LMFDB - Embedded newform 1764.2.bm.b.1697.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.bm (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1697.3
Root			$-0.744857 + 1.56371i$ of defining polynomial
Character	$\chi$	$=$	1764.1697
Dual form			1764.2.bm.b.1685.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.744857 + 1.56371i) q^{3} -0.553827 q^{5} +(-1.89038 - 2.32948i) q^{9} +O(q^{10})$	\(q+(-0.744857 + 1.56371i) q^{3} -0.553827 q^{5} +(-1.89038 - 2.32948i) q^{9} +4.65896i q^{11} +(3.58265 + 2.06844i) q^{13} +(0.412522 - 0.866025i) q^{15} +(3.62264 - 6.27459i) q^{17} +(5.81722 - 3.35857i) q^{19} +5.60371i q^{23} -4.69328 q^{25} +(5.05069 - 1.22087i) q^{27} +(1.16599 - 0.673187i) q^{29} +(0.830741 - 0.479629i) q^{31} +(-7.28526 - 3.47026i) q^{33} +(3.53478 + 6.12241i) q^{37} +(-5.90301 + 4.06153i) q^{39} +(-2.39152 + 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(1.04694 + 1.29013i) q^{45} +(-4.90301 + 8.49226i) q^{47} +(7.11329 + 10.3384i) q^{51} +(-7.30235 - 4.21601i) q^{53} -2.58026i q^{55} +(0.918838 + 11.5981i) q^{57} +(3.89955 + 6.75422i) q^{59} +(5.37336 + 3.10231i) q^{61} +(-1.98417 - 1.14556i) q^{65} +(1.68814 + 2.92394i) q^{67} +(-8.76257 - 4.17396i) q^{69} +0.407556i q^{71} +(-7.47870 - 4.31783i) q^{73} +(3.49582 - 7.33892i) q^{75} +(-0.318176 + 0.551097i) q^{79} +(-1.85295 + 8.80719i) q^{81} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(0.184170 + 2.32470i) q^{87} +(3.46568 + 6.00274i) q^{89} +(0.131217 + 1.65629i) q^{93} +(-3.22174 + 1.86007i) q^{95} +(7.48798 - 4.32318i) q^{97} +(10.8530 - 8.80719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^9	$ 16 q + 6 q^{9} - 12 q^{15} + 16 q^{25} - 12 q^{29} - 2 q^{37} + 18 q^{39} + 4 q^{43} + 6 q^{51} - 36 q^{53} - 42 q^{57} + 24 q^{65} + 14 q^{67} + 20 q^{79} + 54 q^{81} + 6 q^{85} + 30 q^{93} + 60 q^{95} + 90 q^{99}+O(q^{100}) $ 16 * q + 6 * q^9 - 12 * q^15 + 16 * q^25 - 12 * q^29 - 2 * q^37 + 18 * q^39 + 4 * q^43 + 6 * q^51 - 36 * q^53 - 42 * q^57 + 24 * q^65 + 14 * q^67 + 20 * q^79 + 54 * q^81 + 6 * q^85 + 30 * q^93 + 60 * q^95 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.744857	+	1.56371i	−0.430043	+	0.902808i
$3$	−0.744857	+	1.56371i	−0.430043	+	0.902808i
$4$		0			0
$5$	−0.553827			−0.247679			−0.123840	−	0.992302i	$-0.539521\pi$
$5$	−0.553827			−0.247679			−0.123840	+	0.992302i	$0.539521\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.89038	−	2.32948i	−0.630125	−	0.776493i
$10$		0			0
$11$			4.65896i			1.40473i	0.711817	+	0.702365i	$0.247872\pi$
$11$			4.65896i			1.40473i	−0.711817	+	0.702365i	$0.752128\pi$
$12$		0			0
$13$	3.58265	+	2.06844i	0.993648	+	0.573683i	0.906363	−	0.422500i	$-0.138847\pi$
$13$	3.58265	+	2.06844i	0.993648	+	0.573683i	0.0872856	+	0.996183i	$0.472181\pi$
$14$		0			0
$15$	0.412522	−	0.866025i	0.106513	−	0.223607i
$16$		0			0
$17$	3.62264	−	6.27459i	0.878619	−	1.52181i	0.0257612	−	0.999668i	$-0.491799\pi$
$17$	3.62264	−	6.27459i	0.878619	−	1.52181i	0.852857	−	0.522144i	$-0.174868\pi$
$18$		0			0
$19$	5.81722	−	3.35857i	1.33456	−	0.770510i	0.348567	−	0.937284i	$-0.386668\pi$
$19$	5.81722	−	3.35857i	1.33456	−	0.770510i	0.985995	+	0.166774i	$0.0533351\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			5.60371i			1.16845i	0.811590	+	0.584227i	$0.198602\pi$
$23$			5.60371i			1.16845i	−0.811590	+	0.584227i	$0.801398\pi$
$24$		0			0
$25$	−4.69328			−0.938655
$26$		0			0
$27$	5.05069	−	1.22087i	0.972006	−	0.234957i
$28$		0			0
$29$	1.16599	−	0.673187i	0.216520	−	0.125008i	−0.387818	−	0.921736i	$-0.626771\pi$
$29$	1.16599	−	0.673187i	0.216520	−	0.125008i	0.604338	+	0.796728i	$0.293438\pi$
$30$		0			0
$31$	0.830741	−	0.479629i	0.149206	−	0.0861438i	−0.423539	−	0.905878i	$-0.639212\pi$
$31$	0.830741	−	0.479629i	0.149206	−	0.0861438i	0.572744	+	0.819734i	$0.305879\pi$
$32$		0			0
$33$	−7.28526	−	3.47026i	−1.26820	−	0.604094i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.53478	+	6.12241i	0.581114	+	1.00652i	0.995348	+	0.0963482i	$0.0307162\pi$
$37$	3.53478	+	6.12241i	0.581114	+	1.00652i	−0.414234	+	0.910170i	$0.635950\pi$
$38$		0			0
$39$	−5.90301	+	4.06153i	−0.945238	+	0.650365i
$40$		0			0
$41$	−2.39152	+	4.14224i	−0.373493	+	0.646909i	−0.990100	−	0.140362i	$-0.955173\pi$
$41$	−2.39152	+	4.14224i	−0.373493	+	0.646909i	0.616607	+	0.787271i	$0.288507\pi$
$42$		0			0
$43$	−1.02846	−	1.78135i	−0.156839	−	0.271653i	0.776888	−	0.629639i	$-0.216797\pi$
$43$	−1.02846	−	1.78135i	−0.156839	−	0.271653i	−0.933727	+	0.357986i	$0.883464\pi$
$44$		0			0
$45$	1.04694	+	1.29013i	0.156069	+	0.192321i
$46$		0			0
$47$	−4.90301	+	8.49226i	−0.715177	+	1.23872i	0.247714	+	0.968833i	$0.420321\pi$
$47$	−4.90301	+	8.49226i	−0.715177	+	1.23872i	−0.962891	+	0.269890i	$0.913013\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	7.11329	+	10.3384i	0.996060	+	1.44767i
$52$		0			0
$53$	−7.30235	−	4.21601i	−1.00305	−	0.579114i	−0.0939038	−	0.995581i	$-0.529935\pi$
$53$	−7.30235	−	4.21601i	−1.00305	−	0.579114i	−0.909151	+	0.416468i	$0.863268\pi$
$54$		0			0
$55$		−	2.58026i		−	0.347922i
$56$		0			0
$57$	0.918838	+	11.5981i	0.121703	+	1.53621i
$58$		0			0
$59$	3.89955	+	6.75422i	0.507678	+	0.879325i	0.999960	+	0.00888893i	$0.00282947\pi$
$59$	3.89955	+	6.75422i	0.507678	+	0.879325i	−0.492282	+	0.870436i	$0.663837\pi$
$60$		0			0
$61$	5.37336	+	3.10231i	0.687989	+	0.397211i	0.802858	−	0.596170i	$-0.203312\pi$
$61$	5.37336	+	3.10231i	0.687989	+	0.397211i	−0.114869	+	0.993381i	$0.536645\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.98417	−	1.14556i	−0.246106	−	0.142089i
$66$		0			0
$67$	1.68814	+	2.92394i	0.206239	+	0.357217i	0.950527	−	0.310642i	$-0.100544\pi$
$67$	1.68814	+	2.92394i	0.206239	+	0.357217i	−0.744288	+	0.667859i	$0.767211\pi$
$68$		0			0
$69$	−8.76257	−	4.17396i	−1.05489	−	0.502486i
$70$		0			0
$71$			0.407556i			0.0483680i	0.999708	+	0.0241840i	$0.00769875\pi$
$71$			0.407556i			0.0483680i	−0.999708	+	0.0241840i	$0.992301\pi$
$72$		0			0
$73$	−7.47870	−	4.31783i	−0.875316	−	0.505364i	−0.00620487	−	0.999981i	$-0.501975\pi$
$73$	−7.47870	−	4.31783i	−0.875316	−	0.505364i	−0.869111	+	0.494617i	$0.835308\pi$
$74$		0			0
$75$	3.49582	−	7.33892i	0.403662	−	0.847426i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.318176	+	0.551097i	−0.0357976	+	0.0620032i	−0.883369	−	0.468678i	$-0.844730\pi$
$79$	−0.318176	+	0.551097i	−0.0357976	+	0.0620032i	0.847572	+	0.530681i	$0.178064\pi$
$80$		0			0
$81$	−1.85295	+	8.80719i	−0.205884	+	0.978576i
$82$		0			0
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	0.977498	−	0.210944i	$-0.0676537\pi$
