Properties

Label 1110.2.ba.a.619.12
Level $1110$
Weight $2$
Character 1110.619
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
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] = [1110,2,Mod(529,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.ba (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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 619.12
Character \(\chi\) \(=\) 1110.619
Dual form 1110.2.ba.a.529.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.12688 - 0.690199i) q^{5} +1.00000i q^{6} +(3.89483 - 2.24868i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.12688 - 0.690199i) q^{5} +1.00000i q^{6} +(3.89483 - 2.24868i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.66117 - 1.49683i) q^{10} +0.412574 q^{11} +(-0.866025 - 0.500000i) q^{12} +(1.10249 + 1.90957i) q^{13} +4.49736i q^{14} +(-2.18703 + 0.465711i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.63267 + 2.82787i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.06416 - 1.19174i) q^{19} +(0.465711 + 2.18703i) q^{20} +(2.24868 - 3.89483i) q^{21} +(-0.206287 + 0.357299i) q^{22} -1.63566 q^{23} +(0.866025 - 0.500000i) q^{24} +(4.04725 + 2.93594i) q^{25} -2.20498 q^{26} -1.00000i q^{27} +(-3.89483 - 2.24868i) q^{28} -9.16257i q^{29} +(0.690199 - 2.12688i) q^{30} -6.51360i q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.357299 - 0.206287i) q^{33} +(-1.63267 - 2.82787i) q^{34} +(-9.83588 + 2.09447i) q^{35} -1.00000 q^{36} +(5.42955 - 2.74226i) q^{37} +2.38348i q^{38} +(1.90957 + 1.10249i) q^{39} +(-2.12688 - 0.690199i) q^{40} +(-1.68174 - 2.91286i) q^{41} +(2.24868 + 3.89483i) q^{42} -9.32116 q^{43} +(-0.206287 - 0.357299i) q^{44} +(-1.66117 + 1.49683i) q^{45} +(0.817829 - 1.41652i) q^{46} -6.71516i q^{47} +1.00000i q^{48} +(6.61313 - 11.4543i) q^{49} +(-4.56623 + 2.03705i) q^{50} +3.26535i q^{51} +(1.10249 - 1.90957i) q^{52} +(10.0924 + 5.82686i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.877496 - 0.284758i) q^{55} +(3.89483 - 2.24868i) q^{56} +(1.19174 - 2.06416i) q^{57} +(7.93502 + 4.58129i) q^{58} +(4.76276 + 2.74978i) q^{59} +(1.49683 + 1.66117i) q^{60} +(6.46982 - 3.73535i) q^{61} +(5.64095 + 3.25680i) q^{62} -4.49736i q^{63} +1.00000 q^{64} +(-1.02688 - 4.82237i) q^{65} +0.412574i q^{66} +(2.71578 - 1.56796i) q^{67} +3.26535 q^{68} +(-1.41652 + 0.817829i) q^{69} +(3.10407 - 9.56535i) q^{70} +(-1.01489 - 1.75784i) q^{71} +(0.500000 - 0.866025i) q^{72} +6.57476i q^{73} +(-0.339909 + 6.07326i) q^{74} +(4.97299 + 0.518977i) q^{75} +(-2.06416 - 1.19174i) q^{76} +(1.60690 - 0.927747i) q^{77} +(-1.90957 + 1.10249i) q^{78} +(-7.72926 + 4.46249i) q^{79} +(1.66117 - 1.49683i) q^{80} +(-0.500000 - 0.866025i) q^{81} +3.36348 q^{82} +(3.38588 + 1.95484i) q^{83} -4.49736 q^{84} +(5.42430 - 4.88768i) q^{85} +(4.66058 - 8.07236i) q^{86} +(-4.58129 - 7.93502i) q^{87} +0.412574 q^{88} +(-2.49674 - 1.44149i) q^{89} +(-0.465711 - 2.18703i) q^{90} +(8.58804 + 4.95830i) q^{91} +(0.817829 + 1.41652i) q^{92} +(-3.25680 - 5.64095i) q^{93} +(5.81550 + 3.35758i) q^{94} +(-5.21275 + 1.11001i) q^{95} +(-0.866025 - 0.500000i) q^{96} +10.9274 q^{97} +(6.61313 + 11.4543i) q^{98} +(0.206287 - 0.357299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −2.12688 0.690199i −0.951170 0.308666i
\(6\) 1.00000i 0.408248i
\(7\) 3.89483 2.24868i 1.47211 0.849921i 0.472599 0.881278i \(-0.343316\pi\)
0.999508 + 0.0313565i \(0.00998272\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 1.66117 1.49683i 0.525308 0.473340i
\(11\) 0.412574 0.124396 0.0621979 0.998064i \(-0.480189\pi\)
0.0621979 + 0.998064i \(0.480189\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) 1.10249 + 1.90957i 0.305776 + 0.529620i 0.977434 0.211242i \(-0.0677507\pi\)
−0.671658 + 0.740862i \(0.734417\pi\)
\(14\) 4.49736i 1.20197i
\(15\) −2.18703 + 0.465711i −0.564690 + 0.120246i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.63267 + 2.82787i −0.395981 + 0.685860i −0.993226 0.116199i \(-0.962929\pi\)
0.597245 + 0.802059i \(0.296262\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 2.06416 1.19174i 0.473550 0.273404i −0.244175 0.969731i \(-0.578517\pi\)
0.717725 + 0.696327i \(0.245184\pi\)
\(20\) 0.465711 + 2.18703i 0.104136 + 0.489035i
\(21\) 2.24868 3.89483i 0.490702 0.849921i
\(22\) −0.206287 + 0.357299i −0.0439805 + 0.0761765i
\(23\) −1.63566 −0.341058 −0.170529 0.985353i \(-0.554548\pi\)
−0.170529 + 0.985353i \(0.554548\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 4.04725 + 2.93594i 0.809450 + 0.587189i
\(26\) −2.20498 −0.432433
\(27\) 1.00000i 0.192450i
\(28\) −3.89483 2.24868i −0.736053 0.424961i
\(29\) 9.16257i 1.70145i −0.525614 0.850723i \(-0.676164\pi\)
0.525614 0.850723i \(-0.323836\pi\)
\(30\) 0.690199 2.12688i 0.126013 0.388314i
\(31\) 6.51360i 1.16988i −0.811077 0.584939i \(-0.801118\pi\)
0.811077 0.584939i \(-0.198882\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.357299 0.206287i 0.0621979 0.0359099i
\(34\) −1.63267 2.82787i −0.280001 0.484976i
\(35\) −9.83588 + 2.09447i −1.66257 + 0.354030i
\(36\) −1.00000 −0.166667
\(37\) 5.42955 2.74226i 0.892613 0.450825i
\(38\) 2.38348i 0.386652i
\(39\) 1.90957 + 1.10249i 0.305776 + 0.176540i
\(40\) −2.12688 0.690199i −0.336289 0.109130i
\(41\) −1.68174 2.91286i −0.262644 0.454913i 0.704300 0.709903i \(-0.251261\pi\)
−0.966944 + 0.254990i \(0.917928\pi\)
\(42\) 2.24868 + 3.89483i 0.346979 + 0.600985i
\(43\) −9.32116 −1.42146 −0.710732 0.703463i \(-0.751636\pi\)
−0.710732 + 0.703463i \(0.751636\pi\)
\(44\) −0.206287 0.357299i −0.0310989 0.0538649i
\(45\) −1.66117 + 1.49683i −0.247633 + 0.223135i
\(46\) 0.817829 1.41652i 0.120582 0.208855i
\(47\) 6.71516i 0.979507i −0.871861 0.489753i \(-0.837087\pi\)
0.871861 0.489753i \(-0.162913\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.61313 11.4543i 0.944732 1.63632i
\(50\) −4.56623 + 2.03705i −0.645762 + 0.288082i
\(51\) 3.26535i 0.457240i
\(52\) 1.10249 1.90957i 0.152888 0.264810i
\(53\) 10.0924 + 5.82686i 1.38630 + 0.800380i 0.992896 0.118986i \(-0.0379643\pi\)
0.393403 + 0.919366i \(0.371298\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) −0.877496 0.284758i −0.118322 0.0383968i
\(56\) 3.89483 2.24868i 0.520468 0.300493i
\(57\) 1.19174 2.06416i 0.157850 0.273404i
\(58\) 7.93502 + 4.58129i 1.04192 + 0.601552i
\(59\) 4.76276 + 2.74978i 0.620058 + 0.357991i 0.776892 0.629634i \(-0.216795\pi\)
−0.156834 + 0.987625i \(0.550129\pi\)
\(60\) 1.49683 + 1.66117i 0.193240 + 0.214456i
\(61\) 6.46982 3.73535i 0.828376 0.478263i −0.0249202 0.999689i \(-0.507933\pi\)
0.853296 + 0.521426i \(0.174600\pi\)
\(62\) 5.64095 + 3.25680i 0.716401 + 0.413614i
\(63\) 4.49736i 0.566614i
\(64\) 1.00000 0.125000
\(65\) −1.02688 4.82237i −0.127369 0.598142i
\(66\) 0.412574i 0.0507843i
\(67\) 2.71578 1.56796i 0.331785 0.191556i −0.324848 0.945766i \(-0.605313\pi\)
0.656633 + 0.754210i \(0.271980\pi\)
\(68\) 3.26535 0.395981
\(69\) −1.41652 + 0.817829i −0.170529 + 0.0984550i
\(70\) 3.10407 9.56535i 0.371008 1.14328i
\(71\) −1.01489 1.75784i −0.120445 0.208617i 0.799498 0.600669i \(-0.205099\pi\)
−0.919943 + 0.392051i \(0.871766\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 6.57476i 0.769517i 0.923017 + 0.384759i \(0.125715\pi\)
−0.923017 + 0.384759i \(0.874285\pi\)
