LMFDB - Embedded newform 693.2.m.j.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.2
Root			$-1.07866 - 0.783695i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.j.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07866 + 0.783695i) q^{2} +(-0.0686960 + 0.211425i) q^{4} +(-0.706442 - 0.513260i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.915619 - 2.81798i) q^{8} +O(q^{10})$	\(q+(-1.07866 + 0.783695i) q^{2} +(-0.0686960 + 0.211425i) q^{4} +(-0.706442 - 0.513260i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.915619 - 2.81798i) q^{8} +1.16425 q^{10} +(-1.79514 + 2.78881i) q^{11} +(-0.0319918 + 0.0232434i) q^{13} +(-0.412013 - 1.26805i) q^{14} +(2.83639 + 2.06076i) q^{16} +(1.65552 + 1.20280i) q^{17} +(-1.75961 - 5.41551i) q^{19} +(0.157046 - 0.114100i) q^{20} +(-0.249220 - 4.41504i) q^{22} -5.97870 q^{23} +(-1.30946 - 4.03011i) q^{25} +(0.0162926 - 0.0501436i) q^{26} +(-0.179849 - 0.130668i) q^{28} +(1.44389 - 4.44385i) q^{29} +(-6.05057 + 4.39599i) q^{31} +1.25149 q^{32} -2.72838 q^{34} +(0.706442 - 0.513260i) q^{35} +(3.57546 - 11.0041i) q^{37} +(6.14214 + 4.46252i) q^{38} +(-0.799528 + 2.46069i) q^{40} +(1.90009 + 5.84788i) q^{41} -1.79689 q^{43} +(-0.466304 - 0.571118i) q^{44} +(6.44901 - 4.68548i) q^{46} +(-1.86885 - 5.75173i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(4.57084 + 3.32091i) q^{50} +(-0.00271652 - 0.00836058i) q^{52} +(-0.100643 + 0.0731211i) q^{53} +(2.69955 - 1.04876i) q^{55} +2.96300 q^{56} +(1.92515 + 5.92499i) q^{58} +(4.43316 - 13.6439i) q^{59} +(-6.11572 - 4.44333i) q^{61} +(3.08141 - 9.48360i) q^{62} +(-7.02272 + 5.10230i) q^{64} +0.0345302 q^{65} +4.85938 q^{67} +(-0.368030 + 0.267389i) q^{68} +(-0.359774 + 1.10727i) q^{70} +(-9.10168 - 6.61275i) q^{71} +(0.189413 - 0.582954i) q^{73} +(4.76718 + 14.6719i) q^{74} +1.26585 q^{76} +(-2.09759 - 2.56907i) q^{77} +(0.125581 - 0.0912401i) q^{79} +(-0.946040 - 2.91161i) q^{80} +(-6.63251 - 4.81880i) q^{82} +(7.21319 + 5.24069i) q^{83} +(-0.552176 - 1.69942i) q^{85} +(1.93824 - 1.40822i) q^{86} +(9.50249 + 2.50520i) q^{88} -5.17689 q^{89} +(-0.0122198 - 0.0376086i) q^{91} +(0.410713 - 1.26404i) q^{92} +(6.52347 + 4.73958i) q^{94} +(-1.53651 + 4.72888i) q^{95} +(-6.42539 + 4.66832i) q^{97} +1.33330 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.07866	+	0.783695i	−0.762731	+	0.554156i	−0.899747	−	0.436412i	$-0.856249\pi$
$2$	−1.07866	+	0.783695i	−0.762731	+	0.554156i	0.137016	+	0.990569i	$0.456249\pi$
$3$		0			0
$3$		0			0
$4$	−0.0686960	+	0.211425i	−0.0343480	+	0.105712i
$5$	−0.706442	−	0.513260i	−0.315931	−	0.229537i	0.418507	−	0.908214i	$-0.362554\pi$
$5$	−0.706442	−	0.513260i	−0.315931	−	0.229537i	−0.734437	+	0.678677i	$0.762554\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.915619	−	2.81798i	−0.323720	−	0.996308i
$9$		0			0
$10$	1.16425			0.368169
$11$	−1.79514	+	2.78881i	−0.541256	+	0.840858i
$11$	−1.79514	+	2.78881i	−0.541256	+	0.840858i
$12$		0			0
$13$	−0.0319918	+	0.0232434i	−0.00887292	+	0.00644656i	−0.592213	−	0.805782i	$-0.701746\pi$
$13$	−0.0319918	+	0.0232434i	−0.00887292	+	0.00644656i	0.583340	+	0.812228i	$0.301746\pi$
$14$	−0.412013	−	1.26805i	−0.110115	−	0.338900i
$15$		0			0
$16$	2.83639	+	2.06076i	0.709097	+	0.515189i
$17$	1.65552	+	1.20280i	0.401522	+	0.291723i	0.770161	−	0.637850i	$-0.220176\pi$
$17$	1.65552	+	1.20280i	0.401522	+	0.291723i	−0.368639	+	0.929573i	$0.620176\pi$
$18$		0			0
$19$	−1.75961	−	5.41551i	−0.403681	−	1.24240i	−0.921991	−	0.387211i	$-0.873439\pi$
$19$	−1.75961	−	5.41551i	−0.403681	−	1.24240i	0.518310	−	0.855193i	$-0.326561\pi$
$20$	0.157046	−	0.114100i	0.0351165	−	0.0255136i
$21$		0			0
$22$	−0.249220	−	4.41504i	−0.0531340	−	0.941289i
$23$	−5.97870			−1.24665			−0.623323	−	0.781965i	$-0.714218\pi$
$23$	−5.97870			−1.24665			−0.623323	+	0.781965i	$0.714218\pi$
$24$		0			0
$25$	−1.30946	−	4.03011i	−0.261892	−	0.806021i
$26$	0.0162926	−	0.0501436i	0.00319525	−	0.00983397i
$27$		0			0
$28$	−0.179849	−	0.130668i	−0.0339882	−	0.0246939i
$29$	1.44389	−	4.44385i	0.268124	−	0.825202i	−0.722833	−	0.691023i	$-0.757160\pi$
$29$	1.44389	−	4.44385i	0.268124	−	0.825202i	0.990957	−	0.134179i	$-0.0428397\pi$
$30$		0			0
$31$	−6.05057	+	4.39599i	−1.08671	+	0.789544i	−0.978841	−	0.204621i	$-0.934404\pi$
$31$	−6.05057	+	4.39599i	−1.08671	+	0.789544i	−0.107872	+	0.994165i	$0.534404\pi$
$32$	1.25149			0.221234
$33$		0			0
$34$	−2.72838			−0.467913
$35$	0.706442	−	0.513260i	0.119411	−	0.0867568i
$36$		0			0
$37$	3.57546	−	11.0041i	0.587803	−	1.80907i	9.16819e−5	−	1.00000i	$-0.499971\pi$
$37$	3.57546	−	11.0041i	0.587803	−	1.80907i	0.587711	−	0.809071i	$-0.300029\pi$
$38$	6.14214	+	4.46252i	0.996386	+	0.723917i
$39$		0			0
$40$	−0.799528	+	2.46069i	−0.126416	+	0.389070i
$41$	1.90009	+	5.84788i	0.296744	+	0.913285i	0.982630	+	0.185576i	$0.0594150\pi$
$41$	1.90009	+	5.84788i	0.296744	+	0.913285i	−0.685886	+	0.727709i	$0.740585\pi$
$42$		0			0
$43$	−1.79689			−0.274024			−0.137012	−	0.990569i	$-0.543750\pi$
$43$	−1.79689			−0.274024			−0.137012	+	0.990569i	$0.543750\pi$
$44$	−0.466304	−	0.571118i	−0.0702979	−	0.0860992i
$45$		0			0
$46$	6.44901	−	4.68548i	0.950855	−	0.690837i
$47$	−1.86885	−	5.75173i	−0.272600	−	0.838977i	−0.989844	−	0.142155i	$-0.954597\pi$
$47$	−1.86885	−	5.75173i	−0.272600	−	0.838977i	0.717244	−	0.696822i	$-0.245403\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	4.57084	+	3.32091i	0.646415	+	0.469648i
$51$		0			0
$52$	−0.00271652	−	0.00836058i	−0.000376713	−	0.00115940i
$53$	−0.100643	+	0.0731211i	−0.0138243	+	0.0100440i	−0.594676	−	0.803965i	$-0.702720\pi$
$53$	−0.100643	+	0.0731211i	−0.0138243	+	0.0100440i	0.580852	+	0.814009i	$0.302720\pi$
$54$		0			0
$55$	2.69955	−	1.04876i	0.364007	−	0.141414i
$56$	2.96300			0.395948
$57$		0			0
$58$	1.92515	+	5.92499i	0.252784	+	0.777990i
$59$	4.43316	−	13.6439i	0.577148	−	1.77628i	−0.0515991	−	0.998668i	$-0.516432\pi$
$59$	4.43316	−	13.6439i	0.577148	−	1.77628i	0.628747	−	0.777610i	$-0.283568\pi$
$60$		0			0
$61$	−6.11572	−	4.44333i	−0.783037	−	0.568910i	0.122852	−	0.992425i	$-0.460796\pi$
$61$	−6.11572	−	4.44333i	−0.783037	−	0.568910i	−0.905889	+	0.423515i	$0.860796\pi$
$62$	3.08141	−	9.48360i	0.391339	−	1.20442i
$63$		0			0
$64$	−7.02272	+	5.10230i	−0.877840	+	0.637788i
$65$	0.0345302			0.00428295
$66$		0			0
$67$	4.85938			0.593668			0.296834	−	0.954929i	$-0.404069\pi$
$67$	4.85938			0.593668			0.296834	+	0.954929i	$0.404069\pi$
$68$	−0.368030	+	0.267389i	−0.0446301	+	0.0324257i
$69$		0			0
$70$	−0.359774	+	1.10727i	−0.0430012	+	0.132344i
$71$	−9.10168	−	6.61275i	−1.08017	−	0.784790i	−0.102458	−	0.994737i	$-0.532671\pi$
$71$	−9.10168	−	6.61275i	−1.08017	−	0.784790i	−0.977713	+	0.209948i	$0.932671\pi$
$72$		0			0
$73$	0.189413	−	0.582954i	0.0221692	−	0.0682296i	−0.939360	−	0.342933i	$-0.888580\pi$
$73$	0.189413	−	0.582954i	0.0221692	−	0.0682296i	0.961529	+	0.274703i	$0.0885796\pi$
$74$	4.76718	+	14.6719i	0.554173	+	1.70557i
$75$		0			0
$76$	1.26585			0.145203
$77$	−2.09759	−	2.56907i	−0.239042	−	0.292773i
$78$		0			0
$79$	0.125581	−	0.0912401i	0.0141290	−	0.0102653i	−0.580698	−	0.814119i	$-0.697220\pi$
$79$	0.125581	−	0.0912401i	0.0141290	−	0.0102653i	0.594827	+	0.803853i	$0.297220\pi$
$80$	−0.946040	−	2.91161i	−0.105771	−	0.325528i
$81$		0			0
$82$	−6.63251	−	4.81880i	−0.732439	−	0.532148i
