Properties

Label 280.2.w.a.43.3
Level $280$
Weight $2$
Character 280.43
Analytic conductor $2.236$
Analytic rank $0$
Dimension $72$
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] = [280,2,Mod(43,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.w (of order \(4\), 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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.3
Character \(\chi\) \(=\) 280.43
Dual form 280.2.w.a.267.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33794 - 0.458170i) q^{2} +(2.03802 + 2.03802i) q^{3} +(1.58016 + 1.22601i) q^{4} +(-1.56810 + 1.59407i) q^{5} +(-1.79299 - 3.66051i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-1.55244 - 2.36430i) q^{8} +5.30708i q^{9} +O(q^{10})\) \(q+(-1.33794 - 0.458170i) q^{2} +(2.03802 + 2.03802i) q^{3} +(1.58016 + 1.22601i) q^{4} +(-1.56810 + 1.59407i) q^{5} +(-1.79299 - 3.66051i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-1.55244 - 2.36430i) q^{8} +5.30708i q^{9} +(2.82837 - 1.41432i) q^{10} +1.12517 q^{11} +(0.721774 + 5.71904i) q^{12} +(1.14209 - 1.14209i) q^{13} +(-0.622091 - 1.27004i) q^{14} +(-6.44458 + 0.0529419i) q^{15} +(0.993815 + 3.87457i) q^{16} +(-3.40113 + 3.40113i) q^{17} +(2.43155 - 7.10055i) q^{18} -6.04642i q^{19} +(-4.43219 + 0.596396i) q^{20} +2.88220i q^{21} +(-1.50541 - 0.515519i) q^{22} +(-4.27148 + 4.27148i) q^{23} +(1.65460 - 7.98242i) q^{24} +(-0.0821439 - 4.99933i) q^{25} +(-2.05133 + 1.00478i) q^{26} +(-4.70189 + 4.70189i) q^{27} +(0.250425 + 1.98426i) q^{28} +5.08560 q^{29} +(8.64671 + 2.88188i) q^{30} +1.17687i q^{31} +(0.445550 - 5.63928i) q^{32} +(2.29312 + 2.29312i) q^{33} +(6.10880 - 2.99221i) q^{34} +(-2.23599 + 0.0183686i) q^{35} +(-6.50652 + 8.38605i) q^{36} +(2.57874 + 2.57874i) q^{37} +(-2.77029 + 8.08974i) q^{38} +4.65523 q^{39} +(6.20325 + 1.23276i) q^{40} +3.89085 q^{41} +(1.32054 - 3.85621i) q^{42} +(8.80877 + 8.80877i) q^{43} +(1.77795 + 1.37947i) q^{44} +(-8.45989 - 8.32202i) q^{45} +(7.67204 - 3.75792i) q^{46} +(-1.04379 - 1.04379i) q^{47} +(-5.87106 + 9.92190i) q^{48} +1.00000i q^{49} +(-2.18064 + 6.72643i) q^{50} -13.8632 q^{51} +(3.20491 - 0.404477i) q^{52} +(7.09313 - 7.09313i) q^{53} +(8.44511 - 4.13658i) q^{54} +(-1.76438 + 1.79360i) q^{55} +(0.574075 - 2.76956i) q^{56} +(12.3228 - 12.3228i) q^{57} +(-6.80422 - 2.33007i) q^{58} -13.0335i q^{59} +(-10.2484 - 7.81744i) q^{60} -14.1452i q^{61} +(0.539209 - 1.57459i) q^{62} +(-3.75268 + 3.75268i) q^{63} +(-3.17987 + 7.34088i) q^{64} +(0.0296683 + 3.61150i) q^{65} +(-2.01742 - 4.11870i) q^{66} +(-8.52477 + 8.52477i) q^{67} +(-9.54415 + 1.20452i) q^{68} -17.4108 q^{69} +(3.00004 + 0.999889i) q^{70} +3.20531i q^{71} +(12.5476 - 8.23892i) q^{72} +(0.661851 + 0.661851i) q^{73} +(-2.26869 - 4.63169i) q^{74} +(10.0213 - 10.3562i) q^{75} +(7.41295 - 9.55432i) q^{76} +(0.795615 + 0.795615i) q^{77} +(-6.22841 - 2.13289i) q^{78} +7.84196 q^{79} +(-7.73476 - 4.49149i) q^{80} -3.24389 q^{81} +(-5.20572 - 1.78267i) q^{82} +(-4.69230 - 4.69230i) q^{83} +(-3.53360 + 4.55434i) q^{84} +(-0.0883515 - 10.7550i) q^{85} +(-7.74968 - 15.8215i) q^{86} +(10.3646 + 10.3646i) q^{87} +(-1.74676 - 2.66024i) q^{88} -4.54385i q^{89} +(7.50591 + 15.0104i) q^{90} +1.61516 q^{91} +(-11.9865 + 1.51276i) q^{92} +(-2.39850 + 2.39850i) q^{93} +(0.918297 + 1.87477i) q^{94} +(9.63844 + 9.48138i) q^{95} +(12.4010 - 10.5849i) q^{96} +(8.93455 - 8.93455i) q^{97} +(0.458170 - 1.33794i) q^{98} +5.97137i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33794 0.458170i −0.946066 0.323975i
\(3\) 2.03802 + 2.03802i 1.17665 + 1.17665i 0.980591 + 0.196062i \(0.0628155\pi\)
0.196062 + 0.980591i \(0.437185\pi\)
\(4\) 1.58016 + 1.22601i 0.790080 + 0.613003i
\(5\) −1.56810 + 1.59407i −0.701274 + 0.712892i
\(6\) −1.79299 3.66051i −0.731985 1.49440i
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) −1.55244 2.36430i −0.548870 0.835908i
\(9\) 5.30708i 1.76903i
\(10\) 2.82837 1.41432i 0.894411 0.447247i
\(11\) 1.12517 0.339251 0.169626 0.985509i \(-0.445744\pi\)
0.169626 + 0.985509i \(0.445744\pi\)
\(12\) 0.721774 + 5.71904i 0.208358 + 1.65094i
\(13\) 1.14209 1.14209i 0.316760 0.316760i −0.530761 0.847521i \(-0.678094\pi\)
0.847521 + 0.530761i \(0.178094\pi\)
\(14\) −0.622091 1.27004i −0.166261 0.339433i
\(15\) −6.44458 + 0.0529419i −1.66398 + 0.0136695i
\(16\) 0.993815 + 3.87457i 0.248454 + 0.968644i
\(17\) −3.40113 + 3.40113i −0.824896 + 0.824896i −0.986806 0.161910i \(-0.948235\pi\)
0.161910 + 0.986806i \(0.448235\pi\)
\(18\) 2.43155 7.10055i 0.573121 1.67362i
\(19\) 6.04642i 1.38714i −0.720387 0.693572i \(-0.756036\pi\)
0.720387 0.693572i \(-0.243964\pi\)
\(20\) −4.43219 + 0.596396i −0.991068 + 0.133358i
\(21\) 2.88220i 0.628948i
\(22\) −1.50541 0.515519i −0.320954 0.109909i
\(23\) −4.27148 + 4.27148i −0.890665 + 0.890665i −0.994586 0.103921i \(-0.966861\pi\)
0.103921 + 0.994586i \(0.466861\pi\)
\(24\) 1.65460 7.98242i 0.337744 1.62940i
\(25\) −0.0821439 4.99933i −0.0164288 0.999865i
\(26\) −2.05133 + 1.00478i −0.402298 + 0.197053i
\(27\) −4.70189 + 4.70189i −0.904880 + 0.904880i
\(28\) 0.250425 + 1.98426i 0.0473258 + 0.374990i
\(29\) 5.08560 0.944372 0.472186 0.881499i \(-0.343465\pi\)
0.472186 + 0.881499i \(0.343465\pi\)
\(30\) 8.64671 + 2.88188i 1.57867 + 0.526157i
\(31\) 1.17687i 0.211373i 0.994400 + 0.105686i \(0.0337040\pi\)
−0.994400 + 0.105686i \(0.966296\pi\)
\(32\) 0.445550 5.63928i 0.0787628 0.996893i
\(33\) 2.29312 + 2.29312i 0.399181 + 0.399181i
\(34\) 6.10880 2.99221i 1.04765 0.513160i
\(35\) −2.23599 + 0.0183686i −0.377952 + 0.00310485i
\(36\) −6.50652 + 8.38605i −1.08442 + 1.39767i
\(37\) 2.57874 + 2.57874i 0.423942 + 0.423942i 0.886558 0.462617i \(-0.153089\pi\)
−0.462617 + 0.886558i \(0.653089\pi\)
\(38\) −2.77029 + 8.08974i −0.449400 + 1.31233i
\(39\) 4.65523 0.745433
\(40\) 6.20325 + 1.23276i 0.980820 + 0.194916i
\(41\) 3.89085 0.607649 0.303824 0.952728i \(-0.401736\pi\)
0.303824 + 0.952728i \(0.401736\pi\)
\(42\) 1.32054 3.85621i 0.203763 0.595026i
\(43\) 8.80877 + 8.80877i 1.34333 + 1.34333i 0.892727 + 0.450599i \(0.148789\pi\)
0.450599 + 0.892727i \(0.351211\pi\)
\(44\) 1.77795 + 1.37947i 0.268036 + 0.207962i
\(45\) −8.45989 8.32202i −1.26113 1.24057i
\(46\) 7.67204 3.75792i 1.13118 0.554074i
\(47\) −1.04379 1.04379i −0.152253 0.152253i 0.626870 0.779123i \(-0.284336\pi\)
−0.779123 + 0.626870i \(0.784336\pi\)
\(48\) −5.87106 + 9.92190i −0.847414 + 1.43210i
\(49\) 1.00000i 0.142857i
\(50\) −2.18064 + 6.72643i −0.308389 + 0.951260i
\(51\) −13.8632 −1.94123
\(52\) 3.20491 0.404477i 0.444441 0.0560909i
\(53\) 7.09313 7.09313i 0.974316 0.974316i −0.0253624 0.999678i \(-0.508074\pi\)
0.999678 + 0.0253624i \(0.00807395\pi\)
\(54\) 8.44511 4.13658i 1.14923 0.562917i
\(55\) −1.76438 + 1.79360i −0.237908 + 0.241849i
\(56\) 0.574075 2.76956i 0.0767140 0.370097i
\(57\) 12.3228 12.3228i 1.63219 1.63219i
\(58\) −6.80422 2.33007i −0.893437 0.305953i
\(59\) 13.0335i 1.69682i −0.529341 0.848409i \(-0.677561\pi\)
0.529341 0.848409i \(-0.322439\pi\)
\(60\) −10.2484 7.81744i −1.32306 1.00923i
\(61\) 14.1452i 1.81111i −0.424232 0.905553i \(-0.639456\pi\)
0.424232 0.905553i \(-0.360544\pi\)
\(62\) 0.539209 1.57459i 0.0684795 0.199973i
\(63\) −3.75268 + 3.75268i −0.472793 + 0.472793i
\(64\) −3.17987 + 7.34088i −0.397483 + 0.917609i
\(65\) 0.0296683 + 3.61150i 0.00367989 + 0.447951i
\(66\) −2.01742 4.11870i −0.248327 0.506977i
\(67\) −8.52477 + 8.52477i −1.04147 + 1.04147i −0.0423637 + 0.999102i \(0.513489\pi\)
