Properties

Label 1014.2.e.l.529.1
Level $1014$
Weight $2$
Character 1014.529
Analytic conductor $8.097$
Analytic rank $0$
Dimension $6$
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] = [1014,2,Mod(529,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("1014.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.1
Root \(-0.623490 + 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 1014.529
Dual form 1014.2.e.l.991.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -4.29590 q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.17845 - 3.77318i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -4.29590 q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.17845 - 3.77318i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.14795 - 3.72036i) q^{10} +(0.579417 - 1.00358i) q^{11} -1.00000 q^{12} +4.35690 q^{14} +(-2.14795 + 3.72036i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.246980 - 0.427781i) q^{17} +1.00000 q^{18} +(0.890084 + 1.54167i) q^{19} +(2.14795 + 3.72036i) q^{20} -4.35690 q^{21} +(0.579417 + 1.00358i) q^{22} +(-1.69202 + 2.93067i) q^{23} +(0.500000 - 0.866025i) q^{24} +13.4547 q^{25} -1.00000 q^{27} +(-2.17845 + 3.77318i) q^{28} +(-3.46950 + 6.00935i) q^{29} +(-2.14795 - 3.72036i) q^{30} +2.22521 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.579417 - 1.00358i) q^{33} +0.493959 q^{34} +(9.35839 + 16.2092i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.93900 + 3.35845i) q^{37} -1.78017 q^{38} -4.29590 q^{40} +(-3.15883 + 5.47126i) q^{41} +(2.17845 - 3.77318i) q^{42} +(-3.69202 - 6.39477i) q^{43} -1.15883 q^{44} +(2.14795 + 3.72036i) q^{45} +(-1.69202 - 2.93067i) q^{46} +1.78017 q^{47} +(0.500000 + 0.866025i) q^{48} +(-5.99127 + 10.3772i) q^{49} +(-6.72737 + 11.6521i) q^{50} -0.493959 q^{51} -2.51573 q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.48911 + 4.31127i) q^{55} +(-2.17845 - 3.77318i) q^{56} +1.78017 q^{57} +(-3.46950 - 6.00935i) q^{58} +(3.31551 + 5.74263i) q^{59} +4.29590 q^{60} +(-5.24698 - 9.08804i) q^{61} +(-1.11260 + 1.92709i) q^{62} +(-2.17845 + 3.77318i) q^{63} +1.00000 q^{64} +1.15883 q^{66} +(2.04892 - 3.54883i) q^{67} +(-0.246980 + 0.427781i) q^{68} +(1.69202 + 2.93067i) q^{69} -18.7168 q^{70} +(4.69202 + 8.12682i) q^{71} +(-0.500000 - 0.866025i) q^{72} -0.374354 q^{73} +(-1.93900 - 3.35845i) q^{74} +(6.72737 - 11.6521i) q^{75} +(0.890084 - 1.54167i) q^{76} -5.04892 q^{77} +2.65519 q^{79} +(2.14795 - 3.72036i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.15883 - 5.47126i) q^{82} +14.2784 q^{83} +(2.17845 + 3.77318i) q^{84} +(1.06100 + 1.83770i) q^{85} +7.38404 q^{86} +(3.46950 + 6.00935i) q^{87} +(0.579417 - 1.00358i) q^{88} +(0.417895 - 0.723815i) q^{89} -4.29590 q^{90} +3.38404 q^{92} +(1.11260 - 1.92709i) q^{93} +(-0.890084 + 1.54167i) q^{94} +(-3.82371 - 6.62286i) q^{95} -1.00000 q^{96} +(9.19687 + 15.9294i) q^{97} +(-5.99127 - 10.3772i) q^{98} -1.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8} - 3 q^{9} - q^{10} - 5 q^{11} - 6 q^{12} + 18 q^{14} + q^{15} - 3 q^{16} + 8 q^{17} + 6 q^{18} + 4 q^{19} - q^{20} - 18 q^{21} - 5 q^{22} + 3 q^{24} + 36 q^{25} - 6 q^{27} - 9 q^{28} - 11 q^{29} + q^{30} + 10 q^{31} - 3 q^{32} + 5 q^{33} - 16 q^{34} + 4 q^{35} - 3 q^{36} + 8 q^{37} - 8 q^{38} + 2 q^{40} - 2 q^{41} + 9 q^{42} - 12 q^{43} + 10 q^{44} - q^{45} + 8 q^{47} + 3 q^{48} - 20 q^{49} - 18 q^{50} + 16 q^{51} + 10 q^{53} + 3 q^{54} - 18 q^{55} - 9 q^{56} + 8 q^{57} - 11 q^{58} + 5 q^{59} - 2 q^{60} - 22 q^{61} - 5 q^{62} - 9 q^{63} + 6 q^{64} - 10 q^{66} - 6 q^{67} + 8 q^{68} - 8 q^{70} + 18 q^{71} - 3 q^{72} - 26 q^{73} + 8 q^{74} + 18 q^{75} + 4 q^{76} - 12 q^{77} + 62 q^{79} - q^{80} - 3 q^{81} - 2 q^{82} + 26 q^{83} + 9 q^{84} + 26 q^{85} + 24 q^{86} + 11 q^{87} - 5 q^{88} + 14 q^{89} + 2 q^{90} + 5 q^{93} - 4 q^{94} - 8 q^{95} - 6 q^{96} + 23 q^{97} - 20 q^{98} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −4.29590 −1.92118 −0.960592 0.277963i \(-0.910341\pi\)
−0.960592 + 0.277963i \(0.910341\pi\)
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −2.17845 3.77318i −0.823376 1.42613i −0.903154 0.429316i \(-0.858755\pi\)
0.0797783 0.996813i \(-0.474579\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 2.14795 3.72036i 0.679241 1.17648i
\(11\) 0.579417 1.00358i 0.174701 0.302591i −0.765357 0.643606i \(-0.777438\pi\)
0.940058 + 0.341016i \(0.110771\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 4.35690 1.16443
\(15\) −2.14795 + 3.72036i −0.554598 + 0.960592i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.246980 0.427781i −0.0599014 0.103752i 0.834520 0.550978i \(-0.185745\pi\)
−0.894421 + 0.447226i \(0.852412\pi\)
\(18\) 1.00000 0.235702
\(19\) 0.890084 + 1.54167i 0.204199 + 0.353683i 0.949877 0.312623i \(-0.101208\pi\)
−0.745678 + 0.666306i \(0.767874\pi\)
\(20\) 2.14795 + 3.72036i 0.480296 + 0.831897i
\(21\) −4.35690 −0.950753
\(22\) 0.579417 + 1.00358i 0.123532 + 0.213964i
\(23\) −1.69202 + 2.93067i −0.352811 + 0.611086i −0.986741 0.162304i \(-0.948107\pi\)
0.633930 + 0.773391i \(0.281441\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 13.4547 2.69095
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −2.17845 + 3.77318i −0.411688 + 0.713064i
\(29\) −3.46950 + 6.00935i −0.644270 + 1.11591i 0.340200 + 0.940353i \(0.389505\pi\)
−0.984470 + 0.175555i \(0.943828\pi\)
\(30\) −2.14795 3.72036i −0.392160 0.679241i
\(31\) 2.22521 0.399659 0.199830 0.979831i \(-0.435961\pi\)
0.199830 + 0.979831i \(0.435961\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.579417 1.00358i −0.100864 0.174701i
\(34\) 0.493959 0.0847133
\(35\) 9.35839 + 16.2092i 1.58186 + 2.73986i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −1.93900 + 3.35845i −0.318770 + 0.552126i −0.980232 0.197853i \(-0.936603\pi\)
0.661462 + 0.749979i \(0.269936\pi\)
\(38\) −1.78017 −0.288781
\(39\) 0 0
\(40\) −4.29590 −0.679241
\(41\) −3.15883 + 5.47126i −0.493327 + 0.854467i −0.999970 0.00768834i \(-0.997553\pi\)
0.506644 + 0.862156i \(0.330886\pi\)
\(42\) 2.17845 3.77318i 0.336142 0.582215i
\(43\) −3.69202 6.39477i −0.563028 0.975193i −0.997230 0.0743776i \(-0.976303\pi\)
0.434202 0.900815i \(-0.357030\pi\)
\(44\) −1.15883 −0.174701
\(45\) 2.14795 + 3.72036i 0.320197 + 0.554598i
\(46\) −1.69202 2.93067i −0.249475 0.432103i
\(47\) 1.78017 0.259664 0.129832 0.991536i \(-0.458556\pi\)
0.129832 + 0.991536i \(0.458556\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −5.99127 + 10.3772i −0.855896 + 1.48246i
\(50\) −6.72737 + 11.6521i −0.951393 + 1.64786i
\(51\) −0.493959 −0.0691681
\(52\) 0 0
\(53\) −2.51573 −0.345562 −0.172781 0.984960i \(-0.555275\pi\)
−0.172781 + 0.984960i \(0.555275\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −2.48911 + 4.31127i −0.335632 + 0.581332i
\(56\) −2.17845 3.77318i −0.291107 0.504213i
\(57\) 1.78017 0.235789
\(58\) −3.46950 6.00935i −0.455568 0.789066i
\(59\) 3.31551 + 5.74263i 0.431643 + 0.747627i 0.997015 0.0772087i \(-0.0246008\pi\)