\(74\) −0.339909 + 6.07326i −0.0395136 + 0.706002i
\(75\) 4.97299 + 0.518977i 0.574232 + 0.0599263i
\(76\) −2.06416 1.19174i −0.236775 0.136702i
\(77\) 1.60690 0.927747i 0.183124 0.105727i
\(78\) −1.90957 + 1.10249i −0.216216 + 0.124833i
\(79\) −7.72926 + 4.46249i −0.869610 + 0.502069i −0.867219 0.497928i \(-0.834095\pi\)
−0.00239128 + 0.999997i \(0.500761\pi\)
\(80\) 1.66117 1.49683i 0.185725 0.167351i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.36348 0.371435
\(83\) 3.38588 + 1.95484i 0.371649 + 0.214571i 0.674178 0.738568i \(-0.264498\pi\)
−0.302530 + 0.953140i \(0.597831\pi\)
\(84\) −4.49736 −0.490702
\(85\) 5.42430 4.88768i 0.588348 0.530143i
\(86\) 4.66058 8.07236i 0.502563 0.870465i
\(87\) −4.58129 7.93502i −0.491165 0.850723i
\(88\) 0.412574 0.0439805
\(89\) −2.49674 1.44149i −0.264654 0.152798i 0.361802 0.932255i \(-0.382162\pi\)
−0.626456 + 0.779457i \(0.715495\pi\)
\(90\) −0.465711 2.18703i −0.0490902 0.230534i
\(91\) 8.58804 + 4.95830i 0.900271 + 0.519772i
\(92\) 0.817829 + 1.41652i 0.0852646 + 0.147683i
\(93\) −3.25680 5.64095i −0.337715 0.584939i
\(94\) 5.81550 + 3.35758i 0.599823 + 0.346308i
\(95\) −5.21275 + 1.11001i −0.534817 + 0.113885i
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) 10.9274 1.10951 0.554753 0.832015i \(-0.312813\pi\)
0.554753 + 0.832015i \(0.312813\pi\)
\(98\) 6.61313 + 11.4543i 0.668027 + 1.15706i
\(99\) 0.206287 0.357299i 0.0207326 0.0359099i
\(100\) 0.518977 4.97299i 0.0518977 0.497299i
\(101\) −17.2184 −1.71329 −0.856647 0.515903i \(-0.827457\pi\)
−0.856647 + 0.515903i \(0.827457\pi\)
\(102\) −2.82787 1.63267i −0.280001 0.161659i
\(103\) −16.9033 −1.66554 −0.832768 0.553622i \(-0.813245\pi\)
−0.832768 + 0.553622i \(0.813245\pi\)
\(104\) 1.10249 + 1.90957i 0.108108 + 0.187249i
\(105\) −7.47088 + 6.73180i −0.729084 + 0.656957i
\(106\) −10.0924 + 5.82686i −0.980262 + 0.565954i
\(107\) 7.58132 4.37708i 0.732914 0.423148i −0.0865732 0.996245i \(-0.527592\pi\)
0.819487 + 0.573097i \(0.194258\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) 9.65596 + 5.57487i 0.924873 + 0.533976i 0.885186 0.465236i \(-0.154031\pi\)
0.0396866 + 0.999212i \(0.487364\pi\)
\(110\) 0.685356 0.617555i 0.0653461 0.0588815i
\(111\) 3.33100 5.08964i 0.316164 0.483087i
\(112\) 4.49736i 0.424961i
\(113\) 0.817025 1.41513i 0.0768593 0.133124i −0.825034 0.565083i \(-0.808844\pi\)
0.901893 + 0.431959i \(0.142177\pi\)
\(114\) 1.19174 + 2.06416i 0.111617 + 0.193326i
\(115\) 3.47885 + 1.12893i 0.324404 + 0.105273i
\(116\) −7.93502 + 4.58129i −0.736748 + 0.425362i
\(117\) 2.20498 0.203851
\(118\) −4.76276 + 2.74978i −0.438447 + 0.253138i
\(119\) 14.6854i 1.34621i
\(120\) −2.18703 + 0.465711i −0.199648 + 0.0425134i
\(121\) −10.8298 −0.984526
\(122\) 7.47071i 0.676366i
\(123\) −2.91286 1.68174i −0.262644 0.151638i
\(124\) −5.64095 + 3.25680i −0.506572 + 0.292469i
\(125\) −6.58164 9.03781i −0.588679 0.808367i
\(126\) 3.89483 + 2.24868i 0.346979 + 0.200328i
\(127\) 7.90697 + 4.56509i 0.701630 + 0.405086i 0.807954 0.589245i \(-0.200575\pi\)
−0.106324 + 0.994332i \(0.533908\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −8.07236 + 4.66058i −0.710732 + 0.410341i
\(130\) 4.68974 + 1.52188i 0.411317 + 0.133478i
\(131\) −9.85183 5.68796i −0.860758 0.496959i 0.00350776 0.999994i \(-0.498883\pi\)
−0.864266 + 0.503035i \(0.832217\pi\)
\(132\) −0.357299 0.206287i −0.0310989 0.0179550i
\(133\) 5.35969 9.28325i 0.464744 0.804960i
\(134\) 3.13591i 0.270902i
\(135\) −0.690199 + 2.12688i −0.0594029 + 0.183053i
\(136\) −1.63267 + 2.82787i −0.140001 + 0.242488i
\(137\) 2.47409i 0.211376i −0.994399 0.105688i \(-0.966296\pi\)
0.994399 0.105688i \(-0.0337044\pi\)
\(138\) 1.63566i 0.139236i
\(139\) 9.45191 16.3712i 0.801701 1.38859i −0.116795 0.993156i \(-0.537262\pi\)
0.918496 0.395431i \(-0.129405\pi\)
\(140\) 6.73180 + 7.47088i 0.568941 + 0.631405i
\(141\) −3.35758 5.81550i −0.282759 0.489753i
\(142\) 2.02978 0.170335
\(143\) 0.454859 + 0.787840i 0.0380373 + 0.0658825i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −6.32400 + 19.4877i −0.525180 + 1.61837i
\(146\) −5.69391 3.28738i −0.471231 0.272065i
\(147\) 13.2263i 1.09088i
\(148\) −5.08964 3.33100i −0.418366 0.273806i
\(149\) 7.98719 0.654336 0.327168 0.944966i \(-0.393906\pi\)
0.327168 + 0.944966i \(0.393906\pi\)
\(150\) −2.93594 + 4.04725i −0.239719 + 0.330457i
\(151\) −2.15436 3.73146i −0.175319 0.303662i 0.764952 0.644087i \(-0.222762\pi\)
−0.940272 + 0.340425i \(0.889429\pi\)
\(152\) 2.06416 1.19174i 0.167425 0.0966630i
\(153\) 1.63267 + 2.82787i 0.131994 + 0.228620i
\(154\) 1.85549i 0.149520i
\(155\) −4.49568 + 13.8537i −0.361102 + 1.11275i
\(156\) 2.20498i 0.176540i
\(157\) −3.79620 2.19174i −0.302970 0.174920i 0.340806 0.940133i \(-0.389300\pi\)
−0.643776 + 0.765214i \(0.722633\pi\)
\(158\) 8.92498i 0.710033i
\(159\) 11.6537 0.924199
\(160\) 0.465711 + 2.18703i 0.0368177 + 0.172900i
\(161\) −6.37061 + 3.67807i −0.502074 + 0.289873i
\(162\) 1.00000 0.0785674
\(163\) −8.00959 + 13.8730i −0.627360 + 1.08662i 0.360720 + 0.932674i \(0.382531\pi\)
−0.988079 + 0.153945i \(0.950802\pi\)
\(164\) −1.68174 + 2.91286i −0.131322 + 0.227456i
\(165\) −0.902313 + 0.192140i −0.0702450 + 0.0149581i
\(166\) −3.38588 + 1.95484i −0.262795 + 0.151725i
\(167\) 6.66540 + 11.5448i 0.515784 + 0.893365i 0.999832 + 0.0183231i \(0.00583275\pi\)
−0.484048 + 0.875042i \(0.660834\pi\)
\(168\) 2.24868 3.89483i 0.173489 0.300493i
\(169\) 4.06902 7.04775i 0.313002 0.542135i
\(170\) 1.52071 + 7.14142i 0.116633 + 0.547722i
\(171\) 2.38348i 0.182269i
\(172\) 4.66058 + 8.07236i 0.355366 + 0.615512i
\(173\) 22.0473 + 12.7290i 1.67622 + 0.967768i 0.964033 + 0.265781i \(0.0856299\pi\)
0.712190 + 0.701987i \(0.247703\pi\)
\(174\) 9.16257 0.694613
\(175\) 22.3653 + 2.33403i 1.69066 + 0.176436i
\(176\) −0.206287 + 0.357299i −0.0155495 + 0.0269325i
\(177\) 5.49956 0.413372
\(178\) 2.49674 1.44149i 0.187138 0.108044i
\(179\) 3.35687i 0.250904i 0.992100 + 0.125452i \(0.0400382\pi\)
−0.992100 + 0.125452i \(0.959962\pi\)
\(180\) 2.12688 + 0.690199i 0.158528 + 0.0514444i
\(181\) 4.85498 + 8.40907i 0.360868 + 0.625041i 0.988104 0.153788i \(-0.0491472\pi\)
−0.627236 + 0.778829i \(0.715814\pi\)
\(182\) −8.58804 + 4.95830i −0.636588 + 0.367534i
\(183\) 3.73535 6.46982i 0.276125 0.478263i
\(184\) −1.63566 −0.120582
\(185\) −13.4407 + 2.08499i −0.988181 + 0.153292i
\(186\) 6.51360 0.477601
\(187\) −0.673598 + 1.16671i −0.0492584 + 0.0853180i
\(188\) −5.81550 + 3.35758i −0.424139 + 0.244877i
\(189\) −2.24868 3.89483i −0.163567 0.283307i
\(190\) 1.64508 5.06938i 0.119346 0.367772i
\(191\) 18.7526i 1.35689i 0.734651 + 0.678446i \(0.237346\pi\)
−0.734651 + 0.678446i \(0.762654\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −25.6781 −1.84835 −0.924174 0.381971i \(-0.875245\pi\)
−0.924174 + 0.381971i \(0.875245\pi\)
\(194\) −5.46368 + 9.46337i −0.392269 + 0.679431i
\(195\) −3.30049 3.66286i −0.236353 0.262303i
\(196\) −13.2263 −0.944732
\(197\) 15.5562 + 8.98138i 1.10833 + 0.639897i 0.938397 0.345558i \(-0.112311\pi\)
0.169936 + 0.985455i \(0.445644\pi\)
\(198\) 0.206287 + 0.357299i 0.0146602 + 0.0253922i
\(199\) 8.12120i 0.575697i −0.957676 0.287848i \(-0.907060\pi\)
0.957676 0.287848i \(-0.0929399\pi\)
\(200\) 4.04725 + 2.93594i 0.286184 + 0.207603i
