LMFDB - Embedded newform 1040.2.dh.a.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(289,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("1040.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.dh (of order $6$, 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 $ x^12 - 8x^10 + 54x^8 - 78x^6 + 92x^4 - 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.3
Root			$-1.02826 + 0.593667i$ of defining polynomial
Character	$\chi$	$=$	1040.529
Dual form			1040.2.dh.a.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.298874 - 0.172555i) q^{3} +(1.44045 - 1.71029i) q^{5} +(-1.75765 + 1.01478i) q^{7} +(-1.44045 - 2.49493i) q^{9} +O(q^{10})$	\(q+(-0.298874 - 0.172555i) q^{3} +(1.44045 - 1.71029i) q^{5} +(-1.75765 + 1.01478i) q^{7} +(-1.44045 - 2.49493i) q^{9} +(1.94045 - 3.36096i) q^{11} +(2.96232 + 2.05540i) q^{13} +(-0.725633 + 0.262606i) q^{15} +(-4.71996 + 2.72507i) q^{17} +(-2.94045 - 5.09301i) q^{19} +0.700420 q^{21} +(0.298874 + 0.172555i) q^{23} +(-0.850210 - 4.92718i) q^{25} +2.02956i q^{27} +(1.50000 - 2.59808i) q^{29} -1.18048 q^{31} +(-1.15990 + 0.669668i) q^{33} +(-0.796234 + 4.46783i) q^{35} +(-4.71996 - 2.72507i) q^{37} +(-0.530689 - 1.12547i) q^{39} +(-0.0902394 + 0.156299i) q^{41} +(-1.15990 + 0.669668i) q^{43} +(-6.34196 - 1.13023i) q^{45} -12.2807i q^{47} +(-1.44045 + 2.49493i) q^{49} +1.88090 q^{51} -2.42636i q^{53} +(-2.95310 - 8.16003i) q^{55} +2.02956i q^{57} +(3.53069 + 6.11533i) q^{59} +(-3.38090 - 5.85589i) q^{61} +(5.06361 + 2.92347i) q^{63} +(7.78241 - 2.10573i) q^{65} +(-3.81417 - 2.20211i) q^{67} +(-0.0595504 - 0.103144i) q^{69} +(-0.940450 - 1.62891i) q^{71} -8.86014i q^{73} +(-0.596104 + 1.61932i) q^{75} +7.87651i q^{77} +11.1805 q^{79} +(-3.97114 + 6.87821i) q^{81} +7.83540i q^{83} +(-2.13820 + 11.9979i) q^{85} +(-0.896622 + 0.517665i) q^{87} +(6.12093 - 10.6018i) q^{89} +(-7.29249 - 0.606582i) q^{91} +(0.352814 + 0.203698i) q^{93} +(-12.9461 - 2.30719i) q^{95} +(-5.02801 + 2.90292i) q^{97} -11.1805 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^5 + 6 * q^9	$ 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65} - 24 q^{69} + 12 q^{71} - 2 q^{75} + 104 q^{79} + 14 q^{81} + 21 q^{85} + 20 q^{89} + 44 q^{91} - 20 q^{95} - 104 q^{99}+O(q^{100}) $ 12 * q - 6 * q^5 + 6 * q^9 + 4 * q^15 - 12 * q^19 - 8 * q^21 - 2 * q^25 + 18 * q^29 + 16 * q^31 - 10 * q^35 + 32 * q^39 + 14 * q^41 - 29 * q^45 + 6 * q^49 - 24 * q^51 + 26 * q^55 + 4 * q^59 + 6 * q^61 + 23 * q^65 - 24 * q^69 + 12 * q^71 - 2 * q^75 + 104 * q^79 + 14 * q^81 + 21 * q^85 + 20 * q^89 + 44 * q^91 - 20 * q^95 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.298874	−	0.172555i	−0.172555	−	0.0996247i	0.411235	−	0.911529i	$-0.365098\pi$
$3$	−0.298874	−	0.172555i	−0.172555	−	0.0996247i	−0.583790	+	0.811905i	$0.698431\pi$
$4$		0			0
$5$	1.44045	−	1.71029i	0.644189	−	0.764867i
$5$	1.44045	−	1.71029i	0.644189	−	0.764867i
$6$		0			0
$7$	−1.75765	+	1.01478i	−0.664328	+	0.383550i	−0.793924	−	0.608017i	$-0.791965\pi$
$7$	−1.75765	+	1.01478i	−0.664328	+	0.383550i	0.129596	+	0.991567i	$0.458632\pi$
$8$		0			0
$9$	−1.44045	−	2.49493i	−0.480150	−	0.831644i
$10$		0			0
$11$	1.94045	−	3.36096i	0.585068	−	1.01337i	−0.409799	−	0.912176i	$-0.634401\pi$
$11$	1.94045	−	3.36096i	0.585068	−	1.01337i	0.994867	−	0.101191i	$-0.0322653\pi$
$12$		0			0
$13$	2.96232	+	2.05540i	0.821599	+	0.570066i
$13$	2.96232	+	2.05540i	0.821599	+	0.570066i
$14$		0			0
$15$	−0.725633	+	0.262606i	−0.187358	+	0.0678045i
$16$		0			0
$17$	−4.71996	+	2.72507i	−1.14476	+	0.660927i	−0.947605	−	0.319445i	$-0.896503\pi$
$17$	−4.71996	+	2.72507i	−1.14476	+	0.660927i	−0.197155	+	0.980372i	$0.563170\pi$
$18$		0			0
$19$	−2.94045	−	5.09301i	−0.674585	−	1.16842i	−0.976590	−	0.215110i	$-0.930989\pi$
$19$	−2.94045	−	5.09301i	−0.674585	−	1.16842i	0.302005	−	0.953306i	$-0.402344\pi$
$20$		0			0
$21$	0.700420			0.152844
$22$		0			0
$23$	0.298874	+	0.172555i	0.0623195	+	0.0359802i	0.530836	−	0.847475i	$-0.321878\pi$
$23$	0.298874	+	0.172555i	0.0623195	+	0.0359802i	−0.468516	+	0.883455i	$0.655211\pi$
$24$		0			0
$25$	−0.850210	−	4.92718i	−0.170042	−	0.985437i
$26$		0			0
$27$			2.02956i			0.390588i
$28$		0			0
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$	−1.18048			−0.212020			−0.106010	−	0.994365i	$-0.533808\pi$
$31$	−1.18048			−0.212020			−0.106010	+	0.994365i	$0.533808\pi$
$32$		0			0
$33$	−1.15990	+	0.669668i	−0.201913	+	0.116574i
$34$		0			0
$35$	−0.796234	+	4.46783i	−0.134588	+	0.755201i
$36$		0			0
$37$	−4.71996	−	2.72507i	−0.775957	−	0.447999i	0.0590384	−	0.998256i	$-0.481197\pi$
$37$	−4.71996	−	2.72507i	−0.775957	−	0.447999i	−0.834996	+	0.550257i	$0.814530\pi$
$38$		0			0
$39$	−0.530689	−	1.12547i	−0.0849782	−	0.180219i
$40$		0			0
$41$	−0.0902394	+	0.156299i	−0.0140930	+	0.0244098i	−0.872986	−	0.487745i	$-0.837819\pi$
$41$	−0.0902394	+	0.156299i	−0.0140930	+	0.0244098i	0.858893	+	0.512155i	$0.171153\pi$
$42$		0			0
$43$	−1.15990	+	0.669668i	−0.176883	+	0.102123i	−0.585827	−	0.810436i	$-0.699230\pi$
$43$	−1.15990	+	0.669668i	−0.176883	+	0.102123i	0.408944	+	0.912559i	$0.365897\pi$
$44$		0			0
$45$	−6.34196	−	1.13023i	−0.945404	−	0.168485i
$46$		0			0
$47$		−	12.2807i		−	1.79133i	−0.444731	−	0.895664i	$-0.646701\pi$
$47$		−	12.2807i		−	1.79133i	0.444731	−	0.895664i	$-0.353299\pi$
$48$		0			0
$49$	−1.44045	+	2.49493i	−0.205779	+	0.356419i
$50$		0			0
$51$	1.88090			0.263379
$52$		0			0
$53$		−	2.42636i		−	0.333286i	−0.986017	−	0.166643i	$-0.946707\pi$
$53$		−	2.42636i		−	0.333286i	0.986017	−	0.166643i	$-0.0532928\pi$
$54$		0			0
$55$	−2.95310	−	8.16003i	−0.398197	−	1.10030i
$56$		0			0
$57$			2.02956i			0.268821i
$58$		0			0
$59$	3.53069	+	6.11533i	0.459657	+	0.796149i	0.998943	−	0.0459741i	$-0.0146392\pi$
$59$	3.53069	+	6.11533i	0.459657	+	0.796149i	−0.539286	+	0.842123i	$0.681306\pi$
$60$		0			0
$61$	−3.38090	−	5.85589i	−0.432880	−	0.749770i	0.564240	−	0.825611i	$-0.309169\pi$
$61$	−3.38090	−	5.85589i	−0.432880	−	0.749770i	−0.997120	+	0.0758409i	$0.975836\pi$
$62$		0			0
$63$	5.06361	+	2.92347i	0.637954	+	0.368323i
$64$		0			0
$65$	7.78241	−	2.10573i	0.965289	−	0.261183i
$66$		0			0
$67$	−3.81417	−	2.20211i	−0.465975	−	0.269031i	0.248578	−	0.968612i	$-0.420037\pi$
$67$	−3.81417	−	2.20211i	−0.465975	−	0.269031i	−0.714553	+	0.699581i	$0.753370\pi$
$68$		0			0
$69$	−0.0595504	−	0.103144i	−0.00716903	−	0.0124171i
$70$		0			0
$71$	−0.940450	−	1.62891i	−0.111611	−	0.193316i	0.804809	−	0.593534i	$-0.202268\pi$
$71$	−0.940450	−	1.62891i	−0.111611	−	0.193316i	−0.916420	+	0.400218i	$0.868934\pi$
$72$		0			0
$73$		−	8.86014i		−	1.03700i	−0.855077	−	0.518501i	$-0.826490\pi$
$73$		−	8.86014i		−	1.03700i	0.855077	−	0.518501i	$-0.173510\pi$
$74$		0			0
$75$	−0.596104	+	1.61932i	−0.0688322	+	0.186982i
$76$		0			0
$77$			7.87651i			0.897611i
$78$		0			0
$79$	11.1805			1.25790			0.628951	−	0.777445i	$-0.283485\pi$
