LMFDB - Embedded newform 585.2.bs.a.289.5

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			289.5
Root			$1.02826 + 0.593667i$ of defining polynomial
Character	$\chi$	$=$	585.289
Dual form			585.2.bs.a.334.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02826 - 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(1.75765 + 1.01478i) q^{7} +3.07548i q^{8} +O(q^{10})$	\(q+(1.02826 - 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(1.75765 + 1.01478i) q^{7} +3.07548i q^{8} +(-2.49650 - 0.903481i) q^{10} +(1.94045 + 3.36096i) q^{11} +(2.96232 - 2.05540i) q^{13} +2.40976 q^{14} +(1.23557 + 2.14007i) q^{16} +(4.71996 + 2.72507i) q^{17} +(2.94045 - 5.09301i) q^{19} +(1.29934 - 0.231562i) q^{20} +(3.99058 + 2.30396i) q^{22} +(0.298874 - 0.172555i) q^{23} +(-0.850210 + 4.92718i) q^{25} +(1.82581 - 3.87212i) q^{26} +(-1.03743 + 0.598962i) q^{28} +(-1.50000 - 2.59808i) q^{29} +1.18048 q^{31} +(-2.78591 - 1.60845i) q^{32} +6.47114 q^{34} +(-0.796234 - 4.46783i) q^{35} +(-4.71996 + 2.72507i) q^{37} -6.98259i q^{38} +(5.25997 - 4.43007i) q^{40} +(0.0902394 + 0.156299i) q^{41} +(1.15990 + 0.669668i) q^{43} -2.29066 q^{44} +(0.204880 - 0.354863i) q^{46} +12.2807i q^{47} +(-1.44045 - 2.49493i) q^{49} +(2.05087 + 5.57117i) q^{50} +(0.176407 + 2.12081i) q^{52} -2.42636i q^{53} +(2.95310 - 8.16003i) q^{55} +(-3.12093 + 5.40561i) q^{56} +(-3.08478 - 1.78100i) q^{58} +(3.53069 - 6.11533i) q^{59} +(-3.38090 + 5.85589i) q^{61} +(1.21384 - 0.700811i) q^{62} -8.76180 q^{64} +(-7.78241 - 2.10573i) q^{65} +(3.81417 - 2.20211i) q^{67} +(-2.78591 + 1.60845i) q^{68} +(-3.47114 - 4.12140i) q^{70} +(-0.940450 + 1.62891i) q^{71} +8.86014i q^{73} +(-3.23557 + 5.60417i) q^{74} +(1.73557 + 3.00609i) q^{76} +7.87651i q^{77} -11.1805 q^{79} +(1.88037 - 5.19585i) q^{80} +(0.185579 + 0.107144i) q^{82} -7.83540i q^{83} +(-2.13820 - 11.9979i) q^{85} +1.59024 q^{86} +(-10.3365 + 5.96781i) q^{88} +(-6.12093 - 10.6018i) q^{89} +(7.29249 - 0.606582i) q^{91} +0.203698i q^{92} +(7.29066 + 12.6278i) q^{94} +(-12.9461 + 2.30719i) q^{95} +(-5.02801 - 2.90292i) q^{97} +(-2.96232 - 1.71029i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.0902665	−	0.995918i	$-0.528772\pi$
$2$	1.02826	−	0.593667i	0.727090	−	0.419786i	0.817357	+	0.576132i	$0.195439\pi$
$3$		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	0.793924	−	0.608017i	$-0.208035\pi$
$7$	1.75765	+	1.01478i	0.664328	+	0.383550i	−0.129596	+	0.991567i	$0.541368\pi$
$8$			3.07548i			1.08735i
$9$		0			0
$10$	−2.49650	−	0.903481i	−0.789463	−	0.285706i
$11$	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	0.947605	−	0.319445i	$-0.103497\pi$
$17$	4.71996	+	2.72507i	1.14476	+	0.660927i	0.197155	+	0.980372i	$0.436830\pi$
$18$		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	$-0.0690109\pi$
$20$	1.29934	−	0.231562i	0.290542	−	0.0517789i
$21$		0			0
$22$	3.99058	+	2.30396i	0.850794	+	0.491206i
$23$	0.298874	−	0.172555i	0.0623195	−	0.0359802i	−0.468516	−	0.883455i	$-0.655211\pi$
$23$	0.298874	−	0.172555i	0.0623195	−	0.0359802i	0.530836	+	0.847475i	$0.321878\pi$
$24$		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
$35$	−0.796234	−	4.46783i	−0.134588	−	0.755201i
$36$		0			0
$37$	−4.71996	+	2.72507i	−0.775957	+	0.447999i	−0.834996	−	0.550257i	$-0.814530\pi$
$37$	−4.71996	+	2.72507i	−0.775957	+	0.447999i	0.0590384	+	0.998256i	$0.481197\pi$
$38$		−	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	0.585827	−	0.810436i	$-0.300770\pi$
$43$	1.15990	+	0.669668i	0.176883	+	0.102123i	−0.408944	+	0.912559i	$0.634103\pi$
$44$	−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	$0.353299\pi$
$47$			12.2807i			1.79133i	−0.444731	+	0.895664i	$0.646701\pi$
$48$		0			0
$49$	−1.44045	−	2.49493i	−0.205779	−	0.356419i
$50$	2.05087	+	5.57117i	0.290036	+	0.787883i
$51$		0			0
$52$	0.176407	+	2.12081i	0.0244633	+	0.294104i
