LMFDB - Embedded newform 1638.2.bj.b.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.b.1135.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.36603 - 2.36603i) q^{10} +(-1.50000 + 0.866025i) q^{11} +(-3.59808 + 0.232051i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.133975 + 0.232051i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(2.36603 + 1.36603i) q^{20} +(0.866025 - 1.50000i) q^{22} +(-1.73205 - 3.00000i) q^{23} -2.46410 q^{25} +(3.00000 - 2.00000i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-0.232051 - 0.401924i) q^{29} -8.19615i q^{31} +(0.866025 + 0.500000i) q^{32} -0.267949i q^{34} +(1.36603 - 2.36603i) q^{35} +(-2.83013 + 1.63397i) q^{37} +1.00000 q^{38} -2.73205 q^{40} +(2.59808 - 1.50000i) q^{41} +(3.36603 - 5.83013i) q^{43} +1.73205i q^{44} +(3.00000 + 1.73205i) q^{46} +4.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(2.13397 - 1.23205i) q^{50} +(-1.59808 + 3.23205i) q^{52} -7.00000 q^{53} +(-2.36603 - 4.09808i) q^{55} +(0.500000 - 0.866025i) q^{56} +(0.401924 + 0.232051i) q^{58} +(-11.1962 - 6.46410i) q^{59} +(2.59808 - 4.50000i) q^{61} +(4.09808 + 7.09808i) q^{62} -1.00000 q^{64} +(-0.633975 - 9.83013i) q^{65} +(4.26795 - 2.46410i) q^{67} +(0.133975 + 0.232051i) q^{68} +2.73205i q^{70} +(7.09808 + 4.09808i) q^{71} +1.46410i q^{73} +(1.63397 - 2.83013i) q^{74} +(-0.866025 + 0.500000i) q^{76} +1.73205 q^{77} +15.9282 q^{79} +(2.36603 - 1.36603i) q^{80} +(-1.50000 + 2.59808i) q^{82} +10.1962i q^{83} +(-0.633975 - 0.366025i) q^{85} +6.73205i q^{86} +(-0.866025 - 1.50000i) q^{88} +(-3.06218 + 1.76795i) q^{89} +(3.23205 + 1.59808i) q^{91} -3.46410 q^{92} +(-2.23205 - 3.86603i) q^{94} +(1.36603 - 2.36603i) q^{95} +(1.43782 + 0.830127i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} - 2 q^{10} - 6 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 6 q^{29} + 2 q^{35} + 6 q^{37} + 4 q^{38} - 4 q^{40} + 10 q^{43} + 12 q^{46} + 2 q^{49} + 12 q^{50} + 4 q^{52} - 28 q^{53} - 6 q^{55} + 2 q^{56} + 12 q^{58} - 24 q^{59} + 6 q^{62} - 4 q^{64} - 6 q^{65} + 24 q^{67} + 4 q^{68} + 18 q^{71} + 10 q^{74} + 36 q^{79} + 6 q^{80} - 6 q^{82} - 6 q^{85} + 12 q^{89} + 6 q^{91} - 2 q^{94} + 2 q^{95} + 30 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^10 - 6 * q^11 - 4 * q^13 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 6 * q^20 + 4 * q^25 + 12 * q^26 + 6 * q^29 + 2 * q^35 + 6 * q^37 + 4 * q^38 - 4 * q^40 + 10 * q^43 + 12 * q^46 + 2 * q^49 + 12 * q^50 + 4 * q^52 - 28 * q^53 - 6 * q^55 + 2 * q^56 + 12 * q^58 - 24 * q^59 + 6 * q^62 - 4 * q^64 - 6 * q^65 + 24 * q^67 + 4 * q^68 + 18 * q^71 + 10 * q^74 + 36 * q^79 + 6 * q^80 - 6 * q^82 - 6 * q^85 + 12 * q^89 + 6 * q^91 - 2 * q^94 + 2 * q^95 + 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			2.73205i			1.22181i	0.791704	+	0.610905i	$0.209194\pi$
$5$			2.73205i			1.22181i	−0.791704	+	0.610905i	$0.790806\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.36603	−	2.36603i	−0.431975	−	0.748203i
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	−0.708787	−	0.705422i	$-0.750757\pi$
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	0.256520	+	0.966539i	$0.417424\pi$
$12$		0			0
$13$	−3.59808	+	0.232051i	−0.997927	+	0.0643593i
$13$	−3.59808	+	0.232051i	−0.997927	+	0.0643593i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.133975	+	0.232051i	−0.0324936	+	0.0562806i	−0.881815	−	0.471596i	$-0.843678\pi$
$17$	−0.133975	+	0.232051i	−0.0324936	+	0.0562806i	0.849321	+	0.527876i	$0.177012\pi$
$18$		0			0
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	0.397360	−	0.917663i	$-0.369927\pi$
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	−0.596040	+	0.802955i	$0.703260\pi$
$20$	2.36603	+	1.36603i	0.529059	+	0.305453i
$21$		0			0
$22$	0.866025	−	1.50000i	0.184637	−	0.319801i
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	0.626994	−	0.779024i	$-0.284285\pi$
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	−0.988152	+	0.153481i	$0.950952\pi$
$24$		0			0
$25$	−2.46410			−0.492820
$26$	3.00000	−	2.00000i	0.588348	−	0.392232i
$27$		0			0
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	−0.232051	−	0.401924i	−0.0430908	−	0.0746354i	0.843676	−	0.536853i	$-0.180387\pi$
$29$	−0.232051	−	0.401924i	−0.0430908	−	0.0746354i	−0.886766	+	0.462218i	$0.847054\pi$
$30$		0			0
$31$		−	8.19615i		−	1.47207i	−0.676942	−	0.736036i	$-0.736695\pi$
$31$		−	8.19615i		−	1.47207i	0.676942	−	0.736036i	$-0.263305\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	0.267949i		−	0.0459529i
$35$	1.36603	−	2.36603i	0.230900	−	0.399931i
$36$		0			0
$37$	−2.83013	+	1.63397i	−0.465270	+	0.268624i	−0.714258	−	0.699883i	$-0.753235\pi$
$37$	−2.83013	+	1.63397i	−0.465270	+	0.268624i	0.248988	+	0.968507i	$0.419902\pi$
$38$	1.00000			0.162221
$39$		0			0
$40$	−2.73205			−0.431975
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$		0			0
$43$	3.36603	−	5.83013i	0.513314	−	0.889086i	−0.486567	−	0.873643i	$-0.661751\pi$
$43$	3.36603	−	5.83013i	0.513314	−	0.889086i	0.999881	−	0.0154426i	$-0.00491573\pi$
$44$			1.73205i			0.261116i
$45$		0			0
$46$	3.00000	+	1.73205i	0.442326	+	0.255377i
$47$			4.46410i			0.651156i	0.945515	+	0.325578i	$0.105559\pi$
$47$			4.46410i			0.651156i	−0.945515	+	0.325578i	$0.894441\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	2.13397	−	1.23205i	0.301790	−	0.174238i
$51$		0			0
$52$	−1.59808	+	3.23205i	−0.221613	+	0.448205i
$53$	−7.00000			−0.961524			−0.480762	−	0.876851i	$-0.659640\pi$
$53$	−7.00000			−0.961524			−0.480762	+	0.876851i	$0.659640\pi$
$54$		0			0
$55$	−2.36603	−	4.09808i	−0.319035	−	0.552584i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	0.401924	+	0.232051i	0.0527752	+	0.0304698i
$59$	−11.1962	−	6.46410i	−1.45761	−	0.841554i	−0.458721	−	0.888580i	$-0.651692\pi$
$59$	−11.1962	−	6.46410i	−1.45761	−	0.841554i	−0.998894	+	0.0470259i	$0.985026\pi$
$60$		0			0
$61$	2.59808	−	4.50000i	0.332650	−	0.576166i	−0.650381	−	0.759608i	$-0.725391\pi$
$61$	2.59808	−	4.50000i	0.332650	−	0.576166i	0.983030	+	0.183442i	$0.0587240\pi$
$62$	4.09808	+	7.09808i	0.520456	+	0.901457i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.633975	−	9.83013i	−0.0786349	−	1.21928i
$66$		0			0
$67$	4.26795	−	2.46410i	0.521413	−	0.301038i	−0.216100	−	0.976371i	$-0.569334\pi$
$67$	4.26795	−	2.46410i	0.521413	−	0.301038i	0.737513	+	0.675333i	$0.236000\pi$
$68$	0.133975	+	0.232051i	0.0162468	+	0.0281403i
$69$		0			0
$70$			2.73205i			0.326543i
$71$	7.09808	+	4.09808i	0.842387	+	0.486352i	0.858075	−	0.513525i	$-0.171661\pi$
$71$	7.09808	+	4.09808i	0.842387	+	0.486352i	−0.0156881	+	0.999877i	$0.504994\pi$
$72$		0			0
$73$			1.46410i			0.171360i	0.996323	+	0.0856801i	$0.0273063\pi$
$73$			1.46410i			0.171360i	−0.996323	+	0.0856801i	$0.972694\pi$
$74$	1.63397	−	2.83013i	0.189946	−	0.328996i
$75$		0			0
$76$	−0.866025	+	0.500000i	−0.0993399	+	0.0573539i
$77$	1.73205			0.197386
$78$		0			0
$79$	15.9282			1.79206			0.896031	−	0.443991i	$-0.146438\pi$
$79$	15.9282			1.79206			0.896031	+	0.443991i	$0.146438\pi$
$80$	2.36603	−	1.36603i	0.264530	−	0.152726i
$81$		0			0
