^{25} - 20 q^{26} - 22 q^{27} + 8 q^{29} - 24 q^{30} - 32 q^{31} + 48 q^{32} - 14 q^{33} - 4 q^{34} + 6 q^{35} - 10 q^{36} - 20 q^{37} + 20 q^{38} - 6 q^{39} + 22 q^{44} + 12 q^{45} + 20 q^{46} + 20 q^{47} - 4 q^{48} + 12 q^{49} + 28 q^{50} + 8 q^{51} + 20 q^{52} + 20 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{57} + 8 q^{58} + 30 q^{59} - 4 q^{60} - 20 q^{61} + 8 q^{62} + 4 q^{63} - 12 q^{64} - 14 q^{66} + 36 q^{67} - 24 q^{68} - 70 q^{69} - 4 q^{70} + 10 q^{72} - 20 q^{73} - 20 q^{74} - 30 q^{75} - 16 q^{77} - 16 q^{78} - 20 q^{79} + 26 q^{81} - 10 q^{82} - 46 q^{83} - 10 q^{84} + 10 q^{85} - 30 q^{86} + 8 q^{87} - 8 q^{88} - 38 q^{90} - 36 q^{91} + 10 q^{92} - 36 q^{93} + 50 q^{95} - 4 q^{96} - 2 q^{97} - 48 q^{98} + 70 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\)

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
\(3\) 1.23159 + 1.21786i 0.711060 + 0.703132i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 1.20361 0.391077i 0.538271 0.174895i −0.0272501 0.999629i \(-0.508675\pi\)
0.565521 + 0.824734i \(0.308675\pi\)
\(6\) 1.53884 0.794973i 0.628227 0.324547i
\(7\) 0.587785 0.809017i 0.222162 0.305780i
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) 0.0336340 + 2.99981i 0.0112113 + 0.999937i
\(10\) 1.26555i 0.400202i
\(11\) 3.11275 1.14489i 0.938531 0.345196i
\(12\) −0.280538 1.70918i −0.0809844 0.493398i
\(13\) −0.142725 0.0463742i −0.0395848 0.0128619i 0.289158 0.957281i \(-0.406625\pi\)
−0.328742 + 0.944420i \(0.606625\pi\)
\(14\) −0.587785 0.809017i −0.157092 0.216219i
\(15\) 1.95863 + 0.984183i 0.505717 + 0.254115i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −0.379364 1.16756i −0.0920093 0.283176i 0.894453 0.447161i \(-0.147565\pi\)
−0.986463 + 0.163986i \(0.947565\pi\)
\(18\) 2.86338 + 0.895005i 0.674906 + 0.210955i
\(19\) 2.43237 + 3.34788i 0.558025 + 0.768056i 0.991074 0.133315i \(-0.0425622\pi\)
−0.433049 + 0.901371i \(0.642562\pi\)
\(20\) −1.20361 0.391077i −0.269136 0.0874475i
\(21\) 1.70918 0.280538i 0.372974 0.0612184i
\(22\) −0.126956 3.31419i −0.0270672 0.706589i
\(23\) 7.98930i 1.66588i −0.553360 0.832942i \(-0.686655\pi\)
0.553360 0.832942i \(-0.313345\pi\)
\(24\) −1.71222 0.261358i −0.349505 0.0533495i
\(25\) −2.74935 + 1.99752i −0.549869 + 0.399503i
\(26\) −0.0882090 + 0.121409i −0.0172992 + 0.0238103i
\(27\) −3.61193 + 3.73550i −0.695116 + 0.718898i
\(28\) −0.951057 + 0.309017i −0.179733 + 0.0583987i
\(29\) 4.28495 + 3.11320i 0.795695 + 0.578106i 0.909648 0.415380i \(-0.136351\pi\)
−0.113953 + 0.993486i \(0.536351\pi\)
\(30\) 1.54126 1.55864i 0.281395 0.284568i
\(31\) −1.38692 + 4.26849i −0.249097 + 0.766643i 0.745838 + 0.666127i \(0.232049\pi\)
−0.994935 + 0.100516i \(0.967951\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.22795 + 2.38087i 0.910069 + 0.414456i
\(34\) −1.22765 −0.210540
\(35\) 0.391077 1.20361i 0.0661041 0.203447i
\(36\) 1.73603 2.44667i 0.289339 0.407778i
\(37\) −6.04544 4.39227i −0.993864 0.722085i −0.0331002 0.999452i \(-0.510538\pi\)
−0.960764 + 0.277368i \(0.910538\pi\)
\(38\) 3.93566 1.27878i 0.638449 0.207445i
\(39\) −0.119302 0.230933i −0.0191036 0.0369789i
\(40\) −0.743872 + 1.02385i −0.117617 + 0.161885i
\(41\) 7.89214 5.73398i 1.23255 0.895496i 0.235467 0.971882i \(-0.424338\pi\)
0.997078 + 0.0763859i \(0.0243381\pi\)
\(42\) 0.261358 1.71222i 0.0403285 0.264201i
\(43\) 4.38794i 0.669154i 0.942368 + 0.334577i \(0.108593\pi\)
−0.942368 + 0.334577i \(0.891407\pi\)
\(44\) −3.19122 0.903399i −0.481094 0.136193i
\(45\) 1.21364 + 3.59745i 0.180919 + 0.536277i
\(46\) −7.59828 2.46883i −1.12030 0.364009i
\(47\) −1.64278 2.26109i −0.239623 0.329813i 0.672220 0.740351i \(-0.265341\pi\)
−0.911843 + 0.410538i \(0.865341\pi\)
\(48\) −0.777671 + 1.54765i −0.112247 + 0.223384i
\(49\) −0.309017 0.951057i −0.0441453 0.135865i
\(50\) 1.05016 + 3.23205i 0.148515 + 0.457081i
\(51\) 0.954706 1.89997i 0.133686 0.266049i
\(52\) 0.0882090 + 0.121409i 0.0122324 + 0.0168364i
\(53\) −5.52399 1.79485i −0.758779 0.246542i −0.0960245 0.995379i \(-0.530613\pi\)
−0.662755 + 0.748837i \(0.730613\pi\)
\(54\) 2.43653 + 4.58948i 0.331569 + 0.624549i
\(55\) 3.29881 2.59532i 0.444811 0.349953i
\(56\) 1.00000i 0.133631i
\(57\) −1.08155 + 7.08551i −0.143255 + 0.938498i
\(58\) 4.28495 3.11320i 0.562641 0.408783i
\(59\) −8.64390 + 11.8973i −1.12534 + 1.54890i −0.328708 + 0.944432i \(0.606613\pi\)
−0.796632 + 0.604465i \(0.793387\pi\)
\(60\) −1.00608 1.94748i −0.129884 0.251418i
\(61\) −2.40987 + 0.783013i −0.308552 + 0.100255i −0.459200 0.888333i \(-0.651864\pi\)
0.150648 + 0.988587i \(0.451864\pi\)
\(62\) 3.63099 + 2.63807i 0.461137 + 0.335035i
\(63\) 2.44667 + 1.73603i 0.308251 + 0.218720i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −0.189921 −0.0235569
\(66\) 3.87987 4.23635i 0.477578 0.521458i
\(67\) −12.1494 −1.48428 −0.742142 0.670242i \(-0.766190\pi\)
−0.742142 + 0.670242i \(0.766190\pi\)
\(68\) −0.379364 + 1.16756i −0.0460047 + 0.141588i
\(69\) 9.72985 9.83955i 1.17134 1.18454i
\(70\) −1.02385 0.743872i −0.122374 0.0889098i
\(71\) −5.97482 + 1.94134i −0.709081 + 0.230394i −0.641283 0.767305i \(-0.721597\pi\)
−0.0677982 + 0.997699i \(0.521597\pi\)
\(72\) −1.79046 2.40713i −0.211007 0.283683i
\(73\) 6.32399 8.70422i 0.740166 1.01875i −0.258443 0.966027i \(-0.583209\pi\)
0.998609 0.0527251i \(-0.0167907\pi\)
\(74\) −6.04544 + 4.39227i −0.702768 + 0.510591i
\(75\) −5.81877 0.888195i −0.671893 0.102560i
\(76\) 4.13820i 0.474684i
\(77\) 0.903399 3.19122i 0.102952 0.363673i
\(78\) −0.256497 + 0.0421004i −0.0290426 + 0.00476693i
\(79\) −10.3548 3.36448i −1.16501 0.378534i −0.338230 0.941063i \(-0.609828\pi\)
−0.826777 + 0.562529i \(0.809828\pi\)
\(80\) 0.743872 + 1.02385i 0.0831675 + 0.114470i
\(81\) −8.99774 + 0.201791i −0.999749 + 0.0224213i
\(82\) −3.01453 9.27777i −0.332899 1.02456i
\(83\) −3.01551 9.28079i −0.330995 1.01870i −0.968661 0.248386i \(-0.920100\pi\)
0.637666 0.770313i \(-0.279900\pi\)
\(84\) −1.54765 0.777671i −0.168863 0.0848509i
\(85\) −0.913213 1.25693i −0.0990519 0.136333i
\(86\) 4.17318 + 1.35595i 0.450005 + 0.146216i
\(87\) 1.48587 + 9.05266i 0.159302 + 0.970547i
\(88\) −1.84532 + 2.75586i −0.196712 + 0.293776i
\(89\) 1.07013i 0.113433i −0.998390 0.0567166i \(-0.981937\pi\)
0.998390 0.0567166i \(-0.0180632\pi\)
\(90\) 3.79642 0.0425656i 0.400177 0.00448681i
\(91\) −0.121409 + 0.0882090i −0.0127271 + 0.00924681i
\(92\) −4.69599 + 6.46348i −0.489591 + 0.673864i
\(93\) −6.90654 + 3.56796i −0.716174 + 0.369981i
\(94\) −2.65807 + 0.863658i −0.274159 + 0.0890795i
\(95\) 4.23691 + 3.07830i 0.434698 + 0.315826i
\(96\) 1.23159 + 1.21786i 0.125699 + 0.124297i
\(97\) −3.06249 + 9.42539i −0.310949 + 0.957003i 0.666441 + 0.745558i \(0.267817\pi\)
−0.977390 + 0.211445i \(0.932183\pi\)
\(98\) −1.00000 −0.101015
\(99\) 3.53913 + 9.29917i 0.355696 + 0.934602i
\(100\) 3.39838 0.339838
\(101\) −0.471591 + 1.45141i −0.0469250 + 0.144420i −0.971774 0.235915i \(-0.924191\pi\)
0.924849 + 0.380335i \(0.124191\pi\)
\(102\) −1.51196 1.49510i −0.149706 0.148037i
\(103\) 3.25945 + 2.36813i 0.321164 + 0.233339i 0.736672 0.676250i \(-0.236396\pi\)
−0.415508 + 0.909589i \(0.636396\pi\)
\(104\) 0.142725 0.0463742i 0.0139954 0.00454737i
\(105\) 1.94748 1.00608i 0.190054 0.0981833i
\(106\) −3.41402 + 4.69899i −0.331599 + 0.456406i
\(107\) −2.67801 + 1.94569i −0.258893 + 0.188097i −0.709659 0.704545i \(-0.751151\pi\)
0.450766 + 0.892642i \(0.351151\pi\)
