LMFDB - Embedded newform 1323.2.o.e.440.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (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			440.19
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.e.881.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28562 + 0.742253i) q^{2} +(0.101880 + 0.176462i) q^{4} +(-0.154215 - 0.267109i) q^{5} -2.66653i q^{8} +O(q^{10})$	\(q+(1.28562 + 0.742253i) q^{2} +(0.101880 + 0.176462i) q^{4} +(-0.154215 - 0.267109i) q^{5} -2.66653i q^{8} -0.457868i q^{10} +(2.73879 + 1.58124i) q^{11} +(-3.00394 + 1.73432i) q^{13} +(2.18300 - 3.78107i) q^{16} +4.88248 q^{17} -5.34116i q^{19} +(0.0314230 - 0.0544262i) q^{20} +(2.34736 + 4.06575i) q^{22} +(5.17269 - 2.98645i) q^{23} +(2.45244 - 4.24774i) q^{25} -5.14923 q^{26} +(-2.70372 - 1.56099i) q^{29} +(-6.51414 + 3.76094i) q^{31} +(0.994457 - 0.574150i) q^{32} +(6.27702 + 3.62404i) q^{34} +11.8514 q^{37} +(3.96450 - 6.86671i) q^{38} +(-0.712254 + 0.411220i) q^{40} +(2.58920 + 4.48462i) q^{41} +(2.75159 - 4.76589i) q^{43} +0.644388i q^{44} +8.86682 q^{46} +(4.23198 - 7.33000i) q^{47} +(6.30580 - 3.64066i) q^{50} +(-0.612084 - 0.353387i) q^{52} +0.0855080i q^{53} -0.975406i q^{55} +(-2.31731 - 4.01369i) q^{58} +(-1.04433 - 1.80884i) q^{59} +(-4.69964 - 2.71334i) q^{61} -11.1663 q^{62} -7.02734 q^{64} +(0.926507 + 0.534919i) q^{65} +(0.0554134 + 0.0959787i) q^{67} +(0.497429 + 0.861572i) q^{68} +7.78899i q^{71} -9.61495i q^{73} +(15.2364 + 8.79672i) q^{74} +(0.942510 - 0.544159i) q^{76} +(-2.56825 + 4.44834i) q^{79} -1.34661 q^{80} +7.68736i q^{82} +(-4.42464 + 7.66370i) q^{83} +(-0.752954 - 1.30416i) q^{85} +(7.07500 - 4.08475i) q^{86} +(4.21642 - 7.30306i) q^{88} +1.87377 q^{89} +(1.05399 + 0.608521i) q^{92} +(10.8814 - 6.28240i) q^{94} +(-1.42667 + 0.823689i) q^{95} +(10.9813 + 6.34007i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.28562	+	0.742253i	0.909071	+	0.524852i	0.880132	−	0.474729i	$-0.157454\pi$
$2$	1.28562	+	0.742253i	0.909071	+	0.524852i	0.0289389	+	0.999581i	$0.490787\pi$
$3$		0			0
$3$		0			0
$4$	0.101880	+	0.176462i	0.0509401	+	0.0882308i
$5$	−0.154215	−	0.267109i	−0.0689672	−	0.119455i	0.829480	−	0.558537i	$-0.188637\pi$
$5$	−0.154215	−	0.267109i	−0.0689672	−	0.119455i	−0.898447	+	0.439082i	$0.855304\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	2.66653i		−	0.942761i
$9$		0			0
$10$		−	0.457868i		−	0.144790i
$11$	2.73879	+	1.58124i	0.825775	+	0.476761i	0.852404	−	0.522884i	$-0.175144\pi$
$11$	2.73879	+	1.58124i	0.825775	+	0.476761i	−0.0266288	+	0.999645i	$0.508477\pi$
$12$		0			0
$13$	−3.00394	+	1.73432i	−0.833143	+	0.481015i	−0.854927	−	0.518748i	$-0.826398\pi$
$13$	−3.00394	+	1.73432i	−0.833143	+	0.481015i	0.0217849	+	0.999763i	$0.493065\pi$
$14$		0			0
$15$		0			0
$16$	2.18300	−	3.78107i	0.545750	−	0.945267i
$17$	4.88248			1.18418			0.592088	−	0.805873i	$-0.298304\pi$
$17$	4.88248			1.18418			0.592088	+	0.805873i	$0.298304\pi$
$18$		0			0
$19$		−	5.34116i		−	1.22535i	−0.790336	−	0.612673i	$-0.790094\pi$
$19$		−	5.34116i		−	1.22535i	0.790336	−	0.612673i	$-0.209906\pi$
$20$	0.0314230	−	0.0544262i	0.00702639	−	0.0121701i
$21$		0			0
$22$	2.34736	+	4.06575i	0.500459	+	0.866820i
$23$	5.17269	−	2.98645i	1.07858	−	0.622719i	0.148067	−	0.988977i	$-0.452695\pi$
$23$	5.17269	−	2.98645i	1.07858	−	0.622719i	0.930513	+	0.366259i	$0.119361\pi$
$24$		0			0
$25$	2.45244	−	4.24774i	0.490487	−	0.849548i
$26$	−5.14923			−1.00985
$27$		0			0
$28$		0			0
$29$	−2.70372	−	1.56099i	−0.502069	−	0.289869i	0.227499	−	0.973778i	$-0.426945\pi$
$29$	−2.70372	−	1.56099i	−0.502069	−	0.289869i	−0.729567	+	0.683909i	$0.760279\pi$
$30$		0			0
$31$	−6.51414	+	3.76094i	−1.16997	+	0.675485i	−0.953674	−	0.300842i	$-0.902732\pi$
$31$	−6.51414	+	3.76094i	−1.16997	+	0.675485i	−0.216300	+	0.976327i	$0.569399\pi$
$32$	0.994457	−	0.574150i	0.175797	−	0.101496i
$33$		0			0
$34$	6.27702	+	3.62404i	1.07650	+	0.621518i
$35$		0			0
$36$		0			0
$37$	11.8514			1.94835			0.974176	−	0.225788i	$-0.0724957\pi$
$37$	11.8514			1.94835			0.974176	+	0.225788i	$0.0724957\pi$
$38$	3.96450	−	6.86671i	0.643126	−	1.11393i
$39$		0			0
$40$	−0.712254	+	0.411220i	−0.112617	+	0.0650196i
$41$	2.58920	+	4.48462i	0.404365	+	0.700380i	0.994247	−	0.107109i	$-0.0341593\pi$
$41$	2.58920	+	4.48462i	0.404365	+	0.700380i	−0.589883	+	0.807489i	$0.700826\pi$
$42$		0			0
$43$	2.75159	−	4.76589i	0.419613	−	0.726792i	−0.576287	−	0.817247i	$-0.695499\pi$
$43$	2.75159	−	4.76589i	0.419613	−	0.726792i	0.995900	+	0.0904557i	$0.0288323\pi$
$44$			0.644388i			0.0971451i
$45$		0			0
$46$	8.86682			1.30734
$47$	4.23198	−	7.33000i	0.617298	−	1.06919i	−0.372679	−	0.927960i	$-0.621561\pi$
$47$	4.23198	−	7.33000i	0.617298	−	1.06919i	0.989977	−	0.141231i	$-0.0451059\pi$
$48$		0			0
$49$		0			0
$50$	6.30580	−	3.64066i	0.891775	−	0.514867i
$51$		0			0
$52$	−0.612084	−	0.353387i	−0.0848807	−	0.0490059i
$53$			0.0855080i			0.0117454i	0.999983	+	0.00587272i	$0.00186935\pi$
$53$			0.0855080i			0.0117454i	−0.999983	+	0.00587272i	$0.998131\pi$
$54$		0			0
$55$		−	0.975406i		−	0.131524i
$56$		0			0
$57$		0			0
$58$	−2.31731	−	4.01369i	−0.304277	−	0.527024i
$59$	−1.04433	−	1.80884i	−0.135960	−	0.235490i	0.790004	−	0.613102i	$-0.210079\pi$
$59$	−1.04433	−	1.80884i	−0.135960	−	0.235490i	−0.925964	+	0.377612i	$0.876745\pi$
$60$		0			0
$61$	−4.69964	−	2.71334i	−0.601727	−	0.347407i	0.167994	−	0.985788i	$-0.446271\pi$
$61$	−4.69964	−	2.71334i	−0.601727	−	0.347407i	−0.769721	+	0.638381i	$0.779604\pi$
$62$	−11.1663			−1.41812
$63$		0			0
$64$	−7.02734			−0.878418
$65$	0.926507	+	0.534919i	0.114919	+	0.0663485i
$66$		0			0
$67$	0.0554134	+	0.0959787i	0.00676982	+	0.0117257i	0.869390	−	0.494126i	$-0.164512\pi$
$67$	0.0554134	+	0.0959787i	0.00676982	+	0.0117257i	−0.862621	+	0.505851i	$0.831178\pi$
$68$	0.497429	+	0.861572i	0.0603221	+	0.104481i
$69$		0			0
$70$		0			0
$71$			7.78899i			0.924384i	0.886780	+	0.462192i	$0.152937\pi$
$71$			7.78899i			0.924384i	−0.886780	+	0.462192i	$0.847063\pi$
$72$		0			0
$73$		−	9.61495i		−	1.12534i	−0.826680	−	0.562672i	$-0.809773\pi$
$73$		−	9.61495i		−	1.12534i	0.826680	−	0.562672i	$-0.190227\pi$
$74$	15.2364	+	8.79672i	1.77119	+	1.02260i
$75$		0			0
$76$	0.942510	−	0.544159i	0.108113	−	0.0624193i
$77$		0			0
$78$		0			0
$79$	−2.56825	+	4.44834i	−0.288951	+	0.500477i	−0.973560	−	0.228433i	$-0.926640\pi$
$79$	−2.56825	+	4.44834i	−0.288951	+	0.500477i	0.684609	+	0.728911i	$0.259973\pi$
$80$	−1.34661			−0.150556
$81$		0			0
$82$			7.68736i			0.848927i
$83$	−4.42464	+	7.66370i	−0.485667	+	0.841201i	−0.999864	−	0.0164715i	$-0.994757\pi$
$83$	−4.42464	+	7.66370i	−0.485667	+	0.841201i	0.514197	+	0.857672i	$0.328090\pi$
$84$		0			0
$85$	−0.752954	−	1.30416i	−0.0816694	−	0.141455i