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$			10.1962i			1.11917i	0.828772	+	0.559587i	$0.189040\pi$
$83$			10.1962i			1.11917i	−0.828772	+	0.559587i	$0.810960\pi$
$84$		0			0
$85$	−0.633975	−	0.366025i	−0.0687642	−	0.0397010i
$86$			6.73205i			0.725936i
$87$		0			0
$88$	−0.866025	−	1.50000i	−0.0923186	−	0.159901i
$89$	−3.06218	+	1.76795i	−0.324590	+	0.187402i	−0.653437	−	0.756981i	$-0.726673\pi$
$89$	−3.06218	+	1.76795i	−0.324590	+	0.187402i	0.328847	+	0.944383i	$0.393340\pi$
$90$		0			0
$91$	3.23205	+	1.59808i	0.338811	+	0.167524i
$92$	−3.46410			−0.361158
$93$		0			0
$94$	−2.23205	−	3.86603i	−0.230218	−	0.398750i
$95$	1.36603	−	2.36603i	0.140151	−	0.242749i
$96$		0			0
$97$	1.43782	+	0.830127i	0.145989	+	0.0842866i	0.571215	−	0.820800i	$-0.306472\pi$
$97$	1.43782	+	0.830127i	0.145989	+	0.0842866i	−0.425226	+	0.905087i	$0.639806\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	−1.23205	+	2.13397i	−0.123205	+	0.213397i
$101$	−8.46410	−	14.6603i	−0.842210	−	1.45875i	−0.888023	−	0.459800i	$-0.847921\pi$
$101$	−8.46410	−	14.6603i	−0.842210	−	1.45875i	0.0458130	−	0.998950i	$-0.485412\pi$
$102$		0			0
$103$	−11.2679			−1.11026			−0.555132	−	0.831762i	$-0.687332\pi$
$103$	−11.2679			−1.11026			−0.555132	+	0.831762i	$0.687332\pi$
$104$	−0.232051	−	3.59808i	−0.0227545	−	0.352820i
$105$		0			0
$106$	6.06218	−	3.50000i	0.588811	−	0.339950i
$107$	−8.42820	−	14.5981i	−0.814785	−	1.41125i	−0.909482	−	0.415743i	$-0.863522\pi$
$107$	−8.42820	−	14.5981i	−0.814785	−	1.41125i	0.0946969	−	0.995506i	$-0.469812\pi$
$108$		0			0
$109$			1.26795i			0.121448i	0.998155	+	0.0607238i	$0.0193409\pi$
$109$			1.26795i			0.121448i	−0.998155	+	0.0607238i	$0.980659\pi$
$110$	4.09808	+	2.36603i	0.390736	+	0.225592i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	9.36603	−	16.2224i	0.881082	−	1.52608i	0.0309416	−	0.999521i	$-0.490149\pi$
$113$	9.36603	−	16.2224i	0.881082	−	1.52608i	0.850140	−	0.526557i	$-0.176517\pi$
$114$		0			0
$115$	8.19615	−	4.73205i	0.764295	−	0.441266i
$116$	−0.464102			−0.0430908
$117$		0			0
$118$	12.9282			1.19014
$119$	0.232051	−	0.133975i	0.0212721	−	0.0122814i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$			5.19615i			0.470438i
$123$		0			0
$124$	−7.09808	−	4.09808i	−0.637426	−	0.368018i
$125$			6.92820i			0.619677i
$126$		0			0
$127$	−4.26795	−	7.39230i	−0.378719	−	0.655961i	0.612157	−	0.790736i	$-0.290302\pi$
$127$	−4.26795	−	7.39230i	−0.378719	−	0.655961i	−0.990876	+	0.134775i	$0.956969\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	5.46410	+	8.19615i	0.479233	+	0.718850i
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$		0			0
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	−2.46410	+	4.26795i	−0.212866	+	0.368695i
$135$		0			0
$136$	−0.232051	−	0.133975i	−0.0198982	−	0.0114882i
$137$	−5.53590	−	3.19615i	−0.472964	−	0.273066i	0.244516	−	0.969645i	$-0.421371\pi$
$137$	−5.53590	−	3.19615i	−0.472964	−	0.273066i	−0.717480	+	0.696580i	$0.754704\pi$
$138$		0			0
$139$	9.79423	−	16.9641i	0.830736	−	1.43888i	−0.0667201	−	0.997772i	$-0.521253\pi$
$139$	9.79423	−	16.9641i	0.830736	−	1.43888i	0.897456	−	0.441105i	$-0.145413\pi$
$140$	−1.36603	−	2.36603i	−0.115450	−	0.199966i
$141$		0			0
$142$	−8.19615			−0.687806
$143$	5.19615	−	3.46410i	0.434524	−	0.289683i
$144$		0			0
$145$	1.09808	−	0.633975i	0.0911903	−	0.0526487i
$146$	−0.732051	−	1.26795i	−0.0605850	−	0.104936i
$147$		0			0
$148$			3.26795i			0.268624i
$149$	−12.0000	−	6.92820i	−0.983078	−	0.567581i	−0.0798802	−	0.996804i	$-0.525454\pi$
$149$	−12.0000	−	6.92820i	−0.983078	−	0.567581i	−0.903198	+	0.429224i	$0.858787\pi$
$150$		0			0
$151$		−	5.19615i		−	0.422857i	−0.977393	−	0.211428i	$-0.932188\pi$
$151$		−	5.19615i		−	0.422857i	0.977393	−	0.211428i	$-0.0678115\pi$
$152$	0.500000	−	0.866025i	0.0405554	−	0.0702439i
$153$		0			0
$154$	−1.50000	+	0.866025i	−0.120873	+	0.0697863i
$155$	22.3923			1.79859
$156$		0			0
$157$	−7.46410			−0.595700			−0.297850	−	0.954613i	$-0.596270\pi$
$157$	−7.46410			−0.595700			−0.297850	+	0.954613i	$0.596270\pi$
$158$	−13.7942	+	7.96410i	−1.09741	+	0.633590i
$159$		0			0
$160$	−1.36603	+	2.36603i	−0.107994	+	0.187051i
$161$			3.46410i			0.273009i
$162$		0			0
$163$	0.633975	+	0.366025i	0.0496567	+	0.0286693i	0.524623	−	0.851335i	$-0.324206\pi$
$163$	0.633975	+	0.366025i	0.0496567	+	0.0286693i	−0.474966	+	0.880004i	$0.657540\pi$
$164$		−	3.00000i		−	0.234261i
$165$		0			0
$166$	−5.09808	−	8.83013i	−0.395687	−	0.685351i
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.0422232	−	0.999108i	$-0.486556\pi$
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.886365	+	0.462988i	$0.153223\pi$
$168$		0			0
$169$	12.8923	−	1.66987i	0.991716	−	0.128452i
$170$	0.732051			0.0561457
$171$		0			0
$172$	−3.36603	−	5.83013i	−0.256657	−	0.444543i
$173$	−7.56218	+	13.0981i	−0.574942	+	0.995828i	0.421106	+	0.907011i	$0.361642\pi$
$173$	−7.56218	+	13.0981i	−0.574942	+	0.995828i	−0.996048	+	0.0888170i	$0.971691\pi$
$174$		0			0
$175$	2.13397	+	1.23205i	0.161313	+	0.0931343i
$176$	1.50000	+	0.866025i	0.113067	+	0.0652791i
$177$		0			0
$178$	1.76795	−	3.06218i	0.132513	−	0.229520i
$179$	−2.26795	−	3.92820i	−0.169514	−	0.293608i	0.768735	−	0.639568i	$-0.220887\pi$
$179$	−2.26795	−	3.92820i	−0.169514	−	0.293608i	−0.938249	+	0.345960i	$0.887553\pi$
$180$		0			0
$181$	−14.6603			−1.08969			−0.544844	−	0.838537i	$-0.683411\pi$
$181$	−14.6603			−1.08969			−0.544844	+	0.838537i	$0.683411\pi$
$182$	−3.59808	+	0.232051i	−0.266707	+	0.0172008i
$183$		0			0
$184$	3.00000	−	1.73205i	0.221163	−	0.127688i
$185$	−4.46410	−	7.73205i	−0.328207	−	0.568472i
$186$		0			0
$187$		−	0.464102i		−	0.0339385i
$188$	3.86603	+	2.23205i	0.281959	+	0.162789i
$189$		0			0
$190$			2.73205i			0.198204i
$191$	−0.562178	+	0.973721i	−0.0406778	+	0.0704559i	−0.885647	−	0.464358i	$-0.846285\pi$
$191$	−0.562178	+	0.973721i	−0.0406778	+	0.0704559i	0.844970	+	0.534814i	$0.179618\pi$
$192$		0			0
$193$	−7.96410	+	4.59808i	−0.573269	+	0.330977i	−0.758454	−	0.651727i	$-0.774045\pi$
$193$	−7.96410	+	4.59808i	−0.573269	+	0.330977i	0.185185	+	0.982704i	$0.440712\pi$
$194$	−1.66025			−0.119199
$195$		0			0
$196$	1.00000			0.0714286
$197$	8.08846	−	4.66987i	0.576279	−	0.332715i	−0.183374	−	0.983043i	$-0.558702\pi$
$197$	8.08846	−	4.66987i	0.576279	−	0.332715i	0.759653	+	0.650328i	$0.225369\pi$
$198$		0			0
$199$	−2.90192	+	5.02628i	−0.205712	+	0.356304i	−0.950359	−	0.311155i	$-0.899284\pi$
$199$	−2.90192	+	5.02628i	−0.205712	+	0.356304i	0.744647	+	0.667458i	$0.232618\pi$
$200$		−	2.46410i		−	0.174238i
$201$		0			0
$202$	14.6603	+	8.46410i	1.03149	+	0.595532i
$203$			0.464102i			0.0325735i
$204$		0			0
$205$	4.09808	+	7.09808i	0.286222	+	0.495751i
$206$	9.75833	−	5.63397i	0.679895	−	0.392538i
$207$		0			0
$208$	2.00000	+	3.00000i	0.138675	+	0.208013i
$209$	1.73205			0.119808
$210$		0			0
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.833858	−	0.551979i	$-0.813873\pi$
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.0610990	−	0.998132i	$-0.519461\pi$
$212$	−3.50000	+	6.06218i	−0.240381	+	0.416352i
$213$		0			0