\(108\) 5.11778 0.899048i 0.492459 0.0865109i
\(109\) 1.95947i 0.187683i 0.995587 + 0.0938414i \(0.0299147\pi\)
−0.995587 + 0.0938414i \(0.970085\pi\)
\(110\) −1.44891 3.93935i −0.138148 0.375602i
\(111\) −2.09634 12.7720i −0.198976 1.21226i
\(112\) 0.951057 + 0.309017i 0.0898664 + 0.0291994i
\(113\) 10.7866 + 14.8465i 1.01472 + 1.39664i 0.915843 + 0.401538i \(0.131524\pi\)
0.0988740 + 0.995100i \(0.468476\pi\)
\(114\) 6.40450 + 3.21816i 0.599836 + 0.301408i
\(115\) −3.12443 9.61601i −0.291355 0.896697i
\(116\) −1.63671 5.03726i −0.151964 0.467698i
\(117\) 0.134313 0.429708i 0.0124173 0.0397265i
\(118\) 8.64390 + 11.8973i 0.795735 + 1.09524i
\(119\) −1.16756 0.379364i −0.107030 0.0347762i
\(120\) −2.16306 + 0.355035i −0.197459 + 0.0324101i
\(121\) 8.37848 7.12749i 0.761680 0.647954i
\(122\) 2.53388i 0.229407i
\(123\) 16.7031 + 2.54961i 1.50607 + 0.229890i
\(124\) 3.63099 2.63807i 0.326073 0.236906i
\(125\) −6.24732 + 8.59870i −0.558778 + 0.769091i
\(126\) 2.40713 1.79046i 0.214444 0.159506i
\(127\) −9.83031 + 3.19406i −0.872299 + 0.283427i −0.710756 0.703439i \(-0.751647\pi\)
−0.161543 + 0.986866i \(0.551647\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) −5.34389 + 5.40414i −0.470503 + 0.475808i
\(130\) −0.0586889 + 0.180626i −0.00514736 + 0.0158419i
\(131\) −3.13040 −0.273505 −0.136752 0.990605i \(-0.543666\pi\)
−0.136752 + 0.990605i \(0.543666\pi\)
\(132\) −2.83006 4.99908i −0.246325 0.435114i
\(133\) 4.13820 0.358828
\(134\) −3.75437 + 11.5548i −0.324328 + 0.998179i
\(135\) −2.88649 + 5.90863i −0.248429 + 0.508534i
\(136\) 0.993188 + 0.721593i 0.0851652 + 0.0618761i
\(137\) 0.810649 0.263396i 0.0692584 0.0225034i −0.274183 0.961678i \(-0.588407\pi\)
0.343441 + 0.939174i \(0.388407\pi\)
\(138\) −6.35128 12.2942i −0.540657 1.04655i
\(139\) −4.49572 + 6.18783i −0.381322 + 0.524845i −0.955934 0.293581i \(-0.905153\pi\)
0.574612 + 0.818426i \(0.305153\pi\)
\(140\) −1.02385 + 0.743872i −0.0865313 + 0.0628687i
\(141\) 0.730459 4.78540i 0.0615157 0.403004i
\(142\) 6.28230i 0.527199i
\(143\) −0.497361 + 0.0190524i −0.0415914 + 0.00159324i
\(144\) −2.84260 + 0.958981i −0.236883 + 0.0799150i
\(145\) 6.37491 + 2.07133i 0.529408 + 0.172015i
\(146\) −6.32399 8.70422i −0.523377 0.720366i
\(147\) 0.777671 1.54765i 0.0641412 0.127648i
\(148\) 2.30915 + 7.10684i 0.189811 + 0.584179i
\(149\) −0.275104 0.846682i −0.0225374 0.0693629i 0.939155 0.343493i \(-0.111610\pi\)
−0.961693 + 0.274130i \(0.911610\pi\)
\(150\) −2.64282 + 5.25951i −0.215785 + 0.429437i
\(151\) 8.56766 + 11.7924i 0.697227 + 0.959650i 0.999978 + 0.00658065i \(0.00209470\pi\)
−0.302752 + 0.953069i \(0.597905\pi\)
\(152\) −3.93566 1.27878i −0.319225 0.103722i
\(153\) 3.48971 1.17729i 0.282126 0.0951783i
\(154\) −2.75586 1.84532i −0.222074 0.148700i
\(155\) 5.67999i 0.456228i
\(156\) −0.0392221 + 0.256953i −0.00314028 + 0.0205727i
\(157\) 17.4409 12.6716i 1.39194 1.01130i 0.396290 0.918126i \(-0.370298\pi\)
0.995650 0.0931775i \(-0.0297024\pi\)
\(158\) −6.39963 + 8.80833i −0.509127 + 0.700753i
\(159\) −4.61742 8.93798i −0.366185 0.708828i
\(160\) 1.20361 0.391077i 0.0951538 0.0309173i
\(161\) −6.46348 4.69599i −0.509394 0.370096i
\(162\) −2.58854 + 8.61971i −0.203375 + 0.677229i
\(163\) −2.92839 + 9.01266i −0.229369 + 0.705926i 0.768449 + 0.639911i \(0.221029\pi\)
−0.997819 + 0.0660154i \(0.978971\pi\)
\(164\) −9.75522 −0.761755
\(165\) 7.22352 + 0.821108i 0.562350 + 0.0639232i
\(166\) −9.75840 −0.757399
\(167\) 3.49984 10.7714i 0.270826 0.833517i −0.719468 0.694526i \(-0.755614\pi\)
0.990294 0.138991i \(-0.0443859\pi\)
\(168\) −1.21786 + 1.23159i −0.0939599 + 0.0950193i
\(169\) −10.4990 7.62797i −0.807615 0.586767i
\(170\) −1.47761 + 0.480105i −0.113328 + 0.0368224i
\(171\) −9.96119 + 7.40927i −0.761751 + 0.566601i
\(172\) 2.57916 3.54991i 0.196659 0.270678i
\(173\) 13.8568 10.0675i 1.05351 0.765420i 0.0806333 0.996744i \(-0.474306\pi\)
0.972877 + 0.231324i \(0.0743057\pi\)
\(174\) 9.06875 + 1.38428i 0.687500 + 0.104942i
\(175\) 3.39838i 0.256893i
\(176\) 2.05074 + 2.60662i 0.154581 + 0.196481i
\(177\) −25.1350 + 4.12556i −1.88926 + 0.310096i
\(178\) −1.01775 0.330687i −0.0762837 0.0247861i
\(179\) −0.221144 0.304378i −0.0165291 0.0227503i 0.800672 0.599102i \(-0.204476\pi\)
−0.817202 + 0.576352i \(0.804476\pi\)
\(180\) 1.13267 3.62376i 0.0844246 0.270099i
\(181\) −5.34329 16.4450i −0.397163 1.22234i −0.927264 0.374409i \(-0.877846\pi\)
0.530100 0.847935i \(-0.322154\pi\)
\(182\) 0.0463742 + 0.142725i 0.00343749 + 0.0105795i
\(183\) −3.92157 1.97053i −0.289891 0.145666i
\(184\) 4.69599 + 6.46348i 0.346193 + 0.476494i
\(185\) −8.99407 2.92235i −0.661257 0.214856i
\(186\) 1.25910 + 7.67107i 0.0923216 + 0.562470i
\(187\) −2.51759 3.20001i −0.184105 0.234008i
\(188\) 2.79486i 0.203836i
\(189\) 0.899048 + 5.11778i 0.0653961 + 0.372264i
\(190\) 4.23691 3.07830i 0.307378 0.223323i
\(191\) 6.77637 9.32688i 0.490321 0.674869i −0.490126 0.871652i \(-0.663049\pi\)
0.980447 + 0.196782i \(0.0630492\pi\)
\(192\) 1.53884 0.794973i 0.111056 0.0573723i
\(193\) −10.3428 + 3.36058i −0.744492 + 0.241900i −0.656609 0.754231i \(-0.728010\pi\)
−0.0878823 + 0.996131i \(0.528010\pi\)
\(194\) 8.01771 + 5.82521i 0.575638 + 0.418226i
\(195\) −0.233906 0.231298i −0.0167503 0.0165636i
\(196\) −0.309017 + 0.951057i −0.0220726 + 0.0679326i
\(197\) 9.73907 0.693880 0.346940 0.937887i \(-0.387221\pi\)
0.346940 + 0.937887i \(0.387221\pi\)
\(198\) 9.93769 0.492315i 0.706241 0.0349873i
\(199\) 19.1382 1.35667 0.678337 0.734751i \(-0.262701\pi\)
0.678337 + 0.734751i \(0.262701\pi\)
\(200\) 1.05016 3.23205i 0.0742573 0.228541i
\(201\) −14.9631 14.7963i −1.05541 1.04365i
\(202\) 1.23464 + 0.897019i 0.0868690 + 0.0631141i
\(203\) 5.03726 1.63671i 0.353546 0.114874i
\(204\) −1.88915 + 0.975947i −0.132267 + 0.0683300i
\(205\) 7.25664 9.98791i 0.506826 0.697586i
\(206\) 3.25945 2.36813i 0.227097 0.164996i
\(207\) 23.9664 0.268712i 1.66578 0.0186768i
\(208\) 0.150070i 0.0104055i
\(209\) 11.4043 + 7.63633i 0.788853 + 0.528216i
\(210\) −0.355035 2.16306i −0.0244998 0.149265i
\(211\) −0.412712 0.134098i −0.0284122 0.00923169i 0.294776 0.955566i \(-0.404755\pi\)
−0.323189 + 0.946335i \(0.604755\pi\)
\(212\) 3.41402 + 4.69899i 0.234476 + 0.322728i
\(213\) −9.72281 4.88556i −0.666196 0.334753i
\(214\) 1.02291 + 3.14819i 0.0699246 + 0.215206i
\(215\) 1.71602 + 5.28137i 0.117032 + 0.360186i
\(216\) 0.726437 5.14512i 0.0494278 0.350081i
\(217\) 2.63807 + 3.63099i 0.179084 + 0.246488i
\(218\) 1.86356 + 0.605508i 0.126216 + 0.0410102i
\(219\) 18.3891 3.01831i 1.24262 0.203959i
\(220\) −4.19428 + 0.160670i −0.282778 + 0.0108324i
\(221\) 0.184233i 0.0123929i
\(222\) −12.7947 1.95302i −0.858723 0.131078i
\(223\) −14.7261 + 10.6992i −0.986136 + 0.716470i −0.959071 0.283164i \(-0.908616\pi\)
−0.0270643 + 0.999634i \(0.508616\pi\)
\(224\) 0.587785 0.809017i 0.0392731 0.0540547i
\(225\) −6.08465 8.18034i −0.405643 0.545356i
\(226\) 17.4531 5.67084i 1.16096 0.377219i
\(227\) 15.9273 + 11.5718i 1.05713 + 0.768049i 0.973555 0.228453i \(-0.0733666\pi\)
0.0835737 + 0.996502i \(0.473367\pi\)
\(228\) 5.03975 5.09657i 0.333766 0.337529i
\(229\) 3.02746 9.31756i 0.200060 0.615722i −0.799820 0.600240i \(-0.795072\pi\)
0.999880 0.0154820i \(-0.00492827\pi\)
\(230\) −10.1109 −0.666691
\(231\) 4.99908 2.83006i 0.328915 0.186204i
\(232\) −5.29649 −0.347732
\(233\) 9.31781 28.6773i 0.610430 1.87871i 0.156485 0.987680i \(-0.449984\pi\)
