LMFDB - Embedded newform 585.2.bs.a.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, 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:	$4.67124851824$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.2
Root			$-1.02826 - 0.593667i$ of defining polynomial
Character	$\chi$	$=$	585.289
Dual form			585.2.bs.a.334.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02826 + 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 + 1.71029i) q^{5} +(-1.75765 - 1.01478i) q^{7} -3.07548i q^{8} +O(q^{10})$	\(q+(-1.02826 + 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 + 1.71029i) q^{5} +(-1.75765 - 1.01478i) q^{7} -3.07548i q^{8} +(0.465813 - 2.61378i) q^{10} +(1.94045 + 3.36096i) q^{11} +(-2.96232 + 2.05540i) q^{13} +2.40976 q^{14} +(1.23557 + 2.14007i) q^{16} +(-4.71996 - 2.72507i) q^{17} +(2.94045 - 5.09301i) q^{19} +(-0.449133 - 1.24105i) q^{20} +(-3.99058 - 2.30396i) q^{22} +(-0.298874 + 0.172555i) q^{23} +(-0.850210 - 4.92718i) q^{25} +(1.82581 - 3.87212i) q^{26} +(1.03743 - 0.598962i) q^{28} +(-1.50000 - 2.59808i) q^{29} +1.18048 q^{31} +(2.78591 + 1.60845i) q^{32} +6.47114 q^{34} +(4.26737 - 1.54436i) q^{35} +(4.71996 - 2.72507i) q^{37} +6.98259i q^{38} +(5.25997 + 4.43007i) q^{40} +(0.0902394 + 0.156299i) q^{41} +(-1.15990 - 0.669668i) q^{43} -2.29066 q^{44} +(0.204880 - 0.354863i) q^{46} -12.2807i q^{47} +(-1.44045 - 2.49493i) q^{49} +(3.79934 + 4.56169i) q^{50} +(-0.176407 - 2.12081i) q^{52} +2.42636i q^{53} +(-8.54334 - 1.52255i) q^{55} +(-3.12093 + 5.40561i) q^{56} +(3.08478 + 1.78100i) q^{58} +(3.53069 - 6.11533i) q^{59} +(-3.38090 + 5.85589i) q^{61} +(-1.21384 + 0.700811i) q^{62} -8.76180 q^{64} +(0.751722 - 8.02714i) q^{65} +(-3.81417 + 2.20211i) q^{67} +(2.78591 - 1.60845i) q^{68} +(-3.47114 + 4.12140i) q^{70} +(-0.940450 + 1.62891i) q^{71} -8.86014i q^{73} +(-3.23557 + 5.60417i) q^{74} +(1.73557 + 3.00609i) q^{76} -7.87651i q^{77} -11.1805 q^{79} +(-5.43992 - 0.969475i) q^{80} +(-0.185579 - 0.107144i) q^{82} +7.83540i q^{83} +(11.4595 - 4.14720i) q^{85} +1.59024 q^{86} +(10.3365 - 5.96781i) q^{88} +(-6.12093 - 10.6018i) q^{89} +(7.29249 - 0.606582i) q^{91} -0.203698i q^{92} +(7.29066 + 12.6278i) q^{94} +(4.47497 + 12.3653i) q^{95} +(5.02801 + 2.90292i) q^{97} +(2.96232 + 1.71029i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5	$ 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 7 * q^10 + 44 * q^14 - 16 * q^16 + 12 * q^19 + q^20 - 2 * q^25 - 24 * q^26 - 18 * q^29 - 16 * q^31 + 16 * q^34 - 10 * q^35 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 10 * q^46 + 6 * q^49 + 31 * q^50 - 26 * q^55 + 16 * q^56 + 4 * q^59 + 6 * q^61 - 12 * q^64 - 23 * q^65 + 20 * q^70 + 12 * q^71 - 8 * q^74 - 10 * q^76 - 104 * q^79 - 33 * q^80 + 21 * q^85 + 4 * q^86 - 20 * q^89 - 44 * q^91 + 56 * q^94 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.02826	+	0.593667i	−0.727090	+	0.419786i	−0.817357	−	0.576132i	$-0.804561\pi$
$2$	−1.02826	+	0.593667i	−0.727090	+	0.419786i	0.0902665	+	0.995918i	$0.471228\pi$
$3$		0			0
$3$		0			0
$4$	−0.295120	+	0.511162i	−0.147560	+	0.255581i
$5$	−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	0.129596	−	0.991567i	$-0.458632\pi$
$7$	−1.75765	−	1.01478i	−0.664328	−	0.383550i	−0.793924	+	0.608017i	$0.791965\pi$
$8$		−	3.07548i		−	1.08735i
$9$		0			0
$10$	0.465813	−	2.61378i	0.147303	−	0.826548i
$11$	1.94045	+	3.36096i	0.585068	+	1.01337i	0.994867	+	0.101191i	$0.0322653\pi$
$11$	1.94045	+	3.36096i	0.585068	+	1.01337i	−0.409799	+	0.912176i	$0.634401\pi$
$12$		0			0
$13$	−2.96232	+	2.05540i	−0.821599	+	0.570066i
$13$	−2.96232	+	2.05540i	−0.821599	+	0.570066i
$14$	2.40976			0.644036
$15$		0			0
$16$	1.23557	+	2.14007i	0.308892	+	0.535017i
$17$	−4.71996	−	2.72507i	−1.14476	−	0.660927i	−0.197155	−	0.980372i	$-0.563170\pi$
$17$	−4.71996	−	2.72507i	−1.14476	−	0.660927i	−0.947605	+	0.319445i	$0.896503\pi$
$18$		0			0
$19$	2.94045	−	5.09301i	0.674585	−	1.16842i	−0.302005	−	0.953306i	$-0.597656\pi$
$19$	2.94045	−	5.09301i	0.674585	−	1.16842i	0.976590	−	0.215110i	$-0.0690109\pi$
$20$	−0.449133	−	1.24105i	−0.100429	−	0.277506i
$21$		0			0
$22$	−3.99058	−	2.30396i	−0.850794	−	0.491206i
$23$	−0.298874	+	0.172555i	−0.0623195	+	0.0359802i	−0.530836	−	0.847475i	$-0.678122\pi$
$23$	−0.298874	+	0.172555i	−0.0623195	+	0.0359802i	0.468516	+	0.883455i	$0.344789\pi$
$24$		0			0
$25$	−0.850210	−	4.92718i	−0.170042	−	0.985437i
$26$	1.82581	−	3.87212i	0.358071	−	0.759385i
$27$		0			0
$28$	1.03743	−	0.598962i	0.196056	−	0.113193i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	1.18048			0.212020			0.106010	−	0.994365i	$-0.466192\pi$
$31$	1.18048			0.212020			0.106010	+	0.994365i	$0.466192\pi$
$32$	2.78591	+	1.60845i	0.492484	+	0.284336i
$33$		0			0
$34$	6.47114			1.10979
$35$	4.26737	−	1.54436i	0.721318	−	0.261044i
$36$		0			0
$37$	4.71996	−	2.72507i	0.775957	−	0.447999i	−0.0590384	−	0.998256i	$-0.518803\pi$
$37$	4.71996	−	2.72507i	0.775957	−	0.447999i	0.834996	+	0.550257i	$0.185470\pi$
$38$			6.98259i			1.13273i
$39$		0			0
$40$	5.25997	+	4.43007i	0.831674	+	0.700456i
$41$	0.0902394	+	0.156299i	0.0140930	+	0.0244098i	0.872986	−	0.487745i	$-0.162181\pi$
$41$	0.0902394	+	0.156299i	0.0140930	+	0.0244098i	−0.858893	+	0.512155i	$0.828847\pi$
$42$		0			0
$43$	−1.15990	−	0.669668i	−0.176883	−	0.102123i	0.408944	−	0.912559i	$-0.365897\pi$
$43$	−1.15990	−	0.669668i	−0.176883	−	0.102123i	−0.585827	+	0.810436i	$0.699230\pi$
$44$	−2.29066			−0.345330
$45$		0			0
$46$	0.204880	−	0.354863i	0.0302079	−	0.0523217i
$47$		−	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
$50$	3.79934	+	4.56169i	0.537308	+	0.645120i
$51$		0			0
$52$	−0.176407	−	2.12081i	−0.0244633	−	0.294104i
$53$			2.42636i			0.333286i	0.986017	+	0.166643i	$0.0532928\pi$
$53$			2.42636i			0.333286i	−0.986017	+	0.166643i	$0.946707\pi$
$54$		0			0
$55$	−8.54334	−	1.52255i	−1.15198	−	0.205301i
$56$	−3.12093	+	5.40561i	−0.417052	+	0.722355i
$57$		0			0
$58$	3.08478	+	1.78100i	0.405052	+	0.233857i
$59$	3.53069	−	6.11533i	0.459657	−	0.796149i	−0.539286	−	0.842123i	$-0.681306\pi$
$59$	3.53069	−	6.11533i	0.459657	−	0.796149i	0.998943	+	0.0459741i	$0.0146392\pi$
$60$		0			0
$61$	−3.38090	+	5.85589i	−0.432880	+	0.749770i	−0.997120	−	0.0758409i	$-0.975836\pi$
$61$	−3.38090	+	5.85589i	−0.432880	+	0.749770i	0.564240	+	0.825611i	$0.309169\pi$
$62$	−1.21384	+	0.700811i	−0.154158	+	0.0890031i
$63$		0			0
$64$	−8.76180			−1.09522
$65$	0.751722	−	8.02714i	0.0932396	−	0.995644i
$66$		0			0
$67$	−3.81417	+	2.20211i	−0.465975	+	0.269031i	−0.714553	−	0.699581i	$-0.753370\pi$
$67$	−3.81417	+	2.20211i	−0.465975	+	0.269031i	0.248578	+	0.968612i	$0.420037\pi$
$68$	2.78591	−	1.60845i	0.337841	−	0.195053i
$69$		0			0
$70$	−3.47114	+	4.12140i	−0.414880	+	0.492601i
$71$	−0.940450	+	1.62891i	−0.111611	+	0.193316i	−0.916420	−	0.400218i	$-0.868934\pi$
$71$	−0.940450	+	1.62891i	−0.111611	+	0.193316i	0.804809	+	0.593534i	$0.202268\pi$
$72$		0			0
$73$		−	8.86014i		−	1.03700i	−0.855077	−	0.518501i	$-0.826490\pi$
$73$		−	8.86014i		−	1.03700i	0.855077	−	0.518501i	$-0.173510\pi$
$74$	−3.23557	+	5.60417i	−0.376127	+	0.651472i
$75$		0			0
$76$	1.73557	+	3.00609i	0.199083	+	0.344823i
$77$		−	7.87651i		−	0.897611i
$78$		0			0
$79$	−11.1805			−1.25790			−0.628951	−	0.777445i	$-0.716515\pi$
