LMFDB - Embedded newform 585.2.dp.a.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(28,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 1]))

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

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

chi := DirichletCharacter("585.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.dp (of order $12$, 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:	$4.67124851824$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.1
Root			$1.51805i$ of defining polynomial
Character	$\chi$	$=$	585.28
Dual form			585.2.dp.a.397.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31467 + 0.759023i) q^{2} +(0.152233 - 0.263675i) q^{4} +(2.15400 + 0.600231i) q^{5} +(-1.29744 + 2.24723i) q^{7} -2.57390i q^{8} +(-3.28738 + 0.845834i) q^{10} +(-1.29395 + 4.82908i) q^{11} +(-2.37567 - 2.71223i) q^{13} -3.93915i q^{14} +(2.25812 + 3.91117i) q^{16} +(-0.0790751 + 0.0211881i) q^{17} +(-2.71143 + 0.726525i) q^{19} +(0.486175 - 0.476581i) q^{20} +(-1.96427 - 7.33077i) q^{22} +(3.91925 + 1.05016i) q^{23} +(4.27945 + 2.58580i) q^{25} +(5.18186 + 1.76249i) q^{26} +(0.395026 + 0.684205i) q^{28} +(-4.31701 + 2.49243i) q^{29} +(-2.32124 + 2.32124i) q^{31} +(-1.47921 - 0.854024i) q^{32} +(0.0878751 - 0.0878751i) q^{34} +(-4.14355 + 4.06178i) q^{35} +(-0.285750 - 0.494934i) q^{37} +(3.01318 - 3.01318i) q^{38} +(1.54493 - 5.54419i) q^{40} +(-10.0563 - 2.69458i) q^{41} +(0.0354017 + 0.132121i) q^{43} +(1.07633 + 1.07633i) q^{44} +(-5.94960 + 1.59419i) q^{46} +2.30053 q^{47} +(0.133293 + 0.230870i) q^{49} +(-7.58873 - 0.151261i) q^{50} +(-1.07680 + 0.213514i) q^{52} +(-6.70735 - 6.70735i) q^{53} +(-5.68573 + 9.62518i) q^{55} +(5.78416 + 3.33948i) q^{56} +(3.78362 - 6.55343i) q^{58} +(0.694109 + 2.59045i) q^{59} +(-2.74237 + 4.74992i) q^{61} +(1.28978 - 4.81352i) q^{62} -6.43957 q^{64} +(-3.48923 - 7.26810i) q^{65} +(-13.6718 + 7.89339i) q^{67} +(-0.00645104 + 0.0240756i) q^{68} +(2.36440 - 8.48494i) q^{70} +(1.98951 + 7.42495i) q^{71} -6.61894i q^{73} +(0.751333 + 0.433783i) q^{74} +(-0.221202 + 0.825536i) q^{76} +(-9.17326 - 9.17326i) q^{77} -5.71054i q^{79} +(2.51638 + 9.78006i) q^{80} +(15.2660 - 4.09050i) q^{82} -3.70736 q^{83} +(-0.183046 - 0.00182408i) q^{85} +(-0.146824 - 0.146824i) q^{86} +(12.4296 + 3.33050i) q^{88} +(17.2829 + 4.63094i) q^{89} +(9.17731 - 1.81973i) q^{91} +(0.873538 - 0.873538i) q^{92} +(-3.02443 + 1.74616i) q^{94} +(-6.27651 - 0.0625465i) q^{95} +(4.65043 + 2.68493i) q^{97} +(-0.350471 - 0.202345i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} + 6 q^{4} - 2 q^{7} - 2 q^{10} + 16 q^{11} - 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 16 q^{22} + 10 q^{23} + 18 q^{25} + 24 q^{26} + 18 q^{28} - 48 q^{32} + 2 q^{34} - 40 q^{35} - 4 q^{37}+ \cdots + 30 q^{98}+O(q^{100}) $ 20 * q + 6 * q^2 + 6 * q^4 - 2 * q^7 - 2 * q^10 + 16 * q^11 - 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 16 * q^22 + 10 * q^23 + 18 * q^25 + 24 * q^26 + 18 * q^28 - 48 * q^32 + 2 * q^34 - 40 * q^35 - 4 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 + 10 * q^43 + 36 * q^44 + 4 * q^46 + 40 * q^47 + 18 * q^49 - 36 * q^50 - 30 * q^52 + 10 * q^53 - 10 * q^55 + 16 * q^59 - 16 * q^61 + 44 * q^62 + 20 * q^64 + 14 * q^65 + 18 * q^67 - 22 * q^68 - 12 * q^70 + 16 * q^71 - 18 * q^74 - 64 * q^76 + 28 * q^77 + 2 * q^80 + 56 * q^82 - 48 * q^83 - 26 * q^85 - 60 * q^86 + 82 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^94 + 26 * q^95 + 66 * q^97 + 30 * q^98

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−1.31467	+	0.759023i	−0.929610	+	0.536710i	−0.886688	−	0.462368i	$-0.847000\pi$
$2$	−1.31467	+	0.759023i	−0.929610	+	0.536710i	−0.0429217	+	0.999078i	$0.513667\pi$
$3$		0			0
$3$		0			0
