Basic properties
Modulus: | \(8640\) | |
Conductor: | \(4320\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4320}(2819,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8640.ho
\(\chi_{8640}(119,\cdot)\) \(\chi_{8640}(599,\cdot)\) \(\chi_{8640}(839,\cdot)\) \(\chi_{8640}(1319,\cdot)\) \(\chi_{8640}(1559,\cdot)\) \(\chi_{8640}(2039,\cdot)\) \(\chi_{8640}(2279,\cdot)\) \(\chi_{8640}(2759,\cdot)\) \(\chi_{8640}(2999,\cdot)\) \(\chi_{8640}(3479,\cdot)\) \(\chi_{8640}(3719,\cdot)\) \(\chi_{8640}(4199,\cdot)\) \(\chi_{8640}(4439,\cdot)\) \(\chi_{8640}(4919,\cdot)\) \(\chi_{8640}(5159,\cdot)\) \(\chi_{8640}(5639,\cdot)\) \(\chi_{8640}(5879,\cdot)\) \(\chi_{8640}(6359,\cdot)\) \(\chi_{8640}(6599,\cdot)\) \(\chi_{8640}(7079,\cdot)\) \(\chi_{8640}(7319,\cdot)\) \(\chi_{8640}(7799,\cdot)\) \(\chi_{8640}(8039,\cdot)\) \(\chi_{8640}(8519,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,3781,6401,3457)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{13}{18}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 8640 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{19}{36}\right)\) |