Basic properties
Modulus: | \(4012\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1003}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.bb
\(\chi_{4012}(169,\cdot)\) \(\chi_{4012}(373,\cdot)\) \(\chi_{4012}(441,\cdot)\) \(\chi_{4012}(577,\cdot)\) \(\chi_{4012}(713,\cdot)\) \(\chi_{4012}(985,\cdot)\) \(\chi_{4012}(1189,\cdot)\) \(\chi_{4012}(1325,\cdot)\) \(\chi_{4012}(1393,\cdot)\) \(\chi_{4012}(1461,\cdot)\) \(\chi_{4012}(1597,\cdot)\) \(\chi_{4012}(1733,\cdot)\) \(\chi_{4012}(1937,\cdot)\) \(\chi_{4012}(2141,\cdot)\) \(\chi_{4012}(2209,\cdot)\) \(\chi_{4012}(2277,\cdot)\) \(\chi_{4012}(2413,\cdot)\) \(\chi_{4012}(2481,\cdot)\) \(\chi_{4012}(2549,\cdot)\) \(\chi_{4012}(2617,\cdot)\) \(\chi_{4012}(2821,\cdot)\) \(\chi_{4012}(2889,\cdot)\) \(\chi_{4012}(2957,\cdot)\) \(\chi_{4012}(3025,\cdot)\) \(\chi_{4012}(3093,\cdot)\) \(\chi_{4012}(3501,\cdot)\) \(\chi_{4012}(3569,\cdot)\) \(\chi_{4012}(3909,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((2007,3777,3129)\) → \((1,-1,e\left(\frac{16}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 4012 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{45}{58}\right)\) |