LMFDB - Embedded newform 162.2.e.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			37.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	162.37
Dual form			162.2.e.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.26604 - 0.460802i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.26604 - 0.460802i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.673648 - 1.16679i) q^{10} +(3.49273 + 1.27125i) q^{11} +(-4.64543 - 3.89798i) q^{13} +(-0.0923963 - 0.0775297i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-2.58512 + 4.47756i) q^{17} +(2.96064 + 5.12797i) q^{19} +(-0.233956 - 1.32683i) q^{20} +(3.49273 - 1.27125i) q^{22} +(0.826352 - 4.68647i) q^{23} +(-2.43969 + 2.04715i) q^{25} -6.06418 q^{26} -0.120615 q^{28} +(-4.55303 + 3.82045i) q^{29} +(-0.875515 + 4.96529i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.897804 + 5.09170i) q^{34} +(-0.0812519 - 0.140732i) q^{35} +(-0.145430 + 0.251892i) q^{37} +(5.56418 + 2.02520i) q^{38} +(-1.03209 - 0.866025i) q^{40} +(-4.44356 - 3.72859i) q^{41} +(-0.426022 - 0.155059i) q^{43} +(1.85844 - 3.21891i) q^{44} +(-2.37939 - 4.12122i) q^{46} +(0.134285 + 0.761570i) q^{47} +(6.56418 - 2.38917i) q^{49} +(-0.553033 + 3.13641i) q^{50} +(-4.64543 + 3.89798i) q^{52} +7.29086 q^{53} +5.00774 q^{55} +(-0.0923963 + 0.0775297i) q^{56} +(-1.03209 + 5.85327i) q^{58} +(-1.40033 + 0.509678i) q^{59} +(-0.656574 - 3.72362i) q^{61} +(2.52094 + 4.36640i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-7.67752 - 2.79439i) q^{65} +(-5.08512 - 4.26692i) q^{67} +(3.96064 + 3.32337i) q^{68} +(-0.152704 - 0.0555796i) q^{70} +(2.87211 - 4.97464i) q^{71} +(-5.20961 - 9.02330i) q^{73} +(0.0505072 + 0.286441i) q^{74} +(5.56418 - 2.02520i) q^{76} +(0.0778483 - 0.441500i) q^{77} +(10.7194 - 8.99465i) q^{79} -1.34730 q^{80} -5.80066 q^{82} +(1.81521 - 1.52314i) q^{83} +(-1.20961 + 6.86002i) q^{85} +(-0.426022 + 0.155059i) q^{86} +(-0.645430 - 3.66041i) q^{88} +(-1.08512 - 1.87949i) q^{89} +(-0.365715 + 0.633436i) q^{91} +(-4.47178 - 1.62760i) q^{92} +(0.592396 + 0.497079i) q^{94} +(6.11128 + 5.12797i) q^{95} +(3.21941 + 1.17177i) q^{97} +(3.49273 - 6.04958i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8	$ 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{11} - 12 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} - 6 q^{20} + 3 q^{22} + 6 q^{23} - 9 q^{25} - 18 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} + 6 q^{34} - 3 q^{35} + 15 q^{37} + 15 q^{38} + 3 q^{40} + 3 q^{41} - 18 q^{43} + 3 q^{44} - 3 q^{46} - 9 q^{47} + 21 q^{49} + 9 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 3 q^{56} + 3 q^{58} + 6 q^{59} + 18 q^{61} + 12 q^{62} - 3 q^{64} - 21 q^{65} - 9 q^{67} + 15 q^{68} - 3 q^{70} - 12 q^{71} + 3 q^{73} + 3 q^{74} + 15 q^{76} - 39 q^{77} + 33 q^{79} - 6 q^{80} - 6 q^{82} + 18 q^{83} + 27 q^{85} - 18 q^{86} + 12 q^{88} + 15 q^{89} - 12 q^{91} - 12 q^{92} - 21 q^{95} - 12 q^{97} + 3 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 3 * q^11 - 12 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 - 6 * q^20 + 3 * q^22 + 6 * q^23 - 9 * q^25 - 18 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 + 6 * q^34 - 3 * q^35 + 15 * q^37 + 15 * q^38 + 3 * q^40 + 3 * q^41 - 18 * q^43 + 3 * q^44 - 3 * q^46 - 9 * q^47 + 21 * q^49 + 9 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 3 * q^58 + 6 * q^59 + 18 * q^61 + 12 * q^62 - 3 * q^64 - 21 * q^65 - 9 * q^67 + 15 * q^68 - 3 * q^70 - 12 * q^71 + 3 * q^73 + 3 * q^74 + 15 * q^76 - 39 * q^77 + 33 * q^79 - 6 * q^80 - 6 * q^82 + 18 * q^83 + 27 * q^85 - 18 * q^86 + 12 * q^88 + 15 * q^89 - 12 * q^91 - 12 * q^92 - 21 * q^95 - 12 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	1.26604	−	0.460802i	0.566192	−	0.206077i	−0.0430339	−	0.999074i	$-0.513702\pi$
$5$	1.26604	−	0.460802i	0.566192	−	0.206077i	0.609226	+	0.792996i	$0.291480\pi$
$6$		0			0
$7$	−0.0209445	−	0.118782i	−0.00791629	−	0.0448955i	0.980594	−	0.196051i	$-0.0628118\pi$
$7$	−0.0209445	−	0.118782i	−0.00791629	−	0.0448955i	−0.988510	+	0.151155i	$0.951701\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	0.673648	−	1.16679i	0.213026	−	0.368972i
$11$	3.49273	+	1.27125i	1.05310	+	0.383296i	0.809831	−	0.586664i	$-0.199559\pi$
$11$	3.49273	+	1.27125i	1.05310	+	0.383296i	0.243266	+	0.969960i	$0.421781\pi$
$12$		0			0
$13$	−4.64543	−	3.89798i	−1.28841	−	1.08110i	−0.992026	−	0.126036i	$-0.959775\pi$
$13$	−4.64543	−	3.89798i	−1.28841	−	1.08110i	−0.296385	−	0.955069i	$-0.595781\pi$
$14$	−0.0923963	−	0.0775297i	−0.0246939	−	0.0207207i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−2.58512	+	4.47756i	−0.626984	+	1.08597i	0.361169	+	0.932500i	$0.382378\pi$
$17$	−2.58512	+	4.47756i	−0.626984	+	1.08597i	−0.988154	+	0.153468i	$0.950956\pi$
$18$		0			0
$19$	2.96064	+	5.12797i	0.679217	+	1.17644i	0.975217	+	0.221250i	$0.0710137\pi$
$19$	2.96064	+	5.12797i	0.679217	+	1.17644i	−0.296000	+	0.955188i	$0.595653\pi$
$20$	−0.233956	−	1.32683i	−0.0523141	−	0.296688i
$21$		0			0
$22$	3.49273	−	1.27125i	0.744652	−	0.271031i
$23$	0.826352	−	4.68647i	0.172306	−	0.977197i	−0.768901	−	0.639368i	$-0.779196\pi$
$23$	0.826352	−	4.68647i	0.172306	−	0.977197i	0.941207	−	0.337830i	$-0.109693\pi$
$24$		0			0
$25$	−2.43969	+	2.04715i	−0.487939	+	0.409429i
$26$	−6.06418			−1.18928
$27$		0			0
$28$	−0.120615			−0.0227940
$29$	−4.55303	+	3.82045i	−0.845477	+	0.709440i	−0.958789	−	0.284120i	$-0.908299\pi$
$29$	−4.55303	+	3.82045i	−0.845477	+	0.709440i	0.113312	+	0.993559i	$0.463854\pi$
$30$		0			0
$31$	−0.875515	+	4.96529i	−0.157247	+	0.891793i	0.799455	+	0.600725i	$0.205121\pi$
$31$	−0.875515	+	4.96529i	−0.157247	+	0.891793i	−0.956703	+	0.291067i	$0.905990\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$		0			0
$34$	0.897804	+	5.09170i	0.153972	+	0.873219i
$35$	−0.0812519	−	0.140732i	−0.0137341	−	0.0237881i
$36$		0			0
$37$	−0.145430	+	0.251892i	−0.0239085	+	0.0414107i	−0.877732	−	0.479152i	$-0.840944\pi$
$37$	−0.145430	+	0.251892i	−0.0239085	+	0.0414107i	0.853824	+	0.520562i	$0.174278\pi$
$38$	5.56418	+	2.02520i	0.902629	+	0.328530i
$39$		0			0
$40$	−1.03209	−	0.866025i	−0.163188	−	0.136931i
$41$	−4.44356	−	3.72859i	−0.693968	−	0.582308i	0.226082	−	0.974108i	$-0.427408\pi$
$41$	−4.44356	−	3.72859i	−0.693968	−	0.582308i	−0.920050	+	0.391800i	$0.871853\pi$
$42$		0			0
$43$	−0.426022	−	0.155059i	−0.0649678	−	0.0236463i	0.309332	−	0.950954i	$-0.399895\pi$
$43$	−0.426022	−	0.155059i	−0.0649678	−	0.0236463i	−0.374300	+	0.927308i	$0.622117\pi$
$44$	1.85844	−	3.21891i	0.280170	−	0.485270i
$45$		0			0
$46$	−2.37939	−	4.12122i	−0.350821	−	0.607640i
$47$	0.134285	+	0.761570i	0.0195875	+	0.111086i	0.993034	−	0.117829i	$-0.0375933\pi$
$47$	0.134285	+	0.761570i	0.0195875	+	0.111086i	−0.973446	+	0.228915i	$0.926482\pi$
$48$		0			0
$49$	6.56418	−	2.38917i	0.937740	−	0.341309i
$50$	−0.553033	+	3.13641i	−0.0782107	+	0.443555i
$51$		0			0
$52$	−4.64543	+	3.89798i	−0.644205	+	0.540552i
$53$	7.29086			1.00148			0.500738	−	0.865599i	$-0.333062\pi$
$53$	7.29086			1.00148			0.500738	+	0.865599i	$0.333062\pi$
$54$		0			0
$55$	5.00774			0.675244
$56$	−0.0923963	+	0.0775297i	−0.0123470	+	0.0103603i
$57$		0			0
$58$	−1.03209	+	5.85327i	−0.135520	+	0.768572i
$59$	−1.40033	+	0.509678i	−0.182307	+	0.0663545i	−0.431561	−	0.902084i	$-0.642037\pi$
$59$	−1.40033	+	0.509678i	−0.182307	+	0.0663545i	0.249253	+	0.968438i	$0.419815\pi$
$60$		0			0
$61$	−0.656574	−	3.72362i	−0.0840657	−	0.476760i	−0.997554	−	0.0698959i	$-0.977733\pi$
$61$	−0.656574	−	3.72362i	−0.0840657	−	0.476760i	0.913489	−	0.406864i	$-0.133378\pi$
$62$	2.52094	+	4.36640i	0.320160	+	0.554534i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−7.67752	−	2.79439i	−0.952279	−	0.346601i
$66$		0			0
$67$	−5.08512	−	4.26692i	−0.621247	−	0.521288i	0.276949	−	0.960885i	$-0.410677\pi$
$67$	−5.08512	−	4.26692i	−0.621247	−	0.521288i	−0.898195	+	0.439597i	$0.855121\pi$
$68$	3.96064	+	3.32337i	0.480298	+	0.403018i
