LMFDB - Embedded newform 585.2.cf.a.262.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(163,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.163"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.cf (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
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} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.1
Root			$-1.51805i$ of defining polynomial
Character	$\chi$	$=$	585.262
Dual form			585.2.cf.a.163.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.759023 - 1.31467i) q^{2} +(-0.152233 + 0.263675i) q^{4} +(-0.600231 - 2.15400i) q^{5} +(-2.24723 - 1.29744i) q^{7} -2.57390 q^{8} +(-2.37621 + 2.42404i) q^{10} +(-1.29395 + 4.82908i) q^{11} +(-2.71223 + 2.37567i) q^{13} +3.93915i q^{14} +(2.25812 + 3.91117i) q^{16} +(-0.0211881 - 0.0790751i) q^{17} +(2.71143 - 0.726525i) q^{19} +(0.659330 + 0.169644i) q^{20} +(7.33077 - 1.96427i) q^{22} +(1.05016 - 3.91925i) q^{23} +(-4.27945 + 2.58580i) q^{25} +(5.18186 + 1.76249i) q^{26} +(0.684205 - 0.395026i) q^{28} +(4.31701 - 2.49243i) q^{29} +(-2.32124 + 2.32124i) q^{31} +(0.854024 - 1.47921i) q^{32} +(-0.0878751 + 0.0878751i) q^{34} +(-1.44583 + 5.61931i) q^{35} +(0.494934 - 0.285750i) q^{37} +(-3.01318 - 3.01318i) q^{38} +(1.54493 + 5.54419i) q^{40} +(-10.0563 - 2.69458i) q^{41} +(0.132121 - 0.0354017i) q^{43} +(-1.07633 - 1.07633i) q^{44} +(-5.94960 + 1.59419i) q^{46} +2.30053i q^{47} +(-0.133293 - 0.230870i) q^{49} +(6.64766 + 3.66337i) q^{50} +(-0.213514 - 1.07680i) q^{52} +(-6.70735 + 6.70735i) q^{53} +(11.1785 - 0.111396i) q^{55} +(5.78416 + 3.33948i) q^{56} +(-6.55343 - 3.78362i) q^{58} +(-0.694109 - 2.59045i) q^{59} +(-2.74237 + 4.74992i) q^{61} +(4.81352 + 1.28978i) q^{62} +6.43957 q^{64} +(6.74516 + 4.41620i) q^{65} +(-7.89339 - 13.6718i) q^{67} +(0.0240756 + 0.00645104i) q^{68} +(8.48494 - 2.36440i) q^{70} +(1.98951 + 7.42495i) q^{71} -6.61894 q^{73} +(-0.751333 - 0.433783i) q^{74} +(-0.221202 + 0.825536i) q^{76} +(9.17326 - 9.17326i) q^{77} +5.71054i q^{79} +(7.06928 - 7.21159i) q^{80} +(4.09050 + 15.2660i) q^{82} +3.70736i q^{83} +(-0.157610 + 0.0931025i) q^{85} +(-0.146824 - 0.146824i) q^{86} +(3.33050 - 12.4296i) q^{88} +(-17.2829 - 4.63094i) q^{89} +(9.17731 - 1.81973i) q^{91} +(0.873538 + 0.873538i) q^{92} +(3.02443 - 1.74616i) q^{94} +(-3.19242 - 5.40434i) q^{95} +(-2.68493 + 4.65043i) q^{97} +(-0.202345 + 0.350471i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 12 q^{8} - 10 q^{10} + 16 q^{11} + 2 q^{13} - 2 q^{16} + 10 q^{17} + 20 q^{19} - 14 q^{20} + 16 q^{22} + 2 q^{23} - 18 q^{25} + 24 q^{26} + 6 q^{28} + 6 q^{32}+ \cdots - 4 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 12 * q^8 - 10 * q^10 + 16 * q^11 + 2 * q^13 - 2 * q^16 + 10 * q^17 + 20 * q^19 - 14 * q^20 + 16 * q^22 + 2 * q^23 - 18 * q^25 + 24 * q^26 + 6 * q^28 + 6 * q^32 - 2 * q^34 + 20 * q^35 + 42 * q^37 - 8 * q^38 - 16 * q^40 - 10 * q^41 - 22 * q^43 - 36 * q^44 + 4 * q^46 - 18 * q^49 - 44 * q^50 + 46 * q^52 + 10 * q^53 + 26 * q^55 - 90 * q^58 - 16 * q^59 - 16 * q^61 + 40 * q^62 - 20 * q^64 - 8 * q^65 - 58 * q^67 - 28 * q^68 + 32 * q^70 + 16 * q^71 + 72 * q^73 + 18 * q^74 - 64 * q^76 - 28 * q^77 + 34 * q^80 + 22 * q^82 - 6 * q^85 - 60 * q^86 + 50 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 + 48 * q^94 - 14 * q^95 - 22 * q^97 - 4 * q^98

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	−0.759023	−	1.31467i	−0.536710	−	0.929610i	−0.999078	−	0.0429217i	$-0.986333\pi$
$2$	−0.759023	−	1.31467i	−0.536710	−	0.929610i	0.462368	−	0.886688i	$-0.347000\pi$
$3$		0			0
$3$		0			0
$4$	−0.152233	+	0.263675i	−0.0761163	+	0.131837i
$5$	−0.600231	−	2.15400i	−0.268431	−	0.963299i
$5$	−0.600231	−	2.15400i	−0.268431	−	0.963299i
$6$		0			0
$7$	−2.24723	−	1.29744i	−0.849375	−	0.490387i	0.0110652	−	0.999939i	$-0.496478\pi$
$7$	−2.24723	−	1.29744i	−0.849375	−	0.490387i	−0.860440	+	0.509552i	$0.829811\pi$
$8$	−2.57390			−0.910011
$9$		0			0
$10$	−2.37621	+	2.42404i	−0.751422	+	0.766549i
$11$	−1.29395	+	4.82908i	−0.390140	+	1.45602i	0.439762	+	0.898114i	$0.355063\pi$
$11$	−1.29395	+	4.82908i	−0.390140	+	1.45602i	−0.829902	+	0.557909i	$0.811604\pi$
$12$		0			0
$13$	−2.71223	+	2.37567i	−0.752237	+	0.658892i
$13$	−2.71223	+	2.37567i	−0.752237	+	0.658892i
$14$			3.93915i			1.05278i
$15$		0			0
$16$	2.25812	+	3.91117i	0.564529	+	0.977793i
$17$	−0.0211881	−	0.0790751i	−0.00513887	−	0.0191785i	0.963309	−	0.268396i	$-0.0864934\pi$
$17$	−0.0211881	−	0.0790751i	−0.00513887	−	0.0191785i	−0.968448	+	0.249217i	$0.919827\pi$
$18$		0			0
$19$	2.71143	−	0.726525i	0.622045	−	0.166676i	0.0659876	−	0.997820i	$-0.478980\pi$
$19$	2.71143	−	0.726525i	0.622045	−	0.166676i	0.556057	+	0.831144i	$0.312314\pi$
$20$	0.659330	+	0.169644i	0.147431	+	0.0379335i
$21$		0			0
$22$	7.33077	−	1.96427i	1.56293	−	0.418785i
$23$	1.05016	−	3.91925i	0.218973	−	0.817220i	−0.765756	−	0.643131i	$-0.777635\pi$
$23$	1.05016	−	3.91925i	0.218973	−	0.817220i	0.984730	−	0.174089i	$-0.0556982\pi$
$24$		0			0
$25$	−4.27945	+	2.58580i	−0.855889	+	0.517159i
$26$	5.18186	+	1.76249i	1.01625	+	0.345653i
$27$		0			0
$28$	0.684205	−	0.395026i	0.129303	−	0.0746528i
$29$	4.31701	−	2.49243i	0.801649	−	0.462833i	−0.0423981	−	0.999101i	$-0.513500\pi$
$29$	4.31701	−	2.49243i	0.801649	−	0.462833i	0.844048	+	0.536268i	$0.180166\pi$
$30$		0			0
$31$	−2.32124	+	2.32124i	−0.416906	+	0.416906i	−0.884136	−	0.467230i	$-0.845252\pi$
$31$	−2.32124	+	2.32124i	−0.416906	+	0.416906i	0.467230	+	0.884136i	$0.345252\pi$
$32$	0.854024	−	1.47921i	0.150972	−	0.261490i
$33$		0			0
$34$	−0.0878751	+	0.0878751i	−0.0150705	+	0.0150705i
$35$	−1.44583	+	5.61931i	−0.244390	+	0.949837i
$36$		0			0
$37$	0.494934	−	0.285750i	0.0813667	−	0.0469771i	−0.458765	−	0.888558i	$-0.651708\pi$
$37$	0.494934	−	0.285750i	0.0813667	−	0.0469771i	0.540131	+	0.841581i	$0.318375\pi$
$38$	−3.01318	−	3.01318i	−0.488802	−	0.488802i
$39$		0			0
$40$	1.54493	+	5.54419i	0.244276	+	0.876613i
$41$	−10.0563	−	2.69458i	−1.57053	−	0.420823i	−0.634554	−	0.772879i	$-0.718816\pi$
$41$	−10.0563	−	2.69458i	−1.57053	−	0.420823i	−0.935979	+	0.352056i	$0.885483\pi$
$42$		0			0
$43$	0.132121	−	0.0354017i	0.0201483	−	0.00539871i	−0.248731	−	0.968573i	$-0.580013\pi$
$43$	0.132121	−	0.0354017i	0.0201483	−	0.00539871i	0.268879	+	0.963174i	$0.413347\pi$
$44$	−1.07633	−	1.07633i	−0.162262	−	0.162262i
$45$		0			0
$46$	−5.94960	+	1.59419i	−0.877221	+	0.235051i
$47$			2.30053i			0.335567i	0.985824	+	0.167784i	$0.0536610\pi$
$47$			2.30053i			0.335567i	−0.985824	+	0.167784i	$0.946339\pi$
$48$		0			0
$49$	−0.133293	−	0.230870i	−0.0190418	−	0.0329814i
$50$	6.64766	+	3.66337i	0.940121	+	0.518078i
$51$		0			0
$52$	−0.213514	−	1.07680i	−0.0296090	−	0.149325i
$53$	−6.70735	+	6.70735i	−0.921326	+	0.921326i	−0.997123	−	0.0757974i	$-0.975850\pi$
$53$	−6.70735	+	6.70735i	−0.921326	+	0.921326i	0.0757974	+	0.997123i	$0.475850\pi$
$54$		0			0
$55$	11.1785	−	0.111396i	1.50731	−	0.0150206i
$56$	5.78416	+	3.33948i	0.772941	+	0.446257i
$57$		0			0
$58$	−6.55343	−	3.78362i	−0.860507	−	0.496814i
$59$	−0.694109	−	2.59045i	−0.0903653	−	0.337248i	0.905911	−	0.423469i	$-0.139188\pi$
$59$	−0.694109	−	2.59045i	−0.0903653	−	0.337248i	−0.996276	+	0.0862207i	$0.972521\pi$
$60$		0			0
$61$	−2.74237	+	4.74992i	−0.351124	+	0.608165i	−0.986447	−	0.164082i	$-0.947534\pi$
$61$	−2.74237	+	4.74992i	−0.351124	+	0.608165i	0.635322	+	0.772247i	$0.280867\pi$
$62$	4.81352	+	1.28978i	0.611318	+	0.163802i
$63$		0			0
$64$	6.43957			0.804946
$65$	6.74516	+	4.41620i	0.836634	+	0.547762i
$66$		0			0
$67$	−7.89339	−	13.6718i	−0.964331	−	1.67027i	−0.711401	−	0.702786i	$-0.751939\pi$
$67$	−7.89339	−	13.6718i	−0.964331	−	1.67027i	−0.252930	−	0.967485i	$-0.581394\pi$
$68$	0.0240756	+	0.00645104i	0.00291960	+	0.000782303i
$69$		0			0
$70$	8.48494	−	2.36440i	1.01414	−	0.282600i
$71$	1.98951	+	7.42495i	0.236111	+	0.881180i	0.977645	+	0.210264i	$0.0674322\pi$
