LMFDB - Embedded newform 666.2.bs.b.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.b.431.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.55188 - 0.310750i) q^{5} +(3.11397 + 2.61293i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.55188 - 0.310750i) q^{5} +(3.11397 + 2.61293i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-1.78273 + 3.08777i) q^{10} +(-0.00168590 - 0.00292006i) q^{11} +(1.48479 + 0.692367i) q^{13} +(-3.92649 + 1.05210i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-6.72035 + 3.13375i) q^{17} +(5.40925 - 3.78760i) q^{19} +(-1.50683 - 3.23140i) q^{20} +(0.00335897 + 0.000293872i) q^{22} +(-1.87861 - 7.01106i) q^{23} +(7.59528 - 1.33925i) q^{25} +(-1.41879 + 0.819140i) q^{26} +(1.39031 - 3.81985i) q^{28} +(0.451637 - 1.68553i) q^{29} +(-6.34406 + 6.34406i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(1.28762 - 7.30243i) q^{34} +(11.8724 + 8.31317i) q^{35} +(5.96785 - 1.17677i) q^{37} +6.60347i q^{38} +(3.51129 + 0.619134i) q^{40} +(-8.09602 + 2.94671i) q^{41} +(-3.92740 - 3.92740i) q^{43} +(-0.00216735 + 0.00258295i) q^{44} +(6.82065 + 2.48251i) q^{46} +(0.830808 + 0.479667i) q^{47} +(1.65387 + 9.37955i) q^{49} +(-3.25942 + 6.98986i) q^{50} +(0.142786 - 1.63205i) q^{52} +(7.38951 + 8.80648i) q^{53} +(-0.00689553 - 0.00984784i) q^{55} +(2.33159 + 3.32985i) q^{56} +(1.12166 + 1.33674i) q^{58} +(0.918352 - 10.4968i) q^{59} +(-4.66422 + 10.0025i) q^{61} +(-1.55795 - 8.83555i) q^{62} +(0.866025 + 0.500000i) q^{64} +(5.48894 + 1.99781i) q^{65} +(6.84313 - 8.15532i) q^{67} +(5.24325 + 5.24325i) q^{68} +(-13.6195 + 4.95709i) q^{70} +(-6.56350 - 1.15732i) q^{71} +1.04063i q^{73} +(-2.45906 + 5.56354i) q^{74} +(-5.40925 - 3.78760i) q^{76} +(0.00238009 - 0.0134981i) q^{77} +(0.482790 + 5.51832i) q^{79} +(-2.52116 + 2.52116i) q^{80} +(2.22988 - 8.32204i) q^{82} +(-0.623717 + 1.71365i) q^{83} +(-22.8961 + 13.2191i) q^{85} +(5.46980 - 0.964473i) q^{86} +(-0.000872686 - 0.00325691i) q^{88} +(3.68659 + 0.322535i) q^{89} +(2.81447 + 6.03566i) q^{91} +(-5.94572 + 4.16324i) q^{92} +(-0.869453 + 0.405432i) q^{94} +(18.0360 - 15.1340i) q^{95} +(-4.41394 + 1.18271i) q^{97} +(-8.63189 - 4.02512i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{7}{36}\right)$

Coefficient data

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

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

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

$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$3$		0			0
$3$		0			0
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$	3.55188	−	0.310750i	1.58845	−	0.138971i	0.741615	−	0.670826i	$-0.234060\pi$
$5$	3.55188	−	0.310750i	1.58845	−	0.138971i	0.846836	+	0.531854i	$0.178505\pi$
$6$		0			0
$7$	3.11397	+	2.61293i	1.17697	+	0.987596i	0.999994	+	0.00338075i	$0.00107613\pi$
$7$	3.11397	+	2.61293i	1.17697	+	0.987596i	0.176977	+	0.984215i	$0.443368\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	−1.78273	+	3.08777i	−0.563748	+	0.976439i
$11$	−0.00168590	−	0.00292006i	−0.000508318	−	0.000880433i	0.865771	−	0.500440i	$-0.166828\pi$
$11$	−0.00168590	−	0.00292006i	−0.000508318	−	0.000880433i	−0.866279	+	0.499560i	$0.833495\pi$
$12$		0			0
$13$	1.48479	+	0.692367i	0.411806	+	0.192028i	0.617470	−	0.786594i	$-0.288158\pi$
$13$	1.48479	+	0.692367i	0.411806	+	0.192028i	−0.205664	+	0.978623i	$0.565935\pi$
$14$	−3.92649	+	1.05210i	−1.04940	+	0.281186i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−6.72035	+	3.13375i	−1.62992	+	0.760046i	−0.999864	−	0.0165015i	$-0.994747\pi$
$17$	−6.72035	+	3.13375i	−1.62992	+	0.760046i	−0.630059	+	0.776547i	$0.716969\pi$
$18$		0			0
$19$	5.40925	−	3.78760i	1.24097	−	0.868934i	0.246013	−	0.969267i	$-0.420879\pi$
$19$	5.40925	−	3.78760i	1.24097	−	0.868934i	0.994954	+	0.100332i	$0.0319906\pi$
$20$	−1.50683	−	3.23140i	−0.336936	−	0.722562i
$21$		0			0
$22$	0.00335897		0.000293872i	0.000716135		6.26537e-5i
$23$	−1.87861	−	7.01106i	−0.391717	−	1.46191i	−0.827301	−	0.561758i	$-0.810125\pi$
$23$	−1.87861	−	7.01106i	−0.391717	−	1.46191i	0.435585	−	0.900148i	$-0.356542\pi$
$24$		0			0
$25$	7.59528	−	1.33925i	1.51906	−	0.267851i
$26$	−1.41879	+	0.819140i	−0.278248	+	0.160647i
$27$		0			0
$28$	1.39031	−	3.81985i	0.262744	−	0.721884i
$29$	0.451637	−	1.68553i	0.0838669	−	0.312995i	−0.911230	−	0.411897i	$-0.864866\pi$
$29$	0.451637	−	1.68553i	0.0838669	−	0.312995i	0.995097	+	0.0989018i	$0.0315330\pi$
$30$		0			0
$31$	−6.34406	+	6.34406i	−1.13943	+	1.13943i	−0.150873	+	0.988553i	$0.548209\pi$
$31$	−6.34406	+	6.34406i	−1.13943	+	1.13943i	−0.988553	+	0.150873i	$0.951791\pi$
$32$	−0.0871557	−	0.996195i	−0.0154071	−	0.176104i
$33$		0			0
$34$	1.28762	−	7.30243i	0.220824	−	1.25236i
$35$	11.8724	+	8.31317i	2.00681	+	1.40518i
$36$		0			0
$37$	5.96785	−	1.17677i	0.981108	−	0.193460i
$37$	5.96785	−	1.17677i	0.981108	−	0.193460i
$38$			6.60347i			1.07122i
$39$		0			0
$40$	3.51129	+	0.619134i	0.555183	+	0.0978937i
$41$	−8.09602	+	2.94671i	−1.26439	+	0.460199i	−0.885239	−	0.465137i	$-0.846005\pi$
$41$	−8.09602	+	2.94671i	−1.26439	+	0.460199i	−0.379148	+	0.925336i	$0.623783\pi$
$42$		0			0
$43$	−3.92740	−	3.92740i	−0.598923	−	0.598923i	0.341103	−	0.940026i	$-0.389199\pi$
$43$	−3.92740	−	3.92740i	−0.598923	−	0.598923i	−0.940026	+	0.341103i	$0.889199\pi$
$44$	−0.00216735	+	0.00258295i	−0.000326741	+	0.000389394i
$45$		0			0
$46$	6.82065	+	2.48251i	1.00565	+	0.366026i
$47$	0.830808	+	0.479667i	0.121186	+	0.0699667i	0.559368	−	0.828920i	$-0.311044\pi$
$47$	0.830808	+	0.479667i	0.121186	+	0.0699667i	−0.438182	+	0.898886i	$0.644377\pi$
$48$		0			0
$49$	1.65387	+	9.37955i	0.236267	+	1.33994i
$50$	−3.25942	+	6.98986i	−0.460952	+	0.988515i
$51$		0			0
$52$	0.142786	−	1.63205i	0.0198008	−	0.226324i
$53$	7.38951	+	8.80648i	1.01503	+	1.20966i	0.977623	+	0.210362i	$0.0674644\pi$
$53$	7.38951	+	8.80648i	1.01503	+	1.20966i	0.0374040	+	0.999300i	$0.488091\pi$
$54$		0			0
$55$	−0.00689553	−	0.00984784i	−0.000929793	−	0.00132788i
$56$	2.33159	+	3.32985i	0.311572	+	0.444971i
$57$		0			0
$58$	1.12166	+	1.33674i	0.147281	+	0.175523i
$59$	0.918352	−	10.4968i	0.119559	−	1.36657i	−0.665152	−	0.746708i	$-0.731633\pi$