$69$		0			0
$70$	−0.152704	−	0.0555796i	−0.0182516	−	0.00664303i
$71$	2.87211	−	4.97464i	0.340857	−	0.590381i	−0.643735	−	0.765248i	$-0.722616\pi$
$71$	2.87211	−	4.97464i	0.340857	−	0.590381i	0.984592	+	0.174867i	$0.0559495\pi$
$72$		0			0
$73$	−5.20961	−	9.02330i	−0.609738	−	1.05610i	−0.991283	−	0.131748i	$-0.957941\pi$
$73$	−5.20961	−	9.02330i	−0.609738	−	1.05610i	0.381545	−	0.924350i	$-0.375392\pi$
$74$	0.0505072	+	0.286441i	0.00587134	+	0.0332980i
$75$		0			0
$76$	5.56418	−	2.02520i	0.638255	−	0.232306i
$77$	0.0778483	−	0.441500i	0.00887164	−	0.0503136i
$78$		0			0
$79$	10.7194	−	8.99465i	1.20603	−	1.01198i	0.206591	−	0.978427i	$-0.433763\pi$
$79$	10.7194	−	8.99465i	1.20603	−	1.01198i	0.999437	−	0.0335498i	$-0.0106812\pi$
$80$	−1.34730			−0.150632
$81$		0			0
$82$	−5.80066			−0.640576
$83$	1.81521	−	1.52314i	0.199245	−	0.167186i	−0.537706	−	0.843132i	$-0.680709\pi$
$83$	1.81521	−	1.52314i	0.199245	−	0.167186i	0.736951	+	0.675946i	$0.236265\pi$
$84$		0			0
$85$	−1.20961	+	6.86002i	−0.131200	+	0.744074i
$86$	−0.426022	+	0.155059i	−0.0459391	+	0.0167205i
$87$		0			0
$88$	−0.645430	−	3.66041i	−0.0688030	−	0.390201i
$89$	−1.08512	−	1.87949i	−0.115023	−	0.199225i	0.802766	−	0.596294i	$-0.203361\pi$
$89$	−1.08512	−	1.87949i	−0.115023	−	0.199225i	−0.917789	+	0.397069i	$0.870027\pi$
$90$		0			0
$91$	−0.365715	+	0.633436i	−0.0383373	+	0.0664022i
$92$	−4.47178	−	1.62760i	−0.466215	−	0.169689i
$93$		0			0
$94$	0.592396	+	0.497079i	0.0611010	+	0.0512698i
$95$	6.11128	+	5.12797i	0.627004	+	0.526119i
$96$		0			0
$97$	3.21941	+	1.17177i	0.326881	+	0.118975i	0.500248	−	0.865882i	$-0.333242\pi$
$97$	3.21941	+	1.17177i	0.326881	+	0.118975i	−0.173366	+	0.984857i	$0.555464\pi$
$98$	3.49273	−	6.04958i	0.352819	−	0.611100i
$99$		0			0
$100$	1.59240	+	2.75811i	0.159240	+	0.275811i
$101$	−1.49660	−	8.48762i	−0.148917	−	0.844550i	−0.964138	−	0.265400i	$-0.914496\pi$
$101$	−1.49660	−	8.48762i	−0.148917	−	0.844550i	0.815221	−	0.579149i	$-0.196615\pi$
$102$		0			0
$103$	2.05303	−	0.747243i	0.202291	−	0.0736280i	−0.238887	−	0.971047i	$-0.576783\pi$
$103$	2.05303	−	0.747243i	0.202291	−	0.0736280i	0.441179	+	0.897419i	$0.354560\pi$
$104$	−1.05303	+	5.97205i	−0.103258	+	0.585608i
$105$		0			0
$106$	5.58512	−	4.68647i	0.542475	−	0.455191i
$107$	10.2909			0.994855			0.497427	−	0.867506i	$-0.334278\pi$
$107$	10.2909			0.994855			0.497427	+	0.867506i	$0.334278\pi$
$108$		0			0
$109$	−11.0915			−1.06237			−0.531187	−	0.847254i	$-0.678254\pi$
$109$	−11.0915			−1.06237			−0.531187	+	0.847254i	$0.678254\pi$
$110$	3.83615	−	3.21891i	0.365763	−	0.306911i
$111$		0			0
$112$	−0.0209445	+	0.118782i	−0.00197907	+	0.0112239i
$113$	5.56670	−	2.02611i	0.523671	−	0.190601i	−0.0666389	−	0.997777i	$-0.521228\pi$
$113$	5.56670	−	2.02611i	0.523671	−	0.190601i	0.590310	+	0.807176i	$0.299005\pi$
$114$		0			0
$115$	−1.11334	−	6.31407i	−0.103820	−	0.588790i
$116$	2.97178	+	5.14728i	0.275923	+	0.477913i
$117$		0			0
$118$	−0.745100	+	1.29055i	−0.0685920	+	0.118805i
$119$	0.586000	+	0.213286i	0.0537185	+	0.0195519i
$120$		0			0
$121$	2.15657	+	1.80958i	0.196052	+	0.164507i
$122$	−2.89646	−	2.43042i	−0.262233	−	0.220040i
$123$		0			0
$124$	4.73783	+	1.72443i	0.425469	+	0.154858i
$125$	−5.51367	+	9.54996i	−0.493158	+	0.854174i
$126$		0			0
$127$	2.86959	+	4.97027i	0.254634	+	0.441040i	0.964796	−	0.262999i	$-0.0847115\pi$
$127$	2.86959	+	4.97027i	0.254634	+	0.441040i	−0.710162	+	0.704039i	$0.751378\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$		0			0
$130$	−7.67752	+	2.79439i	−0.673363	+	0.245084i
$131$	−2.99020	+	16.9583i	−0.261255	+	1.48165i	0.518236	+	0.855237i	$0.326589\pi$
$131$	−2.99020	+	16.9583i	−0.261255	+	1.48165i	−0.779491	+	0.626413i	$0.784522\pi$
$132$		0			0
$133$	0.547104	−	0.459074i	0.0474399	−	0.0398068i
$134$	−6.63816			−0.573449
$135$		0			0
$136$	5.17024			0.443345
$137$	−0.0662372	+	0.0555796i	−0.00565902	+	0.00474848i	−0.645613	−	0.763665i	$-0.723398\pi$
$137$	−0.0662372	+	0.0555796i	−0.00565902	+	0.00474848i	0.639954	+	0.768413i	$0.278954\pi$
$138$		0			0
$139$	−3.18866	+	18.0838i	−0.270459	+	1.53385i	0.482568	+	0.875859i	$0.339704\pi$
$139$	−3.18866	+	18.0838i	−0.270459	+	1.53385i	−0.753027	+	0.657990i	$0.771407\pi$
$140$	−0.152704	+	0.0555796i	−0.0129058	+	0.00469733i
$141$		0			0
$142$	−0.997474	−	5.65695i	−0.0837061	−	0.474721i
$143$	−11.2699	−	19.5201i	−0.942438	−	1.63235i
$144$		0			0
$145$	−4.00387	+	6.93491i	−0.332503	+	0.575913i
$146$	−9.79086	−	3.56358i	−0.810297	−	0.294924i
$147$		0			0
$148$	0.222811	+	0.186961i	0.0183150	+	0.0153681i
$149$	3.75490	+	3.15074i	0.307613	+	0.258118i	0.783505	−	0.621386i	$-0.213430\pi$
$149$	3.75490	+	3.15074i	0.307613	+	0.258118i	−0.475891	+	0.879504i	$0.657874\pi$
$150$		0			0
$151$	−1.62701	−	0.592184i	−0.132404	−	0.0481912i	0.274968	−	0.961453i	$-0.411333\pi$
$151$	−1.62701	−	0.592184i	−0.132404	−	0.0481912i	−0.407372	+	0.913262i	$0.633555\pi$
$152$	2.96064	−	5.12797i	0.240139	−	0.415934i
$153$		0			0
$154$	−0.224155	−	0.388249i	−0.0180630	−	0.0312860i
$155$	1.17958	+	6.68972i	0.0947460	+	0.537331i
$156$		0			0
$157$	5.46451	−	1.98892i	0.436115	−	0.158733i	−0.114627	−	0.993409i	$-0.536567\pi$
$157$	5.46451	−	1.98892i	0.436115	−	0.158733i	0.550742	+	0.834676i	$0.314345\pi$
$158$	2.42989	−	13.7806i	0.193312	−	1.09633i
$159$		0			0
$160$	−1.03209	+	0.866025i	−0.0815938	+	0.0684653i
$161$	−0.573978			−0.0452358
$162$		0			0
$163$	−2.70914			−0.212196			−0.106098	−	0.994356i	$-0.533836\pi$
$163$	−2.70914			−0.212196			−0.106098	+	0.994356i	$0.533836\pi$
$164$	−4.44356	+	3.72859i	−0.346984	+	0.291154i
$165$		0			0
$166$	0.411474	−	2.33359i	0.0319366	−	0.181121i
$167$	−23.1202	+	8.41507i	−1.78910	+	0.651177i	−0.789811	+	0.613351i	$0.789821\pi$
$167$	−23.1202	+	8.41507i	−1.78910	+	0.651177i	−0.999284	+	0.0378268i	$0.987956\pi$
$168$		0			0
$169$	4.12836	+	23.4131i	0.317566	+	1.80101i
$170$	3.48293	+	6.03260i	0.267128	+	0.462680i
$171$		0			0
$172$	−0.226682	+	0.392624i	−0.0172843	+	0.0299373i
$173$	−10.0753	−	3.66712i	−0.766013	−	0.278806i	−0.0706849	−	0.997499i	$-0.522518\pi$
$173$	−10.0753	−	3.66712i	−0.766013	−	0.278806i	−0.695328	+	0.718693i	$0.744741\pi$
$174$		0			0
$175$	0.294263	+	0.246916i	0.0222442	+	0.0186651i
$176$	−2.84730	−	2.38917i	−0.214623	−	0.180090i
$177$		0			0
$178$	−2.03936	−	0.742267i	−0.152857	−	0.0556353i
$179$	−6.92262	+	11.9903i	−0.517421	+	0.896199i	0.482374	+	0.875965i	$0.339774\pi$
$179$	−6.92262	+	11.9903i	−0.517421	+	0.896199i	−0.999795	+	0.0202340i	$0.993559\pi$
$180$		0			0
$181$	−1.75490	−	3.03958i	−0.130441	−	0.225930i	0.793406	−	0.608693i	$-0.208306\pi$
$181$	−1.75490	−	3.03958i	−0.130441	−	0.225930i	−0.923847	+	0.382763i	$0.874973\pi$
$182$	0.127011	+	0.720317i	0.00941471	+	0.0533935i
$183$		0			0
$184$	−4.47178	+	1.62760i	−0.329664	+	0.119988i
$185$	−0.0680482	+	0.385920i	−0.00500300	+	0.0283734i
$186$		0			0
$187$	−14.7212	+	12.3526i	−1.07652	+	0.903309i
$188$	0.773318			0.0564000
$189$		0			0
$190$	7.97771			0.578764
$191$	16.7704	−	14.0720i	1.21346	−	1.01822i	0.214322	−	0.976763i	$-0.431246\pi$
$191$	16.7704	−	14.0720i	1.21346	−	1.01822i	0.999140	−	0.0414526i	$-0.0131986\pi$
$192$		0			0
$193$	4.44743	−	25.2226i	0.320133	−	1.81557i	−0.221740	−	0.975106i	$-0.571174\pi$
$193$	4.44743	−	25.2226i	0.320133	−	1.81557i	0.541873	−	0.840460i	$-0.317715\pi$
$194$	3.21941	−	1.17177i	0.231140	−	0.0841281i
$195$		0			0
$196$	−1.21301	−	6.87933i	−0.0866436	−	0.491381i
$197$	6.84255	+	11.8516i	0.487511	+	0.844395i	0.999897	−	0.0143611i	$-0.00457142\pi$
$197$	6.84255	+	11.8516i	0.487511	+	0.844395i	−0.512385	+	0.858756i	$0.671238\pi$
$198$		0			0
$199$	6.19981	−	10.7384i	0.439493	−	0.761224i	−0.558158	−	0.829735i	$-0.688492\pi$
$199$	6.19981	−	10.7384i	0.439493	−	0.761224i	0.997650	+	0.0685113i	$0.0218249\pi$
$200$	2.99273	+	1.08926i	0.211618	+	0.0770225i
$201$		0			0
$202$	−6.60220	−	5.53990i	−0.464529	−	0.389786i
