LMFDB - Embedded newform 1323.2.i.d.521.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.11
Character	$\chi$	$=$	1323.521
Dual form			1323.2.i.d.1097.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.122344i q^{2} +1.98503 q^{4} +(0.264715 - 0.458500i) q^{5} +0.487547i q^{8} +O(q^{10})$	\(q+0.122344i q^{2} +1.98503 q^{4} +(0.264715 - 0.458500i) q^{5} +0.487547i q^{8} +(0.0560949 + 0.0323864i) q^{10} +(-3.64120 + 2.10225i) q^{11} +(-1.74714 + 1.00871i) q^{13} +3.91042 q^{16} +(2.19381 - 3.79979i) q^{17} +(4.54391 - 2.62343i) q^{19} +(0.525467 - 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +(5.43444 + 3.13757i) q^{23} +(2.35985 + 4.08738i) q^{25} +(-0.123411 - 0.213753i) q^{26} +(7.27689 + 4.20131i) q^{29} +1.19170i q^{31} +1.45351i q^{32} +(0.464883 + 0.268400i) q^{34} +(1.61626 + 2.79945i) q^{37} +(0.320962 + 0.555922i) q^{38} +(0.223540 + 0.129061i) q^{40} +(0.0994958 + 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} +(-7.22789 + 4.17303i) q^{44} +(-0.383865 + 0.664873i) q^{46} +9.97189 q^{47} +(-0.500069 + 0.288715i) q^{50} +(-3.46814 + 2.00233i) q^{52} +(-3.65249 - 2.10877i) q^{53} +2.22598i q^{55} +(-0.514008 + 0.890287i) q^{58} -13.4392 q^{59} -13.1132i q^{61} -0.145798 q^{62} +7.64300 q^{64} +1.06809i q^{65} -6.58003 q^{67} +(4.35478 - 7.54270i) q^{68} -8.50587i q^{71} +(-4.86015 - 2.80601i) q^{73} +(-0.342497 + 0.197741i) q^{74} +(9.01980 - 5.20758i) q^{76} +0.572684 q^{79} +(1.03514 - 1.79292i) q^{80} +(-0.0210838 + 0.0121728i) q^{82} +(-5.42692 + 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +(0.839806 + 0.484862i) q^{86} +(-1.02494 - 1.77525i) q^{88} +(6.43688 + 11.1490i) q^{89} +(10.7875 + 6.22819i) q^{92} +1.22001i q^{94} -2.77784i q^{95} +(0.493773 + 0.285080i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$			0.122344i			0.0865106i	0.999064	+	0.0432553i	$0.0137729\pi$
$2$			0.122344i			0.0865106i	−0.999064	+	0.0432553i	$0.986227\pi$
$3$		0			0
$3$		0			0
$4$	1.98503			0.992516
$5$	0.264715	−	0.458500i	0.118384	−	0.205047i	−0.800743	−	0.599008i	$-0.795562\pi$
$5$	0.264715	−	0.458500i	0.118384	−	0.205047i	0.919127	+	0.393960i	$0.128895\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			0.487547i			0.172374i
$9$		0			0
$10$	0.0560949	+	0.0323864i	0.0177388	+	0.0102415i
$11$	−3.64120	+	2.10225i	−1.09786	+	0.633851i	−0.935659	−	0.352906i	$-0.885193\pi$
$11$	−3.64120	+	2.10225i	−1.09786	+	0.633851i	−0.162204	+	0.986757i	$0.551860\pi$
$12$		0			0
$13$	−1.74714	+	1.00871i	−0.484570	+	0.279767i	−0.722319	−	0.691560i	$-0.756924\pi$
$13$	−1.74714	+	1.00871i	−0.484570	+	0.279767i	0.237749	+	0.971327i	$0.423590\pi$
$14$		0			0
$15$		0			0
$16$	3.91042			0.977604
$17$	2.19381	−	3.79979i	0.532077	−	0.921584i	−0.467222	−	0.884140i	$-0.654745\pi$
$17$	2.19381	−	3.79979i	0.532077	−	0.921584i	0.999299	−	0.0374442i	$-0.0119216\pi$
$18$		0			0
$19$	4.54391	−	2.62343i	1.04244	−	0.601855i	0.121919	−	0.992540i	$-0.461095\pi$
$19$	4.54391	−	2.62343i	1.04244	−	0.601855i	0.920524	+	0.390685i	$0.127762\pi$
$20$	0.525467	−	0.910136i	0.117498	−	0.203513i
$21$		0			0
$22$	−0.257198	−	0.445480i	−0.0548348	−	0.0949767i
$23$	5.43444	+	3.13757i	1.13316	+	0.654230i	0.944727	−	0.327857i	$-0.106326\pi$
$23$	5.43444	+	3.13757i	1.13316	+	0.654230i	0.188431	+	0.982086i	$0.439660\pi$
$24$		0			0
$25$	2.35985	+	4.08738i	0.471970	+	0.817477i
$26$	−0.123411	−	0.213753i	−0.0242028	−	0.0419205i
$27$		0			0
$28$		0			0
$29$	7.27689	+	4.20131i	1.35128	+	0.780164i	0.988429	−	0.151681i	$-0.0484687\pi$
$29$	7.27689	+	4.20131i	1.35128	+	0.780164i	0.362855	+	0.931846i	$0.381802\pi$
$30$		0			0
$31$			1.19170i			0.214035i	0.994257	+	0.107018i	$0.0341301\pi$
$31$			1.19170i			0.214035i	−0.994257	+	0.107018i	$0.965870\pi$
$32$			1.45351i			0.256947i
$33$		0			0
$34$	0.464883	+	0.268400i	0.0797268	+	0.0460303i
$35$		0			0
$36$		0			0
$37$	1.61626	+	2.79945i	0.265712	+	0.460226i	0.967750	−	0.251913i	$-0.0810597\pi$
$37$	1.61626	+	2.79945i	0.265712	+	0.460226i	−0.702038	+	0.712139i	$0.747726\pi$
$38$	0.320962	+	0.555922i	0.0520668	+	0.0901824i
$39$		0			0
$40$	0.223540	+	0.129061i	0.0353448	+	0.0204063i
$41$	0.0994958	+	0.172332i	0.0155386	+	0.0269137i	0.873690	−	0.486483i	$-0.161720\pi$
$41$	0.0994958	+	0.172332i	0.0155386	+	0.0269137i	−0.858152	+	0.513396i	$0.828387\pi$
$42$		0			0
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	−0.387786	−	0.921750i	$-0.626760\pi$
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	0.992151	−	0.125042i	$-0.0399067\pi$
$44$	−7.22789	+	4.17303i	−1.08965	+	0.629107i
$45$		0			0
$46$	−0.383865	+	0.664873i	−0.0565978	+	0.0980302i
$47$	9.97189			1.45455			0.727275	−	0.686346i	$-0.240787\pi$
$47$	9.97189			1.45455			0.727275	+	0.686346i	$0.240787\pi$
$48$		0			0
$49$		0			0
$50$	−0.500069	+	0.288715i	−0.0707204	+	0.0408304i
$51$		0			0
$52$	−3.46814	+	2.00233i	−0.480944	+	0.277673i
$53$	−3.65249	−	2.10877i	−0.501708	−	0.289661i	0.227711	−	0.973729i	$-0.426876\pi$
$53$	−3.65249	−	2.10877i	−0.501708	−	0.289661i	−0.729419	+	0.684068i	$0.760209\pi$
$54$		0			0
$55$			2.22598i			0.300152i
$56$		0			0
$57$		0			0
$58$	−0.514008	+	0.890287i	−0.0674925	+	0.116900i
$59$	−13.4392			−1.74963			−0.874817	−	0.484454i	$-0.839018\pi$
$59$	−13.4392			−1.74963			−0.874817	+	0.484454i	$0.839018\pi$
$60$		0			0
$61$		−	13.1132i		−	1.67898i	−0.543377	−	0.839489i	$-0.682854\pi$
$61$		−	13.1132i		−	1.67898i	0.543377	−	0.839489i	$-0.317146\pi$
$62$	−0.145798			−0.0185163
$63$		0			0
$64$	7.64300			0.955375
$65$			1.06809i			0.132480i
$66$		0			0
$67$	−6.58003			−0.803878			−0.401939	−	0.915666i	$-0.631664\pi$
$67$	−6.58003			−0.803878			−0.401939	+	0.915666i	$0.631664\pi$
$68$	4.35478	−	7.54270i	0.528095	−	0.914687i
$69$		0			0
$70$		0			0
$71$		−	8.50587i		−	1.00946i	−0.863277	−	0.504730i	$-0.831592\pi$
$71$		−	8.50587i		−	1.00946i	0.863277	−	0.504730i	$-0.168408\pi$
$72$		0			0
$73$	−4.86015	−	2.80601i	−0.568838	−	0.328419i	0.187847	−	0.982198i	$-0.439849\pi$
$73$	−4.86015	−	2.80601i	−0.568838	−	0.328419i	−0.756685	+	0.653780i	$0.773182\pi$
$74$	−0.342497	+	0.197741i	−0.0398145	+	0.0229869i
$75$		0			0
$76$	9.01980	−	5.20758i	1.03464	−	0.597351i
$77$		0			0
$78$		0			0
$79$	0.572684			0.0644320			0.0322160	−	0.999481i	$-0.489744\pi$
$79$	0.572684			0.0644320			0.0322160	+	0.999481i	$0.489744\pi$
$80$	1.03514	−	1.79292i	0.115733	−	0.200455i
$81$		0			0
$82$	−0.0210838	+	0.0121728i	−0.00232832	+	0.00134426i
$83$	−5.42692	+	9.39971i	−0.595682	+	1.03175i	0.397768	+	0.917486i	$0.369785\pi$
$83$	−5.42692	+	9.39971i	−0.595682	+	1.03175i	−0.993450	+	0.114266i	$0.963548\pi$
$84$		0			0
$85$	−1.16147	−	2.01172i	−0.125979	−	0.218202i
$86$	0.839806	+	0.484862i	0.0905586	+	0.0522840i
$87$		0			0
$88$	−1.02494	−	1.77525i	−0.109259	−	0.189243i