$79$	11.1805			1.25790			0.628951	+	0.777445i	$0.283485\pi$
$80$		0			0
$81$	−3.97114	+	6.87821i	−0.441238	+	0.764246i
$82$		0			0
$83$			7.83540i			0.860047i	0.902818	+	0.430024i	$0.141495\pi$
$83$			7.83540i			0.860047i	−0.902818	+	0.430024i	$0.858505\pi$
$84$		0			0
$85$	−2.13820	+	11.9979i	−0.231920	+	1.30135i
$86$		0			0
$87$	−0.896622	+	0.517665i	−0.0961280	+	0.0554995i
$88$		0			0
$89$	6.12093	−	10.6018i	0.648817	−	1.12378i	−0.334589	−	0.942364i	$-0.608597\pi$
$89$	6.12093	−	10.6018i	0.648817	−	1.12378i	0.983406	−	0.181420i	$-0.0580693\pi$
$90$		0			0
$91$	−7.29249	−	0.606582i	−0.764460	−	0.0635870i
$92$		0			0
$93$	0.352814	+	0.203698i	0.0365852	+	0.0211224i
$94$		0			0
$95$	−12.9461	−	2.30719i	−1.32824	−	0.236713i
$96$		0			0
$97$	−5.02801	+	2.90292i	−0.510517	+	0.294747i	−0.733046	−	0.680179i	$-0.761902\pi$
$97$	−5.02801	+	2.90292i	−0.510517	+	0.294747i	0.222529	+	0.974926i	$0.428569\pi$
$98$		0			0
$99$	−11.1805			−1.12368
$100$		0			0
$101$	2.97114	−	5.14616i	0.295639	−	0.512062i	−0.679494	−	0.733681i	$-0.737801\pi$
$101$	2.97114	−	5.14616i	0.295639	−	0.512062i	0.975133	+	0.221619i	$0.0711340\pi$
$102$		0			0
$103$		−	6.43378i		−	0.633939i	−0.948436	−	0.316970i	$-0.897335\pi$
$103$		−	6.43378i		−	0.633939i	0.948436	−	0.316970i	$-0.102665\pi$
$104$		0			0
$105$	1.00892	−	1.19792i	0.0984605	−	0.116905i
$106$		0			0
$107$	15.3106	+	8.83959i	1.48013	+	0.854555i	0.999747	−	0.0225015i	$-0.00716305\pi$
$107$	15.3106	+	8.83959i	1.48013	+	0.854555i	0.480387	+	0.877057i	$0.340496\pi$
$108$		0			0
$109$	−5.76180			−0.551880			−0.275940	−	0.961175i	$-0.588989\pi$
$109$	−5.76180			−0.551880			−0.275940	+	0.961175i	$0.588989\pi$
$110$		0			0
$111$	0.940450	+	1.62891i	0.0892635	+	0.154609i
$112$		0			0
$113$	4.12222	−	2.37996i	0.387785	−	0.223888i	−0.293415	−	0.955985i	$-0.594792\pi$
$113$	4.12222	−	2.37996i	0.387785	−	0.223888i	0.681200	+	0.732097i	$0.261458\pi$
$114$		0			0
$115$	0.725633	−	0.262606i	0.0676656	−	0.0244881i
$116$		0			0
$117$	0.861026	−	10.3515i	0.0796019	−	0.956995i
$118$		0			0
$119$	5.53069	−	9.57943i	0.506997	−	0.878145i
$120$		0			0
$121$	−2.03069	−	3.51726i	−0.184608	−	0.319751i
$122$		0			0
$123$	0.0539404	−	0.0311425i	0.00486365	−	0.00280803i
$124$		0			0
$125$	−9.65162	−	5.64325i	−0.863267	−	0.504748i
$126$		0			0
$127$	−14.4679	−	8.35307i	−1.28382	−	0.741215i	−0.306277	−	0.951942i	$-0.599083\pi$
$127$	−14.4679	−	8.35307i	−1.28382	−	0.741215i	−0.977545	+	0.210728i	$0.932417\pi$
$128$		0			0
$129$	0.462218			0.0406961
$130$		0			0
$131$	−10.0000			−0.873704			−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000			−0.873704			−0.436852	+	0.899533i	$0.643907\pi$
$132$		0			0
$133$	10.3365	+	5.96781i	0.896292	+	0.517475i
$134$		0			0
$135$	3.47114	+	2.92347i	0.298748	+	0.251613i
$136$		0			0
$137$	1.71288	−	0.988931i	0.146341	−	0.0844901i	−0.425042	−	0.905174i	$-0.639741\pi$
$137$	1.71288	−	0.988931i	0.146341	−	0.0844901i	0.571383	+	0.820684i	$0.306407\pi$
$138$		0			0
$139$	−4.35021	−	7.53478i	−0.368980	−	0.639092i	0.620426	−	0.784265i	$-0.286960\pi$
$139$	−4.35021	−	7.53478i	−0.368980	−	0.639092i	−0.989406	+	0.145173i	$0.953626\pi$
$140$		0			0
$141$	−2.11910	+	3.67039i	−0.178460	+	0.309103i
$142$		0			0
$143$	12.6563	−	5.96781i	1.05838	−	0.499053i
$144$		0			0
$145$	−2.28280	−	6.30784i	−0.189576	−	0.523837i
$146$		0			0
$147$	0.861026	−	0.497113i	0.0710162	−	0.0410012i
$148$		0			0
$149$	11.1516	+	19.3152i	0.913576	+	1.58236i	0.808973	+	0.587846i	$0.200024\pi$
$149$	11.1516	+	19.3152i	0.913576	+	1.58236i	0.104603	+	0.994514i	$0.466643\pi$
$150$		0			0
$151$	19.1626			1.55943			0.779717	−	0.626132i	$-0.215363\pi$
$151$	19.1626			1.55943			0.779717	+	0.626132i	$0.215363\pi$
$152$		0			0
$153$	13.5977	+	7.85066i	1.09931	+	0.634688i
$154$		0			0
$155$	−1.70042	+	2.01897i	−0.136581	+	0.162167i
$156$		0			0
$157$		−	6.20265i		−	0.495025i	−0.968885	−	0.247513i	$-0.920387\pi$
$157$		−	6.20265i		−	0.495025i	0.968885	−	0.247513i	$-0.0796132\pi$
$158$		0			0
$159$	−0.418681	+	0.725176i	−0.0332035	+	0.0575102i
$160$		0			0
$161$	−0.700420			−0.0552008
$162$		0			0
$163$	10.3365	−	5.96781i	0.809621	−	0.467435i	−0.0372032	−	0.999308i	$-0.511845\pi$
$163$	10.3365	−	5.96781i	0.809621	−	0.467435i	0.846824	+	0.531873i	$0.178512\pi$
$164$		0			0
$165$	−0.525447	+	2.94839i	−0.0409060	+	0.229532i
$166$		0			0
$167$	−1.75765	−	1.01478i	−0.136011	−	0.0785259i	0.430451	−	0.902614i	$-0.358355\pi$
$167$	−1.75765	−	1.01478i	−0.136011	−	0.0785259i	−0.566461	+	0.824088i	$0.691688\pi$
$168$		0			0
$169$	4.55063	+	12.1775i	0.350048	+	0.936732i
$170$		0			0
$171$	−8.47114	+	14.6724i	−0.647804	+	1.12203i
$172$		0			0
$173$	−1.15990	+	0.669668i	−0.0881855	+	0.0509139i	−0.543444	−	0.839445i	$-0.682880\pi$
$173$	−1.15990	+	0.669668i	−0.0881855	+	0.0509139i	0.455259	+	0.890359i	$0.349547\pi$
$174$		0			0
$175$	6.49437	+	7.79748i	0.490928	+	0.589434i
$176$		0			0
$177$		−	2.43695i		−	0.183173i
$178$		0			0
$179$	−10.1120	+	17.5145i	−0.755807	+	1.30910i	0.189165	+	0.981945i	$0.439422\pi$
$179$	−10.1120	+	17.5145i	−0.755807	+	1.30910i	−0.944972	+	0.327151i	$0.893911\pi$
$180$		0			0
$181$	19.8232			1.47345			0.736723	−	0.676195i	$-0.236372\pi$
$181$	19.8232			1.47345			0.736723	+	0.676195i	$0.236372\pi$
$182$		0			0
$183$			2.33356i			0.172502i
$184$		0			0
$185$	−11.4595	+	4.14720i	−0.842522	+	0.304908i
$186$		0			0
$187$			21.1515i			1.54675i
$188$		0			0
$189$	−2.05955	−	3.56725i	−0.149810	−	0.259479i
$190$		0			0
$191$	0.768891	+	1.33176i	0.0556350	+	0.0963626i	0.892502	−	0.451044i	$-0.148948\pi$
$191$	0.768891	+	1.33176i	0.0556350	+	0.0963626i	−0.836867	+	0.547407i	$0.815615\pi$
$192$		0			0
$193$	18.3625	+	10.6016i	1.32176	+	0.763118i	0.984009	−	0.178117i	$-0.0570007\pi$
$193$	18.3625	+	10.6016i	1.32176	+	0.763118i	0.337750	+	0.941236i	$0.390334\pi$
$194$		0			0
$195$	−2.68931	−	0.713547i	−0.192586	−	0.0510982i
$196$		0			0
$197$	8.01675	+	4.62847i	0.571170	+	0.329765i	0.757616	−	0.652700i	$-0.226364\pi$
$197$	8.01675	+	4.62847i	0.571170	+	0.329765i	−0.186447	+	0.982465i	$0.559697\pi$
$198$		0			0
$199$	8.70225	+	15.0727i	0.616886	+	1.06848i	0.990050	+	0.140713i	$0.0449394\pi$
$199$	8.70225	+	15.0727i	0.616886	+	1.06848i	−0.373164	+	0.927765i	$0.621727\pi$
$200$		0			0
$201$	0.759971	+	1.31631i	0.0536042	+	0.0928452i
$202$		0			0
$203$			6.08867i			0.427341i
$204$		0			0
$205$	0.137332	+	0.379477i	0.00959171	+	0.0265038i
$206$		0			0
$207$		−	0.994227i		−	0.0691036i
$208$		0			0
$209$	−22.8232			−1.57871
$210$		0			0
$211$	−3.64087	+	6.30617i	−0.250648	+	0.434135i	−0.963704	−	0.266972i	$-0.913977\pi$
$211$	−3.64087	+	6.30617i	−0.250648	+	0.434135i	0.713057	+	0.701107i	$0.247310\pi$
$212$		0			0
$213$			0.649117i			0.0444768i
$214$		0			0
$215$	−0.525447	+	2.94839i	−0.0358352	+	0.201079i
$216$		0			0
$217$	2.07487	−	1.19792i	0.140851	−	0.0813204i
