LMFDB - Embedded newform 270.2.f.a.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(53,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("270.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.f (of order $4$, degree $2$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	270.107
Dual form			270.2.f.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.41421 - 1.73205i) q^{5} +(1.44949 + 1.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.41421 - 1.73205i) q^{5} +(1.44949 + 1.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.22474 + 0.224745i) q^{10} -1.09638i q^{11} +(4.22474 - 4.22474i) q^{13} -2.04989 q^{14} -1.00000 q^{16} +(4.17121 - 4.17121i) q^{17} -4.44949i q^{19} +(-1.73205 + 1.41421i) q^{20} +(0.775255 + 0.775255i) q^{22} +(4.48905 + 4.48905i) q^{23} +(-1.00000 + 4.89898i) q^{25} +5.97469i q^{26} +(1.44949 - 1.44949i) q^{28} -3.14626 q^{29} -1.44949 q^{31} +(0.707107 - 0.707107i) q^{32} +5.89898i q^{34} +(0.460702 - 4.56048i) q^{35} +(3.14626 + 3.14626i) q^{38} +(0.224745 - 2.22474i) q^{40} +4.87832i q^{41} +(-7.22474 + 7.22474i) q^{43} -1.09638 q^{44} -6.34847 q^{46} +(7.31747 - 7.31747i) q^{47} -2.79796i q^{49} +(-2.75699 - 4.17121i) q^{50} +(-4.22474 - 4.22474i) q^{52} +(-5.65685 - 5.65685i) q^{53} +(-1.89898 + 1.55051i) q^{55} +2.04989i q^{56} +(2.22474 - 2.22474i) q^{58} +2.82843 q^{59} -8.44949 q^{61} +(1.02494 - 1.02494i) q^{62} +1.00000i q^{64} +(-13.2922 - 1.34278i) q^{65} +(2.00000 + 2.00000i) q^{67} +(-4.17121 - 4.17121i) q^{68} +(2.89898 + 3.55051i) q^{70} +13.9993i q^{71} +(-4.44949 + 4.44949i) q^{73} -4.44949 q^{76} +(1.58919 - 1.58919i) q^{77} -5.44949i q^{79} +(1.41421 + 1.73205i) q^{80} +(-3.44949 - 3.44949i) q^{82} +(10.2173 + 10.2173i) q^{83} +(-13.1237 - 1.32577i) q^{85} -10.2173i q^{86} +(0.775255 - 0.775255i) q^{88} -17.4634 q^{89} +12.2474 q^{91} +(4.48905 - 4.48905i) q^{92} +10.3485i q^{94} +(-7.70674 + 6.29253i) q^{95} +(8.44949 + 8.44949i) q^{97} +(1.97846 + 1.97846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} + 8 q^{10} + 24 q^{13} - 8 q^{16} + 16 q^{22} - 8 q^{25} - 8 q^{28} + 8 q^{31} - 8 q^{40} - 48 q^{43} + 8 q^{46} - 24 q^{52} + 24 q^{55} + 8 q^{58} - 48 q^{61} + 16 q^{67} - 16 q^{70} - 16 q^{73} - 16 q^{76} - 8 q^{82} - 56 q^{85} + 16 q^{88} + 48 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 + 8 * q^10 + 24 * q^13 - 8 * q^16 + 16 * q^22 - 8 * q^25 - 8 * q^28 + 8 * q^31 - 8 * q^40 - 48 * q^43 + 8 * q^46 - 24 * q^52 + 24 * q^55 + 8 * q^58 - 48 * q^61 + 16 * q^67 - 16 * q^70 - 16 * q^73 - 16 * q^76 - 8 * q^82 - 56 * q^85 + 16 * q^88 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−1.41421	−	1.73205i	−0.632456	−	0.774597i
$5$	−1.41421	−	1.73205i	−0.632456	−	0.774597i
$6$		0			0
$7$	1.44949	+	1.44949i	0.547856	+	0.547856i	0.925820	−	0.377964i	$-0.123376\pi$
$7$	1.44949	+	1.44949i	0.547856	+	0.547856i	−0.377964	+	0.925820i	$0.623376\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	2.22474	+	0.224745i	0.703526	+	0.0710706i
$11$		−	1.09638i		−	0.330570i	−0.986246	−	0.165285i	$-0.947146\pi$
$11$		−	1.09638i		−	0.330570i	0.986246	−	0.165285i	$-0.0528544\pi$
$12$		0			0
$13$	4.22474	−	4.22474i	1.17173	−	1.17173i	0.189937	−	0.981796i	$-0.439172\pi$
$13$	4.22474	−	4.22474i	1.17173	−	1.17173i	0.981796	−	0.189937i	$-0.0608284\pi$
$14$	−2.04989			−0.547856
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.17121	−	4.17121i	1.01167	−	1.01167i	0.0117355	−	0.999931i	$-0.496264\pi$
$17$	4.17121	−	4.17121i	1.01167	−	1.01167i	0.999931	−	0.0117355i	$-0.00373561\pi$
$18$		0			0
$19$		−	4.44949i		−	1.02078i	−0.859942	−	0.510391i	$-0.829501\pi$
$19$		−	4.44949i		−	1.02078i	0.859942	−	0.510391i	$-0.170499\pi$
$20$	−1.73205	+	1.41421i	−0.387298	+	0.316228i
$21$		0			0
$22$	0.775255	+	0.775255i	0.165285	+	0.165285i
$23$	4.48905	+	4.48905i	0.936031	+	0.936031i	0.998073	−	0.0620428i	$-0.0197615\pi$
$23$	4.48905	+	4.48905i	0.936031	+	0.936031i	−0.0620428	+	0.998073i	$0.519762\pi$
$24$		0			0
$25$	−1.00000	+	4.89898i	−0.200000	+	0.979796i
$26$			5.97469i			1.17173i
$27$		0			0
$28$	1.44949	−	1.44949i	0.273928	−	0.273928i
$29$	−3.14626			−0.584247			−0.292123	−	0.956381i	$-0.594362\pi$
$29$	−3.14626			−0.584247			−0.292123	+	0.956381i	$0.594362\pi$
$30$		0			0
$31$	−1.44949			−0.260336			−0.130168	−	0.991492i	$-0.541552\pi$
$31$	−1.44949			−0.260336			−0.130168	+	0.991492i	$0.541552\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			5.89898i			1.01167i
$35$	0.460702	−	4.56048i	0.0778728	−	0.770861i
$36$		0			0
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	3.14626	+	3.14626i	0.510391	+	0.510391i
$39$		0			0
$40$	0.224745	−	2.22474i	0.0355353	−	0.351763i
$41$			4.87832i			0.761865i	0.924603	+	0.380932i	$0.124397\pi$
$41$			4.87832i			0.761865i	−0.924603	+	0.380932i	$0.875603\pi$
$42$		0			0
$43$	−7.22474	+	7.22474i	−1.10176	+	1.10176i	−0.107565	+	0.994198i	$0.534305\pi$
$43$	−7.22474	+	7.22474i	−1.10176	+	1.10176i	−0.994198	+	0.107565i	$0.965695\pi$
$44$	−1.09638			−0.165285
$45$		0			0
$46$	−6.34847			−0.936031
$47$	7.31747	−	7.31747i	1.06736	−	1.06736i	0.0698023	−	0.997561i	$-0.477763\pi$
$47$	7.31747	−	7.31747i	1.06736	−	1.06736i	0.997561	−	0.0698023i	$-0.0222368\pi$
$48$		0			0
$49$		−	2.79796i		−	0.399708i
$50$	−2.75699	−	4.17121i	−0.389898	−	0.589898i
$51$		0			0
$52$	−4.22474	−	4.22474i	−0.585867	−	0.585867i
$53$	−5.65685	−	5.65685i	−0.777029	−	0.777029i	0.202296	−	0.979324i	$-0.435160\pi$
$53$	−5.65685	−	5.65685i	−0.777029	−	0.777029i	−0.979324	+	0.202296i	$0.935160\pi$
$54$		0			0
$55$	−1.89898	+	1.55051i	−0.256058	+	0.209071i
$56$			2.04989i			0.273928i
$57$		0			0
$58$	2.22474	−	2.22474i	0.292123	−	0.292123i
$59$	2.82843			0.368230			0.184115	−	0.982905i	$-0.441058\pi$
$59$	2.82843			0.368230			0.184115	+	0.982905i	$0.441058\pi$
$60$		0			0
$61$	−8.44949			−1.08185			−0.540923	−	0.841072i	$-0.681925\pi$
$61$	−8.44949			−1.08185			−0.540923	+	0.841072i	$0.681925\pi$
$62$	1.02494	−	1.02494i	0.130168	−	0.130168i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−13.2922	−	1.34278i	−1.64869	−	0.166552i
$66$		0			0
$67$	2.00000	+	2.00000i	0.244339	+	0.244339i	0.818642	−	0.574304i	$-0.194727\pi$
$67$	2.00000	+	2.00000i	0.244339	+	0.244339i	−0.574304	+	0.818642i	$0.694727\pi$
$68$	−4.17121	−	4.17121i	−0.505833	−	0.505833i
$69$		0			0
$70$	2.89898	+	3.55051i	0.346494	+	0.424367i
$71$			13.9993i			1.66141i	0.556714	+	0.830704i	$0.312062\pi$
$71$			13.9993i			1.66141i	−0.556714	+	0.830704i	$0.687938\pi$
$72$		0			0
$73$	−4.44949	+	4.44949i	−0.520773	+	0.520773i	−0.917805	−	0.397032i	$-0.870040\pi$
$73$	−4.44949	+	4.44949i	−0.520773	+	0.520773i	0.397032	+	0.917805i	$0.370040\pi$
$74$		0			0
$75$		0			0
$76$	−4.44949			−0.510391
$77$	1.58919	−	1.58919i	0.181105	−	0.181105i
$78$		0			0
$79$		−	5.44949i		−	0.613115i	−0.951852	−	0.306558i	$-0.900823\pi$
$79$		−	5.44949i		−	0.613115i	0.951852	−	0.306558i	$-0.0991773\pi$