$79$	−11.1805			−1.25790			−0.628951	+	0.777445i	$0.716515\pi$
$80$	−5.43992	−	0.969475i	−0.608202	−	0.108391i
$81$		0			0
$82$	−0.185579	−	0.107144i	−0.0204938	−	0.0118321i
$83$			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
$85$	11.4595	−	4.14720i	1.24296	−	0.449827i
$86$	1.59024			0.171480
$87$		0			0
$88$	10.3365	−	5.96781i	1.10188	−	0.636171i
$89$	−6.12093	−	10.6018i	−0.648817	−	1.12378i	−0.983406	−	0.181420i	$-0.941931\pi$
$89$	−6.12093	−	10.6018i	−0.648817	−	1.12378i	0.334589	−	0.942364i	$-0.391403\pi$
$90$		0			0
$91$	7.29249	−	0.606582i	0.764460	−	0.0635870i
$92$		−	0.203698i		−	0.0212369i
$93$		0			0
$94$	7.29066	+	12.6278i	0.751974	+	1.30246i
$95$	4.47497	+	12.3653i	0.459122	+	1.26865i
$96$		0			0
$97$	5.02801	+	2.90292i	0.510517	+	0.294747i	0.733046	−	0.680179i	$-0.238098\pi$
$97$	5.02801	+	2.90292i	0.510517	+	0.294747i	−0.222529	+	0.974926i	$0.571431\pi$
$98$	2.96232	+	1.71029i	0.299239	+	0.172766i
$99$		0			0
$100$	2.76950	+	1.01951i	0.276950	+	0.101951i
$101$	−2.97114	−	5.14616i	−0.295639	−	0.512062i	0.679494	−	0.733681i	$-0.262199\pi$
$101$	−2.97114	−	5.14616i	−0.295639	−	0.512062i	−0.975133	+	0.221619i	$0.928866\pi$
$102$		0			0
$103$			6.43378i			0.633939i	0.948436	+	0.316970i	$0.102665\pi$
$103$			6.43378i			0.633939i	−0.948436	+	0.316970i	$0.897335\pi$
$104$	6.32135	+	9.11054i	0.619859	+	0.893362i
$105$		0			0
$106$	−1.44045	−	2.49493i	−0.139909	−	0.242329i
$107$	−15.3106	+	8.83959i	−1.48013	+	0.854555i	−0.999747	−	0.0225015i	$-0.992837\pi$
$107$	−15.3106	+	8.83959i	−1.48013	+	0.854555i	−0.480387	+	0.877057i	$0.659504\pi$
$108$		0			0
$109$	−5.76180			−0.551880			−0.275940	−	0.961175i	$-0.588989\pi$
$109$	−5.76180			−0.551880			−0.275940	+	0.961175i	$0.588989\pi$
$110$	9.68867	−	3.50632i	0.923779	−	0.334314i
$111$		0			0
$112$		−	5.01532i		−	0.473903i
$113$	4.12222	+	2.37996i	0.387785	+	0.223888i	0.681200	−	0.732097i	$-0.261458\pi$
$113$	4.12222	+	2.37996i	0.387785	+	0.223888i	−0.293415	+	0.955985i	$0.594792\pi$
$114$		0			0
$115$	0.135393	−	0.759719i	0.0126255	−	0.0708442i
$116$	1.77072			0.164407
$117$		0			0
$118$			8.38421i			0.771829i
$119$	5.53069	+	9.57943i	0.506997	+	0.878145i
$120$		0			0
$121$	−2.03069	+	3.51726i	−0.184608	+	0.319751i
$122$		−	8.02851i		−	0.726867i
$123$		0			0
$124$	−0.348383	+	0.603416i	−0.0312857	+	0.0541884i
$125$	9.65162	+	5.64325i	0.863267	+	0.504748i
$126$		0			0
$127$	−14.4679	+	8.35307i	−1.28382	+	0.741215i	−0.977545	−	0.210728i	$-0.932417\pi$
$127$	−14.4679	+	8.35307i	−1.28382	+	0.741215i	−0.306277	+	0.951942i	$0.599083\pi$
$128$	3.43760	−	1.98470i	0.303844	−	0.175424i
$129$		0			0
$130$	3.99248	+	8.70026i	0.350163	+	0.763063i
$131$	−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
$134$	2.61464	−	4.52869i	0.225871	−	0.391219i
$135$		0			0
$136$	−8.38090	+	14.5161i	−0.718656	+	1.24475i
$137$	1.71288	+	0.988931i	0.146341	+	0.0844901i	0.571383	−	0.820684i	$-0.306407\pi$
$137$	1.71288	+	0.988931i	0.146341	+	0.0844901i	−0.425042	+	0.905174i	$0.639741\pi$
$138$		0			0
$139$	4.35021	−	7.53478i	0.368980	−	0.639092i	−0.620426	−	0.784265i	$-0.713040\pi$
$139$	4.35021	−	7.53478i	0.368980	−	0.639092i	0.989406	+	0.145173i	$0.0463737\pi$
$140$	−0.469969	+	2.63709i	−0.0397196	+	0.222875i
$141$		0			0
$142$		−	2.23325i		−	0.187411i
$143$	−12.6563	−	5.96781i	−1.05838	−	0.499053i
$144$		0			0
$145$	6.60415	+	1.17696i	0.548445	+	0.0977410i
$146$	5.25997	+	9.11054i	0.435318	+	0.753993i
$147$		0			0
$148$			3.21689i			0.264427i
$149$	−11.1516	+	19.3152i	−0.913576	+	1.58236i	−0.104603	+	0.994514i	$0.533357\pi$
$149$	−11.1516	+	19.3152i	−0.913576	+	1.58236i	−0.808973	+	0.587846i	$0.799976\pi$
$150$		0			0
$151$	−19.1626			−1.55943			−0.779717	−	0.626132i	$-0.784637\pi$
$151$	−19.1626			−1.55943			−0.779717	+	0.626132i	$0.784637\pi$
$152$	−15.6634	−	9.04329i	−1.27047	−	0.733507i
$153$		0			0
$154$	4.67602	+	8.09910i	0.376804	+	0.652644i
$155$	−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	$-0.0796132\pi$
$158$	11.4964	−	6.63748i	0.914608	−	0.528049i
$159$		0			0
$160$	−6.76387	+	2.44784i	−0.534731	+	0.193519i
$161$	0.700420			0.0552008
$162$		0			0
$163$	10.3365	+	5.96781i	0.809621	+	0.467435i	0.846824	−	0.531873i	$-0.178512\pi$
$163$	10.3365	+	5.96781i	0.809621	+	0.467435i	−0.0372032	+	0.999308i	$0.511845\pi$
$164$	−0.106526			−0.00831826
$165$		0			0
$166$	−4.65162	−	8.05684i	−0.361036	−	0.625332i
$167$	1.75765	−	1.01478i	0.136011	−	0.0785259i	−0.430451	−	0.902614i	$-0.641645\pi$
$167$	1.75765	−	1.01478i	0.136011	−	0.0785259i	0.566461	+	0.824088i	$0.308312\pi$
$168$		0			0
$169$	4.55063	−	12.1775i	0.350048	−	0.936732i
$170$	−9.32135	+	11.0675i	−0.714915	+	0.848842i
$171$		0			0
$172$	0.684619	−	0.395265i	0.0522017	−	0.0301387i
$173$	−1.15990	−	0.669668i	−0.0881855	−	0.0509139i	0.455259	−	0.890359i	$-0.349547\pi$
$173$	−1.15990	−	0.669668i	−0.0881855	−	0.0509139i	−0.543444	+	0.839445i	$0.682880\pi$
$174$		0			0
$175$	−3.50563	+	9.52303i	−0.265001	+	0.719873i
$176$	−4.79512	+	8.30539i	−0.361446	+	0.626042i
$177$		0			0
$178$	12.5878	+	7.26758i	0.943497	+	0.544728i
$179$	−10.1120	−	17.5145i	−0.755807	−	1.30910i	−0.944972	−	0.327151i	$-0.893911\pi$
$179$	−10.1120	−	17.5145i	−0.755807	−	1.30910i	0.189165	−	0.981945i	$-0.439422\pi$
$180$		0			0
$181$	19.8232			1.47345			0.736723	−	0.676195i	$-0.236372\pi$
$181$	19.8232			1.47345			0.736723	+	0.676195i	$0.236372\pi$
$182$	−7.13847	+	4.95303i	−0.529139	+	0.367143i
$183$		0			0
$184$	0.530689	+	0.919180i	0.0391229	+	0.0677629i
$185$	−2.13820	+	11.9979i	−0.157203	+	0.882100i
$186$		0			0
$187$		−	21.1515i		−	1.54675i
$188$	6.27745	+	3.62429i	0.457830	+	0.264328i
$189$		0			0
$190$	−11.9423	−	10.0581i	−0.866384	−	0.729689i
$191$	0.768891	−	1.33176i	0.0556350	−	0.0963626i	−0.836867	−	0.547407i	$-0.815615\pi$
$191$	0.768891	−	1.33176i	0.0556350	−	0.0963626i	0.892502	+	0.451044i	$0.148948\pi$
$192$		0			0
$193$	−18.3625	+	10.6016i	−1.32176	+	0.763118i	−0.984009	−	0.178117i	$-0.942999\pi$
$193$	−18.3625	+	10.6016i	−1.32176	+	0.763118i	−0.337750	+	0.941236i	$0.609666\pi$
$194$	−6.89347			−0.494923
$195$		0			0
$196$	1.70042			0.121459
$197$	8.01675	−	4.62847i	0.571170	−	0.329765i	−0.186447	−	0.982465i	$-0.559697\pi$
$197$	8.01675	−	4.62847i	0.571170	−	0.329765i	0.757616	+	0.652700i	$0.226364\pi$
$198$		0			0
$199$	−8.70225	+	15.0727i	−0.616886	+	1.06848i	0.373164	+	0.927765i	$0.378273\pi$
$199$	−8.70225	+	15.0727i	−0.616886	+	1.06848i	−0.990050	+	0.140713i	$0.955061\pi$
$200$	−15.1534	+	2.61480i	−1.07151	+	0.184894i
$201$		0			0
$202$	6.11021	+	3.52773i	0.429913	+	0.248210i
$203$			6.08867i			0.427341i
$204$		0			0
$205$	−0.397303	−	0.0708053i	−0.0277488	−	0.00494526i
$206$	−3.81952	−	6.61560i	−0.266119	−	0.460931i
$207$		0			0
$208$	−8.05885	−	3.79997i	−0.558781	−	0.263480i
$209$	22.8232			1.57871
$210$		0			0
$211$	3.64087	+	6.30617i	0.250648	+	0.434135i	0.963704	−	0.266972i	$-0.0860231\pi$
$211$	3.64087	+	6.30617i	0.250648	+	0.434135i	−0.713057	+	0.701107i	$0.752690\pi$
$212$	−1.24026	−	0.716067i	−0.0851817	−	0.0491797i
$213$		0			0
$214$	10.4955	−	18.1788i	0.717460	−	1.24268i
$215$	2.81611	−	1.01915i	0.192057	−	0.0695052i
$216$		0			0
$217$	−2.07487	−	1.19792i	−0.140851	−	0.0813204i
$218$	5.92463	−	3.42059i	0.401267	−	0.231671i
