LMFDB - Embedded newform 972.2.i.b.865.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [972,2,Mod(109,972)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(972, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("972.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.i (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			865.3
Root			$1.16555 + 1.28120i$ of defining polynomial
Character	$\chi$	$=$	972.865
Dual form			972.2.i.b.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.16020 + 1.15022i) q^{5} +(-0.333817 + 1.89317i) q^{7} +O(q^{10})$	$q+(3.16020 + 1.15022i) q^{5} +(-0.333817 + 1.89317i) q^{7} +(1.90527 - 0.693460i) q^{11} +(4.50919 - 3.78366i) q^{13} +(-1.69713 - 2.93951i) q^{17} +(-0.0802464 + 0.138991i) q^{19} +(0.746622 + 4.23431i) q^{23} +(4.83365 + 4.05592i) q^{25} +(-6.35331 - 5.33106i) q^{29} +(1.83141 + 10.3865i) q^{31} +(-3.23249 + 5.59884i) q^{35} +(2.17770 + 3.77190i) q^{37} +(0.988175 - 0.829177i) q^{41} +(6.78459 - 2.46939i) q^{43} +(-0.0168525 + 0.0955753i) q^{47} +(3.10519 + 1.13020i) q^{49} -12.8006 q^{53} +6.81866 q^{55} +(-2.28715 - 0.832456i) q^{59} +(1.00156 - 5.68010i) q^{61} +(18.6020 - 6.77058i) q^{65} +(-3.17652 + 2.66542i) q^{67} +(3.09944 + 5.36839i) q^{71} +(2.12803 - 3.68585i) q^{73} +(0.676828 + 3.83848i) q^{77} +(-2.28753 - 1.91947i) q^{79} +(-7.30399 - 6.12877i) q^{83} +(-1.98218 - 11.2415i) q^{85} +(0.821473 - 1.42283i) q^{89} +(5.65787 + 9.79971i) q^{91} +(-0.413465 + 0.346938i) q^{95} +(-2.62231 + 0.954445i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{5}+O(q^{10}) $ 18 * q - 3 * q^5	$ 18 q - 3 q^{5} + 15 q^{11} + 12 q^{17} - 33 q^{23} + 9 q^{25} - 21 q^{29} + 9 q^{31} + 21 q^{35} + 33 q^{41} + 18 q^{43} - 9 q^{47} + 36 q^{49} - 66 q^{53} + 12 q^{59} + 36 q^{61} + 66 q^{65} + 27 q^{67} + 12 q^{71} + 9 q^{73} - 33 q^{77} + 18 q^{79} - 81 q^{83} + 18 q^{85} + 48 q^{89} + 9 q^{91} + 84 q^{95}+O(q^{100}) $ 18 * q - 3 * q^5 + 15 * q^11 + 12 * q^17 - 33 * q^23 + 9 * q^25 - 21 * q^29 + 9 * q^31 + 21 * q^35 + 33 * q^41 + 18 * q^43 - 9 * q^47 + 36 * q^49 - 66 * q^53 + 12 * q^59 + 36 * q^61 + 66 * q^65 + 27 * q^67 + 12 * q^71 + 9 * q^73 - 33 * q^77 + 18 * q^79 - 81 * q^83 + 18 * q^85 + 48 * q^89 + 9 * q^91 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	3.16020	+	1.15022i	1.41329	+	0.514394i	0.932092	−	0.362221i	$-0.117981\pi$
$5$	3.16020	+	1.15022i	1.41329	+	0.514394i	0.481193	+	0.876615i	$0.340204\pi$
$6$		0			0
$7$	−0.333817	+	1.89317i	−0.126171	+	0.715551i	0.854435	+	0.519559i	$0.173904\pi$
$7$	−0.333817	+	1.89317i	−0.126171	+	0.715551i	−0.980606	+	0.195992i	$0.937207\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.90527	−	0.693460i	0.574460	−	0.209086i	−0.0384211	−	0.999262i	$-0.512233\pi$
$11$	1.90527	−	0.693460i	0.574460	−	0.209086i	0.612881	+	0.790175i	$0.290011\pi$
$12$		0			0
$13$	4.50919	−	3.78366i	1.25062	−	1.04940i	0.254009	−	0.967202i	$-0.418251\pi$
$13$	4.50919	−	3.78366i	1.25062	−	1.04940i	0.996616	−	0.0821970i	$-0.0261937\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.69713	−	2.93951i	−0.411613	−	0.712935i	0.583453	−	0.812147i	$-0.301701\pi$
$17$	−1.69713	−	2.93951i	−0.411613	−	0.712935i	−0.995066	+	0.0992115i	$0.968368\pi$
$18$		0			0
$19$	−0.0802464	+	0.138991i	−0.0184098	+	0.0318867i	−0.875084	−	0.483972i	$-0.839194\pi$
$19$	−0.0802464	+	0.138991i	−0.0184098	+	0.0318867i	0.856674	+	0.515859i	$0.172527\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.746622	+	4.23431i	0.155681	+	0.882914i	0.958160	+	0.286233i	$0.0924031\pi$
$23$	0.746622	+	4.23431i	0.155681	+	0.882914i	−0.802479	+	0.596681i	$0.796486\pi$
$24$		0			0
$25$	4.83365	+	4.05592i	0.966731	+	0.811183i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.35331	−	5.33106i	−1.17978	−	0.989954i	−0.999980	−	0.00625040i	$-0.998010\pi$
$29$	−6.35331	−	5.33106i	−1.17978	−	0.989954i	−0.179800	−	0.983703i	$-0.557545\pi$
$30$		0			0
$31$	1.83141	+	10.3865i	0.328932	+	1.86546i	0.480467	+	0.877013i	$0.340467\pi$
$31$	1.83141	+	10.3865i	0.328932	+	1.86546i	−0.151536	+	0.988452i	$0.548422\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.23249	+	5.59884i	−0.546390	+	0.946376i
$36$		0			0
$37$	2.17770	+	3.77190i	0.358012	+	0.620096i	0.987629	−	0.156810i	$-0.0501212\pi$
$37$	2.17770	+	3.77190i	0.358012	+	0.620096i	−0.629616	+	0.776906i	$0.716788\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.988175	−	0.829177i	0.154327	−	0.129496i	−0.562355	−	0.826896i	$-0.690104\pi$
$41$	0.988175	−	0.829177i	0.154327	−	0.129496i	0.716682	+	0.697400i	$0.245660\pi$
$42$		0			0
$43$	6.78459	−	2.46939i	1.03464	−	0.376578i	0.231794	−	0.972765i	$-0.425540\pi$
$43$	6.78459	−	2.46939i	1.03464	−	0.376578i	0.802846	+	0.596186i	$0.203318\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.0168525	+	0.0955753i	−0.00245819	+	0.0139411i	−0.986012	−	0.166673i	$-0.946697\pi$
$47$	−0.0168525	+	0.0955753i	−0.00245819	+	0.0139411i	0.983554	+	0.180614i	$0.0578086\pi$
$48$		0			0
$49$	3.10519	+	1.13020i	0.443599	+	0.161457i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−12.8006			−1.75830			−0.879152	−	0.476541i	$-0.841890\pi$
$53$	−12.8006			−1.75830			−0.879152	+	0.476541i	$0.841890\pi$
$54$		0			0
$55$	6.81866			0.919428
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.28715	−	0.832456i	−0.297762	−	0.108376i	0.188819	−	0.982012i	$-0.439534\pi$
$59$	−2.28715	−	0.832456i	−0.297762	−	0.108376i	−0.486581	+	0.873635i	$0.661756\pi$
$60$		0			0
$61$	1.00156	−	5.68010i	0.128236	−	0.727263i	−0.851097	−	0.525008i	$-0.824062\pi$
$61$	1.00156	−	5.68010i	0.128236	−	0.727263i	0.979333	−	0.202254i	$-0.0648267\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	18.6020	−	6.77058i	2.30729	−	0.839787i
$66$		0			0
$67$	−3.17652	+	2.66542i	−0.388074	+	0.325633i	−0.815862	−	0.578246i	$-0.803737\pi$
$67$	−3.17652	+	2.66542i	−0.388074	+	0.325633i	0.427788	+	0.903879i	$0.359293\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.09944	+	5.36839i	0.367836	+	0.637111i	0.989227	−	0.146390i	$-0.0467654\pi$
$71$	3.09944	+	5.36839i	0.367836	+	0.637111i	−0.621391	+	0.783501i	$0.713432\pi$
$72$		0			0
$73$	2.12803	−	3.68585i	0.249067	−	0.431396i	−0.714200	−	0.699941i	$-0.753209\pi$
