LMFDB - Embedded newform 378.2.k.d.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(215,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("378.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.k (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	378.269
Dual form			378.2.k.d.215.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} +1.00000i q^{8} +(2.12132 + 1.22474i) q^{10} +(-3.67423 - 2.12132i) q^{11} -0.717439i q^{13} +(-0.358719 - 2.62132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.22474 + 2.12132i) q^{17} +(-4.24264 + 2.44949i) q^{19} -2.44949 q^{20} +4.24264 q^{22} +(-5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(0.358719 + 0.621320i) q^{26} +(1.62132 + 2.09077i) q^{28} +1.75736i q^{29} +(-7.86396 - 4.54026i) q^{31} +(0.866025 + 0.500000i) q^{32} -2.44949i q^{34} +(6.42090 - 0.878680i) q^{35} +(-2.62132 - 4.54026i) q^{37} +(2.44949 - 4.24264i) q^{38} +(2.12132 - 1.22474i) q^{40} -2.44949 q^{41} +7.00000 q^{43} +(-3.67423 + 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-6.42090 - 11.1213i) q^{47} +(-5.00000 - 4.89898i) q^{49} -1.00000i q^{50} +(-0.621320 - 0.358719i) q^{52} +(12.5446 + 7.24264i) q^{53} +10.3923i q^{55} +(-2.44949 - 1.00000i) q^{56} +(-0.878680 - 1.52192i) q^{58} +(1.22474 - 2.12132i) q^{59} +(3.62132 - 2.09077i) q^{61} +9.08052 q^{62} -1.00000 q^{64} +(-1.52192 + 0.878680i) q^{65} +(-6.74264 + 11.6786i) q^{67} +(1.22474 + 2.12132i) q^{68} +(-5.12132 + 3.97141i) q^{70} +12.7279i q^{71} +(-4.75736 - 2.74666i) q^{73} +(4.54026 + 2.62132i) q^{74} +4.89898i q^{76} +(8.87039 - 6.87868i) q^{77} +(-0.378680 - 0.655892i) q^{79} +(-1.22474 + 2.12132i) q^{80} +(2.12132 - 1.22474i) q^{82} +15.2913 q^{83} +6.00000 q^{85} +(-6.06218 + 3.50000i) q^{86} +(2.12132 - 3.67423i) q^{88} +(-1.52192 - 2.63604i) q^{89} +(1.75736 + 0.717439i) q^{91} +6.00000i q^{92} +(11.1213 + 6.42090i) q^{94} +(10.3923 + 6.00000i) q^{95} +3.16693i q^{97} +(6.77962 + 1.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 8 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 - 8 * q^7	$ 8 q + 4 q^{4} - 8 q^{7} - 4 q^{16} - 4 q^{25} - 4 q^{28} - 12 q^{31} - 4 q^{37} + 56 q^{43} + 24 q^{46} - 40 q^{49} + 12 q^{52} - 24 q^{58} + 12 q^{61} - 8 q^{64} - 20 q^{67} - 24 q^{70} - 72 q^{73} - 20 q^{79} + 48 q^{85} + 48 q^{91} + 72 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 - 8 * q^7 - 4 * q^16 - 4 * q^25 - 4 * q^28 - 12 * q^31 - 4 * q^37 + 56 * q^43 + 24 * q^46 - 40 * q^49 + 12 * q^52 - 24 * q^58 + 12 * q^61 - 8 * q^64 - 20 * q^67 - 24 * q^70 - 72 * q^73 - 20 * q^79 + 48 * q^85 + 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	−0.998430	−	0.0560116i	$-0.982162\pi$
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	0.450708	−	0.892672i	$-0.351172\pi$
$6$		0			0
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.12132	+	1.22474i	0.670820	+	0.387298i
$11$	−3.67423	−	2.12132i	−1.10782	−	0.639602i	−0.169559	−	0.985520i	$-0.554234\pi$
$11$	−3.67423	−	2.12132i	−1.10782	−	0.639602i	−0.938265	+	0.345918i	$0.887568\pi$
$12$		0			0
$13$		−	0.717439i		−	0.198982i	−0.995038	−	0.0994909i	$-0.968279\pi$
$13$		−	0.717439i		−	0.198982i	0.995038	−	0.0994909i	$-0.0317214\pi$
$14$	−0.358719	−	2.62132i	−0.0958718	−	0.700577i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.22474	+	2.12132i	−0.297044	+	0.514496i	−0.975458	−	0.220184i	$-0.929334\pi$
$17$	−1.22474	+	2.12132i	−0.297044	+	0.514496i	0.678414	+	0.734680i	$0.262668\pi$
$18$		0			0
$19$	−4.24264	+	2.44949i	−0.973329	+	0.561951i	−0.900249	−	0.435375i	$-0.856616\pi$
$19$	−4.24264	+	2.44949i	−0.973329	+	0.561951i	−0.0730792	+	0.997326i	$0.523283\pi$
$20$	−2.44949			−0.547723
$21$		0			0
$22$	4.24264			0.904534
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.358719	+	0.621320i	0.0703507	+	0.121851i
$27$		0			0
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$			1.75736i			0.326333i	0.986599	+	0.163167i	$0.0521708\pi$
$29$			1.75736i			0.326333i	−0.986599	+	0.163167i	$0.947829\pi$
$30$		0			0
$31$	−7.86396	−	4.54026i	−1.41241	−	0.815455i	−0.416794	−	0.909001i	$-0.636846\pi$
$31$	−7.86396	−	4.54026i	−1.41241	−	0.815455i	−0.995615	+	0.0935461i	$0.970180\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	2.44949i		−	0.420084i
$35$	6.42090	−	0.878680i	1.08533	−	0.148524i
$36$		0			0
$37$	−2.62132	−	4.54026i	−0.430942	−	0.746414i	0.566012	−	0.824397i	$-0.308485\pi$
$37$	−2.62132	−	4.54026i	−0.430942	−	0.746414i	−0.996955	+	0.0779826i	$0.975152\pi$
$38$	2.44949	−	4.24264i	0.397360	−	0.688247i
$39$		0			0
$40$	2.12132	−	1.22474i	0.335410	−	0.193649i
$41$	−2.44949			−0.382546			−0.191273	−	0.981537i	$-0.561262\pi$
$41$	−2.44949			−0.382546			−0.191273	+	0.981537i	$0.561262\pi$
$42$		0			0
$43$	7.00000			1.06749			0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000			1.06749			0.533745	+	0.845645i	$0.320784\pi$
$44$	−3.67423	+	2.12132i	−0.553912	+	0.319801i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−6.42090	−	11.1213i	−0.936584	−	1.62221i	−0.771784	−	0.635884i	$-0.780636\pi$
$47$	−6.42090	−	11.1213i	−0.936584	−	1.62221i	−0.164800	−	0.986327i	$-0.552698\pi$
$48$		0			0
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$		−	1.00000i		−	0.141421i
$51$		0			0
$52$	−0.621320	−	0.358719i	−0.0861616	−	0.0497454i
$53$	12.5446	+	7.24264i	1.72314	+	0.994853i	0.912231	+	0.409675i	$0.134358\pi$
$53$	12.5446	+	7.24264i	1.72314	+	0.994853i	0.810905	+	0.585178i	$0.198975\pi$
$54$		0			0
$55$			10.3923i			1.40130i
$56$	−2.44949	−	1.00000i	−0.327327	−	0.133631i
$57$		0			0
$58$	−0.878680	−	1.52192i	−0.115376	−	0.199838i
$59$	1.22474	−	2.12132i	0.159448	−	0.276172i	−0.775222	−	0.631689i	$-0.782362\pi$
$59$	1.22474	−	2.12132i	0.159448	−	0.276172i	0.934670	+	0.355517i	$0.115695\pi$
$60$		0			0
$61$	3.62132	−	2.09077i	0.463663	−	0.267696i	−0.249920	−	0.968266i	$-0.580404\pi$
$61$	3.62132	−	2.09077i	0.463663	−	0.267696i	0.713583	+	0.700571i	$0.247071\pi$
$62$	9.08052			1.15323
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.52192	+	0.878680i	−0.188771	+	0.108987i
$66$		0			0
$67$	−6.74264	+	11.6786i	−0.823745	+	1.42677i	0.0791303	+	0.996864i	$0.474786\pi$
$67$	−6.74264	+	11.6786i	−0.823745	+	1.42677i	−0.902875	+	0.429903i	$0.858548\pi$
$68$	1.22474	+	2.12132i	0.148522	+	0.257248i
$69$		0			0
$70$	−5.12132	+	3.97141i	−0.612115	+	0.474674i
$71$			12.7279i			1.51053i	0.655422	+	0.755263i	$0.272491\pi$
$71$			12.7279i			1.51053i	−0.655422	+	0.755263i	$0.727509\pi$
$72$		0			0
$73$	−4.75736	−	2.74666i	−0.556807	−	0.321473i	0.195056	−	0.980792i	$-0.437511\pi$
$73$	−4.75736	−	2.74666i	−0.556807	−	0.321473i	−0.751863	+	0.659320i	$0.770844\pi$
$74$	4.54026	+	2.62132i	0.527795	+	0.304722i
$75$		0			0
$76$			4.89898i			0.561951i
$77$	8.87039	−	6.87868i	1.01087	−	0.783898i
$78$		0			0
$79$	−0.378680	−	0.655892i	−0.0426048	−	0.0737937i	0.843937	−	0.536443i	$-0.180232\pi$
$79$	−0.378680	−	0.655892i	−0.0426048	−	0.0737937i	−0.886541	+	0.462649i	$0.846899\pi$
$80$	−1.22474	+	2.12132i	−0.136931	+	0.237171i
$81$		0			0
$82$	2.12132	−	1.22474i	0.234261	−	0.135250i
