LMFDB - Embedded newform 1440.2.q.i.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(481,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, 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("1440.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.3010058496.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 6x^{6} + 2x^{5} - 17x^{4} + 6x^{3} + 54x^{2} - 108x + 81 $ x^8 - 4x^7 + 6x^6 + 2x^5 - 17x^4 + 6x^3 + 54x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.3
Root			$-1.54667 - 0.779618i$ of defining polynomial
Character	$\chi$	$=$	1440.961
Dual form			1440.2.q.i.481.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0981673 - 1.72927i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.0981673 + 0.170031i) q^{7} +(-2.98073 - 0.339515i) q^{9} +O(q^{10})$	\(q+(0.0981673 - 1.72927i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.0981673 + 0.170031i) q^{7} +(-2.98073 - 0.339515i) q^{9} +(-2.64484 + 4.58100i) q^{11} +(-1.28439 - 2.22463i) q^{13} +(1.54667 - 0.779618i) q^{15} -5.22524 q^{17} +6.89701 q^{19} +(0.284392 + 0.186449i) q^{21} +(3.66695 + 6.35135i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.879722 + 5.12114i) q^{27} +(-2.39701 + 4.15174i) q^{29} +(1.12028 + 1.94038i) q^{31} +(7.66213 + 5.02334i) q^{33} -0.196335 q^{35} -9.61791 q^{37} +(-3.97307 + 2.00267i) q^{39} +(2.50529 + 4.33929i) q^{41} +(-4.44851 + 7.70504i) q^{43} +(-1.19633 - 2.75114i) q^{45} +(6.44368 - 11.1608i) q^{47} +(3.48073 + 6.02879i) q^{49} +(-0.512948 + 9.03583i) q^{51} -7.53024 q^{53} -5.28968 q^{55} +(0.677061 - 11.9268i) q^{57} +(2.19633 + 3.80416i) q^{59} +(3.30895 - 5.73128i) q^{61} +(0.350338 - 0.473486i) q^{63} +(1.28439 - 2.22463i) q^{65} +(2.74301 + 4.75103i) q^{67} +(11.3431 - 5.71764i) q^{69} -5.49566 q^{71} -2.57936 q^{73} +(1.44851 + 0.949649i) q^{75} +(-0.519274 - 0.899408i) q^{77} +(-1.19633 + 2.07211i) q^{79} +(8.76946 + 2.02400i) q^{81} +(-2.38785 + 4.13587i) q^{83} +(-2.61262 - 4.52519i) q^{85} +(6.94416 + 4.55264i) q^{87} +15.5794 q^{89} +0.504341 q^{91} +(3.46541 - 1.74678i) q^{93} +(3.44851 + 5.97299i) q^{95} +(6.26946 - 10.8590i) q^{97} +(9.43886 - 12.7567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 8 * q^9	$ 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 8 q^{9} - 2 q^{11} - 4 q^{15} - 8 q^{17} + 28 q^{19} - 8 q^{21} + 6 q^{23} - 4 q^{25} - 14 q^{27} + 8 q^{29} + 2 q^{31} + 8 q^{33} + 4 q^{35} - 32 q^{37} - 6 q^{39} - 8 q^{41} - 22 q^{43} - 4 q^{45} + 8 q^{47} + 12 q^{49} + 14 q^{51} - 8 q^{53} - 4 q^{55} - 16 q^{57} + 12 q^{59} + 4 q^{61} - 8 q^{63} + 12 q^{69} - 60 q^{71} + 56 q^{73} - 2 q^{75} - 20 q^{77} - 4 q^{79} + 28 q^{81} + 22 q^{83} - 4 q^{85} + 58 q^{87} + 48 q^{89} - 12 q^{91} - 8 q^{93} + 14 q^{95} + 8 q^{97} + 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 8 * q^9 - 2 * q^11 - 4 * q^15 - 8 * q^17 + 28 * q^19 - 8 * q^21 + 6 * q^23 - 4 * q^25 - 14 * q^27 + 8 * q^29 + 2 * q^31 + 8 * q^33 + 4 * q^35 - 32 * q^37 - 6 * q^39 - 8 * q^41 - 22 * q^43 - 4 * q^45 + 8 * q^47 + 12 * q^49 + 14 * q^51 - 8 * q^53 - 4 * q^55 - 16 * q^57 + 12 * q^59 + 4 * q^61 - 8 * q^63 + 12 * q^69 - 60 * q^71 + 56 * q^73 - 2 * q^75 - 20 * q^77 - 4 * q^79 + 28 * q^81 + 22 * q^83 - 4 * q^85 + 58 * q^87 + 48 * q^89 - 12 * q^91 - 8 * q^93 + 14 * q^95 + 8 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0981673	−	1.72927i	0.0566769	−	0.998393i
$3$	0.0981673	−	1.72927i	0.0566769	−	0.998393i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.0981673	+	0.170031i	−0.0371038	+	0.0642656i	−0.883981	−	0.467523i	$-0.845147\pi$
$7$	−0.0981673	+	0.170031i	−0.0371038	+	0.0642656i	0.846877	+	0.531789i	$0.178480\pi$
$8$		0			0
$9$	−2.98073	−	0.339515i	−0.993575	−	0.113172i
$10$		0			0
$11$	−2.64484	+	4.58100i	−0.797449	+	1.38122i	0.123823	+	0.992304i	$0.460484\pi$
$11$	−2.64484	+	4.58100i	−0.797449	+	1.38122i	−0.921272	+	0.388918i	$0.872849\pi$
$12$		0			0
$13$	−1.28439	−	2.22463i	−0.356226	−	0.617002i	0.631101	−	0.775701i	$-0.282603\pi$
$13$	−1.28439	−	2.22463i	−0.356226	−	0.617002i	−0.987327	+	0.158699i	$0.949270\pi$
$14$		0			0
$15$	1.54667	−	0.779618i	0.399349	−	0.201296i
$16$		0			0
$17$	−5.22524			−1.26731			−0.633653	−	0.773617i	$-0.718445\pi$
$17$	−5.22524			−1.26731			−0.633653	+	0.773617i	$0.718445\pi$
$18$		0			0
$19$	6.89701			1.58228			0.791141	−	0.611633i	$-0.209487\pi$
$19$	6.89701			1.58228			0.791141	+	0.611633i	$0.209487\pi$
$20$		0			0
$21$	0.284392	+	0.186449i	0.0620594	+	0.0406865i
$22$		0			0
$23$	3.66695	+	6.35135i	0.764612	+	1.32435i	0.940451	+	0.339928i	$0.110403\pi$
$23$	3.66695	+	6.35135i	0.764612	+	1.32435i	−0.175839	+	0.984419i	$0.556264\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−0.879722	+	5.12114i	−0.169303	+	0.985564i
$28$		0			0
$29$	−2.39701	+	4.15174i	−0.445114	+	0.770959i	−0.998060	−	0.0622573i	$-0.980170\pi$
$29$	−2.39701	+	4.15174i	−0.445114	+	0.770959i	0.552946	+	0.833217i	$0.313503\pi$
$30$		0			0
$31$	1.12028	+	1.94038i	0.201208	+	0.348502i	0.948918	−	0.315523i	$-0.102180\pi$
$31$	1.12028	+	1.94038i	0.201208	+	0.348502i	−0.747710	+	0.664025i	$0.768847\pi$
$32$		0			0
$33$	7.66213	+	5.02334i	1.33381	+	0.874451i
$34$		0			0
$35$	−0.196335			−0.0331866
$36$		0			0
$37$	−9.61791			−1.58117			−0.790587	−	0.612350i	$-0.790224\pi$
$37$	−9.61791			−1.58117			−0.790587	+	0.612350i	$0.790224\pi$
$38$		0			0
$39$	−3.97307	+	2.00267i	−0.636200	+	0.320684i
$40$		0			0
$41$	2.50529	+	4.33929i	0.391260	+	0.677683i	0.992616	−	0.121299i	$-0.0387059\pi$
$41$	2.50529	+	4.33929i	0.391260	+	0.677683i	−0.601356	+	0.798981i	$0.705373\pi$
$42$		0			0
$43$	−4.44851	+	7.70504i	−0.678391	+	1.17501i	0.297075	+	0.954854i	$0.403989\pi$
$43$	−4.44851	+	7.70504i	−0.678391	+	1.17501i	−0.975465	+	0.220153i	$0.929344\pi$
$44$		0			0
$45$	−1.19633	−	2.75114i	−0.178339	−	0.410116i
$46$		0			0
$47$	6.44368	−	11.1608i	0.939908	−	1.62797i	0.174268	−	0.984698i	$-0.444244\pi$
$47$	6.44368	−	11.1608i	0.939908	−	1.62797i	0.765640	−	0.643270i	$-0.222423\pi$
$48$		0			0
$49$	3.48073	+	6.02879i	0.497247	+	0.861256i
$50$		0			0
$51$	−0.512948	+	9.03583i	−0.0718270	+	1.26527i
$52$		0			0
$53$	−7.53024			−1.03436			−0.517179	−	0.855877i	$-0.673018\pi$
$53$	−7.53024			−1.03436			−0.517179	+	0.855877i	$0.673018\pi$
$54$		0			0
$55$	−5.28968			−0.713260
$56$		0			0
$57$	0.677061	−	11.9268i	0.0896789	−	1.57974i
$58$		0			0
$59$	2.19633	+	3.80416i	0.285938	+	0.495260i	0.972836	−	0.231494i	$-0.0743614\pi$
$59$	2.19633	+	3.80416i	0.285938	+	0.495260i	−0.686898	+	0.726754i	$0.741028\pi$
$60$		0			0
$61$	3.30895	−	5.73128i	0.423668	−	0.733815i	−0.572627	−	0.819816i	$-0.694076\pi$
$61$	3.30895	−	5.73128i	0.423668	−	0.733815i	0.996295	+	0.0860015i	$0.0274090\pi$
$62$		0			0
