LMFDB - Embedded newform 1008.2.r.l.337.4

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			337.4
Root			$0.335492 - 1.69925i$ of defining polynomial
Character	$\chi$	$=$	1008.337
Dual form			1008.2.r.l.673.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30385 + 1.14017i) q^{3} +(-0.164508 + 0.284936i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(0.400030 + 2.97321i) q^{9} +O(q^{10})$	\(q+(1.30385 + 1.14017i) q^{3} +(-0.164508 + 0.284936i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(0.400030 + 2.97321i) q^{9} +(-0.664508 - 1.15096i) q^{11} +(-1.53937 + 2.66626i) q^{13} +(-0.539368 + 0.183946i) q^{15} +7.35741 q^{17} +2.93671 q^{19} +(0.335492 - 1.69925i) q^{21} +(-3.34321 + 5.79062i) q^{23} +(2.44587 + 4.23638i) q^{25} +(-2.86838 + 4.33271i) q^{27} +(3.88258 + 6.72483i) q^{29} +(-1.63555 + 2.83286i) q^{31} +(0.445874 - 2.25833i) q^{33} +0.329016 q^{35} +0.329016 q^{37} +(-5.04709 + 1.72126i) q^{39} +(-0.135552 + 0.234783i) q^{41} +(-5.48255 - 9.49606i) q^{43} +(-0.912983 - 0.375134i) q^{45} +(0.571014 + 0.989025i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(9.59293 + 8.38869i) q^{51} +6.42828 q^{53} +0.437267 q^{55} +(3.82902 + 3.34834i) q^{57} +(0.372170 - 0.644618i) q^{59} +(-4.42195 - 7.65904i) q^{61} +(2.37486 - 1.83304i) q^{63} +(-0.506476 - 0.877243i) q^{65} +(4.28640 - 7.42426i) q^{67} +(-10.9613 + 3.73825i) q^{69} -1.60769 q^{71} -13.4941 q^{73} +(-1.64114 + 8.31230i) q^{75} +(-0.664508 + 1.15096i) q^{77} +(-0.628926 - 1.08933i) q^{79} +(-8.67995 + 2.37875i) q^{81} +(-0.0316459 - 0.0548124i) q^{83} +(-1.21035 + 2.09639i) q^{85} +(-2.60515 + 13.1949i) q^{87} +11.3071 q^{89} +3.07874 q^{91} +(-5.36245 + 1.82881i) q^{93} +(-0.483112 + 0.836774i) q^{95} +(5.51420 + 9.55087i) q^{97} +(3.15623 - 2.43614i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.30385	+	1.14017i	0.752776	+	0.658277i
$3$	1.30385	+	1.14017i	0.752776	+	0.658277i
$4$		0			0
$5$	−0.164508	+	0.284936i	−0.0735702	+	0.127427i	−0.900464	−	0.434931i	$-0.856773\pi$
$5$	−0.164508	+	0.284936i	−0.0735702	+	0.127427i	0.826893	+	0.562359i	$0.190106\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$	0.400030	+	2.97321i	0.133343	+	0.991070i
$10$		0			0
$11$	−0.664508	−	1.15096i	−0.200357	−	0.347028i	0.748287	−	0.663375i	$-0.230877\pi$
$11$	−0.664508	−	1.15096i	−0.200357	−	0.347028i	−0.948643	+	0.316348i	$0.897543\pi$
$12$		0			0
$13$	−1.53937	+	2.66626i	−0.426944	+	0.739489i	−0.996600	−	0.0823948i	$-0.973743\pi$
$13$	−1.53937	+	2.66626i	−0.426944	+	0.739489i	0.569656	+	0.821883i	$0.307076\pi$
$14$		0			0
$15$	−0.539368	+	0.183946i	−0.139264	+	0.0474946i
$16$		0			0
$17$	7.35741			1.78443			0.892217	−	0.451606i	$-0.149149\pi$
$17$	7.35741			1.78443			0.892217	+	0.451606i	$0.149149\pi$
$18$		0			0
$19$	2.93671			0.673727			0.336864	−	0.941553i	$-0.390634\pi$
$19$	2.93671			0.673727			0.336864	+	0.941553i	$0.390634\pi$
$20$		0			0
$21$	0.335492	−	1.69925i	0.0732104	−	0.370806i
$22$		0			0
$23$	−3.34321	+	5.79062i	−0.697108	+	1.20743i	0.272356	+	0.962196i	$0.412197\pi$
$23$	−3.34321	+	5.79062i	−0.697108	+	1.20743i	−0.969465	+	0.245231i	$0.921136\pi$
$24$		0			0
$25$	2.44587	+	4.23638i	0.489175	+	0.847276i
$26$		0			0
$27$	−2.86838	+	4.33271i	−0.552021	+	0.833830i
$28$		0			0
$29$	3.88258	+	6.72483i	0.720977	+	1.24877i	0.960608	+	0.277906i	$0.0896402\pi$
$29$	3.88258	+	6.72483i	0.720977	+	1.24877i	−0.239631	+	0.970864i	$0.577026\pi$
$30$		0			0
$31$	−1.63555	+	2.83286i	−0.293754	+	0.508796i	−0.974694	−	0.223542i	$-0.928238\pi$
$31$	−1.63555	+	2.83286i	−0.293754	+	0.508796i	0.680940	+	0.732339i	$0.261571\pi$
$32$		0			0
$33$	0.445874	−	2.25833i	0.0776168	−	0.393124i
$34$		0			0
$35$	0.329016			0.0556138
$36$		0			0
$37$	0.329016			0.0540899			0.0270449	−	0.999634i	$-0.491390\pi$
$37$	0.329016			0.0540899			0.0270449	+	0.999634i	$0.491390\pi$
$38$		0			0
$39$	−5.04709	+	1.72126i	−0.808181	+	0.275622i
$40$		0			0
$41$	−0.135552	+	0.234783i	−0.0211696	+	0.0366669i	−0.876416	−	0.481555i	$-0.840072\pi$
$41$	−0.135552	+	0.234783i	−0.0211696	+	0.0366669i	0.855247	+	0.518221i	$0.173406\pi$
$42$		0			0
$43$	−5.48255	−	9.49606i	−0.836081	−	1.44814i	−0.893147	−	0.449765i	$-0.851508\pi$
$43$	−5.48255	−	9.49606i	−0.836081	−	1.44814i	0.0570654	−	0.998370i	$-0.481826\pi$
$44$		0			0
$45$	−0.912983	−	0.375134i	−0.136099	−	0.0559216i
$46$		0			0
$47$	0.571014	+	0.989025i	0.0832910	+	0.144264i	0.904662	−	0.426131i	$-0.140124\pi$
$47$	0.571014	+	0.989025i	0.0832910	+	0.144264i	−0.821371	+	0.570395i	$0.806790\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	9.59293	+	8.38869i	1.34328	+	1.17465i
$52$		0			0
$53$	6.42828			0.882992			0.441496	−	0.897263i	$-0.354448\pi$
$53$	6.42828			0.882992			0.441496	+	0.897263i	$0.354448\pi$
$54$		0			0
$55$	0.437267			0.0589611
$56$		0			0
$57$	3.82902	+	3.34834i	0.507166	+	0.443499i
$58$		0			0
$59$	0.372170	−	0.644618i	0.0484525	−	0.0839221i	−0.840782	−	0.541374i	$-0.817904\pi$
$59$	0.372170	−	0.644618i	0.0484525	−	0.0839221i	0.889234	+	0.457452i	$0.151238\pi$
$60$		0			0
$61$	−4.42195	−	7.65904i	−0.566173	−	0.980640i	−0.996940	−	0.0781767i	$-0.975090\pi$
$61$	−4.42195	−	7.65904i	−0.566173	−	0.980640i	0.430767	−	0.902463i	$-0.358243\pi$
$62$		0			0
$63$	2.37486	−	1.83304i	0.299204	−	0.230941i
$64$		0			0
$65$	−0.506476	−	0.877243i	−0.0628207	−	0.108809i
$66$		0			0
$67$	4.28640	−	7.42426i	0.523667	−	0.907018i	−0.475954	−	0.879470i	$-0.657897\pi$
$67$	4.28640	−	7.42426i	0.523667	−	0.907018i	0.999620	−	0.0275474i	$-0.00876971\pi$
$68$		0			0
$69$	−10.9613	+	3.73825i	−1.31959	+	0.450032i
$70$		0			0
$71$	−1.60769			−0.190798			−0.0953990	−	0.995439i	$-0.530413\pi$
$71$	−1.60769			−0.190798			−0.0953990	+	0.995439i	$0.530413\pi$
$72$		0			0
$73$	−13.4941			−1.57936			−0.789680	−	0.613519i	$-0.789754\pi$
$73$	−13.4941			−1.57936			−0.789680	+	0.613519i	$0.789754\pi$
$74$		0			0
$75$	−1.64114	+	8.31230i	−0.189503	+	0.959821i
$76$		0			0
$77$	−0.664508	+	1.15096i	−0.0757277	+	0.131164i
$78$		0			0
$79$	−0.628926	−	1.08933i	−0.0707597	−	0.122559i	0.828475	−	0.560026i	$-0.189209\pi$
$79$	−0.628926	−	1.08933i	−0.0707597	−	0.122559i	−0.899234	+	0.437467i	$0.855876\pi$
$80$		0			0
$81$	−8.67995	+	2.37875i	−0.964439	+	0.264305i
$82$		0			0
$83$	−0.0316459	−	0.0548124i	−0.00347359	−	0.00601644i	0.864283	−	0.503005i	$-0.167772\pi$
$83$	−0.0316459	−	0.0548124i	−0.00347359	−	0.00601644i	−0.867757	+	0.496989i	$0.834439\pi$
$84$		0			0
