Basic properties
Modulus: | \(8100\) | |
Conductor: | \(405\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{405}(32,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8100.cy
\(\chi_{8100}(257,\cdot)\) \(\chi_{8100}(293,\cdot)\) \(\chi_{8100}(857,\cdot)\) \(\chi_{8100}(893,\cdot)\) \(\chi_{8100}(1157,\cdot)\) \(\chi_{8100}(1193,\cdot)\) \(\chi_{8100}(1757,\cdot)\) \(\chi_{8100}(1793,\cdot)\) \(\chi_{8100}(2057,\cdot)\) \(\chi_{8100}(2093,\cdot)\) \(\chi_{8100}(2657,\cdot)\) \(\chi_{8100}(2693,\cdot)\) \(\chi_{8100}(2957,\cdot)\) \(\chi_{8100}(2993,\cdot)\) \(\chi_{8100}(3557,\cdot)\) \(\chi_{8100}(3593,\cdot)\) \(\chi_{8100}(3857,\cdot)\) \(\chi_{8100}(3893,\cdot)\) \(\chi_{8100}(4457,\cdot)\) \(\chi_{8100}(4493,\cdot)\) \(\chi_{8100}(4757,\cdot)\) \(\chi_{8100}(4793,\cdot)\) \(\chi_{8100}(5357,\cdot)\) \(\chi_{8100}(5393,\cdot)\) \(\chi_{8100}(5657,\cdot)\) \(\chi_{8100}(5693,\cdot)\) \(\chi_{8100}(6257,\cdot)\) \(\chi_{8100}(6293,\cdot)\) \(\chi_{8100}(6557,\cdot)\) \(\chi_{8100}(6593,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((4051,6401,7777)\) → \((1,e\left(\frac{5}{54}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 8100 }(2057, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{53}{108}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{83}{108}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{49}{54}\right)\) |