Basic properties
Modulus: | \(4008\) | |
Conductor: | \(4008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.y
\(\chi_{4008}(5,\cdot)\) \(\chi_{4008}(53,\cdot)\) \(\chi_{4008}(101,\cdot)\) \(\chi_{4008}(125,\cdot)\) \(\chi_{4008}(149,\cdot)\) \(\chi_{4008}(197,\cdot)\) \(\chi_{4008}(245,\cdot)\) \(\chi_{4008}(269,\cdot)\) \(\chi_{4008}(389,\cdot)\) \(\chi_{4008}(413,\cdot)\) \(\chi_{4008}(437,\cdot)\) \(\chi_{4008}(485,\cdot)\) \(\chi_{4008}(581,\cdot)\) \(\chi_{4008}(605,\cdot)\) \(\chi_{4008}(773,\cdot)\) \(\chi_{4008}(797,\cdot)\) \(\chi_{4008}(821,\cdot)\) \(\chi_{4008}(845,\cdot)\) \(\chi_{4008}(869,\cdot)\) \(\chi_{4008}(917,\cdot)\) \(\chi_{4008}(941,\cdot)\) \(\chi_{4008}(1037,\cdot)\) \(\chi_{4008}(1061,\cdot)\) \(\chi_{4008}(1085,\cdot)\) \(\chi_{4008}(1133,\cdot)\) \(\chi_{4008}(1157,\cdot)\) \(\chi_{4008}(1229,\cdot)\) \(\chi_{4008}(1325,\cdot)\) \(\chi_{4008}(1349,\cdot)\) \(\chi_{4008}(1373,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((1,-1,-1,e\left(\frac{149}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(941, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{166}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{11}{83}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{93}{166}\right)\) | \(e\left(\frac{30}{83}\right)\) | \(e\left(\frac{66}{83}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{65}{83}\right)\) |