LMFDB - Embedded newform 1008.2.q.g.625.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (of order $3$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	1008.625
Dual form			1008.2.q.g.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933463 - 1.45899i) q^{3} +(-0.296790 - 0.514055i) q^{5} +(-2.32383 - 1.26483i) q^{7} +(-1.25729 + 2.72382i) q^{9} +O(q^{10})$	\(q+(-0.933463 - 1.45899i) q^{3} +(-0.296790 - 0.514055i) q^{5} +(-2.32383 - 1.26483i) q^{7} +(-1.25729 + 2.72382i) q^{9} +(-0.296790 + 0.514055i) q^{11} +(-1.25729 + 2.17770i) q^{13} +(-0.472958 + 0.912864i) q^{15} +(1.46050 + 2.52967i) q^{17} +(-2.69076 + 4.66053i) q^{19} +(0.323832 + 4.57112i) q^{21} +(2.23025 + 3.86291i) q^{23} +(2.32383 - 4.02499i) q^{25} +(5.14766 - 0.708209i) q^{27} +(-3.09718 - 5.36447i) q^{29} +7.86693 q^{31} +(1.02704 - 0.0468383i) q^{33} +(0.0394951 + 1.56997i) q^{35} +(0.500000 - 0.866025i) q^{37} +(4.35087 - 0.198422i) q^{39} +(-0.136673 + 0.236725i) q^{41} +(5.58113 + 9.66679i) q^{43} +(1.77335 - 0.162084i) q^{45} -12.1623 q^{47} +(3.80039 + 5.87852i) q^{49} +(2.32743 - 4.49221i) q^{51} +(4.02704 + 6.97504i) q^{53} +0.352336 q^{55} +(9.31138 - 0.424646i) q^{57} -8.64766 q^{59} -6.64766 q^{61} +(6.36693 - 4.73944i) q^{63} +1.49261 q^{65} +1.91381 q^{67} +(3.55408 - 6.85980i) q^{69} +14.4107 q^{71} +(3.95691 + 6.85356i) q^{73} +(-8.04163 + 0.366739i) q^{75} +(1.33988 - 0.819187i) q^{77} +9.24844 q^{79} +(-5.83842 - 6.84929i) q^{81} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(-4.93560 + 9.52628i) q^{87} +(-6.21780 + 10.7695i) q^{89} +(5.67617 - 3.47033i) q^{91} +(-7.34348 - 11.4778i) q^{93} +3.19436 q^{95} +(5.86693 + 10.1618i) q^{97} +(-1.02704 - 1.45472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9}+O(q^{10}) $ 6 * q - 2 * q^3 + q^5 - 2 * q^7 + 8 * q^9	$ 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9} + q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} + 2 q^{25} + 7 q^{27} - 5 q^{29} + 40 q^{31} - 3 q^{33} + 13 q^{35} + 3 q^{37} + 5 q^{39} + 6 q^{43} + 9 q^{45} - 18 q^{47} + 12 q^{49} - 6 q^{51} + 15 q^{53} + 26 q^{55} + 22 q^{57} - 28 q^{59} - 16 q^{61} + 31 q^{63} + 24 q^{65} + 2 q^{67} + 3 q^{69} - 14 q^{71} + 19 q^{73} - 8 q^{75} + 10 q^{77} + 10 q^{79} + 8 q^{81} - 2 q^{83} - 2 q^{85} + 27 q^{87} - 9 q^{89} + 46 q^{91} - 38 q^{93} - 8 q^{95} + 28 q^{97} + 3 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 + q^5 - 2 * q^7 + 8 * q^9 + q^11 + 8 * q^13 - 12 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 + 2 * q^25 + 7 * q^27 - 5 * q^29 + 40 * q^31 - 3 * q^33 + 13 * q^35 + 3 * q^37 + 5 * q^39 + 6 * q^43 + 9 * q^45 - 18 * q^47 + 12 * q^49 - 6 * q^51 + 15 * q^53 + 26 * q^55 + 22 * q^57 - 28 * q^59 - 16 * q^61 + 31 * q^63 + 24 * q^65 + 2 * q^67 + 3 * q^69 - 14 * q^71 + 19 * q^73 - 8 * q^75 + 10 * q^77 + 10 * q^79 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 27 * q^87 - 9 * q^89 + 46 * q^91 - 38 * q^93 - 8 * q^95 + 28 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−0.933463	−	1.45899i	−0.538935	−	0.842347i
$3$	−0.933463	−	1.45899i	−0.538935	−	0.842347i
$4$		0			0
$5$	−0.296790	−	0.514055i	−0.132728	−	0.229892i	0.791999	−	0.610522i	$-0.209040\pi$
$5$	−0.296790	−	0.514055i	−0.132728	−	0.229892i	−0.924727	+	0.380630i	$0.875707\pi$
$6$		0			0
$7$	−2.32383	−	1.26483i	−0.878326	−	0.478062i
$7$	−2.32383	−	1.26483i	−0.878326	−	0.478062i
$8$		0			0
$9$	−1.25729	+	2.72382i	−0.419098	+	0.907941i
$10$		0			0
$11$	−0.296790	+	0.514055i	−0.0894855	+	0.154993i	−0.907294	−	0.420497i	$-0.861856\pi$
$11$	−0.296790	+	0.514055i	−0.0894855	+	0.154993i	0.817808	+	0.575491i	$0.195189\pi$
$12$		0			0
$13$	−1.25729	+	2.17770i	−0.348711	+	0.603985i	−0.986021	−	0.166623i	$-0.946714\pi$
$13$	−1.25729	+	2.17770i	−0.348711	+	0.603985i	0.637310	+	0.770608i	$0.280047\pi$
$14$		0			0
$15$	−0.472958	+	0.912864i	−0.122117	+	0.235700i
$16$		0			0
$17$	1.46050	+	2.52967i	0.354224	+	0.613535i	0.986985	−	0.160813i	$-0.0514116\pi$
$17$	1.46050	+	2.52967i	0.354224	+	0.613535i	−0.632760	+	0.774348i	$0.718078\pi$
$18$		0			0
$19$	−2.69076	+	4.66053i	−0.617302	+	1.06920i	0.372674	+	0.927962i	$0.378441\pi$
$19$	−2.69076	+	4.66053i	−0.617302	+	1.06920i	−0.989976	+	0.141236i	$0.954892\pi$
$20$		0			0
$21$	0.323832	+	4.57112i	0.0706659	+	0.997500i
$22$		0			0
$23$	2.23025	+	3.86291i	0.465040	+	0.805473i	0.999203	−	0.0399086i	$-0.0127067\pi$
$23$	2.23025	+	3.86291i	0.465040	+	0.805473i	−0.534164	+	0.845381i	$0.679373\pi$
$24$		0			0
$25$	2.32383	−	4.02499i	0.464766	−	0.804999i
$26$		0			0
$27$	5.14766	−	0.708209i	0.990668	−	0.136295i
$28$		0			0
$29$	−3.09718	−	5.36447i	−0.575132	−	0.996157i	−0.996027	−	0.0890480i	$-0.971618\pi$
$29$	−3.09718	−	5.36447i	−0.575132	−	0.996157i	0.420896	−	0.907109i	$-0.361716\pi$
$30$		0			0
$31$	7.86693			1.41294			0.706471	−	0.707742i	$-0.250286\pi$
$31$	7.86693			1.41294			0.706471	+	0.707742i	$0.250286\pi$
$32$		0			0
$33$	1.02704	−	0.0468383i	0.178785	−	0.00815350i
$34$		0			0
$35$	0.0394951	+	1.56997i	0.00667590	+	0.265373i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$	4.35087	−	0.198422i	0.696697	−	0.0317729i
$40$		0			0
$41$	−0.136673	+	0.236725i	−0.0213448	+	0.0369702i	−0.876500	−	0.481401i	$-0.840128\pi$
$41$	−0.136673	+	0.236725i	−0.0213448	+	0.0369702i	0.855156	+	0.518371i	$0.173461\pi$
$42$		0			0
$43$	5.58113	+	9.66679i	0.851114	+	1.47417i	0.880204	+	0.474596i	$0.157406\pi$
$43$	5.58113	+	9.66679i	0.851114	+	1.47417i	−0.0290902	+	0.999577i	$0.509261\pi$
$44$		0			0
$45$	1.77335	−	0.162084i	0.264355	−	0.0241621i
$46$		0			0
$47$	−12.1623			−1.77405			−0.887023	−	0.461724i	$-0.847231\pi$
$47$	−12.1623			−1.77405			−0.887023	+	0.461724i	$0.847231\pi$
$48$		0			0
$49$	3.80039	+	5.87852i	0.542913	+	0.839789i
$50$		0			0
$51$	2.32743	−	4.49221i	0.325905	−	0.629035i
$52$		0			0
$53$	4.02704	+	6.97504i	0.553157	+	0.958096i	0.998044	+	0.0625092i	$0.0199103\pi$
$53$	4.02704	+	6.97504i	0.553157	+	0.958096i	−0.444888	+	0.895586i	$0.646756\pi$
$54$		0			0
$55$	0.352336			0.0475090
$56$		0			0
$57$	9.31138	−	0.424646i	1.23332	−	0.0562457i
$58$		0			0
$59$	−8.64766			−1.12583			−0.562915	−	0.826515i	$-0.690320\pi$
$59$	−8.64766			−1.12583			−0.562915	+	0.826515i	$0.690320\pi$
$60$		0			0
$61$	−6.64766			−0.851146			−0.425573	−	0.904924i	$-0.639927\pi$
$61$	−6.64766			−0.851146			−0.425573	+	0.904924i	$0.639927\pi$
$62$		0			0
$63$	6.36693	−	4.73944i	0.802157	−	0.597113i
$64$		0			0
$65$	1.49261			0.185135
$66$		0			0
$67$	1.91381			0.233809			0.116905	−	0.993143i	$-0.462703\pi$
$67$	1.91381			0.233809			0.116905	+	0.993143i	$0.462703\pi$
$68$		0			0
$69$	3.55408	−	6.85980i	0.427861	−	0.825822i
$70$		0			0
$71$	14.4107			1.71023			0.855117	−	0.518435i	$-0.173485\pi$
$71$	14.4107			1.71023			0.855117	+	0.518435i	$0.173485\pi$
$72$		0			0
$73$	3.95691	+	6.85356i	0.463121	+	0.802149i	0.999115	−	0.0420732i	$-0.0133963\pi$
$73$	3.95691	+	6.85356i	0.463121	+	0.802149i	−0.535994	+	0.844222i	$0.680063\pi$
$74$		0			0
$75$	−8.04163	+	0.366739i	−0.928568	+	0.0423474i
