Basic properties
Modulus: | \(8470\) | |
Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4235}(1203,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.df
\(\chi_{8470}(97,\cdot)\) \(\chi_{8470}(223,\cdot)\) \(\chi_{8470}(377,\cdot)\) \(\chi_{8470}(433,\cdot)\) \(\chi_{8470}(587,\cdot)\) \(\chi_{8470}(643,\cdot)\) \(\chi_{8470}(713,\cdot)\) \(\chi_{8470}(797,\cdot)\) \(\chi_{8470}(867,\cdot)\) \(\chi_{8470}(993,\cdot)\) \(\chi_{8470}(1147,\cdot)\) \(\chi_{8470}(1203,\cdot)\) \(\chi_{8470}(1357,\cdot)\) \(\chi_{8470}(1413,\cdot)\) \(\chi_{8470}(1483,\cdot)\) \(\chi_{8470}(1567,\cdot)\) \(\chi_{8470}(1637,\cdot)\) \(\chi_{8470}(1763,\cdot)\) \(\chi_{8470}(1917,\cdot)\) \(\chi_{8470}(1973,\cdot)\) \(\chi_{8470}(2127,\cdot)\) \(\chi_{8470}(2183,\cdot)\) \(\chi_{8470}(2253,\cdot)\) \(\chi_{8470}(2337,\cdot)\) \(\chi_{8470}(2407,\cdot)\) \(\chi_{8470}(2533,\cdot)\) \(\chi_{8470}(2687,\cdot)\) \(\chi_{8470}(2897,\cdot)\) \(\chi_{8470}(2953,\cdot)\) \(\chi_{8470}(3023,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-i,-1,e\left(\frac{31}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(1203, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{149}{220}\right)\) | \(e\left(\frac{191}{220}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{93}{220}\right)\) |