Basic properties
Modulus: | \(7350\) | |
Conductor: | \(3675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3675}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7350.cs
\(\chi_{7350}(41,\cdot)\) \(\chi_{7350}(461,\cdot)\) \(\chi_{7350}(671,\cdot)\) \(\chi_{7350}(1091,\cdot)\) \(\chi_{7350}(1511,\cdot)\) \(\chi_{7350}(1721,\cdot)\) \(\chi_{7350}(1931,\cdot)\) \(\chi_{7350}(2141,\cdot)\) \(\chi_{7350}(2561,\cdot)\) \(\chi_{7350}(2771,\cdot)\) \(\chi_{7350}(2981,\cdot)\) \(\chi_{7350}(3191,\cdot)\) \(\chi_{7350}(3611,\cdot)\) \(\chi_{7350}(4031,\cdot)\) \(\chi_{7350}(4241,\cdot)\) \(\chi_{7350}(4661,\cdot)\) \(\chi_{7350}(4871,\cdot)\) \(\chi_{7350}(5081,\cdot)\) \(\chi_{7350}(5711,\cdot)\) \(\chi_{7350}(5921,\cdot)\) \(\chi_{7350}(6131,\cdot)\) \(\chi_{7350}(6341,\cdot)\) \(\chi_{7350}(6971,\cdot)\) \(\chi_{7350}(7181,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4901,1177,2551)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{5}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 7350 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{1}{7}\right)\) |