Basic properties
| Modulus: | \(7600\) | |
| Conductor: | \(7600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7600.il
\(\chi_{7600}(309,\cdot)\) \(\chi_{7600}(389,\cdot)\) \(\chi_{7600}(669,\cdot)\) \(\chi_{7600}(709,\cdot)\) \(\chi_{7600}(909,\cdot)\) \(\chi_{7600}(1069,\cdot)\) \(\chi_{7600}(1309,\cdot)\) \(\chi_{7600}(1429,\cdot)\) \(\chi_{7600}(1469,\cdot)\) \(\chi_{7600}(1669,\cdot)\) \(\chi_{7600}(1829,\cdot)\) \(\chi_{7600}(1909,\cdot)\) \(\chi_{7600}(2069,\cdot)\) \(\chi_{7600}(2189,\cdot)\) \(\chi_{7600}(2229,\cdot)\) \(\chi_{7600}(2429,\cdot)\) \(\chi_{7600}(2589,\cdot)\) \(\chi_{7600}(2669,\cdot)\) \(\chi_{7600}(2829,\cdot)\) \(\chi_{7600}(2989,\cdot)\) \(\chi_{7600}(3189,\cdot)\) \(\chi_{7600}(3429,\cdot)\) \(\chi_{7600}(3589,\cdot)\) \(\chi_{7600}(3709,\cdot)\) \(\chi_{7600}(4109,\cdot)\) \(\chi_{7600}(4189,\cdot)\) \(\chi_{7600}(4469,\cdot)\) \(\chi_{7600}(4509,\cdot)\) \(\chi_{7600}(4709,\cdot)\) \(\chi_{7600}(4869,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4751,5701,5777,401)\) → \((1,i,e\left(\frac{7}{10}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7600 }(309, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{180}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{89}{180}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{97}{180}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{47}{180}\right)\) |