$218$		0			0
$219$	−1.52886	+	2.64807i	−0.103311	+	0.178940i
$220$		0			0
$221$	−19.5831	−	1.62891i	−1.31731	−	0.109572i
$222$		0			0
$223$	16.8589	+	9.73351i	1.12896	+	0.651804i	0.943672	−	0.330881i	$-0.107346\pi$
$223$	16.8589	+	9.73351i	1.12896	+	0.651804i	0.185285	+	0.982685i	$0.440679\pi$
$224$		0			0
$225$	−11.0683	+	9.21858i	−0.737887	+	0.614572i
$226$		0			0
$227$	−4.16698	+	2.40581i	−0.276572	+	0.159679i	−0.631871	−	0.775074i	$-0.717713\pi$
$227$	−4.16698	+	2.40581i	−0.276572	+	0.159679i	0.355298	+	0.934753i	$0.384379\pi$
$228$		0			0
$229$	−1.52360			−0.100682			−0.0503410	−	0.998732i	$-0.516031\pi$
$229$	−1.52360			−0.100682			−0.0503410	+	0.998732i	$0.516031\pi$
$230$		0			0
$231$	1.35913	−	2.35408i	0.0894242	−	0.154887i
$232$		0			0
$233$			13.9652i			0.914889i	0.889238	+	0.457445i	$0.151235\pi$
$233$			13.9652i			0.914889i	−0.889238	+	0.457445i	$0.848765\pi$
$234$		0			0
$235$	−21.0037	−	17.6898i	−1.37013	−	1.15395i
$236$		0			0
$237$	−3.34155	−	1.92925i	−0.217057	−	0.125318i
$238$		0			0
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	8.73294	+	15.1259i	0.562538	+	0.974344i	0.997274	+	0.0737864i	$0.0235083\pi$
$241$	8.73294	+	15.1259i	0.562538	+	0.974344i	−0.434736	+	0.900558i	$0.643158\pi$
$242$		0			0
$243$	7.64668	−	4.41481i	0.490535	−	0.283210i
$244$		0			0
$245$	2.19217	+	6.05742i	0.140053	+	0.386994i
$246$		0			0
$247$	1.75765	−	21.1309i	0.111836	−	1.34453i
$248$		0			0
$249$	1.35204	−	2.34180i	0.0856819	−	0.148405i
$250$		0			0
$251$	4.64979	+	8.05367i	0.293492	+	0.508343i	0.974633	−	0.223809i	$-0.0718492\pi$
$251$	4.64979	+	8.05367i	0.293492	+	0.508343i	−0.681141	+	0.732152i	$0.738516\pi$
$252$		0			0
$253$	1.15990	−	0.669668i	0.0729223	−	0.0421017i
$254$		0			0
$255$	2.70934	−	3.21689i	0.169665	−	0.201449i
$256$		0			0
$257$	−9.43076	−	5.44485i	−0.588274	−	0.339640i	0.176141	−	0.984365i	$-0.443639\pi$
$257$	−9.43076	−	5.44485i	−0.588274	−	0.339640i	−0.764415	+	0.644725i	$0.776972\pi$
$258$		0			0
$259$	11.0614			0.687321
$260$		0			0
$261$	−8.64270			−0.534970
$262$		0			0
$263$	11.6399	+	6.72031i	0.717749	+	0.414392i	0.813923	−	0.580972i	$-0.197327\pi$
$263$	11.6399	+	6.72031i	0.717749	+	0.414392i	−0.0961749	+	0.995364i	$0.530661\pi$
$264$		0			0
$265$	−4.14979	−	3.49505i	−0.254920	−	0.214699i
$266$		0			0
$267$	−3.65877	+	2.11239i	−0.223913	+	0.129276i
$268$		0			0
$269$	1.83027	+	3.17012i	0.111593	+	0.193286i	0.916413	−	0.400234i	$-0.131071\pi$
$269$	1.83027	+	3.17012i	0.111593	+	0.193286i	−0.804819	+	0.593520i	$0.797738\pi$
$270$		0			0
$271$	11.0018	−	19.0557i	0.668313	−	1.15755i	−0.310062	−	0.950716i	$-0.600350\pi$
$271$	11.0018	−	19.0557i	0.668313	−	1.15755i	0.978376	−	0.206837i	$-0.0663168\pi$
$272$		0			0
$273$	2.07487	+	1.43965i	0.125577	+	0.0871314i
$274$		0			0
$275$	−18.2098	−	6.70343i	−1.09809	−	0.404232i
$276$		0			0
$277$	8.56973	−	4.94774i	0.514905	−	0.297281i	−0.219943	−	0.975513i	$-0.570587\pi$
$277$	8.56973	−	4.94774i	0.514905	−	0.297281i	0.734848	+	0.678232i	$0.237254\pi$
$278$		0			0
$279$	1.70042	+	2.94521i	0.101801	+	0.176325i
$280$		0			0
$281$	4.06138			0.242281			0.121141	−	0.992635i	$-0.461345\pi$
$281$	4.06138			0.242281			0.121141	+	0.992635i	$0.461345\pi$
$282$		0			0
$283$	5.27294	+	3.04434i	0.313444	+	0.180967i	0.648467	−	0.761243i	$-0.275411\pi$
$283$	5.27294	+	3.04434i	0.313444	+	0.180967i	−0.335023	+	0.942210i	$0.608744\pi$
$284$		0			0
$285$	3.47114	+	2.92347i	0.205613	+	0.173172i
$286$		0			0
$287$		−	0.366292i		−	0.0216215i
$288$		0			0
$289$	6.35204	−	11.0021i	0.373649	−	0.647180i
$290$		0			0
$291$	2.00366			0.117456
$292$		0			0
$293$	8.48019	−	4.89604i	0.495418	−	0.286030i	−0.231401	−	0.972858i	$-0.574331\pi$
$293$	8.48019	−	4.89604i	0.495418	−	0.286030i	0.726819	+	0.686829i	$0.240998\pi$
$294$		0			0
$295$	15.5448	+	2.77031i	0.905053	+	0.161294i
$296$		0			0
$297$	6.82125	+	3.93825i	0.395809	+	0.228521i
$298$		0			0
$299$	0.530689	+	1.12547i	0.0306905	+	0.0650876i
$300$		0			0
$301$	1.35913	−	2.35408i	0.0783390	−	0.135687i
$302$		0			0
$303$	−1.77599	+	1.02537i	−0.102028	+	0.0589059i
$304$		0			0
$305$	−14.8853	−	2.65278i	−0.852330	−	0.151898i
$306$		0			0
$307$			22.1046i			1.26158i	0.775955	+	0.630788i	$0.217268\pi$
$307$			22.1046i			1.26158i	−0.775955	+	0.630788i	$0.782732\pi$
$308$		0			0
$309$	−1.11018	+	1.92289i	−0.0631560	+	0.109389i
$310$		0			0
$311$	−7.63904			−0.433170			−0.216585	−	0.976264i	$-0.569492\pi$
$311$	−7.63904			−0.433170			−0.216585	+	0.976264i	$0.569492\pi$
$312$		0			0
$313$		−	26.1425i		−	1.47766i	−0.673891	−	0.738831i	$-0.735378\pi$
$313$		−	26.1425i		−	1.47766i	0.673891	−	0.738831i	$-0.264622\pi$
$314$		0			0
$315$	12.2939	−	4.44914i	0.692681	−	0.250680i
$316$		0			0
$317$			11.8428i			0.665159i	0.943075	+	0.332580i	$0.107919\pi$
$317$			11.8428i			0.665159i	−0.943075	+	0.332580i	$0.892081\pi$
$318$		0			0
$319$	−5.82135	−	10.0829i	−0.325933	−	0.564532i
$320$		0			0
$321$	−3.05063	−	5.28385i	−0.170270	−	0.294916i
$322$		0			0
$323$	27.7576	+	16.0259i	1.54448	+	0.891704i
$324$		0			0
$325$	7.60876	−	16.3434i	0.422058	−	0.906569i
$326$		0			0
$327$	1.72205	+	0.994227i	0.0952297	+	0.0549809i
$328$		0			0
$329$	12.4622	+	21.5852i	0.687064	+	1.19003i
$330$		0			0
$331$	−6.35021	−	10.9989i	−0.349039	−	0.604553i	0.637040	−	0.770831i	$-0.280159\pi$
$331$	−6.35021	−	10.9989i	−0.349039	−	0.604553i	−0.986079	+	0.166277i	$0.946825\pi$
$332$		0			0
$333$			15.7013i			0.860427i
$334$		0			0
$335$	−9.26038	+	3.35132i	−0.505948	+	0.183102i
$336$		0			0
$337$		−	15.2939i		−	0.833113i	−0.909110	−	0.416556i	$-0.863237\pi$
$337$		−	15.2939i		−	0.833113i	0.909110	−	0.416556i	$-0.136763\pi$
$338$		0			0
$339$	−1.64270			−0.0892191
$340$		0			0
$341$	−2.29066	+	3.96754i	−0.124046	+	0.214854i
$342$		0			0
$343$		−	20.0538i		−	1.08281i
$344$		0			0
$345$	−0.262187	−	0.0467255i	−0.0141157	−	0.00251562i
$346$		0			0
$347$	−10.5998	+	6.11981i	−0.569029	+	0.328529i	−0.756761	−	0.653691i	$-0.773219\pi$
$347$	−10.5998	+	6.11981i	−0.569029	+	0.328529i	0.187733	+	0.982220i	$0.439886\pi$
$348$		0			0
$349$	9.35021	−	16.1950i	0.500505	−	0.866901i	−0.499495	−	0.866317i	$-0.666481\pi$
$349$	9.35021	−	16.1950i	0.500505	−	0.866901i	1.00000		0.000583538i	$-0.000185746\pi$
$350$		0			0
$351$	−4.17156	+	6.01219i	−0.222661	+	0.320907i
$352$		0			0
$353$	1.13348	+	0.654413i	0.0603288	+	0.0348309i	0.529861	−	0.848084i	$-0.322244\pi$
$353$	1.13348	+	0.654413i	0.0603288	+	0.0348309i	−0.469532	+	0.882915i	$0.655577\pi$
$354$		0			0
$355$	−4.14058	−	0.737912i	−0.219759	−	0.0391643i
$356$		0			0
$357$	−3.30596	+	1.90870i	−0.174970	+	0.101019i
$358$		0			0
$359$	−29.4082			−1.55210			−0.776051	−	0.630670i	$-0.782780\pi$
$359$	−29.4082			−1.55210			−0.776051	+	0.630670i	$0.782780\pi$
$360$		0			0
$361$	−7.79249	+	13.4970i	−0.410131	+	0.710368i
$362$		0			0
$363$			1.40162i			0.0735661i
