Properties

Label 770.2.n.b.631.1
Level $770$
Weight $2$
Character 770.631
Analytic conductor $6.148$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [770,2,Mod(71,770)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(770, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("770.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.14848095564\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 631.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 770.631
Dual form 770.2.n.b.421.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(0.118034 - 0.363271i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.309017 - 0.224514i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.30902 + 1.67760i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(0.118034 - 0.363271i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.309017 - 0.224514i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.30902 + 1.67760i) q^{9} +1.00000 q^{10} +(0.309017 - 3.30220i) q^{11} +0.381966 q^{12} +(1.61803 + 1.17557i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-0.118034 - 0.363271i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.500000 - 0.363271i) q^{17} +(0.881966 + 2.71441i) q^{18} +(-0.0450850 + 0.138757i) q^{19} +(0.809017 + 0.587785i) q^{20} -0.381966 q^{21} +(2.19098 - 2.48990i) q^{22} +6.00000 q^{23} +(0.309017 + 0.224514i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.618034 + 1.90211i) q^{26} +(1.80902 - 1.31433i) q^{27} +(0.809017 - 0.587785i) q^{28} +(0.381966 + 1.17557i) q^{29} +(0.118034 - 0.363271i) q^{30} +(-2.61803 - 1.90211i) q^{31} -1.00000 q^{32} +(-1.16312 - 0.502029i) q^{33} +0.618034 q^{34} +(-0.809017 - 0.587785i) q^{35} +(-0.881966 + 2.71441i) q^{36} +(0.763932 + 2.35114i) q^{37} +(-0.118034 + 0.0857567i) q^{38} +(0.618034 - 0.449028i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-1.64590 + 5.06555i) q^{41} +(-0.309017 - 0.224514i) q^{42} +4.85410 q^{43} +(3.23607 - 0.726543i) q^{44} +2.85410 q^{45} +(4.85410 + 3.52671i) q^{46} +(1.47214 - 4.53077i) q^{47} +(0.118034 + 0.363271i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-0.0729490 - 0.224514i) q^{51} +(-0.618034 + 1.90211i) q^{52} +(2.61803 + 1.90211i) q^{53} +2.23607 q^{54} +(-1.69098 - 2.85317i) q^{55} +1.00000 q^{56} +(0.0450850 + 0.0327561i) q^{57} +(-0.381966 + 1.17557i) q^{58} +(-1.66312 - 5.11855i) q^{59} +(0.309017 - 0.224514i) q^{60} +(-10.0902 + 7.33094i) q^{61} +(-1.00000 - 3.07768i) q^{62} +(0.881966 - 2.71441i) q^{63} +(-0.809017 - 0.587785i) q^{64} +2.00000 q^{65} +(-0.645898 - 1.08981i) q^{66} -5.09017 q^{67} +(0.500000 + 0.363271i) q^{68} +(0.708204 - 2.17963i) q^{69} +(-0.309017 - 0.951057i) q^{70} +(-3.00000 + 2.17963i) q^{71} +(-2.30902 + 1.67760i) q^{72} +(-2.20820 - 6.79615i) q^{73} +(-0.763932 + 2.35114i) q^{74} +(-0.309017 - 0.224514i) q^{75} -0.145898 q^{76} +(-3.23607 + 0.726543i) q^{77} +0.763932 q^{78} +(0.381966 + 0.277515i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.38197 + 7.33094i) q^{81} +(-4.30902 + 3.13068i) q^{82} +(-4.30902 + 3.13068i) q^{83} +(-0.118034 - 0.363271i) q^{84} +(0.190983 - 0.587785i) q^{85} +(3.92705 + 2.85317i) q^{86} +0.472136 q^{87} +(3.04508 + 1.31433i) q^{88} +1.90983 q^{89} +(2.30902 + 1.67760i) q^{90} +(0.618034 - 1.90211i) q^{91} +(1.85410 + 5.70634i) q^{92} +(-1.00000 + 0.726543i) q^{93} +(3.85410 - 2.80017i) q^{94} +(0.0450850 + 0.138757i) q^{95} +(-0.118034 + 0.363271i) q^{96} +(-8.54508 - 6.20837i) q^{97} -1.00000 q^{98} +(6.25329 - 7.10642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - 4 q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - 4 q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + 7 q^{9} + 4 q^{10} - q^{11} + 6 q^{12} + 2 q^{13} - q^{14} + 4 q^{15} - q^{16} + 2 q^{17} + 8 q^{18} + 11 q^{19} + q^{20} - 6 q^{21} + 11 q^{22} + 24 q^{23} - q^{24} - q^{25} - 2 q^{26} + 5 q^{27} + q^{28} + 6 q^{29} - 4 q^{30} - 6 q^{31} - 4 q^{32} + 11 q^{33} - 2 q^{34} - q^{35} - 8 q^{36} + 12 q^{37} + 4 q^{38} - 2 q^{39} - q^{40} - 20 q^{41} + q^{42} + 6 q^{43} + 4 q^{44} - 2 q^{45} + 6 q^{46} - 12 q^{47} - 4 q^{48} - q^{49} + q^{50} - 7 q^{51} + 2 q^{52} + 6 q^{53} - 9 q^{55} + 4 q^{56} - 11 q^{57} - 6 q^{58} + 9 q^{59} - q^{60} - 18 q^{61} - 4 q^{62} + 8 q^{63} - q^{64} + 8 q^{65} - 16 q^{66} + 2 q^{67} + 2 q^{68} - 24 q^{69} + q^{70} - 12 q^{71} - 7 q^{72} + 18 q^{73} - 12 q^{74} + q^{75} - 14 q^{76} - 4 q^{77} + 12 q^{78} + 6 q^{79} + q^{80} + 14 q^{81} - 15 q^{82} - 15 q^{83} + 4 q^{84} + 3 q^{85} + 9 q^{86} - 16 q^{87} + q^{88} + 30 q^{89} + 7 q^{90} - 2 q^{91} - 6 q^{92} - 4 q^{93} + 2 q^{94} - 11 q^{95} + 4 q^{96} - 23 q^{97} - 4 q^{98} - 13 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i
\(3\) 0.118034 0.363271i 0.0681470 0.209735i −0.911184 0.412000i \(-0.864830\pi\)
0.979331 + 0.202265i \(0.0648303\pi\)
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 0.809017 0.587785i 0.361803 0.262866i
\(6\) 0.309017 0.224514i 0.126156 0.0916575i
\(7\) −0.309017 0.951057i −0.116797 0.359466i
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) 2.30902 + 1.67760i 0.769672 + 0.559200i
\(10\) 1.00000 0.316228
\(11\) 0.309017 3.30220i 0.0931721 0.995650i
\(12\) 0.381966 0.110264
\(13\) 1.61803 + 1.17557i 0.448762 + 0.326045i 0.789107 0.614256i \(-0.210544\pi\)
−0.340345 + 0.940301i \(0.610544\pi\)
\(14\) 0.309017 0.951057i 0.0825883 0.254181i
\(15\) −0.118034 0.363271i −0.0304762 0.0937962i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 0.500000 0.363271i 0.121268 0.0881062i −0.525498 0.850795i \(-0.676121\pi\)
0.646766 + 0.762688i \(0.276121\pi\)
\(18\) 0.881966 + 2.71441i 0.207881 + 0.639793i
\(19\) −0.0450850 + 0.138757i −0.0103432 + 0.0318331i −0.956095 0.293057i \(-0.905327\pi\)
0.945752 + 0.324890i \(0.105327\pi\)
\(20\) 0.809017 + 0.587785i 0.180902 + 0.131433i
\(21\) −0.381966 −0.0833518
\(22\) 2.19098 2.48990i 0.467119 0.530848i
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0.309017 + 0.224514i 0.0630778 + 0.0458287i
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) 0.618034 + 1.90211i 0.121206 + 0.373035i
\(27\) 1.80902 1.31433i 0.348145 0.252942i
\(28\) 0.809017 0.587785i 0.152890 0.111081i
\(29\) 0.381966 + 1.17557i 0.0709293 + 0.218298i 0.980237 0.197826i \(-0.0633882\pi\)
−0.909308 + 0.416124i \(0.863388\pi\)
\(30\) 0.118034 0.363271i 0.0215500 0.0663240i
\(31\) −2.61803 1.90211i −0.470213 0.341630i 0.327311 0.944917i \(-0.393857\pi\)
−0.797524 + 0.603287i \(0.793857\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.16312 0.502029i −0.202473 0.0873920i
\(34\) 0.618034 0.105992
\(35\) −0.809017 0.587785i −0.136749 0.0993538i
\(36\) −0.881966 + 2.71441i −0.146994 + 0.452402i
\(37\) 0.763932 + 2.35114i 0.125590 + 0.386525i 0.994008 0.109307i \(-0.0348631\pi\)
−0.868418 + 0.495832i \(0.834863\pi\)
\(38\) −0.118034 + 0.0857567i −0.0191476 + 0.0139116i
\(39\) 0.618034 0.449028i 0.0989646 0.0719020i
\(40\) 0.309017 + 0.951057i 0.0488599 + 0.150375i
\(41\) −1.64590 + 5.06555i −0.257046 + 0.791107i 0.736374 + 0.676575i \(0.236537\pi\)
−0.993420 + 0.114531i \(0.963463\pi\)
\(42\) −0.309017 0.224514i −0.0476824 0.0346433i
\(43\) 4.85410 0.740244 0.370122 0.928983i \(-0.379316\pi\)
0.370122 + 0.928983i \(0.379316\pi\)
\(44\) 3.23607 0.726543i 0.487856 0.109530i
\(45\) 2.85410 0.425464
\(46\) 4.85410 + 3.52671i 0.715698 + 0.519985i
\(47\) 1.47214 4.53077i 0.214733 0.660881i −0.784439 0.620206i \(-0.787049\pi\)
0.999172 0.0406750i \(-0.0129508\pi\)
\(48\) 0.118034 + 0.363271i 0.0170367 + 0.0524337i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) 0.809017 0.587785i 0.114412 0.0831254i
\(51\) −0.0729490 0.224514i −0.0102149 0.0314382i
\(52\) −0.618034 + 1.90211i −0.0857059 + 0.263776i
