LMFDB - Embedded newform 324.2.l.a.179.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,2,Mod(35,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.12
Character	$\chi$	$=$	324.179
Dual form			324.2.l.a.143.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.818446 + 1.15332i) q^{2} +(-0.660291 + 1.88786i) q^{4} +(-0.532084 - 0.0938207i) q^{5} +(1.18790 + 1.41568i) q^{7} +(-2.71772 + 0.783586i) q^{8} +(-0.327277 - 0.690450i) q^{10} +(0.867520 + 4.91995i) q^{11} +(-1.52553 + 0.555249i) q^{13} +(-0.660503 + 2.52869i) q^{14} +(-3.12803 - 2.49307i) q^{16} +(0.683630 + 0.394694i) q^{17} +(2.86200 - 1.65238i) q^{19} +(0.528451 - 0.942551i) q^{20} +(-4.96425 + 5.02724i) q^{22} +(3.15234 + 2.64512i) q^{23} +(-4.42415 - 1.61026i) q^{25} +(-1.88895 - 1.30499i) q^{26} +(-3.45697 + 1.30783i) q^{28} +(3.24174 - 8.90660i) q^{29} +(-3.70462 + 4.41499i) q^{31} +(0.315184 - 5.64807i) q^{32} +(0.104306 + 1.11148i) q^{34} +(-0.499242 - 0.864712i) q^{35} +(5.53013 - 9.57846i) q^{37} +(4.24812 + 1.94842i) q^{38} +(1.51957 - 0.161955i) q^{40} +(2.62821 + 7.22095i) q^{41} +(7.88044 - 1.38953i) q^{43} +(-9.86099 - 1.61084i) q^{44} +(-0.470654 + 5.80054i) q^{46} +(2.39693 - 2.01126i) q^{47} +(0.622483 - 3.53027i) q^{49} +(-1.76379 - 6.42037i) q^{50} +(-0.0409360 - 3.24662i) q^{52} +0.933485i q^{53} -2.69922i q^{55} +(-4.33769 - 2.91661i) q^{56} +(12.9253 - 3.55082i) q^{58} +(-0.461077 + 2.61490i) q^{59} +(-4.29949 + 3.60770i) q^{61} +(-8.12393 - 0.659173i) q^{62} +(6.77199 - 4.25913i) q^{64} +(0.863806 - 0.152312i) q^{65} +(-2.15593 - 5.92336i) q^{67} +(-1.19652 + 1.02998i) q^{68} +(0.588687 - 1.28351i) q^{70} +(4.53203 - 7.84970i) q^{71} +(5.77108 + 9.99580i) q^{73} +(15.5731 - 1.46145i) q^{74} +(1.22970 + 6.49411i) q^{76} +(-5.93457 + 7.07254i) q^{77} +(0.275423 - 0.756719i) q^{79} +(1.43047 + 1.62000i) q^{80} +(-6.17702 + 8.94113i) q^{82} +(-15.0247 - 5.46855i) q^{83} +(-0.326718 - 0.274149i) q^{85} +(8.05230 + 7.95141i) q^{86} +(-6.21288 - 12.6913i) q^{88} +(5.41508 - 3.12640i) q^{89} +(-2.59824 - 1.50009i) q^{91} +(-7.07508 + 4.20462i) q^{92} +(4.28138 + 1.11831i) q^{94} +(-1.67785 + 0.610689i) q^{95} +(1.63933 + 9.29708i) q^{97} +(4.58100 - 2.17142i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.818446	+	1.15332i	0.578729	+	0.815520i
$2$	0.818446	+	1.15332i	0.578729	+	0.815520i
$3$		0			0
$3$		0			0
$4$	−0.660291	+	1.88786i	−0.330145	+	0.943930i
$5$	−0.532084	−	0.0938207i	−0.237955	−	0.0419579i	0.0533987	−	0.998573i	$-0.482995\pi$
$5$	−0.532084	−	0.0938207i	−0.237955	−	0.0419579i	−0.291354	+	0.956615i	$0.594106\pi$
$6$		0			0
$7$	1.18790	+	1.41568i	0.448984	+	0.535078i	0.942299	−	0.334773i	$-0.108659\pi$
$7$	1.18790	+	1.41568i	0.448984	+	0.535078i	−0.493315	+	0.869851i	$0.664215\pi$
$8$	−2.71772	+	0.783586i	−0.960859	+	0.277039i
$9$		0			0
$10$	−0.327277	−	0.690450i	−0.103494	−	0.218339i
$11$	0.867520	+	4.91995i	0.261567	+	1.48342i	0.778635	+	0.627477i	$0.215912\pi$
$11$	0.867520	+	4.91995i	0.261567	+	1.48342i	−0.517068	+	0.855944i	$0.672977\pi$
$12$		0			0
$13$	−1.52553	+	0.555249i	−0.423107	+	0.153998i	−0.544793	−	0.838570i	$-0.683392\pi$
$13$	−1.52553	+	0.555249i	−0.423107	+	0.153998i	0.121687	+	0.992569i	$0.461170\pi$
$14$	−0.660503	+	2.52869i	−0.176527	+	0.675821i
$15$		0			0
$16$	−3.12803	−	2.49307i	−0.782008	−	0.623268i
$17$	0.683630	+	0.394694i	0.165805	+	0.0957273i	0.580606	−	0.814185i	$-0.302816\pi$
$17$	0.683630	+	0.394694i	0.165805	+	0.0957273i	−0.414802	+	0.909912i	$0.636149\pi$
$18$		0			0
$19$	2.86200	−	1.65238i	0.656589	−	0.379082i	−0.134387	−	0.990929i	$-0.542907\pi$
$19$	2.86200	−	1.65238i	0.656589	−	0.379082i	0.790976	+	0.611847i	$0.209573\pi$
$20$	0.528451	−	0.942551i	0.118165	−	0.210761i
$21$		0			0
$22$	−4.96425	+	5.02724i	−1.05838	+	1.07181i
$23$	3.15234	+	2.64512i	0.657307	+	0.551546i	0.909278	−	0.416188i	$-0.136634\pi$
$23$	3.15234	+	2.64512i	0.657307	+	0.551546i	−0.251971	+	0.967735i	$0.581079\pi$
$24$		0			0
$25$	−4.42415	−	1.61026i	−0.884830	−	0.322052i
$26$	−1.88895	−	1.30499i	−0.370453	−	0.255929i
$27$		0			0
$28$	−3.45697	+	1.30783i	−0.653306	+	0.247156i
$29$	3.24174	−	8.90660i	0.601976	−	1.65391i	−0.145290	−	0.989389i	$-0.546412\pi$
$29$	3.24174	−	8.90660i	0.601976	−	1.65391i	0.747266	−	0.664525i	$-0.231366\pi$
$30$		0			0
$31$	−3.70462	+	4.41499i	−0.665369	+	0.792956i	−0.988146	−	0.153519i	$-0.950939\pi$
$31$	−3.70462	+	4.41499i	−0.665369	+	0.792956i	0.322777	+	0.946475i	$0.395384\pi$
$32$	0.315184	−	5.64807i	0.0557172	−	0.998447i
$33$		0			0
$34$	0.104306	+	1.11148i	0.0178884	+	0.190617i
$35$	−0.499242	−	0.864712i	−0.0843873	−	0.146163i
$36$		0			0
$37$	5.53013	−	9.57846i	0.909147	−	1.57469i	0.0938963	−	0.995582i	$-0.470068\pi$
$37$	5.53013	−	9.57846i	0.909147	−	1.57469i	0.815251	−	0.579108i	$-0.196599\pi$
$38$	4.24812	+	1.94842i	0.689136	+	0.316076i
$39$		0			0
$40$	1.51957	−	0.161955i	0.240265	−	0.0256074i
$41$	2.62821	+	7.22095i	0.410458	+	1.12772i	0.956948	+	0.290258i	$0.0937412\pi$
$41$	2.62821	+	7.22095i	0.410458	+	1.12772i	−0.546491	+	0.837465i	$0.684037\pi$
$42$		0			0
$43$	7.88044	−	1.38953i	1.20176	−	0.211902i	0.463299	−	0.886202i	$-0.346666\pi$
$43$	7.88044	−	1.38953i	1.20176	−	0.211902i	0.738458	+	0.674300i	$0.235555\pi$
$44$	−9.86099	−	1.61084i	−1.48660	−	0.242844i
$45$		0			0
$46$	−0.470654	+	5.80054i	−0.0693942	+	0.855243i
$47$	2.39693	−	2.01126i	0.349628	−	0.293372i	−0.451013	−	0.892517i	$-0.648937\pi$
$47$	2.39693	−	2.01126i	0.349628	−	0.293372i	0.800640	+	0.599145i	$0.204493\pi$
$48$		0			0
$49$	0.622483	−	3.53027i	0.0889261	−	0.504325i
$50$	−1.76379	−	6.42037i	−0.249437	−	0.907978i
$51$		0			0
$52$	−0.0409360	−	3.24662i	−0.00567681	−	0.450225i
$53$			0.933485i			0.128224i	0.997943	+	0.0641120i	$0.0204215\pi$
$53$			0.933485i			0.128224i	−0.997943	+	0.0641120i	$0.979579\pi$
$54$		0			0
$55$		−	2.69922i		−	0.363962i
$56$	−4.33769	−	2.91661i	−0.579648	−	0.389748i
$57$		0			0
$58$	12.9253	−	3.55082i	1.69718	−	0.466245i
$59$	−0.461077	+	2.61490i	−0.0600271	+	0.340431i	−1.00000		0.000819421i	$-0.999739\pi$
$59$	−0.461077	+	2.61490i	−0.0600271	+	0.340431i	0.939973	+	0.341250i	$0.110850\pi$
$60$		0			0
$61$	−4.29949	+	3.60770i	−0.550493	+	0.461919i	−0.875108	−	0.483928i	$-0.839210\pi$
$61$	−4.29949	+	3.60770i	−0.550493	+	0.461919i	0.324615	+	0.945846i	$0.394765\pi$
$62$	−8.12393	−	0.659173i	−1.03174	−	0.0837151i
$63$		0			0
$64$	6.77199	−	4.25913i	0.846498	−	0.532392i
$65$	0.863806	−	0.152312i	0.107142	−	0.0188920i
$66$		0			0
$67$	−2.15593	−	5.92336i	−0.263388	−	0.723653i	−0.998933	−	0.0461775i	$-0.985296\pi$
$67$	−2.15593	−	5.92336i	−0.263388	−	0.723653i	0.735545	−	0.677476i	$-0.236926\pi$
$68$	−1.19652	+	1.02998i	−0.145100	+	0.124904i
$69$		0			0
$70$	0.588687	−	1.28351i	0.0703615	−	0.153408i
$71$	4.53203	−	7.84970i	0.537853	−	0.931588i	−0.461167	−	0.887313i	$-0.652569\pi$
$71$	4.53203	−	7.84970i	0.537853	−	0.931588i	0.999019	−	0.0442746i	$-0.0140977\pi$
$72$		0			0
$73$	5.77108	+	9.99580i	0.675454	+	1.16992i	0.976336	+	0.216259i	$0.0693855\pi$
$73$	5.77108	+	9.99580i	0.675454	+	1.16992i	−0.300882	+	0.953661i	$0.597281\pi$
$74$	15.5731	−	1.46145i	1.81034	−	0.169891i
$75$		0			0
$76$	1.22970	+	6.49411i	0.141057	+	0.744926i
$77$	−5.93457	+	7.07254i	−0.676307	+	0.805991i
$78$		0			0
$79$	0.275423	−	0.756719i	0.0309875	−	0.0851375i	−0.923234	−	0.384238i	$-0.874464\pi$
$79$	0.275423	−	0.756719i	0.0309875	−	0.0851375i	0.954222	+	0.299100i	$0.0966865\pi$
$80$	1.43047	+	1.62000i	0.159932	+	0.181121i
$81$		0			0
$82$	−6.17702	+	8.94113i	−0.682137	+	0.987383i
$83$	−15.0247	−	5.46855i	−1.64918	−	0.600252i	−0.660570	−	0.750765i	$-0.729685\pi$
$83$	−15.0247	−	5.46855i	−1.64918	−	0.600252i	−0.988608	+	0.150513i	$0.951907\pi$