$364$		0			0
$365$	−15.1534	−	12.7626i	−0.793168	−	0.668024i
$366$		0			0
$367$	−28.9531	−	16.7161i	−1.51134	−	0.872573i	−0.999912	−	0.0132473i	$-0.995783\pi$
$367$	−28.9531	−	16.7161i	−1.51134	−	0.872573i	−0.511429	−	0.859326i	$-0.670884\pi$
$368$		0			0
$369$	0.519941			0.0270671
$370$		0			0
$371$	2.46222	+	4.26469i	0.127832	+	0.221412i
$372$		0			0
$373$	29.8589	−	17.2391i	1.54604	−	0.892604i	0.547598	−	0.836742i	$-0.315542\pi$
$373$	29.8589	−	17.2391i	1.54604	−	0.892604i	0.998438	−	0.0558628i	$-0.0177909\pi$
$374$		0			0
$375$	1.91085	+	3.35206i	0.0986757	+	0.173099i
$376$		0			0
$377$	9.78357	−	4.61322i	0.503879	−	0.237593i
$378$		0			0
$379$	8.70225	−	15.0727i	0.447004	−	0.774234i	−0.551185	−	0.834383i	$-0.685824\pi$
$379$	8.70225	−	15.0727i	0.447004	−	0.774234i	0.998189	+	0.0601487i	$0.0191575\pi$
$380$		0			0
$381$	2.88273	+	4.99303i	0.147687	+	0.255801i
$382$		0			0
$383$	1.51271	−	0.873366i	0.0772961	−	0.0446269i	−0.460854	−	0.887476i	$-0.652457\pi$
$383$	1.51271	−	0.873366i	0.0772961	−	0.0446269i	0.538150	+	0.842849i	$0.319123\pi$
$384$		0			0
$385$	13.4711	+	11.3457i	0.686553	+	0.578231i
$386$		0			0
$387$	3.34155	+	1.92925i	0.169861	+	0.0980692i
$388$		0			0
$389$	−22.0435			−1.11765			−0.558826	−	0.829285i	$-0.688748\pi$
$389$	−22.0435			−1.11765			−0.558826	+	0.829285i	$0.688748\pi$
$390$		0			0
$391$	−1.88090			−0.0951212
$392$		0			0
$393$	2.98874	+	1.72555i	0.150762	+	0.0870425i
$394$		0			0
$395$	16.1049	−	19.1219i	0.810326	−	0.962127i
$396$		0			0
$397$	−19.5132	+	11.2660i	−0.979339	+	0.565422i	−0.902071	−	0.431588i	$-0.857953\pi$
$397$	−19.5132	+	11.2660i	−0.979339	+	0.565422i	−0.0772687	+	0.997010i	$0.524620\pi$
$398$		0			0
$399$	−2.05955	−	3.56725i	−0.103106	−	0.178586i
$400$		0			0
$401$	1.85204	−	3.20782i	0.0924863	−	0.160191i	−0.816070	−	0.577953i	$-0.803852\pi$
$401$	1.85204	−	3.20782i	0.0924863	−	0.160191i	0.908557	+	0.417761i	$0.137185\pi$
$402$		0			0
$403$	−3.49695	−	2.42636i	−0.174196	−	0.120866i
$404$		0			0
$405$	6.04354	+	16.6995i	0.300306	+	0.829807i
$406$		0			0
$407$	−18.3177	+	10.5757i	−0.907975	+	0.524220i
$408$		0			0
$409$	−6.74186	−	11.6772i	−0.333363	−	0.577402i	0.649806	−	0.760100i	$-0.274850\pi$
$409$	−6.74186	−	11.6772i	−0.333363	−	0.577402i	−0.983169	+	0.182698i	$0.941517\pi$
$410$		0			0
$411$	−0.682580			−0.0336692
$412$		0			0
$413$	−12.4114	−	7.16573i	−0.610726	−	0.352603i
$414$		0			0
$415$	13.4008	+	11.2865i	0.657821	+	0.554033i
$416$		0			0
$417$			3.00260i			0.147038i
$418$		0			0
$419$	−8.41159	+	14.5693i	−0.410933	+	0.711757i	−0.994992	−	0.0999544i	$-0.968130\pi$
$419$	−8.41159	+	14.5693i	−0.410933	+	0.711757i	0.584059	+	0.811711i	$0.301464\pi$
$420$		0			0
$421$	17.1013			0.833464			0.416732	−	0.909029i	$-0.363175\pi$
$421$	17.1013			0.833464			0.416732	+	0.909029i	$0.363175\pi$
$422$		0			0
$423$	−30.6396	+	17.6898i	−1.48975	+	0.860106i
$424$		0			0
$425$	17.4399	+	20.9392i	0.845959	+	1.01570i
$426$		0			0
$427$	11.8849	+	6.86173i	0.575149	+	0.332062i
$428$		0			0
$429$	−4.81243	−	0.400293i	−0.232346	−	0.0193263i
$430$		0			0
$431$	4.83027	−	8.36627i	0.232666	−	0.402989i	−0.725926	−	0.687773i	$-0.758588\pi$
$431$	4.83027	−	8.36627i	0.232666	−	0.402989i	0.958592	+	0.284784i	$0.0919218\pi$
$432$		0			0
$433$	−21.4538	+	12.3863i	−1.03100	+	0.595249i	−0.917272	−	0.398262i	$-0.869613\pi$
$433$	−21.4538	+	12.3863i	−1.03100	+	0.595249i	−0.113730	+	0.993512i	$0.536280\pi$
$434$		0			0
$435$	−0.406180	+	2.27916i	−0.0194748	+	0.109277i
$436$		0			0
$437$		−	2.02956i		−	0.0970869i
$438$		0			0
$439$	−3.53069	+	6.11533i	−0.168511	+	0.291869i	−0.937896	−	0.346915i	$-0.887229\pi$
$439$	−3.53069	+	6.11533i	−0.168511	+	0.291869i	0.769386	+	0.638784i	$0.220562\pi$
$440$		0			0
$441$	8.29958			0.395218
$442$		0			0
$443$		−	38.2438i		−	1.81702i	−0.417865	−	0.908509i	$-0.637222\pi$
$443$		−	38.2438i		−	1.81702i	0.417865	−	0.908509i	$-0.362778\pi$
$444$		0			0
$445$	−9.31523	−	25.7399i	−0.441584	−	1.22019i
$446$		0			0
$447$		−	7.69707i		−	0.364059i
$448$		0			0
$449$	−6.24003	−	10.8080i	−0.294485	−	0.510063i	0.680380	−	0.732860i	$-0.261815\pi$
$449$	−6.24003	−	10.8080i	−0.294485	−	0.510063i	−0.974865	+	0.222796i	$0.928481\pi$
$450$		0			0
$451$	0.350210	+	0.606582i	0.0164908	+	0.0285628i
$452$		0			0
$453$	−5.72721	−	3.30661i	−0.269088	−	0.155358i
$454$		0			0
$455$	−11.5419	+	11.5985i	−0.541092	+	0.543748i
$456$		0			0
$457$	−7.12930	−	4.11610i	−0.333495	−	0.192543i	0.323897	−	0.946092i	$-0.395007\pi$
$457$	−7.12930	−	4.11610i	−0.333495	−	0.192543i	−0.657392	+	0.753549i	$0.728340\pi$
$458$		0			0
$459$	−5.53069	−	9.57943i	−0.258150	−	0.447130i
$460$		0			0
$461$	2.27072	+	3.93300i	0.105758	+	0.183178i	0.914048	−	0.405607i	$-0.132940\pi$
$461$	2.27072	+	3.93300i	0.105758	+	0.183178i	−0.808290	+	0.588785i	$0.799606\pi$
$462$		0			0
$463$		−	1.98845i		−	0.0924113i	−0.998932	−	0.0462056i	$-0.985287\pi$
$463$		−	1.98845i		−	0.0924113i	0.998932	−	0.0462056i	$-0.0147130\pi$
$464$		0			0
$465$	0.856594	−	0.310000i	0.0397236	−	0.0143759i
$466$		0			0
$467$			32.8043i			1.51800i	0.651091	+	0.759000i	$0.274312\pi$
$467$			32.8043i			1.51800i	−0.651091	+	0.759000i	$0.725688\pi$
$468$		0			0
$469$	8.93862			0.412747
$470$		0			0
$471$	−1.07030	+	1.85381i	−0.0493167	+	0.0854191i
$472$		0			0
$473$			5.19783i			0.238997i
$474$		0			0
$475$	−22.5942	+	18.8183i	−1.03669	+	0.863441i
$476$		0			0
$477$	−6.05360	+	3.49505i	−0.277176	+	0.160027i
$478$		0			0
$479$	15.4027	−	26.6782i	0.703766	−	1.21896i	−0.263369	−	0.964695i	$-0.584834\pi$
$479$	15.4027	−	26.6782i	0.703766	−	1.21896i	0.967135	−	0.254263i	$-0.0818329\pi$
$480$		0			0
$481$	−8.38090	−	17.7740i	−0.382136	−	0.810423i
$482$		0			0
$483$	0.209337	+	0.120861i	0.00952518	+	0.00549937i
$484$		0			0
$485$	−2.27774	+	12.7809i	−0.103427	+	0.580350i
$486$		0			0
$487$	19.3341	−	11.1626i	0.876113	−	0.505824i	0.00673807	−	0.999977i	$-0.497855\pi$
$487$	19.3341	−	11.1626i	0.876113	−	0.505824i	0.869375	+	0.494153i	$0.164522\pi$
$488$		0			0
$489$	−4.11910			−0.186272
$490$		0			0
$491$	5.34129	−	9.25139i	0.241049	−	0.417509i	−0.719964	−	0.694011i	$-0.755842\pi$
$491$	5.34129	−	9.25139i	0.241049	−	0.417509i	0.961013	+	0.276502i	$0.0891752\pi$
$492$		0			0
$493$			16.3504i			0.736386i
$494$		0			0
$495$	−16.1049	+	19.1219i	−0.723862	+	0.859466i
$496$		0			0
$497$	3.30596	+	1.90870i	0.148292	+	0.0856167i
$498$		0			0
$499$	18.8195			0.842477			0.421239	−	0.906950i	$-0.361595\pi$
$499$	18.8195			0.842477			0.421239	+	0.906950i	$0.361595\pi$
$500$		0			0
$501$	0.350210	+	0.606582i	0.0156462	+	0.0271001i
$502$		0			0
$503$	−4.92013	+	2.84064i	−0.219378	+	0.126658i	−0.605662	−	0.795722i	$-0.707092\pi$
$503$	−4.92013	+	2.84064i	−0.219378	+	0.126658i	0.386284	+	0.922380i	$0.373758\pi$
$504$		0			0
$505$	−4.52168	−	12.4943i	−0.201212	−	0.555989i
$506$		0			0
