Basic properties
| Modulus: | \(4010\) | |
| Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2005}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4010.bp
\(\chi_{4010}(49,\cdot)\) \(\chi_{4010}(69,\cdot)\) \(\chi_{4010}(99,\cdot)\) \(\chi_{4010}(149,\cdot)\) \(\chi_{4010}(419,\cdot)\) \(\chi_{4010}(619,\cdot)\) \(\chi_{4010}(689,\cdot)\) \(\chi_{4010}(709,\cdot)\) \(\chi_{4010}(859,\cdot)\) \(\chi_{4010}(999,\cdot)\) \(\chi_{4010}(1109,\cdot)\) \(\chi_{4010}(1139,\cdot)\) \(\chi_{4010}(1199,\cdot)\) \(\chi_{4010}(1319,\cdot)\) \(\chi_{4010}(1359,\cdot)\) \(\chi_{4010}(1849,\cdot)\) \(\chi_{4010}(1889,\cdot)\) \(\chi_{4010}(2009,\cdot)\) \(\chi_{4010}(2069,\cdot)\) \(\chi_{4010}(2099,\cdot)\) \(\chi_{4010}(2209,\cdot)\) \(\chi_{4010}(2349,\cdot)\) \(\chi_{4010}(2499,\cdot)\) \(\chi_{4010}(2519,\cdot)\) \(\chi_{4010}(2589,\cdot)\) \(\chi_{4010}(2789,\cdot)\) \(\chi_{4010}(3059,\cdot)\) \(\chi_{4010}(3109,\cdot)\) \(\chi_{4010}(3139,\cdot)\) \(\chi_{4010}(3159,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2407,3211)\) → \((-1,e\left(\frac{31}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4010 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{43}{100}\right)\) |