$53$		−	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
$56$	−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
$65$	−7.78241	−	2.10573i	−0.965289	−	0.261183i
$66$		0			0
$67$	3.81417	−	2.20211i	0.465975	−	0.269031i	−0.248578	−	0.968612i	$-0.579963\pi$
$67$	3.81417	−	2.20211i	0.465975	−	0.269031i	0.714553	+	0.699581i	$0.246630\pi$
$68$	−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	$0.173510\pi$
$73$			8.86014i			1.03700i	−0.855077	+	0.518501i	$0.826490\pi$
$74$	−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	$0.716515\pi$
$80$	1.88037	−	5.19585i	0.210232	−	0.580913i
$81$		0			0
$82$	0.185579	+	0.107144i	0.0204938	+	0.0118321i
$83$		−	7.83540i		−	0.860047i	−0.902818	−	0.430024i	$-0.858505\pi$
$83$		−	7.83540i		−	0.860047i	0.902818	−	0.430024i	$-0.141495\pi$
$84$		0			0
$85$	−2.13820	−	11.9979i	−0.231920	−	1.30135i
$86$	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
$95$	−12.9461	+	2.30719i	−1.32824	+	0.236713i
$96$		0			0
$97$	−5.02801	−	2.90292i	−0.510517	−	0.294747i	0.222529	−	0.974926i	$-0.428569\pi$
$97$	−5.02801	−	2.90292i	−0.510517	−	0.294747i	−0.733046	+	0.680179i	$0.761902\pi$
$98$	−2.96232	−	1.71029i	−0.299239	−	0.172766i
$99$		0			0
$100$	−2.26768	−	1.88870i	−0.226768	−	0.188870i
$101$	−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	$-0.897335\pi$
$103$		−	6.43378i		−	0.633939i	0.948436	−	0.316970i	$-0.102665\pi$
$104$	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	0.480387	−	0.877057i	$-0.340496\pi$
$107$	15.3106	−	8.83959i	1.48013	−	0.854555i	0.999747	+	0.0225015i	$0.00716305\pi$
$108$		0			0
$109$	−5.76180			−0.551880			−0.275940	−	0.961175i	$-0.588989\pi$
$109$	−5.76180			−0.551880			−0.275940	+	0.961175i	$0.588989\pi$
$110$	−1.80777	−	10.1438i	−0.172365	−	0.967173i
$111$		0			0
$112$			5.01532i			0.473903i
$113$	−4.12222	−	2.37996i	−0.387785	−	0.223888i	0.293415	−	0.955985i	$-0.405208\pi$
$113$	−4.12222	−	2.37996i	−0.387785	−	0.223888i	−0.681200	+	0.732097i	$0.738542\pi$
$114$		0			0
$115$	−0.725633	−	0.262606i	−0.0676656	−	0.0244881i
$116$	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	0.306277	−	0.951942i	$-0.400917\pi$
$127$	14.4679	−	8.35307i	1.28382	−	0.741215i	0.977545	+	0.210728i	$0.0675833\pi$
$128$	−3.43760	+	1.98470i	−0.303844	+	0.175424i
$129$		0			0
$130$	−9.25245	+	2.45492i	−0.811493	+	0.215311i
$131$	−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	0.425042	−	0.905174i	$-0.360259\pi$
$137$	−1.71288	−	0.988931i	−0.146341	−	0.0844901i	−0.571383	+	0.820684i	$0.693593\pi$
$138$		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	$0.0463737\pi$
$140$	2.51877	+	0.911540i	0.212875	+	0.0770392i
$141$		0			0
$142$			2.23325i			0.187411i
$143$	12.6563	+	5.96781i	1.05838	+	0.499053i
$144$		0			0
$145$	−2.28280	+	6.30784i	−0.189576	+	0.523837i
$146$	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	$0.0796132\pi$
$157$			6.20265i			0.495025i	−0.968885	+	0.247513i	$0.920387\pi$
$158$	−11.4964	+	6.63748i	−0.914608	+	0.528049i
$159$		0			0
$160$	1.26205	+	7.08161i	0.0997736	+	0.559850i
$161$	0.700420			0.0552008
$162$		0			0
$163$	−10.3365	−	5.96781i	−0.809621	−	0.467435i	0.0372032	−	0.999308i	$-0.488155\pi$
$163$	−10.3365	−	5.96781i	−0.809621	−	0.467435i	−0.846824	+	0.531873i	$0.821488\pi$
$164$	−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	−0.566461	−	0.824088i	$-0.691688\pi$
$167$	−1.75765	+	1.01478i	−0.136011	+	0.0785259i	0.430451	+	0.902614i	$0.358355\pi$
$168$		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	0.543444	−	0.839445i	$-0.317120\pi$
$173$	1.15990	+	0.669668i	0.0881855	+	0.0509139i	−0.455259	+	0.890359i	$0.650453\pi$
$174$		0			0
$175$	−6.49437	+	7.79748i	−0.490928	+	0.589434i
$176$	−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
$185$	11.4595	+	4.14720i	0.842522	+	0.304908i
