Basic properties
Modulus: | \(7605\) | |
Conductor: | \(2535\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2535}(44,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.ep
\(\chi_{7605}(44,\cdot)\) \(\chi_{7605}(359,\cdot)\) \(\chi_{7605}(629,\cdot)\) \(\chi_{7605}(1214,\cdot)\) \(\chi_{7605}(1529,\cdot)\) \(\chi_{7605}(1799,\cdot)\) \(\chi_{7605}(2114,\cdot)\) \(\chi_{7605}(2384,\cdot)\) \(\chi_{7605}(2699,\cdot)\) \(\chi_{7605}(2969,\cdot)\) \(\chi_{7605}(3284,\cdot)\) \(\chi_{7605}(3554,\cdot)\) \(\chi_{7605}(3869,\cdot)\) \(\chi_{7605}(4139,\cdot)\) \(\chi_{7605}(4454,\cdot)\) \(\chi_{7605}(4724,\cdot)\) \(\chi_{7605}(5039,\cdot)\) \(\chi_{7605}(5624,\cdot)\) \(\chi_{7605}(5894,\cdot)\) \(\chi_{7605}(6209,\cdot)\) \(\chi_{7605}(6479,\cdot)\) \(\chi_{7605}(6794,\cdot)\) \(\chi_{7605}(7064,\cdot)\) \(\chi_{7605}(7379,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((6761,1522,6931)\) → \((-1,-1,e\left(\frac{35}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 7605 }(44, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(-i\) | \(-1\) |