$83$	15.2913			1.67844			0.839218	−	0.543795i	$-0.183013\pi$
$83$	15.2913			1.67844			0.839218	+	0.543795i	$0.183013\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$	−6.06218	+	3.50000i	−0.653701	+	0.377415i
$87$		0			0
$88$	2.12132	−	3.67423i	0.226134	−	0.391675i
$89$	−1.52192	−	2.63604i	−0.161323	−	0.279420i	0.774020	−	0.633161i	$-0.218243\pi$
$89$	−1.52192	−	2.63604i	−0.161323	−	0.279420i	−0.935343	+	0.353741i	$0.884909\pi$
$90$		0			0
$91$	1.75736	+	0.717439i	0.184221	+	0.0752080i
$92$			6.00000i			0.625543i
$93$		0			0
$94$	11.1213	+	6.42090i	1.14708	+	0.662265i
$95$	10.3923	+	6.00000i	1.06623	+	0.615587i
$96$		0			0
$97$			3.16693i			0.321553i	0.986991	+	0.160776i	$0.0513998\pi$
$97$			3.16693i			0.321553i	−0.986991	+	0.160776i	$0.948600\pi$
$98$	6.77962	+	1.74264i	0.684845	+	0.176033i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−3.67423	+	6.36396i	−0.365600	+	0.633238i	−0.988872	−	0.148767i	$-0.952470\pi$
$101$	−3.67423	+	6.36396i	−0.365600	+	0.633238i	0.623272	+	0.782005i	$0.285803\pi$
$102$		0			0
$103$	9.62132	−	5.55487i	0.948017	−	0.547338i	0.0555525	−	0.998456i	$-0.482308\pi$
$103$	9.62132	−	5.55487i	0.948017	−	0.547338i	0.892464	+	0.451118i	$0.148975\pi$
$104$	0.717439			0.0703507
$105$		0			0
$106$	−14.4853			−1.40693
$107$	2.15232	−	1.24264i	0.208072	−	0.120131i	−0.392343	−	0.919819i	$-0.628335\pi$
$107$	2.15232	−	1.24264i	0.208072	−	0.120131i	0.600415	+	0.799688i	$0.295002\pi$
$108$		0			0
$109$	8.86396	−	15.3528i	0.849013	−	1.47053i	−0.0330761	−	0.999453i	$-0.510530\pi$
$109$	8.86396	−	15.3528i	0.849013	−	1.47053i	0.882090	−	0.471082i	$-0.156136\pi$
$110$	−5.19615	−	9.00000i	−0.495434	−	0.858116i
$111$		0			0
$112$	2.62132	−	0.358719i	0.247691	−	0.0338958i
$113$		−	10.2426i		−	0.963547i	−0.876296	−	0.481773i	$-0.839993\pi$
$113$		−	10.2426i		−	0.963547i	0.876296	−	0.481773i	$-0.160007\pi$
$114$		0			0
$115$	12.7279	+	7.34847i	1.18688	+	0.685248i
$116$	1.52192	+	0.878680i	0.141307	+	0.0815834i
$117$		0			0
$118$			2.44949i			0.225494i
$119$	−3.97141	−	5.12132i	−0.364058	−	0.469471i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−2.09077	+	3.62132i	−0.189289	+	0.327859i
$123$		0			0
$124$	−7.86396	+	4.54026i	−0.706205	+	0.407727i
$125$	−9.79796			−0.876356
$126$		0			0
$127$	−7.72792			−0.685742			−0.342871	−	0.939382i	$-0.611399\pi$
$127$	−7.72792			−0.685742			−0.342871	+	0.939382i	$0.611399\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	0.878680	−	1.52192i	0.0770653	−	0.133481i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	−1.75736	−	12.8418i	−0.152382	−	1.11352i
$134$		−	13.4853i		−	1.16495i
$135$		0			0
$136$	−2.12132	−	1.22474i	−0.181902	−	0.105021i
$137$	5.19615	+	3.00000i	0.443937	+	0.256307i	0.705266	−	0.708942i	$-0.250827\pi$
$137$	5.19615	+	3.00000i	0.443937	+	0.256307i	−0.261329	+	0.965250i	$0.584161\pi$
$138$		0			0
$139$			8.06591i			0.684141i	0.939674	+	0.342071i	$0.111128\pi$
$139$			8.06591i			0.684141i	−0.939674	+	0.342071i	$0.888872\pi$
$140$	2.44949	−	6.00000i	0.207020	−	0.507093i
$141$		0			0
$142$	−6.36396	−	11.0227i	−0.534052	−	0.925005i
$143$	−1.52192	+	2.63604i	−0.127269	+	0.220437i
$144$		0			0
$145$	3.72792	−	2.15232i	0.309587	−	0.178740i
$146$	5.49333			0.454631
$147$		0			0
$148$	−5.24264			−0.430942
$149$	−14.0665	+	8.12132i	−1.15238	+	0.665324i	−0.949465	−	0.313873i	$-0.898373\pi$
$149$	−14.0665	+	8.12132i	−1.15238	+	0.665324i	−0.202911	+	0.979197i	$0.565040\pi$
$150$		0			0
$151$	−4.37868	+	7.58410i	−0.356332	+	0.617185i	−0.987345	−	0.158587i	$-0.949306\pi$
$151$	−4.37868	+	7.58410i	−0.356332	+	0.617185i	0.631013	+	0.775772i	$0.282639\pi$
$152$	−2.44949	−	4.24264i	−0.198680	−	0.344124i
$153$		0			0
$154$	−4.24264	+	10.3923i	−0.341882	+	0.837436i
$155$			22.2426i			1.78657i
$156$		0			0
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	0.0958404	−	0.995397i	$-0.469446\pi$
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	−0.814119	+	0.580699i	$0.802779\pi$
$158$	0.655892	+	0.378680i	0.0521800	+	0.0301261i
$159$		0			0
$160$		−	2.44949i		−	0.193649i
$161$	−2.15232	−	15.7279i	−0.169626	−	1.23953i
$162$		0			0
$163$	4.74264	+	8.21449i	0.371472	+	0.643409i	0.989792	−	0.142518i	$-0.0455197\pi$
$163$	4.74264	+	8.21449i	0.371472	+	0.643409i	−0.618320	+	0.785926i	$0.712186\pi$
$164$	−1.22474	+	2.12132i	−0.0956365	+	0.165647i
$165$		0			0
$166$	−13.2426	+	7.64564i	−1.02783	+	0.593417i
$167$	−0.594346			−0.0459919			−0.0229959	−	0.999736i	$-0.507320\pi$
$167$	−0.594346			−0.0459919			−0.0229959	+	0.999736i	$0.507320\pi$
$168$		0			0
$169$	12.4853			0.960406
$170$	−5.19615	+	3.00000i	−0.398527	+	0.230089i
$171$		0			0
$172$	3.50000	−	6.06218i	0.266872	−	0.462237i
$173$	−10.3923	−	18.0000i	−0.790112	−	1.36851i	−0.925897	−	0.377776i	$-0.876689\pi$
$173$	−10.3923	−	18.0000i	−0.790112	−	1.36851i	0.135785	−	0.990738i	$-0.456644\pi$
$174$		0			0
$175$	−1.62132	−	2.09077i	−0.122560	−	0.158047i
$176$			4.24264i			0.319801i
$177$		0			0
$178$	2.63604	+	1.52192i	0.197579	+	0.114073i
$179$	−5.82655	−	3.36396i	−0.435497	−	0.251434i	0.266189	−	0.963921i	$-0.414236\pi$
$179$	−5.82655	−	3.36396i	−0.435497	−	0.251434i	−0.701686	+	0.712487i	$0.747569\pi$
$180$		0			0
$181$		−	9.79796i		−	0.728277i	−0.931345	−	0.364138i	$-0.881364\pi$
$181$		−	9.79796i		−	0.728277i	0.931345	−	0.364138i	$-0.118636\pi$
$182$	−1.88064	+	0.257359i	−0.139402	+	0.0190767i
$183$		0			0
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$	−6.42090	+	11.1213i	−0.472074	+	0.817656i
$186$		0			0
$187$	9.00000	−	5.19615i	0.658145	−	0.379980i
$188$	−12.8418			−0.936584
$189$		0			0
$190$	−12.0000			−0.870572
$191$	−18.3712	+	10.6066i	−1.32929	+	0.767467i	−0.985190	−	0.171466i	$-0.945150\pi$
$191$	−18.3712	+	10.6066i	−1.32929	+	0.767467i	−0.344101	+	0.938933i	$0.611816\pi$
$192$		0			0
$193$	0.742641	−	1.28629i	0.0534564	−	0.0925893i	−0.838059	−	0.545580i	$-0.816310\pi$
$193$	0.742641	−	1.28629i	0.0534564	−	0.0925893i	0.891515	+	0.452990i	$0.149643\pi$
$194$	−1.58346	−	2.74264i	−0.113686	−	0.196910i
$195$		0			0
$196$	−6.74264	+	1.88064i	−0.481617	+	0.134331i
$197$		−	16.9706i		−	1.20910i	−0.796566	−	0.604551i	$-0.793352\pi$
$197$		−	16.9706i		−	1.20910i	0.796566	−	0.604551i	$-0.206648\pi$
$198$		0			0
$199$	−18.1066	−	10.4539i	−1.28354	−	0.741054i	−0.306049	−	0.952016i	$-0.599007\pi$
$199$	−18.1066	−	10.4539i	−1.28354	−	0.741054i	−0.977494	+	0.210962i	$0.932340\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$		0			0
$202$		−	7.34847i		−	0.517036i
$203$	−4.30463	−	1.75736i	−0.302126	−	0.123342i
$204$		0			0
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	−5.55487	+	9.62132i	−0.387026	+	0.670349i
$207$		0			0
$208$	−0.621320	+	0.358719i	−0.0430808	+	0.0248727i
$209$	20.7846			1.43770
$210$		0			0
$211$	3.48528			0.239937			0.119968	−	0.992778i	$-0.461721\pi$
$211$	3.48528			0.239937			0.119968	+	0.992778i	$0.461721\pi$
$212$	12.5446	−	7.24264i	0.861568	−	0.497427i
$213$		0			0
$214$	−1.24264	+	2.15232i	−0.0849452	+	0.147129i
$215$	−8.57321	−	14.8492i	−0.584688	−	1.01271i
$216$		0			0
$217$	18.9853	−	14.7224i	1.28880	−	0.999424i