$186$		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	0.337750	−	0.941236i	$-0.390334\pi$
$193$	18.3625	−	10.6016i	1.32176	−	0.763118i	0.984009	+	0.178117i	$0.0570007\pi$
$194$	−6.89347			−0.494923
$195$		0			0
$196$	1.70042			0.121459
$197$	−8.01675	+	4.62847i	−0.571170	+	0.329765i	−0.757616	−	0.652700i	$-0.773636\pi$
$197$	−8.01675	+	4.62847i	−0.571170	+	0.329765i	0.186447	+	0.982465i	$0.440303\pi$
$198$		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
$205$	0.137332	−	0.379477i	0.00959171	−	0.0265038i
$206$	−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
$215$	−0.525447	−	2.94839i	−0.0358352	−	0.201079i
$216$		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	−0.943672	−	0.330881i	$-0.892654\pi$
$223$	−16.8589	+	9.73351i	−1.12896	+	0.651804i	−0.185285	+	0.982685i	$0.559321\pi$
$224$	−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	0.355298	−	0.934753i	$-0.384379\pi$
$227$	−4.16698	−	2.40581i	−0.276572	−	0.159679i	−0.631871	+	0.775074i	$0.717713\pi$
$228$		0			0
$229$	−1.52360			−0.100682			−0.0503410	−	0.998732i	$-0.516031\pi$
$229$	−1.52360			−0.100682			−0.0503410	+	0.998732i	$0.516031\pi$
$230$	−0.902040	+	0.160757i	−0.0594787	+	0.0106000i
$231$		0			0
$232$	7.99033	−	4.61322i	0.524591	−	0.302873i
$233$			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
$236$	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
$245$	−2.19217	+	6.05742i	−0.140053	+	0.386994i
$246$		0			0
$247$	−1.75765	−	21.1309i	−0.111836	−	1.34453i
$248$			3.63054i			0.230539i
$249$		0			0
$250$	6.57417	−	11.5326i	0.415787	−	0.729384i
$251$	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	−0.176141	−	0.984365i	$-0.556361\pi$
$257$	9.43076	−	5.44485i	0.588274	−	0.339640i	0.764415	+	0.644725i	$0.223028\pi$
$258$		0			0
$259$	−11.0614			−0.687321
$260$	3.37311	−	3.35663i	0.209191	−	0.208170i
$261$		0			0
$262$	−10.2826	+	5.93667i	−0.635262	+	0.366769i
$263$	11.6399	−	6.72031i	0.717749	−	0.414392i	−0.0961749	−	0.995364i	$-0.530661\pi$
$263$	11.6399	−	6.72031i	0.717749	−	0.414392i	0.813923	+	0.580972i	$0.197327\pi$
$264$		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
$275$	−18.2098	+	6.70343i	−1.09809	+	0.404232i
$276$		0			0
$277$	8.56973	+	4.94774i	0.514905	+	0.297281i	0.734848	−	0.678232i	$-0.237254\pi$
$277$	8.56973	+	4.94774i	0.514905	+	0.297281i	−0.219943	+	0.975513i	$0.570587\pi$
$278$		−	10.3303i		−	0.619570i
$279$		0			0
$280$	13.7407	−	2.44880i	0.821165	−	0.146344i
$281$	−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	−0.648467	−	0.761243i	$-0.724589\pi$
$283$	−5.27294	+	3.04434i	−0.313444	+	0.180967i	0.335023	+	0.942210i	$0.391256\pi$
$284$	−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
$290$	1.39744	+	7.84133i	0.0820605	+	0.460458i
$291$		0			0
$292$	−4.52897	−	2.61480i	−0.265038	−	0.153020i
$293$	−8.48019	−	4.89604i	−0.495418	−	0.286030i	0.231401	−	0.972858i	$-0.425669\pi$
$293$	−8.48019	−	4.89604i	−0.495418	−	0.286030i	−0.726819	+	0.686829i	$0.759002\pi$
$294$		0			0
$295$	−15.5448	+	2.77031i	−0.905053	+	0.161294i
$296$	−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
$305$	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	$0.782732\pi$
$308$	−4.02617	−	2.32451i	−0.229412	−	0.132451i
$309$		0			0
$310$	−2.94707	−	1.06654i	−0.167382	−	0.0605754i
$311$	−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	$0.264622\pi$
$313$			26.1425i			1.47766i	−0.673891	+	0.738831i	$0.735378\pi$
$314$	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	$0.107919\pi$
$317$			11.8428i			0.665159i	−0.943075	+	0.332580i	$0.892081\pi$
$318$		0			0
$319$	5.82135	−	10.0829i	0.325933	−	0.564532i
$320$	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
$325$	7.60876	+	16.3434i	0.422058	+	0.906569i
$326$	−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
$335$	−9.26038	−	3.35132i	−0.505948	−	0.183102i
