LMFDB - Embedded newform 756.2.bx.a.41.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(41,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 17, 9]))

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

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

chi := DirichletCharacter("756.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bx (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.18
Character	$\chi$	$=$	756.41
Dual form			756.2.bx.a.461.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.885631 - 1.48851i) q^{3} +(-0.580812 - 0.487359i) q^{5} +(-0.274713 - 2.63145i) q^{7} +(-1.43132 - 2.63654i) q^{9} +O(q^{10})$	\(q+(0.885631 - 1.48851i) q^{3} +(-0.580812 - 0.487359i) q^{5} +(-0.274713 - 2.63145i) q^{7} +(-1.43132 - 2.63654i) q^{9} +(2.03560 + 2.42593i) q^{11} +(3.63164 + 0.640357i) q^{13} +(-1.23982 + 0.432924i) q^{15} +(1.64486 - 2.84899i) q^{17} +(-0.322117 + 0.185975i) q^{19} +(-4.16023 - 1.92158i) q^{21} +(-1.58709 - 4.36050i) q^{23} +(-0.768417 - 4.35791i) q^{25} +(-5.19213 - 0.204470i) q^{27} +(-10.5919 + 1.86764i) q^{29} +(-2.98491 - 8.20097i) q^{31} +(5.41381 - 0.881527i) q^{33} +(-1.12291 + 1.66226i) q^{35} +(-2.91021 + 5.04063i) q^{37} +(4.16947 - 4.83861i) q^{39} +(-1.27317 + 7.22051i) q^{41} +(5.33314 - 4.47504i) q^{43} +(-0.453615 + 2.22890i) q^{45} +(9.81459 + 3.57222i) q^{47} +(-6.84907 + 1.44579i) q^{49} +(-2.78400 - 4.97154i) q^{51} -2.23537i q^{53} -2.40108i q^{55} +(-0.00845222 + 0.644179i) q^{57} +(7.93795 + 6.66073i) q^{59} +(3.02231 - 8.30373i) q^{61} +(-6.54472 + 4.49073i) q^{63} +(-1.79722 - 2.14184i) q^{65} +(-1.68948 + 9.58153i) q^{67} +(-7.89622 - 1.49939i) q^{69} +(6.78533 + 3.91751i) q^{71} +(8.24898 - 4.76255i) q^{73} +(-7.16732 - 2.71570i) q^{75} +(5.82452 - 6.02301i) q^{77} +(-0.249457 - 1.41474i) q^{79} +(-4.90266 + 7.54744i) q^{81} +(-0.0799053 - 0.453166i) q^{83} +(-2.34384 + 0.853087i) q^{85} +(-6.60053 + 17.4202i) q^{87} +(2.54964 + 4.41610i) q^{89} +(0.687409 - 9.73241i) q^{91} +(-14.8507 - 2.81997i) q^{93} +(0.277726 + 0.0489706i) q^{95} +(-2.99639 - 3.57096i) q^{97} +(3.48247 - 8.83921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

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
$3$	0.885631	−	1.48851i	0.511319	−	0.859391i
$3$	0.885631	−	1.48851i	0.511319	−	0.859391i
$4$		0			0
$5$	−0.580812	−	0.487359i	−0.259747	−	0.217954i	0.503609	−	0.863932i	$-0.332005\pi$
$5$	−0.580812	−	0.487359i	−0.259747	−	0.217954i	−0.763356	+	0.645978i	$0.776450\pi$
$6$		0			0
$7$	−0.274713	−	2.63145i	−0.103832	−	0.994595i
$7$	−0.274713	−	2.63145i	−0.103832	−	0.994595i
$8$		0			0
$9$	−1.43132	−	2.63654i	−0.477106	−	0.878846i
$10$		0			0
$11$	2.03560	+	2.42593i	0.613756	+	0.731446i	0.979983	−	0.199079i	$-0.0637951\pi$
$11$	2.03560	+	2.42593i	0.613756	+	0.731446i	−0.366227	+	0.930525i	$0.619351\pi$
$12$		0			0
$13$	3.63164	+	0.640357i	1.00724	+	0.177603i	0.652843	−	0.757493i	$-0.273576\pi$
$13$	3.63164	+	0.640357i	1.00724	+	0.177603i	0.354394	+	0.935096i	$0.384687\pi$
$14$		0			0
$15$	−1.23982	+	0.432924i	−0.320121	+	0.111780i
$16$		0			0
$17$	1.64486	−	2.84899i	0.398938	−	0.690981i	−0.594657	−	0.803979i	$-0.702712\pi$
$17$	1.64486	−	2.84899i	0.398938	−	0.690981i	0.993595	+	0.112998i	$0.0360455\pi$
$18$		0			0
$19$	−0.322117	+	0.185975i	−0.0738988	+	0.0426655i	−0.536494	−	0.843904i	$-0.680252\pi$
$19$	−0.322117	+	0.185975i	−0.0738988	+	0.0426655i	0.462595	+	0.886570i	$0.346918\pi$
$20$		0			0
$21$	−4.16023	−	1.92158i	−0.907837	−	0.419323i
$22$		0			0
$23$	−1.58709	−	4.36050i	−0.330931	−	0.909227i	−0.987870	−	0.155283i	$-0.950371\pi$
$23$	−1.58709	−	4.36050i	−0.330931	−	0.909227i	0.656939	−	0.753944i	$-0.271851\pi$
$24$		0			0
$25$	−0.768417	−	4.35791i	−0.153683	−	0.871582i
$26$		0			0
$27$	−5.19213	−	0.204470i	−0.999225	−	0.0393503i
$28$		0			0
$29$	−10.5919	+	1.86764i	−1.96687	+	0.346812i	−0.974271	+	0.225381i	$0.927637\pi$
$29$	−10.5919	+	1.86764i	−1.96687	+	0.346812i	−0.992600	+	0.121431i	$0.961252\pi$
$30$		0			0
$31$	−2.98491	−	8.20097i	−0.536106	−	1.47294i	−0.851693	−	0.524042i	$-0.824424\pi$
$31$	−2.98491	−	8.20097i	−0.536106	−	1.47294i	0.315587	−	0.948897i	$-0.397799\pi$
$32$		0			0
$33$	5.41381	−	0.881527i	0.942423	−	0.153454i
$34$		0			0
$35$	−1.12291	+	1.66226i	−0.189806	+	0.280974i
$36$		0			0
$37$	−2.91021	+	5.04063i	−0.478435	+	0.828674i	−0.999694	−	0.0247245i	$-0.992129\pi$
$37$	−2.91021	+	5.04063i	−0.478435	+	0.828674i	0.521259	+	0.853398i	$0.325462\pi$
$38$		0			0
$39$	4.16947	−	4.83861i	0.667650	−	0.774798i
$40$		0			0
$41$	−1.27317	+	7.22051i	−0.198836	+	1.12765i	0.708013	+	0.706199i	$0.249592\pi$
$41$	−1.27317	+	7.22051i	−0.198836	+	1.12765i	−0.906849	+	0.421456i	$0.861519\pi$
$42$		0			0
$43$	5.33314	−	4.47504i	0.813296	−	0.682437i	−0.138096	−	0.990419i	$-0.544098\pi$
$43$	5.33314	−	4.47504i	0.813296	−	0.682437i	0.951392	+	0.307982i	$0.0996538\pi$
$44$		0			0
$45$	−0.453615	+	2.22890i	−0.0676209	+	0.332264i
$46$		0			0
$47$	9.81459	+	3.57222i	1.43160	+	0.521062i	0.937391	−	0.348279i	$-0.113234\pi$
$47$	9.81459	+	3.57222i	1.43160	+	0.521062i	0.494214	+	0.869340i	$0.335456\pi$
$48$		0			0
$49$	−6.84907	+	1.44579i	−0.978438	+	0.206541i
$50$		0			0
$51$	−2.78400	−	4.97154i	−0.389838	−	0.696155i
$52$		0			0
$53$		−	2.23537i		−	0.307052i	−0.988145	−	0.153526i	$-0.950937\pi$
$53$		−	2.23537i		−	0.307052i	0.988145	−	0.153526i	$-0.0490629\pi$
$54$		0			0
$55$		−	2.40108i		−	0.323761i
$56$		0			0
$57$	−0.00845222	+	0.644179i	−0.00111952	+	0.0853236i
$58$		0			0
$59$	7.93795	+	6.66073i	1.03343	+	0.867153i	0.991255	−	0.131957i	$-0.0421260\pi$
$59$	7.93795	+	6.66073i	1.03343	+	0.867153i	0.0421777	+	0.999110i	$0.486570\pi$
$60$		0			0
$61$	3.02231	−	8.30373i	0.386967	−	1.06318i	−0.581392	−	0.813623i	$-0.697492\pi$
$61$	3.02231	−	8.30373i	0.386967	−	1.06318i	0.968359	−	0.249560i	$-0.0802860\pi$
$62$		0			0
$63$	−6.54472	+	4.49073i	−0.824557	+	0.565779i
$64$		0			0
$65$	−1.79722	−	2.14184i	−0.222917	−	0.265663i
$66$		0			0
$67$	−1.68948	+	9.58153i	−0.206403	+	1.17057i	0.688814	+	0.724939i	$0.258132\pi$
$67$	−1.68948	+	9.58153i	−0.206403	+	1.17057i	−0.895217	+	0.445631i	$0.852979\pi$
$68$		0			0
$69$	−7.89622	−	1.49939i	−0.950593	−	0.180505i
$70$		0			0
$71$	6.78533	+	3.91751i	0.805271	+	0.464923i	0.845311	−	0.534275i	$-0.179415\pi$
$71$	6.78533	+	3.91751i	0.805271	+	0.464923i	−0.0400400	+	0.999198i	$0.512749\pi$
$72$		0			0
$73$	8.24898	−	4.76255i	0.965470	−	0.557414i	0.0676176	−	0.997711i	$-0.478460\pi$
$73$	8.24898	−	4.76255i	0.965470	−	0.557414i	0.897852	+	0.440297i	$0.145127\pi$
$74$		0			0
$75$	−7.16732	−	2.71570i	−0.827611	−	0.313582i
$76$		0			0
$77$	5.82452	−	6.02301i	0.663765	−	0.686386i
$78$		0			0
$79$	−0.249457	−	1.41474i	−0.0280661	−	0.159171i	0.967554	−	0.252666i	$-0.0813073\pi$
