LMFDB - Embedded newform 144.4.k.a.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("144.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 $ x^10 - 2x^9 - x^8 + 6x^7 + 14x^6 - 80x^5 + 56x^4 + 96x^3 - 64x^2 - 512x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.3
Root			$-1.62580 + 1.16481i$ of defining polynomial
Character	$\chi$	$=$	144.109
Dual form			144.4.k.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.460984 - 2.79061i) q^{2} +(-7.57499 + 2.57285i) q^{4} +(-8.22587 + 8.22587i) q^{5} -2.67171i q^{7} +(10.6718 + 19.9528i) q^{8} +O(q^{10})$	\(q+(-0.460984 - 2.79061i) q^{2} +(-7.57499 + 2.57285i) q^{4} +(-8.22587 + 8.22587i) q^{5} -2.67171i q^{7} +(10.6718 + 19.9528i) q^{8} +(26.7472 + 19.1632i) q^{10} +(45.2213 - 45.2213i) q^{11} +(35.3968 + 35.3968i) q^{13} +(-7.45568 + 1.23161i) q^{14} +(50.7609 - 38.9786i) q^{16} +72.4991 q^{17} +(19.4427 + 19.4427i) q^{19} +(41.1470 - 83.4748i) q^{20} +(-147.041 - 105.349i) q^{22} +139.462i q^{23} -10.3299i q^{25} +(82.4612 - 115.096i) q^{26} +(6.87389 + 20.2381i) q^{28} +(-66.0434 - 66.0434i) q^{29} +188.682 q^{31} +(-132.174 - 123.685i) q^{32} +(-33.4209 - 202.317i) q^{34} +(21.9771 + 21.9771i) q^{35} +(-84.0653 + 84.0653i) q^{37} +(45.2941 - 63.2196i) q^{38} +(-251.914 - 76.3445i) q^{40} -104.629i q^{41} +(-31.4857 + 31.4857i) q^{43} +(-226.203 + 458.898i) q^{44} +(389.183 - 64.2896i) q^{46} +488.151 q^{47} +335.862 q^{49} +(-28.8266 + 4.76190i) q^{50} +(-359.201 - 177.060i) q^{52} +(-149.560 + 149.560i) q^{53} +743.968i q^{55} +(53.3080 - 28.5118i) q^{56} +(-153.856 + 214.746i) q^{58} +(-284.698 + 284.698i) q^{59} +(-228.069 - 228.069i) q^{61} +(-86.9792 - 526.537i) q^{62} +(-284.227 + 425.863i) q^{64} -582.338 q^{65} +(139.151 + 139.151i) q^{67} +(-549.180 + 186.529i) q^{68} +(51.1984 - 71.4606i) q^{70} +453.655i q^{71} -259.747i q^{73} +(273.346 + 195.841i) q^{74} +(-197.301 - 97.2550i) q^{76} +(-120.818 - 120.818i) q^{77} +323.190 q^{79} +(-96.9197 + 738.185i) q^{80} +(-291.979 + 48.2323i) q^{82} +(563.897 + 563.897i) q^{83} +(-596.368 + 596.368i) q^{85} +(102.379 + 73.3499i) q^{86} +(1384.88 + 419.700i) q^{88} -866.853i q^{89} +(94.5697 - 94.5697i) q^{91} +(-358.814 - 1056.42i) q^{92} +(-225.030 - 1362.24i) q^{94} -319.866 q^{95} -936.077 q^{97} +(-154.827 - 937.259i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) $ 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8	$ 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8 - 68 * q^10 - 18 * q^11 - 2 * q^13 - 188 * q^14 + 280 * q^16 + 4 * q^17 - 26 * q^19 + 196 * q^20 - 588 * q^22 + 264 * q^26 + 280 * q^28 + 202 * q^29 + 368 * q^31 - 968 * q^32 + 436 * q^34 - 476 * q^35 - 10 * q^37 + 1232 * q^38 - 1336 * q^40 - 838 * q^43 - 868 * q^44 + 1132 * q^46 + 944 * q^47 + 94 * q^49 - 726 * q^50 - 236 * q^52 + 378 * q^53 + 488 * q^56 + 8 * q^58 - 1706 * q^59 + 910 * q^61 + 80 * q^62 + 512 * q^64 + 492 * q^65 + 1942 * q^67 + 880 * q^68 + 160 * q^70 + 452 * q^74 - 1228 * q^76 + 268 * q^77 - 4416 * q^79 + 2648 * q^80 - 704 * q^82 + 2562 * q^83 - 12 * q^85 - 3764 * q^86 + 1528 * q^88 + 3332 * q^91 - 632 * q^92 - 3248 * q^94 - 6900 * q^95 - 4 * q^97 - 314 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.460984	−	2.79061i	−0.162982	−	0.986629i
$2$	−0.460984	−	2.79061i	−0.162982	−	0.986629i
$3$		0			0
$3$		0			0
$4$	−7.57499	+	2.57285i	−0.946874	+	0.321606i
$5$	−8.22587	+	8.22587i	−0.735744	+	0.735744i	−0.971751	−	0.236007i	$-0.924161\pi$
$5$	−8.22587	+	8.22587i	−0.735744	+	0.735744i	0.236007	+	0.971751i	$0.424161\pi$
$6$		0			0
$7$		−	2.67171i		−	0.144259i	−0.997395	−	0.0721293i	$-0.977021\pi$
$7$		−	2.67171i		−	0.144259i	0.997395	−	0.0721293i	$-0.0229794\pi$
$8$	10.6718	+	19.9528i	0.471630	+	0.881797i
$9$		0			0
$10$	26.7472	+	19.1632i	0.845820	+	0.605993i
$11$	45.2213	−	45.2213i	1.23952	−	1.23952i	0.279323	−	0.960197i	$-0.409890\pi$
$11$	45.2213	−	45.2213i	1.23952	−	1.23952i	0.960197	−	0.279323i	$-0.0901099\pi$
$12$		0			0
$13$	35.3968	+	35.3968i	0.755176	+	0.755176i	0.975440	−	0.220264i	$-0.0706918\pi$
$13$	35.3968	+	35.3968i	0.755176	+	0.755176i	−0.220264	+	0.975440i	$0.570692\pi$
$14$	−7.45568	+	1.23161i	−0.142330	+	0.0235116i
$15$		0			0
$16$	50.7609	−	38.9786i	0.793139	−	0.609041i
$17$	72.4991			1.03433			0.517165	−	0.855886i	$-0.326987\pi$
$17$	72.4991			1.03433			0.517165	+	0.855886i	$0.326987\pi$
$18$		0			0
$19$	19.4427	+	19.4427i	0.234761	+	0.234761i	0.814676	−	0.579916i	$-0.196915\pi$
$19$	19.4427	+	19.4427i	0.234761	+	0.234761i	−0.579916	+	0.814676i	$0.696915\pi$
$20$	41.1470	−	83.4748i	0.460037	−	0.933277i
$21$		0			0
$22$	−147.041	−	105.349i	−1.42497	−	1.02093i
$23$			139.462i			1.26434i	0.774830	+	0.632170i	$0.217835\pi$
$23$			139.462i			1.26434i	−0.774830	+	0.632170i	$0.782165\pi$
$24$		0			0
$25$		−	10.3299i		−	0.0826390i
$26$	82.4612	−	115.096i	0.621999	−	0.868159i
$27$		0			0
$28$	6.87389	+	20.2381i	0.0463944	+	0.136595i
$29$	−66.0434	−	66.0434i	−0.422895	−	0.422895i	0.463304	−	0.886199i	$-0.346664\pi$
$29$	−66.0434	−	66.0434i	−0.422895	−	0.422895i	−0.886199	+	0.463304i	$0.846664\pi$
$30$		0			0
$31$	188.682			1.09317			0.546584	−	0.837404i	$-0.315928\pi$
$31$	188.682			1.09317			0.546584	+	0.837404i	$0.315928\pi$
$32$	−132.174	−	123.685i	−0.730165	−	0.683271i
$33$		0			0
$34$	−33.4209	−	202.317i	−0.168577	−	1.02050i
$35$	21.9771	+	21.9771i	0.106137	+	0.106137i
$36$		0			0
$37$	−84.0653	+	84.0653i	−0.373520	+	0.373520i	−0.868758	−	0.495237i	$-0.835081\pi$
$37$	−84.0653	+	84.0653i	−0.373520	+	0.373520i	0.495237	+	0.868758i	$0.335081\pi$
$38$	45.2941	−	63.2196i	0.193360	−	0.269884i
$39$		0			0
$40$	−251.914	−	76.3445i	−0.995776	−	0.301778i
$41$		−	104.629i		−	0.398545i	−0.979944	−	0.199272i	$-0.936142\pi$
$41$		−	104.629i		−	0.398545i	0.979944	−	0.199272i	$-0.0638578\pi$
$42$		0			0
$43$	−31.4857	+	31.4857i	−0.111663	+	0.111663i	−0.760731	−	0.649067i	$-0.775159\pi$
$43$	−31.4857	+	31.4857i	−0.111663	+	0.111663i	0.649067	+	0.760731i	$0.275159\pi$
$44$	−226.203	+	458.898i	−0.775032	+	1.57231i
$45$		0			0
$46$	389.183	−	64.2896i	1.24743	−	0.206065i
$47$	488.151			1.51498			0.757491	−	0.652846i	$-0.226425\pi$
$47$	488.151			1.51498			0.757491	+	0.652846i	$0.226425\pi$
$48$		0			0
$49$	335.862			0.979189
$50$	−28.8266	+	4.76190i	−0.0815341	+	0.0134687i
$51$		0			0
$52$	−359.201	−	177.060i	−0.957926	−	0.472187i
$53$	−149.560	+	149.560i	−0.387617	+	0.387617i	−0.873837	−	0.486220i	$-0.838376\pi$
$53$	−149.560	+	149.560i	−0.387617	+	0.387617i	0.486220	+	0.873837i	$0.338376\pi$
$54$		0			0
$55$			743.968i			1.82394i
$56$	53.3080	−	28.5118i	0.127207	−	0.0680366i
$57$		0			0
$58$	−153.856	+	214.746i	−0.348316	+	0.486165i
$59$	−284.698	+	284.698i	−0.628212	+	0.628212i	−0.947618	−	0.319406i	$-0.896517\pi$
$59$	−284.698	+	284.698i	−0.628212	+	0.628212i	0.319406	+	0.947618i	$0.396517\pi$
$60$		0			0
$61$	−228.069	−	228.069i	−0.478709	−	0.478709i	0.426010	−	0.904719i	$-0.359919\pi$
$61$	−228.069	−	228.069i	−0.478709	−	0.478709i	−0.904719	+	0.426010i	$0.859919\pi$
$62$	−86.9792	−	526.537i	−0.178167	−	1.07855i
$63$		0			0
$64$	−284.227	+	425.863i	−0.555131	+	0.831763i
$65$	−582.338			−1.11123
$66$		0			0
$67$	139.151	+	139.151i	0.253730	+	0.253730i	0.822498	−	0.568768i	$-0.192580\pi$
$67$	139.151	+	139.151i	0.253730	+	0.253730i	−0.568768	+	0.822498i	$0.692580\pi$
$68$	−549.180	+	186.529i	−0.979380	+	0.332647i