$76$		0			0
$77$	1.33988	−	0.819187i	0.152694	−	0.0933550i
$78$		0			0
$79$	9.24844			1.04053			0.520265	−	0.854005i	$-0.325833\pi$
$79$	9.24844			1.04053			0.520265	+	0.854005i	$0.325833\pi$
$80$		0			0
$81$	−5.83842	−	6.84929i	−0.648713	−	0.761033i
$82$		0			0
$83$	−3.85087	−	6.66991i	−0.422688	−	0.732118i	0.573513	−	0.819196i	$-0.305580\pi$
$83$	−3.85087	−	6.66991i	−0.422688	−	0.732118i	−0.996201	+	0.0870787i	$0.972247\pi$
$84$		0			0
$85$	0.866926	−	1.50156i	0.0940313	−	0.162867i
$86$		0			0
$87$	−4.93560	+	9.52628i	−0.529152	+	1.02132i
$88$		0			0
$89$	−6.21780	+	10.7695i	−0.659085	+	1.14157i	0.321767	+	0.946819i	$0.395723\pi$
$89$	−6.21780	+	10.7695i	−0.659085	+	1.14157i	−0.980853	+	0.194751i	$0.937610\pi$
$90$		0			0
$91$	5.67617	−	3.47033i	0.595024	−	0.363790i
$92$		0			0
$93$	−7.34348	−	11.4778i	−0.761484	−	1.19019i
$94$		0			0
$95$	3.19436			0.327734
$96$		0			0
$97$	5.86693	+	10.1618i	0.595696	+	1.03178i	0.993448	+	0.114283i	$0.0364570\pi$
$97$	5.86693	+	10.1618i	0.595696	+	1.03178i	−0.397752	+	0.917493i	$0.630210\pi$
$98$		0			0
$99$	−1.02704	−	1.45472i	−0.103222	−	0.146205i
$100$		0			0
$101$	0.811379	−	1.40535i	0.0807352	−	0.139837i	−0.822831	−	0.568287i	$-0.807607\pi$
$101$	0.811379	−	1.40535i	0.0807352	−	0.139837i	0.903566	+	0.428449i	$0.140940\pi$
$102$		0			0
$103$	3.19076	+	5.52655i	0.314395	+	0.544548i	0.979309	−	0.202372i	$-0.0648651\pi$
$103$	3.19076	+	5.52655i	0.314395	+	0.544548i	−0.664914	+	0.746920i	$0.731532\pi$
$104$		0			0
$105$	2.25370	−	1.52313i	0.219938	−	0.148642i
$106$		0			0
$107$	−9.35447	+	16.2024i	−0.904331	+	1.56635i	−0.0825182	+	0.996590i	$0.526296\pi$
$107$	−9.35447	+	16.2024i	−0.904331	+	1.56635i	−0.821813	+	0.569758i	$0.807037\pi$
$108$		0			0
$109$	−1.43346	−	2.48283i	−0.137301	−	0.237812i	0.789173	−	0.614171i	$-0.210509\pi$
$109$	−1.43346	−	2.48283i	−0.137301	−	0.237812i	−0.926474	+	0.376359i	$0.877176\pi$
$110$		0			0
$111$	−1.73025	+	0.0789082i	−0.164228	+	0.00748964i
$112$		0			0
$113$	−6.16012	+	10.6696i	−0.579495	+	1.00371i	0.416042	+	0.909345i	$0.363417\pi$
$113$	−6.16012	+	10.6696i	−0.579495	+	1.00371i	−0.995537	+	0.0943695i	$0.969916\pi$
$114$		0			0
$115$	1.32383	−	2.29294i	0.123448	−	0.213818i
$116$		0			0
$117$	−4.35087	−	6.16266i	−0.402238	−	0.569738i
$118$		0			0
$119$	−0.194356	−	7.72582i	−0.0178166	−	0.708225i
$120$		0			0
$121$	5.32383	+	9.22115i	0.483985	+	0.838286i
$122$		0			0
$123$	0.472958	−	0.0215693i	0.0426452	−	0.00194484i
$124$		0			0
$125$	−5.72665			−0.512207
$126$		0			0
$127$	−12.3346			−1.09452			−0.547261	−	0.836962i	$-0.684329\pi$
$127$	−12.3346			−1.09452			−0.547261	+	0.836962i	$0.684329\pi$
$128$		0			0
$129$	8.89397	−	17.1664i	0.783070	−	1.51142i
$130$		0			0
$131$	−0.593579	−	1.02811i	−0.0518613	−	0.0898264i	0.838929	−	0.544240i	$-0.183182\pi$
$131$	−0.593579	−	1.02811i	−0.0518613	−	0.0898264i	−0.890791	+	0.454414i	$0.849849\pi$
$132$		0			0
$133$	12.1477	−	7.42692i	1.05334	−	0.643996i
$134$		0			0
$135$	−1.89183	−	2.43599i	−0.162823	−	0.209657i
$136$		0			0
$137$	−1.26089	+	2.18393i	−0.107725	+	0.186586i	−0.914848	−	0.403797i	$-0.867690\pi$
$137$	−1.26089	+	2.18393i	−0.107725	+	0.186586i	0.807123	+	0.590383i	$0.201023\pi$
$138$		0			0
$139$	−2.45691	+	4.25549i	−0.208392	+	0.360946i	−0.951208	−	0.308550i	$-0.900156\pi$
$139$	−2.45691	+	4.25549i	−0.208392	+	0.360946i	0.742816	+	0.669496i	$0.233490\pi$
$140$		0			0
$141$	11.3530	+	17.7446i	0.956096	+	1.49436i
$142$		0			0
$143$	−0.746304	−	1.29264i	−0.0624091	−	0.108096i
$144$		0			0
$145$	−1.83842	+	3.18424i	−0.152673	+	0.264437i
$146$		0			0
$147$	5.02918	−	11.0321i	0.414800	−	0.909913i
$148$		0			0
$149$	−9.02558	−	15.6328i	−0.739404	−	1.28069i	−0.952764	−	0.303712i	$-0.901774\pi$
$149$	−9.02558	−	15.6328i	−0.739404	−	1.28069i	0.213360	−	0.976974i	$-0.431559\pi$
$150$		0			0
$151$	0.823832	−	1.42692i	0.0670425	−	0.116121i	−0.830556	−	0.556936i	$-0.811977\pi$
$151$	0.823832	−	1.42692i	0.0670425	−	0.116121i	0.897598	+	0.440815i	$0.145310\pi$
$152$		0			0
$153$	−8.72665	+	0.797618i	−0.705508	+	0.0644836i
$154$		0			0
$155$	−2.33482	−	4.04403i	−0.187537	−	0.324824i
$156$		0			0
$157$	−6.60078			−0.526799			−0.263400	−	0.964687i	$-0.584844\pi$
$157$	−6.60078			−0.526799			−0.263400	+	0.964687i	$0.584844\pi$
$158$		0			0
$159$	6.41741	−	12.3863i	0.508934	−	0.982301i
$160$		0			0
$161$	−0.296790	−	11.7977i	−0.0233903	−	0.929785i
$162$		0			0
$163$	2.99115	−	5.18082i	0.234285	−	0.405793i	−0.724780	−	0.688980i	$-0.758059\pi$
$163$	2.99115	−	5.18082i	0.234285	−	0.405793i	0.959065	+	0.283188i	$0.0913919\pi$
$164$		0			0
$165$	−0.328893	−	0.514055i	−0.0256043	−	0.0400191i
$166$		0			0
$167$	−3.73025	+	6.46099i	−0.288656	+	0.499966i	−0.973489	−	0.228733i	$-0.926542\pi$
$167$	−3.73025	+	6.46099i	−0.288656	+	0.499966i	0.684833	+	0.728700i	$0.259875\pi$
$168$		0			0
$169$	3.33842	+	5.78231i	0.256802	+	0.444793i
$170$		0			0
$171$	−9.31138	−	13.1888i	−0.712059	−	1.00857i
$172$		0			0
$173$	−25.6591			−1.95083			−0.975414	−	0.220381i	$-0.929270\pi$
$173$	−25.6591			−1.95083			−0.975414	+	0.220381i	$0.929270\pi$
$174$		0			0
$175$	−10.4911	+	6.41415i	−0.793056	+	0.484864i
$176$		0			0
$177$	8.07227	+	12.6168i	0.606749	+	0.948340i
$178$		0			0
$179$	−7.51819	−	13.0219i	−0.561936	−	0.973301i	−0.997328	−	0.0730602i	$-0.976723\pi$
$179$	−7.51819	−	13.0219i	−0.561936	−	0.973301i	0.435392	−	0.900241i	$-0.356610\pi$
$180$		0			0
$181$	−0.0861875			−0.00640627			−0.00320313	−	0.999995i	$-0.501020\pi$
$181$	−0.0861875			−0.00640627			−0.00320313	+	0.999995i	$0.501020\pi$
$182$		0			0
$183$	6.20535	+	9.69886i	0.458712	+	0.716961i
$184$		0			0
$185$	−0.593579			−0.0436408
$186$		0			0
$187$	−1.73385			−0.126792
$188$		0			0
$189$	−12.8581	−	4.86518i	−0.935287	−	0.353890i
$190$		0			0
$191$	−3.98229			−0.288148			−0.144074	−	0.989567i	$-0.546020\pi$
$191$	−3.98229			−0.288148			−0.144074	+	0.989567i	$0.546020\pi$
$192$		0			0
$193$	6.78074			0.488088			0.244044	−	0.969764i	$-0.421526\pi$
$193$	6.78074			0.488088			0.244044	+	0.969764i	$0.421526\pi$
$194$		0			0
$195$	−1.39329	−	2.17770i	−0.0997759	−	0.155948i
$196$		0			0
$197$	11.0584			0.787875			0.393938	−	0.919137i	$-0.371113\pi$
$197$	11.0584			0.787875			0.393938	+	0.919137i	$0.371113\pi$
$198$		0			0
$199$	−2.80924	−	4.86575i	−0.199142	−	0.344924i	0.749109	−	0.662447i	$-0.230482\pi$
$199$	−2.80924	−	4.86575i	−0.199142	−	0.344924i	−0.948250	+	0.317523i	$0.897149\pi$
$200$		0			0
$201$	−1.78647	−	2.79223i	−0.126008	−	0.196949i
$202$		0			0
$203$	0.412155	+	16.3835i	0.0289276	+	1.14990i
$204$		0			0
$205$	0.162253			0.0113322
$206$		0			0
$207$	−13.3260	+	1.21800i	−0.926219	+	0.0846566i
$208$		0			0
$209$	−1.59718	−	2.76639i	−0.110479	−	0.191355i
$210$		0			0
$211$	−9.66225	+	16.7355i	−0.665177	+	1.15212i	0.314060	+	0.949403i	$0.398311\pi$
$211$	−9.66225	+	16.7355i	−0.665177	+	1.15212i	−0.979237	+	0.202717i	$0.935023\pi$
$212$		0			0
$213$	−13.4518	−	21.0250i	−0.921705	−	1.44061i
$214$		0			0
$215$	3.31284	−	5.73801i	0.225934	−	0.391329i