$89$	6.43688	+	11.1490i	0.682307	+	1.18179i	0.974275	+	0.225363i	$0.0723568\pi$
$89$	6.43688	+	11.1490i	0.682307	+	1.18179i	−0.291968	+	0.956428i	$0.594310\pi$
$90$		0			0
$91$		0			0
$92$	10.7875	+	6.22819i	1.12468	+	0.649333i
$93$		0			0
$94$			1.22001i			0.125834i
$95$		−	2.77784i		−	0.285000i
$96$		0			0
$97$	0.493773	+	0.285080i	0.0501351	+	0.0289455i	0.524858	−	0.851190i	$-0.324118\pi$
$97$	0.493773	+	0.285080i	0.0501351	+	0.0289455i	−0.474723	+	0.880135i	$0.657452\pi$
$98$		0			0
$99$		0			0
$100$	4.68438	+	8.11359i	0.468438	+	0.811359i
$101$	5.81552	+	10.0728i	0.578666	+	1.00228i	0.995633	+	0.0933576i	$0.0297600\pi$
$101$	5.81552	+	10.0728i	0.578666	+	1.00228i	−0.416966	+	0.908922i	$0.636907\pi$
$102$		0			0
$103$	−5.54001	−	3.19853i	−0.545874	−	0.315160i	0.201582	−	0.979472i	$-0.435392\pi$
$103$	−5.54001	−	3.19853i	−0.545874	−	0.315160i	−0.747456	+	0.664311i	$0.768725\pi$
$104$	−0.491795	−	0.851814i	−0.0482245	−	0.0835272i
$105$		0			0
$106$	0.257996	−	0.446862i	0.0250588	−	0.0434031i
$107$	−0.219332	+	0.126632i	−0.0212037	+	0.0122419i	−0.510564	−	0.859840i	$-0.670563\pi$
$107$	−0.219332	+	0.126632i	−0.0212037	+	0.0122419i	0.489361	+	0.872081i	$0.337230\pi$
$108$		0			0
$109$	−5.98602	+	10.3681i	−0.573357	+	0.993084i	0.422861	+	0.906195i	$0.361026\pi$
$109$	−5.98602	+	10.3681i	−0.573357	+	0.993084i	−0.996218	+	0.0868891i	$0.972307\pi$
$110$	−0.272337			−0.0259663
$111$		0			0
$112$		0			0
$113$	−4.28636	+	2.47473i	−0.403227	+	0.232803i	−0.687875	−	0.725829i	$-0.741456\pi$
$113$	−4.28636	+	2.47473i	−0.403227	+	0.232803i	0.284648	+	0.958632i	$0.408123\pi$
$114$		0			0
$115$	2.87715	−	1.66113i	0.268296	−	0.154901i
$116$	14.4449	+	8.33974i	1.34117	+	0.774326i
$117$		0			0
$118$		−	1.64421i		−	0.151362i
$119$		0			0
$120$		0			0
$121$	3.33888	−	5.78311i	0.303535	−	0.525737i
$122$	1.60433			0.145249
$123$		0			0
$124$			2.36556i			0.212433i
$125$	5.14590			0.460263
$126$		0			0
$127$	−3.68446			−0.326943			−0.163472	−	0.986548i	$-0.552269\pi$
$127$	−3.68446			−0.326943			−0.163472	+	0.986548i	$0.552269\pi$
$128$			3.84210i			0.339597i
$129$		0			0
$130$	−0.130674			−0.0114609
$131$	2.72837	−	4.72567i	0.238379	−	0.412884i	−0.721871	−	0.692028i	$-0.756717\pi$
$131$	2.72837	−	4.72567i	0.238379	−	0.412884i	0.960249	+	0.279144i	$0.0900508\pi$
$132$		0			0
$133$		0			0
$134$		−	0.805030i		−	0.0695440i
$135$		0			0
$136$	1.85257	+	1.06958i	0.158857	+	0.0917161i
$137$	−1.39996	+	0.808270i	−0.119607	+	0.0690551i	−0.558610	−	0.829431i	$-0.688665\pi$
$137$	−1.39996	+	0.808270i	−0.119607	+	0.0690551i	0.439003	+	0.898486i	$0.355332\pi$
$138$		0			0
$139$	−9.79085	+	5.65275i	−0.830449	+	0.479460i	−0.854006	−	0.520262i	$-0.825834\pi$
$139$	−9.79085	+	5.65275i	−0.830449	+	0.479460i	0.0235572	+	0.999722i	$0.492501\pi$
$140$		0			0
$141$		0			0
$142$	1.04065			0.0873291
$143$	4.24113	−	7.34585i	0.354661	−	0.614291i
$144$		0			0
$145$	3.85260	−	2.22430i	0.319941	−	0.184718i
$146$	0.343300	−	0.594613i	0.0284117	−	0.0492105i
$147$		0			0
$148$	3.20833	+	5.55699i	0.263723	+	0.456782i
$149$	4.61426	+	2.66404i	0.378015	+	0.218247i	0.676954	−	0.736025i	$-0.263300\pi$
$149$	4.61426	+	2.66404i	0.378015	+	0.218247i	−0.298939	+	0.954272i	$0.596633\pi$
$150$		0			0
$151$	1.32132	+	2.28859i	0.107527	+	0.186243i	0.914768	−	0.403980i	$-0.132373\pi$
$151$	1.32132	+	2.28859i	0.107527	+	0.186243i	−0.807241	+	0.590222i	$0.799040\pi$
$152$	1.27904	+	2.21537i	0.103744	+	0.179690i
$153$		0			0
$154$		0			0
$155$	0.546393	+	0.315460i	0.0438873	+	0.0253384i
$156$		0			0
$157$		−	13.0690i		−	1.04302i	−0.853246	−	0.521508i	$-0.825370\pi$
$157$		−	13.0690i		−	1.04302i	0.853246	−	0.521508i	$-0.174630\pi$
$158$			0.0700647i			0.00557405i
$159$		0			0
$160$	0.666434	+	0.384766i	0.0526862	+	0.0304184i
$161$		0			0
$162$		0			0
$163$	−8.51345	−	14.7457i	−0.666825	−	1.15498i	−0.978787	−	0.204880i	$-0.934319\pi$
$163$	−8.51345	−	14.7457i	−0.666825	−	1.15498i	0.311962	−	0.950095i	$-0.399014\pi$
$164$	0.197502	+	0.342084i	0.0154223	+	0.0267123i
$165$		0			0
$166$	−1.15000	−	0.663954i	−0.0892575	−	0.0515328i
$167$	−10.6605	−	18.4645i	−0.824932	−	1.42882i	−0.901971	−	0.431796i	$-0.857880\pi$
$167$	−10.6605	−	18.4645i	−0.824932	−	1.42882i	0.0770396	−	0.997028i	$-0.475453\pi$
$168$		0			0
$169$	−4.46499	+	7.73360i	−0.343461	+	0.594892i
$170$	0.246123	−	0.142099i	0.0188768	−	0.0108985i
$171$		0			0
$172$	7.86686	−	13.6258i	0.599842	−	1.03896i
$173$	−20.4865			−1.55756			−0.778781	−	0.627296i	$-0.784162\pi$
$173$	−20.4865			−1.55756			−0.778781	+	0.627296i	$0.784162\pi$
$174$		0			0
$175$		0			0
$176$	−14.2386	+	8.22066i	−1.07327	+	0.619655i
$177$		0			0
$178$	−1.36402	+	0.787516i	−0.102237	+	0.0590268i
$179$	−12.4770	−	7.20357i	−0.932571	−	0.538420i	−0.0449475	−	0.998989i	$-0.514312\pi$
$179$	−12.4770	−	7.20357i	−0.932571	−	0.538420i	−0.887624	+	0.460569i	$0.847645\pi$
$180$		0			0
$181$			6.97309i			0.518306i	0.965836	+	0.259153i	$0.0834434\pi$
$181$			6.97309i			0.518306i	−0.965836	+	0.259153i	$0.916557\pi$
$182$		0			0
$183$		0			0
$184$	−1.52971	+	2.64954i	−0.112772	+	0.195327i
$185$	1.71139			0.125824
$186$		0			0
$187$			18.4477i			1.34903i
$188$	19.7945			1.44366
$189$		0			0
$190$	0.339853			0.0246555
$191$		−	10.8347i		−	0.783969i	−0.919972	−	0.391985i	$-0.871789\pi$
$191$		−	10.8347i		−	0.783969i	0.919972	−	0.391985i	$-0.128211\pi$
$192$		0			0
$193$	10.5245			0.757567			0.378783	−	0.925485i	$-0.376343\pi$
$193$	10.5245			0.757567			0.378783	+	0.925485i	$0.376343\pi$
$194$	−0.0348780	+	0.0604104i	−0.00250409	+	0.00433722i
$195$		0			0
$196$		0			0
$197$		−	15.5156i		−	1.10544i	−0.833366	−	0.552721i	$-0.813590\pi$
$197$		−	15.5156i		−	1.10544i	0.833366	−	0.552721i	$-0.186410\pi$
$198$		0			0
$199$	10.8668	+	6.27394i	0.770326	+	0.444748i	0.832991	−	0.553287i	$-0.186627\pi$
$199$	10.8668	+	6.27394i	0.770326	+	0.444748i	−0.0626651	+	0.998035i	$0.519960\pi$
$200$	−1.99279	+	1.15054i	−0.140912	+	0.0813553i
$201$		0			0
$202$	−1.23235	+	0.711497i	−0.0867078	+	0.0500608i
$203$		0			0
$204$		0			0
$205$	0.105352			0.00735810
$206$	0.391322	−	0.677790i	0.0272647	−	0.0472238i
$207$		0			0
$208$	−6.83206	+	3.94449i	−0.473718	+	0.273501i
$209$	−11.0302	+	19.1048i	−0.762973	+	1.32151i
$210$		0			0
$211$	−1.19765	−	2.07438i	−0.0824494	−	0.142807i	0.821852	−	0.569701i	$-0.192941\pi$
$211$	−1.19765	−	2.07438i	−0.0824494	−	0.142807i	−0.904302	+	0.426894i	$0.859608\pi$
$212$	−7.25031	−	4.18597i	−0.497953	−	0.287493i
$213$		0			0
$214$	−0.0154927	−	0.0268341i	−0.00105906	−	0.00183434i
$215$	−2.09818	−	3.63415i	−0.143095	−	0.247847i
$216$		0			0
$217$		0			0
$218$	−1.26848	−	0.732357i	−0.0859123	−	0.0496015i
$219$		0			0
$220$			4.41865i			0.297905i
$221$			8.85170i			0.595430i
$222$		0			0