$83$	7.21319	+	5.24069i	0.791750	+	0.575240i	0.908482	−	0.417923i	$-0.137242\pi$
$83$	7.21319	+	5.24069i	0.791750	+	0.575240i	−0.116732	+	0.993163i	$0.537242\pi$
$84$		0			0
$85$	−0.552176	−	1.69942i	−0.0598919	−	0.184328i
$86$	1.93824	−	1.40822i	0.209006	−	0.151852i
$87$		0			0
$88$	9.50249	+	2.50520i	1.01297	+	0.267055i
$89$	−5.17689			−0.548749			−0.274374	−	0.961623i	$-0.588471\pi$
$89$	−5.17689			−0.548749			−0.274374	+	0.961623i	$0.588471\pi$
$90$		0			0
$91$	−0.0122198	−	0.0376086i	−0.00128098	−	0.00394245i
$92$	0.410713	−	1.26404i	0.0428198	−	0.131786i
$93$		0			0
$94$	6.52347	+	4.73958i	0.672845	+	0.488850i
$95$	−1.53651	+	4.72888i	−0.157642	+	0.485173i
$96$		0			0
$97$	−6.42539	+	4.66832i	−0.652399	+	0.473996i	−0.864088	−	0.503341i	$-0.832104\pi$
$97$	−6.42539	+	4.66832i	−0.652399	+	0.473996i	0.211688	+	0.977337i	$0.432104\pi$
$98$	1.33330			0.134684
$99$		0			0
$100$	0.942018			0.0942018
$101$	−7.35849	+	5.34626i	−0.732198	+	0.531973i	−0.890258	−	0.455457i	$-0.849476\pi$
$101$	−7.35849	+	5.34626i	−0.732198	+	0.531973i	0.158060	+	0.987429i	$0.449476\pi$
$102$		0			0
$103$	1.06225	−	3.26926i	0.104666	−	0.322130i	−0.884986	−	0.465618i	$-0.845832\pi$
$103$	1.06225	−	3.26926i	0.104666	−	0.322130i	0.989652	+	0.143489i	$0.0458320\pi$
$104$	0.0947918	+	0.0688703i	0.00929510	+	0.00675328i
$105$		0			0
$106$	0.0512548	−	0.157746i	0.00497831	−	0.0153217i
$107$	−1.01716	−	3.13050i	−0.0983328	−	0.302637i	0.889775	−	0.456399i	$-0.150861\pi$
$107$	−1.01716	−	3.13050i	−0.0983328	−	0.302637i	−0.988108	+	0.153762i	$0.950861\pi$
$108$		0			0
$109$	9.99510			0.957357			0.478678	−	0.877990i	$-0.341116\pi$
$109$	9.99510			0.957357			0.478678	+	0.877990i	$0.341116\pi$
$110$	−2.09000	+	3.24688i	−0.199274	+	0.309578i
$111$		0			0
$112$	−2.83639	+	2.06076i	−0.268014	+	0.194723i
$113$	−1.36048	−	4.18713i	−0.127983	−	0.393892i	0.866449	−	0.499265i	$-0.166397\pi$
$113$	−1.36048	−	4.18713i	−0.127983	−	0.393892i	−0.994433	+	0.105372i	$0.966397\pi$
$114$		0			0
$115$	4.22361	+	3.06863i	0.393853	+	0.286151i
$116$	0.840349	+	0.610549i	0.0780245	+	0.0566881i
$117$		0			0
$118$	5.91074	+	18.1914i	0.544127	+	1.67465i
$119$	−1.65552	+	1.20280i	−0.151761	+	0.110261i
$120$		0			0
$121$	−4.55492	−	10.0126i	−0.414084	−	0.910239i
$122$	10.0790			0.912512
$123$		0			0
$124$	−0.513771	−	1.58123i	−0.0461380	−	0.141998i
$125$	−2.49262	+	7.67149i	−0.222947	+	0.686159i
$126$		0			0
$127$	−10.5029	−	7.63082i	−0.931984	−	0.677126i	0.0144941	−	0.999895i	$-0.495386\pi$
$127$	−10.5029	−	7.63082i	−0.931984	−	0.677126i	−0.946478	+	0.322769i	$0.895386\pi$
$128$	2.80304	−	8.62687i	0.247756	−	0.762515i
$129$		0			0
$130$	−0.0372465	+	0.0270612i	−0.00326674	+	0.00237342i
$131$	−18.1255			−1.58363			−0.791817	−	0.610758i	$-0.790865\pi$
$131$	−18.1255			−1.58363			−0.791817	+	0.610758i	$0.790865\pi$
$132$		0			0
$133$	5.69421			0.493750
$134$	−5.24164	+	3.80827i	−0.452809	+	0.328985i
$135$		0			0
$136$	1.87366	−	5.76653i	0.160665	−	0.494476i
$137$	4.21254	+	3.06059i	0.359902	+	0.261484i	0.753011	−	0.658008i	$-0.228601\pi$
$137$	4.21254	+	3.06059i	0.359902	+	0.261484i	−0.393109	+	0.919492i	$0.628601\pi$
$138$		0			0
$139$	−5.60812	+	17.2600i	−0.475674	+	1.46397i	0.369372	+	0.929282i	$0.379573\pi$
$139$	−5.60812	+	17.2600i	−0.475674	+	1.46397i	−0.845046	+	0.534693i	$0.820427\pi$
$140$	0.0599861	+	0.184618i	0.00506975	+	0.0156031i
$141$		0			0
$142$	15.0000			1.25878
$143$	−0.00739155	−	0.130944i	−0.000618113	−	0.0109501i
$144$		0			0
$145$	−3.30088	+	2.39823i	−0.274123	+	0.199162i
$146$	0.252545	+	0.777254i	0.0209008	+	0.0643260i
$147$		0			0
$148$	2.08093	+	1.51188i	0.171051	+	0.124276i
$149$	8.93925	+	6.49475i	0.732332	+	0.532070i	0.890300	−	0.455374i	$-0.150494\pi$
$149$	8.93925	+	6.49475i	0.732332	+	0.532070i	−0.157968	+	0.987444i	$0.550494\pi$
$150$		0			0
$151$	4.92308	+	15.1517i	0.400634	+	1.23303i	0.924486	+	0.381216i	$0.124495\pi$
$151$	4.92308	+	15.1517i	0.400634	+	1.23303i	−0.523852	+	0.851810i	$0.675505\pi$
$152$	−13.6497	+	9.91709i	−1.10714	+	0.804382i
$153$		0			0
$154$	4.27596	+	1.12730i	0.344567	+	0.0908403i
$155$	6.53066			0.524555
$156$		0			0
$157$	4.94536	+	15.2203i	0.394683	+	1.21471i	0.929208	+	0.369556i	$0.120490\pi$
$157$	4.94536	+	15.2203i	0.394683	+	1.21471i	−0.534526	+	0.845152i	$0.679510\pi$
$158$	−0.0639555	+	0.196835i	−0.00508803	+	0.0156593i
$159$		0			0
$160$	−0.884105	−	0.642340i	−0.0698947	−	0.0507814i
$161$	1.84752	−	5.68608i	0.145605	−	0.448126i
$162$		0			0
$163$	−17.8012	+	12.9333i	−1.39429	+	1.01301i	−0.398915	+	0.916988i	$0.630613\pi$
$163$	−17.8012	+	12.9333i	−1.39429	+	1.01301i	−0.995379	+	0.0960257i	$0.969387\pi$
$164$	−1.36691			−0.106738
$165$		0			0
$166$	−11.8877			−0.922665
$167$	−3.81938	+	2.77494i	−0.295553	+	0.214731i	−0.725673	−	0.688040i	$-0.758471\pi$
$167$	−3.81938	+	2.77494i	−0.295553	+	0.214731i	0.430120	+	0.902772i	$0.358471\pi$
$168$		0			0
$169$	−4.01674	+	12.3622i	−0.308980	+	0.950942i
$170$	1.92744	+	1.40037i	0.147828	+	0.107403i
$171$		0			0
$172$	0.123439	−	0.379907i	0.00941216	−	0.0289677i
$173$	2.92816	+	9.01194i	0.222624	+	0.685165i	0.998524	+	0.0543100i	$0.0172959\pi$
$173$	2.92816	+	9.01194i	0.222624	+	0.685165i	−0.775900	+	0.630855i	$0.782704\pi$
$174$		0			0
$175$	4.23750			0.320325
$176$	−10.8388	+	4.21080i	−0.817004	+	0.317401i
$177$		0			0
$178$	5.58412	−	4.05710i	0.418548	−	0.304093i
$179$	−5.47531	−	16.8513i	−0.409244	−	1.25952i	−0.917299	−	0.398199i	$-0.869636\pi$
$179$	−5.47531	−	16.8513i	−0.409244	−	1.25952i	0.508055	−	0.861324i	$-0.330364\pi$
$180$		0			0
$181$	−13.1661	−	9.56574i	−0.978629	−	0.711016i	−0.0212275	−	0.999775i	$-0.506757\pi$
$181$	−13.1661	−	9.56574i	−0.978629	−	0.711016i	−0.957402	+	0.288759i	$0.906757\pi$
$182$	0.0426547	+	0.0309905i	0.00316178	+	0.00229717i
$183$		0			0
$184$	5.47421	+	16.8479i	0.403564	+	1.24204i
$185$	−8.17385	+	5.93865i	−0.600953	+	0.436618i
$186$		0			0
$187$	−6.32628	+	2.45772i	−0.462623	+	0.179726i
$188$	1.34444			0.0980534
$189$		0			0
$190$	−2.04863	−	6.30503i	−0.148623	−	0.457415i
$191$	−1.99194	+	6.13055i	−0.144131	+	0.443591i	−0.996898	−	0.0787007i	$-0.974923\pi$
$191$	−1.99194	+	6.13055i	−0.144131	+	0.443591i	0.852767	+	0.522292i	$0.174923\pi$
$192$		0			0
$193$	1.46492	+	1.06433i	0.105447	+	0.0766120i	0.639259	−	0.768991i	$-0.279241\pi$
$193$	1.46492	+	1.06433i	0.105447	+	0.0766120i	−0.533812	+	0.845603i	$0.679241\pi$
$194$	3.27230	−	10.0711i	0.234937	−	0.723062i
$195$		0			0
$196$	0.179849	−	0.130668i	0.0128463	−	0.00933340i
$197$	6.85772			0.488592			0.244296	−	0.969701i	$-0.421443\pi$
$197$	6.85772			0.488592			0.244296	+	0.969701i	$0.421443\pi$
$198$		0			0
$199$	−5.07400			−0.359687			−0.179843	−	0.983695i	$-0.557559\pi$
$199$	−5.07400			−0.359687			−0.179843	+	0.983695i	$0.557559\pi$
$200$	−10.1578	+	7.38008i	−0.718265	+	0.521850i
$201$		0			0
$202$	3.74751	−	11.5336i	0.263674	−	0.811504i
$203$	3.78016	+	2.74645i	0.265315	+	0.192763i
$204$		0			0
$205$	1.65918	−	5.10643i	0.115882	−	0.356648i
$206$	1.41630	+	4.35891i	0.0986780	+	0.303700i
$207$		0			0
$208$	−0.138640			−0.00961296
$209$	18.2616	+	4.81441i	1.26318	+	0.333020i
$210$		0			0
$211$	−6.55861	+	4.76511i	−0.451513	+	0.328044i	−0.790193	−	0.612858i	$-0.790020\pi$
$211$	−6.55861	+	4.76511i	−0.451513	+	0.328044i	0.338680	+	0.940902i	$0.390020\pi$