$216$		0			0
$217$	−18.2814	−	9.95036i	−1.24102	−	0.675474i
$218$		0			0
$219$	6.30564	−	12.1706i	0.426096	−	0.822415i
$220$		0			0
$221$	−7.34514			−0.494088
$222$		0			0
$223$	−12.6623	−	21.9317i	−0.847927	−	1.46865i	−0.883055	−	0.469270i	$-0.844517\pi$
$223$	−12.6623	−	21.9317i	−0.847927	−	1.46865i	0.0351275	−	0.999383i	$-0.488816\pi$
$224$		0			0
$225$	8.04163	+	11.3903i	0.536109	+	0.759354i
$226$		0			0
$227$	2.40856	−	4.17174i	0.159862	−	0.276888i	−0.774957	−	0.632014i	$-0.782229\pi$
$227$	2.40856	−	4.17174i	0.159862	−	0.276888i	0.934819	+	0.355126i	$0.115562\pi$
$228$		0			0
$229$	4.64766	+	8.04999i	0.307126	+	0.531958i	0.977732	−	0.209855i	$-0.0672993\pi$
$229$	4.64766	+	8.04999i	0.307126	+	0.531958i	−0.670606	+	0.741814i	$0.733966\pi$
$230$		0			0
$231$	−2.44592	−	1.19019i	−0.160929	−	0.0783090i
$232$		0			0
$233$	0.0971780	−	0.168317i	0.00636634	−	0.0110268i	−0.862825	−	0.505503i	$-0.831307\pi$
$233$	0.0971780	−	0.168317i	0.00636634	−	0.0110268i	0.869191	+	0.494476i	$0.164640\pi$
$234$		0			0
$235$	3.60963	+	6.25206i	0.235466	+	0.407840i
$236$		0			0
$237$	−8.63307	−	13.4934i	−0.560778	−	0.876488i
$238$		0			0
$239$	6.82743	−	11.8255i	0.441630	−	0.764925i	−0.556181	−	0.831061i	$-0.687734\pi$
$239$	6.82743	−	11.8255i	0.441630	−	0.764925i	0.997811	+	0.0661361i	$0.0210672\pi$
$240$		0			0
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	−0.577107	−	0.816668i	$-0.695819\pi$
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	0.995809	+	0.0914555i	$0.0291519\pi$
$242$		0			0
$243$	−4.54309	+	14.9118i	−0.291440	+	0.956589i
$244$		0			0
$245$	1.89397	−	3.69829i	0.121001	−	0.236275i
$246$		0			0
$247$	−6.76615	−	11.7193i	−0.430520	−	0.745682i
$248$		0			0
$249$	−6.13667	+	11.8445i	−0.388896	+	0.750614i
$250$		0			0
$251$	19.5438			1.23359			0.616796	−	0.787123i	$-0.288430\pi$
$251$	19.5438			1.23359			0.616796	+	0.787123i	$0.288430\pi$
$252$		0			0
$253$	−2.64766			−0.166457
$254$		0			0
$255$	−3.00000	+	0.136815i	−0.187867	+	0.00856770i
$256$		0			0
$257$	−4.16372	−	7.21177i	−0.259725	−	0.449858i	0.706443	−	0.707770i	$-0.250299\pi$
$257$	−4.16372	−	7.21177i	−0.259725	−	0.449858i	−0.966168	+	0.257912i	$0.916965\pi$
$258$		0			0
$259$	−2.25729	+	1.38008i	−0.140261	+	0.0857540i
$260$		0			0
$261$	18.5059	−	1.69145i	1.14549	−	0.104698i
$262$		0			0
$263$	−8.54523	+	14.8008i	−0.526921	+	0.912655i	0.472586	+	0.881284i	$0.343320\pi$
$263$	−8.54523	+	14.8008i	−0.526921	+	0.912655i	−0.999508	+	0.0313704i	$0.990013\pi$
$264$		0			0
$265$	2.39037	−	4.14024i	0.146839	−	0.254333i
$266$		0			0
$267$	21.5167	−	0.981271i	1.31680	−	0.0600528i
$268$		0			0
$269$	−5.00720	−	8.67272i	−0.305294	−	0.528785i	0.672033	−	0.740522i	$-0.265421\pi$
$269$	−5.00720	−	8.67272i	−0.305294	−	0.528785i	−0.977327	+	0.211737i	$0.932088\pi$
$270$		0			0
$271$	−5.10457	+	8.84137i	−0.310081	+	0.537075i	−0.978380	−	0.206818i	$-0.933689\pi$
$271$	−5.10457	+	8.84137i	−0.310081	+	0.537075i	0.668299	+	0.743893i	$0.267023\pi$
$272$		0			0
$273$	−10.3617	−	5.04204i	−0.627117	−	0.305158i
$274$		0			0
$275$	1.37938	+	2.38915i	0.0831797	+	0.144071i
$276$		0			0
$277$	−9.67111	+	16.7508i	−0.581081	+	1.00646i	0.414271	+	0.910154i	$0.364037\pi$
$277$	−9.67111	+	16.7508i	−0.581081	+	1.00646i	−0.995352	+	0.0963074i	$0.969297\pi$
$278$		0			0
$279$	−9.89104	+	21.4281i	−0.592161	+	1.28287i
$280$		0			0
$281$	−6.40136	−	11.0875i	−0.381873	−	0.661424i	0.609457	−	0.792819i	$-0.291388\pi$
$281$	−6.40136	−	11.0875i	−0.381873	−	0.661424i	−0.991330	+	0.131396i	$0.958054\pi$
$282$		0			0
$283$	16.3523			0.972046			0.486023	−	0.873946i	$-0.338447\pi$
$283$	16.3523			0.972046			0.486023	+	0.873946i	$0.338447\pi$
$284$		0			0
$285$	−2.98181	−	4.66053i	−0.176627	−	0.276066i
$286$		0			0
$287$	0.617023	−	0.377240i	0.0364217	−	0.0222678i
$288$		0			0
$289$	4.23385	−	7.33325i	0.249050	−	0.431367i
$290$		0			0
$291$	9.34941	−	18.0455i	0.548072	−	1.05784i
$292$		0			0
$293$	−10.3889	+	17.9941i	−0.606926	+	1.05123i	0.384817	+	0.922993i	$0.374264\pi$
$293$	−10.3889	+	17.9941i	−0.606926	+	1.05123i	−0.991744	+	0.128235i	$0.959069\pi$
$294$		0			0
$295$	2.56654	+	4.44537i	0.149430	+	0.258820i
$296$		0			0
$297$	−1.16372	+	2.85637i	−0.0675256	+	0.165743i
$298$		0			0
$299$	−11.2163			−0.648658
$300$		0			0
$301$	−0.742705	−	29.5232i	−0.0428088	−	1.70169i
$302$		0			0
$303$	−2.80778	+	0.128049i	−0.161303	+	0.00735622i
$304$		0			0
$305$	1.97296	+	3.41726i	0.112971	+	0.195672i
$306$		0			0
$307$	22.6768			1.29424			0.647118	−	0.762390i	$-0.275974\pi$
$307$	22.6768			1.29424			0.647118	+	0.762390i	$0.275974\pi$
$308$		0			0
$309$	5.08472	−	9.81411i	0.289260	−	0.558305i
$310$		0			0
$311$	6.51459			0.369408			0.184704	−	0.982794i	$-0.440867\pi$
$311$	6.51459			0.369408			0.184704	+	0.982794i	$0.440867\pi$
$312$		0			0
$313$	0.266149			0.0150436			0.00752181	−	0.999972i	$-0.497606\pi$
$313$	0.266149			0.0150436			0.00752181	+	0.999972i	$0.497606\pi$
$314$		0			0
$315$	−4.32597	−	1.86633i	−0.243741	−	0.105156i
$316$		0			0
$317$	15.7237			0.883133			0.441566	−	0.897229i	$-0.354423\pi$
$317$	15.7237			0.883133			0.441566	+	0.897229i	$0.354423\pi$
$318$		0			0
$319$	3.67684			0.205864
$320$		0			0
$321$	32.3712	−	1.47629i	1.80678	−	0.0823985i
$322$		0			0
$323$	−15.7195			−0.874654
$324$		0			0
$325$	5.84348	+	10.1212i	0.324138	+	0.561424i
$326$		0			0
$327$	−2.28434	+	4.40904i	−0.126324	+	0.243820i
$328$		0			0
$329$	28.2630	+	15.3832i	1.55819	+	0.848105i
$330$		0			0
$331$	25.1623			1.38304			0.691521	−	0.722356i	$-0.256941\pi$
$331$	25.1623			1.38304			0.691521	+	0.722356i	$0.256941\pi$
$332$		0			0
$333$	1.73025	+	2.45076i	0.0948172	+	0.134301i
$334$		0			0
$335$	−0.568000	−	0.983804i	−0.0310331	−	0.0537510i
$336$		0			0
$337$	−9.36693	+	16.2240i	−0.510249	+	0.883777i	0.489681	+	0.871902i	$0.337113\pi$
$337$	−9.36693	+	16.2240i	−0.510249	+	0.883777i	−0.999929	+	0.0118752i	$0.996220\pi$
$338$		0			0
$339$	21.3171	−	0.972168i	1.15779	−	0.0528009i
$340$		0			0
$341$	−2.33482	+	4.04403i	−0.126438	+	0.218997i
$342$		0			0
$343$	−1.39610	−	18.4676i	−0.0753825	−	0.997155i
$344$		0			0
$345$	−4.58113	+	0.208922i	−0.246640	+	0.0112480i
$346$		0			0
$347$	−22.5438			−1.21021			−0.605106	−	0.796145i	$-0.706869\pi$
$347$	−22.5438			−1.21021			−0.605106	+	0.796145i	$0.706869\pi$
$348$		0			0
$349$	1.89543	+	3.28298i	0.101460	+	0.175734i	0.912286	−	0.409553i	$-0.134315\pi$
$349$	1.89543	+	3.28298i	0.101460	+	0.175734i	−0.810826	+	0.585287i	$0.800982\pi$
$350$		0			0
$351$	−4.92986	+	12.1005i	−0.263137	+	0.645876i
$352$		0			0
$353$	−3.41741	+	5.91913i	−0.181890	+	0.315043i	−0.942524	−	0.334138i	$-0.891555\pi$
$353$	−3.41741	+	5.91913i	−0.181890	+	0.315043i	0.760634	+	0.649181i	$0.224888\pi$
$354$		0			0
$355$	−4.27694	−	7.40789i	−0.226997	−	0.393170i
$356$		0			0
$357$	−11.0905	+	7.49533i	−0.586969	+	0.396695i
$358$		0			0
$359$	6.32237	−	10.9507i	0.333682	−	0.577954i	−0.649549	−	0.760320i	$-0.725042\pi$
$359$	6.32237	−	10.9507i	0.333682	−	0.577954i	0.983231	+	0.182366i	$0.0583755\pi$
