Basic properties
| Modulus: | \(8035\) | |
| Conductor: | \(1607\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(73\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1607}(96,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8035.m
\(\chi_{8035}(96,\cdot)\) \(\chi_{8035}(286,\cdot)\) \(\chi_{8035}(296,\cdot)\) \(\chi_{8035}(381,\cdot)\) \(\chi_{8035}(441,\cdot)\) \(\chi_{8035}(531,\cdot)\) \(\chi_{8035}(736,\cdot)\) \(\chi_{8035}(886,\cdot)\) \(\chi_{8035}(911,\cdot)\) \(\chi_{8035}(1156,\cdot)\) \(\chi_{8035}(1181,\cdot)\) \(\chi_{8035}(1261,\cdot)\) \(\chi_{8035}(1436,\cdot)\) \(\chi_{8035}(1446,\cdot)\) \(\chi_{8035}(1586,\cdot)\) \(\chi_{8035}(1641,\cdot)\) \(\chi_{8035}(1686,\cdot)\) \(\chi_{8035}(1816,\cdot)\) \(\chi_{8035}(1976,\cdot)\) \(\chi_{8035}(2161,\cdot)\) \(\chi_{8035}(2221,\cdot)\) \(\chi_{8035}(2316,\cdot)\) \(\chi_{8035}(2526,\cdot)\) \(\chi_{8035}(2561,\cdot)\) \(\chi_{8035}(2686,\cdot)\) \(\chi_{8035}(2766,\cdot)\) \(\chi_{8035}(2921,\cdot)\) \(\chi_{8035}(3051,\cdot)\) \(\chi_{8035}(3176,\cdot)\) \(\chi_{8035}(3296,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{73})$ |
| Fixed field: | Number field defined by a degree 73 polynomial |
Values on generators
\((4822,4826)\) → \((1,e\left(\frac{30}{73}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8035 }(96, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{73}\right)\) | \(e\left(\frac{45}{73}\right)\) | \(e\left(\frac{18}{73}\right)\) | \(e\left(\frac{54}{73}\right)\) | \(e\left(\frac{41}{73}\right)\) | \(e\left(\frac{27}{73}\right)\) | \(e\left(\frac{17}{73}\right)\) | \(e\left(\frac{58}{73}\right)\) | \(e\left(\frac{63}{73}\right)\) | \(e\left(\frac{9}{73}\right)\) |