LMFDB - Embedded newform 693.2.m.g.190.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.1
Root			$0.453245 - 1.39494i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.g.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18661 + 0.862123i) q^{2} +(0.0467549 - 0.143897i) q^{4} +(0.377594 + 0.274338i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.837913 - 2.57883i) q^{8} +O(q^{10})$	\(q+(-1.18661 + 0.862123i) q^{2} +(0.0467549 - 0.143897i) q^{4} +(0.377594 + 0.274338i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.837913 - 2.57883i) q^{8} -0.684570 q^{10} +(2.22899 - 2.45593i) q^{11} +(1.28012 - 0.930062i) q^{13} +(-0.453245 - 1.39494i) q^{14} +(3.46236 + 2.51555i) q^{16} +(4.22899 + 3.07254i) q^{17} +(1.30464 + 4.01528i) q^{19} +(0.0571308 - 0.0415079i) q^{20} +(-0.527635 + 4.83590i) q^{22} +1.80505 q^{23} +(-1.47777 - 4.54811i) q^{25} +(-0.717177 + 2.20724i) q^{26} +(0.122406 + 0.0889332i) q^{28} +(-0.840363 + 2.58637i) q^{29} +(-1.04675 + 0.760512i) q^{31} -0.854102 q^{32} -7.66708 q^{34} +(-0.377594 + 0.274338i) q^{35} +(-0.600175 + 1.84715i) q^{37} +(-5.00978 - 3.63982i) q^{38} +(0.391081 - 1.20362i) q^{40} +(0.321724 + 0.990166i) q^{41} +8.70820 q^{43} +(-0.249184 - 0.435572i) q^{44} +(-2.14190 + 1.55618i) q^{46} +(1.97626 + 6.08229i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(5.67457 + 4.12281i) q^{50} +(-0.0739811 - 0.227690i) q^{52} +(-10.6826 + 7.76137i) q^{53} +(1.51541 - 0.315846i) q^{55} +2.71154 q^{56} +(-1.23259 - 3.79351i) q^{58} +(2.65875 - 8.18278i) q^{59} +(12.3295 + 8.95793i) q^{61} +(0.586436 - 1.80486i) q^{62} +(-5.91123 + 4.29476i) q^{64} +0.738517 q^{65} -4.67583 q^{67} +(0.639856 - 0.464883i) q^{68} +(0.211544 - 0.651065i) q^{70} +(7.88234 + 5.72685i) q^{71} +(-4.11611 + 12.6681i) q^{73} +(-0.880296 - 2.70927i) q^{74} +0.638786 q^{76} +(1.64693 + 2.87882i) q^{77} +(-2.89815 + 2.10563i) q^{79} +(0.617255 + 1.89971i) q^{80} +(-1.23541 - 0.897575i) q^{82} +(-13.9627 - 10.1445i) q^{83} +(0.753927 + 2.32035i) q^{85} +(-10.3333 + 7.50755i) q^{86} +(-8.20113 - 3.69034i) q^{88} +8.91982 q^{89} +(0.488963 + 1.50487i) q^{91} +(0.0843952 - 0.259742i) q^{92} +(-7.58873 - 5.51353i) q^{94} +(-0.608919 + 1.87406i) q^{95} +(2.18727 - 1.58915i) q^{97} +1.46673 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) $ 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8	$ 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{13} - q^{14} - 3 q^{16} + 11 q^{17} - 9 q^{19} - 21 q^{20} - q^{22} + 16 q^{23} + 5 q^{25} - 21 q^{26} + 7 q^{28} + 9 q^{29} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 6 q^{37} - 35 q^{38} - 16 q^{40} + 22 q^{41} + 16 q^{43} - 29 q^{44} + 29 q^{46} - 7 q^{47} - 2 q^{49} + 34 q^{50} + 21 q^{52} - 2 q^{53} + 26 q^{55} + 18 q^{56} - 39 q^{58} - 25 q^{59} + 7 q^{61} + 5 q^{62} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} - 2 q^{70} + 14 q^{71} + 3 q^{73} + 9 q^{74} - 52 q^{76} + 5 q^{77} - 9 q^{79} + 33 q^{80} + 31 q^{82} - 23 q^{83} - 10 q^{85} + 17 q^{86} - 7 q^{88} + 34 q^{89} + 5 q^{91} + 34 q^{92} - 30 q^{94} - 24 q^{95} + 30 q^{97} - 4 q^{98}+O(q^{100}) $ 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^13 - q^14 - 3 * q^16 + 11 * q^17 - 9 * q^19 - 21 * q^20 - q^22 + 16 * q^23 + 5 * q^25 - 21 * q^26 + 7 * q^28 + 9 * q^29 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 6 * q^37 - 35 * q^38 - 16 * q^40 + 22 * q^41 + 16 * q^43 - 29 * q^44 + 29 * q^46 - 7 * q^47 - 2 * q^49 + 34 * q^50 + 21 * q^52 - 2 * q^53 + 26 * q^55 + 18 * q^56 - 39 * q^58 - 25 * q^59 + 7 * q^61 + 5 * q^62 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 - 2 * q^70 + 14 * q^71 + 3 * q^73 + 9 * q^74 - 52 * q^76 + 5 * q^77 - 9 * q^79 + 33 * q^80 + 31 * q^82 - 23 * q^83 - 10 * q^85 + 17 * q^86 - 7 * q^88 + 34 * q^89 + 5 * q^91 + 34 * q^92 - 30 * q^94 - 24 * q^95 + 30 * q^97 - 4 * q^98

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 $

$2$	−1.18661	+	0.862123i	−0.839061	+	0.609613i	−0.922108	−	0.386932i	$-0.873535\pi$
$2$	−1.18661	+	0.862123i	−0.839061	+	0.609613i	0.0830475	+	0.996546i	$0.473535\pi$
$3$		0			0
$3$		0			0
$4$	0.0467549	−	0.143897i	0.0233775	−	0.0719485i
$5$	0.377594	+	0.274338i	0.168865	+	0.122688i	0.669008	−	0.743255i	$-0.266719\pi$
$5$	0.377594	+	0.274338i	0.168865	+	0.122688i	−0.500143	+	0.865943i	$0.666719\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.837913	−	2.57883i	−0.296247	−	0.911755i
$9$		0			0
$10$	−0.684570			−0.216480
$11$	2.22899	−	2.45593i	0.672067	−	0.740490i
$11$	2.22899	−	2.45593i	0.672067	−	0.740490i
$12$		0			0
$13$	1.28012	−	0.930062i	0.355042	−	0.257953i	−0.395939	−	0.918277i	$-0.629581\pi$
$13$	1.28012	−	0.930062i	0.355042	−	0.257953i	0.750981	+	0.660324i	$0.229581\pi$
$14$	−0.453245	−	1.39494i	−0.121135	−	0.372815i
$15$		0			0
$16$	3.46236	+	2.51555i	0.865590	+	0.628888i
$17$	4.22899	+	3.07254i	1.02568	+	0.745201i	0.967440	−	0.253101i	$-0.0814505\pi$
$17$	4.22899	+	3.07254i	1.02568	+	0.745201i	0.0582418	+	0.998303i	$0.481451\pi$
$18$		0			0
$19$	1.30464	+	4.01528i	0.299306	+	0.921169i	0.981741	+	0.190223i	$0.0609211\pi$
$19$	1.30464	+	4.01528i	0.299306	+	0.921169i	−0.682435	+	0.730946i	$0.739079\pi$
$20$	0.0571308	−	0.0415079i	0.0127748	−	0.00928146i
$21$		0			0
$22$	−0.527635	+	4.83590i	−0.112492	+	1.03102i
$23$	1.80505			0.376380			0.188190	−	0.982133i	$-0.439738\pi$
$23$	1.80505			0.376380			0.188190	+	0.982133i	$0.439738\pi$
$24$		0			0
$25$	−1.47777	−	4.54811i	−0.295554	−	0.909621i
$26$	−0.717177	+	2.20724i	−0.140650	+	0.432876i
$27$		0			0
$28$	0.122406	+	0.0889332i	0.0231326	+	0.0168068i
$29$	−0.840363	+	2.58637i	−0.156051	+	0.480277i	−0.998266	−	0.0588657i	$-0.981252\pi$
$29$	−0.840363	+	2.58637i	−0.156051	+	0.480277i	0.842215	+	0.539143i	$0.181252\pi$
$30$		0			0
$31$	−1.04675	+	0.760512i	−0.188003	+	0.136592i	−0.677805	−	0.735241i	$-0.737069\pi$
$31$	−1.04675	+	0.760512i	−0.188003	+	0.136592i	0.489803	+	0.871833i	$0.337069\pi$
$32$	−0.854102			−0.150985
$33$		0			0
$34$	−7.66708			−1.31489
$35$	−0.377594	+	0.274338i	−0.0638250	+	0.0463716i
$36$		0			0
$37$	−0.600175	+	1.84715i	−0.0986682	+	0.303669i	−0.988192	−	0.153219i	$-0.951036\pi$
$37$	−0.600175	+	1.84715i	−0.0986682	+	0.303669i	0.889524	+	0.456888i	$0.151036\pi$
$38$	−5.00978	−	3.63982i	−0.812693	−	0.590456i
$39$		0			0
$40$	0.391081	−	1.20362i	0.0618353	−	0.190309i
$41$	0.321724	+	0.990166i	0.0502449	+	0.154638i	0.973031	−	0.230675i	$-0.0740935\pi$
$41$	0.321724	+	0.990166i	0.0502449	+	0.154638i	−0.922786	+	0.385313i	$0.874093\pi$
$42$		0			0
$43$	8.70820			1.32799			0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820			1.32799			0.663994	+	0.747738i	$0.268860\pi$
$44$	−0.249184	−	0.435572i	−0.0375659	−	0.0656650i
$45$		0			0
$46$	−2.14190	+	1.55618i	−0.315805	+	0.229446i
$47$	1.97626	+	6.08229i	0.288266	+	0.887193i	0.985401	+	0.170252i	$0.0544582\pi$
$47$	1.97626	+	6.08229i	0.288266	+	0.887193i	−0.697134	+	0.716941i	$0.745542\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	5.67457	+	4.12281i	0.802505	+	0.583054i
$51$		0			0
$52$	−0.0739811	−	0.227690i	−0.0102593	−	0.0315750i
$53$	−10.6826	+	7.76137i	−1.46737	+	1.06611i	−0.486004	+	0.873957i	$0.661546\pi$
$53$	−10.6826	+	7.76137i	−1.46737	+	1.06611i	−0.981366	+	0.192149i	$0.938454\pi$
$54$		0			0
$55$	1.51541	−	0.315846i	0.204338	−	0.0425887i
$56$	2.71154			0.362345
$57$		0			0
$58$	−1.23259	−	3.79351i	−0.161847	−	0.498112i
$59$	2.65875	−	8.18278i	0.346139	−	1.06531i	−0.614832	−	0.788658i	$-0.710776\pi$
$59$	2.65875	−	8.18278i	0.346139	−	1.06531i	0.960971	−	0.276649i	$-0.0892239\pi$
$60$		0			0
$61$	12.3295	+	8.95793i	1.57864	+	1.14695i	0.918237	+	0.396031i	$0.129613\pi$
$61$	12.3295	+	8.95793i	1.57864	+	1.14695i	0.660399	+	0.750915i	$0.270387\pi$
$62$	0.586436	−	1.80486i	0.0744774	−	0.229218i
$63$		0			0
$64$	−5.91123	+	4.29476i	−0.738904	+	0.536845i
$65$	0.738517			0.0916018