$4$	0.152233	−	0.263675i	0.0761163	−	0.131837i
$5$	2.15400	+	0.600231i	0.963299	+	0.268431i
$5$	2.15400	+	0.600231i	0.963299	+	0.268431i
$6$		0			0
$7$	−1.29744	+	2.24723i	−0.490387	+	0.849375i	−0.999939	−	0.0110652i	$-0.996478\pi$
$7$	−1.29744	+	2.24723i	−0.490387	+	0.849375i	0.509552	+	0.860440i	$0.329811\pi$
$8$		−	2.57390i		−	0.910011i
$9$		0			0
$10$	−3.28738	+	0.845834i	−1.03956	+	0.267476i
$11$	−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
$13$	−2.37567	−	2.71223i	−0.658892	−	0.752237i
$13$	−2.37567	−	2.71223i	−0.658892	−	0.752237i
$14$		−	3.93915i		−	1.05278i
$15$		0			0
$16$	2.25812	+	3.91117i	0.564529	+	0.977793i
$17$	−0.0790751	+	0.0211881i	−0.0191785	+	0.00513887i	−0.268396	−	0.963309i	$-0.586493\pi$
$17$	−0.0790751	+	0.0211881i	−0.0191785	+	0.00513887i	0.249217	+	0.968448i	$0.419827\pi$
$18$		0			0
$19$	−2.71143	+	0.726525i	−0.622045	+	0.166676i	−0.556057	−	0.831144i	$-0.687686\pi$
$19$	−2.71143	+	0.726525i	−0.622045	+	0.166676i	−0.0659876	+	0.997820i	$0.521020\pi$
$20$	0.486175	−	0.476581i	0.108712	−	0.106567i
$21$		0			0
$22$	−1.96427	−	7.33077i	−0.418785	−	1.56293i
$23$	3.91925	+	1.05016i	0.817220	+	0.218973i	0.643131	−	0.765756i	$-0.277635\pi$
$23$	3.91925	+	1.05016i	0.817220	+	0.218973i	0.174089	+	0.984730i	$0.444302\pi$
$24$		0			0
$25$	4.27945	+	2.58580i	0.855889	+	0.517159i
$26$	5.18186	+	1.76249i	1.01625	+	0.345653i
$27$		0			0
$28$	0.395026	+	0.684205i	0.0746528	+	0.129303i
$29$	−4.31701	+	2.49243i	−0.801649	+	0.462833i	−0.844048	−	0.536268i	$-0.819834\pi$
$29$	−4.31701	+	2.49243i	−0.801649	+	0.462833i	0.0423981	+	0.999101i	$0.486500\pi$
$30$		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	$0.345252\pi$
$32$	−1.47921	−	0.854024i	−0.261490	−	0.150972i
$33$		0			0
$34$	0.0878751	−	0.0878751i	0.0150705	−	0.0150705i
$35$	−4.14355	+	4.06178i	−0.700388	+	0.686566i
$36$		0			0
$37$	−0.285750	−	0.494934i	−0.0469771	−	0.0813667i	0.841581	−	0.540131i	$-0.181625\pi$
$37$	−0.285750	−	0.494934i	−0.0469771	−	0.0813667i	−0.888558	+	0.458765i	$0.848292\pi$
$38$	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
$43$	0.0354017	+	0.132121i	0.00539871	+	0.0201483i	0.968573	−	0.248731i	$-0.0800135\pi$
$43$	0.0354017	+	0.132121i	0.00539871	+	0.0201483i	−0.963174	+	0.268879i	$0.913347\pi$
$44$	1.07633	+	1.07633i	0.162262	+	0.162262i
$45$		0			0
$46$	−5.94960	+	1.59419i	−0.877221	+	0.235051i
$47$	2.30053			0.335567			0.167784	−	0.985824i	$-0.446339\pi$
$47$	2.30053			0.335567			0.167784	+	0.985824i	$0.446339\pi$
$48$		0			0
$49$	0.133293	+	0.230870i	0.0190418	+	0.0329814i
$50$	−7.58873	−	0.151261i	−1.07321	−	0.0213915i
$51$		0			0
$52$	−1.07680	+	0.213514i	−0.149325	+	0.0296090i
$53$	−6.70735	−	6.70735i	−0.921326	−	0.921326i	0.0757974	−	0.997123i	$-0.475850\pi$
$53$	−6.70735	−	6.70735i	−0.921326	−	0.921326i	−0.997123	+	0.0757974i	$0.975850\pi$
$54$		0			0
$55$	−5.68573	+	9.62518i	−0.766664	+	1.29786i
$56$	5.78416	+	3.33948i	0.772941	+	0.446257i
$57$		0			0
$58$	3.78362	−	6.55343i	0.496814	−	0.860507i
$59$	0.694109	+	2.59045i	0.0903653	+	0.337248i	0.996276	−	0.0862207i	$-0.0274790\pi$
$59$	0.694109	+	2.59045i	0.0903653	+	0.337248i	−0.905911	+	0.423469i	$0.860812\pi$
$60$		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	$0.280867\pi$
$62$	1.28978	−	4.81352i	0.163802	−	0.611318i
$63$		0			0
$64$	−6.43957			−0.804946
$65$	−3.48923	−	7.26810i	−0.432786	−	0.901497i
$66$		0			0
$67$	−13.6718	+	7.89339i	−1.67027	+	0.964331i	−0.702786	+	0.711401i	$0.748061\pi$
$67$	−13.6718	+	7.89339i	−1.67027	+	0.964331i	−0.967485	+	0.252930i	$0.918606\pi$
$68$	−0.00645104	+	0.0240756i	−0.000782303	+	0.00291960i
$69$		0			0
$70$	2.36440	−	8.48494i	0.282600	−	1.01414i
$71$	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