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	−0.671432	+	0.741066i	$0.734320\pi$
$84$		0			0
$85$	−2.00632	+	3.47504i	−0.217616	+	0.376921i
$86$		0			0
$87$	0.184170	+	2.32470i	0.0197451	+	0.249235i
$88$		0			0
$89$	3.46568	+	6.00274i	0.367362	+	0.636289i	0.989152	−	0.146895i	$-0.0469278\pi$
$89$	3.46568	+	6.00274i	0.367362	+	0.636289i	−0.621790	+	0.783184i	$0.713594\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	0.131217	+	1.65629i	0.0136065	+	0.171750i
$94$		0			0
$95$	−3.22174	+	1.86007i	−0.330543	+	0.190839i
$96$		0			0
$97$	7.48798	−	4.32318i	0.760289	−	0.438953i	−0.0691107	−	0.997609i	$-0.522016\pi$
$97$	7.48798	−	4.32318i	0.760289	−	0.438953i	0.829399	+	0.558656i	$0.188683\pi$
$98$		0			0
$99$	10.8530	−	8.80719i	1.09076	−	0.885156i
$100$		0			0
$101$	−4.68453			−0.466128			−0.233064	−	0.972461i	$-0.574875\pi$
$101$	−4.68453			−0.466128			−0.233064	+	0.972461i	$0.574875\pi$
$102$		0			0
$103$			7.39937i			0.729082i	0.931187	+	0.364541i	$0.118774\pi$
$103$			7.39937i			0.729082i	−0.931187	+	0.364541i	$0.881226\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.38260	−	2.53029i	0.423682	−	0.244613i	−0.272970	−	0.962023i	$-0.588006\pi$
$107$	4.38260	−	2.53029i	0.423682	−	0.244613i	0.696651	+	0.717410i	$0.254673\pi$
$108$		0			0
$109$	−5.88142	+	10.1869i	−0.563337	+	0.975729i	0.433865	+	0.900978i	$0.357150\pi$
$109$	−5.88142	+	10.1869i	−0.563337	+	0.975729i	−0.997202	+	0.0747510i	$0.976184\pi$
$110$		0			0
$111$	−12.2066	+	0.967044i	−1.15860	+	0.0917877i
$112$		0			0
$113$	−1.51895	−	0.876965i	−0.142891	−	0.0824979i	0.426850	−	0.904322i	$-0.359623\pi$
$113$	−1.51895	−	0.876965i	−0.142891	−	0.0824979i	−0.569741	+	0.821824i	$0.692956\pi$
$114$		0			0
$115$		−	3.10349i		−	0.289402i
$116$		0			0
$117$	−1.95416	−	12.2559i	−0.180662	−	1.13305i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.7059			−0.973264
$122$		0			0
$123$	−4.69592	−	6.82503i	−0.423417	−	0.615392i
$124$		0			0
$125$	5.36840			0.480164
$126$		0			0
$127$	11.0822			0.983385			0.491693	−	0.870769i	$-0.336378\pi$
$127$	11.0822			0.983385			0.491693	+	0.870769i	$0.336378\pi$
$128$		0			0
$129$	3.55157	−	0.281366i	0.312698	−	0.0247729i
$130$		0			0
$131$	−18.4729			−1.61398			−0.806990	−	0.590565i	$-0.798905\pi$
$131$	−18.4729			−1.61398			−0.806990	+	0.590565i	$0.798905\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.79721	+	0.676152i	−0.240746	+	0.0581939i
$136$		0			0
$137$			22.0013i			1.87970i	0.341585	+	0.939851i	$0.389036\pi$
$137$			22.0013i			1.87970i	−0.341585	+	0.939851i	$0.610964\pi$
$138$		0			0
$139$	−8.55986	−	4.94204i	−0.726038	−	0.419178i	0.0909332	−	0.995857i	$-0.471015\pi$
$139$	−8.55986	−	4.94204i	−0.726038	−	0.419178i	−0.816971	+	0.576679i	$0.804348\pi$
$140$		0			0
$141$	−9.62739	−	13.9924i	−0.810773	−	1.17837i
$142$		0			0
$143$	−9.63680	+	16.6914i	−0.805870	+	1.39581i
$144$		0			0
$145$	−0.645760	+	0.372830i	−0.0536274	+	0.0309618i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			7.35171i			0.602275i	0.953581	+	0.301138i	$0.0973664\pi$
$149$			7.35171i			0.602275i	−0.953581	+	0.301138i	$0.902634\pi$
$150$		0			0
$151$	−4.33199			−0.352532			−0.176266	−	0.984343i	$-0.556402\pi$
$151$	−4.33199			−0.352532			−0.176266	+	0.984343i	$0.556402\pi$
$152$		0			0
$153$	−21.4647	+	3.42248i	−1.73532	+	0.276691i
$154$		0			0
$155$	−0.460087	+	0.265632i	−0.0369551	+	0.0213360i
$156$		0			0
$157$	1.54152	−	0.889998i	0.123027	−	0.0710296i	−0.437224	−	0.899353i	$-0.644038\pi$
$157$	1.54152	−	0.889998i	0.123027	−	0.0710296i	0.560251	+	0.828323i	$0.310705\pi$
$158$		0			0
$159$	12.0318	−	8.27842i	0.954185	−	0.656522i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.81818	+	4.88122i	0.220737	+	0.382327i	0.955032	−	0.296503i	$-0.0958206\pi$
$163$	2.81818	+	4.88122i	0.220737	+	0.382327i	−0.734295	+	0.678830i	$0.762487\pi$
$164$		0			0
$165$	4.03478	+	1.92192i	0.314107	+	0.149622i
$166$		0			0
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	−0.943506	−	0.331355i	$-0.892494\pi$
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	0.758715	+	0.651423i	$0.225827\pi$
$168$		0			0
$169$	2.05692	+	3.56270i	0.158225	+	0.274054i
$170$		0			0
$171$	−18.8205	−	7.20213i	−1.43924	−	0.550761i
$172$		0			0
$173$	−2.83766	+	4.91497i	−0.215743	+	0.373678i	−0.953502	−	0.301386i	$-0.902551\pi$
$173$	−2.83766	+	4.91497i	−0.215743	+	0.373678i	0.737759	+	0.675064i	$0.235884\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−13.4662	+	1.06684i	−1.01219	+	0.0801885i
$178$		0			0
$179$	−10.9383	−	6.31525i	−0.817570	−	0.472024i	0.0320079	−	0.999488i	$-0.489810\pi$
$179$	−10.9383	−	6.31525i	−0.817570	−	0.472024i	−0.849578	+	0.527463i	$0.823143\pi$
$180$		0			0
$181$		−	22.7424i		−	1.69043i	−0.534426	−	0.845215i	$-0.679472\pi$
$181$		−	22.7424i		−	1.69043i	0.534426	−	0.845215i	$-0.320528\pi$
$182$		0			0
$183$	−8.85351	+	6.09160i	−0.654470	+	0.450304i
$184$		0			0
$185$	−1.95766	−	3.39076i	−0.143930	−	0.249294i
$186$		0			0
$187$	29.2331	+	16.8777i	2.13773	+	1.23422i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.0537	+	5.80452i	0.727462	+	0.420000i	0.817493	−	0.575939i	$-0.195363\pi$
$191$	10.0537	+	5.80452i	0.727462	+	0.420000i	−0.0900309	+	0.995939i	$0.528697\pi$
$192$		0			0
$193$	−3.16599	−	5.48366i	−0.227893	−	0.394723i	0.729290	−	0.684204i	$-0.239850\pi$
$193$	−3.16599	−	5.48366i	−0.227893	−	0.394723i	−0.957184	+	0.289482i	$0.906517\pi$
$194$		0			0
$195$	3.26925	−	2.24939i	0.234116	−	0.161082i
$196$		0			0
$197$			3.10030i			0.220888i	0.993882	+	0.110444i	$0.0352272\pi$
$197$			3.10030i			0.220888i	−0.993882	+	0.110444i	$0.964773\pi$
$198$		0			0
$199$	13.6198	+	7.86341i	0.965484	+	0.557422i	0.897856	−	0.440288i	$-0.145124\pi$
$199$	13.6198	+	7.86341i	0.965484	+	0.557422i	0.0676272	+	0.997711i	$0.478457\pi$
$200$		0			0
$201$	−5.82962	+	0.461841i	−0.411190	+	0.0325758i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.32449	−	2.29409i	0.0925065	−	0.160226i
$206$		0			0
$207$	13.0537	−	10.5931i	0.907297	−	0.736273i
$208$		0			0
$209$	15.6475	+	27.1022i	1.08236	+	1.87470i
$210$		0			0
$211$	3.51263	−	6.08406i	0.241820	−	0.418844i	−0.719413	−	0.694582i	$-0.755589\pi$
$211$	3.51263	−	6.08406i	0.241820	−	0.418844i	0.961233	+	0.275739i	$0.0889225\pi$
$212$		0			0
$213$	−0.637299	−	0.303571i	−0.0436670	−	0.0208003i
$214$		0			0
$215$	0.569590	+	0.986559i	0.0388457	+	0.0672828i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	12.3224	−	8.47836i	0.832671	−	0.572914i
$220$		0			0