\(53\) 2.61803 + 1.90211i 0.359615 + 0.261275i 0.752891 0.658145i \(-0.228659\pi\)
−0.393277 + 0.919420i \(0.628659\pi\)
\(54\) 2.23607 0.304290
\(55\) −1.69098 2.85317i −0.228012 0.384721i
\(56\) 1.00000 0.133631
\(57\) 0.0450850 + 0.0327561i 0.00597165 + 0.00433866i
\(58\) −0.381966 + 1.17557i −0.0501546 + 0.154360i
\(59\) −1.66312 5.11855i −0.216520 0.666379i −0.999042 0.0437567i \(-0.986067\pi\)
0.782523 0.622622i \(-0.213933\pi\)
\(60\) 0.309017 0.224514i 0.0398939 0.0289846i
\(61\) −10.0902 + 7.33094i −1.29191 + 0.938630i −0.999842 0.0177660i \(-0.994345\pi\)
−0.292072 + 0.956396i \(0.594345\pi\)
\(62\) −1.00000 3.07768i −0.127000 0.390866i
\(63\) 0.881966 2.71441i 0.111117 0.341984i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 2.00000 0.248069
\(66\) −0.645898 1.08981i −0.0795046 0.134147i
\(67\) −5.09017 −0.621863 −0.310932 0.950432i \(-0.600641\pi\)
−0.310932 + 0.950432i \(0.600641\pi\)
\(68\) 0.500000 + 0.363271i 0.0606339 + 0.0440531i
\(69\) 0.708204 2.17963i 0.0852577 0.262396i
\(70\) −0.309017 0.951057i −0.0369346 0.113673i
\(71\) −3.00000 + 2.17963i −0.356034 + 0.258674i −0.751396 0.659851i \(-0.770619\pi\)
0.395362 + 0.918526i \(0.370619\pi\)
\(72\) −2.30902 + 1.67760i −0.272120 + 0.197707i
\(73\) −2.20820 6.79615i −0.258451 0.795430i −0.993130 0.117015i \(-0.962667\pi\)
0.734679 0.678414i \(-0.237333\pi\)
\(74\) −0.763932 + 2.35114i −0.0888053 + 0.273315i
\(75\) −0.309017 0.224514i −0.0356822 0.0259246i
\(76\) −0.145898 −0.0167357
\(77\) −3.23607 + 0.726543i −0.368784 + 0.0827972i
\(78\) 0.763932 0.0864983
\(79\) 0.381966 + 0.277515i 0.0429745 + 0.0312228i 0.609065 0.793120i \(-0.291545\pi\)
−0.566091 + 0.824343i \(0.691545\pi\)
\(80\) −0.309017 + 0.951057i −0.0345492 + 0.106331i
\(81\) 2.38197 + 7.33094i 0.264663 + 0.814549i
\(82\) −4.30902 + 3.13068i −0.475851 + 0.345726i
\(83\) −4.30902 + 3.13068i −0.472976 + 0.343637i −0.798600 0.601862i \(-0.794426\pi\)
0.325624 + 0.945499i \(0.394426\pi\)
\(84\) −0.118034 0.363271i −0.0128786 0.0396361i
\(85\) 0.190983 0.587785i 0.0207150 0.0637543i
\(86\) 3.92705 + 2.85317i 0.423465 + 0.307665i
\(87\) 0.472136 0.0506183
\(88\) 3.04508 + 1.31433i 0.324607 + 0.140108i
\(89\) 1.90983 0.202442 0.101221 0.994864i \(-0.467725\pi\)
0.101221 + 0.994864i \(0.467725\pi\)
\(90\) 2.30902 + 1.67760i 0.243392 + 0.176834i
\(91\) 0.618034 1.90211i 0.0647876 0.199396i
\(92\) 1.85410 + 5.70634i 0.193303 + 0.594927i
\(93\) −1.00000 + 0.726543i −0.103695 + 0.0753390i
\(94\) 3.85410 2.80017i 0.397520 0.288815i
\(95\) 0.0450850 + 0.138757i 0.00462562 + 0.0142362i
\(96\) −0.118034 + 0.363271i −0.0120468 + 0.0370762i
\(97\) −8.54508 6.20837i −0.867622 0.630364i 0.0623259 0.998056i \(-0.480148\pi\)
−0.929948 + 0.367692i \(0.880148\pi\)
\(98\) −1.00000 −0.101015
\(99\) 6.25329 7.10642i 0.628479 0.714222i
\(100\) 1.00000 0.100000
\(101\) −7.23607 5.25731i −0.720016 0.523122i 0.166374 0.986063i \(-0.446794\pi\)
−0.886389 + 0.462941i \(0.846794\pi\)
\(102\) 0.0729490 0.224514i 0.00722303 0.0222302i
\(103\) 0.291796 + 0.898056i 0.0287515 + 0.0884881i 0.964403 0.264438i \(-0.0851866\pi\)
−0.935651 + 0.352926i \(0.885187\pi\)
\(104\) −1.61803 + 1.17557i −0.158661 + 0.115274i
\(105\) −0.309017 + 0.224514i −0.0301570 + 0.0219103i
\(106\) 1.00000 + 3.07768i 0.0971286 + 0.298931i
\(107\) −5.44427 + 16.7557i −0.526318 + 1.61984i 0.235378 + 0.971904i \(0.424367\pi\)
−0.761695 + 0.647935i \(0.775633\pi\)
\(108\) 1.80902 + 1.31433i 0.174073 + 0.126471i
\(109\) −8.47214 −0.811483 −0.405742 0.913988i \(-0.632987\pi\)
−0.405742 + 0.913988i \(0.632987\pi\)
\(110\) 0.309017 3.30220i 0.0294636 0.314852i
\(111\) 0.944272 0.0896263
\(112\) 0.809017 + 0.587785i 0.0764449 + 0.0555405i
\(113\) 1.95492 6.01661i 0.183903 0.565995i −0.816025 0.578017i \(-0.803827\pi\)
0.999928 + 0.0120219i \(0.00382677\pi\)
\(114\) 0.0172209 + 0.0530006i 0.00161289 + 0.00496396i
\(115\) 4.85410 3.52671i 0.452647 0.328868i
\(116\) −1.00000 + 0.726543i −0.0928477 + 0.0674578i
\(117\) 1.76393 + 5.42882i 0.163076 + 0.501895i
\(118\) 1.66312 5.11855i 0.153103 0.471201i
\(119\) −0.500000 0.363271i −0.0458349 0.0333010i
\(120\) 0.381966 0.0348686
\(121\) −10.8090 2.04087i −0.982638 0.185534i
\(122\) −12.4721 −1.12917
\(123\) 1.64590 + 1.19581i 0.148406 + 0.107823i
\(124\) 1.00000 3.07768i 0.0898027 0.276384i
\(125\) −0.309017 0.951057i −0.0276393 0.0850651i
\(126\) 2.30902 1.67760i 0.205704 0.149452i
\(127\) 12.4721 9.06154i 1.10672 0.804081i 0.124579 0.992210i \(-0.460242\pi\)
0.982144 + 0.188128i \(0.0602421\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) 0.572949 1.76336i 0.0504453 0.155255i
\(130\) 1.61803 + 1.17557i 0.141911 + 0.103104i
\(131\) −16.7984 −1.46768 −0.733840 0.679322i \(-0.762274\pi\)
−0.733840 + 0.679322i \(0.762274\pi\)
\(132\) 0.118034 1.26133i 0.0102735 0.109784i
\(133\) 0.145898 0.0126510
\(134\) −4.11803 2.99193i −0.355744 0.258463i
\(135\) 0.690983 2.12663i 0.0594703 0.183031i
\(136\) 0.190983 + 0.587785i 0.0163767 + 0.0504022i
\(137\) −8.16312 + 5.93085i −0.697422 + 0.506707i −0.879092 0.476653i \(-0.841850\pi\)
0.181669 + 0.983360i \(0.441850\pi\)
\(138\) 1.85410 1.34708i 0.157832 0.114671i
\(139\) −2.94427 9.06154i −0.249730 0.768590i −0.994822 0.101628i \(-0.967595\pi\)
0.745093 0.666961i \(-0.232405\pi\)
\(140\) 0.309017 0.951057i 0.0261167 0.0803789i
\(141\) −1.47214 1.06957i −0.123976 0.0900740i
\(142\) −3.70820 −0.311186
\(143\) 4.38197 4.97980i 0.366438 0.416432i
\(144\) −2.85410 −0.237842
\(145\) 1.00000 + 0.726543i 0.0830455 + 0.0603361i
\(146\) 2.20820 6.79615i 0.182752 0.562454i
\(147\) 0.118034 + 0.363271i 0.00973528 + 0.0299621i
\(148\) −2.00000 + 1.45309i −0.164399 + 0.119443i
\(149\) 1.47214 1.06957i 0.120602 0.0876225i −0.525849 0.850578i \(-0.676252\pi\)
0.646451 + 0.762955i \(0.276252\pi\)
\(150\) −0.118034 0.363271i −0.00963743 0.0296610i
\(151\) −4.85410 + 14.9394i −0.395021 + 1.21575i 0.533924 + 0.845533i \(0.320717\pi\)
−0.928945 + 0.370218i \(0.879283\pi\)
\(152\) −0.118034 0.0857567i −0.00957382 0.00695579i
\(153\) 1.76393 0.142605
\(154\) −3.04508 1.31433i −0.245380 0.105912i
\(155\) −3.23607 −0.259927
\(156\) 0.618034 + 0.449028i 0.0494823 + 0.0359510i
\(157\) 4.23607 13.0373i 0.338075 1.04049i −0.627112 0.778929i \(-0.715763\pi\)
0.965187 0.261559i \(-0.0842367\pi\)
\(158\) 0.145898 + 0.449028i 0.0116070 + 0.0357227i
\(159\) 1.00000 0.726543i 0.0793052 0.0576186i
\(160\) −0.809017 + 0.587785i −0.0639584 + 0.0464685i
\(161\) −1.85410 5.70634i −0.146124 0.449723i
\(162\) −2.38197 + 7.33094i −0.187145 + 0.575973i
\(163\) 3.11803 + 2.26538i 0.244223 + 0.177439i 0.703163 0.711029i \(-0.251771\pi\)
−0.458939 + 0.888468i \(0.651771\pi\)
\(164\) −5.32624 −0.415909
\(165\) −1.23607 + 0.277515i −0.0962278 + 0.0216045i
\(166\) −5.32624 −0.413396
\(167\) −2.00000 1.45309i −0.154765 0.112443i 0.507708 0.861529i \(-0.330493\pi\)
−0.662473 + 0.749086i \(0.730493\pi\)
\(168\) 0.118034 0.363271i 0.00910652 0.0280270i
\(169\) −2.78115 8.55951i −0.213935 0.658424i
\(170\) 0.500000 0.363271i 0.0383482 0.0278616i
\(171\) −0.336881 + 0.244758i −0.0257619 + 0.0187171i
\(172\) 1.50000 + 4.61653i 0.114374 + 0.352007i
\(173\) −3.70820 + 11.4127i −0.281930 + 0.867690i 0.705373 + 0.708837i \(0.250780\pi\)
−0.987302 + 0.158853i \(0.949220\pi\)
\(174\) 0.381966 + 0.277515i 0.0289568 + 0.0210383i
\(175\) −1.00000 −0.0755929
\(176\) 1.69098 + 2.85317i 0.127463 + 0.215066i
\(177\) −2.05573 −0.154518
\(178\) 1.54508 + 1.12257i 0.115809 + 0.0841402i
\(179\) −2.66312 + 8.19624i −0.199051 + 0.612616i 0.800855 + 0.598859i \(0.204379\pi\)
−0.999905 + 0.0137566i \(0.995621\pi\)
\(180\) 0.881966 + 2.71441i 0.0657379 + 0.202320i
\(181\) −10.0902 + 7.33094i −0.749996 + 0.544904i −0.895826 0.444405i \(-0.853415\pi\)
0.145829 + 0.989310i \(0.453415\pi\)
