LMFDB - Embedded newform 756.2.ca.a.173.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(173,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 13, 15]))

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

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

chi := DirichletCharacter("756.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ca (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.8
Character	$\chi$	$=$	756.173
Dual form			756.2.ca.a.437.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04679 - 1.37994i) q^{3} +(0.700470 - 0.587764i) q^{5} +(-0.673988 + 2.55846i) q^{7} +(-0.808445 + 2.88902i) q^{9} +O(q^{10})$	\(q+(-1.04679 - 1.37994i) q^{3} +(0.700470 - 0.587764i) q^{5} +(-0.673988 + 2.55846i) q^{7} +(-0.808445 + 2.88902i) q^{9} +(2.40709 - 2.86865i) q^{11} +(2.48376 + 2.96003i) q^{13} +(-1.54432 - 0.351336i) q^{15} +(-3.05270 + 5.28743i) q^{17} +(4.82172 - 2.78382i) q^{19} +(4.23604 - 1.74813i) q^{21} +(-0.548926 + 1.50816i) q^{23} +(-0.723049 + 4.10062i) q^{25} +(4.83293 - 1.90860i) q^{27} +(4.21794 - 5.02674i) q^{29} +(1.54773 + 1.84452i) q^{31} +(-6.47828 - 0.318735i) q^{33} +(1.03167 + 2.18827i) q^{35} -2.43591 q^{37} +(1.48467 - 6.52598i) q^{39} +(4.95635 - 4.15887i) q^{41} +(7.68736 - 2.79797i) q^{43} +(1.13177 + 2.49884i) q^{45} +(3.52092 + 2.95440i) q^{47} +(-6.09148 - 3.44875i) q^{49} +(10.4919 - 1.32232i) q^{51} +(9.92435 - 5.72983i) q^{53} -3.42420i q^{55} +(-8.88885 - 3.73958i) q^{57} +(-0.154736 - 0.877551i) q^{59} +(-7.92124 + 9.44017i) q^{61} +(-6.84656 - 4.01554i) q^{63} +(3.47960 + 0.613548i) q^{65} +(-12.2484 - 4.45805i) q^{67} +(2.65578 - 0.821252i) q^{69} +(11.1044 - 6.41115i) q^{71} +4.85770i q^{73} +(6.41547 - 3.29474i) q^{75} +(5.71700 + 8.09188i) q^{77} +(5.29825 - 1.92841i) q^{79} +(-7.69283 - 4.67122i) q^{81} +(6.26479 + 5.25678i) q^{83} +(0.969437 + 5.49795i) q^{85} +(-11.3519 - 0.558520i) q^{87} +(2.04328 + 3.53906i) q^{89} +(-9.24716 + 4.35959i) q^{91} +(0.925156 - 4.06660i) q^{93} +(1.74124 - 4.78402i) q^{95} +(4.13766 + 11.3681i) q^{97} +(6.34159 + 9.27326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.04679	−	1.37994i	−0.604367	−	0.796706i
$3$	−1.04679	−	1.37994i	−0.604367	−	0.796706i
$4$		0			0
$5$	0.700470	−	0.587764i	0.313260	−	0.262856i	−0.472578	−	0.881289i	$-0.656677\pi$
$5$	0.700470	−	0.587764i	0.313260	−	0.262856i	0.785838	+	0.618433i	$0.212232\pi$
$6$		0			0
$7$	−0.673988	+	2.55846i	−0.254743	+	0.967009i
$7$	−0.673988	+	2.55846i	−0.254743	+	0.967009i
$8$		0			0
$9$	−0.808445	+	2.88902i	−0.269482	+	0.963006i
$10$		0			0
$11$	2.40709	−	2.86865i	0.725764	−	0.864931i	−0.269414	−	0.963025i	$-0.586830\pi$
$11$	2.40709	−	2.86865i	0.725764	−	0.864931i	0.995177	+	0.0980932i	$0.0312743\pi$
$12$		0			0
$13$	2.48376	+	2.96003i	0.688872	+	0.820965i	0.991219	−	0.132233i	$-0.0422146\pi$
$13$	2.48376	+	2.96003i	0.688872	+	0.820965i	−0.302347	+	0.953198i	$0.597770\pi$
$14$		0			0
$15$	−1.54432	−	0.351336i	−0.398743	−	0.0907145i
$16$		0			0
$17$	−3.05270	+	5.28743i	−0.740388	+	1.28239i	0.211931	+	0.977285i	$0.432025\pi$
$17$	−3.05270	+	5.28743i	−0.740388	+	1.28239i	−0.952319	+	0.305105i	$0.901309\pi$
$18$		0			0
$19$	4.82172	−	2.78382i	1.10618	−	0.638653i	0.168342	−	0.985729i	$-0.446159\pi$
$19$	4.82172	−	2.78382i	1.10618	−	0.638653i	0.937837	+	0.347076i	$0.112825\pi$
$20$		0			0
$21$	4.23604	−	1.74813i	0.924380	−	0.381472i
$22$		0			0
$23$	−0.548926	+	1.50816i	−0.114459	+	0.314474i	−0.983674	−	0.179961i	$-0.942403\pi$
$23$	−0.548926	+	1.50816i	−0.114459	+	0.314474i	0.869215	+	0.494435i	$0.164625\pi$
$24$		0			0
$25$	−0.723049	+	4.10062i	−0.144610	+	0.820123i
$26$		0			0
$27$	4.83293	−	1.90860i	0.930098	−	0.367311i
$28$		0			0
$29$	4.21794	−	5.02674i	0.783251	−	0.933443i	−0.215824	−	0.976432i	$-0.569244\pi$
$29$	4.21794	−	5.02674i	0.783251	−	0.933443i	0.999076	+	0.0429895i	$0.0136882\pi$
$30$		0			0
$31$	1.54773	+	1.84452i	0.277981	+	0.331285i	0.886912	−	0.461938i	$-0.152846\pi$
$31$	1.54773	+	1.84452i	0.277981	+	0.331285i	−0.608931	+	0.793223i	$0.708401\pi$
$32$		0			0
$33$	−6.47828	−	0.318735i	−1.12772	−	0.0554846i
$34$		0			0
$35$	1.03167	+	2.18827i	0.174383	+	0.369886i
$36$		0			0
$37$	−2.43591			−0.400460			−0.200230	−	0.979749i	$-0.564169\pi$
$37$	−2.43591			−0.400460			−0.200230	+	0.979749i	$0.564169\pi$
$38$		0			0
$39$	1.48467	−	6.52598i	0.237737	−	1.04499i
$40$		0			0
$41$	4.95635	−	4.15887i	0.774052	−	0.649506i	−0.167691	−	0.985840i	$-0.553631\pi$
$41$	4.95635	−	4.15887i	0.774052	−	0.649506i	0.941743	+	0.336333i	$0.109187\pi$
$42$		0			0
$43$	7.68736	−	2.79797i	1.17231	−	0.426686i	0.318831	−	0.947812i	$-0.396710\pi$
$43$	7.68736	−	2.79797i	1.17231	−	0.426686i	0.853480	+	0.521125i	$0.174488\pi$
$44$		0			0
$45$	1.13177	+	2.49884i	0.168714	+	0.372506i
$46$		0			0
$47$	3.52092	+	2.95440i	0.513579	+	0.430944i	0.862386	−	0.506251i	$-0.168969\pi$
$47$	3.52092	+	2.95440i	0.513579	+	0.430944i	−0.348808	+	0.937194i	$0.613413\pi$
$48$		0			0
$49$	−6.09148	−	3.44875i	−0.870212	−	0.492678i
$50$		0			0
$51$	10.4919	−	1.32232i	1.46915	−	0.185162i
$52$		0			0
$53$	9.92435	−	5.72983i	1.36321	−	0.787052i	0.373164	−	0.927765i	$-0.378273\pi$
$53$	9.92435	−	5.72983i	1.36321	−	0.787052i	0.990050	+	0.140713i	$0.0449396\pi$
$54$		0			0
$55$		−	3.42420i		−	0.461720i
$56$		0			0
$57$	−8.88885	−	3.73958i	−1.17736	−	0.495319i
$58$		0			0
$59$	−0.154736	−	0.877551i	−0.0201449	−	0.114247i	0.973077	−	0.230479i	$-0.0740295\pi$
$59$	−0.154736	−	0.877551i	−0.0201449	−	0.114247i	−0.993222	+	0.116232i	$0.962918\pi$
$60$		0			0
$61$	−7.92124	+	9.44017i	−1.01421	+	1.20869i	−0.0363705	+	0.999338i	$0.511580\pi$
$61$	−7.92124	+	9.44017i	−1.01421	+	1.20869i	−0.977841	+	0.209351i	$0.932865\pi$
$62$		0			0
$63$	−6.84656	−	4.01554i	−0.862586	−	0.505910i
$64$		0			0
$65$	3.47960	+	0.613548i	0.431592	+	0.0761012i
$66$		0			0
$67$	−12.2484	−	4.45805i	−1.49638	−	0.544637i	−0.541258	−	0.840856i	$-0.682052\pi$
$67$	−12.2484	−	4.45805i	−1.49638	−	0.544637i	−0.955120	+	0.296219i	$0.904274\pi$
$68$		0			0
$69$	2.65578	−	0.821252i	0.319718	−	0.0988671i
$70$		0			0
$71$	11.1044	−	6.41115i	1.31785	−	0.760864i	0.334471	−	0.942406i	$-0.391442\pi$
$71$	11.1044	−	6.41115i	1.31785	−	0.760864i	0.983383	+	0.181542i	$0.0581089\pi$
$72$		0			0
$73$			4.85770i			0.568551i	0.958743	+	0.284275i	$0.0917530\pi$
$73$			4.85770i			0.568551i	−0.958743	+	0.284275i	$0.908247\pi$
$74$		0			0
$75$	6.41547	−	3.29474i	0.740795	−	0.380444i
$76$		0			0
$77$	5.71700	+	8.09188i	0.651513	+	0.922155i
$78$		0			0
$79$	5.29825	−	1.92841i	0.596100	−	0.216963i	−0.0263101	−	0.999654i	$-0.508376\pi$
$79$	5.29825	−	1.92841i	0.596100	−	0.216963i	0.622410	+	0.782691i	$0.286154\pi$
$80$		0			0
$81$	−7.69283	−	4.67122i	−0.854759	−	0.519025i
