LMFDB - Embedded newform 552.2.q.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	552.25
Dual form			552.2.q.a.265.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{3} +(-0.768760 - 0.225728i) q^{5} +(-0.186229 + 0.214919i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{3} +(-0.768760 - 0.225728i) q^{5} +(-0.186229 + 0.214919i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(2.11480 - 1.35910i) q^{11} +(-3.65149 - 4.21404i) q^{13} +(-0.114025 + 0.793060i) q^{15} +(1.96639 - 4.30580i) q^{17} +(0.447851 + 0.980658i) q^{19} +(0.239235 + 0.153747i) q^{21} +(-4.37764 - 1.95864i) q^{23} +(-3.66623 - 2.35614i) q^{25} +(0.415415 + 0.909632i) q^{27} +(3.56853 - 7.81398i) q^{29} +(-0.721324 + 5.01692i) q^{31} +(-1.64623 - 1.89985i) q^{33} +(0.191679 - 0.123184i) q^{35} +(-7.59475 + 2.23002i) q^{37} +(-3.65149 + 4.21404i) q^{39} +(0.420523 + 0.123477i) q^{41} +(-0.861815 - 5.99406i) q^{43} +0.801215 q^{45} -1.21283 q^{47} +(0.984695 + 6.84870i) q^{49} +(-4.54182 - 1.33360i) q^{51} +(4.94980 - 5.71238i) q^{53} +(-1.93256 + 0.567451i) q^{55} +(0.906940 - 0.582855i) q^{57} +(3.68578 + 4.25362i) q^{59} +(1.36861 - 9.51888i) q^{61} +(0.118135 - 0.258680i) q^{63} +(1.85589 + 4.06383i) q^{65} +(10.8406 + 6.96685i) q^{67} +(-1.31570 + 4.61182i) q^{69} +(5.46102 + 3.50958i) q^{71} +(-1.56864 - 3.43484i) q^{73} +(-1.81040 + 3.96423i) q^{75} +(-0.101740 + 0.707615i) q^{77} +(0.567717 + 0.655180i) q^{79} +(0.841254 - 0.540641i) q^{81} +(0.408517 - 0.119951i) q^{83} +(-2.48363 + 2.86626i) q^{85} +(-8.24230 - 2.42016i) q^{87} +(-1.24569 - 8.66393i) q^{89} +1.58569 q^{91} +5.06851 q^{93} +(-0.122928 - 0.854983i) q^{95} +(6.70654 + 1.96922i) q^{97} +(-1.64623 + 1.89985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$4$		0			0
$5$	−0.768760	−	0.225728i	−0.343800	−	0.100949i	0.105274	−	0.994443i	$-0.466428\pi$
$5$	−0.768760	−	0.225728i	−0.343800	−	0.100949i	−0.449074	+	0.893494i	$0.648246\pi$
$6$		0			0
$7$	−0.186229	+	0.214919i	−0.0703878	+	0.0812319i	−0.789851	−	0.613298i	$-0.789842\pi$
$7$	−0.186229	+	0.214919i	−0.0703878	+	0.0812319i	0.719463	+	0.694530i	$0.244388\pi$
$8$		0			0
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$		0			0
$11$	2.11480	−	1.35910i	0.637636	−	0.409784i	−0.181494	−	0.983392i	$-0.558093\pi$
$11$	2.11480	−	1.35910i	0.637636	−	0.409784i	0.819130	+	0.573608i	$0.194457\pi$
$12$		0			0
$13$	−3.65149	−	4.21404i	−1.01274	−	1.16877i	−0.985593	−	0.169134i	$-0.945903\pi$
$13$	−3.65149	−	4.21404i	−1.01274	−	1.16877i	−0.0271480	−	0.999631i	$-0.508643\pi$
$14$		0			0
$15$	−0.114025	+	0.793060i	−0.0294411	+	0.204767i
$16$		0			0
$17$	1.96639	−	4.30580i	0.476921	−	1.04431i	−0.506378	−	0.862312i	$-0.669016\pi$
$17$	1.96639	−	4.30580i	0.476921	−	1.04431i	0.983299	−	0.181999i	$-0.0582568\pi$
$18$		0			0
$19$	0.447851	+	0.980658i	0.102744	+	0.224978i	0.954022	−	0.299737i	$-0.0968990\pi$
$19$	0.447851	+	0.980658i	0.102744	+	0.224978i	−0.851278	+	0.524715i	$0.824172\pi$
$20$		0			0
$21$	0.239235	+	0.153747i	0.0522053	+	0.0335503i
$22$		0			0
$23$	−4.37764	−	1.95864i	−0.912801	−	0.408405i
$23$	−4.37764	−	1.95864i	−0.912801	−	0.408405i
$24$		0			0
$25$	−3.66623	−	2.35614i	−0.733246	−	0.471228i
$26$		0			0
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$		0			0
$29$	3.56853	−	7.81398i	0.662659	−	1.45102i	−0.217365	−	0.976090i	$-0.569746\pi$
$29$	3.56853	−	7.81398i	0.662659	−	1.45102i	0.880024	−	0.474930i	$-0.157527\pi$
$30$		0			0
$31$	−0.721324	+	5.01692i	−0.129554	+	0.901065i	0.816567	+	0.577251i	$0.195874\pi$
$31$	−0.721324	+	5.01692i	−0.129554	+	0.901065i	−0.946121	+	0.323815i	$0.895035\pi$
$32$		0			0
$33$	−1.64623	−	1.89985i	−0.286572	−	0.330722i
$34$		0			0
$35$	0.191679	−	0.123184i	0.0323996	−	0.0208220i
$36$		0			0
$37$	−7.59475	+	2.23002i	−1.24857	+	0.366613i	−0.838228	−	0.545319i	$-0.816408\pi$
$37$	−7.59475	+	2.23002i	−1.24857	+	0.366613i	−0.410341	+	0.911932i	$0.634590\pi$
$38$		0			0
$39$	−3.65149	+	4.21404i	−0.584706	+	0.674787i
$40$		0			0
$41$	0.420523	+	0.123477i	0.0656747	+	0.0192838i	0.314405	−	0.949289i	$-0.398195\pi$
$41$	0.420523	+	0.123477i	0.0656747	+	0.0192838i	−0.248730	+	0.968573i	$0.580013\pi$
$42$		0			0
$43$	−0.861815	−	5.99406i	−0.131426	−	0.914085i	−0.943698	−	0.330807i	$-0.892679\pi$
$43$	−0.861815	−	5.99406i	−0.131426	−	0.914085i	0.812273	−	0.583278i	$-0.198230\pi$
$44$		0			0
$45$	0.801215			0.119438
$46$		0			0
$47$	−1.21283			−0.176909			−0.0884547	−	0.996080i	$-0.528193\pi$
$47$	−1.21283			−0.176909			−0.0884547	+	0.996080i	$0.528193\pi$
$48$		0			0
$49$	0.984695	+	6.84870i	0.140671	+	0.978386i
$50$		0			0
$51$	−4.54182	−	1.33360i	−0.635982	−	0.186741i
$52$		0			0
$53$	4.94980	−	5.71238i	0.679908	−	0.784656i	−0.305984	−	0.952037i	$-0.598986\pi$
$53$	4.94980	−	5.71238i	0.679908	−	0.784656i	0.985892	+	0.167381i	$0.0535310\pi$
$54$		0			0
$55$	−1.93256	+	0.567451i	−0.260587	+	0.0765151i
$56$		0			0
$57$	0.906940	−	0.582855i	0.120127	−	0.0772010i
$58$		0			0
$59$	3.68578	+	4.25362i	0.479848	+	0.553774i	0.943124	−	0.332440i	$-0.107872\pi$
$59$	3.68578	+	4.25362i	0.479848	+	0.553774i	−0.463277	+	0.886214i	$0.653326\pi$
$60$		0			0
$61$	1.36861	−	9.51888i	0.175232	−	1.21877i	−0.692382	−	0.721531i	$-0.743439\pi$
$61$	1.36861	−	9.51888i	0.175232	−	1.21877i	0.867615	−	0.497237i	$-0.165652\pi$
$62$		0			0
$63$	0.118135	−	0.258680i	0.0148837	−	0.0325907i
$64$		0			0
$65$	1.85589	+	4.06383i	0.230195	+	0.504057i
$66$		0			0
$67$	10.8406	+	6.96685i	1.32439	+	0.851136i	0.995640	−	0.0932793i	$-0.0297350\pi$
$67$	10.8406	+	6.96685i	1.32439	+	0.851136i	0.328754	+	0.944416i	$0.393371\pi$
$68$		0			0
$69$	−1.31570	+	4.61182i	−0.158392	+	0.555198i
$70$		0			0
$71$	5.46102	+	3.50958i	0.648104	+	0.416511i	0.822973	−	0.568081i	$-0.192314\pi$
$71$	5.46102	+	3.50958i	0.648104	+	0.416511i	−0.174869	+	0.984592i	$0.555950\pi$
$72$		0			0
$73$	−1.56864	−	3.43484i	−0.183596	−	0.402018i	0.795347	−	0.606154i	$-0.207289\pi$
$73$	−1.56864	−	3.43484i	−0.183596	−	0.402018i	−0.978942	+	0.204136i	$0.934561\pi$
$74$		0			0
$75$	−1.81040	+	3.96423i	−0.209047	+	0.457749i
$76$		0			0
$77$	−0.101740	+	0.707615i	−0.0115943	+	0.0806402i
$78$		0			0
$79$	0.567717	+	0.655180i	0.0638731	+	0.0737135i	0.786787	−	0.617225i	$-0.211743\pi$
$79$	0.567717	+	0.655180i	0.0638731	+	0.0737135i	−0.722914	+	0.690938i	$0.757198\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$		0			0
$83$	0.408517	−	0.119951i	0.0448405	−	0.0131664i	−0.259235	−	0.965814i	$-0.583471\pi$
$83$	0.408517	−	0.119951i	0.0448405	−	0.0131664i	0.304076	+	0.952648i	$0.401652\pi$
$84$		0			0
$85$	−2.48363	+	2.86626i	−0.269387	+	0.310889i
$86$		0			0
$87$	−8.24230	−	2.42016i	−0.883668	−	0.259468i