$63$	0.350338	−	0.473486i	0.0441384	−	0.0596536i
$64$		0			0
$65$	1.28439	−	2.22463i	0.159309	−	0.275932i
$66$		0			0
$67$	2.74301	+	4.75103i	0.335112	+	0.580430i	0.983506	−	0.180874i	$-0.0578926\pi$
$67$	2.74301	+	4.75103i	0.335112	+	0.580430i	−0.648395	+	0.761304i	$0.724559\pi$
$68$		0			0
$69$	11.3431	−	5.71764i	1.36555	−	0.688323i
$70$		0			0
$71$	−5.49566			−0.652215			−0.326107	−	0.945333i	$-0.605737\pi$
$71$	−5.49566			−0.652215			−0.326107	+	0.945333i	$0.605737\pi$
$72$		0			0
$73$	−2.57936			−0.301891			−0.150946	−	0.988542i	$-0.548232\pi$
$73$	−2.57936			−0.301891			−0.150946	+	0.988542i	$0.548232\pi$
$74$		0			0
$75$	1.44851	+	0.949649i	0.167259	+	0.109656i
$76$		0			0
$77$	−0.519274	−	0.899408i	−0.0591767	−	0.102497i
$78$		0			0
$79$	−1.19633	+	2.07211i	−0.134598	+	0.233131i	−0.925444	−	0.378885i	$-0.876308\pi$
$79$	−1.19633	+	2.07211i	−0.134598	+	0.233131i	0.790846	+	0.612016i	$0.209641\pi$
$80$		0			0
$81$	8.76946	+	2.02400i	0.974384	+	0.224889i
$82$		0			0
$83$	−2.38785	+	4.13587i	−0.262100	+	0.453971i	−0.966800	−	0.255535i	$-0.917748\pi$
$83$	−2.38785	+	4.13587i	−0.262100	+	0.453971i	0.704700	+	0.709506i	$0.251082\pi$
$84$		0			0
$85$	−2.61262	−	4.52519i	−0.283378	−	0.490826i
$86$		0			0
$87$	6.94416	+	4.55264i	0.744493	+	0.488094i
$88$		0			0
$89$	15.5794			1.65141			0.825704	−	0.564103i	$-0.190778\pi$
$89$	15.5794			1.65141			0.825704	+	0.564103i	$0.190778\pi$
$90$		0			0
$91$	0.504341			0.0528693
$92$		0			0
$93$	3.46541	−	1.74678i	0.359346	−	0.181132i
$94$		0			0
$95$	3.44851	+	5.97299i	0.353809	+	0.612815i
$96$		0			0
$97$	6.26946	−	10.8590i	0.636567	−	1.10257i	−0.349614	−	0.936894i	$-0.613687\pi$
$97$	6.26946	−	10.8590i	0.636567	−	1.10257i	0.986181	−	0.165673i	$-0.0529795\pi$
$98$		0			0
$99$	9.43886	−	12.7567i	0.948641	−	1.28210i
$100$		0			0
$101$	−9.55914	+	16.5569i	−0.951170	+	1.64747i	−0.208271	+	0.978071i	$0.566783\pi$
$101$	−9.55914	+	16.5569i	−0.951170	+	1.64747i	−0.742899	+	0.669403i	$0.766550\pi$
$102$		0			0
$103$	−3.01729	−	5.22610i	−0.297302	−	0.514943i	0.678216	−	0.734863i	$-0.262754\pi$
$103$	−3.01729	−	5.22610i	−0.297302	−	0.514943i	−0.975518	+	0.219920i	$0.929420\pi$
$104$		0			0
$105$	−0.0192736	+	0.339515i	−0.00188091	+	0.0331333i
$106$		0			0
$107$	−7.86147			−0.759997			−0.379999	−	0.924987i	$-0.624076\pi$
$107$	−7.86147			−0.759997			−0.379999	+	0.924987i	$0.624076\pi$
$108$		0			0
$109$	−9.49169			−0.909139			−0.454569	−	0.890711i	$-0.650207\pi$
$109$	−9.49169			−0.909139			−0.454569	+	0.890711i	$0.650207\pi$
$110$		0			0
$111$	−0.944164	+	16.6319i	−0.0896161	+	1.57863i
$112$		0			0
$113$	8.05480	+	13.9513i	0.757732	+	1.31243i	0.944005	+	0.329932i	$0.107026\pi$
$113$	8.05480	+	13.9513i	0.757732	+	1.31243i	−0.186273	+	0.982498i	$0.559641\pi$
$114$		0			0
$115$	−3.66695	+	6.35135i	−0.341945	+	0.592266i
$116$		0			0
$117$	3.07312	+	7.06709i	0.284110	+	0.653353i
$118$		0			0
$119$	0.512948	−	0.888451i	0.0470218	−	0.0814442i
$120$		0			0
$121$	−8.49036	−	14.7057i	−0.771850	−	1.33688i
$122$		0			0
$123$	7.74972	−	3.90633i	0.698769	−	0.352222i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.82956			0.606025			0.303013	−	0.952987i	$-0.402008\pi$
$127$	6.82956			0.606025			0.303013	+	0.952987i	$0.402008\pi$
$128$		0			0
$129$	12.8874	+	8.44903i	1.13467	+	0.743896i
$130$		0			0
$131$	−2.42157	−	4.19429i	−0.211574	−	0.366456i	0.740633	−	0.671909i	$-0.234526\pi$
$131$	−2.42157	−	4.19429i	−0.211574	−	0.366456i	−0.952207	+	0.305453i	$0.901192\pi$
$132$		0			0
$133$	−0.677061	+	1.17270i	−0.0587086	+	0.101686i
$134$		0			0
$135$	−4.87490	+	1.79871i	−0.419565	+	0.154808i
$136$		0			0
$137$	−5.59769	+	9.69548i	−0.478243	+	0.828340i	−0.999689	−	0.0249436i	$-0.992059\pi$
$137$	−5.59769	+	9.69548i	−0.478243	+	0.828340i	0.521446	+	0.853284i	$0.325393\pi$
$138$		0			0
$139$	−1.43122	−	2.47894i	−0.121394	−	0.210261i	0.798924	−	0.601433i	$-0.205403\pi$
$139$	−1.43122	−	2.47894i	−0.121394	−	0.210261i	−0.920318	+	0.391172i	$0.872070\pi$
$140$		0			0
$141$	−18.6674	−	12.2385i	−1.57208	−	1.03067i
$142$		0			0
$143$	13.5880			1.13629
$144$		0			0
$145$	−4.79402			−0.398122
$146$		0			0
$147$	10.7671	−	5.42727i	0.888054	−	0.447634i
$148$		0			0
$149$	0.112619	+	0.195061i	0.00922608	+	0.0159800i	0.870602	−	0.491989i	$-0.163730\pi$
$149$	0.112619	+	0.195061i	0.00922608	+	0.0159800i	−0.861376	+	0.507969i	$0.830397\pi$
$150$		0			0
$151$	−2.14050	+	3.70745i	−0.174191	+	0.301708i	−0.939881	−	0.341502i	$-0.889064\pi$
$151$	−2.14050	+	3.70745i	−0.174191	+	0.301708i	0.765690	+	0.643210i	$0.222398\pi$
$152$		0			0
$153$	15.5750	+	1.77405i	1.25916	+	0.143423i
$154$		0			0
$155$	−1.12028	+	1.94038i	−0.0899829	+	0.155855i
$156$		0			0
$157$	−3.38302	−	5.85957i	−0.269995	−	0.467645i	0.698865	−	0.715253i	$-0.253689\pi$
$157$	−3.38302	−	5.85957i	−0.269995	−	0.467645i	−0.968860	+	0.247609i	$0.920355\pi$
$158$		0			0
$159$	−0.739223	+	13.0218i	−0.0586242	+	1.03269i
$160$		0			0
$161$	−1.43990			−0.113480
$162$		0			0
$163$	−2.97410			−0.232950			−0.116475	−	0.993194i	$-0.537159\pi$
$163$	−2.97410			−0.232950			−0.116475	+	0.993194i	$0.537159\pi$
$164$		0			0
$165$	−0.519274	+	9.14727i	−0.0404254	+	0.712114i
$166$		0			0
$167$	7.20313	+	12.4762i	0.557395	+	0.965436i	0.997713	+	0.0675941i	$0.0215323\pi$
$167$	7.20313	+	12.4762i	0.557395	+	0.965436i	−0.440318	+	0.897842i	$0.645134\pi$
$168$		0			0
$169$	3.20068	−	5.54373i	0.246206	−	0.426441i
$170$		0			0
$171$	−20.5581	−	2.34164i	−1.57212	−	0.179070i
$172$		0			0
$173$	10.2511	−	17.7555i	0.779379	−	1.34992i	−0.152921	−	0.988238i	$-0.548868\pi$
$173$	10.2511	−	17.7555i	0.779379	−	1.34992i	0.932300	−	0.361686i	$-0.117799\pi$
$174$		0			0
$175$	−0.0981673	−	0.170031i	−0.00742075	−	0.0128531i
$176$		0			0
$177$	6.79402	−	3.42460i	0.510670	−	0.257409i
$178$		0			0
$179$	−1.84789			−0.138118			−0.0690588	−	0.997613i	$-0.522000\pi$
$179$	−1.84789			−0.138118			−0.0690588	+	0.997613i	$0.522000\pi$
$180$		0			0
$181$	10.0087			0.743939			0.371970	−	0.928245i	$-0.378683\pi$
$181$	10.0087			0.743939			0.371970	+	0.928245i	$0.378683\pi$
$182$		0			0
$183$	−9.58607	−	6.28469i	−0.708623	−	0.464577i
$184$		0			0
$185$	−4.80895	−	8.32935i	−0.353561	−	0.612386i
$186$		0			0
$187$	13.8199	−	23.9368i	1.01061	−	1.75043i
$188$		0			0
$189$	−0.784392	−	0.652308i	−0.0570561	−	0.0474485i
$190$		0			0
$191$	−0.689062	+	1.19349i	−0.0498588	+	0.0863579i	−0.889878	−	0.456199i	$-0.849210\pi$
$191$	−0.689062	+	1.19349i	−0.0498588	+	0.0863579i	0.840019	+	0.542557i	$0.182544\pi$
$192$		0			0
$193$	−7.01397	−	12.1486i	−0.504877	−	0.874472i	−0.999984	−	0.00564022i	$-0.998205\pi$
$193$	−7.01397	−	12.1486i	−0.504877	−	0.874472i	0.495107	−	0.868832i	$-0.335129\pi$
$194$		0			0