$73$	2.12803	−	3.68585i	0.249067	−	0.431396i	0.963267	+	0.268545i	$0.0865428\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.676828	+	3.83848i	0.0771317	+	0.437436i
$78$		0			0
$79$	−2.28753	−	1.91947i	−0.257368	−	0.215957i	0.504969	−	0.863137i	$-0.331504\pi$
$79$	−2.28753	−	1.91947i	−0.257368	−	0.215957i	−0.762337	+	0.647180i	$0.775948\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.30399	−	6.12877i	−0.801717	−	0.672720i	0.146899	−	0.989152i	$-0.453071\pi$
$83$	−7.30399	−	6.12877i	−0.801717	−	0.672720i	−0.948615	+	0.316431i	$0.897515\pi$
$84$		0			0
$85$	−1.98218	−	11.2415i	−0.214998	−	1.21931i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.821473	−	1.42283i	0.0870760	−	0.150820i	−0.819198	−	0.573511i	$-0.805581\pi$
$89$	0.821473	−	1.42283i	0.0870760	−	0.150820i	0.906274	+	0.422691i	$0.138914\pi$
$90$		0			0
$91$	5.65787	+	9.79971i	0.593106	+	1.02729i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.413465	+	0.346938i	−0.0424206	+	0.0355951i
$96$		0			0
$97$	−2.62231	+	0.954445i	−0.266256	+	0.0969092i	−0.471698	−	0.881760i	$-0.656359\pi$
$97$	−2.62231	+	0.954445i	−0.266256	+	0.0969092i	0.205443	+	0.978669i	$0.434137\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.51750	+	8.60618i	−0.150997	+	0.856347i	0.811358	+	0.584550i	$0.198729\pi$
$101$	−1.51750	+	8.60618i	−0.150997	+	0.856347i	−0.962355	+	0.271797i	$0.912382\pi$
$102$		0			0
$103$	5.06083	+	1.84199i	0.498659	+	0.181497i	0.579091	−	0.815263i	$-0.303408\pi$
$103$	5.06083	+	1.84199i	0.498659	+	0.181497i	−0.0804319	+	0.996760i	$0.525630\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.7899			1.42979			0.714896	−	0.699231i	$-0.246474\pi$
$107$	14.7899			1.42979			0.714896	+	0.699231i	$0.246474\pi$
$108$		0			0
$109$	2.68614			0.257286			0.128643	−	0.991691i	$-0.458938\pi$
$109$	2.68614			0.257286			0.128643	+	0.991691i	$0.458938\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.5359	+	4.56268i	1.17927	+	0.429221i	0.855946	−	0.517066i	$-0.172976\pi$
$113$	12.5359	+	4.56268i	1.17927	+	0.429221i	0.323329	+	0.946287i	$0.395198\pi$
$114$		0			0
$115$	−2.51090	+	14.2400i	−0.234143	+	1.32789i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.13152	−	2.23169i	0.562075	−	0.204579i
$120$		0			0
$121$	−5.27733	+	4.42821i	−0.479758	+	0.402564i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.20259	+	3.81499i	0.197005	+	0.341223i
$126$		0			0
$127$	−4.80710	+	8.32614i	−0.426561	+	0.738826i	−0.996565	−	0.0828165i	$-0.973608\pi$
$127$	−4.80710	+	8.32614i	−0.426561	+	0.738826i	0.570004	+	0.821642i	$0.306942\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.16012	−	17.9219i	−0.276101	−	1.56585i	−0.735443	−	0.677586i	$-0.763026\pi$
$131$	−3.16012	−	17.9219i	−0.276101	−	1.56585i	0.459342	−	0.888259i	$-0.348085\pi$
$132$		0			0
$133$	−0.236346	−	0.198317i	−0.0204938	−	0.0171963i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.59418	−	3.01588i	−0.307072	−	0.257664i	0.476209	−	0.879332i	$-0.342011\pi$
$137$	−3.59418	−	3.01588i	−0.307072	−	0.257664i	−0.783281	+	0.621668i	$0.786455\pi$
$138$		0			0
$139$	−1.97436	−	11.1971i	−0.167463	−	0.949729i	−0.946489	−	0.322737i	$-0.895397\pi$
$139$	−1.97436	−	11.1971i	−0.167463	−	0.949729i	0.779026	−	0.626992i	$-0.215714\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.96740	−	10.3358i	0.499019	−	0.864326i
$144$		0			0
$145$	−13.9459	−	24.1549i	−1.15814	−	2.00596i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.85974	+	4.91690i	−0.480048	+	0.402808i	−0.850444	−	0.526066i	$-0.823667\pi$
$149$	−5.85974	+	4.91690i	−0.480048	+	0.402808i	0.370396	+	0.928874i	$0.379222\pi$
$150$		0			0
$151$	−11.3541	+	4.13255i	−0.923982	+	0.336302i	−0.759821	−	0.650132i	$-0.774714\pi$
$151$	−11.3541	+	4.13255i	−0.923982	+	0.336302i	−0.164160	+	0.986434i	$0.552491\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.15908	+	34.9299i	−0.494709	+	2.80563i
$156$		0			0
$157$	2.40284	+	0.874563i	0.191768	+	0.0697977i	0.436119	−	0.899889i	$-0.356353\pi$
$157$	2.40284	+	0.874563i	0.191768	+	0.0697977i	−0.244351	+	0.969687i	$0.578575\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.26549			−0.651412
$162$		0			0
$163$	−19.1557			−1.50039			−0.750195	−	0.661217i	$-0.770040\pi$
$163$	−19.1557			−1.50039			−0.750195	+	0.661217i	$0.770040\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.7597	−	6.82797i	−1.45167	−	0.528364i	−0.508611	−	0.860996i	$-0.669841\pi$
$167$	−18.7597	−	6.82797i	−1.45167	−	0.528364i	−0.943057	+	0.332632i	$0.892063\pi$
$168$		0			0
$169$	3.75929	−	21.3200i	0.289176	−	1.64000i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−11.4606	+	4.17132i	−0.871333	+	0.317139i	−0.738707	−	0.674027i	$-0.764563\pi$
$173$	−11.4606	+	4.17132i	−0.871333	+	0.317139i	−0.132626	+	0.991166i	$0.542341\pi$
$174$		0			0
$175$	−9.29209	+	7.79699i	−0.702416	+	0.589397i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.8419	−	18.7786i	−0.810358	−	1.40358i	−0.912613	−	0.408824i	$-0.865939\pi$
$179$	−10.8419	−	18.7786i	−0.810358	−	1.40358i	0.102255	−	0.994758i	$-0.467394\pi$
$180$		0			0
$181$	2.99749	−	5.19181i	0.222802	−	0.385904i	−0.732856	−	0.680384i	$-0.761813\pi$
$181$	2.99749	−	5.19181i	0.222802	−	0.385904i	0.955658	+	0.294480i	$0.0951464\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.54348	+	14.4248i	0.187000	+	1.06053i
$186$		0			0
$187$	−5.27191	−	4.42366i	−0.385520	−	0.323490i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−14.6702	−	12.3097i	−1.06150	−	0.890701i	−0.0672413	−	0.997737i	$-0.521420\pi$
$191$	−14.6702	−	12.3097i	−1.06150	−	0.890701i	−0.994255	+	0.107035i	$0.965864\pi$
$192$		0			0
$193$	−0.0782126	−	0.443566i	−0.00562986	−	0.0319285i	0.981863	−	0.189590i	$-0.0607158\pi$
$193$	−0.0782126	−	0.443566i	−0.00562986	−	0.0319285i	−0.987493	+	0.157661i	$0.949605\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.79534	−	3.10963i	0.127913	−	0.221552i	−0.794955	−	0.606669i	$-0.792506\pi$
$197$	1.79534	−	3.10963i	0.127913	−	0.221552i	0.922868	+	0.385117i	$0.125839\pi$
$198$		0			0
$199$	−3.63803	−	6.30125i	−0.257893	−	0.446684i	0.707784	−	0.706429i	$-0.249695\pi$
$199$	−3.63803	−	6.30125i	−0.257893	−	0.446684i	−0.965677	+	0.259745i	$0.916362\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	12.2134	−	10.2483i	0.857216	−	0.719290i
$204$		0			0
