LMFDB - Embedded newform 592.2.bq.b.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(65,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("592.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bq (of order $18$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			337.1
Root			$0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	592.337
Dual form			592.2.bq.b.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.266044 + 1.50881i) q^{3} +(-1.97937 - 2.35892i) q^{5} +(-0.153180 + 0.128533i) q^{7} +(0.613341 - 0.223238i) q^{9} +O(q^{10})$	\(q+(0.266044 + 1.50881i) q^{3} +(-1.97937 - 2.35892i) q^{5} +(-0.153180 + 0.128533i) q^{7} +(0.613341 - 0.223238i) q^{9} +(-2.17174 + 3.76157i) q^{11} +(-1.59735 + 4.38867i) q^{13} +(3.03256 - 3.61407i) q^{15} +(2.32445 + 6.38637i) q^{17} +(-4.07964 + 0.719350i) q^{19} +(-0.234685 - 0.196924i) q^{21} +(0.896915 - 0.517834i) q^{23} +(-0.778357 + 4.41428i) q^{25} +(2.79813 + 4.84651i) q^{27} +(1.25937 + 0.727100i) q^{29} +5.10852i q^{31} +(-6.25329 - 2.27601i) q^{33} +(0.606398 + 0.106924i) q^{35} +(5.64160 - 2.27429i) q^{37} +(-7.04665 - 1.24252i) q^{39} +(-4.46505 - 1.62515i) q^{41} -0.399970i q^{43} +(-1.74063 - 1.00495i) q^{45} +(-4.10475 - 7.10963i) q^{47} +(-1.20859 + 6.85428i) q^{49} +(-9.01743 + 5.20621i) q^{51} +(-8.65606 - 7.26330i) q^{53} +(13.1719 - 2.32256i) q^{55} +(-2.17073 - 5.96403i) q^{57} +(2.69714 - 3.21433i) q^{59} +(-3.60153 + 9.89514i) q^{61} +(-0.0652579 + 0.113030i) q^{63} +(13.5143 - 4.91879i) q^{65} +(-6.67299 + 5.59930i) q^{67} +(1.01993 + 1.21551i) q^{69} +(-2.45953 - 13.9487i) q^{71} +7.27588 q^{73} -6.86740 q^{75} +(-0.150819 - 0.855337i) q^{77} +(4.04665 + 4.82261i) q^{79} +(-5.06805 + 4.25260i) q^{81} +(14.4861 - 5.27251i) q^{83} +(10.4640 - 18.1241i) q^{85} +(-0.762009 + 2.09360i) q^{87} +(2.06611 - 2.46229i) q^{89} +(-0.319409 - 0.877568i) q^{91} +(-7.70781 + 1.35909i) q^{93} +(9.77198 + 8.19967i) q^{95} +(2.07350 - 1.19713i) q^{97} +(-0.492294 + 2.79194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$	$1$

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
$3$	0.266044	+	1.50881i	0.153601	+	0.871114i	0.960054	+	0.279815i	$0.0902733\pi$
$3$	0.266044	+	1.50881i	0.153601	+	0.871114i	−0.806453	+	0.591298i	$0.798616\pi$
$4$		0			0
$5$	−1.97937	−	2.35892i	−0.885199	−	1.05494i	−0.998117	−	0.0613353i	$-0.980464\pi$
$5$	−1.97937	−	2.35892i	−0.885199	−	1.05494i	0.112918	−	0.993604i	$-0.463980\pi$
$6$		0			0
$7$	−0.153180	+	0.128533i	−0.0578965	+	0.0485809i	−0.671277	−	0.741207i	$-0.734254\pi$
$7$	−0.153180	+	0.128533i	−0.0578965	+	0.0485809i	0.613380	+	0.789788i	$0.289809\pi$
$8$		0			0
$9$	0.613341	−	0.223238i	0.204447	−	0.0744126i
$10$		0			0
$11$	−2.17174	+	3.76157i	−0.654805	+	1.13416i	0.327137	+	0.944977i	$0.393916\pi$
$11$	−2.17174	+	3.76157i	−0.654805	+	1.13416i	−0.981943	+	0.189179i	$0.939417\pi$
$12$		0			0
$13$	−1.59735	+	4.38867i	−0.443024	+	1.21720i	0.494469	+	0.869195i	$0.335363\pi$
$13$	−1.59735	+	4.38867i	−0.443024	+	1.21720i	−0.937493	+	0.348004i	$0.886860\pi$
$14$		0			0
$15$	3.03256	−	3.61407i	0.783005	−	0.933149i
$16$		0			0
$17$	2.32445	+	6.38637i	0.563761	+	1.54892i	0.814077	+	0.580757i	$0.197243\pi$
$17$	2.32445	+	6.38637i	0.563761	+	1.54892i	−0.250316	+	0.968164i	$0.580534\pi$
$18$		0			0
$19$	−4.07964	+	0.719350i	−0.935933	+	0.165030i	−0.620757	−	0.784003i	$-0.713175\pi$
$19$	−4.07964	+	0.719350i	−0.935933	+	0.165030i	−0.315176	+	0.949033i	$0.602064\pi$
$20$		0			0
$21$	−0.234685	−	0.196924i	−0.0512125	−	0.0429724i
$22$		0			0
$23$	0.896915	−	0.517834i	0.187020	−	0.107976i	−0.403567	−	0.914950i	$-0.632230\pi$
$23$	0.896915	−	0.517834i	0.187020	−	0.107976i	0.590587	+	0.806974i	$0.298896\pi$
$24$		0			0
$25$	−0.778357	+	4.41428i	−0.155671	+	0.882856i
$26$		0			0
$27$	2.79813	+	4.84651i	0.538501	+	0.932711i
$28$		0			0
$29$	1.25937	+	0.727100i	0.233860	+	0.135019i	0.612351	−	0.790586i	$-0.290224\pi$
$29$	1.25937	+	0.727100i	0.233860	+	0.135019i	−0.378492	+	0.925605i	$0.623557\pi$
$30$		0			0
$31$			5.10852i			0.917518i	0.888561	+	0.458759i	$0.151706\pi$
$31$			5.10852i			0.917518i	−0.888561	+	0.458759i	$0.848294\pi$
$32$		0			0
$33$	−6.25329	−	2.27601i	−1.08856	−	0.396202i
$34$		0			0
$35$	0.606398	+	0.106924i	0.102500	+	0.0180735i
$36$		0			0
$37$	5.64160	−	2.27429i	0.927473	−	0.373891i
$37$	5.64160	−	2.27429i	0.927473	−	0.373891i
$38$		0			0
$39$	−7.04665	−	1.24252i	−1.12837	−	0.198962i
$40$		0			0
$41$	−4.46505	−	1.62515i	−0.697324	−	0.253805i	−0.0310562	−	0.999518i	$-0.509887\pi$
$41$	−4.46505	−	1.62515i	−0.697324	−	0.253805i	−0.666268	+	0.745712i	$0.732109\pi$
$42$		0			0
$43$		−	0.399970i		−	0.0609948i	−0.999535	−	0.0304974i	$-0.990291\pi$
$43$		−	0.399970i		−	0.0609948i	0.999535	−	0.0304974i	$-0.00970913\pi$
$44$		0			0
$45$	−1.74063	−	1.00495i	−0.259477	−	0.149809i
$46$		0			0
$47$	−4.10475	−	7.10963i	−0.598739	−	1.03705i	−0.993008	−	0.118051i	$-0.962335\pi$
$47$	−4.10475	−	7.10963i	−0.598739	−	1.03705i	0.394269	−	0.918995i	$-0.370998\pi$
$48$		0			0
$49$	−1.20859	+	6.85428i	−0.172656	+	0.979182i
$50$		0			0
$51$	−9.01743	+	5.20621i	−1.26269	+	0.729016i
$52$		0			0
$53$	−8.65606	−	7.26330i	−1.18900	−	0.997690i	−0.999876	−	0.0157372i	$-0.994990\pi$
$53$	−8.65606	−	7.26330i	−1.18900	−	0.997690i	−0.189125	−	0.981953i	$-0.560565\pi$
$54$		0			0
$55$	13.1719	−	2.32256i	1.77610	−	0.313174i
$56$		0			0
$57$	−2.17073	−	5.96403i	−0.287520	−	0.789955i
$58$		0			0
$59$	2.69714	−	3.21433i	0.351138	−	0.418470i	−0.561347	−	0.827581i	$-0.689717\pi$
$59$	2.69714	−	3.21433i	0.351138	−	0.418470i	0.912485	+	0.409111i	$0.134161\pi$
$60$		0			0
$61$	−3.60153	+	9.89514i	−0.461129	+	1.26694i	0.463508	+	0.886093i	$0.346591\pi$
$61$	−3.60153	+	9.89514i	−0.461129	+	1.26694i	−0.924637	+	0.380849i	$0.875632\pi$
$62$		0			0
$63$	−0.0652579	+	0.113030i	−0.00822173	+	0.0142404i
$64$		0			0
$65$	13.5143	−	4.91879i	1.67624	−	0.610100i
$66$		0			0
$67$	−6.67299	+	5.59930i	−0.815235	+	0.684063i	−0.951851	−	0.306561i	$-0.900822\pi$
$67$	−6.67299	+	5.59930i	−0.815235	+	0.684063i	0.136616	+	0.990624i	$0.456377\pi$
$68$		0			0
$69$	1.01993	+	1.21551i	0.122786	+	0.146330i
$70$		0			0
$71$	−2.45953	−	13.9487i	−0.291893	−	1.65541i	−0.679569	−	0.733612i	$-0.737833\pi$
$71$	−2.45953	−	13.9487i	−0.291893	−	1.65541i	0.387675	−	0.921796i	$-0.373278\pi$
$72$		0			0
$73$	7.27588			0.851577			0.425789	−	0.904823i	$-0.359997\pi$
$73$	7.27588			0.851577			0.425789	+	0.904823i	$0.359997\pi$
$74$		0			0
$75$	−6.86740			−0.792979
$76$		0			0
$77$	−0.150819	−	0.855337i	−0.0171874	−	0.0974747i
$78$		0			0
$79$	4.04665	+	4.82261i	0.455284	+	0.542587i	0.944039	−	0.329835i	$-0.106993\pi$
$79$	4.04665	+	4.82261i	0.455284	+	0.542587i	−0.488754	+	0.872421i	$0.662549\pi$
$80$		0			0