\(182\) 1.61803 1.17557i 0.119937 0.0871391i
\(183\) 1.47214 + 4.53077i 0.108823 + 0.334924i
\(184\) −1.85410 + 5.70634i −0.136686 + 0.420677i
\(185\) 2.00000 + 1.45309i 0.147043 + 0.106833i
\(186\) −1.23607 −0.0906329
\(187\) −1.04508 1.76336i −0.0764242 0.128949i
\(188\) 4.76393 0.347445
\(189\) −1.80902 1.31433i −0.131587 0.0956033i
\(190\) −0.0450850 + 0.138757i −0.00327081 + 0.0100665i
\(191\) −3.23607 9.95959i −0.234154 0.720651i −0.997233 0.0743455i \(-0.976313\pi\)
0.763079 0.646305i \(-0.223687\pi\)
\(192\) −0.309017 + 0.224514i −0.0223014 + 0.0162029i
\(193\) −1.61803 + 1.17557i −0.116469 + 0.0846194i −0.644495 0.764609i \(-0.722932\pi\)
0.528026 + 0.849228i \(0.322932\pi\)
\(194\) −3.26393 10.0453i −0.234337 0.721214i
\(195\) 0.236068 0.726543i 0.0169052 0.0520288i
\(196\) −0.809017 0.587785i −0.0577869 0.0419847i
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 9.23607 2.07363i 0.656379 0.147366i
\(199\) 7.41641 0.525735 0.262868 0.964832i \(-0.415332\pi\)
0.262868 + 0.964832i \(0.415332\pi\)
\(200\) 0.809017 + 0.587785i 0.0572061 + 0.0415627i
\(201\) −0.600813 + 1.84911i −0.0423781 + 0.130426i
\(202\) −2.76393 8.50651i −0.194470 0.598516i
\(203\) 1.00000 0.726543i 0.0701862 0.0509933i
\(204\) 0.190983 0.138757i 0.0133715 0.00971495i
\(205\) 1.64590 + 5.06555i 0.114955 + 0.353794i
\(206\) −0.291796 + 0.898056i −0.0203304 + 0.0625705i
\(207\) 13.8541 + 10.0656i 0.962927 + 0.699607i
\(208\) −2.00000 −0.138675
\(209\) 0.444272 + 0.191758i 0.0307309 + 0.0132642i
\(210\) −0.381966 −0.0263582
\(211\) −18.0172 13.0903i −1.24036 0.901172i −0.242735 0.970093i \(-0.578044\pi\)
−0.997622 + 0.0689209i \(0.978044\pi\)
\(212\) −1.00000 + 3.07768i −0.0686803 + 0.211376i
\(213\) 0.437694 + 1.34708i 0.0299903 + 0.0923007i
\(214\) −14.2533 + 10.3556i −0.974335 + 0.707896i
\(215\) 3.92705 2.85317i 0.267823 0.194585i
\(216\) 0.690983 + 2.12663i 0.0470154 + 0.144699i
\(217\) −1.00000 + 3.07768i −0.0678844 + 0.208927i
\(218\) −6.85410 4.97980i −0.464218 0.337274i
\(219\) −2.72949 −0.184442
\(220\) 2.19098 2.48990i 0.147716 0.167869i
\(221\) 1.23607 0.0831469
\(222\) 0.763932 + 0.555029i 0.0512718 + 0.0372511i
\(223\) 6.09017 18.7436i 0.407828 1.25517i −0.510683 0.859769i \(-0.670607\pi\)
0.918511 0.395396i \(-0.129393\pi\)
\(224\) 0.309017 + 0.951057i 0.0206471 + 0.0635451i
\(225\) 2.30902 1.67760i 0.153934 0.111840i
\(226\) 5.11803 3.71847i 0.340447 0.247349i
\(227\) −2.86475 8.81678i −0.190140 0.585190i 0.809859 0.586624i \(-0.199543\pi\)
−0.999999 + 0.00143420i \(0.999543\pi\)
\(228\) −0.0172209 + 0.0530006i −0.00114048 + 0.00351005i
\(229\) 23.5623 + 17.1190i 1.55704 + 1.13126i 0.938384 + 0.345596i \(0.112323\pi\)
0.618657 + 0.785661i \(0.287677\pi\)
\(230\) 6.00000 0.395628
\(231\) −0.118034 + 1.26133i −0.00776607 + 0.0829892i
\(232\) −1.23607 −0.0811518
\(233\) 17.8713 + 12.9843i 1.17079 + 0.850628i 0.991103 0.133096i \(-0.0424918\pi\)
0.179686 + 0.983724i \(0.442492\pi\)
\(234\) −1.76393 + 5.42882i −0.115312 + 0.354893i
\(235\) −1.47214 4.53077i −0.0960316 0.295555i
\(236\) 4.35410 3.16344i 0.283428 0.205922i
\(237\) 0.145898 0.106001i 0.00947710 0.00688551i
\(238\) −0.190983 0.587785i −0.0123796 0.0381005i
\(239\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(240\) 0.309017 + 0.224514i 0.0199470 + 0.0144923i
\(241\) −27.2705 −1.75665 −0.878324 0.478066i \(-0.841338\pi\)
−0.878324 + 0.478066i \(0.841338\pi\)
\(242\) −7.54508 8.00448i −0.485016 0.514547i
\(243\) 9.65248 0.619207
\(244\) −10.0902 7.33094i −0.645957 0.469315i
\(245\) −0.309017 + 0.951057i −0.0197424 + 0.0607608i
\(246\) 0.628677 + 1.93487i 0.0400830 + 0.123363i
\(247\) −0.236068 + 0.171513i −0.0150206 + 0.0109131i
\(248\) 2.61803 1.90211i 0.166245 0.120784i
\(249\) 0.628677 + 1.93487i 0.0398408 + 0.122617i
\(250\) 0.309017 0.951057i 0.0195440 0.0601501i
\(251\) 21.7082 + 15.7719i 1.37021 + 0.995516i 0.997721 + 0.0674790i \(0.0214956\pi\)
0.372489 + 0.928037i \(0.378504\pi\)
\(252\) 2.85410 0.179792
\(253\) 1.85410 19.8132i 0.116566 1.24564i
\(254\) 15.4164 0.967311
\(255\) −0.190983 0.138757i −0.0119598 0.00868932i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 2.91641 + 8.97578i 0.181921 + 0.559894i 0.999882 0.0153796i \(-0.00489567\pi\)
−0.817961 + 0.575273i \(0.804896\pi\)
\(258\) 1.50000 1.08981i 0.0933859 0.0678488i
\(259\) 2.00000 1.45309i 0.124274 0.0902903i
\(260\) 0.618034 + 1.90211i 0.0383288 + 0.117964i
\(261\) −1.09017 + 3.35520i −0.0674798 + 0.207682i
\(262\) −13.5902 9.87384i −0.839604 0.610008i
\(263\) 2.18034 0.134446 0.0672228 0.997738i \(-0.478586\pi\)
0.0672228 + 0.997738i \(0.478586\pi\)
\(264\) 0.836881 0.951057i 0.0515065 0.0585335i
\(265\) 3.23607 0.198790
\(266\) 0.118034 + 0.0857567i 0.00723713 + 0.00525808i
\(267\) 0.225425 0.693786i 0.0137958 0.0424590i
\(268\) −1.57295 4.84104i −0.0960832 0.295714i
\(269\) −8.23607 + 5.98385i −0.502162 + 0.364842i −0.809842 0.586648i \(-0.800447\pi\)
0.307680 + 0.951490i \(0.400447\pi\)
\(270\) 1.80902 1.31433i 0.110093 0.0799874i
\(271\) −5.38197 16.5640i −0.326931 1.00619i −0.970561 0.240854i \(-0.922573\pi\)
0.643630 0.765337i \(-0.277427\pi\)
\(272\) −0.190983 + 0.587785i −0.0115800 + 0.0356397i
\(273\) −0.618034 0.449028i −0.0374051 0.0271764i
\(274\) −10.0902 −0.609569
\(275\) −3.04508 1.31433i −0.183626 0.0792569i
\(276\) 2.29180 0.137950
\(277\) 15.9443 + 11.5842i 0.957998 + 0.696027i 0.952685 0.303959i \(-0.0983087\pi\)
0.00531342 + 0.999986i \(0.498309\pi\)
\(278\) 2.94427 9.06154i 0.176586 0.543475i
\(279\) −2.85410 8.78402i −0.170871 0.525886i
\(280\) 0.809017 0.587785i 0.0483480 0.0351269i
\(281\) 4.07295 2.95917i 0.242972 0.176529i −0.459634 0.888108i \(-0.652020\pi\)
0.702606 + 0.711579i \(0.252020\pi\)
\(282\) −0.562306 1.73060i −0.0334848 0.103056i
\(283\) 3.70820 11.4127i 0.220430 0.678413i −0.778294 0.627901i \(-0.783914\pi\)
0.998723 0.0505127i \(-0.0160855\pi\)
\(284\) −3.00000 2.17963i −0.178017 0.129337i
\(285\) 0.0557281 0.00330105
\(286\) 6.47214 1.45309i 0.382705 0.0859227i
\(287\) 5.32624 0.314398
\(288\) −2.30902 1.67760i −0.136060 0.0988535i
\(289\) −5.13525 + 15.8047i −0.302074 + 0.929688i
\(290\) 0.381966 + 1.17557i 0.0224298 + 0.0690319i
\(291\) −3.26393 + 2.37139i −0.191335 + 0.139013i
\(292\) 5.78115 4.20025i 0.338316 0.245801i
\(293\) −2.32624 7.15942i −0.135900 0.418258i 0.859829 0.510583i \(-0.170570\pi\)
−0.995729 + 0.0923246i \(0.970570\pi\)
\(294\) −0.118034 + 0.363271i −0.00688388 + 0.0211864i
\(295\) −4.35410 3.16344i −0.253506 0.184183i
\(296\) −2.47214 −0.143690
\(297\) −3.78115 6.37988i −0.219405 0.370198i
\(298\) 1.81966 0.105410
\(299\) 9.70820 + 7.05342i 0.561440 + 0.407910i
\(300\) 0.118034 0.363271i 0.00681470 0.0209735i
\(301\) −1.50000 4.61653i −0.0864586 0.266092i
\(302\) −12.7082 + 9.23305i −0.731275 + 0.531302i
\(303\) −2.76393 + 2.00811i −0.158784 + 0.115363i
\(304\) −0.0450850 0.138757i −0.00258580 0.00795828i
\(305\) −3.85410 + 11.8617i −0.220685 + 0.679199i
\(306\) 1.42705 + 1.03681i 0.0815791 + 0.0592707i
\(307\) 7.43769 0.424492 0.212246 0.977216i \(-0.431922\pi\)
0.212246 + 0.977216i \(0.431922\pi\)
\(308\) −1.69098 2.85317i −0.0963527 0.162574i
\(309\) 0.360680 0.0205184
\(310\) −2.61803 1.90211i −0.148694 0.108033i
\(311\) 3.43769 10.5801i 0.194934 0.599944i −0.805044 0.593216i \(-0.797858\pi\)
0.999977 0.00672876i \(-0.00214185\pi\)
\(312\) 0.236068 + 0.726543i 0.0133647 + 0.0411324i
\(313\) −4.73607 + 3.44095i −0.267698 + 0.194494i −0.713534 0.700621i \(-0.752907\pi\)
0.445836 + 0.895115i \(0.352907\pi\)
\(314\) 11.0902 8.05748i 0.625854 0.454710i
\(315\) −0.881966 2.71441i −0.0496932 0.152940i
\(316\) −0.145898 + 0.449028i −0.00820741 + 0.0252598i
\(317\) 20.4164 + 14.8334i 1.14670 + 0.833126i 0.988039 0.154207i \(-0.0492823\pi\)
