LMFDB - Embedded newform 1100.2.q.b.221.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,2,Mod(221,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("1100.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.q (of order $5$, degree $4$, 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:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.8
Character	$\chi$	$=$	1100.221
Dual form			1100.2.q.b.881.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.722709 + 0.525079i) q^{3} +(1.39423 + 1.74818i) q^{5} +1.78111 q^{7} +(-0.680451 - 2.09421i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(1.61178 + 4.96054i) q^{13} +(0.0896884 + 1.99550i) q^{15} +(2.21980 - 1.61278i) q^{17} +(0.400006 - 0.290622i) q^{19} +(1.28723 + 0.935224i) q^{21} +(-0.601937 + 1.85257i) q^{23} +(-1.11226 + 4.87472i) q^{25} +(1.43601 - 4.41958i) q^{27} +(0.705083 + 0.512273i) q^{29} +(3.23288 - 2.34883i) q^{31} +(-0.722709 + 0.525079i) q^{33} +(2.48327 + 3.11370i) q^{35} +(1.67890 + 5.16713i) q^{37} +(-1.43983 + 4.43133i) q^{39} +(-2.01543 - 6.20285i) q^{41} -3.82844 q^{43} +(2.71236 - 4.10936i) q^{45} +(4.24705 + 3.08567i) q^{47} -3.82764 q^{49} +2.45111 q^{51} +(2.54764 + 1.85097i) q^{53} +(-2.09346 + 0.785772i) q^{55} +0.441687 q^{57} +(-1.01123 - 3.11226i) q^{59} +(-2.80371 + 8.62892i) q^{61} +(-1.21196 - 3.73003i) q^{63} +(-6.42473 + 9.73379i) q^{65} +(-3.65535 + 2.65577i) q^{67} +(-1.40777 + 1.02280i) q^{69} +(3.86992 + 2.81166i) q^{71} +(2.51385 - 7.73684i) q^{73} +(-3.36345 + 2.93898i) q^{75} +(-0.550394 + 1.69394i) q^{77} +(-5.06666 - 3.68114i) q^{79} +(-1.98589 + 1.44283i) q^{81} +(1.96298 - 1.42619i) q^{83} +(5.91433 + 1.63203i) q^{85} +(0.240586 + 0.740448i) q^{87} +(-0.446707 + 1.37482i) q^{89} +(2.87076 + 8.83528i) q^{91} +3.56975 q^{93} +(1.06576 + 0.294090i) q^{95} +(3.05092 + 2.21662i) q^{97} +2.20198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) $ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.722709	+	0.525079i	0.417256	+	0.303154i	0.776533	−	0.630077i	$-0.216977\pi$
$3$	0.722709	+	0.525079i	0.417256	+	0.303154i	−0.359277	+	0.933231i	$0.616977\pi$
$4$		0			0
$5$	1.39423	+	1.74818i	0.623517	+	0.781810i
$5$	1.39423	+	1.74818i	0.623517	+	0.781810i
$6$		0			0
$7$	1.78111			0.673197			0.336599	−	0.941648i	$-0.390723\pi$
$7$	1.78111			0.673197			0.336599	+	0.941648i	$0.390723\pi$
$8$		0			0
$9$	−0.680451	−	2.09421i	−0.226817	−	0.698071i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$		0			0
$13$	1.61178	+	4.96054i	0.447026	+	1.37581i	0.880246	+	0.474518i	$0.157377\pi$
$13$	1.61178	+	4.96054i	0.447026	+	1.37581i	−0.433220	+	0.901288i	$0.642623\pi$
$14$		0			0
$15$	0.0896884	+	1.99550i	0.0231575	+	0.515237i
$16$		0			0
$17$	2.21980	−	1.61278i	0.538381	−	0.391157i	−0.285103	−	0.958497i	$-0.592028\pi$
$17$	2.21980	−	1.61278i	0.538381	−	0.391157i	0.823483	+	0.567341i	$0.192028\pi$
$18$		0			0
$19$	0.400006	−	0.290622i	0.0917677	−	0.0666732i	−0.540955	−	0.841051i	$-0.681937\pi$
$19$	0.400006	−	0.290622i	0.0917677	−	0.0666732i	0.632723	+	0.774378i	$0.281937\pi$
$20$		0			0
$21$	1.28723	+	0.935224i	0.280896	+	0.204083i
$22$		0			0
$23$	−0.601937	+	1.85257i	−0.125512	+	0.386288i	−0.993994	−	0.109434i	$-0.965096\pi$
$23$	−0.601937	+	1.85257i	−0.125512	+	0.386288i	0.868482	+	0.495721i	$0.165096\pi$
$24$		0			0
$25$	−1.11226	+	4.87472i	−0.222452	+	0.974944i
$26$		0			0
$27$	1.43601	−	4.41958i	0.276360	−	0.850549i
$28$		0			0
$29$	0.705083	+	0.512273i	0.130931	+	0.0951267i	0.651323	−	0.758801i	$-0.274214\pi$
$29$	0.705083	+	0.512273i	0.130931	+	0.0951267i	−0.520392	+	0.853927i	$0.674214\pi$
$30$		0			0
$31$	3.23288	−	2.34883i	0.580643	−	0.421862i	−0.258313	−	0.966061i	$-0.583167\pi$
$31$	3.23288	−	2.34883i	0.580643	−	0.421862i	0.838956	+	0.544200i	$0.183167\pi$
$32$		0			0
$33$	−0.722709	+	0.525079i	−0.125807	+	0.0914045i
$34$		0			0
$35$	2.48327	+	3.11370i	0.419750	+	0.526312i
$36$		0			0
$37$	1.67890	+	5.16713i	0.276010	+	0.849471i	0.988950	+	0.148247i	$0.0473630\pi$
$37$	1.67890	+	5.16713i	0.276010	+	0.849471i	−0.712940	+	0.701225i	$0.752637\pi$
$38$		0			0
$39$	−1.43983	+	4.43133i	−0.230557	+	0.709581i
$40$		0			0
$41$	−2.01543	−	6.20285i	−0.314757	−	0.968722i	−0.975854	−	0.218422i	$-0.929909\pi$
$41$	−2.01543	−	6.20285i	−0.314757	−	0.968722i	0.661097	−	0.750300i	$-0.270091\pi$
$42$		0			0
$43$	−3.82844			−0.583832			−0.291916	−	0.956444i	$-0.594293\pi$
$43$	−3.82844			−0.583832			−0.291916	+	0.956444i	$0.594293\pi$
$44$		0			0
$45$	2.71236	−	4.10936i	0.404334	−	0.612587i
$46$		0			0
$47$	4.24705	+	3.08567i	0.619497	+	0.450091i	0.852746	−	0.522326i	$-0.174936\pi$
$47$	4.24705	+	3.08567i	0.619497	+	0.450091i	−0.233249	+	0.972417i	$0.574936\pi$
$48$		0			0
$49$	−3.82764			−0.546806
$50$		0			0
$51$	2.45111			0.343223
$52$		0			0
$53$	2.54764	+	1.85097i	0.349945	+	0.254250i	0.748846	−	0.662744i	$-0.230608\pi$
$53$	2.54764	+	1.85097i	0.349945	+	0.254250i	−0.398901	+	0.916994i	$0.630608\pi$
$54$		0			0
$55$	−2.09346	+	0.785772i	−0.282282	+	0.105953i
$56$		0			0
$57$	0.441687			0.0585029
$58$		0			0
$59$	−1.01123	−	3.11226i	−0.131651	−	0.405181i	0.863403	−	0.504515i	$-0.168329\pi$
$59$	−1.01123	−	3.11226i	−0.131651	−	0.405181i	−0.995054	+	0.0993340i	$0.968329\pi$
$60$		0			0
$61$	−2.80371	+	8.62892i	−0.358978	+	1.10482i	0.594689	+	0.803956i	$0.297275\pi$
$61$	−2.80371	+	8.62892i	−0.358978	+	1.10482i	−0.953667	+	0.300865i	$0.902725\pi$
$62$		0			0
$63$	−1.21196	−	3.73003i	−0.152692	−	0.469939i
$64$		0			0
$65$	−6.42473	+	9.73379i	−0.796890	+	1.20733i
$66$		0			0
$67$	−3.65535	+	2.65577i	−0.446573	+	0.324454i	−0.788241	−	0.615367i	$-0.789008\pi$
$67$	−3.65535	+	2.65577i	−0.446573	+	0.324454i	0.341669	+	0.939821i	$0.389008\pi$
$68$		0			0
$69$	−1.40777	+	1.02280i	−0.169476	+	0.123131i
$70$		0			0
$71$	3.86992	+	2.81166i	0.459275	+	0.333683i	0.793247	−	0.608900i	$-0.208389\pi$
$71$	3.86992	+	2.81166i	0.459275	+	0.333683i	−0.333972	+	0.942583i	$0.608389\pi$
$72$		0			0
$73$	2.51385	−	7.73684i	0.294224	−	0.905529i	−0.689257	−	0.724517i	$-0.742063\pi$
$73$	2.51385	−	7.73684i	0.294224	−	0.905529i	0.983481	−	0.181012i	$-0.0579372\pi$
$74$		0			0
$75$	−3.36345	+	2.93898i	−0.388378	+	0.339364i
$76$		0			0
$77$	−0.550394	+	1.69394i	−0.0627232	+	0.193042i
$78$		0			0
$79$	−5.06666	−	3.68114i	−0.570043	−	0.414161i	0.265078	−	0.964227i	$-0.414602\pi$
$79$	−5.06666	−	3.68114i	−0.570043	−	0.414161i	−0.835121	+	0.550066i	$0.814602\pi$
$80$		0			0
$81$	−1.98589	+	1.44283i	−0.220654	+	0.160315i
$82$		0			0