$79$	−0.249457	−	1.41474i	−0.0280661	−	0.159171i	−0.995620	+	0.0934947i	$0.970196\pi$
$80$		0			0
$81$	−4.90266	+	7.54744i	−0.544740	+	0.838605i
$82$		0			0
$83$	−0.0799053	−	0.453166i	−0.00877075	−	0.0497414i	0.980108	−	0.198463i	$-0.0635951\pi$
$83$	−0.0799053	−	0.453166i	−0.00877075	−	0.0497414i	−0.988879	+	0.148722i	$0.952484\pi$
$84$		0			0
$85$	−2.34384	+	0.853087i	−0.254225	+	0.0925302i
$86$		0			0
$87$	−6.60053	+	17.4202i	−0.707651	+	1.86764i
$88$		0			0
$89$	2.54964	+	4.41610i	0.270261	+	0.468106i	0.968929	−	0.247341i	$-0.0795567\pi$
$89$	2.54964	+	4.41610i	0.270261	+	0.468106i	−0.698668	+	0.715446i	$0.746223\pi$
$90$		0			0
$91$	0.687409	−	9.73241i	0.0720600	−	1.02023i
$92$		0			0
$93$	−14.8507	−	2.81997i	−1.53995	−	0.292417i
$94$		0			0
$95$	0.277726	+	0.0489706i	0.0284941	+	0.00502428i
$96$		0			0
$97$	−2.99639	−	3.57096i	−0.304238	−	0.362576i	0.592165	−	0.805817i	$-0.298273\pi$
$97$	−2.99639	−	3.57096i	−0.304238	−	0.362576i	−0.896403	+	0.443240i	$0.853829\pi$
$98$		0			0
$99$	3.48247	−	8.83921i	0.350002	−	0.888374i
$100$		0			0
$101$	−7.14051	−	2.59893i	−0.710507	−	0.258603i	−0.0386167	−	0.999254i	$-0.512295\pi$
$101$	−7.14051	−	2.59893i	−0.710507	−	0.258603i	−0.671890	+	0.740651i	$0.734517\pi$
$102$		0			0
$103$	8.98237	−	10.7048i	0.885059	−	1.05477i	−0.113068	−	0.993587i	$-0.536068\pi$
$103$	8.98237	−	10.7048i	0.885059	−	1.05477i	0.998126	−	0.0611847i	$-0.0194879\pi$
$104$		0			0
$105$	1.47981	+	3.14360i	0.144415	+	0.306784i
$106$		0			0
$107$			14.1706i			1.36993i	0.728577	+	0.684963i	$0.240182\pi$
$107$			14.1706i			1.36993i	−0.728577	+	0.684963i	$0.759818\pi$
$108$		0			0
$109$	18.1324			1.73677			0.868384	−	0.495892i	$-0.165159\pi$
$109$	18.1324			1.73677			0.868384	+	0.495892i	$0.165159\pi$
$110$		0			0
$111$	4.92565	+	8.79600i	0.467522	+	0.834880i
$112$		0			0
$113$	−2.80894	+	3.34756i	−0.264243	+	0.314912i	−0.881809	−	0.471607i	$-0.843674\pi$
$113$	−2.80894	+	3.34756i	−0.264243	+	0.314912i	0.617566	+	0.786519i	$0.288119\pi$
$114$		0			0
$115$	−1.20333	+	3.30611i	−0.112211	+	0.308297i
$116$		0			0
$117$	−3.50971	−	10.4915i	−0.324473	−	0.969941i
$118$		0			0
$119$	−7.94884	−	3.54572i	−0.728669	−	0.325036i
$120$		0			0
$121$	0.168645	−	0.956433i	0.0153314	−	0.0869485i
$122$		0			0
$123$	9.62024	+	8.28983i	0.867428	+	0.747469i
$124$		0			0
$125$	−3.57305	+	6.18871i	−0.319583	+	0.553535i
$126$		0			0
$127$	9.97682	+	17.2804i	0.885300	+	1.53338i	0.845370	+	0.534181i	$0.179380\pi$
$127$	9.97682	+	17.2804i	0.885300	+	1.53338i	0.0399295	+	0.999202i	$0.487287\pi$
$128$		0			0
$129$	−1.93794	−	11.9017i	−0.170626	−	1.04788i
$130$		0			0
$131$	10.4263	−	3.79485i	0.910947	−	0.331557i	0.156316	−	0.987707i	$-0.450038\pi$
$131$	10.4263	−	3.79485i	0.910947	−	0.331557i	0.754631	+	0.656150i	$0.227816\pi$
$132$		0			0
$133$	0.577873	+	0.796546i	0.0501079	+	0.0690693i
$134$		0			0
$135$	2.91600	+	2.64919i	0.250969	+	0.228006i
$136$		0			0
$137$	5.88144	−	1.03706i	0.502485	−	0.0886017i	0.0833406	−	0.996521i	$-0.473441\pi$
$137$	5.88144	−	1.03706i	0.502485	−	0.0886017i	0.419145	+	0.907919i	$0.362330\pi$
$138$		0			0
$139$	−2.14512	−	5.89367i	−0.181947	−	0.499895i	0.814868	−	0.579647i	$-0.196809\pi$
$139$	−2.14512	−	5.89367i	−0.181947	−	0.499895i	−0.996815	+	0.0797520i	$0.974587\pi$
$140$		0			0
$141$	14.0094	−	11.4454i	1.17980	−	0.963880i
$142$		0			0
$143$	5.83911	+	10.1136i	0.488291	+	0.845744i
$144$		0			0
$145$	7.06213	+	4.07732i	0.586478	+	0.338603i
$146$		0			0
$147$	−3.91368	+	11.4753i	−0.322795	+	0.946469i
$148$		0			0
$149$	9.52983	+	1.68037i	0.780714	+	0.137661i	0.549781	−	0.835309i	$-0.314711\pi$
$149$	9.52983	+	1.68037i	0.780714	+	0.137661i	0.230933	+	0.972970i	$0.425822\pi$
$150$		0			0
$151$	3.33262	−	2.79640i	0.271205	−	0.227568i	−0.497034	−	0.867731i	$-0.665578\pi$
$151$	3.33262	−	2.79640i	0.271205	−	0.227568i	0.768239	+	0.640163i	$0.221133\pi$
$152$		0			0
$153$	−9.86578	−	0.258941i	−0.797601	−	0.0209341i
$154$		0			0
$155$	−2.26315	+	6.21795i	−0.181780	+	0.499437i
$156$		0			0
$157$	1.14269	−	1.36181i	0.0911967	−	0.108684i	−0.718516	−	0.695510i	$-0.755178\pi$
$157$	1.14269	−	1.36181i	0.0911967	−	0.108684i	0.809713	+	0.586826i	$0.199623\pi$
$158$		0			0
$159$	−3.32737	−	1.97971i	−0.263878	−	0.157001i
$160$		0			0
$161$	−11.0384	+	5.37424i	−0.869951	+	0.423549i
$162$		0			0
$163$	14.6403			1.14672			0.573359	−	0.819304i	$-0.305640\pi$
$163$	14.6403			1.14672			0.573359	+	0.819304i	$0.305640\pi$
$164$		0			0
$165$	−3.57403	−	2.12647i	−0.278238	−	0.165545i
$166$		0			0
$167$	−5.85974	−	4.91691i	−0.453441	−	0.380482i	0.387270	−	0.921966i	$-0.373418\pi$
$167$	−5.85974	−	4.91691i	−0.453441	−	0.380482i	−0.840711	+	0.541484i	$0.817862\pi$
$168$		0			0
$169$	0.562775	+	0.204833i	0.0432904	+	0.0157564i
$170$		0			0
$171$	0.951381	+	0.583086i	0.0727539	+	0.0445897i
$172$		0			0
$173$	14.0203	−	11.7644i	1.06594	−	0.894432i	0.0712635	−	0.997458i	$-0.477297\pi$
$173$	14.0203	−	11.7644i	1.06594	−	0.894432i	0.994679	+	0.103026i	$0.0328524\pi$
$174$		0			0
$175$	−11.2565	+	3.21923i	−0.850914	+	0.243351i
$176$		0			0
$177$	16.9446	−	5.91676i	1.27364	−	0.444731i
$178$		0			0
$179$	15.2922	+	8.82896i	1.14299	+	0.659907i	0.947170	−	0.320732i	$-0.103929\pi$
$179$	15.2922	+	8.82896i	1.14299	+	0.659907i	0.195823	+	0.980639i	$0.437262\pi$
$180$		0			0
$181$	−19.6886	+	11.3672i	−1.46344	+	0.844920i	−0.999169	−	0.0407705i	$-0.987019\pi$
$181$	−19.6886	+	11.3672i	−1.46344	+	0.844920i	−0.464276	+	0.885691i	$0.653685\pi$
$182$		0			0
$183$	−9.68352	−	11.8528i	−0.715827	−	0.876182i
$184$		0			0
$185$	4.14688	−	1.50934i	0.304885	−	0.110969i
$186$		0			0
$187$	10.2597	−	1.80907i	0.750266	−	0.132292i
$188$		0			0
$189$	0.888290	+	13.7190i	0.0646136	+	0.997910i
$190$		0			0
$191$	−22.7735	+	4.01558i	−1.64783	+	0.290557i	−0.919036	−	0.394175i	$-0.871031\pi$
$191$	−22.7735	+	4.01558i	−1.64783	+	0.290557i	−0.728795	+	0.684732i	$0.759919\pi$
$192$		0			0
$193$	−12.7613	+	4.64473i	−0.918578	+	0.334335i	−0.757673	−	0.652635i	$-0.773664\pi$
$193$	−12.7613	+	4.64473i	−0.918578	+	0.334335i	−0.160905	+	0.986970i	$0.551441\pi$
$194$		0			0
$195$	−4.77982	+	0.778295i	−0.342290	+	0.0557349i
$196$		0			0
$197$	−13.5242	+	7.80820i	−0.963560	+	0.556311i	−0.897267	−	0.441489i	$-0.854450\pi$
$197$	−13.5242	+	7.80820i	−0.963560	+	0.556311i	−0.0662928	+	0.997800i	$0.521117\pi$
$198$		0			0
$199$	−5.52621	−	3.19056i	−0.391743	−	0.226173i	0.291172	−	0.956671i	$-0.405955\pi$
$199$	−5.52621	−	3.19056i	−0.391743	−	0.226173i	−0.682915	+	0.730498i	$0.739288\pi$
$200$		0			0
$201$	12.7659	+	11.0005i	0.900439	+	0.775916i
$202$		0			0
$203$	7.82434	+	27.3591i	0.549161	+	1.92023i
$204$		0			0
$205$	4.25846	−	3.57327i	0.297423	−	0.249568i
$206$		0			0