$360$		0			0
$361$	−4.98035	−	8.62622i	−0.262124	−	0.454012i
$362$		0			0
$363$	8.48395	−	16.3750i	0.445292	−	0.859465i
$364$		0			0
$365$	2.34874	−	4.06813i	0.122939	−	0.212936i
$366$		0			0
$367$	3.27188	−	5.66707i	0.170791	−	0.295819i	−0.767906	−	0.640563i	$-0.778701\pi$
$367$	3.27188	−	5.66707i	0.170791	−	0.295819i	0.938697	+	0.344744i	$0.112034\pi$
$368$		0			0
$369$	−0.472958	−	0.669906i	−0.0246212	−	0.0348739i
$370$		0			0
$371$	−0.535897	−	21.3024i	−0.0278224	−	1.10596i
$372$		0			0
$373$	−4.71420	−	8.16524i	−0.244092	−	0.422780i	0.717784	−	0.696266i	$-0.245157\pi$
$373$	−4.71420	−	8.16524i	−0.244092	−	0.422780i	−0.961876	+	0.273486i	$0.911823\pi$
$374$		0			0
$375$	5.34562	+	8.35512i	0.276047	+	0.431457i
$376$		0			0
$377$	15.5763			0.802218
$378$		0			0
$379$	7.27762			0.373826			0.186913	−	0.982376i	$-0.440152\pi$
$379$	7.27762			0.373826			0.186913	+	0.982376i	$0.440152\pi$
$380$		0			0
$381$	11.5139	+	17.9961i	0.589876	+	0.921967i
$382$		0			0
$383$	−12.0416	−	20.8567i	−0.615299	−	1.06573i	−0.990332	−	0.138717i	$-0.955702\pi$
$383$	−12.0416	−	20.8567i	−0.615299	−	1.06573i	0.375033	−	0.927011i	$-0.377631\pi$
$384$		0			0
$385$	−0.818771	−	0.445647i	−0.0417284	−	0.0227123i
$386$		0			0
$387$	−33.3478	+	3.04799i	−1.69516	+	0.154938i
$388$		0			0
$389$	8.14913	−	14.1147i	0.413177	−	0.715644i	−0.582058	−	0.813147i	$-0.697752\pi$
$389$	8.14913	−	14.1147i	0.413177	−	0.715644i	0.995235	+	0.0975035i	$0.0310857\pi$
$390$		0			0
$391$	−6.51459	+	11.2836i	−0.329457	+	0.570636i
$392$		0			0
$393$	−0.945916	+	1.82573i	−0.0477151	+	0.0920958i
$394$		0			0
$395$	−2.74484	−	4.75420i	−0.138108	−	0.239210i
$396$		0			0
$397$	−6.08619	+	10.5416i	−0.305457	+	0.529067i	−0.977363	−	0.211569i	$-0.932143\pi$
$397$	−6.08619	+	10.5416i	−0.305457	+	0.529067i	0.671906	+	0.740636i	$0.265476\pi$
$398$		0			0
$399$	−22.1752	−	10.7905i	−1.11015	−	0.540203i
$400$		0			0
$401$	16.6804	+	28.8914i	0.832981	+	1.44277i	0.895663	+	0.444733i	$0.146701\pi$
$401$	16.6804	+	28.8914i	0.832981	+	1.44277i	−0.0626819	+	0.998034i	$0.519965\pi$
$402$		0			0
$403$	−9.89104	+	17.1318i	−0.492708	+	0.853395i
$404$		0			0
$405$	−1.78813	+	5.03407i	−0.0888529	+	0.250145i
$406$		0			0
$407$	0.296790	+	0.514055i	0.0147113	+	0.0254808i
$408$		0			0
$409$	−5.78074			−0.285839			−0.142920	−	0.989734i	$-0.545649\pi$
$409$	−5.78074			−0.285839			−0.142920	+	0.989734i	$0.545649\pi$
$410$		0			0
$411$	4.36333	−	0.198990i	0.215227	−	0.00981544i
$412$		0			0
$413$	20.0957	+	10.9379i	0.988846	+	0.538217i
$414$		0			0
$415$	−2.28580	+	3.95912i	−0.112205	+	0.194346i
$416$		0			0
$417$	8.50214	−	0.387740i	0.416351	−	0.0189877i
$418$		0			0
$419$	−15.4356	+	26.7352i	−0.754078	+	1.30610i	0.191753	+	0.981443i	$0.438583\pi$
$419$	−15.4356	+	26.7352i	−0.754078	+	1.30610i	−0.945831	+	0.324659i	$0.894751\pi$
$420$		0			0
$421$	−1.86693	−	3.23361i	−0.0909884	−	0.157597i	0.816939	−	0.576724i	$-0.195669\pi$
$421$	−1.86693	−	3.23361i	−0.0909884	−	0.157597i	−0.907927	+	0.419128i	$0.862336\pi$
$422$		0			0
$423$	15.2915	−	33.1278i	0.743500	−	1.61073i
$424$		0			0
$425$	13.5759			0.658526
$426$		0			0
$427$	15.4481	+	8.40819i	0.747584	+	0.406901i
$428$		0			0
$429$	−1.18929	+	2.29548i	−0.0574197	+	0.110827i
$430$		0			0
$431$	14.0979	+	24.4182i	0.679070	+	1.17618i	0.975261	+	0.221055i	$0.0709499\pi$
$431$	14.0979	+	24.4182i	0.679070	+	1.17618i	−0.296192	+	0.955128i	$0.595717\pi$
$432$		0			0
$433$	12.5438			0.602815			0.301407	−	0.953495i	$-0.402544\pi$
$433$	12.5438			0.602815			0.301407	+	0.953495i	$0.402544\pi$
$434$		0			0
$435$	6.36186	−	0.290133i	0.305028	−	0.0139108i
$436$		0			0
$437$	−24.0043			−1.14828
$438$		0			0
$439$	−26.0406			−1.24285			−0.621426	−	0.783473i	$-0.713446\pi$
$439$	−26.0406			−1.24285			−0.621426	+	0.783473i	$0.713446\pi$
$440$		0			0
$441$	−20.7903	+	2.96055i	−0.990013	+	0.140978i
$442$		0			0
$443$	23.5729			1.11998			0.559992	−	0.828498i	$-0.310804\pi$
$443$	23.5729			1.11998			0.559992	+	0.828498i	$0.310804\pi$
$444$		0			0
$445$	7.38151			0.349917
$446$		0			0
$447$	−14.3830	+	27.7608i	−0.680291	+	1.31304i
$448$		0			0
$449$	13.6870			0.645928			0.322964	−	0.946411i	$-0.395321\pi$
$449$	13.6870			0.645928			0.322964	+	0.946411i	$0.395321\pi$
$450$		0			0
$451$	−0.0811263	−	0.140515i	−0.00382009	−	0.00661659i
$452$		0			0
$453$	−2.85087	+	0.130014i	−0.133946	+	0.00610860i
$454$		0			0
$455$	−3.46857	−	1.88790i	−0.162609	−	0.0885062i
$456$		0			0
$457$	−22.3523			−1.04560			−0.522799	−	0.852456i	$-0.675112\pi$
$457$	−22.3523			−1.04560			−0.522799	+	0.852456i	$0.675112\pi$
$458$		0			0
$459$	9.30972	+	11.9875i	0.434541	+	0.559530i
$460$		0			0
$461$	−3.98755	−	6.90663i	−0.185719	−	0.321674i	0.758100	−	0.652138i	$-0.226128\pi$
$461$	−3.98755	−	6.90663i	−0.185719	−	0.321674i	−0.943818	+	0.330464i	$0.892795\pi$
$462$		0			0
$463$	14.3676	−	24.8854i	0.667719	−	1.15652i	−0.310821	−	0.950468i	$-0.600604\pi$
$463$	14.3676	−	24.8854i	0.667719	−	1.15652i	0.978540	−	0.206055i	$-0.0660625\pi$
$464$		0			0
$465$	−3.72072	+	7.18143i	−0.172544	+	0.333031i
$466$		0			0
$467$	−16.7829	+	29.0688i	−0.776619	+	1.34514i	0.157261	+	0.987557i	$0.449733\pi$
$467$	−16.7829	+	29.0688i	−0.776619	+	1.34514i	−0.933880	+	0.357586i	$0.883600\pi$
$468$		0			0
$469$	−4.44738	−	2.42066i	−0.205361	−	0.111775i
$470$		0			0
$471$	6.16158	+	9.63046i	0.283911	+	0.443748i
$472$		0			0
$473$	−6.62568			−0.304649
$474$		0			0
$475$	12.5057	+	21.6606i	0.573802	+	0.993855i
$476$		0			0
$477$	−24.0620	+	2.19927i	−1.10172	+	0.100698i
$478$		0			0
$479$	0.183560	−	0.317935i	0.00838707	−	0.0145268i	−0.861801	−	0.507246i	$-0.830664\pi$
$479$	0.183560	−	0.317935i	0.00838707	−	0.0145268i	0.870188	+	0.492719i	$0.163997\pi$
$480$		0			0
$481$	1.25729	+	2.17770i	0.0573277	+	0.0992945i
$482$		0			0
$483$	−16.9356	+	11.4457i	−0.770596	+	0.520797i
$484$		0			0
$485$	3.48249	−	6.03184i	0.158132	−	0.273892i
$486$		0			0
$487$	14.9538	+	25.9007i	0.677621	+	1.17367i	0.975695	+	0.219131i	$0.0703222\pi$
$487$	14.9538	+	25.9007i	0.677621	+	1.17367i	−0.298075	+	0.954543i	$0.596344\pi$
$488$		0			0
$489$	−10.3509	+	0.472052i	−0.468083	+	0.0213469i
$490$		0			0
$491$	0.255158	−	0.441947i	0.0115151	−	0.0199448i	−0.860210	−	0.509939i	$-0.829668\pi$
$491$	0.255158	−	0.441947i	0.0115151	−	0.0199448i	0.871726	+	0.489994i	$0.163001\pi$
$492$		0			0
$493$	9.04689	−	15.6697i	0.407451	−	0.705726i
$494$		0			0
$495$	−0.442991	+	0.959702i	−0.0199110	+	0.0431354i
$496$		0			0
$497$	−33.4880	−	18.2271i	−1.50214	−	0.817599i
$498$		0			0
$499$	−9.50953	−	16.4710i	−0.425705	−	0.737343i	0.570781	−	0.821102i	$-0.306641\pi$
$499$	−9.50953	−	16.4710i	−0.425705	−	0.737343i	−0.996486	+	0.0837597i	$0.973307\pi$
$500$		0			0
$501$	12.9086	−	0.588695i	0.576712	−	0.0263010i
$502$		0			0
$503$	37.7807			1.68456			0.842280	−	0.539040i	$-0.181213\pi$
$503$	37.7807			1.68456			0.842280	+	0.539040i	$0.181213\pi$
$504$		0			0
$505$	−0.963235			−0.0428634
$506$		0			0
