Properties

Label 930.2.s.c.439.3
Level $930$
Weight $2$
Character 930.439
Analytic conductor $7.426$
Analytic rank $0$
Dimension $24$
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] = [930,2,Mod(439,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.439");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.s (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 439.3
Character \(\chi\) \(=\) 930.439
Dual form 930.2.s.c.769.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.291362 - 2.21700i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(3.11266 + 1.79709i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.291362 - 2.21700i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(3.11266 + 1.79709i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.21700 + 0.291362i) q^{10} +(2.97645 + 5.15537i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-4.69019 + 2.70788i) q^{13} +(1.79709 - 3.11266i) q^{14} +(-0.856175 + 2.06566i) q^{15} +1.00000 q^{16} +(-4.44932 - 2.56882i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.31842 + 4.01562i) q^{19} +(0.291362 + 2.21700i) q^{20} +(-1.79709 - 3.11266i) q^{21} +(5.15537 - 2.97645i) q^{22} +9.06476i q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.83022 + 1.29190i) q^{25} +(2.70788 + 4.69019i) q^{26} -1.00000i q^{27} +(-3.11266 - 1.79709i) q^{28} +5.52189 q^{29} +(2.06566 + 0.856175i) q^{30} +(-1.89486 + 5.23541i) q^{31} -1.00000i q^{32} -5.95290i q^{33} +(-2.56882 + 4.44932i) q^{34} +(3.07725 - 7.42438i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-7.15835 - 4.13288i) q^{37} +(4.01562 + 2.31842i) q^{38} +5.41576 q^{39} +(2.21700 - 0.291362i) q^{40} +(4.35396 + 7.54127i) q^{41} +(-3.11266 + 1.79709i) q^{42} +(1.99052 + 1.14923i) q^{43} +(-2.97645 - 5.15537i) q^{44} +(1.77430 - 1.36083i) q^{45} +9.06476 q^{46} -5.05582i q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.95909 + 5.12530i) q^{49} +(1.29190 + 4.83022i) q^{50} +(2.56882 + 4.44932i) q^{51} +(4.69019 - 2.70788i) q^{52} +(4.26701 - 2.46356i) q^{53} -1.00000 q^{54} +(10.5622 - 8.10088i) q^{55} +(-1.79709 + 3.11266i) q^{56} +(4.01562 - 2.31842i) q^{57} -5.52189i q^{58} +(6.67355 - 11.5589i) q^{59} +(0.856175 - 2.06566i) q^{60} +1.14657 q^{61} +(5.23541 + 1.89486i) q^{62} +3.59419i q^{63} -1.00000 q^{64} +(7.36993 + 9.60920i) q^{65} -5.95290 q^{66} +(-4.83998 + 2.79437i) q^{67} +(4.44932 + 2.56882i) q^{68} +(4.53238 - 7.85031i) q^{69} +(-7.42438 - 3.07725i) q^{70} +(-2.38791 - 4.13598i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(1.61832 - 0.934337i) q^{73} +(-4.13288 + 7.15835i) q^{74} +(4.82904 + 1.29629i) q^{75} +(2.31842 - 4.01562i) q^{76} +21.3959i q^{77} -5.41576i q^{78} +(-2.00321 + 3.46966i) q^{79} +(-0.291362 - 2.21700i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.54127 - 4.35396i) q^{82} +(-8.58415 + 4.95606i) q^{83} +(1.79709 + 3.11266i) q^{84} +(-4.39872 + 10.6126i) q^{85} +(1.14923 - 1.99052i) q^{86} +(-4.78210 - 2.76095i) q^{87} +(-5.15537 + 2.97645i) q^{88} +11.6216 q^{89} +(-1.36083 - 1.77430i) q^{90} -19.4653 q^{91} -9.06476i q^{92} +(4.25870 - 3.58656i) q^{93} -5.05582 q^{94} +(9.57816 + 3.96995i) q^{95} +(-0.500000 + 0.866025i) q^{96} -6.45060i q^{97} +(5.12530 - 2.95909i) q^{98} +(-2.97645 + 5.15537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) −1.00000 −0.500000
\(5\) −0.291362 2.21700i −0.130301 0.991474i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 3.11266 + 1.79709i 1.17647 + 0.679238i 0.955196 0.295973i \(-0.0956439\pi\)
0.221278 + 0.975211i \(0.428977\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −2.21700 + 0.291362i −0.701078 + 0.0921368i
\(11\) 2.97645 + 5.15537i 0.897434 + 1.55440i 0.830763 + 0.556626i \(0.187904\pi\)
0.0666710 + 0.997775i \(0.478762\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) −4.69019 + 2.70788i −1.30082 + 0.751031i −0.980546 0.196292i \(-0.937110\pi\)
−0.320279 + 0.947323i \(0.603777\pi\)
\(14\) 1.79709 3.11266i 0.480293 0.831893i
\(15\) −0.856175 + 2.06566i −0.221063 + 0.533352i
\(16\) 1.00000 0.250000
\(17\) −4.44932 2.56882i −1.07912 0.623030i −0.148461 0.988918i \(-0.547432\pi\)
−0.930659 + 0.365888i \(0.880765\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −2.31842 + 4.01562i −0.531882 + 0.921247i 0.467425 + 0.884033i \(0.345182\pi\)
−0.999307 + 0.0372146i \(0.988151\pi\)
\(20\) 0.291362 + 2.21700i 0.0651505 + 0.495737i
\(21\) −1.79709 3.11266i −0.392158 0.679238i
\(22\) 5.15537 2.97645i 1.09913 0.634582i
\(23\) 9.06476i 1.89013i 0.326879 + 0.945066i \(0.394003\pi\)
−0.326879 + 0.945066i \(0.605997\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −4.83022 + 1.29190i −0.966043 + 0.258380i
\(26\) 2.70788 + 4.69019i 0.531059 + 0.919822i
\(27\) 1.00000i 0.192450i
\(28\) −3.11266 1.79709i −0.588237 0.339619i
\(29\) 5.52189 1.02539 0.512695 0.858571i \(-0.328647\pi\)
0.512695 + 0.858571i \(0.328647\pi\)
\(30\) 2.06566 + 0.856175i 0.377137 + 0.156315i
\(31\) −1.89486 + 5.23541i −0.340328 + 0.940307i
\(32\) 1.00000i 0.176777i
\(33\) 5.95290i 1.03627i
\(34\) −2.56882 + 4.44932i −0.440549 + 0.763053i
\(35\) 3.07725 7.42438i 0.520151 1.25495i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −7.15835 4.13288i −1.17683 0.679441i −0.221548 0.975150i \(-0.571111\pi\)
−0.955278 + 0.295709i \(0.904444\pi\)
\(38\) 4.01562 + 2.31842i 0.651420 + 0.376098i
\(39\) 5.41576 0.867216
\(40\) 2.21700 0.291362i 0.350539 0.0460684i
\(41\) 4.35396 + 7.54127i 0.679974 + 1.17775i 0.974988 + 0.222256i \(0.0713421\pi\)
−0.295015 + 0.955493i \(0.595325\pi\)
\(42\) −3.11266 + 1.79709i −0.480293 + 0.277298i
\(43\) 1.99052 + 1.14923i 0.303552 + 0.175256i 0.644037 0.764994i \(-0.277258\pi\)
−0.340486 + 0.940250i \(0.610591\pi\)
\(44\) −2.97645 5.15537i −0.448717 0.777201i
\(45\) 1.77430 1.36083i 0.264497 0.202860i
\(46\) 9.06476 1.33653
\(47\) 5.05582i 0.737467i −0.929535 0.368734i \(-0.879791\pi\)
0.929535 0.368734i \(-0.120209\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) 2.95909 + 5.12530i 0.422727 + 0.732185i
\(50\) 1.29190 + 4.83022i 0.182703 + 0.683096i
\(51\) 2.56882 + 4.44932i 0.359707 + 0.623030i
\(52\) 4.69019 2.70788i 0.650412 0.375516i
\(53\) 4.26701 2.46356i 0.586119 0.338396i −0.177443 0.984131i \(-0.556782\pi\)
0.763561 + 0.645735i \(0.223449\pi\)
\(54\) −1.00000 −0.136083
\(55\) 10.5622 8.10088i 1.42421 1.09232i
\(56\) −1.79709 + 3.11266i −0.240147 + 0.415946i
\(57\) 4.01562 2.31842i 0.531882 0.307082i
\(58\) 5.52189i 0.725060i
\(59\) 6.67355 11.5589i 0.868823 1.50485i 0.00562217 0.999984i \(-0.498210\pi\)
0.863201 0.504861i \(-0.168456\pi\)
\(60\) 0.856175 2.06566i 0.110532 0.266676i
\(61\) 1.14657 0.146804 0.0734019 0.997302i \(-0.476614\pi\)
0.0734019 + 0.997302i \(0.476614\pi\)
\(62\) 5.23541 + 1.89486i 0.664897 + 0.240648i
\(63\) 3.59419i 0.452825i
\(64\) −1.00000 −0.125000
\(65\) 7.36993 + 9.60920i 0.914127 + 1.19187i
\(66\) −5.95290 −0.732752
\(67\) −4.83998 + 2.79437i −0.591298 + 0.341386i −0.765611 0.643304i \(-0.777563\pi\)
0.174313 + 0.984690i \(0.444230\pi\)
\(68\) 4.44932 + 2.56882i 0.539560 + 0.311515i
\(69\) 4.53238 7.85031i 0.545634 0.945066i
\(70\) −7.42438 3.07725i −0.887383 0.367802i
\(71\) −2.38791 4.13598i −0.283393 0.490851i 0.688825 0.724927i \(-0.258127\pi\)