$207$	−9.22499	+	10.4257i	−0.641181	+	0.724635i
$208$		0			0
$209$	−1.10686	−	0.402865i	−0.0765633	−	0.0278668i
$210$		0			0
$211$	17.6446	+	14.8056i	1.21470	+	1.01926i	0.999084	+	0.0427808i	$0.0136217\pi$
$211$	17.6446	+	14.8056i	1.21470	+	1.01926i	0.215620	+	0.976477i	$0.430823\pi$
$212$		0			0
$213$	11.8406	−	6.63056i	0.811301	−	0.454318i
$214$		0			0
$215$	−5.27850			−0.359991
$216$		0			0
$217$	−20.7605	+	10.1076i	−1.40931	+	0.686146i
$218$		0			0
$219$	0.216450	−	16.4965i	0.0146263	−	1.11473i
$220$		0			0
$221$	7.79793	−	9.29321i	0.524545	−	0.625129i
$222$		0			0
$223$	1.29796	−	3.56610i	0.0869176	−	0.238804i	−0.888617	−	0.458650i	$-0.848333\pi$
$223$	1.29796	−	3.56610i	0.0869176	−	0.238804i	0.975535	+	0.219846i	$0.0705554\pi$
$224$		0			0
$225$	−10.3899	+	8.26351i	−0.692663	+	0.550901i
$226$		0			0
$227$	−6.50525	+	5.45855i	−0.431769	+	0.362297i	−0.832619	−	0.553847i	$-0.813159\pi$
$227$	−6.50525	+	5.45855i	−0.431769	+	0.362297i	0.400850	+	0.916144i	$0.368715\pi$
$228$		0			0
$229$	−8.95145	−	1.57838i	−0.591529	−	0.104302i	−0.130132	−	0.991497i	$-0.541540\pi$
$229$	−8.95145	−	1.57838i	−0.591529	−	0.104302i	−0.461396	+	0.887194i	$0.652651\pi$
$230$		0			0
$231$	−3.80694	−	14.0040i	−0.250478	−	0.921396i
$232$		0			0
$233$	−1.89811	−	1.09588i	−0.124350	−	0.0717932i	0.436535	−	0.899687i	$-0.356206\pi$
$233$	−1.89811	−	1.09588i	−0.124350	−	0.0717932i	−0.560885	+	0.827894i	$0.689539\pi$
$234$		0			0
$235$	−3.95948	−	6.85802i	−0.258288	−	0.447368i
$236$		0			0
$237$	−2.32678	−	0.881620i	−0.151141	−	0.0572674i
$238$		0			0
$239$	−0.443055	−	1.21728i	−0.0286588	−	0.0787395i	0.924538	−	0.381090i	$-0.124451\pi$
$239$	−0.443055	−	1.21728i	−0.0286588	−	0.0787395i	−0.953197	+	0.302350i	$0.902229\pi$
$240$		0			0
$241$	14.8370	−	2.61616i	0.955733	−	0.168521i	0.326031	−	0.945359i	$-0.394288\pi$
$241$	14.8370	−	2.61616i	0.955733	−	0.168521i	0.629701	+	0.776837i	$0.283177\pi$
$242$		0			0
$243$	6.89249	+	13.9819i	0.442153	+	0.896939i
$244$		0			0
$245$	4.68264	+	2.49822i	0.299163	+	0.159606i
$246$		0			0
$247$	−1.28891	+	0.469123i	−0.0820111	+	0.0298496i
$248$		0			0
$249$	−0.745308	−	0.282398i	−0.0472320	−	0.0178962i
$250$		0			0
$251$	10.9824	+	19.0220i	0.693201	+	1.20066i	0.970783	+	0.239958i	$0.0771336\pi$
$251$	10.9824	+	19.0220i	0.693201	+	1.20066i	−0.277582	+	0.960702i	$0.589533\pi$
$252$		0			0
$253$	7.34759	−	12.7264i	0.461939	−	0.800102i
$254$		0			0
$255$	−0.805946	+	4.24434i	−0.0504703	+	0.265791i
$256$		0			0
$257$	−0.495949	+	2.81267i	−0.0309365	+	0.175449i	−0.996361	−	0.0852332i	$-0.972836\pi$
$257$	−0.495949	+	2.81267i	−0.0309365	+	0.175449i	0.965425	+	0.260683i	$0.0839476\pi$
$258$		0			0
$259$	14.0636	+	6.27334i	0.873872	+	0.389807i
$260$		0			0
$261$	20.0845	+	25.2528i	1.24320	+	1.56311i
$262$		0			0
$263$	−2.49305	+	6.84959i	−0.153728	+	0.422364i	−0.992519	−	0.122089i	$-0.961041\pi$
$263$	−2.49305	+	6.84959i	−0.153728	+	0.422364i	0.838791	+	0.544453i	$0.183263\pi$
$264$		0			0
$265$	−1.08943	+	1.29833i	−0.0669231	+	0.0797558i
$266$		0			0
$267$	8.83144	+	0.115877i	0.540475	+	0.00709153i
$268$		0			0
$269$	−13.7990			−0.841341			−0.420670	−	0.907214i	$-0.638205\pi$
$269$	−13.7990			−0.841341			−0.420670	+	0.907214i	$0.638205\pi$
$270$		0			0
$271$			6.87579i			0.417675i	0.977950	+	0.208837i	$0.0669679\pi$
$271$			6.87579i			0.417675i	−0.977950	+	0.208837i	$0.933032\pi$
$272$		0			0
$273$	−13.8780	−	9.64253i	−0.839934	−	0.583592i
$274$		0			0
$275$	9.00781	−	10.7351i	0.543191	−	0.647350i
$276$		0			0
$277$	−24.4022	−	8.88168i	−1.46619	−	0.533649i	−0.519125	−	0.854698i	$-0.673742\pi$
$277$	−24.4022	−	8.88168i	−1.46619	−	0.533649i	−0.947062	+	0.321049i	$0.895964\pi$
$278$		0			0
$279$	−17.3498	+	19.6080i	−1.03871	+	1.17390i
$280$		0			0
$281$	−10.8817	−	12.9683i	−0.649150	−	0.773627i	0.336636	−	0.941635i	$-0.390711\pi$
$281$	−10.8817	−	12.9683i	−0.649150	−	0.773627i	−0.985786	+	0.168008i	$0.946266\pi$
$282$		0			0
$283$	7.55158	+	1.33155i	0.448895	+	0.0791522i	0.393525	−	0.919314i	$-0.371255\pi$
$283$	7.55158	+	1.33155i	0.448895	+	0.0791522i	0.0553692	+	0.998466i	$0.482366\pi$
$284$		0			0
$285$	0.318856	−	0.370028i	0.0188874	−	0.0219185i
$286$		0			0
$287$	19.3502	+	1.36672i	1.14221	+	0.0806750i
$288$		0			0
$289$	3.08885	+	5.35004i	0.181697	+	0.314708i
$290$		0			0
$291$	−7.96910	+	1.29760i	−0.467157	+	0.0760669i
$292$		0			0
$293$	−0.905744	+	0.329664i	−0.0529142	+	0.0192592i	−0.368342	−	0.929691i	$-0.620074\pi$
$293$	−0.905744	+	0.329664i	−0.0529142	+	0.0192592i	0.315427	+	0.948950i	$0.397852\pi$
$294$		0			0
$295$	−1.36429	−	7.73726i	−0.0794319	−	0.450481i
$296$		0			0
$297$	−10.0731	−	13.0120i	−0.584498	−	0.755031i
$298$		0			0
$299$	−2.97148	−	16.8521i	−0.171845	−	0.974581i
$300$		0			0
$301$	−13.2409	−	12.8045i	−0.763194	−	0.738042i
$302$		0			0
$303$	−10.1924	+	8.32701i	−0.585537	+	0.478374i
$304$		0			0
$305$	−5.80229	+	3.34995i	−0.332238	+	0.191818i
$306$		0			0
$307$	−1.50572	−	0.869326i	−0.0859358	−	0.0496151i	0.456416	−	0.889766i	$-0.349133\pi$
$307$	−1.50572	−	0.869326i	−0.0859358	−	0.0496151i	−0.542352	+	0.840151i	$0.682466\pi$
$308$		0			0
$309$	−7.97908	−	22.8508i	−0.453914	−	1.29994i
$310$		0			0
$311$	5.38235	−	30.5248i	0.305205	−	1.73090i	−0.317334	−	0.948314i	$-0.602787\pi$
$311$	5.38235	−	30.5248i	0.305205	−	1.73090i	0.622538	−	0.782589i	$-0.286101\pi$
$312$		0			0
$313$	8.97130	+	10.6916i	0.507088	+	0.604324i	0.957477	−	0.288508i	$-0.0931592\pi$
$313$	8.97130	+	10.6916i	0.507088	+	0.604324i	−0.450389	+	0.892832i	$0.648715\pi$
$314$		0			0
$315$	5.98985	+	0.581358i	0.337490	+	0.0327558i
$316$		0			0
$317$	0.819774	−	2.25231i	0.0460431	−	0.126502i	−0.914540	−	0.404496i	$-0.867447\pi$
$317$	0.819774	−	2.25231i	0.0460431	−	0.126502i	0.960583	+	0.277993i	$0.0896693\pi$
$318$		0			0
$319$	−26.0917	−	21.8935i	−1.46085	−	1.22580i
$320$		0			0
$321$	21.0931	+	12.5499i	1.17730	+	0.700470i
$322$		0			0
$323$			1.22361i			0.0680835i
$324$		0			0
$325$		−	16.3184i		−	0.905184i
$326$		0			0
$327$	16.0586	−	26.9902i	0.888043	−	1.49256i
$328$		0			0
$329$	6.70392	−	26.8079i	0.369599	−	1.47797i
$330$		0			0
$331$	−8.54493	−	3.11010i	−0.469672	−	0.170947i	0.0963319	−	0.995349i	$-0.469289\pi$
$331$	−8.54493	−	3.11010i	−0.469672	−	0.170947i	−0.566004	+	0.824403i	$0.691511\pi$
$332$		0			0
$333$	17.4552	+	0.458136i	0.956541	+	0.0251057i
$334$		0			0
$335$	5.65092	−	4.74168i	0.308742	−	0.259066i
$336$		0			0
$337$	−2.82194	+	16.0040i	−0.153721	+	0.871793i	0.806225	+	0.591608i	$0.201507\pi$
$337$	−2.82194	+	16.0040i	−0.153721	+	0.871793i	−0.959946	+	0.280185i	$0.909604\pi$
$338$		0			0
$339$	2.49520	+	7.14583i	0.135520	+	0.388108i
$340$		0			0
$341$	13.8189	−	23.9351i	0.748337	−	1.29616i
$342$		0			0
$343$	5.68604	+	17.6258i	0.307017	+	0.951704i
