LMFDB - Embedded newform 567.2.i.f.269.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(215,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("567.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.i (of order $6$, degree $2$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.3
Root			$1.65604 - 0.956115i$ of defining polynomial
Character	$\chi$	$=$	567.269
Dual form			567.2.i.f.215.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.656620i q^{2} +1.56885 q^{4} +(-1.65604 + 2.86834i) q^{5} +(1.78442 - 1.95341i) q^{7} -2.34338i q^{8} +O(q^{10})$	\(q-0.656620i q^{2} +1.56885 q^{4} +(-1.65604 + 2.86834i) q^{5} +(1.78442 - 1.95341i) q^{7} -2.34338i q^{8} +(1.88341 + 1.08739i) q^{10} +(2.02943 - 1.17169i) q^{11} +(-1.36834 + 0.790014i) q^{13} +(-1.28265 - 1.17169i) q^{14} +1.59899 q^{16} +(-0.568650 + 0.984931i) q^{17} +(3.85327 - 2.22469i) q^{19} +(-2.59808 + 4.50000i) q^{20} +(-0.769355 - 1.33256i) q^{22} +(8.13484 + 4.69665i) q^{23} +(-2.98493 - 5.17005i) q^{25} +(0.518739 + 0.898482i) q^{26} +(2.79949 - 3.06461i) q^{28} +(3.16673 + 1.82831i) q^{29} +7.31873i q^{31} -5.73669i q^{32} +(0.646726 + 0.373387i) q^{34} +(2.64799 + 8.35327i) q^{35} +(2.58392 + 4.47548i) q^{37} +(-1.46078 - 2.53014i) q^{38} +(6.72162 + 3.88073i) q^{40} +(-4.82277 - 8.35327i) q^{41} +(1.08392 - 1.87740i) q^{43} +(3.18386 - 1.83821i) q^{44} +(3.08392 - 5.34150i) q^{46} -5.58668 q^{47} +(-0.631656 - 6.97144i) q^{49} +(-3.39476 + 1.95997i) q^{50} +(-2.14673 + 1.23941i) q^{52} +(-8.70349 - 5.02496i) q^{53} +7.76146i q^{55} +(-4.57759 - 4.18158i) q^{56} +(1.20051 - 2.07934i) q^{58} +2.17478 q^{59} +4.00665i q^{61} +4.80563 q^{62} -0.568850 q^{64} -5.23317i q^{65} -10.7668 q^{67} +(-0.892126 + 1.54521i) q^{68} +(5.48493 - 1.73872i) q^{70} -6.39331i q^{71} +(-9.25176 - 5.34150i) q^{73} +(2.93869 - 1.69665i) q^{74} +(6.04521 - 3.49020i) q^{76} +(1.33256 - 6.05510i) q^{77} +1.23317 q^{79} +(-2.64799 + 4.58645i) q^{80} +(-5.48493 + 3.16673i) q^{82} +(0.518739 - 0.898482i) q^{83} +(-1.88341 - 3.26217i) q^{85} +(-1.23274 - 0.711723i) q^{86} +(-2.74571 - 4.75572i) q^{88} +(-3.73538 - 6.46986i) q^{89} +(-0.898482 + 4.08266i) q^{91} +(12.7623 + 7.36834i) q^{92} +3.66833i q^{94} +14.7367i q^{95} +(11.7367 + 6.77618i) q^{97} +(-4.57759 + 0.414758i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} + 4 q^{7}+O(q^{10}) $ 12 * q - 16 * q^4 + 4 * q^7	$ 12 q - 16 q^{4} + 4 q^{7} - 6 q^{10} + 24 q^{13} + 8 q^{16} - 6 q^{19} + 20 q^{22} - 24 q^{25} + 28 q^{28} + 60 q^{34} + 8 q^{37} - 12 q^{40} - 10 q^{43} + 14 q^{46} - 48 q^{49} - 78 q^{52} + 20 q^{58} + 28 q^{64} - 72 q^{67} + 54 q^{70} - 42 q^{73} + 108 q^{76} + 72 q^{79} - 54 q^{82} + 6 q^{85} - 74 q^{88} + 6 q^{91} + 60 q^{97}+O(q^{100}) $ 12 * q - 16 * q^4 + 4 * q^7 - 6 * q^10 + 24 * q^13 + 8 * q^16 - 6 * q^19 + 20 * q^22 - 24 * q^25 + 28 * q^28 + 60 * q^34 + 8 * q^37 - 12 * q^40 - 10 * q^43 + 14 * q^46 - 48 * q^49 - 78 * q^52 + 20 * q^58 + 28 * q^64 - 72 * q^67 + 54 * q^70 - 42 * q^73 + 108 * q^76 + 72 * q^79 - 54 * q^82 + 6 * q^85 - 74 * q^88 + 6 * q^91 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	0.656620i		−	0.464301i	−0.972680	−	0.232150i	$-0.925424\pi$
$2$		−	0.656620i		−	0.464301i	0.972680	−	0.232150i	$-0.0745761\pi$
$3$		0			0
$3$		0			0
$4$	1.56885			0.784425
$5$	−1.65604	+	2.86834i	−0.740603	+	1.28276i	0.211618	+	0.977352i	$0.432127\pi$
$5$	−1.65604	+	2.86834i	−0.740603	+	1.28276i	−0.952221	+	0.305410i	$0.901207\pi$
$6$		0			0
$7$	1.78442	−	1.95341i	0.674449	−	0.738321i
$7$	1.78442	−	1.95341i	0.674449	−	0.738321i
$8$		−	2.34338i		−	0.828510i
$9$		0			0
$10$	1.88341	+	1.08739i	0.595588	+	0.343863i
$11$	2.02943	−	1.17169i	0.611895	−	0.353278i	−0.161812	−	0.986822i	$-0.551734\pi$
$11$	2.02943	−	1.17169i	0.611895	−	0.353278i	0.773707	+	0.633544i	$0.218400\pi$
$12$		0			0
$13$	−1.36834	+	0.790014i	−0.379510	+	0.219110i	−0.677605	−	0.735426i	$-0.736982\pi$
$13$	−1.36834	+	0.790014i	−0.379510	+	0.219110i	0.298095	+	0.954536i	$0.403649\pi$
$14$	−1.28265	−	1.17169i	−0.342803	−	0.313147i
$15$		0			0
$16$	1.59899			0.399747
$17$	−0.568650	+	0.984931i	−0.137918	+	0.238881i	−0.926708	−	0.375781i	$-0.877374\pi$
$17$	−0.568650	+	0.984931i	−0.137918	+	0.238881i	0.788790	+	0.614662i	$0.210708\pi$
$18$		0			0
$19$	3.85327	−	2.22469i	0.884002	−	0.510379i	0.0120260	−	0.999928i	$-0.496172\pi$
$19$	3.85327	−	2.22469i	0.884002	−	0.510379i	0.871976	+	0.489549i	$0.162839\pi$
$20$	−2.59808	+	4.50000i	−0.580948	+	1.00623i
$21$		0			0
$22$	−0.769355	−	1.33256i	−0.164027	−	0.284103i
$23$	8.13484	+	4.69665i	1.69623	+	0.979320i	0.949275	+	0.314448i	$0.101819\pi$
$23$	8.13484	+	4.69665i	1.69623	+	0.979320i	0.746957	+	0.664872i	$0.231514\pi$
$24$		0			0
$25$	−2.98493	−	5.17005i	−0.596986	−	1.03401i
$26$	0.518739	+	0.898482i	0.101733	+	0.176207i
$27$		0			0
$28$	2.79949	−	3.06461i	0.529055	−	0.579158i
$29$	3.16673	+	1.82831i	0.588046	+	0.339509i	0.764325	−	0.644832i	$-0.223073\pi$
$29$	3.16673	+	1.82831i	0.588046	+	0.339509i	−0.176278	+	0.984340i	$0.556406\pi$
$30$		0			0
$31$			7.31873i			1.31448i	0.753680	+	0.657241i	$0.228277\pi$
$31$			7.31873i			1.31448i	−0.753680	+	0.657241i	$0.771723\pi$
$32$		−	5.73669i		−	1.01411i
$33$		0			0
$34$	0.646726	+	0.373387i	0.110913	+	0.0640354i
$35$	2.64799	+	8.35327i	0.447592	+	1.41196i
$36$		0			0
$37$	2.58392	+	4.47548i	0.424794	+	0.735764i	0.996401	−	0.0847630i	$-0.0270133\pi$
$37$	2.58392	+	4.47548i	0.424794	+	0.735764i	−0.571607	+	0.820527i	$0.693680\pi$
$38$	−1.46078	−	2.53014i	−0.236969	−	0.410443i
$39$		0			0
$40$	6.72162	+	3.88073i	1.06278	+	0.613597i
$41$	−4.82277	−	8.35327i	−0.753189	−	1.30456i	−0.946269	−	0.323379i	$-0.895181\pi$
$41$	−4.82277	−	8.35327i	−0.753189	−	1.30456i	0.193080	−	0.981183i	$-0.438152\pi$
$42$		0			0
$43$	1.08392	−	1.87740i	0.165296	−	0.286301i	−0.771464	−	0.636273i	$-0.780475\pi$
$43$	1.08392	−	1.87740i	0.165296	−	0.286301i	0.936760	+	0.349971i	$0.113809\pi$
$44$	3.18386	−	1.83821i	0.479986	−	0.277120i
$45$		0			0
$46$	3.08392	−	5.34150i	0.454699	−	0.787562i
$47$	−5.58668			−0.814901			−0.407450	−	0.913227i	$-0.633582\pi$
$47$	−5.58668			−0.814901			−0.407450	+	0.913227i	$0.633582\pi$
$48$		0			0
$49$	−0.631656	−	6.97144i	−0.0902366	−	0.995920i
$50$	−3.39476	+	1.95997i	−0.480092	+	0.277181i
$51$		0			0
$52$	−2.14673	+	1.23941i	−0.297697	+	0.171876i
$53$	−8.70349	−	5.02496i	−1.19552	−	0.690232i	−0.235964	−	0.971762i	$-0.575825\pi$
$53$	−8.70349	−	5.02496i	−1.19552	−	0.690232i	−0.959552	+	0.281530i	$0.909158\pi$
$54$		0			0
$55$			7.76146i			1.04655i
$56$	−4.57759	−	4.18158i	−0.611706	−	0.558788i
$57$		0			0
$58$	1.20051	−	2.07934i	0.157634	−	0.273030i
$59$	2.17478			0.283132			0.141566	−	0.989929i	$-0.454786\pi$
$59$	2.17478			0.283132			0.141566	+	0.989929i	$0.454786\pi$
$60$		0			0
$61$			4.00665i			0.512999i	0.966544	+	0.256500i	$0.0825692\pi$
$61$			4.00665i			0.512999i	−0.966544	+	0.256500i	$0.917431\pi$
$62$	4.80563			0.610315
$63$		0			0
$64$	−0.568850			−0.0711062
$65$		−	5.23317i		−	0.649095i
$66$		0			0
$67$	−10.7668			−1.31538			−0.657689	−	0.753290i	$-0.728466\pi$
$67$	−10.7668			−1.31538			−0.657689	+	0.753290i	$0.728466\pi$
$68$	−0.892126	+	1.54521i	−0.108186	+	0.187384i
$69$		0			0
$70$	5.48493	−	1.73872i	0.655575	−	0.207817i
$71$		−	6.39331i		−	0.758746i	−0.925244	−	0.379373i	$-0.876140\pi$
