LMFDB - Embedded newform 432.2.u.b.385.1

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			385.1
Root			$0.500000 - 1.96356i$ of defining polynomial
Character	$\chi$	$=$	432.385
Dual form			432.2.u.b.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.552775 + 1.64147i) q^{3} +(-0.177398 - 1.00607i) q^{5} +(-2.04289 - 1.71418i) q^{7} +(-2.38888 - 1.81473i) q^{9} +O(q^{10})$	\(q+(-0.552775 + 1.64147i) q^{3} +(-0.177398 - 1.00607i) q^{5} +(-2.04289 - 1.71418i) q^{7} +(-2.38888 - 1.81473i) q^{9} +(0.720058 - 4.08365i) q^{11} +(-3.68356 - 1.34071i) q^{13} +(1.74950 + 0.264938i) q^{15} +(0.925795 + 1.60352i) q^{17} +(3.21653 - 5.57120i) q^{19} +(3.94305 - 2.40579i) q^{21} +(-6.69746 + 5.61984i) q^{23} +(3.71775 - 1.35315i) q^{25} +(4.29935 - 2.91815i) q^{27} +(-1.17759 + 0.428609i) q^{29} +(2.56758 - 2.15445i) q^{31} +(6.30518 + 3.43930i) q^{33} +(-1.36219 + 2.35938i) q^{35} +(-4.58887 - 7.94816i) q^{37} +(4.23692 - 5.30537i) q^{39} +(-3.53914 - 1.28814i) q^{41} +(-0.536567 + 3.04303i) q^{43} +(-1.40197 + 2.72531i) q^{45} +(2.11809 + 1.77729i) q^{47} +(0.0194152 + 0.110109i) q^{49} +(-3.14390 + 0.633281i) q^{51} -0.231576 q^{53} -4.23618 q^{55} +(7.36696 + 8.35948i) q^{57} +(-0.613793 - 3.48099i) q^{59} +(0.405075 + 0.339899i) q^{61} +(1.76942 + 7.80227i) q^{63} +(-0.695393 + 3.94377i) q^{65} +(-7.67276 - 2.79266i) q^{67} +(-5.52263 - 14.1002i) q^{69} +(4.03086 + 6.98165i) q^{71} +(1.57397 - 2.72620i) q^{73} +(0.166083 + 6.85058i) q^{75} +(-8.47113 + 7.10812i) q^{77} +(-2.43473 + 0.886167i) q^{79} +(2.41349 + 8.67036i) q^{81} +(-7.55488 + 2.74975i) q^{83} +(1.44903 - 1.21588i) q^{85} +(-0.0526065 - 2.16991i) q^{87} +(-6.12693 + 10.6122i) q^{89} +(5.22688 + 9.05322i) q^{91} +(2.11719 + 5.40555i) q^{93} +(-6.17564 - 2.24775i) q^{95} +(-1.51264 + 8.57862i) q^{97} +(-9.13087 + 8.44864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

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
$3$	−0.552775	+	1.64147i	−0.319145	+	0.947706i
$3$	−0.552775	+	1.64147i	−0.319145	+	0.947706i
$4$		0			0
$5$	−0.177398	−	1.00607i	−0.0793347	−	0.449929i	−0.998436	−	0.0559078i	$-0.982195\pi$
$5$	−0.177398	−	1.00607i	−0.0793347	−	0.449929i	0.919101	−	0.394021i	$-0.128916\pi$
$6$		0			0
$7$	−2.04289	−	1.71418i	−0.772138	−	0.647901i	0.169118	−	0.985596i	$-0.445908\pi$
$7$	−2.04289	−	1.71418i	−0.772138	−	0.647901i	−0.941256	+	0.337695i	$0.890353\pi$
$8$		0			0
$9$	−2.38888	−	1.81473i	−0.796293	−	0.604911i
$10$		0			0
$11$	0.720058	−	4.08365i	0.217106	−	1.23127i	−0.660109	−	0.751169i	$-0.729490\pi$
$11$	0.720058	−	4.08365i	0.217106	−	1.23127i	0.877215	−	0.480098i	$-0.159399\pi$
$12$		0			0
$13$	−3.68356	−	1.34071i	−1.02164	−	0.371845i	−0.223746	−	0.974647i	$-0.571829\pi$
$13$	−3.68356	−	1.34071i	−1.02164	−	0.371845i	−0.797891	+	0.602802i	$0.794051\pi$
$14$		0			0
$15$	1.74950	+	0.264938i	0.451720	+	0.0684067i
$16$		0			0
$17$	0.925795	+	1.60352i	0.224538	+	0.388912i	0.956181	−	0.292777i	$-0.0945793\pi$
$17$	0.925795	+	1.60352i	0.224538	+	0.388912i	−0.731643	+	0.681688i	$0.761246\pi$
$18$		0			0
$19$	3.21653	−	5.57120i	0.737923	−	1.27812i	−0.215505	−	0.976503i	$-0.569140\pi$
$19$	3.21653	−	5.57120i	0.737923	−	1.27812i	0.953429	−	0.301618i	$-0.0975268\pi$
$20$		0			0
$21$	3.94305	−	2.40579i	0.860443	−	0.524986i
$22$		0			0
$23$	−6.69746	+	5.61984i	−1.39652	+	1.17182i	−0.433897	+	0.900963i	$0.642862\pi$
$23$	−6.69746	+	5.61984i	−1.39652	+	1.17182i	−0.962620	+	0.270854i	$0.912694\pi$
$24$		0			0
$25$	3.71775	−	1.35315i	0.743550	−	0.270630i
$26$		0			0
$27$	4.29935	−	2.91815i	0.827411	−	0.561598i
$28$		0			0
$29$	−1.17759	+	0.428609i	−0.218674	+	0.0795907i	−0.449034	−	0.893515i	$-0.648232\pi$
$29$	−1.17759	+	0.428609i	−0.218674	+	0.0795907i	0.230360	+	0.973105i	$0.426010\pi$
$30$		0			0
$31$	2.56758	−	2.15445i	0.461151	−	0.386952i	−0.382403	−	0.923995i	$-0.624904\pi$
$31$	2.56758	−	2.15445i	0.461151	−	0.386952i	0.843554	+	0.537044i	$0.180459\pi$
$32$		0			0
$33$	6.30518	+	3.43930i	1.09759	+	0.598705i
$34$		0			0
$35$	−1.36219	+	2.35938i	−0.230252	+	0.398808i
$36$		0			0
$37$	−4.58887	−	7.94816i	−0.754406	−	1.30667i	−0.945669	−	0.325131i	$-0.894592\pi$
$37$	−4.58887	−	7.94816i	−0.754406	−	1.30667i	0.191263	−	0.981539i	$-0.438742\pi$
$38$		0			0
$39$	4.23692	−	5.30537i	0.678450	−	0.849539i
$40$		0			0
$41$	−3.53914	−	1.28814i	−0.552720	−	0.201174i	0.0505345	−	0.998722i	$-0.483908\pi$
$41$	−3.53914	−	1.28814i	−0.552720	−	0.201174i	−0.603255	+	0.797549i	$0.706130\pi$
$42$		0			0
$43$	−0.536567	+	3.04303i	−0.0818258	+	0.464057i	0.916171	+	0.400788i	$0.131264\pi$
$43$	−0.536567	+	3.04303i	−0.0818258	+	0.464057i	−0.997997	+	0.0632688i	$0.979847\pi$
$44$		0			0
$45$	−1.40197	+	2.72531i	−0.208993	+	0.406266i
$46$		0			0
$47$	2.11809	+	1.77729i	0.308956	+	0.259244i	0.784060	−	0.620685i	$-0.213145\pi$
$47$	2.11809	+	1.77729i	0.308956	+	0.259244i	−0.475105	+	0.879929i	$0.657590\pi$
$48$		0			0
$49$	0.0194152	+	0.110109i	0.00277360	+	0.0157298i
$50$		0			0
$51$	−3.14390	+	0.633281i	−0.440234	+	0.0886771i
$52$		0			0
$53$	−0.231576			−0.0318094			−0.0159047	−	0.999874i	$-0.505063\pi$
$53$	−0.231576			−0.0318094			−0.0159047	+	0.999874i	$0.505063\pi$
$54$		0			0
$55$	−4.23618			−0.571207
$56$		0			0
$57$	7.36696	+	8.35948i	0.975778	+	1.10724i
$58$		0			0
$59$	−0.613793	−	3.48099i	−0.0799090	−	0.453187i	−0.998339	−	0.0576042i	$-0.981654\pi$
$59$	−0.613793	−	3.48099i	−0.0799090	−	0.453187i	0.918430	−	0.395582i	$-0.129457\pi$
$60$		0			0
$61$	0.405075	+	0.339899i	0.0518646	+	0.0435196i	0.668351	−	0.743846i	$-0.267000\pi$
$61$	0.405075	+	0.339899i	0.0518646	+	0.0435196i	−0.616487	+	0.787365i	$0.711445\pi$
$62$		0			0
$63$	1.76942	+	7.80227i	0.222926	+	0.982994i
$64$		0			0
$65$	−0.695393	+	3.94377i	−0.0862529	+	0.489164i
$66$		0			0
$67$	−7.67276	−	2.79266i	−0.937377	−	0.341177i	−0.172247	−	0.985054i	$-0.555103\pi$
$67$	−7.67276	−	2.79266i	−0.937377	−	0.341177i	−0.765130	+	0.643876i	$0.777325\pi$
$68$		0			0
$69$	−5.52263	−	14.1002i	−0.664847	−	1.69747i
$70$		0			0
$71$	4.03086	+	6.98165i	0.478375	+	0.828570i	0.999693	−	0.0247929i	$-0.00789263\pi$
$71$	4.03086	+	6.98165i	0.478375	+	0.828570i	−0.521318	+	0.853363i	$0.674559\pi$
$72$		0			0
$73$	1.57397	−	2.72620i	0.184219	−	0.319078i	−0.759094	−	0.650981i	$-0.774358\pi$
$73$	1.57397	−	2.72620i	0.184219	−	0.319078i	0.943313	+	0.331904i	$0.107691\pi$
$74$		0			0
$75$	0.166083	+	6.85058i	0.0191776	+	0.791037i
$76$		0			0
$77$	−8.47113	+	7.10812i	−0.965374	+	0.810045i
$78$		0			0
$79$	−2.43473	+	0.886167i	−0.273928	+	0.0997016i	−0.475332	−	0.879807i	$-0.657672\pi$
$79$	−2.43473	+	0.886167i	−0.273928	+	0.0997016i	0.201404	+	0.979508i	$0.435450\pi$
$80$		0			0
$81$	2.41349	+	8.67036i	0.268165	+	0.963373i
$82$		0			0
$83$	−7.55488	+	2.74975i	−0.829256	+	0.301824i	−0.721553	−	0.692359i	$-0.756572\pi$
$83$	−7.55488	+	2.74975i	−0.829256	+	0.301824i	−0.107702	+	0.994183i	$0.534349\pi$