−0.565372 + 0.824836i \(0.691267\pi\)
\(60\) 4.29590 0.554598
\(61\) −5.24698 9.08804i −0.671807 1.16360i −0.977391 0.211439i \(-0.932185\pi\)
0.305584 0.952165i \(-0.401148\pi\)
\(62\) −1.11260 + 1.92709i −0.141301 + 0.244740i
\(63\) −2.17845 + 3.77318i −0.274459 + 0.475376i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.15883 0.142643
\(67\) 2.04892 3.54883i 0.250315 0.433558i −0.713297 0.700861i \(-0.752799\pi\)
0.963613 + 0.267303i \(0.0861325\pi\)
\(68\) −0.246980 + 0.427781i −0.0299507 + 0.0518761i
\(69\) 1.69202 + 2.93067i 0.203695 + 0.352811i
\(70\) −18.7168 −2.23708
\(71\) 4.69202 + 8.12682i 0.556841 + 0.964476i 0.997758 + 0.0669283i \(0.0213199\pi\)
−0.440917 + 0.897548i \(0.645347\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −0.374354 −0.0438149 −0.0219074 0.999760i \(-0.506974\pi\)
−0.0219074 + 0.999760i \(0.506974\pi\)
\(74\) −1.93900 3.35845i −0.225404 0.390412i
\(75\) 6.72737 11.6521i 0.776809 1.34547i
\(76\) 0.890084 1.54167i 0.102100 0.176842i
\(77\) −5.04892 −0.575378
\(78\) 0 0
\(79\) 2.65519 0.298732 0.149366 0.988782i \(-0.452277\pi\)
0.149366 + 0.988782i \(0.452277\pi\)
\(80\) 2.14795 3.72036i 0.240148 0.415948i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.15883 5.47126i −0.348835 0.604200i
\(83\) 14.2784 1.56726 0.783631 0.621226i \(-0.213365\pi\)
0.783631 + 0.621226i \(0.213365\pi\)
\(84\) 2.17845 + 3.77318i 0.237688 + 0.411688i
\(85\) 1.06100 + 1.83770i 0.115081 + 0.199327i
\(86\) 7.38404 0.796242
\(87\) 3.46950 + 6.00935i 0.371970 + 0.644270i
\(88\) 0.579417 1.00358i 0.0617660 0.106982i
\(89\) 0.417895 0.723815i 0.0442968 0.0767242i −0.843027 0.537871i \(-0.819229\pi\)
0.887324 + 0.461147i \(0.152562\pi\)
\(90\) −4.29590 −0.452827
\(91\) 0 0
\(92\) 3.38404 0.352811
\(93\) 1.11260 1.92709i 0.115372 0.199830i
\(94\) −0.890084 + 1.54167i −0.0918051 + 0.159011i
\(95\) −3.82371 6.62286i −0.392304 0.679491i
\(96\) −1.00000 −0.102062
\(97\) 9.19687 + 15.9294i 0.933800 + 1.61739i 0.776759 + 0.629797i \(0.216862\pi\)
0.157041 + 0.987592i \(0.449805\pi\)
\(98\) −5.99127 10.3772i −0.605210 1.04825i
\(99\) −1.15883 −0.116467
\(100\) −6.72737 11.6521i −0.672737 1.16521i
\(101\) 2.73341 4.73440i 0.271984 0.471090i −0.697386 0.716696i \(-0.745654\pi\)
0.969370 + 0.245606i \(0.0789869\pi\)
\(102\) 0.246980 0.427781i 0.0244546 0.0423567i
\(103\) 7.00969 0.690685 0.345343 0.938477i \(-0.387763\pi\)
0.345343 + 0.938477i \(0.387763\pi\)
\(104\) 0 0
\(105\) 18.7168 1.82657
\(106\) 1.25786 2.17869i 0.122175 0.211613i
\(107\) 0.958615 1.66037i 0.0926728 0.160514i −0.815962 0.578105i \(-0.803792\pi\)
0.908635 + 0.417591i \(0.137126\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −18.7681 −1.79766 −0.898828 0.438301i \(-0.855580\pi\)
−0.898828 + 0.438301i \(0.855580\pi\)
\(110\) −2.48911 4.31127i −0.237328 0.411064i
\(111\) 1.93900 + 3.35845i 0.184042 + 0.318770i
\(112\) 4.35690 0.411688
\(113\) −5.20775 9.02009i −0.489904 0.848539i 0.510028 0.860158i \(-0.329635\pi\)
−0.999932 + 0.0116189i \(0.996302\pi\)
\(114\) −0.890084 + 1.54167i −0.0833640 + 0.144391i
\(115\) 7.26875 12.5898i 0.677814 1.17401i
\(116\) 6.93900 0.644270
\(117\) 0 0
\(118\) −6.63102 −0.610435
\(119\) −1.07606 + 1.86380i −0.0986427 + 0.170854i
\(120\) −2.14795 + 3.72036i −0.196080 + 0.339620i
\(121\) 4.82855 + 8.36330i 0.438959 + 0.760300i
\(122\) 10.4940 0.950078
\(123\) 3.15883 + 5.47126i 0.284822 + 0.493327i
\(124\) −1.11260 1.92709i −0.0999148 0.173058i
\(125\) −36.3207 −3.24862
\(126\) −2.17845 3.77318i −0.194072 0.336142i
\(127\) −4.19687 + 7.26918i −0.372412 + 0.645036i −0.989936 0.141516i \(-0.954802\pi\)
0.617524 + 0.786552i \(0.288136\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −7.38404 −0.650129
\(130\) 0 0
\(131\) −13.5036 −1.17982 −0.589910 0.807469i \(-0.700837\pi\)
−0.589910 + 0.807469i \(0.700837\pi\)
\(132\) −0.579417 + 1.00358i −0.0504318 + 0.0873504i
\(133\) 3.87800 6.71690i 0.336265 0.582429i
\(134\) 2.04892 + 3.54883i 0.176999 + 0.306572i
\(135\) 4.29590 0.369732
\(136\) −0.246980 0.427781i −0.0211783 0.0366819i
\(137\) 2.00000 + 3.46410i 0.170872 + 0.295958i 0.938725 0.344668i \(-0.112008\pi\)
−0.767853 + 0.640626i \(0.778675\pi\)
\(138\) −3.38404 −0.288069
\(139\) 7.51573 + 13.0176i 0.637476 + 1.10414i 0.985985 + 0.166835i \(0.0533548\pi\)
−0.348509 + 0.937305i \(0.613312\pi\)
\(140\) 9.35839 16.2092i 0.790928 1.36993i
\(141\) 0.890084 1.54167i 0.0749586 0.129832i
\(142\) −9.38404 −0.787491
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 14.9046 25.8156i 1.23776 2.14387i
\(146\) 0.187177 0.324200i 0.0154909 0.0268310i
\(147\) 5.99127 + 10.3772i 0.494152 + 0.855896i
\(148\) 3.87800 0.318770
\(149\) −1.96346 3.40081i −0.160853 0.278605i 0.774322 0.632792i \(-0.218091\pi\)
−0.935175 + 0.354187i \(0.884758\pi\)
\(150\) 6.72737 + 11.6521i 0.549287 + 0.951393i
\(151\) −9.62863 −0.783567 −0.391783 0.920057i \(-0.628142\pi\)
−0.391783 + 0.920057i \(0.628142\pi\)
\(152\) 0.890084 + 1.54167i 0.0721953 + 0.125046i
\(153\) −0.246980 + 0.427781i −0.0199671 + 0.0345841i
\(154\) 2.52446 4.37249i 0.203427 0.352345i
\(155\) −9.55927 −0.767819
\(156\) 0 0
\(157\) −17.3840 −1.38740 −0.693699 0.720265i \(-0.744020\pi\)
−0.693699 + 0.720265i \(0.744020\pi\)
\(158\) −1.32759 + 2.29946i −0.105618 + 0.182935i
\(159\) −1.25786 + 2.17869i −0.0997552 + 0.172781i
\(160\) 2.14795 + 3.72036i 0.169810 + 0.294120i
\(161\) 14.7439 1.16198
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −11.2349 19.4594i −0.879985 1.52418i −0.851356 0.524589i \(-0.824219\pi\)
−0.0286294 0.999590i \(-0.509114\pi\)
\(164\) 6.31767 0.493327
\(165\) 2.48911 + 4.31127i 0.193777 + 0.335632i
\(166\) −7.13922 + 12.3655i −0.554111 + 0.959748i
\(167\) −0.417895 + 0.723815i −0.0323377 + 0.0560105i −0.881741 0.471733i \(-0.843629\pi\)
0.849404 + 0.527744i \(0.176962\pi\)
\(168\) −4.35690 −0.336142
\(169\) 0 0
\(170\) −2.12200 −0.162750
\(171\) 0.890084 1.54167i 0.0680664 0.117894i
\(172\) −3.69202 + 6.39477i −0.281514 + 0.487597i
\(173\) 2.08546 + 3.61212i 0.158554 + 0.274624i 0.934348 0.356363i \(-0.115983\pi\)
−0.775793 + 0.630987i \(0.782650\pi\)
\(174\) −6.93900 −0.526044
\(175\) −29.3104 50.7672i −2.21566 3.83764i
\(176\) 0.579417 + 1.00358i 0.0436752 + 0.0756476i
\(177\) 6.63102 0.498418
\(178\) 0.417895 + 0.723815i 0.0313225 + 0.0542522i
\(179\) −11.4438 + 19.8213i −0.855353 + 1.48152i 0.0209638 + 0.999780i \(0.493327\pi\)
−0.876317 + 0.481735i \(0.840007\pi\)
\(180\) 2.14795 3.72036i 0.160099 0.277299i
\(181\) 11.6039 0.862509 0.431255 0.902230i \(-0.358071\pi\)
0.431255 + 0.902230i \(0.358071\pi\)
\(182\) 0 0
\(183\) −10.4940 −0.775736
\(184\) −1.69202 + 2.93067i −0.124737 + 0.216052i
\(185\) 8.32975 14.4275i 0.612415 1.06073i
\(186\) 1.11260 + 1.92709i 0.0815801 + 0.141301i
\(187\) −0.572417 −0.0418592
\(188\) −0.890084 1.54167i −0.0649160 0.112438i
\(189\) 2.17845 + 3.77318i 0.158459 + 0.274459i
\(190\) 7.64742 0.554802