$336$		0			0
$337$			15.2939i			0.833113i	0.909110	+	0.416556i	$0.136763\pi$
$337$			15.2939i			0.833113i	−0.909110	+	0.416556i	$0.863237\pi$
$338$	−2.55015	−	15.2232i	−0.138710	−	0.828034i
$339$		0			0
$340$	6.76387	+	2.44784i	0.366823	+	0.132753i
$341$	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	0.187733	−	0.982220i	$-0.439886\pi$
$347$	−10.5998	−	6.11981i	−0.569029	−	0.328529i	−0.756761	+	0.653691i	$0.773219\pi$
$348$		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	−0.529861	−	0.848084i	$-0.677756\pi$
$353$	−1.13348	+	0.654413i	−0.0603288	+	0.0348309i	0.469532	+	0.882915i	$0.344423\pi$
$354$		0			0
$355$	4.14058	−	0.737912i	0.219759	−	0.0391643i
$356$	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	$-0.329116\pi$
$367$	28.9531	−	16.7161i	1.51134	−	0.872573i	0.999912	−	0.0132473i	$-0.00421687\pi$
$368$	0.738559	+	0.426407i	0.0385001	+	0.0222280i
$369$		0			0
$370$	14.2455	−	2.53875i	0.740586	−	0.131983i
$371$	2.46222	−	4.26469i	0.127832	−	0.221412i
$372$		0			0
$373$	29.8589	+	17.2391i	1.54604	+	0.892604i	0.998438	+	0.0558628i	$0.0177909\pi$
$373$	29.8589	+	17.2391i	1.54604	+	0.892604i	0.547598	+	0.836742i	$0.315542\pi$
$374$	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	$0.980843\pi$
$380$	2.64130	−	7.29846i	0.135496	−	0.374403i
$381$		0			0
$382$		−	1.82586i		−	0.0934191i
$383$	1.51271	+	0.873366i	0.0772961	+	0.0446269i	0.538150	−	0.842849i	$-0.319123\pi$
$383$	1.51271	+	0.873366i	0.0772961	+	0.0446269i	−0.460854	+	0.887476i	$0.652457\pi$
$384$		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	−0.0772687	−	0.997010i	$-0.524620\pi$
$397$	−19.5132	−	11.2660i	−0.979339	−	0.565422i	−0.902071	+	0.431588i	$0.857953\pi$
$398$			20.6649i			1.03584i
$399$		0			0
$400$	−11.5950	+	4.26837i	−0.579750	+	0.213418i
$401$	−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	$0.274850\pi$
$410$	−0.0840695	−	0.471731i	−0.00415190	−	0.0232971i
$411$		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
$425$	−17.4399	+	20.9392i	−0.845959	+	1.01570i
$426$		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	−0.113730	−	0.993512i	$-0.536280\pi$
$433$	−21.4538	−	12.3863i	−1.03100	−	0.595249i	−0.917272	+	0.398262i	$0.869613\pi$
$434$	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	$0.779438\pi$
$440$	25.0960	+	9.08221i	1.19640	+	0.432977i
$441$		0			0
$442$	19.1696	−	13.3008i	0.911803	−	0.632655i
$443$			38.2438i			1.81702i	0.417865	+	0.908509i	$0.362778\pi$
$443$			38.2438i			1.81702i	−0.417865	+	0.908509i	$0.637222\pi$
$444$		0			0
$445$	−9.31523	+	25.7399i	−0.441584	+	1.22019i
$446$	−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
$455$	−11.5419	−	11.5985i	−0.541092	−	0.543748i
$456$		0			0
$457$	−7.12930	+	4.11610i	−0.333495	+	0.192543i	−0.657392	−	0.753549i	$-0.728340\pi$
$457$	−7.12930	+	4.11610i	−0.333495	+	0.192543i	0.323897	+	0.946092i	$0.395007\pi$
$458$	−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	$-0.985287\pi$
$463$		−	1.98845i		−	0.0924113i	0.998932	−	0.0462056i	$-0.0147130\pi$
$464$	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	$-0.725688\pi$
$467$		−	32.8043i		−	1.51800i	0.651091	−	0.759000i	$-0.274312\pi$
$468$		0			0
$469$	8.93862			0.412747
$470$	11.0954	−	30.6589i	0.511793	−	1.41419i
$471$		0			0
$472$	18.8076	+	10.8586i	0.865689	+	0.499806i
$473$			5.19783i			0.238997i
$474$		0			0
$475$	22.5942	+	18.8183i	1.03669	+	0.863441i
$476$	−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
$485$	2.27774	+	12.7809i	0.103427	+	0.580350i
$486$		0			0
$487$	−19.3341	−	11.1626i	−0.876113	−	0.505824i	−0.00673807	−	0.999977i	$-0.502145\pi$
$487$	−19.3341	−	11.1626i	−0.876113	−	0.505824i	−0.869375	+	0.494153i	$0.835478\pi$
$488$	−18.0097	−	10.3979i	−0.815259	−	0.470690i
$489$		0			0
$490$	1.34196	+	7.53002i	0.0606236	+	0.340172i
$491$	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	$0.638405\pi$