$80$	1.41421	+	1.73205i	0.158114	+	0.193649i
$81$		0			0
$82$	−3.44949	−	3.44949i	−0.380932	−	0.380932i
$83$	10.2173	+	10.2173i	1.12150	+	1.12150i	0.991516	+	0.129981i	$0.0414918\pi$
$83$	10.2173	+	10.2173i	1.12150	+	1.12150i	0.129981	+	0.991516i	$0.458508\pi$
$84$		0			0
$85$	−13.1237	−	1.32577i	−1.42347	−	0.143799i
$86$		−	10.2173i		−	1.10176i
$87$		0			0
$88$	0.775255	−	0.775255i	0.0826425	−	0.0826425i
$89$	−17.4634			−1.85111			−0.925557	−	0.378609i	$-0.876403\pi$
$89$	−17.4634			−1.85111			−0.925557	+	0.378609i	$0.876403\pi$
$90$		0			0
$91$	12.2474			1.28388
$92$	4.48905	−	4.48905i	0.468015	−	0.468015i
$93$		0			0
$94$			10.3485i			1.06736i
$95$	−7.70674	+	6.29253i	−0.790695	+	0.645600i
$96$		0			0
$97$	8.44949	+	8.44949i	0.857916	+	0.857916i	0.991092	−	0.133177i	$-0.0425178\pi$
$97$	8.44949	+	8.44949i	0.857916	+	0.857916i	−0.133177	+	0.991092i	$0.542518\pi$
$98$	1.97846	+	1.97846i	0.199854	+	0.199854i
$99$		0			0
$100$	4.89898	+	1.00000i	0.489898	+	0.100000i
$101$		−	8.16744i		−	0.812691i	−0.913719	−	0.406346i	$-0.866803\pi$
$101$		−	8.16744i		−	0.812691i	0.913719	−	0.406346i	$-0.133197\pi$
$102$		0			0
$103$	1.55051	−	1.55051i	0.152776	−	0.152776i	−0.626580	−	0.779357i	$-0.715546\pi$
$103$	1.55051	−	1.55051i	0.152776	−	0.152776i	0.779357	+	0.626580i	$0.215546\pi$
$104$	5.97469			0.585867
$105$		0			0
$106$	8.00000			0.777029
$107$	3.60697	−	3.60697i	0.348699	−	0.348699i	−0.510926	−	0.859625i	$-0.670697\pi$
$107$	3.60697	−	3.60697i	0.348699	−	0.348699i	0.859625	+	0.510926i	$0.170697\pi$
$108$		0			0
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$	0.246405	−	2.43916i	0.0234938	−	0.232565i
$111$		0			0
$112$	−1.44949	−	1.44949i	−0.136964	−	0.136964i
$113$	5.72829	+	5.72829i	0.538872	+	0.538872i	0.923198	−	0.384326i	$-0.125566\pi$
$113$	5.72829	+	5.72829i	0.538872	+	0.538872i	−0.384326	+	0.923198i	$0.625566\pi$
$114$		0			0
$115$	1.42679	−	14.1237i	0.133048	−	1.31704i
$116$			3.14626i			0.292123i
$117$		0			0
$118$	−2.00000	+	2.00000i	−0.184115	+	0.184115i
$119$	12.0922			1.10849
$120$		0			0
$121$	9.79796			0.890724
$122$	5.97469	−	5.97469i	0.540923	−	0.540923i
$123$		0			0
$124$			1.44949i			0.130168i
$125$	9.89949	−	5.19615i	0.885438	−	0.464758i
$126$		0			0
$127$	−4.55051	−	4.55051i	−0.403792	−	0.403792i	0.475775	−	0.879567i	$-0.342168\pi$
$127$	−4.55051	−	4.55051i	−0.403792	−	0.403792i	−0.879567	+	0.475775i	$0.842168\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	10.3485	−	8.44949i	0.907621	−	0.741069i
$131$			9.29593i			0.812189i	0.913831	+	0.406095i	$0.133110\pi$
$131$			9.29593i			0.812189i	−0.913831	+	0.406095i	$0.866890\pi$
$132$		0			0
$133$	6.44949	−	6.44949i	0.559242	−	0.559242i
$134$	−2.82843			−0.244339
$135$		0			0
$136$	5.89898			0.505833
$137$	−15.4135	+	15.4135i	−1.31686	+	1.31686i	−0.400617	+	0.916245i	$0.631204\pi$
$137$	−15.4135	+	15.4135i	−1.31686	+	1.31686i	−0.916245	+	0.400617i	$0.868796\pi$
$138$		0			0
$139$			8.24745i			0.699539i	0.936836	+	0.349770i	$0.113740\pi$
$139$			8.24745i			0.699539i	−0.936836	+	0.349770i	$0.886260\pi$
$140$	−4.56048	−	0.460702i	−0.385431	−	0.0389364i
$141$		0			0
$142$	−9.89898	−	9.89898i	−0.830704	−	0.830704i
$143$	−4.63191	−	4.63191i	−0.387340	−	0.387340i
$144$		0			0
$145$	4.44949	+	5.44949i	0.369510	+	0.452555i
$146$		−	6.29253i		−	0.520773i
$147$		0			0
$148$		0			0
$149$	4.41761			0.361905			0.180952	−	0.983492i	$-0.442082\pi$
$149$	4.41761			0.361905			0.180952	+	0.983492i	$0.442082\pi$
$150$		0			0
$151$	24.1464			1.96501			0.982504	−	0.186240i	$-0.0596303\pi$
$151$	24.1464			1.96501			0.982504	+	0.186240i	$0.0596303\pi$
$152$	3.14626	−	3.14626i	0.255196	−	0.255196i
$153$		0			0
$154$			2.24745i			0.181105i
$155$	2.04989	+	2.51059i	0.164651	+	0.201655i
$156$		0			0
$157$	8.02270	+	8.02270i	0.640281	+	0.640281i	0.950625	−	0.310343i	$-0.100444\pi$
$157$	8.02270	+	8.02270i	0.640281	+	0.640281i	−0.310343	+	0.950625i	$0.600444\pi$
$158$	3.85337	+	3.85337i	0.306558	+	0.306558i
$159$		0			0
$160$	−2.22474	−	0.224745i	−0.175882	−	0.0177676i
$161$			13.0137i			1.02562i
$162$		0			0
$163$	−4.12372	+	4.12372i	−0.322995	+	0.322995i	−0.849915	−	0.526920i	$-0.823347\pi$
$163$	−4.12372	+	4.12372i	−0.322995	+	0.322995i	0.526920	+	0.849915i	$0.323347\pi$
$164$	4.87832			0.380932
$165$		0			0
$166$	−14.4495			−1.12150
$167$	−5.51399	+	5.51399i	−0.426685	+	0.426685i	−0.887498	−	0.460812i	$-0.847558\pi$
$167$	−5.51399	+	5.51399i	−0.426685	+	0.426685i	0.460812	+	0.887498i	$0.347558\pi$
$168$		0			0
$169$		−	22.6969i		−	1.74592i
$170$	10.2173	−	8.34242i	0.783634	−	0.639834i
$171$		0			0
$172$	7.22474	+	7.22474i	0.550882	+	0.550882i
$173$	−5.33902	−	5.33902i	−0.405918	−	0.405918i	0.474394	−	0.880312i	$-0.342667\pi$
$173$	−5.33902	−	5.33902i	−0.405918	−	0.405918i	−0.880312	+	0.474394i	$0.842667\pi$
$174$		0			0
$175$	−8.55051	+	5.65153i	−0.646358	+	0.427216i
$176$			1.09638i			0.0826425i
$177$		0			0
$178$	12.3485	−	12.3485i	0.925557	−	0.925557i
$179$	−7.84961			−0.586707			−0.293354	−	0.956004i	$-0.594771\pi$
$179$	−7.84961			−0.586707			−0.293354	+	0.956004i	$0.594771\pi$
$180$		0			0
$181$	−4.24745			−0.315710			−0.157855	−	0.987462i	$-0.550458\pi$
$181$	−4.24745			−0.315710			−0.157855	+	0.987462i	$0.550458\pi$
$182$	−8.66025	+	8.66025i	−0.641941	+	0.641941i
$183$		0			0
$184$			6.34847i			0.468015i
$185$		0			0
$186$		0			0
$187$	−4.57321	−	4.57321i	−0.334427	−	0.334427i
$188$	−7.31747	−	7.31747i	−0.533682	−	0.533682i
$189$		0			0
$190$	1.00000	−	9.89898i	0.0725476	−	0.718147i
$191$		−	16.0492i		−	1.16128i	−0.814162	−	0.580638i	$-0.802803\pi$
$191$		−	16.0492i		−	1.16128i	0.814162	−	0.580638i	$-0.197197\pi$
$192$		0			0
$193$	−6.79796	+	6.79796i	−0.489328	+	0.489328i	−0.908094	−	0.418766i	$-0.862463\pi$
$193$	−6.79796	+	6.79796i	−0.489328	+	0.489328i	0.418766	+	0.908094i	$0.362463\pi$
$194$	−11.9494			−0.857916
$195$		0			0
$196$	−2.79796			−0.199854
$197$	6.75323	−	6.75323i	0.481148	−	0.481148i	−0.424350	−	0.905498i	$-0.639497\pi$
$197$	6.75323	−	6.75323i	0.481148	−	0.481148i	0.905498	+	0.424350i	$0.139497\pi$
$198$		0			0
$199$			12.5505i			0.889682i	0.895610	+	0.444841i	$0.146740\pi$
$199$			12.5505i			0.889682i	−0.895610	+	0.444841i	$0.853260\pi$
$200$	−4.17121	+	2.75699i	−0.294949	+	0.194949i
$201$		0			0
$202$	5.77526	+	5.77526i	0.406346	+	0.406346i
$203$	−4.56048	−	4.56048i	−0.320083	−	0.320083i
$204$		0			0
$205$	8.44949	−	6.89898i	0.590138	−	0.481846i
$206$			2.19275i			0.152776i
$207$		0			0
$208$	−4.22474	+	4.22474i	−0.292933	+	0.292933i
$209$	−4.87832			−0.337440
$210$		0			0
$211$	8.24745			0.567778			0.283889	−	0.958857i	$-0.408375\pi$
$211$	8.24745			0.567778			0.283889	+	0.958857i	$0.408375\pi$
$212$	−5.65685	+	5.65685i	−0.388514	+	0.388514i
$213$		0			0
$214$			5.10102i			0.348699i
$215$	22.7310	+	2.29629i	1.55024	+	0.156606i
$216$		0			0
$217$	−2.10102	−	2.10102i	−0.142627	−	0.142627i