$219$		0			0
$220$	3.29958	−	3.91770i	0.222458	−	0.264131i
$221$	19.5831	−	1.62891i	1.31731	−	0.109572i
$222$		0			0
$223$	16.8589	−	9.73351i	1.12896	−	0.651804i	0.185285	−	0.982685i	$-0.440679\pi$
$223$	16.8589	−	9.73351i	1.12896	−	0.651804i	0.943672	+	0.330881i	$0.107346\pi$
$224$	−3.26443	−	5.65416i	−0.218114	−	0.377784i
$225$		0			0
$226$	−5.65162			−0.375940
$227$	4.16698	+	2.40581i	0.276572	+	0.159679i	0.631871	−	0.775074i	$-0.282287\pi$
$227$	4.16698	+	2.40581i	0.276572	+	0.159679i	−0.355298	+	0.934753i	$0.615621\pi$
$228$		0			0
$229$	−1.52360			−0.100682			−0.0503410	−	0.998732i	$-0.516031\pi$
$229$	−1.52360			−0.100682			−0.0503410	+	0.998732i	$0.516031\pi$
$230$	0.311800	+	0.861568i	0.0205595	+	0.0568101i
$231$		0			0
$232$	−7.99033	+	4.61322i	−0.524591	+	0.302873i
$233$		−	13.9652i		−	0.914889i	−0.889238	−	0.457445i	$-0.848765\pi$
$233$		−	13.9652i		−	0.914889i	0.889238	−	0.457445i	$-0.151235\pi$
$234$		0			0
$235$	21.0037	+	17.6898i	1.37013	+	1.15395i
$236$	2.08395	+	3.60951i	0.135654	+	0.234959i
$237$		0			0
$238$	−11.3740	−	6.56677i	−0.737266	−	0.425661i
$239$	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	−0.434736	−	0.900558i	$-0.643158\pi$
$241$	8.73294	−	15.1259i	0.562538	−	0.974344i	0.997274	−	0.0737864i	$-0.0235083\pi$
$242$		−	4.82221i		−	0.309983i
$243$		0			0
$244$	−1.99554	−	3.45638i	−0.127751	−	0.221272i
$245$	6.34196	+	1.13023i	0.405173	+	0.0722078i
$246$		0			0
$247$	1.75765	+	21.1309i	0.111836	+	1.34453i
$248$		−	3.63054i		−	0.230539i
$249$		0			0
$250$	−13.2746	−	0.0728904i	−0.839559	−	0.00460999i
$251$	4.64979	−	8.05367i	0.293492	−	0.508343i	−0.681141	−	0.732152i	$-0.738516\pi$
$251$	4.64979	−	8.05367i	0.293492	−	0.508343i	0.974633	+	0.223809i	$0.0718492\pi$
$252$		0			0
$253$	−1.15990	−	0.669668i	−0.0729223	−	0.0421017i
$254$	9.91788	−	17.1783i	0.622303	−	1.07786i
$255$		0			0
$256$	6.40530	−	11.0943i	0.400331	−	0.693394i
$257$	−9.43076	+	5.44485i	−0.588274	+	0.339640i	−0.764415	−	0.644725i	$-0.776972\pi$
$257$	−9.43076	+	5.44485i	−0.588274	+	0.339640i	0.176141	+	0.984365i	$0.443639\pi$
$258$		0			0
$259$	−11.0614			−0.687321
$260$	3.88132	+	2.75322i	0.240709	+	0.170747i
$261$		0			0
$262$	10.2826	−	5.93667i	0.635262	−	0.366769i
$263$	−11.6399	+	6.72031i	−0.717749	+	0.414392i	−0.813923	−	0.580972i	$-0.802673\pi$
$263$	−11.6399	+	6.72031i	−0.717749	+	0.414392i	0.0961749	+	0.995364i	$0.469339\pi$
$264$		0			0
$265$	−4.14979	−	3.49505i	−0.254920	−	0.214699i
$266$	7.08578	−	12.2729i	0.434457	−	0.752502i
$267$		0			0
$268$		−	2.59955i		−	0.158793i
$269$	−1.83027	+	3.17012i	−0.111593	+	0.193286i	−0.916413	−	0.400234i	$-0.868929\pi$
$269$	−1.83027	+	3.17012i	−0.111593	+	0.193286i	0.804819	+	0.593520i	$0.202262\pi$
$270$		0			0
$271$	−11.0018	−	19.0557i	−0.668313	−	1.15755i	−0.978376	−	0.206837i	$-0.933683\pi$
$271$	−11.0018	−	19.0557i	−0.668313	−	1.15755i	0.310062	−	0.950716i	$-0.399650\pi$
$272$		−	13.4681i		−	0.816621i
$273$		0			0
$274$	−2.34838			−0.141871
$275$	14.9103	−	12.4185i	0.899123	−	0.748862i
$276$		0			0
$277$	−8.56973	−	4.94774i	−0.514905	−	0.297281i	0.219943	−	0.975513i	$-0.429413\pi$
$277$	−8.56973	−	4.94774i	−0.514905	−	0.297281i	−0.734848	+	0.678232i	$0.762746\pi$
$278$			10.3303i			0.619570i
$279$		0			0
$280$	−4.74964	−	13.1242i	−0.283845	−	0.784321i
$281$	−4.06138			−0.242281			−0.121141	−	0.992635i	$-0.538655\pi$
$281$	−4.06138			−0.242281			−0.121141	+	0.992635i	$0.538655\pi$
$282$		0			0
$283$	5.27294	−	3.04434i	0.313444	−	0.180967i	−0.335023	−	0.942210i	$-0.608744\pi$
$283$	5.27294	−	3.04434i	0.313444	−	0.180967i	0.648467	+	0.761243i	$0.275411\pi$
$284$	−0.555090	−	0.961445i	−0.0329386	−	0.0570513i
$285$		0			0
$286$	16.5569	−	1.37719i	0.979031	−	0.0814348i
$287$		−	0.366292i		−	0.0216215i
$288$		0			0
$289$	6.35204	+	11.0021i	0.373649	+	0.647180i
$290$	−7.48951	+	2.71044i	−0.439799	+	0.159163i
$291$		0			0
$292$	4.52897	+	2.61480i	0.265038	+	0.153020i
$293$	8.48019	+	4.89604i	0.495418	+	0.286030i	0.726819	−	0.686829i	$-0.240998\pi$
$293$	8.48019	+	4.89604i	0.495418	+	0.286030i	−0.231401	+	0.972858i	$0.574331\pi$
$294$		0			0
$295$	5.37324	+	14.8473i	0.312842	+	0.864446i
$296$	−8.38090	−	14.5161i	−0.487130	−	0.843734i
$297$		0			0
$298$		−	26.4814i		−	1.53402i
$299$	0.530689	−	1.12547i	0.0306905	−	0.0650876i
$300$		0			0
$301$	1.35913	+	2.35408i	0.0783390	+	0.135687i
$302$	19.7042	−	11.3762i	1.13385	−	0.654628i
$303$		0			0
$304$	14.5325			0.833497
$305$	−5.14528	−	14.2174i	−0.294618	−	0.814088i
$306$		0			0
$307$		−	22.1046i		−	1.26158i	−0.775955	−	0.630788i	$-0.782732\pi$
$307$		−	22.1046i		−	1.26158i	0.775955	−	0.630788i	$-0.217268\pi$
$308$	4.02617	+	2.32451i	0.229412	+	0.132451i
$309$		0			0
$310$	0.549883	−	3.08551i	0.0312313	−	0.175245i
$311$	−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	$-0.264622\pi$
$314$	3.68231	+	6.37794i	0.207805	+	0.359928i
$315$		0			0
$316$	3.29958	−	5.71504i	0.185616	−	0.321496i
$317$		−	11.8428i		−	0.665159i	−0.943075	−	0.332580i	$-0.892081\pi$
$317$		−	11.8428i		−	0.665159i	0.943075	−	0.332580i	$-0.107919\pi$
$318$		0			0
$319$	5.82135	−	10.0829i	0.325933	−	0.564532i
$320$	12.6209	−	14.9852i	0.705531	−	0.837701i
$321$		0			0
$322$	−0.720215	+	0.415816i	−0.0401360	+	0.0231725i
$323$	−27.7576	+	16.0259i	−1.54448	+	0.891704i
$324$		0			0
$325$	12.6459	+	12.8484i	0.701471	+	0.712698i
$326$	−14.1716			−0.784890
$327$		0			0
$328$	0.480695	−	0.277529i	0.0265419	−	0.0153240i
$329$	−12.4622	+	21.5852i	−0.687064	+	1.19003i
$330$		0			0
$331$	6.35021	−	10.9989i	0.349039	−	0.604553i	−0.637040	−	0.770831i	$-0.719841\pi$
$331$	6.35021	−	10.9989i	0.349039	−	0.604553i	0.986079	+	0.166277i	$0.0531747\pi$
$332$	−4.00516	−	2.31238i	−0.219812	−	0.126908i
$333$		0			0
$334$	−1.20488	+	2.08691i	−0.0659281	+	0.114191i
$335$	1.72786	−	9.69538i	0.0944031	−	0.529715i
$336$		0			0
$337$		−	15.2939i		−	0.833113i	−0.909110	−	0.416556i	$-0.863237\pi$
$337$		−	15.2939i		−	0.833113i	0.909110	−	0.416556i	$-0.136763\pi$
$338$	2.55015	+	15.2232i	0.138710	+	0.828034i
$339$		0			0
$340$	−1.26205	+	7.08161i	−0.0684441	+	0.384054i
$341$	2.29066	+	3.96754i	0.124046	+	0.214854i
$342$		0			0
$343$			20.0538i			1.08281i
$344$	−2.05955	+	3.56725i	−0.111044	+	0.192333i
$345$		0			0
$346$	1.59024			0.0854918
$347$	10.5998	+	6.11981i	0.569029	+	0.328529i	0.756761	−	0.653691i	$-0.226781\pi$
$347$	10.5998	+	6.11981i	0.569029	+	0.328529i	−0.187733	+	0.982220i	$0.560114\pi$
$348$		0			0
$349$	9.35021	+	16.1950i	0.500505	+	0.866901i	1.00000		0.000583538i	$0.000185746\pi$
$349$	9.35021	+	16.1950i	0.500505	+	0.866901i	−0.499495	+	0.866317i	$0.666481\pi$
$350$	−2.04880	−	11.8733i	−0.109513	−	0.634656i
$351$		0			0
$352$			12.4844i			0.665422i
$353$	1.13348	−	0.654413i	0.0603288	−	0.0348309i	−0.469532	−	0.882915i	$-0.655577\pi$
$353$	1.13348	−	0.654413i	0.0603288	−	0.0348309i	0.529861	+	0.848084i	$0.322244\pi$
$354$		0			0
$355$	−1.43124	−	3.95480i	−0.0759623	−	0.209899i
$356$	7.22563			0.382957
$357$		0			0
$358$	20.7956	+	12.0063i	1.09908	+	0.634554i
$359$	−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
$362$	−20.3834	+	11.7684i	−1.07133	+	0.618531i
$363$		0			0
$364$	−1.84210	+	3.90666i	−0.0965520	+	0.204765i
$365$	15.1534	+	12.7626i	0.793168	+	0.668024i
$366$		0			0