$500$	0.0362348	+	6.59898i	0.00162047	+	0.295115i
$501$		0			0
$502$		−	11.0417i		−	0.492815i
$503$	−4.92013	−	2.84064i	−0.219378	−	0.126658i	0.386284	−	0.922380i	$-0.373758\pi$
$503$	−4.92013	−	2.84064i	−0.219378	−	0.126658i	−0.605662	+	0.795722i	$0.707092\pi$
$504$		0			0
$505$	−4.52168	+	12.4943i	−0.201212	+	0.555989i
$506$	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
$520$	6.47611	−	23.9346i	0.283996	−	1.04960i
$521$	−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	−0.000305526	−	1.00000i	$-0.500097\pi$
$523$	19.7948	−	11.4285i	0.865567	−	0.499735i	0.865873	+	0.500265i	$0.166764\pi$
$524$	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
$530$	−2.19217	+	6.05742i	−0.0952219	+	0.263117i
$531$		0			0
$532$			7.04487i			0.305434i
$533$	0.588576	+	0.277529i	0.0254940	+	0.0120211i
$534$		0			0
$535$	−37.1725	−	13.4527i	−1.60711	−	0.581610i
$536$	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	$-0.746950\pi$
$547$		−	33.3911i		−	1.42770i	0.700299	−	0.713850i	$-0.253050\pi$
$548$	1.01101	−	0.583706i	0.0431882	−	0.0249347i
$549$		0			0
$550$	−14.7449	+	17.7035i	−0.628723	+	0.754878i
$551$	−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	−0.992835	−	0.119495i	$-0.961873\pi$
$557$	−32.7053	+	18.8824i	−1.38577	+	0.800073i	−0.392932	+	0.919567i	$0.628539\pi$
$558$		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	0.891631	−	0.452762i	$-0.149561\pi$
$563$	22.4307	+	12.9504i	0.945343	+	0.545794i	0.0537120	+	0.998556i	$0.482895\pi$
$564$		0			0
$565$	1.86741	+	10.4784i	0.0785625	+	0.440830i
$566$	−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
$575$	0.596104	+	1.61932i	0.0248593	+	0.0675301i
$576$		0			0
$577$		−	6.20265i		−	0.258220i	−0.991630	−	0.129110i	$-0.958788\pi$
$577$		−	6.20265i		−	0.258220i	0.991630	−	0.129110i	$-0.0412120\pi$
$578$	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	−0.466956	−	0.884280i	$-0.654649\pi$
$587$	1.58391	−	0.914469i	0.0653748	−	0.0377442i	0.532331	+	0.846536i	$0.321316\pi$
$588$		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	$-0.999524\pi$
$593$		−	0.0728761i		−	0.00299266i	0.999999	−	0.00149633i	$-0.000476297\pi$
$594$		0			0
$595$	8.41697	−	23.2578i	0.345062	−	0.953477i
$596$	−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
$605$	8.94065	−	1.59336i	0.363489	−	0.0647791i
$606$		0			0
$607$	−31.3808	−	18.1177i	−1.27371	−	0.735375i	−0.298024	−	0.954558i	$-0.596328\pi$
$607$	−31.3808	−	18.1177i	−1.27371	−	0.735375i	−0.975684	+	0.219183i	$0.929661\pi$
$608$	−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	−0.557583	−	0.830121i	$-0.688271\pi$
$613$	−2.90838	+	1.67915i	−0.117468	+	0.0678203i	0.440115	+	0.897942i	$0.354938\pi$
$614$	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	0.0830194	−	0.996548i	$-0.473544\pi$
$617$	−18.3441	−	10.5910i	−0.738507	−	0.426377i	−0.821526	+	0.570171i	$0.806877\pi$
$618$		0			0
$619$	−25.4082			−1.02124			−0.510620	−	0.859807i	$-0.670584\pi$
$619$	−25.4082			−1.02124			−0.510620	+	0.859807i	$0.670584\pi$
$620$	1.53385	−	0.273354i	0.0616008	−	0.0109782i
$621$		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
$635$	−35.1265	−	12.7123i	−1.39395	−	0.504470i
$636$		0			0
$637$	−9.39516	−	4.43007i	−0.372250	−	0.175526i
$638$		−	13.8238i		−	0.547288i
$639$		0			0
$640$	8.34610	+	3.02044i	0.329909	+	0.119394i
$641$	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	0.998250	−	0.0591344i	$-0.0188341\pi$
$643$	36.6710	+	21.1720i	1.44616	+	0.834943i	0.447913	+	0.894077i	$0.352167\pi$
$644$	−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	−0.954008	−	0.299781i	$-0.903086\pi$
$647$	−29.7958	+	17.2026i	−1.17139	+	0.676305i	−0.217386	+	0.976086i	$0.569753\pi$
$648$		0			0
$649$	27.4045			1.07572
$650$	17.5263	+	12.2882i	0.687439	+	0.481983i
$651$		0			0