$218$	2.82843	+	2.82843i	0.191565	+	0.191565i
$219$		0			0
$220$	1.55051	+	1.89898i	0.104535	+	0.128029i
$221$		−	35.2446i		−	2.37081i
$222$		0			0
$223$	−12.7980	+	12.7980i	−0.857015	+	0.857015i	−0.990985	−	0.133971i	$-0.957227\pi$
$223$	−12.7980	+	12.7980i	−0.857015	+	0.857015i	0.133971	+	0.990985i	$0.457227\pi$
$224$	2.04989			0.136964
$225$		0			0
$226$	−8.10102			−0.538872
$227$	−5.33902	+	5.33902i	−0.354363	+	0.354363i	−0.861730	−	0.507367i	$-0.830619\pi$
$227$	−5.33902	+	5.33902i	−0.354363	+	0.354363i	0.507367	+	0.861730i	$0.330619\pi$
$228$		0			0
$229$			4.65153i			0.307382i	0.988119	+	0.153691i	$0.0491160\pi$
$229$			4.65153i			0.307382i	−0.988119	+	0.153691i	$0.950884\pi$
$230$	8.97809	+	10.9959i	0.591998	+	0.725046i
$231$		0			0
$232$	−2.22474	−	2.22474i	−0.146062	−	0.146062i
$233$	−3.46410	−	3.46410i	−0.226941	−	0.226941i	0.584473	−	0.811413i	$-0.301301\pi$
$233$	−3.46410	−	3.46410i	−0.226941	−	0.226941i	−0.811413	+	0.584473i	$0.801301\pi$
$234$		0			0
$235$	−23.0227	−	2.32577i	−1.50184	−	0.151716i
$236$		−	2.82843i		−	0.184115i
$237$		0			0
$238$	−8.55051	+	8.55051i	−0.554247	+	0.554247i
$239$	−6.14966			−0.397789			−0.198894	−	0.980021i	$-0.563735\pi$
$239$	−6.14966			−0.397789			−0.198894	+	0.980021i	$0.563735\pi$
$240$		0			0
$241$	−19.6969			−1.26879			−0.634396	−	0.773008i	$-0.718751\pi$
$241$	−19.6969			−1.26879			−0.634396	+	0.773008i	$0.718751\pi$
$242$	−6.92820	+	6.92820i	−0.445362	+	0.445362i
$243$		0			0
$244$			8.44949i			0.540923i
$245$	−4.84621	+	3.95691i	−0.309613	+	0.252798i
$246$		0			0
$247$	−18.7980	−	18.7980i	−1.19609	−	1.19609i
$248$	−1.02494	−	1.02494i	−0.0650840	−	0.0650840i
$249$		0			0
$250$	−3.32577	+	10.6742i	−0.210340	+	0.675098i
$251$		−	1.73205i		−	0.109326i	−0.998505	−	0.0546630i	$-0.982592\pi$
$251$		−	1.73205i		−	0.109326i	0.998505	−	0.0546630i	$-0.0174085\pi$
$252$		0			0
$253$	4.92168	−	4.92168i	0.309424	−	0.309424i
$254$	6.43539			0.403792
$255$		0			0
$256$	1.00000			0.0625000
$257$	−2.61413	+	2.61413i	−0.163065	+	0.163065i	−0.783923	−	0.620858i	$-0.786784\pi$
$257$	−2.61413	+	2.61413i	−0.163065	+	0.163065i	0.620858	+	0.783923i	$0.286784\pi$
$258$		0			0
$259$		0			0
$260$	−1.34278	+	13.2922i	−0.0832758	+	0.824345i
$261$		0			0
$262$	−6.57321	−	6.57321i	−0.406095	−	0.406095i
$263$	0.921404	+	0.921404i	0.0568162	+	0.0568162i	0.734944	−	0.678128i	$-0.237208\pi$
$263$	0.921404	+	0.921404i	0.0568162	+	0.0568162i	−0.678128	+	0.734944i	$0.737208\pi$
$264$		0			0
$265$	−1.79796	+	17.7980i	−0.110448	+	1.09332i
$266$			9.12096i			0.559242i
$267$		0			0
$268$	2.00000	−	2.00000i	0.122169	−	0.122169i
$269$	24.5665			1.49785			0.748924	−	0.662655i	$-0.230571\pi$
$269$	24.5665			1.49785			0.748924	+	0.662655i	$0.230571\pi$
$270$		0			0
$271$	−6.00000			−0.364474			−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000			−0.364474			−0.182237	+	0.983255i	$0.558334\pi$
$272$	−4.17121	+	4.17121i	−0.252917	+	0.252917i
$273$		0			0
$274$		−	21.7980i		−	1.31686i
$275$	5.37113	+	1.09638i	0.323891	+	0.0661140i
$276$		0			0
$277$	9.55051	+	9.55051i	0.573835	+	0.573835i	0.933198	−	0.359363i	$-0.117006\pi$
$277$	9.55051	+	9.55051i	0.573835	+	0.573835i	−0.359363	+	0.933198i	$0.617006\pi$
$278$	−5.83183	−	5.83183i	−0.349770	−	0.349770i
$279$		0			0
$280$	3.55051	−	2.89898i	0.212184	−	0.173247i
$281$			8.83523i			0.527065i	0.964650	+	0.263533i	$0.0848877\pi$
$281$			8.83523i			0.527065i	−0.964650	+	0.263533i	$0.915112\pi$
$282$		0			0
$283$	0.898979	−	0.898979i	0.0534388	−	0.0534388i	−0.679882	−	0.733321i	$-0.737969\pi$
$283$	0.898979	−	0.898979i	0.0534388	−	0.0534388i	0.733321	+	0.679882i	$0.237969\pi$
$284$	13.9993			0.830704
$285$		0			0
$286$	6.55051			0.387340
$287$	−7.07107	+	7.07107i	−0.417392	+	0.417392i
$288$		0			0
$289$		−	17.7980i		−	1.04694i
$290$	−6.99964	−	0.707107i	−0.411033	−	0.0415227i
$291$		0			0
$292$	4.44949	+	4.44949i	0.260387	+	0.260387i
$293$	−4.24264	−	4.24264i	−0.247858	−	0.247858i	0.572233	−	0.820091i	$-0.306077\pi$
$293$	−4.24264	−	4.24264i	−0.247858	−	0.247858i	−0.820091	+	0.572233i	$0.806077\pi$
$294$		0			0
$295$	−4.00000	−	4.89898i	−0.232889	−	0.285230i
$296$		0			0
$297$		0			0
$298$	−3.12372	+	3.12372i	−0.180952	+	0.180952i
$299$	37.9301			2.19356
$300$		0			0
$301$	−20.9444			−1.20721
$302$	−17.0741	+	17.0741i	−0.982504	+	0.982504i
$303$		0			0
$304$			4.44949i			0.255196i
$305$	11.9494	+	14.6349i	0.684220	+	0.837995i
$306$		0			0
$307$	21.6742	+	21.6742i	1.23701	+	1.23701i	0.961216	+	0.275798i	$0.0889422\pi$
$307$	21.6742	+	21.6742i	1.23701	+	1.23701i	0.275798	+	0.961216i	$0.411058\pi$
$308$	−1.58919	−	1.58919i	−0.0905523	−	0.0905523i
$309$		0			0
$310$	−3.22474	−	0.325765i	−0.183153	−	0.0185022i
$311$		−	32.2412i		−	1.82823i	−0.405455	−	0.914115i	$-0.632887\pi$
$311$		−	32.2412i		−	1.82823i	0.405455	−	0.914115i	$-0.367113\pi$
$312$		0			0
$313$	3.24745	−	3.24745i	0.183557	−	0.183557i	−0.609347	−	0.792904i	$-0.708568\pi$
$313$	3.24745	−	3.24745i	0.183557	−	0.183557i	0.792904	+	0.609347i	$0.208568\pi$
$314$	−11.3458			−0.640281
$315$		0			0
$316$	−5.44949			−0.306558
$317$	1.55708	−	1.55708i	0.0874542	−	0.0874542i	−0.662026	−	0.749481i	$-0.730303\pi$
$317$	1.55708	−	1.55708i	0.0874542	−	0.0874542i	0.749481	+	0.662026i	$0.230303\pi$
$318$		0			0
$319$			3.44949i			0.193134i
$320$	1.73205	−	1.41421i	0.0968246	−	0.0790569i
$321$		0			0
$322$	−9.20204	−	9.20204i	−0.512810	−	0.512810i
$323$	−18.5597	−	18.5597i	−1.03269	−	1.03269i
$324$		0			0
$325$	16.4722	+	24.9217i	0.913713	+	1.38241i
$326$		−	5.83183i		−	0.322995i
$327$		0			0
$328$	−3.44949	+	3.44949i	−0.190466	+	0.190466i
$329$	21.2132			1.16952
$330$		0			0
$331$	−21.1010			−1.15982			−0.579908	−	0.814682i	$-0.696912\pi$
$331$	−21.1010			−1.15982			−0.579908	+	0.814682i	$0.696912\pi$
$332$	10.2173	−	10.2173i	0.560749	−	0.560749i
$333$		0			0
$334$		−	7.79796i		−	0.426685i
$335$	0.635674	−	6.29253i	0.0347306	−	0.343798i
$336$		0			0
$337$	−7.10102	−	7.10102i	−0.386817	−	0.386817i	0.486733	−	0.873551i	$-0.338188\pi$
$337$	−7.10102	−	7.10102i	−0.386817	−	0.386817i	−0.873551	+	0.486733i	$0.838188\pi$
$338$	16.0492	+	16.0492i	0.872959	+	0.872959i
$339$		0			0
$340$	−1.32577	+	13.1237i	−0.0718997	+	0.711734i
$341$			1.58919i			0.0860593i
$342$		0			0
$343$	14.2020	−	14.2020i	0.766838	−	0.766838i
$344$	−10.2173			−0.550882
$345$		0			0
$346$	7.55051			0.405918
$347$	−10.0745	+	10.0745i	−0.540826	+	0.540826i	−0.923771	−	0.382945i	$-0.874910\pi$
$347$	−10.0745	+	10.0745i	−0.540826	+	0.540826i	0.382945	+	0.923771i	$0.374910\pi$
$348$		0			0
$349$			20.0454i			1.07301i	0.843898	+	0.536503i	$0.180255\pi$
$349$			20.0454i			1.07301i	−0.843898	+	0.536503i	$0.819745\pi$
$350$	2.04989	−	10.0424i	0.109571	−	0.536787i
$351$		0			0
$352$	−0.775255	−	0.775255i	−0.0413212	−	0.0413212i
$353$	−1.34278	−	1.34278i	−0.0714690	−	0.0714690i	0.670469	−	0.741938i	$-0.266093\pi$