$223$	−2.42193	−	1.39830i	−0.162184	−	0.0936370i	0.416711	−	0.909039i	$-0.363183\pi$
$223$	−2.42193	−	1.39830i	−0.162184	−	0.0936370i	−0.578895	+	0.815402i	$0.696516\pi$
$224$		0			0
$225$		0			0
$226$	−0.302770	−	0.524413i	−0.0201400	−	0.0348834i
$227$	1.42300	+	2.46471i	0.0944480	+	0.163589i	0.909378	−	0.415970i	$-0.136558\pi$
$227$	1.42300	+	2.46471i	0.0944480	+	0.163589i	−0.814930	+	0.579559i	$0.803225\pi$
$228$		0			0
$229$	20.5460	+	11.8623i	1.35772	+	0.783880i	0.989316	−	0.145786i	$-0.0465711\pi$
$229$	20.5460	+	11.8623i	1.35772	+	0.783880i	0.368404	+	0.929666i	$0.379904\pi$
$230$	0.203229	+	0.352004i	0.0134006	+	0.0232104i
$231$		0			0
$232$	−2.04834	+	3.54782i	−0.134480	+	0.232926i
$233$	16.2205	−	9.36488i	1.06264	−	0.613514i	0.136477	−	0.990643i	$-0.456422\pi$
$233$	16.2205	−	9.36488i	1.06264	−	0.613514i	0.926161	+	0.377129i	$0.123089\pi$
$234$		0			0
$235$	2.63971	−	4.57211i	0.172196	−	0.298251i
$236$	−26.6772			−1.73654
$237$		0			0
$238$		0			0
$239$	−11.1421	+	6.43288i	−0.720721	+	0.416109i	−0.815018	−	0.579436i	$-0.803273\pi$
$239$	−11.1421	+	6.43288i	−0.720721	+	0.416109i	0.0942969	+	0.995544i	$0.469940\pi$
$240$		0			0
$241$	−3.64082	+	2.10203i	−0.234526	+	0.135403i	−0.612658	−	0.790348i	$-0.709900\pi$
$241$	−3.64082	+	2.10203i	−0.234526	+	0.135403i	0.378132	+	0.925752i	$0.376566\pi$
$242$	0.707531	+	0.408493i	0.0454818	+	0.0262590i
$243$		0			0
$244$		−	26.0302i		−	1.66641i
$245$		0			0
$246$		0			0
$247$	−5.29257	+	9.16700i	−0.336758	+	0.583282i
$248$	−0.581008			−0.0368941
$249$		0			0
$250$			0.629572i			0.0398177i
$251$	7.50592			0.473770			0.236885	−	0.971538i	$-0.423874\pi$
$251$	7.50592			0.473770			0.236885	+	0.971538i	$0.423874\pi$
$252$		0			0
$253$	−26.3838			−1.65874
$254$		−	0.450774i		−	0.0282840i
$255$		0			0
$256$	14.8159			0.925996
$257$	−2.51960	+	4.36408i	−0.157169	+	0.272224i	−0.933847	−	0.357674i	$-0.883570\pi$
$257$	−2.51960	+	4.36408i	−0.157169	+	0.272224i	0.776678	+	0.629898i	$0.216903\pi$
$258$		0			0
$259$		0			0
$260$			2.12018i			0.131488i
$261$		0			0
$262$	0.578160	+	0.333801i	0.0357188	+	0.0206223i
$263$	12.2494	−	7.07220i	0.755331	−	0.436091i	−0.0722856	−	0.997384i	$-0.523029\pi$
$263$	12.2494	−	7.07220i	0.755331	−	0.436091i	0.827617	+	0.561293i	$0.189696\pi$
$264$		0			0
$265$	−1.93374	+	1.11644i	−0.118789	+	0.0685826i
$266$		0			0
$267$		0			0
$268$	−13.0616			−0.797862
$269$	7.88856	−	13.6634i	0.480974	−	0.833071i	−0.518788	−	0.854903i	$-0.673616\pi$
$269$	7.88856	−	13.6634i	0.480974	−	0.833071i	0.999762	+	0.0218318i	$0.00694983\pi$
$270$		0			0
$271$	−14.5560	+	8.40390i	−0.884213	+	0.510501i	−0.872045	−	0.489425i	$-0.837207\pi$
$271$	−14.5560	+	8.40390i	−0.884213	+	0.510501i	−0.0121677	+	0.999926i	$0.503873\pi$
$272$	8.57871	−	14.8588i	0.520160	−	0.900944i
$273$		0			0
$274$	−0.0988873	−	0.171278i	−0.00597400	−	0.0103473i
$275$	−17.1854	−	9.92198i	−1.03632	−	0.598318i
$276$		0			0
$277$	−8.91066	−	15.4337i	−0.535390	−	0.927322i	−0.999144	−	0.0413586i	$-0.986831\pi$
$277$	−8.91066	−	15.4337i	−0.535390	−	0.927322i	0.463755	−	0.885964i	$-0.346502\pi$
$278$	−0.691583	−	1.19786i	−0.0414784	−	0.0718427i
$279$		0			0
$280$		0			0
$281$	−7.59774	−	4.38656i	−0.453243	−	0.261680i	0.255956	−	0.966688i	$-0.417610\pi$
$281$	−7.59774	−	4.38656i	−0.453243	−	0.261680i	−0.709199	+	0.705008i	$0.750943\pi$
$282$		0			0
$283$			21.5983i			1.28388i	0.766753	+	0.641942i	$0.221871\pi$
$283$			21.5983i			1.28388i	−0.766753	+	0.641942i	$0.778129\pi$
$284$		−	16.8844i		−	1.00191i
$285$		0			0
$286$	0.898724	+	0.518879i	0.0531427	+	0.0306819i
$287$		0			0
$288$		0			0
$289$	−1.12560	−	1.94960i	−0.0662118	−	0.114682i
$290$	0.272131	+	0.471344i	0.0159801	+	0.0276783i
$291$		0			0
$292$	−9.64756	−	5.57002i	−0.564581	−	0.325961i
$293$	−9.79756	−	16.9699i	−0.572379	−	0.991390i	−0.996321	−	0.0857006i	$-0.972687\pi$
$293$	−9.79756	−	16.9699i	−0.572379	−	0.991390i	0.423942	−	0.905690i	$-0.360646\pi$
$294$		0			0
$295$	−3.55755	+	6.16186i	−0.207129	+	0.358758i
$296$	−1.36486	+	0.788003i	−0.0793309	+	0.0458017i
$297$		0			0
$298$	−0.325931	+	0.564529i	−0.0188807	+	0.0327023i
$299$	−12.6597			−0.732127
$300$		0			0
$301$		0			0
$302$	−0.279996	+	0.161656i	−0.0161120	+	0.00930224i
$303$		0			0
$304$	17.7686	−	10.2587i	1.01910	−	0.588376i
$305$	−6.01241	−	3.47127i	−0.344270	−	0.198764i
$306$		0			0
$307$			27.7677i			1.58478i	0.610012	+	0.792392i	$0.291165\pi$
$307$			27.7677i			1.58478i	−0.610012	+	0.792392i	$0.708835\pi$
$308$		0			0
$309$		0			0
$310$	−0.0385948	+	0.0668482i	−0.00219204	+	0.00379672i
$311$	−20.0160			−1.13500			−0.567501	−	0.823373i	$-0.692090\pi$
$311$	−20.0160			−1.13500			−0.567501	+	0.823373i	$0.692090\pi$
$312$		0			0
$313$			18.4353i			1.04202i	0.853549	+	0.521012i	$0.174445\pi$
$313$			18.4353i			1.04202i	−0.853549	+	0.521012i	$0.825555\pi$
$314$	1.59891			0.0902320
$315$		0			0
$316$	1.13680			0.0639498
$317$		−	14.5483i		−	0.817115i	−0.912733	−	0.408558i	$-0.866032\pi$
$317$		−	14.5483i		−	0.817115i	0.912733	−	0.408558i	$-0.133968\pi$
$318$		0			0
$319$	−35.3288			−1.97803
$320$	2.02322	−	3.50431i	0.113101	−	0.195897i
$321$		0			0
$322$		0			0
$323$		−	23.0212i		−	1.28093i
$324$		0			0
$325$	−8.24600	−	4.76083i	−0.457406	−	0.264083i
$326$	1.80406	−	1.04157i	0.0999176	−	0.0576874i
$327$		0			0
$328$	−0.0840197	+	0.0485088i	−0.00463921	+	0.00267845i
$329$		0			0
$330$		0			0
$331$	−29.6891			−1.63186			−0.815930	−	0.578150i	$-0.803775\pi$
$331$	−29.6891			−1.63186			−0.815930	+	0.578150i	$0.803775\pi$
$332$	−10.7726	+	18.6587i	−0.591224	+	1.02403i
$333$		0			0
$334$	2.25903	−	1.30425i	0.123608	−	0.0713653i
$335$	−1.74183	+	3.01694i	−0.0951664	+	0.164833i
$336$		0			0
$337$	−4.60606	−	7.97793i	−0.250908	−	0.434586i	0.712868	−	0.701298i	$-0.247396\pi$
$337$	−4.60606	−	7.97793i	−0.250908	−	0.434586i	−0.963776	+	0.266713i	$0.914063\pi$
$338$	−0.946163	−	0.546267i	−0.0514645	−	0.0297130i
$339$		0			0
$340$	−2.30555	−	3.99333i	−0.125036	−	0.216569i
$341$	−2.50524	−	4.33921i	−0.135667	−	0.234981i
$342$		0			0
$343$		0			0
$344$	3.34665	+	1.93219i	0.180439	+	0.104177i
$345$		0			0
$346$		−	2.50641i		−	0.134746i
$347$		−	18.1649i		−	0.975145i	−0.873082	−	0.487573i	$-0.837882\pi$
$347$		−	18.1649i		−	0.975145i	0.873082	−	0.487573i	$-0.162118\pi$
$348$		0			0
$349$	−5.70494	−	3.29375i	−0.305378	−	0.176310i	0.339478	−	0.940614i	$-0.389750\pi$
$349$	−5.70494	−	3.29375i	−0.305378	−	0.176310i	−0.644856	+	0.764304i	$0.723083\pi$
$350$		0			0
$351$		0			0
$352$	−3.05564	−	5.29252i	−0.162866	−	0.282092i
$353$	10.4692	+	18.1332i	0.557221	+	0.965135i	0.997727	+	0.0673857i	$0.0214658\pi$
$353$	10.4692	+	18.1332i	0.557221	+	0.965135i	−0.440506	+	0.897750i	$0.645201\pi$
$354$		0			0
$355$	−3.89994	−	2.25163i	−0.206987	−	0.119504i
