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 \(\chi_{4235}(2197,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.de
\(\chi_{8470}(13,\cdot)\) \(\chi_{8470}(83,\cdot)\) \(\chi_{8470}(167,\cdot)\) \(\chi_{8470}(237,\cdot)\) \(\chi_{8470}(293,\cdot)\) \(\chi_{8470}(447,\cdot)\) \(\chi_{8470}(503,\cdot)\) \(\chi_{8470}(657,\cdot)\) \(\chi_{8470}(783,\cdot)\) \(\chi_{8470}(853,\cdot)\) \(\chi_{8470}(937,\cdot)\) \(\chi_{8470}(1007,\cdot)\) \(\chi_{8470}(1063,\cdot)\) \(\chi_{8470}(1217,\cdot)\) \(\chi_{8470}(1273,\cdot)\) \(\chi_{8470}(1427,\cdot)\) \(\chi_{8470}(1553,\cdot)\) \(\chi_{8470}(1623,\cdot)\) \(\chi_{8470}(1707,\cdot)\) \(\chi_{8470}(1777,\cdot)\) \(\chi_{8470}(1833,\cdot)\) \(\chi_{8470}(1987,\cdot)\) \(\chi_{8470}(2043,\cdot)\) \(\chi_{8470}(2197,\cdot)\) \(\chi_{8470}(2323,\cdot)\) \(\chi_{8470}(2477,\cdot)\) \(\chi_{8470}(2547,\cdot)\) \(\chi_{8470}(2603,\cdot)\) \(\chi_{8470}(2757,\cdot)\) \(\chi_{8470}(2813,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((i,-1,e\left(\frac{83}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(2197, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{101}{220}\right)\) | \(e\left(\frac{159}{220}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{207}{220}\right)\) |