$84$		0			0
$85$	1.44903	−	1.21588i	0.157169	−	0.131880i
$86$		0			0
$87$	−0.0526065	−	2.16991i	−0.00564001	−	0.232639i
$88$		0			0
$89$	−6.12693	+	10.6122i	−0.649453	+	1.12489i	0.333800	+	0.942644i	$0.391669\pi$
$89$	−6.12693	+	10.6122i	−0.649453	+	1.12489i	−0.983254	+	0.182242i	$0.941664\pi$
$90$		0			0
$91$	5.22688	+	9.05322i	0.547926	+	0.949035i
$92$		0			0
$93$	2.11719	+	5.40555i	0.219542	+	0.560529i
$94$		0			0
$95$	−6.17564	−	2.24775i	−0.633607	−	0.230614i
$96$		0			0
$97$	−1.51264	+	8.57862i	−0.153586	+	0.871027i	0.806482	+	0.591259i	$0.201369\pi$
$97$	−1.51264	+	8.57862i	−0.153586	+	0.871027i	−0.960068	+	0.279768i	$0.909742\pi$
$98$		0			0
$99$	−9.13087	+	8.44864i	−0.917687	+	0.849120i
$100$		0			0
$101$	−4.14121	−	3.47489i	−0.412066	−	0.345764i	0.413069	−	0.910700i	$-0.364457\pi$
$101$	−4.14121	−	3.47489i	−0.412066	−	0.345764i	−0.825135	+	0.564935i	$0.808901\pi$
$102$		0			0
$103$	−1.87292	−	10.6218i	−0.184544	−	1.04660i	−0.926540	−	0.376197i	$-0.877232\pi$
$103$	−1.87292	−	10.6218i	−0.184544	−	1.04660i	0.741996	−	0.670405i	$-0.233880\pi$
$104$		0			0
$105$	−3.11988	−	3.54021i	−0.304469	−	0.345489i
$106$		0			0
$107$	14.8511			1.43571			0.717856	−	0.696191i	$-0.245124\pi$
$107$	14.8511			1.43571			0.717856	+	0.696191i	$0.245124\pi$
$108$		0			0
$109$	17.6598			1.69150			0.845752	−	0.533576i	$-0.179152\pi$
$109$	17.6598			1.69150			0.845752	+	0.533576i	$0.179152\pi$
$110$		0			0
$111$	15.5833	−	3.13897i	1.47910	−	0.297938i
$112$		0			0
$113$	0.339716	+	1.92663i	0.0319578	+	0.181242i	0.996608	−	0.0822905i	$-0.0262235\pi$
$113$	0.339716	+	1.92663i	0.0319578	+	0.181242i	−0.964651	+	0.263532i	$0.915112\pi$
$114$		0			0
$115$	6.84208	+	5.74118i	0.638027	+	0.535368i
$116$		0			0
$117$	6.36656	+	9.88747i	0.588589	+	0.914097i
$118$		0			0
$119$	0.857442	−	4.86280i	0.0786016	−	0.445772i
$120$		0			0
$121$	−5.82110	−	2.11871i	−0.529191	−	0.192610i
$122$		0			0
$123$	4.07080	−	5.09735i	0.367051	−	0.459613i
$124$		0			0
$125$	−4.57487	−	7.92391i	−0.409189	−	0.708736i
$126$		0			0
$127$	2.78998	−	4.83239i	0.247571	−	0.428805i	−0.715281	−	0.698837i	$-0.753701\pi$
$127$	2.78998	−	4.83239i	0.247571	−	0.428805i	0.962851	+	0.270032i	$0.0870344\pi$
$128$		0			0
$129$	−4.69845	−	2.56287i	−0.413675	−	0.225648i
$130$		0			0
$131$	−1.18532	+	0.994600i	−0.103562	+	0.0868986i	−0.693098	−	0.720843i	$-0.743755\pi$
$131$	−1.18532	+	0.994600i	−0.103562	+	0.0868986i	0.589537	+	0.807742i	$0.299310\pi$
$132$		0			0
$133$	−16.1211	+	5.86759i	−1.39787	+	0.508785i
$134$		0			0
$135$	−3.69856	−	3.80779i	−0.318321	−	0.327722i
$136$		0			0
$137$	18.8496	−	6.86070i	1.61043	−	0.586149i	0.628906	−	0.777481i	$-0.283503\pi$
$137$	18.8496	−	6.86070i	1.61043	−	0.586149i	0.981525	+	0.191332i	$0.0612807\pi$
$138$		0			0
$139$	−2.98779	+	2.50705i	−0.253421	+	0.212645i	−0.760644	−	0.649170i	$-0.775117\pi$
$139$	−2.98779	+	2.50705i	−0.253421	+	0.212645i	0.507223	+	0.861815i	$0.330672\pi$
$140$		0			0
$141$	−4.08821	+	2.49435i	−0.344289	+	0.210062i
$142$		0			0
$143$	−8.12736	+	14.0770i	−0.679644	+	1.17718i
$144$		0			0
$145$	0.640114	+	1.10871i	0.0531586	+	0.0920734i
$146$		0			0
$147$	−0.191473	−	0.0289960i	−0.0157925	−	0.00239155i
$148$		0			0
$149$	9.24128	+	3.36355i	0.757075	+	0.275553i	0.691580	−	0.722300i	$-0.256915\pi$
$149$	9.24128	+	3.36355i	0.757075	+	0.275553i	0.0654951	+	0.997853i	$0.479137\pi$
$150$		0			0
$151$	−0.697011	+	3.95294i	−0.0567219	+	0.321686i	−0.999945	−	0.0104735i	$-0.996666\pi$
$151$	−0.697011	+	3.95294i	−0.0567219	+	0.321686i	0.943223	+	0.332160i	$0.107777\pi$
$152$		0			0
$153$	0.698355	−	5.51070i	0.0564587	−	0.445513i
$154$		0			0
$155$	−2.62302	−	2.20098i	−0.210686	−	0.176787i
$156$		0			0
$157$	−2.48817	−	14.1111i	−0.198578	−	1.12619i	−0.907231	−	0.420634i	$-0.861808\pi$
$157$	−2.48817	−	14.1111i	−0.198578	−	1.12619i	0.708653	−	0.705557i	$-0.249303\pi$
$158$		0			0
$159$	0.128010	−	0.380127i	0.0101518	−	0.0301460i
$160$		0			0
$161$	23.3156			1.83753
$162$		0			0
$163$	14.2911			1.11937			0.559683	−	0.828707i	$-0.310923\pi$
$163$	14.2911			1.11937			0.559683	+	0.828707i	$0.310923\pi$
$164$		0			0
$165$	2.34166	−	6.95359i	0.182298	−	0.541336i
$166$		0			0
$167$	1.65921	+	9.40983i	0.128393	+	0.728154i	0.979234	+	0.202731i	$0.0649818\pi$
$167$	1.65921	+	9.40983i	0.128393	+	0.728154i	−0.850841	+	0.525423i	$0.823907\pi$
$168$		0			0
$169$	1.81256	+	1.52092i	0.139428	+	0.116994i
$170$		0			0
$171$	−17.7941	+	7.47177i	−1.36075	+	0.571381i
$172$		0			0
$173$	1.73345	−	9.83089i	0.131792	−	0.747429i	−0.845248	−	0.534374i	$-0.820547\pi$
$173$	1.73345	−	9.83089i	0.131792	−	0.747429i	0.977040	−	0.213055i	$-0.0683414\pi$
$174$		0			0
$175$	−9.91449	−	3.60858i	−0.749465	−	0.272783i
$176$		0			0
$177$	6.05325	+	0.916681i	0.454990	+	0.0689019i
$178$		0			0
$179$	−11.2541	−	19.4927i	−0.841174	−	1.45696i	−0.888903	−	0.458096i	$-0.848532\pi$
$179$	−11.2541	−	19.4927i	−0.841174	−	1.45696i	0.0477290	−	0.998860i	$-0.484802\pi$
$180$		0			0
$181$	−0.248078	+	0.429684i	−0.0184395	+	0.0319382i	−0.875098	−	0.483946i	$-0.839203\pi$
$181$	−0.248078	+	0.429684i	−0.0184395	+	0.0319382i	0.856658	+	0.515884i	$0.172536\pi$
$182$		0			0
$183$	−0.781851	+	0.477034i	−0.0577961	+	0.0352633i
$184$		0			0
$185$	−7.18237	+	6.02672i	−0.528058	+	0.443093i
$186$		0			0
$187$	7.21486	−	2.62599i	0.527603	−	0.192032i
$188$		0			0
$189$	−13.7853	−	1.40844i	−1.00273	−	0.102449i
$190$		0			0
$191$	6.75481	−	2.45855i	0.488761	−	0.177894i	−0.0858713	−	0.996306i	$-0.527367\pi$
$191$	6.75481	−	2.45855i	0.488761	−	0.177894i	0.574632	+	0.818412i	$0.305145\pi$
$192$		0			0
$193$	−10.3185	+	8.65825i	−0.742742	+	0.623234i	−0.933572	−	0.358389i	$-0.883326\pi$
$193$	−10.3185	+	8.65825i	−0.742742	+	0.623234i	0.190831	+	0.981623i	$0.438882\pi$
$194$		0			0
$195$	−6.08920	−	3.32149i	−0.436057	−	0.237857i
$196$		0			0
$197$	−2.53340	+	4.38797i	−0.180497	+	0.312630i	−0.942050	−	0.335473i	$-0.891104\pi$
$197$	−2.53340	+	4.38797i	−0.180497	+	0.312630i	0.761553	+	0.648103i	$0.224437\pi$
$198$		0			0
$199$	−8.97242	−	15.5407i	−0.636038	−	1.10165i	−0.986294	−	0.164996i	$-0.947239\pi$
$199$	−8.97242	−	15.5407i	−0.636038	−	1.10165i	0.350256	−	0.936654i	$-0.386094\pi$
$200$		0			0
$201$	8.82539	−	11.0509i	0.622495	−	0.779473i
$202$		0			0
$203$	3.14040	+	1.14301i	0.220413	+	0.0802238i
$204$		0			0
$205$	−0.668128	+	3.78914i	−0.0466641	+	0.264645i
$206$		0			0
$207$	26.1979	−	1.27101i	1.82088	−	0.0883413i
$208$		0			0
$209$	−20.4347	−	17.1468i	−1.41350	−	1.18607i
$210$		0			0
$211$	0.884489	+	5.01618i	0.0608907	+	0.345328i	0.999999	+	0.00170581i	$0.000542977\pi$
$211$	0.884489	+	5.01618i	0.0608907	+	0.345328i	−0.939108	+	0.343623i	$0.888346\pi$
$212$		0			0
$213$	−13.6884	+	2.75727i	−0.937912	+	0.188925i
$214$		0			0
$215$	3.15669			0.215284
$216$		0			0
$217$	−8.93840			−0.606778
$218$		0			0
$219$	3.60494	+	4.09061i	0.243599	+	0.276418i
$220$		0			0