$356$	12.7774	+	22.1311i	0.677201	+	1.17295i
$357$		0			0
$358$	0.881317	−	1.52649i	0.0465791	−	0.0806773i
$359$	−12.3205	+	7.11324i	−0.650251	+	0.375422i	−0.788552	−	0.614968i	$-0.789169\pi$
$359$	−12.3205	+	7.11324i	−0.650251	+	0.375422i	0.138302	+	0.990390i	$0.455836\pi$
$360$		0			0
$361$	4.26472	−	7.38671i	0.224459	−	0.388774i
$362$	−0.853120			−0.0448390
$363$		0			0
$364$		0			0
$365$	−2.57311	+	1.48559i	−0.134683	+	0.0777591i
$366$		0			0
$367$	−10.7237	+	6.19136i	−0.559775	+	0.323186i	−0.753055	−	0.657957i	$-0.771421\pi$
$367$	−10.7237	+	6.19136i	−0.559775	+	0.323186i	0.193280	+	0.981144i	$0.438087\pi$
$368$	21.2509	+	12.2692i	1.10778	+	0.639577i
$369$		0			0
$370$			0.209380i			0.0108851i
$371$		0			0
$372$		0			0
$373$	10.6559	−	18.4565i	0.551740	−	0.955642i	−0.446409	−	0.894829i	$-0.647297\pi$
$373$	10.6559	−	18.4565i	0.551740	−	0.955642i	0.998149	−	0.0608130i	$-0.0193693\pi$
$374$	−2.25698			−0.116705
$375$		0			0
$376$			4.86176i			0.250726i
$377$	−16.9517			−0.873057
$378$		0			0
$379$	10.6001			0.544489			0.272244	−	0.962228i	$-0.412234\pi$
$379$	10.6001			0.544489			0.272244	+	0.962228i	$0.412234\pi$
$380$		−	5.51410i		−	0.282867i
$381$		0			0
$382$	1.32556			0.0678217
$383$	−6.32174	+	10.9496i	−0.323026	+	0.559497i	−0.981111	−	0.193446i	$-0.938033\pi$
$383$	−6.32174	+	10.9496i	−0.323026	+	0.559497i	0.658085	+	0.752944i	$0.271367\pi$
$384$		0			0
$385$		0			0
$386$			1.28761i			0.0655375i
$387$		0			0
$388$	0.980156	+	0.565893i	0.0497599	+	0.0287289i
$389$	11.4538	−	6.61286i	0.580732	−	0.335286i	−0.180692	−	0.983540i	$-0.557834\pi$
$389$	11.4538	−	6.61286i	0.580732	−	0.335286i	0.761424	+	0.648254i	$0.224501\pi$
$390$		0			0
$391$	23.8442	−	13.7665i	1.20586	−	0.696201i
$392$		0			0
$393$		0			0
$394$	1.89825			0.0956324
$395$	0.151598	−	0.262575i	0.00762772	−	0.0132116i
$396$		0			0
$397$	−21.4672	+	12.3941i	−1.07741	+	0.622043i	−0.930197	−	0.367062i	$-0.880364\pi$
$397$	−21.4672	+	12.3941i	−1.07741	+	0.622043i	−0.147214	+	0.989105i	$0.547030\pi$
$398$	−0.767582	+	1.32949i	−0.0384754	+	0.0666413i
$399$		0			0
$400$	9.22800	+	15.9834i	0.461400	+	0.799168i
$401$	3.19615	+	1.84530i	0.159608	+	0.0921499i	0.577677	−	0.816266i	$-0.303959\pi$
$401$	3.19615	+	1.84530i	0.159608	+	0.0921499i	−0.418068	+	0.908416i	$0.637293\pi$
$402$		0			0
$403$	−1.20208	−	2.08207i	−0.0598800	−	0.103715i
$404$	11.5440	+	19.9948i	0.574336	+	0.994778i
$405$		0			0
$406$		0			0
$407$	−11.7703	−	6.79556i	−0.583430	−	0.336843i
$408$		0			0
$409$		−	18.5370i		−	0.916597i	−0.888798	−	0.458299i	$-0.848459\pi$
$409$		−	18.5370i		−	0.916597i	0.888798	−	0.458299i	$-0.151541\pi$
$410$			0.0128892i			0.000636554i
$411$		0			0
$412$	−10.9971	−	6.34918i	−0.541788	−	0.312802i
$413$		0			0
$414$		0			0
$415$	2.87317	+	4.97648i	0.141039	+	0.244286i
$416$	−1.46618	−	2.53949i	−0.0718852	−	0.124509i
$417$		0			0
$418$	−2.33737	−	1.34948i	−0.114324	−	0.0660053i
$419$	−1.46994	−	2.54600i	−0.0718111	−	0.124380i	0.827884	−	0.560899i	$-0.189545\pi$
$419$	−1.46994	−	2.54600i	−0.0718111	−	0.124380i	−0.899695	+	0.436519i	$0.856211\pi$
$420$		0			0
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	0.285031	+	0.958518i	$0.407996\pi$
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	−0.972617	+	0.232415i	$0.925337\pi$
$422$	0.253790	−	0.146525i	0.0123543	−	0.00713275i
$423$		0			0
$424$	1.02812	−	1.78076i	0.0499300	−	0.0864813i
$425$	20.7083			1.00450
$426$		0			0
$427$		0			0
$428$	−0.435382	+	0.251368i	−0.0210450	+	0.0121503i
$429$		0			0
$430$	0.444618	−	0.256700i	0.0214414	−	0.0123792i
$431$	5.85836	+	3.38232i	0.282187	+	0.162921i	0.634413	−	0.772994i	$-0.281242\pi$
$431$	5.85836	+	3.38232i	0.282187	+	0.162921i	−0.352226	+	0.935915i	$0.614575\pi$
$432$		0			0
$433$		−	28.3475i		−	1.36229i	−0.732146	−	0.681147i	$-0.761481\pi$
$433$		−	28.3475i		−	1.36229i	0.732146	−	0.681147i	$-0.238519\pi$
$434$		0			0
$435$		0			0
$436$	−11.8824	+	20.5810i	−0.569066	+	0.985651i
$437$	32.9248			1.57501
$438$		0			0
$439$		−	26.3512i		−	1.25767i	−0.777537	−	0.628837i	$-0.783531\pi$
$439$		−	26.3512i		−	1.25767i	0.777537	−	0.628837i	$-0.216469\pi$
$440$	−1.08527			−0.0517382
$441$		0			0
$442$	−1.08296			−0.0515110
$443$		−	5.49589i		−	0.261118i	−0.991441	−	0.130559i	$-0.958323\pi$
$443$		−	5.49589i		−	0.261118i	0.991441	−	0.130559i	$-0.0416772\pi$
$444$		0			0
$445$	6.81575			0.323097
$446$	0.171074	−	0.296309i	0.00810060	−	0.0140306i
$447$		0			0
$448$		0			0
$449$			7.38342i			0.348445i	0.984706	+	0.174223i	$0.0557412\pi$
$449$			7.38342i			0.348445i	−0.984706	+	0.174223i	$0.944259\pi$
$450$		0			0
$451$	−0.724568	−	0.418329i	−0.0341186	−	0.0196984i
$452$	−8.50857	+	4.91242i	−0.400209	+	0.231061i
$453$		0			0
$454$	−0.301544	+	0.174097i	−0.0141522	+	0.00817076i
$455$		0			0
$456$		0			0
$457$	41.4219			1.93763			0.968817	−	0.247779i	$-0.0797006\pi$
$457$	41.4219			1.93763			0.968817	+	0.247779i	$0.0797006\pi$
$458$	−1.45128	+	2.51369i	−0.0678139	+	0.117457i
$459$		0			0
$460$	5.71124	−	3.29739i	0.266288	−	0.153741i
$461$	−5.44638	+	9.43341i	−0.253663	+	0.439357i	−0.964532	−	0.263968i	$-0.914969\pi$
$461$	−5.44638	+	9.43341i	−0.253663	+	0.439357i	0.710868	+	0.703325i	$0.248302\pi$
$462$		0			0
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	0.791316	−	0.611407i	$-0.209396\pi$
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	−0.925152	+	0.379597i	$0.876063\pi$
$464$	28.4557	+	16.4289i	1.32102	+	0.762692i
$465$		0			0
$466$	1.14574	+	1.98448i	0.0530755	+	0.0919294i
$467$	−11.9441	−	20.6878i	−0.552707	−	0.957316i	−0.998078	−	0.0619701i	$-0.980262\pi$
$467$	−11.9441	−	20.6878i	−0.552707	−	0.957316i	0.445371	−	0.895346i	$-0.353072\pi$
$468$		0			0
$469$		0			0
$470$	0.559372	+	0.322954i	0.0258019	+	0.0148967i
$471$		0			0
$472$		−	6.55223i		−	0.301591i
$473$			33.3256i			1.53231i
$474$		0			0
$475$	21.4459	+	12.3818i	0.984005	+	0.568116i
$476$		0			0
$477$		0			0
$478$	−0.787028	−	1.36317i	−0.0359978	−	0.0623500i
$479$	−0.947645	−	1.64137i	−0.0432990	−	0.0749961i	0.843564	−	0.537029i	$-0.180453\pi$
$479$	−0.947645	−	1.64137i	−0.0432990	−	0.0749961i	−0.886863	+	0.462033i	$0.847120\pi$
$480$		0			0
$481$	−5.64768	−	3.26069i	−0.257512	−	0.148675i
$482$	−0.257171	−	0.445434i	−0.0117138	−	0.0202890i
$483$		0			0
$484$	6.62778	−	11.4797i	0.301263	−	0.521803i
$485$	0.261418	−	0.150930i	0.0118704	−	0.00685337i
$486$		0			0
$487$	−14.1124	+	24.4434i	−0.639494	+	1.10764i	0.346050	+	0.938216i	$0.387523\pi$
$487$	−14.1124	+	24.4434i	−0.639494	+	1.10764i	−0.985544	+	0.169420i	$0.945811\pi$
$488$	6.39331			0.289412
$489$		0			0
$490$		0			0
$491$	2.30250	−	1.32935i	0.103910	−	0.0599927i	−0.447144	−	0.894462i	$-0.647559\pi$
$491$	2.30250	−	1.32935i	0.103910	−	0.0599927i	0.551055	+	0.834469i	$0.314226\pi$