\(191\) −8.34481 14.4536i −0.603810 1.04583i −0.992238 0.124350i \(-0.960315\pi\)
0.388429 0.921479i \(-0.373018\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −4.82371 + 8.35491i −0.347218 + 0.601399i −0.985754 0.168193i \(-0.946207\pi\)
0.638536 + 0.769592i \(0.279540\pi\)
\(194\) −18.3937 −1.32059
\(195\) 0 0
\(196\) 11.9825 0.855896
\(197\) −9.81916 + 17.0073i −0.699586 + 1.21172i 0.269024 + 0.963133i \(0.413299\pi\)
−0.968610 + 0.248585i \(0.920034\pi\)
\(198\) 0.579417 1.00358i 0.0411774 0.0713213i
\(199\) 9.21044 + 15.9529i 0.652911 + 1.13087i 0.982413 + 0.186720i \(0.0597857\pi\)
−0.329502 + 0.944155i \(0.606881\pi\)
\(200\) 13.4547 0.951393
\(201\) −2.04892 3.54883i −0.144519 0.250315i
\(202\) 2.73341 + 4.73440i 0.192322 + 0.333111i
\(203\) 30.2325 2.12191
\(204\) 0.246980 + 0.427781i 0.0172920 + 0.0299507i
\(205\) 13.5700 23.5040i 0.947772 1.64159i
\(206\) −3.50484 + 6.07057i −0.244194 + 0.422957i
\(207\) 3.38404 0.235207
\(208\) 0 0
\(209\) 2.06292 0.142695
\(210\) −9.35839 + 16.2092i −0.645790 + 1.11854i
\(211\) −7.96077 + 13.7885i −0.548042 + 0.949237i 0.450367 + 0.892844i \(0.351293\pi\)
−0.998409 + 0.0563930i \(0.982040\pi\)
\(212\) 1.25786 + 2.17869i 0.0863905 + 0.149633i
\(213\) 9.38404 0.642984
\(214\) 0.958615 + 1.66037i 0.0655296 + 0.113501i
\(215\) 15.8605 + 27.4713i 1.08168 + 1.87352i
\(216\) −1.00000 −0.0680414
\(217\) −4.84750 8.39612i −0.329070 0.569966i
\(218\) 9.38404 16.2536i 0.635568 1.10084i
\(219\) −0.187177 + 0.324200i −0.0126483 + 0.0219074i
\(220\) 4.97823 0.335632
\(221\) 0 0
\(222\) −3.87800 −0.260274
\(223\) 2.59179 4.48912i 0.173559 0.300614i −0.766102 0.642719i \(-0.777806\pi\)
0.939662 + 0.342105i \(0.111140\pi\)
\(224\) −2.17845 + 3.77318i −0.145554 + 0.252106i
\(225\) −6.72737 11.6521i −0.448491 0.776809i
\(226\) 10.4155 0.692829
\(227\) −7.44385 12.8931i −0.494065 0.855746i 0.505911 0.862586i \(-0.331156\pi\)
−0.999977 + 0.00683921i \(0.997823\pi\)
\(228\) −0.890084 1.54167i −0.0589472 0.102100i
\(229\) 23.4577 1.55013 0.775065 0.631882i \(-0.217717\pi\)
0.775065 + 0.631882i \(0.217717\pi\)
\(230\) 7.26875 + 12.5898i 0.479287 + 0.830150i
\(231\) −2.52446 + 4.37249i −0.166097 + 0.287689i
\(232\) −3.46950 + 6.00935i −0.227784 + 0.394533i
\(233\) −11.8780 −0.778154 −0.389077 0.921205i \(-0.627206\pi\)
−0.389077 + 0.921205i \(0.627206\pi\)
\(234\) 0 0
\(235\) −7.64742 −0.498862
\(236\) 3.31551 5.74263i 0.215821 0.373814i
\(237\) 1.32759 2.29946i 0.0862364 0.149366i
\(238\) −1.07606 1.86380i −0.0697509 0.120812i
\(239\) −25.3599 −1.64039 −0.820197 0.572081i \(-0.806136\pi\)
−0.820197 + 0.572081i \(0.806136\pi\)
\(240\) −2.14795 3.72036i −0.138649 0.240148i
\(241\) −6.01089 10.4112i −0.387195 0.670642i 0.604876 0.796320i \(-0.293223\pi\)
−0.992071 + 0.125678i \(0.959889\pi\)
\(242\) −9.65710 −0.620782
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −5.24698 + 9.08804i −0.335903 + 0.581802i
\(245\) 25.7379 44.5793i 1.64433 2.84807i
\(246\) −6.31767 −0.402800
\(247\) 0 0
\(248\) 2.22521 0.141301
\(249\) 7.13922 12.3655i 0.452430 0.783631i
\(250\) 18.1603 31.4546i 1.14856 1.98936i
\(251\) 7.67241 + 13.2890i 0.484278 + 0.838794i 0.999837 0.0180600i \(-0.00574899\pi\)
−0.515559 + 0.856854i \(0.672416\pi\)
\(252\) 4.35690 0.274459
\(253\) 1.96077 + 3.39616i 0.123273 + 0.213514i
\(254\) −4.19687 7.26918i −0.263335 0.456109i
\(255\) 2.12200 0.132885
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.75302 6.50042i 0.234107 0.405485i −0.724906 0.688848i \(-0.758117\pi\)
0.959013 + 0.283363i \(0.0914501\pi\)
\(258\) 3.69202 6.39477i 0.229855 0.398121i
\(259\) 16.8961 1.04987
\(260\) 0 0
\(261\) 6.93900 0.429513
\(262\) 6.75182 11.6945i 0.417129 0.722489i
\(263\) 6.11529 10.5920i 0.377085 0.653131i −0.613552 0.789655i \(-0.710260\pi\)
0.990637 + 0.136524i \(0.0435931\pi\)
\(264\) −0.579417 1.00358i −0.0356606 0.0617660i
\(265\) 10.8073 0.663888
\(266\) 3.87800 + 6.71690i 0.237776 + 0.411839i
\(267\) −0.417895 0.723815i −0.0255747 0.0442968i
\(268\) −4.09783 −0.250315
\(269\) −1.35809 2.35228i −0.0828044 0.143421i 0.821649 0.569994i \(-0.193054\pi\)
−0.904453 + 0.426572i \(0.859721\pi\)
\(270\) −2.14795 + 3.72036i −0.130720 + 0.226414i
\(271\) −6.19687 + 10.7333i −0.376433 + 0.652001i −0.990540 0.137222i \(-0.956183\pi\)
0.614108 + 0.789222i \(0.289516\pi\)
\(272\) 0.493959 0.0299507
\(273\) 0 0
\(274\) −4.00000 −0.241649
\(275\) 7.79590 13.5029i 0.470110 0.814255i
\(276\) 1.69202 2.93067i 0.101848 0.176405i
\(277\) 12.0640 + 20.8954i 0.724854 + 1.25548i 0.959034 + 0.283291i \(0.0914264\pi\)
−0.234179 + 0.972193i \(0.575240\pi\)
\(278\) −15.0315 −0.901527
\(279\) −1.11260 1.92709i −0.0666099 0.115372i
\(280\) 9.35839 + 16.2092i 0.559271 + 0.968685i
\(281\) 12.8358 0.765719 0.382860 0.923807i \(-0.374939\pi\)
0.382860 + 0.923807i \(0.374939\pi\)
\(282\) 0.890084 + 1.54167i 0.0530037 + 0.0918051i
\(283\) −2.82371 + 4.89081i −0.167852 + 0.290728i −0.937664 0.347542i \(-0.887016\pi\)
0.769812 + 0.638270i \(0.220350\pi\)
\(284\) 4.69202 8.12682i 0.278420 0.482238i
\(285\) −7.64742 −0.452994
\(286\) 0 0
\(287\) 27.5254 1.62477
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 8.37800 14.5111i 0.492824 0.853596i
\(290\) 14.9046 + 25.8156i 0.875229 + 1.51594i
\(291\) 18.3937 1.07826
\(292\) 0.187177 + 0.324200i 0.0109537 + 0.0189724i
\(293\) −10.6826 18.5029i −0.624086 1.08095i −0.988717 0.149796i \(-0.952138\pi\)
0.364631 0.931152i \(-0.381195\pi\)
\(294\) −11.9825 −0.698836
\(295\) −14.2431 24.6698i −0.829265 1.43633i
\(296\) −1.93900 + 3.35845i −0.112702 + 0.195206i
\(297\) −0.579417 + 1.00358i −0.0336212 + 0.0582336i
\(298\) 3.92692 0.227480
\(299\) 0 0
\(300\) −13.4547 −0.776809
\(301\) −16.0858 + 27.8613i −0.927167 + 1.60590i
\(302\) 4.81431 8.33864i 0.277033 0.479835i
\(303\) −2.73341 4.73440i −0.157030 0.271984i
\(304\) −1.78017 −0.102100
\(305\) 22.5405 + 39.0413i 1.29066 + 2.23550i
\(306\) −0.246980 0.427781i −0.0141189 0.0244546i
\(307\) −28.8853 −1.64857 −0.824286 0.566174i \(-0.808423\pi\)
−0.824286 + 0.566174i \(0.808423\pi\)
\(308\) 2.52446 + 4.37249i 0.143844 + 0.249146i
\(309\) 3.50484 6.07057i 0.199384 0.345343i
\(310\) 4.77963 8.27857i 0.271465 0.470191i
\(311\) 3.38404 0.191891 0.0959457 0.995387i \(-0.469412\pi\)
0.0959457 + 0.995387i \(0.469412\pi\)
\(312\) 0 0
\(313\) 14.3502 0.811121 0.405560 0.914068i \(-0.367076\pi\)
0.405560 + 0.914068i \(0.367076\pi\)
\(314\) 8.69202 15.0550i 0.490519 0.849604i
\(315\) 9.35839 16.2092i 0.527285 0.913285i
\(316\) −1.32759 2.29946i −0.0746829 0.129355i
\(317\) −18.5332 −1.04093 −0.520464 0.853884i \(-0.674241\pi\)
−0.520464 + 0.853884i \(0.674241\pi\)
\(318\) −1.25786 2.17869i −0.0705376 0.122175i
\(319\) 4.02057 + 6.96384i 0.225109 + 0.389900i
\(320\) −4.29590 −0.240148
\(321\) −0.958615 1.66037i −0.0535047 0.0926728i
\(322\) −7.37196 + 12.7686i −0.410823 + 0.711567i
\(323\) 0.439665 0.761522i 0.0244636 0.0423722i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 22.4698 1.24449