$85$	−1.21035	+	2.09639i	−0.131281	+	0.227386i
$86$		0			0
$87$	−2.60515	+	13.1949i	−0.279302	+	1.41465i
$88$		0			0
$89$	11.3071			1.19855			0.599274	−	0.800544i	$-0.295456\pi$
$89$	11.3071			1.19855			0.599274	+	0.800544i	$0.295456\pi$
$90$		0			0
$91$	3.07874			0.322739
$92$		0			0
$93$	−5.36245	+	1.82881i	−0.556060	+	0.189638i
$94$		0			0
$95$	−0.483112	+	0.836774i	−0.0495662	+	0.0858512i
$96$		0			0
$97$	5.51420	+	9.55087i	0.559882	+	0.969744i	0.997506	+	0.0705859i	$0.0224869\pi$
$97$	5.51420	+	9.55087i	0.559882	+	0.969744i	−0.437624	+	0.899158i	$0.644180\pi$
$98$		0			0
$99$	3.15623	−	2.43614i	0.317213	−	0.244841i
$100$		0			0
$101$	−7.12079	−	12.3336i	−0.708546	−	1.22724i	−0.965397	−	0.260786i	$-0.916018\pi$
$101$	−7.12079	−	12.3336i	−0.708546	−	1.22724i	0.256851	−	0.966451i	$-0.417315\pi$
$102$		0			0
$103$	5.29288	−	9.16753i	0.521522	−	0.903303i	−0.478164	−	0.878270i	$-0.658698\pi$
$103$	5.29288	−	9.16753i	0.521522	−	0.903303i	0.999687	−	0.0250330i	$-0.00796907\pi$
$104$		0			0
$105$	0.428986	+	0.375134i	0.0418647	+	0.0366093i
$106$		0			0
$107$	15.5574			1.50399			0.751993	−	0.659171i	$-0.229093\pi$
$107$	15.5574			1.50399			0.751993	+	0.659171i	$0.229093\pi$
$108$		0			0
$109$	−14.3574			−1.37519			−0.687595	−	0.726094i	$-0.741334\pi$
$109$	−14.3574			−1.37519			−0.687595	+	0.726094i	$0.741334\pi$
$110$		0			0
$111$	0.428986	+	0.375134i	0.0407175	+	0.0356061i
$112$		0			0
$113$	1.94966	−	3.37691i	0.183409	−	0.317673i	−0.759630	−	0.650355i	$-0.774620\pi$
$113$	1.94966	−	3.37691i	0.183409	−	0.317673i	0.943039	+	0.332682i	$0.107954\pi$
$114$		0			0
$115$	−1.09997	−	1.90520i	−0.102573	−	0.177661i
$116$		0			0
$117$	−8.54315	−	3.51028i	−0.789815	−	0.324525i
$118$		0			0
$119$	−3.67871	−	6.37171i	−0.337226	−	0.584093i
$120$		0			0
$121$	4.61686	−	7.99663i	0.419714	−	0.726967i
$122$		0			0
$123$	−0.444430	+	0.151568i	−0.0400729	+	0.0136665i
$124$		0			0
$125$	−3.25454			−0.291095
$126$		0			0
$127$	7.00787			0.621848			0.310924	−	0.950435i	$-0.399362\pi$
$127$	7.00787			0.621848			0.310924	+	0.950435i	$0.399362\pi$
$128$		0			0
$129$	3.67871	−	18.6324i	0.323892	−	1.64049i
$130$		0			0
$131$	3.33280	−	5.77258i	0.291188	−	0.504353i	−0.682903	−	0.730509i	$-0.739283\pi$
$131$	3.33280	−	5.77258i	0.291188	−	0.504353i	0.974091	+	0.226156i	$0.0726161\pi$
$132$		0			0
$133$	−1.46835	−	2.54326i	−0.127322	−	0.220529i
$134$		0			0
$135$	−0.762673	−	1.53007i	−0.0656405	−	0.131688i
$136$		0			0
$137$	8.41926	+	14.5826i	0.719306	+	1.24587i	0.961275	+	0.275591i	$0.0888734\pi$
$137$	8.41926	+	14.5826i	0.719306	+	1.24587i	−0.241969	+	0.970284i	$0.577793\pi$
$138$		0			0
$139$	−7.81032	+	13.5279i	−0.662463	+	1.14742i	0.317504	+	0.948257i	$0.397155\pi$
$139$	−7.81032	+	13.5279i	−0.662463	+	1.14742i	−0.979967	+	0.199162i	$0.936178\pi$
$140$		0			0
$141$	−0.383141	+	1.94059i	−0.0322663	+	0.163427i
$142$		0			0
$143$	4.09169			0.342164
$144$		0			0
$145$	−2.55486			−0.212170
$146$		0			0
$147$	−1.63934	+	0.559079i	−0.135210	+	0.0461121i
$148$		0			0
$149$	7.53233	−	13.0464i	0.617073	−	1.06880i	−0.372944	−	0.927854i	$-0.621652\pi$
$149$	7.53233	−	13.0464i	0.617073	−	1.06880i	0.990017	−	0.140948i	$-0.0450149\pi$
$150$		0			0
$151$	−3.86714	−	6.69808i	−0.314703	−	0.545082i	0.664671	−	0.747136i	$-0.268572\pi$
$151$	−3.86714	−	6.69808i	−0.314703	−	0.545082i	−0.979374	+	0.202054i	$0.935238\pi$
$152$		0			0
$153$	2.94318	+	21.8751i	0.237942	+	1.76850i
$154$		0			0
$155$	−0.538122	−	0.932055i	−0.0432230	−	0.0748645i
$156$		0			0
$157$	4.35812	−	7.54849i	0.347816	−	0.602435i	−0.638045	−	0.769999i	$-0.720257\pi$
$157$	4.35812	−	7.54849i	0.347816	−	0.602435i	0.985861	+	0.167564i	$0.0535901\pi$
$158$		0			0
$159$	8.38149	+	7.32932i	0.664695	+	0.581253i
$160$		0			0
$161$	6.68643			0.526964
$162$		0			0
$163$	−13.4513			−1.05359			−0.526793	−	0.849993i	$-0.676606\pi$
$163$	−13.4513			−1.05359			−0.526793	+	0.849993i	$0.676606\pi$
$164$		0			0
$165$	0.570129	+	0.498558i	0.0443845	+	0.0388127i
$166$		0			0
$167$	−5.81804	+	10.0771i	−0.450214	+	0.779793i	−0.998399	−	0.0565638i	$-0.981986\pi$
$167$	−5.81804	+	10.0771i	−0.450214	+	0.779793i	0.548185	+	0.836357i	$0.315319\pi$
$168$		0			0
$169$	1.76069	+	3.04961i	0.135438	+	0.234585i
$170$		0			0
$171$	1.17477	+	8.73145i	0.0898370	+	0.667711i
$172$		0			0
$173$	−0.885831	−	1.53430i	−0.0673485	−	0.116651i	0.830385	−	0.557190i	$-0.188121\pi$
$173$	−0.885831	−	1.53430i	−0.0673485	−	0.116651i	−0.897733	+	0.440539i	$0.854787\pi$
$174$		0			0
$175$	2.44587	−	4.23638i	0.184891	−	0.320240i
$176$		0			0
$177$	1.22023	−	0.416146i	0.0917178	−	0.0312794i
$178$		0			0
$179$	6.73139			0.503128			0.251564	−	0.967841i	$-0.419055\pi$
$179$	6.73139			0.503128			0.251564	+	0.967841i	$0.419055\pi$
$180$		0			0
$181$	−13.2711			−0.986433			−0.493217	−	0.869906i	$-0.664179\pi$
$181$	−13.2711			−0.986433			−0.493217	+	0.869906i	$0.664179\pi$
$182$		0			0
$183$	2.96706	−	15.0280i	0.219331	−	1.11090i
$184$		0			0
$185$	−0.0541257	+	0.0937484i	−0.00397940	+	0.00689252i
$186$		0			0
$187$	−4.88906	−	8.46810i	−0.357523	−	0.619249i
$188$		0			0
$189$	5.18643	+	0.317738i	0.377257	+	0.0231121i
$190$		0			0
$191$	10.4083	+	18.0277i	0.753117	+	1.30444i	0.946305	+	0.323276i	$0.104784\pi$
$191$	10.4083	+	18.0277i	0.753117	+	1.30444i	−0.193187	+	0.981162i	$0.561883\pi$
$192$		0			0
$193$	10.2585	−	17.7683i	0.738426	−	1.27899i	−0.214778	−	0.976663i	$-0.568903\pi$
$193$	10.2585	−	17.7683i	0.738426	−	1.27899i	0.953204	−	0.302328i	$-0.0977638\pi$
$194$		0			0
$195$	0.339838	−	1.72126i	0.0243363	−	0.123262i
$196$		0			0
$197$	7.20781			0.513535			0.256768	−	0.966473i	$-0.417342\pi$
$197$	7.20781			0.513535			0.256768	+	0.966473i	$0.417342\pi$
$198$		0			0
$199$	14.3276			1.01566			0.507828	−	0.861458i	$-0.330448\pi$
$199$	14.3276			1.01566			0.507828	+	0.861458i	$0.330448\pi$
$200$		0			0
$201$	14.0537	−	4.79288i	0.991273	−	0.338063i
$202$		0			0
$203$	3.88258	−	6.72483i	0.272504	−	0.471991i
$204$		0			0
$205$	−0.0445987	−	0.0772471i	−0.00311491	−	0.00539517i
$206$		0			0
$207$	−18.5541	−	7.62366i	−1.28960	−	0.529881i
$208$		0			0
$209$	−1.95147	−	3.38004i	−0.134986	−	0.233802i
$210$		0			0
$211$	−3.68897	+	6.38948i	−0.253959	+	0.439870i	−0.964612	−	0.263672i	$-0.915066\pi$
$211$	−3.68897	+	6.38948i	−0.253959	+	0.439870i	0.710653	+	0.703543i	$0.248400\pi$
$212$		0			0
$213$	−2.09618	−	1.83304i	−0.143628	−	0.125598i
$214$		0			0
$215$	3.60769			0.246043
$216$		0			0
$217$	3.27110			0.222057
$218$		0			0