$492$		0			0
$493$	31.9282	−	18.4338i	1.43797	−	0.830215i
$494$	−1.12153	−	0.647517i	−0.0504601	−	0.0291332i
$495$		0			0
$496$			4.66003i			0.209242i
$497$		0			0
$498$		0			0
$499$	6.27844	−	10.8746i	0.281062	−	0.486813i	−0.690585	−	0.723251i	$-0.742647\pi$
$499$	6.27844	−	10.8746i	0.281062	−	0.486813i	0.971646	+	0.236438i	$0.0759801\pi$
$500$	10.2148			0.456819
$501$		0			0
$502$			0.918308i			0.0409861i
$503$	−18.1502			−0.809278			−0.404639	−	0.914476i	$-0.632603\pi$
$503$	−18.1502			−0.809278			−0.404639	+	0.914476i	$0.632603\pi$
$504$		0			0
$505$	6.15782			0.274020
$506$		−	3.22791i		−	0.143498i
$507$		0			0
$508$	−7.31377			−0.324496
$509$	−9.33827	+	16.1744i	−0.413912	+	0.716916i	−0.995314	−	0.0967005i	$-0.969171\pi$
$509$	−9.33827	+	16.1744i	−0.413912	+	0.716916i	0.581402	+	0.813617i	$0.302504\pi$
$510$		0			0
$511$		0			0
$512$			9.49685i			0.419705i
$513$		0			0
$514$	−0.533921	−	0.308260i	−0.0235503	−	0.0135967i
$515$	−2.93305	+	1.69340i	−0.129245	+	0.0746199i
$516$		0			0
$517$	−36.3096	+	20.9634i	−1.59690	+	0.921968i
$518$		0			0
$519$		0			0
$520$	−0.520742			−0.0228360
$521$	9.03326	−	15.6461i	0.395754	−	0.685466i	−0.597443	−	0.801911i	$-0.703817\pi$
$521$	9.03326	−	15.6461i	0.395754	−	0.685466i	0.993197	+	0.116445i	$0.0371499\pi$
$522$		0			0
$523$	18.3024	−	10.5669i	0.800308	−	0.462058i	−0.0432710	−	0.999063i	$-0.513778\pi$
$523$	18.3024	−	10.5669i	0.800308	−	0.462058i	0.843579	+	0.537005i	$0.180445\pi$
$524$	5.41590	−	9.38061i	0.236595	−	0.409794i
$525$		0			0
$526$	0.865245	+	1.49865i	0.0377265	+	0.0653442i
$527$	4.52820	+	2.61436i	0.197252	+	0.113883i
$528$		0			0
$529$	8.18875	+	14.1833i	0.356033	+	0.616666i
$530$	−0.136591	−	0.236582i	−0.00593312	−	0.0102765i
$531$		0			0
$532$		0			0
$533$	−0.347667	−	0.200725i	−0.0150591	−	0.00869439i
$534$		0			0
$535$			0.134085i			0.00579700i
$536$		−	3.20807i		−	0.138567i
$537$		0			0
$538$	1.67164	+	0.965122i	0.0720695	+	0.0416093i
$539$		0			0
$540$		0			0
$541$	−8.88661	−	15.3921i	−0.382065	−	0.661757i	0.609292	−	0.792946i	$-0.291454\pi$
$541$	−8.88661	−	15.3921i	−0.382065	−	0.661757i	−0.991357	+	0.131189i	$0.958120\pi$
$542$	−1.02817	−	1.78084i	−0.0441637	−	0.0764938i
$543$		0			0
$544$	5.52304	+	3.18873i	0.236798	+	0.136715i
$545$	3.16918	+	5.48918i	0.135753	+	0.235131i
$546$		0			0
$547$	14.1560	−	24.5190i	0.605268	−	1.04835i	−0.386741	−	0.922188i	$-0.626399\pi$
$547$	14.1560	−	24.5190i	0.605268	−	1.04835i	0.992009	−	0.126166i	$-0.0402673\pi$
$548$	−2.77897	+	1.60444i	−0.118712	+	0.0685383i
$549$		0			0
$550$	1.21390	−	2.10254i	0.0517608	−	0.0896524i
$551$	44.0873			1.87818
$552$		0			0
$553$		0			0
$554$	1.88823	−	1.09017i	0.0802232	−	0.0463169i
$555$		0			0
$556$	−19.4352	+	11.2209i	−0.824234	+	0.475872i
$557$	−10.1510	−	5.86069i	−0.430113	−	0.248326i	0.269282	−	0.963061i	$-0.413214\pi$
$557$	−10.1510	−	5.86069i	−0.430113	−	0.248326i	−0.699395	+	0.714736i	$0.746547\pi$
$558$		0			0
$559$			15.9905i			0.676326i
$560$		0			0
$561$		0			0
$562$	0.536671	−	0.929541i	0.0226381	−	0.0392103i
$563$	−36.6029			−1.54263			−0.771314	−	0.636455i	$-0.780400\pi$
$563$	−36.6029			−1.54263			−0.771314	+	0.636455i	$0.780400\pi$
$564$		0			0
$565$			2.62039i			0.110241i
$566$	−2.64243			−0.111070
$567$		0			0
$568$	4.14701			0.174005
$569$			37.6973i			1.58035i	0.612880	+	0.790176i	$0.290011\pi$
$569$			37.6973i			1.58035i	−0.612880	+	0.790176i	$0.709989\pi$
$570$		0			0
$571$	28.2246			1.18116			0.590581	−	0.806979i	$-0.298899\pi$
$571$	28.2246			1.18116			0.590581	+	0.806979i	$0.298899\pi$
$572$	8.41878	−	14.5817i	0.352007	−	0.609694i
$573$		0			0
$574$		0			0
$575$			29.6168i			1.23511i
$576$		0			0
$577$	−8.12775	−	4.69256i	−0.338363	−	0.195354i	0.321185	−	0.947016i	$-0.395919\pi$
$577$	−8.12775	−	4.69256i	−0.338363	−	0.195354i	−0.659548	+	0.751663i	$0.729252\pi$
$578$	0.238523	−	0.137711i	0.00992123	−	0.00572802i
$579$		0			0
$580$	7.64754	−	4.41531i	0.317547	−	0.183336i
$581$		0			0
$582$		0			0
$583$	17.7326			0.734409
$584$	1.36806	−	2.36955i	0.0566108	−	0.0980527i
$585$		0			0
$586$	2.07617	−	1.19868i	0.0857657	−	0.0495169i
$587$	23.1819	−	40.1523i	0.956821	−	1.65726i	0.226675	−	0.973971i	$-0.427215\pi$
$587$	23.1819	−	40.1523i	0.956821	−	1.65726i	0.730146	−	0.683291i	$-0.239452\pi$
$588$		0			0
$589$	3.12633	+	5.41496i	0.128818	+	0.223120i
$590$	−0.753870	−	0.435247i	−0.0310363	−	0.0179188i
$591$		0			0
$592$	6.32025	+	10.9470i	0.259761	+	0.449919i
$593$	−9.07080	−	15.7111i	−0.372493	−	0.645177i	0.617455	−	0.786606i	$-0.288164\pi$
$593$	−9.07080	−	15.7111i	−0.372493	−	0.645177i	−0.989948	+	0.141429i	$0.954830\pi$
$594$		0			0
$595$		0			0
$596$	9.15945	+	5.28821i	0.375186	+	0.216613i
$597$		0			0
$598$		−	1.54884i		−	0.0633367i
$599$		−	6.96020i		−	0.284386i	−0.989839	−	0.142193i	$-0.954585\pi$
$599$		−	6.96020i		−	0.284386i	0.989839	−	0.142193i	$-0.0454154\pi$
$600$		0			0
$601$	2.08865	+	1.20588i	0.0851976	+	0.0491889i	0.541994	−	0.840383i	$-0.317670\pi$
$601$	2.08865	+	1.20588i	0.0851976	+	0.0491889i	−0.456796	+	0.889572i	$0.651003\pi$
$602$		0			0
$603$		0			0
$604$	2.62285	+	4.54292i	0.106722	+	0.184849i
$605$	−1.76770	−	3.06175i	−0.0718673	−	0.124478i
$606$		0			0
$607$	11.0306	+	6.36850i	0.447717	+	0.258489i	0.706865	−	0.707348i	$-0.250109\pi$
$607$	11.0306	+	6.36850i	0.447717	+	0.258489i	−0.259149	+	0.965837i	$0.583442\pi$
$608$	3.81318	+	6.60462i	0.154645	+	0.267853i
$609$		0			0
$610$	0.424690	−	0.735585i	0.0171952	−	0.0297830i
$611$	−17.4223	+	10.0588i	−0.704832	+	0.406935i
$612$		0			0
$613$	5.16761	−	8.95057i	0.208718	−	0.361510i	−0.742593	−	0.669743i	$-0.766404\pi$
$613$	5.16761	−	8.95057i	0.208718	−	0.361510i	0.951311	+	0.308233i	$0.0997376\pi$
$614$	−3.39722			−0.137101
$615$		0			0
$616$		0			0
$617$	41.3741	−	23.8873i	1.66566	−	0.961668i	0.695721	−	0.718313i	$-0.255085\pi$
$617$	41.3741	−	23.8873i	1.66566	−	0.961668i	0.969937	−	0.243355i	$-0.0782481\pi$
$618$		0			0
$619$	−35.2626	+	20.3588i	−1.41732	+	0.818291i	−0.996063	−	0.0886491i	$-0.971745\pi$
$619$	−35.2626	+	20.3588i	−1.41732	+	0.818291i	−0.421259	+	0.906940i	$0.638412\pi$
$620$	1.08461	+	0.626198i	0.0435589	+	0.0251487i
$621$		0			0
$622$		−	2.44884i		−	0.0981897i
$623$		0			0
$624$		0			0
$625$	−10.4371	+	18.0775i	−0.417483	+	0.723101i
$626$	−2.25546			−0.0901462
$627$		0			0
$628$		−	25.9423i		−	1.03521i
$629$	14.1831			0.565517
$630$		0			0
$631$	11.4782			0.456942			0.228471	−	0.973551i	$-0.426627\pi$
$631$	11.4782			0.456942			0.228471	+	0.973551i	$0.426627\pi$
$632$			0.279210i			0.0111064i
$633$		0			0
$634$	1.77991			0.0706891
$635$	−0.975332	+	1.68932i	−0.0387049	+	0.0670388i
$636$		0			0
$637$		0			0
$638$		−	4.32228i		−	0.171121i
$639$		0			0
$640$	1.76160	+	1.01706i	0.0696334	+	0.0402029i