$214$	14.5981	+	8.42820i	0.997904	+	0.576140i
$215$	15.9282	+	9.19615i	1.08629	+	0.627172i
$216$		0			0
$217$	−4.09808	+	7.09808i	−0.278196	+	0.481849i
$218$	−0.633975	−	1.09808i	−0.0429382	−	0.0743711i
$219$		0			0
$220$	−4.73205			−0.319035
$221$	0.428203	−	0.866025i	0.0288041	−	0.0582552i
$222$		0			0
$223$	−3.12436	+	1.80385i	−0.209222	+	0.120795i	−0.600950	−	0.799287i	$-0.705211\pi$
$223$	−3.12436	+	1.80385i	−0.209222	+	0.120795i	0.391728	+	0.920081i	$0.371878\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$			18.7321i			1.24604i
$227$	−2.07180	−	1.19615i	−0.137510	−	0.0793914i	0.429667	−	0.902988i	$-0.358631\pi$
$227$	−2.07180	−	1.19615i	−0.137510	−	0.0793914i	−0.567177	+	0.823596i	$0.691964\pi$
$228$		0			0
$229$		−	6.07180i		−	0.401236i	−0.979670	−	0.200618i	$-0.935705\pi$
$229$		−	6.07180i		−	0.401236i	0.979670	−	0.200618i	$-0.0642949\pi$
$230$	−4.73205	+	8.19615i	−0.312022	+	0.540438i
$231$		0			0
$232$	0.401924	−	0.232051i	0.0263876	−	0.0152349i
$233$	15.1244			0.990829			0.495415	−	0.868657i	$-0.335016\pi$
$233$	15.1244			0.990829			0.495415	+	0.868657i	$0.335016\pi$
$234$		0			0
$235$	−12.1962			−0.795589
$236$	−11.1962	+	6.46410i	−0.728807	+	0.420777i
$237$		0			0
$238$	−0.133975	+	0.232051i	−0.00868428	+	0.0150416i
$239$			2.73205i			0.176722i	0.996089	+	0.0883608i	$0.0281629\pi$
$239$			2.73205i			0.176722i	−0.996089	+	0.0883608i	$0.971837\pi$
$240$		0			0
$241$	6.92820	+	4.00000i	0.446285	+	0.257663i	0.706260	−	0.707953i	$-0.250381\pi$
$241$	6.92820	+	4.00000i	0.446285	+	0.257663i	−0.259975	+	0.965615i	$0.583714\pi$
$242$		−	8.00000i		−	0.514259i
$243$		0			0
$244$	−2.59808	−	4.50000i	−0.166325	−	0.288083i
$245$	−2.36603	+	1.36603i	−0.151160	+	0.0872722i
$246$		0			0
$247$	3.23205	+	1.59808i	0.205650	+	0.101683i
$248$	8.19615			0.520456
$249$		0			0
$250$	−3.46410	−	6.00000i	−0.219089	−	0.379473i
$251$	5.56218	−	9.63397i	0.351082	−	0.608091i	−0.635358	−	0.772218i	$-0.719147\pi$
$251$	5.56218	−	9.63397i	0.351082	−	0.608091i	0.986439	+	0.164127i	$0.0524807\pi$
$252$		0			0
$253$	5.19615	+	3.00000i	0.326679	+	0.188608i
$254$	7.39230	+	4.26795i	0.463834	+	0.267795i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.66987	−	2.89230i	−0.104164	−	0.180417i	0.809232	−	0.587489i	$-0.199883\pi$
$257$	−1.66987	−	2.89230i	−0.104164	−	0.180417i	−0.913396	+	0.407072i	$0.866550\pi$
$258$		0			0
$259$	3.26795			0.203060
$260$	−8.83013	−	4.36603i	−0.547621	−	0.270769i
$261$		0			0
$262$	12.0000	−	6.92820i	0.741362	−	0.428026i
$263$	4.56218	+	7.90192i	0.281316	+	0.487253i	0.971709	−	0.236181i	$-0.0758958\pi$
$263$	4.56218	+	7.90192i	0.281316	+	0.487253i	−0.690393	+	0.723434i	$0.742562\pi$
$264$		0			0
$265$		−	19.1244i		−	1.17480i
$266$	−0.866025	−	0.500000i	−0.0530994	−	0.0306570i
$267$		0			0
$268$		−	4.92820i		−	0.301038i
$269$	8.92820	−	15.4641i	0.544362	−	0.942863i	−0.454285	−	0.890857i	$-0.650105\pi$
$269$	8.92820	−	15.4641i	0.544362	−	0.942863i	0.998647	−	0.0520063i	$-0.0165616\pi$
$270$		0			0
$271$	−8.70577	+	5.02628i	−0.528838	+	0.305325i	−0.740543	−	0.672009i	$-0.765432\pi$
$271$	−8.70577	+	5.02628i	−0.528838	+	0.305325i	0.211705	+	0.977334i	$0.432098\pi$
$272$	0.267949			0.0162468
$273$		0			0
$274$	6.39230			0.386173
$275$	3.69615	−	2.13397i	0.222886	−	0.128684i
$276$		0			0
$277$	−12.6603	+	21.9282i	−0.760681	+	1.31754i	0.181819	+	0.983332i	$0.441801\pi$
$277$	−12.6603	+	21.9282i	−0.760681	+	1.31754i	−0.942500	+	0.334206i	$0.891532\pi$
$278$			19.5885i			1.17484i
$279$		0			0
$280$	2.36603	+	1.36603i	0.141397	+	0.0816356i
$281$			17.6603i			1.05352i	0.850013	+	0.526761i	$0.176594\pi$
$281$			17.6603i			1.05352i	−0.850013	+	0.526761i	$0.823406\pi$
$282$		0			0
$283$	8.92820	+	15.4641i	0.530727	+	0.919245i	0.999357	+	0.0358512i	$0.0114142\pi$
$283$	8.92820	+	15.4641i	0.530727	+	0.919245i	−0.468631	+	0.883394i	$0.655252\pi$
$284$	7.09808	−	4.09808i	0.421193	−	0.243176i
$285$		0			0
$286$	−2.76795	+	5.59808i	−0.163672	+	0.331021i
$287$	−3.00000			−0.177084
$288$		0			0
$289$	8.46410	+	14.6603i	0.497888	+	0.862368i
$290$	−0.633975	+	1.09808i	−0.0372283	+	0.0644813i
$291$		0			0
$292$	1.26795	+	0.732051i	0.0742011	+	0.0428400i
$293$	−26.7846	−	15.4641i	−1.56477	−	0.903422i	−0.996763	−	0.0804015i	$-0.974380\pi$
$293$	−26.7846	−	15.4641i	−1.56477	−	0.903422i	−0.568011	−	0.823021i	$-0.692287\pi$
$294$		0			0
$295$	17.6603	−	30.5885i	1.02822	−	1.78093i
$296$	−1.63397	−	2.83013i	−0.0949728	−	0.164498i
$297$		0			0
$298$	13.8564			0.802680
$299$	6.92820	+	10.3923i	0.400668	+	0.601003i
$300$		0			0
$301$	−5.83013	+	3.36603i	−0.336043	+	0.194014i
$302$	2.59808	+	4.50000i	0.149502	+	0.258946i
$303$		0			0
$304$			1.00000i			0.0573539i
$305$	12.2942	+	7.09808i	0.703965	+	0.406435i
$306$		0			0
$307$			29.3923i			1.67751i	0.544511	+	0.838754i	$0.316715\pi$
$307$			29.3923i			1.67751i	−0.544511	+	0.838754i	$0.683285\pi$
$308$	0.866025	−	1.50000i	0.0493464	−	0.0854704i
$309$		0			0
$310$	−19.3923	+	11.1962i	−1.10141	+	0.635899i
$311$	7.73205			0.438444			0.219222	−	0.975675i	$-0.429648\pi$
$311$	7.73205			0.438444			0.219222	+	0.975675i	$0.429648\pi$
$312$		0			0
$313$	−31.5167			−1.78143			−0.890713	−	0.454565i	$-0.849795\pi$
$313$	−31.5167			−1.78143			−0.890713	+	0.454565i	$0.849795\pi$
$314$	6.46410	−	3.73205i	0.364790	−	0.210612i
$315$		0			0
$316$	7.96410	−	13.7942i	0.448016	−	0.775986i
$317$			15.8564i			0.890585i	0.895385	+	0.445292i	$0.146900\pi$
$317$			15.8564i			0.890585i	−0.895385	+	0.445292i	$0.853100\pi$
$318$		0			0
$319$	0.696152	+	0.401924i	0.0389771	+	0.0225034i
$320$		−	2.73205i		−	0.152726i
$321$		0			0
$322$	−1.73205	−	3.00000i	−0.0965234	−	0.167183i
$323$	0.232051	−	0.133975i	0.0129117	−	0.00745455i
$324$		0			0
$325$	8.86603	−	0.571797i	0.491799	−	0.0317176i
$326$	−0.732051			−0.0405445
$327$		0			0
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	2.23205	−	3.86603i	0.123057	−	0.213141i
$330$		0			0
$331$	−0.124356	−	0.0717968i	−0.00683520	−	0.00394631i	0.496579	−	0.867992i	$-0.334589\pi$
$331$	−0.124356	−	0.0717968i	−0.00683520	−	0.00394631i	−0.503414	+	0.864046i	$0.667923\pi$
$332$	8.83013	+	5.09808i	0.484616	+	0.279793i
$333$		0			0
$334$	−6.92820	+	12.0000i	−0.379094	+	0.656611i
$335$	6.73205	+	11.6603i	0.367811	+	0.637068i
$336$		0			0
$337$	−19.0000			−1.03500			−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000			−1.03500			−0.517498	+	0.855684i	$0.673136\pi$
$338$	−10.3301	+	7.89230i	−0.561885	+	0.429285i
$339$		0			0
$340$	−0.633975	+	0.366025i	−0.0343821	+	0.0198505i
$341$	7.09808	+	12.2942i	0.384382	+	0.665770i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	5.83013	+	3.36603i	0.314339	+	0.181484i
$345$		0			0
$346$		−	15.1244i		−	0.813090i
$347$	−7.69615	+	13.3301i	−0.413151	+	0.715599i	−0.995232	−	0.0975319i	$-0.968905\pi$
$347$	−7.69615	+	13.3301i	−0.413151	+	0.715599i	0.582081	+	0.813131i	$0.302239\pi$
$348$		0			0
$349$	−27.4641	+	15.8564i	−1.47012	+	0.848774i	−0.999438	−	0.0335290i	$-0.989325\pi$
$349$	−27.4641	+	15.8564i	−1.47012	+	0.848774i	−0.470682	+	0.882303i	$0.655992\pi$
$350$	−2.46410			−0.131712
$351$		0			0
