Properties

Label 152.2.o.c.107.13
Level $152$
Weight $2$
Character 152.107
Analytic conductor $1.214$
Analytic rank $0$
Dimension $28$
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] = [152,2,Mod(27,152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(152, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.o (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: \(1.21372611072\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.13
Character \(\chi\) \(=\) 152.107
Dual form 152.2.o.c.27.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37418 + 0.334110i) q^{2} +(1.27630 - 0.736872i) q^{3} +(1.77674 + 0.918256i) q^{4} +(-2.34524 + 1.35403i) q^{5} +(2.00006 - 0.586169i) q^{6} -3.01597i q^{7} +(2.13476 + 1.85548i) q^{8} +(-0.414040 + 0.717138i) q^{9} +O(q^{10})\) \(q+(1.37418 + 0.334110i) q^{2} +(1.27630 - 0.736872i) q^{3} +(1.77674 + 0.918256i) q^{4} +(-2.34524 + 1.35403i) q^{5} +(2.00006 - 0.586169i) q^{6} -3.01597i q^{7} +(2.13476 + 1.85548i) q^{8} +(-0.414040 + 0.717138i) q^{9} +(-3.67518 + 1.07711i) q^{10} -3.11370 q^{11} +(2.94429 - 0.137261i) q^{12} +(0.218909 - 0.379162i) q^{13} +(1.00767 - 4.14449i) q^{14} +(-1.99549 + 3.45629i) q^{15} +(2.31361 + 3.26300i) q^{16} +(-3.22274 - 5.58194i) q^{17} +(-0.808569 + 0.847142i) q^{18} +(3.58731 + 2.47613i) q^{19} +(-5.41023 + 0.252221i) q^{20} +(-2.22238 - 3.84928i) q^{21} +(-4.27879 - 1.04032i) q^{22} +(-1.81421 - 1.04744i) q^{23} +(4.09184 + 0.795097i) q^{24} +(1.16678 - 2.02092i) q^{25} +(0.427502 - 0.447896i) q^{26} +5.64161i q^{27} +(2.76943 - 5.35860i) q^{28} +(-1.58443 + 2.74431i) q^{29} +(-3.89694 + 4.08285i) q^{30} +9.77556 q^{31} +(2.08912 + 5.25696i) q^{32} +(-3.97402 + 2.29440i) q^{33} +(-2.56363 - 8.74735i) q^{34} +(4.08371 + 7.07319i) q^{35} +(-1.39416 + 0.893974i) q^{36} -8.36258 q^{37} +(4.10230 + 4.60121i) q^{38} -0.645232i q^{39} +(-7.51890 - 1.46102i) q^{40} +(4.66208 - 2.69165i) q^{41} +(-1.76787 - 6.03213i) q^{42} +(-2.43347 - 4.21489i) q^{43} +(-5.53225 - 2.85918i) q^{44} -2.24248i q^{45} +(-2.14310 - 2.04551i) q^{46} +(-1.22865 - 0.709359i) q^{47} +(5.35728 + 2.45973i) q^{48} -2.09609 q^{49} +(2.27857 - 2.38727i) q^{50} +(-8.22635 - 4.74949i) q^{51} +(0.737112 - 0.472657i) q^{52} +(1.63792 - 2.83695i) q^{53} +(-1.88492 + 7.75258i) q^{54} +(7.30239 - 4.21604i) q^{55} +(5.59606 - 6.43838i) q^{56} +(6.40307 + 0.516904i) q^{57} +(-3.09420 + 3.24181i) q^{58} +(-1.70599 + 0.984956i) q^{59} +(-6.71922 + 4.30856i) q^{60} +(9.56035 + 5.51967i) q^{61} +(13.4334 + 3.26612i) q^{62} +(2.16287 + 1.24873i) q^{63} +(1.11442 + 7.92200i) q^{64} +1.18563i q^{65} +(-6.22760 + 1.82516i) q^{66} +(4.49875 + 2.59735i) q^{67} +(-0.600315 - 12.8770i) q^{68} -3.08731 q^{69} +(3.24852 + 11.0842i) q^{70} +(4.40927 + 7.63707i) q^{71} +(-2.21451 + 0.762678i) q^{72} +(-6.90160 - 11.9539i) q^{73} +(-11.4917 - 2.79403i) q^{74} -3.43906i q^{75} +(4.09999 + 7.69351i) q^{76} +9.39085i q^{77} +(0.215579 - 0.886664i) q^{78} +(-0.939415 - 1.62711i) q^{79} +(-9.84418 - 4.51984i) q^{80} +(2.91502 + 5.04897i) q^{81} +(7.30584 - 2.14116i) q^{82} +3.79468 q^{83} +(-0.413974 - 8.87989i) q^{84} +(15.1162 + 8.72734i) q^{85} +(-1.93578 - 6.60506i) q^{86} +4.67009i q^{87} +(-6.64702 - 5.77740i) q^{88} +(10.7709 + 6.21857i) q^{89} +(0.749238 - 3.08158i) q^{90} +(-1.14354 - 0.660224i) q^{91} +(-2.26157 - 3.52694i) q^{92} +(12.4765 - 7.20333i) q^{93} +(-1.45138 - 1.38529i) q^{94} +(-11.7659 - 0.949828i) q^{95} +(6.54004 + 5.17004i) q^{96} +(-16.1008 + 9.29578i) q^{97} +(-2.88040 - 0.700325i) q^{98} +(1.28920 - 2.23296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32} + 36 q^{33} - 12 q^{34} - 28 q^{35} - 8 q^{36} + 38 q^{38} - 48 q^{40} + 6 q^{41} + 14 q^{42} + 30 q^{43} + 5 q^{44} - 15 q^{48} - 68 q^{49} - 42 q^{51} + 36 q^{52} + 23 q^{54} - 26 q^{57} + 20 q^{58} - 18 q^{59} - 42 q^{60} + 22 q^{62} + 70 q^{64} - 27 q^{66} + 78 q^{67} + 4 q^{68} + 18 q^{70} - 24 q^{72} + 14 q^{73} + 4 q^{74} + 47 q^{76} - 30 q^{78} - 20 q^{80} + 6 q^{81} + 23 q^{82} - 32 q^{83} + 42 q^{86} - 18 q^{89} - 96 q^{90} - 12 q^{91} + 46 q^{92} + 50 q^{96} + 30 q^{97} + 15 q^{98} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).

\(n\) \(39\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37418 + 0.334110i 0.971692 + 0.236252i
\(3\) 1.27630 0.736872i 0.736872 0.425433i −0.0840591 0.996461i \(-0.526788\pi\)
0.820931 + 0.571028i \(0.193455\pi\)
\(4\) 1.77674 + 0.918256i 0.888370 + 0.459128i
\(5\) −2.34524 + 1.35403i −1.04882 + 0.605539i −0.922320 0.386427i \(-0.873709\pi\)
−0.126504 + 0.991966i \(0.540376\pi\)
\(6\) 2.00006 0.586169i 0.816522 0.239303i
\(7\) 3.01597i 1.13993i −0.821669 0.569965i \(-0.806957\pi\)
0.821669 0.569965i \(-0.193043\pi\)
\(8\) 2.13476 + 1.85548i 0.754752 + 0.656010i
\(9\) −0.414040 + 0.717138i −0.138013 + 0.239046i
\(10\) −3.67518 + 1.07711i −1.16219 + 0.340611i
\(11\) −3.11370 −0.938817 −0.469409 0.882981i \(-0.655533\pi\)
−0.469409 + 0.882981i \(0.655533\pi\)
\(12\) 2.94429 0.137261i 0.849943 0.0396237i
\(13\) 0.218909 0.379162i 0.0607144 0.105160i −0.834071 0.551658i \(-0.813995\pi\)
0.894785 + 0.446497i \(0.147329\pi\)
\(14\) 1.00767 4.14449i 0.269311 1.10766i
\(15\) −1.99549 + 3.45629i −0.515233 + 0.892409i
\(16\) 2.31361 + 3.26300i 0.578403 + 0.815751i
\(17\) −3.22274 5.58194i −0.781629 1.35382i −0.930993 0.365038i \(-0.881056\pi\)
0.149364 0.988782i \(-0.452277\pi\)
\(18\) −0.808569 + 0.847142i −0.190582 + 0.199673i
\(19\) 3.58731 + 2.47613i 0.822984 + 0.568064i
\(20\) −5.41023 + 0.252221i −1.20976 + 0.0563984i
\(21\) −2.22238 3.84928i −0.484964 0.839982i
\(22\) −4.27879 1.04032i −0.912241 0.221797i
\(23\) −1.81421 1.04744i −0.378290 0.218406i 0.298784 0.954321i \(-0.403419\pi\)
−0.677074 + 0.735915i \(0.736752\pi\)
\(24\) 4.09184 + 0.795097i 0.835244 + 0.162298i
\(25\) 1.16678 2.02092i 0.233355 0.404183i
\(26\) 0.427502 0.447896i 0.0838401 0.0878397i
\(27\) 5.64161i 1.08573i
\(28\) 2.76943 5.35860i 0.523374 1.01268i
\(29\) −1.58443 + 2.74431i −0.294221 + 0.509606i −0.974803 0.223066i \(-0.928394\pi\)
0.680582 + 0.732672i \(0.261727\pi\)
\(30\) −3.89694 + 4.08285i −0.711481 + 0.745422i
\(31\) 9.77556 1.75574 0.877871 0.478897i \(-0.158963\pi\)
0.877871 + 0.478897i \(0.158963\pi\)
\(32\) 2.08912 + 5.25696i 0.369307 + 0.929307i
\(33\) −3.97402 + 2.29440i −0.691788 + 0.399404i
\(34\) −2.56363 8.74735i −0.439660 1.50016i
\(35\) 4.08371 + 7.07319i 0.690272 + 1.19559i
\(36\) −1.39416 + 0.893974i −0.232360 + 0.148996i
\(37\) −8.36258 −1.37480 −0.687400 0.726279i \(-0.741248\pi\)
−0.687400 + 0.726279i \(0.741248\pi\)
\(38\) 4.10230 + 4.60121i 0.665481 + 0.746415i
\(39\) 0.645232i 0.103320i
\(40\) −7.51890 1.46102i −1.18884 0.231007i
\(41\) 4.66208 2.69165i 0.728094 0.420365i −0.0896306 0.995975i \(-0.528569\pi\)
0.817724 + 0.575610i \(0.195235\pi\)
\(42\) −1.76787 6.03213i −0.272788 0.930778i
\(43\) −2.43347 4.21489i −0.371100 0.642764i 0.618635 0.785679i \(-0.287686\pi\)
−0.989735 + 0.142914i \(0.954353\pi\)
\(44\) −5.53225 2.85918i −0.834017 0.431037i
\(45\) 2.24248i 0.334290i
\(46\) −2.14310 2.04551i −0.315982 0.301595i
\(47\) −1.22865 0.709359i −0.179216 0.103471i 0.407708 0.913112i \(-0.366328\pi\)
−0.586924 + 0.809642i \(0.699661\pi\)
\(48\) 5.35728 + 2.45973i 0.773256 + 0.355032i
\(49\) −2.09609 −0.299441
\(50\) 2.27857 2.38727i 0.322238 0.337611i
\(51\) −8.22635 4.74949i −1.15192 0.665061i
\(52\) 0.737112 0.472657i 0.102219 0.0655458i
\(53\) 1.63792 2.83695i 0.224985 0.389686i −0.731330 0.682024i \(-0.761100\pi\)
0.956315 + 0.292338i \(0.0944333\pi\)
\(54\) −1.88492 + 7.75258i −0.256505 + 1.05499i
\(55\) 7.30239 4.21604i 0.984655 0.568491i
\(56\) 5.59606 6.43838i 0.747805 0.860365i
\(57\) 6.40307 + 0.516904i 0.848107 + 0.0684655i