$66$		0			0
$67$	−4.67583			−0.571243			−0.285622	−	0.958342i	$-0.592200\pi$
$67$	−4.67583			−0.571243			−0.285622	+	0.958342i	$0.592200\pi$
$68$	0.639856	−	0.464883i	0.0775939	−	0.0563753i
$69$		0			0
$70$	0.211544	−	0.651065i	0.0252843	−	0.0778172i
$71$	7.88234	+	5.72685i	0.935461	+	0.679652i	0.947324	−	0.320277i	$-0.103776\pi$
$71$	7.88234	+	5.72685i	0.935461	+	0.679652i	−0.0118626	+	0.999930i	$0.503776\pi$
$72$		0			0
$73$	−4.11611	+	12.6681i	−0.481754	+	1.48269i	0.354873	+	0.934915i	$0.384524\pi$
$73$	−4.11611	+	12.6681i	−0.481754	+	1.48269i	−0.836627	+	0.547773i	$0.815476\pi$
$74$	−0.880296	−	2.70927i	−0.102332	−	0.314947i
$75$		0			0
$76$	0.638786			0.0732737
$77$	1.64693	+	2.87882i	0.187685	+	0.328072i
$78$		0			0
$79$	−2.89815	+	2.10563i	−0.326068	+	0.236902i	−0.738760	−	0.673968i	$-0.764588\pi$
$79$	−2.89815	+	2.10563i	−0.326068	+	0.236902i	0.412692	+	0.910870i	$0.364588\pi$
$80$	0.617255	+	1.89971i	0.0690112	+	0.212395i
$81$		0			0
$82$	−1.23541	−	0.897575i	−0.136428	−	0.0991206i
$83$	−13.9627	−	10.1445i	−1.53261	−	1.11351i	−0.954766	−	0.297357i	$-0.903895\pi$
$83$	−13.9627	−	10.1445i	−1.53261	−	1.11351i	−0.577842	−	0.816148i	$-0.696105\pi$
$84$		0			0
$85$	0.753927	+	2.32035i	0.0817748	+	0.251677i
$86$	−10.3333	+	7.50755i	−1.11426	+	0.809559i
$87$		0			0
$88$	−8.20113	−	3.69034i	−0.874243	−	0.393392i
$89$	8.91982			0.945499			0.472750	−	0.881197i	$-0.343262\pi$
$89$	8.91982			0.945499			0.472750	+	0.881197i	$0.343262\pi$
$90$		0			0
$91$	0.488963	+	1.50487i	0.0512572	+	0.157753i
$92$	0.0843952	−	0.259742i	0.00879881	−	0.0270799i
$93$		0			0
$94$	−7.58873	−	5.51353i	−0.782718	−	0.568678i
$95$	−0.608919	+	1.87406i	−0.0624738	+	0.192275i
$96$		0			0
$97$	2.18727	−	1.58915i	0.222084	−	0.161353i	−0.471180	−	0.882037i	$-0.656172\pi$
$97$	2.18727	−	1.58915i	0.222084	−	0.161353i	0.693264	+	0.720684i	$0.256172\pi$
$98$	1.46673			0.148162
$99$		0			0
$100$	−0.723551			−0.0723551
$101$	0.144637	−	0.105085i	0.0143919	−	0.0104563i	−0.580566	−	0.814213i	$-0.697169\pi$
$101$	0.144637	−	0.105085i	0.0143919	−	0.0104563i	0.594958	+	0.803757i	$0.297169\pi$
$102$		0			0
$103$	5.21535	−	16.0512i	0.513884	−	1.58157i	−0.271420	−	0.962461i	$-0.587493\pi$
$103$	5.21535	−	16.0512i	0.513884	−	1.58157i	0.785304	−	0.619111i	$-0.212507\pi$
$104$	−3.47110	−	2.52190i	−0.340370	−	0.247293i
$105$		0			0
$106$	5.98484	−	18.4195i	0.581299	−	1.78906i
$107$	4.78241	+	14.7188i	0.462333	+	1.42292i	0.862305	+	0.506389i	$0.169020\pi$
$107$	4.78241	+	14.7188i	0.462333	+	1.42292i	−0.399972	+	0.916527i	$0.630980\pi$
$108$		0			0
$109$	11.0349			1.05695			0.528476	−	0.848948i	$-0.322764\pi$
$109$	11.0349			1.05695			0.528476	+	0.848948i	$0.322764\pi$
$110$	−1.52590	+	1.68126i	−0.145489	+	0.160301i
$111$		0			0
$112$	−3.46236	+	2.51555i	−0.327162	+	0.237697i
$113$	−0.546984	−	1.68344i	−0.0514559	−	0.158365i	0.922027	−	0.387127i	$-0.126532\pi$
$113$	−0.546984	−	1.68344i	−0.0514559	−	0.158365i	−0.973482	+	0.228762i	$0.926532\pi$
$114$		0			0
$115$	0.681577	+	0.495195i	0.0635574	+	0.0461772i
$116$	0.332880	+	0.241851i	0.0309071	+	0.0224553i
$117$		0			0
$118$	3.89967	+	12.0019i	0.358994	+	1.10487i
$119$	−4.22899	+	3.07254i	−0.387671	+	0.281660i
$120$		0			0
$121$	−1.06317	−	10.9485i	−0.0966521	−	0.995318i
$122$	−22.3532			−2.02376
$123$		0			0
$124$	0.0604944	+	0.186183i	0.00543255	+	0.0167197i
$125$	1.41086	−	4.34219i	0.126191	−	0.388377i
$126$		0			0
$127$	6.90919	+	5.01982i	0.613092	+	0.445437i	0.850502	−	0.525972i	$-0.176298\pi$
$127$	6.90919	+	5.01982i	0.613092	+	0.445437i	−0.237410	+	0.971410i	$0.576298\pi$
$128$	3.83958	−	11.8170i	0.339374	−	1.04449i
$129$		0			0
$130$	−0.876333	+	0.636693i	−0.0768595	+	0.0558417i
$131$	9.66708			0.844617			0.422308	−	0.906452i	$-0.361220\pi$
$131$	9.66708			0.844617			0.422308	+	0.906452i	$0.361220\pi$
$132$		0			0
$133$	−4.22192			−0.366087
$134$	5.54839	−	4.03114i	0.479308	−	0.348237i
$135$		0			0
$136$	4.38004	−	13.4804i	0.375586	−	1.15593i
$137$	−11.3350	−	8.23535i	−0.968413	−	0.703593i	−0.0133236	−	0.999911i	$-0.504241\pi$
$137$	−11.3350	−	8.23535i	−0.968413	−	0.703593i	−0.955089	+	0.296318i	$0.904241\pi$
$138$		0			0
$139$	2.95966	−	9.10889i	0.251035	−	0.772606i	−0.743550	−	0.668680i	$-0.766860\pi$
$139$	2.95966	−	9.10889i	0.251035	−	0.772606i	0.994585	−	0.103926i	$-0.0331404\pi$
$140$	0.0218220	+	0.0671613i	0.00184430	+	0.00567616i
$141$		0			0
$142$	−14.2905			−1.19923
$143$	0.569215	−	5.21699i	0.0476001	−	0.436267i
$144$		0			0
$145$	−1.02686	+	0.746054i	−0.0852757	+	0.0619564i
$146$	−6.03723	−	18.5807i	−0.499645	−	1.53775i
$147$		0			0
$148$	0.237738	+	0.172727i	0.0195419	+	0.0141980i
$149$	12.1049	+	8.79474i	0.991674	+	0.720493i	0.960287	−	0.279014i	$-0.0900077\pi$
$149$	12.1049	+	8.79474i	0.991674	+	0.720493i	0.0313866	+	0.999507i	$0.490008\pi$
$150$		0			0
$151$	−0.887599	−	2.73175i	−0.0722318	−	0.222307i	0.908423	−	0.418053i	$-0.137287\pi$
$151$	−0.887599	−	2.73175i	−0.0722318	−	0.222307i	−0.980655	+	0.195746i	$0.937287\pi$
$152$	9.26156	−	6.72892i	0.751212	−	0.545787i
$153$		0			0
$154$	−4.43617	−	1.99619i	−0.357476	−	0.160857i
$155$	−0.603886			−0.0485053
$156$		0			0
$157$	−5.83496	−	17.9582i	−0.465680	−	1.43322i	−0.858125	−	0.513441i	$-0.828370\pi$
$157$	−5.83496	−	17.9582i	−0.465680	−	1.43322i	0.392444	−	0.919776i	$-0.371630\pi$
$158$	1.62367	−	4.99713i	0.129172	−	0.397551i
$159$		0			0
$160$	−0.322504	−	0.234313i	−0.0254962	−	0.0185240i
$161$	−0.557792	+	1.71671i	−0.0439602	+	0.135296i
$162$		0			0
$163$	−9.38067	+	6.81545i	−0.734751	+	0.533827i	−0.891063	−	0.453880i	$-0.850039\pi$
$163$	−9.38067	+	6.81545i	−0.734751	+	0.533827i	0.156312	+	0.987708i	$0.450039\pi$
$164$	0.157524			0.0123006
$165$		0			0
$166$	25.3142			1.96476
$167$	5.11696	−	3.71769i	0.395963	−	0.287684i	−0.371932	−	0.928260i	$-0.621305\pi$
$167$	5.11696	−	3.71769i	0.395963	−	0.287684i	0.767894	+	0.640576i	$0.221305\pi$
$168$		0			0
$169$	−3.24353	+	9.98255i	−0.249502	+	0.767889i
$170$	−2.89504	−	2.10337i	−0.222040	−	0.161321i
$171$		0			0
$172$	0.407152	−	1.25308i	0.0310450	−	0.0955467i
$173$	−0.413793	−	1.27352i	−0.0314601	−	0.0968243i	0.934093	−	0.357029i	$-0.116210\pi$
$173$	−0.413793	−	1.27352i	−0.0314601	−	0.0968243i	−0.965554	+	0.260204i	$0.916210\pi$
$174$		0			0
$175$	4.78216			0.361497
$176$	13.8956	−	2.89616i	1.04742	−	0.218306i
$177$		0			0
$178$	−10.5844	+	7.68999i	−0.793331	+	0.576389i
$179$	−5.49705	−	16.9182i	−0.410868	−	1.26452i	−0.915895	−	0.401419i	$-0.868517\pi$
$179$	−5.49705	−	16.9182i	−0.410868	−	1.26452i	0.505026	−	0.863104i	$-0.331483\pi$
$180$		0			0
$181$	0.779712	+	0.566494i	0.0579555	+	0.0421072i	0.616386	−	0.787444i	$-0.288596\pi$
$181$	0.779712	+	0.566494i	0.0579555	+	0.0421072i	−0.558430	+	0.829551i	$0.688596\pi$
$182$	−1.87759	−	1.36415i	−0.139177	−	0.101118i
$183$		0			0
$184$	−1.51248	−	4.65493i	−0.111501	−	0.343166i
$185$	−0.733366	+	0.532822i	−0.0539181	+	0.0391738i
$186$		0			0
$187$	16.9724	−	3.53743i	1.24114	−	0.258682i
$188$	0.967622			0.0705711
$189$		0			0
$190$	−0.893121	−	2.74874i	−0.0647938	−	0.199415i
$191$	4.97173	−	15.3014i	0.359742	−	1.10717i	−0.593467	−	0.804858i	$-0.702241\pi$
$191$	4.97173	−	15.3014i	0.359742	−	1.10717i	0.953209	−	0.302313i	$-0.0977586\pi$
$192$		0			0
$193$	−9.82750	−	7.14010i	−0.707399	−	0.513955i	0.174935	−	0.984580i	$-0.444029\pi$
$193$	−9.82750	−	7.14010i	−0.707399	−	0.513955i	−0.882333	+	0.470625i	$0.844029\pi$
$194$	−1.22540	+	3.77140i	−0.0879787	+	0.270771i
$195$		0			0
$196$	−0.122406	+	0.0889332i	−0.00874329	+	0.00635237i
$197$	2.30179			0.163996			0.0819978	−	0.996633i	$-0.473870\pi$
$197$	2.30179			0.163996			0.0819978	+	0.996633i	$0.473870\pi$
$198$		0			0
$199$	20.2797			1.43759			0.718795	−	0.695222i	$-0.244694\pi$
$199$	20.2797			1.43759			0.718795	+	0.695222i	$0.244694\pi$
$200$	−10.4906	+	7.62184i	−0.741794	+	0.538945i