$352$	−1.73205			−0.0923186
$353$	−2.19615	+	1.26795i	−0.116889	+	0.0674861i	−0.557305	−	0.830308i	$-0.688165\pi$
$353$	−2.19615	+	1.26795i	−0.116889	+	0.0674861i	0.440415	+	0.897794i	$0.354831\pi$
$354$		0			0
$355$	−11.1962	+	19.3923i	−0.594230	+	1.02924i
$356$			3.53590i			0.187402i
$357$		0			0
$358$	3.92820	+	2.26795i	0.207612	+	0.119865i
$359$			14.1962i			0.749244i	0.927178	+	0.374622i	$0.122228\pi$
$359$			14.1962i			0.749244i	−0.927178	+	0.374622i	$0.877772\pi$
$360$		0			0
$361$	−9.00000	−	15.5885i	−0.473684	−	0.820445i
$362$	12.6962	−	7.33013i	0.667295	−	0.385263i
$363$		0			0
$364$	3.00000	−	2.00000i	0.157243	−	0.104828i
$365$	−4.00000			−0.209370
$366$		0			0
$367$	4.66025	+	8.07180i	0.243263	+	0.421344i	0.961642	−	0.274308i	$-0.0884488\pi$
$367$	4.66025	+	8.07180i	0.243263	+	0.421344i	−0.718379	+	0.695652i	$0.755115\pi$
$368$	−1.73205	+	3.00000i	−0.0902894	+	0.156386i
$369$		0			0
$370$	7.73205	+	4.46410i	0.401970	+	0.232078i
$371$	6.06218	+	3.50000i	0.314733	+	0.181711i
$372$		0			0
$373$	3.83013	−	6.63397i	0.198316	−	0.343494i	−0.749666	−	0.661816i	$-0.769786\pi$
$373$	3.83013	−	6.63397i	0.198316	−	0.343494i	0.947983	+	0.318322i	$0.103119\pi$
$374$	0.232051	+	0.401924i	0.0119991	+	0.0207830i
$375$		0			0
$376$	−4.46410			−0.230218
$377$	0.928203	+	1.39230i	0.0478049	+	0.0717073i
$378$		0			0
$379$	26.3660	−	15.2224i	1.35433	−	0.781924i	0.365479	−	0.930820i	$-0.380905\pi$
$379$	26.3660	−	15.2224i	1.35433	−	0.781924i	0.988853	+	0.148896i	$0.0475719\pi$
$380$	−1.36603	−	2.36603i	−0.0700756	−	0.121375i
$381$		0			0
$382$		−	1.12436i		−	0.0575270i
$383$	−10.7942	−	6.23205i	−0.551559	−	0.318443i	0.198191	−	0.980163i	$-0.436493\pi$
$383$	−10.7942	−	6.23205i	−0.551559	−	0.318443i	−0.749751	+	0.661720i	$0.769827\pi$
$384$		0			0
$385$			4.73205i			0.241168i
$386$	4.59808	−	7.96410i	0.234036	−	0.405362i
$387$		0			0
$388$	1.43782	−	0.830127i	0.0729944	−	0.0421433i
$389$	−12.3923			−0.628315			−0.314157	−	0.949371i	$-0.601722\pi$
$389$	−12.3923			−0.628315			−0.314157	+	0.949371i	$0.601722\pi$
$390$		0			0
$391$	0.928203			0.0469413
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	−4.66987	+	8.08846i	−0.235265	+	0.407491i
$395$			43.5167i			2.18956i
$396$		0			0
$397$	−18.9904	−	10.9641i	−0.953100	−	0.550272i	−0.0590574	−	0.998255i	$-0.518809\pi$
$397$	−18.9904	−	10.9641i	−0.953100	−	0.550272i	−0.894043	+	0.447982i	$0.852143\pi$
$398$		−	5.80385i		−	0.290921i
$399$		0			0
$400$	1.23205	+	2.13397i	0.0616025	+	0.106699i
$401$	2.41154	−	1.39230i	0.120427	−	0.0695284i	−0.438577	−	0.898694i	$-0.644517\pi$
$401$	2.41154	−	1.39230i	0.120427	−	0.0695284i	0.559003	+	0.829165i	$0.311184\pi$
$402$		0			0
$403$	1.90192	+	29.4904i	0.0947416	+	1.46902i
$404$	−16.9282			−0.842210
$405$		0			0
$406$	−0.232051	−	0.401924i	−0.0115165	−	0.0199471i
$407$	2.83013	−	4.90192i	0.140284	−	0.242979i
$408$		0			0
$409$	30.5429	+	17.6340i	1.51025	+	0.871944i	0.999928	+	0.0119609i	$0.00380738\pi$
$409$	30.5429	+	17.6340i	1.51025	+	0.871944i	0.510323	+	0.859983i	$0.329526\pi$
$410$	−7.09808	−	4.09808i	−0.350549	−	0.202390i
$411$		0			0
$412$	−5.63397	+	9.75833i	−0.277566	+	0.480758i
$413$	6.46410	+	11.1962i	0.318078	+	0.550927i
$414$		0			0
$415$	−27.8564			−1.36742
$416$	−3.23205	−	1.59808i	−0.158464	−	0.0783521i
$417$		0			0
$418$	−1.50000	+	0.866025i	−0.0733674	+	0.0423587i
$419$	−1.36603	−	2.36603i	−0.0667347	−	0.115588i	0.830727	−	0.556679i	$-0.187925\pi$
$419$	−1.36603	−	2.36603i	−0.0667347	−	0.115588i	−0.897462	+	0.441091i	$0.854591\pi$
$420$		0			0
$421$			1.60770i			0.0783543i	0.999232	+	0.0391771i	$0.0124737\pi$
$421$			1.60770i			0.0783543i	−0.999232	+	0.0391771i	$0.987526\pi$
$422$	22.5167	+	13.0000i	1.09609	+	0.632830i
$423$		0			0
$424$		−	7.00000i		−	0.339950i
$425$	0.330127	−	0.571797i	0.0160135	−	0.0277362i
$426$		0			0
$427$	−4.50000	+	2.59808i	−0.217770	+	0.125730i
$428$	−16.8564			−0.814785
$429$		0			0
$430$	−18.3923			−0.886956
$431$	−3.29423	+	1.90192i	−0.158677	+	0.0916124i	−0.577236	−	0.816577i	$-0.695869\pi$
$431$	−3.29423	+	1.90192i	−0.158677	+	0.0916124i	0.418559	+	0.908190i	$0.362535\pi$
$432$		0			0
$433$	−20.4641	+	35.4449i	−0.983442	+	1.70337i	−0.334777	+	0.942297i	$0.608661\pi$
$433$	−20.4641	+	35.4449i	−0.983442	+	1.70337i	−0.648665	+	0.761074i	$0.724672\pi$
$434$		−	8.19615i		−	0.393428i
$435$		0			0
$436$	1.09808	+	0.633975i	0.0525883	+	0.0303619i
$437$			3.46410i			0.165710i
$438$		0			0
$439$	18.5885	+	32.1962i	0.887179	+	1.53664i	0.843196	+	0.537606i	$0.180671\pi$
$439$	18.5885	+	32.1962i	0.887179	+	1.53664i	0.0439826	+	0.999032i	$0.485995\pi$
$440$	4.09808	−	2.36603i	0.195368	−	0.112796i
$441$		0			0
$442$	0.0621778	+	0.964102i	0.00295750	+	0.0458576i
$443$	−35.6410			−1.69336			−0.846678	−	0.532106i	$-0.821401\pi$
$443$	−35.6410			−1.69336			−0.846678	+	0.532106i	$0.821401\pi$
$444$		0			0
$445$	−4.83013	−	8.36603i	−0.228970	−	0.396588i
$446$	1.80385	−	3.12436i	0.0854147	−	0.147943i
$447$		0			0
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	−9.16987	−	5.29423i	−0.432753	−	0.249850i	0.267766	−	0.963484i	$-0.413715\pi$
$449$	−9.16987	−	5.29423i	−0.432753	−	0.249850i	−0.700519	+	0.713634i	$0.747048\pi$
$450$		0			0
$451$	−2.59808	+	4.50000i	−0.122339	+	0.211897i
$452$	−9.36603	−	16.2224i	−0.440541	−	0.763039i
$453$		0			0
$454$	2.39230			0.112276
$455$	−4.36603	+	8.83013i	−0.204682	+	0.413963i
$456$		0			0
$457$	13.7321	−	7.92820i	0.642358	−	0.370866i	−0.143164	−	0.989699i	$-0.545728\pi$
$457$	13.7321	−	7.92820i	0.642358	−	0.370866i	0.785522	+	0.618833i	$0.212394\pi$
$458$	3.03590	+	5.25833i	0.141858	+	0.245706i
$459$		0			0
$460$		−	9.46410i		−	0.441266i
$461$	−11.3205	−	6.53590i	−0.527249	−	0.304407i	0.212647	−	0.977129i	$-0.431792\pi$
$461$	−11.3205	−	6.53590i	−0.527249	−	0.304407i	−0.739895	+	0.672722i	$0.765125\pi$
$462$		0			0
$463$		−	9.73205i		−	0.452287i	−0.974094	−	0.226143i	$-0.927388\pi$
$463$		−	9.73205i		−	0.452287i	0.974094	−	0.226143i	$-0.0726118\pi$
$464$	−0.232051	+	0.401924i	−0.0107727	+	0.0186588i
$465$		0			0
$466$	−13.0981	+	7.56218i	−0.606757	+	0.350311i
$467$	13.8564			0.641198			0.320599	−	0.947215i	$-0.396116\pi$
$467$	13.8564			0.641198			0.320599	+	0.947215i	$0.396116\pi$
$468$		0			0
$469$	−4.92820			−0.227563
$470$	10.5622	−	6.09808i	0.487197	−	0.281283i
$471$		0			0
$472$	6.46410	−	11.1962i	0.297534	−	0.515345i
$473$			11.6603i			0.536139i
$474$		0			0
$475$	2.13397	+	1.23205i	0.0979135	+	0.0565304i
$476$		−	0.267949i		−	0.0122814i
$477$		0			0
$478$	−1.36603	−	2.36603i	−0.0624805	−	0.108219i
$479$	−22.1147	+	12.7679i	−1.01045	+	0.583382i	−0.911323	−	0.411692i	$-0.864938\pi$
$479$	−22.1147	+	12.7679i	−1.01045	+	0.583382i	−0.0991253	+	0.995075i	$0.531604\pi$
$480$		0			0
$481$	9.80385	−	6.53590i	0.447017	−	0.298011i
$482$	−8.00000			−0.364390
$483$		0			0
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$	−2.26795	+	3.92820i	−0.102982	+	0.178371i
$486$		0			0
$487$	−0.571797	−	0.330127i	−0.0259106	−	0.0149595i	0.486989	−	0.873408i	$-0.338095\pi$
$487$	−0.571797	−	0.330127i	−0.0259106	−	0.0149595i	−0.512899	+	0.858449i	$0.671429\pi$