−0.999102 + 0.0423637i \(0.986511\pi\)
\(68\) −9.54415 + 1.20452i −1.15740 + 0.146070i
\(69\) −17.4108 −2.09601
\(70\) 3.00004 + 0.999889i 0.358573 + 0.119510i
\(71\) 3.20531i 0.380400i 0.981745 + 0.190200i \(0.0609136\pi\)
−0.981745 + 0.190200i \(0.939086\pi\)
\(72\) 12.5476 8.23892i 1.47874 0.970967i
\(73\) 0.661851 + 0.661851i 0.0774638 + 0.0774638i 0.744777 0.667313i \(-0.232556\pi\)
−0.667313 + 0.744777i \(0.732556\pi\)
\(74\) −2.26869 4.63169i −0.263730 0.538424i
\(75\) 10.0213 10.3562i 1.15716 1.19583i
\(76\) 7.41295 9.55432i 0.850324 1.09596i
\(77\) 0.795615 + 0.795615i 0.0906688 + 0.0906688i
\(78\) −6.22841 2.13289i −0.705229 0.241502i
\(79\) 7.84196 0.882290 0.441145 0.897436i \(-0.354572\pi\)
0.441145 + 0.897436i \(0.354572\pi\)
\(80\) −7.73476 4.49149i −0.864772 0.502164i
\(81\) −3.24389 −0.360432
\(82\) −5.20572 1.78267i −0.574875 0.196863i
\(83\) −4.69230 4.69230i −0.515047 0.515047i 0.401022 0.916069i \(-0.368655\pi\)
−0.916069 + 0.401022i \(0.868655\pi\)
\(84\) −3.53360 + 4.55434i −0.385547 + 0.496919i
\(85\) −0.0883515 10.7550i −0.00958306 1.16654i
\(86\) −7.74968 15.8215i −0.835670 1.70608i
\(87\) 10.3646 + 10.3646i 1.11120 + 1.11120i
\(88\) −1.74676 2.66024i −0.186205 0.283583i
\(89\) 4.54385i 0.481647i −0.970569 0.240824i \(-0.922582\pi\)
0.970569 0.240824i \(-0.0774176\pi\)
\(90\) 7.50591 + 15.0104i 0.791192 + 1.58224i
\(91\) 1.61516 0.169315
\(92\) −11.9865 + 1.51276i −1.24968 + 0.157716i
\(93\) −2.39850 + 2.39850i −0.248713 + 0.248713i
\(94\) 0.918297 + 1.87477i 0.0947151 + 0.193367i
\(95\) 9.63844 + 9.48138i 0.988884 + 0.972769i
\(96\) 12.4010 10.5849i 1.26567 1.08032i
\(97\) 8.93455 8.93455i 0.907166 0.907166i −0.0888762 0.996043i \(-0.528328\pi\)
0.996043 + 0.0888762i \(0.0283275\pi\)
\(98\) 0.458170 1.33794i 0.0462822 0.135152i
\(99\) 5.97137i 0.600145i
\(100\) 5.99941 8.00045i 0.599941 0.800045i
\(101\) 5.60617i 0.557834i 0.960315 + 0.278917i \(0.0899755\pi\)
−0.960315 + 0.278917i \(0.910025\pi\)
\(102\) 18.5481 + 6.35169i 1.83653 + 0.628911i
\(103\) −4.23937 + 4.23937i −0.417718 + 0.417718i −0.884416 0.466699i \(-0.845443\pi\)
0.466699 + 0.884416i \(0.345443\pi\)
\(104\) −4.47329 0.927226i −0.438642 0.0909220i
\(105\) −4.59444 4.51957i −0.448372 0.441065i
\(106\) −12.7400 + 6.24031i −1.23742 + 0.606113i
\(107\) −0.0282900 + 0.0282900i −0.00273490 + 0.00273490i −0.708473 0.705738i \(-0.750616\pi\)
0.705738 + 0.708473i \(0.250616\pi\)
\(108\) −13.1943 + 1.66519i −1.26962 + 0.160233i
\(109\) 12.2940 1.17756 0.588778 0.808295i \(-0.299609\pi\)
0.588778 + 0.808295i \(0.299609\pi\)
\(110\) 3.18240 1.59135i 0.303430 0.151729i
\(111\) 10.5111i 0.997666i
\(112\) −2.03700 + 3.44247i −0.192479 + 0.325283i
\(113\) 0.542652 + 0.542652i 0.0510484 + 0.0510484i 0.732170 0.681122i \(-0.238508\pi\)
−0.681122 + 0.732170i \(0.738508\pi\)
\(114\) −22.1330 + 10.8412i −2.07295 + 1.01537i
\(115\) −0.110961 13.5071i −0.0103471 1.25955i
\(116\) 8.03606 + 6.23497i 0.746129 + 0.578903i
\(117\) 6.06119 + 6.06119i 0.560357 + 0.560357i
\(118\) −5.97156 + 17.4380i −0.549727 + 1.60530i
\(119\) −4.80993 −0.440925
\(120\) 10.1300 + 15.1548i 0.924737 + 1.38343i
\(121\) −9.73399 −0.884908
\(122\) −6.48090 + 18.9254i −0.586753 + 1.71343i
\(123\) 7.92964 + 7.92964i 0.714992 + 0.714992i
\(124\) −1.44286 + 1.85965i −0.129572 + 0.167002i
\(125\) 8.09810 + 7.70848i 0.724316 + 0.689468i
\(126\) 6.74021 3.30149i 0.600466 0.294120i
\(127\) −14.5948 14.5948i −1.29508 1.29508i −0.931603 0.363478i \(-0.881589\pi\)
−0.363478 0.931603i \(-0.618411\pi\)
\(128\) 7.61784 8.36472i 0.673328 0.739344i
\(129\) 35.9050i 3.16126i
\(130\) 1.61498 4.84555i 0.141644 0.424983i
\(131\) −9.64508 −0.842694 −0.421347 0.906899i \(-0.638443\pi\)
−0.421347 + 0.906899i \(0.638443\pi\)
\(132\) 0.812119 + 6.43489i 0.0706859 + 0.560085i
\(133\) 4.27547 4.27547i 0.370730 0.370730i
\(134\) 15.3114 7.49982i 1.32270 0.647886i
\(135\) −0.122141 14.8682i −0.0105123 1.27965i
\(136\) 13.3214 + 2.76126i 1.14230 + 0.236776i
\(137\) −0.237816 + 0.237816i −0.0203180 + 0.0203180i −0.717193 0.696875i \(-0.754573\pi\)
0.696875 + 0.717193i \(0.254573\pi\)
\(138\) 23.2945 + 7.97709i 1.98296 + 0.679055i
\(139\) 15.6138i 1.32435i 0.749350 + 0.662174i \(0.230366\pi\)
−0.749350 + 0.662174i \(0.769634\pi\)
\(140\) −3.55575 2.71232i −0.300516 0.229233i
\(141\) 4.25455i 0.358298i
\(142\) 1.46857 4.28850i 0.123240 0.359883i
\(143\) 1.28505 1.28505i 0.107461 0.107461i
\(144\) −20.5627 + 5.27426i −1.71356 + 0.439522i
\(145\) −7.97471 + 8.10682i −0.662263 + 0.673234i
\(146\) −0.582276 1.18876i −0.0481895 0.0983822i
\(147\) −2.03802 + 2.03802i −0.168093 + 0.168093i
\(148\) 0.913270 + 7.23637i 0.0750704 + 0.594826i
\(149\) 13.1459 1.07696 0.538479 0.842639i \(-0.318999\pi\)
0.538479 + 0.842639i \(0.318999\pi\)
\(150\) −18.1528 + 9.26443i −1.48217 + 0.756438i
\(151\) 10.6597i 0.867477i −0.901039 0.433739i \(-0.857194\pi\)
0.901039 0.433739i \(-0.142806\pi\)
\(152\) −14.2956 + 9.38670i −1.15952 + 0.761362i
\(153\) −18.0501 18.0501i −1.45926 1.45926i
\(154\) −0.699957 1.42901i −0.0564042 0.115153i
\(155\) −1.87603 1.84545i −0.150686 0.148230i
\(156\) 7.35601 + 5.70734i 0.588952 + 0.456953i
\(157\) −6.91900 6.91900i −0.552196 0.552196i 0.374878 0.927074i \(-0.377685\pi\)
−0.927074 + 0.374878i \(0.877685\pi\)
\(158\) −10.4921 3.59295i −0.834704 0.285840i
\(159\) 28.9119 2.29287
\(160\) 8.29077 + 9.55318i 0.655443 + 0.755245i
\(161\) −6.04078 −0.476081
\(162\) 4.34013 + 1.48625i 0.340993 + 0.116771i
\(163\) −5.43455 5.43455i −0.425667 0.425667i 0.461483 0.887149i \(-0.347318\pi\)
−0.887149 + 0.461483i \(0.847318\pi\)
\(164\) 6.14817 + 4.77021i 0.480091 + 0.372491i
\(165\) −7.25125 + 0.0595686i −0.564509 + 0.00463741i
\(166\) 4.12814 + 8.42788i 0.320406 + 0.654130i
\(167\) −7.37047 7.37047i −0.570344 0.570344i 0.361881 0.932224i \(-0.382135\pi\)
−0.932224 + 0.361881i \(0.882135\pi\)
\(168\) 6.81440 4.47444i 0.525742 0.345211i
\(169\) 10.3912i 0.799326i
\(170\) −4.80939 + 14.4300i −0.368864 + 1.10673i
\(171\) 32.0889 2.45390
\(172\) 3.11966 + 24.7189i 0.237872 + 1.88480i
\(173\) −2.51488 + 2.51488i −0.191203 + 0.191203i −0.796216 0.605013i \(-0.793168\pi\)
0.605013 + 0.796216i \(0.293168\pi\)
\(174\) −9.11842 18.6159i −0.691266 1.41127i
\(175\) 3.47697 3.59314i 0.262834 0.271616i
\(176\) 1.11821 + 4.35955i 0.0842883 + 0.328614i
\(177\) 26.5626 26.5626i 1.99657 1.99657i
\(178\) −2.08186 + 6.07940i −0.156042 + 0.455670i
\(179\) 15.2275i 1.13816i −0.822282 0.569080i \(-0.807299\pi\)
0.822282 0.569080i \(-0.192701\pi\)
\(180\) −3.16512 23.5220i −0.235914 1.75323i
\(181\) 16.1726i 1.20210i 0.799211 + 0.601050i \(0.205251\pi\)
−0.799211 + 0.601050i \(0.794749\pi\)
\(182\) −2.16099 0.740020i −0.160183 0.0548539i
\(183\) 28.8283 28.8283i 2.13105 2.13105i
\(184\) 16.7303 + 3.46787i 1.23337 + 0.255654i
\(185\) −8.15441 + 0.0669881i −0.599524 + 0.00492506i
\(186\) 4.30796 2.11012i 0.315875 0.154722i
\(187\) −3.82685 + 3.82685i −0.279847 + 0.279847i
\(188\) −0.369664 2.92906i −0.0269605 0.213624i
\(189\) −6.64948 −0.483679
\(190\) −8.55157 17.1015i −0.620396 1.24068i
\(191\) 0.150312i 0.0108762i 0.999985 + 0.00543811i \(0.00173101\pi\)
−0.999985 + 0.00543811i \(0.998269\pi\)
\(192\) −21.4415 + 8.48024i −1.54741 + 0.612008i
\(193\) 1.53880 + 1.53880i 0.110766 + 0.110766i 0.760317 0.649552i \(-0.225043\pi\)
−0.649552 + 0.760317i \(0.725043\pi\)
\(194\) −16.0474 + 7.86034i −1.15214 + 0.564340i
\(195\) −7.29985 + 7.42078i −0.522753 + 0.531413i
\(196\) −1.22601 + 1.58016i −0.0875719 + 0.112869i