0.453945 0.891030i \(-0.350016\pi\)
\(234\) −0.367172 0.260527i −0.0240028 0.0170312i
\(235\) −2.86152 2.07902i −0.186665 0.135620i
\(236\) 13.9861 4.54436i 0.910419 0.295813i
\(237\) −8.65543 16.7544i −0.562231 1.08831i
\(238\) −0.721593 + 0.993188i −0.0467739 + 0.0643788i
\(239\) −2.40266 + 1.74564i −0.155415 + 0.112916i −0.662775 0.748818i \(-0.730621\pi\)
0.507360 + 0.861734i \(0.330621\pi\)
\(240\) −0.330762 + 2.16690i −0.0213506 + 0.139873i
\(241\) 4.21213i 0.271327i 0.990755 + 0.135664i \(0.0433166\pi\)
−0.990755 + 0.135664i \(0.956683\pi\)
\(242\) −4.18956 10.1709i −0.269315 0.653812i
\(243\) −11.3273 10.7095i −0.726646 0.687012i
\(244\) 2.40987 + 0.783013i 0.154276 + 0.0501273i
\(245\) −0.743872 1.02385i −0.0475243 0.0654115i
\(246\) 7.58635 15.0977i 0.483688 0.962594i
\(247\) −0.191906 0.590626i −0.0122107 0.0375806i
\(248\) −1.38692 4.26849i −0.0880693 0.271049i
\(249\) 7.58882 15.1026i 0.480922 0.957089i
\(250\) 6.24732 + 8.59870i 0.395115 + 0.543830i
\(251\) 9.73610 + 3.16345i 0.614537 + 0.199675i 0.599713 0.800215i \(-0.295281\pi\)
0.0148239 + 0.999890i \(0.495281\pi\)
\(252\) −0.958981 2.84260i −0.0604101 0.179067i
\(253\) −9.14683 24.8687i −0.575056 1.56348i
\(254\) 10.3362i 0.648551i
\(255\) 0.406060 2.66019i 0.0254284 0.166588i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 16.0700 22.1184i 1.00242 1.37971i 0.0785877 0.996907i \(-0.474959\pi\)
0.923830 0.382803i \(-0.125041\pi\)
\(258\) 3.48829 + 6.75232i 0.217172 + 0.420381i
\(259\) −7.10684 + 2.30915i −0.441598 + 0.143484i
\(260\) 0.153650 + 0.111633i 0.00952895 + 0.00692319i
\(261\) −9.19489 + 12.9588i −0.569149 + 0.802127i
\(262\) −0.967348 + 2.97719i −0.0597630 + 0.183932i
\(263\) −19.8950 −1.22678 −0.613391 0.789780i \(-0.710195\pi\)
−0.613391 + 0.789780i \(0.710195\pi\)
\(264\) −5.62894 + 1.14675i −0.346437 + 0.0705775i
\(265\) −7.35067 −0.451548
\(266\) 1.27878 3.93566i 0.0784067 0.241311i
\(267\) 1.30326 1.31796i 0.0797585 0.0806578i
\(268\) 9.82907 + 7.14124i 0.600406 + 0.436220i
\(269\) 0.602463 0.195752i 0.0367328 0.0119352i −0.290593 0.956847i \(-0.593853\pi\)
0.327326 + 0.944912i \(0.393853\pi\)
\(270\) 4.72747 + 4.57108i 0.287705 + 0.278187i
\(271\) 15.4216 21.2260i 0.936796 1.28939i −0.0203534 0.999793i \(-0.506479\pi\)
0.957149 0.289596i \(-0.0935209\pi\)
\(272\) 0.993188 0.721593i 0.0602209 0.0437530i
\(273\) −0.256953 0.0392221i −0.0155515 0.00237383i
\(274\) 0.852366i 0.0514933i
\(275\) −6.27111 + 9.36547i −0.378162 + 0.564759i
\(276\) −13.6552 + 2.24130i −0.821944 + 0.134911i
\(277\) 26.8393 + 8.72062i 1.61262 + 0.523971i 0.970184 0.242371i \(-0.0779250\pi\)
0.642433 + 0.766342i \(0.277925\pi\)
\(278\) 4.49572 + 6.18783i 0.269635 + 0.371121i
\(279\) −12.8513 4.01692i −0.769388 0.240487i
\(280\) 0.391077 + 1.20361i 0.0233713 + 0.0719295i
\(281\) 1.44118 + 4.43549i 0.0859735 + 0.264599i 0.984796 0.173713i \(-0.0555765\pi\)
−0.898823 + 0.438312i \(0.855576\pi\)
\(282\) −4.32547 2.17348i −0.257578 0.129429i
\(283\) 14.3709 + 19.7799i 0.854263 + 1.17579i 0.982907 + 0.184101i \(0.0589375\pi\)
−0.128644 + 0.991691i \(0.541063\pi\)
\(284\) 5.97482 + 1.94134i 0.354540 + 0.115197i
\(285\) 1.46921 + 8.95116i 0.0870284 + 0.530221i
\(286\) −0.135573 + 0.478906i −0.00801661 + 0.0283183i
\(287\) 9.75522i 0.575833i
\(288\) 0.0336340 + 2.99981i 0.00198190 + 0.176766i
\(289\) 12.5340 9.10649i 0.737294 0.535676i
\(290\) 3.93991 5.42282i 0.231360 0.318439i
\(291\) −15.2505 + 7.87854i −0.894003 + 0.461848i
\(292\) −10.2324 + 3.32472i −0.598807 + 0.194564i
\(293\) 5.76112 + 4.18570i 0.336568 + 0.244531i 0.743212 0.669056i \(-0.233301\pi\)
−0.406644 + 0.913587i \(0.633301\pi\)
\(294\) −1.23159 1.21786i −0.0718279 0.0710270i
\(295\) −5.75113 + 17.7001i −0.334844 + 1.03054i
\(296\) 7.47257 0.434335
\(297\) −6.96632 + 15.7629i −0.404227 + 0.914659i
\(298\) −0.890254 −0.0515711
\(299\) −0.370497 + 1.14027i −0.0214264 + 0.0659437i
\(300\) 4.18541 + 4.13875i 0.241645 + 0.238951i
\(301\) 3.54991 + 2.57916i 0.204614 + 0.148661i
\(302\) 13.8628 4.50429i 0.797713 0.259193i
\(303\) −2.34842 + 1.21321i −0.134913 + 0.0696970i
\(304\) −2.43237 + 3.34788i −0.139506 + 0.192014i
\(305\) −2.59432 + 1.88489i −0.148551 + 0.107928i
\(306\) −0.0412907 3.68271i −0.00236043 0.210527i
\(307\) 25.5876i 1.46036i −0.683253 0.730181i \(-0.739436\pi\)
0.683253 0.730181i \(-0.260564\pi\)
\(308\) −2.60662 + 2.05074i −0.148526 + 0.116852i
\(309\) 1.13026 + 6.88613i 0.0642984 + 0.391738i
\(310\) 5.40199 + 1.75521i 0.306813 + 0.0996894i
\(311\) 3.00067 + 4.13007i 0.170152 + 0.234195i 0.885574 0.464498i \(-0.153765\pi\)
−0.715422 + 0.698693i \(0.753765\pi\)
\(312\) 0.232256 + 0.116705i 0.0131489 + 0.00660713i
\(313\) 4.99132 + 15.3617i 0.282126 + 0.868294i 0.987245 + 0.159206i \(0.0508933\pi\)
−0.705120 + 0.709088i \(0.749107\pi\)
\(314\) −6.66185 20.5031i −0.375950 1.15705i
\(315\) 3.62376 + 1.13267i 0.204176 + 0.0638190i
\(316\) 6.39963 + 8.80833i 0.360007 + 0.495507i
\(317\) −16.0129 5.20290i −0.899372 0.292224i −0.177394 0.984140i \(-0.556767\pi\)
−0.721978 + 0.691916i \(0.756767\pi\)
\(318\) −9.92739 + 1.62944i −0.556700 + 0.0913745i
\(319\) 16.9022 + 4.78485i 0.946344 + 0.267900i
\(320\) 1.26555i 0.0707465i
\(321\) −5.66779 0.865148i −0.316345 0.0482879i
\(322\) −6.46348 + 4.69599i −0.360196 + 0.261697i
\(323\) 2.98610 4.11001i 0.166151 0.228687i
\(324\) 7.39793 + 5.12548i 0.410996 + 0.284749i
\(325\) 0.485034 0.157597i 0.0269049 0.00874192i
\(326\) 7.66663 + 5.57013i 0.424615 + 0.308501i
\(327\) −2.38636 + 2.41326i −0.131966 + 0.133454i
\(328\) −3.01453 + 9.27777i −0.166450 + 0.512279i
\(329\) −2.79486 −0.154085
\(330\) 3.01311 6.61624i 0.165866 0.364212i
\(331\) −5.03168 −0.276566 −0.138283 0.990393i \(-0.544158\pi\)
−0.138283 + 0.990393i \(0.544158\pi\)
\(332\) −3.01551 + 9.28079i −0.165498 + 0.509349i
\(333\) 12.9726 18.2829i 0.710897 1.00190i
\(334\) −9.16271 6.65710i −0.501361 0.364260i
\(335\) −14.6231 + 4.75135i −0.798948 + 0.259594i
\(336\) 0.794973 + 1.53884i 0.0433694 + 0.0839504i
\(337\) −13.2501 + 18.2372i −0.721779 + 0.993444i 0.277684 + 0.960673i \(0.410433\pi\)
−0.999463 + 0.0327711i \(0.989567\pi\)
\(338\) −10.4990 + 7.62797i −0.571070 + 0.414907i
\(339\) −4.79625 + 31.4213i −0.260496 + 1.70657i
\(340\) 1.55365i 0.0842586i
\(341\) 0.569800 + 14.8746i 0.0308564 + 0.805506i
\(342\) 3.96846 + 11.7632i 0.214590 + 0.636083i
\(343\) −0.951057 0.309017i −0.0513522 0.0166853i
\(344\) −2.57916 3.54991i −0.139059 0.191399i
\(345\) 7.86293 15.6481i 0.423326 0.842466i
\(346\) −5.29281 16.2896i −0.284543 0.875734i
\(347\) 6.29845 + 19.3846i 0.338119 + 1.04062i 0.965165 + 0.261641i \(0.0842636\pi\)
−0.627047 + 0.778982i \(0.715736\pi\)
\(348\) 4.11893 8.19712i 0.220798 0.439412i
\(349\) 12.7756 + 17.5842i 0.683864 + 0.941259i 0.999972 0.00746472i \(-0.00237612\pi\)
−0.316108 + 0.948723i \(0.602376\pi\)
\(350\) 3.23205 + 1.05016i 0.172760 + 0.0561333i
\(351\) 0.688744 0.365650i 0.0367624 0.0195169i
\(352\) 3.11275 1.14489i 0.165910 0.0610226i
\(353\) 12.1839i 0.648486i −0.945974 0.324243i \(-0.894890\pi\)
0.945974 0.324243i \(-0.105110\pi\)
\(354\) −3.84350 + 25.1797i −0.204280 + 1.33828i
\(355\) −6.43215 + 4.67323i −0.341383 + 0.248029i
\(356\) −0.629005 + 0.865751i −0.0333372 + 0.0458847i
\(357\) −0.975947 1.88915i −0.0516526 0.0999844i
\(358\) −0.357818 + 0.116262i −0.0189113 + 0.00614465i