0.158661 + 0.987333i \(0.449282\pi\)
\(318\) 1.23607 0.0693153
\(319\) 4.00000 0.898056i 0.223957 0.0502815i
\(320\) −1.00000 −0.0559017
\(321\) 5.44427 + 3.95550i 0.303870 + 0.220774i
\(322\) 1.85410 5.70634i 0.103325 0.318002i
\(323\) 0.0278640 + 0.0857567i 0.00155040 + 0.00477163i
\(324\) −6.23607 + 4.53077i −0.346448 + 0.251709i
\(325\) 1.61803 1.17557i 0.0897524 0.0652089i
\(326\) 1.19098 + 3.66547i 0.0659624 + 0.203012i
\(327\) −1.00000 + 3.07768i −0.0553001 + 0.170196i
\(328\) −4.30902 3.13068i −0.237926 0.172863i
\(329\) −4.76393 −0.262644
\(330\) −1.16312 0.502029i −0.0640276 0.0276358i
\(331\) −23.0344 −1.26609 −0.633044 0.774116i \(-0.718195\pi\)
−0.633044 + 0.774116i \(0.718195\pi\)
\(332\) −4.30902 3.13068i −0.236488 0.171819i
\(333\) −2.18034 + 6.71040i −0.119482 + 0.367727i
\(334\) −0.763932 2.35114i −0.0418005 0.128649i
\(335\) −4.11803 + 2.99193i −0.224992 + 0.163466i
\(336\) 0.309017 0.224514i 0.0168583 0.0122482i
\(337\) 4.13525 + 12.7270i 0.225262 + 0.693284i 0.998265 + 0.0588821i \(0.0187536\pi\)
−0.773003 + 0.634402i \(0.781246\pi\)
\(338\) 2.78115 8.55951i 0.151275 0.465576i
\(339\) −1.95492 1.42033i −0.106176 0.0771417i
\(340\) 0.618034 0.0335176
\(341\) −7.09017 + 8.05748i −0.383954 + 0.436337i
\(342\) −0.416408 −0.0225168
\(343\) 0.809017 + 0.587785i 0.0436828 + 0.0317374i
\(344\) −1.50000 + 4.61653i −0.0808746 + 0.248906i
\(345\) −0.708204 2.17963i −0.0381284 0.117347i
\(346\) −9.70820 + 7.05342i −0.521916 + 0.379194i
\(347\) −8.35410 + 6.06961i −0.448472 + 0.325834i −0.788992 0.614403i \(-0.789397\pi\)
0.340520 + 0.940237i \(0.389397\pi\)
\(348\) 0.145898 + 0.449028i 0.00782096 + 0.0240704i
\(349\) −4.47214 + 13.7638i −0.239388 + 0.736760i 0.757121 + 0.653275i \(0.226605\pi\)
−0.996509 + 0.0834857i \(0.973395\pi\)
\(350\) −0.809017 0.587785i −0.0432438 0.0314184i
\(351\) 4.47214 0.238705
\(352\) −0.309017 + 3.30220i −0.0164707 + 0.176008i
\(353\) 27.4508 1.46106 0.730531 0.682880i \(-0.239273\pi\)
0.730531 + 0.682880i \(0.239273\pi\)
\(354\) −1.66312 1.20833i −0.0883938 0.0642218i
\(355\) −1.14590 + 3.52671i −0.0608180 + 0.187178i
\(356\) 0.590170 + 1.81636i 0.0312789 + 0.0962667i
\(357\) −0.190983 + 0.138757i −0.0101079 + 0.00734381i
\(358\) −6.97214 + 5.06555i −0.368489 + 0.267723i
\(359\) 3.90983 + 12.0332i 0.206353 + 0.635089i 0.999655 + 0.0262609i \(0.00836008\pi\)
−0.793302 + 0.608828i \(0.791640\pi\)
\(360\) −0.881966 + 2.71441i −0.0464837 + 0.143062i
\(361\) 15.3541 + 11.1554i 0.808111 + 0.587127i
\(362\) −12.4721 −0.655521
\(363\) −2.01722 + 3.68571i −0.105877 + 0.193450i
\(364\) 2.00000 0.104828
\(365\) −5.78115 4.20025i −0.302599 0.219851i
\(366\) −1.47214 + 4.53077i −0.0769498 + 0.236827i
\(367\) 1.79837 + 5.53483i 0.0938744 + 0.288916i 0.986959 0.160974i \(-0.0514634\pi\)
−0.893084 + 0.449889i \(0.851463\pi\)
\(368\) −4.85410 + 3.52671i −0.253038 + 0.183843i
\(369\) −12.2984 + 8.93529i −0.640228 + 0.465153i
\(370\) 0.763932 + 2.35114i 0.0397149 + 0.122230i
\(371\) 1.00000 3.07768i 0.0519174 0.159785i
\(372\) −1.00000 0.726543i −0.0518476 0.0376695i
\(373\) 15.5279 0.804002 0.402001 0.915639i \(-0.368315\pi\)
0.402001 + 0.915639i \(0.368315\pi\)
\(374\) 0.190983 2.04087i 0.00987550 0.105531i
\(375\) −0.381966 −0.0197246
\(376\) 3.85410 + 2.80017i 0.198760 + 0.144408i
\(377\) −0.763932 + 2.35114i −0.0393445 + 0.121090i
\(378\) −0.690983 2.12663i −0.0355403 0.109382i
\(379\) 17.1074 12.4292i 0.878748 0.638448i −0.0541722 0.998532i \(-0.517252\pi\)
0.932920 + 0.360084i \(0.117252\pi\)
\(380\) −0.118034 + 0.0857567i −0.00605502 + 0.00439923i
\(381\) −1.81966 5.60034i −0.0932240 0.286914i
\(382\) 3.23607 9.95959i 0.165572 0.509577i
\(383\) 19.4164 + 14.1068i 0.992132 + 0.720826i 0.960387 0.278670i \(-0.0898935\pi\)
0.0317451 + 0.999496i \(0.489894\pi\)
\(384\) −0.381966 −0.0194921
\(385\) −2.19098 + 2.48990i −0.111663 + 0.126897i
\(386\) −2.00000 −0.101797
\(387\) 11.2082 + 8.14324i 0.569745 + 0.413944i
\(388\) 3.26393 10.0453i 0.165701 0.509975i
\(389\) 6.43769 + 19.8132i 0.326404 + 1.00457i 0.970803 + 0.239879i \(0.0771077\pi\)
−0.644399 + 0.764690i \(0.722892\pi\)
\(390\) 0.618034 0.449028i 0.0312954 0.0227374i
\(391\) 3.00000 2.17963i 0.151717 0.110229i
\(392\) −0.309017 0.951057i −0.0156077 0.0480356i
\(393\) −1.98278 + 6.10237i −0.100018 + 0.307824i
\(394\) −4.85410 3.52671i −0.244546 0.177673i
\(395\) 0.472136 0.0237557
\(396\) 8.69098 + 3.75123i 0.436738 + 0.188506i
\(397\) 0.944272 0.0473916 0.0236958 0.999719i \(-0.492457\pi\)
0.0236958 + 0.999719i \(0.492457\pi\)
\(398\) 6.00000 + 4.35926i 0.300753 + 0.218510i
\(399\) 0.0172209 0.0530006i 0.000862125 0.00265335i
\(400\) 0.309017 + 0.951057i 0.0154508 + 0.0475528i
\(401\) −9.30902 + 6.76340i −0.464870 + 0.337748i −0.795439 0.606034i \(-0.792760\pi\)
0.330569 + 0.943782i \(0.392760\pi\)
\(402\) −1.57295 + 1.14281i −0.0784516 + 0.0569984i
\(403\) −2.00000 6.15537i −0.0996271 0.306621i
\(404\) 2.76393 8.50651i 0.137511 0.423215i
\(405\) 6.23607 + 4.53077i 0.309873 + 0.225136i
\(406\) 1.23607 0.0613450
\(407\) 8.00000 1.79611i 0.396545 0.0890300i
\(408\) 0.236068 0.0116871
\(409\) −6.38197 4.63677i −0.315568 0.229274i 0.418714 0.908118i \(-0.362481\pi\)
−0.734282 + 0.678845i \(0.762481\pi\)
\(410\) −1.64590 + 5.06555i −0.0812851 + 0.250170i
\(411\) 1.19098 + 3.66547i 0.0587469 + 0.180804i
\(412\) −0.763932 + 0.555029i −0.0376362 + 0.0273443i
\(413\) −4.35410 + 3.16344i −0.214251 + 0.155663i
\(414\) 5.29180 + 16.2865i 0.260078 + 0.800437i
\(415\) −1.64590 + 5.06555i −0.0807940 + 0.248658i
\(416\) −1.61803 1.17557i −0.0793306 0.0576371i
\(417\) −3.63932 −0.178218
\(418\) 0.246711 + 0.416272i 0.0120670 + 0.0203605i
\(419\) −3.32624 −0.162497 −0.0812487 0.996694i \(-0.525891\pi\)
−0.0812487 + 0.996694i \(0.525891\pi\)
\(420\) −0.309017 0.224514i −0.0150785 0.0109552i
\(421\) 11.8541 36.4832i 0.577734 1.77808i −0.0489429 0.998802i \(-0.515585\pi\)
0.626676 0.779280i \(-0.284415\pi\)
\(422\) −6.88197 21.1805i −0.335009 1.03105i
\(423\) 11.0000 7.99197i 0.534838 0.388583i
\(424\) −2.61803 + 1.90211i −0.127143 + 0.0923748i
\(425\) −0.190983 0.587785i −0.00926404 0.0285118i
\(426\) −0.437694 + 1.34708i −0.0212063 + 0.0652664i
\(427\) 10.0902 + 7.33094i 0.488298 + 0.354769i
\(428\) −17.6180 −0.851600
\(429\) −1.29180 2.17963i −0.0623685 0.105233i
\(430\) 4.85410 0.234086
\(431\) 21.6525 + 15.7314i 1.04296 + 0.757757i 0.970862 0.239640i \(-0.0770295\pi\)
0.0721013 + 0.997397i \(0.477030\pi\)
\(432\) −0.690983 + 2.12663i −0.0332449 + 0.102317i
\(433\) −12.1910 37.5200i −0.585861 1.80310i −0.595784 0.803145i \(-0.703159\pi\)
0.00992266 0.999951i \(-0.496841\pi\)
\(434\) −2.61803 + 1.90211i −0.125670 + 0.0913043i
\(435\) 0.381966 0.277515i 0.0183139 0.0133058i
\(436\) −2.61803 8.05748i −0.125381 0.385883i
\(437\) −0.270510 + 0.832544i −0.0129402 + 0.0398260i
\(438\) −2.20820 1.60435i −0.105512 0.0766590i
\(439\) −2.65248 −0.126596 −0.0632979 0.997995i \(-0.520162\pi\)
−0.0632979 + 0.997995i \(0.520162\pi\)
\(440\) 3.23607 0.726543i 0.154273 0.0346366i
\(441\) −2.85410 −0.135910
\(442\) 1.00000 + 0.726543i 0.0475651 + 0.0345581i
\(443\) −0.319660 + 0.983813i −0.0151875 + 0.0467424i −0.958363 0.285553i \(-0.907823\pi\)
0.943176 + 0.332295i \(0.107823\pi\)
\(444\) 0.291796 + 0.898056i 0.0138480 + 0.0426198i
\(445\) 1.54508 1.12257i 0.0732441 0.0532149i
\(446\) 15.9443 11.5842i 0.754983 0.548527i
\(447\) −0.214782 0.661030i −0.0101588 0.0312657i
\(448\) −0.309017 + 0.951057i −0.0145997 + 0.0449332i
\(449\) 25.4443 + 18.4863i 1.20079 + 0.872425i 0.994362 0.106037i \(-0.0338163\pi\)
0.206427 + 0.978462i \(0.433816\pi\)
\(450\) 2.85410 0.134544
\(451\) 16.2188 + 7.00042i 0.763716 + 0.329637i
\(452\) 6.32624 0.297561