\(197\) 12.2359 + 12.2359i 0.871771 + 0.871771i 0.992665 0.120894i \(-0.0385763\pi\)
−0.120894 + 0.992665i \(0.538576\pi\)
\(198\) 2.73590 7.98933i 0.194432 0.567777i
\(199\) −5.52414 −0.391596 −0.195798 0.980644i \(-0.562730\pi\)
−0.195798 + 0.980644i \(0.562730\pi\)
\(200\) −11.6924 + 7.95536i −0.826778 + 0.562529i
\(201\) −34.7474 −2.45089
\(202\) 2.56858 7.50071i 0.180724 0.527748i
\(203\) 3.59606 + 3.59606i 0.252394 + 0.252394i
\(204\) −21.9061 16.9964i −1.53373 1.18998i
\(205\) −6.10123 + 6.20230i −0.426128 + 0.433188i
\(206\) 7.61437 3.72967i 0.530518 0.259858i
\(207\) −22.6691 22.6691i −1.57561 1.57561i
\(208\) 5.56016 + 3.29010i 0.385528 + 0.228127i
\(209\) 6.80325i 0.470591i
\(210\) 4.07635 + 8.15194i 0.281295 + 0.562538i
\(211\) −14.6760 −1.01034 −0.505170 0.863020i \(-0.668570\pi\)
−0.505170 + 0.863020i \(0.668570\pi\)
\(212\) 19.9045 2.51206i 1.36705 0.172529i
\(213\) −6.53249 + 6.53249i −0.447599 + 0.447599i
\(214\) 0.0508119 0.0248886i 0.00347343 0.00170135i
\(215\) −27.8548 + 0.228826i −1.89968 + 0.0156058i
\(216\) 18.4161 + 3.81730i 1.25306 + 0.259735i
\(217\) −0.832176 + 0.832176i −0.0564918 + 0.0564918i
\(218\) −16.4487 5.63276i −1.11405 0.381499i
\(219\) 2.69774i 0.182296i
\(220\) −4.98697 + 0.671046i −0.336221 + 0.0452419i
\(221\) 7.76883i 0.522588i
\(222\) 4.81585 14.0632i 0.323219 0.943857i
\(223\) −6.10264 + 6.10264i −0.408663 + 0.408663i −0.881272 0.472609i \(-0.843312\pi\)
0.472609 + 0.881272i \(0.343312\pi\)
\(224\) 4.30262 3.67252i 0.287481 0.245381i
\(225\) 26.5318 0.435945i 1.76879 0.0290630i
\(226\) −0.477409 0.974662i −0.0317567 0.0648336i
\(227\) 10.3883 10.3883i 0.689496 0.689496i −0.272625 0.962120i \(-0.587892\pi\)
0.962120 + 0.272625i \(0.0878918\pi\)
\(228\) 34.5797 4.36415i 2.29010 0.289023i
\(229\) −11.8631 −0.783937 −0.391969 0.919979i \(-0.628206\pi\)
−0.391969 + 0.919979i \(0.628206\pi\)
\(230\) −6.04011 + 18.1226i −0.398273 + 1.19497i
\(231\) 3.24297i 0.213371i
\(232\) −7.89508 12.0239i −0.518337 0.789407i
\(233\) 3.55821 + 3.55821i 0.233106 + 0.233106i 0.813988 0.580882i \(-0.197292\pi\)
−0.580882 + 0.813988i \(0.697292\pi\)
\(234\) −5.33245 10.8866i −0.348593 0.711676i
\(235\) 3.30065 0.0271147i 0.215311 0.00176877i
\(236\) 15.9792 20.5950i 1.04016 1.34062i
\(237\) 15.9821 + 15.9821i 1.03815 + 1.03815i
\(238\) 6.43539 + 2.20376i 0.417144 + 0.142849i
\(239\) −19.4118 −1.25565 −0.627824 0.778355i \(-0.716054\pi\)
−0.627824 + 0.778355i \(0.716054\pi\)
\(240\) −6.60985 24.9174i −0.426664 1.60841i
\(241\) 3.80736 0.245253 0.122627 0.992453i \(-0.460868\pi\)
0.122627 + 0.992453i \(0.460868\pi\)
\(242\) 13.0235 + 4.45982i 0.837181 + 0.286688i
\(243\) 7.49455 + 7.49455i 0.480776 + 0.480776i
\(244\) 17.3421 22.3517i 1.11021 1.43092i
\(245\) −1.59407 1.56810i −0.101842 0.100182i
\(246\) −6.97625 14.2425i −0.444790 0.908069i
\(247\) −6.90558 6.90558i −0.439392 0.439392i
\(248\) 2.78249 1.82703i 0.176688 0.116016i
\(249\) 19.1260i 1.21206i
\(250\) −7.30297 14.0238i −0.461881 0.886942i
\(251\) −7.38557 −0.466173 −0.233086 0.972456i \(-0.574883\pi\)
−0.233086 + 0.972456i \(0.574883\pi\)
\(252\) −10.5306 + 1.32902i −0.663368 + 0.0837207i
\(253\) −4.80614 + 4.80614i −0.302159 + 0.302159i
\(254\) 12.8401 + 26.2139i 0.805658 + 1.64481i
\(255\) 21.7388 22.0989i 1.36134 1.38389i
\(256\) −14.0247 + 7.70122i −0.876541 + 0.481327i
\(257\) −11.3747 + 11.3747i −0.709532 + 0.709532i −0.966437 0.256904i \(-0.917297\pi\)
0.256904 + 0.966437i \(0.417297\pi\)
\(258\) 16.4506 48.0387i 1.02417 2.99076i
\(259\) 3.64689i 0.226606i
\(260\) −4.38084 + 5.74312i −0.271688 + 0.356173i
\(261\) 26.9897i 1.67062i
\(262\) 12.9045 + 4.41908i 0.797244 + 0.273012i
\(263\) −1.88534 + 1.88534i −0.116255 + 0.116255i −0.762841 0.646586i \(-0.776196\pi\)
0.646586 + 0.762841i \(0.276196\pi\)
\(264\) 1.86171 8.98157i 0.114580 0.552778i
\(265\) 0.184259 + 22.4297i 0.0113189 + 1.37784i
\(266\) −7.67920 + 3.76142i −0.470842 + 0.230628i
\(267\) 9.26048 9.26048i 0.566732 0.566732i
\(268\) −23.9219 + 3.01908i −1.46126 + 0.184420i
\(269\) 4.32967 0.263985 0.131992 0.991251i \(-0.457863\pi\)
0.131992 + 0.991251i \(0.457863\pi\)
\(270\) −6.64874 + 19.9487i −0.404629 + 1.21404i
\(271\) 20.9148i 1.27049i 0.772313 + 0.635243i \(0.219100\pi\)
−0.772313 + 0.635243i \(0.780900\pi\)
\(272\) −16.5580 9.79785i −1.00398 0.594082i
\(273\) 3.29175 + 3.29175i 0.199225 + 0.199225i
\(274\) 0.427143 0.209223i 0.0258046 0.0126396i
\(275\) −0.0924259 5.62509i −0.00557349 0.339206i
\(276\) −27.5118 21.3457i −1.65602 1.28486i
\(277\) −22.2493 22.2493i −1.33683 1.33683i −0.899114 0.437714i \(-0.855788\pi\)
−0.437714 0.899114i \(-0.644212\pi\)
\(278\) 7.15379 20.8903i 0.429056 1.25292i
\(279\) −6.24577 −0.373925
\(280\) 3.51467 + 5.25805i 0.210042 + 0.314229i
\(281\) 5.70890 0.340564 0.170282 0.985395i \(-0.445532\pi\)
0.170282 + 0.985395i \(0.445532\pi\)
\(282\) −1.94931 + 5.69233i −0.116080 + 0.338974i
\(283\) 3.91652 + 3.91652i 0.232813 + 0.232813i 0.813866 0.581053i \(-0.197359\pi\)
−0.581053 + 0.813866i \(0.697359\pi\)
\(284\) −3.92973 + 5.06490i −0.233186 + 0.300546i
\(285\) 0.320109 + 38.9667i 0.0189616 + 2.30819i
\(286\) −2.30809 + 1.13055i −0.136480 + 0.0668506i
\(287\) 2.75125 + 2.75125i 0.162401 + 0.162401i
\(288\) 29.9281 + 2.36457i 1.76353 + 0.139334i
\(289\) 6.13541i 0.360907i
\(290\) 14.3840 7.19265i 0.844656 0.422367i
\(291\) 36.4177 2.13484
\(292\) 0.234397 + 1.85726i 0.0137171 + 0.108688i
\(293\) 20.6522 20.6522i 1.20651 1.20651i 0.234364 0.972149i \(-0.424699\pi\)
0.972149 0.234364i \(-0.0753007\pi\)
\(294\) 3.66051 1.79299i 0.213485 0.104569i
\(295\) 20.7764 + 20.4378i 1.20965 + 1.18994i
\(296\) 2.09359 10.1003i 0.121687 0.587065i
\(297\) −5.29043 + 5.29043i −0.306982 + 0.306982i
\(298\) −17.5885 6.02307i −1.01887 0.348907i
\(299\) 9.75686i 0.564254i
\(300\) 28.5320 4.07817i 1.64730 0.235453i
\(301\) 12.4575i 0.718038i
\(302\) −4.88397 + 14.2621i −0.281041 + 0.820690i
\(303\) −11.4255 + 11.4255i −0.656378 + 0.656378i
\(304\) 23.4273 6.00903i 1.34365 0.344641i
\(305\) 22.5485 + 22.1810i 1.29112 + 1.27008i
\(306\) 15.8799 + 32.4199i 0.907794 + 1.85332i
\(307\) 0.372304 0.372304i 0.0212485 0.0212485i −0.696403 0.717651i \(-0.745217\pi\)
0.717651 + 0.696403i \(0.245217\pi\)
\(308\) 0.281770 + 2.23263i 0.0160554 + 0.127216i
\(309\) −17.2799 −0.983018
\(310\) 1.66448 + 3.32864i 0.0945359 + 0.189054i
\(311\) 13.0674i 0.740984i 0.928836 + 0.370492i \(0.120811\pi\)
−0.928836 + 0.370492i \(0.879189\pi\)
\(312\) −7.22696 11.0064i −0.409146 0.623114i
\(313\) −11.0791 11.0791i −0.626230 0.626230i 0.320887 0.947117i \(-0.396019\pi\)
−0.947117 + 0.320887i \(0.896019\pi\)
\(314\) 6.08712 + 12.4273i 0.343516 + 0.701312i
\(315\) −0.0974835 11.8666i −0.00549257 0.668607i
\(316\) 12.3916 + 9.61430i 0.697080 + 0.540847i
\(317\) −15.8196 15.8196i −0.888515 0.888515i 0.105865 0.994380i \(-0.466239\pi\)
−0.994380 + 0.105865i \(0.966239\pi\)
\(318\) −38.6824 13.2466i −2.16920 0.742831i
\(319\) 5.72216 0.320379
\(320\) −6.71556 16.5801i −0.375411 0.926858i
\(321\) −0.115311 −0.00643605
\(322\) 8.08220 + 2.76771i 0.450403 + 0.154238i
\(323\) 20.5647 + 20.5647i 1.14425 + 1.14425i
\(324\) −5.12587 3.97703i −0.284771 0.220946i
\(325\) −5.80352 5.61588i −0.321921 0.311513i
\(326\) 4.78115 + 9.76104i 0.264803 + 0.540614i
\(327\) 25.0556 + 25.0556i 1.38558 + 1.38558i
\(328\) −6.04031 9.19915i −0.333520 0.507938i
\(329\) 1.47615i 0.0813826i
\(330\) 9.72902 + 3.24260i 0.535565 + 0.178499i