$212$	−0.00854585	−	0.0263014i	−0.000586932	−	0.00180639i
$213$		0			0
$214$	3.55054	+	2.57962i	0.242710	+	0.176339i
$215$	1.26940	+	0.922274i	0.0865724	+	0.0628985i
$216$		0			0
$217$	−2.31111	−	7.11287i	−0.156888	−	0.482853i
$218$	−10.7814	+	7.83311i	−0.730205	+	0.530525i
$219$		0			0
$220$	0.0362847	+	0.642797i	0.00244631	+	0.0433373i
$221$	−0.0809201			−0.00544328
$222$		0			0
$223$	−5.00761	−	15.4119i	−0.335335	−	1.03205i	−0.966557	−	0.256452i	$-0.917446\pi$
$223$	−5.00761	−	15.4119i	−0.335335	−	1.03205i	0.631222	−	0.775602i	$-0.282554\pi$
$224$	−0.386732	+	1.19024i	−0.0258396	+	0.0795261i
$225$		0			0
$226$	4.74894	+	3.45031i	0.315895	+	0.229511i
$227$	−7.31572	+	22.5155i	−0.485561	+	1.49440i	0.345605	+	0.938380i	$0.387674\pi$
$227$	−7.31572	+	22.5155i	−0.485561	+	1.49440i	−0.831166	+	0.556024i	$0.812326\pi$
$228$		0			0
$229$	−8.21697	+	5.96998i	−0.542993	+	0.394507i	−0.825195	−	0.564848i	$-0.808935\pi$
$229$	−8.21697	+	5.96998i	−0.542993	+	0.394507i	0.282203	+	0.959355i	$0.408935\pi$
$230$	−6.96073			−0.458977
$231$		0			0
$232$	−13.8448			−0.908952
$233$	19.0247	−	13.8223i	1.24635	−	0.905527i	0.248346	−	0.968671i	$-0.420113\pi$
$233$	19.0247	−	13.8223i	1.24635	−	0.905527i	0.998004	+	0.0631448i	$0.0201130\pi$
$234$		0			0
$235$	−1.63190	+	5.02247i	−0.106453	+	0.327630i
$236$	2.58011	+	1.87456i	0.167951	+	0.122023i
$237$		0			0
$238$	0.843115	−	2.59484i	0.0546510	−	0.168199i
$239$	−2.41823	−	7.44253i	−0.156422	−	0.481417i	0.841880	−	0.539664i	$-0.181449\pi$
$239$	−2.41823	−	7.44253i	−0.156422	−	0.481417i	−0.998302	+	0.0582470i	$0.981449\pi$
$240$		0			0
$241$	−6.86139			−0.441981			−0.220991	−	0.975276i	$-0.570929\pi$
$241$	−6.86139			−0.441981			−0.220991	+	0.975276i	$0.570929\pi$
$242$	12.7601	+	7.23059i	0.820249	+	0.464800i
$243$		0			0
$244$	1.35955	−	0.987774i	0.0870366	−	0.0632358i
$245$	0.269837	+	0.830472i	0.0172392	+	0.0530569i
$246$		0			0
$247$	0.182168	+	0.132353i	0.0115911	+	0.00842140i
$248$	17.9279	+	13.0253i	1.13842	+	0.827110i
$249$		0			0
$250$	−3.32341	−	10.2284i	−0.210191	−	0.646902i
$251$	−2.07682	+	1.50890i	−0.131088	+	0.0952407i	−0.651397	−	0.758737i	$-0.725817\pi$
$251$	−2.07682	+	1.50890i	−0.131088	+	0.0952407i	0.520309	+	0.853978i	$0.325817\pi$
$252$		0			0
$253$	10.7326	−	16.6735i	0.674755	−	1.04825i
$254$	17.3094			1.08609
$255$		0			0
$256$	−1.62758	−	5.00918i	−0.101724	−	0.313074i
$257$	6.05411	−	18.6326i	0.377645	−	1.16227i	−0.564032	−	0.825753i	$-0.690750\pi$
$257$	6.05411	−	18.6326i	0.377645	−	1.16227i	0.941677	−	0.336519i	$-0.109250\pi$
$258$		0			0
$259$	9.36069	+	6.80094i	0.581645	+	0.422590i
$260$	−0.00237209	+	0.00730054i	−0.000147111	+	0.000452760i
$261$		0			0
$262$	19.5514	−	14.2049i	1.20789	−	0.877581i
$263$	26.5306			1.63595			0.817974	−	0.575255i	$-0.195097\pi$
$263$	26.5306			1.63595			0.817974	+	0.575255i	$0.195097\pi$
$264$		0			0
$265$	0.108628			0.00667298
$266$	−6.14214	+	4.46252i	−0.376599	+	0.273615i
$267$		0			0
$268$	−0.333820	+	1.02739i	−0.0203913	+	0.0627580i
$269$	−13.8542	−	10.0657i	−0.844708	−	0.613716i	0.0789736	−	0.996877i	$-0.474836\pi$
$269$	−13.8542	−	10.0657i	−0.844708	−	0.613716i	−0.923682	+	0.383160i	$0.874836\pi$
$270$		0			0
$271$	1.63641	−	5.03635i	0.0994049	−	0.305937i	−0.888972	−	0.457962i	$-0.848580\pi$
$271$	1.63641	−	5.03635i	0.0994049	−	0.305937i	0.988377	+	0.152025i	$0.0485795\pi$
$272$	2.21700	+	6.82324i	0.134426	+	0.413720i
$273$		0			0
$274$	−6.94249			−0.419411
$275$	13.5899	+	3.58278i	0.819500	+	0.216050i
$276$		0			0
$277$	−1.98213	+	1.44010i	−0.119094	+	0.0865272i	−0.645738	−	0.763559i	$-0.723450\pi$
$277$	−1.98213	+	1.44010i	−0.119094	+	0.0865272i	0.526644	+	0.850086i	$0.323450\pi$
$278$	−7.47731	−	23.0128i	−0.448459	−	1.38022i
$279$		0			0
$280$	−2.09319	−	1.52079i	−0.125092	−	0.0908847i
$281$	0.244117	+	0.177362i	0.0145628	+	0.0105805i	0.595043	−	0.803694i	$-0.297135\pi$
$281$	0.244117	+	0.177362i	0.0145628	+	0.0105805i	−0.580480	+	0.814274i	$0.697135\pi$
$282$		0			0
$283$	7.41931	+	22.8343i	0.441032	+	1.35736i	0.886777	+	0.462198i	$0.152939\pi$
$283$	7.41931	+	22.8343i	0.441032	+	1.35736i	−0.445745	+	0.895160i	$0.647061\pi$
$284$	2.02335	−	1.47005i	0.120064	−	0.0872313i
$285$		0			0
$286$	0.110593	+	0.135452i	0.00653952	+	0.00800945i
$287$	−6.14882			−0.362954
$288$		0			0
$289$	−3.95929	−	12.1854i	−0.232899	−	0.716791i
$290$	1.68106	−	5.17377i	0.0987151	−	0.303814i
$291$		0			0
$292$	0.110239	+	0.0800933i	0.00645124	+	0.00468710i
$293$	0.606919	−	1.86791i	0.0354566	−	0.109124i	−0.931762	−	0.363070i	$-0.881729\pi$
$293$	0.606919	−	1.86791i	0.0354566	−	0.109124i	0.967218	+	0.253946i	$0.0817285\pi$
$294$		0			0
$295$	−10.1346	+	7.36323i	−0.590060	+	0.428704i
$296$	−34.2833			−1.99268
$297$		0			0
$298$	−14.7324			−0.853422
$299$	0.191269	−	0.138965i	0.0110614	−	0.00803657i
$300$		0			0
$301$	0.555270	−	1.70895i	0.0320053	−	0.0985020i
$302$	−17.1846	−	12.4854i	−0.988865	−	0.718453i
$303$		0			0
$304$	6.16913	−	18.9866i	0.353824	−	1.08896i
$305$	2.03982	+	6.27791i	0.116800	+	0.359472i
$306$		0			0
$307$	20.0180			1.14249			0.571243	−	0.820781i	$-0.306462\pi$
$307$	20.0180			1.14249			0.571243	+	0.820781i	$0.306462\pi$
$308$	0.687261	−	0.266996i	0.0391603	−	0.0152135i
$309$		0			0
$310$	−7.04439	+	5.11805i	−0.400095	+	0.290686i
$311$	−5.47087	−	16.8376i	−0.310225	−	0.954773i	−0.977676	−	0.210119i	$-0.932615\pi$
$311$	−5.47087	−	16.8376i	−0.310225	−	0.954773i	0.667451	−	0.744654i	$-0.267385\pi$
$312$		0			0
$313$	−22.9207	−	16.6529i	−1.29555	−	0.941276i	−0.295653	−	0.955295i	$-0.595537\pi$
$313$	−22.9207	−	16.6529i	−1.29555	−	0.941276i	−0.999902	+	0.0140197i	$0.995537\pi$
$314$	−17.2624	−	12.5419i	−0.974175	−	0.707780i
$315$		0			0
$316$	0.0106635	+	0.0328188i	0.000599867	+	0.00184620i
$317$	−17.7623	+	12.9051i	−0.997631	+	0.724821i	−0.961579	−	0.274529i	$-0.911478\pi$
$317$	−17.7623	+	12.9051i	−0.997631	+	0.724821i	−0.0360518	+	0.999350i	$0.511478\pi$
$318$		0			0
$319$	9.80105	+	12.0041i	0.548753	+	0.672100i
$320$	7.57995			0.423732
$321$		0			0
$322$	2.46330	+	7.58127i	0.137275	+	0.422488i
$323$	3.60074	−	11.0819i	0.200350	−	0.616615i
$324$		0			0
$325$	0.135565	+	0.0984939i	0.00751981	+	0.00546346i
$326$	9.06570	−	27.9014i	0.502103	−	1.54531i
$327$		0			0
$328$	14.7395	−	10.7089i	0.813851	−	0.591297i
$329$	6.04773			0.333422
$330$		0			0
$331$	23.1465			1.27225			0.636123	−	0.771587i	$-0.280537\pi$
$331$	23.1465			1.27225			0.636123	+	0.771587i	$0.280537\pi$
$332$	−1.60353	+	1.16503i	−0.0880050	+	0.0639394i
$333$		0			0
$334$	1.94512	−	5.98646i	0.106432	−	0.327565i
$335$	−3.43287	−	2.49413i	−0.187558	−	0.136269i
$336$		0			0
$337$	10.8190	−	33.2975i	0.589349	−	1.81383i	0.00829520	−	0.999966i	$-0.497360\pi$
$337$	10.8190	−	33.2975i	0.589349	−	1.81383i	0.581054	−	0.813865i	$-0.302640\pi$
$338$	−5.35553	−	16.4826i	−0.291302	−	0.896536i
$339$		0			0
$340$	0.397232			0.0215429
$341$	−1.39796	−	24.7653i	−0.0757035	−	1.34112i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	1.64527	+	5.06362i	0.0887069	+	0.273012i
$345$		0			0
$346$	−10.2211	−	7.42608i	−0.549491	−	0.399228i
$347$	−3.04157	−	2.20983i	−0.163280	−	0.118630i	0.503145	−	0.864202i	$-0.332176\pi$
$347$	−3.04157	−	2.20983i	−0.163280	−	0.118630i	−0.666425	+	0.745572i	$0.732176\pi$
$348$		0			0
$349$	−3.76196	−	11.5781i	−0.201373	−	0.619764i	−0.999843	−	0.0177282i	$-0.994357\pi$