$221$	25.9573	−	14.9864i	1.74608	−	1.00810i
$222$		0			0
$223$	21.3477	−	12.3251i	1.42955	−	0.825350i	0.432464	−	0.901651i	$-0.357644\pi$
$223$	21.3477	−	12.3251i	1.42955	−	0.825350i	0.997085	+	0.0763008i	$0.0243109\pi$
$224$		0			0
$225$	8.87206	+	10.9329i	0.591470	+	0.728859i
$226$		0			0
$227$	20.0743			1.33238			0.666190	−	0.745782i	$-0.267924\pi$
$227$	20.0743			1.33238			0.666190	+	0.745782i	$0.267924\pi$
$228$		0			0
$229$		−	7.80422i		−	0.515717i	−0.966183	−	0.257859i	$-0.916983\pi$
$229$		−	7.80422i		−	0.515717i	0.966183	−	0.257859i	$-0.0830169\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.89843	+	3.98281i	−0.451931	+	0.260922i	−0.708645	−	0.705565i	$-0.750693\pi$
$233$	−6.89843	+	3.98281i	−0.451931	+	0.260922i	0.256714	+	0.966487i	$0.417360\pi$
$234$		0			0
$235$	2.71542	−	4.70325i	0.177135	−	0.306806i
$236$		0			0
$237$	−0.624760	−	0.908023i	−0.0405825	−	0.0589824i
$238$		0			0
$239$	23.2059	+	13.3979i	1.50107	+	0.866640i	0.999999	+	0.00123146i	$0.000391987\pi$
$239$	23.2059	+	13.3979i	1.50107	+	0.866640i	0.501066	+	0.865409i	$0.332941\pi$
$240$		0			0
$241$			0.874407i			0.0563255i	0.999603	+	0.0281628i	$0.00896567\pi$
$241$			0.874407i			0.0563255i	−0.999603	+	0.0281628i	$0.991034\pi$
$242$		0			0
$243$	−12.3917	−	9.45758i	−0.794928	−	0.606704i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	27.7881			1.76811
$248$		0			0
$249$	−9.62912	+	0.762849i	−0.610221	+	0.0483436i
$250$		0			0
$251$	−2.32082			−0.146489			−0.0732445	−	0.997314i	$-0.523335\pi$
$251$	−2.32082			−0.146489			−0.0732445	+	0.997314i	$0.523335\pi$
$252$		0			0
$253$	−26.1075			−1.64136
$254$		0			0
$255$	−3.93954	−	5.72570i	−0.246703	−	0.358558i
$256$		0			0
$257$	−24.6035			−1.53472			−0.767361	−	0.641215i	$-0.778431\pi$
$257$	−24.6035			−1.53472			−0.767361	+	0.641215i	$0.778431\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.77234	−	1.44358i	−0.233502	−	0.0893556i
$262$		0			0
$263$		−	23.7024i		−	1.46155i	−0.682619	−	0.730775i	$-0.739159\pi$
$263$		−	23.7024i		−	1.46155i	0.682619	−	0.730775i	$-0.260841\pi$
$264$		0			0
$265$	4.04424	+	2.33494i	0.248436	+	0.143434i
$266$		0			0
$267$	−11.9680	+	0.948141i	−0.732429	+	0.0580253i
$268$		0			0
$269$	10.3106	−	17.8585i	0.628648	−	1.08885i	−0.359176	−	0.933270i	$-0.616942\pi$
$269$	10.3106	−	17.8585i	0.628648	−	1.08885i	0.987823	−	0.155580i	$-0.0497245\pi$
$270$		0			0
$271$	12.0771	−	6.97270i	0.733630	−	0.423562i	−0.0861186	−	0.996285i	$-0.527446\pi$
$271$	12.0771	−	6.97270i	0.733630	−	0.423562i	0.819749	+	0.572723i	$0.194113\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	21.8658i		−	1.31856i
$276$		0			0
$277$	20.7881			1.24904			0.624518	−	0.781011i	$-0.285296\pi$
$277$	20.7881			1.24904			0.624518	+	0.781011i	$0.285296\pi$
$278$		0			0
$279$	−2.68770	−	1.02852i	−0.160908	−	0.0615757i
$280$		0			0
$281$	−20.3371	+	11.7416i	−1.21321	+	0.700448i	−0.963457	−	0.267862i	$-0.913683\pi$
$281$	−20.3371	+	11.7416i	−1.21321	+	0.700448i	−0.249754	+	0.968309i	$0.580350\pi$
$282$		0			0
$283$	11.1906	−	6.46089i	0.665211	−	0.384060i	−0.129048	−	0.991638i	$-0.541192\pi$
$283$	11.1906	−	6.46089i	0.665211	−	0.384060i	0.794260	+	0.607578i	$0.207859\pi$
$284$		0			0
$285$	−0.508878	−	6.42335i	−0.0301433	−	0.380486i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−17.7470	−	30.7387i	−1.04394	−	1.80816i
$290$		0			0
$291$	1.18274	+	14.9292i	0.0693332	+	0.875164i
$292$		0			0
$293$	−1.99115	+	3.44878i	−0.116324	+	0.201480i	−0.918308	−	0.395866i	$-0.870445\pi$
$293$	−1.99115	+	3.44878i	−0.116324	+	0.201480i	0.801984	+	0.597346i	$0.203778\pi$
$294$		0			0
$295$	−2.15968	−	3.74067i	−0.125741	−	0.217790i
$296$		0			0
$297$	5.68799	+	23.5310i	0.330051	+	1.36541i
$298$		0			0
$299$	−11.5910	+	20.0761i	−0.670322	+	1.16103i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	3.48931	−	7.32525i	0.200455	−	0.420824i
$304$		0			0
$305$	−2.97592	−	1.71815i	−0.170401	−	0.0983808i
$306$		0			0
$307$			22.3162i			1.27365i	0.771008	+	0.636825i	$0.219753\pi$
$307$			22.3162i			1.27365i	−0.771008	+	0.636825i	$0.780247\pi$
$308$		0			0
$309$	−11.5705	−	5.51147i	−0.658221	−	0.313537i
$310$		0			0
$311$	−8.18371	−	14.1746i	−0.464056	−	0.803768i	0.535103	−	0.844787i	$-0.320273\pi$
$311$	−8.18371	−	14.1746i	−0.464056	−	0.803768i	−0.999158	+	0.0410190i	$0.986940\pi$
$312$		0			0
$313$	16.5547	+	9.55785i	0.935726	+	0.540242i	0.888618	−	0.458648i	$-0.151666\pi$
$313$	16.5547	+	9.55785i	0.935726	+	0.540242i	0.0471079	+	0.998890i	$0.485000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.8798	−	12.0550i	−1.17273	−	0.677074i	−0.218405	−	0.975858i	$-0.570086\pi$
$317$	−20.8798	−	12.0550i	−1.17273	−	0.677074i	−0.954321	+	0.298784i	$0.903419\pi$
$318$		0			0
$319$	3.13635	+	5.43232i	0.175602	+	0.304152i
$320$		0			0
$321$	0.692237	+	8.73781i	0.0386369	+	0.487697i
$322$		0			0
$323$		−	48.6676i		−	2.70794i
$324$		0			0
$325$	−16.8144	−	9.70778i	−0.932693	−	0.538491i
$326$		0			0
$327$	−11.5486	−	16.7846i	−0.638637	−	0.928191i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−5.70077	+	9.87403i	−0.313343	+	0.542726i	−0.979084	−	0.203457i	$-0.934782\pi$
$331$	−5.70077	+	9.87403i	−0.313343	+	0.542726i	0.665741	+	0.746183i	$0.268116\pi$
$332$		0			0
$333$	7.57998	−	19.8079i	0.415380	−	1.08546i
$334$		0			0
$335$	−0.934938	−	1.61936i	−0.0510811	−	0.0884751i
$336$		0			0
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	−0.800981	−	0.598689i	$-0.795689\pi$
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	0.918971	+	0.394326i	$0.129022\pi$
$338$		0			0
$339$	2.50272	−	1.72198i	0.135929	−	0.0935251i
$340$		0			0
$341$	2.23457	+	3.87039i	0.121009	+	0.209593i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4.85295	+	2.31165i	0.261274	+	0.124455i
$346$		0			0
$347$	4.62254	−	2.66882i	0.248151	−	0.143270i	−0.370766	−	0.928726i	$-0.620905\pi$
$347$	4.62254	−	2.66882i	0.248151	−	0.143270i	0.618917	+	0.785456i	$0.287572\pi$
$348$		0			0
$349$	8.78031	−	5.06931i	0.469999	−	0.271354i	−0.246240	−	0.969209i	$-0.579195\pi$
$349$	8.78031	−	5.06931i	0.469999	−	0.271354i	0.716239	+	0.697855i	$0.245862\pi$
$350$		0			0
$351$	20.6202	+	6.07312i	1.10062	+	0.324159i
$352$		0			0
$353$	15.3513			0.817067			0.408533	−	0.912743i	$-0.366040\pi$
$353$	15.3513			0.817067			0.408533	+	0.912743i	$0.366040\pi$
$354$		0			0
$355$		−	0.225715i		−	0.0119797i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.51381	+	0.874000i	−0.0798960	+	0.0461280i	−0.539416	−	0.842040i	$-0.681355\pi$
$359$	−1.51381	+	0.874000i	−0.0798960	+	0.0461280i	0.459520	+	0.888168i	$0.348022\pi$