$81$	−5.06805	+	4.25260i	−0.563116	+	0.472511i
$82$		0			0
$83$	14.4861	−	5.27251i	1.59006	−	0.578733i	0.612696	−	0.790318i	$-0.290085\pi$
$83$	14.4861	−	5.27251i	1.59006	−	0.578733i	0.977360	+	0.211585i	$0.0678626\pi$
$84$		0			0
$85$	10.4640	−	18.1241i	1.13498	−	1.96584i
$86$		0			0
$87$	−0.762009	+	2.09360i	−0.0816959	+	0.224458i
$88$		0			0
$89$	2.06611	−	2.46229i	0.219007	−	0.261002i	−0.645343	−	0.763893i	$-0.723286\pi$
$89$	2.06611	−	2.46229i	0.219007	−	0.261002i	0.864350	+	0.502890i	$0.167730\pi$
$90$		0			0
$91$	−0.319409	−	0.877568i	−0.0334831	−	0.0919941i
$92$		0			0
$93$	−7.70781	+	1.35909i	−0.799262	+	0.140932i
$94$		0			0
$95$	9.77198	+	8.19967i	1.00258	+	0.841268i
$96$		0			0
$97$	2.07350	−	1.19713i	0.210532	−	0.121551i	−0.391027	−	0.920379i	$-0.627880\pi$
$97$	2.07350	−	1.19713i	0.210532	−	0.121551i	0.601559	+	0.798829i	$0.294547\pi$
$98$		0			0
$99$	−0.492294	+	2.79194i	−0.0494774	+	0.280600i
$100$		0			0
$101$	5.48150	+	9.49423i	0.545429	+	0.944711i	0.998580	+	0.0532773i	$0.0169667\pi$
$101$	5.48150	+	9.49423i	0.545429	+	0.944711i	−0.453150	+	0.891434i	$0.649700\pi$
$102$		0			0
$103$	13.6274	+	7.86780i	1.34275	+	0.775238i	0.987210	−	0.159423i	$-0.0509635\pi$
$103$	13.6274	+	7.86780i	1.34275	+	0.775238i	0.355541	+	0.934661i	$0.384297\pi$
$104$		0			0
$105$			0.943387i			0.0920652i
$106$		0			0
$107$	−17.4933	−	6.36704i	−1.69114	−	0.615525i	−0.696373	−	0.717680i	$-0.745204\pi$
$107$	−17.4933	−	6.36704i	−1.69114	−	0.615525i	−0.994769	+	0.102154i	$0.967426\pi$
$108$		0			0
$109$	0.00691666	+	0.00121959i	0.000662495	+	0.000116816i	0.173979	−	0.984749i	$-0.444337\pi$
$109$	0.00691666	+	0.00121959i	0.000662495	+	0.000116816i	−0.173317	+	0.984866i	$0.555448\pi$
$110$		0			0
$111$	4.93239	+	7.90705i	0.468162	+	0.750504i
$112$		0			0
$113$	2.52369	+	0.444994i	0.237408	+	0.0418615i	0.291086	−	0.956697i	$-0.405983\pi$
$113$	2.52369	+	0.444994i	0.237408	+	0.0418615i	−0.0536779	+	0.998558i	$0.517094\pi$
$114$		0			0
$115$	−2.99685	−	1.09076i	−0.279458	−	0.101714i
$116$		0			0
$117$			3.04834i			0.281819i
$118$		0			0
$119$	−1.17692	−	0.679493i	−0.107888	−	0.0622891i
$120$		0			0
$121$	−3.93294	−	6.81205i	−0.357540	−	0.619277i
$122$		0			0
$123$	1.26414	−	7.16929i	0.113984	−	0.646433i
$124$		0			0
$125$	−1.38039	+	0.796967i	−0.123466	+	0.0712829i
$126$		0			0
$127$	4.44843	+	3.73268i	0.394735	+	0.331222i	0.818454	−	0.574572i	$-0.194831\pi$
$127$	4.44843	+	3.73268i	0.394735	+	0.331222i	−0.423720	+	0.905793i	$0.639276\pi$
$128$		0			0
$129$	0.603479	−	0.106410i	0.0531334	−	0.00936885i
$130$		0			0
$131$	2.86257	+	7.86484i	0.250104	+	0.687154i	0.999681	+	0.0252378i	$0.00803431\pi$
$131$	2.86257	+	7.86484i	0.250104	+	0.687154i	−0.749578	+	0.661916i	$0.769743\pi$
$132$		0			0
$133$	0.532457	−	0.634558i	0.0461699	−	0.0550232i
$134$		0			0
$135$	5.89398	−	16.1936i	0.507273	−	1.39372i
$136$		0			0
$137$	0.788995	−	1.36658i	0.0674084	−	0.116755i	−0.830351	−	0.557240i	$-0.811860\pi$
$137$	0.788995	−	1.36658i	0.0674084	−	0.116755i	0.897760	+	0.440485i	$0.145194\pi$
$138$		0			0
$139$	9.32521	−	3.39410i	0.790954	−	0.287884i	0.0852214	−	0.996362i	$-0.472840\pi$
$139$	9.32521	−	3.39410i	0.790954	−	0.287884i	0.705733	+	0.708478i	$0.250618\pi$
$140$		0			0
$141$	9.63506	−	8.08477i	0.811418	−	0.680861i
$142$		0			0
$143$	−13.0393	−	15.5396i	−1.09040	−	1.29949i
$144$		0			0
$145$	−0.777594	−	4.40996i	−0.0645757	−	0.366227i
$146$		0			0
$147$	−10.6634			−0.879499
$148$		0			0
$149$	12.8504			1.05274			0.526372	−	0.850254i	$-0.323552\pi$
$149$	12.8504			1.05274			0.526372	+	0.850254i	$0.323552\pi$
$150$		0			0
$151$	−0.900597	−	5.10754i	−0.0732895	−	0.415646i	−0.999274	−	0.0380852i	$-0.987874\pi$
$151$	−0.900597	−	5.10754i	−0.0732895	−	0.415646i	0.925985	−	0.377560i	$-0.123237\pi$
$152$		0			0
$153$	2.85136	+	3.39811i	0.230519	+	0.274721i
$154$		0			0
$155$	12.0506	−	10.1116i	0.967926	−	0.812186i
$156$		0			0
$157$	−11.2421	+	4.09177i	−0.897214	+	0.326559i	−0.749136	−	0.662416i	$-0.769531\pi$
$157$	−11.2421	+	4.09177i	−0.897214	+	0.326559i	−0.148078	+	0.988976i	$0.547309\pi$
$158$		0			0
$159$	8.65606	−	14.9927i	0.686470	−	1.18900i
$160$		0			0
$161$	−0.0708304	+	0.194605i	−0.00558222	+	0.0153370i
$162$		0			0
$163$	0.454390	−	0.541521i	0.0355906	−	0.0424152i	−0.747956	−	0.663749i	$-0.768964\pi$
$163$	0.454390	−	0.541521i	0.0355906	−	0.0424152i	0.783546	+	0.621334i	$0.213409\pi$
$164$		0			0
$165$	7.00862	+	19.2560i	0.545621	+	1.49908i
$166$		0			0
$167$	6.50943	−	1.14779i	0.503715	−	0.0888185i	0.0839840	−	0.996467i	$-0.473236\pi$
$167$	6.50943	−	1.14779i	0.503715	−	0.0888185i	0.419731	+	0.907649i	$0.362124\pi$
$168$		0			0
$169$	−6.75037	−	5.66423i	−0.519259	−	0.435710i
$170$		0			0
$171$	−2.34162	+	1.35194i	−0.179068	+	0.103385i
$172$		0			0
$173$	2.67447	−	15.1676i	0.203336	−	1.15317i	−0.696701	−	0.717361i	$-0.745350\pi$
$173$	2.67447	−	15.1676i	0.203336	−	1.15317i	0.900037	−	0.435813i	$-0.143539\pi$
$174$		0			0
$175$	−0.448153	−	0.776223i	−0.0338771	−	0.0586769i
$176$		0			0
$177$	5.56739	+	3.21433i	0.418470	+	0.241604i
$178$		0			0
$179$			2.55438i			0.190923i	0.995433	+	0.0954617i	$0.0304328\pi$
$179$			2.55438i			0.190923i	−0.995433	+	0.0954617i	$0.969567\pi$
$180$		0			0
$181$	−7.88211	−	2.86885i	−0.585873	−	0.213240i	0.0320404	−	0.999487i	$-0.489799\pi$
$181$	−7.88211	−	2.86885i	−0.585873	−	0.213240i	−0.617913	+	0.786246i	$0.712022\pi$
$182$		0			0
$183$	−15.8881	−	2.80150i	−1.17448	−	0.207093i
$184$		0			0
$185$	−16.5316	−	8.80641i	−1.21543	−	0.647460i
$186$		0			0
$187$	−29.0709	−	5.12598i	−2.12587	−	0.374849i
$188$		0			0
$189$	−1.05155	−	0.382734i	−0.0764893	−	0.0278398i
$190$		0			0
$191$		−	6.48182i		−	0.469008i	−0.972115	−	0.234504i	$-0.924653\pi$
$191$		−	6.48182i		−	0.469008i	0.972115	−	0.234504i	$-0.0753466\pi$
$192$		0			0
$193$	−18.1716	−	10.4914i	−1.30802	−	0.755186i	−0.326255	−	0.945282i	$-0.605787\pi$
$193$	−18.1716	−	10.4914i	−1.30802	−	0.755186i	−0.981766	+	0.190096i	$0.939120\pi$
$194$		0			0
$195$	11.0169	+	19.0819i	0.788938	+	1.36648i
$196$		0			0
$197$	−0.287925	+	1.63290i	−0.0205138	+	0.116340i	−0.993345	−	0.115175i	$-0.963257\pi$
$197$	−0.287925	+	1.63290i	−0.0205138	+	0.116340i	0.972831	+	0.231515i	$0.0743682\pi$
$198$		0			0
$199$	−6.25254	+	3.60991i	−0.443231	+	0.255900i	−0.704967	−	0.709240i	$-0.749038\pi$
$199$	−6.25254	+	3.60991i	−0.443231	+	0.255900i	0.261736	+	0.965139i	$0.415705\pi$
$200$		0			0
$201$	−10.2236	−	8.57863i	−0.721118	−	0.605090i
$202$		0			0
$203$	−0.286367	+	0.0504942i	−0.0200990	+	0.00354400i
$204$		0			0
$205$	5.00439	+	13.7495i	0.349522	+	0.960303i
$206$		0			0
$207$	0.434515	−	0.517834i	0.0302009	−	0.0359920i
$208$		0			0
$209$	6.15404	−	16.9081i	0.425684	−	1.16956i
$210$		0			0