$88$		0			0
$89$	−1.24569	−	8.66393i	−0.132042	−	0.918375i	−0.942887	−	0.333113i	$-0.891901\pi$
$89$	−1.24569	−	8.66393i	−0.132042	−	0.918375i	0.810844	−	0.585262i	$-0.199008\pi$
$90$		0			0
$91$	1.58569			0.166226
$92$		0			0
$93$	5.06851			0.525580
$94$		0			0
$95$	−0.122928	−	0.854983i	−0.0126122	−	0.0877194i
$96$		0			0
$97$	6.70654	+	1.96922i	0.680946	+	0.199944i	0.603871	−	0.797082i	$-0.293624\pi$
$97$	6.70654	+	1.96922i	0.680946	+	0.199944i	0.0770741	+	0.997025i	$0.475442\pi$
$98$		0			0
$99$	−1.64623	+	1.89985i	−0.165453	+	0.190943i
$100$		0			0
$101$	13.2336	−	3.88573i	1.31679	−	0.386644i	0.453456	−	0.891279i	$-0.350191\pi$
$101$	13.2336	−	3.88573i	1.31679	−	0.386644i	0.863333	+	0.504634i	$0.168373\pi$
$102$		0			0
$103$	−5.48808	+	3.52697i	−0.540756	+	0.347523i	−0.782335	−	0.622858i	$-0.785971\pi$
$103$	−5.48808	+	3.52697i	−0.540756	+	0.347523i	0.241578	+	0.970381i	$0.422335\pi$
$104$		0			0
$105$	−0.149209	−	0.172197i	−0.0145613	−	0.0168047i
$106$		0			0
$107$	−0.662265	+	4.60615i	−0.0640235	+	0.445293i	0.932444	+	0.361315i	$0.117672\pi$
$107$	−0.662265	+	4.60615i	−0.0640235	+	0.445293i	−0.996468	+	0.0839789i	$0.973237\pi$
$108$		0			0
$109$	−5.78793	+	12.6738i	−0.554383	+	1.21393i	0.400321	+	0.916375i	$0.368898\pi$
$109$	−5.78793	+	12.6738i	−0.554383	+	1.21393i	−0.954705	+	0.297555i	$0.903829\pi$
$110$		0			0
$111$	3.28817	+	7.20008i	0.312099	+	0.683402i
$112$		0			0
$113$	10.2602	+	6.59381i	0.965195	+	0.620293i	0.925431	−	0.378916i	$-0.123703\pi$
$113$	10.2602	+	6.59381i	0.965195	+	0.620293i	0.0397637	+	0.999209i	$0.487339\pi$
$114$		0			0
$115$	2.92323	+	2.49388i	0.272593	+	0.232556i
$116$		0			0
$117$	4.69081	+	3.01460i	0.433666	+	0.278700i
$118$		0			0
$119$	0.559202	+	1.22448i	0.0512619	+	0.112248i
$120$		0			0
$121$	−1.94434	+	4.25751i	−0.176758	+	0.387046i
$122$		0			0
$123$	0.0623733	−	0.433816i	0.00562401	−	0.0391158i
$124$		0			0
$125$	4.91002	+	5.66647i	0.439166	+	0.506824i
$126$		0			0
$127$	−3.23641	+	2.07991i	−0.287185	+	0.184563i	−0.676299	−	0.736627i	$-0.736417\pi$
$127$	−3.23641	+	2.07991i	−0.287185	+	0.184563i	0.389114	+	0.921189i	$0.372781\pi$
$128$		0			0
$129$	−5.81040	+	1.70609i	−0.511577	+	0.150213i
$130$		0			0
$131$	12.7839	−	14.7535i	1.11694	−	1.28902i	0.163796	−	0.986494i	$-0.447626\pi$
$131$	12.7839	−	14.7535i	1.11694	−	1.28902i	0.953143	−	0.302521i	$-0.0978284\pi$
$132$		0			0
$133$	−0.294165	−	0.0863747i	−0.0255074	−	0.00748964i
$134$		0			0
$135$	−0.114025	−	0.793060i	−0.00981369	−	0.0682557i
$136$		0			0
$137$	−0.944499			−0.0806940			−0.0403470	−	0.999186i	$-0.512846\pi$
$137$	−0.944499			−0.0806940			−0.0403470	+	0.999186i	$0.512846\pi$
$138$		0			0
$139$	9.77599			0.829189			0.414594	−	0.910006i	$-0.363923\pi$
$139$	9.77599			0.829189			0.414594	+	0.910006i	$0.363923\pi$
$140$		0			0
$141$	0.172604	+	1.20049i	0.0145359	+	0.101099i
$142$		0			0
$143$	−13.4495	−	3.94912i	−1.12470	−	0.330242i
$144$		0			0
$145$	−4.50718	+	5.20156i	−0.374301	+	0.431966i
$146$		0			0
$147$	6.63886	−	1.94934i	0.547564	−	0.160779i
$148$		0			0
$149$	−9.07071	+	5.82939i	−0.743101	+	0.477562i	−0.856603	−	0.515975i	$-0.827430\pi$
$149$	−9.07071	+	5.82939i	−0.743101	+	0.477562i	0.113502	+	0.993538i	$0.463793\pi$
$150$		0			0
$151$	2.71821	+	3.13698i	0.221205	+	0.255284i	0.855495	−	0.517811i	$-0.173253\pi$
$151$	2.71821	+	3.13698i	0.221205	+	0.255284i	−0.634290	+	0.773095i	$0.718708\pi$
$152$		0			0
$153$	−0.673657	+	4.68538i	−0.0544619	+	0.378791i
$154$		0			0
$155$	1.68699	−	3.69398i	0.135502	−	0.296708i
$156$		0			0
$157$	−5.50397	−	12.0520i	−0.439264	−	0.961854i	−0.991733	−	0.128321i	$-0.959041\pi$
$157$	−5.50397	−	12.0520i	−0.439264	−	0.961854i	0.552468	−	0.833534i	$-0.313686\pi$
$158$		0			0
$159$	−6.35867	−	4.08647i	−0.504275	−	0.324078i
$160$		0			0
$161$	1.23619	−	0.576084i	0.0974256	−	0.0454018i
$162$		0			0
$163$	13.3839	+	8.60128i	1.04830	+	0.673704i	0.947027	−	0.321154i	$-0.104071\pi$
$163$	13.3839	+	8.60128i	1.04830	+	0.673704i	0.101277	+	0.994858i	$0.467707\pi$
$164$		0			0
$165$	0.836708	+	1.83213i	0.0651376	+	0.142631i
$166$		0			0
$167$	−0.0568154	+	0.124408i	−0.00439651	+	0.00962701i	−0.911818	−	0.410596i	$-0.865321\pi$
$167$	−0.0568154	+	0.124408i	−0.00439651	+	0.00962701i	0.907421	+	0.420223i	$0.138048\pi$
$168$		0			0
$169$	−2.57470	+	17.9074i	−0.198053	+	1.37749i
$170$		0			0
$171$	−0.705993	−	0.814760i	−0.0539887	−	0.0623062i
$172$		0			0
$173$	−9.69427	+	6.23013i	−0.737041	+	0.473668i	−0.854527	−	0.519407i	$-0.826153\pi$
$173$	−9.69427	+	6.23013i	−0.737041	+	0.473668i	0.117486	+	0.993075i	$0.462517\pi$
$174$		0			0
$175$	1.18914	−	0.349162i	0.0898904	−	0.0263942i
$176$		0			0
$177$	3.68578	−	4.25362i	0.277040	−	0.319721i
$178$		0			0
$179$	8.08264	+	2.37328i	0.604125	+	0.177387i	0.569470	−	0.822012i	$-0.307149\pi$
$179$	8.08264	+	2.37328i	0.604125	+	0.177387i	0.0346551	+	0.999399i	$0.488967\pi$
$180$		0			0
$181$	−1.52298	−	10.5926i	−0.113202	−	0.787340i	−0.964770	−	0.263095i	$-0.915257\pi$
$181$	−1.52298	−	10.5926i	−0.113202	−	0.787340i	0.851567	−	0.524245i	$-0.175652\pi$
$182$		0			0
$183$	−9.61677			−0.710892
$184$		0			0
$185$	6.34192			0.466267
$186$		0			0
$187$	−1.69348	−	11.7784i	−0.123840	−	0.861325i
$188$		0			0
$189$	−0.272860	−	0.0801189i	−0.0198476	−	0.00582779i
$190$		0			0
$191$	−14.9363	+	17.2375i	−1.08076	+	1.24726i	−0.113478	+	0.993541i	$0.536199\pi$
$191$	−14.9363	+	17.2375i	−1.08076	+	1.24726i	−0.967278	+	0.253719i	$0.918346\pi$
$192$		0			0
$193$	−17.7069	+	5.19921i	−1.27457	+	0.374247i	−0.847898	−	0.530159i	$-0.822132\pi$
$193$	−17.7069	+	5.19921i	−1.27457	+	0.374247i	−0.426672	+	0.904407i	$0.640314\pi$
$194$		0			0
$195$	3.75835	−	2.41534i	0.269141	−	0.172966i
$196$		0			0
$197$	13.2891	+	15.3365i	0.946811	+	1.09268i	0.995585	+	0.0938679i	$0.0299231\pi$
$197$	13.2891	+	15.3365i	0.946811	+	1.09268i	−0.0487740	+	0.998810i	$0.515531\pi$
$198$		0			0
$199$	−0.966279	+	6.72062i	−0.0684977	+	0.476412i	0.926482	+	0.376338i	$0.122817\pi$
$199$	−0.966279	+	6.72062i	−0.0684977	+	0.476412i	−0.994980	+	0.100074i	$0.968092\pi$
$200$		0			0
$201$	5.35316	−	11.7218i	0.377582	−	0.826790i
$202$		0			0
$203$	1.01481	+	2.22213i	0.0712260	+	0.155963i
$204$		0			0
$205$	−0.295409	−	0.189848i	−0.0206323	−	0.0132596i
$206$		0			0
$207$	4.75213	+	0.645979i	0.330296	+	0.0448986i
$208$		0			0
$209$	2.27993	+	1.46522i	0.157706	+	0.101351i
$210$		0			0
$211$	−7.72335	−	16.9118i	−0.531697	−	1.16425i	−0.964818	−	0.262918i	$-0.915315\pi$
$211$	−7.72335	−	16.9118i	−0.531697	−	1.16425i	0.433121	−	0.901336i	$-0.357412\pi$
$212$		0			0
$213$	2.69668	−	5.90490i	0.184773	−	0.404597i