−0.972218 + 0.234077i \(0.924793\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 1.61832 0.934337i 0.189410 0.109356i −0.402296 0.915509i \(-0.631788\pi\)
0.591706 + 0.806154i \(0.298455\pi\)
\(74\) −4.13288 + 7.15835i −0.480437 + 0.832142i
\(75\) 4.82904 + 1.29629i 0.557610 + 0.149682i
\(76\) 2.31842 4.01562i 0.265941 0.460624i
\(77\) 21.3959i 2.43828i
\(78\) 5.41576i 0.613215i
\(79\) −2.00321 + 3.46966i −0.225379 + 0.390368i −0.956433 0.291952i \(-0.905695\pi\)
0.731054 + 0.682319i \(0.239029\pi\)
\(80\) −0.291362 2.21700i −0.0325753 0.247869i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 7.54127 4.35396i 0.832794 0.480814i
\(83\) −8.58415 + 4.95606i −0.942233 + 0.543998i −0.890659 0.454671i \(-0.849757\pi\)
−0.0515731 + 0.998669i \(0.516424\pi\)
\(84\) 1.79709 + 3.11266i 0.196079 + 0.339619i
\(85\) −4.39872 + 10.6126i −0.477108 + 1.15110i
\(86\) 1.14923 1.99052i 0.123925 0.214644i
\(87\) −4.78210 2.76095i −0.512695 0.296004i
\(88\) −5.15537 + 2.97645i −0.549564 + 0.317291i
\(89\) 11.6216 1.23189 0.615943 0.787790i \(-0.288775\pi\)
0.615943 + 0.787790i \(0.288775\pi\)
\(90\) −1.36083 1.77430i −0.143444 0.187028i
\(91\) −19.4653 −2.04051
\(92\) 9.06476i 0.945066i
\(93\) 4.25870 3.58656i 0.441607 0.371909i
\(94\) −5.05582 −0.521468
\(95\) 9.57816 + 3.96995i 0.982698 + 0.407308i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 6.45060i 0.654959i −0.944858 0.327479i \(-0.893801\pi\)
0.944858 0.327479i \(-0.106199\pi\)
\(98\) 5.12530 2.95909i 0.517733 0.298913i
\(99\) −2.97645 + 5.15537i −0.299145 + 0.518134i
\(100\) 4.83022 1.29190i 0.483022 0.129190i
\(101\) −9.76731 −0.971884 −0.485942 0.873991i \(-0.661523\pi\)
−0.485942 + 0.873991i \(0.661523\pi\)
\(102\) 4.44932 2.56882i 0.440549 0.254351i
\(103\) 1.45146 0.838003i 0.143017 0.0825709i −0.426784 0.904354i \(-0.640354\pi\)
0.569801 + 0.821783i \(0.307020\pi\)
\(104\) −2.70788 4.69019i −0.265530 0.459911i
\(105\) −6.37717 + 4.89107i −0.622348 + 0.477320i
\(106\) −2.46356 4.26701i −0.239282 0.414449i
\(107\) 2.12044 + 1.22423i 0.204990 + 0.118351i 0.598981 0.800763i \(-0.295572\pi\)
−0.393991 + 0.919114i \(0.628906\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 1.67713 0.160640 0.0803201 0.996769i \(-0.474406\pi\)
0.0803201 + 0.996769i \(0.474406\pi\)
\(110\) −8.10088 10.5622i −0.772389 1.00707i
\(111\) 4.13288 + 7.15835i 0.392275 + 0.679441i
\(112\) 3.11266 + 1.79709i 0.294118 + 0.169809i
\(113\) −3.36747 + 1.94421i −0.316785 + 0.182896i −0.649959 0.759970i \(-0.725214\pi\)
0.333174 + 0.942865i \(0.391880\pi\)
\(114\) −2.31842 4.01562i −0.217140 0.376098i
\(115\) 20.0966 2.64113i 1.87402 0.246286i
\(116\) −5.52189 −0.512695
\(117\) −4.69019 2.70788i −0.433608 0.250344i
\(118\) −11.5589 6.67355i −1.06409 0.614350i
\(119\) −9.23282 15.9917i −0.846371 1.46596i
\(120\) −2.06566 0.856175i −0.188568 0.0781577i
\(121\) −12.2185 + 21.1631i −1.11078 + 1.92392i
\(122\) 1.14657i 0.103806i
\(123\) 8.70791i 0.785166i
\(124\) 1.89486 5.23541i 0.170164 0.470153i
\(125\) 4.27149 + 10.3322i 0.382054 + 0.924140i
\(126\) 3.59419 0.320196
\(127\) 11.9460 + 6.89703i 1.06004 + 0.612013i 0.925443 0.378888i \(-0.123693\pi\)
0.134595 + 0.990901i \(0.457027\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −1.14923 1.99052i −0.101184 0.175256i
\(130\) 9.60920 7.36993i 0.842782 0.646386i
\(131\) 10.1483 17.5774i 0.886663 1.53575i 0.0428672 0.999081i \(-0.486351\pi\)
0.843796 0.536664i \(-0.180316\pi\)
\(132\) 5.95290i 0.518134i
\(133\) −14.4329 + 8.33284i −1.25149 + 0.722549i
\(134\) 2.79437 + 4.83998i 0.241396 + 0.418111i
\(135\) −2.21700 + 0.291362i −0.190809 + 0.0250765i
\(136\) 2.56882 4.44932i 0.220274 0.381526i
\(137\) −10.9454 + 6.31936i −0.935133 + 0.539899i −0.888431 0.459010i \(-0.848204\pi\)
−0.0467015 + 0.998909i \(0.514871\pi\)
\(138\) −7.85031 4.53238i −0.668263 0.385822i
\(139\) −6.62791 −0.562172 −0.281086 0.959683i \(-0.590695\pi\)
−0.281086 + 0.959683i \(0.590695\pi\)
\(140\) −3.07725 + 7.42438i −0.260075 + 0.627475i
\(141\) −2.52791 + 4.37847i −0.212888 + 0.368734i
\(142\) −4.13598 + 2.38791i −0.347084 + 0.200389i
\(143\) −27.9202 16.1198i −2.33481 1.34800i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −1.60887 12.2421i −0.133609 1.01665i
\(146\) −0.934337 1.61832i −0.0773263 0.133933i
\(147\) 5.91818i 0.488123i
\(148\) 7.15835 + 4.13288i 0.588413 + 0.339720i
\(149\) 0.371288 0.643090i 0.0304171 0.0526840i −0.850416 0.526111i \(-0.823650\pi\)
0.880833 + 0.473427i \(0.156983\pi\)
\(150\) 1.29629 4.82904i 0.105841 0.394290i
\(151\) −4.11608 −0.334962 −0.167481 0.985875i \(-0.553563\pi\)
−0.167481 + 0.985875i \(0.553563\pi\)
\(152\) −4.01562 2.31842i −0.325710 0.188049i
\(153\) 5.13764i 0.415353i
\(154\) 21.3959 1.72413
\(155\) 12.1590 + 2.67552i 0.976635 + 0.214903i
\(156\) −5.41576 −0.433608
\(157\) 7.83784i 0.625528i −0.949831 0.312764i \(-0.898745\pi\)
0.949831 0.312764i \(-0.101255\pi\)
\(158\) 3.46966 + 2.00321i 0.276032 + 0.159367i
\(159\) −4.92712 −0.390746
\(160\) −2.21700 + 0.291362i −0.175270 + 0.0230342i
\(161\) −16.2902 + 28.2155i −1.28385 + 2.22369i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 10.7682i 0.843428i −0.906729 0.421714i \(-0.861429\pi\)
0.906729 0.421714i \(-0.138571\pi\)
\(164\) −4.35396 7.54127i −0.339987 0.588874i
\(165\) −13.1976 + 1.73445i −1.02743 + 0.135027i
\(166\) 4.95606 + 8.58415i 0.384665 + 0.666259i
\(167\) 10.0883 + 5.82450i 0.780658 + 0.450713i 0.836663 0.547717i \(-0.184503\pi\)
−0.0560056 + 0.998430i \(0.517836\pi\)
\(168\) 3.11266 1.79709i 0.240147 0.138649i
\(169\) 8.16525 14.1426i 0.628096 1.08790i
\(170\) 10.6126 + 4.39872i 0.813951 + 0.337366i
\(171\) −4.63684 −0.354588
\(172\) −1.99052 1.14923i −0.151776 0.0876279i
\(173\) 9.86029 5.69284i 0.749664 0.432819i −0.0759084 0.997115i \(-0.524186\pi\)
0.825573 + 0.564296i \(0.190852\pi\)
\(174\) −2.76095 + 4.78210i −0.209307 + 0.362530i
\(175\) −17.3565 4.65910i −1.31203 0.352195i
\(176\) 2.97645 + 5.15537i 0.224359 + 0.388600i
\(177\) −11.5589 + 6.67355i −0.868823 + 0.501615i
\(178\) 11.6216i 0.871075i
\(179\) −3.83263 + 6.63830i −0.286464 + 0.496170i −0.972963 0.230960i \(-0.925813\pi\)
0.686499 + 0.727131i \(0.259147\pi\)
\(180\) −1.77430 + 1.36083i −0.132249 + 0.101430i
\(181\) −2.30528 3.99286i −0.171350 0.296787i 0.767542 0.640999i \(-0.221480\pi\)
−0.938892 + 0.344212i \(0.888146\pi\)
\(182\) 19.4653i 1.44286i
\(183\) −0.992962 0.573287i −0.0734019 0.0423786i
\(184\) −9.06476 −0.668263
\(185\) −7.07693 + 17.0743i −0.520306 + 1.25532i
\(186\) −3.58656 4.25870i −0.262980 0.312263i
\(187\) 30.5839i 2.23651i
\(188\) 5.05582i 0.368734i
\(189\) 1.79709 3.11266i 0.130719 0.226413i
\(190\) 3.96995 9.57816i 0.288010 0.694873i
\(191\) 7.63804 + 13.2295i 0.552669 + 0.957251i 0.998081 + 0.0619254i \(0.0197241\pi\)
−0.445411 + 0.895326i \(0.646943\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 3.56077 + 2.05581i 0.256310 + 0.147981i 0.622650 0.782500i \(-0.286056\pi\)
−0.366340 + 0.930481i \(0.619389\pi\)
\(194\) −6.45060 −0.463126
\(195\) −1.57795 12.0068i −0.112999 0.859823i
\(196\) −2.95909 5.12530i −0.211364 0.366093i
\(197\) 10.0616 5.80908i 0.716861 0.413880i −0.0967354 0.995310i \(-0.530840\pi\)
0.813596 + 0.581430i \(0.197507\pi\)
\(198\) 5.15537 + 2.97645i 0.366376 + 0.211527i