$84$		0			0
$85$	−0.326718	−	0.274149i	−0.0354375	−	0.0297356i
$86$	8.05230	+	7.95141i	0.868302	+	0.857422i
$87$		0			0
$88$	−6.21288	−	12.6913i	−0.662295	−	1.35289i
$89$	5.41508	−	3.12640i	0.573997	−	0.331398i	−0.184747	−	0.982786i	$-0.559147\pi$
$89$	5.41508	−	3.12640i	0.573997	−	0.331398i	0.758744	+	0.651389i	$0.225813\pi$
$90$		0			0
$91$	−2.59824	−	1.50009i	−0.272369	−	0.157252i
$92$	−7.07508	+	4.20462i	−0.737628	+	0.438362i
$93$		0			0
$94$	4.28138	+	1.11831i	0.441591	+	0.115345i
$95$	−1.67785	+	0.610689i	−0.172144	+	0.0626553i
$96$		0			0
$97$	1.63933	+	9.29708i	0.166448	+	0.943975i	0.947559	+	0.319582i	$0.103543\pi$
$97$	1.63933	+	9.29708i	0.166448	+	0.943975i	−0.781110	+	0.624393i	$0.785346\pi$
$98$	4.58100	−	2.17142i	0.462751	−	0.219346i
$99$		0			0
$100$	5.96117	−	7.28894i	0.596117	−	0.728894i
$101$	−6.31653	−	7.52775i	−0.628518	−	0.749039i	0.353992	−	0.935249i	$-0.384824\pi$
$101$	−6.31653	−	7.52775i	−0.628518	−	0.749039i	−0.982510	+	0.186210i	$0.940380\pi$
$102$		0			0
$103$	6.85056	+	1.20794i	0.675005	+	0.119022i	0.500635	−	0.865658i	$-0.333100\pi$
$103$	6.85056	+	1.20794i	0.675005	+	0.119022i	0.174370	+	0.984680i	$0.444211\pi$
$104$	3.71089	−	2.70440i	0.363882	−	0.265188i
$105$		0			0
$106$	−1.07661	+	0.764008i	−0.104569	+	0.0742070i
$107$	2.51779			0.243404			0.121702	−	0.992567i	$-0.461165\pi$
$107$	2.51779			0.243404			0.121702	+	0.992567i	$0.461165\pi$
$108$		0			0
$109$	5.76924			0.552593			0.276296	−	0.961072i	$-0.410893\pi$
$109$	5.76924			0.552593			0.276296	+	0.961072i	$0.410893\pi$
$110$	3.11306	−	2.20916i	0.296819	−	0.210636i
$111$		0			0
$112$	−0.186384	−	7.38983i	−0.0176116	−	0.698273i
$113$	−4.36693	−	0.770007i	−0.410806	−	0.0724362i	−0.0355738	−	0.999367i	$-0.511326\pi$
$113$	−4.36693	−	0.770007i	−0.410806	−	0.0724362i	−0.375232	+	0.926931i	$0.622437\pi$
$114$		0			0
$115$	−1.42914	−	1.70318i	−0.133268	−	0.158823i
$116$	14.6739	+	12.0009i	1.36244	+	1.11426i
$117$		0			0
$118$	−3.39318	+	1.60838i	−0.312367	+	0.148064i
$119$	0.253322	+	1.43666i	0.0232220	+	0.131698i
$120$		0			0
$121$	−13.1167	+	4.77409i	−1.19243	+	0.434008i
$122$	−7.67973	−	2.00598i	−0.695290	−	0.181612i
$123$		0			0
$124$	−5.88876	−	9.90898i	−0.528826	−	0.889853i
$125$	4.54248	+	2.62260i	0.406292	+	0.234573i
$126$		0			0
$127$	−3.47118	+	2.00409i	−0.308018	+	0.177834i	−0.646039	−	0.763304i	$-0.723576\pi$
$127$	−3.47118	+	2.00409i	−0.308018	+	0.177834i	0.338021	+	0.941138i	$0.390242\pi$
$128$	10.4546	+	4.32439i	0.924069	+	0.382226i
$129$		0			0
$130$	0.882643	+	0.871584i	0.0774129	+	0.0764430i
$131$	−1.84218	−	1.54577i	−0.160952	−	0.135055i	0.558755	−	0.829333i	$-0.311279\pi$
$131$	−1.84218	−	1.54577i	−0.160952	−	0.135055i	−0.719707	+	0.694278i	$0.755724\pi$
$132$		0			0
$133$	5.73902	+	2.08883i	0.497636	+	0.181125i
$134$	5.06701	−	7.33442i	0.437723	−	0.633598i
$135$		0			0
$136$	−2.16719	−	0.536984i	−0.185835	−	0.0460460i
$137$	−1.46523	+	4.02570i	−0.125183	+	0.343939i	−0.986415	−	0.164275i	$-0.947472\pi$
$137$	−1.46523	+	4.02570i	−0.125183	+	0.343939i	0.861231	+	0.508213i	$0.169694\pi$
$138$		0			0
$139$	−11.4619	+	13.6598i	−0.972187	+	1.15861i	0.0151364	+	0.999885i	$0.495182\pi$
$139$	−11.4619	+	13.6598i	−0.972187	+	1.15861i	−0.987323	+	0.158722i	$0.949263\pi$
$140$	1.96210	−	0.371537i	0.165828	−	0.0314006i
$141$		0			0
$142$	12.7624	−	1.19769i	1.07100	−	0.100508i
$143$	−4.05523	−	7.02386i	−0.339115	−	0.587365i
$144$		0			0
$145$	−2.56050	+	4.43492i	−0.212638	+	0.368300i
$146$	−6.80503	+	14.8369i	−0.563188	+	1.22791i
$147$		0			0
$148$	14.4313	+	16.7647i	1.18625	+	1.37805i
$149$	−4.08657	−	11.2278i	−0.334785	−	0.919814i	−0.986848	−	0.161650i	$-0.948319\pi$
$149$	−4.08657	−	11.2278i	−0.334785	−	0.919814i	0.652063	−	0.758165i	$-0.273904\pi$
$150$		0			0
$151$	−18.0852	+	3.18891i	−1.47175	+	0.259510i	−0.851277	−	0.524716i	$-0.824171\pi$
$151$	−18.0852	+	3.18891i	−1.47175	+	0.259510i	−0.620475	+	0.784226i	$0.713060\pi$
$152$	−6.48334	+	6.73333i	−0.525868	+	0.546145i
$153$		0			0
$154$	−13.0140	−	1.05595i	−1.04870	−	0.0850912i
$155$	2.38539	−	2.00158i	0.191599	−	0.160770i
$156$		0			0
$157$	3.60079	−	20.4211i	0.287374	−	1.62978i	−0.409306	−	0.912397i	$-0.634229\pi$
$157$	3.60079	−	20.4211i	0.287374	−	1.62978i	0.696680	−	0.717382i	$-0.254660\pi$
$158$	1.09816	−	0.301683i	0.0873647	−	0.0240006i
$159$		0			0
$160$	−0.697610	+	2.97567i	−0.0551509	+	0.235248i
$161$			7.60485i			0.599346i
$162$		0			0
$163$			2.03697i			0.159548i	0.996813	+	0.0797739i	$0.0254198\pi$
$163$			2.03697i			0.159548i	−0.996813	+	0.0797739i	$0.974580\pi$
$164$	−15.3675	+	0.193767i	−1.20000	+	0.0151306i
$165$		0			0
$166$	−5.98994	−	21.8040i	−0.464910	−	1.69232i
$167$	−1.07213	+	6.08034i	−0.0829637	+	0.470511i	0.914814	+	0.403876i	$0.132337\pi$
$167$	−1.07213	+	6.08034i	−0.0829637	+	0.470511i	−0.997777	+	0.0666346i	$0.978774\pi$
$168$		0			0
$169$	−7.93963	+	6.66214i	−0.610741	+	0.512472i
$170$	0.0487801	−	0.601186i	0.00374126	−	0.0461089i
$171$		0			0
$172$	−2.58014	+	15.7947i	−0.196734	+	1.20433i
$173$	−14.6443	+	2.58218i	−1.11338	+	0.196320i	−0.699934	−	0.714207i	$-0.746787\pi$
$173$	−14.6443	+	2.58218i	−1.11338	+	0.196320i	−0.413450	+	0.910527i	$0.635676\pi$
$174$		0			0
$175$	−2.97583	−	8.17603i	−0.224952	−	0.618050i
$176$	9.55217	−	17.5526i	0.720022	−	1.32307i
$177$		0			0
$178$	8.03769	+	3.68653i	0.602450	+	0.276317i
$179$	−2.80761	+	4.86292i	−0.209850	+	0.363472i	−0.951667	−	0.307131i	$-0.900631\pi$
$179$	−2.80761	+	4.86292i	−0.209850	+	0.363472i	0.741817	+	0.670603i	$0.233964\pi$
$180$		0			0
$181$	−3.04279	−	5.27027i	−0.226169	−	0.391736i	0.730500	−	0.682912i	$-0.239287\pi$
$181$	−3.04279	−	5.27027i	−0.226169	−	0.391736i	−0.956670	+	0.291176i	$0.905954\pi$
$182$	−0.396432	−	4.22434i	−0.0293855	−	0.313129i
$183$		0			0
$184$	−10.6398	−	4.71857i	−0.784379	−	0.347858i
$185$	−3.84115	+	4.57770i	−0.282407	+	0.336560i
$186$		0			0
$187$	−1.34881	+	3.70583i	−0.0986349	+	0.270997i
$188$	2.21431	+	5.85308i	0.161495	+	0.426880i
$189$		0			0
$190$	−2.07755	−	1.43528i	−0.150721	−	0.104126i
$191$	−4.55974	−	1.65961i	−0.329931	−	0.120085i	0.171743	−	0.985142i	$-0.445060\pi$
$191$	−4.55974	−	1.65961i	−0.329931	−	0.120085i	−0.501674	+	0.865057i	$0.667282\pi$
$192$		0			0
$193$	4.04332	+	3.39275i	0.291044	+	0.244215i	0.776605	−	0.629988i	$-0.216940\pi$
$193$	4.04332	+	3.39275i	0.291044	+	0.244215i	−0.485561	+	0.874203i	$0.661385\pi$
$194$	−9.38080	+	9.49982i	−0.673502	+	0.682048i
$195$		0			0
$196$	6.25364	+	3.50617i	0.446689	+	0.250441i
$197$	−2.31117	+	1.33435i	−0.164664	+	0.0950687i	−0.580067	−	0.814569i	$-0.696974\pi$
$197$	−2.31117	+	1.33435i	−0.164664	+	0.0950687i	0.415403	+	0.909637i	$0.363640\pi$
$198$		0			0
$199$	−9.82614	−	5.67313i	−0.696557	−	0.402157i	0.109507	−	0.993986i	$-0.465073\pi$
$199$	−9.82614	−	5.67313i	−0.696557	−	0.402157i	−0.806064	+	0.591829i	$0.798406\pi$
$200$	13.2854	+	0.909529i	0.939418	+	0.0643134i
$201$		0			0
$202$	3.51216	−	13.4460i	0.247114	−	0.946060i
$203$	16.4598	−	5.99087i	1.15525	−	0.420477i
$204$		0			0
$205$	−0.720954	−	4.08873i	−0.0503536	−	0.285570i
$206$	4.21368	+	8.88951i	0.293581	+	0.619362i
$207$		0			0
$208$	6.15619	+	2.06643i	0.426855	+	0.143281i
$209$	10.6125	+	12.6474i	0.734080	+	0.874842i
$210$		0			0
$211$	4.51015	+	0.795260i	0.310491	+	0.0547480i	0.326723	−	0.945120i	$-0.394056\pi$
$211$	4.51015	+	0.795260i	0.310491	+	0.0547480i	−0.0162314	+	0.999868i	$0.505167\pi$
$212$	−1.76229	−	0.616372i	−0.121035	−	0.0423326i
$213$		0			0
$214$	2.06067	+	2.90381i	0.140865	+	0.198501i
$215$	−4.32342			−0.294855
$216$		0			0
$217$	−10.6509			−0.723033
$218$	4.72181	+	6.65378i	0.319802	+	0.450651i
$219$		0			0