$360$		0			0
$361$	13.0600	−	22.6207i	0.687371	−	1.19056i
$362$		0			0
$363$	7.97437	−	16.7409i	0.418546	−	0.878671i
$364$		0			0
$365$	4.14191	+	2.39133i	0.216798	+	0.125168i
$366$		0			0
$367$		−	12.9004i		−	0.673393i	−0.941613	−	0.336697i	$-0.890690\pi$
$367$		−	12.9004i		−	0.673393i	0.941613	−	0.336697i	$-0.109310\pi$
$368$		0			0
$369$	14.1702	−	2.25939i	0.737669	−	0.117619i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−10.6956			−0.553799			−0.276900	−	0.960899i	$-0.589307\pi$
$373$	−10.6956			−0.553799			−0.276900	+	0.960899i	$0.589307\pi$
$374$		0			0
$375$	−3.99869	+	8.39462i	−0.206492	+	0.433496i
$376$		0			0
$377$	5.56980			0.286859
$378$		0			0
$379$	0.566797			0.0291144			0.0145572	−	0.999894i	$-0.495366\pi$
$379$	0.566797			0.0291144			0.0145572	+	0.999894i	$0.495366\pi$
$380$		0			0
$381$	−8.25464	+	17.3293i	−0.422898	+	0.887808i
$382$		0			0
$383$	18.8612			0.963761			0.481880	−	0.876237i	$-0.339954\pi$
$383$	18.8612			0.963761			0.481880	+	0.876237i	$0.339954\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.20543	+	5.76320i	−0.112109	+	0.292960i
$388$		0			0
$389$			16.5332i			0.838267i	0.907925	+	0.419133i	$0.137666\pi$
$389$			16.5332i			0.838267i	−0.907925	+	0.419133i	$0.862334\pi$
$390$		0			0
$391$	35.1610	+	20.3002i	1.77817	+	1.02663i
$392$		0			0
$393$	13.7596	−	28.8862i	0.694082	−	1.45712i
$394$		0			0
$395$	0.176215	−	0.305213i	0.00886632	−	0.0153569i
$396$		0			0
$397$	29.5384	−	17.0540i	1.48249	−	0.855917i	0.482688	−	0.875792i	$-0.339660\pi$
$397$	29.5384	−	17.0540i	1.48249	−	0.855917i	0.999802	+	0.0198756i	$0.00632700\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	21.5230i		−	1.07481i	−0.843325	−	0.537404i	$-0.819405\pi$
$401$		−	21.5230i		−	1.07481i	0.843325	−	0.537404i	$-0.180595\pi$
$402$		0			0
$403$	3.96834			0.197677
$404$		0			0
$405$	1.02622	−	4.87766i	0.0509931	−	0.242373i
$406$		0			0
$407$	−28.5241	+	16.4684i	−1.41389	+	0.816308i
$408$		0			0
$409$	−19.2516	+	11.1149i	−0.951933	+	0.549599i	−0.893681	−	0.448703i	$-0.851886\pi$
$409$	−19.2516	+	11.1149i	−0.951933	+	0.549599i	−0.0582520	+	0.998302i	$0.518553\pi$
$410$		0			0
$411$	−34.4037	−	16.3879i	−1.69701	−	0.808353i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.54429	−	2.67479i	−0.0758063	−	0.131300i
$416$		0			0
$417$	14.1038	−	9.70402i	0.690665	−	0.475208i
$418$		0			0
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	−0.983085	−	0.183150i	$-0.941371\pi$
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	0.650155	+	0.759802i	$0.274704\pi$
$420$		0			0
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	0.978451	+	0.206480i	$0.0662009\pi$
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	−0.310408	+	0.950603i	$0.600466\pi$
$422$		0			0
$423$	29.0511	−	4.63211i	1.41251	−	0.225221i
$424$		0			0
$425$	−17.0020	+	29.4484i	−0.824720	+	1.42846i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−18.9225	−	27.5019i	−0.913587	−	1.32780i
$430$		0			0
$431$	30.1663	+	17.4165i	1.45306	+	0.838925i	0.998654	−	0.0518699i	$-0.0165181\pi$
$431$	30.1663	+	17.4165i	1.45306	+	0.838925i	0.454406	+	0.890795i	$0.349851\pi$
$432$		0			0
$433$		−	19.5648i		−	0.940223i	−0.882607	−	0.470112i	$-0.844214\pi$
$433$		−	19.5648i		−	0.940223i	0.882607	−	0.470112i	$-0.155786\pi$
$434$		0			0
$435$	−0.101999	−	1.28749i	−0.00489046	−	0.0617302i
$436$		0			0
$437$	18.8205	+	32.5980i	0.900305	+	1.55937i
$438$		0			0
$439$	−24.7361	−	14.2814i	−1.18059	−	0.681614i	−0.224439	−	0.974488i	$-0.572055\pi$
$439$	−24.7361	−	14.2814i	−1.18059	−	0.681614i	−0.956151	+	0.292874i	$0.905388\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	21.8612	+	12.6216i	1.03866	+	0.599669i	0.919453	−	0.393201i	$-0.128632\pi$
$443$	21.8612	+	12.6216i	1.03866	+	0.599669i	0.119205	+	0.992870i	$0.461966\pi$
$444$		0			0
$445$	−1.91939	−	3.32448i	−0.0909878	−	0.157596i
$446$		0			0
$447$	−11.4959	−	5.47597i	−0.543739	−	0.259005i
$448$		0			0
$449$		−	15.1042i		−	0.712811i	−0.934331	−	0.356405i	$-0.884002\pi$
$449$		−	15.1042i		−	0.712811i	0.934331	−	0.356405i	$-0.115998\pi$
$450$		0			0
$451$	−19.2985	−	11.1420i	−0.908733	−	0.524657i
$452$		0			0
$453$	3.22671	−	6.77397i	0.151604	−	0.318269i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.75138	+	3.03348i	−0.0819261	+	0.141900i	−0.904077	−	0.427369i	$-0.859440\pi$
$457$	−1.75138	+	3.03348i	−0.0819261	+	0.141900i	0.822151	+	0.569269i	$0.192774\pi$
$458$		0			0
$459$	10.6364	−	36.1138i	0.496462	−	1.68565i
$460$		0			0
$461$	1.98765	+	3.44272i	0.0925743	+	0.160343i	0.908594	−	0.417681i	$-0.137157\pi$
$461$	1.98765	+	3.44272i	0.0925743	+	0.160343i	−0.816019	+	0.578025i	$0.803824\pi$
$462$		0			0
$463$	−5.18494	+	8.98058i	−0.240965	+	0.417363i	−0.960989	−	0.276585i	$-0.910797\pi$
$463$	−5.18494	+	8.98058i	−0.240965	+	0.417363i	0.720025	+	0.693948i	$0.244130\pi$
$464$		0			0
$465$	−0.0726714	−	0.917300i	−0.00337006	−	0.0425388i
$466$		0			0
$467$	9.80952	+	16.9906i	0.453930	+	0.786230i	0.998626	−	0.0524035i	$-0.0166882\pi$
$467$	9.80952	+	16.9906i	0.453930	+	0.786230i	−0.544696	+	0.838634i	$0.683355\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.243486	+	3.07342i	0.0112192	+	0.141615i
$472$		0			0
$473$	8.29923	−	4.79156i	0.381599	−	0.220316i
$474$		0			0
$475$	−27.3018	+	15.7627i	−1.25269	+	0.723243i
$476$		0			0
$477$	3.98307	+	24.9805i	0.182372	+	1.14378i
$478$		0			0
$479$	−31.6474			−1.44600			−0.723002	−	0.690846i	$-0.757238\pi$
$479$	−31.6474			−1.44600			−0.723002	+	0.690846i	$0.757238\pi$
$480$		0			0
$481$			29.2460i			1.33350i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.14705	+	2.39430i	−0.188308	+	0.108719i
$486$		0			0
$487$	9.72923	−	16.8515i	0.440874	−	0.763616i	−0.556881	−	0.830592i	$-0.688002\pi$
$487$	9.72923	−	16.8515i	0.440874	−	0.763616i	0.997755	+	0.0669768i	$0.0213353\pi$
$488$		0			0
$489$	−9.73196	+	0.770996i	−0.440094	+	0.0348656i
$490$		0			0
$491$	23.9525	+	13.8290i	1.08096	+	0.624094i	0.931156	−	0.364622i	$-0.118802\pi$
$491$	23.9525	+	13.8290i	1.08096	+	0.624094i	0.149806	+	0.988715i	$0.452135\pi$
$492$		0			0
$493$		−	9.75485i		−	0.439336i
$494$		0			0
$495$	−6.01066	+	4.87766i	−0.270159	+	0.219235i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−9.01263			−0.403461			−0.201730	−	0.979441i	$-0.564656\pi$
$499$	−9.01263			−0.403461			−0.201730	+	0.979441i	$0.564656\pi$
$500$		0			0
$501$	−4.68905	−	6.81504i	−0.209491	−	0.304474i
$502$		0			0
$503$	−27.1572			−1.21088			−0.605440	−	0.795891i	$-0.707003\pi$
