LMFDB - Embedded newform 432.2.u.b.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			241.1
Root			$0.500000 - 2.42499i$ of defining polynomial
Character	$\chi$	$=$	432.241
Dual form			432.2.u.b.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.56529 + 0.741539i) q^{3} +(-3.10057 + 2.60168i) q^{5} +(-0.144365 + 0.0525446i) q^{7} +(1.90024 - 2.32144i) q^{9} +(-0.169211 - 0.141985i) q^{11} +(0.103202 + 0.585289i) q^{13} +(2.92402 - 6.37157i) q^{15} +(-2.78255 - 4.81952i) q^{17} +(1.91041 - 3.30893i) q^{19} +(0.187009 - 0.189300i) q^{21} +(-5.50570 - 2.00391i) q^{23} +(1.97651 - 11.2093i) q^{25} +(-1.25298 + 5.04282i) q^{27} +(0.129880 - 0.736585i) q^{29} +(4.77702 + 1.73869i) q^{31} +(0.370152 + 0.0967705i) q^{33} +(0.310909 - 0.538510i) q^{35} +(-1.87388 - 3.24566i) q^{37} +(-0.595555 - 0.839616i) q^{39} +(0.690156 + 3.91407i) q^{41} +(-7.81896 - 6.56088i) q^{43} +(0.147838 + 12.1416i) q^{45} +(-0.447025 + 0.162704i) q^{47} +(-5.34423 + 4.48434i) q^{49} +(7.92935 + 5.48056i) q^{51} +3.29955 q^{53} +0.894051 q^{55} +(-0.536639 + 6.59606i) q^{57} +(-5.57221 + 4.67564i) q^{59} +(-3.16654 + 1.15253i) q^{61} +(-0.152349 + 0.434982i) q^{63} +(-1.84272 - 1.54623i) q^{65} +(-1.29509 - 7.34481i) q^{67} +(10.1040 - 0.945999i) q^{69} +(1.42889 + 2.47490i) q^{71} +(0.638922 - 1.10665i) q^{73} +(5.21836 + 19.0115i) q^{75} +(0.0318887 + 0.0116066i) q^{77} +(0.574268 - 3.25684i) q^{79} +(-1.77818 - 8.82259i) q^{81} +(1.43627 - 8.14551i) q^{83} +(21.1664 + 7.70392i) q^{85} +(0.342907 + 1.24928i) q^{87} +(2.47882 - 4.29345i) q^{89} +(-0.0456525 - 0.0790725i) q^{91} +(-8.76671 + 0.820795i) q^{93} +(2.68543 + 15.2298i) q^{95} +(4.33127 + 3.63437i) q^{97} +(-0.651152 + 0.123008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9} + 12 q^{11} + 12 q^{13} + 18 q^{15} - 6 q^{17} + 9 q^{19} + 24 q^{21} - 30 q^{23} - 9 q^{25} + 15 q^{29} + 36 q^{33} - 3 q^{35} - 15 q^{37} + 42 q^{39} - 12 q^{41} - 9 q^{43}+ \cdots - 9 q^{99}+O(q^{100}) $ 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9 + 12 * q^11 + 12 * q^13 + 18 * q^15 - 6 * q^17 + 9 * q^19 + 24 * q^21 - 30 * q^23 - 9 * q^25 + 15 * q^29 + 36 * q^33 - 3 * q^35 - 15 * q^37 + 42 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^45 + 9 * q^47 - 39 * q^49 + 27 * q^51 - 12 * q^53 - 18 * q^55 + 18 * q^57 - 12 * q^59 - 36 * q^61 - 3 * q^63 - 15 * q^65 - 36 * q^67 + 18 * q^69 - 12 * q^71 - 21 * q^73 - 30 * q^75 + 3 * q^77 - 39 * q^79 - 18 * q^83 + 45 * q^85 - 27 * q^87 + 12 * q^89 + 6 * q^91 - 33 * q^93 + 15 * q^95 + 39 * q^97 - 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

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			0
$2$		0			0
$3$	−1.56529	+	0.741539i	−0.903718	+	0.428128i
$3$	−1.56529	+	0.741539i	−0.903718	+	0.428128i
$4$		0			0
$5$	−3.10057	+	2.60168i	−1.38661	+	1.16351i	−0.419925	+	0.907559i	$0.637944\pi$
$5$	−3.10057	+	2.60168i	−1.38661	+	1.16351i	−0.966690	+	0.255949i	$0.917612\pi$
$6$		0			0
$7$	−0.144365	+	0.0525446i	−0.0545648	+	0.0198600i	−0.369158	−	0.929366i	$-0.620354\pi$
$7$	−0.144365	+	0.0525446i	−0.0545648	+	0.0198600i	0.314594	+	0.949226i	$0.398132\pi$
$8$		0			0
$9$	1.90024	−	2.32144i	0.633413	−	0.773814i
$10$		0			0
$11$	−0.169211	−	0.141985i	−0.0510191	−	0.0428101i	0.616922	−	0.787025i	$-0.288380\pi$
$11$	−0.169211	−	0.141985i	−0.0510191	−	0.0428101i	−0.667941	+	0.744215i	$0.732824\pi$
$12$		0			0
$13$	0.103202	+	0.585289i	0.0286231	+	0.162330i	0.995769	−	0.0918925i	$-0.0292916\pi$
$13$	0.103202	+	0.585289i	0.0286231	+	0.162330i	−0.967146	+	0.254222i	$0.918180\pi$
$14$		0			0
$15$	2.92402	−	6.37157i	0.754979	−	1.64513i
$16$		0			0
$17$	−2.78255	−	4.81952i	−0.674868	−	1.16891i	−0.976507	−	0.215484i	$-0.930867\pi$
$17$	−2.78255	−	4.81952i	−0.674868	−	1.16891i	0.301639	−	0.953422i	$-0.402466\pi$
$18$		0			0
$19$	1.91041	−	3.30893i	0.438278	−	0.759120i	−0.559279	−	0.828980i	$-0.688922\pi$
$19$	1.91041	−	3.30893i	0.438278	−	0.759120i	0.997557	+	0.0698599i	$0.0222552\pi$
$20$		0			0
$21$	0.187009	−	0.189300i	0.0408086	−	0.0413086i
$22$		0			0
$23$	−5.50570	−	2.00391i	−1.14802	−	0.417844i	−0.303215	−	0.952922i	$-0.598060\pi$
$23$	−5.50570	−	2.00391i	−1.14802	−	0.417844i	−0.844803	+	0.535078i	$0.820282\pi$
$24$		0			0
$25$	1.97651	−	11.2093i	0.395302	−	2.24187i
$26$		0			0
$27$	−1.25298	+	5.04282i	−0.241136	+	0.970491i
$28$		0			0
$29$	0.129880	−	0.736585i	0.0241181	−	0.136780i	−0.970371	−	0.241619i	$-0.922322\pi$
$29$	0.129880	−	0.736585i	0.0241181	−	0.136780i	0.994489	+	0.104839i	$0.0334327\pi$
$30$		0			0
$31$	4.77702	+	1.73869i	0.857978	+	0.312278i	0.733289	−	0.679917i	$-0.237984\pi$
$31$	4.77702	+	1.73869i	0.857978	+	0.312278i	0.124689	+	0.992196i	$0.460207\pi$
$32$		0			0
$33$	0.370152	+	0.0967705i	0.0644351	+	0.0168456i
$34$		0			0
$35$	0.310909	−	0.538510i	0.0525532	−	0.0910248i
$36$		0			0
$37$	−1.87388	−	3.24566i	−0.308065	−	0.533584i	0.669874	−	0.742474i	$-0.266348\pi$
$37$	−1.87388	−	3.24566i	−0.308065	−	0.533584i	−0.977939	+	0.208891i	$0.933015\pi$
$38$		0			0
$39$	−0.595555	−	0.839616i	−0.0953652	−	0.134446i
$40$		0			0
$41$	0.690156	+	3.91407i	0.107784	+	0.611275i	0.990072	+	0.140564i	$0.0448915\pi$
$41$	0.690156	+	3.91407i	0.107784	+	0.611275i	−0.882287	+	0.470711i	$0.843997\pi$
$42$		0			0
$43$	−7.81896	−	6.56088i	−1.19238	−	1.00053i	−0.999815	−	0.0192411i	$-0.993875\pi$
$43$	−7.81896	−	6.56088i	−1.19238	−	1.00053i	−0.192565	−	0.981284i	$-0.561681\pi$
$44$		0			0
$45$	0.147838	+	12.1416i	0.0220384	+	1.80996i
$46$		0			0
$47$	−0.447025	+	0.162704i	−0.0652054	+	0.0237328i	−0.374417	−	0.927260i	$-0.622157\pi$
$47$	−0.447025	+	0.162704i	−0.0652054	+	0.0237328i	0.309212	+	0.950993i	$0.399935\pi$
$48$		0			0
$49$	−5.34423	+	4.48434i	−0.763462	+	0.640620i
$50$		0			0
$51$	7.92935	+	5.48056i	1.11033	+	0.767432i
$52$		0			0
$53$	3.29955			0.453228			0.226614	−	0.973985i	$-0.427234\pi$
$53$	3.29955			0.453228			0.226614	+	0.973985i	$0.427234\pi$
$54$		0			0
$55$	0.894051			0.120554
$56$		0			0
$57$	−0.536639	+	6.59606i	−0.0710795	+	0.873669i
$58$		0			0
$59$	−5.57221	+	4.67564i	−0.725440	+	0.608716i	−0.928884	−	0.370370i	$-0.879231\pi$
$59$	−5.57221	+	4.67564i	−0.725440	+	0.608716i	0.203444	+	0.979086i	$0.434786\pi$
$60$		0			0
$61$	−3.16654	+	1.15253i	−0.405434	+	0.147566i	−0.536684	−	0.843783i	$-0.680323\pi$
$61$	−3.16654	+	1.15253i	−0.405434	+	0.147566i	0.131250	+	0.991349i	$0.458101\pi$
$62$		0			0
$63$	−0.152349	+	0.434982i	−0.0191942	+	0.0548026i
$64$		0			0
$65$	−1.84272	−	1.54623i	−0.228561	−	0.191786i
$66$		0			0
$67$	−1.29509	−	7.34481i	−0.158220	−	0.897312i	−0.955782	−	0.294075i	$-0.904989\pi$
$67$	−1.29509	−	7.34481i	−0.158220	−	0.897312i	0.797562	−	0.603237i	$-0.206123\pi$
$68$		0			0
$69$	10.1040	−	0.945999i	1.21638	−	0.113885i
$70$		0			0
$71$	1.42889	+	2.47490i	0.169578	+	0.293717i	0.938271	−	0.345900i	$-0.112426\pi$
$71$	1.42889	+	2.47490i	0.169578	+	0.293717i	−0.768694	+	0.639617i	$0.779093\pi$
$72$		0			0
$73$	0.638922	−	1.10665i	0.0747802	−	0.129523i	−0.826210	−	0.563362i	$-0.809508\pi$