$201$		0			0
$202$	−0.0810316	+	0.249390i	−0.00570136	+	0.0175470i
$203$	−2.20010	−	1.59846i	−0.154417	−	0.112190i
$204$		0			0
$205$	−0.150159	+	0.462142i	−0.0104876	+	0.0322774i
$206$	7.64952	+	23.5428i	0.532967	+	1.64030i
$207$		0			0
$208$	6.77186			0.469544
$209$	12.7693	+	5.74593i	0.883271	+	0.397454i
$210$		0			0
$211$	−4.34062	+	3.15364i	−0.298820	+	0.217106i	−0.727085	−	0.686548i	$-0.759125\pi$
$211$	−4.34062	+	3.15364i	−0.298820	+	0.217106i	0.428264	+	0.903654i	$0.359125\pi$
$212$	0.617372	+	1.90008i	0.0424013	+	0.130498i
$213$		0			0
$214$	−18.3642	−	13.3424i	−1.25535	−	0.912068i
$215$	3.28817	+	2.38899i	0.224251	+	0.162928i
$216$		0			0
$217$	−0.399825	−	1.23053i	−0.0271419	−	0.0835341i
$218$	−13.0941	+	9.51344i	−0.886847	+	0.644332i
$219$		0			0
$220$	0.0254036	−	0.232830i	0.00171271	−	0.0156974i
$221$	8.27128			0.556387
$222$		0			0
$223$	−7.85614	−	24.1787i	−0.526086	−	1.61913i	−0.762158	−	0.647391i	$-0.775860\pi$
$223$	−7.85614	−	24.1787i	−0.526086	−	1.61913i	0.236072	−	0.971736i	$-0.424140\pi$
$224$	0.263932	−	0.812299i	0.0176347	−	0.0542740i
$225$		0			0
$226$	2.10039	+	1.52602i	0.139716	+	0.101510i
$227$	6.70869	−	20.6472i	0.445271	−	1.37040i	−0.436915	−	0.899503i	$-0.643929\pi$
$227$	6.70869	−	20.6472i	0.445271	−	1.37040i	0.882186	−	0.470901i	$-0.156071\pi$
$228$		0			0
$229$	−16.6097	+	12.0676i	−1.09760	+	0.797451i	−0.980666	−	0.195689i	$-0.937306\pi$
$229$	−16.6097	+	12.0676i	−1.09760	+	0.797451i	−0.116931	+	0.993140i	$0.537306\pi$
$230$	−1.23569			−0.0814787
$231$		0			0
$232$	7.37396			0.484124
$233$	0.561503	−	0.407956i	0.0367853	−	0.0267261i	−0.569241	−	0.822171i	$-0.692763\pi$
$233$	0.561503	−	0.407956i	0.0367853	−	0.0267261i	0.606026	+	0.795445i	$0.292763\pi$
$234$		0			0
$235$	−0.922381	+	2.83880i	−0.0601695	+	0.185183i
$236$	−1.05317	−	0.765171i	−0.0685554	−	0.0498084i
$237$		0			0
$238$	2.36926	−	7.29183i	0.153576	−	0.472659i
$239$	−0.107093	−	0.329599i	−0.00692728	−	0.0213200i	0.947533	−	0.319658i	$-0.103568\pi$
$239$	−0.107093	−	0.329599i	−0.00692728	−	0.0213200i	−0.954460	+	0.298338i	$0.903568\pi$
$240$		0			0
$241$	−10.4372			−0.672317			−0.336158	−	0.941806i	$-0.609128\pi$
$241$	−10.4372			−0.672317			−0.336158	+	0.941806i	$0.609128\pi$
$242$	10.7005	+	12.0750i	0.687856	+	0.776212i
$243$		0			0
$244$	1.86549	−	1.35536i	0.119426	−	0.0867677i
$245$	−0.144228	−	0.443888i	−0.00921439	−	0.0283590i
$246$		0			0
$247$	5.40457	+	3.92665i	0.343884	+	0.249847i
$248$	2.83832	+	2.06216i	0.180234	+	0.130947i
$249$		0			0
$250$	2.06936	+	6.36882i	0.130878	+	0.402800i
$251$	−5.65909	+	4.11157i	−0.357199	+	0.259520i	−0.751883	−	0.659297i	$-0.770854\pi$
$251$	−5.65909	+	4.11157i	−0.357199	+	0.259520i	0.394684	+	0.918817i	$0.370854\pi$
$252$		0			0
$253$	4.02345	−	4.43308i	0.252952	−	0.278706i
$254$	−12.5262			−0.785965
$255$		0			0
$256$	1.11586	+	3.43426i	0.0697412	+	0.214641i
$257$	3.07423	−	9.46152i	0.191765	−	0.590193i	−0.808234	−	0.588862i	$-0.799576\pi$
$257$	3.07423	−	9.46152i	0.191765	−	0.590193i	0.999999	−	0.00133144i	$-0.000423809\pi$
$258$		0			0
$259$	−1.57128	−	1.14160i	−0.0976345	−	0.0709356i
$260$	0.0345293	−	0.106270i	0.00214142	−	0.00659061i
$261$		0			0
$262$	−11.4711	+	8.33422i	−0.708685	+	0.514890i
$263$	−14.1803			−0.874397			−0.437199	−	0.899365i	$-0.644029\pi$
$263$	−14.1803			−0.874397			−0.437199	+	0.899365i	$0.644029\pi$
$264$		0			0
$265$	−6.16293			−0.378586
$266$	5.00978	−	3.63982i	0.307169	−	0.223171i
$267$		0			0
$268$	−0.218618	+	0.672837i	−0.0133542	+	0.0411001i
$269$	−14.8884	−	10.8171i	−0.907762	−	0.659528i	0.0326859	−	0.999466i	$-0.489594\pi$
$269$	−14.8884	−	10.8171i	−0.907762	−	0.659528i	−0.940448	+	0.339938i	$0.889594\pi$
$270$		0			0
$271$	0.225765	−	0.694833i	0.0137142	−	0.0422081i	−0.943965	−	0.330045i	$-0.892936\pi$
$271$	0.225765	−	0.694833i	0.0137142	−	0.0422081i	0.957679	+	0.287837i	$0.0929361\pi$
$272$	6.91316	+	21.2765i	0.419172	+	1.29008i
$273$		0			0
$274$	20.5501			1.24148
$275$	−14.4638	−	6.50840i	−0.872198	−	0.392472i
$276$		0			0
$277$	−12.1874	+	8.85463i	−0.732267	+	0.532023i	−0.890280	−	0.455414i	$-0.849491\pi$
$277$	−12.1874	+	8.85463i	−0.732267	+	0.532023i	0.158013	+	0.987437i	$0.449491\pi$
$278$	4.34102	+	13.3603i	0.260357	+	0.801297i
$279$		0			0
$280$	1.02386	+	0.743880i	0.0611875	+	0.0444553i
$281$	−8.65334	−	6.28702i	−0.516215	−	0.375052i	0.298961	−	0.954265i	$-0.403360\pi$
$281$	−8.65334	−	6.28702i	−0.516215	−	0.375052i	−0.815176	+	0.579213i	$0.803360\pi$
$282$		0			0
$283$	2.81481	+	8.66308i	0.167323	+	0.514967i	0.999200	−	0.0399931i	$-0.0127336\pi$
$283$	2.81481	+	8.66308i	0.167323	+	0.514967i	−0.831877	+	0.554960i	$0.812734\pi$
$284$	1.19261	−	0.866485i	0.0707687	−	0.0514164i
$285$		0			0
$286$	3.82225	+	6.68127i	0.226014	+	0.395072i
$287$	−1.04112			−0.0614555
$288$		0			0
$289$	3.19057	+	9.81958i	0.187681	+	0.577622i
$290$	0.575287	−	1.77055i	0.0337820	−	0.103970i
$291$		0			0
$292$	1.63045	+	1.18459i	0.0954149	+	0.0693230i
$293$	−3.67390	+	11.3071i	−0.214632	+	0.660569i	0.784548	+	0.620068i	$0.212895\pi$
$293$	−3.67390	+	11.3071i	−0.214632	+	0.660569i	−0.999180	+	0.0405002i	$0.987105\pi$
$294$		0			0
$295$	3.24878	−	2.36037i	0.189151	−	0.137426i
$296$	5.26638			0.306102
$297$		0			0
$298$	−21.9460			−1.27130
$299$	2.31069	−	1.67881i	0.133630	−	0.0970882i
$300$		0			0
$301$	−2.69098	+	8.28199i	−0.155106	+	0.477366i
$302$	3.40834	+	2.47630i	0.196128	+	0.142495i
$303$		0			0
$304$	−5.58350	+	17.1843i	−0.320236	+	0.985585i
$305$	2.19806	+	6.76492i	0.125860	+	0.387358i
$306$		0			0
$307$	2.22072			0.126743			0.0633716	−	0.997990i	$-0.479815\pi$
$307$	2.22072			0.126743			0.0633716	+	0.997990i	$0.479815\pi$
$308$	0.491256	−	0.102389i	0.0279919	−	0.00583415i
$309$		0			0
$310$	0.716577	−	0.520624i	0.0406989	−	0.0295695i
$311$	6.61685	+	20.3646i	0.375207	+	1.15477i	0.943339	+	0.331831i	$0.107666\pi$
$311$	6.61685	+	20.3646i	0.375207	+	1.15477i	−0.568132	+	0.822937i	$0.692334\pi$
$312$		0			0
$313$	25.5283	+	18.5474i	1.44295	+	1.04836i	0.987416	+	0.158142i	$0.0505505\pi$
$313$	25.5283	+	18.5474i	1.44295	+	1.04836i	0.455531	+	0.890220i	$0.349450\pi$
$314$	22.4060	+	16.2789i	1.26444	+	0.918671i
$315$		0			0
$316$	0.167491	+	0.515484i	0.00942211	+	0.0289983i
$317$	−10.6796	+	7.75915i	−0.599824	+	0.435798i	−0.845816	−	0.533474i	$-0.820886\pi$
$317$	−10.6796	+	7.75915i	−0.599824	+	0.435798i	0.245992	+	0.969272i	$0.420886\pi$
$318$		0			0
$319$	4.47878	+	7.82887i	0.250763	+	0.438333i
$320$	−3.41026			−0.190639
$321$		0			0
$322$	−0.818132	−	2.51795i	−0.0455927	−	0.140320i
$323$	−6.81980	+	20.9892i	−0.379464	+	1.16787i
$324$		0			0
$325$	−6.12174	−	4.44771i	−0.339573	−	0.246714i
$326$	5.25544	−	16.1746i	0.291072	−	0.895827i
$327$		0			0
$328$	2.28389	−	1.65935i	0.126107	−	0.0916220i
$329$	−6.39530			−0.352584
$330$		0			0
$331$	9.47653			0.520877			0.260439	−	0.965490i	$-0.416133\pi$
$331$	9.47653			0.520877			0.260439	+	0.965490i	$0.416133\pi$
$332$	−2.11259	+	1.53489i	−0.115944	+	0.0842379i
$333$		0			0
$334$	−2.86674	+	8.82291i	−0.156861	+	0.482768i
$335$	−1.76556	−	1.28276i	−0.0964631	−	0.0700845i
$336$		0			0
$337$	−5.93346	+	18.2613i	−0.323216	+	0.994758i	0.649023	+	0.760769i	$0.275178\pi$
$337$	−5.93346	+	18.2613i	−0.323216	+	0.994758i	−0.972239	+	0.233989i	$0.924822\pi$
$338$	−4.75738	−	14.6417i	−0.258768	−	0.796405i
$339$		0			0
$340$	0.369141			0.0200195
$341$	−0.465447	+	4.26593i	−0.0252054	+	0.231013i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−7.29672	−	22.4570i	−0.393413	−	1.21080i
$345$		0			0
$346$	1.58895	+	1.15444i	0.0854223	+	0.0620629i
$347$	2.46613	+	1.79175i	0.132389	+	0.0961862i	0.652009	−	0.758211i	$-0.273926\pi$
$347$	2.46613	+	1.79175i	0.132389	+	0.0961862i	−0.519620	+	0.854397i	$0.673926\pi$
$348$		0			0
$349$	5.99373	+	18.4468i	0.320837	+	0.987435i	0.973285	+	0.229601i	$0.0737421\pi$