$652$	6.10104	−	3.52244i	0.238935	−	0.137949i
$653$	12.4114	−	7.16573i	0.485696	−	0.280417i	−0.237091	−	0.971487i	$-0.576194\pi$
$653$	12.4114	−	7.16573i	0.485696	−	0.280417i	0.722787	+	0.691071i	$0.242861\pi$
$654$		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
$665$	−25.0960	−	9.08221i	−0.973181	−	0.352193i
$666$		0			0
$667$	−0.896622	−	0.517665i	−0.0347173	−	0.0200441i
$668$		−	1.19792i		−	0.0463491i
$669$		0			0
$670$	−11.5117	+	2.05155i	−0.444734	+	0.0792582i
$671$	−26.2419			−1.01306
$672$		0			0
$673$	−29.5956	+	17.0871i	−1.14083	+	0.658657i	−0.946636	−	0.322306i	$-0.895542\pi$
$673$	−29.5956	+	17.0871i	−1.14083	+	0.658657i	−0.194193	+	0.980963i	$0.562209\pi$
$674$	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	$0.0358404\pi$
$677$			5.84695i			0.224716i	−0.993668	+	0.112358i	$0.964160\pi$
$678$		0			0
$679$	−5.89165	−	10.2046i	−0.226101	−	0.391618i
$680$	36.8991	−	6.57597i	1.41502	−	0.252177i
$681$		0			0
$682$	4.71079	+	2.71978i	0.180386	+	0.104146i
$683$	−9.82834	−	5.67439i	−0.376071	−	0.217125i	0.300036	−	0.953928i	$-0.403001\pi$
$683$	−9.82834	−	5.67439i	−0.376071	−	0.217125i	−0.676107	+	0.736803i	$0.736334\pi$
$684$		0			0
$685$	0.775953	+	4.35403i	0.0296476	+	0.166359i
$686$	−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
$695$	−19.1530	+	3.41334i	−0.726513	+	0.129475i
$696$		0			0
$697$			0.983636i			0.0372579i
$698$	19.2289	+	11.1018i	0.727825	+	0.420210i
$699$		0			0
$700$	−2.06916	−	5.62087i	−0.0782069	−	0.212449i
$701$	−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
$715$	−8.02412	−	30.2424i	−0.300085	−	1.13100i
$716$	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
$725$	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	$-0.155954\pi$
$728$	1.86553	+	22.4279i	0.0691411	+	0.831233i
$729$		0			0
$730$	8.00497	−	22.1194i	0.296277	−	0.818674i
$731$	3.64979	+	6.32162i	0.134992	+	0.233814i
$732$		0			0
$733$		−	10.6692i		−	0.394074i	−0.980396	−	0.197037i	$-0.936868\pi$
$733$		−	10.6692i		−	0.394074i	0.980396	−	0.197037i	$-0.0631320\pi$
$734$	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	0.0564064	−	0.998408i	$-0.482036\pi$
$743$	25.8748	−	14.9389i	0.949256	−	0.548053i	0.892850	+	0.450355i	$0.148702\pi$
$744$		0			0
$745$	49.0980	−	8.74998i	1.79881	−	0.320575i
$746$	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	−0.206266	−	0.978496i	$-0.566131\pi$
$757$	14.8024	−	8.54617i	0.538003	−	0.310616i	0.744269	+	0.667880i	$0.232798\pi$
$758$	−17.8964	−	10.3325i	−0.650025	−	0.375292i
$759$		0			0
$760$	−7.09571	−	39.8155i	−0.257388	−	1.44426i
$761$	−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	$0.974292\pi$
$770$	7.11628	−	19.6637i	0.256453	−	0.708631i
$771$		0			0
$772$			12.5149i			0.450422i
$773$	−0.246026	−	0.142043i	−0.00884894	−	0.00510894i	0.495569	−	0.868569i	$-0.334960\pi$
$773$	−0.246026	−	0.142043i	−0.00884894	−	0.00510894i	−0.504418	+	0.863460i	$0.668293\pi$
$774$		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	0.823896	−	0.566741i	$-0.191796\pi$
$787$	20.9008	+	12.0671i	0.745032	+	0.430145i	−0.0788638	+	0.996885i	$0.525129\pi$
$788$		−	5.46381i		−	0.194640i
$789$		0			0
$790$	27.9121	+	10.1014i	0.993068	+	0.359390i
$791$	−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	0.923641	−	0.383259i	$-0.125198\pi$
$797$	29.7430	+	17.1721i	1.05355	+	0.608267i	0.129909	+	0.991526i	$0.458532\pi$
$798$		0			0
$799$	−33.4659	+	57.9646i	−1.18394	+	2.05064i
$800$	10.2937	−	12.3592i	0.363938	−	0.436963i
$801$		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
$815$	4.68257	+	26.2749i	0.164023	+	0.920368i
$816$		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	0.903171	−	0.429280i	$-0.141233\pi$
$823$	28.2000	+	16.2813i	0.982990	+	0.567529i	0.0798182	+	0.996809i	$0.474566\pi$
$824$	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	$-0.913315\pi$