$86$	7.07500	−	4.08475i	0.762917	−	0.440470i
$87$		0			0
$88$	4.21642	−	7.30306i	0.449472	−	0.778508i
$89$	1.87377			0.198619			0.0993096	−	0.995057i	$-0.468337\pi$
$89$	1.87377			0.198619			0.0993096	+	0.995057i	$0.468337\pi$
$90$		0			0
$91$		0			0
$92$	1.05399	+	0.608521i	0.109886	+	0.0634427i
$93$		0			0
$94$	10.8814	−	6.28240i	1.12233	−	0.647980i
$95$	−1.42667	+	0.823689i	−0.146373	+	0.0845087i
$96$		0			0
$97$	10.9813	+	6.34007i	1.11498	+	0.643736i	0.940116	−	0.340855i	$-0.110717\pi$
$97$	10.9813	+	6.34007i	1.11498	+	0.643736i	0.174868	+	0.984592i	$0.444050\pi$
$98$		0			0
$99$		0			0
$100$	0.999418			0.0999418
$101$	−3.68322	+	6.37952i	−0.366494	+	0.634786i	−0.989015	−	0.147817i	$-0.952775\pi$
$101$	−3.68322	+	6.37952i	−0.366494	+	0.634786i	0.622521	+	0.782603i	$0.286109\pi$
$102$		0			0
$103$	6.91120	−	3.99019i	0.680981	−	0.393165i	−0.119244	−	0.992865i	$-0.538047\pi$
$103$	6.91120	−	3.99019i	0.680981	−	0.393165i	0.800225	+	0.599700i	$0.204714\pi$
$104$	4.62463	+	8.01009i	0.453482	+	0.785454i
$105$		0			0
$106$	−0.0634686	+	0.109931i	−0.00616462	+	0.0106774i
$107$			16.7694i			1.62116i	0.585625	+	0.810582i	$0.300849\pi$
$107$			16.7694i			1.62116i	−0.585625	+	0.810582i	$0.699151\pi$
$108$		0			0
$109$	−8.86509			−0.849122			−0.424561	−	0.905399i	$-0.639572\pi$
$109$	−8.86509			−0.849122			−0.424561	+	0.905399i	$0.639572\pi$
$110$	0.723998	−	1.25400i	0.0690305	−	0.119564i
$111$		0			0
$112$		0			0
$113$	−13.5621	+	7.83007i	−1.27581	+	0.736591i	−0.976076	−	0.217430i	$-0.930233\pi$
$113$	−13.5621	+	7.83007i	−1.27581	+	0.736591i	−0.299738	+	0.954022i	$0.596899\pi$
$114$		0			0
$115$	−1.59542	−	0.921114i	−0.148773	−	0.0858943i
$116$		−	0.636138i		−	0.0590639i
$117$		0			0
$118$		−	3.10063i		−	0.285437i
$119$		0			0
$120$		0			0
$121$	−0.499366	−	0.864928i	−0.0453969	−	0.0786298i
$122$	−4.02797	−	6.97664i	−0.364675	−	0.631635i
$123$		0			0
$124$	−1.32732	−	0.766330i	−0.119197	−	0.0688185i
$125$	−3.05497			−0.273245
$126$		0			0
$127$	−6.78064			−0.601685			−0.300842	−	0.953674i	$-0.597268\pi$
$127$	−6.78064			−0.601685			−0.300842	+	0.953674i	$0.597268\pi$
$128$	−11.0234	−	6.36437i	−0.974341	−	0.562536i
$129$		0			0
$130$	0.794091	+	1.37541i	0.0696464	+	0.120631i
$131$	9.77105	+	16.9240i	0.853701	+	1.47865i	0.877845	+	0.478944i	$0.158980\pi$
$131$	9.77105	+	16.9240i	0.853701	+	1.47865i	−0.0241447	+	0.999708i	$0.507686\pi$
$132$		0			0
$133$		0			0
$134$			0.164523i			0.0142126i
$135$		0			0
$136$		−	13.0193i		−	1.11640i
$137$	1.37570	+	0.794262i	0.117534	+	0.0678584i	0.557615	−	0.830100i	$-0.311717\pi$
$137$	1.37570	+	0.794262i	0.117534	+	0.0678584i	−0.440080	+	0.897958i	$0.645050\pi$
$138$		0			0
$139$	−3.97274	+	2.29366i	−0.336963	+	0.194546i	−0.658928	−	0.752206i	$-0.728990\pi$
$139$	−3.97274	+	2.29366i	−0.336963	+	0.194546i	0.321965	+	0.946752i	$0.395657\pi$
$140$		0			0
$141$		0			0
$142$	−5.78141	+	10.0137i	−0.485165	+	0.840330i
$143$	−10.9695			−0.917318
$144$		0			0
$145$			0.962918i			0.0799660i
$146$	7.13673	−	12.3612i	0.590640	−	1.02302i
$147$		0			0
$148$	1.20742	+	2.09131i	0.0992493	+	0.171905i
$149$	−8.42966	+	4.86686i	−0.690584	+	0.398709i	−0.803831	−	0.594858i	$-0.797208\pi$
$149$	−8.42966	+	4.86686i	−0.690584	+	0.398709i	0.113247	+	0.993567i	$0.463875\pi$
$150$		0			0
$151$	3.00916	−	5.21203i	0.244882	−	0.424149i	−0.717216	−	0.696851i	$-0.754584\pi$
$151$	3.00916	−	5.21203i	0.244882	−	0.424149i	0.962099	+	0.272702i	$0.0879173\pi$
$152$	−14.2424			−1.15521
$153$		0			0
$154$		0			0
$155$	2.00916	+	1.15999i	0.161380	+	0.0931726i
$156$		0			0
$157$	−14.1600	+	8.17531i	−1.13009	+	0.652461i	−0.943959	−	0.330063i	$-0.892930\pi$
$157$	−14.1600	+	8.17531i	−1.13009	+	0.652461i	−0.186136	+	0.982524i	$0.559597\pi$
$158$	−6.60359	+	3.81258i	−0.525353	+	0.303313i
$159$		0			0
$160$	−0.306721	−	0.177086i	−0.0242484	−	0.0139998i
$161$		0			0
$162$		0			0
$163$	−6.46471			−0.506355			−0.253177	−	0.967420i	$-0.581476\pi$
$163$	−6.46471			−0.506355			−0.253177	+	0.967420i	$0.581476\pi$
$164$	−0.527576	+	0.913788i	−0.0411968	+	0.0713549i
$165$		0			0
$166$	−11.3768	+	6.56841i	−0.883012	+	0.509807i
$167$	1.33556	+	2.31325i	0.103348	+	0.179005i	0.913062	−	0.407820i	$-0.133711\pi$
$167$	1.33556	+	2.31325i	0.103348	+	0.179005i	−0.809714	+	0.586825i	$0.800378\pi$
$168$		0			0
$169$	−0.484236	+	0.838722i	−0.0372489	+	0.0645171i
$170$		−	2.23553i		−	0.171457i
$171$		0			0
$172$	1.12133			0.0855006
$173$	10.0983	−	17.4908i	0.767760	−	1.32980i	−0.171015	−	0.985268i	$-0.554705\pi$
$173$	10.0983	−	17.4908i	0.767760	−	1.32980i	0.938775	−	0.344531i	$-0.111962\pi$
$174$		0			0
$175$		0			0
$176$	11.9575	−	6.90369i	0.901334	−	0.520385i
$177$		0			0
$178$	2.40896	+	1.39081i	0.180559	+	0.104246i
$179$		−	21.9622i		−	1.64153i	−0.571266	−	0.820765i	$-0.693548\pi$
$179$		−	21.9622i		−	1.64153i	0.571266	−	0.820765i	$-0.306452\pi$
$180$		0			0
$181$		−	2.50569i		−	0.186246i	−0.995655	−	0.0931232i	$-0.970315\pi$
$181$		−	2.50569i		−	0.186246i	0.995655	−	0.0931232i	$-0.0296850\pi$
$182$		0			0
$183$		0			0
$184$	−7.96347	−	13.7931i	−0.587075	−	1.01684i
$185$	−1.82766	−	3.16561i	−0.134372	−	0.232740i
$186$		0			0
$187$	13.3721	+	7.72038i	0.977864	+	0.564570i
$188$	1.72462			0.125781
$189$		0			0
$190$	−2.44554			−0.177418
$191$	1.82276	+	1.05237i	0.131891	+	0.0761470i	0.564494	−	0.825437i	$-0.309071\pi$
$191$	1.82276	+	1.05237i	0.131891	+	0.0761470i	−0.432603	+	0.901584i	$0.642405\pi$
$192$		0			0
$193$	2.97730	+	5.15683i	0.214311	+	0.371197i	0.953059	−	0.302784i	$-0.0979162\pi$
$193$	2.97730	+	5.15683i	0.214311	+	0.371197i	−0.738748	+	0.673981i	$0.764583\pi$
$194$	9.41187	+	16.3018i	0.675733	+	1.17040i
$195$		0			0
$196$		0			0
$197$			7.64511i			0.544692i	0.962199	+	0.272346i	$0.0877995\pi$
$197$			7.64511i			0.544692i	−0.962199	+	0.272346i	$0.912200\pi$
$198$		0			0
$199$			6.85193i			0.485720i	0.970061	+	0.242860i	$0.0780856\pi$
$199$			6.85193i			0.485720i	−0.970061	+	0.242860i	$0.921914\pi$
$200$	−11.3267	−	6.53949i	−0.800921	−	0.462412i
$201$		0			0
$202$	−9.47044	+	5.46776i	−0.666338	+	0.384710i
$203$		0			0
$204$		0			0
$205$	0.798588	−	1.38320i	0.0557758	−	0.0966066i
$206$	11.8469			0.825414
$207$		0			0
$208$			15.1441i			1.05006i
$209$	8.44565	−	14.6283i	0.584198	−	1.01186i
$210$		0			0
$211$	−2.74784	−	4.75940i	−0.189169	−	0.327651i	0.755804	−	0.654798i	$-0.227246\pi$
$211$	−2.74784	−	4.75940i	−0.189169	−	0.327651i	−0.944974	+	0.327147i	$0.893913\pi$
$212$	−0.0150889	+	0.00871157i	−0.00103631	+	0.000598313i
$213$		0			0
$214$	−12.4472	+	21.5591i	−0.850872	+	1.47375i
$215$	−1.69735			−0.115758
$216$		0			0
$217$		0			0
$218$	−11.3971	−	6.58015i	−0.771912	−	0.445664i
$219$		0			0
$220$	0.172122	−	0.0993745i	0.0116044	−	0.00669983i
