Basic properties
| Modulus: | \(1002\) | |
| Conductor: | \(501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{501}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1002.f
\(\chi_{1002}(5,\cdot)\) \(\chi_{1002}(17,\cdot)\) \(\chi_{1002}(23,\cdot)\) \(\chi_{1002}(35,\cdot)\) \(\chi_{1002}(41,\cdot)\) \(\chi_{1002}(53,\cdot)\) \(\chi_{1002}(59,\cdot)\) \(\chi_{1002}(71,\cdot)\) \(\chi_{1002}(83,\cdot)\) \(\chi_{1002}(95,\cdot)\) \(\chi_{1002}(101,\cdot)\) \(\chi_{1002}(113,\cdot)\) \(\chi_{1002}(119,\cdot)\) \(\chi_{1002}(125,\cdot)\) \(\chi_{1002}(131,\cdot)\) \(\chi_{1002}(143,\cdot)\) \(\chi_{1002}(149,\cdot)\) \(\chi_{1002}(155,\cdot)\) \(\chi_{1002}(161,\cdot)\) \(\chi_{1002}(197,\cdot)\) \(\chi_{1002}(227,\cdot)\) \(\chi_{1002}(245,\cdot)\) \(\chi_{1002}(257,\cdot)\) \(\chi_{1002}(269,\cdot)\) \(\chi_{1002}(287,\cdot)\) \(\chi_{1002}(305,\cdot)\) \(\chi_{1002}(323,\cdot)\) \(\chi_{1002}(347,\cdot)\) \(\chi_{1002}(371,\cdot)\) \(\chi_{1002}(377,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,673)\) → \((-1,e\left(\frac{1}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1002 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{42}{83}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{111}{166}\right)\) | \(e\left(\frac{103}{166}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{29}{83}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{1}{83}\right)\) | \(e\left(\frac{67}{166}\right)\) | \(e\left(\frac{45}{83}\right)\) |