Basic properties
Modulus: | \(2004\) | |
Conductor: | \(2004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2004.o
\(\chi_{2004}(11,\cdot)\) \(\chi_{2004}(47,\cdot)\) \(\chi_{2004}(107,\cdot)\) \(\chi_{2004}(179,\cdot)\) \(\chi_{2004}(191,\cdot)\) \(\chi_{2004}(203,\cdot)\) \(\chi_{2004}(215,\cdot)\) \(\chi_{2004}(239,\cdot)\) \(\chi_{2004}(251,\cdot)\) \(\chi_{2004}(263,\cdot)\) \(\chi_{2004}(275,\cdot)\) \(\chi_{2004}(299,\cdot)\) \(\chi_{2004}(311,\cdot)\) \(\chi_{2004}(359,\cdot)\) \(\chi_{2004}(383,\cdot)\) \(\chi_{2004}(395,\cdot)\) \(\chi_{2004}(419,\cdot)\) \(\chi_{2004}(431,\cdot)\) \(\chi_{2004}(455,\cdot)\) \(\chi_{2004}(467,\cdot)\) \(\chi_{2004}(491,\cdot)\) \(\chi_{2004}(503,\cdot)\) \(\chi_{2004}(515,\cdot)\) \(\chi_{2004}(539,\cdot)\) \(\chi_{2004}(551,\cdot)\) \(\chi_{2004}(563,\cdot)\) \(\chi_{2004}(599,\cdot)\) \(\chi_{2004}(623,\cdot)\) \(\chi_{2004}(671,\cdot)\) \(\chi_{2004}(695,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((1003,1337,673)\) → \((-1,-1,e\left(\frac{44}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2004 }(215, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{166}\right)\) | \(e\left(\frac{9}{166}\right)\) | \(e\left(\frac{70}{83}\right)\) | \(e\left(\frac{50}{83}\right)\) | \(e\left(\frac{99}{166}\right)\) | \(e\left(\frac{41}{166}\right)\) | \(e\left(\frac{40}{83}\right)\) | \(e\left(\frac{5}{83}\right)\) | \(e\left(\frac{3}{166}\right)\) | \(e\left(\frac{35}{166}\right)\) |