$349$	5.99373	+	18.4468i	0.320837	+	0.987435i	−0.652448	+	0.757834i	$0.726258\pi$
$350$	−5.67457	+	4.12281i	−0.303318	+	0.220374i
$351$		0			0
$352$	−1.90379	+	2.09761i	−0.101472	+	0.111803i
$353$	10.7585			0.572619			0.286309	−	0.958137i	$-0.407572\pi$
$353$	10.7585			0.572619			0.286309	+	0.958137i	$0.407572\pi$
$354$		0			0
$355$	1.40523	+	4.32485i	0.0745818	+	0.229539i
$356$	0.417046	−	1.28353i	0.0221034	−	0.0680272i
$357$		0			0
$358$	21.1084	+	15.3361i	1.11561	+	0.810541i
$359$	−0.187643	+	0.577506i	−0.00990342	+	0.0304796i	−0.955886	−	0.293738i	$-0.905101\pi$
$359$	−0.187643	+	0.577506i	−0.00990342	+	0.0304796i	0.945983	+	0.324217i	$0.105101\pi$
$360$		0			0
$361$	0.950914	−	0.690879i	0.0500481	−	0.0363621i
$362$	−1.41360			−0.0742973
$363$		0			0
$364$	0.239408			0.0125484
$365$	−5.02956	+	3.65419i	−0.263259	+	0.191269i
$366$		0			0
$367$	8.54829	−	26.3089i	0.446217	−	1.37332i	−0.434926	−	0.900466i	$-0.643226\pi$
$367$	8.54829	−	26.3089i	0.446217	−	1.37332i	0.881143	−	0.472849i	$-0.156774\pi$
$368$	6.24975	+	4.54071i	0.325791	+	0.236701i
$369$		0			0
$370$	0.410862	−	1.26450i	0.0213597	−	0.0657384i
$371$	−4.08039	−	12.5582i	−0.211843	−	0.651987i
$372$		0			0
$373$	−29.4513			−1.52493			−0.762465	−	0.647029i	$-0.776011\pi$
$373$	−29.4513			−1.52493			−0.762465	+	0.647029i	$0.776011\pi$
$374$	−17.0899	+	18.8298i	−0.883697	+	0.973666i
$375$		0			0
$376$	14.0293	−	10.1929i	0.723504	−	0.525657i
$377$	1.32972	+	4.09246i	0.0684840	+	0.210772i
$378$		0			0
$379$	−20.5034	−	14.8966i	−1.05319	−	0.765188i	−0.0803745	−	0.996765i	$-0.525612\pi$
$379$	−20.5034	−	14.8966i	−1.05319	−	0.765188i	−0.972817	+	0.231577i	$0.925612\pi$
$380$	0.241202	+	0.175243i	0.0123734	+	0.00898979i
$381$		0			0
$382$	7.29219	+	22.4431i	0.373101	+	1.14829i
$383$	−25.8337	+	18.7693i	−1.32004	+	0.959065i	−0.320108	+	0.947381i	$0.603719\pi$
$383$	−25.8337	+	18.7693i	−1.32004	+	0.959065i	−0.999932	+	0.0116837i	$0.996281\pi$
$384$		0			0
$385$	−0.167900	+	1.53884i	−0.00855697	+	0.0784266i
$386$	17.8171			0.906865
$387$		0			0
$388$	−0.126407	−	0.389042i	−0.00641737	−	0.0197506i
$389$	−5.48558	+	16.8829i	−0.278130	+	0.855996i	0.710244	+	0.703955i	$0.248584\pi$
$389$	−5.48558	+	16.8829i	−0.278130	+	0.855996i	−0.988374	+	0.152040i	$0.951416\pi$
$390$		0			0
$391$	7.63356	+	5.54611i	0.386046	+	0.280479i
$392$	−0.837913	+	2.57883i	−0.0423210	+	0.130251i
$393$		0			0
$394$	−2.73133	+	1.98442i	−0.137602	+	0.0999738i
$395$	−1.67198			−0.0841265
$396$		0			0
$397$	−13.3047			−0.667742			−0.333871	−	0.942619i	$-0.608355\pi$
$397$	−13.3047			−0.667742			−0.333871	+	0.942619i	$0.608355\pi$
$398$	−24.0641	+	17.4836i	−1.20623	+	0.876374i
$399$		0			0
$400$	6.32443	−	19.4646i	0.316221	−	0.973229i
$401$	−2.82317	−	2.05115i	−0.140982	−	0.102430i	0.515059	−	0.857155i	$-0.327770\pi$
$401$	−2.82317	−	2.05115i	−0.140982	−	0.102430i	−0.656041	+	0.754725i	$0.727770\pi$
$402$		0			0
$403$	−0.632649	+	1.94709i	−0.0315145	+	0.0969917i
$404$	−0.00835890	−	0.0257260i	−0.000415871	−	0.00127992i
$405$		0			0
$406$	3.98873			0.197958
$407$	3.19868	+	5.59127i	0.158553	+	0.277149i
$408$		0			0
$409$	23.9675	−	17.4134i	1.18512	−	0.861039i	0.192379	−	0.981321i	$-0.438380\pi$
$409$	23.9675	−	17.4134i	1.18512	−	0.861039i	0.992740	+	0.120282i	$0.0383799\pi$
$410$	−0.220243	−	0.677838i	−0.0108770	−	0.0334760i
$411$		0			0
$412$	−2.06587	−	1.50095i	−0.101778	−	0.0739463i
$413$	6.96069	+	5.05724i	0.342513	+	0.248850i
$414$		0			0
$415$	−2.48922	−	7.66102i	−0.122191	−	0.376065i
$416$	−1.09335	+	0.794368i	−0.0536061	+	0.0389471i
$417$		0			0
$418$	−20.1059	+	4.19053i	−0.983411	+	0.204965i
$419$	11.6452			0.568907			0.284454	−	0.958690i	$-0.408188\pi$
$419$	11.6452			0.568907			0.284454	+	0.958690i	$0.408188\pi$
$420$		0			0
$421$	6.14475	+	18.9116i	0.299477	+	0.921696i	0.981681	+	0.190533i	$0.0610217\pi$
$421$	6.14475	+	18.9116i	0.299477	+	0.921696i	−0.682204	+	0.731162i	$0.738978\pi$
$422$	2.43179	−	7.48429i	0.118378	−	0.364330i
$423$		0			0
$424$	28.9664	+	21.0453i	1.40673	+	1.02205i
$425$	7.72478	−	23.7744i	0.374707	−	1.15323i
$426$		0			0
$427$	−12.3295	+	8.95793i	−0.596668	+	0.433505i
$428$	2.34159			0.113185
$429$		0			0
$430$	−5.96138			−0.287483
$431$	24.4698	−	17.7784i	1.17867	−	0.856354i	0.186649	−	0.982427i	$-0.440237\pi$
$431$	24.4698	−	17.7784i	1.17867	−	0.856354i	0.992021	+	0.126073i	$0.0402372\pi$
$432$		0			0
$433$	−1.76362	+	5.42786i	−0.0847542	+	0.260846i	−0.984448	−	0.175674i	$-0.943789\pi$
$433$	−1.76362	+	5.42786i	−0.0847542	+	0.260846i	0.899694	+	0.436521i	$0.143789\pi$
$434$	1.53531	+	1.11547i	0.0736972	+	0.0535441i
$435$		0			0
$436$	0.515936	−	1.58789i	0.0247089	−	0.0760461i
$437$	2.35495	+	7.24780i	0.112653	+	0.346709i
$438$		0			0
$439$	6.84875			0.326873			0.163436	−	0.986554i	$-0.447742\pi$
$439$	6.84875			0.326873			0.163436	+	0.986554i	$0.447742\pi$
$440$	−2.08430	−	3.64333i	−0.0993649	−	0.173689i
$441$		0			0
$442$	−9.81479	+	7.13086i	−0.466842	+	0.339181i
$443$	−0.0311165	−	0.0957668i	−0.00147839	−	0.00455002i	0.950315	−	0.311291i	$-0.100761\pi$
$443$	−0.0311165	−	0.0957668i	−0.00147839	−	0.00455002i	−0.951793	+	0.306741i	$0.900761\pi$
$444$		0			0
$445$	3.36807	+	2.44705i	0.159662	+	0.116001i
$446$	30.1672	+	21.9178i	1.42846	+	1.03784i
$447$		0			0
$448$	−2.25789	−	6.94907i	−0.106675	−	0.328313i
$449$	−24.9216	+	18.1066i	−1.17612	+	0.854502i	−0.991729	−	0.128351i	$-0.959032\pi$
$449$	−24.9216	+	18.1066i	−1.17612	+	0.854502i	−0.184392	+	0.982853i	$0.559032\pi$
$450$		0			0
$451$	3.14890	+	1.41694i	0.148276	+	0.0667211i
$452$	−0.267817			−0.0125970
$453$		0			0
$454$	9.83984	+	30.2839i	0.461807	+	1.42129i
$455$	−0.228214	+	0.702372i	−0.0106989	+	0.0329277i
$456$		0			0
$457$	−18.7171	−	13.5987i	−0.875547	−	0.636122i	0.0565223	−	0.998401i	$-0.481999\pi$
$457$	−18.7171	−	13.5987i	−0.875547	−	0.636122i	−0.932070	+	0.362279i	$0.881999\pi$
$458$	9.30542	−	28.6392i	0.434814	−	1.33822i
$459$		0			0
$460$	0.103124	−	0.0749241i	0.00480819	−	0.00349335i
$461$	2.77839			0.129403			0.0647013	−	0.997905i	$-0.479391\pi$
$461$	2.77839			0.129403			0.0647013	+	0.997905i	$0.479391\pi$
$462$		0			0
$463$	−26.0950			−1.21274			−0.606369	−	0.795184i	$-0.707374\pi$
$463$	−26.0950			−1.21274			−0.606369	+	0.795184i	$0.707374\pi$
$464$	−9.41578	+	6.84097i	−0.437117	+	0.317584i
$465$		0			0
$466$	−0.314577	+	0.968169i	−0.0145725	+	0.0448496i
$467$	−2.15060	−	1.56250i	−0.0995180	−	0.0723041i	0.536913	−	0.843637i	$-0.319590\pi$
$467$	−2.15060	−	1.56250i	−0.0995180	−	0.0723041i	−0.636431	+	0.771333i	$0.719590\pi$
$468$		0			0
$469$	1.44491	−	4.44698i	0.0667197	−	0.205342i
$470$	−1.35289	−	4.16375i	−0.0624040	−	0.192060i
$471$		0			0
$472$	−23.3298			−1.07384
$473$	19.4105	−	21.3867i	0.892497	−	0.983363i
$474$		0			0
$475$	16.3340	−	11.8673i	0.749454	−	0.544510i
$476$	0.244403	+	0.752196i	0.0112022	+	0.0344768i
$477$		0			0
$478$	0.411233	+	0.298778i	0.0188093	+	0.0136658i
$479$	−6.70047	−	4.86818i	−0.306152	−	0.222433i	0.424091	−	0.905619i	$-0.360593\pi$
$479$	−6.70047	−	4.86818i	−0.306152	−	0.222433i	−0.730244	+	0.683187i	$0.760593\pi$
$480$		0			0
$481$	0.949667	+	2.92277i	0.0433011	+	0.133267i
$482$	12.3848	−	8.99812i	0.564114	−	0.409853i
$483$		0			0
$484$	−1.62516	−	0.358909i	−0.0738711	−	0.0163141i
$485$	1.26186			0.0572983
$486$		0			0
$487$	−6.05536	−	18.6365i	−0.274395	−	0.844500i	−0.989379	−	0.145360i	$-0.953566\pi$
$487$	−6.05536	−	18.6365i	−0.274395	−	0.844500i	0.714984	−	0.699141i	$-0.246434\pi$
$488$	12.7699	−	39.3018i	0.578067	−	1.77911i
$489$		0			0
$490$	0.553829	+	0.402380i	0.0250194	+	0.0181777i
$491$	8.86312	−	27.2779i	0.399987	−	1.23103i	−0.525022	−	0.851089i	$-0.675943\pi$
$491$	8.86312	−	27.2779i	0.399987	−	1.23103i	0.925009	−	0.379945i	$-0.124057\pi$
$492$		0			0
$493$	−11.5006	+	8.35569i	−0.517962	+	0.376321i
$494$	−9.79837			−0.440850
$495$		0			0
$496$	−5.53735			−0.248634