$205$	4.07657	−	1.48375i	0.284720	−	0.103630i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0565062	+	0.320462i	−0.00390861	+	0.0221668i
$210$		0			0
$211$	−6.09882	−	2.21979i	−0.419860	−	0.152816i	0.123446	−	0.992351i	$-0.460605\pi$
$211$	−6.09882	−	2.21979i	−0.419860	−	0.152816i	−0.543306	+	0.839535i	$0.682828\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	24.2810			1.65595
$216$		0			0
$217$	−20.2747			−1.37634
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−18.7748	−	6.83346i	−1.26293	−	0.459668i
$222$		0			0
$223$	−2.57206	+	14.5869i	−0.172238	+	0.976811i	0.769046	+	0.639194i	$0.220732\pi$
$223$	−2.57206	+	14.5869i	−0.172238	+	0.976811i	−0.941284	+	0.337617i	$0.890379\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.779996	−	0.283895i	0.0517701	−	0.0188428i	−0.316005	−	0.948757i	$-0.602342\pi$
$227$	0.779996	−	0.283895i	0.0517701	−	0.0188428i	0.367775	+	0.929915i	$0.380120\pi$
$228$		0			0
$229$	12.0063	−	10.0745i	0.793402	−	0.665743i	−0.153183	−	0.988198i	$-0.548952\pi$
$229$	12.0063	−	10.0745i	0.793402	−	0.665743i	0.946585	+	0.322455i	$0.104508\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.29551	+	12.6362i	0.477945	+	0.827824i	0.999680	−	0.0252828i	$-0.00804864\pi$
$233$	7.29551	+	12.6362i	0.477945	+	0.827824i	−0.521736	+	0.853107i	$0.674715\pi$
$234$		0			0
$235$	−0.163190	+	0.282653i	−0.0106453	+	0.0184383i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.53189	−	8.68779i	−0.0990899	−	0.561967i	−0.993417	−	0.114553i	$-0.963456\pi$
$239$	−1.53189	−	8.68779i	−0.0990899	−	0.561967i	0.894327	−	0.447413i	$-0.147655\pi$
$240$		0			0
$241$	−10.4015	−	8.72790i	−0.670020	−	0.562213i	0.243052	−	0.970013i	$-0.421852\pi$
$241$	−10.4015	−	8.72790i	−0.670020	−	0.562213i	−0.913071	+	0.407800i	$0.866296\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.51306	+	7.14331i	0.543880	+	0.456369i
$246$		0			0
$247$	0.164048	+	0.930362i	0.0104381	+	0.0591975i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.80404	+	10.0529i	−0.366348	+	0.634533i	−0.988992	−	0.147972i	$-0.952725\pi$
$251$	−5.80404	+	10.0529i	−0.366348	+	0.634533i	0.622643	+	0.782506i	$0.286059\pi$
$252$		0			0
$253$	4.35884	+	7.54973i	0.274038	+	0.474647i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.63129	+	5.56431i	−0.413648	+	0.347092i	−0.825741	−	0.564050i	$-0.809243\pi$
$257$	−6.63129	+	5.56431i	−0.413648	+	0.347092i	0.412092	+	0.911142i	$0.364798\pi$
$258$		0			0
$259$	−7.86779	+	2.86364i	−0.488881	+	0.177938i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.51513	+	14.2640i	−0.155089	+	0.879556i	0.803614	+	0.595150i	$0.202907\pi$
$263$	−2.51513	+	14.2640i	−0.155089	+	0.879556i	−0.958704	+	0.284406i	$0.908204\pi$
$264$		0			0
$265$	−40.4526	−	14.7236i	−2.48499	−	0.904461i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.3063			0.872273			0.436137	−	0.899880i	$-0.356346\pi$
$269$	14.3063			0.872273			0.436137	+	0.899880i	$0.356346\pi$
$270$		0			0
$271$	9.43403			0.573077			0.286538	−	0.958069i	$-0.407495\pi$
$271$	9.43403			0.573077			0.286538	+	0.958069i	$0.407495\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.0220	+	4.37566i	0.724955	+	0.263862i
$276$		0			0
$277$	0.264170	−	1.49819i	0.0158725	−	0.0900172i	−0.975842	−	0.218475i	$-0.929892\pi$
$277$	0.264170	−	1.49819i	0.0158725	−	0.0900172i	0.991715	+	0.128458i	$0.0410028\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	24.0779	−	8.76362i	1.43636	−	0.522794i	0.497616	−	0.867397i	$-0.334209\pi$
$281$	24.0779	−	8.76362i	1.43636	−	0.522794i	0.938748	+	0.344604i	$0.111987\pi$
$282$		0			0
$283$	4.84455	−	4.06506i	0.287978	−	0.241643i	−0.487341	−	0.873212i	$-0.662033\pi$
$283$	4.84455	−	4.06506i	0.287978	−	0.241643i	0.775320	+	0.631569i	$0.217589\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.23990	+	2.14757i	0.0731892	+	0.126767i
$288$		0			0
$289$	2.73953	−	4.74500i	0.161149	−	0.279118i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.84078	−	21.7822i	−0.224381	−	1.27253i	−0.863865	−	0.503723i	$-0.831963\pi$
$293$	−3.84078	−	21.7822i	−0.224381	−	1.27253i	0.639484	−	0.768804i	$-0.279148\pi$
$294$		0			0
$295$	−6.27036	−	5.26146i	−0.365074	−	0.306334i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	19.3878	+	16.2683i	1.12123	+	0.940822i
$300$		0			0
$301$	2.41016	+	13.6687i	0.138919	+	0.787851i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.69849	−	16.7983i	0.555334	−	0.961866i
$306$		0			0
$307$	3.48009	+	6.02769i	0.198619	+	0.344019i	0.948081	−	0.318029i	$-0.103021\pi$
$307$	3.48009	+	6.02769i	0.198619	+	0.344019i	−0.749462	+	0.662048i	$0.769688\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.33377	+	6.15376i	−0.415860	+	0.348948i	−0.826586	−	0.562811i	$-0.809720\pi$
$311$	−7.33377	+	6.15376i	−0.415860	+	0.348948i	0.410726	+	0.911759i	$0.365275\pi$
$312$		0			0
$313$	−11.5061	+	4.18788i	−0.650363	+	0.236713i	−0.646070	−	0.763278i	$-0.723589\pi$
$313$	−11.5061	+	4.18788i	−0.650363	+	0.236713i	−0.00429307	+	0.999991i	$0.501367\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.89608	−	10.7532i	0.106494	−	0.603960i	−0.884118	−	0.467263i	$-0.845240\pi$
$317$	1.89608	−	10.7532i	0.106494	−	0.603960i	0.990613	−	0.136697i	$-0.0436487\pi$
$318$		0			0
$319$	−15.8016	−	5.75133i	−0.884722	−	0.322012i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.544753			0.0303109
$324$		0			0
$325$	37.1421			2.06027
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.175315	−	0.0638093i	−0.00966541	−	0.00351792i
$330$		0			0
$331$	3.64802	−	20.6890i	0.200514	−	1.13717i	−0.703832	−	0.710367i	$-0.748529\pi$
$331$	3.64802	−	20.6890i	0.200514	−	1.13717i	0.904345	−	0.426802i	$-0.140360\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.1043	+	4.76957i	−0.715963	+	0.260589i
$336$		0			0
$337$	−5.21291	+	4.37415i	−0.283965	+	0.238275i	−0.773633	−	0.633634i	$-0.781563\pi$
$337$	−5.21291	+	4.37415i	−0.283965	+	0.238275i	0.489668	+	0.871909i	$0.337118\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	10.6919	+	18.5190i	0.579001	+	1.00286i
$342$		0			0
$343$	−9.90453	+	17.1552i	−0.534794	+	0.926291i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.818830	−	4.64382i	−0.0439571	−	0.249293i	0.954909	−	0.296898i	$-0.0959522\pi$
$347$	−0.818830	−	4.64382i	−0.0439571	−	0.249293i	−0.998866	+	0.0476051i	$0.984841\pi$