$349$	−3.76196	−	11.5781i	−0.201373	−	0.619764i	0.798469	−	0.602035i	$-0.205643\pi$
$350$	−4.57084	+	3.32091i	−0.244322	+	0.177510i
$351$		0			0
$352$	−2.24660	+	3.49017i	−0.119744	+	0.186027i
$353$	5.79059			0.308202			0.154101	−	0.988055i	$-0.450752\pi$
$353$	5.79059			0.308202			0.154101	+	0.988055i	$0.450752\pi$
$354$		0			0
$355$	3.03574	+	9.34306i	0.161121	+	0.495878i
$356$	0.355631	−	1.09452i	0.0188484	−	0.0580095i
$357$		0			0
$358$	19.1123	+	13.8859i	1.01012	+	0.733892i
$359$	−1.78020	+	5.47890i	−0.0939555	+	0.289165i	−0.986980	−	0.160843i	$-0.948579\pi$
$359$	−1.78020	+	5.47890i	−0.0939555	+	0.289165i	0.893025	+	0.450008i	$0.148579\pi$
$360$		0			0
$361$	−10.8602	+	7.89042i	−0.571591	+	0.415285i
$362$	21.6984			1.14044
$363$		0			0
$364$	0.00879083			0.000460765
$365$	−0.433017	+	0.314605i	−0.0226651	+	0.0164672i
$366$		0			0
$367$	4.40597	−	13.5602i	0.229990	−	0.707836i	−0.767757	−	0.640742i	$-0.778627\pi$
$367$	4.40597	−	13.5602i	0.229990	−	0.707836i	0.997747	−	0.0670949i	$-0.0213730\pi$
$368$	−16.9579	−	12.3207i	−0.883993	−	0.642259i
$369$		0			0
$370$	4.16275	−	12.8116i	0.216411	−	0.666044i
$371$	−0.0384420	−	0.118312i	−0.00199581	−	0.00614247i
$372$		0			0
$373$	32.2223			1.66841			0.834203	−	0.551458i	$-0.185928\pi$
$373$	32.2223			1.66841			0.834203	+	0.551458i	$0.185928\pi$
$374$	4.89783	−	7.60893i	0.253261	−	0.393448i
$375$		0			0
$376$	−14.4971	+	10.5328i	−0.747633	+	0.543187i
$377$	0.0570974	+	0.175728i	0.00294066	+	0.00905043i
$378$		0			0
$379$	23.1196	+	16.7973i	1.18757	+	0.862822i	0.993006	−	0.118068i	$-0.0376699\pi$
$379$	23.1196	+	16.7973i	1.18757	+	0.862822i	0.194567	+	0.980889i	$0.437670\pi$
$380$	−0.894250	−	0.649711i	−0.0458741	−	0.0333295i
$381$		0			0
$382$	−2.65585	−	8.17388i	−0.135885	−	0.418212i
$383$	−16.3108	+	11.8505i	−0.833444	+	0.605533i	−0.920532	−	0.390668i	$-0.872244\pi$
$383$	−16.3108	+	11.8505i	−0.833444	+	0.605533i	0.0870873	+	0.996201i	$0.472244\pi$
$384$		0			0
$385$	0.163220	+	2.89151i	0.00831847	+	0.147365i
$386$	−2.41427			−0.122883
$387$		0			0
$388$	−0.545599	−	1.67918i	−0.0276986	−	0.0852474i
$389$	5.11755	−	15.7502i	0.259470	−	0.798567i	−0.733446	−	0.679748i	$-0.762089\pi$
$389$	5.11755	−	15.7502i	0.259470	−	0.798567i	0.992916	−	0.118819i	$-0.0379109\pi$
$390$		0			0
$391$	−9.89784	−	7.19120i	−0.500555	−	0.363675i
$392$	−0.915619	+	2.81798i	−0.0462457	+	0.142330i
$393$		0			0
$394$	−7.39718	+	5.37436i	−0.372664	+	0.270757i
$395$	−0.135546			−0.00682005
$396$		0			0
$397$	30.9920			1.55545			0.777723	−	0.628607i	$-0.216375\pi$
$397$	30.9920			1.55545			0.777723	+	0.628607i	$0.216375\pi$
$398$	5.47315	−	3.97647i	0.274344	−	0.199323i
$399$		0			0
$400$	4.59093	−	14.1294i	0.229547	−	0.706472i
$401$	2.81752	+	2.04705i	0.140700	+	0.102225i	0.655909	−	0.754840i	$-0.272286\pi$
$401$	2.81752	+	2.04705i	0.140700	+	0.102225i	−0.515209	+	0.857065i	$0.672286\pi$
$402$		0			0
$403$	0.0913906	−	0.281271i	0.00455249	−	0.0140111i
$404$	−0.624831	−	1.92303i	−0.0310865	−	0.0956745i
$405$		0			0
$406$	−6.22991			−0.309185
$407$	24.2700	+	29.7253i	1.20302	+	1.47343i
$408$		0			0
$409$	21.5104	−	15.6282i	1.06362	−	0.772765i	0.0888652	−	0.996044i	$-0.471676\pi$
$409$	21.5104	−	15.6282i	1.06362	−	0.772765i	0.974755	+	0.223279i	$0.0716760\pi$
$410$	2.21219	+	6.80841i	0.109252	+	0.336244i
$411$		0			0
$412$	0.618229	+	0.449170i	0.0304580	+	0.0221290i
$413$	11.6062	+	8.43236i	0.571101	+	0.414929i
$414$		0			0
$415$	−2.40586	−	7.40448i	−0.118099	−	0.363472i
$416$	−0.0400374	+	0.0290889i	−0.00196299	+	0.00142620i
$417$		0			0
$418$	−23.4711	+	9.11838i	−1.14801	+	0.445995i
$419$	−29.1491			−1.42402			−0.712012	−	0.702167i	$-0.752216\pi$
$419$	−29.1491			−1.42402			−0.712012	+	0.702167i	$0.752216\pi$
$420$		0			0
$421$	−6.17753	−	19.0125i	−0.301074	−	0.926611i	−0.981113	−	0.193435i	$-0.938037\pi$
$421$	−6.17753	−	19.0125i	−0.301074	−	0.926611i	0.680039	−	0.733176i	$-0.261963\pi$
$422$	3.34014	−	10.2799i	0.162596	−	0.500418i
$423$		0			0
$424$	0.298204	+	0.216658i	0.0144821	+	0.0105218i
$425$	2.67959	−	8.24693i	0.129979	−	0.400035i
$426$		0			0
$427$	6.11572	−	4.44333i	0.295960	−	0.215028i
$428$	0.731740			0.0353700
$429$		0			0
$430$	−2.09204			−0.100887
$431$	13.6954	−	9.95033i	0.659687	−	0.479290i	−0.206870	−	0.978368i	$-0.566328\pi$
$431$	13.6954	−	9.95033i	0.659687	−	0.479290i	0.866557	+	0.499078i	$0.166328\pi$
$432$		0			0
$433$	−2.64255	+	8.13294i	−0.126993	+	0.390844i	−0.994259	−	0.107001i	$-0.965875\pi$
$433$	−2.64255	+	8.13294i	−0.126993	+	0.390844i	0.867266	+	0.497845i	$0.165875\pi$
$434$	8.06723	+	5.86119i	0.387240	+	0.281346i
$435$		0			0
$436$	−0.686623	+	2.11321i	−0.0328833	+	0.101204i
$437$	10.5202	+	32.3777i	0.503248	+	1.54884i
$438$		0			0
$439$	−33.9408			−1.61990			−0.809952	−	0.586496i	$-0.800507\pi$
$439$	−33.9408			−1.61990			−0.809952	+	0.586496i	$0.800507\pi$
$440$	−5.42714	−	6.64703i	−0.258729	−	0.316885i
$441$		0			0
$442$	0.0872857	−	0.0634167i	0.00415176	−	0.00301643i
$443$	10.8651	+	33.4393i	0.516216	+	1.58875i	0.781059	+	0.624457i	$0.214680\pi$
$443$	10.8651	+	33.4393i	0.516216	+	1.58875i	−0.264844	+	0.964291i	$0.585320\pi$
$444$		0			0
$445$	3.65717	+	2.65709i	0.173366	+	0.125958i
$446$	17.4797	+	12.6998i	0.827689	+	0.601352i
$447$		0			0
$448$	−2.68244	−	8.25570i	−0.126733	−	0.390045i
$449$	−1.55978	+	1.13325i	−0.0736107	+	0.0534813i	−0.623982	−	0.781439i	$-0.714486\pi$
$449$	−1.55978	+	1.13325i	−0.0736107	+	0.0534813i	0.550371	+	0.834920i	$0.314486\pi$
$450$		0			0
$451$	−19.7196	−	5.19879i	−0.928558	−	0.244801i
$452$	0.978723			0.0460352
$453$		0			0
$454$	−9.75407	−	30.0199i	−0.457781	−	1.40891i
$455$	−0.0106704	+	0.0328402i	−0.000500238	+	0.00153957i
$456$		0			0
$457$	6.19032	+	4.49753i	0.289571	+	0.210386i	0.723081	−	0.690763i	$-0.242725\pi$
$457$	6.19032	+	4.49753i	0.289571	+	0.210386i	−0.433510	+	0.901149i	$0.642725\pi$
$458$	4.18471	−	12.8792i	0.195539	−	0.601806i
$459$		0			0
$460$	−0.938929	+	0.682172i	−0.0437778	+	0.0318064i
$461$	−40.7525			−1.89803			−0.949017	−	0.315224i	$-0.897920\pi$
$461$	−40.7525			−1.89803			−0.949017	+	0.315224i	$0.897920\pi$
$462$		0			0
$463$	−8.37407			−0.389176			−0.194588	−	0.980885i	$-0.562337\pi$
$463$	−8.37407			−0.389176			−0.194588	+	0.980885i	$0.562337\pi$
$464$	13.2531	−	9.62897i	0.615262	−	0.447014i
$465$		0			0
$466$	−9.68883	+	29.8192i	−0.448827	+	1.38135i
$467$	7.68254	+	5.58169i	0.355505	+	0.258290i	0.751175	−	0.660103i	$-0.229487\pi$
$467$	7.68254	+	5.58169i	0.355505	+	0.258290i	−0.395670	+	0.918393i	$0.629487\pi$
$468$		0			0
$469$	−1.50163	+	4.62154i	−0.0693389	+	0.213403i
$470$	−2.17582	−	6.69648i	−0.100363	−	0.308885i
$471$		0			0
$472$	−42.5072			−1.95655
$473$	3.22568	−	5.01119i	0.148317	−	0.230415i
$474$		0			0
$475$	−19.5209	+	14.1828i	−0.895683	+	0.650751i
$476$	−0.140575	−	0.432645i	−0.00644323	−	0.0198302i
$477$		0			0
$478$	8.44113	+	6.13284i	0.386088	+	0.280510i
$479$	−29.3659	−	21.3356i	−1.34176	−	0.974849i	−0.999377	−	0.0352896i	$-0.988765\pi$
$479$	−29.3659	−	21.3356i	−1.34176	−	0.974849i	−0.342387	−	0.939559i	$-0.611235\pi$
$480$		0			0
$481$	0.141388	+	0.435148i	0.00644675	+	0.0198410i
$482$	7.40114	−	5.37724i	0.337113	−	0.244927i
$483$		0			0
$484$	2.42982	−	0.275194i	0.110446	−	0.0125088i
$485$	6.93523			0.314912
$486$		0			0