$73$	0.638922	−	1.10665i	0.0747802	−	0.129523i	0.900991	+	0.433838i	$0.142841\pi$
$74$		0			0
$75$	5.21836	+	19.0115i	0.602564	+	2.19526i
$76$		0			0
$77$	0.0318887	+	0.0116066i	0.00363406	+	0.00132269i
$78$		0			0
$79$	0.574268	−	3.25684i	0.0646102	−	0.366423i	−0.935310	−	0.353828i	$-0.884880\pi$
$79$	0.574268	−	3.25684i	0.0646102	−	0.366423i	0.999921	−	0.0125947i	$-0.00400912\pi$
$80$		0			0
$81$	−1.77818	−	8.82259i	−0.197575	−	0.980288i
$82$		0			0
$83$	1.43627	−	8.14551i	0.157651	−	0.894085i	−0.798670	−	0.601769i	$-0.794463\pi$
$83$	1.43627	−	8.14551i	0.157651	−	0.894085i	0.956322	−	0.292316i	$-0.0944261\pi$
$84$		0			0
$85$	21.1664	+	7.70392i	2.29581	+	0.835608i
$86$		0			0
$87$	0.342907	+	1.24928i	0.0367635	+	0.133937i
$88$		0			0
$89$	2.47882	−	4.29345i	0.262755	−	0.455105i	−0.704218	−	0.709984i	$-0.748702\pi$
$89$	2.47882	−	4.29345i	0.262755	−	0.455105i	0.966973	+	0.254879i	$0.0820356\pi$
$90$		0			0
$91$	−0.0456525	−	0.0790725i	−0.00478569	−	0.00828905i
$92$		0			0
$93$	−8.76671	+	0.820795i	−0.909065	+	0.0851125i
$94$		0			0
$95$	2.68543	+	15.2298i	0.275519	+	1.56255i
$96$		0			0
$97$	4.33127	+	3.63437i	0.439774	+	0.369014i	0.835625	−	0.549301i	$-0.185106\pi$
$97$	4.33127	+	3.63437i	0.439774	+	0.369014i	−0.395851	+	0.918315i	$0.629550\pi$
$98$		0			0
$99$	−0.651152	+	0.123008i	−0.0654433	+	0.0123628i
$100$		0			0
$101$	−14.8467	+	5.40376i	−1.47730	+	0.537694i	−0.950072	−	0.312029i	$-0.898991\pi$
$101$	−14.8467	+	5.40376i	−1.47730	+	0.537694i	−0.527229	+	0.849723i	$0.676769\pi$
$102$		0			0
$103$	−8.19426	+	6.87580i	−0.807404	+	0.677493i	−0.949987	−	0.312290i	$-0.898904\pi$
$103$	−8.19426	+	6.87580i	−0.807404	+	0.677493i	0.142582	+	0.989783i	$0.454459\pi$
$104$		0			0
$105$	−0.0873351	+	1.07347i	−0.00852303	+	0.104760i
$106$		0			0
$107$	−1.85236			−0.179075			−0.0895374	−	0.995983i	$-0.528539\pi$
$107$	−1.85236			−0.179075			−0.0895374	+	0.995983i	$0.528539\pi$
$108$		0			0
$109$	−14.5495			−1.39359			−0.696793	−	0.717273i	$-0.745390\pi$
$109$	−14.5495			−1.39359			−0.696793	+	0.717273i	$0.745390\pi$
$110$		0			0
$111$	5.33995	+	3.69083i	0.506846	+	0.350318i
$112$		0			0
$113$	−10.2514	+	8.60195i	−0.964371	+	0.809204i	−0.981659	−	0.190647i	$-0.938941\pi$
$113$	−10.2514	+	8.60195i	−0.964371	+	0.809204i	0.0172875	+	0.999851i	$0.494497\pi$
$114$		0			0
$115$	22.2843	−	8.11083i	2.07802	−	0.756339i
$116$		0			0
$117$	1.55482	+	0.872611i	0.143743	+	0.0806729i
$118$		0			0
$119$	0.654943	+	0.549562i	0.0600385	+	0.0503783i
$120$		0			0
$121$	−1.90166	−	10.7848i	−0.172878	−	0.980439i
$122$		0			0
$123$	−3.98273	−	5.61486i	−0.359110	−	0.506275i
$124$		0			0
$125$	12.9161	+	22.3713i	1.15525	+	2.00095i
$126$		0			0
$127$	−9.31545	+	16.1348i	−0.826612	+	1.43173i	0.0740688	+	0.997253i	$0.476402\pi$
$127$	−9.31545	+	16.1348i	−0.826612	+	1.43173i	−0.900681	+	0.434481i	$0.856932\pi$
$128$		0			0
$129$	17.1041	+	4.47160i	1.50593	+	0.393702i
$130$		0			0
$131$	−6.45330	−	2.34881i	−0.563828	−	0.205217i	0.0443519	−	0.999016i	$-0.485878\pi$
$131$	−6.45330	−	2.34881i	−0.563828	−	0.205217i	−0.608180	+	0.793799i	$0.708100\pi$
$132$		0			0
$133$	−0.101930	+	0.578075i	−0.00883847	+	0.0501254i
$134$		0			0
$135$	−9.23488	−	18.8954i	−0.794812	−	1.62626i
$136$		0			0
$137$	2.60219	−	14.7577i	0.222320	−	1.26084i	−0.645423	−	0.763826i	$-0.723319\pi$
$137$	2.60219	−	14.7577i	0.222320	−	1.26084i	0.867743	−	0.497014i	$-0.165570\pi$
$138$		0			0
$139$	17.0110	+	6.19150i	1.44286	+	0.525156i	0.940586	−	0.339555i	$-0.110276\pi$
$139$	17.0110	+	6.19150i	1.44286	+	0.525156i	0.502269	+	0.864711i	$0.332499\pi$
$140$		0			0
$141$	0.579071	−	0.586165i	0.0487666	−	0.0493640i
$142$		0			0
$143$	0.0656393	−	0.113691i	0.00548904	−	0.00950729i
$144$		0			0
$145$	1.51366	+	2.62174i	0.125703	+	0.217723i
$146$		0			0
$147$	5.03993	−	10.9822i	0.415687	−	0.905799i
$148$		0			0
$149$	−2.60884	−	14.7955i	−0.213725	−	1.21209i	−0.883106	−	0.469174i	$-0.844552\pi$
$149$	−2.60884	−	14.7955i	−0.213725	−	1.21209i	0.669381	−	0.742919i	$-0.266559\pi$
$150$		0			0
$151$	4.32258	+	3.62708i	0.351767	+	0.295167i	0.801499	−	0.597996i	$-0.204036\pi$
$151$	4.32258	+	3.62708i	0.351767	+	0.295167i	−0.449732	+	0.893163i	$0.648481\pi$
$152$		0			0
$153$	−16.4758	−	2.69871i	−1.33199	−	0.218178i
$154$		0			0
$155$	−19.3350	+	7.03736i	−1.55302	+	0.565254i
$156$		0			0
$157$	5.54978	−	4.65682i	0.442921	−	0.371655i	−0.393880	−	0.919162i	$-0.628868\pi$
$157$	5.54978	−	4.65682i	0.442921	−	0.371655i	0.836801	+	0.547507i	$0.184423\pi$
$158$		0			0
$159$	−5.16474	+	2.44675i	−0.409591	+	0.194040i
$160$		0			0
$161$	0.900125			0.0709398
$162$		0			0
$163$	−14.1079			−1.10501			−0.552506	−	0.833509i	$-0.686328\pi$
$163$	−14.1079			−1.10501			−0.552506	+	0.833509i	$0.686328\pi$
$164$		0			0
$165$	−1.39945	+	0.662974i	−0.108947	+	0.0516124i
$166$		0			0
$167$	10.5889	−	8.88510i	0.819390	−	0.687550i	−0.133439	−	0.991057i	$-0.542602\pi$
$167$	10.5889	−	8.88510i	0.819390	−	0.687550i	0.952829	+	0.303507i	$0.0981576\pi$
$168$		0			0
$169$	11.8841	−	4.32546i	0.914161	−	0.332727i
$170$		0			0
$171$	−4.05124	−	10.7227i	−0.309806	−	0.819982i
$172$		0			0
$173$	−3.00999	−	2.52568i	−0.228845	−	0.192024i	0.521154	−	0.853463i	$-0.325502\pi$
$173$	−3.00999	−	2.52568i	−0.228845	−	0.192024i	−0.749999	+	0.661439i	$0.769946\pi$
$174$		0			0
$175$	0.303651	+	1.72209i	0.0229539	+	0.130178i
$176$		0			0
$177$	5.25493	−	11.4507i	0.394985	−	0.860689i
$178$		0			0
$179$	1.42211	+	2.46317i	0.106294	+	0.184106i	0.914266	−	0.405115i	$-0.132768\pi$
$179$	1.42211	+	2.46317i	0.106294	+	0.184106i	−0.807972	+	0.589220i	$0.799435\pi$
$180$		0			0
$181$	−6.46274	+	11.1938i	−0.480372	+	0.832028i	−0.999746	−	0.0225186i	$-0.992832\pi$
$181$	−6.46274	+	11.1938i	−0.480372	+	0.832028i	0.519375	+	0.854547i	$0.326165\pi$
$182$		0			0
$183$	4.10190	−	4.15215i	0.303221	−	0.306936i
$184$		0			0
$185$	14.2543	+	5.18813i	1.04800	+	0.381439i
$186$		0			0
$187$	−0.213461	+	1.21060i	−0.0156098	+	0.0885277i
$188$		0			0
$189$	−0.0840866	−	0.793844i	−0.00611640	−	0.0577437i
$190$		0			0
$191$	3.49774	−	19.8367i	0.253088	−	1.43533i	−0.547846	−	0.836579i	$-0.684552\pi$
$191$	3.49774	−	19.8367i	0.253088	−	1.43533i	0.800934	−	0.598753i	$-0.204337\pi$
$192$		0			0
$193$	−9.03669	−	3.28909i	−0.650476	−	0.236754i	−0.00435663	−	0.999991i	$-0.501387\pi$
$193$	−9.03669	−	3.28909i	−0.650476	−	0.236754i	−0.646119	+	0.763237i	$0.723609\pi$
$194$		0			0
$195$	4.03097	+	1.05384i	0.288664	+	0.0754668i
$196$		0			0
$197$	−3.77527	+	6.53895i	−0.268977	+	0.465881i	−0.968598	−	0.248633i	$-0.920019\pi$
$197$	−3.77527	+	6.53895i	−0.268977	+	0.465881i	0.699621	+	0.714514i	$0.253352\pi$
$198$		0			0
$199$	−6.07071	−	10.5148i	−0.430341	−	0.745372i	0.566562	−	0.824019i	$-0.308273\pi$
$199$	−6.07071	−	10.5148i	−0.430341	−	0.745372i	−0.996903	+	0.0786471i	$0.974940\pi$
$200$		0			0
$201$	7.47365	+	10.5364i	0.527151	+	0.743178i
$202$		0			0
$203$	0.0199534	+	0.113162i	0.00140046	+	0.00794238i
$204$		0			0
$205$	−12.3230	−	10.3403i	−0.860678	−	0.722195i