$497$	−7.88234	+	5.72685i	−0.353571	+	0.256884i
$498$		0			0
$499$	8.63700	−	26.5819i	0.386645	−	1.18997i	−0.548635	−	0.836062i	$-0.684852\pi$
$499$	8.63700	−	26.5819i	0.386645	−	1.18997i	0.935280	−	0.353909i	$-0.115148\pi$
$500$	−0.558863	−	0.406037i	−0.0249931	−	0.0181585i
$501$		0			0
$502$	3.17046	−	9.75767i	0.141505	−	0.435506i
$503$	2.50222	+	7.70104i	0.111568	+	0.343373i	0.991216	−	0.132254i	$-0.0422214\pi$
$503$	2.50222	+	7.70104i	0.111568	+	0.343373i	−0.879647	+	0.475626i	$0.842221\pi$
$504$		0			0
$505$	0.0834428			0.00371316
$506$	−0.952410	+	8.72906i	−0.0423398	+	0.388054i
$507$		0			0
$508$	1.04538	−	0.759510i	0.0463811	−	0.0336978i
$509$	−5.03702	−	15.5024i	−0.223262	−	0.687130i	−0.998463	−	0.0554159i	$-0.982352\pi$
$509$	−5.03702	−	15.5024i	−0.223262	−	0.687130i	0.775201	−	0.631714i	$-0.217648\pi$
$510$		0			0
$511$	−10.7761	−	7.82931i	−0.476707	−	0.346348i
$512$	15.8195	+	11.4935i	0.699129	+	0.507947i
$513$		0			0
$514$	4.50908	+	13.8775i	0.198887	+	0.612111i
$515$	6.37274	−	4.63007i	0.280816	−	0.204025i
$516$		0			0
$517$	19.3427	+	8.70384i	0.850692	+	0.382795i
$518$	2.84870			0.125165
$519$		0			0
$520$	−0.618813	−	1.90451i	−0.0271368	−	0.0835184i
$521$	−2.37512	+	7.30987i	−0.104056	+	0.320251i	−0.989508	−	0.144480i	$-0.953849\pi$
$521$	−2.37512	+	7.30987i	−0.104056	+	0.320251i	0.885452	+	0.464731i	$0.153849\pi$
$522$		0			0
$523$	−21.1339	−	15.3547i	−0.924121	−	0.671413i	0.0204256	−	0.999791i	$-0.493498\pi$
$523$	−21.1339	−	15.3547i	−0.924121	−	0.671413i	−0.944546	+	0.328378i	$0.893498\pi$
$524$	0.451984	−	1.39106i	0.0197450	−	0.0607689i
$525$		0			0
$526$	16.8265	−	12.2252i	0.733672	−	0.533044i
$527$	−6.76343			−0.294619
$528$		0			0
$529$	−19.7418			−0.858338
$530$	7.31300	−	5.31320i	0.317656	−	0.230791i
$531$		0			0
$532$	−0.197396	+	0.607521i	−0.00855819	+	0.0263394i
$533$	1.33276	+	0.968308i	0.0577283	+	0.0419421i
$534$		0			0
$535$	−2.23210	+	6.86971i	−0.0965023	+	0.297004i
$536$	3.91794	+	12.0582i	0.169229	+	0.520834i
$537$		0			0
$538$	26.9924			1.16372
$539$	−3.24685	+	0.676718i	−0.139852	+	0.0291483i
$540$		0			0
$541$	20.9355	−	15.2105i	0.900086	−	0.653951i	−0.0384021	−	0.999262i	$-0.512227\pi$
$541$	20.9355	−	15.2105i	0.900086	−	0.653951i	0.938488	+	0.345312i	$0.112227\pi$
$542$	0.331137	+	1.01913i	0.0142235	+	0.0437756i
$543$		0			0
$544$	−3.61199	−	2.62427i	−0.154863	−	0.112514i
$545$	4.16671	+	3.02729i	0.178482	+	0.129675i
$546$		0			0
$547$	−11.7726	−	36.2322i	−0.503359	−	1.54918i	−0.803513	−	0.595288i	$-0.797038\pi$
$547$	−11.7726	−	36.2322i	−0.503359	−	1.54918i	0.300154	−	0.953891i	$-0.402962\pi$
$548$	−1.71501	+	1.24603i	−0.0732615	+	0.0532276i
$549$		0			0
$550$	22.7739	−	4.74660i	0.971083	−	0.202396i
$551$	−11.4814			−0.489123
$552$		0			0
$553$	−1.10700	−	3.40699i	−0.0470743	−	0.144880i
$554$	6.82786	−	21.0140i	0.290088	−	0.892799i
$555$		0			0
$556$	−1.17236	−	0.851771i	−0.0497192	−	0.0361231i
$557$	−10.6741	+	32.8516i	−0.452277	+	1.39197i	0.422026	+	0.906584i	$0.361319\pi$
$557$	−10.6741	+	32.8516i	−0.452277	+	1.39197i	−0.874303	+	0.485381i	$0.838681\pi$
$558$		0			0
$559$	11.1476	−	8.09917i	0.471491	−	0.342558i
$560$	−1.99748			−0.0844088
$561$		0			0
$562$	15.6883			0.661773
$563$	15.7612	−	11.4512i	0.664256	−	0.482610i	−0.203842	−	0.979004i	$-0.565343\pi$
$563$	15.7612	−	11.4512i	0.664256	−	0.482610i	0.868098	+	0.496394i	$0.165343\pi$
$564$		0			0
$565$	0.255295	−	0.785717i	0.0107403	−	0.0330553i
$566$	−10.8087	−	7.85300i	−0.454325	−	0.330086i
$567$		0			0
$568$	8.16387	−	25.1258i	0.342549	−	1.05426i
$569$	−5.29308	−	16.2904i	−0.221897	−	0.682930i	−0.998592	−	0.0530524i	$-0.983105\pi$
$569$	−5.29308	−	16.2904i	−0.221897	−	0.682930i	0.776694	−	0.629878i	$-0.216895\pi$
$570$		0			0
$571$	−3.85581			−0.161360			−0.0806802	−	0.996740i	$-0.525709\pi$
$571$	−3.85581			−0.161360			−0.0806802	+	0.996740i	$0.525709\pi$
$572$	−0.724095	−	0.325828i	−0.0302759	−	0.0136236i
$573$		0			0
$574$	1.23541	−	0.897575i	0.0515649	−	0.0374641i
$575$	−2.66745	−	8.20958i	−0.111240	−	0.342363i
$576$		0			0
$577$	7.91368	+	5.74963i	0.329451	+	0.239360i	0.740198	−	0.672389i	$-0.234732\pi$
$577$	7.91368	+	5.74963i	0.329451	+	0.239360i	−0.410747	+	0.911750i	$0.634732\pi$
$578$	−12.2517	−	8.90135i	−0.509602	−	0.370247i
$579$		0			0
$580$	0.0593443	+	0.182643i	0.00246414	+	0.00758384i
$581$	13.9627	−	10.1445i	0.579272	−	0.420865i
$582$		0			0
$583$	−4.75010	+	43.5358i	−0.196729	+	1.80307i
$584$	36.1178			1.49457
$585$		0			0
$586$	−5.38863	−	16.5845i	−0.222602	−	0.685099i
$587$	1.88467	−	5.80041i	0.0777886	−	0.239409i	−0.904599	−	0.426264i	$-0.859830\pi$
$587$	1.88467	−	5.80041i	0.0777886	−	0.239409i	0.982387	+	0.186855i	$0.0598295\pi$
$588$		0			0
$589$	−4.41932	−	3.21082i	−0.182095	−	0.132300i
$590$	−1.82010	+	5.60169i	−0.0749323	+	0.230618i
$591$		0			0
$592$	−6.72462	+	4.88572i	−0.276380	+	0.200802i
$593$	−13.2330			−0.543413			−0.271706	−	0.962380i	$-0.587588\pi$
$593$	−13.2330			−0.543413			−0.271706	+	0.962380i	$0.587588\pi$
$594$		0			0
$595$	−2.43976			−0.100020
$596$	1.83150	−	1.33066i	0.0750212	−	0.0545061i
$597$		0			0
$598$	−1.29454	+	3.98419i	−0.0529378	+	0.162926i
$599$	−4.79355	−	3.48271i	−0.195859	−	0.142300i	0.485534	−	0.874218i	$-0.338625\pi$
$599$	−4.79355	−	3.48271i	−0.195859	−	0.142300i	−0.681393	+	0.731918i	$0.738625\pi$
$600$		0			0
$601$	3.93712	−	12.1172i	0.160599	−	0.494272i	−0.838086	−	0.545538i	$-0.816326\pi$
$601$	3.93712	−	12.1172i	0.160599	−	0.494272i	0.998685	+	0.0512657i	$0.0163255\pi$
$602$	−3.94695	−	12.1475i	−0.160866	−	0.495094i
$603$		0			0
$604$	−0.434590			−0.0176832
$605$	2.60214	−	4.42576i	0.105792	−	0.179933i
$606$		0			0
$607$	−6.76452	+	4.91471i	−0.274563	+	0.199482i	−0.716543	−	0.697543i	$-0.754276\pi$
$607$	−6.76452	+	4.91471i	−0.274563	+	0.199482i	0.441979	+	0.897025i	$0.354276\pi$
$608$	−1.11430	−	3.42946i	−0.0451908	−	0.139083i
$609$		0			0
$610$	−8.44044	−	6.13234i	−0.341743	−	0.248291i
$611$	8.18675	+	5.94802i	0.331201	+	0.240631i
$612$		0			0
$613$	−2.06514	−	6.35585i	−0.0834102	−	0.256710i	0.900650	−	0.434545i	$-0.143091\pi$
$613$	−2.06514	−	6.35585i	−0.0834102	−	0.256710i	−0.984060	+	0.177835i	$0.943091\pi$
$614$	−2.63513	+	1.91453i	−0.106345	+	0.0772643i
$615$		0			0
$616$	6.04401	−	6.65936i	0.243520	−	0.268313i
$617$	−11.8669			−0.477741			−0.238871	−	0.971051i	$-0.576777\pi$
$617$	−11.8669			−0.477741			−0.238871	+	0.971051i	$0.576777\pi$
$618$		0			0
$619$	6.37213	+	19.6114i	0.256118	+	0.788249i	0.993607	+	0.112891i	$0.0360109\pi$
$619$	6.37213	+	19.6114i	0.256118	+	0.788249i	−0.737490	+	0.675358i	$0.763989\pi$
$620$	−0.0282346	+	0.0868973i	−0.00113393	+	0.00348988i
$621$		0			0
$622$	−25.4084	−	18.4603i	−1.01878	−	0.740189i
$623$	−2.75638	+	8.48325i	−0.110432	+	0.339874i
$624$		0			0
$625$	−17.6203	+	12.8019i	−0.704812	+	0.512076i
$626$	−46.2824			−1.84982
$627$		0			0
$628$	−2.85694			−0.114004
$629$	−8.21358	+	5.96752i	−0.327497	+	0.237941i
$630$		0			0
$631$	−4.78342	+	14.7219i	−0.190425	+	0.586068i	−1.00000		0.000949112i	$-0.999698\pi$
$631$	−4.78342	+	14.7219i	−0.190425	+	0.586068i	0.809575	+	0.587017i	$0.199698\pi$
$632$	7.85847	+	5.70952i	0.312593	+	0.227112i
$633$		0			0
$634$	5.98314	−	18.4142i	0.237621	−	0.731321i
$635$	1.23174	+	3.79091i	0.0488801	+	0.150438i
$636$		0			0
$637$	−1.58232			−0.0626937
$638$	−12.0640	−	5.42857i	−0.477619	−	0.214919i
$639$		0			0
$640$	4.69166	−	3.40869i	0.185454	−	0.134740i
$641$	7.28615	+	22.4245i	0.287786	+	0.885713i	0.985550	+	0.169385i	$0.0541783\pi$
$641$	7.28615	+	22.4245i	0.287786	+	0.885713i	−0.697764	+	0.716327i	$0.745822\pi$
$642$		0			0
$643$	−23.2031	−	16.8581i	−0.915042	−	0.664817i	0.0272428	−	0.999629i	$-0.491327\pi$
$643$	−23.2031	−	16.8581i	−0.915042	−	0.664817i	−0.942285	+	0.334812i	$0.891327\pi$
$644$	0.220949	+	0.160529i	0.00870663	+	0.00632574i
$645$		0			0