$211$	2.25434	−	3.90463i	0.155195	−	0.268806i	−0.777935	−	0.628345i	$-0.783733\pi$
$211$	2.25434	−	3.90463i	0.155195	−	0.268806i	0.933130	+	0.359539i	$0.117066\pi$
$212$		0			0
$213$	20.3917	−	7.42196i	1.39721	−	0.508544i
$214$		0			0
$215$	−0.943495	+	0.791686i	−0.0643458	+	0.0539926i
$216$		0			0
$217$	−0.656614	−	0.782522i	−0.0445739	−	0.0531211i
$218$		0			0
$219$	1.93571	+	10.9779i	0.130803	+	0.741821i
$220$		0			0
$221$	−31.7406			−2.13511
$222$		0			0
$223$	−13.6418			−0.913526			−0.456763	−	0.889588i	$-0.650991\pi$
$223$	−13.6418			−0.913526			−0.456763	+	0.889588i	$0.650991\pi$
$224$		0			0
$225$	0.508036	+	2.88122i	0.0338691	+	0.192081i
$226$		0			0
$227$	17.5084	+	20.8657i	1.16207	+	1.38490i	0.908657	+	0.417544i	$0.137109\pi$
$227$	17.5084	+	20.8657i	1.16207	+	1.38490i	0.253414	+	0.967358i	$0.418446\pi$
$228$		0			0
$229$	1.56117	−	1.30998i	0.103165	−	0.0865658i	−0.589746	−	0.807589i	$-0.700772\pi$
$229$	1.56117	−	1.30998i	0.103165	−	0.0865658i	0.692911	+	0.721023i	$0.256328\pi$
$230$		0			0
$231$	1.25042	−	0.455115i	0.0822715	−	0.0299444i
$232$		0			0
$233$	1.94247	−	3.36446i	0.127256	−	0.220413i	−0.795357	−	0.606142i	$-0.792716\pi$
$233$	1.94247	−	3.36446i	0.127256	−	0.220413i	0.922612	+	0.385728i	$0.126050\pi$
$234$		0			0
$235$	−8.64623	+	23.7553i	−0.564018	+	1.54963i
$236$		0			0
$237$	−6.19983	+	7.38867i	−0.402722	+	0.479946i
$238$		0			0
$239$	6.35148	+	17.4506i	0.410843	+	1.12878i	0.956744	+	0.290933i	$0.0939656\pi$
$239$	6.35148	+	17.4506i	0.410843	+	1.12878i	−0.545900	+	0.837850i	$0.683812\pi$
$240$		0			0
$241$	24.9528	−	4.39985i	1.60735	−	0.283420i	0.703317	−	0.710877i	$-0.251702\pi$
$241$	24.9528	−	4.39985i	1.60735	−	0.283420i	0.904036	+	0.427457i	$0.140591\pi$
$242$		0			0
$243$	5.09627	+	4.27628i	0.326926	+	0.274323i
$244$		0			0
$245$	18.5609	−	10.7162i	1.18581	−	0.684630i
$246$		0			0
$247$	3.35960	−	19.0533i	0.213766	−	1.21233i
$248$		0			0
$249$	11.8092	+	20.4541i	0.748376	+	1.29623i
$250$		0			0
$251$	−11.0092	−	6.35615i	−0.694893	−	0.401197i	0.110549	−	0.993871i	$-0.464739\pi$
$251$	−11.0092	−	6.35615i	−0.694893	−	0.401197i	−0.805443	+	0.592674i	$0.798072\pi$
$252$		0			0
$253$			4.49841i			0.282813i
$254$		0			0
$255$	30.1298	+	10.9664i	1.88680	+	0.686740i
$256$		0			0
$257$	4.28106	+	0.754866i	0.267045	+	0.0470873i	0.305567	−	0.952170i	$-0.401154\pi$
$257$	4.28106	+	0.754866i	0.267045	+	0.0470873i	−0.0385222	+	0.999258i	$0.512265\pi$
$258$		0			0
$259$	−0.571857	+	1.07351i	−0.0355335	+	0.0667044i
$260$		0			0
$261$	0.934742	+	0.164820i	0.0578591	+	0.0102021i
$262$		0			0
$263$	−6.11870	−	2.22703i	−0.377295	−	0.137324i	0.146409	−	0.989224i	$-0.453228\pi$
$263$	−6.11870	−	2.22703i	−0.377295	−	0.137324i	−0.523705	+	0.851900i	$0.675451\pi$
$264$		0			0
$265$			34.7956i			2.13748i
$266$		0			0
$267$	4.26481	+	2.46229i	0.261002	+	0.150690i
$268$		0			0
$269$	4.95106	+	8.57549i	0.301872	+	0.522857i	0.976560	−	0.215246i	$-0.0690552\pi$
$269$	4.95106	+	8.57549i	0.301872	+	0.522857i	−0.674688	+	0.738103i	$0.735722\pi$
$270$		0			0
$271$	−1.56719	+	8.88797i	−0.0951999	+	0.539906i	0.899486	+	0.436950i	$0.143941\pi$
$271$	−1.56719	+	8.88797i	−0.0951999	+	0.539906i	−0.994686	+	0.102956i	$0.967170\pi$
$272$		0			0
$273$	1.23911	−	0.715400i	0.0749943	−	0.0432980i
$274$		0			0
$275$	−14.9142	−	12.5145i	−0.899362	−	0.754655i
$276$		0			0
$277$	−0.204926	+	0.0361340i	−0.0123128	+	0.00217108i	−0.179801	−	0.983703i	$-0.557545\pi$
$277$	−0.204926	+	0.0361340i	−0.0123128	+	0.00217108i	0.167488	+	0.985874i	$0.446434\pi$
$278$		0			0
$279$	1.14042	+	3.13327i	0.0682749	+	0.187584i
$280$		0			0
$281$	−17.3934	+	20.7286i	−1.03760	+	1.23657i	−0.0665281	+	0.997785i	$0.521192\pi$
$281$	−17.3934	+	20.7286i	−1.03760	+	1.23657i	−0.971073	+	0.238781i	$0.923252\pi$
$282$		0			0
$283$	−0.278026	+	0.763870i	−0.0165269	+	0.0454074i	−0.947682	−	0.319217i	$-0.896580\pi$
$283$	−0.278026	+	0.763870i	−0.0165269	+	0.0454074i	0.931155	+	0.364624i	$0.118802\pi$
$284$		0			0
$285$	−9.77198	+	16.9256i	−0.578842	+	1.00258i
$286$		0			0
$287$	0.892841	−	0.324967i	0.0527027	−	0.0191822i
$288$		0			0
$289$	−22.3599	+	18.7621i	−1.31529	+	1.10366i
$290$		0			0
$291$	2.35789	+	2.81003i	0.138222	+	0.164727i
$292$		0			0
$293$	−1.52803	−	8.66589i	−0.0892684	−	0.506266i	−0.996354	−	0.0853194i	$-0.972809\pi$
$293$	−1.52803	−	8.66589i	−0.0892684	−	0.506266i	0.907085	−	0.420947i	$-0.138302\pi$
$294$		0			0
$295$	−12.9210			−0.752288
$296$		0			0
$297$	−24.3073			−1.41045
$298$		0			0
$299$	0.839921	+	4.76343i	0.0485739	+	0.275476i
$300$		0			0
$301$	0.0514093	+	0.0612672i	0.00296318	+	0.00353138i
$302$		0			0
$303$	−12.8667	+	10.7964i	−0.739173	+	0.620239i
$304$		0			0
$305$	30.4706	−	11.0904i	1.74474	−	0.635033i
$306$		0			0
$307$	12.2271	−	21.1779i	0.697836	−	1.20869i	−0.271379	−	0.962472i	$-0.587480\pi$
$307$	12.2271	−	21.1779i	0.697836	−	1.20869i	0.969215	−	0.246215i	$-0.0791869\pi$
$308$		0			0
$309$	−8.24554	+	22.6544i	−0.469072	+	1.28877i
$310$		0			0
$311$	−0.00816038	+	0.00972517i	−0.000462733	+	0.000551464i	−0.766276	−	0.642512i	$-0.777892\pi$
$311$	−0.00816038	+	0.00972517i	−0.000462733	+	0.000551464i	0.765813	+	0.643063i	$0.222337\pi$
$312$		0			0
$313$	5.97456	+	16.4150i	0.337702	+	0.927829i	0.986045	+	0.166480i	$0.0532402\pi$
$313$	5.97456	+	16.4150i	0.337702	+	0.927829i	−0.648343	+	0.761349i	$0.724538\pi$
$314$		0			0
$315$	0.395798	−	0.0697898i	0.0223007	−	0.00393221i
$316$		0			0
$317$	2.09046	+	1.75410i	0.117412	+	0.0985203i	0.699603	−	0.714531i	$-0.253360\pi$
$317$	2.09046	+	1.75410i	0.117412	+	0.0985203i	−0.582191	+	0.813052i	$0.697805\pi$
$318$		0			0
$319$	−5.47008	+	3.15815i	−0.306266	+	0.176822i
$320$		0			0
$321$	4.95268	−	28.0880i	0.276432	−	1.56772i
$322$		0			0
$323$	−14.0769	−	24.3820i	−0.783262	−	1.35665i
$324$		0			0
$325$	−18.1295	−	10.4671i	−1.00565	−	0.580610i
$326$		0			0
$327$			0.0107604i			0.000595052i
$328$		0			0
$329$	1.54259	+	0.561455i	0.0850455	+	0.0309540i
$330$		0			0
$331$	23.2573	+	4.10088i	1.27834	+	0.225405i	0.771273	−	0.636504i	$-0.219620\pi$
$331$	23.2573	+	4.10088i	1.27834	+	0.225405i	0.507062	+	0.861909i	$0.330731\pi$
$332$		0			0
$333$	2.95251	−	2.65433i	0.161797	−	0.145456i
$334$		0			0
$335$	26.4166	+	4.65795i	1.44329	+	0.254491i
$336$		0			0
$337$	21.0920	+	7.67685i	1.14895	+	0.418185i	0.845139	−	0.534546i	$-0.179517\pi$
$337$	21.0920	+	7.67685i	1.14895	+	0.418185i	0.303814	+	0.952731i	$0.401740\pi$
$338$		0			0
$339$			3.92616i			0.213240i
$340$		0			0
$341$	−19.2161	−	11.0944i	−1.04061	−	0.600796i
$342$		0			0
$343$	−1.39574	−	2.41749i	−0.0753626	−	0.130532i
$344$		0			0
$345$	0.848464	−	4.81188i	0.0456798	−	0.259063i
$346$		0			0
$347$	1.05232	−	0.607556i	0.0564914	−	0.0326153i	−0.471488	−	0.881872i	$-0.656283\pi$