$59$	0.918352	−	10.4968i	0.119559	−	1.36657i	0.784712	−	0.619861i	$-0.212811\pi$
$60$		0			0
$61$	−4.66422	+	10.0025i	−0.597193	+	1.28068i	0.342774	+	0.939418i	$0.388633\pi$
$61$	−4.66422	+	10.0025i	−0.597193	+	1.28068i	−0.939967	+	0.341266i	$0.889144\pi$
$62$	−1.55795	−	8.83555i	−0.197859	−	1.12212i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	5.48894	+	1.99781i	0.680820	+	0.247798i
$66$		0			0
$67$	6.84313	−	8.15532i	0.836021	−	0.996331i	−0.163930	−	0.986472i	$-0.552417\pi$
$67$	6.84313	−	8.15532i	0.836021	−	0.996331i	0.999951	−	0.00985913i	$-0.00313831\pi$
$68$	5.24325	+	5.24325i	0.635838	+	0.635838i
$69$		0			0
$70$	−13.6195	+	4.95709i	−1.62784	+	0.592486i
$71$	−6.56350	−	1.15732i	−0.778944	−	0.137349i	−0.229981	−	0.973195i	$-0.573866\pi$
$71$	−6.56350	−	1.15732i	−0.778944	−	0.137349i	−0.548964	+	0.835846i	$0.684977\pi$
$72$		0			0
$73$			1.04063i			0.121796i	0.998144	+	0.0608982i	$0.0193965\pi$
$73$			1.04063i			0.121796i	−0.998144	+	0.0608982i	$0.980603\pi$
$74$	−2.45906	+	5.56354i	−0.285860	+	0.646749i
$75$		0			0
$76$	−5.40925	−	3.78760i	−0.620483	−	0.434467i
$77$	0.00238009	−	0.0134981i	0.000271236	−	0.00153826i
$78$		0			0
$79$	0.482790	+	5.51832i	0.0543181	+	0.620859i	0.973752	+	0.227613i	$0.0730922\pi$
$79$	0.482790	+	5.51832i	0.0543181	+	0.620859i	−0.919433	+	0.393246i	$0.871352\pi$
$80$	−2.52116	+	2.52116i	−0.281874	+	0.281874i
$81$		0			0
$82$	2.22988	−	8.32204i	0.246249	−	0.919016i
$83$	−0.623717	+	1.71365i	−0.0684618	+	0.188097i	−0.969205	−	0.246254i	$-0.920800\pi$
$83$	−0.623717	+	1.71365i	−0.0684618	+	0.188097i	0.900743	+	0.434351i	$0.143022\pi$
$84$		0			0
$85$	−22.8961	+	13.2191i	−2.48343	+	1.43381i
$86$	5.46980	−	0.964473i	0.589824	−	0.104002i
$87$		0			0
$88$	−0.000872686	−	0.00325691i	−9.30286e−5	−	0.000347188i
$89$	3.68659	+	0.322535i	0.390778	+	0.0341886i	0.280852	−	0.959751i	$-0.409383\pi$
$89$	3.68659	+	0.322535i	0.390778	+	0.0341886i	0.109926	+	0.993940i	$0.464939\pi$
$90$		0			0
$91$	2.81447	+	6.03566i	0.295037	+	0.632709i
$92$	−5.94572	+	4.16324i	−0.619884	+	0.434047i
$93$		0			0
$94$	−0.869453	+	0.405432i	−0.0896772	+	0.0418172i
$95$	18.0360	−	15.1340i	1.85046	−	1.55272i
$96$		0			0
$97$	−4.41394	+	1.18271i	−0.448168	+	0.120086i	−0.475842	−	0.879531i	$-0.657857\pi$
$97$	−4.41394	+	1.18271i	−0.448168	+	0.120086i	0.0276742	+	0.999617i	$0.491190\pi$
$98$	−8.63189	−	4.02512i	−0.871953	−	0.406598i
$99$		0			0
$100$	−3.85623	−	6.67918i	−0.385623	−	0.667918i
$101$	−0.0461206	+	0.0798833i	−0.00458917	+	0.00794868i	−0.868311	−	0.496020i	$-0.834794\pi$
$101$	−0.0461206	+	0.0798833i	−0.00458917	+	0.00794868i	0.863722	+	0.503969i	$0.168127\pi$
$102$		0			0
$103$	−5.68882	−	1.52431i	−0.560536	−	0.150195i	−0.0325833	−	0.999469i	$-0.510373\pi$
$103$	−5.68882	−	1.52431i	−0.560536	−	0.150195i	−0.527952	+	0.849274i	$0.677040\pi$
$104$	1.25500	+	1.05307i	0.123062	+	0.103262i
$105$		0			0
$106$	−11.4523	+	1.00195i	−1.11235	+	0.0973176i
$107$	−1.35290	−	3.71707i	−0.130790	−	0.359343i	0.856961	−	0.515382i	$-0.172350\pi$
$107$	−1.35290	−	3.71707i	−0.130790	−	0.359343i	−0.987751	+	0.156039i	$0.950128\pi$
$108$		0			0
$109$	4.72339	−	6.74570i	0.452419	−	0.646121i	−0.526547	−	0.850146i	$-0.676514\pi$
$109$	4.72339	−	6.74570i	0.452419	−	0.646121i	0.978966	+	0.204025i	$0.0654024\pi$
$110$	0.0120220			0.00114625
$111$		0			0
$112$	−4.06500			−0.384107
$113$	3.97766	−	5.68069i	0.374187	−	0.534395i	−0.587255	−	0.809402i	$-0.699791\pi$
$113$	3.97766	−	5.68069i	0.374187	−	0.534395i	0.961442	+	0.275007i	$0.0886803\pi$
$114$		0			0
$115$	−8.85128	−	24.3187i	−0.825386	−	2.26773i
$116$	−1.73835	+	0.152086i	−0.161402	+	0.0141208i
$117$		0			0
$118$	8.07174	+	6.77299i	0.743064	+	0.623505i
$119$	−29.1152	−	7.80141i	−2.66899	−	0.715154i
$120$		0			0
$121$	5.49999	−	9.52627i	0.499999	−	0.866025i
$122$	−5.51825	−	9.55788i	−0.499599	−	0.865330i
$123$		0			0
$124$	8.13126	+	3.79167i	0.730209	+	0.340502i
$125$	9.34158	−	2.50307i	0.835537	−	0.223881i
$126$		0			0
$127$	2.05515	−	1.72448i	0.182365	−	0.153023i	−0.547035	−	0.837110i	$-0.684244\pi$
$127$	2.05515	−	1.72448i	0.182365	−	0.153023i	0.729400	+	0.684087i	$0.239799\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$		0			0
$130$	−4.78484	+	3.35038i	−0.419658	+	0.293848i
$131$	−3.38409	−	7.25720i	−0.295669	−	0.634064i	0.701215	−	0.712950i	$-0.252641\pi$
$131$	−3.38409	−	7.25720i	−0.295669	−	0.634064i	−0.996884	+	0.0788860i	$0.974864\pi$
$132$		0			0
$133$	26.7410	+	2.33953i	2.31874	+	0.202863i
$134$	2.75539	+	10.2833i	0.238030	+	0.888338i
$135$		0			0
$136$	−7.30243	+	1.28762i	−0.626178	+	0.110412i
$137$	10.6929	−	6.17353i	0.913553	−	0.527440i	0.0319803	−	0.999489i	$-0.489819\pi$
$137$	10.6929	−	6.17353i	0.913553	−	0.527440i	0.881573	+	0.472049i	$0.156485\pi$
$138$		0			0
$139$	0.0881489	−	0.242187i	0.00747669	−	0.0205420i	−0.935898	−	0.352271i	$-0.885410\pi$
$139$	0.0881489	−	0.242187i	0.00747669	−	0.0205420i	0.943375	+	0.331729i	$0.107632\pi$
$140$	3.75121	−	13.9997i	0.317035	−	1.18319i
$141$		0			0
$142$	4.71269	−	4.71269i	0.395480	−	0.395480i
$143$	−0.000481444	−	0.00550293i	−4.02604e−5	−	0.000460178i
$144$		0			0
$145$	1.08038	−	6.12716i	0.0897210	−	0.508833i
$146$	−0.852433	−	0.596880i	−0.0705479	−	0.0493982i
$147$		0			0
$148$	−3.14693	−	5.20546i	−0.258676	−	0.427886i
$149$			23.0030i			1.88448i	0.334937	+	0.942241i	$0.391285\pi$
$149$			23.0030i			1.88448i	−0.334937	+	0.942241i	$0.608715\pi$
$150$		0			0
$151$	−9.17838	−	1.61840i	−0.746926	−	0.131703i	−0.212786	−	0.977099i	$-0.568254\pi$
$151$	−9.17838	−	1.61840i	−0.746926	−	0.131703i	−0.534141	+	0.845396i	$0.679365\pi$
$152$	6.20524	−	2.25852i	0.503311	−	0.183190i
$153$		0			0
$154$	0.00969187	+	0.00969187i	0.000780993	+	0.000780993i
$155$	−20.5620	+	24.5048i	−1.65158	+	1.96827i
$156$		0			0
$157$	−16.4279	−	5.97928i	−1.31109	−	0.477198i	−0.410498	−	0.911861i	$-0.634645\pi$
$157$	−16.4279	−	5.97928i	−1.31109	−	0.477198i	−0.900593	+	0.434663i	$0.856867\pi$
$158$	−4.79726	−	2.76970i	−0.381649	−	0.220345i
$159$		0			0
$160$	−0.619134	−	3.51129i	−0.0489469	−	0.277591i
$161$	12.4695	−	26.7409i	0.982733	−	2.10748i