$214$		0			0
$215$	−0.690499	+	4.80253i	−0.0470917	+	0.327530i
$216$		0			0
$217$	−0.943902	−	1.08932i	−0.0640762	−	0.0739479i
$218$		0			0
$219$	−3.17664	+	2.04150i	−0.214658	+	0.137952i
$220$		0			0
$221$	−25.3251	+	7.43612i	−1.70355	+	0.500208i
$222$		0			0
$223$	16.5423	−	19.0908i	1.10775	−	1.27841i	0.150674	−	0.988584i	$-0.451856\pi$
$223$	16.5423	−	19.0908i	1.10775	−	1.27841i	0.957078	−	0.289830i	$-0.0935989\pi$
$224$		0			0
$225$	4.18152	+	1.22781i	0.278768	+	0.0818537i
$226$		0			0
$227$	−3.32248	−	23.1083i	−0.220520	−	1.53375i	−0.736077	−	0.676898i	$-0.763324\pi$
$227$	−3.32248	−	23.1083i	−0.220520	−	1.53375i	0.515556	−	0.856856i	$-0.327585\pi$
$228$		0			0
$229$	5.09358			0.336593			0.168297	−	0.985736i	$-0.446173\pi$
$229$	5.09358			0.336593			0.168297	+	0.985736i	$0.446173\pi$
$230$		0			0
$231$	0.714892			0.0470364
$232$		0			0
$233$	−1.13976	−	7.92718i	−0.0746679	−	0.519327i	−0.992489	−	0.122333i	$-0.960962\pi$
$233$	−1.13976	−	7.92718i	−0.0746679	−	0.519327i	0.917821	−	0.396994i	$-0.129947\pi$
$234$		0			0
$235$	0.932376	+	0.273770i	0.0608215	+	0.0178588i
$236$		0			0
$237$	0.567717	−	0.655180i	0.0368772	−	0.0425585i
$238$		0			0
$239$	11.8161	−	3.46951i	0.764318	−	0.224424i	0.123737	−	0.992315i	$-0.460512\pi$
$239$	11.8161	−	3.46951i	0.764318	−	0.224424i	0.640580	+	0.767891i	$0.278694\pi$
$240$		0			0
$241$	2.66798	−	1.71461i	0.171860	−	0.110447i	−0.451883	−	0.892077i	$-0.649248\pi$
$241$	2.66798	−	1.71461i	0.171860	−	0.110447i	0.623743	+	0.781630i	$0.285611\pi$
$242$		0			0
$243$	−0.654861	−	0.755750i	−0.0420093	−	0.0484814i
$244$		0			0
$245$	0.788952	−	5.48728i	0.0504043	−	0.350570i
$246$		0			0
$247$	2.49721	−	5.46813i	0.158894	−	0.347929i
$248$		0			0
$249$	−0.176868	−	0.387288i	−0.0112086	−	0.0245434i
$250$		0			0
$251$	−18.0482	−	11.5989i	−1.13919	−	0.732116i	−0.171735	−	0.985143i	$-0.554937\pi$
$251$	−18.0482	−	11.5989i	−1.13919	−	0.732116i	−0.967459	+	0.253028i	$0.918574\pi$
$252$		0			0
$253$	−11.9198	+	1.80751i	−0.749393	+	0.113637i
$254$		0			0
$255$	3.19054	+	2.05044i	0.199799	+	0.128403i
$256$		0			0
$257$	−5.74664	−	12.5834i	−0.358466	−	0.784930i	−0.999843	−	0.0177048i	$-0.994364\pi$
$257$	−5.74664	−	12.5834i	−0.358466	−	0.784930i	0.641378	−	0.767225i	$-0.278363\pi$
$258$		0			0
$259$	0.935086	−	2.04755i	0.0581034	−	0.127229i
$260$		0			0
$261$	−1.22252	+	8.50283i	−0.0756723	+	0.526312i
$262$		0			0
$263$	−14.8575	−	17.1465i	−0.916152	−	1.05730i	−0.998158	−	0.0606641i	$-0.980678\pi$
$263$	−14.8575	−	17.1465i	−0.916152	−	1.05730i	0.0820061	−	0.996632i	$-0.473867\pi$
$264$		0			0
$265$	−5.09466	+	3.27414i	−0.312962	+	0.201129i
$266$		0			0
$267$	−8.39846	+	2.46601i	−0.513978	+	0.150917i
$268$		0			0
$269$	5.05215	−	5.83049i	0.308035	−	0.355492i	−0.580533	−	0.814237i	$-0.697156\pi$
$269$	5.05215	−	5.83049i	0.308035	−	0.355492i	0.888568	+	0.458746i	$0.151701\pi$
$270$		0			0
$271$	−7.53025	−	2.21108i	−0.457430	−	0.134314i	0.0448964	−	0.998992i	$-0.485704\pi$
$271$	−7.53025	−	2.21108i	−0.457430	−	0.134314i	−0.502326	+	0.864678i	$0.667522\pi$
$272$		0			0
$273$	−0.225668	−	1.56955i	−0.0136580	−	0.0949936i
$274$		0			0
$275$	−10.9556			−0.660646
$276$		0			0
$277$	21.1224			1.26912			0.634562	−	0.772872i	$-0.281180\pi$
$277$	21.1224			1.26912			0.634562	+	0.772872i	$0.281180\pi$
$278$		0			0
$279$	−0.721324	−	5.01692i	−0.0431845	−	0.300355i
$280$		0			0
$281$	−0.111461	−	0.0327279i	−0.00664920	−	0.00195238i	0.278406	−	0.960463i	$-0.410194\pi$
$281$	−0.111461	−	0.0327279i	−0.00664920	−	0.00195238i	−0.285055	+	0.958511i	$0.592012\pi$
$282$		0			0
$283$	18.2776	−	21.0935i	1.08649	−	1.25388i	0.121218	−	0.992626i	$-0.461320\pi$
$283$	18.2776	−	21.0935i	1.08649	−	1.25388i	0.965271	−	0.261250i	$-0.0841347\pi$
$284$		0			0
$285$	−0.828786	+	0.243354i	−0.0490931	+	0.0144150i
$286$		0			0
$287$	−0.104851	+	0.0673837i	−0.00618916	+	0.00397753i
$288$		0			0
$289$	−3.54060	−	4.08607i	−0.208270	−	0.240357i
$290$		0			0
$291$	0.994733	−	6.91852i	0.0583123	−	0.405571i
$292$		0			0
$293$	−4.73051	+	10.3584i	−0.276359	+	0.605143i	−0.996015	−	0.0891888i	$-0.971573\pi$
$293$	−4.73051	+	10.3584i	−0.276359	+	0.605143i	0.719655	+	0.694331i	$0.244300\pi$
$294$		0			0
$295$	−1.87332	−	4.10200i	−0.109069	−	0.238828i
$296$		0			0
$297$	2.11480	+	1.35910i	0.122713	+	0.0788629i
$298$		0			0
$299$	7.73111	+	25.5995i	0.447101	+	1.48046i
$300$		0			0
$301$	1.44873	+	0.931045i	0.0835036	+	0.0536645i
$302$		0			0
$303$	−5.72951	−	12.5459i	−0.329152	−	0.720742i
$304$		0			0
$305$	−3.20081	+	7.00881i	−0.183278	+	0.401323i
$306$		0			0
$307$	−1.72326	+	11.9855i	−0.0983514	+	0.684049i	0.879676	+	0.475573i	$0.157759\pi$
$307$	−1.72326	+	11.9855i	−0.0983514	+	0.684049i	−0.978028	+	0.208476i	$0.933150\pi$
$308$		0			0
$309$	4.27211	+	4.93028i	0.243032	+	0.280474i
$310$		0			0
$311$	−8.32410	+	5.34958i	−0.472017	+	0.303347i	−0.754938	−	0.655797i	$-0.772333\pi$
$311$	−8.32410	+	5.34958i	−0.472017	+	0.303347i	0.282921	+	0.959143i	$0.408697\pi$
$312$		0			0
$313$	5.53810	−	1.62613i	0.313032	−	0.0919145i	−0.121443	−	0.992598i	$-0.538752\pi$
$313$	5.53810	−	1.62613i	0.313032	−	0.0919145i	0.434475	+	0.900684i	$0.356934\pi$
$314$		0			0
$315$	−0.149209	+	0.172197i	−0.00840699	+	0.00970218i
$316$		0			0
$317$	−13.6919	−	4.02031i	−0.769015	−	0.225803i	−0.126386	−	0.991981i	$-0.540338\pi$
$317$	−13.6919	−	4.02031i	−0.769015	−	0.225803i	−0.642629	+	0.766178i	$0.722156\pi$
$318$		0			0
$319$	−3.07326	−	21.3750i	−0.172070	−	1.19677i
$320$		0			0
$321$	4.65352			0.259734
$322$		0			0
$323$	5.10317			0.283948
$324$		0			0
$325$	3.45831	+	24.0531i	0.191833	+	1.33422i
$326$		0			0
$327$	13.3685	+	3.92535i	0.739280	+	0.217072i
$328$		0			0
$329$	0.225864	−	0.260661i	0.0124523	−	0.0143707i
$330$		0			0
$331$	18.9294	−	5.55816i	1.04045	−	0.305504i	0.283498	−	0.958973i	$-0.408505\pi$
$331$	18.9294	−	5.55816i	1.04045	−	0.305504i	0.756954	+	0.653469i	$0.226687\pi$
$332$		0			0
$333$	6.65884	−	4.27938i	0.364902	−	0.234508i
$334$		0			0
$335$	−6.76123	−	7.80288i	−0.369405	−	0.426317i
$336$		0			0
$337$	0.972836	−	6.76622i	0.0529937	−	0.368580i	−0.946017	−	0.324116i	$-0.894933\pi$
$337$	0.972836	−	6.76622i	0.0529937	−	0.368580i	0.999011	−	0.0444633i	$-0.0141578\pi$
$338$		0			0
$339$	5.06652	−	11.0941i	0.275175	−	0.602550i
$340$		0			0
$341$	5.29304	+	11.5901i	0.286634	+	0.627641i
$342$		0			0
$343$	−3.32994	−	2.14002i	−0.179800	−	0.115550i
$344$		0			0
$345$	2.05248	−	3.24840i	0.110502	−	0.174888i
$346$		0			0
$347$	6.68706	+	4.29752i	0.358980	+	0.230703i	0.707682	−	0.706531i	$-0.249741\pi$
$347$	6.68706	+	4.29752i	0.358980	+	0.230703i	−0.348702	+	0.937234i	$0.613377\pi$