$221$	−1.26037	−	7.14790i	−0.0847815	−	0.480820i
$222$		0			0
$223$	−2.92334	−	2.45297i	−0.195761	−	0.164263i	0.539638	−	0.841897i	$-0.318561\pi$
$223$	−2.92334	−	2.45297i	−0.195761	−	0.164263i	−0.735399	+	0.677634i	$0.763005\pi$
$224$		0			0
$225$	−11.3369	−	3.51421i	−0.755791	−	0.234281i
$226$		0			0
$227$	3.53875	−	20.0693i	0.234875	−	1.33204i	−0.608001	−	0.793936i	$-0.708028\pi$
$227$	3.53875	−	20.0693i	0.234875	−	1.33204i	0.842876	−	0.538108i	$-0.180861\pi$
$228$		0			0
$229$	1.41711	+	0.515787i	0.0936455	+	0.0340842i	0.388418	−	0.921483i	$-0.373022\pi$
$229$	1.41711	+	0.515787i	0.0936455	+	0.0340842i	−0.294773	+	0.955567i	$0.595244\pi$
$230$		0			0
$231$	−6.98517	−	17.8343i	−0.459590	−	1.17341i
$232$		0			0
$233$	10.0838	+	17.4656i	0.660610	+	1.14421i	0.980456	+	0.196741i	$0.0630357\pi$
$233$	10.0838	+	17.4656i	0.660610	+	1.14421i	−0.319845	+	0.947470i	$0.603631\pi$
$234$		0			0
$235$	1.41234	−	2.44624i	0.0921308	−	0.159575i
$236$		0			0
$237$	−0.108766	−	4.48639i	−0.00706512	−	0.291422i
$238$		0			0
$239$	9.68541	−	8.12702i	0.626497	−	0.525693i	−0.273341	−	0.961917i	$-0.588129\pi$
$239$	9.68541	−	8.12702i	0.626497	−	0.525693i	0.899838	+	0.436224i	$0.143684\pi$
$240$		0			0
$241$	26.1605	−	9.52166i	1.68515	−	0.613344i	0.691148	−	0.722713i	$-0.257105\pi$
$241$	26.1605	−	9.52166i	1.68515	−	0.613344i	0.994001	+	0.109369i	$0.0348831\pi$
$242$		0			0
$243$	−15.5663	−	0.831075i	−0.998578	−	0.0533135i
$244$		0			0
$245$	0.107333	−	0.0390661i	0.00685728	−	0.00249584i
$246$		0			0
$247$	−19.3177	+	16.2094i	−1.22915	+	1.03138i
$248$		0			0
$249$	−0.337498	−	13.9211i	−0.0213881	−	0.882216i
$250$		0			0
$251$	−0.336641	+	0.583079i	−0.0212486	+	0.0368036i	−0.876454	−	0.481485i	$-0.840097\pi$
$251$	−0.336641	+	0.583079i	−0.0212486	+	0.0368036i	0.855206	+	0.518289i	$0.173431\pi$
$252$		0			0
$253$	18.1269	+	31.3967i	1.13963	+	1.97389i
$254$		0			0
$255$	1.19485	+	3.05065i	0.0748242	+	0.191039i
$256$		0			0
$257$	−28.7904	−	10.4789i	−1.79590	−	0.653653i	−0.998756	−	0.0498599i	$-0.984123\pi$
$257$	−28.7904	−	10.4789i	−1.79590	−	0.653653i	−0.797141	−	0.603793i	$-0.793655\pi$
$258$		0			0
$259$	−4.25007	+	24.1033i	−0.264087	+	1.49771i
$260$		0			0
$261$	3.59094	+	1.11312i	0.222274	+	0.0689006i
$262$		0			0
$263$	4.54929	+	3.81731i	0.280521	+	0.235385i	0.772182	−	0.635402i	$-0.219165\pi$
$263$	4.54929	+	3.81731i	0.280521	+	0.235385i	−0.491661	+	0.870787i	$0.663610\pi$
$264$		0			0
$265$	0.0410811	+	0.232982i	0.00252359	+	0.0143120i
$266$		0			0
$267$	−14.0328	−	15.9233i	−0.858792	−	0.974492i
$268$		0			0
$269$	15.3624			0.936661			0.468330	−	0.883553i	$-0.344856\pi$
$269$	15.3624			0.936661			0.468330	+	0.883553i	$0.344856\pi$
$270$		0			0
$271$	14.5939			0.886516			0.443258	−	0.896394i	$-0.353823\pi$
$271$	14.5939			0.886516			0.443258	+	0.896394i	$0.353823\pi$
$272$		0			0
$273$	−17.7499	+	3.57539i	−1.07427	+	0.216393i
$274$		0			0
$275$	−2.84880	−	16.1563i	−0.171789	−	0.974264i
$276$		0			0
$277$	4.35786	+	3.65668i	0.261838	+	0.219709i	0.764250	−	0.644920i	$-0.223109\pi$
$277$	4.35786	+	3.65668i	0.261838	+	0.219709i	−0.502412	+	0.864629i	$0.667554\pi$
$278$		0			0
$279$	−10.0434	+	0.487262i	−0.601282	+	0.0291716i
$280$		0			0
$281$	2.37136	−	13.4487i	0.141464	−	0.802281i	−0.828675	−	0.559730i	$-0.810905\pi$
$281$	2.37136	−	13.4487i	0.141464	−	0.802281i	0.970139	−	0.242551i	$-0.0779841\pi$
$282$		0			0
$283$	24.3720	+	8.87068i	1.44876	+	0.527307i	0.942246	−	0.334922i	$-0.108710\pi$
$283$	24.3720	+	8.87068i	1.44876	+	0.527307i	0.506519	+	0.862229i	$0.330932\pi$
$284$		0			0
$285$	7.10336	−	8.89465i	0.420767	−	0.526874i
$286$		0			0
$287$	5.02194	+	8.69825i	0.296436	+	0.513442i
$288$		0			0
$289$	6.78581	−	11.7534i	0.399165	−	0.691374i
$290$		0			0
$291$	−13.2454	−	7.22501i	−0.776461	−	0.423538i
$292$		0			0
$293$	15.2378	−	12.7860i	0.890199	−	0.746966i	−0.0780511	−	0.996949i	$-0.524870\pi$
$293$	15.2378	−	12.7860i	0.890199	−	0.746966i	0.968250	+	0.249984i	$0.0804253\pi$
$294$		0			0
$295$	−3.39325	+	1.23504i	−0.197562	+	0.0719068i
$296$		0			0
$297$	−8.82091	−	19.6583i	−0.511841	−	1.14069i
$298$		0			0
$299$	32.2051	−	11.7217i	1.86247	−	0.677883i
$300$		0			0
$301$	6.31245	−	5.29678i	0.363844	−	0.305301i
$302$		0			0
$303$	7.99310	−	4.87686i	0.459192	−	0.280168i
$304$		0			0
$305$	0.270103	−	0.467832i	0.0154661	−	0.0267880i
$306$		0			0
$307$	−4.75733	−	8.23993i	−0.271515	−	0.470278i	0.697735	−	0.716356i	$-0.254191\pi$
$307$	−4.75733	−	8.23993i	−0.271515	−	0.470278i	−0.969250	+	0.246078i	$0.920858\pi$
$308$		0			0
$309$	18.4708	+	2.79714i	1.05077	+	0.159124i
$310$		0			0
$311$	−13.5916	−	4.94693i	−0.770707	−	0.280514i	−0.0734150	−	0.997301i	$-0.523390\pi$
$311$	−13.5916	−	4.94693i	−0.770707	−	0.280514i	−0.697292	+	0.716787i	$0.745612\pi$
$312$		0			0
$313$	−2.32518	+	13.1867i	−0.131427	+	0.745359i	0.845855	+	0.533414i	$0.179091\pi$
$313$	−2.32518	+	13.1867i	−0.131427	+	0.745359i	−0.977281	+	0.211946i	$0.932020\pi$
$314$		0			0
$315$	7.53576	−	3.16427i	0.424592	−	0.178286i
$316$		0			0
$317$	19.2768	+	16.1751i	1.08269	+	0.908487i	0.996142	−	0.0877609i	$-0.0279711\pi$
$317$	19.2768	+	16.1751i	1.08269	+	0.908487i	0.0865506	+	0.996247i	$0.472416\pi$
$318$		0			0
$319$	0.902354	+	5.11750i	0.0505221	+	0.286525i
$320$		0			0
$321$	−8.20933	+	24.3777i	−0.458200	+	1.36063i
$322$		0			0
$323$	11.9114			0.662768
$324$		0			0
$325$	−15.5088			−0.860271
$326$		0			0
$327$	−9.76191	+	28.9882i	−0.539835	+	1.60305i
$328$		0			0
$329$	−1.28042	−	7.26160i	−0.0705916	−	0.400345i
$330$		0			0
$331$	16.1905	+	13.5855i	0.889912	+	0.746725i	0.968193	−	0.250206i	$-0.0804984\pi$
$331$	16.1905	+	13.5855i	0.889912	+	0.746725i	−0.0782802	+	0.996931i	$0.524943\pi$
$332$		0			0
$333$	−3.46152	+	27.3148i	−0.189690	+	1.49684i
$334$		0			0
$335$	−1.44848	+	8.21476i	−0.0791392	+	0.448820i
$336$		0			0
$337$	−4.48414	−	1.63209i	−0.244267	−	0.0889058i	0.216986	−	0.976175i	$-0.430378\pi$
$337$	−4.48414	−	1.63209i	−0.244267	−	0.0889058i	−0.461252	+	0.887269i	$0.652600\pi$
$338$		0			0
$339$	−3.35030	−	0.507356i	−0.181963	−	0.0275558i
$340$		0			0
$341$	−6.94924	−	12.0364i	−0.376322	−	0.651809i
$342$		0			0
$343$	−9.18471	+	15.9084i	−0.495928	+	0.858972i
$344$		0			0
$345$	−13.2061	+	8.05751i	−0.710995	+	0.433802i
$346$		0			0
$347$	−12.0020	+	10.0708i	−0.644299	+	0.540631i	−0.905335	−	0.424698i	$-0.860380\pi$
$347$	−12.0020	+	10.0708i	−0.644299	+	0.540631i	0.261036	+	0.965329i	$0.415936\pi$
$348$		0			0
$349$	−18.6170	+	6.77604i	−0.996547	+	0.362713i	−0.788252	−	0.615353i	$-0.789014\pi$
$349$	−18.6170	+	6.77604i	−0.996547	+	0.362713i	−0.208295	+	0.978066i	$0.566791\pi$
$350$		0			0
$351$	−19.7493	+	4.98500i	−1.05414	+	0.266080i
$352$		0			0
$353$	14.8445	−	5.40296i	0.790093	−	0.287570i	0.0847183	−	0.996405i	$-0.473001\pi$
$353$	14.8445	−	5.40296i	0.790093	−	0.287570i	0.705375	+	0.708835i	$0.250779\pi$
$354$		0			0
$355$	6.30898	−	5.29387i	0.334846	−	0.280969i