$220$	5.09574	+	1.78227i	0.343555	+	0.120161i
$221$	−1.26205	−	0.222534i	−0.0848949	−	0.0149693i
$222$		0			0
$223$	11.8712	+	14.1475i	0.794953	+	0.947388i	0.999505	−	0.0314676i	$-0.0100181\pi$
$223$	11.8712	+	14.1475i	0.794953	+	0.947388i	−0.204552	+	0.978856i	$0.565574\pi$
$224$	8.37028	−	6.26314i	0.559263	−	0.418473i
$225$		0			0
$226$	−2.68603	−	5.66667i	−0.178672	−	0.376941i
$227$	2.30342	+	13.0633i	0.152883	+	0.867043i	0.960696	+	0.277604i	$0.0895402\pi$
$227$	2.30342	+	13.0633i	0.152883	+	0.867043i	−0.807813	+	0.589439i	$0.799349\pi$
$228$		0			0
$229$	3.24361	−	1.18058i	0.214344	−	0.0780147i	−0.232617	−	0.972569i	$-0.574729\pi$
$229$	3.24361	−	1.18058i	0.214344	−	0.0780147i	0.446960	+	0.894554i	$0.352507\pi$
$230$	0.794639	−	3.04222i	0.0523969	−	0.200598i
$231$		0			0
$232$	−1.83104	+	26.7458i	−0.120214	+	1.75595i
$233$	14.1574	+	8.17379i	0.927483	+	0.535483i	0.886015	−	0.463657i	$-0.153463\pi$
$233$	14.1574	+	8.17379i	0.927483	+	0.535483i	0.0414686	+	0.999140i	$0.486796\pi$
$234$		0			0
$235$	−1.46406	+	0.845277i	−0.0955050	+	0.0551398i
$236$	−4.63212	−	2.59704i	−0.301525	−	0.169053i
$237$		0			0
$238$	−1.44960	+	1.46799i	−0.0939634	+	0.0951557i
$239$	−0.797855	−	0.669480i	−0.0516089	−	0.0433050i	0.616618	−	0.787262i	$-0.288502\pi$
$239$	−0.797855	−	0.669480i	−0.0516089	−	0.0433050i	−0.668227	+	0.743957i	$0.732947\pi$
$240$		0			0
$241$	15.4743	+	5.63219i	0.996788	+	0.362801i	0.788345	−	0.615233i	$-0.210938\pi$
$241$	15.4743	+	5.63219i	0.996788	+	0.362801i	0.208443	+	0.978035i	$0.433160\pi$
$242$	−16.2414	−	11.2204i	−1.04403	−	0.721275i
$243$		0			0
$244$	−3.97192	−	10.4990i	−0.254276	−	0.672128i
$245$	−0.662426	+	1.82000i	−0.0423208	+	0.116276i
$246$		0			0
$247$	−3.44860	+	4.10988i	−0.219429	+	0.261506i
$248$	6.60858	−	14.9016i	0.419645	−	0.946252i
$249$		0			0
$250$	0.693078	+	7.38539i	0.0438341	+	0.467093i
$251$	6.70961	+	11.6214i	0.423507	+	0.733535i	0.996280	−	0.0861790i	$-0.0274657\pi$
$251$	6.70961	+	11.6214i	0.423507	+	0.733535i	−0.572773	+	0.819714i	$0.694132\pi$
$252$		0			0
$253$	−10.2792	+	17.8040i	−0.646245	+	1.11933i
$254$	−5.15233	−	2.36314i	−0.323286	−	0.148277i
$255$		0			0
$256$	3.56916	+	15.5968i	0.223073	+	0.974802i
$257$	−0.987706	−	2.71370i	−0.0616114	−	0.169276i	0.905068	−	0.425268i	$-0.139820\pi$
$257$	−0.987706	−	2.71370i	−0.0616114	−	0.169276i	−0.966679	+	0.255992i	$0.917598\pi$
$258$		0			0
$259$	20.1293	−	3.54934i	1.25077	−	0.220545i
$260$	−0.282819	+	1.73131i	−0.0175397	+	0.107372i
$261$		0			0
$262$	0.275044	−	3.38975i	0.0169922	−	0.209420i
$263$	10.7439	−	9.01519i	0.662496	−	0.555900i	−0.248338	−	0.968674i	$-0.579884\pi$
$263$	10.7439	−	9.01519i	0.662496	−	0.555900i	0.910834	+	0.412773i	$0.135440\pi$
$264$		0			0
$265$	0.0875803	−	0.496692i	0.00538001	−	0.0305116i
$266$	2.28799	+	8.32852i	0.140286	+	0.510654i
$267$		0			0
$268$	12.6060	−	0.158947i	0.770035	−	0.00970923i
$269$		−	20.1185i		−	1.22665i	−0.789831	−	0.613325i	$-0.789832\pi$
$269$		−	20.1185i		−	1.22665i	0.789831	−	0.613325i	$-0.210168\pi$
$270$		0			0
$271$		−	19.1968i		−	1.16612i	−0.812428	−	0.583062i	$-0.801855\pi$
$271$		−	19.1968i		−	1.16612i	0.812428	−	0.583062i	$-0.198145\pi$
$272$	−1.15441	−	2.93895i	−0.0699967	−	0.178200i
$273$		0			0
$274$	−5.84213	+	1.60493i	−0.352936	+	0.0969577i
$275$	4.08436	−	23.1635i	0.246296	−	1.39681i
$276$		0			0
$277$	20.3674	−	17.0903i	1.22376	−	1.02686i	0.225141	−	0.974326i	$-0.427716\pi$
$277$	20.3674	−	17.0903i	1.22376	−	1.02686i	0.998619	−	0.0525311i	$-0.0167289\pi$
$278$	−25.1350	−	2.03945i	−1.50750	−	0.122318i
$279$		0			0
$280$	2.03437	+	1.95885i	0.121577	+	0.117063i
$281$	−2.17919	+	0.384249i	−0.129999	+	0.0229224i	−0.238269	−	0.971199i	$-0.576580\pi$
$281$	−2.17919	+	0.384249i	−0.129999	+	0.0229224i	0.108270	+	0.994122i	$0.465469\pi$
$282$		0			0
$283$	−8.19432	−	22.5137i	−0.487102	−	1.33830i	−0.903293	−	0.429024i	$-0.858858\pi$
$283$	−8.19432	−	22.5137i	−0.487102	−	1.33830i	0.416192	−	0.909277i	$-0.363365\pi$
$284$	11.8267	+	13.7389i	0.701784	+	0.815255i
$285$		0			0
$286$	4.78177	−	10.4256i	0.282752	−	0.616480i
$287$	−7.10053	+	12.2985i	−0.419131	+	0.725957i
$288$		0			0
$289$	−8.18843	−	14.1828i	−0.481673	−	0.834281i
$290$	−7.21051	+	0.676667i	−0.423416	+	0.0397353i
$291$		0			0
$292$	−22.6813	+	4.29485i	−1.32732	+	0.251337i
$293$	17.5281	−	20.8891i	1.02400	−	1.22036i	0.0488514	−	0.998806i	$-0.484444\pi$
$293$	17.5281	−	20.8891i	1.02400	−	1.22036i	0.975149	−	0.221550i	$-0.0711116\pi$
$294$		0			0
$295$	0.490663	−	1.34809i	0.0285675	−	0.0784886i
$296$	−7.52378	+	30.3649i	−0.437311	+	1.76492i
$297$		0			0
$298$	9.60456	−	13.9024i	0.556377	−	0.805347i
$299$	−6.27769	−	2.28489i	−0.363048	−	0.132139i
$300$		0			0
$301$	11.3283	+	9.50559i	0.652953	+	0.547893i
$302$	−18.4796	−	18.2481i	−1.06338	−	1.05006i
$303$		0			0
$304$	−13.0719	−	1.96649i	−0.749727	−	0.112786i
$305$	2.62617	−	1.51622i	0.150374	−	0.0868184i
$306$		0			0
$307$	21.0055	+	12.1276i	1.19885	+	0.692156i	0.960299	−	0.278974i	$-0.0899944\pi$
$307$	21.0055	+	12.1276i	1.19885	+	0.692156i	0.238551	+	0.971130i	$0.423328\pi$
$308$	−9.43343	−	15.8736i	−0.537519	−	0.904480i
$309$		0			0
$310$	4.26077	+	1.11293i	0.241995	+	0.0632101i
$311$	−18.0900	+	6.58424i	−1.02579	+	0.373358i	−0.799477	−	0.600696i	$-0.794890\pi$
$311$	−18.0900	+	6.58424i	−1.02579	+	0.373358i	−0.226315	+	0.974054i	$0.572668\pi$
$312$		0			0
$313$	−1.18433	−	6.71666i	−0.0669422	−	0.379648i	−0.999811	−	0.0194321i	$-0.993814\pi$
$313$	−1.18433	−	6.71666i	−0.0669422	−	0.379648i	0.932869	−	0.360216i	$-0.117297\pi$
$314$	26.4991	−	12.5607i	1.49543	−	0.708841i
$315$		0			0
$316$	1.24672	+	1.01961i	0.0701335	+	0.0573578i
$317$	7.41728	+	8.83957i	0.416596	+	0.496480i	0.933006	−	0.359862i	$-0.117176\pi$
$317$	7.41728	+	8.83957i	0.416596	+	0.496480i	−0.516409	+	0.856342i	$0.672732\pi$
$318$		0			0
$319$	46.6323	+	8.22253i	2.61091	+	0.460373i
$320$	−4.00286	+	1.63086i	−0.223767	+	0.0911680i
$321$		0			0
$322$	−8.77082	+	6.22416i	−0.488779	+	0.346859i
$323$	2.60873			0.145154
$324$		0			0
$325$	7.64329			0.423973
$326$	−2.34928	+	1.66715i	−0.130114	+	0.0923349i
$327$		0			0
$328$	−12.8010	−	17.5651i	−0.706816	−	0.969870i
$329$	5.69461	+	1.00411i	0.313954	+	0.0553586i
$330$		0			0
$331$	−13.2173	−	15.7517i	−0.726487	−	0.865793i	0.268757	−	0.963208i	$-0.413387\pi$
$331$	−13.2173	−	15.7517i	−0.726487	−	0.865793i	−0.995244	+	0.0974147i	$0.968943\pi$
$332$	20.2446	−	24.7537i	1.11106	−	1.35854i
$333$		0			0
$334$	−7.89005	+	3.73993i	−0.431724	+	0.204640i
$335$	0.591400	+	3.35399i	0.0323116	+	0.183248i
$336$		0			0
$337$	−10.0326	+	3.65156i	−0.546509	+	0.198913i	−0.600495	−	0.799629i	$-0.705030\pi$
$337$	−10.0326	+	3.65156i	−0.546509	+	0.198913i	0.0539858	+	0.998542i	$0.482807\pi$
$338$	−14.1817	−	3.70432i	−0.771384	−	0.201489i
$339$		0			0
$340$	0.733284	−	0.435780i	0.0397679	−	0.0236335i
$341$	−24.9354	−	14.3964i	−1.35033	−	0.779611i
$342$		0			0
$343$	16.9404	−	9.78053i	0.914694	−	0.528099i
$344$	−20.3280	+	9.95137i	−1.09601	+	0.536542i
$345$		0			0
$346$	−14.9636	−	14.7762i	−0.804451	−	0.794371i
$347$	0.957389	+	0.803344i	0.0513953	+	0.0431258i	0.668123	−	0.744050i	$-0.267098\pi$
$347$	0.957389	+	0.803344i	0.0513953	+	0.0431258i	−0.616728	+	0.787176i	$0.711542\pi$
$348$		0			0
$349$	−18.0738	−	6.57834i	−0.967470	−	0.352130i	−0.190514	−	0.981685i	$-0.561015\pi$
$349$	−18.0738	−	6.57834i	−0.967470	−	0.352130i	−0.776957	+	0.629554i	$0.783238\pi$
$350$	6.99401	−	10.1237i	0.373846	−	0.541136i
$351$		0			0
$352$	28.0616	−	3.34912i	1.49569	−	0.178509i
$353$	2.12947	−	5.85067i	0.113340	−	0.311400i	−0.870034	−	0.492992i	$-0.835903\pi$
$353$	2.12947	−	5.85067i	0.113340	−	0.311400i	0.983374	+	0.181593i	$0.0581253\pi$