$203$	0.549163	+	0.460802i	0.0385437	+	0.0323420i
$204$		0			0
$205$	−7.34389	−	2.67296i	−0.512920	−	0.186688i
$206$	1.09240	−	1.89209i	0.0761109	−	0.131828i
$207$		0			0
$208$	3.03209	+	5.25173i	0.210238	+	0.364142i
$209$	3.82177	+	21.6743i	0.264357	+	1.49924i
$210$		0			0
$211$	−13.9474	+	5.07645i	−0.960181	+	0.349477i	−0.774104	−	0.633058i	$-0.781799\pi$
$211$	−13.9474	+	5.07645i	−0.960181	+	0.349477i	−0.186077	+	0.982535i	$0.559577\pi$
$212$	1.26604	−	7.18009i	0.0869523	−	0.493131i
$213$		0			0
$214$	7.88326	−	6.61484i	0.538888	−	0.452181i
$215$	−0.610815			−0.0416572
$216$		0			0
$217$	0.608126			0.0412823
$218$	−8.49660	+	7.12949i	−0.575462	+	0.482870i
$219$		0			0
$220$	0.869585	−	4.93166i	0.0586274	−	0.332493i
$221$	29.4624	−	10.7235i	1.98186	−	0.721338i
$222$		0			0
$223$	−1.16890	−	6.62916i	−0.0782754	−	0.443922i	−0.998606	−	0.0527806i	$-0.983192\pi$
$223$	−1.16890	−	6.62916i	−0.0782754	−	0.443922i	0.920331	−	0.391141i	$-0.127920\pi$
$224$	0.0603074	+	0.104455i	0.00402946	+	0.00697922i
$225$		0			0
$226$	2.96198	−	5.13030i	0.197028	−	0.341263i
$227$	13.6211	+	4.95767i	0.904063	+	0.329052i	0.751880	−	0.659300i	$-0.229147\pi$
$227$	13.6211	+	4.95767i	0.904063	+	0.329052i	0.152183	+	0.988352i	$0.451370\pi$
$228$		0			0
$229$	19.7540	+	16.5756i	1.30538	+	1.09535i	0.989188	+	0.146652i	$0.0468496\pi$
$229$	19.7540	+	16.5756i	1.30538	+	1.09535i	0.316194	+	0.948694i	$0.397595\pi$
$230$	−4.91147	−	4.12122i	−0.323853	−	0.271745i
$231$		0			0
$232$	5.58512	+	2.03282i	0.366681	+	0.133461i
$233$	5.19846	−	9.00400i	0.340563	−	0.589872i	−0.643975	−	0.765047i	$-0.722716\pi$
$233$	5.19846	−	9.00400i	0.340563	−	0.589872i	0.984537	+	0.175175i	$0.0560491\pi$
$234$		0			0
$235$	0.520945	+	0.902302i	0.0339827	+	0.0588597i
$236$	0.258770	+	1.46756i	0.0168445	+	0.0955300i
$237$		0			0
$238$	0.586000	−	0.213286i	0.0379847	−	0.0138253i
$239$	3.97906	−	22.5663i	0.257384	−	1.45970i	−0.532495	−	0.846433i	$-0.678746\pi$
$239$	3.97906	−	22.5663i	0.257384	−	1.45970i	0.789879	−	0.613263i	$-0.210143\pi$
$240$		0			0
$241$	−9.25150	+	7.76293i	−0.595941	+	0.500054i	−0.890138	−	0.455691i	$-0.849392\pi$
$241$	−9.25150	+	7.76293i	−0.595941	+	0.500054i	0.294197	+	0.955745i	$0.404948\pi$
$242$	2.81521			0.180968
$243$		0			0
$244$	−3.78106			−0.242058
$245$	7.20961	−	6.04958i	0.460605	−	0.386493i
$246$		0			0
$247$	6.23530	−	35.3621i	0.396743	−	2.25004i
$248$	4.73783	−	1.72443i	0.300852	−	0.109501i
$249$		0			0
$250$	1.91488	+	10.8598i	0.121107	+	0.686835i
$251$	−7.02347	−	12.1650i	−0.443318	−	0.767849i	0.554616	−	0.832107i	$-0.312865\pi$
$251$	−7.02347	−	12.1650i	−0.443318	−	0.767849i	−0.997933	+	0.0642581i	$0.979532\pi$
$252$		0			0
$253$	8.84389	−	15.3181i	0.556011	−	0.963039i
$254$	5.39306	+	1.96291i	0.338390	+	0.123164i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−13.8983	−	11.6620i	−0.866950	−	0.727458i	0.0965034	−	0.995333i	$-0.469234\pi$
$257$	−13.8983	−	11.6620i	−0.866950	−	0.727458i	−0.963454	+	0.267875i	$0.913679\pi$
$258$		0			0
$259$	0.0329662	+	0.0119987i	0.00204842	+	0.000745565i
$260$	−4.08512	+	7.07564i	−0.253349	+	0.438813i
$261$		0			0
$262$	8.60994	+	14.9128i	0.531924	+	0.921319i
$263$	−0.742107	−	4.20870i	−0.0457603	−	0.259519i	0.953342	−	0.301894i	$-0.0976188\pi$
$263$	−0.742107	−	4.20870i	−0.0457603	−	0.259519i	−0.999102	+	0.0423745i	$0.986508\pi$
$264$		0			0
$265$	9.23055	−	3.35965i	0.567028	−	0.206381i
$266$	0.124018	−	0.703343i	0.00760405	−	0.0431247i
$267$		0			0
$268$	−5.08512	+	4.26692i	−0.310623	+	0.260644i
$269$	−13.0615			−0.796373			−0.398187	−	0.917304i	$-0.630360\pi$
$269$	−13.0615			−0.796373			−0.398187	+	0.917304i	$0.630360\pi$
$270$		0			0
$271$	8.48751			0.515580			0.257790	−	0.966201i	$-0.417006\pi$
$271$	8.48751			0.515580			0.257790	+	0.966201i	$0.417006\pi$
$272$	3.96064	−	3.32337i	0.240149	−	0.201509i
$273$		0			0
$274$	−0.0150147	+	0.0851529i	−0.000907074	+	0.00514427i
$275$	−11.1236	+	4.04866i	−0.670779	+	0.244144i
$276$		0			0
$277$	1.14842	+	6.51303i	0.0690020	+	0.391330i	0.999675	+	0.0254787i	$0.00811100\pi$
$277$	1.14842	+	6.51303i	0.0690020	+	0.391330i	−0.930673	+	0.365851i	$0.880778\pi$
$278$	9.18139	+	15.9026i	0.550663	+	0.953776i
$279$		0			0
$280$	−0.0812519	+	0.140732i	−0.00485573	+	0.00841037i
$281$	27.9320	+	10.1664i	1.66628	+	0.606478i	0.991332	−	0.131384i	$-0.0419420\pi$
$281$	27.9320	+	10.1664i	1.66628	+	0.606478i	0.674952	+	0.737861i	$0.264164\pi$
$282$		0			0
$283$	−2.15657	−	1.80958i	−0.128195	−	0.107568i	0.576436	−	0.817142i	$-0.304443\pi$
$283$	−2.15657	−	1.80958i	−0.128195	−	0.107568i	−0.704631	+	0.709574i	$0.748887\pi$
$284$	−4.40033	−	3.69232i	−0.261112	−	0.219099i
$285$		0			0
$286$	−21.1805	−	7.70908i	−1.25243	−	0.455847i
$287$	−0.349823	+	0.605910i	−0.0206494	+	0.0357658i
$288$		0			0
$289$	−4.86571	−	8.42767i	−0.286219	−	0.495745i
$290$	1.39053	+	7.88609i	0.0816547	+	0.463087i
$291$		0			0
$292$	−9.79086	+	3.56358i	−0.572967	+	0.208543i
$293$	−1.70796	+	9.68631i	−0.0997800	+	0.565881i	0.893397	+	0.449267i	$0.148315\pi$
$293$	−1.70796	+	9.68631i	−0.0997800	+	0.565881i	−0.993177	+	0.116613i	$0.962796\pi$
$294$		0			0
$295$	−1.53802	+	1.29055i	−0.0895469	+	0.0751388i
$296$	0.290859			0.0169059
$297$		0			0
$298$	4.90167			0.283946
$299$	−22.1065	+	18.5496i	−1.27845	+	1.07275i
$300$		0			0
$301$	−0.00949548	+	0.0538515i	−0.000547310	+	0.00310395i
$302$	−1.62701	+	0.592184i	−0.0936240	+	0.0340763i
$303$		0			0
$304$	−1.02822	−	5.83132i	−0.0589724	−	0.334449i
$305$	−2.54710	−	4.41171i	−0.145847	−	0.252614i
$306$		0			0
$307$	−6.78106	+	11.7451i	−0.387015	+	0.670330i	−0.992047	−	0.125871i	$-0.959827\pi$
$307$	−6.78106	+	11.7451i	−0.387015	+	0.670330i	0.605031	+	0.796202i	$0.293161\pi$
$308$	−0.421274	−	0.153331i	−0.0240043	−	0.00873686i
$309$		0			0
$310$	5.20368	+	4.36640i	0.295549	+	0.247995i
$311$	8.10220	+	6.79855i	0.459433	+	0.385510i	0.842922	−	0.538035i	$-0.180833\pi$
$311$	8.10220	+	6.79855i	0.459433	+	0.385510i	−0.383489	+	0.923545i	$0.625278\pi$
$312$		0			0
$313$	10.0544	+	3.65949i	0.568307	+	0.206847i	0.610162	−	0.792277i	$-0.291104\pi$
$313$	10.0544	+	3.65949i	0.568307	+	0.206847i	−0.0418547	+	0.999124i	$0.513327\pi$
$314$	2.90760	−	5.03612i	0.164086	−	0.284205i
$315$		0			0
$316$	−6.99660	−	12.1185i	−0.393589	−	0.681717i
$317$	−5.06717	−	28.7374i	−0.284601	−	1.61405i	−0.706708	−	0.707505i	$-0.749821\pi$
$317$	−5.06717	−	28.7374i	−0.284601	−	1.61405i	0.422108	−	0.906546i	$-0.361290\pi$
$318$		0			0
$319$	−20.7592	+	7.55574i	−1.16229	+	0.423040i
$320$	−0.233956	+	1.32683i	−0.0130785	+	0.0741719i
$321$		0			0
$322$	−0.439693	+	0.368946i	−0.0245031	+	0.0205606i
$323$	−30.6144			−1.70343
$324$		0			0
$325$	19.3131			1.07130
$326$	−2.07532	+	1.74140i	−0.114941	+	0.0964473i
$327$		0			0
$328$	−1.00727	+	5.71253i	−0.0556174	+	0.315422i
$329$	0.0876485	−	0.0319015i	0.00483222	−	0.00175878i
$330$		0			0
$331$	−1.26739	−	7.18772i	−0.0696620	−	0.395073i	−0.999624	−	0.0274173i	$-0.991272\pi$
$331$	−1.26739	−	7.18772i	−0.0696620	−	0.395073i	0.929962	−	0.367655i	$-0.119839\pi$
$332$	−1.18479	−	2.05212i	−0.0650239	−	0.112625i
$333$		0			0
$334$	−12.3020	+	21.3077i	−0.673136	+	1.16591i
$335$	−8.40420	−	3.05888i	−0.459171	−	0.167124i
$336$		0			0
$337$	−1.24376	−	1.04363i	−0.0677517	−	0.0568504i	0.608283	−	0.793720i	$-0.291859\pi$
$337$	−1.24376	−	1.04363i	−0.0677517	−	0.0568504i	−0.676035	+	0.736870i	$0.736303\pi$
$338$	18.2121	+	15.2818i	0.990609	+	0.831220i
$339$		0			0
$340$	6.54576	+	2.38246i	0.354994	+	0.129207i
$341$	−9.37005	+	16.2294i	−0.507417	+	0.878872i
$342$		0			0
$343$	−0.843426	−	1.46086i	−0.0455407	−	0.0788788i
$344$	0.0787257	+	0.446476i	0.00424460	+	0.0240724i
$345$		0			0
$346$	−10.0753	+	3.66712i	−0.541653	+	0.197145i
$347$	0.949655	−	5.38576i	0.0509801	−	0.289123i	−0.948650	−	0.316329i	$-0.897550\pi$
$347$	0.949655	−	5.38576i	0.0509801	−	0.289123i	0.999630	+	0.0272057i	$0.00866092\pi$
$348$		0			0