$356$		0			0
$357$	7.50819	+	4.09550i	0.397375	+	0.216757i
$358$		0			0
$359$	2.43474	−	4.21710i	0.128501	−	0.222570i	−0.794595	−	0.607140i	$-0.792317\pi$
$359$	2.43474	−	4.21710i	0.128501	−	0.222570i	0.923096	+	0.384570i	$0.125650\pi$
$360$		0			0
$361$	−11.1922	−	19.3854i	−0.589062	−	1.02028i
$362$		0			0
$363$	6.69557	−	8.38402i	0.351426	−	0.440047i
$364$		0			0
$365$	−3.02197	−	1.09991i	−0.158177	−	0.0575718i
$366$		0			0
$367$	1.47394	−	8.35914i	0.0769392	−	0.436344i	−0.921868	−	0.387505i	$-0.873337\pi$
$367$	1.47394	−	8.35914i	0.0769392	−	0.436344i	0.998807	−	0.0488385i	$-0.0155520\pi$
$368$		0			0
$369$	6.11694	+	9.49980i	0.318435	+	0.494540i
$370$		0			0
$371$	0.473084	+	0.396964i	0.0245613	+	0.0206094i
$372$		0			0
$373$	0.783900	+	4.44572i	0.0405888	+	0.230190i	0.998353	−	0.0573629i	$-0.0182692\pi$
$373$	0.783900	+	4.44572i	0.0405888	+	0.230190i	−0.957765	+	0.287553i	$0.907158\pi$
$374$		0			0
$375$	15.5358	−	3.12940i	0.802264	−	0.161601i
$376$		0			0
$377$	4.91238			0.253000
$378$		0			0
$379$	−11.1018			−0.570262			−0.285131	−	0.958489i	$-0.592037\pi$
$379$	−11.1018			−0.570262			−0.285131	+	0.958489i	$0.592037\pi$
$380$		0			0
$381$	6.39001	+	7.25091i	0.327370	+	0.371475i
$382$		0			0
$383$	3.82767	+	21.7078i	0.195585	+	1.10922i	0.911584	+	0.411114i	$0.134860\pi$
$383$	3.82767	+	21.7078i	0.195585	+	1.10922i	−0.715999	+	0.698101i	$0.754029\pi$
$384$		0			0
$385$	8.65404	+	7.26160i	0.441051	+	0.370085i
$386$		0			0
$387$	6.80407	−	6.29569i	0.345870	−	0.320028i
$388$		0			0
$389$	−2.95836	+	16.7777i	−0.149995	+	0.850663i	0.813225	+	0.581949i	$0.197710\pi$
$389$	−2.95836	+	16.7777i	−0.149995	+	0.850663i	−0.963220	+	0.268714i	$0.913401\pi$
$390$		0			0
$391$	−15.2120	−	5.53672i	−0.769305	−	0.280004i
$392$		0			0
$393$	−0.977396	−	2.49546i	−0.0493031	−	0.125879i
$394$		0			0
$395$	1.32346	+	2.29231i	0.0665907	+	0.115338i
$396$		0			0
$397$	7.80452	−	13.5178i	0.391698	−	0.678441i	−0.600976	−	0.799267i	$-0.705221\pi$
$397$	7.80452	−	13.5178i	0.391698	−	0.678441i	0.992674	+	0.120827i	$0.0385545\pi$
$398$		0			0
$399$	−0.720175	−	29.7058i	−0.0360538	−	1.48715i
$400$		0			0
$401$	−2.82242	+	2.36829i	−0.140945	+	0.118267i	−0.710534	−	0.703663i	$-0.751547\pi$
$401$	−2.82242	+	2.36829i	−0.140945	+	0.118267i	0.569589	+	0.821929i	$0.307102\pi$
$402$		0			0
$403$	−12.3463	+	4.49370i	−0.615015	+	0.223847i
$404$		0			0
$405$	8.29486	−	3.96625i	0.412175	−	0.197084i
$406$		0			0
$407$	−35.7618	+	13.0162i	−1.77264	+	0.645190i
$408$		0			0
$409$	−10.3077	+	8.64918i	−0.509682	+	0.427674i	−0.861017	−	0.508576i	$-0.830172\pi$
$409$	−10.3077	+	8.64918i	−0.509682	+	0.427674i	0.351335	+	0.936250i	$0.385728\pi$
$410$		0			0
$411$	0.842067	+	34.7336i	0.0415361	+	1.71328i
$412$		0			0
$413$	−4.71316	+	8.16342i	−0.231919	+	0.401696i
$414$		0			0
$415$	4.10667	+	7.11296i	0.201588	+	0.349161i
$416$		0			0
$417$	−2.46369	−	6.29022i	−0.120647	−	0.308033i
$418$		0			0
$419$	1.29440	+	0.471124i	0.0632357	+	0.0230159i	0.373444	−	0.927653i	$-0.378177\pi$
$419$	1.29440	+	0.471124i	0.0632357	+	0.0230159i	−0.310209	+	0.950668i	$0.600399\pi$
$420$		0			0
$421$	−1.39368	+	7.90398i	−0.0679240	+	0.385216i	0.931827	+	0.362903i	$0.118214\pi$
$421$	−1.39368	+	7.90398i	−0.0679240	+	0.385216i	−0.999751	+	0.0223134i	$0.992897\pi$
$422$		0			0
$423$	−1.83456	−	8.08950i	−0.0891993	−	0.393325i
$424$		0			0
$425$	5.61168	+	4.70876i	0.272207	+	0.228409i
$426$		0			0
$427$	−0.244874	−	1.38875i	−0.0118503	−	0.0672062i
$428$		0			0
$429$	−18.6144	−	21.1223i	−0.898714	−	1.01979i
$430$		0			0
$431$	34.6923			1.67107			0.835534	−	0.549438i	$-0.185158\pi$
$431$	34.6923			1.67107			0.835534	+	0.549438i	$0.185158\pi$
$432$		0			0
$433$	0.605990			0.0291220			0.0145610	−	0.999894i	$-0.495365\pi$
$433$	0.605990			0.0291220			0.0145610	+	0.999894i	$0.495365\pi$
$434$		0			0
$435$	−2.17376	+	0.437864i	−0.104224	+	0.0209940i
$436$		0			0
$437$	9.76663	+	55.3893i	0.467201	+	2.64963i
$438$		0			0
$439$	0.853735	+	0.716369i	0.0407466	+	0.0341904i	0.662934	−	0.748678i	$-0.269311\pi$
$439$	0.853735	+	0.716369i	0.0407466	+	0.0341904i	−0.622187	+	0.782869i	$0.713756\pi$
$440$		0			0
$441$	0.153438	−	0.298270i	0.00730656	−	0.0142033i
$442$		0			0
$443$	−1.06252	+	6.02583i	−0.0504817	+	0.286296i	−0.999589	−	0.0286559i	$-0.990877\pi$
$443$	−1.06252	+	6.02583i	−0.0504817	+	0.286296i	0.949108	+	0.314952i	$0.101988\pi$
$444$		0			0
$445$	11.7635	+	4.28156i	0.557643	+	0.202966i
$446$		0			0
$447$	−10.6295	+	13.3100i	−0.502759	+	0.629543i
$448$		0			0
$449$	−18.1443	−	31.4269i	−0.856283	−	1.48313i	−0.875450	−	0.483310i	$-0.839435\pi$
$449$	−18.1443	−	31.4269i	−0.856283	−	1.48313i	0.0191664	−	0.999816i	$-0.493899\pi$
$450$		0			0
$451$	−7.80870	+	13.5251i	−0.367697	+	0.636870i
$452$		0			0
$453$	−6.10337	−	3.32922i	−0.286761	−	0.156420i
$454$		0			0
$455$	8.18096	−	6.86464i	0.383529	−	0.321819i
$456$		0			0
$457$	−19.4942	+	7.09531i	−0.911900	+	0.331905i	−0.755011	−	0.655712i	$-0.772369\pi$
$457$	−19.4942	+	7.09531i	−0.911900	+	0.331905i	−0.156889	+	0.987616i	$0.550146\pi$
$458$		0			0
$459$	8.65963	+	4.19251i	0.404197	+	0.195689i
$460$		0			0
$461$	−38.8668	+	14.1464i	−1.81021	+	0.658861i	−0.813162	+	0.582037i	$0.802256\pi$
$461$	−38.8668	+	14.1464i	−1.81021	+	0.658861i	−0.997045	+	0.0768243i	$0.975522\pi$
$462$		0			0
$463$	18.1032	−	15.1904i	0.841328	−	0.705958i	−0.116534	−	0.993187i	$-0.537178\pi$
$463$	18.1032	−	15.1904i	0.841328	−	0.705958i	0.957862	+	0.287229i	$0.0927340\pi$
$464$		0			0
$465$	5.06279	−	3.08898i	0.234781	−	0.143248i
$466$		0			0
$467$	−10.5877	+	18.3384i	−0.489939	+	0.848599i	−0.999933	−	0.0115789i	$-0.996314\pi$
$467$	−10.5877	+	18.3384i	−0.489939	+	0.848599i	0.509994	+	0.860178i	$0.329648\pi$
$468$		0			0
$469$	10.8874	+	18.8576i	0.502735	+	0.870763i
$470$		0			0
$471$	24.5385	+	3.71601i	1.13067	+	0.171225i
$472$		0			0
$473$	12.0403	+	4.38231i	0.553613	+	0.201499i
$474$		0			0
$475$	4.41960	−	25.0648i	0.202785	−	1.15005i
$476$		0			0
$477$	0.553208	+	0.420249i	0.0253296	+	0.0192419i
$478$		0			0
$479$	−10.2101	−	8.56728i	−0.466511	−	0.391449i	0.379009	−	0.925393i	$-0.376265\pi$
$479$	−10.2101	−	8.56728i	−0.466511	−	0.391449i	−0.845520	+	0.533944i	$0.820709\pi$
$480$		0			0
$481$	6.24724	+	35.4299i	0.284850	+	1.61546i
$482$		0			0
$483$	−12.8883	+	38.2719i	−0.586437	+	1.74143i
$484$		0			0
$485$	8.89905			0.404085
$486$		0			0
$487$	18.3872			0.833202			0.416601	−	0.909090i	$-0.363221\pi$
$487$	18.3872			0.833202			0.416601	+	0.909090i	$0.363221\pi$
$488$		0			0
$489$	−7.89976	+	23.4585i	−0.357240	+	1.06083i
$490$		0			0
$491$	−3.35081	−	19.0034i	−0.151220	−	0.857610i	−0.962161	−	0.272482i	$-0.912155\pi$
$491$	−3.35081	−	19.0034i	−0.151220	−	0.857610i	0.810941	−	0.585128i	$-0.198956\pi$
$492$		0			0
$493$	−1.77749	−	1.49150i	−0.0800543	−	0.0671736i
$494$		0			0
$495$	10.1197	+	7.68754i	0.454848	+	0.345529i