$206$		0			0
$207$	−15.1141	+	8.97325i	−1.05050	+	0.623684i
$208$		0			0
$209$	−0.793081	+	0.288658i	−0.0548586	+	0.0199669i
$210$		0			0
$211$	5.53378	−	4.64340i	0.380961	−	0.319665i	−0.432118	−	0.901817i	$-0.642234\pi$
$211$	5.53378	−	4.64340i	0.380961	−	0.319665i	0.813080	+	0.582152i	$0.197789\pi$
$212$		0			0
$213$	−4.07185	−	2.81436i	−0.278999	−	0.192837i
$214$		0			0
$215$	41.3125			2.81749
$216$		0			0
$217$	−0.780993			−0.0530173
$218$		0			0
$219$	−0.179475	+	2.20600i	−0.0121278	+	0.149068i
$220$		0			0
$221$	2.53365	−	2.12598i	0.170432	−	0.143009i
$222$		0			0
$223$	−23.9856	+	8.73004i	−1.60619	+	0.584607i	−0.980682	−	0.195607i	$-0.937332\pi$
$223$	−23.9856	+	8.73004i	−1.60619	+	0.584607i	−0.625512	+	0.780214i	$0.715110\pi$
$224$		0			0
$225$	−22.2660	−	25.8888i	−1.48440	−	1.72592i
$226$		0			0
$227$	−10.9999	−	9.22998i	−0.730086	−	0.612615i	0.200069	−	0.979782i	$-0.435883\pi$
$227$	−10.9999	−	9.22998i	−0.730086	−	0.612615i	−0.930155	+	0.367167i	$0.880328\pi$
$228$		0			0
$229$	0.704853	+	3.99742i	0.0465780	+	0.264157i	0.999200	−	0.0400010i	$-0.0127361\pi$
$229$	0.704853	+	3.99742i	0.0465780	+	0.264157i	−0.952622	+	0.304158i	$0.901625\pi$
$230$		0			0
$231$	−0.0585217	+	0.00547918i	−0.00385045	+	0.000360503i
$232$		0			0
$233$	−8.48936	−	14.7040i	−0.556157	−	0.963292i	−0.997813	−	0.0661072i	$-0.978942\pi$
$233$	−8.48936	−	14.7040i	−0.556157	−	0.963292i	0.441656	−	0.897185i	$-0.354391\pi$
$234$		0			0
$235$	0.962728	−	1.66749i	0.0628014	−	0.108775i
$236$		0			0
$237$	1.51618	+	5.52372i	0.0984864	+	0.358804i
$238$		0			0
$239$	20.0419	+	7.29464i	1.29640	+	0.471851i	0.895823	−	0.444412i	$-0.146587\pi$
$239$	20.0419	+	7.29464i	1.29640	+	0.471851i	0.400577	+	0.916263i	$0.368810\pi$
$240$		0			0
$241$	−1.86745	+	10.5909i	−0.120293	+	0.682217i	0.863699	+	0.504007i	$0.168142\pi$
$241$	−1.86745	+	10.5909i	−0.120293	+	0.682217i	−0.983993	+	0.178210i	$0.942970\pi$
$242$		0			0
$243$	9.32565	+	12.4913i	0.598241	+	0.801316i
$244$		0			0
$245$	4.90330	−	27.8080i	0.313260	−	1.77659i
$246$		0			0
$247$	2.13384	+	0.776653i	0.135773	+	0.0494172i
$248$		0			0
$249$	3.79203	+	13.8151i	0.240310	+	0.875496i
$250$		0			0
$251$	2.08811	−	3.61672i	0.131801	−	0.228285i	−0.792570	−	0.609781i	$-0.791257\pi$
$251$	2.08811	−	3.61672i	0.131801	−	0.228285i	0.924371	+	0.381495i	$0.124591\pi$
$252$		0			0
$253$	0.647101	+	1.12081i	0.0406829	+	0.0704649i
$254$		0			0
$255$	−38.8442	+	3.63684i	−2.43252	+	0.227748i
$256$		0			0
$257$	2.83797	+	16.0949i	0.177028	+	1.00397i	0.935777	+	0.352592i	$0.114699\pi$
$257$	2.83797	+	16.0949i	0.177028	+	1.00397i	−0.758750	+	0.651382i	$0.774189\pi$
$258$		0			0
$259$	0.441065	+	0.370098i	0.0274065	+	0.0229967i
$260$		0			0
$261$	−1.46314	−	1.70120i	−0.0905658	−	0.105301i
$262$		0			0
$263$	−2.51963	+	0.917071i	−0.155367	+	0.0565490i	−0.418533	−	0.908202i	$-0.637456\pi$
$263$	−2.51963	+	0.917071i	−0.155367	+	0.0565490i	0.263166	+	0.964751i	$0.415233\pi$
$264$		0			0
$265$	−10.2305	+	8.58439i	−0.628453	+	0.527335i
$266$		0			0
$267$	−0.696308	+	8.55862i	−0.0426133	+	0.523779i
$268$		0			0
$269$	22.3509			1.36276			0.681380	−	0.731930i	$-0.261380\pi$
$269$	22.3509			1.36276			0.681380	+	0.731930i	$0.261380\pi$
$270$		0			0
$271$	−25.4813			−1.54788			−0.773941	−	0.633258i	$-0.781717\pi$
$271$	−25.4813			−1.54788			−0.773941	+	0.633258i	$0.781717\pi$
$272$		0			0
$273$	0.130095	+	0.0899179i	0.00787369	+	0.00544208i
$274$		0			0
$275$	−1.92601	+	1.61611i	−0.116143	+	0.0974552i
$276$		0			0
$277$	2.41221	−	0.877972i	0.144936	−	0.0527523i	−0.268534	−	0.963270i	$-0.586539\pi$
$277$	2.41221	−	0.877972i	0.144936	−	0.0527523i	0.413469	+	0.910518i	$0.364317\pi$
$278$		0			0
$279$	13.1138	−	7.78564i	0.785100	−	0.466114i
$280$		0			0
$281$	16.2374	+	13.6248i	0.968642	+	0.812787i	0.982337	−	0.187119i	$-0.0599151\pi$
$281$	16.2374	+	13.6248i	0.968642	+	0.812787i	−0.0136956	+	0.999906i	$0.504360\pi$
$282$		0			0
$283$	3.40928	+	19.3350i	0.202660	+	1.14934i	0.901079	+	0.433655i	$0.142776\pi$
$283$	3.40928	+	19.3350i	0.202660	+	1.14934i	−0.698419	+	0.715689i	$0.746113\pi$
$284$		0			0
$285$	−15.4970	−	21.8477i	−0.917961	−	1.29414i
$286$		0			0
$287$	−0.305297	−	0.528791i	−0.0180211	−	0.0312135i
$288$		0			0
$289$	−6.98519	+	12.0987i	−0.410894	+	0.711689i
$290$		0			0
$291$	−9.47470	−	2.47702i	−0.555417	−	0.145205i
$292$		0			0
$293$	−20.1808	−	7.34522i	−1.17898	−	0.429112i	−0.323136	−	0.946352i	$-0.604737\pi$
$293$	−20.1808	−	7.34522i	−1.17898	−	0.429112i	−0.855840	+	0.517240i	$0.826959\pi$
$294$		0			0
$295$	5.11247	−	28.9942i	0.297659	−	1.68811i
$296$		0			0
$297$	0.928024	−	0.675398i	0.0538494	−	0.0391906i
$298$		0			0
$299$	0.604666	−	3.42923i	0.0349688	−	0.198318i
$300$		0			0
$301$	1.47352	+	0.536318i	0.0849324	+	0.0309129i
$302$		0			0
$303$	19.2322	−	19.4678i	1.10486	−	1.11840i
$304$		0			0
$305$	6.81956	−	11.8118i	0.390487	−	0.676343i
$306$		0			0
$307$	2.82636	+	4.89540i	0.161309	+	0.279395i	0.935338	−	0.353754i	$-0.115095\pi$
$307$	2.82636	+	4.89540i	0.161309	+	0.279395i	−0.774029	+	0.633150i	$0.781762\pi$
$308$		0			0
$309$	7.72768	−	16.8390i	0.439613	−	0.957935i
$310$		0			0
$311$	−1.61574	−	9.16334i	−0.0916205	−	0.519605i	−0.995731	−	0.0923061i	$-0.970576\pi$
$311$	−1.61574	−	9.16334i	−0.0916205	−	0.519605i	0.904110	−	0.427299i	$-0.140535\pi$
$312$		0			0
$313$	−2.05976	−	1.72835i	−0.116425	−	0.0976920i	0.582717	−	0.812675i	$-0.301990\pi$
$313$	−2.05976	−	1.72835i	−0.116425	−	0.0976920i	−0.699141	+	0.714983i	$0.746434\pi$
$314$		0			0
$315$	−0.659318	−	1.74505i	−0.0371484	−	0.0983227i
$316$		0			0
$317$	26.2511	−	9.55461i	1.47441	−	0.536641i	0.525114	−	0.851032i	$-0.324023\pi$
$317$	26.2511	−	9.55461i	1.47441	−	0.536641i	0.949294	+	0.314391i	$0.101800\pi$
$318$		0			0
$319$	−0.126561	+	0.106197i	−0.00708607	+	0.00594592i
$320$		0			0
$321$	2.89948	−	1.37360i	0.161833	−	0.0766669i
$322$		0			0
$323$	−21.2633			−1.18312
$324$		0			0
$325$	6.76468			0.375237
$326$		0			0
$327$	22.7741	−	10.7890i	1.25941	−	0.596633i
$328$		0			0
$329$	0.0559856	−	0.0469775i	0.00308659	−	0.00258995i
$330$		0			0
$331$	0.794144	−	0.289045i	0.0436501	−	0.0158873i	−0.320103	−	0.947383i	$-0.603717\pi$
$331$	0.794144	−	0.289045i	0.0436501	−	0.0158873i	0.363753	+	0.931495i	$0.381495\pi$
$332$		0			0
$333$	−11.0954	−	1.81742i	−0.608026	−	0.0995942i
$334$		0			0
$335$	23.1244	+	19.4037i	1.26342	+	1.06014i
$336$		0			0
$337$	5.09088	+	28.8718i	0.277318	+	1.57275i	0.731501	+	0.681840i	$0.238820\pi$
$337$	5.09088	+	28.8718i	0.277318	+	1.57275i	−0.454183	+	0.890908i	$0.650069\pi$
$338$		0			0
$339$	9.66770	−	21.0663i	0.525077	−	1.14417i
$340$		0			0
$341$	−0.561457	−	0.972472i	−0.0304046	−	0.0526623i
$342$		0			0
$343$	1.07360	−	1.85953i	0.0579688	−	0.100405i
$344$		0			0
$345$	−28.8668	+	29.2205i	−1.55414	+	1.57318i
$346$		0			0
$347$	−18.9820	−	6.90888i	−1.01901	−	0.370888i	−0.222121	−	0.975019i	$-0.571298\pi$
$347$	−18.9820	−	6.90888i	−1.01901	−	0.370888i	−0.796885	+	0.604131i	$0.793520\pi$
$348$		0			0