\(199\) −2.53294 4.38718i −0.179555 0.310999i 0.762173 0.647373i \(-0.224132\pi\)
−0.941728 + 0.336375i \(0.890799\pi\)
\(200\) −1.29190 4.83022i −0.0913513 0.341548i
\(201\) 5.58873 0.394199
\(202\) 9.76731i 0.687226i
\(203\) 17.1878 + 9.92336i 1.20634 + 0.696483i
\(204\) −2.56882 4.44932i −0.179853 0.311515i
\(205\) 15.4505 11.8500i 1.07911 0.827638i
\(206\) −0.838003 1.45146i −0.0583864 0.101128i
\(207\) −7.85031 + 4.53238i −0.545634 + 0.315022i
\(208\) −4.69019 + 2.70788i −0.325206 + 0.187758i
\(209\) −27.6027 −1.90932
\(210\) 4.89107 + 6.37717i 0.337516 + 0.440067i
\(211\) −3.91582 + 6.78240i −0.269576 + 0.466920i −0.968752 0.248030i \(-0.920217\pi\)
0.699176 + 0.714949i \(0.253550\pi\)
\(212\) −4.26701 + 2.46356i −0.293059 + 0.169198i
\(213\) 4.77582i 0.327234i
\(214\) 1.22423 2.12044i 0.0836870 0.144950i
\(215\) 1.96788 4.74784i 0.134208 0.323800i
\(216\) 1.00000 0.0680414
\(217\) −15.3066 + 12.8908i −1.03908 + 0.875083i
\(218\) 1.67713i 0.113590i
\(219\) −1.86867 −0.126273
\(220\) −10.5622 + 8.10088i −0.712106 + 0.546162i
\(221\) 27.8242 1.87166
\(222\) 7.15835 4.13288i 0.480437 0.277381i
\(223\) 11.0560 + 6.38320i 0.740366 + 0.427451i 0.822203 0.569195i \(-0.192745\pi\)
−0.0818361 + 0.996646i \(0.526078\pi\)
\(224\) 1.79709 3.11266i 0.120073 0.207973i
\(225\) −3.53393 3.53714i −0.235595 0.235809i
\(226\) 1.94421 + 3.36747i 0.129327 + 0.224001i
\(227\) −2.87642 + 1.66070i −0.190915 + 0.110225i −0.592411 0.805636i \(-0.701824\pi\)
0.401496 + 0.915861i \(0.368490\pi\)
\(228\) −4.01562 + 2.31842i −0.265941 + 0.153541i
\(229\) −2.61956 + 4.53720i −0.173105 + 0.299827i −0.939504 0.342538i \(-0.888713\pi\)
0.766399 + 0.642365i \(0.222047\pi\)
\(230\) −2.64113 20.0966i −0.174151 1.32513i
\(231\) 10.6979 18.5294i 0.703872 1.21914i
\(232\) 5.52189i 0.362530i
\(233\) 14.5392i 0.952492i −0.879312 0.476246i \(-0.841997\pi\)
0.879312 0.476246i \(-0.158003\pi\)
\(234\) −2.70788 + 4.69019i −0.177020 + 0.306607i
\(235\) −11.2088 + 1.47307i −0.731180 + 0.0960928i
\(236\) −6.67355 + 11.5589i −0.434411 + 0.752423i
\(237\) 3.46966 2.00321i 0.225379 0.130123i
\(238\) −15.9917 + 9.23282i −1.03659 + 0.598475i
\(239\) 11.1198 + 19.2600i 0.719278 + 1.24583i 0.961286 + 0.275551i \(0.0888604\pi\)
−0.242009 + 0.970274i \(0.577806\pi\)
\(240\) −0.856175 + 2.06566i −0.0552659 + 0.133338i
\(241\) −1.12616 + 1.95057i −0.0725424 + 0.125647i −0.900015 0.435859i \(-0.856445\pi\)
0.827473 + 0.561506i \(0.189778\pi\)
\(242\) 21.1631 + 12.2185i 1.36042 + 0.785437i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −1.14657 −0.0734019
\(245\) 10.5006 8.05363i 0.670861 0.514528i
\(246\) −8.70791 −0.555196
\(247\) 25.1121i 1.59784i
\(248\) −5.23541 1.89486i −0.332449 0.120324i
\(249\) 9.91212 0.628155
\(250\) 10.3322 4.27149i 0.653466 0.270153i
\(251\) 7.60189 13.1669i 0.479827 0.831085i −0.519905 0.854224i \(-0.674033\pi\)
0.999732 + 0.0231388i \(0.00736598\pi\)
\(252\) 3.59419i 0.226413i
\(253\) −46.7321 + 26.9808i −2.93802 + 1.69627i
\(254\) 6.89703 11.9460i 0.432758 0.749559i
\(255\) 9.11572 6.99145i 0.570848 0.437821i
\(256\) 1.00000 0.0625000
\(257\) −2.77882 + 1.60435i −0.173338 + 0.100077i −0.584159 0.811639i \(-0.698576\pi\)
0.410821 + 0.911716i \(0.365242\pi\)
\(258\) −1.99052 + 1.14923i −0.123925 + 0.0715479i
\(259\) −14.8543 25.7285i −0.923003 1.59869i
\(260\) −7.36993 9.60920i −0.457064 0.595937i
\(261\) 2.76095 + 4.78210i 0.170898 + 0.296004i
\(262\) −17.5774 10.1483i −1.08594 0.626965i
\(263\) 21.1070i 1.30151i 0.759286 + 0.650757i \(0.225549\pi\)
−0.759286 + 0.650757i \(0.774451\pi\)
\(264\) 5.95290 0.366376
\(265\) −6.70496 8.74219i −0.411883 0.537028i
\(266\) 8.33284 + 14.4329i 0.510919 + 0.884938i
\(267\) −10.0646 5.81080i −0.615943 0.355615i
\(268\) 4.83998 2.79437i 0.295649 0.170693i
\(269\) 8.35872 + 14.4777i 0.509640 + 0.882722i 0.999938 + 0.0111673i \(0.00355472\pi\)
−0.490298 + 0.871555i \(0.663112\pi\)
\(270\) 0.291362 + 2.21700i 0.0177317 + 0.134923i
\(271\) −8.95467 −0.543958 −0.271979 0.962303i \(-0.587678\pi\)
−0.271979 + 0.962303i \(0.587678\pi\)
\(272\) −4.44932 2.56882i −0.269780 0.155758i
\(273\) 16.8574 + 9.73264i 1.02026 + 0.589046i
\(274\) 6.31936 + 10.9454i 0.381766 + 0.661239i
\(275\) −21.0371 21.0562i −1.26859 1.26974i
\(276\) −4.53238 + 7.85031i −0.272817 + 0.472533i
\(277\) 0.851610i 0.0511683i −0.999673 0.0255842i \(-0.991855\pi\)
0.999673 0.0255842i \(-0.00814458\pi\)
\(278\) 6.62791i 0.397515i
\(279\) −5.48143 + 0.976703i −0.328165 + 0.0584737i
\(280\) 7.42438 + 3.07725i 0.443692 + 0.183901i
\(281\) 3.72310 0.222102 0.111051 0.993815i \(-0.464578\pi\)
0.111051 + 0.993815i \(0.464578\pi\)
\(282\) 4.37847 + 2.52791i 0.260734 + 0.150535i
\(283\) 21.3862i 1.27128i 0.771988 + 0.635638i \(0.219263\pi\)
−0.771988 + 0.635638i \(0.780737\pi\)
\(284\) 2.38791 + 4.13598i 0.141696 + 0.245425i
\(285\) −6.30995 8.22716i −0.373769 0.487335i
\(286\) −16.1198 + 27.9202i −0.953182 + 1.65096i
\(287\) 31.2979i 1.84745i
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) 4.69766 + 8.13659i 0.276333 + 0.478623i
\(290\) −12.2421 + 1.60887i −0.718878 + 0.0944761i
\(291\) −3.22530 + 5.58638i −0.189070 + 0.327479i
\(292\) −1.61832 + 0.934337i −0.0947050 + 0.0546779i
\(293\) −7.79125 4.49828i −0.455170 0.262792i 0.254841 0.966983i \(-0.417977\pi\)
−0.710011 + 0.704190i \(0.751310\pi\)
\(294\) −5.91818 −0.345155
\(295\) −27.5706 11.4275i −1.60522 0.665333i
\(296\) 4.13288 7.15835i 0.240219 0.416071i
\(297\) 5.15537 2.97645i 0.299145 0.172711i
\(298\) −0.643090 0.371288i −0.0372532 0.0215082i
\(299\) −24.5463 42.5154i −1.41955 2.45873i
\(300\) −4.82904 1.29629i −0.278805 0.0748412i
\(301\) 4.13054 + 7.15431i 0.238081 + 0.412368i
\(302\) 4.11608i 0.236854i
\(303\) 8.45874 + 4.88366i 0.485942 + 0.280559i
\(304\) −2.31842 + 4.01562i −0.132971 + 0.230312i
\(305\) −0.334068 2.54196i −0.0191287 0.145552i
\(306\) −5.13764 −0.293699
\(307\) 14.7208 + 8.49904i 0.840158 + 0.485066i 0.857318 0.514787i \(-0.172129\pi\)
−0.0171597 + 0.999853i \(0.505462\pi\)
\(308\) 21.3959i 1.21914i
\(309\) −1.67601 −0.0953446
\(310\) 2.67552 12.1590i 0.151960 0.690585i
\(311\) −17.4831 −0.991378 −0.495689 0.868500i \(-0.665084\pi\)
−0.495689 + 0.868500i \(0.665084\pi\)
\(312\) 5.41576i 0.306607i
\(313\) 28.9556 + 16.7175i 1.63667 + 0.944931i 0.981969 + 0.189041i \(0.0605381\pi\)
0.654699 + 0.755889i \(0.272795\pi\)
\(314\) −7.83784 −0.442315
\(315\) 7.96833 1.04721i 0.448964 0.0590036i
\(316\) 2.00321 3.46966i 0.112689 0.195184i
\(317\) 12.0309 + 6.94602i 0.675720 + 0.390127i 0.798241 0.602339i \(-0.205764\pi\)
−0.122520 + 0.992466i \(0.539098\pi\)
\(318\) 4.92712i 0.276299i
\(319\) 16.4356 + 28.4674i 0.920219 + 1.59387i
\(320\) 0.291362 + 2.21700i 0.0162876 + 0.123934i
\(321\) −1.22423 2.12044i −0.0683301 0.118351i
\(322\) 28.2155 + 16.2902i 1.57239 + 0.907818i
\(323\) 20.6308 11.9112i 1.14793 0.662758i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) 19.1563 19.1389i 1.06260 1.06164i
\(326\) −10.7682 −0.596394
\(327\) −1.45244 0.838566i −0.0803201 0.0463728i
\(328\) −7.54127 + 4.35396i −0.416397 + 0.240407i
\(329\) 9.08578 15.7370i 0.500915 0.867611i
\(330\) 1.73445 + 13.1976i 0.0954784 + 0.726505i
\(331\) −2.20296 3.81564i −0.121086 0.209726i 0.799110 0.601184i \(-0.205304\pi\)