$71$	1.98951	+	7.42495i	0.236111	+	0.881180i	−0.741533	+	0.670916i	$0.765901\pi$
$72$		0			0
$73$	−6.61894			−0.774688			−0.387344	−	0.921935i	$-0.626607\pi$
$73$	−6.61894			−0.774688			−0.387344	+	0.921935i	$0.626607\pi$
$74$	−0.751333	−	0.433783i	−0.0873407	−	0.0504262i
$75$		0			0
$76$	−0.221202	+	0.825536i	−0.0253736	+	0.0946955i
$77$	9.17326	−	9.17326i	1.04539	−	1.04539i
$78$		0			0
$79$			5.71054i			0.642486i	0.946997	+	0.321243i	$0.104101\pi$
$79$			5.71054i			0.642486i	−0.946997	+	0.321243i	$0.895899\pi$
$80$	7.06928	−	7.21159i	0.790369	−	0.806280i
$81$		0			0
$82$	4.09050	+	15.2660i	0.451720	+	1.68584i
$83$			3.70736i			0.406936i	0.979082	+	0.203468i	$0.0652213\pi$
$83$			3.70736i			0.406936i	−0.979082	+	0.203468i	$0.934779\pi$
$84$		0			0
$85$	−0.157610	+	0.0931025i	−0.0170952	+	0.0100984i
$86$	−0.146824	−	0.146824i	−0.0158325	−	0.0158325i
$87$		0			0
$88$	3.33050	−	12.4296i	0.355032	−	1.32500i
$89$	−17.2829	−	4.63094i	−1.83198	−	0.490878i	−0.833851	−	0.551989i	$-0.813869\pi$
$89$	−17.2829	−	4.63094i	−1.83198	−	0.490878i	−0.998131	+	0.0611111i	$0.980536\pi$
$90$		0			0
$91$	9.17731	−	1.81973i	0.962043	−	0.190759i
$92$	0.873538	+	0.873538i	0.0910726	+	0.0910726i
$93$		0			0
$94$	3.02443	−	1.74616i	0.311946	−	0.180102i
$95$	−3.19242	−	5.40434i	−0.327535	−	0.554474i
$96$		0			0
$97$	−2.68493	+	4.65043i	−0.272613	+	0.472180i	−0.969530	−	0.244972i	$-0.921221\pi$
$97$	−2.68493	+	4.65043i	−0.272613	+	0.472180i	0.696917	+	0.717152i	$0.254555\pi$
$98$	−0.202345	+	0.350471i	−0.0204399	+	0.0354029i
$99$		0			0
$100$	−0.0303375	−	1.52202i	−0.00303375	−	0.152202i
$101$	−2.17443	+	1.25541i	−0.216363	+	0.124918i	−0.604265	−	0.796783i	$-0.706533\pi$
$101$	−2.17443	+	1.25541i	−0.216363	+	0.124918i	0.387902	+	0.921701i	$0.373200\pi$
$102$		0			0
$103$	−4.71738	−	4.71738i	−0.464817	−	0.464817i	0.435414	−	0.900230i	$-0.356602\pi$
$103$	−4.71738	−	4.71738i	−0.464817	−	0.464817i	−0.900230	+	0.435414i	$0.856602\pi$
$104$	6.98101	−	6.11474i	0.684545	−	0.599599i
$105$		0			0
$106$	13.9090	+	3.72690i	1.35096	+	0.361988i
$107$	−0.939155	+	3.50497i	−0.0907915	+	0.338838i	−0.996348	−	0.0853876i	$-0.972787\pi$
$107$	−0.939155	+	3.50497i	−0.0907915	+	0.338838i	0.905556	+	0.424226i	$0.139454\pi$
$108$		0			0
$109$	−1.58528	−	1.58528i	−0.151843	−	0.151843i	0.627098	−	0.778941i	$-0.284243\pi$
$109$	−1.58528	−	1.58528i	−0.151843	−	0.151843i	−0.778941	+	0.627098i	$0.784243\pi$
$110$	−8.63120	−	14.6115i	−0.822953	−	1.39315i
$111$		0			0
$112$		−	11.7191i		−	1.10735i
$113$	−1.48231	−	5.53206i	−0.139444	−	0.520412i	−0.999940	−	0.0109551i	$-0.996513\pi$
$113$	−1.48231	−	5.53206i	−0.139444	−	0.520412i	0.860496	−	0.509457i	$-0.170154\pi$
$114$		0			0
$115$	−9.07241	+	0.0904081i	−0.846006	+	0.00843060i
$116$			1.51772i			0.140916i
$117$		0			0
$118$	−2.87873	+	2.87873i	−0.265009	+	0.265009i
$119$	−0.0549806	+	0.205190i	−0.00504007	+	0.0188098i
$120$		0			0
$121$	−12.1195	−	6.99717i	−1.10177	−	0.636106i
$122$	8.32609			0.753809
$123$		0			0
$124$	−0.258683	−	0.965419i	−0.0232304	−	0.0866972i
$125$	8.13846	+	7.66586i	0.727926	+	0.685655i
$126$		0			0
$127$	0.786718	+	0.210801i	0.0698100	+	0.0187055i	0.293555	−	0.955942i	$-0.405162\pi$
$127$	0.786718	+	0.210801i	0.0698100	+	0.0187055i	−0.223745	+	0.974648i	$0.571828\pi$
$128$	−6.59583	−	11.4243i	−0.582994	−	1.00978i
$129$		0			0
$130$	0.686097	−	12.2196i	0.0601747	−	1.07173i
$131$	16.1062			1.40721			0.703604	−	0.710592i	$-0.251573\pi$
$131$	16.1062			1.40721			0.703604	+	0.710592i	$0.251573\pi$
$132$		0			0
$133$	−7.03584	−	1.88525i	−0.610085	−	0.163472i
$134$	−11.9825	+	20.7544i	−1.03513	+	1.79290i
$135$		0			0
$136$	0.0545361	+	0.203531i	0.00467643	+	0.0174527i
$137$	−16.6601	−	9.61871i	−1.42337	−	0.821782i	−0.426783	−	0.904354i	$-0.640353\pi$
$137$	−16.6601	−	9.61871i	−1.42337	−	0.821782i	−0.996585	+	0.0825721i	$0.973687\pi$
$138$		0			0
$139$	−13.7257	−	7.92451i	−1.16419	−	0.672148i	−0.211889	−	0.977294i	$-0.567962\pi$
$139$	−13.7257	−	7.92451i	−1.16419	−	0.672148i	−0.952306	+	0.305146i	$0.901295\pi$
$140$	−1.26157	−	1.23667i	−0.106622	−	0.104518i
$141$		0			0
$142$	8.25125	−	8.25125i	0.692430	−	0.692430i
$143$	−7.96282	−	16.1716i	−0.665884	−	1.35234i
$144$		0			0
$145$	−7.95990	−	7.80282i	−0.661034	−	0.647989i
$146$	5.02393	+	8.70170i	0.415783	+	0.720158i
$147$		0			0
$148$			0.174002i			0.0143029i
$149$	−1.39120	+	0.372772i	−0.113972	+	0.0305387i	−0.315354	−	0.948974i	$-0.602123\pi$
$149$	−1.39120	+	0.372772i	−0.113972	+	0.0305387i	0.201382	+	0.979513i	$0.435457\pi$
$150$		0			0
$151$	13.9253	+	13.9253i	1.13322	+	1.13322i	0.989638	+	0.143585i	$0.0458631\pi$
$151$	13.9253	+	13.9253i	1.13322	+	1.13322i	0.143585	+	0.989638i	$0.454137\pi$
$152$	−6.97895	+	1.87000i	−0.566068	+	0.151677i
$153$		0			0
$154$	−19.0225	−	5.09706i	−1.53288	−	0.410733i
$155$	6.39322	+	3.60667i	0.513516	+	0.289695i
$156$		0			0
$157$	4.54644	+	4.54644i	0.362845	+	0.362845i	0.864859	−	0.502014i	$-0.167408\pi$
$157$	4.54644	+	4.54644i	0.362845	+	0.362845i	−0.502014	+	0.864859i	$0.667408\pi$
$158$	7.50746	−	4.33444i	0.597262	−	0.344829i
$159$		0			0
$160$	−3.69884	−	0.951700i	−0.292419	−	0.0752385i
$161$	−7.44495	+	7.44495i	−0.586744	+	0.586744i
$162$		0			0
$163$	6.56789	−	11.3759i	0.514437	−	0.891031i	−0.485423	−	0.874280i	$-0.661334\pi$
$163$	6.56789	−	11.3759i	0.514437	−	0.891031i	0.999860	−	0.0167516i	$-0.00533245\pi$
$164$	2.24139	−	2.24139i	0.175023	−	0.175023i
$165$		0			0
$166$	4.87395	−	2.81398i	0.378292	−	0.218407i
$167$	−2.84503	+	1.64258i	−0.220155	+	0.127107i	−0.606022	−	0.795448i	$-0.707236\pi$
$167$	−2.84503	+	1.64258i	−0.220155	+	0.127107i	0.385867	+	0.922554i	$0.373902\pi$
$168$		0			0
$169$	1.71239	−	12.8867i	0.131722	−	0.991287i
$170$	0.242028	+	0.136538i	0.0185627	+	0.0104720i
$171$		0			0
$172$	−0.0107786	+	0.0402263i	−0.000821860	+	0.00306722i
$173$	4.09367	−	1.09689i	0.311236	−	0.0833953i	−0.0998202	−	0.995005i	$-0.531827\pi$
$173$	4.09367	−	1.09689i	0.311236	−	0.0833953i	0.411056	+	0.911610i	$0.365160\pi$
$174$		0			0
$175$	12.9718	−	0.258559i	0.980579	−	0.0195452i
$176$	−21.8093	+	5.84377i	−1.64393	+	0.440491i
$177$		0			0
$178$	7.02997	+	26.2362i	0.526919	+	1.96649i
$179$	−6.98083	−	12.0912i	−0.521772	−	0.903735i	−0.999679	−	0.0253252i	$-0.991938\pi$
$179$	−6.98083	−	12.0912i	−0.521772	−	0.903735i	0.477907	−	0.878410i	$-0.341395\pi$
$180$		0			0
$181$		−	8.64775i		−	0.642782i	−0.946947	−	0.321391i	$-0.895850\pi$
$181$		−	8.64775i		−	0.642782i	0.946947	−	0.321391i	$-0.104150\pi$
$182$	−9.35812	−	10.6839i	−0.693670	−	0.791942i
$183$		0			0
$184$	−2.70301	+	10.0878i	−0.199268	+	0.743680i
$185$	−0.912582	−	0.894573i	−0.0670944	−	0.0657703i
$186$		0			0
$187$	0.409276			0.0299292
$188$	−0.606592	−	0.350216i	−0.0442402	−	0.0255421i
$189$		0			0
$190$	−4.68179	+	8.29899i	−0.339653	+	0.602072i
$191$	8.45647	−	14.6470i	0.611889	−	1.05982i	−0.379033	−	0.925383i	$-0.623743\pi$
$191$	8.45647	−	14.6470i	0.611889	−	1.05982i	0.990922	−	0.134439i	$-0.0429232\pi$
$192$		0			0
$193$	−4.27780	−	7.40936i	−0.307923	−	0.533338i	0.669985	−	0.742375i	$-0.266300\pi$
$193$	−4.27780	−	7.40936i	−0.307923	−	0.533338i	−0.977908	+	0.209037i	$0.932967\pi$
$194$	8.15169			0.585257
$195$		0			0
$196$	0.0811660			0.00579757
$197$	3.82842	+	6.63101i	0.272764	+	0.472440i	0.969568	−	0.244820i	$-0.0787290\pi$
$197$	3.82842	+	6.63101i	0.272764	+	0.472440i	−0.696805	+	0.717261i	$0.745396\pi$
$198$		0			0
$199$	−7.66380	+	13.2741i	−0.543272	+	0.940975i	0.455441	+	0.890266i	$0.349481\pi$
$199$	−7.66380	+	13.2741i	−0.543272	+	0.940975i	−0.998713	+	0.0507092i	$0.983852\pi$
$200$	11.0149	−	6.65558i	0.778869	−	0.470621i
$201$		0			0
$202$	3.30088	+	1.90576i	0.232249	+	0.134089i
$203$	−12.9351			−0.907868
$204$		0			0
$205$	0.231976	+	23.2787i	0.0162019	+	1.62585i
$206$	−2.62118	+	9.78238i	−0.182626	+	0.681570i
$207$		0			0