$349$	1.66866	−	9.46343i	0.0893212	−	0.506566i	−0.907019	−	0.421090i	$-0.861648\pi$
$349$	1.66866	−	9.46343i	0.0893212	−	0.506566i	0.996340	−	0.0854761i	$-0.0272411\pi$
$350$		0			0
$351$	−3.08082	−	0.212924i	−0.164442	−	0.0113650i
$352$		0			0
$353$	−1.70637	+	9.67729i	−0.0908208	+	0.515070i	0.905127	+	0.425141i	$0.139775\pi$
$353$	−1.70637	+	9.67729i	−0.0908208	+	0.515070i	−0.995948	+	0.0899297i	$0.971336\pi$
$354$		0			0
$355$	−10.8693	−	3.95609i	−0.576881	−	0.209968i
$356$		0			0
$357$	−1.43269	−	0.374556i	−0.0758262	−	0.0198236i
$358$		0			0
$359$	5.94469	−	10.2965i	0.313749	−	0.543429i	−0.665422	−	0.746467i	$-0.731748\pi$
$359$	5.94469	−	10.2965i	0.313749	−	0.543429i	0.979171	+	0.203039i	$0.0650817\pi$
$360$		0			0
$361$	2.20067	+	3.81167i	0.115825	+	0.200614i
$362$		0			0
$363$	10.9740	+	15.4712i	0.575986	+	0.812027i
$364$		0			0
$365$	0.898122	+	5.09350i	0.0470098	+	0.266606i
$366$		0			0
$367$	27.7867	+	23.3158i	1.45045	+	1.21708i	0.932248	+	0.361821i	$0.117845\pi$
$367$	27.7867	+	23.3158i	1.45045	+	1.21708i	0.518207	+	0.855255i	$0.326600\pi$
$368$		0			0
$369$	10.3977	+	5.83551i	0.541285	+	0.303785i
$370$		0			0
$371$	−0.476340	+	0.173374i	−0.0247303	+	0.00900111i
$372$		0			0
$373$	10.8389	−	9.09489i	0.561215	−	0.470916i	−0.317502	−	0.948258i	$-0.602844\pi$
$373$	10.8389	−	9.09489i	0.561215	−	0.470916i	0.878718	+	0.477342i	$0.158400\pi$
$374$		0			0
$375$	−36.8066	−	25.4398i	−1.90069	−	1.31370i
$376$		0			0
$377$	0.444519			0.0228939
$378$		0			0
$379$	29.5237			1.51653			0.758265	−	0.651946i	$-0.226047\pi$
$379$	29.5237			1.51653			0.758265	+	0.651946i	$0.226047\pi$
$380$		0			0
$381$	2.61673	−	32.1634i	0.134059	−	1.64778i
$382$		0			0
$383$	−18.9404	+	15.8929i	−0.967811	+	0.812090i	−0.982206	−	0.187807i	$-0.939862\pi$
$383$	−18.9404	+	15.8929i	−0.967811	+	0.812090i	0.0143953	+	0.999896i	$0.495418\pi$
$384$		0			0
$385$	−0.129070	+	0.0469775i	−0.00657800	+	0.00239420i
$386$		0			0
$387$	−30.0886	+	5.68400i	−1.52949	+	0.288934i
$388$		0			0
$389$	11.1425	+	9.34969i	0.564948	+	0.474048i	0.879965	−	0.475038i	$-0.157566\pi$
$389$	11.1425	+	9.34969i	0.564948	+	0.474048i	−0.315017	+	0.949086i	$0.602010\pi$
$390$		0			0
$391$	5.66201	+	32.1108i	0.286340	+	1.62391i
$392$		0			0
$393$	11.8430	−	1.10882i	0.597400	−	0.0559324i
$394$		0			0
$395$	6.69270	+	11.5921i	0.336746	+	0.583262i
$396$		0			0
$397$	−2.10870	+	3.65238i	−0.105833	+	0.183308i	−0.914078	−	0.405538i	$-0.867084\pi$
$397$	−2.10870	+	3.65238i	−0.105833	+	0.183308i	0.808245	+	0.588846i	$0.200418\pi$
$398$		0			0
$399$	−0.269115	−	0.980438i	−0.0134726	−	0.0490833i
$400$		0			0
$401$	15.2143	+	5.53755i	0.759765	+	0.276532i	0.692709	−	0.721217i	$-0.256417\pi$
$401$	15.2143	+	5.53755i	0.759765	+	0.276532i	0.0670561	+	0.997749i	$0.478639\pi$
$402$		0			0
$403$	−0.524638	+	2.97537i	−0.0261341	+	0.148214i
$404$		0			0
$405$	28.4669	+	22.7288i	1.41453	+	1.12940i
$406$		0			0
$407$	−0.143753	+	0.815266i	−0.00712559	+	0.0404112i
$408$		0			0
$409$	−3.70550	−	1.34869i	−0.183225	−	0.0666885i	0.248778	−	0.968560i	$-0.419971\pi$
$409$	−3.70550	−	1.34869i	−0.183225	−	0.0666885i	−0.432003	+	0.901872i	$0.642193\pi$
$410$		0			0
$411$	6.87028	+	25.0297i	0.338886	+	1.23463i
$412$		0			0
$413$	0.558753	−	0.967788i	0.0274944	−	0.0476217i
$414$		0			0
$415$	16.7388	+	28.9924i	0.821674	+	1.42318i
$416$		0			0
$417$	−31.2183	+	2.92286i	−1.52877	+	0.143133i
$418$		0			0
$419$	5.98994	+	33.9707i	0.292628	+	1.65957i	0.676690	+	0.736268i	$0.263414\pi$
$419$	5.98994	+	33.9707i	0.292628	+	1.65957i	−0.384062	+	0.923307i	$0.625475\pi$
$420$		0			0
$421$	−8.80184	−	7.38562i	−0.428976	−	0.359953i	0.402589	−	0.915381i	$-0.368110\pi$
$421$	−8.80184	−	7.38562i	−0.428976	−	0.359953i	−0.831565	+	0.555427i	$0.812555\pi$
$422$		0			0
$423$	−0.471748	+	1.34692i	−0.0229372	+	0.0654895i
$424$		0			0
$425$	−59.5234	+	21.6647i	−2.88731	+	1.05089i
$426$		0			0
$427$	0.396579	−	0.332769i	0.0191918	−	0.0161038i
$428$		0			0
$429$	−0.0184382	+	0.226632i	−0.000890207	+	0.0109419i
$430$		0			0
$431$	−24.6371			−1.18673			−0.593364	−	0.804934i	$-0.702201\pi$
$431$	−24.6371			−1.18673			−0.593364	+	0.804934i	$0.702201\pi$
$432$		0			0
$433$	12.8011			0.615181			0.307590	−	0.951519i	$-0.400477\pi$
$433$	12.8011			0.615181			0.307590	+	0.951519i	$0.400477\pi$
$434$		0			0
$435$	−4.31343	−	2.98133i	−0.206813	−	0.142944i
$436$		0			0
$437$	−17.1489	+	14.3897i	−0.820345	+	0.688351i
$438$		0			0
$439$	−34.1541	+	12.4311i	−1.63009	+	0.593303i	−0.985266	−	0.171029i	$-0.945291\pi$
$439$	−34.1541	+	12.4311i	−1.63009	+	0.593303i	−0.644822	+	0.764333i	$0.723068\pi$
$440$		0			0
$441$	0.254818	+	20.9276i	0.0121342	+	0.996554i
$442$		0			0
$443$	29.5753	+	24.8166i	1.40516	+	1.17907i	0.958752	+	0.284245i	$0.0917428\pi$
$443$	29.5753	+	24.8166i	1.40516	+	1.17907i	0.446412	+	0.894828i	$0.352702\pi$
$444$		0			0
$445$	3.48444	+	19.7612i	0.165178	+	0.936772i
$446$		0			0
$447$	15.0550	+	21.2246i	0.712077	+	1.00389i
$448$		0			0
$449$	7.76357	+	13.4469i	0.366385	+	0.634598i	0.988997	−	0.147932i	$-0.0472618\pi$
$449$	7.76357	+	13.4469i	0.366385	+	0.634598i	−0.622612	+	0.782531i	$0.713928\pi$
$450$		0			0
$451$	0.438957	−	0.760296i	0.0206697	−	0.0358010i
$452$		0			0
$453$	−9.45569	−	2.47205i	−0.444267	−	0.116147i
$454$		0			0
$455$	0.347270	+	0.126396i	0.0162803	+	0.00592554i
$456$		0			0
$457$	−6.26933	+	35.5551i	−0.293267	+	1.66320i	0.380897	+	0.924618i	$0.375615\pi$
$457$	−6.26933	+	35.5551i	−0.293267	+	1.66320i	−0.674164	+	0.738582i	$0.735496\pi$
$458$		0			0
$459$	27.7905	−	7.99316i	1.29715	−	0.373089i
$460$		0			0
$461$	1.72646	−	9.79122i	0.0804091	−	0.456023i	−0.917844	−	0.396941i	$-0.870072\pi$
$461$	1.72646	−	9.79122i	0.0804091	−	0.456023i	0.998253	−	0.0590816i	$-0.0188172\pi$
$462$		0			0
$463$	−18.0852	−	6.58248i	−0.840492	−	0.305914i	−0.114334	−	0.993442i	$-0.536473\pi$
$463$	−18.0852	−	6.58248i	−0.840492	−	0.305914i	−0.726158	+	0.687528i	$0.758696\pi$
$464$		0			0
$465$	25.0463	−	25.3531i	1.16149	−	1.17572i
$466$		0			0
$467$	15.7918	−	27.3521i	0.730756	−	1.26571i	−0.225805	−	0.974173i	$-0.572501\pi$
$467$	15.7918	−	27.3521i	0.730756	−	1.26571i	0.956561	−	0.291534i	$-0.0941655\pi$
$468$		0			0
$469$	0.572895	+	0.992284i	0.0264539	+	0.0458194i
$470$		0			0
$471$	−5.23378	+	11.4046i	−0.241160	+	0.525498i
$472$		0			0
$473$	0.391508	+	2.22035i	0.0180015	+	0.102092i
$474$		0			0
$475$	−33.3149	−	27.9545i	−1.52859	−	1.28264i
$476$		0			0
$477$	6.26994	−	7.65972i	0.287081	−	0.350714i
$478$		0			0
$479$	10.6027	−	3.85905i	0.484448	−	0.176325i	−0.0882381	−	0.996099i	$-0.528124\pi$
$479$	10.6027	−	3.85905i	0.484448	−	0.176325i	0.572686	+	0.819775i	$0.305901\pi$
$480$		0			0
$481$	1.70626	−	1.43172i	0.0777988	−	0.0652809i
$482$		0			0
$483$	−1.40895	+	0.667478i	−0.0641096	+	0.0303713i
$484$		0			0
$485$	−22.8849			−1.03915
$486$		0			0
$487$	29.3219			1.32870			0.664352	−	0.747420i	$-0.268708\pi$
$487$	29.3219			1.32870			0.664352	+	0.747420i	$0.268708\pi$
$488$		0			0
$489$	22.0828	−	10.4615i	0.998620	−	0.473087i