\(327\) −9.38404 + 16.2536i −0.518939 + 0.898828i
\(328\) −3.15883 + 5.47126i −0.174417 + 0.302100i
\(329\) −3.87800 6.71690i −0.213801 0.370315i
\(330\) −4.97823 −0.274043
\(331\) −3.93900 6.82255i −0.216507 0.375001i 0.737231 0.675641i \(-0.236133\pi\)
−0.953738 + 0.300640i \(0.902800\pi\)
\(332\) −7.13922 12.3655i −0.391816 0.678644i
\(333\) 3.87800 0.212513
\(334\) −0.417895 0.723815i −0.0228662 0.0396054i
\(335\) −8.80194 + 15.2454i −0.480901 + 0.832945i
\(336\) 2.17845 3.77318i 0.118844 0.205844i
\(337\) −13.7265 −0.747728 −0.373864 0.927484i \(-0.621967\pi\)
−0.373864 + 0.927484i \(0.621967\pi\)
\(338\) 0 0
\(339\) −10.4155 −0.565692
\(340\) 1.06100 1.83770i 0.0575407 0.0996635i
\(341\) 1.28932 2.23317i 0.0698208 0.120933i
\(342\) 0.890084 + 1.54167i 0.0481302 + 0.0833640i
\(343\) 21.7084 1.17214
\(344\) −3.69202 6.39477i −0.199060 0.344783i
\(345\) −7.26875 12.5898i −0.391336 0.677814i
\(346\) −4.17092 −0.224230
\(347\) 2.42543 + 4.20096i 0.130204 + 0.225520i 0.923755 0.382984i \(-0.125104\pi\)
−0.793551 + 0.608503i \(0.791770\pi\)
\(348\) 3.46950 6.00935i 0.185985 0.322135i
\(349\) 14.1739 24.5499i 0.758711 1.31413i −0.184797 0.982777i \(-0.559163\pi\)
0.943508 0.331350i \(-0.107504\pi\)
\(350\) 58.6209 3.13342
\(351\) 0 0
\(352\) −1.15883 −0.0617660
\(353\) 14.2228 24.6346i 0.757004 1.31117i −0.187368 0.982290i \(-0.559996\pi\)
0.944372 0.328880i \(-0.106671\pi\)
\(354\) −3.31551 + 5.74263i −0.176217 + 0.305218i
\(355\) −20.1564 34.9120i −1.06979 1.85294i
\(356\) −0.835790 −0.0442968
\(357\) 1.07606 + 1.86380i 0.0569514 + 0.0986427i
\(358\) −11.4438 19.8213i −0.604826 1.04759i
\(359\) 11.2271 0.592545 0.296273 0.955103i \(-0.404256\pi\)
0.296273 + 0.955103i \(0.404256\pi\)
\(360\) 2.14795 + 3.72036i 0.113207 + 0.196080i
\(361\) 7.91550 13.7101i 0.416605 0.721582i
\(362\) −5.80194 + 10.0493i −0.304943 + 0.528177i
\(363\) 9.65710 0.506867
\(364\) 0 0
\(365\) 1.60819 0.0841764
\(366\) 5.24698 9.08804i 0.274264 0.475039i
\(367\) −8.41335 + 14.5723i −0.439173 + 0.760670i −0.997626 0.0688662i \(-0.978062\pi\)
0.558453 + 0.829536i \(0.311395\pi\)
\(368\) −1.69202 2.93067i −0.0882027 0.152772i
\(369\) 6.31767 0.328885
\(370\) 8.32975 + 14.4275i 0.433043 + 0.750053i
\(371\) 5.48039 + 9.49231i 0.284527 + 0.492816i
\(372\) −2.22521 −0.115372
\(373\) 13.2664 + 22.9780i 0.686906 + 1.18976i 0.972834 + 0.231505i \(0.0743649\pi\)
−0.285928 + 0.958251i \(0.592302\pi\)
\(374\) 0.286208 0.495727i 0.0147995 0.0256334i
\(375\) −18.1603 + 31.4546i −0.937795 + 1.62431i
\(376\) 1.78017 0.0918051
\(377\) 0 0
\(378\) −4.35690 −0.224095
\(379\) −10.9879 + 19.0316i −0.564411 + 0.977589i 0.432693 + 0.901541i \(0.357564\pi\)
−0.997104 + 0.0760479i \(0.975770\pi\)
\(380\) −3.82371 + 6.62286i −0.196152 + 0.339745i
\(381\) 4.19687 + 7.26918i 0.215012 + 0.372412i
\(382\) 16.6896 0.853916
\(383\) 0.307979 + 0.533434i 0.0157370 + 0.0272572i 0.873787 0.486309i \(-0.161657\pi\)
−0.858050 + 0.513567i \(0.828324\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 21.6896 1.10541
\(386\) −4.82371 8.35491i −0.245520 0.425254i
\(387\) −3.69202 + 6.39477i −0.187676 + 0.325064i
\(388\) 9.19687 15.9294i 0.466900 0.808695i
\(389\) −35.5260 −1.80124 −0.900620 0.434607i \(-0.856887\pi\)
−0.900620 + 0.434607i \(0.856887\pi\)
\(390\) 0 0
\(391\) 1.67158 0.0845354
\(392\) −5.99127 + 10.3772i −0.302605 + 0.524127i
\(393\) −6.75182 + 11.6945i −0.340584 + 0.589910i
\(394\) −9.81916 17.0073i −0.494682 0.856815i
\(395\) −11.4064 −0.573918
\(396\) 0.579417 + 1.00358i 0.0291168 + 0.0504318i
\(397\) 8.03923 + 13.9244i 0.403477 + 0.698843i 0.994143 0.108073i \(-0.0344681\pi\)
−0.590666 + 0.806916i \(0.701135\pi\)
\(398\) −18.4209 −0.923355
\(399\) −3.87800 6.71690i −0.194143 0.336265i
\(400\) −6.72737 + 11.6521i −0.336368 + 0.582607i
\(401\) −11.4547 + 19.8402i −0.572022 + 0.990771i 0.424336 + 0.905505i \(0.360507\pi\)
−0.996358 + 0.0852664i \(0.972826\pi\)
\(402\) 4.09783 0.204381
\(403\) 0 0
\(404\) −5.46681 −0.271984
\(405\) 2.14795 3.72036i 0.106732 0.184866i
\(406\) −15.1163 + 26.1821i −0.750207 + 1.29940i
\(407\) 2.24698 + 3.89188i 0.111379 + 0.192913i
\(408\) −0.493959 −0.0244546
\(409\) 0.623490 + 1.07992i 0.0308296 + 0.0533984i 0.881029 0.473063i \(-0.156852\pi\)
−0.850199 + 0.526462i \(0.823518\pi\)
\(410\) 13.5700 + 23.5040i 0.670176 + 1.16078i
\(411\) 4.00000 0.197305
\(412\) −3.50484 6.07057i −0.172671 0.299075i
\(413\) 14.4453 25.0201i 0.710809 1.23116i
\(414\) −1.69202 + 2.93067i −0.0831583 + 0.144034i
\(415\) −61.3387 −3.01100
\(416\) 0 0
\(417\) 15.0315 0.736094
\(418\) −1.03146 + 1.78654i −0.0504503 + 0.0873825i
\(419\) −14.7315 + 25.5158i −0.719683 + 1.24653i 0.241442 + 0.970415i \(0.422380\pi\)
−0.961125 + 0.276112i \(0.910954\pi\)
\(420\) −9.35839 16.2092i −0.456643 0.790928i
\(421\) −17.3491 −0.845545 −0.422772 0.906236i \(-0.638943\pi\)
−0.422772 + 0.906236i \(0.638943\pi\)
\(422\) −7.96077 13.7885i −0.387524 0.671212i
\(423\) −0.890084 1.54167i −0.0432774 0.0749586i
\(424\) −2.51573 −0.122175
\(425\) −3.32304 5.75568i −0.161191 0.279192i
\(426\) −4.69202 + 8.12682i −0.227329 + 0.393746i
\(427\) −22.8605 + 39.5956i −1.10630 + 1.91617i
\(428\) −1.91723 −0.0926728
\(429\) 0 0
\(430\) −31.7211 −1.52973
\(431\) −12.6920 + 21.9832i −0.611353 + 1.05889i 0.379659 + 0.925126i \(0.376041\pi\)
−0.991013 + 0.133768i \(0.957292\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −10.0027 17.3252i −0.480699 0.832594i 0.519056 0.854740i \(-0.326284\pi\)
−0.999755 + 0.0221458i \(0.992950\pi\)
\(434\) 9.69501 0.465375
\(435\) −14.9046 25.8156i −0.714622 1.23776i
\(436\) 9.38404 + 16.2536i 0.449414 + 0.778408i
\(437\) −6.02416 −0.288175
\(438\) −0.187177 0.324200i −0.00894367 0.0154909i
\(439\) −0.271971 + 0.471067i −0.0129805 + 0.0224828i −0.872443 0.488716i \(-0.837465\pi\)
0.859462 + 0.511199i \(0.170799\pi\)
\(440\) −2.48911 + 4.31127i −0.118664 + 0.205532i
\(441\) 11.9825 0.570597
\(442\) 0 0
\(443\) −18.1360 −0.861667 −0.430834 0.902431i \(-0.641780\pi\)
−0.430834 + 0.902431i \(0.641780\pi\)
\(444\) 1.93900 3.35845i 0.0920209 0.159385i
\(445\) −1.79523 + 3.10943i −0.0851022 + 0.147401i
\(446\) 2.59179 + 4.48912i 0.122725 + 0.212566i
\(447\) −3.92692 −0.185737
\(448\) −2.17845 3.77318i −0.102922 0.178266i
\(449\) −14.6896 25.4432i −0.693246 1.20074i −0.970768 0.240019i \(-0.922846\pi\)
0.277522 0.960719i \(-0.410487\pi\)
\(450\) 13.4547 0.634262
\(451\) 3.66056 + 6.34028i 0.172369 + 0.298552i
\(452\) −5.20775 + 9.02009i −0.244952 + 0.424269i
\(453\) −4.81431 + 8.33864i −0.226196 + 0.391783i
\(454\) 14.8877 0.698714
\(455\) 0 0
\(456\) 1.78017 0.0833640
\(457\) 4.17360 7.22889i 0.195233 0.338153i −0.751744 0.659455i \(-0.770787\pi\)
0.946977 + 0.321302i \(0.104120\pi\)
\(458\) −11.7289 + 20.3150i −0.548054 + 0.949257i
\(459\) 0.246980 + 0.427781i 0.0115280 + 0.0199671i
\(460\) −14.5375 −0.677814
\(461\) −10.7485 18.6169i −0.500606 0.867075i −1.00000 0.000700154i \(-0.999777\pi\)