$162$		0			0
$163$	0.0228049	−	0.260661i	0.00178622	−	0.0204166i	−0.995249	−	0.0973595i	$-0.968960\pi$
$163$	0.0228049	−	0.260661i	0.00178622	−	0.0204166i	0.997036	+	0.0769429i	$0.0245159\pi$
$164$	5.53801	+	6.59994i	0.432446	+	0.515369i
$165$		0			0
$166$	−1.04599	−	1.49383i	−0.0811845	−	0.115943i
$167$	2.85957	+	4.08389i	0.221280	+	0.316021i	0.914408	−	0.404794i	$-0.132657\pi$
$167$	2.85957	+	4.08389i	0.221280	+	0.316021i	−0.693128	+	0.720815i	$0.743768\pi$
$168$		0			0
$169$	−6.63102	−	7.90254i	−0.510079	−	0.607888i
$170$	2.30423	−	26.3375i	0.176727	−	2.01999i
$171$		0			0
$172$	−2.34730	+	5.03380i	−0.178980	+	0.383823i
$173$	−0.740764	−	4.20108i	−0.0563192	−	0.319402i	0.943613	−	0.331051i	$-0.107403\pi$
$173$	−0.740764	−	4.20108i	−0.0563192	−	0.319402i	−0.999932	+	0.0116486i	$0.996292\pi$
$174$		0			0
$175$	27.1509	+	15.6756i	2.05241	+	1.18496i
$176$	0.00316846	+	0.00115322i	0.000238831	+	8.69275e-5i
$177$		0			0
$178$	−2.37874	+	2.83488i	−0.178294	+	0.212483i
$179$	−1.93041	−	1.93041i	−0.144286	−	0.144286i	0.631274	−	0.775560i	$-0.282532\pi$
$179$	−1.93041	−	1.93041i	−0.144286	−	0.144286i	−0.775560	+	0.631274i	$0.782532\pi$
$180$		0			0
$181$	−7.04931	+	2.56574i	−0.523971	+	0.190710i	−0.590444	−	0.807078i	$-0.701047\pi$
$181$	−7.04931	+	2.56574i	−0.523971	+	0.190710i	0.0664735	+	0.997788i	$0.478825\pi$
$182$	−6.55844	−	1.15643i	−0.486144	−	0.0857203i
$183$		0			0
$184$		−	7.25838i		−	0.535095i
$185$	20.8314	−	6.03427i	1.53156	−	0.443648i
$186$		0			0
$187$	0.0204806	+	0.0143407i	0.00149769	+	0.00104869i
$188$	0.166587	−	0.944760i	0.0121496	−	0.0689037i
$189$		0			0
$190$	2.05203	+	23.4548i	0.148870	+	1.70159i
$191$	−11.6275	+	11.6275i	−0.841335	+	0.841335i	−0.989033	−	0.147697i	$-0.952814\pi$
$191$	−11.6275	+	11.6275i	−0.841335	+	0.841335i	0.147697	+	0.989033i	$0.452814\pi$
$192$		0			0
$193$	−0.356593	+	1.33082i	−0.0256681	+	0.0957946i	−0.977572	−	0.210603i	$-0.932457\pi$
$193$	−0.356593	+	1.33082i	−0.0256681	+	0.0957946i	0.951904	+	0.306398i	$0.0991238\pi$
$194$	1.56291	−	4.29406i	0.112211	−	0.308296i
$195$		0			0
$196$	8.24823	−	4.76212i	0.589160	−	0.340151i
$197$	11.8613	−	2.09147i	0.845084	−	0.149011i	0.265690	−	0.964059i	$-0.414400\pi$
$197$	11.8613	−	2.09147i	0.845084	−	0.149011i	0.579394	+	0.815047i	$0.303289\pi$
$198$		0			0
$199$	−3.62271	−	13.5201i	−0.256807	−	0.958418i	−0.967076	−	0.254487i	$-0.918093\pi$
$199$	−3.62271	−	13.5201i	−0.256807	−	0.958418i	0.710269	−	0.703931i	$-0.248573\pi$
$200$	7.68310	+	0.672184i	0.543277	+	0.0475306i
$201$		0			0
$202$	−0.0389828	−	0.0835990i	−0.00274282	−	0.00588200i
$203$	5.81057	−	4.06860i	0.407822	−	0.285560i
$204$		0			0
$205$	−27.8405	+	12.9822i	−1.94446	+	0.906717i
$206$	4.51162	−	3.78570i	0.314339	−	0.263762i
$207$		0			0
$208$	−1.58246	+	0.424018i	−0.109724	+	0.0294004i
$209$	−0.0201795	−	0.00940985i	−0.00139584	−	0.000650893i
$210$		0			0
$211$	−10.0144	−	17.3454i	−0.689418	−	1.19411i	−0.972026	−	0.234871i	$-0.924533\pi$
$211$	−10.0144	−	17.3454i	−0.689418	−	1.19411i	0.282609	−	0.959235i	$-0.408800\pi$
$212$	5.74802	−	9.95586i	0.394776	−	0.683771i
$213$		0			0
$214$	3.82084	+	1.02379i	0.261187	+	0.0699850i
$215$	−15.1701	−	12.7292i	−1.03459	−	0.868126i
$216$		0			0
$217$	−36.3318	+	3.17862i	−2.46636	+	0.215779i
$218$	2.81653	+	7.73835i	0.190759	+	0.524107i
$219$		0			0
$220$	−0.00689553	+	0.00984784i	−0.000464897	+	0.000663941i
$221$	−12.1480			−0.817162
$222$		0			0
$223$	4.17196			0.279375			0.139688	−	0.990196i	$-0.455390\pi$
$223$	4.17196			0.279375			0.139688	+	0.990196i	$0.455390\pi$
$224$	2.33159	−	3.32985i	0.155786	−	0.222485i
$225$		0			0
$226$	2.37186	+	6.51662i	0.157774	+	0.433479i
$227$	1.71222	−	0.149800i	0.113644	−	0.00994255i	−0.0301919	−	0.999544i	$-0.509612\pi$
$227$	1.71222	−	0.149800i	0.113644	−	0.00994255i	0.143836	+	0.989602i	$0.454056\pi$
$228$		0			0
$229$	1.07852	+	0.904984i	0.0712705	+	0.0598030i	0.677727	−	0.735314i	$-0.262965\pi$
$229$	1.07852	+	0.904984i	0.0712705	+	0.0598030i	−0.606457	+	0.795117i	$0.707410\pi$
$230$	24.9976	+	6.69808i	1.64829	+	0.441659i
$231$		0			0
$232$	0.872496	−	1.51121i	0.0572821	−	0.0992156i
$233$	−8.03419	−	13.9156i	−0.526337	−	0.911643i	−0.999529	−	0.0306833i	$-0.990232\pi$
$233$	−8.03419	−	13.9156i	−0.526337	−	0.911643i	0.473192	−	0.880959i	$-0.343102\pi$
$234$		0			0
$235$	3.09999	+	1.44555i	0.202221	+	0.0942973i
$236$	−10.1779	+	2.72715i	−0.662523	+	0.177522i
$237$		0			0
$238$	23.0904	−	19.3751i	1.49673	−	1.25590i
$239$	−15.8497	+	7.39083i	−1.02523	+	0.478073i	−0.861138	−	0.508372i	$-0.830248\pi$
$239$	−15.8497	+	7.39083i	−1.02523	+	0.478073i	−0.164093	+	0.986445i	$0.552470\pi$
$240$		0			0
$241$	−21.6237	+	15.1410i	−1.39290	+	0.975321i	−0.394495	+	0.918898i	$0.629081\pi$
$241$	−21.6237	+	15.1410i	−1.39290	+	0.975321i	−0.998407	+	0.0564229i	$0.982030\pi$
$242$	4.64880	+	9.96938i	0.298836	+	0.640856i
$243$		0			0
$244$	10.9945	+	0.961894i	0.703850	+	0.0615789i
$245$	8.78904	+	32.8011i	0.561511	+	2.09559i
$246$		0			0
$247$	10.6540	−	1.87859i	0.677897	−	0.119532i
$248$	−7.76985	+	4.48593i	−0.493386	+	0.284857i
$249$		0			0
$250$	−3.30772	+	9.08788i	−0.209198	+	0.574768i
$251$	3.07617	−	11.4804i	0.194166	−	0.724639i	−0.798315	−	0.602240i	$-0.794275\pi$
$251$	3.07617	−	11.4804i	0.194166	−	0.724639i	0.992481	−	0.122398i	$-0.0390585\pi$
$252$		0			0
$253$	−0.0173056	+	0.0173056i	−0.00108799	+	0.00108799i
$254$	0.233823	+	2.67260i	0.0146713	+	0.167694i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−10.8686	−	7.61028i	−0.677965	−	0.474716i	0.183178	−	0.983080i	$-0.441362\pi$
$257$	−10.8686	−	7.61028i	−0.677965	−	0.474716i	−0.861142	+	0.508364i	$0.830251\pi$
$258$		0			0
$259$	21.6585	+	11.9291i	1.34580	+	0.741241i
$260$		−	5.84121i		−	0.362257i
$261$		0			0
$262$	7.88578	+	1.39048i	0.487185	+	0.0859039i
$263$	−15.0672	+	5.48401i	−0.929084	+	0.338159i	−0.761846	−	0.647758i	$-0.775707\pi$
$263$	−15.0672	+	5.48401i	−0.929084	+	0.338159i	−0.167237	+	0.985917i	$0.553485\pi$
$264$		0			0
$265$	28.9833	+	28.9833i	1.78043	+	1.78043i
$266$	−17.2544	+	20.5630i	−1.05794	+	1.26080i
$267$		0			0
$268$	−10.0040	−	3.64115i	−0.611090	−	0.222419i