$348$		0			0
$349$	−12.5452	−	27.4702i	−0.671530	−	1.47044i	−0.871375	−	0.490617i	$-0.836771\pi$
$349$	−12.5452	−	27.4702i	−0.671530	−	1.47044i	0.199846	−	0.979827i	$-0.435956\pi$
$350$		0			0
$351$	2.31635	−	5.07209i	0.123637	−	0.270728i
$352$		0			0
$353$	1.96891	−	13.6941i	0.104794	−	0.728861i	−0.867894	−	0.496749i	$-0.834527\pi$
$353$	1.96891	−	13.6941i	0.104794	−	0.728861i	0.972689	−	0.232113i	$-0.0745638\pi$
$354$		0			0
$355$	−3.40600	−	3.93074i	−0.180772	−	0.208622i
$356$		0			0
$357$	1.13243	−	0.727771i	0.0599348	−	0.0385177i
$358$		0			0
$359$	−23.9461	+	7.03120i	−1.26383	+	0.371093i	−0.843917	−	0.536474i	$-0.819756\pi$
$359$	−23.9461	+	7.03120i	−1.26383	+	0.371093i	−0.419909	+	0.907566i	$0.637938\pi$
$360$		0			0
$361$	11.6812	−	13.4809i	0.614802	−	0.709519i
$362$		0			0
$363$	4.49088	+	1.31864i	0.235710	+	0.0692107i
$364$		0			0
$365$	0.430567	+	2.99466i	0.0225369	+	0.156748i
$366$		0			0
$367$	−19.0746			−0.995684			−0.497842	−	0.867268i	$-0.665874\pi$
$367$	−19.0746			−0.995684			−0.497842	+	0.867268i	$0.665874\pi$
$368$		0			0
$369$	−0.438277			−0.0228158
$370$		0			0
$371$	0.305905	+	2.12762i	0.0158818	+	0.110460i
$372$		0			0
$373$	−21.5728	−	6.33436i	−1.11700	−	0.327981i	−0.329414	−	0.944186i	$-0.606851\pi$
$373$	−21.5728	−	6.33436i	−1.11700	−	0.327981i	−0.787586	+	0.616205i	$0.788669\pi$
$374$		0			0
$375$	4.91002	−	5.66647i	0.253553	−	0.292615i
$376$		0			0
$377$	−45.9589	+	13.4948i	−2.36700	+	0.695015i
$378$		0			0
$379$	−31.2750	+	20.0992i	−1.60649	+	1.03243i	−0.642568	+	0.766229i	$0.722131\pi$
$379$	−31.2750	+	20.0992i	−1.60649	+	1.03243i	−0.963919	+	0.266197i	$0.914233\pi$
$380$		0			0
$381$	2.51933	+	2.90746i	0.129069	+	0.148954i
$382$		0			0
$383$	−0.641536	+	4.46198i	−0.0327810	+	0.227997i	−0.999625	−	0.0273696i	$-0.991287\pi$
$383$	−0.641536	+	4.46198i	−0.0327810	+	0.227997i	0.966844	+	0.255366i	$0.0821960\pi$
$384$		0			0
$385$	0.237942	−	0.521021i	0.0121267	−	0.0265537i
$386$		0			0
$387$	2.51563	+	5.50845i	0.127876	+	0.280010i
$388$		0			0
$389$	28.6674	+	18.4234i	1.45350	+	0.934105i	0.999061	+	0.0433245i	$0.0137949\pi$
$389$	28.6674	+	18.4234i	1.45350	+	0.934105i	0.454434	+	0.890780i	$0.349841\pi$
$390$		0			0
$391$	−17.0417	+	14.9978i	−0.861835	+	0.758471i
$392$		0			0
$393$	−16.4226	−	10.5542i	−0.828412	−	0.532388i
$394$		0			0
$395$	−0.288545	−	0.631826i	−0.0145183	−	0.0317906i
$396$		0			0
$397$	2.67222	−	5.85134i	0.134115	−	0.293670i	−0.830645	−	0.556802i	$-0.812028\pi$
$397$	2.67222	−	5.85134i	0.134115	−	0.293670i	0.964760	+	0.263132i	$0.0847555\pi$
$398$		0			0
$399$	−0.0436314	+	0.303463i	−0.00218430	+	0.0151922i
$400$		0			0
$401$	8.92990	+	10.3056i	0.445938	+	0.514640i	0.933563	−	0.358413i	$-0.116682\pi$
$401$	8.92990	+	10.3056i	0.445938	+	0.514640i	−0.487625	+	0.873053i	$0.662137\pi$
$402$		0			0
$403$	23.7754	−	15.2795i	1.18434	−	0.761128i
$404$		0			0
$405$	−0.768760	+	0.225728i	−0.0382000	+	0.0112165i
$406$		0			0
$407$	−13.0306	+	15.0381i	−0.645901	+	0.745409i
$408$		0			0
$409$	32.0655	+	9.41528i	1.58554	+	0.465555i	0.951475	−	0.307727i	$-0.0995684\pi$
$409$	32.0655	+	9.41528i	1.58554	+	0.465555i	0.634062	+	0.773282i	$0.281387\pi$
$410$		0			0
$411$	0.134416	+	0.934885i	0.00663026	+	0.0461145i
$412$		0			0
$413$	−1.60058			−0.0787596
$414$		0			0
$415$	−0.341128			−0.0167453
$416$		0			0
$417$	−1.39127	−	9.67649i	−0.0681307	−	0.473860i
$418$		0			0
$419$	−12.4508	−	3.65587i	−0.608259	−	0.178601i	−0.0369244	−	0.999318i	$-0.511756\pi$
$419$	−12.4508	−	3.65587i	−0.608259	−	0.178601i	−0.571335	+	0.820717i	$0.693574\pi$
$420$		0			0
$421$	17.3713	−	20.0476i	0.846628	−	0.977060i	−0.153310	−	0.988178i	$-0.548993\pi$
$421$	17.3713	−	20.0476i	0.846628	−	0.977060i	0.999938	+	0.0111176i	$0.00353891\pi$
$422$		0			0
$423$	1.16370	−	0.341694i	0.0565811	−	0.0166137i
$424$		0			0
$425$	−17.3543	+	11.1530i	−0.841809	+	0.540998i
$426$		0			0
$427$	1.79092	+	2.06683i	0.0866686	+	0.100021i
$428$		0			0
$429$	−1.99487	+	13.8746i	−0.0963130	+	0.669872i
$430$		0			0
$431$	8.10742	−	17.7528i	0.390521	−	0.855121i	−0.607623	−	0.794225i	$-0.707877\pi$
$431$	8.10742	−	17.7528i	0.390521	−	0.855121i	0.998144	−	0.0608960i	$-0.0193958\pi$
$432$		0			0
$433$	15.0777	+	33.0155i	0.724587	+	1.58663i	0.807362	+	0.590057i	$0.200895\pi$
$433$	15.0777	+	33.0155i	0.724587	+	1.58663i	−0.0827741	+	0.996568i	$0.526378\pi$
$434$		0			0
$435$	5.79006	+	3.72104i	0.277612	+	0.178410i
$436$		0			0
$437$	−0.0397755	−	5.17015i	−0.00190272	−	0.247322i
$438$		0			0
$439$	25.2702	+	16.2402i	1.20608	+	0.775102i	0.979998	−	0.199006i	$-0.0637712\pi$
$439$	25.2702	+	16.2402i	1.20608	+	0.775102i	0.226084	+	0.974108i	$0.427408\pi$
$440$		0			0
$441$	−2.87431	−	6.29386i	−0.136872	−	0.299708i
$442$		0			0
$443$	3.50223	−	7.66881i	0.166396	−	0.364356i	−0.808004	−	0.589176i	$-0.799452\pi$
$443$	3.50223	−	7.66881i	0.166396	−	0.364356i	0.974400	+	0.224820i	$0.0721796\pi$
$444$		0			0
$445$	−0.998062	+	6.94167i	−0.0473127	+	0.329067i
$446$		0			0
$447$	7.06095	+	8.14877i	0.333972	+	0.385424i
$448$		0			0
$449$	−15.4504	+	9.92938i	−0.729150	+	0.468596i	−0.851809	−	0.523853i	$-0.824494\pi$
$449$	−15.4504	+	9.92938i	−0.729150	+	0.468596i	0.122659	+	0.992449i	$0.460858\pi$
$450$		0			0
$451$	1.05714	−	0.310404i	0.0497788	−	0.0146164i
$452$		0			0
$453$	2.71821	−	3.13698i	0.127713	−	0.147388i
$454$		0			0
$455$	−1.21902	−	0.357936i	−0.0571484	−	0.0167803i
$456$		0			0
$457$	−4.08848	−	28.4360i	−0.191251	−	1.33018i	−0.828702	−	0.559690i	$-0.810920\pi$
$457$	−4.08848	−	28.4360i	−0.191251	−	1.33018i	0.637451	−	0.770491i	$-0.279989\pi$
$458$		0			0
$459$	4.73357			0.220944
$460$		0			0
$461$	30.4181			1.41671			0.708356	−	0.705855i	$-0.249437\pi$
$461$	30.4181			1.41671			0.708356	+	0.705855i	$0.249437\pi$
$462$		0			0
$463$	3.52870	+	24.5427i	0.163993	+	1.14059i	0.891013	+	0.453978i	$0.149996\pi$
$463$	3.52870	+	24.5427i	0.163993	+	1.14059i	−0.727020	+	0.686616i	$0.759095\pi$
$464$		0			0
$465$	−3.89647	−	1.14411i	−0.180694	−	0.0530567i
$466$		0			0
$467$	−6.89639	+	7.95885i	−0.319127	+	0.368292i	−0.892535	−	0.450978i	$-0.851075\pi$
$467$	−6.89639	+	7.95885i	−0.319127	+	0.368292i	0.573408	+	0.819270i	$0.305621\pi$
$468$		0			0
$469$	−3.51615	+	1.03243i	−0.162361	+	0.0476734i
$470$		0			0
$471$	−11.1460	+	7.16312i	−0.513582	+	0.330059i
$472$		0			0
$473$	−9.96908	−	11.5049i	−0.458379	−	0.528998i
$474$		0			0
$475$	0.668643	−	4.65052i	0.0306795	−	0.213380i
$476$		0			0
$477$	−3.13994	+	6.87551i	−0.143768	+	0.314808i
$478$		0			0
$479$	13.7116	+	30.0243i	0.626501	+	1.37184i	0.910695	+	0.413078i	$0.135546\pi$
$479$	13.7116	+	30.0243i	0.626501	+	1.37184i	−0.284195	+	0.958767i	$0.591726\pi$