\(201\) 1.56796 2.71578i 0.110595 0.191556i
\(202\) 8.60920 14.9116i 0.605741 1.04917i
\(203\) −20.6037 35.6866i −1.44610 2.50471i
\(204\) 2.82787 1.63267i 0.197991 0.114310i
\(205\) 1.56641 + 7.35605i 0.109403 + 0.513769i
\(206\) 8.45167 14.6387i 0.588856 1.01993i
\(207\) −0.817829 + 1.41652i −0.0568430 + 0.0984550i
\(208\) −2.20498 −0.152888
\(209\) 0.851617 0.491681i 0.0589076 0.0340103i
\(210\) −2.09447 9.83588i −0.144532 0.678740i
\(211\) −8.47435 −0.583399 −0.291699 0.956510i \(-0.594221\pi\)
−0.291699 + 0.956510i \(0.594221\pi\)
\(212\) 11.6537i 0.800380i
\(213\) −1.75784 1.01489i −0.120445 0.0695391i
\(214\) 8.75416i 0.598422i
\(215\) 19.8250 + 6.43346i 1.35205 + 0.438758i
\(216\) 1.00000i 0.0680414i
\(217\) −14.6470 25.3694i −0.994304 1.72219i
\(218\) −9.65596 + 5.57487i −0.653984 + 0.377578i
\(219\) 3.28738 + 5.69391i 0.222140 + 0.384759i
\(220\) 0.192140 + 0.902313i 0.0129541 + 0.0608339i
\(221\) −7.20004 −0.484327
\(222\) 2.74226 + 5.42955i 0.184048 + 0.364408i
\(223\) 18.7191i 1.25352i −0.779212 0.626761i \(-0.784380\pi\)
0.779212 0.626761i \(-0.215620\pi\)
\(224\) −3.89483 2.24868i −0.260234 0.150246i
\(225\) 4.56623 2.03705i 0.304415 0.135803i
\(226\) 0.817025 + 1.41513i 0.0543477 + 0.0941330i
\(227\) 2.24825 + 3.89408i 0.149222 + 0.258459i 0.930940 0.365172i \(-0.118990\pi\)
−0.781718 + 0.623632i \(0.785657\pi\)
\(228\) −2.38348 −0.157850
\(229\) 10.1818 + 17.6353i 0.672829 + 1.16537i 0.977098 + 0.212788i \(0.0682545\pi\)
−0.304269 + 0.952586i \(0.598412\pi\)
\(230\) −2.71711 + 2.44831i −0.179161 + 0.161437i
\(231\) 0.927747 1.60690i 0.0610413 0.105727i
\(232\) 9.16257i 0.601552i
\(233\) 2.94072i 0.192653i −0.995350 0.0963266i \(-0.969291\pi\)
0.995350 0.0963266i \(-0.0307093\pi\)
\(234\) −1.10249 + 1.90957i −0.0720722 + 0.124833i
\(235\) −4.63480 + 14.2823i −0.302341 + 0.931678i
\(236\) 5.49956i 0.357991i
\(237\) −4.46249 + 7.72926i −0.289870 + 0.502069i
\(238\) −12.7180 7.34272i −0.824383 0.475958i
\(239\) −8.01145 4.62541i −0.518218 0.299193i 0.217987 0.975952i \(-0.430051\pi\)
−0.736205 + 0.676758i \(0.763384\pi\)
\(240\) 0.690199 2.12688i 0.0445522 0.137290i
\(241\) 0.691167 0.399045i 0.0445220 0.0257048i −0.477574 0.878592i \(-0.658484\pi\)
0.522096 + 0.852887i \(0.325150\pi\)
\(242\) 5.41489 9.37887i 0.348082 0.602896i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −6.46982 3.73535i −0.414188 0.239132i
\(245\) −21.9711 + 19.7975i −1.40368 + 1.26482i
\(246\) 2.91286 1.68174i 0.185717 0.107224i
\(247\) 4.55143 + 2.62777i 0.289601 + 0.167201i
\(248\) 6.51360i 0.413614i
\(249\) 3.90968 0.247766
\(250\) 11.1178 1.18096i 0.703151 0.0746902i
\(251\) 13.7566i 0.868306i 0.900839 + 0.434153i \(0.142952\pi\)
−0.900839 + 0.434153i \(0.857048\pi\)
\(252\) −3.89483 + 2.24868i −0.245351 + 0.141654i
\(253\) −0.674830 −0.0424262
\(254\) −7.90697 + 4.56509i −0.496127 + 0.286439i
\(255\) 2.25374 6.94500i 0.141135 0.434913i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.61645 + 16.6562i −0.599858 + 1.03898i 0.392984 + 0.919545i \(0.371443\pi\)
−0.992842 + 0.119439i \(0.961890\pi\)
\(258\) 9.32116i 0.580310i
\(259\) 14.9807 22.8900i 0.930856 1.42231i
\(260\) −3.66286 + 3.30049i −0.227161 + 0.204688i
\(261\) −7.93502 4.58129i −0.491165 0.283574i
\(262\) 9.85183 5.68796i 0.608648 0.351403i
\(263\) 5.05664 2.91945i 0.311806 0.180021i −0.335929 0.941887i \(-0.609050\pi\)
0.647734 + 0.761866i \(0.275717\pi\)
\(264\) 0.357299 0.206287i 0.0219903 0.0126961i
\(265\) −17.4437 19.3588i −1.07156 1.18920i
\(266\) 5.35969 + 9.28325i 0.328624 + 0.569193i
\(267\) −2.88298 −0.176436
\(268\) −2.71578 1.56796i −0.165893 0.0957782i
\(269\) −21.9627 −1.33909 −0.669545 0.742771i \(-0.733511\pi\)
−0.669545 + 0.742771i \(0.733511\pi\)
\(270\) −1.49683 1.66117i −0.0910944 0.101096i
\(271\) −1.50615 + 2.60873i −0.0914920 + 0.158469i −0.908139 0.418668i \(-0.862497\pi\)
0.816647 + 0.577137i \(0.195830\pi\)
\(272\) −1.63267 2.82787i −0.0989953 0.171465i
\(273\) 9.91661 0.600180
\(274\) 2.14262 + 1.23704i 0.129441 + 0.0747325i
\(275\) 1.66979 + 1.21129i 0.100692 + 0.0730438i
\(276\) 1.41652 + 0.817829i 0.0852646 + 0.0492275i
\(277\) 7.28820 + 12.6235i 0.437905 + 0.758475i 0.997528 0.0702733i \(-0.0223871\pi\)
−0.559622 + 0.828748i \(0.689054\pi\)
\(278\) 9.45191 + 16.3712i 0.566888 + 0.981879i
\(279\) −5.64095 3.25680i −0.337715 0.194980i
\(280\) −9.83588 + 2.09447i −0.587806 + 0.125168i
\(281\) 12.4391 + 7.18169i 0.742052 + 0.428424i 0.822815 0.568310i \(-0.192402\pi\)
−0.0807631 + 0.996733i \(0.525736\pi\)
\(282\) 6.71516 0.399882
\(283\) 13.5334 + 23.4405i 0.804478 + 1.39340i 0.916643 + 0.399706i \(0.130888\pi\)
−0.112166 + 0.993690i \(0.535779\pi\)
\(284\) −1.01489 + 1.75784i −0.0602227 + 0.104309i
\(285\) −3.95937 + 3.56768i −0.234533 + 0.211331i
\(286\) −0.909719 −0.0537928
\(287\) −13.1002 7.56340i −0.773280 0.446453i
\(288\) −1.00000 −0.0589256
\(289\) 3.16876 + 5.48845i 0.186397 + 0.322850i
\(290\) −13.7148 15.2206i −0.805364 0.893784i
\(291\) 9.46337 5.46368i 0.554753 0.320287i
\(292\) 5.69391 3.28738i 0.333211 0.192379i
\(293\) −15.0447 + 8.68606i −0.878920 + 0.507445i −0.870302 0.492518i \(-0.836077\pi\)
−0.00861800 + 0.999963i \(0.502743\pi\)
\(294\) 11.4543 + 6.61313i 0.668027 + 0.385685i
\(295\) −8.23192 9.13570i −0.479281 0.531901i
\(296\) 5.42955 2.74226i 0.315586 0.159391i
\(297\) 0.412574i 0.0239400i
\(298\) −3.99360 + 6.91711i −0.231343 + 0.400697i
\(299\) −1.80330 3.12341i −0.104288 0.180631i
\(300\) −2.03705 4.56623i −0.117609 0.263631i
\(301\) −36.3043 + 20.9603i −2.09255 + 1.20813i
\(302\) 4.30872 0.247939
\(303\) −14.9116 + 8.60920i −0.856647 + 0.494585i
\(304\) 2.38348i 0.136702i
\(305\) −16.3387 + 3.47919i −0.935551 + 0.199218i
\(306\) −3.26535 −0.186667
\(307\) 19.0895i 1.08949i −0.838600 0.544747i \(-0.816626\pi\)
0.838600 0.544747i \(-0.183374\pi\)
\(308\) −1.60690 0.927747i −0.0915619 0.0528633i
\(309\) −14.6387 + 8.45167i −0.832768 + 0.480799i
\(310\) −9.74978 10.8202i −0.553750 0.614547i
\(311\) 1.51782 + 0.876316i 0.0860679 + 0.0496913i 0.542416 0.840110i \(-0.317510\pi\)
−0.456348 + 0.889801i \(0.650843\pi\)
\(312\) 1.90957 + 1.10249i 0.108108 + 0.0624163i
\(313\) −3.08712 + 5.34705i −0.174495 + 0.302233i −0.939986 0.341212i \(-0.889162\pi\)
0.765492 + 0.643446i \(0.222496\pi\)
\(314\) 3.79620 2.19174i 0.214232 0.123687i
\(315\) −3.10407 + 9.56535i −0.174895 + 0.538947i
\(316\) 7.72926 + 4.46249i 0.434805 + 0.251035i
\(317\) 14.2460 + 8.22494i 0.800136 + 0.461959i 0.843519 0.537100i \(-0.180480\pi\)
−0.0433825 + 0.999059i \(0.513813\pi\)
\(318\) −5.82686 + 10.0924i −0.326754 + 0.565954i
\(319\) 3.78024i 0.211653i
\(320\) −2.12688 0.690199i −0.118896 0.0385833i
\(321\) 4.37708 7.58132i 0.244305 0.423148i
\(322\) 7.35614i 0.409942i
\(323\) 7.78289i 0.433052i
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −1.14434 + 10.9654i −0.0634764 + 0.608249i
\(326\) −8.00959 13.8730i −0.443610 0.768356i
\(327\) 11.1497 0.616582
\(328\) −1.68174 2.91286i −0.0928587 0.160836i
\(329\) −15.1002 26.1544i −0.832504 1.44194i
\(330\) 0.284758 0.877496i 0.0156754 0.0483046i
\(331\) 9.69676 + 5.59843i 0.532982 + 0.307717i 0.742230 0.670145i \(-0.233768\pi\)
−0.209248 + 0.977863i \(0.567102\pi\)
\(332\) 3.90968i 0.214571i