$353$	−1.34278	−	1.34278i	−0.0714690	−	0.0714690i	−0.741938	+	0.670469i	$0.766093\pi$
$354$		0			0
$355$	24.2474	−	19.7980i	1.28692	−	1.05077i
$356$			17.4634i			0.925557i
$357$		0			0
$358$	5.55051	−	5.55051i	0.293354	−	0.293354i
$359$	−24.0416			−1.26887			−0.634434	−	0.772977i	$-0.718767\pi$
$359$	−24.0416			−1.26887			−0.634434	+	0.772977i	$0.718767\pi$
$360$		0			0
$361$	−0.797959			−0.0419978
$362$	3.00340	−	3.00340i	0.157855	−	0.157855i
$363$		0			0
$364$		−	12.2474i		−	0.641941i
$365$	13.9993	+	1.41421i	0.732755	+	0.0740233i
$366$		0			0
$367$	20.2474	+	20.2474i	1.05691	+	1.05691i	0.998280	+	0.0586283i	$0.0186727\pi$
$367$	20.2474	+	20.2474i	1.05691	+	1.05691i	0.0586283	+	0.998280i	$0.481327\pi$
$368$	−4.48905	−	4.48905i	−0.234008	−	0.234008i
$369$		0			0
$370$		0			0
$371$		−	16.3991i		−	0.851399i
$372$		0			0
$373$	19.3712	−	19.3712i	1.00300	−	1.00300i	0.00300584	−	0.999995i	$-0.499043\pi$
$373$	19.3712	−	19.3712i	1.00300	−	1.00300i	0.999995	−	0.00300584i	$-0.000956790\pi$
$374$	6.46750			0.334427
$375$		0			0
$376$	10.3485			0.533682
$377$	−13.2922	+	13.2922i	−0.684581	+	0.684581i
$378$		0			0
$379$			4.00000i			0.205466i	0.994709	+	0.102733i	$0.0327588\pi$
$379$			4.00000i			0.205466i	−0.994709	+	0.102733i	$0.967241\pi$
$380$	6.29253	+	7.70674i	0.322800	+	0.395348i
$381$		0			0
$382$	11.3485	+	11.3485i	0.580638	+	0.580638i
$383$	−14.2457	−	14.2457i	−0.727920	−	0.727920i	0.242285	−	0.970205i	$-0.422103\pi$
$383$	−14.2457	−	14.2457i	−0.727920	−	0.727920i	−0.970205	+	0.242285i	$0.922103\pi$
$384$		0			0
$385$	−5.00000	−	0.505103i	−0.254824	−	0.0257424i
$386$		−	9.61377i		−	0.489328i
$387$		0			0
$388$	8.44949	−	8.44949i	0.428958	−	0.428958i
$389$	−9.43879			−0.478566			−0.239283	−	0.970950i	$-0.576912\pi$
$389$	−9.43879			−0.478566			−0.239283	+	0.970950i	$0.576912\pi$
$390$		0			0
$391$	37.4495			1.89390
$392$	1.97846	−	1.97846i	0.0999271	−	0.0999271i
$393$		0			0
$394$			9.55051i			0.481148i
$395$	−9.43879	+	7.70674i	−0.474917	+	0.387768i
$396$		0			0
$397$	−19.5732	−	19.5732i	−0.982351	−	0.982351i	0.0174955	−	0.999847i	$-0.494431\pi$
$397$	−19.5732	−	19.5732i	−0.982351	−	0.982351i	−0.999847	+	0.0174955i	$0.994431\pi$
$398$	−8.87455	−	8.87455i	−0.444841	−	0.444841i
$399$		0			0
$400$	1.00000	−	4.89898i	0.0500000	−	0.244949i
$401$			10.0424i			0.501492i	0.968053	+	0.250746i	$0.0806758\pi$
$401$			10.0424i			0.501492i	−0.968053	+	0.250746i	$0.919324\pi$
$402$		0			0
$403$	−6.12372	+	6.12372i	−0.305044	+	0.305044i
$404$	−8.16744			−0.406346
$405$		0			0
$406$	6.44949			0.320083
$407$		0			0
$408$		0			0
$409$		−	30.7980i		−	1.52286i	−0.648247	−	0.761431i	$-0.724497\pi$
$409$		−	30.7980i		−	1.52286i	0.648247	−	0.761431i	$-0.275503\pi$
$410$	−1.09638	+	10.8530i	−0.0541462	+	0.535992i
$411$		0			0
$412$	−1.55051	−	1.55051i	−0.0763882	−	0.0763882i
$413$	4.09978	+	4.09978i	0.201737	+	0.201737i
$414$		0			0
$415$	3.24745	−	32.1464i	0.159411	−	1.57801i
$416$		−	5.97469i		−	0.292933i
$417$		0			0
$418$	3.44949	−	3.44949i	0.168720	−	0.168720i
$419$	−34.1161			−1.66668			−0.833340	−	0.552760i	$-0.813574\pi$
$419$	−34.1161			−1.66668			−0.833340	+	0.552760i	$0.813574\pi$
$420$		0			0
$421$	−13.5505			−0.660411			−0.330206	−	0.943909i	$-0.607118\pi$
$421$	−13.5505			−0.660411			−0.330206	+	0.943909i	$0.607118\pi$
$422$	−5.83183	+	5.83183i	−0.283889	+	0.283889i
$423$		0			0
$424$		−	8.00000i		−	0.388514i
$425$	16.2635	+	24.6059i	0.788893	+	1.19356i
$426$		0			0
$427$	−12.2474	−	12.2474i	−0.592696	−	0.592696i
$428$	−3.60697	−	3.60697i	−0.174349	−	0.174349i
$429$		0			0
$430$	−17.6969	+	14.4495i	−0.853422	+	0.696816i
$431$			22.6274i			1.08992i	0.838461	+	0.544962i	$0.183456\pi$
$431$			22.6274i			1.08992i	−0.838461	+	0.544962i	$0.816544\pi$
$432$		0			0
$433$	14.2474	−	14.2474i	0.684689	−	0.684689i	−0.276364	−	0.961053i	$-0.589130\pi$
$433$	14.2474	−	14.2474i	0.684689	−	0.684689i	0.961053	+	0.276364i	$0.0891296\pi$
$434$	2.97129			0.142627
$435$		0			0
$436$	−4.00000			−0.191565
$437$	19.9740	−	19.9740i	0.955484	−	0.955484i
$438$		0			0
$439$			3.59592i			0.171624i	0.996311	+	0.0858119i	$0.0273484\pi$
$439$			3.59592i			0.171624i	−0.996311	+	0.0858119i	$0.972652\pi$
$440$	−2.43916	−	0.246405i	−0.116282	−	0.0117469i
$441$		0			0
$442$	24.9217	+	24.9217i	1.18540	+	1.18540i
$443$	4.41761	+	4.41761i	0.209887	+	0.209887i	0.804220	−	0.594332i	$-0.202584\pi$
$443$	4.41761	+	4.41761i	0.209887	+	0.209887i	−0.594332	+	0.804220i	$0.702584\pi$
$444$		0			0
$445$	24.6969	+	30.2474i	1.17075	+	1.43387i
$446$		−	18.0990i		−	0.857015i
$447$		0			0
$448$	−1.44949	+	1.44949i	−0.0684820	+	0.0684820i
$449$	15.5563			0.734150			0.367075	−	0.930191i	$-0.380359\pi$
$449$	15.5563			0.734150			0.367075	+	0.930191i	$0.380359\pi$
$450$		0			0
$451$	5.34847			0.251850
$452$	5.72829	−	5.72829i	0.269436	−	0.269436i
$453$		0			0
$454$		−	7.55051i		−	0.354363i
$455$	−17.3205	−	21.2132i	−0.811998	−	0.994490i
$456$		0			0
$457$	14.6969	+	14.6969i	0.687494	+	0.687494i	0.961677	−	0.274184i	$-0.0884076\pi$
$457$	14.6969	+	14.6969i	0.687494	+	0.687494i	−0.274184	+	0.961677i	$0.588408\pi$
$458$	−3.28913	−	3.28913i	−0.153691	−	0.153691i
$459$		0			0
$460$	−14.1237	−	1.42679i	−0.658522	−	0.0665242i
$461$		−	2.82843i		−	0.131733i	−0.997828	−	0.0658665i	$-0.979019\pi$
$461$		−	2.82843i		−	0.131733i	0.997828	−	0.0658665i	$-0.0209811\pi$
$462$		0			0
$463$	−11.3485	+	11.3485i	−0.527408	+	0.527408i	−0.919799	−	0.392391i	$-0.871648\pi$
$463$	−11.3485	+	11.3485i	−0.527408	+	0.527408i	0.392391	+	0.919799i	$0.371648\pi$
$464$	3.14626			0.146062
$465$		0			0
$466$	4.89898			0.226941
$467$	−6.61037	+	6.61037i	−0.305891	+	0.305891i	−0.843313	−	0.537422i	$-0.819398\pi$
$467$	−6.61037	+	6.61037i	−0.305891	+	0.305891i	0.537422	+	0.843313i	$0.319398\pi$
$468$		0			0
$469$			5.79796i			0.267725i
$470$	17.9241	−	14.6349i	0.826776	−	0.675060i
$471$		0			0
$472$	2.00000	+	2.00000i	0.0920575	+	0.0920575i
$473$	7.92104	+	7.92104i	0.364210	+	0.364210i
$474$		0			0
$475$	21.7980	+	4.44949i	1.00016	+	0.204157i
$476$		−	12.0922i		−	0.554247i
$477$		0			0
$478$	4.34847	−	4.34847i	0.198894	−	0.198894i
$479$	−18.3848			−0.840022			−0.420011	−	0.907519i	$-0.637974\pi$
$479$	−18.3848			−0.840022			−0.420011	+	0.907519i	$0.637974\pi$
$480$		0			0
$481$		0			0
$482$	13.9278	−	13.9278i	0.634396	−	0.634396i
$483$		0			0
$484$		−	9.79796i		−	0.445362i
$485$	2.68556	−	26.5843i	0.121945	−	1.20713i
$486$		0			0
$487$	−14.6969	−	14.6969i	−0.665982	−	0.665982i	0.290802	−	0.956783i	$-0.406078\pi$
$487$	−14.6969	−	14.6969i	−0.665982	−	0.665982i	−0.956783	+	0.290802i	$0.906078\pi$
$488$	−5.97469	−	5.97469i	−0.270462	−	0.270462i
$489$		0			0
$490$	0.628827	−	6.22474i	0.0284075	−	0.281205i
$491$			25.1701i			1.13591i	0.823059	+	0.567956i	$0.192266\pi$
$491$			25.1701i			1.13591i	−0.823059	+	0.567956i	$0.807734\pi$
$492$		0			0