$82$		0			0
$83$	6.26479	+	5.25678i	0.687650	+	0.577006i	0.918230	−	0.396047i	$-0.129618\pi$
$83$	6.26479	+	5.25678i	0.687650	+	0.577006i	−0.230581	+	0.973053i	$0.574063\pi$
$84$		0			0
$85$	0.969437	+	5.49795i	0.105150	+	0.596336i
$86$		0			0
$87$	−11.3519	−	0.558520i	−1.21705	−	0.0598796i
$88$		0			0
$89$	2.04328	+	3.53906i	0.216587	+	0.375139i	0.953762	−	0.300562i	$-0.0971742\pi$
$89$	2.04328	+	3.53906i	0.216587	+	0.375139i	−0.737175	+	0.675701i	$0.763841\pi$
$90$		0			0
$91$	−9.24716	+	4.35959i	−0.969366	+	0.457009i
$92$		0			0
$93$	0.925156	−	4.06660i	0.0959342	−	0.421687i
$94$		0			0
$95$	1.74124	−	4.78402i	0.178648	−	0.490830i
$96$		0			0
$97$	4.13766	+	11.3681i	0.420115	+	1.15426i	0.951640	+	0.307215i	$0.0993971\pi$
$97$	4.13766	+	11.3681i	0.420115	+	1.15426i	−0.531525	+	0.847043i	$0.678381\pi$
$98$		0			0
$99$	6.34159	+	9.27326i	0.637354	+	0.931998i
$100$		0			0
$101$	−2.79081	+	1.01577i	−0.277696	+	0.101073i	−0.477114	−	0.878842i	$-0.658317\pi$
$101$	−2.79081	+	1.01577i	−0.277696	+	0.101073i	0.199418	+	0.979914i	$0.436095\pi$
$102$		0			0
$103$	5.85295	+	6.97527i	0.576708	+	0.687294i	0.972993	−	0.230834i	$-0.0741453\pi$
$103$	5.85295	+	6.97527i	0.576708	+	0.687294i	−0.396285	+	0.918127i	$0.629701\pi$
$104$		0			0
$105$	1.93974	−	3.71430i	0.189299	−	0.362479i
$106$		0			0
$107$	−12.5146	−	7.22532i	−1.20983	−	0.698498i	−0.247111	−	0.968987i	$-0.579481\pi$
$107$	−12.5146	−	7.22532i	−1.20983	−	0.698498i	−0.962723	+	0.270489i	$0.912815\pi$
$108$		0			0
$109$	4.51287	+	7.81653i	0.432255	+	0.748688i	0.997067	−	0.0765319i	$-0.0243847\pi$
$109$	4.51287	+	7.81653i	0.432255	+	0.748688i	−0.564812	+	0.825220i	$0.691051\pi$
$110$		0			0
$111$	2.54989	+	3.36139i	0.242025	+	0.319049i
$112$		0			0
$113$	−3.84867	+	10.5741i	−0.362053	+	0.994732i	0.616250	+	0.787551i	$0.288651\pi$
$113$	−3.84867	+	10.5741i	−0.362053	+	0.994732i	−0.978303	+	0.207181i	$0.933571\pi$
$114$		0			0
$115$	0.501937	+	1.37906i	0.0468059	+	0.128598i
$116$		0			0
$117$	−10.5596	+	4.78261i	−0.976233	+	0.442152i
$118$		0			0
$119$	−11.4702	−	11.3739i	−1.05147	−	1.04264i
$120$		0			0
$121$	−0.524979	−	2.97730i	−0.0477253	−	0.270664i
$122$		0			0
$123$	−10.9273	−	2.48596i	−0.985277	−	0.224152i
$124$		0			0
$125$	4.18972	+	7.25680i	0.374740	+	0.649068i
$126$		0			0
$127$	1.76290	−	3.05343i	0.156432	−	0.270948i	−0.777148	−	0.629318i	$-0.783334\pi$
$127$	1.76290	−	3.05343i	0.156432	−	0.270948i	0.933579	+	0.358370i	$0.116668\pi$
$128$		0			0
$129$	−11.9081	−	7.67916i	−1.04845	−	0.676112i
$130$		0			0
$131$	−10.8842	−	3.96153i	−0.950957	−	0.346120i	−0.180474	−	0.983580i	$-0.557763\pi$
$131$	−10.8842	−	3.96153i	−0.950957	−	0.346120i	−0.770484	+	0.637460i	$0.779985\pi$
$132$		0			0
$133$	3.87253	+	14.2125i	0.335791	+	1.23238i
$134$		0			0
$135$	2.26352	−	4.17754i	0.194812	−	0.359546i
$136$		0			0
$137$	−4.58013	−	0.807600i	−0.391307	−	0.0689980i	−0.0254667	−	0.999676i	$-0.508107\pi$
$137$	−4.58013	−	0.807600i	−0.391307	−	0.0689980i	−0.365840	+	0.930678i	$0.619218\pi$
$138$		0			0
$139$	−20.6952	+	3.64913i	−1.75535	+	0.309515i	−0.956438	−	0.291935i	$-0.905701\pi$
$139$	−20.6952	+	3.64913i	−1.75535	+	0.309515i	−0.798910	+	0.601450i	$0.794590\pi$
$140$		0			0
$141$	0.391208	−	7.95129i	0.0329457	−	0.669619i
$142$		0			0
$143$	14.4699			1.21004
$144$		0			0
$145$		−	6.00024i		−	0.498292i
$146$		0			0
$147$	1.61748	+	12.0160i	0.133407	+	0.991061i
$148$		0			0
$149$	−13.2104	+	2.32935i	−1.08224	+	0.190827i	−0.686204	−	0.727409i	$-0.740724\pi$
$149$	−13.2104	+	2.32935i	−1.08224	+	0.190827i	−0.396032	+	0.918237i	$0.629613\pi$
$150$		0			0
$151$	−8.01271	−	6.72346i	−0.652065	−	0.547148i	0.255632	−	0.966774i	$-0.417717\pi$
$151$	−8.01271	−	6.72346i	−0.652065	−	0.547148i	−0.907697	+	0.419627i	$0.862161\pi$
$152$		0			0
$153$	−12.8075	−	13.0939i	−1.03543	−	1.05858i
$154$		0			0
$155$	2.16828	+	0.382326i	0.174160	+	0.0307092i
$156$		0			0
$157$	−19.5690	+	3.45055i	−1.56178	+	0.275384i	−0.886694	−	0.462357i	$-0.847004\pi$
$157$	−19.5690	+	3.45055i	−1.56178	+	0.275384i	−0.675084	+	0.737741i	$0.735893\pi$
$158$		0			0
$159$	−18.2955	−	7.69702i	−1.45093	−	0.610413i
$160$		0			0
$161$	−3.48861	−	2.42089i	−0.274941	−	0.190793i
$162$		0			0
$163$	7.01252	−	12.1460i	0.549263	−	0.951352i	−0.449062	−	0.893501i	$-0.648242\pi$
$163$	7.01252	−	12.1460i	0.549263	−	0.951352i	0.998325	−	0.0578512i	$-0.0184249\pi$
$164$		0			0
$165$	−4.72518	+	3.58444i	−0.367855	+	0.279048i
$166$		0			0
$167$	2.12777	+	0.774444i	0.164652	+	0.0599283i	0.423031	−	0.906115i	$-0.360966\pi$
$167$	2.12777	+	0.774444i	0.164652	+	0.0599283i	−0.258379	+	0.966044i	$0.583188\pi$
$168$		0			0
$169$	−0.335292	+	1.90154i	−0.0257917	+	0.146272i
$170$		0			0
$171$	4.14441	+	16.1806i	0.316931	+	1.23736i
$172$		0			0
$173$	4.40574	−	24.9862i	0.334962	−	1.89967i	−0.0926401	−	0.995700i	$-0.529531\pi$
$173$	4.40574	−	24.9862i	0.334962	−	1.89967i	0.427603	−	0.903967i	$-0.359358\pi$
$174$		0			0
$175$	−10.0040	−	4.61366i	−0.756228	−	0.348760i
$176$		0			0
$177$	−1.04899	+	1.13214i	−0.0788467	+	0.0850969i
$178$		0			0
$179$	3.76744	+	2.17513i	0.281591	+	0.162577i	0.634144	−	0.773215i	$-0.281353\pi$
$179$	3.76744	+	2.17513i	0.281591	+	0.162577i	−0.352552	+	0.935792i	$0.614686\pi$
$180$		0			0
$181$	2.32397	+	1.34175i	0.172740	+	0.0997313i	0.583877	−	0.811842i	$-0.301535\pi$
$181$	2.32397	+	1.34175i	0.172740	+	0.0997313i	−0.411137	+	0.911573i	$0.634868\pi$
$182$		0			0
$183$	21.3187	+	1.04889i	1.57593	+	0.0775364i
$184$		0			0
$185$	−1.70628	+	1.43174i	−0.125448	+	0.105263i
$186$		0			0
$187$	7.81969	+	21.4844i	0.571832	+	1.57110i
$188$		0			0
$189$	1.62576	+	13.6513i	0.118256	+	0.992983i
$190$		0			0
$191$	5.63477	+	15.4814i	0.407717	+	1.12019i	0.958387	+	0.285471i	$0.0921501\pi$
$191$	5.63477	+	15.4814i	0.407717	+	1.12019i	−0.550670	+	0.834723i	$0.685628\pi$
$192$		0			0
$193$	7.76210	−	6.51318i	0.558728	−	0.468829i	−0.319156	−	0.947702i	$-0.603399\pi$
$193$	7.76210	−	6.51318i	0.558728	−	0.468829i	0.877884	+	0.478874i	$0.158955\pi$
$194$		0			0
$195$	−2.79577	−	5.44389i	−0.200209	−	0.389845i
$196$		0			0
$197$	23.3394	+	13.4750i	1.66286	+	0.960054i	0.971338	+	0.237701i	$0.0763939\pi$
$197$	23.3394	+	13.4750i	1.66286	+	0.960054i	0.691524	+	0.722353i	$0.256939\pi$
$198$		0			0
$199$	−10.8742	−	6.27825i	−0.770855	−	0.445053i	0.0623246	−	0.998056i	$-0.480149\pi$
$199$	−10.8742	−	6.27825i	−0.770855	−	0.445053i	−0.833180	+	0.553003i	$0.813482\pi$
$200$		0			0
$201$	6.66972	+	21.5686i	0.470445	+	1.52133i
$202$		0			0
$203$	10.0179	+	14.1794i	0.703119	+	0.995199i
$204$		0			0
$205$	1.02734	−	5.82633i	0.0717525	−	0.406928i
$206$		0			0
$207$	−3.91333	−	2.80512i	−0.271995	−	0.194969i
$208$		0			0