\(333\) 0.339909 6.07326i 0.0186269 0.332812i
\(334\) −13.3308 −0.729429
\(335\) −6.85834 + 1.46043i −0.374711 + 0.0797917i
\(336\) 2.24868 + 3.89483i 0.122676 + 0.212480i
\(337\) −26.6165 + 15.3670i −1.44989 + 0.837095i −0.998474 0.0552182i \(-0.982415\pi\)
−0.451417 + 0.892313i \(0.649081\pi\)
\(338\) 4.06902 + 7.04775i 0.221326 + 0.383347i
\(339\) 1.63405i 0.0887495i
\(340\) −6.94500 2.25374i −0.376646 0.122226i
\(341\) 2.68734i 0.145528i
\(342\) 2.06416 + 1.19174i 0.111617 + 0.0644420i
\(343\) 28.0017i 1.51195i
\(344\) −9.32116 −0.502563
\(345\) 3.57724 0.761743i 0.192592 0.0410109i
\(346\) −22.0473 + 12.7290i −1.18527 + 0.684315i
\(347\) −6.51035 −0.349494 −0.174747 0.984613i \(-0.555911\pi\)
−0.174747 + 0.984613i \(0.555911\pi\)
\(348\) −4.58129 + 7.93502i −0.245583 + 0.425362i
\(349\) −5.75901 + 9.97489i −0.308273 + 0.533944i −0.977985 0.208677i \(-0.933084\pi\)
0.669712 + 0.742621i \(0.266418\pi\)
\(350\) −13.2040 + 18.2019i −0.705783 + 0.972935i
\(351\) 1.90957 1.10249i 0.101925 0.0588467i
\(352\) −0.206287 0.357299i −0.0109951 0.0190441i
\(353\) −13.7639 + 23.8398i −0.732580 + 1.26887i 0.223197 + 0.974773i \(0.428351\pi\)
−0.955777 + 0.294093i \(0.904983\pi\)
\(354\) −2.74978 + 4.76276i −0.146149 + 0.253138i
\(355\) 0.945290 + 4.43920i 0.0501708 + 0.235608i
\(356\) 2.88298i 0.152798i
\(357\) 7.34272 + 12.7180i 0.388618 + 0.673106i
\(358\) −2.90714 1.67844i −0.153647 0.0887081i
\(359\) −10.4314 −0.550546 −0.275273 0.961366i \(-0.588768\pi\)
−0.275273 + 0.961366i \(0.588768\pi\)
\(360\) −1.66117 + 1.49683i −0.0875514 + 0.0788901i
\(361\) −6.65951 + 11.5346i −0.350500 + 0.607084i
\(362\) −9.70996 −0.510344
\(363\) −9.37887 + 5.41489i −0.492263 + 0.284208i
\(364\) 9.91661i 0.519772i
\(365\) 4.53789 13.9837i 0.237524 0.731942i
\(366\) 3.73535 + 6.46982i 0.195250 + 0.338183i
\(367\) −6.94787 + 4.01136i −0.362676 + 0.209391i −0.670254 0.742132i \(-0.733815\pi\)
0.307578 + 0.951523i \(0.400481\pi\)
\(368\) 0.817829 1.41652i 0.0426323 0.0738413i
\(369\) −3.36348 −0.175096
\(370\) 4.91470 12.6825i 0.255503 0.659332i
\(371\) 52.4109 2.72104
\(372\) −3.25680 + 5.64095i −0.168857 + 0.292469i
\(373\) 20.3157 11.7293i 1.05191 0.607318i 0.128724 0.991680i \(-0.458912\pi\)
0.923182 + 0.384362i \(0.125579\pi\)
\(374\) −0.673598 1.16671i −0.0348309 0.0603290i
\(375\) −10.2188 4.53616i −0.527695 0.234246i
\(376\) 6.71516i 0.346308i
\(377\) 17.4966 10.1017i 0.901120 0.520262i
\(378\) 4.49736 0.231319
\(379\) −8.83500 + 15.3027i −0.453823 + 0.786045i −0.998620 0.0525234i \(-0.983274\pi\)
0.544796 + 0.838568i \(0.316607\pi\)
\(380\) 3.56768 + 3.95937i 0.183018 + 0.203111i
\(381\) 9.13018 0.467753
\(382\) −16.2402 9.37630i −0.830923 0.479733i
\(383\) 11.8360 + 20.5006i 0.604793 + 1.04753i 0.992084 + 0.125575i \(0.0400775\pi\)
−0.387291 + 0.921957i \(0.626589\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −4.05803 + 0.864123i −0.206816 + 0.0440398i
\(386\) 12.8390 22.2379i 0.653490 1.13188i
\(387\) −4.66058 + 8.07236i −0.236911 + 0.410341i
\(388\) −5.46368 9.46337i −0.277376 0.480430i
\(389\) −12.3967 + 7.15722i −0.628536 + 0.362886i −0.780185 0.625549i \(-0.784875\pi\)
0.151649 + 0.988434i \(0.451542\pi\)
\(390\) 4.82237 1.02688i 0.244190 0.0519983i
\(391\) 2.67049 4.62543i 0.135053 0.233918i
\(392\) 6.61313 11.4543i 0.334013 0.578528i
\(393\) −11.3759 −0.573839
\(394\) −15.5562 + 8.98138i −0.783710 + 0.452475i
\(395\) 19.5192 4.15646i 0.982119 0.209134i
\(396\) −0.412574 −0.0207326
\(397\) 30.2416i 1.51778i 0.651218 + 0.758891i \(0.274258\pi\)
−0.651218 + 0.758891i \(0.725742\pi\)
\(398\) 7.03317 + 4.06060i 0.352541 + 0.203540i
\(399\) 10.7194i 0.536640i
\(400\) −4.56623 + 2.03705i −0.228311 + 0.101852i
\(401\) 3.30061i 0.164824i −0.996598 0.0824122i \(-0.973738\pi\)
0.996598 0.0824122i \(-0.0262624\pi\)
\(402\) 1.56796 + 2.71578i 0.0782025 + 0.135451i
\(403\) 12.4382 7.18120i 0.619591 0.357721i
\(404\) 8.60920 + 14.9116i 0.428324 + 0.741878i
\(405\) 0.465711 + 2.18703i 0.0231414 + 0.108675i
\(406\) 41.2074 2.04509
\(407\) 2.24009 1.13138i 0.111037 0.0560807i
\(408\) 3.26535i 0.161659i
\(409\) −24.6098 14.2085i −1.21688 0.702565i −0.252630 0.967563i \(-0.581295\pi\)
−0.964249 + 0.264998i \(0.914629\pi\)
\(410\) −7.15373 2.32147i −0.353298 0.114649i
\(411\) −1.23704 2.14262i −0.0610189 0.105688i
\(412\) 8.45167 + 14.6387i 0.416384 + 0.721198i
\(413\) 24.7335 1.21706
\(414\) −0.817829 1.41652i −0.0401941 0.0696182i
\(415\) −5.85214 6.49464i −0.287270 0.318809i
\(416\) 1.10249 1.90957i 0.0540541 0.0936245i
\(417\) 18.9038i 0.925724i
\(418\) 0.983363i 0.0480978i
\(419\) 2.15871 3.73900i 0.105460 0.182662i −0.808466 0.588543i \(-0.799702\pi\)
0.913926 + 0.405881i \(0.133035\pi\)
\(420\) 9.56535 + 3.10407i 0.466741 + 0.151463i
\(421\) 31.2190i 1.52152i 0.649034 + 0.760759i \(0.275173\pi\)
−0.649034 + 0.760759i \(0.724827\pi\)
\(422\) 4.23718 7.33901i 0.206263 0.357257i
\(423\) −5.81550 3.35758i −0.282759 0.163251i
\(424\) 10.0924 + 5.82686i 0.490131 + 0.282977i
\(425\) −14.9103 + 6.65167i −0.723256 + 0.322653i
\(426\) 1.75784 1.01489i 0.0851677 0.0491716i
\(427\) 16.7992 29.0971i 0.812972 1.40811i
\(428\) −7.58132 4.37708i −0.366457 0.211574i
\(429\) 0.787840 + 0.454859i 0.0380373 + 0.0219608i
\(430\) −15.4840 + 13.9522i −0.746707 + 0.672836i
\(431\) 19.5309 11.2762i 0.940770 0.543154i 0.0505684 0.998721i \(-0.483897\pi\)
0.890202 + 0.455567i \(0.150563\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 3.06164i 0.147133i −0.997290 0.0735664i \(-0.976562\pi\)
0.997290 0.0735664i \(-0.0234381\pi\)
\(434\) 29.2940 1.40616
\(435\) 4.26711 + 20.0388i 0.204592 + 0.960789i
\(436\) 11.1497i 0.533976i
\(437\) −3.37625 + 1.94928i −0.161508 + 0.0932467i
\(438\) −6.57476 −0.314154
\(439\) 3.33982 1.92824i 0.159401 0.0920301i −0.418178 0.908365i \(-0.637331\pi\)
0.577579 + 0.816335i \(0.303998\pi\)
\(440\) −0.877496 0.284758i −0.0418330 0.0135753i
\(441\) −6.61313 11.4543i −0.314911 0.545442i
\(442\) 3.60002 6.23541i 0.171235 0.296588i
\(443\) 25.4109i 1.20731i −0.797247 0.603654i \(-0.793711\pi\)
0.797247 0.603654i \(-0.206289\pi\)
\(444\) −6.07326 0.339909i −0.288224 0.0161313i
\(445\) 4.31535 + 4.78913i 0.204567 + 0.227026i
\(446\) 16.2112 + 9.35953i 0.767622 + 0.443187i
\(447\) 6.91711 3.99360i 0.327168 0.188891i
\(448\) 3.89483 2.24868i 0.184013 0.106240i
\(449\) 29.8241 17.2189i 1.40749 0.812612i 0.412340 0.911030i \(-0.364712\pi\)
0.995145 + 0.0984178i \(0.0313782\pi\)
\(450\) −0.518977 + 4.97299i −0.0244648 + 0.234429i
\(451\) −0.693843 1.20177i −0.0326718 0.0565892i
\(452\) −1.63405 −0.0768593
\(453\) −3.73146 2.15436i −0.175319 0.101221i
\(454\) −4.49650 −0.211031
\(455\) −14.8435 16.4732i −0.695875 0.772275i
\(456\) 1.19174 2.06416i 0.0558084 0.0966630i
\(457\) −0.681427 1.18027i −0.0318758 0.0552105i 0.849647 0.527351i \(-0.176815\pi\)
−0.881523 + 0.472141i \(0.843481\pi\)
\(458\) −20.3635 −0.951524
\(459\) 2.82787 + 1.63267i 0.131994 + 0.0762067i
\(460\) −0.761743 3.57724i −0.0355165 0.166790i
\(461\) −10.7687 6.21733i −0.501550 0.289570i 0.227803 0.973707i \(-0.426846\pi\)
−0.729353 + 0.684137i \(0.760179\pi\)
\(462\) 0.927747 + 1.60690i 0.0431627 + 0.0747600i
\(463\) −2.33045 4.03646i −0.108305 0.187590i 0.806778 0.590854i \(-0.201209\pi\)