$73$		−	6.61894i		−	0.774688i	−0.921935	−	0.387344i	$-0.873393\pi$
$73$		−	6.61894i		−	0.774688i	0.921935	−	0.387344i	$-0.126607\pi$
$74$	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	$-0.895899\pi$
$79$		−	5.71054i		−	0.642486i	0.946997	−	0.321243i	$-0.104101\pi$
$80$	2.51638	+	9.78006i	0.281340	+	1.09344i
$81$		0			0
$82$	15.2660	−	4.09050i	1.68584	−	0.451720i
$83$	−3.70736			−0.406936			−0.203468	−	0.979082i	$-0.565221\pi$
$83$	−3.70736			−0.406936			−0.203468	+	0.979082i	$0.565221\pi$
$84$		0			0
$85$	−0.183046	−	0.00182408i	−0.0198541	−	0.000197849i
$86$	−0.146824	−	0.146824i	−0.0158325	−	0.0158325i
$87$		0			0
$88$	12.4296	+	3.33050i	1.32500	+	0.355032i
$89$	17.2829	+	4.63094i	1.83198	+	0.490878i	0.998131	−	0.0611111i	$-0.0194644\pi$
$89$	17.2829	+	4.63094i	1.83198	+	0.490878i	0.833851	+	0.551989i	$0.186131\pi$
$90$		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
$95$	−6.27651	−	0.0625465i	−0.643956	−	0.00641713i
$96$		0			0
$97$	4.65043	+	2.68493i	0.472180	+	0.272613i	0.717152	−	0.696917i	$-0.245445\pi$
$97$	4.65043	+	2.68493i	0.472180	+	0.272613i	−0.244972	+	0.969530i	$0.578779\pi$
$98$	−0.350471	−	0.202345i	−0.0354029	−	0.0204399i
$99$		0			0
$100$	1.33328	−	0.734739i	0.133328	−	0.0734739i
$101$	−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	$-0.643398\pi$
$103$	4.71738	−	4.71738i	0.464817	−	0.464817i	0.900230	+	0.435414i	$0.143398\pi$
$104$	−6.98101	+	6.11474i	−0.684545	+	0.599599i
$105$		0			0
$106$	13.9090	+	3.72690i	1.35096	+	0.361988i
$107$	3.50497	+	0.939155i	0.338838	+	0.0907915i	0.424226	−	0.905556i	$-0.360546\pi$
$107$	3.50497	+	0.939155i	0.338838	+	0.0907915i	−0.0853876	+	0.996348i	$0.527213\pi$
$108$		0			0
$109$	1.58528	+	1.58528i	0.151843	+	0.151843i	0.778941	−	0.627098i	$-0.215757\pi$
$109$	1.58528	+	1.58528i	0.151843	+	0.151843i	−0.627098	+	0.778941i	$0.715757\pi$
$110$	0.169104	−	16.9695i	0.0161234	−	1.61798i
$111$		0			0
$112$	−11.7191			−1.10735
$113$	5.53206	−	1.48231i	0.520412	−	0.139444i	0.0109551	−	0.999940i	$-0.496513\pi$
$113$	5.53206	−	1.48231i	0.520412	−	0.139444i	0.509457	+	0.860496i	$0.329846\pi$
$114$		0			0
$115$	7.81173	+	4.61450i	0.728448	+	0.430304i
$116$			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
$122$		−	8.32609i		−	0.753809i
$123$		0			0
$124$	0.258683	+	0.965419i	0.0232304	+	0.0866972i
$125$	7.66586	+	8.13846i	0.685655	+	0.727926i
$126$		0			0
$127$	0.210801	−	0.786718i	0.0187055	−	0.0698100i	−0.955942	−	0.293555i	$-0.905162\pi$
$127$	0.210801	−	0.786718i	0.0187055	−	0.0698100i	0.974648	+	0.223745i	$0.0718283\pi$
$128$	11.4243	−	6.59583i	1.00978	−	0.582994i
$129$		0			0
$130$	10.1038	+	6.90672i	0.886165	+	0.605759i
$131$	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
$133$	1.88525	−	7.03584i	0.163472	−	0.610085i
$134$	11.9825	−	20.7544i	1.03513	−	1.79290i
$135$		0			0
$136$	0.0545361	+	0.203531i	0.00467643	+	0.0174527i
$137$	−9.61871	+	16.6601i	−0.821782	+	1.42337i	0.0825721	+	0.996585i	$0.473687\pi$
$137$	−9.61871	+	16.6601i	−0.821782	+	1.42337i	−0.904354	+	0.426783i	$0.859647\pi$
$138$		0			0
$139$	13.7257	+	7.92451i	1.16419	+	0.672148i	0.952306	−	0.305146i	$-0.0987052\pi$
$139$	13.7257	+	7.92451i	1.16419	+	0.672148i	0.211889	+	0.977294i	$0.432038\pi$
$140$	0.440205	+	1.71088i	0.0372041	+	0.144596i
$141$		0			0
$142$	−8.25125	−	8.25125i	−0.692430	−	0.692430i
$143$	16.1716	−	7.96282i	1.35234	−	0.665884i
$144$		0			0
$145$	−10.7949	+	2.77749i	−0.896467	+	0.230658i
$146$	5.02393	+	8.70170i	0.415783	+	0.720158i
$147$		0			0
$148$	−0.174002			−0.0143029
$149$	1.39120	−	0.372772i	0.113972	−	0.0305387i	−0.201382	−	0.979513i	$-0.564543\pi$
$149$	1.39120	−	0.372772i	0.113972	−	0.0305387i	0.315354	+	0.948974i	$0.397877\pi$
$150$		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	$0.454137\pi$