−0.920196 + 0.391458i \(0.871971\pi\)
\(332\) 8.58415 4.95606i 0.471116 0.271999i
\(333\) 8.26575i 0.452960i
\(334\) 5.82450 10.0883i 0.318702 0.552008i
\(335\) 7.60531 + 9.91609i 0.415522 + 0.541774i
\(336\) −1.79709 3.11266i −0.0980395 0.169809i
\(337\) 8.34153i 0.454392i 0.973849 + 0.227196i \(0.0729558\pi\)
−0.973849 + 0.227196i \(0.927044\pi\)
\(338\) −14.1426 8.16525i −0.769258 0.444131i
\(339\) 3.88842 0.211190
\(340\) 4.39872 10.6126i 0.238554 0.575551i
\(341\) −32.6304 + 5.81422i −1.76704 + 0.314858i
\(342\) 4.63684i 0.250732i
\(343\) 3.88826i 0.209946i
\(344\) −1.14923 + 1.99052i −0.0619623 + 0.107322i
\(345\) −18.7247 7.76102i −1.00811 0.417839i
\(346\) −5.69284 9.86029i −0.306049 0.530093i
\(347\) −26.5275 15.3156i −1.42407 0.822186i −0.427425 0.904051i \(-0.640579\pi\)
−0.996643 + 0.0818642i \(0.973913\pi\)
\(348\) 4.78210 + 2.76095i 0.256347 + 0.148002i
\(349\) 15.2039 0.813846 0.406923 0.913462i \(-0.366602\pi\)
0.406923 + 0.913462i \(0.366602\pi\)
\(350\) −4.65910 + 17.3565i −0.249040 + 0.927743i
\(351\) 2.70788 + 4.69019i 0.144536 + 0.250344i
\(352\) 5.15537 2.97645i 0.274782 0.158645i
\(353\) −11.1325 6.42736i −0.592524 0.342094i 0.173571 0.984821i \(-0.444469\pi\)
−0.766095 + 0.642728i \(0.777803\pi\)
\(354\) 6.67355 + 11.5589i 0.354695 + 0.614350i
\(355\) −8.47374 + 6.49908i −0.449740 + 0.344935i
\(356\) −11.6216 −0.615943
\(357\) 18.4656i 0.977305i
\(358\) 6.63830 + 3.83263i 0.350845 + 0.202561i
\(359\) 8.85258 + 15.3331i 0.467222 + 0.809251i 0.999299 0.0374444i \(-0.0119217\pi\)
−0.532077 + 0.846696i \(0.678588\pi\)
\(360\) 1.36083 + 1.77430i 0.0717220 + 0.0935139i
\(361\) −1.25016 2.16534i −0.0657978 0.113965i
\(362\) −3.99286 + 2.30528i −0.209860 + 0.121163i
\(363\) 21.1631 12.2185i 1.11078 0.641307i
\(364\) 19.4653 1.02026
\(365\) −2.54295 3.31559i −0.133104 0.173546i
\(366\) −0.573287 + 0.992962i −0.0299662 + 0.0519030i
\(367\) −3.85157 + 2.22370i −0.201050 + 0.116076i −0.597145 0.802133i \(-0.703698\pi\)
0.396095 + 0.918210i \(0.370365\pi\)
\(368\) 9.06476i 0.472533i
\(369\) −4.35396 + 7.54127i −0.226658 + 0.392583i
\(370\) 17.0743 + 7.07693i 0.887649 + 0.367912i
\(371\) 17.7090 0.919405
\(372\) −4.25870 + 3.58656i −0.220804 + 0.185955i
\(373\) 17.9531i 0.929577i −0.885422 0.464788i \(-0.846130\pi\)
0.885422 0.464788i \(-0.153870\pi\)
\(374\) −30.5839 −1.58145
\(375\) 1.46688 11.0837i 0.0757492 0.572359i
\(376\) 5.05582 0.260734
\(377\) −25.8987 + 14.9526i −1.33385 + 0.770100i
\(378\) −3.11266 1.79709i −0.160098 0.0924325i
\(379\) −4.35115 + 7.53641i −0.223503 + 0.387119i −0.955869 0.293792i \(-0.905083\pi\)
0.732366 + 0.680911i \(0.238416\pi\)
\(380\) −9.57816 3.96995i −0.491349 0.203654i
\(381\) −6.89703 11.9460i −0.353346 0.612013i
\(382\) 13.2295 7.63804i 0.676879 0.390796i
\(383\) 24.1554 13.9461i 1.23428 0.712613i 0.266362 0.963873i \(-0.414178\pi\)
0.967919 + 0.251261i \(0.0808451\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 47.4347 6.23394i 2.41750 0.317711i
\(386\) 2.05581 3.56077i 0.104638 0.181238i
\(387\) 2.29846i 0.116837i
\(388\) 6.45060i 0.327479i
\(389\) 16.0896 27.8681i 0.815777 1.41297i −0.0929919 0.995667i \(-0.529643\pi\)
0.908769 0.417300i \(-0.137024\pi\)
\(390\) −12.0068 + 1.57795i −0.607987 + 0.0799025i
\(391\) 23.2857 40.3320i 1.17761 2.03968i
\(392\) −5.12530 + 2.95909i −0.258867 + 0.149457i
\(393\) −17.5774 + 10.1483i −0.886663 + 0.511915i
\(394\) −5.80908 10.0616i −0.292657 0.506897i
\(395\) 8.27592 + 3.43020i 0.416407 + 0.172592i
\(396\) 2.97645 5.15537i 0.149572 0.259067i
\(397\) 4.00201 + 2.31056i 0.200855 + 0.115964i 0.597054 0.802201i \(-0.296338\pi\)
−0.396199 + 0.918165i \(0.629671\pi\)
\(398\) −4.38718 + 2.53294i −0.219909 + 0.126965i
\(399\) 16.6657 0.834328
\(400\) −4.83022 + 1.29190i −0.241511 + 0.0645951i
\(401\) 2.12856 0.106295 0.0531477 0.998587i \(-0.483075\pi\)
0.0531477 + 0.998587i \(0.483075\pi\)
\(402\) 5.58873i 0.278741i
\(403\) −5.28959 29.6861i −0.263493 1.47877i
\(404\) 9.76731 0.485942
\(405\) 2.06566 + 0.856175i 0.102644 + 0.0425437i
\(406\) 9.92336 17.1878i 0.492488 0.853014i
\(407\) 49.2052i 2.43901i
\(408\) −4.44932 + 2.56882i −0.220274 + 0.127175i
\(409\) 9.55496 16.5497i 0.472463 0.818329i −0.527041 0.849840i \(-0.676699\pi\)
0.999503 + 0.0315108i \(0.0100319\pi\)
\(410\) −11.8500 15.4505i −0.585229 0.763044i
\(411\) 12.6387 0.623422
\(412\) −1.45146 + 0.838003i −0.0715085 + 0.0412854i
\(413\) 41.5450 23.9860i 2.04429 1.18027i
\(414\) 4.53238 + 7.85031i 0.222754 + 0.385822i
\(415\) 13.4887 + 17.5871i 0.662134 + 0.863316i
\(416\) 2.70788 + 4.69019i 0.132765 + 0.229955i
\(417\) 5.73994 + 3.31395i 0.281086 + 0.162285i
\(418\) 27.6027i 1.35009i
\(419\) −30.6580 −1.49774 −0.748870 0.662717i \(-0.769403\pi\)
−0.748870 + 0.662717i \(0.769403\pi\)
\(420\) 6.37717 4.89107i 0.311174 0.238660i
\(421\) 17.2976 + 29.9603i 0.843032 + 1.46017i 0.887319 + 0.461156i \(0.152565\pi\)
−0.0442873 + 0.999019i \(0.514102\pi\)
\(422\) 6.78240 + 3.91582i 0.330162 + 0.190619i
\(423\) 4.37847 2.52791i 0.212888 0.122911i
\(424\) 2.46356 + 4.26701i 0.119641 + 0.207224i
\(425\) 24.8099 + 6.65986i 1.20346 + 0.323051i
\(426\) 4.77582 0.231389
\(427\) 3.56889 + 2.06050i 0.172711 + 0.0997146i
\(428\) −2.12044 1.22423i −0.102495 0.0591756i
\(429\) 16.1198 + 27.9202i 0.778270 + 1.34800i
\(430\) −4.74784 1.96788i −0.228961 0.0948997i
\(431\) 3.79252 6.56884i 0.182679 0.316410i −0.760113 0.649791i \(-0.774856\pi\)
0.942792 + 0.333381i \(0.108190\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 23.7371i 1.14073i 0.821390 + 0.570366i \(0.193199\pi\)
−0.821390 + 0.570366i \(0.806801\pi\)
\(434\) 12.8908 + 15.3066i 0.618777 + 0.734739i
\(435\) −4.72771 + 11.4064i −0.226676 + 0.546893i
\(436\) −1.67713 −0.0803201
\(437\) −36.4007 21.0159i −1.74128 1.00533i
\(438\) 1.86867i 0.0892887i
\(439\) 5.10170 + 8.83640i 0.243491 + 0.421738i 0.961706 0.274082i \(-0.0883741\pi\)
−0.718215 + 0.695821i \(0.755041\pi\)
\(440\) 8.10088 + 10.5622i 0.386195 + 0.503535i
\(441\) −2.95909 + 5.12530i −0.140909 + 0.244062i
\(442\) 27.8242i 1.32346i
\(443\) 33.0182 19.0631i 1.56874 0.905715i 0.572429 0.819955i \(-0.306001\pi\)
0.996316 0.0857604i \(-0.0273320\pi\)
\(444\) −4.13288 7.15835i −0.196138 0.339720i
\(445\) −3.38609 25.7651i −0.160516 1.22138i
\(446\) 6.38320 11.0560i 0.302253 0.523518i
\(447\) −0.643090 + 0.371288i −0.0304171 + 0.0175613i
\(448\) −3.11266 1.79709i −0.147059 0.0849047i
\(449\) 30.7843 1.45280 0.726400 0.687272i \(-0.241192\pi\)
0.726400 + 0.687272i \(0.241192\pi\)
\(450\) −3.53714 + 3.53393i −0.166742 + 0.166591i
\(451\) −25.9187 + 44.8925i −1.22046 + 2.11390i
\(452\) 3.36747 1.94421i 0.158392 0.0914479i
\(453\) 3.56463 + 2.05804i 0.167481 + 0.0966951i
\(454\) 1.66070 + 2.87642i 0.0779407 + 0.134997i
\(455\) 5.67144 + 43.1546i 0.265881 + 2.02312i
\(456\) 2.31842 + 4.01562i 0.108570 + 0.188049i
\(457\) 22.5321i 1.05401i 0.849862 + 0.527005i \(0.176685\pi\)
−0.849862 + 0.527005i \(0.823315\pi\)
\(458\) 4.53720 + 2.61956i 0.212010 + 0.122404i
\(459\) −2.56882 + 4.44932i −0.119902 + 0.207677i
\(460\) −20.0966 + 2.64113i −0.937009 + 0.123143i
\(461\) −40.8334 −1.90180 −0.950899 0.309500i \(-0.899838\pi\)
−0.950899 + 0.309500i \(0.899838\pi\)
\(462\) −18.5294 10.6979i −0.862063 0.497713i