$221$	−14.6667	+	8.46781i	−0.986588	+	0.569607i
$222$		0			0
$223$	−17.6080	−	10.1660i	−1.17912	−	0.680764i	−0.223307	−	0.974748i	$-0.571685\pi$
$223$	−17.6080	−	10.1660i	−1.17912	−	0.680764i	−0.955810	+	0.293985i	$0.905019\pi$
$224$		0			0
$225$		0			0
$226$	−23.2476			−1.54641
$227$	0.161235	−	0.279268i	0.0107016	−	0.0185356i	−0.860625	−	0.509239i	$-0.829927\pi$
$227$	0.161235	−	0.279268i	0.0107016	−	0.0185356i	0.871327	+	0.490704i	$0.163260\pi$
$228$		0			0
$229$	2.30171	−	1.32889i	0.152101	−	0.0878157i	−0.422018	−	0.906588i	$-0.638678\pi$
$229$	2.30171	−	1.32889i	0.152101	−	0.0878157i	0.574119	+	0.818772i	$0.305345\pi$
$230$	−1.36740	−	2.36841i	−0.0901637	−	0.156168i
$231$		0			0
$232$	−4.16244	+	7.20956i	−0.273278	+	0.473331i
$233$			23.2575i			1.52365i	0.647785	+	0.761823i	$0.275696\pi$
$233$			23.2575i			1.52365i	−0.647785	+	0.761823i	$0.724304\pi$
$234$		0			0
$235$	−2.61055			−0.170293
$236$	0.212793	−	0.368569i	0.0138517	−	0.0239918i
$237$		0			0
$238$		0			0
$239$	0.291265	−	0.168162i	0.0188404	−	0.0108775i	−0.490550	−	0.871413i	$-0.663204\pi$
$239$	0.291265	−	0.168162i	0.0188404	−	0.0108775i	0.509391	+	0.860535i	$0.329871\pi$
$240$		0			0
$241$	19.1846	+	11.0762i	1.23579	+	0.713483i	0.968231	−	0.250059i	$-0.0804500\pi$
$241$	19.1846	+	11.0762i	1.23579	+	0.713483i	0.267558	+	0.963542i	$0.413783\pi$
$242$		−	1.48263i		−	0.0953068i
$243$		0			0
$244$		−	1.10574i		−	0.0707878i
$245$		0			0
$246$		0			0
$247$	9.26331	+	16.0445i	0.589410	+	1.02089i
$248$	10.0287	+	17.3701i	0.636820	+	1.10301i
$249$		0			0
$250$	−3.92753	−	2.26756i	−0.248399	−	0.143413i
$251$	13.9800			0.882409			0.441205	−	0.897407i	$-0.354551\pi$
$251$	13.9800			0.882409			0.441205	+	0.897407i	$0.354551\pi$
$252$		0			0
$253$	18.8892			1.18755
$254$	−8.71734	−	5.03296i	−0.546974	−	0.315796i
$255$		0			0
$256$	−2.42061	−	4.19261i	−0.151288	−	0.262038i
$257$	−9.69064	−	16.7847i	−0.604486	−	1.04700i	−0.992133	−	0.125192i	$-0.960045\pi$
$257$	−9.69064	−	16.7847i	−0.604486	−	1.04700i	0.387647	−	0.921808i	$-0.373288\pi$
$258$		0			0
$259$		0			0
$260$			0.217991i			0.0135192i
$261$		0			0
$262$			29.0104i			1.79227i
$263$	−4.40776	−	2.54482i	−0.271794	−	0.156920i	0.357909	−	0.933757i	$-0.383490\pi$
$263$	−4.40776	−	2.54482i	−0.271794	−	0.156920i	−0.629703	+	0.776836i	$0.716823\pi$
$264$		0			0
$265$	0.0228400	−	0.0131867i	0.00140305	−	0.000810050i
$266$		0			0
$267$		0			0
$268$	−0.0112910	+	0.0195567i	−0.000689710	+	0.00119461i
$269$	−5.05601			−0.308270			−0.154135	−	0.988050i	$-0.549259\pi$
$269$	−5.05601			−0.308270			−0.154135	+	0.988050i	$0.549259\pi$
$270$		0			0
$271$		−	31.3809i		−	1.90626i	−0.302567	−	0.953128i	$-0.597844\pi$
$271$		−	31.3809i		−	1.90626i	0.302567	−	0.953128i	$-0.402156\pi$
$272$	10.6585	−	18.4610i	0.646265	−	1.11936i
$273$		0			0
$274$	1.17909	+	2.04224i	0.0712313	+	0.123376i
$275$	13.4334	−	7.75577i	0.810064	−	0.467691i
$276$		0			0
$277$	−13.0279	+	22.5650i	−0.782771	+	1.35580i	0.147551	+	0.989054i	$0.452861\pi$
$277$	−13.0279	+	22.5650i	−0.782771	+	1.35580i	−0.930322	+	0.366744i	$0.880473\pi$
$278$	−6.80991			−0.408431
$279$		0			0
$280$		0			0
$281$	4.14335	+	2.39217i	0.247172	+	0.142705i	0.618469	−	0.785810i	$-0.287753\pi$
$281$	4.14335	+	2.39217i	0.247172	+	0.142705i	−0.371297	+	0.928514i	$0.621087\pi$
$282$		0			0
$283$	−0.927241	+	0.535343i	−0.0551188	+	0.0318228i	−0.527306	−	0.849675i	$-0.676798\pi$
$283$	−0.927241	+	0.535343i	−0.0551188	+	0.0318228i	0.472187	+	0.881498i	$0.343465\pi$
$284$	−1.37446	+	0.793544i	−0.0815591	+	0.0470882i
$285$		0			0
$286$	−14.1026	−	8.14217i	−0.833907	−	0.481457i
$287$		0			0
$288$		0			0
$289$	6.83866			0.402274
$290$	−0.714729	+	1.23795i	−0.0419703	+	0.0726947i
$291$		0			0
$292$	1.69667	−	0.979573i	0.0992901	−	0.0573252i
$293$	−1.36267	−	2.36021i	−0.0796079	−	0.137885i	0.823473	−	0.567356i	$-0.192033\pi$
$293$	−1.36267	−	2.36021i	−0.0796079	−	0.137885i	−0.903081	+	0.429471i	$0.858700\pi$
$294$		0			0
$295$	−0.322104	+	0.557900i	−0.0187536	+	0.0324822i
$296$		−	31.6020i		−	1.83683i
$297$		0			0
$298$	−14.4498			−0.837054
$299$	−10.3590	+	17.9422i	−0.599074	+	1.03763i
$300$		0			0
$301$		0			0
$302$	7.73729	−	4.46713i	0.445231	−	0.257054i
$303$		0			0
$304$	−20.1953	−	11.6598i	−1.15828	−	0.668733i
$305$			1.67375i			0.0958388i
$306$		0			0
$307$		−	8.31294i		−	0.474444i	−0.971455	−	0.237222i	$-0.923763\pi$
$307$		−	8.31294i		−	0.474444i	0.971455	−	0.237222i	$-0.0762369\pi$
$308$		0			0
$309$		0			0
$310$	1.72201	+	2.98261i	0.0978037	+	0.169401i
$311$	3.00023	+	5.19656i	0.170128	+	0.294670i	0.938464	−	0.345376i	$-0.112249\pi$
$311$	3.00023	+	5.19656i	0.170128	+	0.294670i	−0.768337	+	0.640046i	$0.778915\pi$
$312$		0			0
$313$	10.2410	+	5.91263i	0.578854	+	0.334201i	0.760678	−	0.649130i	$-0.224867\pi$
$313$	10.2410	+	5.91263i	0.578854	+	0.334201i	−0.181824	+	0.983331i	$0.558200\pi$
$314$	−24.2726			−1.36978
$315$		0			0
$316$	−1.04662			−0.0588767
$317$	−25.6726	−	14.8221i	−1.44192	−	0.832491i	−0.443940	−	0.896057i	$-0.646420\pi$
$317$	−25.6726	−	14.8221i	−1.44192	−	0.832491i	−0.997978	+	0.0635652i	$0.979753\pi$
$318$		0			0
$319$	−4.93661	−	8.55046i	−0.276397	−	0.478734i
$320$	1.08372	+	1.87707i	0.0605821	+	0.104931i
$321$		0			0
$322$		0			0
$323$		−	26.0781i		−	1.45103i
$324$		0			0
$325$			17.0133i			0.943727i
$326$	−8.31116	−	4.79845i	−0.460313	−	0.265762i
$327$		0			0
$328$	11.9584	−	6.90417i	0.660291	−	0.381219i
$329$		0			0
$330$		0			0
$331$	8.52504	−	14.7658i	0.468579	−	0.811602i	−0.530776	−	0.847512i	$-0.678100\pi$
$331$	8.52504	−	14.7658i	0.468579	−	0.811602i	0.999355	+	0.0359097i	$0.0114329\pi$
$332$	−1.80313			−0.0989598
$333$		0			0
$334$			3.96529i			0.216971i
$335$	0.0170912	−	0.0296028i	0.000933791	−	0.00161737i
$336$		0			0
$337$	10.1065	+	17.5050i	0.550536	+	0.953556i	0.998236	+	0.0593723i	$0.0189099\pi$
$337$	10.1065	+	17.5050i	0.550536	+	0.953556i	−0.447700	+	0.894184i	$0.647757\pi$
$338$	−1.24509	+	0.718852i	−0.0677239	+	0.0391004i
$339$		0			0
$340$	0.153422	−	0.265735i	0.00832049	−	0.0144115i
$341$	−23.7878			−1.28818
$342$		0			0
$343$		0			0
$344$	−12.7084	−	7.33719i	−0.685191	−	0.395595i
$345$		0			0
$346$	25.9652	−	14.9910i	1.39590	−	0.805921i
$347$	−15.3128	+	8.84086i	−0.822036	+	0.474602i	−0.851118	−	0.524975i	$-0.824075\pi$
$347$	−15.3128	+	8.84086i	−0.822036	+	0.474602i	0.0290824	+	0.999577i	$0.490741\pi$
$348$		0			0
$349$	−3.62628	−	2.09363i	−0.194110	−	0.112070i	0.399795	−	0.916605i	$-0.369081\pi$
$349$	−3.62628	−	2.09363i	−0.194110	−	0.112070i	−0.593905	+	0.804535i	$0.702415\pi$
$350$		0			0
$351$		0			0
$352$	3.63148			0.193558
$353$	−15.2477	+	26.4097i	−0.811551	+	1.40565i	0.100227	+	0.994965i	$0.468043\pi$
$353$	−15.2477	+	26.4097i	−0.811551	+	1.40565i	−0.911778	+	0.410684i	$0.865290\pi$