$152$	1.87000	+	6.97895i	0.151677	+	0.566068i
$153$		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	−0.502014	−	0.864859i	$-0.667408\pi$
$157$	4.54644	−	4.54644i	0.362845	−	0.362845i	0.864859	+	0.502014i	$0.167408\pi$
$158$	4.33444	+	7.50746i	0.344829	+	0.597262i
$159$		0			0
$160$	−2.67362	−	2.72744i	−0.211368	−	0.215623i
$161$	−7.44495	+	7.44495i	−0.586744	+	0.586744i
$162$		0			0
$163$	11.3759	+	6.56789i	0.891031	+	0.514437i	0.874280	−	0.485423i	$-0.161334\pi$
$163$	11.3759	+	6.56789i	0.891031	+	0.514437i	0.0167516	+	0.999860i	$0.494668\pi$
$164$	−2.24139	+	2.24139i	−0.175023	+	0.175023i
$165$		0			0
$166$	4.87395	−	2.81398i	0.378292	−	0.218407i
$167$	1.64258	+	2.84503i	0.127107	+	0.220155i	0.922554	−	0.385867i	$-0.126098\pi$
$167$	1.64258	+	2.84503i	0.127107	+	0.220155i	−0.795448	+	0.606022i	$0.792764\pi$
$168$		0			0
$169$	−1.71239	+	12.8867i	−0.131722	+	0.991287i
$170$	0.242028	−	0.136538i	0.0185627	−	0.0104720i
$171$		0			0
$172$	0.0402263	+	0.0107786i	0.00306722	+	0.000821860i
$173$	1.09689	+	4.09367i	0.0833953	+	0.311236i	0.995005	−	0.0998202i	$-0.0318268\pi$
$173$	1.09689	+	4.09367i	0.0833953	+	0.311236i	−0.911610	+	0.411056i	$0.865160\pi$
$174$		0			0
$175$	−11.3632	+	6.26200i	−0.858979	+	0.473363i
$176$	−21.8093	+	5.84377i	−1.64393	+	0.440491i
$177$		0			0
$178$	−26.2362	+	7.02997i	−1.96649	+	0.526919i
$179$	6.98083	+	12.0912i	0.521772	+	0.903735i	0.999679	+	0.0253252i	$0.00806213\pi$
$179$	6.98083	+	12.0912i	0.521772	+	0.903735i	−0.477907	+	0.878410i	$0.658605\pi$
$180$		0			0
$181$		−	8.64775i		−	0.642782i	−0.946947	−	0.321391i	$-0.895850\pi$
$181$		−	8.64775i		−	0.642782i	0.946947	−	0.321391i	$-0.104150\pi$
$182$	−10.6839	+	9.35812i	−0.791942	+	0.693670i
$183$		0			0
$184$	2.70301	−	10.0878i	0.199268	−	0.743680i
$185$	−0.318432	−	1.23761i	−0.0234116	−	0.0909906i
$186$		0			0
$187$		−	0.409276i		−	0.0299292i
$188$	0.350216	−	0.606592i	0.0255421	−	0.0442402i
$189$		0			0
$190$	8.29899	−	4.68179i	0.602072	−	0.339653i
$191$	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
$193$	7.40936	−	4.27780i	0.533338	−	0.307923i	−0.209037	−	0.977908i	$-0.567033\pi$
$193$	7.40936	−	4.27780i	0.533338	−	0.307923i	0.742375	+	0.669985i	$0.233700\pi$
$194$	−8.15169			−0.585257
$195$		0			0
$196$	0.0811660			0.00579757
$197$	6.63101	−	3.82842i	0.472440	−	0.272764i	−0.244820	−	0.969568i	$-0.578729\pi$
$197$	6.63101	−	3.82842i	0.472440	−	0.272764i	0.717261	+	0.696805i	$0.245396\pi$
$198$		0			0
$199$	7.66380	−	13.2741i	0.543272	−	0.940975i	−0.455441	−	0.890266i	$-0.650519\pi$
$199$	7.66380	−	13.2741i	0.543272	−	0.940975i	0.998713	−	0.0507092i	$-0.0161482\pi$
$200$	6.65558	−	11.0149i	0.470621	−	0.778869i
$201$		0			0
$202$	1.90576	−	3.30088i	0.134089	−	0.232249i
$203$		−	12.9351i		−	0.907868i
$204$		0			0
$205$	−20.0440	−	11.8402i	−1.39993	−	0.826959i
$206$	−2.62118	+	9.78238i	−0.182626	+	0.681570i
$207$		0			0
$208$	5.24346	−	15.4162i	0.363569	−	1.06892i
$209$		−	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	$-0.405894\pi$
$212$	−2.78964	+	0.747481i	−0.191593	+	0.0513372i
$213$		0			0
$214$	−5.32071	+	1.42568i	−0.363716	+	0.0974575i
$215$	−0.00304773	+	0.305838i	−0.000207854	+	0.0208580i
$216$		0			0
$217$	−2.20469	−	8.22803i	−0.149664	−	0.558555i
$218$	−3.28739	−	0.880853i	−0.222650	−	0.0596589i
$219$		0			0
$220$	1.67236	+	2.96445i	0.112751	+	0.199863i
$221$	0.245323	+	0.164134i	0.0165022	+	0.0110408i
$222$		0			0
$223$	9.48653	+	16.4311i	0.635265	+	1.10031i	0.986459	+	0.164008i	$0.0524424\pi$
$223$	9.48653	+	16.4311i	0.635265	+	1.10031i	−0.351194	+	0.936303i	$0.614224\pi$
$224$	3.83838	−	2.21609i	0.256463	−	0.148069i
$225$		0			0
$226$	−6.14771	+	6.14771i	−0.408939	+	0.408939i