$195$	−3.72090	−	2.43944i	−0.266459	−	0.174692i
$196$		0			0
$197$	−4.26378			−0.303782			−0.151891	−	0.988397i	$-0.548536\pi$
$197$	−4.26378			−0.303782			−0.151891	+	0.988397i	$0.548536\pi$
$198$		0			0
$199$	−0.691031			−0.0489859			−0.0244930	−	0.999700i	$-0.507797\pi$
$199$	−0.691031			−0.0489859			−0.0244930	+	0.999700i	$0.507797\pi$
$200$		0			0
$201$	8.48507	−	4.27700i	0.598491	−	0.301676i
$202$		0			0
$203$	−0.470616	−	0.815131i	−0.0330308	−	0.0572110i
$204$		0			0
$205$	−2.50529	+	4.33929i	−0.174977	+	0.303069i
$206$		0			0
$207$	−8.77380	−	20.1766i	−0.609821	−	1.40237i
$208$		0			0
$209$	−18.2415	+	31.5952i	−1.26179	+	2.18548i
$210$		0			0
$211$	11.3359	+	19.6343i	0.780394	+	1.35168i	0.931713	+	0.363196i	$0.118315\pi$
$211$	11.3359	+	19.6343i	0.780394	+	1.35168i	−0.151319	+	0.988485i	$0.548352\pi$
$212$		0			0
$213$	−0.539494	+	9.50346i	−0.0369655	+	0.651166i
$214$		0			0
$215$	−8.89701			−0.606771
$216$		0			0
$217$	−0.439899			−0.0298623
$218$		0			0
$219$	−0.253209	+	4.46040i	−0.0171103	+	0.301406i
$220$		0			0
$221$	6.71125	+	11.6242i	0.451448	+	0.781930i
$222$		0			0
$223$	7.07123	−	12.2477i	0.473525	−	0.820169i	−0.526016	−	0.850475i	$-0.676315\pi$
$223$	7.07123	−	12.2477i	0.473525	−	0.820169i	0.999541	+	0.0303057i	$0.00964807\pi$
$224$		0			0
$225$	1.78439	−	2.41163i	0.118959	−	0.160775i
$226$		0			0
$227$	4.22327	−	7.31491i	0.280308	−	0.485508i	−0.691152	−	0.722709i	$-0.742897\pi$
$227$	4.22327	−	7.31491i	0.280308	−	0.485508i	0.971461	+	0.237201i	$0.0762300\pi$
$228$		0			0
$229$	−10.2555	−	17.7630i	−0.677701	−	1.17381i	−0.975672	−	0.219237i	$-0.929643\pi$
$229$	−10.2555	−	17.7630i	−0.677701	−	1.17381i	0.297971	−	0.954575i	$-0.403690\pi$
$230$		0			0
$231$	−1.60629	+	0.809670i	−0.105686	+	0.0532724i
$232$		0			0
$233$	−6.40325			−0.419491			−0.209745	−	0.977756i	$-0.567263\pi$
$233$	−6.40325			−0.419491			−0.209745	+	0.977756i	$0.567263\pi$
$234$		0			0
$235$	12.8874			0.840679
$236$		0			0
$237$	3.46579	+	2.27220i	0.225128	+	0.147595i
$238$		0			0
$239$	−8.14814	−	14.1130i	−0.527060	−	0.912894i	−0.999503	−	0.0315328i	$-0.989961\pi$
$239$	−8.14814	−	14.1130i	−0.527060	−	0.912894i	0.472443	−	0.881361i	$-0.343372\pi$
$240$		0			0
$241$	−8.41194	+	14.5699i	−0.541861	+	0.938531i	0.456936	+	0.889499i	$0.348947\pi$
$241$	−8.41194	+	14.5699i	−0.541861	+	0.938531i	−0.998797	+	0.0490312i	$0.984387\pi$
$242$		0			0
$243$	4.36091	−	14.9660i	0.279753	−	0.960072i
$244$		0			0
$245$	−3.48073	+	6.02879i	−0.222375	+	0.385166i
$246$		0			0
$247$	−8.85846	−	15.3433i	−0.563651	−	0.976271i
$248$		0			0
$249$	6.91762	+	4.53523i	0.438386	+	0.287409i
$250$		0			0
$251$	−23.6053			−1.48995			−0.744975	−	0.667092i	$-0.767539\pi$
$251$	−23.6053			−1.48995			−0.744975	+	0.667092i	$0.767539\pi$
$252$		0			0
$253$	−38.7940			−2.43896
$254$		0			0
$255$	−8.08173	+	4.07369i	−0.506098	+	0.255104i
$256$		0			0
$257$	2.04912	+	3.54919i	0.127821	+	0.221392i	0.922832	−	0.385203i	$-0.125868\pi$
$257$	2.04912	+	3.54919i	0.127821	+	0.221392i	−0.795011	+	0.606595i	$0.792535\pi$
$258$		0			0
$259$	0.944164	−	1.63534i	0.0586675	−	0.101615i
$260$		0			0
$261$	8.55441	−	11.5614i	0.529505	−	0.715632i
$262$		0			0
$263$	12.1309	−	21.0113i	0.748021	−	1.29561i	−0.200750	−	0.979643i	$-0.564338\pi$
$263$	12.1309	−	21.0113i	0.748021	−	1.29561i	0.948770	−	0.315967i	$-0.102329\pi$
$264$		0			0
$265$	−3.76512	−	6.52138i	−0.231289	−	0.400605i
$266$		0			0
$267$	1.52938	−	26.9409i	0.0935968	−	1.64875i
$268$		0			0
$269$	−11.1357			−0.678954			−0.339477	−	0.940614i	$-0.610250\pi$
$269$	−11.1357			−0.678954			−0.339477	+	0.940614i	$0.610250\pi$
$270$		0			0
$271$	−27.8804			−1.69361			−0.846806	−	0.531901i	$-0.821478\pi$
$271$	−27.8804			−1.69361			−0.846806	+	0.531901i	$0.821478\pi$
$272$		0			0
$273$	0.0495098	−	0.872140i	0.00299647	−	0.0527843i
$274$		0			0
$275$	−2.64484	−	4.58100i	−0.159490	−	0.276245i
$276$		0			0
$277$	−2.74150	+	4.74842i	−0.164721	+	0.285305i	−0.936556	−	0.350518i	$-0.886006\pi$
$277$	−2.74150	+	4.74842i	−0.164721	+	0.285305i	0.771835	+	0.635823i	$0.219339\pi$
$278$		0			0
$279$	−2.68046	−	6.16409i	−0.160475	−	0.369034i
$280$		0			0
$281$	−2.14152	+	3.70922i	−0.127752	+	0.221274i	−0.922805	−	0.385266i	$-0.874110\pi$
$281$	−2.14152	+	3.70922i	−0.127752	+	0.221274i	0.795053	+	0.606540i	$0.207443\pi$
$282$		0			0
$283$	−0.338724	−	0.586687i	−0.0201350	−	0.0348749i	0.855782	−	0.517336i	$-0.173076\pi$
$283$	−0.338724	−	0.586687i	−0.0201350	−	0.0348749i	−0.875917	+	0.482461i	$0.839743\pi$
$284$		0			0
$285$	10.6674	−	5.37703i	0.631883	−	0.318508i
$286$		0			0
$287$	−0.983750			−0.0580689
$288$		0			0
$289$	10.3031			0.606065
$290$		0			0
$291$	−18.1627	−	11.9076i	−1.06472	−	0.698034i
$292$		0			0
$293$	3.32294	+	5.75550i	0.194128	+	0.336240i	0.946614	−	0.322368i	$-0.104479\pi$
$293$	3.32294	+	5.75550i	0.194128	+	0.336240i	−0.752486	+	0.658608i	$0.771146\pi$
$294$		0			0
$295$	−2.19633	+	3.80416i	−0.127876	+	0.221487i
$296$		0			0
$297$	−21.1332	−	17.5746i	−1.22627	−	1.01978i
$298$		0			0
$299$	9.41960	−	16.3152i	0.544750	−	0.943534i
$300$		0			0
$301$	−0.873396	−	1.51277i	−0.0503417	−	0.0871944i
$302$		0			0
$303$	27.6929	+	18.1556i	1.59092	+	1.04301i
$304$		0			0
$305$	6.61791			0.378940
$306$		0			0
$307$	4.89323			0.279271			0.139636	−	0.990203i	$-0.455407\pi$
$307$	4.89323			0.279271			0.139636	+	0.990203i	$0.455407\pi$
$308$		0			0
$309$	−9.33351	+	4.70466i	−0.530965	+	0.267639i
$310$		0			0
$311$	12.8113	+	22.1898i	0.726463	+	1.25827i	0.958369	+	0.285532i	$0.0921704\pi$
$311$	12.8113	+	22.1898i	0.726463	+	1.25827i	−0.231906	+	0.972738i	$0.574496\pi$
$312$		0			0
$313$	−14.9571	+	25.9065i	−0.845425	+	1.46432i	0.0398265	+	0.999207i	$0.487319\pi$
$313$	−14.9571	+	25.9065i	−0.845425	+	1.46432i	−0.885252	+	0.465113i	$0.846014\pi$
$314$		0			0
$315$	0.585220	+	0.0666585i	0.0329734	+	0.00375578i
$316$		0			0
$317$	−10.3883	+	17.9931i	−0.583466	+	1.01059i	0.411599	+	0.911365i	$0.364970\pi$
$317$	−10.3883	+	17.9931i	−0.583466	+	1.01059i	−0.995065	+	0.0992273i	$0.968363\pi$
$318$		0			0
$319$	−12.6794	−	21.9614i	−0.709911	−	1.22960i
$320$		0			0
$321$	−0.771739	+	13.5946i	−0.0430743	+	0.758775i
$322$		0			0
$323$	−36.0385			−2.00524
$324$		0			0
$325$	2.56878			0.142490
$326$		0			0
$327$	−0.931774	+	16.4137i	−0.0515272	+	0.907678i
$328$		0			0
$329$	1.26512	+	2.19125i	0.0697482	+	0.120807i
$330$		0			0
$331$	−11.4456	+	19.8243i	−0.629106	+	1.08964i	0.358626	+	0.933481i	$0.383245\pi$
$331$	−11.4456	+	19.8243i	−0.629106	+	1.08964i	−0.987732	+	0.156162i	$0.950088\pi$
$332$		0			0
$333$	28.6683	+	3.26542i	1.57102	+	0.178944i
$334$		0			0
$335$	−2.74301	+	4.75103i	−0.149866	+	0.259576i
$336$		0			0
$337$	−11.8787	−	20.5745i	−0.647073	−	1.12076i	−0.983819	−	0.179168i	$-0.942660\pi$
