Basic properties
Modulus: | \(8034\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1339}(407,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.dg
\(\chi_{8034}(49,\cdot)\) \(\chi_{8034}(517,\cdot)\) \(\chi_{8034}(673,\cdot)\) \(\chi_{8034}(907,\cdot)\) \(\chi_{8034}(979,\cdot)\) \(\chi_{8034}(1603,\cdot)\) \(\chi_{8034}(1681,\cdot)\) \(\chi_{8034}(1993,\cdot)\) \(\chi_{8034}(2461,\cdot)\) \(\chi_{8034}(2695,\cdot)\) \(\chi_{8034}(3013,\cdot)\) \(\chi_{8034}(3085,\cdot)\) \(\chi_{8034}(3325,\cdot)\) \(\chi_{8034}(3871,\cdot)\) \(\chi_{8034}(4021,\cdot)\) \(\chi_{8034}(4099,\cdot)\) \(\chi_{8034}(4255,\cdot)\) \(\chi_{8034}(4333,\cdot)\) \(\chi_{8034}(4573,\cdot)\) \(\chi_{8034}(4651,\cdot)\) \(\chi_{8034}(4801,\cdot)\) \(\chi_{8034}(4879,\cdot)\) \(\chi_{8034}(4963,\cdot)\) \(\chi_{8034}(5035,\cdot)\) \(\chi_{8034}(5041,\cdot)\) \(\chi_{8034}(5587,\cdot)\) \(\chi_{8034}(5899,\cdot)\) \(\chi_{8034}(6127,\cdot)\) \(\chi_{8034}(6445,\cdot)\) \(\chi_{8034}(7381,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{26}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(3085, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{15}{17}\right)\) |