$208$	−15.4162	−	5.24346i	−1.06892	−	0.363569i
$209$			14.0338i			0.970739i
$210$		0			0
$211$	−9.91788	−	17.1783i	−0.682775	−	1.18260i	−0.974130	−	0.225986i	$-0.927440\pi$
$211$	−9.91788	−	17.1783i	−0.682775	−	1.18260i	0.291355	−	0.956615i	$-0.405894\pi$
$212$	−0.747481	−	2.78964i	−0.0513372	−	0.191593i
$213$		0			0
$214$	5.32071	−	1.42568i	0.363716	−	0.0974575i
$215$	−0.155559	−	0.263340i	−0.0106090	−	0.0179596i
$216$		0			0
$217$	8.22803	−	2.20469i	0.558555	−	0.149664i
$218$	−0.880853	+	3.28739i	−0.0596589	+	0.222650i
$219$		0			0
$220$	−1.67236	+	2.96445i	−0.112751	+	0.199863i
$221$	0.245323	+	0.164134i	0.0165022	+	0.0110408i
$222$		0			0
$223$	16.4311	−	9.48653i	1.10031	−	0.635265i	0.164008	−	0.986459i	$-0.447558\pi$
$223$	16.4311	−	9.48653i	1.10031	−	0.635265i	0.936303	+	0.351194i	$0.114224\pi$
$224$	−3.83838	+	2.21609i	−0.256463	+	0.148069i
$225$		0			0
$226$	−6.14771	+	6.14771i	−0.408939	+	0.408939i
$227$	13.4794	−	23.3469i	0.894656	−	1.54959i	0.0604265	−	0.998173i	$-0.480754\pi$
$227$	13.4794	−	23.3469i	0.894656	−	1.54959i	0.834230	−	0.551417i	$-0.185913\pi$
$228$		0			0
$229$	11.1801	−	11.1801i	0.738799	−	0.738799i	−0.233547	−	0.972346i	$-0.575033\pi$
$229$	11.1801	−	11.1801i	0.738799	−	0.738799i	0.972346	+	0.233547i	$0.0750331\pi$
$230$	7.00503	+	11.8586i	0.461898	+	0.781931i
$231$		0			0
$232$	−11.1116	+	6.41527i	−0.729510	+	0.421183i
$233$	6.75797	+	6.75797i	0.442729	+	0.442729i	0.892928	−	0.450199i	$-0.148647\pi$
$233$	6.75797	+	6.75797i	0.442729	+	0.442729i	−0.450199	+	0.892928i	$0.648647\pi$
$234$		0			0
$235$	4.95535	−	1.38085i	0.323251	−	0.0900767i
$236$	0.788702	+	0.211332i	0.0513401	+	0.0137565i
$237$		0			0
$238$	0.311489	−	0.0834631i	0.0201908	−	0.00541011i
$239$	1.98766	+	1.98766i	0.128571	+	0.128571i	0.768464	−	0.639893i	$-0.221021\pi$
$239$	1.98766	+	1.98766i	0.128571	+	0.128571i	−0.639893	+	0.768464i	$0.721021\pi$
$240$		0			0
$241$	−2.65141	+	0.710443i	−0.170792	+	0.0457637i	−0.343202	−	0.939262i	$-0.611511\pi$
$241$	−2.65141	+	0.710443i	−0.170792	+	0.0457637i	0.172409	+	0.985025i	$0.444845\pi$
$242$			21.2441i			1.36562i
$243$		0			0
$244$	−0.834956	−	1.44619i	−0.0534526	−	0.0925826i
$245$	−0.417287	+	0.425688i	−0.0266595	+	0.0271962i
$246$		0			0
$247$	−5.62804	+	8.41197i	−0.358104	+	0.535241i
$248$	5.97463	−	5.97463i	0.379389	−	0.379389i
$249$		0			0
$250$	3.90077	−	16.5179i	0.246706	−	1.04469i
$251$	2.45414	+	1.41690i	0.154904	+	0.0894337i	0.575448	−	0.817838i	$-0.304828\pi$
$251$	2.45414	+	1.41690i	0.154904	+	0.0894337i	−0.420545	+	0.907272i	$0.638161\pi$
$252$		0			0
$253$	17.5675	+	10.1426i	1.10446	+	0.637661i
$254$	−0.320005	−	1.19428i	−0.0200789	−	0.0749355i
$255$		0			0
$256$	−3.57321	+	6.18898i	−0.223325	+	0.386811i
$257$	19.3784	+	5.19242i	1.20879	+	0.323894i	0.806287	−	0.591525i	$-0.201474\pi$
$257$	19.3784	+	5.19242i	1.20879	+	0.323894i	0.402502	+	0.915419i	$0.368141\pi$
$258$		0			0
$259$	−1.48298			−0.0921478
$260$	−2.19127	+	1.10624i	−0.135897	+	0.0686060i
$261$		0			0
$262$	−12.2250	−	21.1743i	−0.755264	−	1.30815i
$263$	9.10077	+	2.43854i	0.561177	+	0.150367i	0.528247	−	0.849091i	$-0.322849\pi$
$263$	9.10077	+	2.43854i	0.561177	+	0.150367i	0.0329302	+	0.999458i	$0.489516\pi$
$264$		0			0
$265$	18.4736	+	10.4217i	1.13482	+	0.640199i
$266$	2.86189	+	10.6807i	0.175474	+	0.654878i
$267$		0			0
$268$	4.80653			0.293605
$269$	−2.78417	−	1.60744i	−0.169754	−	0.0980075i	0.412716	−	0.910860i	$-0.364580\pi$
$269$	−2.78417	−	1.60744i	−0.169754	−	0.0980075i	−0.582470	+	0.812852i	$0.697914\pi$
$270$		0			0
$271$	−3.93065	+	14.6694i	−0.238770	+	0.891102i	0.737643	+	0.675191i	$0.235939\pi$
$271$	−3.93065	+	14.6694i	−0.238770	+	0.891102i	−0.976413	+	0.215911i	$0.930728\pi$
$272$	0.261431	−	0.261431i	0.0158516	−	0.0158516i
$273$		0			0
$274$			29.2033i			1.76424i
$275$	−6.94964	−	24.0117i	−0.419079	−	1.44796i
$276$		0			0
$277$	2.76028	+	10.3015i	0.165849	+	0.618956i	0.997930	+	0.0643031i	$0.0204824\pi$
$277$	2.76028	+	10.3015i	0.165849	+	0.618956i	−0.832082	+	0.554653i	$0.812851\pi$
$278$			24.0595i			1.44300i
$279$		0			0
$280$	3.72143	−	14.4635i	0.222398	−	0.864362i
$281$	12.7630	+	12.7630i	0.761379	+	0.761379i	0.976572	−	0.215193i	$-0.0690380\pi$
$281$	12.7630	+	12.7630i	0.761379	+	0.761379i	−0.215193	+	0.976572i	$0.569038\pi$
$282$		0			0
$283$	−1.49018	+	5.56143i	−0.0885820	+	0.330592i	−0.995968	−	0.0897050i	$-0.971408\pi$
$283$	−1.49018	+	5.56143i	−0.0885820	+	0.330592i	0.907386	+	0.420297i	$0.138074\pi$
$284$	−2.26064	−	0.605736i	−0.134144	−	0.0359438i
$285$		0			0
$286$	−15.2163	+	22.7431i	−0.899757	+	1.34483i
$287$	19.1028	+	19.1028i	1.12760	+	1.12760i
$288$		0			0
$289$	14.7166	−	8.49665i	0.865684	−	0.499803i
$290$	−4.21636	+	16.3871i	−0.247593	+	0.962286i
$291$		0			0
$292$	1.00762	−	1.74525i	0.0589664	−	0.102133i
$293$	−1.59804	+	2.76788i	−0.0933583	+	0.161701i	−0.908922	−	0.416966i	$-0.863094\pi$
$293$	−1.59804	+	2.76788i	−0.0933583	+	0.161701i	0.815564	+	0.578667i	$0.196427\pi$
$294$		0			0
$295$	−5.16321	+	3.04998i	−0.300614	+	0.177577i
$296$	−1.27391	+	0.735493i	−0.0740446	+	0.0427497i
$297$		0			0
$298$	1.54603	+	1.54603i	0.0895590	+	0.0895590i
$299$	6.46257	+	13.1247i	0.373740	+	0.759023i
$300$		0			0
$301$	−0.342839	−	0.0918633i	−0.0197609	−	0.00529491i
$302$	7.73749	−	28.8767i	0.445243	−	1.66167i
$303$		0			0
$304$	8.96429	+	8.96429i	0.514137	+	0.514137i
$305$	11.8774	+	3.05602i	0.680098	+	0.174987i
$306$		0			0
$307$			24.2740i			1.38539i	0.721231	+	0.692695i	$0.243577\pi$
$307$			24.2740i			1.38539i	−0.721231	+	0.692695i	$0.756423\pi$
$308$	1.02229	+	3.81522i	0.0582501	+	0.217393i
$309$		0			0
$310$	−0.111037	−	11.1425i	−0.00630648	−	0.632852i
$311$		−	16.9053i		−	0.958614i	−0.877647	−	0.479307i	$-0.840888\pi$
$311$		−	16.9053i		−	0.958614i	0.877647	−	0.479307i	$-0.159112\pi$
$312$		0			0
$313$	−8.40997	+	8.40997i	−0.475359	+	0.475359i	−0.903644	−	0.428285i	$-0.859118\pi$
$313$	−8.40997	+	8.40997i	−0.475359	+	0.475359i	0.428285	+	0.903644i	$0.359118\pi$
$314$	2.52620	−	9.42790i	0.142562	−	0.532047i
$315$		0			0
$316$	−1.50573	−	0.869331i	−0.0847037	−	0.0489037i
$317$	−11.9484			−0.671087			−0.335543	−	0.942025i	$-0.608920\pi$
$317$	−11.9484			−0.671087			−0.335543	+	0.942025i	$0.608920\pi$
$318$		0			0
$319$	6.45015	+	24.0723i	0.361139	+	1.34779i
$320$	−3.86523	−	13.8708i	−0.216073	−	0.775403i
$321$		0			0
$322$	15.4385	+	4.13674i	0.860355	+	0.230531i
$323$	−0.114900	−	0.199013i	−0.00639321	−	0.0110734i
$324$		0			0
$325$	5.46385	−	17.1798i	0.303080	−	0.952965i
$326$	−19.9407			−1.10442
$327$		0			0
$328$	25.8840	+	6.93559i	1.42920	+	0.382954i
$329$	2.98480	−	5.16983i	0.164558	−	0.285022i
$330$		0			0
$331$	−5.55136	−	20.7179i	−0.305130	−	1.13876i	−0.932833	−	0.360308i	$-0.882671\pi$
$331$	−5.55136	−	20.7179i	−0.305130	−	1.13876i	0.627703	−	0.778453i	$-0.283995\pi$
$332$	−0.977538	−	0.564382i	−0.0536494	−	0.0309745i
$333$		0			0
$334$	4.31889	+	2.49351i	0.236319	+	0.136439i
$335$	−24.7111	+	25.2086i	−1.35011	+	1.37729i
$336$		0			0
$337$	−14.1264	+	14.1264i	−0.769514	+	0.769514i	−0.978021	−	0.208507i	$-0.933140\pi$
$337$	−14.1264	+	14.1264i	−0.769514	+	0.769514i	0.208507	+	0.978021i	$0.433140\pi$
$338$	−18.2415	+	7.53011i	−0.992206	+	0.409584i
$339$		0			0
$340$	−0.000555369	−	0.0557310i	−3.01191e−5	−	0.00302244i
$341$	−8.20588	−	14.2130i	−0.444373	−	0.769677i
$342$		0			0
$343$			18.8559i			1.01812i
$344$	−0.340067	+	0.0911205i	−0.0183352	+	0.00491289i
$345$		0			0
$346$	−4.54924	−	4.54924i	−0.244569	−	0.244569i
$347$	−23.7906	+	6.37467i	−1.27715	+	0.342210i	−0.832765	−	0.553627i	$-0.813243\pi$
$347$	−23.7906	+	6.37467i	−1.27715	+	0.342210i	−0.444382	+	0.895837i	$0.646577\pi$
$348$		0			0
$349$	−26.3190	−	7.05214i	−1.40882	−	0.377493i	−0.527317	−	0.849669i	$-0.676802\pi$
$349$	−26.3190	−	7.05214i	−1.40882	−	0.377493i	−0.881504	+	0.472176i	$0.843469\pi$
$350$	−10.1858	−	16.8574i	−0.544456	−	0.901065i