$488$	4.50000	+	2.59808i	0.203705	+	0.117609i
$489$		0			0
$490$	1.36603	−	2.36603i	0.0617107	−	0.106886i
$491$	−14.2679	−	24.7128i	−0.643904	−	1.11527i	−0.984554	−	0.175083i	$-0.943980\pi$
$491$	−14.2679	−	24.7128i	−0.643904	−	1.11527i	0.340650	−	0.940190i	$-0.389353\pi$
$492$		0			0
$493$	0.124356			0.00560070
$494$	−3.59808	+	0.232051i	−0.161885	+	0.0104405i
$495$		0			0
$496$	−7.09808	+	4.09808i	−0.318713	+	0.184009i
$497$	−4.09808	−	7.09808i	−0.183824	−	0.318392i
$498$		0			0
$499$			33.5167i			1.50041i	0.661204	+	0.750206i	$0.270046\pi$
$499$			33.5167i			1.50041i	−0.661204	+	0.750206i	$0.729954\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$		0			0
$502$			11.1244i			0.496504i
$503$	−3.46410	+	6.00000i	−0.154457	+	0.267527i	−0.932861	−	0.360236i	$-0.882696\pi$
$503$	−3.46410	+	6.00000i	−0.154457	+	0.267527i	0.778404	+	0.627763i	$0.216029\pi$
$504$		0			0
$505$	40.0526	−	23.1244i	1.78232	−	1.02902i
$506$	−6.00000			−0.266733
$507$		0			0
$508$	−8.53590			−0.378719
$509$	−34.3468	+	19.8301i	−1.52239	+	0.878955i	−0.522745	+	0.852489i	$0.675092\pi$
$509$	−34.3468	+	19.8301i	−1.52239	+	0.878955i	−0.999650	+	0.0264657i	$0.991575\pi$
$510$		0			0
$511$	0.732051	−	1.26795i	0.0323840	−	0.0560908i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	2.89230	+	1.66987i	0.127574	+	0.0736549i
$515$		−	30.7846i		−	1.35653i
$516$		0			0
$517$	−3.86603	−	6.69615i	−0.170028	−	0.294496i
$518$	−2.83013	+	1.63397i	−0.124349	+	0.0717927i
$519$		0			0
$520$	9.83013	−	0.633975i	0.431080	−	0.0278016i
$521$	31.0526			1.36044			0.680219	−	0.733009i	$-0.261885\pi$
$521$	31.0526			1.36044			0.680219	+	0.733009i	$0.261885\pi$
$522$		0			0
$523$	19.0622	+	33.0167i	0.833531	+	1.44372i	0.895221	+	0.445622i	$0.147018\pi$
$523$	19.0622	+	33.0167i	0.833531	+	1.44372i	−0.0616902	+	0.998095i	$0.519649\pi$
$524$	−6.92820	+	12.0000i	−0.302660	+	0.524222i
$525$		0			0
$526$	−7.90192	−	4.56218i	−0.344540	−	0.198920i
$527$	1.90192	+	1.09808i	0.0828491	+	0.0478330i
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	9.56218	+	16.5622i	0.415354	+	0.719415i
$531$		0			0
$532$	1.00000			0.0433555
$533$	−9.00000	+	6.00000i	−0.389833	+	0.259889i
$534$		0			0
$535$	39.8827	−	23.0263i	1.72428	−	0.995513i
$536$	2.46410	+	4.26795i	0.106433	+	0.184347i
$537$		0			0
$538$			17.8564i			0.769844i
$539$	−1.50000	−	0.866025i	−0.0646096	−	0.0373024i
$540$		0			0
$541$		−	41.6603i		−	1.79111i	−0.444947	−	0.895557i	$-0.646777\pi$
$541$		−	41.6603i		−	1.79111i	0.444947	−	0.895557i	$-0.353223\pi$
$542$	5.02628	−	8.70577i	0.215897	−	0.373945i
$543$		0			0
$544$	−0.232051	+	0.133975i	−0.00994910	+	0.00574411i
$545$	−3.46410			−0.148386
$546$		0			0
$547$	−4.73205			−0.202328			−0.101164	−	0.994870i	$-0.532257\pi$
$547$	−4.73205			−0.202328			−0.101164	+	0.994870i	$0.532257\pi$
$548$	−5.53590	+	3.19615i	−0.236482	+	0.136533i
$549$		0			0
$550$	−2.13397	+	3.69615i	−0.0909930	+	0.157604i
$551$			0.464102i			0.0197714i
$552$		0			0
$553$	−13.7942	−	7.96410i	−0.586590	−	0.338668i
$554$		−	25.3205i		−	1.07577i
$555$		0			0
$556$	−9.79423	−	16.9641i	−0.415368	−	0.719438i
$557$	−21.6962	+	12.5263i	−0.919295	+	0.530755i	−0.883410	−	0.468600i	$-0.844758\pi$
$557$	−21.6962	+	12.5263i	−0.919295	+	0.530755i	−0.0358852	+	0.999356i	$0.511425\pi$
$558$		0			0
$559$	−10.7583	+	21.7583i	−0.455029	+	0.920279i
$560$	−2.73205			−0.115450
$561$		0			0
$562$	−8.83013	−	15.2942i	−0.372476	−	0.645148i
$563$	12.9019	−	22.3468i	0.543751	−	0.941805i	−0.454933	−	0.890526i	$-0.650337\pi$
$563$	12.9019	−	22.3468i	0.543751	−	0.941805i	0.998684	−	0.0512792i	$-0.0163298\pi$
$564$		0			0
$565$	44.3205	+	25.5885i	1.86458	+	1.07651i
$566$	−15.4641	−	8.92820i	−0.650005	−	0.375280i
$567$		0			0
$568$	−4.09808	+	7.09808i	−0.171951	+	0.297829i
$569$	−10.2224	−	17.7058i	−0.428547	−	0.742265i	0.568198	−	0.822892i	$-0.307641\pi$
$569$	−10.2224	−	17.7058i	−0.428547	−	0.742265i	−0.996744	+	0.0806276i	$0.974308\pi$
$570$		0			0
$571$	34.9808			1.46390			0.731950	−	0.681359i	$-0.238611\pi$
$571$	34.9808			1.46390			0.731950	+	0.681359i	$0.238611\pi$
$572$	−0.401924	−	6.23205i	−0.0168053	−	0.260575i
$573$		0			0
$574$	2.59808	−	1.50000i	0.108442	−	0.0626088i
$575$	4.26795	+	7.39230i	0.177986	+	0.308280i
$576$		0			0
$577$		−	27.6603i		−	1.15151i	−0.817622	−	0.575756i	$-0.804708\pi$
$577$		−	27.6603i		−	1.15151i	0.817622	−	0.575756i	$-0.195292\pi$
$578$	−14.6603	−	8.46410i	−0.609786	−	0.352060i
$579$		0			0
$580$		−	1.26795i		−	0.0526487i
$581$	5.09808	−	8.83013i	0.211504	−	0.366335i
$582$		0			0
$583$	10.5000	−	6.06218i	0.434866	−	0.251070i
$584$	−1.46410			−0.0605850
$585$		0			0
$586$	30.9282			1.27763
$587$	25.6865	−	14.8301i	1.06020	−	0.612105i	0.134710	−	0.990885i	$-0.456990\pi$
$587$	25.6865	−	14.8301i	1.06020	−	0.612105i	0.925487	+	0.378780i	$0.123656\pi$
$588$		0			0
$589$	−4.09808	+	7.09808i	−0.168858	+	0.292471i
$590$			35.3205i			1.45412i
$591$		0			0
$592$	2.83013	+	1.63397i	0.116318	+	0.0671559i
$593$			6.46410i			0.265449i	0.991153	+	0.132724i	$0.0423725\pi$
$593$			6.46410i			0.265449i	−0.991153	+	0.132724i	$0.957627\pi$
$594$		0			0
$595$	0.366025	+	0.633975i	0.0150056	+	0.0259904i
$596$	−12.0000	+	6.92820i	−0.491539	+	0.283790i
$597$		0			0
$598$	−11.1962	−	5.53590i	−0.457845	−	0.226380i
$599$	−40.6410			−1.66055			−0.830273	−	0.557356i	$-0.811816\pi$
$599$	−40.6410			−1.66055			−0.830273	+	0.557356i	$0.811816\pi$
$600$		0			0
$601$	9.63397	+	16.6865i	0.392978	+	0.680658i	0.992841	−	0.119445i	$-0.0381115\pi$
$601$	9.63397	+	16.6865i	0.392978	+	0.680658i	−0.599863	+	0.800103i	$0.704778\pi$
$602$	3.36603	−	5.83013i	0.137189	−	0.237618i
$603$		0			0
$604$	−4.50000	−	2.59808i	−0.183102	−	0.105714i
$605$	−18.9282	−	10.9282i	−0.769541	−	0.444295i
$606$		0			0
$607$	−6.75833	+	11.7058i	−0.274312	+	0.475123i	−0.969961	−	0.243259i	$-0.921783\pi$
$607$	−6.75833	+	11.7058i	−0.274312	+	0.475123i	0.695649	+	0.718382i	$0.255117\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$		0			0
$610$	−14.1962			−0.574785
$611$	−1.03590	−	16.0622i	−0.0419080	−	0.649806i
$612$		0			0
$613$	−3.46410	+	2.00000i	−0.139914	+	0.0807792i	−0.568323	−	0.822806i	$-0.692408\pi$
$613$	−3.46410	+	2.00000i	−0.139914	+	0.0807792i	0.428409	+	0.903585i	$0.359074\pi$
$614$	−14.6962	−	25.4545i	−0.593088	−	1.02726i
$615$		0			0
$616$			1.73205i			0.0697863i
$617$	−7.09808	−	4.09808i	−0.285758	−	0.164982i	0.350269	−	0.936649i	$-0.386090\pi$
$617$	−7.09808	−	4.09808i	−0.285758	−	0.164982i	−0.636027	+	0.771667i	$0.719423\pi$
$618$		0			0
$619$			35.9282i			1.44408i	0.691853	+	0.722038i	$0.256795\pi$
$619$			35.9282i			1.44408i	−0.691853	+	0.722038i	$0.743205\pi$
$620$	11.1962	−	19.3923i	0.449648	−	0.778814i
$621$		0			0
$622$	−6.69615	+	3.86603i	−0.268491	+	0.155013i
$623$	3.53590			0.141663
$624$		0			0
$625$	−31.2487			−1.24995
$626$	27.2942	−	15.7583i	1.09090	−	0.629830i
$627$		0			0
$628$	−3.73205	+	6.46410i	−0.148925	+	0.257946i
$629$		−	0.875644i		−	0.0349142i
$630$		0			0
$631$	−23.5526	−	13.5981i	−0.937613	−	0.541331i	−0.0484014	−	0.998828i	$-0.515413\pi$