$209$	3.62048	−	20.5328i	0.250434	−	1.42028i
$210$		0			0
$211$	4.63971	+	1.68871i	0.319411	+	0.116256i	0.496750	−	0.867894i	$-0.334527\pi$
$211$	4.63971	+	1.68871i	0.319411	+	0.116256i	−0.177339	+	0.984150i	$0.556749\pi$
$212$		0			0
$213$	−20.4710	−	8.61226i	−1.40265	−	0.590102i
$214$		0			0
$215$	3.74022	−	6.47825i	0.255081	−	0.441813i
$216$		0			0
$217$	−5.76228	+	2.71664i	−0.391169	+	0.184417i
$218$		0			0
$219$	6.70331	−	5.08501i	0.452968	−	0.343613i
$220$		0			0
$221$	−23.2331	+	4.09663i	−1.56283	+	0.275569i
$222$		0			0
$223$	−12.8650	−	2.26844i	−0.861502	−	0.151906i	−0.274595	−	0.961560i	$-0.588544\pi$
$223$	−12.8650	−	2.26844i	−0.861502	−	0.151906i	−0.586908	+	0.809654i	$0.699655\pi$
$224$		0			0
$225$	−11.2622	−	5.40402i	−0.750814	−	0.360268i
$226$		0			0
$227$	−11.7375	−	9.84892i	−0.779044	−	0.653696i	0.163963	−	0.986466i	$-0.447572\pi$
$227$	−11.7375	−	9.84892i	−0.779044	−	0.653696i	−0.943008	+	0.332770i	$0.892017\pi$
$228$		0			0
$229$	9.15063	−	1.61350i	0.604691	−	0.106623i	0.137083	−	0.990560i	$-0.456227\pi$
$229$	9.15063	−	1.61350i	0.604691	−	0.106623i	0.467608	+	0.883936i	$0.345116\pi$
$230$		0			0
$231$	5.18175	−	16.3596i	0.340934	−	1.07638i
$232$		0			0
$233$		−	9.39194i		−	0.615286i	−0.951502	−	0.307643i	$-0.900460\pi$
$233$		−	9.39194i		−	0.615286i	0.951502	−	0.307643i	$-0.0995403\pi$
$234$		0			0
$235$	4.20279			0.274160
$236$		0			0
$237$	−8.20726	−	5.29261i	−0.533119	−	0.343792i
$238$		0			0
$239$	−8.59351	+	1.51527i	−0.555868	+	0.0980145i	−0.444523	−	0.895767i	$-0.646627\pi$
$239$	−8.59351	+	1.51527i	−0.555868	+	0.0980145i	−0.111345	+	0.993782i	$0.535516\pi$
$240$		0			0
$241$	−5.56319	−	0.980941i	−0.358357	−	0.0631880i	−0.00842855	−	0.999964i	$-0.502683\pi$
$241$	−5.56319	−	0.980941i	−0.358357	−	0.0631880i	−0.349928	+	0.936777i	$0.613794\pi$
$242$		0			0
$243$	1.60682	+	15.5054i	0.103078	+	0.994673i
$244$		0			0
$245$	−6.29395	+	1.16461i	−0.402106	+	0.0744043i
$246$		0			0
$247$	20.2162	+	7.35811i	1.28633	+	0.468185i
$248$		0			0
$249$	0.696078	−	14.1478i	0.0441121	−	0.896578i
$250$		0			0
$251$	−0.593298	+	1.02762i	−0.0374487	+	0.0648630i	−0.884142	−	0.467218i	$-0.845256\pi$
$251$	−0.593298	+	1.02762i	−0.0374487	+	0.0648630i	0.846694	+	0.532081i	$0.178590\pi$
$252$		0			0
$253$	3.00508	+	5.20495i	0.188928	+	0.327233i
$254$		0			0
$255$	6.57202	−	7.09298i	0.411556	−	0.444180i
$256$		0			0
$257$	2.10237	+	11.9231i	0.131142	+	0.743743i	0.977469	+	0.211080i	$0.0676979\pi$
$257$	2.10237	+	11.9231i	0.131142	+	0.743743i	−0.846327	+	0.532664i	$0.821191\pi$
$258$		0			0
$259$	1.64177	−	6.23218i	0.102015	−	0.387249i
$260$		0			0
$261$	11.1124	+	16.2495i	0.687839	+	1.00582i
$262$		0			0
$263$	−0.490567	−	1.34782i	−0.0302497	−	0.0831103i	0.923649	−	0.383241i	$-0.125192\pi$
$263$	−0.490567	−	1.34782i	−0.0302497	−	0.0831103i	−0.953898	+	0.300130i	$0.902970\pi$
$264$		0			0
$265$	3.58392	−	9.84675i	0.220159	−	0.604881i
$266$		0			0
$267$	2.74478	−	6.52425i	0.167978	−	0.399278i
$268$		0			0
$269$	−5.22031	−	9.04184i	−0.318288	−	0.551291i	0.661843	−	0.749642i	$-0.269775\pi$
$269$	−5.22031	−	9.04184i	−0.318288	−	0.551291i	−0.980131	+	0.198352i	$0.936441\pi$
$270$		0			0
$271$	11.2170	+	6.47615i	0.681386	+	0.393398i	0.800377	−	0.599497i	$-0.204633\pi$
$271$	11.2170	+	6.47615i	0.681386	+	0.393398i	−0.118991	+	0.992895i	$0.537966\pi$
$272$		0			0
$273$	15.6958	+	8.19690i	0.949955	+	0.496099i
$274$		0			0
$275$	10.0228	+	11.9447i	0.604398	+	0.720293i
$276$		0			0
$277$	19.0041	−	6.91693i	1.14185	−	0.415598i	0.299267	−	0.954169i	$-0.403258\pi$
$277$	19.0041	−	6.91693i	1.14185	−	0.415598i	0.842580	+	0.538571i	$0.181036\pi$
$278$		0			0
$279$	−6.58009	+	2.98024i	−0.393940	+	0.178422i
$280$		0			0
$281$	−9.35867	−	25.7127i	−0.558291	−	1.53389i	−0.822115	−	0.569322i	$-0.807206\pi$
$281$	−9.35867	−	25.7127i	−0.558291	−	1.53389i	0.263824	−	0.964571i	$-0.415016\pi$
$282$		0			0
$283$	−7.50273	+	20.6136i	−0.445991	+	1.22535i	0.489501	+	0.872003i	$0.337179\pi$
$283$	−7.50273	+	20.6136i	−0.445991	+	1.22535i	−0.935492	+	0.353347i	$0.885043\pi$
$284$		0			0
$285$	−8.42436	+	2.60508i	−0.499016	+	0.154312i
$286$		0			0
$287$	7.29981	+	15.4837i	0.430894	+	0.913972i
$288$		0			0
$289$	−10.1379	−	17.5594i	−0.596348	−	1.03291i
$290$		0			0
$291$	11.3560	−	17.6098i	0.665701	−	1.03230i
$292$		0			0
$293$	−2.68082	−	15.2037i	−0.156615	−	0.888209i	−0.957294	−	0.289116i	$-0.906639\pi$
$293$	−2.68082	−	15.2037i	−0.156615	−	0.888209i	0.800679	−	0.599094i	$-0.204472\pi$
$294$		0			0
$295$	−0.624181	−	0.523750i	−0.0363412	−	0.0304939i
$296$		0			0
$297$	6.15816	−	18.4582i	0.357333	−	1.07105i
$298$		0			0
$299$	−5.82761	+	2.12108i	−0.337019	+	0.122665i
$300$		0			0
$301$	1.97732	+	21.5536i	0.113971	+	1.24233i
$302$		0			0
$303$	4.32310	+	2.78783i	0.248355	+	0.160157i
$304$		0			0
$305$			11.2684i			0.645225i
$306$		0			0
$307$	22.4632	−	12.9691i	1.28204	−	0.740187i	0.304820	−	0.952410i	$-0.401404\pi$
$307$	22.4632	−	12.9691i	1.28204	−	0.740187i	0.977221	+	0.212223i	$0.0680704\pi$
$308$		0			0
$309$	3.49860	−	15.3784i	0.199028	−	0.874844i
$310$		0			0
$311$	−0.873505	−	0.317930i	−0.0495319	−	0.0180281i	0.317135	−	0.948380i	$-0.397279\pi$
$311$	−0.873505	−	0.317930i	−0.0495319	−	0.0180281i	−0.366667	+	0.930352i	$0.619501\pi$
$312$		0			0
$313$	4.73809	+	0.835452i	0.267812	+	0.0472226i	0.305942	−	0.952050i	$-0.401029\pi$
$313$	4.73809	+	0.835452i	0.267812	+	0.0472226i	−0.0381292	+	0.999273i	$0.512140\pi$
$314$		0			0
$315$	−7.15600	+	1.21140i	−0.403195	+	0.0682547i
$316$		0			0
$317$	8.42285	−	10.0380i	0.473074	−	0.563788i	−0.475755	−	0.879578i	$-0.657825\pi$
$317$	8.42285	−	10.0380i	0.473074	−	0.563788i	0.948829	+	0.315790i	$0.102269\pi$
$318$		0			0
$319$	−4.26704	−	24.1996i	−0.238909	−	1.35492i
$320$		0			0
$321$	3.12975	+	24.8328i	0.174686	+	1.38603i
$322$		0			0
$323$			33.9927i			1.89140i
$324$		0			0
$325$	−13.9338	+	8.04471i	−0.772910	+	0.446240i
$326$		0			0
$327$	6.06226	−	14.4098i	0.335244	−	0.796862i
$328$		0			0
$329$	−9.93179	+	7.01692i	−0.547557	+	0.386855i
$330$		0			0
$331$	−14.0616	−	11.7991i	−0.772897	−	0.648537i	0.168552	−	0.985693i	$-0.446091\pi$
$331$	−14.0616	−	11.7991i	−0.772897	−	0.648537i	−0.941449	+	0.337156i	$0.890535\pi$
$332$		0			0
$333$	1.96930	−	7.03737i	0.107917	−	0.385646i
$334$		0			0
$335$	−11.1999	+	4.07643i	−0.611916	+	0.222719i
$336$		0			0
$337$	−19.7150	+	16.5428i	−1.07394	+	0.901145i	−0.995404	−	0.0957659i	$-0.969470\pi$
$337$	−19.7150	+	16.5428i	−1.07394	+	0.901145i	−0.0785390	+	0.996911i	$0.525026\pi$
$338$		0			0
$339$	18.6204	−	5.75803i	1.01132	−	0.312733i
$340$		0			0
$341$	9.01680			0.488287
$342$		0			0
$343$	12.9291	−	13.2604i	0.698105	−	0.715996i
$344$		0			0