$354$		0			0
$355$	2.08051	−	1.20118i	0.110422	−	0.0637522i
$356$	0.190900	+	0.330649i	0.0101177	+	0.0175243i
$357$		0			0
$358$	16.3015	−	28.2350i	0.861561	−	1.49227i
$359$		−	5.39131i		−	0.284542i	−0.989828	−	0.142271i	$-0.954559\pi$
$359$		−	5.39131i		−	0.284542i	0.989828	−	0.142271i	$-0.0454405\pi$
$360$		0			0
$361$	−9.52801			−0.501474
$362$	1.85986	−	3.22137i	0.0977519	−	0.169311i
$363$		0			0
$364$		0			0
$365$	−2.56824	+	1.48277i	−0.134428	+	0.0776119i
$366$		0			0
$367$	17.3218	+	10.0007i	0.904188	+	0.522033i	0.878557	−	0.477638i	$-0.158507\pi$
$367$	17.3218	+	10.0007i	0.904188	+	0.522033i	0.0256317	+	0.999671i	$0.491840\pi$
$368$		−	26.0777i		−	1.35940i
$369$		0			0
$370$		−	5.42636i		−	0.282103i
$371$		0			0
$372$		0			0
$373$	13.0474	+	22.5988i	0.675571	+	1.17012i	0.976302	+	0.216414i	$0.0694363\pi$
$373$	13.0474	+	22.5988i	0.675571	+	1.17012i	−0.300730	+	0.953709i	$0.597230\pi$
$374$	11.4609	+	19.8509i	0.592632	+	1.02647i
$375$		0			0
$376$	−19.5457	−	11.2847i	−1.00799	−	0.581964i
$377$	10.8291			0.557726
$378$		0			0
$379$	30.5222			1.56782			0.783910	−	0.620875i	$-0.213222\pi$
$379$	30.5222			1.56782			0.783910	+	0.620875i	$0.213222\pi$
$380$	−0.290699	−	0.167835i	−0.0149126	−	0.00860977i
$381$		0			0
$382$	1.56225	+	2.70590i	0.0799319	+	0.138446i
$383$	11.3543	+	19.6662i	0.580177	+	1.00490i	0.995458	+	0.0952034i	$0.0303501\pi$
$383$	11.3543	+	19.6662i	0.580177	+	1.00490i	−0.415280	+	0.909693i	$0.636317\pi$
$384$		0			0
$385$		0			0
$386$			8.83964i			0.449926i
$387$		0			0
$388$			2.58371i			0.131168i
$389$	3.89121	+	2.24659i	0.197292	+	0.113907i	0.595392	−	0.803436i	$-0.296997\pi$
$389$	3.89121	+	2.24659i	0.197292	+	0.113907i	−0.398100	+	0.917342i	$0.630330\pi$
$390$		0			0
$391$	25.2556	−	14.5813i	1.27723	−	0.737409i
$392$		0			0
$393$		0			0
$394$	−5.67461	+	9.82872i	−0.285883	+	0.495164i
$395$	1.58425			0.0797125
$396$		0			0
$397$			9.65161i			0.484400i	0.970226	+	0.242200i	$0.0778691\pi$
$397$			9.65161i			0.484400i	−0.970226	+	0.242200i	$0.922131\pi$
$398$	−5.08587	+	8.80898i	−0.254931	+	0.441554i
$399$		0			0
$400$	−10.7073	−	18.5457i	−0.535367	−	0.927283i
$401$	17.2356	−	9.95098i	0.860705	−	0.496928i	−0.00354346	−	0.999994i	$-0.501128\pi$
$401$	17.2356	−	9.95098i	0.860705	−	0.496928i	0.864248	+	0.503066i	$0.167795\pi$
$402$		0			0
$403$	13.0454	−	22.5953i	0.649837	−	1.12555i
$404$	−1.50099			−0.0746769
$405$		0			0
$406$		0			0
$407$	32.4584	+	18.7398i	1.60890	+	0.928900i
$408$		0			0
$409$	2.10072	−	1.21285i	0.103874	−	0.0599718i	−0.447163	−	0.894453i	$-0.647566\pi$
$409$	2.10072	−	1.21285i	0.103874	−	0.0599718i	0.551037	+	0.834481i	$0.314232\pi$
$410$	2.05336	−	1.18551i	0.101408	−	0.0585482i
$411$		0			0
$412$	1.40823	+	0.813042i	0.0693785	+	0.0400557i
$413$		0			0
$414$		0			0
$415$	2.72939			0.133981
$416$	−1.99153	+	3.44942i	−0.0976426	+	0.169122i
$417$		0			0
$418$	21.7158	−	12.5376i	1.06216	−	0.613236i
$419$	−14.6878	−	25.4399i	−0.717544	−	1.24282i	−0.961970	−	0.273155i	$-0.911933\pi$
$419$	−14.6878	−	25.4399i	−0.717544	−	1.24282i	0.244426	−	0.969668i	$-0.421400\pi$
$420$		0			0
$421$	−18.2078	+	31.5368i	−0.887392	+	1.53701i	−0.0444443	+	0.999012i	$0.514152\pi$
$421$	−18.2078	+	31.5368i	−0.887392	+	1.53701i	−0.842948	+	0.537996i	$0.819182\pi$
$422$		−	8.15838i		−	0.397144i
$423$		0			0
$424$	0.228010			0.0110731
$425$	11.9740	−	20.7395i	0.580823	−	1.00602i
$426$		0			0
$427$		0			0
$428$	−2.95916	+	1.70847i	−0.143037	+	0.0825822i
$429$		0			0
$430$	−2.18215	−	1.25986i	−0.105232	−	0.0607560i
$431$			19.4520i			0.936968i	0.883472	+	0.468484i	$0.155200\pi$
$431$			19.4520i			0.936968i	−0.883472	+	0.468484i	$0.844800\pi$
$432$		0			0
$433$			9.94623i			0.477985i	0.971021	+	0.238993i	$0.0768172\pi$
$433$			9.94623i			0.477985i	−0.971021	+	0.238993i	$0.923183\pi$
$434$		0			0
$435$		0			0
$436$	−0.903178	−	1.56435i	−0.0432544	−	0.0749188i
$437$	−15.9511	−	27.6282i	−0.763046	−	1.32163i
$438$		0			0
$439$	−6.38746	−	3.68780i	−0.304857	−	0.176009i	0.339766	−	0.940510i	$-0.389652\pi$
$439$	−6.38746	−	3.68780i	−0.304857	−	0.176009i	−0.644623	+	0.764501i	$0.722986\pi$
$440$	−2.60095			−0.123995
$441$		0			0
$442$	−25.1411			−1.19584
$443$	−0.744629	−	0.429911i	−0.0353784	−	0.0204257i	0.482207	−	0.876058i	$-0.339835\pi$
$443$	−0.744629	−	0.429911i	−0.0353784	−	0.0204257i	−0.517585	+	0.855632i	$0.673169\pi$
$444$		0			0
$445$	−0.288964	−	0.500501i	−0.0136982	−	0.0237260i
$446$	−15.0914	−	26.1392i	−0.714601	−	1.23772i
$447$		0			0
$448$		0			0
$449$			15.6497i			0.738556i	0.929319	+	0.369278i	$0.120395\pi$
$449$			15.6497i			0.738556i	−0.929319	+	0.369278i	$0.879605\pi$
$450$		0			0
$451$			16.3766i			0.771142i
$452$	−2.76342	−	1.59546i	−0.129980	−	0.0750441i
$453$		0			0
$454$	0.414575	−	0.239355i	0.0194570	−	0.0112335i
$455$		0			0
$456$		0			0
$457$	2.81559	−	4.87675i	0.131708	−	0.228125i	−0.792627	−	0.609707i	$-0.791287\pi$
$457$	2.81559	−	4.87675i	0.131708	−	0.228125i	0.924335	+	0.381582i	$0.124621\pi$
$458$	3.94550			0.184361
$459$		0			0
$460$		−	0.375373i		−	0.0175019i
$461$	−11.3342	+	19.6314i	−0.527886	+	0.914326i	0.471585	+	0.881821i	$0.343682\pi$
$461$	−11.3342	+	19.6314i	−0.527886	+	0.914326i	−0.999472	+	0.0325056i	$0.989651\pi$
$462$		0			0
$463$	−21.0052	−	36.3821i	−0.976194	−	1.69082i	−0.675937	−	0.736960i	$-0.736261\pi$
$463$	−21.0052	−	36.3821i	−0.976194	−	1.69082i	−0.300257	−	0.953858i	$-0.597073\pi$
$464$	−11.8045	+	6.81531i	−0.548008	+	0.316393i
$465$		0			0
$466$	−17.2629	+	29.9003i	−0.799690	+	1.38510i
$467$	24.8033			1.14776			0.573879	−	0.818940i	$-0.305438\pi$
$467$	24.8033			1.14776			0.573879	+	0.818940i	$0.305438\pi$
$468$		0			0
$469$		0			0
$470$	−3.35617	−	1.93769i	−0.154809	−	0.0893788i
$471$		0			0
$472$	−4.82331	+	2.78474i	−0.222011	+	0.128178i
$473$	15.0720	−	8.70184i	0.693013	−	0.400111i
$474$		0			0
$475$	−22.6879	−	13.0989i	−1.04099	−	0.601017i
$476$		0			0
$477$		0			0
$478$	0.499275			0.0228363
$479$	1.64647	−	2.85177i	0.0752291	−	0.130301i	−0.825957	−	0.563733i	$-0.809365\pi$
$479$	1.64647	−	2.85177i	0.0752291	−	0.130301i	0.901186	+	0.433433i	$0.142698\pi$
$480$		0			0
$481$	−35.6008	+	20.5541i	−1.62326	+	0.937187i
$482$	16.4427	+	28.4797i	0.748946	+	1.29721i
$483$		0			0
$484$	0.101751	−	0.176238i	0.00462505	−	0.00801082i
$485$		−	3.91094i		−	0.177587i
$486$		0			0
$487$	10.4448			0.473299			0.236650	−	0.971595i	$-0.423951\pi$
$487$	10.4448			0.473299			0.236650	+	0.971595i	$0.423951\pi$
$488$	−7.23519	+	12.5317i	−0.327522	+	0.567284i
$489$		0			0
$490$		0			0
$491$	26.2797	−	15.1726i	1.18599	−	0.684731i	0.228596	−	0.973521i	$-0.426587\pi$
$491$	26.2797	−	15.1726i	1.18599	−	0.684731i	0.957392	+	0.288791i	$0.0932532\pi$
$492$		0			0