$349$	2.37346	−	1.99157i	0.127048	−	0.106606i	−0.577050	−	0.816709i	$-0.695796\pi$
$349$	2.37346	−	1.99157i	0.127048	−	0.106606i	0.704098	+	0.710103i	$0.251352\pi$
$350$	0.384133			0.0205328
$351$		0			0
$352$	−3.71688			−0.198110
$353$	−0.233956	+	0.196312i	−0.0124522	+	0.0104486i	−0.648992	−	0.760795i	$-0.724809\pi$
$353$	−0.233956	+	0.196312i	−0.0124522	+	0.0104486i	0.636540	+	0.771243i	$0.280365\pi$
$354$		0			0
$355$	1.34389	−	7.62159i	0.0713264	−	0.404512i
$356$	−2.03936	+	0.742267i	−0.108086	+	0.0393401i
$357$		0			0
$358$	2.40420	+	13.6349i	0.127066	+	0.720627i
$359$	5.28493	+	9.15377i	0.278928	+	0.483117i	0.971119	−	0.238597i	$-0.0766876\pi$
$359$	5.28493	+	9.15377i	0.278928	+	0.483117i	−0.692191	+	0.721715i	$0.743354\pi$
$360$		0			0
$361$	−8.03074	+	13.9097i	−0.422671	+	0.732087i
$362$	−3.29813	−	1.20042i	−0.173346	−	0.0630928i
$363$		0			0
$364$	0.560307	+	0.470154i	0.0293681	+	0.0246428i
$365$	−10.7536	−	9.02330i	−0.562867	−	0.472301i
$366$		0			0
$367$	−2.51842	−	0.916629i	−0.131460	−	0.0478477i	0.275452	−	0.961315i	$-0.411172\pi$
$367$	−2.51842	−	0.916629i	−0.131460	−	0.0478477i	−0.406913	+	0.913467i	$0.633395\pi$
$368$	−2.37939	+	4.12122i	−0.124034	+	0.214833i
$369$		0			0
$370$	0.195937	+	0.339373i	0.0101863	+	0.0176431i
$371$	−0.152704	−	0.866025i	−0.00792798	−	0.0449618i
$372$		0			0
$373$	−22.9008	+	8.33521i	−1.18576	+	0.431581i	−0.858232	−	0.513261i	$-0.828437\pi$
$373$	−22.9008	+	8.33521i	−1.18576	+	0.431581i	−0.327526	+	0.944842i	$0.606215\pi$
$374$	−3.33703	+	18.9252i	−0.172554	+	0.978601i
$375$		0			0
$376$	0.592396	−	0.497079i	0.0305505	−	0.0256349i
$377$	36.0428			1.85630
$378$		0			0
$379$	−4.08647			−0.209908			−0.104954	−	0.994477i	$-0.533469\pi$
$379$	−4.08647			−0.209908			−0.104954	+	0.994477i	$0.533469\pi$
$380$	6.11128	−	5.12797i	0.313502	−	0.263060i
$381$		0			0
$382$	3.80154	−	21.5596i	0.194504	−	1.10308i
$383$	−15.4017	+	5.60575i	−0.786989	+	0.286440i	−0.704084	−	0.710117i	$-0.748642\pi$
$383$	−15.4017	+	5.60575i	−0.786989	+	0.286440i	−0.0829050	+	0.996557i	$0.526420\pi$
$384$		0			0
$385$	−0.104885	−	0.594831i	−0.00534542	−	0.0303154i
$386$	−12.8059	−	22.1804i	−0.651802	−	1.12895i
$387$		0			0
$388$	1.71301	−	2.96702i	0.0869650	−	0.150628i
$389$	−26.2263	−	9.54558i	−1.32972	−	0.483980i	−0.423163	−	0.906054i	$-0.639080\pi$
$389$	−26.2263	−	9.54558i	−1.32972	−	0.483980i	−0.906562	+	0.422073i	$0.861302\pi$
$390$		0			0
$391$	18.8478	+	15.8152i	0.953172	+	0.799807i
$392$	−5.35117	−	4.49016i	−0.270275	−	0.226787i
$393$		0			0
$394$	12.8598	+	4.68058i	0.647867	+	0.235804i
$395$	9.42649	−	16.3272i	0.474298	−	0.821508i
$396$		0			0
$397$	16.2469	+	28.1405i	0.815409	+	1.41233i	0.909034	+	0.416722i	$0.136821\pi$
$397$	16.2469	+	28.1405i	0.815409	+	1.41233i	−0.0936247	+	0.995608i	$0.529845\pi$
$398$	−2.15317	−	12.2112i	−0.107929	−	0.612094i
$399$		0			0
$400$	2.99273	−	1.08926i	0.149636	−	0.0544632i
$401$	−2.67096	+	15.1478i	−0.133381	+	0.756443i	0.842592	+	0.538553i	$0.181029\pi$
$401$	−2.67096	+	15.1478i	−0.133381	+	0.756443i	−0.975973	+	0.217891i	$0.930082\pi$
$402$		0			0
$403$	23.4217	−	19.6532i	1.16672	−	0.978994i
$404$	−8.61856			−0.428789
$405$		0			0
$406$	0.716881			0.0355782
$407$	−0.828163	+	0.694911i	−0.0410505	+	0.0344455i
$408$		0			0
$409$	−1.65822	+	9.40425i	−0.0819938	+	0.465010i	0.915971	+	0.401244i	$0.131422\pi$
$409$	−1.65822	+	9.40425i	−0.0819938	+	0.465010i	−0.997965	+	0.0637658i	$0.979689\pi$
$410$	−7.34389	+	2.67296i	−0.362689	+	0.132008i
$411$		0			0
$412$	−0.379385	−	2.15160i	−0.0186910	−	0.106002i
$413$	0.0898700	+	0.155659i	0.00442222	+	0.00765950i
$414$		0			0
$415$	1.59627	−	2.76481i	0.0783576	−	0.135719i
$416$	5.69846	+	2.07407i	0.279390	+	0.101690i
$417$		0			0
$418$	16.8596	+	14.1469i	0.824631	+	0.691948i
$419$	26.0239	+	21.8367i	1.27135	+	1.06679i	0.994375	+	0.105915i	$0.0337771\pi$
$419$	26.0239	+	21.8367i	1.27135	+	1.06679i	0.276977	+	0.960876i	$0.410667\pi$
$420$		0			0
$421$	11.8229	+	4.30320i	0.576215	+	0.209725i	0.613656	−	0.789574i	$-0.289698\pi$
$421$	11.8229	+	4.30320i	0.576215	+	0.209725i	−0.0374406	+	0.999299i	$0.511920\pi$
$422$	−7.42127	+	12.8540i	−0.361262	+	0.625724i
$423$		0			0
$424$	−3.64543	−	6.31407i	−0.177038	−	0.306638i
$425$	−2.85932	−	16.2160i	−0.138697	−	0.786591i
$426$		0			0
$427$	−0.428548	+	0.155979i	−0.0207389	+	0.00754834i
$428$	1.78699	−	10.1345i	0.0863774	−	0.489870i
$429$		0			0
$430$	−0.467911	+	0.392624i	−0.0225647	+	0.0189340i
$431$	7.77601			0.374557			0.187279	−	0.982307i	$-0.440033\pi$
$431$	7.77601			0.374557			0.187279	+	0.982307i	$0.440033\pi$
$432$		0			0
$433$	−40.6536			−1.95369			−0.976845	−	0.213950i	$-0.931367\pi$
$433$	−40.6536			−1.95369			−0.976845	+	0.213950i	$0.931367\pi$
$434$	0.465852	−	0.390896i	0.0223616	−	0.0187636i
$435$		0			0
$436$	−1.92602	+	10.9230i	−0.0922397	+	0.523117i
$437$	26.4786	−	9.63744i	1.26665	−	0.461021i
$438$		0			0
$439$	−3.07280	−	17.4267i	−0.146657	−	0.831731i	−0.966022	−	0.258459i	$-0.916785\pi$
$439$	−3.07280	−	17.4267i	−0.146657	−	0.831731i	0.819366	−	0.573271i	$-0.194326\pi$
$440$	−2.50387	−	4.33683i	−0.119367	−	0.206750i
$441$		0			0
$442$	15.6766	−	27.1527i	0.745662	−	1.29152i
$443$	13.5086	+	4.91673i	0.641814	+	0.233601i	0.642365	−	0.766399i	$-0.277953\pi$
$443$	13.5086	+	4.91673i	0.641814	+	0.233601i	−0.000551343		1.00000i	$0.500175\pi$
$444$		0			0
$445$	−2.23989	−	1.87949i	−0.106181	−	0.0890962i
$446$	−5.15657	−	4.32688i	−0.244171	−	0.204884i
$447$		0			0
$448$	0.113341	+	0.0412527i	0.00535485	+	0.00194901i
$449$	13.9859	−	24.2243i	0.660036	−	1.14322i	−0.320569	−	0.947225i	$-0.603874\pi$
$449$	13.9859	−	24.2243i	0.660036	−	1.14322i	0.980606	−	0.195991i	$-0.0627925\pi$
$450$		0			0
$451$	−10.7802	−	18.6718i	−0.507619	−	0.879222i
$452$	−1.02869	−	5.83396i	−0.0483853	−	0.274407i
$453$		0			0
$454$	13.6211	−	4.95767i	0.639269	−	0.232675i
$455$	−0.171122	+	0.970481i	−0.00802232	+	0.0454968i
$456$		0			0
$457$	6.53280	−	5.48167i	0.305592	−	0.256422i	−0.477075	−	0.878862i	$-0.658303\pi$
$457$	6.53280	−	5.48167i	0.305592	−	0.256422i	0.782667	+	0.622440i	$0.213859\pi$
$458$	25.7870			1.20495
$459$		0			0
$460$	−6.41147			−0.298937
$461$	−16.6361	+	13.9593i	−0.774820	+	0.650151i	−0.941938	−	0.335785i	$-0.890998\pi$
$461$	−16.6361	+	13.9593i	−0.774820	+	0.650151i	0.167118	+	0.985937i	$0.446554\pi$
$462$		0			0
$463$	−3.43882	+	19.5025i	−0.159815	+	0.906358i	0.794435	+	0.607349i	$0.207767\pi$
$463$	−3.43882	+	19.5025i	−0.159815	+	0.906358i	−0.954250	+	0.299009i	$0.903344\pi$
$464$	5.58512	−	2.03282i	0.259283	−	0.0943712i
$465$		0			0
$466$	−1.80541	−	10.2390i	−0.0836339	−	0.474311i
$467$	18.4927	+	32.0303i	0.855741	+	1.48219i	0.875956	+	0.482392i	$0.160232\pi$
$467$	18.4927	+	32.0303i	0.855741	+	1.48219i	−0.0202143	+	0.999796i	$0.506435\pi$
$468$		0			0
$469$	−0.400330	+	0.693392i	−0.0184855	+	0.0320178i
$470$	0.979055	+	0.356347i	0.0451605	+	0.0164371i
$471$		0			0
$472$	1.14156	+	0.957882i	0.0525445	+	0.0440901i
$473$	−1.29086	−	1.08316i	−0.0593538	−	0.0498037i
$474$		0			0
$475$	−17.7208	−	6.44983i	−0.813084	−	0.295938i
$476$	0.311804	−	0.540060i	0.0142915	−	0.0247536i
$477$		0			0
$478$	−11.4572	−	19.8445i	−0.524042	−	0.907667i
$479$	1.97131	+	11.1799i	0.0900717	+	0.510822i	0.996147	+	0.0877044i	$0.0279531\pi$
$479$	1.97131	+	11.1799i	0.0900717	+	0.510822i	−0.906075	+	0.423117i	$0.860936\pi$
$480$		0			0
$481$	1.65745	−	0.603263i	0.0755733	−	0.0275064i
$482$	−2.09714	+	11.8935i	−0.0955223	+	0.541734i
$483$		0			0
$484$	2.15657	−	1.80958i	0.0980261	−	0.0822537i
$485$	4.61587			0.209596
$486$		0			0
$487$	1.13785			0.0515610			0.0257805	−	0.999668i	$-0.491793\pi$
$487$	1.13785			0.0515610			0.0257805	+	0.999668i	$0.491793\pi$
$488$	−2.89646	+	2.43042i	−0.131117	+	0.110020i
$489$		0			0
$490$	1.63429	−	9.26849i	0.0738295	−	0.418708i
$491$	−14.3880	+	5.23680i	−0.649322	+	0.236334i	−0.645619	−	0.763659i	$-0.723401\pi$