$345$	1.37759	−	2.13623i	0.0741670	−	0.115011i
$346$		0			0
$347$	−12.4203	−	14.8019i	−0.666756	−	0.794609i	0.321582	−	0.946882i	$-0.395785\pi$
$347$	−12.4203	−	14.8019i	−0.666756	−	0.794609i	−0.988339	+	0.152272i	$0.951341\pi$
$348$		0			0
$349$	5.91691	−	7.05150i	0.316725	−	0.377458i	−0.584070	−	0.811704i	$-0.698541\pi$
$349$	5.91691	−	7.05150i	0.316725	−	0.377458i	0.900795	+	0.434245i	$0.142985\pi$
$350$		0			0
$351$	17.6534	+	9.56512i	0.942268	+	0.510548i
$352$		0			0
$353$	−4.49925	+	25.5165i	−0.239471	+	1.35811i	0.593520	+	0.804820i	$0.297738\pi$
$353$	−4.49925	+	25.5165i	−0.239471	+	1.35811i	−0.832990	+	0.553287i	$0.813373\pi$
$354$		0			0
$355$	4.01008	−	11.0176i	0.212833	−	0.584754i
$356$		0			0
$357$	−3.68827	+	27.7343i	−0.195204	+	1.46785i
$358$		0			0
$359$	−18.8538	+	10.8853i	−0.995068	+	0.574503i	−0.906785	−	0.421593i	$-0.861471\pi$
$359$	−18.8538	+	10.8853i	−0.995068	+	0.574503i	−0.0882827	+	0.996095i	$0.528138\pi$
$360$		0			0
$361$	5.99935	−	10.3912i	0.315755	−	0.546904i
$362$		0			0
$363$	−3.55894	+	3.84106i	−0.186796	+	0.201603i
$364$		0			0
$365$	2.85518	+	3.40267i	0.149447	+	0.178104i
$366$		0			0
$367$	−10.0506	+	11.9778i	−0.524635	+	0.625235i	−0.961670	−	0.274209i	$-0.911584\pi$
$367$	−10.0506	+	11.9778i	−0.524635	+	0.625235i	0.437035	+	0.899444i	$0.356028\pi$
$368$		0			0
$369$	8.00811	+	17.6812i	0.416886	+	0.920446i
$370$		0			0
$371$	7.97067	+	29.2529i	0.413816	+	1.51874i
$372$		0			0
$373$	−18.2009	+	15.2724i	−0.942409	+	0.790775i	−0.978003	−	0.208591i	$-0.933112\pi$
$373$	−18.2009	+	15.2724i	−0.942409	+	0.790775i	0.0355936	+	0.999366i	$0.488668\pi$
$374$		0			0
$375$	5.62815	−	13.3779i	0.290636	−	0.690833i
$376$		0			0
$377$	25.3557			1.30588
$378$		0			0
$379$	−2.22199			−0.114136			−0.0570680	−	0.998370i	$-0.518175\pi$
$379$	−2.22199			−0.114136			−0.0570680	+	0.998370i	$0.518175\pi$
$380$		0			0
$381$	−6.05892	+	0.763625i	−0.310408	+	0.0391217i
$382$		0			0
$383$	15.8539	−	13.3030i	0.810095	−	0.679751i	−0.140535	−	0.990076i	$-0.544882\pi$
$383$	15.8539	−	13.3030i	0.810095	−	0.679751i	0.950631	+	0.310325i	$0.100438\pi$
$384$		0			0
$385$	8.76070	+	2.30787i	0.446487	+	0.117620i
$386$		0			0
$387$	1.86857	+	24.4709i	0.0949849	+	1.24393i
$388$		0			0
$389$	18.8479	−	22.4621i	0.955626	−	1.13887i	−0.0345999	−	0.999401i	$-0.511016\pi$
$389$	18.8479	−	22.4621i	0.955626	−	1.13887i	0.990226	−	0.139470i	$-0.0445399\pi$
$390$		0			0
$391$	−6.29859	−	7.50637i	−0.318533	−	0.379613i
$392$		0			0
$393$	5.92687	+	19.1664i	0.298971	+	0.966817i
$394$		0			0
$395$	2.57782	−	4.46492i	0.129704	−	0.224654i
$396$		0			0
$397$	27.6163	−	15.9443i	1.38602	−	0.800220i	0.393158	−	0.919471i	$-0.371383\pi$
$397$	27.6163	−	15.9443i	1.38602	−	0.800220i	0.992864	+	0.119251i	$0.0380494\pi$
$398$		0			0
$399$	15.5586	−	20.2214i	0.778902	−	1.01234i
$400$		0			0
$401$	3.57887	−	9.83286i	0.178720	−	0.491030i	−0.817693	−	0.575655i	$-0.804747\pi$
$401$	3.57887	−	9.83286i	0.178720	−	0.491030i	0.996413	+	0.0846254i	$0.0269694\pi$
$402$		0			0
$403$	−1.61563	+	9.16268i	−0.0804801	+	0.456426i
$404$		0			0
$405$	−8.13418	+	1.24952i	−0.404190	+	0.0620892i
$406$		0			0
$407$	−5.86343	+	6.98777i	−0.290640	+	0.346371i
$408$		0			0
$409$	−0.632612	−	0.753918i	−0.0312807	−	0.0372788i	0.750177	−	0.661237i	$-0.229968\pi$
$409$	−0.632612	−	0.753918i	−0.0312807	−	0.0372788i	−0.781458	+	0.623958i	$0.785524\pi$
$410$		0			0
$411$	3.68001	+	7.16567i	0.181522	+	0.353457i
$412$		0			0
$413$	2.34947	+	0.195572i	0.115610	+	0.00962347i
$414$		0			0
$415$	7.47804			0.367083
$416$		0			0
$417$	26.6992	+	24.7382i	1.30747	+	1.21144i
$418$		0			0
$419$	−10.6223	+	8.91314i	−0.518931	+	0.435435i	−0.864259	−	0.503047i	$-0.832212\pi$
$419$	−10.6223	+	8.91314i	−0.518931	+	0.435435i	0.345328	+	0.938482i	$0.387768\pi$
$420$		0			0
$421$	6.03019	−	2.19481i	0.293893	−	0.106968i	−0.190866	−	0.981616i	$-0.561130\pi$
$421$	6.03019	−	2.19481i	0.293893	−	0.106968i	0.484759	+	0.874648i	$0.338907\pi$
$422$		0			0
$423$	−11.3818	+	7.78352i	−0.553401	+	0.378448i
$424$		0			0
$425$	−19.4745	−	16.3410i	−0.944650	−	0.792655i
$426$		0			0
$427$	−18.8135	−	26.6288i	−0.910450	−	1.28866i
$428$		0			0
$429$	−15.1470	−	19.9676i	−0.731306	−	0.964044i
$430$		0			0
$431$	−8.73432	+	5.04276i	−0.420717	+	0.242901i	−0.695384	−	0.718638i	$-0.744766\pi$
$431$	−8.73432	+	5.04276i	−0.420717	+	0.242901i	0.274667	+	0.961539i	$0.411432\pi$
$432$		0			0
$433$			15.6232i			0.750805i	0.926862	+	0.375403i	$0.122496\pi$
$433$			15.6232i			0.750805i	−0.926862	+	0.375403i	$0.877504\pi$
$434$		0			0
$435$	−8.27994	+	6.28101i	−0.396993	+	0.301151i
$436$		0			0
$437$	1.55169	+	8.80005i	0.0742273	+	0.420964i
$438$		0			0
$439$	17.3026	−	20.6205i	0.825809	−	0.984161i	−0.174191	−	0.984712i	$-0.555731\pi$
$439$	17.3026	−	20.6205i	0.825809	−	0.984161i	1.00000		0.000551317i	$0.000175490\pi$
$440$		0			0
$441$	14.8881	−	14.8103i	0.708958	−	0.705251i
$442$		0			0
$443$	−33.6691	−	5.93677i	−1.59967	−	0.282064i	−0.698524	−	0.715587i	$-0.746159\pi$
$443$	−33.6691	−	5.93677i	−1.59967	−	0.282064i	−0.901143	+	0.433522i	$0.857270\pi$
$444$		0			0
$445$	3.51138	+	1.27804i	0.166456	+	0.0605849i
$446$		0			0
$447$	17.0429	+	15.7911i	0.806101	+	0.746895i
$448$		0			0
$449$	21.9379	−	12.6659i	1.03531	−	0.597739i	0.116812	−	0.993154i	$-0.462733\pi$
$449$	21.9379	−	12.6659i	1.03531	−	0.597739i	0.918502	+	0.395415i	$0.129399\pi$
$450$		0			0
$451$		−	24.2288i		−	1.14089i
$452$		0			0
$453$	−0.890289	+	18.0951i	−0.0418294	+	0.850182i
$454$		0			0
$455$	−3.91495	+	8.48892i	−0.183536	+	0.397966i
$456$		0			0
$457$	28.2998	−	10.3003i	1.32381	−	0.481828i	0.419133	−	0.907925i	$-0.362334\pi$
$457$	28.2998	−	10.3003i	1.32381	−	0.481828i	0.904677	+	0.426097i	$0.140112\pi$
$458$		0			0
$459$	−4.66188	+	31.3802i	−0.217598	+	1.46470i
$460$		0			0
$461$	−16.9479	−	14.2210i	−0.789344	−	0.662338i	0.156239	−	0.987719i	$-0.450063\pi$
$461$	−16.9479	−	14.2210i	−0.789344	−	0.662338i	−0.945583	+	0.325381i	$0.894507\pi$
$462$		0			0
$463$	−6.48204	−	36.7614i	−0.301246	−	1.70845i	−0.640670	−	0.767816i	$-0.721343\pi$
$463$	−6.48204	−	36.7614i	−0.301246	−	1.70845i	0.339425	−	0.940633i	$-0.389768\pi$
$464$		0			0
$465$	−1.74216	−	3.39230i	−0.0807906	−	0.157314i
$466$		0			0
$467$	−8.81347	−	15.2654i	−0.407839	−	0.706397i	0.586809	−	0.809726i	$-0.300384\pi$
$467$	−8.81347	−	15.2654i	−0.407839	−	0.706397i	−0.994647	+	0.103328i	$0.967051\pi$
$468$		0			0
$469$	19.6610	−	28.3324i	0.907861	−	1.30827i
$470$		0			0
$471$	25.2463	+	23.3920i	1.16329	+	1.07785i
$472$		0			0
$473$	10.4777	−	28.7873i	0.481766	−	1.32364i
$474$		0			0
$475$	7.92905	+	21.7849i	0.363810	+	0.999559i
$476$		0			0
$477$	8.53027	+	33.3039i	0.390574	+	1.52488i
$478$		0			0
