Basic properties
Modulus: | \(2300\) | |
Conductor: | \(575\) | 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 \(\chi_{575}(259,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2300.bo
\(\chi_{2300}(9,\cdot)\) \(\chi_{2300}(29,\cdot)\) \(\chi_{2300}(169,\cdot)\) \(\chi_{2300}(209,\cdot)\) \(\chi_{2300}(269,\cdot)\) \(\chi_{2300}(289,\cdot)\) \(\chi_{2300}(409,\cdot)\) \(\chi_{2300}(469,\cdot)\) \(\chi_{2300}(489,\cdot)\) \(\chi_{2300}(509,\cdot)\) \(\chi_{2300}(629,\cdot)\) \(\chi_{2300}(669,\cdot)\) \(\chi_{2300}(729,\cdot)\) \(\chi_{2300}(809,\cdot)\) \(\chi_{2300}(869,\cdot)\) \(\chi_{2300}(909,\cdot)\) \(\chi_{2300}(929,\cdot)\) \(\chi_{2300}(969,\cdot)\) \(\chi_{2300}(1089,\cdot)\) \(\chi_{2300}(1129,\cdot)\) \(\chi_{2300}(1189,\cdot)\) \(\chi_{2300}(1209,\cdot)\) \(\chi_{2300}(1269,\cdot)\) \(\chi_{2300}(1329,\cdot)\) \(\chi_{2300}(1369,\cdot)\) \(\chi_{2300}(1389,\cdot)\) \(\chi_{2300}(1409,\cdot)\) \(\chi_{2300}(1429,\cdot)\) \(\chi_{2300}(1589,\cdot)\) \(\chi_{2300}(1669,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{9}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
\( \chi_{ 2300 }(1409, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{7}{55}\right)\) |