$367$	−28.9531	+	16.7161i	−1.51134	+	0.872573i	−0.511429	+	0.859326i	$0.670884\pi$
$367$	−28.9531	+	16.7161i	−1.51134	+	0.872573i	−0.999912	+	0.0132473i	$0.995783\pi$
$368$	−0.738559	−	0.426407i	−0.0385001	−	0.0222280i
$369$		0			0
$370$	−4.92410	−	13.6063i	−0.255992	−	0.707358i
$371$	2.46222	−	4.26469i	0.127832	−	0.221412i
$372$		0			0
$373$	−29.8589	−	17.2391i	−1.54604	−	0.892604i	−0.998438	−	0.0558628i	$-0.982209\pi$
$373$	−29.8589	−	17.2391i	−1.54604	−	0.892604i	−0.547598	−	0.836742i	$-0.684458\pi$
$374$	12.5569	+	21.7492i	0.649303	+	1.12463i
$375$		0			0
$376$	−37.7691			−1.94779
$377$	9.78357	+	4.61322i	0.503879	+	0.237593i
$378$		0			0
$379$	−8.70225	−	15.0727i	−0.447004	−	0.774234i	0.551185	−	0.834383i	$-0.314176\pi$
$379$	−8.70225	−	15.0727i	−0.447004	−	0.774234i	−0.998189	+	0.0601487i	$0.980843\pi$
$380$	−7.64130	−	1.36179i	−0.391991	−	0.0698585i
$381$		0			0
$382$			1.82586i			0.0934191i
$383$	−1.51271	−	0.873366i	−0.0772961	−	0.0446269i	0.460854	−	0.887476i	$-0.347543\pi$
$383$	−1.51271	−	0.873366i	−0.0772961	−	0.0446269i	−0.538150	+	0.842849i	$0.680877\pi$
$384$		0			0
$385$	13.4711	+	11.3457i	0.686553	+	0.578231i
$386$	12.5876	−	21.8024i	0.640692	−	1.10971i
$387$		0			0
$388$	−2.96773	+	1.71342i	−0.150664	+	0.0869857i
$389$	22.0435			1.11765			0.558826	−	0.829285i	$-0.311252\pi$
$389$	22.0435			1.11765			0.558826	+	0.829285i	$0.311252\pi$
$390$		0			0
$391$	1.88090			0.0951212
$392$	−7.67311	+	4.43007i	−0.387550	+	0.223752i
$393$		0			0
$394$	−5.49554	+	9.51855i	−0.276861	+	0.479538i
$395$	16.1049	−	19.1219i	0.810326	−	0.962127i
$396$		0			0
$397$	19.5132	+	11.2660i	0.979339	+	0.565422i	0.902071	−	0.431588i	$-0.142047\pi$
$397$	19.5132	+	11.2660i	0.979339	+	0.565422i	0.0772687	+	0.997010i	$0.475380\pi$
$398$		−	20.6649i		−	1.03584i
$399$		0			0
$400$	9.49402	−	7.90739i	0.474701	−	0.395369i
$401$	−1.85204	−	3.20782i	−0.0924863	−	0.160191i	0.816070	−	0.577953i	$-0.196148\pi$
$401$	−1.85204	−	3.20782i	−0.0924863	−	0.160191i	−0.908557	+	0.417761i	$0.862815\pi$
$402$		0			0
$403$	−3.49695	+	2.42636i	−0.174196	+	0.120866i
$404$	3.50737			0.174498
$405$		0			0
$406$	−3.61464	−	6.26074i	−0.179392	−	0.310715i
$407$	18.3177	+	10.5757i	0.907975	+	0.524220i
$408$		0			0
$409$	−6.74186	+	11.6772i	−0.333363	+	0.577402i	−0.983169	−	0.182698i	$-0.941517\pi$
$409$	−6.74186	+	11.6772i	−0.333363	+	0.577402i	0.649806	+	0.760100i	$0.274850\pi$
$410$	0.450566	−	0.163059i	0.0222519	−	0.00805292i
$411$		0			0
$412$	−3.28871	−	1.89874i	−0.162023	−	0.0935440i
$413$	−12.4114	+	7.16573i	−0.610726	+	0.352603i
$414$		0			0
$415$	−13.4008	−	11.2865i	−0.657821	−	0.554033i
$416$	−11.5587	+	0.961445i	−0.566714	+	0.0471387i
$417$		0			0
$418$	−23.4682	+	13.5494i	−1.14787	+	0.662721i
$419$	−8.41159	−	14.5693i	−0.410933	−	0.711757i	0.584059	−	0.811711i	$-0.301464\pi$
$419$	−8.41159	−	14.5693i	−0.410933	−	0.711757i	−0.994992	+	0.0999544i	$0.968130\pi$
$420$		0			0
$421$	17.1013			0.833464			0.416732	−	0.909029i	$-0.363175\pi$
$421$	17.1013			0.833464			0.416732	+	0.909029i	$0.363175\pi$
$422$	−7.48753	−	4.32293i	−0.364487	−	0.210437i
$423$		0			0
$424$	7.46222			0.362397
$425$	−9.41397	+	25.5730i	−0.456645	+	1.24047i
$426$		0			0
$427$	11.8849	−	6.86173i	0.575149	−	0.332062i
$428$		−	10.4349i		−	0.504392i
$429$		0			0
$430$	−2.29066	+	2.71978i	−0.110465	+	0.131159i
$431$	4.83027	+	8.36627i	0.232666	+	0.402989i	0.958592	−	0.284784i	$-0.0919218\pi$
$431$	4.83027	+	8.36627i	0.232666	+	0.402989i	−0.725926	+	0.687773i	$0.758588\pi$
$432$		0			0
$433$	21.4538	+	12.3863i	1.03100	+	0.595249i	0.917272	−	0.398262i	$-0.130387\pi$
$433$	21.4538	+	12.3863i	1.03100	+	0.595249i	0.113730	+	0.993512i	$0.463720\pi$
$434$	2.84467			0.136549
$435$		0			0
$436$	1.70042	−	2.94521i	0.0814354	−	0.141050i
$437$			2.02956i			0.0970869i
$438$		0			0
$439$	3.53069	+	6.11533i	0.168511	+	0.291869i	0.937896	−	0.346915i	$-0.112771\pi$
$439$	3.53069	+	6.11533i	0.168511	+	0.291869i	−0.769386	+	0.638784i	$0.779438\pi$
$440$	−4.68257	+	26.2749i	−0.223233	+	1.25261i
$441$		0			0
$442$	−19.1696	+	13.3008i	−0.911803	+	0.632655i
$443$		−	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
$445$	26.9490	+	4.80271i	1.27751	+	0.227670i
$446$	−11.5569	+	20.0172i	−0.547236	+	0.947840i
$447$		0			0
$448$	15.4002	+	8.89128i	0.727589	+	0.420074i
$449$	6.24003	−	10.8080i	0.294485	−	0.510063i	−0.680380	−	0.732860i	$-0.738185\pi$
$449$	6.24003	−	10.8080i	0.294485	−	0.510063i	0.974865	+	0.222796i	$0.0715185\pi$
$450$		0			0
$451$	−0.350210	+	0.606582i	−0.0164908	+	0.0285628i
$452$	−2.43309	+	1.40475i	−0.114443	+	0.0660738i
$453$		0			0
$454$	−5.71300			−0.268124
$455$	−9.46703	+	13.3460i	−0.443821	+	0.625672i
$456$		0			0
$457$	7.12930	−	4.11610i	0.333495	−	0.192543i	−0.323897	−	0.946092i	$-0.604993\pi$
$457$	7.12930	−	4.11610i	0.333495	−	0.192543i	0.657392	+	0.753549i	$0.271660\pi$
$458$	1.56665	−	0.904508i	0.0732050	−	0.0422649i
$459$		0			0
$460$	0.348383	+	0.293416i	0.0162434	+	0.0136806i
$461$	−2.27072	+	3.93300i	−0.105758	+	0.183178i	−0.914048	−	0.405607i	$-0.867060\pi$
$461$	−2.27072	+	3.93300i	−0.105758	+	0.183178i	0.808290	+	0.588785i	$0.200394\pi$
$462$		0			0
$463$			1.98845i			0.0924113i	0.998932	+	0.0462056i	$0.0147130\pi$
$463$			1.98845i			0.0924113i	−0.998932	+	0.0462056i	$0.985287\pi$
$464$	3.70671	−	6.42021i	0.172080	−	0.298051i
$465$		0			0
$466$	8.29066	+	14.3598i	0.384057	+	0.665207i
$467$			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
$470$	−32.0991	−	5.72053i	−1.48062	−	0.263868i
$471$		0			0
$472$	−18.8076	−	10.8586i	−0.865689	−	0.499806i
$473$		−	5.19783i		−	0.238997i
$474$		0			0
$475$	−27.5942	−	10.1580i	−1.26611	−	0.466081i
$476$	−6.52886			−0.299250
$477$		0			0
$478$	−4.11304	+	2.37467i	−0.188126	+	0.108615i
$479$	15.4027	+	26.6782i	0.703766	+	1.21896i	0.967135	+	0.254263i	$0.0818329\pi$
$479$	15.4027	+	26.6782i	0.703766	+	1.21896i	−0.263369	+	0.964695i	$0.584834\pi$
$480$		0			0
$481$	−8.38090	+	17.7740i	−0.382136	+	0.810423i
$482$			20.7378i			0.944582i
$483$		0			0
$484$	−1.19859	−	2.07602i	−0.0544815	−	0.0943647i
$485$	−12.2074	+	4.41786i	−0.554312	+	0.200605i
$486$		0			0
$487$	19.3341	+	11.1626i	0.876113	+	0.505824i	0.869375	−	0.494153i	$-0.164522\pi$
$487$	19.3341	+	11.1626i	0.876113	+	0.505824i	0.00673807	+	0.999977i	$0.497855\pi$
$488$	18.0097	+	10.3979i	0.815259	+	0.470690i
$489$		0			0
$490$	−7.19217	+	2.60284i	−0.324909	+	0.117584i
$491$	5.34129	+	9.25139i	0.241049	+	0.417509i	0.961013	−	0.276502i	$-0.0891752\pi$
$491$	5.34129	+	9.25139i	0.241049	+	0.417509i	−0.719964	+	0.694011i	$0.755842\pi$
$492$		0			0
$493$			16.3504i			0.736386i
$494$	−14.3520	−	20.6846i	−0.645729	−	0.930646i
$495$		0			0
$496$	1.45856	+	2.52631i	0.0654914	+	0.113434i
$497$	3.30596	−	1.90870i	0.148292	−	0.0856167i
$498$		0			0
$499$	−18.8195			−0.842477			−0.421239	−	0.906950i	$-0.638405\pi$
$499$	−18.8195			−0.842477			−0.421239	+	0.906950i	$0.638405\pi$
$500$	−5.73300	+	3.26811i	−0.256388	+	0.146154i
$501$		0			0
$502$			11.0417i			0.492815i
$503$	4.92013	+	2.84064i	0.219378	+	0.126658i	0.605662	−	0.795722i	$-0.292908\pi$
$503$	4.92013	+	2.84064i	0.219378	+	0.126658i	−0.386284	+	0.922380i	$0.626242\pi$
$504$		0			0
$505$	13.0812	+	2.33127i	0.582107	+	0.103740i