$641$	−30.5823	+	17.6567i	−1.20793	+	0.697398i	−0.962306	−	0.271968i	$-0.912326\pi$
$641$	−30.5823	+	17.6567i	−1.20793	+	0.697398i	−0.245622	+	0.969366i	$0.578992\pi$
$642$		0			0
$643$	6.09416	−	3.51846i	0.240330	−	0.138755i	−0.374998	−	0.927025i	$-0.622357\pi$
$643$	6.09416	−	3.51846i	0.240330	−	0.138755i	0.615328	+	0.788271i	$0.289023\pi$
$644$		0			0
$645$		0			0
$646$	2.81651			0.110814
$647$	−7.49709	+	12.9853i	−0.294741	+	0.510507i	−0.974925	−	0.222535i	$-0.928567\pi$
$647$	−7.49709	+	12.9853i	−0.294741	+	0.510507i	0.680184	+	0.733042i	$0.261900\pi$
$648$		0			0
$649$	48.9347	−	28.2525i	1.92086	−	1.10901i
$650$	0.582461	−	1.00885i	0.0228460	−	0.0395704i
$651$		0			0
$652$	−16.8995	−	29.2708i	−0.661835	−	1.14633i
$653$	4.15597	+	2.39945i	0.162636	+	0.0938977i	0.579109	−	0.815250i	$-0.303401\pi$
$653$	4.15597	+	2.39945i	0.162636	+	0.0938977i	−0.416473	+	0.909148i	$0.636734\pi$
$654$		0			0
$655$	−1.44448	−	2.50191i	−0.0564405	−	0.0977577i
$656$	0.389070	+	0.673889i	0.0151906	+	0.0263109i
$657$		0			0
$658$		0			0
$659$	13.4562	+	7.76893i	0.524179	+	0.302635i	0.738643	−	0.674097i	$-0.235467\pi$
$659$	13.4562	+	7.76893i	0.524179	+	0.302635i	−0.214464	+	0.976732i	$0.568800\pi$
$660$		0			0
$661$			21.0307i			0.818001i	0.912534	+	0.409000i	$0.134123\pi$
$661$			21.0307i			0.818001i	−0.912534	+	0.409000i	$0.865877\pi$
$662$		−	3.63230i		−	0.141173i
$663$		0			0
$664$	−4.58280	−	2.64588i	−0.177847	−	0.102680i
$665$		0			0
$666$		0			0
$667$	26.3639	+	45.6636i	1.02081	+	1.76810i
$668$	−21.1614	−	36.6526i	−0.818758	−	1.41813i
$669$		0			0
$670$	−0.369106	−	0.213103i	−0.0142598	−	0.00823290i
$671$	27.5673	+	47.7479i	1.06422	+	1.84329i
$672$		0			0
$673$	10.7194	−	18.5665i	0.413201	−	0.715686i	−0.582036	−	0.813163i	$-0.697744\pi$
$673$	10.7194	−	18.5665i	0.413201	−	0.715686i	0.995238	+	0.0974770i	$0.0310772\pi$
$674$	0.976056	−	0.563526i	0.0375963	−	0.0217062i
$675$		0			0
$676$	−8.86315	+	15.3514i	−0.340891	+	0.590440i
$677$	18.0630			0.694217			0.347109	−	0.937825i	$-0.387164\pi$
$677$	18.0630			0.694217			0.347109	+	0.937825i	$0.387164\pi$
$678$		0			0
$679$		0			0
$680$	0.980808	−	0.566270i	0.0376123	−	0.0217155i
$681$		0			0
$682$	0.530878	−	0.306503i	0.0203284	−	0.0117366i
$683$	−39.4602	−	22.7824i	−1.50990	−	0.871743i	−0.999933	−	0.0115508i	$-0.996323\pi$
$683$	−39.4602	−	22.7824i	−1.50990	−	0.871743i	−0.509970	−	0.860192i	$-0.670343\pi$
$684$		0			0
$685$			0.855844i			0.0327001i
$686$		0			0
$687$		0			0
$688$	15.4973	−	26.8422i	0.590830	−	1.02335i
$689$	8.50857			0.324151
$690$		0			0
$691$		−	3.85240i		−	0.146552i	−0.997312	−	0.0732760i	$-0.976655\pi$
$691$		−	3.85240i		−	0.146552i	0.997312	−	0.0732760i	$-0.0233454\pi$
$692$	−40.6664			−1.54590
$693$		0			0
$694$	2.22238			0.0843604
$695$			5.98547i			0.227042i
$696$		0			0
$697$	0.873099			0.0330710
$698$	0.402972	−	0.697967i	0.0152527	−	0.0264185i
$699$		0			0
$700$		0			0
$701$			46.5216i			1.75710i	0.477653	+	0.878549i	$0.341488\pi$
$701$			46.5216i			1.75710i	−0.477653	+	0.878549i	$0.658512\pi$
$702$		0			0
$703$	14.6883	+	8.48028i	0.553979	+	0.319840i
$704$	−27.8297	+	16.0675i	−1.04887	+	0.605566i
$705$		0			0
$706$	−2.21850	+	1.28085i	−0.0834944	+	0.0482055i
$707$		0			0
$708$		0			0
$709$	−29.2374			−1.09803			−0.549017	−	0.835811i	$-0.684998\pi$
$709$	−29.2374			−1.09803			−0.549017	+	0.835811i	$0.684998\pi$
$710$	0.275474	−	0.477136i	0.0103384	−	0.0179066i
$711$		0			0
$712$	−5.43565	+	3.13828i	−0.203710	+	0.117612i
$713$	−3.73904	+	6.47621i	−0.140028	+	0.242536i
$714$		0			0
$715$	−2.24538	−	3.88911i	−0.0839724	−	0.145445i
$716$	−24.7672	−	14.2993i	−0.925592	−	0.534391i
$717$		0			0
$718$	−0.870265	−	1.50734i	−0.0324780	−	0.0562536i
$719$	1.68561	+	2.91956i	0.0628627	+	0.108881i	0.895744	−	0.444570i	$-0.146644\pi$
$719$	1.68561	+	2.91956i	0.0628627	+	0.108881i	−0.832881	+	0.553452i	$0.813310\pi$
$720$		0			0
$721$		0			0
$722$	0.903723	+	0.521765i	0.0336331	+	0.0194181i
$723$		0			0
$724$			13.8418i			0.514427i
$725$			39.6579i			1.47286i
$726$		0			0
$727$	−4.34397	−	2.50799i	−0.161109	−	0.0930164i	0.417278	−	0.908779i	$-0.362984\pi$
$727$	−4.34397	−	2.50799i	−0.161109	−	0.0930164i	−0.578387	+	0.815763i	$0.696318\pi$
$728$		0			0
$729$		0			0
$730$	−0.181753	−	0.314806i	−0.00672698	−	0.0116515i
$731$	−17.3885	−	30.1178i	−0.643138	−	1.11395i
$732$		0			0
$733$	−19.6875	−	11.3666i	−0.727175	−	0.419835i	0.0902126	−	0.995923i	$-0.471245\pi$
$733$	−19.6875	−	11.3666i	−0.727175	−	0.419835i	−0.817388	+	0.576088i	$0.804579\pi$
$734$	−0.757478	−	1.31199i	−0.0279590	−	0.0484265i
$735$		0			0
$736$	−4.56050	+	7.89901i	−0.168102	+	0.291162i
$737$	23.9592	−	13.8328i	0.882547	−	0.509539i
$738$		0			0
$739$	1.19511	−	2.06999i	0.0439628	−	0.0761458i	−0.843207	−	0.537589i	$-0.819335\pi$
$739$	1.19511	−	2.06999i	0.0439628	−	0.0761458i	0.887170	+	0.461444i	$0.152668\pi$
$740$	3.39717			0.124883
$741$		0			0
$742$		0			0
$743$	36.1039	−	20.8446i	1.32453	−	0.764715i	0.340078	−	0.940397i	$-0.389546\pi$
$743$	36.1039	−	20.8446i	1.32453	−	0.764715i	0.984447	+	0.175682i	$0.0562131\pi$
$744$		0			0
$745$	2.44292	−	1.41042i	0.0895018	−	0.0516739i
$746$	2.25805	+	1.30369i	0.0826732	+	0.0477314i
$747$		0			0
$748$			36.6193i			1.33893i
$749$		0			0
$750$		0			0
$751$	−13.2710	+	22.9861i	−0.484267	+	0.838775i	−0.999837	−	0.0180728i	$-0.994247\pi$
$751$	−13.2710	+	22.9861i	−0.484267	+	0.838775i	0.515570	+	0.856848i	$0.327580\pi$
$752$	38.9942			1.42197
$753$		0			0
$754$		−	2.07395i		−	0.0755287i
$755$	1.39909			0.0509180
$756$		0			0
$757$	20.3580			0.739923			0.369961	−	0.929047i	$-0.379371\pi$
$757$	20.3580			0.739923			0.369961	+	0.929047i	$0.379371\pi$
$758$			1.29686i			0.0471041i
$759$		0			0
$760$	1.35433			0.0491266
$761$	12.9578	−	22.4436i	0.469720	−	0.813578i	−0.529681	−	0.848197i	$-0.677688\pi$
$761$	12.9578	−	22.4436i	0.469720	−	0.813578i	0.999401	+	0.0346186i	$0.0110217\pi$
$762$		0			0
$763$		0			0
$764$		−	21.5072i		−	0.778102i
$765$		0			0
$766$	−1.33962	−	0.773430i	−0.0484024	−	0.0279452i
$767$	23.4802	−	13.5563i	0.847821	−	0.489489i
$768$		0			0
$769$	18.8269	−	10.8697i	0.678914	−	0.391971i	−0.120532	−	0.992709i	$-0.538460\pi$
$769$	18.8269	−	10.8697i	0.678914	−	0.391971i	0.799446	+	0.600738i	$0.205127\pi$
$770$		0			0
$771$		0			0
$772$	20.8914			0.751897
$773$	−10.1606	+	17.5987i	−0.365453	+	0.632982i	−0.988849	−	0.148924i	$-0.952419\pi$
$773$	−10.1606	+	17.5987i	−0.365453	+	0.632982i	0.623396	+	0.781906i	$0.285752\pi$
$774$		0			0
$775$	−4.87093	+	2.81223i	−0.174969	+	0.101018i
$776$	−0.138990	+	0.240738i	−0.00498945	+	0.00864197i
$777$		0			0
$778$	0.809047	+	1.40131i	0.0290058	+	0.0502394i
$779$	0.904199	+	0.522039i	0.0323963	+	0.0187040i
$780$		0			0