\(58\) −3.09420 + 3.24181i −0.406288 + 0.425670i
\(59\) −1.70599 + 0.984956i −0.222102 + 0.128230i −0.606923 0.794761i \(-0.707596\pi\)
0.384821 + 0.922991i \(0.374263\pi\)
\(60\) −6.71922 + 4.30856i −0.867447 + 0.556232i
\(61\) 9.56035 + 5.51967i 1.22408 + 0.706722i 0.965785 0.259345i \(-0.0835067\pi\)
0.258293 + 0.966067i \(0.416840\pi\)
\(62\) 13.4334 + 3.26612i 1.70604 + 0.414797i
\(63\) 2.16287 + 1.24873i 0.272496 + 0.157326i
\(64\) 1.11442 + 7.92200i 0.139302 + 0.990250i
\(65\) 1.18563i 0.147060i
\(66\) −6.22760 + 1.82516i −0.766565 + 0.224661i
\(67\) 4.49875 + 2.59735i 0.549609 + 0.317317i 0.748964 0.662610i \(-0.230551\pi\)
−0.199355 + 0.979927i \(0.563885\pi\)
\(68\) −0.600315 12.8770i −0.0727989 1.56156i
\(69\) −3.08731 −0.371668
\(70\) 3.24852 + 11.0842i 0.388273 + 1.32482i
\(71\) 4.40927 + 7.63707i 0.523284 + 0.906354i 0.999633 + 0.0270976i \(0.00862647\pi\)
−0.476349 + 0.879256i \(0.658040\pi\)
\(72\) −2.21451 + 0.762678i −0.260983 + 0.0898825i
\(73\) −6.90160 11.9539i −0.807772 1.39910i −0.914404 0.404803i \(-0.867340\pi\)
0.106632 0.994299i \(-0.465993\pi\)
\(74\) −11.4917 2.79403i −1.33588 0.324799i
\(75\) 3.43906i 0.397108i
\(76\) 4.09999 + 7.69351i 0.470301 + 0.882506i
\(77\) 9.39085i 1.07019i
\(78\) 0.215579 0.886664i 0.0244095 0.100395i
\(79\) −0.939415 1.62711i −0.105692 0.183065i 0.808328 0.588732i \(-0.200373\pi\)
−0.914021 + 0.405667i \(0.867039\pi\)
\(80\) −9.84418 4.51984i −1.10061 0.505334i
\(81\) 2.91502 + 5.04897i 0.323891 + 0.560996i
\(82\) 7.30584 2.14116i 0.806795 0.236452i
\(83\) 3.79468 0.416520 0.208260 0.978073i \(-0.433220\pi\)
0.208260 + 0.978073i \(0.433220\pi\)
\(84\) −0.413974 8.87989i −0.0451683 0.968876i
\(85\) 15.1162 + 8.72734i 1.63958 + 0.946613i
\(86\) −1.93578 6.60506i −0.208741 0.712242i
\(87\) 4.67009i 0.500686i
\(88\) −6.64702 5.77740i −0.708575 0.615873i
\(89\) 10.7709 + 6.21857i 1.14171 + 0.659167i 0.946854 0.321664i \(-0.104242\pi\)
0.194857 + 0.980832i \(0.437576\pi\)
\(90\) 0.749238 3.08158i 0.0789766 0.324827i
\(91\) −1.14354 0.660224i −0.119876 0.0692102i
\(92\) −2.26157 3.52694i −0.235785 0.367708i
\(93\) 12.4765 7.20333i 1.29376 0.746951i
\(94\) −1.45138 1.38529i −0.149698 0.142882i
\(95\) −11.7659 0.949828i −1.20715 0.0974503i
\(96\) 6.54004 + 5.17004i 0.667490 + 0.527665i
\(97\) −16.1008 + 9.29578i −1.63479 + 0.943844i −0.652197 + 0.758050i \(0.726152\pi\)
−0.982589 + 0.185794i \(0.940514\pi\)
\(98\) −2.88040 0.700325i −0.290964 0.0707435i
\(99\) 1.28920 2.23296i 0.129569 0.224421i
\(100\) 3.92878 2.51924i 0.392878 0.251924i
\(101\) 1.29368 + 0.746904i 0.128726 + 0.0743198i 0.562980 0.826470i \(-0.309655\pi\)
−0.434254 + 0.900790i \(0.642988\pi\)
\(102\) −9.71764 9.27516i −0.962189 0.918378i
\(103\) 5.61948 0.553704 0.276852 0.960913i \(-0.410709\pi\)
0.276852 + 0.960913i \(0.410709\pi\)
\(104\) 1.17084 0.403239i 0.114811 0.0395409i
\(105\) 10.4241 + 6.01834i 1.01728 + 0.587329i
\(106\) 3.19865 3.35124i 0.310680 0.325501i
\(107\) 9.01090i 0.871117i −0.900160 0.435558i \(-0.856551\pi\)
0.900160 0.435558i \(-0.143449\pi\)
\(108\) −5.18044 + 10.0237i −0.498488 + 0.964528i
\(109\) −5.62286 9.73908i −0.538573 0.932835i −0.998981 0.0451280i \(-0.985630\pi\)
0.460409 0.887707i \(-0.347703\pi\)
\(110\) 11.4434 3.35379i 1.09109 0.319771i
\(111\) −10.6732 + 6.16215i −1.01305 + 0.584885i
\(112\) 9.84113 6.97779i 0.929899 0.659339i
\(113\) 4.22083i 0.397063i 0.980095 + 0.198531i \(0.0636171\pi\)
−0.980095 + 0.198531i \(0.936383\pi\)
\(114\) 8.62626 + 2.84965i 0.807924 + 0.266894i
\(115\) 5.67303 0.529013
\(116\) −5.33510 + 3.42102i −0.495352 + 0.317634i
\(117\) 0.181274 + 0.313976i 0.0167588 + 0.0290271i
\(118\) −2.67343 + 0.783517i −0.246109 + 0.0721286i
\(119\) −16.8350 + 9.71969i −1.54326 + 0.891002i
\(120\) −10.6729 + 3.67577i −0.974302 + 0.335550i
\(121\) −1.30484 −0.118622
\(122\) 11.2935 + 10.7792i 1.02246 + 0.975906i
\(123\) 3.96680 6.87070i 0.357675 0.619510i
\(124\) 17.3686 + 8.97646i 1.55975 + 0.806110i
\(125\) 7.22088i 0.645855i
\(126\) 2.55496 + 2.43862i 0.227614 + 0.217250i
\(127\) 7.86010 13.6141i 0.697471 1.20806i −0.271869 0.962334i \(-0.587642\pi\)
0.969340 0.245721i \(-0.0790248\pi\)
\(128\) −1.11541 + 11.2586i −0.0985895 + 0.995128i
\(129\) −6.21166 3.58631i −0.546906 0.315757i
\(130\) −0.396133 + 1.62928i −0.0347432 + 0.142897i
\(131\) −5.08127 8.80102i −0.443953 0.768948i 0.554026 0.832499i \(-0.313091\pi\)
−0.997979 + 0.0635510i \(0.979757\pi\)
\(132\) −9.16765 + 0.427389i −0.797941 + 0.0371995i
\(133\) 7.46795 10.8192i 0.647553 0.938145i
\(134\) 5.31429 + 5.07231i 0.459084 + 0.438181i
\(135\) −7.63889 13.2309i −0.657451 1.13874i
\(136\) 3.47739 17.8958i 0.298184 1.53456i
\(137\) −7.17527 + 12.4279i −0.613024 + 1.06179i 0.377703 + 0.925927i \(0.376714\pi\)
−0.990728 + 0.135863i \(0.956619\pi\)
\(138\) −4.24251 1.03150i −0.361147 0.0878072i
\(139\) 5.30773 9.19326i 0.450196 0.779763i −0.548202 0.836346i \(-0.684687\pi\)
0.998398 + 0.0565836i \(0.0180207\pi\)
\(140\) 0.760692 + 16.3171i 0.0642902 + 1.37905i
\(141\) −2.09083 −0.176079
\(142\) 3.50750 + 11.9679i 0.294343 + 1.00432i
\(143\) −0.681618 + 1.18060i −0.0569998 + 0.0987265i
\(144\) −3.29795 + 0.308166i −0.274829 + 0.0256805i
\(145\) 8.58144i 0.712650i
\(146\) −5.49011 18.7327i −0.454365 1.55033i
\(147\) −2.67523 + 1.54455i −0.220650 + 0.127392i
\(148\) −14.8581 7.67899i −1.22133 0.631209i
\(149\) −16.0045 + 9.24023i −1.31114 + 0.756989i −0.982286 0.187390i \(-0.939997\pi\)
−0.328858 + 0.944379i \(0.606664\pi\)
\(150\) 1.14902 4.72588i 0.0938175 0.385867i
\(151\) −18.5105 −1.50637 −0.753183 0.657811i \(-0.771483\pi\)
−0.753183 + 0.657811i \(0.771483\pi\)
\(152\) 3.06364 + 11.9421i 0.248494 + 0.968633i
\(153\) 5.33737 0.431501
\(154\) −3.13758 + 12.9047i −0.252833 + 1.03989i
\(155\) −22.9261 + 13.2364i −1.84147 + 1.06317i
\(156\) 0.592488 1.14641i 0.0474370 0.0917862i
\(157\) −21.2242 + 12.2538i −1.69388 + 0.977961i −0.742545 + 0.669796i \(0.766382\pi\)
−0.951333 + 0.308165i \(0.900285\pi\)
\(158\) −0.747289 2.54982i −0.0594511 0.202852i
\(159\) 4.82774i 0.382864i
\(160\) −12.0175 9.50012i −0.950070 0.751050i
\(161\) −3.15904 + 5.47162i −0.248967 + 0.431224i
\(162\) 2.31885 + 7.91213i 0.182186 + 0.621635i
\(163\) −6.00269 −0.470167 −0.235084 0.971975i \(-0.575536\pi\)
−0.235084 + 0.971975i \(0.575536\pi\)
\(164\) 10.7549 0.501387i 0.839818 0.0391517i
\(165\) 6.21336 10.7619i 0.483709 0.837809i
\(166\) 5.21458 + 1.26784i 0.404730 + 0.0984037i
\(167\) −3.39245 + 5.87589i −0.262515 + 0.454690i −0.966910 0.255119i \(-0.917885\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(168\) 2.39799 12.3409i 0.185009 0.952120i
\(169\) 6.40416 + 11.0923i 0.492628 + 0.853256i
\(170\) 17.8565 + 17.0434i 1.36953 + 1.30717i
\(171\) −3.26102 + 1.54738i −0.249376 + 0.118331i
\(172\) −0.453294 9.72331i −0.0345633 0.741395i
\(173\) −8.69543 15.0609i −0.661101 1.14506i −0.980327 0.197382i \(-0.936756\pi\)
0.319225 0.947679i \(-0.396577\pi\)
\(174\) −1.56033 + 6.41754i −0.118288 + 0.486512i
\(175\) −6.09502 3.51896i −0.460741 0.266009i
\(176\) −7.20391 10.1600i −0.543015 0.765841i
\(177\) −1.45157 + 2.51420i −0.109107 + 0.188979i
\(178\) 12.7234 + 12.1441i 0.953662 + 0.910239i
\(179\) 3.28473i 0.245513i −0.992437 0.122756i \(-0.960827\pi\)
0.992437 0.122756i \(-0.0391733\pi\)
\(180\) 2.05917 3.98431i 0.153482 0.296973i
\(181\) 4.17326 7.22829i 0.310196 0.537275i −0.668209 0.743974i \(-0.732939\pi\)
0.978405 + 0.206699i \(0.0662721\pi\)
\(182\) −1.35084 1.28933i −0.100131 0.0955718i
\(183\) 16.2692 1.20265
\(184\) −1.92942 5.60226i −0.142239 0.413004i
\(185\) 19.6123 11.3232i 1.44192 0.832495i
\(186\) 19.5517 5.73013i 1.43360 0.420154i