$69$		0			0
$70$	51.1984	−	71.4606i	0.0874197	−	0.122017i
$71$			453.655i			0.758294i	0.925336	+	0.379147i	$0.123783\pi$
$71$			453.655i			0.758294i	−0.925336	+	0.379147i	$0.876217\pi$
$72$		0			0
$73$		−	259.747i		−	0.416454i	−0.978081	−	0.208227i	$-0.933231\pi$
$73$		−	259.747i		−	0.416454i	0.978081	−	0.208227i	$-0.0667692\pi$
$74$	273.346	+	195.841i	0.429403	+	0.307649i
$75$		0			0
$76$	−197.301	−	97.2550i	−0.297789	−	0.146788i
$77$	−120.818	−	120.818i	−0.178811	−	0.178811i
$78$		0			0
$79$	323.190			0.460275			0.230138	−	0.973158i	$-0.426082\pi$
$79$	323.190			0.460275			0.230138	+	0.973158i	$0.426082\pi$
$80$	−96.9197	+	738.185i	−0.135449	+	1.03165i
$81$		0			0
$82$	−291.979	+	48.2323i	−0.393216	+	0.0649557i
$83$	563.897	+	563.897i	0.745732	+	0.745732i	0.973674	−	0.227943i	$-0.0732000\pi$
$83$	563.897	+	563.897i	0.745732	+	0.745732i	−0.227943	+	0.973674i	$0.573200\pi$
$84$		0			0
$85$	−596.368	+	596.368i	−0.761002	+	0.761002i
$86$	102.379	+	73.3499i	0.128369	+	0.0919711i
$87$		0			0
$88$	1384.88	+	419.700i	1.67760	+	0.508411i
$89$		−	866.853i		−	1.03243i	−0.856459	−	0.516215i	$-0.827341\pi$
$89$		−	866.853i		−	1.03243i	0.856459	−	0.516215i	$-0.172659\pi$
$90$		0			0
$91$	94.5697	−	94.5697i	0.108941	−	0.108941i
$92$	−358.814	−	1056.42i	−0.406619	−	1.19717i
$93$		0			0
$94$	−225.030	−	1362.24i	−0.246915	−	1.49472i
$95$	−319.866			−0.345448
$96$		0			0
$97$	−936.077			−0.979837			−0.489919	−	0.871768i	$-0.662974\pi$
$97$	−936.077			−0.979837			−0.489919	+	0.871768i	$0.662974\pi$
$98$	−154.827	−	937.259i	−0.159591	−	0.966097i
$99$		0			0
$100$	26.5772	+	78.2487i	0.0265772	+	0.0782487i
$101$	1.58844	−	1.58844i	0.00156491	−	0.00156491i	−0.706324	−	0.707889i	$-0.749648\pi$
$101$	1.58844	−	1.58844i	0.00156491	−	0.00156491i	0.707889	+	0.706324i	$0.249648\pi$
$102$		0			0
$103$		−	1388.28i		−	1.32807i	−0.747700	−	0.664036i	$-0.768842\pi$
$103$		−	1388.28i		−	1.32807i	0.747700	−	0.664036i	$-0.231158\pi$
$104$	−328.518	+	1084.01i	−0.309749	+	1.02208i
$105$		0			0
$106$	486.310	+	348.420i	0.445609	+	0.319260i
$107$	821.526	−	821.526i	0.742243	−	0.742243i	−0.230767	−	0.973009i	$-0.574123\pi$
$107$	821.526	−	821.526i	0.742243	−	0.742243i	0.973009	+	0.230767i	$0.0741234\pi$
$108$		0			0
$109$	532.797	+	532.797i	0.468190	+	0.468190i	0.901328	−	0.433138i	$-0.142594\pi$
$109$	532.797	+	532.797i	0.468190	+	0.468190i	−0.433138	+	0.901328i	$0.642594\pi$
$110$	2076.12	−	342.957i	1.79955	−	0.297270i
$111$		0			0
$112$	−104.139	−	135.618i	−0.0878593	−	0.114417i
$113$	67.2680			0.0560003			0.0280002	−	0.999608i	$-0.491086\pi$
$113$	67.2680			0.0560003			0.0280002	+	0.999608i	$0.491086\pi$
$114$		0			0
$115$	−1147.19	−	1147.19i	−0.930230	−	0.930230i
$116$	670.198	+	330.359i	0.536434	+	0.264423i
$117$		0			0
$118$	925.722	+	663.240i	0.722200	+	0.517425i
$119$		−	193.696i		−	0.149211i
$120$		0			0
$121$		−	2758.92i		−	2.07282i
$122$	−531.315	+	741.587i	−0.394287	+	0.550329i
$123$		0			0
$124$	−1429.26	+	485.449i	−1.03509	+	0.351570i
$125$	−943.262	−	943.262i	−0.674943	−	0.674943i
$126$		0			0
$127$	1903.59			1.33005			0.665026	−	0.746820i	$-0.268421\pi$
$127$	1903.59			1.33005			0.665026	+	0.746820i	$0.268421\pi$
$128$	1319.44	+	596.851i	0.911118	+	0.412146i
$129$		0			0
$130$	268.448	+	1625.08i	0.181111	+	1.09638i
$131$	−918.430	−	918.430i	−0.612546	−	0.612546i	0.331062	−	0.943609i	$-0.392593\pi$
$131$	−918.430	−	918.430i	−0.612546	−	0.612546i	−0.943609	+	0.331062i	$0.892593\pi$
$132$		0			0
$133$	51.9451	−	51.9451i	0.0338662	−	0.0338662i
$134$	324.169	−	452.461i	0.208984	−	0.291691i
$135$		0			0
$136$	773.693	+	1446.56i	0.487821	+	0.912069i
$137$		−	477.234i		−	0.297612i	−0.988866	−	0.148806i	$-0.952457\pi$
$137$		−	477.234i		−	0.297612i	0.988866	−	0.148806i	$-0.0475430\pi$
$138$		0			0
$139$	−1513.89	+	1513.89i	−0.923788	+	0.923788i	−0.997295	−	0.0735064i	$-0.976581\pi$
$139$	−1513.89	+	1513.89i	−0.923788	+	0.923788i	0.0735064	+	0.997295i	$0.476581\pi$
$140$	−223.020	−	109.933i	−0.134633	−	0.0663642i
$141$		0			0
$142$	1265.97	−	209.127i	0.748155	−	0.123589i
$143$	3201.37			1.87211
$144$		0			0
$145$	1086.53			0.622285
$146$	−724.853	+	119.739i	−0.410885	+	0.0678746i
$147$		0			0
$148$	420.507	−	853.081i	0.233550	−	0.473803i
$149$	−375.353	+	375.353i	−0.206377	+	0.206377i	−0.802725	−	0.596349i	$-0.796618\pi$
$149$	−375.353	+	375.353i	−0.206377	+	0.206377i	0.596349	+	0.802725i	$0.296618\pi$
$150$		0			0
$151$			2997.52i			1.61546i	0.589553	+	0.807730i	$0.299304\pi$
$151$			2997.52i			1.61546i	−0.589553	+	0.807730i	$0.700696\pi$
$152$	−180.448	+	595.423i	−0.0962912	+	0.317731i
$153$		0			0
$154$	−281.460	+	392.850i	−0.147277	+	0.205564i
$155$	−1552.07	+	1552.07i	−0.804293	+	0.804293i
$156$		0			0
$157$	−1509.01	−	1509.01i	−0.767082	−	0.767082i	0.210510	−	0.977592i	$-0.432488\pi$
$157$	−1509.01	−	1509.01i	−0.767082	−	0.767082i	−0.977592	+	0.210510i	$0.932488\pi$
$158$	−148.985	−	901.897i	−0.0750167	−	0.454121i
$159$		0			0
$160$	2104.66	−	69.8265i	1.03993	−	0.0345017i
$161$	372.601			0.182392
$162$		0			0
$163$	−1425.19	−	1425.19i	−0.684844	−	0.684844i	0.276244	−	0.961088i	$-0.410910\pi$
$163$	−1425.19	−	1425.19i	−0.684844	−	0.684844i	−0.961088	+	0.276244i	$0.910910\pi$
$164$	269.195	+	792.565i	0.128174	+	0.377371i
$165$		0			0
$166$	1313.67	−	1833.56i	0.614219	−	0.857301i
$167$			792.415i			0.367179i	0.983003	+	0.183590i	$0.0587717\pi$
$167$			792.415i			0.367179i	−0.983003	+	0.183590i	$0.941228\pi$
$168$		0			0
$169$			308.861i			0.140583i
$170$	1939.15	+	1389.31i	0.874857	+	0.626797i
$171$		0			0
$172$	157.496	−	319.512i	0.0698195	−	0.141643i
$173$	773.594	+	773.594i	0.339972	+	0.339972i	0.856357	−	0.516384i	$-0.172722\pi$
$173$	773.594	+	773.594i	0.339972	+	0.339972i	−0.516384	+	0.856357i	$0.672722\pi$
$174$		0			0
$175$	−27.5984			−0.0119214
$176$	532.810	−	4058.13i	0.228194	−	1.73803i
$177$		0			0
$178$	−2419.05	+	399.605i	−1.01862	+	0.168268i
$179$	−426.050	−	426.050i	−0.177902	−	0.177902i	0.612539	−	0.790441i	$-0.290148\pi$
$179$	−426.050	−	426.050i	−0.177902	−	0.177902i	−0.790441	+	0.612539i	$0.790148\pi$
$180$		0			0
$181$	−2618.06	+	2618.06i	−1.07513	+	1.07513i	−0.0781951	+	0.996938i	$0.524916\pi$
$181$	−2618.06	+	2618.06i	−1.07513	+	1.07513i	−0.996938	+	0.0781951i	$0.975084\pi$
$182$	−307.502	−	220.312i	−0.125239	−	0.0897286i
$183$		0			0
$184$	−2782.65	+	1488.30i	−1.11489	+	0.596300i
$185$		−	1383.02i		−	0.549631i
$186$		0			0
$187$	3278.50	−	3278.50i	1.28207	−	1.28207i
$188$	−3697.74	+	1255.94i	−1.43450	+	0.487227i
$189$		0			0
$190$	147.453	+	892.620i	0.0563019	+	0.340829i
$191$	−3216.39			−1.21848			−0.609240	−	0.792986i	$-0.708525\pi$
$191$	−3216.39			−1.21848			−0.609240	+	0.792986i	$0.708525\pi$
$192$		0			0
$193$	2852.57			1.06390			0.531950	−	0.846776i	$-0.321459\pi$
$193$	2852.57			1.06390			0.531950	+	0.846776i	$0.321459\pi$
$194$	431.516	+	2612.22i	0.159696	+	0.966736i
$195$		0			0
$196$	−2544.15	+	864.122i	−0.927169	+	0.314913i
$197$	−1609.02	+	1609.02i	−0.581918	+	0.581918i	−0.935430	−	0.353512i	$-0.884987\pi$
$197$	−1609.02	+	1609.02i	−0.581918	+	0.581918i	0.353512	+	0.935430i	$0.384987\pi$
$198$		0			0
$199$			747.136i			0.266146i	0.991106	+	0.133073i	$0.0424845\pi$
$199$			747.136i			0.266146i	−0.991106	+	0.133073i	$0.957516\pi$
$200$	206.110	−	110.238i	0.0728708	−	0.0389750i
$201$		0			0
$202$	−5.16496	−	3.70047i	−0.00179904	−	0.00128893i