0.499394 0.866375i \(-0.333556\pi\)
\(462\) −2.52446 4.37249i −0.117448 0.203427i
\(463\) 26.1715 1.21629 0.608147 0.793825i \(-0.291913\pi\)
0.608147 + 0.793825i \(0.291913\pi\)
\(464\) −3.46950 6.00935i −0.161068 0.278977i
\(465\) −4.77963 + 8.27857i −0.221650 + 0.383910i
\(466\) 5.93900 10.2867i 0.275119 0.476520i
\(467\) −9.81269 −0.454077 −0.227039 0.973886i \(-0.572904\pi\)
−0.227039 + 0.973886i \(0.572904\pi\)
\(468\) 0 0
\(469\) −17.8538 −0.824414
\(470\) 3.82371 6.62286i 0.176374 0.305490i
\(471\) −8.69202 + 15.0550i −0.400507 + 0.693699i
\(472\) 3.31551 + 5.74263i 0.152609 + 0.264326i
\(473\) −8.55688 −0.393446
\(474\) 1.32759 + 2.29946i 0.0609784 + 0.105618i
\(475\) 11.9758 + 20.7428i 0.549489 + 0.951743i
\(476\) 2.15213 0.0986427
\(477\) 1.25786 + 2.17869i 0.0575937 + 0.0997552i
\(478\) 12.6799 21.9623i 0.579967 1.00453i
\(479\) −8.64071 + 14.9662i −0.394804 + 0.683821i −0.993076 0.117472i \(-0.962521\pi\)
0.598272 + 0.801293i \(0.295854\pi\)
\(480\) 4.29590 0.196080
\(481\) 0 0
\(482\) 12.0218 0.547577
\(483\) 7.37196 12.7686i 0.335436 0.580992i
\(484\) 4.82855 8.36330i 0.219480 0.380150i
\(485\) −39.5088 68.4312i −1.79400 3.10730i
\(486\) −1.00000 −0.0453609
\(487\) 15.8443 + 27.4431i 0.717973 + 1.24357i 0.961802 + 0.273747i \(0.0882632\pi\)
−0.243829 + 0.969818i \(0.578403\pi\)
\(488\) −5.24698 9.08804i −0.237520 0.411396i
\(489\) −22.4698 −1.01612
\(490\) 25.7379 + 44.5793i 1.16272 + 2.01389i
\(491\) −1.15183 + 1.99503i −0.0519815 + 0.0900346i −0.890845 0.454307i \(-0.849887\pi\)
0.838864 + 0.544341i \(0.183220\pi\)
\(492\) 3.15883 5.47126i 0.142411 0.246663i
\(493\) 3.42758 0.154371
\(494\) 0 0
\(495\) 4.97823 0.223755
\(496\) −1.11260 + 1.92709i −0.0499574 + 0.0865288i
\(497\) 20.4426 35.4077i 0.916978 1.58825i
\(498\) 7.13922 + 12.3655i 0.319916 + 0.554111i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 18.1603 + 31.4546i 0.812154 + 1.40669i
\(501\) 0.417895 + 0.723815i 0.0186702 + 0.0323377i
\(502\) −15.3448 −0.684873
\(503\) 17.6843 + 30.6300i 0.788502 + 1.36573i 0.926885 + 0.375346i \(0.122476\pi\)
−0.138383 + 0.990379i \(0.544190\pi\)
\(504\) −2.17845 + 3.77318i −0.0970358 + 0.168071i
\(505\) −11.7424 + 20.3385i −0.522531 + 0.905051i
\(506\) −3.92154 −0.174334
\(507\) 0 0
\(508\) 8.39373 0.372412
\(509\) −14.3056 + 24.7780i −0.634084 + 1.09827i 0.352624 + 0.935765i \(0.385289\pi\)
−0.986708 + 0.162501i \(0.948044\pi\)
\(510\) −1.06100 + 1.83770i −0.0469818 + 0.0813749i
\(511\) 0.815511 + 1.41251i 0.0360761 + 0.0624856i
\(512\) 1.00000 0.0441942
\(513\) −0.890084 1.54167i −0.0392982 0.0680664i
\(514\) 3.75302 + 6.50042i 0.165539 + 0.286721i
\(515\) −30.1129 −1.32693
\(516\) 3.69202 + 6.39477i 0.162532 + 0.281514i
\(517\) 1.03146 1.78654i 0.0453635 0.0785719i
\(518\) −8.44803 + 14.6324i −0.371185 + 0.642911i
\(519\) 4.17092 0.183083
\(520\) 0 0
\(521\) −17.1594 −0.751768 −0.375884 0.926667i \(-0.622661\pi\)
−0.375884 + 0.926667i \(0.622661\pi\)
\(522\) −3.46950 + 6.00935i −0.151856 + 0.263022i
\(523\) −8.25667 + 14.3010i −0.361039 + 0.625338i −0.988132 0.153607i \(-0.950911\pi\)
0.627093 + 0.778944i \(0.284245\pi\)
\(524\) 6.75182 + 11.6945i 0.294955 + 0.510877i
\(525\) −58.6209 −2.55842
\(526\) 6.11529 + 10.5920i 0.266639 + 0.461833i
\(527\) −0.549581 0.951903i −0.0239401 0.0414655i
\(528\) 1.15883 0.0504318
\(529\) 5.77413 + 10.0011i 0.251049 + 0.434830i
\(530\) −5.40366 + 9.35941i −0.234720 + 0.406547i
\(531\) 3.31551 5.74263i 0.143881 0.249209i
\(532\) −7.75600 −0.336265
\(533\) 0 0
\(534\) 0.835790 0.0361682
\(535\) −4.11811 + 7.13278i −0.178042 + 0.308377i
\(536\) 2.04892 3.54883i 0.0884997 0.153286i
\(537\) 11.4438 + 19.8213i 0.493838 + 0.855353i
\(538\) 2.71618 0.117103
\(539\) 6.94289 + 12.0254i 0.299051 + 0.517972i
\(540\) −2.14795 3.72036i −0.0924330 0.160099i
\(541\) −25.0858 −1.07852 −0.539260 0.842139i \(-0.681296\pi\)
−0.539260 + 0.842139i \(0.681296\pi\)
\(542\) −6.19687 10.7333i −0.266178 0.461034i
\(543\) 5.80194 10.0493i 0.248985 0.431255i
\(544\) −0.246980 + 0.427781i −0.0105892 + 0.0183410i
\(545\) 80.6258 3.45363
\(546\) 0 0
\(547\) 31.1594 1.33228 0.666140 0.745826i \(-0.267945\pi\)
0.666140 + 0.745826i \(0.267945\pi\)
\(548\) 2.00000 3.46410i 0.0854358 0.147979i
\(549\) −5.24698 + 9.08804i −0.223936 + 0.387868i
\(550\) 7.79590 + 13.5029i 0.332418 + 0.575765i
\(551\) −12.3526 −0.526238
\(552\) 1.69202 + 2.93067i 0.0720172 + 0.124737i
\(553\) −5.78418 10.0185i −0.245969 0.426030i
\(554\) −24.1280 −1.02510
\(555\) −8.32975 14.4275i −0.353578 0.612415i
\(556\) 7.51573 13.0176i 0.318738 0.552070i
\(557\) −1.98792 + 3.44318i −0.0842308 + 0.145892i −0.905063 0.425277i \(-0.860177\pi\)
0.820832 + 0.571169i \(0.193510\pi\)
\(558\) 2.22521 0.0942006
\(559\) 0 0
\(560\) −18.7168 −0.790928
\(561\) −0.286208 + 0.495727i −0.0120837 + 0.0209296i
\(562\) −6.41789 + 11.1161i −0.270723 + 0.468905i
\(563\) −0.301405 0.522049i −0.0127027 0.0220018i 0.859604 0.510961i \(-0.170710\pi\)
−0.872307 + 0.488959i \(0.837377\pi\)
\(564\) −1.78017 −0.0749586
\(565\) 22.3720 + 38.7494i 0.941195 + 1.63020i
\(566\) −2.82371 4.89081i −0.118689 0.205576i
\(567\) 4.35690 0.182972
\(568\) 4.69202 + 8.12682i 0.196873 + 0.340994i
\(569\) −1.10992 + 1.92243i −0.0465301 + 0.0805925i −0.888352 0.459162i \(-0.848150\pi\)
0.841822 + 0.539755i \(0.181483\pi\)
\(570\) 3.82371 6.62286i 0.160158 0.277401i
\(571\) 24.4155 1.02176 0.510878 0.859653i \(-0.329320\pi\)
0.510878 + 0.859653i \(0.329320\pi\)
\(572\) 0 0
\(573\) −16.6896 −0.697219
\(574\) −13.7627 + 23.8377i −0.574444 + 0.994967i
\(575\) −22.7657 + 39.4313i −0.949395 + 1.64440i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −20.7375 −0.863313 −0.431656 0.902038i \(-0.642071\pi\)
−0.431656 + 0.902038i \(0.642071\pi\)
\(578\) 8.37800 + 14.5111i 0.348479 + 0.603583i
\(579\) 4.82371 + 8.35491i 0.200466 + 0.347218i
\(580\) −29.8092 −1.23776
\(581\) −31.1048 53.8752i −1.29045 2.23512i
\(582\) −9.19687 + 15.9294i −0.381222 + 0.660296i
\(583\) −1.45766 + 2.52473i −0.0603699 + 0.104564i
\(584\) −0.374354 −0.0154909
\(585\) 0 0
\(586\) 21.3653 0.882591
\(587\) 5.68396 9.84490i 0.234602 0.406343i −0.724555 0.689217i \(-0.757955\pi\)
0.959157 + 0.282874i \(0.0912880\pi\)
\(588\) 5.99127 10.3772i 0.247076 0.427948i
\(589\) 1.98062 + 3.43054i 0.0816101 + 0.141353i
\(590\) 28.4862 1.17276
\(591\) 9.81916 + 17.0073i 0.403906 + 0.699586i
\(592\) −1.93900 3.35845i −0.0796925 0.138031i
\(593\) 36.7198 1.50790 0.753950 0.656932i \(-0.228146\pi\)
0.753950 + 0.656932i \(0.228146\pi\)
\(594\) −0.579417 1.00358i −0.0237738 0.0411774i
\(595\) 4.62266 8.00669i 0.189511 0.328242i
\(596\) −1.96346 + 3.40081i −0.0804264 + 0.139303i
\(597\) 18.4209 0.753916
\(598\) 0 0
\(599\) −47.4965 −1.94065 −0.970327 0.241798i \(-0.922263\pi\)
−0.970327 + 0.241798i \(0.922263\pi\)
\(600\) 6.72737 11.6521i 0.274644 0.475697i
\(601\) −3.87531 + 6.71224i −0.158077 + 0.273798i −0.934175 0.356814i \(-0.883863\pi\)
0.776098 + 0.630612i \(0.217196\pi\)