$71$		−	6.39331i		−	0.758746i	0.925244	−	0.379373i	$-0.123860\pi$
$72$		0			0
$73$	−9.25176	−	5.34150i	−1.08284	−	0.625176i	−0.151176	−	0.988507i	$-0.548306\pi$
$73$	−9.25176	−	5.34150i	−1.08284	−	0.625176i	−0.931660	+	0.363331i	$0.881639\pi$
$74$	2.93869	−	1.69665i	0.341616	−	0.197232i
$75$		0			0
$76$	6.04521	−	3.49020i	0.693433	−	0.400354i
$77$	1.33256	−	6.05510i	0.151860	−	0.690043i
$78$		0			0
$79$	1.23317			0.138743			0.0693714	−	0.997591i	$-0.477901\pi$
$79$	1.23317			0.138743			0.0693714	+	0.997591i	$0.477901\pi$
$80$	−2.64799	+	4.58645i	−0.296054	+	0.512780i
$81$		0			0
$82$	−5.48493	+	3.16673i	−0.605709	+	0.349706i
$83$	0.518739	−	0.898482i	0.0569390	−	0.0986213i	−0.836151	−	0.548499i	$-0.815199\pi$
$83$	0.518739	−	0.898482i	0.0569390	−	0.0986213i	0.893090	+	0.449878i	$0.148533\pi$
$84$		0			0
$85$	−1.88341	−	3.26217i	−0.204285	−	0.353832i
$86$	−1.23274	−	0.711723i	−0.132930	−	0.0767471i
$87$		0			0
$88$	−2.74571	−	4.75572i	−0.292694	−	0.506961i
$89$	−3.73538	−	6.46986i	−0.395949	−	0.685804i	0.597273	−	0.802038i	$-0.296251\pi$
$89$	−3.73538	−	6.46986i	−0.395949	−	0.685804i	−0.993222	+	0.116234i	$0.962918\pi$
$90$		0			0
$91$	−0.898482	+	4.08266i	−0.0941866	+	0.427979i
$92$	12.7623	+	7.36834i	1.33057	+	0.768203i
$93$		0			0
$94$			3.66833i			0.378359i
$95$			14.7367i			1.51195i
$96$		0			0
$97$	11.7367	+	6.77618i	1.19168	+	0.688017i	0.958687	−	0.284462i	$-0.0918149\pi$
$97$	11.7367	+	6.77618i	1.19168	+	0.688017i	0.232993	+	0.972478i	$0.425148\pi$
$98$	−4.57759	+	0.414758i	−0.462407	+	0.0418969i
$99$		0			0
$100$	−4.68291	−	8.11103i	−0.468291	−	0.811103i
$101$	6.85219	+	11.8683i	0.681819	+	1.18094i	0.974425	+	0.224711i	$0.0721440\pi$
$101$	6.85219	+	11.8683i	0.681819	+	1.18094i	−0.292607	+	0.956233i	$0.594523\pi$
$102$		0			0
$103$	−4.23669	−	2.44605i	−0.417453	−	0.241017i	0.276534	−	0.961004i	$-0.410814\pi$
$103$	−4.23669	−	2.44605i	−0.417453	−	0.241017i	−0.693987	+	0.719987i	$0.744148\pi$
$104$	1.85130	+	3.20655i	0.181535	+	0.314428i
$105$		0			0
$106$	−3.29949	+	5.71489i	−0.320475	+	0.555079i
$107$	−2.12487	+	1.22679i	−0.205419	+	0.118599i	−0.599180	−	0.800614i	$-0.704507\pi$
$107$	−2.12487	+	1.22679i	−0.205419	+	0.118599i	0.393762	+	0.919213i	$0.371173\pi$
$108$		0			0
$109$	−2.16784	+	3.75481i	−0.207641	+	0.359645i	−0.950971	−	0.309280i	$-0.899912\pi$
$109$	−2.16784	+	3.75481i	−0.207641	+	0.359645i	0.743330	+	0.668925i	$0.233245\pi$
$110$	5.09633			0.485916
$111$		0			0
$112$	2.85327	−	3.12349i	0.269609	−	0.295142i
$113$	−6.20086	+	3.58007i	−0.583328	+	0.336784i	−0.762455	−	0.647042i	$-0.776006\pi$
$113$	−6.20086	+	3.58007i	−0.583328	+	0.336784i	0.179127	+	0.983826i	$0.442673\pi$
$114$		0			0
$115$	−26.9432	+	15.5557i	−2.51247	+	1.45058i
$116$	4.96812	+	2.86834i	0.461278	+	0.266319i
$117$		0			0
$118$		−	1.42800i		−	0.131458i
$119$	0.909265	+	2.86834i	0.0833522	+	0.262941i
$120$		0			0
$121$	−2.75429	+	4.77056i	−0.250390	+	0.433688i
$122$	2.63085			0.238186
$123$		0			0
$124$			11.4820i			1.03111i
$125$	3.21226			0.287313
$126$		0			0
$127$	−17.7065			−1.57120			−0.785601	−	0.618733i	$-0.787646\pi$
$127$	−17.7065			−1.57120			−0.785601	+	0.618733i	$0.787646\pi$
$128$		−	11.0999i		−	0.981098i
$129$		0			0
$130$	−3.43621			−0.301375
$131$	6.80228	−	11.7819i	0.594318	−	1.02939i	−0.399325	−	0.916810i	$-0.630755\pi$
$131$	6.80228	−	11.7819i	0.594318	−	1.02939i	0.993643	−	0.112579i	$-0.0359113\pi$
$132$		0			0
$133$	2.53014	−	11.4968i	0.219391	−	0.996902i
$134$			7.06972i			0.610731i
$135$		0			0
$136$	2.30807	+	1.33256i	0.197915	+	0.114266i
$137$	−8.79893	+	5.08007i	−0.751744	+	0.434019i	−0.826324	−	0.563196i	$-0.809572\pi$
$137$	−8.79893	+	5.08007i	−0.751744	+	0.434019i	0.0745799	+	0.997215i	$0.476238\pi$
$138$		0			0
$139$	3.33821	−	1.92731i	0.283143	−	0.163473i	−0.351703	−	0.936112i	$-0.614397\pi$
$139$	3.33821	−	1.92731i	0.283143	−	0.163473i	0.634845	+	0.772639i	$0.281064\pi$
$140$	4.15429	+	13.1050i	0.351102	+	1.10758i
$141$		0			0
$142$	−4.19798			−0.352286
$143$	−1.85130	+	3.20655i	−0.154814	+	0.268145i
$144$		0			0
$145$	−10.4884	+	6.05551i	−0.871018	+	0.502882i
$146$	−3.50734	+	6.07489i	−0.290270	+	0.502762i
$147$		0			0
$148$	4.05378	+	7.02135i	0.333219	+	0.577152i
$149$	−4.39947	−	2.54003i	−0.360418	−	0.208088i	0.308846	−	0.951112i	$-0.400057\pi$
$149$	−4.39947	−	2.54003i	−0.360418	−	0.208088i	−0.669264	+	0.743024i	$0.733391\pi$
$150$		0			0
$151$	−9.15277	−	15.8531i	−0.744842	−	1.29010i	−0.950269	−	0.311431i	$-0.899192\pi$
$151$	−9.15277	−	15.8531i	−0.744842	−	1.29010i	0.205427	−	0.978672i	$-0.434142\pi$
$152$	−5.21329	−	9.02968i	−0.422854	−	0.732404i
$153$		0			0
$154$	−3.97590	−	0.874988i	−0.320387	−	0.0705085i
$155$	−20.9926	−	12.1201i	−1.68617	−	0.973510i
$156$		0			0
$157$		−	3.31208i		−	0.264333i	−0.991228	−	0.132166i	$-0.957807\pi$
$157$		−	3.31208i		−	0.264333i	0.991228	−	0.132166i	$-0.0421933\pi$
$158$		−	0.809727i		−	0.0644184i
$159$		0			0
$160$	16.4548	+	9.50018i	1.30087	+	0.751055i
$161$	23.6905	−	7.50989i	1.86708	−	0.591863i
$162$		0			0
$163$	1.14673	+	1.98619i	0.0898185	+	0.155570i	0.907434	−	0.420194i	$-0.138038\pi$
$163$	1.14673	+	1.98619i	0.0898185	+	0.155570i	−0.817616	+	0.575764i	$0.804705\pi$
$164$	−7.56619	−	13.1050i	−0.590820	−	1.02333i
$165$		0			0
$166$	−0.589962	−	0.340615i	−0.0457899	−	0.0264368i
$167$	−1.33256	−	2.30807i	−0.103117	−	0.178604i	0.809850	−	0.586636i	$-0.199548\pi$
$167$	−1.33256	−	2.30807i	−0.103117	−	0.178604i	−0.912967	+	0.408033i	$0.866215\pi$
$168$		0			0
$169$	−5.25176	+	9.09631i	−0.403981	+	0.699716i
$170$	−2.14201	+	1.23669i	−0.164284	+	0.0948496i
$171$		0			0
$172$	1.70051	−	2.94536i	0.129662	−	0.224582i
$173$	2.56530			0.195036			0.0975182	−	0.995234i	$-0.468910\pi$
$173$	2.56530			0.195036			0.0975182	+	0.995234i	$0.468910\pi$
$174$		0			0
$175$	−15.4256	−	3.39476i	−1.16607	−	0.256620i
$176$	3.24503	−	1.87352i	0.244603	−	0.141222i
$177$		0			0
$178$	−4.24824	+	2.45272i	−0.318419	+	0.183839i
$179$	11.9828	+	6.91827i	0.895636	+	0.517096i	0.875782	−	0.482707i	$-0.160346\pi$
$179$	11.9828	+	6.91827i	0.895636	+	0.517096i	0.0198545	+	0.999803i	$0.493680\pi$
$180$		0			0
$181$		−	4.74008i		−	0.352328i	−0.984361	−	0.176164i	$-0.943631\pi$
$181$		−	4.74008i		−	0.352328i	0.984361	−	0.176164i	$-0.0563688\pi$
$182$	2.68076	+	0.589962i	0.198711	+	0.0437309i
$183$		0			0
$184$	11.0060	−	19.0630i	0.811376	−	1.40534i
$185$	−17.1163			−1.25841
$186$		0			0
$187$			2.66513i			0.194893i
$188$	−8.76466			−0.639228
$189$		0			0
$190$	9.67641			0.702001
$191$			8.34338i			0.603706i	0.953355	+	0.301853i	$0.0976051\pi$
$191$			8.34338i			0.603706i	−0.953355	+	0.301853i	$0.902395\pi$
$192$		0			0
$193$	−17.8442			−1.28446			−0.642229	−	0.766513i	$-0.721990\pi$
$193$	−17.8442			−1.28446			−0.642229	+	0.766513i	$0.721990\pi$
$194$	4.44938	−	7.70655i	0.319447	−	0.553298i
$195$		0			0
$196$	−0.990974	−	10.9371i	−0.0707838	−	0.781225i
$197$			15.1102i			1.07656i	0.842767	+	0.538279i	$0.180925\pi$
$197$			15.1102i			1.07656i	−0.842767	+	0.538279i	$0.819075\pi$
$198$		0			0
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	0.210032	−	0.977695i	$-0.432643\pi$
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	−0.741693	+	0.670740i	$0.765977\pi$
$200$	−12.1154	+	6.99483i	−0.856688	+	0.494609i
$201$		0			0
$202$	7.79300	−	4.49929i	0.548313	−	0.316569i