−0.915084 + 0.403264i \(0.867876\pi\)
\(464\) 7.93502 + 4.58129i 0.368374 + 0.212681i
\(465\) 3.03345 + 14.2455i 0.140673 + 0.660618i
\(466\) 2.54674 + 1.47036i 0.117975 + 0.0681132i
\(467\) 24.9564 1.15484 0.577422 0.816446i \(-0.304059\pi\)
0.577422 + 0.816446i \(0.304059\pi\)
\(468\) −1.10249 1.90957i −0.0509627 0.0882700i
\(469\) 7.05166 12.2138i 0.325616 0.563983i
\(470\) −10.0515 11.1550i −0.463640 0.514543i
\(471\) −4.38347 −0.201980
\(472\) 4.76276 + 2.74978i 0.219224 + 0.126569i
\(473\) −3.84567 −0.176824
\(474\) −4.46249 7.72926i −0.204969 0.355017i
\(475\) 11.8530 + 1.23697i 0.543855 + 0.0567562i
\(476\) 12.7180 7.34272i 0.582927 0.336553i
\(477\) 10.0924 5.82686i 0.462100 0.266793i
\(478\) 8.01145 4.62541i 0.366435 0.211562i
\(479\) −10.0078 5.77801i −0.457268 0.264004i 0.253627 0.967302i \(-0.418377\pi\)
−0.710895 + 0.703298i \(0.751710\pi\)
\(480\) 1.49683 + 1.66117i 0.0683208 + 0.0758217i
\(481\) 11.2226 + 7.34480i 0.511706 + 0.334894i
\(482\) 0.798091i 0.0363520i
\(483\) −3.67807 + 6.37061i −0.167358 + 0.289873i
\(484\) 5.41489 + 9.37887i 0.246131 + 0.426312i
\(485\) −23.2412 7.54206i −1.05533 0.342467i
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 34.7877 1.57638 0.788190 0.615432i \(-0.211019\pi\)
0.788190 + 0.615432i \(0.211019\pi\)
\(488\) 6.46982 3.73535i 0.292875 0.169092i
\(489\) 16.0192i 0.724413i
\(490\) −6.15961 28.9263i −0.278263 1.30675i
\(491\) 4.56055 0.205815 0.102907 0.994691i \(-0.467186\pi\)
0.102907 + 0.994691i \(0.467186\pi\)
\(492\) 3.36348i 0.151638i
\(493\) 25.9106 + 14.9595i 1.16695 + 0.673741i
\(494\) −4.55143 + 2.62777i −0.204779 + 0.118229i
\(495\) −0.685356 + 0.617555i −0.0308044 + 0.0277570i
\(496\) 5.64095 + 3.25680i 0.253286 + 0.146235i
\(497\) −7.90565 4.56433i −0.354617 0.204738i
\(498\) −1.95484 + 3.38588i −0.0875984 + 0.151725i
\(499\) 3.45818 1.99658i 0.154809 0.0893792i −0.420594 0.907249i \(-0.638178\pi\)
0.575404 + 0.817870i \(0.304845\pi\)
\(500\) −4.53616 + 10.2188i −0.202863 + 0.456997i
\(501\) 11.5448 + 6.66540i 0.515784 + 0.297788i
\(502\) −11.9135 6.87828i −0.531727 0.306993i
\(503\) 11.2212 19.4356i 0.500327 0.866593i −0.499672 0.866214i \(-0.666546\pi\)
1.00000 0.000378200i \(-0.000120385\pi\)
\(504\) 4.49736i 0.200328i
\(505\) 36.6215 + 11.8841i 1.62963 + 0.528836i
\(506\) 0.337415 0.584420i 0.0149999 0.0259806i
\(507\) 8.13804i 0.361423i
\(508\) 9.13018i 0.405086i
\(509\) 16.6264 28.7978i 0.736952 1.27644i −0.216910 0.976192i \(-0.569598\pi\)
0.953862 0.300246i \(-0.0970689\pi\)
\(510\) 4.88768 + 5.42430i 0.216430 + 0.240192i
\(511\) 14.7845 + 25.6076i 0.654029 + 1.13281i
\(512\) 1.00000 0.0441942
\(513\) −1.19174 2.06416i −0.0526167 0.0911347i
\(514\) −9.61645 16.6562i −0.424164 0.734673i
\(515\) 35.9514 + 11.6667i 1.58421 + 0.514095i
\(516\) 8.07236 + 4.66058i 0.355366 + 0.205171i
\(517\) 2.77050i 0.121846i
\(518\) 12.3329 + 24.4186i 0.541878 + 1.07289i
\(519\) 25.4580 1.11748
\(520\) −1.02688 4.82237i −0.0450319 0.211475i
\(521\) −7.83325 13.5676i −0.343181 0.594407i 0.641841 0.766838i \(-0.278171\pi\)
−0.985022 + 0.172431i \(0.944838\pi\)
\(522\) 7.93502 4.58129i 0.347306 0.200517i
\(523\) 9.39805 + 16.2779i 0.410948 + 0.711783i 0.994994 0.0999381i \(-0.0318645\pi\)
−0.584046 + 0.811721i \(0.698531\pi\)
\(524\) 11.3759i 0.496959i
\(525\) 20.5360 9.16135i 0.896263 0.399834i
\(526\) 5.83890i 0.254588i
\(527\) 18.4196 + 10.6346i 0.802372 + 0.463250i
\(528\) 0.412574i 0.0179550i
\(529\) −20.3246 −0.883679
\(530\) 25.4871 5.42726i 1.10709 0.235745i
\(531\) 4.76276 2.74978i 0.206686 0.119330i
\(532\) −10.7194 −0.464744
\(533\) 3.70821 6.42282i 0.160621 0.278203i
\(534\) 1.44149 2.49674i 0.0623795 0.108044i
\(535\) −19.1456 + 4.07690i −0.827738 + 0.176260i
\(536\) 2.71578 1.56796i 0.117304 0.0677254i
\(537\) 1.67844 + 2.90714i 0.0724299 + 0.125452i
\(538\) 10.9814 19.0203i 0.473440 0.820022i
\(539\) 2.72840 4.72573i 0.117521 0.203552i
\(540\) 2.18703 0.465711i 0.0941149 0.0200410i
\(541\) 21.1376i 0.908776i 0.890804 + 0.454388i \(0.150142\pi\)
−0.890804 + 0.454388i \(0.849858\pi\)
\(542\) −1.50615 2.60873i −0.0646946 0.112054i
\(543\) 8.40907 + 4.85498i 0.360868 + 0.208347i
\(544\) 3.26535 0.140001
\(545\) −16.6893 18.5216i −0.714891 0.793379i
\(546\) −4.95830 + 8.58804i −0.212196 + 0.367534i
\(547\) 12.0432 0.514932 0.257466 0.966287i \(-0.417112\pi\)
0.257466 + 0.966287i \(0.417112\pi\)
\(548\) −2.14262 + 1.23704i −0.0915283 + 0.0528439i
\(549\) 7.47071i 0.318842i
\(550\) −1.88391 + 0.840433i −0.0803300 + 0.0358362i
\(551\) −10.9194 18.9130i −0.465183 0.805720i
\(552\) −1.41652 + 0.817829i −0.0602911 + 0.0348091i
\(553\) −20.0694 + 34.7613i −0.853439 + 1.47820i
\(554\) −14.5764 −0.619292
\(555\) −10.5975 + 8.52601i −0.449839 + 0.361909i
\(556\) −18.9038 −0.801701
\(557\) 9.83047 17.0269i 0.416530 0.721452i −0.579057 0.815287i \(-0.696579\pi\)
0.995588 + 0.0938350i \(0.0299126\pi\)
\(558\) 5.64095 3.25680i 0.238800 0.137871i
\(559\) −10.2765 17.7994i −0.434650 0.752836i
\(560\) 3.10407 9.56535i 0.131171 0.404210i
\(561\) 1.34720i 0.0568787i
\(562\) −12.4391 + 7.18169i −0.524710 + 0.302941i
\(563\) 40.6424 1.71287 0.856436 0.516252i \(-0.172673\pi\)
0.856436 + 0.516252i \(0.172673\pi\)
\(564\) −3.35758 + 5.81550i −0.141380 + 0.244877i
\(565\) −2.71444 + 2.44590i −0.114197 + 0.102900i
\(566\) −27.0668 −1.13770
\(567\) −3.89483 2.24868i −0.163567 0.0944357i
\(568\) −1.01489 1.75784i −0.0425838 0.0737574i
\(569\) 12.5423i 0.525799i −0.964823 0.262900i \(-0.915321\pi\)
0.964823 0.262900i \(-0.0846788\pi\)
\(570\) −1.11001 5.21275i −0.0464933 0.218338i
\(571\) −19.7682 + 34.2396i −0.827275 + 1.43288i 0.0728934 + 0.997340i \(0.476777\pi\)
−0.900168 + 0.435542i \(0.856557\pi\)
\(572\) 0.454859 0.787840i 0.0190186 0.0329412i
\(573\) 9.37630 + 16.2402i 0.391701 + 0.678446i
\(574\) 13.1002 7.56340i 0.546791 0.315690i
\(575\) −6.61992 4.80220i −0.276070 0.200266i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −16.0103 + 27.7306i −0.666516 + 1.15444i 0.312356 + 0.949965i \(0.398882\pi\)
−0.978872 + 0.204474i \(0.934452\pi\)
\(578\) −6.33751 −0.263606
\(579\) −22.2379 + 12.8390i −0.924174 + 0.533572i
\(580\) 20.0388 4.26711i 0.832068 0.177182i
\(581\) 17.5832 0.729475
\(582\) 10.9274i 0.452954i
\(583\) 4.16386 + 2.40401i 0.172450 + 0.0995639i
\(584\) 6.57476i 0.272065i
\(585\) −4.68974 1.52188i −0.193897 0.0629219i
\(586\) 17.3721i 0.717635i
\(587\) −23.6410 40.9474i −0.975769 1.69008i −0.677373 0.735639i \(-0.736882\pi\)
−0.298396 0.954442i \(-0.596451\pi\)
\(588\) −11.4543 + 6.61313i −0.472366 + 0.272721i
\(589\) −7.76253 13.4451i −0.319849 0.553995i
\(590\) 12.0277 2.56120i 0.495173 0.105443i
\(591\) 17.9628 0.738889
\(592\) −0.339909 + 6.07326i −0.0139702 + 0.249609i
\(593\) 33.0223i 1.35606i −0.735033 0.678032i \(-0.762833\pi\)
0.735033 0.678032i \(-0.237167\pi\)
\(594\) 0.357299 + 0.206287i 0.0146602 + 0.00846406i
\(595\) 10.1359 31.2342i 0.415531 1.28048i
\(596\) −3.99360 6.91711i −0.163584 0.283336i
\(597\) −4.06060 7.03317i −0.166189 0.287848i
\(598\) 3.60660 0.147485
\(599\) 7.17181 + 12.4219i 0.293032 + 0.507547i 0.974525 0.224278i \(-0.0720024\pi\)
−0.681493 + 0.731825i \(0.738669\pi\)
\(600\) 4.97299 + 0.518977i 0.203022 + 0.0211871i
\(601\) 15.3756 26.6314i 0.627185 1.08632i −0.360929 0.932593i \(-0.617540\pi\)