$480$		0			0
$481$	37.1296	+	23.8617i	1.69296	+	1.08800i
$482$		0			0
$483$	−0.746149	−	1.14162i	−0.0339510	−	0.0519457i
$484$		0			0
$485$	−4.71121	−	3.02771i	−0.213925	−	0.137481i
$486$		0			0
$487$	5.95654	+	13.0430i	0.269917	+	0.591035i	0.995249	−	0.0973641i	$-0.0310411\pi$
$487$	5.95654	+	13.0430i	0.269917	+	0.591035i	−0.725332	+	0.688399i	$0.758314\pi$
$488$		0			0
$489$	6.60901	−	14.4717i	0.298870	−	0.654434i
$490$		0			0
$491$	−2.68132	+	18.6490i	−0.121006	+	0.841618i	0.835413	+	0.549622i	$0.185228\pi$
$491$	−2.68132	+	18.6490i	−0.121006	+	0.841618i	−0.956420	+	0.291996i	$0.905681\pi$
$492$		0			0
$493$	−26.6283	−	30.7307i	−1.19928	−	1.38404i
$494$		0			0
$495$	1.69441	−	1.08893i	0.0761580	−	0.0489438i
$496$		0			0
$497$	−1.77128	+	0.520094i	−0.0794526	+	0.0233294i
$498$		0			0
$499$	−25.7949	+	29.7690i	−1.15474	+	1.33264i	−0.220755	+	0.975329i	$0.570852\pi$
$499$	−25.7949	+	29.7690i	−1.15474	+	1.33264i	−0.933985	+	0.357312i	$0.883693\pi$
$500$		0			0
$501$	0.131228	+	0.0385320i	0.00586283	+	0.00172148i
$502$		0			0
$503$	0.199512	+	1.38764i	0.00889580	+	0.0618716i	0.993786	−	0.111309i	$-0.0355045\pi$
$503$	0.199512	+	1.38764i	0.00889580	+	0.0618716i	−0.984890	+	0.173181i	$0.944595\pi$
$504$		0			0
$505$	−11.0506			−0.491743
$506$		0			0
$507$	18.0915			0.803474
$508$		0			0
$509$	−0.0178196	−	0.123938i	−0.000789842	−	0.00549347i	0.989423	−	0.145061i	$-0.0463379\pi$
$509$	−0.0178196	−	0.123938i	−0.000789842	−	0.00549347i	−0.990213	+	0.139568i	$0.955429\pi$
$510$		0			0
$511$	1.03034	+	0.302535i	0.0455796	+	0.0133834i
$512$		0			0
$513$	−0.705993	+	0.814760i	−0.0311704	+	0.0359725i
$514$		0			0
$515$	5.01515	−	1.47258i	0.220994	−	0.0648897i
$516$		0			0
$517$	−2.56489	+	1.64836i	−0.112804	+	0.0724947i
$518$		0			0
$519$	7.54635	+	8.70895i	0.331248	+	0.382281i
$520$		0			0
$521$	4.61322	−	32.0857i	0.202109	−	1.40570i	−0.595902	−	0.803057i	$-0.703206\pi$
$521$	4.61322	−	32.0857i	0.202109	−	1.40570i	0.798011	−	0.602642i	$-0.205885\pi$
$522$		0			0
$523$	9.18096	−	20.1035i	0.401455	−	0.879065i	−0.595665	−	0.803233i	$-0.703111\pi$
$523$	9.18096	−	20.1035i	0.401455	−	0.879065i	0.997121	−	0.0758320i	$-0.0241613\pi$
$524$		0			0
$525$	−0.514840	−	1.12734i	−0.0224695	−	0.0492013i
$526$		0			0
$527$	20.1835	+	12.9711i	0.879205	+	0.565031i
$528$		0			0
$529$	15.3275	+	17.1484i	0.666411	+	0.745585i
$530$		0			0
$531$	−4.73486	−	3.04291i	−0.205476	−	0.132051i
$532$		0			0
$533$	−1.01520	−	2.22298i	−0.0439732	−	0.0962879i
$534$		0			0
$535$	1.54886	−	3.39153i	0.0669631	−	0.146629i
$536$		0			0
$537$	1.19884	−	8.33812i	0.0517338	−	0.359817i
$538$		0			0
$539$	11.3905	+	13.1453i	0.490624	+	0.566210i
$540$		0			0
$541$	−9.80447	+	6.30095i	−0.421527	+	0.270899i	−0.734162	−	0.678974i	$-0.762425\pi$
$541$	−9.80447	+	6.30095i	−0.421527	+	0.270899i	0.312635	+	0.949873i	$0.398788\pi$
$542$		0			0
$543$	−10.2680	+	3.01496i	−0.440643	+	0.129384i
$544$		0			0
$545$	7.31037	−	8.43661i	0.313142	−	0.361385i
$546$		0			0
$547$	23.9008	+	7.01790i	1.02192	+	0.300064i	0.749423	−	0.662092i	$-0.230331\pi$
$547$	23.9008	+	7.01790i	1.02192	+	0.300064i	0.272501	+	0.962156i	$0.412149\pi$
$548$		0			0
$549$	1.36861	+	9.51888i	0.0584108	+	0.406256i
$550$		0			0
$551$	9.26101			0.394532
$552$		0			0
$553$	−0.246536			−0.0104838
$554$		0			0
$555$	−0.902549	−	6.27737i	−0.0383111	−	0.266459i
$556$		0			0
$557$	−9.28714	−	2.72695i	−0.393509	−	0.115545i	0.0789911	−	0.996875i	$-0.474830\pi$
$557$	−9.28714	−	2.72695i	−0.393509	−	0.115545i	−0.472500	+	0.881331i	$0.656648\pi$
$558$		0			0
$559$	−22.1123	+	25.5190i	−0.935251	+	1.07934i
$560$		0			0
$561$	−11.4175	+	3.35249i	−0.482049	+	0.141542i
$562$		0			0
$563$	28.4885	−	18.3084i	1.20065	−	0.771609i	0.221579	−	0.975142i	$-0.428879\pi$
$563$	28.4885	−	18.3084i	1.20065	−	0.771609i	0.979068	+	0.203533i	$0.0652426\pi$
$564$		0			0
$565$	−6.39919	−	7.38506i	−0.269216	−	0.310692i
$566$		0			0
$567$	−0.0404714	+	0.281485i	−0.00169964	+	0.0118212i
$568$		0			0
$569$	3.70343	−	8.10937i	0.155256	−	0.339962i	−0.815981	−	0.578079i	$-0.803803\pi$
$569$	3.70343	−	8.10937i	0.155256	−	0.339962i	0.971237	+	0.238116i	$0.0765299\pi$
$570$		0			0
$571$	8.68500	+	19.0175i	0.363456	+	0.795858i	0.999703	+	0.0243721i	$0.00775866\pi$
$571$	8.68500	+	19.0175i	0.363456	+	0.795858i	−0.636247	+	0.771485i	$0.719514\pi$
$572$		0			0
$573$	19.1877	+	12.3312i	0.801577	+	0.515142i
$574$		0			0
$575$	11.4346	+	17.4952i	0.476855	+	0.729599i
$576$		0			0
$577$	17.2937	+	11.1140i	0.719948	+	0.462682i	0.848619	−	0.529005i	$-0.177435\pi$
$577$	17.2937	+	11.1140i	0.719948	+	0.462682i	−0.128671	+	0.991687i	$0.541071\pi$
$578$		0			0
$579$	7.66624	+	16.7867i	0.318598	+	0.697633i
$580$		0			0
$581$	−0.0502977	+	0.110137i	−0.00208670	+	0.00456923i
$582$		0			0
$583$	2.70416	−	18.8078i	0.111995	−	0.778940i
$584$		0			0
$585$	−2.92563	−	3.37636i	−0.120960	−	0.139595i
$586$		0			0
$587$	−34.1743	+	21.9625i	−1.41052	+	0.906489i	−0.999986	−	0.00535401i	$-0.998296\pi$
$587$	−34.1743	+	21.9625i	−1.41052	+	0.906489i	−0.410539	+	0.911843i	$0.634659\pi$
$588$		0			0
$589$	−5.24293	+	1.53946i	−0.216031	+	0.0634324i
$590$		0			0
$591$	13.2891	−	15.3365i	0.546641	−	0.630858i
$592$		0			0
$593$	13.9097	+	4.08425i	0.571202	+	0.167720i	0.554563	−	0.832141i	$-0.312885\pi$
$593$	13.9097	+	4.08425i	0.571202	+	0.167720i	0.0166389	+	0.999862i	$0.494703\pi$
$594$		0			0
$595$	−0.153492	−	1.06756i	−0.00629255	−	0.0437657i
$596$		0			0
$597$	6.78972			0.277885
$598$		0			0
$599$	28.7623			1.17520			0.587598	−	0.809153i	$-0.300074\pi$
$599$	28.7623			1.17520			0.587598	+	0.809153i	$0.300074\pi$
$600$		0			0
$601$	2.94956	+	20.5146i	0.120315	+	0.836809i	0.957199	+	0.289430i	$0.0934656\pi$
$601$	2.94956	+	20.5146i	0.120315	+	0.836809i	−0.836884	+	0.547380i	$0.815625\pi$
$602$		0			0
$603$	−12.3643	−	3.63049i	−0.503513	−	0.147845i
$604$		0			0
$605$	2.45577	−	2.83411i	0.0998412	−	0.115223i
$606$		0			0
$607$	13.4059	−	3.93631i	0.544127	−	0.159770i	0.00189387	−	0.999998i	$-0.499397\pi$
$607$	13.4059	−	3.93631i	0.544127	−	0.159770i	0.542233	+	0.840228i	$0.317579\pi$
$608$		0			0
$609$	2.05509	−	1.32073i	0.0832766	−	0.0535186i
$610$		0			0
$611$	4.42864	+	5.11092i	0.179163	+	0.206766i
$612$		0			0
$613$	2.24911	−	15.6429i	0.0908407	−	0.631811i	−0.892636	−	0.450778i	$-0.851147\pi$
$613$	2.24911	−	15.6429i	0.0908407	−	0.631811i	0.983477	−	0.181033i	$-0.0579442\pi$
$614$		0			0
$615$	−0.145875	+	0.319421i	−0.00588223	+	0.0128803i
$616$		0			0
$617$	−4.14526	−	9.07685i	−0.166882	−	0.365420i	0.807652	−	0.589659i	$-0.200738\pi$
$617$	−4.14526	−	9.07685i	−0.166882	−	0.365420i	−0.974534	+	0.224239i	$0.928011\pi$