$479$	24.5142	−	8.92243i	1.12008	−	0.407676i	0.285399	−	0.958409i	$-0.407874\pi$
$479$	24.5142	−	8.92243i	1.12008	−	0.407676i	0.834682	+	0.550733i	$0.185652\pi$
$480$		0			0
$481$	−6.05021	−	7.21036i	−0.275866	−	0.328764i
$482$		0			0
$483$	0.311182	+	7.34823i	0.0141593	+	0.334356i
$484$		0			0
$485$	9.58008	+	5.53106i	0.435009	+	0.251153i
$486$		0			0
$487$	1.88377	+	3.26279i	0.0853619	+	0.147851i	0.905545	−	0.424249i	$-0.139462\pi$
$487$	1.88377	+	3.26279i	0.0853619	+	0.147851i	−0.820183	+	0.572101i	$0.806129\pi$
$488$		0			0
$489$	−24.1014	+	3.03758i	−1.08990	+	0.137364i
$490$		0			0
$491$	−10.2584	+	28.1847i	−0.462955	+	1.27196i	0.460298	+	0.887764i	$0.347743\pi$
$491$	−10.2584	+	28.1847i	−0.462955	+	1.27196i	−0.923253	+	0.384193i	$0.874480\pi$
$492$		0			0
$493$	13.7024	+	37.6472i	0.617127	+	1.69554i
$494$		0			0
$495$	9.89258	+	2.76828i	0.444638	+	0.124425i
$496$		0			0
$497$	8.91845	+	32.7314i	0.400047	+	1.46820i
$498$		0			0
$499$	−3.23287	−	18.3345i	−0.144723	−	0.820766i	−0.967589	−	0.252530i	$-0.918737\pi$
$499$	−3.23287	−	18.3345i	−0.144723	−	0.820766i	0.822866	−	0.568236i	$-0.192374\pi$
$500$		0			0
$501$	−1.15865	−	3.74686i	−0.0517647	−	0.167398i
$502$		0			0
$503$	−21.0298	−	36.4246i	−0.937670	−	1.62409i	−0.769801	−	0.638284i	$-0.779645\pi$
$503$	−21.0298	−	36.4246i	−0.937670	−	1.62409i	−0.167869	−	0.985809i	$-0.553689\pi$
$504$		0			0
$505$	−1.35784	+	2.35185i	−0.0604232	+	0.104656i
$506$		0			0
$507$	2.97498	−	1.52783i	0.132123	−	0.0678535i
$508$		0			0
$509$	−22.9472	−	8.35211i	−1.01712	−	0.370201i	−0.220956	−	0.975284i	$-0.570918\pi$
$509$	−22.9472	−	8.35211i	−1.01712	−	0.370201i	−0.796162	+	0.605083i	$0.793140\pi$
$510$		0			0
$511$	−12.4283	−	3.27403i	−0.549794	−	0.144835i
$512$		0			0
$513$	17.9899	−	22.6568i	0.794271	−	1.00032i
$514$		0			0
$515$	8.19963	+	1.44582i	0.361319	+	0.0637102i
$516$		0			0
$517$	16.9503	−	2.98880i	0.745474	−	0.131447i
$518$		0			0
$519$	−39.0913	+	20.0758i	−1.71592	+	0.881229i
$520$		0			0
$521$	16.6726			0.730441			0.365220	−	0.930921i	$-0.380994\pi$
$521$	16.6726			0.730441			0.365220	+	0.930921i	$0.380994\pi$
$522$		0			0
$523$		−	9.76741i		−	0.427099i	−0.976932	−	0.213549i	$-0.931498\pi$
$523$		−	9.76741i		−	0.427099i	0.976932	−	0.213549i	$-0.0685024\pi$
$524$		0			0
$525$	4.10552	+	18.6344i	0.179180	+	0.813270i
$526$		0			0
$527$	−14.4775	+	2.55277i	−0.630650	+	0.111201i
$528$		0			0
$529$	15.6458	+	13.1284i	0.680252	+	0.570799i
$530$		0			0
$531$	2.66035	+	0.262417i	0.115450	+	0.0113879i
$532$		0			0
$533$	24.6208	+	4.34131i	1.06644	+	0.188043i
$534$		0			0
$535$	−13.0129	+	2.29453i	−0.562597	+	0.0992010i
$536$		0			0
$537$	−0.942189	−	7.47573i	−0.0406585	−	0.322602i
$538$		0			0
$539$	−24.5560	+	9.17292i	−1.05770	+	0.395106i
$540$		0			0
$541$	15.0773	−	26.1147i	0.648224	−	1.12276i	−0.335322	−	0.942103i	$-0.608845\pi$
$541$	15.0773	−	26.1147i	0.648224	−	1.12276i	0.983547	−	0.180654i	$-0.0578214\pi$
$542$		0			0
$543$	−0.581197	−	4.61147i	−0.0249416	−	0.197897i
$544$		0			0
$545$	7.75541	+	2.82274i	0.332205	+	0.120913i
$546$		0			0
$547$	−8.06550	+	45.7417i	−0.344856	+	1.95578i	−0.0558860	+	0.998437i	$0.517798\pi$
$547$	−8.06550	+	45.7417i	−0.344856	+	1.95578i	−0.288970	+	0.957338i	$0.593313\pi$
$548$		0			0
$549$	−20.8689	−	30.5165i	−0.890663	−	1.30241i
$550$		0			0
$551$	6.34417	−	35.9796i	0.270271	−	1.53278i
$552$		0			0
$553$	1.36280	+	14.8551i	0.0579523	+	0.631704i
$554$		0			0
$555$	3.76183	+	0.855820i	0.159681	+	0.0363276i
$556$		0			0
$557$	−29.5500	−	17.0607i	−1.25207	−	0.722886i	−0.280554	−	0.959838i	$-0.590518\pi$
$557$	−29.5500	−	17.0607i	−1.25207	−	0.722886i	−0.971521	+	0.236953i	$0.923851\pi$
$558$		0			0
$559$	27.3756	+	15.8053i	1.15787	+	0.668494i
$560$		0			0
$561$	21.4615	−	33.2804i	0.906106	−	1.40510i
$562$		0			0
$563$	−4.17263	+	3.50125i	−0.175855	+	0.147560i	−0.726467	−	0.687201i	$-0.758839\pi$
$563$	−4.17263	+	3.50125i	−0.175855	+	0.147560i	0.550612	+	0.834762i	$0.314395\pi$
$564$		0			0
$565$	3.51922	+	9.66898i	0.148055	+	0.406777i
$566$		0			0
$567$	17.1360	−	16.5335i	0.719646	−	0.694342i
$568$		0			0
$569$	−0.348275	−	0.956878i	−0.0146005	−	0.0401144i	0.932178	−	0.361999i	$-0.117906\pi$
$569$	−0.348275	−	0.956878i	−0.0146005	−	0.0401144i	−0.946779	+	0.321885i	$0.895684\pi$
$570$		0			0
$571$	2.74392	−	2.30242i	0.114830	−	0.0963534i	−0.583565	−	0.812067i	$-0.698343\pi$
$571$	2.74392	−	2.30242i	0.114830	−	0.0963534i	0.698394	+	0.715713i	$0.253898\pi$
$572$		0			0
$573$	15.4649	−	23.9814i	0.646055	−	1.00184i
$574$		0			0
$575$	−5.78749	−	3.34141i	−0.241355	−	0.139346i
$576$		0			0
$577$	−19.9959	−	11.5446i	−0.832440	−	0.480609i	0.0222476	−	0.999752i	$-0.492918\pi$
$577$	−19.9959	−	11.5446i	−0.832440	−	0.480609i	−0.854687	+	0.519143i	$0.826251\pi$
$578$		0			0
$579$	−17.1131	−	3.89325i	−0.711196	−	0.161798i
$580$		0			0
$581$	−17.6717	+	12.4852i	−0.733144	+	0.517974i
$582$		0			0
$583$	7.45188	−	42.2617i	0.308625	−	1.75030i
$584$		0			0
$585$	−4.58562	+	9.55661i	−0.189592	+	0.395117i
$586$		0			0
$587$	0.0818717	−	0.464317i	0.00337921	−	0.0191644i	−0.983072	−	0.183222i	$-0.941347\pi$
$587$	0.0818717	−	0.464317i	0.00337921	−	0.0191644i	0.986451	+	0.164058i	$0.0524583\pi$
$588$		0			0
$589$	12.5975	+	4.58513i	0.519073	+	0.188927i
$590$		0			0
$591$	−5.83689	−	46.3124i	−0.240098	−	1.90504i
$592$		0			0
$593$	−19.0760	+	33.0406i	−0.783357	+	1.35681i	0.146619	+	0.989193i	$0.453161\pi$
$593$	−19.0760	+	33.0406i	−0.783357	+	1.35681i	−0.929976	+	0.367621i	$0.880172\pi$
$594$		0			0
$595$	−14.7197	−	1.22528i	−0.603449	−	0.0502316i
$596$		0			0
$597$	2.71951	+	21.5778i	0.111302	+	0.883120i
$598$		0			0
$599$	−26.2990	+	4.63723i	−1.07455	+	0.189472i	−0.682804	−	0.730602i	$-0.739240\pi$
$599$	−26.2990	+	4.63723i	−1.07455	+	0.189472i	−0.391745	+	0.920074i	$0.628128\pi$
$600$		0			0
$601$	−26.0201	−	4.58804i	−1.06138	−	0.187150i	−0.384412	−	0.923162i	$-0.625596\pi$
$601$	−26.0201	−	4.58804i	−1.06138	−	0.187150i	−0.676969	+	0.736012i	$0.736707\pi$
$602$		0			0
$603$	22.7815	−	31.7817i	0.927735	−	1.29425i
$604$		0			0
$605$	−2.11768	−	1.77695i	−0.0860960	−	0.0722432i
$606$		0			0
$607$	−6.92812	+	1.22162i	−0.281204	+	0.0495838i	−0.312471	−	0.949927i	$-0.601157\pi$
$607$	−6.92812	+	1.22162i	−0.281204	+	0.0495838i	0.0312673	+	0.999511i	$0.490046\pi$
$608$		0			0
$609$	9.07999	−	28.6670i	0.367940	−	1.16164i
$610$		0			0
$611$			17.7601i			0.718495i
$612$		0			0
$613$	−21.2303			−0.857485			−0.428743	−	0.903427i	$-0.641043\pi$
$613$	−21.2303			−0.857485			−0.428743	+	0.903427i	$0.641043\pi$
$614$		0			0
$615$	−9.11537	+	4.68130i	−0.367567	+	0.188768i
$616$		0			0
$617$	−16.1973	+	2.85602i	−0.652079	+	0.114979i	−0.489895	−	0.871782i	$-0.662965\pi$