$507$	5.32004	−	10.2683i	0.236271	−	0.456031i
$508$		0			0
$509$	5.60817	+	9.71363i	0.248578	+	0.430549i	0.963131	−	0.269031i	$-0.0867035\pi$
$509$	5.60817	+	9.71363i	0.248578	+	0.430549i	−0.714554	+	0.699581i	$0.753370\pi$
$510$		0			0
$511$	−0.526563	−	20.9314i	−0.0232938	−	0.925949i
$512$		0			0
$513$	−10.5505	+	25.8965i	−0.465815	+	1.14336i
$514$		0			0
$515$	1.89397	−	3.28045i	0.0834582	−	0.144554i
$516$		0			0
$517$	3.60963	−	6.25206i	0.158751	−	0.274965i
$518$		0			0
$519$	23.9518	+	37.4364i	1.05137	+	1.64327i
$520$		0			0
$521$	−13.7360	−	23.7914i	−0.601785	−	1.04232i	−0.992551	−	0.121831i	$-0.961123\pi$
$521$	−13.7360	−	23.7914i	−0.601785	−	1.04232i	0.390766	−	0.920490i	$-0.372210\pi$
$522$		0			0
$523$	−11.0919	+	19.2118i	−0.485016	+	0.840072i	−0.999852	−	0.0172166i	$-0.994520\pi$
$523$	−11.0919	+	19.2118i	−0.485016	+	0.840072i	0.514836	+	0.857289i	$0.327853\pi$
$524$		0			0
$525$	19.1513	+	9.31909i	0.835830	+	0.406718i
$526$		0			0
$527$	11.4897	+	19.9007i	0.500498	+	0.866889i
$528$		0			0
$529$	1.55195	−	2.68805i	0.0674760	−	0.116872i
$530$		0			0
$531$	10.8727	−	23.5547i	0.471833	−	1.02219i
$532$		0			0
$533$	−0.343677	−	0.595265i	−0.0148863	−	0.0257838i
$534$		0			0
$535$	11.1052			0.480122
$536$		0			0
$537$	−11.9808	+	23.1244i	−0.517011	+	0.997891i
$538$		0			0
$539$	−4.14980	+	0.208922i	−0.178745	+	0.00899893i
$540$		0			0
$541$	14.9246	−	25.8502i	0.641659	−	1.11139i	−0.343403	−	0.939188i	$-0.611580\pi$
$541$	14.9246	−	25.8502i	0.641659	−	1.11139i	0.985062	−	0.172198i	$-0.0550869\pi$
$542$		0			0
$543$	0.0804528	+	0.125747i	0.00345256	+	0.00539630i
$544$		0			0
$545$	−0.850874	+	1.47376i	−0.0364474	+	0.0631288i
$546$		0			0
$547$	−8.84348	−	15.3174i	−0.378120	−	0.654923i	0.612669	−	0.790340i	$-0.290096\pi$
$547$	−8.84348	−	15.3174i	−0.378120	−	0.654923i	−0.990789	+	0.135417i	$0.956763\pi$
$548$		0			0
$549$	8.35807	−	18.1071i	0.356714	−	0.772790i
$550$		0			0
$551$	33.3350			1.42012
$552$		0			0
$553$	−21.4918	−	11.6977i	−0.913925	−	0.497439i
$554$		0			0
$555$	0.554084	+	0.866025i	0.0235196	+	0.0367607i
$556$		0			0
$557$	15.0651	+	26.0935i	0.638328	+	1.10562i	0.985800	+	0.167926i	$0.0537069\pi$
$557$	15.0651	+	26.0935i	0.638328	+	1.10562i	−0.347472	+	0.937690i	$0.612960\pi$
$558$		0			0
$559$	−28.0685			−1.18717
$560$		0			0
$561$	1.61849	+	2.52967i	0.0683325	+	0.106803i
$562$		0			0
$563$	−4.09766			−0.172696			−0.0863478	−	0.996265i	$-0.527520\pi$
$563$	−4.09766			−0.172696			−0.0863478	+	0.996265i	$0.527520\pi$
$564$		0			0
$565$	7.31304			0.307662
$566$		0			0
$567$	4.90428	+	23.3012i	0.205961	+	0.978560i
$568$		0			0
$569$	6.23697			0.261467			0.130734	−	0.991418i	$-0.458267\pi$
$569$	6.23697			0.261467			0.130734	+	0.991418i	$0.458267\pi$
$570$		0			0
$571$	−35.6021			−1.48990			−0.744951	−	0.667119i	$-0.767527\pi$
$571$	−35.6021			−1.48990			−0.744951	+	0.667119i	$0.767527\pi$
$572$		0			0
$573$	3.71732	+	5.81012i	0.155293	+	0.242721i
$574$		0			0
$575$	20.7309			0.864539
$576$		0			0
$577$	23.1388	+	40.0776i	0.963281	+	1.66845i	0.714164	+	0.699979i	$0.246807\pi$
$577$	23.1388	+	40.0776i	0.963281	+	1.66845i	0.249118	+	0.968473i	$0.419859\pi$
$578$		0			0
$579$	−6.32957	−	9.89302i	−0.263048	−	0.411140i
$580$		0			0
$581$	0.512453	+	20.3705i	0.0212601	+	0.845109i
$582$		0			0
$583$	−4.78074			−0.197998
$584$		0			0
$585$	−1.87665	+	4.06560i	−0.0775898	+	0.168092i
$586$		0			0
$587$	−1.13161	−	1.96001i	−0.0467066	−	0.0808982i	0.841727	−	0.539903i	$-0.181539\pi$
$587$	−1.13161	−	1.96001i	−0.0467066	−	0.0808982i	−0.888434	+	0.459005i	$0.848206\pi$
$588$		0			0
$589$	−21.1680	+	36.6640i	−0.872212	+	1.51072i
$590$		0			0
$591$	−10.3226	−	16.1340i	−0.424614	−	0.663665i
$592$		0			0
$593$	23.0979	−	40.0067i	0.948515	−	1.64288i	0.199960	−	0.979804i	$-0.435919\pi$
$593$	23.0979	−	40.0067i	0.948515	−	1.64288i	0.748555	−	0.663072i	$-0.230748\pi$
$594$		0			0
$595$	−3.91381	+	2.39285i	−0.160451	+	0.0980974i
$596$		0			0
$597$	−4.47675	+	8.64065i	−0.183221	+	0.353638i
$598$		0			0
$599$	16.7807			0.685642			0.342821	−	0.939401i	$-0.388618\pi$
$599$	16.7807			0.685642			0.342821	+	0.939401i	$0.388618\pi$
$600$		0			0
$601$	−5.69961	−	9.87202i	−0.232492	−	0.402688i	0.726049	−	0.687643i	$-0.241355\pi$
$601$	−5.69961	−	9.87202i	−0.232492	−	0.402688i	−0.958541	+	0.284955i	$0.908021\pi$
$602$		0			0
$603$	−2.40623	+	5.21289i	−0.0979891	+	0.212285i
$604$		0			0
$605$	3.16012	−	5.47348i	0.128477	−	0.222529i
$606$		0			0
$607$	−7.21420	−	12.4954i	−0.292815	−	0.507171i	0.681659	−	0.731670i	$-0.261259\pi$
$607$	−7.21420	−	12.4954i	−0.292815	−	0.507171i	−0.974474	+	0.224499i	$0.927925\pi$
$608$		0			0
$609$	23.5187	−	15.8948i	0.953024	−	0.644088i
$610$		0			0
$611$	15.2915	−	26.4857i	0.618629	−	1.07150i
$612$		0			0
$613$	12.2053	+	21.1403i	0.492969	+	0.853848i	0.999967	−	0.00809942i	$-0.00257815\pi$
$613$	12.2053	+	21.1403i	0.492969	+	0.853848i	−0.506998	+	0.861947i	$0.669245\pi$
$614$		0			0
$615$	−0.151457	−	0.236725i	−0.00610733	−	0.00954566i
$616$		0			0
$617$	24.4698	−	42.3830i	0.985119	−	1.70628i	0.343710	−	0.939076i	$-0.388316\pi$
$617$	24.4698	−	42.3830i	0.985119	−	1.70628i	0.641408	−	0.767200i	$-0.278350\pi$
$618$		0			0
$619$	−22.3296	+	38.6759i	−0.897501	+	1.55452i	−0.0668227	+	0.997765i	$0.521286\pi$
$619$	−22.3296	+	38.6759i	−0.897501	+	1.55452i	−0.830678	+	0.556753i	$0.812047\pi$
$620$		0			0
$621$	14.2163	+	18.3055i	0.570482	+	0.734574i
$622$		0			0
$623$	28.0708	−	17.1621i	1.12463	−	0.687586i
$624$		0			0
$625$	−9.91955	−	17.1812i	−0.396782	−	0.687246i
$626$		0			0
$627$	−2.54523	+	4.91259i	−0.101647	+	0.196190i
$628$		0			0
$629$	2.92101			0.116468
$630$		0			0
$631$	−33.2852			−1.32506			−0.662532	−	0.749034i	$-0.730518\pi$
$631$	−33.2852			−1.32506			−0.662532	+	0.749034i	$0.730518\pi$
$632$		0			0
$633$	33.4363	−	1.52486i	1.32897	−	0.0606079i
$634$		0			0
$635$	3.66079	+	6.34067i	0.145274	+	0.251622i
$636$		0			0
$637$	−17.5799	+	0.885061i	−0.696539	+	0.0350674i
$638$		0			0
$639$	−18.1185	+	39.2522i	−0.716756	+	1.55279i
$640$		0			0
$641$	−15.3940	+	26.6631i	−0.608025	+	1.05313i	0.383540	+	0.923524i	$0.374705\pi$
$641$	−15.3940	+	26.6631i	−0.608025	+	1.05313i	−0.991566	+	0.129606i	$0.958629\pi$
$642$		0			0
$643$	13.7345	−	23.7889i	0.541637	−	0.938142i	−0.457174	−	0.889378i	$-0.651138\pi$
$643$	13.7345	−	23.7889i	0.541637	−	0.938142i	0.998810	−	0.0487649i	$-0.0155285\pi$
$644$		0			0
$645$	−11.4641	+	0.522821i	−0.451399	+	0.0205861i
$646$		0			0
$647$	6.63521	+	11.4925i	0.260857	+	0.451818i	0.966470	−	0.256780i	$-0.0826615\pi$
$647$	6.63521	+	11.4925i	0.260857	+	0.451818i	−0.705613	+	0.708598i	$0.749328\pi$
$648$		0			0
$649$	2.56654	−	4.44537i	0.100745	−	0.174496i
$650$		0			0
$651$	2.54756	+	35.9607i	0.0998468	+	1.40941i
$652$		0			0
$653$	8.57081	+	14.8451i	0.335402	+	0.580933i	0.983562	−	0.180571i	$-0.0577946\pi$
$653$	8.57081	+	14.8451i	0.335402	+	0.580933i	−0.648160	+	0.761504i	$0.724461\pi$
$654$		0			0
$655$	−0.352336	+	0.610265i	−0.0137669	+	0.0238450i
$656$		0			0