$83$	1.96298	−	1.42619i	0.215465	−	0.156544i	−0.474818	−	0.880084i	$-0.657486\pi$
$83$	1.96298	−	1.42619i	0.215465	−	0.156544i	0.690283	+	0.723540i	$0.257486\pi$
$84$		0			0
$85$	5.91433	+	1.63203i	0.641500	+	0.177018i
$86$		0			0
$87$	0.240586	+	0.740448i	0.0257935	+	0.0793844i
$88$		0			0
$89$	−0.446707	+	1.37482i	−0.0473509	+	0.145731i	−0.971937	−	0.235243i	$-0.924411\pi$
$89$	−0.446707	+	1.37482i	−0.0473509	+	0.145731i	0.924586	+	0.380974i	$0.124411\pi$
$90$		0			0
$91$	2.87076	+	8.83528i	0.300937	+	0.926189i
$92$		0			0
$93$	3.56975			0.370166
$94$		0			0
$95$	1.06576	+	0.294090i	0.109344	+	0.0301730i
$96$		0			0
$97$	3.05092	+	2.21662i	0.309774	+	0.225064i	0.731799	−	0.681520i	$-0.238681\pi$
$97$	3.05092	+	2.21662i	0.309774	+	0.225064i	−0.422026	+	0.906584i	$0.638681\pi$
$98$		0			0
$99$	2.20198			0.221308
$100$		0			0
$101$	10.8417			1.07878			0.539392	−	0.842055i	$-0.318654\pi$
$101$	10.8417			1.07878			0.539392	+	0.842055i	$0.318654\pi$
$102$		0			0
$103$	−14.9081	−	10.8314i	−1.46894	−	1.06725i	−0.980919	−	0.194417i	$-0.937719\pi$
$103$	−14.9081	−	10.8314i	−1.46894	−	1.06725i	−0.488022	−	0.872831i	$-0.662281\pi$
$104$		0			0
$105$	0.159745	+	3.55421i	0.0155895	+	0.346856i
$106$		0			0
$107$	9.07446			0.877261			0.438630	−	0.898668i	$-0.355464\pi$
$107$	9.07446			0.877261			0.438630	+	0.898668i	$0.355464\pi$
$108$		0			0
$109$	4.42222	+	13.6102i	0.423572	+	1.30362i	0.904355	+	0.426780i	$0.140352\pi$
$109$	4.42222	+	13.6102i	0.423572	+	1.30362i	−0.480784	+	0.876839i	$0.659648\pi$
$110$		0			0
$111$	−1.49979	+	4.61589i	−0.142354	+	0.438121i
$112$		0			0
$113$	−0.000908882	−	0.00279725i	−8.55004e−5	−	0.000263143i	0.951014	−	0.309149i	$-0.100044\pi$
$113$	−0.000908882	−	0.00279725i	−8.55004e−5	−	0.000263143i	−0.951099	+	0.308885i	$0.900044\pi$
$114$		0			0
$115$	−4.07786	+	1.53061i	−0.380263	+	0.142730i
$116$		0			0
$117$	9.29168	−	6.75080i	0.859017	−	0.624112i
$118$		0			0
$119$	3.95371	−	2.87254i	0.362436	−	0.263325i
$120$		0			0
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$		0			0
$123$	1.80042	−	5.54111i	0.162338	−	0.499625i
$124$		0			0
$125$	−10.0726	+	4.85203i	−0.900923	+	0.433979i
$126$		0			0
$127$	5.32151	−	16.3779i	0.472207	−	1.45330i	−0.377480	−	0.926018i	$-0.623209\pi$
$127$	5.32151	−	16.3779i	0.472207	−	1.45330i	0.849687	−	0.527287i	$-0.176791\pi$
$128$		0			0
$129$	−2.76685	−	2.01023i	−0.243607	−	0.176991i
$130$		0			0
$131$	10.1056	−	7.34216i	0.882932	−	0.641488i	−0.0510937	−	0.998694i	$-0.516271\pi$
$131$	10.1056	−	7.34216i	0.882932	−	0.641488i	0.934025	+	0.357206i	$0.116271\pi$
$132$		0			0
$133$	0.712456	−	0.517630i	0.0617778	−	0.0448842i
$134$		0			0
$135$	9.72834	−	3.65150i	0.837282	−	0.314271i
$136$		0			0
$137$	−1.88364	−	5.79724i	−0.160930	−	0.495292i	0.837783	−	0.546003i	$-0.183851\pi$
$137$	−1.88364	−	5.79724i	−0.160930	−	0.495292i	−0.998713	+	0.0507112i	$0.983851\pi$
$138$		0			0
$139$	4.67841	−	14.3987i	0.396817	−	1.22128i	−0.530720	−	0.847547i	$-0.678078\pi$
$139$	4.67841	−	14.3987i	0.396817	−	1.22128i	0.927537	−	0.373731i	$-0.121922\pi$
$140$		0			0
$141$	1.44917	+	4.46007i	0.122042	+	0.375606i
$142$		0			0
$143$	−5.21582			−0.436169
$144$		0			0
$145$	0.0875011	+	1.94684i	0.00726657	+	0.161676i
$146$		0			0
$147$	−2.76627	−	2.00981i	−0.228158	−	0.165766i
$148$		0			0
$149$	−8.15553			−0.668127			−0.334063	−	0.942551i	$-0.608420\pi$
$149$	−8.15553			−0.668127			−0.334063	+	0.942551i	$0.608420\pi$
$150$		0			0
$151$	1.90530			0.155051			0.0775254	−	0.996990i	$-0.475298\pi$
$151$	1.90530			0.155051			0.0775254	+	0.996990i	$0.475298\pi$
$152$		0			0
$153$	−4.88797	−	3.55132i	−0.395169	−	0.287107i
$154$		0			0
$155$	8.61354	+	2.37686i	0.691856	+	0.190914i
$156$		0			0
$157$	−5.04002			−0.402238			−0.201119	−	0.979567i	$-0.564458\pi$
$157$	−5.04002			−0.402238			−0.201119	+	0.979567i	$0.564458\pi$
$158$		0			0
$159$	0.869298	+	2.67542i	0.0689398	+	0.212175i
$160$		0			0
$161$	−1.07212	+	3.29964i	−0.0844946	+	0.260048i
$162$		0			0
$163$	−2.20080	−	6.77335i	−0.172380	−	0.530530i	0.827124	−	0.562019i	$-0.189975\pi$
$163$	−2.20080	−	6.77335i	−0.172380	−	0.530530i	−0.999504	+	0.0314887i	$0.989975\pi$
$164$		0			0
$165$	−1.92555	−	0.531346i	−0.149904	−	0.0413652i
$166$		0			0
$167$	3.61926	−	2.62954i	0.280067	−	0.203480i	−0.438880	−	0.898546i	$-0.644625\pi$
$167$	3.61926	−	2.62954i	0.280067	−	0.203480i	0.718946	+	0.695065i	$0.244625\pi$
$168$		0			0
$169$	−11.4919	+	8.34936i	−0.883992	+	0.642258i
$170$		0			0
$171$	−0.880808	−	0.639944i	−0.0673570	−	0.0489378i
$172$		0			0
$173$	2.74310	−	8.44239i	0.208554	−	0.641863i	−0.790995	−	0.611823i	$-0.790436\pi$
$173$	2.74310	−	8.44239i	0.208554	−	0.641863i	0.999549	−	0.0300403i	$-0.00956356\pi$
$174$		0			0
$175$	−1.98106	+	8.68242i	−0.149754	+	0.656329i
$176$		0			0
$177$	0.903352	−	2.78023i	0.0679001	−	0.208975i
$178$		0			0
$179$	−13.4932	−	9.80337i	−1.00853	−	0.732739i	−0.0446283	−	0.999004i	$-0.514210\pi$
$179$	−13.4932	−	9.80337i	−1.00853	−	0.732739i	−0.963900	+	0.266265i	$0.914210\pi$
$180$		0			0
$181$	−17.8674	+	12.9814i	−1.32807	+	0.964903i	−0.328281	+	0.944580i	$0.606469\pi$
$181$	−17.8674	+	12.9814i	−1.32807	+	0.964903i	−0.999793	+	0.0203225i	$0.993531\pi$
$182$		0			0
$183$	−6.55713	+	4.76403i	−0.484717	+	0.352167i
$184$		0			0
$185$	−6.69230	+	10.1392i	−0.492028	+	0.745447i
$186$		0			0
$187$	0.847888	+	2.60953i	0.0620037	+	0.190828i
$188$		0			0
$189$	2.55769	−	7.87177i	0.186045	−	0.572587i
$190$		0			0
$191$	−2.97223	−	9.14758i	−0.215063	−	0.661896i	−0.999149	−	0.0412437i	$-0.986868\pi$
$191$	−2.97223	−	9.14758i	−0.215063	−	0.661896i	0.784086	−	0.620652i	$-0.213132\pi$
$192$		0			0
$193$	−17.4383			−1.25524			−0.627619	−	0.778521i	$-0.715970\pi$
$193$	−17.4383			−1.25524			−0.627619	+	0.778521i	$0.715970\pi$
$194$		0			0
$195$	−9.75421	+	3.66121i	−0.698514	+	0.262185i
$196$		0			0
$197$	5.78387	+	4.20223i	0.412084	+	0.299396i	0.774445	−	0.632641i	$-0.218029\pi$
$197$	5.78387	+	4.20223i	0.412084	+	0.299396i	−0.362361	+	0.932038i	$0.618029\pi$
$198$		0			0
$199$	−24.3258			−1.72441			−0.862206	−	0.506558i	$-0.830918\pi$
$199$	−24.3258			−1.72441			−0.862206	+	0.506558i	$0.830918\pi$
$200$		0			0
$201$	−4.03624			−0.284695
$202$		0			0
$203$	1.25583	+	0.912415i	0.0881421	+	0.0640390i
$204$		0			0
$205$	8.03373	−	12.1715i	0.561100	−	0.850095i
$206$		0			0
$207$	4.28926			0.298124
$208$		0			0
$209$	0.152789	+	0.470236i	0.0105686	+	0.0325269i
$210$		0			0
$211$	0.0454974	−	0.140027i	0.00313217	−	0.00963984i	−0.949478	−	0.313833i	$-0.898387\pi$