$503$	−27.1572			−1.21088			−0.605440	+	0.795891i	$0.707003\pi$
$504$		0			0
$505$	2.59442			0.115450
$506$		0			0
$507$	−7.10314	+	0.562733i	−0.315461	+	0.0249918i
$508$		0			0
$509$	13.1360			0.582242			0.291121	−	0.956686i	$-0.405972\pi$
$509$	13.1360			0.582242			0.291121	+	0.956686i	$0.405972\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	25.2806	−	24.0652i	1.11617	−	1.06250i
$514$		0			0
$515$		−	4.09797i		−	0.180578i
$516$		0			0
$517$	−39.5651	−	22.8429i	−1.74007	−	1.00463i
$518$		0			0
$519$	−5.57193	−	8.09822i	−0.244581	−	0.355472i
$520$		0			0
$521$	−2.01609	+	3.49198i	−0.0883266	+	0.152986i	−0.906804	−	0.421553i	$-0.861485\pi$
$521$	−2.01609	+	3.49198i	−0.0883266	+	0.152986i	0.818477	+	0.574539i	$0.194819\pi$
$522$		0			0
$523$	0.516117	−	0.297980i	0.0225682	−	0.0130298i	−0.488673	−	0.872467i	$-0.662519\pi$
$523$	0.516117	−	0.297980i	0.0225682	−	0.0130298i	0.511242	+	0.859437i	$0.329186\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	6.95008i		−	0.302750i
$528$		0			0
$529$	−8.40154			−0.365285
$530$		0			0
$531$	8.36220	−	21.8519i	0.362889	−	0.948294i
$532$		0			0
$533$	−17.1360	+	9.89347i	−0.742242	+	0.428534i
$534$		0			0
$535$	−2.42720	+	1.40135i	−0.104937	+	0.0605855i
$536$		0			0
$537$	18.0227	−	12.4004i	0.777738	−	0.535118i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	7.05061	+	12.2120i	0.303129	+	0.525035i	0.976843	−	0.213957i	$-0.0686353\pi$
$541$	7.05061	+	12.2120i	0.303129	+	0.525035i	−0.673714	+	0.738992i	$0.735302\pi$
$542$		0			0
$543$	35.5625	+	16.9398i	1.52613	+	0.726958i
$544$		0			0
$545$	3.25729	−	5.64179i	0.139527	−	0.241668i
$546$		0			0
$547$	−18.9921	−	32.8952i	−0.812042	−	1.40650i	−0.911433	−	0.411450i	$-0.865023\pi$
$547$	−18.9921	−	32.8952i	−0.812042	−	1.40650i	0.0993905	−	0.995049i	$-0.468311\pi$
$548$		0			0
$549$	−2.93091	−	18.3817i	−0.125088	−	0.784511i
$550$		0			0
$551$	4.52190	−	7.83216i	0.192639	−	0.333661i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	6.76034	−	0.535575i	0.286960	−	0.0227339i
$556$		0			0
$557$	−36.1181	−	20.8528i	−1.53037	−	0.883562i	−0.999344	−	0.0362098i	$-0.988472\pi$
$557$	−36.1181	−	20.8528i	−1.53037	−	0.883562i	−0.531031	−	0.847353i	$-0.678195\pi$
$558$		0			0
$559$		−	8.50926i		−	0.359903i
$560$		0			0
$561$	−48.1663	+	33.1406i	−2.03358	+	1.39920i
$562$		0			0
$563$	−0.938436	−	1.62542i	−0.0395504	−	0.0685033i	0.845573	−	0.533860i	$-0.179259\pi$
$563$	−0.938436	−	1.62542i	−0.0395504	−	0.0685033i	−0.885123	+	0.465357i	$0.845926\pi$
$564$		0			0
$565$	0.841235	+	0.485687i	0.0353910	+	0.0204330i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	20.6391	+	11.9160i	0.865237	+	0.499545i	0.865762	−	0.500455i	$-0.166834\pi$
$569$	20.6391	+	11.9160i	0.865237	+	0.499545i	−0.000525844		1.00000i	$0.500167\pi$
$570$		0			0
$571$	−14.8719	−	25.7589i	−0.622370	−	1.07798i	−0.989043	−	0.147626i	$-0.952837\pi$
$571$	−14.8719	−	25.7589i	−0.622370	−	1.07798i	0.366674	−	0.930350i	$-0.380497\pi$
$572$		0			0
$573$	−16.5652	+	11.3976i	−0.692020	+	0.476140i
$574$		0			0
$575$		−	26.2997i		−	1.09678i
$576$		0			0
$577$	12.6950	+	7.32947i	0.528501	+	0.305130i	0.740406	−	0.672160i	$-0.234633\pi$
$577$	12.6950	+	7.32947i	0.528501	+	0.305130i	−0.211905	+	0.977290i	$0.567967\pi$
$578$		0			0
$579$	10.9331	−	0.866152i	0.454363	−	0.0359961i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	19.6422	−	34.0213i	0.813498	−	1.40902i
$584$		0			0
$585$	1.08227	+	6.78763i	0.0447462	+	0.280634i
$586$		0			0
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.803836	−	0.594851i	$-0.797211\pi$
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.113238	−	0.993568i	$-0.536122\pi$
$588$		0			0
$589$	3.22174	−	5.58021i	0.132749	−	0.229929i
$590$		0			0
$591$	−4.84798	−	2.30928i	−0.199419	−	0.0949912i
$592$		0			0
$593$	−18.5593	−	32.1457i	−0.762140	−	1.32006i	−0.941746	−	0.336326i	$-0.890816\pi$
$593$	−18.5593	−	32.1457i	−0.762140	−	1.32006i	0.179606	−	0.983739i	$-0.442518\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−22.4409	+	15.4403i	−0.918445	+	0.631931i
$598$		0			0
$599$	12.0534	−	6.95901i	0.492487	−	0.284338i	−0.233119	−	0.972448i	$-0.574893\pi$
$599$	12.0534	−	6.95901i	0.492487	−	0.284338i	0.725606	+	0.688111i	$0.241560\pi$
$600$		0			0
$601$	0.377613	−	0.218015i	0.0154032	−	0.00889301i	−0.492279	−	0.870438i	$-0.663836\pi$
$601$	0.377613	−	0.218015i	0.0154032	−	0.00889301i	0.507682	+	0.861545i	$0.330503\pi$
$602$		0			0
$603$	3.62005	−	9.45984i	0.147420	−	0.385235i
$604$		0			0
$605$	5.92923			0.241057
$606$		0			0
$607$		−	2.21837i		−	0.0900410i	−0.998986	−	0.0450205i	$-0.985665\pi$
$607$		−	2.21837i		−	0.0900410i	0.998986	−	0.0450205i	$-0.0143353\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−35.1315	+	20.2832i	−1.42127	+	0.820570i
$612$		0			0
$613$	−19.1011	+	33.0841i	−0.771488	+	1.33626i	0.165260	+	0.986250i	$0.447154\pi$
$613$	−19.1011	+	33.0841i	−0.771488	+	1.33626i	−0.936748	+	0.350006i	$0.886180\pi$
$614$		0			0
$615$	2.60073	+	3.77989i	0.104872	+	0.152420i
$616$		0			0
$617$	21.1043	+	12.1846i	0.849628	+	0.490533i	0.860525	−	0.509407i	$-0.170135\pi$
$617$	21.1043	+	12.1846i	0.849628	+	0.490533i	−0.0108970	+	0.999941i	$0.503469\pi$
$618$		0			0
$619$			29.3845i			1.18106i	0.807015	+	0.590531i	$0.201082\pi$
$619$			29.3845i			1.18106i	−0.807015	+	0.590531i	$0.798918\pi$
$620$		0			0
$621$	6.84140	+	28.3026i	0.274536	+	1.13574i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	20.4932			0.819728
$626$		0			0
$627$	−54.0351	+	4.28083i	−2.15795	+	0.170960i
$628$		0			0
$629$	51.2209			2.04231
$630$		0			0
$631$	5.17077			0.205845			0.102923	−	0.994689i	$-0.467181\pi$
$631$	5.17077			0.205845			0.102923	+	0.994689i	$0.467181\pi$
$632$		0			0
$633$	6.89729	+	10.0245i	0.274143	+	0.398438i
$634$		0			0
$635$	−6.13762			−0.243564
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.949393	−	0.770434i	0.0375574	−	0.0304779i
$640$		0			0
$641$		−	6.14769i		−	0.242819i	−0.992603	−	0.121410i	$-0.961259\pi$
$641$		−	6.14769i		−	0.242819i	0.992603	−	0.121410i	$-0.0387414\pi$
$642$		0			0
$643$	23.9599	+	13.8333i	0.944886	+	0.545530i	0.891489	−	0.453043i	$-0.149662\pi$
$643$	23.9599	+	13.8333i	0.944886	+	0.545530i	0.0533976	+	0.998573i	$0.482995\pi$
$644$		0			0
$645$	−1.96696	+	0.155828i	−0.0774488	+	0.00613574i
$646$		0			0
$647$	−2.40729	+	4.16954i	−0.0946402	+	0.163922i	−0.909458	−	0.415795i	$-0.863503\pi$
$647$	−2.40729	+	4.16954i	−0.0946402	+	0.163922i	0.814818	+	0.579717i	$0.196837\pi$
$648$		0			0