\(453\) 4.85410 + 3.52671i 0.228066 + 0.165699i
\(454\) 2.86475 8.81678i 0.134449 0.413792i
\(455\) −0.618034 1.90211i −0.0289739 0.0891724i
\(456\) −0.0450850 + 0.0327561i −0.00211130 + 0.00153395i
\(457\) 1.83688 1.33457i 0.0859257 0.0624287i −0.543993 0.839090i \(-0.683088\pi\)
0.629919 + 0.776661i \(0.283088\pi\)
\(458\) 9.00000 + 27.6992i 0.420542 + 1.29430i
\(459\) 0.427051 1.31433i 0.0199330 0.0613476i
\(460\) 4.85410 + 3.52671i 0.226324 + 0.164434i
\(461\) 10.9443 0.509726 0.254863 0.966977i \(-0.417970\pi\)
0.254863 + 0.966977i \(0.417970\pi\)
\(462\) −0.836881 + 0.951057i −0.0389352 + 0.0442472i
\(463\) 19.4164 0.902357 0.451178 0.892434i \(-0.351004\pi\)
0.451178 + 0.892434i \(0.351004\pi\)
\(464\) −1.00000 0.726543i −0.0464238 0.0337289i
\(465\) −0.381966 + 1.17557i −0.0177132 + 0.0545158i
\(466\) 6.82624 + 21.0090i 0.316219 + 0.973223i
\(467\) −14.4721 + 10.5146i −0.669691 + 0.486559i −0.869922 0.493190i \(-0.835831\pi\)
0.200231 + 0.979749i \(0.435831\pi\)
\(468\) −4.61803 + 3.35520i −0.213469 + 0.155094i
\(469\) 1.57295 + 4.84104i 0.0726320 + 0.223538i
\(470\) 1.47214 4.53077i 0.0679046 0.208989i
\(471\) −4.23607 3.07768i −0.195188 0.141812i
\(472\) 5.38197 0.247725
\(473\) 1.50000 16.0292i 0.0689701 0.737024i
\(474\) 0.180340 0.00828329
\(475\) 0.118034 + 0.0857567i 0.00541577 + 0.00393479i
\(476\) 0.190983 0.587785i 0.00875369 0.0269411i
\(477\) 2.85410 + 8.78402i 0.130680 + 0.402193i
\(478\) 0 0
\(479\) −1.70820 + 1.24108i −0.0780498 + 0.0567065i −0.626126 0.779722i \(-0.715360\pi\)
0.548076 + 0.836428i \(0.315360\pi\)
\(480\) 0.118034 + 0.363271i 0.00538749 + 0.0165810i
\(481\) −1.52786 + 4.70228i −0.0696646 + 0.214406i
\(482\) −22.0623 16.0292i −1.00491 0.730110i
\(483\) −2.29180 −0.104280
\(484\) −1.39919 10.9106i −0.0635994 0.495939i
\(485\) −10.5623 −0.479610
\(486\) 7.80902 + 5.67358i 0.354224 + 0.257359i
\(487\) 8.29180 25.5195i 0.375737 1.15640i −0.567243 0.823551i \(-0.691990\pi\)
0.942980 0.332849i \(-0.108010\pi\)
\(488\) −3.85410 11.8617i −0.174467 0.536954i
\(489\) 1.19098 0.865300i 0.0538581 0.0391302i
\(490\) −0.809017 + 0.587785i −0.0365477 + 0.0265534i
\(491\) −1.70163 5.23707i −0.0767933 0.236346i 0.905290 0.424795i \(-0.139654\pi\)
−0.982083 + 0.188449i \(0.939654\pi\)
\(492\) −0.628677 + 1.93487i −0.0283430 + 0.0872306i
\(493\) 0.618034 + 0.449028i 0.0278349 + 0.0202232i
\(494\) −0.291796 −0.0131285
\(495\) 0.881966 9.42481i 0.0396414 0.423614i
\(496\) 3.23607 0.145304
\(497\) 3.00000 + 2.17963i 0.134568 + 0.0977697i
\(498\) −0.628677 + 1.93487i −0.0281717 + 0.0867036i
\(499\) −12.2984 37.8505i −0.550551 1.69442i −0.707413 0.706801i \(-0.750138\pi\)
0.156862 0.987621i \(-0.449862\pi\)
\(500\) 0.809017 0.587785i 0.0361803 0.0262866i
\(501\) −0.763932 + 0.555029i −0.0341300 + 0.0247969i
\(502\) 8.29180 + 25.5195i 0.370081 + 1.13899i
\(503\) −7.14590 + 21.9928i −0.318620 + 0.980611i 0.655619 + 0.755092i \(0.272408\pi\)
−0.974239 + 0.225519i \(0.927592\pi\)
\(504\) 2.30902 + 1.67760i 0.102852 + 0.0747262i
\(505\) −8.94427 −0.398015
\(506\) 13.1459 14.9394i 0.584406 0.664137i
\(507\) −3.43769 −0.152673
\(508\) 12.4721 + 9.06154i 0.553362 + 0.402041i
\(509\) −10.6525 + 32.7849i −0.472163 + 1.45317i 0.377584 + 0.925975i \(0.376755\pi\)
−0.849746 + 0.527192i \(0.823245\pi\)
\(510\) −0.0729490 0.224514i −0.00323024 0.00994165i
\(511\) −5.78115 + 4.20025i −0.255743 + 0.185808i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) 0.100813 + 0.310271i 0.00445101 + 0.0136988i
\(514\) −2.91641 + 8.97578i −0.128637 + 0.395905i
\(515\) 0.763932 + 0.555029i 0.0336629 + 0.0244575i
\(516\) 1.85410 0.0816223
\(517\) −14.5066 6.26137i −0.637999 0.275375i
\(518\) 2.47214 0.108619
\(519\) 3.70820 + 2.69417i 0.162772 + 0.118261i
\(520\) −0.618034 + 1.90211i −0.0271026 + 0.0834132i
\(521\) 3.46149 + 10.6534i 0.151651 + 0.466733i 0.997806 0.0662032i \(-0.0210886\pi\)
−0.846155 + 0.532936i \(0.821089\pi\)
\(522\) −2.85410 + 2.07363i −0.124921 + 0.0907602i
\(523\) −33.1525 + 24.0867i −1.44966 + 1.05324i −0.463745 + 0.885969i \(0.653495\pi\)
−0.985911 + 0.167269i \(0.946505\pi\)
\(524\) −5.19098 15.9762i −0.226769 0.697924i
\(525\) −0.118034 + 0.363271i −0.00515143 + 0.0158545i
\(526\) 1.76393 + 1.28157i 0.0769111 + 0.0558792i
\(527\) −2.00000 −0.0871214
\(528\) 1.23607 0.277515i 0.0537930 0.0120773i
\(529\) 13.0000 0.565217
\(530\) 2.61803 + 1.90211i 0.113720 + 0.0826225i
\(531\) 4.74671 14.6089i 0.205990 0.633971i
\(532\) 0.0450850 + 0.138757i 0.00195468 + 0.00601589i
\(533\) −8.61803 + 6.26137i −0.373288 + 0.271210i
\(534\) 0.590170 0.428784i 0.0255392 0.0185553i
\(535\) 5.44427 + 16.7557i 0.235376 + 0.724414i
\(536\) 1.57295 4.84104i 0.0679410 0.209101i
\(537\) 2.66312 + 1.93487i 0.114922 + 0.0834958i
\(538\) −10.1803 −0.438906
\(539\) 1.69098 + 2.85317i 0.0728358 + 0.122895i
\(540\) 2.23607 0.0962250
\(541\) −31.4164 22.8254i −1.35070 0.981339i −0.998976 0.0452336i \(-0.985597\pi\)
−0.351720 0.936105i \(-0.614403\pi\)
\(542\) 5.38197 16.5640i 0.231175 0.711484i
\(543\) 1.47214 + 4.53077i 0.0631754 + 0.194434i
\(544\) −0.500000 + 0.363271i −0.0214373 + 0.0155751i
\(545\) −6.85410 + 4.97980i −0.293597 + 0.213311i
\(546\) −0.236068 0.726543i −0.0101028 0.0310931i
\(547\) 8.98936 27.6664i 0.384357 1.18293i −0.552588 0.833454i \(-0.686360\pi\)
0.936946 0.349475i \(-0.113640\pi\)
\(548\) −8.16312 5.93085i −0.348711 0.253353i
\(549\) −35.5967 −1.51923
\(550\) −1.69098 2.85317i −0.0721038 0.121660i
\(551\) −0.180340 −0.00768274
\(552\) 1.85410 + 1.34708i 0.0789158 + 0.0573357i
\(553\) 0.145898 0.449028i 0.00620422 0.0190946i
\(554\) 6.09017 + 18.7436i 0.258747 + 0.796340i
\(555\) 0.763932 0.555029i 0.0324271 0.0235597i
\(556\) 7.70820 5.60034i 0.326901 0.237507i
\(557\) −4.88854 15.0454i −0.207134 0.637494i −0.999619 0.0276019i \(-0.991213\pi\)
0.792485 0.609892i \(-0.208787\pi\)
\(558\) 2.85410 8.78402i 0.120824 0.371857i
\(559\) 7.85410 + 5.70634i 0.332193 + 0.241352i
\(560\) 1.00000 0.0422577
\(561\) −0.763932 + 0.171513i −0.0322532 + 0.00724130i
\(562\) 5.03444 0.212365
\(563\) 33.5795 + 24.3970i 1.41521 + 1.02821i 0.992539 + 0.121925i \(0.0389067\pi\)
0.422669 + 0.906284i \(0.361093\pi\)
\(564\) 0.562306 1.73060i 0.0236773 0.0728714i
\(565\) −1.95492 6.01661i −0.0822439 0.253121i
\(566\) 9.70820 7.05342i 0.408066 0.296477i
\(567\) 6.23607 4.53077i 0.261890 0.190274i
\(568\) −1.14590 3.52671i −0.0480808 0.147978i
\(569\) −0.954915 + 2.93893i −0.0400321 + 0.123206i −0.969075 0.246765i \(-0.920632\pi\)
0.929043 + 0.369971i \(0.120632\pi\)
\(570\) 0.0450850 + 0.0327561i 0.00188840 + 0.00137200i
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 6.09017 + 2.62866i 0.254643 + 0.109910i
\(573\) −4.00000 −0.167102
\(574\) 4.30902 + 3.13068i 0.179855 + 0.130672i
\(575\) 1.85410 5.70634i 0.0773214 0.237971i
\(576\) −0.881966 2.71441i −0.0367486 0.113101i
\(577\) 21.2082 15.4087i 0.882909 0.641471i −0.0511104 0.998693i \(-0.516276\pi\)
0.934020 + 0.357222i \(0.116276\pi\)
\(578\) −13.4443 + 9.76784i −0.559208 + 0.406288i
\(579\) 0.236068 + 0.726543i 0.00981065 + 0.0301941i
\(580\) −0.381966 + 1.17557i −0.0158603 + 0.0488129i
\(581\) 4.30902 + 3.13068i 0.178768 + 0.129883i
\(582\) −4.03444 −0.167233
\(583\) 7.09017 8.05748i 0.293645 0.333707i
\(584\) 7.14590 0.295699
\(585\) 4.61803 + 3.35520i 0.190932 + 0.138720i
\(586\) 2.32624 7.15942i 0.0960960 0.295753i
\(587\) −12.2812 37.7975i −0.506897 1.56007i −0.797557 0.603243i \(-0.793875\pi\)
0.290660 0.956826i \(-0.406125\pi\)
\(588\) −0.309017 + 0.224514i −0.0127436 + 0.00925880i
\(589\) 0.381966 0.277515i 0.0157386 0.0114348i
\(590\) −1.66312 5.11855i −0.0684695 0.210728i
\(591\) −0.708204 + 2.17963i −0.0291316 + 0.0896579i
\(592\) −2.00000 1.45309i −0.0821995 0.0597214i