$218$			17.7279i			1.20069i
$219$		0			0
$220$	9.00000	+	5.19615i	0.606780	+	0.350325i
$221$	1.52192	+	0.878680i	0.102375	+	0.0591064i
$222$		0			0
$223$		−	10.3923i		−	0.695920i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$		−	10.3923i		−	0.695920i	0.937509	−	0.347960i	$-0.113126\pi$
$224$	−2.09077	+	1.62132i	−0.139695	+	0.108329i
$225$		0			0
$226$	5.12132	+	8.87039i	0.340665	+	0.590049i
$227$	12.5446	−	21.7279i	0.832616	−	1.44213i	−0.0633412	−	0.997992i	$-0.520176\pi$
$227$	12.5446	−	21.7279i	0.832616	−	1.44213i	0.895957	−	0.444141i	$-0.146491\pi$
$228$		0			0
$229$	−4.86396	+	2.80821i	−0.321420	+	0.185572i	−0.652025	−	0.758197i	$-0.726080\pi$
$229$	−4.86396	+	2.80821i	−0.321420	+	0.185572i	0.330606	+	0.943769i	$0.392747\pi$
$230$	−14.6969			−0.969087
$231$		0			0
$232$	−1.75736			−0.115376
$233$	−17.7408	+	10.2426i	−1.16224	+	0.671018i	−0.951839	−	0.306598i	$-0.900809\pi$
$233$	−17.7408	+	10.2426i	−1.16224	+	0.671018i	−0.210398	+	0.977616i	$0.567476\pi$
$234$		0			0
$235$	−15.7279	+	27.2416i	−1.02598	+	1.77704i
$236$	−1.22474	−	2.12132i	−0.0797241	−	0.138086i
$237$		0			0
$238$	6.00000	+	2.44949i	0.388922	+	0.158777i
$239$		−	16.2426i		−	1.05065i	−0.850902	−	0.525325i	$-0.823944\pi$
$239$		−	16.2426i		−	1.05065i	0.850902	−	0.525325i	$-0.176056\pi$
$240$		0			0
$241$	−0.985281	−	0.568852i	−0.0634676	−	0.0366430i	0.467930	−	0.883765i	$-0.345000\pi$
$241$	−0.985281	−	0.568852i	−0.0634676	−	0.0366430i	−0.531398	+	0.847122i	$0.678333\pi$
$242$	−6.06218	−	3.50000i	−0.389692	−	0.224989i
$243$		0			0
$244$		−	4.18154i		−	0.267696i
$245$	−4.26858	+	16.6066i	−0.272710	+	1.06096i
$246$		0			0
$247$	1.75736	+	3.04384i	0.111818	+	0.193675i
$248$	4.54026	−	7.86396i	0.288307	−	0.499362i
$249$		0			0
$250$	8.48528	−	4.89898i	0.536656	−	0.309839i
$251$	−15.2913			−0.965177			−0.482589	−	0.875847i	$-0.660303\pi$
$251$	−15.2913			−0.965177			−0.482589	+	0.875847i	$0.660303\pi$
$252$		0			0
$253$	25.4558			1.60040
$254$	6.69258	−	3.86396i	0.419930	−	0.242446i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.5446	+	21.7279i	0.782512	+	1.35535i	0.930474	+	0.366358i	$0.119395\pi$
$257$	12.5446	+	21.7279i	0.782512	+	1.35535i	−0.147962	+	0.988993i	$0.547271\pi$
$258$		0			0
$259$	13.7426	−	1.88064i	0.853926	−	0.116857i
$260$			1.75736i			0.108987i
$261$		0			0
$262$		0			0
$263$	5.82655	+	3.36396i	0.359281	+	0.207431i	0.668765	−	0.743474i	$-0.266823\pi$
$263$	5.82655	+	3.36396i	0.359281	+	0.207431i	−0.309485	+	0.950904i	$0.600157\pi$
$264$		0			0
$265$		−	35.4815i		−	2.17961i
$266$	7.94282	+	10.2426i	0.487005	+	0.628017i
$267$		0			0
$268$	6.74264	+	11.6786i	0.411872	+	0.713384i
$269$	4.89898	−	8.48528i	0.298696	−	0.517357i	−0.677142	−	0.735853i	$-0.736782\pi$
$269$	4.89898	−	8.48528i	0.298696	−	0.517357i	0.975838	+	0.218496i	$0.0701150\pi$
$270$		0			0
$271$	−16.3492	+	9.43924i	−0.993146	+	0.573393i	−0.906213	−	0.422821i	$-0.861040\pi$
$271$	−16.3492	+	9.43924i	−0.993146	+	0.573393i	−0.0869326	+	0.996214i	$0.527706\pi$
$272$	2.44949			0.148522
$273$		0			0
$274$	−6.00000			−0.362473
$275$	3.67423	−	2.12132i	0.221565	−	0.127920i
$276$		0			0
$277$	−11.8640	+	20.5490i	−0.712836	+	1.23467i	0.250952	+	0.968000i	$0.419256\pi$
$277$	−11.8640	+	20.5490i	−0.712836	+	1.23467i	−0.963788	+	0.266669i	$0.914077\pi$
$278$	−4.03295	−	6.98528i	−0.241881	−	0.418949i
$279$		0			0
$280$	0.878680	+	6.42090i	0.0525112	+	0.383722i
$281$			13.7574i			0.820695i	0.911929	+	0.410348i	$0.134593\pi$
$281$			13.7574i			0.820695i	−0.911929	+	0.410348i	$0.865407\pi$
$282$		0			0
$283$	5.22792	+	3.01834i	0.310768	+	0.179422i	0.647270	−	0.762261i	$-0.275911\pi$
$283$	5.22792	+	3.01834i	0.310768	+	0.179422i	−0.336502	+	0.941683i	$0.609244\pi$
$284$	11.0227	+	6.36396i	0.654077	+	0.377632i
$285$		0			0
$286$		−	3.04384i		−	0.179986i
$287$	2.44949	−	6.00000i	0.144589	−	0.354169i
$288$		0			0
$289$	5.50000	+	9.52628i	0.323529	+	0.560369i
$290$	−2.15232	+	3.72792i	−0.126388	+	0.218911i
$291$		0			0
$292$	−4.75736	+	2.74666i	−0.278403	+	0.160736i
$293$	−12.8418			−0.750226			−0.375113	−	0.926979i	$-0.622396\pi$
$293$	−12.8418			−0.750226			−0.375113	+	0.926979i	$0.622396\pi$
$294$		0			0
$295$	−6.00000			−0.349334
$296$	4.54026	−	2.62132i	0.263897	−	0.152361i
$297$		0			0
$298$	8.12132	−	14.0665i	0.470455	−	0.814853i
$299$	2.15232	+	3.72792i	0.124472	+	0.215591i
$300$		0			0
$301$	−7.00000	+	17.1464i	−0.403473	+	0.988304i
$302$		−	8.75736i		−	0.503929i
$303$		0			0
$304$	4.24264	+	2.44949i	0.243332	+	0.140488i
$305$	−8.87039	−	5.12132i	−0.507917	−	0.293246i
$306$		0			0
$307$			26.8213i			1.53077i	0.643571	+	0.765386i	$0.277452\pi$
$307$			26.8213i			1.53077i	−0.643571	+	0.765386i	$0.722548\pi$
$308$	−1.52192	−	11.1213i	−0.0867193	−	0.633696i
$309$		0			0
$310$	−11.1213	−	19.2627i	−0.631649	−	1.09405i
$311$	−8.57321	+	14.8492i	−0.486142	+	0.842023i	−0.999873	−	0.0159282i	$-0.994930\pi$
$311$	−8.57321	+	14.8492i	−0.486142	+	0.842023i	0.513731	+	0.857951i	$0.328263\pi$
$312$		0			0
$313$	−17.4853	+	10.0951i	−0.988327	+	0.570611i	−0.904774	−	0.425893i	$-0.859960\pi$
$313$	−17.4853	+	10.0951i	−0.988327	+	0.570611i	−0.0835529	+	0.996503i	$0.526627\pi$
$314$	10.3923			0.586472
$315$		0			0
$316$	−0.757359			−0.0426048
$317$	19.2627	−	11.1213i	1.08190	−	0.624636i	0.150492	−	0.988611i	$-0.451914\pi$
$317$	19.2627	−	11.1213i	1.08190	−	0.624636i	0.931408	+	0.363976i	$0.118581\pi$
$318$		0			0
$319$	3.72792	−	6.45695i	0.208724	−	0.361520i
$320$	1.22474	+	2.12132i	0.0684653	+	0.118585i
$321$		0			0
$322$	9.72792	+	12.5446i	0.542116	+	0.699084i
$323$		−	12.0000i		−	0.667698i
$324$		0			0
$325$	0.621320	+	0.358719i	0.0344647	+	0.0198982i
$326$	−8.21449	−	4.74264i	−0.454959	−	0.262671i
$327$		0			0
$328$		−	2.44949i		−	0.135250i
$329$	33.6625	−	4.60660i	1.85587	−	0.253970i
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$	7.64564	−	13.2426i	0.419609	−	0.726784i
$333$		0			0
$334$	0.514719	−	0.297173i	0.0281642	−	0.0162606i
$335$	33.0321			1.80473
$336$		0			0
$337$	−21.4558			−1.16877			−0.584387	−	0.811475i	$-0.698665\pi$
$337$	−21.4558			−1.16877			−0.584387	+	0.811475i	$0.698665\pi$
$338$	−10.8126	+	6.24264i	−0.588126	+	0.339555i
$339$		0			0
$340$	3.00000	−	5.19615i	0.162698	−	0.281801i
$341$	19.2627	+	33.3640i	1.04313	+	1.80676i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$			7.00000i			0.377415i
$345$		0			0
$346$	18.0000	+	10.3923i	0.967686	+	0.558694i
$347$	4.30463	+	2.48528i	0.231085	+	0.133417i	0.611072	−	0.791575i	$-0.290738\pi$
$347$	4.30463	+	2.48528i	0.231085	+	0.133417i	−0.379988	+	0.924992i	$0.624072\pi$
$348$		0			0
$349$		−	0.123093i		−	0.00658902i	−0.999995	−	0.00329451i	$-0.998951\pi$
$349$		−	0.123093i		−	0.00658902i	0.999995	−	0.00329451i	$-0.00104868\pi$
$350$	2.44949	+	1.00000i	0.130931	+	0.0534522i
$351$		0			0
$352$	−2.12132	−	3.67423i	−0.113067	−	0.195837i
$353$	5.49333	−	9.51472i	0.292380	−	0.506417i	−0.681992	−	0.731360i	$-0.738886\pi$
$353$	5.49333	−	9.51472i	0.292380	−	0.506417i	0.974372	+	0.224942i	$0.0722194\pi$
$354$		0			0
$355$	27.0000	−	15.5885i	1.43301	−	0.827349i