$493$	−13.1237	+	13.1237i	−0.591063	+	0.591063i
$494$	26.5843			1.19609
$495$		0			0
$496$	1.44949			0.0650840
$497$	−20.2918	+	20.2918i	−0.910212	+	0.910212i
$498$		0			0
$499$			5.79796i			0.259552i	0.991543	+	0.129776i	$0.0414259\pi$
$499$			5.79796i			0.259552i	−0.991543	+	0.129776i	$0.958574\pi$
$500$	−5.19615	−	9.89949i	−0.232379	−	0.442719i
$501$		0			0
$502$	1.22474	+	1.22474i	0.0546630	+	0.0546630i
$503$	26.1951	+	26.1951i	1.16798	+	1.16798i	0.982682	+	0.185297i	$0.0593249\pi$
$503$	26.1951	+	26.1951i	1.16798	+	1.16798i	0.185297	+	0.982682i	$0.440675\pi$
$504$		0			0
$505$	−14.1464	+	11.5505i	−0.629508	+	0.513991i
$506$			6.96031i			0.309424i
$507$		0			0
$508$	−4.55051	+	4.55051i	−0.201896	+	0.201896i
$509$	18.8455			0.835311			0.417656	−	0.908605i	$-0.362852\pi$
$509$	18.8455			0.835311			0.417656	+	0.908605i	$0.362852\pi$
$510$		0			0
$511$	−12.8990			−0.570617
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	3.69694i		−	0.163065i
$515$	−4.87832	−	0.492810i	−0.214964	−	0.0217158i
$516$		0			0
$517$	−8.02270	−	8.02270i	−0.352838	−	0.352838i
$518$		0			0
$519$		0			0
$520$	−8.44949	−	10.3485i	−0.370535	−	0.453810i
$521$			4.59259i			0.201205i	0.994927	+	0.100602i	$0.0320770\pi$
$521$			4.59259i			0.201205i	−0.994927	+	0.100602i	$0.967923\pi$
$522$		0			0
$523$	4.77526	−	4.77526i	0.208807	−	0.208807i	−0.594953	−	0.803760i	$-0.702829\pi$
$523$	4.77526	−	4.77526i	0.208807	−	0.208807i	0.803760	+	0.594953i	$0.202829\pi$
$524$	9.29593			0.406095
$525$		0			0
$526$	−1.30306			−0.0568162
$527$	−6.04612	+	6.04612i	−0.263373	+	0.263373i
$528$		0			0
$529$			17.3031i			0.752307i
$530$	−11.3137	−	13.8564i	−0.491436	−	0.601884i
$531$		0			0
$532$	−6.44949	−	6.44949i	−0.279621	−	0.279621i
$533$	20.6096	+	20.6096i	0.892702	+	0.892702i
$534$		0			0
$535$	−11.3485	−	1.14643i	−0.490637	−	0.0495644i
$536$			2.82843i			0.122169i
$537$		0			0
$538$	−17.3712	+	17.3712i	−0.748924	+	0.748924i
$539$	−3.06762			−0.132132
$540$		0			0
$541$	−9.59592			−0.412561			−0.206280	−	0.978493i	$-0.566136\pi$
$541$	−9.59592			−0.412561			−0.206280	+	0.978493i	$0.566136\pi$
$542$	4.24264	−	4.24264i	0.182237	−	0.182237i
$543$		0			0
$544$		−	5.89898i		−	0.252917i
$545$	−6.92820	+	5.65685i	−0.296772	+	0.242313i
$546$		0			0
$547$	−13.4722	−	13.4722i	−0.576029	−	0.576029i	0.357777	−	0.933807i	$-0.383535\pi$
$547$	−13.4722	−	13.4722i	−0.576029	−	0.576029i	−0.933807	+	0.357777i	$0.883535\pi$
$548$	15.4135	+	15.4135i	0.658431	+	0.658431i
$549$		0			0
$550$	−4.57321	+	3.02270i	−0.195003	+	0.128889i
$551$			13.9993i			0.596389i
$552$		0			0
$553$	7.89898	−	7.89898i	0.335899	−	0.335899i
$554$	−13.5065			−0.573835
$555$		0			0
$556$	8.24745			0.349770
$557$	12.1244	−	12.1244i	0.513725	−	0.513725i	−0.401940	−	0.915666i	$-0.631664\pi$
$557$	12.1244	−	12.1244i	0.513725	−	0.513725i	0.915666	+	0.401940i	$0.131664\pi$
$558$		0			0
$559$			61.0454i			2.58195i
$560$	−0.460702	+	4.56048i	−0.0194682	+	0.192715i
$561$		0			0
$562$	−6.24745	−	6.24745i	−0.263533	−	0.263533i
$563$	−13.6814	−	13.6814i	−0.576604	−	0.576604i	0.357362	−	0.933966i	$-0.383676\pi$
$563$	−13.6814	−	13.6814i	−0.576604	−	0.576604i	−0.933966	+	0.357362i	$0.883676\pi$
$564$		0			0
$565$	1.82066	−	18.0227i	0.0765959	−	0.758221i
$566$			1.27135i			0.0534388i
$567$		0			0
$568$	−9.89898	+	9.89898i	−0.415352	+	0.415352i
$569$	−22.0560			−0.924634			−0.462317	−	0.886715i	$-0.652982\pi$
$569$	−22.0560			−0.924634			−0.462317	+	0.886715i	$0.652982\pi$
$570$		0			0
$571$	−1.55051			−0.0648868			−0.0324434	−	0.999474i	$-0.510329\pi$
$571$	−1.55051			−0.0648868			−0.0324434	+	0.999474i	$0.510329\pi$
$572$	−4.63191	+	4.63191i	−0.193670	+	0.193670i
$573$		0			0
$574$		−	10.0000i		−	0.417392i
$575$	−26.4808	+	17.5027i	−1.10433	+	0.729913i
$576$		0			0
$577$	4.00000	+	4.00000i	0.166522	+	0.166522i	0.785449	−	0.618927i	$-0.212432\pi$
$577$	4.00000	+	4.00000i	0.166522	+	0.166522i	−0.618927	+	0.785449i	$0.712432\pi$
$578$	12.5851	+	12.5851i	0.523469	+	0.523469i
$579$		0			0
$580$	5.44949	−	4.44949i	0.226278	−	0.184755i
$581$			29.6198i			1.22884i
$582$		0			0
$583$	−6.20204	+	6.20204i	−0.256862	+	0.256862i
$584$	−6.29253			−0.260387
$585$		0			0
$586$	6.00000			0.247858
$587$	24.0737	−	24.0737i	0.993630	−	0.993630i	−0.00635031	−	0.999980i	$-0.502021\pi$
$587$	24.0737	−	24.0737i	0.993630	−	0.993630i	0.999980	+	0.00635031i	$0.00202138\pi$
$588$		0			0
$589$			6.44949i			0.265747i
$590$	6.29253	+	0.635674i	0.259059	+	0.0261703i
$591$		0			0
$592$		0			0
$593$	23.9702	+	23.9702i	0.984338	+	0.984338i	0.999879	−	0.0155412i	$-0.00494711\pi$
$593$	23.9702	+	23.9702i	0.984338	+	0.984338i	−0.0155412	+	0.999879i	$0.504947\pi$
$594$		0			0
$595$	−17.1010	−	20.9444i	−0.701073	−	0.858636i
$596$		−	4.41761i		−	0.180952i
$597$		0			0
$598$	−26.8207	+	26.8207i	−1.09678	+	1.09678i
$599$	18.5919			0.759643			0.379821	−	0.925060i	$-0.375985\pi$
$599$	18.5919			0.759643			0.379821	+	0.925060i	$0.375985\pi$
$600$		0			0
$601$	−18.3939			−0.750302			−0.375151	−	0.926964i	$-0.622409\pi$
$601$	−18.3939			−0.750302			−0.375151	+	0.926964i	$0.622409\pi$
$602$	14.8099	−	14.8099i	0.603607	−	0.603607i
$603$		0			0
$604$		−	24.1464i		−	0.982504i
$605$	−13.8564	−	16.9706i	−0.563343	−	0.689951i
$606$		0			0
$607$	−16.6515	−	16.6515i	−0.675865	−	0.675865i	0.283197	−	0.959062i	$-0.408605\pi$
$607$	−16.6515	−	16.6515i	−0.675865	−	0.675865i	−0.959062	+	0.283197i	$0.908605\pi$
$608$	−3.14626	−	3.14626i	−0.127598	−	0.127598i
$609$		0			0
$610$	−18.7980	−	1.89898i	−0.761107	−	0.0768874i
$611$		−	61.8289i		−	2.50133i
$612$		0			0
$613$	−10.4722	+	10.4722i	−0.422968	+	0.422968i	−0.886224	−	0.463256i	$-0.846681\pi$
$613$	−10.4722	+	10.4722i	−0.422968	+	0.422968i	0.463256	+	0.886224i	$0.346681\pi$
$614$	−30.6520			−1.23701
$615$		0			0
$616$	2.24745			0.0905523
$617$	−3.67840	+	3.67840i	−0.148087	+	0.148087i	−0.777263	−	0.629176i	$-0.783392\pi$
$617$	−3.67840	+	3.67840i	−0.148087	+	0.148087i	0.629176	+	0.777263i	$0.283392\pi$
$618$		0			0
$619$			8.69694i			0.349559i	0.984608	+	0.174780i	$0.0559213\pi$
$619$			8.69694i			0.349559i	−0.984608	+	0.174780i	$0.944079\pi$
$620$	2.51059	−	2.04989i	0.100828	−	0.0823255i
$621$		0			0
$622$	22.7980	+	22.7980i	0.914115	+	0.914115i
$623$	−25.3130	−	25.3130i	−1.01414	−	1.01414i
$624$		0			0
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$			4.59259i			0.183557i
$627$		0			0
$628$	8.02270	−	8.02270i	0.320141	−	0.320141i
$629$		0			0
$630$		0			0
$631$	4.49490			0.178939			0.0894695	−	0.995990i	$-0.471483\pi$
$631$	4.49490			0.178939			0.0894695	+	0.995990i	$0.471483\pi$
$632$	3.85337	−	3.85337i	0.153279	−	0.153279i
$633$		0			0
$634$			2.20204i			0.0874542i
$635$	−1.44632	+	14.3171i	−0.0573955	+	0.568157i
$636$		0			0
$637$	−11.8207	−	11.8207i	−0.468352	−	0.468352i
$638$	−2.43916	−	2.43916i	−0.0965672	−	0.0965672i
$639$		0			0
$640$	−0.224745	+	2.22474i	−0.00888382	+	0.0879408i