$657$	−23.6429	+	2.16096i	−0.922397	+	0.0843072i
$658$		0			0
$659$	−4.26089	−	7.38008i	−0.165981	−	0.287487i	0.771022	−	0.636808i	$-0.219746\pi$
$659$	−4.26089	−	7.38008i	−0.165981	−	0.287487i	−0.937003	+	0.349321i	$0.886412\pi$
$660$		0			0
$661$	34.3360			1.33551			0.667757	−	0.744379i	$-0.267254\pi$
$661$	34.3360			1.33551			0.667757	+	0.744379i	$0.267254\pi$
$662$		0			0
$663$	6.85641	+	10.7165i	0.266281	+	0.416193i
$664$		0			0
$665$	−7.42315	−	4.04033i	−0.287857	−	0.156677i
$666$		0			0
$667$	13.8150	−	23.9282i	0.534918	−	0.926505i
$668$		0			0
$669$	−20.1783	+	38.9465i	−0.780138	+	1.50576i
$670$		0			0
$671$	1.97296	−	3.41726i	0.0761652	−	0.131922i
$672$		0			0
$673$	−7.70155	−	13.3395i	−0.296873	−	0.514199i	0.678546	−	0.734558i	$-0.262610\pi$
$673$	−7.70155	−	13.3395i	−0.296873	−	0.514199i	−0.975419	+	0.220359i	$0.929277\pi$
$674$		0			0
$675$	9.11177	−	22.3651i	0.350712	−	0.860832i
$676$		0			0
$677$	−7.38151			−0.283695			−0.141847	−	0.989889i	$-0.545304\pi$
$677$	−7.38151			−0.283695			−0.141847	+	0.989889i	$0.545304\pi$
$678$		0			0
$679$	−0.780738	−	31.0350i	−0.0299620	−	1.19102i
$680$		0			0
$681$	−8.33482	+	0.380110i	−0.319391	+	0.0145658i
$682$		0			0
$683$	−4.79893	−	8.31198i	−0.183626	−	0.318049i	0.759487	−	0.650523i	$-0.225450\pi$
$683$	−4.79893	−	8.31198i	−0.183626	−	0.318049i	−0.943113	+	0.332474i	$0.892117\pi$
$684$		0			0
$685$	1.49688			0.0571929
$686$		0			0
$687$	7.40642	−	14.2953i	0.282573	−	0.545398i
$688$		0			0
$689$	−20.2527			−0.771567
$690$		0			0
$691$	14.1445			0.538084			0.269042	−	0.963128i	$-0.413293\pi$
$691$	14.1445			0.538084			0.269042	+	0.963128i	$0.413293\pi$
$692$		0			0
$693$	0.546692	+	4.67956i	0.0207671	+	0.177762i
$694$		0			0
$695$	2.91674			0.110638
$696$		0			0
$697$	−0.798447			−0.0302433
$698$		0			0
$699$	−0.336285	+	0.0153363i	−0.0127195	+	0.000580072i
$700$		0			0
$701$	37.3753			1.41164			0.705822	−	0.708389i	$-0.250578\pi$
$701$	37.3753			1.41164			0.705822	+	0.708389i	$0.250578\pi$
$702$		0			0
$703$	2.69076	+	4.66053i	0.101484	+	0.175775i
$704$		0			0
$705$	5.75223	−	11.1025i	0.216642	−	0.418144i
$706$		0			0
$707$	−3.66304	+	2.23954i	−0.137763	+	0.0842264i
$708$		0			0
$709$	−10.4868			−0.393838			−0.196919	−	0.980420i	$-0.563094\pi$
$709$	−10.4868			−0.393838			−0.196919	+	0.980420i	$0.563094\pi$
$710$		0			0
$711$	−11.6280	+	25.1911i	−0.436085	+	0.944741i
$712$		0			0
$713$	17.5452	+	30.3892i	0.657074	+	1.13809i
$714$		0			0
$715$	−0.442991	+	0.767282i	−0.0165669	+	0.0286947i
$716$		0			0
$717$	−23.6264	+	1.07748i	−0.882342	+	0.0402393i
$718$		0			0
$719$	−1.11995	+	1.93981i	−0.0417670	+	0.0723426i	−0.886153	−	0.463392i	$-0.846632\pi$
$719$	−1.11995	+	1.93981i	−0.0417670	+	0.0723426i	0.844386	+	0.535735i	$0.179965\pi$
$720$		0			0
$721$	−0.424608	−	16.8786i	−0.0158132	−	0.628590i
$722$		0			0
$723$	−22.4933	+	1.02581i	−0.836534	+	0.0381502i
$724$		0			0
$725$	−28.7893			−1.06921
$726$		0			0
$727$	−0.185023	−	0.320469i	−0.00686211	−	0.0118855i	0.862574	−	0.505931i	$-0.168851\pi$
$727$	−0.185023	−	0.320469i	−0.00686211	−	0.0118855i	−0.869436	+	0.494045i	$0.835518\pi$
$728$		0			0
$729$	25.9969	−	7.29124i	0.962847	−	0.270046i
$730$		0			0
$731$	−16.3025	+	28.2368i	−0.602971	+	1.04438i
$732$		0			0
$733$	−7.00953	−	12.1409i	−0.258903	−	0.448433i	0.707045	−	0.707168i	$-0.250028\pi$
$733$	−7.00953	−	12.1409i	−0.258903	−	0.448433i	−0.965948	+	0.258735i	$0.916694\pi$
$734$		0			0
$735$	−7.16372	+	0.688942i	−0.264238	+	0.0254120i
$736$		0			0
$737$	−0.568000	+	0.983804i	−0.0209225	+	0.0362389i
$738$		0			0
$739$	−13.3872	−	23.1874i	−0.492458	−	0.852962i	0.507504	−	0.861649i	$-0.330568\pi$
$739$	−13.3872	−	23.1874i	−0.492458	−	0.852962i	−0.999962	+	0.00868705i	$0.997235\pi$
$740$		0			0
$741$	−10.7824	+	20.8113i	−0.396101	+	0.764521i
$742$		0			0
$743$	5.04669	−	8.74113i	0.185145	−	0.320681i	−0.758480	−	0.651696i	$-0.774058\pi$
$743$	5.04669	−	8.74113i	0.185145	−	0.320681i	0.943625	+	0.331015i	$0.107391\pi$
$744$		0			0
$745$	−5.35740	+	9.27928i	−0.196280	+	0.339967i
$746$		0			0
$747$	23.0093	−	2.10306i	0.841867	−	0.0769468i
$748$		0			0
$749$	42.2316	−	25.8198i	1.54311	−	0.943437i
$750$		0			0
$751$	5.75729	+	9.97193i	0.210087	+	0.363881i	0.951741	−	0.306901i	$-0.0992921\pi$
$751$	5.75729	+	9.97193i	0.210087	+	0.363881i	−0.741655	+	0.670782i	$0.765959\pi$
$752$		0			0
$753$	−18.2434	−	28.5141i	−0.664826	−	1.03911i
$754$		0			0
$755$	−0.978019			−0.0355938
$756$		0			0
$757$	−15.2484			−0.554214			−0.277107	−	0.960839i	$-0.589376\pi$
$757$	−15.2484			−0.554214			−0.277107	+	0.960839i	$0.589376\pi$
$758$		0			0
$759$	2.47150	+	3.86291i	0.0897096	+	0.140215i
$760$		0			0
$761$	0.850874	+	1.47376i	0.0308442	+	0.0534236i	0.881035	−	0.473050i	$-0.156847\pi$
$761$	0.850874	+	1.47376i	0.0308442	+	0.0534236i	−0.850191	+	0.526474i	$0.823514\pi$
$762$		0			0
$763$	0.190757	+	7.58277i	0.00690588	+	0.274515i
$764$		0			0
$765$	3.00000	+	4.24925i	0.108465	+	0.153632i
$766$		0			0
$767$	10.8727	−	18.8320i	0.392589	−	0.679984i
$768$		0			0
$769$	24.1211	−	41.7790i	0.869829	−	1.50659i	0.00765823	−	0.999971i	$-0.497562\pi$
$769$	24.1211	−	41.7790i	0.869829	−	1.50659i	0.862171	−	0.506618i	$-0.169104\pi$
$770$		0			0
$771$	−6.63521	+	12.8067i	−0.238961	+	0.461223i
$772$		0			0
$773$	3.10243	+	5.37357i	0.111587	+	0.193274i	0.916410	−	0.400240i	$-0.131073\pi$
$773$	3.10243	+	5.37357i	0.111587	+	0.193274i	−0.804823	+	0.593514i	$0.797740\pi$
$774$		0			0
$775$	18.2814	−	31.6643i	0.656688	−	1.13742i
$776$		0			0
$777$	4.12062	+	2.00511i	0.147826	+	0.0719330i
$778$		0			0
$779$	−0.735508	−	1.27394i	−0.0263523	−	0.0456436i
$780$		0			0
$781$	−4.27694	+	7.40789i	−0.153041	+	0.265075i
$782$		0			0
$783$	−19.7424	−	25.4210i	−0.705536	−	0.908474i
$784$		0			0
$785$	1.95904	+	3.39316i	0.0699212	+	0.121107i
$786$		0			0
$787$	−6.09766			−0.217358			−0.108679	−	0.994077i	$-0.534662\pi$
$787$	−6.09766			−0.217358			−0.108679	+	0.994077i	$0.534662\pi$
$788$		0			0
$789$	29.5708	−	1.34858i	1.05275	−	0.0480107i
$790$		0			0
$791$	27.8104	−	17.0029i	0.988824	−	0.604554i
$792$		0			0
$793$	8.35807	−	14.4766i	0.296804	−	0.514079i
$794$		0			0
$795$	−8.27188	+	0.377240i	−0.293373	+	0.0133793i
$796$		0			0
$797$	−6.22860	+	10.7882i	−0.220628	+	0.382139i	−0.954999	−	0.296609i	$-0.904144\pi$
$797$	−6.22860	+	10.7882i	−0.220628	+	0.382139i	0.734371	+	0.678749i	$0.237477\pi$
$798$		0			0
$799$	−17.7630	−	30.7665i	−0.628411	−	1.08844i
$800$		0			0
$801$	−21.5167	−	30.4767i	−0.760256	−	1.07684i
$802$		0			0
$803$	−4.69748			−0.165770
$804$		0			0
$805$	−5.97656	+	3.65399i	−0.210646	+	0.128786i
$806$		0			0
$807$	−7.97937	+	15.4011i	−0.280887	+	0.542145i
$808$		0			0
$809$	−2.81644	−	4.87822i	−0.0990208	−	0.171509i	0.812259	−	0.583297i	$-0.198238\pi$
$809$	−2.81644	−	4.87822i	−0.0990208	−	0.171509i	−0.911280	+	0.411788i	$0.864904\pi$
$810$		0			0
$811$	45.6414			1.60269			0.801344	−	0.598204i	$-0.204119\pi$
$811$	45.6414			1.60269			0.801344	+	0.598204i	$0.204119\pi$
$812$		0			0