$354$		0			0
$355$	−3.14788	+	3.75150i	−0.167072	+	0.199109i
$356$	2.32667	+	12.2872i	0.123313	+	0.651223i
$357$		0			0
$358$	−7.90637	+	0.741970i	−0.417865	+	0.0392143i
$359$	−4.51666	−	7.82308i	−0.238380	−	0.412886i	0.721870	−	0.692029i	$-0.243283\pi$
$359$	−4.51666	−	7.82308i	−0.238380	−	0.412886i	−0.960250	+	0.279143i	$0.909950\pi$
$360$		0			0
$361$	−4.03929	+	6.99626i	−0.212594	+	0.368224i
$362$	3.58794	−	7.82275i	0.188578	−	0.411155i
$363$		0			0
$364$	4.54756	−	3.91461i	0.238357	−	0.205181i
$365$	−2.13288	−	5.86005i	−0.111640	−	0.306729i
$366$		0			0
$367$	−7.28951	+	1.28534i	−0.380509	+	0.0670941i	−0.360632	−	0.932708i	$-0.617439\pi$
$367$	−7.28951	+	1.28534i	−0.380509	+	0.0670941i	−0.0198778	+	0.999802i	$0.506328\pi$
$368$	−3.26612	−	16.1330i	−0.170258	−	0.840993i
$369$		0			0
$370$	−8.42333	−	0.683467i	−0.437908	−	0.0355318i
$371$	−1.32152	+	1.10889i	−0.0686099	+	0.0575705i
$372$		0			0
$373$	0.532880	−	3.02211i	0.0275915	−	0.156479i	−0.967899	−	0.251339i	$-0.919129\pi$
$373$	0.532880	−	3.02211i	0.0275915	−	0.156479i	0.995491	+	0.0948598i	$0.0302403\pi$
$374$	−5.37793	+	1.47741i	−0.278086	+	0.0763952i
$375$		0			0
$376$	−4.93817	+	7.34423i	−0.254667	+	0.378750i
$377$			15.3873i			0.792486i
$378$		0			0
$379$			30.1832i			1.55041i	0.631712	+	0.775203i	$0.282353\pi$
$379$			30.1832i			1.55041i	−0.631712	+	0.775203i	$0.717647\pi$
$380$	−0.0450234	−	3.57078i	−0.00230965	−	0.183177i
$381$		0			0
$382$	−1.81784	−	6.61714i	−0.0930090	−	0.338562i
$383$	−3.37652	+	19.1492i	−0.172532	+	0.978479i	0.768422	+	0.639944i	$0.221042\pi$
$383$	−3.37652	+	19.1492i	−0.172532	+	0.978479i	−0.940954	+	0.338535i	$0.890069\pi$
$384$		0			0
$385$	3.82124	−	3.20640i	0.194748	−	0.163413i
$386$	−0.603681	+	7.44002i	−0.0307266	+	0.378687i
$387$		0			0
$388$	−18.6340	−	3.04396i	−0.945999	−	0.154534i
$389$	20.0904	−	3.54247i	1.01862	−	0.179610i	0.360688	−	0.932687i	$-0.382542\pi$
$389$	20.0904	−	3.54247i	1.01862	−	0.179610i	0.657933	+	0.753076i	$0.271431\pi$
$390$		0			0
$391$	1.11102	+	3.05249i	0.0561865	+	0.154371i
$392$	1.07454	+	10.0821i	0.0542725	+	0.509221i
$393$		0			0
$394$	−3.43050	−	1.57342i	−0.172826	−	0.0792676i
$395$	−0.217544	+	0.376797i	−0.0109458	+	0.0189587i
$396$		0			0
$397$	−8.78858	−	15.2223i	−0.441086	−	0.763984i	0.556684	−	0.830724i	$-0.312073\pi$
$397$	−8.78858	−	15.2223i	−0.441086	−	0.763984i	−0.997770	+	0.0667406i	$0.978740\pi$
$398$	−1.49924	−	15.9758i	−0.0751504	−	0.800796i
$399$		0			0
$400$	9.82439	+	16.0667i	0.491220	+	0.803334i
$401$	15.5813	−	18.5691i	0.778094	−	0.927297i	−0.220751	−	0.975330i	$-0.570851\pi$
$401$	15.5813	−	18.5691i	0.778094	−	0.927297i	0.998846	+	0.0480334i	$0.0152954\pi$
$402$		0			0
$403$	3.20010	−	8.79220i	0.159408	−	0.437971i
$404$	18.3821	−	6.95422i	0.914543	−	0.345986i
$405$		0			0
$406$	20.3808	+	14.0802i	1.01148	+	0.698788i
$407$	51.9231	+	18.8984i	2.57373	+	0.936761i
$408$		0			0
$409$	15.8369	+	13.2887i	0.783085	+	0.657086i	0.944024	−	0.329878i	$-0.107008\pi$
$409$	15.8369	+	13.2887i	0.783085	+	0.657086i	−0.160939	+	0.986964i	$0.551452\pi$
$410$	4.12555	−	4.17790i	0.203747	−	0.206332i
$411$		0			0
$412$	−6.80378	+	12.1353i	−0.335198	+	0.597863i
$413$	−4.24958	+	2.45350i	−0.209108	+	0.120729i
$414$		0			0
$415$	7.48135	+	4.31936i	0.367245	+	0.212029i
$416$	2.65526	+	8.79132i	0.130185	+	0.431030i
$417$		0			0
$418$	−5.90081	+	22.5908i	−0.288618	+	1.10495i
$419$	−8.00463	+	2.91345i	−0.391052	+	0.142331i	−0.530060	−	0.847960i	$-0.677831\pi$
$419$	−8.00463	+	2.91345i	−0.391052	+	0.142331i	0.139009	+	0.990291i	$0.455608\pi$
$420$		0			0
$421$	−2.47727	−	14.0493i	−0.120735	−	0.684721i	−0.983750	−	0.179543i	$-0.942538\pi$
$421$	−2.47727	−	14.0493i	−0.120735	−	0.684721i	0.863015	−	0.505178i	$-0.168573\pi$
$422$	2.77412	+	5.85252i	0.135042	+	0.284896i
$423$		0			0
$424$	−0.731466	−	2.53695i	−0.0355231	−	0.123205i
$425$	−2.38892	−	2.84701i	−0.115880	−	0.138100i
$426$		0			0
$427$	−10.2147	−	1.80113i	−0.494325	−	0.0871629i
$428$	−1.66247	+	4.75323i	−0.0803586	+	0.229756i
$429$		0			0
$430$	−3.53849	−	4.98629i	−0.170641	−	0.240460i
$431$	−1.49028			−0.0717841			−0.0358920	−	0.999356i	$-0.511427\pi$
$431$	−1.49028			−0.0717841			−0.0358920	+	0.999356i	$0.511427\pi$
$432$		0			0
$433$	2.83288			0.136139			0.0680697	−	0.997681i	$-0.478316\pi$
$433$	2.83288			0.136139			0.0680697	+	0.997681i	$0.478316\pi$
$434$	−8.71723	−	12.2839i	−0.418440	−	0.589648i
$435$		0			0
$436$	−3.80938	+	10.8915i	−0.182436	+	0.521609i
$437$	13.3927	+	2.36150i	0.640662	+	0.112966i
$438$		0			0
$439$	−17.2666	−	20.5775i	−0.824089	−	0.982112i	0.175908	−	0.984407i	$-0.443714\pi$
$439$	−17.2666	−	20.5775i	−0.824089	−	0.982112i	−0.999997	+	0.00229504i	$0.999269\pi$
$440$	2.11507	+	7.33571i	0.100832	+	0.349716i
$441$		0			0
$442$	−0.776270	−	1.63768i	−0.0369234	−	0.0778966i
$443$	−4.52430	−	25.6586i	−0.214956	−	1.21908i	−0.880983	−	0.473148i	$-0.843118\pi$
$443$	−4.52430	−	25.6586i	−0.214956	−	1.21908i	0.666027	−	0.745928i	$-0.267994\pi$
$444$		0			0
$445$	−3.17460	+	1.15546i	−0.150490	+	0.0547740i
$446$	−6.60069	+	25.2703i	−0.312552	+	1.19658i
$447$		0			0
$448$	14.0740	+	4.52757i	0.664935	+	0.213908i
$449$	−19.5356	−	11.2789i	−0.921940	−	0.532282i	−0.0376867	−	0.999290i	$-0.511999\pi$
$449$	−19.5356	−	11.2789i	−0.921940	−	0.532282i	−0.884254	+	0.467007i	$0.845332\pi$
$450$		0			0
$451$	−33.2467	+	19.1950i	−1.56553	+	0.903857i
$452$	4.33711	−	7.73572i	0.204000	−	0.363858i
$453$		0			0
$454$	−13.1810	+	13.3482i	−0.618613	+	0.626462i
$455$	1.24174	+	1.04194i	0.0582137	+	0.0488471i
$456$		0			0
$457$	−13.9247	−	5.06817i	−0.651370	−	0.237079i	−0.00486385	−	0.999988i	$-0.501548\pi$
$457$	−13.9247	−	5.06817i	−0.651370	−	0.237079i	−0.646506	+	0.762909i	$0.723770\pi$
$458$	4.01630	+	2.77468i	0.187669	+	0.129652i
$459$		0			0
$460$	4.15902	−	1.57342i	0.193915	−	0.0733611i
$461$	−10.5924	+	29.1025i	−0.493339	+	1.35544i	0.404267	+	0.914641i	$0.367527\pi$
$461$	−10.5924	+	29.1025i	−0.493339	+	1.35544i	−0.897606	+	0.440798i	$0.854696\pi$
$462$		0			0
$463$	14.7162	−	17.5380i	0.683918	−	0.815062i	−0.306687	−	0.951810i	$-0.599221\pi$
$463$	14.7162	−	17.5380i	0.683918	−	0.815062i	0.990606	+	0.136748i	$0.0436651\pi$
$464$	−32.3451	+	19.7782i	−1.50158	+	0.918182i
$465$		0			0
$466$	2.16010	+	23.0178i	0.100065	+	1.06628i
$467$	17.9763	+	31.1359i	0.831844	+	1.44080i	0.896575	+	0.442893i	$0.146048\pi$
$467$	17.9763	+	31.1359i	0.831844	+	1.44080i	−0.0647308	+	0.997903i	$0.520619\pi$
$468$		0			0
$469$	5.82458	−	10.0885i	0.268954	−	0.465842i
$470$	−2.17313	−	0.996718i	−0.100239	−	0.0459752i
$471$		0			0
$472$	−0.795920	−	7.46785i	−0.0366352	−	0.343736i
$473$	13.6729	+	37.5659i	0.628680	+	1.72728i
$474$		0			0
$475$	−15.3227	+	2.70181i	−0.703054	+	0.123967i
$476$	−2.87948	−	0.470377i	−0.131981	−	0.0215597i
$477$		0			0
$478$	0.119122	−	1.46811i	0.00544853	−	0.0671500i
$479$	−15.6682	+	13.1472i	−0.715899	+	0.600711i	−0.926248	−	0.376916i	$-0.876985\pi$
$479$	−15.6682	+	13.1472i	−0.715899	+	0.600711i	0.210348	+	0.977627i	$0.432540\pi$
$480$		0			0
$481$	−3.11797	+	17.6829i	−0.142167	+	0.806269i
$482$	6.16918	+	22.4565i	0.280998	+	1.02286i
$483$		0			0
$484$	−0.351972	−	27.9148i	−0.0159987	−	1.26885i
$485$		−	5.10063i		−	0.231608i
$486$		0			0
$487$			17.0248i			0.771469i	0.922610	+	0.385734i	$0.126052\pi$
$487$			17.0248i			0.771469i	−0.922610	+	0.385734i	$0.873948\pi$
$488$	8.85786	−	13.1737i	0.400976	−	0.596347i
$489$		0			0
$490$	−2.64120	+	0.725584i	−0.119317	+	0.0327785i
$491$	2.46802	−	13.9968i	0.111380	−	0.631668i	−0.877099	−	0.480310i	$-0.840524\pi$
$491$	2.46802	−	13.9968i	0.111380	−	0.631668i	0.988479	−	0.151358i	$-0.0483647\pi$
$492$		0			0