$617$	−16.1973	+	2.85602i	−0.652079	+	0.114979i	−0.162184	+	0.986761i	$0.551854\pi$
$618$		0			0
$619$	28.5343	+	5.03136i	1.14689	+	0.202227i	0.714617	−	0.699516i	$-0.246601\pi$
$619$	28.5343	+	5.03136i	1.14689	+	0.202227i	0.432272	+	0.901743i	$0.357712\pi$
$620$		0			0
$621$	0.225560	+	8.33653i	0.00905139	+	0.334533i
$622$		0			0
$623$	−10.4317	+	2.84237i	−0.417937	+	0.113877i
$624$		0			0
$625$	−12.3638	−	4.50004i	−0.494550	−	0.180002i
$626$		0			0
$627$	−32.1238	+	16.4975i	−1.28290	+	0.658848i
$628$		0			0
$629$	7.43608	−	12.8797i	0.296496	−	0.513546i
$630$		0			0
$631$	−7.51188	−	13.0110i	−0.299043	−	0.517958i	0.676874	−	0.736099i	$-0.263334\pi$
$631$	−7.51188	−	13.0110i	−0.299043	−	0.517958i	−0.975917	+	0.218141i	$0.930001\pi$
$632$		0			0
$633$	−2.52650	−	8.17023i	−0.100419	−	0.324738i
$634$		0			0
$635$	−0.559839	−	3.17500i	−0.0222165	−	0.125996i
$636$		0			0
$637$	−4.92139	−	26.5969i	−0.194993	−	1.05381i
$638$		0			0
$639$	9.54459	+	37.2640i	0.377578	+	1.47414i
$640$		0			0
$641$	2.72963	+	7.49959i	0.107814	+	0.296216i	0.981854	−	0.189637i	$-0.0607312\pi$
$641$	2.72963	+	7.49959i	0.107814	+	0.296216i	−0.874040	+	0.485853i	$0.838509\pi$
$642$		0			0
$643$	10.8529	−	29.8181i	0.427996	−	1.17591i	−0.519031	−	0.854756i	$-0.673707\pi$
$643$	10.8529	−	29.8181i	0.427996	−	1.17591i	0.947027	−	0.321154i	$-0.104071\pi$
$644$		0			0
$645$	−12.8548	+	1.62013i	−0.506157	+	0.0637925i
$646$		0			0
$647$	0.285978	+	0.495329i	0.0112430	+	0.0194734i	0.871592	−	0.490232i	$-0.163088\pi$
$647$	0.285978	+	0.495329i	0.0112430	+	0.0194734i	−0.860349	+	0.509705i	$0.829755\pi$
$648$		0			0
$649$	−2.88985	−	1.66846i	−0.113437	−	0.0654926i
$650$		0			0
$651$	9.78071	+	5.10782i	0.383336	+	0.200191i
$652$		0			0
$653$	−26.4290	−	31.4968i	−1.03425	−	1.23257i	−0.972116	−	0.234499i	$-0.924655\pi$
$653$	−26.4290	−	31.4968i	−1.03425	−	1.23257i	−0.0621301	−	0.998068i	$-0.519789\pi$
$654$		0			0
$655$	−9.95250	+	3.62241i	−0.388876	+	0.141539i
$656$		0			0
$657$	−14.0340	−	3.92718i	−0.547518	−	0.153214i
$658$		0			0
$659$	−4.33314	−	11.9052i	−0.168795	−	0.463761i	0.826236	−	0.563324i	$-0.190478\pi$
$659$	−4.33314	−	11.9052i	−0.168795	−	0.463761i	−0.995031	+	0.0995628i	$0.968256\pi$
$660$		0			0
$661$	2.80824	−	7.71557i	0.109228	−	0.300101i	−0.873021	−	0.487682i	$-0.837843\pi$
$661$	2.80824	−	7.71557i	0.109228	−	0.300101i	0.982249	+	0.187581i	$0.0600648\pi$
$662$		0			0
$663$	29.9734	+	27.7719i	1.16407	+	1.07857i
$664$		0			0
$665$	11.0662	+	7.67928i	0.429128	+	0.297790i
$666$		0			0
$667$	5.26581	+	9.12064i	0.203893	+	0.353153i
$668$		0			0
$669$	10.3367	+	20.1274i	0.399639	+	0.778171i
$670$		0			0
$671$	8.01346	+	45.4466i	0.309356	+	1.75445i
$672$		0			0
$673$	−33.8139	−	28.3732i	−1.30343	−	1.09371i	−0.989542	−	0.144248i	$-0.953924\pi$
$673$	−33.8139	−	28.3732i	−1.30343	−	1.09371i	−0.313889	−	0.949460i	$-0.601632\pi$
$674$		0			0
$675$	4.33200	+	21.1980i	0.166739	+	0.815912i
$676$		0			0
$677$	−21.2078	+	7.71902i	−0.815084	+	0.296666i	−0.715722	−	0.698385i	$-0.753902\pi$
$677$	−21.2078	+	7.71902i	−0.815084	+	0.296666i	−0.0993616	+	0.995051i	$0.531680\pi$
$678$		0			0
$679$	−31.8737	+	2.92408i	−1.22320	+	0.112216i
$680$		0			0
$681$	−1.30415	+	26.5068i	−0.0499751	+	1.01574i
$682$		0			0
$683$			11.7561i			0.449836i	0.974378	+	0.224918i	$0.0722114\pi$
$683$			11.7561i			0.449836i	−0.974378	+	0.224918i	$0.927789\pi$
$684$		0			0
$685$	−3.68292	+	2.12634i	−0.140717	+	0.0812431i
$686$		0			0
$687$	−11.8054	−	10.9383i	−0.450403	−	0.417321i
$688$		0			0
$689$	41.6102	+	15.1449i	1.58522	+	0.576974i
$690$		0			0
$691$	17.9020	+	3.15660i	0.681023	+	0.120083i	0.503449	−	0.864025i	$-0.332064\pi$
$691$	17.9020	+	3.15660i	0.681023	+	0.120083i	0.177574	+	0.984107i	$0.443175\pi$
$692$		0			0
$693$	−27.9995	+	9.97467i	−1.06361	+	0.378906i
$694$		0			0
$695$	−12.3516	+	14.7200i	−0.468522	+	0.558363i
$696$		0			0
$697$	6.85949	+	38.9021i	0.259822	+	1.47352i
$698$		0			0
$699$	−12.9603	+	9.83142i	−0.490202	+	0.371859i
$700$		0			0
$701$		−	10.7142i		−	0.404669i	−0.979317	−	0.202334i	$-0.935147\pi$
$701$		−	10.7142i		−	0.404669i	0.979317	−	0.202334i	$-0.0648527\pi$
$702$		0			0
$703$	−11.7453	+	6.78113i	−0.442981	+	0.255755i
$704$		0			0
$705$	−4.39945	−	5.79958i	−0.165693	−	0.218425i
$706$		0			0
$707$	−0.717844	−	7.82480i	−0.0269973	−	0.294282i
$708$		0			0
$709$	5.48560	+	4.60297i	0.206016	+	0.172868i	0.739958	−	0.672653i	$-0.234845\pi$
$709$	5.48560	+	4.60297i	0.206016	+	0.172868i	−0.533942	+	0.845521i	$0.679290\pi$
$710$		0			0
$711$	1.28785	+	16.8658i	0.0482982	+	0.632515i
$712$		0			0
$713$	−3.63142	+	1.32173i	−0.135998	+	0.0494991i
$714$		0			0
$715$	10.1358	−	8.50491i	0.379056	−	0.318066i
$716$		0			0
$717$	11.0866	+	10.2723i	0.414037	+	0.383627i
$718$		0			0
$719$	12.8506			0.479247			0.239624	−	0.970866i	$-0.422976\pi$
$719$	12.8506			0.479247			0.239624	+	0.970866i	$0.422976\pi$
$720$		0			0
$721$	−21.7908	+	10.2733i	−0.811532	+	0.382598i
$722$		0			0
$723$	4.46988	+	8.70369i	0.166237	+	0.323694i
$724$		0			0
$725$	17.5630	+	20.9307i	0.652272	+	0.777348i
$726$		0			0
$727$	−25.2662	+	30.1111i	−0.937071	+	1.11676i	0.0559043	+	0.998436i	$0.482196\pi$
$727$	−25.2662	+	30.1111i	−0.937071	+	1.11676i	−0.992975	+	0.118322i	$0.962249\pi$
$728$		0			0
$729$	19.7145	−	18.4483i	0.730166	−	0.683270i
$730$		0			0
$731$	−8.67311	+	49.1877i	−0.320787	+	1.81927i
$732$		0			0
$733$	−2.35387	+	6.46721i	−0.0869422	+	0.238872i	−0.975543	−	0.219810i	$-0.929456\pi$
$733$	−2.35387	+	6.46721i	−0.0869422	+	0.238872i	0.888600	+	0.458682i	$0.151678\pi$
$734$		0			0
$735$	8.19556	+	7.46614i	0.302298	+	0.275393i
$736$		0			0
$737$	−42.2715	+	24.4055i	−1.55709	+	0.898987i
$738$		0			0
$739$	−8.13308	+	14.0869i	−0.299180	+	0.518195i	−0.975949	−	0.218001i	$-0.930046\pi$
$739$	−8.13308	+	14.0869i	−0.299180	+	0.518195i	0.676768	+	0.736196i	$0.263380\pi$
$740$		0			0
$741$	−11.0085	−	35.5995i	−0.404408	−	1.30778i
$742$		0			0
$743$	−4.66918	−	5.56451i	−0.171296	−	0.204142i	0.673566	−	0.739127i	$-0.264762\pi$
$743$	−4.66918	−	5.56451i	−0.171296	−	0.204142i	−0.844862	+	0.534985i	$0.820317\pi$
$744$		0			0
$745$	−7.88437	+	9.39622i	−0.288861	+	0.344251i
$746$		0			0
$747$	−20.2517	+	13.8493i	−0.740969	+	0.506718i
$748$		0			0
$749$	26.9204	−	27.1484i	0.983651	−	0.991982i
$750$		0			0
$751$	22.4704	−	18.8549i	0.819956	−	0.688024i	−0.133006	−	0.991115i	$-0.542463\pi$
$751$	22.4704	−	18.8549i	0.819956	−	0.688024i	0.952962	+	0.303091i	$0.0980185\pi$
$752$		0			0
$753$	2.03911	−	0.256996i	0.0743095	−	0.00936545i
$754$		0			0
$755$	−9.56447			−0.348087
$756$		0			0
$757$	20.1619			0.732796			0.366398	−	0.930458i	$-0.380591\pi$
$757$	20.1619			0.732796			0.366398	+	0.930458i	$0.380591\pi$
$758$		0			0