$211$	0.0454974	−	0.140027i	0.00313217	−	0.00963984i	0.952610	+	0.304193i	$0.0983868\pi$
$212$		0			0
$213$	1.32048	+	4.06402i	0.0904779	+	0.278462i
$214$		0			0
$215$	−5.33771	−	6.69280i	−0.364029	−	0.456445i
$216$		0			0
$217$	5.75813	−	4.18352i	0.390887	−	0.283996i
$218$		0			0
$219$	5.87923	−	4.27151i	0.397282	−	0.288642i
$220$		0			0
$221$	11.5781	+	8.41197i	0.778826	+	0.565850i
$222$		0			0
$223$	5.60909	−	17.2630i	0.375613	−	1.15602i	−0.567452	−	0.823407i	$-0.692071\pi$
$223$	5.60909	−	17.2630i	0.375613	−	1.15602i	0.943064	−	0.332610i	$-0.107929\pi$
$224$		0			0
$225$	10.9655	−	0.987693i	0.731035	−	0.0658462i
$226$		0			0
$227$	2.36311	−	7.27291i	0.156845	−	0.482720i	−0.841498	−	0.540260i	$-0.818326\pi$
$227$	2.36311	−	7.27291i	0.156845	−	0.482720i	0.998343	+	0.0575403i	$0.0183258\pi$
$228$		0			0
$229$	−0.958318	−	0.696259i	−0.0633274	−	0.0460101i	0.555671	−	0.831402i	$-0.312461\pi$
$229$	−0.958318	−	0.696259i	−0.0633274	−	0.0460101i	−0.618999	+	0.785392i	$0.712461\pi$
$230$		0			0
$231$	−1.28723	+	0.935224i	−0.0846932	+	0.0615332i
$232$		0			0
$233$	16.0295	−	11.6461i	1.05013	−	0.762962i	0.0778906	−	0.996962i	$-0.475182\pi$
$233$	16.0295	−	11.6461i	1.05013	−	0.762962i	0.972237	+	0.234000i	$0.0751815\pi$
$234$		0			0
$235$	0.527061	+	11.7267i	0.0343817	+	0.764968i
$236$		0			0
$237$	−1.72883	−	5.32079i	−0.112299	−	0.345622i
$238$		0			0
$239$	2.99542	−	9.21894i	0.193757	−	0.596324i	−0.806231	−	0.591600i	$-0.798496\pi$
$239$	2.99542	−	9.21894i	0.193757	−	0.596324i	0.999989	−	0.00472368i	$-0.00150360\pi$
$240$		0			0
$241$	−4.42040	−	13.6046i	−0.284743	−	0.876350i	−0.986475	−	0.163909i	$-0.947590\pi$
$241$	−4.42040	−	13.6046i	−0.284743	−	0.876350i	0.701732	−	0.712441i	$-0.252410\pi$
$242$		0			0
$243$	−16.1339			−1.03499
$244$		0			0
$245$	−5.33660	−	6.69140i	−0.340943	−	0.427498i
$246$		0			0
$247$	2.08636	+	1.51583i	0.132752	+	0.0964499i
$248$		0			0
$249$	2.16752			0.137361
$250$		0			0
$251$	7.29984			0.460762			0.230381	−	0.973101i	$-0.426003\pi$
$251$	7.29984			0.460762			0.230381	+	0.973101i	$0.426003\pi$
$252$		0			0
$253$	−1.57589	−	1.14495i	−0.0990754	−	0.0719825i
$254$		0			0
$255$	3.41740	+	4.28497i	0.214006	+	0.268335i
$256$		0			0
$257$	2.60768			0.162663			0.0813313	−	0.996687i	$-0.474083\pi$
$257$	2.60768			0.162663			0.0813313	+	0.996687i	$0.474083\pi$
$258$		0			0
$259$	2.99031	+	9.20324i	0.185809	+	0.571862i
$260$		0			0
$261$	0.593034	−	1.82517i	0.0367079	−	0.112975i
$262$		0			0
$263$	−5.47673	−	16.8556i	−0.337709	−	1.03936i	−0.965372	−	0.260877i	$-0.915988\pi$
$263$	−5.47673	−	16.8556i	−0.337709	−	1.03936i	0.627663	−	0.778485i	$-0.284012\pi$
$264$		0			0
$265$	0.316163	+	7.03440i	0.0194218	+	0.432120i
$266$		0			0
$267$	−1.04473	+	0.759040i	−0.0639364	+	0.0464525i
$268$		0			0
$269$	−22.4976	+	16.3454i	−1.37170	+	0.996599i	−0.374099	+	0.927389i	$0.622048\pi$
$269$	−22.4976	+	16.3454i	−1.37170	+	0.996599i	−0.997602	+	0.0692106i	$0.977952\pi$
$270$		0			0
$271$	16.3054	+	11.8466i	0.990483	+	0.719628i	0.960027	−	0.279908i	$-0.0903040\pi$
$271$	16.3054	+	11.8466i	0.990483	+	0.719628i	0.0304563	+	0.999536i	$0.490304\pi$
$272$		0			0
$273$	−2.56449	+	7.89270i	−0.155210	+	0.477688i
$274$		0			0
$275$	−4.29242	−	2.56419i	−0.258843	−	0.154627i
$276$		0			0
$277$	9.17213	−	28.2289i	0.551100	−	1.69611i	−0.154928	−	0.987926i	$-0.549515\pi$
$277$	9.17213	−	28.2289i	0.551100	−	1.69611i	0.706027	−	0.708184i	$-0.250485\pi$
$278$		0			0
$279$	−7.11876	−	5.17208i	−0.426189	−	0.309644i
$280$		0			0
$281$	−1.57648	+	1.14538i	−0.0940447	+	0.0683275i	−0.633814	−	0.773486i	$-0.718512\pi$
$281$	−1.57648	+	1.14538i	−0.0940447	+	0.0683275i	0.539769	+	0.841813i	$0.318512\pi$
$282$		0			0
$283$	7.09409	−	5.15416i	0.421700	−	0.306383i	−0.356621	−	0.934249i	$-0.616071\pi$
$283$	7.09409	−	5.15416i	0.421700	−	0.306383i	0.778322	+	0.627866i	$0.216071\pi$
$284$		0			0
$285$	0.615812	+	0.772148i	0.0364776	+	0.0457381i
$286$		0			0
$287$	−3.58970	−	11.0480i	−0.211893	−	0.652141i
$288$		0			0
$289$	−2.92683	+	9.00786i	−0.172167	+	0.529874i
$290$		0			0
$291$	1.04102	+	3.20394i	0.0610259	+	0.187818i
$292$		0			0
$293$	−16.6811			−0.974519			−0.487260	−	0.873257i	$-0.662003\pi$
$293$	−16.6811			−0.974519			−0.487260	+	0.873257i	$0.662003\pi$
$294$		0			0
$295$	4.03089	−	6.10701i	0.234688	−	0.355564i
$296$		0			0
$297$	3.75952	+	2.73145i	0.218149	+	0.158495i
$298$		0			0
$299$	−10.1599			−0.587564
$300$		0			0
$301$	−6.81888			−0.393034
$302$		0			0
$303$	7.83536	+	5.69272i	0.450129	+	0.327038i
$304$		0			0
$305$	−18.9939	+	7.12930i	−1.08759	+	0.408222i
$306$		0			0
$307$	8.72717			0.498086			0.249043	−	0.968492i	$-0.419884\pi$
$307$	8.72717			0.498086			0.249043	+	0.968492i	$0.419884\pi$
$308$		0			0
$309$	−5.08690	−	15.6559i	−0.289384	−	0.890631i
$310$		0			0
$311$	8.84864	−	27.2333i	0.501761	−	1.54426i	−0.304389	−	0.952548i	$-0.598452\pi$
$311$	8.84864	−	27.2333i	0.501761	−	1.54426i	0.806149	−	0.591712i	$-0.201548\pi$
$312$		0			0
$313$	3.98735	+	12.2718i	0.225378	+	0.693642i	0.998253	+	0.0590841i	$0.0188180\pi$
$313$	3.98735	+	12.2718i	0.225378	+	0.693642i	−0.772875	+	0.634558i	$0.781182\pi$
$314$		0			0
$315$	4.83101	−	7.31922i	0.272196	−	0.412392i
$316$		0			0
$317$	14.1322	−	10.2677i	0.793744	−	0.576689i	−0.115328	−	0.993327i	$-0.536792\pi$
$317$	14.1322	−	10.2677i	0.793744	−	0.576689i	0.909072	+	0.416639i	$0.136792\pi$
$318$		0			0
$319$	−0.705083	+	0.512273i	−0.0394771	+	0.0286818i
$320$		0			0
$321$	6.55819	+	4.76480i	0.366042	+	0.265945i
$322$		0			0
$323$	0.419226	−	1.29024i	0.0233263	−	0.0717911i
$324$		0			0
$325$	−25.9739	+	2.33954i	−1.44078	+	0.129774i
$326$		0			0
$327$	−3.95044	+	12.1582i	−0.218460	+	0.672350i
$328$		0			0
$329$	7.56448	+	5.49592i	0.417043	+	0.303000i
$330$		0			0
$331$	3.06555	−	2.22726i	0.168498	−	0.122421i	−0.500340	−	0.865829i	$-0.666792\pi$
$331$	3.06555	−	2.22726i	0.168498	−	0.122421i	0.668838	+	0.743408i	$0.266792\pi$
$332$		0			0
$333$	9.67866	−	7.03196i	0.530387	−	0.385349i
$334$		0			0
$335$	−9.73916	−	2.68747i	−0.532107	−	0.146832i
$336$		0			0
$337$	0.815897	+	2.51107i	0.0444447	+	0.136787i	0.970817	−	0.239823i	$-0.0770896\pi$
$337$	0.815897	+	2.51107i	0.0444447	+	0.136787i	−0.926372	+	0.376610i	$0.877090\pi$
$338$		0			0
$339$	0.000811919	−	0.00249883i	4.40974e−5	−	0.000135718i
$340$		0			0
$341$	1.23485	+	3.80048i	0.0668709	+	0.205808i
$342$		0			0
$343$	−19.2852			−1.04131
$344$		0			0
$345$	−3.75080	−	1.03501i	−0.201936	−	0.0557232i