$507$	0.741225	−	4.42478i	0.0329190	−	0.196511i
$508$		0			0
$509$	13.9622	−	24.1833i	0.618864	−	1.07190i	−0.370829	−	0.928701i	$-0.620926\pi$
$509$	13.9622	−	24.1833i	0.618864	−	1.07190i	0.989693	−	0.143203i	$-0.0457403\pi$
$510$		0			0
$511$	8.99108	+	15.5730i	0.397742	+	0.688909i
$512$		0			0
$513$	10.3365	−	5.96781i	0.456370	−	0.263485i
$514$		0			0
$515$	−11.0037	−	9.26754i	−0.484879	−	0.408376i
$516$		0			0
$517$	−41.2750	−	23.8301i	−1.81527	−	1.04805i
$518$		0			0
$519$	0.462218			0.0202891
$520$		0			0
$521$	6.29958			0.275990			0.137995	−	0.990433i	$-0.455934\pi$
$521$	6.29958			0.275990			0.137995	+	0.990433i	$0.455934\pi$
$522$		0			0
$523$	−19.7948	−	11.4285i	−0.865567	−	0.499735i	0.000305526	−	1.00000i	$-0.499903\pi$
$523$	−19.7948	−	11.4285i	−0.865567	−	0.499735i	−0.865873	+	0.500265i	$0.833236\pi$
$524$		0			0
$525$	−0.595504	−	3.45110i	−0.0259899	−	0.150618i
$526$		0			0
$527$	5.57182	−	3.21689i	0.242712	−	0.140130i
$528$		0			0
$529$	−11.4404	−	19.8154i	−0.497411	−	0.861541i
$530$		0			0
$531$	10.1716	−	17.6177i	0.441408	−	0.764541i
$532$		0			0
$533$	−0.588576	+	0.277529i	−0.0254940	+	0.0120211i
$534$		0			0
$535$	37.1725	−	13.4527i	1.60711	−	0.581610i
$536$		0			0
$537$	6.04443	−	3.48975i	0.260837	−	0.150594i
$538$		0			0
$539$	5.59024	+	9.68258i	0.240789	+	0.417058i
$540$		0			0
$541$	−9.48006			−0.407580			−0.203790	−	0.979015i	$-0.565326\pi$
$541$	−9.48006			−0.407580			−0.203790	+	0.979015i	$0.565326\pi$
$542$		0			0
$543$	−5.92463	−	3.42059i	−0.254250	−	0.146791i
$544$		0			0
$545$	−8.29958	+	9.85437i	−0.355515	+	0.422115i
$546$		0			0
$547$		−	33.3911i		−	1.42770i	−0.700299	−	0.713850i	$-0.746950\pi$
$547$		−	33.3911i		−	1.42770i	0.700299	−	0.713850i	$-0.253050\pi$
$548$		0			0
$549$	−9.74003	+	16.8702i	−0.415694	+	0.720004i
$550$		0			0
$551$	−17.6427			−0.751604
$552$		0			0
$553$	−19.6513	+	11.3457i	−0.835660	+	0.482469i
$554$		0			0
$555$	4.14058	+	0.737912i	0.175758	+	0.0313226i
$556$		0			0
$557$	32.7053	+	18.8824i	1.38577	+	0.800073i	0.992835	−	0.119495i	$-0.0381274\pi$
$557$	32.7053	+	18.8824i	1.38577	+	0.800073i	0.392932	+	0.919567i	$0.371461\pi$
$558$		0			0
$559$	−4.81243	−	0.400293i	−0.203544	−	0.0169306i
$560$		0			0
$561$	3.64979	−	6.32162i	0.154094	−	0.266899i
$562$		0			0
$563$	22.4307	−	12.9504i	0.945343	−	0.545794i	0.0537120	−	0.998556i	$-0.482895\pi$
$563$	22.4307	−	12.9504i	0.945343	−	0.545794i	0.891631	+	0.452762i	$0.149561\pi$
$564$		0			0
$565$	1.86741	−	10.4784i	0.0785625	−	0.440830i
$566$		0			0
$567$		−	16.1193i		−	0.676947i
$568$		0			0
$569$	−10.7725	+	18.6586i	−0.451609	+	0.782209i	−0.998486	−	0.0550035i	$-0.982483\pi$
$569$	−10.7725	+	18.6586i	−0.451609	+	0.782209i	0.546878	+	0.837213i	$0.315816\pi$
$570$		0			0
$571$	2.22036			0.0929192			0.0464596	−	0.998920i	$-0.485206\pi$
$571$	2.22036			0.0929192			0.0464596	+	0.998920i	$0.485206\pi$
$572$		0			0
$573$		−	0.530704i		−	0.0221705i
$574$		0			0
$575$	0.596104	−	1.61932i	0.0248593	−	0.0675301i
$576$		0			0
$577$			6.20265i			0.258220i	0.991630	+	0.129110i	$0.0412120\pi$
$577$			6.20265i			0.258220i	−0.991630	+	0.129110i	$0.958788\pi$
$578$		0			0
$579$	−3.65871	−	6.33707i	−0.152051	−	0.263360i
$580$		0			0
$581$	−7.95120	−	13.7719i	−0.329871	−	0.571354i
$582$		0			0
$583$	−8.15489	−	4.70823i	−0.337741	−	0.194995i
$584$		0			0
$585$	−16.4638	−	16.3834i	−0.680695	−	0.677370i
$586$		0			0
$587$	1.58391	+	0.914469i	0.0653748	+	0.0377442i	0.532331	−	0.846536i	$-0.321316\pi$
$587$	1.58391	+	0.914469i	0.0653748	+	0.0377442i	−0.466956	+	0.884280i	$0.654649\pi$
$588$		0			0
$589$	3.47114	+	6.01219i	0.143026	+	0.247728i
$590$		0			0
$591$	−1.59733	−	2.76666i	−0.0657055	−	0.113805i
$592$		0			0
$593$		−	0.0728761i		−	0.00299266i	−0.999999	−	0.00149633i	$-0.999524\pi$
$593$		−	0.0728761i		−	0.00299266i	0.999999	−	0.00149633i	$-0.000476297\pi$
$594$		0			0
$595$	−8.41697	−	23.2578i	−0.345062	−	0.953477i
$596$		0			0
$597$		−	6.00646i		−	0.245828i
$598$		0			0
$599$	−14.5813			−0.595777			−0.297888	−	0.954601i	$-0.596282\pi$
$599$	−14.5813			−0.595777			−0.297888	+	0.954601i	$0.596282\pi$
$600$		0			0
$601$	22.2041	−	38.4586i	0.905723	−	1.56876i	0.0857795	−	0.996314i	$-0.472662\pi$
$601$	22.2041	−	38.4586i	0.905723	−	1.56876i	0.819944	−	0.572444i	$-0.194005\pi$
$602$		0			0
$603$			12.6881i			0.516700i
$604$		0			0
$605$	−8.94065	−	1.59336i	−0.363489	−	0.0647791i
$606$		0			0
$607$	31.3808	−	18.1177i	1.27371	−	0.735375i	0.298024	−	0.954558i	$-0.403672\pi$
$607$	31.3808	−	18.1177i	1.27371	−	0.735375i	0.975684	+	0.219183i	$0.0703392\pi$
$608$		0			0
$609$	1.05063	−	1.81975i	0.0425737	−	0.0737398i
$610$		0			0
$611$	25.2419	−	36.3794i	1.02118	−	1.47175i
$612$		0			0
$613$	−2.90838	−	1.67915i	−0.117468	−	0.0678203i	0.440115	−	0.897942i	$-0.354938\pi$
$613$	−2.90838	−	1.67915i	−0.117468	−	0.0678203i	−0.557583	+	0.830121i	$0.688271\pi$
$614$		0			0
$615$	0.0244356	−	0.137113i	0.000985339	−	0.00552894i
$616$		0			0
$617$	18.3441	−	10.5910i	0.738507	−	0.426377i	−0.0830194	−	0.996548i	$-0.526456\pi$
$617$	18.3441	−	10.5910i	0.738507	−	0.426377i	0.821526	+	0.570171i	$0.193123\pi$
$618$		0			0
$619$	25.4082			1.02124			0.510620	−	0.859807i	$-0.329416\pi$
$619$	25.4082			1.02124			0.510620	+	0.859807i	$0.329416\pi$
$620$		0			0
$621$	−0.350210	+	0.606582i	−0.0140534	+	0.0243413i
$622$		0			0
$623$			24.8455i			0.995416i
$624$		0			0
$625$	−23.5543	+	8.37828i	−0.942171	+	0.335131i
$626$		0			0
$627$	6.82125	+	3.93825i	0.272415	+	0.157279i
$628$		0			0
$629$	29.7041			1.18438
$630$		0			0
$631$	21.7725	+	37.7112i	0.866751	+	1.50126i	0.865298	+	0.501258i	$0.167129\pi$
$631$	21.7725	+	37.7112i	0.866751	+	1.50126i	0.00145375	+	0.999999i	$0.499537\pi$
$632$		0			0
$633$	2.17632	−	1.25650i	0.0865011	−	0.0499414i
$634$		0			0
$635$	−35.1265	+	12.7123i	−1.39395	+	0.504470i
$636$		0			0
$637$	−9.39516	+	4.43007i	−0.372250	+	0.175526i
$638$		0			0
$639$	−2.70934	+	4.69272i	−0.107180	+	0.185641i
$640$		0			0
$641$	−24.1427	−	41.8164i	−0.953579	−	1.65165i	−0.737586	−	0.675253i	$-0.764035\pi$
$641$	−24.1427	−	41.8164i	−0.953579	−	1.65165i	−0.215993	−	0.976395i	$-0.569299\pi$
$642$		0			0
$643$	−36.6710	+	21.1720i	−1.44616	+	0.834943i	−0.998250	−	0.0591344i	$-0.981166\pi$
$643$	−36.6710	+	21.1720i	−1.44616	+	0.834943i	−0.447913	+	0.894077i	$0.647833\pi$
$644$		0			0
$645$	0.665802	−	0.790529i	0.0262159	−	0.0311271i
$646$		0			0
$647$	−29.7958	−	17.2026i	−1.17139	−	0.676305i	−0.217386	−	0.976086i	$-0.569753\pi$
$647$	−29.7958	−	17.2026i	−1.17139	−	0.676305i	−0.954008	+	0.299781i	$0.903086\pi$
$648$		0			0
$649$	27.4045			1.07572
$650$		0			0
$651$	−0.826831			−0.0324061
$652$		0			0
$653$	−12.4114	−	7.16573i	−0.485696	−	0.280417i	0.237091	−	0.971487i	$-0.423806\pi$
$653$	−12.4114	−	7.16573i	−0.485696	−	0.280417i	−0.722787	+	0.691071i	$0.757139\pi$
$654$		0			0