0.988114 0.153723i \(-0.0491263\pi\)
\(602\) 41.9206i 1.70856i
\(603\) 3.13591i 0.127704i
\(604\) −2.15436 + 3.73146i −0.0876597 + 0.151831i
\(605\) 23.0337 + 7.47471i 0.936452 + 0.303890i
\(606\) 17.2184i 0.699449i
\(607\) −9.17110 + 15.8848i −0.372243 + 0.644745i −0.989910 0.141695i \(-0.954745\pi\)
0.617667 + 0.786440i \(0.288078\pi\)
\(608\) −2.06416 1.19174i −0.0837126 0.0483315i
\(609\) −35.6866 20.6037i −1.44610 0.834904i
\(610\) 5.15628 15.8893i 0.208772 0.643340i
\(611\) 12.8231 7.40341i 0.518766 0.299510i
\(612\) 1.63267 2.82787i 0.0659969 0.114310i
\(613\) 16.8714 + 9.74069i 0.681429 + 0.393423i 0.800393 0.599476i \(-0.204624\pi\)
−0.118965 + 0.992899i \(0.537957\pi\)
\(614\) 16.5320 + 9.54474i 0.667176 + 0.385194i
\(615\) 5.03458 + 5.58732i 0.203014 + 0.225303i
\(616\) 1.60690 0.927747i 0.0647440 0.0373800i
\(617\) 26.0408 + 15.0346i 1.04836 + 0.605272i 0.922190 0.386737i \(-0.126398\pi\)
0.126171 + 0.992008i \(0.459731\pi\)
\(618\) 16.9033i 0.679952i
\(619\) −25.2132 −1.01340 −0.506702 0.862121i \(-0.669135\pi\)
−0.506702 + 0.862121i \(0.669135\pi\)
\(620\) 14.2455 3.03345i 0.572112 0.121826i
\(621\) 1.63566i 0.0656367i
\(622\) −1.51782 + 0.876316i −0.0608592 + 0.0351371i
\(623\) −12.9658 −0.519465
\(624\) −1.90957 + 1.10249i −0.0764441 + 0.0441350i
\(625\) 7.76047 + 23.7650i 0.310419 + 0.950600i
\(626\) −3.08712 5.34705i −0.123386 0.213711i
\(627\) 0.491681 0.851617i 0.0196359 0.0340103i
\(628\) 4.38347i 0.174920i
\(629\) −1.10992 + 19.8313i −0.0442554 + 0.790725i
\(630\) −6.73180 7.47088i −0.268201 0.297647i
\(631\) −3.21095 1.85384i −0.127826 0.0738003i 0.434724 0.900564i \(-0.356846\pi\)
−0.562549 + 0.826764i \(0.690179\pi\)
\(632\) −7.72926 + 4.46249i −0.307454 + 0.177508i
\(633\) −7.33901 + 4.23718i −0.291699 + 0.168413i
\(634\) −14.2460 + 8.22494i −0.565782 + 0.326654i
\(635\) −13.6664 15.1668i −0.542333 0.601876i
\(636\) −5.82686 10.0924i −0.231050 0.400190i
\(637\) 29.1637 1.15551
\(638\) 3.27378 + 1.89012i 0.129610 + 0.0748305i
\(639\) −2.02978 −0.0802969
\(640\) 1.66117 1.49683i 0.0656635 0.0591676i
\(641\) −21.6941 + 37.5752i −0.856864 + 1.48413i 0.0180408 + 0.999837i \(0.494257\pi\)
−0.874905 + 0.484295i \(0.839076\pi\)
\(642\) 4.37708 + 7.58132i 0.172750 + 0.299211i
\(643\) −20.0324 −0.790003 −0.395001 0.918681i \(-0.629256\pi\)
−0.395001 + 0.918681i \(0.629256\pi\)
\(644\) 6.37061 + 3.67807i 0.251037 + 0.144936i
\(645\) 20.3857 4.34097i 0.802686 0.170925i
\(646\) −6.74018 3.89145i −0.265189 0.153107i
\(647\) −3.87468 6.71115i −0.152329 0.263842i 0.779754 0.626086i \(-0.215344\pi\)
−0.932083 + 0.362244i \(0.882011\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 1.96499 + 1.13449i 0.0771326 + 0.0445325i
\(650\) −8.92412 6.47371i −0.350033 0.253920i
\(651\) −25.3694 14.6470i −0.994304 0.574062i
\(652\) 16.0192 0.627360
\(653\) −16.5210 28.6152i −0.646516 1.11980i −0.983949 0.178449i \(-0.942892\pi\)
0.337433 0.941350i \(-0.390441\pi\)
\(654\) −5.57487 + 9.65596i −0.217995 + 0.377578i
\(655\) 17.0279 + 18.8973i 0.665333 + 0.738380i
\(656\) 3.36348 0.131322
\(657\) 5.69391 + 3.28738i 0.222140 + 0.128253i
\(658\) 30.2005 1.17734
\(659\) 7.97035 + 13.8051i 0.310481 + 0.537768i 0.978467 0.206406i \(-0.0661766\pi\)
−0.667986 + 0.744174i \(0.732843\pi\)
\(660\) 0.617555 + 0.685356i 0.0240383 + 0.0266774i
\(661\) 22.0245 12.7158i 0.856653 0.494589i −0.00623711 0.999981i \(-0.501985\pi\)
0.862890 + 0.505392i \(0.168652\pi\)
\(662\) −9.69676 + 5.59843i −0.376875 + 0.217589i
\(663\) −6.23541 + 3.60002i −0.242163 + 0.139813i
\(664\) 3.38588 + 1.95484i 0.131398 + 0.0758625i
\(665\) −17.8067 + 16.0451i −0.690515 + 0.622203i
\(666\) 5.08964 + 3.33100i 0.197220 + 0.129074i
\(667\) 14.9868i 0.580292i
\(668\) 6.66540 11.5448i 0.257892 0.446682i
\(669\) −9.35953 16.2112i −0.361860 0.626761i
\(670\) 2.16440 6.66971i 0.0836182 0.257674i
\(671\) 2.66928 1.54111i 0.103046 0.0594939i
\(672\) −4.49736 −0.173489
\(673\) −29.2455 + 16.8849i −1.12733 + 0.650866i −0.943263 0.332047i \(-0.892261\pi\)
−0.184070 + 0.982913i \(0.558927\pi\)
\(674\) 30.7340i 1.18383i
\(675\) 2.93594 4.04725i 0.113005 0.155779i
\(676\) −8.13804 −0.313002
\(677\) 15.8792i 0.610288i 0.952306 + 0.305144i \(0.0987045\pi\)
−0.952306 + 0.305144i \(0.901295\pi\)
\(678\) 1.41513 + 0.817025i 0.0543477 + 0.0313777i
\(679\) 42.5602 24.5721i 1.63331 0.942992i
\(680\) 5.42430 4.88768i 0.208012 0.187434i
\(681\) 3.89408 + 2.24825i 0.149222 + 0.0861531i
\(682\) 2.32731 + 1.34367i 0.0891172 + 0.0514518i
\(683\) −16.4618 + 28.5127i −0.629894 + 1.09101i 0.357678 + 0.933845i \(0.383569\pi\)
−0.987572 + 0.157164i \(0.949765\pi\)
\(684\) −2.06416 + 1.19174i −0.0789250 + 0.0455674i
\(685\) −1.70761 + 5.26209i −0.0652445 + 0.201054i
\(686\) 24.2502 + 14.0009i 0.925877 + 0.534555i
\(687\) 17.6353 + 10.1818i 0.672829 + 0.388458i
\(688\) 4.66058 8.07236i 0.177683 0.307756i
\(689\) 25.6962i 0.978949i
\(690\) −1.12893 + 3.47885i −0.0429776 + 0.132438i
\(691\) −18.6030 + 32.2214i −0.707693 + 1.22576i 0.258018 + 0.966140i \(0.416930\pi\)
−0.965711 + 0.259619i \(0.916403\pi\)
\(692\) 25.4580i 0.967768i
\(693\) 1.85549i 0.0704844i
\(694\) 3.25518 5.63813i 0.123565 0.214020i
\(695\) −31.4025 + 28.2959i −1.19116 + 1.07332i
\(696\) −4.58129 7.93502i −0.173653 0.300776i
\(697\) 10.9829 0.416008
\(698\) −5.75901 9.97489i −0.217982 0.377555i
\(699\) −1.47036 2.54674i −0.0556142 0.0963266i
\(700\) −9.16135 20.5360i −0.346266 0.776187i
\(701\) 7.57252 + 4.37200i 0.286010 + 0.165128i 0.636141 0.771573i \(-0.280530\pi\)
−0.350131 + 0.936701i \(0.613863\pi\)
\(702\) 2.20498i 0.0832218i
\(703\) 7.93938 12.1311i 0.299439 0.457532i
\(704\) 0.412574 0.0155495
\(705\) 3.12732 + 14.6863i 0.117782 + 0.553117i
\(706\) −13.7639 23.8398i −0.518012 0.897224i
\(707\) −67.0627 + 38.7187i −2.52215 + 1.45617i
\(708\) −2.74978 4.76276i −0.103343 0.178995i
\(709\) 8.59568i 0.322817i −0.986888 0.161409i \(-0.948396\pi\)
0.986888 0.161409i \(-0.0516037\pi\)
\(710\) −4.31710 1.40095i −0.162018 0.0525768i
\(711\) 8.92498i 0.334713i
\(712\) −2.49674 1.44149i −0.0935692 0.0540222i
\(713\) 10.6540i 0.398996i
\(714\) −14.6854 −0.549589
\(715\) −0.423666 1.98959i −0.0158442 0.0744063i
\(716\) 2.90714 1.67844i 0.108645 0.0627261i
\(717\) −9.25083 −0.345478
\(718\) 5.21568 9.03383i 0.194648 0.337139i
\(719\) −18.9145 + 32.7608i −0.705391 + 1.22177i 0.261160 + 0.965296i \(0.415895\pi\)
−0.966550 + 0.256477i \(0.917438\pi\)
\(720\) −0.465711 2.18703i −0.0173560 0.0815059i
\(721\) −65.8356 + 38.0102i −2.45185 + 1.41557i
\(722\) −6.65951 11.5346i −0.247841 0.429273i
\(723\) 0.399045 0.691167i 0.0148407 0.0257048i
\(724\) 4.85498 8.40907i 0.180434 0.312521i
\(725\) 26.9008 37.0832i 0.999071 1.37724i
\(726\) 10.8298i 0.401931i
\(727\) 11.9500 + 20.6980i 0.443200 + 0.767646i 0.997925 0.0643884i \(-0.0205096\pi\)
−0.554724 + 0.832034i \(0.687176\pi\)
\(728\) 8.58804 + 4.95830i 0.318294 + 0.183767i
\(729\) −1.00000 −0.0370370
\(730\) 9.84132 + 10.9218i 0.364244 + 0.404234i
\(731\) 15.2184 26.3591i 0.562873 0.974925i
\(732\) −7.47071 −0.276125
\(733\) −18.4978 + 10.6797i −0.683233 + 0.394465i −0.801072 0.598568i \(-0.795737\pi\)
0.117839 + 0.993033i \(0.462403\pi\)
\(734\) 8.02271i 0.296124i