$344$		0			0
$345$	3.85547	+	4.71916i	0.207572	+	0.254071i
$346$		0			0
$347$	−9.78183	−	26.8754i	−0.525116	−	1.44275i	−0.864757	−	0.502190i	$-0.832528\pi$
$347$	−9.78183	−	26.8754i	−0.525116	−	1.44275i	0.339641	−	0.940555i	$-0.389694\pi$
$348$		0			0
$349$	−6.58677	+	1.16143i	−0.352582	+	0.0621697i	−0.347134	−	0.937815i	$-0.612845\pi$
$349$	−6.58677	+	1.16143i	−0.352582	+	0.0621697i	−0.00544760	+	0.999985i	$0.501734\pi$
$350$		0			0
$351$	−18.7250	−	4.06738i	−0.999468	−	0.217101i
$352$		0			0
$353$	−0.525929	−	2.98269i	−0.0279924	−	0.158753i	0.967607	−	0.252460i	$-0.0812395\pi$
$353$	−0.525929	−	2.98269i	−0.0279924	−	0.158753i	−0.995600	+	0.0937069i	$0.970128\pi$
$354$		0			0
$355$	−2.03177	−	5.58223i	−0.107835	−	0.296274i
$356$		0			0
$357$	−12.3176	+	8.69171i	−0.651915	+	0.460014i
$358$		0			0
$359$	−10.7244	+	6.19172i	−0.566011	+	0.326787i	−0.755555	−	0.655086i	$-0.772633\pi$
$359$	−10.7244	+	6.19172i	−0.566011	+	0.326787i	0.189544	+	0.981872i	$0.439299\pi$
$360$		0			0
$361$	−9.43083	+	16.3347i	−0.496359	+	0.859720i
$362$		0			0
$363$	−1.27430	−	1.09808i	−0.0668835	−	0.0576341i
$364$		0			0
$365$	−7.11218	−	1.25407i	−0.372268	−	0.0656409i
$366$		0			0
$367$	0.689314	+	0.821493i	0.0359819	+	0.0428816i	0.783735	−	0.621095i	$-0.213312\pi$
$367$	0.689314	+	0.821493i	0.0359819	+	0.0428816i	−0.747753	+	0.663977i	$0.768867\pi$
$368$		0			0
$369$	20.8595	−	6.97808i	1.08590	−	0.363264i
$370$		0			0
$371$	−5.88227	+	0.614085i	−0.305392	+	0.0318817i
$372$		0			0
$373$	5.67292	+	4.76015i	0.293733	+	0.246471i	0.777730	−	0.628598i	$-0.216371\pi$
$373$	5.67292	+	4.76015i	0.293733	+	0.246471i	−0.483997	+	0.875070i	$0.660816\pi$
$374$		0			0
$375$	6.04754	+	10.7994i	0.312294	+	0.557680i
$376$		0			0
$377$	−39.6620			−2.04270
$378$		0			0
$379$	26.9337			1.38349			0.691745	−	0.722142i	$-0.256842\pi$
$379$	26.9337			1.38349			0.691745	+	0.722142i	$0.256842\pi$
$380$		0			0
$381$	34.5577	+	0.453429i	1.77045	+	0.0232299i
$382$		0			0
$383$	26.6839	+	22.3904i	1.36348	+	1.14410i	0.974890	+	0.222689i	$0.0714833\pi$
$383$	26.6839	+	22.3904i	1.36348	+	1.14410i	0.388593	+	0.921409i	$0.372961\pi$
$384$		0			0
$385$	−6.31832	+	0.659607i	−0.322011	+	0.0336167i
$386$		0			0
$387$	−19.4320	−	7.65583i	−0.987785	−	0.389168i
$388$		0			0
$389$	−13.0365	−	15.5363i	−0.660977	−	0.787722i	0.326548	−	0.945181i	$-0.394114\pi$
$389$	−13.0365	−	15.5363i	−0.660977	−	0.787722i	−0.987526	+	0.157458i	$0.949670\pi$
$390$		0			0
$391$	−15.0336	−	2.65082i	−0.760279	−	0.134058i
$392$		0			0
$393$	3.58515	−	18.8804i	0.180847	−	0.952391i
$394$		0			0
$395$	−0.544600	+	0.943275i	−0.0274018	+	0.0474613i
$396$		0			0
$397$	7.02081	−	4.05347i	0.352364	−	0.203438i	−0.313362	−	0.949634i	$-0.601455\pi$
$397$	7.02081	−	4.05347i	0.352364	−	0.203438i	0.665726	+	0.746196i	$0.268122\pi$
$398$		0			0
$399$	1.69745	−	0.154723i	0.0849787	−	0.00774582i
$400$		0			0
$401$	−1.96007	−	5.38524i	−0.0978811	−	0.268926i	0.881082	−	0.472964i	$-0.156816\pi$
$401$	−1.96007	−	5.38524i	−0.0978811	−	0.268926i	−0.978963	+	0.204037i	$0.934594\pi$
$402$		0			0
$403$	−5.58858	−	31.6944i	−0.278387	−	1.57881i
$404$		0			0
$405$	6.52584	−	1.99429i	0.324272	−	0.0990970i
$406$		0			0
$407$	−18.1522	+	3.20073i	−0.899773	+	0.158654i
$408$		0			0
$409$	10.2787	+	28.2404i	0.508247	+	1.39640i	0.883044	+	0.469290i	$0.155490\pi$
$409$	10.2787	+	28.2404i	0.508247	+	1.39640i	−0.374797	+	0.927107i	$0.622288\pi$
$410$		0			0
$411$	3.66512	−	9.67303i	0.180787	−	0.477135i
$412$		0			0
$413$	15.3467	−	22.7181i	0.755163	−	1.11789i
$414$		0			0
$415$	−0.174444	+	0.302147i	−0.00856314	+	0.0148318i
$416$		0			0
$417$	−10.6726	−	2.02658i	−0.522638	−	0.0992422i
$418$		0			0
$419$	2.02546	−	11.4870i	0.0989504	−	0.561176i	−0.894515	−	0.447039i	$-0.852479\pi$
$419$	2.02546	−	11.4870i	0.0989504	−	0.561176i	0.993465	−	0.114137i	$-0.0364103\pi$
$420$		0			0
$421$	0.622585	−	0.522411i	0.0303429	−	0.0254608i	−0.627490	−	0.778625i	$-0.715918\pi$
$421$	0.622585	−	0.522411i	0.0303429	−	0.0254608i	0.657833	+	0.753164i	$0.271473\pi$
$422$		0			0
$423$	−4.62950	−	30.9895i	−0.225094	−	1.50676i
$424$		0			0
$425$	−13.6796	−	4.97896i	−0.663557	−	0.241515i
$426$		0			0
$427$	−22.6811	−	5.67192i	−1.09762	−	0.274483i
$428$		0			0
$429$	20.2255	+	0.265377i	0.976497	+	0.0128125i
$430$		0			0
$431$		−	17.3542i		−	0.835924i	−0.908465	−	0.417962i	$-0.862745\pi$
$431$		−	17.3542i		−	0.835924i	0.908465	−	0.417962i	$-0.137255\pi$
$432$		0			0
$433$			30.4315i			1.46245i	0.682139	+	0.731223i	$0.261050\pi$
$433$			30.4315i			1.46245i	−0.682139	+	0.731223i	$0.738950\pi$
$434$		0			0
$435$	12.3236	−	6.90104i	0.590870	−	0.330879i
$436$		0			0
$437$	1.32217	+	1.10943i	0.0632480	+	0.0530714i
$438$		0			0
$439$	9.18800	−	25.2438i	0.438519	−	1.20482i	−0.501936	−	0.864905i	$-0.667379\pi$
$439$	9.18800	−	25.2438i	0.438519	−	1.20482i	0.940455	−	0.339917i	$-0.110399\pi$
$440$		0			0
$441$	13.6151	+	15.9884i	0.648336	+	0.761354i
$442$		0			0
$443$	7.22306	+	8.60810i	0.343178	+	0.408983i	0.909835	−	0.414970i	$-0.136208\pi$
$443$	7.22306	+	8.60810i	0.343178	+	0.408983i	−0.566657	+	0.823954i	$0.691764\pi$
$444$		0			0
$445$	0.671367	−	3.80751i	0.0318259	−	0.180493i
$446$		0			0
$447$	10.9412	−	12.6971i	0.517499	−	0.600550i
$448$		0			0
$449$	3.02045	+	1.74385i	0.142544	+	0.0822976i	0.569576	−	0.821939i	$-0.307108\pi$
$449$	3.02045	+	1.74385i	0.142544	+	0.0822976i	−0.427032	+	0.904236i	$0.640441\pi$
$450$		0			0
$451$	−20.1081	+	11.6094i	−0.946856	+	0.546667i
$452$		0			0
$453$	−1.21100	−	7.43721i	−0.0568976	−	0.349431i
$454$		0			0
$455$	−5.14243	+	5.31768i	−0.241081	+	0.249297i
$456$		0			0
$457$	−2.04648	−	11.6062i	−0.0957303	−	0.542913i	−0.994521	−	0.104536i	$-0.966664\pi$
$457$	−2.04648	−	11.6062i	−0.0957303	−	0.542913i	0.898791	−	0.438378i	$-0.144447\pi$
$458$		0			0
$459$	−9.12288	+	14.4560i	−0.425819	+	0.674747i
$460$		0			0
$461$	−3.51700	−	19.9459i	−0.163803	−	0.928973i	−0.950290	−	0.311366i	$-0.899213\pi$
$461$	−3.51700	−	19.9459i	−0.163803	−	0.928973i	0.786487	−	0.617607i	$-0.211898\pi$
$462$		0			0
$463$	−34.2382	+	12.4617i	−1.59119	+	0.579144i	−0.977598	−	0.210481i	$-0.932497\pi$
$463$	−34.2382	+	12.4617i	−1.59119	+	0.579144i	−0.613589	+	0.789626i	$0.710275\pi$
$464$		0			0
$465$	7.25116	+	8.87552i	0.336264	+	0.411592i
$466$		0			0
$467$	−1.66258	−	2.87968i	−0.0769351	−	0.133255i	0.824991	−	0.565146i	$-0.191180\pi$
$467$	−1.66258	−	2.87968i	−0.0769351	−	0.133255i	−0.901926	+	0.431890i	$0.857847\pi$
$468$		0			0
$469$	25.6774	+	1.81362i	1.18567	+	0.0837452i
$470$		0			0
$471$	−1.01506	−	2.90696i	−0.0467714	−	0.133946i
$472$		0			0
$473$	21.7123	+	3.82846i	0.998331	+	0.176033i
$474$		0			0
$475$	1.05798	+	1.26085i	0.0485435	+	0.0578519i
$476$		0			0