$346$		0			0
$347$	−24.0417	−	17.4673i	−1.29063	−	0.937696i	−0.290810	−	0.956781i	$-0.593925\pi$
$347$	−24.0417	−	17.4673i	−1.29063	−	0.937696i	−0.999818	+	0.0190845i	$0.993925\pi$
$348$		0			0
$349$	−4.94331			−0.264610			−0.132305	−	0.991209i	$-0.542238\pi$
$349$	−4.94331			−0.264610			−0.132305	+	0.991209i	$0.542238\pi$
$350$		0			0
$351$	24.2380			1.29373
$352$		0			0
$353$	−8.96195	−	6.51124i	−0.476996	−	0.346558i	0.323165	−	0.946343i	$-0.395253\pi$
$353$	−8.96195	−	6.51124i	−0.476996	−	0.346558i	−0.800162	+	0.599784i	$0.795253\pi$
$354$		0			0
$355$	0.480259	+	10.6854i	0.0254895	+	0.567123i
$356$		0			0
$357$	4.36569			0.231057
$358$		0			0
$359$	−0.622813	−	1.91682i	−0.0328708	−	0.101166i	0.933275	−	0.359163i	$-0.116938\pi$
$359$	−0.622813	−	1.91682i	−0.0328708	−	0.101166i	−0.966146	+	0.257997i	$0.916938\pi$
$360$		0			0
$361$	−5.79578	+	17.8376i	−0.305041	+	0.938820i
$362$		0			0
$363$	−0.276050	−	0.849595i	−0.0144889	−	0.0445922i
$364$		0			0
$365$	17.0303	−	6.39225i	0.891405	−	0.334586i
$366$		0			0
$367$	−25.2227	+	18.3254i	−1.31662	+	0.956577i	−0.316648	+	0.948543i	$0.602557\pi$
$367$	−25.2227	+	18.3254i	−1.31662	+	0.956577i	−0.999968	+	0.00803434i	$0.997443\pi$
$368$		0			0
$369$	−11.6187	+	8.44147i	−0.604844	+	0.439445i
$370$		0			0
$371$	4.53763	+	3.29678i	0.235582	+	0.171160i
$372$		0			0
$373$	6.65298	−	20.4758i	0.344478	−	1.06020i	−0.617384	−	0.786662i	$-0.711808\pi$
$373$	6.65298	−	20.4758i	0.344478	−	1.06020i	0.961863	−	0.273533i	$-0.0881924\pi$
$374$		0			0
$375$	−9.82727	−	1.78232i	−0.507478	−	0.0920384i
$376$		0			0
$377$	−1.40471	+	4.32326i	−0.0723464	+	0.222659i
$378$		0			0
$379$	−18.3653	−	13.3432i	−0.943363	−	0.685393i	0.00586519	−	0.999983i	$-0.498133\pi$
$379$	−18.3653	−	13.3432i	−0.943363	−	0.685393i	−0.949228	+	0.314590i	$0.898133\pi$
$380$		0			0
$381$	12.4456	−	9.04225i	0.637607	−	0.463249i
$382$		0			0
$383$	30.1246	−	21.8868i	1.53929	−	1.11836i	0.588517	−	0.808485i	$-0.299712\pi$
$383$	30.1246	−	21.8868i	1.53929	−	1.11836i	0.950777	−	0.309877i	$-0.100288\pi$
$384$		0			0
$385$	−3.72868	+	1.39955i	−0.190031	+	0.0713275i
$386$		0			0
$387$	2.60506	+	8.01756i	0.132423	+	0.407556i
$388$		0			0
$389$	−1.42593	+	4.38856i	−0.0722975	+	0.222509i	−0.980676	−	0.195641i	$-0.937321\pi$
$389$	−1.42593	+	4.38856i	−0.0722975	+	0.222509i	0.908378	+	0.418150i	$0.137321\pi$
$390$		0			0
$391$	1.65161	+	5.08313i	0.0835254	+	0.257065i
$392$		0			0
$393$	11.1586			0.562878
$394$		0			0
$395$	−0.628774	−	13.9898i	−0.0316371	−	0.703902i
$396$		0			0
$397$	−2.77311	−	2.01478i	−0.139178	−	0.101119i	0.516018	−	0.856578i	$-0.327414\pi$
$397$	−2.77311	−	2.01478i	−0.139178	−	0.101119i	−0.655196	+	0.755459i	$0.727414\pi$
$398$		0			0
$399$	0.786694			0.0393840
$400$		0			0
$401$	−12.2691			−0.612690			−0.306345	−	0.951921i	$-0.599106\pi$
$401$	−12.2691			−0.612690			−0.306345	+	0.951921i	$0.599106\pi$
$402$		0			0
$403$	16.8621	+	12.2511i	0.839963	+	0.610269i
$404$		0			0
$405$	−5.29110	−	1.46005i	−0.262917	−	0.0725505i
$406$		0			0
$407$	−5.43305			−0.269306
$408$		0			0
$409$	11.6088	+	35.7282i	0.574019	+	1.76665i	0.639496	+	0.768794i	$0.279143\pi$
$409$	11.6088	+	35.7282i	0.574019	+	1.76665i	−0.0654776	+	0.997854i	$0.520857\pi$
$410$		0			0
$411$	1.68269	−	5.17877i	0.0830007	−	0.255450i
$412$		0			0
$413$	−1.80112	−	5.54328i	−0.0886273	−	0.272767i
$414$		0			0
$415$	5.23007	+	1.44321i	0.256734	+	0.0708444i
$416$		0			0
$417$	10.9416	−	7.94950i	0.535810	−	0.389289i
$418$		0			0
$419$	−18.7510	+	13.6234i	−0.916046	+	0.665546i	−0.942537	−	0.334103i	$-0.891567\pi$
$419$	−18.7510	+	13.6234i	−0.916046	+	0.665546i	0.0264910	+	0.999649i	$0.491567\pi$
$420$		0			0
$421$	27.5067	+	19.9848i	1.34059	+	0.973999i	0.999422	+	0.0339980i	$0.0108240\pi$
$421$	27.5067	+	19.9848i	1.34059	+	0.973999i	0.341172	+	0.940001i	$0.389176\pi$
$422$		0			0
$423$	3.57213	−	10.9939i	0.173683	−	0.534540i
$424$		0			0
$425$	5.39285	+	12.6147i	0.261591	+	0.611905i
$426$		0			0
$427$	−4.99372	+	15.3691i	−0.241663	+	0.743762i
$428$		0			0
$429$	−3.76952	−	2.73872i	−0.181994	−	0.132226i
$430$		0			0
$431$	5.56113	−	4.04040i	0.267870	−	0.194619i	−0.445739	−	0.895163i	$-0.647059\pi$
$431$	5.56113	−	4.04040i	0.267870	−	0.194619i	0.713609	+	0.700544i	$0.247059\pi$
$432$		0			0
$433$	−11.5807	+	8.41387i	−0.556533	+	0.404345i	−0.830188	−	0.557483i	$-0.811767\pi$
$433$	−11.5807	+	8.41387i	−0.556533	+	0.404345i	0.273656	+	0.961828i	$0.411767\pi$
$434$		0			0
$435$	−0.959004	+	1.45294i	−0.0459807	+	0.0696632i
$436$		0			0
$437$	0.297618	+	0.915976i	0.0142370	+	0.0438171i
$438$		0			0
$439$	0.859739	−	2.64600i	0.0410331	−	0.126287i	−0.928442	−	0.371479i	$-0.878851\pi$
$439$	0.859739	−	2.64600i	0.0410331	−	0.126287i	0.969475	+	0.245192i	$0.0788509\pi$
$440$		0			0
$441$	2.60452	+	8.01589i	0.124025	+	0.381709i
$442$		0			0
$443$	−5.90139			−0.280383			−0.140192	−	0.990124i	$-0.544772\pi$
$443$	−5.90139			−0.280383			−0.140192	+	0.990124i	$0.544772\pi$
$444$		0			0
$445$	−3.02625	+	1.13589i	−0.143458	+	0.0538464i
$446$		0			0
$447$	−5.89407	−	4.28229i	−0.278780	−	0.202545i
$448$		0			0
$449$	42.2314			1.99302			0.996512	−	0.0834554i	$-0.0265956\pi$
$449$	42.2314			1.99302			0.996512	+	0.0834554i	$0.0265956\pi$
$450$		0			0
$451$	6.52206			0.307112
$452$		0			0
$453$	1.37697	+	1.00043i	0.0646959	+	0.0470043i
$454$		0			0
$455$	−11.4432	+	17.3370i	−0.536464	+	0.812770i
$456$		0			0
$457$	−1.70577			−0.0797927			−0.0398964	−	0.999204i	$-0.512703\pi$
$457$	−1.70577			−0.0797927			−0.0398964	+	0.999204i	$0.512703\pi$
$458$		0			0
$459$	−3.94016	−	12.1266i	−0.183911	−	0.566019i
$460$		0			0
$461$	8.76981	−	26.9907i	0.408451	−	1.25708i	−0.509528	−	0.860454i	$-0.670180\pi$
$461$	8.76981	−	26.9907i	0.408451	−	1.25708i	0.917979	−	0.396629i	$-0.129820\pi$
$462$		0			0
$463$	−0.391461	−	1.20479i	−0.0181927	−	0.0559914i	0.941548	−	0.336879i	$-0.109371\pi$
$463$	−0.391461	−	1.20479i	−0.0181927	−	0.0559914i	−0.959741	+	0.280887i	$0.909371\pi$
$464$		0			0
$465$	4.97704	+	6.24056i	0.230805	+	0.289399i
$466$		0			0
$467$	−5.15793	+	3.74746i	−0.238681	+	0.173412i	−0.700695	−	0.713461i	$-0.747127\pi$
$467$	−5.15793	+	3.74746i	−0.238681	+	0.173412i	0.462015	+	0.886872i	$0.347127\pi$
$468$		0			0
$469$	−6.51060	+	4.73022i	−0.300631	+	0.218421i
$470$		0			0
$471$	−3.64247	−	2.64641i	−0.167836	−	0.121940i
$472$		0			0
$473$	1.18305	−	3.64106i	0.0543968	−	0.167416i
$474$		0			0
$475$	0.971786	+	2.27316i	0.0445886	+	0.104300i
$476$		0			0
