Basic properties
Modulus: | \(3630\) | |
Conductor: | \(1815\) | 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 \(\chi_{1815}(854,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bp
\(\chi_{3630}(29,\cdot)\) \(\chi_{3630}(149,\cdot)\) \(\chi_{3630}(299,\cdot)\) \(\chi_{3630}(359,\cdot)\) \(\chi_{3630}(479,\cdot)\) \(\chi_{3630}(569,\cdot)\) \(\chi_{3630}(629,\cdot)\) \(\chi_{3630}(689,\cdot)\) \(\chi_{3630}(809,\cdot)\) \(\chi_{3630}(899,\cdot)\) \(\chi_{3630}(1019,\cdot)\) \(\chi_{3630}(1139,\cdot)\) \(\chi_{3630}(1229,\cdot)\) \(\chi_{3630}(1289,\cdot)\) \(\chi_{3630}(1349,\cdot)\) \(\chi_{3630}(1469,\cdot)\) \(\chi_{3630}(1559,\cdot)\) \(\chi_{3630}(1619,\cdot)\) \(\chi_{3630}(1679,\cdot)\) \(\chi_{3630}(1799,\cdot)\) \(\chi_{3630}(1889,\cdot)\) \(\chi_{3630}(1949,\cdot)\) \(\chi_{3630}(2009,\cdot)\) \(\chi_{3630}(2129,\cdot)\) \(\chi_{3630}(2219,\cdot)\) \(\chi_{3630}(2279,\cdot)\) \(\chi_{3630}(2459,\cdot)\) \(\chi_{3630}(2549,\cdot)\) \(\chi_{3630}(2609,\cdot)\) \(\chi_{3630}(2669,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((-1,-1,e\left(\frac{7}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 3630 }(2669, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) |