Basic properties
| Modulus: | \(4010\) | |
| Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2005}(153,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4010.bm
\(\chi_{4010}(153,\cdot)\) \(\chi_{4010}(157,\cdot)\) \(\chi_{4010}(243,\cdot)\) \(\chi_{4010}(253,\cdot)\) \(\chi_{4010}(317,\cdot)\) \(\chi_{4010}(353,\cdot)\) \(\chi_{4010}(477,\cdot)\) \(\chi_{4010}(613,\cdot)\) \(\chi_{4010}(647,\cdot)\) \(\chi_{4010}(683,\cdot)\) \(\chi_{4010}(957,\cdot)\) \(\chi_{4010}(973,\cdot)\) \(\chi_{4010}(1127,\cdot)\) \(\chi_{4010}(1287,\cdot)\) \(\chi_{4010}(1433,\cdot)\) \(\chi_{4010}(1447,\cdot)\) \(\chi_{4010}(1637,\cdot)\) \(\chi_{4010}(1723,\cdot)\) \(\chi_{4010}(1793,\cdot)\) \(\chi_{4010}(1897,\cdot)\) \(\chi_{4010}(1937,\cdot)\) \(\chi_{4010}(2053,\cdot)\) \(\chi_{4010}(2147,\cdot)\) \(\chi_{4010}(2153,\cdot)\) \(\chi_{4010}(2163,\cdot)\) \(\chi_{4010}(2253,\cdot)\) \(\chi_{4010}(2833,\cdot)\) \(\chi_{4010}(3467,\cdot)\) \(\chi_{4010}(3583,\cdot)\) \(\chi_{4010}(3677,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2407,3211)\) → \((-i,e\left(\frac{77}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4010 }(153, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) |