$203$	9.22223	−	2.92345i	0.647274	−	0.205186i
$204$		0			0
$205$	31.9468			2.23126
$206$	−1.60613	+	2.78190i	−0.111904	+	0.193824i
$207$		0			0
$208$	−2.18797	+	1.26322i	−0.151708	+	0.0875887i
$209$	5.21329	−	9.02968i	0.360611	−	0.624596i
$210$		0			0
$211$	7.29047	+	12.6275i	0.501897	+	0.869310i	0.999998	+	0.00219128i	$0.000697506\pi$
$211$	7.29047	+	12.6275i	0.501897	+	0.869310i	−0.498101	+	0.867119i	$0.665969\pi$
$212$	−13.6545	−	7.88341i	−0.937793	−	0.541435i
$213$		0			0
$214$	0.805537	+	1.39523i	0.0550654	+	0.0953760i
$215$	3.59002	+	6.21810i	0.244838	+	0.424071i
$216$		0			0
$217$	14.2965	+	13.0597i	0.970510	+	0.886552i
$218$	2.46548	+	1.42345i	0.166984	+	0.0964080i
$219$		0			0
$220$			12.1766i			0.820943i
$221$		−	1.79696i		−	0.120877i
$222$		0			0
$223$	−9.16531	−	5.29159i	−0.613754	−	0.354351i	0.160679	−	0.987007i	$-0.448632\pi$
$223$	−9.16531	−	5.29159i	−0.613754	−	0.354351i	−0.774433	+	0.632655i	$0.781965\pi$
$224$	−11.2061	−	10.2367i	−0.748741	−	0.683967i
$225$		0			0
$226$	2.35075	+	4.07161i	0.156369	+	0.270839i
$227$	3.36199	+	5.82314i	0.223143	+	0.386495i	0.955761	−	0.294145i	$-0.0950350\pi$
$227$	3.36199	+	5.82314i	0.223143	+	0.386495i	−0.732618	+	0.680640i	$0.761702\pi$
$228$		0			0
$229$	10.6201	+	6.13152i	0.701796	+	0.405182i	0.808016	−	0.589161i	$-0.200541\pi$
$229$	10.6201	+	6.13152i	0.701796	+	0.405182i	−0.106220	+	0.994343i	$0.533875\pi$
$230$	10.2142	+	17.6915i	0.673503	+	1.16654i
$231$		0			0
$232$	4.28442	−	7.42084i	0.281286	−	0.487202i
$233$	−4.87268	+	2.81324i	−0.319220	+	0.184302i	−0.651045	−	0.759039i	$-0.725669\pi$
$233$	−4.87268	+	2.81324i	−0.319220	+	0.184302i	0.331825	+	0.943341i	$0.392336\pi$
$234$		0			0
$235$	9.25176	−	16.0245i	0.603518	−	1.04532i
$236$	3.41190			0.222096
$237$		0			0
$238$	1.88341	−	0.597042i	0.122084	−	0.0387005i
$239$	13.8213	−	7.97976i	0.894028	−	0.516168i	0.0187704	−	0.999824i	$-0.494025\pi$
$239$	13.8213	−	7.97976i	0.894028	−	0.516168i	0.875258	+	0.483656i	$0.160692\pi$
$240$		0			0
$241$	3.97338	−	2.29403i	0.255948	−	0.147771i	−0.366537	−	0.930403i	$-0.619457\pi$
$241$	3.97338	−	2.29403i	0.255948	−	0.147771i	0.622485	+	0.782632i	$0.286123\pi$
$242$	3.13245	+	1.80852i	0.201361	+	0.116256i
$243$		0			0
$244$			6.28583i			0.402409i
$245$	21.0425	+	9.73317i	1.34436	+	0.621830i
$246$		0			0
$247$	−3.51507	+	6.08828i	−0.223659	+	0.387388i
$248$	17.1506			1.08906
$249$		0			0
$250$		−	2.10923i		−	0.133400i
$251$	−13.8042			−0.871314			−0.435657	−	0.900113i	$-0.643484\pi$
$251$	−13.8042			−0.871314			−0.435657	+	0.900113i	$0.643484\pi$
$252$		0			0
$253$	22.0121			1.38389
$254$			11.6265i			0.729510i
$255$		0			0
$256$	−8.42609			−0.526631
$257$	−4.48215	+	7.76331i	−0.279589	+	0.484262i	−0.971283	−	0.237929i	$-0.923531\pi$
$257$	−4.48215	+	7.76331i	−0.279589	+	0.484262i	0.691694	+	0.722191i	$0.256865\pi$
$258$		0			0
$259$	13.3533	+	2.93869i	0.829732	+	0.182601i
$260$		−	8.21006i		−	0.509166i
$261$		0			0
$262$	−7.73623	−	4.46652i	−0.477946	−	0.275942i
$263$	24.7280	−	14.2767i	1.52479	−	0.880340i	0.525226	−	0.850963i	$-0.323981\pi$
$263$	24.7280	−	14.2767i	1.52479	−	0.880340i	0.999568	−	0.0293774i	$-0.00935247\pi$
$264$		0			0
$265$	28.8266	−	16.6431i	1.77081	−	1.02238i
$266$	−7.54905	−	1.66134i	−0.462862	−	0.101863i
$267$		0			0
$268$	−16.8915			−1.03181
$269$	11.9657	−	20.7251i	0.729559	−	1.26363i	−0.227510	−	0.973776i	$-0.573059\pi$
$269$	11.9657	−	20.7251i	0.729559	−	1.26363i	0.957070	−	0.289858i	$-0.0936081\pi$
$270$		0			0
$271$	12.6467	−	7.30159i	0.768234	−	0.443540i	−0.0640103	−	0.997949i	$-0.520389\pi$
$271$	12.6467	−	7.30159i	0.768234	−	0.443540i	0.832244	+	0.554409i	$0.187056\pi$
$272$	−0.909265	+	1.57489i	−0.0551323	+	0.0954919i
$273$		0			0
$274$	3.33568	+	5.77756i	0.201516	+	0.349035i
$275$	−12.1154	−	6.99483i	−0.730586	−	0.421804i
$276$		0			0
$277$	−11.1915	−	19.3842i	−0.672431	−	1.16468i	−0.977213	−	0.212262i	$-0.931917\pi$
$277$	−11.1915	−	19.3842i	−0.672431	−	1.16468i	0.304782	−	0.952422i	$-0.401416\pi$
$278$	−1.26551	−	2.19193i	−0.0759005	−	0.131463i
$279$		0			0
$280$	19.5749	−	6.20524i	1.16982	−	0.370834i
$281$	−10.0517	−	5.80335i	−0.599634	−	0.346199i	0.169264	−	0.985571i	$-0.445861\pi$
$281$	−10.0517	−	5.80335i	−0.599634	−	0.346199i	−0.768897	+	0.639372i	$0.779194\pi$
$282$		0			0
$283$			14.9937i			0.891283i	0.895211	+	0.445642i	$0.147024\pi$
$283$			14.9937i			0.891283i	−0.895211	+	0.445642i	$0.852976\pi$
$284$		−	10.0301i		−	0.595179i
$285$		0			0
$286$	2.10549	+	1.21560i	0.124500	+	0.0718801i
$287$	−24.9233	−	5.48493i	−1.47117	−	0.323765i
$288$		0			0
$289$	7.85327	+	13.6023i	0.461957	+	0.800134i
$290$	3.97617	+	6.88693i	0.233489	+	0.404414i
$291$		0			0
$292$	−14.5146	−	8.38002i	−0.849404	−	0.490403i
$293$	8.16762	+	14.1467i	0.477157	+	0.826461i	0.999657	−	0.0261787i	$-0.00833389\pi$
$293$	8.16762	+	14.1467i	0.477157	+	0.826461i	−0.522500	+	0.852639i	$0.675001\pi$
$294$		0			0
$295$	−3.60152	+	6.23801i	−0.209688	+	0.363191i
$296$	10.4877	−	6.05510i	0.609588	−	0.351946i
$297$		0			0
$298$	−1.66784	+	2.88878i	−0.0966153	+	0.167343i
$299$	−14.8417			−0.858317
$300$		0			0
$301$	−1.73317	−	5.46743i	−0.0998985	−	0.315137i
$302$	−10.4094	+	6.00989i	−0.598996	+	0.345831i
$303$		0			0
$304$	6.16134	−	3.55725i	0.353377	−	0.204022i
$305$	−11.4925	−	6.63517i	−0.658056	−	0.379929i
$306$		0			0
$307$		−	3.17340i		−	0.181115i	−0.995891	−	0.0905577i	$-0.971135\pi$
$307$		−	3.17340i		−	0.181115i	0.995891	−	0.0905577i	$-0.0288650\pi$
$308$	2.09059	−	9.49955i	0.119122	−	0.541287i
$309$		0			0
$310$	−7.95831	+	13.7842i	−0.452001	+	0.782889i
$311$	−25.1342			−1.42523			−0.712614	−	0.701556i	$-0.752489\pi$
$311$	−25.1342			−1.42523			−0.712614	+	0.701556i	$0.752489\pi$
$312$		0			0
$313$		−	18.6441i		−	1.05383i	−0.849919	−	0.526914i	$-0.823349\pi$
$313$		−	18.6441i		−	1.05383i	0.849919	−	0.526914i	$-0.176651\pi$
$314$	−2.17478			−0.122730
$315$		0			0
$316$	1.93466			0.108833
$317$			7.98965i			0.448744i	0.974504	+	0.224372i	$0.0720330\pi$
$317$			7.98965i			0.448744i	−0.974504	+	0.224372i	$0.927967\pi$
$318$		0			0
$319$	8.56885			0.479763
$320$	0.942037	−	1.63166i	0.0526615	−	0.0912124i
$321$		0			0
$322$	−4.93115	−	15.5557i	−0.274802	−	0.866884i
$323$			5.06028i			0.281561i
$324$		0			0
$325$	8.16882	+	4.71627i	0.453125	+	0.261612i
$326$	1.30417	−	0.752963i	0.0722313	−	0.0417028i
$327$		0			0
$328$	−19.5749	+	11.3016i	−1.08084	+	0.624025i
$329$	−9.96901	+	10.9131i	−0.549609	+	0.601659i
$330$		0			0
$331$	−8.93466			−0.491094			−0.245547	−	0.969385i	$-0.578967\pi$
$331$	−8.93466			−0.491094			−0.245547	+	0.969385i	$0.578967\pi$
$332$	0.813824	−	1.40958i	0.0446644	−	0.0773610i
$333$		0			0
$334$	−1.51552	+	0.874988i	−0.0829258	+	0.0478772i
$335$	17.8303	−	30.8830i	0.974173	−	1.68732i
$336$		0			0
$337$	−2.12263	−	3.67650i	−0.115627	−	0.200272i	0.802403	−	0.596782i	$-0.203554\pi$
$337$	−2.12263	−	3.67650i	−0.115627	−	0.200272i	−0.918030	+	0.396510i	$0.870221\pi$
$338$	5.97282	+	3.44841i	0.324879	+	0.187569i
$339$		0			0
$340$	−2.95479	−	5.11785i	−0.160246	−	0.277554i
$341$	8.57528	+	14.8528i	0.464377	+	0.804325i
$342$		0			0
$343$	−14.7453	−	11.2061i	−0.796169	−	0.605074i
$344$	−4.39947	−	2.54003i	−0.237203	−	0.136949i
$345$		0			0
$346$		−	1.68443i		−	0.0905556i
$347$		−	2.62648i		−	0.140997i	−0.997512	−	0.0704985i	$-0.977541\pi$