$219$	−17.5942	−	15.3855i	−1.18890	−	1.03966i
$220$		0			0
$221$	−11.3258	+	19.6168i	−0.761854	+	1.31957i
$222$		0			0
$223$	−13.3549	−	23.1313i	−0.894308	−	1.54899i	−0.834658	−	0.550768i	$-0.814335\pi$
$223$	−13.3549	−	23.1313i	−0.894308	−	1.54899i	−0.0596502	−	0.998219i	$-0.518999\pi$
$224$		0			0
$225$	−11.6172	+	8.96678i	−0.774481	+	0.597785i
$226$		0			0
$227$	−8.46386	−	14.6598i	−0.561766	−	0.973007i	−0.997342	−	0.0728556i	$-0.976789\pi$
$227$	−8.46386	−	14.6598i	−0.561766	−	0.973007i	0.435576	−	0.900152i	$-0.356545\pi$
$228$		0			0
$229$	8.22580	−	14.2475i	0.543576	−	0.941501i	−0.455119	−	0.890431i	$-0.650403\pi$
$229$	8.22580	−	14.2475i	0.543576	−	0.941501i	0.998695	−	0.0510706i	$-0.0162633\pi$
$230$		0			0
$231$	−2.17871	+	0.743025i	−0.143348	+	0.0488875i
$232$		0			0
$233$	4.10855			0.269160			0.134580	−	0.990903i	$-0.457031\pi$
$233$	4.10855			0.269160			0.134580	+	0.990903i	$0.457031\pi$
$234$		0			0
$235$	−0.375745			−0.0245109
$236$		0			0
$237$	0.422000	−	2.13740i	0.0274118	−	0.138839i
$238$		0			0
$239$	10.4182	−	18.0448i	0.673895	−	1.16722i	−0.302896	−	0.953024i	$-0.597953\pi$
$239$	10.4182	−	18.0448i	0.673895	−	1.16722i	0.976791	−	0.214197i	$-0.0687133\pi$
$240$		0			0
$241$	−11.3477	−	19.6548i	−0.730969	−	1.26608i	−0.956470	−	0.291832i	$-0.905735\pi$
$241$	−11.3477	−	19.6548i	−0.730969	−	1.26608i	0.225501	−	0.974243i	$-0.427598\pi$
$242$		0			0
$243$	−14.0295	−	6.79509i	−0.899992	−	0.435905i
$244$		0			0
$245$	−0.164508	−	0.284936i	−0.0105100	−	0.0182039i
$246$		0			0
$247$	−4.52067	+	7.83004i	−0.287644	+	0.498213i
$248$		0			0
$249$	0.0212339	−	0.107549i	0.00134564	−	0.00681561i
$250$		0			0
$251$	−4.00030			−0.252497			−0.126248	−	0.991999i	$-0.540294\pi$
$251$	−4.00030			−0.252497			−0.126248	+	0.991999i	$0.540294\pi$
$252$		0			0
$253$	8.88637			0.558681
$254$		0			0
$255$	−3.96835	+	1.35337i	−0.248508	+	0.0847511i
$256$		0			0
$257$	−0.254753	+	0.441245i	−0.0158911	+	0.0275241i	−0.873862	−	0.486175i	$-0.838392\pi$
$257$	−0.254753	+	0.441245i	−0.0158911	+	0.0275241i	0.857971	+	0.513699i	$0.171725\pi$
$258$		0			0
$259$	−0.164508	−	0.284936i	−0.0102220	−	0.0177051i
$260$		0			0
$261$	−18.4412	+	14.2339i	−1.14148	+	0.881054i
$262$		0			0
$263$	−1.56344	−	2.70796i	−0.0964059	−	0.166980i	0.813789	−	0.581161i	$-0.197401\pi$
$263$	−1.56344	−	2.70796i	−0.0964059	−	0.166980i	−0.910194	+	0.414181i	$0.864068\pi$
$264$		0			0
$265$	−1.05750	+	1.83165i	−0.0649619	+	0.112517i
$266$		0			0
$267$	14.7427	+	12.8920i	0.902238	+	0.788976i
$268$		0			0
$269$	−4.16505			−0.253947			−0.126974	−	0.991906i	$-0.540526\pi$
$269$	−4.16505			−0.253947			−0.126974	+	0.991906i	$0.540526\pi$
$270$		0			0
$271$	13.0230			0.791092			0.395546	−	0.918446i	$-0.370555\pi$
$271$	13.0230			0.791092			0.395546	+	0.918446i	$0.370555\pi$
$272$		0			0
$273$	4.01420	+	3.51028i	0.242950	+	0.212452i
$274$		0			0
$275$	3.25061	−	5.63021i	0.196019	−	0.339515i
$276$		0			0
$277$	0.347709	+	0.602250i	0.0208918	+	0.0361857i	0.876282	−	0.481798i	$-0.160016\pi$
$277$	0.347709	+	0.602250i	0.0208918	+	0.0361857i	−0.855390	+	0.517984i	$0.826683\pi$
$278$		0			0
$279$	−9.07695	−	3.72961i	−0.543423	−	0.223286i
$280$		0			0
$281$	−16.1488	−	27.9706i	−0.963359	−	1.66859i	−0.713960	−	0.700186i	$-0.753100\pi$
$281$	−16.1488	−	27.9706i	−0.963359	−	1.66859i	−0.249399	−	0.968401i	$-0.580233\pi$
$282$		0			0
$283$	−7.06383	+	12.2349i	−0.419901	+	0.727290i	−0.995929	−	0.0901399i	$-0.971269\pi$
$283$	−7.06383	+	12.2349i	−0.419901	+	0.727290i	0.576028	+	0.817430i	$0.304602\pi$
$284$		0			0
$285$	−1.58397	+	0.540196i	−0.0938261	+	0.0319984i
$286$		0			0
$287$	0.271104			0.0160027
$288$		0			0
$289$	37.1315			2.18421
$290$		0			0
$291$	−3.69994	+	18.7400i	−0.216894	+	1.09856i
$292$		0			0
$293$	−8.33818	+	14.4422i	−0.487122	+	0.843720i	−0.999890	−	0.0148072i	$-0.995287\pi$
$293$	−8.33818	+	14.4422i	−0.487122	+	0.843720i	0.512769	+	0.858527i	$0.328620\pi$
$294$		0			0
$295$	0.122450	+	0.212090i	0.00712931	+	0.0123483i
$296$		0			0
$297$	6.89285	+	0.422279i	0.399963	+	0.0245031i
$298$		0			0
$299$	−10.2929	−	17.8278i	−0.595252	−	1.03101i
$300$		0			0
$301$	−5.48255	+	9.49606i	−0.316009	+	0.547344i
$302$		0			0
$303$	4.77794	−	24.2000i	0.274486	−	1.39025i
$304$		0			0
$305$	2.90978			0.166614
$306$		0			0
$307$	−27.0345			−1.54294			−0.771469	−	0.636267i	$-0.780478\pi$
$307$	−27.0345			−1.54294			−0.771469	+	0.636267i	$0.780478\pi$
$308$		0			0
$309$	17.3536	−	5.91828i	0.987213	−	0.336679i
$310$		0			0
$311$	−11.7377	+	20.3302i	−0.665581	+	1.15282i	0.313546	+	0.949573i	$0.398483\pi$
$311$	−11.7377	+	20.3302i	−0.665581	+	1.15282i	−0.979127	+	0.203248i	$0.934850\pi$
$312$		0			0
$313$	0.364597	+	0.631501i	0.0206083	+	0.0356946i	0.876146	−	0.482047i	$-0.160106\pi$
$313$	0.364597	+	0.631501i	0.0206083	+	0.0356946i	−0.855537	+	0.517741i	$0.826773\pi$
$314$		0			0
$315$	0.131616	+	0.978233i	0.00741573	+	0.0551172i
$316$		0			0
$317$	−16.7398	−	28.9943i	−0.940203	−	1.62848i	−0.765082	−	0.643933i	$-0.777301\pi$
$317$	−16.7398	−	28.9943i	−0.940203	−	1.62848i	−0.175122	−	0.984547i	$-0.556032\pi$
$318$		0			0
$319$	5.16001	−	8.93741i	0.288905	−	0.500399i
$320$		0			0
$321$	20.2844	+	17.7380i	1.13216	+	0.990039i
$322$		0			0
$323$	21.6066			1.20222
$324$		0			0
$325$	−15.0604			−0.835401
$326$		0			0
$327$	−18.7199	−	16.3699i	−1.03521	−	0.905256i
$328$		0			0
$329$	0.571014	−	0.989025i	0.0314810	−	0.0545267i
$330$		0			0
$331$	−4.92051	−	8.52257i	−0.270456	−	0.468443i	0.698523	−	0.715588i	$-0.253841\pi$
$331$	−4.92051	−	8.52257i	−0.270456	−	0.468443i	−0.968979	+	0.247145i	$0.920508\pi$
$332$		0			0
$333$	0.131616	+	0.978233i	0.00721252	+	0.0536068i
$334$		0			0
$335$	1.41029	+	2.44270i	0.0770525	+	0.133459i
$336$		0			0
$337$	3.93490	−	6.81545i	0.214348	−	0.371261i	−0.738723	−	0.674009i	$-0.764571\pi$
$337$	3.93490	−	6.81545i	0.214348	−	0.371261i	0.953071	+	0.302748i	$0.0979041\pi$
$338$		0			0
$339$	6.39231	−	2.18003i	0.347182	−	0.118403i
$340$		0			0
$341$	4.34735			0.235422
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	0.738063	−	3.73825i	0.0397360	−	0.201260i
$346$		0			0
$347$	−8.14721	+	14.1114i	−0.437365	+	0.757539i	−0.997485	−	0.0708727i	$-0.977422\pi$
$347$	−8.14721	+	14.1114i	−0.437365	+	0.757539i	0.560120	+	0.828411i	$0.310755\pi$
$348$		0			0
$349$	1.79219	+	3.10416i	0.0959336	+	0.166162i	0.909998	−	0.414613i	$-0.136083\pi$
$349$	1.79219	+	3.10416i	0.0959336	+	0.166162i	−0.814064	+	0.580775i	$0.802750\pi$