\(331\) −6.31429 −0.347065 −0.173533 0.984828i \(-0.555518\pi\)
−0.173533 + 0.984828i \(0.555518\pi\)
\(332\) −1.66180 13.1674i −0.0912029 0.722654i
\(333\) −13.6856 + 13.6856i −0.749965 + 0.749965i
\(334\) 6.48431 + 13.2382i 0.354805 + 0.724360i
\(335\) −0.221448 26.9568i −0.0120990 1.47281i
\(336\) −11.1673 + 2.86438i −0.609226 + 0.156265i
\(337\) −4.49695 + 4.49695i −0.244965 + 0.244965i −0.818900 0.573936i \(-0.805416\pi\)
0.573936 + 0.818900i \(0.305416\pi\)
\(338\) 4.76095 13.9028i 0.258962 0.756215i
\(339\) 2.21188i 0.120133i
\(340\) 13.0460 17.1029i 0.707521 0.927534i
\(341\) 1.32418i 0.0717086i
\(342\) −42.9330 14.7022i −2.32155 0.795002i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 7.15153 34.5017i 0.385585 1.86021i
\(345\) 27.3018 27.7540i 1.46988 1.49423i
\(346\) 4.51700 2.21251i 0.242835 0.118946i
\(347\) −2.39194 + 2.39194i −0.128406 + 0.128406i −0.768389 0.639983i \(-0.778941\pi\)
0.639983 + 0.768389i \(0.278941\pi\)
\(348\) 3.67065 + 29.0847i 0.196768 + 1.55910i
\(349\) −6.54354 −0.350268 −0.175134 0.984545i \(-0.556036\pi\)
−0.175134 + 0.984545i \(0.556036\pi\)
\(350\) −6.29825 + 3.21436i −0.336655 + 0.171815i
\(351\) 10.7400i 0.573259i
\(352\) 0.501319 6.34515i 0.0267204 0.338198i
\(353\) −11.0648 11.0648i −0.588921 0.588921i 0.348418 0.937339i \(-0.386719\pi\)
−0.937339 + 0.348418i \(0.886719\pi\)
\(354\) −47.7093 + 23.3690i −2.53572 + 1.24205i
\(355\) −5.10950 5.02623i −0.271184 0.266765i
\(356\) 5.57079 7.18002i 0.295252 0.380540i
\(357\) −9.80275 9.80275i −0.518817 0.518817i
\(358\) −6.97680 + 20.3735i −0.368735 + 1.07677i
\(359\) −11.7640 −0.620879 −0.310439 0.950593i \(-0.600476\pi\)
−0.310439 + 0.950593i \(0.600476\pi\)
\(360\) −6.54234 + 32.9212i −0.344811 + 1.73510i
\(361\) −17.5592 −0.924170
\(362\) 7.40980 21.6380i 0.389450 1.13727i
\(363\) −19.8381 19.8381i −1.04123 1.04123i
\(364\) 2.55222 + 1.98020i 0.133773 + 0.103791i
\(365\) −2.09289 + 0.0171929i −0.109547 + 0.000899920i
\(366\) −51.7787 + 25.3622i −2.70651 + 1.32570i
\(367\) −13.3311 13.3311i −0.695879 0.695879i 0.267640 0.963519i \(-0.413756\pi\)
−0.963519 + 0.267640i \(0.913756\pi\)
\(368\) −20.7952 12.3051i −1.08403 0.641448i
\(369\) 20.6491i 1.07495i
\(370\) 10.9408 + 3.64648i 0.568785 + 0.189571i
\(371\) 10.0312 0.520794
\(372\) −6.73059 + 0.849438i −0.348965 + 0.0440413i
\(373\) 1.31759 1.31759i 0.0682224 0.0682224i −0.672172 0.740395i \(-0.734639\pi\)
0.740395 + 0.672172i \(0.234639\pi\)
\(374\) 6.87344 3.36675i 0.355417 0.174090i
\(375\) 0.794057 + 32.2142i 0.0410049 + 1.66353i
\(376\) −0.847420 + 4.08827i −0.0437023 + 0.210837i
\(377\) 5.80823 5.80823i 0.299139 0.299139i
\(378\) 8.89660 + 3.04659i 0.457592 + 0.156700i
\(379\) 15.0827i 0.774744i 0.921923 + 0.387372i \(0.126617\pi\)
−0.921923 + 0.387372i \(0.873383\pi\)
\(380\) 3.60606 + 26.7989i 0.184987 + 1.37475i
\(381\) 59.4892i 3.04772i
\(382\) 0.0688686 0.201109i 0.00352362 0.0102896i
\(383\) 6.10560 6.10560i 0.311981 0.311981i −0.533695 0.845677i \(-0.679197\pi\)
0.845677 + 0.533695i \(0.179197\pi\)
\(384\) 32.5728 1.52217i 1.66223 0.0776781i
\(385\) −2.51587 + 0.0206677i −0.128221 + 0.00105333i
\(386\) −1.35379 2.76386i −0.0689062 0.140677i
\(387\) −46.7489 + 46.7489i −2.37638 + 2.37638i
\(388\) 25.0719 3.16421i 1.27283 0.160638i
\(389\) 6.14729 0.311680 0.155840 0.987782i \(-0.450192\pi\)
0.155840 + 0.987782i \(0.450192\pi\)
\(390\) 13.1667 6.58398i 0.666724 0.333393i
\(391\) 29.0557i 1.46941i
\(392\) 2.36430 1.55244i 0.119415 0.0784100i
\(393\) −19.6569 19.6569i −0.991559 0.991559i
\(394\) −10.7648 21.9770i −0.542320 1.10718i
\(395\) −12.2970 + 12.5007i −0.618727 + 0.628977i
\(396\) −7.32094 + 9.43573i −0.367891 + 0.474163i
\(397\) −17.8446 17.8446i −0.895593 0.895593i 0.0994493 0.995043i \(-0.468292\pi\)
−0.995043 + 0.0994493i \(0.968292\pi\)
\(398\) 7.39096 + 2.53100i 0.370476 + 0.126867i
\(399\) 17.4270 0.872442
\(400\) 19.2886 5.28668i 0.964431 0.264334i
\(401\) 6.09484 0.304362 0.152181 0.988353i \(-0.451370\pi\)
0.152181 + 0.988353i \(0.451370\pi\)
\(402\) 46.4898 + 15.9202i 2.31870 + 0.794027i
\(403\) 1.34410 + 1.34410i 0.0669545 + 0.0669545i
\(404\) −6.87320 + 8.85864i −0.341954 + 0.440734i
\(405\) 5.08674 5.17100i 0.252762 0.256949i
\(406\) −3.16370 6.45891i −0.157012 0.320551i
\(407\) 2.90152 + 2.90152i 0.143823 + 0.143823i
\(408\) 21.5217 + 32.7768i 1.06549 + 1.62269i
\(409\) 31.1733i 1.54142i −0.637187 0.770709i \(-0.719902\pi\)
0.637187 0.770709i \(-0.280098\pi\)
\(410\) 11.0048 5.50290i 0.543487 0.271769i
\(411\) −0.969347 −0.0478144
\(412\) −11.8964 + 1.50139i −0.586093 + 0.0739682i
\(413\) 9.21608 9.21608i 0.453494 0.453494i
\(414\) 19.9436 + 40.7162i 0.980173 + 2.00109i
\(415\) 14.8379 0.121892i 0.728362 0.00598345i
\(416\) −5.93173 6.94945i −0.290827 0.340725i
\(417\) −31.8214 + 31.8214i −1.55830 + 1.55830i
\(418\) −3.11705 + 9.10233i −0.152460 + 0.445210i
\(419\) 20.5774i 1.00527i −0.864499 0.502635i \(-0.832364\pi\)
0.864499 0.502635i \(-0.167636\pi\)
\(420\) −1.71893 12.7745i −0.0838753 0.623330i
\(421\) 31.4588i 1.53321i −0.642121 0.766604i \(-0.721945\pi\)
0.642121 0.766604i \(-0.278055\pi\)
\(422\) 19.6356 + 6.72411i 0.955847 + 0.327325i
\(423\) 5.53950 5.53950i 0.269340 0.269340i
\(424\) −27.7820 5.75866i −1.34921 0.279665i
\(425\) 17.2828 + 16.7240i 0.838337 + 0.811233i
\(426\) 11.7331 5.74708i 0.568469 0.278447i
\(427\) 10.0022 10.0022i 0.484039 0.484039i
\(428\) −0.0793864 + 0.0100190i −0.00383729 + 0.000484287i
\(429\) 5.23792 0.252889
\(430\) 37.3729 + 12.4561i 1.80228 + 0.600686i
\(431\) 0.859240i 0.0413881i −0.999786 0.0206941i \(-0.993412\pi\)
0.999786 0.0206941i \(-0.00658759\pi\)
\(432\) −22.8907 13.5450i −1.10133 0.651685i
\(433\) 25.0843 + 25.0843i 1.20548 + 1.20548i 0.972477 + 0.232998i \(0.0748537\pi\)
0.232998 + 0.972477i \(0.425146\pi\)
\(434\) 1.49468 0.732123i 0.0717469 0.0351430i
\(435\) −32.7745 + 0.269241i −1.57142 + 0.0129091i
\(436\) 19.4266 + 15.0726i 0.930364 + 0.721846i
\(437\) 25.8272 + 25.8272i 1.23548 + 1.23548i
\(438\) 1.23602 3.60941i 0.0590594 0.172464i
\(439\) −15.3973 −0.734873 −0.367437 0.930049i \(-0.619765\pi\)
−0.367437 + 0.930049i \(0.619765\pi\)
\(440\) 6.97971 + 1.38706i 0.332745 + 0.0661254i
\(441\) −5.30708 −0.252718
\(442\) 3.55944 10.3942i 0.169305 0.494402i
\(443\) 8.67120 + 8.67120i 0.411981 + 0.411981i 0.882428 0.470447i \(-0.155907\pi\)
−0.470447 + 0.882428i \(0.655907\pi\)
\(444\) −12.8866 + 16.6092i −0.611572 + 0.788236i
\(445\) 7.24324 + 7.12520i 0.343362 + 0.337767i
\(446\) 10.9610 5.36892i 0.519019 0.254226i
\(447\) 26.7917 + 26.7917i 1.26721 + 1.26721i
\(448\) −7.43929 + 2.94228i −0.351473 + 0.139010i
\(449\) 5.60819i 0.264667i 0.991205 + 0.132333i \(0.0422469\pi\)
−0.991205 + 0.132333i \(0.957753\pi\)
\(450\) −35.6977 11.5728i −1.68281 0.545548i
\(451\) 4.37787 0.206146
\(452\) 0.192182 + 1.52277i 0.00903950 + 0.0716252i
\(453\) 21.7248 21.7248i 1.02072 1.02072i
\(454\) −18.6585 + 9.13930i −0.875688 + 0.428929i
\(455\) −2.53274 + 2.57469i −0.118736 + 0.120703i
\(456\) −48.2651 10.0044i −2.26022 0.468500i
\(457\) −5.78603 + 5.78603i −0.270659 + 0.270659i −0.829365 0.558706i \(-0.811298\pi\)
0.558706 + 0.829365i \(0.311298\pi\)
\(458\) 15.8721 + 5.43533i 0.741656 + 0.253976i
\(459\) 31.9835i 1.49286i
\(460\) 16.3845 21.4795i 0.763932 1.00149i
\(461\) 4.56485i 0.212606i 0.994334 + 0.106303i \(0.0339014\pi\)
−0.994334 + 0.106303i \(0.966099\pi\)
\(462\) 1.48583 4.33889i 0.0691270 0.201863i
\(463\) 4.57165 4.57165i 0.212463 0.212463i −0.592850 0.805313i \(-0.701997\pi\)