$641$			27.8557i			1.10023i	0.835088	+	0.550117i	$0.185417\pi$
$641$			27.8557i			1.10023i	−0.835088	+	0.550117i	$0.814583\pi$
$642$		0			0
$643$	−32.8207	+	32.8207i	−1.29432	+	1.29432i	−0.362233	+	0.932088i	$0.617986\pi$
$643$	−32.8207	+	32.8207i	−1.29432	+	1.29432i	−0.932088	+	0.362233i	$0.882014\pi$
$644$	13.0137			0.512810
$645$		0			0
$646$	26.2474			1.03269
$647$	6.00680	−	6.00680i	0.236152	−	0.236152i	−0.579103	−	0.815254i	$-0.696597\pi$
$647$	6.00680	−	6.00680i	0.236152	−	0.236152i	0.815254	+	0.579103i	$0.196597\pi$
$648$		0			0
$649$		−	3.10102i		−	0.121726i
$650$	−29.2699	−	5.97469i	−1.14806	−	0.234347i
$651$		0			0
$652$	4.12372	+	4.12372i	0.161498	+	0.161498i
$653$	10.5673	+	10.5673i	0.413530	+	0.413530i	0.882966	−	0.469437i	$-0.155543\pi$
$653$	10.5673	+	10.5673i	0.413530	+	0.413530i	−0.469437	+	0.882966i	$0.655543\pi$
$654$		0			0
$655$	16.1010	−	13.1464i	0.629119	−	0.513673i
$656$		−	4.87832i		−	0.190466i
$657$		0			0
$658$	−15.0000	+	15.0000i	−0.584761	+	0.584761i
$659$	−32.0983			−1.25037			−0.625186	−	0.780475i	$-0.714977\pi$
$659$	−32.0983			−1.25037			−0.625186	+	0.780475i	$0.714977\pi$
$660$		0			0
$661$	−20.0454			−0.779676			−0.389838	−	0.920883i	$-0.627469\pi$
$661$	−20.0454			−0.779676			−0.389838	+	0.920883i	$0.627469\pi$
$662$	14.9207	−	14.9207i	0.579908	−	0.579908i
$663$		0			0
$664$			14.4495i			0.560749i
$665$	−20.2918	−	2.04989i	−0.786882	−	0.0794912i
$666$		0			0
$667$	−14.1237	−	14.1237i	−0.546873	−	0.546873i
$668$	5.51399	+	5.51399i	0.213343	+	0.213343i
$669$		0			0
$670$	4.00000	+	4.89898i	0.154533	+	0.189264i
$671$			9.26382i			0.357626i
$672$		0			0
$673$	34.7980	−	34.7980i	1.34136	−	1.34136i	0.446658	−	0.894705i	$-0.352614\pi$
$673$	34.7980	−	34.7980i	1.34136	−	1.34136i	0.894705	−	0.446658i	$-0.147386\pi$
$674$	10.0424			0.386817
$675$		0			0
$676$	−22.6969			−0.872959
$677$	33.6554	−	33.6554i	1.29348	−	1.29348i	0.360863	−	0.932619i	$-0.382482\pi$
$677$	33.6554	−	33.6554i	1.29348	−	1.29348i	0.932619	−	0.360863i	$-0.117518\pi$
$678$		0			0
$679$			24.4949i			0.940028i
$680$	−8.34242	−	10.2173i	−0.319917	−	0.391817i
$681$		0			0
$682$	−1.12372	−	1.12372i	−0.0430296	−	0.0430296i
$683$	−6.92820	−	6.92820i	−0.265100	−	0.265100i	0.562022	−	0.827122i	$-0.310024\pi$
$683$	−6.92820	−	6.92820i	−0.265100	−	0.265100i	−0.827122	+	0.562022i	$0.810024\pi$
$684$		0			0
$685$	48.4949	+	4.89898i	1.85289	+	0.187180i
$686$			20.0847i			0.766838i
$687$		0			0
$688$	7.22474	−	7.22474i	0.275441	−	0.275441i
$689$	−47.7975			−1.82094
$690$		0			0
$691$	22.8990			0.871118			0.435559	−	0.900160i	$-0.356551\pi$
$691$	22.8990			0.871118			0.435559	+	0.900160i	$0.356551\pi$
$692$	−5.33902	+	5.33902i	−0.202959	+	0.202959i
$693$		0			0
$694$		−	14.2474i		−	0.540826i
$695$	14.2850	−	11.6637i	0.541861	−	0.442428i
$696$		0			0
$697$	20.3485	+	20.3485i	0.770753	+	0.770753i
$698$	−14.1742	−	14.1742i	−0.536503	−	0.536503i
$699$		0			0
$700$	5.65153	+	8.55051i	0.213608	+	0.323179i
$701$		−	13.8243i		−	0.522137i	−0.965320	−	0.261068i	$-0.915925\pi$
$701$		−	13.8243i		−	0.522137i	0.965320	−	0.261068i	$-0.0840748\pi$
$702$		0			0
$703$		0			0
$704$	1.09638			0.0413212
$705$		0			0
$706$	1.89898			0.0714690
$707$	11.8386	−	11.8386i	0.445237	−	0.445237i
$708$		0			0
$709$		−	8.00000i		−	0.300446i	−0.988652	−	0.150223i	$-0.952001\pi$
$709$		−	8.00000i		−	0.300446i	0.988652	−	0.150223i	$-0.0479992\pi$
$710$	−3.14626	+	31.1448i	−0.118077	+	1.16884i
$711$		0			0
$712$	−12.3485	−	12.3485i	−0.462778	−	0.462778i
$713$	−6.50683	−	6.50683i	−0.243683	−	0.243683i
$714$		0			0
$715$	−1.47219	+	14.5732i	−0.0550569	+	0.545007i
$716$			7.84961i			0.293354i
$717$		0			0
$718$	17.0000	−	17.0000i	0.634434	−	0.634434i
$719$	29.7627			1.10996			0.554981	−	0.831863i	$-0.312726\pi$
$719$	29.7627			1.10996			0.554981	+	0.831863i	$0.312726\pi$
$720$		0			0
$721$	4.49490			0.167399
$722$	0.564242	−	0.564242i	0.0209989	−	0.0209989i
$723$		0			0
$724$			4.24745i			0.157855i
$725$	3.14626	−	15.4135i	0.116849	−	0.572442i
$726$		0			0
$727$	−24.4949	−	24.4949i	−0.908465	−	0.908465i	0.0876830	−	0.996148i	$-0.472054\pi$
$727$	−24.4949	−	24.4949i	−0.908465	−	0.908465i	−0.996148	+	0.0876830i	$0.972054\pi$
$728$	8.66025	+	8.66025i	0.320970	+	0.320970i
$729$		0			0
$730$	−10.8990	+	8.89898i	−0.403389	+	0.329366i
$731$			60.2718i			2.22923i
$732$		0			0
$733$	23.5959	−	23.5959i	0.871535	−	0.871535i	−0.121105	−	0.992640i	$-0.538644\pi$
$733$	23.5959	−	23.5959i	0.871535	−	0.871535i	0.992640	+	0.121105i	$0.0386437\pi$
$734$	−28.6342			−1.05691
$735$		0			0
$736$	6.34847			0.234008
$737$	2.19275	−	2.19275i	0.0807711	−	0.0807711i
$738$		0			0
$739$			9.84337i			0.362094i	0.983474	+	0.181047i	$0.0579486\pi$
$739$			9.84337i			0.362094i	−0.983474	+	0.181047i	$0.942051\pi$
$740$		0			0
$741$		0			0
$742$	11.5959	+	11.5959i	0.425700	+	0.425700i
$743$	19.7597	+	19.7597i	0.724912	+	0.724912i	0.969601	−	0.244690i	$-0.0786861\pi$
$743$	19.7597	+	19.7597i	0.724912	+	0.724912i	−0.244690	+	0.969601i	$0.578686\pi$
$744$		0			0
$745$	−6.24745	−	7.65153i	−0.228889	−	0.280330i
$746$			27.3950i			1.00300i
$747$		0			0
$748$	−4.57321	+	4.57321i	−0.167213	+	0.167213i
$749$	10.4565			0.382073
$750$		0			0
$751$	25.0454			0.913920			0.456960	−	0.889487i	$-0.348938\pi$
$751$	25.0454			0.913920			0.456960	+	0.889487i	$0.348938\pi$
$752$	−7.31747	+	7.31747i	−0.266841	+	0.266841i
$753$		0			0
$754$		−	18.7980i		−	0.684581i
$755$	−34.1482	−	41.8228i	−1.24278	−	1.52209i
$756$		0			0
$757$	2.02270	+	2.02270i	0.0735164	+	0.0735164i	0.742909	−	0.669393i	$-0.233446\pi$
$757$	2.02270	+	2.02270i	0.0735164	+	0.0735164i	−0.669393	+	0.742909i	$0.733446\pi$
$758$	−2.82843	−	2.82843i	−0.102733	−	0.102733i
$759$		0			0
$760$	−9.89898	−	1.00000i	−0.359074	−	0.0362738i
$761$			4.52837i			0.164153i	0.996626	+	0.0820766i	$0.0261552\pi$
$761$			4.52837i			0.164153i	−0.996626	+	0.0820766i	$0.973845\pi$
$762$		0			0
$763$	5.79796	−	5.79796i	0.209900	−	0.209900i
$764$	−16.0492			−0.580638
$765$		0			0
$766$	20.1464			0.727920
$767$	11.9494	−	11.9494i	0.431467	−	0.431467i
$768$		0			0
$769$			31.6969i			1.14302i	0.820595	+	0.571510i	$0.193642\pi$
$769$			31.6969i			1.14302i	−0.820595	+	0.571510i	$0.806358\pi$
$770$	3.89270	−	3.17837i	0.140283	−	0.114541i
$771$		0			0
$772$	6.79796	+	6.79796i	0.244664	+	0.244664i
$773$	−1.12848	−	1.12848i	−0.0405888	−	0.0405888i	0.686521	−	0.727110i	$-0.259137\pi$
$773$	−1.12848	−	1.12848i	−0.0405888	−	0.0405888i	−0.727110	+	0.686521i	$0.759137\pi$
$774$		0			0
$775$	1.44949	−	7.10102i	0.0520672	−	0.255076i
$776$			11.9494i			0.428958i
$777$		0			0
$778$	6.67423	−	6.67423i	0.239283	−	0.239283i
$779$	21.7060			0.777699
$780$		0			0
$781$	15.3485			0.549211
$782$	−26.4808	+	26.4808i	−0.946951	+	0.946951i
$783$		0			0
$784$			2.79796i			0.0999271i
$785$	2.54991	−	25.2415i	0.0910103	−	0.900909i
$786$		0			0