$490$		0			0
$491$	7.76464	−	6.51531i	0.350413	−	0.294032i	−0.450543	−	0.892755i	$-0.648769\pi$
$491$	7.76464	−	6.51531i	0.350413	−	0.294032i	0.800956	+	0.598723i	$0.204325\pi$
$492$		0			0
$493$	−3.91138	+	1.42363i	−0.176160	+	0.0641169i
$494$		0			0
$495$	1.69891	−	2.07549i	0.0763604	−	0.0932862i
$496$		0			0
$497$	−0.336324	−	0.282209i	−0.0150862	−	0.0126588i
$498$		0			0
$499$	−3.87086	−	21.9527i	−0.173284	−	0.982740i	−0.940106	−	0.340881i	$-0.889275\pi$
$499$	−3.87086	−	21.9527i	−0.173284	−	0.982740i	0.766823	−	0.641859i	$-0.221836\pi$
$500$		0			0
$501$	−9.98593	+	21.7598i	−0.446139	+	0.972155i
$502$		0			0
$503$	−7.31535	−	12.6706i	−0.326175	−	0.564952i	0.655574	−	0.755131i	$-0.272427\pi$
$503$	−7.31535	−	12.6706i	−0.326175	−	0.564952i	−0.981750	+	0.190179i	$0.939093\pi$
$504$		0			0
$505$	31.9743	−	55.3811i	1.42284	−	2.46443i
$506$		0			0
$507$	−15.3945	+	15.5831i	−0.683694	+	0.692069i
$508$		0			0
$509$	−6.70321	−	2.43977i	−0.297115	−	0.108141i	0.189162	−	0.981946i	$-0.439423\pi$
$509$	−6.70321	−	2.43977i	−0.297115	−	0.108141i	−0.486276	+	0.873805i	$0.661645\pi$
$510$		0			0
$511$	−0.0340898	+	0.193333i	−0.00150804	+	0.00855254i
$512$		0			0
$513$	14.2926	+	13.7799i	0.631035	+	0.608396i
$514$		0			0
$515$	7.51818	−	42.6377i	0.331291	−	1.87884i
$516$		0			0
$517$	0.0987433	+	0.0359396i	0.00434273	+	0.00158062i
$518$		0			0
$519$	6.58438	+	1.72139i	0.289022	+	0.0755605i
$520$		0			0
$521$	4.12053	−	7.13696i	0.180524	−	0.312676i	−0.761535	−	0.648123i	$-0.775554\pi$
$521$	4.12053	−	7.13696i	0.180524	−	0.312676i	0.942059	+	0.335447i	$0.108887\pi$
$522$		0			0
$523$	−11.2705	−	19.5211i	−0.492826	−	0.853599i	0.507140	−	0.861864i	$-0.330703\pi$
$523$	−11.2705	−	19.5211i	−0.492826	−	0.853599i	−0.999966	+	0.00826425i	$0.997369\pi$
$524$		0			0
$525$	−1.75230	−	2.47040i	−0.0764766	−	0.107817i
$526$		0			0
$527$	−4.91264	−	27.8610i	−0.213998	−	1.21364i
$528$		0			0
$529$	8.67807	+	7.28176i	0.377307	+	0.316598i
$530$		0			0
$531$	0.265689	+	21.8204i	0.0115299	+	0.946924i
$532$		0			0
$533$	−2.21963	+	0.807881i	−0.0961430	+	0.0349932i
$534$		0			0
$535$	5.74337	−	4.81926i	0.248308	−	0.208355i
$536$		0			0
$537$	−4.05254	−	2.80101i	−0.174880	−	0.120873i
$538$		0			0
$539$	1.54101			0.0663762
$540$		0			0
$541$	−31.4683			−1.35293			−0.676464	−	0.736476i	$-0.736488\pi$
$541$	−31.4683			−1.35293			−0.676464	+	0.736476i	$0.736488\pi$
$542$		0			0
$543$	1.81540	−	22.3139i	0.0779062	−	0.957579i
$544$		0			0
$545$	45.1115	−	37.8531i	1.93237	−	1.62145i
$546$		0			0
$547$	28.3635	−	10.3235i	1.21274	−	0.441400i	0.345085	−	0.938571i	$-0.387850\pi$
$547$	28.3635	−	10.3235i	1.21274	−	0.441400i	0.867652	+	0.497171i	$0.165628\pi$
$548$		0			0
$549$	−3.34167	+	9.54102i	−0.142619	+	0.407201i
$550$		0			0
$551$	−2.18918	−	1.83694i	−0.0932623	−	0.0782563i
$552$		0			0
$553$	0.0882249	+	0.500348i	0.00375170	+	0.0212770i
$554$		0			0
$555$	−26.1592	+	2.44919i	−1.11040	+	0.103963i
$556$		0			0
$557$	−16.4210	−	28.4420i	−0.695779	−	1.20512i	−0.969917	−	0.243434i	$-0.921726\pi$
$557$	−16.4210	−	28.4420i	−0.695779	−	1.20512i	0.274138	−	0.961690i	$-0.411607\pi$
$558$		0			0
$559$	3.03308	−	5.25345i	0.128286	−	0.222197i
$560$		0			0
$561$	−0.563578	−	2.05322i	−0.0237943	−	0.0866871i
$562$		0			0
$563$	17.5885	+	6.40168i	0.741266	+	0.269799i	0.684926	−	0.728613i	$-0.259835\pi$
$563$	17.5885	+	6.40168i	0.741266	+	0.269799i	0.0563401	+	0.998412i	$0.482057\pi$
$564$		0			0
$565$	9.40560	−	53.3418i	0.395697	−	2.24411i
$566$		0			0
$567$	0.720286	+	1.18024i	0.0302492	+	0.0495654i
$568$		0			0
$569$	−1.38771	+	7.87008i	−0.0581757	+	0.329931i	−0.999981	−	0.00622922i	$-0.998017\pi$
$569$	−1.38771	+	7.87008i	−0.0581757	+	0.329931i	0.941805	+	0.336160i	$0.109128\pi$
$570$		0			0
$571$	−26.7013	−	9.71847i	−1.11741	−	0.406705i	−0.283706	−	0.958911i	$-0.591564\pi$
$571$	−26.7013	−	9.71847i	−1.11741	−	0.406705i	−0.833708	+	0.552206i	$0.813786\pi$
$572$		0			0
$573$	9.23471	+	33.6438i	0.385786	+	1.40549i
$574$		0			0
$575$	−33.3446	+	57.7545i	−1.39057	+	2.40853i
$576$		0			0
$577$	−23.5780	−	40.8383i	−0.981564	−	1.70012i	−0.656307	−	0.754494i	$-0.727883\pi$
$577$	−23.5780	−	40.8383i	−0.981564	−	1.70012i	−0.325257	−	0.945626i	$-0.605451\pi$
$578$		0			0
$579$	16.5840	−	1.55270i	0.689207	−	0.0645280i
$580$		0			0
$581$	0.220655	+	1.25139i	0.00915429	+	0.0519166i
$582$		0			0
$583$	−0.558322	−	0.468487i	−0.0231233	−	0.0194028i
$584$		0			0
$585$	−7.09109	+	1.33957i	−0.293180	+	0.0553843i
$586$		0			0
$587$	−16.5971	+	6.04086i	−0.685036	+	0.249333i	−0.661008	−	0.750378i	$-0.729871\pi$
$587$	−16.5971	+	6.04086i	−0.685036	+	0.249333i	−0.0240279	+	0.999711i	$0.507649\pi$
$588$		0			0
$589$	14.8793	−	12.4852i	0.613090	−	0.514443i
$590$		0			0
$591$	1.06048	−	13.0348i	0.0436224	−	0.536182i
$592$		0			0
$593$	4.89941			0.201195			0.100597	−	0.994927i	$-0.467925\pi$
$593$	4.89941			0.201195			0.100597	+	0.994927i	$0.467925\pi$
$594$		0			0
$595$	−3.46048			−0.141866
$596$		0			0
$597$	17.2995	+	11.9570i	0.708021	+	0.489366i
$598$		0			0
$599$	−13.8351	+	11.6090i	−0.565288	+	0.474333i	−0.880078	−	0.474828i	$-0.842510\pi$
$599$	−13.8351	+	11.6090i	−0.565288	+	0.474333i	0.314791	+	0.949161i	$0.398066\pi$
$600$		0			0
$601$	−3.04117	+	1.10690i	−0.124052	+	0.0451513i	−0.403300	−	0.915068i	$-0.632137\pi$
$601$	−3.04117	+	1.10690i	−0.124052	+	0.0451513i	0.279248	+	0.960219i	$0.409915\pi$
$602$		0			0
$603$	−19.5115	−	10.9504i	−0.794571	−	0.445936i
$604$		0			0
$605$	33.9549	+	28.4916i	1.38046	+	1.15835i
$606$		0			0
$607$	−4.71790	−	26.7566i	−0.191494	−	1.08602i	−0.917324	−	0.398141i	$-0.869655\pi$
$607$	−4.71790	−	26.7566i	−0.191494	−	1.08602i	0.725830	−	0.687874i	$-0.241456\pi$
$608$		0			0
$609$	−0.115147	−	0.162334i	−0.00466597	−	0.00657810i
$610$		0			0
$611$	−0.141363	−	0.244848i	−0.00571893	−	0.00990547i
$612$		0			0
$613$	−13.6622	+	23.6636i	−0.551810	+	0.955763i	0.446334	+	0.894866i	$0.352729\pi$
$613$	−13.6622	+	23.6636i	−0.551810	+	0.955763i	−0.998144	+	0.0608964i	$0.980604\pi$
$614$		0			0
$615$	26.9568	+	7.04744i	1.08700	+	0.284180i
$616$		0			0
$617$	−25.0923	−	9.13284i	−1.01018	−	0.367674i	−0.216676	−	0.976244i	$-0.569522\pi$
$617$	−25.0923	−	9.13284i	−1.01018	−	0.367674i	−0.793501	+	0.608569i	$0.791744\pi$
$618$		0			0
$619$	−6.92886	+	39.2955i	−0.278494	+	1.57942i	0.449145	+	0.893459i	$0.351729\pi$
$619$	−6.92886	+	39.2955i	−0.278494	+	1.57942i	−0.727639	+	0.685960i	$0.759382\pi$
$620$		0			0
$621$	17.0039	−	25.2534i	0.682343	−	1.01338i
$622$		0			0
$623$	−0.132258	+	0.750073i	−0.00529881	+	0.0300510i
$624$		0			0
$625$	−44.7712	−	16.2954i	−1.79085	−	0.651816i
$626$		0			0
$627$	1.02735	−	1.03993i	0.0410283	−	0.0415309i
$628$		0			0
$629$	−10.4284	+	18.0624i	−0.415806	+	0.720197i
$630$		0			0
$631$	−4.36875	−	7.56690i	−0.173917	−	0.301234i	0.765869	−	0.642997i	$-0.222309\pi$
$631$	−4.36875	−	7.56690i	−0.173917	−	0.301234i	−0.939786	+	0.341763i	$0.888976\pi$
$632$		0			0
$633$	−5.21869	+	11.3718i	−0.207424	+	0.451987i
$634$		0			0