\(359\) −21.3205 15.4903i −1.12526 0.817546i −0.140258 0.990115i \(-0.544793\pi\)
−0.984997 + 0.172569i \(0.944793\pi\)
\(360\) −3.09638 2.19704i −0.163194 0.115794i
\(361\) 0.579492 1.78349i 0.0304996 0.0938681i
\(362\) −17.2912 −0.908808
\(363\) 18.9991 + 1.42566i 0.997196 + 0.0748275i
\(364\) 0.150070 0.00786581
\(365\) 4.20760 12.9497i 0.220236 0.677816i
\(366\) −3.08592 + 3.12071i −0.161303 + 0.163122i
\(367\) 14.4897 + 10.5274i 0.756357 + 0.549525i 0.897791 0.440422i \(-0.145171\pi\)
−0.141434 + 0.989948i \(0.545171\pi\)
\(368\) 7.59828 2.46883i 0.396088 0.128697i
\(369\) 17.4663 + 23.4821i 0.909259 + 1.22243i
\(370\) −5.55864 + 7.65081i −0.288980 + 0.397747i
\(371\) −4.69899 + 3.41402i −0.243959 + 0.177247i
\(372\) 7.68470 + 1.17302i 0.398433 + 0.0608181i
\(373\) 11.2227i 0.581089i 0.956862 + 0.290544i \(0.0938364\pi\)
−0.956862 + 0.290544i \(0.906164\pi\)
\(374\) −3.82137 + 1.40552i −0.197598 + 0.0726775i
\(375\) −18.1662 + 2.98172i −0.938097 + 0.153975i
\(376\) 2.65807 + 0.863658i 0.137079 + 0.0445398i
\(377\) −0.467198 0.643043i −0.0240619 0.0331184i
\(378\) 5.14512 + 0.726437i 0.264637 + 0.0373639i
\(379\) 5.42840 + 16.7069i 0.278838 + 0.858176i 0.988178 + 0.153310i \(0.0489932\pi\)
−0.709340 + 0.704867i \(0.751007\pi\)
\(380\) −1.61836 4.98079i −0.0830199 0.255509i
\(381\) −15.9968 8.03816i −0.819543 0.411808i
\(382\) −6.77637 9.32688i −0.346709 0.477205i
\(383\) −23.9018 7.76617i −1.22133 0.396833i −0.373761 0.927525i \(-0.621932\pi\)
−0.847565 + 0.530692i \(0.821932\pi\)
\(384\) −0.280538 1.70918i −0.0143162 0.0872213i
\(385\) −0.160670 4.19428i −0.00818850 0.213760i
\(386\) 10.8751i 0.553527i
\(387\) −13.1630 + 0.147584i −0.669112 + 0.00750211i
\(388\) 8.01771 5.82521i 0.407038 0.295730i
\(389\) −6.53645 + 8.99665i −0.331411 + 0.456148i −0.941908 0.335870i \(-0.890970\pi\)
0.610497 + 0.792018i \(0.290970\pi\)
\(390\) −0.292258 + 0.150982i −0.0147991 + 0.00764530i
\(391\) −9.32801 + 3.03085i −0.471738 + 0.153277i
\(392\) 0.809017 + 0.587785i 0.0408615 + 0.0296876i
\(393\) −3.85538 3.81239i −0.194478 0.192310i
\(394\) 3.00954 9.26241i 0.151618 0.466633i
\(395\) −13.7789 −0.693294
\(396\) 2.60269 9.60344i 0.130790 0.482591i
\(397\) 22.4138 1.12492 0.562459 0.826825i \(-0.309855\pi\)
0.562459 + 0.826825i \(0.309855\pi\)
\(398\) 5.91404 18.2015i 0.296444 0.912361i
\(399\) 5.09657 + 5.03975i 0.255148 + 0.252303i
\(400\) −2.74935 1.99752i −0.137467 0.0998759i
\(401\) −5.07008 + 1.64737i −0.253188 + 0.0822656i −0.432861 0.901461i \(-0.642496\pi\)
0.179673 + 0.983726i \(0.442496\pi\)
\(402\) −18.6959 + 9.65845i −0.932468 + 0.481720i
\(403\) 0.395896 0.544904i 0.0197210 0.0271436i
\(404\) 1.23464 0.897019i 0.0614257 0.0446284i
\(405\) −10.7509 + 3.76169i −0.534214 + 0.186920i
\(406\) 5.29649i 0.262860i
\(407\) −23.8466 6.75072i −1.18203 0.334621i
\(408\) 0.344402 + 2.09827i 0.0170504 + 0.103880i
\(409\) −15.3374 4.98341i −0.758384 0.246414i −0.0957990 0.995401i \(-0.530541\pi\)
−0.662585 + 0.748987i \(0.730541\pi\)
\(410\) −7.25664 9.98791i −0.358380 0.493268i
\(411\) 1.31917 + 0.662861i 0.0650697 + 0.0326965i
\(412\) −1.24500 3.83172i −0.0613368 0.188775i
\(413\) 4.54436 + 13.9861i 0.223614 + 0.688212i
\(414\) 7.15046 22.8764i 0.351426 1.12432i
\(415\) −7.25900 9.99116i −0.356330 0.490447i
\(416\) −0.142725 0.0463742i −0.00699768 0.00227368i
\(417\) −13.0728 + 2.14572i −0.640177 + 0.105076i
\(418\) 10.7867 8.48640i 0.527595 0.415083i
\(419\) 18.7529i 0.916137i 0.888917 + 0.458069i \(0.151459\pi\)
−0.888917 + 0.458069i \(0.848541\pi\)
\(420\) −2.16690 0.330762i −0.105734 0.0161395i
\(421\) 6.14224 4.46260i 0.299355 0.217494i −0.427961 0.903797i \(-0.640768\pi\)
0.727315 + 0.686304i \(0.240768\pi\)
\(422\) −0.255070 + 0.351073i −0.0124166 + 0.0170900i
\(423\) 6.72758 5.00407i 0.327106 0.243306i
\(424\) 5.52399 1.79485i 0.268269 0.0871659i
\(425\) 3.37523 + 2.45225i 0.163723 + 0.118952i
\(426\) −7.65096 + 7.73722i −0.370690 + 0.374870i
\(427\) −0.783013 + 2.40987i −0.0378927 + 0.116622i
\(428\) 3.31020 0.160005
\(429\) −0.635749 0.582252i −0.0306943 0.0281114i
\(430\) 5.55316 0.267797
\(431\) 7.03075 21.6384i 0.338659 1.04229i −0.626232 0.779637i \(-0.715404\pi\)
0.964891 0.262649i \(-0.0845963\pi\)
\(432\) −4.66882 2.28081i −0.224629 0.109736i
\(433\) 8.15913 + 5.92796i 0.392103 + 0.284879i 0.766317 0.642463i \(-0.222087\pi\)
−0.374214 + 0.927342i \(0.622087\pi\)
\(434\) 4.26849 1.38692i 0.204894 0.0665741i
\(435\) 5.32869 + 10.3148i 0.255491 + 0.494556i
\(436\) 1.15175 1.58524i 0.0551586 0.0759193i
\(437\) 26.7472 19.4330i 1.27949 0.929605i
\(438\) 2.81196 18.4218i 0.134360 0.880226i
\(439\) 2.63248i 0.125641i −0.998025 0.0628206i \(-0.979990\pi\)
0.998025 0.0628206i \(-0.0200096\pi\)
\(440\) −1.14330 + 4.03865i −0.0545046 + 0.192535i
\(441\) 2.84260 0.958981i 0.135362 0.0456657i
\(442\) 0.175216 + 0.0569312i 0.00833419 + 0.00270794i
\(443\) 11.9073 + 16.3890i 0.565733 + 0.778665i 0.992041 0.125913i \(-0.0401861\pi\)
−0.426308 + 0.904578i \(0.640186\pi\)
\(444\) −5.81120 + 11.5649i −0.275788 + 0.548848i
\(445\) −0.418502 1.28802i −0.0198389 0.0610578i
\(446\) 5.62489 + 17.3116i 0.266346 + 0.819729i
\(447\) 0.692325 1.37780i 0.0327459 0.0651679i
\(448\) −0.587785 0.809017i −0.0277702 0.0382225i
\(449\) −24.5056 7.96236i −1.15649 0.375767i −0.332907 0.942960i \(-0.608030\pi\)
−0.823585 + 0.567193i \(0.808030\pi\)
\(450\) −9.66022 + 3.25898i −0.455387 + 0.153630i
\(451\) 18.0015 26.8840i 0.847660 1.26592i
\(452\) 18.3512i 0.863169i
\(453\) −3.80961 + 24.9576i −0.178991 + 1.17261i
\(454\) 15.9273 11.5718i 0.747503 0.543093i
\(455\) −0.111633 + 0.153650i −0.00523344 + 0.00720321i
\(456\) −3.28976 6.36802i −0.154057 0.298210i
\(457\) −22.5834 + 7.33780i −1.05641 + 0.343248i −0.785180 0.619268i \(-0.787430\pi\)
−0.271228 + 0.962515i \(0.587430\pi\)
\(458\) −7.92599 5.75857i −0.370357 0.269080i
\(459\) 5.73167 + 2.80004i 0.267531 + 0.130694i
\(460\) −3.12443 + 9.61601i −0.145677 + 0.448349i
\(461\) 2.78562 0.129739 0.0648696 0.997894i \(-0.479337\pi\)
0.0648696 + 0.997894i \(0.479337\pi\)
\(462\) −1.14675 5.62894i −0.0533516 0.261882i
\(463\) −2.99874 −0.139363 −0.0696816 0.997569i \(-0.522198\pi\)
−0.0696816 + 0.997569i \(0.522198\pi\)
\(464\) −1.63671 + 5.03726i −0.0759821 + 0.233849i
\(465\) −6.91743 + 6.99543i −0.320788 + 0.324405i
\(466\) −24.3943 17.7235i −1.13005 0.821026i
\(467\) −5.15927 + 1.67635i −0.238743 + 0.0775722i −0.425945 0.904749i \(-0.640058\pi\)
0.187202 + 0.982321i \(0.440058\pi\)
\(468\) −0.361238 + 0.268694i −0.0166982 + 0.0124204i
\(469\) −7.14124 + 9.82907i −0.329752 + 0.453864i
\(470\) −2.86152 + 2.07902i −0.131992 + 0.0958979i
\(471\) 36.9123 + 5.63441i 1.70083 + 0.259620i
\(472\) 14.7059i 0.676893i
\(473\) 5.02368 + 13.6586i 0.230989 + 0.628022i
\(474\) −18.6090 + 3.05441i −0.854742 + 0.140294i
\(475\) −13.3749 4.34576i −0.613682 0.199397i
\(476\) 0.721593 + 0.993188i 0.0330742 + 0.0455227i
\(477\) 5.19843 16.6313i 0.238020 0.761495i
\(478\) 0.917735 + 2.82450i 0.0419762 + 0.129190i
\(479\) 8.33856 + 25.6634i 0.380998 + 1.17259i 0.939342 + 0.342983i \(0.111437\pi\)
−0.558343 + 0.829610i \(0.688563\pi\)
\(480\) 1.95863 + 0.984183i 0.0893990 + 0.0449216i
\(481\) 0.659148 + 0.907240i 0.0300546 + 0.0413666i
\(482\) 4.00597 + 1.30162i 0.182467 + 0.0592872i
\(483\) −2.24130 13.6552i −0.101983 0.621331i
\(484\) −10.9678 + 0.841517i −0.498535 + 0.0382508i
\(485\) 12.5422i 0.569511i