0.805313 + 0.592850i \(0.201997\pi\)
\(464\) 5.05414 + 19.7045i 0.234633 + 0.914760i
\(465\) −0.0623060 7.58446i −0.00288937 0.351721i
\(466\) −3.13040 6.39093i −0.145013 0.296054i
\(467\) 16.3006 16.3006i 0.754300 0.754300i −0.220978 0.975279i \(-0.570925\pi\)
0.975279 + 0.220978i \(0.0709250\pi\)
\(468\) 2.14659 + 17.0087i 0.0992264 + 0.786228i
\(469\) −12.0558 −0.556687
\(470\) −4.42850 1.47598i −0.204271 0.0680820i
\(471\) 28.2022i 1.29949i
\(472\) −30.8152 + 20.2337i −1.41838 + 0.931333i
\(473\) 9.91136 + 9.91136i 0.455725 + 0.455725i
\(474\) −14.0606 28.7056i −0.645823 1.31849i
\(475\) −30.2280 + 0.496677i −1.38696 + 0.0227891i
\(476\) −7.60046 5.89700i −0.348366 0.270289i
\(477\) 37.6438 + 37.6438i 1.72359 + 1.72359i
\(478\) 25.9719 + 8.89392i 1.18793 + 0.406799i
\(479\) −40.3109 −1.84185 −0.920925 0.389740i \(-0.872565\pi\)
−0.920925 + 0.389740i \(0.872565\pi\)
\(480\) −2.57283 + 36.3664i −0.117433 + 1.65989i
\(481\) 5.89032 0.268576
\(482\) −5.09401 1.74442i −0.232026 0.0794560i
\(483\) −12.3113 12.3113i −0.560182 0.560182i
\(484\) −15.3813 11.9339i −0.699149 0.542452i
\(485\) 0.232094 + 28.2526i 0.0105388 + 1.28288i
\(486\) −6.59347 13.4610i −0.299086 0.610605i
\(487\) 1.49444 + 1.49444i 0.0677194 + 0.0677194i 0.740155 0.672436i \(-0.234752\pi\)
−0.672436 + 0.740155i \(0.734752\pi\)
\(488\) −33.4435 + 21.9596i −1.51392 + 0.994062i
\(489\) 22.1515i 1.00172i
\(490\) 1.41432 + 2.82837i 0.0638924 + 0.127773i
\(491\) 18.9508 0.855239 0.427619 0.903959i \(-0.359352\pi\)
0.427619 + 0.903959i \(0.359352\pi\)
\(492\) 2.80832 + 22.2519i 0.126609 + 1.00319i
\(493\) −17.2968 + 17.2968i −0.779008 + 0.779008i
\(494\) 6.07532 + 12.4032i 0.273341 + 0.558045i
\(495\) −9.51881 9.36369i −0.427839 0.420866i
\(496\) −4.55989 + 1.16960i −0.204745 + 0.0525164i
\(497\) −2.26649 + 2.26649i −0.101666 + 0.101666i
\(498\) −8.76298 + 25.5895i −0.392678 + 1.14669i
\(499\) 31.3478i 1.40332i 0.712512 + 0.701660i \(0.247557\pi\)
−0.712512 + 0.701660i \(0.752443\pi\)
\(500\) 3.34565 + 22.1090i 0.149622 + 0.988743i
\(501\) 30.0424i 1.34219i
\(502\) 9.88144 + 3.38384i 0.441030 + 0.151028i
\(503\) −4.67127 + 4.67127i −0.208281 + 0.208281i −0.803537 0.595255i \(-0.797051\pi\)
0.595255 + 0.803537i \(0.297051\pi\)
\(504\) 14.6983 + 3.04667i 0.654713 + 0.135709i
\(505\) −8.93664 8.79101i −0.397675 0.391195i
\(506\) 8.63235 4.22829i 0.383755 0.187971i
\(507\) −21.1776 + 21.1776i −0.940530 + 0.940530i
\(508\) −5.16881 40.9555i −0.229329 1.81711i
\(509\) −20.1361 −0.892516 −0.446258 0.894904i \(-0.647244\pi\)
−0.446258 + 0.894904i \(0.647244\pi\)
\(510\) −39.2103 + 19.6070i −1.73626 + 0.868211i
\(511\) 0.935999i 0.0414061i
\(512\) 22.2926 3.87809i 0.985203 0.171389i
\(513\) 28.4296 + 28.4296i 1.25520 + 1.25520i
\(514\) 20.4301 10.0071i 0.901135 0.441393i
\(515\) −0.110126 13.4056i −0.00485275 0.590722i
\(516\) −44.0197 + 56.7356i −1.93786 + 2.49765i
\(517\) −1.17445 1.17445i −0.0516520 0.0516520i
\(518\) 1.67089 4.87931i 0.0734149 0.214385i
\(519\) −10.2508 −0.449959
\(520\) 8.49262 5.67677i 0.372426 0.248943i
\(521\) 2.40321 0.105286 0.0526432 0.998613i \(-0.483235\pi\)
0.0526432 + 0.998613i \(0.483235\pi\)
\(522\) 12.3659 36.1106i 0.541239 1.58052i
\(523\) −19.2772 19.2772i −0.842935 0.842935i 0.146305 0.989240i \(-0.453262\pi\)
−0.989240 + 0.146305i \(0.953262\pi\)
\(524\) −15.2408 11.8249i −0.665796 0.516574i
\(525\) 14.4091 0.236755i 0.628863 0.0103329i
\(526\) 3.38627 1.65866i 0.147649 0.0723211i
\(527\) −4.00271 4.00271i −0.174361 0.174361i
\(528\) −6.60594 + 11.1638i −0.287486 + 0.485843i
\(529\) 13.4911i 0.586569i
\(530\) 10.0301 30.0940i 0.435679 1.30720i
\(531\) 69.1699 3.00172
\(532\) 11.9977 1.51417i 0.520165 0.0656477i
\(533\) 4.44372 4.44372i 0.192479 0.192479i
\(534\) −16.6328 + 8.14708i −0.719773 + 0.352559i
\(535\) −0.000734891 0.0894578i −3.17721e−5 0.00386760i
\(536\) 33.3893 + 6.92096i 1.44220 + 0.298940i
\(537\) 31.0341 31.0341i 1.33922 1.33922i
\(538\) −5.79284 1.98373i −0.249747 0.0855245i
\(539\) 1.12517i 0.0484645i
\(540\) 18.0355 23.6439i 0.776124 1.01747i
\(541\) 1.46872i 0.0631452i −0.999501 0.0315726i \(-0.989948\pi\)
0.999501 0.0315726i \(-0.0100515\pi\)
\(542\) 9.58254 27.9828i 0.411605 1.20196i
\(543\) −32.9602 + 32.9602i −1.41446 + 1.41446i
\(544\) 17.6646 + 20.6953i 0.757362 + 0.887304i
\(545\) −19.2783 + 19.5976i −0.825790 + 0.839470i
\(546\) −2.89597 5.91233i −0.123936 0.253024i
\(547\) 23.7167 23.7167i 1.01405 1.01405i 0.0141527 0.999900i \(-0.495495\pi\)
0.999900 0.0141527i \(-0.00450509\pi\)
\(548\) −0.667350 + 0.0842233i −0.0285078 + 0.00359784i
\(549\) 75.0698 3.20390
\(550\) −2.45359 + 7.56837i −0.104621 + 0.322716i
\(551\) 30.7497i 1.30998i
\(552\) 27.0291 + 41.1643i 1.15044 + 1.75207i
\(553\) 5.54511 + 5.54511i 0.235802 + 0.235802i
\(554\) 19.5742 + 39.9621i 0.831628 + 1.69783i
\(555\) −16.7554 16.4824i −0.711228 0.699637i
\(556\) −19.1427 + 24.6724i −0.811829 + 1.04634i
\(557\) 19.5468 + 19.5468i 0.828226 + 0.828226i 0.987271 0.159045i \(-0.0508416\pi\)
−0.159045 + 0.987271i \(0.550842\pi\)
\(558\) 8.35646 + 2.86163i 0.353757 + 0.121142i
\(559\) 20.1209 0.851023
\(560\) −2.29333 8.64527i −0.0969111 0.365329i
\(561\) −15.5984 −0.658566
\(562\) −7.63815 2.61564i −0.322196 0.110334i
\(563\) 13.3343 + 13.3343i 0.561973 + 0.561973i 0.929868 0.367895i \(-0.119921\pi\)
−0.367895 + 0.929868i \(0.619921\pi\)
\(564\) 5.21611 6.72288i 0.219638 0.283084i
\(565\) −1.71596 + 0.0140965i −0.0721909 + 0.000593045i
\(566\) −3.44564 7.03450i −0.144831 0.295682i
\(567\) −2.29378 2.29378i −0.0963296 0.0963296i
\(568\) 7.57832 4.97604i 0.317979 0.208790i
\(569\) 39.6529i 1.66234i −0.556020 0.831169i \(-0.687672\pi\)
0.556020 0.831169i \(-0.312328\pi\)
\(570\) 17.4251 52.2817i 0.729856 2.18984i
\(571\) −14.7413 −0.616904 −0.308452 0.951240i \(-0.599811\pi\)
−0.308452 + 0.951240i \(0.599811\pi\)
\(572\) 3.60606 0.455105i 0.150777 0.0190289i
\(573\) −0.306340 + 0.306340i −0.0127975 + 0.0127975i
\(574\) −2.42046 4.94154i −0.101028 0.206256i
\(575\) 21.7054 + 21.0036i 0.905177 + 0.875912i
\(576\) −38.9586 16.8758i −1.62328 0.703159i
\(577\) 6.52078 6.52078i 0.271464 0.271464i −0.558226 0.829689i \(-0.688518\pi\)
0.829689 + 0.558226i \(0.188518\pi\)
\(578\) −2.81106 + 8.20881i −0.116925 + 0.341441i
\(579\) 6.27224i 0.260665i
\(580\) −22.5403 + 3.03303i −0.935936 + 0.125940i
\(581\) 6.63591i 0.275304i
\(582\) −48.7246 16.6855i −2.01970 0.691635i
\(583\) 7.98097 7.98097i 0.330538 0.330538i
\(584\) 0.537334 2.59230i 0.0222350 0.107270i
\(585\) −19.1665 + 0.157452i −0.792438 + 0.00650984i
\(586\) −37.0935 + 18.1691i −1.53232 + 0.750560i
\(587\) −20.1293 + 20.1293i −0.830826 + 0.830826i −0.987630 0.156804i \(-0.949881\pi\)
0.156804 + 0.987630i \(0.449881\pi\)
\(588\) −5.71904 + 0.721774i −0.235849 + 0.0297655i
\(589\) 7.11588 0.293205
\(590\) −18.4335 36.8636i −0.758897 1.51765i
\(591\) 49.8741i 2.05154i
\(592\) −7.42872 + 12.5543i −0.305319 + 0.515979i
\(593\) −11.4414 11.4414i −0.469841 0.469841i 0.432022 0.901863i \(-0.357800\pi\)
−0.901863 + 0.432022i \(0.857800\pi\)
\(594\) 9.50218 4.65435i 0.389879 0.190970i
\(595\) 7.54243 7.66738i 0.309210 0.314332i
\(596\) 20.7727 + 16.1170i 0.850883 + 0.660178i
\(597\) −11.2583 11.2583i −0.460773 0.460773i
\(598\) 4.47030 13.0541i 0.182804 0.533821i
\(599\) 19.4712 0.795570 0.397785 0.917479i \(-0.369779\pi\)
0.397785 + 0.917479i \(0.369779\pi\)
\(600\) −40.0426 7.61618i −1.63473 0.310929i
\(601\) 32.2378 1.31501 0.657503 0.753452i \(-0.271613\pi\)