$646$	−10.0028	−	30.7855i	−0.393556	−	1.21124i
$647$	4.39104	−	3.19028i	0.172630	−	0.125423i	−0.498115	−	0.867111i	$-0.665974\pi$
$647$	4.39104	−	3.19028i	0.172630	−	0.125423i	0.670745	+	0.741688i	$0.265974\pi$
$648$		0			0
$649$	−14.1700	−	24.7691i	−0.556221	−	0.972271i
$650$	11.0986			0.435323
$651$		0			0
$652$	0.542130	+	1.66851i	0.0212315	+	0.0653437i
$653$	3.81392	−	11.7380i	0.149250	−	0.459344i	−0.848283	−	0.529543i	$-0.822363\pi$
$653$	3.81392	−	11.7380i	0.149250	−	0.459344i	0.997533	+	0.0701988i	$0.0223634\pi$
$654$		0			0
$655$	3.65023	+	2.65205i	0.142626	+	0.103624i
$656$	−1.37689	+	4.23762i	−0.0537584	+	0.165451i
$657$		0			0
$658$	7.58873	−	5.51353i	0.295839	−	0.214940i
$659$	−16.2115			−0.631512			−0.315756	−	0.948840i	$-0.602258\pi$
$659$	−16.2115			−0.631512			−0.315756	+	0.948840i	$0.602258\pi$
$660$		0			0
$661$	43.7050			1.69993			0.849964	−	0.526840i	$-0.176623\pi$
$661$	43.7050			1.69993			0.849964	+	0.526840i	$0.176623\pi$
$662$	−11.2450	+	8.16994i	−0.437048	+	0.317534i
$663$		0			0
$664$	−14.4614	+	44.5078i	−0.561213	+	1.72724i
$665$	−1.59417	−	1.15823i	−0.0618193	−	0.0449144i
$666$		0			0
$667$	−1.51690	+	4.66854i	−0.0587346	+	0.180766i
$668$	−0.295721	−	0.910136i	−0.0114418	−	0.0352142i
$669$		0			0
$670$	3.20093			0.123663
$671$	49.4825	−	10.3133i	1.91025	−	0.398140i
$672$		0			0
$673$	4.74166	−	3.44502i	0.182778	−	0.132796i	−0.492634	−	0.870237i	$-0.663966\pi$
$673$	4.74166	−	3.44502i	0.182778	−	0.132796i	0.675412	+	0.737441i	$0.263966\pi$
$674$	−8.70280	−	26.7845i	−0.335219	−	1.03170i
$675$		0			0
$676$	1.28481	+	0.933467i	0.0494157	+	0.0359026i
$677$	−16.6074	−	12.0660i	−0.638275	−	0.463734i	0.220982	−	0.975278i	$-0.429074\pi$
$677$	−16.6074	−	12.0660i	−0.638275	−	0.463734i	−0.859257	+	0.511544i	$0.829074\pi$
$678$		0			0
$679$	0.835464	+	2.57129i	0.0320622	+	0.0986772i
$680$	5.35206	−	3.88850i	0.205242	−	0.149117i
$681$		0			0
$682$	−3.12546	−	5.46327i	−0.119680	−	0.209200i
$683$	−38.7055			−1.48103			−0.740513	−	0.672042i	$-0.765417\pi$
$683$	−38.7055			−1.48103			−0.740513	+	0.672042i	$0.765417\pi$
$684$		0			0
$685$	−2.02075	−	6.21923i	−0.0772090	−	0.237625i
$686$	−0.453245	+	1.39494i	−0.0173050	+	0.0532592i
$687$		0			0
$688$	30.1509	+	21.9059i	1.14949	+	0.835156i
$689$	−6.45647	+	19.8710i	−0.245972	+	0.757024i
$690$		0			0
$691$	18.7126	−	13.5955i	0.711860	−	0.517197i	−0.171913	−	0.985112i	$-0.554995\pi$
$691$	18.7126	−	13.5955i	0.711860	−	0.517197i	0.883773	+	0.467916i	$0.154995\pi$
$692$	−0.202603			−0.00770182
$693$		0			0
$694$	−4.47105			−0.169719
$695$	3.61646	−	2.62751i	0.137180	−	0.0996673i
$696$		0			0
$697$	−1.68176	+	5.17592i	−0.0637011	+	0.196052i
$698$	−23.0156	−	16.7218i	−0.871155	−	0.632931i
$699$		0			0
$700$	0.223590	−	0.688138i	0.00845090	−	0.0260092i
$701$	−10.9734	−	33.7727i	−0.414460	−	1.27558i	−0.912733	−	0.408557i	$-0.866032\pi$
$701$	−10.9734	−	33.7727i	−0.414460	−	1.27558i	0.498273	−	0.867020i	$-0.333968\pi$
$702$		0			0
$703$	−8.19985			−0.309263
$704$	−2.62847	+	24.0906i	−0.0990643	+	0.907947i
$705$		0			0
$706$	−12.7662	+	9.27518i	−0.480462	+	0.349076i
$707$	0.0552464	+	0.170031i	0.00207775	+	0.00639467i
$708$		0			0
$709$	−35.4386	−	25.7476i	−1.33092	−	0.966972i	−0.999726	−	0.0234107i	$-0.992547\pi$
$709$	−35.4386	−	25.7476i	−1.33092	−	0.966972i	−0.331197	−	0.943562i	$-0.607453\pi$
$710$	−5.39601	−	3.92043i	−0.202509	−	0.147131i
$711$		0			0
$712$	−7.47403	−	23.0027i	−0.280101	−	0.862063i
$713$	−1.88945	+	1.37277i	−0.0707604	+	0.0514105i
$714$		0			0
$715$	1.64615	−	1.81375i	0.0615625	−	0.0678303i
$716$	−2.69149			−0.100586
$717$		0			0
$718$	−0.275222	−	0.847046i	−0.0102712	−	0.0316115i
$719$	−4.90115	+	15.0842i	−0.182782	+	0.562546i	−0.999903	−	0.0139205i	$-0.995569\pi$
$719$	−4.90115	+	15.0842i	−0.182782	+	0.562546i	0.817121	+	0.576466i	$0.195569\pi$
$720$		0			0
$721$	13.6540	+	9.92019i	0.508500	+	0.369447i
$722$	−0.532741	+	1.63961i	−0.0198266	+	0.0610199i
$723$		0			0
$724$	0.117972	−	0.0857118i	0.00438440	−	0.00318545i
$725$	13.0049			0.482992
$726$		0			0
$727$	13.7719			0.510770			0.255385	−	0.966839i	$-0.417798\pi$
$727$	13.7719			0.510770			0.255385	+	0.966839i	$0.417798\pi$
$728$	3.47110	−	2.52190i	0.128648	−	0.0934680i
$729$		0			0
$730$	2.81777	−	8.67220i	0.104290	−	0.320972i
$731$	36.8269	+	26.7563i	1.36209	+	0.989619i
$732$		0			0
$733$	−6.04675	+	18.6100i	−0.223342	+	0.687376i	0.775114	+	0.631822i	$0.217693\pi$
$733$	−6.04675	+	18.6100i	−0.223342	+	0.687376i	−0.998456	+	0.0555542i	$0.982307\pi$
$734$	12.5380	+	38.5881i	0.462788	+	1.42431i
$735$		0			0
$736$	−1.54170			−0.0568278
$737$	−10.4224	+	11.4835i	−0.383914	+	0.423000i
$738$		0			0
$739$	9.02392	−	6.55626i	0.331950	−	0.241176i	−0.409307	−	0.912397i	$-0.634230\pi$
$739$	9.02392	−	6.55626i	0.331950	−	0.241176i	0.741258	+	0.671220i	$0.234230\pi$
$740$	0.0423829	+	0.130441i	0.00155803	+	0.00479511i
$741$		0			0
$742$	15.6685	+	11.3838i	0.575210	+	0.417914i
$743$	16.7102	+	12.1407i	0.613038	+	0.445398i	0.850483	−	0.526003i	$-0.176310\pi$
$743$	16.7102	+	12.1407i	0.613038	+	0.445398i	−0.237445	+	0.971401i	$0.576310\pi$
$744$		0			0
$745$	2.15801	+	6.64168i	0.0790635	+	0.243332i
$746$	34.9472	−	25.3907i	1.27951	−	0.929618i
$747$		0			0
$748$	0.284517	−	2.60766i	0.0104030	−	0.0953455i
$749$	−15.4762			−0.565489
$750$		0			0
$751$	8.21957	+	25.2972i	0.299936	+	0.923109i	0.981518	+	0.191367i	$0.0612922\pi$
$751$	8.21957	+	25.2972i	0.299936	+	0.923109i	−0.681582	+	0.731742i	$0.738708\pi$
$752$	−8.45780	+	26.0304i	−0.308424	+	0.949233i
$753$		0			0
$754$	−5.10606	−	3.70977i	−0.185952	−	0.135102i
$755$	0.414271	−	1.27499i	0.0150769	−	0.0464018i
$756$		0			0
$757$	−17.0702	+	12.4022i	−0.620427	+	0.450767i	−0.853071	−	0.521796i	$-0.825262\pi$
$757$	−17.0702	+	12.4022i	−0.620427	+	0.450767i	0.232644	+	0.972562i	$0.425262\pi$
$758$	37.1723			1.35016
$759$		0			0
$760$	5.34311			0.193815
$761$	−6.47006	+	4.70077i	−0.234539	+	0.170403i	−0.698847	−	0.715271i	$-0.746303\pi$
$761$	−6.47006	+	4.70077i	−0.234539	+	0.170403i	0.464308	+	0.885674i	$0.346303\pi$
$762$		0			0
$763$	−3.40997	+	10.4948i	−0.123449	+	0.379938i
$764$	−1.96937	−	1.43083i	−0.0712494	−	0.0517657i
$765$		0			0
$766$	14.4731	−	44.5436i	0.522935	−	1.60943i
$767$	−4.20698	−	12.9477i	−0.151905	−	0.467516i
$768$		0			0
$769$	−52.0476			−1.87689			−0.938443	−	0.345435i	$-0.887731\pi$
$769$	−52.0476			−1.87689			−0.938443	+	0.345435i	$0.887731\pi$
$770$	−1.12744	−	1.97076i	−0.0406301	−	0.0710211i
$771$		0			0
$772$	−1.48692	+	1.08031i	−0.0535155	+	0.0388813i
$773$	0.488554	+	1.50361i	0.0175721	+	0.0540812i	0.959458	−	0.281851i	$-0.0909485\pi$
$773$	0.488554	+	1.50361i	0.0175721	+	0.0540812i	−0.941886	+	0.335933i	$0.890949\pi$
$774$		0			0
$775$	5.00575	+	3.63689i	0.179812	+	0.130641i
$776$	−5.93089	−	4.30904i	−0.212906	−	0.154686i
$777$		0			0
$778$	−8.04587	−	24.7626i	−0.288458	−	0.887784i
$779$	−3.55606	+	2.58363i	−0.127409	+	0.0925681i
$780$		0			0
$781$	31.6344	−	6.59334i	1.13197	−	0.235928i
$782$	−13.8395			−0.494899
$783$		0			0
$784$	−1.32250	−	4.07025i	−0.0472323	−	0.145366i
$785$	2.72336	−	8.38164i	0.0972009	−	0.299154i
$786$		0			0
$787$	−18.9235	−	13.7487i	−0.674549	−	0.490089i	0.196996	−	0.980404i	$-0.436882\pi$
$787$	−18.9235	−	13.7487i	−0.674549	−	0.490089i	−0.871545	+	0.490316i	$0.836882\pi$
$788$	0.107620	−	0.331220i	0.00383380	−	0.0117992i
$789$		0			0
$790$	1.98399	−	1.44145i	0.0705872	−	0.0512846i
$791$	1.77008			0.0629367
$792$		0			0
$793$	24.1147			0.856339
$794$	15.7875	−	11.4703i	0.560276	−	0.407064i
$795$		0			0
$796$	0.948177	−	2.91819i	0.0336072	−	0.103432i
$797$	−37.3376	−	27.1274i	−1.32257	−	0.960900i	−0.999896	−	0.0143887i	$-0.995420\pi$
$797$	−37.3376	−	27.1274i	−1.32257	−	0.960900i	−0.322669	−	0.946512i	$-0.604580\pi$
$798$		0			0
$799$	−10.3305	+	31.7941i	−0.365468	+	1.12479i
$800$	1.26217	+	3.88455i	0.0446243	+	0.137339i