$350$		0			0
$351$	−7.13665	−	14.3175i	−0.380926	−	0.764212i
$352$		0			0
$353$	9.80329	+	16.9798i	0.521776	+	0.903743i	0.999679	+	0.0253304i	$0.00806378\pi$
$353$	9.80329	+	16.9798i	0.521776	+	0.903743i	−0.477903	+	0.878413i	$0.658603\pi$
$354$		0			0
$355$	0.264478	−	0.458089i	0.0140370	−	0.0243129i
$356$		0			0
$357$	2.46835	−	12.5021i	0.130639	−	0.661680i
$358$		0			0
$359$	16.8040			0.886882			0.443441	−	0.896303i	$-0.353757\pi$
$359$	16.8040			0.886882			0.443441	+	0.896303i	$0.353757\pi$
$360$		0			0
$361$	−10.3757			−0.546092
$362$		0			0
$363$	15.1372	−	5.16238i	0.794496	−	0.270955i
$364$		0			0
$365$	2.21988	−	3.84494i	0.116194	−	0.201254i
$366$		0			0
$367$	16.8160	+	29.1262i	0.877790	+	1.52038i	0.853760	+	0.520666i	$0.174316\pi$
$367$	16.8160	+	29.1262i	0.877790	+	1.52038i	0.0240298	+	0.999711i	$0.492350\pi$
$368$		0			0
$369$	−0.752282	−	0.309104i	−0.0391623	−	0.0160913i
$370$		0			0
$371$	−3.21414	−	5.56705i	−0.166870	−	0.289027i
$372$		0			0
$373$	17.2159	−	29.8189i	0.891407	−	1.54396i	0.0532169	−	0.998583i	$-0.483053\pi$
$373$	17.2159	−	29.8189i	0.891407	−	1.54396i	0.838190	−	0.545379i	$-0.183614\pi$
$374$		0			0
$375$	−4.24342	−	3.71073i	−0.219129	−	0.191621i
$376$		0			0
$377$	−23.9069			−1.23127
$378$		0			0
$379$	−18.0913			−0.929287			−0.464644	−	0.885498i	$-0.653818\pi$
$379$	−18.0913			−0.929287			−0.464644	+	0.885498i	$0.653818\pi$
$380$		0			0
$381$	9.13719	+	7.99016i	0.468112	+	0.409348i
$382$		0			0
$383$	−5.03792	+	8.72594i	−0.257426	+	0.445875i	−0.965552	−	0.260212i	$-0.916208\pi$
$383$	−5.03792	+	8.72594i	−0.257426	+	0.445875i	0.708126	+	0.706086i	$0.249541\pi$
$384$		0			0
$385$	−0.218634	−	0.378684i	−0.0111426	−	0.0192995i
$386$		0			0
$387$	26.0406	−	20.0995i	1.32372	−	1.02171i
$388$		0			0
$389$	0.715236	+	1.23882i	0.0362639	+	0.0628109i	0.883588	−	0.468266i	$-0.155121\pi$
$389$	0.715236	+	1.23882i	0.0362639	+	0.0628109i	−0.847324	+	0.531077i	$0.821788\pi$
$390$		0			0
$391$	−24.5974	+	42.6040i	−1.24394	+	2.15457i
$392$		0			0
$393$	10.9272	−	3.72660i	0.551203	−	0.187982i
$394$		0			0
$395$	0.413853			0.0208232
$396$		0			0
$397$	−10.5433			−0.529152			−0.264576	−	0.964365i	$-0.585232\pi$
$397$	−10.5433			−0.529152			−0.264576	+	0.964365i	$0.585232\pi$
$398$		0			0
$399$	0.985242	−	4.99020i	0.0493238	−	0.249822i
$400$		0			0
$401$	−0.804044	+	1.39265i	−0.0401521	+	0.0695454i	−0.885403	−	0.464824i	$-0.846118\pi$
$401$	−0.804044	+	1.39265i	−0.0401521	+	0.0695454i	0.845251	+	0.534369i	$0.179451\pi$
$402$		0			0
$403$	−5.03543	−	8.72162i	−0.250833	−	0.434455i
$404$		0			0
$405$	0.750130	−	2.86455i	0.0372743	−	0.142341i
$406$		0			0
$407$	−0.218634	−	0.378684i	−0.0108373	−	0.0187707i
$408$		0			0
$409$	−13.0174	+	22.5468i	−0.643670	+	1.11487i	0.340937	+	0.940086i	$0.389256\pi$
$409$	−13.0174	+	22.5468i	−0.643670	+	1.11487i	−0.984607	+	0.174783i	$0.944077\pi$
$410$		0			0
$411$	−5.64919	+	28.6128i	−0.278654	+	1.41137i
$412$		0			0
$413$	−0.744341			−0.0366266
$414$		0			0
$415$	0.0208240			0.00102221
$416$		0			0
$417$	−25.6075	+	8.73318i	−1.25401	+	0.427666i
$418$		0			0
$419$	2.00882	−	3.47938i	0.0981372	−	0.169979i	−0.812776	−	0.582576i	$-0.802045\pi$
$419$	2.00882	−	3.47938i	0.0981372	−	0.169979i	0.910914	+	0.412597i	$0.135378\pi$
$420$		0			0
$421$	−2.63431	−	4.56275i	−0.128388	−	0.222375i	0.794664	−	0.607049i	$-0.207647\pi$
$421$	−2.63431	−	4.56275i	−0.128388	−	0.222375i	−0.923052	+	0.384675i	$0.874314\pi$
$422$		0			0
$423$	−2.71216	+	2.09338i	−0.131870	+	0.101784i
$424$		0			0
$425$	17.9953	+	31.1688i	0.872901	+	1.51191i
$426$		0			0
$427$	−4.42195	+	7.65904i	−0.213993	+	0.370647i
$428$		0			0
$429$	5.33493	+	4.66522i	0.257573	+	0.225239i
$430$		0			0
$431$	17.7343			0.854230			0.427115	−	0.904197i	$-0.359530\pi$
$431$	17.7343			0.854230			0.427115	+	0.904197i	$0.359530\pi$
$432$		0			0
$433$	−4.76835			−0.229152			−0.114576	−	0.993414i	$-0.536551\pi$
$433$	−4.76835			−0.229152			−0.114576	+	0.993414i	$0.536551\pi$
$434$		0			0
$435$	−3.33115	−	2.91297i	−0.159716	−	0.139666i
$436$		0			0
$437$	−9.81804	+	17.0054i	−0.469661	+	0.813476i
$438$		0			0
$439$	18.1134	+	31.3733i	0.864506	+	1.49737i	0.867537	+	0.497373i	$0.165702\pi$
$439$	18.1134	+	31.3733i	0.864506	+	1.49737i	−0.00303091	+	0.999995i	$0.500965\pi$
$440$		0			0
$441$	−2.77489	−	1.14017i	−0.132138	−	0.0542938i
$442$		0			0
$443$	7.81211	+	13.5310i	0.371164	+	0.642876i	0.989745	−	0.142846i	$-0.0456253\pi$
$443$	7.81211	+	13.5310i	0.371164	+	0.642876i	−0.618581	+	0.785721i	$0.712292\pi$
$444$		0			0
$445$	−1.86010	+	3.22179i	−0.0881773	+	0.152728i
$446$		0			0
$447$	24.6961	−	8.42235i	1.16808	−	0.398363i
$448$		0			0
$449$	−15.4142			−0.727441			−0.363721	−	0.931508i	$-0.618494\pi$
$449$	−15.4142			−0.727441			−0.363721	+	0.931508i	$0.618494\pi$
$450$		0			0
$451$	0.360301			0.0169659
$452$		0			0
$453$	2.59479	−	13.1425i	0.121914	−	0.617486i
$454$		0			0
$455$	−0.506476	+	0.877243i	−0.0237440	+	0.0411258i
$456$		0			0
$457$	4.71214	+	8.16166i	0.220424	+	0.381786i	0.954937	−	0.296809i	$-0.0959224\pi$
$457$	4.71214	+	8.16166i	0.220424	+	0.381786i	−0.734512	+	0.678595i	$0.762589\pi$
$458$		0			0
$459$	−21.1039	+	31.8775i	−0.985045	+	1.48792i
$460$		0			0
$461$	−20.0406	−	34.7113i	−0.933383	−	1.61667i	−0.777491	−	0.628893i	$-0.783508\pi$
$461$	−20.0406	−	34.7113i	−0.933383	−	1.61667i	−0.155892	−	0.987774i	$-0.549825\pi$
$462$		0			0
$463$	10.9717	−	19.0036i	0.509900	−	0.883172i	−0.490035	−	0.871703i	$-0.663016\pi$
$463$	10.9717	−	19.0036i	0.509900	−	0.883172i	0.999934	−	0.0114690i	$-0.00365078\pi$
$464$		0			0
$465$	0.361072	−	1.82881i	0.0167443	−	0.0848089i
$466$		0			0
$467$	20.9808			0.970878			0.485439	−	0.874271i	$-0.338660\pi$
$467$	20.9808			0.970878			0.485439	+	0.874271i	$0.338660\pi$
$468$		0			0
$469$	−8.57280			−0.395855
$470$		0			0
$471$	14.2889	−	4.87307i	0.658396	−	0.224539i
$472$		0			0
$473$	−7.28640	+	12.6204i	−0.335029	+	0.580287i
$474$		0			0
$475$	7.18282	+	12.4410i	0.329570	+	0.570833i
$476$		0			0
$477$	2.57150	+	19.1126i	0.117741	+	0.875107i
$478$		0			0
$479$	−6.65194	−	11.5215i	−0.303935	−	0.526431i	0.673089	−	0.739562i	$-0.264967\pi$
$479$	−6.65194	−	11.5215i	−0.303935	−	0.526431i	−0.977024	+	0.213131i	$0.931634\pi$
$480$		0			0
$481$	−0.506476	+	0.877243i	−0.0230933	+	0.0399988i
$482$		0			0
$483$	8.71807	+	7.62366i	0.396686	+	0.346888i
$484$		0			0
$485$	−3.62852			−0.164762
$486$		0			0
$487$	38.5519			1.74695			0.873477	−	0.486865i	$-0.161860\pi$