$635$	−13.0946	−	74.2629i	−0.519642	−	2.94703i
$636$		0			0
$637$	−3.17617	−	2.66512i	−0.125845	−	0.105596i
$638$		0			0
$639$	8.46057	+	1.38583i	0.334695	+	0.0548228i
$640$		0			0
$641$	−17.0222	+	6.19556i	−0.672335	+	0.244710i	−0.655553	−	0.755149i	$-0.727564\pi$
$641$	−17.0222	+	6.19556i	−0.672335	+	0.244710i	−0.0167821	+	0.999859i	$0.505342\pi$
$642$		0			0
$643$	24.5762	−	20.6219i	0.969191	−	0.813247i	−0.0132331	−	0.999912i	$-0.504212\pi$
$643$	24.5762	−	20.6219i	0.969191	−	0.813247i	0.982424	+	0.186665i	$0.0597679\pi$
$644$		0			0
$645$	−64.6659	+	30.6349i	−2.54622	+	1.20625i
$646$		0			0
$647$	11.1390			0.437918			0.218959	−	0.975734i	$-0.429734\pi$
$647$	11.1390			0.437918			0.218959	+	0.975734i	$0.429734\pi$
$648$		0			0
$649$	1.60675			0.0630705
$650$		0			0
$651$	1.22248	−	0.579137i	0.0479127	−	0.0226982i
$652$		0			0
$653$	1.15447	−	0.968718i	0.0451780	−	0.0379089i	−0.619919	−	0.784666i	$-0.712835\pi$
$653$	1.15447	−	0.968718i	0.0451780	−	0.0379089i	0.665097	+	0.746757i	$0.268390\pi$
$654$		0			0
$655$	26.1197	−	9.50681i	1.02058	−	0.371462i
$656$		0			0
$657$	−1.35491	−	3.58611i	−0.0528600	−	0.139908i
$658$		0			0
$659$	6.06158	+	5.08627i	0.236126	+	0.198133i	0.753171	−	0.657825i	$-0.228523\pi$
$659$	6.06158	+	5.08627i	0.236126	+	0.198133i	−0.517045	+	0.855958i	$0.672968\pi$
$660$		0			0
$661$	−5.26138	−	29.8388i	−0.204644	−	1.16059i	−0.897999	−	0.439998i	$-0.854979\pi$
$661$	−5.26138	−	29.8388i	−0.204644	−	1.16059i	0.693355	−	0.720597i	$-0.256132\pi$
$662$		0			0
$663$	−2.38938	+	5.20657i	−0.0927959	+	0.202206i
$664$		0			0
$665$	−1.18793	−	2.05755i	−0.0460658	−	0.0797883i
$666$		0			0
$667$	−2.19113	+	3.79515i	−0.0848409	+	0.146949i
$668$		0			0
$669$	31.0707	−	31.4513i	1.20126	−	1.21598i
$670$		0			0
$671$	0.699457	+	0.254581i	0.0270022	+	0.00982801i
$672$		0			0
$673$	−3.85949	+	21.8883i	−0.148772	+	0.843731i	0.815488	+	0.578774i	$0.196469\pi$
$673$	−3.85949	+	21.8883i	−0.148772	+	0.843731i	−0.964260	+	0.264956i	$0.914642\pi$
$674$		0			0
$675$	54.0502	+	24.0122i	2.08039	+	0.924232i
$676$		0			0
$677$	7.00672	−	39.7371i	0.269290	−	1.52722i	−0.487245	−	0.873266i	$-0.661998\pi$
$677$	7.00672	−	39.7371i	0.269290	−	1.52722i	0.756535	−	0.653954i	$-0.226891\pi$
$678$		0			0
$679$	−0.816250	−	0.297091i	−0.0313248	−	0.0114013i
$680$		0			0
$681$	24.0623	+	6.29073i	0.922070	+	0.241061i
$682$		0			0
$683$	−12.5504	+	21.7380i	−0.480229	+	0.831780i	−0.999743	−	0.0226815i	$-0.992780\pi$
$683$	−12.5504	+	21.7380i	−0.480229	+	0.831780i	0.519514	+	0.854462i	$0.326113\pi$
$684$		0			0
$685$	30.3267	+	52.5274i	1.15872	+	2.00697i
$686$		0			0
$687$	−4.06754	−	5.73443i	−0.155186	−	0.218782i
$688$		0			0
$689$	0.340521	+	1.93119i	0.0129728	+	0.0735725i
$690$		0			0
$691$	2.21137	+	1.85556i	0.0841245	+	0.0705889i	0.683880	−	0.729594i	$-0.260291\pi$
$691$	2.21137	+	1.85556i	0.0841245	+	0.0705889i	−0.599756	+	0.800183i	$0.704736\pi$
$692$		0			0
$693$	0.0875402	−	0.0519726i	0.00332538	−	0.00197428i
$694$		0			0
$695$	−68.8521	+	25.0601i	−2.61171	+	0.950584i
$696$		0			0
$697$	16.9435	−	14.2173i	0.641782	−	0.538519i
$698$		0			0
$699$	24.1919	+	16.7208i	0.915021	+	0.632438i
$700$		0			0
$701$	−24.5608			−0.927648			−0.463824	−	0.885927i	$-0.653523\pi$
$701$	−24.5608			−0.927648			−0.463824	+	0.885927i	$0.653523\pi$
$702$		0			0
$703$	−14.3195			−0.540072
$704$		0			0
$705$	−0.270433	+	3.32400i	−0.0101851	+	0.125189i
$706$		0			0
$707$	1.85941	−	1.56023i	0.0699302	−	0.0586784i
$708$		0			0
$709$	20.9978	−	7.64257i	0.788588	−	0.287023i	0.0838392	−	0.996479i	$-0.473282\pi$
$709$	20.9978	−	7.64257i	0.788588	−	0.287023i	0.704749	+	0.709457i	$0.251060\pi$
$710$		0			0
$711$	−6.46931	−	7.52190i	−0.242618	−	0.282093i
$712$		0			0
$713$	−22.8167	−	19.1454i	−0.854490	−	0.717003i
$714$		0			0
$715$	0.0922680	+	0.523278i	0.00345063	+	0.0195695i
$716$		0			0
$717$	−36.7805	+	3.44362i	−1.37359	+	0.128605i
$718$		0			0
$719$	−18.3086	−	31.7114i	−0.682796	−	1.18264i	−0.974124	−	0.226014i	$-0.927430\pi$
$719$	−18.3086	−	31.7114i	−0.682796	−	1.18264i	0.291328	−	0.956623i	$-0.405903\pi$
$720$		0			0
$721$	0.821678	−	1.42319i	0.0306009	−	0.0530023i
$722$		0			0
$723$	−4.93043	−	17.9625i	−0.183365	−	0.668033i
$724$		0			0
$725$	−7.99992	−	2.91173i	−0.297110	−	0.108139i
$726$		0			0
$727$	−2.38849	+	13.5458i	−0.0885842	+	0.502386i	0.907941	+	0.419097i	$0.137653\pi$
$727$	−2.38849	+	13.5458i	−0.0885842	+	0.502386i	−0.996525	+	0.0832885i	$0.973458\pi$
$728$		0			0
$729$	−23.8601	−	12.6371i	−0.883707	−	0.468040i
$730$		0			0
$731$	−9.86367	+	55.9396i	−0.364821	+	2.06900i
$732$		0			0
$733$	−30.6892	−	11.1699i	−1.13353	−	0.412571i	−0.293957	−	0.955819i	$-0.594972\pi$
$733$	−30.6892	−	11.1699i	−1.13353	−	0.412571i	−0.839573	+	0.543247i	$0.817195\pi$
$734$		0			0
$735$	12.9456	+	47.1634i	0.477507	+	1.73965i
$736$		0			0
$737$	−0.823710	+	1.42671i	−0.0303418	+	0.0525535i
$738$		0			0
$739$	−14.0540	−	24.3423i	−0.516986	−	0.895445i	−0.999805	−	0.0197257i	$-0.993721\pi$
$739$	−14.0540	−	24.3423i	−0.516986	−	0.895445i	0.482820	−	0.875720i	$-0.339613\pi$
$740$		0			0
$741$	−3.91598	+	0.366639i	−0.143857	+	0.0134688i
$742$		0			0
$743$	2.01338	+	11.4184i	0.0738636	+	0.418901i	0.999209	+	0.0397752i	$0.0126642\pi$
$743$	2.01338	+	11.4184i	0.0738636	+	0.418901i	−0.925345	+	0.379126i	$0.876225\pi$
$744$		0			0
$745$	46.5820	+	39.0870i	1.70663	+	1.43204i
$746$		0			0
$747$	−16.1801	−	18.8126i	−0.591997	−	0.688318i
$748$		0			0
$749$	0.267417	−	0.0973316i	0.00977119	−	0.00355642i
$750$		0			0
$751$	31.0515	−	26.0553i	1.13309	−	0.950772i	0.133896	−	0.990995i	$-0.457251\pi$
$751$	31.0515	−	26.0553i	1.13309	−	0.950772i	0.999191	+	0.0402230i	$0.0128068\pi$
$752$		0			0
$753$	−0.586556	+	7.20962i	−0.0213753	+	0.262733i
$754$		0			0
$755$	−22.8390			−0.831194
$756$		0			0
$757$	51.1841			1.86032			0.930158	−	0.367159i	$-0.119669\pi$
$757$	51.1841			1.86032			0.930158	+	0.367159i	$0.119669\pi$
$758$		0			0
$759$	−1.84402	−	1.27454i	−0.0669338	−	0.0462629i
$760$		0			0
$761$	3.01606	−	2.53078i	0.109332	−	0.0917406i	−0.586483	−	0.809962i	$-0.699488\pi$
$761$	3.01606	−	2.53078i	0.109332	−	0.0917406i	0.695815	+	0.718221i	$0.255043\pi$
$762$		0			0
$763$	2.10043	−	0.764495i	0.0760408	−	0.0276766i
$764$		0			0
$765$	58.1053	−	34.4971i	2.10080	−	1.24725i
$766$		0			0
$767$	−3.31166	−	2.77882i	−0.119577	−	0.100337i
$768$		0			0
$769$	−7.45807	−	42.2968i	−0.268945	−	1.52526i	−0.757562	−	0.652763i	$-0.773610\pi$
$769$	−7.45807	−	42.2968i	−0.268945	−	1.52526i	0.488617	−	0.872498i	$-0.337501\pi$
$770$		0			0
$771$	−16.3773	−	23.0887i	−0.589812	−	0.831519i
$772$		0			0
$773$	10.6680	+	18.4775i	0.383702	+	0.664591i	0.991588	−	0.129433i	$-0.0413157\pi$
$773$	10.6680	+	18.4775i	0.383702	+	0.664591i	−0.607886	+	0.794024i	$0.707982\pi$
$774$		0			0
$775$	28.9314	−	50.1107i	1.03925	−	1.80003i
$776$		0			0
$777$	−0.964835	−	0.252241i	−0.0346133	−	0.00904911i
$778$		0			0
$779$	14.2698	+	5.19380i	0.511270	+	0.186087i
$780$		0			0
$781$	0.109616	−	0.621662i	0.00392236	−	0.0222448i