$655$	−14.4045	+	17.1029i	−0.562830	+	0.668267i
$656$		0			0
$657$	−22.1054	+	12.7626i	−0.862416	+	0.497916i
$658$		0			0
$659$	−11.4116	−	19.7655i	−0.444532	−	0.769953i	0.553487	−	0.832858i	$-0.313297\pi$
$659$	−11.4116	−	19.7655i	−0.444532	−	0.769953i	−0.998020	+	0.0629051i	$0.979963\pi$
$660$		0			0
$661$	−7.20934	+	12.4869i	−0.280411	+	0.485686i	−0.971486	−	0.237097i	$-0.923804\pi$
$661$	−7.20934	+	12.4869i	−0.280411	+	0.485686i	0.691075	+	0.722783i	$0.257137\pi$
$662$		0			0
$663$	5.57182	+	3.86601i	0.216391	+	0.150143i
$664$		0			0
$665$	25.0960	−	9.08221i	0.973181	−	0.352193i
$666$		0			0
$667$	0.896622	−	0.517665i	0.0347173	−	0.0200441i
$668$		0			0
$669$	−3.35913	−	5.81818i	−0.129871	−	0.224944i
$670$		0			0
$671$	−26.2419			−1.01306
$672$		0			0
$673$	−29.5956	−	17.0871i	−1.14083	−	0.658657i	−0.194193	−	0.980963i	$-0.562209\pi$
$673$	−29.5956	−	17.0871i	−1.14083	−	0.658657i	−0.946636	+	0.322306i	$0.895542\pi$
$674$		0			0
$675$	10.0000	−	1.72555i	0.384900	−	0.0664164i
$676$		0			0
$677$			5.84695i			0.224716i	0.993668	+	0.112358i	$0.0358404\pi$
$677$			5.84695i			0.224716i	−0.993668	+	0.112358i	$0.964160\pi$
$678$		0			0
$679$	5.89165	−	10.2046i	0.226101	−	0.391618i
$680$		0			0
$681$	1.66054			0.0636319
$682$		0			0
$683$	−9.82834	+	5.67439i	−0.376071	+	0.217125i	−0.676107	−	0.736803i	$-0.736334\pi$
$683$	−9.82834	+	5.67439i	−0.376071	+	0.217125i	0.300036	+	0.953928i	$0.403001\pi$
$684$		0			0
$685$	0.775953	−	4.35403i	0.0296476	−	0.166359i
$686$		0			0
$687$	0.455363	+	0.262904i	0.0173732	+	0.0100304i
$688$		0			0
$689$	4.98715	−	7.18765i	0.189995	−	0.273828i
$690$		0			0
$691$	−9.41159	+	16.3013i	−0.358034	+	0.620133i	−0.987632	−	0.156788i	$-0.949886\pi$
$691$	−9.41159	+	16.3013i	−0.358034	+	0.620133i	0.629599	+	0.776921i	$0.283219\pi$
$692$		0			0
$693$	19.6513	−	11.3457i	0.746493	−	0.430988i
$694$		0			0
$695$	−19.1530	−	3.41334i	−0.726513	−	0.129475i
$696$		0			0
$697$		−	0.983636i		−	0.0372579i
$698$		0			0
$699$	2.40976	−	4.17383i	0.0911455	−	0.157869i
$700$		0			0
$701$	19.1626			0.723763			0.361881	−	0.932224i	$-0.382135\pi$
$701$	19.1626			0.723763			0.361881	+	0.932224i	$0.382135\pi$
$702$		0			0
$703$			32.0518i			1.20885i
$704$		0			0
$705$	3.22499	+	8.91130i	0.121460	+	0.335619i
$706$		0			0
$707$			12.0602i			0.453570i
$708$		0			0
$709$	11.7419	+	20.3375i	0.440975	+	0.763791i	0.997762	−	0.0668645i	$-0.0212995\pi$
$709$	11.7419	+	20.3375i	0.440975	+	0.763791i	−0.556787	+	0.830655i	$0.687966\pi$
$710$		0			0
$711$	−16.1049	−	27.8945i	−0.603982	−	1.04613i
$712$		0			0
$713$	−0.352814	−	0.203698i	−0.0132130	−	0.00762853i
$714$		0			0
$715$	8.02412	−	30.2424i	0.300085	−	1.13100i
$716$		0			0
$717$	−1.19550	−	0.690220i	−0.0446466	−	0.0257767i
$718$		0			0
$719$	7.05429	+	12.2184i	0.263080	+	0.455669i	0.967059	−	0.254553i	$-0.0819282\pi$
$719$	7.05429	+	12.2184i	0.263080	+	0.455669i	−0.703978	+	0.710221i	$0.748595\pi$
$720$		0			0
$721$	6.52886	+	11.3083i	0.243148	+	0.421144i
$722$		0			0
$723$		−	6.02765i		−	0.224171i
$724$		0			0
$725$	−14.0765	−	5.18187i	−0.522789	−	0.192450i
$726$		0			0
$727$		−	25.3762i		−	0.941153i	−0.882359	−	0.470576i	$-0.844046\pi$
$727$		−	25.3762i		−	0.941153i	0.882359	−	0.470576i	$-0.155954\pi$
$728$		0			0
$729$	20.7796			0.769616
$730$		0			0
$731$	3.64979	−	6.32162i	0.134992	−	0.233814i
$732$		0			0
$733$			10.6692i			0.394074i	0.980396	+	0.197037i	$0.0631320\pi$
$733$			10.6692i			0.394074i	−0.980396	+	0.197037i	$0.936868\pi$
$734$		0			0
$735$	0.390054	−	2.18867i	0.0143874	−	0.0807305i
$736$		0			0
$737$	−14.8024	+	8.54617i	−0.545254	+	0.314802i
$738$		0			0
$739$	0.707513	−	1.22545i	0.0260263	−	0.0450788i	−0.852719	−	0.522370i	$-0.825048\pi$
$739$	0.707513	−	1.22545i	0.0260263	−	0.0450788i	0.878745	+	0.477291i	$0.158381\pi$
$740$		0			0
$741$	−4.17156	+	6.01219i	−0.153246	+	0.220863i
$742$		0			0
$743$	25.8748	+	14.9389i	0.949256	+	0.548053i	0.892850	−	0.450355i	$-0.148702\pi$
$743$	25.8748	+	14.9389i	0.949256	+	0.548053i	0.0564064	+	0.998408i	$0.482036\pi$
$744$		0			0
$745$	49.0980	+	8.74998i	1.79881	+	0.320575i
$746$		0			0
$747$	19.5488	−	11.2865i	0.715253	−	0.412952i
$748$		0			0
$749$	−35.8809			−1.31106
$750$		0			0
$751$	−9.99291	+	17.3082i	−0.364646	+	0.631586i	−0.988719	−	0.149780i	$-0.952143\pi$
$751$	−9.99291	+	17.3082i	−0.364646	+	0.631586i	0.624073	+	0.781366i	$0.285477\pi$
$752$		0			0
$753$		−	3.20938i		−	0.116956i
$754$		0			0
$755$	27.6028	−	32.7737i	1.00457	−	1.19276i
$756$		0			0
$757$	14.8024	+	8.54617i	0.538003	+	0.310616i	0.744269	−	0.667880i	$-0.232798\pi$
$757$	14.8024	+	8.54617i	0.538003	+	0.310616i	−0.206266	+	0.978496i	$0.566131\pi$
$758$		0			0
$759$	−0.462218			−0.0167775
$760$		0			0
$761$	21.1120	+	36.5671i	0.765310	+	1.32556i	0.940083	+	0.340947i	$0.110748\pi$
$761$	21.1120	+	36.5671i	0.765310	+	1.32556i	−0.174773	+	0.984609i	$0.555919\pi$
$762$		0			0
$763$	10.1272	−	5.84695i	0.366630	−	0.211674i
$764$		0			0
$765$	33.0138	−	11.9477i	1.19362	−	0.431968i
$766$		0			0
$767$	−2.11046	+	25.3725i	−0.0762044	+	0.916149i
$768$		0			0
$769$	−11.8827	+	20.5815i	−0.428502	+	0.742187i	−0.996740	−	0.0806767i	$-0.974292\pi$
$769$	−11.8827	+	20.5815i	−0.428502	+	0.742187i	0.568238	+	0.822864i	$0.307625\pi$
$770$		0			0
$771$	1.87907	+	3.25465i	0.0676731	+	0.117213i
$772$		0			0
$773$	0.246026	−	0.142043i	0.00884894	−	0.00510894i	−0.495569	−	0.868569i	$-0.665040\pi$
$773$	0.246026	−	0.142043i	0.00884894	−	0.00510894i	0.504418	+	0.863460i	$0.331707\pi$
$774$		0			0
$775$	1.00366	+	5.81644i	0.0360524	+	0.208933i
$776$		0			0
$777$	−3.30596	−	1.90870i	−0.118601	−	0.0684741i
$778$		0			0
$779$	1.06138			0.0380278
$780$		0			0
$781$	−7.29958			−0.261199
$782$		0			0
$783$	5.27294	+	3.04434i	0.188440	+	0.108796i
$784$		0			0
$785$	−10.6084	−	8.93460i	−0.378628	−	0.318890i
$786$		0			0
$787$	−20.9008	+	12.0671i	−0.745032	+	0.430145i	−0.823896	−	0.566741i	$-0.808204\pi$
$787$	−20.9008	+	12.0671i	−0.745032	+	0.430145i	0.0788638	+	0.996885i	$0.474871\pi$
$788$		0			0
$789$	−2.31925	−	4.01705i	−0.0825674	−	0.143011i
$790$		0			0
$791$	−4.83027	+	8.36627i	−0.171745	+	0.297470i
$792$		0			0
$793$	2.02093	−	24.2961i	0.0717652	−	0.862780i
$794$		0			0
$795$	0.637176	+	1.76065i	0.0225983	+	0.0624437i
$796$		0			0
$797$	−29.7430	+	17.1721i	−1.05355	+	0.608267i	−0.923641	−	0.383259i	$-0.874802\pi$
$797$	−29.7430	+	17.1721i	−1.05355	+	0.608267i	−0.129909	+	0.991526i	$0.541468\pi$
$798$		0			0
$799$	33.4659	+	57.9646i	1.18394	+	2.05064i
$800$		0			0
$801$	−35.2676			−1.24612
$802$		0			0
$803$	−29.7786	−	17.1927i	−1.05086	−	0.606716i
$804$		0			0
$805$	−1.00892	+	1.19792i	−0.0355598	+	0.0422213i
$806$		0			0
$807$		−	1.26329i		−	0.0444698i
$808$		0			0
$809$	−23.8431	+	41.2975i	−0.838279	+	1.45194i	0.0530528	+	0.998592i	$0.483105\pi$
$809$	−23.8431	+	41.2975i	−0.838279	+	1.45194i	−0.891332	+	0.453351i	$0.850229\pi$
