Basic properties
Modulus: | \(8034\) | |
Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4017}(203,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.cv
\(\chi_{8034}(203,\cdot)\) \(\chi_{8034}(317,\cdot)\) \(\chi_{8034}(473,\cdot)\) \(\chi_{8034}(785,\cdot)\) \(\chi_{8034}(905,\cdot)\) \(\chi_{8034}(941,\cdot)\) \(\chi_{8034}(1373,\cdot)\) \(\chi_{8034}(1451,\cdot)\) \(\chi_{8034}(1877,\cdot)\) \(\chi_{8034}(2033,\cdot)\) \(\chi_{8034}(2153,\cdot)\) \(\chi_{8034}(2345,\cdot)\) \(\chi_{8034}(3515,\cdot)\) \(\chi_{8034}(3635,\cdot)\) \(\chi_{8034}(3671,\cdot)\) \(\chi_{8034}(4025,\cdot)\) \(\chi_{8034}(4181,\cdot)\) \(\chi_{8034}(4295,\cdot)\) \(\chi_{8034}(4493,\cdot)\) \(\chi_{8034}(4529,\cdot)\) \(\chi_{8034}(4649,\cdot)\) \(\chi_{8034}(5231,\cdot)\) \(\chi_{8034}(5585,\cdot)\) \(\chi_{8034}(5699,\cdot)\) \(\chi_{8034}(5741,\cdot)\) \(\chi_{8034}(5777,\cdot)\) \(\chi_{8034}(6053,\cdot)\) \(\chi_{8034}(6479,\cdot)\) \(\chi_{8034}(7223,\cdot)\) \(\chi_{8034}(7379,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{68})$ |
Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((5357,1237,5773)\) → \((-1,i,e\left(\frac{15}{17}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(203, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{57}{68}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{31}{34}\right)\) |