$618$		0			0
$619$	−16.6614	−	10.7076i	−0.669679	−	0.430377i	0.161131	−	0.986933i	$-0.448486\pi$
$619$	−16.6614	−	10.7076i	−0.669679	−	0.430377i	−0.830810	+	0.556556i	$0.812122\pi$
$620$		0			0
$621$	−0.0368947	−	4.79569i	−0.00148053	−	0.192444i
$622$		0			0
$623$	2.09403	+	1.34575i	0.0838955	+	0.0539164i
$624$		0			0
$625$	6.55646	+	14.3566i	0.262258	+	0.574266i
$626$		0			0
$627$	1.12584	−	2.46524i	0.0449617	−	0.0984523i
$628$		0			0
$629$	−5.33225	+	37.0866i	−0.212611	+	1.47874i
$630$		0			0
$631$	−20.4558	−	23.6073i	−0.814333	−	0.939790i	0.184743	−	0.982787i	$-0.440855\pi$
$631$	−20.4558	−	23.6073i	−0.814333	−	0.939790i	−0.999075	+	0.0429969i	$0.986309\pi$
$632$		0			0
$633$	−15.6405	+	10.0515i	−0.621653	+	0.399512i
$634$		0			0
$635$	2.95752	−	0.868406i	0.117366	−	0.0344616i
$636$		0			0
$637$	25.2651	−	29.1575i	1.00104	−	1.15526i
$638$		0			0
$639$	−6.22857	−	1.82887i	−0.246399	−	0.0723491i
$640$		0			0
$641$	−2.39950	−	16.6889i	−0.0947746	−	0.659172i	−0.980725	−	0.195392i	$-0.937402\pi$
$641$	−2.39950	−	16.6889i	−0.0947746	−	0.659172i	0.885951	−	0.463780i	$-0.153507\pi$
$642$		0			0
$643$	−36.1508			−1.42565			−0.712823	−	0.701344i	$-0.752584\pi$
$643$	−36.1508			−1.42565			−0.712823	+	0.701344i	$0.752584\pi$
$644$		0			0
$645$	4.85191			0.191044
$646$		0			0
$647$	1.14075	+	7.93408i	0.0448474	+	0.311921i	0.999881	+	0.0154233i	$0.00490957\pi$
$647$	1.14075	+	7.93408i	0.0448474	+	0.311921i	−0.955034	+	0.296498i	$0.904181\pi$
$648$		0			0
$649$	13.5758	+	3.98621i	0.532896	+	0.156472i
$650$		0			0
$651$	−0.943902	+	1.08932i	−0.0369944	+	0.0426939i
$652$		0			0
$653$	−20.2351	+	5.94155i	−0.791859	+	0.232511i	−0.652557	−	0.757739i	$-0.726304\pi$
$653$	−20.2351	+	5.94155i	−0.791859	+	0.232511i	−0.139301	+	0.990250i	$0.544486\pi$
$654$		0			0
$655$	−13.1581	+	8.45617i	−0.514128	+	0.330410i
$656$		0			0
$657$	2.47281	+	2.85377i	0.0964734	+	0.111336i
$658$		0			0
$659$	−6.23547	+	43.3686i	−0.242899	+	1.68940i	0.394522	+	0.918887i	$0.370910\pi$
$659$	−6.23547	+	43.3686i	−0.242899	+	1.68940i	−0.637421	+	0.770516i	$0.719999\pi$
$660$		0			0
$661$	2.32213	−	5.08476i	0.0903205	−	0.197774i	−0.859081	−	0.511840i	$-0.828964\pi$
$661$	2.32213	−	5.08476i	0.0903205	−	0.197774i	0.949401	+	0.314066i	$0.101691\pi$
$662$		0			0
$663$	10.9646	+	24.0091i	0.425829	+	0.932435i
$664$		0			0
$665$	0.206645	+	0.132803i	0.00801336	+	0.00514987i
$666$		0			0
$667$	−30.9265	+	27.2173i	−1.19748	+	1.05386i
$668$		0			0
$669$	−21.2507	−	13.6570i	−0.821599	−	0.528010i
$670$		0			0
$671$	−10.0428	−	21.9906i	−0.387697	−	0.848938i
$672$		0			0
$673$	8.87299	−	19.4291i	0.342029	−	0.748939i	−0.657963	−	0.753050i	$-0.728582\pi$
$673$	8.87299	−	19.4291i	0.342029	−	0.748939i	0.999992	+	0.00411190i	$0.00130886\pi$
$674$		0			0
$675$	0.620216	−	4.31370i	0.0238721	−	0.166034i
$676$		0			0
$677$	−2.58538	−	2.98369i	−0.0993643	−	0.114672i	0.703889	−	0.710310i	$-0.251445\pi$
$677$	−2.58538	−	2.98369i	−0.0993643	−	0.114672i	−0.803254	+	0.595637i	$0.796900\pi$
$678$		0			0
$679$	−1.67217	+	1.07464i	−0.0641721	+	0.0412409i
$680$		0			0
$681$	−22.4003	+	6.57732i	−0.858381	+	0.252043i
$682$		0			0
$683$	31.8437	−	36.7496i	1.21847	−	1.40619i	0.332074	−	0.943253i	$-0.392252\pi$
$683$	31.8437	−	36.7496i	1.21847	−	1.40619i	0.886393	−	0.462933i	$-0.153203\pi$
$684$		0			0
$685$	0.726093	+	0.213200i	0.0277426	+	0.00814596i
$686$		0			0
$687$	−0.724892	−	5.04173i	−0.0276564	−	0.192354i
$688$		0			0
$689$	−42.1464			−1.60565
$690$		0			0
$691$	−41.5476			−1.58055			−0.790273	−	0.612754i	$-0.790061\pi$
$691$	−41.5476			−1.58055			−0.790273	+	0.612754i	$0.790061\pi$
$692$		0			0
$693$	−0.101740	−	0.707615i	−0.00386477	−	0.0268801i
$694$		0			0
$695$	−7.51539	−	2.20672i	−0.285075	−	0.0837056i
$696$		0			0
$697$	1.35858	−	1.56789i	0.0514599	−	0.0593879i
$698$		0			0
$699$	−7.68429	+	2.25631i	−0.290647	+	0.0853415i
$700$		0			0
$701$	25.8629	−	16.6211i	0.976827	−	0.627769i	0.0482213	−	0.998837i	$-0.484645\pi$
$701$	25.8629	−	16.6211i	0.976827	−	0.627769i	0.928606	+	0.371068i	$0.121008\pi$
$702$		0			0
$703$	−5.58821	−	6.44913i	−0.210763	−	0.243234i
$704$		0			0
$705$	0.138293	−	0.961847i	0.00520840	−	0.0362253i
$706$		0			0
$707$	−1.62935	+	3.56778i	−0.0612781	+	0.134180i
$708$		0			0
$709$	−9.76858	−	21.3902i	−0.366867	−	0.803326i	−0.999581	−	0.0289409i	$-0.990787\pi$
$709$	−9.76858	−	21.3902i	−0.366867	−	0.803326i	0.632714	−	0.774385i	$-0.281941\pi$
$710$		0			0
$711$	−0.729306	−	0.468696i	−0.0273511	−	0.0175775i
$712$		0			0
$713$	12.9840	−	20.5494i	0.486256	−	0.769583i
$714$		0			0
$715$	9.44799	+	6.07186i	0.353335	+	0.227075i
$716$		0			0
$717$	−5.11580	−	11.2020i	−0.191053	−	0.418347i
$718$		0			0
$719$	19.2668	−	42.1884i	0.718530	−	1.57336i	−0.0974237	−	0.995243i	$-0.531060\pi$
$719$	19.2668	−	42.1884i	0.718530	−	1.57336i	0.815953	−	0.578118i	$-0.196213\pi$
$720$		0			0
$721$	0.264023	−	1.83632i	0.00983272	−	0.0683881i
$722$		0			0
$723$	−2.07685	−	2.39681i	−0.0772387	−	0.0891382i
$724$		0			0
$725$	−31.4939	+	20.2399i	−1.16965	+	0.751691i
$726$		0			0
$727$	42.8348	−	12.5774i	1.58866	−	0.466471i	0.636295	−	0.771446i	$-0.280466\pi$
$727$	42.8348	−	12.5774i	1.58866	−	0.466471i	0.952361	+	0.304974i	$0.0986479\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$		0			0
$731$	−27.5039	−	8.07587i	−1.01727	−	0.298697i
$732$		0			0
$733$	−4.34817	−	30.2422i	−0.160603	−	1.11702i	−0.897500	−	0.441015i	$-0.854618\pi$
$733$	−4.34817	−	30.2422i	−0.160603	−	1.11702i	0.736896	−	0.676006i	$-0.236291\pi$
$734$		0			0
$735$	−5.54371			−0.204483
$736$		0			0
$737$	32.3944			1.19326
$738$		0			0
$739$	1.97775	+	13.7556i	0.0727527	+	0.506006i	0.993317	+	0.115416i	$0.0368201\pi$
$739$	1.97775	+	13.7556i	0.0727527	+	0.506006i	−0.920565	+	0.390591i	$0.872271\pi$
$740$		0			0
$741$	−5.76786	−	1.69360i	−0.211888	−	0.0622158i
$742$		0			0
$743$	30.3321	−	35.0051i	1.11278	−	1.28421i	0.157821	−	0.987468i	$-0.449553\pi$
$743$	30.3321	−	35.0051i	1.11278	−	1.28421i	0.954957	−	0.296746i	$-0.0959014\pi$
$744$		0			0
$745$	8.28906	−	2.43389i	0.303688	−	0.0891707i
$746$		0			0
$747$	−0.358175	+	0.230185i	−0.0131049	+	0.00842202i
$748$		0			0
$749$	−0.866619	−	1.00013i	−0.0316656	−	0.0365440i
$750$		0			0
$751$	−6.75096	+	46.9539i	−0.246346	+	1.71337i	0.372644	+	0.927974i	$0.378451\pi$
$751$	−6.75096	+	46.9539i	−0.246346	+	1.71337i	−0.618990	+	0.785399i	$0.712458\pi$
$752$		0			0
$753$	−8.91230	+	19.5152i	−0.324782	+	0.711174i
$754$		0			0
$755$	−1.38155	−	3.02516i	−0.0502796	−	0.110097i
$756$		0			0
$757$	12.8714	+	8.27192i	0.467817	+	0.300648i	0.753231	−	0.657757i	$-0.228494\pi$