$801$		0			0
$802$	5.11834			0.180735
$803$	21.9371	+	38.3460i	0.774145	+	1.35320i
$804$		0			0
$805$	−0.681577	+	0.495195i	−0.0240224	+	0.0174533i
$806$	−0.927927	−	2.85587i	−0.0326848	−	0.100594i
$807$		0			0
$808$	−0.392189	−	0.284942i	−0.0137972	−	0.0100242i
$809$	27.3044	+	19.8378i	0.959972	+	0.697461i	0.953144	−	0.302516i	$-0.0978266\pi$
$809$	27.3044	+	19.8378i	0.959972	+	0.697461i	0.00682787	+	0.999977i	$0.497827\pi$
$810$		0			0
$811$	−9.50690	−	29.2592i	−0.333833	−	1.02743i	−0.967294	−	0.253657i	$-0.918367\pi$
$811$	−9.50690	−	29.2592i	−0.333833	−	1.02743i	0.633462	−	0.773774i	$-0.281633\pi$
$812$	−0.332880	+	0.241851i	−0.0116818	+	0.00848731i
$813$		0			0
$814$	−8.61596	−	3.87701i	−0.301989	−	0.135889i
$815$	−5.41182			−0.189568
$816$		0			0
$817$	11.3611	+	34.9659i	0.397475	+	1.22330i
$818$	−13.4276	+	41.3259i	−0.469485	+	1.44493i
$819$		0			0
$820$	0.0594801	+	0.0432148i	0.00207714	+	0.00150913i
$821$	−3.73242	+	11.4872i	−0.130262	+	0.400906i	−0.994823	−	0.101622i	$-0.967597\pi$
$821$	−3.73242	+	11.4872i	−0.130262	+	0.400906i	0.864561	+	0.502528i	$0.167597\pi$
$822$		0			0
$823$	20.0787	−	14.5880i	0.699900	−	0.508507i	−0.179999	−	0.983667i	$-0.557610\pi$
$823$	20.0787	−	14.5880i	0.699900	−	0.508507i	0.879900	+	0.475159i	$0.157610\pi$
$824$	−45.7634			−1.59424
$825$		0			0
$826$	−12.6196			−0.439092
$827$	4.18529	−	3.04079i	0.145537	−	0.105739i	−0.512634	−	0.858607i	$-0.671330\pi$
$827$	4.18529	−	3.04079i	0.145537	−	0.105739i	0.658171	+	0.752868i	$0.271330\pi$
$828$		0			0
$829$	9.75057	−	30.0092i	0.338651	−	1.04226i	−0.626244	−	0.779627i	$-0.715409\pi$
$829$	9.75057	−	30.0092i	0.338651	−	1.04226i	0.964895	−	0.262635i	$-0.0845914\pi$
$830$	9.55847	+	6.94464i	0.331779	+	0.241052i
$831$		0			0
$832$	−3.57270	+	10.9956i	−0.123861	+	0.381205i
$833$	−1.61533	−	4.97148i	−0.0559679	−	0.172252i
$834$		0			0
$835$	2.95204			0.102160
$836$	1.42385	−	1.56881i	0.0492449	−	0.0542585i
$837$		0			0
$838$	−13.8184	+	10.0396i	−0.477348	+	0.346813i
$839$	1.80355	+	5.55077i	0.0622656	+	0.191634i	0.977350	−	0.211628i	$-0.0678765\pi$
$839$	1.80355	+	5.55077i	0.0622656	+	0.191634i	−0.915085	+	0.403262i	$0.867876\pi$
$840$		0			0
$841$	17.4784	+	12.6988i	0.602703	+	0.437889i
$842$	−23.5956	−	17.1432i	−0.813157	−	0.590793i
$843$		0			0
$844$	0.250854	+	0.772050i	0.00863475	+	0.0265750i
$845$	−3.96333	+	2.87953i	−0.136343	+	0.0990588i
$846$		0			0
$847$	10.7412	+	2.37214i	0.369071	+	0.0815075i
$848$	−56.5112			−1.94060
$849$		0			0
$850$	11.3302	+	34.8707i	0.388622	+	1.19606i
$851$	−1.08335	+	3.33420i	−0.0371367	+	0.114295i
$852$		0			0
$853$	16.4604	+	11.9592i	0.563593	+	0.409475i	0.832772	−	0.553616i	$-0.186752\pi$
$853$	16.4604	+	11.9592i	0.563593	+	0.409475i	−0.269179	+	0.963090i	$0.586752\pi$
$854$	6.90752	−	21.2592i	0.236371	−	0.727474i
$855$		0			0
$856$	33.9499	−	24.6661i	1.16039	−	0.843069i
$857$	15.1087			0.516104			0.258052	−	0.966131i	$-0.416919\pi$
$857$	15.1087			0.516104			0.258052	+	0.966131i	$0.416919\pi$
$858$		0			0
$859$	−33.9641			−1.15884			−0.579420	−	0.815029i	$-0.696721\pi$
$859$	−33.9641			−1.15884			−0.579420	+	0.815029i	$0.696721\pi$
$860$	0.497507	−	0.361460i	0.0169648	−	0.0123257i
$861$		0			0
$862$	−13.7090	+	42.1920i	−0.466931	+	1.43707i
$863$	−2.24691	−	1.63248i	−0.0764859	−	0.0555702i	0.548885	−	0.835898i	$-0.315052\pi$
$863$	−2.24691	−	1.63248i	−0.0764859	−	0.0555702i	−0.625371	+	0.780327i	$0.715052\pi$
$864$		0			0
$865$	0.193130	−	0.594395i	0.00656663	−	0.0202100i
$866$	−2.58676	−	7.96122i	−0.0879016	−	0.270533i
$867$		0			0
$868$	−0.195764			−0.00664466
$869$	−1.28869	+	11.8111i	−0.0437156	+	0.400664i
$870$		0			0
$871$	−5.98562	+	4.34881i	−0.202815	+	0.147354i
$872$	−9.24629	−	28.4571i	−0.313119	−	0.963681i
$873$		0			0
$874$	−9.04292	−	6.57006i	−0.305881	−	0.222236i
$875$	3.69369	+	2.68362i	0.124869	+	0.0907229i
$876$		0			0
$877$	15.3514	+	47.2469i	0.518381	+	1.59541i	0.777044	+	0.629446i	$0.216718\pi$
$877$	15.3514	+	47.2469i	0.518381	+	1.59541i	−0.258662	+	0.965968i	$0.583282\pi$
$878$	−8.12680	+	5.90446i	−0.274266	+	0.199266i
$879$		0			0
$880$	6.04142	+	2.71852i	0.203656	+	0.0916412i
$881$	27.3064			0.919975			0.459988	−	0.887925i	$-0.347854\pi$
$881$	27.3064			0.919975			0.459988	+	0.887925i	$0.347854\pi$
$882$		0			0
$883$	−5.50388	−	16.9392i	−0.185220	−	0.570049i	0.814732	−	0.579838i	$-0.196884\pi$
$883$	−5.50388	−	16.9392i	−0.185220	−	0.570049i	−0.999952	+	0.00978852i	$0.996884\pi$
$884$	0.386723	−	1.19021i	0.0130069	−	0.0400312i
$885$		0			0
$886$	0.119486	+	0.0868116i	0.00401421	+	0.00291649i
$887$	5.09040	−	15.6666i	0.170919	−	0.526034i	−0.828505	−	0.559982i	$-0.810808\pi$
$887$	5.09040	−	15.6666i	0.170919	−	0.526034i	0.999424	+	0.0339479i	$0.0108080\pi$
$888$		0			0
$889$	−6.90919	+	5.01982i	−0.231727	+	0.168359i
$890$	−6.10625			−0.204682
$891$		0			0
$892$	−3.84656			−0.128792
$893$	−21.8438	+	15.8705i	−0.730975	+	0.531084i
$894$		0			0
$895$	2.56565	−	7.89625i	0.0857601	−	0.263942i
$896$	10.0522	+	7.30332i	0.335819	+	0.243987i
$897$		0			0
$898$	13.9621	−	42.9709i	0.465921	−	1.43396i
$899$	−1.08731	−	3.34640i	−0.0362639	−	0.111609i
$900$		0			0
$901$	−69.0238			−2.29952
$902$	−4.95809	+	1.03338i	−0.165086	+	0.0344078i
$903$		0			0
$904$	−3.88299	+	2.82116i	−0.129146	+	0.0938304i
$905$	0.139004	+	0.427809i	0.00462064	+	0.0142209i
$906$		0			0
$907$	−23.0470	−	16.7446i	−0.765264	−	0.555997i	0.135257	−	0.990811i	$-0.456814\pi$
$907$	−23.0470	−	16.7446i	−0.765264	−	0.555997i	−0.900520	+	0.434814i	$0.856814\pi$
$908$	−2.65741	−	1.93072i	−0.0881891	−	0.0640731i
$909$		0			0
$910$	−0.334729	−	1.03019i	−0.0110962	−	0.0341505i
$911$	−9.08955	+	6.60394i	−0.301150	+	0.218798i	−0.728090	−	0.685482i	$-0.759592\pi$
$911$	−9.08955	+	6.60394i	−0.301150	+	0.218798i	0.426940	+	0.904280i	$0.359592\pi$
$912$		0			0
$913$	−56.0371	+	11.6794i	−1.85456	+	0.386532i
$914$	33.9337			1.12243
$915$		0			0
$916$	0.959910	+	2.95430i	0.0317163	+	0.0976128i
$917$	−2.98729	+	9.19394i	−0.0986491	+	0.303611i
$918$		0			0
$919$	−0.631403	−	0.458741i	−0.0208281	−	0.0151325i	0.577323	−	0.816516i	$-0.304098\pi$
$919$	−0.631403	−	0.458741i	−0.0208281	−	0.0151325i	−0.598151	+	0.801384i	$0.704098\pi$
$920$	0.705922	−	2.17260i	0.0232735	−	0.0716286i
$921$		0			0
$922$	−3.29687	+	2.39532i	−0.108577	+	0.0788856i
$923$	15.4167			0.507446
$924$		0			0
$925$	9.28795			0.305386
$926$	30.9646	−	22.4971i	1.01756	−	0.739301i
$927$		0			0
$928$	0.717755	−	2.20902i	0.0235615	−	0.0725148i
$929$	21.5169	+	15.6329i	0.705946	+	0.512899i	0.881863	−	0.471505i	$-0.156289\pi$
$929$	21.5169	+	15.6329i	0.705946	+	0.512899i	−0.175918	+	0.984405i	$0.556289\pi$
$930$		0			0
$931$	1.30464	−	4.01528i	0.0427580	−	0.131596i
$932$	−0.0324505	−	0.0998725i	−0.00106295	−	0.00327143i
$933$		0			0
$934$	3.89900			0.127579
$935$	7.37911	+	3.32045i	0.241323	+	0.108590i
$936$		0			0
$937$	−33.9542	+	24.6691i	−1.10923	+	0.805906i	−0.982543	−	0.186036i	$-0.940436\pi$
$937$	−33.9542	+	24.6691i	−1.10923	+	0.805906i	−0.126691	+	0.991942i	$0.540436\pi$
$938$	2.11930	+	6.52252i	0.0691974	+	0.212968i
$939$		0			0
$940$	0.365368	+	0.265456i	0.0119170	+	0.00865821i
$941$	−39.6685	−	28.8209i	−1.29316	−	0.939533i	−0.293292	−	0.956023i	$-0.594751\pi$
$941$	−39.6685	−	28.8209i	−1.29316	−	0.939533i	−0.999864	+	0.0164899i	$0.994751\pi$
$942$		0			0
$943$	0.580730	+	1.78730i	0.0189112	+	0.0582026i
$944$	29.7897	−	21.6435i	0.969574	−	0.704437i
$945$		0			0
$946$	−4.59475	+	42.1120i	−0.149388	+	1.36918i
$947$	27.2953			0.886978			0.443489	−	0.896280i	$-0.353741\pi$
$947$	27.2953			0.886978			0.443489	+	0.896280i	$0.353741\pi$
$948$		0			0
$949$	6.51299	+	20.0449i	0.211421	+	0.650686i
$950$	−9.15097	+	28.1638i	−0.296897	+	0.913754i
$951$		0			0
$952$	11.4671	+	8.33134i	0.371651	+	0.270020i
$953$	−6.10023	+	18.7746i	−0.197606	+	0.608169i	0.802330	+	0.596880i	$0.203593\pi$