$227$	−23.3469	−	13.4794i	−1.54959	−	0.894656i	−0.998173	−	0.0604265i	$-0.980754\pi$
$227$	−23.3469	−	13.4794i	−1.54959	−	0.894656i	−0.551417	−	0.834230i	$-0.685913\pi$
$228$		0			0
$229$	−11.1801	+	11.1801i	−0.738799	+	0.738799i	−0.972346	−	0.233547i	$-0.924967\pi$
$229$	−11.1801	+	11.1801i	−0.738799	+	0.738799i	0.233547	+	0.972346i	$0.424967\pi$
$230$	−13.7723	−	0.137244i	−0.908121	−	0.00904959i
$231$		0			0
$232$	6.41527	+	11.1116i	0.421183	+	0.729510i
$233$	−6.75797	+	6.75797i	−0.442729	+	0.442729i	−0.892928	−	0.450199i	$-0.851353\pi$
$233$	−6.75797	+	6.75797i	−0.442729	+	0.442729i	0.450199	+	0.892928i	$0.351353\pi$
$234$		0			0
$235$	4.95535	+	1.38085i	0.323251	+	0.0900767i
$236$	0.788702	+	0.211332i	0.0513401	+	0.0137565i
$237$		0			0
$238$	0.0834631	+	0.311489i	0.00541011	+	0.0201908i
$239$	−1.98766	−	1.98766i	−0.128571	−	0.128571i	0.639893	−	0.768464i	$-0.278979\pi$
$239$	−1.98766	−	1.98766i	−0.128571	−	0.128571i	−0.768464	+	0.639893i	$0.778979\pi$
$240$		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	$0.444845\pi$
$242$	21.2441			1.36562
$243$		0			0
$244$	0.834956	+	1.44619i	0.0534526	+	0.0925826i
$245$	0.148538	+	0.577300i	0.00948972	+	0.0368824i
$246$		0			0
$247$	8.41197	+	5.62804i	0.535241	+	0.358104i
$248$	5.97463	+	5.97463i	0.379389	+	0.379389i
$249$		0			0
$250$	−16.2553	−	4.88080i	−1.02808	−	0.308689i
$251$	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
$253$	−10.1426	+	17.5675i	−0.637661	+	1.10446i
$254$	0.320005	+	1.19428i	0.0200789	+	0.0749355i
$255$		0			0
$256$	−3.57321	+	6.18898i	−0.223325	+	0.386811i
$257$	5.19242	−	19.3784i	0.323894	−	1.20879i	−0.591525	−	0.806287i	$-0.701474\pi$
$257$	5.19242	−	19.3784i	0.323894	−	1.20879i	0.915419	−	0.402502i	$-0.131859\pi$
$258$		0			0
$259$	1.48298			0.0921478
$260$	−2.44759	−	0.186420i	−0.151793	−	0.0115613i
$261$		0			0
$262$	−21.1743	+	12.2250i	−1.30815	+	0.755264i
$263$	−2.43854	+	9.10077i	−0.150367	+	0.561177i	0.849091	+	0.528247i	$0.177151\pi$
$263$	−2.43854	+	9.10077i	−0.150367	+	0.561177i	−0.999458	+	0.0329302i	$0.989516\pi$
$264$		0			0
$265$	−10.4217	−	18.4736i	−0.640199	−	1.13482i
$266$	2.86189	+	10.6807i	0.175474	+	0.654878i
$267$		0			0
$268$			4.80653i			0.293605i
$269$	2.78417	+	1.60744i	0.169754	+	0.0980075i	0.582470	−	0.812852i	$-0.302086\pi$
$269$	2.78417	+	1.60744i	0.169754	+	0.0980075i	−0.412716	+	0.910860i	$0.635420\pi$
$270$		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
$275$	−18.0244	+	17.3199i	−1.08691	+	1.04443i
$276$		0			0
$277$	10.3015	−	2.76028i	0.618956	−	0.165849i	0.0643031	−	0.997930i	$-0.479518\pi$
$277$	10.3015	−	2.76028i	0.618956	−	0.165849i	0.554653	+	0.832082i	$0.312851\pi$
$278$	−24.0595			−1.44300
$279$		0			0
$280$	10.4546	+	10.6651i	0.624783	+	0.637361i
$281$	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
$283$	−5.56143	−	1.49018i	−0.330592	−	0.0885820i	0.0897050	−	0.995968i	$-0.471408\pi$
$283$	−5.56143	−	1.49018i	−0.330592	−	0.0885820i	−0.420297	+	0.907386i	$0.638074\pi$
$284$	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
$290$	12.0835	−	11.8450i	0.709568	−	0.695565i
$291$		0			0
$292$	−1.74525	−	1.00762i	−0.102133	−	0.0589664i
$293$	−2.76788	−	1.59804i	−0.161701	−	0.0933583i	0.416966	−	0.908922i	$-0.363094\pi$
$293$	−2.76788	−	1.59804i	−0.161701	−	0.0933583i	−0.578667	+	0.815564i	$0.696427\pi$
$294$		0			0
$295$	−0.0597558	+	5.99646i	−0.00347912	+	0.349127i
$296$	−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
$302$	−28.8767	−	7.73749i	−1.66167	−	0.445243i
$303$		0			0
$304$	−8.96429	−	8.96429i	−0.514137	−	0.514137i
$305$	−8.75812	+	8.58529i	−0.501488	+	0.491592i
$306$		0			0
$307$	24.2740			1.38539			0.692695	−	0.721231i	$-0.256423\pi$
$307$	24.2740			1.38539			0.692695	+	0.721231i	$0.256423\pi$
$308$	−3.81522	+	1.02229i	−0.217393	+	0.0582501i