$757$	12.8714	+	8.27192i	0.467817	+	0.300648i	−0.285413	+	0.958405i	$0.592131\pi$
$758$		0			0
$759$	3.48548	+	11.5413i	0.126515	+	0.418921i
$760$		0			0
$761$	−28.2144	−	18.1323i	−1.02277	−	0.657294i	−0.0821021	−	0.996624i	$-0.526163\pi$
$761$	−28.2144	−	18.1323i	−1.02277	−	0.657294i	−0.940667	+	0.339330i	$0.889800\pi$
$762$		0			0
$763$	−1.64597	−	3.60416i	−0.0595880	−	0.130480i
$764$		0			0
$765$	1.57550	−	3.44987i	0.0569625	−	0.124730i
$766$		0			0
$767$	4.46634	−	31.0641i	0.161270	−	1.12166i
$768$		0			0
$769$	14.7944	+	17.0736i	0.533498	+	0.615690i	0.956958	−	0.290225i	$-0.0937302\pi$
$769$	14.7944	+	17.0736i	0.533498	+	0.615690i	−0.423460	+	0.905915i	$0.639185\pi$
$770$		0			0
$771$	−11.6375	+	7.47895i	−0.419113	+	0.269348i
$772$		0			0
$773$	7.42885	−	2.18131i	0.267197	−	0.0784561i	−0.145390	−	0.989374i	$-0.546444\pi$
$773$	7.42885	−	2.18131i	0.267197	−	0.0784561i	0.412587	+	0.910918i	$0.364625\pi$
$774$		0			0
$775$	14.4651	−	16.6936i	0.519602	−	0.599653i
$776$		0			0
$777$	−2.15979	−	0.634171i	−0.0774820	−	0.0227508i
$778$		0			0
$779$	0.0672435	+	0.467689i	0.00240925	+	0.0167567i
$780$		0			0
$781$	16.3188			0.583934
$782$		0			0
$783$	8.59027			0.306991
$784$		0			0
$785$	1.51075	+	10.5075i	0.0539210	+	0.375029i
$786$		0			0
$787$	−37.9101	−	11.1314i	−1.35135	−	0.396792i	−0.475644	−	0.879638i	$-0.657785\pi$
$787$	−37.9101	−	11.1314i	−1.35135	−	0.396792i	−0.875706	+	0.482845i	$0.839603\pi$
$788$		0			0
$789$	−14.8575	+	17.1465i	−0.528941	+	0.610430i
$790$		0			0
$791$	−3.32787	+	0.977152i	−0.118326	+	0.0347435i
$792$		0			0
$793$	−45.1105	+	28.9907i	−1.60192	+	1.02949i
$794$		0			0
$795$	3.96586	+	4.57684i	0.140654	+	0.162324i
$796$		0			0
$797$	4.45285	−	30.9702i	0.157728	−	1.09702i	−0.745079	−	0.666976i	$-0.767588\pi$
$797$	4.45285	−	30.9702i	0.157728	−	1.09702i	0.902807	−	0.430046i	$-0.141503\pi$
$798$		0			0
$799$	−2.38490	+	5.22221i	−0.0843718	+	0.184748i
$800$		0			0
$801$	3.63614	+	7.96203i	0.128477	+	0.281325i
$802$		0			0
$803$	−7.98566	−	5.13207i	−0.281808	−	0.181107i
$804$		0			0
$805$	−1.08037	+	0.163827i	−0.0380782	+	0.00577415i
$806$		0			0
$807$	−6.49015	−	4.17096i	−0.228464	−	0.146825i
$808$		0			0
$809$	0.740733	+	1.62198i	0.0260428	+	0.0570258i	0.922206	−	0.386698i	$-0.126384\pi$
$809$	0.740733	+	1.62198i	0.0260428	+	0.0570258i	−0.896164	+	0.443724i	$0.853657\pi$
$810$		0			0
$811$	−14.6244	+	32.0230i	−0.513533	+	1.12448i	0.458298	+	0.888799i	$0.348459\pi$
$811$	−14.6244	+	32.0230i	−0.513533	+	1.12448i	−0.971830	+	0.235681i	$0.924268\pi$
$812$		0			0
$813$	−1.11691	+	7.76827i	−0.0391717	+	0.272445i
$814$		0			0
$815$	−8.34742	−	9.63344i	−0.292397	−	0.337445i
$816$		0			0
$817$	5.49215	−	3.52959i	0.192146	−	0.123485i
$818$		0			0
$819$	−1.52146	+	0.446741i	−0.0531641	+	0.0156104i
$820$		0			0
$821$	9.50018	−	10.9638i	0.331559	−	0.382639i	−0.565353	−	0.824849i	$-0.691260\pi$
$821$	9.50018	−	10.9638i	0.331559	−	0.382639i	0.896911	+	0.442210i	$0.145805\pi$
$822$		0			0
$823$	−10.2925	−	3.02215i	−0.358773	−	0.105345i	0.0973782	−	0.995247i	$-0.468954\pi$
$823$	−10.2925	−	3.02215i	−0.358773	−	0.105345i	−0.456152	+	0.889902i	$0.650773\pi$
$824$		0			0
$825$	1.55914	+	10.8441i	0.0542823	+	0.377542i
$826$		0			0
$827$	−45.3920			−1.57843			−0.789217	−	0.614114i	$-0.789513\pi$
$827$	−45.3920			−1.57843			−0.789217	+	0.614114i	$0.789513\pi$
$828$		0			0
$829$	−14.2674			−0.495527			−0.247763	−	0.968821i	$-0.579696\pi$
$829$	−14.2674			−0.495527			−0.247763	+	0.968821i	$0.579696\pi$
$830$		0			0
$831$	−3.00604	−	20.9075i	−0.104278	−	0.725271i
$832$		0			0
$833$	31.4255	+	9.22735i	1.08883	+	0.319709i
$834$		0			0
$835$	0.0717600	−	0.0828154i	0.00248336	−	0.00286595i
$836$		0			0
$837$	−4.86320	+	1.42796i	−0.168097	+	0.0493577i
$838$		0			0
$839$	−2.18452	+	1.40391i	−0.0754181	+	0.0484683i	−0.577806	−	0.816174i	$-0.696091\pi$
$839$	−2.18452	+	1.40391i	−0.0754181	+	0.0484683i	0.502388	+	0.864642i	$0.332455\pi$
$840$		0			0
$841$	−29.3330	−	33.8521i	−1.01148	−	1.16731i
$842$		0			0
$843$	−0.0165322	+	0.114984i	−0.000569400	+	0.00396026i
$844$		0			0
$845$	6.02153	−	13.1853i	0.207147	−	0.453589i
$846$		0			0
$847$	−0.552929	−	1.21075i	−0.0189989	−	0.0416017i
$848$		0			0
$849$	−23.4799	−	15.0896i	−0.805829	−	0.517875i
$850$		0			0
$851$	37.6149	+	5.11317i	1.28942	+	0.175277i
$852$		0			0
$853$	31.2792	+	20.1019i	1.07098	+	0.688276i	0.952456	−	0.304675i	$-0.0985479\pi$
$853$	31.2792	+	20.1019i	1.07098	+	0.688276i	0.118522	+	0.992951i	$0.462184\pi$
$854$		0			0
$855$	0.358825	+	0.785718i	0.0122716	+	0.0268710i
$856$		0			0
$857$	3.66963	−	8.03537i	0.125352	−	0.274483i	−0.836543	−	0.547901i	$-0.815427\pi$
$857$	3.66963	−	8.03537i	0.125352	−	0.274483i	0.961895	+	0.273418i	$0.0881543\pi$
$858$		0			0
$859$	4.82398	−	33.5515i	0.164592	−	1.14476i	−0.725247	−	0.688489i	$-0.758275\pi$
$859$	4.82398	−	33.5515i	0.164592	−	1.14476i	0.889839	−	0.456274i	$-0.150816\pi$
$860$		0			0
$861$	0.0816197	+	0.0941942i	0.00278159	+	0.00321013i
$862$		0			0
$863$	29.9169	−	19.2264i	1.01838	−	0.654475i	0.0788339	−	0.996888i	$-0.474880\pi$
$863$	29.9169	−	19.2264i	1.01838	−	0.654475i	0.939550	+	0.342412i	$0.111244\pi$
$864$		0			0
$865$	8.85888	−	2.60120i	0.301211	−	0.0884435i
$866$		0			0
$867$	−3.54060	+	4.08607i	−0.120245	+	0.138770i
$868$		0			0
$869$	2.09106	+	0.613991i	0.0709344	+	0.0208282i
$870$		0			0
$871$	−10.2258	−	71.1223i	−0.346489	−	2.40989i
$872$		0			0
$873$	−6.98967			−0.236564
$874$		0			0
$875$	−2.13222			−0.0720823
$876$		0			0
$877$	−1.23727	−	8.60541i	−0.0417797	−	0.290584i	−0.999990	−	0.00451870i	$-0.998562\pi$
$877$	−1.23727	−	8.60541i	−0.0417797	−	0.290584i	0.958210	−	0.286065i	$-0.0923474\pi$
$878$		0			0
$879$	10.9262	+	3.20821i	0.368530	+	0.108210i
$880$		0			0
$881$	14.4705	−	16.6998i	0.487523	−	0.562632i	−0.457679	−	0.889118i	$-0.651319\pi$
$881$	14.4705	−	16.6998i	0.487523	−	0.562632i	0.945202	+	0.326486i	$0.105864\pi$
$882$		0			0
$883$	−37.3357	+	10.9628i	−1.25645	+	0.368926i	−0.841171	−	0.540769i	$-0.818133\pi$
$883$	−37.3357	+	10.9628i	−1.25645	+	0.368926i	−0.415276	+	0.909695i	$0.636315\pi$
$884$		0			0
$885$	−3.79364	+	2.43803i	−0.127522	+	0.0819534i
$886$		0			0
$887$	8.69737	+	10.0373i	0.292029	+	0.337020i	0.882738	−	0.469865i	$-0.155697\pi$
$887$	8.69737	+	10.0373i	0.292029	+	0.337020i	−0.590709	+	0.806885i	$0.701152\pi$
$888$		0			0
$889$	0.155699	−	1.08291i	0.00522196	−	0.0363195i
$890$		0			0
$891$	1.04430	−	2.28669i	0.0349853	−	0.0766071i
$892$		0			0
$893$	−0.543168	−	1.18937i	−0.0181764	−	0.0398008i
$894$		0			0
$895$	−5.67790	−	3.64896i	−0.189791	−	0.121971i
$896$		0			0
$897$	24.2387	−	11.2956i	0.809307	−	0.377149i