$649$	−31.4676	+	18.1679i	−1.23521	+	0.713151i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	24.4518i		−	0.956874i	−0.878122	−	0.478437i	$-0.841204\pi$
$653$		−	24.4518i		−	0.956874i	0.878122	−	0.478437i	$-0.158796\pi$
$654$		0			0
$655$	10.2308			0.399749
$656$		0			0
$657$	4.07926	+	25.5838i	0.159147	+	0.998120i
$658$		0			0
$659$	−20.7514	+	11.9808i	−0.808359	+	0.466706i	−0.846386	−	0.532570i	$-0.821226\pi$
$659$	−20.7514	+	11.9808i	−0.808359	+	0.466706i	0.0380267	+	0.999277i	$0.487893\pi$
$660$		0			0
$661$	6.73275	−	3.88715i	0.261874	−	0.151193i	−0.363315	−	0.931666i	$-0.618355\pi$
$661$	6.73275	−	3.88715i	0.261874	−	0.151193i	0.625189	+	0.780473i	$0.285022\pi$
$662$		0			0
$663$	4.09999	+	51.7524i	0.159230	+	2.00990i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.77234	+	6.53389i	0.146066	+	0.252993i
$668$		0			0
$669$	3.37190	+	42.5621i	0.130365	+	1.64554i
$670$		0			0
$671$	−14.4536	+	25.0343i	−0.557973	+	0.966438i
$672$		0			0
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	−0.996790	−	0.0800548i	$-0.974490\pi$
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	0.429066	−	0.903273i	$-0.358843\pi$
$674$		0			0
$675$	−23.7043	+	5.72988i	−0.912378	+	0.220543i
$676$		0			0
$677$	17.8293	−	30.8812i	0.685235	−	1.18686i	−0.288128	−	0.957592i	$-0.593033\pi$
$677$	17.8293	−	30.8812i	0.685235	−	1.18686i	0.973363	−	0.229270i	$-0.0736337\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−14.9525	+	31.3904i	−0.572981	+	1.20288i
$682$		0			0
$683$	−11.3423	−	6.54846i	−0.433999	−	0.250570i	0.267050	−	0.963683i	$-0.413951\pi$
$683$	−11.3423	−	6.54846i	−0.433999	−	0.250570i	−0.701049	+	0.713113i	$0.747285\pi$
$684$		0			0
$685$		−	12.1850i		−	0.465563i
$686$		0			0
$687$	12.2035	+	5.81302i	0.465594	+	0.221781i
$688$		0			0
$689$	−17.4412	−	30.2090i	−0.664456	−	1.15087i
$690$		0			0
$691$	−7.81992	−	4.51483i	−0.297484	−	0.171752i	0.343828	−	0.939033i	$-0.388276\pi$
$691$	−7.81992	−	4.51483i	−0.297484	−	0.171752i	−0.641312	+	0.767280i	$0.721610\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.74068	+	2.73704i	0.179824	+	0.103822i
$696$		0			0
$697$	17.3273	+	30.0117i	0.656316	+	1.13677i
$698$		0			0
$699$	−1.08962	−	13.7538i	−0.0412131	−	0.520215i
$700$		0			0
$701$		−	0.259274i		−	0.00979264i	−0.999988	−	0.00489632i	$-0.998441\pi$
$701$		−	0.259274i		−	0.00979264i	0.999988	−	0.00489632i	$-0.00155855\pi$
$702$		0			0
$703$	41.1252	+	23.7436i	1.55107	+	0.895508i
$704$		0			0
$705$	5.33191	+	7.74938i	0.200811	+	0.291858i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.08574	+	5.34467i	−0.115888	+	0.200723i	−0.918134	−	0.396270i	$-0.870305\pi$
$709$	−3.08574	+	5.34467i	−0.115888	+	0.200723i	0.802247	+	0.596993i	$0.203638\pi$
$710$		0			0
$711$	1.88524	−	0.300596i	0.0707021	−	0.0112732i
$712$		0			0
$713$	2.68770	+	4.65523i	0.100655	+	0.174340i
$714$		0			0
$715$	5.33712	−	9.24417i	0.199597	−	0.345712i
$716$		0			0
$717$	−38.2356	+	26.3078i	−1.42793	+	0.982481i
$718$		0			0
$719$	−9.76375	−	16.9113i	−0.364127	−	0.630686i	0.624509	−	0.781018i	$-0.285299\pi$
$719$	−9.76375	−	16.9113i	−0.364127	−	0.630686i	−0.988636	+	0.150332i	$0.951966\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.36732	−	0.651308i	−0.0508511	−	0.0242224i
$724$		0			0
$725$	−5.47233	+	3.15945i	−0.203237	+	0.117339i
$726$		0			0
$727$	0.425312	−	0.245554i	0.0157740	−	0.00910710i	−0.492092	−	0.870543i	$-0.663768\pi$
$727$	0.425312	−	0.245554i	0.0157740	−	0.00910710i	0.507866	+	0.861436i	$0.330434\pi$
$728$		0			0
$729$	24.0189	−	12.3325i	0.889591	−	0.456759i
$730$		0			0
$731$	−14.9030			−0.551206
$732$		0			0
$733$		−	7.71829i		−	0.285082i	−0.989789	−	0.142541i	$-0.954473\pi$
$733$		−	7.71829i		−	0.285082i	0.989789	−	0.142541i	$-0.0455272\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−13.6225	+	7.86498i	−0.501793	+	0.289710i
$738$		0			0
$739$	−5.45417	+	9.44690i	−0.200635	+	0.347510i	−0.948733	−	0.316078i	$-0.897634\pi$
$739$	−5.45417	+	9.44690i	−0.200635	+	0.347510i	0.748098	+	0.663588i	$0.230967\pi$
$740$		0			0
$741$	−20.6982	+	43.4525i	−0.760366	+	1.59627i
$742$		0			0
$743$	27.0051	+	15.5914i	0.990722	+	0.571994i	0.905490	−	0.424367i	$-0.139503\pi$
$743$	27.0051	+	15.5914i	0.990722	+	0.571994i	0.0852322	+	0.996361i	$0.472837\pi$
$744$		0			0
$745$		−	4.07158i		−	0.149171i
$746$		0			0
$747$	5.97944	−	15.6254i	0.218776	−	0.571702i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−46.0734			−1.68124			−0.840622	−	0.541623i	$-0.817810\pi$
$751$	−46.0734			−1.68124			−0.840622	+	0.541623i	$0.817810\pi$
$752$		0			0
$753$	1.72868	−	3.62909i	0.0629966	−	0.132252i
$754$		0			0
$755$	2.39917			0.0873149
$756$		0			0
$757$	40.6419			1.47715			0.738577	−	0.674169i	$-0.235498\pi$
$757$	40.6419			1.47715			0.738577	+	0.674169i	$0.235498\pi$
$758$		0			0
$759$	19.4463	−	40.8245i	0.705856	−	1.48183i
$760$		0			0
$761$	−7.28380			−0.264037			−0.132019	−	0.991247i	$-0.542146\pi$
$761$	−7.28380			−0.264037			−0.132019	+	0.991247i	$0.542146\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.8877	−	1.89546i	0.429802	−	0.0685306i
$766$		0			0
$767$			32.2640i			1.16499i
$768$		0			0
$769$	−35.8261	−	20.6842i	−1.29192	−	0.745892i	−0.312927	−	0.949777i	$-0.601310\pi$
$769$	−35.8261	−	20.6842i	−1.29192	−	0.745892i	−0.978995	+	0.203886i	$0.934643\pi$
$770$		0			0
$771$	18.3261	−	38.4727i	0.659997	−	1.38556i
$772$		0			0
$773$	−8.55914	+	14.8249i	−0.307851	+	0.533213i	−0.977892	−	0.209111i	$-0.932943\pi$
$773$	−8.55914	+	14.8249i	−0.307851	+	0.533213i	0.670041	+	0.742324i	$0.266276\pi$
$774$		0			0
$775$	−3.89890	+	2.25103i	−0.140053	+	0.0808594i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			32.1284i			1.15112i
$780$		0			0
$781$	−1.89879			−0.0679439
$782$		0			0
$783$	5.06720	−	4.82359i	0.181087	−	0.172381i
$784$		0			0
$785$	−0.853737	+	0.492906i	−0.0304712	+	0.0175926i
$786$		0			0
$787$	25.7426	−	14.8625i	0.917623	−	0.529790i	0.0347472	−	0.999396i	$-0.488937\pi$
$787$	25.7426	−	14.8625i	0.917623	−	0.529790i	0.882876	+	0.469606i	$0.155604\pi$
$788$		0			0
$789$	37.0636	+	17.6549i	1.31950	+	0.628530i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	12.8339	+	22.2290i	0.455746	+	0.789375i
$794$		0			0
$795$	−6.66355	+	4.58482i	−0.236332	+	0.162607i
$796$		0			0
$797$	20.6019	−	35.6836i	0.729757	−	1.26398i	−0.227229	−	0.973841i	$-0.572966\pi$
$797$	20.6019	−	35.6836i	0.729757	−	1.26398i	0.956986	−	0.290135i	$-0.0937002\pi$
$798$		0			0
$799$	35.5236	+	61.5288i	1.25674	+	2.17673i
$800$		0			0
$801$	7.43182	−	19.4207i	0.262590	−	0.686196i
$802$		0			0
