Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(400\) | 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 4001.s
\(\chi_{4001}(58,\cdot)\) \(\chi_{4001}(59,\cdot)\) \(\chi_{4001}(63,\cdot)\) \(\chi_{4001}(69,\cdot)\) \(\chi_{4001}(127,\cdot)\) \(\chi_{4001}(129,\cdot)\) \(\chi_{4001}(132,\cdot)\) \(\chi_{4001}(144,\cdot)\) \(\chi_{4001}(217,\cdot)\) \(\chi_{4001}(223,\cdot)\) \(\chi_{4001}(241,\cdot)\) \(\chi_{4001}(290,\cdot)\) \(\chi_{4001}(295,\cdot)\) \(\chi_{4001}(303,\cdot)\) \(\chi_{4001}(315,\cdot)\) \(\chi_{4001}(329,\cdot)\) \(\chi_{4001}(345,\cdot)\) \(\chi_{4001}(394,\cdot)\) \(\chi_{4001}(397,\cdot)\) \(\chi_{4001}(401,\cdot)\) \(\chi_{4001}(409,\cdot)\) \(\chi_{4001}(427,\cdot)\) \(\chi_{4001}(429,\cdot)\) \(\chi_{4001}(581,\cdot)\) \(\chi_{4001}(605,\cdot)\) \(\chi_{4001}(607,\cdot)\) \(\chi_{4001}(623,\cdot)\) \(\chi_{4001}(645,\cdot)\) \(\chi_{4001}(660,\cdot)\) \(\chi_{4001}(684,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{400})$ |
| Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{31}{400}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(58, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{31}{400}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{83}{400}\right)\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{31}{200}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{7}{16}\right)\) |