$477$	−5.89364	+	3.19953i	−0.269851	+	0.146496i
$478$		0			0
$479$	−2.58586	−	0.941175i	−0.118151	−	0.0430034i	0.282268	−	0.959336i	$-0.408913\pi$
$479$	−2.58586	−	0.941175i	−0.118151	−	0.0430034i	−0.400419	+	0.916332i	$0.631135\pi$
$480$		0			0
$481$	−13.7966	+	16.4422i	−0.629072	+	0.749699i
$482$		0			0
$483$	−1.77638	+	21.1904i	−0.0808281	+	0.964197i
$484$		0			0
$485$			3.53438i			0.160488i
$486$		0			0
$487$	−6.75517			−0.306106			−0.153053	−	0.988218i	$-0.548911\pi$
$487$	−6.75517			−0.306106			−0.153053	+	0.988218i	$0.548911\pi$
$488$		0			0
$489$	12.9659	−	21.7922i	0.586339	−	0.985479i
$490$		0			0
$491$	−6.44850	+	7.68503i	−0.291017	+	0.346820i	−0.891667	−	0.452691i	$-0.850464\pi$
$491$	−6.44850	+	7.68503i	−0.291017	+	0.346820i	0.600650	+	0.799512i	$0.294908\pi$
$492$		0			0
$493$	−12.1014	+	33.2483i	−0.545019	+	1.49743i
$494$		0			0
$495$	−6.33053	+	3.43670i	−0.284536	+	0.154468i
$496$		0			0
$497$	8.44473	−	18.9315i	0.378798	−	0.849192i
$498$		0			0
$499$	−0.778363	+	4.41432i	−0.0348443	+	0.197612i	−0.997261	−	0.0739660i	$-0.976434\pi$
$499$	−0.778363	+	4.41432i	−0.0348443	+	0.197612i	0.962416	+	0.271578i	$0.0875455\pi$
$500$		0			0
$501$	−12.5084	+	4.36772i	−0.558835	+	0.195135i
$502$		0			0
$503$	7.20120	−	12.4728i	0.321086	−	0.556137i	−0.659627	−	0.751593i	$-0.729286\pi$
$503$	7.20120	−	12.4728i	0.321086	−	0.556137i	0.980712	+	0.195457i	$0.0626189\pi$
$504$		0			0
$505$	2.88068	+	4.98948i	0.128189	+	0.222029i
$506$		0			0
$507$	0.803308	−	0.656289i	0.0356761	−	0.0291468i
$508$		0			0
$509$	−39.0931	+	14.2287i	−1.73277	+	0.630677i	−0.998822	−	0.0485267i	$-0.984547\pi$
$509$	−39.0931	+	14.2287i	−1.73277	+	0.630677i	−0.733950	+	0.679204i	$0.762325\pi$
$510$		0			0
$511$	−14.7985	−	20.3984i	−0.654648	−	0.902374i
$512$		0			0
$513$	1.71050	−	0.899740i	0.0755204	−	0.0397245i
$514$		0			0
$515$	−10.4341	+	1.83982i	−0.459783	+	0.0810721i
$516$		0			0
$517$	11.3126	+	31.0811i	0.497528	+	1.36695i
$518$		0			0
$519$	−5.09464	−	31.2882i	−0.223630	−	1.37340i
$520$		0			0
$521$	8.77828	+	15.2044i	0.384583	+	0.666118i	0.991711	−	0.128486i	$-0.0410117\pi$
$521$	8.77828	+	15.2044i	0.384583	+	0.666118i	−0.607128	+	0.794604i	$0.707678\pi$
$522$		0			0
$523$	9.12872	+	5.27047i	0.399171	+	0.230462i	0.686126	−	0.727482i	$-0.259310\pi$
$523$	9.12872	+	5.27047i	0.399171	+	0.230462i	−0.286955	+	0.957944i	$0.592643\pi$
$524$		0			0
$525$	−5.17728	+	19.6065i	−0.225955	+	0.855698i
$526$		0			0
$527$	−28.2742	−	4.98551i	−1.23165	−	0.217172i
$528$		0			0
$529$	1.12394	−	0.943099i	0.0488671	−	0.0410043i
$530$		0			0
$531$	6.19955	−	30.4623i	0.269037	−	1.32195i
$532$		0			0
$533$	−9.24741	+	25.4070i	−0.400550	+	1.10050i
$534$		0			0
$535$	6.90619	−	8.23047i	0.298581	−	0.355834i
$536$		0			0
$537$	26.6852	−	14.9434i	1.15155	−	0.644855i
$538$		0			0
$539$	−17.4493	−	13.6723i	−0.751596	−	0.588909i
$540$		0			0
$541$	6.04178			0.259756			0.129878	−	0.991530i	$-0.458541\pi$
$541$	6.04178			0.259756			0.129878	+	0.991530i	$0.458541\pi$
$542$		0			0
$543$	−0.516621	+	39.3739i	−0.0221703	+	1.68969i
$544$		0			0
$545$	−10.5315	−	8.83699i	−0.451120	−	0.378535i
$546$		0			0
$547$	32.8469	+	11.9553i	1.40443	+	0.511172i	0.929491	−	0.368845i	$-0.120247\pi$
$547$	32.8469	+	11.9553i	1.40443	+	0.511172i	0.474942	+	0.880017i	$0.342469\pi$
$548$		0			0
$549$	−26.2190	+	3.91683i	−1.11900	+	0.167166i
$550$		0			0
$551$	3.06451	−	2.57143i	0.130552	−	0.109546i
$552$		0			0
$553$	−3.65430	+	1.04508i	−0.155397	+	0.0444414i
$554$		0			0
$555$	1.42594	−	7.50938i	0.0605276	−	0.318756i
$556$		0			0
$557$	26.9399	+	15.5538i	1.14148	+	0.659034i	0.946797	−	0.321832i	$-0.104299\pi$
$557$	26.9399	+	15.5538i	1.14148	+	0.659034i	0.194684	+	0.980866i	$0.437632\pi$
$558$		0			0
$559$	22.2337	−	12.8366i	0.940385	−	0.542931i
$560$		0			0
$561$	6.39352	−	16.8739i	0.269935	−	0.712415i
$562$		0			0
$563$	−2.93215	+	1.06721i	−0.123575	+	0.0449777i	−0.403068	−	0.915170i	$-0.632056\pi$
$563$	−2.93215	+	1.06721i	−0.123575	+	0.0449777i	0.279492	+	0.960148i	$0.409834\pi$
$564$		0			0
$565$	3.26293	−	0.575343i	0.137273	−	0.0242048i
$566$		0			0
$567$	21.2075	+	10.8277i	0.890633	+	0.454722i
$568$		0			0
$569$	17.8105	−	3.14048i	0.746656	−	0.131656i	0.212641	−	0.977130i	$-0.431794\pi$
$569$	17.8105	−	3.14048i	0.746656	−	0.131656i	0.534015	+	0.845475i	$0.320683\pi$
$570$		0			0
$571$	−7.02115	+	2.55549i	−0.293826	+	0.106944i	−0.484727	−	0.874665i	$-0.661081\pi$
$571$	−7.02115	+	2.55549i	−0.293826	+	0.106944i	0.190901	+	0.981609i	$0.438859\pi$
$572$		0			0
$573$	−14.1917	+	37.4548i	−0.592865	+	1.56470i
$574$		0			0
$575$	−17.7831	+	10.2671i	−0.741607	+	0.428167i
$576$		0			0
$577$	−16.7017	−	9.64275i	−0.695302	−	0.401433i	0.110293	−	0.993899i	$-0.464821\pi$
$577$	−16.7017	−	9.64275i	−0.695302	−	0.401433i	−0.805595	+	0.592466i	$0.798154\pi$
$578$		0			0
$579$	−4.38807	+	23.1088i	−0.182362	+	0.960369i
$580$		0			0
$581$	−1.17053	+	0.334757i	−0.0485619	+	0.0138881i
$582$		0			0
$583$	5.42286	−	4.55032i	0.224592	−	0.188455i
$584$		0			0
$585$	−3.07466	+	7.80409i	−0.127121	+	0.322659i
$586$		0			0
$587$	−15.9146	−	5.79243i	−0.656864	−	0.239079i	−0.00798237	−	0.999968i	$-0.502541\pi$
$587$	−15.9146	−	5.79243i	−0.656864	−	0.239079i	−0.648882	+	0.760889i	$0.724763\pi$
$588$		0			0
$589$	2.48666	+	2.08656i	0.102461	+	0.0859751i
$590$		0			0
$591$	−0.354869	+	27.0461i	−0.0145974	+	1.11253i
$592$		0			0
$593$	−44.1513			−1.81308			−0.906538	−	0.422125i	$-0.861284\pi$
$593$	−44.1513			−1.81308			−0.906538	+	0.422125i	$0.861284\pi$
$594$		0			0
$595$	2.88874	+	5.93334i	0.118427	+	0.243243i
$596$		0			0
$597$	−9.64336	+	5.40016i	−0.394676	+	0.221014i
$598$		0			0
$599$	23.6707	−	28.2097i	0.967160	−	1.15262i	−0.0210911	−	0.999778i	$-0.506714\pi$
$599$	23.6707	−	28.2097i	0.967160	−	1.15262i	0.988251	−	0.152839i	$-0.0488415\pi$
$600$		0			0
$601$	−8.31816	+	22.8540i	−0.339305	+	0.932233i	0.646287	+	0.763094i	$0.276321\pi$
$601$	−8.31816	+	22.8540i	−0.339305	+	0.932233i	−0.985592	+	0.169138i	$0.945901\pi$
$602$		0			0
$603$	27.6802	−	9.25982i	1.12723	−	0.377089i
$604$		0			0
$605$	−0.564078	+	0.473317i	−0.0229330	+	0.0192431i
$606$		0			0
$607$	−13.5872	−	2.39579i	−0.551487	−	0.0972420i	−0.109041	−	0.994037i	$-0.534778\pi$
$607$	−13.5872	−	2.39579i	−0.551487	−	0.0972420i	−0.442446	+	0.896795i	$0.645889\pi$
$608$		0			0
$609$	47.6537	+	12.5834i	1.93102	+	0.509906i
$610$		0			0
$611$	33.3556	+	19.2579i	1.34942	+	0.779090i
$612$		0			0
$613$	−17.8206	−	30.8661i	−0.719766	−	1.24667i	−0.961092	−	0.276228i	$-0.910916\pi$
$613$	−17.8206	−	30.8661i	−0.719766	−	1.24667i	0.241326	−	0.970444i	$-0.422418\pi$
$614$		0			0
$615$	−1.54742	−	9.50335i	−0.0623981	−	0.383212i
$616$		0			0
$617$	−0.342056	−	0.939792i	−0.0137707	−	0.0378346i	0.932617	−	0.360868i	$-0.117520\pi$