\(486\) −13.6856 + 7.46349i −0.620793 + 0.338551i
\(487\) 14.1964 10.3143i 0.643299 0.467384i −0.217683 0.976019i \(-0.569850\pi\)
0.860982 + 0.508636i \(0.169850\pi\)
\(488\) 1.48938 2.04995i 0.0674210 0.0927971i
\(489\) −14.5827 + 7.53354i −0.659454 + 0.340679i
\(490\) −1.20361 + 0.391077i −0.0543736 + 0.0176671i
\(491\) −27.3069 19.8396i −1.23234 0.895351i −0.235281 0.971927i \(-0.575601\pi\)
−0.997064 + 0.0765768i \(0.975601\pi\)
\(492\) −12.0144 11.8805i −0.541653 0.535614i
\(493\) 2.00930 6.18398i 0.0904942 0.278513i
\(494\) −0.621020 −0.0279410
\(495\) 7.89643 + 9.80851i 0.354918 + 0.440860i
\(496\) −4.48815 −0.201524
\(497\) −1.94134 + 5.97482i −0.0870809 + 0.268007i
\(498\) −12.0184 11.8844i −0.538556 0.532551i
\(499\) 6.19831 + 4.50333i 0.277474 + 0.201597i 0.717815 0.696234i \(-0.245142\pi\)
−0.440341 + 0.897831i \(0.645142\pi\)
\(500\) 10.1084 3.28441i 0.452061 0.146883i
\(501\) 17.4284 9.00366i 0.778646 0.402254i
\(502\) 6.01724 8.28202i 0.268563 0.369645i
\(503\) −7.37887 + 5.36106i −0.329008 + 0.239038i −0.740009 0.672596i \(-0.765179\pi\)
0.411002 + 0.911635i \(0.365179\pi\)
\(504\) −2.99981 + 0.0336340i −0.133622 + 0.00149818i
\(505\) 1.93136i 0.0859443i
\(506\) −26.4781 + 1.01429i −1.17709 + 0.0450908i
\(507\) −3.64068 22.1809i −0.161688 0.985086i
\(508\) 9.83031 + 3.19406i 0.436150 + 0.141714i
\(509\) 21.3108 + 29.3318i 0.944584 + 1.30011i 0.953891 + 0.300152i \(0.0970375\pi\)
−0.00930679 + 0.999957i \(0.502962\pi\)
\(510\) −2.40451 1.20823i −0.106474 0.0535013i
\(511\) −3.32472 10.2324i −0.147077 0.452656i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) −21.2916 3.00614i −0.940045 0.132724i
\(514\) −16.0700 22.1184i −0.708816 0.975602i
\(515\) 4.84924 + 1.57561i 0.213683 + 0.0694298i
\(516\) 7.49978 1.23098i 0.330159 0.0541910i
\(517\) −7.70224 5.15742i −0.338744 0.226823i
\(518\) 7.47257i 0.328326i
\(519\) 29.3267 + 4.47652i 1.28730 + 0.196497i
\(520\) 0.153650 0.111633i 0.00673798 0.00489543i
\(521\) −8.17594 + 11.2532i −0.358194 + 0.493012i −0.949645 0.313329i \(-0.898556\pi\)
0.591450 + 0.806342i \(0.298556\pi\)
\(522\) 9.48313 + 12.7493i 0.415065 + 0.558023i
\(523\) 10.1304 3.29157i 0.442971 0.143930i −0.0790347 0.996872i \(-0.525184\pi\)
0.522006 + 0.852942i \(0.325184\pi\)
\(524\) 2.53255 + 1.84001i 0.110635 + 0.0803810i
\(525\) −4.13875 + 4.18541i −0.180630 + 0.182666i
\(526\) −6.14791 + 18.9213i −0.268062 + 0.825009i
\(527\) 5.50987 0.240014
\(528\) −0.648815 + 5.70781i −0.0282360 + 0.248400i
\(529\) −40.8289 −1.77517
\(530\) −2.27148 + 6.99090i −0.0986668 + 0.303665i
\(531\) −35.9804 25.5299i −1.56142 1.10790i
\(532\) −3.34788 2.43237i −0.145149 0.105457i
\(533\) −1.39232 + 0.452391i −0.0603079 + 0.0195952i
\(534\) −0.850723 1.64675i −0.0368144 0.0712619i
\(535\) −2.46237 + 3.38916i −0.106457 + 0.146526i
\(536\) 9.82907 7.14124i 0.424551 0.308454i
\(537\) 0.0983314 0.644192i 0.00424331 0.0277989i
\(538\) 0.633467i 0.0273107i
\(539\) −2.05074 2.60662i −0.0883318 0.112275i
\(540\) 5.80822 3.08355i 0.249946 0.132695i
\(541\) 9.36982 + 3.04444i 0.402840 + 0.130891i 0.503427 0.864038i \(-0.332072\pi\)
−0.100587 + 0.994928i \(0.532072\pi\)
\(542\) −15.4216 21.2260i −0.662415 0.911735i
\(543\) 13.4469 26.7608i 0.577062 1.14842i
\(544\) −0.379364 1.16756i −0.0162651 0.0500588i
\(545\) 0.766302 + 2.35843i 0.0328248 + 0.101024i
\(546\) −0.116705 + 0.232256i −0.00499452 + 0.00993965i
\(547\) 0.276221 + 0.380186i 0.0118104 + 0.0162556i 0.814881 0.579628i \(-0.196802\pi\)
−0.803071 + 0.595883i \(0.796802\pi\)
\(548\) −0.810649 0.263396i −0.0346292 0.0112517i
\(549\) −2.42994 7.20281i −0.103708 0.307408i
\(550\) 6.96921 + 8.85827i 0.297168 + 0.377718i
\(551\) 21.9179i 0.933736i
\(552\) −2.08807 + 13.6794i −0.0888741 + 0.582235i
\(553\) −8.80833 + 6.39963i −0.374568 + 0.272140i
\(554\) 16.5876 22.8309i 0.704739 0.969991i
\(555\) −7.51801 14.5527i −0.319122 0.617726i
\(556\) 7.27423 2.36354i 0.308496 0.100236i
\(557\) 7.59992 + 5.52167i 0.322019 + 0.233961i 0.737037 0.675853i \(-0.236225\pi\)
−0.415017 + 0.909813i \(0.636225\pi\)
\(558\) −7.79159 + 10.9810i −0.329844 + 0.464864i
\(559\) 0.203487 0.626269i 0.00860659 0.0264883i
\(560\) 1.26555 0.0534793
\(561\) 0.796516 7.00718i 0.0336289 0.295843i
\(562\) 4.66375 0.196728
\(563\) 12.2573 37.7240i 0.516583 1.58988i −0.263800 0.964577i \(-0.584976\pi\)
0.780383 0.625302i \(-0.215024\pi\)
\(564\) −3.40374 + 3.44212i −0.143323 + 0.144939i
\(565\) 18.7890 + 13.6510i 0.790457 + 0.574301i
\(566\) 23.2527 7.55524i 0.977382 0.317571i
\(567\) −5.12548 + 7.39793i −0.215250 + 0.310684i
\(568\) 3.69264 5.08249i 0.154940 0.213256i
\(569\) −14.1470 + 10.2784i −0.593073 + 0.430893i −0.843414 0.537265i \(-0.819458\pi\)
0.250340 + 0.968158i \(0.419458\pi\)
\(570\) 8.96707 + 1.36876i 0.375589 + 0.0573311i
\(571\) 42.0315i 1.75896i 0.475934 + 0.879481i \(0.342110\pi\)
−0.475934 + 0.879481i \(0.657890\pi\)
\(572\) 0.413573 + 0.276928i 0.0172923 + 0.0115789i
\(573\) 19.7046 3.23423i 0.823170 0.135112i
\(574\) −9.27777 3.01453i −0.387247 0.125824i
\(575\) 15.9588 + 21.9654i 0.665527 + 0.916019i
\(576\) 2.86338 + 0.895005i 0.119308 + 0.0372919i
\(577\) 2.37227 + 7.30108i 0.0987587 + 0.303948i 0.988215 0.153072i \(-0.0489167\pi\)
−0.889456 + 0.457020i \(0.848917\pi\)
\(578\) −4.78756 14.7346i −0.199136 0.612879i
\(579\) −16.8308 8.45723i −0.699465 0.351470i
\(580\) −3.93991 5.42282i −0.163596 0.225171i
\(581\) −9.28079 3.01551i −0.385032 0.125104i
\(582\) 2.78026 + 16.9387i 0.115245 + 0.702133i
\(583\) −19.2497 + 0.737398i −0.797243 + 0.0305399i
\(584\) 10.7590i 0.445211i
\(585\) −0.00638782 0.569728i −0.000264104 0.0235554i
\(586\) 5.76112 4.18570i 0.237990 0.172910i
\(587\) −23.2807 + 32.0431i −0.960898 + 1.32256i −0.0143847 + 0.999897i \(0.504579\pi\)
−0.946513 + 0.322666i \(0.895421\pi\)
\(588\) −1.53884 + 0.794973i −0.0634605 + 0.0327842i
\(589\) −17.6639 + 5.73934i −0.727827 + 0.236485i
\(590\) 15.0566 + 10.9393i 0.619872 + 0.450364i
\(591\) 11.9946 + 11.8608i 0.493390 + 0.487889i
\(592\) 2.30915 7.10684i 0.0949056 0.292089i
\(593\) 0.505509 0.0207588 0.0103794 0.999946i \(-0.496696\pi\)
0.0103794 + 0.999946i \(0.496696\pi\)
\(594\) 12.8387 + 11.4964i 0.526780 + 0.471702i
\(595\) −1.55365 −0.0636935
\(596\) −0.275104 + 0.846682i −0.0112687 + 0.0346815i
\(597\) 23.5705 + 23.3077i 0.964676 + 0.953920i
\(598\) 0.969975 + 0.704728i 0.0396652 + 0.0288185i
\(599\) 7.13291 2.31762i 0.291443 0.0946956i −0.159647 0.987174i \(-0.551035\pi\)
0.451090 + 0.892479i \(0.351035\pi\)
\(600\) 5.22955 2.70162i 0.213495 0.110293i
\(601\) −25.9777 + 35.7552i −1.05965 + 1.45849i −0.179521 + 0.983754i \(0.557455\pi\)
−0.880131 + 0.474732i \(0.842545\pi\)
\(602\) 3.54991 2.57916i 0.144684 0.105119i
\(603\) −0.408633 36.4459i −0.0166408 1.48419i
\(604\) 14.5762i 0.593096i
\(605\) 7.29703 11.8554i 0.296666 0.481989i
\(606\) 0.428129 + 2.60838i 0.0173916 + 0.105958i
\(607\) −11.3469 3.68682i −0.460555 0.149643i 0.0695446 0.997579i \(-0.477845\pi\)
−0.530099 + 0.847936i \(0.677845\pi\)
\(608\) 2.43237 + 3.34788i 0.0986458 + 0.135774i
\(609\) 8.19712 + 4.11893i 0.332164 + 0.166907i
\(610\) 0.990943 + 3.04981i 0.0401221 + 0.123483i
\(611\) 0.129609 + 0.398896i 0.00524343 + 0.0161376i
\(612\) −3.51523 1.09875i −0.142095 0.0444144i
\(613\) −23.1639 31.8824i −0.935581 1.28772i −0.957642 0.287961i \(-0.907023\pi\)
0.0220609 0.999757i \(-0.492977\pi\)
\(614\) −24.3353 7.90701i −0.982092 0.319101i