$348$		0			0
$349$	−6.74711	−	5.66150i	−0.361165	−	0.303053i	0.444090	−	0.895982i	$-0.353527\pi$
$349$	−6.74711	−	5.66150i	−0.361165	−	0.303053i	−0.805255	+	0.592929i	$0.797971\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.4124	−	11.2544i	−0.713871	−	0.599009i	0.211811	−	0.977311i	$-0.432064\pi$
$353$	−13.4124	−	11.2544i	−0.713871	−	0.599009i	−0.925682	+	0.378302i	$0.876508\pi$
$354$		0			0
$355$	3.62004	+	20.5302i	0.192132	+	1.08963i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.44318	+	16.3561i	−0.498392	+	0.863240i	−0.999998	−	0.00185580i	$-0.999409\pi$
$359$	−9.44318	+	16.3561i	−0.498392	+	0.863240i	0.501606	+	0.865096i	$0.332743\pi$
$360$		0			0
$361$	9.48712	+	16.4322i	0.499322	+	0.864851i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.9645	−	9.20034i	0.573910	−	0.481568i
$366$		0			0
$367$	12.8981	−	4.69454i	0.673278	−	0.245053i	0.0173193	−	0.999850i	$-0.494487\pi$
$367$	12.8981	−	4.69454i	0.673278	−	0.245053i	0.655959	+	0.754797i	$0.272265\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.27307	−	24.2338i	0.221847	−	1.25816i
$372$		0			0
$373$	34.5677	+	12.5816i	1.78985	+	0.651451i	0.999234	+	0.0391369i	$0.0124608\pi$
$373$	34.5677	+	12.5816i	1.78985	+	0.651451i	0.790614	+	0.612315i	$0.209761\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−48.8192			−2.51432
$378$		0			0
$379$	−28.9790			−1.48855			−0.744276	−	0.667872i	$-0.767205\pi$
$379$	−28.9790			−1.48855			−0.744276	+	0.667872i	$0.767205\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.13070	+	2.59536i	0.364362	+	0.132617i	0.517712	−	0.855555i	$-0.326784\pi$
$383$	7.13070	+	2.59536i	0.364362	+	0.132617i	−0.153350	+	0.988172i	$0.549006\pi$
$384$		0			0
$385$	−2.27618	+	12.9089i	−0.116005	+	0.657897i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−5.53093	+	2.01310i	−0.280429	+	0.102068i	−0.478406	−	0.878139i	$-0.658785\pi$
$389$	−5.53093	+	2.01310i	−0.280429	+	0.102068i	0.197976	+	0.980207i	$0.436563\pi$
$390$		0			0
$391$	11.1797	−	9.38085i	0.565380	−	0.474410i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.02126	−	8.69708i	−0.252647	−	0.437597i
$396$		0			0
$397$	9.47451	−	16.4103i	0.475512	−	0.823611i	−0.524094	−	0.851660i	$-0.675596\pi$
$397$	9.47451	−	16.4103i	0.475512	−	0.823611i	0.999607	+	0.0280490i	$0.00892943\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.68567	+	20.9025i	0.184054	+	1.04382i	0.927165	+	0.374653i	$0.122238\pi$
$401$	3.68567	+	20.9025i	0.184054	+	1.04382i	−0.743112	+	0.669167i	$0.766651\pi$
$402$		0			0
$403$	47.5571	+	39.9051i	2.36899	+	1.98782i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.76477	+	5.67632i	0.335317	+	0.281365i
$408$		0			0
$409$	−2.22439	−	12.6152i	−0.109989	−	0.623779i	−0.989110	−	0.147180i	$-0.952980\pi$
$409$	−2.22439	−	12.6152i	−0.109989	−	0.623779i	0.879121	−	0.476599i	$-0.158131\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.33947	−	4.05208i	0.115118	−	0.199390i
$414$		0			0
$415$	−16.0326	−	27.7694i	−0.787012	−	1.36314i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−20.9306	+	17.5629i	−1.02253	+	0.858003i	−0.989943	−	0.141466i	$-0.954818\pi$
$419$	−20.9306	+	17.5629i	−1.02253	+	0.858003i	−0.0325852	+	0.999469i	$0.510374\pi$
$420$		0			0
$421$	26.8121	−	9.75882i	1.30674	−	0.475616i	0.407556	−	0.913180i	$-0.366381\pi$
$421$	26.8121	−	9.75882i	1.30674	−	0.475616i	0.899187	+	0.437564i	$0.144159\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.71908	−	21.0920i	0.180402	−	1.02311i
$426$		0			0
$427$	10.4191	+	3.79223i	0.504214	+	0.183519i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−3.44020			−0.165709			−0.0828544	−	0.996562i	$-0.526404\pi$
$431$	−3.44020			−0.165709			−0.0828544	+	0.996562i	$0.526404\pi$
$432$		0			0
$433$	−1.84486			−0.0886584			−0.0443292	−	0.999017i	$-0.514115\pi$
$433$	−1.84486			−0.0886584			−0.0443292	+	0.999017i	$0.514115\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.648443	−	0.236014i	−0.0310193	−	0.0112901i
$438$		0			0
$439$	0.942527	−	5.34534i	0.0449844	−	0.255119i	−0.954019	−	0.299745i	$-0.903098\pi$
$439$	0.942527	−	5.34534i	0.0449844	−	0.255119i	0.999004	+	0.0446258i	$0.0142095\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−25.3266	+	9.21813i	−1.20330	+	0.437966i	−0.864376	−	0.502846i	$-0.832286\pi$
$443$	−25.3266	+	9.21813i	−1.20330	+	0.437966i	−0.338927	+	0.940813i	$0.610064\pi$
$444$		0			0
$445$	4.23259	−	3.55157i	0.200644	−	0.168360i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11.3097	−	19.5890i	−0.533737	−	0.924460i	−0.999223	−	0.0394051i	$-0.987454\pi$
$449$	−11.3097	−	19.5890i	−0.533737	−	0.924460i	0.465486	−	0.885055i	$-0.345880\pi$
$450$		0			0
$451$	1.30773	−	2.26506i	0.0615788	−	0.106658i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.60818	+	37.4769i	0.309796	+	1.75694i
$456$		0			0
$457$	−16.4290	−	13.7856i	−0.768517	−	0.644862i	0.171812	−	0.985130i	$-0.445038\pi$
$457$	−16.4290	−	13.7856i	−0.768517	−	0.644862i	−0.940329	+	0.340268i	$0.889482\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.54324	−	5.49043i	−0.304749	−	0.255715i	0.477569	−	0.878594i	$-0.341518\pi$
$461$	−6.54324	−	5.49043i	−0.304749	−	0.255715i	−0.782318	+	0.622880i	$0.785963\pi$
$462$		0			0
$463$	0.741810	+	4.20702i	0.0344748	+	0.195517i	0.997181	−	0.0750322i	$-0.0239060\pi$
$463$	0.741810	+	4.20702i	0.0344748	+	0.195517i	−0.962706	+	0.270549i	$0.912795\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.12319	+	7.14157i	−0.190798	+	0.330472i	−0.945515	−	0.325578i	$-0.894441\pi$
$467$	−4.12319	+	7.14157i	−0.190798	+	0.330472i	0.754717	+	0.656051i	$0.227774\pi$
$468$		0			0
$469$	−3.98571	−	6.90346i	−0.184043	−	0.318772i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	11.2140	−	9.40969i	0.515622	−	0.432658i
$474$		0			0
$475$	−0.951619	+	0.346361i	−0.0436633	+	0.0158921i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.86743	−	21.9333i	0.176708	−	1.00216i	−0.759447	−	0.650569i	$-0.774530\pi$
$479$	3.86743	−	21.9333i	0.176708	−	1.00216i	0.936154	−	0.351589i	$-0.114359\pi$
$480$		0			0
$481$	24.0913	+	8.76850i	1.09847	+	0.399809i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−9.38487			−0.426145
$486$		0			0
$487$	36.7759			1.66647			0.833237	−	0.552916i	$-0.186485\pi$