$506$	1.59024			0.0706948
$507$		0			0
$508$		−	9.86062i		−	0.437494i
$509$	−13.9622	−	24.1833i	−0.618864	−	1.07190i	−0.989693	−	0.143203i	$-0.954260\pi$
$509$	−13.9622	−	24.1833i	−0.618864	−	1.07190i	0.370829	−	0.928701i	$-0.379074\pi$
$510$		0			0
$511$	−8.99108	+	15.5730i	−0.397742	+	0.688909i
$512$			23.1492i			1.02306i
$513$		0			0
$514$	6.46485	−	11.1975i	0.285152	−	0.493898i
$515$	−11.0037	−	9.26754i	−0.484879	−	0.408376i
$516$		0			0
$517$	41.2750	−	23.8301i	1.81527	−	1.04805i
$518$	11.3740	−	6.56677i	0.499744	−	0.288527i
$519$		0			0
$520$	−24.6873	−	2.31190i	−1.08261	−	0.101384i
$521$	−6.29958			−0.275990			−0.137995	−	0.990433i	$-0.544066\pi$
$521$	−6.29958			−0.275990			−0.137995	+	0.990433i	$0.544066\pi$
$522$		0			0
$523$	−19.7948	+	11.4285i	−0.865567	+	0.499735i	−0.865873	−	0.500265i	$-0.833236\pi$
$523$	−19.7948	+	11.4285i	−0.865567	+	0.499735i	0.000305526		1.00000i	$0.499903\pi$
$524$	2.95120	−	5.11162i	0.128924	−	0.223302i
$525$		0			0
$526$	7.97925	−	13.8205i	0.347912	−	0.602601i
$527$	−5.57182	−	3.21689i	−0.242712	−	0.140130i
$528$		0			0
$529$	−11.4404	+	19.8154i	−0.497411	+	0.861541i
$530$	6.34196	+	1.13023i	0.275477	+	0.0490941i
$531$		0			0
$532$		−	7.04487i		−	0.305434i
$533$	−0.588576	−	0.277529i	−0.0254940	−	0.0120211i
$534$		0			0
$535$	6.93588	−	38.9186i	0.299864	−	1.68260i
$536$	6.77255	+	11.7304i	0.292529	+	0.506676i
$537$		0			0
$538$		−	4.34628i		−	0.187381i
$539$	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	$0.565326\pi$
$542$	22.6255	+	13.0628i	0.971848	+	0.561097i
$543$		0			0
$544$	−8.76626	−	15.1836i	−0.375850	−	0.650992i
$545$	8.29958	−	9.85437i	0.355515	−	0.422115i
$546$		0			0
$547$			33.3911i			1.42770i	0.700299	+	0.713850i	$0.253050\pi$
$547$			33.3911i			1.42770i	−0.700299	+	0.713850i	$0.746950\pi$
$548$	−1.01101	+	0.583706i	−0.0431882	+	0.0249347i
$549$		0			0
$550$	−7.95921	+	21.6212i	−0.339382	+	0.921929i
$551$	−17.6427			−0.751604
$552$		0			0
$553$	19.6513	+	11.3457i	0.835660	+	0.482469i
$554$	11.7492			0.499177
$555$		0			0
$556$	2.56767	+	4.44733i	0.108893	+	0.188609i
$557$	32.7053	−	18.8824i	1.38577	−	0.800073i	0.392932	−	0.919567i	$-0.371461\pi$
$557$	32.7053	−	18.8824i	1.38577	−	0.800073i	0.992835	+	0.119495i	$0.0381274\pi$
$558$		0			0
$559$	4.81243	−	0.400293i	0.203544	−	0.0169306i
$560$	8.57766	+	7.22431i	0.362472	+	0.305283i
$561$		0			0
$562$	4.17616	−	2.41110i	0.176161	−	0.101706i
$563$	−22.4307	−	12.9504i	−0.945343	−	0.545794i	−0.0537120	−	0.998556i	$-0.517105\pi$
$563$	−22.4307	−	12.9504i	−0.945343	−	0.545794i	−0.891631	+	0.452762i	$0.850439\pi$
$564$		0			0
$565$	−10.0083	+	3.62198i	−0.421051	+	0.152378i
$566$	−3.61464	+	6.26074i	−0.151935	+	0.263159i
$567$		0			0
$568$	5.00967	+	2.89233i	0.210201	+	0.121360i
$569$	10.7725	+	18.6586i	0.451609	+	0.782209i	0.998486	−	0.0550035i	$-0.0175170\pi$
$569$	10.7725	+	18.6586i	0.451609	+	0.782209i	−0.546878	+	0.837213i	$0.684184\pi$
$570$		0			0
$571$	−2.22036			−0.0929192			−0.0464596	−	0.998920i	$-0.514794\pi$
$571$	−2.22036			−0.0929192			−0.0464596	+	0.998920i	$0.514794\pi$
$572$	6.78566	−	4.70823i	0.283723	−	0.196861i
$573$		0			0
$574$	0.217455	+	0.376644i	0.00907641	+	0.0157208i
$575$	1.10432	+	1.32590i	0.0460532	+	0.0552938i
$576$		0			0
$577$			6.20265i			0.258220i	0.991630	+	0.129110i	$0.0412120\pi$
$577$			6.20265i			0.258220i	−0.991630	+	0.129110i	$0.958788\pi$
$578$	−13.0631	−	7.54199i	−0.543353	−	0.313705i
$579$		0			0
$580$	−2.55063	+	3.02845i	−0.105909	+	0.125749i
$581$	7.95120	−	13.7719i	0.329871	−	0.571354i
$582$		0			0
$583$	−8.15489	+	4.70823i	−0.337741	+	0.194995i
$584$	−27.2492			−1.12758
$585$		0			0
$586$	−11.6265			−0.480285
$587$	−1.58391	+	0.914469i	−0.0653748	+	0.0377442i	−0.532331	−	0.846536i	$-0.678684\pi$
$587$	−1.58391	+	0.914469i	−0.0653748	+	0.0377442i	0.466956	+	0.884280i	$0.345351\pi$
$588$		0			0
$589$	3.47114	−	6.01219i	0.143026	−	0.247728i
$590$	−14.3395	−	12.0770i	−0.590346	−	0.497204i
$591$		0			0
$592$	11.6637	+	6.73403i	0.479374	+	0.276767i
$593$			0.0728761i			0.00299266i	0.999999	+	0.00149633i	$0.000476297\pi$
$593$			0.0728761i			0.00299266i	−0.999999	+	0.00149633i	$0.999524\pi$
$594$		0			0
$595$	−24.3503	−	4.33959i	−0.998266	−	0.177906i
$596$	−6.58212	−	11.4006i	−0.269614	−	0.466986i
$597$		0			0
$598$	0.122467	+	1.47233i	0.00500804	+	0.0602080i
$599$	−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	0.819944	+	0.572444i	$0.194005\pi$
$601$	22.2041	+	38.4586i	0.905723	+	1.56876i	0.0857795	+	0.996314i	$0.472662\pi$
$602$	−2.79508	−	1.61374i	−0.113919	−	0.0657712i
$603$		0			0
$604$	5.65527	−	9.79522i	0.230110	−	0.398562i
$605$	−3.09044	−	8.53951i	−0.125644	−	0.347180i
$606$		0			0
$607$	31.3808	+	18.1177i	1.27371	+	0.735375i	0.975684	−	0.219183i	$-0.0703392\pi$
$607$	31.3808	+	18.1177i	1.27371	+	0.735375i	0.298024	+	0.954558i	$0.403672\pi$
$608$	16.3836	−	9.45910i	0.664445	−	0.383617i
$609$		0			0
$610$	13.7311	+	11.5647i	0.555956	+	0.468239i
$611$	25.2419	+	36.3794i	1.02118	+	1.47175i
$612$		0			0
$613$	2.90838	−	1.67915i	0.117468	−	0.0678203i	−0.440115	−	0.897942i	$-0.645062\pi$
$613$	2.90838	−	1.67915i	0.117468	−	0.0678203i	0.557583	+	0.830121i	$0.311729\pi$
$614$	13.1228	+	22.7293i	0.529591	+	0.917279i
$615$		0			0
$616$	−24.2240			−0.976013
$617$	18.3441	+	10.5910i	0.738507	+	0.426377i	0.821526	−	0.570171i	$-0.193123\pi$
$617$	18.3441	+	10.5910i	0.738507	+	0.426377i	−0.0830194	+	0.996548i	$0.526456\pi$
$618$		0			0
$619$	−25.4082			−1.02124			−0.510620	−	0.859807i	$-0.670584\pi$
$619$	−25.4082			−1.02124			−0.510620	+	0.859807i	$0.670584\pi$
$620$	−0.530192	−	1.46503i	−0.0212930	−	0.0588369i
$621$		0			0
$622$	7.85493	−	4.53504i	0.314954	−	0.181839i
$623$			24.8455i			0.995416i
$624$		0			0
$625$	−23.5543	+	8.37828i	−0.942171	+	0.335131i
$626$	15.5199	+	26.8813i	0.620302	+	1.07439i
$627$		0			0
$628$	3.17056	+	1.83052i	0.126519	+	0.0730459i
$629$	−29.7041			−1.18438
$630$		0			0
$631$	−21.7725	+	37.7112i	−0.866751	+	1.50126i	−0.00145375	+	0.999999i	$0.500463\pi$
$631$	−21.7725	+	37.7112i	−0.866751	+	1.50126i	−0.865298	+	0.501258i	$0.832871\pi$
$632$			34.3853i			1.36777i
$633$		0			0
$634$	7.03069	+	12.1775i	0.279224	+	0.483631i
$635$	6.55413	−	36.7766i	0.260093	−	1.45943i
$636$		0			0
$637$	9.39516	+	4.43007i	0.372250	+	0.175526i
$638$			13.8238i			0.547288i
$639$		0			0
$640$	−1.55727	+	8.73816i	−0.0615565	+	0.345406i
$641$	24.1427	−	41.8164i	0.953579	−	1.65165i	0.215993	−	0.976395i	$-0.430701\pi$
$641$	24.1427	−	41.8164i	0.953579	−	1.65165i	0.737586	−	0.675253i	$-0.235965\pi$
$642$		0			0
$643$	−36.6710	−	21.1720i	−1.44616	−	0.834943i	−0.447913	−	0.894077i	$-0.647833\pi$
$643$	−36.6710	−	21.1720i	−1.44616	−	0.834943i	−0.998250	+	0.0591344i	$0.981166\pi$
$644$	−0.206708	+	0.358028i	−0.00814543	+	0.0141083i
$645$		0			0
$646$	19.0281	−	32.9576i	0.748649	−	1.29670i
$647$	29.7958	−	17.2026i	1.17139	−	0.676305i	0.217386	−	0.976086i	$-0.430247\pi$
$647$	29.7958	−	17.2026i	1.17139	−	0.676305i	0.954008	+	0.299781i	$0.0969136\pi$
$648$		0			0
$649$	27.4045			1.07572
$650$	−20.6310	−	5.70398i	−0.809213	−	0.223729i
$651$		0			0
$652$	−6.10104	+	3.52244i	−0.238935	+	0.137949i
$653$	−12.4114	+	7.16573i	−0.485696	+	0.280417i	−0.722787	−	0.691071i	$-0.757139\pi$