$477$	2.14278	−	6.59479i	0.0981111	−	0.301955i
$478$		0			0
$479$	−7.04194	−	5.11627i	−0.321754	−	0.233768i	0.415169	−	0.909744i	$-0.363722\pi$
$479$	−7.04194	−	5.11627i	−0.321754	−	0.233768i	−0.736924	+	0.675976i	$0.763722\pi$
$480$		0			0
$481$	−22.9257	+	16.6565i	−1.04532	+	0.759472i
$482$		0			0
$483$	−2.50740	+	1.82173i	−0.114090	+	0.0828916i
$484$		0			0
$485$	0.378620	+	8.42402i	0.0171922	+	0.382515i
$486$		0			0
$487$	7.61594	+	23.4394i	0.345111	+	1.06214i	0.961524	+	0.274720i	$0.0885851\pi$
$487$	7.61594	+	23.4394i	0.345111	+	1.06214i	−0.616413	+	0.787423i	$0.711415\pi$
$488$		0			0
$489$	1.96601	−	6.05075i	0.0889060	−	0.273625i
$490$		0			0
$491$	8.80966	+	27.1133i	0.397574	+	1.22361i	0.926939	+	0.375213i	$0.122430\pi$
$491$	8.80966	+	27.1133i	0.397574	+	1.22361i	−0.529364	+	0.848395i	$0.677570\pi$
$492$		0			0
$493$	2.39133			0.107700
$494$		0			0
$495$	3.07007	+	3.84946i	0.137989	+	0.173021i
$496$		0			0
$497$	6.89276	+	5.00788i	0.309183	+	0.224634i
$498$		0			0
$499$	−16.4530			−0.736538			−0.368269	−	0.929719i	$-0.620049\pi$
$499$	−16.4530			−0.736538			−0.368269	+	0.929719i	$0.620049\pi$
$500$		0			0
$501$	3.99639			0.178545
$502$		0			0
$503$	22.5029	+	16.3493i	1.00335	+	0.728980i	0.962805	−	0.270198i	$-0.0870890\pi$
$503$	22.5029	+	16.3493i	1.00335	+	0.728980i	0.0405500	+	0.999178i	$0.487089\pi$
$504$		0			0
$505$	15.1157	+	18.9532i	0.672641	+	0.843404i
$506$		0			0
$507$	−12.6894			−0.563554
$508$		0			0
$509$	3.71812	+	11.4432i	0.164803	+	0.507211i	0.999022	−	0.0442226i	$-0.0140811\pi$
$509$	3.71812	+	11.4432i	0.164803	+	0.507211i	−0.834219	+	0.551433i	$0.814081\pi$
$510$		0			0
$511$	4.47745	−	13.7802i	0.198071	−	0.609600i
$512$		0			0
$513$	−0.710013	−	2.18519i	−0.0313478	−	0.0964787i
$514$		0			0
$515$	−1.85010	−	41.1635i	−0.0815253	−	1.81388i
$516$		0			0
$517$	−4.24705	+	3.08567i	−0.186785	+	0.135707i
$518$		0			0
$519$	6.41538	−	4.66105i	0.281604	−	0.204597i
$520$		0			0
$521$	7.45112	+	5.41356i	0.326440	+	0.237172i	0.738918	−	0.673795i	$-0.235337\pi$
$521$	7.45112	+	5.41356i	0.326440	+	0.237172i	−0.412479	+	0.910967i	$0.635337\pi$
$522$		0			0
$523$	−9.84712	+	30.3063i	−0.430585	+	1.32520i	0.466960	+	0.884279i	$0.345349\pi$
$523$	−9.84712	+	30.3063i	−0.430585	+	1.32520i	−0.897544	+	0.440924i	$0.854651\pi$
$524$		0			0
$525$	−5.99068	+	5.23465i	−0.261455	+	0.228459i
$526$		0			0
$527$	3.38822	−	10.4279i	0.147593	−	0.454244i
$528$		0			0
$529$	15.5377	+	11.2888i	0.675552	+	0.490817i
$530$		0			0
$531$	−5.82963	+	4.23547i	−0.252984	+	0.183804i
$532$		0			0
$533$	27.5211	−	19.9952i	1.19207	−	0.866089i
$534$		0			0
$535$	12.6519	+	15.8638i	0.546987	+	0.685851i
$536$		0			0
$537$	−4.60410	−	14.1700i	−0.198682	−	0.611479i
$538$		0			0
$539$	1.18281	−	3.64030i	0.0509470	−	0.156799i
$540$		0			0
$541$	6.27016	+	19.2976i	0.269575	+	0.829667i	0.990604	+	0.136762i	$0.0436696\pi$
$541$	6.27016	+	19.2976i	0.269575	+	0.829667i	−0.721029	+	0.692905i	$0.756330\pi$
$542$		0			0
$543$	−19.7292			−0.846661
$544$		0			0
$545$	−17.6275	+	26.7065i	−0.755078	+	1.14398i
$546$		0			0
$547$	7.18934	+	5.22336i	0.307394	+	0.223335i	0.730777	−	0.682616i	$-0.239158\pi$
$547$	7.18934	+	5.22336i	0.307394	+	0.223335i	−0.423384	+	0.905951i	$0.639158\pi$
$548$		0			0
$549$	19.9786			0.852665
$550$		0			0
$551$	0.430915			0.0183576
$552$		0			0
$553$	−9.02428	−	6.55652i	−0.383752	−	0.278812i
$554$		0			0
$555$	−10.1605	+	3.81369i	−0.431287	+	0.161882i
$556$		0			0
$557$	32.3214			1.36950			0.684751	−	0.728777i	$-0.259911\pi$
$557$	32.3214			1.36950			0.684751	+	0.728777i	$0.259911\pi$
$558$		0			0
$559$	−6.17059	−	18.9911i	−0.260988	−	0.803239i
$560$		0			0
$561$	−0.757433	+	2.33114i	−0.0319789	+	0.0984208i
$562$		0			0
$563$	1.82666	+	5.62189i	0.0769847	+	0.236935i	0.982142	−	0.188143i	$-0.0602468\pi$
$563$	1.82666	+	5.62189i	0.0769847	+	0.236935i	−0.905157	+	0.425078i	$0.860247\pi$
$564$		0			0
$565$	0.00362291	−	0.00548889i	0.000152417	−	0.000230919i
$566$		0			0
$567$	−3.53709	+	2.56984i	−0.148544	+	0.107923i
$568$		0			0
$569$	−16.9877	+	12.3423i	−0.712161	+	0.517415i	−0.883870	−	0.467733i	$-0.845071\pi$
$569$	−16.9877	+	12.3423i	−0.712161	+	0.517415i	0.171709	+	0.985148i	$0.445071\pi$
$570$		0			0
$571$	11.5793	+	8.41287i	0.484579	+	0.352068i	0.803096	−	0.595850i	$-0.203185\pi$
$571$	11.5793	+	8.41287i	0.484579	+	0.352068i	−0.318516	+	0.947917i	$0.603185\pi$
$572$		0			0
$573$	2.65514	−	8.17169i	0.110920	−	0.341377i
$574$		0			0
$575$	−8.36125	−	4.99481i	−0.348688	−	0.208298i
$576$		0			0
$577$	−5.15954	+	15.8794i	−0.214794	+	0.661069i	0.784374	+	0.620288i	$0.212984\pi$
$577$	−5.15954	+	15.8794i	−0.214794	+	0.661069i	−0.999168	+	0.0407805i	$0.987016\pi$
$578$		0			0
$579$	−12.6028	−	9.15649i	−0.523756	−	0.380531i
$580$		0			0
$581$	3.49628	−	2.54020i	0.145050	−	0.105385i
$582$		0			0
$583$	−2.54764	+	1.85097i	−0.105512	+	0.0766593i
$584$		0			0
$585$	24.7563	+	6.83138i	1.02355	+	0.282443i
$586$		0			0
$587$	0.711519	+	2.18983i	0.0293675	+	0.0903840i	0.964666	−	0.263476i	$-0.0848690\pi$
$587$	0.711519	+	2.18983i	0.0293675	+	0.0903840i	−0.935298	+	0.353860i	$0.884869\pi$
$588$		0			0
$589$	0.610554	−	1.87909i	0.0251574	−	0.0774266i
$590$		0			0
$591$	1.97355	+	6.07398i	0.0811812	+	0.249850i
$592$		0			0
$593$	−4.55374			−0.187000			−0.0934999	−	0.995619i	$-0.529805\pi$
$593$	−4.55374			−0.187000			−0.0934999	+	0.995619i	$0.529805\pi$
$594$		0			0
$595$	10.5341	+	2.90683i	0.431856	+	0.119168i
$596$		0			0
$597$	−17.5805	−	12.7730i	−0.719521	−	0.522763i
$598$		0			0
$599$	23.7752			0.971427			0.485713	−	0.874118i	$-0.338560\pi$
$599$	23.7752			0.971427			0.485713	+	0.874118i	$0.338560\pi$
$600$		0			0
$601$	−9.44908			−0.385436			−0.192718	−	0.981254i	$-0.561730\pi$
$601$	−9.44908			−0.385436			−0.192718	+	0.981254i	$0.561730\pi$
$602$		0			0
$603$	8.04903	+	5.84796i	0.327782	+	0.238148i
$604$		0			0
$605$	−0.100399	−	2.23381i	−0.00408181	−	0.0908174i
$606$		0			0
$607$	14.0296			0.569444			0.284722	−	0.958610i	$-0.408099\pi$
$607$	14.0296			0.569444			0.284722	+	0.958610i	$0.408099\pi$
$608$		0			0
$609$	0.428511	+	1.31882i	0.0173641	+	0.0534413i
$610$		0			0
$611$	−8.46126	+	26.0411i	−0.342306	+	1.05351i
$612$		0			0
$613$	5.89336	+	18.1379i	0.238030	+	0.732583i	0.996705	+	0.0811126i	$0.0258473\pi$
$613$	5.89336	+	18.1379i	0.238030	+	0.732583i	−0.758674	+	0.651470i	$0.774153\pi$
$614$		0			0
$615$	12.1970	−	4.57812i	0.491832	−	0.184607i
$616$		0			0
$617$	9.62986	−	6.99650i	0.387683	−	0.281669i	−0.376822	−	0.926286i	$-0.622983\pi$