\(463\) 3.98680i 0.185282i 0.995700 + 0.0926412i \(0.0295310\pi\)
−0.995700 + 0.0926412i \(0.970469\pi\)
\(464\) 5.52189 0.256347
\(465\) −9.19225 8.39658i −0.426280 0.389382i
\(466\) −14.5392 −0.673513
\(467\) 21.0286i 0.973087i −0.873656 0.486544i \(-0.838257\pi\)
0.873656 0.486544i \(-0.161743\pi\)
\(468\) 4.69019 + 2.70788i 0.216804 + 0.125172i
\(469\) −20.0869 −0.927529
\(470\) 1.47307 + 11.2088i 0.0679478 + 0.517022i
\(471\) −3.91892 + 6.78777i −0.180574 + 0.312764i
\(472\) 11.5589 + 6.67355i 0.532043 + 0.307175i
\(473\) 13.6825i 0.629122i
\(474\) −2.00321 3.46966i −0.0920105 0.159367i
\(475\) 6.01069 22.3915i 0.275789 1.02739i
\(476\) 9.23282 + 15.9917i 0.423185 + 0.732979i
\(477\) 4.26701 + 2.46356i 0.195373 + 0.112799i
\(478\) 19.2600 11.1198i 0.880932 0.508606i
\(479\) −5.43490 + 9.41352i −0.248327 + 0.430115i −0.963062 0.269281i \(-0.913214\pi\)
0.714735 + 0.699395i \(0.246547\pi\)
\(480\) 2.06566 + 0.856175i 0.0942842 + 0.0390789i
\(481\) 44.7654 2.04113
\(482\) 1.95057 + 1.12616i 0.0888459 + 0.0512952i
\(483\) 28.2155 16.2902i 1.28385 0.741230i
\(484\) 12.2185 21.1631i 0.555388 0.961960i
\(485\) −14.3010 + 1.87946i −0.649375 + 0.0853419i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −27.4811 + 15.8662i −1.24529 + 0.718966i −0.970166 0.242444i \(-0.922051\pi\)
−0.275120 + 0.961410i \(0.588718\pi\)
\(488\) 1.14657i 0.0519030i
\(489\) −5.38408 + 9.32551i −0.243477 + 0.421714i
\(490\) −8.05363 10.5006i −0.363826 0.474370i
\(491\) −3.62646 6.28121i −0.163660 0.283467i 0.772519 0.634992i \(-0.218997\pi\)
−0.936179 + 0.351525i \(0.885663\pi\)
\(492\) 8.70791i 0.392583i
\(493\) −24.5687 14.1847i −1.10652 0.638849i
\(494\) −25.1121 −1.12984
\(495\) 12.2967 + 5.09673i 0.552695 + 0.229081i
\(496\) −1.89486 + 5.23541i −0.0850819 + 0.235077i
\(497\) 17.1652i 0.769964i
\(498\) 9.91212i 0.444173i
\(499\) 10.9674 18.9961i 0.490969 0.850383i −0.508977 0.860780i \(-0.669976\pi\)
0.999946 + 0.0103971i \(0.00330957\pi\)
\(500\) −4.27149 10.3322i −0.191027 0.462070i
\(501\) −5.82450 10.0883i −0.260219 0.450713i
\(502\) −13.1669 7.60189i −0.587666 0.339289i
\(503\) −7.31796 4.22503i −0.326292 0.188385i 0.327902 0.944712i \(-0.393659\pi\)
−0.654194 + 0.756327i \(0.726992\pi\)
\(504\) −3.59419 −0.160098
\(505\) 2.84582 + 21.6542i 0.126638 + 0.963598i
\(506\) 26.9808 + 46.7321i 1.19944 + 2.07750i
\(507\) −14.1426 + 8.16525i −0.628096 + 0.362632i
\(508\) −11.9460 6.89703i −0.530019 0.306006i
\(509\) −5.61256 9.72123i −0.248772 0.430886i 0.714413 0.699724i \(-0.246694\pi\)
−0.963185 + 0.268838i \(0.913360\pi\)
\(510\) −6.99145 9.11572i −0.309586 0.403651i
\(511\) 6.71636 0.297114
\(512\) 1.00000i 0.0441942i
\(513\) 4.01562 + 2.31842i 0.177294 + 0.102361i
\(514\) 1.60435 + 2.77882i 0.0707650 + 0.122568i
\(515\) −2.28076 2.97374i −0.100502 0.131039i
\(516\) 1.14923 + 1.99052i 0.0505920 + 0.0876279i
\(517\) 26.0646 15.0484i 1.14632 0.661828i
\(518\) −25.7285 + 14.8543i −1.13044 + 0.652662i
\(519\) −11.3857 −0.499776
\(520\) −9.60920 + 7.36993i −0.421391 + 0.323193i
\(521\) 13.8234 23.9428i 0.605613 1.04895i −0.386341 0.922356i \(-0.626261\pi\)
0.991954 0.126597i \(-0.0404054\pi\)
\(522\) 4.78210 2.76095i 0.209307 0.120843i
\(523\) 36.5883i 1.59989i 0.600070 + 0.799947i \(0.295139\pi\)
−0.600070 + 0.799947i \(0.704861\pi\)
\(524\) −10.1483 + 17.5774i −0.443331 + 0.767873i
\(525\) 12.7016 + 12.7131i 0.554343 + 0.554847i
\(526\) 21.1070 0.920310
\(527\) 21.8797 18.4265i 0.953094 0.802669i
\(528\) 5.95290i 0.259067i
\(529\) −59.1698 −2.57260
\(530\) −8.74219 + 6.70496i −0.379736 + 0.291245i
\(531\) 13.3471 0.579215
\(532\) 14.4329 8.33284i 0.625746 0.361275i
\(533\) −40.8418 23.5800i −1.76905 1.02136i
\(534\) −5.81080 + 10.0646i −0.251458 + 0.435538i
\(535\) 2.09632 5.05771i 0.0906318 0.218664i
\(536\) −2.79437 4.83998i −0.120698 0.209055i
\(537\) 6.63830 3.83263i 0.286464 0.165390i
\(538\) 14.4777 8.35872i 0.624179 0.360370i
\(539\) −17.6152 + 30.5104i −0.758740 + 1.31418i
\(540\) 2.21700 0.291362i 0.0954047 0.0125382i
\(541\) 2.94961 5.10887i 0.126813 0.219647i −0.795627 0.605787i \(-0.792858\pi\)
0.922440 + 0.386140i \(0.126192\pi\)
\(542\) 8.95467i 0.384636i
\(543\) 4.61056i 0.197858i
\(544\) −2.56882 + 4.44932i −0.110137 + 0.190763i
\(545\) −0.488653 3.71821i −0.0209316 0.159271i
\(546\) 9.73264 16.8574i 0.416518 0.721431i
\(547\) 9.81072 5.66422i 0.419476 0.242185i −0.275377 0.961336i \(-0.588803\pi\)
0.694853 + 0.719152i \(0.255469\pi\)
\(548\) 10.9454 6.31936i 0.467566 0.269950i
\(549\) 0.573287 + 0.992962i 0.0244673 + 0.0423786i
\(550\) −21.0562 + 21.0371i −0.897841 + 0.897026i
\(551\) −12.8021 + 22.1738i −0.545387 + 0.944637i
\(552\) 7.85031 + 4.53238i 0.334131 + 0.192911i
\(553\) −12.4706 + 7.19992i −0.530305 + 0.306172i
\(554\) −0.851610 −0.0361815
\(555\) 14.6659 11.2483i 0.622534 0.477463i
\(556\) 6.62791 0.281086
\(557\) 6.90212i 0.292452i 0.989251 + 0.146226i \(0.0467127\pi\)
−0.989251 + 0.146226i \(0.953287\pi\)
\(558\) 0.976703 + 5.48143i 0.0413471 + 0.232047i
\(559\) −12.4479 −0.526490
\(560\) 3.07725 7.42438i 0.130038 0.313737i
\(561\) −15.2919 + 26.4864i −0.645626 + 1.11826i
\(562\) 3.72310i 0.157050i
\(563\) 30.7052 17.7277i 1.29407 0.747131i 0.314697 0.949192i \(-0.398097\pi\)
0.979373 + 0.202061i \(0.0647639\pi\)
\(564\) 2.52791 4.37847i 0.106444 0.184367i
\(565\) 5.29147 + 6.89922i 0.222614 + 0.290253i
\(566\) 21.3862 0.898927
\(567\) −3.11266 + 1.79709i −0.130719 + 0.0754708i
\(568\) 4.13598 2.38791i 0.173542 0.100194i
\(569\) 2.76691 + 4.79243i 0.115995 + 0.200909i 0.918177 0.396170i \(-0.129661\pi\)
−0.802182 + 0.597080i \(0.796328\pi\)
\(570\) −8.22716 + 6.30995i −0.344598 + 0.264295i
\(571\) 22.6987 + 39.3153i 0.949911 + 1.64529i 0.745606 + 0.666387i \(0.232160\pi\)
0.204305 + 0.978907i \(0.434506\pi\)
\(572\) 27.9202 + 16.1198i 1.16740 + 0.674001i
\(573\) 15.2761i 0.638168i
\(574\) 31.2979 1.30635
\(575\) −11.7108 43.7847i −0.488373 1.82595i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 10.3544 + 5.97812i 0.431060 + 0.248872i 0.699798 0.714341i \(-0.253273\pi\)
−0.268738 + 0.963213i \(0.586607\pi\)
\(578\) 8.13659 4.69766i 0.338437 0.195397i
\(579\) −2.05581 3.56077i −0.0854366 0.147981i
\(580\) 1.60887 + 12.2421i 0.0668047 + 0.508324i
\(581\) −35.6260 −1.47802
\(582\) 5.58638 + 3.22530i 0.231563 + 0.133693i
\(583\) 25.4011 + 14.6653i 1.05201 + 0.607376i
\(584\) 0.934337 + 1.61832i 0.0386631 + 0.0669665i
\(585\) −4.63684 + 11.1871i −0.191710 + 0.462532i
\(586\) −4.49828 + 7.79125i −0.185822 + 0.321854i
\(587\) 24.8671i 1.02637i −0.858277 0.513187i \(-0.828465\pi\)
0.858277 0.513187i \(-0.171535\pi\)
\(588\) 5.91818i 0.244062i
\(589\) −16.6303 19.7469i −0.685241 0.813659i
\(590\) −11.4275 + 27.5706i −0.470461 + 1.13506i
\(591\) −11.6182 −0.477907
\(592\) −7.15835 4.13288i −0.294206 0.169860i
\(593\) 43.5200i 1.78715i 0.448910 + 0.893577i \(0.351812\pi\)
−0.448910 + 0.893577i \(0.648188\pi\)
\(594\) −2.97645 5.15537i −0.122125 0.211527i
\(595\) −32.7636 + 25.1286i −1.34318 + 1.03017i
\(596\) −0.371288 + 0.643090i −0.0152086 + 0.0263420i
\(597\) 5.06587i 0.207332i
\(598\) −42.5154 + 24.5463i −1.73858 + 1.00377i
\(599\) 0.472384 + 0.818193i 0.0193011 + 0.0334304i 0.875515 0.483192i \(-0.160523\pi\)
−0.856214 + 0.516622i \(0.827189\pi\)
