LMFDB - Embedded newform 1008.2.r.l.337.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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, 2, 0]))

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.2091141441.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 $ x^8 - x^7 + x^6 + 3x^5 - 15x^4 + 9x^3 + 9x^2 - 27*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			337.3
Root			$-1.69047 - 0.377226i$ of defining polynomial
Character	$\chi$	$=$	1008.337
Dual form			1008.2.r.l.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17192 - 1.27538i) q^{3} +(-2.19047 + 3.79401i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.253189 - 2.98930i) q^{9} +O(q^{10})$	\(q+(1.17192 - 1.27538i) q^{3} +(-2.19047 + 3.79401i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.253189 - 2.98930i) q^{9} +(-2.69047 - 4.66004i) q^{11} +(1.27174 - 2.20272i) q^{13} +(2.27174 + 7.23998i) q^{15} -2.58058 q^{17} +6.72479 q^{19} +(-1.69047 - 0.377226i) q^{21} +(-0.400185 + 0.693141i) q^{23} +(-7.09635 - 12.2912i) q^{25} +(-4.10921 - 3.18032i) q^{27} +(-1.87155 - 3.24163i) q^{29} +(1.69685 - 2.93903i) q^{31} +(-9.09635 - 2.02983i) q^{33} +4.38095 q^{35} +4.38095 q^{37} +(-1.31892 - 4.20337i) q^{39} +(3.19685 - 5.53711i) q^{41} +(-0.381635 - 0.661012i) q^{43} +(11.8960 + 5.58737i) q^{45} +(-4.13414 - 7.16053i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-3.02424 + 3.29122i) q^{51} -4.94877 q^{53} +23.5736 q^{55} +(7.88095 - 8.57667i) q^{57} +(2.78751 - 4.82811i) q^{59} +(4.14329 + 7.17639i) q^{61} +(-2.46221 + 1.71392i) q^{63} +(5.57142 + 9.64998i) q^{65} +(-0.946441 + 1.63928i) q^{67} +(0.415032 + 1.32270i) q^{69} -1.34385 q^{71} -8.65060 q^{73} +(-23.9924 - 5.35385i) q^{75} +(-2.69047 + 4.66004i) q^{77} +(-6.64051 - 11.5017i) q^{79} +(-8.87179 + 1.51371i) q^{81} +(1.86240 + 3.22577i) q^{83} +(5.65269 - 9.79074i) q^{85} +(-6.32762 - 1.41200i) q^{87} -6.99862 q^{89} -2.54348 q^{91} +(-1.75980 - 5.60845i) q^{93} +(-14.7305 + 25.5139i) q^{95} +(-1.48076 - 2.56476i) q^{97} +(-13.2490 + 9.22249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 3 q^{5} - 4 q^{7} - q^{9}+O(q^{10}) $ 8 * q + q^3 - 3 * q^5 - 4 * q^7 - q^9	$ 8 q + q^{3} - 3 q^{5} - 4 q^{7} - q^{9} - 7 q^{11} + 3 q^{13} + 11 q^{15} + 6 q^{17} + 8 q^{19} + q^{21} - 2 q^{23} - 5 q^{25} - 11 q^{27} - 9 q^{29} - 3 q^{31} - 21 q^{33} + 6 q^{35} + 6 q^{37} - 2 q^{39} + 9 q^{41} - 8 q^{43} + 7 q^{45} - 3 q^{47} - 4 q^{49} + 18 q^{51} + 12 q^{53} + 56 q^{55} + 34 q^{57} - 10 q^{59} + 20 q^{61} + 2 q^{63} + q^{65} - 11 q^{67} - 17 q^{69} + 6 q^{71} - 48 q^{73} - 52 q^{75} - 7 q^{77} - 21 q^{79} - 25 q^{81} - 8 q^{83} + 9 q^{85} + 15 q^{87} + 12 q^{89} - 6 q^{91} + 29 q^{93} - 36 q^{95} + 16 q^{97} - 18 q^{99}+O(q^{100}) $ 8 * q + q^3 - 3 * q^5 - 4 * q^7 - q^9 - 7 * q^11 + 3 * q^13 + 11 * q^15 + 6 * q^17 + 8 * q^19 + q^21 - 2 * q^23 - 5 * q^25 - 11 * q^27 - 9 * q^29 - 3 * q^31 - 21 * q^33 + 6 * q^35 + 6 * q^37 - 2 * q^39 + 9 * q^41 - 8 * q^43 + 7 * q^45 - 3 * q^47 - 4 * q^49 + 18 * q^51 + 12 * q^53 + 56 * q^55 + 34 * q^57 - 10 * q^59 + 20 * q^61 + 2 * q^63 + q^65 - 11 * q^67 - 17 * q^69 + 6 * q^71 - 48 * q^73 - 52 * q^75 - 7 * q^77 - 21 * q^79 - 25 * q^81 - 8 * q^83 + 9 * q^85 + 15 * q^87 + 12 * q^89 - 6 * q^91 + 29 * q^93 - 36 * q^95 + 16 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.17192	−	1.27538i	0.676611	−	0.736341i
$3$	1.17192	−	1.27538i	0.676611	−	0.736341i
$4$		0			0
$5$	−2.19047	+	3.79401i	−0.979610	+	1.69673i	−0.315811	+	0.948822i	$0.602277\pi$
$5$	−2.19047	+	3.79401i	−0.979610	+	1.69673i	−0.663799	+	0.747911i	$0.731057\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$	−0.253189	−	2.98930i	−0.0843964	−	0.996432i
$10$		0			0
$11$	−2.69047	−	4.66004i	−0.811208	−	1.40505i	−0.912019	−	0.410148i	$-0.865477\pi$
$11$	−2.69047	−	4.66004i	−0.811208	−	1.40505i	0.100811	−	0.994906i	$-0.467856\pi$
$12$		0			0
$13$	1.27174	−	2.20272i	0.352717	−	0.610924i	−0.634008	−	0.773327i	$-0.718591\pi$
$13$	1.27174	−	2.20272i	0.352717	−	0.610924i	0.986724	+	0.162403i	$0.0519245\pi$
$14$		0			0
$15$	2.27174	+	7.23998i	0.586560	+	1.86935i
$16$		0			0
$17$	−2.58058			−0.625882			−0.312941	−	0.949773i	$-0.601314\pi$
$17$	−2.58058			−0.625882			−0.312941	+	0.949773i	$0.601314\pi$
$18$		0			0
$19$	6.72479			1.54277			0.771387	−	0.636366i	$-0.219563\pi$
$19$	6.72479			1.54277			0.771387	+	0.636366i	$0.219563\pi$
$20$		0			0
$21$	−1.69047	−	0.377226i	−0.368892	−	0.0823174i
$22$		0			0
$23$	−0.400185	+	0.693141i	−0.0834443	+	0.144530i	−0.904727	−	0.425991i	$-0.859925\pi$
$23$	−0.400185	+	0.693141i	−0.0834443	+	0.144530i	0.821283	+	0.570521i	$0.193259\pi$
$24$		0			0
$25$	−7.09635	−	12.2912i	−1.41927	−	2.45825i
$26$		0			0
$27$	−4.10921	−	3.18032i	−0.790817	−	0.612052i
$28$		0			0
$29$	−1.87155	−	3.24163i	−0.347539	−	0.601955i	0.638273	−	0.769810i	$-0.279649\pi$
$29$	−1.87155	−	3.24163i	−0.347539	−	0.601955i	−0.985812	+	0.167855i	$0.946316\pi$
$30$		0			0
$31$	1.69685	−	2.93903i	0.304764	−	0.527866i	−0.672445	−	0.740147i	$-0.734756\pi$
$31$	1.69685	−	2.93903i	0.304764	−	0.527866i	0.977209	+	0.212281i	$0.0680892\pi$
$32$		0			0
$33$	−9.09635	−	2.02983i	−1.58347	−	0.353348i
$34$		0			0
$35$	4.38095			0.740515
$36$		0			0
$37$	4.38095			0.720223			0.360112	−	0.932909i	$-0.382739\pi$
$37$	4.38095			0.720223			0.360112	+	0.932909i	$0.382739\pi$
$38$		0			0
$39$	−1.31892	−	4.20337i	−0.211196	−	0.673077i
$40$		0			0
$41$	3.19685	−	5.53711i	0.499264	−	0.864751i	−0.500735	−	0.865600i	$-0.666937\pi$
$41$	3.19685	−	5.53711i	0.499264	−	0.864751i	1.00000		0.000849221i	$0.000270315\pi$
$42$		0			0
$43$	−0.381635	−	0.661012i	−0.0581988	−	0.100803i	0.835458	−	0.549554i	$-0.185202\pi$
$43$	−0.381635	−	0.661012i	−0.0581988	−	0.100803i	−0.893657	+	0.448751i	$0.851869\pi$
$44$		0			0
$45$	11.8960	+	5.58737i	1.77336	+	0.832916i
$46$		0			0
$47$	−4.13414	−	7.16053i	−0.603026	−	1.04447i	−0.992360	−	0.123375i	$-0.960628\pi$
$47$	−4.13414	−	7.16053i	−0.603026	−	1.04447i	0.389334	−	0.921096i	$-0.372705\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−3.02424	+	3.29122i	−0.423478	+	0.460863i
$52$		0			0
$53$	−4.94877			−0.679766			−0.339883	−	0.940468i	$-0.610387\pi$
$53$	−4.94877			−0.679766			−0.339883	+	0.940468i	$0.610387\pi$
$54$		0			0
$55$	23.5736			3.17867
$56$		0			0
$57$	7.88095	−	8.57667i	1.04386	−	1.13601i
$58$		0			0
$59$	2.78751	−	4.82811i	0.362903	−	0.628566i	−0.625534	−	0.780197i	$-0.715119\pi$
$59$	2.78751	−	4.82811i	0.362903	−	0.628566i	0.988437	+	0.151630i	$0.0484523\pi$
$60$		0			0
$61$	4.14329	+	7.17639i	0.530494	+	0.918843i	0.999367	+	0.0355773i	$0.0113270\pi$
$61$	4.14329	+	7.17639i	0.530494	+	0.918843i	−0.468873	+	0.883266i	$0.655340\pi$
$62$		0			0
$63$	−2.46221	+	1.71392i	−0.310210	+	0.215933i