$803$	20.1166	−	34.8430i	0.709900	−	1.22958i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	20.2455	+	29.4248i	0.712677	+	1.03580i
$808$		0			0
$809$	−10.7589	−	6.21165i	−0.378262	−	0.218390i	0.298800	−	0.954316i	$-0.403414\pi$
$809$	−10.7589	−	6.21165i	−0.378262	−	0.218390i	−0.677062	+	0.735926i	$0.736747\pi$
$810$		0			0
$811$			32.8713i			1.15427i	0.816650	+	0.577133i	$0.195829\pi$
$811$			32.8713i			1.15427i	−0.816650	+	0.577133i	$0.804171\pi$
$812$		0			0
$813$	1.90759	+	24.0787i	0.0669021	+	0.844477i
$814$		0			0
$815$	−1.56078	−	2.70336i	−0.0546719	−	0.0946944i
$816$		0			0
$817$	−11.9656	−	6.90833i	−0.418623	−	0.241692i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.7411	+	6.77873i	0.409768	+	0.236579i	0.690690	−	0.723151i	$-0.257307\pi$
$821$	11.7411	+	6.77873i	0.409768	+	0.236579i	−0.280922	+	0.959731i	$0.590640\pi$
$822$		0			0
$823$	12.2565	+	21.2289i	0.427235	+	0.739993i	0.996626	−	0.0820737i	$-0.0261543\pi$
$823$	12.2565	+	21.2289i	0.427235	+	0.739993i	−0.569391	+	0.822067i	$0.692821\pi$
$824$		0			0
$825$	34.1917	+	16.2869i	1.19040	+	0.567036i
$826$		0			0
$827$		−	14.7323i		−	0.512292i	−0.966638	−	0.256146i	$-0.917547\pi$
$827$		−	14.7323i		−	0.512292i	0.966638	−	0.256146i	$-0.0824527\pi$
$828$		0			0
$829$	11.7079	+	6.75957i	0.406633	+	0.234770i	0.689342	−	0.724436i	$-0.257900\pi$
$829$	11.7079	+	6.75957i	0.406633	+	0.234770i	−0.282709	+	0.959206i	$0.591233\pi$
$830$		0			0
$831$	−15.4842	+	32.5065i	−0.537139	+	1.12764i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.32255	−	2.29073i	0.0457689	−	0.0792740i
$836$		0			0
$837$	3.61025	−	3.43668i	0.124789	−	0.118789i
$838$		0			0
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	0.857067	−	0.515205i	$-0.172284\pi$
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	−0.874714	+	0.484639i	$0.838951\pi$
$840$		0			0
$841$	−13.5936	+	23.5449i	−0.468746	+	0.811892i
$842$		0			0
$843$	−3.21228	−	40.5472i	−0.110637	−	1.39652i
$844$		0			0
$845$	−1.13918	−	1.97312i	−0.0391890	−	0.0678773i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.76757	+	22.3113i	0.0606628	+	0.765721i
$850$		0			0
$851$	−34.3082	+	19.8079i	−1.17607	+	0.679005i
$852$		0			0
$853$	8.70682	−	5.02689i	0.298116	−	0.172117i	−0.343480	−	0.939160i	$-0.611606\pi$
$853$	8.70682	−	5.02689i	0.298116	−	0.172117i	0.641596	+	0.767043i	$0.278273\pi$
$854$		0			0
$855$	10.4233	+	3.98874i	0.356469	+	0.136412i
$856$		0			0
$857$	28.2543			0.965150			0.482575	−	0.875855i	$-0.339702\pi$
$857$	28.2543			0.965150			0.482575	+	0.875855i	$0.339702\pi$
$858$		0			0
$859$		−	31.1538i		−	1.06295i	−0.847073	−	0.531476i	$-0.821637\pi$
$859$		−	31.1538i		−	1.06295i	0.847073	−	0.531476i	$-0.178363\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	49.4703	−	28.5617i	1.68399	−	0.972252i	0.725026	−	0.688722i	$-0.241828\pi$
$863$	49.4703	−	28.5617i	1.68399	−	0.972252i	0.958963	−	0.283530i	$-0.0915055\pi$
$864$		0			0
$865$	1.57157	−	2.72204i	0.0534351	−	0.0925522i
$866$		0			0
$867$	61.2854	−	4.85522i	2.08136	−	0.164892i
$868$		0			0
$869$	−2.56754	−	1.48237i	−0.0870978	−	0.0502859i
$870$		0			0
$871$			13.9673i			0.473264i
$872$		0			0
$873$	−24.2259	−	9.27064i	−0.819921	−	0.313764i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−31.3382			−1.05822			−0.529108	−	0.848554i	$-0.677473\pi$
$877$	−31.3382			−1.05822			−0.529108	+	0.848554i	$0.677473\pi$
$878$		0			0
$879$	−3.90976	−	5.68243i	−0.131873	−	0.191664i
$880$		0			0
$881$	12.2822			0.413799			0.206900	−	0.978362i	$-0.433663\pi$
$881$	12.2822			0.413799			0.206900	+	0.978362i	$0.433663\pi$
$882$		0			0
$883$	3.61496			0.121653			0.0608266	−	0.998148i	$-0.480626\pi$
$883$	3.61496			0.121653			0.0608266	+	0.998148i	$0.480626\pi$
$884$		0			0
$885$	7.45798	−	0.590844i	0.250697	−	0.0198610i
$886$		0			0
$887$	18.8853			0.634106			0.317053	−	0.948408i	$-0.397307\pi$
$887$	18.8853			0.634106			0.317053	+	0.948408i	$0.397307\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−41.0323	−	8.63284i	−1.37463	−	0.289211i
$892$		0			0
$893$			65.8685i			2.20420i
$894$		0			0
$895$	6.05795	+	3.49756i	0.202495	+	0.116911i
$896$		0			0
$897$	−22.7596	−	33.0787i	−0.759922	−	1.10447i
$898$		0			0
$899$	0.645760	−	1.11849i	0.0215373	−	0.0373037i
$900$		0			0
$901$	−52.9075	+	30.5462i	−1.76260	+	1.01764i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			12.5954i			0.418684i
$906$		0			0
$907$	−57.7603			−1.91790			−0.958950	−	0.283576i	$-0.908479\pi$
$907$	−57.7603			−1.91790			−0.958950	+	0.283576i	$0.908479\pi$
$908$		0			0
$909$	8.85553	+	10.9125i	0.293719	+	0.361945i
$910$		0			0
$911$	−33.7810	+	19.5034i	−1.11921	+	0.646178i	−0.941200	−	0.337850i	$-0.890300\pi$
$911$	−33.7810	+	19.5034i	−1.11921	+	0.646178i	−0.178013	+	0.984028i	$0.556967\pi$
$912$		0			0
$913$	−22.5011	+	12.9910i	−0.744679	+	0.429940i
$914$		0			0
$915$	4.90331	−	3.37370i	0.162099	−	0.111531i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	15.9047	+	27.5478i	0.524649	+	0.908719i	0.999588	+	0.0287001i	$0.00913677\pi$
$919$	15.9047	+	27.5478i	0.524649	+	0.908719i	−0.474939	+	0.880019i	$0.657530\pi$
$920$		0			0
$921$	−34.8960	−	16.6223i	−1.14986	−	0.547725i
$922$		0			0
$923$	−0.843006	+	1.46013i	−0.0277479	+	0.0480607i
$924$		0			0
$925$	−16.5897	−	28.7342i	−0.545465	−	0.944774i
$926$		0			0
$927$	17.2367	−	13.9876i	0.566127	−	0.459413i
$928$		0			0
$929$	19.0424	−	32.9825i	0.624762	−	1.08212i	−0.363824	−	0.931468i	$-0.618529\pi$
$929$	19.0424	−	32.9825i	0.624762	−	1.08212i	0.988587	−	0.150653i	$-0.0481375\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	28.2607	−	2.23890i	0.925212	−	0.0732982i
$934$		0			0
$935$	−16.1901	−	9.34735i	−0.529472	−	0.305691i
$936$		0			0
$937$			37.6261i			1.22919i	0.788842	+	0.614596i	$0.210681\pi$
$937$			37.6261i			1.22919i	−0.788842	+	0.614596i	$0.789319\pi$
$938$		0			0
$939$	−27.2766	+	18.7675i	−0.890137	+	0.612454i
$940$		0			0
$941$	−0.837737	−	1.45100i	−0.0273094	−	0.0473014i	0.852048	−	0.523464i	$-0.175361\pi$
$941$	−0.837737	−	1.45100i	−0.0273094	−	0.0473014i	−0.879357	+	0.476163i	$0.842027\pi$
$942$		0			0
$943$	−23.2119	−	13.4014i	−0.755884	−	0.436410i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.2331	−	11.1042i	−0.624992	−	0.360839i	0.153818	−	0.988099i	$-0.450843\pi$
$947$	−19.2331	−	11.1042i	−0.624992	−	0.360839i	−0.778810	+	0.627260i	$0.784176\pi$
$948$		0			0
$949$	−17.8624	−	30.9386i	−0.579838	−	1.00431i
$950$		0			0
$951$	34.4029	−	23.6707i	1.11559	−	0.767576i
$952$		0			0
$953$		−	27.1505i		−	0.879491i	−0.898122	−	0.439746i	$-0.855069\pi$