$347$		−	2.62648i		−	0.140997i	0.997512	−	0.0704985i	$-0.0224590\pi$
$348$		0			0
$349$	28.1387	+	16.2459i	1.50623	+	0.869622i	0.999974	+	0.00723825i	$0.00230403\pi$
$349$	28.1387	+	16.2459i	1.50623	+	0.869622i	0.506255	+	0.862384i	$0.331029\pi$
$350$	−2.22907	+	10.1288i	−0.119149	+	0.541407i
$351$		0			0
$352$	−6.72162	−	11.6422i	−0.358263	−	0.620531i
$353$	−11.6921	−	20.2513i	−0.622307	−	1.07787i	−0.989055	−	0.147548i	$-0.952862\pi$
$353$	−11.6921	−	20.2513i	−0.622307	−	1.07787i	0.366748	−	0.930321i	$-0.380471\pi$
$354$		0			0
$355$	18.3382	+	10.5876i	0.973291	+	0.561930i
$356$	−5.86024	−	10.1502i	−0.310592	−	0.537962i
$357$		0			0
$358$	4.54268	−	7.86815i	0.240088	−	0.415845i
$359$	18.4900	−	10.6752i	0.975865	−	0.563416i	0.0748455	−	0.997195i	$-0.476154\pi$
$359$	18.4900	−	10.6752i	0.975865	−	0.563416i	0.901019	+	0.433779i	$0.142820\pi$
$360$		0			0
$361$	0.398482	−	0.690192i	0.0209728	−	0.0363259i
$362$	−3.11243			−0.163586
$363$		0			0
$364$	−1.40958	+	6.40508i	−0.0738823	+	0.335718i
$365$	30.6425	−	17.6915i	1.60390	−	0.926014i
$366$		0			0
$367$	−13.4432	+	7.76146i	−0.701731	+	0.405145i	−0.807992	−	0.589194i	$-0.799446\pi$
$367$	−13.4432	+	7.76146i	−0.701731	+	0.405145i	0.106261	+	0.994338i	$0.466112\pi$
$368$	13.0075	+	7.50989i	0.678064	+	0.391480i
$369$		0			0
$370$			11.2389i			0.584283i
$371$	−25.3466	+	8.03486i	−1.31593	+	0.417149i
$372$		0			0
$373$	11.6764	−	20.2241i	0.604582	−	1.04717i	−0.387536	−	0.921855i	$-0.626674\pi$
$373$	11.6764	−	20.2241i	0.604582	−	1.04717i	0.992117	−	0.125311i	$-0.0399930\pi$
$374$	1.74998			0.0904891
$375$		0			0
$376$			13.0917i			0.675153i
$377$	−5.77756			−0.297559
$378$		0			0
$379$	2.53871			0.130405			0.0652024	−	0.997872i	$-0.479231\pi$
$379$	2.53871			0.130405			0.0652024	+	0.997872i	$0.479231\pi$
$380$			23.1196i			1.18601i
$381$		0			0
$382$	5.47843			0.280301
$383$	−8.10207	+	14.0332i	−0.413996	+	0.717063i	−0.995323	−	0.0966078i	$-0.969201\pi$
$383$	−8.10207	+	14.0332i	−0.413996	+	0.717063i	0.581326	+	0.813671i	$0.302534\pi$
$384$		0			0
$385$	15.1613	+	13.8497i	0.772693	+	0.705848i
$386$			11.7169i			0.596374i
$387$		0			0
$388$	18.4131	+	10.6308i	0.934783	+	0.539697i
$389$	−19.3410	+	11.1665i	−0.980626	+	0.566165i	−0.902459	−	0.430775i	$-0.858240\pi$
$389$	−19.3410	+	11.1665i	−0.980626	+	0.566165i	−0.0781671	+	0.996940i	$0.524907\pi$
$390$		0			0
$391$	−9.25176	+	5.34150i	−0.467881	+	0.270131i
$392$	−16.3367	+	1.48021i	−0.825130	+	0.0747619i
$393$		0			0
$394$	9.92167			0.499847
$395$	−2.04218	+	3.53717i	−0.102753	+	0.177974i
$396$		0			0
$397$	28.3116	−	16.3457i	1.42092	−	0.820367i	0.424540	−	0.905409i	$-0.360436\pi$
$397$	28.3116	−	16.3457i	1.42092	−	0.820367i	0.996377	+	0.0850420i	$0.0271025\pi$
$398$	−2.84325	+	4.92465i	−0.142519	+	0.246851i
$399$		0			0
$400$	−4.77287	−	8.26685i	−0.238643	−	0.413343i
$401$	25.0515	+	14.4635i	1.25101	+	0.722272i	0.971310	−	0.237815i	$-0.0764313\pi$
$401$	25.0515	+	14.4635i	1.25101	+	0.722272i	0.279701	+	0.960087i	$0.409765\pi$
$402$		0			0
$403$	−5.78190	−	10.0145i	−0.288017	−	0.498860i
$404$	10.7501	+	18.6196i	0.534835	+	0.926362i
$405$		0			0
$406$	−1.91959	−	6.05551i	−0.0952679	−	0.300530i
$407$	10.4877	+	6.05510i	0.519858	+	0.300140i
$408$		0			0
$409$		−	1.05082i		−	0.0519598i	−0.999662	−	0.0259799i	$-0.991729\pi$
$409$		−	1.05082i		−	0.0519598i	0.999662	−	0.0259799i	$-0.00827059\pi$
$410$		−	20.9769i		−	1.03597i
$411$		0			0
$412$	−6.64673	−	3.83749i	−0.327461	−	0.189060i
$413$	3.88073	−	4.24824i	0.190958	−	0.209042i
$414$		0			0
$415$	1.71810	+	2.97584i	0.0843384	+	0.146078i
$416$	4.53206	+	7.84976i	0.222203	+	0.384866i
$417$		0			0
$418$	−5.92908	−	3.42315i	−0.290001	−	0.167432i
$419$	−1.56060	−	2.70304i	−0.0762402	−	0.132052i	0.825385	−	0.564571i	$-0.190958\pi$
$419$	−1.56060	−	2.70304i	−0.0762402	−	0.132052i	−0.901625	+	0.432519i	$0.857625\pi$
$420$		0			0
$421$	4.35327	−	7.54009i	0.212166	−	0.367482i	−0.740226	−	0.672358i	$-0.765282\pi$
$421$	4.35327	−	7.54009i	0.212166	−	0.367482i	0.952392	+	0.304876i	$0.0986150\pi$
$422$	8.29145	−	4.78707i	0.403621	−	0.233031i
$423$		0			0
$424$	−11.7754	+	20.3956i	−0.571864	+	0.990497i
$425$	6.78952			0.329340
$426$		0			0
$427$	7.82665	+	7.14957i	0.378758	+	0.345992i
$428$	−3.33360	+	1.92465i	−0.161136	+	0.0930316i
$429$		0			0
$430$	4.08293	−	2.35728i	0.196897	−	0.113678i
$431$	−23.6279	−	13.6416i	−1.13811	−	0.657090i	−0.192151	−	0.981365i	$-0.561546\pi$
$431$	−23.6279	−	13.6416i	−1.13811	−	0.657090i	−0.945963	+	0.324275i	$0.894880\pi$
$432$		0			0
$433$		−	12.8711i		−	0.618547i	−0.950973	−	0.309274i	$-0.899914\pi$
$433$		−	12.8711i		−	0.618547i	0.950973	−	0.309274i	$-0.100086\pi$
$434$	8.57528	−	9.38738i	0.411627	−	0.450609i
$435$		0			0
$436$	−3.40101	+	5.89073i	−0.162879	+	0.282115i
$437$	41.7944			1.99930
$438$		0			0
$439$			18.4445i			0.880306i	0.897923	+	0.440153i	$0.145076\pi$
$439$			18.4445i			0.880306i	−0.897923	+	0.440153i	$0.854924\pi$
$440$	18.1880			0.867081
$441$		0			0
$442$	−1.17992			−0.0561233
$443$			2.87000i			0.136358i	0.997673	+	0.0681790i	$0.0217189\pi$
$443$			2.87000i			0.136358i	−0.997673	+	0.0681790i	$0.978281\pi$
$444$		0			0
$445$	24.7437			1.17296
$446$	−3.47457	+	6.01813i	−0.164526	+	0.284967i
$447$		0			0
$448$	−1.01507	+	1.11120i	−0.0479575	+	0.0524992i
$449$			1.81675i			0.0857380i	0.999081	+	0.0428690i	$0.0136498\pi$
$449$			1.81675i			0.0857380i	−0.999081	+	0.0428690i	$0.986350\pi$
$450$		0			0
$451$	−19.5749	−	11.3016i	−0.921746	−	0.532170i
$452$	−9.72821	+	5.61659i	−0.457577	+	0.264182i
$453$		0			0
$454$	3.82359	−	2.20755i	0.179450	−	0.103605i
$455$	−10.2226	−	9.33821i	−0.479241	−	0.437782i
$456$		0			0
$457$	6.15575			0.287954			0.143977	−	0.989581i	$-0.454011\pi$
$457$	6.15575			0.287954			0.143977	+	0.989581i	$0.454011\pi$
$458$	4.02608	−	6.97338i	0.188126	−	0.325844i
$459$		0			0
$460$	−42.2699	+	24.4045i	−1.97084	+	1.13787i
$461$	−8.52537	+	14.7664i	−0.397066	+	0.687739i	−0.993363	−	0.115026i	$-0.963305\pi$
$461$	−8.52537	+	14.7664i	−0.397066	+	0.687739i	0.596296	+	0.802764i	$0.296638\pi$
$462$		0			0
$463$	−14.7065	−	25.4725i	−0.683471	−	1.18381i	−0.973915	−	0.226915i	$-0.927136\pi$
$463$	−14.7065	−	25.4725i	−0.683471	−	1.18381i	0.290443	−	0.956892i	$-0.406197\pi$
$464$	5.06356	+	2.92345i	0.235070	+	0.135718i
$465$		0			0
$466$	1.84723	+	3.19950i	0.0855713	+	0.148214i
$467$	13.5590	+	23.4849i	0.627437	+	1.08675i	0.988064	+	0.154043i	$0.0492294\pi$
$467$	13.5590	+	23.4849i	0.627437	+	1.08675i	−0.360627	+	0.932710i	$0.617437\pi$
$468$		0			0
$469$	−19.2126	+	21.0321i	−0.887155	+	0.971171i
$470$	−10.5220	−	6.07489i	−0.485345	−	0.280214i
$471$		0			0
$472$		−	5.09633i		−	0.234578i
$473$		−	5.08007i		−	0.233582i
$474$		0			0
$475$	−23.0035	−	13.2811i	−1.05547	−	0.609378i
$476$	1.42650	+	4.50000i	0.0653835	+	0.206257i
$477$		0			0
$478$	−5.23967	−	9.07538i	−0.239657	−	0.415098i
$479$	10.7784	+	18.6688i	0.492480	+	0.853000i	0.999962	−	0.00866176i	$-0.00275716\pi$
$479$	10.7784	+	18.6688i	0.492480	+	0.853000i	−0.507483	+	0.861662i	$0.669424\pi$
$480$		0			0
$481$	−7.07138	−	4.08266i	−0.322427	−	0.186153i
$482$	−1.50631	−	2.60900i	−0.0686104	−	0.118837i
$483$		0			0
$484$	−4.32106	+	7.48430i	−0.196412	+	0.340195i
$485$	−38.8728	+	22.4432i	−1.76512	+	1.01909i
$486$		0			0