$487$	1.65861	+	5.10466i	0.0751586	+	0.231314i	0.981577	−	0.191066i	$-0.0611945\pi$
$487$	1.65861	+	5.10466i	0.0751586	+	0.231314i	−0.906419	+	0.422381i	$0.861195\pi$
$488$	−6.92157	+	21.3024i	−0.313325	+	0.964314i
$489$		0			0
$490$	−0.941901	−	0.684331i	−0.0425507	−	0.0309149i
$491$	−7.12636	+	21.9327i	−0.321608	+	0.989808i	0.651340	+	0.758786i	$0.274207\pi$
$491$	−7.12636	+	21.9327i	−0.321608	+	0.989808i	−0.972948	+	0.231022i	$0.925793\pi$
$492$		0			0
$493$	7.73547	−	5.62014i	0.348388	−	0.253119i
$494$	−0.300222			−0.0135076
$495$		0			0
$496$	−26.2208			−1.17735
$497$	9.10168	−	6.61275i	0.408266	−	0.296623i
$498$		0			0
$499$	10.2406	−	31.5172i	0.458431	−	1.41090i	−0.408629	−	0.912700i	$-0.633993\pi$
$499$	10.2406	−	31.5172i	0.458431	−	1.41090i	0.867060	−	0.498204i	$-0.166007\pi$
$500$	−1.45071	−	1.05400i	−0.0648777	−	0.0471364i
$501$		0			0
$502$	1.05767	−	3.25518i	0.0472063	−	0.145286i
$503$	5.59684	+	17.2253i	0.249551	+	0.768038i	0.994855	+	0.101313i	$0.0323045\pi$
$503$	5.59684	+	17.2253i	0.249551	+	0.768038i	−0.745304	+	0.666725i	$0.767696\pi$
$504$		0			0
$505$	7.94237			0.353431
$506$	1.49001	+	26.3962i	0.0662392	+	1.17345i
$507$		0			0
$508$	2.33485	−	1.69637i	0.103592	−	0.0752642i
$509$	4.81817	+	14.8288i	0.213562	+	0.657275i	0.999253	+	0.0386557i	$0.0123076\pi$
$509$	4.81817	+	14.8288i	0.213562	+	0.657275i	−0.785691	+	0.618619i	$0.787692\pi$
$510$		0			0
$511$	0.495890	+	0.360286i	0.0219369	+	0.0159381i
$512$	20.3582	+	14.7911i	0.899713	+	0.653680i
$513$		0			0
$514$	8.07196	+	24.8429i	0.356039	+	1.09577i
$515$	−2.42840	+	1.76433i	−0.107008	+	0.0777458i
$516$		0			0
$517$	19.3953	+	5.11332i	0.853006	+	0.224883i
$518$	−15.4269			−0.677819
$519$		0			0
$520$	−0.0316165	−	0.0973057i	−0.00138648	−	0.00426714i
$521$	4.78023	−	14.7120i	0.209426	−	0.644546i	−0.790077	−	0.613008i	$-0.789959\pi$
$521$	4.78023	−	14.7120i	0.209426	−	0.644546i	0.999503	−	0.0315383i	$-0.0100406\pi$
$522$		0			0
$523$	14.0335	+	10.1959i	0.613643	+	0.445837i	0.850695	−	0.525659i	$-0.176181\pi$
$523$	14.0335	+	10.1959i	0.613643	+	0.445837i	−0.237053	+	0.971497i	$0.576181\pi$
$524$	1.24515	−	3.83218i	0.0543947	−	0.167410i
$525$		0			0
$526$	−28.6176	+	20.7919i	−1.24779	+	0.906571i
$527$	−15.3043			−0.666667
$528$		0			0
$529$	12.7449			0.554126
$530$	−0.117173	+	0.0851315i	−0.00508969	+	0.00369788i
$531$		0			0
$532$	−0.391169	+	1.20390i	−0.0169593	+	0.0521955i
$533$	−0.196712	−	0.142919i	−0.00852053	−	0.00619053i
$534$		0			0
$535$	−0.888197	+	2.73359i	−0.0384001	+	0.118183i
$536$	−4.44934	−	13.6937i	−0.192182	−	0.591476i
$537$		0			0
$538$	22.8325			0.984380
$539$	3.09152	−	1.20104i	0.133161	−	0.0517323i
$540$		0			0
$541$	−24.5088	+	17.8067i	−1.05372	+	0.765569i	−0.972916	−	0.231161i	$-0.925748\pi$
$541$	−24.5088	+	17.8067i	−1.05372	+	0.765569i	−0.0808002	+	0.996730i	$0.525748\pi$
$542$	2.18183	+	6.71498i	0.0937176	+	0.288433i
$543$		0			0
$544$	2.07186	+	1.50530i	0.0888304	+	0.0645390i
$545$	−7.06096	−	5.13009i	−0.302458	−	0.219749i
$546$		0			0
$547$	−9.40927	−	28.9588i	−0.402311	−	1.23819i	−0.923119	−	0.384513i	$-0.874369\pi$
$547$	−9.40927	−	28.9588i	−0.402311	−	1.23819i	0.520808	−	0.853674i	$-0.325631\pi$
$548$	−0.936469	+	0.680384i	−0.0400040	+	0.0290646i
$549$		0			0
$550$	−17.4667	+	6.78570i	−0.744783	+	0.289343i
$551$	−26.6064			−1.13347
$552$		0			0
$553$	0.0479677	+	0.147630i	0.00203980	+	0.00627785i
$554$	1.00945	−	3.10677i	0.0428874	−	0.131994i
$555$		0			0
$556$	−3.26393	−	2.37139i	−0.138422	−	0.100569i
$557$	−2.21706	+	6.82341i	−0.0939399	+	0.289117i	−0.986976	−	0.160868i	$-0.948571\pi$
$557$	−2.21706	+	6.82341i	−0.0939399	+	0.289117i	0.893036	+	0.449985i	$0.148571\pi$
$558$		0			0
$559$	0.0574858	−	0.0417659i	0.00243139	−	0.00176651i
$560$	3.06145			0.129370
$561$		0			0
$562$	−0.402318			−0.0169708
$563$	7.29219	−	5.29809i	0.307329	−	0.223288i	−0.423421	−	0.905933i	$-0.639171\pi$
$563$	7.29219	−	5.29809i	0.307329	−	0.223288i	0.730750	+	0.682646i	$0.239171\pi$
$564$		0			0
$565$	−1.18799	+	3.65625i	−0.0499790	+	0.153820i
$566$	−25.8981	−	18.8161i	−1.08858	−	0.790898i
$567$		0			0
$568$	−10.3010	+	31.7031i	−0.432219	+	1.33023i
$569$	−2.30526	−	7.09487i	−0.0966417	−	0.297433i	0.891036	−	0.453932i	$-0.149979\pi$
$569$	−2.30526	−	7.09487i	−0.0966417	−	0.297433i	−0.987678	+	0.156499i	$0.949979\pi$
$570$		0			0
$571$	−37.5921			−1.57318			−0.786590	−	0.617475i	$-0.788156\pi$
$571$	−37.5921			−1.57318			−0.786590	+	0.617475i	$0.788156\pi$
$572$	0.0281926	+	0.00743259i	0.00117879	+	0.000310772i
$573$		0			0
$574$	6.63251	−	4.81880i	0.276836	−	0.201133i
$575$	7.82888	+	24.0948i	0.326487	+	1.00482i
$576$		0			0
$577$	9.80773	+	7.12573i	0.408301	+	0.296648i	0.772914	−	0.634511i	$-0.218799\pi$
$577$	9.80773	+	7.12573i	0.408301	+	0.296648i	−0.364613	+	0.931159i	$0.618799\pi$
$578$	13.8204	+	10.0411i	0.574854	+	0.417656i
$579$		0			0
$580$	−0.280287	−	0.862635i	−0.0116383	−	0.0358190i
$581$	−7.21319	+	5.24069i	−0.299253	+	0.217420i
$582$		0			0
$583$	−0.0232530	−	0.411936i	−0.000963041	−	0.0170606i
$584$	−1.81619			−0.0751543
$585$		0			0
$586$	0.809207	+	2.49048i	0.0334280	+	0.102881i
$587$	0.395768	−	1.21805i	0.0163351	−	0.0502743i	−0.942557	−	0.334046i	$-0.891586\pi$
$587$	0.395768	−	1.21805i	0.0163351	−	0.0502743i	0.958892	+	0.283772i	$0.0915859\pi$
$588$		0			0
$589$	34.4532	+	25.0317i	1.41962	+	1.03141i
$590$	5.16132	−	15.8849i	0.212488	−	0.653971i
$591$		0			0
$592$	32.8183	−	23.8439i	1.34882	−	0.979978i
$593$	24.7324			1.01564			0.507819	−	0.861464i	$-0.330452\pi$
$593$	24.7324			1.01564			0.507819	+	0.861464i	$0.330452\pi$
$594$		0			0
$595$	1.78688			0.0732548
$596$	−1.98724	+	1.44381i	−0.0814005	+	0.0591409i
$597$		0			0
$598$	−0.0974089	+	0.299794i	−0.00398335	+	0.0122595i
$599$	−22.5718	−	16.3994i	−0.922260	−	0.670061i	0.0218257	−	0.999762i	$-0.493052\pi$
$599$	−22.5718	−	16.3994i	−0.922260	−	0.670061i	−0.944085	+	0.329701i	$0.893052\pi$
$600$		0			0
$601$	−10.6381	+	32.7407i	−0.433936	+	1.33552i	0.460236	+	0.887797i	$0.347765\pi$
$601$	−10.6381	+	32.7407i	−0.433936	+	1.33552i	−0.894173	+	0.447722i	$0.852235\pi$
$602$	0.740343	+	2.27854i	0.0301741	+	0.0928665i
$603$		0			0
$604$	−3.54163			−0.144107
$605$	−1.92130	+	9.41120i	−0.0781118	+	0.382620i
$606$		0			0
$607$	21.3777	−	15.5318i	0.867693	−	0.630416i	−0.0622737	−	0.998059i	$-0.519835\pi$
$607$	21.3777	−	15.5318i	0.867693	−	0.630416i	0.929967	+	0.367643i	$0.119835\pi$
$608$	−2.20213	−	6.77746i	−0.0893082	−	0.274862i
$609$		0			0
$610$	−7.12025	−	5.17316i	−0.288290	−	0.209455i
$611$	0.193478	+	0.140570i	0.00782727	+	0.00568684i
$612$		0			0
$613$	−12.2373	−	37.6625i	−0.494260	−	1.52118i	−0.818107	−	0.575066i	$-0.804976\pi$
$613$	−12.2373	−	37.6625i	−0.494260	−	1.52118i	0.323847	−	0.946109i	$-0.395024\pi$
$614$	−21.5927	+	15.6880i	−0.871409	+	0.633115i
$615$		0			0
$616$	−5.31902	+	8.26326i	−0.214309	+	0.332936i
$617$	−17.0640			−0.686971			−0.343486	−	0.939158i	$-0.611608\pi$
$617$	−17.0640			−0.686971			−0.343486	+	0.939158i	$0.611608\pi$
$618$		0			0
$619$	9.04822	+	27.8476i	0.363679	+	1.11929i	0.950804	+	0.309792i	$0.100259\pi$
$619$	9.04822	+	27.8476i	0.363679	+	1.11929i	−0.587126	+	0.809496i	$0.699741\pi$
$620$	−0.448630	+	1.38074i	−0.0180174	+	0.0554520i
$621$		0			0
$622$	19.0968	+	13.8746i	0.765711	+	0.556322i