$493$	5.73153	−	4.80932i	0.258135	−	0.216601i
$494$	−7.56250	−	0.613620i	−0.340253	−	0.0276080i
$495$		0			0
$496$	22.5951	−	4.57435i	1.01455	−	0.205394i
$497$	16.4963	−	2.90874i	0.739960	−	0.130475i
$498$		0			0
$499$	−2.45044	−	6.73253i	−0.109697	−	0.301390i	0.872682	−	0.488288i	$-0.162379\pi$
$499$	−2.45044	−	6.73253i	−0.109697	−	0.301390i	−0.982379	+	0.186899i	$0.940156\pi$
$500$	−7.95046	+	6.84388i	−0.355555	+	0.306068i
$501$		0			0
$502$	−7.91171	+	17.2498i	−0.353117	+	0.769896i
$503$	2.15953	−	3.74041i	0.0962886	−	0.166777i	−0.813857	−	0.581065i	$-0.802636\pi$
$503$	2.15953	−	3.74041i	0.0962886	−	0.166777i	0.910146	+	0.414288i	$0.135969\pi$
$504$		0			0
$505$	2.65467	+	4.59802i	0.118131	+	0.204609i
$506$	−28.9467	+	2.71649i	−1.28684	+	0.120763i
$507$		0			0
$508$	−1.49145	−	7.87639i	−0.0661723	−	0.349458i
$509$	−25.4341	+	30.3112i	−1.12735	+	1.34352i	−0.195488	+	0.980706i	$0.562629\pi$
$509$	−25.4341	+	30.3112i	−1.12735	+	1.34352i	−0.931861	+	0.362816i	$0.881815\pi$
$510$		0			0
$511$	−7.29543	+	20.0440i	−0.322731	+	0.886696i
$512$	−15.0670	+	16.8816i	−0.665872	+	0.746066i
$513$		0			0
$514$	2.32138	−	3.36016i	0.102392	−	0.148210i
$515$	−3.53174	−	1.28545i	−0.155627	−	0.0566436i
$516$		0			0
$517$	11.9747	+	10.0479i	0.526646	+	0.441908i
$518$	20.5683	+	20.3106i	0.903719	+	0.892396i
$519$		0			0
$520$	−2.22823	+	1.09081i	−0.0977144	+	0.0478351i
$521$	−39.1169	+	22.5841i	−1.71374	+	0.989429i	−0.784360	+	0.620305i	$0.787009\pi$
$521$	−39.1169	+	22.5841i	−1.71374	+	0.989429i	−0.929380	+	0.369123i	$0.879658\pi$
$522$		0			0
$523$	2.99933	+	1.73166i	0.131152	+	0.0757204i	0.564140	−	0.825679i	$-0.309208\pi$
$523$	2.99933	+	1.73166i	0.131152	+	0.0757204i	−0.432989	+	0.901399i	$0.642541\pi$
$524$	4.13457	−	2.45712i	0.180620	−	0.107340i
$525$		0			0
$526$	19.1907	+	5.01268i	0.836754	+	0.218563i
$527$	−4.27516	+	1.55603i	−0.186229	+	0.0677817i
$528$		0			0
$529$	−1.05337	−	5.97395i	−0.0457986	−	0.259737i
$530$	0.644525	−	0.305508i	0.0279964	−	0.0132704i
$531$		0			0
$532$	−7.73284	+	9.45523i	−0.335261	+	0.409936i
$533$	−8.01885	−	9.55650i	−0.347335	−	0.413938i
$534$		0			0
$535$	−1.33967	−	0.236221i	−0.0579192	−	0.0102127i
$536$	10.5007	+	14.4087i	0.453559	+	0.622360i
$537$		0			0
$538$	23.2031	−	16.4660i	1.00036	−	0.709898i
$539$	17.9088			0.771386
$540$		0			0
$541$	−14.6206			−0.628588			−0.314294	−	0.949326i	$-0.601768\pi$
$541$	−14.6206			−0.628588			−0.314294	+	0.949326i	$0.601768\pi$
$542$	22.1401	−	15.7116i	0.950997	−	0.674869i
$543$		0			0
$544$	2.44473	−	3.73679i	0.104817	−	0.160213i
$545$	−3.06972	−	0.541274i	−0.131492	−	0.0231856i
$546$		0			0
$547$	8.74169	+	10.4179i	0.373768	+	0.445439i	0.919837	−	0.392301i	$-0.128321\pi$
$547$	8.74169	+	10.4179i	0.373768	+	0.445439i	−0.546069	+	0.837740i	$0.683876\pi$
$548$	−6.63247	−	5.42429i	−0.283325	−	0.231714i
$549$		0			0
$550$	30.0578	−	14.2475i	1.28167	−	0.607517i
$551$	−5.43921	−	30.8473i	−0.231718	−	1.31414i
$552$		0			0
$553$	1.39845	−	0.508994i	0.0594681	−	0.0216446i
$554$	36.3802	+	9.50266i	1.54565	+	0.403729i
$555$		0			0
$556$	−18.2196	−	30.6579i	−0.772681	−	1.30019i
$557$	−5.66207	−	3.26900i	−0.239909	−	0.138512i	0.375226	−	0.926933i	$-0.377565\pi$
$557$	−5.66207	−	3.26900i	−0.239909	−	0.138512i	−0.615135	+	0.788422i	$0.710899\pi$
$558$		0			0
$559$	−11.2503	+	6.49539i	−0.475839	+	0.274726i
$560$	−0.594147	+	3.94949i	−0.0251073	+	0.166897i
$561$		0			0
$562$	−2.22671	−	2.19881i	−0.0939280	−	0.0927512i
$563$	−18.1068	−	15.1934i	−0.763110	−	0.640325i	0.175824	−	0.984422i	$-0.443741\pi$
$563$	−18.1068	−	15.1934i	−0.763110	−	0.640325i	−0.938934	+	0.344096i	$0.888185\pi$
$564$		0			0
$565$	2.25133	+	0.819417i	0.0947141	+	0.0344731i
$566$	19.2589	−	27.8769i	0.809511	−	1.17175i
$567$		0			0
$568$	−6.16586	+	24.8845i	−0.258714	+	1.04413i
$569$	−3.88872	+	10.6842i	−0.163024	+	0.447904i	−0.994128	−	0.108213i	$-0.965487\pi$
$569$	−3.88872	+	10.6842i	−0.163024	+	0.447904i	0.831104	+	0.556117i	$0.187709\pi$
$570$		0			0
$571$	−14.2613	+	16.9960i	−0.596818	+	0.711260i	−0.976901	−	0.213692i	$-0.931451\pi$
$571$	−14.2613	+	16.9960i	−0.596818	+	0.711260i	0.380083	+	0.924952i	$0.375895\pi$
$572$	15.9377	−	3.01791i	0.666388	−	0.126185i
$573$		0			0
$574$	−19.9955	+	1.87647i	−0.834596	+	0.0783223i
$575$	−9.68708	−	16.7785i	−0.403979	−	0.699712i
$576$		0			0
$577$	5.30268	−	9.18452i	0.220754	−	0.382357i	−0.734283	−	0.678843i	$-0.762482\pi$
$577$	5.30268	−	9.18452i	0.220754	−	0.382357i	0.955037	+	0.296487i	$0.0958150\pi$
$578$	9.65548	−	21.0517i	0.401615	−	0.875636i
$579$		0			0
$580$	−6.68183	−	7.76220i	−0.277448	−	0.322308i
$581$	−10.1061	−	27.7664i	−0.419273	−	1.15194i
$582$		0			0
$583$	−4.59270	+	0.809817i	−0.190210	+	0.0335392i
$584$	−23.5167	−	22.6436i	−0.973129	−	0.937000i
$585$		0			0
$586$	38.4376	+	3.11882i	1.58784	+	0.128837i
$587$	−8.09141	+	6.78950i	−0.333968	+	0.280233i	−0.794314	−	0.607507i	$-0.792170\pi$
$587$	−8.09141	+	6.78950i	−0.333968	+	0.280233i	0.460346	+	0.887740i	$0.347725\pi$
$588$		0			0
$589$	−3.30739	+	18.7572i	−0.136279	+	0.772875i
$590$	1.95636	−	0.537445i	0.0805419	−	0.0221263i
$591$		0			0
$592$	−41.1782	+	16.1747i	−1.69241	+	0.664777i
$593$		−	27.5676i		−	1.13207i	−0.824383	−	0.566033i	$-0.808478\pi$
$593$		−	27.5676i		−	1.13207i	0.824383	−	0.566033i	$-0.191522\pi$
$594$		0			0
$595$		−	0.788191i		−	0.0323127i
$596$	23.8948	−	0.301285i	0.978768	−	0.0123411i
$597$		0			0
$598$	−2.50274	−	9.11025i	−0.102345	−	0.372546i
$599$	−2.13432	+	12.1044i	−0.0872061	+	0.494571i	0.909653	+	0.415370i	$0.136348\pi$
$599$	−2.13432	+	12.1044i	−0.0872061	+	0.494571i	−0.996859	+	0.0792006i	$0.974763\pi$
$600$		0			0
$601$	−9.68745	+	8.12873i	−0.395159	+	0.331578i	−0.818619	−	0.574337i	$-0.805260\pi$
$601$	−9.68745	+	8.12873i	−0.395159	+	0.331578i	0.423460	+	0.905915i	$0.360815\pi$
$602$	−1.69136	+	20.8450i	−0.0689346	+	0.849578i
$603$		0			0
$604$	5.92128	−	36.2479i	0.240933	−	1.47491i
$605$	7.42709	−	1.30960i	0.301954	−	0.0532427i
$606$		0			0
$607$	−2.12432	−	5.83652i	−0.0862235	−	0.236897i	0.889086	−	0.457741i	$-0.151341\pi$
$607$	−2.12432	−	5.83652i	−0.0862235	−	0.236897i	−0.975309	+	0.220844i	$0.929119\pi$
$608$	−8.43069	−	16.6856i	−0.341909	−	0.676690i
$609$		0			0
$610$	3.89806	+	1.78787i	0.157828	+	0.0723886i
$611$	−2.53984	+	4.39913i	−0.102751	+	0.177970i
$612$		0			0
$613$	12.5009	+	21.6522i	0.504907	+	0.874524i	0.999984	+	0.00567529i	$0.00180651\pi$
$613$	12.5009	+	21.6522i	0.504907	+	0.874524i	−0.495077	+	0.868849i	$0.664860\pi$
$614$	3.20497	+	34.1518i	0.129342	+	1.37826i
$615$		0			0
$616$	10.5865	−	23.8714i	0.426544	−	0.961807i
$617$	20.9893	−	25.0141i	0.844997	−	1.00703i	−0.154821	−	0.987943i	$-0.549480\pi$
$617$	20.9893	−	25.0141i	0.844997	−	1.00703i	0.999818	−	0.0190859i	$-0.00607561\pi$
$618$		0			0
$619$	13.2843	−	36.4984i	0.533942	−	1.46699i	−0.320401	−	0.947282i	$-0.603818\pi$
$619$	13.2843	−	36.4984i	0.533942	−	1.46699i	0.854342	−	0.519711i	$-0.173960\pi$
$620$	2.20365	+	5.82490i	0.0885006	+	0.233933i
$621$		0			0
$622$	−22.3995	−	15.4748i	−0.898136	−	0.620481i
$623$	10.8586	+	3.95219i	0.435039	+	0.158341i
$624$		0			0
$625$	15.8621	+	13.3099i	0.634483	+	0.532395i
$626$	6.77714	−	6.86313i	0.270869	−	0.274306i
$627$		0			0
$628$	36.1746	+	20.2816i	1.44352	+	0.809325i
$629$	7.56112	−	4.36541i	0.301482	−	0.174060i
$630$		0			0
$631$	−27.2601	−	15.7386i	−1.08521	−	0.626544i	−0.152911	−	0.988240i	$-0.548865\pi$
$631$	−27.2601	−	15.7386i	−1.08521	−	0.626544i	−0.932296	+	0.361696i	$0.882198\pi$
$632$	−0.155568	+	2.27237i	−0.00618817	+	0.0903899i
$633$		0			0
$634$	−4.12420	+	15.7892i	−0.163793	+	0.627070i
$635$	2.03499	−	0.740675i	0.0807560	−	0.0293928i
$636$		0			0