$787$	12.5732	+	12.5732i	0.448187	+	0.448187i	0.894751	−	0.446565i	$-0.147353\pi$
$787$	12.5732	+	12.5732i	0.448187	+	0.448187i	−0.446565	+	0.894751i	$0.647353\pi$
$788$	−6.75323	−	6.75323i	−0.240574	−	0.240574i
$789$		0			0
$790$	1.22474	−	12.1237i	0.0435745	−	0.431343i
$791$			16.6062i			0.590448i
$792$		0			0
$793$	−35.6969	+	35.6969i	−1.26764	+	1.26764i
$794$	27.6807			0.982351
$795$		0			0
$796$	12.5505			0.444841
$797$	18.7026	−	18.7026i	0.662481	−	0.662481i	−0.293484	−	0.955964i	$-0.594815\pi$
$797$	18.7026	−	18.7026i	0.662481	−	0.662481i	0.955964	+	0.293484i	$0.0948146\pi$
$798$		0			0
$799$		−	61.0454i		−	2.15963i
$800$	2.75699	+	4.17121i	0.0974745	+	0.147474i
$801$		0			0
$802$	−7.10102	−	7.10102i	−0.250746	−	0.250746i
$803$	4.87832	+	4.87832i	0.172152	+	0.172152i
$804$		0			0
$805$	22.5403	−	18.4041i	0.794441	−	0.648659i
$806$		−	8.66025i		−	0.305044i
$807$		0			0
$808$	5.77526	−	5.77526i	0.203173	−	0.203173i
$809$	15.6992			0.551955			0.275977	−	0.961164i	$-0.410998\pi$
$809$	15.6992			0.551955			0.275977	+	0.961164i	$0.410998\pi$
$810$		0			0
$811$	30.8990			1.08501			0.542505	−	0.840053i	$-0.317476\pi$
$811$	30.8990			1.08501			0.542505	+	0.840053i	$0.317476\pi$
$812$	−4.56048	+	4.56048i	−0.160041	+	0.160041i
$813$		0			0
$814$		0			0
$815$	12.9743	+	1.31067i	0.454471	+	0.0459109i
$816$		0			0
$817$	32.1464	+	32.1464i	1.12466	+	1.12466i
$818$	21.7774	+	21.7774i	0.761431	+	0.761431i
$819$		0			0
$820$	−6.89898	−	8.44949i	−0.240923	−	0.295069i
$821$		−	5.08540i		−	0.177482i	−0.996055	−	0.0887408i	$-0.971716\pi$
$821$		−	5.08540i		−	0.177482i	0.996055	−	0.0887408i	$-0.0282843\pi$
$822$		0			0
$823$	−4.00000	+	4.00000i	−0.139431	+	0.139431i	−0.773377	−	0.633946i	$-0.781434\pi$
$823$	−4.00000	+	4.00000i	−0.139431	+	0.139431i	0.633946	+	0.773377i	$0.281434\pi$
$824$	2.19275			0.0763882
$825$		0			0
$826$	−5.79796			−0.201737
$827$	17.7491	−	17.7491i	0.617197	−	0.617197i	−0.327615	−	0.944811i	$-0.606245\pi$
$827$	17.7491	−	17.7491i	0.617197	−	0.617197i	0.944811	+	0.327615i	$0.106245\pi$
$828$		0			0
$829$		−	25.7980i		−	0.896000i	−0.894034	−	0.448000i	$-0.852136\pi$
$829$		−	25.7980i		−	0.896000i	0.894034	−	0.448000i	$-0.147864\pi$
$830$	20.4347	+	25.0273i	0.709298	+	0.868709i
$831$		0			0
$832$	4.22474	+	4.22474i	0.146467	+	0.146467i
$833$	−11.6709	−	11.6709i	−0.404372	−	0.404372i
$834$		0			0
$835$	17.3485	+	1.75255i	0.600369	+	0.0606495i
$836$			4.87832i			0.168720i
$837$		0			0
$838$	24.1237	−	24.1237i	0.833340	−	0.833340i
$839$	−8.54950			−0.295161			−0.147581	−	0.989050i	$-0.547149\pi$
$839$	−8.54950			−0.295161			−0.147581	+	0.989050i	$0.547149\pi$
$840$		0			0
$841$	−19.1010			−0.658656
$842$	9.58166	−	9.58166i	0.330206	−	0.330206i
$843$		0			0
$844$		−	8.24745i		−	0.283889i
$845$	−39.3123	+	32.0983i	−1.35238	+	1.10422i
$846$		0			0
$847$	14.2020	+	14.2020i	0.487988	+	0.487988i
$848$	5.65685	+	5.65685i	0.194257	+	0.194257i
$849$		0			0
$850$	−28.8990	−	5.89898i	−0.991227	−	0.202333i
$851$		0			0
$852$		0			0
$853$	16.4268	−	16.4268i	0.562442	−	0.562442i	−0.367558	−	0.930001i	$-0.619806\pi$
$853$	16.4268	−	16.4268i	0.562442	−	0.562442i	0.930001	+	0.367558i	$0.119806\pi$
$854$	17.3205			0.592696
$855$		0			0
$856$	5.10102			0.174349
$857$	24.2487	−	24.2487i	0.828320	−	0.828320i	−0.158964	−	0.987284i	$-0.550815\pi$
$857$	24.2487	−	24.2487i	0.828320	−	0.828320i	0.987284	+	0.158964i	$0.0508154\pi$
$858$		0			0
$859$		−	2.89898i		−	0.0989119i	−0.998776	−	0.0494560i	$-0.984251\pi$
$859$		−	2.89898i		−	0.0989119i	0.998776	−	0.0494560i	$-0.0157487\pi$
$860$	2.29629	−	22.7310i	0.0783029	−	0.775119i
$861$		0			0
$862$	−16.0000	−	16.0000i	−0.544962	−	0.544962i
$863$	7.95315	+	7.95315i	0.270728	+	0.270728i	0.829393	−	0.558665i	$-0.188686\pi$
$863$	7.95315	+	7.95315i	0.270728	+	0.270728i	−0.558665	+	0.829393i	$0.688686\pi$
$864$		0			0
$865$	−1.69694	+	16.7980i	−0.0576976	+	0.571148i
$866$			20.1489i			0.684689i
$867$		0			0
$868$	−2.10102	+	2.10102i	−0.0713133	+	0.0713133i
$869$	−5.97469			−0.202678
$870$		0			0
$871$	16.8990			0.572600
$872$	2.82843	−	2.82843i	0.0957826	−	0.0957826i
$873$		0			0
$874$			28.2474i			0.955484i
$875$	21.8810	+	6.81745i	0.739712	+	0.230472i
$876$		0			0
$877$	−24.9217	−	24.9217i	−0.841545	−	0.841545i	0.147514	−	0.989060i	$-0.452873\pi$
$877$	−24.9217	−	24.9217i	−0.841545	−	0.841545i	−0.989060	+	0.147514i	$0.952873\pi$
$878$	−2.54270	−	2.54270i	−0.0858119	−	0.0858119i
$879$		0			0
$880$	1.89898	−	1.55051i	0.0640146	−	0.0522677i
$881$		−	40.2337i		−	1.35551i	−0.735290	−	0.677753i	$-0.762954\pi$
$881$		−	40.2337i		−	1.35551i	0.735290	−	0.677753i	$-0.237046\pi$
$882$		0			0
$883$	33.1464	−	33.1464i	1.11547	−	1.11547i	0.123068	−	0.992398i	$-0.460727\pi$
$883$	33.1464	−	33.1464i	1.11547	−	1.11547i	0.992398	−	0.123068i	$-0.0392733\pi$
$884$	−35.2446			−1.18540
$885$		0			0
$886$	−6.24745			−0.209887
$887$	10.4316	−	10.4316i	0.350260	−	0.350260i	−0.509946	−	0.860206i	$-0.670335\pi$
$887$	10.4316	−	10.4316i	0.350260	−	0.350260i	0.860206	+	0.509946i	$0.170335\pi$
$888$		0			0
$889$		−	13.1918i		−	0.442440i
$890$	−38.8515	−	3.92480i	−1.30231	−	0.131560i
$891$		0			0
$892$	12.7980	+	12.7980i	0.428507	+	0.428507i
$893$	−32.5590	−	32.5590i	−1.08955	−	1.08955i
$894$		0			0
$895$	11.1010	+	13.5959i	0.371066	+	0.454461i
$896$		−	2.04989i		−	0.0684820i
$897$		0			0
$898$	−11.0000	+	11.0000i	−0.367075	+	0.367075i
$899$	4.56048			0.152100
$900$		0			0
$901$	−47.1918			−1.57219
$902$	−3.78194	+	3.78194i	−0.125925	+	0.125925i
$903$		0			0
$904$			8.10102i			0.269436i
$905$	6.00680	+	7.35680i	0.199673	+	0.244548i
$906$		0			0
$907$	−1.62883	−	1.62883i	−0.0540843	−	0.0540843i	0.679547	−	0.733632i	$-0.262176\pi$
$907$	−1.62883	−	1.62883i	−0.0540843	−	0.0540843i	−0.733632	+	0.679547i	$0.762176\pi$
$908$	5.33902	+	5.33902i	0.177182	+	0.177182i
$909$		0			0
$910$	27.2474	+	2.75255i	0.903244	+	0.0912462i
$911$		−	43.4120i		−	1.43830i	−0.694852	−	0.719152i	$-0.744530\pi$
$911$		−	43.4120i		−	1.43830i	0.694852	−	0.719152i	$-0.255470\pi$
$912$		0			0
$913$	11.2020	−	11.2020i	0.370733	−	0.370733i
$914$	−20.7846			−0.687494
$915$		0			0
$916$	4.65153			0.153691
$917$	−13.4744	+	13.4744i	−0.444962	+	0.444962i
$918$		0			0
$919$		−	5.65153i		−	0.186427i	−0.995646	−	0.0932134i	$-0.970286\pi$
$919$		−	5.65153i		−	0.186427i	0.995646	−	0.0932134i	$-0.0297139\pi$
$920$	10.9959	−	8.97809i	0.362523	−	0.295999i
$921$		0			0
$922$	2.00000	+	2.00000i	0.0658665	+	0.0658665i
$923$	59.1433	+	59.1433i	1.94673	+	1.94673i
$924$		0			0
$925$		0			0
$926$		−	16.0492i		−	0.527408i
$927$		0			0
$928$	−2.22474	+	2.22474i	−0.0730308	+	0.0730308i
$929$	39.8051			1.30596			0.652981	−	0.757374i	$-0.273518\pi$
$929$	39.8051			1.30596			0.652981	+	0.757374i	$0.273518\pi$
$930$		0			0
$931$	−12.4495			−0.408016
$932$	−3.46410	+	3.46410i	−0.113470	+	0.113470i
$933$		0			0
$934$		−	9.34847i		−	0.305891i