$493$	−13.2009	−	7.62153i	−0.594538	−	0.343257i
$494$			27.5029i			1.23741i
$495$		0			0
$496$			32.8405i			1.47458i
$497$		0			0
$498$		0			0
$499$	−0.984757	−	1.70565i	−0.0440838	−	0.0763554i	0.843142	−	0.537692i	$-0.180704\pi$
$499$	−0.984757	−	1.70565i	−0.0440838	−	0.0763554i	−0.887225	+	0.461336i	$0.847370\pi$
$500$	−0.311241	−	0.539085i	−0.0139191	−	0.0241086i
$501$		0			0
$502$	17.9730	+	10.3767i	0.802173	+	0.463135i
$503$	−17.3024			−0.771477			−0.385739	−	0.922608i	$-0.626053\pi$
$503$	−17.3024			−0.771477			−0.385739	+	0.922608i	$0.626053\pi$
$504$		0			0
$505$	2.27203			0.101104
$506$	24.2843	+	14.0206i	1.07957	+	0.623290i
$507$		0			0
$508$	−0.690813	−	1.19652i	−0.0306499	−	0.0530872i
$509$	−0.240892	−	0.417237i	−0.0106774	−	0.0184937i	0.860637	−	0.509218i	$-0.170065\pi$
$509$	−0.240892	−	0.417237i	−0.0106774	−	0.0184937i	−0.871315	+	0.490725i	$0.836732\pi$
$510$		0			0
$511$		0			0
$512$			18.2707i			0.807457i
$513$		0			0
$514$		−	28.7717i		−	1.26906i
$515$	−2.13163	−	1.23070i	−0.0939307	−	0.0542309i
$516$		0			0
$517$	23.1810	−	13.3835i	1.01950	−	0.588607i
$518$		0			0
$519$		0			0
$520$	1.42638	−	2.47056i	0.0625508	−	0.108341i
$521$	14.4154			0.631550			0.315775	−	0.948834i	$-0.397735\pi$
$521$	14.4154			0.631550			0.315775	+	0.948834i	$0.397735\pi$
$522$		0			0
$523$			6.81956i			0.298198i	0.988822	+	0.149099i	$0.0476374\pi$
$523$			6.81956i			0.298198i	−0.988822	+	0.149099i	$0.952363\pi$
$524$	−1.99095	+	3.44843i	−0.0869752	+	0.150645i
$525$		0			0
$526$	−3.77780	−	6.54334i	−0.164720	−	0.285303i
$527$	−31.8052	+	18.3627i	−1.38546	+	0.799893i
$528$		0			0
$529$	6.33781	−	10.9774i	0.275557	−	0.477278i
$530$	0.0391514			0.00170063
$531$		0			0
$532$		0			0
$533$	−15.5556	−	8.98102i	−0.673787	−	0.389011i
$534$		0			0
$535$	4.47927	−	2.58611i	0.193656	−	0.111807i
$536$	0.255930	−	0.147761i	0.0110545	−	0.00638232i
$537$		0			0
$538$	−6.50011	−	3.75284i	−0.280240	−	0.161796i
$539$		0			0
$540$		0			0
$541$	−17.8226			−0.766252			−0.383126	−	0.923696i	$-0.625153\pi$
$541$	−17.8226			−0.766252			−0.383126	+	0.923696i	$0.625153\pi$
$542$	23.2926	−	40.3440i	1.00050	−	1.73292i
$543$		0			0
$544$	4.85542	−	2.80328i	0.208175	−	0.120190i
$545$	1.36713	+	2.36795i	0.0585616	+	0.101432i
$546$		0			0
$547$	−6.79325	+	11.7663i	−0.290458	+	0.503089i	−0.973918	−	0.226900i	$-0.927141\pi$
$547$	−6.79325	+	11.7663i	−0.290458	+	0.503089i	0.683460	+	0.729988i	$0.260474\pi$
$548$			0.323678i			0.0138268i
$549$		0			0
$550$	23.0270			0.981874
$551$	−8.33752	+	14.4410i	−0.355191	+	0.615208i
$552$		0			0
$553$		0			0
$554$	−33.4979	+	19.3400i	−1.42319	+	0.821678i
$555$		0			0
$556$	−0.809487	−	0.467357i	−0.0343299	−	0.0198204i
$557$		−	7.21412i		−	0.305672i	−0.988252	−	0.152836i	$-0.951159\pi$
$557$		−	7.21412i		−	0.305672i	0.988252	−	0.152836i	$-0.0488406\pi$
$558$		0			0
$559$			19.0886i			0.807361i
$560$		0			0
$561$		0			0
$562$	3.55119	+	6.15084i	0.149798	+	0.259457i
$563$	−11.5472	−	20.0004i	−0.486657	−	0.842915i	0.513225	−	0.858254i	$-0.328451\pi$
$563$	−11.5472	−	20.0004i	−0.486657	−	0.842915i	−0.999882	+	0.0153392i	$0.995117\pi$
$564$		0			0
$565$	4.18296	+	2.41504i	0.175979	+	0.101601i
$566$	−1.58944			−0.0668092
$567$		0			0
$568$	20.7696			0.871473
$569$	22.6039	+	13.0504i	0.947605	+	0.547100i	0.892336	−	0.451372i	$-0.149065\pi$
$569$	22.6039	+	13.0504i	0.947605	+	0.547100i	0.0552688	+	0.998472i	$0.482398\pi$
$570$		0			0
$571$	12.3318	+	21.3594i	0.516071	+	0.893862i	0.999826	+	0.0186582i	$0.00593945\pi$
$571$	12.3318	+	21.3594i	0.516071	+	0.893862i	−0.483754	+	0.875204i	$0.660727\pi$
$572$	−1.11758	−	1.93570i	−0.0467283	−	0.0809357i
$573$		0			0
$574$		0			0
$575$		−	29.2963i		−	1.22174i
$576$		0			0
$577$		−	19.3300i		−	0.804719i	−0.915482	−	0.402360i	$-0.868190\pi$
$577$		−	19.3300i		−	0.804719i	0.915482	−	0.402360i	$-0.131810\pi$
$578$	8.79192	+	5.07602i	0.365696	+	0.211135i
$579$		0			0
$580$	−0.169918	+	0.0981022i	−0.00705546	+	0.00407347i
$581$		0			0
$582$		0			0
$583$	−0.135209	+	0.234188i	−0.00559977	+	0.00969908i
$584$	−25.6386			−1.06093
$585$		0			0
$586$		−	4.04578i		−	0.167130i
$587$	7.65692	−	13.2622i	0.316035	−	0.547389i	−0.663622	−	0.748068i	$-0.730982\pi$
$587$	7.65692	−	13.2622i	0.316035	−	0.547389i	0.979657	+	0.200679i	$0.0643150\pi$
$588$		0			0
$589$	20.0878	+	34.7931i	0.827703	+	1.43362i
$590$	−0.828207	+	0.478166i	−0.0340967	+	0.0196858i
$591$		0			0
$592$	25.8716	−	44.8108i	1.06331	−	1.84171i
$593$	39.2391			1.61136			0.805678	−	0.592354i	$-0.201801\pi$
$593$	39.2391			1.61136			0.805678	+	0.592354i	$0.201801\pi$
$594$		0			0
$595$		0			0
$596$	−1.71763	−	0.991674i	−0.0703569	−	0.0406206i
$597$		0			0
$598$	−26.6354	+	15.3779i	−1.08920	+	0.628851i
$599$	29.7113	−	17.1538i	1.21397	−	0.700887i	0.250350	−	0.968155i	$-0.419454\pi$
$599$	29.7113	−	17.1538i	1.21397	−	0.700887i	0.963622	+	0.267269i	$0.0861211\pi$
$600$		0			0
$601$	24.0139	+	13.8644i	0.979547	+	0.565541i	0.902133	−	0.431458i	$-0.142001\pi$
$601$	24.0139	+	13.8644i	0.979547	+	0.565541i	0.0774133	+	0.996999i	$0.475334\pi$
$602$		0			0
$603$		0			0
$604$	1.22630			0.0498973
$605$	−0.154020	+	0.266770i	−0.00626180	+	0.0108458i
$606$		0			0
$607$	13.0526	−	7.53592i	0.529788	−	0.305873i	−0.211142	−	0.977455i	$-0.567718\pi$
$607$	13.0526	−	7.53592i	0.529788	−	0.305873i	0.740930	+	0.671582i	$0.234385\pi$
$608$	−3.06663	−	5.31156i	−0.124368	−	0.215412i
$609$		0			0
$610$	−1.24235	+	2.15181i	−0.0503012	+	0.0871243i
$611$			29.3585i			1.18772i
$612$		0			0
$613$	9.65889			0.390119			0.195059	−	0.980791i	$-0.437510\pi$
$613$	9.65889			0.390119			0.195059	+	0.980791i	$0.437510\pi$
$614$	6.17031	−	10.6873i	0.249013	−	0.431304i
$615$		0			0
$616$		0			0
$617$	−15.9761	+	9.22381i	−0.643174	+	0.371337i	−0.785836	−	0.618435i	$-0.787767\pi$
$617$	−15.9761	+	9.22381i	−0.643174	+	0.371337i	0.142662	+	0.989771i	$0.454434\pi$
$618$		0			0
$619$	−29.3519	−	16.9463i	−1.17975	−	0.681130i	−0.223795	−	0.974636i	$-0.571845\pi$
$619$	−29.3519	−	16.9463i	−1.17975	−	0.681130i	−0.955957	+	0.293506i	$0.905178\pi$
$620$			0.472720i			0.0189849i
$621$		0			0
$622$			8.90774i			0.357168i
$623$		0			0
$624$		0			0
$625$	−11.7911	−	20.4227i	−0.471642	−	0.816908i
$626$	8.77733	+	15.2028i	0.350813	+	0.607626i
$627$		0			0
$628$	−2.88526	−	1.66580i	−0.115134	−	0.0664728i
$629$	57.8641			2.30719
$630$		0			0
$631$	−10.0134			−0.398629			−0.199314	−	0.979936i	$-0.563871\pi$
$631$	−10.0134			−0.398629			−0.199314	+	0.979936i	$0.563871\pi$
$632$	11.8616	+	6.84831i	0.471830	+	0.272411i
$633$		0			0
$634$	−22.0035	−	38.1112i	−0.873870	−	1.51359i
$635$	1.04568	+	1.81117i	0.0414965	+	0.0718741i
$636$		0			0
$637$		0			0
$638$		−	14.6569i		−	0.580271i
$639$		0			0
$640$			3.92594i			0.155186i