$337$	−11.8787	−	20.5745i	−0.647073	−	1.12076i	0.336745	−	0.941596i	$-0.390674\pi$
$338$		0			0
$339$	24.9163	−	12.5593i	1.35327	−	0.682129i
$340$		0			0
$341$	−11.8518			−0.641812
$342$		0			0
$343$	−2.74112			−0.148006
$344$		0			0
$345$	10.6232	+	6.96463i	0.571934	+	0.374963i
$346$		0			0
$347$	2.66506	+	4.61602i	0.143068	+	0.247801i	0.928650	−	0.370956i	$-0.120970\pi$
$347$	2.66506	+	4.61602i	0.143068	+	0.247801i	−0.785583	+	0.618757i	$0.787637\pi$
$348$		0			0
$349$	10.0505	−	17.4079i	0.537989	−	0.931824i	−0.461024	−	0.887388i	$-0.652518\pi$
$349$	10.0505	−	17.4079i	0.537989	−	0.931824i	0.999012	−	0.0444357i	$-0.0141490\pi$
$350$		0			0
$351$	12.5226	−	4.62049i	0.668405	−	0.246624i
$352$		0			0
$353$	13.5880	−	23.5352i	0.723218	−	1.25265i	−0.236485	−	0.971635i	$-0.575995\pi$
$353$	13.5880	−	23.5352i	0.723218	−	1.25265i	0.959703	−	0.281016i	$-0.0906714\pi$
$354$		0			0
$355$	−2.74783	−	4.75938i	−0.145840	−	0.252602i
$356$		0			0
$357$	−1.48601	−	0.974240i	−0.0786482	−	0.0515622i
$358$		0			0
$359$	19.8497			1.04763			0.523815	−	0.851832i	$-0.324508\pi$
$359$	19.8497			1.04763			0.523815	+	0.851832i	$0.324508\pi$
$360$		0			0
$361$	28.5688			1.50362
$362$		0			0
$363$	−26.2636	+	13.2385i	−1.37848	+	0.694839i
$364$		0			0
$365$	−1.28968	−	2.23379i	−0.0675049	−	0.116922i
$366$		0			0
$367$	2.18472	−	3.78405i	0.114041	−	0.197526i	−0.803355	−	0.595501i	$-0.796954\pi$
$367$	2.18472	−	3.78405i	0.114041	−	0.197526i	0.917396	+	0.397975i	$0.130287\pi$
$368$		0			0
$369$	−5.99433	−	13.7848i	−0.312052	−	0.717608i
$370$		0			0
$371$	0.739223	−	1.28037i	0.0383785	−	0.0664736i
$372$		0			0
$373$	0.363767	+	0.630062i	0.0188351	+	0.0326234i	0.875289	−	0.483600i	$-0.160671\pi$
$373$	0.363767	+	0.630062i	0.0188351	+	0.0326234i	−0.856454	+	0.516223i	$0.827338\pi$
$374$		0			0
$375$	−0.0981673	+	1.72927i	−0.00506934	+	0.0892989i
$376$		0			0
$377$	12.3148			0.634245
$378$		0			0
$379$	3.04912			0.156623			0.0783115	−	0.996929i	$-0.475047\pi$
$379$	3.04912			0.156623			0.0783115	+	0.996929i	$0.475047\pi$
$380$		0			0
$381$	0.670440	−	11.8101i	0.0343477	−	0.605051i
$382$		0			0
$383$	−10.3070	−	17.8522i	−0.526661	−	0.912204i	−0.999517	−	0.0310647i	$-0.990110\pi$
$383$	−10.3070	−	17.8522i	−0.526661	−	0.912204i	0.472856	−	0.881140i	$-0.343223\pi$
$384$		0			0
$385$	0.519274	−	0.899408i	0.0264646	−	0.0458381i
$386$		0			0
$387$	15.8758	−	21.4563i	0.807010	−	1.09068i
$388$		0			0
$389$	5.58806	−	9.67880i	0.283326	−	0.490735i	−0.688876	−	0.724879i	$-0.741896\pi$
$389$	5.58806	−	9.67880i	0.283326	−	0.490735i	0.972202	+	0.234145i	$0.0752289\pi$
$390$		0			0
$391$	−19.1607	−	33.1873i	−0.968998	−	1.67835i
$392$		0			0
$393$	−7.49076	+	3.77580i	−0.377859	+	0.190464i
$394$		0			0
$395$	−2.39267			−0.120388
$396$		0			0
$397$	15.6863			0.787272			0.393636	−	0.919266i	$-0.371217\pi$
$397$	15.6863			0.787272			0.393636	+	0.919266i	$0.371217\pi$
$398$		0			0
$399$	1.96145	+	1.28594i	0.0981955	+	0.0643775i
$400$		0			0
$401$	11.7997	+	20.4377i	0.589249	+	1.02061i	0.994331	+	0.106328i	$0.0339095\pi$
$401$	11.7997	+	20.4377i	0.589249	+	1.02061i	−0.405082	+	0.914280i	$0.632757\pi$
$402$		0			0
$403$	2.87775	−	4.98441i	0.143351	−	0.248291i
$404$		0			0
$405$	2.63189	+	8.60658i	0.130780	+	0.427664i
$406$		0			0
$407$	25.4378	−	44.0596i	1.26091	−	2.18395i
$408$		0			0
$409$	−5.17611	−	8.96529i	−0.255942	−	0.443305i	0.709209	−	0.704999i	$-0.249052\pi$
$409$	−5.17611	−	8.96529i	−0.255942	−	0.443305i	−0.965151	+	0.261693i	$0.915719\pi$
$410$		0			0
$411$	16.2166	+	10.6317i	0.799904	+	0.524422i
$412$		0			0
$413$	−0.862433			−0.0424376
$414$		0			0
$415$	−4.77569			−0.234430
$416$		0			0
$417$	−4.42725	+	2.23160i	−0.216803	+	0.109282i
$418$		0			0
$419$	4.14050	+	7.17155i	0.202277	+	0.350353i	0.949262	−	0.314488i	$-0.101833\pi$
$419$	4.14050	+	7.17155i	0.202277	+	0.350353i	−0.746985	+	0.664841i	$0.768499\pi$
$420$		0			0
$421$	11.7555	−	20.3611i	0.572927	−	0.992338i	−0.423337	−	0.905972i	$-0.639141\pi$
$421$	11.7555	−	20.3611i	0.572927	−	0.992338i	0.996263	−	0.0863658i	$-0.0275254\pi$
$422$		0			0
$423$	−22.9961	+	31.0795i	−1.11811	+	1.51114i
$424$		0			0
$425$	2.61262	−	4.52519i	0.126731	−	0.219504i
$426$		0			0
$427$	0.649662	+	1.12525i	0.0314394	+	0.0544546i
$428$		0			0
$429$	1.33390	−	23.4973i	0.0644014	−	1.13446i
$430$		0			0
$431$	−1.73622			−0.0836306			−0.0418153	−	0.999125i	$-0.513314\pi$
$431$	−1.73622			−0.0836306			−0.0418153	+	0.999125i	$0.513314\pi$
$432$		0			0
$433$	−10.0797			−0.484401			−0.242200	−	0.970226i	$-0.577869\pi$
$433$	−10.0797			−0.484401			−0.242200	+	0.970226i	$0.577869\pi$
$434$		0			0
$435$	−0.470616	+	8.29014i	−0.0225643	+	0.397482i
$436$		0			0
$437$	25.2910	+	43.8053i	1.20983	+	2.09549i
$438$		0			0
$439$	2.53024	−	4.38250i	0.120762	−	0.209165i	−0.799307	−	0.600923i	$-0.794800\pi$
$439$	2.53024	−	4.38250i	0.120762	−	0.209165i	0.920068	+	0.391758i	$0.128133\pi$
$440$		0			0
$441$	−8.32823	−	19.1519i	−0.396582	−	0.911997i
$442$		0			0
$443$	5.61111	−	9.71874i	0.266592	−	0.461751i	−0.701387	−	0.712780i	$-0.747436\pi$
$443$	5.61111	−	9.71874i	0.266592	−	0.461751i	0.967980	+	0.251029i	$0.0807690\pi$
$444$		0			0
$445$	7.78968	+	13.4921i	0.369266	+	0.639588i
$446$		0			0
$447$	0.348368	−	0.175599i	0.0164773	−	0.00830555i
$448$		0			0
$449$	−15.7056			−0.741192			−0.370596	−	0.928794i	$-0.620847\pi$
$449$	−15.7056			−0.741192			−0.370596	+	0.928794i	$0.620847\pi$
$450$		0			0
$451$	−26.5043			−1.24804
$452$		0			0
$453$	6.20105	+	4.06544i	0.291351	+	0.191011i
$454$		0			0
$455$	0.252171	+	0.436772i	0.0118219	+	0.0204762i
$456$		0			0
$457$	6.31519	−	10.9382i	0.295412	−	0.511669i	−0.679669	−	0.733519i	$-0.737876\pi$
$457$	6.31519	−	10.9382i	0.295412	−	0.511669i	0.975081	+	0.221851i	$0.0712097\pi$
$458$		0			0
$459$	4.59675	−	26.7592i	0.214558	−	1.24901i
$460$		0			0
$461$	−4.86280	+	8.42262i	−0.226483	+	0.392281i	−0.956763	−	0.290867i	$-0.906056\pi$
$461$	−4.86280	+	8.42262i	−0.226483	+	0.392281i	0.730280	+	0.683148i	$0.239390\pi$
$462$		0			0
$463$	11.3714	+	19.6959i	0.528474	+	0.915344i	0.999449	+	0.0331975i	$0.0105690\pi$
$463$	11.3714	+	19.6959i	0.528474	+	0.915344i	−0.470975	+	0.882147i	$0.656098\pi$
$464$		0			0
$465$	3.24546	+	2.12774i	0.150505	+	0.0986717i
$466$		0			0
$467$	3.40722			0.157667			0.0788336	−	0.996888i	$-0.474880\pi$
$467$	3.40722			0.157667			0.0788336	+	0.996888i	$0.474880\pi$
$468$		0			0
$469$	−1.07709			−0.0497356
$470$		0			0
$471$	−10.4649	+	5.27493i	−0.482195	+	0.243056i
$472$		0			0
$473$	−23.5312	−	40.7572i	−1.08196	−	1.87402i
$474$		0			0
$475$	−3.44851	+	5.97299i	−0.158228	+	0.274059i
$476$		0			0
$477$	22.4456	+	2.55663i	1.02771	+	0.117060i
$478$		0			0