$347$	1.05232	−	0.607556i	0.0564914	−	0.0326153i	0.527980	+	0.849257i	$0.322950\pi$
$348$		0			0
$349$	13.5892	+	11.4027i	0.727415	+	0.610374i	0.929426	−	0.369010i	$-0.120303\pi$
$349$	13.5892	+	11.4027i	0.727415	+	0.610374i	−0.202011	+	0.979383i	$0.564748\pi$
$350$		0			0
$351$	−25.7393	+	4.53854i	−1.37386	+	0.242249i
$352$		0			0
$353$	0.549304	+	1.50920i	0.0292365	+	0.0803266i	0.953452	−	0.301544i	$-0.0975021\pi$
$353$	0.549304	+	1.50920i	0.0292365	+	0.0803266i	−0.924216	+	0.381871i	$0.875280\pi$
$354$		0			0
$355$	−28.0355	+	33.4115i	−1.48797	+	1.77330i
$356$		0			0
$357$	0.712116	−	1.95652i	0.0376892	−	0.103550i
$358$		0			0
$359$	−16.0062	+	27.7236i	−0.844775	+	1.46319i	0.0410405	+	0.999157i	$0.486933\pi$
$359$	−16.0062	+	27.7236i	−0.844775	+	1.46319i	−0.885816	+	0.464037i	$0.846401\pi$
$360$		0			0
$361$	−1.72818	+	0.629006i	−0.0909568	+	0.0331056i
$362$		0			0
$363$	9.23177	−	7.74638i	0.484542	−	0.406579i
$364$		0			0
$365$	−14.4016	−	17.1632i	−0.753816	−	0.898363i
$366$		0			0
$367$	−2.78467	−	15.7927i	−0.145359	−	0.824371i	−0.967078	−	0.254479i	$-0.918096\pi$
$367$	−2.78467	−	15.7927i	−0.145359	−	0.824371i	0.821720	−	0.569892i	$-0.193015\pi$
$368$		0			0
$369$	−3.10139			−0.161452
$370$		0			0
$371$	2.25951			0.117308
$372$		0			0
$373$	−0.193859	−	1.09943i	−0.0100376	−	0.0569262i	0.979378	−	0.202039i	$-0.0647567\pi$
$373$	−0.193859	−	1.09943i	−0.0100376	−	0.0569262i	−0.989415	+	0.145113i	$0.953646\pi$
$374$		0			0
$375$	−1.56972	−	1.87072i	−0.0810600	−	0.0966035i
$376$		0			0
$377$	−5.20266	+	4.36555i	−0.267951	+	0.224837i
$378$		0			0
$379$	34.2433	−	12.4636i	1.75896	−	0.640210i	0.759021	−	0.651066i	$-0.225678\pi$
$379$	34.2433	−	12.4636i	1.75896	−	0.640210i	0.999941	+	0.0108561i	$0.00345568\pi$
$380$		0			0
$381$	−4.44843	+	7.70491i	−0.227900	+	0.394735i
$382$		0			0
$383$	−2.06267	+	5.66715i	−0.105398	+	0.289578i	−0.981170	−	0.193147i	$-0.938131\pi$
$383$	−2.06267	+	5.66715i	−0.105398	+	0.289578i	0.875772	+	0.482725i	$0.160353\pi$
$384$		0			0
$385$	−1.71914	+	2.04879i	−0.0876156	+	0.104416i
$386$		0			0
$387$	−0.0892883	−	0.245318i	−0.00453878	−	0.0124702i
$388$		0			0
$389$	18.5468	−	3.27030i	0.940361	−	0.165811i	0.317601	−	0.948224i	$-0.397123\pi$
$389$	18.5468	−	3.27030i	0.940361	−	0.165811i	0.622759	+	0.782413i	$0.286012\pi$
$390$		0			0
$391$	5.39191	+	4.52435i	0.272681	+	0.228806i
$392$		0			0
$393$	−11.1050	+	6.41147i	−0.560173	+	0.323416i
$394$		0			0
$395$	3.36634	−	19.0914i	0.169379	−	0.960595i
$396$		0			0
$397$	−13.7557	−	23.8255i	−0.690378	−	1.19577i	−0.971714	−	0.236160i	$-0.924111\pi$
$397$	−13.7557	−	23.8255i	−0.690378	−	1.19577i	0.281336	−	0.959609i	$-0.409222\pi$
$398$		0			0
$399$	1.09909	+	0.634558i	0.0550232	+	0.0317676i
$400$		0			0
$401$		−	22.0721i		−	1.10223i	−0.834430	−	0.551114i	$-0.814203\pi$
$401$		−	22.0721i		−	1.10223i	0.834430	−	0.551114i	$-0.185797\pi$
$402$		0			0
$403$	−22.4196	−	8.16008i	−1.11680	−	0.406483i
$404$		0			0
$405$	20.0630	+	3.53766i	0.996941	+	0.175788i
$406$		0			0
$407$	−3.69721	+	26.1604i	−0.183264	+	1.29672i
$408$		0			0
$409$	−1.39932	−	0.246737i	−0.0691917	−	0.0122004i	0.138945	−	0.990300i	$-0.455629\pi$
$409$	−1.39932	−	0.246737i	−0.0691917	−	0.0122004i	−0.208137	+	0.978100i	$0.566740\pi$
$410$		0			0
$411$	2.27182	+	0.826875i	0.112061	+	0.0407867i
$412$		0			0
$413$			0.839043i			0.0412866i
$414$		0			0
$415$	−41.1107	−	23.7353i	−2.01805	−	1.16512i
$416$		0			0
$417$	7.60198	+	13.1670i	0.372271	+	0.644792i
$418$		0			0
$419$	2.36856	−	13.4328i	0.115712	−	0.656235i	−0.870683	−	0.491844i	$-0.836323\pi$
$419$	2.36856	−	13.4328i	0.115712	−	0.656235i	0.986395	−	0.164391i	$-0.0525658\pi$
$420$		0			0
$421$	−24.2468	+	13.9989i	−1.18172	+	0.682264i	−0.956411	−	0.292024i	$-0.905671\pi$
$421$	−24.2468	+	13.9989i	−1.18172	+	0.682264i	−0.225306	+	0.974288i	$0.572338\pi$
$422$		0			0
$423$	−4.10475	−	3.44429i	−0.199580	−	0.167467i
$424$		0			0
$425$	−30.0005	+	5.28989i	−1.45524	+	0.256597i
$426$		0			0
$427$	−0.720170	−	1.97865i	−0.0348515	−	0.0957536i
$428$		0			0
$429$	19.9773	−	23.8081i	0.964515	−	1.14946i
$430$		0			0
$431$	0.974582	−	2.67764i	0.0469440	−	0.128977i	−0.914005	−	0.405703i	$-0.867027\pi$
$431$	0.974582	−	2.67764i	0.0469440	−	0.128977i	0.960949	+	0.276725i	$0.0892491\pi$
$432$		0			0
$433$	15.5676	−	26.9638i	0.748130	−	1.29580i	−0.200588	−	0.979676i	$-0.564285\pi$
$433$	15.5676	−	26.9638i	0.748130	−	1.29580i	0.948718	−	0.316123i	$-0.102381\pi$
$434$		0			0
$435$	6.44693	−	2.34649i	0.309106	−	0.112506i
$436$		0			0
$437$	−3.28659	+	2.75777i	−0.157219	+	0.131922i
$438$		0			0
$439$	18.4994	+	22.0467i	0.882929	+	1.05223i	0.998263	+	0.0589066i	$0.0187614\pi$
$439$	18.4994	+	22.0467i	0.882929	+	1.05223i	−0.115335	+	0.993327i	$0.536794\pi$
$440$		0			0
$441$	0.788854	+	4.47381i	0.0375645	+	0.213039i
$442$		0			0
$443$	19.3903			0.921259			0.460630	−	0.887592i	$-0.347624\pi$
$443$	19.3903			0.921259			0.460630	+	0.887592i	$0.347624\pi$
$444$		0			0
$445$	−9.89793			−0.469207
$446$		0			0
$447$	3.41877	+	19.3888i	0.161702	+	0.917060i
$448$		0			0
$449$	10.9788	+	13.0840i	0.518120	+	0.617472i	0.960135	−	0.279536i	$-0.0901806\pi$
$449$	10.9788	+	13.0840i	0.518120	+	0.617472i	−0.442015	+	0.897008i	$0.645736\pi$
$450$		0			0
$451$	15.8101	−	13.2662i	0.744466	−	0.624681i
$452$		0			0
$453$	7.46672	−	2.71766i	0.350817	−	0.127687i
$454$		0			0
$455$	−1.43788	+	2.49049i	−0.0674090	+	0.116756i
$456$		0			0
$457$	−0.826507	+	2.27081i	−0.0386623	+	0.106224i	−0.957522	−	0.288361i	$-0.906890\pi$
$457$	−0.826507	+	2.27081i	−0.0386623	+	0.106224i	0.918859	+	0.394585i	$0.129112\pi$
$458$		0			0
$459$	−24.4475	+	29.1354i	−1.14111	+	1.35992i
$460$		0			0
$461$	−6.40945	−	17.6098i	−0.298518	−	0.820171i	−0.994748	−	0.102353i	$-0.967363\pi$
$461$	−6.40945	−	17.6098i	−0.298518	−	0.820171i	0.696230	−	0.717819i	$-0.254859\pi$
$462$		0			0
$463$	−5.08108	+	0.895932i	−0.236138	+	0.0416375i	−0.290465	−	0.956886i	$-0.593810\pi$
$463$	−5.08108	+	0.895932i	−0.236138	+	0.0416375i	0.0543267	+	0.998523i	$0.482699\pi$
$464$		0			0
$465$	18.4626	+	15.4919i	0.856181	+	0.718421i
$466$		0			0
$467$	26.7874	−	15.4657i	1.23957	−	0.715668i	0.270566	−	0.962701i	$-0.412789\pi$
$467$	26.7874	−	15.4657i	1.23957	−	0.715668i	0.969007	+	0.247034i	$0.0794558\pi$
$468$		0			0
$469$	0.302471	−	1.71540i	0.0139668	−	0.0792097i
$470$		0			0
$471$	−9.16461	−	15.8736i	−0.422283	−	0.731416i
$472$		0			0
$473$	1.50451	+	0.868631i	0.0691776	+	0.0399397i
$474$		0			0
$475$		−	18.5686i		−	0.851985i
$476$		0			0
$477$	−6.93056	−	2.52252i	−0.317328	−	0.115498i
$478$		0			0
$479$	−12.6827	−	2.23629i	−0.579485	−	0.102179i	−0.123780	−	0.992310i	$-0.539502\pi$
$479$	−12.6827	−	2.23629i	−0.579485	−	0.102179i	−0.455705	+	0.890131i	$0.650613\pi$