\(187\) 10.0347 + 17.3805i 0.733806 + 1.27099i
\(188\) −1.53161 2.38856i −0.111704 0.174204i
\(189\) 17.0149 1.23765
\(190\) −15.8511 5.23633i −1.14996 0.379883i
\(191\) 4.43183i 0.320676i −0.987062 0.160338i \(-0.948742\pi\)
0.987062 0.160338i \(-0.0512584\pi\)
\(192\) 7.25983 + 9.28966i 0.523933 + 0.670423i
\(193\) −6.12690 + 3.53737i −0.441024 + 0.254625i −0.704032 0.710168i \(-0.748619\pi\)
0.263008 + 0.964794i \(0.415286\pi\)
\(194\) −25.2312 + 7.39464i −1.81149 + 0.530904i
\(195\) 0.873661 + 1.51322i 0.0625641 + 0.108364i
\(196\) −3.72420 1.92474i −0.266014 0.137482i
\(197\) 11.2899i 0.804372i 0.915558 + 0.402186i \(0.131750\pi\)
−0.915558 + 0.402186i \(0.868250\pi\)
\(198\) 2.51765 2.63775i 0.178921 0.187457i
\(199\) −6.12926 3.53873i −0.434492 0.250854i 0.266766 0.963761i \(-0.414045\pi\)
−0.701258 + 0.712907i \(0.747378\pi\)
\(200\) 6.24055 2.14925i 0.441273 0.151975i
\(201\) 7.65566 0.539989
\(202\) 1.52820 + 1.45861i 0.107523 + 0.102628i
\(203\) 8.27677 + 4.77860i 0.580916 + 0.335392i
\(204\) −10.2549 15.9925i −0.717983 1.11970i
\(205\) −7.28913 + 12.6251i −0.509095 + 0.881779i
\(206\) 7.72217 + 1.87753i 0.538029 + 0.130813i
\(207\) 1.50231 0.867362i 0.104418 0.0602858i
\(208\) 1.74368 0.162932i 0.120902 0.0112973i
\(209\) −11.1698 7.70995i −0.772632 0.533308i
\(210\) 12.3137 + 11.7531i 0.849729 + 0.811038i
\(211\) 15.7615 9.09989i 1.08506 0.626462i 0.152806 0.988256i \(-0.451169\pi\)
0.932258 + 0.361794i \(0.117836\pi\)
\(212\) 5.51520 3.53651i 0.378786 0.242888i
\(213\) 11.2551 + 6.49813i 0.771186 + 0.445244i
\(214\) 3.01064 12.3826i 0.205803 0.846457i
\(215\) 11.4141 + 6.58996i 0.778438 + 0.449431i
\(216\) −10.4679 + 12.0435i −0.712248 + 0.819456i
\(217\) 29.4828i 2.00142i
\(218\) −4.47289 15.2619i −0.302943 1.03367i
\(219\) −17.6170 10.1712i −1.19045 0.687306i
\(220\) 16.8459 0.785342i 1.13575 0.0529477i
\(221\) −2.82195 −0.189825
\(222\) −16.7257 + 4.90189i −1.12255 + 0.328993i
\(223\) 0.772936 + 1.33877i 0.0517596 + 0.0896503i 0.890744 0.454505i \(-0.150184\pi\)
−0.838985 + 0.544155i \(0.816850\pi\)
\(224\) 15.8548 6.30072i 1.05935 0.420984i
\(225\) 0.966184 + 1.67348i 0.0644123 + 0.111565i
\(226\) −1.41022 + 5.80018i −0.0938067 + 0.385823i
\(227\) 3.30271i 0.219209i −0.993975 0.109604i \(-0.965042\pi\)
0.993975 0.109604i \(-0.0349584\pi\)
\(228\) 10.9019 + 6.79806i 0.721999 + 0.450212i
\(229\) 8.81252i 0.582348i 0.956670 + 0.291174i \(0.0940458\pi\)
−0.956670 + 0.291174i \(0.905954\pi\)
\(230\) 7.79576 + 1.89542i 0.514037 + 0.124980i
\(231\) 6.91985 + 11.9855i 0.455293 + 0.788590i
\(232\) −8.47439 + 2.91858i −0.556371 + 0.191614i
\(233\) 3.15790 + 5.46965i 0.206881 + 0.358329i 0.950730 0.310019i \(-0.100335\pi\)
−0.743849 + 0.668347i \(0.767002\pi\)
\(234\) 0.144201 + 0.492025i 0.00942669 + 0.0321647i
\(235\) 3.84197 0.250622
\(236\) −3.93555 + 0.183473i −0.256183 + 0.0119430i
\(237\) −2.39795 1.38446i −0.155764 0.0899301i
\(238\) −26.3818 + 7.73185i −1.71007 + 0.501181i
\(239\) 26.2612i 1.69870i 0.527834 + 0.849348i \(0.323004\pi\)
−0.527834 + 0.849348i \(0.676996\pi\)
\(240\) −15.8947 + 1.48522i −1.02600 + 0.0958708i
\(241\) 1.61651 + 0.933290i 0.104128 + 0.0601185i 0.551160 0.834400i \(-0.314185\pi\)
−0.447031 + 0.894518i \(0.647519\pi\)
\(242\) −1.79309 0.435961i −0.115264 0.0280247i
\(243\) −7.21645 4.16642i −0.462935 0.267276i
\(244\) 11.9178 + 18.5859i 0.762959 + 1.18984i
\(245\) 4.91583 2.83816i 0.314061 0.181323i
\(246\) 7.74667 8.11623i 0.493910 0.517472i
\(247\) 1.72415 0.818120i 0.109705 0.0520558i
\(248\) 20.8685 + 18.1383i 1.32515 + 1.15178i
\(249\) 4.84315 2.79619i 0.306922 0.177202i
\(250\) 2.41257 9.92279i 0.152584 0.627572i
\(251\) 10.1173 17.5236i 0.638596 1.10608i −0.347145 0.937811i \(-0.612849\pi\)
0.985741 0.168269i \(-0.0538177\pi\)
\(252\) 2.69620 + 4.20474i 0.169845 + 0.264874i
\(253\) 5.64893 + 3.26141i 0.355145 + 0.205043i
\(254\) 15.3498 16.0821i 0.963132 1.00908i
\(255\) 25.7237 1.61088
\(256\) −5.29439 + 15.0987i −0.330899 + 0.943666i
\(257\) −10.3865 5.99663i −0.647890 0.374060i 0.139757 0.990186i \(-0.455368\pi\)
−0.787647 + 0.616126i \(0.788701\pi\)
\(258\) −7.33772 7.00361i −0.456827 0.436026i
\(259\) 25.2213i 1.56718i
\(260\) −1.08872 + 2.10656i −0.0675193 + 0.130644i
\(261\) −1.31204 2.27251i −0.0812129 0.140665i
\(262\) −4.04207 13.7919i −0.249720 0.852065i
\(263\) 24.8302 14.3357i 1.53109 0.883978i 0.531783 0.846881i \(-0.321522\pi\)
0.999312 0.0370975i \(-0.0118112\pi\)
\(264\) −12.7408 2.47570i −0.784142 0.152369i
\(265\) 8.87113i 0.544949i
\(266\) 13.8771 12.3724i 0.850861 0.758602i
\(267\) 18.3292 1.12173
\(268\) 5.60807 + 8.74582i 0.342568 + 0.534236i
\(269\) −7.77990 13.4752i −0.474349 0.821596i 0.525220 0.850967i \(-0.323983\pi\)
−0.999569 + 0.0293704i \(0.990650\pi\)
\(270\) −6.07661 20.7339i −0.369811 1.26183i
\(271\) −2.99285 + 1.72792i −0.181803 + 0.104964i −0.588139 0.808760i \(-0.700139\pi\)
0.406337 + 0.913723i \(0.366806\pi\)
\(272\) 10.7577 23.4303i 0.652284 1.42067i
\(273\) −1.94600 −0.117777
\(274\) −14.0124 + 14.6809i −0.846520 + 0.886904i
\(275\) −3.63300 + 6.29253i −0.219078 + 0.379454i
\(276\) −5.48534 2.83494i −0.330179 0.170643i
\(277\) 1.41483i 0.0850090i 0.999096 + 0.0425045i \(0.0135337\pi\)
−0.999096 + 0.0425045i \(0.986466\pi\)
\(278\) 10.3653 10.8598i 0.621672 0.651329i
\(279\) −4.04747 + 7.01043i −0.242316 + 0.419703i
\(280\) −4.40639 + 22.6768i −0.263332 + 1.35520i
\(281\) 4.69854 + 2.71270i 0.280291 + 0.161826i 0.633555 0.773697i \(-0.281595\pi\)
−0.353264 + 0.935524i \(0.614928\pi\)
\(282\) −2.87317 0.698567i −0.171095 0.0415991i
\(283\) 8.05693 + 13.9550i 0.478935 + 0.829540i 0.999708 0.0241553i \(-0.00768962\pi\)
−0.520773 + 0.853695i \(0.674356\pi\)
\(284\) 0.821335 + 17.6179i 0.0487373 + 1.04543i
\(285\) −15.7167 + 7.45766i −0.930974 + 0.441754i
\(286\) −1.33112 + 1.39462i −0.0787105 + 0.0824654i
\(287\) −8.11794 14.0607i −0.479187 0.829976i
\(288\) −4.63494 0.678405i −0.273117 0.0399754i
\(289\) −12.2721 + 21.2559i −0.721887 + 1.25034i
\(290\) 2.86715 11.7924i 0.168365 0.692476i
\(291\) −13.6996 + 23.7284i −0.803085 + 1.39098i
\(292\) −1.28560 27.5765i −0.0752338 1.61379i
\(293\) 23.7978 1.39028 0.695142 0.718872i \(-0.255341\pi\)
0.695142 + 0.718872i \(0.255341\pi\)
\(294\) −4.19230 + 1.22866i −0.244500 + 0.0716570i
\(295\) 2.66731 4.61992i 0.155297 0.268982i
\(296\) −17.8521 15.5166i −1.03763 0.901882i
\(297\) 17.5663i 1.01930i
\(298\) −25.0804 + 7.35045i −1.45287 + 0.425800i
\(299\) −0.794296 + 0.458587i −0.0459353 + 0.0265208i
\(300\) 3.15793 6.11031i 0.182323 0.352779i
\(301\) −12.7120 + 7.33927i −0.732707 + 0.423028i
\(302\) −25.4368 6.18457i −1.46372 0.355882i
\(303\) 2.20149 0.126472
\(304\) 0.220002 + 17.4342i 0.0126180 + 0.999920i
\(305\) −29.8951 −1.71179
\(306\) 7.33451 + 1.78327i 0.419286 + 0.101943i
\(307\) −1.43431 + 0.828099i −0.0818604 + 0.0472621i −0.540371 0.841427i \(-0.681716\pi\)
0.458511 + 0.888689i \(0.348383\pi\)
\(308\) −8.62320 + 16.6851i −0.491352 + 0.950722i
\(309\) 7.17214 4.14084i 0.408009 0.235564i
\(310\) −35.9269 + 10.5293i −2.04051 + 0.598025i
\(311\) 0.650991i 0.0369143i 0.999830 + 0.0184572i \(0.00587543\pi\)
−0.999830 + 0.0184572i \(0.994125\pi\)
\(312\) 1.19721 1.37742i 0.0677788 0.0779808i
\(313\) 9.66128 16.7338i 0.546088 0.945852i −0.452450 0.891790i \(-0.649450\pi\)
0.998538 0.0540617i \(-0.0172168\pi\)
\(314\) −33.2600 + 9.74771i −1.87697 + 0.550095i
\(315\) −6.76327 −0.381067
\(316\) −0.174989 3.75358i −0.00984392 0.211156i
\(317\) 10.4707 18.1358i 0.588093 1.01861i −0.406389 0.913700i \(-0.633212\pi\)
0.994482 0.104907i \(-0.0334545\pi\)
\(318\) 1.61300 6.63418i 0.0904524 0.372026i
\(319\) 4.93345 8.54498i 0.276220 0.478427i