$309$		0			0
$310$	5.66741	−	9.59417i	0.321887	−	0.544912i
$311$		−	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	0.428285	−	0.903644i	$-0.359118\pi$
$313$	−8.40997	−	8.40997i	−0.475359	−	0.475359i	−0.903644	+	0.428285i	$0.859118\pi$
$314$	−2.52620	+	9.42790i	−0.142562	+	0.532047i
$315$		0			0
$316$	−1.50573	−	0.869331i	−0.0847037	−	0.0489037i
$317$			11.9484i			0.671087i	0.942025	+	0.335543i	$0.108920\pi$
$317$			11.9484i			0.671087i	−0.942025	+	0.335543i	$0.891080\pi$
$318$		0			0
$319$	−6.45015	−	24.0723i	−0.361139	−	1.34779i
$320$	−13.8708	−	3.86523i	−0.775403	−	0.216073i
$321$		0			0
$322$	4.13674	−	15.4385i	0.230531	−	0.860355i
$323$	0.199013	−	0.114900i	0.0110734	−	0.00639321i
$324$		0			0
$325$	−3.15328	−	17.7498i	−0.174912	−	0.984584i
$326$	−19.9407			−1.10442
$327$		0			0
$328$	−6.93559	+	25.8840i	−0.382954	+	1.42920i
$329$	−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	$-0.283995\pi$
$332$	−0.564382	+	0.977538i	−0.0309745	+	0.0536494i
$333$		0			0
$334$	−4.31889	−	2.49351i	−0.236319	−	0.136439i
$335$	−34.1868	+	8.79617i	−1.86783	+	0.480586i
$336$		0			0
$337$	14.1264	+	14.1264i	0.769514	+	0.769514i	0.978021	−	0.208507i	$-0.0668604\pi$
$337$	14.1264	+	14.1264i	0.769514	+	0.769514i	−0.208507	+	0.978021i	$0.566860\pi$
$338$	−7.53011	−	18.2415i	−0.409584	−	0.992206i
$339$		0			0
$340$	−0.0283465	+	0.0479868i	−0.00153730	+	0.00260245i
$341$	−8.20588	−	14.2130i	−0.444373	−	0.769677i
$342$		0			0
$343$	−18.8559			−1.01812
$344$	0.340067	−	0.0911205i	0.0183352	−	0.00491289i
$345$		0			0
$346$	−4.54924	−	4.54924i	−0.244569	−	0.244569i
$347$	6.37467	+	23.7906i	0.342210	+	1.27715i	0.895837	+	0.444382i	$0.146577\pi$
$347$	6.37467	+	23.7906i	0.342210	+	1.27715i	−0.553627	+	0.832765i	$0.686757\pi$
$348$		0			0
$349$	26.3190	+	7.05214i	1.40882	+	0.377493i	0.881504	−	0.472176i	$-0.156531\pi$
$349$	26.3190	+	7.05214i	1.40882	+	0.377493i	0.527317	+	0.849669i	$0.323198\pi$
$350$	10.1858	−	16.8574i	0.544456	−	0.901065i
$351$		0			0
$352$	6.03818	−	6.03818i	0.321836	−	0.321836i
$353$	−4.39963	−	7.62038i	−0.234169	−	0.405592i	0.724862	−	0.688894i	$-0.241903\pi$
$353$	−4.39963	−	7.62038i	−0.234169	−	0.405592i	−0.959031	+	0.283302i	$0.908570\pi$
$354$		0			0
$355$	−0.171277	+	17.1875i	−0.00909042	+	0.912219i
$356$	3.85208	−	3.85208i	0.204160	−	0.204160i
$357$		0			0
$358$	−18.3549	−	10.5972i	−0.970089	−	0.560081i
$359$	−11.1256	+	11.1256i	−0.587186	+	0.587186i	−0.936868	−	0.349683i	$-0.886289\pi$
$359$	−11.1256	+	11.1256i	−0.587186	+	0.587186i	0.349683	+	0.936868i	$0.386289\pi$
$360$		0			0
$361$	−9.63047	+	5.56015i	−0.506867	+	0.292640i
$362$	6.56385	+	11.3689i	0.344988	+	0.597537i
$363$		0			0
$364$	0.917270	−	2.69684i	0.0480780	−	0.141353i
$365$	3.97289	−	14.2572i	0.207951	−	0.746256i
$366$		0			0
$367$	−10.6044	−	2.84144i	−0.553545	−	0.148322i	−0.0288057	−	0.999585i	$-0.509170\pi$
$367$	−10.6044	−	2.84144i	−0.553545	−	0.148322i	−0.524739	+	0.851263i	$0.675837\pi$
$368$	4.74276	+	17.7002i	0.247234	+	0.922689i
$369$		0			0
$370$	1.35800	+	1.38534i	0.0705993	+	0.0720205i
$371$	23.7754	−	6.37060i	1.23436	−	0.330745i
$372$		0			0
$373$	−10.2193	+	2.73825i	−0.529135	+	0.141781i	−0.513489	−	0.858096i	$-0.671647\pi$
$373$	−10.2193	+	2.73825i	−0.529135	+	0.141781i	−0.0156462	+	0.999878i	$0.504981\pi$
$374$	0.310650	+	0.538062i	0.0160633	+	0.0278225i
$375$		0			0
$376$		−	5.92134i		−	0.305370i
$377$	17.0158	+	5.78755i	0.876361	+	0.298074i
$378$		0			0
$379$	−2.53694	+	9.46800i	−0.130314	+	0.486338i	−0.999973	−	0.00731411i	$-0.997672\pi$
$379$	−2.53694	+	9.46800i	−0.130314	+	0.486338i	0.869659	+	0.493652i	$0.164338\pi$
$380$	−0.971981	+	1.64543i	−0.0498616	+	0.0844090i
$381$		0			0
$382$			25.6746i			1.31363i