$480$		0			0
$481$	0.969525	+	28.3920i	0.0442065	+	1.29456i
$482$		0			0
$483$	−0.312467	−	0.0550963i	−0.0142177	−	0.00250697i
$484$		0			0
$485$	−6.92815	−	2.52164i	−0.314591	−	0.114502i
$486$		0			0
$487$			17.2601i			0.782130i	0.920363	+	0.391065i	$0.127893\pi$
$487$			17.2601i			0.782130i	−0.920363	+	0.391065i	$0.872107\pi$
$488$		0			0
$489$	0.937942	+	0.541521i	0.0424152	+	0.0244884i
$490$		0			0
$491$	8.55331	+	14.8148i	0.386005	+	0.668581i	0.991908	−	0.126958i	$-0.0405212\pi$
$491$	8.55331	+	14.8148i	0.386005	+	0.668581i	−0.605903	+	0.795539i	$0.707188\pi$
$492$		0			0
$493$	−1.71618	+	9.73293i	−0.0772928	+	0.438349i
$494$		0			0
$495$	7.56038	−	4.36499i	0.339814	−	0.196192i
$496$		0			0
$497$	2.16962	+	1.82053i	0.0973208	+	0.0816619i
$498$		0			0
$499$	18.2596	−	3.21965i	0.817410	−	0.144131i	0.250717	−	0.968060i	$-0.419334\pi$
$499$	18.2596	−	3.21965i	0.817410	−	0.144131i	0.566693	+	0.823929i	$0.308223\pi$
$500$		0			0
$501$	3.46360	+	9.51615i	0.154742	+	0.425150i
$502$		0			0
$503$	−2.15713	+	2.57077i	−0.0961818	+	0.114625i	−0.811988	−	0.583674i	$-0.801615\pi$
$503$	−2.15713	+	2.57077i	−0.0961818	+	0.114625i	0.715807	+	0.698299i	$0.246059\pi$
$504$		0			0
$505$	11.5462	−	31.7230i	0.513800	−	1.41165i
$506$		0			0
$507$	6.75037	−	11.6920i	0.299794	−	0.519259i
$508$		0			0
$509$	10.3552	−	3.76897i	0.458984	−	0.167057i	−0.102171	−	0.994767i	$-0.532579\pi$
$509$	10.3552	−	3.76897i	0.458984	−	0.167057i	0.561156	+	0.827710i	$0.310357\pi$
$510$		0			0
$511$	−1.11452	+	0.935191i	−0.0493033	+	0.0413704i
$512$		0			0
$513$	−14.9017	−	17.7592i	−0.657926	−	0.784086i
$514$		0			0
$515$	−8.41419	−	47.7192i	−0.370774	−	2.10276i
$516$		0			0
$517$	35.6578			1.56823
$518$		0			0
$519$	23.5967			1.03578
$520$		0			0
$521$	−1.36004	−	7.71318i	−0.0595845	−	0.337921i	0.940413	−	0.340034i	$-0.110439\pi$
$521$	−1.36004	−	7.71318i	−0.0595845	−	0.337921i	−0.999998	+	0.00211306i	$0.999327\pi$
$522$		0			0
$523$	−1.16527	−	1.38872i	−0.0509538	−	0.0607244i	0.739966	−	0.672645i	$-0.234842\pi$
$523$	−1.16527	−	1.38872i	−0.0509538	−	0.0607244i	−0.790919	+	0.611920i	$0.790397\pi$
$524$		0			0
$525$	1.05195	−	0.882688i	0.0459107	−	0.0385237i
$526$		0			0
$527$	−32.6249	+	11.8745i	−1.42116	+	0.517261i
$528$		0			0
$529$	−10.9637	+	18.9897i	−0.476682	+	0.825638i
$530$		0			0
$531$	0.936708	−	2.57359i	0.0406497	−	0.111684i
$532$		0			0
$533$	14.2645	−	16.9997i	0.617863	−	0.736341i
$534$		0			0
$535$	19.6063	+	53.8680i	0.847656	+	2.32892i
$536$		0			0
$537$	−3.85408	+	0.679579i	−0.166316	+	0.0293260i
$538$		0			0
$539$	−23.1581	−	19.4319i	−0.997489	−	0.836993i
$540$		0			0
$541$	−6.02197	+	3.47679i	−0.258905	+	0.149479i	−0.623835	−	0.781556i	$-0.714426\pi$
$541$	−6.02197	+	3.47679i	−0.258905	+	0.149479i	0.364930	+	0.931035i	$0.381093\pi$
$542$		0			0
$543$	2.23157	−	12.6559i	0.0957659	−	0.543116i
$544$		0			0
$545$	−0.0108137	−	0.0187298i	−0.000463207	−	0.000802298i
$546$		0			0
$547$	−4.21435	−	2.43316i	−0.180193	−	0.104034i	0.407191	−	0.913343i	$-0.366508\pi$
$547$	−4.21435	−	2.43316i	−0.180193	−	0.104034i	−0.587383	+	0.809309i	$0.699842\pi$
$548$		0			0
$549$			6.87309i			0.293336i
$550$		0			0
$551$	−5.66083	−	2.06037i	−0.241160	−	0.0877749i
$552$		0			0
$553$	−1.23973	−	0.218598i	−0.0527187	−	0.00929573i
$554$		0			0
$555$	8.88907	−	27.2861i	0.377320	−	1.15823i
$556$		0			0
$557$	−7.17172	−	1.26457i	−0.303876	−	0.0535815i	0.0196313	−	0.999807i	$-0.493751\pi$
$557$	−7.17172	−	1.26457i	−0.303876	−	0.0535815i	−0.323507	+	0.946226i	$0.604862\pi$
$558$		0			0
$559$	1.75534	+	0.638890i	0.0742428	+	0.0270222i
$560$		0			0
$561$		−	45.2262i		−	1.90945i
$562$		0			0
$563$	−23.9124	−	13.8058i	−1.00779	−	0.581845i	−0.0972430	−	0.995261i	$-0.531002\pi$
$563$	−23.9124	−	13.8058i	−1.00779	−	0.581845i	−0.910543	+	0.413415i	$0.864336\pi$
$564$		0			0
$565$	−3.94560	−	6.83397i	−0.165992	−	0.287507i
$566$		0			0
$567$	0.229723	−	1.30282i	0.00964746	−	0.0547134i
$568$		0			0
$569$	−4.89110	+	2.82388i	−0.205046	+	0.118383i	−0.599007	−	0.800744i	$-0.704438\pi$
$569$	−4.89110	+	2.82388i	−0.205046	+	0.118383i	0.393961	+	0.919127i	$0.371104\pi$
$570$		0			0
$571$	−10.3379	−	8.67450i	−0.432626	−	0.363016i	0.400315	−	0.916377i	$-0.368901\pi$
$571$	−10.3379	−	8.67450i	−0.432626	−	0.363016i	−0.832942	+	0.553361i	$0.813345\pi$
$572$		0			0
$573$	9.77986	−	1.72445i	0.408560	−	0.0720401i
$574$		0			0
$575$	1.58775	+	4.36230i	0.0662136	+	0.181920i
$576$		0			0
$577$	27.0708	−	32.2617i	1.12697	−	1.34307i	0.194888	−	0.980825i	$-0.437566\pi$
$577$	27.0708	−	32.2617i	1.12697	−	1.34307i	0.932083	−	0.362246i	$-0.117990\pi$
$578$		0			0
$579$	10.9951	−	30.2087i	0.456940	−	1.25543i
$580$		0			0
$581$	−1.54128	+	2.66958i	−0.0639433	+	0.110753i
$582$		0			0
$583$	46.1201	−	16.7864i	1.91010	−	0.695220i
$584$		0			0
$585$	7.19078	−	6.03378i	0.297302	−	0.249466i
$586$		0			0
$587$	26.6651	+	31.7782i	1.10059	+	1.31163i	0.946188	+	0.323618i	$0.104899\pi$
$587$	26.6651	+	31.7782i	1.10059	+	1.31163i	0.154398	+	0.988009i	$0.450656\pi$
$588$		0			0
$589$	−3.67482	−	20.8409i	−0.151418	−	0.858735i
$590$		0			0
$591$	−2.54035			−0.104496
$592$		0			0
$593$	−29.6746			−1.21859			−0.609295	−	0.792944i	$-0.708548\pi$
$593$	−29.6746			−1.21859			−0.609295	+	0.792944i	$0.708548\pi$
$594$		0			0
$595$	0.726682	+	4.12122i	0.0297910	+	0.168953i
$596$		0			0
$597$	−7.11013	−	8.47352i	−0.290998	−	0.346798i
$598$		0			0
$599$	3.43909	−	2.88574i	0.140517	−	0.117908i	−0.569820	−	0.821770i	$-0.692987\pi$
$599$	3.43909	−	2.88574i	0.140517	−	0.117908i	0.710337	+	0.703862i	$0.248543\pi$
$600$		0			0
$601$	13.3480	−	4.85827i	0.544476	−	0.198173i	−0.0551145	−	0.998480i	$-0.517552\pi$
$601$	13.3480	−	4.85827i	0.544476	−	0.198173i	0.599590	+	0.800307i	$0.295330\pi$
$602$		0			0
$603$	−2.84284	+	4.92394i	−0.115769	+	0.200518i
$604$		0			0
$605$	−8.28433	+	22.7610i	−0.336806	+	0.925367i
$606$		0			0
$607$	16.2460	−	19.3612i	0.659405	−	0.785848i	−0.327895	−	0.944714i	$-0.606339\pi$
$607$	16.2460	−	19.3612i	0.659405	−	0.785848i	0.987300	+	0.158866i	$0.0507838\pi$
$608$		0			0
$609$	−0.152373	−	0.418641i	−0.00617445	−	0.0169642i
$610$		0			0
$611$	37.7585	−	6.65785i	1.52755	−	0.269348i
$612$		0			0
$613$	1.12722	+	0.945851i	0.0455280	+	0.0382025i	0.665268	−	0.746605i	$-0.268317\pi$
$613$	1.12722	+	0.945851i	0.0455280	+	0.0382025i	−0.619740	+	0.784807i	$0.712762\pi$
$614$		0			0
$615$	−19.4140	+	11.2087i	−0.782846	+	0.451977i
$616$		0			0
$617$	−2.72180	+	15.4361i	−0.109575	+	0.621433i	0.879718	+	0.475495i	$0.157731\pi$
$617$	−2.72180	+	15.4361i	−0.109575	+	0.621433i	−0.989294	+	0.145938i	$0.953380\pi$
$618$		0			0
$619$	20.1519	+	34.9042i	0.809974	+	1.40292i	0.912881	+	0.408226i	$0.133852\pi$