$953$		−	27.1505i		−	0.879491i	0.898122	−	0.439746i	$-0.144931\pi$
$954$		0			0
$955$	−5.56803	−	3.21470i	−0.180177	−	0.104025i
$956$		0			0
$957$	−10.8307	+	0.858043i	−0.350107	+	0.0277366i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.0399	+	26.0499i	−0.485158	+	0.840319i
$962$		0			0
$963$	−14.1790	−	5.42596i	−0.456913	−	0.174849i
$964$		0			0
$965$	1.75341	+	3.03700i	0.0564444	+	0.0977646i
$966$		0			0
$967$	−16.7553	+	29.0211i	−0.538815	+	0.933255i	0.460153	+	0.887840i	$0.347795\pi$
$967$	−16.7553	+	29.0211i	−0.538815	+	0.933255i	−0.998968	+	0.0454157i	$0.985539\pi$
$968$		0			0
$969$	76.1020	+	36.2504i	2.44475	+	1.16453i
$970$		0			0
$971$	17.8733	+	30.9574i	0.573580	+	0.993470i	0.996194	+	0.0871606i	$0.0277793\pi$
$971$	17.8733	+	30.9574i	0.573580	+	0.993470i	−0.422614	+	0.906310i	$0.638887\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	27.7044	−	19.0619i	0.887252	−	0.610469i
$976$		0			0
$977$	39.5696	−	22.8455i	1.26594	−	0.730892i	0.291725	−	0.956502i	$-0.405771\pi$
$977$	39.5696	−	22.8455i	1.26594	−	0.730892i	0.974218	+	0.225610i	$0.0724376\pi$
$978$		0			0
$979$	−27.9665	+	16.1465i	−0.893814	+	0.516044i
$980$		0			0
$981$	34.8483	−	5.55646i	1.11262	−	0.177404i
$982$		0			0
$983$	−18.6743			−0.595616			−0.297808	−	0.954626i	$-0.596256\pi$
$983$	−18.6743			−0.595616			−0.297808	+	0.954626i	$0.596256\pi$
$984$		0			0
$985$		−	1.71703i		−	0.0547092i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.98215	−	5.76320i	0.317414	−	0.183259i
$990$		0			0
$991$	−24.2806	+	42.0552i	−0.771299	+	1.33593i	0.165553	+	0.986201i	$0.447059\pi$
$991$	−24.2806	+	42.0552i	−0.771299	+	1.33593i	−0.936851	+	0.349727i	$0.886274\pi$
$992$		0			0
$993$	−11.1939	−	16.2691i	−0.355226	−	0.516284i
$994$		0			0
$995$	−7.54303	−	4.35497i	−0.239130	−	0.138062i
$996$		0			0
$997$		−	52.1903i		−	1.65288i	−0.563022	−	0.826442i	$-0.690361\pi$
$997$		−	52.1903i		−	1.65288i	0.563022	−	0.826442i	$-0.309639\pi$
$998$		0			0
$999$	25.3277	+	26.6069i	0.801334	+	0.841805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.bm.b.1697.3		16
3.2	odd	2		5292.2.bm.b.2285.6		16
7.2	even	3		1764.2.w.a.509.3		16
7.3	odd	6		252.2.x.a.41.1	✓	16
7.4	even	3		252.2.x.a.41.8	yes	16
7.5	odd	6		1764.2.w.a.509.6		16
7.6	odd	2	inner	1764.2.bm.b.1697.6		16
9.2	odd	6		1764.2.w.a.1109.6		16
9.7	even	3		5292.2.w.a.521.6		16
21.2	odd	6		5292.2.w.a.1097.3		16
21.5	even	6		5292.2.w.a.1097.6		16
21.11	odd	6		756.2.x.a.125.3		16
21.17	even	6		756.2.x.a.125.6		16
21.20	even	2		5292.2.bm.b.2285.3		16
28.3	even	6		1008.2.cc.c.545.8		16
28.11	odd	6		1008.2.cc.c.545.1		16
63.2	odd	6	inner	1764.2.bm.b.1685.6		16
63.4	even	3		2268.2.f.b.1133.5		16
63.11	odd	6		252.2.x.a.209.1	yes	16
63.16	even	3		5292.2.bm.b.4625.3		16
63.20	even	6		1764.2.w.a.1109.3		16
63.25	even	3		756.2.x.a.629.6		16
63.31	odd	6		2268.2.f.b.1133.12		16
63.32	odd	6		2268.2.f.b.1133.11		16
63.34	odd	6		5292.2.w.a.521.3		16
63.38	even	6		252.2.x.a.209.8	yes	16
63.47	even	6	inner	1764.2.bm.b.1685.3		16
63.52	odd	6		756.2.x.a.629.3		16
63.59	even	6		2268.2.f.b.1133.6		16
63.61	odd	6		5292.2.bm.b.4625.6		16
84.11	even	6		3024.2.cc.c.881.3		16
84.59	odd	6		3024.2.cc.c.881.6		16
252.11	even	6		1008.2.cc.c.209.8		16
252.115	even	6		3024.2.cc.c.2897.3		16
252.151	odd	6		3024.2.cc.c.2897.6		16
252.227	odd	6		1008.2.cc.c.209.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.1	✓	16	7.3	odd	6
252.2.x.a.41.8	yes	16	7.4	even	3
252.2.x.a.209.1	yes	16	63.11	odd	6
252.2.x.a.209.8	yes	16	63.38	even	6
756.2.x.a.125.3		16	21.11	odd	6
756.2.x.a.125.6		16	21.17	even	6
756.2.x.a.629.3		16	63.52	odd	6
756.2.x.a.629.6		16	63.25	even	3
1008.2.cc.c.209.1		16	252.227	odd	6
1008.2.cc.c.209.8		16	252.11	even	6
1008.2.cc.c.545.1		16	28.11	odd	6
1008.2.cc.c.545.8		16	28.3	even	6
1764.2.w.a.509.3		16	7.2	even	3
1764.2.w.a.509.6		16	7.5	odd	6
1764.2.w.a.1109.3		16	63.20	even	6
1764.2.w.a.1109.6		16	9.2	odd	6
1764.2.bm.b.1685.3		16	63.47	even	6	inner
1764.2.bm.b.1685.6		16	63.2	odd	6	inner
1764.2.bm.b.1697.3		16	1.1	even	1	trivial
1764.2.bm.b.1697.6		16	7.6	odd	2	inner
2268.2.f.b.1133.5		16	63.4	even	3
2268.2.f.b.1133.6		16	63.59	even	6
2268.2.f.b.1133.11		16	63.32	odd	6
2268.2.f.b.1133.12		16	63.31	odd	6
3024.2.cc.c.881.3		16	84.11	even	6
3024.2.cc.c.881.6		16	84.59	odd	6
3024.2.cc.c.2897.3		16	252.115	even	6
3024.2.cc.c.2897.6		16	252.151	odd	6
5292.2.w.a.521.3		16	63.34	odd	6
5292.2.w.a.521.6		16	9.7	even	3
5292.2.w.a.1097.3		16	21.2	odd	6
5292.2.w.a.1097.6		16	21.5	even	6
5292.2.bm.b.2285.3		16	21.20	even	2
5292.2.bm.b.2285.6		16	3.2	odd	2
5292.2.bm.b.4625.3		16	63.16	even	3
5292.2.bm.b.4625.6		16	63.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.744857 + 1.56371i) q^{3} -0.553827 q^{5} +(-1.89038 - 2.32948i) q^{9} +O(q^{10})\)	\(q+(-0.744857 + 1.56371i) q^{3} -0.553827 q^{5} +(-1.89038 - 2.32948i) q^{9} +4.65896i q^{11} +(3.58265 + 2.06844i) q^{13} +(0.412522 - 0.866025i) q^{15} +(3.62264 - 6.27459i) q^{17} +(5.81722 - 3.35857i) q^{19} +5.60371i q^{23} -4.69328 q^{25} +(5.05069 - 1.22087i) q^{27} +(1.16599 - 0.673187i) q^{29} +(0.830741 - 0.479629i) q^{31} +(-7.28526 - 3.47026i) q^{33} +(3.53478 + 6.12241i) q^{37} +(-5.90301 + 4.06153i) q^{39} +(-2.39152 + 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(1.04694 + 1.29013i) q^{45} +(-4.90301 + 8.49226i) q^{47} +(7.11329 + 10.3384i) q^{51} +(-7.30235 - 4.21601i) q^{53} -2.58026i q^{55} +(0.918838 + 11.5981i) q^{57} +(3.89955 + 6.75422i) q^{59} +(5.37336 + 3.10231i) q^{61} +(-1.98417 - 1.14556i) q^{65} +(1.68814 + 2.92394i) q^{67} +(-8.76257 - 4.17396i) q^{69} +0.407556i q^{71} +(-7.47870 - 4.31783i) q^{73} +(3.49582 - 7.33892i) q^{75} +(-0.318176 + 0.551097i) q^{79} +(-1.85295 + 8.80719i) q^{81} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(0.184170 + 2.32470i) q^{87} +(3.46568 + 6.00274i) q^{89} +(0.131217 + 1.65629i) q^{93} +(-3.22174 + 1.86007i) q^{95} +(7.48798 - 4.32318i) q^{97} +(10.8530 - 8.80719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^9	\( 16 q + 6 q^{9} - 12 q^{15} + 16 q^{25} - 12 q^{29} - 2 q^{37} + 18 q^{39} + 4 q^{43} + 6 q^{51} - 36 q^{53} - 42 q^{57} + 24 q^{65} + 14 q^{67} + 20 q^{79} + 54 q^{81} + 6 q^{85} + 30 q^{93} + 60 q^{95} + 90 q^{99}+O(q^{100}) \) 16 * q + 6 * q^9 - 12 * q^15 + 16 * q^25 - 12 * q^29 - 2 * q^37 + 18 * q^39 + 4 * q^43 + 6 * q^51 - 36 * q^53 - 42 * q^57 + 24 * q^65 + 14 * q^67 + 20 * q^79 + 54 * q^81 + 6 * q^85 + 30 * q^93 + 60 * q^95 + 90 * q^99

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