$496$		0			0
$497$	3.73326	−	21.1724i	0.167459	−	0.949710i
$498$		0			0
$499$	−15.3641	−	5.59206i	−0.687790	−	0.250335i	−0.0256013	−	0.999672i	$-0.508150\pi$
$499$	−15.3641	−	5.59206i	−0.687790	−	0.250335i	−0.662189	+	0.749337i	$0.730372\pi$
$500$		0			0
$501$	−16.3632	−	2.47797i	−0.731052	−	0.110708i
$502$		0			0
$503$	−19.9756	−	34.5988i	−0.890670	−	1.54269i	−0.839074	−	0.544018i	$-0.816902\pi$
$503$	−19.9756	−	34.5988i	−0.890670	−	1.54269i	−0.0515962	−	0.998668i	$-0.516431\pi$
$504$		0			0
$505$	−2.76135	+	4.78280i	−0.122878	+	0.212832i
$506$		0			0
$507$	−3.49850	+	2.13455i	−0.155374	+	0.0947987i
$508$		0			0
$509$	24.7041	−	20.7292i	1.09499	−	0.918805i	0.0979108	−	0.995195i	$-0.468784\pi$
$509$	24.7041	−	20.7292i	1.09499	−	0.918805i	0.997078	+	0.0763905i	$0.0243396\pi$
$510$		0			0
$511$	−7.88865	+	2.87123i	−0.348973	+	0.127016i
$512$		0			0
$513$	−2.42857	−	33.3389i	−0.107224	−	1.47195i
$514$		0			0
$515$	−10.3541	+	3.76858i	−0.456256	+	0.166064i
$516$		0			0
$517$	8.78298	−	7.36980i	0.386275	−	0.324123i
$518$		0			0
$519$	15.1790	+	8.27969i	0.666282	+	0.363438i
$520$		0			0
$521$	−18.6915	+	32.3746i	−0.818890	+	1.41836i	0.0876112	+	0.996155i	$0.472077\pi$
$521$	−18.6915	+	32.3746i	−0.818890	+	1.41836i	−0.906501	+	0.422204i	$0.861257\pi$
$522$		0			0
$523$	14.5920	+	25.2740i	0.638062	+	1.10516i	0.985858	+	0.167586i	$0.0535971\pi$
$523$	14.5920	+	25.2740i	0.638062	+	1.10516i	−0.347795	+	0.937570i	$0.613070\pi$
$524$		0			0
$525$	11.4039	−	14.2797i	0.497706	−	0.623215i
$526$		0			0
$527$	5.83177	+	2.12259i	0.254036	+	0.0924615i
$528$		0			0
$529$	9.27951	−	52.6267i	0.403457	−	2.28812i
$530$		0			0
$531$	−4.85080	+	9.42954i	−0.210507	+	0.409207i
$532$		0			0
$533$	11.3096	+	9.48989i	0.489874	+	0.411053i
$534$		0			0
$535$	−2.63456	−	14.9413i	−0.113902	−	0.645969i
$536$		0			0
$537$	38.2179	−	7.69828i	1.64922	−	0.332206i
$538$		0			0
$539$	0.463627			0.0199698
$540$		0			0
$541$	12.6132			0.542283			0.271142	−	0.962539i	$-0.412599\pi$
$541$	12.6132			0.542283			0.271142	+	0.962539i	$0.412599\pi$
$542$		0			0
$543$	−0.568185	−	0.644733i	−0.0243831	−	0.0276682i
$544$		0			0
$545$	−3.13281	−	17.7671i	−0.134195	−	0.761057i
$546$		0			0
$547$	−22.3688	−	18.7696i	−0.956419	−	0.802531i	0.0239476	−	0.999713i	$-0.492377\pi$
$547$	−22.3688	−	18.7696i	−0.956419	−	0.802531i	−0.980367	+	0.197182i	$0.936821\pi$
$548$		0			0
$549$	−0.350851	−	1.54708i	−0.0149740	−	0.0660278i
$550$		0			0
$551$	−1.39990	+	7.93924i	−0.0596379	+	0.338223i
$552$		0			0
$553$	6.49292	+	2.36323i	0.276107	+	0.100495i
$554$		0			0
$555$	−5.92248	−	15.1211i	−0.251395	−	0.641855i
$556$		0			0
$557$	−21.6137	−	37.4361i	−0.915804	−	1.58622i	−0.805720	−	0.592296i	$-0.798222\pi$
$557$	−21.6137	−	37.4361i	−0.915804	−	1.58622i	−0.110083	−	0.993922i	$-0.535112\pi$
$558$		0			0
$559$	6.05629	−	10.4898i	0.256154	−	0.443671i
$560$		0			0
$561$	0.322308	+	13.2946i	0.0136079	+	0.561298i
$562$		0			0
$563$	5.18375	−	4.34968i	0.218469	−	0.183317i	−0.526984	−	0.849875i	$-0.676677\pi$
$563$	5.18375	−	4.34968i	0.218469	−	0.183317i	0.745454	+	0.666558i	$0.232233\pi$
$564$		0			0
$565$	1.87806	−	0.683558i	0.0790106	−	0.0287575i
$566$		0			0
$567$	9.93211	−	21.8497i	0.417109	−	0.917601i
$568$		0			0
$569$	1.78951	−	0.651329i	0.0750203	−	0.0273051i	−0.304237	−	0.952596i	$-0.598402\pi$
$569$	1.78951	−	0.651329i	0.0750203	−	0.0273051i	0.379258	+	0.925291i	$0.376179\pi$
$570$		0			0
$571$	8.59231	−	7.20980i	0.359577	−	0.301721i	−0.445045	−	0.895508i	$-0.646812\pi$
$571$	8.59231	−	7.20980i	0.359577	−	0.301721i	0.804622	+	0.593787i	$0.202368\pi$
$572$		0			0
$573$	0.301757	+	12.4469i	0.0126061	+	0.519976i
$574$		0			0
$575$	−17.2950	+	29.9558i	−0.721252	+	1.24924i
$576$		0			0
$577$	−19.6634	−	34.0581i	−0.818600	−	1.41786i	−0.906714	−	0.421746i	$-0.861417\pi$
$577$	−19.6634	−	34.0581i	−0.818600	−	1.41786i	0.0881143	−	0.996110i	$-0.471916\pi$
$578$		0			0
$579$	−8.50849	−	21.7236i	−0.353601	−	0.902803i
$580$		0			0
$581$	20.1473	+	7.33303i	0.835852	+	0.304225i
$582$		0			0
$583$	−0.166748	+	0.945677i	−0.00690601	+	0.0391659i
$584$		0			0
$585$	8.81810	−	8.15924i	0.364583	−	0.337343i
$586$		0			0
$587$	−5.98030	−	5.01807i	−0.246834	−	0.207118i	0.510974	−	0.859596i	$-0.329285\pi$
$587$	−5.98030	−	5.01807i	−0.246834	−	0.207118i	−0.757807	+	0.652478i	$0.773729\pi$
$588$		0			0
$589$	−3.74419	−	21.2344i	−0.154277	−	0.874947i
$590$		0			0
$591$	−5.80235	−	6.58407i	−0.238677	−	0.270832i
$592$		0			0
$593$	−12.2602			−0.503465			−0.251733	−	0.967797i	$-0.581000\pi$
$593$	−12.2602			−0.503465			−0.251733	+	0.967797i	$0.581000\pi$
$594$		0			0
$595$	−5.04444			−0.206802
$596$		0			0
$597$	30.4694	−	6.13750i	1.24703	−	0.251191i
$598$		0			0
$599$	3.40179	+	19.2925i	0.138993	+	0.788271i	0.971995	+	0.235001i	$0.0755093\pi$
$599$	3.40179	+	19.2925i	0.138993	+	0.788271i	−0.833002	+	0.553270i	$0.813380\pi$
$600$		0			0
$601$	−3.14380	−	2.63796i	−0.128238	−	0.107605i	0.576413	−	0.817159i	$-0.304452\pi$
$601$	−3.14380	−	2.63796i	−0.128238	−	0.107605i	−0.704651	+	0.709554i	$0.748896\pi$
$602$		0			0
$603$	13.2614	+	20.5953i	0.540045	+	0.838707i
$604$		0			0
$605$	−1.09892	+	6.23230i	−0.0446776	+	0.253379i
$606$		0			0
$607$	15.2753	+	5.55976i	0.620006	+	0.225664i	0.632876	−	0.774253i	$-0.281874\pi$
$607$	15.2753	+	5.55976i	0.620006	+	0.225664i	−0.0128694	+	0.999917i	$0.504097\pi$
$608$		0			0
$609$	−3.61216	+	4.52306i	−0.146372	+	0.183284i
$610$		0			0
$611$	−5.41930	−	9.38650i	−0.219241	−	0.379737i
$612$		0			0
$613$	−8.52562	+	14.7668i	−0.344347	+	0.596426i	−0.985235	−	0.171208i	$-0.945233\pi$
$613$	−8.52562	+	14.7668i	−0.344347	+	0.596426i	0.640888	+	0.767634i	$0.278566\pi$
$614$		0			0
$615$	−5.85045	−	3.19126i	−0.235913	−	0.128684i
$616$		0			0
$617$	−21.2848	+	17.8601i	−0.856895	+	0.719020i	−0.961297	−	0.275515i	$-0.911152\pi$
$617$	−21.2848	+	17.8601i	−0.856895	+	0.719020i	0.104402	+	0.994535i	$0.466707\pi$
$618$		0			0
$619$	7.09199	−	2.58127i	0.285051	−	0.103750i	−0.195538	−	0.980696i	$-0.562645\pi$
$619$	7.09199	−	2.58127i	0.285051	−	0.103750i	0.480589	+	0.876946i	$0.340423\pi$
$620$		0			0
$621$	−12.3952	+	43.7058i	−0.497404	+	1.75385i
$622$		0			0
$623$	30.7078	−	11.1767i	1.23028	−	0.447786i
$624$		0			0
$625$	7.99324	−	6.70713i	0.319730	−	0.268285i
$626$		0			0
$627$	39.4418	−	24.0648i	1.57516	−	0.961056i
$628$		0			0
$629$	8.49671	−	14.7167i	0.338786	−	0.586794i
$630$		0			0
$631$	−12.3054	−	21.3136i	−0.489872	−	0.848483i	0.510060	−	0.860139i	$-0.329623\pi$
$631$	−12.3054	−	21.3136i	−0.489872	−	0.848483i	−0.999932	+	0.0116559i	$0.996290\pi$
$632$		0			0
$633$	−8.72286	−	1.32096i	−0.346703	−	0.0525033i
$634$		0			0
$635$	−5.35667	−	1.94967i	−0.212573	−	0.0773702i
$636$		0			0
$637$	0.0761068	−	0.431623i	0.00301546	−	0.0171015i
$638$		0			0
$639$	3.04060	−	23.9933i	0.120284	−	0.949159i
$640$		0			0
$641$	23.1248	+	19.4040i	0.913373	+	0.766411i	0.972758	−	0.231824i	$-0.0744695\pi$