$653$	−12.4114	+	7.16573i	−0.485696	+	0.280417i	0.237091	+	0.971487i	$0.423806\pi$
$654$		0			0
$655$	14.4045	−	17.1029i	0.562830	−	0.668267i
$656$	−0.222994	+	0.386237i	−0.00870646	+	0.0150800i
$657$		0			0
$658$		−	29.5936i		−	1.15368i
$659$	−11.4116	+	19.7655i	−0.444532	+	0.769953i	−0.998020	−	0.0629051i	$-0.979963\pi$
$659$	−11.4116	+	19.7655i	−0.444532	+	0.769953i	0.553487	+	0.832858i	$0.313297\pi$
$660$		0			0
$661$	−7.20934	−	12.4869i	−0.280411	−	0.485686i	0.691075	−	0.722783i	$-0.257137\pi$
$661$	−7.20934	−	12.4869i	−0.280411	−	0.485686i	−0.971486	+	0.237097i	$0.923804\pi$
$662$			15.0796i			0.586087i
$663$		0			0
$664$	24.0976			0.935168
$665$	4.68257	−	26.2749i	0.181582	−	1.01890i
$666$		0			0
$667$	0.896622	+	0.517665i	0.0347173	+	0.0200441i
$668$			1.19792i			0.0463491i
$669$		0			0
$670$	3.97913	+	10.9952i	0.153727	+	0.424780i
$671$	−26.2419			−1.01306
$672$		0			0
$673$	29.5956	−	17.0871i	1.14083	−	0.658657i	0.194193	−	0.980963i	$-0.437791\pi$
$673$	29.5956	−	17.0871i	1.14083	−	0.658657i	0.946636	+	0.322306i	$0.104458\pi$
$674$	9.07949	+	15.7261i	0.349729	+	0.605748i
$675$		0			0
$676$	4.88170	+	5.91993i	0.187758	+	0.227690i
$677$		−	5.84695i		−	0.224716i	−0.993668	−	0.112358i	$-0.964160\pi$
$677$		−	5.84695i		−	0.224716i	0.993668	−	0.112358i	$-0.0358404\pi$
$678$		0			0
$679$	−5.89165	−	10.2046i	−0.226101	−	0.391618i
$680$	−12.7546	−	35.2436i	−0.489117	−	1.35153i
$681$		0			0
$682$	−4.71079	−	2.71978i	−0.180386	−	0.104146i
$683$	9.82834	+	5.67439i	0.376071	+	0.217125i	0.676107	−	0.736803i	$-0.263666\pi$
$683$	9.82834	+	5.67439i	0.376071	+	0.217125i	−0.300036	+	0.953928i	$0.596999\pi$
$684$		0			0
$685$	−4.15868	+	1.50502i	−0.158895	+	0.0575039i
$686$	−11.9053	−	20.6206i	−0.454546	−	0.787298i
$687$		0			0
$688$		−	3.30969i		−	0.126181i
$689$	−4.98715	−	7.18765i	−0.189995	−	0.273828i
$690$		0			0
$691$	9.41159	+	16.3013i	0.358034	+	0.620133i	0.987632	−	0.156788i	$-0.0501140\pi$
$691$	9.41159	+	16.3013i	0.358034	+	0.620133i	−0.629599	+	0.776921i	$0.716781\pi$
$692$	0.684619	−	0.395265i	0.0260253	−	0.0150257i
$693$		0			0
$694$	−14.5325			−0.551647
$695$	6.62044	+	18.2936i	0.251128	+	0.693916i
$696$		0			0
$697$		−	0.983636i		−	0.0372579i
$698$	−19.2289	−	11.1018i	−0.727825	−	0.420210i
$699$		0			0
$700$	−3.83323	−	4.60238i	−0.144883	−	0.173954i
$701$	−19.1626			−0.723763			−0.361881	−	0.932224i	$-0.617865\pi$
$701$	−19.1626			−0.723763			−0.361881	+	0.932224i	$0.617865\pi$
$702$		0			0
$703$		−	32.0518i		−	1.20885i
$704$	−17.0018	−	29.4480i	−0.640780	−	1.10986i
$705$		0			0
$706$	−0.777006	+	1.34581i	−0.0292430	+	0.0506504i
$707$			12.0602i			0.453570i
$708$		0			0
$709$	11.7419	−	20.3375i	0.440975	−	0.763791i	−0.556787	−	0.830655i	$-0.687966\pi$
$709$	11.7419	−	20.3375i	0.440975	−	0.763791i	0.997762	+	0.0668645i	$0.0212995\pi$
$710$	3.81952	+	3.21689i	0.143344	+	0.120728i
$711$		0			0
$712$	−32.6055	+	18.8248i	−1.22194	+	0.705488i
$713$	−0.352814	+	0.203698i	−0.0132130	+	0.00762853i
$714$		0			0
$715$	28.4375	−	13.0497i	1.06350	−	0.488033i
$716$	11.9370			0.446107
$717$		0			0
$718$	30.2393	−	17.4586i	1.12852	−	0.651551i
$719$	7.05429	−	12.2184i	0.263080	−	0.455669i	−0.703978	−	0.710221i	$-0.748595\pi$
$719$	7.05429	−	12.2184i	0.263080	−	0.455669i	0.967059	+	0.254553i	$0.0819282\pi$
$720$		0			0
$721$	6.52886	−	11.3083i	0.243148	−	0.421144i
$722$	16.0254	+	9.25228i	0.596404	+	0.344334i
$723$		0			0
$724$	−5.85021	+	10.1329i	−0.217421	+	0.376585i
$725$	−11.5259	+	9.59969i	−0.428061	+	0.356523i
$726$		0			0
$727$			25.3762i			0.941153i	0.882359	+	0.470576i	$0.155954\pi$
$727$			25.3762i			0.941153i	−0.882359	+	0.470576i	$0.844046\pi$
$728$	−1.86553	−	22.4279i	−0.0691411	−	0.831233i
$729$		0			0
$730$	−23.1584	−	4.12717i	−0.857131	−	0.152754i
$731$	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	$0.936868\pi$
$734$	19.8476	−	34.3770i	0.732587	−	1.26888i
$735$		0			0
$736$	−1.11018			−0.0409218
$737$	−14.8024	−	8.54617i	−0.545254	−	0.314802i
$738$		0			0
$739$	−0.707513	−	1.22545i	−0.0260263	−	0.0450788i	0.852719	−	0.522370i	$-0.174952\pi$
$739$	−0.707513	−	1.22545i	−0.0260263	−	0.0450788i	−0.878745	+	0.477291i	$0.841619\pi$
$740$	−5.50183	−	4.63377i	−0.202251	−	0.170341i
$741$		0			0
$742$			5.84695i			0.214648i
$743$	−25.8748	+	14.9389i	−0.949256	+	0.548053i	−0.892850	−	0.450355i	$-0.851298\pi$
$743$	−25.8748	+	14.9389i	−0.949256	+	0.548053i	−0.0564064	+	0.998408i	$0.517964\pi$
$744$		0			0
$745$	−16.9713	−	46.8951i	−0.621779	−	1.71810i
$746$	40.9370			1.49881
$747$		0			0
$748$	10.8118	+	6.24221i	0.395320	+	0.228238i
$749$	35.8809			1.31106
$750$		0			0
$751$	9.99291	+	17.3082i	0.364646	+	0.631586i	0.988719	−	0.149780i	$-0.0478565\pi$
$751$	9.99291	+	17.3082i	0.364646	+	0.631586i	−0.624073	+	0.781366i	$0.714523\pi$
$752$	26.2816	−	15.1737i	0.958391	−	0.553328i
$753$		0			0
$754$	−12.7988	+	1.06459i	−0.466104	+	0.0387701i
$755$	27.6028	−	32.7737i	1.00457	−	1.19276i
$756$		0			0
$757$	−14.8024	+	8.54617i	−0.538003	+	0.310616i	−0.744269	−	0.667880i	$-0.767202\pi$
$757$	−14.8024	+	8.54617i	−0.538003	+	0.310616i	0.206266	+	0.978496i	$0.433869\pi$
$758$	17.8964	+	10.3325i	0.650025	+	0.375292i
$759$		0			0
$760$	38.0291	−	13.7627i	1.37946	−	0.499225i
$761$	−21.1120	+	36.5671i	−0.765310	+	1.32556i	0.174773	+	0.984609i	$0.444081\pi$
$761$	−21.1120	+	36.5671i	−0.765310	+	1.32556i	−0.940083	+	0.340947i	$0.889252\pi$
$762$		0			0
$763$	10.1272	+	5.84695i	0.366630	+	0.211674i
$764$	0.453830	+	0.786056i	0.0164190	+	0.0284385i
$765$		0			0
$766$	2.07395			0.0749350
$767$	2.11046	+	25.3725i	0.0762044	+	0.916149i
$768$		0			0
$769$	−11.8827	−	20.5815i	−0.428502	−	0.742187i	0.568238	−	0.822864i	$-0.307625\pi$
$769$	−11.8827	−	20.5815i	−0.428502	−	0.742187i	−0.996740	+	0.0806767i	$0.974292\pi$
$770$	−20.5874	−	3.66898i	−0.741919	−	0.132221i
$771$		0			0
$772$		−	12.5149i		−	0.450422i
$773$	0.246026	+	0.142043i	0.00884894	+	0.00510894i	0.504418	−	0.863460i	$-0.331707\pi$
$773$	0.246026	+	0.142043i	0.00884894	+	0.00510894i	−0.495569	+	0.868569i	$0.665040\pi$
$774$		0			0
$775$	−1.00366	−	5.81644i	−0.0360524	−	0.208933i
$776$	8.92787	−	15.4635i	0.320492	−	0.555108i
$777$		0			0
$778$	−22.6665	+	13.0865i	−0.812634	+	0.469174i
$779$	1.06138			0.0380278
$780$		0			0
$781$	−7.29958			−0.261199
$782$	−1.93405	+	1.11663i	−0.0691617	+	0.0399305i
$783$		0			0
$784$	3.55955	−	6.16532i	0.127127	−	0.220190i
$785$	10.6084	+	8.93460i	0.378628	+	0.318890i
$786$		0			0
$787$	−20.9008	−	12.0671i	−0.745032	−	0.430145i	0.0788638	−	0.996885i	$-0.474871\pi$
$787$	−20.9008	−	12.0671i	−0.745032	−	0.430145i	−0.823896	+	0.566741i	$0.808204\pi$
$788$			5.46381i			0.194640i
$789$		0			0
$790$	−5.20802	+	29.2233i	−0.185293	+	1.03972i
$791$	−4.83027	−	8.36627i	−0.171745	−	0.297470i
$792$		0			0
$793$	−2.02093	−	24.2961i	−0.0717652	−	0.862780i
$794$	−26.7529			−0.949424
$795$		0			0
$796$	−5.13641	−	8.89652i	−0.182055	−	0.315329i
$797$	−29.7430	−	17.1721i	−1.05355	−	0.608267i	−0.129909	−	0.991526i	$-0.541468\pi$
$797$	−29.7430	−	17.1721i	−1.05355	−	0.608267i	−0.923641	+	0.383259i	$0.874802\pi$
$798$		0			0
$799$	−33.4659	+	57.9646i	−1.18394	+	2.05064i
$800$	5.55650	−	15.0942i	0.196452	−	0.533661i
$801$		0			0
$802$	3.80876	+	2.19899i	0.134492	+	0.0776489i
$803$	29.7786	−	17.1927i	1.05086	−	0.606716i