\(320\) −13.3402 17.0701i −0.745739 0.954245i
\(321\) −6.63988 11.5006i −0.370602 0.641901i
\(322\) −6.16921 + 6.46352i −0.343797 + 0.360198i
\(323\) 2.26070 28.0041i 0.125789 1.55819i
\(324\) 0.542995 + 11.6474i 0.0301664 + 0.647080i
\(325\) −0.510836 0.884793i −0.0283361 0.0490795i
\(326\) −8.24878 2.00556i −0.456858 0.111078i
\(327\) −14.3529 8.28666i −0.793718 0.458253i
\(328\) 14.9467 + 2.90434i 0.825294 + 0.160365i
\(329\) −2.13941 + 3.70556i −0.117949 + 0.204294i
\(330\) 12.1339 12.7128i 0.667950 0.699815i
\(331\) 7.37076i 0.405134i 0.979268 + 0.202567i \(0.0649284\pi\)
−0.979268 + 0.202567i \(0.935072\pi\)
\(332\) 6.74216 + 3.48449i 0.370024 + 0.191236i
\(333\) 3.46244 5.99713i 0.189741 0.328641i
\(334\) −6.62503 + 6.94108i −0.362505 + 0.379799i
\(335\) −14.0675 −0.768592
\(336\) 7.41849 16.1574i 0.404712 0.881458i
\(337\) −9.00098 + 5.19672i −0.490315 + 0.283083i −0.724705 0.689059i \(-0.758024\pi\)
0.234390 + 0.972143i \(0.424691\pi\)
\(338\) 5.09440 + 17.3825i 0.277099 + 0.945486i
\(339\) 3.11021 + 5.38705i 0.168924 + 0.292584i
\(340\) 18.8436 + 29.3868i 1.02194 + 1.59372i
\(341\) −30.4382 −1.64832
\(342\) −4.99822 + 1.03683i −0.270273 + 0.0560655i
\(343\) 14.7901i 0.798588i
\(344\) 2.62575 13.5130i 0.141571 0.728573i
\(345\) 7.24048 4.18029i 0.389814 0.225060i
\(346\) −6.91707 23.6017i −0.371864 1.26883i
\(347\) 9.25966 + 16.0382i 0.497085 + 0.860976i 0.999994 0.00336302i \(-0.00107049\pi\)
−0.502910 + 0.864339i \(0.667737\pi\)
\(348\) −4.28833 + 8.29753i −0.229879 + 0.444794i
\(349\) 16.1158i 0.862661i 0.902194 + 0.431330i \(0.141956\pi\)
−0.902194 + 0.431330i \(0.858044\pi\)
\(350\) −7.19994 6.87210i −0.384853 0.367329i
\(351\) 2.13908 + 1.23500i 0.114176 + 0.0659194i
\(352\) −6.50489 16.3686i −0.346712 0.872450i
\(353\) 32.0716 1.70700 0.853500 0.521093i \(-0.174476\pi\)
0.853500 + 0.521093i \(0.174476\pi\)
\(354\) −2.83474 + 2.96997i −0.150665 + 0.157852i
\(355\) −20.6816 11.9405i −1.09767 0.633737i
\(356\) 13.4268 + 20.9392i 0.711620 + 1.10978i
\(357\) −14.3243 + 24.8105i −0.758124 + 1.31311i
\(358\) 1.09746 4.51382i 0.0580028 0.238563i
\(359\) 3.07083 1.77294i 0.162072 0.0935724i −0.416770 0.909012i \(-0.636838\pi\)
0.578842 + 0.815440i \(0.303505\pi\)
\(360\) 4.16088 4.78717i 0.219297 0.252306i
\(361\) 6.73752 + 17.7653i 0.354607 + 0.935016i
\(362\) 8.14985 8.53864i 0.428347 0.448781i
\(363\) −1.66537 + 0.961501i −0.0874092 + 0.0504657i
\(364\) −1.42552 2.22311i −0.0747176 0.116523i
\(365\) 32.3719 + 18.6899i 1.69442 + 0.978275i
\(366\) 22.3568 + 5.43570i 1.16861 + 0.284128i
\(367\) 30.3020 + 17.4948i 1.58175 + 0.913224i 0.994604 + 0.103742i \(0.0330817\pi\)
0.587145 + 0.809481i \(0.300252\pi\)
\(368\) −0.779598 8.34315i −0.0406393 0.434917i
\(369\) 4.45780i 0.232064i
\(370\) 30.7340 9.00738i 1.59778 0.468272i
\(371\) −8.55617 4.93991i −0.444214 0.256467i
\(372\) 28.7821 1.34180i 1.49228 0.0695691i
\(373\) −6.14462 −0.318157 −0.159078 0.987266i \(-0.550852\pi\)
−0.159078 + 0.987266i \(0.550852\pi\)
\(374\) 7.98240 + 27.2367i 0.412760 + 1.40837i
\(375\) −5.32086 9.21601i −0.274768 0.475913i
\(376\) −1.30667 3.79404i −0.0673863 0.195663i
\(377\) 0.693692 + 1.20151i 0.0357270 + 0.0618809i
\(378\) 23.3816 + 5.68487i 1.20262 + 0.292398i
\(379\) 16.1488i 0.829507i 0.909934 + 0.414753i \(0.136132\pi\)
−0.909934 + 0.414753i \(0.863868\pi\)
\(380\) −20.0327 12.4917i −1.02765 0.640809i
\(381\) 23.1675i 1.18691i
\(382\) 1.48072 6.09013i 0.0757603 0.311598i
\(383\) 5.82205 + 10.0841i 0.297493 + 0.515272i 0.975562 0.219726i \(-0.0705163\pi\)
−0.678069 + 0.734998i \(0.737183\pi\)
\(384\) 6.87254 + 15.1912i 0.350713 + 0.775225i
\(385\) −12.7155 22.0238i −0.648040 1.12244i
\(386\) −9.60134 + 2.81392i −0.488695 + 0.143225i
\(387\) 4.03021 0.204867
\(388\) −37.1428 + 1.73157i −1.88564 + 0.0879072i
\(389\) −12.0060 6.93167i −0.608729 0.351450i 0.163739 0.986504i \(-0.447645\pi\)
−0.772468 + 0.635054i \(0.780978\pi\)
\(390\) 0.694983 + 2.37134i 0.0351918 + 0.120078i
\(391\) 13.5025i 0.682848i
\(392\) −4.47465 3.88924i −0.226004 0.196436i
\(393\) −12.9704 7.48849i −0.654272 0.377744i
\(394\) −3.77208 + 15.5144i −0.190034 + 0.781602i
\(395\) 4.40631 + 2.54399i 0.221706 + 0.128002i
\(396\) 4.34100 2.78357i 0.218143 0.139880i
\(397\) −10.1183 + 5.84182i −0.507825 + 0.293193i −0.731939 0.681370i \(-0.761384\pi\)
0.224114 + 0.974563i \(0.428051\pi\)
\(398\) −7.24038 6.91070i −0.362928 0.346402i
\(399\) 1.55897 19.3115i 0.0780459 0.966783i
\(400\) 9.29372 0.868421i 0.464686 0.0434210i
\(401\) 21.4038 12.3575i 1.06886 0.617105i 0.140988 0.990011i \(-0.454972\pi\)
0.927869 + 0.372907i \(0.121639\pi\)
\(402\) 10.5203 + 2.55784i 0.524703 + 0.127573i
\(403\) 2.13996 3.70652i 0.106599 0.184635i
\(404\) 1.61268 + 2.51498i 0.0802337 + 0.125125i
\(405\) −13.6729 7.89403i −0.679410 0.392258i
\(406\) 9.77720 + 9.33201i 0.485234 + 0.463140i
\(407\) 26.0386 1.29069
\(408\) −8.74875 25.4028i −0.433128 1.25763i
\(409\) 16.4212 + 9.48080i 0.811978 + 0.468796i 0.847642 0.530568i \(-0.178021\pi\)
−0.0356645 + 0.999364i \(0.511355\pi\)
\(410\) −14.2348 + 14.9138i −0.703005 + 0.736542i
\(411\) 21.1490i 1.04320i
\(412\) 9.98435 + 5.16012i 0.491894 + 0.254221i
\(413\) 2.97060 + 5.14523i 0.146174 + 0.253180i
\(414\) 2.35424 0.689972i 0.115705 0.0339103i
\(415\) −8.89945 + 5.13810i −0.436857 + 0.252219i
\(416\) 2.45056 + 0.358683i 0.120149 + 0.0175859i
\(417\) 15.6445i 0.766113i
\(418\) −12.7734 14.3268i −0.624765 0.700747i
\(419\) 8.83253 0.431497 0.215749 0.976449i \(-0.430781\pi\)
0.215749 + 0.976449i \(0.430781\pi\)
\(420\) 12.9945 + 20.2650i 0.634066 + 0.988830i
\(421\) 0.915408 + 1.58553i 0.0446143 + 0.0772742i 0.887470 0.460865i \(-0.152461\pi\)
−0.842856 + 0.538139i \(0.819127\pi\)
\(422\) 24.6995 7.23881i 1.20235 0.352380i
\(423\) 1.01742 0.587406i 0.0494685 0.0285607i
\(424\) 8.76046 3.01711i 0.425446 0.146524i
\(425\) −15.0409 −0.729588
\(426\) 13.2954 + 12.6900i 0.644165 + 0.614834i
\(427\) 16.6472 28.8338i 0.805613 1.39536i
\(428\) 8.27431 16.0100i 0.399954 0.773874i
\(429\) 2.00906i 0.0969984i
\(430\) 13.4833 + 12.8694i 0.650223 + 0.620616i
\(431\) −11.5493 + 20.0040i −0.556310 + 0.963557i 0.441490 + 0.897266i \(0.354450\pi\)
−0.997800 + 0.0662911i \(0.978883\pi\)
\(432\) −18.4086 + 13.0525i −0.885684 + 0.627989i
\(433\) 1.33452 + 0.770486i 0.0641330 + 0.0370272i 0.531724 0.846918i \(-0.321545\pi\)
−0.467591 + 0.883945i \(0.654878\pi\)
\(434\) 9.85051 40.5147i 0.472840 1.94477i
\(435\) −6.32342 10.9525i −0.303185 0.525132i
\(436\) −1.04740 22.4671i −0.0501613 1.07598i
\(437\) −3.91455 8.24971i −0.187258 0.394637i
\(438\) −20.8107 19.8631i −0.994372 0.949095i
\(439\) −18.4223 31.9083i −0.879246 1.52290i −0.852169 0.523266i \(-0.824713\pi\)
−0.0270772 0.999633i \(-0.508620\pi\)
\(440\) 23.4116 + 4.54918i 1.11611 + 0.216874i
\(441\) 0.867864 1.50318i 0.0413269 0.0715802i
\(442\) −3.87786 0.942841i −0.184451 0.0448464i
\(443\) −12.8595 + 22.2732i −0.610971 + 1.05823i 0.380106 + 0.924943i \(0.375887\pi\)
−0.991077 + 0.133290i \(0.957446\pi\)
\(444\) −24.6219 + 1.14785i −1.16850 + 0.0544747i
\(445\) −33.6804 −1.59661
\(446\) 0.614858 + 2.09795i 0.0291144 + 0.0993408i
\(447\) −13.6177 + 23.5866i −0.644097 + 1.11561i
\(448\) 23.8925 3.36105i 1.12882 0.158795i
\(449\) 12.6228i 0.595707i −0.954612 0.297853i \(-0.903729\pi\)
0.954612 0.297853i \(-0.0962706\pi\)
\(450\) 0.768583 + 2.62247i 0.0362314 + 0.123625i
\(451\) −14.5163 + 8.38100i −0.683547 + 0.394646i
\(452\) −3.87580 + 7.49933i −0.182303 + 0.352739i
\(453\) −23.6250 + 13.6399i −1.11000 + 0.640858i
\(454\) 1.10347 4.53852i 0.0517884 0.213003i
\(455\) 3.57584 0.167638
\(456\) 12.7099 + 12.9842i 0.595197 + 0.608041i
\(457\) 3.27588 0.153239 0.0766197 0.997060i \(-0.475587\pi\)