$356$	−3.04384			−0.161323
$357$		0			0
$358$	6.72792			0.355582
$359$	12.5446	−	7.24264i	0.662080	−	0.382252i	−0.130989	−	0.991384i	$-0.541815\pi$
$359$	12.5446	−	7.24264i	0.662080	−	0.382252i	0.793069	+	0.609132i	$0.208482\pi$
$360$		0			0
$361$	2.50000	−	4.33013i	0.131579	−	0.227901i
$362$	4.89898	+	8.48528i	0.257485	+	0.445976i
$363$		0			0
$364$	1.50000	−	1.16320i	0.0786214	−	0.0609682i
$365$			13.4558i			0.704311i
$366$		0			0
$367$	−25.9706	−	14.9941i	−1.35565	−	0.782686i	−0.366618	−	0.930372i	$-0.619484\pi$
$367$	−25.9706	−	14.9941i	−1.35565	−	0.782686i	−0.989034	+	0.147685i	$0.952818\pi$
$368$	5.19615	+	3.00000i	0.270868	+	0.156386i
$369$		0			0
$370$		−	12.8418i		−	0.667613i
$371$	−30.2854	+	23.4853i	−1.57234	+	1.21930i
$372$		0			0
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	0.996610	+	0.0822766i	$0.0262191\pi$
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	−0.427051	+	0.904227i	$0.640448\pi$
$374$	−5.19615	+	9.00000i	−0.268687	+	0.465379i
$375$		0			0
$376$	11.1213	−	6.42090i	0.573538	−	0.331132i
$377$	1.26080			0.0649344
$378$		0			0
$379$	−7.48528			−0.384493			−0.192247	−	0.981347i	$-0.561577\pi$
$379$	−7.48528			−0.384493			−0.192247	+	0.981347i	$0.561577\pi$
$380$	10.3923	−	6.00000i	0.533114	−	0.307794i
$381$		0			0
$382$	10.6066	−	18.3712i	0.542681	−	0.939951i
$383$	2.74666	+	4.75736i	0.140348	+	0.243090i	0.927628	−	0.373506i	$-0.121845\pi$
$383$	2.74666	+	4.75736i	0.140348	+	0.243090i	−0.787280	+	0.616596i	$0.788511\pi$
$384$		0			0
$385$	−25.4558	−	10.3923i	−1.29735	−	0.529641i
$386$			1.48528i			0.0755988i
$387$		0			0
$388$	2.74264	+	1.58346i	0.139236	+	0.0803882i
$389$	−13.4361	−	7.75736i	−0.681239	−	0.393314i	0.119082	−	0.992884i	$-0.462005\pi$
$389$	−13.4361	−	7.75736i	−0.681239	−	0.393314i	−0.800322	+	0.599571i	$0.795338\pi$
$390$		0			0
$391$		−	14.6969i		−	0.743256i
$392$	4.89898	−	5.00000i	0.247436	−	0.252538i
$393$		0			0
$394$	8.48528	+	14.6969i	0.427482	+	0.740421i
$395$	−0.927572	+	1.60660i	−0.0466712	+	0.0808369i
$396$		0			0
$397$	−13.1360	+	7.58410i	−0.659279	+	0.380635i	−0.792002	−	0.610518i	$-0.790961\pi$
$397$	−13.1360	+	7.58410i	−0.659279	+	0.380635i	0.132723	+	0.991153i	$0.457628\pi$
$398$	20.9077			1.04801
$399$		0			0
$400$	1.00000			0.0500000
$401$	17.1104	−	9.87868i	0.854451	−	0.493318i	−0.00769892	−	0.999970i	$-0.502451\pi$
$401$	17.1104	−	9.87868i	0.854451	−	0.493318i	0.862150	+	0.506653i	$0.169117\pi$
$402$		0			0
$403$	−3.25736	+	5.64191i	−0.162261	+	0.281044i
$404$	3.67423	+	6.36396i	0.182800	+	0.316619i
$405$		0			0
$406$	4.60660	−	0.630399i	0.228622	−	0.0312862i
$407$			22.2426i			1.10253i
$408$		0			0
$409$	−3.25736	−	1.88064i	−0.161066	−	0.0929915i	0.417300	−	0.908769i	$-0.362976\pi$
$409$	−3.25736	−	1.88064i	−0.161066	−	0.0929915i	−0.578366	+	0.815777i	$0.696310\pi$
$410$	−5.19615	−	3.00000i	−0.256620	−	0.148159i
$411$		0			0
$412$		−	11.1097i		−	0.547338i
$413$	3.97141	+	5.12132i	0.195420	+	0.252004i
$414$		0			0
$415$	−18.7279	−	32.4377i	−0.919318	−	1.59230i
$416$	0.358719	−	0.621320i	0.0175877	−	0.0304627i
$417$		0			0
$418$	−18.0000	+	10.3923i	−0.880409	+	0.508304i
$419$	−7.94282			−0.388032			−0.194016	−	0.980998i	$-0.562151\pi$
$419$	−7.94282			−0.388032			−0.194016	+	0.980998i	$0.562151\pi$
$420$		0			0
$421$	−23.4558			−1.14317			−0.571584	−	0.820544i	$-0.693671\pi$
$421$	−23.4558			−1.14317			−0.571584	+	0.820544i	$0.693671\pi$
$422$	−3.01834	+	1.74264i	−0.146931	+	0.0848304i
$423$		0			0
$424$	−7.24264	+	12.5446i	−0.351734	+	0.609221i
$425$	−1.22474	−	2.12132i	−0.0594089	−	0.102899i
$426$		0			0
$427$	1.50000	+	10.9612i	0.0725901	+	0.530448i
$428$		−	2.48528i		−	0.120131i
$429$		0			0
$430$	14.8492	+	8.57321i	0.716094	+	0.413437i
$431$	−1.52192	−	0.878680i	−0.0733082	−	0.0423245i	0.462898	−	0.886412i	$-0.346810\pi$
$431$	−1.52192	−	0.878680i	−0.0733082	−	0.0423245i	−0.536206	+	0.844087i	$0.680143\pi$
$432$		0			0
$433$			2.57258i			0.123630i	0.998088	+	0.0618152i	$0.0196889\pi$
$433$			2.57258i			0.123630i	−0.998088	+	0.0618152i	$0.980311\pi$
$434$	−9.08052	+	22.2426i	−0.435879	+	1.06768i
$435$		0			0
$436$	−8.86396	−	15.3528i	−0.424507	−	0.735267i
$437$	14.6969	−	25.4558i	0.703050	−	1.21772i
$438$		0			0
$439$	3.72792	−	2.15232i	0.177924	−	0.102724i	−0.408393	−	0.912806i	$-0.633911\pi$
$439$	3.72792	−	2.15232i	0.177924	−	0.102724i	0.586317	+	0.810082i	$0.300577\pi$
$440$	−10.3923			−0.495434
$441$		0			0
$442$	−1.75736			−0.0835891
$443$	22.0454	−	12.7279i	1.04741	−	0.604722i	0.125486	−	0.992095i	$-0.459951\pi$
$443$	22.0454	−	12.7279i	1.04741	−	0.604722i	0.921923	+	0.387374i	$0.126618\pi$
$444$		0			0
$445$	−3.72792	+	6.45695i	−0.176720	+	0.306089i
$446$	5.19615	+	9.00000i	0.246045	+	0.426162i
$447$		0			0
$448$	1.00000	−	2.44949i	0.0472456	−	0.115728i
$449$		−	5.27208i		−	0.248805i	−0.992232	−	0.124402i	$-0.960299\pi$
$449$		−	5.27208i		−	0.248805i	0.992232	−	0.124402i	$-0.0397014\pi$
$450$		0			0
$451$	9.00000	+	5.19615i	0.423793	+	0.244677i
$452$	−8.87039	−	5.12132i	−0.417228	−	0.240887i
$453$		0			0
$454$			25.0892i			1.17750i
$455$	−0.630399	−	4.60660i	−0.0295536	−	0.215961i
$456$		0			0
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	0.999014	+	0.0443868i	$0.0141334\pi$
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	−0.461067	+	0.887365i	$0.652533\pi$
$458$	2.80821	−	4.86396i	0.131219	−	0.227278i
$459$		0			0
$460$	12.7279	−	7.34847i	0.593442	−	0.342624i
$461$	−21.4511			−0.999076			−0.499538	−	0.866292i	$-0.666497\pi$
$461$	−21.4511			−0.999076			−0.499538	+	0.866292i	$0.666497\pi$
$462$		0			0
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$	1.52192	−	0.878680i	0.0706533	−	0.0407917i
$465$		0			0
$466$	10.2426	−	17.7408i	0.474481	−	0.821825i
$467$	8.87039	+	15.3640i	0.410473	+	0.710959i	0.994941	−	0.100457i	$-0.0320304\pi$
$467$	8.87039	+	15.3640i	0.410473	+	0.710959i	−0.584469	+	0.811416i	$0.698697\pi$
$468$		0			0
$469$	−21.8640	−	28.1946i	−1.00958	−	1.30191i
$470$		−	31.4558i		−	1.45095i
$471$		0			0
$472$	2.12132	+	1.22474i	0.0976417	+	0.0563735i
$473$	−25.7196	−	14.8492i	−1.18259	−	0.682769i
$474$		0			0
$475$		−	4.89898i		−	0.224781i
$476$	−6.42090	+	0.878680i	−0.294301	+	0.0402742i
$477$		0			0
$478$	8.12132	+	14.0665i	0.371461	+	0.643389i
$479$	1.22474	−	2.12132i	0.0559600	−	0.0969256i	−0.836688	−	0.547679i	$-0.815511\pi$
$479$	1.22474	−	2.12132i	0.0559600	−	0.0969256i	0.892648	+	0.450754i	$0.148845\pi$
$480$		0			0
$481$	−3.25736	+	1.88064i	−0.148523	+	0.0857497i
$482$	1.13770			0.0518210
$483$		0			0
$484$	7.00000			0.318182
$485$	6.71807	−	3.87868i	0.305052	−	0.176122i
$486$		0			0
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	−0.999998	−	0.00178012i	$-0.999433\pi$
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	0.501541	+	0.865134i	$0.332767\pi$
$488$	2.09077	+	3.62132i	0.0946447	+	0.163929i
$489$		0			0
$490$	−4.60660	−	16.5160i	−0.208105	−	0.746118i
$491$		−	34.9706i		−	1.57820i	−0.614265	−	0.789100i	$-0.710547\pi$
$491$		−	34.9706i		−	1.57820i	0.614265	−	0.789100i	$-0.289453\pi$
$492$		0			0