$810$		0			0
$811$	−24.5992			−0.863793			−0.431897	−	0.901923i	$-0.642155\pi$
$811$	−24.5992			−0.863793			−0.431897	+	0.901923i	$0.642155\pi$
$812$		0			0
$813$	−6.57632	+	3.79684i	−0.230642	+	0.133161i
$814$		0			0
$815$	4.68257	−	26.2749i	0.164023	−	0.920368i
$816$		0			0
$817$	6.82125	+	3.93825i	0.238645	+	0.137782i
$818$		0			0
$819$	8.99108	+	19.0680i	0.314174	+	0.666290i
$820$		0			0
$821$	−8.64979	+	14.9819i	−0.301880	+	0.522871i	−0.976562	−	0.215237i	$-0.930947\pi$
$821$	−8.64979	+	14.9819i	−0.301880	+	0.522871i	0.674682	+	0.738109i	$0.264281\pi$
$822$		0			0
$823$	−28.2000	+	16.2813i	−0.982990	+	0.567529i	−0.903171	−	0.429280i	$-0.858767\pi$
$823$	−28.2000	+	16.2813i	−0.982990	+	0.567529i	−0.0798182	+	0.996809i	$0.525434\pi$
$824$		0			0
$825$	4.28574	+	5.14568i	0.149210	+	0.179150i
$826$		0			0
$827$			15.4702i			0.537951i	0.963147	+	0.268976i	$0.0866851\pi$
$827$			15.4702i			0.537951i	−0.963147	+	0.268976i	$0.913315\pi$
$828$		0			0
$829$	−7.26180	+	12.5778i	−0.252213	+	0.436845i	−0.964135	−	0.265413i	$-0.914492\pi$
$829$	−7.26180	+	12.5778i	−0.252213	+	0.436845i	0.711922	+	0.702258i	$0.247825\pi$
$830$		0			0
$831$	−3.41503			−0.118466
$832$		0			0
$833$		−	15.7013i		−	0.544018i
$834$		0			0
$835$	−4.26737	+	1.54436i	−0.147679	+	0.0534447i
$836$		0			0
$837$		−	2.39585i		−	0.0828127i
$838$		0			0
$839$	−0.407933	−	0.706561i	−0.0140834	−	0.0243932i	0.858898	−	0.512147i	$-0.171150\pi$
$839$	−0.407933	−	0.706561i	−0.0140834	−	0.0243932i	−0.872981	+	0.487754i	$0.837816\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	−1.21384	−	0.700811i	−0.0418069	−	0.0241372i
$844$		0			0
$845$	27.3821	+	9.75817i	0.941972	+	0.335691i
$846$		0			0
$847$	7.13847	+	4.12140i	0.245281	+	0.141613i
$848$		0			0
$849$	−1.05063	−	1.81975i	−0.0360575	−	0.0624535i
$850$		0			0
$851$	−0.940450	−	1.62891i	−0.0322382	−	0.0558382i
$852$		0			0
$853$		−	20.0856i		−	0.687719i	−0.939021	−	0.343859i	$-0.888266\pi$
$853$		−	20.0856i		−	0.687719i	0.939021	−	0.343859i	$-0.111734\pi$
$854$		0			0
$855$	12.8919	+	35.6230i	0.440895	+	1.21828i
$856$		0			0
$857$			40.7886i			1.39331i	0.717406	+	0.696656i	$0.245329\pi$
$857$			40.7886i			1.39331i	−0.717406	+	0.696656i	$0.754671\pi$
$858$		0			0
$859$	−40.1301			−1.36922			−0.684610	−	0.728909i	$-0.740028\pi$
$859$	−40.1301			−1.36922			−0.684610	+	0.728909i	$0.740028\pi$
$860$		0			0
$861$	−0.0632055	+	0.109475i	−0.00215404	+	0.00373090i
$862$		0			0
$863$		−	20.8275i		−	0.708977i	−0.935060	−	0.354489i	$-0.884655\pi$
$863$		−	20.8275i		−	0.708977i	0.935060	−	0.354489i	$-0.115345\pi$
$864$		0			0
$865$	−0.525447	+	2.94839i	−0.0178657	+	0.100248i
$866$		0			0
$867$	−3.79692	+	2.19215i	−0.128950	+	0.0744494i
$868$		0			0
$869$	21.6952	−	37.5771i	0.735958	−	1.27472i
$870$		0			0
$871$	−6.77255	−	14.3630i	−0.229479	−	0.486672i
$872$		0			0
$873$	14.4852	+	8.36303i	0.490249	+	0.283046i
$874$		0			0
$875$	22.6908	+	0.124594i	0.767089	+	0.00421206i
$876$		0			0
$877$	40.3520	−	23.2972i	1.36259	−	0.786691i	0.372621	−	0.927984i	$-0.378459\pi$
$877$	40.3520	−	23.2972i	1.36259	−	0.786691i	0.989968	+	0.141293i	$0.0451258\pi$
$878$		0			0
$879$	−3.37935			−0.113982
$880$		0			0
$881$	−11.9223	+	20.6501i	−0.401674	+	0.695719i	−0.993928	−	0.110032i	$-0.964905\pi$
$881$	−11.9223	+	20.6501i	−0.401674	+	0.695719i	0.592254	+	0.805751i	$0.298238\pi$
$882$		0			0
$883$		−	37.2496i		−	1.25355i	−0.779201	−	0.626774i	$-0.784375\pi$
$883$		−	37.2496i		−	1.25355i	0.779201	−	0.626774i	$-0.215625\pi$
$884$		0			0
$885$	−4.16790	−	3.51031i	−0.140103	−	0.117998i
$886$		0			0
$887$	24.7505	+	14.2897i	0.831042	+	0.479802i	0.854209	−	0.519929i	$-0.174042\pi$
$887$	24.7505	+	14.2897i	0.831042	+	0.479802i	−0.0231673	+	0.999732i	$0.507375\pi$
$888$		0			0
$889$	33.9060			1.13717
$890$		0			0
$891$	15.4116	+	26.6937i	0.516308	+	0.894271i
$892$		0			0
$893$	−62.5459	+	36.1109i	−2.09302	+	1.20840i
$894$		0			0
$895$	15.3891	+	42.5233i	0.514402	+	1.42140i
$896$		0			0
$897$	0.0355962	−	0.427946i	0.00118852	−	0.0142887i
$898$		0			0
$899$	−1.77072	+	3.06697i	−0.0590568	+	0.102289i
$900$		0			0
$901$	6.61201	+	11.4523i	0.220278	+	0.381533i
$902$		0			0
$903$	−0.812417	+	0.469049i	−0.0270356	+	0.0156090i
$904$		0			0
$905$	28.5543	−	33.9035i	0.949177	−	1.12699i
$906$		0			0
$907$	5.55457	+	3.20693i	0.184436	+	0.106484i	0.589375	−	0.807859i	$-0.299374\pi$
$907$	5.55457	+	3.20693i	0.184436	+	0.106484i	−0.404939	+	0.914344i	$0.632707\pi$
$908$		0			0
$909$	−17.1191			−0.567805
$910$		0			0
$911$	−22.2204			−0.736193			−0.368097	−	0.929788i	$-0.619990\pi$
$911$	−22.2204			−0.736193			−0.368097	+	0.929788i	$0.619990\pi$
$912$		0			0
$913$	26.3345	+	15.2042i	0.871543	+	0.503186i
$914$		0			0
$915$	3.99108	+	3.36138i	0.131941	+	0.111124i
$916$		0			0
$917$	17.5765	−	10.1478i	0.580426	−	0.335109i
$918$		0			0
$919$	−13.0632	−	22.6261i	−0.430915	−	0.746367i	0.566037	−	0.824380i	$-0.308476\pi$
$919$	−13.0632	−	22.6261i	−0.430915	−	0.746367i	−0.996952	+	0.0780125i	$0.975143\pi$
$920$		0			0
$921$	3.81426	−	6.60649i	0.125684	−	0.217691i
$922$		0			0
$923$	0.562152	−	6.75834i	0.0185035	−	0.222453i
$924$		0			0
$925$	−9.41397	+	25.5730i	−0.309529	+	0.840836i
$926$		0			0
$927$	−16.0518	+	9.26754i	−0.527212	+	0.304386i
$928$		0			0
$929$	−11.9711	−	20.7346i	−0.392760	−	0.680281i	0.600052	−	0.799961i	$-0.295146\pi$
$929$	−11.9711	−	20.7346i	−0.392760	−	0.680281i	−0.992813	+	0.119680i	$0.961813\pi$
$930$		0			0
$931$	16.9423			0.555261
$932$		0			0
$933$	2.28311	+	1.31815i	0.0747457	+	0.0431544i
$934$		0			0
$935$	36.1752	+	30.4676i	1.18306	+	0.996397i
$936$		0			0
$937$		−	18.5046i		−	0.604518i	−0.953226	−	0.302259i	$-0.902259\pi$
$937$		−	18.5046i		−	0.604518i	0.953226	−	0.302259i	$-0.0977407\pi$
$938$		0			0
$939$	−4.51102	+	7.81332i	−0.147212	+	0.254978i
$940$		0			0
$941$	−14.3788			−0.468735			−0.234368	−	0.972148i	$-0.575302\pi$
$941$	−14.3788			−0.468735			−0.234368	+	0.972148i	$0.575302\pi$
$942$		0			0
$943$	−0.0539404	+	0.0311425i	−0.00175654	+	0.00101414i
$944$		0			0
$945$	−9.06772	−	1.61600i	−0.294973	−	0.0525685i
$946$		0			0
$947$	50.5056	+	29.1594i	1.64121	+	0.947554i	0.980404	+	0.196998i	$0.0631194\pi$
$947$	50.5056	+	29.1594i	1.64121	+	0.947554i	0.660807	+	0.750555i	$0.270214\pi$
$948$		0			0
$949$	18.2112	−	26.2465i	0.591160	−	0.851999i
$950$		0			0
$951$	2.04354	−	3.53951i	0.0662663	−	0.114777i
$952$		0			0
$953$	11.9507	−	6.89975i	0.387122	−	0.223505i	−0.293791	−	0.955870i	$-0.594917\pi$
$953$	11.9507	−	6.89975i	0.387122	−	0.223505i	0.680912	+	0.732365i	$0.261583\pi$
$954$		0			0
$955$	3.38525	+	0.603301i	0.109544	+	0.0195224i
$956$		0			0
$957$			4.01801i			0.129884i
$958$		0			0
$959$	−2.00709	+	3.47639i	−0.0648124	+	0.112258i
$960$		0			0
$961$	−29.6065			−0.955047
$962$		0			0
$963$		−	50.9319i		−	1.64126i
$964$		0			0
$965$	44.5820	−	16.1342i	1.43515	−	0.519378i