$64$		0			0
$65$	5.57142	+	9.64998i	0.691050	+	1.19693i
$66$		0			0
$67$	−0.946441	+	1.63928i	−0.115626	+	0.200270i	−0.918030	−	0.396511i	$-0.870221\pi$
$67$	−0.946441	+	1.63928i	−0.115626	+	0.200270i	0.802404	+	0.596782i	$0.203554\pi$
$68$		0			0
$69$	0.415032	+	1.32270i	0.0499639	+	0.159234i
$70$		0			0
$71$	−1.34385			−0.159485			−0.0797427	−	0.996815i	$-0.525410\pi$
$71$	−1.34385			−0.159485			−0.0797427	+	0.996815i	$0.525410\pi$
$72$		0			0
$73$	−8.65060			−1.01248			−0.506238	−	0.862394i	$-0.668964\pi$
$73$	−8.65060			−1.01248			−0.506238	+	0.862394i	$0.668964\pi$
$74$		0			0
$75$	−23.9924	−	5.35385i	−2.77040	−	0.618209i
$76$		0			0
$77$	−2.69047	+	4.66004i	−0.306608	+	0.531060i
$78$		0			0
$79$	−6.64051	−	11.5017i	−0.747116	−	1.29404i	−0.949199	−	0.314675i	$-0.898104\pi$
$79$	−6.64051	−	11.5017i	−0.747116	−	1.29404i	0.202083	−	0.979368i	$-0.435229\pi$
$80$		0			0
$81$	−8.87179	+	1.51371i	−0.985755	+	0.168191i
$82$		0			0
$83$	1.86240	+	3.22577i	0.204425	+	0.354074i	0.949949	−	0.312404i	$-0.101134\pi$
$83$	1.86240	+	3.22577i	0.204425	+	0.354074i	−0.745525	+	0.666478i	$0.767801\pi$
$84$		0			0
$85$	5.65269	−	9.79074i	0.613120	−	1.06195i
$86$		0			0
$87$	−6.32762	−	1.41200i	−0.678393	−	0.151382i
$88$		0			0
$89$	−6.99862			−0.741853			−0.370926	−	0.928662i	$-0.620960\pi$
$89$	−6.99862			−0.741853			−0.370926	+	0.928662i	$0.620960\pi$
$90$		0			0
$91$	−2.54348			−0.266629
$92$		0			0
$93$	−1.75980	−	5.60845i	−0.182483	−	0.581570i
$94$		0			0
$95$	−14.7305	+	25.5139i	−1.51132	+	2.61768i
$96$		0			0
$97$	−1.48076	−	2.56476i	−0.150349	−	0.260411i	0.781007	−	0.624522i	$-0.214706\pi$
$97$	−1.48076	−	2.56476i	−0.150349	−	0.260411i	−0.931356	+	0.364111i	$0.881373\pi$
$98$		0			0
$99$	−13.2490	+	9.22249i	−1.33158	+	0.926896i
$100$		0			0
$101$	8.56494	+	14.8349i	0.852243	+	1.47613i	0.879179	+	0.476492i	$0.158092\pi$
$101$	8.56494	+	14.8349i	0.852243	+	1.47613i	−0.0269357	+	0.999637i	$0.508575\pi$
$102$		0			0
$103$	−6.01786	+	10.4232i	−0.592958	+	1.02703i	0.400874	+	0.916133i	$0.368706\pi$
$103$	−6.01786	+	10.4232i	−0.592958	+	1.02703i	−0.993832	+	0.110899i	$0.964627\pi$
$104$		0			0
$105$	5.13414	−	5.58737i	0.501040	−	0.545272i
$106$		0			0
$107$	6.92580			0.669542			0.334771	−	0.942299i	$-0.391341\pi$
$107$	6.92580			0.669542			0.334771	+	0.942299i	$0.391341\pi$
$108$		0			0
$109$	−4.41942			−0.423304			−0.211652	−	0.977345i	$-0.567884\pi$
$109$	−4.41942			−0.423304			−0.211652	+	0.977345i	$0.567884\pi$
$110$		0			0
$111$	5.13414	−	5.58737i	0.487311	−	0.530330i
$112$		0			0
$113$	−6.41805	+	11.1164i	−0.603759	+	1.04574i	0.388487	+	0.921454i	$0.372998\pi$
$113$	−6.41805	+	11.1164i	−0.603759	+	1.04574i	−0.992246	+	0.124287i	$0.960336\pi$
$114$		0			0
$115$	−1.75319	−	3.03661i	−0.163486	−	0.283166i
$116$		0			0
$117$	−6.90656	−	3.24390i	−0.638512	−	0.299899i
$118$		0			0
$119$	1.29029	+	2.23485i	0.118281	+	0.204868i
$120$		0			0
$121$	−8.97730	+	15.5491i	−0.816118	+	1.41356i
$122$		0			0
$123$	−3.31545	−	10.5663i	−0.298944	−	0.952729i
$124$		0			0
$125$	40.2727			3.60210
$126$		0			0
$127$	2.82471			0.250653			0.125326	−	0.992116i	$-0.460002\pi$
$127$	2.82471			0.250653			0.125326	+	0.992116i	$0.460002\pi$
$128$		0			0
$129$	−1.29029	−	0.287925i	−0.113604	−	0.0253504i
$130$		0			0
$131$	8.55925	−	14.8251i	0.747825	−	1.29527i	−0.201038	−	0.979583i	$-0.564432\pi$
$131$	8.55925	−	14.8251i	0.747825	−	1.29527i	0.948863	−	0.315688i	$-0.102235\pi$
$132$		0			0
$133$	−3.36240	−	5.82384i	−0.291557	−	0.504991i
$134$		0			0
$135$	21.0673	−	8.62399i	1.81318	−	0.742235i
$136$		0			0
$137$	7.10643	+	12.3087i	0.607143	+	1.05160i	0.991709	+	0.128505i	$0.0410179\pi$
$137$	7.10643	+	12.3087i	0.607143	+	1.05160i	−0.384566	+	0.923098i	$0.625649\pi$
$138$		0			0
$139$	−1.60050	+	2.77215i	−0.135753	+	0.235131i	−0.925885	−	0.377806i	$-0.876679\pi$
$139$	−1.60050	+	2.77215i	−0.135753	+	0.235131i	0.790132	+	0.612937i	$0.210012\pi$
$140$		0			0
$141$	−13.9773	−	3.11900i	−1.17710	−	0.262668i
$142$		0			0
$143$	−13.6863			−1.14451
$144$		0			0
$145$	16.3984			1.36181
$146$		0			0
$147$	0.518550	+	1.65261i	0.0427693	+	0.136305i
$148$		0			0
$149$	−8.54917	+	14.8076i	−0.700375	+	1.21309i	0.267960	+	0.963430i	$0.413651\pi$
$149$	−8.54917	+	14.8076i	−0.700375	+	1.21309i	−0.968335	+	0.249655i	$0.919683\pi$
$150$		0			0
$151$	0.0528709	+	0.0915750i	0.00430257	+	0.00745227i	0.868169	−	0.496269i	$-0.165297\pi$
$151$	0.0528709	+	0.0915750i	0.00430257	+	0.00745227i	−0.863866	+	0.503722i	$0.831964\pi$
$152$		0			0
$153$	0.653374	+	7.71411i	0.0528222	+	0.623649i
$154$		0			0
$155$	7.43382	+	12.8758i	0.597099	+	1.03421i
$156$		0			0
$157$	10.5023	−	18.1906i	0.838177	−	1.45177i	−0.0532404	−	0.998582i	$-0.516955\pi$
$157$	10.5023	−	18.1906i	0.838177	−	1.45177i	0.891417	−	0.453183i	$-0.149712\pi$
$158$		0			0
$159$	−5.79958	+	6.31156i	−0.459937	+	0.500539i
$160$		0			0
$161$	0.800370			0.0630780
$162$		0			0
$163$	−2.58915			−0.202798			−0.101399	−	0.994846i	$-0.532332\pi$
$163$	−2.58915			−0.202798			−0.101399	+	0.994846i	$0.532332\pi$
$164$		0			0
$165$	27.6265	−	30.0654i	2.15072	−	2.34058i
$166$		0			0
$167$	1.30884	−	2.26697i	0.101281	−	0.175424i	−0.810932	−	0.585141i	$-0.801039\pi$
$167$	1.30884	−	2.26697i	0.101281	−	0.175424i	0.912213	+	0.409717i	$0.134373\pi$
$168$		0			0
$169$	3.26536	+	5.65577i	0.251182	+	0.435059i
$170$		0			0
$171$	−1.70264	−	20.1024i	−0.130205	−	1.53727i
$172$		0			0
$173$	−7.22757	−	12.5185i	−0.549502	−	0.951766i	−0.998309	−	0.0581367i	$-0.981484\pi$
$173$	−7.22757	−	12.5185i	−0.549502	−	0.951766i	0.448806	−	0.893629i	$-0.351849\pi$
$174$		0			0
$175$	−7.09635	+	12.2912i	−0.536434	+	0.929130i
$176$		0			0
$177$	−2.89093	−	9.21331i	−0.217295	−	0.692515i
$178$		0			0
$179$	23.7179			1.77276			0.886378	−	0.462962i	$-0.153213\pi$
$179$	23.7179			1.77276			0.886378	+	0.462962i	$0.153213\pi$
$180$		0			0
$181$	−6.60630			−0.491042			−0.245521	−	0.969391i	$-0.578959\pi$
$181$	−6.60630			−0.491042			−0.245521	+	0.969391i	$0.578959\pi$
$182$		0			0
$183$	14.0083	+	3.12591i	1.03552	+	0.231074i
$184$		0			0
$185$	−9.59635	+	16.6214i	−0.705538	+	1.22203i
$186$		0			0
$187$	6.94297	+	12.0256i	0.507721	+	0.879398i
$188$		0			0
$189$	−0.699630	+	5.14884i	−0.0508906	+	0.374523i
$190$		0			0
$191$	−2.08336	−	3.60848i	−0.150746	−	0.261100i	0.780756	−	0.624836i	$-0.214834\pi$
$191$	−2.08336	−	3.60848i	−0.150746	−	0.261100i	−0.931502	+	0.363736i	$0.881501\pi$
$192$		0			0
$193$	8.09426	−	14.0197i	0.582637	−	1.00916i	−0.412528	−	0.910945i	$-0.635354\pi$
$193$	8.09426	−	14.0197i	0.582637	−	1.00916i	0.995165	−	0.0982128i	$-0.0313126\pi$
$194$		0			0
$195$	18.8367	+	4.20337i	1.34892	+	0.301009i
$196$		0			0
$197$	4.33109			0.308577			0.154289	−	0.988026i	$-0.450691\pi$