0.0766197 + 0.997060i \(0.475587\pi\)
\(458\) −2.94435 + 12.1100i −0.137581 + 0.565862i
\(459\) 31.4911 18.1814i 1.46988 0.848636i
\(460\) 10.0795 + 5.20929i 0.469959 + 0.242884i
\(461\) 14.3820 8.30348i 0.669839 0.386732i −0.126177 0.992008i \(-0.540271\pi\)
0.796015 + 0.605276i \(0.206937\pi\)
\(462\) 5.50463 + 18.7823i 0.256098 + 0.873830i
\(463\) 29.2576i 1.35972i −0.733344 0.679858i \(-0.762042\pi\)
0.733344 0.679858i \(-0.237958\pi\)
\(464\) −12.6205 + 1.17928i −0.585890 + 0.0547466i
\(465\) −19.5070 + 33.7871i −0.904616 + 1.56684i
\(466\) 2.51206 + 8.57137i 0.116369 + 0.397061i
\(467\) −7.69409 −0.356040 −0.178020 0.984027i \(-0.556969\pi\)
−0.178020 + 0.984027i \(0.556969\pi\)
\(468\) 0.0337668 + 0.724310i 0.00156087 + 0.0334813i
\(469\) 7.83354 13.5681i 0.361719 0.626516i
\(470\) 5.27955 + 1.28364i 0.243528 + 0.0592099i
\(471\) −18.0590 + 31.2791i −0.832114 + 1.44126i
\(472\) −5.46946 1.06278i −0.251752 0.0489186i
\(473\) 7.57710 + 13.1239i 0.348395 + 0.603438i
\(474\) −2.83265 2.70367i −0.130108 0.124184i
\(475\) 9.18964 4.36055i 0.421650 0.200076i
\(476\) −38.8366 + 1.81053i −1.78007 + 0.0829856i
\(477\) 1.35633 + 2.34923i 0.0621019 + 0.107564i
\(478\) −8.77414 + 36.0876i −0.401320 + 1.65061i
\(479\) 30.9763 + 17.8841i 1.41534 + 0.817148i 0.995885 0.0906279i \(-0.0288874\pi\)
0.419456 + 0.907776i \(0.362221\pi\)
\(480\) −22.3384 3.26961i −1.01960 0.149237i
\(481\) −1.83064 + 3.17077i −0.0834702 + 0.144575i
\(482\) 1.90955 + 1.82260i 0.0869775 + 0.0830171i
\(483\) 9.31123i 0.423676i
\(484\) −2.31837 1.19818i −0.105380 0.0544627i
\(485\) 25.1735 43.6017i 1.14307 1.97985i
\(486\) −8.52465 8.13650i −0.386686 0.369079i
\(487\) −2.98739 −0.135372 −0.0676858 0.997707i \(-0.521562\pi\)
−0.0676858 + 0.997707i \(0.521562\pi\)
\(488\) 10.1675 + 29.5222i 0.460259 + 1.33641i
\(489\) −7.66123 + 4.42321i −0.346453 + 0.200025i
\(490\) 7.70350 2.25771i 0.348008 0.101993i
\(491\) −16.2391 28.1269i −0.732858 1.26935i −0.955657 0.294483i \(-0.904853\pi\)
0.222798 0.974865i \(-0.428481\pi\)
\(492\) 13.3570 8.56492i 0.602182 0.386136i
\(493\) 20.4248 0.919887
\(494\) 2.64263 0.548189i 0.118898 0.0246642i
\(495\) 6.98244i 0.313837i
\(496\) 22.6169 + 31.8977i 1.01553 + 1.43225i
\(497\) 23.0332 13.2982i 1.03318 0.596507i
\(498\) 7.58960 2.22433i 0.340098 0.0996744i
\(499\) −4.86494 8.42632i −0.217785 0.377214i 0.736346 0.676605i \(-0.236550\pi\)
−0.954130 + 0.299391i \(0.903216\pi\)
\(500\) 6.63062 12.8296i 0.296530 0.573759i
\(501\) 9.99919i 0.446731i
\(502\) 19.7578 20.7003i 0.881832 0.923900i
\(503\) −15.8302 9.13954i −0.705832 0.407512i 0.103684 0.994610i \(-0.466937\pi\)
−0.809516 + 0.587098i \(0.800270\pi\)
\(504\) 2.30022 + 6.67890i 0.102460 + 0.297502i
\(505\) −4.04531 −0.180014
\(506\) 6.67297 + 6.36913i 0.296650 + 0.283142i
\(507\) 16.3472 + 9.43809i 0.726007 + 0.419160i
\(508\) 26.4666 16.9711i 1.17426 0.752972i
\(509\) 2.39384 4.14625i 0.106105 0.183779i −0.808084 0.589067i \(-0.799495\pi\)
0.914189 + 0.405288i \(0.132829\pi\)
\(510\) 35.3490 + 8.59457i 1.56528 + 0.380574i
\(511\) −36.0527 + 20.8150i −1.59488 + 0.920803i
\(512\) −12.3201 + 18.9794i −0.544475 + 0.838777i
\(513\) −13.9694 + 20.2382i −0.616763 + 0.893537i
\(514\) −12.2693 11.7107i −0.541177 0.516536i
\(515\) −13.1790 + 7.60892i −0.580738 + 0.335289i
\(516\) −7.74337 12.0758i −0.340883 0.531609i
\(517\) 3.82564 + 2.20874i 0.168252 + 0.0971401i
\(518\) −8.42670 + 34.6586i −0.370248 + 1.52281i
\(519\) −22.1959 12.8148i −0.974294 0.562509i
\(520\) −2.19992 + 2.53105i −0.0964727 + 0.110994i
\(521\) 14.4161i 0.631582i −0.948829 0.315791i \(-0.897730\pi\)
0.948829 0.315791i \(-0.102270\pi\)
\(522\) −1.04370 3.56120i −0.0456816 0.155870i
\(523\) −13.5585 7.82801i −0.592873 0.342295i 0.173360 0.984859i \(-0.444538\pi\)
−0.766233 + 0.642563i \(0.777871\pi\)
\(524\) −0.946513 20.3030i −0.0413486 0.886942i
\(525\) −10.3721 −0.452676
\(526\) 38.9109 11.4038i 1.69659 0.497230i
\(527\) −31.5041 54.5666i −1.37234 2.37696i
\(528\) −16.6810 7.65889i −0.725947 0.333310i
\(529\) −9.30575 16.1180i −0.404598 0.700784i
\(530\) −2.96394 + 12.1905i −0.128745 + 0.529523i
\(531\) 1.63125i 0.0707900i
\(532\) 23.2034 12.3654i 1.00600 0.536110i
\(533\) 2.35691i 0.102089i
\(534\) 25.1876 + 6.12396i 1.08997 + 0.265010i
\(535\) 12.2010 + 21.1328i 0.527495 + 0.913649i
\(536\) 4.78443 + 13.8920i 0.206656 + 0.600045i
\(537\) −2.42043 4.19230i −0.104449 0.180911i
\(538\) −6.18878 21.1167i −0.266817 0.910404i
\(539\) 6.52660 0.281120
\(540\) −1.42293 30.5224i −0.0612333 1.31347i
\(541\) 7.10566 + 4.10246i 0.305496 + 0.176378i 0.644909 0.764259i \(-0.276895\pi\)
−0.339413 + 0.940637i \(0.610228\pi\)
\(542\) −4.69003 + 1.37453i −0.201454 + 0.0590413i
\(543\) 12.3006i 0.527870i
\(544\) 22.6114 28.6031i 0.969454 1.22635i
\(545\) 26.3740 + 15.2270i 1.12974 + 0.652254i
\(546\) −2.67415 0.650179i −0.114443 0.0278251i
\(547\) 25.9507 + 14.9826i 1.10957 + 0.640611i 0.938718 0.344685i \(-0.112014\pi\)
0.170853 + 0.985297i \(0.445348\pi\)
\(548\) −24.1606 + 15.4925i −1.03209 + 0.661805i
\(549\) −7.91674 + 4.57073i −0.337878 + 0.195074i
\(550\) −7.09479 + 7.43325i −0.302523 + 0.316955i
\(551\) −12.4791 + 5.92143i −0.531629 + 0.252261i
\(552\) −6.59066 5.72842i −0.280517 0.243818i
\(553\) −4.90733 + 2.83325i −0.208681 + 0.120482i
\(554\) −0.472710 + 1.94423i −0.0200835 + 0.0826025i
\(555\) 16.6874 28.9035i 0.708342 1.22688i
\(556\) 17.8722 11.4602i 0.757952 0.486020i
\(557\) 33.2847 + 19.2169i 1.41032 + 0.814247i 0.995418 0.0956198i \(-0.0304833\pi\)
0.414900 + 0.909867i \(0.363817\pi\)
\(558\) −7.90421 + 8.28129i −0.334612 + 0.350575i
\(559\) −2.13083 −0.0901246
\(560\) −13.6317 + 29.6898i −0.576045 + 1.25462i
\(561\) 25.6144 + 14.7885i 1.08144 + 0.624371i
\(562\) 5.55030 + 5.29757i 0.234125 + 0.223465i
\(563\) 0.0334791i 0.00141098i −1.00000 0.000705488i \(-0.999775\pi\)
1.00000 0.000705488i \(-0.000224564\pi\)
\(564\) −3.71486 1.91991i −0.156424 0.0808430i
\(565\) −5.71512 9.89888i −0.240437 0.416449i
\(566\) 6.40916 + 21.8686i 0.269397 + 0.919206i
\(567\) 15.2275 8.79162i 0.639496 0.369213i
\(568\) −4.75767 + 24.4846i −0.199627 + 1.02735i
\(569\) 0.534632i 0.0224129i 0.999937 + 0.0112065i \(0.00356720\pi\)
−0.999937 + 0.0112065i \(0.996433\pi\)
\(570\) −24.0892 + 4.99707i −1.00899 + 0.209304i
\(571\) −37.1365 −1.55411 −0.777057 0.629430i \(-0.783288\pi\)
−0.777057 + 0.629430i \(0.783288\pi\)
\(572\) −2.29515 + 1.47172i −0.0959650 + 0.0615355i
\(573\) −3.26569 5.65634i −0.136426 0.236297i
\(574\) −6.45769 22.0342i −0.269539 0.919690i
\(575\) −4.23356 + 2.44425i −0.176552 + 0.101932i
\(576\) −6.14258 2.48083i −0.255941 0.103368i
\(577\) −25.7080 −1.07024 −0.535118 0.844777i \(-0.679733\pi\)
−0.535118 + 0.844777i \(0.679733\pi\)
\(578\) −23.9658 + 25.1091i −0.996847 + 1.04440i
\(579\) −5.21318 + 9.02949i −0.216652 + 0.375253i
\(580\) 7.87996 15.2470i 0.327198 0.633097i
\(581\) 11.4447i 0.474804i
\(582\) −26.7536 + 28.0299i −1.10897 + 1.16188i
\(583\) −5.09999 + 8.83344i −0.211220 + 0.365844i
\(584\) 7.44695 38.3245i 0.308157 1.58588i
\(585\) −0.850264 0.490900i −0.0351541 0.0202962i
\(586\) 32.7025 + 7.95110i 1.35093 + 0.328457i
\(587\) −9.70642 16.8120i −0.400627 0.693906i 0.593175 0.805074i \(-0.297874\pi\)
−0.993802 + 0.111168i \(0.964541\pi\)
\(588\) −6.17149 + 0.287710i −0.254508 + 0.0118650i
\(589\) 35.0679 + 24.2056i 1.44495 + 0.997374i
\(590\) 5.20893 5.45743i 0.214448 0.224679i
\(591\) 8.31921 + 14.4093i 0.342207 + 0.592719i
\(592\) −19.3478 27.2871i −0.795189 1.12149i
\(593\) −14.9132 + 25.8304i −0.612411 + 1.06073i 0.378422 + 0.925633i \(0.376467\pi\)
−0.990833 + 0.135093i \(0.956867\pi\)
\(594\) 5.86909 24.1393i 0.240811 0.990446i