$383$	−13.0283	+	22.5658i	−0.665718	+	1.15306i	0.313373	+	0.949630i	$0.398541\pi$
$383$	−13.0283	+	22.5658i	−0.665718	+	1.15306i	−0.979090	+	0.203426i	$0.934792\pi$
$384$		0			0
$385$	−14.2531	−	25.2653i	−0.726407	−	1.28764i
$386$	−6.49390	+	11.2478i	−0.330531	+	0.572496i
$387$		0			0
$388$	1.41589	−	0.817467i	0.0718812	−	0.0415006i
$389$	32.4888			1.64725			0.823623	−	0.567138i	$-0.191950\pi$
$389$	32.4888			1.64725			0.823623	+	0.567138i	$0.191950\pi$
$390$		0			0
$391$	−0.332166			−0.0167983
$392$	0.594236	−	0.343082i	0.0300134	−	0.0173283i
$393$		0			0
$394$	−5.81172	+	10.0662i	−0.292790	+	0.507127i
$395$	3.42764	−	12.3005i	0.172463	−	0.618906i
$396$		0			0
$397$	−12.0927	+	20.9451i	−0.606914	+	1.05121i	0.384832	+	0.922987i	$0.374259\pi$
$397$	−12.0927	+	20.9451i	−0.606914	+	1.05121i	−0.991746	+	0.128219i	$0.959074\pi$
$398$			23.2680i			1.16632i
$399$		0			0
$400$	−0.450006	+	22.5767i	−0.0225003	+	1.12883i
$401$	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
$403$	11.8102	+	0.781237i	0.588309	+	0.0389162i
$404$			0.764454i			0.0380330i
$405$		0			0
$406$	9.81806	+	17.0054i	0.487262	+	0.843963i
$407$	2.75983	−	0.739493i	0.136799	−	0.0366553i
$408$		0			0
$409$	13.4843	−	3.61312i	0.666758	−	0.178657i	0.0904639	−	0.995900i	$-0.471165\pi$
$409$	13.4843	−	3.61312i	0.666758	−	0.178657i	0.576294	+	0.817243i	$0.304498\pi$
$410$	35.3381	+	0.352151i	1.74523	+	0.0173915i
$411$		0			0
$412$	−0.525714	−	1.96199i	−0.0259001	−	0.0966603i
$413$	−6.72192	−	1.80113i	−0.330764	−	0.0886279i
$414$		0			0
$415$	−7.98567	−	2.22527i	−0.392001	−	0.109234i
$416$	1.19781	+	6.04084i	0.0587275	+	0.296177i
$417$		0			0
$418$	10.6520	+	18.4498i	0.521006	+	0.902408i
$419$	1.92240	−	1.10990i	0.0939155	−	0.0542221i	−0.452307	−	0.891862i	$-0.649399\pi$
$419$	1.92240	−	1.10990i	0.0939155	−	0.0542221i	0.546222	+	0.837640i	$0.316065\pi$
$420$		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	$-0.0695792\pi$
$422$	26.0774	+	15.0558i	1.26943	+	0.732905i
$423$		0			0
$424$	−17.2641	+	17.2641i	−0.838417	+	0.838417i
$425$	−0.393186	−	0.113799i	−0.0190723	−	0.00552004i
$426$		0			0
$427$	−7.11613	−	12.3255i	−0.344374	−	0.596472i
$428$	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
$433$	−3.83465	−	14.3111i	−0.184281	−	0.687748i	−0.994783	−	0.102012i	$-0.967472\pi$
$433$	−3.83465	−	14.3111i	−0.184281	−	0.687748i	0.810502	−	0.585736i	$-0.199195\pi$
$434$	9.14370	+	9.14370i	0.438912	+	0.438912i
$435$		0			0
$436$	0.659331	−	0.176667i	0.0315762	−	0.00846083i
$437$	−11.3897			−0.544845
$438$		0			0
$439$	10.9363	+	18.9422i	0.521959	+	0.904060i	0.999674	+	0.0255448i	$0.00813206\pi$
$439$	10.9363	+	18.9422i	0.521959	+	0.904060i	−0.477714	+	0.878515i	$0.658535\pi$
$440$	24.7743	+	14.6345i	1.18107	+	0.697673i
$441$		0			0
$442$	−0.447100	−	0.0295753i	−0.0212664	−	0.00140675i
$443$	6.14972	+	6.14972i	0.292182	+	0.292182i	0.837942	−	0.545760i	$-0.183759\pi$
$443$	6.14972	+	6.14972i	0.292182	+	0.292182i	−0.545760	+	0.837942i	$0.683759\pi$
$444$		0			0
$445$	34.4477	+	20.3488i	1.63298	+	0.964624i
$446$	−24.9432	−	14.4010i	−1.18110	−	0.681907i
$447$		0			0
$448$	8.35496	−	14.4712i	0.394735	−	0.683701i
$449$	−1.20994	−	4.51557i	−0.0571008	−	0.213103i	0.931481	−	0.363791i	$-0.118518\pi$
$449$	−1.20994	−	4.51557i	−0.0571008	−	0.213103i	−0.988581	+	0.150688i	$0.951851\pi$
$450$		0			0
$451$	26.0247	−	45.0761i	1.22546	−	2.12255i
$452$	0.451312	−	1.68432i	0.0212279	−	0.0792237i
$453$		0			0
$454$	40.9246			1.92069
$455$	20.8602	+	1.58881i	0.977941	+	0.0744845i
$456$		0			0
$457$	26.0120	−	15.0180i	1.21679	−	0.702514i	0.252560	−	0.967581i	$-0.418727\pi$
$457$	26.0120	−	15.0180i	1.21679	−	0.702514i	0.964230	+	0.265067i	$0.0853941\pi$
$458$	6.21213	−	23.1840i	0.290274	−	1.08332i
$459$		0			0