$617$	−0.342056	−	0.939792i	−0.0137707	−	0.0378346i	−0.946388	+	0.323034i	$0.895297\pi$
$618$		0			0
$619$	−24.7736	+	4.36825i	−0.995735	+	0.175575i	−0.647691	−	0.761903i	$-0.724265\pi$
$619$	−24.7736	+	4.36825i	−0.995735	+	0.175575i	−0.348044	+	0.937478i	$0.613154\pi$
$620$		0			0
$621$	7.34879	+	22.9648i	0.294897	+	0.921545i
$622$		0			0
$623$	10.9203	−	7.92240i	0.437514	−	0.317404i
$624$		0			0
$625$	−15.7000	+	5.71432i	−0.627998	+	0.228573i
$626$		0			0
$627$	−1.57994	+	1.29079i	−0.0630967	+	0.0515490i
$628$		0			0
$629$	9.57379	+	16.5823i	0.381732	+	0.661179i
$630$		0			0
$631$	−8.81809	+	15.2734i	−0.351043	+	0.608024i	−0.986432	−	0.164168i	$-0.947506\pi$
$631$	−8.81809	+	15.2734i	−0.351043	+	0.608024i	0.635390	+	0.772192i	$0.280839\pi$
$632$		0			0
$633$	37.6648	−	13.1519i	1.49704	−	0.522740i
$634$		0			0
$635$	2.62708	−	14.8989i	0.104253	−	0.591246i
$636$		0			0
$637$	−25.7992	+	0.864733i	−1.02220	+	0.0342620i
$638$		0			0
$639$	0.616710	−	23.4970i	0.0243967	−	0.929527i
$640$		0			0
$641$	14.5683	−	40.0260i	0.575411	−	1.58093i	−0.220416	−	0.975406i	$-0.570741\pi$
$641$	14.5683	−	40.0260i	0.575411	−	1.58093i	0.795827	−	0.605524i	$-0.207036\pi$
$642$		0			0
$643$	18.0323	−	21.4901i	0.711126	−	0.847487i	−0.282611	−	0.959235i	$-0.591200\pi$
$643$	18.0323	−	21.4901i	0.711126	−	0.847487i	0.993737	+	0.111748i	$0.0356448\pi$
$644$		0			0
$645$	−4.67480	+	7.85709i	−0.184070	+	0.309373i
$646$		0			0
$647$	−1.52315			−0.0598813			−0.0299407	−	0.999552i	$-0.509532\pi$
$647$	−1.52315			−0.0598813			−0.0299407	+	0.999552i	$0.509532\pi$
$648$		0			0
$649$			32.8155i			1.28812i
$650$		0			0
$651$	−3.34092	+	39.8537i	−0.130941	+	1.56199i
$652$		0			0
$653$	9.91571	−	11.8171i	0.388032	−	0.462438i	−0.536300	−	0.844027i	$-0.680179\pi$
$653$	9.91571	−	11.8171i	0.388032	−	0.462438i	0.924332	+	0.381589i	$0.124623\pi$
$654$		0			0
$655$	−7.90515	−	2.87724i	−0.308880	−	0.112423i
$656$		0			0
$657$	−24.3635	−	14.9320i	−0.950512	−	0.582554i
$658$		0			0
$659$	−9.37220	−	11.1694i	−0.365089	−	0.435096i	0.551960	−	0.833871i	$-0.313880\pi$
$659$	−9.37220	−	11.1694i	−0.365089	−	0.435096i	−0.917049	+	0.398774i	$0.869436\pi$
$660$		0			0
$661$	22.4478	+	3.95815i	0.873118	+	0.153954i	0.592213	−	0.805781i	$-0.298254\pi$
$661$	22.4478	+	3.95815i	0.873118	+	0.153954i	0.280905	+	0.959736i	$0.409365\pi$
$662$		0			0
$663$	−6.92694	−	19.8376i	−0.269020	−	0.770430i
$664$		0			0
$665$	0.0525688	−	0.744275i	0.00203853	−	0.0288617i
$666$		0			0
$667$	24.9542	+	43.2219i	0.966230	+	1.67356i
$668$		0			0
$669$	−4.15867	−	5.09027i	−0.160783	−	0.196801i
$670$		0			0
$671$	26.2965	−	9.57114i	1.01517	−	0.369490i
$672$		0			0
$673$	7.00771	+	39.7427i	0.270127	+	1.53197i	0.754026	+	0.656845i	$0.228109\pi$
$673$	7.00771	+	39.7427i	0.270127	+	1.53197i	−0.483898	+	0.875124i	$0.660780\pi$
$674$		0			0
$675$	3.09866	+	22.7839i	0.119267	+	0.876955i
$676$		0			0
$677$	4.58819	+	26.0209i	0.176338	+	1.00006i	0.936588	+	0.350433i	$0.113966\pi$
$677$	4.58819	+	26.0209i	0.176338	+	1.00006i	−0.760249	+	0.649631i	$0.774923\pi$
$678$		0			0
$679$	−8.57366	+	8.86585i	−0.329027	+	0.340240i
$680$		0			0
$681$	2.36386	+	14.5174i	0.0905831	+	0.556307i
$682$		0			0
$683$	19.4784	−	11.2459i	0.745322	−	0.430312i	−0.0786790	−	0.996900i	$-0.525070\pi$
$683$	19.4784	−	11.2459i	0.745322	−	0.430312i	0.824001	+	0.566588i	$0.191737\pi$
$684$		0			0
$685$	−3.92143	−	2.26404i	−0.149830	−	0.0865045i
$686$		0			0
$687$	−10.2771	+	11.9265i	−0.392096	+	0.455022i
$688$		0			0
$689$	1.43144	−	8.11807i	0.0545333	−	0.309274i
$690$		0			0
$691$	2.74733	+	3.27414i	0.104513	+	0.124554i	0.815765	−	0.578383i	$-0.196316\pi$
$691$	2.74733	+	3.27414i	0.104513	+	0.124554i	−0.711252	+	0.702937i	$0.751872\pi$
$692$		0			0
$693$	−24.2166	−	6.73572i	−0.919914	−	0.255869i
$694$		0			0
$695$	−1.62642	+	4.46856i	−0.0616937	+	0.169502i
$696$		0			0
$697$	18.4770	+	15.5040i	0.699865	+	0.587256i
$698$		0			0
$699$	−3.31225	+	1.85482i	−0.125281	+	0.0701556i
$700$		0			0
$701$			23.7848i			0.898340i	0.893446	+	0.449170i	$0.148280\pi$
$701$			23.7848i			0.898340i	−0.893446	+	0.449170i	$0.851720\pi$
$702$		0			0
$703$		−	2.16490i		−	0.0816507i
$704$		0			0
$705$	−13.7149	−	0.179951i	−0.516531	−	0.00677736i
$706$		0			0
$707$	−4.87737	+	19.5039i	−0.183433	+	0.733518i
$708$		0			0
$709$	−4.38703	−	1.59675i	−0.164758	−	0.0599672i	0.258324	−	0.966058i	$-0.416830\pi$
$709$	−4.38703	−	1.59675i	−0.164758	−	0.0599672i	−0.423083	+	0.906091i	$0.639052\pi$
$710$		0			0
$711$	−3.37297	+	2.68265i	−0.126496	+	0.100607i
$712$		0			0
$713$	−31.0230	+	26.0314i	−1.16182	+	0.974883i
$714$		0			0
$715$	1.53755	−	8.71986i	0.0575010	−	0.326104i
$716$		0			0
$717$	−2.20432	−	0.418572i	−0.0823218	−	0.0156319i
$718$		0			0
$719$	11.7175	−	20.2952i	0.436988	−	0.756885i	−0.560468	−	0.828176i	$-0.689379\pi$
$719$	11.7175	−	20.2952i	0.436988	−	0.756885i	0.997456	+	0.0712912i	$0.0227120\pi$
$720$		0			0
$721$	−30.6366	−	20.6959i	−1.14097	−	0.770756i
$722$		0			0
$723$	9.24589	−	24.4019i	0.343858	−	0.907516i
$724$		0			0
$725$	16.2780	+	44.7235i	0.604551	+	1.66099i
$726$		0			0
$727$	13.2926	−	2.34385i	0.492996	−	0.0869285i	0.0783772	−	0.996924i	$-0.475026\pi$
$727$	13.2926	−	2.34385i	0.492996	−	0.0869285i	0.414619	+	0.909995i	$0.363915\pi$
$728$		0			0
$729$	26.9164	+	2.12327i	0.996903	+	0.0786397i
$730$		0			0
$731$	−3.97703	−	22.5549i	−0.147096	−	0.834222i
$732$		0			0
$733$	−7.19663	−	19.7726i	−0.265813	−	0.730317i	−0.998748	−	0.0500177i	$-0.984072\pi$
$733$	−7.19663	−	19.7726i	−0.265813	−	0.730317i	0.732935	−	0.680299i	$-0.238150\pi$
$734$		0			0
$735$	7.86572	−	4.75764i	0.290131	−	0.175488i
$736$		0			0
$737$	−26.6832	+	15.4056i	−0.982890	+	0.567472i
$738$		0			0
$739$	−11.7112	+	20.2844i	−0.430803	+	0.746173i	−0.996943	−	0.0781363i	$-0.975103\pi$
$739$	−11.7112	+	20.2844i	−0.430803	+	0.746173i	0.566139	+	0.824310i	$0.308436\pi$
$740$		0			0
$741$	−0.443200	+	2.33402i	−0.0162814	+	0.0857423i
$742$		0			0
$743$	−31.0839	−	5.48093i	−1.14036	−	0.201076i	−0.428596	−	0.903496i	$-0.640992\pi$
$743$	−31.0839	−	5.48093i	−1.14036	−	0.201076i	−0.711762	+	0.702420i	$0.752103\pi$
$744$		0			0
$745$	−4.71610	−	5.62043i	−0.172784	−	0.205917i
$746$		0			0
$747$	−1.08042	+	0.859297i	−0.0395305	+	0.0314400i
$748$		0			0
$749$	37.2893	−	3.89285i	1.36252	−	0.142242i
$750$		0			0
$751$	0.0408859	+	0.0343073i	0.00149195	+	0.00125189i	0.643533	−	0.765418i	$-0.277468\pi$
$751$	0.0408859	+	0.0343073i	0.00149195	+	0.00125189i	−0.642041	+	0.766670i	$0.721912\pi$
$752$		0			0
$753$	38.0408	+	0.499130i	1.38628	+	0.0181893i
$754$		0			0
$755$	−3.29848			−0.120044
$756$		0			0
$757$	21.5650			0.783794			0.391897	−	0.920009i	$-0.371819\pi$
$757$	21.5650			0.783794			0.391897	+	0.920009i	$0.371819\pi$