\(593\) −0.909830 −0.0373622 −0.0186811 0.999825i \(-0.505947\pi\)
−0.0186811 + 0.999825i \(0.505947\pi\)
\(594\) 0.690983 7.38394i 0.0283514 0.302967i
\(595\) −0.618034 −0.0253369
\(596\) 1.47214 + 1.06957i 0.0603010 + 0.0438113i
\(597\) 0.875388 2.69417i 0.0358273 0.110265i
\(598\) 3.70820 + 11.4127i 0.151640 + 0.466699i
\(599\) 16.7984 12.2047i 0.686363 0.498672i −0.189100 0.981958i \(-0.560557\pi\)
0.875463 + 0.483286i \(0.160557\pi\)
\(600\) 0.309017 0.224514i 0.0126156 0.00916575i
\(601\) 5.53444 + 17.0333i 0.225755 + 0.694801i 0.998214 + 0.0597372i \(0.0190263\pi\)
−0.772460 + 0.635064i \(0.780974\pi\)
\(602\) 1.50000 4.61653i 0.0611354 0.188156i
\(603\) −11.7533 8.53926i −0.478631 0.347746i
\(604\) −15.7082 −0.639158
\(605\) −9.94427 + 4.70228i −0.404292 + 0.191175i
\(606\) −3.41641 −0.138782
\(607\) 15.8541 + 11.5187i 0.643498 + 0.467529i 0.861050 0.508520i \(-0.169807\pi\)
−0.217552 + 0.976049i \(0.569807\pi\)
\(608\) 0.0450850 0.138757i 0.00182844 0.00562735i
\(609\) −0.145898 0.449028i −0.00591209 0.0181955i
\(610\) −10.0902 + 7.33094i −0.408539 + 0.296821i
\(611\) 7.70820 5.60034i 0.311841 0.226565i
\(612\) 0.545085 + 1.67760i 0.0220338 + 0.0678129i
\(613\) 3.27051 10.0656i 0.132095 0.406546i −0.863032 0.505149i \(-0.831438\pi\)
0.995127 + 0.0986035i \(0.0314375\pi\)
\(614\) 6.01722 + 4.37177i 0.242835 + 0.176430i
\(615\) 2.03444 0.0820366
\(616\) 0.309017 3.30220i 0.0124506 0.133049i
\(617\) −6.03444 −0.242937 −0.121469 0.992595i \(-0.538760\pi\)
−0.121469 + 0.992595i \(0.538760\pi\)
\(618\) 0.291796 + 0.212002i 0.0117378 + 0.00852798i
\(619\) 10.6074 32.6462i 0.426347 1.31216i −0.475352 0.879796i \(-0.657679\pi\)
0.901699 0.432365i \(-0.142321\pi\)
\(620\) −1.00000 3.07768i −0.0401610 0.123603i
\(621\) 10.8541 7.88597i 0.435560 0.316453i
\(622\) 9.00000 6.53888i 0.360867 0.262185i
\(623\) −0.590170 1.81636i −0.0236447 0.0727708i
\(624\) −0.236068 + 0.726543i −0.00945028 + 0.0290850i
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) −5.85410 −0.233977
\(627\) 0.122099 0.138757i 0.00487618 0.00554143i
\(628\) 13.7082 0.547017
\(629\) 1.23607 + 0.898056i 0.0492853 + 0.0358078i
\(630\) 0.881966 2.71441i 0.0351384 0.108145i
\(631\) −3.18034 9.78808i −0.126607 0.389657i 0.867583 0.497292i \(-0.165672\pi\)
−0.994190 + 0.107635i \(0.965672\pi\)
\(632\) −0.381966 + 0.277515i −0.0151938 + 0.0110389i
\(633\) −6.88197 + 5.00004i −0.273534 + 0.198734i
\(634\) 7.79837 + 24.0009i 0.309713 + 0.953199i
\(635\) 4.76393 14.6619i 0.189051 0.581839i
\(636\) 1.00000 + 0.726543i 0.0396526 + 0.0288093i
\(637\) −2.00000 −0.0792429
\(638\) 3.76393 + 1.62460i 0.149015 + 0.0643185i
\(639\) −10.5836 −0.418680
\(640\) −0.809017 0.587785i −0.0319792 0.0232343i
\(641\) 7.62461 23.4661i 0.301154 0.926857i −0.679930 0.733277i \(-0.737990\pi\)
0.981084 0.193580i \(-0.0620100\pi\)
\(642\) 2.07953 + 6.40013i 0.0820724 + 0.252593i
\(643\) −25.8713 + 18.7966i −1.02027 + 0.741266i −0.966337 0.257279i \(-0.917174\pi\)
−0.0539281 + 0.998545i \(0.517174\pi\)
\(644\) 4.85410 3.52671i 0.191278 0.138972i
\(645\) −0.572949 1.76336i −0.0225598 0.0694321i
\(646\) −0.0278640 + 0.0857567i −0.00109630 + 0.00337405i
\(647\) 17.9443 + 13.0373i 0.705462 + 0.512548i 0.881707 0.471798i \(-0.156395\pi\)
−0.176244 + 0.984346i \(0.556395\pi\)
\(648\) −7.70820 −0.302807
\(649\) −17.4164 + 3.91023i −0.683654 + 0.153490i
\(650\) 2.00000 0.0784465
\(651\) 1.00000 + 0.726543i 0.0391931 + 0.0284754i
\(652\) −1.19098 + 3.66547i −0.0466425 + 0.143551i
\(653\) −8.29180 25.5195i −0.324483 0.998656i −0.971673 0.236328i \(-0.924056\pi\)
0.647190 0.762328i \(-0.275944\pi\)
\(654\) −2.61803 + 1.90211i −0.102373 + 0.0743785i
\(655\) −13.5902 + 9.87384i −0.531012 + 0.385803i
\(656\) −1.64590 5.06555i −0.0642615 0.197777i
\(657\) 6.30244 19.3969i 0.245882 0.756746i
\(658\) −3.85410 2.80017i −0.150249 0.109162i
\(659\) 7.09017 0.276194 0.138097 0.990419i \(-0.455901\pi\)
0.138097 + 0.990419i \(0.455901\pi\)
\(660\) −0.645898 1.08981i −0.0251415 0.0424209i
\(661\) −10.1115 −0.393290 −0.196645 0.980475i \(-0.563005\pi\)
−0.196645 + 0.980475i \(0.563005\pi\)
\(662\) −18.6353 13.5393i −0.724280 0.526220i
\(663\) 0.145898 0.449028i 0.00566621 0.0174388i
\(664\) −1.64590 5.06555i −0.0638732 0.196582i
\(665\) 0.118034 0.0857567i 0.00457716 0.00332550i
\(666\) −5.70820 + 4.14725i −0.221188 + 0.160703i
\(667\) 2.29180 + 7.05342i 0.0887387 + 0.273110i
\(668\) 0.763932 2.35114i 0.0295574 0.0909684i
\(669\) −6.09017 4.42477i −0.235460 0.171071i
\(670\) −5.09017 −0.196650
\(671\) 21.0902 + 35.5851i 0.814177 + 1.37375i
\(672\) 0.381966 0.0147347
\(673\) −26.0066 18.8949i −1.00248 0.728344i −0.0398614 0.999205i \(-0.512692\pi\)
−0.962618 + 0.270861i \(0.912692\pi\)
\(674\) −4.13525 + 12.7270i −0.159284 + 0.490226i
\(675\) −0.690983 2.12663i −0.0265959 0.0818539i
\(676\) 7.28115 5.29007i 0.280044 0.203464i
\(677\) 28.7984 20.9232i 1.10681 0.804146i 0.124653 0.992200i \(-0.460218\pi\)
0.982159 + 0.188055i \(0.0602183\pi\)
\(678\) −0.746711 2.29814i −0.0286773 0.0882596i
\(679\) −3.26393 + 10.0453i −0.125258 + 0.385505i
\(680\) 0.500000 + 0.363271i 0.0191741 + 0.0139308i
\(681\) −3.54102 −0.135692
\(682\) −10.4721 + 2.35114i −0.400999 + 0.0900298i
\(683\) −48.9443 −1.87280 −0.936400 0.350934i \(-0.885864\pi\)
−0.936400 + 0.350934i \(0.885864\pi\)
\(684\) −0.336881 0.244758i −0.0128810 0.00935857i
\(685\) −3.11803 + 9.59632i −0.119134 + 0.366657i
\(686\) 0.309017 + 0.951057i 0.0117983 + 0.0363115i
\(687\) 9.00000 6.53888i 0.343371 0.249474i
\(688\) −3.92705 + 2.85317i −0.149717 + 0.108776i
\(689\) 2.00000 + 6.15537i 0.0761939 + 0.234501i
\(690\) 0.708204 2.17963i 0.0269609 0.0829770i
\(691\) −22.5344 16.3722i −0.857251 0.622829i 0.0698850 0.997555i \(-0.477737\pi\)
−0.927136 + 0.374726i \(0.877737\pi\)
\(692\) −12.0000 −0.456172
\(693\) −8.69098 3.75123i −0.330143 0.142497i
\(694\) −10.3262 −0.391979
\(695\) −7.70820 5.60034i −0.292389 0.212433i
\(696\) −0.145898 + 0.449028i −0.00553025 + 0.0170204i
\(697\) 1.01722 + 3.13068i 0.0385300 + 0.118583i
\(698\) −11.7082 + 8.50651i −0.443162 + 0.321976i
\(699\) 6.82624 4.95955i 0.258192 0.187587i
\(700\) −0.309017 0.951057i −0.0116797 0.0359466i
\(701\) −3.14590 + 9.68208i −0.118819 + 0.365687i −0.992724 0.120409i \(-0.961579\pi\)
0.873905 + 0.486096i \(0.161579\pi\)
\(702\) 3.61803 + 2.62866i 0.136554 + 0.0992122i
\(703\) −0.360680 −0.0136033
\(704\) −2.19098 + 2.48990i −0.0825758 + 0.0938416i
\(705\) −1.81966 −0.0685324
\(706\) 22.2082 + 16.1352i 0.835817 + 0.607256i
\(707\) −2.76393 + 8.50651i −0.103948 + 0.319920i
\(708\) −0.635255 1.95511i −0.0238743 0.0734777i
\(709\) 5.70820 4.14725i 0.214376 0.155753i −0.475415 0.879761i \(-0.657702\pi\)
0.689791 + 0.724008i \(0.257702\pi\)
\(710\) −3.00000 + 2.17963i −0.112588 + 0.0818000i
\(711\) 0.416408 + 1.28157i 0.0156165 + 0.0480627i
\(712\) −0.590170 + 1.81636i −0.0221176 + 0.0680708i
\(713\) −15.7082 11.4127i −0.588277 0.427408i
\(714\) −0.236068 −0.00883462
\(715\) 0.618034 6.60440i 0.0231132 0.246990i
\(716\) −8.61803 −0.322071
\(717\) 0 0
\(718\) −3.90983 + 12.0332i −0.145914 + 0.449076i
\(719\) −3.81966 11.7557i −0.142449 0.438414i 0.854225 0.519904i \(-0.174032\pi\)
−0.996674 + 0.0814899i \(0.974032\pi\)
\(720\) −2.30902 + 1.67760i −0.0860520 + 0.0625204i
\(721\) 0.763932 0.555029i 0.0284503 0.0206704i
\(722\) 5.86475 + 18.0498i 0.218263 + 0.671745i
\(723\) −3.21885 + 9.90659i −0.119710 + 0.368430i
\(724\) −10.0902 7.33094i −0.374998 0.272452i
\(725\) 1.23607 0.0459064
\(726\) −3.79837 + 1.79611i −0.140971 + 0.0666600i
\(727\) −14.8328 −0.550119 −0.275059 0.961427i \(-0.588698\pi\)
−0.275059 + 0.961427i \(0.588698\pi\)
\(728\) 1.61803 + 1.17557i 0.0599683 + 0.0435695i