$759$	4.03680	−	9.59533i	0.146527	−	0.348288i
$760$		0			0
$761$	−34.3005	+	28.7816i	−1.24339	+	1.04333i	−0.246143	+	0.969234i	$0.579163\pi$
$761$	−34.3005	+	28.7816i	−1.24339	+	1.04333i	−0.997251	+	0.0740978i	$0.976392\pi$
$762$		0			0
$763$	−23.0399	+	6.27779i	−0.834102	+	0.227271i
$764$		0			0
$765$	−16.6674	−	1.64407i	−0.602611	−	0.0594415i
$766$		0			0
$767$	2.21325	−	2.63765i	0.0799159	−	0.0952400i
$768$		0			0
$769$	7.23057	+	8.61705i	0.260741	+	0.310739i	0.880493	−	0.474058i	$-0.157211\pi$
$769$	7.23057	+	8.61705i	0.260741	+	0.310739i	−0.619752	+	0.784797i	$0.712767\pi$
$770$		0			0
$771$	14.2524	−	15.3822i	0.513287	−	0.553976i
$772$		0			0
$773$	10.1685	−	17.6124i	0.365737	−	0.633476i	−0.623157	−	0.782097i	$-0.714150\pi$
$773$	10.1685	−	17.6124i	0.365737	−	0.633476i	0.988894	+	0.148621i	$0.0474835\pi$
$774$		0			0
$775$	−8.68274	+	5.01298i	−0.311893	+	0.180072i
$776$		0			0
$777$	−10.3186	+	4.25827i	−0.370178	+	0.152765i
$778$		0			0
$779$	12.3206	−	33.8505i	0.441431	−	1.21282i
$780$		0			0
$781$	8.33797	−	47.2870i	0.298356	−	1.69206i
$782$		0			0
$783$	10.7910	−	32.3443i	0.385637	−	1.15589i
$784$		0			0
$785$	−11.6794	+	13.9190i	−0.416856	+	0.496789i
$786$		0			0
$787$	14.2686	+	17.0047i	0.508621	+	0.606151i	0.957851	−	0.287265i	$-0.0927461\pi$
$787$	14.2686	+	17.0047i	0.508621	+	0.606151i	−0.449230	+	0.893416i	$0.648302\pi$
$788$		0			0
$789$	−1.34639	+	2.08784i	−0.0479326	+	0.0743292i
$790$		0			0
$791$	−24.4596	−	16.9735i	−0.869684	−	0.603510i
$792$		0			0
$793$	−47.6177			−1.69095
$794$		0			0
$795$	−17.3395	+	5.36193i	−0.614969	+	0.190168i
$796$		0			0
$797$	−2.21466	+	1.85832i	−0.0784473	+	0.0658251i	−0.681168	−	0.732127i	$-0.738528\pi$
$797$	−2.21466	+	1.85832i	−0.0784473	+	0.0658251i	0.602721	+	0.797952i	$0.294083\pi$
$798$		0			0
$799$	−26.3695	+	9.59770i	−0.932885	+	0.339542i
$800$		0			0
$801$	−11.8763	+	3.04192i	−0.419627	+	0.107481i
$802$		0			0
$803$	13.9351	+	11.6929i	0.491757	+	0.412634i
$804$		0			0
$805$	−3.86658	+	0.354718i	−0.136279	+	0.0125022i
$806$		0			0
$807$	−7.01257	+	16.6686i	−0.246854	+	0.586764i
$808$		0			0
$809$	13.6590	−	7.88602i	0.480224	−	0.277258i	−0.240286	−	0.970702i	$-0.577241\pi$
$809$	13.6590	−	7.88602i	0.480224	−	0.277258i	0.720510	+	0.693445i	$0.243908\pi$
$810$		0			0
$811$			14.4836i			0.508589i	0.967127	+	0.254294i	$0.0818432\pi$
$811$			14.4836i			0.508589i	−0.967127	+	0.254294i	$0.918157\pi$
$812$		0			0
$813$	−2.80524	−	22.2580i	−0.0983841	−	0.780621i
$814$		0			0
$815$	−2.22695	−	12.6297i	−0.0780066	−	0.442397i
$816$		0			0
$817$	29.2773	−	34.8913i	1.02428	−	1.22069i
$818$		0			0
$819$	−5.11911	−	30.2397i	−0.178876	−	1.05666i
$820$		0			0
$821$	−33.3906	−	5.88767i	−1.16534	−	0.205481i	−0.442678	−	0.896681i	$-0.645971\pi$
$821$	−33.3906	−	5.88767i	−1.16534	−	0.205481i	−0.722664	+	0.691200i	$0.757083\pi$
$822$		0			0
$823$	8.60231	+	3.13099i	0.299858	+	0.109139i	0.487568	−	0.873085i	$-0.337884\pi$
$823$	8.60231	+	3.13099i	0.299858	+	0.109139i	−0.187710	+	0.982225i	$0.560106\pi$
$824$		0			0
$825$	5.99113	−	26.3345i	0.208584	−	0.916849i
$826$		0			0
$827$	−10.4030	+	6.00615i	−0.361746	+	0.208854i	−0.669846	−	0.742500i	$-0.733640\pi$
$827$	−10.4030	+	6.00615i	−0.361746	+	0.208854i	0.308100	+	0.951354i	$0.400307\pi$
$828$		0			0
$829$		−	0.0554541i		−	0.00192600i	−1.00000		0.000963000i	$-0.999693\pi$
$829$		−	0.0554541i		−	0.00192600i	1.00000		0.000963000i	$-0.000306533\pi$
$830$		0			0
$831$	−29.4383	−	18.9839i	−1.02120	−	0.658543i
$832$		0			0
$833$	36.8304	−	21.6803i	1.27610	−	0.751177i
$834$		0			0
$835$	1.94563	−	0.708150i	0.0673312	−	0.0245066i
$836$		0			0
$837$	11.0005	+	5.96041i	0.380234	+	0.206022i
$838$		0			0
$839$	−35.6042	−	29.8755i	−1.22919	−	1.03142i	−0.998291	−	0.0584391i	$-0.981388\pi$
$839$	−35.6042	−	29.8755i	−1.22919	−	1.03142i	−0.230903	−	0.972977i	$-0.574168\pi$
$840$		0			0
$841$	−2.44135	−	13.8456i	−0.0841843	−	0.477433i
$842$		0			0
$843$	−25.6853	+	39.8303i	−0.884649	+	1.37183i
$844$		0			0
$845$	0.882792	+	1.52904i	0.0303690	+	0.0526006i
$846$		0			0
$847$	7.97115	+	0.663525i	0.273892	+	0.0227990i
$848$		0			0
$849$	36.2992	−	11.2249i	1.24579	−	0.385237i
$850$		0			0
$851$	1.33713	−	3.67374i	0.0458363	−	0.125934i
$852$		0			0
$853$	13.7813	+	37.8638i	0.471862	+	1.29643i	0.916254	+	0.400599i	$0.131198\pi$
$853$	13.7813	+	37.8638i	0.471862	+	1.29643i	−0.444391	+	0.895833i	$0.646580\pi$
$854$		0			0
$855$	12.4134	+	8.89809i	0.424530	+	0.304308i
$856$		0			0
$857$	53.0459	−	19.3071i	1.81201	−	0.659519i	0.815252	−	0.579106i	$-0.196598\pi$
$857$	53.0459	−	19.3071i	1.81201	−	0.659519i	0.996762	−	0.0804131i	$-0.0256240\pi$
$858$		0			0
$859$	6.21588	+	7.40780i	0.212083	+	0.252751i	0.861590	−	0.507605i	$-0.169469\pi$
$859$	6.21588	+	7.40780i	0.212083	+	0.252751i	−0.649507	+	0.760356i	$0.725025\pi$
$860$		0			0
$861$	13.7251	−	26.2815i	0.467749	−	0.895670i
$862$		0			0
$863$	−7.71069	−	4.45177i	−0.262475	−	0.151540i	0.362988	−	0.931794i	$-0.381757\pi$
$863$	−7.71069	−	4.45177i	−0.262475	−	0.151540i	−0.625463	+	0.780254i	$0.715090\pi$
$864$		0			0
$865$	−11.5999	−	20.0916i	−0.394409	−	0.683136i
$866$		0			0
$867$	−13.6185	+	32.3707i	−0.462509	+	1.09937i
$868$		0			0
$869$	7.22142	−	19.8407i	0.244970	−	0.673049i
$870$		0			0
$871$	−17.2261	−	47.3284i	−0.583685	−	1.60366i
$872$		0			0
$873$	−36.1878	+	2.76326i	−1.22477	+	0.0935222i
$874$		0			0
$875$	−21.3901	+	5.82825i	−0.723117	+	0.197031i
$876$		0			0
$877$	3.94549	+	22.3760i	0.133230	+	0.755584i	0.976076	+	0.217429i	$0.0697672\pi$
$877$	3.94549	+	22.3760i	0.133230	+	0.755584i	−0.842846	+	0.538155i	$0.819122\pi$
$878$		0			0
$879$	−18.1739	+	19.6145i	−0.612989	+	0.661580i
$880$		0			0
$881$	20.5916	+	35.6656i	0.693748	+	1.20161i	0.970601	+	0.240694i	$0.0773750\pi$
$881$	20.5916	+	35.6656i	0.693748	+	1.20161i	−0.276854	+	0.960912i	$0.589292\pi$
$882$		0			0
$883$	−22.4947	+	38.9620i	−0.757008	+	1.31118i	0.187361	+	0.982291i	$0.440006\pi$
$883$	−22.4947	+	38.9620i	−0.757008	+	1.31118i	−0.944370	+	0.328886i	$0.893327\pi$
$884$		0			0
$885$	−0.0693525	+	1.40959i	−0.00233126	+	0.0473828i
$886$		0			0
$887$	−26.8588	−	9.77580i	−0.901830	−	0.328239i	−0.150844	−	0.988558i	$-0.548199\pi$
$887$	−26.8588	−	9.77580i	−0.901830	−	0.328239i	−0.750986	+	0.660318i	$0.770421\pi$
$888$		0			0
$889$	6.62392	+	6.56828i	0.222159	+	0.220293i
$890$		0			0
$891$	−31.9174	+	10.8240i	−1.06927	+	0.362619i
$892$		0			0
$893$	25.2014	+	4.44369i	0.843334	+	0.148702i
$894$		0			0
$895$	3.91744	−	0.690750i	0.130946	−	0.0230892i
$896$		0			0
$897$	9.02726	+	5.82140i	0.301411	+	0.194371i
$898$		0			0
$899$	15.8001			0.526964
$900$		0			0
$901$			69.9657i			2.33089i
$902$		0			0
$903$	27.6728	−	25.2908i	0.920892	−	0.841624i