$813$	17.6644	−	0.805585i	0.619517	−	0.0282531i
$814$		0			0
$815$	−3.55096			−0.124385
$816$		0			0
$817$	−60.0698			−2.10158
$818$		0			0
$819$	2.31596	+	19.8241i	0.0809262	+	0.692710i
$820$		0			0
$821$	32.6946			1.14105			0.570524	−	0.821281i	$-0.306740\pi$
$821$	32.6946			1.14105			0.570524	+	0.821281i	$0.306740\pi$
$822$		0			0
$823$	10.4399			0.363911			0.181956	−	0.983307i	$-0.441757\pi$
$823$	10.4399			0.363911			0.181956	+	0.983307i	$0.441757\pi$
$824$		0			0
$825$	2.19815	−	4.24268i	0.0765297	−	0.147711i
$826$		0			0
$827$	−16.7060			−0.580925			−0.290463	−	0.956886i	$-0.593809\pi$
$827$	−16.7060			−0.580925			−0.290463	+	0.956886i	$0.593809\pi$
$828$		0			0
$829$	−13.1046	−	22.6978i	−0.455141	−	0.788327i	0.543556	−	0.839373i	$-0.317078\pi$
$829$	−13.1046	−	22.6978i	−0.455141	−	0.788327i	−0.998696	+	0.0510466i	$0.983744\pi$
$830$		0			0
$831$	33.4669	−	1.52626i	1.16095	−	0.0529454i
$832$		0			0
$833$	−9.32023	+	18.1993i	−0.322927	+	0.630570i
$834$		0			0
$835$	4.42840			0.153251
$836$		0			0
$837$	40.4963	−	5.57143i	1.39976	−	0.192577i
$838$		0			0
$839$	−11.1886	−	19.3793i	−0.386274	−	0.669046i	0.605671	−	0.795715i	$-0.292905\pi$
$839$	−11.1886	−	19.3793i	−0.386274	−	0.669046i	−0.991945	+	0.126669i	$0.959571\pi$
$840$		0			0
$841$	−4.68502	+	8.11470i	−0.161553	+	0.279817i
$842$		0			0
$843$	−10.2011	+	19.6893i	−0.351344	+	0.678134i
$844$		0			0
$845$	1.98162	−	3.43226i	0.0681697	−	0.118073i
$846$		0			0
$847$	−0.708466	−	28.1622i	−0.0243432	−	0.967663i
$848$		0			0
$849$	−15.2643	−	23.8579i	−0.523869	−	0.818800i
$850$		0			0
$851$	4.46050			0.152904
$852$		0			0
$853$	4.96264	+	8.59555i	0.169918	+	0.294306i	0.938391	−	0.345576i	$-0.112317\pi$
$853$	4.96264	+	8.59555i	0.169918	+	0.294306i	−0.768473	+	0.639882i	$0.778983\pi$
$854$		0			0
$855$	−4.01625	+	8.70086i	−0.137353	+	0.297563i
$856$		0			0
$857$	−3.89776	+	6.75112i	−0.133145	+	0.230614i	−0.924887	−	0.380241i	$-0.875841\pi$
$857$	−3.89776	+	6.75112i	−0.133145	+	0.230614i	0.791742	+	0.610855i	$0.209174\pi$
$858$		0			0
$859$	8.17111	+	14.1528i	0.278795	+	0.482886i	0.971085	−	0.238732i	$-0.0767318\pi$
$859$	8.17111	+	14.1528i	0.278795	+	0.482886i	−0.692291	+	0.721619i	$0.743398\pi$
$860$		0			0
$861$	−1.12636	−	0.548090i	−0.0383861	−	0.0186789i
$862$		0			0
$863$	−0.730252	+	1.26483i	−0.0248581	+	0.0430555i	−0.878187	−	0.478318i	$-0.841247\pi$
$863$	−0.730252	+	1.26483i	−0.0248581	+	0.0430555i	0.853329	+	0.521373i	$0.174580\pi$
$864$		0			0
$865$	7.61537	+	13.1902i	0.258930	+	0.448480i
$866$		0			0
$867$	−14.6513	+	0.668172i	−0.497583	+	0.0226923i
$868$		0			0
$869$	−2.74484	+	4.75420i	−0.0931124	+	0.161275i
$870$		0			0
$871$	−2.40623	+	4.16771i	−0.0815319	+	0.141217i
$872$		0			0
$873$	−35.0554	+	3.20407i	−1.18645	+	0.108441i
$874$		0			0
$875$	13.3078	+	7.24327i	0.449885	+	0.244867i
$876$		0			0
$877$	1.20467	+	2.08655i	0.0406789	+	0.0704579i	0.885648	−	0.464357i	$-0.153715\pi$
$877$	1.20467	+	2.08655i	0.0406789	+	0.0704579i	−0.844969	+	0.534815i	$0.820381\pi$
$878$		0			0
$879$	35.9509	−	1.63954i	1.21259	−	0.0553003i
$880$		0			0
$881$	−18.9607			−0.638802			−0.319401	−	0.947620i	$-0.603482\pi$
$881$	−18.9607			−0.638802			−0.319401	+	0.947620i	$0.603482\pi$
$882$		0			0
$883$	−3.64008			−0.122498			−0.0612492	−	0.998123i	$-0.519508\pi$
$883$	−3.64008			−0.122498			−0.0612492	+	0.998123i	$0.519508\pi$
$884$		0			0
$885$	4.08998	−	7.89414i	0.137483	−	0.265359i
$886$		0			0
$887$	−12.2286	−	21.1805i	−0.410596	−	0.711173i	0.584359	−	0.811495i	$-0.301346\pi$
$887$	−12.2286	−	21.1805i	−0.410596	−	0.711173i	−0.994955	+	0.100322i	$0.968013\pi$
$888$		0			0
$889$	28.6636	+	15.6013i	0.961346	+	0.523249i
$890$		0			0
$891$	5.25370	−	0.968468i	0.176005	−	0.0324449i
$892$		0			0
$893$	32.7257	−	56.6825i	1.09512	−	1.89681i
$894$		0			0
$895$	−4.46264	+	7.72952i	−0.149170	+	0.258369i
$896$		0			0
$897$	10.4700	+	16.3645i	0.349584	+	0.546395i
$898$		0			0
$899$	−24.3653	−	42.2019i	−0.812627	−	1.40751i
$900$		0			0
$901$	−11.7630	+	20.3742i	−0.391883	+	0.678762i
$902$		0			0
$903$	−42.3807	+	28.6424i	−1.41034	+	0.953160i
$904$		0			0
$905$	0.0255796	+	0.0443051i	0.000850293	+	0.00147275i
$906$		0			0
$907$	5.01838	−	8.69209i	0.166633	−	0.288616i	−0.770601	−	0.637318i	$-0.780044\pi$
$907$	5.01838	−	8.69209i	0.166633	−	0.288616i	0.937234	+	0.348701i	$0.113377\pi$
$908$		0			0
$909$	2.80778	+	3.97699i	0.0931282	+	0.131908i
$910$		0			0
$911$	−11.4459	−	19.8249i	−0.379220	−	0.656828i	0.611729	−	0.791067i	$-0.290474\pi$
$911$	−11.4459	−	19.8249i	−0.379220	−	0.656828i	−0.990949	+	0.134239i	$0.957141\pi$
$912$		0			0
$913$	4.57160			0.151298
$914$		0			0
$915$	3.14406	−	6.06841i	0.103940	−	0.200615i
$916$		0			0
$917$	0.0789903	+	3.13993i	0.00260849	+	0.103690i
$918$		0			0
$919$	−10.8910	+	18.8638i	−0.359262	+	0.622261i	−0.987838	−	0.155488i	$-0.950305\pi$
$919$	−10.8910	+	18.8638i	−0.359262	+	0.622261i	0.628575	+	0.777749i	$0.283638\pi$
$920$		0			0
$921$	−21.1680	−	33.0852i	−0.697509	−	1.09020i
$922$		0			0
$923$	−18.1185	+	31.3821i	−0.596377	+	1.03296i
$924$		0			0
$925$	−2.32383	−	4.02499i	−0.0764071	−	0.132341i
$926$		0			0
$927$	−19.0651	+	1.74255i	−0.626179	+	0.0572329i
$928$		0			0
$929$	−32.8377			−1.07737			−0.538686	−	0.842507i	$-0.681079\pi$
$929$	−32.8377			−1.07737			−0.538686	+	0.842507i	$0.681079\pi$
$930$		0			0
$931$	−37.6230	+	1.89413i	−1.23304	+	0.0620778i
$932$		0			0
$933$	−6.08113	−	9.50471i	−0.199087	−	0.311170i
$934$		0			0
$935$	0.514589	+	0.891294i	0.0168289	+	0.0291484i
$936$		0			0
$937$	−8.78074			−0.286854			−0.143427	−	0.989661i	$-0.545812\pi$
$937$	−8.78074			−0.286854			−0.143427	+	0.989661i	$0.545812\pi$
$938$		0			0
$939$	−0.248440	−	0.388308i	−0.00810754	−	0.0126720i
$940$		0			0
$941$	4.26615			0.139072			0.0695362	−	0.997579i	$-0.477848\pi$
$941$	4.26615			0.139072			0.0695362	+	0.997579i	$0.477848\pi$
$942$		0			0
$943$	−1.21926			−0.0397046
$944$		0			0
$945$	1.31517	+	8.05369i	0.0427825	+	0.261987i
$946$		0			0
$947$	23.0584			0.749296			0.374648	−	0.927167i	$-0.377764\pi$
$947$	23.0584			0.749296			0.374648	+	0.927167i	$0.377764\pi$
$948$		0			0
$949$	−19.9000			−0.645981
$950$		0			0
$951$	−14.6775	−	22.9407i	−0.475951	−	0.743904i
$952$		0			0
$953$	−36.5552			−1.18414			−0.592070	−	0.805886i	$-0.701689\pi$
$953$	−36.5552			−1.18414			−0.592070	+	0.805886i	$0.701689\pi$
$954$		0			0
$955$	1.18190	+	2.04712i	0.0382455	+	0.0662431i
$956$		0			0
$957$	−3.43219	−	5.36447i	−0.110947	−	0.173409i
$958$		0			0
$959$	5.69241	−	3.48027i	0.183818	−	0.112384i
$960$		0			0
$961$	30.8885			0.996404
$962$		0			0
$963$	−32.3712	−	45.8511i	−1.04315	−	1.47753i
$964$		0			0
$965$	−2.01245	−	3.48567i	−0.0647832	−	0.112208i
$966$		0			0
$967$	−26.7719	+	46.3703i	−0.860926	+	1.49117i	0.0101108	+	0.999949i	$0.496782\pi$
$967$	−26.7719	+	46.3703i	−0.860926	+	1.49117i	−0.871037	+	0.491218i	$0.836552\pi$
$968$		0			0
$969$	14.6735	+	22.9345i	0.471382	+	0.736762i
$970$		0			0
$971$	15.9897	−	27.6949i	0.513133	−	0.888773i	−0.486751	−	0.873541i	$-0.661818\pi$