$641$	23.1248	+	19.4040i	0.913373	+	0.766411i	−0.0593849	+	0.998235i	$0.518914\pi$
$642$		0			0
$643$	2.06856	+	11.7314i	0.0815762	+	0.462641i	0.998043	+	0.0625308i	$0.0199172\pi$
$643$	2.06856	+	11.7314i	0.0815762	+	0.462641i	−0.916467	+	0.400111i	$0.868972\pi$
$644$		0			0
$645$	−1.74494	+	5.18163i	−0.0687069	+	0.204026i
$646$		0			0
$647$	−20.4896			−0.805528			−0.402764	−	0.915304i	$-0.631951\pi$
$647$	−20.4896			−0.805528			−0.402764	+	0.915304i	$0.631951\pi$
$648$		0			0
$649$	−14.6571			−0.575343
$650$		0			0
$651$	4.94093	−	14.6722i	0.193650	−	0.575047i
$652$		0			0
$653$	−8.53662	−	48.4136i	−0.334064	−	1.89457i	−0.436286	−	0.899808i	$-0.643706\pi$
$653$	−8.53662	−	48.4136i	−0.334064	−	1.89457i	0.102222	−	0.994762i	$-0.467405\pi$
$654$		0			0
$655$	1.21091	+	1.01608i	0.0473142	+	0.0397014i
$656$		0			0
$657$	−8.70735	+	3.65622i	−0.339706	+	0.142643i
$658$		0			0
$659$	−4.93483	+	27.9868i	−0.192234	+	1.09021i	0.724070	+	0.689727i	$0.242269\pi$
$659$	−4.93483	+	27.9868i	−0.192234	+	1.09021i	−0.916303	+	0.400485i	$0.868842\pi$
$660$		0			0
$661$	−40.5404	−	14.7555i	−1.57684	−	0.573923i	−0.602326	−	0.798251i	$-0.705759\pi$
$661$	−40.5404	−	14.7555i	−1.57684	−	0.573923i	−0.974514	+	0.224328i	$0.927981\pi$
$662$		0			0
$663$	12.4298	+	1.88232i	0.482733	+	0.0731032i
$664$		0			0
$665$	8.76306	+	15.1781i	0.339817	+	0.588580i
$666$		0			0
$667$	5.47817	−	9.48848i	0.212116	−	0.367395i
$668$		0			0
$669$	5.64244	−	3.44264i	0.218149	−	0.133100i
$670$		0			0
$671$	1.67971	−	1.40944i	0.0648443	−	0.0544108i
$672$		0			0
$673$	33.9219	−	12.3466i	1.30759	−	0.475926i	0.408132	−	0.912923i	$-0.366180\pi$
$673$	33.9219	−	12.3466i	1.30759	−	0.475926i	0.899463	+	0.436997i	$0.143958\pi$
$674$		0			0
$675$	12.0352	−	16.6666i	0.463236	−	0.641498i
$676$		0			0
$677$	−40.5216	+	14.7487i	−1.55737	+	0.566837i	−0.970132	−	0.242576i	$-0.922008\pi$
$677$	−40.5216	+	14.7487i	−1.55737	+	0.566837i	−0.587239	+	0.809413i	$0.699785\pi$
$678$		0			0
$679$	17.7955	−	14.9322i	0.682928	−	0.573045i
$680$		0			0
$681$	30.9871	+	16.9026i	1.18743	+	0.647708i
$682$		0			0
$683$	0.0895535	−	0.155111i	0.00342667	−	0.00593517i	−0.864307	−	0.502965i	$-0.832243\pi$
$683$	0.0895535	−	0.155111i	0.00342667	−	0.00593517i	0.867734	+	0.497029i	$0.165576\pi$
$684$		0			0
$685$	−10.2462	−	17.7470i	−0.391489	−	0.678078i
$686$		0			0
$687$	−1.63000	+	2.04104i	−0.0621882	+	0.0778706i
$688$		0			0
$689$	0.853026	+	0.310476i	0.0324977	+	0.0118282i
$690$		0			0
$691$	5.97830	−	33.9046i	0.227425	−	1.28979i	−0.630568	−	0.776134i	$-0.717178\pi$
$691$	5.97830	−	33.9046i	0.227425	−	1.28979i	0.857994	−	0.513660i	$-0.171711\pi$
$692$		0			0
$693$	33.1358	−	1.60761i	1.25873	−	0.0610680i
$694$		0			0
$695$	3.05230	+	2.56119i	0.115780	+	0.0971514i
$696$		0			0
$697$	−1.21095	−	6.86764i	−0.0458680	−	0.260130i
$698$		0			0
$699$	−34.2434	+	6.89771i	−1.29521	+	0.260895i
$700$		0			0
$701$	−17.3215			−0.654224			−0.327112	−	0.944985i	$-0.606076\pi$
$701$	−17.3215			−0.654224			−0.327112	+	0.944985i	$0.606076\pi$
$702$		0			0
$703$	−59.0410			−2.22677
$704$		0			0
$705$	3.23474	+	3.67054i	0.121827	+	0.138240i
$706$		0			0
$707$	2.50342	+	14.1976i	0.0941508	+	0.533956i
$708$		0			0
$709$	−28.0038	−	23.4980i	−1.05171	−	0.882485i	−0.0584333	−	0.998291i	$-0.518611\pi$
$709$	−28.0038	−	23.4980i	−1.05171	−	0.882485i	−0.993272	+	0.115806i	$0.963055\pi$
$710$		0			0
$711$	7.42442	+	2.30143i	0.278438	+	0.0863103i
$712$		0			0
$713$	−5.08858	+	28.8588i	−0.190569	+	1.08077i
$714$		0			0
$715$	15.6043	+	5.67948i	0.583566	+	0.212401i
$716$		0			0
$717$	7.98645	+	20.3908i	0.298259	+	0.761507i
$718$		0			0
$719$	−22.8804	−	39.6301i	−0.853296	−	1.47795i	−0.878216	−	0.478263i	$-0.841266\pi$
$719$	−22.8804	−	39.6301i	−0.853296	−	1.47795i	0.0249200	−	0.999689i	$-0.492067\pi$
$720$		0			0
$721$	−14.3816	+	24.9097i	−0.535601	+	0.927687i
$722$		0			0
$723$	1.16867	+	48.2052i	0.0434632	+	1.79277i
$724$		0			0
$725$	−3.79803	+	3.18692i	−0.141055	+	0.118359i
$726$		0			0
$727$	8.24873	−	3.00229i	0.305928	−	0.111349i	−0.184494	−	0.982834i	$-0.559065\pi$
$727$	8.24873	−	3.00229i	0.305928	−	0.111349i	0.490423	+	0.871485i	$0.336842\pi$
$728$		0			0
$729$	9.96884	−	25.0923i	0.369216	−	0.929343i
$730$		0			0
$731$	−5.37632	+	1.95682i	−0.198850	+	0.0723756i
$732$		0			0
$733$	25.4717	−	21.3733i	0.940820	−	0.789441i	−0.0369082	−	0.999319i	$-0.511751\pi$
$733$	25.4717	−	21.3733i	0.940820	−	0.789441i	0.977728	+	0.209877i	$0.0673065\pi$
$734$		0			0
$735$	0.00479489	+	0.197780i	0.000176862	+	0.00729522i
$736$		0			0
$737$	−16.9291	+	29.3220i	−0.623590	+	1.08009i
$738$		0			0
$739$	−1.03598	−	1.79437i	−0.0381091	−	0.0660069i	0.846342	−	0.532640i	$-0.178800\pi$
$739$	−1.03598	−	1.79437i	−0.0381091	−	0.0660069i	−0.884451	+	0.466633i	$0.845467\pi$
$740$		0			0
$741$	−15.9291	−	40.6696i	−0.585169	−	1.49404i
$742$		0			0
$743$	3.31599	+	1.20692i	0.121652	+	0.0442777i	0.402129	−	0.915583i	$-0.368270\pi$
$743$	3.31599	+	1.20692i	0.121652	+	0.0442777i	−0.280477	+	0.959861i	$0.590493\pi$
$744$		0			0
$745$	1.74459	−	9.89408i	0.0639169	−	0.362491i
$746$		0			0
$747$	23.0378	+	7.14126i	0.842908	+	0.261285i
$748$		0			0
$749$	−30.3391	−	25.4576i	−1.10857	−	0.930199i
$750$		0			0
$751$	6.65211	+	37.7260i	0.242739	+	1.37664i	0.825685	+	0.564131i	$0.190789\pi$
$751$	6.65211	+	37.7260i	0.242739	+	1.37664i	−0.582946	+	0.812511i	$0.698100\pi$
$752$		0			0
$753$	−0.771023	−	0.874899i	−0.0280976	−	0.0318831i
$754$		0			0
$755$	4.10060			0.149236
$756$		0			0
$757$	12.3900			0.450322			0.225161	−	0.974322i	$-0.427709\pi$
$757$	12.3900			0.450322			0.225161	+	0.974322i	$0.427709\pi$
$758$		0			0
$759$	−61.5570	+	12.3995i	−2.23438	+	0.450074i
$760$		0			0
$761$	−1.41032	−	7.99834i	−0.0511241	−	0.289939i	0.948517	−	0.316726i	$-0.102584\pi$
$761$	−1.41032	−	7.99834i	−0.0511241	−	0.289939i	−0.999641	+	0.0267867i	$0.991473\pi$
$762$		0			0
$763$	−36.0770	−	30.2722i	−1.30607	−	1.09593i
$764$		0			0
$765$	−5.66804	+	0.274989i	−0.204929	+	0.00994225i
$766$		0			0
$767$	−2.40605	+	13.6454i	−0.0868774	+	0.492706i
$768$		0			0
$769$	24.7906	+	9.02303i	0.893971	+	0.325379i	0.747834	−	0.663885i	$-0.231094\pi$
$769$	24.7906	+	9.02303i	0.893971	+	0.325379i	0.146137	+	0.989264i	$0.453316\pi$
$770$		0			0
$771$	33.1154	−	41.4663i	1.19262	−	1.49337i
$772$		0			0
$773$	−5.39129	−	9.33798i	−0.193911	−	0.335864i	0.752632	−	0.658442i	$-0.228784\pi$
$773$	−5.39129	−	9.33798i	−0.193911	−	0.335864i	−0.946543	+	0.322578i	$0.895451\pi$
$774$		0			0
$775$	6.63032	−	11.4840i	0.238168	−	0.412519i
$776$		0			0
$777$	−37.2157	−	20.3001i	−1.33511	−	0.728263i
$778$		0			0
$779$	−18.5602	+	15.5739i	−0.664989	+	0.557992i
$780$		0			0
$781$	31.4131	−	11.4334i	1.12405	−	0.409120i
$782$		0			0
$783$	−3.81214	+	5.27913i	−0.136235	+	0.188661i
$784$		0			0
$785$	−13.7554	+	5.00657i	−0.490952	+	0.178692i
$786$		0			0