$487$	7.29047	−	12.6275i	0.330363	−	0.572205i	−0.652220	−	0.758029i	$-0.726162\pi$
$487$	7.29047	−	12.6275i	0.330363	−	0.572205i	0.982583	+	0.185825i	$0.0594956\pi$
$488$	9.38910			0.425025
$489$		0			0
$490$	6.39100	−	13.8170i	0.288716	−	0.624187i
$491$	0.245174	−	0.141551i	0.0110645	−	0.00638811i	−0.494458	−	0.869202i	$-0.664633\pi$
$491$	0.245174	−	0.141551i	0.0110645	−	0.00638811i	0.505522	+	0.862814i	$0.331300\pi$
$492$		0			0
$493$	−3.60152	+	2.07934i	−0.162204	+	0.0936486i
$494$	3.99769	+	2.30807i	0.179864	+	0.103845i
$495$		0			0
$496$			11.7026i			0.525461i
$497$	−12.4888	−	11.4084i	−0.560198	−	0.511736i
$498$		0			0
$499$	−6.15277	+	10.6569i	−0.275436	+	0.477069i	−0.970245	−	0.242125i	$-0.922155\pi$
$499$	−6.15277	+	10.6569i	−0.275436	+	0.477069i	0.694809	+	0.719194i	$0.255489\pi$
$500$	5.03955			0.225375
$501$		0			0
$502$			9.06412i			0.404552i
$503$	1.78425			0.0795559			0.0397779	−	0.999209i	$-0.487335\pi$
$503$	1.78425			0.0795559			0.0397779	+	0.999209i	$0.487335\pi$
$504$		0			0
$505$	−45.3900			−2.01983
$506$		−	14.4536i		−	0.642540i
$507$		0			0
$508$	−27.7789			−1.23249
$509$	−19.5362	+	33.8378i	−0.865928	+	1.49983i	0.000194027		1.00000i	$0.499938\pi$
$509$	−19.5362	+	33.8378i	−0.865928	+	1.49983i	−0.866122	+	0.499832i	$0.833395\pi$
$510$		0			0
$511$	−26.9432	+	8.54100i	−1.19190	+	0.377832i
$512$		−	16.6670i		−	0.736583i
$513$		0			0
$514$	5.09755	+	2.94307i	0.224843	+	0.129813i
$515$	14.0322	−	8.10152i	0.618334	−	0.356996i
$516$		0			0
$517$	−11.3378	+	6.54585i	−0.498634	+	0.287886i
$518$	1.92960	−	8.76803i	0.0847820	−	0.385245i
$519$		0			0
$520$	−12.2633			−0.537782
$521$	10.1814	−	17.6347i	0.446056	−	0.772591i	−0.552070	−	0.833798i	$-0.686162\pi$
$521$	10.1814	−	17.6347i	0.446056	−	0.772591i	0.998125	+	0.0612072i	$0.0194950\pi$
$522$		0			0
$523$	1.24066	−	0.716293i	0.0542501	−	0.0313213i	−0.472630	−	0.881261i	$-0.656695\pi$
$523$	1.24066	−	0.716293i	0.0542501	−	0.0313213i	0.526880	+	0.849940i	$0.323362\pi$
$524$	10.6718	−	18.4840i	0.466198	−	0.807478i
$525$		0			0
$526$	−9.37439	−	16.2369i	−0.408743	−	0.707963i
$527$	−7.20844	−	4.16179i	−0.314005	−	0.181291i
$528$		0			0
$529$	32.6171	+	56.4945i	1.41814	+	2.45628i
$530$	−10.9282	−	18.9282i	−0.474690	−	0.822187i
$531$		0			0
$532$	3.96941	−	18.0368i	0.172096	−	0.781994i
$533$	13.1984	+	7.62010i	0.571686	+	0.330063i
$534$		0			0
$535$		−	8.12647i		−	0.351338i
$536$			25.2308i			1.08980i
$537$		0			0
$538$	−13.6085	−	7.85690i	−0.586706	−	0.338735i
$539$	−9.45027	−	13.4079i	−0.407052	−	0.577520i
$540$		0			0
$541$	5.04521	+	8.73856i	0.216910	+	0.375700i	0.953862	−	0.300246i	$-0.0970687\pi$
$541$	5.04521	+	8.73856i	0.216910	+	0.375700i	−0.736951	+	0.675946i	$0.763735\pi$
$542$	−4.79437	−	8.30410i	−0.205936	−	0.356692i
$543$		0			0
$544$	5.65024	+	3.26217i	0.242252	+	0.139864i
$545$	−7.18005	−	12.4362i	−0.307559	−	0.532709i
$546$		0			0
$547$	−3.65024	+	6.32240i	−0.156073	+	0.270326i	−0.933449	−	0.358710i	$-0.883217\pi$
$547$	−3.65024	+	6.32240i	−0.156073	+	0.270326i	0.777376	+	0.629036i	$0.216550\pi$
$548$	−13.8042	+	7.96986i	−0.589686	+	0.340456i
$549$		0			0
$550$	−4.59295	+	7.95521i	−0.195844	+	0.339211i
$551$	16.2697			0.693112
$552$		0			0
$553$	2.20051	−	2.40890i	0.0935750	−	0.102437i
$554$	−12.7281	+	7.34855i	−0.540764	+	0.312210i
$555$		0			0
$556$	5.23714	−	3.02367i	0.222104	−	0.128232i
$557$	19.7970	+	11.4298i	0.838828	+	0.484297i	0.856866	−	0.515540i	$-0.172409\pi$
$557$	19.7970	+	11.4298i	0.838828	+	0.484297i	−0.0180379	+	0.999837i	$0.505742\pi$
$558$		0			0
$559$			3.42524i			0.144872i
$560$	4.23410	+	13.3568i	0.178923	+	0.564427i
$561$		0			0
$562$	−3.81060	+	6.60015i	−0.160740	+	0.278410i
$563$	−21.1096			−0.889663			−0.444832	−	0.895614i	$-0.646736\pi$
$563$	−21.1096			−0.889663			−0.444832	+	0.895614i	$0.646736\pi$
$564$		0			0
$565$		−	23.7149i		−	0.997694i
$566$	9.84517			0.413824
$567$		0			0
$568$	−14.9819			−0.628629
$569$		−	26.4536i		−	1.10899i	−0.832186	−	0.554496i	$-0.812911\pi$
$569$		−	26.4536i		−	1.10899i	0.832186	−	0.554496i	$-0.187089\pi$
$570$		0			0
$571$	12.0301			0.503446			0.251723	−	0.967799i	$-0.419003\pi$
$571$	12.0301			0.503446			0.251723	+	0.967799i	$0.419003\pi$
$572$	−2.90441	+	5.03059i	−0.121440	+	0.210340i
$573$		0			0
$574$	−3.60152	+	16.3651i	−0.150324	+	0.683067i
$575$		−	56.0767i		−	2.33856i
$576$		0			0
$577$	−31.9055	−	18.4207i	−1.32824	−	0.766862i	−0.343216	−	0.939257i	$-0.611516\pi$
$577$	−31.9055	−	18.4207i	−1.32824	−	0.766862i	−0.985028	+	0.172395i	$0.944850\pi$
$578$	8.93153	−	5.15662i	0.371503	−	0.214487i
$579$		0			0
$580$	−16.4548	+	9.50018i	−0.683248	+	0.394473i
$581$	−0.829458	−	2.61659i	−0.0344117	−	0.108554i
$582$		0			0
$583$	−23.5508			−0.975374
$584$	−12.5172	+	21.6804i	−0.517964	+	0.897140i
$585$		0			0
$586$	9.28903	−	5.36302i	0.383726	−	0.221544i
$587$	−14.3856	+	24.9166i	−0.593758	+	1.02842i	0.399963	+	0.916531i	$0.369023\pi$
$587$	−14.3856	+	24.9166i	−0.593758	+	1.02842i	−0.993721	+	0.111887i	$0.964310\pi$
$588$		0			0
$589$	16.2819	+	28.2011i	0.670884	+	1.16200i
$590$	4.09601	+	2.36483i	0.168630	+	0.0973585i
$591$		0			0
$592$	4.13166	+	7.15624i	0.169810	+	0.294120i
$593$	−5.29159	−	9.16531i	−0.217300	−	0.376374i	0.736682	−	0.676240i	$-0.236392\pi$
$593$	−5.29159	−	9.16531i	−0.217300	−	0.376374i	−0.953982	+	0.299865i	$0.903058\pi$
$594$		0			0
$595$	−9.73317	−	2.14201i	−0.399021	−	0.0878137i
$596$	−6.90210	−	3.98493i	−0.282721	−	0.163229i
$597$		0			0
$598$			9.74535i			0.398517i
$599$			18.1927i			0.743333i	0.928366	+	0.371666i	$0.121214\pi$
$599$			18.1927i			0.743333i	−0.928366	+	0.371666i	$0.878786\pi$
$600$		0			0
$601$	−22.8719	−	13.2051i	−0.932963	−	0.538646i	−0.0452152	−	0.998977i	$-0.514397\pi$
$601$	−22.8719	−	13.2051i	−0.932963	−	0.538646i	−0.887747	+	0.460331i	$0.847731\pi$
$602$	−3.59002	+	1.13804i	−0.146318	+	0.0463829i
$603$		0			0
$604$	−14.3593	−	24.8711i	−0.584272	−	1.01199i
$605$	−9.12241	−	15.8005i	−0.370879	−	0.642381i
$606$		0			0
$607$	21.6312	+	12.4888i	0.877983	+	0.506904i	0.869993	−	0.493064i	$-0.164123\pi$
$607$	21.6312	+	12.4888i	0.877983	+	0.506904i	0.00799043	+	0.999968i	$0.497457\pi$
$608$	−12.7623	−	22.1050i	−0.517581	−	0.896477i
$609$		0			0
$610$	−4.35679	+	7.54618i	−0.176401	+	0.305536i
$611$	7.64450	−	4.41355i	0.309263	−	0.178553i
$612$		0			0
$613$	7.05631	−	12.2219i	0.285002	−	0.493637i	−0.687608	−	0.726082i	$-0.741339\pi$
$613$	7.05631	−	12.2219i	0.285002	−	0.493637i	0.972610	+	0.232445i	$0.0746725\pi$
$614$	−2.08372			−0.0840920
$615$		0			0
$616$	−14.1894	−	3.12270i	−0.571707	−	0.125817i
$617$	−12.6669	+	7.31324i	−0.509950	+	0.294420i	−0.732813	−	0.680430i	$-0.761793\pi$
$617$	−12.6669	+	7.31324i	−0.509950	+	0.294420i	0.222863	+	0.974850i	$0.428460\pi$
$618$		0			0
$619$	22.9880	−	13.2721i	0.923965	−	0.533452i	0.0390674	−	0.999237i	$-0.487561\pi$
$619$	22.9880	−	13.2721i	0.923965	−	0.533452i	0.884898	+	0.465785i	$0.154228\pi$
$620$	−32.9343	−	19.0146i	−1.32267	−	0.763645i
$621$		0			0
$622$			16.5036i			0.661734i
$623$	−19.3038	−	4.24824i	−0.773391	−	0.170202i
$624$		0			0
$625$	9.60503	−	16.6364i	0.384201	−	0.665456i
$626$	−12.2421			−0.489293
$627$		0			0
$628$		−	5.19615i		−	0.207349i
$629$	−5.87738			−0.234347
$630$		0			0
$631$	−8.20304			−0.326558			−0.163279	−	0.986580i	$-0.552207\pi$
$631$	−8.20304			−0.326558			−0.163279	+	0.986580i	$0.552207\pi$