$479$	9.87679	−	17.1071i	0.451282	−	0.781643i	−0.547184	−	0.837012i	$-0.684300\pi$
$479$	9.87679	−	17.1071i	0.451282	−	0.781643i	0.998466	+	0.0553690i	$0.0176335\pi$
$480$		0			0
$481$	12.3532	+	21.3963i	0.563256	+	0.975587i
$482$		0			0
$483$	−0.141351	+	2.48997i	−0.00643169	+	0.113298i
$484$		0			0
$485$	12.5389			0.569363
$486$		0			0
$487$	14.9182			0.676006			0.338003	−	0.941145i	$-0.390249\pi$
$487$	14.9182			0.676006			0.338003	+	0.941145i	$0.390249\pi$
$488$		0			0
$489$	−0.291960	+	5.14302i	−0.0132029	+	0.232575i
$490$		0			0
$491$	17.2984	+	29.9616i	0.780664	+	1.35215i	0.931555	+	0.363600i	$0.118452\pi$
$491$	17.2984	+	29.9616i	0.780664	+	1.35215i	−0.150891	+	0.988550i	$0.548214\pi$
$492$		0			0
$493$	12.5249	−	21.6938i	0.564095	−	0.977042i
$494$		0			0
$495$	15.7671	+	1.79593i	0.708678	+	0.0807208i
$496$		0			0
$497$	0.539494	−	0.934431i	0.0241996	−	0.0419150i
$498$		0			0
$499$	10.2358	+	17.7289i	0.458218	+	0.793657i	0.998867	−	0.0475916i	$-0.0151546\pi$
$499$	10.2358	+	17.7289i	0.458218	+	0.793657i	−0.540649	+	0.841248i	$0.681821\pi$
$500$		0			0
$501$	22.2818	−	11.2314i	0.995475	−	0.501781i
$502$		0			0
$503$	−19.3878			−0.864458			−0.432229	−	0.901764i	$-0.642273\pi$
$503$	−19.3878			−0.864458			−0.432229	+	0.901764i	$0.642273\pi$
$504$		0			0
$505$	−19.1183			−0.850752
$506$		0			0
$507$	−9.27239	−	6.07904i	−0.411801	−	0.269979i
$508$		0			0
$509$	−17.7415	−	30.7292i	−0.786378	−	1.36205i	−0.928173	−	0.372150i	$-0.878621\pi$
$509$	−17.7415	−	30.7292i	−0.786378	−	1.36205i	0.141795	−	0.989896i	$-0.454713\pi$
$510$		0			0
$511$	0.253209	−	0.438570i	0.0112013	−	0.0194012i
$512$		0			0
$513$	−6.06745	+	35.3206i	−0.267884	+	1.55944i
$514$		0			0
$515$	3.01729	−	5.22610i	0.132958	−	0.230289i
$516$		0			0
$517$	34.0850	+	59.0370i	1.49906	+	2.59644i
$518$		0			0
$519$	−29.6976	−	19.4699i	−1.30358	−	0.854636i
$520$		0			0
$521$	−39.6081			−1.73526			−0.867631	−	0.497209i	$-0.834358\pi$
$521$	−39.6081			−1.73526			−0.867631	+	0.497209i	$0.834358\pi$
$522$		0			0
$523$	43.2415			1.89082			0.945408	−	0.325888i	$-0.105663\pi$
$523$	43.2415			1.89082			0.945408	+	0.325888i	$0.105663\pi$
$524$		0			0
$525$	−0.303665	+	0.153066i	−0.0132530	+	0.00668035i
$526$		0			0
$527$	−5.85372	−	10.1389i	−0.254992	−	0.441659i
$528$		0			0
$529$	−15.3931	+	26.6616i	−0.669263	+	1.15920i
$530$		0			0
$531$	−5.25510	−	12.0849i	−0.228052	−	0.524438i
$532$		0			0
$533$	6.43554	−	11.1467i	0.278754	−	0.482817i
$534$		0			0
$535$	−3.93074	−	6.80823i	−0.169941	−	0.294346i
$536$		0			0
$537$	−0.181402	+	3.19549i	−0.00782808	+	0.137896i
$538$		0			0
$539$	−36.8239			−1.58612
$540$		0			0
$541$	−10.2340			−0.439992			−0.219996	−	0.975501i	$-0.570604\pi$
$541$	−10.2340			−0.439992			−0.219996	+	0.975501i	$0.570604\pi$
$542$		0			0
$543$	0.982525	−	17.3077i	0.0421642	−	0.742744i
$544$		0			0
$545$	−4.74584	−	8.22004i	−0.203290	−	0.352108i
$546$		0			0
$547$	−13.7709	+	23.8518i	−0.588800	+	1.01983i	0.405590	+	0.914055i	$0.367066\pi$
$547$	−13.7709	+	23.8518i	−0.588800	+	1.01983i	−0.994390	+	0.105776i	$0.966267\pi$
$548$		0			0
$549$	−11.8089	+	15.9599i	−0.503993	+	0.681153i
$550$		0			0
$551$	−16.5322	+	28.6346i	−0.704296	+	1.21988i
$552$		0			0
$553$	−0.234882	−	0.406827i	−0.00998819	−	0.0173001i
$554$		0			0
$555$	−14.8758	+	7.49829i	−0.631440	+	0.318285i
$556$		0			0
$557$	4.73355			0.200567			0.100283	−	0.994959i	$-0.468025\pi$
$557$	4.73355			0.200567			0.100283	+	0.994959i	$0.468025\pi$
$558$		0			0
$559$	22.8545			0.966642
$560$		0			0
$561$	−40.0364	−	26.2481i	−1.69034	−	1.10820i
$562$		0			0
$563$	10.6497	+	18.4458i	0.448830	+	0.777396i	0.998310	−	0.0581107i	$-0.0185076\pi$
$563$	10.6497	+	18.4458i	0.448830	+	0.777396i	−0.549480	+	0.835507i	$0.685174\pi$
$564$		0			0
$565$	−8.05480	+	13.9513i	−0.338868	+	0.586936i
$566$		0			0
$567$	−1.20502	+	1.29239i	−0.0506060	+	0.0542752i
$568$		0			0
$569$	2.13757	−	3.70237i	0.0896115	−	0.155212i	−0.817735	−	0.575594i	$-0.804771\pi$
$569$	2.13757	−	3.70237i	0.0896115	−	0.155212i	0.907347	+	0.420383i	$0.138104\pi$
$570$		0			0
$571$	18.5495	+	32.1287i	0.776272	+	1.34454i	0.934077	+	0.357072i	$0.116225\pi$
$571$	18.5495	+	32.1287i	0.776272	+	1.34454i	−0.157805	+	0.987470i	$0.550442\pi$
$572$		0			0
$573$	1.99622	+	1.30873i	0.0833932	+	0.0546731i
$574$		0			0
$575$	−7.33390			−0.305845
$576$		0			0
$577$	32.7354			1.36279			0.681396	−	0.731914i	$-0.261373\pi$
$577$	32.7354			1.36279			0.681396	+	0.731914i	$0.261373\pi$
$578$		0			0
$579$	−21.6966	+	10.9364i	−0.901681	+	0.454503i
$580$		0			0
$581$	−0.468817	−	0.812015i	−0.0194498	−	0.0336881i
$582$		0			0
$583$	19.9163	−	34.4960i	0.824848	−	1.42868i
$584$		0			0
$585$	−4.58372	+	6.19495i	−0.189513	+	0.256130i
$586$		0			0
$587$	−14.7796	+	25.5989i	−0.610017	+	1.05658i	0.381219	+	0.924485i	$0.375504\pi$
$587$	−14.7796	+	25.5989i	−0.610017	+	1.05658i	−0.991237	+	0.132097i	$0.957829\pi$
$588$		0			0
$589$	7.72657	+	13.3828i	0.318368	+	0.551429i
$590$		0			0
$591$	−0.418564	+	7.37322i	−0.0172174	+	0.303294i
$592$		0			0
$593$	33.1251			1.36028			0.680142	−	0.733081i	$-0.261918\pi$
$593$	33.1251			1.36028			0.680142	+	0.733081i	$0.261918\pi$
$594$		0			0
$595$	1.02590			0.0420576
$596$		0			0
$597$	−0.0678367	+	1.19498i	−0.00277637	+	0.0489072i
$598$		0			0
$599$	19.0249	+	32.9522i	0.777338	+	1.34639i	0.933471	+	0.358652i	$0.116764\pi$
$599$	19.0249	+	32.9522i	0.777338	+	1.34639i	−0.156134	+	0.987736i	$0.549903\pi$
$600$		0			0
$601$	22.2232	−	38.4916i	0.906502	−	1.57011i	0.0876129	−	0.996155i	$-0.472076\pi$
$601$	22.2232	−	38.4916i	0.906502	−	1.57011i	0.818889	−	0.573952i	$-0.194591\pi$
$602$		0			0
$603$	−6.56311	−	15.0928i	−0.267270	−	0.614627i
$604$		0			0
$605$	8.49036	−	14.7057i	0.345182	−	0.597873i
$606$		0			0
$607$	6.66024	+	11.5359i	0.270331	+	0.468227i	0.968946	−	0.247270i	$-0.0795336\pi$
$607$	6.66024	+	11.5359i	0.270331	+	0.468227i	−0.698616	+	0.715497i	$0.746200\pi$
$608$		0			0
$609$	−1.45578	+	0.733802i	−0.0589911	+	0.0297351i
$610$		0			0
$611$	−33.1049			−1.33928
$612$		0			0
$613$	−28.1780			−1.13810			−0.569049	−	0.822304i	$-0.692688\pi$
$613$	−28.1780			−1.13810			−0.569049	+	0.822304i	$0.692688\pi$
$614$		0			0
$615$	7.25785	+	4.75829i	0.292665	+	0.191873i
$616$		0			0
$617$	−13.7910	−	23.8867i	−0.555205	−	0.961644i	−0.997888	−	0.0649652i	$-0.979306\pi$
$617$	−13.7910	−	23.8867i	−0.555205	−	0.961644i	0.442682	−	0.896679i	$-0.354027\pi$
$618$		0			0
$619$	9.99800	−	17.3170i	0.401854	−	0.696031i	−0.592096	−	0.805867i	$-0.701699\pi$
$619$	9.99800	−	17.3170i	0.401854	−	0.696031i	0.993950	+	0.109837i	$0.0350328\pi$
$620$		0			0
$621$	−35.7520	+	13.1916i	−1.43468	+	0.529359i
$622$		0			0