$781$	17.8814	+	30.9715i	0.639848	+	1.10825i
$782$	1.68425	+	2.91721i	0.0602288	+	0.104319i
$783$		0			0
$784$		0			0
$785$	−5.99211	−	3.45955i	−0.213868	−	0.123477i
$786$		0			0
$787$			18.9446i			0.675303i	0.941271	+	0.337652i	$0.109633\pi$
$787$			18.9446i			0.675303i	−0.941271	+	0.337652i	$0.890367\pi$
$788$		−	30.7990i		−	1.09717i
$789$		0			0
$790$	0.0321246	+	0.0185472i	0.00114294	+	0.000659879i
$791$		0			0
$792$		0			0
$793$	13.2275	+	22.9107i	0.469722	+	0.813583i
$794$	−1.51635	−	2.62640i	−0.0538133	−	0.0932074i
$795$		0			0
$796$	21.5709	+	12.4540i	0.764560	+	0.441419i
$797$	−11.4342	−	19.8047i	−0.405022	−	0.701518i	0.589302	−	0.807913i	$-0.299403\pi$
$797$	−11.4342	−	19.8047i	−0.405022	−	0.701518i	−0.994324	+	0.106394i	$0.966069\pi$
$798$		0			0
$799$	21.8764	−	37.8911i	0.773932	−	1.34049i
$800$	−5.94106	+	3.43007i	−0.210048	+	0.121271i
$801$		0			0
$802$	−0.225762	+	0.391032i	−0.00797194	+	0.0138078i
$803$	23.5957			0.832674
$804$		0			0
$805$		0			0
$806$	0.254729	−	0.147068i	0.00897246	−	0.00518025i
$807$		0			0
$808$	−4.91095	+	2.83534i	−0.172767	+	0.0997469i
$809$	10.3762	+	5.99072i	0.364809	+	0.210622i	0.671188	−	0.741287i	$-0.265784\pi$
$809$	10.3762	+	5.99072i	0.364809	+	0.210622i	−0.306379	+	0.951909i	$0.599118\pi$
$810$		0			0
$811$		−	36.9371i		−	1.29704i	−0.761199	−	0.648519i	$-0.775389\pi$
$811$		−	36.9371i		−	1.29704i	0.761199	−	0.648519i	$-0.224611\pi$
$812$		0			0
$813$		0			0
$814$	0.831399	−	1.44003i	0.0291405	−	0.0504729i
$815$	−9.01455			−0.315766
$816$		0			0
$817$		−	41.5875i		−	1.45496i
$818$	2.26790			0.0792954
$819$		0			0
$820$	0.209127			0.00730304
$821$			37.7480i			1.31741i	0.752400	+	0.658707i	$0.228896\pi$
$821$			37.7480i			1.31741i	−0.752400	+	0.658707i	$0.771104\pi$
$822$		0			0
$823$	−21.0164			−0.732586			−0.366293	−	0.930499i	$-0.619373\pi$
$823$	−21.0164			−0.732586			−0.366293	+	0.930499i	$0.619373\pi$
$824$	1.55943	−	2.70101i	0.0543253	−	0.0940943i
$825$		0			0
$826$		0			0
$827$			23.9104i			0.831447i	0.909491	+	0.415724i	$0.136472\pi$
$827$			23.9104i			0.831447i	−0.909491	+	0.415724i	$0.863528\pi$
$828$		0			0
$829$	−21.7251	−	12.5430i	−0.754542	−	0.435635i	0.0727906	−	0.997347i	$-0.476810\pi$
$829$	−21.7251	−	12.5430i	−0.754542	−	0.435635i	−0.827333	+	0.561712i	$0.810143\pi$
$830$	−0.608845	+	0.351517i	−0.0211333	+	0.0122013i
$831$		0			0
$832$	−13.3534	+	7.70960i	−0.462946	+	0.267282i
$833$		0			0
$834$		0			0
$835$	−11.2879			−0.390635
$836$	−21.8952	+	37.9237i	−0.757263	+	1.31162i
$837$		0			0
$838$	0.311489	−	0.179838i	0.0107602	−	0.00621242i
$839$	−3.72840	+	6.45777i	−0.128719	+	0.222947i	−0.923180	−	0.384367i	$-0.874420\pi$
$839$	−3.72840	+	6.45777i	−0.128719	+	0.222947i	0.794462	+	0.607314i	$0.207753\pi$
$840$		0			0
$841$	20.8021	+	36.0303i	0.717313	+	1.24242i
$842$	−2.98960	−	1.72604i	−0.103028	−	0.0594834i
$843$		0			0
$844$	−2.37737	−	4.11772i	−0.0818323	−	0.141738i
$845$	2.36390	+	4.09439i	0.0813206	+	0.140851i
$846$		0			0
$847$		0			0
$848$	−14.2828	−	8.24615i	−0.490472	−	0.283174i
$849$		0			0
$850$			2.53354i			0.0868998i
$851$			20.2846i			0.695346i
$852$		0			0
$853$	−2.19184	−	1.26546i	−0.0750472	−	0.0433285i	0.462007	−	0.886876i	$-0.347130\pi$
$853$	−2.19184	−	1.26546i	−0.0750472	−	0.0433285i	−0.537054	+	0.843548i	$0.680463\pi$
$854$		0			0
$855$		0			0
$856$	−0.0617388	−	0.106935i	−0.00211019	−	0.00365495i
$857$	−9.52098	−	16.4908i	−0.325231	−	0.563316i	0.656328	−	0.754475i	$-0.272109\pi$
$857$	−9.52098	−	16.4908i	−0.325231	−	0.563316i	−0.981559	+	0.191159i	$0.938775\pi$
$858$		0			0
$859$	−8.88415	−	5.12927i	−0.303123	−	0.175008i	0.340722	−	0.940164i	$-0.389329\pi$
$859$	−8.88415	−	5.12927i	−0.303123	−	0.175008i	−0.643845	+	0.765156i	$0.722662\pi$
$860$	−4.16495	−	7.21390i	−0.142024	−	0.245992i
$861$		0			0
$862$	−0.413809	+	0.716738i	−0.0140944	+	0.0244122i
$863$	−3.81858	+	2.20466i	−0.129986	+	0.0750475i	−0.563583	−	0.826059i	$-0.690578\pi$
$863$	−3.81858	+	2.20466i	−0.129986	+	0.0750475i	0.433597	+	0.901107i	$0.357244\pi$
$864$		0			0
$865$	−5.42309	+	9.39306i	−0.184390	+	0.319374i
$866$	3.46816			0.117853
$867$		0			0
$868$		0			0
$869$	−2.08526	+	1.20392i	−0.0707375	+	0.0408403i
$870$		0			0
$871$	11.4962	−	6.63736i	0.389535	−	0.224898i
$872$	−5.05493	−	2.91847i	−0.171182	−	0.0988317i
$873$		0			0
$874$			4.02816i			0.136255i
$875$		0			0
$876$		0			0
$877$	25.0586	−	43.4028i	0.846170	−	1.46561i	−0.0384307	−	0.999261i	$-0.512236\pi$
$877$	25.0586	−	43.4028i	0.846170	−	1.46561i	0.884601	−	0.466349i	$-0.154431\pi$
$878$	3.22392			0.108802
$879$		0			0
$880$			8.70452i			0.293429i
$881$	42.5809			1.43459			0.717294	−	0.696771i	$-0.245381\pi$
$881$	42.5809			1.43459			0.717294	+	0.696771i	$0.245381\pi$
$882$		0			0
$883$	−15.6590			−0.526967			−0.263483	−	0.964664i	$-0.584871\pi$
$883$	−15.6590			−0.526967			−0.263483	+	0.964664i	$0.584871\pi$
$884$			17.5709i			0.590974i
$885$		0			0
$886$	0.672392			0.0225895
$887$	−12.3919	+	21.4634i	−0.416080	+	0.720671i	−0.995541	−	0.0943286i	$-0.969930\pi$
$887$	−12.3919	+	21.4634i	−0.416080	+	0.720671i	0.579461	+	0.815000i	$0.303263\pi$
$888$		0			0
$889$		0			0
$890$			0.833869i			0.0279513i
$891$		0			0
$892$	−4.80760	−	2.77567i	−0.160970	−	0.0929363i
$893$	45.3113	−	26.1605i	1.51629	−	0.875428i
$894$		0			0
$895$	−6.60567	+	3.81379i	−0.220803	+	0.127481i
$896$		0			0
$897$		0			0
$898$	−0.903321			−0.0301442
$899$	−5.00670	+	8.67186i	−0.166983	+	0.289223i
$900$		0			0
$901$	−16.0257	+	9.25246i	−0.533895	+	0.308244i
$902$	0.0511803	−	0.0886468i	0.00170412	−	0.00295162i
$903$		0			0
$904$	−1.20655	−	2.08980i	−0.0401292	−	0.0695058i
$905$	3.19716	+	1.84588i	0.106277	+	0.0613592i
$906$		0			0
$907$	−22.0517	−	38.1946i	−0.732213	−	1.26823i	−0.955935	−	0.293577i	$-0.905154\pi$
$907$	−22.0517	−	38.1946i	−0.732213	−	1.26823i	0.223722	−	0.974653i	$-0.428179\pi$
$908$	2.82471	+	4.89254i	0.0937412	+	0.162365i
$909$		0			0
$910$		0			0
$911$	−22.3259	−	12.8899i	−0.739691	−	0.427061i	0.0822657	−	0.996610i	$-0.473784\pi$
$911$	−22.3259	−	12.8899i	−0.739691	−	0.427061i	−0.821957	+	0.569549i	$0.807118\pi$
$912$		0			0
$913$		−	45.6349i		−	1.51030i
$914$			5.06774i			0.167626i
$915$		0			0
$916$	40.7845	+	23.5470i	1.34756	+	0.778013i
$917$		0			0
$918$		0			0
$919$	−26.3551	−	45.6484i	−0.869375	−	1.50580i	−0.862637	−	0.505824i	$-0.831189\pi$
$919$	−26.3551	−	45.6484i	−0.869375	−	1.50580i	−0.00673776	−	0.999977i	$-0.502145\pi$
$920$	0.809876	+	1.40275i	0.0267008	+	0.0462472i
$921$		0			0
$922$	−1.15412	−	0.666334i	−0.0380091	−	0.0219446i
$923$	8.57999	+	14.8610i	0.282414	+	0.489155i
$924$		0			0
$925$	−7.62828	+	13.2126i	−0.250816	+	0.434426i
$926$	0.610249	−	0.352327i	0.0200540	−	0.0115782i
$927$		0			0
$928$	−6.10666	+	10.5770i	−0.200461	+	0.347208i