$632$		−	2.88979i		−	0.114950i
$633$		0			0
$634$	5.24617			0.208352
$635$	29.3227	−	50.7885i	1.16364	−	2.01548i
$636$		0			0
$637$	6.37186	+	9.04031i	0.252462	+	0.358190i
$638$		−	5.62648i		−	0.222755i
$639$		0			0
$640$	31.8382	+	18.3818i	1.25852	+	0.726604i
$641$	13.8996	−	8.02496i	0.549003	−	0.316967i	−0.199717	−	0.979854i	$-0.564002\pi$
$641$	13.8996	−	8.02496i	0.549003	−	0.316967i	0.748720	+	0.662887i	$0.230669\pi$
$642$		0			0
$643$	−22.8719	+	13.2051i	−0.901978	+	0.520757i	−0.877841	−	0.478951i	$-0.841017\pi$
$643$	−22.8719	+	13.2051i	−0.901978	+	0.520757i	−0.0241366	+	0.999709i	$0.507684\pi$
$644$	37.1669	−	11.7819i	1.46458	−	0.464272i
$645$		0			0
$646$	3.32268			0.130729
$647$	−15.8508	+	27.4543i	−0.623158	+	1.07934i	0.365736	+	0.930719i	$0.380817\pi$
$647$	−15.8508	+	27.4543i	−0.623158	+	1.07934i	−0.988894	+	0.148623i	$0.952516\pi$
$648$		0			0
$649$	4.41355	−	2.54817i	0.173247	−	0.100024i
$650$	3.09680	−	5.36382i	0.121467	−	0.210386i
$651$		0			0
$652$	1.79904	+	3.11603i	0.0704558	+	0.122033i
$653$	−11.5096	−	6.64506i	−0.450405	−	0.260041i	0.257596	−	0.966253i	$-0.417070\pi$
$653$	−11.5096	−	6.64506i	−0.450405	−	0.260041i	−0.708001	+	0.706211i	$0.750403\pi$
$654$		0			0
$655$	22.5297	+	39.0226i	0.880308	+	1.52474i
$656$	−7.71155	−	13.3568i	−0.301085	−	0.521495i
$657$		0			0
$658$	7.16576	+	6.54585i	0.279351	+	0.255184i
$659$	31.3609	+	18.1062i	1.22165	+	0.705319i	0.965269	−	0.261257i	$-0.0841372\pi$
$659$	31.3609	+	18.1062i	1.22165	+	0.705319i	0.256379	+	0.966576i	$0.417470\pi$
$660$		0			0
$661$		−	50.7930i		−	1.97562i	−0.155674	−	0.987809i	$-0.549755\pi$
$661$		−	50.7930i		−	1.97562i	0.155674	−	0.987809i	$-0.450245\pi$
$662$			5.86668i			0.228015i
$663$		0			0
$664$	−2.10549	−	1.21560i	−0.0817087	−	0.0471745i
$665$	28.7869	+	26.2965i	1.11631	+	1.01973i
$666$		0			0
$667$	17.1739	+	29.7460i	0.664975	+	1.15177i
$668$	−2.09059	−	3.62101i	−0.0808874	−	0.140101i
$669$		0			0
$670$	−20.2784	−	11.7077i	−0.783422	−	0.452309i
$671$	4.69455	+	8.13120i	0.181231	+	0.313902i
$672$		0			0
$673$	−1.66432	+	2.88269i	−0.0641550	+	0.111120i	−0.896319	−	0.443410i	$-0.853769\pi$
$673$	−1.66432	+	2.88269i	−0.0641550	+	0.111120i	0.832164	+	0.554530i	$0.187102\pi$
$674$	−2.41407	+	1.39376i	−0.0929864	+	0.0536857i
$675$		0			0
$676$	−8.23922	+	14.2707i	−0.316893	+	0.548875i
$677$	19.9380			0.766280			0.383140	−	0.923690i	$-0.374843\pi$
$677$	19.9380			0.766280			0.383140	+	0.923690i	$0.374843\pi$
$678$		0			0
$679$	34.1799	−	10.8350i	1.31171	−	0.415810i
$680$	−7.64450	+	4.41355i	−0.293153	+	0.169252i
$681$		0			0
$682$	9.75267	−	5.63070i	0.373449	−	0.215611i
$683$	24.8234	+	14.3318i	0.949843	+	0.548392i	0.893032	−	0.449993i	$-0.148574\pi$
$683$	24.8234	+	14.3318i	0.949843	+	0.548392i	0.0568107	+	0.998385i	$0.481907\pi$
$684$		0			0
$685$		−	33.6512i		−	1.28574i
$686$	−7.35817	+	9.68204i	−0.280936	+	0.369662i
$687$		0			0
$688$	1.73317	−	3.00195i	0.0660766	−	0.114448i
$689$	15.8792			0.604948
$690$		0			0
$691$		−	20.3674i		−	0.774812i	−0.921909	−	0.387406i	$-0.873371\pi$
$691$		−	20.3674i		−	0.774812i	0.921909	−	0.387406i	$-0.126629\pi$
$692$	4.02458			0.152991
$693$		0			0
$694$	−1.72460			−0.0654650
$695$			12.7668i			0.484273i
$696$		0			0
$697$	10.9699			0.415513
$698$	10.6674	−	18.4764i	0.403766	−	0.699343i
$699$		0			0
$700$	−24.2005	−	5.32587i	−0.914693	−	0.201299i
$701$			49.1172i			1.85513i	0.373659	+	0.927566i	$0.378103\pi$
$701$			49.1172i			1.85513i	−0.373659	+	0.927566i	$0.621897\pi$
$702$		0			0
$703$	19.9131	+	11.4968i	0.751037	+	0.433611i
$704$	−1.15444	+	0.666515i	−0.0435095	+	0.0251202i
$705$		0			0
$706$	−13.2974	+	7.67727i	−0.500455	+	0.288938i
$707$	35.4110	+	7.79300i	1.33177	+	0.293086i
$708$		0			0
$709$	23.3658			0.877522			0.438761	−	0.898604i	$-0.355418\pi$
$709$	23.3658			0.877522			0.438761	+	0.898604i	$0.355418\pi$
$710$	6.95201	−	12.0412i	0.260904	−	0.451900i
$711$		0			0
$712$	−15.1613	+	8.75340i	−0.568195	+	0.328048i
$713$	−34.3735	+	59.5367i	−1.28730	+	2.22967i
$714$		0			0
$715$	−6.13166	−	10.6203i	−0.229311	−	0.397178i
$716$	18.7992	+	10.8537i	0.702559	+	0.405623i
$717$		0			0
$718$	−7.00956	−	12.1409i	−0.261594	−	0.453095i
$719$	−6.33345	−	10.9699i	−0.236198	−	0.409107i	0.723422	−	0.690406i	$-0.242568\pi$
$719$	−6.33345	−	10.9699i	−0.236198	−	0.409107i	−0.959620	+	0.281299i	$0.909235\pi$
$720$		0			0
$721$	−12.3382	+	3.91121i	−0.459499	+	0.145661i
$722$	−0.453194	−	0.261652i	−0.0168661	−	0.00973767i
$723$		0			0
$724$		−	7.43648i		−	0.276374i
$725$		−	21.8295i		−	0.810728i
$726$		0			0
$727$	2.34172	+	1.35199i	0.0868495	+	0.0501426i	0.542796	−	0.839865i	$-0.317366\pi$
$727$	2.34172	+	1.35199i	0.0868495	+	0.0501426i	−0.455946	+	0.890007i	$0.650699\pi$
$728$	9.56723	+	2.10549i	0.354585	+	0.0780345i
$729$		0			0
$730$	−11.6166	−	20.1205i	−0.429949	−	0.744694i
$731$	1.23274	+	2.13517i	0.0455946	+	0.0789721i
$732$		0			0
$733$	−18.8869	−	10.9044i	−0.697605	−	0.402762i	0.108850	−	0.994058i	$-0.465283\pi$
$733$	−18.8869	−	10.9044i	−0.697605	−	0.402762i	−0.806455	+	0.591296i	$0.798616\pi$
$734$	5.09633	+	8.82710i	0.188109	+	0.325814i
$735$		0			0
$736$	26.9432	−	46.6671i	0.993141	−	1.72017i
$737$	−21.8505	+	12.6154i	−0.804873	+	0.464694i
$738$		0			0
$739$	−16.0633	+	27.8225i	−0.590899	+	1.02347i	0.403212	+	0.915107i	$0.367894\pi$
$739$	−16.0633	+	27.8225i	−0.590899	+	1.02347i	−0.994112	+	0.108361i	$0.965440\pi$
$740$	−26.8529			−0.987131
$741$		0			0
$742$	5.27585	+	16.6431i	0.193683	+	0.610986i
$743$	−35.7433	+	20.6364i	−1.31129	+	0.757075i	−0.982310	−	0.187261i	$-0.940039\pi$
$743$	−35.7433	+	20.6364i	−1.31129	+	0.757075i	−0.328983	+	0.944336i	$0.606706\pi$
$744$		0			0
$745$	14.5714	−	8.41279i	0.533854	−	0.308221i
$746$	−13.2796	−	7.66697i	−0.486200	−	0.280708i
$747$		0			0
$748$			4.18118i			0.152879i
$749$	−1.39523	+	6.33987i	−0.0509806	+	0.231654i
$750$		0			0
$751$	−22.9045	+	39.6718i	−0.835798	+	1.44764i	0.0575810	+	0.998341i	$0.481661\pi$
$751$	−22.9045	+	39.6718i	−0.835798	+	1.44764i	−0.893379	+	0.449304i	$0.851672\pi$
$752$	−8.93303			−0.325754
$753$		0			0
$754$			3.79366i			0.138157i
$755$	60.6294			2.20653
$756$		0			0
$757$	50.3427			1.82974			0.914868	−	0.403752i	$-0.132294\pi$
$757$	50.3427			1.82974			0.914868	+	0.403752i	$0.132294\pi$
$758$		−	1.66697i		−	0.0605471i
$759$		0			0
$760$	34.5337			1.25267
$761$	15.1823	−	26.2965i	0.550358	−	0.953248i	−0.447891	−	0.894088i	$-0.647825\pi$
$761$	15.1823	−	26.2965i	0.550358	−	0.953248i	0.998249	−	0.0591594i	$-0.0188420\pi$
$762$		0			0
$763$	3.46635	+	10.9349i	0.125490	+	0.395868i
$764$			13.0895i			0.473562i
$765$		0			0
$766$	9.21448	+	5.31999i	0.332933	+	0.192219i
$767$	−2.97584	+	1.71810i	−0.107452	+	0.0620372i
$768$		0			0
$769$	35.8000	−	20.6692i	1.29098	−	0.745349i	0.312154	−	0.950032i	$-0.398950\pi$
$769$	35.8000	−	20.6692i	1.29098	−	0.745349i	0.978828	+	0.204683i	$0.0656163\pi$
$770$	9.09402	−	9.95525i	0.327726	−	0.358762i
$771$		0			0
$772$	−27.9949			−1.00756
$773$	6.99754	−	12.1201i	0.251684	−	0.435930i	−0.712305	−	0.701870i	$-0.752349\pi$
$773$	6.99754	−	12.1201i	0.251684	−	0.435930i	0.963990	+	0.265940i	$0.0856823\pi$
$774$		0			0
$775$	37.8382	−	21.8459i	1.35919	−	0.784728i
$776$	15.8792	−	27.5035i	0.570029	−	0.987319i
$777$		0			0
$778$	7.33216	+	12.6997i	0.262871	+	0.455305i