$935$	−1.45354	+	14.3885i	−0.0475358	+	0.470556i
$936$		0			0
$937$	19.4949	+	19.4949i	0.636871	+	0.636871i	0.949782	−	0.312912i	$-0.101304\pi$
$937$	19.4949	+	19.4949i	0.636871	+	0.636871i	−0.312912	+	0.949782i	$0.601304\pi$
$938$	−4.09978	−	4.09978i	−0.133862	−	0.133862i
$939$		0			0
$940$	−2.32577	+	23.0227i	−0.0758581	+	0.750918i
$941$			33.3376i			1.08677i	0.839483	+	0.543387i	$0.182858\pi$
$941$			33.3376i			1.08677i	−0.839483	+	0.543387i	$0.817142\pi$
$942$		0			0
$943$	−21.8990	+	21.8990i	−0.713129	+	0.713129i
$944$	−2.82843			−0.0920575
$945$		0			0
$946$	−11.2020			−0.364210
$947$	−33.4804	+	33.4804i	−1.08797	+	1.08797i	−0.0922298	+	0.995738i	$0.529399\pi$
$947$	−33.4804	+	33.4804i	−1.08797	+	1.08797i	−0.995738	+	0.0922298i	$0.970601\pi$
$948$		0			0
$949$			37.5959i			1.22042i
$950$	−18.5597	+	12.2672i	−0.602158	+	0.398001i
$951$		0			0
$952$	8.55051	+	8.55051i	0.277124	+	0.277124i
$953$	3.67840	+	3.67840i	0.119155	+	0.119155i	0.764170	−	0.645015i	$-0.223149\pi$
$953$	3.67840	+	3.67840i	0.119155	+	0.119155i	−0.645015	+	0.764170i	$0.723149\pi$
$954$		0			0
$955$	−27.7980	+	22.6969i	−0.899521	+	0.734456i
$956$			6.14966i			0.198894i
$957$		0			0
$958$	13.0000	−	13.0000i	0.420011	−	0.420011i
$959$	−44.6834			−1.44290
$960$		0			0
$961$	−28.8990			−0.932225
$962$		0			0
$963$		0			0
$964$			19.6969i			0.634396i
$965$	21.3882	+	2.16064i	0.688510	+	0.0695536i
$966$		0			0
$967$	11.3485	+	11.3485i	0.364942	+	0.364942i	0.865629	−	0.500687i	$-0.166919\pi$
$967$	11.3485	+	11.3485i	0.364942	+	0.364942i	−0.500687	+	0.865629i	$0.666919\pi$
$968$	6.92820	+	6.92820i	0.222681	+	0.222681i
$969$		0			0
$970$	16.8990	+	20.6969i	0.542594	+	0.664539i
$971$		−	37.8659i		−	1.21518i	−0.794253	−	0.607588i	$-0.792137\pi$
$971$		−	37.8659i		−	1.21518i	0.794253	−	0.607588i	$-0.207863\pi$
$972$		0			0
$973$	−11.9546	+	11.9546i	−0.383247	+	0.383247i
$974$	20.7846			0.665982
$975$		0			0
$976$	8.44949			0.270462
$977$	−14.0707	+	14.0707i	−0.450162	+	0.450162i	−0.895408	−	0.445246i	$-0.853116\pi$
$977$	−14.0707	+	14.0707i	−0.450162	+	0.450162i	0.445246	+	0.895408i	$0.353116\pi$
$978$		0			0
$979$			19.1464i			0.611922i
$980$	3.95691	+	4.84621i	0.126399	+	0.154806i
$981$		0			0
$982$	−17.7980	−	17.7980i	−0.567956	−	0.567956i
$983$	−12.1958	−	12.1958i	−0.388985	−	0.388985i	0.485340	−	0.874325i	$-0.338696\pi$
$983$	−12.1958	−	12.1958i	−0.388985	−	0.388985i	−0.874325	+	0.485340i	$0.838696\pi$
$984$		0			0
$985$	−21.2474	−	2.14643i	−0.677000	−	0.0683909i
$986$		−	18.5597i		−	0.591063i
$987$		0			0
$988$	−18.7980	+	18.7980i	−0.598043	+	0.598043i
$989$	−64.8644			−2.06257
$990$		0			0
$991$	−41.7423			−1.32599			−0.662995	−	0.748624i	$-0.730715\pi$
$991$	−41.7423			−1.32599			−0.662995	+	0.748624i	$0.730715\pi$
$992$	−1.02494	+	1.02494i	−0.0325420	+	0.0325420i
$993$		0			0
$994$		−	28.6969i		−	0.910212i
$995$	21.7381	−	17.7491i	0.689145	−	0.562684i
$996$		0			0
$997$	−14.9217	−	14.9217i	−0.472574	−	0.472574i	0.430172	−	0.902747i	$-0.358453\pi$
$997$	−14.9217	−	14.9217i	−0.472574	−	0.472574i	−0.902747	+	0.430172i	$0.858453\pi$
$998$	−4.09978	−	4.09978i	−0.129776	−	0.129776i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.f.a.107.1	yes	8
3.2	odd	2	inner	270.2.f.a.107.4	yes	8
4.3	odd	2		2160.2.w.f.1457.1		8
5.2	odd	4		1350.2.f.f.593.1		8
5.3	odd	4	inner	270.2.f.a.53.3	yes	8
5.4	even	2		1350.2.f.f.107.3		8
9.2	odd	6		810.2.m.a.377.1		8
9.4	even	3		810.2.m.a.107.1		8
9.5	odd	6		810.2.m.h.107.2		8
9.7	even	3		810.2.m.h.377.2		8
12.11	even	2		2160.2.w.f.1457.4		8
15.2	even	4		1350.2.f.f.593.3		8
15.8	even	4	inner	270.2.f.a.53.2	✓	8
15.14	odd	2		1350.2.f.f.107.1		8
20.3	even	4		2160.2.w.f.593.3		8
45.13	odd	12		810.2.m.a.593.1		8
45.23	even	12		810.2.m.h.593.2		8
45.38	even	12		810.2.m.a.53.1		8
45.43	odd	12		810.2.m.h.53.2		8
60.23	odd	4		2160.2.w.f.593.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.f.a.53.2	✓	8	15.8	even	4	inner
270.2.f.a.53.3	yes	8	5.3	odd	4	inner
270.2.f.a.107.1	yes	8	1.1	even	1	trivial
270.2.f.a.107.4	yes	8	3.2	odd	2	inner
810.2.m.a.53.1		8	45.38	even	12
810.2.m.a.107.1		8	9.4	even	3
810.2.m.a.377.1		8	9.2	odd	6
810.2.m.a.593.1		8	45.13	odd	12
810.2.m.h.53.2		8	45.43	odd	12
810.2.m.h.107.2		8	9.5	odd	6
810.2.m.h.377.2		8	9.7	even	3
810.2.m.h.593.2		8	45.23	even	12
1350.2.f.f.107.1		8	15.14	odd	2
1350.2.f.f.107.3		8	5.4	even	2
1350.2.f.f.593.1		8	5.2	odd	4
1350.2.f.f.593.3		8	15.2	even	4
2160.2.w.f.593.2		8	60.23	odd	4
2160.2.w.f.593.3		8	20.3	even	4
2160.2.w.f.1457.1		8	4.3	odd	2
2160.2.w.f.1457.4		8	12.11	even	2

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.41421 - 1.73205i) q^{5} +(1.44949 + 1.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.41421 - 1.73205i) q^{5} +(1.44949 + 1.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.22474 + 0.224745i) q^{10} -1.09638i q^{11} +(4.22474 - 4.22474i) q^{13} -2.04989 q^{14} -1.00000 q^{16} +(4.17121 - 4.17121i) q^{17} -4.44949i q^{19} +(-1.73205 + 1.41421i) q^{20} +(0.775255 + 0.775255i) q^{22} +(4.48905 + 4.48905i) q^{23} +(-1.00000 + 4.89898i) q^{25} +5.97469i q^{26} +(1.44949 - 1.44949i) q^{28} -3.14626 q^{29} -1.44949 q^{31} +(0.707107 - 0.707107i) q^{32} +5.89898i q^{34} +(0.460702 - 4.56048i) q^{35} +(3.14626 + 3.14626i) q^{38} +(0.224745 - 2.22474i) q^{40} +4.87832i q^{41} +(-7.22474 + 7.22474i) q^{43} -1.09638 q^{44} -6.34847 q^{46} +(7.31747 - 7.31747i) q^{47} -2.79796i q^{49} +(-2.75699 - 4.17121i) q^{50} +(-4.22474 - 4.22474i) q^{52} +(-5.65685 - 5.65685i) q^{53} +(-1.89898 + 1.55051i) q^{55} +2.04989i q^{56} +(2.22474 - 2.22474i) q^{58} +2.82843 q^{59} -8.44949 q^{61} +(1.02494 - 1.02494i) q^{62} +1.00000i q^{64} +(-13.2922 - 1.34278i) q^{65} +(2.00000 + 2.00000i) q^{67} +(-4.17121 - 4.17121i) q^{68} +(2.89898 + 3.55051i) q^{70} +13.9993i q^{71} +(-4.44949 + 4.44949i) q^{73} -4.44949 q^{76} +(1.58919 - 1.58919i) q^{77} -5.44949i q^{79} +(1.41421 + 1.73205i) q^{80} +(-3.44949 - 3.44949i) q^{82} +(10.2173 + 10.2173i) q^{83} +(-13.1237 - 1.32577i) q^{85} -10.2173i q^{86} +(0.775255 - 0.775255i) q^{88} -17.4634 q^{89} +12.2474 q^{91} +(4.48905 - 4.48905i) q^{92} +10.3485i q^{94} +(-7.70674 + 6.29253i) q^{95} +(8.44949 + 8.44949i) q^{97} +(1.97846 + 1.97846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} + 8 q^{10} + 24 q^{13} - 8 q^{16} + 16 q^{22} - 8 q^{25} - 8 q^{28} + 8 q^{31} - 8 q^{40} - 48 q^{43} + 8 q^{46} - 24 q^{52} + 24 q^{55} + 8 q^{58} - 48 q^{61} + 16 q^{67} - 16 q^{70} - 16 q^{73} - 16 q^{76} - 8 q^{82} - 56 q^{85} + 16 q^{88} + 48 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 + 8 * q^10 + 24 * q^13 - 8 * q^16 + 16 * q^22 - 8 * q^25 - 8 * q^28 + 8 * q^31 - 8 * q^40 - 48 * q^43 + 8 * q^46 - 24 * q^52 + 24 * q^55 + 8 * q^58 - 48 * q^61 + 16 * q^67 - 16 * q^70 - 16 * q^73 - 16 * q^76 - 8 * q^82 - 56 * q^85 + 16 * q^88 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more