$493$	−3.72792	−	2.15232i	−0.167897	−	0.0969355i
$494$	−3.04384	−	1.75736i	−0.136949	−	0.0790673i
$495$		0			0
$496$			9.08052i			0.407727i
$497$	−31.1769	−	12.7279i	−1.39848	−	0.570925i
$498$		0			0
$499$	12.2279	+	21.1794i	0.547397	+	0.948119i	0.998452	+	0.0556231i	$0.0177145\pi$
$499$	12.2279	+	21.1794i	0.547397	+	0.948119i	−0.451055	+	0.892496i	$0.648952\pi$
$500$	−4.89898	+	8.48528i	−0.219089	+	0.379473i
$501$		0			0
$502$	13.2426	−	7.64564i	0.591048	−	0.341242i
$503$	0.594346			0.0265006			0.0132503	−	0.999912i	$-0.495782\pi$
$503$	0.594346			0.0265006			0.0132503	+	0.999912i	$0.495782\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	−22.0454	+	12.7279i	−0.980038	+	0.565825i
$507$		0			0
$508$	−3.86396	+	6.69258i	−0.171436	+	0.296935i
$509$	−4.60181	−	7.97056i	−0.203971	−	0.353289i	0.745833	−	0.666133i	$-0.232052\pi$
$509$	−4.60181	−	7.97056i	−0.203971	−	0.353289i	−0.949805	+	0.312844i	$0.898718\pi$
$510$		0			0
$511$	11.4853	−	8.90644i	0.508079	−	0.393998i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−21.7279	−	12.5446i	−0.958378	−	0.553320i
$515$	−23.5673	−	13.6066i	−1.03850	−	0.599579i
$516$		0			0
$517$			54.4831i			2.39616i
$518$	−10.9612	+	8.50000i	−0.481606	+	0.373469i
$519$		0			0
$520$	−0.878680	−	1.52192i	−0.0385327	−	0.0667405i
$521$	−14.9941	+	25.9706i	−0.656904	+	1.13779i	0.324509	+	0.945883i	$0.394801\pi$
$521$	−14.9941	+	25.9706i	−0.656904	+	1.13779i	−0.981413	+	0.191908i	$0.938532\pi$
$522$		0			0
$523$	23.7426	−	13.7078i	1.03819	−	0.599401i	0.118872	−	0.992910i	$-0.462072\pi$
$523$	23.7426	−	13.7078i	1.03819	−	0.599401i	0.919321	+	0.393508i	$0.128739\pi$
$524$		0			0
$525$		0			0
$526$	−6.72792			−0.293351
$527$	19.2627	−	11.1213i	0.839096	−	0.484452i
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$	17.7408	+	30.7279i	0.770610	+	1.33474i
$531$		0			0
$532$	−12.0000	−	4.89898i	−0.520266	−	0.212398i
$533$			1.75736i			0.0761197i
$534$		0			0
$535$	−5.27208	−	3.04384i	−0.227932	−	0.131596i
$536$	−11.6786	−	6.74264i	−0.504439	−	0.291238i
$537$		0			0
$538$			9.79796i			0.422420i
$539$	7.97887	+	28.6066i	0.343674	+	1.23217i
$540$		0			0
$541$	2.72792	+	4.72490i	0.117283	+	0.203139i	0.918690	−	0.394980i	$-0.129248\pi$
$541$	2.72792	+	4.72490i	0.117283	+	0.203139i	−0.801407	+	0.598119i	$0.795915\pi$
$542$	9.43924	−	16.3492i	0.405450	−	0.702260i
$543$		0			0
$544$	−2.12132	+	1.22474i	−0.0909509	+	0.0525105i
$545$	−43.4244			−1.86010
$546$		0			0
$547$	39.9706			1.70902			0.854509	−	0.519437i	$-0.173858\pi$
$547$	39.9706			1.70902			0.854509	+	0.519437i	$0.173858\pi$
$548$	5.19615	−	3.00000i	0.221969	−	0.128154i
$549$		0			0
$550$	−2.12132	+	3.67423i	−0.0904534	+	0.156670i
$551$	−4.30463	−	7.45584i	−0.183384	−	0.317630i
$552$		0			0
$553$	1.98528	−	0.271680i	0.0844228	−	0.0115530i
$554$		−	23.7279i		−	1.00810i
$555$		0			0
$556$	6.98528	+	4.03295i	0.296242	+	0.171035i
$557$	18.3712	+	10.6066i	0.778412	+	0.449416i	0.835867	−	0.548932i	$-0.184965\pi$
$557$	18.3712	+	10.6066i	0.778412	+	0.449416i	−0.0574555	+	0.998348i	$0.518299\pi$
$558$		0			0
$559$		−	5.02207i		−	0.212411i
$560$	−3.97141	−	5.12132i	−0.167823	−	0.216415i
$561$		0			0
$562$	−6.87868	−	11.9142i	−0.290160	−	0.502571i
$563$	−22.9369	+	39.7279i	−0.966676	+	1.67433i	−0.261634	+	0.965167i	$0.584261\pi$
$563$	−22.9369	+	39.7279i	−0.966676	+	1.67433i	−0.705043	+	0.709165i	$0.749072\pi$
$564$		0			0
$565$	−21.7279	+	12.5446i	−0.914101	+	0.527756i
$566$	−6.03668			−0.253741
$567$		0			0
$568$	−12.7279			−0.534052
$569$	8.87039	−	5.12132i	0.371866	−	0.214697i	−0.302407	−	0.953179i	$-0.597790\pi$
$569$	8.87039	−	5.12132i	0.371866	−	0.214697i	0.674273	+	0.738482i	$0.264457\pi$
$570$		0			0
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	−0.538642	−	0.842535i	$-0.681062\pi$
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	0.998978	+	0.0452101i	$0.0143957\pi$
$572$	1.52192	+	2.63604i	0.0636346	+	0.110218i
$573$		0			0
$574$	0.878680	+	6.42090i	0.0366754	+	0.268003i
$575$		−	6.00000i		−	0.250217i
$576$		0			0
$577$	23.7426	+	13.7078i	0.988419	+	0.570664i	0.904801	−	0.425834i	$-0.140019\pi$
$577$	23.7426	+	13.7078i	0.988419	+	0.570664i	0.0836177	+	0.996498i	$0.473353\pi$
$578$	−9.52628	−	5.50000i	−0.396241	−	0.228770i
$579$		0			0
$580$		−	4.30463i		−	0.178740i
$581$	−15.2913	+	37.4558i	−0.634389	+	1.55393i
$582$		0			0
$583$	−30.7279	−	53.2223i	−1.27262	−	2.20424i
$584$	2.74666	−	4.75736i	0.113658	−	0.196861i
$585$		0			0
$586$	11.1213	−	6.42090i	0.459418	−	0.265245i
$587$	−32.4377			−1.33885			−0.669424	−	0.742881i	$-0.733459\pi$
$587$	−32.4377			−1.33885			−0.669424	+	0.742881i	$0.733459\pi$
$588$		0			0
$589$	44.4853			1.83298
$590$	5.19615	−	3.00000i	0.213922	−	0.123508i
$591$		0			0
$592$	−2.62132	+	4.54026i	−0.107736	+	0.186604i
$593$	−0.927572	−	1.60660i	−0.0380908	−	0.0659752i	0.846352	−	0.532625i	$-0.178794\pi$
$593$	−0.927572	−	1.60660i	−0.0380908	−	0.0659752i	−0.884442	+	0.466650i	$0.845461\pi$
$594$		0			0
$595$	−6.00000	+	14.6969i	−0.245976	+	0.602516i
$596$			16.2426i			0.665324i
$597$		0			0
$598$	−3.72792	−	2.15232i	−0.152446	−	0.0880148i
$599$	−3.04384	−	1.75736i	−0.124368	−	0.0718038i	0.436526	−	0.899692i	$-0.356209\pi$
$599$	−3.04384	−	1.75736i	−0.124368	−	0.0718038i	−0.560893	+	0.827888i	$0.689542\pi$
$600$		0			0
$601$			41.5182i			1.69356i	0.531940	+	0.846782i	$0.321463\pi$
$601$			41.5182i			1.69356i	−0.531940	+	0.846782i	$0.678537\pi$
$602$	−2.51104	−	18.3492i	−0.102342	−	0.747859i
$603$		0			0
$604$	4.37868	+	7.58410i	0.178166	+	0.308592i
$605$	8.57321	−	14.8492i	0.348551	−	0.603708i
$606$		0			0
$607$	31.2426	−	18.0379i	1.26810	−	0.732138i	0.293471	−	0.955968i	$-0.405189\pi$
$607$	31.2426	−	18.0379i	1.26810	−	0.732138i	0.974628	+	0.223830i	$0.0718561\pi$
$608$	−4.89898			−0.198680
$609$		0			0
$610$	10.2426			0.414712
$611$	−7.97887	+	4.60660i	−0.322790	+	0.186363i
$612$		0			0
$613$	14.1066	−	24.4334i	0.569760	−	0.986854i	−0.426829	−	0.904332i	$-0.640369\pi$
$613$	14.1066	−	24.4334i	0.569760	−	0.986854i	0.996589	−	0.0825214i	$-0.0262973\pi$
$614$	−13.4106	−	23.2279i	−0.541210	−	0.937403i
$615$		0			0
$616$	6.87868	+	8.87039i	0.277150	+	0.357398i
$617$		−	4.24264i		−	0.170802i	−0.996347	−	0.0854011i	$-0.972783\pi$
$617$		−	4.24264i		−	0.170802i	0.996347	−	0.0854011i	$-0.0272172\pi$
$618$		0			0
$619$	−11.0147	−	6.35935i	−0.442719	−	0.255604i	0.262031	−	0.965059i	$-0.415608\pi$
$619$	−11.0147	−	6.35935i	−0.442719	−	0.255604i	−0.704750	+	0.709455i	$0.748941\pi$
$620$	19.2627	+	11.1213i	0.773608	+	0.446643i
$621$		0			0
$622$		−	17.1464i		−	0.687509i
$623$	7.97887	−	1.09188i	0.319667	−	0.0437454i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	10.0951	−	17.4853i	0.403483	−	0.698852i
$627$		0			0
$628$	−9.00000	+	5.19615i	−0.359139	+	0.207349i
$629$	12.8418			0.512036
$630$		0			0
$631$	−14.7574			−0.587481			−0.293741	−	0.955885i	$-0.594900\pi$
$631$	−14.7574			−0.587481			−0.293741	+	0.955885i	$0.594900\pi$
$632$	0.655892	−	0.378680i	0.0260900	−	0.0150631i
$633$		0			0
$634$	−11.1213	+	19.2627i	−0.441684	+	0.765019i
$635$	9.46473	+	16.3934i	0.375596	+	0.650552i