$641$	34.7673	+	20.0729i	1.37323	+	0.792833i	0.991333	−	0.131373i	$-0.0419387\pi$
$641$	34.7673	+	20.0729i	1.37323	+	0.792833i	0.381894	+	0.924206i	$0.375272\pi$
$642$		0			0
$643$	−30.0552	+	17.3524i	−1.18526	+	0.684311i	−0.957226	−	0.289342i	$-0.906564\pi$
$643$	−30.0552	+	17.3524i	−1.18526	+	0.684311i	−0.228036	+	0.973653i	$0.573230\pi$
$644$		0			0
$645$		0			0
$646$	19.3566	−	33.5266i	0.761575	−	1.31909i
$647$	−14.3693			−0.564916			−0.282458	−	0.959280i	$-0.591150\pi$
$647$	−14.3693			−0.564916			−0.282458	+	0.959280i	$0.591150\pi$
$648$		0			0
$649$		−	6.60535i		−	0.259283i
$650$	−12.6282	+	21.8726i	−0.495317	+	0.857915i
$651$		0			0
$652$	−0.658626	−	1.14077i	−0.0257938	−	0.0446761i
$653$	0.971455	−	0.560870i	0.0380160	−	0.0219485i	−0.480872	−	0.876791i	$-0.659680\pi$
$653$	0.971455	−	0.560870i	0.0380160	−	0.0219485i	0.518888	+	0.854843i	$0.326346\pi$
$654$		0			0
$655$	3.01369	−	5.21987i	0.117755	−	0.203957i
$656$	22.6089			0.882729
$657$		0			0
$658$		0			0
$659$	5.45240	+	3.14795i	0.212395	+	0.122627i	0.602424	−	0.798176i	$-0.294202\pi$
$659$	5.45240	+	3.14795i	0.212395	+	0.122627i	−0.390029	+	0.920803i	$0.627535\pi$
$660$		0			0
$661$	37.6913	−	21.7611i	1.46602	−	0.846409i	0.466745	−	0.884392i	$-0.345427\pi$
$661$	37.6913	−	21.7611i	1.46602	−	0.846409i	0.999278	+	0.0379828i	$0.0120932\pi$
$662$	21.9199	−	12.6555i	0.851943	−	0.491869i
$663$		0			0
$664$	20.4355	+	11.7984i	0.793051	+	0.457868i
$665$		0			0
$666$		0			0
$667$	−18.6474			−0.722028
$668$	−0.272134	+	0.471349i	−0.0105292	+	0.0182370i
$669$		0			0
$670$	0.0439456	−	0.0253720i	0.00169776	−	0.000980205i
$671$	−8.58086	−	14.8625i	−0.331261	−	0.573760i
$672$		0			0
$673$	−11.6052	+	20.1008i	−0.447347	+	0.774827i	−0.998212	−	0.0597668i	$-0.980964\pi$
$673$	−11.6052	+	20.1008i	−0.447347	+	0.774827i	0.550866	+	0.834594i	$0.314298\pi$
$674$			30.0063i			1.15580i
$675$		0			0
$676$	−0.197336			−0.00758986
$677$	−22.8213	+	39.5276i	−0.877093	+	1.51917i	−0.0225758	+	0.999745i	$0.507187\pi$
$677$	−22.8213	+	39.5276i	−0.877093	+	1.51917i	−0.854517	+	0.519424i	$0.826147\pi$
$678$		0			0
$679$		0			0
$680$	−3.47757	+	2.00778i	−0.133359	+	0.0769947i
$681$		0			0
$682$	−30.5821	−	17.6566i	−1.17105	−	0.676104i
$683$			4.40243i			0.168454i	0.996447	+	0.0842272i	$0.0268421\pi$
$683$			4.40243i			0.168454i	−0.996447	+	0.0842272i	$0.973158\pi$
$684$		0			0
$685$		−	0.489950i		−	0.0187200i
$686$		0			0
$687$		0			0
$688$	−12.0134	−	20.8079i	−0.458008	−	0.793294i
$689$	−0.148299	−	0.256861i	−0.00564973	−	0.00978562i
$690$		0			0
$691$	−8.08070	−	4.66539i	−0.307404	−	0.177480i	0.338360	−	0.941017i	$-0.390128\pi$
$691$	−8.08070	−	4.66539i	−0.307404	−	0.177480i	−0.645764	+	0.763537i	$0.723461\pi$
$692$	4.11527			0.156439
$693$		0			0
$694$	−26.2486			−0.996385
$695$	1.22531	+	0.707436i	0.0464788	+	0.0268346i
$696$		0			0
$697$	12.6417	+	21.8961i	0.478839	+	0.829374i
$698$	−3.10802	−	5.38324i	−0.117640	−	0.203759i
$699$		0			0
$700$		0			0
$701$			22.9051i			0.865116i	0.901606	+	0.432558i	$0.142389\pi$
$701$			22.9051i			0.865116i	−0.901606	+	0.432558i	$0.857611\pi$
$702$		0			0
$703$		−	63.3001i		−	2.38741i
$704$	−19.2464	−	11.1119i	−0.725376	−	0.418796i
$705$		0			0
$706$	−39.2054	+	22.6353i	−1.47552	+	0.851889i
$707$		0			0
$708$		0			0
$709$	−2.78180	+	4.81822i	−0.104473	+	0.180952i	−0.913523	−	0.406788i	$-0.866649\pi$
$709$	−2.78180	+	4.81822i	−0.104473	+	0.180952i	0.809050	+	0.587740i	$0.199982\pi$
$710$	3.56633			0.133842
$711$		0			0
$712$		−	4.99647i		−	0.187250i
$713$	−22.4637	+	38.9083i	−0.841274	+	1.45713i
$714$		0			0
$715$	1.69167	+	2.93006i	0.0632649	+	0.109578i
$716$	3.87548	−	2.23751i	0.144834	−	0.0836197i
$717$		0			0
$718$	4.00172	−	6.93118i	0.149343	−	0.258669i
$719$	−19.9978			−0.745790			−0.372895	−	0.927873i	$-0.621635\pi$
$719$	−19.9978			−0.745790			−0.372895	+	0.927873i	$0.621635\pi$
$720$		0			0
$721$		0			0
$722$	−12.2494	−	7.07220i	−0.455876	−	0.263200i
$723$		0			0
$724$	0.442158	−	0.255280i	0.0164327	−	0.00948741i
$725$	−13.2614	+	7.65648i	−0.492516	+	0.284354i
$726$		0			0
$727$	25.0380	+	14.4557i	0.928610	+	0.536133i	0.886372	−	0.462975i	$-0.153218\pi$
$727$	25.0380	+	14.4557i	0.928610	+	0.536133i	0.0422381	+	0.999108i	$0.486551\pi$
$728$		0			0
$729$		0			0
$730$	−4.40237			−0.162939
$731$	13.4346	−	23.2694i	0.496896	−	0.860650i
$732$		0			0
$733$	−27.5498	+	15.9059i	−1.01757	+	0.587496i	−0.913400	−	0.407063i	$-0.866553\pi$
$733$	−27.5498	+	15.9059i	−1.01757	+	0.587496i	−0.104173	+	0.994559i	$0.533220\pi$
$734$	14.8461	+	25.7143i	0.547981	+	0.949131i
$735$		0			0
$736$	3.42935	−	5.93980i	0.126407	−	0.218944i
$737$			0.350487i			0.0129104i
$738$		0			0
$739$	22.7871			0.838236			0.419118	−	0.907932i	$-0.362339\pi$
$739$	22.7871			0.838236			0.419118	+	0.907932i	$0.362339\pi$
$740$	0.372405	−	0.645025i	0.0136899	−	0.0237116i
$741$		0			0
$742$		0			0
$743$	−11.8554	+	6.84471i	−0.434932	+	0.251108i	−0.701446	−	0.712723i	$-0.747462\pi$
$743$	−11.8554	+	6.84471i	−0.434932	+	0.251108i	0.266513	+	0.963831i	$0.414128\pi$
$744$		0			0
$745$	2.59997	+	1.50109i	0.0952554	+	0.0549957i
$746$			38.7380i			1.41830i
$747$		0			0
$748$			3.14621i			0.115037i
$749$		0			0
$750$		0			0
$751$	−10.2030	−	17.6721i	−0.372312	−	0.644864i	0.617608	−	0.786486i	$-0.288102\pi$
$751$	−10.2030	−	17.6721i	−0.372312	−	0.644864i	−0.989921	+	0.141622i	$0.954768\pi$
$752$	−18.4768	−	32.0028i	−0.673781	−	1.16702i
$753$		0			0
$754$	13.9221	+	8.03793i	0.507013	+	0.292724i
$755$	−1.85624			−0.0675554
$756$		0			0
$757$	−4.02306			−0.146221			−0.0731104	−	0.997324i	$-0.523293\pi$
$757$	−4.02306			−0.146221			−0.0731104	+	0.997324i	$0.523293\pi$
$758$	39.2400	+	22.6552i	1.42526	+	0.822874i
$759$		0			0
$760$	2.19639	+	3.80426i	0.0796715	+	0.137995i
$761$	−22.9595	−	39.7670i	−0.832280	−	1.44155i	−0.896226	−	0.443598i	$-0.853702\pi$
$761$	−22.9595	−	39.7670i	−0.832280	−	1.44155i	0.0639453	−	0.997953i	$-0.479632\pi$
$762$		0			0
$763$		0			0
$764$			0.428864i			0.0155157i
$765$		0			0
$766$			33.7111i			1.21803i
$767$	6.27422	+	3.62242i	0.226549	+	0.130798i
$768$		0			0
$769$	5.22983	−	3.01944i	0.188592	−	0.108884i	−0.402731	−	0.915318i	$-0.631939\pi$
$769$	5.22983	−	3.01944i	0.188592	−	0.108884i	0.591323	+	0.806434i	$0.298606\pi$
$770$		0			0
$771$		0			0
$772$	−0.606656	+	1.05076i	−0.0218340	+	0.0378176i
$773$	38.2314			1.37509			0.687545	−	0.726142i	$-0.258689\pi$
$773$	38.2314			1.37509			0.687545	+	0.726142i	$0.258689\pi$
$774$		0			0
$775$			36.8938i			1.32527i
$776$	16.9060	−	29.2820i	0.606889	−	1.05116i
$777$		0			0
$778$	3.33508	+	5.77653i	0.119568	+	0.207098i
$779$	23.9531	−	13.8293i	0.858209	−	0.495487i
$780$		0			0
$781$	−12.3163	+	21.3324i	−0.440711	+	0.763333i
$782$	43.2921			1.54812
$783$		0			0