$929$	3.38018			0.110900			0.0554500	−	0.998461i	$-0.482341\pi$
$929$	3.38018			0.110900			0.0554500	+	0.998461i	$0.482341\pi$
$930$		0			0
$931$		0			0
$932$	32.1981	−	18.5896i	1.05468	−	0.608922i
$933$		0			0
$934$	2.53103	−	1.46129i	0.0828180	−	0.0478150i
$935$	8.45827	+	4.88338i	0.276615	+	0.159704i
$936$		0			0
$937$			8.26186i			0.269903i	0.990852	+	0.134952i	$0.0430879\pi$
$937$			8.26186i			0.269903i	−0.990852	+	0.134952i	$0.956912\pi$
$938$		0			0
$939$		0			0
$940$	5.23990	−	9.07578i	0.170907	−	0.296019i
$941$	52.3763			1.70742			0.853710	−	0.520749i	$-0.174347\pi$
$941$	52.3763			1.70742			0.853710	+	0.520749i	$0.174347\pi$
$942$		0			0
$943$			1.24870i			0.0406633i
$944$	−52.5528			−1.71045
$945$		0			0
$946$	−4.07720			−0.132561
$947$		−	7.54421i		−	0.245154i	−0.992459	−	0.122577i	$-0.960884\pi$
$947$		−	7.54421i		−	0.245154i	0.992459	−	0.122577i	$-0.0391158\pi$
$948$		0			0
$949$	11.3218			0.367523
$950$	−1.51484	+	2.62379i	−0.0491480	+	0.0851269i
$951$		0			0
$952$		0			0
$953$			45.2795i			1.46675i	0.679825	+	0.733374i	$0.262056\pi$
$953$			45.2795i			1.46675i	−0.679825	+	0.733374i	$0.737944\pi$
$954$		0			0
$955$	−4.96769	−	2.86810i	−0.160751	−	0.0928095i
$956$	−22.1174	+	12.7695i	−0.715327	+	0.412994i
$957$		0			0
$958$	0.200812	−	0.115939i	0.00648795	−	0.00374582i
$959$		0			0
$960$		0			0
$961$	29.5799			0.954189
$962$	0.398927	−	0.690963i	0.0128619	−	0.0222775i
$963$		0			0
$964$	−7.22714	+	4.17259i	−0.232770	+	0.134390i
$965$	2.78598	−	4.82546i	0.0896838	−	0.155337i
$966$		0			0
$967$	−6.82403	−	11.8196i	−0.219446	−	0.380092i	0.735193	−	0.677858i	$-0.237092\pi$
$967$	−6.82403	−	11.8196i	−0.219446	−	0.380092i	−0.954639	+	0.297766i	$0.903758\pi$
$968$	2.81954	+	1.62786i	0.0906233	+	0.0523214i
$969$		0			0
$970$	0.0184654	+	0.0319831i	0.000592889	+	0.00102691i
$971$	−1.73552	−	3.00601i	−0.0556955	−	0.0964675i	0.836833	−	0.547458i	$-0.184404\pi$
$971$	−1.73552	−	3.00601i	−0.0556955	−	0.0964675i	−0.892529	+	0.450990i	$0.851071\pi$
$972$		0			0
$973$		0			0
$974$	−2.99051	−	1.72657i	−0.0958222	−	0.0553230i
$975$		0			0
$976$		−	51.2782i		−	1.64138i
$977$			2.56232i			0.0819759i	0.999160	+	0.0409880i	$0.0130505\pi$
$977$			2.56232i			0.0819759i	−0.999160	+	0.0409880i	$0.986949\pi$
$978$		0			0
$979$	−46.8759	−	27.0638i	−1.49816	−	0.864963i
$980$		0			0
$981$		0			0
$982$	0.162638	+	0.281698i	0.00519000	+	0.00898935i
$983$	19.5749	+	33.9047i	0.624343	+	1.08139i	0.988668	+	0.150122i	$0.0479665\pi$
$983$	19.5749	+	33.9047i	0.624343	+	1.08139i	−0.364325	+	0.931272i	$0.618700\pi$
$984$		0			0
$985$	−7.11390	−	4.10721i	−0.226668	−	0.130867i
$986$	2.25527	+	3.90624i	0.0718224	+	0.124400i
$987$		0			0
$988$	−10.5059	+	18.1968i	−0.334238	+	0.578917i
$989$	43.0743	−	24.8690i	1.36968	−	0.790788i
$990$		0			0
$991$	8.10333	−	14.0354i	0.257411	−	0.445848i	−0.708137	−	0.706075i	$-0.750464\pi$
$991$	8.10333	−	14.0354i	0.257411	−	0.445848i	0.965547	+	0.260227i	$0.0837974\pi$
$992$	−1.73215			−0.0549957
$993$		0			0
$994$		0			0
$995$	5.75320	−	3.32161i	0.182389	−	0.105302i
$996$		0			0
$997$	21.5007	−	12.4134i	0.680933	−	0.393137i	−0.119273	−	0.992861i	$-0.538057\pi$
$997$	21.5007	−	12.4134i	0.680933	−	0.393137i	0.800207	+	0.599725i	$0.204723\pi$
$998$	1.33044	+	0.768132i	0.0421145	+	0.0243148i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.i.d.521.11		48
3.2	odd	2		441.2.i.d.227.12		48
7.2	even	3		1323.2.s.d.656.14		48
7.3	odd	6		1323.2.o.e.440.11		48
7.4	even	3		1323.2.o.e.440.12		48
7.5	odd	6		1323.2.s.d.656.13		48
7.6	odd	2	inner	1323.2.i.d.521.12		48
9.4	even	3		441.2.s.d.374.12		48
9.5	odd	6		1323.2.s.d.962.13		48
21.2	odd	6		441.2.s.d.362.11		48
21.5	even	6		441.2.s.d.362.12		48
21.11	odd	6		441.2.o.e.146.14	yes	48
21.17	even	6		441.2.o.e.146.13	✓	48
21.20	even	2		441.2.i.d.227.11		48
63.4	even	3		441.2.o.e.293.13	yes	48
63.5	even	6	inner	1323.2.i.d.1097.11		48
63.13	odd	6		441.2.s.d.374.11		48
63.23	odd	6	inner	1323.2.i.d.1097.12		48
63.31	odd	6		441.2.o.e.293.14	yes	48
63.32	odd	6		1323.2.o.e.881.11		48
63.40	odd	6		441.2.i.d.68.14		48
63.41	even	6		1323.2.s.d.962.14		48
63.58	even	3		441.2.i.d.68.13		48
63.59	even	6		1323.2.o.e.881.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.13		48	63.58	even	3
441.2.i.d.68.14		48	63.40	odd	6
441.2.i.d.227.11		48	21.20	even	2
441.2.i.d.227.12		48	3.2	odd	2
441.2.o.e.146.13	✓	48	21.17	even	6
441.2.o.e.146.14	yes	48	21.11	odd	6
441.2.o.e.293.13	yes	48	63.4	even	3
441.2.o.e.293.14	yes	48	63.31	odd	6
441.2.s.d.362.11		48	21.2	odd	6
441.2.s.d.362.12		48	21.5	even	6
441.2.s.d.374.11		48	63.13	odd	6
441.2.s.d.374.12		48	9.4	even	3
1323.2.i.d.521.11		48	1.1	even	1	trivial
1323.2.i.d.521.12		48	7.6	odd	2	inner
1323.2.i.d.1097.11		48	63.5	even	6	inner
1323.2.i.d.1097.12		48	63.23	odd	6	inner
1323.2.o.e.440.11		48	7.3	odd	6
1323.2.o.e.440.12		48	7.4	even	3
1323.2.o.e.881.11		48	63.32	odd	6
1323.2.o.e.881.12		48	63.59	even	6
1323.2.s.d.656.13		48	7.5	odd	6
1323.2.s.d.656.14		48	7.2	even	3
1323.2.s.d.962.13		48	9.5	odd	6
1323.2.s.d.962.14		48	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.122344i q^{2} +1.98503 q^{4} +(0.264715 - 0.458500i) q^{5} +0.487547i q^{8} +O(q^{10})\)	\(q+0.122344i q^{2} +1.98503 q^{4} +(0.264715 - 0.458500i) q^{5} +0.487547i q^{8} +(0.0560949 + 0.0323864i) q^{10} +(-3.64120 + 2.10225i) q^{11} +(-1.74714 + 1.00871i) q^{13} +3.91042 q^{16} +(2.19381 - 3.79979i) q^{17} +(4.54391 - 2.62343i) q^{19} +(0.525467 - 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +(5.43444 + 3.13757i) q^{23} +(2.35985 + 4.08738i) q^{25} +(-0.123411 - 0.213753i) q^{26} +(7.27689 + 4.20131i) q^{29} +1.19170i q^{31} +1.45351i q^{32} +(0.464883 + 0.268400i) q^{34} +(1.61626 + 2.79945i) q^{37} +(0.320962 + 0.555922i) q^{38} +(0.223540 + 0.129061i) q^{40} +(0.0994958 + 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} +(-7.22789 + 4.17303i) q^{44} +(-0.383865 + 0.664873i) q^{46} +9.97189 q^{47} +(-0.500069 + 0.288715i) q^{50} +(-3.46814 + 2.00233i) q^{52} +(-3.65249 - 2.10877i) q^{53} +2.22598i q^{55} +(-0.514008 + 0.890287i) q^{58} -13.4392 q^{59} -13.1132i q^{61} -0.145798 q^{62} +7.64300 q^{64} +1.06809i q^{65} -6.58003 q^{67} +(4.35478 - 7.54270i) q^{68} -8.50587i q^{71} +(-4.86015 - 2.80601i) q^{73} +(-0.342497 + 0.197741i) q^{74} +(9.01980 - 5.20758i) q^{76} +0.572684 q^{79} +(1.03514 - 1.79292i) q^{80} +(-0.0210838 + 0.0121728i) q^{82} +(-5.42692 + 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +(0.839806 + 0.484862i) q^{86} +(-1.02494 - 1.77525i) q^{88} +(6.43688 + 11.1490i) q^{89} +(10.7875 + 6.22819i) q^{92} +1.22001i q^{94} -2.77784i q^{95} +(0.493773 + 0.285080i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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