$269$	14.7079	+	8.49160i	0.896755	+	0.517742i	0.876146	−	0.482046i	$-0.160106\pi$
$269$	14.7079	+	8.49160i	0.896755	+	0.517742i	0.0206093	+	0.999788i	$0.493439\pi$
$270$		0			0
$271$	5.31338	+	30.1337i	0.322765	+	1.83049i	0.524938	+	0.851141i	$0.324089\pi$
$271$	5.31338	+	30.1337i	0.322765	+	1.83049i	−0.202173	+	0.979350i	$0.564800\pi$
$272$	3.13375	−	6.72035i	0.190011	−	0.407481i
$273$		0			0
$274$	−1.07612	+	12.3001i	−0.0650106	+	0.743074i
$275$	−0.0167156	−	0.0199209i	−0.00100799	−	0.00120127i
$276$		0			0
$277$	−5.89228	−	8.41505i	−0.354033	−	0.505611i	0.602149	−	0.798383i	$-0.294311\pi$
$277$	−5.89228	−	8.41505i	−0.354033	−	0.505611i	−0.956182	+	0.292772i	$0.905422\pi$
$278$	0.147828	+	0.211120i	0.00886613	+	0.0126622i
$279$		0			0
$280$	9.31629	+	11.1027i	0.556755	+	0.663514i
$281$	−1.42594	+	16.2985i	−0.0850643	+	0.972289i	0.826989	+	0.562218i	$0.190052\pi$
$281$	−1.42594	+	16.2985i	−0.0850643	+	0.972289i	−0.912053	+	0.410071i	$0.865504\pi$
$282$		0			0
$283$	12.0051	−	25.7450i	0.713629	−	1.53038i	−0.128856	−	0.991663i	$-0.541131\pi$
$283$	12.0051	−	25.7450i	0.713629	−	1.53038i	0.842485	−	0.538719i	$-0.181092\pi$
$284$	1.15732	+	6.56350i	0.0686745	+	0.389472i
$285$		0			0
$286$	0.00478389	+	0.00276198i	0.000282877	+	0.000163319i
$287$	−32.9104	−	11.9784i	−1.94264	−	0.707062i
$288$		0			0
$289$	24.4153	−	29.0970i	1.43619	−	1.71159i
$290$	4.39939	+	4.39939i	0.258341	+	0.258341i
$291$		0			0
$292$	0.977871	−	0.355916i	0.0572256	−	0.0208284i
$293$	−10.9385	−	1.92874i	−0.639031	−	0.112678i	−0.155261	−	0.987873i	$-0.549622\pi$
$293$	−10.9385	−	1.92874i	−0.639031	−	0.112678i	−0.483770	+	0.875195i	$0.660733\pi$
$294$		0			0
$295$		−	37.5688i		−	2.18734i
$296$	6.06907	+	0.407916i	0.352757	+	0.0237097i
$297$		0			0
$298$	−18.8430	−	13.1940i	−1.09154	−	0.764307i
$299$	2.06490	−	11.7106i	0.119416	−	0.677242i
$300$		0			0
$301$	−1.96778	−	22.4918i	−0.113421	−	1.29641i
$302$	6.59022	−	6.59022i	0.379224	−	0.379224i
$303$		0			0
$304$	−1.70910	+	6.37847i	−0.0980239	+	0.365830i
$305$	−13.4585	+	36.9770i	−0.770633	+	2.11730i
$306$		0			0
$307$	−11.3461	+	6.55069i	−0.647558	+	0.373868i	−0.787520	−	0.616289i	$-0.788635\pi$
$307$	−11.3461	+	6.55069i	−0.647558	+	0.373868i	0.139962	+	0.990157i	$0.455302\pi$
$308$	−0.0134981	+	0.00238009i	−0.000769128	+	0.000135618i
$309$		0			0
$310$	−8.27929	−	30.8987i	−0.470232	−	1.75493i
$311$	27.8046	+	2.43259i	1.57665	+	0.137939i	0.841612	−	0.540083i	$-0.181607\pi$
$311$	27.8046	+	2.43259i	1.57665	+	0.137939i	0.735041	+	0.678022i	$0.237163\pi$
$312$		0			0
$313$	2.37961	+	5.10310i	0.134504	+	0.288444i	0.962011	−	0.273011i	$-0.0880195\pi$
$313$	2.37961	+	5.10310i	0.134504	+	0.288444i	−0.827507	+	0.561455i	$0.810242\pi$
$314$	14.3206	−	10.0274i	0.808159	−	0.565879i
$315$		0			0
$316$	5.02040	−	2.34105i	0.282419	−	0.131694i
$317$	−5.45144	+	4.57430i	−0.306183	+	0.256918i	−0.782912	−	0.622132i	$-0.786267\pi$
$317$	−5.45144	+	4.57430i	−0.306183	+	0.256918i	0.476729	+	0.879050i	$0.341822\pi$
$318$		0			0
$319$	−0.00568328	+	0.00152283i	−0.000318202	+	8.52621e-5i
$320$	3.23140	+	1.50683i	0.180641	+	0.0842341i
$321$		0			0
$322$	14.7527	+	25.5524i	0.822134	+	1.42398i
$323$	−24.4826	+	42.4052i	−1.36225	+	2.35949i
$324$		0			0
$325$	12.2046	+	3.27022i	0.676991	+	0.181399i
$326$	0.200441	+	0.168190i	0.0111014	+	0.00931518i
$327$		0			0
$328$	−8.58282	+	0.750900i	−0.473907	+	0.0414615i
$329$	1.33378	+	3.66452i	0.0735334	+	0.202031i
$330$		0			0
$331$	−2.76390	+	3.94725i	−0.151917	+	0.216961i	−0.887896	−	0.460044i	$-0.847834\pi$
$331$	−2.76390	+	3.94725i	−0.151917	+	0.216961i	0.735979	+	0.677005i	$0.236722\pi$
$332$	1.82363			0.100084
$333$		0			0
$334$	−4.98551			−0.272795
$335$	21.7717	−	31.0933i	1.18952	−	1.69881i
$336$		0			0
$337$	8.14958	+	22.3908i	0.443936	+	1.21970i	0.936883	+	0.349644i	$0.113697\pi$
$337$	8.14958	+	22.3908i	0.443936	+	1.21970i	−0.492947	+	0.870059i	$0.664080\pi$
$338$	10.2768	−	0.899102i	0.558983	−	0.0489047i
$339$		0			0
$340$	20.2528	+	16.9941i	1.09836	+	0.921634i
$341$	0.0292205	+	0.00782961i	0.00158238	+	0.000423997i
$342$		0			0
$343$	−5.13052	+	8.88633i	−0.277022	+	0.479817i
$344$	−2.77709	−	4.81006i	−0.149731	−	0.259341i
$345$		0			0
$346$	3.86621	+	1.80284i	0.207849	+	0.0969214i
$347$	3.72691	−	0.998623i	0.200071	−	0.0536089i	−0.157392	−	0.987536i	$-0.550309\pi$
$347$	3.72691	−	0.998623i	0.200071	−	0.0536089i	0.357463	+	0.933927i	$0.383642\pi$
$348$		0			0
$349$	−19.7307	+	16.5560i	−1.05616	+	0.886222i	−0.993728	−	0.111828i	$-0.964330\pi$
$349$	−19.7307	+	16.5560i	−1.05616	+	0.886222i	−0.0624303	+	0.998049i	$0.519885\pi$
$350$	−28.4138	+	13.2496i	−1.51878	+	0.708219i
$351$		0			0
$352$	−0.00276202	+	0.00193399i	−0.000147216	+	0.000103082i
$353$	7.25723	+	15.5632i	0.386263	+	0.828344i	0.999268	+	0.0382648i	$0.0121830\pi$
$353$	7.25723	+	15.5632i	0.386263	+	0.828344i	−0.613004	+	0.790080i	$0.710039\pi$
$354$		0			0
$355$	−23.6724	−	2.07107i	−1.25640	−	0.109921i
$356$	−0.957804	−	3.57457i	−0.0507635	−	0.189452i
$357$		0			0
$358$	2.68854	−	0.474062i	0.142094	−	0.0250550i
$359$	−2.17060	+	1.25319i	−0.114560	+	0.0661411i	−0.556185	−	0.831059i	$-0.687735\pi$
$359$	−2.17060	+	1.25319i	−0.114560	+	0.0661411i	0.441625	+	0.897200i	$0.354402\pi$
$360$		0			0
$361$	8.41570	−	23.1219i	0.442932	−	1.21694i
$362$	1.94159	−	7.24610i	0.102048	−	0.380847i
$363$		0			0
$364$	4.70906	−	4.70906i	0.246822	−	0.246822i
$365$	0.323375	+	3.69619i	0.0169262	+	0.193468i
$366$		0			0
$367$	3.37470	−	19.1389i	0.176158	−	0.999042i	−0.760641	−	0.649173i	$-0.775115\pi$
$367$	3.37470	−	19.1389i	0.176158	−	0.999042i	0.936799	−	0.349869i	$-0.113774\pi$
$368$	5.94572	+	4.16324i	0.309942	+	0.217024i
$369$		0			0
$370$	−7.00543	+	20.5252i	−0.364195	+	1.06706i
$371$			46.7314i			2.42617i
$372$		0			0
$373$	29.8587	+	5.26489i	1.54602	+	0.272606i	0.880600	−	0.473860i	$-0.157140\pi$
$373$	29.8587	+	5.26489i	1.54602	+	0.272606i	0.665424	+	0.746466i	$0.268251\pi$
$374$	−0.0234944	+	0.00855125i	−0.00121486	+	0.000442174i
$375$		0			0
$376$	0.678352	+	0.678352i	0.0349833	+	0.0349833i
$377$	1.83759	−	2.18996i	0.0946408	−	0.112788i