$619$	20.1519	+	34.9042i	0.809974	+	1.40292i	−0.102907	+	0.994691i	$0.532814\pi$
$620$		0			0
$621$	5.01938	+	2.89794i	0.201421	+	0.116290i
$622$		0			0
$623$			0.642736i			0.0257507i
$624$		0			0
$625$	25.6726	+	9.34405i	1.02690	+	0.373762i
$626$		0			0
$627$	27.1484	+	4.78699i	1.08420	+	0.191174i
$628$		0			0
$629$	27.6380	+	30.7428i	1.10200	+	1.22580i
$630$		0			0
$631$	−29.0845	−	5.12838i	−1.15783	−	0.204158i	−0.438441	−	0.898760i	$-0.644469\pi$
$631$	−29.0845	−	5.12838i	−1.15783	−	0.204158i	−0.719394	+	0.694602i	$0.755580\pi$
$632$		0			0
$633$	6.49111	+	2.36257i	0.257999	+	0.0939038i
$634$		0			0
$635$		−	17.8818i		−	0.709618i
$636$		0			0
$637$	−28.1506	−	16.2528i	−1.11537	−	0.643959i
$638$		0			0
$639$	−4.62241	−	8.00626i	−0.182860	−	0.316723i
$640$		0			0
$641$	−4.14227	+	23.4920i	−0.163610	+	0.927877i	0.786876	+	0.617111i	$0.211697\pi$
$641$	−4.14227	+	23.4920i	−0.163610	+	0.927877i	−0.950486	+	0.310767i	$0.899414\pi$
$642$		0			0
$643$	−17.4120	+	10.0528i	−0.686663	+	0.396445i	−0.802361	−	0.596839i	$-0.796423\pi$
$643$	−17.4120	+	10.0528i	−0.686663	+	0.396445i	0.115698	+	0.993284i	$0.463090\pi$
$644$		0			0
$645$	−1.44552	−	1.21293i	−0.0569172	−	0.0477592i
$646$		0			0
$647$	−15.3079	+	2.69919i	−0.601815	+	0.106116i	−0.466251	−	0.884652i	$-0.654396\pi$
$647$	−15.3079	+	2.69919i	−0.601815	+	0.106116i	−0.135564	+	0.990769i	$0.543285\pi$
$648$		0			0
$649$	6.23343	+	17.1262i	0.244683	+	0.672262i
$650$		0			0
$651$	1.00599	−	1.19889i	0.0394279	−	0.0469883i
$652$		0			0
$653$	1.10893	−	3.04676i	0.0433958	−	0.119229i	−0.916102	−	0.400946i	$-0.868682\pi$
$653$	1.10893	−	3.04676i	0.0433958	−	0.119229i	0.959498	+	0.281717i	$0.0909038\pi$
$654$		0			0
$655$	12.8864	−	22.3199i	0.503514	−	0.872113i
$656$		0			0
$657$	4.46259	−	1.62425i	0.174102	−	0.0633681i
$658$		0			0
$659$	10.8426	−	9.09798i	0.422366	−	0.354407i	−0.406696	−	0.913563i	$-0.633319\pi$
$659$	10.8426	−	9.09798i	0.422366	−	0.354407i	0.829062	+	0.559156i	$0.188875\pi$
$660$		0			0
$661$	30.2776	+	36.0835i	1.17766	+	1.40348i	0.896049	+	0.443956i	$0.146425\pi$
$661$	30.2776	+	36.0835i	1.17766	+	1.40348i	0.281614	+	0.959528i	$0.409130\pi$
$662$		0			0
$663$	−8.44442	−	47.8907i	−0.327954	−	1.85992i
$664$		0			0
$665$	−2.55080			−0.0989157
$666$		0			0
$667$	1.50607			0.0583153
$668$		0			0
$669$	−3.62934	−	20.5830i	−0.140318	−	0.795785i
$670$		0			0
$671$	−29.3996	−	35.0371i	−1.13496	−	1.35259i
$672$		0			0
$673$	−3.74538	+	3.14274i	−0.144374	+	0.121144i	−0.712114	−	0.702064i	$-0.752262\pi$
$673$	−3.74538	+	3.14274i	−0.144374	+	0.121144i	0.567740	+	0.823208i	$0.307818\pi$
$674$		0			0
$675$	−23.5718	+	8.57943i	−0.907279	+	0.330223i
$676$		0			0
$677$	−2.95124	+	5.11171i	−0.113426	+	0.196459i	−0.917149	−	0.398544i	$-0.869516\pi$
$677$	−2.95124	+	5.11171i	−0.113426	+	0.196459i	0.803724	+	0.595003i	$0.202849\pi$
$678$		0			0
$679$	−0.163746	+	0.449890i	−0.00628401	+	0.0172652i
$680$		0			0
$681$	−26.8244	+	31.9680i	−1.02791	+	1.22502i
$682$		0			0
$683$	−7.74555	−	21.2807i	−0.296375	−	0.814285i	−0.995098	−	0.0988921i	$-0.968470\pi$
$683$	−7.74555	−	21.2807i	−0.296375	−	0.814285i	0.698723	−	0.715392i	$-0.253752\pi$
$684$		0			0
$685$	−4.78536	+	0.843787i	−0.182839	+	0.0322395i
$686$		0			0
$687$	2.39185	+	2.00700i	0.0912549	+	0.0765720i
$688$		0			0
$689$	45.7030	−	26.3866i	1.74114	−	1.00525i
$690$		0			0
$691$	−7.27318	+	41.2483i	−0.276685	+	1.56916i	0.456874	+	0.889531i	$0.348969\pi$
$691$	−7.27318	+	41.2483i	−0.276685	+	1.56916i	−0.733559	+	0.679626i	$0.762142\pi$
$692$		0			0
$693$	−0.283447	−	0.490945i	−0.0107673	−	0.0186494i
$694$		0			0
$695$	−26.4644	−	15.2792i	−1.00385	−	0.579574i
$696$		0			0
$697$		−	32.2930i		−	1.22319i
$698$		0			0
$699$	5.59313	+	2.03573i	0.211552	+	0.0769985i
$700$		0			0
$701$	8.72989	+	1.53931i	0.329723	+	0.0581391i	0.336059	−	0.941841i	$-0.390906\pi$
$701$	8.72989	+	1.53931i	0.329723	+	0.0581391i	−0.00633605	+	0.999980i	$0.502017\pi$
$702$		0			0
$703$	−21.3797	+	13.3366i	−0.806349	+	0.502998i
$704$		0			0
$705$	−38.1426	−	6.72557i	−1.43653	−	0.253300i
$706$		0			0
$707$	−2.05998	−	0.749770i	−0.0774734	−	0.0281980i
$708$		0			0
$709$		−	45.8415i		−	1.72161i	−0.508931	−	0.860807i	$-0.669959\pi$
$709$		−	45.8415i		−	1.72161i	0.508931	−	0.860807i	$-0.330041\pi$
$710$		0			0
$711$	3.55857	+	2.05454i	0.133457	+	0.0770513i
$712$		0			0
$713$	2.64537	+	4.58191i	0.0990698	+	0.171594i
$714$		0			0
$715$	−10.8471	+	61.5171i	−0.405660	+	2.30061i
$716$		0			0
$717$	−24.6399	+	14.2258i	−0.920192	+	0.531273i
$718$		0			0
$719$	4.97255	+	4.17246i	0.185445	+	0.155607i	0.730784	−	0.682609i	$-0.239155\pi$
$719$	4.97255	+	4.17246i	0.185445	+	0.155607i	−0.545339	+	0.838215i	$0.683599\pi$
$720$		0			0
$721$	−3.09872	+	0.546388i	−0.115402	+	0.0203485i
$722$		0			0
$723$	13.2771	+	36.4786i	0.493781	+	1.35665i
$724$		0			0
$725$	−4.18987	+	4.99329i	−0.155608	+	0.185446i
$726$		0			0
$727$	−9.11998	+	25.0569i	−0.338241	+	0.929310i	0.647652	+	0.761936i	$0.275751\pi$
$727$	−9.11998	+	25.0569i	−0.338241	+	0.929310i	−0.985893	+	0.167374i	$0.946471\pi$
$728$		0			0
$729$	−15.0201	+	26.0155i	−0.556299	+	0.963538i
$730$		0			0
$731$	2.55435	−	0.929708i	0.0944761	−	0.0343865i
$732$		0			0
$733$	−37.4593	+	31.4321i	−1.38359	+	1.16097i	−0.415729	+	0.909489i	$0.636473\pi$
$733$	−37.4593	+	31.4321i	−1.38359	+	1.16097i	−0.967862	+	0.251482i	$0.919082\pi$
$734$		0			0
$735$	21.1067	+	25.1540i	0.778532	+	0.927819i
$736$		0			0
$737$	−6.57015	−	37.2611i	−0.242014	−	1.37253i
$738$		0			0
$739$	53.7875			1.97861			0.989303	−	0.145878i	$-0.0466006\pi$
$739$	53.7875			1.97861			0.989303	+	0.145878i	$0.0466006\pi$
$740$		0			0
$741$	29.6416			1.08891
$742$		0			0
$743$	3.90547	+	22.1490i	0.143278	+	0.812569i	0.968734	+	0.248103i	$0.0798070\pi$
$743$	3.90547	+	22.1490i	0.143278	+	0.812569i	−0.825456	+	0.564467i	$0.809082\pi$
$744$		0			0
$745$	−25.4356	−	30.3130i	−0.931889	−	1.11058i
$746$		0			0
$747$	7.70789	−	6.46769i	0.282017	−	0.236640i
$748$		0			0
$749$	3.49800	−	1.27317i	0.127814	−	0.0465205i
$750$		0			0
$751$	3.56277	−	6.17090i	0.130007	−	0.225179i	−0.793672	−	0.608346i	$-0.791833\pi$
$751$	3.56277	−	6.17090i	0.130007	−	0.225179i	0.923679	+	0.383167i	$0.125167\pi$
$752$		0			0
$753$	6.66131	−	18.3018i	0.242752	−	0.666955i
$754$		0			0
$755$	−10.2656	+	12.2341i	−0.373605	+	0.445245i
$756$		0			0
$757$	−1.85286	−	5.09070i	−0.0673434	−	0.185024i	0.901456	−	0.432871i	$-0.142499\pi$
$757$	−1.85286	−	5.09070i	−0.0673434	−	0.185024i	−0.968799	+	0.247846i	$0.920277\pi$
$758$		0			0
$759$	−6.78726	+	1.19678i	−0.246362	+	0.0434403i
$760$		0			0
$761$	19.7639	+	16.5839i	0.716440	+	0.601165i	0.926398	−	0.376546i	$-0.122888\pi$
$761$	19.7639	+	16.5839i	0.716440	+	0.601165i	−0.209958	+	0.977710i	$0.567333\pi$