$487$	38.5519			1.74695			0.873477	+	0.486865i	$0.161860\pi$
$488$		0			0
$489$	−17.5384	−	15.3367i	−0.793115	−	0.693552i
$490$		0			0
$491$	−3.25959	+	5.64578i	−0.147103	+	0.254791i	−0.930156	−	0.367165i	$-0.880328\pi$
$491$	−3.25959	+	5.64578i	−0.147103	+	0.254791i	0.783052	+	0.621956i	$0.213662\pi$
$492$		0			0
$493$	28.5658	+	49.4774i	1.28654	+	2.22835i
$494$		0			0
$495$	0.174920	+	1.30009i	0.00786206	+	0.0584346i
$496$		0			0
$497$	0.803846	+	1.39230i	0.0360574	+	0.0624533i
$498$		0			0
$499$	14.3259	−	24.8132i	0.641316	−	1.11079i	−0.343823	−	0.939034i	$-0.611722\pi$
$499$	14.3259	−	24.8132i	0.641316	−	1.11079i	0.985139	−	0.171758i	$-0.0549446\pi$
$500$		0			0
$501$	−19.0755	+	6.50550i	−0.852230	+	0.290644i
$502$		0			0
$503$	−16.2801			−0.725892			−0.362946	−	0.931810i	$-0.618229\pi$
$503$	−16.2801			−0.725892			−0.362946	+	0.931810i	$0.618229\pi$
$504$		0			0
$505$	4.68571			0.208511
$506$		0			0
$507$	−1.18140	+	5.98370i	−0.0524676	+	0.265746i
$508$		0			0
$509$	−13.2296	+	22.9143i	−0.586391	+	1.01566i	0.408309	+	0.912844i	$0.366118\pi$
$509$	−13.2296	+	22.9143i	−0.586391	+	1.01566i	−0.994700	+	0.102815i	$0.967215\pi$
$510$		0			0
$511$	6.74703	+	11.6862i	0.298471	+	0.516967i
$512$		0			0
$513$	−8.42361	+	12.7239i	−0.371911	+	0.561774i
$514$		0			0
$515$	1.74144	+	3.01626i	0.0767370	+	0.132912i
$516$		0			0
$517$	0.758887	−	1.31443i	0.0333758	−	0.0578086i
$518$		0			0
$519$	0.594379	−	3.01049i	0.0260903	−	0.132146i
$520$		0			0
$521$	−7.72559			−0.338464			−0.169232	−	0.985576i	$-0.554129\pi$
$521$	−7.72559			−0.338464			−0.169232	+	0.985576i	$0.554129\pi$
$522$		0			0
$523$	16.9546			0.741375			0.370687	−	0.928758i	$-0.379122\pi$
$523$	16.9546			0.741375			0.370687	+	0.928758i	$0.379122\pi$
$524$		0			0
$525$	8.01923	−	2.73488i	0.349988	−	0.119360i
$526$		0			0
$527$	−12.0334	+	20.8425i	−0.524184	+	0.907914i
$528$		0			0
$529$	−10.8542	−	18.8000i	−0.471920	−	0.817390i
$530$		0			0
$531$	2.06546	+	0.848674i	0.0896335	+	0.0368293i
$532$		0			0
$533$	−0.417328	−	0.722833i	−0.0180765	−	0.0313094i
$534$		0			0
$535$	−2.55931	+	4.43285i	−0.110648	+	0.191649i
$536$		0			0
$537$	8.77669	+	7.67492i	0.378742	+	0.331197i
$538$		0			0
$539$	1.32902			0.0572448
$540$		0			0
$541$	21.9353			0.943072			0.471536	−	0.881847i	$-0.343700\pi$
$541$	21.9353			0.943072			0.471536	+	0.881847i	$0.343700\pi$
$542$		0			0
$543$	−17.3035	−	15.1313i	−0.742563	−	0.649346i
$544$		0			0
$545$	2.36191	−	4.09094i	0.101173	−	0.175237i
$546$		0			0
$547$	21.4034	+	37.0718i	0.915144	+	1.58508i	0.806691	+	0.590974i	$0.201256\pi$
$547$	21.4034	+	37.0718i	0.915144	+	1.58508i	0.108453	+	0.994102i	$0.465410\pi$
$548$		0			0
$549$	21.0030	−	16.2112i	0.896387	−	0.691879i
$550$		0			0
$551$	11.4020	+	19.7489i	0.485742	+	0.841330i
$552$		0			0
$553$	−0.628926	+	1.08933i	−0.0267447	+	0.0463231i
$554$		0			0
$555$	−0.177461	+	0.0605211i	−0.00753278	+	0.00256898i
$556$		0			0
$557$	36.5498			1.54866			0.774332	−	0.632780i	$-0.218086\pi$
$557$	36.5498			1.54866			0.774332	+	0.632780i	$0.218086\pi$
$558$		0			0
$559$	33.7587			1.42784
$560$		0			0
$561$	3.28048	−	16.6155i	0.138502	−	0.701505i
$562$		0			0
$563$	19.8582	−	34.3955i	0.836925	−	1.44960i	−0.0555277	−	0.998457i	$-0.517684\pi$
$563$	19.8582	−	34.3955i	0.836925	−	1.44960i	0.892453	−	0.451140i	$-0.148983\pi$
$564$		0			0
$565$	0.641469	+	1.11106i	0.0269868	+	0.0467425i
$566$		0			0
$567$	6.40003	+	6.32769i	0.268776	+	0.265738i
$568$		0			0
$569$	−15.4173	−	26.7035i	−0.646325	−	1.11947i	−0.983994	−	0.178203i	$-0.942972\pi$
$569$	−15.4173	−	26.7035i	−0.646325	−	1.11947i	0.337669	−	0.941265i	$-0.390362\pi$
$570$		0			0
$571$	−19.4009	+	33.6033i	−0.811901	+	1.40625i	0.0996310	+	0.995024i	$0.468234\pi$
$571$	−19.4009	+	33.6033i	−0.811901	+	1.40625i	−0.911532	+	0.411229i	$0.865100\pi$
$572$		0			0
$573$	−6.98380	+	35.3725i	−0.291752	+	1.47771i
$574$		0			0
$575$	−32.7083			−1.36403
$576$		0			0
$577$	−2.10713			−0.0877211			−0.0438606	−	0.999038i	$-0.513966\pi$
$577$	−2.10713			−0.0877211			−0.0438606	+	0.999038i	$0.513966\pi$
$578$		0			0
$579$	33.6344	−	11.4707i	1.39780	−	0.476705i
$580$		0			0
$581$	−0.0316459	+	0.0548124i	−0.00131289	+	0.00227400i
$582$		0			0
$583$	−4.27164	−	7.39870i	−0.176913	−	0.306423i
$584$		0			0
$585$	2.40562	−	1.85678i	0.0994602	−	0.0767686i
$586$		0			0
$587$	3.46457	+	6.00081i	0.142998	+	0.247680i	0.928624	−	0.371022i	$-0.120992\pi$
$587$	3.46457	+	6.00081i	0.142998	+	0.247680i	−0.785626	+	0.618701i	$0.787659\pi$
$588$		0			0
$589$	−4.80314	+	8.31928i	−0.197910	+	0.342790i
$590$		0			0
$591$	9.39788	+	8.21812i	0.386577	+	0.338048i
$592$		0			0
$593$	−10.0323			−0.411977			−0.205989	−	0.978554i	$-0.566041\pi$
$593$	−10.0323			−0.411977			−0.205989	+	0.978554i	$0.566041\pi$
$594$		0			0
$595$	2.42070			0.0992392
$596$		0			0
$597$	18.6810	+	16.3359i	0.764562	+	0.668583i
$598$		0			0
$599$	−21.6645	+	37.5240i	−0.885187	+	1.53319i	−0.0396877	+	0.999212i	$0.512636\pi$
$599$	−21.6645	+	37.5240i	−0.885187	+	1.53319i	−0.845499	+	0.533977i	$0.820697\pi$
$600$		0			0
$601$	23.2578	+	40.2837i	0.948707	+	1.64321i	0.748154	+	0.663525i	$0.230941\pi$
$601$	23.2578	+	40.2837i	0.948707	+	1.64321i	0.200553	+	0.979683i	$0.435726\pi$
$602$		0			0
$603$	23.7886	+	9.77444i	0.968746	+	0.398046i
$604$		0			0
$605$	1.51902	+	2.63102i	0.0617569	+	0.106966i
$606$		0			0
$607$	18.9227	−	32.7751i	0.768048	−	1.33030i	−0.170572	−	0.985345i	$-0.554561\pi$
$607$	18.9227	−	32.7751i	0.768048	−	1.33030i	0.938620	−	0.344953i	$-0.112105\pi$
$608$		0			0
$609$	12.7297	−	4.34134i	0.515835	−	0.175920i
$610$		0			0
$611$	−3.51600			−0.142242
$612$		0			0
$613$	30.2811			1.22304			0.611522	−	0.791228i	$-0.290558\pi$
$613$	30.2811			1.22304			0.611522	+	0.791228i	$0.290558\pi$
$614$		0			0
$615$	0.0299250	−	0.151568i	0.00120669	−	0.00611183i
$616$		0			0
$617$	8.08770	−	14.0083i	0.325599	−	0.563954i	−0.656035	−	0.754731i	$-0.727767\pi$
$617$	8.08770	−	14.0083i	0.325599	−	0.563954i	0.981633	+	0.190777i	$0.0611008\pi$
$618$		0			0
$619$	−12.9377	−	22.4088i	−0.520012	−	0.900687i	−0.999729	−	0.0232638i	$-0.992594\pi$
$619$	−12.9377	−	22.4088i	−0.520012	−	0.900687i	0.479718	−	0.877423i	$-0.340739\pi$
$620$		0			0
$621$	−15.4994	−	31.0949i	−0.621971	−	1.24779i
$622$		0			0
$623$	−5.65354	−	9.79221i	−0.226504	−	0.392317i
$624$		0			0
$625$	−11.6940	+	20.2546i	−0.467759	+	0.810182i
$626$		0			0
$627$	1.30940	−	6.63205i	0.0522925	−	0.264859i