$203$	−176.449	+	176.449i	−0.0610062	+	0.0610062i
$204$		0			0
$205$	860.666	+	860.666i	0.293227	+	0.293227i
$206$	−3874.15	+	639.975i	−1.31032	+	0.216452i
$207$		0			0
$208$	3176.49	+	417.055i	1.05889	+	0.139027i
$209$	1758.44			0.581981
$210$		0			0
$211$	−2227.13	−	2227.13i	−0.726645	−	0.726645i	0.243305	−	0.969950i	$-0.421769\pi$
$211$	−2227.13	−	2227.13i	−0.726645	−	0.726645i	−0.969950	+	0.243305i	$0.921769\pi$
$212$	748.122	−	1517.72i	0.242364	−	0.491684i
$213$		0			0
$214$	−2671.27	−	1913.85i	−0.853290	−	0.611346i
$215$		−	517.995i		−	0.164311i
$216$		0			0
$217$		−	504.102i		−	0.157699i
$218$	1241.22	−	1732.44i	0.385623	−	0.538237i
$219$		0			0
$220$	−1914.12	−	5635.55i	−0.586590	−	1.72704i
$221$	2566.23	+	2566.23i	0.781102	+	0.781102i
$222$		0			0
$223$	−358.053			−0.107520			−0.0537601	−	0.998554i	$-0.517121\pi$
$223$	−358.053			−0.107520			−0.0537601	+	0.998554i	$0.517121\pi$
$224$	−330.451	+	353.130i	−0.0985677	+	0.105332i
$225$		0			0
$226$	−31.0094	−	187.719i	−0.00912706	−	0.0552516i
$227$	−3455.40	−	3455.40i	−1.01032	−	1.01032i	−0.999946	−	0.0103741i	$-0.996698\pi$
$227$	−3455.40	−	3455.40i	−1.01032	−	1.01032i	−0.0103741	−	0.999946i	$-0.503302\pi$
$228$		0			0
$229$	−1430.03	+	1430.03i	−0.412659	+	0.412659i	−0.882664	−	0.470005i	$-0.844252\pi$
$229$	−1430.03	+	1430.03i	−0.412659	+	0.412659i	0.470005	+	0.882664i	$0.344252\pi$
$230$	−2672.53	+	3730.21i	−0.766181	+	1.06940i
$231$		0			0
$232$	612.951	−	2022.55i	0.173458	−	0.572357i
$233$			926.479i			0.260496i	0.991481	+	0.130248i	$0.0415774\pi$
$233$			926.479i			0.260496i	−0.991481	+	0.130248i	$0.958423\pi$
$234$		0			0
$235$	−4015.47	+	4015.47i	−1.11464	+	1.11464i
$236$	1424.10	−	2889.07i	0.392801	−	0.796875i
$237$		0			0
$238$	−540.530	+	89.2908i	−0.147216	+	0.0243187i
$239$	792.472			0.214480			0.107240	−	0.994233i	$-0.465799\pi$
$239$	792.472			0.214480			0.107240	+	0.994233i	$0.465799\pi$
$240$		0			0
$241$	1449.01			0.387299			0.193650	−	0.981071i	$-0.437967\pi$
$241$	1449.01			0.387299			0.193650	+	0.981071i	$0.437967\pi$
$242$	−7699.07	+	1271.82i	−2.04510	+	0.337833i
$243$		0			0
$244$	2314.41	+	1140.83i	0.607233	+	0.299321i
$245$	−2762.76	+	2762.76i	−0.720433	+	0.720433i
$246$		0			0
$247$			1376.42i			0.354572i
$248$	2013.57	+	3764.73i	0.515571	+	0.963953i
$249$		0			0
$250$	−2197.45	+	3067.10i	−0.555915	+	0.775922i
$251$	3580.04	−	3580.04i	0.900280	−	0.900280i	−0.0951802	−	0.995460i	$-0.530343\pi$
$251$	3580.04	−	3580.04i	0.900280	−	0.900280i	0.995460	+	0.0951802i	$0.0303427\pi$
$252$		0			0
$253$	6306.64	+	6306.64i	1.56717	+	1.56717i
$254$	−877.525	−	5312.18i	−0.216775	−	1.31227i
$255$		0			0
$256$	1057.34	−	3957.18i	0.258139	−	0.966108i
$257$	4708.87			1.14292			0.571461	−	0.820629i	$-0.306377\pi$
$257$	4708.87			1.14292			0.571461	+	0.820629i	$0.306377\pi$
$258$		0			0
$259$	224.598	+	224.598i	0.0538835	+	0.0538835i
$260$	4411.21	−	1498.27i	1.05220	−	0.357379i
$261$		0			0
$262$	−2139.60	+	2986.36i	−0.504522	+	0.704190i
$263$			2967.82i			0.695830i	0.937526	+	0.347915i	$0.113110\pi$
$263$			2967.82i			0.695830i	−0.937526	+	0.347915i	$0.886890\pi$
$264$		0			0
$265$		−	2460.53i		−	0.570374i
$266$	−168.904	−	121.013i	−0.0389330	−	0.0278938i
$267$		0			0
$268$	−1412.08	−	696.050i	−0.321852	−	0.158649i
$269$	663.633	+	663.633i	0.150418	+	0.150418i	0.778305	−	0.627887i	$-0.216080\pi$
$269$	663.633	+	663.633i	0.150418	+	0.150418i	−0.627887	+	0.778305i	$0.716080\pi$
$270$		0			0
$271$	8058.74			1.80640			0.903199	−	0.429223i	$-0.141212\pi$
$271$	8058.74			1.80640			0.903199	+	0.429223i	$0.141212\pi$
$272$	3680.12	−	2825.91i	0.820368	−	0.629949i
$273$		0			0
$274$	−1331.77	+	219.997i	−0.293633	+	0.0485055i
$275$	−467.130	−	467.130i	−0.102433	−	0.102433i
$276$		0			0
$277$	482.477	−	482.477i	0.104654	−	0.104654i	−0.652841	−	0.757495i	$-0.726423\pi$
$277$	482.477	−	482.477i	0.104654	−	0.104654i	0.757495	+	0.652841i	$0.226423\pi$
$278$	4922.56	+	3526.80i	1.06200	+	0.760875i
$279$		0			0
$280$	−203.970	+	673.039i	−0.0435341	+	0.143649i
$281$			5899.10i			1.25235i	0.779682	+	0.626175i	$0.215381\pi$
$281$			5899.10i			1.25235i	−0.779682	+	0.626175i	$0.784619\pi$
$282$		0			0
$283$	−679.897	+	679.897i	−0.142812	+	0.142812i	−0.774898	−	0.632086i	$-0.782199\pi$
$283$	−679.897	+	679.897i	−0.142812	+	0.142812i	0.632086	+	0.774898i	$0.282199\pi$
$284$	−1167.18	−	3436.43i	−0.243872	−	0.718009i
$285$		0			0
$286$	−1475.78	−	8933.77i	−0.305121	−	1.84708i
$287$	−279.538			−0.0574935
$288$		0			0
$289$	343.118			0.0698388
$290$	−500.872	−	3032.08i	−0.101421	−	0.613965i
$291$		0			0
$292$	668.290	+	1967.58i	0.133934	+	0.394329i
$293$	3552.87	−	3552.87i	0.708398	−	0.708398i	−0.257800	−	0.966198i	$-0.582998\pi$
$293$	3552.87	−	3552.87i	0.708398	−	0.708398i	0.966198	+	0.257800i	$0.0829976\pi$
$294$		0			0
$295$		−	4683.78i		−	0.924407i
$296$	−2574.46	−	780.213i	−0.505532	−	0.153206i
$297$		0			0
$298$	1220.49	+	874.432i	0.237253	+	0.169981i
$299$	−4936.50	+	4936.50i	−0.954799	+	0.954799i
$300$		0			0
$301$	84.1205	+	84.1205i	0.0161084	+	0.0161084i
$302$	8364.89	−	1381.81i	1.59386	−	0.263291i
$303$		0			0
$304$	1744.78	+	229.079i	0.329177	+	0.0432191i
$305$	3752.13			0.704415
$306$		0			0
$307$	2735.56	+	2735.56i	0.508556	+	0.508556i	0.914083	−	0.405527i	$-0.132912\pi$
$307$	2735.56	+	2735.56i	0.508556	+	0.508556i	−0.405527	+	0.914083i	$0.632912\pi$
$308$	1226.04	+	604.348i	0.226819	+	0.111805i
$309$		0			0
$310$	5046.70	+	3615.74i	0.924624	+	0.662453i
$311$		−	5796.70i		−	1.05692i	−0.848960	−	0.528458i	$-0.822771\pi$
$311$		−	5796.70i		−	1.05692i	0.848960	−	0.528458i	$-0.177229\pi$
$312$		0			0
$313$			8362.62i			1.51017i	0.655627	+	0.755085i	$0.272404\pi$
$313$			8362.62i			1.51017i	−0.655627	+	0.755085i	$0.727596\pi$
$314$	−3515.42	+	4906.67i	−0.631804	+	0.881846i
$315$		0			0
$316$	−2448.16	+	831.519i	−0.435822	+	0.148027i
$317$	344.406	+	344.406i	0.0610214	+	0.0610214i	0.736959	−	0.675938i	$-0.236261\pi$
$317$	344.406	+	344.406i	0.0610214	+	0.0610214i	−0.675938	+	0.736959i	$0.736261\pi$
$318$		0			0
$319$	−5973.13			−1.04837
$320$	−1165.07	−	5841.11i	−0.203530	−	1.02040i
$321$		0			0
$322$	−171.763	−	1039.78i	−0.0297266	−	0.179953i
$323$	1409.58	+	1409.58i	0.242820	+	0.242820i
$324$		0			0
$325$	365.644	−	365.644i	0.0624071	−	0.0624071i
$326$	−3320.16	+	4634.14i	−0.564069	+	0.787304i
$327$		0			0
$328$	2087.64	−	1116.58i	0.351435	−	0.187965i
$329$		−	1304.20i		−	0.218549i
$330$		0			0
$331$	2687.86	−	2687.86i	0.446339	−	0.446339i	−0.447797	−	0.894135i	$-0.647791\pi$
$331$	2687.86	−	2687.86i	0.446339	−	0.446339i	0.894135	+	0.447797i	$0.147791\pi$
$332$	−5722.33	−	2820.69i	−0.945945	−	0.466282i
$333$		0			0
$334$	2211.32	−	365.290i	0.362270	−	0.0598437i
$335$	−2289.27			−0.373361
$336$		0			0
$337$	−1795.31			−0.290199			−0.145099	−	0.989417i	$-0.546350\pi$
$337$	−1795.31			−0.290199			−0.145099	+	0.989417i	$0.546350\pi$
$338$	861.910	−	142.380i	0.138703	−	0.0229125i
$339$		0			0
$340$	2983.12	−	6051.85i	0.475830	−	0.965316i
$341$	8532.42	−	8532.42i	1.35500	−	1.35500i
$342$		0			0
$343$		−	1813.72i		−	0.285515i
$344$	−964.235	−	292.220i	−0.151128	−	0.0458007i
$345$		0			0
$346$	1802.18	−	2515.41i	0.280017	−	0.390836i
$347$	1967.33	−	1967.33i	0.304357	−	0.304357i	−0.538359	−	0.842716i	$-0.680955\pi$
$347$	1967.33	−	1967.33i	0.304357	−	0.304357i	0.842716	+	0.538359i	$0.180955\pi$