$787$	−21.9933	+	18.4546i	−0.783976	+	0.657834i	−0.944247	−	0.329239i	$-0.893208\pi$
$787$	−21.9933	+	18.4546i	−0.783976	+	0.657834i	0.160270	+	0.987073i	$0.448763\pi$
$788$		0			0
$789$	−8.78074	+	5.35743i	−0.312603	+	0.190730i
$790$		0			0
$791$	2.60859	−	4.51821i	0.0927509	−	0.160649i
$792$		0			0
$793$	−1.03642	−	1.79513i	−0.0368042	−	0.0637468i
$794$		0			0
$795$	−0.405143	−	0.0613533i	−0.0143690	−	0.00217598i
$796$		0			0
$797$	18.3516	+	6.67942i	0.650045	+	0.236597i	0.645933	−	0.763394i	$-0.276469\pi$
$797$	18.3516	+	6.67942i	0.650045	+	0.236597i	0.00411268	+	0.999992i	$0.498691\pi$
$798$		0			0
$799$	−0.889009	+	5.04182i	−0.0314509	+	0.178367i
$800$		0			0
$801$	33.8947	−	14.2324i	1.19761	−	0.502878i
$802$		0			0
$803$	−9.99950	−	8.39057i	−0.352875	−	0.296097i
$804$		0			0
$805$	−4.13613	−	23.4572i	−0.145779	−	0.826756i
$806$		0			0
$807$	−8.49194	+	25.2170i	−0.298931	+	0.887679i
$808$		0			0
$809$	44.3315			1.55861			0.779307	−	0.626643i	$-0.215571\pi$
$809$	44.3315			1.55861			0.779307	+	0.626643i	$0.215571\pi$
$810$		0			0
$811$	−47.8398			−1.67988			−0.839941	−	0.542677i	$-0.817411\pi$
$811$	−47.8398			−1.67988			−0.839941	+	0.542677i	$0.817411\pi$
$812$		0			0
$813$	−8.06714	+	23.9555i	−0.282927	+	0.840156i
$814$		0			0
$815$	−2.53521	−	14.3779i	−0.0888045	−	0.503635i
$816$		0			0
$817$	15.2274	+	12.7773i	0.532740	+	0.447022i
$818$		0			0
$819$	3.94279	−	31.1124i	0.137772	−	1.08716i
$820$		0			0
$821$	−5.56302	+	31.5494i	−0.194151	+	1.10108i	0.719473	+	0.694521i	$0.244384\pi$
$821$	−5.56302	+	31.5494i	−0.194151	+	1.10108i	−0.913623	+	0.406562i	$0.866728\pi$
$822$		0			0
$823$	7.96990	+	2.90081i	0.277813	+	0.101116i	0.477169	−	0.878811i	$-0.341663\pi$
$823$	7.96990	+	2.90081i	0.277813	+	0.101116i	−0.199356	+	0.979927i	$0.563885\pi$
$824$		0			0
$825$	28.0950	+	4.25459i	0.978142	+	0.148126i
$826$		0			0
$827$	10.8012	+	18.7083i	0.375596	+	0.650552i	0.990416	−	0.138116i	$-0.0441047\pi$
$827$	10.8012	+	18.7083i	0.375596	+	0.650552i	−0.614820	+	0.788668i	$0.710771\pi$
$828$		0			0
$829$	−23.3196	+	40.3907i	−0.809922	+	1.40283i	0.102996	+	0.994682i	$0.467157\pi$
$829$	−23.3196	+	40.3907i	−0.809922	+	1.40283i	−0.912918	+	0.408144i	$0.866176\pi$
$830$		0			0
$831$	−8.41126	+	5.13200i	−0.291783	+	0.178027i
$832$		0			0
$833$	−0.158588	+	0.133071i	−0.00549474	+	0.00461064i
$834$		0			0
$835$	9.17263	−	3.33856i	0.317432	−	0.115536i
$836$		0			0
$837$	4.75191	−	16.7553i	0.164250	−	0.579149i
$838$		0			0
$839$	12.8905	−	4.69176i	0.445030	−	0.161978i	−0.109778	−	0.993956i	$-0.535014\pi$
$839$	12.8905	−	4.69176i	0.445030	−	0.161978i	0.554808	+	0.831978i	$0.312792\pi$
$840$		0			0
$841$	−21.0123	+	17.6314i	−0.724561	+	0.607979i
$842$		0			0
$843$	20.7648	+	11.3266i	0.715179	+	0.390110i
$844$		0			0
$845$	1.20861	−	2.09338i	0.0415775	−	0.0720144i
$846$		0			0
$847$	8.25999	+	14.3067i	0.283817	+	0.491585i
$848$		0			0
$849$	−28.0332	+	35.1025i	−0.962098	+	1.20472i
$850$		0			0
$851$	75.4011	+	27.4438i	2.58472	+	0.940760i
$852$		0			0
$853$	3.39926	−	19.2781i	0.116388	−	0.660071i	−0.869665	−	0.493642i	$-0.835665\pi$
$853$	3.39926	−	19.2781i	0.116388	−	0.660071i	0.986053	−	0.166429i	$-0.0532236\pi$
$854$		0			0
$855$	10.6738	+	16.5767i	0.365036	+	0.566912i
$856$		0			0
$857$	−4.11703	−	3.45460i	−0.140635	−	0.118007i	0.569756	−	0.821814i	$-0.307038\pi$
$857$	−4.11703	−	3.45460i	−0.140635	−	0.118007i	−0.710391	+	0.703807i	$0.751482\pi$
$858$		0			0
$859$	−5.41073	−	30.6858i	−0.184612	−	1.04698i	−0.926453	−	0.376410i	$-0.877159\pi$
$859$	−5.41073	−	30.6858i	−0.184612	−	1.04698i	0.741842	−	0.670575i	$-0.233953\pi$
$860$		0			0
$861$	−17.0540	+	3.43521i	−0.581198	+	0.117072i
$862$		0			0
$863$	2.34241			0.0797367			0.0398683	−	0.999205i	$-0.487306\pi$
$863$	2.34241			0.0797367			0.0398683	+	0.999205i	$0.487306\pi$
$864$		0			0
$865$	−10.1981			−0.346746
$866$		0			0
$867$	15.5418	+	17.6357i	0.527828	+	0.598940i
$868$		0			0
$869$	1.86566	+	10.5807i	0.0632880	+	0.358924i
$870$		0			0
$871$	24.5190	+	20.5739i	0.830793	+	0.697118i
$872$		0			0
$873$	19.1814	−	17.7482i	0.649193	−	0.600687i
$874$		0			0
$875$	−4.23710	+	24.0298i	−0.143240	+	0.812356i
$876$		0			0
$877$	42.5834	+	15.4991i	1.43794	+	0.523367i	0.939196	−	0.343383i	$-0.111573\pi$
$877$	42.5834	+	15.4991i	1.43794	+	0.523367i	0.498743	+	0.866750i	$0.333795\pi$
$878$		0			0
$879$	12.5648	+	32.0802i	0.423801	+	1.08204i
$880$		0			0
$881$	5.46101	+	9.45874i	0.183986	+	0.318673i	0.943234	−	0.332128i	$-0.107767\pi$
$881$	5.46101	+	9.45874i	0.183986	+	0.318673i	−0.759248	+	0.650801i	$0.774433\pi$
$882$		0			0
$883$	12.8886	−	22.3238i	0.433737	−	0.751254i	−0.563455	−	0.826147i	$-0.690528\pi$
$883$	12.8886	−	22.3238i	0.433737	−	0.751254i	0.997192	+	0.0748928i	$0.0238615\pi$
$884$		0			0
$885$	−0.151586	−	6.25263i	−0.00509551	−	0.210180i
$886$		0			0
$887$	31.1646	−	26.1502i	1.04640	−	0.878038i	0.0536937	−	0.998557i	$-0.482901\pi$
$887$	31.1646	−	26.1502i	1.04640	−	0.878038i	0.992711	+	0.120520i	$0.0384561\pi$
$888$		0			0
$889$	−13.9832	+	5.08947i	−0.468982	+	0.170695i
$890$		0			0
$891$	37.1446	−	3.61269i	1.24439	−	0.121030i
$892$		0			0
$893$	16.7146	−	6.08360i	0.559331	−	0.203580i
$894$		0			0
$895$	−17.6147	+	14.7804i	−0.588793	+	0.494056i
$896$		0			0
$897$	1.43869	+	59.3433i	0.0480366	+	1.98141i
$898$		0			0
$899$	−2.10015	+	3.63756i	−0.0700438	+	0.121319i
$900$		0			0
$901$	−0.214392	−	0.371338i	−0.00714244	−	0.0123711i
$902$		0			0
$903$	5.20516	+	13.2897i	0.173217	+	0.442252i
$904$		0			0
$905$	0.476302	+	0.173360i	0.0158328	+	0.00576267i
$906$		0			0
$907$	0.940619	−	5.33451i	0.0312327	−	0.177130i	−0.965201	−	0.261509i	$-0.915780\pi$
$907$	0.940619	−	5.33451i	0.0312327	−	0.177130i	0.996434	+	0.0843797i	$0.0268909\pi$
$908$		0			0
$909$	3.58686	+	15.8163i	0.118969	+	0.524593i
$910$		0			0
$911$	−3.30707	−	2.77496i	−0.109568	−	0.0919385i	0.586358	−	0.810052i	$-0.300561\pi$
$911$	−3.30707	−	2.77496i	−0.109568	−	0.0919385i	−0.695926	+	0.718114i	$0.745006\pi$
$912$		0			0
$913$	5.78907	+	32.8315i	0.191590	+	1.08656i
$914$		0			0
$915$	0.618629	+	0.701974i	0.0204512	+	0.0232065i
$916$		0			0
$917$	4.12640			0.136266
$918$		0			0
$919$	33.7655			1.11382			0.556911	−	0.830572i	$-0.311987\pi$
$919$	33.7655			1.11382			0.556911	+	0.830572i	$0.311987\pi$
$920$		0			0
$921$	16.1554	−	3.25420i	0.532337	−	0.107230i
$922$		0			0
$923$	−5.48757	−	31.1216i	−0.180626	−	1.02438i
$924$		0			0
$925$	−27.8153	−	23.3398i	−0.914563	−	0.767409i
$926$		0			0
$927$	−14.8016	+	28.7732i	−0.486150	+	0.945035i
$928$		0			0
$929$	7.86087	−	44.5812i	0.257907	−	1.46266i	−0.530593	−	0.847626i	$-0.678031\pi$
$929$	7.86087	−	44.5812i	0.257907	−	1.46266i	0.788500	−	0.615035i	$-0.210858\pi$
$930$		0			0
$931$	0.675888	+	0.246003i	0.0221513	+	0.00806243i
$932$		0			0
$933$	15.6333	−	19.5757i	0.511812	−	0.640879i
$934$		0			0
$935$	−3.92184	−	6.79282i	−0.128258	−	0.222149i
$936$		0			0