$631$	−23.5526	−	13.5981i	−0.937613	−	0.541331i	−0.889211	+	0.457497i	$0.848746\pi$
$632$			15.9282i			0.633590i
$633$		0			0
$634$	−7.92820	−	13.7321i	−0.314869	−	0.545369i
$635$	20.1962	−	11.6603i	0.801460	−	0.462723i
$636$		0			0
$637$	−2.00000	−	3.00000i	−0.0792429	−	0.118864i
$638$	−0.803848			−0.0318246
$639$		0			0
$640$	1.36603	+	2.36603i	0.0539969	+	0.0935254i
$641$	15.5885	−	27.0000i	0.615707	−	1.06644i	−0.374553	−	0.927206i	$-0.622204\pi$
$641$	15.5885	−	27.0000i	0.615707	−	1.06644i	0.990260	−	0.139230i	$-0.0444629\pi$
$642$		0			0
$643$	−4.45448	−	2.57180i	−0.175668	−	0.101422i	0.409588	−	0.912271i	$-0.365672\pi$
$643$	−4.45448	−	2.57180i	−0.175668	−	0.101422i	−0.585256	+	0.810849i	$0.699006\pi$
$644$	3.00000	+	1.73205i	0.118217	+	0.0682524i
$645$		0			0
$646$	−0.133975	+	0.232051i	−0.00527116	+	0.00912992i
$647$	21.9186	+	37.9641i	0.861708	+	1.49252i	0.870279	+	0.492560i	$0.163939\pi$
$647$	21.9186	+	37.9641i	0.861708	+	1.49252i	−0.00857027	+	0.999963i	$0.502728\pi$
$648$		0			0
$649$	22.3923			0.878975
$650$	−7.39230	+	4.92820i	−0.289950	+	0.193300i
$651$		0			0
$652$	0.633975	−	0.366025i	0.0248284	−	0.0143347i
$653$	−4.35641	−	7.54552i	−0.170479	−	0.295279i	0.768108	−	0.640320i	$-0.221198\pi$
$653$	−4.35641	−	7.54552i	−0.170479	−	0.295279i	−0.938588	+	0.345041i	$0.887865\pi$
$654$		0			0
$655$		−	37.8564i		−	1.47917i
$656$	−2.59808	−	1.50000i	−0.101438	−	0.0585652i
$657$		0			0
$658$			4.46410i			0.174029i
$659$	19.6962	−	34.1147i	0.767253	−	1.32892i	−0.171794	−	0.985133i	$-0.554956\pi$
$659$	19.6962	−	34.1147i	0.767253	−	1.32892i	0.939047	−	0.343789i	$-0.111710\pi$
$660$		0			0
$661$	7.26795	−	4.19615i	0.282690	−	0.163211i	−0.351950	−	0.936019i	$-0.614481\pi$
$661$	7.26795	−	4.19615i	0.282690	−	0.163211i	0.634641	+	0.772807i	$0.281148\pi$
$662$	0.143594			0.00558092
$663$		0			0
$664$	−10.1962			−0.395687
$665$	−2.36603	+	1.36603i	−0.0917505	+	0.0529722i
$666$		0			0
$667$	−0.803848	+	1.39230i	−0.0311251	+	0.0539103i
$668$		−	13.8564i		−	0.536120i
$669$		0			0
$670$	−11.6603	−	6.73205i	−0.450475	−	0.260082i
$671$			9.00000i			0.347441i
$672$		0			0
$673$	11.3564	+	19.6699i	0.437757	+	0.758218i	0.997516	−	0.0704376i	$-0.0224396\pi$
$673$	11.3564	+	19.6699i	0.437757	+	0.758218i	−0.559759	+	0.828656i	$0.689106\pi$
$674$	16.4545	−	9.50000i	0.633803	−	0.365926i
$675$		0			0
$676$	5.00000	−	12.0000i	0.192308	−	0.461538i
$677$	−33.2679			−1.27859			−0.639296	−	0.768961i	$-0.720774\pi$
$677$	−33.2679			−1.27859			−0.639296	+	0.768961i	$0.720774\pi$
$678$		0			0
$679$	−0.830127	−	1.43782i	−0.0318574	−	0.0551786i
$680$	0.366025	−	0.633975i	0.0140364	−	0.0243118i
$681$		0			0
$682$	−12.2942	−	7.09808i	−0.470770	−	0.271799i
$683$	43.6410	+	25.1962i	1.66988	+	0.964104i	0.967701	+	0.252101i	$0.0811214\pi$
$683$	43.6410	+	25.1962i	1.66988	+	0.964104i	0.702176	+	0.712003i	$0.252212\pi$
$684$		0			0
$685$	8.73205	−	15.1244i	0.333635	−	0.577872i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−6.73205			−0.256657
$689$	25.1865	−	1.62436i	0.959531	−	0.0618830i
$690$		0			0
$691$	10.1436	−	5.85641i	0.385880	−	0.222788i	−0.294493	−	0.955654i	$-0.595151\pi$
$691$	10.1436	−	5.85641i	0.385880	−	0.222788i	0.680374	+	0.732865i	$0.261817\pi$
$692$	7.56218	+	13.0981i	0.287471	+	0.497914i
$693$		0			0
$694$		−	15.3923i		−	0.584284i
$695$	46.3468	+	26.7583i	1.75803	+	1.01500i
$696$		0			0
$697$			0.803848i			0.0304479i
$698$	15.8564	−	27.4641i	0.600174	−	1.03953i
$699$		0			0
$700$	2.13397	−	1.23205i	0.0806567	−	0.0465671i
$701$	28.8564			1.08989			0.544946	−	0.838471i	$-0.316550\pi$
$701$	28.8564			1.08989			0.544946	+	0.838471i	$0.316550\pi$
$702$		0			0
$703$	3.26795			0.123253
$704$	1.50000	−	0.866025i	0.0565334	−	0.0326396i
$705$		0			0
$706$	1.26795	−	2.19615i	0.0477199	−	0.0826533i
$707$			16.9282i			0.636651i
$708$		0			0
$709$	−5.24167	−	3.02628i	−0.196855	−	0.113654i	0.398333	−	0.917241i	$-0.369589\pi$
$709$	−5.24167	−	3.02628i	−0.196855	−	0.113654i	−0.595188	+	0.803587i	$0.702922\pi$
$710$		−	22.3923i		−	0.840368i
$711$		0			0
$712$	−1.76795	−	3.06218i	−0.0662567	−	0.114760i
$713$	−24.5885	+	14.1962i	−0.920845	+	0.531650i
$714$		0			0
$715$	9.46410	+	14.1962i	0.353937	+	0.530906i
$716$	−4.53590			−0.169514
$717$		0			0
$718$	−7.09808	−	12.2942i	−0.264898	−	0.458817i
$719$	9.25833	−	16.0359i	0.345277	−	0.598038i	−0.640127	−	0.768269i	$-0.721118\pi$
$719$	9.25833	−	16.0359i	0.345277	−	0.598038i	0.985404	+	0.170231i	$0.0544515\pi$
$720$		0			0
$721$	9.75833	+	5.63397i	0.363419	+	0.209820i
$722$	15.5885	+	9.00000i	0.580142	+	0.334945i
$723$		0			0
$724$	−7.33013	+	12.6962i	−0.272422	+	0.471849i
$725$	0.571797	+	0.990381i	0.0212360	+	0.0367818i
$726$		0			0
$727$	−15.3205			−0.568206			−0.284103	−	0.958794i	$-0.591696\pi$
$727$	−15.3205			−0.568206			−0.284103	+	0.958794i	$0.591696\pi$
$728$	−1.59808	+	3.23205i	−0.0592286	+	0.119788i
$729$		0			0
$730$	3.46410	−	2.00000i	0.128212	−	0.0740233i
$731$	0.901924	+	1.56218i	0.0333589	+	0.0577792i
$732$		0			0
$733$			14.1769i			0.523636i	0.965117	+	0.261818i	$0.0843221\pi$
$733$			14.1769i			0.523636i	−0.965117	+	0.261818i	$0.915678\pi$
$734$	−8.07180	−	4.66025i	−0.297935	−	0.172013i
$735$		0			0
$736$		−	3.46410i		−	0.127688i
$737$	−4.26795	+	7.39230i	−0.157212	+	0.272299i
$738$		0			0
$739$	40.8564	−	23.5885i	1.50293	−	0.867715i	0.502933	−	0.864325i	$-0.332254\pi$
$739$	40.8564	−	23.5885i	1.50293	−	0.867715i	0.999994	−	0.00339000i	$-0.00107907\pi$
$740$	−8.92820			−0.328207
$741$		0			0
$742$	−7.00000			−0.256978
$743$	20.8301	−	12.0263i	0.764183	−	0.441201i	−0.0666124	−	0.997779i	$-0.521219\pi$
$743$	20.8301	−	12.0263i	0.764183	−	0.441201i	0.830796	+	0.556578i	$0.187886\pi$
$744$		0			0
$745$	18.9282	−	32.7846i	0.693476	−	1.20114i
$746$			7.66025i			0.280462i
$747$		0			0
$748$	−0.401924	−	0.232051i	−0.0146958	−	0.00848462i
$749$			16.8564i			0.615920i
$750$		0			0
$751$	−23.4282	−	40.5788i	−0.854907	−	1.48074i	−0.876731	−	0.480981i	$-0.840281\pi$
$751$	−23.4282	−	40.5788i	−0.854907	−	1.48074i	0.0218237	−	0.999762i	$-0.493053\pi$
$752$	3.86603	−	2.23205i	0.140979	−	0.0813945i
$753$		0			0
$754$	−1.50000	−	0.741670i	−0.0546268	−	0.0270100i
$755$	14.1962			0.516651
$756$		0			0
$757$	−15.2942	−	26.4904i	−0.555878	−	0.962809i	−0.997835	−	0.0657728i	$-0.979049\pi$
$757$	−15.2942	−	26.4904i	−0.555878	−	0.962809i	0.441956	−	0.897037i	$-0.354285\pi$
$758$	−15.2224	+	26.3660i	−0.552904	+	0.957657i
$759$		0			0
$760$	2.36603	+	1.36603i	0.0858248	+	0.0495509i
$761$	−16.7321	−	9.66025i	−0.606536	−	0.350184i	0.165072	−	0.986281i	$-0.447214\pi$
$761$	−16.7321	−	9.66025i	−0.606536	−	0.350184i	−0.771609	+	0.636098i	$0.780548\pi$
$762$		0			0
$763$	0.633975	−	1.09808i	0.0229514	−	0.0397530i
$764$	0.562178	+	0.973721i	0.0203389	+	0.0352280i
$765$		0			0
$766$	12.4641			0.450346
$767$	41.7846	+	20.6603i	1.50875	+	0.745999i
$768$		0			0
$769$	38.3660	−	22.1506i	1.38351	−	0.798772i	0.390940	−	0.920416i	$-0.372150\pi$
$769$	38.3660	−	22.1506i	1.38351	−	0.798772i	0.992574	+	0.121644i	$0.0388165\pi$
$770$	−2.36603	−	4.09808i	−0.0852656	−	0.147684i
$771$		0			0
$772$			9.19615i			0.330977i