$804$		0			0
$805$	−1.00892	+	1.19792i	−0.0355598	+	0.0422213i
$806$	2.15533	−	4.57096i	0.0759182	−	0.161005i
$807$		0			0
$808$	−15.8269	+	9.13767i	−0.556789	+	0.321462i
$809$	23.8431	+	41.2975i	0.838279	+	1.45194i	0.891332	+	0.453351i	$0.149771\pi$
$809$	23.8431	+	41.2975i	0.838279	+	1.45194i	−0.0530528	+	0.998592i	$0.516895\pi$
$810$		0			0
$811$	24.5992			0.863793			0.431897	−	0.901923i	$-0.357845\pi$
$811$	24.5992			0.863793			0.431897	+	0.901923i	$0.357845\pi$
$812$	−3.11230	−	1.79689i	−0.109220	−	0.0630584i
$813$		0			0
$814$	−25.1138			−0.880239
$815$	−25.0960	+	9.08221i	−0.879074	+	0.318136i
$816$		0			0
$817$	−6.82125	+	3.93825i	−0.238645	+	0.137782i
$818$		−	16.0097i		−	0.559765i
$819$		0			0
$820$	0.153445	−	0.182190i	0.00535853	−	0.00636236i
$821$	8.64979	+	14.9819i	0.301880	+	0.522871i	0.976562	−	0.215237i	$-0.0690526\pi$
$821$	8.64979	+	14.9819i	0.301880	+	0.522871i	−0.674682	+	0.738109i	$0.735719\pi$
$822$		0			0
$823$	−28.2000	−	16.2813i	−0.982990	−	0.567529i	−0.0798182	−	0.996809i	$-0.525434\pi$
$823$	−28.2000	−	16.2813i	−0.982990	−	0.567529i	−0.903171	+	0.429280i	$0.858767\pi$
$824$	19.7869			0.689311
$825$		0			0
$826$	8.50812	−	14.7365i	0.296035	−	0.512748i
$827$			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	0.711922	−	0.702258i	$-0.247825\pi$
$829$	−7.26180	−	12.5778i	−0.252213	−	0.436845i	−0.964135	+	0.265413i	$0.914492\pi$
$830$	20.4800	+	3.64984i	0.710870	+	0.126688i
$831$		0			0
$832$	25.9552	−	18.0090i	0.899835	−	0.624351i
$833$			15.7013i			0.544018i
$834$		0			0
$835$	−0.796234	+	4.46783i	−0.0275548	+	0.154616i
$836$	−6.73557	+	11.6663i	−0.232955	+	0.403489i
$837$		0			0
$838$	17.2986	+	9.98736i	0.597571	+	0.345008i
$839$	−0.407933	+	0.706561i	−0.0140834	+	0.0243932i	−0.872981	−	0.487754i	$-0.837816\pi$
$839$	−0.407933	+	0.706561i	−0.0140834	+	0.0243932i	0.858898	+	0.512147i	$0.171150\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−17.5846	+	10.1524i	−0.606004	+	0.349876i
$843$		0			0
$844$	−4.29797			−0.147942
$845$	14.2722	+	25.3240i	0.490978	+	0.871172i
$846$		0			0
$847$	7.13847	−	4.12140i	0.245281	−	0.141613i
$848$	−5.19258	+	2.99794i	−0.178314	+	0.102950i
$849$		0			0
$850$	−5.50183	−	31.8845i	−0.188711	−	1.09363i
$851$	−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	$-0.111734\pi$
$854$	−8.14716	+	14.1113i	−0.278790	+	0.482878i
$855$		0			0
$856$	27.1860	+	47.0875i	0.929197	+	1.60942i
$857$		−	40.7886i		−	1.39331i	−0.717406	−	0.696656i	$-0.754671\pi$
$857$		−	40.7886i		−	1.39331i	0.717406	−	0.696656i	$-0.245329\pi$
$858$		0			0
$859$	40.1301			1.36922			0.684610	−	0.728909i	$-0.259972\pi$
$859$	40.1301			1.36922			0.684610	+	0.728909i	$0.259972\pi$
$860$	−0.310140	+	1.74026i	−0.0105757	+	0.0593423i
$861$		0			0
$862$	−9.93355	−	5.73514i	−0.338338	−	0.195340i
$863$		−	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
$865$	2.81611	−	1.01915i	0.0957505	−	0.0346520i
$866$	−29.4134			−0.999509
$867$		0			0
$868$	1.22467	−	0.707062i	0.0415679	−	0.0239993i
$869$	−21.6952	−	37.5771i	−0.735958	−	1.27472i
$870$		0			0
$871$	6.77255	−	14.3630i	0.229479	−	0.486672i
$872$			17.7203i			0.600084i
$873$		0			0
$874$	−1.20488	−	2.08691i	−0.0407557	−	0.0705909i
$875$	−11.2375	−	19.7131i	−0.379897	−	0.666424i
$876$		0			0
$877$	−40.3520	−	23.2972i	−1.36259	−	0.786691i	−0.372621	−	0.927984i	$-0.621541\pi$
$877$	−40.3520	−	23.2972i	−1.36259	−	0.786691i	−0.989968	+	0.141293i	$0.954874\pi$
$878$	−7.26094	−	4.19210i	−0.245045	−	0.141477i
$879$		0			0
$880$	−7.29753	−	20.1646i	−0.246000	−	0.679747i
$881$	11.9223	+	20.6501i	0.401674	+	0.695719i	0.993928	−	0.110032i	$-0.0350953\pi$
$881$	11.9223	+	20.6501i	0.401674	+	0.695719i	−0.592254	+	0.805751i	$0.701762\pi$
$882$		0			0
$883$			37.2496i			1.25355i	0.779201	+	0.626774i	$0.215625\pi$
$883$			37.2496i			1.25355i	−0.779201	+	0.626774i	$0.784375\pi$
$884$	−4.94674	+	10.4909i	−0.166377	+	0.352847i
$885$		0			0
$886$	22.7041	+	39.3246i	0.762758	+	1.32114i
$887$	−24.7505	+	14.2897i	−0.831042	+	0.479802i	−0.854209	−	0.519929i	$-0.825958\pi$
$887$	−24.7505	+	14.2897i	−0.831042	+	0.479802i	0.0231673	+	0.999732i	$0.492625\pi$
$888$		0			0
$889$	33.9060			1.13717
$890$	−30.5618	+	11.0603i	−1.02443	+	0.370742i
$891$		0			0
$892$			11.4902i			0.384720i
$893$	−62.5459	−	36.1109i	−2.09302	−	1.20840i
$894$		0			0
$895$	44.5208	+	7.93427i	1.48817	+	0.265213i
$896$	−8.05611			−0.269136
$897$		0			0
$898$			14.8180i			0.494483i
$899$	−1.77072	−	3.06697i	−0.0590568	−	0.102289i
$900$		0			0
$901$	6.61201	−	11.4523i	0.220278	−	0.381533i
$902$		−	0.831632i		−	0.0276903i
$903$		0			0
$904$	7.31952	−	12.6778i	0.243444	−	0.421657i
$905$	−28.5543	+	33.9035i	−0.949177	+	1.12699i
$906$		0			0
$907$	5.55457	−	3.20693i	0.184436	−	0.106484i	−0.404939	−	0.914344i	$-0.632707\pi$
$907$	5.55457	−	3.20693i	0.184436	−	0.106484i	0.589375	+	0.807859i	$0.299374\pi$
$908$	−2.45952	+	1.42000i	−0.0816220	+	0.0471245i
$909$		0			0
$910$	1.81147	−	19.3435i	0.0600497	−	0.641230i
$911$	−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
$914$	−4.88719	+	8.46486i	−0.161654	+	0.279993i
$915$		0			0
$916$	0.449643	−	0.778805i	0.0148566	−	0.0257324i
$917$	17.5765	+	10.1478i	0.580426	+	0.335109i
$918$		0			0
$919$	13.0632	−	22.6261i	0.430915	−	0.746367i	−0.566037	−	0.824380i	$-0.691524\pi$
$919$	13.0632	−	22.6261i	0.430915	−	0.746367i	0.996952	+	0.0780125i	$0.0248574\pi$
$920$	−2.33650	−	0.416399i	−0.0770321	−	0.0137283i
$921$		0			0
$922$		−	5.39220i		−	0.177583i
$923$	−0.562152	−	6.75834i	−0.0185035	−	0.222453i
$924$		0			0
$925$	−17.4399	−	20.9392i	−0.573420	−	0.688478i
$926$	−1.18048	−	2.04465i	−0.0387929	−	0.0671913i
$927$		0			0
$928$		−	9.65067i		−	0.316799i
$929$	11.9711	−	20.7346i	0.392760	−	0.680281i	−0.600052	−	0.799961i	$-0.704854\pi$
$929$	11.9711	−	20.7346i	0.392760	−	0.680281i	0.992813	+	0.119680i	$0.0381869\pi$
$930$		0			0
$931$	−16.9423			−0.555261
$932$	7.13847	+	4.12140i	0.233828	+	0.135001i
$933$		0			0
$934$	−19.4748	−	33.7313i	−0.637235	−	1.10372i
$935$	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	$-0.0977407\pi$
$938$	−9.19124	+	5.30656i	−0.300104	+	0.173265i
$939$		0			0
$940$	−15.2409	+	5.51568i	−0.497105	+	0.179902i
$941$	14.3788			0.468735			0.234368	−	0.972148i	$-0.424698\pi$
$941$	14.3788			0.468735			0.234368	+	0.972148i	$0.424698\pi$
$942$		0			0
$943$	−0.0539404	−	0.0311425i	−0.00175654	−	0.00101414i
$944$	17.4496			0.567938
$945$		0			0
$946$	3.08578	+	5.34473i	0.100327	+	0.173772i
$947$	−50.5056	+	29.1594i	−1.64121	+	0.947554i	−0.660807	+	0.750555i	$0.729786\pi$
$947$	−50.5056	+	29.1594i	−1.64121	+	0.947554i	−0.980404	+	0.196998i	$0.936881\pi$
$948$		0			0
$949$	18.2112	+	26.2465i	0.591160	+	0.851999i
$950$	34.4045	−	5.93667i	1.11623	−	0.192611i
$951$		0			0
$952$	29.4613	−	17.0095i	0.954847	−	0.551281i
$953$	11.9507	+	6.89975i	0.387122	+	0.223505i	0.680912	−	0.732365i	$-0.261583\pi$
$953$	11.9507	+	6.89975i	0.387122	+	0.223505i	−0.293791	+	0.955870i	$0.594917\pi$
$954$		0			0
$955$	1.17015	+	3.23336i	0.0378651	+	0.104629i
$956$	−1.18048	+	2.04465i	−0.0381794	+	0.0661287i
$957$		0			0
$958$	−31.6759	−	18.2881i	−1.02340	−	0.590862i
$959$	−2.00709	−	3.47639i	−0.0648124	−	0.112258i
$960$		0			0
$961$	−29.6065			−0.955047
