Basic properties
| Modulus: | \(8020\) | |
| 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 8020.dd
\(\chi_{8020}(49,\cdot)\) \(\chi_{8020}(69,\cdot)\) \(\chi_{8020}(149,\cdot)\) \(\chi_{8020}(689,\cdot)\) \(\chi_{8020}(709,\cdot)\) \(\chi_{8020}(1109,\cdot)\) \(\chi_{8020}(1849,\cdot)\) \(\chi_{8020}(1889,\cdot)\) \(\chi_{8020}(2009,\cdot)\) \(\chi_{8020}(2069,\cdot)\) \(\chi_{8020}(2209,\cdot)\) \(\chi_{8020}(2349,\cdot)\) \(\chi_{8020}(2589,\cdot)\) \(\chi_{8020}(2789,\cdot)\) \(\chi_{8020}(3109,\cdot)\) \(\chi_{8020}(3289,\cdot)\) \(\chi_{8020}(3329,\cdot)\) \(\chi_{8020}(3509,\cdot)\) \(\chi_{8020}(3709,\cdot)\) \(\chi_{8020}(3889,\cdot)\) \(\chi_{8020}(3929,\cdot)\) \(\chi_{8020}(4109,\cdot)\) \(\chi_{8020}(4429,\cdot)\) \(\chi_{8020}(4629,\cdot)\) \(\chi_{8020}(4869,\cdot)\) \(\chi_{8020}(5009,\cdot)\) \(\chi_{8020}(5149,\cdot)\) \(\chi_{8020}(5209,\cdot)\) \(\chi_{8020}(5329,\cdot)\) \(\chi_{8020}(5369,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((4011,6417,7221)\) → \((1,-1,e\left(\frac{31}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 8020 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{43}{100}\right)\) |