$197$	4.33109			0.308577			0.154289	+	0.988026i	$0.450691\pi$
$198$		0			0
$199$	−13.7849			−0.977183			−0.488591	−	0.872513i	$-0.662489\pi$
$199$	−13.7849			−0.977183			−0.488591	+	0.872513i	$0.662489\pi$
$200$		0			0
$201$	0.981553	+	3.12819i	0.0692334	+	0.220645i
$202$		0			0
$203$	−1.87155	+	3.24163i	−0.131357	+	0.227518i
$204$		0			0
$205$	14.0052	+	24.2578i	0.978168	+	1.69424i
$206$		0			0
$207$	2.17333	+	1.02078i	0.151057	+	0.0709488i
$208$		0			0
$209$	−18.0929	−	31.3378i	−1.25151	−	2.16768i
$210$		0			0
$211$	6.18341	−	10.7100i	0.425683	−	0.737305i	−0.570801	−	0.821089i	$-0.693367\pi$
$211$	6.18341	−	10.7100i	0.425683	−	0.737305i	0.996484	+	0.0837836i	$0.0267004\pi$
$212$		0			0
$213$	−1.57489	+	1.71392i	−0.107909	+	0.117436i
$214$		0			0
$215$	3.34385			0.228049
$216$		0			0
$217$	−3.39370			−0.230380
$218$		0			0
$219$	−10.1378	+	11.0328i	−0.685052	+	0.745527i
$220$		0			0
$221$	−3.28182	+	5.68428i	−0.220759	+	0.382366i
$222$		0			0
$223$	−7.40320	−	12.8227i	−0.495755	−	0.858673i	0.504233	−	0.863568i	$-0.331775\pi$
$223$	−7.40320	−	12.8227i	−0.495755	−	0.858673i	−0.999988	+	0.00489487i	$0.998442\pi$
$224$		0			0
$225$	−34.9454	+	24.3251i	−2.32970	+	1.62167i
$226$		0			0
$227$	6.89881	+	11.9491i	0.457890	+	0.793089i	0.998849	−	0.0479600i	$-0.0152720\pi$
$227$	6.89881	+	11.9491i	0.457890	+	0.793089i	−0.540959	+	0.841049i	$0.681939\pi$
$228$		0			0
$229$	−0.471369	+	0.816435i	−0.0311489	+	0.0539515i	−0.881180	−	0.472782i	$-0.843250\pi$
$229$	−0.471369	+	0.816435i	−0.0311489	+	0.0539515i	0.850031	+	0.526733i	$0.176583\pi$
$230$		0			0
$231$	2.79029	+	8.89258i	0.183588	+	0.585089i
$232$		0			0
$233$	16.6608			1.09149			0.545743	−	0.837953i	$-0.316248\pi$
$233$	16.6608			1.09149			0.545743	+	0.837953i	$0.316248\pi$
$234$		0			0
$235$	36.2229			2.36292
$236$		0			0
$237$	−22.4512	−	5.00995i	−1.45836	−	0.325431i
$238$		0			0
$239$	0.678405	−	1.17503i	0.0438824	−	0.0760065i	−0.843250	−	0.537522i	$-0.819361\pi$
$239$	0.678405	−	1.17503i	0.0438824	−	0.0760065i	0.887132	+	0.461515i	$0.152694\pi$
$240$		0			0
$241$	4.60828	+	7.98178i	0.296846	+	0.514152i	0.975413	−	0.220387i	$-0.0707320\pi$
$241$	4.60828	+	7.98178i	0.296846	+	0.514152i	−0.678567	+	0.734539i	$0.737399\pi$
$242$		0			0
$243$	−8.46650	+	13.0889i	−0.543126	+	0.839651i
$244$		0			0
$245$	−2.19047	−	3.79401i	−0.139944	−	0.242391i
$246$		0			0
$247$	8.55218	−	14.8128i	0.544162	−	0.942517i
$248$		0			0
$249$	6.29667	+	1.40509i	0.399035	+	0.0890439i
$250$		0			0
$251$	2.53189			0.159812			0.0799058	−	0.996802i	$-0.474538\pi$
$251$	2.53189			0.159812			0.0799058	+	0.996802i	$0.474538\pi$
$252$		0			0
$253$	4.30675			0.270763
$254$		0			0
$255$	−5.86240	−	18.6833i	−0.367118	−	1.17000i
$256$		0			0
$257$	3.08404	−	5.34172i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$257$	3.08404	−	5.34172i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$258$		0			0
$259$	−2.19047	−	3.79401i	−0.136109	−	0.235748i
$260$		0			0
$261$	−9.21633	+	6.41537i	−0.570476	+	0.397102i
$262$		0			0
$263$	5.49074	+	9.51024i	0.338574	+	0.586427i	0.984165	−	0.177257i	$-0.0567223\pi$
$263$	5.49074	+	9.51024i	0.338574	+	0.586427i	−0.645591	+	0.763683i	$0.723389\pi$
$264$		0			0
$265$	10.8401	−	18.7757i	0.665905	−	1.15338i
$266$		0			0
$267$	−8.20185	+	8.92591i	−0.501945	+	0.546257i
$268$		0			0
$269$	4.73035			0.288415			0.144207	−	0.989547i	$-0.453937\pi$
$269$	4.73035			0.288415			0.144207	+	0.989547i	$0.453937\pi$
$270$		0			0
$271$	13.5379			0.822370			0.411185	−	0.911552i	$-0.365115\pi$
$271$	13.5379			0.822370			0.411185	+	0.911552i	$0.365115\pi$
$272$		0			0
$273$	−2.98076	+	3.24390i	−0.180404	+	0.196330i
$274$		0			0
$275$	−38.1851	+	66.1385i	−2.30265	+	3.98830i
$276$		0			0
$277$	14.6614	+	25.3943i	0.880918	+	1.52579i	0.850322	+	0.526262i	$0.176407\pi$
$277$	14.6614	+	25.3943i	0.880918	+	1.52579i	0.0305952	+	0.999532i	$0.490260\pi$
$278$		0			0
$279$	−9.21527	−	4.32826i	−0.551704	−	0.259126i
$280$		0			0
$281$	−7.31336	−	12.6671i	−0.436279	−	0.755657i	0.561120	−	0.827734i	$-0.310370\pi$
$281$	−7.31336	−	12.6671i	−0.436279	−	0.755657i	−0.997399	+	0.0720774i	$0.977037\pi$
$282$		0			0
$283$	7.64562	−	13.2426i	0.454485	−	0.787191i	−0.544174	−	0.838973i	$-0.683157\pi$
$283$	7.64562	−	13.2426i	0.454485	−	0.787191i	0.998658	+	0.0517817i	$0.0164900\pi$
$284$		0			0
$285$	15.2770	+	48.6874i	0.904930	+	2.88399i
$286$		0			0
$287$	−6.39370			−0.377408
$288$		0			0
$289$	−10.3406			−0.608272
$290$		0			0
$291$	−5.00638	−	1.11716i	−0.293479	−	0.0654893i
$292$		0			0
$293$	0.940196	−	1.62847i	0.0549268	−	0.0951361i	−0.837255	−	0.546813i	$-0.815841\pi$
$293$	0.940196	−	1.62847i	0.0549268	−	0.0951361i	0.892181	+	0.451677i	$0.149174\pi$
$294$		0			0
$295$	12.2119	+	21.1517i	0.711006	+	1.23150i
$296$		0			0
$297$	−3.76467	+	27.7056i	−0.218448	+	1.60764i
$298$		0			0
$299$	1.01786	+	1.76299i	0.0588645	+	0.101956i
$300$		0			0
$301$	−0.381635	+	0.661012i	−0.0219971	+	0.0381001i
$302$		0			0
$303$	28.9576	+	6.46183i	1.66357	+	0.371222i
$304$		0			0
$305$	−36.3031			−2.07871
$306$		0			0
$307$	−11.8451			−0.676038			−0.338019	−	0.941139i	$-0.609757\pi$
$307$	−11.8451			−0.676038			−0.338019	+	0.941139i	$0.609757\pi$
$308$		0			0
$309$	6.24112	+	19.8903i	0.355045	+	1.13152i
$310$		0			0
$311$	17.5422	−	30.3840i	0.994729	−	1.72292i	0.408562	−	0.912730i	$-0.366030\pi$
$311$	17.5422	−	30.3840i	0.994729	−	1.72292i	0.586167	−	0.810190i	$-0.300636\pi$
$312$		0			0
$313$	0.430906	+	0.746351i	0.0243563	+	0.0421863i	0.877947	−	0.478759i	$-0.158913\pi$
$313$	0.430906	+	0.746351i	0.0243563	+	0.0421863i	−0.853590	+	0.520945i	$0.825580\pi$
$314$		0			0
$315$	−1.10921	−	13.0960i	−0.0624968	−	0.737873i
$316$		0			0
$317$	−4.31381	−	7.47175i	−0.242288	−	0.419655i	0.719078	−	0.694930i	$-0.244565\pi$
$317$	−4.31381	−	7.47175i	−0.242288	−	0.419655i	−0.961366	+	0.275275i	$0.911231\pi$
$318$		0			0
$319$	−10.0707	+	17.4430i	−0.563853	+	0.976622i
$320$		0			0
$321$	8.11651	−	8.83303i	0.453019	−	0.493012i
$322$		0			0
$323$	−17.3539			−0.965594
$324$		0			0
$325$	−36.0988			−2.00240
$326$		0			0
$327$	−5.17923	+	5.63644i	−0.286412	+	0.311696i
$328$		0			0
$329$	−4.13414	+	7.16053i	−0.227922	+	0.394773i
$330$		0			0
$331$	−8.76851	−	15.1875i	−0.481961	−	0.834781i	0.517825	−	0.855487i	$-0.326742\pi$
$331$	−8.76851	−	15.1875i	−0.481961	−	0.834781i	−0.999786	+	0.0207060i	$0.993409\pi$
$332$		0			0
$333$	−1.10921	−	13.0960i	−0.0607842	−	0.717654i
$334$		0			0
$335$	−4.14631	−	7.18162i	−0.226537	−	0.392374i
$336$		0			0
$337$	−16.7861	+	29.0744i	−0.914399	+	1.58379i	−0.106620	+	0.994300i	$0.534003\pi$
$337$	−16.7861	+	29.0744i	−0.914399	+	1.58379i	−0.807779	+	0.589486i	$0.799330\pi$
$338$		0			0
$339$	6.65615	+	21.2130i	0.361513	+	1.15213i
