Basic properties
| Modulus: | \(5400\) | |
| Conductor: | \(2700\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2700}(191,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5400.eu
\(\chi_{5400}(191,\cdot)\) \(\chi_{5400}(311,\cdot)\) \(\chi_{5400}(671,\cdot)\) \(\chi_{5400}(911,\cdot)\) \(\chi_{5400}(1031,\cdot)\) \(\chi_{5400}(1271,\cdot)\) \(\chi_{5400}(1391,\cdot)\) \(\chi_{5400}(1631,\cdot)\) \(\chi_{5400}(1991,\cdot)\) \(\chi_{5400}(2111,\cdot)\) \(\chi_{5400}(2471,\cdot)\) \(\chi_{5400}(2711,\cdot)\) \(\chi_{5400}(2831,\cdot)\) \(\chi_{5400}(3071,\cdot)\) \(\chi_{5400}(3191,\cdot)\) \(\chi_{5400}(3431,\cdot)\) \(\chi_{5400}(3791,\cdot)\) \(\chi_{5400}(3911,\cdot)\) \(\chi_{5400}(4271,\cdot)\) \(\chi_{5400}(4511,\cdot)\) \(\chi_{5400}(4631,\cdot)\) \(\chi_{5400}(4871,\cdot)\) \(\chi_{5400}(4991,\cdot)\) \(\chi_{5400}(5231,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1351,2701,1001,2377)\) → \((-1,1,e\left(\frac{1}{18}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5400 }(191, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{67}{90}\right)\) |