\(615\) 21.1011 3.46345i 0.850878 0.139660i
\(616\) 1.14489 + 3.11275i 0.0461287 + 0.125416i
\(617\) 14.7927i 0.595530i −0.954639 0.297765i \(-0.903759\pi\)
0.954639 0.297765i \(-0.0962412\pi\)
\(618\) 6.89837 + 1.05299i 0.277493 + 0.0423574i
\(619\) 11.0014 7.99297i 0.442183 0.321264i −0.344319 0.938853i \(-0.611890\pi\)
0.786502 + 0.617588i \(0.211890\pi\)
\(620\) 3.33861 4.59521i 0.134082 0.184548i
\(621\) 29.8441 + 28.8568i 1.19760 + 1.15798i
\(622\) 4.85519 1.57755i 0.194675 0.0632538i
\(623\) −0.865751 0.629005i −0.0346856 0.0252005i
\(624\) 0.182764 0.184825i 0.00731643 0.00739892i
\(625\) 1.09419 3.36758i 0.0437677 0.134703i
\(626\) 16.1522 0.645573
\(627\) 4.74548 + 23.2937i 0.189516 + 0.930261i
\(628\) −21.5582 −0.860266
\(629\) −2.83483 + 8.72470i −0.113032 + 0.347876i
\(630\) 2.19704 3.09638i 0.0875322 0.123363i
\(631\) 38.2813 + 27.8130i 1.52395 + 1.10722i 0.959483 + 0.281766i \(0.0909201\pi\)
0.564472 + 0.825452i \(0.309080\pi\)
\(632\) 10.3548 3.36448i 0.411892 0.133832i
\(633\) −0.344979 0.667779i −0.0137117 0.0265418i
\(634\) −9.89650 + 13.6214i −0.393040 + 0.540973i
\(635\) −10.5827 + 7.68882i −0.419963 + 0.305121i
\(636\) −1.51804 + 9.94503i −0.0601942 + 0.394346i
\(637\) 0.150070i 0.00594599i
\(638\) 9.77374 14.5964i 0.386946 0.577877i
\(639\) −6.02460 17.8580i −0.238330 0.706453i
\(640\) −1.20361 0.391077i −0.0475769 0.0154587i
\(641\) 10.4106 + 14.3290i 0.411195 + 0.565961i 0.963509 0.267674i \(-0.0862552\pi\)
−0.552314 + 0.833636i \(0.686255\pi\)
\(642\) −2.57425 + 5.12304i −0.101597 + 0.202190i
\(643\) −10.2501 31.5465i −0.404223 1.24407i −0.921542 0.388279i \(-0.873070\pi\)
0.517319 0.855793i \(-0.326930\pi\)
\(644\) 2.46883 + 7.59828i 0.0972855 + 0.299414i
\(645\) −4.31853 + 8.59436i −0.170042 + 0.338403i
\(646\) −2.98610 4.11001i −0.117487 0.161706i
\(647\) −35.8161 11.6374i −1.40808 0.457512i −0.496282 0.868161i \(-0.665302\pi\)
−0.911793 + 0.410650i \(0.865302\pi\)
\(648\) 7.16071 5.45199i 0.281299 0.214174i
\(649\) −13.2853 + 46.9296i −0.521493 + 1.84215i
\(650\) 0.509995i 0.0200037i
\(651\) −1.17302 + 7.68470i −0.0459741 + 0.301187i
\(652\) 7.66663 5.57013i 0.300248 0.218143i
\(653\) 23.9367 32.9460i 0.936715 1.28928i −0.0204664 0.999791i \(-0.506515\pi\)
0.957182 0.289488i \(-0.0934849\pi\)
\(654\) 1.55772 + 3.01530i 0.0609118 + 0.117907i
\(655\) −3.76779 + 1.22423i −0.147220 + 0.0478346i
\(656\) 7.89214 + 5.73398i 0.308136 + 0.223874i
\(657\) 26.3237 + 18.6780i 1.02699 + 0.728698i
\(658\) −0.863658 + 2.65807i −0.0336689 + 0.103622i
\(659\) 3.77335 0.146989 0.0734945 0.997296i \(-0.476585\pi\)
0.0734945 + 0.997296i \(0.476585\pi\)
\(660\) −5.36132 4.91017i −0.208689 0.191128i
\(661\) 35.5412 1.38239 0.691196 0.722667i \(-0.257084\pi\)
0.691196 + 0.722667i \(0.257084\pi\)
\(662\) −1.55487 + 4.78541i −0.0604319 + 0.185990i
\(663\) −0.224370 + 0.226900i −0.00871382 + 0.00881207i
\(664\) 7.89471 + 5.73584i 0.306374 + 0.222594i
\(665\) 4.98079 1.61836i 0.193147 0.0627571i
\(666\) −13.3793 17.9874i −0.518438 0.696999i
\(667\) 24.8723 34.2337i 0.963058 1.32554i
\(668\) −9.16271 + 6.65710i −0.354516 + 0.257571i
\(669\) −31.1667 4.75738i −1.20497 0.183931i
\(670\) 15.3757i 0.594015i
\(671\) −6.60486 + 5.19635i −0.254978 + 0.200603i
\(672\) 1.70918 0.280538i 0.0659331 0.0108220i
\(673\) −31.3630 10.1905i −1.20895 0.392813i −0.365907 0.930652i \(-0.619241\pi\)
−0.843048 + 0.537838i \(0.819241\pi\)
\(674\) 13.2501 + 18.2372i 0.510375 + 0.702471i
\(675\) 2.46871 17.4851i 0.0950206 0.673001i
\(676\) 4.01026 + 12.3423i 0.154241 + 0.474704i
\(677\) 0.576976 + 1.77575i 0.0221750 + 0.0682476i 0.961532 0.274694i \(-0.0885766\pi\)
−0.939357 + 0.342942i \(0.888577\pi\)
\(678\) 28.4013 + 14.2712i 1.09075 + 0.548083i
\(679\) 5.82521 + 8.01771i 0.223551 + 0.307692i
\(680\) 1.47761 + 0.480105i 0.0566638 + 0.0184112i
\(681\) 5.52300 + 33.6489i 0.211642 + 1.28943i
\(682\) 14.3227 + 4.05460i 0.548444 + 0.155259i
\(683\) 39.4696i 1.51026i −0.655573 0.755132i \(-0.727573\pi\)
0.655573 0.755132i \(-0.272427\pi\)
\(684\) 12.4138 0.139184i 0.474655 0.00532185i
\(685\) 0.872697 0.634052i 0.0333441 0.0242259i
\(686\) −0.587785 + 0.809017i −0.0224417 + 0.0308884i
\(687\) 15.0761 7.78841i 0.575188 0.297146i
\(688\) −4.17318 + 1.35595i −0.159101 + 0.0516950i
\(689\) 0.705178 + 0.512342i 0.0268651 + 0.0195187i
\(690\) −12.4525 12.3136i −0.474057 0.468772i
\(691\) 6.90773 21.2598i 0.262783 0.808762i −0.729413 0.684073i \(-0.760207\pi\)
0.992196 0.124688i \(-0.0397931\pi\)
\(692\) −17.1279 −0.651105
\(693\) 9.60344 + 2.60269i 0.364804 + 0.0988682i
\(694\) 20.3822 0.773699
\(695\) −2.99118 + 9.20591i −0.113462 + 0.349200i
\(696\) −6.52311 6.45038i −0.247258 0.244501i
\(697\) −9.68877 7.03930i −0.366988 0.266633i
\(698\) 20.6714 6.71655i 0.782425 0.254225i
\(699\) 46.4006 23.9709i 1.75503 0.906662i
\(700\) 1.99752 2.74935i 0.0754991 0.103916i
\(701\) 36.2208 26.3160i 1.36804 0.993941i 0.370155 0.928970i \(-0.379305\pi\)
0.997887 0.0649706i \(-0.0206954\pi\)
\(702\) −0.134920 0.768026i −0.00509224 0.0289873i
\(703\) 30.9230i 1.16628i
\(704\) −0.126956 3.31419i −0.00478485 0.124908i
\(705\) −0.992273 6.04543i −0.0373712 0.227684i
\(706\) −11.5876 3.76505i −0.436106 0.141699i
\(707\) 0.897019 + 1.23464i 0.0337359 + 0.0464335i
\(708\) 22.7596 + 11.4363i 0.855357 + 0.429804i
\(709\) −8.93914 27.5119i −0.335717 1.03323i −0.966368 0.257163i \(-0.917212\pi\)
0.630651 0.776066i \(-0.282788\pi\)
\(710\) 2.45686 + 7.56144i 0.0922044 + 0.283776i
\(711\) 9.74454 31.1757i 0.365449 1.16918i
\(712\) 0.629005 + 0.865751i 0.0235730 + 0.0324454i
\(713\) 34.1022 + 11.0805i 1.27714 + 0.414968i
\(714\) −2.09827 + 0.344402i −0.0785259 + 0.0128889i
\(715\) −0.591179 + 0.217438i −0.0221088 + 0.00813173i
\(716\) 0.376232i 0.0140605i
\(717\) −5.08504 0.776196i −0.189904 0.0289876i
\(718\) −21.3205 + 15.4903i −0.795676 + 0.578092i
\(719\) −11.0692 + 15.2355i −0.412812 + 0.568187i −0.963901 0.266259i \(-0.914212\pi\)
0.551090 + 0.834446i \(0.314212\pi\)
\(720\) −3.04635 + 2.26591i −0.113531 + 0.0844456i
\(721\) 3.83172 1.24500i 0.142701 0.0463663i
\(722\) −1.51713 1.10226i −0.0564617 0.0410219i
\(723\) −5.12978 + 5.18762i −0.190779 + 0.192930i
\(724\) −5.34329 + 16.4450i −0.198582 + 0.611172i
\(725\) −17.9995 −0.668484
\(726\) 7.22694 17.6287i 0.268217 0.654263i
\(727\) 45.8398 1.70010 0.850051 0.526700i \(-0.176571\pi\)
0.850051 + 0.526700i \(0.176571\pi\)
\(728\) 0.0463742 0.142725i 0.00171874 0.00528975i
\(729\) −0.907966 26.9847i −0.0336284 0.999434i
\(730\) −11.0156 8.00333i −0.407707 0.296216i
\(731\) 5.12319 1.66463i 0.189488 0.0615684i
\(732\) 2.01437 + 3.89923i 0.0744533 + 0.144120i
\(733\) 4.64612 6.39483i 0.171608 0.236199i −0.714546 0.699588i \(-0.753367\pi\)
0.886155 + 0.463389i \(0.153367\pi\)
\(734\) 14.4897 10.5274i 0.534825 0.388573i
\(735\) 0.330762 2.16690i 0.0122004 0.0799273i
\(736\) 7.98930i 0.294490i
\(737\) −37.8181 + 13.9097i −1.39305 + 0.512369i
\(738\) 27.7302 9.35507i 1.02076 0.344365i
\(739\) −30.1398 9.79303i −1.10871 0.360242i −0.303263 0.952907i \(-0.598076\pi\)
−0.805449 + 0.592665i \(0.798076\pi\)
\(740\) 5.55864 + 7.65081i 0.204340 + 0.281250i
\(741\) 0.482950 0.961124i 0.0177416 0.0353078i
\(742\) 1.79485 + 5.52399i 0.0658912 + 0.202792i
\(743\) −8.62955 26.5590i −0.316587 0.974356i −0.975096 0.221783i \(-0.928812\pi\)
0.658509 0.752573i \(-0.271188\pi\)
\(744\) 3.49031 6.94610i 0.127961 0.254656i