$487$	36.7759			1.66647			0.833237	+	0.552916i	$0.186485\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	27.1604	+	9.88558i	1.22573	+	0.446130i	0.872134	−	0.489268i	$-0.162736\pi$
$491$	27.1604	+	9.88558i	1.22573	+	0.446130i	0.353598	+	0.935398i	$0.384958\pi$
$492$		0			0
$493$	−4.88833	+	27.7231i	−0.220159	+	1.24859i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−11.1979	+	4.07571i	−0.502295	+	0.182821i
$498$		0			0
$499$	−10.7558	+	9.02523i	−0.481498	+	0.404025i	−0.850968	−	0.525218i	$-0.823984\pi$
$499$	−10.7558	+	9.02523i	−0.481498	+	0.404025i	0.369470	+	0.929243i	$0.379539\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.4453	−	18.0917i	−0.465731	−	0.806669i	0.533503	−	0.845798i	$-0.320875\pi$
$503$	−10.4453	−	18.0917i	−0.465731	−	0.806669i	−0.999234	+	0.0391285i	$0.987542\pi$
$504$		0			0
$505$	−14.6946	+	25.4518i	−0.653902	+	1.13259i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.18398	+	6.71466i	0.0524788	+	0.297622i	0.999739	−	0.0228431i	$-0.00727183\pi$
$509$	1.18398	+	6.71466i	0.0524788	+	0.297622i	−0.947260	+	0.320465i	$0.896161\pi$
$510$		0			0
$511$	6.26757	+	5.25911i	0.277261	+	0.232649i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	13.8746	+	11.6421i	0.611386	+	0.513014i
$516$		0			0
$517$	0.0341692	+	0.193783i	0.00150276	+	0.00852257i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.17259	−	5.49509i	0.138994	−	0.240744i	−0.788122	−	0.615519i	$-0.788947\pi$
$521$	3.17259	−	5.49509i	0.138994	−	0.240744i	0.927116	+	0.374774i	$0.122280\pi$
$522$		0			0
$523$	22.3401	+	38.6942i	0.976864	+	1.69198i	0.673641	+	0.739059i	$0.264730\pi$
$523$	22.3401	+	38.6942i	0.976864	+	1.69198i	0.303224	+	0.952919i	$0.401937\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	27.4230	−	23.0106i	1.19456	−	1.00236i
$528$		0			0
$529$	4.24104	−	1.54361i	0.184393	−	0.0671135i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.31854	−	7.47784i	0.0571125	−	0.323901i
$534$		0			0
$535$	46.7390	+	17.0116i	2.02070	+	0.735476i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.69997			0.288588
$540$		0			0
$541$	−11.3563			−0.488244			−0.244122	−	0.969745i	$-0.578500\pi$
$541$	−11.3563			−0.488244			−0.244122	+	0.969745i	$0.578500\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.48876	+	3.08965i	0.363618	+	0.132346i
$546$		0			0
$547$	0.0180989	−	0.102644i	0.000773855	−	0.00438875i	−0.984418	−	0.175842i	$-0.943735\pi$
$547$	0.0180989	−	0.102644i	0.000773855	−	0.00438875i	0.985192	+	0.171453i	$0.0548463\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.25080	−	0.455254i	0.0532858	−	0.0193945i
$552$		0			0
$553$	4.39750	−	3.68994i	0.187001	−	0.156912i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.7684	+	23.8476i	0.583385	+	1.01045i	0.995075	+	0.0991289i	$0.0316056\pi$
$557$	13.7684	+	23.8476i	0.583385	+	1.01045i	−0.411689	+	0.911324i	$0.635061\pi$
$558$		0			0
$559$	21.2497	−	36.8055i	0.898766	−	1.55671i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.564927	−	3.20386i	−0.0238088	−	0.135027i	0.970586	−	0.240753i	$-0.0773943\pi$
$563$	−0.564927	−	3.20386i	−0.0238088	−	0.135027i	−0.994395	+	0.105726i	$0.966283\pi$
$564$		0			0
$565$	34.3678	+	28.8380i	1.44586	+	1.21322i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	29.0436	+	24.3704i	1.21757	+	1.02166i	0.998948	+	0.0458523i	$0.0146004\pi$
$569$	29.0436	+	24.3704i	1.21757	+	1.02166i	0.218621	+	0.975810i	$0.429844\pi$
$570$		0			0
$571$	−5.10803	−	28.9691i	−0.213765	−	1.21232i	−0.883038	−	0.469302i	$-0.844505\pi$
$571$	−5.10803	−	28.9691i	−0.213765	−	1.21232i	0.669273	−	0.743017i	$-0.266606\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−13.5651	+	23.4954i	−0.565703	+	0.979826i
$576$		0			0
$577$	13.3737	+	23.1640i	0.556755	+	0.964329i	0.997765	+	0.0668261i	$0.0212873\pi$
$577$	13.3737	+	23.1640i	0.556755	+	0.964329i	−0.441009	+	0.897503i	$0.645379\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	14.0410	−	11.7818i	0.582519	−	0.488791i
$582$		0			0
$583$	−24.3886	+	8.87674i	−1.01007	+	0.367637i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.25043	−	46.7905i	0.340532	−	1.93125i	−0.0231618	−	0.999732i	$-0.507373\pi$
$587$	8.25043	−	46.7905i	0.340532	−	1.93125i	0.363693	−	0.931519i	$-0.381516\pi$
$588$		0			0
$589$	−1.59059	−	0.578927i	−0.0655390	−	0.0238543i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.40677			−0.386290			−0.193145	−	0.981170i	$-0.561869\pi$
$593$	−9.40677			−0.386290			−0.193145	+	0.981170i	$0.561869\pi$
$594$		0			0
$595$	21.9438			0.899607
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.33263	−	1.21298i	−0.136168	−	0.0495610i	0.273037	−	0.962003i	$-0.411972\pi$
$599$	−3.33263	−	1.21298i	−0.136168	−	0.0495610i	−0.409205	+	0.912442i	$0.634194\pi$
$600$		0			0
$601$	−7.39590	+	41.9442i	−0.301685	+	1.71094i	0.337027	+	0.941495i	$0.390579\pi$
$601$	−7.39590	+	41.9442i	−0.301685	+	1.71094i	−0.638712	+	0.769446i	$0.720532\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−21.7709	+	7.92395i	−0.885111	+	0.322154i
$606$		0			0
$607$	−8.32057	+	6.98179i	−0.337722	+	0.283382i	−0.795837	−	0.605510i	$-0.792969\pi$
$607$	−8.32057	+	6.98179i	−0.337722	+	0.283382i	0.458116	+	0.888893i	$0.348525\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.285633	+	0.494732i	0.0115555	+	0.0200147i
$612$		0			0
$613$	−12.6149	+	21.8496i	−0.509510	+	0.882497i	0.490429	+	0.871481i	$0.336840\pi$
$613$	−12.6149	+	21.8496i	−0.509510	+	0.882497i	−0.999939	+	0.0110162i	$0.996493\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.49515	+	8.47940i	0.0601923	+	0.341368i	1.00000		0.000336372i	$-0.000107071\pi$
$617$	1.49515	+	8.47940i	0.0601923	+	0.341368i	−0.939808	+	0.341704i	$0.888996\pi$
$618$		0			0
$619$	−27.6743	−	23.2215i	−1.11233	−	0.933352i	−0.114134	−	0.993465i	$-0.536409\pi$
$619$	−27.6743	−	23.2215i	−1.11233	−	0.933352i	−0.998192	+	0.0601136i	$0.980854\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.41944	+	2.03015i	0.0969329	+	0.0813364i
$624$		0			0
$625$	−2.90596	−	16.4805i	−0.116238	−	0.659221i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	7.39168	−	12.8028i	0.294726	−	0.510480i
$630$		0			0
$631$	−0.0668013	−	0.115703i	−0.00265932	−	0.00460607i	0.864693	−	0.502301i	$-0.167513\pi$