$623$	1.59975	−	4.92351i	0.0640925	−	0.197256i
$624$		0			0
$625$	−11.4427	+	8.31361i	−0.457708	+	0.332544i
$626$	37.7745			1.50977
$627$		0			0
$628$	−3.55766			−0.141966
$629$	19.1551	−	13.9170i	0.763763	−	0.554906i
$630$		0			0
$631$	−12.4517	+	38.3223i	−0.495693	+	1.52559i	0.320182	+	0.947356i	$0.396256\pi$
$631$	−12.4517	+	38.3223i	−0.495693	+	1.52559i	−0.815875	+	0.578229i	$0.803744\pi$
$632$	−0.372098	−	0.270345i	−0.0148012	−	0.0107537i
$633$		0			0
$634$	9.04592	−	27.8405i	0.359259	−	1.10569i
$635$	3.50311	+	10.7815i	0.139017	+	0.427849i
$636$		0			0
$637$	0.0395440			0.00156679
$638$	−19.9796	−	5.26734i	−0.791000	−	0.208536i
$639$		0			0
$640$	−6.40801	+	4.65569i	−0.253299	+	0.184032i
$641$	3.88039	+	11.9426i	0.153266	+	0.471705i	0.997981	−	0.0635114i	$-0.0202299\pi$
$641$	3.88039	+	11.9426i	0.153266	+	0.471705i	−0.844715	+	0.535217i	$0.820230\pi$
$642$		0			0
$643$	3.34694	+	2.43170i	0.131991	+	0.0958968i	0.651822	−	0.758372i	$-0.274005\pi$
$643$	3.34694	+	2.43170i	0.131991	+	0.0958968i	−0.519831	+	0.854269i	$0.674005\pi$
$644$	1.07526	+	0.781223i	0.0423712	+	0.0307845i
$645$		0			0
$646$	4.80087	+	14.7756i	0.188888	+	0.581337i
$647$	−30.4262	+	22.1059i	−1.19618	+	0.869073i	−0.993903	−	0.110256i	$-0.964833\pi$
$647$	−30.4262	+	22.1059i	−1.19618	+	0.869073i	−0.202273	+	0.979329i	$0.564833\pi$
$648$		0			0
$649$	30.0920	+	36.8559i	1.18121	+	1.44672i
$650$	−0.223419			−0.00876320
$651$		0			0
$652$	−1.51155	−	4.65207i	−0.0591968	−	0.182189i
$653$	−1.86070	+	5.72666i	−0.0728150	+	0.224102i	−0.980840	−	0.194814i	$-0.937590\pi$
$653$	−1.86070	+	5.72666i	−0.0728150	+	0.224102i	0.908025	+	0.418916i	$0.137590\pi$
$654$		0			0
$655$	12.8046	+	9.30311i	0.500319	+	0.363503i
$656$	−6.66166	+	20.5025i	−0.260094	+	0.800488i
$657$		0			0
$658$	−6.52347	+	4.73958i	−0.254311	+	0.184768i
$659$	38.6192			1.50439			0.752195	−	0.658940i	$-0.228995\pi$
$659$	38.6192			1.50439			0.752195	+	0.658940i	$0.228995\pi$
$660$		0			0
$661$	43.0833			1.67575			0.837874	−	0.545864i	$-0.183798\pi$
$661$	43.0833			1.67575			0.837874	+	0.545864i	$0.183798\pi$
$662$	−24.9673	+	18.1398i	−0.970382	+	0.705024i
$663$		0			0
$664$	8.16364	−	25.1251i	0.316811	−	0.975044i
$665$	−4.02263	−	2.92261i	−0.155991	−	0.113334i
$666$		0			0
$667$	−8.63261	+	26.5685i	−0.334256	+	1.02873i
$668$	−0.324315	−	0.998138i	−0.0125481	−	0.0386191i
$669$		0			0
$670$	5.65755			0.218570
$671$	23.3702	−	9.07916i	0.902196	−	0.350497i
$672$		0			0
$673$	17.0032	−	12.3535i	0.655425	−	0.476194i	−0.209690	−	0.977768i	$-0.567246\pi$
$673$	17.0032	−	12.3535i	0.655425	−	0.476194i	0.865115	+	0.501574i	$0.167246\pi$
$674$	14.4250	+	44.3956i	0.555631	+	1.71006i
$675$		0			0
$676$	−2.33775	−	1.69847i	−0.0899134	−	0.0653259i
$677$	−19.3263	−	14.0414i	−0.742770	−	0.539654i	0.150807	−	0.988563i	$-0.451813\pi$
$677$	−19.3263	−	14.0414i	−0.742770	−	0.539654i	−0.893578	+	0.448909i	$0.851813\pi$
$678$		0			0
$679$	−2.45428	−	7.55350i	−0.0941866	−	0.289877i
$680$	−4.28336	+	3.11204i	−0.164259	+	0.119341i
$681$		0			0
$682$	20.9164	+	25.6179i	0.800930	+	0.980960i
$683$	13.5672			0.519134			0.259567	−	0.965725i	$-0.416420\pi$
$683$	13.5672			0.519134			0.259567	+	0.965725i	$0.416420\pi$
$684$		0			0
$685$	−1.40504	−	4.32426i	−0.0536837	−	0.165221i
$686$	−0.412013	+	1.26805i	−0.0157307	+	0.0484142i
$687$		0			0
$688$	−5.09669	−	3.70296i	−0.194309	−	0.141174i
$689$	0.00152015	−	0.00467855i	5.79132e−5	−	0.000178238i
$690$		0			0
$691$	3.97366	−	2.88703i	0.151165	−	0.109828i	−0.509632	−	0.860393i	$-0.670218\pi$
$691$	3.97366	−	2.88703i	0.151165	−	0.109828i	0.660797	+	0.750565i	$0.270218\pi$
$692$	−2.10650			−0.0800771
$693$		0			0
$694$	5.01266			0.190278
$695$	12.8207	−	9.31477i	0.486316	−	0.353329i
$696$		0			0
$697$	−3.88821	+	11.9667i	−0.147277	+	0.453271i
$698$	13.1316	+	9.54069i	0.497040	+	0.361120i
$699$		0			0
$700$	−0.291100	+	0.895912i	−0.0110025	+	0.0338623i
$701$	−11.4102	−	35.1170i	−0.430958	−	1.32635i	−0.897173	−	0.441680i	$-0.854383\pi$
$701$	−11.4102	−	35.1170i	−0.430958	−	1.32635i	0.466215	−	0.884672i	$-0.345617\pi$
$702$		0			0
$703$	−65.8845			−2.48488
$704$	−1.62257	−	28.7444i	−0.0611528	−	1.08334i
$705$		0			0
$706$	−6.24610	+	4.53806i	−0.235075	+	0.170792i
$707$	−2.81069	−	8.65043i	−0.105707	−	0.325333i
$708$		0			0
$709$	−0.395914	−	0.287648i	−0.0148688	−	0.0108028i	0.580326	−	0.814384i	$-0.302925\pi$
$709$	−0.395914	−	0.287648i	−0.0148688	−	0.0108028i	−0.595195	+	0.803581i	$0.702925\pi$
$710$	−10.5967	−	7.69892i	−0.397685	−	0.288935i
$711$		0			0
$712$	4.74005	+	14.5884i	0.177641	+	0.546723i
$713$	36.1745	−	26.2823i	1.35475	−	0.984281i
$714$		0			0
$715$	−0.0619867	+	0.0962983i	−0.00231817	+	0.00360135i
$716$	3.93890			0.147204
$717$		0			0
$718$	−2.37355	−	7.30503i	−0.0885800	−	0.272621i
$719$	−3.13317	+	9.64292i	−0.116848	+	0.359620i	−0.992328	−	0.123634i	$-0.960545\pi$
$719$	−3.13317	+	9.64292i	−0.116848	+	0.359620i	0.875480	+	0.483254i	$0.160545\pi$
$720$		0			0
$721$	2.78100	+	2.02051i	0.103570	+	0.0752478i
$722$	5.53086	−	17.0222i	0.205837	−	0.633502i
$723$		0			0
$724$	2.92689	−	2.12651i	0.108777	−	0.0790312i
$725$	−19.7999			−0.735350
$726$		0			0
$727$	−10.5834			−0.392516			−0.196258	−	0.980552i	$-0.562879\pi$
$727$	−10.5834			−0.392516			−0.196258	+	0.980552i	$0.562879\pi$
$728$	−0.0947918	+	0.0688703i	−0.00351322	+	0.00255250i
$729$		0			0
$730$	0.220525	−	0.678707i	0.00816200	−	0.0251201i
$731$	−2.97479	−	2.16131i	−0.110026	−	0.0799389i
$732$		0			0
$733$	3.88595	−	11.9597i	0.143531	−	0.441742i	−0.853288	−	0.521439i	$-0.825395\pi$
$733$	3.88595	−	11.9597i	0.143531	−	0.441742i	0.996819	+	0.0796971i	$0.0253953\pi$
$734$	5.87450	+	18.0798i	0.216832	+	0.667339i
$735$		0			0
$736$	−7.48229			−0.275801
$737$	−8.72328	+	13.5519i	−0.321326	+	0.499190i
$738$		0			0
$739$	1.13052	−	0.821374i	0.0415870	−	0.0302147i	−0.566798	−	0.823857i	$-0.691818\pi$
$739$	1.13052	−	0.821374i	0.0415870	−	0.0302147i	0.608385	+	0.793642i	$0.291818\pi$
$740$	−0.694066	−	2.13611i	−0.0255144	−	0.0785251i
$741$		0			0
$742$	0.134187	+	0.0974925i	0.00492616	+	0.00357906i
$743$	19.5111	+	14.1756i	0.715791	+	0.520053i	0.885037	−	0.465521i	$-0.154133\pi$
$743$	19.5111	+	14.1756i	0.715791	+	0.520053i	−0.169245	+	0.985574i	$0.554133\pi$
$744$		0			0
$745$	−2.98157	−	9.17632i	−0.109236	−	0.336194i
$746$	−34.7570	+	25.2524i	−1.27254	+	0.924557i
$747$		0			0
$748$	−0.0850315	−	1.50637i	−0.00310906	−	0.0550782i
$749$	3.29161			0.120273
$750$		0			0
$751$	−5.94079	−	18.2839i	−0.216783	−	0.667188i	−0.999022	−	0.0442106i	$-0.985923\pi$
$751$	−5.94079	−	18.2839i	−0.216783	−	0.667188i	0.782240	−	0.622978i	$-0.214077\pi$
$752$	6.55214	−	20.1654i	0.238932	−	0.735357i
$753$		0			0
$754$	−0.199306	−	0.144804i	−0.00725829	−	0.00527346i
$755$	4.29888	−	13.2306i	0.156452	−	0.481511i
$756$		0			0
$757$	34.3682	−	24.9699i	1.24913	−	0.907548i	0.250961	−	0.967997i	$-0.419253\pi$
$757$	34.3682	−	24.9699i	1.24913	−	0.907548i	0.998171	+	0.0604493i	$0.0192533\pi$
$758$	−38.1023			−1.38394
$759$		0			0
$760$	14.7328			0.534414
$761$	11.8940	−	8.64149i	0.431157	−	0.313254i	−0.350954	−	0.936393i	$-0.614143\pi$
$761$	11.8940	−	8.64149i	0.431157	−	0.313254i	0.782111	+	0.623139i	$0.214143\pi$
$762$		0			0
$763$	−3.08865	+	9.50590i	−0.111817	+	0.344137i
$764$	−1.15931	−	0.842289i	−0.0419424	−	0.0304729i
$765$		0			0
