Basic properties
| Modulus: | \(2004\) | |
| Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{167}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2004.m
\(\chi_{2004}(13,\cdot)\) \(\chi_{2004}(37,\cdot)\) \(\chi_{2004}(73,\cdot)\) \(\chi_{2004}(109,\cdot)\) \(\chi_{2004}(145,\cdot)\) \(\chi_{2004}(193,\cdot)\) \(\chi_{2004}(241,\cdot)\) \(\chi_{2004}(253,\cdot)\) \(\chi_{2004}(277,\cdot)\) \(\chi_{2004}(301,\cdot)\) \(\chi_{2004}(313,\cdot)\) \(\chi_{2004}(325,\cdot)\) \(\chi_{2004}(349,\cdot)\) \(\chi_{2004}(373,\cdot)\) \(\chi_{2004}(385,\cdot)\) \(\chi_{2004}(445,\cdot)\) \(\chi_{2004}(457,\cdot)\) \(\chi_{2004}(469,\cdot)\) \(\chi_{2004}(493,\cdot)\) \(\chi_{2004}(541,\cdot)\) \(\chi_{2004}(553,\cdot)\) \(\chi_{2004}(637,\cdot)\) \(\chi_{2004}(649,\cdot)\) \(\chi_{2004}(661,\cdot)\) \(\chi_{2004}(673,\cdot)\) \(\chi_{2004}(685,\cdot)\) \(\chi_{2004}(709,\cdot)\) \(\chi_{2004}(721,\cdot)\) \(\chi_{2004}(769,\cdot)\) \(\chi_{2004}(781,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((1003,1337,673)\) → \((1,1,e\left(\frac{103}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2004 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{166}\right)\) | \(e\left(\frac{18}{83}\right)\) | \(e\left(\frac{31}{83}\right)\) | \(e\left(\frac{151}{166}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{82}{83}\right)\) | \(e\left(\frac{71}{166}\right)\) | \(e\left(\frac{20}{83}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{70}{83}\right)\) |