$351$		0			0
$352$	6.03818	+	6.03818i	0.321836	+	0.321836i
$353$	−7.62038	+	4.39963i	−0.405592	+	0.234169i	−0.688894	−	0.724862i	$-0.741903\pi$
$353$	−7.62038	+	4.39963i	−0.405592	+	0.234169i	0.283302	+	0.959031i	$0.408570\pi$
$354$		0			0
$355$	14.7992	−	8.74209i	0.785460	−	0.463982i
$356$	3.85208	−	3.85208i	0.204160	−	0.204160i
$357$		0			0
$358$	−10.5972	+	18.3549i	−0.560081	+	0.970089i
$359$	11.1256	−	11.1256i	0.587186	−	0.587186i	−0.349683	−	0.936868i	$-0.613711\pi$
$359$	11.1256	−	11.1256i	0.587186	−	0.587186i	0.936868	+	0.349683i	$0.113711\pi$
$360$		0			0
$361$	−9.63047	+	5.56015i	−0.506867	+	0.292640i
$362$	−11.3689	+	6.56385i	−0.597537	+	0.344988i
$363$		0			0
$364$	−0.917270	+	2.69684i	−0.0480780	+	0.141353i
$365$	3.97289	+	14.2572i	0.207951	+	0.746256i
$366$		0			0
$367$	2.84144	−	10.6044i	0.148322	−	0.553545i	−0.851263	−	0.524739i	$-0.824163\pi$
$367$	2.84144	−	10.6044i	0.148322	−	0.553545i	0.999585	−	0.0288057i	$-0.00917042\pi$
$368$	17.7002	−	4.74276i	0.922689	−	0.247234i
$369$		0			0
$370$	−0.483395	+	1.87874i	−0.0251305	+	0.0976712i
$371$	23.7754	−	6.37060i	1.23436	−	0.330745i
$372$		0			0
$373$	2.73825	+	10.2193i	0.141781	+	0.529135i	0.999878	+	0.0156462i	$0.00498054\pi$
$373$	2.73825	+	10.2193i	0.141781	+	0.529135i	−0.858096	+	0.513489i	$0.828353\pi$
$374$	−0.310650	−	0.538062i	−0.0160633	−	0.0278225i
$375$		0			0
$376$		−	5.92134i		−	0.305370i
$377$	−5.78755	+	17.0158i	−0.298074	+	0.876361i
$378$		0			0
$379$	2.53694	−	9.46800i	0.130314	−	0.486338i	−0.869659	−	0.493652i	$-0.835662\pi$
$379$	2.53694	−	9.46800i	0.130314	−	0.486338i	0.999973	+	0.00731411i	$0.00232818\pi$
$380$	1.91098	−	0.0190432i	0.0980311	−	0.000976897i
$381$		0			0
$382$	−25.6746			−1.31363
$383$	22.5658	+	13.0283i	1.15306	+	0.665718i	0.949630	−	0.313373i	$-0.101459\pi$
$383$	22.5658	+	13.0283i	1.15306	+	0.665718i	0.203426	+	0.979090i	$0.434792\pi$
$384$		0			0
$385$	−25.2653	−	14.2531i	−1.28764	−	0.726407i
$386$	−6.49390	+	11.2478i	−0.330531	+	0.572496i
$387$		0			0
$388$	−0.817467	−	1.41589i	−0.0415006	−	0.0718812i
$389$	−32.4888			−1.64725			−0.823623	−	0.567138i	$-0.808050\pi$
$389$	−32.4888			−1.64725			−0.823623	+	0.567138i	$0.808050\pi$
$390$		0			0
$391$	−0.332166			−0.0167983
$392$	0.343082	+	0.594236i	0.0173283	+	0.0300134i
$393$		0			0
$394$	5.81172	−	10.0662i	0.292790	−	0.507127i
$395$	12.3005	−	3.42764i	0.618906	−	0.172463i
$396$		0			0
$397$	−20.9451	−	12.0927i	−1.05121	−	0.606914i	−0.128219	−	0.991746i	$-0.540926\pi$
$397$	−20.9451	−	12.0927i	−1.05121	−	0.606914i	−0.922987	+	0.384832i	$0.874259\pi$
$398$	23.2680			1.16632
$399$		0			0
$400$	−19.7770	−	10.8986i	−0.988849	−	0.544931i
$401$	8.49918	−	31.7194i	0.424429	−	1.58399i	−0.340738	−	0.940158i	$-0.610677\pi$
$401$	8.49918	−	31.7194i	0.424429	−	1.58399i	0.765167	−	0.643832i	$-0.222657\pi$
$402$		0			0
$403$	0.781237	−	11.8102i	0.0389162	−	0.588309i
$404$		−	0.764454i		−	0.0380330i
$405$		0			0
$406$	9.81806	+	17.0054i	0.487262	+	0.843963i
$407$	0.739493	+	2.75983i	0.0366553	+	0.136799i
$408$		0			0
$409$	−13.4843	+	3.61312i	−0.666758	+	0.178657i	−0.576294	−	0.817243i	$-0.695502\pi$
$409$	−13.4843	+	3.61312i	−0.666758	+	0.178657i	−0.0904639	+	0.995900i	$0.528835\pi$
$410$	30.4277	−	17.9740i	1.50271	−	0.887675i
$411$		0			0
$412$	1.96199	−	0.525714i	0.0966603	−	0.0259001i
$413$	−1.80113	+	6.72192i	−0.0886279	+	0.330764i
$414$		0			0
$415$	7.98567	−	2.22527i	0.392001	−	0.109234i
$416$	1.19781	+	6.04084i	0.0587275	+	0.296177i
$417$		0			0
$418$	18.4498	−	10.6520i	0.902408	−	0.521006i
$419$	−1.92240	+	1.10990i	−0.0939155	+	0.0542221i	−0.546222	−	0.837640i	$-0.683935\pi$
$419$	−1.92240	+	1.10990i	−0.0939155	+	0.0542221i	0.452307	+	0.891862i	$0.350601\pi$
$420$		0			0
$421$	24.4795	−	24.4795i	1.19306	−	1.19306i	0.216853	−	0.976204i	$-0.430421\pi$
$421$	24.4795	−	24.4795i	1.19306	−	1.19306i	0.976204	−	0.216853i	$-0.0695792\pi$
$422$	−15.0558	+	26.0774i	−0.732905	+	1.26943i
$423$		0			0
$424$	17.2641	−	17.2641i	0.838417	−	0.838417i
$425$	0.295145	+	0.283609i	0.0143166	+	0.0137571i
$426$		0			0
$427$	12.3255	−	7.11613i	0.596472	−	0.344374i
$428$	−0.781202	−	0.781202i	−0.0377608	−	0.0377608i
$429$		0			0
$430$	−0.228132	+	0.404389i	−0.0110015	+	0.0195014i
$431$	−1.59621	−	0.427704i	−0.0768868	−	0.0206018i	0.220171	−	0.975461i	$-0.429339\pi$
$431$	−1.59621	−	0.427704i	−0.0768868	−	0.0206018i	−0.297057	+	0.954860i	$0.596005\pi$
$432$		0			0
$433$	−14.3111	+	3.83465i	−0.687748	+	0.184281i	−0.585736	−	0.810502i	$-0.699195\pi$
$433$	−14.3111	+	3.83465i	−0.687748	+	0.184281i	−0.102012	+	0.994783i	$0.532528\pi$
$434$	−9.14370	−	9.14370i	−0.438912	−	0.438912i
$435$		0			0
$436$	0.659331	−	0.176667i	0.0315762	−	0.00846083i
$437$		−	11.3897i		−	0.544845i
$438$		0			0
$439$	−10.9363	−	18.9422i	−0.521959	−	0.904060i	−0.999674	−	0.0255448i	$-0.991868\pi$
$439$	−10.9363	−	18.9422i	−0.521959	−	0.904060i	0.477714	−	0.878515i	$-0.341465\pi$
$440$	−28.7724	+	0.286722i	−1.37167	+	0.0136689i
$441$		0			0
$442$	0.0295753	−	0.447100i	0.00140675	−	0.0212664i
$443$	6.14972	−	6.14972i	0.292182	−	0.292182i	−0.545760	−	0.837942i	$-0.683759\pi$
$443$	6.14972	−	6.14972i	0.292182	−	0.292182i	0.837942	+	0.545760i	$0.183759\pi$
$444$		0			0
$445$	0.398677	+	40.0070i	0.0188991	+	1.89651i
$446$	−24.9432	−	14.4010i	−1.18110	−	0.681907i
$447$		0			0
$448$	−14.4712	−	8.35496i	−0.683701	−	0.394735i
$449$	1.20994	+	4.51557i	0.0571008	+	0.213103i	0.988581	−	0.150688i	$-0.0481489\pi$
$449$	1.20994	+	4.51557i	0.0571008	+	0.213103i	−0.931481	+	0.363791i	$0.881482\pi$
$450$		0			0
$451$	26.0247	−	45.0761i	1.22546	−	2.12255i
$452$	1.68432	+	0.451312i	0.0792237	+	0.0212279i
$453$		0			0
$454$	−40.9246			−1.92069
$455$	−9.42820	−	18.6757i	−0.442001	−	0.875529i
$456$		0			0
$457$	15.0180	+	26.0120i	0.702514	+	1.21679i	0.967581	+	0.252560i	$0.0812725\pi$
$457$	15.0180	+	26.0120i	0.702514	+	1.21679i	−0.265067	+	0.964230i	$0.585394\pi$
$458$	−23.1840	−	6.21213i	−1.08332	−	0.290274i
$459$		0			0
$460$	1.35728	−	2.40593i	0.0632834	−	0.112177i
$461$	−0.680045	−	2.53796i	−0.0316729	−	0.118205i	0.948280	−	0.317436i	$-0.102822\pi$
$461$	−0.680045	−	2.53796i	−0.0316729	−	0.118205i	−0.979952	+	0.199232i	$0.936155\pi$
$462$		0			0
$463$	25.1475			1.16870			0.584352	−	0.811500i	$-0.301349\pi$
$463$	25.1475			1.16870			0.584352	+	0.811500i	$0.301349\pi$
$464$	19.4966	+	11.2564i	0.905109	+	0.522565i
$465$		0			0
$466$	3.75502	−	14.0139i	0.173948	−	0.649183i
$467$	−14.9907	+	14.9907i	−0.693688	+	0.693688i	−0.963041	−	0.269354i	$-0.913190\pi$
$467$	−14.9907	+	14.9907i	−0.693688	+	0.693688i	0.269354	+	0.963041i	$0.413190\pi$
$468$		0			0
$469$			40.9648i			1.89158i
$470$	−5.57658	−	5.46654i	−0.257229	−	0.252152i
$471$		0			0
$472$	1.78657	+	6.66756i	0.0822335	+	0.306899i
$473$			0.683832i			0.0314426i
$474$		0			0
$475$	−9.72477	+	10.1203i	−0.446203	+	0.464353i
$476$	−0.0457337	−	0.0457337i	−0.00209620	−	0.00209620i
$477$		0			0
$478$	1.10443	−	4.12178i	0.0505154	−	0.188526i
$479$	2.21157	+	0.592587i	0.101049	+	0.0270760i	0.308989	−	0.951066i	$-0.400009\pi$
$479$	2.21157	+	0.592587i	0.101049	+	0.0270760i	−0.207940	+	0.978142i	$0.566676\pi$
$480$		0			0
$481$	−0.663527	+	1.95082i	−0.0302542	+	0.0889498i
$482$	2.94648	+	2.94648i	0.134208	+	0.134208i
$483$		0			0
$484$	3.68995	−	2.13039i	0.167725	−	0.0968361i
$485$	11.6286	+	2.99201i	0.528028	+	0.135860i
$486$		0			0
$487$	2.78321	−	4.82067i	0.126119	−	0.218445i	−0.796050	−	0.605230i	$-0.793081\pi$
$487$	2.78321	−	4.82067i	0.126119	−	0.218445i	0.922170	+	0.386785i	$0.126414\pi$
$488$	7.05859	−	12.2258i	0.319527	−	0.553437i
$489$		0			0
$490$	0.876368	+	0.225487i	0.0395903	+	0.0101865i
$491$	−5.29139	+	3.05498i	−0.238797	+	0.137869i	−0.614624	−	0.788820i	$-0.710692\pi$
$491$	−5.29139	+	3.05498i	−0.238797	+	0.137869i	0.375827	+	0.926690i	$0.377359\pi$
$492$		0			0
$493$	−0.288558	−	0.288558i	−0.0129960	−	0.0129960i