$782$		0			0
$783$	3.55173	+	1.57789i	0.126928	+	0.0563890i
$784$		0			0
$785$	−5.09189	+	28.8776i	−0.181737	+	1.03068i
$786$		0			0
$787$	−6.97310	−	2.53800i	−0.248564	−	0.0904699i	0.214734	−	0.976673i	$-0.431112\pi$
$787$	−6.97310	−	2.53800i	−0.248564	−	0.0904699i	−0.463298	+	0.886203i	$0.653334\pi$
$788$		0			0
$789$	3.26390	−	3.30388i	0.116198	−	0.117621i
$790$		0			0
$791$	1.02796	−	1.78048i	0.0365500	−	0.0633065i
$792$		0			0
$793$	−1.00136	−	1.73440i	−0.0355592	−	0.0615903i
$794$		0			0
$795$	9.64796	−	21.0233i	0.342178	−	0.745620i
$796$		0			0
$797$	2.06082	+	11.6875i	0.0729980	+	0.413992i	0.999307	+	0.0372272i	$0.0118525\pi$
$797$	2.06082	+	11.6875i	0.0729980	+	0.413992i	−0.926309	+	0.376765i	$0.877036\pi$
$798$		0			0
$799$	2.02803	+	1.70172i	0.0717464	+	0.0602024i
$800$		0			0
$801$	−5.25663	−	13.9130i	−0.185734	−	0.491593i
$802$		0			0
$803$	−0.265240	+	0.0965395i	−0.00936012	+	0.00340681i
$804$		0			0
$805$	−2.79090	+	2.34184i	−0.0983662	+	0.0825391i
$806$		0			0
$807$	−34.9856	+	16.5741i	−1.23155	+	0.583436i
$808$		0			0
$809$	−46.8455			−1.64700			−0.823500	−	0.567316i	$-0.807982\pi$
$809$	−46.8455			−1.64700			−0.823500	+	0.567316i	$0.807982\pi$
$810$		0			0
$811$	1.66252			0.0583791			0.0291895	−	0.999574i	$-0.490707\pi$
$811$	1.66252			0.0583791			0.0291895	+	0.999574i	$0.490707\pi$
$812$		0			0
$813$	39.8856	−	18.8954i	1.39885	−	0.662691i
$814$		0			0
$815$	43.7423	−	36.7042i	1.53223	−	1.28569i
$816$		0			0
$817$	−36.6469	+	13.3384i	−1.28211	+	0.466651i
$818$		0			0
$819$	−0.270313	−	0.0442770i	−0.00944550	−	0.00154716i
$820$		0			0
$821$	6.93192	+	5.81657i	0.241926	+	0.203000i	0.755686	−	0.654934i	$-0.227304\pi$
$821$	6.93192	+	5.81657i	0.241926	+	0.203000i	−0.513761	+	0.857934i	$0.671748\pi$
$822$		0			0
$823$	−2.04514	−	11.5986i	−0.0712892	−	0.404301i	−0.999481	−	0.0322000i	$-0.989749\pi$
$823$	−2.04514	−	11.5986i	−0.0712892	−	0.404301i	0.928192	−	0.372101i	$-0.121362\pi$
$824$		0			0
$825$	1.81634	−	3.95789i	0.0632369	−	0.137796i
$826$		0			0
$827$	16.9625	+	29.3798i	0.589843	+	1.02164i	0.994253	+	0.107060i	$0.0341436\pi$
$827$	16.9625	+	29.3798i	0.589843	+	1.02164i	−0.404410	+	0.914578i	$0.632523\pi$
$828$		0			0
$829$	−7.37389	+	12.7719i	−0.256106	+	0.443588i	−0.965195	−	0.261530i	$-0.915773\pi$
$829$	−7.37389	+	12.7719i	−0.256106	+	0.443588i	0.709090	+	0.705118i	$0.249106\pi$
$830$		0			0
$831$	−3.12475	+	3.16303i	−0.108396	+	0.109724i
$832$		0			0
$833$	36.4830	+	13.2787i	1.26406	+	0.460080i
$834$		0			0
$835$	−9.71521	+	55.0977i	−0.336209	+	1.90673i
$836$		0			0
$837$	−14.7534	+	21.9111i	−0.509953	+	0.757359i
$838$		0			0
$839$	4.77160	−	27.0611i	0.164734	−	0.934252i	−0.784605	−	0.619996i	$-0.787134\pi$
$839$	4.77160	−	27.0611i	0.164734	−	0.934252i	0.949338	−	0.314256i	$-0.101755\pi$
$840$		0			0
$841$	26.7254	+	9.72725i	0.921565	+	0.335422i
$842$		0			0
$843$	−35.5195	−	9.28603i	−1.22336	−	0.319828i
$844$		0			0
$845$	−25.5939	+	44.3300i	−0.880458	+	1.52500i
$846$		0			0
$847$	0.841217	+	1.45703i	0.0289046	+	0.0500642i
$848$		0			0
$849$	−19.6741	−	27.7366i	−0.675214	−	0.951919i
$850$		0			0
$851$	3.81303	+	21.6247i	0.130709	+	0.741287i
$852$		0			0
$853$	4.59134	+	3.85259i	0.157205	+	0.131910i	0.717997	−	0.696046i	$-0.245059\pi$
$853$	4.59134	+	3.85259i	0.157205	+	0.131910i	−0.560793	+	0.827956i	$0.689503\pi$
$854$		0			0
$855$	40.4581	+	22.7062i	1.38364	+	0.776537i
$856$		0			0
$857$	−17.8493	+	6.49663i	−0.609722	+	0.221921i	−0.628381	−	0.777905i	$-0.716282\pi$
$857$	−17.8493	+	6.49663i	−0.609722	+	0.221921i	0.0186598	+	0.999826i	$0.494060\pi$
$858$		0			0
$859$	−13.8575	+	11.6278i	−0.472812	+	0.396737i	−0.847819	−	0.530285i	$-0.822085\pi$
$859$	−13.8575	+	11.6278i	−0.472812	+	0.396737i	0.375007	+	0.927022i	$0.377640\pi$
$860$		0			0
$861$	0.869997	+	0.601318i	0.0296494	+	0.0204929i
$862$		0			0
$863$	8.17235			0.278190			0.139095	−	0.990279i	$-0.455581\pi$
$863$	8.17235			0.278190			0.139095	+	0.990279i	$0.455581\pi$
$864$		0			0
$865$	15.9037			0.540741
$866$		0			0
$867$	1.96216	−	24.1177i	0.0666384	−	0.819081i
$868$		0			0
$869$	−0.559595	+	0.469556i	−0.0189830	+	0.0159286i
$870$		0			0
$871$	4.16518	−	1.51600i	0.141132	−	0.0513678i
$872$		0			0
$873$	16.6674	−	3.14862i	0.564107	−	0.106565i
$874$		0			0
$875$	−3.04013	−	2.55097i	−0.102775	−	0.0862385i
$876$		0			0
$877$	3.12176	+	17.7044i	0.105414	+	0.597835i	0.991054	+	0.133462i	$0.0426093\pi$
$877$	3.12176	+	17.7044i	0.105414	+	0.597835i	−0.885639	+	0.464373i	$0.846280\pi$
$878$		0			0
$879$	37.0355	−	3.46750i	1.24918	−	0.116956i
$880$		0			0
$881$	−13.9064	−	24.0865i	−0.468518	−	0.811496i	0.530835	−	0.847475i	$-0.321878\pi$
$881$	−13.9064	−	24.0865i	−0.468518	−	0.811496i	−0.999353	+	0.0359788i	$0.988545\pi$
$882$		0			0
$883$	−5.86589	+	10.1600i	−0.197403	+	0.341912i	−0.947686	−	0.319205i	$-0.896584\pi$
$883$	−5.86589	+	10.1600i	−0.197403	+	0.341912i	0.750283	+	0.661117i	$0.229917\pi$
$884$		0			0
$885$	13.4979	+	49.1754i	0.453727	+	1.65301i
$886$		0			0
$887$	−18.0700	−	6.57694i	−0.606731	−	0.220832i	0.0203412	−	0.999793i	$-0.493525\pi$
$887$	−18.0700	−	6.57694i	−0.606731	−	0.220832i	−0.627072	+	0.778961i	$0.715747\pi$
$888$		0			0
$889$	0.497027	−	2.81878i	0.0166698	−	0.0945389i
$890$		0			0
$891$	−0.951788	+	1.74536i	−0.0318861	+	0.0584716i
$892$		0			0
$893$	−0.315626	+	1.79001i	−0.0105620	+	0.0599003i
$894$		0			0
$895$	−10.8177	−	3.93733i	−0.361597	−	0.131610i
$896$		0			0
$897$	1.59644	+	5.81611i	0.0533034	+	0.194194i
$898$		0			0
$899$	1.90113	−	3.29286i	0.0634063	−	0.109823i
$900$		0			0
$901$	−9.18118	−	15.9023i	−0.305869	−	0.529781i
$902$		0			0
$903$	−2.70419	+	0.253183i	−0.0899896	+	0.00842541i
$904$		0			0
$905$	−9.08456	−	51.5211i	−0.301981	−	1.71262i
$906$		0			0
$907$	−0.795661	−	0.667639i	−0.0264195	−	0.0221686i	0.629482	−	0.777015i	$-0.283267\pi$
$907$	−0.795661	−	0.667639i	−0.0264195	−	0.0221686i	−0.655902	+	0.754846i	$0.727711\pi$
$908$		0			0
$909$	−15.6678	+	44.7342i	−0.519667	+	1.48374i
$910$		0			0
$911$	8.97004	−	3.26483i	0.297191	−	0.108169i	−0.189121	−	0.981954i	$-0.560564\pi$
$911$	8.97004	−	3.26483i	0.297191	−	0.108169i	0.486312	+	0.873785i	$0.338342\pi$
$912$		0			0
$913$	−1.39957	+	1.17438i	−0.0463191	+	0.0388664i
$914$		0			0
$915$	−1.91563	+	23.5459i	−0.0633288	+	0.778402i
$916$		0			0
$917$	1.05505			0.0348408
$918$		0			0
$919$	−2.76185			−0.0911049			−0.0455525	−	0.998962i	$-0.514505\pi$
$919$	−2.76185			−0.0911049			−0.0455525	+	0.998962i	$0.514505\pi$
$920$		0			0
$921$	−8.05420	−	5.56685i	−0.265395	−	0.183434i
$922$		0			0
$923$	−1.30107	+	1.09173i	−0.0428252	+	0.0359346i
$924$		0			0
$925$	−40.0855	+	14.5899i	−1.31800	+	0.479714i
$926$		0			0
$927$	0.390711	+	32.0882i	0.0128326	+	1.05391i
$928$		0			0
$929$	41.9258	+	35.1799i	1.37554	+	1.15421i	0.970830	+	0.239769i	$0.0770718\pi$
$929$	41.9258	+	35.1799i	1.37554	+	1.15421i	0.404710	+	0.914445i	$0.367373\pi$
$930$		0			0
$931$	4.62869	+	26.2506i	0.151699	+	0.860329i
$932$		0			0
$933$	9.32408	+	13.1451i	0.305257	+	0.430352i