$491$	−14.3880	+	5.23680i	−0.649322	+	0.236334i	−0.00370223	+	0.999993i	$0.501178\pi$
$492$		0			0
$493$	−5.33615	−	30.2628i	−0.240328	−	1.36297i
$494$	−17.9538	−	31.0969i	−0.807781	−	1.39912i
$495$		0			0
$496$	2.52094	−	4.36640i	0.113194	−	0.196057i
$497$	−0.651055	−	0.236965i	−0.0292038	−	0.0106293i
$498$		0			0
$499$	1.77584	+	1.49011i	0.0794977	+	0.0667065i	0.681671	−	0.731659i	$-0.261254\pi$
$499$	1.77584	+	1.49011i	0.0794977	+	0.0667065i	−0.602173	+	0.798366i	$0.705698\pi$
$500$	8.44743	+	7.08824i	0.377781	+	0.316996i
$501$		0			0
$502$	−13.1998	−	4.80434i	−0.589136	−	0.214428i
$503$	4.02869	−	6.97789i	0.179630	−	0.311129i	−0.762124	−	0.647431i	$-0.775843\pi$
$503$	4.02869	−	6.97789i	0.179630	−	0.311129i	0.941754	+	0.336303i	$0.109177\pi$
$504$		0			0
$505$	−5.80587	−	10.0561i	−0.258358	−	0.447489i
$506$	−3.07145	−	17.4191i	−0.136543	−	0.774372i
$507$		0			0
$508$	5.39306	−	1.96291i	0.239278	−	0.0870901i
$509$	−1.24944	+	7.08591i	−0.0553803	+	0.314077i	−0.999896	−	0.0143875i	$-0.995420\pi$
$509$	−1.24944	+	7.08591i	−0.0553803	+	0.314077i	0.944516	+	0.328465i	$0.106531\pi$
$510$		0			0
$511$	−0.962697	+	0.807798i	−0.0425872	+	0.0357349i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−18.1429			−0.800249
$515$	2.25490	−	1.89209i	0.0993628	−	0.0833753i
$516$		0			0
$517$	−0.499123	+	2.83067i	−0.0219514	+	0.124493i
$518$	0.0329662	−	0.0119987i	0.00144845	−	0.000527194i
$519$		0			0
$520$	1.41875	+	8.04612i	0.0622162	+	0.352846i
$521$	4.84343	+	8.38906i	0.212194	+	0.367531i	0.952401	−	0.304848i	$-0.0986057\pi$
$521$	4.84343	+	8.38906i	0.212194	+	0.367531i	−0.740207	+	0.672379i	$0.765272\pi$
$522$		0			0
$523$	−7.29339	+	12.6325i	−0.318917	+	0.552381i	−0.980262	−	0.197701i	$-0.936653\pi$
$523$	−7.29339	+	12.6325i	−0.318917	+	0.552381i	0.661345	+	0.750082i	$0.269986\pi$
$524$	16.1814	+	5.88954i	0.706887	+	0.257286i
$525$		0			0
$526$	−3.27379	−	2.74703i	−0.142744	−	0.119776i
$527$	−19.9691	−	16.7561i	−0.869867	−	0.729905i
$528$		0			0
$529$	0.332748	+	0.121111i	0.0144673	+	0.00526568i
$530$	4.91147	−	8.50692i	0.213341	−	0.369517i
$531$		0			0
$532$	−0.357097	−	0.618509i	−0.0154821	−	0.0268158i
$533$	6.10829	+	34.6418i	0.264579	+	1.50050i
$534$		0			0
$535$	13.0287	−	4.74205i	0.563279	−	0.205017i
$536$	−1.15270	+	6.53731i	−0.0497892	+	0.282369i
$537$		0			0
$538$	−10.0057	+	8.39576i	−0.431376	+	0.361967i
$539$	25.9641			1.11835
$540$		0			0
$541$	23.9786			1.03092			0.515461	−	0.856913i	$-0.327621\pi$
$541$	23.9786			1.03092			0.515461	+	0.856913i	$0.327621\pi$
$542$	6.50181	−	5.45567i	0.279277	−	0.234341i
$543$		0			0
$544$	0.897804	−	5.09170i	0.0384930	−	0.218305i
$545$	−14.0424	+	5.11100i	−0.601508	+	0.218931i
$546$		0			0
$547$	6.94269	+	39.3739i	0.296848	+	1.68351i	0.659596	+	0.751620i	$0.270727\pi$
$547$	6.94269	+	39.3739i	0.296848	+	1.68351i	−0.362748	+	0.931887i	$0.618161\pi$
$548$	0.0432332	+	0.0748822i	0.00184683	+	0.00319881i
$549$		0			0
$550$	−5.91875	+	10.2516i	−0.252376	+	0.437129i
$551$	−33.0710	−	12.0369i	−1.40887	−	0.512788i
$552$		0			0
$553$	−1.29292	−	1.08489i	−0.0549805	−	0.0461341i
$554$	5.06624	+	4.25108i	0.215244	+	0.180611i
$555$		0			0
$556$	17.2554	+	6.28044i	0.731791	+	0.266350i
$557$	1.17958	−	2.04309i	0.0499803	−	0.0865685i	−0.839953	−	0.542659i	$-0.817417\pi$
$557$	1.17958	−	2.04309i	0.0499803	−	0.0865685i	0.889933	+	0.456091i	$0.150751\pi$
$558$		0			0
$559$	1.37464	+	2.38094i	0.0581410	+	0.100703i
$560$	0.0282185	+	0.160035i	0.00119245	+	0.00676271i
$561$		0			0
$562$	27.9320	−	10.1664i	1.17824	−	0.428845i
$563$	7.55825	−	42.8650i	0.318542	−	1.80654i	−0.233090	−	0.972455i	$-0.574884\pi$
$563$	7.55825	−	42.8650i	0.318542	−	1.80654i	0.551632	−	0.834087i	$-0.314005\pi$
$564$		0			0
$565$	6.11406	−	5.13030i	0.257220	−	0.215833i
$566$	−2.81521			−0.118332
$567$		0			0
$568$	−5.74422			−0.241022
$569$	−11.2187	+	9.41360i	−0.470312	+	0.394639i	−0.846908	−	0.531739i	$-0.821539\pi$
$569$	−11.2187	+	9.41360i	−0.470312	+	0.394639i	0.376596	+	0.926377i	$0.377094\pi$
$570$		0			0
$571$	−2.57145	+	14.5834i	−0.107612	+	0.610297i	0.882533	+	0.470251i	$0.155836\pi$
$571$	−2.57145	+	14.5834i	−0.107612	+	0.610297i	−0.990145	+	0.140047i	$0.955275\pi$
$572$	−21.1805	+	7.70908i	−0.885602	+	0.322333i
$573$		0			0
$574$	0.121492	+	0.689016i	0.00507098	+	0.0287590i
$575$	7.57785	+	13.1252i	0.316018	+	0.547359i
$576$		0			0
$577$	16.0706	−	27.8351i	0.669027	−	1.15879i	−0.309150	−	0.951013i	$-0.600044\pi$
$577$	16.0706	−	27.8351i	0.669027	−	1.15879i	0.978177	−	0.207775i	$-0.0666222\pi$
$578$	−9.14455	−	3.32834i	−0.380363	−	0.138441i
$579$		0			0
$580$	6.13429	+	5.14728i	0.254712	+	0.213729i
$581$	−0.218941	−	0.183713i	−0.00908320	−	0.00762171i
$582$		0			0
$583$	25.4650	+	9.26849i	1.05465	+	0.383862i
$584$	−5.20961	+	9.02330i	−0.215575	+	0.373387i
$585$		0			0
$586$	4.91787	+	8.51800i	0.203155	+	0.351875i
$587$	−4.75918	−	26.9907i	−0.196432	−	1.11402i	−0.910364	−	0.413808i	$-0.864198\pi$
$587$	−4.75918	−	26.9907i	−0.196432	−	1.11402i	0.713932	−	0.700215i	$-0.246913\pi$
$588$		0			0
$589$	−28.0540	+	10.2108i	−1.15594	+	0.420729i
$590$	−0.348641	+	1.97724i	−0.0143533	+	0.0814016i
$591$		0			0
$592$	0.222811	−	0.186961i	0.00915748	−	0.00768404i
$593$	−36.2377			−1.48810			−0.744052	−	0.668121i	$-0.767099\pi$
$593$	−36.2377			−1.48810			−0.744052	+	0.668121i	$0.767099\pi$
$594$		0			0
$595$	0.840185			0.0344442
$596$	3.75490	−	3.15074i	0.153807	−	0.129059i
$597$		0			0
$598$	−5.01114	+	28.4196i	−0.204921	+	1.16216i
$599$	43.2438	−	15.7395i	1.76689	−	0.643097i	0.766895	−	0.641772i	$-0.221801\pi$
$599$	43.2438	−	15.7395i	1.76689	−	0.643097i	0.999999	−	0.00132449i	$-0.000421598\pi$
$600$		0			0
$601$	0.294673	+	1.67118i	0.0120200	+	0.0681687i	0.990228	−	0.139460i	$-0.0445366\pi$
$601$	0.294673	+	1.67118i	0.0120200	+	0.0681687i	−0.978208	+	0.207628i	$0.933425\pi$
$602$	0.0273411	+	0.0473563i	0.00111434	+	0.00193010i
$603$		0			0
$604$	−0.865715	+	1.49946i	−0.0352254	+	0.0610122i
$605$	3.56418	+	1.29725i	0.144904	+	0.0527409i
$606$		0			0
$607$	−10.7779	−	9.04374i	−0.437462	−	0.367074i	0.397297	−	0.917690i	$-0.369948\pi$
$607$	−10.7779	−	9.04374i	−0.437462	−	0.367074i	−0.834758	+	0.550616i	$0.814393\pi$
$608$	−4.53596	−	3.80612i	−0.183957	−	0.154359i
$609$		0			0
$610$	−4.78699	−	1.74232i	−0.193820	−	0.0705445i
$611$	2.34477	−	4.06126i	0.0948592	−	0.164301i
$612$		0			0
$613$	12.8314	+	22.2246i	0.518256	+	0.897645i	0.999775	+	0.0212096i	$0.00675172\pi$
$613$	12.8314	+	22.2246i	0.518256	+	0.897645i	−0.481520	+	0.876435i	$0.659915\pi$
$614$	2.35504	+	13.3561i	0.0950416	+	0.539007i
$615$		0			0
$616$	−0.421274	+	0.153331i	−0.0169736	+	0.00617789i
$617$	−5.46822	+	31.0118i	−0.220142	+	1.24849i	0.651615	+	0.758550i	$0.274092\pi$
$617$	−5.46822	+	31.0118i	−0.220142	+	1.24849i	−0.871757	+	0.489938i	$0.837019\pi$
$618$		0			0
$619$	−2.42674	+	2.03627i	−0.0975388	+	0.0818448i	−0.690253	−	0.723568i	$-0.742501\pi$
$619$	−2.42674	+	2.03627i	−0.0975388	+	0.0818448i	0.592714	+	0.805413i	$0.298056\pi$
$620$	6.79292			0.272810
$621$		0			0
$622$	10.5767			0.424086
$623$	−0.200522	+	0.168258i	−0.00803376	+	0.00674113i
$624$		0			0
$625$	0.185259	−	1.05066i	0.00741037	−	0.0420263i
$626$	10.0544	−	3.65949i	0.401854	−	0.146263i
$627$		0			0
$628$	−1.00980	−	5.72686i	−0.0402954	−	0.228527i
$629$	−0.751907	−	1.30234i	−0.0299805	−	0.0519277i
$630$		0			0
$631$	−11.2961	+	19.5654i	−0.449690	+	0.778885i	−0.998366	−	0.0571498i	$-0.981799\pi$
$631$	−11.2961	+	19.5654i	−0.449690	+	0.778885i	0.548676	+	0.836035i	$0.315132\pi$
$632$	−13.1493	−	4.78595i	−0.523051	−	0.190375i
$633$		0			0
$634$	−22.3537	−	18.7570i	−0.887779	−	0.744935i
$635$	5.92333	+	4.97027i	0.235060	+	0.197239i
$636$		0			0
$637$	−39.8063	−	14.4883i	−1.57718	−	0.574048i
$638$	−11.0458	+	19.1318i	−0.437306	+	0.757436i
$639$		0			0
$640$	0.673648	+	1.16679i	0.0266283	+	0.0461215i
$641$	3.04323	+	17.2590i	0.120200	+	0.681691i	0.984043	+	0.177929i	$0.0569398\pi$