$773$	13.1436	+	7.58846i	0.472742	+	0.272938i	0.717387	−	0.696675i	$-0.245338\pi$
$773$	13.1436	+	7.58846i	0.472742	+	0.272938i	−0.244645	+	0.969613i	$0.578671\pi$
$774$		0			0
$775$			20.1962i			0.725467i
$776$	−0.830127	+	1.43782i	−0.0297998	+	0.0516148i
$777$		0			0
$778$	10.7321	−	6.19615i	0.384763	−	0.222143i
$779$	−3.00000			−0.107486
$780$		0			0
$781$	−14.1962			−0.507978
$782$	−0.803848	+	0.464102i	−0.0287455	+	0.0165962i
$783$		0			0
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	20.3923i		−	0.727833i
$786$		0			0
$787$	−33.1865	−	19.1603i	−1.18297	−	0.682989i	−0.226272	−	0.974064i	$-0.572654\pi$
$787$	−33.1865	−	19.1603i	−1.18297	−	0.682989i	−0.956700	+	0.291075i	$0.905987\pi$
$788$		−	9.33975i		−	0.332715i
$789$		0			0
$790$	−21.7583	−	37.6865i	−0.774127	−	1.34083i
$791$	−16.2224	+	9.36603i	−0.576803	+	0.333018i
$792$		0			0
$793$	−8.30385	+	16.7942i	−0.294878	+	0.596381i
$794$	21.9282			0.778203
$795$		0			0
$796$	2.90192	+	5.02628i	0.102856	+	0.178152i
$797$	13.5622	−	23.4904i	0.480397	−	0.832072i	−0.519350	−	0.854562i	$-0.673826\pi$
$797$	13.5622	−	23.4904i	0.480397	−	0.832072i	0.999747	+	0.0224896i	$0.00715926\pi$
$798$		0			0
$799$	−1.03590	−	0.598076i	−0.0366475	−	0.0211584i
$800$	−2.13397	−	1.23205i	−0.0754474	−	0.0435596i
$801$		0			0
$802$	−1.39230	+	2.41154i	−0.0491640	+	0.0851545i
$803$	−1.26795	−	2.19615i	−0.0447450	−	0.0775005i
$804$		0			0
$805$	−9.46410			−0.333566
$806$	−16.3923	−	24.5885i	−0.577394	−	0.866091i
$807$		0			0
$808$	14.6603	−	8.46410i	0.515746	−	0.297766i
$809$	26.2224	+	45.4186i	0.921932	+	1.59683i	0.796423	+	0.604740i	$0.206723\pi$
$809$	26.2224	+	45.4186i	0.921932	+	1.59683i	0.125509	+	0.992093i	$0.459944\pi$
$810$		0			0
$811$		−	31.4641i		−	1.10485i	−0.833561	−	0.552427i	$-0.813702\pi$
$811$		−	31.4641i		−	1.10485i	0.833561	−	0.552427i	$-0.186298\pi$
$812$	0.401924	+	0.232051i	0.0141048	+	0.00814339i
$813$		0			0
$814$			5.66025i			0.198392i
$815$	−1.00000	+	1.73205i	−0.0350285	+	0.0606711i
$816$		0			0
$817$	−5.83013	+	3.36603i	−0.203970	+	0.117762i
$818$	−35.2679			−1.23311
$819$		0			0
$820$	8.19615			0.286222
$821$	24.1077	−	13.9186i	0.841364	−	0.485762i	−0.0163634	−	0.999866i	$-0.505209\pi$
$821$	24.1077	−	13.9186i	0.841364	−	0.485762i	0.857728	+	0.514104i	$0.171876\pi$
$822$		0			0
$823$	17.3923	−	30.1244i	0.606258	−	1.05007i	−0.385594	−	0.922669i	$-0.626003\pi$
$823$	17.3923	−	30.1244i	0.606258	−	1.05007i	0.991851	−	0.127400i	$-0.0406633\pi$
$824$		−	11.2679i		−	0.392538i
$825$		0			0
$826$	−11.1962	−	6.46410i	−0.389564	−	0.224915i
$827$		−	27.3205i		−	0.950027i	−0.879978	−	0.475014i	$-0.842443\pi$
$827$		−	27.3205i		−	0.950027i	0.879978	−	0.475014i	$-0.157557\pi$
$828$		0			0
$829$	−17.3301	−	30.0167i	−0.601900	−	1.04252i	−0.992533	−	0.121975i	$-0.961077\pi$
$829$	−17.3301	−	30.0167i	−0.601900	−	1.04252i	0.390633	−	0.920547i	$-0.372256\pi$
$830$	24.1244	−	13.9282i	0.837369	−	0.483455i
$831$		0			0
$832$	3.59808	−	0.232051i	0.124741	−	0.00804491i
$833$	−0.267949			−0.00928389
$834$		0			0
$835$	18.9282	+	32.7846i	0.655037	+	1.13456i
$836$	0.866025	−	1.50000i	0.0299521	−	0.0518786i
$837$		0			0
$838$	2.36603	+	1.36603i	0.0817330	+	0.0471886i
$839$	36.4641	+	21.0526i	1.25888	+	0.726815i	0.972857	−	0.231408i	$-0.0743331\pi$
$839$	36.4641	+	21.0526i	1.25888	+	0.726815i	0.286024	+	0.958223i	$0.407666\pi$
$840$		0			0
$841$	14.3923	−	24.9282i	0.496286	−	0.859593i
$842$	−0.803848	−	1.39230i	−0.0277024	−	0.0479820i
$843$		0			0
$844$	−26.0000			−0.894957
$845$	4.56218	+	35.2224i	0.156944	+	1.21169i
$846$		0			0
$847$	6.92820	−	4.00000i	0.238056	−	0.137442i
$848$	3.50000	+	6.06218i	0.120190	+	0.208176i
$849$		0			0
$850$			0.660254i			0.0226465i
$851$	9.80385	+	5.66025i	0.336072	+	0.194031i
$852$		0			0
$853$			5.92820i			0.202978i	0.994837	+	0.101489i	$0.0323606\pi$
$853$			5.92820i			0.202978i	−0.994837	+	0.101489i	$0.967639\pi$
$854$	2.59808	−	4.50000i	0.0889043	−	0.153987i
$855$		0			0
$856$	14.5981	−	8.42820i	0.498952	−	0.288070i
$857$	−39.4641			−1.34807			−0.674034	−	0.738700i	$-0.735440\pi$
$857$	−39.4641			−1.34807			−0.674034	+	0.738700i	$0.735440\pi$
$858$		0			0
$859$	−50.7654			−1.73209			−0.866046	−	0.499964i	$-0.833346\pi$
$859$	−50.7654			−1.73209			−0.866046	+	0.499964i	$0.833346\pi$
$860$	15.9282	−	9.19615i	0.543147	−	0.313586i
$861$		0			0
$862$	1.90192	−	3.29423i	0.0647798	−	0.112202i
$863$		−	16.9282i		−	0.576243i	−0.957594	−	0.288121i	$-0.906969\pi$
$863$		−	16.9282i		−	0.576243i	0.957594	−	0.288121i	$-0.0930307\pi$
$864$		0			0
$865$	−35.7846	−	20.6603i	−1.21671	−	0.702470i
$866$		−	40.9282i		−	1.39080i
$867$		0			0
$868$	4.09808	+	7.09808i	0.139098	+	0.240924i
$869$	−23.8923	+	13.7942i	−0.810491	+	0.467937i
$870$		0			0
$871$	−14.7846	+	9.85641i	−0.500957	+	0.333972i
$872$	−1.26795			−0.0429382
$873$		0			0
$874$	−1.73205	−	3.00000i	−0.0585875	−	0.101477i
$875$	3.46410	−	6.00000i	0.117108	−	0.202837i
$876$		0			0
$877$	−23.1506	−	13.3660i	−0.781741	−	0.451339i	0.0553057	−	0.998469i	$-0.482387\pi$
$877$	−23.1506	−	13.3660i	−0.781741	−	0.451339i	−0.837047	+	0.547131i	$0.815720\pi$
$878$	−32.1962	−	18.5885i	−1.08657	−	0.627330i
$879$		0			0
$880$	−2.36603	+	4.09808i	−0.0797587	+	0.138146i
$881$	−4.53590	−	7.85641i	−0.152818	−	0.264689i	0.779444	−	0.626472i	$-0.215502\pi$
$881$	−4.53590	−	7.85641i	−0.152818	−	0.264689i	−0.932262	+	0.361783i	$0.882168\pi$
$882$		0			0
$883$	−30.0526			−1.01135			−0.505675	−	0.862724i	$-0.668756\pi$
$883$	−30.0526			−1.01135			−0.505675	+	0.862724i	$0.668756\pi$
$884$	−0.535898	−	0.803848i	−0.0180242	−	0.0270363i
$885$		0			0
$886$	30.8660	−	17.8205i	1.03696	−	0.598692i
$887$	21.7224	+	37.6244i	0.729368	+	1.26330i	0.957151	+	0.289590i	$0.0935190\pi$
$887$	21.7224	+	37.6244i	0.729368	+	1.26330i	−0.227783	+	0.973712i	$0.573148\pi$
$888$		0			0
$889$			8.53590i			0.286285i
$890$	8.36603	+	4.83013i	0.280430	+	0.161906i
$891$		0			0
$892$			3.60770i			0.120795i
$893$	2.23205	−	3.86603i	0.0746927	−	0.129372i
$894$		0			0
$895$	10.7321	−	6.19615i	0.358733	−	0.207115i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	10.5885			0.353341
$899$	−3.29423	+	1.90192i	−0.109869	+	0.0634327i
$900$		0			0
$901$	0.937822	−	1.62436i	0.0312434	−	0.0541151i
$902$		−	5.19615i		−	0.173013i
$903$		0			0
$904$	16.2224	+	9.36603i	0.539550	+	0.311509i
$905$		−	40.0526i		−	1.33139i
$906$		0			0
$907$	−11.1962	−	19.3923i	−0.371762	−	0.643911i	0.618075	−	0.786119i	$-0.287913\pi$
$907$	−11.1962	−	19.3923i	−0.371762	−	0.643911i	−0.989837	+	0.142209i	$0.954580\pi$
$908$	−2.07180	+	1.19615i	−0.0687550	+	0.0396957i
$909$		0			0
$910$	−0.633975	−	9.83013i	−0.0210161	−	0.325866i
$911$	−28.8372			−0.955418			−0.477709	−	0.878518i	$-0.658533\pi$
$911$	−28.8372			−0.955418			−0.477709	+	0.878518i	$0.658533\pi$
$912$		0			0
$913$	−8.83013	−	15.2942i	−0.292235	−	0.506165i
$914$	−7.92820	+	13.7321i	−0.262242	+	0.454216i
$915$		0			0
$916$	−5.25833	−	3.03590i	−0.173740	−	0.100309i
$917$	12.0000	+	6.92820i	0.396275	+	0.228789i
$918$		0			0
$919$	−2.57180	+	4.45448i	−0.0848357	+	0.146940i	−0.905321	−	0.424728i	$-0.860370\pi$