$637$	1.01056	+	5.73118i	0.0400399	+	0.227078i
$638$	28.6828	+	60.5116i	1.13556	+	2.39568i
$639$		0			0
$640$	−5.15703	−	3.28180i	−0.203850	−	0.129725i
$641$	−6.98262	−	8.32156i	−0.275797	−	0.328682i	0.610310	−	0.792163i	$-0.291045\pi$
$641$	−6.98262	−	8.32156i	−0.275797	−	0.328682i	−0.886107	+	0.463481i	$0.846600\pi$
$642$		0			0
$643$	−10.8032	−	1.90489i	−0.426036	−	0.0751217i	−0.0434808	−	0.999054i	$-0.513845\pi$
$643$	−10.8032	−	1.90489i	−0.426036	−	0.0751217i	−0.382555	+	0.923933i	$0.624956\pi$
$644$	−14.3569	−	5.02141i	−0.565741	−	0.197871i
$645$		0			0
$646$	2.13511	+	3.00870i	0.0840047	+	0.118376i
$647$	−47.2138			−1.85616			−0.928082	−	0.372375i	$-0.878544\pi$
$647$	−47.2138			−1.85616			−0.928082	+	0.372375i	$0.878544\pi$
$648$		0			0
$649$	−13.2652			−0.520703
$650$	6.25562	+	8.81515i	0.245366	+	0.345759i
$651$		0			0
$652$	−3.84551	−	1.34499i	−0.150602	−	0.0526740i
$653$	28.9484	+	5.10438i	1.13284	+	0.199750i	0.708471	−	0.705740i	$-0.249385\pi$
$653$	28.9484	+	5.10438i	1.13284	+	0.199750i	0.424367	+	0.905490i	$0.360497\pi$
$654$		0			0
$655$	0.835168	+	0.995314i	0.0326327	+	0.0388902i
$656$	9.78124	−	29.1397i	0.381893	−	1.13771i
$657$		0			0
$658$	3.50267	+	7.38952i	0.136548	+	0.288074i
$659$	−0.0149056	−	0.0845336i	−0.000580638	−	0.00329296i	0.984516	−	0.175294i	$-0.0560877\pi$
$659$	−0.0149056	−	0.0845336i	−0.000580638	−	0.00329296i	−0.985097	+	0.172001i	$0.944977\pi$
$660$		0			0
$661$	−12.6865	+	4.61752i	−0.493449	+	0.179601i	−0.576745	−	0.816924i	$-0.695677\pi$
$661$	−12.6865	+	4.61752i	−0.493449	+	0.179601i	0.0832963	+	0.996525i	$0.473455\pi$
$662$	7.34915	−	28.1357i	0.285633	−	1.09352i
$663$		0			0
$664$	45.1181	+	3.08882i	1.75092	+	0.119870i
$665$	−2.85766	−	1.64987i	−0.110815	−	0.0639793i
$666$		0			0
$667$	33.7781	−	19.5018i	1.30789	−	0.755113i
$668$	−10.7709	−	6.03882i	−0.416739	−	0.233649i
$669$		0			0
$670$	−3.38420	+	3.42714i	−0.130743	+	0.132402i
$671$	−21.4796	−	18.0235i	−0.829211	−	0.695790i
$672$		0			0
$673$	−5.01426	−	1.82504i	−0.193285	−	0.0703501i	0.243564	−	0.969885i	$-0.421683\pi$
$673$	−5.01426	−	1.82504i	−0.193285	−	0.0703501i	−0.436849	+	0.899535i	$0.643906\pi$
$674$	−12.4225	−	8.58215i	−0.478498	−	0.330572i
$675$		0			0
$676$	−7.33472	−	19.3879i	−0.282105	−	0.745687i
$677$	8.95953	−	24.6161i	0.344343	−	0.946074i	−0.639776	−	0.768562i	$-0.720973\pi$
$677$	8.95953	−	24.6161i	0.344343	−	0.946074i	0.984119	−	0.177512i	$-0.0568050\pi$
$678$		0			0
$679$	−11.2144	+	13.3648i	−0.430368	+	0.512892i
$680$	1.10275	+	0.489048i	0.0422884	+	0.0187541i
$681$		0			0
$682$	−3.80457	−	40.5412i	−0.145684	−	1.55240i
$683$	−16.4032	−	28.4113i	−0.627653	−	1.08713i	−0.988021	−	0.154317i	$-0.950682\pi$
$683$	−16.4032	−	28.4113i	−0.627653	−	1.08713i	0.360369	−	0.932810i	$-0.382651\pi$
$684$		0			0
$685$	1.15732	−	2.00454i	0.0442190	−	0.0765895i
$686$	25.1449	+	11.5328i	0.960035	+	0.440325i
$687$		0			0
$688$	−28.1145	−	15.3000i	−1.07185	−	0.583308i
$689$	−0.518316	−	1.42406i	−0.0197463	−	0.0542525i
$690$		0			0
$691$	5.03144	−	0.887178i	0.191405	−	0.0337498i	−0.0771239	−	0.997022i	$-0.524574\pi$
$691$	5.03144	−	0.887178i	0.191405	−	0.0337498i	0.268529	+	0.963272i	$0.413463\pi$
$692$	4.79469	−	29.3514i	0.182267	−	1.11577i
$693$		0			0
$694$	−0.142941	+	1.76167i	−0.00542598	+	0.0668721i
$695$	7.38027	−	6.19278i	0.279950	−	0.234906i
$696$		0			0
$697$	−1.05334	+	5.97380i	−0.0398982	+	0.226274i
$698$	−7.20554	−	26.2289i	−0.272734	−	0.992779i
$699$		0			0
$700$	17.4001	−	0.219395i	0.657662	−	0.00829235i
$701$			40.9095i			1.54513i	0.634936	+	0.772565i	$0.281026\pi$
$701$			40.9095i			1.54513i	−0.634936	+	0.772565i	$0.718974\pi$
$702$		0			0
$703$		−	36.5515i		−	1.37856i
$704$	26.8295	+	29.6230i	1.01118	+	1.11646i
$705$		0			0
$706$	8.49054	−	2.33250i	0.319546	−	0.0877848i
$707$	3.15351	−	17.8844i	0.118600	−	0.672613i
$708$		0			0
$709$	−12.2104	+	10.2458i	−0.458572	+	0.384787i	−0.842605	−	0.538532i	$-0.818979\pi$
$709$	−12.2104	+	10.2458i	−0.458572	+	0.384787i	0.384033	+	0.923319i	$0.374535\pi$
$710$	−6.90305	−	0.560112i	−0.259067	−	0.0210206i
$711$		0			0
$712$	−12.2669	+	12.7399i	−0.459720	+	0.477446i
$713$	−23.3564	+	4.11836i	−0.874704	+	0.154234i
$714$		0			0
$715$	1.49874	+	4.11775i	0.0560496	+	0.153995i
$716$	−7.32667	−	8.51131i	−0.273811	−	0.318083i
$717$		0			0
$718$	5.32587	−	11.6119i	0.198760	−	0.433353i
$719$	15.8103	−	27.3843i	0.589626	−	1.02126i	−0.404655	−	0.914469i	$-0.632608\pi$
$719$	15.8103	−	27.3843i	0.589626	−	1.02126i	0.994281	−	0.106793i	$-0.0340582\pi$
$720$		0			0
$721$	6.42772	+	11.1331i	0.239381	+	0.414619i
$722$	−11.3749	+	1.06747i	−0.423328	+	0.0397271i
$723$		0			0
$724$	11.9587	−	2.26446i	0.444440	−	0.0841578i
$725$	−28.6839	+	34.1841i	−1.06529	+	1.26957i
$726$		0			0
$727$	−9.85979	+	27.0896i	−0.365680	+	1.00470i	0.611307	+	0.791394i	$0.290644\pi$
$727$	−9.85979	+	27.0896i	−0.365680	+	1.00470i	−0.976986	+	0.213302i	$0.931578\pi$
$728$	8.23673	+	2.04089i	0.305273	+	0.0756403i
$729$		0			0
$730$	5.01286	−	7.25603i	0.185534	−	0.268558i
$731$	5.93575	+	2.16044i	0.219542	+	0.0799066i
$732$		0			0
$733$	−25.8057	−	21.6536i	−0.953157	−	0.799793i	0.0266696	−	0.999644i	$-0.491510\pi$
$733$	−25.8057	−	21.6536i	−0.953157	−	0.799793i	−0.979826	+	0.199851i	$0.935954\pi$
$734$	−7.44848	−	7.35515i	−0.274928	−	0.271484i
$735$		0			0
$736$	15.9334	−	16.9709i	0.587313	−	0.625556i
$737$	27.2723	−	15.7457i	1.00459	−	0.580000i
$738$		0			0
$739$	10.3214	+	5.95905i	0.379678	+	0.219207i	0.677678	−	0.735359i	$-0.262986\pi$
$739$	10.3214	+	5.95905i	0.379678	+	0.219207i	−0.298000	+	0.954566i	$0.596320\pi$
$740$	−6.10579	−	10.2742i	−0.224453	−	0.377686i
$741$		0			0
$742$	−2.36049	−	0.616570i	−0.0866564	−	0.0226350i
$743$	9.08444	−	3.30647i	0.333276	−	0.121302i	−0.169962	−	0.985451i	$-0.554364\pi$
$743$	9.08444	−	3.30647i	0.333276	−	0.121302i	0.503237	+	0.864148i	$0.332142\pi$
$744$		0			0
$745$	1.12100	+	6.35752i	0.0410703	+	0.232921i
$746$	3.92160	−	1.85886i	0.143580	−	0.0680576i
$747$		0			0
$748$	−6.10548	−	4.99329i	−0.223238	−	0.182573i
$749$	2.99088	+	3.56439i	0.109284	+	0.130240i
$750$		0			0
$751$	−22.0213	−	3.88295i	−0.803570	−	0.141691i	−0.243246	−	0.969965i	$-0.578212\pi$
$751$	−22.0213	−	3.88295i	−0.803570	−	0.141691i	−0.560324	+	0.828274i	$0.689323\pi$
$752$	−12.5119	+	0.315570i	−0.456261	+	0.0115077i
$753$		0			0
$754$	−17.7465	+	12.5937i	−0.646288	+	0.458634i
$755$	9.92203			0.361100
$756$		0			0
$757$	3.40365			0.123708			0.0618540	−	0.998085i	$-0.480299\pi$
$757$	3.40365			0.123708			0.0618540	+	0.998085i	$0.480299\pi$
$758$	−34.8109	+	24.7033i	−1.26439	+	0.897265i
$759$		0			0
$760$	4.08141	−	2.97442i	0.148048	−	0.107894i
$761$	−43.2514	−	7.62639i	−1.56786	−	0.276457i	−0.678829	−	0.734297i	$-0.737512\pi$
$761$	−43.2514	−	7.62639i	−1.56786	−	0.276457i	−0.889034	+	0.457840i	$0.848623\pi$
$762$		0			0
$763$	6.85328	+	8.16742i	0.248105	+	0.295680i
$764$	6.14387	−	7.51233i	0.222277	−	0.271787i
$765$		0			0
$766$	−24.8486	+	11.7784i	−0.897818	+	0.425571i
$767$	−0.748530	−	4.24513i	−0.0270279	−	0.153283i
$768$		0			0
$769$	43.4127	−	15.8009i	1.56550	−	0.569797i	0.593514	−	0.804823i	$-0.297740\pi$
$769$	43.4127	−	15.8009i	1.56550	−	0.569797i	0.971989	+	0.235027i	$0.0755178\pi$
$770$	6.82548	+	1.78284i	0.245973	+	0.0642492i
$771$		0			0
$772$	−9.07480	+	5.39302i	−0.326609	+	0.194099i
$773$	35.3857	+	20.4299i	1.27273	+	0.734813i	0.975502	−	0.219992i	$-0.0706031\pi$
$773$	35.3857	+	20.4299i	1.27273	+	0.734813i	0.297232	+	0.954805i	$0.403936\pi$
$774$		0			0
$775$	23.4991	−	13.5672i	0.844112	−	0.487348i
$776$	−11.7403	−	23.9823i	−0.421452	−	0.860914i
$777$		0			0
$778$	20.5285	+	20.2713i	0.735982	+	0.726760i