$340$		0			0
$341$	−18.2613			−0.988907
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−5.92744	−	1.32270i	−0.319123	−	0.0712116i
$346$		0			0
$347$	−1.80616	+	3.12837i	−0.0969599	+	0.167939i	−0.910425	−	0.413674i	$-0.864245\pi$
$347$	−1.80616	+	3.12837i	−0.0969599	+	0.167939i	0.813465	+	0.581614i	$0.197579\pi$
$348$		0			0
$349$	4.66891	+	8.08679i	0.249921	+	0.432876i	0.963504	−	0.267695i	$-0.0862620\pi$
$349$	4.66891	+	8.08679i	0.249921	+	0.432876i	−0.713583	+	0.700571i	$0.752929\pi$
$350$		0			0
$351$	−12.2312	+	5.00689i	−0.652852	+	0.267248i
$352$		0			0
$353$	−9.67693	−	16.7609i	−0.515051	−	0.892094i	−0.999847	−	0.0174672i	$-0.994440\pi$
$353$	−9.67693	−	16.7609i	−0.515051	−	0.892094i	0.484797	−	0.874627i	$-0.338894\pi$
$354$		0			0
$355$	2.94366	−	5.09857i	0.156233	−	0.270604i
$356$		0			0
$357$	4.36240	+	0.973460i	0.230883	+	0.0515210i
$358$		0			0
$359$	−31.1716			−1.64518			−0.822588	−	0.568638i	$-0.807471\pi$
$359$	−31.1716			−1.64518			−0.822588	+	0.568638i	$0.807471\pi$
$360$		0			0
$361$	26.2229			1.38015
$362$		0			0
$363$	9.31035	+	29.6719i	0.488667	+	1.55737i
$364$		0			0
$365$	18.9489	−	32.8205i	0.991831	−	1.71790i
$366$		0			0
$367$	2.75411	+	4.77027i	0.143764	+	0.249006i	0.928911	−	0.370303i	$-0.120746\pi$
$367$	2.75411	+	4.77027i	0.143764	+	0.249006i	−0.785147	+	0.619309i	$0.787413\pi$
$368$		0			0
$369$	−17.3615	−	8.15440i	−0.903802	−	0.424501i
$370$		0			0
$371$	2.47438	+	4.28576i	0.128464	+	0.222505i
$372$		0			0
$373$	5.76687	−	9.98851i	0.298597	−	0.517186i	−0.677218	−	0.735782i	$-0.736815\pi$
$373$	5.76687	−	9.98851i	0.298597	−	0.517186i	0.975815	+	0.218597i	$0.0701479\pi$
$374$		0			0
$375$	47.1966	−	51.3630i	2.43722	−	2.65238i
$376$		0			0
$377$	−9.52051			−0.490331
$378$		0			0
$379$	−35.4614			−1.82153			−0.910766	−	0.412923i	$-0.864508\pi$
$379$	−35.4614			−1.82153			−0.910766	+	0.412923i	$0.864508\pi$
$380$		0			0
$381$	3.31035	−	3.60258i	0.169594	−	0.184566i
$382$		0			0
$383$	−14.6401	+	25.3573i	−0.748072	+	1.29570i	0.200673	+	0.979658i	$0.435687\pi$
$383$	−14.6401	+	25.3573i	−0.748072	+	1.29570i	−0.948746	+	0.316041i	$0.897646\pi$
$384$		0			0
$385$	−11.7868	−	20.4154i	−0.600712	−	1.04046i
$386$		0			0
$387$	−1.87933	+	1.30818i	−0.0955319	+	0.0664986i
$388$		0			0
$389$	3.45364	+	5.98188i	0.175107	+	0.303293i	0.940198	−	0.340628i	$-0.110640\pi$
$389$	3.45364	+	5.98188i	0.175107	+	0.303293i	−0.765092	+	0.643921i	$0.777306\pi$
$390$		0			0
$391$	1.03271	−	1.78870i	0.0522263	−	0.0904586i
$392$		0			0
$393$	−8.87679	−	28.2901i	−0.447775	−	1.42705i
$394$		0			0
$395$	58.1835			2.92753
$396$		0			0
$397$	24.6291			1.23610			0.618048	−	0.786140i	$-0.287924\pi$
$397$	24.6291			1.23610			0.618048	+	0.786140i	$0.287924\pi$
$398$		0			0
$399$	−11.3681	−	2.53677i	−0.569116	−	0.126997i
$400$		0			0
$401$	16.9020	−	29.2750i	0.844043	−	1.46193i	−0.0424059	−	0.999100i	$-0.513502\pi$
$401$	16.9020	−	29.2750i	0.844043	−	1.46193i	0.886449	−	0.462826i	$-0.153164\pi$
$402$		0			0
$403$	−4.31590	−	7.47537i	−0.214991	−	0.372375i
$404$		0			0
$405$	13.6904	−	36.9754i	0.680280	−	1.83732i
$406$		0			0
$407$	−11.7868	−	20.4154i	−0.584251	−	1.01195i
$408$		0			0
$409$	12.1513	−	21.0467i	0.600844	−	1.04069i	−0.391850	−	0.920029i	$-0.628165\pi$
$409$	12.1513	−	21.0467i	0.600844	−	1.04069i	0.992694	−	0.120663i	$-0.0385019\pi$
$410$		0			0
$411$	24.0265	+	5.36146i	1.18514	+	0.264461i
$412$		0			0
$413$	−5.57502			−0.274329
$414$		0			0
$415$	−16.3181			−0.801025
$416$		0			0
$417$	1.65988	+	5.29000i	0.0812847	+	0.259053i
$418$		0			0
$419$	9.51868	−	16.4868i	0.465018	−	0.805435i	−0.534184	−	0.845368i	$-0.679381\pi$
$419$	9.51868	−	16.4868i	0.465018	−	0.805435i	0.999202	+	0.0399331i	$0.0127145\pi$
$420$		0			0
$421$	5.85893	+	10.1480i	0.285547	+	0.494582i	0.972742	−	0.231892i	$-0.0744915\pi$
$421$	5.85893	+	10.1480i	0.285547	+	0.494582i	−0.687195	+	0.726473i	$0.741158\pi$
$422$		0			0
$423$	−20.3582	+	14.1711i	−0.989852	+	0.689024i
$424$		0			0
$425$	18.3127	+	31.7185i	0.888295	+	1.53857i
$426$		0			0
$427$	4.14329	−	7.17639i	0.200508	−	0.347290i
$428$		0			0
$429$	−16.0393	+	17.4553i	−0.774386	+	0.842748i
$430$		0			0
$431$	9.89426			0.476590			0.238295	−	0.971193i	$-0.423412\pi$
$431$	9.89426			0.476590			0.238295	+	0.971193i	$0.423412\pi$
$432$		0			0
$433$	38.0986			1.83090			0.915451	−	0.402429i	$-0.131834\pi$
$433$	38.0986			1.83090			0.915451	+	0.402429i	$0.131834\pi$
$434$		0			0
$435$	19.2176	−	20.9141i	0.921415	−	1.00276i
$436$		0			0
$437$	−2.69116	+	4.66123i	−0.128736	+	0.222977i
$438$		0			0
$439$	9.99746	+	17.3161i	0.477153	+	0.826453i	0.999657	−	0.0261839i	$-0.00833554\pi$
$439$	9.99746	+	17.3161i	0.477153	+	0.826453i	−0.522504	+	0.852637i	$0.675002\pi$
$440$		0			0
$441$	2.71540	+	1.27538i	0.129305	+	0.0607324i
$442$		0			0
$443$	−4.15824	−	7.20229i	−0.197564	−	0.342191i	0.750174	−	0.661240i	$-0.229970\pi$
$443$	−4.15824	−	7.20229i	−0.197564	−	0.342191i	−0.947738	+	0.319049i	$0.896636\pi$
$444$		0			0
$445$	15.3303	−	26.5529i	0.726726	−	1.25873i
$446$		0			0
$447$	8.86634	+	28.2568i	0.419363	+	1.33650i
$448$		0			0
$449$	22.5036			1.06201			0.531006	−	0.847368i	$-0.321814\pi$
$449$	22.5036			1.06201			0.531006	+	0.847368i	$0.321814\pi$
$450$		0			0
$451$	−34.4042			−1.62003
$452$		0			0
$453$	0.178754	+	0.0398885i	0.00839858	+	0.00187413i
$454$		0			0
$455$	5.57142	−	9.64998i	0.261192	−	0.452398i
$456$		0			0
$457$	−7.91143	−	13.7030i	−0.370081	−	0.640999i	0.619497	−	0.784999i	$-0.287337\pi$
$457$	−7.91143	−	13.7030i	−0.370081	−	0.640999i	−0.989578	+	0.144000i	$0.954003\pi$
$458$		0			0
$459$	10.6041	+	8.20705i	0.494958	+	0.383072i
$460$		0			0
$461$	7.87933	+	13.6474i	0.366977	+	0.635623i	0.989091	−	0.147303i	$-0.0470594\pi$
$461$	7.87933	+	13.6474i	0.366977	+	0.635623i	−0.622114	+	0.782927i	$0.713726\pi$
$462$		0			0
$463$	−8.57410	+	14.8508i	−0.398472	+	0.690174i	−0.993538	−	0.113503i	$-0.963793\pi$
$463$	−8.57410	+	14.8508i	−0.398472	+	0.690174i	0.595066	+	0.803677i	$0.297126\pi$
$464$		0			0
$465$	25.1333	+	5.60845i	1.16553	+	0.260086i
$466$		0			0
$467$	2.41270			0.111646			0.0558231	−	0.998441i	$-0.482222\pi$
$467$	2.41270			0.111646			0.0558231	+	0.998441i	$0.482222\pi$
$468$		0			0
$469$	1.89288			0.0874052
$470$		0			0
$471$	−10.8920	−	34.7124i	−0.501875	−	1.59946i
$472$		0			0
$473$	−2.05356	+	3.55687i	−0.0944227	+	0.163545i
$474$		0			0
$475$	−47.7215	−	82.6560i	−2.18961	−	3.79252i
$476$		0			0
$477$	1.25297	+	14.7933i	0.0573697	+	0.677340i
$478$		0			0
$479$	−13.1784	−	22.8257i	−0.602138	−	1.04293i	−0.992497	−	0.122271i	$-0.960982\pi$
$479$	−13.1784	−	22.8257i	−0.602138	−	1.04293i	0.390359	−	0.920663i	$-0.372351\pi$
$480$		0			0
$481$	5.57142	−	9.64998i	0.254035	−	0.440001i