$348$		0			0
$349$	−7363.37	−	7363.37i	−1.12938	−	1.12938i	−0.990279	−	0.139097i	$-0.955580\pi$
$349$	−7363.37	−	7363.37i	−1.12938	−	1.12938i	−0.139097	−	0.990279i	$-0.544420\pi$
$350$	12.7224	+	77.0163i	0.00194297	+	0.0117620i
$351$		0			0
$352$	−11570.3	+	383.867i	−1.75198	+	0.0581255i
$353$	−10644.3			−1.60493			−0.802466	−	0.596698i	$-0.796479\pi$
$353$	−10644.3			−1.60493			−0.802466	+	0.596698i	$0.796479\pi$
$354$		0			0
$355$	−3731.70	−	3731.70i	−0.557911	−	0.557911i
$356$	2230.28	+	6566.40i	0.332036	+	0.977580i
$357$		0			0
$358$	−992.537	+	1385.34i	−0.146529	+	0.204518i
$359$		−	7459.42i		−	1.09664i	−0.836269	−	0.548319i	$-0.815268\pi$
$359$		−	7459.42i		−	1.09664i	0.836269	−	0.548319i	$-0.184732\pi$
$360$		0			0
$361$		−	6102.96i		−	0.889775i
$362$	8512.87	+	6099.10i	1.23599	+	0.885530i
$363$		0			0
$364$	−473.051	+	959.678i	−0.0681170	+	0.138189i
$365$	2136.65	+	2136.65i	0.306403	+	0.306403i
$366$		0			0
$367$	−6251.35			−0.889149			−0.444574	−	0.895742i	$-0.646645\pi$
$367$	−6251.35			−0.889149			−0.444574	+	0.895742i	$0.646645\pi$
$368$	5436.03	+	7079.21i	0.770034	+	1.00280i
$369$		0			0
$370$	−3859.47	+	637.550i	−0.542282	+	0.0895801i
$371$	399.582	+	399.582i	0.0559171	+	0.0559171i
$372$		0			0
$373$	8911.86	−	8911.86i	1.23710	−	1.23710i	0.275921	−	0.961180i	$-0.411017\pi$
$373$	8911.86	−	8911.86i	1.23710	−	1.23710i	0.961180	−	0.275921i	$-0.0889827\pi$
$374$	−10660.3	−	7637.67i	−1.47389	−	1.05598i
$375$		0			0
$376$	5209.43	+	9739.97i	0.714510	+	1.33591i
$377$		−	4675.45i		−	0.638721i
$378$		0			0
$379$	1184.03	−	1184.03i	0.160473	−	0.160473i	−0.622303	−	0.782776i	$-0.713803\pi$
$379$	1184.03	−	1184.03i	0.160473	−	0.160473i	0.782776	+	0.622303i	$0.213803\pi$
$380$	2422.98	−	822.966i	0.327095	−	0.111098i
$381$		0			0
$382$	1482.70	+	8975.67i	0.198591	+	1.20219i
$383$	2880.38			0.384283			0.192142	−	0.981367i	$-0.438457\pi$
$383$	2880.38			0.384283			0.192142	+	0.981367i	$0.438457\pi$
$384$		0			0
$385$	1987.66			0.263119
$386$	−1314.99	−	7960.42i	−0.173397	−	1.04968i
$387$		0			0
$388$	7090.77	−	2408.38i	0.927782	−	0.315122i
$389$	−9244.24	+	9244.24i	−1.20489	+	1.20489i	−0.232226	+	0.972662i	$0.574601\pi$
$389$	−9244.24	+	9244.24i	−1.20489	+	1.20489i	−0.972662	+	0.232226i	$0.925399\pi$
$390$		0			0
$391$			10110.9i			1.30774i
$392$	3584.24	+	6701.38i	0.461815	+	0.863446i
$393$		0			0
$394$	5231.87	+	3748.41i	0.668979	+	0.479295i
$395$	−2658.52	+	2658.52i	−0.338645	+	0.338645i
$396$		0			0
$397$	−4257.80	−	4257.80i	−0.538270	−	0.538270i	0.384751	−	0.923020i	$-0.374287\pi$
$397$	−4257.80	−	4257.80i	−0.538270	−	0.538270i	−0.923020	+	0.384751i	$0.874287\pi$
$398$	2084.96	−	344.417i	0.262587	−	0.0433771i
$399$		0			0
$400$	−402.644	−	524.354i	−0.0503305	−	0.0655442i
$401$	−12722.6			−1.58437			−0.792187	−	0.610278i	$-0.791058\pi$
$401$	−12722.6			−1.58437			−0.792187	+	0.610278i	$0.791058\pi$
$402$		0			0
$403$	6678.72	+	6678.72i	0.825535	+	0.825535i
$404$	−7.94560	+	16.1192i	−0.000978486	+	0.00198505i
$405$		0			0
$406$	573.739	+	411.059i	0.0701335	+	0.0502476i
$407$			7603.08i			0.925972i
$408$		0			0
$409$			232.991i			0.0281678i	0.999901	+	0.0140839i	$0.00448320\pi$
$409$			232.991i			0.0281678i	−0.999901	+	0.0140839i	$0.995517\pi$
$410$	2005.03	−	2798.53i	0.241515	−	0.337097i
$411$		0			0
$412$	3571.84	+	10516.2i	0.427116	+	1.25752i
$413$	760.629	+	760.629i	0.0906250	+	0.0906250i
$414$		0			0
$415$	−9277.08			−1.09734
$416$	−300.471	−	9056.59i	−0.0354129	−	1.06739i
$417$		0			0
$418$	−810.614	−	4907.13i	−0.0948527	−	0.574200i
$419$	6125.69	+	6125.69i	0.714223	+	0.714223i	0.967416	−	0.253193i	$-0.0814807\pi$
$419$	6125.69	+	6125.69i	0.714223	+	0.714223i	−0.253193	+	0.967416i	$0.581481\pi$
$420$		0			0
$421$	−8308.44	+	8308.44i	−0.961825	+	0.961825i	−0.999298	−	0.0374725i	$-0.988069\pi$
$421$	−8308.44	+	8308.44i	−0.961825	+	0.961825i	0.0374725	+	0.999298i	$0.488069\pi$
$422$	−5188.38	+	7241.73i	−0.598499	+	0.835360i
$423$		0			0
$424$	−4580.22	−	1388.07i	−0.524611	−	0.158988i
$425$		−	748.907i		−	0.0854760i
$426$		0			0
$427$	−609.333	+	609.333i	−0.0690579	+	0.0690579i
$428$	−4109.39	+	8336.72i	−0.464100	+	0.941520i
$429$		0			0
$430$	−1445.52	+	238.787i	−0.162114	+	0.0267798i
$431$	−8737.57			−0.976506			−0.488253	−	0.872702i	$-0.662366\pi$
$431$	−8737.57			−0.976506			−0.488253	+	0.872702i	$0.662366\pi$
$432$		0			0
$433$	−11627.5			−1.29049			−0.645247	−	0.763974i	$-0.723245\pi$
$433$	−11627.5			−1.29049			−0.645247	+	0.763974i	$0.723245\pi$
$434$	−1406.75	+	232.383i	−0.155590	+	0.0257021i
$435$		0			0
$436$	−5406.74	−	2665.13i	−0.593890	−	0.292744i
$437$	−2711.51	+	2711.51i	−0.296817	+	0.296817i
$438$		0			0
$439$		−	17631.8i		−	1.91690i	−0.285261	−	0.958450i	$-0.592080\pi$
$439$		−	17631.8i		−	1.91690i	0.285261	−	0.958450i	$-0.407920\pi$
$440$	−14844.2	+	7939.45i	−1.60834	+	0.860224i
$441$		0			0
$442$	5978.36	−	8344.34i	0.643352	−	0.897963i
$443$	4549.81	−	4549.81i	0.487964	−	0.487964i	−0.419699	−	0.907663i	$-0.637864\pi$
$443$	4549.81	−	4549.81i	0.487964	−	0.487964i	0.907663	+	0.419699i	$0.137864\pi$
$444$		0			0
$445$	7130.62	+	7130.62i	0.759604	+	0.759604i
$446$	165.057	+	999.186i	0.0175239	+	0.106083i
$447$		0			0
$448$	1137.78	+	759.371i	0.119989	+	0.0800824i
$449$	12926.5			1.35867			0.679334	−	0.733830i	$-0.262269\pi$
$449$	12926.5			1.35867			0.679334	+	0.733830i	$0.262269\pi$
$450$		0			0
$451$	−4731.46	−	4731.46i	−0.494004	−	0.494004i
$452$	−509.554	+	173.070i	−0.0530252	+	0.0180101i
$453$		0			0
$454$	−8049.78	+	11235.5i	−0.832147	+	1.16148i
$455$			1555.84i			0.160305i
$456$		0			0
$457$			9320.32i			0.954018i	0.878898	+	0.477009i	$0.158279\pi$
$457$			9320.32i			0.954018i	−0.878898	+	0.477009i	$0.841721\pi$
$458$	4649.87	+	3331.43i	0.474398	+	0.339886i
$459$		0			0
$460$	11641.5	+	5738.43i	1.17998	+	0.581643i
$461$	−12885.0	−	12885.0i	−1.30177	−	1.30177i	−0.927200	−	0.374566i	$-0.877792\pi$
$461$	−12885.0	−	12885.0i	−1.30177	−	1.30177i	−0.374566	−	0.927200i	$-0.622208\pi$
$462$		0			0
$463$	7038.37			0.706482			0.353241	−	0.935532i	$-0.385080\pi$
$463$	7038.37			0.706482			0.353241	+	0.935532i	$0.385080\pi$
$464$	−5926.71	−	778.144i	−0.592975	−	0.0778543i
$465$		0			0
$466$	2585.44	−	427.091i	0.257013	−	0.0424563i
$467$	−6001.76	−	6001.76i	−0.594707	−	0.594707i	0.344192	−	0.938899i	$-0.388153\pi$
$467$	−6001.76	−	6001.76i	−0.594707	−	0.594707i	−0.938899	+	0.344192i	$0.888153\pi$
$468$		0			0
$469$	371.769	−	371.769i	0.0366028	−	0.0366028i
$470$	13056.7	+	9354.53i	1.28140	+	0.918069i
$471$		0			0
$472$	−8718.75	−	2642.29i	−0.850239	−	0.257672i
$473$			2847.65i			0.276818i
$474$		0			0
$475$	200.840	−	200.840i	0.0194004	−	0.0194004i
$476$	498.351	+	1467.25i	0.0479872	+	0.141284i
$477$		0			0
$478$	−365.317	−	2211.48i	−0.0349565	−	0.211612i
$479$	587.317			0.0560234			0.0280117	−	0.999608i	$-0.491082\pi$
$479$	587.317			0.0560234			0.0280117	+	0.999608i	$0.491082\pi$
$480$		0			0
$481$	−5951.28			−0.564148
$482$	−667.971	−	4043.63i	−0.0631229	−	0.382121i
$483$		0			0
$484$	7098.29	+	20898.8i	0.666631	+	1.96270i
$485$	7700.05	−	7700.05i	0.720910	−	0.720910i
$486$		0			0
$487$		−	8366.45i		−	0.778481i	−0.921136	−	0.389240i	$-0.872738\pi$
$487$		−	8366.45i		−	0.778481i	0.921136	−	0.389240i	$-0.127262\pi$
$488$	2116.71	−	6984.51i	0.196351	−	0.647897i
$489$		0			0
$490$	8983.36	+	6436.19i	0.828218	+	0.593382i