$623$	−1.52938	+	2.64897i	−0.0612735	+	0.106129i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	52.8458	+	34.6460i	2.11046	+	1.38363i
$628$		0			0
$629$	50.2558			2.00383
$630$		0			0
$631$	−22.0423			−0.877490			−0.438745	−	0.898612i	$-0.644577\pi$
$631$	−22.0423			−0.877490			−0.438745	+	0.898612i	$0.644577\pi$
$632$		0			0
$633$	35.0658	−	17.6753i	1.39374	−	0.702530i
$634$		0			0
$635$	3.41478	+	5.91457i	0.135511	+	0.234713i
$636$		0			0
$637$	8.94123	−	15.4867i	0.354265	−	0.613604i
$638$		0			0
$639$	16.3811	+	1.86586i	0.648025	+	0.0738122i
$640$		0			0
$641$	−9.49564	+	16.4469i	−0.375055	+	0.649615i	−0.990335	−	0.138694i	$-0.955710\pi$
$641$	−9.49564	+	16.4469i	−0.375055	+	0.649615i	0.615280	+	0.788309i	$0.289043\pi$
$642$		0			0
$643$	4.67366	+	8.09502i	0.184311	+	0.319237i	0.943344	−	0.331816i	$-0.107661\pi$
$643$	4.67366	+	8.09502i	0.184311	+	0.319237i	−0.759033	+	0.651052i	$0.774328\pi$
$644$		0			0
$645$	−0.873396	+	15.3853i	−0.0343899	+	0.605796i
$646$		0			0
$647$	33.6708			1.32373			0.661867	−	0.749621i	$-0.269764\pi$
$647$	33.6708			1.32373			0.661867	+	0.749621i	$0.269764\pi$
$648$		0			0
$649$	−23.2358			−0.912085
$650$		0			0
$651$	−0.0431837	+	0.760702i	−0.00169250	+	0.0298143i
$652$		0			0
$653$	−20.8887	−	36.1803i	−0.817437	−	1.41584i	−0.907564	−	0.419913i	$-0.862061\pi$
$653$	−20.8887	−	36.1803i	−0.817437	−	1.41584i	0.0901271	−	0.995930i	$-0.471273\pi$
$654$		0			0
$655$	2.42157	−	4.19429i	0.0946186	−	0.163884i
$656$		0			0
$657$	7.68836	+	0.875731i	0.299952	+	0.0341655i
$658$		0			0
$659$	−7.09902	+	12.2959i	−0.276539	+	0.478979i	−0.970522	−	0.241012i	$-0.922521\pi$
$659$	−7.09902	+	12.2959i	−0.276539	+	0.478979i	0.693984	+	0.719991i	$0.255854\pi$
$660$		0			0
$661$	17.2984	+	29.9616i	0.672828	+	1.16537i	0.977099	+	0.212787i	$0.0682541\pi$
$661$	17.2984	+	29.9616i	0.672828	+	1.16537i	−0.304270	+	0.952586i	$0.598413\pi$
$662$		0			0
$663$	20.7602	−	10.4644i	0.806260	−	0.406405i
$664$		0			0
$665$	−1.35412			−0.0525106
$666$		0			0
$667$	−35.1589			−1.36136
$668$		0			0
$669$	−20.4854	−	13.4304i	−0.792013	−	0.519248i
$670$		0			0
$671$	17.5033	+	30.3166i	0.675708	+	1.17036i
$672$		0			0
$673$	−16.2594	+	28.1622i	−0.626755	+	1.08557i	0.361444	+	0.932394i	$0.382284\pi$
$673$	−16.2594	+	28.1622i	−0.626755	+	1.08557i	−0.988199	+	0.153177i	$0.951049\pi$
$674$		0			0
$675$	−3.99518	−	3.32243i	−0.153774	−	0.127880i
$676$		0			0
$677$	−0.0149325	+	0.0258638i	−0.000573903	+	0.000994028i	−0.866312	−	0.499503i	$-0.833516\pi$
$677$	−0.0149325	+	0.0258638i	−0.000573903	+	0.000994028i	0.865738	+	0.500497i	$0.166849\pi$
$678$		0			0
$679$	1.23091	+	2.13200i	0.0472381	+	0.0818187i
$680$		0			0
$681$	−12.2349	−	8.02124i	−0.468841	−	0.307375i
$682$		0			0
$683$	11.1241			0.425653			0.212827	−	0.977090i	$-0.431733\pi$
$683$	11.1241			0.425653			0.212827	+	0.977090i	$0.431733\pi$
$684$		0			0
$685$	−11.1954			−0.427753
$686$		0			0
$687$	−31.7237	+	15.9907i	−1.21034	+	0.610083i
$688$		0			0
$689$	9.67177	+	16.7520i	0.368465	+	0.638200i
$690$		0			0
$691$	0.299324	−	0.518445i	0.0113868	−	0.0197226i	−0.860276	−	0.509829i	$-0.829709\pi$
$691$	0.299324	−	0.518445i	0.0113868	−	0.0197226i	0.871663	+	0.490106i	$0.163042\pi$
$692$		0			0
$693$	1.24245	+	2.85719i	0.0471968	+	0.108536i
$694$		0			0
$695$	1.43122	−	2.47894i	0.0542891	−	0.0940315i
$696$		0			0
$697$	−13.0907	−	22.6738i	−0.495847	−	0.858831i
$698$		0			0
$699$	−0.628589	+	11.0729i	−0.0237754	+	0.418816i
$700$		0			0
$701$	15.6784			0.592164			0.296082	−	0.955162i	$-0.404320\pi$
$701$	15.6784			0.592164			0.296082	+	0.955162i	$0.404320\pi$
$702$		0			0
$703$	−66.3348			−2.50186
$704$		0			0
$705$	1.26512	−	22.2857i	0.0476471	−	0.839328i
$706$		0			0
$707$	−1.87679	−	3.25070i	−0.0705840	−	0.122255i
$708$		0			0
$709$	−1.37112	+	2.37484i	−0.0514933	+	0.0891890i	−0.890623	−	0.454742i	$-0.849731\pi$
$709$	−1.37112	+	2.37484i	−0.0514933	+	0.0891890i	0.839130	+	0.543931i	$0.183065\pi$
$710$		0			0
$711$	4.26946	−	5.77023i	0.160117	−	0.216400i
$712$		0			0
$713$	−8.21601	+	14.2305i	−0.307692	+	0.532938i
$714$		0			0
$715$	6.79402	+	11.7676i	0.254082	+	0.440083i
$716$		0			0
$717$	−25.2050	+	12.7049i	−0.941299	+	0.474472i
$718$		0			0
$719$	−17.7056			−0.660307			−0.330153	−	0.943927i	$-0.607100\pi$
$719$	−17.7056			−0.660307			−0.330153	+	0.943927i	$0.607100\pi$
$720$		0			0
$721$	1.18480			0.0441241
$722$		0			0
$723$	24.3695	+	15.9768i	0.906311	+	0.594183i
$724$		0			0
$725$	−2.39701	−	4.15174i	−0.0890227	−	0.154192i
$726$		0			0
$727$	5.24167	−	9.07885i	0.194403	−	0.336716i	−0.752302	−	0.658819i	$-0.771056\pi$
$727$	5.24167	−	9.07885i	0.194403	−	0.336716i	0.946705	+	0.322103i	$0.104390\pi$
$728$		0			0
$729$	−25.4522	−	9.01036i	−0.942673	−	0.333717i
$730$		0			0
$731$	23.2445	−	40.2606i	0.859729	−	1.48909i
$732$		0			0
$733$	−7.20012	−	12.4710i	−0.265942	−	0.460626i	0.701868	−	0.712307i	$-0.252350\pi$
$733$	−7.20012	−	12.4710i	−0.265942	−	0.460626i	−0.967810	+	0.251682i	$0.919016\pi$
$734$		0			0
$735$	10.0837	+	6.61093i	0.371943	+	0.243848i
$736$		0			0
$737$	−29.0193			−1.06894
$738$		0			0
$739$	18.8564			0.693645			0.346822	−	0.937931i	$-0.387261\pi$
$739$	18.8564			0.693645			0.346822	+	0.937931i	$0.387261\pi$
$740$		0			0
$741$	−27.4023	+	13.8124i	−1.00665	+	0.507412i
$742$		0			0
$743$	22.9413	+	39.7355i	0.841635	+	1.45775i	0.888512	+	0.458854i	$0.151740\pi$
$743$	22.9413	+	39.7355i	0.841635	+	1.45775i	−0.0468766	+	0.998901i	$0.514927\pi$
$744$		0			0
$745$	−0.112619	+	0.195061i	−0.00412603	+	0.00714649i
$746$		0			0
$747$	8.52171	−	11.5172i	0.311793	−	0.421392i
$748$		0			0
$749$	0.771739	−	1.33669i	0.0281987	−	0.0488417i
$750$		0			0
$751$	10.5178	+	18.2174i	0.383802	+	0.664764i	0.991602	−	0.129326i	$-0.0412813\pi$
$751$	10.5178	+	18.2174i	0.383802	+	0.664764i	−0.607800	+	0.794090i	$0.707948\pi$
$752$		0			0
$753$	−2.31726	+	40.8198i	−0.0844458	+	1.48756i
$754$		0			0
$755$	−4.28100			−0.155801
$756$		0			0
$757$	38.8360			1.41152			0.705759	−	0.708452i	$-0.250606\pi$
$757$	38.8360			1.41152			0.705759	+	0.708452i	$0.250606\pi$
$758$		0			0
$759$	−3.80830	+	67.0852i	−0.138233	+	2.43504i
$760$		0			0
$761$	12.6425	+	21.8974i	0.458289	+	0.793780i	0.998871	−	0.0475116i	$-0.0151291\pi$
$761$	12.6425	+	21.8974i	0.458289	+	0.793780i	−0.540582	+	0.841292i	$0.681796\pi$
$762$		0			0
$763$	0.931774	−	1.61388i	0.0337325	−	0.0584264i
$764$		0			0
$765$	6.25113	+	14.3754i	0.226010	+	0.519743i
$766$		0			0
$767$	5.64191	−	9.77207i	0.203717	−	0.352849i
$768$		0			0
$769$	11.5249	+	19.9618i	0.415600	+	0.719840i	0.995491	−	0.0948539i	$-0.0302384\pi$
$769$	11.5249	+	19.9618i	0.415600	+	0.719840i	−0.579891	+	0.814694i	$0.696905\pi$
$770$		0			0
$771$	6.33864	−	3.19507i	0.228281	−	0.115068i
$772$		0			0