$919$	−2.57180	+	4.45448i	−0.0848357	+	0.146940i	0.820485	+	0.571667i	$0.193703\pi$
$920$	4.73205	+	8.19615i	0.156011	+	0.270219i
$921$		0			0
$922$	13.0718			0.430497
$923$	−26.4904	−	13.0981i	−0.871942	−	0.431128i
$924$		0			0
$925$	6.97372	−	4.02628i	0.229295	−	0.132383i
$926$	4.86603	+	8.42820i	0.159908	+	0.276968i
$927$		0			0
$928$		−	0.464102i		−	0.0152349i
$929$	−27.9904	−	16.1603i	−0.918335	−	0.530201i	−0.0352312	−	0.999379i	$-0.511217\pi$
$929$	−27.9904	−	16.1603i	−0.918335	−	0.530201i	−0.883103	+	0.469178i	$0.844550\pi$
$930$		0			0
$931$		−	1.00000i		−	0.0327737i
$932$	7.56218	−	13.0981i	0.247707	−	0.429042i
$933$		0			0
$934$	−12.0000	+	6.92820i	−0.392652	+	0.226698i
$935$	1.26795			0.0414664
$936$		0			0
$937$	14.9282			0.487683			0.243842	−	0.969815i	$-0.421592\pi$
$937$	14.9282			0.487683			0.243842	+	0.969815i	$0.421592\pi$
$938$	4.26795	−	2.46410i	0.139353	−	0.0804558i
$939$		0			0
$940$	−6.09808	+	10.5622i	−0.198897	+	0.344500i
$941$			32.3923i			1.05596i	0.849257	+	0.527979i	$0.177050\pi$
$941$			32.3923i			1.05596i	−0.849257	+	0.527979i	$0.822950\pi$
$942$		0			0
$943$	−9.00000	−	5.19615i	−0.293080	−	0.169210i
$944$			12.9282i			0.420777i
$945$		0			0
$946$	−5.83013	−	10.0981i	−0.189554	−	0.328317i
$947$	10.8397	−	6.25833i	0.352244	−	0.203368i	−0.313429	−	0.949612i	$-0.601478\pi$
$947$	10.8397	−	6.25833i	0.352244	−	0.203368i	0.665673	+	0.746243i	$0.268144\pi$
$948$		0			0
$949$	−0.339746	−	5.26795i	−0.0110286	−	0.171005i
$950$	−2.46410			−0.0799460
$951$		0			0
$952$	0.133975	+	0.232051i	0.00434214	+	0.00752081i
$953$	−11.9019	+	20.6147i	−0.385541	+	0.667777i	−0.991844	−	0.127457i	$-0.959319\pi$
$953$	−11.9019	+	20.6147i	−0.385541	+	0.667777i	0.606303	+	0.795234i	$0.292652\pi$
$954$		0			0
$955$	−2.66025	−	1.53590i	−0.0860838	−	0.0497005i
$956$	2.36603	+	1.36603i	0.0765227	+	0.0441804i
$957$		0			0
$958$	12.7679	−	22.1147i	0.412514	−	0.714495i
$959$	3.19615	+	5.53590i	0.103209	+	0.178763i
$960$		0			0
$961$	−36.1769			−1.16700
$962$	−5.22243	+	10.5622i	−0.168378	+	0.340538i
$963$		0			0
$964$	6.92820	−	4.00000i	0.223142	−	0.128831i
$965$	−12.5622	−	21.7583i	−0.404391	−	0.700425i
$966$		0			0
$967$			55.7128i			1.79160i	0.444454	+	0.895802i	$0.353398\pi$
$967$			55.7128i			1.79160i	−0.444454	+	0.895802i	$0.646602\pi$
$968$	−6.92820	−	4.00000i	−0.222681	−	0.128565i
$969$		0			0
$970$		−	4.53590i		−	0.145639i
$971$	11.0526	−	19.1436i	0.354693	−	0.614347i	−0.632372	−	0.774665i	$-0.717919\pi$
$971$	11.0526	−	19.1436i	0.354693	−	0.614347i	0.987065	+	0.160318i	$0.0512519\pi$
$972$		0			0
$973$	−16.9641	+	9.79423i	−0.543844	+	0.313989i
$974$	0.660254			0.0211559
$975$		0			0
$976$	−5.19615			−0.166325
$977$	3.80385	−	2.19615i	0.121696	−	0.0702611i	−0.437916	−	0.899016i	$-0.644283\pi$
$977$	3.80385	−	2.19615i	0.121696	−	0.0702611i	0.559612	+	0.828755i	$0.310950\pi$
$978$		0			0
$979$	3.06218	−	5.30385i	0.0978676	−	0.169512i
$980$			2.73205i			0.0872722i
$981$		0			0
$982$	24.7128	+	14.2679i	0.788618	+	0.455309i
$983$			8.14359i			0.259740i	0.991531	+	0.129870i	$0.0414560\pi$
$983$			8.14359i			0.259740i	−0.991531	+	0.129870i	$0.958544\pi$
$984$		0			0
$985$	12.7583	+	22.0981i	0.406514	+	0.704103i
$986$	−0.107695	+	0.0621778i	−0.00342971	+	0.00198015i
$987$		0			0
$988$	3.00000	−	2.00000i	0.0954427	−	0.0636285i
$989$	−23.3205			−0.741549
$990$		0			0
$991$	5.37564	+	9.31089i	0.170763	+	0.295770i	0.938687	−	0.344771i	$-0.112043\pi$
$991$	5.37564	+	9.31089i	0.170763	+	0.295770i	−0.767924	+	0.640541i	$0.778710\pi$
$992$	4.09808	−	7.09808i	0.130114	−	0.225364i
$993$		0			0
$994$	7.09808	+	4.09808i	0.225137	+	0.129983i
$995$	−13.7321	−	7.92820i	−0.435335	−	0.251341i
$996$		0			0
$997$	−8.52628	+	14.7679i	−0.270030	+	0.467706i	−0.968869	−	0.247573i	$-0.920367\pi$
$997$	−8.52628	+	14.7679i	−0.270030	+	0.467706i	0.698839	+	0.715279i	$0.253700\pi$
$998$	−16.7583	−	29.0263i	−0.530476	−	0.918811i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.b.127.1		4
3.2	odd	2		546.2.s.a.127.2	yes	4
13.4	even	6	inner	1638.2.bj.b.1135.1		4
39.2	even	12		7098.2.a.bx.1.1		2
39.11	even	12		7098.2.a.bp.1.2		2
39.17	odd	6		546.2.s.a.43.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.a.43.2	✓	4	39.17	odd	6
546.2.s.a.127.2	yes	4	3.2	odd	2
1638.2.bj.b.127.1		4	1.1	even	1	trivial
1638.2.bj.b.1135.1		4	13.4	even	6	inner
7098.2.a.bp.1.2		2	39.11	even	12
7098.2.a.bx.1.1		2	39.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.36603 - 2.36603i) q^{10} +(-1.50000 + 0.866025i) q^{11} +(-3.59808 + 0.232051i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.133975 + 0.232051i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(2.36603 + 1.36603i) q^{20} +(0.866025 - 1.50000i) q^{22} +(-1.73205 - 3.00000i) q^{23} -2.46410 q^{25} +(3.00000 - 2.00000i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-0.232051 - 0.401924i) q^{29} -8.19615i q^{31} +(0.866025 + 0.500000i) q^{32} -0.267949i q^{34} +(1.36603 - 2.36603i) q^{35} +(-2.83013 + 1.63397i) q^{37} +1.00000 q^{38} -2.73205 q^{40} +(2.59808 - 1.50000i) q^{41} +(3.36603 - 5.83013i) q^{43} +1.73205i q^{44} +(3.00000 + 1.73205i) q^{46} +4.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(2.13397 - 1.23205i) q^{50} +(-1.59808 + 3.23205i) q^{52} -7.00000 q^{53} +(-2.36603 - 4.09808i) q^{55} +(0.500000 - 0.866025i) q^{56} +(0.401924 + 0.232051i) q^{58} +(-11.1962 - 6.46410i) q^{59} +(2.59808 - 4.50000i) q^{61} +(4.09808 + 7.09808i) q^{62} -1.00000 q^{64} +(-0.633975 - 9.83013i) q^{65} +(4.26795 - 2.46410i) q^{67} +(0.133975 + 0.232051i) q^{68} +2.73205i q^{70} +(7.09808 + 4.09808i) q^{71} +1.46410i q^{73} +(1.63397 - 2.83013i) q^{74} +(-0.866025 + 0.500000i) q^{76} +1.73205 q^{77} +15.9282 q^{79} +(2.36603 - 1.36603i) q^{80} +(-1.50000 + 2.59808i) q^{82} +10.1962i q^{83} +(-0.633975 - 0.366025i) q^{85} +6.73205i q^{86} +(-0.866025 - 1.50000i) q^{88} +(-3.06218 + 1.76795i) q^{89} +(3.23205 + 1.59808i) q^{91} -3.46410 q^{92} +(-2.23205 - 3.86603i) q^{94} +(1.36603 - 2.36603i) q^{95} +(1.43782 + 0.830127i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} - 2 q^{10} - 6 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 6 q^{29} + 2 q^{35} + 6 q^{37} + 4 q^{38} - 4 q^{40} + 10 q^{43} + 12 q^{46} + 2 q^{49} + 12 q^{50} + 4 q^{52} - 28 q^{53} - 6 q^{55} + 2 q^{56} + 12 q^{58} - 24 q^{59} + 6 q^{62} - 4 q^{64} - 6 q^{65} + 24 q^{67} + 4 q^{68} + 18 q^{71} + 10 q^{74} + 36 q^{79} + 6 q^{80} - 6 q^{82} - 6 q^{85} + 12 q^{89} + 6 q^{91} - 2 q^{94} + 2 q^{95} + 30 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^10 - 6 * q^11 - 4 * q^13 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 6 * q^20 + 4 * q^25 + 12 * q^26 + 6 * q^29 + 2 * q^35 + 6 * q^37 + 4 * q^38 - 4 * q^40 + 10 * q^43 + 12 * q^46 + 2 * q^49 + 12 * q^50 + 4 * q^52 - 28 * q^53 - 6 * q^55 + 2 * q^56 + 12 * q^58 - 24 * q^59 + 6 * q^62 - 4 * q^64 - 6 * q^65 + 24 * q^67 + 4 * q^68 + 18 * q^71 + 10 * q^74 + 36 * q^79 + 6 * q^80 - 6 * q^82 - 6 * q^85 + 12 * q^89 + 6 * q^91 - 2 * q^94 + 2 * q^95 + 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more