$491$	−1529.30	+	1529.30i	−0.140563	+	0.140563i	−0.773887	−	0.633324i	$-0.781690\pi$
$491$	−1529.30	+	1529.30i	−0.140563	+	0.140563i	0.633324	+	0.773887i	$0.281690\pi$
$492$		0			0
$493$	−4788.09	−	4788.09i	−0.437413	−	0.437413i
$494$	3841.04	−	634.505i	0.349831	−	0.0577889i
$495$		0			0
$496$	9577.65	−	7354.55i	0.867035	−	0.665784i
$497$	1212.03			0.109390
$498$		0			0
$499$	11364.5	+	11364.5i	1.01952	+	1.01952i	0.999806	+	0.0197191i	$0.00627718\pi$
$499$	11364.5	+	11364.5i	1.01952	+	1.01952i	0.0197191	+	0.999806i	$0.493723\pi$
$500$	9572.06	+	4718.33i	0.856151	+	0.422020i
$501$		0			0
$502$	−11640.8	−	8340.15i	−1.03497	−	0.741513i
$503$			12570.2i			1.11427i	0.830421	+	0.557137i	$0.188100\pi$
$503$			12570.2i			1.11427i	−0.830421	+	0.557137i	$0.811900\pi$
$504$		0			0
$505$			26.1326i			0.00230274i
$506$	14692.1	−	20506.6i	1.29080	−	1.80164i
$507$		0			0
$508$	−14419.7	+	4897.66i	−1.25939	+	0.427753i
$509$	−11880.4	−	11880.4i	−1.03456	−	1.03456i	−0.999381	−	0.0351750i	$-0.988801\pi$
$509$	−11880.4	−	11880.4i	−1.03456	−	1.03456i	−0.0351750	−	0.999381i	$-0.511199\pi$
$510$		0			0
$511$	−693.968			−0.0600770
$512$	−11530.3	−	1126.42i	−0.995262	−	0.0972291i
$513$		0			0
$514$	−2170.71	−	13140.6i	−0.186276	−	1.12764i
$515$	11419.8	+	11419.8i	0.977122	+	0.977122i
$516$		0			0
$517$	22074.8	−	22074.8i	1.87785	−	1.87785i
$518$	523.229	−	730.300i	0.0443810	−	0.0619451i
$519$		0			0
$520$	−6214.57	−	11619.3i	−0.524090	−	0.979882i
$521$			6612.98i			0.556085i	0.960569	+	0.278042i	$0.0896856\pi$
$521$			6612.98i			0.556085i	−0.960569	+	0.278042i	$0.910314\pi$
$522$		0			0
$523$	5129.30	−	5129.30i	0.428850	−	0.428850i	−0.459387	−	0.888236i	$-0.651931\pi$
$523$	5129.30	−	5129.30i	0.428850	−	0.428850i	0.888236	+	0.459387i	$0.151931\pi$
$524$	9320.07	+	4594.11i	0.777003	+	0.383005i
$525$		0			0
$526$	8282.01	−	1368.11i	0.686526	−	0.113408i
$527$	13679.3			1.13070
$528$		0			0
$529$	−7282.60			−0.598553
$530$	−6866.38	+	1134.26i	−0.562748	+	0.0929609i
$531$		0			0
$532$	−259.837	+	527.130i	−0.0211755	+	0.0429586i
$533$	3703.53	−	3703.53i	0.300972	−	0.300972i
$534$		0			0
$535$			13515.5i			1.09220i
$536$	−1291.46	+	4261.42i	−0.104072	+	0.343406i
$537$		0			0
$538$	1546.02	−	2157.86i	0.123891	−	0.172922i
$539$	15188.1	−	15188.1i	1.21372	−	1.21372i
$540$		0			0
$541$	−10968.5	−	10968.5i	−0.871672	−	0.871672i	0.120983	−	0.992655i	$-0.461395\pi$
$541$	−10968.5	−	10968.5i	−0.871672	−	0.871672i	−0.992655	+	0.120983i	$0.961395\pi$
$542$	−3714.95	−	22488.8i	−0.294411	−	1.78224i
$543$		0			0
$544$	−9582.49	−	8967.07i	−0.755231	−	0.706728i
$545$	−8765.44			−0.688936
$546$		0			0
$547$	13088.8	+	13088.8i	1.02311	+	1.02311i	0.999727	+	0.0233784i	$0.00744226\pi$
$547$	13088.8	+	13088.8i	1.02311	+	1.02311i	0.0233784	+	0.999727i	$0.492558\pi$
$548$	1227.85	+	3615.04i	0.0957138	+	0.281801i
$549$		0			0
$550$	−1088.24	+	1518.92i	−0.0843684	+	0.117758i
$551$		−	2568.12i		−	0.198558i
$552$		0			0
$553$		−	863.469i		−	0.0663986i
$554$	−1568.82	−	1123.99i	−0.120312	−	0.0861981i
$555$		0			0
$556$	7572.70	−	15362.7i	0.577615	−	1.17181i
$557$	−5049.87	−	5049.87i	−0.384147	−	0.384147i	0.488447	−	0.872594i	$-0.337564\pi$
$557$	−5049.87	−	5049.87i	−0.384147	−	0.384147i	−0.872594	+	0.488447i	$0.837564\pi$
$558$		0			0
$559$	−2228.98			−0.168651
$560$	1972.21	+	258.941i	0.148824	+	0.0195397i
$561$		0			0
$562$	16462.1	−	2719.39i	1.23561	−	0.204111i
$563$	3249.06	+	3249.06i	0.243217	+	0.243217i	0.818180	−	0.574962i	$-0.194983\pi$
$563$	3249.06	+	3249.06i	0.243217	+	0.243217i	−0.574962	+	0.818180i	$0.694983\pi$
$564$		0			0
$565$	−553.338	+	553.338i	−0.0412019	+	0.0412019i
$566$	2210.75	+	1583.90i	0.164178	+	0.117626i
$567$		0			0
$568$	−9051.67	+	4841.29i	−0.668661	+	0.357634i
$569$		−	2806.05i		−	0.206741i	−0.994643	−	0.103371i	$-0.967037\pi$
$569$		−	2806.05i		−	0.206741i	0.994643	−	0.103371i	$-0.0329628\pi$
$570$		0			0
$571$	−12038.8	+	12038.8i	−0.882324	+	0.882324i	−0.993770	−	0.111446i	$-0.964452\pi$
$571$	−12038.8	+	12038.8i	−0.882324	+	0.882324i	0.111446	+	0.993770i	$0.464452\pi$
$572$	−24250.3	+	8236.64i	−1.77265	+	0.602083i
$573$		0			0
$574$	128.863	+	780.082i	0.00937042	+	0.0567247i
$575$	1440.62			0.104484
$576$		0			0
$577$	7206.84			0.519973			0.259987	−	0.965612i	$-0.416282\pi$
$577$	7206.84			0.519973			0.259987	+	0.965612i	$0.416282\pi$
$578$	−158.172	−	957.508i	−0.0113825	−	0.0689050i
$579$		0			0
$580$	−8230.45	+	2795.48i	−0.589226	+	0.200131i
$581$	1506.57	−	1506.57i	0.107578	−	0.107578i
$582$		0			0
$583$			13526.6i			0.960918i
$584$	5182.68	−	2771.96i	0.367227	−	0.196412i
$585$		0			0
$586$	−11552.5	−	8276.84i	−0.814382	−	0.583470i
$587$	−10377.0	+	10377.0i	−0.729647	+	0.729647i	−0.970549	−	0.240903i	$-0.922557\pi$
$587$	−10377.0	+	10377.0i	−0.729647	+	0.729647i	0.240903	+	0.970549i	$0.422557\pi$
$588$		0			0
$589$	3668.48	+	3668.48i	0.256633	+	0.256633i
$590$	−13070.6	+	2159.14i	−0.912047	+	0.150662i
$591$		0			0
$592$	−990.483	+	7543.98i	−0.0687645	+	0.523743i
$593$	4758.60			0.329531			0.164766	−	0.986333i	$-0.447313\pi$
$593$	4758.60			0.329531			0.164766	+	0.986333i	$0.447313\pi$
$594$		0			0
$595$	1593.32	+	1593.32i	0.109781	+	0.109781i
$596$	1877.57	−	3809.02i	0.129041	−	0.261785i
$597$		0			0
$598$	16051.5	+	11500.2i	1.09765	+	0.786417i
$599$		−	14256.4i		−	0.972455i	−0.873832	−	0.486227i	$-0.838373\pi$
$599$		−	14256.4i		−	0.972455i	0.873832	−	0.486227i	$-0.161627\pi$
$600$		0			0
$601$			10385.2i			0.704862i	0.935838	+	0.352431i	$0.114645\pi$
$601$			10385.2i			0.704862i	−0.935838	+	0.352431i	$0.885355\pi$
$602$	195.969	−	273.526i	0.0132676	−	0.0185184i
$603$		0			0
$604$	−7712.16	−	22706.2i	−0.519542	−	1.52964i
$605$	22694.5	+	22694.5i	1.52506	+	1.52506i
$606$		0			0
$607$	−16243.6			−1.08618			−0.543088	−	0.839676i	$-0.682745\pi$
$607$	−16243.6			−1.08618			−0.543088	+	0.839676i	$0.682745\pi$
$608$	−165.042	−	4974.59i	−0.0110088	−	0.331819i
$609$		0			0
$610$	−1729.67	−	10470.7i	−0.114807	−	0.694996i
$611$	17279.0	+	17279.0i	1.14408	+	1.14408i
$612$		0			0
$613$	−500.502	+	500.502i	−0.0329773	+	0.0329773i	−0.723403	−	0.690426i	$-0.757423\pi$
$613$	−500.502	+	500.502i	−0.0329773	+	0.0329773i	0.690426	+	0.723403i	$0.257423\pi$
$614$	6372.83	−	8894.92i	0.418870	−	0.584642i
$615$		0			0
$616$	1121.31	−	3699.99i	0.0733426	−	0.242008i
$617$		−	11575.9i		−	0.755316i	−0.925945	−	0.377658i	$-0.876729\pi$
$617$		−	11575.9i		−	0.755316i	0.925945	−	0.377658i	$-0.123271\pi$
$618$		0			0
$619$	18356.1	−	18356.1i	1.19191	−	1.19191i	0.215380	−	0.976530i	$-0.430901\pi$
$619$	18356.1	−	18356.1i	1.19191	−	1.19191i	0.976530	−	0.215380i	$-0.0690992\pi$
$620$	7763.68	−	15750.2i	0.502898	−	1.02023i
$621$		0			0
$622$	−16176.3	+	2672.18i	−1.04278	+	0.172258i
$623$	−2315.98			−0.148937
$624$		0			0
$625$	16809.5			1.07581
$626$	23336.8	−	3855.03i	1.48998	−	0.246131i
$627$		0			0
$628$	15313.2	+	7548.26i	0.973027	+	0.479631i
$629$	−6094.66	+	6094.66i	−0.386343	+	0.386343i
$630$		0			0
$631$		−	10224.8i		−	0.645079i	−0.946556	−	0.322539i	$-0.895463\pi$
$631$		−	10224.8i		−	0.645079i	0.946556	−	0.322539i	$-0.104537\pi$
$632$	3449.01	+	6448.54i	0.217079	+	0.405869i
$633$		0			0
$634$	802.338	−	1119.87i	0.0502601	−	0.0701509i
$635$	−15658.7	+	15658.7i	−0.978578	+	0.978578i
$636$		0			0
$637$	11888.4	+	11888.4i	0.739461	+	0.739461i
$638$	2753.52	+	16668.7i	0.170866	+	1.03436i