$636$		0			0
$637$	−3.51472	+	3.58719i	−0.139258	+	0.142130i
$638$			7.45584i			0.295180i
$639$		0			0
$640$	−2.12132	−	1.22474i	−0.0838525	−	0.0484123i
$641$	−28.7635	−	16.6066i	−1.13609	−	0.655921i	−0.190630	−	0.981662i	$-0.561053\pi$
$641$	−28.7635	−	16.6066i	−1.13609	−	0.655921i	−0.945459	+	0.325741i	$0.894386\pi$
$642$		0			0
$643$		−	1.73205i		−	0.0683054i	−0.999417	−	0.0341527i	$-0.989127\pi$
$643$		−	1.73205i		−	0.0683054i	0.999417	−	0.0341527i	$-0.0108733\pi$
$644$	−14.6969	−	6.00000i	−0.579141	−	0.236433i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	10.3923	−	18.0000i	0.408564	−	0.707653i	−0.586165	−	0.810191i	$-0.699363\pi$
$647$	10.3923	−	18.0000i	0.408564	−	0.707653i	0.994729	+	0.102538i	$0.0326965\pi$
$648$		0			0
$649$	−9.00000	+	5.19615i	−0.353281	+	0.203967i
$650$	−0.717439			−0.0281403
$651$		0			0
$652$	9.48528			0.371472
$653$	2.15232	−	1.24264i	0.0842267	−	0.0486283i	−0.457295	−	0.889315i	$-0.651182\pi$
$653$	2.15232	−	1.24264i	0.0842267	−	0.0486283i	0.541522	+	0.840687i	$0.317848\pi$
$654$		0			0
$655$		0			0
$656$	1.22474	+	2.12132i	0.0478183	+	0.0828236i
$657$		0			0
$658$	−26.8492	+	20.8207i	−1.04669	+	0.811674i
$659$		−	22.2426i		−	0.866450i	−0.901286	−	0.433225i	$-0.857376\pi$
$659$		−	22.2426i		−	0.866450i	0.901286	−	0.433225i	$-0.142624\pi$
$660$		0			0
$661$	−4.24264	−	2.44949i	−0.165020	−	0.0952741i	0.415216	−	0.909723i	$-0.363706\pi$
$661$	−4.24264	−	2.44949i	−0.165020	−	0.0952741i	−0.580235	+	0.814449i	$0.697039\pi$
$662$	8.66025	+	5.00000i	0.336590	+	0.194331i
$663$		0			0
$664$			15.2913i			0.593417i
$665$	−25.0892	+	19.4558i	−0.972919	+	0.754465i
$666$		0			0
$667$	−5.27208	−	9.13151i	−0.204136	−	0.353573i
$668$	−0.297173	+	0.514719i	−0.0114980	+	0.0199151i
$669$		0			0
$670$	−28.6066	+	16.5160i	−1.10517	+	0.638070i
$671$	−17.7408			−0.684875
$672$		0			0
$673$	−45.4558			−1.75219			−0.876097	−	0.482135i	$-0.839862\pi$
$673$	−45.4558			−1.75219			−0.876097	+	0.482135i	$0.839862\pi$
$674$	18.5813	−	10.7279i	0.715725	−	0.413224i
$675$		0			0
$676$	6.24264	−	10.8126i	0.240102	−	0.415868i
$677$	−7.34847	−	12.7279i	−0.282425	−	0.489174i	0.689557	−	0.724232i	$-0.257805\pi$
$677$	−7.34847	−	12.7279i	−0.282425	−	0.489174i	−0.971981	+	0.235058i	$0.924472\pi$
$678$		0			0
$679$	−7.75736	−	3.16693i	−0.297700	−	0.121536i
$680$			6.00000i			0.230089i
$681$		0			0
$682$	−33.3640	−	19.2627i	−1.27757	−	0.737607i
$683$	−8.87039	−	5.12132i	−0.339416	−	0.195962i	0.320598	−	0.947215i	$-0.396116\pi$
$683$	−8.87039	−	5.12132i	−0.339416	−	0.195962i	−0.660014	+	0.751254i	$0.729450\pi$
$684$		0			0
$685$		−	14.6969i		−	0.561541i
$686$	−11.0482	+	14.8640i	−0.421822	+	0.567509i
$687$		0			0
$688$	−3.50000	−	6.06218i	−0.133436	−	0.231118i
$689$	5.19615	−	9.00000i	0.197958	−	0.342873i
$690$		0			0
$691$	2.22792	−	1.28629i	0.0847541	−	0.0489328i	−0.457024	−	0.889454i	$-0.651085\pi$
$691$	2.22792	−	1.28629i	0.0847541	−	0.0489328i	0.541778	+	0.840522i	$0.317751\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	−4.97056			−0.188680
$695$	17.1104	−	9.87868i	0.649034	−	0.374720i
$696$		0			0
$697$	3.00000	−	5.19615i	0.113633	−	0.196818i
$698$	0.0615465	+	0.106602i	0.00232957	+	0.00403493i
$699$		0			0
$700$	−2.62132	+	0.358719i	−0.0990766	+	0.0135583i
$701$		−	20.4853i		−	0.773718i	−0.922139	−	0.386859i	$-0.873560\pi$
$701$		−	20.4853i		−	0.773718i	0.922139	−	0.386859i	$-0.126440\pi$
$702$		0			0
$703$	22.2426	+	12.8418i	0.838897	+	0.484337i
$704$	3.67423	+	2.12132i	0.138478	+	0.0799503i
$705$		0			0
$706$			10.9867i			0.413488i
$707$	−11.9142	−	15.3640i	−0.448080	−	0.577821i
$708$		0			0
$709$	−8.10660	−	14.0410i	−0.304450	−	0.527323i	0.672689	−	0.739925i	$-0.265139\pi$
$709$	−8.10660	−	14.0410i	−0.304450	−	0.527323i	−0.977139	+	0.212603i	$0.931806\pi$
$710$	−15.5885	+	27.0000i	−0.585024	+	1.01329i
$711$		0			0
$712$	2.63604	−	1.52192i	0.0987897	−	0.0570363i
$713$	54.4831			2.04041
$714$		0			0
$715$	7.45584			0.278833
$716$	−5.82655	+	3.36396i	−0.217748	+	0.125717i
$717$		0			0
$718$	−7.24264	+	12.5446i	−0.270293	+	0.468161i
$719$	26.3140	+	45.5772i	0.981346	+	1.69974i	0.657166	+	0.753746i	$0.271755\pi$
$719$	26.3140	+	45.5772i	0.981346	+	1.69974i	0.324181	+	0.945995i	$0.394911\pi$
$720$		0			0
$721$	3.98528	+	29.1222i	0.148420	+	1.08457i
$722$			5.00000i			0.186081i
$723$		0			0
$724$	−8.48528	−	4.89898i	−0.315353	−	0.182069i
$725$	−1.52192	−	0.878680i	−0.0565226	−	0.0326333i
$726$		0			0
$727$		−	28.0821i		−	1.04151i	−0.853707	−	0.520754i	$-0.825651\pi$
$727$		−	28.0821i		−	1.04151i	0.853707	−	0.520754i	$-0.174349\pi$
$728$	−0.717439	+	1.75736i	−0.0265901	+	0.0651321i
$729$		0			0
$730$	−6.72792	−	11.6531i	−0.249012	−	0.431301i
$731$	−8.57321	+	14.8492i	−0.317092	+	0.549219i
$732$		0			0
$733$	1.13604	−	0.655892i	0.0419606	−	0.0242259i	−0.478873	−	0.877884i	$-0.658955\pi$
$733$	1.13604	−	0.655892i	0.0419606	−	0.0242259i	0.520834	+	0.853658i	$0.325621\pi$
$734$	29.9882			1.10689
$735$		0			0
$736$	−6.00000			−0.221163
$737$	49.5481	−	28.6066i	1.82513	−	1.05374i
$738$		0			0
$739$	4.22792	−	7.32298i	0.155527	−	0.269380i	−0.777724	−	0.628606i	$-0.783626\pi$
$739$	4.22792	−	7.32298i	0.155527	−	0.269380i	0.933251	+	0.359226i	$0.116959\pi$
$740$	6.42090	+	11.1213i	0.236037	+	0.408828i
$741$		0			0
$742$	14.4853	−	35.4815i	0.531771	−	1.30257i
$743$		−	18.7279i		−	0.687061i	−0.939142	−	0.343530i	$-0.888377\pi$
$743$		−	18.7279i		−	0.687061i	0.939142	−	0.343530i	$-0.111623\pi$
$744$		0			0
$745$	34.4558	+	19.8931i	1.26236	+	0.728826i
$746$	−19.0526	−	11.0000i	−0.697564	−	0.402739i
$747$		0			0
$748$		−	10.3923i		−	0.379980i
$749$	0.891519	+	6.51472i	0.0325754	+	0.238043i
$750$		0			0
$751$	−26.7279	−	46.2941i	−0.975316	−	1.68930i	−0.678889	−	0.734241i	$-0.737538\pi$
$751$	−26.7279	−	46.2941i	−0.975316	−	1.68930i	−0.296427	−	0.955056i	$-0.595795\pi$
$752$	−6.42090	+	11.1213i	−0.234146	+	0.405553i
$753$		0			0
$754$	−1.09188	+	0.630399i	−0.0397640	+	0.0229578i
$755$	21.4511			0.780684
$756$		0			0
$757$	32.7574			1.19059			0.595293	−	0.803509i	$-0.297036\pi$
$757$	32.7574			1.19059			0.595293	+	0.803509i	$0.297036\pi$
$758$	6.48244	−	3.74264i	0.235453	−	0.135939i
$759$		0			0
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	12.2474	+	21.2132i	0.443970	+	0.768978i	0.997980	−	0.0635319i	$-0.0202365\pi$
$761$	12.2474	+	21.2132i	0.443970	+	0.768978i	−0.554010	+	0.832510i	$0.686903\pi$
$762$		0			0
$763$	28.7426	+	37.0650i	1.04055	+	1.34184i
$764$			21.2132i			0.767467i
$765$		0			0
$766$	−4.75736	−	2.74666i	−0.171890	−	0.0992410i
$767$	−1.52192	−	0.878680i	−0.0549533	−	0.0317273i
$768$		0			0
$769$		−	40.3805i		−	1.45616i	−0.685493	−	0.728080i	$-0.740413\pi$
$769$		−	40.3805i		−	1.45616i	0.685493	−	0.728080i	$-0.259587\pi$
$770$	27.2416	−	3.72792i	0.981718	−	0.134345i
$771$		0			0
$772$	−0.742641	−	1.28629i	−0.0267282	−	0.0462946i
$773$	−4.89898	+	8.48528i	−0.176204	+	0.305194i	−0.940577	−	0.339580i	$-0.889715\pi$
$773$	−4.89898	+	8.48528i	−0.176204	+	0.305194i	0.764373	+	0.644774i	$0.223049\pi$
$774$		0			0