\(600\) −1.29629 + 4.82904i −0.0529207 + 0.197145i
\(601\) 16.3314 28.2868i 0.666172 1.15384i −0.312795 0.949821i \(-0.601265\pi\)
0.978966 0.204022i \(-0.0654015\pi\)
\(602\) 7.15431 4.13054i 0.291588 0.168348i
\(603\) −4.83998 2.79437i −0.197099 0.113795i
\(604\) 4.11608 0.167481
\(605\) 50.4787 + 20.9224i 2.05225 + 0.850617i
\(606\) 4.88366 8.45874i 0.198385 0.343613i
\(607\) −3.54336 + 2.04576i −0.143820 + 0.0830347i −0.570184 0.821517i \(-0.693128\pi\)
0.426363 + 0.904552i \(0.359795\pi\)
\(608\) 4.01562 + 2.31842i 0.162855 + 0.0940244i
\(609\) −9.92336 17.1878i −0.402115 0.696483i
\(610\) −2.54196 + 0.334068i −0.102921 + 0.0135260i
\(611\) 13.6906 + 23.7128i 0.553861 + 0.959315i
\(612\) 5.13764i 0.207677i
\(613\) −7.25064 4.18616i −0.292851 0.169077i 0.346376 0.938096i \(-0.387412\pi\)
−0.639227 + 0.769018i \(0.720745\pi\)
\(614\) 8.49904 14.7208i 0.342993 0.594082i
\(615\) −19.3055 + 2.53715i −0.778472 + 0.102308i
\(616\) −21.3959 −0.862063
\(617\) −6.05354 3.49502i −0.243706 0.140704i 0.373173 0.927762i \(-0.378270\pi\)
−0.616879 + 0.787058i \(0.711603\pi\)
\(618\) 1.67601i 0.0674188i
\(619\) 21.1473 0.849982 0.424991 0.905197i \(-0.360277\pi\)
0.424991 + 0.905197i \(0.360277\pi\)
\(620\) −12.1590 2.67552i −0.488318 0.107452i
\(621\) 9.06476 0.363756
\(622\) 17.4831i 0.701010i
\(623\) 36.1740 + 20.8851i 1.44928 + 0.836744i
\(624\) 5.41576 0.216804
\(625\) 21.6620 12.4803i 0.866479 0.499213i
\(626\) 16.7175 28.9556i 0.668167 1.15730i
\(627\) 23.9046 + 13.8013i 0.954659 + 0.551173i
\(628\) 7.83784i 0.312764i
\(629\) 21.2332 + 36.7770i 0.846624 + 1.46640i
\(630\) −1.04721 7.96833i −0.0417218 0.317466i
\(631\) 10.9873 + 19.0306i 0.437399 + 0.757598i 0.997488 0.0708346i \(-0.0225662\pi\)
−0.560089 + 0.828433i \(0.689233\pi\)
\(632\) −3.46966 2.00321i −0.138016 0.0796835i
\(633\) 6.78240 3.91582i 0.269576 0.155640i
\(634\) 6.94602 12.0309i 0.275862 0.477806i
\(635\) 11.8101 28.4939i 0.468671 1.13075i
\(636\) 4.92712 0.195373
\(637\) −27.7574 16.0257i −1.09979 0.634963i
\(638\) 28.4674 16.4356i 1.12703 0.650693i
\(639\) 2.38791 4.13598i 0.0944643 0.163617i
\(640\) 2.21700 0.291362i 0.0876348 0.0115171i
\(641\) −19.2323 33.3113i −0.759631 1.31572i −0.943039 0.332682i \(-0.892046\pi\)
0.183409 0.983037i \(-0.441287\pi\)
\(642\) −2.12044 + 1.22423i −0.0836870 + 0.0483167i
\(643\) 20.6335i 0.813704i 0.913494 + 0.406852i \(0.133374\pi\)
−0.913494 + 0.406852i \(0.866626\pi\)
\(644\) 16.2902 28.2155i 0.641924 1.11185i
\(645\) −4.07816 + 3.12781i −0.160577 + 0.123157i
\(646\) −11.9112 20.6308i −0.468640 0.811709i
\(647\) 4.89104i 0.192287i −0.995367 0.0961434i \(-0.969349\pi\)
0.995367 0.0961434i \(-0.0306507\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 79.4541 3.11884
\(650\) −19.1389 19.1563i −0.750690 0.751372i
\(651\) 19.7013 3.51045i 0.772154 0.137585i
\(652\) 10.7682i 0.421714i
\(653\) 12.9123i 0.505297i 0.967558 + 0.252648i \(0.0813016\pi\)
−0.967558 + 0.252648i \(0.918698\pi\)
\(654\) −0.838566 + 1.45244i −0.0327905 + 0.0567949i
\(655\) −41.9260 17.3775i −1.63819 0.678994i
\(656\) 4.35396 + 7.54127i 0.169993 + 0.294437i
\(657\) 1.61832 + 0.934337i 0.0631366 + 0.0364520i
\(658\) −15.7370 9.08578i −0.613493 0.354201i
\(659\) −10.7331 −0.418103 −0.209051 0.977905i \(-0.567038\pi\)
−0.209051 + 0.977905i \(0.567038\pi\)
\(660\) 13.1976 1.73445i 0.513716 0.0675134i
\(661\) −18.9020 32.7391i −0.735201 1.27341i −0.954635 0.297778i \(-0.903755\pi\)
0.219434 0.975627i \(-0.429579\pi\)
\(662\) −3.81564 + 2.20296i −0.148299 + 0.0856204i
\(663\) −24.0965 13.9121i −0.935830 0.540302i
\(664\) −4.95606 8.58415i −0.192332 0.333130i
\(665\) 22.6791 + 29.5699i 0.879460 + 1.14667i
\(666\) −8.26575 −0.320291
\(667\) 50.0546i 1.93812i
\(668\) −10.0883 5.82450i −0.390329 0.225356i
\(669\) −6.38320 11.0560i −0.246789 0.427451i
\(670\) 9.91609 7.60531i 0.383092 0.293819i
\(671\) 3.41272 + 5.91101i 0.131747 + 0.228192i
\(672\) −3.11266 + 1.79709i −0.120073 + 0.0693244i
\(673\) 7.29082 4.20935i 0.281040 0.162259i −0.352854 0.935678i \(-0.614789\pi\)
0.633894 + 0.773420i \(0.281455\pi\)
\(674\) 8.34153 0.321304
\(675\) 1.29190 + 4.83022i 0.0497253 + 0.185915i
\(676\) −8.16525 + 14.1426i −0.314048 + 0.543948i
\(677\) −5.96039 + 3.44123i −0.229076 + 0.132257i −0.610146 0.792289i \(-0.708889\pi\)
0.381070 + 0.924546i \(0.375556\pi\)
\(678\) 3.88842i 0.149334i
\(679\) 11.5923 20.0785i 0.444873 0.770542i
\(680\) −10.6126 4.39872i −0.406976 0.168683i
\(681\) 3.32141 0.127277
\(682\) 5.81422 + 32.6304i 0.222638 + 1.24948i
\(683\) 17.2994i 0.661945i −0.943640 0.330973i \(-0.892623\pi\)
0.943640 0.330973i \(-0.107377\pi\)
\(684\) 4.63684 0.177294
\(685\) 17.1991 + 22.4249i 0.657145 + 0.856811i
\(686\) −3.88826 −0.148454
\(687\) 4.53720 2.61956i 0.173105 0.0999423i
\(688\) 1.99052 + 1.14923i 0.0758880 + 0.0438139i
\(689\) −13.3421 + 23.1091i −0.508292 + 0.880387i
\(690\) −7.76102 + 18.7247i −0.295457 + 0.712838i
\(691\) −24.1447 41.8198i −0.918508 1.59090i −0.801683 0.597749i \(-0.796062\pi\)
−0.116825 0.993153i \(-0.537272\pi\)
\(692\) −9.86029 + 5.69284i −0.374832 + 0.216409i
\(693\) −18.5294 + 10.6979i −0.703872 + 0.406381i
\(694\) −15.3156 + 26.5275i −0.581374 + 1.00697i
\(695\) 1.93112 + 14.6941i 0.0732516 + 0.557379i
\(696\) 2.76095 4.78210i 0.104653 0.181265i
\(697\) 44.7381i 1.69458i
\(698\) 15.2039i 0.575476i
\(699\) −7.26958 + 12.5913i −0.274961 + 0.476246i
\(700\) 17.3565 + 4.65910i 0.656013 + 0.176098i
\(701\) 7.46350 12.9272i 0.281893 0.488252i −0.689958 0.723849i \(-0.742371\pi\)
0.971851 + 0.235597i \(0.0757045\pi\)
\(702\) 4.69019 2.70788i 0.177020 0.102202i
\(703\) 33.1922 19.1635i 1.25187 0.722765i
\(704\) −2.97645 5.15537i −0.112179 0.194300i
\(705\) 10.4436 + 4.32867i 0.393329 + 0.163027i
\(706\) −6.42736 + 11.1325i −0.241897 + 0.418977i
\(707\) −30.4023 17.5528i −1.14340 0.660140i
\(708\) 11.5589 6.67355i 0.434411 0.250808i
\(709\) −35.9212 −1.34905 −0.674525 0.738252i \(-0.735651\pi\)
−0.674525 + 0.738252i \(0.735651\pi\)
\(710\) 6.49908 + 8.47374i 0.243906 + 0.318014i
\(711\) −4.00642 −0.150253
\(712\) 11.6216i 0.435538i
\(713\) −47.4577 17.1765i −1.77730 0.643264i
\(714\) 18.4656 0.691059
\(715\) −27.6027 + 66.5960i −1.03228 + 2.49055i
\(716\) 3.83263 6.63830i 0.143232 0.248085i
\(717\) 22.2395i 0.830550i
\(718\) 15.3331 8.85258i 0.572227 0.330376i
\(719\) 22.3875 38.7763i 0.834914 1.44611i −0.0591865 0.998247i \(-0.518851\pi\)
0.894100 0.447866i \(-0.147816\pi\)
\(720\) 1.77430 1.36083i 0.0661243 0.0507151i
\(721\) 6.02388 0.224341
\(722\) −2.16534 + 1.25016i −0.0805856 + 0.0465261i
\(723\) 1.95057 1.12616i 0.0725424 0.0418824i
\(724\) 2.30528 + 3.99286i 0.0856751 + 0.148394i
\(725\) −26.6719 + 7.13374i −0.990571 + 0.264941i
\(726\) −12.2185 21.1631i −0.453472 0.785437i
\(727\) −6.22980 3.59677i −0.231050 0.133397i 0.380006 0.924984i \(-0.375922\pi\)
−0.611057 + 0.791587i \(0.709255\pi\)
\(728\) 19.4653i 0.721431i
\(729\) −1.00000 −0.0370370
\(730\) −3.31559 + 2.54295i −0.122715 + 0.0941186i
\(731\) −5.90432 10.2266i −0.218379 0.378244i
\(732\) 0.992962 + 0.573287i 0.0367009 + 0.0211893i
\(733\) −7.10090 + 4.09970i −0.262278 + 0.151426i −0.625373 0.780326i \(-0.715053\pi\)
0.363095 + 0.931752i \(0.381720\pi\)
\(734\) 2.22370 + 3.85157i 0.0820784 + 0.142164i