\(595\) 26.3214 45.5900i 1.07907 1.86901i
\(596\) −36.9208 + 1.72122i −1.51234 + 0.0705040i
\(597\) −10.4304 −0.426886
\(598\) −1.24472 + 0.364798i −0.0509005 + 0.0149177i
\(599\) 3.62259 6.27451i 0.148015 0.256369i −0.782479 0.622677i \(-0.786045\pi\)
0.930494 + 0.366308i \(0.119378\pi\)
\(600\) 6.38109 7.34157i 0.260507 0.299718i
\(601\) 23.7575i 0.969088i 0.874767 + 0.484544i \(0.161015\pi\)
−0.874767 + 0.484544i \(0.838985\pi\)
\(602\) −19.9207 + 5.83827i −0.811906 + 0.237950i
\(603\) −3.72532 + 2.15082i −0.151707 + 0.0875880i
\(604\) −32.8884 16.9974i −1.33821 0.691615i
\(605\) 3.06017 1.76679i 0.124414 0.0718303i
\(606\) 3.02524 + 0.735541i 0.122892 + 0.0298793i
\(607\) 15.5235 0.630081 0.315041 0.949078i \(-0.397982\pi\)
0.315041 + 0.949078i \(0.397982\pi\)
\(608\) −5.52263 + 24.0312i −0.223972 + 0.974596i
\(609\) 14.0849 0.570747
\(610\) −41.0813 9.98828i −1.66333 0.404413i
\(611\) −0.537924 + 0.310570i −0.0217621 + 0.0125643i
\(612\) 9.48312 + 4.90107i 0.383332 + 0.198114i
\(613\) 6.02011 3.47571i 0.243150 0.140383i −0.373474 0.927641i \(-0.621833\pi\)
0.616624 + 0.787258i \(0.288500\pi\)
\(614\) −2.24768 + 0.658739i −0.0907088 + 0.0265845i
\(615\) 21.4846i 0.866344i
\(616\) −17.4245 + 20.0472i −0.702053 + 0.807726i
\(617\) −13.4941 + 23.3725i −0.543253 + 0.940943i 0.455461 + 0.890256i \(0.349474\pi\)
−0.998715 + 0.0506869i \(0.983859\pi\)
\(618\) 11.2393 3.29397i 0.452111 0.132503i
\(619\) −21.2410 −0.853747 −0.426874 0.904311i \(-0.640385\pi\)
−0.426874 + 0.904311i \(0.640385\pi\)
\(620\) −52.8880 + 2.46560i −2.12403 + 0.0990210i
\(621\) 5.90923 10.2351i 0.237129 0.410720i
\(622\) −0.217503 + 0.894579i −0.00872108 + 0.0358694i
\(623\) 18.7550 32.4847i 0.751405 1.30147i
\(624\) 2.10539 1.49282i 0.0842832 0.0597605i
\(625\) 15.6111 + 27.0393i 0.624446 + 1.08157i
\(626\) 18.8673 19.7673i 0.754088 0.790062i
\(627\) −19.9373 1.60948i −0.796218 0.0642766i
\(628\) −48.9621 + 2.28258i −1.95380 + 0.0910848i
\(629\) 26.9504 + 46.6795i 1.07458 + 1.86123i
\(630\) −9.29395 2.25968i −0.370280 0.0900278i
\(631\) −7.72930 4.46251i −0.307699 0.177650i 0.338198 0.941075i \(-0.390183\pi\)
−0.645896 + 0.763425i \(0.723516\pi\)
\(632\) 1.01364 5.21656i 0.0403206 0.207504i
\(633\) 13.4109 23.2284i 0.533036 0.923245i
\(634\) 20.4480 21.4235i 0.812093 0.850834i
\(635\) 42.5711i 1.68938i
\(636\) 4.43310 8.57764i 0.175784 0.340125i
\(637\) −0.458852 + 0.794756i −0.0181804 + 0.0314894i
\(638\) 9.63441 10.0940i 0.381430 0.399626i
\(639\) −7.30245 −0.288880
\(640\) −12.6285 27.9144i −0.499186 1.10341i
\(641\) 1.70881 0.986580i 0.0674938 0.0389675i −0.465873 0.884851i \(-0.654260\pi\)
0.533367 + 0.845884i \(0.320926\pi\)
\(642\) −5.28191 18.0224i −0.208461 0.711286i
\(643\) −6.70192 11.6081i −0.264298 0.457777i 0.703082 0.711109i \(-0.251807\pi\)
−0.967379 + 0.253332i \(0.918474\pi\)
\(644\) −10.6371 + 6.82084i −0.419162 + 0.268779i
\(645\) 19.4238 0.764812
\(646\) 12.4631 37.7273i 0.490352 1.48436i
\(647\) 25.2982i 0.994575i −0.867586 0.497288i \(-0.834329\pi\)
0.867586 0.497288i \(-0.165671\pi\)
\(648\) −3.14536 + 16.1871i −0.123561 + 0.635889i
\(649\) 5.31196 3.06686i 0.208513 0.120385i
\(650\) −0.406361 1.38654i −0.0159388 0.0543846i
\(651\) −21.7250 37.6289i −0.851472 1.47479i
\(652\) −10.6652 5.51201i −0.417682 0.215867i
\(653\) 2.28865i 0.0895618i 0.998997 + 0.0447809i \(0.0142590\pi\)
−0.998997 + 0.0447809i \(0.985741\pi\)
\(654\) −16.9548 16.1828i −0.662986 0.632798i
\(655\) 23.8336 + 13.7603i 0.931257 + 0.537661i
\(656\) 19.5691 + 8.98493i 0.764045 + 0.350803i
\(657\) 11.4302 0.445933
\(658\) −4.17800 + 4.37731i −0.162875 + 0.170645i
\(659\) −6.55373 3.78380i −0.255297 0.147396i 0.366890 0.930264i \(-0.380422\pi\)
−0.622187 + 0.782868i \(0.713756\pi\)
\(660\) 20.9217 13.4156i 0.814375 0.522200i
\(661\) −7.23786 + 12.5363i −0.281520 + 0.487607i −0.971759 0.235974i \(-0.924172\pi\)
0.690239 + 0.723581i \(0.257505\pi\)
\(662\) −2.46265 + 10.1288i −0.0957136 + 0.393665i
\(663\) −3.60165 + 2.07941i −0.139876 + 0.0807577i
\(664\) 8.10074 + 7.04094i 0.314370 + 0.273242i
\(665\) −2.86465 + 35.4855i −0.111086 + 1.37607i
\(666\) 6.76172 7.08429i 0.262011 0.274511i
\(667\) 5.74899 3.31918i 0.222602 0.128519i
\(668\) −11.4231 + 7.32480i −0.441972 + 0.283405i
\(669\) 1.97300 + 1.13911i 0.0762804 + 0.0440405i
\(670\) −19.3313 4.70011i −0.746834 0.181581i
\(671\) −29.7681 17.1866i −1.14919 0.663482i
\(672\) 15.5927 19.7246i 0.601501 0.760892i
\(673\) 26.5226i 1.02237i 0.859470 + 0.511186i \(0.170794\pi\)
−0.859470 + 0.511186i \(0.829206\pi\)
\(674\) −14.1052 + 4.13390i −0.543314 + 0.159232i
\(675\) 11.4012 + 6.58249i 0.438833 + 0.253360i
\(676\) 1.19293 + 25.5888i 0.0458821 + 0.984186i
\(677\) −6.15109 −0.236405 −0.118203 0.992989i \(-0.537713\pi\)
−0.118203 + 0.992989i \(0.537713\pi\)
\(678\) 2.47412 + 8.44193i 0.0950181 + 0.324210i
\(679\) 28.0358 + 48.5595i 1.07592 + 1.86354i
\(680\) 16.0761 + 46.6786i 0.616491 + 1.79004i
\(681\) −2.43367 4.21525i −0.0932586 0.161529i
\(682\) −41.8276 10.1697i −1.60166 0.389419i
\(683\) 2.04240i 0.0781501i 0.999236 + 0.0390750i \(0.0124411\pi\)
−0.999236 + 0.0390750i \(0.987559\pi\)
\(684\) −7.21487 0.245163i −0.275867 0.00937406i
\(685\) 38.8620i 1.48484i
\(686\) 4.94152 20.3242i 0.188668 0.775982i
\(687\) 6.49370 + 11.2474i 0.247750 + 0.429115i
\(688\) 8.12310 17.6920i 0.309690 0.674502i
\(689\) −0.717109 1.24207i −0.0273197 0.0473191i
\(690\) 11.3464 3.32536i 0.431950 0.126594i
\(691\) 45.7370 1.73992 0.869960 0.493123i \(-0.164145\pi\)
0.869960 + 0.493123i \(0.164145\pi\)
\(692\) −1.61974 34.7440i −0.0615733 1.32077i
\(693\) −6.73454 3.88819i −0.255824 0.147700i
\(694\) 7.36591 + 25.1331i 0.279606 + 0.954041i
\(695\) 28.7473i 1.09045i
\(696\) −8.66524 + 9.96953i −0.328455 + 0.377894i
\(697\) −30.0493 17.3490i −1.13820 0.657139i
\(698\) −5.38447 + 22.1461i −0.203805 + 0.838240i
\(699\) 8.06086 + 4.65394i 0.304890 + 0.176028i
\(700\) −7.59797 11.8491i −0.287176 0.447853i
\(701\) 24.5743 14.1880i 0.928159 0.535873i 0.0419298 0.999121i \(-0.486649\pi\)
0.886229 + 0.463248i \(0.153316\pi\)
\(702\) 2.52686 + 2.41180i 0.0953700 + 0.0910275i
\(703\) −29.9991 20.7069i −1.13144 0.780974i
\(704\) −3.46997 24.6668i −0.130779 0.929664i
\(705\) 4.90350 2.83104i 0.184676 0.106623i
\(706\) 44.0722 + 10.7155i 1.65868 + 0.403282i
\(707\) 2.25264 3.90169i 0.0847193 0.146738i
\(708\) −4.88775 + 3.13416i −0.183693 + 0.117789i
\(709\) −4.47396 2.58304i −0.168023 0.0970082i 0.413630 0.910445i \(-0.364261\pi\)
−0.581653 + 0.813437i \(0.697594\pi\)
\(710\) −24.4308 23.3184i −0.916871 0.875123i
\(711\) 1.55582 0.0583479
\(712\) 11.4549 + 33.2603i 0.429289 + 1.24648i
\(713\) −17.7350 10.2393i −0.664179 0.383464i
\(714\) −27.9736 + 29.3081i −1.04689 + 1.09683i
\(715\) 3.69172i 0.138062i
\(716\) 3.01623 5.83612i 0.112722 0.218106i
\(717\) 19.3511 + 33.5171i 0.722681 + 1.25172i
\(718\) 4.81223 1.41035i 0.179591 0.0526337i
\(719\) 30.3540 17.5249i 1.13201 0.653568i 0.187573 0.982251i \(-0.439938\pi\)
0.944441 + 0.328682i \(0.106605\pi\)
\(720\) 7.31724 5.18824i 0.272697 0.193354i
\(721\) 16.9482i 0.631184i
\(722\) 3.32300 + 26.6638i 0.123669 + 0.992324i
\(723\) 2.75086 0.102306
\(724\) 14.0522 9.01068i 0.522246 0.334879i
\(725\) 3.69735 + 6.40400i 0.137316 + 0.237839i
\(726\) −2.60976 + 0.764858i −0.0968574 + 0.0283866i
\(727\) 7.95388 4.59217i 0.294993 0.170314i −0.345198 0.938530i \(-0.612188\pi\)
0.640191 + 0.768215i \(0.278855\pi\)
\(728\) −1.21616 3.53123i −0.0450738 0.130876i
\(729\) −29.7706 −1.10261
\(730\) 38.2403 + 36.4991i 1.41534 + 1.35089i
\(731\) −15.6848 + 27.1670i −0.580125 + 1.00481i
\(732\) 28.9061 + 14.9393i 1.06840 + 0.552171i
\(733\) 1.04212i 0.0384918i 0.999815 + 0.0192459i \(0.00612653\pi\)