$827$		−	15.4702i		−	0.537951i	0.963147	−	0.268976i	$-0.0866851\pi$
$828$		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	$0.914492\pi$
$830$	−7.07914	+	19.5611i	−0.245721	+	0.678976i
$831$		0			0
$832$	−25.9552	+	18.0090i	−0.899835	+	0.624351i
$833$		−	15.7013i		−	0.544018i
$834$		0			0
$835$	4.26737	+	1.54436i	0.147679	+	0.0534447i
$836$	−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
$845$	−27.3821	+	9.75817i	−0.941972	+	0.335691i
$846$		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	$0.111734\pi$
$853$			20.0856i			0.687719i	−0.939021	+	0.343859i	$0.888266\pi$
$854$	−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	$0.245329\pi$
$857$			40.7886i			1.39331i	−0.717406	+	0.696656i	$0.754671\pi$
$858$		0			0
$859$	40.1301			1.36922			0.684610	−	0.728909i	$-0.259972\pi$
$859$	40.1301			1.36922			0.684610	+	0.728909i	$0.259972\pi$
$860$	1.66218	+	0.601540i	0.0566798	+	0.0205123i
$861$		0			0
$862$	9.93355	+	5.73514i	0.338338	+	0.195340i
$863$			20.8275i			0.708977i	0.935060	+	0.354489i	$0.115345\pi$
$863$			20.8275i			0.708977i	−0.935060	+	0.354489i	$0.884655\pi$
$864$		0			0
$865$	−0.525447	−	2.94839i	−0.0178657	−	0.100248i
$866$	−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
$875$	22.6908	−	0.124594i	0.767089	−	0.00421206i
$876$		0			0
$877$	40.3520	+	23.2972i	1.36259	+	0.786691i	0.989968	−	0.141293i	$-0.0451258\pi$
$877$	40.3520	+	23.2972i	1.36259	+	0.786691i	0.372621	+	0.927984i	$0.378459\pi$
$878$	7.26094	+	4.19210i	0.245045	+	0.141477i
$879$		0			0
$880$	21.1118	−	3.76243i	0.711678	−	0.126832i
$881$	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	$-0.784375\pi$
$883$		−	37.2496i		−	1.25355i	0.779201	−	0.626774i	$-0.215625\pi$
$884$	−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	−0.0231673	−	0.999732i	$-0.507375\pi$
$887$	24.7505	−	14.2897i	0.831042	−	0.479802i	0.854209	+	0.519929i	$0.174042\pi$
$888$		0			0
$889$	33.9060			1.13717
$890$	5.70242	+	31.9975i	0.191146	+	1.07256i
$891$		0			0
$892$		−	11.4902i		−	0.384720i
$893$	62.5459	+	36.1109i	2.09302	+	1.20840i
$894$		0			0
$895$	−15.3891	+	42.5233i	−0.514402	+	1.42140i
$896$	−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	−0.589375	−	0.807859i	$-0.700626\pi$
$907$	−5.55457	+	3.20693i	−0.184436	+	0.106484i	0.404939	+	0.914344i	$0.367293\pi$
$908$	2.45952	−	1.42000i	0.0816220	−	0.0471245i
$909$		0			0
$910$	−18.7537	−	5.07429i	−0.621681	−	0.168211i
$911$	−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	$0.0248574\pi$
$920$	0.807638	−	2.23167i	0.0266270	−	0.0735759i
$921$		0			0
$922$			5.39220i			0.177583i
$923$	0.562152	+	6.75834i	0.0185035	+	0.222453i
$924$		0			0
$925$	−9.41397	−	25.5730i	−0.309529	−	0.840836i
$926$	−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	$0.0977407\pi$
$937$			18.5046i			0.604518i	−0.953226	+	0.302259i	$0.902259\pi$
$938$	9.19124	−	5.30656i	0.300104	−	0.173265i
$939$		0			0
$940$	2.84375	+	15.9569i	0.0927530	+	0.520456i
$941$	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	$-0.270214\pi$
$947$	50.5056	−	29.1594i	1.64121	−	0.947554i	0.980404	−	0.196998i	$-0.0631194\pi$
$948$		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	0.293791	−	0.955870i	$-0.405083\pi$
$953$	−11.9507	−	6.89975i	−0.387122	−	0.223505i	−0.680912	+	0.732365i	$0.738417\pi$
$954$		0			0
$955$	−3.38525	+	0.603301i	−0.109544	+	0.0195224i
$956$	−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
$965$	−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	$-0.162256\pi$
$968$	−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	−0.776271	−	0.630399i	$-0.782891\pi$
$977$	−19.3314	+	11.1610i	−0.618466	+	0.357071i	0.157806	+	0.987470i	$0.449558\pi$
$978$		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	$-0.979488\pi$
$983$		−	4.03793i		−	0.128790i	0.997924	−	0.0643950i	$-0.0205118\pi$
$984$		0			0