$779$	19.4537	+	16.3236i	0.697001	+	0.584853i
$780$		0			0
$781$	42.5518	+	15.4876i	1.52262	+	0.554189i
$782$	−2.61119	+	3.77966i	−0.0933760	+	0.135160i
$783$		0			0
$784$	−10.7484	+	9.49091i	−0.383871	+	0.338961i
$785$	−3.83184	+	10.5279i	−0.136764	+	0.375757i
$786$		0			0
$787$	26.6313	−	31.7379i	0.949302	−	1.13133i	−0.0419189	−	0.999121i	$-0.513347\pi$
$787$	26.6313	−	31.7379i	0.949302	−	1.13133i	0.991221	−	0.132214i	$-0.0422085\pi$
$788$	−0.993029	−	5.24422i	−0.0353752	−	0.186818i
$789$		0			0
$790$	−0.612616	+	0.0574907i	−0.0217959	+	0.00204543i
$791$	−4.09738	−	7.09688i	−0.145686	−	0.252336i
$792$		0			0
$793$	4.55584	−	7.89095i	0.161783	−	0.280216i
$794$	10.3632	−	22.5946i	0.367774	−	0.801854i
$795$		0			0
$796$	17.1982	−	14.8045i	0.609573	−	0.524730i
$797$	−4.25196	−	11.6822i	−0.150612	−	0.413803i	0.841326	−	0.540528i	$-0.181776\pi$
$797$	−4.25196	−	11.6822i	−0.150612	−	0.413803i	−0.991938	+	0.126725i	$0.959553\pi$
$798$		0			0
$799$	2.43244	−	0.428905i	0.0860536	−	0.0151736i
$800$	−10.4893	+	24.4804i	−0.370852	+	0.865512i
$801$		0			0
$802$	34.1686	+	2.77243i	1.20653	+	0.0978979i
$803$	−44.1723	+	37.0650i	−1.55881	+	1.30799i
$804$		0			0
$805$	0.713493	−	4.04642i	0.0251473	−	0.142618i
$806$	12.7593	−	3.50521i	0.449428	−	0.123466i
$807$		0			0
$808$	23.0652	+	15.5088i	0.811431	+	0.545596i
$809$			4.57993i			0.161022i	0.996754	+	0.0805109i	$0.0256552\pi$
$809$			4.57993i			0.161022i	−0.996754	+	0.0805109i	$0.974345\pi$
$810$		0			0
$811$			23.9708i			0.841727i	0.907124	+	0.420864i	$0.138273\pi$
$811$			23.9708i			0.841727i	−0.907124	+	0.420864i	$0.861727\pi$
$812$	0.441681	+	35.0295i	0.0155000	+	1.22929i
$813$		0			0
$814$	20.7003	+	75.3512i	0.725545	+	2.64106i
$815$	0.191110	−	1.08384i	0.00669429	−	0.0379652i
$816$		0			0
$817$	20.2578	−	16.9983i	0.708731	−	0.594696i
$818$	−2.36451	+	29.1411i	−0.0826730	+	1.01890i
$819$		0			0
$820$	8.19500	+	1.33869i	0.286182	+	0.0467492i
$821$	−7.46457	+	1.31620i	−0.260515	+	0.0459359i	−0.302380	−	0.953187i	$-0.597781\pi$
$821$	−7.46457	+	1.31620i	−0.260515	+	0.0459359i	0.0418649	+	0.999123i	$0.486670\pi$
$822$		0			0
$823$	15.9886	+	43.9282i	0.557326	+	1.53124i	0.823500	+	0.567316i	$0.192018\pi$
$823$	15.9886	+	43.9282i	0.557326	+	1.53124i	−0.266174	+	0.963925i	$0.585760\pi$
$824$	−19.5644	+	2.08516i	−0.681558	+	0.0726402i
$825$		0			0
$826$	−6.30772	−	2.89307i	−0.219474	−	0.100663i
$827$	−15.4331	+	26.7308i	−0.536660	+	0.929522i	0.462421	+	0.886661i	$0.346981\pi$
$827$	−15.4331	+	26.7308i	−0.536660	+	0.929522i	−0.999081	+	0.0428620i	$0.986352\pi$
$828$		0			0
$829$	5.56407	+	9.63724i	0.193248	+	0.334715i	0.946325	−	0.323217i	$-0.104764\pi$
$829$	5.56407	+	9.63724i	0.193248	+	0.334715i	−0.753077	+	0.657933i	$0.771431\pi$
$830$	1.14148	+	12.1636i	0.0396215	+	0.422203i
$831$		0			0
$832$	−7.96601	+	10.2576i	−0.276172	+	0.355618i
$833$	1.81892	−	2.16771i	0.0630220	−	0.0751067i
$834$		0			0
$835$	1.14092	−	3.13466i	0.0394833	−	0.108479i
$836$	−30.8839	+	11.6839i	−1.06814	+	0.404095i
$837$		0			0
$838$	−9.91149	−	6.84739i	−0.342387	−	0.236539i
$839$	8.74658	+	3.18349i	0.301965	+	0.109906i	0.488559	−	0.872531i	$-0.337523\pi$
$839$	8.74658	+	3.18349i	0.301965	+	0.109906i	−0.186594	+	0.982437i	$0.559745\pi$
$840$		0			0
$841$	−46.6034	−	39.1049i	−1.60701	−	1.34844i
$842$	14.1758	−	14.3557i	0.488531	−	0.494730i
$843$		0			0
$844$	−4.47935	+	7.98942i	−0.154186	+	0.275007i
$845$	4.84959	−	2.79991i	0.166831	−	0.0963200i
$846$		0			0
$847$	−22.3399	−	12.8980i	−0.767609	−	0.443179i
$848$	2.32725	−	2.91997i	0.0799180	−	0.100272i
$849$		0			0
$850$	1.32830	−	5.08531i	0.0455604	−	0.174425i
$851$	42.7690	−	15.5667i	1.46610	−	0.533618i
$852$		0			0
$853$	2.28870	+	12.9798i	0.0783634	+	0.444421i	0.998592	+	0.0530406i	$0.0168913\pi$
$853$	2.28870	+	12.9798i	0.0783634	+	0.444421i	−0.920229	+	0.391381i	$0.871998\pi$
$854$	−6.28293	−	13.2550i	−0.214997	−	0.453576i
$855$		0			0
$856$	−6.84264	+	1.97290i	−0.233877	+	0.0674324i
$857$	9.69516	+	11.5542i	0.331180	+	0.394685i	0.905779	−	0.423750i	$-0.139286\pi$
$857$	9.69516	+	11.5542i	0.331180	+	0.394685i	−0.574599	+	0.818435i	$0.694842\pi$
$858$		0			0
$859$	−24.5457	−	4.32808i	−0.837490	−	0.147672i	−0.261577	−	0.965183i	$-0.584242\pi$
$859$	−24.5457	−	4.32808i	−0.837490	−	0.147672i	−0.575914	+	0.817511i	$0.695354\pi$
$860$	2.85472	−	8.16202i	0.0973451	−	0.278323i
$861$		0			0
$862$	−1.21971	−	1.71876i	−0.0415435	−	0.0585413i
$863$	22.0216			0.749626			0.374813	−	0.927101i	$-0.377707\pi$
$863$	22.0216			0.749626			0.374813	+	0.927101i	$0.377707\pi$
$864$		0			0
$865$	8.03425			0.273173
$866$	2.31856	+	3.26721i	0.0787879	+	0.111024i
$867$		0			0
$868$	7.03272	−	20.1075i	0.238706	−	0.682493i
$869$	3.96195	+	0.698599i	0.134400	+	0.0236984i
$870$		0			0
$871$	6.57787	+	7.83921i	0.222883	+	0.265621i
$872$	−15.6792	+	4.52070i	−0.530964	+	0.153090i
$873$		0			0
$874$	8.23767	+	17.3789i	0.278643	+	0.587849i
$875$	1.68323	+	9.54610i	0.0569037	+	0.322717i
$876$		0			0
$877$	−20.5090	+	7.46466i	−0.692539	+	0.252064i	−0.664222	−	0.747535i	$-0.731237\pi$
$877$	−20.5090	+	7.46466i	−0.692539	+	0.252064i	−0.0283170	+	0.999599i	$0.509015\pi$
$878$	9.60067	−	36.7555i	0.324007	−	1.24044i
$879$		0			0
$880$	−6.72935	+	8.44324i	−0.226846	+	0.284621i
$881$	7.29454	+	4.21150i	0.245759	+	0.141889i	0.617821	−	0.786319i	$-0.288016\pi$
$881$	7.29454	+	4.21150i	0.245759	+	0.141889i	−0.372062	+	0.928208i	$0.621349\pi$
$882$		0			0
$883$	−21.6426	+	12.4953i	−0.728330	+	0.420502i	−0.817811	−	0.575487i	$-0.804813\pi$
$883$	−21.6426	+	12.4953i	−0.728330	+	0.420502i	0.0894807	+	0.995989i	$0.471479\pi$
$884$	1.25344	−	2.23564i	0.0421576	−	0.0751928i
$885$		0			0
$886$	25.8896	−	26.2181i	0.869779	−	0.880815i
$887$	34.3044	+	28.7848i	1.15183	+	0.966499i	0.999761	−	0.0218707i	$-0.00696222\pi$
$887$	34.3044	+	28.7848i	1.15183	+	0.966499i	0.152068	+	0.988370i	$0.451407\pi$
$888$		0			0
$889$	−6.96058	−	2.53344i	−0.233450	−	0.0849689i
$890$	−3.93085	−	2.71564i	−0.131762	−	0.0910286i
$891$		0			0
$892$	−34.5470	+	13.0696i	−1.15672	+	0.437604i
$893$	3.53665	−	9.71686i	0.118349	−	0.325162i
$894$		0			0
$895$	1.95013	−	2.32407i	0.0651855	−	0.0776850i
$896$	6.29710	+	19.9374i	0.210371	+	0.666062i
$897$		0			0
$898$	−2.98068	−	31.7619i	−0.0994666	−	1.05991i
$899$	27.3132	+	47.3078i	0.910945	+	1.57780i
$900$		0			0
$901$	−0.368441	+	0.638158i	−0.0122745	+	0.0212601i
$902$	−49.3486	−	22.6340i	−1.64313	−	0.753630i
$903$		0			0
$904$	12.4714	−	1.32920i	0.414794	−	0.0442085i
$905$	1.12456	+	3.08970i	0.0373817	+	0.102705i
$906$		0			0
$907$	31.5142	−	5.55680i	1.04641	−	0.184511i	0.376091	−	0.926583i	$-0.377268\pi$
$907$	31.5142	−	5.55680i	1.04641	−	0.184511i	0.670320	+	0.742072i	$0.266157\pi$
$908$	−26.1826	−	4.27707i	−0.868902	−	0.141939i
$909$		0			0
$910$	−0.185396	+	2.28490i	−0.00614582	+	0.0757436i
$911$	21.9054	−	18.3808i	0.725757	−	0.608983i	−0.203214	−	0.979134i	$-0.565139\pi$
$911$	21.9054	−	18.3808i	0.725757	−	0.608983i	0.928971	+	0.370152i	$0.120694\pi$
$912$		0			0
$913$	13.8708	−	78.6650i	0.459055	−	2.60343i
$914$	−5.55139	−	20.2076i	−0.183624	−	0.668410i
$915$		0			0
$916$	0.0870387	+	6.90300i	0.00287584	+	0.228082i
$917$		−	4.44416i		−	0.146759i
$918$		0			0
$919$		−	27.7726i		−	0.916132i	−0.888918	−	0.458066i	$-0.848542\pi$
$919$		−	27.7726i		−	0.916132i	0.888918	−	0.458066i	$-0.151458\pi$
$920$	5.21859	+	3.50892i	0.172052	+	0.115686i
$921$		0			0
$922$	−42.2338	+	11.6024i	−1.39090	+	0.382104i
$923$	−2.55522	+	14.4914i	−0.0841062	+	0.476990i
$924$		0			0
$925$	−39.8899	+	33.4716i	−1.31157	+	1.10054i
$926$	32.2714	+	2.61849i	1.06050	+	0.0860489i
$927$		0			0
$928$	−49.2833	−	21.1168i	−1.61780	−	0.693192i