$934$		0			0
$935$	−2.48774	−	4.30890i	−0.0813579	−	0.140916i
$936$		0			0
$937$	18.8239	−	32.6039i	0.614950	−	1.06512i	−0.375443	−	0.926845i	$-0.622510\pi$
$937$	18.8239	−	32.6039i	0.614950	−	1.06512i	0.990393	−	0.138279i	$-0.0441571\pi$
$938$		0			0
$939$	4.50576	+	1.17796i	0.147040	+	0.0384413i
$940$		0			0
$941$	−39.3948	−	14.3386i	−1.28424	−	0.467423i	−0.392405	−	0.919793i	$-0.628357\pi$
$941$	−39.3948	−	14.3386i	−1.28424	−	0.467423i	−0.891831	+	0.452369i	$0.850579\pi$
$942$		0			0
$943$	4.04365	−	22.9327i	0.131680	−	0.746792i
$944$		0			0
$945$	2.32605	+	2.24260i	0.0756663	+	0.0729518i
$946$		0			0
$947$	1.77265	−	10.0532i	0.0576035	−	0.326686i	−0.942365	−	0.334586i	$-0.891404\pi$
$947$	1.77265	−	10.0532i	0.0576035	−	0.326686i	0.999969	+	0.00790013i	$0.00251471\pi$
$948$		0			0
$949$	0.713646	+	0.259746i	0.0231659	+	0.00843171i
$950$		0			0
$951$	−34.0053	+	34.4219i	−1.10270	+	1.11621i
$952$		0			0
$953$	9.51525	−	16.4809i	0.308229	−	0.533869i	−0.669746	−	0.742590i	$-0.733597\pi$
$953$	9.51525	−	16.4809i	0.308229	−	0.533869i	0.977975	+	0.208722i	$0.0669303\pi$
$954$		0			0
$955$	40.7638	+	70.6050i	1.31909	+	2.28472i
$956$		0			0
$957$	0.119355	−	0.260079i	0.00385820	−	0.00840718i
$958$		0			0
$959$	0.399774	+	2.26723i	0.0129094	+	0.0732128i
$960$		0			0
$961$	−3.95052	−	3.31488i	−0.127436	−	0.106932i
$962$		0			0
$963$	−3.51993	+	4.30015i	−0.113428	+	0.138571i
$964$		0			0
$965$	36.5760	−	13.3126i	1.17742	−	0.428547i
$966$		0			0
$967$	−31.3774	+	26.3288i	−1.00903	+	0.846676i	−0.988210	−	0.153108i	$-0.951072\pi$
$967$	−31.3774	+	26.3288i	−1.00903	+	0.846676i	−0.0208191	+	0.999783i	$0.506627\pi$
$968$		0			0
$969$	33.2831	−	15.7675i	1.06921	−	0.506526i
$970$		0			0
$971$	−45.2142			−1.45099			−0.725497	−	0.688225i	$-0.758390\pi$
$971$	−45.2142			−1.45099			−0.725497	+	0.688225i	$0.758390\pi$
$972$		0			0
$973$	−2.78113			−0.0891588
$974$		0			0
$975$	−10.5887	+	5.01627i	−0.339108	+	0.160649i
$976$		0			0
$977$	27.0072	−	22.6617i	0.864036	−	0.725013i	−0.0987973	−	0.995108i	$-0.531500\pi$
$977$	27.0072	−	22.6617i	0.864036	−	0.725013i	0.962834	+	0.270095i	$0.0870551\pi$
$978$		0			0
$979$	−1.02905	+	0.374544i	−0.0328886	+	0.0119705i
$980$		0			0
$981$	−27.6475	+	33.7757i	−0.882715	+	1.07838i
$982$		0			0
$983$	30.5200	+	25.6093i	0.973437	+	0.816810i	0.983086	−	0.183143i	$-0.0586272\pi$
$983$	30.5200	+	25.6093i	0.973437	+	0.816810i	−0.00964963	+	0.999953i	$0.503072\pi$
$984$		0			0
$985$	−5.30683	−	30.0965i	−0.169090	−	0.958954i
$986$		0			0
$987$	−0.0527978	+	0.115049i	−0.00168057	+	0.00366204i
$988$		0			0
$989$	29.9014	+	51.7908i	0.950810	+	1.64685i
$990$		0			0
$991$	−12.6850	+	21.9711i	−0.402953	+	0.697935i	−0.994081	−	0.108643i	$-0.965350\pi$
$991$	−12.6850	+	21.9711i	−0.402953	+	0.697935i	0.591128	+	0.806578i	$0.298683\pi$
$992$		0			0
$993$	−1.02872	+	1.04133i	−0.0326456	+	0.0330455i
$994$		0			0
$995$	46.1787	+	16.8077i	1.46396	+	0.532839i
$996$		0			0
$997$	−4.67785	+	26.5294i	−0.148149	+	0.840194i	0.816636	+	0.577153i	$0.195836\pi$
$997$	−4.67785	+	26.5294i	−0.148149	+	0.840194i	−0.964785	+	0.263041i	$0.915275\pi$
$998$		0			0
$999$	18.7152	−	5.38292i	0.592124	−	0.170308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.b.241.1		12
4.3	odd	2		54.2.e.b.25.2	yes	12
12.11	even	2		162.2.e.b.73.2		12
27.13	even	9	inner	432.2.u.b.337.1		12
36.7	odd	6		486.2.e.f.55.1		12
36.11	even	6		486.2.e.g.55.2		12
36.23	even	6		486.2.e.e.379.1		12
36.31	odd	6		486.2.e.h.379.2		12
108.7	odd	18		1458.2.c.f.973.6		12
108.11	even	18		1458.2.a.f.1.6		6
108.23	even	18		486.2.e.e.109.1		12
108.31	odd	18		486.2.e.h.109.2		12
108.43	odd	18		1458.2.a.g.1.1		6
108.47	even	18		1458.2.c.g.973.1		12
108.59	even	18		486.2.e.g.433.2		12
108.67	odd	18		54.2.e.b.13.2	✓	12
108.79	odd	18		1458.2.c.f.487.6		12
108.83	even	18		1458.2.c.g.487.1		12
108.95	even	18		162.2.e.b.91.2		12
108.103	odd	18		486.2.e.f.433.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.13.2	✓	12	108.67	odd	18
54.2.e.b.25.2	yes	12	4.3	odd	2
162.2.e.b.73.2		12	12.11	even	2
162.2.e.b.91.2		12	108.95	even	18
432.2.u.b.241.1		12	1.1	even	1	trivial
432.2.u.b.337.1		12	27.13	even	9	inner
486.2.e.e.109.1		12	108.23	even	18
486.2.e.e.379.1		12	36.23	even	6
486.2.e.f.55.1		12	36.7	odd	6
486.2.e.f.433.1		12	108.103	odd	18
486.2.e.g.55.2		12	36.11	even	6
486.2.e.g.433.2		12	108.59	even	18
486.2.e.h.109.2		12	108.31	odd	18
486.2.e.h.379.2		12	36.31	odd	6
1458.2.a.f.1.6		6	108.11	even	18
1458.2.a.g.1.1		6	108.43	odd	18
1458.2.c.f.487.6		12	108.79	odd	18
1458.2.c.f.973.6		12	108.7	odd	18
1458.2.c.g.487.1		12	108.83	even	18
1458.2.c.g.973.1		12	108.47	even	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.56529 + 0.741539i) q^{3} +(-3.10057 + 2.60168i) q^{5} +(-0.144365 + 0.0525446i) q^{7} +(1.90024 - 2.32144i) q^{9} +(-0.169211 - 0.141985i) q^{11} +(0.103202 + 0.585289i) q^{13} +(2.92402 - 6.37157i) q^{15} +(-2.78255 - 4.81952i) q^{17} +(1.91041 - 3.30893i) q^{19} +(0.187009 - 0.189300i) q^{21} +(-5.50570 - 2.00391i) q^{23} +(1.97651 - 11.2093i) q^{25} +(-1.25298 + 5.04282i) q^{27} +(0.129880 - 0.736585i) q^{29} +(4.77702 + 1.73869i) q^{31} +(0.370152 + 0.0967705i) q^{33} +(0.310909 - 0.538510i) q^{35} +(-1.87388 - 3.24566i) q^{37} +(-0.595555 - 0.839616i) q^{39} +(0.690156 + 3.91407i) q^{41} +(-7.81896 - 6.56088i) q^{43} +(0.147838 + 12.1416i) q^{45} +(-0.447025 + 0.162704i) q^{47} +(-5.34423 + 4.48434i) q^{49} +(7.92935 + 5.48056i) q^{51} +3.29955 q^{53} +0.894051 q^{55} +(-0.536639 + 6.59606i) q^{57} +(-5.57221 + 4.67564i) q^{59} +(-3.16654 + 1.15253i) q^{61} +(-0.152349 + 0.434982i) q^{63} +(-1.84272 - 1.54623i) q^{65} +(-1.29509 - 7.34481i) q^{67} +(10.1040 - 0.945999i) q^{69} +(1.42889 + 2.47490i) q^{71} +(0.638922 - 1.10665i) q^{73} +(5.21836 + 19.0115i) q^{75} +(0.0318887 + 0.0116066i) q^{77} +(0.574268 - 3.25684i) q^{79} +(-1.77818 - 8.82259i) q^{81} +(1.43627 - 8.14551i) q^{83} +(21.1664 + 7.70392i) q^{85} +(0.342907 + 1.24928i) q^{87} +(2.47882 - 4.29345i) q^{89} +(-0.0456525 - 0.0790725i) q^{91} +(-8.76671 + 0.820795i) q^{93} +(2.68543 + 15.2298i) q^{95} +(4.33127 + 3.63437i) q^{97} +(-0.651152 + 0.123008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9} + 12 q^{11} + 12 q^{13} + 18 q^{15} - 6 q^{17} + 9 q^{19} + 24 q^{21} - 30 q^{23} - 9 q^{25} + 15 q^{29} + 36 q^{33} - 3 q^{35} - 15 q^{37} + 42 q^{39} - 12 q^{41} - 9 q^{43}+ \cdots - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9 + 12 * q^11 + 12 * q^13 + 18 * q^15 - 6 * q^17 + 9 * q^19 + 24 * q^21 - 30 * q^23 - 9 * q^25 + 15 * q^29 + 36 * q^33 - 3 * q^35 - 15 * q^37 + 42 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^45 + 9 * q^47 - 39 * q^49 + 27 * q^51 - 12 * q^53 - 18 * q^55 + 18 * q^57 - 12 * q^59 - 36 * q^61 - 3 * q^63 - 15 * q^65 - 36 * q^67 + 18 * q^69 - 12 * q^71 - 21 * q^73 - 30 * q^75 + 3 * q^77 - 39 * q^79 - 18 * q^83 + 45 * q^85 - 27 * q^87 + 12 * q^89 + 6 * q^91 - 33 * q^93 + 15 * q^95 + 39 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more