$762$		0			0
$763$	−0.00121625		0.000702202i	−4.40312e−5		2.54214e-5i
$764$		0			0
$765$	2.37199	−	13.4522i	0.0857595	−	0.486366i
$766$		0			0
$767$	9.79838	+	16.9713i	0.353799	+	0.612798i
$768$		0			0
$769$	−1.66740	−	0.962671i	−0.0601278	−	0.0347148i	0.469635	−	0.882861i	$-0.344386\pi$
$769$	−1.66740	−	0.962671i	−0.0601278	−	0.0347148i	−0.529763	+	0.848146i	$0.677719\pi$
$770$		0			0
$771$			6.66015i			0.239859i
$772$		0			0
$773$	−25.7461	−	9.37083i	−0.926025	−	0.337045i	−0.165392	−	0.986228i	$-0.552889\pi$
$773$	−25.7461	−	9.37083i	−0.926025	−	0.337045i	−0.760633	+	0.649183i	$0.775111\pi$
$774$		0			0
$775$	−22.5505	−	3.97625i	−0.810036	−	0.142831i
$776$		0			0
$777$	−1.77186	−	0.577225i	−0.0635651	−	0.0207078i
$778$		0			0
$779$	19.3849	+	3.41807i	0.694534	+	0.122465i
$780$		0			0
$781$	57.8105	+	21.0413i	2.06862	+	0.752918i
$782$		0			0
$783$			8.13809i			0.290832i
$784$		0			0
$785$	31.9043	+	18.4200i	1.13871	+	0.657437i
$786$		0			0
$787$	−17.7666	−	30.7726i	−0.633309	−	1.09692i	−0.986871	−	0.161512i	$-0.948363\pi$
$787$	−17.7666	−	30.7726i	−0.633309	−	1.09692i	0.353562	−	0.935411i	$-0.384970\pi$
$788$		0			0
$789$	1.73232	−	9.82446i	0.0616722	−	0.349760i
$790$		0			0
$791$	−0.443774	+	0.256213i	−0.0157788	+	0.00910989i
$792$		0			0
$793$	−37.6736	−	31.6119i	−1.33783	−	1.12257i
$794$		0			0
$795$	−52.5001	+	9.25719i	−1.86199	+	0.328319i
$796$		0			0
$797$	17.5674	+	48.2661i	0.622271	+	1.70967i	0.701360	+	0.712807i	$0.252576\pi$
$797$	17.5674	+	48.2661i	0.622271	+	1.70967i	−0.0790896	+	0.996868i	$0.525201\pi$
$798$		0			0
$799$	35.8634	−	42.7404i	1.26876	−	1.51205i
$800$		0			0
$801$	0.717552	−	1.97146i	0.0253534	−	0.0696580i
$802$		0			0
$803$	−15.8013	+	27.3687i	−0.557617	+	0.965821i
$804$		0			0
$805$	0.599256	−	0.218111i	0.0211210	−	0.00768742i
$806$		0			0
$807$	−11.6216	+	9.75169i	−0.409100	+	0.343276i
$808$		0			0
$809$	10.7079	+	12.7612i	0.376470	+	0.448660i	0.920697	−	0.390278i	$-0.127621\pi$
$809$	10.7079	+	12.7612i	0.376470	+	0.448660i	−0.544227	+	0.838938i	$0.683177\pi$
$810$		0			0
$811$	5.92190	+	33.5848i	0.207946	+	1.17932i	0.892736	+	0.450581i	$0.148783\pi$
$811$	5.92190	+	33.5848i	0.207946	+	1.17932i	−0.684790	+	0.728741i	$0.740106\pi$
$812$		0			0
$813$	−13.8272			−0.484942
$814$		0			0
$815$	−2.17681			−0.0762503
$816$		0			0
$817$	0.287718	+	1.63173i	0.0100660	+	0.0570870i
$818$		0			0
$819$	−0.391813	−	0.466944i	−0.0136910	−	0.0163163i
$820$		0			0
$821$	16.5679	−	13.9021i	0.578222	−	0.485186i	−0.306140	−	0.951986i	$-0.599038\pi$
$821$	16.5679	−	13.9021i	0.578222	−	0.485186i	0.884363	+	0.466800i	$0.154593\pi$
$822$		0			0
$823$	21.1059	−	7.68190i	0.735704	−	0.267774i	0.0531267	−	0.998588i	$-0.483081\pi$
$823$	21.1059	−	7.68190i	0.735704	−	0.267774i	0.682577	+	0.730813i	$0.260859\pi$
$824$		0			0
$825$	14.9142	−	25.8322i	0.519247	−	0.899362i
$826$		0			0
$827$	11.2613	−	30.9402i	0.391594	−	1.07590i	−0.574680	−	0.818378i	$-0.694873\pi$
$827$	11.2613	−	30.9402i	0.391594	−	1.07590i	0.966274	−	0.257517i	$-0.0829043\pi$
$828$		0			0
$829$	−11.8170	+	14.0829i	−0.410421	+	0.489121i	−0.931168	−	0.364590i	$-0.881209\pi$
$829$	−11.8170	+	14.0829i	−0.410421	+	0.489121i	0.520747	+	0.853711i	$0.325653\pi$
$830$		0			0
$831$	−0.109039	−	0.299582i	−0.00378252	−	0.0103924i
$832$		0			0
$833$	−46.5832	+	8.21388i	−1.61401	+	0.284594i
$834$		0			0
$835$	−15.5921	−	13.0833i	−0.539586	−	0.452767i
$836$		0			0
$837$	−24.7585	+	14.2943i	−0.855779	+	0.494084i
$838$		0			0
$839$	−1.94855	+	11.0508i	−0.0672715	+	0.381516i	0.932520	+	0.361117i	$0.117605\pi$
$839$	−1.94855	+	11.0508i	−0.0672715	+	0.381516i	−0.999792	+	0.0203984i	$0.993507\pi$
$840$		0			0
$841$	−13.4427	−	23.2834i	−0.463540	−	0.802874i
$842$		0			0
$843$	−35.9030	−	20.7286i	−1.23657	−	0.713931i
$844$		0			0
$845$			27.1351i			0.933477i
$846$		0			0
$847$	1.47802	+	0.537955i	0.0507854	+	0.0184844i
$848$		0			0
$849$	−1.22650	−	0.216266i	−0.0420935	−	0.00742223i
$850$		0			0
$851$	3.88233	−	4.96126i	0.133085	−	0.170070i
$852$		0			0
$853$	−0.0959745	−	0.0169229i	−0.00328610	−	0.000579429i	0.172005	−	0.985096i	$-0.444976\pi$
$853$	−0.0959745	−	0.0169229i	−0.00328610	−	0.000579429i	−0.175291	+	0.984517i	$0.556087\pi$
$854$		0			0
$855$	7.82403	+	2.84772i	0.267576	+	0.0973898i
$856$		0			0
$857$			27.1799i			0.928447i	0.885718	+	0.464223i	$0.153667\pi$
$857$			27.1799i			0.928447i	−0.885718	+	0.464223i	$0.846333\pi$
$858$		0			0
$859$	−13.9714	−	8.06637i	−0.476697	−	0.275221i	0.242342	−	0.970191i	$-0.422084\pi$
$859$	−13.9714	−	8.06637i	−0.476697	−	0.275221i	−0.719039	+	0.694970i	$0.755418\pi$
$860$		0			0
$861$	0.727850	+	1.26067i	0.0248051	+	0.0429637i
$862$		0			0
$863$	−7.25123	+	41.1238i	−0.246835	+	1.39987i	0.569358	+	0.822090i	$0.307192\pi$
$863$	−7.25123	+	41.1238i	−0.246835	+	1.39987i	−0.816193	+	0.577780i	$0.803919\pi$
$864$		0			0
$865$	−41.0730	+	23.7135i	−1.39652	+	0.806283i
$866$		0			0
$867$	−34.2573	−	28.7453i	−1.16344	−	0.976241i
$868$		0			0
$869$	−26.9289	+	4.74829i	−0.913500	+	0.161075i
$870$		0			0
$871$	−13.9144	−	38.2296i	−0.471473	−	1.29536i
$872$		0			0
$873$	1.00452	−	1.19713i	0.0339977	−	0.0405169i
$874$		0			0
$875$	0.109011	−	0.299505i	0.00368524	−	0.0101251i
$876$		0			0
$877$	−6.52496	+	11.3016i	−0.220332	+	0.381627i	−0.954909	−	0.296899i	$-0.904048\pi$
$877$	−6.52496	+	11.3016i	−0.220332	+	0.381627i	0.734577	+	0.678526i	$0.237381\pi$
$878$		0			0
$879$	12.6687	−	4.61102i	0.427304	−	0.155526i
$880$		0			0
$881$	−8.00075	+	6.71343i	−0.269552	+	0.226181i	−0.767537	−	0.641005i	$-0.778518\pi$
$881$	−8.00075	+	6.71343i	−0.269552	+	0.226181i	0.497985	+	0.867186i	$0.334073\pi$
$882$		0			0
$883$	−20.7632	−	24.7446i	−0.698736	−	0.832721i	0.293647	−	0.955914i	$-0.405131\pi$
$883$	−20.7632	−	24.7446i	−0.698736	−	0.832721i	−0.992383	+	0.123193i	$0.960687\pi$
$884$		0			0
$885$	−3.43755	−	19.4953i	−0.115552	−	0.655329i
$886$		0			0
$887$	9.33190			0.313334			0.156667	−	0.987651i	$-0.449925\pi$
$887$	9.33190			0.313334			0.156667	+	0.987651i	$0.449925\pi$
$888$		0			0
$889$	−1.16118			−0.0389448
$890$		0			0
$891$	−4.98994	−	28.2994i	−0.167169	−	0.948065i
$892$		0			0
$893$	21.8602	+	26.0520i	0.731523	+	0.871796i
$894$		0			0
$895$	6.02557	−	5.05606i	0.201413	−	0.169005i
$896$		0			0
$897$	−6.96367	+	2.53457i	−0.232510	+	0.0846268i
$898$		0			0
$899$	−3.71441	+	6.43354i	−0.123882	+	0.214571i
$900$		0			0
$901$	26.2655	−	72.1639i	0.875031	−	2.40413i
$902$		0			0
$903$	−0.0787636	+	0.0938668i	−0.00262109	+	0.00312369i
$904$		0			0
$905$	8.83420	+	24.2718i	0.293659	+	0.806821i
$906$		0			0
$907$	−31.2512	+	5.51042i	−1.03768	+	0.182971i	−0.666433	−	0.745565i	$-0.732180\pi$
$907$	−31.2512	+	5.51042i	−1.03768	+	0.182971i	−0.371244	+	0.928535i	$0.621069\pi$