$482$		0			0
$483$	0.937973	−	1.02078i	0.0426792	−	0.0464469i
$484$		0			0
$485$	12.9743			0.589132
$486$		0			0
$487$	−16.1141			−0.730200			−0.365100	−	0.930968i	$-0.618965\pi$
$487$	−16.1141			−0.730200			−0.365100	+	0.930968i	$0.618965\pi$
$488$		0			0
$489$	−3.03429	+	3.30216i	−0.137215	+	0.149329i
$490$		0			0
$491$	3.66266	−	6.34392i	0.165294	−	0.286297i	−0.771466	−	0.636271i	$-0.780476\pi$
$491$	3.66266	−	6.34392i	0.165294	−	0.286297i	0.936760	+	0.349974i	$0.113809\pi$
$492$		0			0
$493$	4.82969	+	8.36527i	0.217518	+	0.376753i
$494$		0			0
$495$	−5.96859	−	70.4686i	−0.268268	−	3.16733i
$496$		0			0
$497$	0.671924	+	1.16381i	0.0301399	+	0.0522038i
$498$		0			0
$499$	3.01587	−	5.22365i	0.135009	−	0.233843i	−0.790592	−	0.612343i	$-0.790227\pi$
$499$	3.01587	−	5.22365i	0.135009	−	0.233843i	0.925601	+	0.378501i	$0.123560\pi$
$500$		0			0
$501$	−1.35740	−	4.32599i	−0.0606440	−	0.193271i
$502$		0			0
$503$	16.4106			0.731714			0.365857	−	0.930671i	$-0.380776\pi$
$503$	16.4106			0.731714			0.365857	+	0.930671i	$0.380776\pi$
$504$		0			0
$505$	−75.0451			−3.33946
$506$		0			0
$507$	11.0400	+	2.46356i	0.490304	+	0.109410i
$508$		0			0
$509$	−5.70693	+	9.88470i	−0.252955	+	0.438132i	−0.964338	−	0.264673i	$-0.914736\pi$
$509$	−5.70693	+	9.88470i	−0.252955	+	0.438132i	0.711383	+	0.702805i	$0.248069\pi$
$510$		0			0
$511$	4.32530	+	7.49164i	0.191340	+	0.331410i
$512$		0			0
$513$	−27.6336	−	21.3870i	−1.22005	−	0.944258i
$514$		0			0
$515$	−26.3639	−	45.6637i	−1.16173	−	2.01218i
$516$		0			0
$517$	−22.2456	+	38.5305i	−0.978359	+	1.69457i
$518$		0			0
$519$	−24.4360	−	5.45285i	−1.07262	−	0.239354i
$520$		0			0
$521$	41.1600			1.80325			0.901627	−	0.432514i	$-0.142373\pi$
$521$	41.1600			1.80325			0.901627	+	0.432514i	$0.142373\pi$
$522$		0			0
$523$	29.2303			1.27815			0.639075	−	0.769144i	$-0.279317\pi$
$523$	29.2303			1.27815			0.639075	+	0.769144i	$0.279317\pi$
$524$		0			0
$525$	7.35962	+	23.4549i	0.321200	+	1.02366i
$526$		0			0
$527$	−4.37886	+	7.58440i	−0.190746	+	0.330382i
$528$		0			0
$529$	11.1797	+	19.3638i	0.486074	+	0.841905i
$530$		0			0
$531$	−15.1384	−	7.11027i	−0.656951	−	0.308559i
$532$		0			0
$533$	−8.13112	−	14.0835i	−0.352198	−	0.610025i
$534$		0			0
$535$	−15.1708	+	26.2766i	−0.655890	+	1.13604i
$536$		0			0
$537$	27.7955	−	30.2493i	1.19947	−	1.30535i
$538$		0			0
$539$	5.38095			0.231774
$540$		0			0
$541$	−6.44101			−0.276921			−0.138460	−	0.990368i	$-0.544215\pi$
$541$	−6.44101			−0.276921			−0.138460	+	0.990368i	$0.544215\pi$
$542$		0			0
$543$	−7.74208	+	8.42554i	−0.332244	+	0.361575i
$544$		0			0
$545$	9.68063	−	16.7673i	0.414673	−	0.718234i
$546$		0			0
$547$	−0.689682	−	1.19456i	−0.0294887	−	0.0510759i	0.850904	−	0.525321i	$-0.176055\pi$
$547$	−0.689682	−	1.19456i	−0.0294887	−	0.0510759i	−0.880393	+	0.474245i	$0.842721\pi$
$548$		0			0
$549$	20.4033	−	14.2025i	0.870793	−	0.606149i
$550$		0			0
$551$	−12.5858	−	21.7993i	−0.536174	−	0.928680i
$552$		0			0
$553$	−6.64051	+	11.5017i	−0.282383	+	0.489102i
$554$		0			0
$555$	9.95237	+	31.7180i	0.422454	+	1.34635i
$556$		0			0
$557$	25.5692			1.08340			0.541701	−	0.840571i	$-0.317781\pi$
$557$	25.5692			1.08340			0.541701	+	0.840571i	$0.317781\pi$
$558$		0			0
$559$	−1.94136			−0.0821108
$560$		0			0
$561$	23.4738	+	5.23814i	0.991066	+	0.221154i
$562$		0			0
$563$	−7.53329	+	13.0480i	−0.317490	+	0.549910i	−0.979964	−	0.199176i	$-0.936173\pi$
$563$	−7.53329	+	13.0480i	−0.317490	+	0.549910i	0.662473	+	0.749086i	$0.269507\pi$
$564$		0			0
$565$	−28.1171	−	48.7003i	−1.18290	−	2.04884i
$566$		0			0
$567$	5.74681	+	6.92634i	0.241343	+	0.290879i
$568$		0			0
$569$	−7.16938	−	12.4177i	−0.300556	−	0.520578i	0.675706	−	0.737171i	$-0.263839\pi$
$569$	−7.16938	−	12.4177i	−0.300556	−	0.520578i	−0.976262	+	0.216593i	$0.930506\pi$
$570$		0			0
$571$	−1.29409	+	2.24144i	−0.0541562	+	0.0938013i	−0.891833	−	0.452366i	$-0.850580\pi$
$571$	−1.29409	+	2.24144i	−0.0541562	+	0.0938013i	0.837676	+	0.546167i	$0.183914\pi$
$572$		0			0
$573$	−7.04371	−	1.57179i	−0.294255	−	0.0656625i
$574$		0			0
$575$	11.3594			0.473720
$576$		0			0
$577$	17.5050			0.728743			0.364371	−	0.931254i	$-0.381284\pi$
$577$	17.5050			0.728743			0.364371	+	0.931254i	$0.381284\pi$
$578$		0			0
$579$	−8.39455	−	26.7532i	−0.348866	−	1.11183i
$580$		0			0
$581$	1.86240	−	3.22577i	0.0772653	−	0.133827i
$582$		0			0
$583$	13.3145	+	23.0614i	0.551431	+	0.955107i
$584$		0			0
$585$	27.4360	−	19.0979i	1.13434	−	0.789601i
$586$		0			0
$587$	4.18410	+	7.24707i	0.172696	+	0.299118i	0.939362	−	0.342928i	$-0.111419\pi$
$587$	4.18410	+	7.24707i	0.172696	+	0.299118i	−0.766665	+	0.642047i	$0.778085\pi$
$588$		0			0
$589$	11.4110	−	19.7644i	0.470181	−	0.814378i
$590$		0			0
$591$	5.07571	−	5.52379i	0.208787	−	0.227218i
$592$		0			0
$593$	−38.5284			−1.58217			−0.791087	−	0.611704i	$-0.790484\pi$
$593$	−38.5284			−1.58217			−0.791087	+	0.611704i	$0.790484\pi$
$594$		0			0
$595$	−11.3054			−0.463475
$596$		0			0
$597$	−16.1548	+	17.5809i	−0.661172	+	0.719540i
$598$		0			0
$599$	6.57920	−	11.3955i	0.268819	−	0.465608i	−0.699738	−	0.714399i	$-0.746700\pi$
$599$	6.57920	−	11.3955i	0.268819	−	0.465608i	0.968557	+	0.248791i	$0.0800334\pi$
$600$		0			0
$601$	5.01135	+	8.67992i	0.204417	+	0.354061i	0.949947	−	0.312411i	$-0.101137\pi$
$601$	5.01135	+	8.67992i	0.204417	+	0.354061i	−0.745530	+	0.666473i	$0.767803\pi$
$602$		0			0
$603$	5.13993	+	2.41414i	0.209314	+	0.0983115i
$604$		0			0
$605$	−39.3291	−	68.1199i	−1.59895	−	2.76947i
$606$		0			0
$607$	−18.1380	+	31.4159i	−0.736199	+	1.27513i	0.217997	+	0.975949i	$0.430048\pi$
$607$	−18.1380	+	31.4159i	−0.736199	+	1.27513i	−0.954195	+	0.299184i	$0.903286\pi$
$608$		0			0
$609$	1.94099	+	6.18588i	0.0786528	+	0.250665i
$610$		0			0
$611$	−21.0302			−0.850789
$612$		0			0
$613$	−24.2523			−0.979541			−0.489770	−	0.871851i	$-0.662919\pi$
$613$	−24.2523			−0.979541			−0.489770	+	0.871851i	$0.662919\pi$
$614$		0			0
$615$	47.3510	+	10.5663i	1.90938	+	0.426073i
$616$		0			0
$617$	6.70926	−	11.6208i	0.270105	−	0.467835i	−0.698784	−	0.715333i	$-0.746275\pi$
$617$	6.70926	−	11.6208i	0.270105	−	0.467835i	0.968888	+	0.247498i	$0.0796084\pi$
$618$		0			0
$619$	18.3018	+	31.6997i	0.735612	+	1.27412i	0.954455	+	0.298356i	$0.0964384\pi$
$619$	18.3018	+	31.6997i	0.735612	+	1.27412i	−0.218843	+	0.975760i	$0.570228\pi$
$620$		0			0
$621$	3.84885	−	1.57554i	0.154449	−	0.0632244i
$622$		0			0
$623$	3.49931	+	6.06099i	0.140197	+	0.242828i
$624$		0			0
$625$	−52.7346	+	91.3390i	−2.10938	+	3.65356i
$626$		0			0
$627$	−61.1711	−	13.6502i	−2.44294	−	0.545137i
$628$		0			0
$629$	−11.3054			−0.450775
$630$		0			0
$631$	−26.9365			−1.07232			−0.536162	−	0.844115i	$-0.680126\pi$
$631$	−26.9365			−1.07232			−0.536162	+	0.844115i	$0.680126\pi$