$641$	3.04323	+	17.2590i	0.120200	+	0.681691i	−0.863843	+	0.503761i	$0.831949\pi$
$642$		0			0
$643$	26.4923	−	9.64241i	1.04475	−	0.380260i	0.238074	−	0.971247i	$-0.423484\pi$
$643$	26.4923	−	9.64241i	1.04475	−	0.380260i	0.806681	+	0.590987i	$0.201262\pi$
$644$	−0.0996702	+	0.565258i	−0.00392756	+	0.0222743i
$645$		0			0
$646$	−23.4520	+	19.6786i	−0.922707	+	0.774243i
$647$	−32.3492			−1.27178			−0.635888	−	0.771781i	$-0.719366\pi$
$647$	−32.3492			−1.27178			−0.635888	+	0.771781i	$0.719366\pi$
$648$		0			0
$649$	−5.53890			−0.217421
$650$	14.7947	−	12.4143i	0.580297	−	0.486927i
$651$		0			0
$652$	−0.470437	+	2.66798i	−0.0184237	+	0.104486i
$653$	−25.9329	+	9.43880i	−1.01483	+	0.369369i	−0.795287	−	0.606234i	$-0.792680\pi$
$653$	−25.9329	+	9.43880i	−1.01483	+	0.369369i	−0.219546	+	0.975602i	$0.570457\pi$
$654$		0			0
$655$	4.02869	+	22.8478i	0.157414	+	0.892738i
$656$	2.90033	+	5.02352i	0.113239	+	0.196135i
$657$		0			0
$658$	0.0466368	−	0.0807773i	0.00181809	−	0.00314903i
$659$	−4.90508	−	1.78530i	−0.191075	−	0.0695455i	0.244711	−	0.969596i	$-0.421307\pi$
$659$	−4.90508	−	1.78530i	−0.191075	−	0.0695455i	−0.435785	+	0.900051i	$0.643529\pi$
$660$		0			0
$661$	−36.7294	−	30.8196i	−1.42861	−	1.19875i	−0.946529	−	0.322618i	$-0.895437\pi$
$661$	−36.7294	−	30.8196i	−1.42861	−	1.19875i	−0.482080	−	0.876127i	$-0.660119\pi$
$662$	−5.59105	−	4.69145i	−0.217302	−	0.182338i
$663$		0			0
$664$	−2.22668	−	0.810446i	−0.0864120	−	0.0314514i
$665$	0.481115	−	0.833315i	0.0186568	−	0.0323146i
$666$		0			0
$667$	14.1420	+	24.4947i	0.547581	+	0.948439i
$668$	4.27244	+	24.2302i	0.165306	+	0.937495i
$669$		0			0
$670$	−8.40420	+	3.05888i	−0.324683	+	0.118175i
$671$	2.44041	−	13.8402i	0.0942109	−	0.534297i
$672$		0			0
$673$	−8.51960	+	7.14879i	−0.328406	+	0.275566i	−0.792050	−	0.610456i	$-0.790986\pi$
$673$	−8.51960	+	7.14879i	−0.328406	+	0.275566i	0.463644	+	0.886022i	$0.346542\pi$
$674$	−1.62361			−0.0625390
$675$		0			0
$676$	23.7743			0.914394
$677$	36.9550	−	31.0089i	1.42030	−	1.19177i	0.469115	−	0.883137i	$-0.344573\pi$
$677$	36.9550	−	31.0089i	1.42030	−	1.19177i	0.951181	−	0.308633i	$-0.0998716\pi$
$678$		0			0
$679$	0.0717564	−	0.406951i	0.00275376	−	0.0156173i
$680$	6.54576	−	2.38246i	0.251018	−	0.0913632i
$681$		0			0
$682$	3.25418	+	18.4554i	0.124609	+	0.706694i
$683$	6.60401	+	11.4385i	0.252695	+	0.437681i	0.964267	−	0.264932i	$-0.0853496\pi$
$683$	6.60401	+	11.4385i	0.252695	+	0.437681i	−0.711572	+	0.702614i	$0.752016\pi$
$684$		0			0
$685$	−0.0582480	+	0.100888i	−0.00222554	+	0.00385475i
$686$	−1.58512	−	0.576937i	−0.0605203	−	0.0220276i
$687$		0			0
$688$	0.347296	+	0.291416i	0.0132405	+	0.0111101i
$689$	−33.8692	−	28.4196i	−1.29031	−	1.08270i
$690$		0			0
$691$	9.37211	+	3.41117i	0.356532	+	0.129767i	0.514075	−	0.857745i	$-0.328135\pi$
$691$	9.37211	+	3.41117i	0.356532	+	0.129767i	−0.157543	+	0.987512i	$0.550357\pi$
$692$	−5.36097	+	9.28547i	−0.203793	+	0.352980i
$693$		0			0
$694$	−2.73442	−	4.73616i	−0.103797	−	0.179782i
$695$	4.29607	+	24.3642i	0.162959	+	0.924189i
$696$		0			0
$697$	28.1822	−	10.2575i	1.06748	−	0.388529i
$698$	0.538019	−	3.05126i	0.0203643	−	0.115492i
$699$		0			0
$700$	0.294263	−	0.246916i	0.0111221	−	0.00933254i
$701$	−46.7588			−1.76605			−0.883027	−	0.469322i	$-0.844498\pi$
$701$	−46.7588			−1.76605			−0.883027	+	0.469322i	$0.844498\pi$
$702$		0			0
$703$	−1.72226			−0.0649562
$704$	−2.84730	+	2.38917i	−0.107312	+	0.0900451i
$705$		0			0
$706$	−0.0530334	+	0.300767i	−0.00199594	+	0.0113195i
$707$	−0.976834	+	0.355538i	−0.0367376	+	0.0133714i
$708$		0			0
$709$	−6.56907	−	37.2550i	−0.246707	−	1.39914i	−0.816496	−	0.577351i	$-0.804086\pi$
$709$	−6.56907	−	37.2550i	−0.246707	−	1.39914i	0.569789	−	0.821791i	$-0.307025\pi$
$710$	−3.86959	−	6.70232i	−0.145223	−	0.251534i
$711$		0			0
$712$	−1.08512	+	1.87949i	−0.0406667	+	0.0704368i
$713$	22.5462	+	8.20616i	0.844363	+	0.307323i
$714$		0			0
$715$	−23.2631	−	19.5201i	−0.869991	−	0.730009i
$716$	10.6061	+	8.89955i	0.396367	+	0.332592i
$717$		0			0
$718$	9.93242	+	3.61510i	0.370675	+	0.134915i
$719$	1.65048	−	2.85872i	0.0615526	−	0.106612i	−0.833607	−	0.552358i	$-0.813728\pi$
$719$	1.65048	−	2.85872i	0.0615526	−	0.106612i	0.895160	+	0.445746i	$0.147061\pi$
$720$		0			0
$721$	−0.131759	−	0.228213i	−0.00490697	−	0.00849911i
$722$	2.78905	+	15.8175i	0.103798	+	0.588666i
$723$		0			0
$724$	−3.29813	+	1.20042i	−0.122574	+	0.0446133i
$725$	3.28699	−	18.6414i	0.122076	−	0.692326i
$726$		0			0
$727$	−16.0548	+	13.4716i	−0.595441	+	0.499635i	−0.889977	−	0.456006i	$-0.849280\pi$
$727$	−16.0548	+	13.4716i	−0.595441	+	0.499635i	0.294535	+	0.955641i	$0.404835\pi$
$728$	0.731429			0.0271086
$729$		0			0
$730$	−14.0378			−0.519561
$731$	1.79561	−	1.50669i	0.0664129	−	0.0557271i
$732$		0			0
$733$	−3.11943	+	17.6912i	−0.115219	+	0.653439i	0.871423	+	0.490533i	$0.163198\pi$
$733$	−3.11943	+	17.6912i	−0.115219	+	0.653439i	−0.986642	+	0.162906i	$0.947913\pi$
$734$	−2.51842	+	0.916629i	−0.0929565	+	0.0338334i
$735$		0			0
$736$	0.826352	+	4.68647i	0.0304597	+	0.172746i
$737$	−12.3366	−	21.3677i	−0.454425	−	0.787088i
$738$		0			0
$739$	19.6630	−	34.0573i	0.723314	−	1.25282i	−0.236350	−	0.971668i	$-0.575951\pi$
$739$	19.6630	−	34.0573i	0.723314	−	1.25282i	0.959664	−	0.281149i	$-0.0907154\pi$
$740$	0.368241	+	0.134029i	0.0135368	+	0.00492699i
$741$		0			0
$742$	−0.673648	−	0.565258i	−0.0247304	−	0.0207513i
$743$	35.7957	+	30.0361i	1.31322	+	1.10192i	0.987696	+	0.156383i	$0.0499835\pi$
$743$	35.7957	+	30.0361i	1.31322	+	1.10192i	0.325519	+	0.945535i	$0.394461\pi$
$744$		0			0
$745$	6.20574	+	2.25870i	0.227361	+	0.0827525i
$746$	−12.1853	+	21.1055i	−0.446134	+	0.772727i
$747$		0			0
$748$	9.60859	+	16.6426i	0.351325	+	0.608513i
$749$	−0.215537	−	1.22237i	−0.00787556	−	0.0446645i
$750$		0			0
$751$	31.3184	−	11.3990i	1.14282	−	0.415954i	0.299891	−	0.953973i	$-0.403050\pi$
$751$	31.3184	−	11.3990i	1.14282	−	0.415954i	0.842932	+	0.538020i	$0.180827\pi$
$752$	0.134285	−	0.761570i	0.00489688	−	0.0277716i
$753$		0			0
$754$	27.6104	−	23.1679i	1.00551	−	0.843724i
$755$	−2.33275			−0.0848974
$756$		0			0
$757$	32.3354			1.17525			0.587626	−	0.809133i	$-0.300063\pi$
$757$	32.3354			1.17525			0.587626	+	0.809133i	$0.300063\pi$
$758$	−3.13041	+	2.62673i	−0.113702	+	0.0954071i
$759$		0			0
$760$	1.38532	−	7.85651i	0.0502507	−	0.284986i
$761$	1.81521	−	0.660681i	0.0658012	−	0.0239497i	−0.308910	−	0.951091i	$-0.599964\pi$
$761$	1.81521	−	0.660681i	0.0658012	−	0.0239497i	0.374711	+	0.927142i	$0.377742\pi$
$762$		0			0
$763$	0.232307	+	1.31748i	0.00841007	+	0.0476959i
$764$	−10.9461	−	18.9592i	−0.396016	−	0.685919i
$765$		0			0
$766$	−8.19506	+	14.1943i	−0.296100	+	0.512859i
$767$	8.49185	+	3.09078i	0.306623	+	0.111602i
$768$		0			0
$769$	−3.66179	−	3.07261i	−0.132047	−	0.110801i	0.574372	−	0.818594i	$-0.305246\pi$
$769$	−3.66179	−	3.07261i	−0.132047	−	0.110801i	−0.706419	+	0.707793i	$0.749691\pi$
$770$	−0.462697	−	0.388249i	−0.0166744	−	0.0139915i
$771$		0			0
$772$	−24.0672	−	8.75973i	−0.866196	−	0.315270i
$773$	−2.95336	+	5.11538i	−0.106225	+	0.183987i	−0.914238	−	0.405177i	$-0.867210\pi$
$773$	−2.95336	+	5.11538i	−0.106225	+	0.183987i	0.808013	+	0.589165i	$0.200543\pi$
$774$		0			0
$775$	−8.02869	−	13.9061i	−0.288399	−	0.499522i
$776$	−0.594922	−	3.37397i	−0.0213565	−	0.121119i
$777$		0			0
$778$	−26.2263	+	9.54558i	−0.940257	+	0.342226i
$779$	5.96435	−	33.8255i	0.213695	−	1.21192i
$780$		0			0
$781$	16.3555	−	13.7239i	0.585246	−	0.491080i
$782$	24.6040			0.879838
$783$		0			0
$784$	−6.98545			−0.249480
$785$	6.00181	−	5.03612i	0.214214	−	0.179747i
$786$		0			0
$787$	2.29220	−	12.9997i	0.0817082	−	0.463390i	−0.916310	−	0.400469i	$-0.868847\pi$
$787$	2.29220	−	12.9997i	0.0817082	−	0.463390i	0.998018	−	0.0629213i	$-0.0200417\pi$
$788$	12.8598	−	4.68058i	0.458111	−	0.166739i
$789$		0			0
$790$	−3.27379	−	18.5666i	−0.116476	−	0.660569i