$628$		0			0
$629$	2.42070			0.0965198
$630$		0			0
$631$	−29.2969			−1.16629			−0.583146	−	0.812368i	$-0.698178\pi$
$631$	−29.2969			−1.16629			−0.583146	+	0.812368i	$0.698178\pi$
$632$		0			0
$633$	−12.0949	+	4.12485i	−0.480731	+	0.163948i
$634$		0			0
$635$	−1.15285	+	1.99679i	−0.0457495	+	0.0792404i
$636$		0			0
$637$	−1.53937	−	2.66626i	−0.0609920	−	0.105641i
$638$		0			0
$639$	−0.643125	−	4.78001i	−0.0254416	−	0.189094i
$640$		0			0
$641$	8.82630	+	15.2876i	0.348618	+	0.603824i	0.986004	−	0.166720i	$-0.0533177\pi$
$641$	8.82630	+	15.2876i	0.348618	+	0.603824i	−0.637386	+	0.770545i	$0.719984\pi$
$642$		0			0
$643$	−14.5426	+	25.1885i	−0.573504	+	0.993338i	0.422698	+	0.906270i	$0.361083\pi$
$643$	−14.5426	+	25.1885i	−0.573504	+	0.993338i	−0.996202	+	0.0870676i	$0.972250\pi$
$644$		0			0
$645$	4.70388	+	4.11338i	0.185215	+	0.161964i
$646$		0			0
$647$	−39.8747			−1.56764			−0.783819	−	0.620989i	$-0.786731\pi$
$647$	−39.8747			−1.56764			−0.783819	+	0.620989i	$0.786731\pi$
$648$		0			0
$649$	−0.989241			−0.0388311
$650$		0			0
$651$	4.26502	+	3.72961i	0.167159	+	0.146175i
$652$		0			0
$653$	−7.08986	+	12.2800i	−0.277448	+	0.480553i	−0.970750	−	0.240094i	$-0.922822\pi$
$653$	−7.08986	+	12.2800i	−0.277448	+	0.480553i	0.693302	+	0.720647i	$0.256155\pi$
$654$		0			0
$655$	1.09654	+	1.89927i	0.0428455	+	0.0742106i
$656$		0			0
$657$	−5.39803	−	40.1207i	−0.210597	−	1.56526i
$658$		0			0
$659$	−11.3592	−	19.6747i	−0.442491	−	0.766418i	0.555382	−	0.831595i	$-0.312572\pi$
$659$	−11.3592	−	19.6747i	−0.442491	−	0.766418i	−0.997874	+	0.0651775i	$0.979239\pi$
$660$		0			0
$661$	−20.0052	+	34.6500i	−0.778111	+	1.34773i	0.154919	+	0.987927i	$0.450488\pi$
$661$	−20.0052	+	34.6500i	−0.778111	+	1.34773i	−0.933030	+	0.359800i	$0.882845\pi$
$662$		0			0
$663$	−37.1335	+	12.6640i	−1.44215	+	0.491829i
$664$		0			0
$665$	0.966223			0.0374685
$666$		0			0
$667$	−51.9212			−2.01040
$668$		0			0
$669$	8.96091	−	45.3865i	0.346449	−	1.75474i
$670$		0			0
$671$	−5.87684	+	10.1790i	−0.226873	+	0.392956i
$672$		0			0
$673$	0.913881	+	1.58289i	0.0352275	+	0.0610159i	0.883102	−	0.469182i	$-0.155451\pi$
$673$	0.913881	+	1.58289i	0.0352275	+	0.0610159i	−0.847874	+	0.530198i	$0.822118\pi$
$674$		0			0
$675$	−25.3707	−	1.55430i	−0.976519	−	0.0598249i
$676$		0			0
$677$	14.2246	+	24.6376i	0.546694	+	0.946902i	0.998498	+	0.0547845i	$0.0174472\pi$
$677$	14.2246	+	24.6376i	0.546694	+	0.946902i	−0.451804	+	0.892117i	$0.649219\pi$
$678$		0			0
$679$	5.51420	−	9.55087i	0.211616	−	0.366529i
$680$		0			0
$681$	5.67912	−	28.7644i	0.217624	−	1.10225i
$682$		0			0
$683$	−0.868335			−0.0332259			−0.0166130	−	0.999862i	$-0.505288\pi$
$683$	−0.868335			−0.0332259			−0.0166130	+	0.999862i	$0.505288\pi$
$684$		0			0
$685$	−5.54014			−0.211678
$686$		0			0
$687$	26.9697	−	9.19775i	1.02896	−	0.350916i
$688$		0			0
$689$	−9.89549	+	17.1395i	−0.376988	+	0.652962i
$690$		0			0
$691$	−8.71932	−	15.1023i	−0.331699	−	0.574519i	0.651146	−	0.758952i	$-0.274288\pi$
$691$	−8.71932	−	15.1023i	−0.331699	−	0.574519i	−0.982845	+	0.184433i	$0.940955\pi$
$692$		0			0
$693$	−3.68787	−	1.51530i	−0.140091	−	0.0575616i
$694$		0			0
$695$	−2.56972	−	4.45088i	−0.0974750	−	0.168832i
$696$		0			0
$697$	−0.997310	+	1.72739i	−0.0377758	+	0.0654296i
$698$		0			0
$699$	5.35692	+	4.68444i	0.202617	+	0.177182i
$700$		0			0
$701$	9.23113			0.348655			0.174327	−	0.984688i	$-0.444225\pi$
$701$	9.23113			0.348655			0.174327	+	0.984688i	$0.444225\pi$
$702$		0			0
$703$	0.966223			0.0364418
$704$		0			0
$705$	−0.489914	−	0.428413i	−0.0184512	−	0.0161350i
$706$		0			0
$707$	−7.12079	+	12.3336i	−0.267805	+	0.463852i
$708$		0			0
$709$	−10.8231	−	18.7461i	−0.406469	−	0.704025i	0.588022	−	0.808845i	$-0.299907\pi$
$709$	−10.8231	−	18.7461i	−0.406469	−	0.704025i	−0.994491	+	0.104820i	$0.966573\pi$
$710$		0			0
$711$	2.98722	−	2.30570i	0.112030	−	0.0864703i
$712$		0			0
$713$	−10.9360	−	18.9417i	−0.409556	−	0.709373i
$714$		0			0
$715$	−0.673115	+	1.16587i	−0.0251731	+	0.0436010i
$716$		0			0
$717$	34.1578	−	11.6492i	1.27565	−	0.435046i
$718$		0			0
$719$	−48.6526			−1.81444			−0.907218	−	0.420661i	$-0.861798\pi$
$719$	−48.6526			−1.81444			−0.907218	+	0.420661i	$0.861798\pi$
$720$		0			0
$721$	−10.5858			−0.394234
$722$		0			0
$723$	7.61412	−	38.5651i	0.283172	−	1.43425i
$724$		0			0
$725$	−18.9926	+	32.8962i	−0.705368	+	1.22173i
$726$		0			0
$727$	1.11417	+	1.92980i	0.0413222	+	0.0715722i	0.885947	−	0.463787i	$-0.153510\pi$
$727$	1.11417	+	1.92980i	0.0413222	+	0.0715722i	−0.844625	+	0.535359i	$0.820176\pi$
$728$		0			0
$729$	−10.5447	−	24.8557i	−0.390546	−	0.920583i
$730$		0			0
$731$	−40.3374	−	69.8664i	−1.49193	−	2.58410i
$732$		0			0
$733$	−19.0129	+	32.9313i	−0.702258	+	1.21635i	0.265415	+	0.964134i	$0.414491\pi$
$733$	−19.0129	+	32.9313i	−0.702258	+	1.21635i	−0.967672	+	0.252211i	$0.918842\pi$
$734$		0			0
$735$	0.110382	−	0.559079i	0.00407151	−	0.0206220i
$736$		0			0
$737$	−11.3934			−0.419681
$738$		0			0
$739$	48.6048			1.78796			0.893978	−	0.448112i	$-0.147903\pi$
$739$	48.6048			1.78796			0.893978	+	0.448112i	$0.147903\pi$
$740$		0			0
$741$	−14.8218	+	5.05483i	−0.544494	+	0.185694i
$742$		0			0
$743$	−21.2700	+	36.8408i	−0.780322	+	1.35156i	0.151432	+	0.988468i	$0.451612\pi$
$743$	−21.2700	+	36.8408i	−0.780322	+	1.35156i	−0.931754	+	0.363090i	$0.881722\pi$
$744$		0			0
$745$	2.47826	+	4.29247i	0.0907963	+	0.157264i
$746$		0			0
$747$	0.150309	−	0.116017i	0.00549953	−	0.00424482i
$748$		0			0
$749$	−7.77868	−	13.4731i	−0.284227	−	0.492295i
$750$		0			0
$751$	4.62893	−	8.01754i	0.168912	−	0.292564i	−0.769126	−	0.639098i	$-0.779308\pi$
$751$	4.62893	−	8.01754i	0.168912	−	0.292564i	0.938038	+	0.346534i	$0.112641\pi$
$752$		0			0
$753$	−5.21577	−	4.56102i	−0.190073	−	0.166213i
$754$		0			0
$755$	2.54470			0.0926111
$756$		0			0
$757$	41.0363			1.49149			0.745744	−	0.666232i	$-0.232094\pi$
$757$	41.0363			1.49149			0.745744	+	0.666232i	$0.232094\pi$
$758$		0			0
$759$	11.5865	+	10.1320i	0.420562	+	0.367767i
$760$		0			0
$761$	19.1859	−	33.2309i	0.695487	−	1.20462i	−0.274529	−	0.961579i	$-0.588522\pi$
$761$	19.1859	−	33.2309i	0.695487	−	1.20462i	0.970016	−	0.243040i	$-0.0781448\pi$
$762$		0			0
$763$	7.17871	+	12.4339i	0.259887	+	0.450137i
$764$		0			0
$765$	−6.71719	−	2.76001i	−0.242861	−	0.0997885i
$766$		0			0
$767$	1.14581	+	1.98461i	0.0413730	+	0.0716601i
$768$		0			0
$769$	0.149772	−	0.259412i	0.00540090	−	0.00935463i	−0.863312	−	0.504670i	$-0.831614\pi$