$937$	6.86473	−	11.8901i	0.224261	−	0.388431i	−0.731837	−	0.681480i	$-0.761337\pi$
$937$	6.86473	−	11.8901i	0.224261	−	0.388431i	0.956097	+	0.293049i	$0.0946699\pi$
$938$		0			0
$939$	−20.3604	−	11.1060i	−0.664437	−	0.362432i
$940$		0			0
$941$	−5.27589	+	4.42700i	−0.171989	+	0.144316i	−0.724719	−	0.689044i	$-0.758031\pi$
$941$	−5.27589	+	4.42700i	−0.171989	+	0.144316i	0.552730	+	0.833360i	$0.313586\pi$
$942$		0			0
$943$	30.9424	−	11.2621i	1.00762	−	0.366744i
$944$		0			0
$945$	1.02849	+	14.1189i	0.0334568	+	0.459287i
$946$		0			0
$947$	−39.5384	+	14.3908i	−1.28483	+	0.467639i	−0.892026	−	0.451985i	$-0.850716\pi$
$947$	−39.5384	+	14.3908i	−1.28483	+	0.467639i	−0.392801	+	0.919624i	$0.628494\pi$
$948$		0			0
$949$	−9.45286	+	7.93189i	−0.306853	+	0.257480i
$950$		0			0
$951$	−37.2068	+	22.7011i	−1.20651	+	0.736135i
$952$		0			0
$953$	7.20010	−	12.4709i	0.233234	−	0.403973i	−0.725524	−	0.688197i	$-0.758403\pi$
$953$	7.20010	−	12.4709i	0.233234	−	0.403973i	0.958758	+	0.284224i	$0.0917359\pi$
$954$		0			0
$955$	−3.67177	−	6.35968i	−0.118816	−	0.205795i
$956$		0			0
$957$	−8.89905	−	1.34764i	−0.287666	−	0.0435629i
$958$		0			0
$959$	−50.2681	−	18.2961i	−1.62324	−	0.590812i
$960$		0			0
$961$	−3.43231	+	19.4656i	−0.110720	+	0.627922i
$962$		0			0
$963$	−35.4775	−	26.9508i	−1.14325	−	0.868478i
$964$		0			0
$965$	10.5413	+	8.84520i	0.339336	+	0.284737i
$966$		0			0
$967$	0.257613	+	1.46100i	0.00828429	+	0.0469825i	0.988670	−	0.150107i	$-0.0479620\pi$
$967$	0.257613	+	1.46100i	0.00828429	+	0.0469825i	−0.980385	+	0.197090i	$0.936851\pi$
$968$		0			0
$969$	−6.58433	+	19.5523i	−0.211519	+	0.628109i
$970$		0			0
$971$	−57.7537			−1.85340			−0.926702	−	0.375797i	$-0.877369\pi$
$971$	−57.7537			−1.85340			−0.926702	+	0.375797i	$0.877369\pi$
$972$		0			0
$973$	10.4013			0.333449
$974$		0			0
$975$	8.57285	−	25.4572i	0.274551	−	0.815284i
$976$		0			0
$977$	6.17780	+	35.0361i	0.197645	+	1.12090i	0.908601	+	0.417666i	$0.137152\pi$
$977$	6.17780	+	35.0361i	0.197645	+	1.12090i	−0.710955	+	0.703237i	$0.751737\pi$
$978$		0			0
$979$	38.9246	+	32.6616i	1.24404	+	1.04387i
$980$		0			0
$981$	−42.1872	−	32.0479i	−1.34693	−	1.02321i
$982$		0			0
$983$	−4.42114	+	25.0735i	−0.141012	+	0.799722i	0.829470	+	0.558551i	$0.188642\pi$
$983$	−4.42114	+	25.0735i	−0.141012	+	0.799722i	−0.970483	+	0.241171i	$0.922469\pi$
$984$		0			0
$985$	4.86404	+	1.77036i	0.154981	+	0.0564085i
$986$		0			0
$987$	12.6275	+	1.91226i	0.401938	+	0.0608679i
$988$		0			0
$989$	−13.5077	−	23.3960i	−0.429519	−	0.743948i
$990$		0			0
$991$	−22.5583	+	39.0722i	−0.716589	+	1.24117i	0.245755	+	0.969332i	$0.420964\pi$
$991$	−22.5583	+	39.0722i	−0.716589	+	1.24117i	−0.962344	+	0.271836i	$0.912369\pi$
$992$		0			0
$993$	−31.2499	+	19.0666i	−0.991687	+	0.605062i
$994$		0			0
$995$	−14.0434	+	11.7838i	−0.445205	+	0.373571i
$996$		0			0
$997$	−49.8376	+	18.1394i	−1.57837	+	0.574481i	−0.974849	−	0.222865i	$-0.928459\pi$
$997$	−49.8376	+	18.1394i	−1.57837	+	0.574481i	−0.603523	+	0.797345i	$0.706237\pi$
$998$		0			0
$999$	−42.9231	−	20.7809i	−1.35803	−	0.657480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.b.385.1		12
4.3	odd	2		54.2.e.b.7.2	✓	12
12.11	even	2		162.2.e.b.19.2		12
27.4	even	9	inner	432.2.u.b.193.1		12
36.7	odd	6		486.2.e.f.379.2		12
36.11	even	6		486.2.e.g.379.1		12
36.23	even	6		486.2.e.e.217.2		12
36.31	odd	6		486.2.e.h.217.1		12
108.7	odd	18		1458.2.c.f.487.5		12
108.11	even	18		1458.2.c.g.973.2		12
108.23	even	18		162.2.e.b.145.2		12
108.31	odd	18		54.2.e.b.31.2	yes	12
108.43	odd	18		1458.2.c.f.973.5		12
108.47	even	18		1458.2.c.g.487.2		12
108.59	even	18		486.2.e.e.271.2		12
108.67	odd	18		486.2.e.f.109.2		12
108.79	odd	18		1458.2.a.g.1.2		6
108.83	even	18		1458.2.a.f.1.5		6
108.95	even	18		486.2.e.g.109.1		12
108.103	odd	18		486.2.e.h.271.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.7.2	✓	12	4.3	odd	2
54.2.e.b.31.2	yes	12	108.31	odd	18
162.2.e.b.19.2		12	12.11	even	2
162.2.e.b.145.2		12	108.23	even	18
432.2.u.b.193.1		12	27.4	even	9	inner
432.2.u.b.385.1		12	1.1	even	1	trivial
486.2.e.e.217.2		12	36.23	even	6
486.2.e.e.271.2		12	108.59	even	18
486.2.e.f.109.2		12	108.67	odd	18
486.2.e.f.379.2		12	36.7	odd	6
486.2.e.g.109.1		12	108.95	even	18
486.2.e.g.379.1		12	36.11	even	6
486.2.e.h.217.1		12	36.31	odd	6
486.2.e.h.271.1		12	108.103	odd	18
1458.2.a.f.1.5		6	108.83	even	18
1458.2.a.g.1.2		6	108.79	odd	18
1458.2.c.f.487.5		12	108.7	odd	18
1458.2.c.f.973.5		12	108.43	odd	18
1458.2.c.g.487.2		12	108.47	even	18
1458.2.c.g.973.2		12	108.11	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)

\(f(q)\)	\(=\)	\(q+(-0.552775 + 1.64147i) q^{3} +(-0.177398 - 1.00607i) q^{5} +(-2.04289 - 1.71418i) q^{7} +(-2.38888 - 1.81473i) q^{9} +O(q^{10})\)	\(q+(-0.552775 + 1.64147i) q^{3} +(-0.177398 - 1.00607i) q^{5} +(-2.04289 - 1.71418i) q^{7} +(-2.38888 - 1.81473i) q^{9} +(0.720058 - 4.08365i) q^{11} +(-3.68356 - 1.34071i) q^{13} +(1.74950 + 0.264938i) q^{15} +(0.925795 + 1.60352i) q^{17} +(3.21653 - 5.57120i) q^{19} +(3.94305 - 2.40579i) q^{21} +(-6.69746 + 5.61984i) q^{23} +(3.71775 - 1.35315i) q^{25} +(4.29935 - 2.91815i) q^{27} +(-1.17759 + 0.428609i) q^{29} +(2.56758 - 2.15445i) q^{31} +(6.30518 + 3.43930i) q^{33} +(-1.36219 + 2.35938i) q^{35} +(-4.58887 - 7.94816i) q^{37} +(4.23692 - 5.30537i) q^{39} +(-3.53914 - 1.28814i) q^{41} +(-0.536567 + 3.04303i) q^{43} +(-1.40197 + 2.72531i) q^{45} +(2.11809 + 1.77729i) q^{47} +(0.0194152 + 0.110109i) q^{49} +(-3.14390 + 0.633281i) q^{51} -0.231576 q^{53} -4.23618 q^{55} +(7.36696 + 8.35948i) q^{57} +(-0.613793 - 3.48099i) q^{59} +(0.405075 + 0.339899i) q^{61} +(1.76942 + 7.80227i) q^{63} +(-0.695393 + 3.94377i) q^{65} +(-7.67276 - 2.79266i) q^{67} +(-5.52263 - 14.1002i) q^{69} +(4.03086 + 6.98165i) q^{71} +(1.57397 - 2.72620i) q^{73} +(0.166083 + 6.85058i) q^{75} +(-8.47113 + 7.10812i) q^{77} +(-2.43473 + 0.886167i) q^{79} +(2.41349 + 8.67036i) q^{81} +(-7.55488 + 2.74975i) q^{83} +(1.44903 - 1.21588i) q^{85} +(-0.0526065 - 2.16991i) q^{87} +(-6.12693 + 10.6122i) q^{89} +(5.22688 + 9.05322i) q^{91} +(2.11719 + 5.40555i) q^{93} +(-6.17564 - 2.24775i) q^{95} +(-1.51264 + 8.57862i) q^{97} +(-9.13087 + 8.44864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9} + 12 q^{11} + 12 q^{13} + 18 q^{15} - 6 q^{17} + 9 q^{19} + 24 q^{21} - 30 q^{23} - 9 q^{25} + 15 q^{29} + 36 q^{33} - 3 q^{35} - 15 q^{37} + 42 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{45} + 9 q^{47} - 39 q^{49} + 27 q^{51} - 12 q^{53} - 18 q^{55} + 18 q^{57} - 12 q^{59} - 36 q^{61} - 3 q^{63} - 15 q^{65} - 36 q^{67} + 18 q^{69} - 12 q^{71} - 21 q^{73} - 30 q^{75} + 3 q^{77} - 39 q^{79} - 18 q^{83} + 45 q^{85} - 27 q^{87} + 12 q^{89} + 6 q^{91} - 33 q^{93} + 15 q^{95} + 39 q^{97} - 9 q^{99}+O(q^{100}) \) 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

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