$632$		0			0
$633$	−6.41281	−	20.4375i	−0.254886	−	0.812316i
$634$		0			0
$635$	−6.18746	+	10.7170i	−0.245542	+	0.425291i
$636$		0			0
$637$	1.27174	+	2.20272i	0.0503881	+	0.0872748i
$638$		0			0
$639$	0.340248	+	4.01716i	0.0134600	+	0.158916i
$640$		0			0
$641$	−10.1390	−	17.5613i	−0.400467	−	0.693629i	0.593316	−	0.804970i	$-0.297819\pi$
$641$	−10.1390	−	17.5613i	−0.400467	−	0.693629i	−0.993782	+	0.111341i	$0.964485\pi$
$642$		0			0
$643$	6.44229	−	11.1584i	0.254059	−	0.440043i	−0.710581	−	0.703616i	$-0.751568\pi$
$643$	6.44229	−	11.1584i	0.254059	−	0.440043i	0.964639	+	0.263573i	$0.0849009\pi$
$644$		0			0
$645$	3.91873	−	4.26468i	0.154300	−	0.167921i
$646$		0			0
$647$	41.4633			1.63009			0.815045	−	0.579397i	$-0.196712\pi$
$647$	41.4633			1.63009			0.815045	+	0.579397i	$0.196712\pi$
$648$		0			0
$649$	−29.9989			−1.17756
$650$		0			0
$651$	−3.97716	+	4.32826i	−0.155877	+	0.169638i
$652$		0			0
$653$	−9.38036	+	16.2473i	−0.367082	+	0.635805i	−0.989108	−	0.147192i	$-0.952976\pi$
$653$	−9.38036	+	16.2473i	−0.367082	+	0.635805i	0.622026	+	0.782997i	$0.286310\pi$
$654$		0			0
$655$	37.4976	+	64.9478i	1.46515	+	2.53772i
$656$		0			0
$657$	2.19024	+	25.8592i	0.0854493	+	1.00886i
$658$		0			0
$659$	4.33932	+	7.51593i	0.169036	+	0.292779i	0.938081	−	0.346415i	$-0.112601\pi$
$659$	4.33932	+	7.51593i	0.169036	+	0.292779i	−0.769045	+	0.639194i	$0.779268\pi$
$660$		0			0
$661$	7.19524	−	12.4625i	0.279862	−	0.484736i	−0.691488	−	0.722388i	$-0.743045\pi$
$661$	7.19524	−	12.4625i	0.279862	−	0.484736i	0.971350	+	0.237652i	$0.0763778\pi$
$662$		0			0
$663$	3.40357	+	10.8471i	0.132184	+	0.421267i
$664$		0			0
$665$	29.4610			1.14245
$666$		0			0
$667$	2.99587			0.116001
$668$		0			0
$669$	−25.0298	−	5.58535i	−0.967709	−	0.215942i
$670$		0			0
$671$	22.2948	−	38.6158i	0.860683	−	1.49075i
$672$		0			0
$673$	14.1059	+	24.4321i	0.543742	+	0.941788i	0.998685	+	0.0512676i	$0.0163261\pi$
$673$	14.1059	+	24.4321i	0.543742	+	0.941788i	−0.454943	+	0.890520i	$0.650341\pi$
$674$		0			0
$675$	−9.92964	+	73.0759i	−0.382192	+	2.81269i
$676$		0			0
$677$	0.366552	+	0.634887i	0.0140877	+	0.0244007i	0.872983	−	0.487750i	$-0.162182\pi$
$677$	0.366552	+	0.634887i	0.0140877	+	0.0244007i	−0.858896	+	0.512151i	$0.828849\pi$
$678$		0			0
$679$	−1.48076	+	2.56476i	−0.0568264	+	0.0984263i
$680$		0			0
$681$	23.3245	+	5.20482i	0.893797	+	0.199449i
$682$		0			0
$683$	−16.4171			−0.628185			−0.314092	−	0.949392i	$-0.601700\pi$
$683$	−16.4171			−0.628185			−0.314092	+	0.949392i	$0.601700\pi$
$684$		0			0
$685$	−62.2658			−2.37905
$686$		0			0
$687$	0.488856	+	1.55797i	0.0186510	+	0.0594404i
$688$		0			0
$689$	−6.29354	+	10.9007i	−0.239765	+	0.415285i
$690$		0			0
$691$	−6.10005	−	10.5656i	−0.232057	−	0.401934i	0.726356	−	0.687318i	$-0.241212\pi$
$691$	−6.10005	−	10.5656i	−0.232057	−	0.401934i	−0.958413	+	0.285384i	$0.907879\pi$
$692$		0			0
$693$	14.6114	+	6.86275i	0.555042	+	0.260694i
$694$		0			0
$695$	−7.01172	−	12.1447i	−0.265970	−	0.460673i
$696$		0			0
$697$	−8.24972	+	14.2889i	−0.312481	+	0.541232i
$698$		0			0
$699$	19.5252	−	21.2489i	0.738511	−	0.803706i
$700$		0			0
$701$	0.337121			0.0127329			0.00636644	−	0.999980i	$-0.497973\pi$
$701$	0.337121			0.0127329			0.00636644	+	0.999980i	$0.497973\pi$
$702$		0			0
$703$	29.4610			1.11114
$704$		0			0
$705$	42.4504	−	46.1979i	1.59878	−	1.73991i
$706$		0			0
$707$	8.56494	−	14.8349i	0.322118	−	0.557924i
$708$		0			0
$709$	−10.0315	−	17.3751i	−0.376743	−	0.652537i	0.613844	−	0.789428i	$-0.289623\pi$
$709$	−10.0315	−	17.3751i	−0.376743	−	0.652537i	−0.990586	+	0.136890i	$0.956289\pi$
$710$		0			0
$711$	−32.7007	+	22.7626i	−1.22637	+	0.853663i
$712$		0			0
$713$	1.35811	+	2.35231i	0.0508616	+	0.0880949i
$714$		0			0
$715$	29.9795	−	51.9261i	1.12117	−	1.94192i
$716$		0			0
$717$	−0.703574	−	2.24227i	−0.0262754	−	0.0837392i
$718$		0			0
$719$	−10.7220			−0.399863			−0.199931	−	0.979810i	$-0.564072\pi$
$719$	−10.7220			−0.399863			−0.199931	+	0.979810i	$0.564072\pi$
$720$		0			0
$721$	12.0357			0.448234
$722$		0			0
$723$	15.5804	+	3.47673i	0.579440	+	0.129301i
$724$		0			0
$725$	−26.5624	+	46.0074i	−0.986503	+	1.70867i
$726$		0			0
$727$	−5.22757	−	9.05442i	−0.193880	−	0.335810i	0.752653	−	0.658418i	$-0.228774\pi$
$727$	−5.22757	−	9.05442i	−0.193880	−	0.335810i	−0.946533	+	0.322608i	$0.895441\pi$
$728$		0			0
$729$	6.77118	+	26.1372i	0.250785	+	0.968043i
$730$		0			0
$731$	0.984839	+	1.70579i	0.0364256	+	0.0630910i
$732$		0			0
$733$	−21.1651	+	36.6590i	−0.781751	+	1.35403i	0.149171	+	0.988811i	$0.452340\pi$
$733$	−21.1651	+	36.6590i	−0.781751	+	1.35403i	−0.930921	+	0.365220i	$0.880994\pi$
$734$		0			0
$735$	−7.40588	−	1.65261i	−0.273170	−	0.0609573i
$736$		0			0
$737$	10.1855			0.375188
$738$		0			0
$739$	12.6281			0.464532			0.232266	−	0.972652i	$-0.425386\pi$
$739$	12.6281			0.464532			0.232266	+	0.972652i	$0.425386\pi$
$740$		0			0
$741$	−8.86946	−	28.2668i	−0.325828	−	1.03841i
$742$		0			0
$743$	−19.3632	+	33.5381i	−0.710368	+	1.23039i	0.254352	+	0.967112i	$0.418138\pi$
$743$	−19.3632	+	33.5381i	−0.710368	+	1.23039i	−0.964719	+	0.263281i	$0.915195\pi$
$744$		0			0
$745$	−37.4535	−	64.8713i	−1.37219	−	2.37670i
$746$		0			0
$747$	9.17124	−	6.38399i	0.335558	−	0.233578i
$748$		0			0
$749$	−3.46290	−	5.99792i	−0.126532	−	0.219159i
$750$		0			0
$751$	10.6405	−	18.4299i	0.388278	−	0.672517i	−0.603940	−	0.797030i	$-0.706403\pi$
$751$	10.6405	−	18.4299i	0.388278	−	0.672517i	0.992218	+	0.124513i	$0.0397367\pi$
$752$		0			0
$753$	2.96718	−	3.22912i	0.108130	−	0.117676i
$754$		0			0
$755$	−0.463249			−0.0168594
$756$		0			0
$757$	22.8632			0.830977			0.415488	−	0.909598i	$-0.363611\pi$
$757$	22.8632			0.830977			0.415488	+	0.909598i	$0.363611\pi$
$758$		0			0
$759$	5.04718	−	5.49274i	0.183201	−	0.199374i
$760$		0			0
$761$	−6.04848	+	10.4763i	−0.219257	+	0.379765i	−0.954581	−	0.297951i	$-0.903697\pi$
$761$	−6.04848	+	10.4763i	−0.219257	+	0.379765i	0.735324	+	0.677716i	$0.237030\pi$
$762$		0			0
$763$	2.20971	+	3.82733i	0.0799969	+	0.138559i
$764$		0			0
$765$	−30.6986	−	14.4186i	−1.10991	−	0.521307i
$766$		0			0
$767$	−7.08997	−	12.2802i	−0.256004	−	0.443412i
$768$		0			0
$769$	20.0921	−	34.8005i	0.724538	−	1.25494i	−0.234626	−	0.972086i	$-0.575386\pi$
$769$	20.0921	−	34.8005i	0.724538	−	1.25494i	0.959164	−	0.282851i	$-0.0912803\pi$
$770$		0			0
$771$	−3.19846	−	10.1934i	−0.115190	−	0.367107i
$772$		0			0
$773$	34.1442			1.22808			0.614041	−	0.789274i	$-0.289543\pi$
$773$	34.1442			1.22808			0.614041	+	0.789274i	$0.289543\pi$
$774$		0			0
$775$	−48.1658			−1.73017
$776$		0			0
$777$	−7.40588	−	1.65261i	−0.265684	−	0.0592869i
$778$		0			0
$779$	21.4982	−	37.2359i	0.770252	−	1.33412i
$780$		0			0