$631$	−0.0668013	−	0.115703i	−0.00265932	−	0.00460607i	−0.867352	+	0.497695i	$0.834180\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−24.7683	+	20.7831i	−0.982900	+	0.824751i
$636$		0			0
$637$	18.2782	−	6.65272i	0.724208	−	0.263590i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.66784	−	9.45878i	0.0658756	−	0.373599i	−0.933991	−	0.357295i	$-0.883699\pi$
$641$	1.66784	−	9.45878i	0.0658756	−	0.373599i	0.999867	−	0.0163039i	$-0.00518994\pi$
$642$		0			0
$643$	−11.8425	−	4.31030i	−0.467021	−	0.169982i	0.0977815	−	0.995208i	$-0.468825\pi$
$643$	−11.8425	−	4.31030i	−0.467021	−	0.169982i	−0.564802	+	0.825226i	$0.691048\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.0753			0.828556			0.414278	−	0.910150i	$-0.364034\pi$
$647$	21.0753			0.828556			0.414278	+	0.910150i	$0.364034\pi$
$648$		0			0
$649$	−4.93491			−0.193712
$650$		0			0
$651$		0			0
$652$		0			0
$653$	29.2602	+	10.6499i	1.14504	+	0.416761i	0.843732	−	0.536765i	$-0.180354\pi$
$653$	29.2602	+	10.6499i	1.14504	+	0.416761i	0.301310	+	0.953526i	$0.402576\pi$
$654$		0			0
$655$	10.6275	−	60.2717i	0.415252	−	2.35501i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	31.5911	−	11.4982i	1.23062	−	0.447907i	0.356807	−	0.934178i	$-0.383865\pi$
$659$	31.5911	−	11.4982i	1.23062	−	0.447907i	0.873808	+	0.486271i	$0.161643\pi$
$660$		0			0
$661$	−28.1828	+	23.6482i	−1.09618	+	0.919808i	−0.997163	−	0.0752777i	$-0.976016\pi$
$661$	−28.1828	+	23.6482i	−1.09618	+	0.919808i	−0.0990214	+	0.995085i	$0.531571\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.518791	−	0.898573i	−0.0201179	−	0.0348452i
$666$		0			0
$667$	17.8298	−	30.8822i	0.690373	−	1.19576i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.03070	−	11.5167i	−0.0783942	−	0.444595i
$672$		0			0
$673$	−4.95789	−	4.16016i	−0.191113	−	0.160363i	0.542211	−	0.840242i	$-0.317587\pi$
$673$	−4.95789	−	4.16016i	−0.191113	−	0.160363i	−0.733323	+	0.679880i	$0.762032\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	29.3272	+	24.6084i	1.12713	+	0.945778i	0.998943	−	0.0459715i	$-0.0146383\pi$
$677$	29.3272	+	24.6084i	1.12713	+	0.945778i	0.128192	+	0.991749i	$0.459083\pi$
$678$		0			0
$679$	−0.931552	−	5.28310i	−0.0357497	−	0.202747i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−13.7010	+	23.7309i	−0.524255	+	0.908037i	0.475346	+	0.879799i	$0.342323\pi$
$683$	−13.7010	+	23.7309i	−0.524255	+	0.908037i	−0.999601	+	0.0282377i	$0.991010\pi$
$684$		0			0
$685$	−7.88943	−	13.6649i	−0.301440	−	0.522109i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−57.7206	+	48.4333i	−2.19898	+	1.84516i
$690$		0			0
$691$	18.9376	−	6.89272i	0.720420	−	0.262211i	0.0443157	−	0.999018i	$-0.485889\pi$
$691$	18.9376	−	6.89272i	0.720420	−	0.262211i	0.676104	+	0.736806i	$0.263667\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.63980	−	37.6562i	0.251862	−	1.42838i
$696$		0			0
$697$	−4.11443	−	1.49753i	−0.155845	−	0.0567230i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	25.8155			0.975036			0.487518	−	0.873113i	$-0.337902\pi$
$701$	25.8155			0.975036			0.487518	+	0.873113i	$0.337902\pi$
$702$		0			0
$703$	−0.699012			−0.0263637
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.7864	−	5.74577i	−0.593708	−	0.216092i
$708$		0			0
$709$	5.43652	−	30.8321i	0.204173	−	1.15792i	−0.694563	−	0.719432i	$-0.744402\pi$
$709$	5.43652	−	30.8321i	0.204173	−	1.15792i	0.898736	−	0.438490i	$-0.144487\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−42.6121	+	15.5095i	−1.59584	+	0.580837i
$714$		0			0
$715$	30.7467	−	25.7995i	1.14986	−	0.964847i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.9508	−	32.8237i	−0.706744	−	1.22412i	−0.966058	−	0.258324i	$-0.916830\pi$
$719$	−18.9508	−	32.8237i	−0.706744	−	1.22412i	0.259314	−	0.965793i	$-0.416504\pi$
$720$		0			0
$721$	−5.17659	+	8.96613i	−0.192786	+	0.333916i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.08737	−	51.5370i	−0.337496	−	1.91404i
$726$		0			0
$727$	2.41552	+	2.02686i	0.0895866	+	0.0751721i	0.686481	−	0.727148i	$-0.259154\pi$
$727$	2.41552	+	2.02686i	0.0895866	+	0.0751721i	−0.596894	+	0.802320i	$0.703599\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−18.7731	−	15.7525i	−0.694348	−	0.582627i
$732$		0			0
$733$	6.98769	+	39.6291i	0.258096	+	1.46374i	0.787999	+	0.615677i	$0.211117\pi$
$733$	6.98769	+	39.6291i	0.258096	+	1.46374i	−0.529903	+	0.848059i	$0.677772\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.20376	+	7.28113i	−0.154848	+	0.268204i
$738$		0			0
$739$	−5.71378	−	9.89656i	−0.210185	−	0.364051i	0.741587	−	0.670856i	$-0.234073\pi$
$739$	−5.71378	−	9.89656i	−0.210185	−	0.364051i	−0.951772	+	0.306805i	$0.900740\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.7753	−	16.5934i	0.725485	−	0.608754i	−0.203412	−	0.979093i	$-0.565203\pi$
$743$	19.7753	−	16.5934i	0.725485	−	0.608754i	0.928897	+	0.370339i	$0.120759\pi$
$744$		0			0
$745$	−24.1735	+	8.79843i	−0.885648	+	0.322349i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−4.93711	+	27.9997i	−0.180398	+	1.02309i
$750$		0			0
$751$	−31.5126	−	11.4697i	−1.14991	−	0.418534i	−0.304428	−	0.952535i	$-0.598465\pi$
$751$	−31.5126	−	11.4697i	−1.14991	−	0.418534i	−0.845483	+	0.534002i	$0.820688\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−40.6345			−1.47884
$756$		0			0
$757$	−8.62121			−0.313343			−0.156672	−	0.987651i	$-0.550076\pi$
$757$	−8.62121			−0.313343			−0.156672	+	0.987651i	$0.550076\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−35.5265	−	12.9306i	−1.28784	−	0.468734i	−0.394820	−	0.918759i	$-0.629193\pi$
$761$	−35.5265	−	12.9306i	−1.28784	−	0.468734i	−0.893016	+	0.450025i	$0.851415\pi$
$762$		0			0
$763$	−0.896680	+	5.08532i	−0.0324620	+	0.184101i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.4629	+	4.90011i	−0.486119	+	0.176933i
$768$		0			0
$769$	−22.0866	+	18.5329i	−0.796464	+	0.668312i	−0.947336	−	0.320241i	$-0.896236\pi$
$769$	−22.0866	+	18.5329i	−0.796464	+	0.668312i	0.150872	+	0.988553i	$0.451792\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.9144	+	32.7607i	0.680304	+	1.17832i	0.974888	+	0.222695i	$0.0714856\pi$
$773$	18.9144	+	32.7607i	0.680304	+	1.17832i	−0.294584	+	0.955626i	$0.595181\pi$
$774$		0			0
$775$	−33.2742	+	57.6326i	−1.19525	+	2.07023i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.0359505	+	0.203886i	0.00128806	+	0.00730496i