$929$	9.40060	−	1.65758i	0.308424	−	0.0543834i	−0.0172941	−	0.999850i	$-0.505505\pi$
$929$	9.40060	−	1.65758i	0.308424	−	0.0543834i	0.325718	+	0.945467i	$0.394394\pi$
$930$		0			0
$931$	−4.05180	−	11.1322i	−0.132792	−	0.364844i
$932$	−24.7790	+	21.3301i	−0.811663	+	0.698692i
$933$		0			0
$934$	−21.1970	+	46.2154i	−0.693585	+	1.51222i
$935$	1.06536	−	1.84527i	0.0348411	−	0.0603466i
$936$		0			0
$937$	−1.13866	−	1.97222i	−0.0371986	−	0.0644298i	0.846827	−	0.531869i	$-0.178510\pi$
$937$	−1.13866	−	1.97222i	−0.0371986	−	0.0644298i	−0.884025	+	0.467439i	$0.845177\pi$
$938$	16.4023	−	1.53927i	0.535555	−	0.0502589i
$939$		0			0
$940$	−0.629058	−	3.32208i	−0.0205176	−	0.108354i
$941$	4.48164	−	5.34101i	0.146097	−	0.174112i	−0.688033	−	0.725679i	$-0.741526\pi$
$941$	4.48164	−	5.34101i	0.146097	−	0.174112i	0.834130	+	0.551567i	$0.185970\pi$
$942$		0			0
$943$	−10.8153	+	29.7148i	−0.352195	+	0.967647i
$944$	7.96140	−	7.02998i	0.259121	−	0.228806i
$945$		0			0
$946$	−32.1350	+	46.5149i	−1.04480	+	1.51233i
$947$	−42.9198	−	15.6215i	−1.39471	−	0.507631i	−0.468103	−	0.883674i	$-0.655063\pi$
$947$	−42.9198	−	15.6215i	−1.39471	−	0.507631i	−0.926603	+	0.376042i	$0.877285\pi$
$948$		0			0
$949$	−14.3541	−	12.0445i	−0.465955	−	0.390982i
$950$	−15.6569	−	15.4607i	−0.507975	−	0.501611i
$951$		0			0
$952$	−1.81420	−	3.70594i	−0.0587987	−	0.120110i
$953$	26.2534	−	15.1574i	0.850431	−	0.490997i	−0.0103652	−	0.999946i	$-0.503299\pi$
$953$	26.2534	−	15.1574i	0.850431	−	0.490997i	0.860796	+	0.508950i	$0.169966\pi$
$954$		0			0
$955$	2.27046	+	1.31085i	0.0734704	+	0.0424181i
$956$	1.79070	−	1.06419i	0.0579154	−	0.0344183i
$957$		0			0
$958$	−27.9865	−	7.31019i	−0.904204	−	0.236181i
$959$	−7.43966	+	2.70782i	−0.240239	+	0.0874400i
$960$		0			0
$961$	−0.384864	−	2.18267i	−0.0124150	−	0.0704089i
$962$	−22.9459	+	10.8765i	−0.739805	+	0.350671i
$963$		0			0
$964$	−20.8503	+	25.4944i	−0.671544	+	0.821121i
$965$	−1.83307	−	2.18457i	−0.0590088	−	0.0703239i
$966$		0			0
$967$	30.8569	+	5.44090i	0.992290	+	0.174967i	0.646146	−	0.763214i	$-0.276380\pi$
$967$	30.8569	+	5.44090i	0.992290	+	0.174967i	0.346144	+	0.938181i	$0.387491\pi$
$968$	31.9066	−	23.2527i	1.02552	−	0.747370i
$969$		0			0
$970$	5.88265	−	4.17459i	0.188881	−	0.134038i
$971$	−1.61116			−0.0517047			−0.0258523	−	0.999666i	$-0.508230\pi$
$971$	−1.61116			−0.0517047			−0.0258523	+	0.999666i	$0.508230\pi$
$972$		0			0
$973$	−32.9535			−1.05644
$974$	−19.6351	+	13.9339i	−0.629148	+	0.446471i
$975$		0			0
$976$	22.4432	−	0.566055i	0.718389	−	0.0181190i
$977$	−26.4012	−	4.65524i	−0.844648	−	0.148934i	−0.265453	−	0.964124i	$-0.585522\pi$
$977$	−26.4012	−	4.65524i	−0.844648	−	0.148934i	−0.579194	+	0.815190i	$0.696633\pi$
$978$		0			0
$979$	20.0794	+	23.9297i	0.641741	+	0.764797i
$980$	−2.99851	−	2.45230i	−0.0957839	−	0.0783358i
$981$		0			0
$982$	18.1628	−	8.60924i	0.579597	−	0.274732i
$983$	4.56612	+	25.8958i	0.145637	+	0.825947i	0.966854	+	0.255331i	$0.0821844\pi$
$983$	4.56612	+	25.8958i	0.145637	+	0.825947i	−0.821217	+	0.570616i	$0.806704\pi$
$984$		0			0
$985$	1.35492	−	0.493152i	0.0431715	−	0.0157131i
$986$	10.2376	+	2.67411i	0.326033	+	0.0851610i
$987$		0			0
$988$	−5.48180	−	9.22419i	−0.174399	−	0.293461i
$989$	28.5173	+	16.4645i	0.906797	+	0.523540i
$990$		0			0
$991$	−20.2827	+	11.7102i	−0.644302	+	0.371988i	−0.786270	−	0.617883i	$-0.787990\pi$
$991$	−20.2827	+	11.7102i	−0.644302	+	0.371988i	0.141968	+	0.989871i	$0.454657\pi$
$992$	23.7685	+	22.3155i	0.754652	+	0.708517i
$993$		0			0
$994$	16.8560	+	16.6448i	0.534641	+	0.527942i
$995$	4.69607	+	3.94047i	0.148876	+	0.124921i
$996$		0			0
$997$	5.48788	+	1.99742i	0.173803	+	0.0632590i	0.427456	−	0.904036i	$-0.359410\pi$
$997$	5.48788	+	1.99742i	0.173803	+	0.0632590i	−0.253653	+	0.967295i	$0.581632\pi$
$998$	5.75921	−	8.33636i	0.182304	−	0.263883i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.179.12		96
3.2	odd	2		108.2.l.a.23.5	✓	96
4.3	odd	2	inner	324.2.l.a.179.1		96
9.2	odd	6		972.2.l.c.215.6		96
9.4	even	3		972.2.l.a.863.1		96
9.5	odd	6		972.2.l.d.863.16		96
9.7	even	3		972.2.l.b.215.11		96
12.11	even	2		108.2.l.a.23.16	yes	96
27.2	odd	18		972.2.l.a.107.10		96
27.7	even	9		108.2.l.a.47.16	yes	96
27.11	odd	18		972.2.l.b.755.12		96
27.16	even	9		972.2.l.c.755.5		96
27.20	odd	18	inner	324.2.l.a.143.1		96
27.25	even	9		972.2.l.d.107.7		96
36.7	odd	6		972.2.l.b.215.12		96
36.11	even	6		972.2.l.c.215.5		96
36.23	even	6		972.2.l.d.863.7		96
36.31	odd	6		972.2.l.a.863.10		96
108.7	odd	18		108.2.l.a.47.5	yes	96
108.11	even	18		972.2.l.b.755.11		96
108.43	odd	18		972.2.l.c.755.6		96
108.47	even	18	inner	324.2.l.a.143.12		96
108.79	odd	18		972.2.l.d.107.16		96
108.83	even	18		972.2.l.a.107.1		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.5	✓	96	3.2	odd	2
108.2.l.a.23.16	yes	96	12.11	even	2
108.2.l.a.47.5	yes	96	108.7	odd	18
108.2.l.a.47.16	yes	96	27.7	even	9
324.2.l.a.143.1		96	27.20	odd	18	inner
324.2.l.a.143.12		96	108.47	even	18	inner
324.2.l.a.179.1		96	4.3	odd	2	inner
324.2.l.a.179.12		96	1.1	even	1	trivial
972.2.l.a.107.1		96	108.83	even	18
972.2.l.a.107.10		96	27.2	odd	18
972.2.l.a.863.1		96	9.4	even	3
972.2.l.a.863.10		96	36.31	odd	6
972.2.l.b.215.11		96	9.7	even	3
972.2.l.b.215.12		96	36.7	odd	6
972.2.l.b.755.11		96	108.11	even	18
972.2.l.b.755.12		96	27.11	odd	18
972.2.l.c.215.5		96	36.11	even	6
972.2.l.c.215.6		96	9.2	odd	6
972.2.l.c.755.5		96	27.16	even	9
972.2.l.c.755.6		96	108.43	odd	18
972.2.l.d.107.7		96	27.25	even	9
972.2.l.d.107.16		96	108.79	odd	18
972.2.l.d.863.7		96	36.23	even	6
972.2.l.d.863.16		96	9.5	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.818446 + 1.15332i) q^{2} +(-0.660291 + 1.88786i) q^{4} +(-0.532084 - 0.0938207i) q^{5} +(1.18790 + 1.41568i) q^{7} +(-2.71772 + 0.783586i) q^{8} +(-0.327277 - 0.690450i) q^{10} +(0.867520 + 4.91995i) q^{11} +(-1.52553 + 0.555249i) q^{13} +(-0.660503 + 2.52869i) q^{14} +(-3.12803 - 2.49307i) q^{16} +(0.683630 + 0.394694i) q^{17} +(2.86200 - 1.65238i) q^{19} +(0.528451 - 0.942551i) q^{20} +(-4.96425 + 5.02724i) q^{22} +(3.15234 + 2.64512i) q^{23} +(-4.42415 - 1.61026i) q^{25} +(-1.88895 - 1.30499i) q^{26} +(-3.45697 + 1.30783i) q^{28} +(3.24174 - 8.90660i) q^{29} +(-3.70462 + 4.41499i) q^{31} +(0.315184 - 5.64807i) q^{32} +(0.104306 + 1.11148i) q^{34} +(-0.499242 - 0.864712i) q^{35} +(5.53013 - 9.57846i) q^{37} +(4.24812 + 1.94842i) q^{38} +(1.51957 - 0.161955i) q^{40} +(2.62821 + 7.22095i) q^{41} +(7.88044 - 1.38953i) q^{43} +(-9.86099 - 1.61084i) q^{44} +(-0.470654 + 5.80054i) q^{46} +(2.39693 - 2.01126i) q^{47} +(0.622483 - 3.53027i) q^{49} +(-1.76379 - 6.42037i) q^{50} +(-0.0409360 - 3.24662i) q^{52} +0.933485i q^{53} -2.69922i q^{55} +(-4.33769 - 2.91661i) q^{56} +(12.9253 - 3.55082i) q^{58} +(-0.461077 + 2.61490i) q^{59} +(-4.29949 + 3.60770i) q^{61} +(-8.12393 - 0.659173i) q^{62} +(6.77199 - 4.25913i) q^{64} +(0.863806 - 0.152312i) q^{65} +(-2.15593 - 5.92336i) q^{67} +(-1.19652 + 1.02998i) q^{68} +(0.588687 - 1.28351i) q^{70} +(4.53203 - 7.84970i) q^{71} +(5.77108 + 9.99580i) q^{73} +(15.5731 - 1.46145i) q^{74} +(1.22970 + 6.49411i) q^{76} +(-5.93457 + 7.07254i) q^{77} +(0.275423 - 0.756719i) q^{79} +(1.43047 + 1.62000i) q^{80} +(-6.17702 + 8.94113i) q^{82} +(-15.0247 - 5.46855i) q^{83} +(-0.326718 - 0.274149i) q^{85} +(8.05230 + 7.95141i) q^{86} +(-6.21288 - 12.6913i) q^{88} +(5.41508 - 3.12640i) q^{89} +(-2.59824 - 1.50009i) q^{91} +(-7.07508 + 4.20462i) q^{92} +(4.28138 + 1.11831i) q^{94} +(-1.67785 + 0.610689i) q^{95} +(1.63933 + 9.29708i) q^{97} +(4.58100 - 2.17142i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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