$617$	9.62986	−	6.99650i	0.387683	−	0.281669i	0.764506	+	0.644617i	$0.222983\pi$
$618$		0			0
$619$	24.3542	−	17.6944i	0.978878	−	0.711197i	0.0214205	−	0.999771i	$-0.493181\pi$
$619$	24.3542	−	17.6944i	0.978878	−	0.711197i	0.957458	+	0.288574i	$0.0931811\pi$
$620$		0			0
$621$	7.32320	+	5.32061i	0.293870	+	0.213509i
$622$		0			0
$623$	−0.795636	+	2.44871i	−0.0318765	+	0.0981057i
$624$		0			0
$625$	−22.5257	−	10.8439i	−0.901030	−	0.433757i
$626$		0			0
$627$	−0.136489	+	0.420069i	−0.00545084	+	0.0167760i
$628$		0			0
$629$	12.0603	+	8.76230i	0.480875	+	0.349376i
$630$		0			0
$631$	−37.8243	+	27.4810i	−1.50576	+	1.09400i	−0.537747	+	0.843106i	$0.680725\pi$
$631$	−37.8243	+	27.4810i	−1.50576	+	1.09400i	−0.968015	+	0.250894i	$0.919275\pi$
$632$		0			0
$633$	0.106406	−	0.0773088i	0.00422928	−	0.00307275i
$634$		0			0
$635$	36.0509	−	13.5316i	1.43064	−	0.536985i
$636$		0			0
$637$	−6.16930	−	18.9872i	−0.244437	−	0.752298i
$638$		0			0
$639$	3.25492	−	10.0176i	0.128763	−	0.396291i
$640$		0			0
$641$	−13.5353	−	41.6575i	−0.534614	−	1.64537i	−0.744482	−	0.667642i	$-0.767304\pi$
$641$	−13.5353	−	41.6575i	−0.534614	−	1.64537i	0.209869	−	0.977730i	$-0.432696\pi$
$642$		0			0
$643$	−11.5909			−0.457099			−0.228550	−	0.973532i	$-0.573398\pi$
$643$	−11.5909			−0.457099			−0.228550	+	0.973532i	$0.573398\pi$
$644$		0			0
$645$	−0.343367	−	7.63966i	−0.0135201	−	0.300811i
$646$		0			0
$647$	34.6651	+	25.1857i	1.36283	+	0.990151i	0.998260	+	0.0589736i	$0.0187828\pi$
$647$	34.6651	+	25.1857i	1.36283	+	0.990151i	0.364566	+	0.931177i	$0.381217\pi$
$648$		0			0
$649$	3.27242			0.128454
$650$		0			0
$651$	6.35813			0.249195
$652$		0			0
$653$	12.7631	+	9.27293i	0.499458	+	0.362878i	0.808810	−	0.588070i	$-0.200112\pi$
$653$	12.7631	+	9.27293i	0.499458	+	0.362878i	−0.309352	+	0.950948i	$0.600112\pi$
$654$		0			0
$655$	26.9249	+	7.42979i	1.05204	+	0.290306i
$656$		0			0
$657$	−17.9131			−0.698858
$658$		0			0
$659$	9.16898	+	28.2192i	0.357173	+	1.09926i	0.954739	+	0.297445i	$0.0961345\pi$
$659$	9.16898	+	28.2192i	0.357173	+	1.09926i	−0.597566	+	0.801820i	$0.703866\pi$
$660$		0			0
$661$	6.43490	−	19.8046i	0.250288	−	0.770309i	−0.744433	−	0.667697i	$-0.767280\pi$
$661$	6.43490	−	19.8046i	0.250288	−	0.770309i	0.994721	−	0.102612i	$-0.0327199\pi$
$662$		0			0
$663$	3.95063	+	12.1588i	0.153430	+	0.472209i
$664$		0			0
$665$	1.89823	+	0.523808i	0.0736104	+	0.0203124i
$666$		0			0
$667$	−1.37344	+	0.997860i	−0.0531797	+	0.0386373i
$668$		0			0
$669$	13.1182	−	9.53091i	0.507178	−	0.368486i
$670$		0			0
$671$	−7.34020	−	5.33297i	−0.283365	−	0.205877i
$672$		0			0
$673$	−7.46617	+	22.9785i	−0.287800	+	0.885756i	0.697746	+	0.716345i	$0.254187\pi$
$673$	−7.46617	+	22.9785i	−0.287800	+	0.885756i	−0.985545	+	0.169411i	$0.945813\pi$
$674$		0			0
$675$	19.9470	+	11.9159i	0.767760	+	0.458642i
$676$		0			0
$677$	−3.33256	+	10.2566i	−0.128081	+	0.394192i	−0.994450	−	0.105212i	$-0.966448\pi$
$677$	−3.33256	+	10.2566i	−0.128081	+	0.394192i	0.866369	+	0.499404i	$0.166448\pi$
$678$		0			0
$679$	5.43402	+	3.94805i	0.208539	+	0.151512i
$680$		0			0
$681$	5.52669	−	4.01538i	0.211783	−	0.153870i
$682$		0			0
$683$	−16.2990	+	11.8419i	−0.623662	+	0.453117i	−0.854199	−	0.519946i	$-0.825952\pi$
$683$	−16.2990	+	11.8419i	−0.623662	+	0.453117i	0.230536	+	0.973064i	$0.425952\pi$
$684$		0			0
$685$	7.50839	−	11.3756i	0.286881	−	0.434639i
$686$		0			0
$687$	−0.326994	−	1.00638i	−0.0124756	−	0.0383960i
$688$		0			0
$689$	−5.07558	+	15.6210i	−0.193364	+	0.595113i
$690$		0			0
$691$	6.71038	+	20.6524i	0.255275	+	0.785655i	0.993775	+	0.111402i	$0.0355342\pi$
$691$	6.71038	+	20.6524i	0.255275	+	0.785655i	−0.738501	+	0.674253i	$0.764466\pi$
$692$		0			0
$693$	3.92198			0.148984
$694$		0			0
$695$	31.6942	−	11.8963i	1.20223	−	0.451252i
$696$		0			0
$697$	−14.4777	−	10.5186i	−0.548381	−	0.398422i
$698$		0			0
$699$	17.6998			0.669467
$700$		0			0
$701$	−45.2417			−1.70875			−0.854377	−	0.519654i	$-0.826061\pi$
$701$	−45.2417			−1.70875			−0.854377	+	0.519654i	$0.826061\pi$
$702$		0			0
$703$	2.17325	+	1.57896i	0.0819657	+	0.0595516i
$704$		0			0
$705$	−5.77654	+	8.75176i	−0.217557	+	0.329610i
$706$		0			0
$707$	19.3102			0.726235
$708$		0			0
$709$	−4.22676	−	13.0086i	−0.158739	−	0.488549i	0.839781	−	0.542925i	$-0.182683\pi$
$709$	−4.22676	−	13.0086i	−0.158739	−	0.488549i	−0.998521	+	0.0543755i	$0.982683\pi$
$710$		0			0
$711$	−4.26148	+	13.1155i	−0.159818	+	0.491869i
$712$		0			0
$713$	2.40538	+	7.40299i	0.0900821	+	0.277244i
$714$		0			0
$715$	−7.27204	−	9.11819i	−0.271959	−	0.341001i
$716$		0			0
$717$	7.00548	−	5.08978i	0.261625	−	0.190081i
$718$		0			0
$719$	−25.5082	+	18.5328i	−0.951294	+	0.691155i	−0.951113	−	0.308845i	$-0.900058\pi$
$719$	−25.5082	+	18.5328i	−0.951294	+	0.691155i	−0.000181220		1.00000i	$0.500058\pi$
$720$		0			0
$721$	−26.5530	−	19.2919i	−0.988887	−	0.718468i
$722$		0			0
$723$	3.94882	−	12.1532i	0.146858	−	0.451983i
$724$		0			0
$725$	−3.28142	+	2.86730i	−0.121869	+	0.106489i
$726$		0			0
$727$	−13.6230	+	41.9273i	−0.505250	+	1.55500i	0.295100	+	0.955466i	$0.404647\pi$
$727$	−13.6230	+	41.9273i	−0.505250	+	1.55500i	−0.800350	+	0.599533i	$0.795353\pi$
$728$		0			0
$729$	−5.70244	−	4.14306i	−0.211201	−	0.153447i
$730$		0			0
$731$	−8.49837	+	6.17443i	−0.314324	+	0.228370i
$732$		0			0
$733$	17.1767	−	12.4796i	0.634437	−	0.460946i	−0.223497	−	0.974705i	$-0.571747\pi$
$733$	17.1767	−	12.4796i	0.634437	−	0.460946i	0.857935	+	0.513759i	$0.171747\pi$
$734$		0			0
$735$	−0.343295	−	7.63807i	−0.0126626	−	0.281734i
$736$		0			0
$737$	−1.39622	−	4.29713i	−0.0514305	−	0.158287i
$738$		0			0
$739$	5.25388	−	16.1698i	0.193267	−	0.594815i	−0.806725	−	0.590927i	$-0.798762\pi$
$739$	5.25388	−	16.1698i	0.193267	−	0.594815i	0.999992	−	0.00388833i	$-0.00123770\pi$
$740$		0			0
$741$	0.711901	+	2.19101i	0.0261523	+	0.0804886i
$742$		0			0
$743$	−52.7509			−1.93524			−0.967622	−	0.252404i	$-0.918779\pi$
$743$	−52.7509			−1.93524			−0.967622	+	0.252404i	$0.918779\pi$
$744$		0			0
$745$	−11.3707	−	14.2573i	−0.416589	−	0.522348i
$746$		0			0
$747$	−4.32245	−	3.14044i	−0.158150	−	0.114903i
$748$		0			0
$749$	16.1626			0.590569
$750$		0			0
$751$	8.58038			0.313103			0.156551	−	0.987670i	$-0.449962\pi$
$751$	8.58038			0.313103			0.156551	+	0.987670i	$0.449962\pi$
$752$		0			0
$753$	5.27566	+	3.83299i	0.192256	+	0.139682i
$754$		0			0
$755$	2.65641	+	3.33080i	0.0966768	+	0.121220i
$756$		0			0
$757$	17.9822			0.653572			0.326786	−	0.945098i	$-0.394034\pi$