$904$		0			0
$905$	2.41651	−	0.426095i	0.0803274	−	0.0141639i
$906$		0			0
$907$	−15.7024	−	13.1759i	−0.521390	−	0.437498i	0.343726	−	0.939070i	$-0.388311\pi$
$907$	−15.7024	−	13.1759i	−0.521390	−	0.437498i	−0.865116	+	0.501572i	$0.832755\pi$
$908$		0			0
$909$	−0.678364	−	8.88388i	−0.0224999	−	0.294660i
$910$		0			0
$911$	26.1535	+	4.61157i	0.866505	+	0.152788i	0.589193	−	0.807992i	$-0.299446\pi$
$911$	26.1535	+	4.61157i	0.866505	+	0.152788i	0.277311	+	0.960780i	$0.410557\pi$
$912$		0			0
$913$	30.1597	−	5.31798i	0.998142	−	0.175999i
$914$		0			0
$915$	15.5496	−	11.7957i	0.514055	−	0.389953i
$916$		0			0
$917$	17.4712	−	25.1768i	0.576951	−	0.831412i
$918$		0			0
$919$	−6.74735	+	11.6868i	−0.222575	+	0.385511i	−0.955589	−	0.294702i	$-0.904779\pi$
$919$	−6.74735	+	11.6868i	−0.222575	+	0.385511i	0.733014	+	0.680213i	$0.238113\pi$
$920$		0			0
$921$	−41.4109	−	17.4217i	−1.36453	−	0.574066i
$922$		0			0
$923$	46.5580	+	16.9457i	1.53248	+	0.557775i
$924$		0			0
$925$	1.76128	−	9.98871i	0.0579105	−	0.328427i
$926$		0			0
$927$	−24.8835	+	11.2701i	−0.817280	+	0.370160i
$928$		0			0
$929$	4.79587	−	27.1987i	0.157347	−	0.892361i	−0.799261	−	0.600984i	$-0.794776\pi$
$929$	4.79587	−	27.1987i	0.157347	−	0.892361i	0.956608	−	0.291377i	$-0.0941133\pi$
$930$		0			0
$931$	−38.9721	+	0.328706i	−1.27726	+	0.0107729i
$932$		0			0
$933$	0.475657	+	1.53819i	0.0155723	+	0.0503580i
$934$		0			0
$935$	18.1052	+	10.4531i	0.592104	+	0.341852i
$936$		0			0
$937$	22.1137	+	12.7673i	0.722423	+	0.417091i	0.815644	−	0.578554i	$-0.196383\pi$
$937$	22.1137	+	12.7673i	0.722423	+	0.417091i	−0.0932208	+	0.995645i	$0.529716\pi$
$938$		0			0
$939$	−3.80693	−	7.41280i	−0.124234	−	0.241908i
$940$		0			0
$941$	11.8983	−	9.98386i	0.387873	−	0.325464i	−0.427911	−	0.903821i	$-0.640750\pi$
$941$	11.8983	−	9.98386i	0.387873	−	0.325464i	0.815784	+	0.578357i	$0.196306\pi$
$942$		0			0
$943$	3.55158	+	9.75789i	0.115655	+	0.317761i
$944$		0			0
$945$	9.16251	+	8.60674i	0.298057	+	0.279977i
$946$		0			0
$947$	16.7798	+	46.1022i	0.545271	+	1.49812i	0.840025	+	0.542547i	$0.182540\pi$
$947$	16.7798	+	46.1022i	0.545271	+	1.49812i	−0.294754	+	0.955573i	$0.595238\pi$
$948$		0			0
$949$	−14.3790	+	12.0654i	−0.466761	+	0.391659i
$950$		0			0
$951$	−22.6687	−	1.11531i	−0.735084	−	0.0361665i
$952$		0			0
$953$	−16.1052	−	9.29833i	−0.521698	−	0.301202i	0.215931	−	0.976409i	$-0.430721\pi$
$953$	−16.1052	−	9.29833i	−0.521698	−	0.301202i	−0.737629	+	0.675206i	$0.764055\pi$
$954$		0			0
$955$	13.0464	+	7.53234i	0.422171	+	0.243741i
$956$		0			0
$957$	−28.9272	+	31.2202i	−0.935083	+	1.00921i
$958$		0			0
$959$	5.15317	−	11.1738i	0.166404	−	0.360820i
$960$		0			0
$961$	4.37633	−	24.8194i	0.141172	−	0.800626i
$962$		0			0
$963$	30.9914	−	30.3137i	0.998685	−	0.976844i
$964$		0			0
$965$	1.60891	−	9.12457i	0.0517926	−	0.293730i
$966$		0			0
$967$	18.0291	+	6.56204i	0.579775	+	0.211021i	0.615226	−	0.788350i	$-0.289065\pi$
$967$	18.0291	+	6.56204i	0.579775	+	0.211021i	−0.0354510	+	0.999371i	$0.511287\pi$
$968$		0			0
$969$	46.9077	−	35.5833i	1.50689	−	1.14310i
$970$		0			0
$971$	21.5511	−	37.3275i	0.691606	−	1.19790i	−0.279705	−	0.960086i	$-0.590237\pi$
$971$	21.5511	−	37.3275i	0.691606	−	1.19790i	0.971311	−	0.237811i	$-0.0764299\pi$
$972$		0			0
$973$	4.61217	−	55.4075i	0.147859	−	1.77628i
$974$		0			0
$975$	25.6870	+	10.8067i	0.822644	+	0.346090i
$976$		0			0
$977$	1.75967	−	0.310277i	0.0562968	−	0.00992665i	−0.145429	−	0.989369i	$-0.546456\pi$
$977$	1.75967	−	0.310277i	0.0562968	−	0.00992665i	0.201726	+	0.979442i	$0.435345\pi$
$978$		0			0
$979$	15.0707	+	2.65737i	0.481661	+	0.0849298i
$980$		0			0
$981$	−26.2305	+	6.71854i	−0.837475	+	0.214506i
$982$		0			0
$983$	−9.03718	−	7.58310i	−0.288241	−	0.241863i	0.487189	−	0.873297i	$-0.338022\pi$
$983$	−9.03718	−	7.58310i	−0.288241	−	0.241863i	−0.775430	+	0.631434i	$0.782467\pi$
$984$		0			0
$985$	24.2687	−	4.27922i	0.773264	−	0.136347i
$986$		0			0
$987$	20.0794	+	6.35996i	0.639135	+	0.202440i
$988$		0			0
$989$			13.1297i			0.417499i
$990$		0			0
$991$	10.0986			0.320792			0.160396	−	0.987053i	$-0.448723\pi$
$991$	10.0986			0.320792			0.160396	+	0.987053i	$0.448723\pi$
$992$		0			0
$993$	−1.56238	+	31.7554i	−0.0495807	+	1.00773i
$994$		0			0
$995$	−11.3072	+	1.99377i	−0.358463	+	0.0632067i
$996$		0			0
$997$	1.21110	+	0.213550i	0.0383560	+	0.00676320i	0.192793	−	0.981239i	$-0.438245\pi$
$997$	1.21110	+	0.213550i	0.0383560	+	0.00676320i	−0.154437	+	0.988003i	$0.549356\pi$
$998$		0			0
$999$	−11.7726	+	4.64918i	−0.372467	+	0.147093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ca.a.173.8	✓	144
7.3	odd	6		756.2.ck.a.605.15	yes	144
27.5	odd	18		756.2.ck.a.5.15	yes	144
189.59	even	18	inner	756.2.ca.a.437.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.8	✓	144	1.1	even	1	trivial
756.2.ca.a.437.8	yes	144	189.59	even	18	inner
756.2.ck.a.5.15	yes	144	27.5	odd	18
756.2.ck.a.605.15	yes	144	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ca (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04679 - 1.37994i) q^{3} +(0.700470 - 0.587764i) q^{5} +(-0.673988 + 2.55846i) q^{7} +(-0.808445 + 2.88902i) q^{9} +O(q^{10})\)	\(q+(-1.04679 - 1.37994i) q^{3} +(0.700470 - 0.587764i) q^{5} +(-0.673988 + 2.55846i) q^{7} +(-0.808445 + 2.88902i) q^{9} +(2.40709 - 2.86865i) q^{11} +(2.48376 + 2.96003i) q^{13} +(-1.54432 - 0.351336i) q^{15} +(-3.05270 + 5.28743i) q^{17} +(4.82172 - 2.78382i) q^{19} +(4.23604 - 1.74813i) q^{21} +(-0.548926 + 1.50816i) q^{23} +(-0.723049 + 4.10062i) q^{25} +(4.83293 - 1.90860i) q^{27} +(4.21794 - 5.02674i) q^{29} +(1.54773 + 1.84452i) q^{31} +(-6.47828 - 0.318735i) q^{33} +(1.03167 + 2.18827i) q^{35} -2.43591 q^{37} +(1.48467 - 6.52598i) q^{39} +(4.95635 - 4.15887i) q^{41} +(7.68736 - 2.79797i) q^{43} +(1.13177 + 2.49884i) q^{45} +(3.52092 + 2.95440i) q^{47} +(-6.09148 - 3.44875i) q^{49} +(10.4919 - 1.32232i) q^{51} +(9.92435 - 5.72983i) q^{53} -3.42420i q^{55} +(-8.88885 - 3.73958i) q^{57} +(-0.154736 - 0.877551i) q^{59} +(-7.92124 + 9.44017i) q^{61} +(-6.84656 - 4.01554i) q^{63} +(3.47960 + 0.613548i) q^{65} +(-12.2484 - 4.45805i) q^{67} +(2.65578 - 0.821252i) q^{69} +(11.1044 - 6.41115i) q^{71} +4.85770i q^{73} +(6.41547 - 3.29474i) q^{75} +(5.71700 + 8.09188i) q^{77} +(5.29825 - 1.92841i) q^{79} +(-7.69283 - 4.67122i) q^{81} +(6.26479 + 5.25678i) q^{83} +(0.969437 + 5.49795i) q^{85} +(-11.3519 - 0.558520i) q^{87} +(2.04328 + 3.53906i) q^{89} +(-9.24716 + 4.35959i) q^{91} +(0.925156 - 4.06660i) q^{93} +(1.74124 - 4.78402i) q^{95} +(4.13766 + 11.3681i) q^{97} +(6.34159 + 9.27326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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