$639$		0			0
$640$	−15763.2	+	5943.92i	−0.973584	+	0.367116i
$641$	−19804.4			−1.22032			−0.610162	−	0.792277i	$-0.708896\pi$
$641$	−19804.4			−1.22032			−0.610162	+	0.792277i	$0.708896\pi$
$642$		0			0
$643$	15680.7	+	15680.7i	0.961723	+	0.961723i	0.999294	−	0.0375712i	$-0.0119621\pi$
$643$	15680.7	+	15680.7i	0.961723	+	0.961723i	−0.0375712	+	0.999294i	$0.511962\pi$
$644$	−2822.45	+	958.646i	−0.172702	+	0.0586583i
$645$		0			0
$646$	3283.78	−	4583.37i	0.199998	−	0.279149i
$647$			9232.26i			0.560985i	0.959856	+	0.280493i	$0.0904978\pi$
$647$			9232.26i			0.560985i	−0.959856	+	0.280493i	$0.909502\pi$
$648$		0			0
$649$			25748.8i			1.55736i
$650$	−1188.93	−	851.814i	−0.0717438	−	0.0514014i
$651$		0			0
$652$	14462.6	+	7129.00i	0.868710	+	0.428210i
$653$	19697.9	+	19697.9i	1.18046	+	1.18046i	0.979626	+	0.200833i	$0.0643648\pi$
$653$	19697.9	+	19697.9i	1.18046	+	1.18046i	0.200833	+	0.979626i	$0.435635\pi$
$654$		0			0
$655$	15109.8			0.901355
$656$	−4078.30	−	5311.07i	−0.242730	−	0.316101i
$657$		0			0
$658$	−3639.50	+	601.213i	−0.215627	+	0.0356196i
$659$	−3888.06	−	3888.06i	−0.229829	−	0.229829i	0.582792	−	0.812621i	$-0.301960\pi$
$659$	−3888.06	−	3888.06i	−0.229829	−	0.229829i	−0.812621	+	0.582792i	$0.801960\pi$
$660$		0			0
$661$	−8110.20	+	8110.20i	−0.477232	+	0.477232i	−0.904245	−	0.427013i	$-0.859566\pi$
$661$	−8110.20	+	8110.20i	−0.477232	+	0.477232i	0.427013	+	0.904245i	$0.359566\pi$
$662$	−8739.82	−	6261.70i	−0.513116	−	0.367625i
$663$		0			0
$664$	−5233.54	+	17269.1i	−0.305875	+	1.00929i
$665$			854.587i			0.0498338i
$666$		0			0
$667$	9210.54	−	9210.54i	0.534683	−	0.534683i
$668$	−2038.76	−	6002.54i	−0.118087	−	0.347672i
$669$		0			0
$670$	1055.31	+	6388.45i	0.0608513	+	0.368369i
$671$	−20627.1			−1.18674
$672$		0			0
$673$	−28428.2			−1.62827			−0.814135	−	0.580676i	$-0.802788\pi$
$673$	−28428.2			−1.62827			−0.814135	+	0.580676i	$0.802788\pi$
$674$	827.610	+	5010.02i	0.0472972	+	0.286318i
$675$		0			0
$676$	−794.652	−	2339.62i	−0.0452124	−	0.133114i
$677$	16967.4	−	16967.4i	0.963235	−	0.963235i	−0.0361128	−	0.999348i	$-0.511498\pi$
$677$	16967.4	−	16967.4i	0.963235	−	0.963235i	0.999348	+	0.0361128i	$0.0114975\pi$
$678$		0			0
$679$			2500.92i			0.141350i
$680$	−18263.5	−	5534.91i	−1.02996	−	0.312138i
$681$		0			0
$682$	−27744.0	−	19877.3i	−1.55773	−	1.11605i
$683$	9550.16	−	9550.16i	0.535032	−	0.535032i	−0.387034	−	0.922066i	$-0.626500\pi$
$683$	9550.16	−	9550.16i	0.535032	−	0.535032i	0.922066	+	0.387034i	$0.126500\pi$
$684$		0			0
$685$	3925.66	+	3925.66i	0.218966	+	0.218966i
$686$	−5061.38	+	836.095i	−0.281697	+	0.0465339i
$687$		0			0
$688$	−370.974	+	2825.51i	−0.0205570	+	0.156572i
$689$	−10587.9			−0.585439
$690$		0			0
$691$	−20859.7	−	20859.7i	−1.14839	−	1.14839i	−0.986868	−	0.161527i	$-0.948358\pi$
$691$	−20859.7	−	20859.7i	−1.14839	−	1.14839i	−0.161527	−	0.986868i	$-0.551642\pi$
$692$	−7850.30	−	3869.62i	−0.431248	−	0.212574i
$693$		0			0
$694$	−6396.96	−	4583.14i	−0.349892	−	0.250683i
$695$		−	24906.1i		−	1.35934i
$696$		0			0
$697$		−	7585.52i		−	0.412227i
$698$	−17153.9	+	23942.7i	−0.930207	+	1.29834i
$699$		0			0
$700$	209.058	−	71.0065i	0.0112880	−	0.00383399i
$701$	−23495.4	−	23495.4i	−1.26592	−	1.26592i	−0.948178	−	0.317740i	$-0.897076\pi$
$701$	−23495.4	−	23495.4i	−1.26592	−	1.26592i	−0.317740	−	0.948178i	$-0.602924\pi$
$702$		0			0
$703$	−3268.91			−0.175376
$704$	6404.93	+	32111.1i	0.342890	+	1.71908i
$705$		0			0
$706$	4906.86	+	29704.2i	0.261575	+	1.58347i
$707$	−4.24384	−	4.24384i	−0.000225751	−	0.000225751i
$708$		0			0
$709$	4559.45	−	4559.45i	0.241515	−	0.241515i	−0.575962	−	0.817477i	$-0.695372\pi$
$709$	4559.45	−	4559.45i	0.241515	−	0.241515i	0.817477	+	0.575962i	$0.195372\pi$
$710$	−8693.47	+	12134.0i	−0.459521	+	0.641380i
$711$		0			0
$712$	17296.1	−	9250.84i	0.910393	−	0.486924i
$713$			26313.9i			1.38214i
$714$		0			0
$715$	−26334.1	+	26334.1i	−1.37740	+	1.37740i
$716$	4323.49	+	2131.16i	0.225665	+	0.111236i
$717$		0			0
$718$	−20816.3	+	3438.67i	−1.08198	+	0.178733i
$719$	6494.67			0.336871			0.168436	−	0.985713i	$-0.446128\pi$
$719$	6494.67			0.336871			0.168436	+	0.985713i	$0.446128\pi$
$720$		0			0
$721$	−3709.08			−0.191586
$722$	−17031.0	+	2813.37i	−0.877878	+	0.145018i
$723$		0			0
$724$	13095.9	−	26567.7i	0.672246	−	1.36378i
$725$	−682.221	+	682.221i	−0.0349476	+	0.0349476i
$726$		0			0
$727$		−	24866.4i		−	1.26856i	−0.773103	−	0.634280i	$-0.781296\pi$
$727$		−	24866.4i		−	1.26856i	0.773103	−	0.634280i	$-0.218704\pi$
$728$	2896.15	+	877.704i	0.147443	+	0.0446839i
$729$		0			0
$730$	4977.59	−	6947.50i	0.252368	−	0.352245i
$731$	−2282.68	+	2282.68i	−0.115497	+	0.115497i
$732$		0			0
$733$	−14914.3	−	14914.3i	−0.751533	−	0.751533i	0.223232	−	0.974765i	$-0.428339\pi$
$733$	−14914.3	−	14914.3i	−0.751533	−	0.751533i	−0.974765	+	0.223232i	$0.928339\pi$
$734$	2881.77	+	17445.1i	0.144916	+	0.877260i
$735$		0			0
$736$	17249.4	−	18433.2i	0.863886	−	0.923176i
$737$	12585.1			0.629008
$738$		0			0
$739$	8451.86	+	8451.86i	0.420713	+	0.420713i	0.885449	−	0.464737i	$-0.153851\pi$
$739$	8451.86	+	8451.86i	0.420713	+	0.420713i	−0.464737	+	0.885449i	$0.653851\pi$
$740$	3558.30	+	10476.4i	0.176765	+	0.520431i
$741$		0			0
$742$	930.875	−	1299.28i	0.0460559	−	0.0642829i
$743$			5622.43i			0.277614i	0.990319	+	0.138807i	$0.0443267\pi$
$743$			5622.43i			0.277614i	−0.990319	+	0.138807i	$0.955673\pi$
$744$		0			0
$745$		−	6175.21i		−	0.303681i
$746$	−28977.7	−	20761.3i	−1.42219	−	1.01893i
$747$		0			0
$748$	−16399.5	+	33269.7i	−0.801638	+	1.62628i
$749$	−2194.88	−	2194.88i	−0.107075	−	0.107075i
$750$		0			0
$751$	−32314.9			−1.57016			−0.785079	−	0.619396i	$-0.787378\pi$
$751$	−32314.9			−1.57016			−0.785079	+	0.619396i	$0.787378\pi$
$752$	24779.0	−	19027.4i	1.20159	−	0.922685i
$753$		0			0
$754$	−13047.3	+	2155.30i	−0.630181	+	0.104100i
$755$	−24657.2	−	24657.2i	−1.18857	−	1.18857i
$756$		0			0
$757$	12692.8	−	12692.8i	0.609418	−	0.609418i	−0.333376	−	0.942794i	$-0.608188\pi$
$757$	12692.8	−	12692.8i	0.609418	−	0.609418i	0.942794	+	0.333376i	$0.108188\pi$
$758$	−3849.97	−	2758.34i	−0.184482	−	0.132173i
$759$		0			0
$760$	−3413.53	−	6382.21i	−0.162923	−	0.304615i
$761$			13108.2i			0.624404i	0.950016	+	0.312202i	$0.101067\pi$
$761$			13108.2i			0.624404i	−0.950016	+	0.312202i	$0.898933\pi$
$762$		0			0
$763$	1423.48	−	1423.48i	0.0675404	−	0.0675404i
$764$	24364.1	−	8275.27i	1.15375	−	0.391870i
$765$		0			0
$766$	−1327.81	−	8038.01i	−0.0626314	−	0.379145i
$767$	−20154.8			−0.948822
$768$		0			0
$769$	23661.2			1.10955			0.554776	−	0.832000i	$-0.312804\pi$
$769$	23661.2			1.10955			0.554776	+	0.832000i	$0.312804\pi$
$770$	−916.280	−	5546.79i	−0.0428837	−	0.259601i
$771$		0			0
$772$	−21608.2	+	7339.24i	−1.00738	+	0.342157i
$773$	−21370.5	+	21370.5i	−0.994362	+	0.994362i	−0.999984	−	0.00562228i	$-0.998210\pi$
$773$	−21370.5	+	21370.5i	−0.994362	+	0.994362i	0.00562228	+	0.999984i	$0.498210\pi$
$774$		0			0
$775$		−	1949.06i		−	0.0903384i
$776$	−9989.59	−	18677.3i	−0.462120	−	0.864018i
$777$		0			0
$778$	30058.5	+	21535.6i	1.38515	+	0.992402i
$779$	2034.27	−	2034.27i	0.0935627	−	0.0935627i
$780$		0			0
$781$	20514.8	+	20514.8i	0.939921	+	0.939921i
$782$	28215.4	−	4660.94i	1.29026	−	0.213139i
$783$		0			0
$784$	17048.7	−	13091.4i	0.776633	−	0.596366i
$785$	24825.8			1.12875
$786$		0			0