$757$	17.9822			0.653572			0.326786	+	0.945098i	$0.394034\pi$
$758$		0			0
$759$	−0.537720	−	1.65493i	−0.0195180	−	0.0600703i
$760$		0			0
$761$	12.3873	−	38.1241i	0.449039	−	1.38200i	−0.428954	−	0.903326i	$-0.641118\pi$
$761$	12.3873	−	38.1241i	0.449039	−	1.38200i	0.877993	−	0.478673i	$-0.158882\pi$
$762$		0			0
$763$	7.87646	+	24.2413i	0.285147	+	0.877593i
$764$		0			0
$765$	−0.606599	−	13.4964i	−0.0219316	−	0.487963i
$766$		0			0
$767$	13.8086	−	10.0325i	0.498599	−	0.362253i
$768$		0			0
$769$	−34.5036	+	25.0683i	−1.24423	+	0.903988i	−0.997873	−	0.0651907i	$-0.979234\pi$
$769$	−34.5036	+	25.0683i	−1.24423	+	0.903988i	−0.246360	+	0.969178i	$0.579234\pi$
$770$		0			0
$771$	1.88459	+	1.36924i	0.0678720	+	0.0493119i
$772$		0			0
$773$	15.1667	−	46.6783i	0.545508	−	1.67890i	−0.174269	−	0.984698i	$-0.555756\pi$
$773$	15.1667	−	46.6783i	0.545508	−	1.67890i	0.719778	−	0.694204i	$-0.244244\pi$
$774$		0			0
$775$	7.85405	+	18.3719i	0.282126	+	0.659938i
$776$		0			0
$777$	−2.67130	+	8.22141i	−0.0958323	+	0.294942i
$778$		0			0
$779$	−2.60887	−	1.89545i	−0.0934723	−	0.0679116i
$780$		0			0
$781$	−3.86992	+	2.81166i	−0.138477	+	0.100609i
$782$		0			0
$783$	3.27654	−	2.38054i	0.117094	−	0.0850737i
$784$		0			0
$785$	−7.02694	−	8.81087i	−0.250802	−	0.314473i
$786$		0			0
$787$	1.74124	+	5.35898i	0.0620684	+	0.191027i	0.977282	−	0.211941i	$-0.0679785\pi$
$787$	1.74124	+	5.35898i	0.0620684	+	0.191027i	−0.915214	+	0.402968i	$0.867979\pi$
$788$		0			0
$789$	4.89245	−	15.0574i	0.174176	−	0.536058i
$790$		0			0
$791$	−0.00161882	−	0.00498222i	−5.75586e−5	−	0.000177147i
$792$		0			0
$793$	−47.3231			−1.68049
$794$		0			0
$795$	−3.46512	+	5.24983i	−0.122895	+	0.186192i
$796$		0			0
$797$	29.1579	+	21.1844i	1.03283	+	0.750392i	0.968872	−	0.247561i	$-0.0796291\pi$
$797$	29.1579	+	21.1844i	1.03283	+	0.750392i	0.0639533	+	0.997953i	$0.479629\pi$
$798$		0			0
$799$	14.4041			0.509581
$800$		0			0
$801$	3.18313			0.112471
$802$		0			0
$803$	6.58135	+	4.78163i	0.232251	+	0.168740i
$804$		0			0
$805$	−7.26313	+	2.72619i	−0.255992	+	0.0960855i
$806$		0			0
$807$	−24.8418			−0.874474
$808$		0			0
$809$	11.6262	+	35.7817i	0.408755	+	1.25802i	0.917719	+	0.397230i	$0.130029\pi$
$809$	11.6262	+	35.7817i	0.408755	+	1.25802i	−0.508964	+	0.860788i	$0.669971\pi$
$810$		0			0
$811$	−3.40132	+	10.4682i	−0.119436	+	0.367587i	−0.992846	−	0.119398i	$-0.961904\pi$
$811$	−3.40132	+	10.4682i	−0.119436	+	0.367587i	0.873410	+	0.486985i	$0.161904\pi$
$812$		0			0
$813$	5.56368	+	17.1232i	0.195127	+	0.600538i
$814$		0			0
$815$	8.77263	−	13.2910i	0.307292	−	0.465563i
$816$		0			0
$817$	−1.53140	+	1.11263i	−0.0535769	+	0.0389259i
$818$		0			0
$819$	16.5495	−	12.0239i	0.578287	−	0.420150i
$820$		0			0
$821$	−44.9307	−	32.6440i	−1.56809	−	1.13928i	−0.928956	−	0.370190i	$-0.879293\pi$
$821$	−44.9307	−	32.6440i	−1.56809	−	1.13928i	−0.639135	−	0.769095i	$-0.720707\pi$
$822$		0			0
$823$	4.15702	−	12.7940i	0.144905	−	0.445970i	−0.852094	−	0.523389i	$-0.824668\pi$
$823$	4.15702	−	12.7940i	0.144905	−	0.445970i	0.996999	+	0.0774181i	$0.0246676\pi$
$824$		0			0
$825$	−1.75577	−	4.10703i	−0.0611280	−	0.142988i
$826$		0			0
$827$	8.66844	−	26.6787i	0.301431	−	0.927710i	−0.679554	−	0.733626i	$-0.737827\pi$
$827$	8.66844	−	26.6787i	0.301431	−	0.927710i	0.980985	−	0.194084i	$-0.0621734\pi$
$828$		0			0
$829$	−41.3452	−	30.0390i	−1.43598	−	1.04330i	−0.988864	−	0.148822i	$-0.952452\pi$
$829$	−41.3452	−	30.0390i	−1.43598	−	1.04330i	−0.447114	−	0.894477i	$-0.647548\pi$
$830$		0			0
$831$	21.4512	−	15.5852i	0.744133	−	0.540644i
$832$		0			0
$833$	−8.49660	+	6.17314i	−0.294390	+	0.213887i
$834$		0			0
$835$	9.64298	+	2.66093i	0.333709	+	0.0920853i
$836$		0			0
$837$	−5.73838	−	17.6609i	−0.198347	−	0.610451i
$838$		0			0
$839$	−6.60569	+	20.3302i	−0.228054	+	0.701878i	0.769913	+	0.638148i	$0.220299\pi$
$839$	−6.60569	+	20.3302i	−0.228054	+	0.701878i	−0.997967	+	0.0637292i	$0.979701\pi$
$840$		0			0
$841$	−8.72677	−	26.8582i	−0.300923	−	0.926147i
$842$		0			0
$843$	−1.74075			−0.0599545
$844$		0			0
$845$	−30.6185	−	8.44901i	−1.05331	−	0.290655i
$846$		0			0
$847$	−1.44095	−	1.04691i	−0.0495116	−	0.0359723i
$848$		0			0
$849$	7.83330			0.268838
$850$		0			0
$851$	−10.5831			−0.362783
$852$		0			0
$853$	−15.8065	−	11.4841i	−0.541204	−	0.393208i	0.283328	−	0.959023i	$-0.408562\pi$
$853$	−15.8065	−	11.4841i	−0.541204	−	0.393208i	−0.824532	+	0.565815i	$0.808562\pi$
$854$		0			0
$855$	−0.109309	−	2.43204i	−0.00373827	−	0.0831739i
$856$		0			0
$857$	−26.9227			−0.919661			−0.459831	−	0.888007i	$-0.652090\pi$
$857$	−26.9227			−0.919661			−0.459831	+	0.888007i	$0.652090\pi$
$858$		0			0
$859$	15.3541	+	47.2551i	0.523875	+	1.61232i	0.766529	+	0.642209i	$0.221982\pi$
$859$	15.3541	+	47.2551i	0.523875	+	1.61232i	−0.242654	+	0.970113i	$0.578018\pi$
$860$		0			0
$861$	3.20674	−	9.86934i	0.109286	−	0.336346i
$862$		0			0
$863$	9.13390	+	28.1113i	0.310922	+	0.956918i	0.977401	+	0.211395i	$0.0678006\pi$
$863$	9.13390	+	28.1113i	0.310922	+	0.956918i	−0.666479	+	0.745524i	$0.732199\pi$
$864$		0			0
$865$	18.5833	−	6.97518i	0.631852	−	0.237163i
$866$		0			0
$867$	−6.84508	+	4.97324i	−0.232471	+	0.168900i
$868$		0			0
$869$	5.06666	−	3.68114i	0.171875	−	0.124874i
$870$		0			0
$871$	−19.0657	−	13.8520i	−0.646015	−	0.469358i
$872$		0			0
$873$	2.56607	−	7.89756i	0.0868484	−	0.267292i
$874$		0			0
$875$	−17.9405	+	8.64201i	−0.606499	+	0.292153i
$876$		0			0
$877$	−12.5209	+	38.5354i	−0.422802	+	1.30125i	0.482282	+	0.876016i	$0.339808\pi$
$877$	−12.5209	+	38.5354i	−0.422802	+	1.30125i	−0.905084	+	0.425233i	$0.860192\pi$
$878$		0			0
$879$	−12.0556	−	8.75888i	−0.406624	−	0.295430i
$880$		0			0
$881$	5.92864	−	4.30741i	0.199741	−	0.145120i	−0.483419	−	0.875389i	$-0.660605\pi$
$881$	5.92864	−	4.30741i	0.199741	−	0.145120i	0.683160	+	0.730269i	$0.260605\pi$
$882$		0			0
$883$	−21.8011	+	15.8395i	−0.733667	+	0.533040i	−0.890721	−	0.454550i	$-0.849800\pi$
$883$	−21.8011	+	15.8395i	−0.733667	+	0.533040i	0.157054	+	0.987590i	$0.449800\pi$
$884$		0			0
$885$	6.11982	−	2.29705i	0.205716	−	0.0772146i
$886$		0			0
$887$	0.0713442	+	0.219575i	0.00239550	+	0.00737260i	0.952247	−	0.305328i	$-0.0987662\pi$
$887$	0.0713442	+	0.219575i	0.00239550	+	0.00737260i	−0.949852	+	0.312701i	$0.898766\pi$
$888$		0			0
$889$	9.47820	−	29.1709i	0.317889	−	0.978361i
$890$		0			0
$891$	−0.758541	−	2.33455i	−0.0254121	−	0.0782103i
$892$		0			0
$893$	2.59561			0.0868587
$894$		0			0
$895$	−1.67451	−	37.2566i	−0.0559727	−	1.24535i