$758$		0			0
$759$	−12.4361	−	22.2078i	−0.451402	−	0.806094i
$760$		0			0
$761$	−1.36733	−	1.14732i	−0.0495656	−	0.0415905i	0.617668	−	0.786439i	$-0.288077\pi$
$761$	−1.36733	−	1.14732i	−0.0495656	−	0.0415905i	−0.667234	+	0.744848i	$0.732522\pi$
$762$		0			0
$763$	−4.98120	−	47.7145i	−0.180331	−	1.72738i
$764$		0			0
$765$	5.60397	+	4.95858i	0.202612	+	0.179278i
$766$		0			0
$767$	24.5626	+	29.2725i	0.886903	+	1.05697i
$768$		0			0
$769$	−16.3648	−	2.88555i	−0.590128	−	0.104056i	−0.129393	−	0.991593i	$-0.541303\pi$
$769$	−16.3648	−	2.88555i	−0.590128	−	0.104056i	−0.460735	+	0.887538i	$0.652414\pi$
$770$		0			0
$771$	3.74745	+	3.22921i	0.134961	+	0.116297i
$772$		0			0
$773$	18.1663	−	31.4649i	0.653395	−	1.13171i	−0.328898	−	0.944365i	$-0.606677\pi$
$773$	18.1663	−	31.4649i	0.653395	−	1.13171i	0.982293	−	0.187349i	$-0.0599894\pi$
$774$		0			0
$775$	−33.4455	+	19.3097i	−1.20140	+	0.693626i
$776$		0			0
$777$	21.7931	−	15.3780i	0.781823	−	0.551682i
$778$		0			0
$779$	−0.932721	−	2.56263i	−0.0334182	−	0.0918158i
$780$		0			0
$781$	4.30859	+	24.4352i	0.154174	+	0.874362i
$782$		0			0
$783$	55.3765	−	7.53130i	1.97899	−	0.269147i
$784$		0			0
$785$	−1.32738	+	0.234052i	−0.0473761	+	0.00835369i
$786$		0			0
$787$	−7.16754	−	19.6927i	−0.255495	−	0.701967i	−0.999431	−	0.0337166i	$-0.989266\pi$
$787$	−7.16754	−	19.6927i	−0.255495	−	0.701967i	0.743936	−	0.668251i	$-0.232957\pi$
$788$		0			0
$789$	7.98776	+	9.77713i	0.284372	+	0.348075i
$790$		0			0
$791$	9.58060	+	6.47197i	0.340647	+	0.230117i
$792$		0			0
$793$	16.2933	−	28.2208i	0.578592	−	1.00215i
$794$		0			0
$795$	0.967745	+	2.77146i	0.0343224	+	0.0982937i
$796$		0			0
$797$	−5.73543	+	32.5273i	−0.203160	+	1.15217i	0.697150	+	0.716925i	$0.254451\pi$
$797$	−5.73543	+	32.5273i	−0.203160	+	1.15217i	−0.900310	+	0.435250i	$0.856660\pi$
$798$		0			0
$799$	26.3209	−	22.0858i	0.931165	−	0.781340i
$800$		0			0
$801$	7.99388	−	13.0431i	0.282450	−	0.460854i
$802$		0			0
$803$	28.3452	+	10.3168i	1.00028	+	0.364073i
$804$		0			0
$805$	9.03044	+	2.25826i	0.318281	+	0.0795933i
$806$		0			0
$807$	−12.2208	+	20.5400i	−0.430194	+	0.723041i
$808$		0			0
$809$		−	3.11659i		−	0.109573i	−0.998498	−	0.0547867i	$-0.982552\pi$
$809$		−	3.11659i		−	0.109573i	0.998498	−	0.0547867i	$-0.0174479\pi$
$810$		0			0
$811$		−	30.6649i		−	1.07679i	−0.842692	−	0.538395i	$-0.819031\pi$
$811$		−	30.6649i		−	1.07679i	0.842692	−	0.538395i	$-0.180969\pi$
$812$		0			0
$813$	10.2347	+	6.08941i	0.358946	+	0.213565i
$814$		0			0
$815$	−8.50327	−	7.13509i	−0.297857	−	0.249931i
$816$		0			0
$817$	−0.885654	+	2.43331i	−0.0309851	+	0.0851309i
$818$		0			0
$819$	−26.6438	+	12.1178i	−0.931008	+	0.423429i
$820$		0			0
$821$	12.8376	+	15.2993i	0.448036	+	0.533949i	0.942035	−	0.335514i	$-0.108910\pi$
$821$	12.8376	+	15.2993i	0.448036	+	0.533949i	−0.493999	+	0.869462i	$0.664465\pi$
$822$		0			0
$823$	1.58071	−	8.96463i	0.0551000	−	0.312487i	−0.944784	−	0.327693i	$-0.893729\pi$
$823$	1.58071	−	8.96463i	0.0551000	−	0.312487i	0.999884	+	0.0152050i	$0.00484010\pi$
$824$		0			0
$825$	−8.00168	−	22.9155i	−0.278583	−	0.797816i
$826$		0			0
$827$	−7.71719	−	4.45552i	−0.268353	−	0.154934i	0.359786	−	0.933035i	$-0.382850\pi$
$827$	−7.71719	−	4.45552i	−0.268353	−	0.154934i	−0.628139	+	0.778101i	$0.716183\pi$
$828$		0			0
$829$	11.0653	−	6.38856i	0.384314	−	0.221884i	−0.295379	−	0.955380i	$-0.595446\pi$
$829$	11.0653	−	6.38856i	0.384314	−	0.221884i	0.679694	+	0.733496i	$0.262113\pi$
$830$		0			0
$831$	−34.8318	+	28.4570i	−1.20830	+	0.987164i
$832$		0			0
$833$	−7.14675	+	21.8910i	−0.247620	+	0.758479i
$834$		0			0
$835$	1.00711	+	5.71160i	0.0348524	+	0.197658i
$836$		0			0
$837$	13.8212	+	43.1908i	0.477730	+	1.49289i
$838$		0			0
$839$	4.35684	+	24.7089i	0.150415	+	0.853044i	0.962859	+	0.270005i	$0.0870254\pi$
$839$	4.35684	+	24.7089i	0.150415	+	0.853044i	−0.812444	+	0.583039i	$0.801863\pi$
$840$		0			0
$841$	81.4496	−	29.6452i	2.80861	−	1.02225i
$842$		0			0
$843$	−28.9407	+	4.71239i	−0.996770	+	0.162303i
$844$		0			0
$845$	−0.227039	−	0.393243i	−0.00781039	−	0.0135280i
$846$		0			0
$847$	−2.56314	−	0.181037i	−0.0880704	−	0.00622049i
$848$		0			0
$849$	8.66993	−	10.0613i	0.297551	−	0.345304i
$850$		0			0
$851$	26.5984	+	4.69002i	0.911782	+	0.160772i
$852$		0			0
$853$	12.5040	+	14.9017i	0.428130	+	0.510226i	0.936382	−	0.350983i	$-0.114152\pi$
$853$	12.5040	+	14.9017i	0.428130	+	0.510226i	−0.508252	+	0.861209i	$0.669708\pi$
$854$		0			0
$855$	−0.268401	−	0.802327i	−0.00917912	−	0.0274390i
$856$		0			0
$857$	−54.8203	−	19.9530i	−1.87263	−	0.681581i	−0.965292	−	0.261172i	$-0.915891\pi$
$857$	−54.8203	−	19.9530i	−1.87263	−	0.681581i	−0.907335	−	0.420409i	$-0.861887\pi$
$858$		0			0
$859$	−20.4664	+	24.3909i	−0.698304	+	0.832206i	−0.992333	−	0.123590i	$-0.960559\pi$
$859$	−20.4664	+	24.3909i	−0.698304	+	0.832206i	0.294029	+	0.955796i	$0.405004\pi$
$860$		0			0
$861$	19.1715	−	27.5925i	0.653363	−	0.940350i
$862$		0			0
$863$		−	56.3306i		−	1.91751i	−0.284226	−	0.958757i	$-0.591737\pi$
$863$		−	56.3306i		−	1.91751i	0.284226	−	0.958757i	$-0.408263\pi$
$864$		0			0
$865$	−13.8766			−0.471820
$866$		0			0
$867$	10.6992	+	0.140383i	0.363362	+	0.00476765i
$868$		0			0
$869$	2.92428	−	3.48502i	0.0991993	−	0.118221i
$870$		0			0
$871$	−12.2712	+	33.7148i	−0.415793	+	1.14238i
$872$		0			0
$873$	−5.12619	+	13.0113i	−0.173495	+	0.440365i
$874$		0			0
$875$	17.2668	+	7.70219i	0.583726	+	0.260382i
$876$		0			0
$877$	−2.43349	+	13.8010i	−0.0821732	+	0.466027i	0.915758	+	0.401731i	$0.131591\pi$
$877$	−2.43349	+	13.8010i	−0.0821732	+	0.466027i	−0.997931	+	0.0642962i	$0.979520\pi$
$878$		0			0
$879$	−0.311447	+	1.64017i	−0.0105049	+	0.0553215i
$880$		0			0
$881$	25.9828	−	45.0035i	0.875383	−	1.51621i	0.0190281	−	0.999819i	$-0.493943\pi$
$881$	25.9828	−	45.0035i	0.875383	−	1.51621i	0.856355	−	0.516388i	$-0.172724\pi$
$882$		0			0
$883$	−5.33882	−	9.24711i	−0.179666	−	0.311190i	0.762100	−	0.647459i	$-0.224168\pi$
$883$	−5.33882	−	9.24711i	−0.179666	−	0.311190i	−0.941766	+	0.336269i	$0.890835\pi$
$884$		0			0
$885$	−12.7252	−	4.82160i	−0.427754	−	0.162076i
$886$		0			0
$887$	−42.6916	+	15.5385i	−1.43344	+	0.521731i	−0.937916	−	0.346862i	$-0.887247\pi$
$887$	−42.6916	+	15.5385i	−1.43344	+	0.521731i	−0.495527	+	0.868593i	$0.665025\pi$
$888$		0			0
$889$	42.7316	−	31.0006i	1.43317	−	1.03973i
$890$		0			0
$891$	−28.2894	+	3.47004i	−0.947732	+	0.116251i
$892$		0			0
$893$	−3.82579	+	0.674590i	−0.128025	+	0.0225743i
$894$		0			0
$895$	−4.57902	−	12.5808i	−0.153060	−	0.420528i
$896$		0			0
$897$	−27.7161	−	10.5016i	−0.925414	−	0.350640i
$898$		0			0
$899$	46.9324	+	81.2893i	1.56528	+	2.71115i
$900$		0			0
$901$	−6.36854	−	3.67688i	−0.212167	−	0.122495i
$902$		0			0