$962$	−1.93405	−	23.2517i	−0.0623564	−	0.749666i
$963$		0			0
$964$	5.15452	+	8.92790i	0.166016	+	0.287548i
$965$	8.31840	−	46.6763i	0.267779	−	1.50256i
$966$		0			0
$967$			30.3474i			0.975906i	0.872870	+	0.487953i	$0.162256\pi$
$967$			30.3474i			0.975906i	−0.872870	+	0.487953i	$0.837744\pi$
$968$	10.8172	+	6.24534i	0.347679	+	0.200733i
$969$		0			0
$970$	9.92970	−	11.7899i	0.318824	−	0.378550i
$971$	22.0506	−	38.1928i	0.707638	−	1.22567i	−0.258092	−	0.966120i	$-0.583094\pi$
$971$	22.0506	−	38.1928i	0.707638	−	1.22567i	0.965731	−	0.259545i	$-0.0835727\pi$
$972$		0			0
$973$	−15.2923	+	8.82900i	−0.490248	+	0.283045i
$974$	−26.5074			−0.849351
$975$		0			0
$976$	−16.7093			−0.534853
$977$	19.3314	−	11.1610i	0.618466	−	0.357071i	−0.157806	−	0.987470i	$-0.550442\pi$
$977$	19.3314	−	11.1610i	0.618466	−	0.357071i	0.776271	+	0.630399i	$0.217109\pi$
$978$		0			0
$979$	23.7547	−	41.1444i	0.759204	−	1.31498i
$980$	−2.44937	+	2.90822i	−0.0782422	+	0.0928996i
$981$		0			0
$982$	−10.9845	−	6.34189i	−0.350529	−	0.202378i
$983$			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
$985$	−3.63168	+	20.3781i	−0.115715	+	0.649300i
$986$	−9.70671	−	16.8125i	−0.309125	−	0.535419i
$987$		0			0
$988$	−11.3200	−	5.33770i	−0.360139	−	0.169815i
$989$	0.462218			0.0146977
$990$		0			0
$991$	−14.8250	−	25.6777i	−0.470932	−	0.815678i	0.528515	−	0.848924i	$-0.322749\pi$
$991$	−14.8250	−	25.6777i	−0.470932	−	0.815678i	−0.999447	+	0.0332459i	$0.989416\pi$
$992$	3.28871	+	1.89874i	0.104417	+	0.0602849i
$993$		0			0
$994$	−2.26626	+	3.92527i	−0.0718813	+	0.124502i
$995$	−13.2437	−	36.5949i	−0.419852	−	1.16014i
$996$		0			0
$997$	−19.2052	−	11.0881i	−0.608233	−	0.351164i	0.164040	−	0.986454i	$-0.447547\pi$
$997$	−19.2052	−	11.0881i	−0.608233	−	0.351164i	−0.772274	+	0.635290i	$0.780881\pi$
$998$	19.3514	−	11.1725i	0.612557	−	0.353660i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.a.289.2		12
3.2	odd	2		65.2.n.a.29.5	yes	12
5.4	even	2	inner	585.2.bs.a.289.5		12
12.11	even	2		1040.2.dh.a.289.4		12
13.9	even	3	inner	585.2.bs.a.334.5		12
15.2	even	4		325.2.e.e.276.5		12
15.8	even	4		325.2.e.e.276.2		12
15.14	odd	2		65.2.n.a.29.2	yes	12
39.2	even	12		845.2.d.d.844.9		12
39.5	even	4		845.2.l.f.699.3		24
39.8	even	4		845.2.l.f.699.9		24
39.11	even	12		845.2.d.d.844.3		12
39.17	odd	6		845.2.n.e.529.5		12
39.20	even	12		845.2.l.f.654.10		24
39.23	odd	6		845.2.b.e.339.2		6
39.29	odd	6		845.2.b.d.339.5		6
39.32	even	12		845.2.l.f.654.4		24
39.35	odd	6		65.2.n.a.9.2	✓	12
39.38	odd	2		845.2.n.e.484.2		12
60.59	even	2		1040.2.dh.a.289.3		12
65.9	even	6	inner	585.2.bs.a.334.2		12
156.35	even	6		1040.2.dh.a.529.3		12
195.23	even	12		4225.2.a.bq.1.2		6
195.29	odd	6		845.2.b.d.339.2		6
195.44	even	4		845.2.l.f.699.10		24
195.59	even	12		845.2.l.f.654.3		24
195.62	even	12		4225.2.a.bq.1.5		6
195.68	even	12		4225.2.a.br.1.5		6
195.74	odd	6		65.2.n.a.9.5	yes	12
195.89	even	12		845.2.d.d.844.10		12
195.107	even	12		4225.2.a.br.1.2		6
195.113	even	12		325.2.e.e.126.2		12
195.119	even	12		845.2.d.d.844.4		12
195.134	odd	6		845.2.n.e.529.2		12
195.149	even	12		845.2.l.f.654.9		24
195.152	even	12		325.2.e.e.126.5		12
195.164	even	4		845.2.l.f.699.4		24
195.179	odd	6		845.2.b.e.339.5		6
195.194	odd	2		845.2.n.e.484.5		12
780.659	even	6		1040.2.dh.a.529.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.2	✓	12	39.35	odd	6
65.2.n.a.9.5	yes	12	195.74	odd	6
65.2.n.a.29.2	yes	12	15.14	odd	2
65.2.n.a.29.5	yes	12	3.2	odd	2
325.2.e.e.126.2		12	195.113	even	12
325.2.e.e.126.5		12	195.152	even	12
325.2.e.e.276.2		12	15.8	even	4
325.2.e.e.276.5		12	15.2	even	4
585.2.bs.a.289.2		12	1.1	even	1	trivial
585.2.bs.a.289.5		12	5.4	even	2	inner
585.2.bs.a.334.2		12	65.9	even	6	inner
585.2.bs.a.334.5		12	13.9	even	3	inner
845.2.b.d.339.2		6	195.29	odd	6
845.2.b.d.339.5		6	39.29	odd	6
845.2.b.e.339.2		6	39.23	odd	6
845.2.b.e.339.5		6	195.179	odd	6
845.2.d.d.844.3		12	39.11	even	12
845.2.d.d.844.4		12	195.119	even	12
845.2.d.d.844.9		12	39.2	even	12
845.2.d.d.844.10		12	195.89	even	12
845.2.l.f.654.3		24	195.59	even	12
845.2.l.f.654.4		24	39.32	even	12
845.2.l.f.654.9		24	195.149	even	12
845.2.l.f.654.10		24	39.20	even	12
845.2.l.f.699.3		24	39.5	even	4
845.2.l.f.699.4		24	195.164	even	4
845.2.l.f.699.9		24	39.8	even	4
845.2.l.f.699.10		24	195.44	even	4
845.2.n.e.484.2		12	39.38	odd	2
845.2.n.e.484.5		12	195.194	odd	2
845.2.n.e.529.2		12	195.134	odd	6
845.2.n.e.529.5		12	39.17	odd	6
1040.2.dh.a.289.3		12	60.59	even	2
1040.2.dh.a.289.4		12	12.11	even	2
1040.2.dh.a.529.3		12	156.35	even	6
1040.2.dh.a.529.4		12	780.659	even	6
4225.2.a.bq.1.2		6	195.23	even	12
4225.2.a.bq.1.5		6	195.62	even	12
4225.2.a.br.1.2		6	195.107	even	12
4225.2.a.br.1.5		6	195.68	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02826 + 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 + 1.71029i) q^{5} +(-1.75765 - 1.01478i) q^{7} -3.07548i q^{8} +O(q^{10})\)	\(q+(-1.02826 + 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 + 1.71029i) q^{5} +(-1.75765 - 1.01478i) q^{7} -3.07548i q^{8} +(0.465813 - 2.61378i) q^{10} +(1.94045 + 3.36096i) q^{11} +(-2.96232 + 2.05540i) q^{13} +2.40976 q^{14} +(1.23557 + 2.14007i) q^{16} +(-4.71996 - 2.72507i) q^{17} +(2.94045 - 5.09301i) q^{19} +(-0.449133 - 1.24105i) q^{20} +(-3.99058 - 2.30396i) q^{22} +(-0.298874 + 0.172555i) q^{23} +(-0.850210 - 4.92718i) q^{25} +(1.82581 - 3.87212i) q^{26} +(1.03743 - 0.598962i) q^{28} +(-1.50000 - 2.59808i) q^{29} +1.18048 q^{31} +(2.78591 + 1.60845i) q^{32} +6.47114 q^{34} +(4.26737 - 1.54436i) q^{35} +(4.71996 - 2.72507i) q^{37} +6.98259i q^{38} +(5.25997 + 4.43007i) q^{40} +(0.0902394 + 0.156299i) q^{41} +(-1.15990 - 0.669668i) q^{43} -2.29066 q^{44} +(0.204880 - 0.354863i) q^{46} -12.2807i q^{47} +(-1.44045 - 2.49493i) q^{49} +(3.79934 + 4.56169i) q^{50} +(-0.176407 - 2.12081i) q^{52} +2.42636i q^{53} +(-8.54334 - 1.52255i) q^{55} +(-3.12093 + 5.40561i) q^{56} +(3.08478 + 1.78100i) q^{58} +(3.53069 - 6.11533i) q^{59} +(-3.38090 + 5.85589i) q^{61} +(-1.21384 + 0.700811i) q^{62} -8.76180 q^{64} +(0.751722 - 8.02714i) q^{65} +(-3.81417 + 2.20211i) q^{67} +(2.78591 - 1.60845i) q^{68} +(-3.47114 + 4.12140i) q^{70} +(-0.940450 + 1.62891i) q^{71} -8.86014i q^{73} +(-3.23557 + 5.60417i) q^{74} +(1.73557 + 3.00609i) q^{76} -7.87651i q^{77} -11.1805 q^{79} +(-5.43992 - 0.969475i) q^{80} +(-0.185579 - 0.107144i) q^{82} +7.83540i q^{83} +(11.4595 - 4.14720i) q^{85} +1.59024 q^{86} +(10.3365 - 5.96781i) q^{88} +(-6.12093 - 10.6018i) q^{89} +(7.29249 - 0.606582i) q^{91} -0.203698i q^{92} +(7.29066 + 12.6278i) q^{94} +(4.47497 + 12.3653i) q^{95} +(5.02801 + 2.90292i) q^{97} +(2.96232 + 1.71029i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5	\( 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 7 * q^10 + 44 * q^14 - 16 * q^16 + 12 * q^19 + q^20 - 2 * q^25 - 24 * q^26 - 18 * q^29 - 16 * q^31 + 16 * q^34 - 10 * q^35 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 10 * q^46 + 6 * q^49 + 31 * q^50 - 26 * q^55 + 16 * q^56 + 4 * q^59 + 6 * q^61 - 12 * q^64 - 23 * q^65 + 20 * q^70 + 12 * q^71 - 8 * q^74 - 10 * q^76 - 104 * q^79 - 33 * q^80 + 21 * q^85 + 4 * q^86 - 20 * q^89 - 44 * q^91 + 56 * q^94 - 20 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more