\(735\) −13.1206 + 1.72433i −0.483962 + 0.0636030i
\(736\) 9.06476 0.334131
\(737\) −28.8120 16.6346i −1.06130 0.612743i
\(738\) 7.54127 + 4.35396i 0.277598 + 0.160271i
\(739\) −14.6917 25.4467i −0.540442 0.936073i −0.998879 0.0473456i \(-0.984924\pi\)
0.458437 0.888727i \(-0.348410\pi\)
\(740\) 7.07693 17.0743i 0.260153 0.627662i
\(741\) −12.5560 + 21.7477i −0.461257 + 0.798921i
\(742\) 17.7090i 0.650117i
\(743\) 4.08220i 0.149761i 0.997193 + 0.0748807i \(0.0238576\pi\)
−0.997193 + 0.0748807i \(0.976142\pi\)
\(744\) 3.58656 + 4.25870i 0.131490 + 0.156132i
\(745\) −1.53391 0.635776i −0.0561982 0.0232930i
\(746\) −17.9531 −0.657310
\(747\) −8.58415 4.95606i −0.314078 0.181333i
\(748\) 30.5839i 1.11826i
\(749\) 4.40013 + 7.62125i 0.160777 + 0.278474i
\(750\) −11.0837 1.46688i −0.404719 0.0535628i
\(751\) −9.28329 + 16.0791i −0.338752 + 0.586736i −0.984198 0.177070i \(-0.943338\pi\)
0.645446 + 0.763806i \(0.276671\pi\)
\(752\) 5.05582i 0.184367i
\(753\) −13.1669 + 7.60189i −0.479827 + 0.277028i
\(754\) 14.9526 + 25.8987i 0.544543 + 0.943176i
\(755\) 1.19927 + 9.12536i 0.0436459 + 0.332106i
\(756\) −1.79709 + 3.11266i −0.0653597 + 0.113206i
\(757\) 10.6644 6.15708i 0.387603 0.223783i −0.293518 0.955954i \(-0.594826\pi\)
0.681121 + 0.732171i \(0.261493\pi\)
\(758\) 7.53641 + 4.35115i 0.273735 + 0.158041i
\(759\) 53.9616 1.95868
\(760\) −3.96995 + 9.57816i −0.144005 + 0.347436i
\(761\) 12.9483 22.4271i 0.469375 0.812981i −0.530012 0.847990i \(-0.677813\pi\)
0.999387 + 0.0350090i \(0.0111460\pi\)
\(762\) −11.9460 + 6.89703i −0.432758 + 0.249853i
\(763\) 5.22034 + 3.01396i 0.188989 + 0.109113i
\(764\) −7.63804 13.2295i −0.276335 0.478626i
\(765\) −11.3902 + 1.49691i −0.411812 + 0.0541210i
\(766\) −13.9461 24.1554i −0.503893 0.872769i
\(767\) 72.2848i 2.61005i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) −18.8752 + 32.6928i −0.680658 + 1.17893i 0.294123 + 0.955768i \(0.404973\pi\)
−0.974780 + 0.223166i \(0.928361\pi\)
\(770\) −6.23394 47.4347i −0.224656 1.70943i
\(771\) 3.20871 0.115559
\(772\) −3.56077 2.05581i −0.128155 0.0739903i
\(773\) 38.3339i 1.37877i 0.724393 + 0.689387i \(0.242120\pi\)
−0.724393 + 0.689387i \(0.757880\pi\)
\(774\) 2.29846 0.0826164
\(775\) 2.38897 27.7361i 0.0858145 0.996311i
\(776\) 6.45060 0.231563
\(777\) 29.7087i 1.06579i
\(778\) −27.8681 16.0896i −0.999118 0.576841i
\(779\) −40.3772 −1.44666
\(780\) 1.57795 + 12.0068i 0.0564996 + 0.429911i
\(781\) 14.2150 24.6211i 0.508653 0.881012i
\(782\) −40.3320 23.2857i −1.44227 0.832695i
\(783\) 5.52189i 0.197336i
\(784\) 2.95909 + 5.12530i 0.105682 + 0.183046i
\(785\) −17.3765 + 2.28365i −0.620195 + 0.0815070i
\(786\) 10.1483 + 17.5774i 0.361979 + 0.626965i
\(787\) −9.92956 5.73283i −0.353951 0.204353i 0.312473 0.949927i \(-0.398843\pi\)
−0.666424 + 0.745573i \(0.732176\pi\)
\(788\) −10.0616 + 5.80908i −0.358430 + 0.206940i
\(789\) 10.5535 18.2792i 0.375715 0.650757i
\(790\) 3.43020 8.27592i 0.122041 0.294444i
\(791\) −13.9757 −0.496919
\(792\) −5.15537 2.97645i −0.183188 0.105764i
\(793\) −5.37765 + 3.10479i −0.190966 + 0.110254i
\(794\) 2.31056 4.00201i 0.0819987 0.142026i
\(795\) 1.43558 + 10.9234i 0.0509146 + 0.387415i
\(796\) 2.53294 + 4.38718i 0.0897776 + 0.155499i
\(797\) −6.64854 + 3.83854i −0.235504 + 0.135968i −0.613108 0.789999i \(-0.710081\pi\)
0.377605 + 0.925967i \(0.376748\pi\)
\(798\) 16.6657i 0.589959i
\(799\) −12.9875 + 22.4950i −0.459464 + 0.795815i
\(800\) 1.29190 + 4.83022i 0.0456756 + 0.170774i
\(801\) 5.81080 + 10.0646i 0.205314 + 0.355615i
\(802\) 2.12856i 0.0751621i
\(803\) 9.63370 + 5.56202i 0.339966 + 0.196279i
\(804\) −5.58873 −0.197099
\(805\) 67.3002 + 27.8946i 2.37202 + 0.983154i
\(806\) −29.6861 + 5.28959i −1.04565 + 0.186318i
\(807\) 16.7174i 0.588482i
\(808\) 9.76731i 0.343613i
\(809\) 7.74541 13.4154i 0.272314 0.471662i −0.697140 0.716935i \(-0.745544\pi\)
0.969454 + 0.245273i \(0.0788777\pi\)
\(810\) 0.856175 2.06566i 0.0300829 0.0725800i
\(811\) 11.1715 + 19.3496i 0.392284 + 0.679456i 0.992750 0.120194i \(-0.0383517\pi\)
−0.600466 + 0.799650i \(0.705018\pi\)
\(812\) −17.1878 9.92336i −0.603172 0.348242i
\(813\) 7.75497 + 4.47734i 0.271979 + 0.157027i
\(814\) −49.2052 −1.72464
\(815\) −23.8731 + 3.13744i −0.836237 + 0.109900i
\(816\) 2.56882 + 4.44932i 0.0899267 + 0.155758i
\(817\) −9.22974 + 5.32879i −0.322908 + 0.186431i
\(818\) −16.5497 9.55496i −0.578646 0.334081i
\(819\) −9.73264 16.8574i −0.340086 0.589046i
\(820\) −15.4505 + 11.8500i −0.539553 + 0.413819i
\(821\) −18.0664 −0.630521 −0.315260 0.949005i \(-0.602092\pi\)
−0.315260 + 0.949005i \(0.602092\pi\)
\(822\) 12.6387i 0.440826i
\(823\) 7.62776 + 4.40389i 0.265887 + 0.153510i 0.627017 0.779006i \(-0.284276\pi\)
−0.361130 + 0.932515i \(0.617609\pi\)
\(824\) 0.838003 + 1.45146i 0.0291932 + 0.0505641i
\(825\) 7.69057 + 28.7538i 0.267751 + 1.00108i
\(826\) −23.9860 41.5450i −0.834580 1.44553i
\(827\) 13.0149 7.51413i 0.452571 0.261292i −0.256344 0.966586i \(-0.582518\pi\)
0.708915 + 0.705294i \(0.249185\pi\)
\(828\) 7.85031 4.53238i 0.272817 0.157511i
\(829\) −26.0810 −0.905831 −0.452916 0.891553i \(-0.649616\pi\)
−0.452916 + 0.891553i \(0.649616\pi\)
\(830\) 17.5871 13.4887i 0.610457 0.468200i
\(831\) −0.425805 + 0.737516i −0.0147710 + 0.0255842i
\(832\) 4.69019 2.70788i 0.162603 0.0938789i
\(833\) 30.4055i 1.05349i
\(834\) 3.31395 5.73994i 0.114753 0.198758i
\(835\) 9.97358 24.0629i 0.345150 0.832731i
\(836\) 27.6027 0.954659
\(837\) 5.23541 + 1.89486i 0.180962 + 0.0654961i
\(838\) 30.6580i 1.05906i
\(839\) 52.7488 1.82109 0.910545 0.413410i \(-0.135662\pi\)
0.910545 + 0.413410i \(0.135662\pi\)
\(840\) −4.89107 6.37717i −0.168758 0.220033i
\(841\) 1.49128 0.0514236
\(842\) 29.9603 17.2976i 1.03250 0.596114i
\(843\) −3.22430 1.86155i −0.111051 0.0641152i
\(844\) 3.91582 6.78240i 0.134788 0.233460i
\(845\) −33.7333 13.9818i −1.16046 0.480988i
\(846\) −2.52791 4.37847i −0.0869113 0.150535i
\(847\) −76.0642 + 43.9157i −2.61360 + 1.50896i
\(848\) 4.26701 2.46356i 0.146530 0.0845990i
\(849\) 10.6931 18.5210i 0.366986 0.635638i
\(850\) 6.65986 24.8099i 0.228431 0.850971i
\(851\) 37.4635 64.8887i 1.28423 2.22436i
\(852\) 4.77582i 0.163617i
\(853\) 12.6356i 0.432634i 0.976323 + 0.216317i \(0.0694045\pi\)
−0.976323 + 0.216317i \(0.930596\pi\)
\(854\) 2.06050 3.56889i 0.0705089 0.122125i
\(855\) 1.35100 + 10.2799i 0.0462032 + 0.351565i
\(856\) −1.22423 + 2.12044i −0.0418435 + 0.0724750i
\(857\) −10.8217 + 6.24790i −0.369662 + 0.213424i −0.673311 0.739360i \(-0.735128\pi\)
0.303649 + 0.952784i \(0.401795\pi\)
\(858\) 27.9202 16.1198i 0.953182 0.550320i
\(859\) −11.5649 20.0310i −0.394589 0.683447i 0.598460 0.801153i \(-0.295780\pi\)
−0.993049 + 0.117705i \(0.962446\pi\)
\(860\) −1.96788 + 4.74784i −0.0671042 + 0.161900i
\(861\) 15.6489 27.1047i 0.533314 0.923727i
\(862\) −6.56884 3.79252i −0.223736 0.129174i
\(863\) −16.5917 + 9.57921i −0.564787 + 0.326080i −0.755065 0.655650i \(-0.772395\pi\)
0.190277 + 0.981730i \(0.439061\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −15.4940 20.2016i −0.526811 0.686876i
\(866\) 23.7371 0.806620
\(867\) 9.39532i 0.319082i
\(868\) 15.3066 12.8908i 0.519539 0.437542i
\(869\) −23.8498 −0.809051
\(870\) 11.4064 + 4.72771i 0.386712 + 0.160284i