$769$	0.149772	−	0.259412i	0.00540090	−	0.00935463i	0.868713	+	0.495315i	$0.164947\pi$
$770$		0			0
$771$	−0.835252	+	0.284854i	−0.0300809	+	0.0102588i
$772$		0			0
$773$	40.2941			1.44928			0.724639	−	0.689128i	$-0.242006\pi$
$773$	40.2941			1.44928			0.724639	+	0.689128i	$0.242006\pi$
$774$		0			0
$775$	−16.0014			−0.574788
$776$		0			0
$777$	0.110382	−	0.559079i	0.00395994	−	0.0200569i
$778$		0			0
$779$	−0.398076	+	0.689488i	−0.0142626	+	0.0247035i
$780$		0			0
$781$	1.06832	+	1.85039i	0.0382276	+	0.0662122i
$782$		0			0
$783$	−40.2735	−	2.46729i	−1.43926	−	0.0881738i
$784$		0			0
$785$	1.43389	+	2.48357i	0.0511777	+	0.0886425i
$786$		0			0
$787$	12.2565	−	21.2289i	0.436897	−	0.756728i	−0.560551	−	0.828120i	$-0.689411\pi$
$787$	12.2565	−	21.2289i	0.436897	−	0.756728i	0.997448	+	0.0713920i	$0.0227441\pi$
$788$		0			0
$789$	1.04904	−	5.31335i	0.0373470	−	0.189160i
$790$		0			0
$791$	−3.89932			−0.138644
$792$		0			0
$793$	27.2280			0.966896
$794$		0			0
$795$	−3.46721	+	1.18246i	−0.122969	+	0.0419374i
$796$		0			0
$797$	26.9140	−	46.6164i	0.953343	−	1.65124i	0.215228	−	0.976564i	$-0.430951\pi$
$797$	26.9140	−	46.6164i	0.953343	−	1.65124i	0.738115	−	0.674675i	$-0.235716\pi$
$798$		0			0
$799$	4.20119	+	7.27667i	0.148627	+	0.257430i
$800$		0			0
$801$	4.52317	+	33.6183i	0.159818	+	1.18784i
$802$		0			0
$803$	8.96691	+	15.5311i	0.316435	+	0.548082i
$804$		0			0
$805$	−1.09997	+	1.90520i	−0.0387689	+	0.0671496i
$806$		0			0
$807$	−5.43058	−	4.74886i	−0.191165	−	0.167168i
$808$		0			0
$809$	7.44011			0.261580			0.130790	−	0.991410i	$-0.458249\pi$
$809$	7.44011			0.261580			0.130790	+	0.991410i	$0.458249\pi$
$810$		0			0
$811$	−2.94854			−0.103537			−0.0517687	−	0.998659i	$-0.516486\pi$
$811$	−2.94854			−0.103537			−0.0517687	+	0.998659i	$0.516486\pi$
$812$		0			0
$813$	16.9800	+	14.8484i	0.595515	+	0.520758i
$814$		0			0
$815$	2.21284	−	3.83276i	0.0775125	−	0.134256i
$816$		0			0
$817$	−16.1007	−	27.8872i	−0.563291	−	0.975648i
$818$		0			0
$819$	1.23159	+	9.15373i	0.0430351	+	0.319857i
$820$		0			0
$821$	8.44331	+	14.6242i	0.294674	+	0.510390i	0.974909	−	0.222604i	$-0.0714557\pi$
$821$	8.44331	+	14.6242i	0.294674	+	0.510390i	−0.680235	+	0.732994i	$0.738122\pi$
$822$		0			0
$823$	24.3829	−	42.2325i	0.849935	−	1.47213i	−0.0313301	−	0.999509i	$-0.509974\pi$
$823$	24.3829	−	42.2325i	0.849935	−	1.47213i	0.881265	−	0.472622i	$-0.156692\pi$
$824$		0			0
$825$	10.6577	−	3.63469i	0.371053	−	0.126544i
$826$		0			0
$827$	14.4541			0.502618			0.251309	−	0.967907i	$-0.419139\pi$
$827$	14.4541			0.502618			0.251309	+	0.967907i	$0.419139\pi$
$828$		0			0
$829$	−32.5659			−1.13106			−0.565530	−	0.824728i	$-0.691328\pi$
$829$	−32.5659			−1.13106			−0.565530	+	0.824728i	$0.691328\pi$
$830$		0			0
$831$	−0.233307	+	1.18169i	−0.00809334	+	0.0409923i
$832$		0			0
$833$	−3.67871	+	6.37171i	−0.127460	+	0.220767i
$834$		0			0
$835$	−1.91423	−	3.31554i	−0.0662446	−	0.114739i
$836$		0			0
$837$	−7.58256	−	15.2121i	−0.262092	−	0.525807i
$838$		0			0
$839$	−24.4412	−	42.3334i	−0.843803	−	1.46151i	−0.886656	−	0.462429i	$-0.846978\pi$
$839$	−24.4412	−	42.3334i	−0.843803	−	1.46151i	0.0428531	−	0.999081i	$-0.486355\pi$
$840$		0			0
$841$	−15.6489	+	27.1047i	−0.539617	+	0.934644i
$842$		0			0
$843$	10.8356	−	54.8818i	0.373199	−	1.89023i
$844$		0			0
$845$	−1.15859			−0.0398567
$846$		0			0
$847$	−9.23372			−0.317274
$848$		0			0
$849$	−23.1600	+	7.89848i	−0.794850	+	0.271075i
$850$		0			0
$851$	−1.09997	+	1.90520i	−0.0377065	+	0.0653096i
$852$		0			0
$853$	10.5285	+	18.2360i	0.360491	+	0.624388i	0.988042	−	0.154187i	$-0.0492760\pi$
$853$	10.5285	+	18.2360i	0.360491	+	0.624388i	−0.627551	+	0.778575i	$0.715943\pi$
$854$		0			0
$855$	−2.68116	−	1.10166i	−0.0916939	−	0.0376759i
$856$		0			0
$857$	−18.7290	−	32.4396i	−0.639771	−	1.10812i	−0.985483	−	0.169776i	$-0.945696\pi$
$857$	−18.7290	−	32.4396i	−0.639771	−	1.10812i	0.345711	−	0.938341i	$-0.387638\pi$
$858$		0			0
$859$	13.2123	−	22.8844i	0.450799	−	0.780807i	−0.547637	−	0.836716i	$-0.684472\pi$
$859$	13.2123	−	22.8844i	0.450799	−	0.780807i	0.998436	+	0.0559093i	$0.0178058\pi$
$860$		0			0
$861$	0.353477	+	0.309104i	0.0120465	+	0.0105342i
$862$		0			0
$863$	29.1888			0.993597			0.496798	−	0.867866i	$-0.334509\pi$
$863$	29.1888			0.993597			0.496798	+	0.867866i	$0.334509\pi$
$864$		0			0
$865$	0.582905			0.0198194
$866$		0			0
$867$	48.4138	+	42.3362i	1.64422	+	1.43781i
$868$		0			0
$869$	−0.835853	+	1.44774i	−0.0283544	+	0.0491112i
$870$		0			0
$871$	13.1967	+	22.8573i	0.447153	+	0.774491i
$872$		0			0
$873$	−26.1909	+	20.2155i	−0.886428	+	0.684191i
$874$		0			0
$875$	1.62727	+	2.81852i	0.0550118	+	0.0952832i
$876$		0			0
$877$	−5.70263	+	9.87725i	−0.192564	+	0.333531i	−0.946099	−	0.323877i	$-0.895014\pi$
$877$	−5.70263	+	9.87725i	−0.192564	+	0.333531i	0.753535	+	0.657408i	$0.228347\pi$
$878$		0			0
$879$	−27.3382	+	9.32341i	−0.922095	+	0.314471i
$880$		0			0
$881$	−16.7109			−0.563005			−0.281503	−	0.959560i	$-0.590833\pi$
$881$	−16.7109			−0.563005			−0.281503	+	0.959560i	$0.590833\pi$
$882$		0			0
$883$	−11.8347			−0.398268			−0.199134	−	0.979972i	$-0.563813\pi$
$883$	−11.8347			−0.398268			−0.199134	+	0.979972i	$0.563813\pi$
$884$		0			0
$885$	−0.0821620	+	0.416146i	−0.00276184	+	0.0139886i
$886$		0			0
$887$	17.8800	−	30.9691i	0.600353	−	1.03984i	−0.392414	−	0.919789i	$-0.628360\pi$
$887$	17.8800	−	30.9691i	0.600353	−	1.03984i	0.992767	−	0.120053i	$-0.0383066\pi$
$888$		0			0
$889$	−3.50394	−	6.06899i	−0.117518	−	0.203548i
$890$		0			0
$891$	8.50574	+	8.40960i	0.284953	+	0.281732i
$892$		0			0
$893$	1.67690	+	2.90448i	0.0561154	+	0.0971947i
$894$		0			0
$895$	−1.10737	+	1.91801i	−0.0370152	+	0.0641122i
$896$		0			0
$897$	6.90636	−	34.9803i	0.230597	−	1.16796i
$898$		0			0
$899$	−25.4007			−0.847159
$900$		0			0
$901$	47.2955			1.57564
$902$		0			0
$903$	−17.9755	+	6.13037i	−0.598188	+	0.204006i
$904$		0			0
$905$	2.18320	−	3.78142i	0.0725721	−	0.125698i
$906$		0			0
$907$	−8.32308	−	14.4160i	−0.276363	−	0.478675i	0.694115	−	0.719864i	$-0.255796\pi$
$907$	−8.32308	−	14.4160i	−0.276363	−	0.478675i	−0.970478	+	0.241189i	$0.922463\pi$
$908$		0			0
$909$	33.8218	−	26.1054i	1.12180	−	0.865862i
$910$		0			0
$911$	9.88258	+	17.1171i	0.327425	+	0.567116i	0.982000	−	0.188881i	$-0.0604859\pi$
$911$	9.88258	+	17.1171i	0.327425	+	0.567116i	−0.654575	+	0.755997i	$0.727153\pi$
$912$		0			0
$913$	−0.0420579	+	0.0728465i	−0.00139191	+	0.00241087i