$791$	−0.357259	−	0.618790i	−0.0127027	−	0.0220016i
$792$		0			0
$793$	−11.4645	+	19.8571i	−0.407117	+	0.705147i
$794$	30.5342	+	11.1135i	1.08362	+	0.394405i
$795$		0			0
$796$	−9.49866	−	7.97032i	−0.336671	−	0.282500i
$797$	−6.86959	−	5.76427i	−0.243333	−	0.204181i	0.512962	−	0.858411i	$-0.328548\pi$
$797$	−6.86959	−	5.76427i	−0.243333	−	0.204181i	−0.756295	+	0.654231i	$0.772993\pi$
$798$		0			0
$799$	−3.75712	−	1.36748i	−0.132917	−	0.0483780i
$800$	1.59240	−	2.75811i	0.0562997	−	0.0975140i
$801$		0			0
$802$	7.69072	+	13.3207i	0.271569	+	0.470371i
$803$	−6.72487	−	38.1386i	−0.237316	−	1.34588i
$804$		0			0
$805$	−0.726682	+	0.264490i	−0.0256122	+	0.00932206i
$806$	5.30928	−	30.1104i	0.187011	−	1.06059i
$807$		0			0
$808$	−6.60220	+	5.53990i	−0.232264	+	0.194893i
$809$	−14.9804			−0.526683			−0.263341	−	0.964703i	$-0.584825\pi$
$809$	−14.9804			−0.526683			−0.263341	+	0.964703i	$0.584825\pi$
$810$		0			0
$811$	41.7529			1.46614			0.733071	−	0.680152i	$-0.238086\pi$
$811$	41.7529			1.46614			0.733071	+	0.680152i	$0.238086\pi$
$812$	0.549163	−	0.460802i	0.0192718	−	0.0161710i
$813$		0			0
$814$	−0.187729	+	1.06467i	−0.00657991	+	0.0373165i
$815$	−3.42989	+	1.24838i	−0.120144	+	0.0437288i
$816$		0			0
$817$	−0.466156	−	2.64370i	−0.0163087	−	0.0924915i
$818$	4.77466	+	8.26996i	0.166942	+	0.289152i
$819$		0			0
$820$	−3.90760	+	6.76817i	−0.136459	+	0.236355i
$821$	7.34730	+	2.67420i	0.256422	+	0.0933301i	0.467033	−	0.884240i	$-0.345323\pi$
$821$	7.34730	+	2.67420i	0.256422	+	0.0933301i	−0.210611	+	0.977570i	$0.567545\pi$
$822$		0			0
$823$	−10.4645	−	8.78076i	−0.364770	−	0.306078i	0.441919	−	0.897055i	$-0.354298\pi$
$823$	−10.4645	−	8.78076i	−0.364770	−	0.306078i	−0.806688	+	0.590977i	$0.798742\pi$
$824$	−1.67365	−	1.40436i	−0.0583043	−	0.0489231i
$825$		0			0
$826$	0.168900	+	0.0614747i	0.00587680	+	0.00213898i
$827$	−10.0679	+	17.4381i	−0.350095	+	0.606382i	−0.986266	−	0.165166i	$-0.947184\pi$
$827$	−10.0679	+	17.4381i	−0.350095	+	0.606382i	0.636171	+	0.771548i	$0.280517\pi$
$828$		0			0
$829$	−20.9491	−	36.2849i	−0.727592	−	1.26023i	−0.957898	−	0.287108i	$-0.907306\pi$
$829$	−20.9491	−	36.2849i	−0.727592	−	1.26023i	0.230307	−	0.973118i	$-0.426027\pi$
$830$	−0.554378	−	3.14403i	−0.0192427	−	0.109131i
$831$		0			0
$832$	5.69846	−	2.07407i	0.197559	−	0.0719055i
$833$	−6.27156	+	35.5678i	−0.217297	+	1.23235i
$834$		0			0
$835$	−25.3935	+	21.3077i	−0.878779	+	0.737383i
$836$	22.0087			0.761186
$837$		0			0
$838$	33.9718			1.17354
$839$	30.0480	−	25.2133i	1.03737	−	0.870460i	0.0456636	−	0.998957i	$-0.485460\pi$
$839$	30.0480	−	25.2133i	1.03737	−	0.870460i	0.991710	+	0.128497i	$0.0410153\pi$
$840$		0			0
$841$	1.09849	−	6.22984i	0.0378789	−	0.214822i
$842$	11.8229	−	4.30320i	0.407446	−	0.148298i
$843$		0			0
$844$	2.57738	+	14.6171i	0.0887171	+	0.503140i
$845$	16.0155	+	27.7396i	0.550949	+	0.954272i
$846$		0			0
$847$	0.169778	−	0.294064i	0.00583363	−	0.0101041i
$848$	−6.85117	−	2.49362i	−0.235270	−	0.0856313i
$849$		0			0
$850$	−12.6138	−	10.5842i	−0.432650	−	0.363036i
$851$	1.06031	+	0.889704i	0.0363469	+	0.0304986i
$852$		0			0
$853$	6.12536	+	2.22945i	0.209728	+	0.0763349i	0.444748	−	0.895656i	$-0.353293\pi$
$853$	6.12536	+	2.22945i	0.209728	+	0.0763349i	−0.235020	+	0.971991i	$0.575515\pi$
$854$	−0.228026	+	0.394952i	−0.00780288	+	0.0135150i
$855$		0			0
$856$	−5.14543	−	8.91215i	−0.175867	−	0.304611i
$857$	3.23514	+	18.3474i	0.110510	+	0.626734i	0.988876	+	0.148745i	$0.0475233\pi$
$857$	3.23514	+	18.3474i	0.110510	+	0.626734i	−0.878365	+	0.477990i	$0.841366\pi$
$858$		0			0
$859$	52.2033	−	19.0004i	1.78115	−	0.648286i	0.781448	−	0.623970i	$-0.214481\pi$
$859$	52.2033	−	19.0004i	1.78115	−	0.648286i	0.999704	−	0.0243163i	$-0.00774089\pi$
$860$	−0.106067	+	0.601535i	−0.00361685	+	0.0205122i
$861$		0			0
$862$	5.95677	−	4.99832i	0.202888	−	0.170243i
$863$	36.1625			1.23099			0.615493	−	0.788142i	$-0.288957\pi$
$863$	36.1625			1.23099			0.615493	+	0.788142i	$0.288957\pi$
$864$		0			0
$865$	−14.4456			−0.491166
$866$	−31.1425	+	26.1317i	−1.05826	+	0.887990i
$867$		0			0
$868$	0.105600	−	0.598887i	0.00358430	−	0.0203276i
$869$	48.8744	−	17.7888i	1.65795	−	0.603444i
$870$		0			0
$871$	6.99020	+	39.6434i	0.236854	+	1.34327i
$872$	5.54576	+	9.60554i	0.187803	+	0.325285i
$873$		0			0
$874$	14.0890	−	24.4029i	0.476567	−	0.825439i
$875$	1.24985	+	0.454907i	0.0422526	+	0.0153787i
$876$		0			0
$877$	−14.8719	−	12.4790i	−0.502187	−	0.421385i	0.356183	−	0.934416i	$-0.384078\pi$
$877$	−14.8719	−	12.4790i	−0.502187	−	0.421385i	−0.858370	+	0.513031i	$0.828522\pi$
$878$	−13.5556	−	11.3745i	−0.457478	−	0.383870i
$879$		0			0
$880$	−4.70574	−	1.71275i	−0.158630	−	0.0577367i
$881$	22.9957	−	39.8298i	0.774745	−	1.34190i	−0.160192	−	0.987086i	$-0.551211\pi$
$881$	22.9957	−	39.8298i	0.774745	−	1.34190i	0.934937	−	0.354813i	$-0.115455\pi$
$882$		0			0
$883$	−11.9081	−	20.6254i	−0.400738	−	0.694099i	0.593077	−	0.805146i	$-0.297913\pi$
$883$	−11.9081	−	20.6254i	−0.400738	−	0.694099i	−0.993815	+	0.111047i	$0.964580\pi$
$884$	−5.44444	−	30.8770i	−0.183116	−	1.03850i
$885$		0			0
$886$	13.5086	−	4.91673i	0.453831	−	0.165181i
$887$	−4.57785	+	25.9623i	−0.153709	+	0.871728i	0.806247	+	0.591579i	$0.201495\pi$
$887$	−4.57785	+	25.9623i	−0.153709	+	0.871728i	−0.959956	+	0.280149i	$0.909616\pi$
$888$		0			0
$889$	0.530278	−	0.444956i	0.0177849	−	0.0149233i
$890$	−2.92396			−0.0980115
$891$		0			0
$892$	−6.73143			−0.225385
$893$	−3.50774	+	2.94334i	−0.117382	+	0.0984953i
$894$		0			0
$895$	−3.23917	+	18.3702i	−0.108274	+	0.614050i
$896$	0.113341	−	0.0412527i	0.00378645	−	0.00137816i
$897$		0			0
$898$	−4.85726	−	27.5469i	−0.162089	−	0.919251i
$899$	−14.9834	−	25.9520i	−0.499724	−	0.865548i
$900$		0			0
$901$	−18.8478	+	32.6453i	−0.627910	+	1.08757i
$902$	−20.2601	−	7.37408i	−0.674588	−	0.245530i
$903$		0			0
$904$	−4.53802	−	3.80785i	−0.150932	−	0.126647i
$905$	−3.62243	−	3.03958i	−0.120414	−	0.101039i
$906$		0			0
$907$	1.99660	+	0.726702i	0.0662959	+	0.0241297i	0.374955	−	0.927043i	$-0.377658\pi$
$907$	1.99660	+	0.726702i	0.0662959	+	0.0241297i	−0.308659	+	0.951173i	$0.599880\pi$
$908$	7.24763	−	12.5533i	0.240521	−	0.416594i
$909$		0			0
$910$	0.492726	+	0.853427i	0.0163337	+	0.0282908i
$911$	8.70661	+	49.3777i	0.288463	+	1.63595i	0.692647	+	0.721277i	$0.256445\pi$
$911$	8.70661	+	49.3777i	0.288463	+	1.63595i	−0.404184	+	0.914678i	$0.632444\pi$
$912$		0			0
$913$	8.27631	−	3.01233i	0.273906	−	0.0996936i
$914$	1.48087	−	8.39841i	0.0489827	−	0.277795i
$915$		0			0
$916$	19.7540	−	16.5756i	0.652691	−	0.547673i
$917$	2.07697			0.0685876
$918$		0			0
$919$	−56.9469			−1.87850			−0.939252	−	0.343229i	$-0.888479\pi$
$919$	−56.9469			−1.87850			−0.939252	+	0.343229i	$0.888479\pi$
$920$	−4.91147	+	4.12122i	−0.161927	+	0.135872i
$921$		0			0
$922$	−3.77110	+	21.3870i	−0.124194	+	0.704342i
$923$	−32.7332	+	11.9139i	−1.07743	+	0.392152i
$924$		0			0
$925$	−0.160855	−	0.912254i	−0.00528888	−	0.0299947i
$926$	9.90167	+	17.1502i	0.325389	+	0.563591i
$927$		0			0
$928$	2.97178	−	5.14728i	0.0975535	−	0.168968i
$929$	0.236177	+	0.0859614i	0.00774872	+	0.00282030i	0.345892	−	0.938274i	$-0.387576\pi$
$929$	0.236177	+	0.0859614i	0.00774872	+	0.00282030i	−0.338143	+	0.941095i	$0.609799\pi$
$930$		0			0
$931$	31.6857	+	26.5875i	1.03846	+	0.871370i
$932$	−7.96451	−	6.68302i	−0.260886	−	0.218909i
$933$		0			0
$934$	34.7550	+	12.6498i	1.13722	+	0.413913i
$935$	−12.9456	+	22.4225i	−0.423367	+	0.733293i
$936$		0			0
$937$	18.4662	+	31.9843i	0.603263	+	1.04488i	0.992323	+	0.123670i	$0.0394664\pi$
$937$	18.4662	+	31.9843i	0.603263	+	1.04488i	−0.389060	+	0.921212i	$0.627200\pi$
$938$	0.139033	+	0.788496i	0.00453959	+	0.0257453i
$939$		0			0
$940$	0.979055	−	0.356347i	0.0319333	−	0.0116228i
$941$	−7.50118	+	42.5413i	−0.244532	+	1.38681i	0.577047	+	0.816711i	$0.304205\pi$
$941$	−7.50118	+	42.5413i	−0.244532	+	1.38681i	−0.821578	+	0.570096i	$0.806906\pi$