0.657503 + 0.753452i \(0.271613\pi\)
\(602\) 5.70765 16.6674i 0.232626 0.679311i
\(603\) −45.2417 45.2417i −1.84238 1.84238i
\(604\) 13.0689 16.8441i 0.531766 0.685377i
\(605\) 15.2638 15.5167i 0.620564 0.630844i
\(606\) 20.5214 10.0518i 0.833627 0.408326i
\(607\) 7.62315 + 7.62315i 0.309414 + 0.309414i 0.844682 0.535268i \(-0.179789\pi\)
−0.535268 + 0.844682i \(0.679789\pi\)
\(608\) −34.0975 2.69398i −1.38284 0.109255i
\(609\) 14.6577i 0.593960i
\(610\) −20.0058 40.0079i −0.810012 1.61987i
\(611\) −2.38422 −0.0964553
\(612\) −6.39252 50.6516i −0.258402 2.04747i
\(613\) −29.3421 + 29.3421i −1.18512 + 1.18512i −0.206717 + 0.978401i \(0.566278\pi\)
−0.978401 + 0.206717i \(0.933722\pi\)
\(614\) −0.668699 + 0.327542i −0.0269865 + 0.0132185i
\(615\) −25.0749 + 0.205989i −1.01112 + 0.00830627i
\(616\) 0.645932 3.11622i 0.0260253 0.125556i
\(617\) −9.56360 + 9.56360i −0.385016 + 0.385016i −0.872905 0.487889i \(-0.837767\pi\)
0.487889 + 0.872905i \(0.337767\pi\)
\(618\) 23.1194 + 7.91712i 0.930000 + 0.318473i
\(619\) 17.2092i 0.691694i −0.938291 0.345847i \(-0.887592\pi\)
0.938291 0.345847i \(-0.112408\pi\)
\(620\) −0.701883 5.21613i −0.0281883 0.209485i
\(621\) 40.1681i 1.61189i
\(622\) 5.98708 17.4834i 0.240060 0.701019i
\(623\) 3.21299 3.21299i 0.128726 0.128726i
\(624\) 4.62644 + 18.0370i 0.185206 + 0.722059i
\(625\) −24.9865 + 0.821328i −0.999460 + 0.0328531i
\(626\) 9.74709 + 19.8994i 0.389572 + 0.795338i
\(627\) 13.8652 13.8652i 0.553722 0.553722i
\(628\) −2.45039 19.4159i −0.0977813 0.774778i
\(629\) −17.5413 −0.699416
\(630\) −5.30649 + 15.9215i −0.211416 + 0.634326i
\(631\) 9.29068i 0.369856i −0.982752 0.184928i \(-0.940795\pi\)
0.982752 0.184928i \(-0.0592052\pi\)
\(632\) −12.1742 18.5408i −0.484263 0.737513i
\(633\) −29.9101 29.9101i −1.18882 1.18882i
\(634\) 13.9176 + 28.4137i 0.552737 + 1.12845i
\(635\) 46.1513 0.379131i 1.83146 0.0150453i
\(636\) 45.6855 + 35.4462i 1.81155 + 1.40553i
\(637\) 1.14209 + 1.14209i 0.0452514 + 0.0452514i
\(638\) −7.65590 2.62172i −0.303100 0.103795i
\(639\) −17.0108 −0.672938
\(640\) 1.38848 + 25.2601i 0.0548846 + 0.998493i
\(641\) 24.5315 0.968937 0.484468 0.874809i \(-0.339013\pi\)
0.484468 + 0.874809i \(0.339013\pi\)
\(642\) 0.154280 + 0.0528322i 0.00608893 + 0.00208512i
\(643\) −8.90235 8.90235i −0.351074 0.351074i 0.509435 0.860509i \(-0.329854\pi\)
−0.860509 + 0.509435i \(0.829854\pi\)
\(644\) −9.54541 7.40604i −0.376142 0.291839i
\(645\) −57.2352 56.3025i −2.25363 2.21691i
\(646\) −18.0922 36.9364i −0.711827 1.45324i
\(647\) 23.3823 + 23.3823i 0.919252 + 0.919252i 0.996975 0.0777226i \(-0.0247648\pi\)
−0.0777226 + 0.996975i \(0.524765\pi\)
\(648\) 5.03594 + 7.66955i 0.197831 + 0.301288i
\(649\) 14.6649i 0.575648i
\(650\) 5.19172 + 10.1727i 0.203636 + 0.399006i
\(651\) −3.39199 −0.132943
\(652\) −1.92467 15.2503i −0.0753758 0.597246i
\(653\) 16.7346 16.7346i 0.654877 0.654877i −0.299286 0.954163i \(-0.596748\pi\)
0.954163 + 0.299286i \(0.0967485\pi\)
\(654\) −22.0431 45.0025i −0.861954 1.75974i
\(655\) 15.1244 15.3750i 0.590960 0.600750i
\(656\) 3.86679 + 15.0754i 0.150973 + 0.588595i
\(657\) −3.51250 + 3.51250i −0.137036 + 0.137036i
\(658\) −0.676326 + 1.97500i −0.0263659 + 0.0769933i
\(659\) 16.9213i 0.659162i −0.944127 0.329581i \(-0.893093\pi\)
0.944127 0.329581i \(-0.106907\pi\)
\(660\) −11.5312 8.79595i −0.448850 0.342382i
\(661\) 38.9846i 1.51633i 0.652066 + 0.758163i \(0.273903\pi\)
−0.652066 + 0.758163i \(0.726097\pi\)
\(662\) 8.44814 + 2.89302i 0.328346 + 0.112440i
\(663\) −15.8331 + 15.8331i −0.614905 + 0.614905i
\(664\) −3.80951 + 18.3785i −0.147838 + 0.713225i
\(665\) 0.111064 + 13.5198i 0.00430688 + 0.524274i
\(666\) 24.5808 12.0401i 0.952486 0.466546i
\(667\) −21.7230 + 21.7230i −0.841119 + 0.841119i
\(668\) −2.61028 20.6828i −0.100995 0.800240i
\(669\) −24.8747 −0.961710
\(670\) −12.0545 + 36.1680i −0.465706 + 1.39729i
\(671\) 15.9157i 0.614421i
\(672\) 16.2535 + 1.28416i 0.626994 + 0.0495377i
\(673\) 19.7476 + 19.7476i 0.761213 + 0.761213i 0.976542 0.215329i \(-0.0690824\pi\)
−0.215329 + 0.976542i \(0.569082\pi\)
\(674\) 8.07702 3.95628i 0.311115 0.152390i
\(675\) 23.8925 + 23.1201i 0.919624 + 0.889892i
\(676\) −12.7397 + 16.4198i −0.489990 + 0.631532i
\(677\) 7.87865 + 7.87865i 0.302801 + 0.302801i 0.842109 0.539308i \(-0.181314\pi\)
−0.539308 + 0.842109i \(0.681314\pi\)
\(678\) 1.01342 2.95936i 0.0389200 0.113653i
\(679\) 12.6354 0.484901
\(680\) −25.2908 + 16.9053i −0.969860 + 0.648289i
\(681\) 42.3432 1.62260
\(682\) 0.606701 1.77168i 0.0232318 0.0678410i
\(683\) −4.99347 4.99347i −0.191070 0.191070i 0.605088 0.796158i \(-0.293138\pi\)
−0.796158 + 0.605088i \(0.793138\pi\)
\(684\) 50.7056 + 39.3412i 1.93878 + 1.50425i
\(685\) −0.00617775 0.752013i −0.000236040 0.0287330i
\(686\) 1.27004 0.622091i 0.0484904 0.0237515i
\(687\) −24.1773 24.1773i −0.922423 0.922423i
\(688\) −25.3760 + 42.8845i −0.967449 + 1.63496i
\(689\) 16.2020i 0.617248i
\(690\) −49.2441 + 24.6244i −1.87469 + 0.937433i
\(691\) 21.0032 0.798999 0.399500 0.916733i \(-0.369184\pi\)
0.399500 + 0.916733i \(0.369184\pi\)
\(692\) −7.05718 + 0.890655i −0.268274 + 0.0338576i
\(693\) −4.22240 + 4.22240i −0.160396 + 0.160396i
\(694\) 4.29618 2.10435i 0.163081 0.0798801i
\(695\) −24.8896 24.4840i −0.944116 0.928731i
\(696\) 8.41463 40.5953i 0.318956 1.53876i
\(697\) −13.2333 + 13.2333i −0.501247 + 0.501247i
\(698\) 8.75486 + 2.99805i 0.331376 + 0.113478i
\(699\) 14.5034i 0.548570i
\(700\) 9.89939 1.41495i 0.374162 0.0534801i
\(701\) 21.8520i 0.825340i 0.910881 + 0.412670i \(0.135404\pi\)
−0.910881 + 0.412670i \(0.864596\pi\)
\(702\) 4.92075 14.3695i 0.185722 0.542341i
\(703\) 15.5921 15.5921i 0.588069 0.588069i
\(704\) −3.57789 + 8.25973i −0.134847 + 0.311300i
\(705\) 6.78207 + 6.67155i 0.255428 + 0.251265i
\(706\) 9.73449 + 19.8736i 0.366362 + 0.747954i
\(707\) −3.96416 + 3.96416i −0.149087 + 0.149087i
\(708\) 74.5391 9.40725i 2.80135 0.353546i
\(709\) 40.1862 1.50922 0.754612 0.656171i \(-0.227825\pi\)
0.754612 + 0.656171i \(0.227825\pi\)
\(710\) 4.53332 + 9.06581i 0.170133 + 0.340234i
\(711\) 41.6180i 1.56080i
\(712\) −10.7431 + 7.05405i −0.402613 + 0.264362i
\(713\) −5.02700 5.02700i −0.188262 0.188262i
\(714\) 8.62415 + 17.6068i 0.322751 + 0.658918i
\(715\) 0.0333818 + 4.06355i 0.00124841 + 0.151968i
\(716\) 18.6691 24.0620i 0.697696 0.899238i
\(717\) −39.5618 39.5618i −1.47746 1.47746i
\(718\) 15.7395 + 5.38990i 0.587392 + 0.201149i
\(719\) −22.1751 −0.826993 −0.413496 0.910506i \(-0.635693\pi\)
−0.413496 + 0.910506i \(0.635693\pi\)
\(720\) 23.8367 41.0490i 0.888343 1.52981i
\(721\) −5.99538 −0.223279
\(722\) 23.4932 + 8.04511i 0.874325 + 0.299408i
\(723\) 7.75948 + 7.75948i 0.288578 + 0.288578i
\(724\) −19.8277 + 25.5553i −0.736891 + 0.949756i
\(725\) −0.417751 25.4245i −0.0155149 0.944244i
\(726\) 17.4530 + 35.6314i 0.647740 + 1.32241i
\(727\) 22.6546 + 22.6546i 0.840213 + 0.840213i 0.988886 0.148674i \(-0.0475004\pi\)
−0.148674 + 0.988886i \(0.547500\pi\)
\(728\) −2.50744 3.81874i −0.0929321 0.141532i
\(729\) 40.2798i 1.49185i
\(730\) 2.80803 + 0.935894i 0.103930 + 0.0346390i
\(731\) −59.9196 −2.21621
\(732\) 80.8969 10.2096i 2.99004 0.377359i
\(733\) 28.2586 28.2586i 1.04375 1.04375i 0.0447571 0.998998i \(-0.485749\pi\)
0.998998 0.0447571i \(-0.0142514\pi\)
\(734\) 11.7283 + 23.9442i 0.432900 + 0.883795i
\(735\) −0.0529419 6.44458i −0.00195279 0.237712i
\(736\) 22.1849 + 25.9912i 0.817747 + 0.958049i