\(871\) 15.1336 26.2122i 0.512783 0.888167i
\(872\) 1.67713i 0.0567949i
\(873\) 5.58638 3.22530i 0.189070 0.109160i
\(874\) −21.0159 + 36.4007i −0.710874 + 1.23127i
\(875\) −5.27223 + 39.8369i −0.178234 + 1.34673i
\(876\) 1.86867 0.0631366
\(877\) −4.46956 + 2.58050i −0.150926 + 0.0871374i −0.573561 0.819163i \(-0.694439\pi\)
0.422635 + 0.906300i \(0.361105\pi\)
\(878\) 8.83640 5.10170i 0.298214 0.172174i
\(879\) 4.49828 + 7.79125i 0.151723 + 0.262792i
\(880\) 10.5622 8.10088i 0.356053 0.273081i
\(881\) 3.89978 + 6.75462i 0.131387 + 0.227569i 0.924211 0.381881i \(-0.124724\pi\)
−0.792824 + 0.609450i \(0.791390\pi\)
\(882\) 5.12530 + 2.95909i 0.172578 + 0.0996378i
\(883\) 12.4007i 0.417316i 0.977989 + 0.208658i \(0.0669096\pi\)
−0.977989 + 0.208658i \(0.933090\pi\)
\(884\) −27.8242 −0.935830
\(885\) 18.1631 + 23.6818i 0.610547 + 0.796055i
\(886\) −19.0631 33.0182i −0.640437 1.10927i
\(887\) −11.7260 6.76998i −0.393719 0.227314i 0.290051 0.957011i \(-0.406328\pi\)
−0.683770 + 0.729697i \(0.739661\pi\)
\(888\) −7.15835 + 4.13288i −0.240219 + 0.138690i
\(889\) 24.7892 + 42.9362i 0.831404 + 1.44003i
\(890\) −25.7651 + 3.38609i −0.863649 + 0.113502i
\(891\) −5.95290 −0.199430
\(892\) −11.0560 6.38320i −0.370183 0.213725i
\(893\) 20.3023 + 11.7215i 0.679390 + 0.392246i
\(894\) 0.371288 + 0.643090i 0.0124177 + 0.0215082i
\(895\) 15.8338 + 6.56280i 0.529267 + 0.219370i
\(896\) −1.79709 + 3.11266i −0.0600367 + 0.103987i
\(897\) 49.0926i 1.63915i
\(898\) 30.7843i 1.02728i
\(899\) −10.4632 + 28.9093i −0.348968 + 0.964181i
\(900\) 3.53393 + 3.53714i 0.117798 + 0.117905i
\(901\) −25.3137 −0.843323
\(902\) 44.8925 + 25.9187i 1.49476 + 0.862998i
\(903\) 8.26109i 0.274912i
\(904\) −1.94421 3.36747i −0.0646634 0.112000i
\(905\) −8.18052 + 6.27419i −0.271930 + 0.208561i
\(906\) 2.05804 3.56463i 0.0683738 0.118427i
\(907\) 47.5948i 1.58036i −0.612876 0.790179i \(-0.709987\pi\)
0.612876 0.790179i \(-0.290013\pi\)
\(908\) 2.87642 1.66070i 0.0954574 0.0551124i
\(909\) −4.88366 8.45874i −0.161981 0.280559i
\(910\) 43.1546 5.67144i 1.43056 0.188006i
\(911\) −12.5857 + 21.7991i −0.416982 + 0.722235i −0.995634 0.0933398i \(-0.970246\pi\)
0.578652 + 0.815575i \(0.303579\pi\)
\(912\) 4.01562 2.31842i 0.132971 0.0767706i
\(913\) −51.1006 29.5029i −1.69118 0.976405i
\(914\) 22.5321 0.745297
\(915\) −0.981668 + 2.36844i −0.0324529 + 0.0782981i
\(916\) 2.61956 4.53720i 0.0865525 0.149913i
\(917\) 63.1765 36.4750i 2.08627 1.20451i
\(918\) 4.44932 + 2.56882i 0.146850 + 0.0847837i
\(919\) 8.71806 + 15.1001i 0.287582 + 0.498107i 0.973232 0.229824i \(-0.0738151\pi\)
−0.685650 + 0.727932i \(0.740482\pi\)
\(920\) 2.64113 + 20.0966i 0.0870753 + 0.662565i
\(921\) −8.49904 14.7208i −0.280053 0.485066i
\(922\) 40.8334i 1.34477i
\(923\) 22.3995 + 12.9324i 0.737289 + 0.425674i
\(924\) −10.6979 + 18.5294i −0.351936 + 0.609571i
\(925\) 39.9157 + 10.7148i 1.31242 + 0.352300i
\(926\) 3.98680 0.131014
\(927\) 1.45146 + 0.838003i 0.0476723 + 0.0275236i
\(928\) 5.52189i 0.181265i
\(929\) −56.6111 −1.85735 −0.928675 0.370894i \(-0.879051\pi\)
−0.928675 + 0.370894i \(0.879051\pi\)
\(930\) −8.39658 + 9.19225i −0.275335 + 0.301426i
\(931\) −27.4417 −0.899365
\(932\) 14.5392i 0.476246i
\(933\) 15.1408 + 8.74157i 0.495689 + 0.286186i
\(934\) −21.0286 −0.688077
\(935\) −67.8046 + 8.91098i −2.21745 + 0.291420i
\(936\) 2.70788 4.69019i 0.0885099 0.153304i
\(937\) 21.7524 + 12.5588i 0.710620 + 0.410277i 0.811291 0.584643i \(-0.198765\pi\)
−0.100670 + 0.994920i \(0.532099\pi\)
\(938\) 20.0869i 0.655862i
\(939\) −16.7175 28.9556i −0.545556 0.944931i
\(940\) 11.2088 1.47307i 0.365590 0.0480464i
\(941\) 18.6613 + 32.3224i 0.608343 + 1.05368i 0.991514 + 0.130003i \(0.0414987\pi\)
−0.383171 + 0.923677i \(0.625168\pi\)
\(942\) 6.78777 + 3.91892i 0.221157 + 0.127685i
\(943\) −68.3598 + 39.4675i −2.22610 + 1.28524i
\(944\) 6.67355 11.5589i 0.217206 0.376211i
\(945\) −7.42438 3.07725i −0.241515 0.100103i
\(946\) 13.6825 0.444856
\(947\) 43.3767 + 25.0436i 1.40955 + 0.813806i 0.995345 0.0963757i \(-0.0307250\pi\)
0.414209 + 0.910182i \(0.364058\pi\)
\(948\) −3.46966 + 2.00321i −0.112689 + 0.0650613i
\(949\) −5.06015 + 8.76444i −0.164259 + 0.284506i
\(950\) −22.3915 6.01069i −0.726476 0.195012i
\(951\) −6.94602 12.0309i −0.225240 0.390127i
\(952\) 15.9917 9.23282i 0.518294 0.299237i
\(953\) 1.90903i 0.0618394i 0.999522 + 0.0309197i \(0.00984361\pi\)
−0.999522 + 0.0309197i \(0.990156\pi\)
\(954\) 2.46356 4.26701i 0.0797607 0.138150i
\(955\) 27.1044 20.7881i 0.877077 0.672688i
\(956\) −11.1198 19.2600i −0.359639 0.622913i
\(957\) 32.8713i 1.06258i
\(958\) 9.41352 + 5.43490i 0.304137 + 0.175594i
\(959\) −45.4259 −1.46688
\(960\) 0.856175 2.06566i 0.0276329 0.0666690i
\(961\) −23.8190 19.8408i −0.768354 0.640025i
\(962\) 44.7654i 1.44329i
\(963\) 2.44847i 0.0789008i
\(964\) 1.12616 1.95057i 0.0362712 0.0628235i
\(965\) 3.52027 8.49323i 0.113322 0.273407i
\(966\) −16.2902 28.2155i −0.524129 0.907818i
\(967\) 16.5586 + 9.56013i 0.532490 + 0.307433i 0.742030 0.670367i \(-0.233863\pi\)
−0.209540 + 0.977800i \(0.567197\pi\)
\(968\) −21.1631 12.2185i −0.680208 0.392718i
\(969\) −23.8224 −0.765286
\(970\) 1.87946 + 14.3010i 0.0603458 + 0.459178i
\(971\) −19.6700 34.0694i −0.631240 1.09334i −0.987299 0.158876i \(-0.949213\pi\)
0.356058 0.934464i \(-0.384120\pi\)
\(972\) −0.866025 + 0.500000i −0.0277778 + 0.0160375i
\(973\) −20.6304 11.9110i −0.661380 0.381848i
\(974\) 15.8662 + 27.4811i 0.508386 + 0.880550i
\(975\) −26.1593 + 6.99664i −0.837769 + 0.224072i
\(976\) 1.14657 0.0367009
\(977\) 11.3539i 0.363244i −0.983368 0.181622i \(-0.941865\pi\)
0.983368 0.181622i \(-0.0581347\pi\)
\(978\) 9.32551 + 5.38408i 0.298197 + 0.172164i
\(979\) 34.5911 + 59.9136i 1.10554 + 1.91485i
\(980\) −10.5006 + 8.05363i −0.335430 + 0.257264i
\(981\) 0.838566 + 1.45244i 0.0267734 + 0.0463728i
\(982\) −6.28121 + 3.62646i −0.200441 + 0.115725i
\(983\) −26.8812 + 15.5199i −0.857376 + 0.495006i −0.863133 0.504977i \(-0.831501\pi\)
0.00575657 + 0.999983i \(0.498168\pi\)
\(984\) 8.70791 0.277598
\(985\) −15.8103 20.6141i −0.503759 0.656820i
\(986\) −14.1847 + 24.5687i −0.451734 + 0.782426i
\(987\) −15.7370 + 9.08578i −0.500915 + 0.289204i
\(988\) 25.1121i 0.798921i
\(989\) −10.4175 + 18.0436i −0.331257 + 0.573753i
\(990\) 5.09673 12.2967i 0.161985 0.390815i
\(991\) −5.06121 −0.160775 −0.0803874 0.996764i \(-0.525616\pi\)
−0.0803874 + 0.996764i \(0.525616\pi\)
\(992\) 5.23541 + 1.89486i 0.166224 + 0.0601620i
\(993\) 4.40592i 0.139818i
\(994\) −17.1652 −0.544447
\(995\) −8.98839 + 6.89379i −0.284951 + 0.218548i
\(996\) −9.91212 −0.314078
\(997\) 35.5407 20.5194i 1.12558 0.649856i 0.182764 0.983157i \(-0.441496\pi\)
0.942821 + 0.333300i \(0.108162\pi\)
\(998\) −18.9961 10.9674i −0.601312 0.347167i
\(999\) −4.13288 + 7.15835i −0.130758 + 0.226480i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 930.2.s.c.439.3 24
5.4 even 2 inner 930.2.s.c.439.8 yes 24
31.25 even 3 inner 930.2.s.c.769.2 yes 24
155.149 even 6 inner 930.2.s.c.769.9 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.s.c.439.3 24 1.1 even 1 trivial
930.2.s.c.439.8 yes 24 5.4 even 2 inner
930.2.s.c.769.2 yes 24 31.25 even 3 inner
930.2.s.c.769.9 yes 24 155.149 even 6 inner