$914$		0			0
$915$	3.79391	+	3.31764i	0.125423	+	0.109678i
$916$		0			0
$917$	−6.66560			−0.220118
$918$		0			0
$919$	10.2384			0.337734			0.168867	−	0.985639i	$-0.445989\pi$
$919$	10.2384			0.337734			0.168867	+	0.985639i	$0.445989\pi$
$920$		0			0
$921$	−35.2488	−	30.8238i	−1.16149	−	1.01568i
$922$		0			0
$923$	2.47483	−	4.28653i	0.0814600	−	0.141093i
$924$		0			0
$925$	0.804731	+	1.39384i	0.0264594	+	0.0458290i
$926$		0			0
$927$	29.3743	+	12.0695i	0.964778	+	0.396416i
$928$		0			0
$929$	17.5842	+	30.4567i	0.576917	+	0.999250i	0.995830	+	0.0912240i	$0.0290779\pi$
$929$	17.5842	+	30.4567i	0.576917	+	0.999250i	−0.418913	+	0.908026i	$0.637589\pi$
$930$		0			0
$931$	−1.46835	+	2.54326i	−0.0481234	+	0.0833521i
$932$		0			0
$933$	−38.4840	+	13.1246i	−1.25991	+	0.429679i
$934$		0			0
$935$	3.21715			0.105212
$936$		0			0
$937$	−31.5829			−1.03177			−0.515884	−	0.856659i	$-0.672536\pi$
$937$	−31.5829			−1.03177			−0.515884	+	0.856659i	$0.672536\pi$
$938$		0			0
$939$	−0.244639	+	1.23908i	−0.00798349	+	0.0404359i
$940$		0			0
$941$	−6.49641	+	11.2521i	−0.211777	+	0.366808i	−0.952271	−	0.305255i	$-0.901258\pi$
$941$	−6.49641	+	11.2521i	−0.211777	+	0.366808i	0.740494	+	0.672063i	$0.234592\pi$
$942$		0			0
$943$	−0.906357	−	1.56986i	−0.0295150	−	0.0511216i
$944$		0			0
$945$	−0.943743	+	1.42553i	−0.0307000	+	0.0463725i
$946$		0			0
$947$	−17.7246	−	30.6998i	−0.575971	−	0.997610i	−0.995935	−	0.0900699i	$-0.971291\pi$
$947$	−17.7246	−	30.6998i	−0.575971	−	0.997610i	0.419965	−	0.907540i	$-0.362042\pi$
$948$		0			0
$949$	20.7723	−	35.9787i	0.674298	−	1.16792i
$950$		0			0
$951$	11.2322	−	56.8903i	0.364228	−	1.84479i
$952$		0			0
$953$	−40.0040			−1.29586			−0.647928	−	0.761702i	$-0.724364\pi$
$953$	−40.0040			−1.29586			−0.647928	+	0.761702i	$0.724364\pi$
$954$		0			0
$955$	−6.84898			−0.221628
$956$		0			0
$957$	16.9180	−	5.76972i	0.546882	−	0.186508i
$958$		0			0
$959$	8.41926	−	14.5826i	0.271872	−	0.470896i
$960$		0			0
$961$	10.1499	+	17.5802i	0.327417	+	0.567104i
$962$		0			0
$963$	6.22341	+	46.2553i	0.200546	+	1.49056i
$964$		0			0
$965$	3.37522	+	5.84605i	0.108652	+	0.188191i
$966$		0			0
$967$	3.03814	−	5.26222i	0.0977001	−	0.169222i	−0.813032	−	0.582219i	$-0.802185\pi$
$967$	3.03814	−	5.26222i	0.0977001	−	0.169222i	0.910732	+	0.412997i	$0.135518\pi$
$968$		0			0
$969$	28.1716	+	24.6351i	0.905004	+	0.791395i
$970$		0			0
$971$	−57.1397			−1.83370			−0.916850	−	0.399232i	$-0.869277\pi$
$971$	−57.1397			−1.83370			−0.916850	+	0.399232i	$0.869277\pi$
$972$		0			0
$973$	15.6206			0.500775
$974$		0			0
$975$	−19.6365	−	17.1714i	−0.628870	−	0.549925i
$976$		0			0
$977$	5.91064	−	10.2375i	0.189098	−	0.327528i	−0.755852	−	0.654743i	$-0.772777\pi$
$977$	5.91064	−	10.2375i	0.189098	−	0.327528i	0.944950	+	0.327215i	$0.106110\pi$
$978$		0			0
$979$	−7.51364	−	13.0140i	−0.240137	−	0.415929i
$980$		0			0
$981$	−5.74339	−	42.6876i	−0.183372	−	1.36291i
$982$		0			0
$983$	9.26336	+	16.0446i	0.295455	+	0.511744i	0.975091	−	0.221806i	$-0.0711953\pi$
$983$	9.26336	+	16.0446i	0.295455	+	0.511744i	−0.679635	+	0.733550i	$0.737862\pi$
$984$		0			0
$985$	−1.18574	+	2.05377i	−0.0377809	+	0.0654384i
$986$		0			0
$987$	1.87217	−	0.638484i	0.0595918	−	0.0203232i
$988$		0			0
$989$	73.3174			2.33136
$990$		0			0
$991$	−12.5408			−0.398371			−0.199186	−	0.979962i	$-0.563830\pi$
$991$	−12.5408			−0.398371			−0.199186	+	0.979962i	$0.563830\pi$
$992$		0			0
$993$	3.30158	−	16.7223i	0.104773	−	0.530667i
$994$		0			0
$995$	−2.35700	+	4.08245i	−0.0747220	+	0.129422i
$996$		0			0
$997$	−7.94209	−	13.7561i	−0.251528	−	0.435660i	0.712418	−	0.701755i	$-0.247600\pi$
$997$	−7.94209	−	13.7561i	−0.251528	−	0.435660i	−0.963947	+	0.266095i	$0.914267\pi$
$998$		0			0
$999$	−0.943743	+	1.42553i	−0.0298587	+	0.0451018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.l.337.4		8
3.2	odd	2		3024.2.r.m.1009.2		8
4.3	odd	2		504.2.r.e.337.1	yes	8
9.2	odd	6		3024.2.r.m.2017.2		8
9.4	even	3		9072.2.a.cj.1.2		4
9.5	odd	6		9072.2.a.cg.1.3		4
9.7	even	3	inner	1008.2.r.l.673.4		8
12.11	even	2		1512.2.r.e.1009.2		8
36.7	odd	6		504.2.r.e.169.1	✓	8
36.11	even	6		1512.2.r.e.505.2		8
36.23	even	6		4536.2.a.y.1.3		4
36.31	odd	6		4536.2.a.z.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.e.169.1	✓	8	36.7	odd	6
504.2.r.e.337.1	yes	8	4.3	odd	2
1008.2.r.l.337.4		8	1.1	even	1	trivial
1008.2.r.l.673.4		8	9.7	even	3	inner
1512.2.r.e.505.2		8	36.11	even	6
1512.2.r.e.1009.2		8	12.11	even	2
3024.2.r.m.1009.2		8	3.2	odd	2
3024.2.r.m.2017.2		8	9.2	odd	6
4536.2.a.y.1.3		4	36.23	even	6
4536.2.a.z.1.2		4	36.31	odd	6
9072.2.a.cg.1.3		4	9.5	odd	6
9072.2.a.cj.1.2		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)

\(f(q)\)	\(=\)	\(q+(1.30385 + 1.14017i) q^{3} +(-0.164508 + 0.284936i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(0.400030 + 2.97321i) q^{9} +O(q^{10})\)	\(q+(1.30385 + 1.14017i) q^{3} +(-0.164508 + 0.284936i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(0.400030 + 2.97321i) q^{9} +(-0.664508 - 1.15096i) q^{11} +(-1.53937 + 2.66626i) q^{13} +(-0.539368 + 0.183946i) q^{15} +7.35741 q^{17} +2.93671 q^{19} +(0.335492 - 1.69925i) q^{21} +(-3.34321 + 5.79062i) q^{23} +(2.44587 + 4.23638i) q^{25} +(-2.86838 + 4.33271i) q^{27} +(3.88258 + 6.72483i) q^{29} +(-1.63555 + 2.83286i) q^{31} +(0.445874 - 2.25833i) q^{33} +0.329016 q^{35} +0.329016 q^{37} +(-5.04709 + 1.72126i) q^{39} +(-0.135552 + 0.234783i) q^{41} +(-5.48255 - 9.49606i) q^{43} +(-0.912983 - 0.375134i) q^{45} +(0.571014 + 0.989025i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(9.59293 + 8.38869i) q^{51} +6.42828 q^{53} +0.437267 q^{55} +(3.82902 + 3.34834i) q^{57} +(0.372170 - 0.644618i) q^{59} +(-4.42195 - 7.65904i) q^{61} +(2.37486 - 1.83304i) q^{63} +(-0.506476 - 0.877243i) q^{65} +(4.28640 - 7.42426i) q^{67} +(-10.9613 + 3.73825i) q^{69} -1.60769 q^{71} -13.4941 q^{73} +(-1.64114 + 8.31230i) q^{75} +(-0.664508 + 1.15096i) q^{77} +(-0.628926 - 1.08933i) q^{79} +(-8.67995 + 2.37875i) q^{81} +(-0.0316459 - 0.0548124i) q^{83} +(-1.21035 + 2.09639i) q^{85} +(-2.60515 + 13.1949i) q^{87} +11.3071 q^{89} +3.07874 q^{91} +(-5.36245 + 1.82881i) q^{93} +(-0.483112 + 0.836774i) q^{95} +(5.51420 + 9.55087i) q^{97} +(3.15623 - 2.43614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 3 q^{5} - 4 q^{7} - q^{9}+O(q^{10}) \) 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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