$378$		0			0
$379$	15.8713	+	5.77669i	0.815256	+	0.296729i	0.715793	−	0.698312i	$-0.246065\pi$
$379$	15.8713	+	5.77669i	0.815256	+	0.296729i	0.0994628	+	0.995041i	$0.468288\pi$
$380$	−20.3900	−	11.7722i	−1.04599	−	0.603900i
$381$		0			0
$382$	−2.85543	−	16.1939i	−0.146096	−	0.828554i
$383$	7.62907	−	16.3606i	0.389827	−	0.835987i	−0.609248	−	0.792980i	$-0.708528\pi$
$383$	7.62907	−	16.3606i	0.389827	−	0.835987i	0.999075	−	0.0430070i	$-0.0136938\pi$
$384$		0			0
$385$	0.00425925	−	0.0486835i	0.000217072	−	0.00248114i
$386$	−0.885612	−	1.05543i	−0.0450765	−	0.0537200i
$387$		0			0
$388$	2.62104	+	3.74324i	0.133063	+	0.190034i
$389$	0.139444	+	0.199146i	0.00707008	+	0.0100971i	0.822672	−	0.568517i	$-0.192483\pi$
$389$	0.139444	+	0.199146i	0.00707008	+	0.0100971i	−0.815601	+	0.578614i	$0.803594\pi$
$390$		0			0
$391$	34.5958	+	41.2296i	1.74958	+	2.08507i
$392$	−0.830092	+	9.48800i	−0.0419260	+	0.479216i
$393$		0			0
$394$	−5.09014	+	10.9158i	−0.256438	+	0.549932i
$395$	3.42963	+	19.4504i	0.172563	+	0.978656i
$396$		0			0
$397$	−23.1979	−	13.3933i	−1.16427	−	0.672192i	−0.211947	−	0.977281i	$-0.567980\pi$
$397$	−23.1979	−	13.3933i	−1.16427	−	0.672192i	−0.952324	+	0.305089i	$0.901314\pi$
$398$	13.1530	+	4.78729i	0.659298	+	0.239965i
$399$		0			0
$400$	−4.95747	+	5.90808i	−0.247873	+	0.295404i
$401$	17.9021	+	17.9021i	0.893988	+	0.893988i	0.994896	−	0.100907i	$-0.0321746\pi$
$401$	17.9021	+	17.9021i	0.893988	+	0.893988i	−0.100907	+	0.994896i	$0.532175\pi$
$402$		0			0
$403$	−13.8120	+	5.02715i	−0.688024	+	0.250420i
$404$	0.0908399	+	0.0160175i	0.00451945	+	0.000796902i
$405$		0			0
$406$			7.09339i			0.352039i
$407$	−0.0134974	−	0.0154426i	−0.000669044	−	0.000765460i
$408$		0			0
$409$	−2.61293	−	1.82960i	−0.129201	−	0.0904677i	0.507189	−	0.861835i	$-0.330684\pi$
$409$	−2.61293	−	1.82960i	−0.129201	−	0.0904677i	−0.636391	+	0.771367i	$0.719573\pi$
$410$	5.33422	−	30.2519i	0.263438	−	1.49403i
$411$		0			0
$412$	0.513303	+	5.86708i	0.0252886	+	0.289051i
$413$	30.2872	−	30.2872i	1.49034	−	1.49034i
$414$		0			0
$415$	−1.68285	+	6.28050i	−0.0826081	+	0.308298i
$416$	0.560325	−	1.53948i	0.0274722	−	0.0754792i
$417$		0			0
$418$	0.0192826	−	0.0111328i	0.000943141	−	0.000544523i
$419$	−18.2736	+	3.22213i	−0.892724	+	0.157411i	−0.601149	−	0.799137i	$-0.705290\pi$
$419$	−18.2736	+	3.22213i	−0.892724	+	0.157411i	−0.291575	+	0.956548i	$0.594179\pi$
$420$		0			0
$421$	−4.33743	−	16.1875i	−0.211393	−	0.788931i	−0.987405	−	0.158213i	$-0.949427\pi$
$421$	−4.33743	−	16.1875i	−0.211393	−	0.788931i	0.776012	−	0.630719i	$-0.217240\pi$
$422$	19.9525	+	1.74562i	0.971274	+	0.0849755i
$423$		0			0
$424$	4.85844	+	10.4189i	0.235947	+	0.505989i
$425$	−46.8460	+	32.8019i	−2.27237	+	1.59113i
$426$		0			0
$427$	−40.6600	+	18.9601i	−1.96768	+	0.917542i
$428$	−3.03019	+	2.54263i	−0.146470	+	0.122903i
$429$		0			0
$430$	19.1284	−	5.12544i	0.922453	−	0.247170i
$431$	33.5757	+	15.6566i	1.61728	+	0.754151i	0.999482	−	0.0321834i	$-0.0102461\pi$
$431$	33.5757	+	15.6566i	1.61728	+	0.754151i	0.617801	+	0.786335i	$0.288024\pi$
$432$		0			0
$433$	−0.479628	−	0.830741i	−0.0230495	−	0.0399228i	0.854271	−	0.519829i	$-0.174004\pi$
$433$	−0.479628	−	0.830741i	−0.0230495	−	0.0399228i	−0.877320	+	0.479906i	$0.840671\pi$
$434$	18.2353	−	31.5845i	0.875322	−	1.51610i
$435$		0			0
$436$	−7.95438	−	2.13137i	−0.380946	−	0.102074i
$437$	−36.7169	−	30.8091i	−1.75641	−	1.47380i
$438$		0			0
$439$	39.3504	−	3.44272i	1.87809	−	0.164312i	0.909952	−	0.414714i	$-0.136118\pi$
$439$	39.3504	−	3.44272i	1.87809	−	0.164312i	0.968142	+	0.250402i	$0.0805627\pi$
$440$	−0.00411176	−	0.0112970i	−0.000196021	−	0.000538562i
$441$		0			0
$442$	6.96780	−	9.95104i	0.331424	−	0.473323i
$443$	3.29403			0.156504			0.0782521	−	0.996934i	$-0.475066\pi$
$443$	3.29403			0.156504			0.0782521	+	0.996934i	$0.475066\pi$
$444$		0			0
$445$	13.1946			0.625482
$446$	−2.39294	+	3.41747i	−0.113309	+	0.161822i
$447$		0			0
$448$	1.39031	+	3.81985i	0.0656861	+	0.180471i
$449$	0.829579	−	0.0725787i	0.0391502	−	0.00342520i	−0.0675638	−	0.997715i	$-0.521523\pi$
$449$	0.829579	−	0.0725787i	0.0391502	−	0.00342520i	0.106714	+	0.994290i	$0.465967\pi$
$450$		0			0
$451$	0.0222537	+	0.0186731i	0.00104788	+	0.000879280i
$452$	−6.69855	−	1.79487i	−0.315073	−	0.0844236i
$453$		0			0
$454$	−0.859379	+	1.48849i	−0.0403326	+	0.0698582i
$455$	11.8723	+	20.5634i	0.556581	+	0.964026i
$456$		0			0
$457$	−17.4986	−	8.15973i	−0.818550	−	0.381696i	−0.0322033	−	0.999481i	$-0.510252\pi$
$457$	−17.4986	−	8.15973i	−0.818550	−	0.381696i	−0.786347	+	0.617785i	$0.788030\pi$
$458$	−1.35993	+	0.364393i	−0.0635454	+	0.0170269i
$459$		0			0
$460$	−19.8248	+	16.6350i	−0.924335	+	0.775609i
$461$	3.95034	−	1.84208i	0.183986	−	0.0857940i	−0.328443	−	0.944524i	$-0.606524\pi$
$461$	3.95034	−	1.84208i	0.183986	−	0.0857940i	0.512428	+	0.858730i	$0.328746\pi$
$462$		0			0
$463$	−2.22242	+	1.55616i	−0.103285	+	0.0723207i	−0.624078	−	0.781362i	$-0.714525\pi$
$463$	−2.22242	+	1.55616i	−0.103285	+	0.0723207i	0.520793	+	0.853683i	$0.325636\pi$
$464$	0.737465	+	1.58150i	0.0342360	+	0.0734192i
$465$		0			0
$466$	16.0072	+	1.40045i	0.741521	+	0.0648746i
$467$	−3.57825	−	13.3542i	−0.165582	−	0.617960i	−0.997965	−	0.0637597i	$-0.979691\pi$
$467$	−3.57825	−	13.3542i	−0.165582	−	0.617960i	0.832383	−	0.554200i	$-0.186976\pi$
$468$		0			0
$469$	42.6186	−	7.51481i	1.96794	−	0.347002i
$470$	−2.96221	+	1.71023i	−0.136636	+	0.0788871i
$471$		0			0
$472$	3.60383	−	9.90145i	0.165880	−	0.455751i
$473$	−0.00484705	+	0.0180895i	−0.000222868	+	0.000831754i
$474$		0			0
$475$	36.0122	−	36.0122i	1.65235	−	1.65235i
$476$	2.62708	+	30.0276i	0.120412	+	1.37631i
$477$		0			0
$478$	3.03679	−	17.2225i	0.138900	−	0.787739i
$479$	−10.1001	−	7.07219i	−0.461487	−	0.323137i	0.319607	−	0.947550i	$-0.396449\pi$
$479$	−10.1001	−	7.07219i	−0.461487	−	0.323137i	−0.781094	+	0.624414i	$0.785338\pi$
$480$		0			0
$481$	9.67574	+	2.38468i	0.441176	+	0.108732i
$482$		−	26.3976i		−	1.20238i
$483$		0			0
$484$	−10.8329	−	1.91013i	−0.492403	−	0.0868240i
$485$	−15.3103	+	5.57249i	−0.695204	+	0.253034i
$486$		0			0