$773$	7.02605			0.252709			0.126355	−	0.991985i	$-0.459672\pi$
$773$	7.02605			0.252709			0.126355	+	0.991985i	$0.459672\pi$
$774$		0			0
$775$	−2.24056			−0.0804832
$776$		0			0
$777$	−2.73525	−	1.79325i	−0.0981267	−	0.0643324i
$778$		0			0
$779$	17.2790	+	29.9281i	0.619084	+	1.07229i
$780$		0			0
$781$	14.5351	−	25.1756i	0.520108	−	0.900854i
$782$		0			0
$783$	−19.1530	−	15.9278i	−0.684471	−	0.569213i
$784$		0			0
$785$	3.38302	−	5.85957i	0.120745	−	0.209137i
$786$		0			0
$787$	−7.73818	−	13.4029i	−0.275837	−	0.477763i	0.694509	−	0.719484i	$-0.255622\pi$
$787$	−7.73818	−	13.4029i	−0.275837	−	0.477763i	−0.970346	+	0.241721i	$0.922288\pi$
$788$		0			0
$789$	−35.1432	−	23.0401i	−1.25113	−	0.820249i
$790$		0			0
$791$	−3.16287			−0.112459
$792$		0			0
$793$	−17.0000			−0.603687
$794$		0			0
$795$	−11.6468	+	5.87071i	−0.413070	+	0.208213i
$796$		0			0
$797$	11.1871	+	19.3766i	0.396267	+	0.686354i	0.993262	−	0.115891i	$-0.0369723\pi$
$797$	11.1871	+	19.3766i	0.396267	+	0.686354i	−0.596995	+	0.802245i	$0.703639\pi$
$798$		0			0
$799$	−33.6698	+	58.3178i	−1.19115	+	2.06313i
$800$		0			0
$801$	−46.4378	−	5.28943i	−1.64080	−	0.186893i
$802$		0			0
$803$	6.82199	−	11.8160i	0.240743	−	0.416979i
$804$		0			0
$805$	−0.719949	−	1.24699i	−0.0253749	−	0.0439506i
$806$		0			0
$807$	−1.09316	+	19.2565i	−0.0384810	+	0.677863i
$808$		0			0
$809$	−2.04044			−0.0717381			−0.0358690	−	0.999356i	$-0.511420\pi$
$809$	−2.04044			−0.0717381			−0.0358690	+	0.999356i	$0.511420\pi$
$810$		0			0
$811$	48.3926			1.69929			0.849647	−	0.527352i	$-0.176815\pi$
$811$	48.3926			1.69929			0.849647	+	0.527352i	$0.176815\pi$
$812$		0			0
$813$	−2.73694	+	48.2126i	−0.0959888	+	1.69089i
$814$		0			0
$815$	−1.48705	−	2.57565i	−0.0520892	−	0.0902211i
$816$		0			0
$817$	−30.6814	+	53.1417i	−1.07341	+	1.85919i
$818$		0			0
$819$	−1.50330	−	0.171231i	−0.0525297	−	0.00598331i
$820$		0			0
$821$	−0.930830	+	1.61224i	−0.0324862	+	0.0562677i	−0.881811	−	0.471602i	$-0.843676\pi$
$821$	−0.930830	+	1.61224i	−0.0324862	+	0.0562677i	0.849325	+	0.527870i	$0.177009\pi$
$822$		0			0
$823$	21.6786	+	37.5484i	0.755667	+	1.30885i	0.945042	+	0.326949i	$0.106021\pi$
$823$	21.6786	+	37.5484i	0.755667	+	1.30885i	−0.189375	+	0.981905i	$0.560646\pi$
$824$		0			0
$825$	−8.18140	+	4.12393i	−0.284840	+	0.143577i
$826$		0			0
$827$	−10.6315			−0.369694			−0.184847	−	0.982767i	$-0.559179\pi$
$827$	−10.6315			−0.369694			−0.184847	+	0.982767i	$0.559179\pi$
$828$		0			0
$829$	37.5109			1.30281			0.651404	−	0.758731i	$-0.274180\pi$
$829$	37.5109			1.30281			0.651404	+	0.758731i	$0.274180\pi$
$830$		0			0
$831$	7.94216	+	5.20693i	0.275511	+	0.180626i
$832$		0			0
$833$	−18.1876	−	31.5019i	−0.630164	−	1.09148i
$834$		0			0
$835$	−7.20313	+	12.4762i	−0.249274	+	0.431756i
$836$		0			0
$837$	−10.9225	+	4.03011i	−0.377536	+	0.139301i
$838$		0			0
$839$	13.6584	−	23.6571i	0.471541	−	0.816733i	−0.527929	−	0.849289i	$-0.677031\pi$
$839$	13.6584	−	23.6571i	0.471541	−	0.816733i	0.999470	+	0.0325554i	$0.0103645\pi$
$840$		0			0
$841$	3.00868	+	5.21119i	0.103748	+	0.179696i
$842$		0			0
$843$	6.20401	+	4.06739i	0.213677	+	0.140088i
$844$		0			0
$845$	6.40135			0.220213
$846$		0			0
$847$	3.33390			0.114554
$848$		0			0
$849$	−1.04779	+	0.528150i	−0.0359600	+	0.0181261i
$850$		0			0
$851$	−35.2684	−	61.0866i	−1.20898	−	2.09402i
$852$		0			0
$853$	−27.3545	+	47.3793i	−0.936599	+	1.62224i	−0.164843	+	0.986320i	$0.552712\pi$
$853$	−27.3545	+	47.3793i	−0.936599	+	1.62224i	−0.771757	+	0.635918i	$0.780622\pi$
$854$		0			0
$855$	−8.25113	−	18.9747i	−0.282183	−	0.648920i
$856$		0			0
$857$	26.8252	−	46.4626i	0.916332	−	1.58713i	0.111391	−	0.993777i	$-0.464469\pi$
$857$	26.8252	−	46.4626i	0.916332	−	1.58713i	0.804940	−	0.593356i	$-0.202197\pi$
$858$		0			0
$859$	−28.1405	−	48.7407i	−0.960140	−	1.66301i	−0.722140	−	0.691747i	$-0.756841\pi$
$859$	−28.1405	−	48.7407i	−0.960140	−	1.66301i	−0.238000	−	0.971265i	$-0.576492\pi$
$860$		0			0
$861$	−0.0965721	+	1.70117i	−0.00329117	+	0.0579756i
$862$		0			0
$863$	2.56199			0.0872111			0.0436056	−	0.999049i	$-0.486116\pi$
$863$	2.56199			0.0872111			0.0436056	+	0.999049i	$0.486116\pi$
$864$		0			0
$865$	20.5023			0.697098
$866$		0			0
$867$	1.01143	−	17.8168i	0.0343499	−	0.605091i
$868$		0			0
$869$	−6.32823	−	10.9608i	−0.214670	−	0.371820i
$870$		0			0
$871$	7.04619	−	12.2044i	0.238751	−	0.413529i
$872$		0			0
$873$	−22.3743	+	30.2392i	−0.757257	+	1.02344i
$874$		0			0
$875$	0.0981673	−	0.170031i	0.00331866	−	0.00574809i
$876$		0			0
$877$	7.63662	+	13.2270i	0.257870	+	0.446645i	0.965671	−	0.259768i	$-0.0836459\pi$
$877$	7.63662	+	13.2270i	0.257870	+	0.446645i	−0.707801	+	0.706412i	$0.750313\pi$
$878$		0			0
$879$	10.2790	−	5.18125i	0.346702	−	0.174759i
$880$		0			0
$881$	2.62392			0.0884022			0.0442011	−	0.999023i	$-0.485926\pi$
$881$	2.62392			0.0884022			0.0442011	+	0.999023i	$0.485926\pi$
$882$		0			0
$883$	−25.8496			−0.869908			−0.434954	−	0.900453i	$-0.643235\pi$
$883$	−25.8496			−0.869908			−0.434954	+	0.900453i	$0.643235\pi$
$884$		0			0
$885$	6.36280	+	4.17149i	0.213883	+	0.140223i
$886$		0			0
$887$	−2.84117	−	4.92106i	−0.0953973	−	0.165233i	0.814377	−	0.580336i	$-0.197079\pi$
$887$	−2.84117	−	4.92106i	−0.0953973	−	0.165233i	−0.909774	+	0.415103i	$0.863745\pi$
$888$		0			0
$889$	−0.670440	+	1.16124i	−0.0224858	+	0.0389466i
$890$		0			0
$891$	−32.4658	+	34.8197i	−1.08764	+	1.16650i
$892$		0			0
$893$	44.4421	−	76.9761i	1.48720	−	2.57591i
$894$		0			0
$895$	−0.923944	−	1.60032i	−0.0308840	−	0.0534927i
$896$		0			0
$897$	−27.2887	−	17.8906i	−0.911143	−	0.597351i
$898$		0			0
$899$	−10.7413			−0.358242
$900$		0			0
$901$	39.3473			1.31085
$902$		0			0
$903$	−2.70171	+	1.36183i	−0.0899074	+	0.0453189i
$904$		0			0
$905$	5.00434	+	8.66777i	0.166350	+	0.288127i
$906$		0			0
$907$	18.3802	−	31.8354i	0.610304	−	1.05708i	−0.380885	−	0.924622i	$-0.624381\pi$
$907$	18.3802	−	31.8354i	0.610304	−	1.05708i	0.991189	−	0.132455i	$-0.0422859\pi$
$908$		0			0
$909$	34.1145	−	46.1062i	1.13151	−	1.52924i
$910$		0			0
$911$	5.03554	−	8.72181i	0.166835	−	0.288966i	−0.770470	−	0.637476i	$-0.779979\pi$
$911$	5.03554	−	8.72181i	0.166835	−	0.288966i	0.937305	+	0.348509i	$0.113312\pi$
$912$		0			0
$913$	−12.6309	−	21.8774i	−0.418023	−	0.724038i
$914$		0			0
$915$	0.649662	−	11.4441i	0.0214772	−	0.378331i
$916$		0			0
$917$	0.950877			0.0314007
$918$		0			0
$919$	16.7143			0.551353			0.275676	−	0.961251i	$-0.411098\pi$
$919$	16.7143			0.551353			0.275676	+	0.961251i	$0.411098\pi$
$920$		0			0
$921$	0.480355	−	8.46170i	0.0158282	−	0.278822i
$922$		0			0
$923$	7.05858	+	12.2258i	0.232336	+	0.402418i
$924$		0			0
$925$	4.80895	−	8.32935i	0.158117	−	0.273867i
$926$		0			0
