Basic properties
| Modulus: | \(9702\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(272,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9702.eu
\(\chi_{9702}(811,\cdot)\) \(\chi_{9702}(937,\cdot)\) \(\chi_{9702}(1063,\cdot)\) \(\chi_{9702}(1315,\cdot)\) \(\chi_{9702}(2197,\cdot)\) \(\chi_{9702}(2323,\cdot)\) \(\chi_{9702}(2701,\cdot)\) \(\chi_{9702}(3583,\cdot)\) \(\chi_{9702}(3709,\cdot)\) \(\chi_{9702}(3835,\cdot)\) \(\chi_{9702}(4087,\cdot)\) \(\chi_{9702}(4969,\cdot)\) \(\chi_{9702}(5221,\cdot)\) \(\chi_{9702}(5473,\cdot)\) \(\chi_{9702}(6355,\cdot)\) \(\chi_{9702}(6481,\cdot)\) \(\chi_{9702}(6607,\cdot)\) \(\chi_{9702}(7867,\cdot)\) \(\chi_{9702}(7993,\cdot)\) \(\chi_{9702}(8245,\cdot)\) \(\chi_{9702}(9127,\cdot)\) \(\chi_{9702}(9253,\cdot)\) \(\chi_{9702}(9379,\cdot)\) \(\chi_{9702}(9631,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4313,199,5293)\) → \((1,e\left(\frac{1}{14}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9702 }(811, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) |