$787$	−20890.9	−	20890.9i	−0.946226	−	0.946226i	0.0524002	−	0.998626i	$-0.483313\pi$
$787$	−20890.9	−	20890.9i	−0.946226	−	0.946226i	−0.998626	+	0.0524002i	$0.983313\pi$
$788$	8048.54	−	16328.1i	0.363854	−	0.738151i
$789$		0			0
$790$	8644.42	+	6193.35i	0.389310	+	0.278924i
$791$		−	179.720i		−	0.00807853i
$792$		0			0
$793$		−	16145.8i		−	0.723020i
$794$	−9919.09	+	13844.6i	−0.443344	+	0.618801i
$795$		0			0
$796$	−1922.27	−	5659.54i	−0.0855942	−	0.252007i
$797$	6834.83	+	6834.83i	0.303767	+	0.303767i	0.842486	−	0.538719i	$-0.181092\pi$
$797$	6834.83	+	6834.83i	0.303767	+	0.303767i	−0.538719	+	0.842486i	$0.681092\pi$
$798$		0			0
$799$	35390.5			1.56699
$800$	−1277.65	+	1365.34i	−0.0564649	+	0.0603401i
$801$		0			0
$802$	5864.89	+	35503.7i	0.258225	+	1.56319i
$803$	−11746.1	−	11746.1i	−0.516203	−	0.516203i
$804$		0			0
$805$	−3064.97	+	3064.97i	−0.134194	+	0.134194i
$806$	15558.9	−	21716.5i	0.679950	−	0.949045i
$807$		0			0
$808$	48.6453	+	14.7424i	0.00211799	+	0.000641874i
$809$			15807.0i			0.686952i	0.939162	+	0.343476i	$0.111604\pi$
$809$			15807.0i			0.686952i	−0.939162	+	0.343476i	$0.888396\pi$
$810$		0			0
$811$	−11522.7	+	11522.7i	−0.498910	+	0.498910i	−0.911099	−	0.412189i	$-0.864764\pi$
$811$	−11522.7	+	11522.7i	−0.498910	+	0.498910i	0.412189	+	0.911099i	$0.364764\pi$
$812$	882.621	−	1790.57i	0.0381452	−	0.0773852i
$813$		0			0
$814$	21217.2	−	3504.89i	0.913591	−	0.150917i
$815$	23446.9			1.00774
$816$		0			0
$817$	−1224.33			−0.0524284
$818$	650.185	−	107.405i	0.0277912	−	0.00459086i
$819$		0			0
$820$	−8733.90	−	4305.17i	−0.371952	−	0.183345i
$821$	−308.824	+	308.824i	−0.0131279	+	0.0131279i	−0.713640	−	0.700512i	$-0.752955\pi$
$821$	−308.824	+	308.824i	−0.0131279	+	0.0131279i	0.700512	+	0.713640i	$0.252955\pi$
$822$		0			0
$823$		−	5633.49i		−	0.238604i	−0.992858	−	0.119302i	$-0.961934\pi$
$823$		−	5633.49i		−	0.238604i	0.992858	−	0.119302i	$-0.0380656\pi$
$824$	27700.1	−	14815.4i	1.17109	−	0.626358i
$825$		0			0
$826$	1771.98	−	2473.26i	0.0746430	−	0.104184i
$827$	15835.5	−	15835.5i	0.665844	−	0.665844i	−0.290908	−	0.956751i	$-0.593957\pi$
$827$	15835.5	−	15835.5i	0.665844	−	0.665844i	0.956751	+	0.290908i	$0.0939572\pi$
$828$		0			0
$829$	−6200.19	−	6200.19i	−0.259761	−	0.259761i	0.565196	−	0.824957i	$-0.308801\pi$
$829$	−6200.19	−	6200.19i	−0.259761	−	0.259761i	−0.824957	+	0.565196i	$0.808801\pi$
$830$	4276.58	+	25888.7i	0.178846	+	1.08266i
$831$		0			0
$832$	−25134.9	+	5013.43i	−1.04735	+	0.208906i
$833$	24349.7			1.01281
$834$		0			0
$835$	−6518.30	−	6518.30i	−0.270150	−	0.270150i
$836$	−13320.2	+	4524.21i	−0.551063	+	0.187169i
$837$		0			0
$838$	14270.6	−	19918.2i	0.588267	−	0.821079i
$839$			30644.3i			1.26098i	0.776199	+	0.630488i	$0.217145\pi$
$839$			30644.3i			1.26098i	−0.776199	+	0.630488i	$0.782855\pi$
$840$		0			0
$841$		−	15665.5i		−	0.642319i
$842$	27015.6	+	19355.5i	1.10573	+	0.792204i
$843$		0			0
$844$	22600.6	+	11140.4i	0.921735	+	0.454348i
$845$	−2540.65	−	2540.65i	−0.103433	−	0.103433i
$846$		0			0
$847$	−7371.03			−0.299022
$848$	−1762.17	+	13421.5i	−0.0713597	+	0.543509i
$849$		0			0
$850$	−2089.91	+	345.234i	−0.0843331	+	0.0139311i
$851$	−11723.9	−	11723.9i	−0.472256	−	0.472256i
$852$		0			0
$853$	−30801.0	+	30801.0i	−1.23635	+	1.23635i	−0.274869	+	0.961482i	$0.588635\pi$
$853$	−30801.0	+	30801.0i	−1.23635	+	1.23635i	−0.961482	+	0.274869i	$0.911365\pi$
$854$	1981.30	+	1419.52i	0.0793897	+	0.0568793i
$855$		0			0
$856$	25158.9	+	7624.61i	1.00457	+	0.304444i
$857$		−	41788.5i		−	1.66566i	−0.553533	−	0.832828i	$-0.686721\pi$
$857$		−	41788.5i		−	1.66566i	0.553533	−	0.832828i	$-0.313279\pi$
$858$		0			0
$859$	11914.5	−	11914.5i	0.473243	−	0.473243i	−0.429719	−	0.902963i	$-0.641388\pi$
$859$	11914.5	−	11914.5i	0.473243	−	0.473243i	0.902963	+	0.429719i	$0.141388\pi$
$860$	1332.72	+	3923.80i	0.0528435	+	0.155582i
$861$		0			0
$862$	4027.88	+	24383.1i	0.159153	+	0.963449i
$863$	−27636.7			−1.09011			−0.545054	−	0.838401i	$-0.683491\pi$
$863$	−27636.7			−1.09011			−0.545054	+	0.838401i	$0.683491\pi$
$864$		0			0
$865$	−12727.0			−0.500266
$866$	5360.10	+	32447.9i	0.210328	+	1.27324i
$867$		0			0
$868$	1296.98	+	3818.57i	0.0507169	+	0.149321i
$869$	14615.1	−	14615.1i	0.570520	−	0.570520i
$870$		0			0
$871$			9850.95i			0.383223i
$872$	−4944.90	+	16316.7i	−0.192036	+	0.633661i
$873$		0			0
$874$	8816.73	+	6316.80i	0.341224	+	0.244473i
$875$	−2520.12	+	2520.12i	−0.0973663	+	0.0973663i
$876$		0			0
$877$	−11918.3	−	11918.3i	−0.458896	−	0.458896i	0.439397	−	0.898293i	$-0.355192\pi$
$877$	−11918.3	−	11918.3i	−0.458896	−	0.458896i	−0.898293	+	0.439397i	$0.855192\pi$
$878$	−49203.4	+	8127.96i	−1.89127	+	0.312421i
$879$		0			0
$880$	28998.8	+	37764.5i	1.11085	+	1.44664i
$881$	13330.0			0.509759			0.254880	−	0.966973i	$-0.417964\pi$
$881$	13330.0			0.509759			0.254880	+	0.966973i	$0.417964\pi$
$882$		0			0
$883$	−25172.1	−	25172.1i	−0.959353	−	0.959353i	0.0398530	−	0.999206i	$-0.487311\pi$
$883$	−25172.1	−	25172.1i	−0.959353	−	0.959353i	−0.999206	+	0.0398530i	$0.987311\pi$
$884$	−26041.7	−	12836.7i	−0.990812	−	0.488398i
$885$		0			0
$886$	−14794.1	−	10599.4i	−0.560969	−	0.401910i
$887$		−	48821.3i		−	1.84810i	−0.382278	−	0.924048i	$-0.624860\pi$
$887$		−	48821.3i		−	1.84810i	0.382278	−	0.924048i	$-0.375140\pi$
$888$		0			0
$889$		−	5085.84i		−	0.191871i
$890$	16611.7	−	23185.9i	0.625645	−	0.873249i
$891$		0			0
$892$	2712.25	−	921.217i	0.101808	−	0.0345792i
$893$	9490.96	+	9490.96i	0.355658	+	0.355658i
$894$		0			0
$895$	7009.27			0.261781
$896$	1594.61	−	3525.15i	0.0594556	−	0.131437i
$897$		0			0
$898$	−5958.93	−	36072.9i	−0.221439	−	1.34050i
$899$	−12461.2	−	12461.2i	−0.462296	−	0.462296i
$900$		0			0
$901$	−10843.0	+	10843.0i	−0.400924	+	0.400924i
$902$	−11022.5	+	15384.8i	−0.406885	+	0.567913i
$903$		0			0
$904$	717.868	+	1342.18i	0.0264114	+	0.0493809i
$905$		−	43071.7i		−	1.58205i
$906$		0			0
$907$	5320.20	−	5320.20i	0.194768	−	0.194768i	−0.602985	−	0.797753i	$-0.706022\pi$
$907$	5320.20	−	5320.20i	0.194768	−	0.194768i	0.797753	+	0.602985i	$0.206022\pi$
$908$	35064.8	+	17284.4i	1.28157	+	0.631720i
$909$		0			0
$910$	4341.73	−	717.215i	0.158161	−	0.0261269i
$911$	26016.0			0.946155			0.473077	−	0.881021i	$-0.343143\pi$
$911$	26016.0			0.946155			0.473077	+	0.881021i	$0.343143\pi$
$912$		0			0
$913$	51000.2			1.84870
$914$	26009.4	−	4296.52i	0.941262	−	0.155488i
$915$		0			0
$916$	7153.21	−	14511.7i	0.258023	−	0.523450i
$917$	−2453.77	+	2453.77i	−0.0883650	+	0.0883650i
$918$		0			0
$919$			24082.1i			0.864413i	0.901775	+	0.432206i	$0.142265\pi$
$919$			24082.1i			0.864413i	−0.901775	+	0.432206i	$0.857735\pi$
$920$	10647.1	−	35132.3i	0.381550	−	1.25900i
$921$		0			0
$922$	−30017.2	+	41896.8i	−1.07220	+	1.49653i
$923$	−16057.9	+	16057.9i	−0.572646	+	0.572646i
$924$		0			0
$925$	868.385	+	868.385i	0.0308674	+	0.0308674i
$926$	−3244.57	−	19641.3i	−0.115144	−	0.697035i
$927$		0			0
$928$	560.619	+	16897.8i	0.0198311	+	0.597735i
$929$	−9324.93			−0.329323			−0.164661	−	0.986350i	$-0.552653\pi$
$929$	−9324.93			−0.329323			−0.164661	+	0.986350i	$0.552653\pi$
$930$		0			0
$931$	6530.06	+	6530.06i	0.229875	+	0.229875i
$932$	−2383.69	−	7018.07i	−0.0837772	−	0.246657i
$933$		0			0
$934$	−13981.8	+	19515.3i	−0.489829	+	0.683682i
$935$			53937.0i			1.88656i
$936$		0			0
$937$		−	15535.2i		−	0.541636i	−0.962631	−	0.270818i	$-0.912706\pi$