$896$		0			0
$897$	−7.34267	−	5.33476i	−0.245165	−	0.178123i
$898$		0			0
$899$	3.48269			0.116154
$900$		0			0
$901$	8.64046			0.287855
$902$		0			0
$903$	−4.92806	−	3.58045i	−0.163996	−	0.119150i
$904$		0			0
$905$	−47.6051	−	13.1364i	−1.58245	−	0.436668i
$906$		0			0
$907$	−37.7167			−1.25236			−0.626181	−	0.779678i	$-0.715383\pi$
$907$	−37.7167			−1.25236			−0.626181	+	0.779678i	$0.715383\pi$
$908$		0			0
$909$	−7.37721	−	22.7047i	−0.244687	−	0.753068i
$910$		0			0
$911$	−11.5944	+	35.6840i	−0.384141	+	1.18226i	0.552961	+	0.833207i	$0.313498\pi$
$911$	−11.5944	+	35.6840i	−0.384141	+	1.18226i	−0.937102	+	0.349057i	$0.886502\pi$
$912$		0			0
$913$	0.749791	+	2.30762i	0.0248145	+	0.0763711i
$914$		0			0
$915$	−17.4705	−	4.82089i	−0.577557	−	0.159374i
$916$		0			0
$917$	17.9992	−	13.0772i	0.594387	−	0.431848i
$918$		0			0
$919$	−10.7330	+	7.79799i	−0.354049	+	0.257232i	−0.750566	−	0.660796i	$-0.770219\pi$
$919$	−10.7330	+	7.79799i	−0.354049	+	0.257232i	0.396516	+	0.918028i	$0.370219\pi$
$920$		0			0
$921$	6.30720	+	4.58245i	0.207829	+	0.150997i
$922$		0			0
$923$	−7.70991	+	23.7287i	−0.253775	+	0.781038i
$924$		0			0
$925$	−27.0557	+	2.43697i	−0.889586	+	0.0801272i
$926$		0			0
$927$	−12.5390	+	38.5910i	−0.411834	+	1.26749i
$928$		0			0
$929$	13.8501	+	10.0627i	0.454408	+	0.330147i	0.791334	−	0.611384i	$-0.209387\pi$
$929$	13.8501	+	10.0627i	0.454408	+	0.330147i	−0.336925	+	0.941531i	$0.609387\pi$
$930$		0			0
$931$	−1.53108	+	1.11239i	−0.0501791	+	0.0364573i
$932$		0			0
$933$	20.6946	−	15.0355i	0.677512	−	0.492241i
$934$		0			0
$935$	−3.37978	+	5.12054i	−0.110531	+	0.167460i
$936$		0			0
$937$	−15.7405	−	48.4442i	−0.514219	−	1.58260i	−0.784699	−	0.619877i	$-0.787182\pi$
$937$	−15.7405	−	48.4442i	−0.514219	−	1.58260i	0.270480	−	0.962726i	$-0.412818\pi$
$938$		0			0
$939$	−3.56196	+	10.9626i	−0.116240	+	0.357751i
$940$		0			0
$941$	−14.2795	−	43.9479i	−0.465499	−	1.43266i	−0.858353	−	0.513059i	$-0.828512\pi$
$941$	−14.2795	−	43.9479i	−0.465499	−	1.43266i	0.392854	−	0.919601i	$-0.371488\pi$
$942$		0			0
$943$	12.7044			0.413711
$944$		0			0
$945$	17.3273	−	6.50373i	0.563656	−	0.211566i
$946$		0			0
$947$	1.30639	+	0.949149i	0.0424520	+	0.0308432i	0.608809	−	0.793317i	$-0.291648\pi$
$947$	1.30639	+	0.949149i	0.0424520	+	0.0308432i	−0.566357	+	0.824160i	$0.691648\pi$
$948$		0			0
$949$	42.4307			1.37736
$950$		0			0
$951$	15.6048			0.506020
$952$		0			0
$953$	43.2550	+	31.4266i	1.40117	+	1.01801i	0.994534	+	0.104417i	$0.0332978\pi$
$953$	43.2550	+	31.4266i	1.40117	+	1.01801i	0.406635	+	0.913591i	$0.366702\pi$
$954$		0			0
$955$	11.8476	−	17.9498i	0.383381	−	0.580842i
$956$		0			0
$957$	−0.778553			−0.0251670
$958$		0			0
$959$	−3.35497	−	10.3255i	−0.108338	−	0.333429i
$960$		0			0
$961$	−4.64498	+	14.2958i	−0.149838	+	0.461155i
$962$		0			0
$963$	−6.17472	−	19.0038i	−0.198978	−	0.612390i
$964$		0			0
$965$	−24.3130	−	30.4853i	−0.782662	−	0.981357i
$966$		0			0
$967$	−17.5370	+	12.7414i	−0.563951	+	0.409734i	−0.832903	−	0.553419i	$-0.813323\pi$
$967$	−17.5370	+	12.7414i	−0.563951	+	0.409734i	0.268952	+	0.963154i	$0.413323\pi$
$968$		0			0
$969$	0.980457	−	0.712344i	0.0314968	−	0.0228838i
$970$		0			0
$971$	3.98749	+	2.89708i	0.127965	+	0.0929717i	0.649926	−	0.759997i	$-0.274800\pi$
$971$	3.98749	+	2.89708i	0.127965	+	0.0929717i	−0.521962	+	0.852969i	$0.674800\pi$
$972$		0			0
$973$	8.33277	−	25.6456i	0.267136	−	0.822161i
$974$		0			0
$975$	−20.0000	−	11.9476i	−0.640514	−	0.382628i
$976$		0			0
$977$	−4.38084	+	13.4828i	−0.140155	+	0.431354i	−0.996356	−	0.0852891i	$-0.972819\pi$
$977$	−4.38084	+	13.4828i	−0.140155	+	0.431354i	0.856201	+	0.516643i	$0.172819\pi$
$978$		0			0
$979$	−1.16949	−	0.849688i	−0.0373772	−	0.0271561i
$980$		0			0
$981$	25.4935	−	18.5221i	0.813945	−	0.591366i
$982$		0			0
$983$	−22.4669	+	16.3232i	−0.716583	+	0.520628i	−0.885291	−	0.465038i	$-0.846041\pi$
$983$	−22.4669	+	16.3232i	−0.716583	+	0.520628i	0.168707	+	0.985666i	$0.446041\pi$
$984$		0			0
$985$	0.717781	+	15.9701i	0.0228704	+	0.508850i
$986$		0			0
$987$	2.58113	+	7.94389i	0.0821582	+	0.252857i
$988$		0			0
$989$	2.30448	−	7.09245i	0.0732781	−	0.225527i
$990$		0			0
$991$	−10.0111	−	30.8109i	−0.318012	−	0.978739i	−0.974497	−	0.224401i	$-0.927958\pi$
$991$	−10.0111	−	30.8109i	−0.318012	−	0.978739i	0.656485	−	0.754339i	$-0.272042\pi$
$992$		0			0
$993$	3.38499			0.107419
$994$		0			0
$995$	−33.9157	−	42.5259i	−1.07520	−	1.34816i
$996$		0			0
$997$	−23.2003	−	16.8560i	−0.734760	−	0.533835i	0.156305	−	0.987709i	$-0.450042\pi$
$997$	−23.2003	−	16.8560i	−0.734760	−	0.533835i	−0.891066	+	0.453874i	$0.850042\pi$
$998$		0			0
$999$	25.2475			0.798795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.221.8	✓	52
25.6	even	5	inner	1100.2.q.b.881.8	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.8	✓	52	1.1	even	1	trivial
1100.2.q.b.881.8	yes	52	25.6	even	5	inner

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:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.722709 + 0.525079i) q^{3} +(1.39423 + 1.74818i) q^{5} +1.78111 q^{7} +(-0.680451 - 2.09421i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(1.61178 + 4.96054i) q^{13} +(0.0896884 + 1.99550i) q^{15} +(2.21980 - 1.61278i) q^{17} +(0.400006 - 0.290622i) q^{19} +(1.28723 + 0.935224i) q^{21} +(-0.601937 + 1.85257i) q^{23} +(-1.11226 + 4.87472i) q^{25} +(1.43601 - 4.41958i) q^{27} +(0.705083 + 0.512273i) q^{29} +(3.23288 - 2.34883i) q^{31} +(-0.722709 + 0.525079i) q^{33} +(2.48327 + 3.11370i) q^{35} +(1.67890 + 5.16713i) q^{37} +(-1.43983 + 4.43133i) q^{39} +(-2.01543 - 6.20285i) q^{41} -3.82844 q^{43} +(2.71236 - 4.10936i) q^{45} +(4.24705 + 3.08567i) q^{47} -3.82764 q^{49} +2.45111 q^{51} +(2.54764 + 1.85097i) q^{53} +(-2.09346 + 0.785772i) q^{55} +0.441687 q^{57} +(-1.01123 - 3.11226i) q^{59} +(-2.80371 + 8.62892i) q^{61} +(-1.21196 - 3.73003i) q^{63} +(-6.42473 + 9.73379i) q^{65} +(-3.65535 + 2.65577i) q^{67} +(-1.40777 + 1.02280i) q^{69} +(3.86992 + 2.81166i) q^{71} +(2.51385 - 7.73684i) q^{73} +(-3.36345 + 2.93898i) q^{75} +(-0.550394 + 1.69394i) q^{77} +(-5.06666 - 3.68114i) q^{79} +(-1.98589 + 1.44283i) q^{81} +(1.96298 - 1.42619i) q^{83} +(5.91433 + 1.63203i) q^{85} +(0.240586 + 0.740448i) q^{87} +(-0.446707 + 1.37482i) q^{89} +(2.87076 + 8.83528i) q^{91} +3.56975 q^{93} +(1.06576 + 0.294090i) q^{95} +(3.05092 + 2.21662i) q^{97} +2.20198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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