Basic properties
Modulus: | \(8470\) | |
Conductor: | \(605\) | 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 \(\chi_{605}(272,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dg
\(\chi_{8470}(57,\cdot)\) \(\chi_{8470}(127,\cdot)\) \(\chi_{8470}(183,\cdot)\) \(\chi_{8470}(337,\cdot)\) \(\chi_{8470}(393,\cdot)\) \(\chi_{8470}(547,\cdot)\) \(\chi_{8470}(673,\cdot)\) \(\chi_{8470}(743,\cdot)\) \(\chi_{8470}(827,\cdot)\) \(\chi_{8470}(897,\cdot)\) \(\chi_{8470}(953,\cdot)\) \(\chi_{8470}(1107,\cdot)\) \(\chi_{8470}(1163,\cdot)\) \(\chi_{8470}(1317,\cdot)\) \(\chi_{8470}(1513,\cdot)\) \(\chi_{8470}(1597,\cdot)\) \(\chi_{8470}(1723,\cdot)\) \(\chi_{8470}(1877,\cdot)\) \(\chi_{8470}(2087,\cdot)\) \(\chi_{8470}(2213,\cdot)\) \(\chi_{8470}(2283,\cdot)\) \(\chi_{8470}(2367,\cdot)\) \(\chi_{8470}(2437,\cdot)\) \(\chi_{8470}(2493,\cdot)\) \(\chi_{8470}(2647,\cdot)\) \(\chi_{8470}(2703,\cdot)\) \(\chi_{8470}(2857,\cdot)\) \(\chi_{8470}(2983,\cdot)\) \(\chi_{8470}(3053,\cdot)\) \(\chi_{8470}(3207,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((i,1,e\left(\frac{53}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(2087, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{91}{220}\right)\) | \(e\left(\frac{189}{220}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{107}{220}\right)\) |