$966$		0			0
$967$		−	30.3474i		−	0.975906i	−0.872870	−	0.487953i	$-0.837744\pi$
$967$		−	30.3474i		−	0.975906i	0.872870	−	0.487953i	$-0.162256\pi$
$968$		0			0
$969$	−5.53069	−	9.57943i	−0.177671	−	0.307736i
$970$		0			0
$971$	22.0506	+	38.1928i	0.707638	+	1.22567i	0.965731	+	0.259545i	$0.0835727\pi$
$971$	22.0506	+	38.1928i	0.707638	+	1.22567i	−0.258092	+	0.966120i	$0.583094\pi$
$972$		0			0
$973$	15.2923	+	8.82900i	0.490248	+	0.283045i
$974$		0			0
$975$	−5.09420	+	3.57169i	−0.163145	+	0.114386i
$976$		0			0
$977$	19.3314	+	11.1610i	0.618466	+	0.357071i	0.776271	−	0.630399i	$-0.217109\pi$
$977$	19.3314	+	11.1610i	0.618466	+	0.357071i	−0.157806	+	0.987470i	$0.550442\pi$
$978$		0			0
$979$	−23.7547	−	41.1444i	−0.759204	−	1.31498i
$980$		0			0
$981$	8.29958	+	14.3753i	0.264985	+	0.458968i
$982$		0			0
$983$			4.03793i			0.128790i	0.997924	+	0.0643950i	$0.0205118\pi$
$983$			4.03793i			0.128790i	−0.997924	+	0.0643950i	$0.979488\pi$
$984$		0			0
$985$	19.4638	−	7.04392i	0.620167	−	0.224438i
$986$		0			0
$987$		−	8.60167i		−	0.273794i
$988$		0			0
$989$	−0.462218			−0.0146977
$990$		0			0
$991$	14.8250	−	25.6777i	0.470932	−	0.815678i	−0.528515	−	0.848924i	$-0.677251\pi$
$991$	14.8250	−	25.6777i	0.470932	−	0.815678i	0.999447	+	0.0332459i	$0.0105845\pi$
$992$		0			0
$993$			4.38304i			0.139092i
$994$		0			0
$995$	38.3140	+	6.82811i	1.21463	+	0.216466i
$996$		0			0
$997$	19.2052	−	11.0881i	0.608233	−	0.351164i	−0.164040	−	0.986454i	$-0.552453\pi$
$997$	19.2052	−	11.0881i	0.608233	−	0.351164i	0.772274	+	0.635290i	$0.219119\pi$
$998$		0			0
$999$	5.53069	−	9.57943i	0.174983	−	0.303080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.dh.a.529.3		12
4.3	odd	2		65.2.n.a.9.2	✓	12
5.4	even	2	inner	1040.2.dh.a.529.4		12
12.11	even	2		585.2.bs.a.334.5		12
13.3	even	3	inner	1040.2.dh.a.289.4		12
20.3	even	4		325.2.e.e.126.2		12
20.7	even	4		325.2.e.e.126.5		12
20.19	odd	2		65.2.n.a.9.5	yes	12
52.3	odd	6		65.2.n.a.29.5	yes	12
52.7	even	12		845.2.d.d.844.3		12
52.11	even	12		845.2.l.f.699.9		24
52.15	even	12		845.2.l.f.699.3		24
52.19	even	12		845.2.d.d.844.9		12
52.23	odd	6		845.2.n.e.484.2		12
52.31	even	4		845.2.l.f.654.4		24
52.35	odd	6		845.2.b.d.339.5		6
52.43	odd	6		845.2.b.e.339.2		6
52.47	even	4		845.2.l.f.654.10		24
52.51	odd	2		845.2.n.e.529.5		12
60.59	even	2		585.2.bs.a.334.2		12
65.29	even	6	inner	1040.2.dh.a.289.3		12
156.107	even	6		585.2.bs.a.289.2		12
260.3	even	12		325.2.e.e.276.2		12
260.19	even	12		845.2.d.d.844.4		12
260.43	even	12		4225.2.a.bq.1.2		6
260.59	even	12		845.2.d.d.844.10		12
260.87	even	12		4225.2.a.br.1.2		6
260.99	even	4		845.2.l.f.654.3		24
260.107	even	12		325.2.e.e.276.5		12
260.119	even	12		845.2.l.f.699.10		24
260.139	odd	6		845.2.b.d.339.2		6
260.147	even	12		4225.2.a.bq.1.5		6
260.159	odd	6		65.2.n.a.29.2	yes	12
260.179	odd	6		845.2.n.e.484.5		12
260.199	odd	6		845.2.b.e.339.5		6
260.219	even	12		845.2.l.f.699.4		24
260.239	even	4		845.2.l.f.654.9		24
260.243	even	12		4225.2.a.br.1.5		6
260.259	odd	2		845.2.n.e.529.2		12
780.419	even	6		585.2.bs.a.289.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.2	✓	12	4.3	odd	2
65.2.n.a.9.5	yes	12	20.19	odd	2
65.2.n.a.29.2	yes	12	260.159	odd	6
65.2.n.a.29.5	yes	12	52.3	odd	6
325.2.e.e.126.2		12	20.3	even	4
325.2.e.e.126.5		12	20.7	even	4
325.2.e.e.276.2		12	260.3	even	12
325.2.e.e.276.5		12	260.107	even	12
585.2.bs.a.289.2		12	156.107	even	6
585.2.bs.a.289.5		12	780.419	even	6
585.2.bs.a.334.2		12	60.59	even	2
585.2.bs.a.334.5		12	12.11	even	2
845.2.b.d.339.2		6	260.139	odd	6
845.2.b.d.339.5		6	52.35	odd	6
845.2.b.e.339.2		6	52.43	odd	6
845.2.b.e.339.5		6	260.199	odd	6
845.2.d.d.844.3		12	52.7	even	12
845.2.d.d.844.4		12	260.19	even	12
845.2.d.d.844.9		12	52.19	even	12
845.2.d.d.844.10		12	260.59	even	12
845.2.l.f.654.3		24	260.99	even	4
845.2.l.f.654.4		24	52.31	even	4
845.2.l.f.654.9		24	260.239	even	4
845.2.l.f.654.10		24	52.47	even	4
845.2.l.f.699.3		24	52.15	even	12
845.2.l.f.699.4		24	260.219	even	12
845.2.l.f.699.9		24	52.11	even	12
845.2.l.f.699.10		24	260.119	even	12
845.2.n.e.484.2		12	52.23	odd	6
845.2.n.e.484.5		12	260.179	odd	6
845.2.n.e.529.2		12	260.259	odd	2
845.2.n.e.529.5		12	52.51	odd	2
1040.2.dh.a.289.3		12	65.29	even	6	inner
1040.2.dh.a.289.4		12	13.3	even	3	inner
1040.2.dh.a.529.3		12	1.1	even	1	trivial
1040.2.dh.a.529.4		12	5.4	even	2	inner
4225.2.a.bq.1.2		6	260.43	even	12
4225.2.a.bq.1.5		6	260.147	even	12
4225.2.a.br.1.2		6	260.87	even	12
4225.2.a.br.1.5		6	260.243	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.dh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.298874 - 0.172555i) q^{3} +(1.44045 - 1.71029i) q^{5} +(-1.75765 + 1.01478i) q^{7} +(-1.44045 - 2.49493i) q^{9} +O(q^{10})\)	\(q+(-0.298874 - 0.172555i) q^{3} +(1.44045 - 1.71029i) q^{5} +(-1.75765 + 1.01478i) q^{7} +(-1.44045 - 2.49493i) q^{9} +(1.94045 - 3.36096i) q^{11} +(2.96232 + 2.05540i) q^{13} +(-0.725633 + 0.262606i) q^{15} +(-4.71996 + 2.72507i) q^{17} +(-2.94045 - 5.09301i) q^{19} +0.700420 q^{21} +(0.298874 + 0.172555i) q^{23} +(-0.850210 - 4.92718i) q^{25} +2.02956i q^{27} +(1.50000 - 2.59808i) q^{29} -1.18048 q^{31} +(-1.15990 + 0.669668i) q^{33} +(-0.796234 + 4.46783i) q^{35} +(-4.71996 - 2.72507i) q^{37} +(-0.530689 - 1.12547i) q^{39} +(-0.0902394 + 0.156299i) q^{41} +(-1.15990 + 0.669668i) q^{43} +(-6.34196 - 1.13023i) q^{45} -12.2807i q^{47} +(-1.44045 + 2.49493i) q^{49} +1.88090 q^{51} -2.42636i q^{53} +(-2.95310 - 8.16003i) q^{55} +2.02956i q^{57} +(3.53069 + 6.11533i) q^{59} +(-3.38090 - 5.85589i) q^{61} +(5.06361 + 2.92347i) q^{63} +(7.78241 - 2.10573i) q^{65} +(-3.81417 - 2.20211i) q^{67} +(-0.0595504 - 0.103144i) q^{69} +(-0.940450 - 1.62891i) q^{71} -8.86014i q^{73} +(-0.596104 + 1.61932i) q^{75} +7.87651i q^{77} +11.1805 q^{79} +(-3.97114 + 6.87821i) q^{81} +7.83540i q^{83} +(-2.13820 + 11.9979i) q^{85} +(-0.896622 + 0.517665i) q^{87} +(6.12093 - 10.6018i) q^{89} +(-7.29249 - 0.606582i) q^{91} +(0.352814 + 0.203698i) q^{93} +(-12.9461 - 2.30719i) q^{95} +(-5.02801 + 2.90292i) q^{97} -11.1805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^5 + 6 * q^9	\( 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65} - 24 q^{69} + 12 q^{71} - 2 q^{75} + 104 q^{79} + 14 q^{81} + 21 q^{85} + 20 q^{89} + 44 q^{91} - 20 q^{95} - 104 q^{99}+O(q^{100}) \) 12 * q - 6 * q^5 + 6 * q^9 + 4 * q^15 - 12 * q^19 - 8 * q^21 - 2 * q^25 + 18 * q^29 + 16 * q^31 - 10 * q^35 + 32 * q^39 + 14 * q^41 - 29 * q^45 + 6 * q^49 - 24 * q^51 + 26 * q^55 + 4 * q^59 + 6 * q^61 + 23 * q^65 - 24 * q^69 + 12 * q^71 - 2 * q^75 + 104 * q^79 + 14 * q^81 + 21 * q^85 + 20 * q^89 + 44 * q^91 - 20 * q^95 - 104 * q^99

Introduction

L-functions

Modular forms

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Database

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