$780$		0			0
$781$	9.62803	+	8.07888i	0.344518	+	0.289085i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.58753	+	5.52759i	0.235119	+	0.197288i
$786$		0			0
$787$	5.87958	+	33.3448i	0.209585	+	1.18861i	0.890060	+	0.455843i	$0.150662\pi$
$787$	5.87958	+	33.3448i	0.209585	+	1.18861i	−0.680476	+	0.732771i	$0.738227\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.8226	+	22.2094i	−0.455919	+	0.789676i
$792$		0			0
$793$	−16.9754	−	29.4022i	−0.602814	−	1.04410i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	40.5217	−	34.0018i	1.43535	−	1.20440i	0.492892	−	0.870090i	$-0.335940\pi$
$797$	40.5217	−	34.0018i	1.43535	−	1.20440i	0.942462	−	0.334314i	$-0.108505\pi$
$798$		0			0
$799$	0.309545	−	0.112665i	0.0109509	−	0.00398581i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.49847	−	8.49823i	0.0528798	−	0.299896i
$804$		0			0
$805$	−26.1206	−	9.50713i	−0.920631	−	0.335082i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−10.9680			−0.385614			−0.192807	−	0.981237i	$-0.561759\pi$
$809$	−10.9680			−0.385614			−0.192807	+	0.981237i	$0.561759\pi$
$810$		0			0
$811$	6.54690			0.229893			0.114946	−	0.993372i	$-0.463330\pi$
$811$	6.54690			0.229893			0.114946	+	0.993372i	$0.463330\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−60.5359	−	22.0333i	−2.12048	−	0.771791i
$816$		0			0
$817$	−0.201217	+	1.14116i	−0.00703967	+	0.0399240i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−40.6377	+	14.7909i	−1.41827	+	0.516207i	−0.933545	−	0.358461i	$-0.883302\pi$
$821$	−40.6377	+	14.7909i	−1.41827	+	0.516207i	−0.484722	+	0.874668i	$0.661079\pi$
$822$		0			0
$823$	−0.333436	+	0.279786i	−0.0116228	+	0.00975272i	−0.648581	−	0.761146i	$-0.724637\pi$
$823$	−0.333436	+	0.279786i	−0.0116228	+	0.00975272i	0.636958	+	0.770899i	$0.280193\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	8.70278	+	15.0737i	0.302625	+	0.524162i	0.976730	−	0.214474i	$-0.0688036\pi$
$827$	8.70278	+	15.0737i	0.302625	+	0.524162i	−0.674105	+	0.738636i	$0.735470\pi$
$828$		0			0
$829$	12.7891	−	22.1513i	0.444183	−	0.769348i	−0.553812	−	0.832642i	$-0.686827\pi$
$829$	12.7891	−	22.1513i	0.444183	−	0.769348i	0.997995	+	0.0632941i	$0.0201606\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.94768	−	11.0458i	−0.0674830	−	0.382715i
$834$		0			0
$835$	−51.4308	−	43.1555i	−1.77983	−	1.49346i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	39.8502	+	33.4383i	1.37578	+	1.15442i	0.970743	+	0.240120i	$0.0771868\pi$
$839$	39.8502	+	33.4383i	1.37578	+	1.15442i	0.405040	+	0.914299i	$0.367258\pi$
$840$		0			0
$841$	6.90856	+	39.1804i	0.238226	+	1.35105i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	36.4028	−	63.0515i	1.25230	−	2.16904i
$846$		0			0
$847$	−6.62169	−	11.4691i	−0.227524	−	0.394083i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−14.3454	+	12.0372i	−0.491755	+	0.412632i
$852$		0			0
$853$	26.5903	−	9.67809i	0.910436	−	0.331371i	0.156009	−	0.987756i	$-0.450137\pi$
$853$	26.5903	−	9.67809i	0.910436	−	0.331371i	0.754427	+	0.656384i	$0.227915\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.02508	+	34.1699i	−0.205813	+	1.16722i	0.690343	+	0.723482i	$0.257460\pi$
$857$	−6.02508	+	34.1699i	−0.205813	+	1.16722i	−0.896156	+	0.443740i	$0.853651\pi$
$858$		0			0
$859$	−29.8538	−	10.8659i	−1.01860	−	0.370739i	−0.221869	−	0.975076i	$-0.571216\pi$
$859$	−29.8538	−	10.8659i	−1.01860	−	0.370739i	−0.796729	+	0.604337i	$0.793438\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	31.0932			1.05843			0.529213	−	0.848489i	$-0.322487\pi$
$863$	31.0932			1.05843			0.529213	+	0.848489i	$0.322487\pi$
$864$		0			0
$865$	−41.0158			−1.39458
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.68944	−	2.07079i	−0.193001	−	0.0702466i
$870$		0			0
$871$	−4.23851	+	24.0378i	−0.143616	+	0.814489i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.95769	+	2.89636i	−0.269019	+	0.0979149i
$876$		0			0
$877$	40.8824	−	34.3044i	1.38050	−	1.15838i	0.411472	−	0.911422i	$-0.365015\pi$
$877$	40.8824	−	34.3044i	1.38050	−	1.15838i	0.969027	−	0.246954i	$-0.0794297\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.55673	+	11.3566i	0.220902	+	0.382613i	0.955082	−	0.296341i	$-0.0957666\pi$
$881$	6.55673	+	11.3566i	0.220902	+	0.382613i	−0.734180	+	0.678955i	$0.762433\pi$
$882$		0			0
$883$	21.0350	−	36.4337i	0.707885	−	1.22609i	−0.257756	−	0.966210i	$-0.582983\pi$
$883$	21.0350	−	36.4337i	0.707885	−	1.22609i	0.965640	−	0.259882i	$-0.0836837\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.1446	+	57.5330i	0.340623	+	1.93177i	0.362441	+	0.932007i	$0.381943\pi$
$887$	10.1446	+	57.5330i	0.340623	+	1.93177i	−0.0218184	+	0.999762i	$0.506946\pi$
$888$		0			0
$889$	−14.1581	−	11.8801i	−0.474848	−	0.398444i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.0119317	−	0.0100119i	−0.000399280	−	0.000335036i
$894$		0			0
$895$	−12.6629	−	71.8148i	−0.423274	−	2.40051i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	43.7354	−	75.7519i	1.45866	−	2.52647i
$900$		0			0
$901$	21.7243	+	37.6276i	0.723742	+	1.25356i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	15.4444	−	12.9594i	0.513389	−	0.430785i
$906$		0			0
$907$	−45.8380	+	16.6837i	−1.52203	+	0.553973i	−0.961654	−	0.274267i	$-0.911565\pi$
$907$	−45.8380	+	16.6837i	−1.52203	+	0.553973i	−0.560374	+	0.828240i	$0.689342\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.20196	+	23.8305i	−0.139217	+	0.789540i	0.832612	+	0.553856i	$0.186844\pi$
$911$	−4.20196	+	23.8305i	−0.139217	+	0.789540i	−0.971830	+	0.235684i	$0.924267\pi$
$912$		0			0
$913$	−18.1661	−	6.61192i	−0.601210	−	0.218823i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	34.9841			1.15528
$918$		0			0
$919$	−42.7812			−1.41122			−0.705610	−	0.708600i	$-0.749327\pi$
$919$	−42.7812			−1.41122			−0.705610	+	0.708600i	$0.749327\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	34.2882	+	12.4799i	1.12861	+	0.410780i
$924$		0			0
$925$	−4.77222	+	27.0646i	−0.156910	+	0.889880i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.86505	−	1.04279i	0.0939993	−	0.0342129i	−0.294592	−	0.955623i	$-0.595184\pi$
$929$	2.86505	−	1.04279i	0.0939993	−	0.0342129i	0.388592	+	0.921410i	$0.372962\pi$
$930$		0			0