$494$	15.3307	+	1.01412i	0.689763	+	0.0456273i
$495$		0			0
$496$	−14.3204	−	3.83713i	−0.643004	−	0.172292i
$497$	5.16254	−	19.2669i	0.231572	−	0.864237i
$498$		0			0
$499$	6.22738	+	6.22738i	0.278776	+	0.278776i	0.832620	−	0.553844i	$-0.186840\pi$
$499$	6.22738	+	6.22738i	0.278776	+	0.278776i	−0.553844	+	0.832620i	$0.686840\pi$
$500$	−3.26023	+	0.978912i	−0.145802	+	0.0437783i
$501$		0			0
$502$		−	4.30183i		−	0.192000i
$503$	−0.951461	−	3.55090i	−0.0424236	−	0.158327i	0.941465	−	0.337112i	$-0.109450\pi$
$503$	−0.951461	−	3.55090i	−0.0424236	−	0.158327i	−0.983888	+	0.178785i	$0.942783\pi$
$504$		0			0
$505$	4.00930	+	3.93018i	0.178412	+	0.174891i
$506$		−	30.7939i		−	1.36896i
$507$		0			0
$508$	−0.175347	+	0.175347i	−0.00777976	+	0.00777976i
$509$	−2.90050	+	10.8248i	−0.128563	+	0.479802i	−0.999942	−	0.0108085i	$-0.996559\pi$
$509$	−2.90050	+	10.8248i	−0.128563	+	0.479802i	0.871379	+	0.490610i	$0.163226\pi$
$510$		0			0
$511$	14.8743	+	8.58768i	0.658000	+	0.379897i
$512$	−15.5347			−0.686544
$513$		0			0
$514$	−7.88233	−	29.4173i	−0.347675	−	1.29754i
$515$	−7.32972	+	12.9927i	−0.322986	+	0.572529i
$516$		0			0
$517$	−11.1095	−	2.97677i	−0.488593	−	0.130918i
$518$	1.12561	+	1.94962i	0.0494567	+	0.0856615i
$519$		0			0
$520$	−17.3614	−	11.3669i	−0.761347	−	0.498470i
$521$	−35.9604			−1.57545			−0.787726	−	0.616026i	$-0.788742\pi$
$521$	−35.9604			−1.57545			−0.787726	+	0.616026i	$0.788742\pi$
$522$		0			0
$523$	8.10636	+	2.17209i	0.354467	+	0.0949790i	0.431658	−	0.902037i	$-0.357929\pi$
$523$	8.10636	+	2.17209i	0.354467	+	0.0949790i	−0.0771917	+	0.997016i	$0.524595\pi$
$524$	−2.45189	+	4.24681i	−0.107112	+	0.185523i
$525$		0			0
$526$	−3.70182	−	13.8154i	−0.161407	−	0.602380i
$527$	0.232734	+	0.134369i	0.0101381	+	0.00585322i
$528$		0			0
$529$	5.66090	+	3.26832i	0.246126	+	0.142101i
$530$	−0.320848	−	32.1969i	−0.0139368	−	1.39855i
$531$		0			0
$532$	1.56818	−	1.56818i	0.0679891	−	0.0679891i
$533$	33.6765	−	16.5822i	1.45869	−	0.718253i
$534$		0			0
$535$	8.11343	−	0.0808517i	0.350774	−	0.00349552i
$536$	20.3168	+	35.1897i	0.877552	+	1.51997i
$537$		0			0
$538$			4.88034i			0.210407i
$539$	1.28736	−	0.344948i	0.0554506	−	0.0148580i
$540$		0			0
$541$	4.13066	+	4.13066i	0.177591	+	0.177591i	0.790305	−	0.612714i	$-0.209922\pi$
$541$	4.13066	+	4.13066i	0.177591	+	0.177591i	−0.612714	+	0.790305i	$0.709922\pi$
$542$	22.2688	−	5.96691i	0.956528	−	0.256301i
$543$		0			0
$544$	−0.135064	−	0.0361903i	−0.00579082	−	0.00155165i
$545$	−2.46317	+	4.36624i	−0.105511	+	0.187029i
$546$		0			0
$547$	−7.90229	−	7.90229i	−0.337877	−	0.337877i	0.517691	−	0.855568i	$-0.326792\pi$
$547$	−7.90229	−	7.90229i	−0.337877	−	0.337877i	−0.855568	+	0.517691i	$0.826792\pi$
$548$	5.07242	−	2.92856i	0.216683	−	0.125102i
$549$		0			0
$550$	−26.2924	+	27.3619i	−1.12111	+	1.16671i
$551$	9.89447	−	9.89447i	0.421519	−	0.421519i
$552$		0			0
$553$	7.40909	−	12.8329i	0.315067	−	0.545712i
$554$	11.4479	−	11.4479i	0.486375	−	0.486375i
$555$		0			0
$556$	4.17898	−	2.41274i	0.177228	−	0.102323i
$557$	10.2077	−	5.89341i	0.432513	−	0.249712i	−0.267903	−	0.963446i	$-0.586331\pi$
$557$	10.2077	−	5.89341i	0.432513	−	0.249712i	0.700417	+	0.713734i	$0.252997\pi$
$558$		0			0
$559$	−0.274240	+	0.409894i	−0.0115991	+	0.0173367i
$560$	−25.2429	+	7.03416i	−1.06671	+	0.297247i
$561$		0			0
$562$	7.09170	−	26.4666i	0.299145	−	1.11643i
$563$	−31.0602	+	8.32255i	−1.30903	+	0.350754i	−0.844858	−	0.534991i	$-0.820315\pi$
$563$	−31.0602	+	8.32255i	−1.30903	+	0.350754i	−0.464172	+	0.885745i	$0.653648\pi$
$564$		0			0
$565$	−11.0263	+	6.51341i	−0.463882	+	0.274021i
$566$	8.44250	−	2.26216i	0.354865	−	0.0950858i
$567$		0			0
$568$	−5.12080	−	19.1111i	−0.214864	−	0.801883i
$569$	4.64237	+	8.04082i	0.194618	+	0.337089i	0.946775	−	0.321895i	$-0.104320\pi$
$569$	4.64237	+	8.04082i	0.194618	+	0.337089i	−0.752157	+	0.658984i	$0.770987\pi$
$570$		0			0
$571$			31.1596i			1.30399i	0.758223	+	0.651995i	$0.226068\pi$
$571$			31.1596i			1.30399i	−0.758223	+	0.651995i	$0.773932\pi$
$572$	5.47623	+	0.362249i	0.228973	+	0.0151464i
$573$		0			0
$574$	10.6144	−	39.6134i	0.443035	−	1.65343i
$575$	5.64028	+	19.4877i	0.235216	+	0.812694i
$576$		0			0
$577$	4.57285			0.190370			0.0951852	−	0.995460i	$-0.469656\pi$
$577$	4.57285			0.190370			0.0951852	+	0.995460i	$0.469656\pi$
$578$	−22.3405	−	12.8983i	−0.929243	−	0.536499i
$579$		0			0
$580$	3.26916	−	0.910980i	0.135745	−	0.0378264i
$581$	4.81009	−	8.33132i	0.199556	−	0.345641i
$582$		0			0
$583$	−23.7114	−	41.0693i	−0.982025	−	1.70092i
$584$	17.0365			0.704975
$585$		0			0
$586$	4.85179			0.200425
$587$	−3.59590	−	6.22829i	−0.148419	−	0.257069i	0.782224	−	0.622997i	$-0.214085\pi$
$587$	−3.59590	−	6.22829i	−0.148419	−	0.257069i	−0.930643	+	0.365928i	$0.880752\pi$
$588$		0			0
$589$	−4.60743	+	7.98031i	−0.189846	+	0.328823i
$590$	7.92870	+	4.47289i	0.326420	+	0.184146i
$591$		0			0
$592$	2.23524	+	1.29052i	0.0918677	+	0.0530399i
$593$	−28.0561			−1.15212			−0.576062	−	0.817406i	$-0.695411\pi$
$593$	−28.0561			−1.15212			−0.576062	+	0.817406i	$0.695411\pi$
$594$		0			0
$595$	0.474982	−	0.00473328i	0.0194724	−	0.000194045i
$596$	0.113496	−	0.423573i	0.00464898	−	0.0173502i
$597$		0			0
$598$	12.3494	−	18.4581i	0.505005	−	0.754808i
$599$		−	0.912959i		−	0.0373025i	−0.999826	−	0.0186513i	$-0.994063\pi$
$599$		−	0.912959i		−	0.0373025i	0.999826	−	0.0186513i	$-0.00593722\pi$
$600$		0			0
$601$	−6.22691	−	10.7853i	−0.254001	−	0.439943i	0.710623	−	0.703573i	$-0.248413\pi$
$601$	−6.22691	−	10.7853i	−0.254001	−	0.439943i	−0.964624	+	0.263631i	$0.915080\pi$
$602$	0.139453	+	0.520445i	0.00568367	+	0.0212118i
$603$		0			0
$604$	−5.79162	+	1.55186i	−0.235658	+	0.0631443i
$605$	−7.79745	+	30.3052i	−0.317011	+	1.23208i
$606$		0			0
$607$	37.4512	−	10.0350i	1.52010	−	0.407309i	0.600324	−	0.799757i	$-0.295038\pi$
$607$	37.4512	−	10.0350i	1.52010	−	0.407309i	0.919774	+	0.392448i	$0.128372\pi$
$608$	1.24094	−	4.63125i	0.0503268	−	0.187822i
$609$		0			0
$610$	−4.99757	−	17.9344i	−0.202346	−	0.726143i
$611$	−5.46530	−	6.23957i	−0.221102	−	0.252426i
$612$		0			0
$613$	−21.3140	+	12.3057i	−0.860865	+	0.497021i	−0.864302	−	0.502973i	$-0.832239\pi$
$613$	−21.3140	+	12.3057i	−0.860865	+	0.497021i	0.00343656	+	0.999994i	$0.498906\pi$
$614$	31.9122	−	18.4245i	1.28787	−	0.743553i
$615$		0			0
$616$	−23.6110	+	23.6110i	−0.951316	+	0.951316i
$617$	−7.70769	+	13.3501i	−0.310300	+	0.537455i	−0.978427	−	0.206592i	$-0.933763\pi$
$617$	−7.70769	+	13.3501i	−0.310300	+	0.537455i	0.668127	+	0.744047i	$0.267096\pi$
$618$		0			0
$619$	20.7915	−	20.7915i	0.835683	−	0.835683i	−0.152604	−	0.988287i	$-0.548766\pi$
$619$	20.7915	−	20.7915i	0.835683	−	0.835683i	0.988287	+	0.152604i	$0.0487661\pi$
$620$	−1.92424	+	1.13668i	−0.0772795	+	0.0456501i
$621$		0			0
$622$	−22.2249	+	12.8316i	−0.891137	+	0.514498i
$623$	32.8303	+	32.8303i	1.31532	+	1.31532i
$624$		0			0
$625$	11.6273	−	22.1315i	0.465093	−	0.885262i
$626$	17.4397	+	4.67294i	0.697029	+	0.186768i
$627$		0			0
$628$	−1.89090	+	0.506664i	−0.0754549	+	0.0202181i
$629$	−0.0330825	−	0.0330825i	−0.00131908	−	0.00131908i
$630$		0			0
$631$	12.1738	−	3.26195i	0.484631	−	0.129856i	−0.00822739	−	0.999966i	$-0.502619\pi$
$631$	12.1738	−	3.26195i	0.484631	−	0.129856i	0.492858	+	0.870110i	$0.335952\pi$
$632$		−	14.6984i		−	0.584670i
$633$		0			0
$634$	9.06908	+	15.7081i	0.360179	+	0.623849i
$635$	−0.0181478	−	1.82112i	−0.000720173	−	0.0722690i
$636$		0			0
$637$	0.909991	+	0.309512i	0.0360551	+	0.0122633i
$638$	26.7512	−	26.7512i	1.05909	−	1.05909i
$639$		0			0
$640$	−20.6490	+	21.0646i	−0.816222	+	0.832653i
$641$	8.45341	+	4.88058i	0.333890	+	0.192771i	0.657567	−	0.753396i	$-0.271586\pi$
$641$	8.45341	+	4.88058i	0.333890	+	0.192771i	−0.323677	+	0.946168i	$0.604919\pi$
$642$		0			0
$643$	24.0854	+	13.9057i	0.949834	+	0.548387i	0.893029	−	0.449999i	$-0.148576\pi$