$487$	−15.8450	−	15.8450i	−0.718004	−	0.718004i	0.250192	−	0.968196i	$-0.419506\pi$
$487$	−15.8450	−	15.8450i	−0.718004	−	0.718004i	−0.968196	+	0.250192i	$0.919506\pi$
$488$	−7.09412	+	8.45444i	−0.321136	+	0.382715i
$489$		0			0
$490$	−31.9103	−	11.6144i	−1.44156	−	0.524685i
$491$	8.29151	+	4.78711i	0.374191	+	0.216039i	0.675288	−	0.737554i	$-0.264019\pi$
$491$	8.29151	+	4.78711i	0.374191	+	0.216039i	−0.301097	+	0.953594i	$0.597353\pi$
$492$		0			0
$493$	2.24688	+	12.7427i	0.101194	+	0.573901i
$494$	−4.57203	+	9.80475i	−0.205705	+	0.441136i
$495$		0			0
$496$	0.781949	−	8.93771i	0.0351105	−	0.401315i
$497$	−17.4146	−	20.7539i	−0.781150	−	0.930938i
$498$		0			0
$499$	0.406534	+	0.580591i	0.0181990	+	0.0259908i	0.828148	−	0.560509i	$-0.189394\pi$
$499$	0.406534	+	0.580591i	0.0181990	+	0.0259908i	−0.809949	+	0.586500i	$0.800506\pi$
$500$	−5.54713	−	7.92212i	−0.248075	−	0.354288i
$501$		0			0
$502$	7.63980	+	9.10476i	0.340981	+	0.406365i
$503$	3.83320	−	43.8137i	0.170914	−	1.95356i	−0.110265	−	0.993902i	$-0.535170\pi$
$503$	3.83320	−	43.8137i	0.170914	−	1.95356i	0.281180	−	0.959655i	$-0.409274\pi$
$504$		0			0
$505$	−0.138991	+	0.298068i	−0.00618504	+	0.0132639i
$506$	−0.00424983	−	0.0241020i	−0.000188928	−	0.00107146i
$507$		0			0
$508$	−2.32338	−	1.34141i	−0.103084	−	0.0595153i
$509$	17.9519	+	6.53396i	0.795704	+	0.289613i	0.707705	−	0.706508i	$-0.249731\pi$
$509$	17.9519	+	6.53396i	0.795704	+	0.289613i	0.0879988	+	0.996121i	$0.471953\pi$
$510$		0			0
$511$	−2.71909	+	3.24049i	−0.120286	+	0.143351i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	12.4679	−	4.53796i	0.549938	−	0.200161i
$515$	−20.6797	−	3.64639i	−0.911257	−	0.160679i
$516$		0			0
$517$		−	0.00323469i		−	0.000142261i
$518$	−22.1946	+	10.8994i	−0.975175	+	0.478891i
$519$		0			0
$520$	4.78484	+	3.35038i	0.209829	+	0.146924i
$521$	−0.512479	+	2.90642i	−0.0224521	+	0.127332i	−0.993974	−	0.109619i	$-0.965037\pi$
$521$	−0.512479	+	2.90642i	−0.0224521	+	0.127332i	0.971522	+	0.236951i	$0.0761481\pi$
$522$		0			0
$523$	−0.994982	−	11.3727i	−0.0435075	−	0.497293i	−0.986419	−	0.164249i	$-0.947480\pi$
$523$	−0.994982	−	11.3727i	−0.0435075	−	0.497293i	0.942911	−	0.333044i	$-0.108076\pi$
$524$	−5.66211	+	5.66211i	−0.247350	+	0.247350i
$525$		0			0
$526$	4.14995	−	15.4878i	0.180947	−	0.675302i
$527$	22.7536	−	62.5149i	0.991161	−	2.72319i
$528$		0			0
$529$	−25.7072	+	14.8420i	−1.11770	+	0.645306i
$530$	−40.3659	+	7.11759i	−1.75338	+	0.309168i
$531$		0			0
$532$	−6.94751	−	25.9285i	−0.301213	−	1.12414i
$533$	−14.0611	−	1.23018i	−0.609053	−	0.0532852i
$534$		0			0
$535$	−5.96044	−	12.7822i	−0.257692	−	0.552623i
$536$	8.72071	−	6.10630i	0.376677	−	0.263752i
$537$		0			0
$538$	−15.3920	+	7.17741i	−0.663596	+	0.309440i
$539$	0.0246006	−	0.0206424i	0.00105962	−	0.000889130i
$540$		0			0
$541$	−3.33999	+	0.894949i	−0.143598	+	0.0384769i	−0.329902	−	0.944015i	$-0.607016\pi$
$541$	−3.33999	+	0.894949i	−0.143598	+	0.0384769i	0.186304	+	0.982492i	$0.440349\pi$
$542$	−27.7317	−	12.9315i	−1.19118	−	0.555456i
$543$		0			0
$544$	3.70754	+	6.42165i	0.158959	+	0.275326i
$545$	14.6807	−	25.4277i	0.628853	−	1.08920i
$546$		0			0
$547$	7.10060	+	1.90260i	0.303600	+	0.0813493i	0.407403	−	0.913249i	$-0.366434\pi$
$547$	7.10060	+	1.90260i	0.303600	+	0.0813493i	−0.103803	+	0.994598i	$0.533101\pi$
$548$	−9.45839	−	7.93653i	−0.404042	−	0.339032i
$549$		0			0
$550$	0.0259059	−	0.00226647i	0.00110463	−	9.66427e-5i
$551$	−3.94110	−	10.8281i	−0.167896	−	0.461292i
$552$		0			0
$553$	−12.9156	+	18.4454i	−0.549227	+	0.784377i
$554$	10.2729			0.436453
$555$		0			0
$556$	−0.257730			−0.0109302
$557$	19.5545	−	27.9267i	0.828551	−	1.18329i	−0.152261	−	0.988340i	$-0.548656\pi$
$557$	19.5545	−	27.9267i	0.828551	−	1.18329i	0.980813	−	0.194953i	$-0.0624556\pi$
$558$		0			0
$559$	−3.11215	−	8.55055i	−0.131630	−	0.361650i
$560$	−14.4384	+	1.26320i	−0.610135	+	0.0533799i
$561$		0			0
$562$	−12.5331	−	10.5165i	−0.528677	−	0.443612i
$563$	10.2691	+	2.75160i	0.432792	+	0.115966i	0.468636	−	0.883391i	$-0.344745\pi$
$563$	10.2691	+	2.75160i	0.432792	+	0.115966i	−0.0358445	+	0.999357i	$0.511412\pi$
$564$		0			0
$565$	12.3629	−	21.4132i	0.520113	−	0.900861i
$566$	14.2032	+	24.6007i	0.597007	+	1.03405i
$567$		0			0
$568$	−6.04032	−	2.81665i	−0.253446	−	0.118184i
$569$	−0.332333	+	0.0890483i	−0.0139321	+	0.00373310i	−0.265778	−	0.964034i	$-0.585629\pi$
$569$	−0.332333	+	0.0890483i	−0.0139321	+	0.00373310i	0.251846	+	0.967767i	$0.418962\pi$
$570$		0			0
$571$	−10.2614	+	8.61031i	−0.429425	+	0.360330i	−0.831735	−	0.555173i	$-0.812652\pi$
$571$	−10.2614	+	8.61031i	−0.429425	+	0.360330i	0.402310	+	0.915504i	$0.368207\pi$
$572$	−0.00500640	+	0.00233452i	−0.000209328	+	9.76114e-5i
$573$		0			0
$574$	28.6887	−	20.0881i	1.19744	−	0.838460i
$575$	−23.6581	−	50.7350i	−0.986612	−	2.11580i
$576$		0			0
$577$	−40.7621	−	3.56622i	−1.69695	−	0.148464i	−0.802803	−	0.596244i	$-0.796659\pi$
$577$	−40.7621	−	3.56622i	−1.69695	−	0.148464i	−0.894144	+	0.447780i	$0.852215\pi$
$578$	9.83083	+	36.6892i	0.408909	+	1.52607i
$579$		0			0
$580$	−6.12716	+	1.08038i	−0.254417	+	0.0448605i
$581$	−6.41988	+	3.70652i	−0.266342	+	0.153772i
$582$		0			0
$583$	0.0132575	−	0.0364247i	0.000549070	−	0.00150856i
$584$	−0.269335	+	1.00517i	−0.0111451	+	0.0415942i
$585$		0			0
$586$	7.85398	−	7.85398i	0.324445	−	0.324445i
$587$	−2.45733	−	28.0875i	−0.101425	−	1.15929i	−0.860906	−	0.508764i	$-0.830103\pi$
$587$	−2.45733	−	28.0875i	−0.101425	−	1.15929i	0.759481	−	0.650529i	$-0.225453\pi$
$588$		0			0
$589$	−10.2879	+	58.3453i	−0.423904	+	2.40408i
$590$	30.7746	+	21.5486i	1.26697	+	0.887142i
$591$		0			0
$592$	−3.81522	+	4.73752i	−0.156805	+	0.194711i
$593$		−	0.186078i		−	0.00764129i	−0.999993	−	0.00382064i	$-0.998784\pi$
$593$		−	0.186078i		−	0.00764129i	0.999993	−	0.00382064i	$-0.00121615\pi$
$594$		0			0
$595$	−105.838	−	18.6621i	−4.33895	−	0.765073i
$596$	21.6158	−	7.86750i	0.885416	−	0.322265i
$597$		0			0
$598$	8.40839	+	8.40839i	0.343845	+	0.343845i
$599$	−11.0025	+	13.1122i	−0.449549	+	0.535752i	−0.942456	−	0.334330i	$-0.891490\pi$