$931$	−0.406268	+	0.340899i	−0.0133149	+	0.0111725i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−11.5721	−	20.0435i	−0.378449	−	0.655493i
$936$		0			0
$937$	−16.1594	+	27.9888i	−0.527903	+	0.914355i	0.471568	+	0.881830i	$0.343688\pi$
$937$	−16.1594	+	27.9888i	−0.527903	+	0.914355i	−0.999471	+	0.0325254i	$0.989645\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−2.74938	−	15.5925i	−0.0896273	−	0.508302i	−0.996262	−	0.0863849i	$-0.972469\pi$
$941$	−2.74938	−	15.5925i	−0.0896273	−	0.508302i	0.906635	−	0.421917i	$-0.138643\pi$
$942$		0			0
$943$	4.24878	+	3.56515i	0.138359	+	0.116097i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.6573	−	12.2990i	−0.476299	−	0.399662i	0.372787	−	0.927917i	$-0.378402\pi$
$947$	−14.6573	−	12.2990i	−0.476299	−	0.399662i	−0.849086	+	0.528255i	$0.822847\pi$
$948$		0			0
$949$	−4.35033	−	24.6719i	−0.141218	−	0.800885i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−14.7660	+	25.5755i	−0.478319	+	0.828472i	−0.999691	−	0.0248569i	$-0.992087\pi$
$953$	−14.7660	+	25.5755i	−0.478319	+	0.828472i	0.521372	+	0.853329i	$0.325420\pi$
$954$		0			0
$955$	−32.2018	−	55.7752i	−1.04203	−	1.80484i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.90937	−	5.79765i	0.223115	−	0.187216i
$960$		0			0
$961$	−75.3941	+	27.4412i	−2.43207	+	0.885201i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.263030	−	1.49172i	0.00846724	−	0.0480201i
$966$		0			0
$967$	−38.6905	−	14.0822i	−1.24420	−	0.452852i	−0.365763	−	0.930708i	$-0.619192\pi$
$967$	−38.6905	−	14.0822i	−1.24420	−	0.452852i	−0.878438	+	0.477856i	$0.841414\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	36.8784			1.18348			0.591742	−	0.806128i	$-0.298440\pi$
$971$	36.8784			1.18348			0.591742	+	0.806128i	$0.298440\pi$
$972$		0			0
$973$	21.8572			0.700708
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.76455	+	1.73415i	0.152432	+	0.0554805i	0.417109	−	0.908856i	$-0.363043\pi$
$977$	4.76455	+	1.73415i	0.152432	+	0.0554805i	−0.264678	+	0.964337i	$0.585266\pi$
$978$		0			0
$979$	0.578447	−	3.28054i	0.0184873	−	0.104846i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.0031	−	8.00849i	0.701791	−	0.255431i	0.0336157	−	0.999435i	$-0.489298\pi$
$983$	22.0031	−	8.00849i	0.701791	−	0.255431i	0.668175	+	0.744004i	$0.267076\pi$
$984$		0			0
$985$	9.25040	−	7.76201i	0.294742	−	0.247318i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	15.5217	+	26.8843i	0.493561	+	0.854872i
$990$		0			0
$991$	5.92671	−	10.2654i	0.188268	−	0.326090i	−0.756405	−	0.654104i	$-0.773046\pi$
$991$	5.92671	−	10.2654i	0.188268	−	0.326090i	0.944673	+	0.328014i	$0.106379\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.24909	−	24.0978i	−0.134705	−	0.763951i
$996$		0			0
$997$	31.2868	+	26.2527i	0.990862	+	0.831432i	0.985692	−	0.168555i	$-0.0539100\pi$
$997$	31.2868	+	26.2527i	0.990862	+	0.831432i	0.00516968	+	0.999987i	$0.498354\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.i.b.865.3		18
3.2	odd	2		972.2.i.c.865.1		18
9.2	odd	6		972.2.i.a.217.3		18
9.4	even	3		324.2.i.a.181.1		18
9.5	odd	6		108.2.i.a.61.3	✓	18
9.7	even	3		972.2.i.d.217.1		18
27.2	odd	18		2916.2.e.c.973.2		18
27.4	even	9		972.2.i.d.757.1		18
27.5	odd	18		972.2.i.c.109.1		18
27.7	even	9		2916.2.a.c.1.2		9
27.11	odd	18		2916.2.e.c.1945.2		18
27.13	even	9		324.2.i.a.145.1		18
27.14	odd	18		108.2.i.a.85.3	yes	18
27.16	even	9		2916.2.e.d.1945.8		18
27.20	odd	18		2916.2.a.d.1.8		9
27.22	even	9	inner	972.2.i.b.109.3		18
27.23	odd	18		972.2.i.a.757.3		18
27.25	even	9		2916.2.e.d.973.8		18
36.23	even	6		432.2.u.d.385.1		18
108.95	even	18		432.2.u.d.193.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.61.3	✓	18	9.5	odd	6
108.2.i.a.85.3	yes	18	27.14	odd	18
324.2.i.a.145.1		18	27.13	even	9
324.2.i.a.181.1		18	9.4	even	3
432.2.u.d.193.1		18	108.95	even	18
432.2.u.d.385.1		18	36.23	even	6
972.2.i.a.217.3		18	9.2	odd	6
972.2.i.a.757.3		18	27.23	odd	18
972.2.i.b.109.3		18	27.22	even	9	inner
972.2.i.b.865.3		18	1.1	even	1	trivial
972.2.i.c.109.1		18	27.5	odd	18
972.2.i.c.865.1		18	3.2	odd	2
972.2.i.d.217.1		18	9.7	even	3
972.2.i.d.757.1		18	27.4	even	9
2916.2.a.c.1.2		9	27.7	even	9
2916.2.a.d.1.8		9	27.20	odd	18
2916.2.e.c.973.2		18	27.2	odd	18
2916.2.e.c.1945.2		18	27.11	odd	18
2916.2.e.d.973.8		18	27.25	even	9
2916.2.e.d.1945.8		18	27.16	even	9

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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.i (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.16020 + 1.15022i) q^{5} +(-0.333817 + 1.89317i) q^{7} +O(q^{10})\)	\(q+(3.16020 + 1.15022i) q^{5} +(-0.333817 + 1.89317i) q^{7} +(1.90527 - 0.693460i) q^{11} +(4.50919 - 3.78366i) q^{13} +(-1.69713 - 2.93951i) q^{17} +(-0.0802464 + 0.138991i) q^{19} +(0.746622 + 4.23431i) q^{23} +(4.83365 + 4.05592i) q^{25} +(-6.35331 - 5.33106i) q^{29} +(1.83141 + 10.3865i) q^{31} +(-3.23249 + 5.59884i) q^{35} +(2.17770 + 3.77190i) q^{37} +(0.988175 - 0.829177i) q^{41} +(6.78459 - 2.46939i) q^{43} +(-0.0168525 + 0.0955753i) q^{47} +(3.10519 + 1.13020i) q^{49} -12.8006 q^{53} +6.81866 q^{55} +(-2.28715 - 0.832456i) q^{59} +(1.00156 - 5.68010i) q^{61} +(18.6020 - 6.77058i) q^{65} +(-3.17652 + 2.66542i) q^{67} +(3.09944 + 5.36839i) q^{71} +(2.12803 - 3.68585i) q^{73} +(0.676828 + 3.83848i) q^{77} +(-2.28753 - 1.91947i) q^{79} +(-7.30399 - 6.12877i) q^{83} +(-1.98218 - 11.2415i) q^{85} +(0.821473 - 1.42283i) q^{89} +(5.65787 + 9.79971i) q^{91} +(-0.413465 + 0.346938i) q^{95} +(-2.62231 + 0.954445i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{5}+O(q^{10}) \) 18 * q - 3 * q^5	\( 18 q - 3 q^{5} + 15 q^{11} + 12 q^{17} - 33 q^{23} + 9 q^{25} - 21 q^{29} + 9 q^{31} + 21 q^{35} + 33 q^{41} + 18 q^{43} - 9 q^{47} + 36 q^{49} - 66 q^{53} + 12 q^{59} + 36 q^{61} + 66 q^{65} + 27 q^{67} + 12 q^{71} + 9 q^{73} - 33 q^{77} + 18 q^{79} - 81 q^{83} + 18 q^{85} + 48 q^{89} + 9 q^{91} + 84 q^{95}+O(q^{100}) \) 18 * q - 3 * q^5 + 15 * q^11 + 12 * q^17 - 33 * q^23 + 9 * q^25 - 21 * q^29 + 9 * q^31 + 21 * q^35 + 33 * q^41 + 18 * q^43 - 9 * q^47 + 36 * q^49 - 66 * q^53 + 12 * q^59 + 36 * q^61 + 66 * q^65 + 27 * q^67 + 12 * q^71 + 9 * q^73 - 33 * q^77 + 18 * q^79 - 81 * q^83 + 18 * q^85 + 48 * q^89 + 9 * q^91 + 84 * q^95

Introduction

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