$643$	24.0854	+	13.9057i	0.949834	+	0.548387i	0.0568044	+	0.998385i	$0.481909\pi$
$644$	−0.829680	−	3.09641i	−0.0326940	−	0.122016i
$645$		0			0
$646$	−0.174424	+	0.302111i	−0.00686261	+	0.0118864i
$647$	17.7967	+	4.76862i	0.699662	+	0.187474i	0.591079	−	0.806613i	$-0.298702\pi$
$647$	17.7967	+	4.76862i	0.699662	+	0.187474i	0.108583	+	0.994087i	$0.465369\pi$
$648$		0			0
$649$	13.4076			0.526296
$650$	−26.7329	+	5.85675i	−1.04855	+	0.229721i
$651$		0			0
$652$	1.99970	+	3.46357i	0.0783141	+	0.135644i
$653$	7.12491	+	1.90911i	0.278819	+	0.0747094i	0.395519	−	0.918458i	$-0.370565\pi$
$653$	7.12491	+	1.90911i	0.278819	+	0.0747094i	−0.116700	+	0.993167i	$0.537231\pi$
$654$		0			0
$655$	−9.66746	−	34.6929i	−0.377739	−	1.35556i
$656$	−12.1694	−	45.4167i	−0.475134	−	1.77322i
$657$		0			0
$658$	−9.06214			−0.353279
$659$	−12.0786	−	6.97358i	−0.470515	−	0.271652i	0.245940	−	0.969285i	$-0.420903\pi$
$659$	−12.0786	−	6.97358i	−0.470515	−	0.271652i	−0.716455	+	0.697633i	$0.754237\pi$
$660$		0			0
$661$	0.0586648	−	0.218940i	0.00228180	−	0.00851578i	−0.964776	−	0.263074i	$-0.915264\pi$
$661$	0.0586648	−	0.218940i	0.00228180	−	0.00851578i	0.967057	+	0.254559i	$0.0819302\pi$
$662$	−23.0236	+	23.0236i	−0.894837	+	0.894837i
$663$		0			0
$664$		−	9.54239i		−	0.370317i
$665$	0.162301	+	16.2868i	0.00629375	+	0.631575i
$666$		0			0
$667$	−5.23490	−	19.5369i	−0.202696	−	0.756472i
$668$		−	1.00022i		−	0.0386996i
$669$		0			0
$670$	51.8972	+	13.3530i	2.00496	+	0.515871i
$671$	−19.3893	−	19.3893i	−0.748515	−	0.748515i
$672$		0			0
$673$	−8.70112	+	32.4730i	−0.335404	+	1.25174i	0.568027	+	0.823010i	$0.307707\pi$
$673$	−8.70112	+	32.4730i	−0.335404	+	1.25174i	−0.903431	+	0.428734i	$0.858960\pi$
$674$	29.2938	+	7.84924i	1.12835	+	0.302341i
$675$		0			0
$676$	3.13722	+	2.41329i	0.120662	+	0.0928190i
$677$	−25.1691	−	25.1691i	−0.967326	−	0.967326i	0.0321566	−	0.999483i	$-0.489762\pi$
$677$	−25.1691	−	25.1691i	−0.967326	−	0.967326i	−0.999483	+	0.0321566i	$0.989762\pi$
$678$		0			0
$679$	12.0673	−	6.96707i	0.463101	−	0.267372i
$680$	0.405673	−	0.239637i	0.0155568	−	0.00918964i
$681$		0			0
$682$	−12.4569	+	21.5760i	−0.477000	+	0.826187i
$683$	−15.3784	+	26.6361i	−0.588437	+	1.01920i	0.406001	+	0.913873i	$0.366923\pi$
$683$	−15.3784	+	26.6361i	−0.588437	+	1.01920i	−0.994437	+	0.105329i	$0.966410\pi$
$684$		0			0
$685$	−10.7188	+	41.6593i	−0.409545	+	1.59172i
$686$	24.7893	−	14.3121i	0.946459	−	0.546438i
$687$		0			0
$688$	0.436807	+	0.436807i	0.0166531	+	0.0166531i
$689$	2.25743	−	34.1263i	0.0860013	−	1.30011i
$690$		0			0
$691$	−37.4215	−	10.0271i	−1.42358	−	0.381447i	−0.536828	−	0.843692i	$-0.680378\pi$
$691$	−37.4215	−	10.0271i	−1.42358	−	0.381447i	−0.886753	+	0.462244i	$0.847044\pi$
$692$	−0.333966	+	1.24638i	−0.0126955	+	0.0473802i
$693$		0			0
$694$	26.4382	+	26.4382i	1.00358	+	1.00358i
$695$	−8.83085	+	34.3216i	−0.334973	+	1.30189i
$696$		0			0
$697$			0.852297i			0.0322831i
$698$	10.7055	+	39.9534i	0.405208	+	1.51226i
$699$		0			0
$700$	−1.90656	+	3.45970i	−0.0720612	+	0.130765i
$701$			19.8876i			0.751143i	0.926793	+	0.375571i	$0.122553\pi$
$701$			19.8876i			0.751143i	−0.926793	+	0.375571i	$0.877447\pi$
$702$		0			0
$703$	1.13437	−	1.13437i	0.0427838	−	0.0427838i
$704$	−8.33247	+	31.0972i	−0.314042	+	1.17202i
$705$		0			0
$706$	11.5681	+	6.67884i	0.435371	+	0.251361i
$707$	6.51526			0.245032
$708$		0			0
$709$	8.24828	+	30.7830i	0.309771	+	1.15608i	0.928760	+	0.370680i	$0.120875\pi$
$709$	8.24828	+	30.7830i	0.309771	+	1.15608i	−0.618990	+	0.785399i	$0.712458\pi$
$710$	−22.7259	−	12.8206i	−0.852887	−	0.481147i
$711$		0			0
$712$	44.4844	+	11.9196i	1.66712	+	0.446705i
$713$	6.65983	+	11.5352i	0.249413	+	0.431996i
$714$		0			0
$715$	−30.0541	+	26.8586i	−1.12396	+	1.00445i
$716$	4.25084			0.158861
$717$		0			0
$718$	−23.0710	−	6.18186i	−0.861002	−	0.230705i
$719$	15.4818	−	26.8152i	0.577372	−	1.00004i	−0.418407	−	0.908260i	$-0.637411\pi$
$719$	15.4818	−	26.8152i	0.577372	−	1.00004i	0.995779	−	0.0917785i	$-0.0292552\pi$
$720$		0			0
$721$	4.48053	+	16.7216i	0.166864	+	0.622744i
$722$	14.6195	+	8.44057i	0.544081	+	0.314126i
$723$		0			0
$724$	2.28019	+	1.31647i	0.0847427	+	0.0489262i
$725$	−12.0295	+	21.8291i	−0.446765	+	0.810714i
$726$		0			0
$727$	−16.2588	+	16.2588i	−0.603007	+	0.603007i	−0.941109	−	0.338103i	$-0.890215\pi$
$727$	−16.2588	+	16.2588i	−0.603007	+	0.603007i	0.338103	+	0.941109i	$0.390215\pi$
$728$	−23.6215	+	4.68379i	−0.875470	+	0.173593i
$729$		0			0
$730$	15.7280	−	16.0446i	0.582118	−	0.593836i
$731$	−0.00559879	−	0.00969739i	−0.000207079	−	0.000358671i
$732$		0			0
$733$		−	31.2515i		−	1.15430i	−0.816638	−	0.577150i	$-0.804165\pi$
$733$		−	31.2515i		−	1.15430i	0.816638	−	0.577150i	$-0.195835\pi$
$734$	−16.0980	+	4.31344i	−0.594187	+	0.159212i
$735$		0			0
$736$	−4.90054	−	4.90054i	−0.180636	−	0.180636i
$737$	76.2357	−	20.4273i	2.80818	−	0.752449i
$738$		0			0
$739$	26.3668	+	7.06496i	0.969918	+	0.259889i	0.708793	−	0.705416i	$-0.249240\pi$
$739$	26.3668	+	7.06496i	0.969918	+	0.259889i	0.261125	+	0.965305i	$0.415907\pi$
$740$	0.374801	−	0.104441i	0.0137780	−	0.00383934i
$741$		0			0
$742$	−26.4213	−	26.4213i	−0.969956	−	0.969956i
$743$	28.5494	−	16.4830i	1.04738	−	0.604703i	0.125463	−	0.992098i	$-0.459958\pi$
$743$	28.5494	−	16.4830i	1.04738	−	0.604703i	0.921914	+	0.387395i	$0.126625\pi$
$744$		0			0
$745$	1.63800	+	2.77291i	0.0600115	+	0.101591i
$746$	11.3566	−	11.3566i	0.415794	−	0.415794i
$747$		0			0
$748$	−0.0623052	+	0.107916i	−0.00227810	+	0.00394579i
$749$	6.65800	−	6.65800i	0.243278	−	0.243278i
$750$		0			0
$751$	26.8241	−	15.4869i	0.978826	−	0.565125i	0.0769103	−	0.997038i	$-0.475494\pi$
$751$	26.8241	−	15.4869i	0.978826	−	0.565125i	0.901915	+	0.431913i	$0.142161\pi$
$752$	−8.99777	+	5.19487i	−0.328115	+	0.189437i
$753$		0			0
$754$	26.7630	−	5.30672i	0.974653	−	0.193259i
$755$	21.6367	−	38.3535i	0.787440	−	1.39583i
$756$		0			0
$757$	13.2249	−	49.3561i	0.480668	−	1.79388i	−0.118154	−	0.992995i	$-0.537698\pi$
$757$	13.2249	−	49.3561i	0.480668	−	1.79388i	0.598822	−	0.800882i	$-0.295636\pi$
$758$	−14.3729	+	3.85120i	−0.522046	+	0.139882i
$759$		0			0
$760$	8.21697	+	13.9102i	0.298061	+	0.504577i
$761$	−1.11809	+	0.299592i	−0.0405308	+	0.0108602i	−0.279027	−	0.960283i	$-0.590012\pi$
$761$	−1.11809	+	0.299592i	−0.0405308	+	0.0108602i	0.238497	+	0.971143i	$0.423345\pi$
$762$		0			0
$763$	1.50569	+	5.61932i	0.0545097	+	0.203433i
$764$	2.57470	+	4.45951i	0.0931494	+	0.161339i
$765$		0			0
$766$		−	39.5553i		−	1.42919i
$767$	8.03664	+	5.37693i	0.290186	+	0.194150i
$768$		0			0
$769$	−7.82422	+	29.2004i	−0.282148	+	1.05299i	0.668750	+	0.743488i	$0.266830\pi$
$769$	−7.82422	+	29.2004i	−0.282148	+	1.05299i	−0.950898	+	0.309505i	$0.899837\pi$
$770$	0.438805	+	44.0339i	0.0158134	+	1.58687i
$771$		0			0
$772$	2.60488			0.0937517
$773$	−6.22916	−	3.59641i	−0.224047	−	0.129354i	0.383776	−	0.923426i	$-0.374624\pi$
$773$	−6.22916	−	3.59641i	−0.224047	−	0.129354i	−0.607823	+	0.794073i	$0.707957\pi$
$774$		0			0
$775$	3.93136	−	15.9358i	0.141219	−	0.572432i
$776$	6.91074	−	11.9698i	0.248081	−	0.429689i
$777$		0			0
$778$	24.6597	+	42.7119i	0.884094	+	1.53130i
$779$	−29.2247			−1.04708
$780$		0			0
$781$	−38.4300			−1.37513
$782$	0.252122	+	0.436687i	0.00901585	+	0.0156159i
$783$		0			0
$784$	0.601981	−	1.04266i	0.0214993	−	0.0372379i
$785$	7.06412	−	12.5219i	0.252129	−	0.446927i
$786$		0			0
$787$	−6.21708	−	3.58943i	−0.221615	−	0.127949i	0.385083	−	0.922882i	$-0.374173\pi$
$787$	−6.21708	−	3.58943i	−0.221615	−	0.127949i	−0.606698	+	0.794933i	$0.707506\pi$
$788$	−2.33124			−0.0830470
$789$		0			0
$790$	−13.8426	−	13.5694i	−0.492497	−	0.482778i
$791$	−3.84642	+	14.3550i	−0.136763	+	0.510407i
$792$		0			0
$793$	−3.84631	−	19.3979i	−0.136586	−	0.688838i
$794$			36.7145i			1.30295i
$795$		0			0
$796$	−2.33336	−	4.04150i	−0.0827037	−	0.143247i