$903$	−30.7862	+	8.36913i	−1.02450	+	0.278507i
$904$		0			0
$905$	16.9753	+	2.99321i	0.564279	+	0.0994976i
$906$		0			0
$907$	−26.4373	+	22.1835i	−0.877836	+	0.736592i	−0.965733	−	0.259538i	$-0.916430\pi$
$907$	−26.4373	+	22.1835i	−0.877836	+	0.736592i	0.0878972	+	0.996130i	$0.471985\pi$
$908$		0			0
$909$	3.36815	+	22.5461i	0.111714	+	0.747807i
$910$		0			0
$911$	−12.5484	+	34.4764i	−0.415747	+	1.14226i	0.538341	+	0.842727i	$0.319051\pi$
$911$	−12.5484	+	34.4764i	−0.415747	+	1.14226i	−0.954087	+	0.299528i	$0.903171\pi$
$912$		0			0
$913$	0.936694	−	1.11631i	0.0310001	−	0.0369444i
$914$		0			0
$915$	−0.152250	+	11.6036i	−0.00503322	+	0.383603i
$916$		0			0
$917$	−12.8502	−	26.3937i	−0.424350	−	0.871597i
$918$		0			0
$919$	−44.2554			−1.45985			−0.729926	−	0.683526i	$-0.760445\pi$
$919$	−44.2554			−1.45985			−0.729926	+	0.683526i	$0.760445\pi$
$920$		0			0
$921$	−2.62751	+	1.47137i	−0.0865794	+	0.0484833i
$922$		0			0
$923$	22.1333	+	18.5720i	0.728527	+	0.611306i
$924$		0			0
$925$	24.2029	+	8.80912i	0.795785	+	0.289642i
$926$		0			0
$927$	−41.0801	−	8.36043i	−1.34925	−	0.274593i
$928$		0			0
$929$	−0.123460	+	0.103595i	−0.00405058	+	0.00339884i	−0.644811	−	0.764342i	$-0.723064\pi$
$929$	−0.123460	+	0.103595i	−0.00405058	+	0.00339884i	0.640760	+	0.767741i	$0.278619\pi$
$930$		0			0
$931$	1.93732	−	1.73946i	0.0634932	−	0.0570086i
$932$		0			0
$933$	−40.6697	−	35.0454i	−1.33147	−	1.14733i
$934$		0			0
$935$	−6.84064	−	3.94945i	−0.223713	−	0.129161i
$936$		0			0
$937$	28.3872	−	16.3894i	0.927369	−	0.535417i	0.0413907	−	0.999143i	$-0.486821\pi$
$937$	28.3872	−	16.3894i	0.927369	−	0.535417i	0.885979	+	0.463726i	$0.153488\pi$
$938$		0			0
$939$	23.8598	−	3.88507i	0.778634	−	0.126785i
$940$		0			0
$941$	47.1036	−	17.1443i	1.53553	−	0.558889i	0.570565	−	0.821252i	$-0.306724\pi$
$941$	47.1036	−	17.1443i	1.53553	−	0.558889i	0.964969	+	0.262363i	$0.0845019\pi$
$942$		0			0
$943$	33.5057	−	5.90795i	1.09109	−	0.192389i
$944$		0			0
$945$	6.17015	−	8.40107i	0.200715	−	0.273287i
$946$		0			0
$947$	−54.5111	+	9.61177i	−1.77137	+	0.312341i	−0.961610	−	0.274419i	$-0.911514\pi$
$947$	−54.5111	+	9.61177i	−1.77137	+	0.312341i	−0.809761	+	0.586760i	$0.800403\pi$
$948$		0			0
$949$	33.0071	−	12.0136i	1.07146	−	0.389978i
$950$		0			0
$951$	−2.62657	−	3.21496i	−0.0851723	−	0.104252i
$952$		0			0
$953$	−40.8446	+	23.5816i	−1.32309	+	0.763884i	−0.984220	−	0.176951i	$-0.943377\pi$
$953$	−40.8446	+	23.5816i	−1.32309	+	0.763884i	−0.338866	+	0.940835i	$0.610043\pi$
$954$		0			0
$955$	15.1841	+	8.76656i	0.491347	+	0.283679i
$956$		0			0
$957$	−55.6963	+	19.4481i	−1.80041	+	0.628669i
$958$		0			0
$959$	−4.34467	−	15.1918i	−0.140297	−	0.490570i
$960$		0			0
$961$	−34.5989	+	29.0319i	−1.11609	+	0.936514i
$962$		0			0
$963$	37.3614	−	20.2827i	1.20395	−	0.653600i
$964$		0			0
$965$	9.67556	+	3.52162i	0.311467	+	0.113365i
$966$		0			0
$967$	7.46649	+	6.26513i	0.240106	+	0.201473i	0.754898	−	0.655842i	$-0.227686\pi$
$967$	7.46649	+	6.26513i	0.240106	+	0.201473i	−0.514792	+	0.857315i	$0.672131\pi$
$968$		0			0
$969$	1.82136	+	1.08367i	0.0585104	+	0.0348124i
$970$		0			0
$971$	−49.8838			−1.60085			−0.800424	−	0.599434i	$-0.795392\pi$
$971$	−49.8838			−1.60085			−0.800424	+	0.599434i	$0.795392\pi$
$972$		0			0
$973$	−14.9196	+	7.26385i	−0.478301	+	0.232868i
$974$		0			0
$975$	−24.2901	−	14.4521i	−0.777907	−	0.462838i
$976$		0			0
$977$	−10.0973	+	12.0335i	−0.323041	+	0.384986i	−0.902986	−	0.429670i	$-0.858630\pi$
$977$	−10.0973	+	12.0335i	−0.323041	+	0.384986i	0.579945	+	0.814656i	$0.303074\pi$
$978$		0			0
$979$	−5.52312	+	15.1747i	−0.176520	+	0.484984i
$980$		0			0
$981$	−25.9532	−	47.8067i	−0.828622	−	1.52635i
$982$		0			0
$983$	−42.7711	+	35.8892i	−1.36418	+	1.14469i	−0.389520	+	0.921018i	$0.627359\pi$
$983$	−42.7711	+	35.8892i	−1.36418	+	1.14469i	−0.974665	+	0.223669i	$0.928197\pi$
$984$		0			0
$985$	11.6604	+	2.05605i	0.371532	+	0.0655111i
$986$		0			0
$987$	−33.9667	−	33.7208i	−1.08117	−	1.07334i
$988$		0			0
$989$	−27.9776	−	16.1529i	−0.889635	−	0.513631i
$990$		0			0
$991$	−6.17459	−	10.6947i	−0.196142	−	0.339728i	0.751132	−	0.660152i	$-0.229508\pi$
$991$	−6.17459	−	10.6947i	−0.196142	−	0.339728i	−0.947274	+	0.320424i	$0.896175\pi$
$992$		0			0
$993$	−12.1971	+	9.96480i	−0.387062	+	0.316223i
$994$		0			0
$995$	1.65474	+	4.54636i	0.0524588	+	0.144129i
$996$		0			0
$997$	−49.4777	+	8.72425i	−1.56697	+	0.276300i	−0.888693	−	0.458502i	$-0.848386\pi$
$997$	−49.4777	+	8.72425i	−1.56697	+	0.276300i	−0.678281	+	0.734802i	$0.737275\pi$
$998$		0			0
$999$	16.1408	−	25.5765i	0.510673	−	0.809206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bx.a.41.18	yes	144
7.6	odd	2	inner	756.2.bx.a.41.7	✓	144
27.2	odd	18	inner	756.2.bx.a.461.7	yes	144
189.83	even	18	inner	756.2.bx.a.461.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bx.a.41.7	✓	144	7.6	odd	2	inner
756.2.bx.a.41.18	yes	144	1.1	even	1	trivial
756.2.bx.a.461.7	yes	144	27.2	odd	18	inner
756.2.bx.a.461.18	yes	144	189.83	even	18	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.885631 - 1.48851i) q^{3} +(-0.580812 - 0.487359i) q^{5} +(-0.274713 - 2.63145i) q^{7} +(-1.43132 - 2.63654i) q^{9} +O(q^{10})\)	\(q+(0.885631 - 1.48851i) q^{3} +(-0.580812 - 0.487359i) q^{5} +(-0.274713 - 2.63145i) q^{7} +(-1.43132 - 2.63654i) q^{9} +(2.03560 + 2.42593i) q^{11} +(3.63164 + 0.640357i) q^{13} +(-1.23982 + 0.432924i) q^{15} +(1.64486 - 2.84899i) q^{17} +(-0.322117 + 0.185975i) q^{19} +(-4.16023 - 1.92158i) q^{21} +(-1.58709 - 4.36050i) q^{23} +(-0.768417 - 4.35791i) q^{25} +(-5.19213 - 0.204470i) q^{27} +(-10.5919 + 1.86764i) q^{29} +(-2.98491 - 8.20097i) q^{31} +(5.41381 - 0.881527i) q^{33} +(-1.12291 + 1.66226i) q^{35} +(-2.91021 + 5.04063i) q^{37} +(4.16947 - 4.83861i) q^{39} +(-1.27317 + 7.22051i) q^{41} +(5.33314 - 4.47504i) q^{43} +(-0.453615 + 2.22890i) q^{45} +(9.81459 + 3.57222i) q^{47} +(-6.84907 + 1.44579i) q^{49} +(-2.78400 - 4.97154i) q^{51} -2.23537i q^{53} -2.40108i q^{55} +(-0.00845222 + 0.644179i) q^{57} +(7.93795 + 6.66073i) q^{59} +(3.02231 - 8.30373i) q^{61} +(-6.54472 + 4.49073i) q^{63} +(-1.79722 - 2.14184i) q^{65} +(-1.68948 + 9.58153i) q^{67} +(-7.89622 - 1.49939i) q^{69} +(6.78533 + 3.91751i) q^{71} +(8.24898 - 4.76255i) q^{73} +(-7.16732 - 2.71570i) q^{75} +(5.82452 - 6.02301i) q^{77} +(-0.249457 - 1.41474i) q^{79} +(-4.90266 + 7.54744i) q^{81} +(-0.0799053 - 0.453166i) q^{83} +(-2.34384 + 0.853087i) q^{85} +(-6.60053 + 17.4202i) q^{87} +(2.54964 + 4.41610i) q^{89} +(0.687409 - 9.73241i) q^{91} +(-14.8507 - 2.81997i) q^{93} +(0.277726 + 0.0489706i) q^{95} +(-2.99639 - 3.57096i) q^{97} +(3.48247 - 8.83921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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