\(735\) −9.12875 + 28.1307i −0.336719 + 1.03762i
\(736\) 0.817829 + 1.41652i 0.0301456 + 0.0522137i
\(737\) 1.12046 0.646898i 0.0412727 0.0238288i
\(738\) 1.68174 2.91286i 0.0619058 0.107224i
\(739\) 40.7382 1.49858 0.749289 0.662243i \(-0.230396\pi\)
0.749289 + 0.662243i \(0.230396\pi\)
\(740\) 8.52601 + 10.5975i 0.313422 + 0.389572i
\(741\) 5.25554 0.193067
\(742\) −26.2055 + 45.3892i −0.962033 + 1.66629i
\(743\) −17.7672 + 10.2579i −0.651816 + 0.376326i −0.789152 0.614199i \(-0.789479\pi\)
0.137336 + 0.990525i \(0.456146\pi\)
\(744\) −3.25680 5.64095i −0.119400 0.206807i
\(745\) −16.9878 5.51275i −0.622385 0.201972i
\(746\) 23.4585i 0.858878i
\(747\) 3.38588 1.95484i 0.123883 0.0715238i
\(748\) 1.34720 0.0492584
\(749\) 19.6853 34.0959i 0.719285 1.24584i
\(750\) 9.03781 6.58164i 0.330014 0.240327i
\(751\) 37.7421 1.37723 0.688614 0.725128i \(-0.258219\pi\)
0.688614 + 0.725128i \(0.258219\pi\)
\(752\) 5.81550 + 3.35758i 0.212069 + 0.122438i
\(753\) 6.87828 + 11.9135i 0.250658 + 0.434153i
\(754\) 20.2033i 0.735762i
\(755\) 2.00662 + 9.42331i 0.0730283 + 0.342949i
\(756\) −2.24868 + 3.89483i −0.0817837 + 0.141654i
\(757\) 16.4384 28.4721i 0.597462 1.03484i −0.395732 0.918366i \(-0.629509\pi\)
0.993194 0.116469i \(-0.0371576\pi\)
\(758\) −8.83500 15.3027i −0.320901 0.555818i
\(759\) −0.584420 + 0.337415i −0.0212131 + 0.0122474i
\(760\) −5.21275 + 1.11001i −0.189086 + 0.0402644i
\(761\) 9.42311 16.3213i 0.341587 0.591647i −0.643140 0.765748i \(-0.722369\pi\)
0.984728 + 0.174102i \(0.0557021\pi\)
\(762\) −4.56509 + 7.90697i −0.165376 + 0.286439i
\(763\) 50.1444 1.81535
\(764\) 16.2402 9.37630i 0.587551 0.339223i
\(765\) −1.52071 7.14142i −0.0549813 0.258199i
\(766\) −23.6721 −0.855306
\(767\) 12.1264i 0.437860i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) 11.5220i 0.415493i −0.978183 0.207746i \(-0.933387\pi\)
0.978183 0.207746i \(-0.0666129\pi\)
\(770\) 1.28066 3.94642i 0.0461518 0.142219i
\(771\) 19.2329i 0.692656i
\(772\) 12.8390 + 22.2379i 0.462087 + 0.800358i
\(773\) −22.3027 + 12.8765i −0.802173 + 0.463135i −0.844230 0.535980i \(-0.819942\pi\)
0.0420574 + 0.999115i \(0.486609\pi\)
\(774\) −4.66058 8.07236i −0.167521 0.290155i
\(775\) 19.1236 26.3622i 0.686939 0.946958i
\(776\) 10.9274 0.392269
\(777\) 1.52869 27.3136i 0.0548415 0.979871i
\(778\) 14.3144i 0.513198i
\(779\) −6.94276 4.00840i −0.248750 0.143616i
\(780\) −1.52188 + 4.68974i −0.0544920 + 0.167920i
\(781\) −0.418717 0.725240i −0.0149829 0.0259511i
\(782\) 2.67049 + 4.62543i 0.0954967 + 0.165405i
\(783\) −9.16257 −0.327444
\(784\) 6.61313 + 11.4543i 0.236183 + 0.409081i
\(785\) 6.56133 + 7.28170i 0.234184 + 0.259895i
\(786\) 5.68796 9.85183i 0.202883 0.351403i
\(787\) 44.7546i 1.59533i −0.603102 0.797664i \(-0.706069\pi\)
0.603102 0.797664i \(-0.293931\pi\)
\(788\) 17.9628i 0.639897i
\(789\) 2.91945 5.05664i 0.103935 0.180021i
\(790\) −6.16002 + 18.9824i −0.219164 + 0.675363i
\(791\) 7.34892i 0.261297i
\(792\) 0.206287 0.357299i 0.00733009 0.0126961i
\(793\) 14.2659 + 8.23640i 0.506596 + 0.292483i
\(794\) −26.1900 15.1208i −0.929448 0.536617i
\(795\) −24.7861 8.04338i −0.879071 0.285269i
\(796\) −7.03317 + 4.06060i −0.249284 + 0.143924i
\(797\) 25.3243 43.8629i 0.897031 1.55370i 0.0657607 0.997835i \(-0.479053\pi\)
0.831270 0.555868i \(-0.187614\pi\)
\(798\) 9.28325 + 5.35969i 0.328624 + 0.189731i
\(799\) 18.9896 + 10.9637i 0.671804 + 0.387866i
\(800\) 0.518977 4.97299i 0.0183486 0.175822i
\(801\) −2.49674 + 1.44149i −0.0882179 + 0.0509326i
\(802\) 2.85841 + 1.65030i 0.100934 + 0.0582742i
\(803\) 2.71257i 0.0957246i
\(804\) −3.13591 −0.110595
\(805\) 16.0881 3.42583i 0.567032 0.120745i
\(806\) 14.3624i 0.505894i
\(807\) −19.0203 + 10.9814i −0.669545 + 0.386562i
\(808\) −17.2184 −0.605741
\(809\) 30.4793 17.5972i 1.07160 0.618686i 0.142979 0.989726i \(-0.454332\pi\)
0.928617 + 0.371040i \(0.120999\pi\)
\(810\) −2.12688 0.690199i −0.0747310 0.0242511i
\(811\) −24.7519 42.8716i −0.869158 1.50543i −0.862858 0.505446i \(-0.831328\pi\)
−0.00629997 0.999980i \(-0.502005\pi\)
\(812\) −20.6037 + 35.6866i −0.723048 + 1.25236i
\(813\) 3.01230i 0.105646i
\(814\) −0.140237 + 2.50567i −0.00491532 + 0.0878236i
\(815\) 26.6106 23.9781i 0.932129 0.839915i
\(816\) −2.82787 1.63267i −0.0989953 0.0571550i
\(817\) −19.2403 + 11.1084i −0.673134 + 0.388634i
\(818\) 24.6098 14.2085i 0.860463 0.496789i
\(819\) 8.58804 4.95830i 0.300090 0.173257i
\(820\) 5.58732 5.03458i 0.195118 0.175815i
\(821\) 12.3439 + 21.3802i 0.430804 + 0.746174i 0.996943 0.0781356i \(-0.0248967\pi\)
−0.566139 + 0.824310i \(0.691563\pi\)
\(822\) 2.47409 0.0862937
\(823\) −19.9965 11.5450i −0.697036 0.402434i 0.109207 0.994019i \(-0.465169\pi\)
−0.806242 + 0.591585i \(0.798502\pi\)
\(824\) −16.9033 −0.588856
\(825\) 2.05173 + 0.214116i 0.0714320 + 0.00745458i
\(826\) −12.3667 + 21.4198i −0.430294 + 0.745291i
\(827\) −26.9683 46.7104i −0.937779 1.62428i −0.769603 0.638523i \(-0.779546\pi\)
−0.168176 0.985757i \(-0.553788\pi\)
\(828\) 1.63566 0.0568430
\(829\) 4.52451 + 2.61222i 0.157143 + 0.0907263i 0.576509 0.817091i \(-0.304414\pi\)
−0.419367 + 0.907817i \(0.637748\pi\)
\(830\) 8.55059 1.82078i 0.296795 0.0632002i
\(831\) 12.6235 + 7.28820i 0.437905 + 0.252825i
\(832\) 1.10249 + 1.90957i 0.0382220 + 0.0662025i
\(833\) 21.5941 + 37.4022i 0.748193 + 1.29591i
\(834\) 16.3712 + 9.45191i 0.566888 + 0.327293i
\(835\) −6.20830 29.1549i −0.214847 1.00895i
\(836\) −0.851617 0.491681i −0.0294538 0.0170052i
\(837\) −6.51360 −0.225143
\(838\) 2.15871 + 3.73900i 0.0745715 + 0.129162i
\(839\) 9.37644 16.2405i 0.323711 0.560684i −0.657540 0.753420i \(-0.728403\pi\)
0.981251 + 0.192736i \(0.0617362\pi\)
\(840\) −7.47088 + 6.73180i −0.257770 + 0.232269i
\(841\) −54.9527 −1.89492
\(842\) −27.0364 15.6095i −0.931736 0.537938i
\(843\) 14.3634 0.494701
\(844\) 4.23718 + 7.33901i 0.145850 + 0.252619i
\(845\) −13.5187 + 12.1813i −0.465057 + 0.419049i
\(846\) 5.81550 3.35758i 0.199941 0.115436i
\(847\) −42.1801 + 24.3527i −1.44933 + 0.836769i
\(848\) −10.0924 + 5.82686i −0.346575 + 0.200095i
\(849\) 23.4405 + 13.5334i 0.804478 + 0.464465i
\(850\) 1.69464 16.2385i 0.0581257 0.556977i
\(851\) −8.88089 + 4.48540i −0.304433 + 0.153757i
\(852\) 2.02978i 0.0695391i
\(853\) −13.8286 + 23.9518i −0.473482 + 0.820095i −0.999539 0.0303541i \(-0.990337\pi\)
0.526057 + 0.850449i \(0.323670\pi\)
\(854\) 16.7992 + 29.0971i 0.574858 + 0.995683i
\(855\) −1.64508 + 5.06938i −0.0562605 + 0.173369i
\(856\) 7.58132 4.37708i 0.259124 0.149605i
\(857\) 45.7437 1.56257 0.781287 0.624172i \(-0.214563\pi\)
0.781287 + 0.624172i \(0.214563\pi\)
\(858\) −0.787840 + 0.454859i −0.0268964 + 0.0155286i
\(859\) 38.2079i 1.30364i −0.758375 0.651819i \(-0.774006\pi\)
0.758375 0.651819i \(-0.225994\pi\)
\(860\) −4.34097 20.3857i −0.148026 0.695146i
\(861\) −15.1268 −0.515520
\(862\) 22.5523i 0.768135i
\(863\) 0.812686 + 0.469204i 0.0276642 + 0.0159719i 0.513768 0.857929i \(-0.328249\pi\)
−0.486104 + 0.873901i \(0.661582\pi\)
\(864\) −0.866025 + 0.500000i −0.0294628 + 0.0170103i
\(865\) −38.1064 42.2901i −1.29566 1.43791i
\(866\) 2.65145 + 1.53082i 0.0901001 + 0.0520193i
\(867\) 5.48845 + 3.16876i 0.186397 + 0.107617i
\(868\) −14.6470 + 25.3694i −0.497152 + 0.861093i
\(869\) −3.18889 + 1.84111i −0.108176 + 0.0624553i