$784$		0			0
$785$	4.36739	+	2.52152i	0.155879	+	0.0899968i
$786$		0			0
$787$	−41.7875	+	24.1260i	−1.48957	+	0.860001i	−0.999929	−	0.0119261i	$-0.996204\pi$
$787$	−41.7875	+	24.1260i	−1.48957	+	0.860001i	−0.489636	+	0.871927i	$0.662870\pi$
$788$	−1.34907	+	0.778886i	−0.0480586	+	0.0277467i
$789$		0			0
$790$	2.03675	+	1.17592i	0.0724643	+	0.0418373i
$791$		0			0
$792$		0			0
$793$	18.8232			0.668432
$794$	−7.16394	+	12.4083i	−0.254239	+	0.440354i
$795$		0			0
$796$	−1.20910	+	0.698076i	−0.0428555	+	0.0247426i
$797$	−12.6517	−	21.9133i	−0.448145	−	0.776209i	0.550121	−	0.835085i	$-0.314582\pi$
$797$	−12.6517	−	21.9133i	−0.448145	−	0.776209i	−0.998265	+	0.0588759i	$0.981248\pi$
$798$		0			0
$799$	20.6626	−	35.7886i	0.730989	−	1.26611i
$800$		−	5.63227i		−	0.199131i
$801$		0			0
$802$	29.5446			1.04326
$803$	15.2035	−	26.3333i	0.536521	−	0.929282i
$804$		0			0
$805$		0			0
$806$	33.5428	−	19.3660i	1.18150	−	0.682137i
$807$		0			0
$808$	17.0112	+	9.82141i	0.598451	+	0.345516i
$809$			11.1541i			0.392158i	0.980588	+	0.196079i	$0.0628209\pi$
$809$			11.1541i			0.392158i	−0.980588	+	0.196079i	$0.937179\pi$
$810$		0			0
$811$			1.90097i			0.0667520i	0.999443	+	0.0333760i	$0.0106259\pi$
$811$			1.90097i			0.0667520i	−0.999443	+	0.0333760i	$0.989374\pi$
$812$		0			0
$813$		0			0
$814$	27.8194	+	48.1847i	0.975070	+	1.68887i
$815$	0.996957	+	1.72678i	0.0349219	+	0.0604865i
$816$		0			0
$817$	−25.4554	−	14.6967i	−0.890572	−	0.514172i
$818$	3.60098			0.125905
$819$		0			0
$820$	0.325441			0.0113649
$821$	8.79955	+	5.08042i	0.307106	+	0.177308i	0.645631	−	0.763650i	$-0.276594\pi$
$821$	8.79955	+	5.08042i	0.307106	+	0.177308i	−0.338524	+	0.940958i	$0.609928\pi$
$822$		0			0
$823$	−15.9763	−	27.6717i	−0.556898	−	0.964576i	−0.997753	−	0.0669975i	$-0.978658\pi$
$823$	−15.9763	−	27.6717i	−0.556898	−	0.964576i	0.440855	−	0.897578i	$-0.354675\pi$
$824$	−10.6399	−	18.4289i	−0.370660	−	0.642002i
$825$		0			0
$826$		0			0
$827$		−	13.7400i		−	0.477787i	−0.971046	−	0.238894i	$-0.923215\pi$
$827$		−	13.7400i		−	0.477787i	0.971046	−	0.238894i	$-0.0767847\pi$
$828$		0			0
$829$			17.9078i			0.621962i	0.950416	+	0.310981i	$0.100658\pi$
$829$			17.9078i			0.621962i	−0.950416	+	0.310981i	$0.899342\pi$
$830$	3.50896	+	2.02590i	0.121798	+	0.0703200i
$831$		0			0
$832$	21.1097	−	12.1877i	0.731848	−	0.422532i
$833$		0			0
$834$		0			0
$835$	0.411927	−	0.713478i	0.0142553	−	0.0246909i
$836$	3.44178			0.119036
$837$		0			0
$838$		−	43.6082i		−	1.50642i
$839$	−27.5601	+	47.7356i	−0.951482	+	1.64802i	−0.209261	+	0.977860i	$0.567106\pi$
$839$	−27.5601	+	47.7356i	−0.951482	+	1.64802i	−0.742221	+	0.670155i	$0.766227\pi$
$840$		0			0
$841$	−9.62659	−	16.6737i	−0.331951	−	0.574957i
$842$	−46.8165	+	27.0295i	−1.61340	+	0.931499i
$843$		0			0
$844$	0.559902	−	0.969778i	0.0192726	−	0.0333811i
$845$	0.298707			0.0102758
$846$		0			0
$847$		0			0
$848$	0.323312	+	0.186664i	0.0111026	+	0.00641007i
$849$		0			0
$850$	30.7880	−	17.7755i	1.05602	−	0.609693i
$851$	61.3034	−	35.3936i	2.10145	−	1.21328i
$852$		0			0
$853$	2.07425	+	1.19757i	0.0710209	+	0.0410039i	0.535090	−	0.844795i	$-0.320278\pi$
$853$	2.07425	+	1.19757i	0.0710209	+	0.0410039i	−0.464069	+	0.885799i	$0.653611\pi$
$854$		0			0
$855$		0			0
$856$	44.7162			1.52837
$857$	15.2461	−	26.4070i	0.520796	−	0.902046i	−0.478911	−	0.877863i	$-0.658968\pi$
$857$	15.2461	−	26.4070i	0.520796	−	0.902046i	0.999708	−	0.0241822i	$-0.00769820\pi$
$858$		0			0
$859$	38.9437	−	22.4841i	1.32874	−	0.767149i	0.343636	−	0.939103i	$-0.388341\pi$
$859$	38.9437	−	22.4841i	1.32874	−	0.767149i	0.985105	+	0.171954i	$0.0550079\pi$
$860$	−0.172926	−	0.299517i	−0.00589674	−	0.0102134i
$861$		0			0
$862$	−14.4383	+	25.0078i	−0.491770	+	0.851770i
$863$		−	52.5198i		−	1.78779i	−0.448272	−	0.893897i	$-0.647960\pi$
$863$		−	52.5198i		−	1.78779i	0.448272	−	0.893897i	$-0.352040\pi$
$864$		0			0
$865$	−6.22926			−0.211801
$866$	−7.38262	+	12.7871i	−0.250872	+	0.434523i
$867$		0			0
$868$		0			0
$869$	−14.0678	+	8.12203i	−0.477217	+	0.275521i
$870$		0			0
$871$	−0.332917	−	0.192209i	−0.0112804	−	0.00651277i
$872$			23.6390i			0.800519i
$873$		0			0
$874$		−	47.3591i		−	1.60195i
$875$		0			0
$876$		0			0
$877$	−0.683876	−	1.18451i	−0.0230929	−	0.0399980i	0.854248	−	0.519866i	$-0.174018\pi$
$877$	−0.683876	−	1.18451i	−0.0230929	−	0.0399980i	−0.877341	+	0.479868i	$0.840685\pi$
$878$	−5.47457	−	9.48224i	−0.184758	−	0.320010i
$879$		0			0
$880$	−3.68808	−	2.12931i	−0.124325	−	0.0717791i
$881$	−20.7141			−0.697876			−0.348938	−	0.937146i	$-0.613458\pi$
$881$	−20.7141			−0.697876			−0.348938	+	0.937146i	$0.613458\pi$
$882$		0			0
$883$	−14.3561			−0.483120			−0.241560	−	0.970386i	$-0.577659\pi$
$883$	−14.3561			−0.483120			−0.241560	+	0.970386i	$0.577659\pi$
$884$	−2.98849	−	1.72541i	−0.100514	−	0.0580317i
$885$		0			0
$886$	−0.638206	−	1.10541i	−0.0214410	−	0.0371368i
$887$	22.0913	+	38.2633i	0.741754	+	1.28475i	0.951696	+	0.307041i	$0.0993390\pi$
$887$	22.0913	+	38.2633i	0.741754	+	1.28475i	−0.209943	+	0.977714i	$0.567328\pi$
$888$		0			0
$889$		0			0
$890$		−	0.857939i		−	0.0287582i
$891$		0			0
$892$		−	4.14284i		−	0.138713i
$893$	−39.1507	−	22.6037i	−1.31013	−	0.756404i
$894$		0			0
$895$	−5.86629	+	3.38691i	−0.196089	+	0.113212i
$896$		0			0
$897$		0			0
$898$	−11.6161	+	20.1196i	−0.387633	+	0.671400i
$899$	23.4832			0.783209
$900$		0			0
$901$			0.417492i			0.0139087i
$902$	−12.1556	+	21.0540i	−0.404736	+	0.701023i
$903$		0			0
$904$	20.8791	+	36.1637i	0.694429	+	1.20279i
$905$	−0.669292	+	0.386416i	−0.0222480	+	0.0128449i
$906$		0			0
$907$	7.18075	−	12.4374i	0.238433	−	0.412978i	−0.721832	−	0.692068i	$-0.756700\pi$
$907$	7.18075	−	12.4374i	0.238433	−	0.412978i	0.960265	+	0.279091i	$0.0900330\pi$
$908$	0.0657067			0.00218055
$909$		0			0
$910$		0			0
$911$	41.6920	+	24.0709i	1.38132	+	0.797505i	0.992316	−	0.123732i	$-0.0394863\pi$
$911$	41.6920	+	24.0709i	1.38132	+	0.797505i	0.389003	+	0.921237i	$0.372820\pi$
$912$		0			0
$913$	−24.2363	+	13.9928i	−0.802104	+	0.463095i
$914$	7.23957	−	4.17977i	0.239464	−	0.138254i
$915$		0			0
$916$	0.468997	+	0.270776i	0.0154961	+	0.00894668i
$917$		0			0
$918$		0			0
$919$	23.0641			0.760816			0.380408	−	0.924819i	$-0.375784\pi$
$919$	23.0641			0.760816			0.380408	+	0.924819i	$0.375784\pi$
$920$	−2.45618	+	4.25423i	−0.0809778	+	0.140258i
$921$		0			0
$922$	−29.1430	+	16.8257i	−0.959773	+	0.554125i
$923$	−13.5086	−	23.3977i	−0.444642	−	0.770143i
$924$		0			0
$925$	29.0647	−	50.3416i	0.955642	−	1.65522i
$926$		−	62.3647i		−	2.04943i
$927$		0			0
$928$	−3.58498			−0.117683
$929$	−18.7804	+	32.5286i	−0.616165	+	1.06723i	0.374014	+	0.927423i	$0.377981\pi$
$929$	−18.7804	+	32.5286i	−0.616165	+	1.06723i	−0.990179	+	0.139806i	$0.955352\pi$