$942$		0			0
$943$	−21.1459	+	17.7435i	−0.688605	+	0.577808i
$944$	1.49020			0.0485019
$945$		0			0
$946$	−1.68510			−0.0547872
$947$	−36.3562	+	30.5065i	−1.18142	+	0.991328i	−0.181450	+	0.983400i	$0.558079\pi$
$947$	−36.3562	+	30.5065i	−1.18142	+	0.991328i	−0.999969	+	0.00792752i	$0.997477\pi$
$948$		0			0
$949$	−10.9718	+	62.2241i	−0.356159	+	2.01988i
$950$	−17.7208	+	6.44983i	−0.574937	+	0.209260i
$951$		0			0
$952$	−0.108288	−	0.614134i	−0.00350965	−	0.0199042i
$953$	−22.6575	−	39.2440i	−0.733949	−	1.27124i	−0.955183	−	0.296016i	$-0.904342\pi$
$953$	−22.6575	−	39.2440i	−0.733949	−	1.27124i	0.221234	−	0.975221i	$-0.428991\pi$
$954$		0			0
$955$	14.7476	−	25.5436i	0.477222	−	0.826573i
$956$	−21.5326	−	7.83721i	−0.696413	−	0.253473i
$957$		0			0
$958$	8.69640	+	7.29715i	0.280968	+	0.235760i
$959$	0.00798918	+	0.00670372i	0.000257984	+	0.000216474i
$960$		0			0
$961$	5.24288	+	1.90825i	0.169125	+	0.0615565i
$962$	0.881911	−	1.52752i	0.0284340	−	0.0492491i
$963$		0			0
$964$	6.03849	+	10.4590i	0.194487	+	0.336861i
$965$	−5.99201	−	33.9824i	−0.192890	−	1.09393i
$966$		0			0
$967$	−42.1559	+	15.3435i	−1.35564	+	0.493413i	−0.914704	−	0.404125i	$-0.867576\pi$
$967$	−42.1559	+	15.3435i	−1.35564	+	0.493413i	−0.440937	+	0.897538i	$0.645354\pi$
$968$	0.488856	−	2.77244i	0.0157124	−	0.0891095i
$969$		0			0
$970$	3.53596	−	2.96702i	0.113533	−	0.0952653i
$971$	6.55438			0.210340			0.105170	−	0.994454i	$-0.466461\pi$
$971$	6.55438			0.210340			0.105170	+	0.994454i	$0.466461\pi$
$972$		0			0
$973$	2.21482			0.0710039
$974$	0.871644	−	0.731397i	0.0279293	−	0.0234355i
$975$		0			0
$976$	−0.656574	+	3.72362i	−0.0210164	+	0.119190i
$977$	−44.3940	+	16.1581i	−1.42029	+	0.516943i	−0.934132	−	0.356928i	$-0.883824\pi$
$977$	−44.3940	+	16.1581i	−1.42029	+	0.516943i	−0.486158	+	0.873871i	$0.661602\pi$
$978$		0			0
$979$	−1.40074	−	7.94399i	−0.0447679	−	0.253891i
$980$	−4.70574	−	8.15058i	−0.150319	−	0.260361i
$981$		0			0
$982$	−7.65570	+	13.2601i	−0.244303	+	0.423145i
$983$	−29.5197	−	10.7443i	−0.941531	−	0.342689i	−0.174761	−	0.984611i	$-0.555915\pi$
$983$	−29.5197	−	10.7443i	−0.941531	−	0.342689i	−0.766770	+	0.641922i	$0.778137\pi$
$984$		0			0
$985$	14.1242	+	11.8516i	0.450036	+	0.377625i
$986$	−23.5403	−	19.7527i	−0.749676	−	0.629053i
$987$		0			0
$988$	−33.7422	−	12.2811i	−1.07348	−	0.390715i
$989$	−1.07873	+	1.86841i	−0.0343015	+	0.0594119i
$990$		0			0
$991$	−23.2126	−	40.2054i	−0.737373	−	1.27717i	−0.953675	−	0.300840i	$-0.902733\pi$
$991$	−23.2126	−	40.2054i	−0.737373	−	1.27717i	0.216302	−	0.976327i	$-0.430600\pi$
$992$	−0.875515	−	4.96529i	−0.0277976	−	0.157648i
$993$		0			0
$994$	−0.651055	+	0.236965i	−0.0206502	+	0.00751606i
$995$	2.90096	−	16.4522i	0.0919666	−	0.521568i
$996$		0			0
$997$	−20.5797	+	17.2684i	−0.651764	+	0.546895i	−0.907606	−	0.419824i	$-0.862092\pi$
$997$	−20.5797	+	17.2684i	−0.651764	+	0.546895i	0.255841	+	0.966719i	$0.417648\pi$
$998$	2.31820			0.0733814
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.e.a.37.1		6
3.2	odd	2		54.2.e.a.49.1	yes	6
9.2	odd	6		486.2.e.d.433.1		6
9.4	even	3		486.2.e.c.271.1		6
9.5	odd	6		486.2.e.b.271.1		6
9.7	even	3		486.2.e.a.433.1		6
12.11	even	2		432.2.u.a.49.1		6
27.2	odd	18		486.2.e.d.55.1		6
27.4	even	9		1458.2.a.d.1.2		3
27.5	odd	18		1458.2.c.d.973.2		6
27.7	even	9		486.2.e.c.217.1		6
27.11	odd	18		54.2.e.a.43.1	✓	6
27.13	even	9		1458.2.c.a.487.2		6
27.14	odd	18		1458.2.c.d.487.2		6
27.16	even	9	inner	162.2.e.a.127.1		6
27.20	odd	18		486.2.e.b.217.1		6
27.22	even	9		1458.2.c.a.973.2		6
27.23	odd	18		1458.2.a.a.1.2		3
27.25	even	9		486.2.e.a.55.1		6
108.11	even	18		432.2.u.a.97.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.a.43.1	✓	6	27.11	odd	18
54.2.e.a.49.1	yes	6	3.2	odd	2
162.2.e.a.37.1		6	1.1	even	1	trivial
162.2.e.a.127.1		6	27.16	even	9	inner
432.2.u.a.49.1		6	12.11	even	2
432.2.u.a.97.1		6	108.11	even	18
486.2.e.a.55.1		6	27.25	even	9
486.2.e.a.433.1		6	9.7	even	3
486.2.e.b.217.1		6	27.20	odd	18
486.2.e.b.271.1		6	9.5	odd	6
486.2.e.c.217.1		6	27.7	even	9
486.2.e.c.271.1		6	9.4	even	3
486.2.e.d.55.1		6	27.2	odd	18
486.2.e.d.433.1		6	9.2	odd	6
1458.2.a.a.1.2		3	27.23	odd	18
1458.2.a.d.1.2		3	27.4	even	9
1458.2.c.a.487.2		6	27.13	even	9
1458.2.c.a.973.2		6	27.22	even	9
1458.2.c.d.487.2		6	27.14	odd	18
1458.2.c.d.973.2		6	27.5	odd	18

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.26604 - 0.460802i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.26604 - 0.460802i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.673648 - 1.16679i) q^{10} +(3.49273 + 1.27125i) q^{11} +(-4.64543 - 3.89798i) q^{13} +(-0.0923963 - 0.0775297i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-2.58512 + 4.47756i) q^{17} +(2.96064 + 5.12797i) q^{19} +(-0.233956 - 1.32683i) q^{20} +(3.49273 - 1.27125i) q^{22} +(0.826352 - 4.68647i) q^{23} +(-2.43969 + 2.04715i) q^{25} -6.06418 q^{26} -0.120615 q^{28} +(-4.55303 + 3.82045i) q^{29} +(-0.875515 + 4.96529i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.897804 + 5.09170i) q^{34} +(-0.0812519 - 0.140732i) q^{35} +(-0.145430 + 0.251892i) q^{37} +(5.56418 + 2.02520i) q^{38} +(-1.03209 - 0.866025i) q^{40} +(-4.44356 - 3.72859i) q^{41} +(-0.426022 - 0.155059i) q^{43} +(1.85844 - 3.21891i) q^{44} +(-2.37939 - 4.12122i) q^{46} +(0.134285 + 0.761570i) q^{47} +(6.56418 - 2.38917i) q^{49} +(-0.553033 + 3.13641i) q^{50} +(-4.64543 + 3.89798i) q^{52} +7.29086 q^{53} +5.00774 q^{55} +(-0.0923963 + 0.0775297i) q^{56} +(-1.03209 + 5.85327i) q^{58} +(-1.40033 + 0.509678i) q^{59} +(-0.656574 - 3.72362i) q^{61} +(2.52094 + 4.36640i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-7.67752 - 2.79439i) q^{65} +(-5.08512 - 4.26692i) q^{67} +(3.96064 + 3.32337i) q^{68} +(-0.152704 - 0.0555796i) q^{70} +(2.87211 - 4.97464i) q^{71} +(-5.20961 - 9.02330i) q^{73} +(0.0505072 + 0.286441i) q^{74} +(5.56418 - 2.02520i) q^{76} +(0.0778483 - 0.441500i) q^{77} +(10.7194 - 8.99465i) q^{79} -1.34730 q^{80} -5.80066 q^{82} +(1.81521 - 1.52314i) q^{83} +(-1.20961 + 6.86002i) q^{85} +(-0.426022 + 0.155059i) q^{86} +(-0.645430 - 3.66041i) q^{88} +(-1.08512 - 1.87949i) q^{89} +(-0.365715 + 0.633436i) q^{91} +(-4.47178 - 1.62760i) q^{92} +(0.592396 + 0.497079i) q^{94} +(6.11128 + 5.12797i) q^{95} +(3.21941 + 1.17177i) q^{97} +(3.49273 - 6.04958i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8	\( 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{11} - 12 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} - 6 q^{20} + 3 q^{22} + 6 q^{23} - 9 q^{25} - 18 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} + 6 q^{34} - 3 q^{35} + 15 q^{37} + 15 q^{38} + 3 q^{40} + 3 q^{41} - 18 q^{43} + 3 q^{44} - 3 q^{46} - 9 q^{47} + 21 q^{49} + 9 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 3 q^{56} + 3 q^{58} + 6 q^{59} + 18 q^{61} + 12 q^{62} - 3 q^{64} - 21 q^{65} - 9 q^{67} + 15 q^{68} - 3 q^{70} - 12 q^{71} + 3 q^{73} + 3 q^{74} + 15 q^{76} - 39 q^{77} + 33 q^{79} - 6 q^{80} - 6 q^{82} + 18 q^{83} + 27 q^{85} - 18 q^{86} + 12 q^{88} + 15 q^{89} - 12 q^{91} - 12 q^{92} - 21 q^{95} - 12 q^{97} + 3 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 3 * q^11 - 12 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 - 6 * q^20 + 3 * q^22 + 6 * q^23 - 9 * q^25 - 18 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 + 6 * q^34 - 3 * q^35 + 15 * q^37 + 15 * q^38 + 3 * q^40 + 3 * q^41 - 18 * q^43 + 3 * q^44 - 3 * q^46 - 9 * q^47 + 21 * q^49 + 9 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 3 * q^58 + 6 * q^59 + 18 * q^61 + 12 * q^62 - 3 * q^64 - 21 * q^65 - 9 * q^67 + 15 * q^68 - 3 * q^70 - 12 * q^71 + 3 * q^73 + 3 * q^74 + 15 * q^76 - 39 * q^77 + 33 * q^79 - 6 * q^80 - 6 * q^82 + 18 * q^83 + 27 * q^85 - 18 * q^86 + 12 * q^88 + 15 * q^89 - 12 * q^91 - 12 * q^92 - 21 * q^95 - 12 * q^97 + 3 * q^98

Introduction

L-functions

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