\(729\) −6.00658 + 18.4863i −0.222466 + 0.684679i
\(730\) −2.20820 6.79615i −0.0817293 0.251537i
\(731\) 2.42705 1.76336i 0.0897677 0.0652201i
\(732\) −3.85410 + 2.80017i −0.142452 + 0.103497i
\(733\) 2.70820 + 8.33499i 0.100030 + 0.307860i 0.988532 0.151013i \(-0.0482534\pi\)
−0.888502 + 0.458873i \(0.848253\pi\)
\(734\) −1.79837 + 5.53483i −0.0663792 + 0.204294i
\(735\) 0.309017 + 0.224514i 0.0113983 + 0.00828132i
\(736\) −6.00000 −0.221163
\(737\) −1.57295 + 16.8087i −0.0579403 + 0.619158i
\(738\) −15.2016 −0.559580
\(739\) −32.6246 23.7032i −1.20012 0.871935i −0.205820 0.978590i \(-0.565986\pi\)
−0.994296 + 0.106655i \(0.965986\pi\)
\(740\) −0.763932 + 2.35114i −0.0280827 + 0.0864297i
\(741\) 0.0344419 + 0.106001i 0.00126525 + 0.00389405i
\(742\) 2.61803 1.90211i 0.0961111 0.0698288i
\(743\) −38.7426 + 28.1482i −1.42133 + 1.03266i −0.429780 + 0.902934i \(0.641409\pi\)
−0.991550 + 0.129723i \(0.958591\pi\)
\(744\) −0.381966 1.17557i −0.0140036 0.0430985i
\(745\) 0.562306 1.73060i 0.0206013 0.0634043i
\(746\) 12.5623 + 9.12705i 0.459939 + 0.334165i
\(747\) −15.2016 −0.556198
\(748\) 1.35410 1.53884i 0.0495109 0.0562656i
\(749\) 17.6180 0.643749
\(750\) −0.309017 0.224514i −0.0112837 0.00819809i
\(751\) −0.416408 + 1.28157i −0.0151949 + 0.0467652i −0.958367 0.285541i \(-0.907827\pi\)
0.943172 + 0.332306i \(0.107827\pi\)
\(752\) 1.47214 + 4.53077i 0.0536833 + 0.165220i
\(753\) 8.29180 6.02434i 0.302170 0.219539i
\(754\) −2.00000 + 1.45309i −0.0728357 + 0.0529182i
\(755\) 4.85410 + 14.9394i 0.176659 + 0.543700i
\(756\) 0.690983 2.12663i 0.0251308 0.0773447i
\(757\) 12.8541 + 9.33905i 0.467190 + 0.339434i 0.796345 0.604842i \(-0.206764\pi\)
−0.329155 + 0.944276i \(0.606764\pi\)
\(758\) 21.1459 0.768054
\(759\) −6.97871 3.01217i −0.253311 0.109335i
\(760\) −0.145898 −0.00529228
\(761\) −5.82624 4.23301i −0.211201 0.153446i 0.477156 0.878819i \(-0.341668\pi\)
−0.688357 + 0.725372i \(0.741668\pi\)
\(762\) 1.81966 5.60034i 0.0659193 0.202879i
\(763\) 2.61803 + 8.05748i 0.0947792 + 0.291700i
\(764\) 8.47214 6.15537i 0.306511 0.222693i
\(765\) 1.42705 1.03681i 0.0515951 0.0374861i
\(766\) 7.41641 + 22.8254i 0.267966 + 0.824714i
\(767\) 3.32624 10.2371i 0.120103 0.369641i
\(768\) −0.309017 0.224514i −0.0111507 0.00810145i
\(769\) −27.8885 −1.00569 −0.502843 0.864378i \(-0.667713\pi\)
−0.502843 + 0.864378i \(0.667713\pi\)
\(770\) −3.23607 + 0.726543i −0.116620 + 0.0261828i
\(771\) 3.60488 0.129827
\(772\) −1.61803 1.17557i −0.0582343 0.0423097i
\(773\) 2.05573 6.32688i 0.0739394 0.227562i −0.907256 0.420579i \(-0.861827\pi\)
0.981196 + 0.193017i \(0.0618271\pi\)
\(774\) 4.28115 + 13.1760i 0.153883 + 0.473603i
\(775\) −2.61803 + 1.90211i −0.0940426 + 0.0683259i
\(776\) 8.54508 6.20837i 0.306751 0.222867i
\(777\) −0.291796 0.898056i −0.0104681 0.0322176i
\(778\) −6.43769 + 19.8132i −0.230803 + 0.710337i
\(779\) −0.628677 0.456761i −0.0225247 0.0163651i
\(780\) 0.763932 0.0273532
\(781\) 6.27051 + 10.5801i 0.224376 + 0.378587i
\(782\) 3.70820 0.132605
\(783\) 2.23607 + 1.62460i 0.0799106 + 0.0580584i
\(784\) 0.309017 0.951057i 0.0110363 0.0339663i
\(785\) −4.23607 13.0373i −0.151192 0.465320i
\(786\) −5.19098 + 3.77147i −0.185156 + 0.134524i
\(787\) −29.2082 + 21.2210i −1.04116 + 0.756447i −0.970512 0.241054i \(-0.922507\pi\)
−0.0706484 + 0.997501i \(0.522507\pi\)
\(788\) −1.85410 5.70634i −0.0660496 0.203280i
\(789\) 0.257354 0.792055i 0.00916205 0.0281979i
\(790\) 0.381966 + 0.277515i 0.0135897 + 0.00987352i
\(791\) −6.32624 −0.224935
\(792\) 4.82624 + 8.14324i 0.171493 + 0.289357i
\(793\) −24.9443 −0.885797
\(794\) 0.763932 + 0.555029i 0.0271109 + 0.0196972i
\(795\) 0.381966 1.17557i 0.0135469 0.0416932i
\(796\) 2.29180 + 7.05342i 0.0812306 + 0.250002i
\(797\) −31.0344 + 22.5478i −1.09930 + 0.798686i −0.980945 0.194286i \(-0.937761\pi\)
−0.118351 + 0.992972i \(0.537761\pi\)
\(798\) 0.0450850 0.0327561i 0.00159599 0.00115956i
\(799\) −0.909830 2.80017i −0.0321875 0.0990629i
\(800\) −0.309017 + 0.951057i −0.0109254 + 0.0336249i
\(801\) 4.40983 + 3.20393i 0.155814 + 0.113205i
\(802\) −11.5066 −0.406311
\(803\) −23.1246 + 5.19180i −0.816050 + 0.183215i
\(804\) −1.94427 −0.0685692
\(805\) −4.85410 3.52671i −0.171085 0.124300i
\(806\) 2.00000 6.15537i 0.0704470 0.216814i
\(807\) 1.20163 + 3.69822i 0.0422992 + 0.130184i
\(808\) 7.23607 5.25731i 0.254564 0.184952i
\(809\) 41.9164 30.4541i 1.47370 1.07071i 0.494183 0.869358i \(-0.335467\pi\)
0.979519 0.201350i \(-0.0645327\pi\)
\(810\) 2.38197 + 7.33094i 0.0836938 + 0.257583i
\(811\) −10.7918 + 33.2137i −0.378951 + 1.16629i 0.561823 + 0.827258i \(0.310100\pi\)
−0.940774 + 0.339034i \(0.889900\pi\)
\(812\) 1.00000 + 0.726543i 0.0350931 + 0.0254966i
\(813\) −6.65248 −0.233313
\(814\) 7.52786 + 3.24920i 0.263851 + 0.113884i
\(815\) 3.85410 0.135003
\(816\) 0.190983 + 0.138757i 0.00668574 + 0.00485748i
\(817\) −0.218847 + 0.673542i −0.00765649 + 0.0235643i
\(818\) −2.43769 7.50245i −0.0852320 0.262317i
\(819\) 4.61803 3.35520i 0.161367 0.117240i
\(820\) −4.30902 + 3.13068i −0.150477 + 0.109328i
\(821\) −15.1246 46.5488i −0.527853 1.62456i −0.758605 0.651551i \(-0.774119\pi\)
0.230752 0.973012i \(-0.425881\pi\)
\(822\) −1.19098 + 3.66547i −0.0415403 + 0.127848i
\(823\) −41.1246 29.8788i −1.43351 1.04151i −0.989349 0.145564i \(-0.953500\pi\)
−0.444165 0.895945i \(-0.646500\pi\)
\(824\) −0.944272 −0.0328953
\(825\) −0.836881 + 0.951057i −0.0291365 + 0.0331115i
\(826\) −5.38197 −0.187263
\(827\) 1.40983 + 1.02430i 0.0490246 + 0.0356185i 0.612028 0.790836i \(-0.290354\pi\)
−0.563003 + 0.826455i \(0.690354\pi\)
\(828\) −5.29180 + 16.2865i −0.183903 + 0.565994i
\(829\) 3.65248 + 11.2412i 0.126856 + 0.390422i 0.994235 0.107227i \(-0.0341970\pi\)
−0.867379 + 0.497648i \(0.834197\pi\)
\(830\) −4.30902 + 3.13068i −0.149568 + 0.108668i
\(831\) 6.09017 4.42477i 0.211266 0.153493i
\(832\) −0.618034 1.90211i −0.0214265 0.0659439i
\(833\) −0.190983 + 0.587785i −0.00661717 + 0.0203656i
\(834\) −2.94427 2.13914i −0.101952 0.0740723i
\(835\) −2.47214 −0.0855518
\(836\) −0.0450850 + 0.481784i −0.00155930 + 0.0166629i
\(837\) −7.23607 −0.250115
\(838\) −2.69098 1.95511i −0.0929585 0.0675383i
\(839\) −1.38197 + 4.25325i −0.0477108 + 0.146839i −0.972074 0.234676i \(-0.924597\pi\)
0.924363 + 0.381514i \(0.124597\pi\)
\(840\) −0.118034 0.363271i −0.00407256 0.0125340i
\(841\) 22.2254 16.1477i 0.766394 0.556818i
\(842\) 31.0344 22.5478i 1.06952 0.777050i
\(843\) −0.594235 1.82887i −0.0204665 0.0629896i
\(844\) 6.88197 21.1805i 0.236887 0.729063i
\(845\) −7.28115 5.29007i −0.250479 0.181984i
\(846\) 13.5967 0.467466
\(847\) 1.39919 + 10.9106i 0.0480766 + 0.374894i
\(848\) −3.23607 −0.111127
\(849\) −3.70820 2.69417i −0.127265 0.0924636i
\(850\) 0.190983 0.587785i 0.00655066 0.0201609i
\(851\) 4.58359 + 14.1068i 0.157124 + 0.483576i
\(852\) −1.14590 + 0.832544i −0.0392578 + 0.0285225i
\(853\) −14.3262 + 10.4086i −0.490521 + 0.356384i −0.805385 0.592753i \(-0.798041\pi\)
0.314864 + 0.949137i \(0.398041\pi\)
\(854\) 3.85410 + 11.8617i 0.131885 + 0.405899i
\(855\) −0.128677 + 0.396027i −0.00440066 + 0.0135439i
\(856\) −14.2533 10.3556i −0.487167 0.353948i
\(857\) −24.2705 −0.829065 −0.414532 0.910035i \(-0.636055\pi\)
−0.414532 + 0.910035i \(0.636055\pi\)
\(858\) 0.236068 2.52265i 0.00805923 0.0861220i
\(859\) −27.5623 −0.940414 −0.470207 0.882556i \(-0.655821\pi\)
−0.470207 + 0.882556i \(0.655821\pi\)
\(860\) 3.92705 + 2.85317i 0.133911 + 0.0972923i
\(861\) 0.628677 1.93487i 0.0214253 0.0659402i
\(862\) 8.27051 + 25.4540i 0.281695 + 0.866967i
\(863\) −9.09017 + 6.60440i −0.309433 + 0.224816i −0.731653 0.681677i \(-0.761251\pi\)
0.422220 + 0.906493i \(0.361251\pi\)
\(864\) −1.80902 + 1.31433i −0.0615440 + 0.0447143i
