Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(1815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1815}(74,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.en
\(\chi_{9075}(74,\cdot)\) \(\chi_{9075}(149,\cdot)\) \(\chi_{9075}(299,\cdot)\) \(\chi_{9075}(899,\cdot)\) \(\chi_{9075}(974,\cdot)\) \(\chi_{9075}(1124,\cdot)\) \(\chi_{9075}(1349,\cdot)\) \(\chi_{9075}(1724,\cdot)\) \(\chi_{9075}(1799,\cdot)\) \(\chi_{9075}(1949,\cdot)\) \(\chi_{9075}(2174,\cdot)\) \(\chi_{9075}(2549,\cdot)\) \(\chi_{9075}(2624,\cdot)\) \(\chi_{9075}(2999,\cdot)\) \(\chi_{9075}(3374,\cdot)\) \(\chi_{9075}(3449,\cdot)\) \(\chi_{9075}(3599,\cdot)\) \(\chi_{9075}(3824,\cdot)\) \(\chi_{9075}(4199,\cdot)\) \(\chi_{9075}(4274,\cdot)\) \(\chi_{9075}(4424,\cdot)\) \(\chi_{9075}(4649,\cdot)\) \(\chi_{9075}(5024,\cdot)\) \(\chi_{9075}(5099,\cdot)\) \(\chi_{9075}(5249,\cdot)\) \(\chi_{9075}(5474,\cdot)\) \(\chi_{9075}(5849,\cdot)\) \(\chi_{9075}(5924,\cdot)\) \(\chi_{9075}(6074,\cdot)\) \(\chi_{9075}(6299,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,-1,e\left(\frac{43}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(74, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{4}{11}\right)\) |