$927$	7.21937	+	16.6020i	0.237115	+	0.545281i
$928$		0			0
$929$	26.1175	−	45.2368i	0.856888	−	1.48417i	−0.0179953	−	0.999838i	$-0.505728\pi$
$929$	26.1175	−	45.2368i	0.856888	−	1.48417i	0.874883	−	0.484335i	$-0.160938\pi$
$930$		0			0
$931$	24.0066	+	41.5807i	0.786785	+	1.36275i
$932$		0			0
$933$	39.6298	−	19.9759i	1.29742	−	0.653980i
$934$		0			0
$935$	27.6398			0.903919
$936$		0			0
$937$	4.94139			0.161428			0.0807141	−	0.996737i	$-0.474280\pi$
$937$	4.94139			0.161428			0.0807141	+	0.996737i	$0.474280\pi$
$938$		0			0
$939$	43.3309	+	28.4080i	1.41405	+	0.927059i
$940$		0			0
$941$	−1.13323	−	1.96280i	−0.0369421	−	0.0639856i	0.846963	−	0.531652i	$-0.178428\pi$
$941$	−1.13323	−	1.96280i	−0.0369421	−	0.0639856i	−0.883905	+	0.467666i	$0.845095\pi$
$942$		0			0
$943$	−18.3735	+	31.8239i	−0.598325	+	1.03633i
$944$		0			0
$945$	0.172720	−	1.00546i	0.00561858	−	0.0327075i
$946$		0			0
$947$	−18.0336	+	31.2351i	−0.586014	+	1.01501i	0.408734	+	0.912653i	$0.365970\pi$
$947$	−18.0336	+	31.2351i	−0.586014	+	1.01501i	−0.994748	+	0.102352i	$0.967363\pi$
$948$		0			0
$949$	3.31291	+	5.73812i	0.107542	+	0.186267i
$950$		0			0
$951$	30.0950	+	19.7305i	0.975899	+	0.639805i
$952$		0			0
$953$	24.2146			0.784389			0.392194	−	0.919882i	$-0.371716\pi$
$953$	24.2146			0.784389			0.392194	+	0.919882i	$0.371716\pi$
$954$		0			0
$955$	−1.37812			−0.0445950
$956$		0			0
$957$	−39.2218	+	19.7702i	−1.26786	+	0.639080i
$958$		0			0
$959$	−1.09902	−	1.90356i	−0.0354892	−	0.0614691i
$960$		0			0
$961$	12.9900	−	22.4993i	0.419031	−	0.725783i
$962$		0			0
$963$	23.4329	+	2.66909i	0.755114	+	0.0860101i
$964$		0			0
$965$	7.01397	−	12.1486i	0.225788	−	0.391076i
$966$		0			0
$967$	23.2348	+	40.2438i	0.747180	+	1.29415i	0.949169	+	0.314766i	$0.101926\pi$
$967$	23.2348	+	40.2438i	0.747180	+	1.29415i	−0.201989	+	0.979388i	$0.564741\pi$
$968$		0			0
$969$	−3.53780	+	62.3202i	−0.113651	+	2.00201i
$970$		0			0
$971$	49.4589			1.58721			0.793607	−	0.608431i	$-0.208201\pi$
$971$	49.4589			1.58721			0.793607	+	0.608431i	$0.208201\pi$
$972$		0			0
$973$	0.561995			0.0180167
$974$		0			0
$975$	0.252171	−	4.44211i	0.00807592	−	0.142261i
$976$		0			0
$977$	−10.3239	−	17.8815i	−0.330290	−	0.572079i	0.652279	−	0.757979i	$-0.273813\pi$
$977$	−10.3239	−	17.8815i	−0.330290	−	0.572079i	−0.982569	+	0.185900i	$0.940480\pi$
$978$		0			0
$979$	−41.2049	+	71.3690i	−1.31691	+	2.28096i
$980$		0			0
$981$	28.2921	+	3.22257i	0.903298	+	0.102889i
$982$		0			0
$983$	0.288827	−	0.500264i	0.00921216	−	0.0159559i	−0.861383	−	0.507957i	$-0.830401\pi$
$983$	0.288827	−	0.500264i	0.00921216	−	0.0159559i	0.870595	+	0.492001i	$0.163734\pi$
$984$		0			0
$985$	−2.13189	−	3.69255i	−0.0679277	−	0.117654i
$986$		0			0
$987$	3.91345	−	1.97262i	0.124566	−	0.0627891i
$988$		0			0
$989$	−65.2498			−2.07482
$990$		0			0
$991$	31.5820			1.00324			0.501618	−	0.865089i	$-0.332738\pi$
$991$	31.5820			1.00324			0.501618	+	0.865089i	$0.332738\pi$
$992$		0			0
$993$	33.1579	+	21.7385i	1.05224	+	0.689852i
$994$		0			0
$995$	−0.345516	−	0.598451i	−0.0109536	−	0.0189722i
$996$		0			0
$997$	5.31858	−	9.21205i	0.168441	−	0.291749i	−0.769431	−	0.638730i	$-0.779460\pi$
$997$	5.31858	−	9.21205i	0.168441	−	0.291749i	0.937872	+	0.346981i	$0.112793\pi$
$998$		0			0
$999$	8.46108	−	49.2547i	0.267697	−	1.55835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.q.i.961.3	yes	8
3.2	odd	2		4320.2.q.k.2881.2		8
4.3	odd	2		1440.2.q.n.961.2	yes	8
9.4	even	3	inner	1440.2.q.i.481.3	✓	8
9.5	odd	6		4320.2.q.k.1441.2		8
12.11	even	2		4320.2.q.i.2881.3		8
36.23	even	6		4320.2.q.i.1441.3		8
36.31	odd	6		1440.2.q.n.481.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.i.481.3	✓	8	9.4	even	3	inner
1440.2.q.i.961.3	yes	8	1.1	even	1	trivial
1440.2.q.n.481.2	yes	8	36.31	odd	6
1440.2.q.n.961.2	yes	8	4.3	odd	2
4320.2.q.i.1441.3		8	36.23	even	6
4320.2.q.i.2881.3		8	12.11	even	2
4320.2.q.k.1441.2		8	9.5	odd	6
4320.2.q.k.2881.2		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0981673 - 1.72927i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.0981673 + 0.170031i) q^{7} +(-2.98073 - 0.339515i) q^{9} +O(q^{10})\)	\(q+(0.0981673 - 1.72927i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.0981673 + 0.170031i) q^{7} +(-2.98073 - 0.339515i) q^{9} +(-2.64484 + 4.58100i) q^{11} +(-1.28439 - 2.22463i) q^{13} +(1.54667 - 0.779618i) q^{15} -5.22524 q^{17} +6.89701 q^{19} +(0.284392 + 0.186449i) q^{21} +(3.66695 + 6.35135i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.879722 + 5.12114i) q^{27} +(-2.39701 + 4.15174i) q^{29} +(1.12028 + 1.94038i) q^{31} +(7.66213 + 5.02334i) q^{33} -0.196335 q^{35} -9.61791 q^{37} +(-3.97307 + 2.00267i) q^{39} +(2.50529 + 4.33929i) q^{41} +(-4.44851 + 7.70504i) q^{43} +(-1.19633 - 2.75114i) q^{45} +(6.44368 - 11.1608i) q^{47} +(3.48073 + 6.02879i) q^{49} +(-0.512948 + 9.03583i) q^{51} -7.53024 q^{53} -5.28968 q^{55} +(0.677061 - 11.9268i) q^{57} +(2.19633 + 3.80416i) q^{59} +(3.30895 - 5.73128i) q^{61} +(0.350338 - 0.473486i) q^{63} +(1.28439 - 2.22463i) q^{65} +(2.74301 + 4.75103i) q^{67} +(11.3431 - 5.71764i) q^{69} -5.49566 q^{71} -2.57936 q^{73} +(1.44851 + 0.949649i) q^{75} +(-0.519274 - 0.899408i) q^{77} +(-1.19633 + 2.07211i) q^{79} +(8.76946 + 2.02400i) q^{81} +(-2.38785 + 4.13587i) q^{83} +(-2.61262 - 4.52519i) q^{85} +(6.94416 + 4.55264i) q^{87} +15.5794 q^{89} +0.504341 q^{91} +(3.46541 - 1.74678i) q^{93} +(3.44851 + 5.97299i) q^{95} +(6.26946 - 10.8590i) q^{97} +(9.43886 - 12.7567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 8 * q^9	\( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 8 q^{9} - 2 q^{11} - 4 q^{15} - 8 q^{17} + 28 q^{19} - 8 q^{21} + 6 q^{23} - 4 q^{25} - 14 q^{27} + 8 q^{29} + 2 q^{31} + 8 q^{33} + 4 q^{35} - 32 q^{37} - 6 q^{39} - 8 q^{41} - 22 q^{43} - 4 q^{45} + 8 q^{47} + 12 q^{49} + 14 q^{51} - 8 q^{53} - 4 q^{55} - 16 q^{57} + 12 q^{59} + 4 q^{61} - 8 q^{63} + 12 q^{69} - 60 q^{71} + 56 q^{73} - 2 q^{75} - 20 q^{77} - 4 q^{79} + 28 q^{81} + 22 q^{83} - 4 q^{85} + 58 q^{87} + 48 q^{89} - 12 q^{91} - 8 q^{93} + 14 q^{95} + 8 q^{97} + 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 8 * q^9 - 2 * q^11 - 4 * q^15 - 8 * q^17 + 28 * q^19 - 8 * q^21 + 6 * q^23 - 4 * q^25 - 14 * q^27 + 8 * q^29 + 2 * q^31 + 8 * q^33 + 4 * q^35 - 32 * q^37 - 6 * q^39 - 8 * q^41 - 22 * q^43 - 4 * q^45 + 8 * q^47 + 12 * q^49 + 14 * q^51 - 8 * q^53 - 4 * q^55 - 16 * q^57 + 12 * q^59 + 4 * q^61 - 8 * q^63 + 12 * q^69 - 60 * q^71 + 56 * q^73 - 2 * q^75 - 20 * q^77 - 4 * q^79 + 28 * q^81 + 22 * q^83 - 4 * q^85 + 58 * q^87 + 48 * q^89 - 12 * q^91 - 8 * q^93 + 14 * q^95 + 8 * q^97 + 2 * q^99

Introduction

L-functions

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