\(602\) −16.0858 27.8613i −0.655606 1.13554i
\(603\) −4.09783 −0.166877
\(604\) 4.81431 + 8.33864i 0.195892 + 0.339294i
\(605\) −20.7430 35.9279i −0.843321 1.46068i
\(606\) 5.46681 0.222074
\(607\) −1.82155 3.15502i −0.0739345 0.128058i 0.826688 0.562661i \(-0.190222\pi\)
−0.900622 + 0.434602i \(0.856889\pi\)
\(608\) 0.890084 1.54167i 0.0360977 0.0625230i
\(609\) 15.1163 26.1821i 0.612541 1.06095i
\(610\) −45.0810 −1.82528
\(611\) 0 0
\(612\) 0.493959 0.0199671
\(613\) 15.2131 26.3499i 0.614452 1.06426i −0.376028 0.926608i \(-0.622710\pi\)
0.990480 0.137654i \(-0.0439564\pi\)
\(614\) 14.4426 25.0154i 0.582858 1.00954i
\(615\) −13.5700 23.5040i −0.547196 0.947772i
\(616\) −5.04892 −0.203427
\(617\) −4.08277 7.07156i −0.164366 0.284690i 0.772064 0.635545i \(-0.219225\pi\)
−0.936430 + 0.350854i \(0.885891\pi\)
\(618\) 3.50484 + 6.07057i 0.140986 + 0.244194i
\(619\) 7.95646 0.319797 0.159899 0.987133i \(-0.448883\pi\)
0.159899 + 0.987133i \(0.448883\pi\)
\(620\) 4.77963 + 8.27857i 0.191955 + 0.332475i
\(621\) 1.69202 2.93067i 0.0678985 0.117604i
\(622\) −1.69202 + 2.93067i −0.0678439 + 0.117509i
\(623\) −3.64145 −0.145892
\(624\) 0 0
\(625\) 88.7561 3.55024
\(626\) −7.17510 + 12.4276i −0.286774 + 0.496708i
\(627\) 1.03146 1.78654i 0.0411925 0.0713475i
\(628\) 8.69202 + 15.0550i 0.346849 + 0.600761i
\(629\) 1.91557 0.0763790
\(630\) 9.35839 + 16.2092i 0.372847 + 0.645790i
\(631\) 7.61679 + 13.1927i 0.303219 + 0.525191i 0.976863 0.213865i \(-0.0686052\pi\)
−0.673644 + 0.739056i \(0.735272\pi\)
\(632\) 2.65519 0.105618
\(633\) 7.96077 + 13.7885i 0.316412 + 0.548042i
\(634\) 9.26659 16.0502i 0.368023 0.637435i
\(635\) 18.0293 31.2277i 0.715471 1.23923i
\(636\) 2.51573 0.0997552
\(637\) 0 0
\(638\) −8.04115 −0.318352
\(639\) 4.69202 8.12682i 0.185614 0.321492i
\(640\) 2.14795 3.72036i 0.0849051 0.147060i
\(641\) 7.09544 + 12.2897i 0.280253 + 0.485413i 0.971447 0.237257i \(-0.0762483\pi\)
−0.691194 + 0.722669i \(0.742915\pi\)
\(642\) 1.91723 0.0756671
\(643\) 11.2784 + 19.5348i 0.444778 + 0.770378i 0.998037 0.0626312i \(-0.0199492\pi\)
−0.553259 + 0.833010i \(0.686616\pi\)
\(644\) −7.37196 12.7686i −0.290496 0.503154i
\(645\) 31.7211 1.24902
\(646\) 0.439665 + 0.761522i 0.0172984 + 0.0299617i
\(647\) 18.4523 31.9604i 0.725436 1.25649i −0.233358 0.972391i \(-0.574971\pi\)
0.958794 0.284102i \(-0.0916953\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 7.68425 0.301633
\(650\) 0 0
\(651\) −9.69501 −0.379977
\(652\) −11.2349 + 19.4594i −0.439993 + 0.762089i
\(653\) 0.924764 1.60174i 0.0361888 0.0626808i −0.847364 0.531013i \(-0.821812\pi\)
0.883553 + 0.468332i \(0.155145\pi\)
\(654\) −9.38404 16.2536i −0.366945 0.635568i
\(655\) 58.0103 2.26665
\(656\) −3.15883 5.47126i −0.123332 0.213617i
\(657\) 0.187177 + 0.324200i 0.00730248 + 0.0126483i
\(658\) 7.75600 0.302361
\(659\) −9.13922 15.8296i −0.356013 0.616633i 0.631277 0.775557i \(-0.282531\pi\)
−0.987291 + 0.158924i \(0.949198\pi\)
\(660\) 2.48911 4.31127i 0.0968887 0.167816i
\(661\) 1.81700 3.14714i 0.0706732 0.122410i −0.828523 0.559955i \(-0.810819\pi\)
0.899197 + 0.437545i \(0.144152\pi\)
\(662\) 7.87800 0.306187
\(663\) 0 0
\(664\) 14.2784 0.554111
\(665\) −16.6595 + 28.8551i −0.646028 + 1.11895i
\(666\) −1.93900 + 3.35845i −0.0751348 + 0.130137i
\(667\) −11.7409 20.3359i −0.454611 0.787409i
\(668\) 0.835790 0.0323377
\(669\) −2.59179 4.48912i −0.100205 0.173559i
\(670\) −8.80194 15.2454i −0.340049 0.588981i
\(671\) −12.1608 −0.469461
\(672\) 2.17845 + 3.77318i 0.0840355 + 0.145554i
\(673\) 3.07391 5.32417i 0.118490 0.205232i −0.800679 0.599093i \(-0.795528\pi\)
0.919170 + 0.393862i \(0.128861\pi\)
\(674\) 6.86323 11.8875i 0.264362 0.457888i
\(675\) −13.4547 −0.517873
\(676\) 0 0
\(677\) −18.2892 −0.702911 −0.351455 0.936205i \(-0.614313\pi\)
−0.351455 + 0.936205i \(0.614313\pi\)
\(678\) 5.20775 9.02009i 0.200002 0.346414i
\(679\) 40.0698 69.4029i 1.53774 2.66344i
\(680\) 1.06100 + 1.83770i 0.0406875 + 0.0704727i
\(681\) −14.8877 −0.570498
\(682\) 1.28932 + 2.23317i 0.0493708 + 0.0855127i
\(683\) 1.79643 + 3.11151i 0.0687385 + 0.119059i 0.898346 0.439288i \(-0.144769\pi\)
−0.829608 + 0.558347i \(0.811436\pi\)
\(684\) −1.78017 −0.0680664
\(685\) −8.59179 14.8814i −0.328276 0.568590i
\(686\) −10.8542 + 18.8000i −0.414416 + 0.717789i
\(687\) 11.7289 20.3150i 0.447484 0.775065i
\(688\) 7.38404 0.281514
\(689\) 0 0
\(690\) 14.5375 0.553433
\(691\) −9.90946 + 17.1637i −0.376974 + 0.652938i −0.990620 0.136643i \(-0.956369\pi\)
0.613647 + 0.789581i \(0.289702\pi\)
\(692\) 2.08546 3.61212i 0.0792772 0.137312i
\(693\) 2.52446 + 4.37249i 0.0958963 + 0.166097i
\(694\) −4.85086 −0.184136
\(695\) −32.2868 55.9224i −1.22471 2.12126i
\(696\) 3.46950 + 6.00935i 0.131511 + 0.227784i
\(697\) 3.12067 0.118204
\(698\) 14.1739 + 24.5499i 0.536490 + 0.929228i
\(699\) −5.93900 + 10.2867i −0.224634 + 0.389077i
\(700\) −29.3104 + 50.7672i −1.10783 + 1.91882i
\(701\) 5.25608 0.198519 0.0992596 0.995062i \(-0.468353\pi\)
0.0992596 + 0.995062i \(0.468353\pi\)
\(702\) 0 0
\(703\) −6.90349 −0.260370
\(704\) 0.579417 1.00358i 0.0218376 0.0378238i
\(705\) −3.82371 + 6.62286i −0.144009 + 0.249431i
\(706\) 14.2228 + 24.6346i 0.535283 + 0.927137i
\(707\) −23.8183 −0.895781
\(708\) −3.31551 5.74263i −0.124605 0.215821i
\(709\) 13.0489 + 22.6014i 0.490062 + 0.848813i 0.999935 0.0114372i \(-0.00364066\pi\)
−0.509872 + 0.860250i \(0.670307\pi\)
\(710\) 40.3129 1.51292
\(711\) −1.32759 2.29946i −0.0497886 0.0862364i
\(712\) 0.417895 0.723815i 0.0156613 0.0271261i
\(713\) −3.76510 + 6.52135i −0.141004 + 0.244226i
\(714\) −2.15213 −0.0805414
\(715\) 0 0
\(716\) 22.8877 0.855353
\(717\) −12.6799 + 21.9623i −0.473541 + 0.820197i
\(718\) −5.61356 + 9.72298i −0.209496 + 0.362858i
\(719\) −25.4155 44.0209i −0.947838 1.64170i −0.749966 0.661476i \(-0.769930\pi\)
−0.197872 0.980228i \(-0.563403\pi\)
\(720\) −4.29590 −0.160099
\(721\) −15.2702 26.4488i −0.568694 0.985006i
\(722\) 7.91550 + 13.7101i 0.294584 + 0.510235i
\(723\) −12.0218 −0.447094
\(724\) −5.80194 10.0493i −0.215627 0.373477i
\(725\) −46.6812 + 80.8542i −1.73370 + 3.00285i
\(726\) −4.82855 + 8.36330i −0.179204 + 0.310391i
\(727\) −20.5042 −0.760460 −0.380230 0.924892i \(-0.624155\pi\)
−0.380230 + 0.924892i \(0.624155\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −0.804094 + 1.39273i −0.0297608 + 0.0515473i
\(731\) −1.82371 + 3.15875i −0.0674523 + 0.116831i
\(732\) 5.24698 + 9.08804i 0.193934 + 0.335903i
\(733\) −3.26205 −0.120486 −0.0602432 0.998184i \(-0.519188\pi\)
−0.0602432 + 0.998184i \(0.519188\pi\)
\(734\) −8.41335 14.5723i −0.310542 0.537875i
\(735\) −25.7379 44.5793i −0.949356 1.64433i
\(736\) 3.38404 0.124737
\(737\) −2.37435 4.11250i −0.0874605 0.151486i
\(738\) −3.15883 + 5.47126i −0.116278 + 0.201400i
\(739\) −16.4101 + 28.4232i −0.603656 + 1.04556i 0.388606 + 0.921404i \(0.372957\pi\)
−0.992262 + 0.124159i \(0.960377\pi\)
\(740\) −16.6595 −0.612415
\(741\) 0 0