$971$	15.9897	−	27.6949i	0.513133	−	0.888773i	0.999884	−	0.0152321i	$-0.00484870\pi$
$972$		0			0
$973$	11.0919	−	6.78146i	0.355591	−	0.217403i
$974$		0			0
$975$	9.31205	−	17.9733i	0.298224	−	0.575608i
$976$		0			0
$977$	−27.4208			−0.877270			−0.438635	−	0.898665i	$-0.644538\pi$
$977$	−27.4208			−0.877270			−0.438635	+	0.898665i	$0.644538\pi$
$978$		0			0
$979$	−3.69076	−	6.39258i	−0.117957	−	0.204308i
$980$		0			0
$981$	8.56507	−	0.782849i	0.273462	−	0.0249945i
$982$		0			0
$983$	−29.5782	+	51.2309i	−0.943398	+	1.63401i	−0.184471	+	0.982838i	$0.559057\pi$
$983$	−29.5782	+	51.2309i	−0.943398	+	1.63401i	−0.758927	+	0.651175i	$0.774276\pi$
$984$		0			0
$985$	−3.28201	−	5.68460i	−0.104573	−	0.181126i
$986$		0			0
$987$	−3.93852	−	55.5951i	−0.125365	−	1.76961i
$988$		0			0
$989$	−24.8946	+	43.1188i	−0.791604	+	1.37110i
$990$		0			0
$991$	−6.41887	−	11.1178i	−0.203902	−	0.353169i	0.745880	−	0.666080i	$-0.232029\pi$
$991$	−6.41887	−	11.1178i	−0.203902	−	0.353169i	−0.949782	+	0.312911i	$0.898696\pi$
$992$		0			0
$993$	−23.4880	−	36.7114i	−0.745370	−	1.16500i
$994$		0			0
$995$	−1.66751	+	2.88821i	−0.0528636	+	0.0915624i
$996$		0			0
$997$	2.89037	−	5.00627i	0.0915389	−	0.158550i	−0.816620	−	0.577176i	$-0.804155\pi$
$997$	2.89037	−	5.00627i	0.0915389	−	0.158550i	0.908159	+	0.418626i	$0.137488\pi$
$998$		0			0
$999$	1.96050	−	4.81211i	0.0620276	−	0.152248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.g.625.2		6
3.2	odd	2		3024.2.q.g.2305.2		6
4.3	odd	2		126.2.e.c.121.2	yes	6
7.4	even	3		1008.2.t.h.193.2		6
9.2	odd	6		3024.2.t.h.289.2		6
9.7	even	3		1008.2.t.h.961.2		6
12.11	even	2		378.2.e.d.37.2		6
21.11	odd	6		3024.2.t.h.1873.2		6
28.3	even	6		882.2.h.p.67.2		6
28.11	odd	6		126.2.h.d.67.2	yes	6
28.19	even	6		882.2.f.o.589.3		6
28.23	odd	6		882.2.f.n.589.1		6
28.27	even	2		882.2.e.o.373.2		6
36.7	odd	6		126.2.h.d.79.2	yes	6
36.11	even	6		378.2.h.c.289.2		6
36.23	even	6		1134.2.g.l.163.2		6
36.31	odd	6		1134.2.g.m.163.2		6
63.11	odd	6		3024.2.q.g.2881.2		6
63.25	even	3	inner	1008.2.q.g.529.2		6
84.11	even	6		378.2.h.c.361.2		6
84.23	even	6		2646.2.f.l.1765.2		6
84.47	odd	6		2646.2.f.m.1765.2		6
84.59	odd	6		2646.2.h.o.361.2		6
84.83	odd	2		2646.2.e.p.1549.2		6
252.11	even	6		378.2.e.d.235.2		6
252.23	even	6		7938.2.a.ca.1.2		3
252.47	odd	6		2646.2.f.m.883.2		6
252.67	odd	6		1134.2.g.m.487.2		6
252.79	odd	6		882.2.f.n.295.1		6
252.83	odd	6		2646.2.h.o.667.2		6
252.95	even	6		1134.2.g.l.487.2		6
252.103	even	6		7938.2.a.bw.1.2		3
252.115	even	6		882.2.e.o.655.2		6
252.131	odd	6		7938.2.a.bz.1.2		3
252.151	odd	6		126.2.e.c.25.2	✓	6
252.187	even	6		882.2.f.o.295.3		6
252.191	even	6		2646.2.f.l.883.2		6
252.223	even	6		882.2.h.p.79.2		6
252.227	odd	6		2646.2.e.p.2125.2		6
252.247	odd	6		7938.2.a.bv.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.2	✓	6	252.151	odd	6
126.2.e.c.121.2	yes	6	4.3	odd	2
126.2.h.d.67.2	yes	6	28.11	odd	6
126.2.h.d.79.2	yes	6	36.7	odd	6
378.2.e.d.37.2		6	12.11	even	2
378.2.e.d.235.2		6	252.11	even	6
378.2.h.c.289.2		6	36.11	even	6
378.2.h.c.361.2		6	84.11	even	6
882.2.e.o.373.2		6	28.27	even	2
882.2.e.o.655.2		6	252.115	even	6
882.2.f.n.295.1		6	252.79	odd	6
882.2.f.n.589.1		6	28.23	odd	6
882.2.f.o.295.3		6	252.187	even	6
882.2.f.o.589.3		6	28.19	even	6
882.2.h.p.67.2		6	28.3	even	6
882.2.h.p.79.2		6	252.223	even	6
1008.2.q.g.529.2		6	63.25	even	3	inner
1008.2.q.g.625.2		6	1.1	even	1	trivial
1008.2.t.h.193.2		6	7.4	even	3
1008.2.t.h.961.2		6	9.7	even	3
1134.2.g.l.163.2		6	36.23	even	6
1134.2.g.l.487.2		6	252.95	even	6
1134.2.g.m.163.2		6	36.31	odd	6
1134.2.g.m.487.2		6	252.67	odd	6
2646.2.e.p.1549.2		6	84.83	odd	2
2646.2.e.p.2125.2		6	252.227	odd	6
2646.2.f.l.883.2		6	252.191	even	6
2646.2.f.l.1765.2		6	84.23	even	6
2646.2.f.m.883.2		6	252.47	odd	6
2646.2.f.m.1765.2		6	84.47	odd	6
2646.2.h.o.361.2		6	84.59	odd	6
2646.2.h.o.667.2		6	252.83	odd	6
3024.2.q.g.2305.2		6	3.2	odd	2
3024.2.q.g.2881.2		6	63.11	odd	6
3024.2.t.h.289.2		6	9.2	odd	6
3024.2.t.h.1873.2		6	21.11	odd	6
7938.2.a.bv.1.2		3	252.247	odd	6
7938.2.a.bw.1.2		3	252.103	even	6
7938.2.a.bz.1.2		3	252.131	odd	6
7938.2.a.ca.1.2		3	252.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.933463 - 1.45899i) q^{3} +(-0.296790 - 0.514055i) q^{5} +(-2.32383 - 1.26483i) q^{7} +(-1.25729 + 2.72382i) q^{9} +O(q^{10})\)	\(q+(-0.933463 - 1.45899i) q^{3} +(-0.296790 - 0.514055i) q^{5} +(-2.32383 - 1.26483i) q^{7} +(-1.25729 + 2.72382i) q^{9} +(-0.296790 + 0.514055i) q^{11} +(-1.25729 + 2.17770i) q^{13} +(-0.472958 + 0.912864i) q^{15} +(1.46050 + 2.52967i) q^{17} +(-2.69076 + 4.66053i) q^{19} +(0.323832 + 4.57112i) q^{21} +(2.23025 + 3.86291i) q^{23} +(2.32383 - 4.02499i) q^{25} +(5.14766 - 0.708209i) q^{27} +(-3.09718 - 5.36447i) q^{29} +7.86693 q^{31} +(1.02704 - 0.0468383i) q^{33} +(0.0394951 + 1.56997i) q^{35} +(0.500000 - 0.866025i) q^{37} +(4.35087 - 0.198422i) q^{39} +(-0.136673 + 0.236725i) q^{41} +(5.58113 + 9.66679i) q^{43} +(1.77335 - 0.162084i) q^{45} -12.1623 q^{47} +(3.80039 + 5.87852i) q^{49} +(2.32743 - 4.49221i) q^{51} +(4.02704 + 6.97504i) q^{53} +0.352336 q^{55} +(9.31138 - 0.424646i) q^{57} -8.64766 q^{59} -6.64766 q^{61} +(6.36693 - 4.73944i) q^{63} +1.49261 q^{65} +1.91381 q^{67} +(3.55408 - 6.85980i) q^{69} +14.4107 q^{71} +(3.95691 + 6.85356i) q^{73} +(-8.04163 + 0.366739i) q^{75} +(1.33988 - 0.819187i) q^{77} +9.24844 q^{79} +(-5.83842 - 6.84929i) q^{81} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(-4.93560 + 9.52628i) q^{87} +(-6.21780 + 10.7695i) q^{89} +(5.67617 - 3.47033i) q^{91} +(-7.34348 - 11.4778i) q^{93} +3.19436 q^{95} +(5.86693 + 10.1618i) q^{97} +(-1.02704 - 1.45472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9}+O(q^{10}) \) 6 * q - 2 * q^3 + q^5 - 2 * q^7 + 8 * q^9	\( 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9} + q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} + 2 q^{25} + 7 q^{27} - 5 q^{29} + 40 q^{31} - 3 q^{33} + 13 q^{35} + 3 q^{37} + 5 q^{39} + 6 q^{43} + 9 q^{45} - 18 q^{47} + 12 q^{49} - 6 q^{51} + 15 q^{53} + 26 q^{55} + 22 q^{57} - 28 q^{59} - 16 q^{61} + 31 q^{63} + 24 q^{65} + 2 q^{67} + 3 q^{69} - 14 q^{71} + 19 q^{73} - 8 q^{75} + 10 q^{77} + 10 q^{79} + 8 q^{81} - 2 q^{83} - 2 q^{85} + 27 q^{87} - 9 q^{89} + 46 q^{91} - 38 q^{93} - 8 q^{95} + 28 q^{97} + 3 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 + q^5 - 2 * q^7 + 8 * q^9 + q^11 + 8 * q^13 - 12 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 + 2 * q^25 + 7 * q^27 - 5 * q^29 + 40 * q^31 - 3 * q^33 + 13 * q^35 + 3 * q^37 + 5 * q^39 + 6 * q^43 + 9 * q^45 - 18 * q^47 + 12 * q^49 - 6 * q^51 + 15 * q^53 + 26 * q^55 + 22 * q^57 - 28 * q^59 - 16 * q^61 + 31 * q^63 + 24 * q^65 + 2 * q^67 + 3 * q^69 - 14 * q^71 + 19 * q^73 - 8 * q^75 + 10 * q^77 + 10 * q^79 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 27 * q^87 - 9 * q^89 + 46 * q^91 - 38 * q^93 - 8 * q^95 + 28 * q^97 + 3 * q^99

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