Basic properties
| Modulus: | \(4002\) | |
| Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2001}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4002.bo
\(\chi_{4002}(35,\cdot)\) \(\chi_{4002}(71,\cdot)\) \(\chi_{4002}(167,\cdot)\) \(\chi_{4002}(179,\cdot)\) \(\chi_{4002}(209,\cdot)\) \(\chi_{4002}(353,\cdot)\) \(\chi_{4002}(473,\cdot)\) \(\chi_{4002}(515,\cdot)\) \(\chi_{4002}(593,\cdot)\) \(\chi_{4002}(647,\cdot)\) \(\chi_{4002}(671,\cdot)\) \(\chi_{4002}(731,\cdot)\) \(\chi_{4002}(767,\cdot)\) \(\chi_{4002}(821,\cdot)\) \(\chi_{4002}(863,\cdot)\) \(\chi_{4002}(905,\cdot)\) \(\chi_{4002}(995,\cdot)\) \(\chi_{4002}(1037,\cdot)\) \(\chi_{4002}(1223,\cdot)\) \(\chi_{4002}(1343,\cdot)\) \(\chi_{4002}(1559,\cdot)\) \(\chi_{4002}(1637,\cdot)\) \(\chi_{4002}(1691,\cdot)\) \(\chi_{4002}(1715,\cdot)\) \(\chi_{4002}(1733,\cdot)\) \(\chi_{4002}(1775,\cdot)\) \(\chi_{4002}(1865,\cdot)\) \(\chi_{4002}(1889,\cdot)\) \(\chi_{4002}(2063,\cdot)\) \(\chi_{4002}(2237,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2669,3133,553)\) → \((-1,e\left(\frac{10}{11}\right),e\left(\frac{3}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 4002 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{45}{77}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{103}{154}\right)\) | \(e\left(\frac{149}{154}\right)\) | \(e\left(\frac{113}{154}\right)\) |