\(737\) −9.59181 + 9.59181i −0.353319 + 0.353319i
\(738\) 9.46078 27.6272i 0.348256 1.01697i
\(739\) 5.77895i 0.212582i 0.994335 + 0.106291i \(0.0338975\pi\)
−0.994335 + 0.106291i \(0.966102\pi\)
\(740\) −12.9674 9.89151i −0.476691 0.363619i
\(741\) 28.1475i 1.03402i
\(742\) −13.4211 4.59599i −0.492705 0.168724i
\(743\) 8.56593 8.56593i 0.314254 0.314254i −0.532301 0.846555i \(-0.678673\pi\)
0.846555 + 0.532301i \(0.178673\pi\)
\(744\) 9.39430 + 1.94726i 0.344412 + 0.0713899i
\(745\) −20.6141 + 20.9556i −0.755242 + 0.767754i
\(746\) −2.36654 + 1.15918i −0.0866452 + 0.0424405i
\(747\) 24.9024 24.9024i 0.911132 0.911132i
\(748\) −10.7388 + 1.35529i −0.392649 + 0.0495545i
\(749\) −0.0400081 −0.00146186
\(750\) 13.6972 43.4644i 0.500150 1.58710i
\(751\) 52.2973i 1.90835i 0.299243 + 0.954177i \(0.403266\pi\)
−0.299243 + 0.954177i \(0.596734\pi\)
\(752\) 3.00692 5.08160i 0.109651 0.185307i
\(753\) −15.0520 15.0520i −0.548524 0.548524i
\(754\) −10.4322 + 5.10990i −0.379919 + 0.186092i
\(755\) 16.9924 + 16.7155i 0.618417 + 0.608339i
\(756\) −10.5072 8.15231i −0.382145 0.296497i
\(757\) −1.86099 1.86099i −0.0676388 0.0676388i 0.672478 0.740117i \(-0.265230\pi\)
−0.740117 + 0.672478i \(0.765230\pi\)
\(758\) 6.91042 20.1797i 0.250998 0.732959i
\(759\) −19.5901 −0.711074
\(760\) 7.45376 37.5075i 0.270376 1.36054i
\(761\) −23.3338 −0.845851 −0.422926 0.906164i \(-0.638997\pi\)
−0.422926 + 0.906164i \(0.638997\pi\)
\(762\) −27.2562 + 79.5929i −0.987387 + 2.88335i
\(763\) 8.69321 + 8.69321i 0.314715 + 0.314715i
\(764\) −0.184284 + 0.237518i −0.00666716 + 0.00859309i
\(765\) 57.0775 0.468889i 2.06364 0.0169527i
\(766\) −10.9663 + 5.37151i −0.396229 + 0.194081i
\(767\) −14.8855 14.8855i −0.537484 0.537484i
\(768\) −44.2779 12.8873i −1.59774 0.465031i
\(769\) 4.91858i 0.177369i 0.996060 + 0.0886843i \(0.0282662\pi\)
−0.996060 + 0.0886843i \(0.971734\pi\)
\(770\) 3.37555 + 1.12504i 0.121646 + 0.0405438i
\(771\) −46.3637 −1.66975
\(772\) 0.544974 + 4.31814i 0.0196140 + 0.155413i
\(773\) −23.3933 + 23.3933i −0.841400 + 0.841400i −0.989041 0.147641i \(-0.952832\pi\)
0.147641 + 0.989041i \(0.452832\pi\)
\(774\) 83.9661 41.1282i 3.01810 1.47832i
\(775\) 5.88358 0.0966731i 0.211344 0.00347260i
\(776\) −34.9944 7.25365i −1.25622 0.260391i
\(777\) −7.43244 + 7.43244i −0.266637 + 0.266637i
\(778\) −8.22470 2.81650i −0.294870 0.100977i
\(779\) 23.5257i 0.842896i
\(780\) −20.6329 + 2.77636i −0.738775 + 0.0994096i
\(781\) 3.60651i 0.129051i
\(782\) −13.3125 + 38.8748i −0.476053 + 1.39016i
\(783\) −23.9119 + 23.9119i −0.854543 + 0.854543i
\(784\) −3.87457 + 0.993815i −0.138378 + 0.0354934i
\(785\) 21.8791 0.179735i 0.780897 0.00641503i
\(786\) 17.2935 + 35.3059i 0.616840 + 1.25932i
\(787\) −3.19923 + 3.19923i −0.114040 + 0.114040i −0.761824 0.647784i \(-0.775696\pi\)
0.647784 + 0.761824i \(0.275696\pi\)
\(788\) 4.33339 + 34.3359i 0.154371 + 1.22317i
\(789\) −7.68473 −0.273584
\(790\) 22.1800 11.0910i 0.789129 0.394601i
\(791\) 0.767426i 0.0272865i
\(792\) 14.1181 9.27019i 0.501666 0.329402i
\(793\) −16.1551 16.1551i −0.573686 0.573686i
\(794\) 15.6991 + 32.0508i 0.557140 + 1.13744i
\(795\) −45.3367 + 46.0878i −1.60793 + 1.63456i
\(796\) −8.72903 6.77263i −0.309392 0.240050i
\(797\) −12.5647 12.5647i −0.445066 0.445066i 0.448645 0.893710i \(-0.351907\pi\)
−0.893710 + 0.448645i \(0.851907\pi\)
\(798\) −23.3163 7.98453i −0.825387 0.282649i
\(799\) 7.10016 0.251186
\(800\) −28.2292 1.76421i −0.998053 0.0623744i
\(801\) 24.1146 0.852048
\(802\) −8.15452 2.79247i −0.287946 0.0986056i
\(803\) 0.744695 + 0.744695i 0.0262797 + 0.0262797i
\(804\) −54.9064 42.6005i −1.93640 1.50240i
\(805\) 9.47254 9.62946i 0.333863 0.339394i
\(806\) −1.18250 2.41415i −0.0416517 0.0850349i
\(807\) 8.82398 + 8.82398i 0.310619 + 0.310619i
\(808\) 13.2547 8.70323i 0.466298 0.306179i
\(809\) 47.6256i 1.67443i 0.546875 + 0.837214i \(0.315817\pi\)
−0.546875 + 0.837214i \(0.684183\pi\)
\(810\) −9.17494 + 4.58790i −0.322375 + 0.161202i
\(811\) 0.00749637 0.000263233 0.000131617 1.00000i \(-0.499958\pi\)
0.000131617 1.00000i \(0.499958\pi\)
\(812\) 1.27356 + 10.0911i 0.0446932 + 0.354130i
\(813\) −42.6249 + 42.6249i −1.49492 + 1.49492i
\(814\) −2.55267 5.21144i −0.0894709 0.182661i
\(815\) 17.1850 0.141174i 0.601963 0.00494510i
\(816\) −13.7774 53.7139i −0.482307 1.88036i
\(817\) 53.2616 53.2616i 1.86339 1.86339i
\(818\) −14.2826 + 41.7079i −0.499381 + 1.45828i
\(819\) 8.57182i 0.299524i
\(820\) −17.2450 + 2.32049i −0.602221 + 0.0810349i
\(821\) 6.37425i 0.222463i −0.993795 0.111232i \(-0.964520\pi\)
0.993795 0.111232i \(-0.0354795\pi\)
\(822\) 1.29693 + 0.444126i 0.0452355 + 0.0154907i
\(823\) 13.8579 13.8579i 0.483058 0.483058i −0.423049 0.906107i \(-0.639040\pi\)
0.906107 + 0.423049i \(0.139040\pi\)
\(824\) 16.6045 + 3.44180i 0.578446 + 0.119901i
\(825\) 11.2757 11.6524i 0.392570 0.405686i
\(826\) −16.5531 + 8.10802i −0.575956 + 0.282114i
\(827\) 1.05891 1.05891i 0.0368221 0.0368221i −0.688456 0.725278i \(-0.741711\pi\)
0.725278 + 0.688456i \(0.241711\pi\)
\(828\) −8.02835 63.6133i −0.279005 2.21071i
\(829\) −36.1123 −1.25423 −0.627115 0.778926i \(-0.715764\pi\)
−0.627115 + 0.778926i \(0.715764\pi\)
\(830\) −19.9080 6.63517i −0.691016 0.230310i
\(831\) 90.6890i 3.14597i
\(832\) 4.75226 + 12.0157i 0.164755 + 0.416569i
\(833\) −3.40113 3.40113i −0.117842 0.117842i
\(834\) 57.1546 27.9954i 1.97910 0.969403i
\(835\) 23.3067 0.191463i 0.806561 0.00662585i
\(836\) 8.34083 10.7502i 0.288474 0.371804i
\(837\) −5.53354 5.53354i −0.191267 0.191267i
\(838\) −9.42793 + 27.5312i −0.325682 + 0.951051i
\(839\) 13.4566 0.464574 0.232287 0.972647i \(-0.425379\pi\)
0.232287 + 0.972647i \(0.425379\pi\)
\(840\) −3.55305 + 17.8790i −0.122592 + 0.616885i
\(841\) −3.13671 −0.108162
\(842\) −14.4135 + 42.0899i −0.496721 + 1.45051i
\(843\) 11.6349 + 11.6349i 0.400726 + 0.400726i
\(844\) −23.1905 17.9929i −0.798249 0.619341i
\(845\) −16.5644 16.2945i −0.569833 0.560547i
\(846\) −9.94955 + 4.87348i −0.342073 + 0.167554i
\(847\) −6.88297 6.88297i −0.236502 0.236502i
\(848\) 34.5321 + 20.4336i 1.18584 + 0.701693i
\(849\) 15.9639i 0.547881i
\(850\) −15.4608 30.2941i −0.530302 1.03908i
\(851\) −22.0301 −0.755181
\(852\) −18.3313 + 2.31351i −0.628019 + 0.0792595i
\(853\) 2.50880 2.50880i 0.0858998 0.0858998i −0.662851 0.748751i \(-0.730654\pi\)
0.748751 + 0.662851i \(0.230654\pi\)
\(854\) −17.9650 + 8.79959i −0.614749 + 0.301116i
\(855\) −50.3185 + 51.1520i −1.72086 + 1.74936i
\(856\) 0.110805 + 0.0229677i 0.00378722 + 0.000785018i
\(857\) 14.7263 14.7263i 0.503040 0.503040i −0.409341 0.912381i \(-0.634241\pi\)
0.912381 + 0.409341i \(0.134241\pi\)
\(858\) −7.00802 2.39986i −0.239250 0.0819298i
\(859\) 37.0552i 1.26431i 0.774844 + 0.632153i \(0.217829\pi\)
−0.774844 + 0.632153i \(0.782171\pi\)
\(860\) −44.2957 33.7886i −1.51047 1.15218i
\(861\) 11.2142i 0.382179i
\(862\) −0.393678 + 1.14961i −0.0134087 + 0.0391559i
\(863\) −39.0206 + 39.0206i −1.32828 + 1.32828i −0.421405 + 0.906873i \(0.638463\pi\)
−0.906873 + 0.421405i \(0.861537\pi\)
\(864\) 24.4204 + 28.6102i 0.830798 + 0.973340i
\(865\) −0.0653293 7.95249i −0.00222126 0.270393i
\(866\) −22.0684 45.0542i −0.749915 1.53100i
\(867\) 12.5041 12.5041i 0.424662 0.424662i
\(868\) −2.33522 + 0.294718i −0.0792627 + 0.0100034i
\(869\) 8.82354 0.299318
\(870\) 43.9737 + 14.6561i 1.49085 + 0.496888i
\(871\) 19.4722i 0.659789i
\(872\) −19.0858 29.0669i −0.646325 0.984328i
\(873\) 47.4164 + 47.4164i 1.60480 + 1.60480i