\(742\) −10.9608 −0.402383
\(743\) 17.4765 30.2702i 0.641151 1.11051i −0.344026 0.938960i \(-0.611791\pi\)
0.985176 0.171545i \(-0.0548760\pi\)
\(744\) 1.11260 1.92709i 0.0407901 0.0706505i
\(745\) 8.43482 + 14.6095i 0.309028 + 0.535252i
\(746\) −26.5327 −0.971432
\(747\) −7.13922 12.3655i −0.261210 0.452430i
\(748\) 0.286208 + 0.495727i 0.0104648 + 0.0181256i
\(749\) −8.35317 −0.305218
\(750\) −18.1603 31.4546i −0.663121 1.14856i
\(751\) 5.08306 8.80413i 0.185484 0.321267i −0.758256 0.651957i \(-0.773948\pi\)
0.943739 + 0.330690i \(0.107281\pi\)
\(752\) −0.890084 + 1.54167i −0.0324580 + 0.0562189i
\(753\) 15.3448 0.559196
\(754\) 0 0
\(755\) 41.3636 1.50538
\(756\) 2.17845 3.77318i 0.0792294 0.137229i
\(757\) 1.23191 2.13374i 0.0447747 0.0775520i −0.842770 0.538275i \(-0.819076\pi\)
0.887544 + 0.460723i \(0.152410\pi\)
\(758\) −10.9879 19.0316i −0.399099 0.691260i
\(759\) 3.92154 0.142343
\(760\) −3.82371 6.62286i −0.138700 0.240236i
\(761\) 21.4034 + 37.0718i 0.775873 + 1.34385i 0.934302 + 0.356482i \(0.116024\pi\)
−0.158429 + 0.987370i \(0.550643\pi\)
\(762\) −8.39373 −0.304073
\(763\) 40.8853 + 70.8154i 1.48015 + 2.56369i
\(764\) −8.34481 + 14.4536i −0.301905 + 0.522914i
\(765\) 1.06100 1.83770i 0.0383605 0.0664423i
\(766\) −0.615957 −0.0222554
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −12.7017 + 22.0000i −0.458035 + 0.793341i −0.998857 0.0477967i \(-0.984780\pi\)
0.540822 + 0.841137i \(0.318113\pi\)
\(770\) −10.8448 + 18.7838i −0.390820 + 0.676920i
\(771\) −3.75302 6.50042i −0.135162 0.234107i
\(772\) 9.64742 0.347218
\(773\) −2.23945 3.87884i −0.0805473 0.139512i 0.822938 0.568131i \(-0.192333\pi\)
−0.903485 + 0.428619i \(0.859000\pi\)
\(774\) −3.69202 6.39477i −0.132707 0.229855i
\(775\) 29.9396 1.07546
\(776\) 9.19687 + 15.9294i 0.330148 + 0.571834i
\(777\) 8.44803 14.6324i 0.303071 0.524935i
\(778\) 17.7630 30.7664i 0.636835 1.10303i
\(779\) −11.2465 −0.402948
\(780\) 0 0
\(781\) 10.8745 0.389122
\(782\) −0.835790 + 1.44763i −0.0298878 + 0.0517671i
\(783\) 3.46950 6.00935i 0.123990 0.214757i
\(784\) −5.99127 10.3772i −0.213974 0.370614i
\(785\) 74.6801 2.66545
\(786\) −6.75182 11.6945i −0.240830 0.417129i
\(787\) −4.71917 8.17384i −0.168220 0.291366i 0.769574 0.638558i \(-0.220469\pi\)
−0.937794 + 0.347192i \(0.887135\pi\)
\(788\) 19.6383 0.699586
\(789\) −6.11529 10.5920i −0.217710 0.377085i
\(790\) 5.70320 9.87824i 0.202911 0.351452i
\(791\) −22.6896 + 39.2996i −0.806750 + 1.39733i
\(792\) −1.15883 −0.0411774
\(793\) 0 0
\(794\) −16.0785 −0.570603
\(795\) 5.40366 9.35941i 0.191648 0.331944i
\(796\) 9.21044 15.9529i 0.326455 0.565437i
\(797\) 12.6230 + 21.8636i 0.447128 + 0.774449i 0.998198 0.0600107i \(-0.0191135\pi\)
−0.551070 + 0.834459i \(0.685780\pi\)
\(798\) 7.75600 0.274560
\(799\) −0.439665 0.761522i −0.0155542 0.0269407i
\(800\) −6.72737 11.6521i −0.237848 0.411965i
\(801\) −0.835790 −0.0295312
\(802\) −11.4547 19.8402i −0.404481 0.700581i
\(803\) −0.216907 + 0.375694i −0.00765449 + 0.0132580i
\(804\) −2.04892 + 3.54883i −0.0722597 + 0.125158i
\(805\) −63.3384 −2.23238
\(806\) 0 0
\(807\) −2.71618 −0.0956142
\(808\) 2.73341 4.73440i 0.0961609 0.166556i
\(809\) −5.85325 + 10.1381i −0.205789 + 0.356437i −0.950384 0.311079i \(-0.899309\pi\)
0.744595 + 0.667517i \(0.232643\pi\)
\(810\) 2.14795 + 3.72036i 0.0754712 + 0.130720i
\(811\) 30.5628 1.07321 0.536603 0.843835i \(-0.319707\pi\)
0.536603 + 0.843835i \(0.319707\pi\)
\(812\) −15.1163 26.1821i −0.530476 0.918812i
\(813\) 6.19687 + 10.7333i 0.217334 + 0.376433i
\(814\) −4.49396 −0.157513
\(815\) 48.2640 + 83.5956i 1.69061 + 2.92823i
\(816\) 0.246980 0.427781i 0.00864602 0.0149753i
\(817\) 6.57242 11.3838i 0.229940 0.398267i
\(818\) −1.24698 −0.0435996
\(819\) 0 0
\(820\) −27.1400 −0.947772
\(821\) 11.2796 19.5369i 0.393662 0.681843i −0.599267 0.800549i \(-0.704541\pi\)
0.992929 + 0.118706i \(0.0378747\pi\)
\(822\) −2.00000 + 3.46410i −0.0697580 + 0.120824i
\(823\) 7.28836 + 12.6238i 0.254056 + 0.440039i 0.964639 0.263575i \(-0.0849018\pi\)
−0.710582 + 0.703614i \(0.751568\pi\)
\(824\) 7.00969 0.244194
\(825\) −7.79590 13.5029i −0.271418 0.470110i
\(826\) 14.4453 + 25.0201i 0.502618 + 0.870559i
\(827\) 20.3666 0.708216 0.354108 0.935205i \(-0.384785\pi\)
0.354108 + 0.935205i \(0.384785\pi\)
\(828\) −1.69202 2.93067i −0.0588018 0.101848i
\(829\) −16.2054 + 28.0685i −0.562835 + 0.974859i 0.434412 + 0.900714i \(0.356956\pi\)
−0.997247 + 0.0741452i \(0.976377\pi\)
\(830\) 30.6694 53.1209i 1.06455 1.84385i
\(831\) 24.1280 0.836990
\(832\) 0 0
\(833\) 5.91889 0.205077
\(834\) −7.51573 + 13.0176i −0.260248 + 0.450763i
\(835\) 1.79523 3.10943i 0.0621266 0.107606i
\(836\) −1.03146 1.78654i −0.0356738 0.0617888i
\(837\) −2.22521 −0.0769145
\(838\) −14.7315 25.5158i −0.508893 0.881428i
\(839\) 14.9705 + 25.9296i 0.516838 + 0.895189i 0.999809 + 0.0195528i \(0.00622426\pi\)
−0.482971 + 0.875636i \(0.660442\pi\)
\(840\) 18.7168 0.645790
\(841\) −9.57487 16.5842i −0.330168 0.571868i
\(842\) 8.67456 15.0248i 0.298945 0.517788i
\(843\) 6.41789 11.1161i 0.221044 0.382860i
\(844\) 15.9215 0.548042
\(845\) 0 0
\(846\) 1.78017 0.0612034
\(847\) 21.0375 36.4380i 0.722857 1.25203i
\(848\) 1.25786 2.17869i 0.0431953 0.0748164i
\(849\) 2.82371 + 4.89081i 0.0969094 + 0.167852i
\(850\) 6.64609 0.227959
\(851\) −6.56166 11.3651i −0.224931 0.389592i
\(852\) −4.69202 8.12682i −0.160746 0.278420i
\(853\) −41.8780 −1.43388 −0.716938 0.697137i \(-0.754457\pi\)
−0.716938 + 0.697137i \(0.754457\pi\)
\(854\) −22.8605 39.5956i −0.782272 1.35493i
\(855\) −3.82371 + 6.62286i −0.130768 + 0.226497i
\(856\) 0.958615 1.66037i 0.0327648 0.0567503i
\(857\) 25.2137 0.861284 0.430642 0.902523i \(-0.358287\pi\)
0.430642 + 0.902523i \(0.358287\pi\)
\(858\) 0 0
\(859\) −46.9939 −1.60341 −0.801705 0.597719i \(-0.796074\pi\)
−0.801705 + 0.597719i \(0.796074\pi\)
\(860\) 15.8605 27.4713i 0.540840 0.936762i
\(861\) 13.7627 23.8377i 0.469032 0.812387i
\(862\) −12.6920 21.9832i −0.432292 0.748752i
\(863\) −43.6969 −1.48746 −0.743730 0.668480i \(-0.766945\pi\)
−0.743730 + 0.668480i \(0.766945\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) −8.95891 15.5173i −0.304612 0.527604i
\(866\) 20.0054 0.679810
\(867\) −8.37800 14.5111i −0.284532 0.492824i
\(868\) −4.84750 + 8.39612i −0.164535 + 0.284983i
\(869\) 1.53846 2.66469i 0.0521887 0.0903934i
\(870\) 29.8092 1.01063
\(871\) 0 0
\(872\) −18.7681 −0.635568
\(873\) 9.19687 15.9294i 0.311267 0.539130i
\(874\) 3.01208 5.21708i 0.101885 0.176470i
\(875\) 79.1226 + 137.044i 2.67483 + 4.63295i
\(876\) 0.374354 0.0126483
\(877\) 6.44504 + 11.1631i 0.217634 + 0.376952i 0.954084 0.299539i \(-0.0968329\pi\)
−0.736450 + 0.676491i \(0.763500\pi\)
\(878\) −0.271971 0.471067i −0.00917857 0.0158977i
\(879\) −21.3653 −0.720632
\(880\) −2.48911 4.31127i −0.0839080 0.145333i
\(881\) 7.47889 12.9538i 0.251970 0.436425i −0.712098 0.702080i \(-0.752255\pi\)
0.964068 + 0.265655i \(0.0855881\pi\)