\(745\) −0.662236 0.911489i −0.0242624 0.0333944i
\(746\) 10.6734 + 3.46800i 0.390781 + 0.126973i
\(747\) 27.7392 9.35811i 1.01492 0.342396i
\(748\) 0.155858 + 4.06866i 0.00569873 + 0.148765i
\(749\) 3.31020i 0.120952i
\(750\) −2.77787 + 18.1985i −0.101433 + 0.664514i
\(751\) −39.9326 + 29.0127i −1.45716 + 1.05869i −0.473068 + 0.881026i \(0.656854\pi\)
−0.984091 + 0.177662i \(0.943146\pi\)
\(752\) 1.64278 2.26109i 0.0599059 0.0824533i
\(753\) 8.13826 + 15.7533i 0.296575 + 0.574082i
\(754\) −0.755942 + 0.245620i −0.0275298 + 0.00894497i
\(755\) 14.9239 + 10.8428i 0.543135 + 0.394611i
\(756\) 2.28081 4.66882i 0.0829524 0.169803i
\(757\) 4.52610 13.9299i 0.164504 0.506291i −0.834495 0.551015i \(-0.814241\pi\)
0.998999 + 0.0447237i \(0.0142408\pi\)
\(758\) 17.5667 0.638051
\(759\) 19.0215 41.7677i 0.690436 1.51607i
\(760\) −5.23711 −0.189970
\(761\) −2.71038 + 8.34169i −0.0982512 + 0.302386i −0.988087 0.153894i \(-0.950819\pi\)
0.889836 + 0.456280i \(0.150819\pi\)
\(762\) −12.5880 + 12.7300i −0.456017 + 0.461158i
\(763\) 1.58524 + 1.15175i 0.0573896 + 0.0416960i
\(764\) −10.9644 + 3.56255i −0.396678 + 0.128889i
\(765\) 3.73984 2.78174i 0.135214 0.100574i
\(766\) −14.7721 + 20.3321i −0.533739 + 0.734629i
\(767\) 1.78543 1.29719i 0.0644681 0.0468388i
\(768\) −1.71222 0.261358i −0.0617844 0.00943095i
\(769\) 7.95794i 0.286971i 0.989652 + 0.143485i \(0.0458310\pi\)
−0.989652 + 0.143485i \(0.954169\pi\)
\(770\) −4.03865 1.14330i −0.145543 0.0412016i
\(771\) 46.7288 7.66988i 1.68290 0.276224i
\(772\) 10.3428 + 3.36058i 0.372246 + 0.120950i
\(773\) 2.00414 + 2.75846i 0.0720839 + 0.0992150i 0.843537 0.537072i \(-0.180470\pi\)
−0.771453 + 0.636287i \(0.780470\pi\)
\(774\) −3.92722 + 12.5643i −0.141161 + 0.451616i
\(775\) −4.71327 14.5059i −0.169306 0.521069i
\(776\) −3.06249 9.42539i −0.109937 0.338352i
\(777\) −11.5649 5.81120i −0.414890 0.208476i
\(778\) 6.53645 + 8.99665i 0.234343 + 0.322545i
\(779\) 38.3933 + 12.4747i 1.37558 + 0.446954i
\(780\) 0.0532802 + 0.324610i 0.00190774 + 0.0116229i
\(781\) −16.3755 + 12.8834i −0.585963 + 0.461004i
\(782\) 9.80805i 0.350735i
\(783\) −27.1063 + 4.76180i −0.968700 + 0.170173i
\(784\) 0.809017 0.587785i 0.0288935 0.0209923i
\(785\) 16.0365 22.0724i 0.572369 0.787798i
\(786\) −4.81718 + 2.48859i −0.171823 + 0.0887650i
\(787\) 8.94226 2.90552i 0.318757 0.103570i −0.145268 0.989392i \(-0.546405\pi\)
0.464026 + 0.885822i \(0.346405\pi\)
\(788\) −7.87907 5.72448i −0.280680 0.203926i
\(789\) −24.5026 24.2294i −0.872314 0.862589i
\(790\) −4.25793 + 13.1046i −0.151490 + 0.466239i
\(791\) 18.3512 0.652495
\(792\) −8.32913 5.44293i −0.295963 0.193406i
\(793\) 0.380260 0.0135034
\(794\) 6.92626 21.3168i 0.245804 0.756506i
\(795\) −9.05302 8.95208i −0.321077 0.317498i
\(796\) −15.4832 11.2492i −0.548786 0.398716i
\(797\) −38.8467 + 12.6221i −1.37602 + 0.447096i −0.901359 0.433072i \(-0.857430\pi\)
−0.474662 + 0.880168i \(0.657430\pi\)
\(798\) 6.36802 3.28976i 0.225425 0.116456i
\(799\) −2.01675 + 2.77582i −0.0713475 + 0.0982014i
\(800\) −2.74935 + 1.99752i −0.0972041 + 0.0706229i
\(801\) 3.21018 0.0359927i 0.113426 0.00127174i
\(802\) 5.33100i 0.188244i
\(803\) 9.71968 34.3343i 0.343000 1.21163i
\(804\) 3.40837 + 20.7655i 0.120204 + 0.732343i
\(805\) −9.61601 3.12443i −0.338920 0.110122i
\(806\) −0.395896 0.544904i −0.0139448 0.0191934i
\(807\) 0.980386 + 0.492629i 0.0345112 + 0.0173414i
\(808\) −0.471591 1.45141i −0.0165905 0.0510603i
\(809\) −0.901007 2.77301i −0.0316777 0.0974939i 0.933968 0.357358i \(-0.116322\pi\)
−0.965645 + 0.259864i \(0.916322\pi\)
\(810\) 0.255377 + 11.3871i 0.00897305 + 0.400102i
\(811\) −20.8639 28.7168i −0.732632 1.00838i −0.999009 0.0445126i \(-0.985827\pi\)
0.266377 0.963869i \(-0.414173\pi\)
\(812\) −5.03726 1.63671i −0.176773 0.0574371i
\(813\) 44.8434 7.36042i 1.57273 0.258141i
\(814\) −13.7893 + 20.5934i −0.483316 + 0.721798i
\(815\) 11.9930i 0.420095i
\(816\) 2.10200 + 0.320856i 0.0735848 + 0.0112322i
\(817\) −14.6903 + 10.6731i −0.513947 + 0.373405i
\(818\) −9.47901 + 13.0467i −0.331426 + 0.456169i
\(819\) −0.268694 0.361238i −0.00938892 0.0126227i
\(820\) −11.7415 + 3.81504i −0.410031 + 0.133227i
\(821\) 35.8961 + 26.0801i 1.25278 + 0.910200i 0.998380 0.0568979i \(-0.0181210\pi\)
0.254403 + 0.967098i \(0.418121\pi\)
\(822\) 1.03806 1.04977i 0.0362066 0.0366148i
\(823\) 13.6996 42.1630i 0.477537 1.46971i −0.364968 0.931020i \(-0.618920\pi\)
0.842505 0.538688i \(-0.181080\pi\)
\(824\) −4.02891 −0.140354
\(825\) −19.1293 + 3.89709i −0.665996 + 0.135679i
\(826\) 14.7059 0.511683
\(827\) 17.7051 54.4908i 0.615667 1.89483i 0.224685 0.974431i \(-0.427865\pi\)
0.390983 0.920398i \(-0.372135\pi\)
\(828\) −19.5472 13.8697i −0.679311 0.482005i
\(829\) −7.96168 5.78450i −0.276521 0.200904i 0.440878 0.897567i \(-0.354667\pi\)
−0.717398 + 0.696663i \(0.754667\pi\)
\(830\) −11.7453 + 3.81628i −0.407686 + 0.132465i
\(831\) 22.4346 + 43.4267i 0.778246 + 1.50646i
\(832\) −0.0882090 + 0.121409i −0.00305810 + 0.00420911i
\(833\) −0.993188 + 0.721593i −0.0344119 + 0.0250017i
\(834\) −1.99902 + 13.0960i −0.0692203 + 0.453478i
\(835\) 14.3333i 0.496024i
\(836\) −4.73777 12.8812i −0.163859 0.445506i
\(837\) −10.9355 20.5983i −0.377987 0.711981i
\(838\) 17.8350 + 5.79495i 0.616101 + 0.200183i
\(839\) 26.2744 + 36.1636i 0.907093 + 1.24851i 0.968150 + 0.250372i \(0.0805528\pi\)
−0.0610572 + 0.998134i \(0.519447\pi\)
\(840\) −0.984183 + 1.95863i −0.0339575 + 0.0675793i
\(841\) −0.292701 0.900843i −0.0100932 0.0310635i
\(842\) −2.34613 7.22064i −0.0808529 0.248840i
\(843\) −3.62686 + 7.21787i −0.124916 + 0.248597i
\(844\) 0.255070 + 0.351073i 0.00877986 + 0.0120844i
\(845\) −15.6198 5.07519i −0.537339 0.174592i
\(846\) −2.68021 7.94465i −0.0921476 0.273143i
\(847\) −0.841517 10.9678i −0.0289149 0.376857i
\(848\) 5.80827i 0.199457i
\(849\) −6.39002 + 41.8625i −0.219305 + 1.43672i
\(850\) 3.37523 2.45225i 0.115769 0.0841114i
\(851\) −35.0912 + 48.2988i −1.20291 + 1.65566i
\(852\) 4.99426 + 9.66743i 0.171101 + 0.331201i
\(853\) −14.8506 + 4.82526i −0.508476 + 0.165214i −0.552009 0.833838i \(-0.686139\pi\)
0.0435333 + 0.999052i \(0.486139\pi\)
\(854\) 2.04995 + 1.48938i 0.0701480 + 0.0509655i
\(855\) −9.09180 + 12.8135i −0.310933 + 0.438211i
\(856\) 1.02291 3.14819i 0.0349623 0.107603i
\(857\) 23.4298 0.800346 0.400173 0.916440i \(-0.368950\pi\)
0.400173 + 0.916440i \(0.368950\pi\)
\(858\) −0.750212 + 0.424708i −0.0256118 + 0.0144993i
\(859\) −45.1419 −1.54022 −0.770110 0.637911i \(-0.779799\pi\)
−0.770110 + 0.637911i \(0.779799\pi\)
\(860\) 1.71602 5.28137i 0.0585158 0.180093i
\(861\) 11.8805 12.0144i 0.404886 0.409451i
\(862\) −18.4067 13.3733i −0.626936 0.455496i
\(863\) −10.9781 + 3.56700i −0.373699 + 0.121422i −0.489844 0.871810i \(-0.662946\pi\)
0.116145 + 0.993232i \(0.462946\pi\)
\(864\) −3.61193 + 3.73550i −0.122880 + 0.127084i
\(865\) 12.7410 17.5364i 0.433206 0.596257i
\(866\) 8.15913 5.92796i 0.277259 0.201440i
\(867\) 26.5272 + 4.04919i 0.900911 + 0.137518i
\(868\) 4.48815i 0.152338i
\(869\) −36.0839 + 1.38226i −1.22406 + 0.0468901i
\(870\) 11.4566 1.88044i 0.388415 0.0637529i
\(871\) 1.73402 + 0.563419i 0.0587552 + 0.0190907i
\(872\) −1.15175 1.58524i −0.0390030 0.0536830i
\(873\) −28.3774 8.86989i −0.960429 0.300200i
\(874\) −10.2165 31.4432i −0.345579 1.06358i
\(875\) 3.28441 + 10.1084i 0.111033 + 0.341726i
\(876\) −16.6512 8.36697i −0.562592 0.282694i