$599$	−11.0025	+	13.1122i	−0.449549	+	0.535752i	0.492907	+	0.870082i	$0.335934\pi$
$600$		0			0
$601$	36.9239	+	13.4392i	1.50616	+	0.548196i	0.957646	−	0.287948i	$-0.0929732\pi$
$601$	36.9239	+	13.4392i	1.50616	+	0.548196i	0.548510	+	0.836144i	$0.315195\pi$
$602$	19.5529	+	11.2889i	0.796917	+	0.460100i
$603$		0			0
$604$	1.61840	+	9.17838i	0.0658516	+	0.373463i
$605$	16.5751	−	35.5453i	0.673872	−	1.44512i
$606$		0			0
$607$	−2.23605	+	25.5581i	−0.0907583	+	1.03737i	0.805132	+	0.593096i	$0.202095\pi$
$607$	−2.23605	+	25.5581i	−0.0907583	+	1.03737i	−0.895890	+	0.444276i	$0.853461\pi$
$608$	−4.24463	−	5.05855i	−0.172143	−	0.205151i
$609$		0			0
$610$	−22.5703	−	32.2337i	−0.913844	−	1.30510i
$611$	0.901467	+	1.28743i	0.0364695	+	0.0520838i
$612$		0			0
$613$	25.5060	+	30.3968i	1.03018	+	1.22772i	0.973348	+	0.229333i	$0.0736543\pi$
$613$	25.5060	+	30.3968i	1.03018	+	1.22772i	0.0568284	+	0.998384i	$0.481901\pi$
$614$	1.14186	−	13.0515i	0.0460818	−	0.526717i
$615$		0			0
$616$	0.00579256	−	0.0124222i	0.000233389	−	0.000500504i
$617$	5.43974	+	30.8503i	0.218996	+	1.24199i	0.873836	+	0.486220i	$0.161625\pi$
$617$	5.43974	+	30.8503i	0.218996	+	1.24199i	−0.654841	+	0.755767i	$0.727264\pi$
$618$		0			0
$619$	−1.93017	−	1.11439i	−0.0775803	−	0.0447910i	0.460708	−	0.887552i	$-0.347596\pi$
$619$	−1.93017	−	1.11439i	−0.0775803	−	0.0447910i	−0.538288	+	0.842761i	$0.680929\pi$
$620$	30.0596	+	10.9408i	1.20722	+	0.439393i
$621$		0			0
$622$	−17.9407	+	21.3809i	−0.719357	+	0.857296i
$623$	10.6372	+	10.6372i	0.426169	+	0.426169i
$624$		0			0
$625$	−3.83427	+	1.39556i	−0.153371	+	0.0558224i
$626$	−5.54510	−	0.977751i	−0.221627	−	0.0390788i
$627$		0			0
$628$			17.4822i			0.697617i
$629$	−36.4183	+	26.6101i	−1.45209	+	1.06101i
$630$		0			0
$631$	7.89783	+	5.53012i	0.314407	+	0.220150i	0.720119	−	0.693851i	$-0.244087\pi$
$631$	7.89783	+	5.53012i	0.314407	+	0.220150i	−0.405711	+	0.914001i	$0.632976\pi$
$632$	−0.961906	+	5.45524i	−0.0382626	+	0.216998i
$633$		0			0
$634$	−0.620230	−	7.08927i	−0.0246325	−	0.281551i
$635$	6.76379	−	6.76379i	0.268413	−	0.268413i
$636$		0			0
$637$	−4.03845	+	15.0717i	−0.160009	+	0.597163i
$638$	0.00201236	−	0.00552893i	7.96703e−5	−	0.000218892i
$639$		0			0
$640$	−3.08777	+	1.78273i	−0.122055	+	0.0704684i
$641$	17.6505	−	3.11225i	0.697152	−	0.122927i	0.186169	−	0.982518i	$-0.440393\pi$
$641$	17.6505	−	3.11225i	0.697152	−	0.122927i	0.510983	+	0.859591i	$0.329282\pi$
$642$		0			0
$643$	0.609877	+	2.27609i	0.0240512	+	0.0897603i	0.976908	−	0.213659i	$-0.0685383\pi$
$643$	0.609877	+	2.27609i	0.0240512	+	0.0897603i	−0.952857	+	0.303420i	$0.901872\pi$
$644$	−29.3930	−	2.57156i	−1.15825	−	0.101334i
$645$		0			0
$646$	−20.6936	−	44.3776i	−0.814180	−	1.74601i
$647$	0.151597	−	0.106150i	0.00595990	−	0.00417317i	−0.570593	−	0.821233i	$-0.693286\pi$
$647$	0.151597	−	0.106150i	0.00595990	−	0.00417317i	0.576553	+	0.817060i	$0.304398\pi$
$648$		0			0
$649$	−0.0321996	+	0.0150149i	−0.00126395	+	0.000589387i
$650$	−9.67909	+	8.12172i	−0.379645	+	0.318560i
$651$		0			0
$652$	−0.252741	+	0.0677219i	−0.00989812	+	0.00265219i
$653$	10.5738	+	4.93064i	0.413784	+	0.192951i	0.618351	−	0.785902i	$-0.287801\pi$
$653$	10.5738	+	4.93064i	0.413784	+	0.192951i	−0.204567	+	0.978853i	$0.565579\pi$
$654$		0			0
$655$	−14.2751	−	24.7251i	−0.557773	−	0.966091i
$656$	4.30780	−	7.46134i	0.168192	−	0.291316i
$657$		0			0
$658$	−3.76682	−	1.00932i	−0.146846	−	0.0393472i
$659$	27.0265	+	22.6779i	1.05280	+	0.883406i	0.993385	−	0.114827i	$-0.0366314\pi$
$659$	27.0265	+	22.6779i	1.05280	+	0.883406i	0.0594169	+	0.998233i	$0.481076\pi$
$660$		0			0
$661$	−24.1453	+	2.11244i	−0.939143	+	0.0821644i	−0.546438	−	0.837500i	$-0.684016\pi$
$661$	−24.1453	+	2.11244i	−0.939143	+	0.0821644i	−0.392706	+	0.919664i	$0.628461\pi$
$662$	−1.64809	−	4.52810i	−0.0640550	−	0.175990i
$663$		0			0
$664$	−1.04599	+	1.49383i	−0.0405922	+	0.0579717i
$665$	95.7079			3.71139
$666$		0			0
$667$	−12.6658			−0.490422
$668$	2.85957	−	4.08389i	0.110640	−	0.158010i
$669$		0			0
$670$	12.9824	+	35.6687i	0.501552	+	1.37800i
$671$	0.0370712	−	0.00324331i	0.00143112	−	0.000125207i
$672$		0			0
$673$	−11.7508	−	9.86011i	−0.452961	−	0.380079i	0.387572	−	0.921839i	$-0.373314\pi$
$673$	−11.7508	−	9.86011i	−0.452961	−	0.380079i	−0.840533	+	0.541760i	$0.817758\pi$
$674$	−23.0159	−	6.16708i	−0.886538	−	0.237547i
$675$		0			0
$676$	−5.15802	+	8.93395i	−0.198385	+	0.343613i
$677$	0.585639	+	1.01436i	0.0225079	+	0.0389849i	0.877060	−	0.480381i	$-0.159502\pi$
$677$	0.585639	+	1.01436i	0.0225079	+	0.0389849i	−0.854552	+	0.519366i	$0.826168\pi$
$678$		0			0
$679$	−16.8352	−	7.85040i	−0.646077	−	0.301271i
$680$	−25.5373	+	6.84269i	−0.979309	+	0.262405i
$681$		0			0
$682$	−0.0231738	+	0.0194452i	−0.000887372	+	0.000744594i
$683$	13.0458	−	6.08336i	0.499184	−	0.232773i	−0.156684	−	0.987649i	$-0.550081\pi$
$683$	13.0458	−	6.08336i	0.499184	−	0.232773i	0.655868	+	0.754876i	$0.272303\pi$
$684$		0			0
$685$	36.0614	−	25.2505i	1.37783	−	0.964770i
$686$	−4.33651	−	9.29967i	−0.165569	−	0.355063i
$687$		0			0
$688$	5.53304	+	0.484079i	0.210945	+	0.0184553i
$689$	4.87453	+	18.1920i	0.185705	+	0.693060i
$690$		0			0
$691$	10.9165	−	1.92487i	0.415283	−	0.0732257i	0.0378972	−	0.999282i	$-0.487934\pi$
$691$	10.9165	−	1.92487i	0.415283	−	0.0732257i	0.377386	+	0.926056i	$0.376823\pi$
$692$	−3.69437	+	2.13295i	−0.140439	+	0.0810824i
$693$		0			0
$694$	−1.31964	+	3.62569i	−0.0500930	+	0.137629i
$695$	0.237835	−	0.887613i	0.00902161	−	0.0336691i
$696$		0			0
$697$	45.1738	−	45.1738i	1.71108	−	1.71108i
$698$	−2.24483	−	25.6585i	−0.0849681	−	0.971190i
$699$		0			0
$700$	5.44407	−	30.8748i	0.205766	−	1.16696i
$701$	−34.4672	−	24.1342i	−1.30181	−	0.911536i	−0.302672	−	0.953095i	$-0.597879\pi$
$701$	−34.4672	−	24.1342i	−1.30181	−	0.911536i	−0.999136	+	0.0415592i	$0.986767\pi$
$702$		0			0
$703$	27.8244	−	28.9693i	1.04942	−	1.09260i
$704$		−	0.00337180i		−	0.000127079i
$705$		0			0
$706$	−16.9112	−	2.98190i	−0.636461	−	0.112225i
$707$	−0.352348	+	0.128244i	−0.0132514	+	0.00482312i
$708$		0			0
$709$	−27.3983	−	27.3983i	−1.02896	−	1.02896i	−0.999568	−	0.0293967i	$-0.990641\pi$