$908$		0			0
$909$	5.48150	+	4.59952i	0.181810	+	0.152557i
$910$		0			0
$911$	−40.7663	+	23.5364i	−1.35065	+	0.779797i	−0.988340	−	0.152262i	$-0.951344\pi$
$911$	−40.7663	+	23.5364i	−1.35065	+	0.779797i	−0.362307	+	0.932059i	$0.618011\pi$
$912$		0			0
$913$	−11.6272	+	65.9410i	−0.384803	+	2.18233i
$914$		0			0
$915$	24.8398	+	43.0238i	0.821179	+	1.42232i
$916$		0			0
$917$	−1.44938	−	0.836799i	−0.0478627	−	0.0276335i
$918$		0			0
$919$		−	36.4389i		−	1.20201i	−0.799246	−	0.601004i	$-0.794767\pi$
$919$		−	36.4389i		−	1.20201i	0.799246	−	0.601004i	$-0.205233\pi$
$920$		0			0
$921$	35.2065	+	12.8141i	1.16009	+	0.422239i
$922$		0			0
$923$	65.1451	+	11.4868i	2.14428	+	0.378094i
$924$		0			0
$925$	5.64817	+	26.6738i	0.185711	+	0.877029i
$926$		0			0
$927$	10.1147	+	1.78349i	0.332209	+	0.0585774i
$928$		0			0
$929$	−32.2285	−	11.7302i	−1.05738	−	0.384856i	−0.245938	−	0.969285i	$-0.579096\pi$
$929$	−32.2285	−	11.7302i	−1.05738	−	0.384856i	−0.811444	+	0.584430i	$0.801318\pi$
$930$		0			0
$931$		−	28.8324i		−	0.944943i
$932$		0			0
$933$	−0.0168445	−	0.00972517i	−0.000551464	−	0.000318388i
$934$		0			0
$935$	45.4501	+	78.7219i	1.48638	+	2.57448i
$936$		0			0
$937$	−0.945344	+	5.36131i	−0.0308830	+	0.175146i	−0.996348	−	0.0853870i	$-0.972787\pi$
$937$	−0.945344	+	5.36131i	−0.0308830	+	0.175146i	0.965465	+	0.260533i	$0.0838984\pi$
$938$		0			0
$939$	−23.1776	+	13.3816i	−0.756373	+	0.436692i
$940$		0			0
$941$	−30.6634	−	25.7296i	−0.999598	−	0.838762i	−0.0126693	−	0.999920i	$-0.504033\pi$
$941$	−30.6634	−	25.7296i	−0.999598	−	0.838762i	−0.986929	+	0.161157i	$0.948477\pi$
$942$		0			0
$943$	−4.84633	+	0.854539i	−0.157818	+	0.0278276i
$944$		0			0
$945$	1.17857	+	3.23810i	0.0383389	+	0.105335i
$946$		0			0
$947$	22.5711	−	26.8992i	0.733462	−	0.874106i	−0.262402	−	0.964959i	$-0.584515\pi$
$947$	22.5711	−	26.8992i	0.733462	−	0.874106i	0.995864	+	0.0908522i	$0.0289591\pi$
$948$		0			0
$949$	−11.6221	+	31.9315i	−0.377269	+	1.03654i
$950$		0			0
$951$	−2.09046	+	3.62078i	−0.0677878	+	0.117412i
$952$		0			0
$953$	8.48235	−	3.08732i	0.274770	−	0.100008i	−0.200960	−	0.979599i	$-0.564406\pi$
$953$	8.48235	−	3.08732i	0.274770	−	0.100008i	0.475730	+	0.879591i	$0.342184\pi$
$954$		0			0
$955$	−15.2901	+	12.8299i	−0.494775	+	0.415166i
$956$		0			0
$957$	−6.22034	−	7.41311i	−0.201075	−	0.239632i
$958$		0			0
$959$	0.0547926	+	0.310744i	0.00176934	+	0.0100344i
$960$		0			0
$961$	4.90299			0.158161
$962$		0			0
$963$	−12.1507			−0.391552
$964$		0			0
$965$	11.2200	+	63.6316i	0.361183	+	2.04837i
$966$		0			0
$967$	−24.9706	−	29.7588i	−0.802999	−	0.956977i	0.196725	−	0.980459i	$-0.436969\pi$
$967$	−24.9706	−	29.7588i	−0.802999	−	0.956977i	−0.999724	+	0.0234813i	$0.992525\pi$
$968$		0			0
$969$	33.0427	−	27.7262i	1.06149	−	0.890692i
$970$		0			0
$971$	−24.8643	+	9.04986i	−0.797933	+	0.290424i	−0.708630	−	0.705581i	$-0.750686\pi$
$971$	−24.8643	+	9.04986i	−0.797933	+	0.290424i	−0.0893032	+	0.996004i	$0.528464\pi$
$972$		0			0
$973$	−0.992179	+	1.71850i	−0.0318078	+	0.0550927i
$974$		0			0
$975$	10.9696	−	30.1388i	0.351309	−	0.965214i
$976$		0			0
$977$	35.4829	−	42.2869i	1.13520	−	1.35288i	0.208079	−	0.978112i	$-0.433279\pi$
$977$	35.4829	−	42.2869i	1.13520	−	1.35288i	0.927120	−	0.374765i	$-0.122277\pi$
$978$		0			0
$979$	4.77503	+	13.1193i	0.152611	+	0.419294i
$980$		0			0
$981$	0.00451453		0.000796033i	0.000144138		2.54154e-5i
$982$		0			0
$983$	22.7515	+	19.0908i	0.725661	+	0.608902i	0.928945	−	0.370218i	$-0.120717\pi$
$983$	22.7515	+	19.0908i	0.725661	+	0.608902i	−0.203284	+	0.979120i	$0.565162\pi$
$984$		0			0
$985$	4.42179	−	2.55292i	0.140890	−	0.0813429i
$986$		0			0
$987$	−0.436735	+	2.47685i	−0.0139014	+	0.0788389i
$988$		0			0
$989$	−0.207118	−	0.358739i	−0.00658597	−	0.0114072i
$990$		0			0
$991$	17.4731	+	10.0881i	0.555050	+	0.320458i	0.751156	−	0.660124i	$-0.229496\pi$
$991$	17.4731	+	10.0881i	0.555050	+	0.320458i	−0.196106	+	0.980583i	$0.562830\pi$
$992$		0			0
$993$			36.1819i			1.14820i
$994$		0			0
$995$	20.8915	+	7.60390i	0.662306	+	0.241060i
$996$		0			0
$997$	36.4291	+	6.42343i	1.15372	+	0.203432i	0.717599	−	0.696456i	$-0.245241\pi$
$997$	36.4291	+	6.42343i	1.15372	+	0.203432i	0.436121	+	0.899888i	$0.356352\pi$
$998$		0			0
$999$	26.8083	+	20.9783i	0.848177	+	0.663724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bq.b.337.1		12
4.3	odd	2		74.2.h.a.41.1	✓	12
12.11	even	2		666.2.bj.c.559.2		12
37.28	even	18	inner	592.2.bq.b.65.1		12
148.19	even	36		2738.2.a.r.1.6		6
148.55	even	36		2738.2.a.s.1.5		6
148.139	odd	18		74.2.h.a.65.1	yes	12
444.287	even	18		666.2.bj.c.361.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.41.1	✓	12	4.3	odd	2
74.2.h.a.65.1	yes	12	148.139	odd	18
592.2.bq.b.65.1		12	37.28	even	18	inner
592.2.bq.b.337.1		12	1.1	even	1	trivial
666.2.bj.c.361.2		12	444.287	even	18
666.2.bj.c.559.2		12	12.11	even	2
2738.2.a.r.1.6		6	148.19	even	36
2738.2.a.s.1.5		6	148.55	even	36

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bq (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.266044 + 1.50881i) q^{3} +(-1.97937 - 2.35892i) q^{5} +(-0.153180 + 0.128533i) q^{7} +(0.613341 - 0.223238i) q^{9} +O(q^{10})\)	\(q+(0.266044 + 1.50881i) q^{3} +(-1.97937 - 2.35892i) q^{5} +(-0.153180 + 0.128533i) q^{7} +(0.613341 - 0.223238i) q^{9} +(-2.17174 + 3.76157i) q^{11} +(-1.59735 + 4.38867i) q^{13} +(3.03256 - 3.61407i) q^{15} +(2.32445 + 6.38637i) q^{17} +(-4.07964 + 0.719350i) q^{19} +(-0.234685 - 0.196924i) q^{21} +(0.896915 - 0.517834i) q^{23} +(-0.778357 + 4.41428i) q^{25} +(2.79813 + 4.84651i) q^{27} +(1.25937 + 0.727100i) q^{29} +5.10852i q^{31} +(-6.25329 - 2.27601i) q^{33} +(0.606398 + 0.106924i) q^{35} +(5.64160 - 2.27429i) q^{37} +(-7.04665 - 1.24252i) q^{39} +(-4.46505 - 1.62515i) q^{41} -0.399970i q^{43} +(-1.74063 - 1.00495i) q^{45} +(-4.10475 - 7.10963i) q^{47} +(-1.20859 + 6.85428i) q^{49} +(-9.01743 + 5.20621i) q^{51} +(-8.65606 - 7.26330i) q^{53} +(13.1719 - 2.32256i) q^{55} +(-2.17073 - 5.96403i) q^{57} +(2.69714 - 3.21433i) q^{59} +(-3.60153 + 9.89514i) q^{61} +(-0.0652579 + 0.113030i) q^{63} +(13.5143 - 4.91879i) q^{65} +(-6.67299 + 5.59930i) q^{67} +(1.01993 + 1.21551i) q^{69} +(-2.45953 - 13.9487i) q^{71} +7.27588 q^{73} -6.86740 q^{75} +(-0.150819 - 0.855337i) q^{77} +(4.04665 + 4.82261i) q^{79} +(-5.06805 + 4.25260i) q^{81} +(14.4861 - 5.27251i) q^{83} +(10.4640 - 18.1241i) q^{85} +(-0.762009 + 2.09360i) q^{87} +(2.06611 - 2.46229i) q^{89} +(-0.319409 - 0.877568i) q^{91} +(-7.70781 + 1.35909i) q^{93} +(9.77198 + 8.19967i) q^{95} +(2.07350 - 1.19713i) q^{97} +(-0.492294 + 2.79194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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