\(865\) 3.70820 + 11.4127i 0.126083 + 0.388043i
\(866\) 12.1910 37.5200i 0.414266 1.27498i
\(867\) 5.13525 + 3.73098i 0.174402 + 0.126711i
\(868\) −3.23607 −0.109839
\(869\) 1.03444 1.17557i 0.0350910 0.0398785i
\(870\) 0.472136 0.0160069
\(871\) −8.23607 5.98385i −0.279069 0.202755i
\(872\) 2.61803 8.05748i 0.0886578 0.272861i
\(873\) −9.31559 28.6705i −0.315285 0.970348i
\(874\) −0.708204 + 0.514540i −0.0239554 + 0.0174046i
\(875\) −0.809017 + 0.587785i −0.0273498 + 0.0198708i
\(876\) −0.843459 2.59590i −0.0284978 0.0877073i
\(877\) −5.56231 + 17.1190i −0.187826 + 0.578068i −0.999986 0.00536681i \(-0.998292\pi\)
0.812160 + 0.583435i \(0.198292\pi\)
\(878\) −2.14590 1.55909i −0.0724206 0.0526166i
\(879\) −2.87539 −0.0969844
\(880\) 3.04508 + 1.31433i 0.102650 + 0.0443060i
\(881\) 10.8541 0.365684 0.182842 0.983142i \(-0.441470\pi\)
0.182842 + 0.983142i \(0.441470\pi\)
\(882\) −2.30902 1.67760i −0.0777486 0.0564877i
\(883\) 6.97214 21.4580i 0.234631 0.722120i −0.762539 0.646942i \(-0.776048\pi\)
0.997170 0.0751780i \(-0.0239525\pi\)
\(884\) 0.381966 + 1.17557i 0.0128469 + 0.0395387i
\(885\) −1.66312 + 1.20833i −0.0559051 + 0.0406175i
\(886\) −0.836881 + 0.608030i −0.0281156 + 0.0204272i
\(887\) −12.4721 38.3853i −0.418773 1.28885i −0.908832 0.417162i \(-0.863025\pi\)
0.490059 0.871689i \(-0.336975\pi\)
\(888\) −0.291796 + 0.898056i −0.00979203 + 0.0301368i
\(889\) −12.4721 9.06154i −0.418302 0.303914i
\(890\) 1.90983 0.0640176
\(891\) 24.9443 5.60034i 0.835665 0.187618i
\(892\) 19.7082 0.659879
\(893\) 0.562306 + 0.408539i 0.0188168 + 0.0136712i
\(894\) 0.214782 0.661030i 0.00718338 0.0221082i
\(895\) 2.66312 + 8.19624i 0.0890182 + 0.273970i
\(896\) −0.809017 + 0.587785i −0.0270274 + 0.0196365i
\(897\) 3.70820 2.69417i 0.123813 0.0899556i
\(898\) 9.71885 + 29.9115i 0.324322 + 0.998161i
\(899\) 1.23607 3.80423i 0.0412252 0.126878i
\(900\) 2.30902 + 1.67760i 0.0769672 + 0.0559200i
\(901\) 2.00000 0.0666297
\(902\) 9.00658 + 15.1967i 0.299886 + 0.505993i
\(903\) −1.85410 −0.0617007
\(904\) 5.11803 + 3.71847i 0.170223 + 0.123674i
\(905\) −3.85410 + 11.8617i −0.128115 + 0.394296i
\(906\) 1.85410 + 5.70634i 0.0615984 + 0.189580i
\(907\) 9.11803 6.62464i 0.302759 0.219968i −0.426024 0.904712i \(-0.640086\pi\)
0.728783 + 0.684744i \(0.240086\pi\)
\(908\) 7.50000 5.44907i 0.248896 0.180834i
\(909\) −7.88854 24.2784i −0.261646 0.805265i
\(910\) 0.618034 1.90211i 0.0204876 0.0630544i
\(911\) 1.94427 + 1.41260i 0.0644166 + 0.0468014i 0.619528 0.784975i \(-0.287324\pi\)
−0.555111 + 0.831776i \(0.687324\pi\)
\(912\) −0.0557281 −0.00184534
\(913\) 9.00658 + 15.1967i 0.298074 + 0.502936i
\(914\) 2.27051 0.0751018
\(915\) 3.85410 + 2.80017i 0.127413 + 0.0925707i
\(916\) −9.00000 + 27.6992i −0.297368 + 0.915206i
\(917\) 5.19098 + 15.9762i 0.171421 + 0.527581i
\(918\) 1.11803 0.812299i 0.0369006 0.0268099i
\(919\) 36.2705 26.3521i 1.19645 0.869275i 0.202522 0.979278i \(-0.435086\pi\)
0.993931 + 0.110003i \(0.0350861\pi\)
\(920\) 1.85410 + 5.70634i 0.0611279 + 0.188132i
\(921\) 0.877901 2.70190i 0.0289278 0.0890306i
\(922\) 8.85410 + 6.43288i 0.291594 + 0.211856i
\(923\) −7.41641 −0.244114
\(924\) −1.23607 + 0.277515i −0.0406637 + 0.00912956i
\(925\) 2.47214 0.0812833
\(926\) 15.7082 + 11.4127i 0.516204 + 0.375044i
\(927\) −0.832816 + 2.56314i −0.0273533 + 0.0841847i
\(928\) −0.381966 1.17557i −0.0125386 0.0385900i
\(929\) 37.0066 26.8869i 1.21415 0.882129i 0.218546 0.975827i \(-0.429869\pi\)
0.995601 + 0.0936977i \(0.0298687\pi\)
\(930\) −1.00000 + 0.726543i −0.0327913 + 0.0238243i
\(931\) −0.0450850 0.138757i −0.00147760 0.00454759i
\(932\) −6.82624 + 21.0090i −0.223601 + 0.688173i
\(933\) −3.43769 2.49763i −0.112545 0.0817688i
\(934\) −17.8885 −0.585331
\(935\) −1.88197 0.812299i −0.0615469 0.0265650i
\(936\) −5.70820 −0.186578
\(937\) −32.6803 23.7437i −1.06762 0.775671i −0.0921372 0.995746i \(-0.529370\pi\)
−0.975483 + 0.220075i \(0.929370\pi\)
\(938\) −1.57295 + 4.84104i −0.0513586 + 0.158066i
\(939\) 0.690983 + 2.12663i 0.0225494 + 0.0693998i
\(940\) 3.85410 2.80017i 0.125707 0.0913314i
\(941\) 9.56231 6.94742i 0.311722 0.226479i −0.420913 0.907101i \(-0.638290\pi\)
0.732635 + 0.680622i \(0.238290\pi\)
\(942\) −1.61803 4.97980i −0.0527184 0.162251i
\(943\) −9.87539 + 30.3933i −0.321587 + 0.989743i
\(944\) 4.35410 + 3.16344i 0.141714 + 0.102961i
\(945\) −2.23607 −0.0727393
\(946\) 10.6353 12.0862i 0.345782 0.392957i
\(947\) −53.0902 −1.72520 −0.862599 0.505888i \(-0.831165\pi\)
−0.862599 + 0.505888i \(0.831165\pi\)
\(948\) 0.145898 + 0.106001i 0.00473855 + 0.00344276i
\(949\) 4.41641 13.5923i 0.143363 0.441225i
\(950\) 0.0450850 + 0.138757i 0.00146275 + 0.00450188i
\(951\) 7.79837 5.66585i 0.252880 0.183728i
\(952\) 0.500000 0.363271i 0.0162051 0.0117737i
\(953\) 8.17376 + 25.1563i 0.264774 + 0.814891i 0.991745 + 0.128223i \(0.0409273\pi\)
−0.726971 + 0.686668i \(0.759073\pi\)
\(954\) −2.85410 + 8.78402i −0.0924050 + 0.284393i
\(955\) −8.47214 6.15537i −0.274152 0.199183i
\(956\) 0 0
\(957\) 0.145898 1.55909i 0.00471621 0.0503981i
\(958\) −2.11146 −0.0682181
\(959\) 8.16312 + 5.93085i 0.263601 + 0.191517i
\(960\) −0.118034 + 0.363271i −0.00380953 + 0.0117245i
\(961\) −6.34346 19.5232i −0.204628 0.629779i
\(962\) −4.00000 + 2.90617i −0.128965 + 0.0936987i
\(963\) −40.6803 + 29.5560i −1.31091 + 0.952429i
\(964\) −8.42705 25.9358i −0.271417 0.835336i
\(965\) −0.618034 + 1.90211i −0.0198952 + 0.0612312i
\(966\) −1.85410 1.34708i −0.0596548 0.0433417i
\(967\) 49.0132 1.57616 0.788078 0.615575i \(-0.211076\pi\)
0.788078 + 0.615575i \(0.211076\pi\)
\(968\) 5.28115 9.64932i 0.169743 0.310141i
\(969\) 0.0344419 0.00110643
\(970\) −8.54508 6.20837i −0.274366 0.199339i
\(971\) 8.29180 25.5195i 0.266096 0.818961i −0.725342 0.688388i \(-0.758319\pi\)
0.991439 0.130572i \(-0.0416815\pi\)
\(972\) 2.98278 + 9.18005i 0.0956727 + 0.294450i
\(973\) −7.70820 + 5.60034i −0.247114 + 0.179539i
\(974\) 21.7082 15.7719i 0.695576 0.505365i
\(975\) −0.236068 0.726543i −0.00756023 0.0232680i
\(976\) 3.85410 11.8617i 0.123367 0.379684i
\(977\) 15.6180 + 11.3472i 0.499665 + 0.363028i 0.808889 0.587961i \(-0.200069\pi\)
−0.309224 + 0.950989i \(0.600069\pi\)
\(978\) 1.47214 0.0470737
\(979\) 0.590170 6.30664i 0.0188619 0.201561i
\(980\) −1.00000 −0.0319438
\(981\) −19.5623 14.2128i −0.624576 0.453781i
\(982\) 1.70163 5.23707i 0.0543011 0.167122i
\(983\) 5.14590 + 15.8374i 0.164129 + 0.505136i 0.998971 0.0453530i \(-0.0144413\pi\)
−0.834842 + 0.550489i \(0.814441\pi\)
\(984\) −1.64590 + 1.19581i −0.0524693 + 0.0381212i
\(985\) −4.85410 + 3.52671i −0.154665 + 0.112370i
\(986\) 0.236068 + 0.726543i 0.00751794 + 0.0231378i
\(987\) −0.562306 + 1.73060i −0.0178984 + 0.0550856i
\(988\) −0.236068 0.171513i −0.00751032 0.00545657i
\(989\) 29.1246 0.926109
\(990\) 6.25329 7.10642i 0.198743 0.225857i
\(991\) −10.6525 −0.338387 −0.169194 0.985583i \(-0.554116\pi\)
−0.169194 + 0.985583i \(0.554116\pi\)
\(992\) 2.61803 + 1.90211i 0.0831227 + 0.0603921i
\(993\) −2.71885 + 8.36775i −0.0862800 + 0.265543i
\(994\) 1.14590 + 3.52671i 0.0363457 + 0.111860i
\(995\) 6.00000 4.35926i 0.190213 0.138198i
\(996\) −1.64590 + 1.19581i −0.0521523 + 0.0378908i
\(997\) −5.29180 16.2865i −0.167593 0.515798i 0.831625 0.555337i \(-0.187411\pi\)
−0.999218 + 0.0395396i \(0.987411\pi\)
\(998\) 12.2984 37.8505i 0.389298 1.19814i
\(999\) 4.47214 + 3.24920i 0.141492 + 0.102800i
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 770.2.n.b.631.1 yes 4
11.3 even 5 inner 770.2.n.b.421.1 4
11.5 even 5 8470.2.a.bt.1.1 2
11.6 odd 10 8470.2.a.cf.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.n.b.421.1 4 11.3 even 5 inner
770.2.n.b.631.1 yes 4 1.1 even 1 trivial
8470.2.a.bt.1.1 2 11.5 even 5
8470.2.a.cf.1.1 2 11.6 odd 10