−0.999815 + 0.0192459i \(0.993873\pi\)
\(734\) 35.7951 + 34.1653i 1.32122 + 1.26106i
\(735\) 4.18272 7.24468i 0.154282 0.267224i
\(736\) 1.71623 11.7255i 0.0632609 0.432206i
\(737\) −14.0078 8.08739i −0.515983 0.297903i
\(738\) −1.48940 + 6.12582i −0.0548255 + 0.225495i
\(739\) 3.24715 + 5.62423i 0.119448 + 0.206891i 0.919549 0.392975i \(-0.128554\pi\)
−0.800101 + 0.599865i \(0.795221\pi\)
\(740\) 45.2435 2.10922i 1.66318 0.0775364i
\(741\) 1.59768 2.31464i 0.0586922 0.0850305i
\(742\) −10.1072 9.64703i −0.371049 0.354154i
\(743\) 21.4582 + 37.1666i 0.787224 + 1.36351i 0.927662 + 0.373422i \(0.121816\pi\)
−0.140438 + 0.990089i \(0.544851\pi\)
\(744\) 40.0000 + 7.77252i 1.46647 + 0.284954i
\(745\) 25.0230 43.3412i 0.916773 1.58790i
\(746\) −8.44382 2.05298i −0.309150 0.0751651i
\(747\) −1.57115 + 2.72131i −0.0574854 + 0.0995676i
\(748\) 1.86920 + 40.0951i 0.0683448 + 1.46602i
\(749\) −27.1766 −0.993012
\(750\) −4.23266 14.4422i −0.154555 0.527355i
\(751\) −21.3186 + 36.9250i −0.777928 + 1.34741i 0.155205 + 0.987882i \(0.450396\pi\)
−0.933134 + 0.359529i \(0.882937\pi\)
\(752\) −0.527970 5.65026i −0.0192531 0.206044i
\(753\) 29.8205i 1.08672i
\(754\) 0.551821 + 1.88286i 0.0200961 + 0.0685697i
\(755\) 43.4117 25.0638i 1.57991 0.912164i
\(756\) 30.2311 + 15.6241i 1.09950 + 0.568242i
\(757\) 33.2731 19.2102i 1.20933 0.698208i 0.246718 0.969087i \(-0.420648\pi\)
0.962613 + 0.270879i \(0.0873144\pi\)
\(758\) −5.39547 + 22.1913i −0.195972 + 0.806025i
\(759\) 9.61296 0.348928
\(760\) −23.3549 23.8589i −0.847172 0.865454i
\(761\) −5.18110 −0.187815 −0.0939074 0.995581i \(-0.529936\pi\)
−0.0939074 + 0.995581i \(0.529936\pi\)
\(762\) 7.74052 31.8364i 0.280409 1.15331i
\(763\) −29.3728 + 16.9584i −1.06337 + 0.613935i
\(764\) 4.06955 7.87421i 0.147231 0.284879i
\(765\) −12.5174 + 7.22694i −0.452569 + 0.261291i
\(766\) 4.63134 + 15.8025i 0.167337 + 0.570969i
\(767\) 0.862463i 0.0311417i
\(768\) 4.36855 + 23.1717i 0.157636 + 0.836136i
\(769\) 23.3360 40.4192i 0.841519 1.45755i −0.0470919 0.998891i \(-0.514995\pi\)
0.888611 0.458663i \(-0.151671\pi\)
\(770\) −10.1149 34.5130i −0.364517 1.24376i
\(771\) −17.6750 −0.636549
\(772\) −14.1341 + 0.658923i −0.508698 + 0.0237152i
\(773\) −16.0227 + 27.7521i −0.576296 + 0.998175i 0.419603 + 0.907708i \(0.362169\pi\)
−0.995899 + 0.0904668i \(0.971164\pi\)
\(774\) 5.53823 + 1.34654i 0.199068 + 0.0484002i
\(775\) 11.4059 19.7556i 0.409712 0.709641i
\(776\) −51.6194 10.0303i −1.85303 0.360067i
\(777\) 18.5849 + 32.1899i 0.666728 + 1.15481i
\(778\) −14.1825 13.5367i −0.508466 0.485314i
\(779\) 23.3892 + 1.88815i 0.838004 + 0.0676500i
\(780\) 0.162741 + 3.49085i 0.00582706 + 0.124993i
\(781\) −13.7292 23.7796i −0.491268 0.850901i
\(782\) −4.51131 + 18.5548i −0.161324 + 0.663518i
\(783\) −15.4823 8.93874i −0.553294 0.319444i
\(784\) −4.84953 6.83954i −0.173198 0.244269i
\(785\) 33.1840 57.4763i 1.18439 2.05142i
\(786\) −15.3217 14.6241i −0.546508 0.521624i
\(787\) 32.2037i 1.14794i 0.818878 + 0.573968i \(0.194597\pi\)
−0.818878 + 0.573968i \(0.805403\pi\)
\(788\) −10.3670 + 20.0592i −0.369310 + 0.714581i
\(789\) 21.1272 36.5933i 0.752147 1.30276i
\(790\) 5.20509 + 4.96809i 0.185189 + 0.176757i
\(791\) 12.7299 0.452624
\(792\) 6.89533 2.37476i 0.245015 0.0843833i
\(793\) 4.18570 2.41661i 0.148638 0.0858164i
\(794\) −15.8562 + 4.64708i −0.562717 + 0.164919i
\(795\) 6.53688 + 11.3222i 0.231839 + 0.401558i
\(796\) −7.64065 11.9156i −0.270816 0.422339i
\(797\) −52.1341 −1.84668 −0.923342 0.383979i \(-0.874554\pi\)
−0.923342 + 0.383979i \(0.874554\pi\)
\(798\) 8.59447 26.0166i 0.304241 0.920977i
\(799\) 9.14431i 0.323503i
\(800\) 13.0614 + 1.91176i 0.461790 + 0.0675911i
\(801\) −8.91915 + 5.14947i −0.315143 + 0.181948i
\(802\) 33.5415 9.83019i 1.18439 0.347116i
\(803\) 21.4896 + 37.2210i 0.758350 + 1.31350i
\(804\) 13.6021 + 7.02986i 0.479710 + 0.247924i
\(805\) 17.1097i 0.603038i
\(806\) 4.17907 4.37844i 0.147202 0.154224i
\(807\) −19.8590 11.4656i −0.699068 0.403607i
\(808\) 1.37583 + 3.99485i 0.0484015 + 0.140538i
\(809\) −28.3362 −0.996249 −0.498124 0.867106i \(-0.665978\pi\)
−0.498124 + 0.867106i \(0.665978\pi\)
\(810\) −16.1515 15.4161i −0.567506 0.541665i
\(811\) −8.67018 5.00573i −0.304451 0.175775i 0.339990 0.940429i \(-0.389576\pi\)
−0.644441 + 0.764654i \(0.722910\pi\)
\(812\) 10.3177 + 16.0905i 0.362080 + 0.564667i
\(813\) −2.54651 + 4.41069i −0.0893101 + 0.154690i
\(814\) 35.7817 + 8.69977i 1.25415 + 0.304927i
\(815\) 14.0778 8.12780i 0.493123 0.284705i
\(816\) −3.53500 37.8311i −0.123750 1.32435i
\(817\) 1.70704 21.1457i 0.0597217 0.739794i
\(818\) 19.3981 + 18.5148i 0.678238 + 0.647356i
\(819\) 0.946943 0.546718i 0.0330889 0.0191039i
\(820\) −24.5440 + 15.7383i −0.857114 + 0.549606i
\(821\) −8.96021 5.17318i −0.312714 0.180545i 0.335427 0.942066i \(-0.391120\pi\)
−0.648140 + 0.761521i \(0.724453\pi\)
\(822\) −7.06610 + 29.0625i −0.246459 + 1.01367i
\(823\) 19.1933 + 11.0812i 0.669036 + 0.386268i 0.795711 0.605676i \(-0.207097\pi\)
−0.126676 + 0.991944i \(0.540431\pi\)
\(824\) 11.9962 + 10.4268i 0.417909 + 0.363235i
\(825\) 10.7082i 0.372812i
\(826\) 2.36306 + 8.06298i 0.0822215 + 0.280547i
\(827\) −15.5457 8.97531i −0.540577 0.312102i 0.204736 0.978817i \(-0.434366\pi\)
−0.745313 + 0.666715i \(0.767700\pi\)
\(828\) 3.46568 0.161568i 0.120441 0.00561486i
\(829\) −30.6699 −1.06521 −0.532605 0.846364i \(-0.678787\pi\)
−0.532605 + 0.846364i \(0.678787\pi\)
\(830\) −13.9461 + 4.08727i −0.484078 + 0.141871i
\(831\) 1.04255 + 1.80575i 0.0361656 + 0.0626407i
\(832\) 3.24767 + 1.31165i 0.112593 + 0.0454734i
\(833\) 6.75514 + 11.7002i 0.234052 + 0.405389i
\(834\) 5.22698 21.4983i 0.180996 0.744426i
\(835\) 18.3739i 0.635853i
\(836\) −12.7661 23.9553i −0.441527 0.828512i
\(837\) 55.1499i 1.90626i
\(838\) 12.1375 + 2.95104i 0.419282 + 0.101942i
\(839\) −18.8792 32.6997i −0.651782 1.12892i −0.982690 0.185256i \(-0.940688\pi\)
0.330908 0.943663i \(-0.392645\pi\)
\(840\) 11.0860 + 32.1893i 0.382504 + 1.11064i
\(841\) 9.47916 + 16.4184i 0.326868 + 0.566151i
\(842\) 0.728192 + 2.48466i 0.0250952 + 0.0856269i
\(843\) 7.99566 0.275385
\(844\) 36.3601 1.69508i 1.25157 0.0583471i
\(845\) −30.0386 17.3428i −1.03336 0.596610i
\(846\) 1.59437 0.467272i 0.0548157 0.0160651i
\(847\) 3.93537i 0.135221i
\(848\) 13.0465 1.21909i 0.448019 0.0418636i
\(849\) 20.5661 + 11.8739i 0.705827 + 0.407510i
\(850\) −20.6688 5.02531i −0.708935 0.172367i
\(851\) 15.1715 + 8.75927i 0.520073 + 0.300264i
\(852\) 14.0304 + 21.8805i 0.480674 + 0.749615i
\(853\) −3.05229 + 1.76224i −0.104508 + 0.0603379i −0.551343 0.834279i \(-0.685884\pi\)
0.446835 + 0.894616i \(0.352551\pi\)
\(854\) 32.5099 34.0608i 1.11246 1.16554i
\(855\) 5.55269 8.04448i 0.189898 0.275115i
\(856\) 16.7195 19.2361i 0.571461 0.657477i
\(857\) −31.7144 + 18.3103i −1.08334 + 0.625468i −0.931796 0.362982i \(-0.881759\pi\)
−0.151547 + 0.988450i \(0.548425\pi\)
\(858\) −0.671248 + 2.76081i −0.0229160 + 0.0942525i
\(859\) −2.99574 + 5.18877i −0.102213 + 0.177038i −0.912596 0.408862i \(-0.865926\pi\)
0.810383 + 0.585900i \(0.199259\pi\)
\(860\) 14.2287 + 22.1897i 0.485195 + 0.756664i
\(861\) −20.7218 11.9638i −0.706199 0.407724i
\(862\) −22.5543 + 23.6303i −0.768204 + 0.804851i
\(863\) −12.3914 −0.421808 −0.210904 0.977507i \(-0.567641\pi\)
−0.210904 + 0.977507i \(0.567641\pi\)
\(864\) −29.6577 + 11.7860i −1.00898 + 0.400967i
\(865\) 40.7858 + 23.5477i 1.38676 + 0.800645i
\(866\) 1.57644 + 1.50466i 0.0535697 + 0.0511305i
\(867\) 36.1718i 1.22846i
\(868\) 27.0728 52.3833i 0.918909 1.77800i
\(869\) 2.92506 + 5.06635i 0.0992259 + 0.171864i
\(870\) −5.03018 17.1634i −0.170539 0.581894i