$775$	7.86396	−	4.54026i	0.282482	−	0.163091i
$776$	−3.16693			−0.113686
$777$		0			0
$778$	15.5147			0.556230
$779$	10.3923	−	6.00000i	0.372343	−	0.214972i
$780$		0			0
$781$	27.0000	−	46.7654i	0.966136	−	1.67340i
$782$	7.34847	+	12.7279i	0.262781	+	0.455150i
$783$		0			0
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$			25.4558i			0.908558i
$786$		0			0
$787$	−24.4706	−	14.1281i	−0.872281	−	0.503612i	−0.00417567	−	0.999991i	$-0.501329\pi$
$787$	−24.4706	−	14.1281i	−0.872281	−	0.503612i	−0.868106	+	0.496379i	$0.834662\pi$
$788$	−14.6969	−	8.48528i	−0.523557	−	0.302276i
$789$		0			0
$790$		−	1.85514i		−	0.0660031i
$791$	25.0892	+	10.2426i	0.892071	+	0.364186i
$792$		0			0
$793$	−1.50000	−	2.59808i	−0.0532666	−	0.0922604i
$794$	7.58410	−	13.1360i	0.269149	−	0.466181i
$795$		0			0
$796$	−18.1066	+	10.4539i	−0.641771	+	0.370527i
$797$	17.7408			0.628410			0.314205	−	0.949355i	$-0.398262\pi$
$797$	17.7408			0.628410			0.314205	+	0.949355i	$0.398262\pi$
$798$		0			0
$799$	31.4558			1.11283
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−9.87868	+	17.1104i	−0.348828	+	0.604188i
$803$	11.6531	+	20.1838i	0.411229	+	0.712270i
$804$		0			0
$805$	−30.7279	+	23.8284i	−1.08302	+	0.839842i
$806$		−	6.51472i		−	0.229471i
$807$		0			0
$808$	−6.36396	−	3.67423i	−0.223883	−	0.129259i
$809$	−12.5446	−	7.24264i	−0.441045	−	0.254638i	0.262996	−	0.964797i	$-0.415290\pi$
$809$	−12.5446	−	7.24264i	−0.441045	−	0.254638i	−0.704041	+	0.710159i	$0.748623\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−3.67423	+	2.84924i	−0.128940	+	0.0999888i
$813$		0			0
$814$	−11.1213	−	19.2627i	−0.389802	−	0.675157i
$815$	11.6170	−	20.1213i	0.406928	−	0.704819i
$816$		0			0
$817$	−29.6985	+	17.1464i	−1.03902	+	0.599878i
$818$	3.76127			0.131510
$819$		0			0
$820$	6.00000			0.209529
$821$	−19.8931	+	11.4853i	−0.694274	+	0.400839i	−0.805211	−	0.592988i	$-0.797948\pi$
$821$	−19.8931	+	11.4853i	−0.694274	+	0.400839i	0.110937	+	0.993827i	$0.464615\pi$
$822$		0			0
$823$	1.37868	−	2.38794i	0.0480578	−	0.0832385i	−0.840996	−	0.541042i	$-0.818030\pi$
$823$	1.37868	−	2.38794i	0.0480578	−	0.0832385i	0.889054	+	0.457803i	$0.151364\pi$
$824$	5.55487	+	9.62132i	0.193513	+	0.335175i
$825$		0			0
$826$	−6.00000	−	2.44949i	−0.208767	−	0.0852286i
$827$			3.51472i			0.122219i	0.998131	+	0.0611094i	$0.0194638\pi$
$827$			3.51472i			0.122219i	−0.998131	+	0.0611094i	$0.980536\pi$
$828$		0			0
$829$	8.48528	+	4.89898i	0.294706	+	0.170149i	0.640062	−	0.768323i	$-0.278909\pi$
$829$	8.48528	+	4.89898i	0.294706	+	0.170149i	−0.345356	+	0.938472i	$0.612242\pi$
$830$	32.4377	+	18.7279i	1.12593	+	0.650056i
$831$		0			0
$832$			0.717439i			0.0248727i
$833$	16.5160	−	4.60660i	0.572246	−	0.159609i
$834$		0			0
$835$	0.727922	+	1.26080i	0.0251908	+	0.0436317i
$836$	10.3923	−	18.0000i	0.359425	−	0.622543i
$837$		0			0
$838$	6.87868	−	3.97141i	0.237620	−	0.137190i
$839$	−15.2913			−0.527914			−0.263957	−	0.964534i	$-0.585028\pi$
$839$	−15.2913			−0.527914			−0.263957	+	0.964534i	$0.585028\pi$
$840$		0			0
$841$	25.9117			0.893506
$842$	20.3134	−	11.7279i	0.700045	−	0.404171i
$843$		0			0
$844$	1.74264	−	3.01834i	0.0599842	−	0.103896i
$845$	−15.2913	−	26.4853i	−0.526036	−	0.911121i
$846$		0			0
$847$	−18.3492	+	2.51104i	−0.630487	+	0.0862802i
$848$		−	14.4853i		−	0.497427i
$849$		0			0
$850$	2.12132	+	1.22474i	0.0727607	+	0.0420084i
$851$	27.2416	+	15.7279i	0.933829	+	0.539146i
$852$		0			0
$853$			31.7713i			1.08783i	0.839141	+	0.543914i	$0.183058\pi$
$853$			31.7713i			1.08783i	−0.839141	+	0.543914i	$0.816942\pi$
$854$	−6.77962	−	8.74264i	−0.231994	−	0.299167i
$855$		0			0
$856$	1.24264	+	2.15232i	0.0424726	+	0.0735647i
$857$	−13.7694	+	23.8492i	−0.470353	+	0.814675i	−0.999425	−	0.0339020i	$-0.989207\pi$
$857$	−13.7694	+	23.8492i	−0.470353	+	0.814675i	0.529073	+	0.848577i	$0.322540\pi$
$858$		0			0
$859$	24.4706	−	14.1281i	0.834925	−	0.482044i	−0.0206111	−	0.999788i	$-0.506561\pi$
$859$	24.4706	−	14.1281i	0.834925	−	0.482044i	0.855536	+	0.517743i	$0.173228\pi$
$860$	−17.1464			−0.584688
$861$		0			0
$862$	1.75736			0.0598559
$863$	−32.4377	+	18.7279i	−1.10419	+	0.637506i	−0.937319	−	0.348472i	$-0.886700\pi$
$863$	−32.4377	+	18.7279i	−1.10419	+	0.637506i	−0.166874	+	0.985978i	$0.553367\pi$
$864$		0			0
$865$	−25.4558	+	44.0908i	−0.865525	+	1.49913i
$866$	−1.28629	−	2.22792i	−0.0437100	−	0.0757079i
$867$		0			0
$868$	−3.25736	−	23.8030i	−0.110562	−	0.807925i
$869$			3.21320i			0.109000i
$870$		0			0
$871$	8.37868	+	4.83743i	0.283901	+	0.163910i
$872$	15.3528	+	8.86396i	0.519912	+	0.300172i
$873$		0			0
$874$			29.3939i			0.994263i
$875$	9.79796	−	24.0000i	0.331231	−	0.811348i
$876$		0			0
$877$	23.1066	+	40.0218i	0.780254	+	1.35144i	0.931793	+	0.362989i	$0.118244\pi$
$877$	23.1066	+	40.0218i	0.780254	+	1.35144i	−0.151539	+	0.988451i	$0.548423\pi$
$878$	−2.15232	+	3.72792i	−0.0726372	+	0.125811i
$879$		0			0
$880$	9.00000	−	5.19615i	0.303390	−	0.175162i
$881$	25.0892			0.845278			0.422639	−	0.906298i	$-0.361104\pi$
$881$	25.0892			0.845278			0.422639	+	0.906298i	$0.361104\pi$
$882$		0			0
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$	1.52192	−	0.878680i	0.0511876	−	0.0295532i
$885$		0			0
$886$	−12.7279	+	22.0454i	−0.427603	+	0.740630i
$887$	4.60181	+	7.97056i	0.154514	+	0.267625i	0.932882	−	0.360183i	$-0.117286\pi$
$887$	4.60181	+	7.97056i	0.154514	+	0.267625i	−0.778368	+	0.627808i	$0.783952\pi$
$888$		0			0
$889$	7.72792	−	18.9295i	0.259186	−	0.634874i
$890$		−	7.45584i		−	0.249920i
$891$		0			0
$892$	−9.00000	−	5.19615i	−0.301342	−	0.173980i
$893$	54.4831	+	31.4558i	1.82321	+	1.05263i
$894$		0			0
$895$			16.4800i			0.550865i
$896$	0.358719	+	2.62132i	0.0119840	+	0.0875722i
$897$		0			0
$898$	2.63604	+	4.56575i	0.0879658	+	0.152361i
$899$	7.97887	−	13.8198i	0.266110	−	0.460916i
$900$		0			0
$901$	−30.7279	+	17.7408i	−1.02370	+	0.591031i
$902$	−10.3923			−0.346026
$903$		0			0
$904$	10.2426			0.340665
$905$	−20.7846	+	12.0000i	−0.690904	+	0.398893i
$906$		0			0
$907$	6.74264	−	11.6786i	0.223886	−	0.387781i	−0.732099	−	0.681198i	$-0.761459\pi$
$907$	6.74264	−	11.6786i	0.223886	−	0.387781i	0.955985	+	0.293417i	$0.0947924\pi$
$908$	−12.5446	−	21.7279i	−0.416308	−	0.721066i
$909$		0			0
$910$	2.84924	+	3.67423i	0.0944515	+	0.121800i
$911$			10.2426i			0.339354i	0.985500	+	0.169677i	$0.0542724\pi$
$911$			10.2426i			0.339354i	−0.985500	+	0.169677i	$0.945728\pi$
$912$		0			0
$913$	−56.1838	−	32.4377i	−1.85941	−	1.07353i
$914$	−19.9186	−	11.5000i	−0.658848	−	0.380386i
$915$		0			0
$916$			5.61642i			0.185572i
$917$		0			0
$918$		0			0
$919$	−12.8640	−	22.2810i	−0.424343	−	0.734983i	0.572016	−	0.820243i	$-0.306162\pi$
$919$	−12.8640	−	22.2810i	−0.424343	−	0.734983i	−0.996359	+	0.0852590i	$0.972828\pi$
$920$	−7.34847	+	12.7279i	−0.242272	+	0.419627i
$921$		0			0
$922$	18.5772	−	10.7255i	0.611806	−	0.353227i
$923$	9.13151			0.300567
$924$		0			0
$925$	5.24264			0.172377
$926$	19.0526	−	11.0000i	0.626106	−	0.361482i
$927$		0			0
$928$	−0.878680	+	1.52192i	−0.0288441	+	0.0499594i
$929$	14.3637	+	24.8787i	0.471258	+	0.816243i	0.999459	−	0.0328762i	$-0.0104667\pi$