\(877\) 23.7693 + 32.7156i 0.802632 + 1.10473i 0.992419 + 0.122903i \(0.0392204\pi\)
−0.189787 + 0.981825i \(0.560780\pi\)
\(878\) −2.50363 0.813480i −0.0844935 0.0274536i
\(879\) 1.99775 + 12.1713i 0.0673824 + 0.410528i
\(880\) 3.48769 + 2.33535i 0.117570 + 0.0787247i
\(881\) 27.0165i 0.910209i 0.890438 + 0.455104i \(0.150398\pi\)
−0.890438 + 0.455104i \(0.849602\pi\)
\(882\) −0.0336340 2.99981i −0.00113252 0.101009i
\(883\) −36.9282 + 26.8299i −1.24273 + 0.902897i −0.997777 0.0666371i \(-0.978773\pi\)
−0.244954 + 0.969535i \(0.578773\pi\)
\(884\) 0.108290 0.149048i 0.00364217 0.00501302i
\(885\) −28.6393 + 14.7953i −0.962701 + 0.497338i
\(886\) 19.2664 6.26004i 0.647268 0.210310i
\(887\) −32.1172 23.3345i −1.07839 0.783495i −0.100988 0.994888i \(-0.532200\pi\)
−0.977401 + 0.211392i \(0.932200\pi\)
\(888\) 9.20316 + 9.10055i 0.308838 + 0.305394i
\(889\) −3.19406 + 9.83031i −0.107125 + 0.329698i
\(890\) −1.35430 −0.0453963
\(891\) −27.7767 + 10.9295i −0.930555 + 0.366152i
\(892\) 18.2025 0.609465
\(893\) 3.57399 10.9996i 0.119599 0.368088i
\(894\) −1.09643 1.08421i −0.0366701 0.0362612i
\(895\) −0.385206 0.279869i −0.0128760 0.00935498i
\(896\) −0.951057 + 0.309017i −0.0317726 + 0.0103235i
\(897\) −1.84500 + 0.953137i −0.0616026 + 0.0318243i
\(898\) −15.1453 + 20.8457i −0.505406 + 0.695631i
\(899\) −19.2315 + 13.9725i −0.641407 + 0.466009i
\(900\) 0.114301 + 10.1945i 0.00381004 + 0.339817i
\(901\) 7.13051i 0.237552i
\(902\) −20.0055 25.4281i −0.666109 0.846664i
\(903\) 1.23098 + 7.49978i 0.0409646 + 0.249577i
\(904\) −17.4531 5.67084i −0.580480 0.188609i
\(905\) −12.8625 17.7037i −0.427563 0.588490i
\(906\) 22.5589 + 11.3355i 0.749468 + 0.376596i
\(907\) 11.5188 + 35.4512i 0.382475 + 1.17714i 0.938295 + 0.345835i \(0.112404\pi\)
−0.555820 + 0.831302i \(0.687596\pi\)
\(908\) −6.08367 18.7236i −0.201894 0.621365i
\(909\) −4.36981 1.36587i −0.144937 0.0453030i
\(910\) 0.111633 + 0.153650i 0.00370060 + 0.00509344i
\(911\) −8.56241 2.78210i −0.283685 0.0921749i 0.163718 0.986507i \(-0.447651\pi\)
−0.447404 + 0.894332i \(0.647651\pi\)
\(912\) −7.07294 + 1.16092i −0.234208 + 0.0384420i
\(913\) −20.0120 25.4364i −0.662300 0.841822i
\(914\) 23.7456i 0.785435i
\(915\) −5.49067 0.838113i −0.181516 0.0277072i
\(916\) −7.92599 + 5.75857i −0.261882 + 0.190269i
\(917\) −1.84001 + 2.53255i −0.0607623 + 0.0836322i
\(918\) 4.43417 4.58588i 0.146350 0.151357i
\(919\) 19.1502 6.22228i 0.631707 0.205254i 0.0243760 0.999703i \(-0.492240\pi\)
0.607331 + 0.794449i \(0.292240\pi\)
\(920\) 8.17987 + 5.94302i 0.269682 + 0.195936i
\(921\) 31.1621 31.5135i 1.02683 1.03840i
\(922\) 0.860804 2.64928i 0.0283491 0.0872495i
\(923\) 0.942785 0.0310322
\(924\) −5.70781 0.648815i −0.187773 0.0213444i
\(925\) 25.3946 0.834971
\(926\) −0.926661 + 2.85197i −0.0304520 + 0.0937216i
\(927\) −6.99432 + 9.85740i −0.229724 + 0.323759i
\(928\) 4.28495 + 3.11320i 0.140660 + 0.102196i
\(929\) −36.4151 + 11.8320i −1.19474 + 0.388195i −0.837823 0.545942i \(-0.816172\pi\)
−0.356917 + 0.934136i \(0.616172\pi\)
\(930\) 4.51544 + 8.74058i 0.148067 + 0.286615i
\(931\) 2.43237 3.34788i 0.0797179 0.109722i
\(932\) −24.3943 + 17.7235i −0.799063 + 0.580553i
\(933\) −1.33425 + 8.74095i −0.0436813 + 0.286166i
\(934\) 5.42478i 0.177504i
\(935\) −4.28165 2.86699i −0.140025 0.0937606i
\(936\) 0.143914 + 0.426589i 0.00470399 + 0.0139435i
\(937\) 47.7321 + 15.5091i 1.55934 + 0.506660i 0.956631 0.291302i \(-0.0940886\pi\)
0.602708 + 0.797962i \(0.294089\pi\)
\(938\) 7.14124 + 9.82907i 0.233170 + 0.320930i
\(939\) −12.5611 + 24.9980i −0.409917 + 0.815780i
\(940\) 1.09300 + 3.36392i 0.0356499 + 0.109719i
\(941\) −6.03396 18.5706i −0.196702 0.605385i −0.999953 0.00974438i \(-0.996898\pi\)
0.803251 0.595641i \(-0.203102\pi\)
\(942\) 16.7652 33.3646i 0.546239 1.08708i
\(943\) −45.8104 63.0527i −1.49179 2.05328i
\(944\) −13.9861 4.54436i −0.455209 0.147906i
\(945\) 3.08355 + 5.80822i 0.100308 + 0.188942i
\(946\) 14.5425 0.557077i 0.472817 0.0181121i
\(947\) 0.232395i 0.00755181i 0.999993 + 0.00377591i \(0.00120191\pi\)
−0.999993 + 0.00377591i \(0.998798\pi\)
\(948\) −2.84559 + 18.6421i −0.0924205 + 0.605468i
\(949\) −1.30624 + 0.949041i −0.0424024 + 0.0308072i
\(950\) −8.26613 + 11.3774i −0.268189 + 0.369130i
\(951\) −13.3849 25.9093i −0.434035 0.840166i
\(952\) 1.16756 0.379364i 0.0378409 0.0122953i
\(953\) 7.79107 + 5.66054i 0.252377 + 0.183363i 0.706780 0.707434i \(-0.250147\pi\)
−0.454402 + 0.890797i \(0.650147\pi\)
\(954\) −14.2109 10.0834i −0.460095 0.326461i
\(955\) 4.50859 13.8760i 0.145895 0.449017i
\(956\) 2.96985 0.0960519
\(957\) 14.9894 + 26.4775i 0.484538 + 0.855898i
\(958\) 26.9841 0.871818
\(959\) 0.263396 0.810649i 0.00850549 0.0261772i
\(960\) 1.54126 1.55864i 0.0497441 0.0503050i
\(961\) 8.78307 + 6.38127i 0.283325 + 0.205847i
\(962\) 1.06652 0.346535i 0.0343861 0.0111727i
\(963\) −5.92677 7.96808i −0.190987 0.256768i
\(964\) 2.47583 3.40768i 0.0797410 0.109754i
\(965\) −11.1345 + 8.08967i −0.358431 + 0.260416i
\(966\) −13.6794 2.08807i −0.440128 0.0671825i
\(967\) 32.6778i 1.05085i −0.850840 0.525424i \(-0.823907\pi\)
0.850840 0.525424i \(-0.176093\pi\)
\(968\) −2.58890 + 10.6910i −0.0832103 + 0.343622i
\(969\) 8.68308 1.42521i 0.278941 0.0457842i
\(970\) 11.9283 + 3.87574i 0.382995 + 0.124443i
\(971\) −9.50365 13.0807i −0.304987 0.419778i 0.628823 0.777549i \(-0.283537\pi\)
−0.933810 + 0.357770i \(0.883537\pi\)
\(972\) 2.86911 + 15.3221i 0.0920266 + 0.491458i
\(973\) 2.36354 + 7.27423i 0.0757716 + 0.233201i
\(974\) −5.42253 16.6888i −0.173749 0.534745i
\(975\) 0.789295 + 0.396608i 0.0252777 + 0.0127016i
\(976\) −1.48938 2.04995i −0.0476739 0.0656174i
\(977\) −3.72468 1.21022i −0.119163 0.0387184i 0.248828 0.968548i \(-0.419954\pi\)
−0.367992 + 0.929829i \(0.619954\pi\)
\(978\) 2.65851 + 16.1970i 0.0850098 + 0.517923i
\(979\) −1.22517 3.33104i −0.0391567 0.106461i
\(980\) 1.26555i 0.0404266i
\(981\) −5.87803 + 0.0659047i −0.187671 + 0.00210418i
\(982\) −27.3069 + 19.8396i −0.871399 + 0.633109i
\(983\) −7.15144 + 9.84312i −0.228096 + 0.313947i −0.907690 0.419641i \(-0.862156\pi\)
0.679594 + 0.733588i \(0.262156\pi\)
\(984\) −15.0117 + 7.75514i −0.478555 + 0.247225i
\(985\) 11.7221 3.80873i 0.373496 0.121356i
\(986\) −5.26041 3.82191i −0.167526 0.121714i
\(987\) −3.44212 3.40374i −0.109564 0.108342i
\(988\) −0.191906 + 0.590626i −0.00610534 + 0.0187903i
\(989\) 35.0565 1.11473
\(990\) 11.7686 4.47896i 0.374030 0.142351i
\(991\) −52.0302 −1.65279 −0.826396 0.563089i \(-0.809613\pi\)
−0.826396 + 0.563089i \(0.809613\pi\)
\(992\) −1.38692 + 4.26849i −0.0440346 + 0.135525i
\(993\) −6.19697 6.12788i −0.196655 0.194462i
\(994\) 5.08249 + 3.69264i 0.161207 + 0.117124i
\(995\) 23.0350 7.48452i 0.730258 0.237275i
\(996\) −15.0166 + 7.75767i −0.475818 + 0.245811i
\(997\) −21.6875 + 29.8502i −0.686849 + 0.945366i −0.999991 0.00433997i \(-0.998619\pi\)
0.313142 + 0.949706i \(0.398619\pi\)
\(998\) 6.19831 4.50333i 0.196204 0.142551i
\(999\) 38.2430 6.71820i 1.20996 0.212555i
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 462.2.w.a.365.10 yes 48
3.2 odd 2 462.2.w.b.365.6 yes 48
11.6 odd 10 462.2.w.b.281.6 yes 48
33.17 even 10 inner 462.2.w.a.281.10 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.w.a.281.10 48 33.17 even 10 inner
462.2.w.a.365.10 yes 48 1.1 even 1 trivial
462.2.w.b.281.6 yes 48 11.6 odd 10
462.2.w.b.365.6 yes 48 3.2 odd 2