$797$	10.1969	+	38.0553i	0.361192	+	1.34799i	0.872510	+	0.488596i	$0.162491\pi$
$797$	10.1969	+	38.0553i	0.361192	+	1.34799i	−0.511318	+	0.859391i	$0.670843\pi$
$798$		0			0
$799$	0.181915	−	0.0487439i	0.00643568	−	0.00172443i
$800$	0.170193	+	8.53854i	0.00601723	+	0.301883i
$801$		0			0
$802$	−48.1515	+	12.9022i	−1.70029	+	0.455591i
$803$	8.56456	−	31.9634i	0.302237	−	1.12796i
$804$		0			0
$805$	20.5051	+	11.5677i	0.722711	+	0.407710i
$806$	−16.1195	+	7.93716i	−0.567784	+	0.279575i
$807$		0			0
$808$	5.59676	−	3.23129i	0.196893	−	0.113676i
$809$	24.2062	−	13.9754i	0.851043	−	0.491350i	−0.00995956	−	0.999950i	$-0.503170\pi$
$809$	24.2062	−	13.9754i	0.851043	−	0.491350i	0.861003	+	0.508600i	$0.169837\pi$
$810$		0			0
$811$	−23.2784	+	23.2784i	−0.817415	+	0.817415i	−0.985733	−	0.168317i	$-0.946167\pi$
$811$	−23.2784	+	23.2784i	−0.817415	+	0.817415i	0.168317	+	0.985733i	$0.446167\pi$
$812$	1.96915	−	3.41066i	0.0691035	−	0.119691i
$813$		0			0
$814$	3.06696	−	3.06696i	0.107497	−	0.107497i
$815$	−28.4460	−	7.31907i	−0.996420	−	0.256376i
$816$		0			0
$817$	0.332517	−	0.191979i	0.0116333	−	0.00671648i
$818$	14.9850	+	14.9850i	0.523937	+	0.523937i
$819$		0			0
$820$	−6.17331	−	3.48261i	−0.215582	−	0.121618i
$821$	−18.8872	−	5.06082i	−0.659169	−	0.176624i	−0.0862981	−	0.996269i	$-0.527504\pi$
$821$	−18.8872	−	5.06082i	−0.659169	−	0.176624i	−0.572871	+	0.819646i	$0.694170\pi$
$822$		0			0
$823$	−39.4302	+	10.5653i	−1.37445	+	0.368283i	−0.869102	−	0.494633i	$-0.835303\pi$
$823$	−39.4302	+	10.5653i	−1.37445	+	0.368283i	−0.505348	+	0.862915i	$0.668636\pi$
$824$	12.1421	+	12.1421i	0.422989	+	0.422989i
$825$		0			0
$826$	10.2042	−	2.73420i	0.355049	−	0.0951350i
$827$		−	31.8649i		−	1.10805i	−0.832499	−	0.554026i	$-0.813091\pi$
$827$		−	31.8649i		−	1.10805i	0.832499	−	0.554026i	$-0.186909\pi$
$828$		0			0
$829$	−27.6391	−	47.8724i	−0.959946	−	1.66268i	−0.722620	−	0.691246i	$-0.757062\pi$
$829$	−27.6391	−	47.8724i	−0.959946	−	1.66268i	−0.237326	−	0.971430i	$-0.576271\pi$
$830$	−8.98680	−	8.80946i	−0.311937	−	0.305781i
$831$		0			0
$832$	−17.4656	+	15.2983i	−0.605510	+	0.530373i
$833$	−0.0154318	+	0.0154318i	−0.000534681	+	0.000534681i
$834$		0			0
$835$	5.24580	+	5.14228i	0.181538	+	0.177956i
$836$	−3.70036	−	2.13640i	−0.127980	−	0.0738890i
$837$		0			0
$838$	2.91830	+	1.68488i	0.100811	+	0.0582032i
$839$	1.00953	+	3.76762i	0.0348528	+	0.130073i	0.981160	−	0.193195i	$-0.0618851\pi$
$839$	1.00953	+	3.76762i	0.0348528	+	0.130073i	−0.946307	+	0.323268i	$0.895218\pi$
$840$		0			0
$841$	−2.07559	+	3.59503i	−0.0715721	+	0.123966i
$842$	−50.7629	−	13.6019i	−1.74940	−	0.468751i
$843$		0			0
$844$	6.03930			0.207881
$845$	−28.7859	+	4.04652i	−0.990264	+	0.139205i
$846$		0			0
$847$	18.1568	+	31.4485i	0.623876	+	1.08058i
$848$	−41.3796	−	11.0876i	−1.42098	−	0.380751i
$849$		0			0
$850$	0.148830	−	0.603284i	0.00510482	−	0.0206925i
$851$	−0.600167	−	2.23986i	−0.0205735	−	0.0767812i
$852$		0			0
$853$	−53.5726			−1.83429			−0.917145	−	0.398554i	$-0.869512\pi$
$853$	−53.5726			−1.83429			−0.917145	+	0.398554i	$0.869512\pi$
$854$	−18.7107	−	10.8026i	−0.640266	−	0.369658i
$855$		0			0
$856$	2.41729	−	9.02145i	0.0826213	−	0.308347i
$857$	−18.9164	+	18.9164i	−0.646171	+	0.646171i	−0.952066	−	0.305894i	$-0.901045\pi$
$857$	−18.9164	+	18.9164i	−0.646171	+	0.646171i	0.305894	+	0.952066i	$0.401045\pi$
$858$		0			0
$859$			18.1203i			0.618258i	0.951020	+	0.309129i	$0.100037\pi$
$859$			18.1203i			0.618258i	−0.951020	+	0.309129i	$0.899963\pi$
$860$	0.0931171		0.000927928i	0.00317527		3.16421e-5i
$861$		0			0
$862$	0.649274	+	2.42312i	0.0221144	+	0.0825320i
$863$			21.4967i			0.731757i	0.930663	+	0.365879i	$0.119232\pi$
$863$			21.4967i			0.731757i	−0.930663	+	0.365879i	$0.880768\pi$
$864$		0			0
$865$	−4.81986	−	8.15937i	−0.163880	−	0.277427i
$866$	15.9037	+	15.9037i	0.540431	+	0.540431i
$867$		0			0
$868$	−0.671252	+	2.50515i	−0.0227838	+	0.0850303i
$869$	−27.5767	−	7.38915i	−0.935475	−	0.250660i
$870$		0			0
$871$	53.8883	+	18.3289i	1.82593	+	0.621050i
$872$	4.08036	+	4.08036i	0.138179	+	0.138179i
$873$		0			0
$874$	−14.9737	+	8.64508i	−0.506493	+	0.292424i
$875$	−8.34303	−	27.7862i	−0.282046	−	0.939344i
$876$		0			0
$877$	10.6745	−	18.4889i	0.360454	−	0.624324i	−0.627582	−	0.778551i	$-0.715955\pi$
$877$	10.6745	−	18.4889i	0.360454	−	0.624324i	0.988036	+	0.154226i	$0.0492885\pi$
$878$	−16.6018	+	28.7551i	−0.560282	+	0.970437i
$879$		0			0
$880$	25.6781	+	43.4696i	0.865608	+	1.46536i
$881$	−11.4703	+	6.62238i	−0.386444	+	0.223114i	−0.680618	−	0.732638i	$-0.738289\pi$
$881$	−11.4703	+	6.62238i	−0.386444	+	0.223114i	0.294174	+	0.955752i	$0.404955\pi$
$882$		0			0
$883$	32.5668	+	32.5668i	1.09596	+	1.09596i	0.994878	+	0.101082i	$0.0322304\pi$
$883$	32.5668	+	32.5668i	1.09596	+	1.09596i	0.101082	+	0.994878i	$0.467770\pi$
$884$	−0.0806241	+	0.0396990i	−0.00271168	+	0.00133522i
$885$		0			0
$886$	−12.7526	−	3.41705i	−0.428432	−	0.114798i
$887$	−4.13600	+	15.4358i	−0.138873	+	0.518282i	0.861079	+	0.508472i	$0.169789\pi$
$887$	−4.13600	+	15.4358i	−0.138873	+	0.518282i	−0.999952	+	0.00981024i	$0.996877\pi$
$888$		0			0
$889$	−1.49444	−	1.49444i	−0.0501219	−	0.0501219i
$890$	52.2933	−	30.8904i	1.75287	−	1.03545i
$891$		0			0
$892$			5.77663i			0.193416i
$893$	1.67139	+	6.23773i	0.0559311	+	0.208738i
$894$		0			0
$895$	−21.8543	+	22.2942i	−0.730507	+	0.745213i
$896$			34.2308i			1.14357i
$897$		0			0
$898$	5.01810	−	5.01810i	0.167456	−	0.167456i
$899$	−4.23529	+	15.8063i	−0.141255	+	0.527170i
$900$		0			0
$901$	0.672500	+	0.388268i	0.0224042	+	0.0129351i
$902$	−79.0135			−2.63086
$903$		0			0
$904$	3.81532	+	14.2390i	0.126896	+	0.473581i
$905$	−18.6273	+	5.19065i	−0.619192	+	0.172543i
$906$		0			0
$907$	5.07458	+	1.35973i	0.168499	+	0.0451491i	0.342082	−	0.939670i	$-0.388868\pi$
$907$	5.07458	+	1.35973i	0.168499	+	0.0451491i	−0.173583	+	0.984819i	$0.555535\pi$
$908$	4.10399	+	7.10833i	0.136196	+	0.235898i
$909$		0			0
$910$	−17.3961	+	26.5702i	−0.576674	+	0.880794i
$911$	−9.49722			−0.314657			−0.157328	−	0.987546i	$-0.550288\pi$
$911$	−9.49722			−0.314657			−0.157328	+	0.987546i	$0.550288\pi$
$912$		0			0
$913$	−17.9032	−	4.79714i	−0.592508	−	0.158762i
$914$	22.7981	−	39.4874i	0.754093	−	1.30613i
$915$		0			0
$916$	1.24593	+	4.64987i	0.0411666	+	0.153636i
$917$	−36.1945	−	20.8969i	−1.19525	−	0.690076i
$918$		0			0
$919$	−45.6207	−	26.3391i	−1.50489	−	0.868847i	−0.999984	−	0.00567026i	$-0.998195\pi$
$919$	−45.6207	−	26.3391i	−1.50489	−	0.868847i	−0.504903	−	0.863176i	$-0.668472\pi$
$920$	23.3515	−	0.232702i	0.769875	−	0.00767194i
$921$		0			0
$922$	−2.82041	+	2.82041i	−0.0928851	+	0.0928851i
$923$	−23.0352	−	15.4118i	−0.758214	−	0.507284i
$924$		0			0
$925$	−1.37915	+	2.50265i	−0.0453463	+	0.0822867i
$926$	−19.0876	−	33.0606i	−0.627256	−	1.08644i
$927$		0			0
$928$		−	8.51438i		−	0.279498i
$929$	−8.04841	+	2.15657i	−0.264060	+	0.0707546i	−0.388420	−	0.921483i	$-0.626979\pi$
$929$	−8.04841	+	2.15657i	−0.264060	+	0.0707546i	0.124360	+	0.992237i	$0.460312\pi$
$930$		0			0
$931$	−0.529147	−	0.529147i	−0.0173421	−	0.0173421i
$932$	−2.81069	+	0.753121i	−0.0920671	+	0.0246693i
$933$		0			0
$934$	31.0861	+	8.32950i	1.01717	+	0.272549i
$935$	−0.245660	−	0.881582i	−0.00803395	−	0.0288308i
$936$		0			0
$937$	16.3814	+	16.3814i	0.535156	+	0.535156i	0.922102	−	0.386947i	$-0.126470\pi$
$937$	16.3814	+	16.3814i	0.535156	+	0.535156i	−0.386947	+	0.922102i	$0.626470\pi$
$938$	53.8551	−	31.0933i	1.75843	−	1.01523i
$939$		0			0
$940$	−0.390271	+	1.51681i	−0.0127292	+	0.0494729i
$941$	24.2325	−	24.2325i	0.789956	−	0.789956i	−0.191530	−	0.981487i	$-0.561345\pi$
$941$	24.2325	−	24.2325i	0.789956	−	0.789956i	0.981487	+	0.191530i	$0.0613451\pi$
$942$		0			0
$943$	−21.1215	+	36.5835i	−0.687810	+	1.19132i
$944$	8.56432	−	8.56432i	0.278745	−	0.278745i
$945$		0			0
$946$	0.899011	−	0.519044i	0.0292294	−	0.0168756i