\(870\) −19.4877 6.32400i −0.660695 0.214404i
\(871\) 5.98825 + 3.45732i 0.202904 + 0.117147i
\(872\) 9.65596 + 5.57487i 0.326992 + 0.188789i
\(873\) 5.46368 9.46337i 0.184918 0.320287i
\(874\) 3.89856i 0.131871i
\(875\) −45.9575 20.4007i −1.55365 0.689671i
\(876\) 3.28738 5.69391i 0.111070 0.192379i
\(877\) 7.26127i 0.245196i 0.992456 + 0.122598i \(0.0391225\pi\)
−0.992456 + 0.122598i \(0.960877\pi\)
\(878\) 3.85649i 0.130150i
\(879\) −8.68606 + 15.0447i −0.292973 + 0.507445i
\(880\) 0.685356 0.617555i 0.0231033 0.0208178i
\(881\) −20.2490 35.0723i −0.682206 1.18161i −0.974306 0.225227i \(-0.927688\pi\)
0.292101 0.956388i \(-0.405646\pi\)
\(882\) 13.2263 0.445351
\(883\) 20.9204 + 36.2352i 0.704028 + 1.21941i 0.967041 + 0.254619i \(0.0819502\pi\)
−0.263014 + 0.964792i \(0.584716\pi\)
\(884\) 3.60002 + 6.23541i 0.121082 + 0.209720i
\(885\) −11.6969 3.79579i −0.393187 0.127594i
\(886\) 22.0065 + 12.7054i 0.739322 + 0.426848i
\(887\) 45.9708i 1.54355i 0.635896 + 0.771775i \(0.280631\pi\)
−0.635896 + 0.771775i \(0.719369\pi\)
\(888\) 3.33100 5.08964i 0.111781 0.170797i
\(889\) 41.0617 1.37717
\(890\) −6.30518 + 1.34264i −0.211350 + 0.0450053i
\(891\) −0.206287 0.357299i −0.00691087 0.0119700i
\(892\) −16.2112 + 9.35953i −0.542791 + 0.313380i
\(893\) −8.00273 13.8611i −0.267801 0.463845i
\(894\) 7.98719i 0.267132i
\(895\) 2.31691 7.13967i 0.0774458 0.238653i
\(896\) 4.49736i 0.150246i
\(897\) −3.12341 1.80330i −0.104288 0.0602104i
\(898\) 34.4379i 1.14921i
\(899\) −59.6814 −1.99048
\(900\) −4.04725 2.93594i −0.134908 0.0978648i
\(901\) −32.9552 + 19.0267i −1.09790 + 0.633871i
\(902\) 1.38769 0.0462049
\(903\) −20.9603 + 36.3043i −0.697516 + 1.20813i
\(904\) 0.817025 1.41513i 0.0271739 0.0470665i
\(905\) −4.52203 21.2360i −0.150317 0.705909i
\(906\) 3.73146 2.15436i 0.123969 0.0715738i
\(907\) −22.9264 39.7096i −0.761257 1.31854i −0.942203 0.335043i \(-0.891249\pi\)
0.180945 0.983493i \(-0.442084\pi\)
\(908\) 2.24825 3.89408i 0.0746108 0.129230i
\(909\) −8.60920 + 14.9116i −0.285549 + 0.494585i
\(910\) 21.6880 4.61827i 0.718949 0.153094i
\(911\) 27.2436i 0.902621i −0.892367 0.451311i \(-0.850957\pi\)
0.892367 0.451311i \(-0.149043\pi\)
\(912\) 1.19174 + 2.06416i 0.0394625 + 0.0683510i
\(913\) 1.39693 + 0.806515i 0.0462315 + 0.0266918i
\(914\) 1.36285 0.0450792
\(915\) −12.4101 + 11.1824i −0.410266 + 0.369679i
\(916\) 10.1818 17.6353i 0.336415 0.582687i
\(917\) −51.1616 −1.68950
\(918\) −2.82787 + 1.63267i −0.0933337 + 0.0538862i
\(919\) 8.75052i 0.288653i 0.989530 + 0.144326i \(0.0461015\pi\)
−0.989530 + 0.144326i \(0.953898\pi\)
\(920\) 3.47885 + 1.12893i 0.114694 + 0.0372197i
\(921\) −9.54474 16.5320i −0.314510 0.544747i
\(922\) 10.7687 6.21733i 0.354649 0.204757i
\(923\) 2.23782 3.87601i 0.0736586 0.127581i
\(924\) −1.85549 −0.0610413
\(925\) 30.0259 + 4.84224i 0.987244 + 0.159212i
\(926\) 4.66091 0.153167
\(927\) −8.45167 + 14.6387i −0.277589 + 0.480799i
\(928\) −7.93502 + 4.58129i −0.260480 + 0.150388i
\(929\) 9.61913 + 16.6608i 0.315593 + 0.546624i 0.979563 0.201135i \(-0.0644631\pi\)
−0.663970 + 0.747759i \(0.731130\pi\)
\(930\) −13.8537 4.49568i −0.454280 0.147419i
\(931\) 31.5245i 1.03318i
\(932\) −2.54674 + 1.47036i −0.0834213 + 0.0481633i
\(933\) 1.75263 0.0573786
\(934\) −12.4782 + 21.6129i −0.408299 + 0.707194i
\(935\) 2.23792 2.01653i 0.0731879 0.0659476i
\(936\) 2.20498 0.0720722
\(937\) −22.5574 13.0235i −0.736917 0.425459i 0.0840301 0.996463i \(-0.473221\pi\)
−0.820947 + 0.571004i \(0.806554\pi\)
\(938\) 7.05166 + 12.2138i 0.230245 + 0.398796i
\(939\) 6.17425i 0.201489i
\(940\) 14.6863 3.12732i 0.479013 0.102002i
\(941\) −0.822234 + 1.42415i −0.0268041 + 0.0464260i −0.879116 0.476607i \(-0.841866\pi\)
0.852312 + 0.523033i \(0.175200\pi\)
\(942\) 2.19174 3.79620i 0.0714107 0.123687i
\(943\) 2.75075 + 4.76445i 0.0895769 + 0.155152i
\(944\) −4.76276 + 2.74978i −0.155015 + 0.0894977i
\(945\) 2.09447 + 9.83588i 0.0681331 + 0.319961i
\(946\) 1.92283 3.33045i 0.0625167 0.108282i
\(947\) −20.1455 + 34.8931i −0.654641 + 1.13387i 0.327342 + 0.944906i \(0.393847\pi\)
−0.981984 + 0.188966i \(0.939486\pi\)
\(948\) 8.92498 0.289870
\(949\) −12.5550 + 7.24862i −0.407552 + 0.235300i
\(950\) −6.99777 + 9.64655i −0.227038 + 0.312975i
\(951\) 16.4499 0.533424
\(952\) 14.6854i 0.475958i
\(953\) −17.7933 10.2730i −0.576381 0.332774i 0.183313 0.983055i \(-0.441318\pi\)
−0.759694 + 0.650281i \(0.774651\pi\)
\(954\) 11.6537i 0.377303i
\(955\) 12.9430 39.8846i 0.418827 1.29063i
\(956\) 9.25083i 0.299193i
\(957\) −1.89012 3.27378i −0.0610989 0.105826i
\(958\) 10.0078 5.77801i 0.323338 0.186679i
\(959\) −5.56343 9.63615i −0.179653 0.311167i
\(960\) −2.18703 + 0.465711i −0.0705862 + 0.0150307i
\(961\) −11.4270 −0.368614
\(962\) −11.9721 + 6.04664i −0.385995 + 0.194951i
\(963\) 8.75416i 0.282099i
\(964\) −0.691167 0.399045i −0.0222610 0.0128524i
\(965\) 54.6142 + 17.7230i 1.75809 + 0.570523i
\(966\) −3.67807 6.37061i −0.118340 0.204971i
\(967\) −22.3500 38.7114i −0.718729 1.24487i −0.961504 0.274792i \(-0.911391\pi\)
0.242775 0.970083i \(-0.421942\pi\)
\(968\) −10.8298 −0.348082
\(969\) 3.89145 + 6.74018i 0.125011 + 0.216526i
\(970\) 18.1522 16.3564i 0.582832 0.525174i
\(971\) −0.443756 + 0.768607i −0.0142408 + 0.0246658i −0.873058 0.487616i \(-0.837866\pi\)
0.858817 + 0.512282i \(0.171200\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 85.0173i 2.72553i
\(974\) −17.3938 + 30.1270i −0.557334 + 0.965331i
\(975\) 4.49166 + 10.0685i 0.143848 + 0.322449i
\(976\) 7.47071i 0.239132i
\(977\) −7.95604 + 13.7803i −0.254536 + 0.440870i −0.964769 0.263097i \(-0.915256\pi\)
0.710233 + 0.703967i \(0.248590\pi\)
\(978\) −13.8730 8.00959i −0.443610 0.256119i
\(979\) −1.03009 0.594722i −0.0329218 0.0190074i
\(980\) 28.1307 + 9.12875i 0.898601 + 0.291607i
\(981\) 9.65596 5.57487i 0.308291 0.177992i
\(982\) −2.28027 + 3.94955i −0.0727664 + 0.126035i
\(983\) −14.3688 8.29582i −0.458293 0.264596i 0.253033 0.967458i \(-0.418572\pi\)
−0.711326 + 0.702862i \(0.751905\pi\)
\(984\) −2.91286 1.68174i −0.0928587 0.0536120i
\(985\) −26.8873 29.8392i −0.856699 0.950756i
\(986\) −25.9106 + 14.9595i −0.825161 + 0.476407i
\(987\) −26.1544 15.1002i −0.832504 0.480646i
\(988\) 5.25554i 0.167201i
\(989\) 15.2462 0.484802
\(990\) −0.192140 0.902313i −0.00610661 0.0286774i
\(991\) 12.0478i 0.382710i −0.981521 0.191355i \(-0.938712\pi\)
0.981521 0.191355i \(-0.0612882\pi\)
\(992\) −5.64095 + 3.25680i −0.179100 + 0.103404i
\(993\) 11.1969 0.355321
\(994\) 7.90565 4.56433i 0.250752 0.144772i
\(995\) −5.60525 + 17.2728i −0.177698 + 0.547586i
\(996\) −1.95484 3.38588i −0.0619414 0.107286i
\(997\) −10.4395 + 18.0817i −0.330621 + 0.572653i −0.982634 0.185555i \(-0.940592\pi\)
0.652013 + 0.758208i \(0.273925\pi\)
\(998\) 3.99316i 0.126401i
\(999\) −2.74226 5.42955i −0.0867613 0.171783i
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 1110.2.ba.a.619.12 yes 36
5.4 even 2 1110.2.ba.b.619.7 yes 36
37.11 even 6 1110.2.ba.b.529.7 yes 36
185.159 even 6 inner 1110.2.ba.a.529.12 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.ba.a.529.12 36 185.159 even 6 inner
1110.2.ba.a.619.12 yes 36 1.1 even 1 trivial
1110.2.ba.b.529.7 yes 36 37.11 even 6
1110.2.ba.b.619.7 yes 36 5.4 even 2