Basic properties
Modulus: | \(8470\) | |
Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{605}(14,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.cv
\(\chi_{8470}(169,\cdot)\) \(\chi_{8470}(379,\cdot)\) \(\chi_{8470}(449,\cdot)\) \(\chi_{8470}(939,\cdot)\) \(\chi_{8470}(1149,\cdot)\) \(\chi_{8470}(1499,\cdot)\) \(\chi_{8470}(1709,\cdot)\) \(\chi_{8470}(1919,\cdot)\) \(\chi_{8470}(1989,\cdot)\) \(\chi_{8470}(2269,\cdot)\) \(\chi_{8470}(2479,\cdot)\) \(\chi_{8470}(2759,\cdot)\) \(\chi_{8470}(3039,\cdot)\) \(\chi_{8470}(3249,\cdot)\) \(\chi_{8470}(3459,\cdot)\) \(\chi_{8470}(3529,\cdot)\) \(\chi_{8470}(3809,\cdot)\) \(\chi_{8470}(4019,\cdot)\) \(\chi_{8470}(4229,\cdot)\) \(\chi_{8470}(4299,\cdot)\) \(\chi_{8470}(4579,\cdot)\) \(\chi_{8470}(4789,\cdot)\) \(\chi_{8470}(4999,\cdot)\) \(\chi_{8470}(5069,\cdot)\) \(\chi_{8470}(5349,\cdot)\) \(\chi_{8470}(5559,\cdot)\) \(\chi_{8470}(5769,\cdot)\) \(\chi_{8470}(5839,\cdot)\) \(\chi_{8470}(6119,\cdot)\) \(\chi_{8470}(6329,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-1,1,e\left(\frac{4}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(3039, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) |