$947$	28.9613	−	16.7208i	0.941114	−	0.543353i	0.0508048	−	0.998709i	$-0.483821\pi$
$947$	28.9613	−	16.7208i	0.941114	−	0.543353i	0.890309	+	0.455356i	$0.150488\pi$
$948$		0			0
$949$	17.9521	−	15.7244i	0.582749	−	0.510436i
$950$	20.6862	+	5.10327i	0.671149	+	0.165572i
$951$		0			0
$952$	0.141515	−	0.528140i	0.00458652	−	0.0171171i
$953$	−14.5138	+	3.88895i	−0.470147	+	0.125975i	−0.486111	−	0.873897i	$-0.661585\pi$
$953$	−14.5138	+	3.88895i	−0.470147	+	0.125975i	0.0159642	+	0.999873i	$0.494918\pi$
$954$		0			0
$955$	−36.6256	−	9.42365i	−1.18518	−	0.304942i
$956$	−0.826681	+	0.221508i	−0.0267368	+	0.00716409i
$957$		0			0
$958$	−0.899575	−	3.35726i	−0.0290640	−	0.108468i
$959$	24.9594	+	43.2310i	0.805982	+	1.39600i
$960$		0			0
$961$			20.2237i			0.652378i
$962$	3.06831	−	0.608402i	0.0989264	−	0.0196157i
$963$		0			0
$964$	0.216305	−	0.807262i	0.00696672	−	0.0260002i
$965$	−13.3921	+	13.6617i	−0.431107	+	0.439786i
$966$		0			0
$967$	7.49252			0.240943			0.120472	−	0.992717i	$-0.461559\pi$
$967$	7.49252			0.240943			0.120472	+	0.992717i	$0.461559\pi$
$968$	31.1943	+	18.0100i	1.00262	+	0.578864i
$969$		0			0
$970$	−4.89290	−	17.5588i	−0.157101	−	0.563778i
$971$	13.9303	−	24.1280i	0.447045	−	0.774304i	−0.551147	−	0.834408i	$-0.685810\pi$
$971$	13.9303	−	24.1280i	0.447045	−	0.774304i	0.998192	+	0.0601036i	$0.0191431\pi$
$972$		0			0
$973$	20.5632	+	35.6165i	0.659225	+	1.14181i
$974$	−8.45010			−0.270759
$975$		0			0
$976$	−24.7704			−0.792880
$977$	19.4382	+	33.6679i	0.621883	+	1.07713i	0.989135	+	0.147011i	$0.0469654\pi$
$977$	19.4382	+	33.6679i	0.621883	+	1.07713i	−0.367252	+	0.930122i	$0.619701\pi$
$978$		0			0
$979$	44.7263	−	77.4683i	1.42946	−	2.47590i
$980$	−0.0487183	−	0.174832i	−0.00155625	−	0.00558479i
$981$		0			0
$982$	8.03257	+	4.63761i	0.256330	+	0.147992i
$983$	−0.207440			−0.00661630			−0.00330815	−	0.999995i	$-0.501053\pi$
$983$	−0.207440			−0.00661630			−0.00330815	+	0.999995i	$0.501053\pi$
$984$		0			0
$985$	11.9853	−	12.2266i	0.381883	−	0.389571i
$986$	−0.160336	+	0.598381i	−0.00510613	+	0.0190563i
$987$		0			0
$988$	−1.36125	−	2.76455i	−0.0433072	−	0.0879519i
$989$		−	0.554993i		−	0.0176477i
$990$		0			0
$991$	12.7480	+	22.0803i	0.404955	+	0.701402i	0.994316	−	0.106467i	$-0.0339539\pi$
$991$	12.7480	+	22.0803i	0.404955	+	0.701402i	−0.589361	+	0.807869i	$0.700621\pi$
$992$	1.45121	+	5.41599i	0.0460760	+	0.171958i
$993$		0			0
$994$	−29.2480	+	7.83698i	−0.927691	+	0.248574i
$995$	33.1924	+	8.54032i	1.05227	+	0.270746i
$996$		0			0
$997$	33.4743	−	8.96942i	1.06014	−	0.284064i	0.313706	−	0.949520i	$-0.398429\pi$
$997$	33.4743	−	8.96942i	1.06014	−	0.284064i	0.746437	+	0.665456i	$0.231763\pi$
$998$	3.46020	−	12.9137i	0.109531	−	0.408774i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.cf.a.262.1		20
3.2	odd	2		65.2.o.a.2.5	✓	20
5.3	odd	4		585.2.dp.a.28.1		20
13.7	odd	12		585.2.dp.a.397.1		20
15.2	even	4		325.2.x.b.93.1		20
15.8	even	4		65.2.t.a.28.5	yes	20
15.14	odd	2		325.2.s.b.132.1		20
39.2	even	12		845.2.f.d.437.9		20
39.5	even	4		845.2.t.e.427.5		20
39.8	even	4		845.2.t.f.427.1		20
39.11	even	12		845.2.f.e.437.2		20
39.17	odd	6		845.2.o.f.357.1		20
39.20	even	12		65.2.t.a.7.5	yes	20
39.23	odd	6		845.2.k.d.577.9		20
39.29	odd	6		845.2.k.e.577.2		20
39.32	even	12		845.2.t.g.657.1		20
39.35	odd	6		845.2.o.e.357.5		20
39.38	odd	2		845.2.o.g.587.1		20
65.33	even	12	inner	585.2.cf.a.163.1		20
195.8	odd	4		845.2.o.e.258.5		20
195.23	even	12		845.2.f.d.408.2		20
195.38	even	4		845.2.t.g.418.1		20
195.59	even	12		325.2.x.b.7.1		20
195.68	even	12		845.2.f.e.408.9		20
195.83	odd	4		845.2.o.f.258.1		20
195.98	odd	12		65.2.o.a.33.5	yes	20
195.113	even	12		845.2.t.f.188.1		20
195.128	odd	12		845.2.k.e.268.2		20
195.137	odd	12		325.2.s.b.293.1		20
195.158	odd	12		845.2.k.d.268.9		20
195.173	even	12		845.2.t.e.188.5		20
195.188	odd	12		845.2.o.g.488.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.5	✓	20	3.2	odd	2
65.2.o.a.33.5	yes	20	195.98	odd	12
65.2.t.a.7.5	yes	20	39.20	even	12
65.2.t.a.28.5	yes	20	15.8	even	4
325.2.s.b.132.1		20	15.14	odd	2
325.2.s.b.293.1		20	195.137	odd	12
325.2.x.b.7.1		20	195.59	even	12
325.2.x.b.93.1		20	15.2	even	4
585.2.cf.a.163.1		20	65.33	even	12	inner
585.2.cf.a.262.1		20	1.1	even	1	trivial
585.2.dp.a.28.1		20	5.3	odd	4
585.2.dp.a.397.1		20	13.7	odd	12
845.2.f.d.408.2		20	195.23	even	12
845.2.f.d.437.9		20	39.2	even	12
845.2.f.e.408.9		20	195.68	even	12
845.2.f.e.437.2		20	39.11	even	12
845.2.k.d.268.9		20	195.158	odd	12
845.2.k.d.577.9		20	39.23	odd	6
845.2.k.e.268.2		20	195.128	odd	12
845.2.k.e.577.2		20	39.29	odd	6
845.2.o.e.258.5		20	195.8	odd	4
845.2.o.e.357.5		20	39.35	odd	6
845.2.o.f.258.1		20	195.83	odd	4
845.2.o.f.357.1		20	39.17	odd	6
845.2.o.g.488.1		20	195.188	odd	12
845.2.o.g.587.1		20	39.38	odd	2
845.2.t.e.188.5		20	195.173	even	12
845.2.t.e.427.5		20	39.5	even	4
845.2.t.f.188.1		20	195.113	even	12
845.2.t.f.427.1		20	39.8	even	4
845.2.t.g.418.1		20	195.38	even	4
845.2.t.g.657.1		20	39.32	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.759023 - 1.31467i) q^{2} +(-0.152233 + 0.263675i) q^{4} +(-0.600231 - 2.15400i) q^{5} +(-2.24723 - 1.29744i) q^{7} -2.57390 q^{8} +(-2.37621 + 2.42404i) q^{10} +(-1.29395 + 4.82908i) q^{11} +(-2.71223 + 2.37567i) q^{13} +3.93915i q^{14} +(2.25812 + 3.91117i) q^{16} +(-0.0211881 - 0.0790751i) q^{17} +(2.71143 - 0.726525i) q^{19} +(0.659330 + 0.169644i) q^{20} +(7.33077 - 1.96427i) q^{22} +(1.05016 - 3.91925i) q^{23} +(-4.27945 + 2.58580i) q^{25} +(5.18186 + 1.76249i) q^{26} +(0.684205 - 0.395026i) q^{28} +(4.31701 - 2.49243i) q^{29} +(-2.32124 + 2.32124i) q^{31} +(0.854024 - 1.47921i) q^{32} +(-0.0878751 + 0.0878751i) q^{34} +(-1.44583 + 5.61931i) q^{35} +(0.494934 - 0.285750i) q^{37} +(-3.01318 - 3.01318i) q^{38} +(1.54493 + 5.54419i) q^{40} +(-10.0563 - 2.69458i) q^{41} +(0.132121 - 0.0354017i) q^{43} +(-1.07633 - 1.07633i) q^{44} +(-5.94960 + 1.59419i) q^{46} +2.30053i q^{47} +(-0.133293 - 0.230870i) q^{49} +(6.64766 + 3.66337i) q^{50} +(-0.213514 - 1.07680i) q^{52} +(-6.70735 + 6.70735i) q^{53} +(11.1785 - 0.111396i) q^{55} +(5.78416 + 3.33948i) q^{56} +(-6.55343 - 3.78362i) q^{58} +(-0.694109 - 2.59045i) q^{59} +(-2.74237 + 4.74992i) q^{61} +(4.81352 + 1.28978i) q^{62} +6.43957 q^{64} +(6.74516 + 4.41620i) q^{65} +(-7.89339 - 13.6718i) q^{67} +(0.0240756 + 0.00645104i) q^{68} +(8.48494 - 2.36440i) q^{70} +(1.98951 + 7.42495i) q^{71} -6.61894 q^{73} +(-0.751333 - 0.433783i) q^{74} +(-0.221202 + 0.825536i) q^{76} +(9.17326 - 9.17326i) q^{77} +5.71054i q^{79} +(7.06928 - 7.21159i) q^{80} +(4.09050 + 15.2660i) q^{82} +3.70736i q^{83} +(-0.157610 + 0.0931025i) q^{85} +(-0.146824 - 0.146824i) q^{86} +(3.33050 - 12.4296i) q^{88} +(-17.2829 - 4.63094i) q^{89} +(9.17731 - 1.81973i) q^{91} +(0.873538 + 0.873538i) q^{92} +(3.02443 - 1.74616i) q^{94} +(-3.19242 - 5.40434i) q^{95} +(-2.68493 + 4.65043i) q^{97} +(-0.202345 + 0.350471i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 12 q^{8} - 10 q^{10} + 16 q^{11} + 2 q^{13} - 2 q^{16} + 10 q^{17} + 20 q^{19} - 14 q^{20} + 16 q^{22} + 2 q^{23} - 18 q^{25} + 24 q^{26} + 6 q^{28} + 6 q^{32}+ \cdots - 4 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 12 * q^8 - 10 * q^10 + 16 * q^11 + 2 * q^13 - 2 * q^16 + 10 * q^17 + 20 * q^19 - 14 * q^20 + 16 * q^22 + 2 * q^23 - 18 * q^25 + 24 * q^26 + 6 * q^28 + 6 * q^32 - 2 * q^34 + 20 * q^35 + 42 * q^37 - 8 * q^38 - 16 * q^40 - 10 * q^41 - 22 * q^43 - 36 * q^44 + 4 * q^46 - 18 * q^49 - 44 * q^50 + 46 * q^52 + 10 * q^53 + 26 * q^55 - 90 * q^58 - 16 * q^59 - 16 * q^61 + 40 * q^62 - 20 * q^64 - 8 * q^65 - 58 * q^67 - 28 * q^68 + 32 * q^70 + 16 * q^71 + 72 * q^73 + 18 * q^74 - 64 * q^76 - 28 * q^77 + 34 * q^80 + 22 * q^82 - 6 * q^85 - 60 * q^86 + 50 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 + 48 * q^94 - 14 * q^95 - 22 * q^97 - 4 * q^98

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