$985$	19.4638	+	7.04392i	0.620167	+	0.224438i
$986$	−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
$995$	38.3140	−	6.82811i	1.21463	−	0.216466i
$996$		0			0
$997$	19.2052	+	11.0881i	0.608233	+	0.351164i	0.772274	−	0.635290i	$-0.219119\pi$
$997$	19.2052	+	11.0881i	0.608233	+	0.351164i	−0.164040	+	0.986454i	$0.552453\pi$
$998$	−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.289.5		12
3.2	odd	2		65.2.n.a.29.2	yes	12
5.4	even	2	inner	585.2.bs.a.289.2		12
12.11	even	2		1040.2.dh.a.289.3		12
13.9	even	3	inner	585.2.bs.a.334.2		12
15.2	even	4		325.2.e.e.276.2		12
15.8	even	4		325.2.e.e.276.5		12
15.14	odd	2		65.2.n.a.29.5	yes	12
39.2	even	12		845.2.d.d.844.4		12
39.5	even	4		845.2.l.f.699.10		24
39.8	even	4		845.2.l.f.699.4		24
39.11	even	12		845.2.d.d.844.10		12
39.17	odd	6		845.2.n.e.529.2		12
39.20	even	12		845.2.l.f.654.3		24
39.23	odd	6		845.2.b.e.339.5		6
39.29	odd	6		845.2.b.d.339.2		6
39.32	even	12		845.2.l.f.654.9		24
39.35	odd	6		65.2.n.a.9.5	yes	12
39.38	odd	2		845.2.n.e.484.5		12
60.59	even	2		1040.2.dh.a.289.4		12
65.9	even	6	inner	585.2.bs.a.334.5		12
156.35	even	6		1040.2.dh.a.529.4		12
195.23	even	12		4225.2.a.bq.1.5		6
195.29	odd	6		845.2.b.d.339.5		6
195.44	even	4		845.2.l.f.699.3		24
195.59	even	12		845.2.l.f.654.10		24
195.62	even	12		4225.2.a.bq.1.2		6
195.68	even	12		4225.2.a.br.1.2		6
195.74	odd	6		65.2.n.a.9.2	✓	12
195.89	even	12		845.2.d.d.844.3		12
195.107	even	12		4225.2.a.br.1.5		6
195.113	even	12		325.2.e.e.126.5		12
195.119	even	12		845.2.d.d.844.9		12
195.134	odd	6		845.2.n.e.529.5		12
195.149	even	12		845.2.l.f.654.4		24
195.152	even	12		325.2.e.e.126.2		12
195.164	even	4		845.2.l.f.699.9		24
195.179	odd	6		845.2.b.e.339.2		6
195.194	odd	2		845.2.n.e.484.2		12
780.659	even	6		1040.2.dh.a.529.3		12

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

\(f(q)\)	\(=\)	\(q+(1.02826 - 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(1.75765 + 1.01478i) q^{7} +3.07548i q^{8} +O(q^{10})\)	\(q+(1.02826 - 0.593667i) q^{2} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(1.75765 + 1.01478i) q^{7} +3.07548i q^{8} +(-2.49650 - 0.903481i) q^{10} +(1.94045 + 3.36096i) q^{11} +(2.96232 - 2.05540i) q^{13} +2.40976 q^{14} +(1.23557 + 2.14007i) q^{16} +(4.71996 + 2.72507i) q^{17} +(2.94045 - 5.09301i) q^{19} +(1.29934 - 0.231562i) q^{20} +(3.99058 + 2.30396i) q^{22} +(0.298874 - 0.172555i) q^{23} +(-0.850210 + 4.92718i) q^{25} +(1.82581 - 3.87212i) q^{26} +(-1.03743 + 0.598962i) q^{28} +(-1.50000 - 2.59808i) q^{29} +1.18048 q^{31} +(-2.78591 - 1.60845i) q^{32} +6.47114 q^{34} +(-0.796234 - 4.46783i) q^{35} +(-4.71996 + 2.72507i) q^{37} -6.98259i q^{38} +(5.25997 - 4.43007i) q^{40} +(0.0902394 + 0.156299i) q^{41} +(1.15990 + 0.669668i) q^{43} -2.29066 q^{44} +(0.204880 - 0.354863i) q^{46} +12.2807i q^{47} +(-1.44045 - 2.49493i) q^{49} +(2.05087 + 5.57117i) q^{50} +(0.176407 + 2.12081i) q^{52} -2.42636i q^{53} +(2.95310 - 8.16003i) q^{55} +(-3.12093 + 5.40561i) q^{56} +(-3.08478 - 1.78100i) q^{58} +(3.53069 - 6.11533i) q^{59} +(-3.38090 + 5.85589i) q^{61} +(1.21384 - 0.700811i) q^{62} -8.76180 q^{64} +(-7.78241 - 2.10573i) q^{65} +(3.81417 - 2.20211i) q^{67} +(-2.78591 + 1.60845i) q^{68} +(-3.47114 - 4.12140i) q^{70} +(-0.940450 + 1.62891i) q^{71} +8.86014i q^{73} +(-3.23557 + 5.60417i) q^{74} +(1.73557 + 3.00609i) q^{76} +7.87651i q^{77} -11.1805 q^{79} +(1.88037 - 5.19585i) q^{80} +(0.185579 + 0.107144i) q^{82} -7.83540i q^{83} +(-2.13820 - 11.9979i) q^{85} +1.59024 q^{86} +(-10.3365 + 5.96781i) q^{88} +(-6.12093 - 10.6018i) q^{89} +(7.29249 - 0.606582i) q^{91} +0.203698i q^{92} +(7.29066 + 12.6278i) q^{94} +(-12.9461 + 2.30719i) q^{95} +(-5.02801 - 2.90292i) q^{97} +(-2.96232 - 1.71029i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) 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