\(871\) 1.96963 1.13717i 0.0667385 0.0385315i
\(872\) 6.06716 31.2237i 0.205460 1.05737i
\(873\) 15.3953i 0.521052i
\(874\) −2.62297 12.6445i −0.0887234 0.427706i
\(875\) −21.7780 −0.736230
\(876\) −21.9611 34.2485i −0.741997 1.15715i
\(877\) 10.4760 + 18.1449i 0.353749 + 0.612711i 0.986903 0.161315i \(-0.0515735\pi\)
−0.633154 + 0.774026i \(0.718240\pi\)
\(878\) −14.6546 50.0028i −0.494569 1.68751i
\(879\) 30.3732 17.5359i 1.02446 0.591473i
\(880\) 30.6519 + 14.0735i 1.03327 + 0.474416i
\(881\) 16.3102 0.549504 0.274752 0.961515i \(-0.411404\pi\)
0.274752 + 0.961515i \(0.411404\pi\)
\(882\) 1.69483 1.77568i 0.0570679 0.0597904i
\(883\) 3.10945 5.38572i 0.104641 0.181244i −0.808950 0.587877i \(-0.799964\pi\)
0.913592 + 0.406633i \(0.133297\pi\)
\(884\) −5.01386 2.59127i −0.168635 0.0871538i
\(885\) 7.86187i 0.264274i
\(886\) −25.1129 + 26.3109i −0.843685 + 0.883933i
\(887\) 0.671412 1.16292i 0.0225438 0.0390470i −0.854533 0.519396i \(-0.826157\pi\)
0.877077 + 0.480349i \(0.159490\pi\)
\(888\) −34.2184 6.64906i −1.14829 0.223128i
\(889\) −41.0597 23.7058i −1.37710 0.795069i
\(890\) −46.2830 11.2530i −1.55141 0.377201i
\(891\) −9.07652 15.7210i −0.304075 0.526673i
\(892\) 0.143979 + 3.08839i 0.00482076 + 0.103407i
\(893\) −2.65106 5.58698i −0.0887144 0.186961i
\(894\) −26.5937 + 27.8624i −0.889428 + 0.931858i
\(895\) 4.44762 + 7.70350i 0.148667 + 0.257500i
\(896\) 33.9556 + 3.36405i 1.13438 + 0.112385i
\(897\) −0.675839 + 1.17059i −0.0225656 + 0.0390848i
\(898\) 4.21741 17.3460i 0.140737 0.578843i
\(899\) −15.4887 + 26.8272i −0.516577 + 0.894737i
\(900\) 0.179976 + 3.86054i 0.00599919 + 0.128685i
\(901\) −21.1143 −0.703419
\(902\) −22.7482 + 6.66695i −0.757433 + 0.221985i
\(903\) −10.8162 + 18.7342i −0.359941 + 0.623435i
\(904\) −7.83166 + 9.01047i −0.260477 + 0.299684i
\(905\) 22.6028i 0.751342i
\(906\) −37.0222 + 10.8503i −1.22998 + 0.360477i
\(907\) 5.49954 3.17516i 0.182609 0.105429i −0.405909 0.913914i \(-0.633045\pi\)
0.588518 + 0.808484i \(0.299712\pi\)
\(908\) 3.03273 5.86806i 0.100645 0.194738i
\(909\) −1.07127 + 0.618497i −0.0355317 + 0.0205142i
\(910\) 4.91385 + 1.19473i 0.162892 + 0.0396048i
\(911\) 32.3135 1.07059 0.535296 0.844664i \(-0.320200\pi\)
0.535296 + 0.844664i \(0.320200\pi\)
\(912\) 13.1276 + 22.0892i 0.434697 + 0.731445i
\(913\) −11.8155 −0.391037
\(914\) 4.50165 + 1.09451i 0.148901 + 0.0362031i
\(915\) −38.1551 + 22.0289i −1.26137 + 0.728252i
\(916\) −8.09215 + 15.6576i −0.267372 + 0.517340i
\(917\) −26.5436 + 15.3250i −0.876547 + 0.506075i
\(918\) 49.3491 14.4630i 1.62876 0.477351i
\(919\) 38.7254i 1.27743i −0.769443 0.638716i \(-0.779466\pi\)
0.769443 0.638716i \(-0.220534\pi\)
\(920\) 12.1106 + 10.5262i 0.399274 + 0.347038i
\(921\) −1.22041 + 2.11380i −0.0402137 + 0.0696522i
\(922\) 22.5378 6.60528i 0.742243 0.217533i
\(923\) 3.86091 0.127083
\(924\) 1.28899 + 27.6494i 0.0424048 + 0.909597i
\(925\) −9.75726 + 16.9001i −0.320817 + 0.555671i
\(926\) 9.77526 40.2052i 0.321235 1.32122i
\(927\) −2.32669 + 4.02994i −0.0764185 + 0.132361i
\(928\) −17.7368 2.59609i −0.582239 0.0852208i
\(929\) −25.4113 44.0137i −0.833719 1.44404i −0.895069 0.445927i \(-0.852874\pi\)
0.0613502 0.998116i \(-0.480459\pi\)
\(930\) −38.0948 + 39.9121i −1.24918 + 1.30877i
\(931\) −7.51930 5.19019i −0.246435 0.170102i
\(932\) 0.588238 + 12.6179i 0.0192684 + 0.413313i
\(933\) 0.479697 + 0.830860i 0.0157046 + 0.0272011i
\(934\) −10.5731 2.57068i −0.345961 0.0841151i
\(935\) −47.0674 27.1744i −1.53927 0.888697i
\(936\) −0.195598 + 1.00661i −0.00639332 + 0.0329022i
\(937\) −16.1691 + 28.0057i −0.528221 + 0.914906i 0.471238 + 0.882006i \(0.343807\pi\)
−0.999459 + 0.0328994i \(0.989526\pi\)
\(938\) 15.2979 16.0277i 0.499495 0.523324i
\(939\) 28.4765i 0.929295i
\(940\) 6.82617 + 3.52791i 0.222645 + 0.115068i
\(941\) −14.0148 + 24.2743i −0.456868 + 0.791319i −0.998793 0.0491078i \(-0.984362\pi\)
0.541925 + 0.840427i \(0.317696\pi\)
\(942\) −35.2670 + 36.9494i −1.14906 + 1.20388i
\(943\) −11.2773 −0.367241
\(944\) −7.16093 3.28786i −0.233068 0.107011i
\(945\) −39.9041 + 23.0387i −1.29808 + 0.749448i
\(946\) 6.02746 + 20.5662i 0.195969 + 0.668665i
\(947\) −7.39400 12.8068i −0.240273 0.416164i 0.720519 0.693435i \(-0.243903\pi\)
−0.960792 + 0.277271i \(0.910570\pi\)
\(948\) −2.98925 4.66175i −0.0970863 0.151407i
\(949\) −6.04329 −0.196174
\(950\) 14.0851 2.92182i 0.456982 0.0947964i
\(951\) 30.8623i 1.00078i
\(952\) −53.9733 10.4877i −1.74929 0.339908i
\(953\) −6.69642 + 3.86618i −0.216918 + 0.125238i −0.604523 0.796588i \(-0.706636\pi\)
0.387604 + 0.921826i \(0.373303\pi\)
\(954\) 1.07893 + 3.68142i 0.0349318 + 0.119190i
\(955\) 6.00082 + 10.3937i 0.194182 + 0.336333i
\(956\) −24.1145 + 46.6593i −0.779918 + 1.50907i
\(957\) 14.5413i 0.470053i
\(958\) 36.5917 + 34.9255i 1.18222 + 1.12839i
\(959\) 37.4823 + 21.6404i 1.21037 + 0.698805i
\(960\) −29.6045 11.9565i −0.955481 0.385895i
\(961\) 64.5615 2.08263
\(962\) −3.57502 + 3.74557i −0.115263 + 0.120762i
\(963\) 6.46206 + 3.73087i 0.208237 + 0.120226i
\(964\) 2.01511 + 3.14258i 0.0649024 + 0.101216i
\(965\) 9.57939 16.5920i 0.308371 0.534115i
\(966\) −3.11098 + 12.7953i −0.100094 + 0.411682i
\(967\) −29.1031 + 16.8027i −0.935892 + 0.540338i −0.888670 0.458547i \(-0.848370\pi\)
−0.0472221 + 0.998884i \(0.515037\pi\)
\(968\) −2.78553 2.42110i −0.0895302 0.0778172i
\(969\) −17.7501 37.4074i −0.570215 1.20170i
\(970\) 49.1607 51.5059i 1.57845 1.65376i
\(971\) 13.6746 7.89505i 0.438840 0.253364i −0.264265 0.964450i \(-0.585130\pi\)
0.703105 + 0.711086i \(0.251796\pi\)
\(972\) −8.99592 14.0292i −0.288544 0.449986i
\(973\) −27.7266 16.0080i −0.888875 0.513192i
\(974\) −4.10521 0.998119i −0.131539 0.0319818i
\(975\) −1.30396 0.752841i −0.0417601 0.0241102i
\(976\) 4.10824 + 43.9659i 0.131502 + 1.40731i
\(977\) 32.5834i 1.04243i −0.853424 0.521217i \(-0.825478\pi\)
0.853424 0.521217i \(-0.174522\pi\)
\(978\) −12.0058 + 3.51859i −0.383902 + 0.112512i
\(979\) −33.5373 19.3628i −1.07186 0.618838i
\(980\) 11.3403 0.528677i 0.362253 0.0168880i
\(981\) 9.31236 0.297321
\(982\) −12.9179 44.0770i −0.412227 1.40655i
\(983\) 3.64307 + 6.30998i 0.116196 + 0.201257i 0.918257 0.395985i \(-0.129597\pi\)
−0.802061 + 0.597242i \(0.796263\pi\)
\(984\) 21.2166 7.30701i 0.676361 0.232939i
\(985\) −15.2868 26.4776i −0.487079 0.843646i
\(986\) 28.0674 + 6.82414i 0.893847 + 0.217325i
\(987\) 6.30588i 0.200718i
\(988\) 3.81461 + 0.129621i 0.121359 + 0.00412381i
\(989\) 10.1956i 0.324202i
\(990\) −2.33291 + 9.59512i −0.0741446 + 0.304953i
\(991\) −1.76345 3.05438i −0.0560177 0.0970256i 0.836657 0.547728i \(-0.184507\pi\)
−0.892674 + 0.450702i \(0.851174\pi\)
\(992\) 20.4223 + 51.3897i 0.648408 + 1.63162i
\(993\) 5.43131 + 9.40730i 0.172357 + 0.298532i
\(994\) 36.0948 10.5785i 1.14486 0.335530i
\(995\) 19.1661 0.607608
\(996\) 11.1726 0.520861i 0.354019 0.0165041i
\(997\) 13.7973 + 7.96589i 0.436966 + 0.252282i 0.702310 0.711871i \(-0.252152\pi\)
−0.265344 + 0.964154i \(0.585485\pi\)
\(998\) −3.86998 13.2047i −0.122502 0.417988i
\(999\) 47.1784i 1.49266i
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 152.2.o.c.107.13 yes 28
4.3 odd 2 608.2.s.c.335.3 28
8.3 odd 2 inner 152.2.o.c.107.9 yes 28
8.5 even 2 608.2.s.c.335.4 28
19.8 odd 6 inner 152.2.o.c.27.9 28
76.27 even 6 608.2.s.c.559.4 28
152.27 even 6 inner 152.2.o.c.27.13 yes 28
152.141 odd 6 608.2.s.c.559.3 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.2.o.c.27.9 28 19.8 odd 6 inner
152.2.o.c.27.13 yes 28 152.27 even 6 inner
152.2.o.c.107.9 yes 28 8.3 odd 2 inner
152.2.o.c.107.13 yes 28 1.1 even 1 trivial
608.2.s.c.335.3 28 4.3 odd 2
608.2.s.c.335.4 28 8.5 even 2
608.2.s.c.559.3 28 152.141 odd 6
608.2.s.c.559.4 28 76.27 even 6