\(882\) −5.99127 + 10.3772i −0.201737 + 0.349418i
\(883\) −20.6896 −0.696261 −0.348131 0.937446i \(-0.613183\pi\)
−0.348131 + 0.937446i \(0.613183\pi\)
\(884\) 0 0
\(885\) −28.4862 −0.957553
\(886\) 9.06800 15.7062i 0.304645 0.527661i
\(887\) −12.0925 + 20.9448i −0.406025 + 0.703256i −0.994440 0.105303i \(-0.966419\pi\)
0.588415 + 0.808559i \(0.299752\pi\)
\(888\) 1.93900 + 3.35845i 0.0650686 + 0.112702i
\(889\) 36.5706 1.22654
\(890\) −1.79523 3.10943i −0.0601763 0.104228i
\(891\) 0.579417 + 1.00358i 0.0194112 + 0.0336212i
\(892\) −5.18359 −0.173559
\(893\) 1.58450 + 2.74443i 0.0530232 + 0.0918389i
\(894\) 1.96346 3.40081i 0.0656679 0.113740i
\(895\) 49.1616 85.1504i 1.64329 2.84626i
\(896\) 4.35690 0.145554
\(897\) 0 0
\(898\) 29.3793 0.980399
\(899\) −7.72037 + 13.3721i −0.257489 + 0.445983i
\(900\) −6.72737 + 11.6521i −0.224246 + 0.388405i
\(901\) 0.621334 + 1.07618i 0.0206996 + 0.0358528i
\(902\) −7.32113 −0.243767
\(903\) 16.0858 + 27.8613i 0.535300 + 0.927167i
\(904\) −5.20775 9.02009i −0.173207 0.300004i
\(905\) −49.8491 −1.65704
\(906\) −4.81431 8.33864i −0.159945 0.277033i
\(907\) −13.6353 + 23.6171i −0.452754 + 0.784193i −0.998556 0.0537214i \(-0.982892\pi\)
0.545802 + 0.837914i \(0.316225\pi\)
\(908\) −7.44385 + 12.8931i −0.247033 + 0.427873i
\(909\) −5.46681 −0.181323
\(910\) 0 0
\(911\) 45.2766 1.50008 0.750041 0.661391i \(-0.230034\pi\)
0.750041 + 0.661391i \(0.230034\pi\)
\(912\) −0.890084 + 1.54167i −0.0294736 + 0.0510498i
\(913\) 8.27317 14.3295i 0.273802 0.474239i
\(914\) 4.17360 + 7.22889i 0.138051 + 0.239111i
\(915\) 45.0810 1.49033
\(916\) −11.7289 20.3150i −0.387532 0.671226i
\(917\) 29.4170 + 50.9517i 0.971435 + 1.68257i
\(918\) −0.493959 −0.0163031
\(919\) −2.34063 4.05410i −0.0772104 0.133732i 0.824835 0.565374i \(-0.191268\pi\)
−0.902045 + 0.431641i \(0.857935\pi\)
\(920\) 7.26875 12.5898i 0.239644 0.415075i
\(921\) −14.4426 + 25.0154i −0.475901 + 0.824286i
\(922\) 21.4969 0.707964
\(923\) 0 0
\(924\) 5.04892 0.166097
\(925\) −26.0887 + 45.1870i −0.857792 + 1.48574i
\(926\) −13.0858 + 22.6652i −0.430025 + 0.744824i
\(927\) −3.50484 6.07057i −0.115114 0.199384i
\(928\) 6.93900 0.227784
\(929\) −1.64550 2.85008i −0.0539870 0.0935082i 0.837769 0.546025i \(-0.183860\pi\)
−0.891756 + 0.452517i \(0.850526\pi\)
\(930\) −4.77963 8.27857i −0.156730 0.271465i
\(931\) −21.3309 −0.699093
\(932\) 5.93900 + 10.2867i 0.194538 + 0.336950i
\(933\) 1.69202 2.93067i 0.0553943 0.0959457i
\(934\) 4.90635 8.49804i 0.160541 0.278064i
\(935\) 2.45904 0.0804193
\(936\) 0 0
\(937\) 6.67563 0.218083 0.109042 0.994037i \(-0.465222\pi\)
0.109042 + 0.994037i \(0.465222\pi\)
\(938\) 8.92692 15.4619i 0.291474 0.504848i
\(939\) 7.17510 12.4276i 0.234150 0.405560i
\(940\) 3.82371 + 6.62286i 0.124716 + 0.216014i
\(941\) 38.9778 1.27064 0.635319 0.772250i \(-0.280869\pi\)
0.635319 + 0.772250i \(0.280869\pi\)
\(942\) −8.69202 15.0550i −0.283201 0.490519i
\(943\) −10.6896 18.5150i −0.348102 0.602931i
\(944\) −6.63102 −0.215821
\(945\) −9.35839 16.2092i −0.304428 0.527285i
\(946\) 4.27844 7.41047i 0.139104 0.240935i
\(947\) 20.3339 35.2194i 0.660764 1.14448i −0.319651 0.947535i \(-0.603566\pi\)
0.980415 0.196941i \(-0.0631009\pi\)
\(948\) −2.65519 −0.0862364
\(949\) 0 0
\(950\) −23.9517 −0.777095
\(951\) −9.26659 + 16.0502i −0.300490 + 0.520464i
\(952\) −1.07606 + 1.86380i −0.0348754 + 0.0604060i
\(953\) 22.4252 + 38.8416i 0.726423 + 1.25820i 0.958386 + 0.285477i \(0.0921520\pi\)
−0.231962 + 0.972725i \(0.574515\pi\)
\(954\) −2.51573 −0.0814497
\(955\) 35.8485 + 62.0914i 1.16003 + 2.00923i
\(956\) 12.6799 + 21.9623i 0.410099 + 0.710312i
\(957\) 8.04115 0.259933
\(958\) −8.64071 14.9662i −0.279169 0.483534i
\(959\) 8.71379 15.0927i 0.281383 0.487370i
\(960\) −2.14795 + 3.72036i −0.0693247 + 0.120074i
\(961\) −26.0484 −0.840272
\(962\) 0 0
\(963\) −1.91723 −0.0617819
\(964\) −6.01089 + 10.4112i −0.193598 + 0.335321i
\(965\) 20.7222 35.8918i 0.667070 1.15540i
\(966\) 7.37196 + 12.7686i 0.237189 + 0.410823i
\(967\) −22.4704 −0.722599 −0.361299 0.932450i \(-0.617667\pi\)
−0.361299 + 0.932450i \(0.617667\pi\)
\(968\) 4.82855 + 8.36330i 0.155196 + 0.268807i
\(969\) −0.439665 0.761522i −0.0141241 0.0244636i
\(970\) 79.0176 2.53710
\(971\) −16.9218 29.3095i −0.543048 0.940586i −0.998727 0.0504421i \(-0.983937\pi\)
0.455679 0.890144i \(-0.349396\pi\)
\(972\) 0.500000 0.866025i 0.0160375 0.0277778i
\(973\) 32.7453 56.7164i 1.04976 1.81825i
\(974\) −31.6886 −1.01537
\(975\) 0 0
\(976\) 10.4940 0.335903
\(977\) 13.6069 23.5678i 0.435322 0.754000i −0.562000 0.827137i \(-0.689968\pi\)
0.997322 + 0.0731375i \(0.0233012\pi\)
\(978\) 11.2349 19.4594i 0.359252 0.622243i
\(979\) −0.484271 0.838781i −0.0154774 0.0268076i
\(980\) −51.4758 −1.64433
\(981\) 9.38404 + 16.2536i 0.299609 + 0.518939i
\(982\) −1.15183 1.99503i −0.0367565 0.0636641i
\(983\) 50.9965 1.62654 0.813269 0.581889i \(-0.197686\pi\)
0.813269 + 0.581889i \(0.197686\pi\)
\(984\) 3.15883 + 5.47126i 0.100700 + 0.174417i
\(985\) 42.1821 73.0615i 1.34403 2.32793i
\(986\) −1.71379 + 2.96837i −0.0545782 + 0.0945323i
\(987\) −7.75600 −0.246876
\(988\) 0 0
\(989\) 24.9879 0.794570
\(990\) −2.48911 + 4.31127i −0.0791093 + 0.137021i
\(991\) 12.1402 21.0274i 0.385645 0.667958i −0.606213 0.795302i \(-0.707312\pi\)
0.991859 + 0.127345i \(0.0406455\pi\)
\(992\) −1.11260 1.92709i −0.0353252 0.0611851i
\(993\) −7.87800 −0.250001
\(994\) 20.4426 + 35.4077i 0.648401 + 1.12306i
\(995\) −39.5671 68.5322i −1.25436 2.17262i
\(996\) −14.2784 −0.452430
\(997\) 2.03252 + 3.52043i 0.0643707 + 0.111493i 0.896415 0.443216i \(-0.146163\pi\)
−0.832044 + 0.554710i \(0.812829\pi\)
\(998\) 0 0
\(999\) 1.93900 3.35845i 0.0613473 0.106257i
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 1014.2.e.l.529.1 6
13.2 odd 12 1014.2.i.h.361.3 12
13.3 even 3 inner 1014.2.e.l.991.1 6
13.4 even 6 1014.2.a.l.1.3 3
13.5 odd 4 1014.2.i.h.823.6 12
13.6 odd 12 1014.2.b.f.337.3 6
13.7 odd 12 1014.2.b.f.337.4 6
13.8 odd 4 1014.2.i.h.823.1 12
13.9 even 3 1014.2.a.n.1.1 yes 3
13.10 even 6 1014.2.e.n.991.3 6
13.11 odd 12 1014.2.i.h.361.4 12
13.12 even 2 1014.2.e.n.529.3 6
39.17 odd 6 3042.2.a.bh.1.1 3
39.20 even 12 3042.2.b.o.1351.3 6
39.32 even 12 3042.2.b.o.1351.4 6
39.35 odd 6 3042.2.a.ba.1.3 3
52.35 odd 6 8112.2.a.cm.1.1 3
52.43 odd 6 8112.2.a.cj.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1014.2.a.l.1.3 3 13.4 even 6
1014.2.a.n.1.1 yes 3 13.9 even 3
1014.2.b.f.337.3 6 13.6 odd 12
1014.2.b.f.337.4 6 13.7 odd 12
1014.2.e.l.529.1 6 1.1 even 1 trivial
1014.2.e.l.991.1 6 13.3 even 3 inner
1014.2.e.n.529.3 6 13.12 even 2
1014.2.e.n.991.3 6 13.10 even 6
1014.2.i.h.361.3 12 13.2 odd 12
1014.2.i.h.361.4 12 13.11 odd 12
1014.2.i.h.823.1 12 13.8 odd 4
1014.2.i.h.823.6 12 13.5 odd 4
3042.2.a.ba.1.3 3 39.35 odd 6
3042.2.a.bh.1.1 3 39.17 odd 6
3042.2.b.o.1351.3 6 39.20 even 12
3042.2.b.o.1351.4 6 39.32 even 12
8112.2.a.cj.1.3 3 52.43 odd 6
8112.2.a.cm.1.1 3 52.35 odd 6