Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(389,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.ei
\(\chi_{9075}(49,\cdot)\) \(\chi_{9075}(499,\cdot)\) \(\chi_{9075}(724,\cdot)\) \(\chi_{9075}(949,\cdot)\) \(\chi_{9075}(1324,\cdot)\) \(\chi_{9075}(1549,\cdot)\) \(\chi_{9075}(1699,\cdot)\) \(\chi_{9075}(1774,\cdot)\) \(\chi_{9075}(2149,\cdot)\) \(\chi_{9075}(2374,\cdot)\) \(\chi_{9075}(2524,\cdot)\) \(\chi_{9075}(2599,\cdot)\) \(\chi_{9075}(2974,\cdot)\) \(\chi_{9075}(3199,\cdot)\) \(\chi_{9075}(3349,\cdot)\) \(\chi_{9075}(3424,\cdot)\) \(\chi_{9075}(3799,\cdot)\) \(\chi_{9075}(4024,\cdot)\) \(\chi_{9075}(4174,\cdot)\) \(\chi_{9075}(4249,\cdot)\) \(\chi_{9075}(4624,\cdot)\) \(\chi_{9075}(4999,\cdot)\) \(\chi_{9075}(5074,\cdot)\) \(\chi_{9075}(5449,\cdot)\) \(\chi_{9075}(5674,\cdot)\) \(\chi_{9075}(5824,\cdot)\) \(\chi_{9075}(5899,\cdot)\) \(\chi_{9075}(6274,\cdot)\) \(\chi_{9075}(6499,\cdot)\) \(\chi_{9075}(6649,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((1,-1,e\left(\frac{51}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(4624, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) |