$930$		0			0
$931$		0			0
$932$	−4.10405	+	2.36947i	−0.134433	+	0.0776147i
$933$		0			0
$934$	31.8876	+	18.4103i	1.04339	+	0.602403i
$935$		−	4.76240i		−	0.155747i
$936$		0			0
$937$		−	18.9436i		−	0.618859i	−0.950922	−	0.309430i	$-0.899862\pi$
$937$		−	18.9436i		−	0.618859i	0.950922	−	0.309430i	$-0.100138\pi$
$938$		0			0
$939$		0			0
$940$	−0.265963	−	0.460661i	−0.00867475	−	0.0150251i
$941$	27.7551	+	48.0733i	0.904792	+	1.56714i	0.821197	+	0.570645i	$0.193307\pi$
$941$	27.7551	+	48.0733i	0.904792	+	1.56714i	0.0835947	+	0.996500i	$0.473360\pi$
$942$		0			0
$943$	26.7862	+	15.4650i	0.872280	+	0.503611i
$944$	−9.11911			−0.296802
$945$		0			0
$946$	25.8359			0.839997
$947$	−16.3036	−	9.41290i	−0.529797	−	0.305878i	0.211137	−	0.977456i	$-0.432283\pi$
$947$	−16.3036	−	9.41290i	−0.529797	−	0.305878i	−0.740934	+	0.671578i	$0.765617\pi$
$948$		0			0
$949$	16.6754	+	28.8827i	0.541308	+	0.937573i
$950$	−19.4453	−	33.6803i	−0.630890	−	1.09273i
$951$		0			0
$952$		0			0
$953$		−	35.0089i		−	1.13405i	−0.823701	−	0.567024i	$-0.808095\pi$
$953$		−	35.0089i		−	1.13405i	0.823701	−	0.567024i	$-0.191905\pi$
$954$		0			0
$955$		−	0.649168i		−	0.0210066i
$956$	0.0593482	+	0.0342647i	0.00191946	+	0.00110820i
$957$		0			0
$958$	4.23347	−	2.44420i	0.136777	−	0.0789684i
$959$		0			0
$960$		0			0
$961$	12.7893	−	22.1518i	0.412559	−	0.714573i
$962$	−61.0255			−1.96754
$963$		0			0
$964$			4.51380i			0.145380i
$965$	0.918291	−	1.59053i	0.0295608	−	0.0512008i
$966$		0			0
$967$	−7.47001	−	12.9384i	−0.240219	−	0.416072i	0.720557	−	0.693395i	$-0.243886\pi$
$967$	−7.47001	−	12.9384i	−0.240219	−	0.416072i	−0.960777	+	0.277323i	$0.910553\pi$
$968$	−2.30636	+	1.33158i	−0.0741291	+	0.0427985i
$969$		0			0
$970$	2.90291	−	5.02799i	0.0932069	−	0.161439i
$971$	−30.3564			−0.974182			−0.487091	−	0.873351i	$-0.661942\pi$
$971$	−30.3564			−0.974182			−0.487091	+	0.873351i	$0.661942\pi$
$972$		0			0
$973$		0			0
$974$	13.4280	+	7.75269i	0.430262	+	0.248412i
$975$		0			0
$976$	−20.5186	+	11.8464i	−0.656785	+	0.379195i
$977$	−47.1306	+	27.2109i	−1.50784	+	0.870554i	−0.507885	+	0.861425i	$0.669572\pi$
$977$	−47.1306	+	27.2109i	−1.50784	+	0.870554i	−0.999958	+	0.00912839i	$0.997094\pi$
$978$		0			0
$979$	5.13186	+	2.96288i	0.164015	+	0.0946940i
$980$		0			0
$981$		0			0
$982$	45.0477			1.43753
$983$	−13.1343	+	22.7493i	−0.418920	+	0.725590i	−0.995831	−	0.0912165i	$-0.970924\pi$
$983$	−13.1343	+	22.7493i	−0.418920	+	0.725590i	0.576911	+	0.816807i	$0.304258\pi$
$984$		0			0
$985$	2.04208	−	1.17899i	0.0650660	−	0.0375659i
$986$	−11.3142	−	19.5968i	−0.360318	−	0.624089i
$987$		0			0
$988$	−1.88750	+	3.26924i	−0.0600492	+	0.104008i
$989$		−	32.8700i		−	1.04520i
$990$		0			0
$991$	−32.4942			−1.03221			−0.516106	−	0.856525i	$-0.672619\pi$
$991$	−32.4942			−1.03221			−0.516106	+	0.856525i	$0.672619\pi$
$992$	−4.31869	+	7.48019i	−0.137118	+	0.237496i
$993$		0			0
$994$		0			0
$995$	1.83021	−	1.05667i	0.0580216	−	0.0334988i
$996$		0			0
$997$	31.8691	+	18.3996i	1.00931	+	0.582723i	0.910988	−	0.412433i	$-0.135321\pi$
$997$	31.8691	+	18.3996i	1.00931	+	0.582723i	0.0983170	+	0.995155i	$0.468654\pi$
$998$		−	2.92376i		−	0.0925499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.440.19		48
3.2	odd	2		441.2.o.e.146.6	yes	48
7.2	even	3		1323.2.i.d.521.13		48
7.3	odd	6		1323.2.s.d.656.6		48
7.4	even	3		1323.2.s.d.656.5		48
7.5	odd	6		1323.2.i.d.521.5		48
7.6	odd	2	inner	1323.2.o.e.440.20		48
9.4	even	3		441.2.o.e.293.5	yes	48
9.5	odd	6	inner	1323.2.o.e.881.20		48
21.2	odd	6		441.2.i.d.227.20		48
21.5	even	6		441.2.i.d.227.19		48
21.11	odd	6		441.2.s.d.362.19		48
21.17	even	6		441.2.s.d.362.20		48
21.20	even	2		441.2.o.e.146.5	✓	48
63.4	even	3		441.2.i.d.68.5		48
63.5	even	6		1323.2.s.d.962.5		48
63.13	odd	6		441.2.o.e.293.6	yes	48
63.23	odd	6		1323.2.s.d.962.6		48
63.31	odd	6		441.2.i.d.68.6		48
63.32	odd	6		1323.2.i.d.1097.5		48
63.40	odd	6		441.2.s.d.374.19		48
63.41	even	6	inner	1323.2.o.e.881.19		48
63.58	even	3		441.2.s.d.374.20		48
63.59	even	6		1323.2.i.d.1097.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.5		48	63.4	even	3
441.2.i.d.68.6		48	63.31	odd	6
441.2.i.d.227.19		48	21.5	even	6
441.2.i.d.227.20		48	21.2	odd	6
441.2.o.e.146.5	✓	48	21.20	even	2
441.2.o.e.146.6	yes	48	3.2	odd	2
441.2.o.e.293.5	yes	48	9.4	even	3
441.2.o.e.293.6	yes	48	63.13	odd	6
441.2.s.d.362.19		48	21.11	odd	6
441.2.s.d.362.20		48	21.17	even	6
441.2.s.d.374.19		48	63.40	odd	6
441.2.s.d.374.20		48	63.58	even	3
1323.2.i.d.521.5		48	7.5	odd	6
1323.2.i.d.521.13		48	7.2	even	3
1323.2.i.d.1097.5		48	63.32	odd	6
1323.2.i.d.1097.13		48	63.59	even	6
1323.2.o.e.440.19		48	1.1	even	1	trivial
1323.2.o.e.440.20		48	7.6	odd	2	inner
1323.2.o.e.881.19		48	63.41	even	6	inner
1323.2.o.e.881.20		48	9.5	odd	6	inner
1323.2.s.d.656.5		48	7.4	even	3
1323.2.s.d.656.6		48	7.3	odd	6
1323.2.s.d.962.5		48	63.5	even	6
1323.2.s.d.962.6		48	63.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.28562 + 0.742253i) q^{2} +(0.101880 + 0.176462i) q^{4} +(-0.154215 - 0.267109i) q^{5} -2.66653i q^{8} +O(q^{10})\)	\(q+(1.28562 + 0.742253i) q^{2} +(0.101880 + 0.176462i) q^{4} +(-0.154215 - 0.267109i) q^{5} -2.66653i q^{8} -0.457868i q^{10} +(2.73879 + 1.58124i) q^{11} +(-3.00394 + 1.73432i) q^{13} +(2.18300 - 3.78107i) q^{16} +4.88248 q^{17} -5.34116i q^{19} +(0.0314230 - 0.0544262i) q^{20} +(2.34736 + 4.06575i) q^{22} +(5.17269 - 2.98645i) q^{23} +(2.45244 - 4.24774i) q^{25} -5.14923 q^{26} +(-2.70372 - 1.56099i) q^{29} +(-6.51414 + 3.76094i) q^{31} +(0.994457 - 0.574150i) q^{32} +(6.27702 + 3.62404i) q^{34} +11.8514 q^{37} +(3.96450 - 6.86671i) q^{38} +(-0.712254 + 0.411220i) q^{40} +(2.58920 + 4.48462i) q^{41} +(2.75159 - 4.76589i) q^{43} +0.644388i q^{44} +8.86682 q^{46} +(4.23198 - 7.33000i) q^{47} +(6.30580 - 3.64066i) q^{50} +(-0.612084 - 0.353387i) q^{52} +0.0855080i q^{53} -0.975406i q^{55} +(-2.31731 - 4.01369i) q^{58} +(-1.04433 - 1.80884i) q^{59} +(-4.69964 - 2.71334i) q^{61} -11.1663 q^{62} -7.02734 q^{64} +(0.926507 + 0.534919i) q^{65} +(0.0554134 + 0.0959787i) q^{67} +(0.497429 + 0.861572i) q^{68} +7.78899i q^{71} -9.61495i q^{73} +(15.2364 + 8.79672i) q^{74} +(0.942510 - 0.544159i) q^{76} +(-2.56825 + 4.44834i) q^{79} -1.34661 q^{80} +7.68736i q^{82} +(-4.42464 + 7.66370i) q^{83} +(-0.752954 - 1.30416i) q^{85} +(7.07500 - 4.08475i) q^{86} +(4.21642 - 7.30306i) q^{88} +1.87377 q^{89} +(1.05399 + 0.608521i) q^{92} +(10.8814 - 6.28240i) q^{94} +(-1.42667 + 0.823689i) q^{95} +(10.9813 + 6.34007i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

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Varieties

Fields

Representations

Groups

Database

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