$766$	8.30672	−	25.5654i	0.300134	−	0.923717i
$767$	0.175305	+	0.539533i	0.00632989	+	0.0194814i
$768$		0			0
$769$	−45.4931			−1.64052			−0.820262	−	0.571988i	$-0.806172\pi$
$769$	−45.4931			−1.64052			−0.820262	+	0.571988i	$0.806172\pi$
$770$	−2.44212	−	2.99105i	−0.0880080	−	0.107790i
$771$		0			0
$772$	−0.325659	+	0.236605i	−0.0117207	+	0.00851562i
$773$	−1.87073	−	5.75752i	−0.0672855	−	0.207084i	0.911761	−	0.410722i	$-0.134723\pi$
$773$	−1.87073	−	5.75752i	−0.0672855	−	0.207084i	−0.979046	+	0.203638i	$0.934723\pi$
$774$		0			0
$775$	25.6393	+	18.6280i	0.920991	+	0.669139i
$776$	19.0385	+	13.8322i	0.683441	+	0.496549i
$777$		0			0
$778$	6.82325	+	20.9998i	0.244625	+	0.752879i
$779$	28.3258	−	20.5799i	1.01488	−	0.737352i
$780$		0			0
$781$	34.7805	−	13.5120i	1.24455	−	0.483497i
$782$	16.3122			0.583322
$783$		0			0
$784$	−1.08340	−	3.33438i	−0.0386930	−	0.119085i
$785$	4.31834	−	13.2905i	0.154128	−	0.474358i
$786$		0			0
$787$	−44.3042	−	32.1889i	−1.57928	−	1.14741i	−0.917520	−	0.397691i	$-0.869812\pi$
$787$	−44.3042	−	32.1889i	−1.57928	−	1.14741i	−0.661756	−	0.749720i	$-0.730188\pi$
$788$	−0.471098	+	1.44989i	−0.0167822	+	0.0516502i
$789$		0			0
$790$	0.146208	−	0.106227i	0.00520186	−	0.00377937i
$791$	4.40261			0.156539
$792$		0			0
$793$	0.298931			0.0106153
$794$	−33.4300	+	24.2883i	−1.18639	+	0.861960i
$795$		0			0
$796$	0.348564	−	1.07277i	0.0123545	−	0.0380233i
$797$	−35.0241	−	25.4465i	−1.24062	−	0.901361i	−0.242978	−	0.970032i	$-0.578124\pi$
$797$	−35.0241	−	25.4465i	−1.24062	−	0.901361i	−0.997639	+	0.0686704i	$0.978124\pi$
$798$		0			0
$799$	3.82429	−	11.7700i	0.135294	−	0.416391i
$800$	−1.63878	−	5.04364i	−0.0579395	−	0.178319i
$801$		0			0
$802$	−4.64342			−0.163965
$803$	1.28572	+	1.57472i	0.0453722	+	0.0555708i
$804$		0			0
$805$	−4.22361	+	3.06863i	−0.148863	+	0.108155i
$806$	0.121851	+	0.375020i	0.00429203	+	0.0132095i
$807$		0			0
$808$	21.8033	+	15.8410i	0.767036	+	0.557284i
$809$	−12.5538	−	9.12083i	−0.441366	−	0.320671i	0.344811	−	0.938672i	$-0.387943\pi$
$809$	−12.5538	−	9.12083i	−0.441366	−	0.320671i	−0.786178	+	0.618001i	$0.787943\pi$
$810$		0			0
$811$	12.8063	+	39.4138i	0.449691	+	1.38401i	0.877257	+	0.480022i	$0.159371\pi$
$811$	12.8063	+	39.4138i	0.449691	+	1.38401i	−0.427566	+	0.903984i	$0.640629\pi$
$812$	−0.840349	+	0.610549i	−0.0294905	+	0.0214261i
$813$		0			0
$814$	−49.4748	−	13.0433i	−1.73409	−	0.457169i
$815$	19.2136			0.673024
$816$		0			0
$817$	3.16182	+	9.73109i	0.110618	+	0.340448i
$818$	−10.9547	+	33.7152i	−0.383023	+	1.17882i
$819$		0			0
$820$	0.965645	+	0.701582i	0.0337218	+	0.0245003i
$821$	12.3892	−	38.1299i	0.432385	−	1.33074i	−0.463359	−	0.886171i	$-0.653356\pi$
$821$	12.3892	−	38.1299i	0.432385	−	1.33074i	0.895743	−	0.444572i	$-0.146644\pi$
$822$		0			0
$823$	−3.42241	+	2.48653i	−0.119298	+	0.0866749i	−0.645834	−	0.763478i	$-0.723490\pi$
$823$	−3.42241	+	2.48653i	−0.119298	+	0.0866749i	0.526537	+	0.850152i	$0.323490\pi$
$824$	−10.1853			−0.354823
$825$		0			0
$826$	−19.1275			−0.665532
$827$	38.5811	−	28.0308i	1.34160	−	0.974727i	0.342212	−	0.939623i	$-0.388824\pi$
$827$	38.5811	−	28.0308i	1.34160	−	0.974727i	0.999384	−	0.0351040i	$-0.0111762\pi$
$828$		0			0
$829$	1.44782	−	4.45592i	0.0502847	−	0.154761i	−0.922761	−	0.385373i	$-0.874073\pi$
$829$	1.44782	−	4.45592i	0.0502847	−	0.154761i	0.973046	+	0.230612i	$0.0740729\pi$
$830$	8.39798	+	6.10149i	0.291498	+	0.211786i
$831$		0			0
$832$	0.106074	−	0.326463i	0.00367747	−	0.0113181i
$833$	−0.632351	−	1.94618i	−0.0219097	−	0.0674310i
$834$		0			0
$835$	4.12244			0.142663
$836$	−2.27238	+	3.53022i	−0.0785920	+	0.122095i
$837$		0			0
$838$	31.4420	−	22.8440i	1.08615	−	0.789132i
$839$	2.14367	+	6.59755i	0.0740078	+	0.227773i	0.981217	−	0.192907i	$-0.0617916\pi$
$839$	2.14367	+	6.59755i	0.0740078	+	0.227773i	−0.907209	+	0.420680i	$0.861792\pi$
$840$		0			0
$841$	5.79854	+	4.21288i	0.199949	+	0.145272i
$842$	21.5635	+	15.6668i	0.743126	+	0.539913i
$843$		0			0
$844$	−0.556911	−	1.71399i	−0.0191697	−	0.0589981i
$845$	9.18264	−	6.67158i	0.315893	−	0.229509i
$846$		0			0
$847$	10.9301	−	1.23791i	0.375563	−	0.0425352i
$848$	−0.436146			−0.0149773
$849$		0			0
$850$	3.57270	+	10.9957i	0.122543	+	0.377148i
$851$	−21.3766	+	65.7905i	−0.732782	+	2.25527i
$852$		0			0
$853$	5.04732	+	3.66709i	0.172817	+	0.125559i	0.670831	−	0.741610i	$-0.265937\pi$
$853$	5.04732	+	3.66709i	0.172817	+	0.125559i	−0.498015	+	0.867169i	$0.665937\pi$
$854$	−3.11459	+	9.58572i	−0.106579	+	0.328017i
$855$		0			0
$856$	−7.89038	+	5.73270i	−0.269688	+	0.195939i
$857$	−26.5684			−0.907559			−0.453779	−	0.891114i	$-0.649925\pi$
$857$	−26.5684			−0.907559			−0.453779	+	0.891114i	$0.649925\pi$
$858$		0			0
$859$	44.6475			1.52335			0.761677	−	0.647957i	$-0.224377\pi$
$859$	44.6475			1.52335			0.761677	+	0.647957i	$0.224377\pi$
$860$	−0.282194	+	0.205026i	−0.00962274	+	0.00699133i
$861$		0			0
$862$	−6.97477	+	21.4661i	−0.237561	+	0.731139i
$863$	−17.1761	−	12.4792i	−0.584682	−	0.424796i	0.255727	−	0.966749i	$-0.417685\pi$
$863$	−17.1761	−	12.4792i	−0.584682	−	0.424796i	−0.840409	+	0.541953i	$0.817685\pi$
$864$		0			0
$865$	2.55690	−	7.86932i	0.0869371	−	0.267565i
$866$	−3.52332	−	10.8437i	−0.119727	−	0.368483i
$867$		0			0
$868$	1.66260			0.0564323
$869$	0.0290150	+	0.514011i	0.000984265	+	0.0174366i
$870$		0			0
$871$	−0.155460	+	0.112948i	−0.00526757	+	0.00382711i
$872$	−9.15170	−	28.1660i	−0.309916	−	0.953822i
$873$		0			0
$874$	−36.7220	−	26.6801i	−1.24214	−	0.902468i
$875$	−6.52576	−	4.74124i	−0.220611	−	0.160283i
$876$		0			0
$877$	2.97741	+	9.16354i	0.100540	+	0.309431i	0.988658	−	0.150185i	$-0.0479870\pi$
$877$	2.97741	+	9.16354i	0.100540	+	0.309431i	−0.888118	+	0.459616i	$0.847987\pi$
$878$	36.6107	−	26.5992i	1.23555	−	0.897680i
$879$		0			0
$880$	9.81821	+	2.58844i	0.330972	+	0.0872561i
$881$	38.9952			1.31378			0.656891	−	0.753985i	$-0.271871\pi$
$881$	38.9952			1.31378			0.656891	+	0.753985i	$0.271871\pi$
$882$		0			0
$883$	4.58283	+	14.1045i	0.154225	+	0.474654i	0.998081	−	0.0619139i	$-0.0197204\pi$
$883$	4.58283	+	14.1045i	0.154225	+	0.474654i	−0.843857	+	0.536568i	$0.819720\pi$
$884$	0.00555889	−	0.0171085i	0.000186966	−	0.000575421i
$885$		0			0
$886$	−37.9260	−	27.5548i	−1.27415	−	0.925723i
$887$	5.44150	−	16.7472i	0.182708	−	0.562316i	−0.817194	−	0.576363i	$-0.804471\pi$
$887$	5.44150	−	16.7472i	0.182708	−	0.562316i	0.999901	+	0.0140468i	$0.00447138\pi$
$888$		0			0
$889$	10.5029	−	7.63082i	0.352257	−	0.255929i
$890$	−6.02721			−0.202032
$891$		0			0
$892$	3.60245			0.120619
$893$	−27.8601	+	20.2416i	−0.932304	+	0.677358i
$894$		0			0
$895$	−4.78110	+	14.7147i	−0.159814	+	0.491858i
$896$	7.33845	+	5.33170i	0.245160	+	0.178119i
$897$		0			0
$898$	0.794360	−	2.44479i	0.0265081	−	0.0815837i
$899$	10.7988	+	33.2351i	0.360159	+	1.10845i
$900$		0			0
$901$	−0.254566			−0.00848081
$902$	25.3450	−	9.84638i	0.843898	−	0.327848i
$903$		0			0
$904$	−10.5536	+	7.66764i	−0.351007	+	0.255022i
$905$	4.39138	+	13.5153i	0.145974	+	0.449263i
$906$		0			0
$907$	−37.2249	−	27.0455i	−1.23603	−	0.898031i	−0.238706	−	0.971092i	$-0.576723\pi$
$907$	−37.2249	−	27.0455i	−1.23603	−	0.898031i	−0.997328	+	0.0730605i	$0.976723\pi$
$908$	−4.25776	−	3.09345i	−0.141299	−	0.102660i
$909$		0			0
$910$	−0.0142269	−	0.0437859i	−0.000471618	−	0.00145149i