$898$		0			0
$899$	36.6281	+	23.5394i	1.22161	+	0.785084i
$900$		0			0
$901$	−14.8631	−	32.5457i	−0.495162	−	1.08425i
$902$		0			0
$903$	0.715392	−	1.56649i	0.0238067	−	0.0521295i
$904$		0			0
$905$	−1.22024	+	8.48693i	−0.0405620	+	0.282115i
$906$		0			0
$907$	−9.03129	−	10.4227i	−0.299879	−	0.346079i	0.585734	−	0.810504i	$-0.300806\pi$
$907$	−9.03129	−	10.4227i	−0.299879	−	0.346079i	−0.885612	+	0.464425i	$0.846261\pi$
$908$		0			0
$909$	−11.6028	+	7.45665i	−0.384840	+	0.247322i
$910$		0			0
$911$	0.487707	−	0.143204i	0.0161584	−	0.00474455i	−0.273643	−	0.961831i	$-0.588229\pi$
$911$	0.487707	−	0.143204i	0.0161584	−	0.00474455i	0.289802	+	0.957087i	$0.406411\pi$
$912$		0			0
$913$	0.700905	−	0.808887i	0.0231966	−	0.0267703i
$914$		0			0
$915$	7.39299	+	2.17078i	0.244405	+	0.0717637i
$916$		0			0
$917$	0.790067	+	5.49504i	0.0260903	+	0.181462i
$918$		0			0
$919$	−41.4751			−1.36814			−0.684068	−	0.729418i	$-0.739791\pi$
$919$	−41.4751			−1.36814			−0.684068	+	0.729418i	$0.739791\pi$
$920$		0			0
$921$	12.1088			0.398997
$922$		0			0
$923$	−5.15132	−	35.8282i	−0.169558	−	1.17930i
$924$		0			0
$925$	33.0983	+	9.71855i	1.08827	+	0.319544i
$926$		0			0
$927$	4.27211	−	4.93028i	0.140314	−	0.161932i
$928$		0			0
$929$	35.3541	−	10.3809i	1.15993	−	0.340587i	0.355526	−	0.934666i	$-0.384302\pi$
$929$	35.3541	−	10.3809i	1.15993	−	0.340587i	0.804406	+	0.594080i	$0.202484\pi$
$930$		0			0
$931$	−6.27524	+	4.03285i	−0.205663	+	0.132171i
$932$		0			0
$933$	6.47977	+	7.47805i	0.212138	+	0.244820i
$934$		0			0
$935$	−1.35684	+	9.43706i	−0.0443736	+	0.308625i
$936$		0			0
$937$	−24.6169	+	53.9036i	−0.804201	+	1.76095i	−0.173647	+	0.984808i	$0.555555\pi$
$937$	−24.6169	+	53.9036i	−0.804201	+	1.76095i	−0.630554	+	0.776146i	$0.717172\pi$
$938$		0			0
$939$	−2.39774	−	5.25031i	−0.0782472	−	0.171337i
$940$		0			0
$941$	−0.610949	−	0.392633i	−0.0199164	−	0.0127995i	0.530645	−	0.847594i	$-0.321950\pi$
$941$	−0.610949	−	0.392633i	−0.0199164	−	0.0127995i	−0.550561	+	0.834795i	$0.685586\pi$
$942$		0			0
$943$	−1.59905	−	1.36419i	−0.0520723	−	0.0444242i
$944$		0			0
$945$	0.191679	+	0.123184i	0.00623531	+	0.00400719i
$946$		0			0
$947$	−14.3192	−	31.3546i	−0.465310	−	1.01889i	−0.986245	−	0.165291i	$-0.947144\pi$
$947$	−14.3192	−	31.3546i	−0.465310	−	1.01889i	0.520935	−	0.853597i	$-0.325584\pi$
$948$		0			0
$949$	−8.74671	+	19.1526i	−0.283930	+	0.621720i
$950$		0			0
$951$	−2.03083	+	14.1247i	−0.0658541	+	0.458025i
$952$		0			0
$953$	−2.61290	−	3.01545i	−0.0846401	−	0.0976799i	0.711850	−	0.702332i	$-0.247858\pi$
$953$	−2.61290	−	3.01545i	−0.0846401	−	0.0976799i	−0.796490	+	0.604652i	$0.793312\pi$
$954$		0			0
$955$	15.3735	−	9.87992i	0.497473	−	0.319707i
$956$		0			0
$957$	−20.7201	+	6.08396i	−0.669784	+	0.196666i
$958$		0			0
$959$	0.175893	−	0.202991i	0.00567987	−	0.00655492i
$960$		0			0
$961$	5.09512	+	1.49606i	0.164359	+	0.0482600i
$962$		0			0
$963$	−0.662265	−	4.60615i	−0.0213412	−	0.148431i
$964$		0			0
$965$	14.7860			0.475977
$966$		0			0
$967$	37.1721			1.19537			0.597687	−	0.801729i	$-0.296086\pi$
$967$	37.1721			1.19537			0.597687	+	0.801729i	$0.296086\pi$
$968$		0			0
$969$	−0.726257	−	5.05123i	−0.0233307	−	0.162269i
$970$		0			0
$971$	−20.4960	−	6.01818i	−0.657749	−	0.193133i	−0.0642086	−	0.997937i	$-0.520452\pi$
$971$	−20.4960	−	6.01818i	−0.657749	−	0.193133i	−0.593541	+	0.804804i	$0.702270\pi$
$972$		0			0
$973$	−1.82057	+	2.10105i	−0.0583648	+	0.0673566i
$974$		0			0
$975$	23.3161	−	6.84622i	0.746712	−	0.219255i
$976$		0			0
$977$	−34.5010	+	22.1725i	−1.10379	+	0.709360i	−0.959930	−	0.280239i	$-0.909586\pi$
$977$	−34.5010	+	22.1725i	−1.10379	+	0.709360i	−0.143855	+	0.989599i	$0.545950\pi$
$978$		0			0
$979$	−14.4095	−	16.6295i	−0.460530	−	0.531480i
$980$		0			0
$981$	1.98286	−	13.7911i	0.0633077	−	0.440315i
$982$		0			0
$983$	17.0255	−	37.2806i	0.543028	−	1.18907i	−0.416935	−	0.908937i	$-0.636896\pi$
$983$	17.0255	−	37.2806i	0.543028	−	1.18907i	0.959962	−	0.280129i	$-0.0903772\pi$
$984$		0			0
$985$	−6.75427	−	14.7898i	−0.215209	−	0.471242i
$986$		0			0
$987$	−0.290151	−	0.186469i	−0.00923562	−	0.00593537i
$988$		0			0
$989$	−7.96749	+	27.9278i	−0.253351	+	0.888052i
$990$		0			0
$991$	40.3611	+	25.9385i	1.28211	+	0.823964i	0.991147	−	0.132770i	$-0.0423871\pi$
$991$	40.3611	+	25.9385i	1.28211	+	0.823964i	0.290966	+	0.956733i	$0.406023\pi$
$992$		0			0
$993$	−8.19552	−	17.9457i	−0.260077	−	0.569489i
$994$		0			0
$995$	2.25987	−	4.94843i	0.0716427	−	0.156876i
$996$		0			0
$997$	−4.99883	+	34.7676i	−0.158315	+	1.10110i	0.743424	+	0.668820i	$0.233201\pi$
$997$	−4.99883	+	34.7676i	−0.158315	+	1.10110i	−0.901739	+	0.432282i	$0.857709\pi$
$998$		0			0
$999$	−5.18347	−	5.98204i	−0.163998	−	0.189264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.a.25.2	✓	30
23.12	even	11	inner	552.2.q.a.265.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.a.25.2	✓	30	1.1	even	1	trivial
552.2.q.a.265.2	yes	30	23.12	even	11	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{3} +(-0.768760 - 0.225728i) q^{5} +(-0.186229 + 0.214919i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{3} +(-0.768760 - 0.225728i) q^{5} +(-0.186229 + 0.214919i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(2.11480 - 1.35910i) q^{11} +(-3.65149 - 4.21404i) q^{13} +(-0.114025 + 0.793060i) q^{15} +(1.96639 - 4.30580i) q^{17} +(0.447851 + 0.980658i) q^{19} +(0.239235 + 0.153747i) q^{21} +(-4.37764 - 1.95864i) q^{23} +(-3.66623 - 2.35614i) q^{25} +(0.415415 + 0.909632i) q^{27} +(3.56853 - 7.81398i) q^{29} +(-0.721324 + 5.01692i) q^{31} +(-1.64623 - 1.89985i) q^{33} +(0.191679 - 0.123184i) q^{35} +(-7.59475 + 2.23002i) q^{37} +(-3.65149 + 4.21404i) q^{39} +(0.420523 + 0.123477i) q^{41} +(-0.861815 - 5.99406i) q^{43} +0.801215 q^{45} -1.21283 q^{47} +(0.984695 + 6.84870i) q^{49} +(-4.54182 - 1.33360i) q^{51} +(4.94980 - 5.71238i) q^{53} +(-1.93256 + 0.567451i) q^{55} +(0.906940 - 0.582855i) q^{57} +(3.68578 + 4.25362i) q^{59} +(1.36861 - 9.51888i) q^{61} +(0.118135 - 0.258680i) q^{63} +(1.85589 + 4.06383i) q^{65} +(10.8406 + 6.96685i) q^{67} +(-1.31570 + 4.61182i) q^{69} +(5.46102 + 3.50958i) q^{71} +(-1.56864 - 3.43484i) q^{73} +(-1.81040 + 3.96423i) q^{75} +(-0.101740 + 0.707615i) q^{77} +(0.567717 + 0.655180i) q^{79} +(0.841254 - 0.540641i) q^{81} +(0.408517 - 0.119951i) q^{83} +(-2.48363 + 2.86626i) q^{85} +(-8.24230 - 2.42016i) q^{87} +(-1.24569 - 8.66393i) q^{89} +1.58569 q^{91} +5.06851 q^{93} +(-0.122928 - 0.854983i) q^{95} +(6.70654 + 1.96922i) q^{97} +(-1.64623 + 1.89985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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