$709$	−27.3983	−	27.3983i	−1.02896	−	1.02896i	−0.0293967	−	0.999568i	$-0.509359\pi$
$710$	15.2745	−	18.2034i	0.573241	−	0.683162i
$711$		0			0
$712$	3.47749	+	1.26570i	0.130325	+	0.0474343i
$713$	56.3965	+	32.5606i	2.11207	+	1.21940i
$714$		0			0
$715$	−0.00342007	−	0.0193962i	−0.000127903	−	0.000725376i
$716$	−1.15375	+	2.47424i	−0.0431178	+	0.0924665i
$717$		0			0
$718$	0.218446	−	2.49685i	0.00815234	−	0.0931817i
$719$	10.4060	+	12.4014i	0.388079	+	0.462495i	0.924347	−	0.381553i	$-0.124611\pi$
$719$	10.4060	+	12.4014i	0.388079	+	0.462495i	−0.536268	+	0.844048i	$0.680166\pi$
$720$		0			0
$721$	−13.7319	−	19.6112i	−0.511402	−	0.730358i
$722$	14.1133	+	20.1559i	0.525244	+	0.750126i
$723$		0			0
$724$	4.82201	+	5.74665i	0.179209	+	0.213572i
$725$	1.17296	−	13.4069i	0.0435625	−	0.497921i
$726$		0			0
$727$	−4.15492	+	8.91025i	−0.154097	+	0.330463i	−0.968167	−	0.250304i	$-0.919469\pi$
$727$	−4.15492	+	8.91025i	−0.154097	+	0.330463i	0.814070	+	0.580767i	$0.197247\pi$
$728$	1.15643	+	6.55844i	0.0428601	+	0.243072i
$729$		0			0
$730$	−3.21323	−	1.85516i	−0.118927	−	0.0686624i
$731$	38.7009	+	14.0860i	1.43141	+	0.520989i
$732$		0			0
$733$	−20.1387	+	24.0004i	−0.743840	+	0.886474i	−0.996712	−	0.0810257i	$-0.974180\pi$
$733$	−20.1387	+	24.0004i	−0.743840	+	0.886474i	0.252872	+	0.967500i	$0.418625\pi$
$734$	13.7420	+	13.7420i	0.507227	+	0.507227i
$735$		0			0
$736$	−6.82065	+	2.48251i	−0.251412	+	0.0915066i
$737$	−0.0353509	−	0.00623332i	−0.00130217	−	0.000229607i
$738$		0			0
$739$		−	2.78918i		−	0.102602i	−0.998683	−	0.0513008i	$-0.983663\pi$
$739$		−	2.78918i		−	0.102602i	0.998683	−	0.0513008i	$-0.0163367\pi$
$740$	−12.7951	−	17.5113i	−0.470358	−	0.643728i
$741$		0			0
$742$	−38.2801	−	26.8040i	−1.40531	−	0.984007i
$743$	−1.20114	+	6.81200i	−0.0440655	+	0.249908i	−0.998881	−	0.0472908i	$-0.984941\pi$
$743$	−1.20114	+	6.81200i	−0.0440655	+	0.249908i	0.954816	+	0.297199i	$0.0960524\pi$
$744$		0			0
$745$	7.14818	+	81.7041i	0.261889	+	2.99341i
$746$	−21.4390	+	21.4390i	−0.784937	+	0.784937i
$747$		0			0
$748$	0.00647104	−	0.0241502i	0.000236605	−	0.000883020i
$749$	5.49956	−	15.1099i	0.200950	−	0.552104i
$750$		0			0
$751$	21.0539	−	12.1555i	0.768267	−	0.443559i	−0.0639889	−	0.997951i	$-0.520382\pi$
$751$	21.0539	−	12.1555i	0.768267	−	0.443559i	0.832256	+	0.554391i	$0.187049\pi$
$752$	−0.944760	+	0.166587i	−0.0344519	+	0.00607479i
$753$		0			0
$754$	0.739908	+	2.76137i	0.0269459	+	0.100563i
$755$	−33.1035	−	2.89618i	−1.20476	−	0.105403i
$756$		0			0
$757$	18.0944	+	38.8035i	0.657651	+	1.41034i	0.898151	+	0.439687i	$0.144911\pi$
$757$	18.0944	+	38.8035i	0.657651	+	1.41034i	−0.240500	+	0.970649i	$0.577311\pi$
$758$	−13.8354	+	9.68766i	−0.502525	+	0.351872i
$759$		0			0
$760$	21.3384	−	9.95028i	0.774027	−	0.360935i
$761$	−37.5989	+	31.5493i	−1.36296	+	1.14366i	−0.387905	+	0.921700i	$0.626801\pi$
$761$	−37.5989	+	31.5493i	−1.36296	+	1.14366i	−0.975056	+	0.221960i	$0.928755\pi$
$762$		0			0
$763$	32.3346	−	8.66402i	1.17059	−	0.313659i
$764$	14.9031	+	6.94943i	0.539175	+	0.251422i
$765$		0			0
$766$	9.02596	+	15.6334i	0.326121	+	0.564858i
$767$	8.63121	−	14.9497i	0.311655	−	0.539802i
$768$		0			0
$769$	−4.95709	−	1.32825i	−0.178757	−	0.0478979i	0.168330	−	0.985731i	$-0.446163\pi$
$769$	−4.95709	−	1.32825i	−0.178757	−	0.0478979i	−0.347087	+	0.937833i	$0.612829\pi$
$770$	0.0374362	+	0.0314127i	0.00134911	+	0.00113203i
$771$		0			0
$772$	1.37253	−	0.120080i	0.0493983	−	0.00432179i
$773$	9.91545	+	27.2425i	0.356634	+	0.979844i	0.980189	+	0.198064i	$0.0634655\pi$
$773$	9.91545	+	27.2425i	0.356634	+	0.979844i	−0.623555	+	0.781779i	$0.714312\pi$
$774$		0			0
$775$	−39.6886	+	56.6812i	−1.42566	+	2.03605i
$776$	−4.56965			−0.164041
$777$		0			0
$778$	−0.243113			−0.00871601
$779$	−32.6325	+	46.6040i	−1.16918	+	1.66976i
$780$		0			0
$781$	0.00768595	+	0.0211170i	0.000275025	+	0.000755625i
$782$	−53.6167	+	4.69085i	−1.91733	+	0.167744i
$783$		0			0
$784$	−7.29599	−	6.12206i	−0.260571	−	0.218645i

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.55188 - 0.310750i) q^{5} +(3.11397 + 2.61293i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.55188 - 0.310750i) q^{5} +(3.11397 + 2.61293i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-1.78273 + 3.08777i) q^{10} +(-0.00168590 - 0.00292006i) q^{11} +(1.48479 + 0.692367i) q^{13} +(-3.92649 + 1.05210i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-6.72035 + 3.13375i) q^{17} +(5.40925 - 3.78760i) q^{19} +(-1.50683 - 3.23140i) q^{20} +(0.00335897 + 0.000293872i) q^{22} +(-1.87861 - 7.01106i) q^{23} +(7.59528 - 1.33925i) q^{25} +(-1.41879 + 0.819140i) q^{26} +(1.39031 - 3.81985i) q^{28} +(0.451637 - 1.68553i) q^{29} +(-6.34406 + 6.34406i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(1.28762 - 7.30243i) q^{34} +(11.8724 + 8.31317i) q^{35} +(5.96785 - 1.17677i) q^{37} +6.60347i q^{38} +(3.51129 + 0.619134i) q^{40} +(-8.09602 + 2.94671i) q^{41} +(-3.92740 - 3.92740i) q^{43} +(-0.00216735 + 0.00258295i) q^{44} +(6.82065 + 2.48251i) q^{46} +(0.830808 + 0.479667i) q^{47} +(1.65387 + 9.37955i) q^{49} +(-3.25942 + 6.98986i) q^{50} +(0.142786 - 1.63205i) q^{52} +(7.38951 + 8.80648i) q^{53} +(-0.00689553 - 0.00984784i) q^{55} +(2.33159 + 3.32985i) q^{56} +(1.12166 + 1.33674i) q^{58} +(0.918352 - 10.4968i) q^{59} +(-4.66422 + 10.0025i) q^{61} +(-1.55795 - 8.83555i) q^{62} +(0.866025 + 0.500000i) q^{64} +(5.48894 + 1.99781i) q^{65} +(6.84313 - 8.15532i) q^{67} +(5.24325 + 5.24325i) q^{68} +(-13.6195 + 4.95709i) q^{70} +(-6.56350 - 1.15732i) q^{71} +1.04063i q^{73} +(-2.45906 + 5.56354i) q^{74} +(-5.40925 - 3.78760i) q^{76} +(0.00238009 - 0.0134981i) q^{77} +(0.482790 + 5.51832i) q^{79} +(-2.52116 + 2.52116i) q^{80} +(2.22988 - 8.32204i) q^{82} +(-0.623717 + 1.71365i) q^{83} +(-22.8961 + 13.2191i) q^{85} +(5.46980 - 0.964473i) q^{86} +(-0.000872686 - 0.00325691i) q^{88} +(3.68659 + 0.322535i) q^{89} +(2.81447 + 6.03566i) q^{91} +(-5.94572 + 4.16324i) q^{92} +(-0.869453 + 0.405432i) q^{94} +(18.0360 - 15.1340i) q^{95} +(-4.41394 + 1.18271i) q^{97} +(-8.63189 - 4.02512i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more