$953$	−6.10023	+	18.7746i	−0.197606	+	0.608169i	−0.999936	+	0.0112883i	$0.996407\pi$
$954$		0			0
$955$	6.07505	−	4.41378i	0.196584	−	0.142827i
$956$	−0.0524354			−0.00169588
$957$		0			0
$958$	12.1478			0.392478
$959$	11.3350	−	8.23535i	0.366026	−	0.265933i
$960$		0			0
$961$	−9.06221	+	27.8906i	−0.292329	+	0.899697i
$962$	−3.64668	−	2.64947i	−0.117574	−	0.0854222i
$963$		0			0
$964$	−0.487989	+	1.50188i	−0.0157171	+	0.0483721i
$965$	−1.75200	−	5.39211i	−0.0563990	−	0.173578i
$966$		0			0
$967$	−12.6734			−0.407551			−0.203775	−	0.979018i	$-0.565321\pi$
$967$	−12.6734			−0.407551			−0.203775	+	0.979018i	$0.565321\pi$
$968$	−27.3435	+	11.9156i	−0.878853	+	0.382983i
$969$		0			0
$970$	−1.49734	+	1.08788i	−0.0480768	+	0.0349298i
$971$	−5.16170	−	15.8861i	−0.165647	−	0.509809i	0.833436	−	0.552615i	$-0.186370\pi$
$971$	−5.16170	−	15.8861i	−0.165647	−	0.509809i	−0.999083	+	0.0428065i	$0.986370\pi$
$972$		0			0
$973$	7.74848	+	5.62960i	0.248405	+	0.180477i
$974$	23.2523	+	16.8938i	0.745052	+	0.541312i
$975$		0			0
$976$	20.1552	+	62.0312i	0.645151	+	1.98557i
$977$	22.1227	−	16.0731i	0.707769	−	0.514224i	−0.174684	−	0.984625i	$-0.555890\pi$
$977$	22.1227	−	16.0731i	0.707769	−	0.514224i	0.882453	+	0.470400i	$0.155890\pi$
$978$		0			0
$979$	19.8822	−	21.9064i	0.635439	−	0.700133i
$980$	−0.0706175			−0.00225579
$981$		0			0
$982$	12.9998	+	40.0093i	0.414841	+	1.27675i
$983$	16.9979	−	52.3143i	0.542150	−	1.66857i	−0.185521	−	0.982640i	$-0.559397\pi$
$983$	16.9979	−	52.3143i	0.542150	−	1.66857i	0.727671	−	0.685926i	$-0.240603\pi$
$984$		0			0
$985$	0.869141	+	0.631468i	0.0276931	+	0.0201202i
$986$	6.44313	−	19.8299i	0.205191	−	0.631513i
$987$		0			0
$988$	0.817723	−	0.594110i	0.0260152	−	0.0189012i
$989$	15.7188			0.499828
$990$		0			0
$991$	53.2327			1.69099			0.845497	−	0.533980i	$-0.179304\pi$
$991$	53.2327			1.69099			0.845497	+	0.533980i	$0.179304\pi$
$992$	0.894035	−	0.649555i	0.0283857	−	0.0206234i
$993$		0			0
$994$	4.41601	−	13.5911i	0.140067	−	0.431083i
$995$	7.65750	+	5.56350i	0.242759	+	0.176375i
$996$		0			0
$997$	10.1217	−	31.1515i	0.320558	−	0.986577i	−0.652848	−	0.757489i	$-0.726426\pi$
$997$	10.1217	−	31.1515i	0.320558	−	0.986577i	0.973406	−	0.229087i	$-0.0735742\pi$
$998$	12.6682	+	38.9886i	0.401004	+	1.23416i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.g.190.1		8
3.2	odd	2		77.2.f.a.36.2	yes	8
11.2	odd	10		7623.2.a.co.1.1		4
11.4	even	5	inner	693.2.m.g.631.1		8
11.9	even	5		7623.2.a.ch.1.4		4
21.2	odd	6		539.2.q.c.410.1		16
21.5	even	6		539.2.q.b.410.1		16
21.11	odd	6		539.2.q.c.520.2		16
21.17	even	6		539.2.q.b.520.2		16
21.20	even	2		539.2.f.d.344.2		8
33.2	even	10		847.2.a.k.1.4		4
33.5	odd	10		847.2.f.p.372.1		8
33.8	even	10		847.2.f.s.148.2		8
33.14	odd	10		847.2.f.p.148.1		8
33.17	even	10		847.2.f.s.372.2		8
33.20	odd	10		847.2.a.l.1.1		4
33.26	odd	10		77.2.f.a.15.2	✓	8
33.29	even	10		847.2.f.q.323.1		8
33.32	even	2		847.2.f.q.729.1		8
231.20	even	10		5929.2.a.bi.1.1		4
231.26	even	30		539.2.q.b.312.2		16
231.59	even	30		539.2.q.b.422.1		16
231.125	even	10		539.2.f.d.246.2		8
231.158	odd	30		539.2.q.c.422.1		16
231.167	odd	10		5929.2.a.bb.1.4		4
231.191	odd	30		539.2.q.c.312.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.2	✓	8	33.26	odd	10
77.2.f.a.36.2	yes	8	3.2	odd	2
539.2.f.d.246.2		8	231.125	even	10
539.2.f.d.344.2		8	21.20	even	2
539.2.q.b.312.2		16	231.26	even	30
539.2.q.b.410.1		16	21.5	even	6
539.2.q.b.422.1		16	231.59	even	30
539.2.q.b.520.2		16	21.17	even	6
539.2.q.c.312.2		16	231.191	odd	30
539.2.q.c.410.1		16	21.2	odd	6
539.2.q.c.422.1		16	231.158	odd	30
539.2.q.c.520.2		16	21.11	odd	6
693.2.m.g.190.1		8	1.1	even	1	trivial
693.2.m.g.631.1		8	11.4	even	5	inner
847.2.a.k.1.4		4	33.2	even	10
847.2.a.l.1.1		4	33.20	odd	10
847.2.f.p.148.1		8	33.14	odd	10
847.2.f.p.372.1		8	33.5	odd	10
847.2.f.q.323.1		8	33.29	even	10
847.2.f.q.729.1		8	33.32	even	2
847.2.f.s.148.2		8	33.8	even	10
847.2.f.s.372.2		8	33.17	even	10
5929.2.a.bb.1.4		4	231.167	odd	10
5929.2.a.bi.1.1		4	231.20	even	10
7623.2.a.ch.1.4		4	11.9	even	5
7623.2.a.co.1.1		4	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)

\(f(q)\)	\(=\)	\(q+(-1.18661 + 0.862123i) q^{2} +(0.0467549 - 0.143897i) q^{4} +(0.377594 + 0.274338i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.837913 - 2.57883i) q^{8} +O(q^{10})\)	\(q+(-1.18661 + 0.862123i) q^{2} +(0.0467549 - 0.143897i) q^{4} +(0.377594 + 0.274338i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-0.837913 - 2.57883i) q^{8} -0.684570 q^{10} +(2.22899 - 2.45593i) q^{11} +(1.28012 - 0.930062i) q^{13} +(-0.453245 - 1.39494i) q^{14} +(3.46236 + 2.51555i) q^{16} +(4.22899 + 3.07254i) q^{17} +(1.30464 + 4.01528i) q^{19} +(0.0571308 - 0.0415079i) q^{20} +(-0.527635 + 4.83590i) q^{22} +1.80505 q^{23} +(-1.47777 - 4.54811i) q^{25} +(-0.717177 + 2.20724i) q^{26} +(0.122406 + 0.0889332i) q^{28} +(-0.840363 + 2.58637i) q^{29} +(-1.04675 + 0.760512i) q^{31} -0.854102 q^{32} -7.66708 q^{34} +(-0.377594 + 0.274338i) q^{35} +(-0.600175 + 1.84715i) q^{37} +(-5.00978 - 3.63982i) q^{38} +(0.391081 - 1.20362i) q^{40} +(0.321724 + 0.990166i) q^{41} +8.70820 q^{43} +(-0.249184 - 0.435572i) q^{44} +(-2.14190 + 1.55618i) q^{46} +(1.97626 + 6.08229i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(5.67457 + 4.12281i) q^{50} +(-0.0739811 - 0.227690i) q^{52} +(-10.6826 + 7.76137i) q^{53} +(1.51541 - 0.315846i) q^{55} +2.71154 q^{56} +(-1.23259 - 3.79351i) q^{58} +(2.65875 - 8.18278i) q^{59} +(12.3295 + 8.95793i) q^{61} +(0.586436 - 1.80486i) q^{62} +(-5.91123 + 4.29476i) q^{64} +0.738517 q^{65} -4.67583 q^{67} +(0.639856 - 0.464883i) q^{68} +(0.211544 - 0.651065i) q^{70} +(7.88234 + 5.72685i) q^{71} +(-4.11611 + 12.6681i) q^{73} +(-0.880296 - 2.70927i) q^{74} +0.638786 q^{76} +(1.64693 + 2.87882i) q^{77} +(-2.89815 + 2.10563i) q^{79} +(0.617255 + 1.89971i) q^{80} +(-1.23541 - 0.897575i) q^{82} +(-13.9627 - 10.1445i) q^{83} +(0.753927 + 2.32035i) q^{85} +(-10.3333 + 7.50755i) q^{86} +(-8.20113 - 3.69034i) q^{88} +8.91982 q^{89} +(0.488963 + 1.50487i) q^{91} +(0.0843952 - 0.259742i) q^{92} +(-7.58873 - 5.51353i) q^{94} +(-0.608919 + 1.87406i) q^{95} +(2.18727 - 1.58915i) q^{97} +1.46673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) \) 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8	\( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{13} - q^{14} - 3 q^{16} + 11 q^{17} - 9 q^{19} - 21 q^{20} - q^{22} + 16 q^{23} + 5 q^{25} - 21 q^{26} + 7 q^{28} + 9 q^{29} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 6 q^{37} - 35 q^{38} - 16 q^{40} + 22 q^{41} + 16 q^{43} - 29 q^{44} + 29 q^{46} - 7 q^{47} - 2 q^{49} + 34 q^{50} + 21 q^{52} - 2 q^{53} + 26 q^{55} + 18 q^{56} - 39 q^{58} - 25 q^{59} + 7 q^{61} + 5 q^{62} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} - 2 q^{70} + 14 q^{71} + 3 q^{73} + 9 q^{74} - 52 q^{76} + 5 q^{77} - 9 q^{79} + 33 q^{80} + 31 q^{82} - 23 q^{83} - 10 q^{85} + 17 q^{86} - 7 q^{88} + 34 q^{89} + 5 q^{91} + 34 q^{92} - 30 q^{94} - 24 q^{95} + 30 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^13 - q^14 - 3 * q^16 + 11 * q^17 - 9 * q^19 - 21 * q^20 - q^22 + 16 * q^23 + 5 * q^25 - 21 * q^26 + 7 * q^28 + 9 * q^29 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 6 * q^37 - 35 * q^38 - 16 * q^40 + 22 * q^41 + 16 * q^43 - 29 * q^44 + 29 * q^46 - 7 * q^47 - 2 * q^49 + 34 * q^50 + 21 * q^52 - 2 * q^53 + 26 * q^55 + 18 * q^56 - 39 * q^58 - 25 * q^59 + 7 * q^61 + 5 * q^62 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 - 2 * q^70 + 14 * q^71 + 3 * q^73 + 9 * q^74 - 52 * q^76 + 5 * q^77 - 9 * q^79 + 33 * q^80 + 31 * q^82 - 23 * q^83 - 10 * q^85 + 17 * q^86 - 7 * q^88 + 34 * q^89 + 5 * q^91 + 34 * q^92 - 30 * q^94 - 24 * q^95 + 30 * q^97 - 4 * q^98

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