$911$	15.7758	−	11.4618i	0.522677	−	0.379747i	−0.294934	−	0.955517i	$-0.595298\pi$
$911$	15.7758	−	11.4618i	0.522677	−	0.379747i	0.817611	+	0.575770i	$0.195298\pi$
$912$		0			0
$913$	−27.5640	+	10.7084i	−0.912235	+	0.354397i
$914$	−10.2020			−0.337451
$915$		0			0
$916$	−0.697727	−	2.14738i	−0.0230536	−	0.0709515i
$917$	5.60110	−	17.2384i	0.184965	−	0.569262i
$918$		0			0
$919$	−9.49601	−	6.89925i	−0.313244	−	0.227585i	0.420043	−	0.907504i	$-0.362015\pi$
$919$	−9.49601	−	6.89925i	−0.313244	−	0.227585i	−0.733287	+	0.679919i	$0.762015\pi$
$920$	4.78014	−	14.7118i	0.157597	−	0.485032i
$921$		0			0
$922$	43.9583	−	31.9376i	1.44769	−	1.05181i
$923$	0.444882			0.0146435
$924$		0			0
$925$	−49.0298			−1.61209
$926$	9.03281	−	6.56272i	0.296837	−	0.215664i
$927$		0			0
$928$	1.80702	−	5.56143i	0.0593183	−	0.182563i
$929$	28.8740	+	20.9782i	0.947326	+	0.688273i	0.950173	−	0.311723i	$-0.100906\pi$
$929$	28.8740	+	20.9782i	0.947326	+	0.688273i	−0.00284654	+	0.999996i	$0.500906\pi$
$930$		0			0
$931$	−1.75961	+	5.41551i	−0.0576688	+	0.177486i
$932$	1.61544	+	4.97183i	0.0529156	+	0.162858i
$933$		0			0
$934$	−12.6612			−0.414288
$935$	5.73060	+	1.51079i	0.187411	+	0.0494082i
$936$		0			0
$937$	−28.6021	+	20.7806i	−0.934390	+	0.678874i	−0.947064	−	0.321046i	$-0.895966\pi$
$937$	−28.6021	+	20.7806i	−0.934390	+	0.678874i	0.0126738	+	0.999920i	$0.495966\pi$
$938$	−2.00213	−	6.16191i	−0.0653718	−	0.201194i
$939$		0			0
$940$	−0.949769	−	0.690048i	−0.0309781	−	0.0225069i
$941$	−24.7099	−	17.9528i	−0.805520	−	0.585245i	0.107008	−	0.994258i	$-0.465873\pi$
$941$	−24.7099	−	17.9528i	−0.805520	−	0.585245i	−0.912528	+	0.409014i	$0.865873\pi$
$942$		0			0
$943$	−11.3601	−	34.9627i	−0.369935	−	1.13854i
$944$	40.6908	−	29.5636i	1.32437	−	0.962214i
$945$		0			0
$946$	0.447822	+	7.93334i	0.0145600	+	0.257935i
$947$	−38.9527			−1.26579			−0.632897	−	0.774236i	$-0.718134\pi$
$947$	−38.9527			−1.26579			−0.632897	+	0.774236i	$0.718134\pi$
$948$		0			0
$949$	0.00749016	+	0.0230523i	0.000243141	+	0.000748311i
$950$	9.94155	−	30.5970i	0.322547	−	0.992696i
$951$		0			0
$952$	4.90530	+	3.56391i	0.158982	+	0.115507i
$953$	−10.9035	+	33.5576i	−0.353200	+	1.08704i	0.603846	+	0.797101i	$0.293634\pi$
$953$	−10.9035	+	33.5576i	−0.353200	+	1.08704i	−0.957046	+	0.289937i	$0.906366\pi$
$954$		0			0
$955$	4.55376	−	3.30850i	0.147356	−	0.107060i
$956$	1.73966			0.0562645
$957$		0			0
$958$	48.3966			1.56362
$959$	−4.21254	+	3.06059i	−0.136030	+	0.0988316i
$960$		0			0
$961$	7.70506	−	23.7137i	0.248550	−	0.764959i
$962$	−0.493534	−	0.358573i	−0.0159122	−	0.0115609i
$963$		0			0
$964$	0.471350	−	1.45067i	0.0151812	−	0.0467228i
$965$	−0.488605	−	1.50377i	−0.0157288	−	0.0484081i
$966$		0			0
$967$	31.4791			1.01230			0.506150	−	0.862445i	$-0.331068\pi$
$967$	31.4791			1.01230			0.506150	+	0.862445i	$0.331068\pi$
$968$	−24.0449	+	22.0034i	−0.772831	+	0.707217i
$969$		0			0
$970$	−7.48078	+	5.43511i	−0.240193	+	0.174511i
$971$	10.6540	+	32.7896i	0.341903	+	1.05227i	0.963221	+	0.268711i	$0.0865975\pi$
$971$	10.6540	+	32.7896i	0.341903	+	1.05227i	−0.621318	+	0.783559i	$0.713402\pi$
$972$		0			0
$973$	−14.6822	−	10.6673i	−0.470691	−	0.341977i
$974$	−5.78958	−	4.20638i	−0.185510	−	0.134781i
$975$		0			0
$976$	−8.18993	−	25.2060i	−0.262153	−	0.806825i
$977$	4.46523	−	3.24418i	0.142855	−	0.103790i	−0.514062	−	0.857753i	$-0.671860\pi$
$977$	4.46523	−	3.24418i	0.142855	−	0.103790i	0.656918	+	0.753962i	$0.271860\pi$
$978$		0			0
$979$	9.29325	−	14.4373i	0.297014	−	0.461420i
$980$	−0.194119			−0.00620090
$981$		0			0
$982$	−9.50159	−	29.2429i	−0.303208	−	0.933178i
$983$	10.1999	−	31.3921i	0.325327	−	1.00125i	−0.645966	−	0.763366i	$-0.723545\pi$
$983$	10.1999	−	31.3921i	0.325327	−	1.00125i	0.971293	−	0.237887i	$-0.0764547\pi$
$984$		0			0
$985$	−4.84458	−	3.51980i	−0.154361	−	0.112150i
$986$	−3.93949	+	12.1245i	−0.125459	+	0.386123i
$987$		0			0
$988$	−0.0404968	+	0.0294226i	−0.00128837	+	0.000936059i
$989$	10.7431			0.341610
$990$		0			0
$991$	−40.9399			−1.30050			−0.650249	−	0.759721i	$-0.725335\pi$
$991$	−40.9399			−1.30050			−0.650249	+	0.759721i	$0.725335\pi$
$992$	−7.57222	+	5.50154i	−0.240418	+	0.174674i
$993$		0			0
$994$	−4.63527	+	14.2659i	−0.147022	+	0.452486i
$995$	3.58449	+	2.60428i	0.113636	+	0.0825614i
$996$		0			0
$997$	−11.7054	+	36.0256i	−0.370714	+	1.14094i	0.575611	+	0.817724i	$0.304764\pi$
$997$	−11.7054	+	36.0256i	−0.370714	+	1.14094i	−0.946325	+	0.323217i	$0.895236\pi$
$998$	13.6538	+	42.0220i	0.432202	+	1.33018i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.j.190.2		20
3.2	odd	2		231.2.j.g.190.4	yes	20
11.2	odd	10		7623.2.a.cy.1.4		10
11.4	even	5	inner	693.2.m.j.631.2		20
11.9	even	5		7623.2.a.cx.1.7		10
33.2	even	10		2541.2.a.br.1.7		10
33.20	odd	10		2541.2.a.bq.1.4		10
33.26	odd	10		231.2.j.g.169.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.4	✓	20	33.26	odd	10
231.2.j.g.190.4	yes	20	3.2	odd	2
693.2.m.j.190.2		20	1.1	even	1	trivial
693.2.m.j.631.2		20	11.4	even	5	inner
2541.2.a.bq.1.4		10	33.20	odd	10
2541.2.a.br.1.7		10	33.2	even	10
7623.2.a.cx.1.7		10	11.9	even	5
7623.2.a.cy.1.4		10	11.2	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07866 + 0.783695i) q^{2} +(-0.0686960 + 0.211425i) q^{4} +(-0.706442 - 0.513260i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.915619 - 2.81798i) q^{8} +O(q^{10})\)	\(q+(-1.07866 + 0.783695i) q^{2} +(-0.0686960 + 0.211425i) q^{4} +(-0.706442 - 0.513260i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.915619 - 2.81798i) q^{8} +1.16425 q^{10} +(-1.79514 + 2.78881i) q^{11} +(-0.0319918 + 0.0232434i) q^{13} +(-0.412013 - 1.26805i) q^{14} +(2.83639 + 2.06076i) q^{16} +(1.65552 + 1.20280i) q^{17} +(-1.75961 - 5.41551i) q^{19} +(0.157046 - 0.114100i) q^{20} +(-0.249220 - 4.41504i) q^{22} -5.97870 q^{23} +(-1.30946 - 4.03011i) q^{25} +(0.0162926 - 0.0501436i) q^{26} +(-0.179849 - 0.130668i) q^{28} +(1.44389 - 4.44385i) q^{29} +(-6.05057 + 4.39599i) q^{31} +1.25149 q^{32} -2.72838 q^{34} +(0.706442 - 0.513260i) q^{35} +(3.57546 - 11.0041i) q^{37} +(6.14214 + 4.46252i) q^{38} +(-0.799528 + 2.46069i) q^{40} +(1.90009 + 5.84788i) q^{41} -1.79689 q^{43} +(-0.466304 - 0.571118i) q^{44} +(6.44901 - 4.68548i) q^{46} +(-1.86885 - 5.75173i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(4.57084 + 3.32091i) q^{50} +(-0.00271652 - 0.00836058i) q^{52} +(-0.100643 + 0.0731211i) q^{53} +(2.69955 - 1.04876i) q^{55} +2.96300 q^{56} +(1.92515 + 5.92499i) q^{58} +(4.43316 - 13.6439i) q^{59} +(-6.11572 - 4.44333i) q^{61} +(3.08141 - 9.48360i) q^{62} +(-7.02272 + 5.10230i) q^{64} +0.0345302 q^{65} +4.85938 q^{67} +(-0.368030 + 0.267389i) q^{68} +(-0.359774 + 1.10727i) q^{70} +(-9.10168 - 6.61275i) q^{71} +(0.189413 - 0.582954i) q^{73} +(4.76718 + 14.6719i) q^{74} +1.26585 q^{76} +(-2.09759 - 2.56907i) q^{77} +(0.125581 - 0.0912401i) q^{79} +(-0.946040 - 2.91161i) q^{80} +(-6.63251 - 4.81880i) q^{82} +(7.21319 + 5.24069i) q^{83} +(-0.552176 - 1.69942i) q^{85} +(1.93824 - 1.40822i) q^{86} +(9.50249 + 2.50520i) q^{88} -5.17689 q^{89} +(-0.0122198 - 0.0376086i) q^{91} +(0.410713 - 1.26404i) q^{92} +(6.52347 + 4.73958i) q^{94} +(-1.53651 + 4.72888i) q^{95} +(-6.42539 + 4.66832i) q^{97} +1.33330 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

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