$781$	3.61559	+	6.26238i	0.129376	+	0.224086i
$782$		0			0
$783$	−2.61879	+	19.2727i	−0.0935879	+	0.688748i
$784$		0			0
$785$	46.0101	+	79.6919i	1.64217	+	2.84433i
$786$		0			0
$787$	−10.0277	+	17.3685i	−0.357450	+	0.619122i	−0.987534	−	0.157405i	$-0.949687\pi$
$787$	−10.0277	+	17.3685i	−0.357450	+	0.619122i	0.630084	+	0.776527i	$0.283020\pi$
$788$		0			0
$789$	18.5639	+	4.14250i	0.660892	+	0.147477i
$790$		0			0
$791$	12.8361			0.456399
$792$		0			0
$793$	21.0767			0.748457
$794$		0			0
$795$	−11.2423	−	35.8290i	−0.398724	−	1.27072i
$796$		0			0
$797$	6.57026	−	11.3800i	0.232730	−	0.403101i	−0.725880	−	0.687821i	$-0.758567\pi$
$797$	6.57026	−	11.3800i	0.232730	−	0.403101i	0.958611	+	0.284720i	$0.0919007\pi$
$798$		0			0
$799$	10.6685	+	18.4783i	0.377423	+	0.653716i
$800$		0			0
$801$	1.77198	+	20.9210i	0.0626097	+	0.739206i
$802$		0			0
$803$	23.2742	+	40.3121i	0.821329	+	1.42258i
$804$		0			0
$805$	−1.75319	+	3.03661i	−0.0617918	+	0.107027i
$806$		0			0
$807$	5.54361	−	6.03300i	0.195144	−	0.212372i
$808$		0			0
$809$	−54.7893			−1.92629			−0.963145	−	0.268984i	$-0.913312\pi$
$809$	−54.7893			−1.92629			−0.963145	+	0.268984i	$0.913312\pi$
$810$		0			0
$811$	44.1157			1.54911			0.774557	−	0.632505i	$-0.217973\pi$
$811$	44.1157			1.54911			0.774557	+	0.632505i	$0.217973\pi$
$812$		0			0
$813$	15.8654	−	17.2660i	0.556424	−	0.605545i
$814$		0			0
$815$	5.67147	−	9.82328i	0.198663	−	0.344094i
$816$		0			0
$817$	−2.56642	−	4.44517i	−0.0897876	−	0.155517i
$818$		0			0
$819$	0.643981	+	7.60321i	0.0225025	+	0.265678i
$820$		0			0
$821$	−27.3822	−	47.4274i	−0.955647	−	1.65523i	−0.732881	−	0.680357i	$-0.761825\pi$
$821$	−27.3822	−	47.4274i	−0.955647	−	1.65523i	−0.222766	−	0.974872i	$-0.571509\pi$
$822$		0			0
$823$	25.2815	−	43.7888i	0.881258	−	1.52638i	0.0313141	−	0.999510i	$-0.490031\pi$
$823$	25.2815	−	43.7888i	0.881258	−	1.52638i	0.849944	−	0.526874i	$-0.176636\pi$
$824$		0			0
$825$	39.6017	+	126.210i	1.37875	+	4.39406i
$826$		0			0
$827$	7.38142			0.256677			0.128339	−	0.991730i	$-0.459036\pi$
$827$	7.38142			0.256677			0.128339	+	0.991730i	$0.459036\pi$
$828$		0			0
$829$	−33.0566			−1.14810			−0.574052	−	0.818819i	$-0.694629\pi$
$829$	−33.0566			−1.14810			−0.574052	+	0.818819i	$0.694629\pi$
$830$		0			0
$831$	49.5694	+	11.0613i	1.71954	+	0.383712i
$832$		0			0
$833$	1.29029	−	2.23485i	0.0447058	−	0.0774328i
$834$		0			0
$835$	5.73395	+	9.93149i	0.198432	+	0.343694i
$836$		0			0
$837$	−16.3198	+	6.68058i	−0.564094	+	0.230914i
$838$		0			0
$839$	−15.2163	−	26.3555i	−0.525326	−	0.909891i	−0.999565	−	0.0294950i	$-0.990610\pi$
$839$	−15.2163	−	26.3555i	−0.525326	−	0.909891i	0.474239	−	0.880396i	$-0.342723\pi$
$840$		0			0
$841$	7.49457	−	12.9810i	0.258434	−	0.447620i
$842$		0			0
$843$	−24.7261	−	5.51758i	−0.851612	−	0.190035i
$844$		0			0
$845$	−28.6107			−0.984240
$846$		0			0
$847$	17.9546			0.616927
$848$		0			0
$849$	−7.92927	−	25.2704i	−0.272132	−	0.867278i
$850$		0			0
$851$	−1.75319	+	3.03661i	−0.0600985	+	0.104094i
$852$		0			0
$853$	−6.72747	−	11.6523i	−0.230344	−	0.398968i	0.727565	−	0.686039i	$-0.240652\pi$
$853$	−6.72747	−	11.6523i	−0.230344	−	0.398968i	−0.957909	+	0.287071i	$0.907319\pi$
$854$		0			0
$855$	79.9984	+	37.5739i	2.73589	+	1.28500i
$856$		0			0
$857$	8.14192	+	14.1022i	0.278123	+	0.481722i	0.970918	−	0.239412i	$-0.0769545\pi$
$857$	8.14192	+	14.1022i	0.278123	+	0.481722i	−0.692796	+	0.721134i	$0.743621\pi$
$858$		0			0
$859$	−16.9853	+	29.4194i	−0.579531	+	1.00378i	0.416002	+	0.909364i	$0.363431\pi$
$859$	−16.9853	+	29.4194i	−0.579531	+	1.00378i	−0.995533	+	0.0944139i	$0.969902\pi$
$860$		0			0
$861$	−7.49293	+	8.15440i	−0.255358	+	0.277901i
$862$		0			0
$863$	−20.8721			−0.710494			−0.355247	−	0.934772i	$-0.615603\pi$
$863$	−20.8721			−0.710494			−0.355247	+	0.934772i	$0.615603\pi$
$864$		0			0
$865$	63.3272			2.15319
$866$		0			0
$867$	−12.1184	+	13.1882i	−0.411563	+	0.447896i
$868$		0			0
$869$	−35.7323	+	61.8901i	−1.21213	+	2.09948i
$870$		0			0
$871$	2.40725	+	4.16948i	0.0815666	+	0.141278i
$872$		0			0
$873$	−7.29190	+	5.07581i	−0.246793	+	0.171790i
$874$		0			0
$875$	−20.1364	−	34.8772i	−0.680733	−	1.17906i
$876$		0			0
$877$	0.243344	−	0.421485i	0.00821716	−	0.0142325i	−0.861888	−	0.507099i	$-0.830718\pi$
$877$	0.243344	−	0.421485i	0.00821716	−	0.0142325i	0.870105	+	0.492867i	$0.164051\pi$
$878$		0			0
$879$	−0.975077	−	3.10755i	−0.0328885	−	0.104815i
$880$		0			0
$881$	45.6511			1.53803			0.769013	−	0.639234i	$-0.220748\pi$
$881$	45.6511			1.53803			0.769013	+	0.639234i	$0.220748\pi$
$882$		0			0
$883$	−27.2622			−0.917448			−0.458724	−	0.888579i	$-0.651693\pi$
$883$	−27.2622			−0.917448			−0.458724	+	0.888579i	$0.651693\pi$
$884$		0			0
$885$	41.2879	+	9.21331i	1.38788	+	0.309702i
$886$		0			0
$887$	16.1122	−	27.9072i	0.540996	−	0.937032i	−0.457852	−	0.889029i	$-0.651381\pi$
$887$	16.1122	−	27.9072i	0.540996	−	0.937032i	0.998847	−	0.0480031i	$-0.0152857\pi$
$888$		0			0
$889$	−1.41236	−	2.44627i	−0.0473689	−	0.0820454i
$890$		0			0
$891$	30.9233	+	37.2703i	1.03597	+	1.24860i
$892$		0			0
$893$	−27.8012	−	48.1531i	−0.930332	−	1.61138i
$894$		0			0
$895$	−51.9533	+	89.9858i	−1.73661	+	3.00789i
$896$		0			0
$897$	3.44134	+	0.767927i	0.114903	+	0.0256403i
$898$		0			0
$899$	−12.7030			−0.423669
$900$		0			0
$901$	12.7707			0.425453
$902$		0			0
$903$	0.395794	+	1.26139i	0.0131712	+	0.0419763i
$904$		0			0
$905$	14.4709	−	25.0644i	0.481030	−	0.833168i
$906$		0			0
$907$	−7.53154	−	13.0450i	−0.250081	−	0.433153i	0.713467	−	0.700689i	$-0.247124\pi$
$907$	−7.53154	−	13.0450i	−0.250081	−	0.433153i	−0.963548	+	0.267536i	$0.913791\pi$
$908$		0			0
$909$	42.1774	−	29.3592i	1.39894	−	0.973783i
$910$		0			0
$911$	4.12845	+	7.15068i	0.136782	+	0.236913i	0.926277	−	0.376844i	$-0.122991\pi$
$911$	4.12845	+	7.15068i	0.136782	+	0.236913i	−0.789495	+	0.613757i	$0.789658\pi$
$912$		0			0
$913$	10.0215	−	17.3577i	0.331662	−	0.574455i
$914$		0			0
$915$	−42.5445	+	46.3002i	−1.40648	+	1.53064i
$916$		0			0
$917$	−17.1185			−0.565303
$918$		0			0
$919$	10.2256			0.337312			0.168656	−	0.985675i	$-0.446057\pi$
$919$	10.2256			0.337312			0.168656	+	0.985675i	$0.446057\pi$
$920$		0			0
$921$	−13.8816	+	15.1071i	−0.457414	+	0.497795i
$922$		0			0
$923$	−1.70902	+	2.96012i	−0.0562532	+	0.0974334i
$924$		0			0
$925$	−31.0887	−	53.8473i	−1.02219	−	1.77049i
$926$		0			0
$927$	32.6818	+	15.3501i	1.07341	+	0.504164i
$928$		0			0
$929$	10.6420	+	18.4325i	0.349153	+	0.604752i	0.986099	−	0.166157i	$-0.0531358\pi$
$929$	10.6420	+	18.4325i	0.349153	+	0.604752i	−0.636946	+	0.770909i	$0.719803\pi$
$930$		0			0
$931$	−3.36240	+	5.82384i	−0.110198	+	0.190869i
$932$		0			0
$933$	−18.1930	−	57.9808i	−0.595613	−	1.89821i
$934$		0			0