$779$	−37.1669	−	21.4583i	−1.33164	−	0.768824i
$780$		0			0
$781$	−7.49097	−	12.9747i	−0.268048	−	0.464273i
$782$	3.50734	+	6.07489i	0.125422	+	0.217238i
$783$		0			0
$784$	−1.01001	−	11.1473i	−0.0360718	−	0.398116i
$785$	9.50018	+	5.48493i	0.339076	+	0.195766i
$786$		0			0
$787$		−	13.4868i		−	0.480753i	−0.970680	−	0.240377i	$-0.922729\pi$
$787$		−	13.4868i		−	0.480753i	0.970680	−	0.240377i	$-0.0772709\pi$
$788$			23.7056i			0.844478i
$789$		0			0
$790$	2.32258	+	1.34094i	0.0826335	+	0.0477085i
$791$	−4.07161	+	18.5012i	−0.144770	+	0.657827i
$792$		0			0
$793$	−3.16531	−	5.48248i	−0.112403	−	0.194688i
$794$	−10.7329	−	18.5900i	−0.380897	−	0.659733i
$795$		0			0
$796$	−11.7664	−	6.79332i	−0.417048	−	0.240783i
$797$	−4.15867	−	7.20304i	−0.147308	−	0.255145i	0.782924	−	0.622118i	$-0.213727\pi$
$797$	−4.15867	−	7.20304i	−0.147308	−	0.255145i	−0.930232	+	0.366973i	$0.880394\pi$
$798$		0			0
$799$	3.17686	−	5.50249i	0.112389	−	0.194664i
$800$	−29.6590	+	17.1236i	−1.04860	+	0.605411i
$801$		0			0
$802$	9.49702	−	16.4493i	0.335351	−	0.580846i
$803$	−25.0343			−0.883443
$804$		0			0
$805$	−17.6915	+	80.3893i	−0.623543	+	2.83335i
$806$	−6.57575	+	3.79651i	−0.231621	+	0.133726i
$807$		0			0
$808$	27.8120	−	16.0573i	0.978424	−	0.564893i
$809$	12.5955	+	7.27200i	0.442833	+	0.255670i	0.704799	−	0.709407i	$-0.251037\pi$
$809$	12.5955	+	7.27200i	0.442833	+	0.255670i	−0.261965	+	0.965077i	$0.584371\pi$
$810$		0			0
$811$		−	41.8287i		−	1.46880i	−0.678715	−	0.734401i	$-0.737463\pi$
$811$		−	41.8287i		−	1.46880i	0.678715	−	0.734401i	$-0.262537\pi$
$812$	14.4683	−	4.58645i	0.507738	−	0.160953i
$813$		0			0
$814$	3.97590	−	6.88647i	0.139355	−	0.241371i
$815$	−7.59609			−0.266079
$816$		0			0
$817$		−	9.64553i		−	0.337454i
$818$	−0.689991			−0.0241250
$819$		0			0
$820$	50.1196			1.75025
$821$		−	46.4828i		−	1.62226i	−0.584865	−	0.811131i	$-0.698852\pi$
$821$		−	46.4828i		−	1.62226i	0.584865	−	0.811131i	$-0.301148\pi$
$822$		0			0
$823$	7.73669			0.269684			0.134842	−	0.990867i	$-0.456947\pi$
$823$	7.73669			0.269684			0.134842	+	0.990867i	$0.456947\pi$
$824$	−5.73203	+	9.92817i	−0.199685	+	0.345864i
$825$		0			0
$826$	−2.78948	−	2.54817i	−0.0970585	−	0.0886620i
$827$		−	20.8898i		−	0.726409i	−0.931709	−	0.363205i	$-0.881683\pi$
$827$		−	20.8898i		−	0.726409i	0.931709	−	0.363205i	$-0.118317\pi$
$828$		0			0
$829$	41.2282	+	23.8031i	1.43191	+	0.826716i	0.997267	−	0.0738846i	$-0.0235396\pi$
$829$	41.2282	+	23.8031i	1.43191	+	0.826716i	0.434647	+	0.900601i	$0.356873\pi$
$830$	1.95400	−	1.12814i	0.0678243	−	0.0391584i
$831$		0			0
$832$	0.778382	−	0.449399i	0.0269855	−	0.0155801i
$833$	7.22558	+	3.34217i	0.250351	+	0.115799i
$834$		0			0
$835$	8.82710			0.305475
$836$	8.17887	−	14.1662i	0.282872	−	0.489949i
$837$		0			0
$838$	−1.77487	+	1.02472i	−0.0613118	+	0.0353984i
$839$	−11.2017	+	19.4020i	−0.386727	+	0.669831i	−0.992007	−	0.126181i	$-0.959728\pi$
$839$	−11.2017	+	19.4020i	−0.386727	+	0.669831i	0.605280	+	0.796013i	$0.293061\pi$
$840$		0			0
$841$	−7.81456	−	13.5352i	−0.269468	−	0.466732i
$842$	−4.95098	−	2.85845i	−0.170622	−	0.0985087i
$843$		0			0
$844$	11.4376	+	19.8106i	0.393700	+	0.681909i
$845$	−17.3942	−	30.1277i	−0.598380	−	1.03642i
$846$		0			0
$847$	4.40407	+	13.8930i	0.151326	+	0.477368i
$848$	−13.9168	−	8.03486i	−0.477904	−	0.275918i
$849$		0			0
$850$		−	4.45814i		−	0.152913i
$851$			48.5431i			1.66404i
$852$		0			0
$853$	−41.9393	−	24.2136i	−1.43597	−	0.829060i	−0.438406	−	0.898777i	$-0.644457\pi$
$853$	−41.9393	−	24.2136i	−1.43597	−	0.829060i	−0.997567	+	0.0697173i	$0.977790\pi$
$854$	4.69455	−	5.13914i	0.160644	−	0.175858i
$855$		0			0
$856$	2.87484	+	4.97937i	0.0982600	+	0.170191i
$857$	−24.5327	−	42.4920i	−0.838023	−	1.45150i	−0.891546	−	0.452931i	$-0.850378\pi$
$857$	−24.5327	−	42.4920i	−0.838023	−	1.45150i	0.0535230	−	0.998567i	$-0.482955\pi$
$858$		0			0
$859$	10.4136	+	6.01227i	0.355306	+	0.205136i	0.667020	−	0.745040i	$-0.267570\pi$
$859$	10.4136	+	6.01227i	0.355306	+	0.205136i	−0.311714	+	0.950176i	$0.600903\pi$
$860$	5.63221	+	9.75527i	0.192057	+	0.332652i
$861$		0			0
$862$	−8.95732	+	15.5145i	−0.305088	+	0.528427i
$863$	39.8804	−	23.0250i	1.35754	−	0.783779i	0.368252	−	0.929726i	$-0.379956\pi$
$863$	39.8804	−	23.0250i	1.35754	−	0.783779i	0.989292	+	0.145947i	$0.0466229\pi$
$864$		0			0
$865$	−4.24824	+	7.35817i	−0.144445	+	0.250185i
$866$	−8.45145			−0.287192
$867$		0			0
$868$	22.4291	+	20.4887i	0.761292	+	0.695433i
$869$	2.50264	−	1.44490i	0.0848961	−	0.0490148i
$870$		0			0
$871$	14.7327	−	8.50594i	0.499199	−	0.288213i
$872$	8.79893	+	5.08007i	0.297970	+	0.172033i
$873$		0			0
$874$		−	27.4430i		−	0.928275i
$875$	5.73203	−	6.27487i	0.193778	−	0.212129i
$876$		0			0
$877$	−6.73669	+	11.6683i	−0.227482	+	0.394010i	−0.957061	−	0.289886i	$-0.906383\pi$
$877$	−6.73669	+	11.6683i	−0.227482	+	0.394010i	0.729579	+	0.683896i	$0.239716\pi$
$878$	12.1110			0.408727
$879$		0			0
$880$			12.4105i			0.418357i
$881$	−25.5247			−0.859949			−0.429974	−	0.902841i	$-0.641477\pi$
$881$	−25.5247			−0.859949			−0.429974	+	0.902841i	$0.641477\pi$
$882$		0			0
$883$	6.45532			0.217239			0.108619	−	0.994083i	$-0.465357\pi$
$883$	6.45532			0.217239			0.108619	+	0.994083i	$0.465357\pi$
$884$		−	2.81917i		−	0.0948189i
$885$		0			0
$886$	1.88450			0.0633111
$887$	−16.5604	+	28.6834i	−0.556043	+	0.963096i	0.441778	+	0.897124i	$0.354348\pi$
$887$	−16.5604	+	28.6834i	−0.556043	+	0.963096i	−0.997822	+	0.0659712i	$0.978985\pi$
$888$		0			0
$889$	−31.5960	+	34.5882i	−1.05970	+	1.16005i
$890$		−	16.2472i		−	0.544608i
$891$		0			0
$892$	−14.3790	−	8.30171i	−0.481444	−	0.277962i
$893$	−21.5270	+	12.4286i	−0.720374	+	0.415908i
$894$		0			0
$895$	−39.6880	+	22.9139i	−1.32662	+	0.765926i
$896$	−21.6826	−	19.8069i	−0.724366	−	0.661701i
$897$		0			0
$898$	1.19292			0.0398082
$899$	−13.3809	+	23.1764i	−0.446278	+	0.772977i
$900$		0			0
$901$	9.89848	−	5.71489i	0.329766	−	0.190391i
$902$	−7.42084	+	12.8533i	−0.247087	+	0.427967i
$903$		0			0
$904$	8.38946	+	14.5310i	0.279029	+	0.483293i
$905$	13.5962	+	7.84976i	0.451952	+	0.260935i
$906$		0			0
$907$	−3.10756	−	5.38245i	−0.103185	−	0.178721i	0.809810	−	0.586692i	$-0.199570\pi$
$907$	−3.10756	−	5.38245i	−0.103185	−	0.178721i	−0.912995	+	0.407970i	$0.866237\pi$
$908$	5.27446	+	9.13562i	0.175039	+	0.303176i
$909$		0			0
$910$	−6.13166	+	6.71234i	−0.203262	+	0.222512i
$911$	15.6296	+	9.02376i	0.517832	+	0.298970i	0.736047	−	0.676930i	$-0.236690\pi$
$911$	15.6296	+	9.02376i	0.517832	+	0.298970i	−0.218215	+	0.975901i	$0.570023\pi$
$912$		0			0
$913$		−	2.43121i		−	0.0804611i
$914$		−	4.04199i		−	0.133697i
$915$		0			0
$916$	16.6613	+	9.61943i	0.550506	+	0.317835i
$917$	−10.8768	−	34.3116i	−0.359182	−	1.13307i
$918$		0			0
$919$	4.12913	+	7.15186i	0.136207	+	0.235918i	0.926058	−	0.377381i	$-0.123175\pi$
$919$	4.12913	+	7.15186i	0.136207	+	0.235918i	−0.789851	+	0.613299i	$0.789842\pi$
$920$	36.4529	+	63.1382i	1.20182	+	2.08161i
$921$		0			0
$922$	9.69590	+	5.59793i	0.319318	+	0.184358i
$923$	5.05080	+	8.74824i	0.166249	+	0.287952i
$924$		0			0
$925$	15.4256	−	26.7180i	0.507192	−	0.878482i
$926$	−16.7258	+	9.65662i	−0.549642	+	0.317336i
$927$		0			0
$928$	10.4884	−	18.1665i	0.344300	−	0.596345i
$929$	34.7709			1.14080			0.570399	−	0.821368i	$-0.306789\pi$