$929$	14.3637	+	24.8787i	0.471258	+	0.816243i	−0.528201	+	0.849119i	$0.677133\pi$
$930$		0			0
$931$	33.2132	+	8.53716i	1.08852	+	0.279794i
$932$			20.4853i			0.671018i
$933$		0			0
$934$	−15.3640	−	8.87039i	−0.502724	−	0.290248i
$935$	−22.0454	−	12.7279i	−0.720962	−	0.416248i
$936$		0			0
$937$		−	33.5033i		−	1.09451i	−0.836967	−	0.547253i	$-0.815674\pi$
$937$		−	33.5033i		−	1.09451i	0.836967	−	0.547253i	$-0.184326\pi$
$938$	33.0321	+	13.4853i	1.07853	+	0.440310i
$939$		0			0
$940$	15.7279	+	27.2416i	0.512988	+	0.888522i
$941$	21.1178	−	36.5772i	0.688422	−	1.19238i	−0.283927	−	0.958846i	$-0.591637\pi$
$941$	21.1178	−	36.5772i	0.688422	−	1.19238i	0.972348	−	0.233535i	$-0.0750295\pi$
$942$		0			0
$943$	12.7279	−	7.34847i	0.414478	−	0.239299i
$944$	−2.44949			−0.0797241
$945$		0			0
$946$	29.6985			0.965581
$947$	14.0665	−	8.12132i	0.457101	−	0.263907i	−0.253723	−	0.967277i	$-0.581655\pi$
$947$	14.0665	−	8.12132i	0.457101	−	0.263907i	0.710825	+	0.703369i	$0.248322\pi$
$948$		0			0
$949$	−1.97056	+	3.41311i	−0.0639672	+	0.110794i
$950$	2.44949	+	4.24264i	0.0794719	+	0.137649i
$951$		0			0
$952$	5.12132	−	3.97141i	0.165983	−	0.128714i
$953$			1.02944i			0.0333467i	0.999861	+	0.0166734i	$0.00530755\pi$
$953$			1.02944i			0.0333467i	−0.999861	+	0.0166734i	$0.994692\pi$
$954$		0			0
$955$	45.0000	+	25.9808i	1.45617	+	0.840718i
$956$	−14.0665	−	8.12132i	−0.454944	−	0.262662i
$957$		0			0
$958$			2.44949i			0.0791394i
$959$	−12.5446	+	9.72792i	−0.405087	+	0.314131i
$960$		0			0
$961$	25.7279	+	44.5621i	0.829933	+	1.43749i
$962$	1.88064	−	3.25736i	0.0606342	−	0.105021i
$963$		0			0
$964$	−0.985281	+	0.568852i	−0.0317338	+	0.0183215i
$965$	−3.63818			−0.117117
$966$		0			0
$967$	−42.6985			−1.37309			−0.686545	−	0.727087i	$-0.740874\pi$
$967$	−42.6985			−1.37309			−0.686545	+	0.727087i	$0.740874\pi$
$968$	−6.06218	+	3.50000i	−0.194846	+	0.112494i
$969$		0			0
$970$	−3.87868	+	6.71807i	−0.124537	+	0.215704i
$971$	−20.1903	−	34.9706i	−0.647936	−	1.12226i	−0.983615	−	0.180282i	$-0.942299\pi$
$971$	−20.1903	−	34.9706i	−0.647936	−	1.12226i	0.335679	−	0.941977i	$-0.391034\pi$
$972$		0			0
$973$	−19.7574	−	8.06591i	−0.633392	−	0.258581i
$974$		−	22.0000i		−	0.704925i
$975$		0			0
$976$	−3.62132	−	2.09077i	−0.115916	−	0.0669239i
$977$	5.19615	+	3.00000i	0.166240	+	0.0959785i	0.580812	−	0.814038i	$-0.302735\pi$
$977$	5.19615	+	3.00000i	0.166240	+	0.0959785i	−0.414572	+	0.910017i	$0.636069\pi$
$978$		0			0
$979$			12.9139i			0.412730i
$980$	12.2474	+	12.0000i	0.391230	+	0.383326i
$981$		0			0
$982$	17.4853	+	30.2854i	0.557978	+	0.966446i
$983$	11.6170	−	20.1213i	0.370526	−	0.641770i	−0.619120	−	0.785296i	$-0.712511\pi$
$983$	11.6170	−	20.1213i	0.370526	−	0.641770i	0.989647	+	0.143526i	$0.0458440\pi$
$984$		0			0
$985$	−36.0000	+	20.7846i	−1.14706	+	0.662253i
$986$	4.30463			0.137087
$987$		0			0
$988$	3.51472			0.111818
$989$	−36.3731	+	21.0000i	−1.15660	+	0.667761i
$990$		0			0
$991$	10.1066	−	17.5051i	0.321047	−	0.556069i	−0.659658	−	0.751566i	$-0.729299\pi$
$991$	10.1066	−	17.5051i	0.321047	−	0.556069i	0.980704	+	0.195497i	$0.0626320\pi$
$992$	−4.54026	−	7.86396i	−0.144153	−	0.249681i
$993$		0			0
$994$	33.3640	−	4.56575i	1.05824	−	0.144817i
$995$			51.2132i			1.62357i
$996$		0			0
$997$	16.8640	+	9.73641i	0.534087	+	0.308355i	0.742679	−	0.669647i	$-0.233555\pi$
$997$	16.8640	+	9.73641i	0.534087	+	0.308355i	−0.208592	+	0.978003i	$0.566888\pi$
$998$	−21.1794	−	12.2279i	−0.670422	−	0.387068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.k.d.269.1	yes	8
3.2	odd	2	inner	378.2.k.d.269.4	yes	8
7.3	odd	6		2646.2.d.d.2645.2		8
7.4	even	3		2646.2.d.d.2645.4		8
7.5	odd	6	inner	378.2.k.d.215.4	yes	8
9.2	odd	6		1134.2.t.f.1025.1		8
9.4	even	3		1134.2.l.e.269.1		8
9.5	odd	6		1134.2.l.e.269.4		8
9.7	even	3		1134.2.t.f.1025.4		8
21.5	even	6	inner	378.2.k.d.215.1	✓	8
21.11	odd	6		2646.2.d.d.2645.5		8
21.17	even	6		2646.2.d.d.2645.7		8
63.5	even	6		1134.2.t.f.593.4		8
63.40	odd	6		1134.2.t.f.593.1		8
63.47	even	6		1134.2.l.e.215.3		8
63.61	odd	6		1134.2.l.e.215.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.d.215.1	✓	8	21.5	even	6	inner
378.2.k.d.215.4	yes	8	7.5	odd	6	inner
378.2.k.d.269.1	yes	8	1.1	even	1	trivial
378.2.k.d.269.4	yes	8	3.2	odd	2	inner
1134.2.l.e.215.2		8	63.61	odd	6
1134.2.l.e.215.3		8	63.47	even	6
1134.2.l.e.269.1		8	9.4	even	3
1134.2.l.e.269.4		8	9.5	odd	6
1134.2.t.f.593.1		8	63.40	odd	6
1134.2.t.f.593.4		8	63.5	even	6
1134.2.t.f.1025.1		8	9.2	odd	6
1134.2.t.f.1025.4		8	9.7	even	3
2646.2.d.d.2645.2		8	7.3	odd	6
2646.2.d.d.2645.4		8	7.4	even	3
2646.2.d.d.2645.5		8	21.11	odd	6
2646.2.d.d.2645.7		8	21.17	even	6

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} +1.00000i q^{8} +(2.12132 + 1.22474i) q^{10} +(-3.67423 - 2.12132i) q^{11} -0.717439i q^{13} +(-0.358719 - 2.62132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.22474 + 2.12132i) q^{17} +(-4.24264 + 2.44949i) q^{19} -2.44949 q^{20} +4.24264 q^{22} +(-5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(0.358719 + 0.621320i) q^{26} +(1.62132 + 2.09077i) q^{28} +1.75736i q^{29} +(-7.86396 - 4.54026i) q^{31} +(0.866025 + 0.500000i) q^{32} -2.44949i q^{34} +(6.42090 - 0.878680i) q^{35} +(-2.62132 - 4.54026i) q^{37} +(2.44949 - 4.24264i) q^{38} +(2.12132 - 1.22474i) q^{40} -2.44949 q^{41} +7.00000 q^{43} +(-3.67423 + 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-6.42090 - 11.1213i) q^{47} +(-5.00000 - 4.89898i) q^{49} -1.00000i q^{50} +(-0.621320 - 0.358719i) q^{52} +(12.5446 + 7.24264i) q^{53} +10.3923i q^{55} +(-2.44949 - 1.00000i) q^{56} +(-0.878680 - 1.52192i) q^{58} +(1.22474 - 2.12132i) q^{59} +(3.62132 - 2.09077i) q^{61} +9.08052 q^{62} -1.00000 q^{64} +(-1.52192 + 0.878680i) q^{65} +(-6.74264 + 11.6786i) q^{67} +(1.22474 + 2.12132i) q^{68} +(-5.12132 + 3.97141i) q^{70} +12.7279i q^{71} +(-4.75736 - 2.74666i) q^{73} +(4.54026 + 2.62132i) q^{74} +4.89898i q^{76} +(8.87039 - 6.87868i) q^{77} +(-0.378680 - 0.655892i) q^{79} +(-1.22474 + 2.12132i) q^{80} +(2.12132 - 1.22474i) q^{82} +15.2913 q^{83} +6.00000 q^{85} +(-6.06218 + 3.50000i) q^{86} +(2.12132 - 3.67423i) q^{88} +(-1.52192 - 2.63604i) q^{89} +(1.75736 + 0.717439i) q^{91} +6.00000i q^{92} +(11.1213 + 6.42090i) q^{94} +(10.3923 + 6.00000i) q^{95} +3.16693i q^{97} +(6.77962 + 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 8 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 - 8 * q^7	\( 8 q + 4 q^{4} - 8 q^{7} - 4 q^{16} - 4 q^{25} - 4 q^{28} - 12 q^{31} - 4 q^{37} + 56 q^{43} + 24 q^{46} - 40 q^{49} + 12 q^{52} - 24 q^{58} + 12 q^{61} - 8 q^{64} - 20 q^{67} - 24 q^{70} - 72 q^{73} - 20 q^{79} + 48 q^{85} + 48 q^{91} + 72 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 - 8 * q^7 - 4 * q^16 - 4 * q^25 - 4 * q^28 - 12 * q^31 - 4 * q^37 + 56 * q^43 + 24 * q^46 - 40 * q^49 + 12 * q^52 - 24 * q^58 + 12 * q^61 - 8 * q^64 - 20 * q^67 - 24 * q^70 - 72 * q^73 - 20 * q^79 + 48 * q^85 + 48 * q^91 + 72 * q^94

Introduction

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