$935$	−60.8336			−1.98947
$936$		0			0
$937$	−33.7879			−1.10380			−0.551901	−	0.833910i	$-0.686097\pi$
$937$	−33.7879			−1.10380			−0.551901	+	0.833910i	$0.686097\pi$
$938$		0			0
$939$	1.45687	+	0.325098i	0.0475432	+	0.0106092i
$940$		0			0
$941$	12.2522	−	21.2214i	0.399410	−	0.691798i	−0.594243	−	0.804285i	$-0.702548\pi$
$941$	12.2522	−	21.2214i	0.399410	−	0.691798i	0.993653	+	0.112487i	$0.0358818\pi$
$942$		0			0
$943$	2.55866	+	4.43174i	0.0833216	+	0.144317i
$944$		0			0
$945$	−18.0022	−	13.9328i	−0.585612	−	0.453234i
$946$		0			0
$947$	−3.86655	−	6.69706i	−0.125646	−	0.217625i	0.796339	−	0.604850i	$-0.206767\pi$
$947$	−3.86655	−	6.69706i	−0.125646	−	0.217625i	−0.921985	+	0.387225i	$0.873434\pi$
$948$		0			0
$949$	−11.0013	+	19.0548i	−0.357117	+	0.618545i
$950$		0			0
$951$	−14.5848	−	3.25456i	−0.472944	−	0.105536i
$952$		0			0
$953$	6.66525			0.215909			0.107954	−	0.994156i	$-0.465570\pi$
$953$	6.66525			0.215909			0.107954	+	0.994156i	$0.465570\pi$
$954$		0			0
$955$	18.2541			0.590690
$956$		0			0
$957$	10.4444	+	33.2859i	0.337618	+	1.07598i
$958$		0			0
$959$	7.10643	−	12.3087i	0.229479	−	0.397469i
$960$		0			0
$961$	9.74139	+	16.8726i	0.314238	+	0.544277i
$962$		0			0
$963$	−1.75354	−	20.7033i	−0.0565070	−	0.667154i
$964$		0			0
$965$	35.4605	+	61.4194i	1.14151	+	1.97716i
$966$		0			0
$967$	25.3359	−	43.8830i	0.814746	−	1.41118i	−0.0947638	−	0.995500i	$-0.530210\pi$
$967$	25.3359	−	43.8830i	0.814746	−	1.41118i	0.909510	−	0.415682i	$-0.136457\pi$
$968$		0			0
$969$	−20.3374	+	22.1328i	−0.653331	+	0.711007i
$970$		0			0
$971$	1.04780			0.0336255			0.0168128	−	0.999859i	$-0.494648\pi$
$971$	1.04780			0.0336255			0.0168128	+	0.999859i	$0.494648\pi$
$972$		0			0
$973$	3.20101			0.102620
$974$		0			0
$975$	−42.3051	+	46.0397i	−1.35485	+	1.47445i
$976$		0			0
$977$	−20.4861	+	35.4830i	−0.655409	+	1.13520i	0.326381	+	0.945238i	$0.394171\pi$
$977$	−20.4861	+	35.4830i	−0.655409	+	1.13520i	−0.981791	+	0.189964i	$0.939163\pi$
$978$		0			0
$979$	18.8296	+	32.6138i	0.601797	+	1.04234i
$980$		0			0
$981$	1.11895	+	13.2110i	0.0357253	+	0.421794i
$982$		0			0
$983$	−26.7540	−	46.3394i	−0.853321	−	1.47800i	−0.878194	−	0.478305i	$-0.841251\pi$
$983$	−26.7540	−	46.3394i	−0.853321	−	1.47800i	0.0248725	−	0.999691i	$-0.492082\pi$
$984$		0			0
$985$	−9.48714	+	16.4322i	−0.302285	+	0.523574i
$986$		0			0
$987$	4.28751	+	13.6642i	0.136473	+	0.434936i
$988$		0			0
$989$	0.610899			0.0194255
$990$		0			0
$991$	32.9532			1.04679			0.523397	−	0.852089i	$-0.324665\pi$
$991$	32.9532			1.04679			0.523397	+	0.852089i	$0.324665\pi$
$992$		0			0
$993$	−29.6459	−	6.61541i	−0.940783	−	0.209934i
$994$		0			0
$995$	30.1954	−	52.2999i	0.957258	−	1.65802i
$996$		0			0
$997$	2.77465	+	4.80584i	0.0878741	+	0.152202i	0.906612	−	0.421965i	$-0.138659\pi$
$997$	2.77465	+	4.80584i	0.0878741	+	0.152202i	−0.818738	+	0.574167i	$0.805326\pi$
$998$		0			0
$999$	−18.0022	−	13.9328i	−0.569565	−	0.440814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.l.337.3		8
3.2	odd	2		3024.2.r.m.1009.4		8
4.3	odd	2		504.2.r.e.337.2	yes	8
9.2	odd	6		3024.2.r.m.2017.4		8
9.4	even	3		9072.2.a.cj.1.4		4
9.5	odd	6		9072.2.a.cg.1.1		4
9.7	even	3	inner	1008.2.r.l.673.3		8
12.11	even	2		1512.2.r.e.1009.4		8
36.7	odd	6		504.2.r.e.169.2	✓	8
36.11	even	6		1512.2.r.e.505.4		8
36.23	even	6		4536.2.a.y.1.1		4
36.31	odd	6		4536.2.a.z.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.e.169.2	✓	8	36.7	odd	6
504.2.r.e.337.2	yes	8	4.3	odd	2
1008.2.r.l.337.3		8	1.1	even	1	trivial
1008.2.r.l.673.3		8	9.7	even	3	inner
1512.2.r.e.505.4		8	36.11	even	6
1512.2.r.e.1009.4		8	12.11	even	2
3024.2.r.m.1009.4		8	3.2	odd	2
3024.2.r.m.2017.4		8	9.2	odd	6
4536.2.a.y.1.1		4	36.23	even	6
4536.2.a.z.1.4		4	36.31	odd	6
9072.2.a.cg.1.1		4	9.5	odd	6
9072.2.a.cj.1.4		4	9.4	even	3

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.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.17192 - 1.27538i) q^{3} +(-2.19047 + 3.79401i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.253189 - 2.98930i) q^{9} +O(q^{10})\)	\(q+(1.17192 - 1.27538i) q^{3} +(-2.19047 + 3.79401i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.253189 - 2.98930i) q^{9} +(-2.69047 - 4.66004i) q^{11} +(1.27174 - 2.20272i) q^{13} +(2.27174 + 7.23998i) q^{15} -2.58058 q^{17} +6.72479 q^{19} +(-1.69047 - 0.377226i) q^{21} +(-0.400185 + 0.693141i) q^{23} +(-7.09635 - 12.2912i) q^{25} +(-4.10921 - 3.18032i) q^{27} +(-1.87155 - 3.24163i) q^{29} +(1.69685 - 2.93903i) q^{31} +(-9.09635 - 2.02983i) q^{33} +4.38095 q^{35} +4.38095 q^{37} +(-1.31892 - 4.20337i) q^{39} +(3.19685 - 5.53711i) q^{41} +(-0.381635 - 0.661012i) q^{43} +(11.8960 + 5.58737i) q^{45} +(-4.13414 - 7.16053i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-3.02424 + 3.29122i) q^{51} -4.94877 q^{53} +23.5736 q^{55} +(7.88095 - 8.57667i) q^{57} +(2.78751 - 4.82811i) q^{59} +(4.14329 + 7.17639i) q^{61} +(-2.46221 + 1.71392i) q^{63} +(5.57142 + 9.64998i) q^{65} +(-0.946441 + 1.63928i) q^{67} +(0.415032 + 1.32270i) q^{69} -1.34385 q^{71} -8.65060 q^{73} +(-23.9924 - 5.35385i) q^{75} +(-2.69047 + 4.66004i) q^{77} +(-6.64051 - 11.5017i) q^{79} +(-8.87179 + 1.51371i) q^{81} +(1.86240 + 3.22577i) q^{83} +(5.65269 - 9.79074i) q^{85} +(-6.32762 - 1.41200i) q^{87} -6.99862 q^{89} -2.54348 q^{91} +(-1.75980 - 5.60845i) q^{93} +(-14.7305 + 25.5139i) q^{95} +(-1.48076 - 2.56476i) q^{97} +(-13.2490 + 9.22249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 3 q^{5} - 4 q^{7} - q^{9}+O(q^{10}) \) 8 * q + q^3 - 3 * q^5 - 4 * q^7 - q^9	\( 8 q + q^{3} - 3 q^{5} - 4 q^{7} - q^{9} - 7 q^{11} + 3 q^{13} + 11 q^{15} + 6 q^{17} + 8 q^{19} + q^{21} - 2 q^{23} - 5 q^{25} - 11 q^{27} - 9 q^{29} - 3 q^{31} - 21 q^{33} + 6 q^{35} + 6 q^{37} - 2 q^{39} + 9 q^{41} - 8 q^{43} + 7 q^{45} - 3 q^{47} - 4 q^{49} + 18 q^{51} + 12 q^{53} + 56 q^{55} + 34 q^{57} - 10 q^{59} + 20 q^{61} + 2 q^{63} + q^{65} - 11 q^{67} - 17 q^{69} + 6 q^{71} - 48 q^{73} - 52 q^{75} - 7 q^{77} - 21 q^{79} - 25 q^{81} - 8 q^{83} + 9 q^{85} + 15 q^{87} + 12 q^{89} - 6 q^{91} + 29 q^{93} - 36 q^{95} + 16 q^{97} - 18 q^{99}+O(q^{100}) \) 8 * q + q^3 - 3 * q^5 - 4 * q^7 - q^9 - 7 * q^11 + 3 * q^13 + 11 * q^15 + 6 * q^17 + 8 * q^19 + q^21 - 2 * q^23 - 5 * q^25 - 11 * q^27 - 9 * q^29 - 3 * q^31 - 21 * q^33 + 6 * q^35 + 6 * q^37 - 2 * q^39 + 9 * q^41 - 8 * q^43 + 7 * q^45 - 3 * q^47 - 4 * q^49 + 18 * q^51 + 12 * q^53 + 56 * q^55 + 34 * q^57 - 10 * q^59 + 20 * q^61 + 2 * q^63 + q^65 - 11 * q^67 - 17 * q^69 + 6 * q^71 - 48 * q^73 - 52 * q^75 - 7 * q^77 - 21 * q^79 - 25 * q^81 - 8 * q^83 + 9 * q^85 + 15 * q^87 + 12 * q^89 - 6 * q^91 + 29 * q^93 - 36 * q^95 + 16 * q^97 - 18 * q^99

Introduction

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