\(874\) −22.7219 46.3884i −0.768581 1.56911i
\(875\) 0.275504 + 11.1769i 0.00931372 + 0.377850i
\(876\) −3.30744 + 4.26286i −0.111748 + 0.144029i
\(877\) 10.9399 + 10.9399i 0.369414 + 0.369414i 0.867264 0.497849i \(-0.165877\pi\)
−0.497849 + 0.867264i \(0.665877\pi\)
\(878\) 20.6007 + 7.05458i 0.695238 + 0.238081i
\(879\) 84.1792 2.83930
\(880\) −8.70292 5.05369i −0.293375 0.170360i
\(881\) 38.4699 1.29608 0.648042 0.761604i \(-0.275588\pi\)
0.648042 + 0.761604i \(0.275588\pi\)
\(882\) 7.10055 + 2.43155i 0.239088 + 0.0818744i
\(883\) 10.9204 + 10.9204i 0.367501 + 0.367501i 0.866565 0.499064i \(-0.166323\pi\)
−0.499064 + 0.866565i \(0.666323\pi\)
\(884\) −9.52463 + 12.2760i −0.320348 + 0.412886i
\(885\) 0.690019 + 83.9955i 0.0231947 + 2.82348i
\(886\) −7.62865 15.5744i −0.256290 0.523233i
\(887\) 33.3314 + 33.3314i 1.11916 + 1.11916i 0.991865 + 0.127294i \(0.0406291\pi\)
0.127294 + 0.991865i \(0.459371\pi\)
\(888\) 24.8513 16.3178i 0.833956 0.547589i
\(889\) 20.6402i 0.692250i
\(890\) −6.42646 12.8517i −0.215415 0.430791i
\(891\) −3.64993 −0.122277
\(892\) −17.1250 + 2.16128i −0.573389 + 0.0723649i
\(893\) −6.31122 + 6.31122i −0.211197 + 0.211197i
\(894\) −23.5705 48.1209i −0.788317 1.60940i
\(895\) 24.2738 + 23.8783i 0.811385 + 0.798162i
\(896\) 11.3014 0.528129i 0.377552 0.0176436i
\(897\) −19.8847 + 19.8847i −0.663932 + 0.663932i
\(898\) 2.56950 7.50341i 0.0857454 0.250392i
\(899\) 5.98511i 0.199615i
\(900\) 42.4590 + 31.8394i 1.41530 + 1.06131i
\(901\) 48.2493i 1.60742i
\(902\) −5.85732 2.00581i −0.195027 0.0667860i
\(903\) −25.3887 + 25.3887i −0.844882 + 0.844882i
\(904\) 0.440560 2.12543i 0.0146528 0.0706907i
\(905\) −25.7803 25.3602i −0.856967 0.843002i
\(906\) −39.0201 + 19.1128i −1.29636 + 0.634980i
\(907\) 4.41436 4.41436i 0.146577 0.146577i −0.630010 0.776587i \(-0.716949\pi\)
0.776587 + 0.630010i \(0.216949\pi\)
\(908\) 29.1513 3.67906i 0.967420 0.122094i
\(909\) −29.7524 −0.986825
\(910\) 4.56829 2.28436i 0.151437 0.0757257i
\(911\) 18.2006i 0.603012i 0.953464 + 0.301506i \(0.0974894\pi\)
−0.953464 + 0.301506i \(0.902511\pi\)
\(912\) 59.9920 + 35.4989i 1.98653 + 1.17549i
\(913\) −5.27963 5.27963i −0.174730 0.174730i
\(914\) 10.3923 5.09037i 0.343748 0.168374i
\(915\) 0.748873 + 91.1599i 0.0247570 + 3.01365i
\(916\) −18.7456 14.5443i −0.619373 0.480556i
\(917\) −6.82010 6.82010i −0.225219 0.225219i
\(918\) −14.6539 + 42.7920i −0.483651 + 1.41235i
\(919\) 45.2644 1.49314 0.746568 0.665310i \(-0.231700\pi\)
0.746568 + 0.665310i \(0.231700\pi\)
\(920\) −31.7627 + 21.2314i −1.04719 + 0.699978i
\(921\) 1.51753 0.0500043
\(922\) 2.09148 6.10749i 0.0688791 0.201140i
\(923\) 3.66076 + 3.66076i 0.120495 + 0.120495i
\(924\) −3.97590 + 5.12441i −0.130797 + 0.168581i
\(925\) 12.6801 13.1038i 0.416920 0.430850i
\(926\) −8.21119 + 4.02200i −0.269836 + 0.132171i
\(927\) −22.4987 22.4987i −0.738954 0.738954i
\(928\) 2.26589 28.6791i 0.0743813 0.941438i
\(929\) 32.9683i 1.08165i 0.841134 + 0.540827i \(0.181889\pi\)
−0.841134 + 0.540827i \(0.818111\pi\)
\(930\) −3.39161 + 10.1761i −0.111215 + 0.333687i
\(931\) 6.04642 0.198163
\(932\) 1.26015 + 9.98493i 0.0412777 + 0.327067i
\(933\) −26.6317 + 26.6317i −0.871881 + 0.871881i
\(934\) −29.2776 + 14.3407i −0.957992 + 0.469243i
\(935\) −0.0994104 12.1012i −0.00325107 0.395750i
\(936\) 4.92087 23.7401i 0.160844 0.775970i
\(937\) −1.18430 + 1.18430i −0.0386894 + 0.0386894i −0.726187 0.687497i \(-0.758709\pi\)
0.687497 + 0.726187i \(0.258709\pi\)
\(938\) 16.1300 + 5.52362i 0.526662 + 0.180353i
\(939\) 45.1591i 1.47371i
\(940\) 5.24881 + 4.00378i 0.171197 + 0.130589i
\(941\) 18.5257i 0.603921i −0.953320 0.301960i \(-0.902359\pi\)
0.953320 0.301960i \(-0.0976411\pi\)
\(942\) −12.9214 + 37.7328i −0.421002 + 1.22940i
\(943\) −16.6197 + 16.6197i −0.541211 + 0.541211i
\(944\) 50.4993 12.9529i 1.64361 0.421581i
\(945\) 10.4270 10.5998i 0.339191 0.344810i
\(946\) −8.71971 17.8019i −0.283502 0.578789i
\(947\) 28.1440 28.1440i 0.914556 0.914556i −0.0820702 0.996627i \(-0.526153\pi\)
0.996627 + 0.0820702i \(0.0261532\pi\)
\(948\) 5.66013 + 44.8485i 0.183832 + 1.45661i
\(949\) 1.51179 0.0490748
\(950\) 40.6708 + 13.1851i 1.31954 + 0.427780i
\(951\) 64.4813i 2.09095i
\(952\) 7.46712 + 11.3721i 0.242011 + 0.368573i
\(953\) −30.9821 30.9821i −1.00361 1.00361i −0.999993 0.00361421i \(-0.998850\pi\)
−0.00361421 0.999993i \(-0.501150\pi\)
\(954\) −33.1179 67.6124i −1.07223 2.18903i
\(955\) −0.239609 0.235704i −0.00775357 0.00762721i
\(956\) −30.6738 23.7990i −0.992063 0.769716i
\(957\) 11.6619 + 11.6619i 0.376976 + 0.376976i
\(958\) 53.9335 + 18.4692i 1.74251 + 0.596713i
\(959\) −0.336322 −0.0108604
\(960\) 20.1043 47.4772i 0.648862 1.53232i
\(961\) 29.6150 0.955321
\(962\) −7.88089 2.69877i −0.254090 0.0870118i
\(963\) −0.150137 0.150137i −0.00483811 0.00483811i
\(964\) 6.01623 + 4.66784i 0.193770 + 0.150341i
\(965\) −4.86596 + 0.0399736i −0.156641 + 0.00128680i
\(966\) 10.8311 + 22.1124i 0.348484 + 0.711454i
\(967\) 1.39596 + 1.39596i 0.0448911 + 0.0448911i 0.729196 0.684305i \(-0.239894\pi\)
−0.684305 + 0.729196i \(0.739894\pi\)
\(968\) 15.1114 + 23.0141i 0.485700 + 0.739702i
\(969\) 83.8227i 2.69277i
\(970\) 12.6340 37.9066i 0.405652 1.21711i
\(971\) −3.19137 −0.102416 −0.0512079 0.998688i \(-0.516307\pi\)
−0.0512079 + 0.998688i \(0.516307\pi\)
\(972\) 2.65423 + 21.0310i 0.0851343 + 0.674568i
\(973\) −11.0406 + 11.0406i −0.353947 + 0.353947i
\(974\) −1.31476 2.68417i −0.0421276 0.0860064i
\(975\) −0.382399 23.2730i −0.0122466 0.745333i
\(976\) 54.8066 14.0577i 1.75432 0.449976i
\(977\) −16.0529 + 16.0529i −0.513578 + 0.513578i −0.915621 0.402043i \(-0.868300\pi\)
0.402043 + 0.915621i \(0.368300\pi\)
\(978\) −10.1491 + 29.6373i −0.324534 + 0.947697i
\(979\) 5.11261i 0.163400i
\(980\) −0.596396 4.43219i −0.0190512 0.141581i
\(981\) 65.2456i 2.08313i
\(982\) −25.3550 8.68270i −0.809112 0.277076i
\(983\) −1.23047 + 1.23047i −0.0392460 + 0.0392460i −0.726457 0.687211i \(-0.758835\pi\)
0.687211 + 0.726457i \(0.258835\pi\)
\(984\) 6.43780 31.0584i 0.205230 0.990105i
\(985\) −38.6920 + 0.317852i −1.23283 + 0.0101276i
\(986\) 31.0669 15.2172i 0.989372 0.484614i
\(987\) 3.00842 3.00842i 0.0957592 0.0957592i
\(988\) −2.44564 19.3782i −0.0778062 0.616503i
\(989\) −75.2530 −2.39291
\(990\) 8.44542 + 16.8893i 0.268413 + 0.536776i
\(991\) 18.7401i 0.595300i −0.954675 0.297650i \(-0.903797\pi\)
0.954675 0.297650i \(-0.0962029\pi\)
\(992\) 6.63673 + 0.524356i 0.210716 + 0.0166483i
\(993\) −12.8687 12.8687i −0.408375 0.408375i
\(994\) 4.07087 1.99399i 0.129120 0.0632455i
\(995\) 8.66239 8.80589i 0.274616 0.279165i
\(996\) 23.4487 30.2222i 0.742999 0.957627i
\(997\) −19.7874 19.7874i −0.626673 0.626673i 0.320557 0.947229i \(-0.396130\pi\)
−0.947229 + 0.320557i \(0.896130\pi\)
\(998\) 14.3626 41.9414i 0.454641 1.32763i
\(999\) −24.2499 −0.767233
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 280.2.w.a.43.3 72
4.3 odd 2 1120.2.bi.a.463.2 72
5.2 odd 4 inner 280.2.w.a.267.23 yes 72
8.3 odd 2 inner 280.2.w.a.43.23 yes 72
8.5 even 2 1120.2.bi.a.463.1 72
20.7 even 4 1120.2.bi.a.687.1 72
40.27 even 4 inner 280.2.w.a.267.3 yes 72
40.37 odd 4 1120.2.bi.a.687.2 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.w.a.43.3 72 1.1 even 1 trivial
280.2.w.a.43.23 yes 72 8.3 odd 2 inner
280.2.w.a.267.3 yes 72 40.27 even 4 inner
280.2.w.a.267.23 yes 72 5.2 odd 4 inner
1120.2.bi.a.463.1 72 8.5 even 2
1120.2.bi.a.463.2 72 4.3 odd 2
1120.2.bi.a.687.1 72 20.7 even 4
1120.2.bi.a.687.2 72 40.37 odd 4