$929$	34.7709			1.14080			0.570399	+	0.821368i	$0.306789\pi$
$930$		0			0
$931$	−17.9432	−	25.4576i	−0.588066	−	0.834341i
$932$	−7.64450	+	4.41355i	−0.250404	+	0.144571i
$933$		0			0
$934$	15.4207	−	8.90314i	0.504580	−	0.291320i
$935$	−7.64450	−	4.41355i	−0.250002	−	0.144339i
$936$		0			0
$937$			51.0703i			1.66839i	0.551466	+	0.834197i	$0.314069\pi$
$937$			51.0703i			1.66839i	−0.551466	+	0.834197i	$0.685931\pi$
$938$	13.8101	+	12.6154i	0.450915	+	0.411907i
$939$		0			0
$940$	14.5146	−	25.1401i	0.473415	−	0.819978i
$941$	−3.47744			−0.113361			−0.0566807	−	0.998392i	$-0.518052\pi$
$941$	−3.47744			−0.113361			−0.0566807	+	0.998392i	$0.518052\pi$
$942$		0			0
$943$		−	90.6034i		−	2.95045i
$944$	3.47744			0.113181
$945$		0			0
$946$	−3.33568			−0.108452
$947$		−	14.3401i		−	0.465989i	−0.972478	−	0.232995i	$-0.925148\pi$
$947$		−	14.3401i		−	0.465989i	0.972478	−	0.232995i	$-0.0748525\pi$
$948$		0			0
$949$	16.8794			0.547930
$950$	−8.72063	+	15.1046i	−0.282935	+	0.490057i
$951$		0			0
$952$	6.72162	−	2.13075i	0.217849	−	0.0690581i
$953$		−	7.53697i		−	0.244147i	−0.992521	−	0.122073i	$-0.961046\pi$
$953$		−	7.53697i		−	0.244147i	0.992521	−	0.122073i	$-0.0389543\pi$
$954$		0			0
$955$	−23.9317	−	13.8170i	−0.774411	−	0.447106i
$956$	21.6836	−	12.5190i	0.701298	−	0.404895i
$957$		0			0
$958$	12.2583	−	7.07735i	0.396049	−	0.228659i
$959$	−5.77756	+	26.2530i	−0.186567	+	0.847752i
$960$		0			0
$961$	−22.5638			−0.727864
$962$	−2.68076	+	4.64321i	−0.0864312	+	0.149703i
$963$		0			0
$964$	6.23363	−	3.59899i	0.200772	−	0.115916i
$965$	29.5508	−	51.1834i	0.951273	−	1.64765i
$966$		0			0
$967$	5.80807	+	10.0599i	0.186775	+	0.323503i	0.944173	−	0.329450i	$-0.106863\pi$
$967$	5.80807	+	10.0599i	0.186775	+	0.323503i	−0.757398	+	0.652953i	$0.773530\pi$
$968$	11.1792	+	6.45434i	0.359314	+	0.207450i
$969$		0			0
$970$	14.7367	+	25.5247i	0.473167	+	0.819548i
$971$	−17.7476	−	30.7397i	−0.569548	−	0.986485i	−0.996611	−	0.0822636i	$-0.973785\pi$
$971$	−17.7476	−	30.7397i	−0.569548	−	0.986485i	0.427063	−	0.904222i	$-0.359548\pi$
$972$		0			0
$973$	2.19193	−	9.96004i	0.0702702	−	0.319304i
$974$	−8.29145	−	4.78707i	−0.265675	−	0.153388i
$975$		0			0
$976$			6.40659i			0.205070i
$977$		−	32.0094i		−	1.02407i	−0.858964	−	0.512036i	$-0.828891\pi$
$977$		−	32.0094i		−	1.02407i	0.858964	−	0.512036i	$-0.171109\pi$
$978$		0			0
$979$	−15.1613	−	8.75340i	−0.484559	−	0.279760i
$980$	33.0126	+	15.2699i	1.05455	+	0.487779i
$981$		0			0
$982$	−0.0929453	−	0.160986i	−0.00296600	−	0.00513727i
$983$	24.7324	+	42.8378i	0.788841	+	1.36631i	0.926678	+	0.375857i	$0.122652\pi$
$983$	24.7324	+	42.8378i	0.788841	+	1.36631i	−0.137837	+	0.990455i	$0.544015\pi$
$984$		0			0
$985$	−43.3413	−	25.0231i	−1.38097	−	0.797302i
$986$	1.36534	+	2.36483i	0.0434811	+	0.0753115i
$987$		0			0
$988$	−5.51462	+	9.55159i	−0.175443	+	0.303877i
$989$	17.6350	−	10.1816i	0.560761	−	0.323756i
$990$		0			0
$991$	−8.97590	+	15.5467i	−0.285129	+	0.493858i	−0.972640	−	0.232316i	$-0.925370\pi$
$991$	−8.97590	+	15.5467i	−0.285129	+	0.493858i	0.687511	+	0.726174i	$0.258703\pi$
$992$	41.9853			1.33303
$993$		0			0
$994$	−7.49097	+	8.20039i	−0.237599	+	0.260101i
$995$	24.8406	−	14.3417i	0.787500	−	0.454663i
$996$		0			0
$997$	29.0151	−	16.7519i	0.918916	−	0.530537i	0.0356272	−	0.999365i	$-0.488657\pi$
$997$	29.0151	−	16.7519i	0.918916	−	0.530537i	0.883289	+	0.468828i	$0.155324\pi$
$998$	6.99754	+	4.04003i	0.221503	+	0.127885i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.i.f.269.3		12
3.2	odd	2	inner	567.2.i.f.269.4		12
7.5	odd	6		567.2.s.f.26.3		12
9.2	odd	6		189.2.p.d.80.4	yes	12
9.4	even	3		567.2.s.f.458.4		12
9.5	odd	6		567.2.s.f.458.3		12
9.7	even	3		189.2.p.d.80.3	yes	12
21.5	even	6		567.2.s.f.26.4		12
63.5	even	6	inner	567.2.i.f.215.4		12
63.11	odd	6		1323.2.c.d.1322.7		12
63.25	even	3		1323.2.c.d.1322.6		12
63.38	even	6		1323.2.c.d.1322.8		12
63.40	odd	6	inner	567.2.i.f.215.3		12
63.47	even	6		189.2.p.d.26.3	✓	12
63.52	odd	6		1323.2.c.d.1322.5		12
63.61	odd	6		189.2.p.d.26.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.3	✓	12	63.47	even	6
189.2.p.d.26.4	yes	12	63.61	odd	6
189.2.p.d.80.3	yes	12	9.7	even	3
189.2.p.d.80.4	yes	12	9.2	odd	6
567.2.i.f.215.3		12	63.40	odd	6	inner
567.2.i.f.215.4		12	63.5	even	6	inner
567.2.i.f.269.3		12	1.1	even	1	trivial
567.2.i.f.269.4		12	3.2	odd	2	inner
567.2.s.f.26.3		12	7.5	odd	6
567.2.s.f.26.4		12	21.5	even	6
567.2.s.f.458.3		12	9.5	odd	6
567.2.s.f.458.4		12	9.4	even	3
1323.2.c.d.1322.5		12	63.52	odd	6
1323.2.c.d.1322.6		12	63.25	even	3
1323.2.c.d.1322.7		12	63.11	odd	6
1323.2.c.d.1322.8		12	63.38	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.656620i q^{2} +1.56885 q^{4} +(-1.65604 + 2.86834i) q^{5} +(1.78442 - 1.95341i) q^{7} -2.34338i q^{8} +O(q^{10})\)	\(q-0.656620i q^{2} +1.56885 q^{4} +(-1.65604 + 2.86834i) q^{5} +(1.78442 - 1.95341i) q^{7} -2.34338i q^{8} +(1.88341 + 1.08739i) q^{10} +(2.02943 - 1.17169i) q^{11} +(-1.36834 + 0.790014i) q^{13} +(-1.28265 - 1.17169i) q^{14} +1.59899 q^{16} +(-0.568650 + 0.984931i) q^{17} +(3.85327 - 2.22469i) q^{19} +(-2.59808 + 4.50000i) q^{20} +(-0.769355 - 1.33256i) q^{22} +(8.13484 + 4.69665i) q^{23} +(-2.98493 - 5.17005i) q^{25} +(0.518739 + 0.898482i) q^{26} +(2.79949 - 3.06461i) q^{28} +(3.16673 + 1.82831i) q^{29} +7.31873i q^{31} -5.73669i q^{32} +(0.646726 + 0.373387i) q^{34} +(2.64799 + 8.35327i) q^{35} +(2.58392 + 4.47548i) q^{37} +(-1.46078 - 2.53014i) q^{38} +(6.72162 + 3.88073i) q^{40} +(-4.82277 - 8.35327i) q^{41} +(1.08392 - 1.87740i) q^{43} +(3.18386 - 1.83821i) q^{44} +(3.08392 - 5.34150i) q^{46} -5.58668 q^{47} +(-0.631656 - 6.97144i) q^{49} +(-3.39476 + 1.95997i) q^{50} +(-2.14673 + 1.23941i) q^{52} +(-8.70349 - 5.02496i) q^{53} +7.76146i q^{55} +(-4.57759 - 4.18158i) q^{56} +(1.20051 - 2.07934i) q^{58} +2.17478 q^{59} +4.00665i q^{61} +4.80563 q^{62} -0.568850 q^{64} -5.23317i q^{65} -10.7668 q^{67} +(-0.892126 + 1.54521i) q^{68} +(5.48493 - 1.73872i) q^{70} -6.39331i q^{71} +(-9.25176 - 5.34150i) q^{73} +(2.93869 - 1.69665i) q^{74} +(6.04521 - 3.49020i) q^{76} +(1.33256 - 6.05510i) q^{77} +1.23317 q^{79} +(-2.64799 + 4.58645i) q^{80} +(-5.48493 + 3.16673i) q^{82} +(0.518739 - 0.898482i) q^{83} +(-1.88341 - 3.26217i) q^{85} +(-1.23274 - 0.711723i) q^{86} +(-2.74571 - 4.75572i) q^{88} +(-3.73538 - 6.46986i) q^{89} +(-0.898482 + 4.08266i) q^{91} +(12.7623 + 7.36834i) q^{92} +3.66833i q^{94} +14.7367i q^{95} +(11.7367 + 6.77618i) q^{97} +(-4.57759 + 0.414758i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) 12 * q - 16 * q^4 + 4 * q^7	\( 12 q - 16 q^{4} + 4 q^{7} - 6 q^{10} + 24 q^{13} + 8 q^{16} - 6 q^{19} + 20 q^{22} - 24 q^{25} + 28 q^{28} + 60 q^{34} + 8 q^{37} - 12 q^{40} - 10 q^{43} + 14 q^{46} - 48 q^{49} - 78 q^{52} + 20 q^{58} + 28 q^{64} - 72 q^{67} + 54 q^{70} - 42 q^{73} + 108 q^{76} + 72 q^{79} - 54 q^{82} + 6 q^{85} - 74 q^{88} + 6 q^{91} + 60 q^{97}+O(q^{100}) \) 12 * q - 16 * q^4 + 4 * q^7 - 6 * q^10 + 24 * q^13 + 8 * q^16 - 6 * q^19 + 20 * q^22 - 24 * q^25 + 28 * q^28 + 60 * q^34 + 8 * q^37 - 12 * q^40 - 10 * q^43 + 14 * q^46 - 48 * q^49 - 78 * q^52 + 20 * q^58 + 28 * q^64 - 72 * q^67 + 54 * q^70 - 42 * q^73 + 108 * q^76 + 72 * q^79 - 54 * q^82 + 6 * q^85 - 74 * q^88 + 6 * q^91 + 60 * q^97

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