$937$		−	15535.2i		−	0.541636i	0.962631	−	0.270818i	$-0.0872941\pi$
$938$	−1208.84	−	866.083i	−0.0420790	−	0.0301478i
$939$		0			0
$940$	20085.9	−	40748.3i	0.696947	−	1.41390i
$941$	34024.8	+	34024.8i	1.17872	+	1.17872i	0.980070	+	0.198651i	$0.0636559\pi$
$941$	34024.8	+	34024.8i	1.17872	+	1.17872i	0.198651	+	0.980070i	$0.436344\pi$
$942$		0			0
$943$	14591.8			0.503896
$944$	−3354.40	+	25548.7i	−0.115653	+	0.880867i
$945$		0			0
$946$	7946.66	−	1312.72i	0.273117	−	0.0451164i
$947$	3816.02	+	3816.02i	0.130944	+	0.130944i	0.769541	−	0.638597i	$-0.220485\pi$
$947$	3816.02	+	3816.02i	0.130944	+	0.130944i	−0.638597	+	0.769541i	$0.720485\pi$
$948$		0			0
$949$	9194.21	−	9194.21i	0.314496	−	0.314496i
$950$	−653.051	−	467.883i	−0.0223029	−	0.0159791i
$951$		0			0
$952$	3864.78	−	2067.08i	0.131574	−	0.0703723i
$953$			21759.7i			0.739629i	0.929106	+	0.369815i	$0.120579\pi$
$953$			21759.7i			0.739629i	−0.929106	+	0.369815i	$0.879421\pi$
$954$		0			0
$955$	26457.6	−	26457.6i	0.896489	−	0.896489i
$956$	−6002.97	+	2038.91i	−0.203086	+	0.0689781i
$957$		0			0
$958$	−270.744	−	1638.97i	−0.00913082	−	0.0552743i
$959$	−1275.03			−0.0429331
$960$		0			0
$961$	5809.78			0.195018
$962$	2743.44	+	16607.7i	0.0919461	+	0.556604i
$963$		0			0
$964$	−10976.3	+	3728.09i	−0.366723	+	0.124558i
$965$	−23464.9	+	23464.9i	−0.782759	+	0.782759i
$966$		0			0
$967$			19338.5i			0.643108i	0.946891	+	0.321554i	$0.104205\pi$
$967$			19338.5i			0.643108i	−0.946891	+	0.321554i	$0.895795\pi$
$968$	55048.2	−	29442.6i	1.82781	−	0.977603i
$969$		0			0
$970$	−25037.4	−	17938.2i	−0.828766	−	0.593775i
$971$	−4184.92	+	4184.92i	−0.138311	+	0.138311i	−0.772873	−	0.634561i	$-0.781181\pi$
$971$	−4184.92	+	4184.92i	−0.138311	+	0.138311i	0.634561	+	0.772873i	$0.281181\pi$
$972$		0			0
$973$	4044.67	+	4044.67i	0.133264	+	0.133264i
$974$	−23347.5	+	3856.80i	−0.768072	+	0.126879i
$975$		0			0
$976$	−20466.8	−	2687.18i	−0.671236	−	0.0881296i
$977$	−17841.9			−0.584249			−0.292125	−	0.956380i	$-0.594362\pi$
$977$	−17841.9			−0.584249			−0.292125	+	0.956380i	$0.594362\pi$
$978$		0			0
$979$	−39200.2	−	39200.2i	−1.27972	−	1.27972i
$980$	13819.7	−	28036.0i	0.450463	−	0.913855i
$981$		0			0
$982$	4972.66	+	3562.69i	0.161593	+	0.115774i
$983$		−	61512.0i		−	1.99586i	−0.0643304	−	0.997929i	$-0.520491\pi$
$983$		−	61512.0i		−	1.99586i	0.0643304	−	0.997929i	$-0.479509\pi$
$984$		0			0
$985$		−	26471.2i		−	0.856286i
$986$	−11154.5	+	15568.9i	−0.360274	+	0.502855i
$987$		0			0
$988$	−3541.31	−	10426.3i	−0.114032	−	0.335735i
$989$	−4391.05	−	4391.05i	−0.141180	−	0.141180i
$990$		0			0
$991$	1827.73			0.0585870			0.0292935	−	0.999571i	$-0.490674\pi$
$991$	1827.73			0.0585870			0.0292935	+	0.999571i	$0.490674\pi$
$992$	−24938.8	−	23337.2i	−0.798193	−	0.746931i
$993$		0			0
$994$	−558.726	−	3382.30i	−0.0178287	−	0.107928i
$995$	−6145.84	−	6145.84i	−0.195815	−	0.195815i
$996$		0			0
$997$	−25017.0	+	25017.0i	−0.794681	+	0.794681i	−0.982251	−	0.187570i	$-0.939939\pi$
$997$	−25017.0	+	25017.0i	−0.794681	+	0.794681i	0.187570	+	0.982251i	$0.439939\pi$
$998$	26474.9	−	36952.6i	0.839728	−	1.17206i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.k.a.109.3		10
3.2	odd	2		16.4.e.a.13.3	yes	10
4.3	odd	2		576.4.k.a.145.2		10
12.11	even	2		64.4.e.a.17.3		10
16.5	even	4	inner	144.4.k.a.37.3		10
16.11	odd	4		576.4.k.a.433.2		10
24.5	odd	2		128.4.e.b.33.3		10
24.11	even	2		128.4.e.a.33.3		10
48.5	odd	4		16.4.e.a.5.3	✓	10
48.11	even	4		64.4.e.a.49.3		10
48.29	odd	4		128.4.e.b.97.3		10
48.35	even	4		128.4.e.a.97.3		10
96.5	odd	8		1024.4.a.n.1.5		10
96.11	even	8		1024.4.a.m.1.5		10
96.29	odd	8		1024.4.b.j.513.6		10
96.35	even	8		1024.4.b.k.513.5		10
96.53	odd	8		1024.4.a.n.1.6		10
96.59	even	8		1024.4.a.m.1.6		10
96.77	odd	8		1024.4.b.j.513.5		10
96.83	even	8		1024.4.b.k.513.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.4.e.a.5.3	✓	10	48.5	odd	4
16.4.e.a.13.3	yes	10	3.2	odd	2
64.4.e.a.17.3		10	12.11	even	2
64.4.e.a.49.3		10	48.11	even	4
128.4.e.a.33.3		10	24.11	even	2
128.4.e.a.97.3		10	48.35	even	4
128.4.e.b.33.3		10	24.5	odd	2
128.4.e.b.97.3		10	48.29	odd	4
144.4.k.a.37.3		10	16.5	even	4	inner
144.4.k.a.109.3		10	1.1	even	1	trivial
576.4.k.a.145.2		10	4.3	odd	2
576.4.k.a.433.2		10	16.11	odd	4
1024.4.a.m.1.5		10	96.11	even	8
1024.4.a.m.1.6		10	96.59	even	8
1024.4.a.n.1.5		10	96.5	odd	8
1024.4.a.n.1.6		10	96.53	odd	8
1024.4.b.j.513.5		10	96.77	odd	8
1024.4.b.j.513.6		10	96.29	odd	8
1024.4.b.k.513.5		10	96.35	even	8
1024.4.b.k.513.6		10	96.83	even	8

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.460984 - 2.79061i) q^{2} +(-7.57499 + 2.57285i) q^{4} +(-8.22587 + 8.22587i) q^{5} -2.67171i q^{7} +(10.6718 + 19.9528i) q^{8} +O(q^{10})\)	\(q+(-0.460984 - 2.79061i) q^{2} +(-7.57499 + 2.57285i) q^{4} +(-8.22587 + 8.22587i) q^{5} -2.67171i q^{7} +(10.6718 + 19.9528i) q^{8} +(26.7472 + 19.1632i) q^{10} +(45.2213 - 45.2213i) q^{11} +(35.3968 + 35.3968i) q^{13} +(-7.45568 + 1.23161i) q^{14} +(50.7609 - 38.9786i) q^{16} +72.4991 q^{17} +(19.4427 + 19.4427i) q^{19} +(41.1470 - 83.4748i) q^{20} +(-147.041 - 105.349i) q^{22} +139.462i q^{23} -10.3299i q^{25} +(82.4612 - 115.096i) q^{26} +(6.87389 + 20.2381i) q^{28} +(-66.0434 - 66.0434i) q^{29} +188.682 q^{31} +(-132.174 - 123.685i) q^{32} +(-33.4209 - 202.317i) q^{34} +(21.9771 + 21.9771i) q^{35} +(-84.0653 + 84.0653i) q^{37} +(45.2941 - 63.2196i) q^{38} +(-251.914 - 76.3445i) q^{40} -104.629i q^{41} +(-31.4857 + 31.4857i) q^{43} +(-226.203 + 458.898i) q^{44} +(389.183 - 64.2896i) q^{46} +488.151 q^{47} +335.862 q^{49} +(-28.8266 + 4.76190i) q^{50} +(-359.201 - 177.060i) q^{52} +(-149.560 + 149.560i) q^{53} +743.968i q^{55} +(53.3080 - 28.5118i) q^{56} +(-153.856 + 214.746i) q^{58} +(-284.698 + 284.698i) q^{59} +(-228.069 - 228.069i) q^{61} +(-86.9792 - 526.537i) q^{62} +(-284.227 + 425.863i) q^{64} -582.338 q^{65} +(139.151 + 139.151i) q^{67} +(-549.180 + 186.529i) q^{68} +(51.1984 - 71.4606i) q^{70} +453.655i q^{71} -259.747i q^{73} +(273.346 + 195.841i) q^{74} +(-197.301 - 97.2550i) q^{76} +(-120.818 - 120.818i) q^{77} +323.190 q^{79} +(-96.9197 + 738.185i) q^{80} +(-291.979 + 48.2323i) q^{82} +(563.897 + 563.897i) q^{83} +(-596.368 + 596.368i) q^{85} +(102.379 + 73.3499i) q^{86} +(1384.88 + 419.700i) q^{88} -866.853i q^{89} +(94.5697 - 94.5697i) q^{91} +(-358.814 - 1056.42i) q^{92} +(-225.030 - 1362.24i) q^{94} -319.866 q^{95} -936.077 q^{97} +(-154.827 - 937.259i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) \) 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8	\( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8 - 68 * q^10 - 18 * q^11 - 2 * q^13 - 188 * q^14 + 280 * q^16 + 4 * q^17 - 26 * q^19 + 196 * q^20 - 588 * q^22 + 264 * q^26 + 280 * q^28 + 202 * q^29 + 368 * q^31 - 968 * q^32 + 436 * q^34 - 476 * q^35 - 10 * q^37 + 1232 * q^38 - 1336 * q^40 - 838 * q^43 - 868 * q^44 + 1132 * q^46 + 944 * q^47 + 94 * q^49 - 726 * q^50 - 236 * q^52 + 378 * q^53 + 488 * q^56 + 8 * q^58 - 1706 * q^59 + 910 * q^61 + 80 * q^62 + 512 * q^64 + 492 * q^65 + 1942 * q^67 + 880 * q^68 + 160 * q^70 + 452 * q^74 - 1228 * q^76 + 268 * q^77 - 4416 * q^79 + 2648 * q^80 - 704 * q^82 + 2562 * q^83 - 12 * q^85 - 3764 * q^86 + 1528 * q^88 + 3332 * q^91 - 632 * q^92 - 3248 * q^94 - 6900 * q^95 - 4 * q^97 - 314 * q^98

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