$460$	2.40593	−	1.35728i	0.112177	−	0.0632834i
$461$	−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
$463$			25.1475i			1.16870i	0.811500	+	0.584352i	$0.198651\pi$
$463$			25.1475i			1.16870i	−0.811500	+	0.584352i	$0.801349\pi$
$464$	−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	$-0.0868100\pi$
$467$	14.9907	+	14.9907i	0.693688	+	0.693688i	−0.269354	+	0.963041i	$0.586810\pi$
$468$		0			0
$469$		−	40.9648i		−	1.89158i
$470$	−7.56273	+	1.94587i	−0.348843	+	0.0897562i
$471$		0			0
$472$	6.66756	−	1.78657i	0.306899	−	0.0822335i
$473$	−0.683832			−0.0314426
$474$		0			0
$475$	−13.4821	−	3.90208i	−0.618600	−	0.179040i
$476$	−0.0457337	−	0.0457337i	−0.00209620	−	0.00209620i
$477$		0			0
$478$	4.12178	+	1.10443i	0.188526	+	0.0505154i
$479$	−2.21157	−	0.592587i	−0.101049	−	0.0270760i	0.207940	−	0.978142i	$-0.433324\pi$
$479$	−2.21157	−	0.592587i	−0.101049	−	0.0270760i	−0.308989	+	0.951066i	$0.599991\pi$
$480$		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
$485$	8.40546	+	8.57467i	0.381672	+	0.389356i
$486$		0			0
$487$	−4.82067	−	2.78321i	−0.218445	−	0.126119i	0.386785	−	0.922170i	$-0.373586\pi$
$487$	−4.82067	−	2.78321i	−0.218445	−	0.126119i	−0.605230	+	0.796050i	$0.706919\pi$
$488$	12.2258	+	7.05859i	0.553437	+	0.319527i
$489$		0			0
$490$	−0.633462	−	0.646214i	−0.0286169	−	0.0291930i
$491$	−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
$497$	−19.2669	−	5.16254i	−0.864237	−	0.231572i
$498$		0			0
$499$	−6.22738	−	6.22738i	−0.278776	−	0.278776i	0.553844	−	0.832620i	$-0.313160\pi$
$499$	−6.22738	−	6.22738i	−0.278776	−	0.278776i	−0.832620	+	0.553844i	$0.813160\pi$
$500$	3.31290	−	0.782353i	0.148157	−	0.0349879i
$501$		0			0
$502$	−4.30183			−0.192000
$503$	3.55090	−	0.951461i	0.158327	−	0.0424236i	−0.178785	−	0.983888i	$-0.557217\pi$
$503$	3.55090	−	0.951461i	0.158327	−	0.0424236i	0.337112	+	0.941465i	$0.390550\pi$
$504$		0			0
$505$	−5.43725	+	1.39899i	−0.241954	+	0.0622542i
$506$		−	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	−0.871379	−	0.490610i	$-0.836774\pi$
$509$	2.90050	−	10.8248i	0.128563	−	0.479802i	0.999942	+	0.0108085i	$0.00344051\pi$
$510$		0			0
$511$	14.8743	+	8.58768i	0.658000	+	0.379897i
$512$			15.5347i			0.686544i
$513$		0			0
$514$	7.88233	+	29.4173i	0.347675	+	1.29754i
$515$	12.9927	−	7.32972i	0.572529	−	0.322986i
$516$		0			0
$517$	−2.97677	+	11.1095i	−0.130918	+	0.488593i
$518$	−1.94962	+	1.12561i	−0.0856615	+	0.0494567i
$519$		0			0
$520$	−18.7074	+	8.98094i	−0.820372	+	0.393840i
$521$	−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
$523$	−2.17209	+	8.10636i	−0.0949790	+	0.354467i	−0.997016	−	0.0771917i	$-0.975405\pi$
$523$	−2.17209	+	8.10636i	−0.0949790	+	0.354467i	0.902037	+	0.431658i	$0.142071\pi$
$524$	2.45189	−	4.24681i	0.107112	−	0.185523i
$525$		0			0
$526$	−3.70182	−	13.8154i	−0.161407	−	0.602380i
$527$	0.134369	−	0.232734i	0.00585322	−	0.0101381i
$528$		0			0
$529$	−5.66090	−	3.26832i	−0.246126	−	0.142101i
$530$	27.7230	+	16.3763i	1.20421	+	0.711343i
$531$		0			0
$532$	−1.56818	−	1.56818i	−0.0679891	−	0.0679891i
$533$	16.5822	+	33.6765i	0.718253	+	1.45869i
$534$		0			0
$535$	6.98601	+	4.12673i	0.302031	+	0.178414i
$536$	20.3168	+	35.1897i	0.877552	+	1.51997i
$537$		0			0
$538$	−4.88034			−0.210407
$539$	−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	$0.709922\pi$
$542$	−5.96691	−	22.2688i	−0.256301	−	0.956528i
$543$		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	−0.855568	−	0.517691i	$-0.826792\pi$
$547$	−7.90229	+	7.90229i	−0.337877	+	0.337877i	0.517691	+	0.855568i	$0.326792\pi$
$548$	2.92856	+	5.07242i	0.125102	+	0.216683i
$549$		0			0
$550$	10.5499	−	36.4509i	0.449848	−	1.55427i
$551$	9.89447	−	9.89447i	0.421519	−	0.421519i
$552$		0			0
$553$	12.8329	+	7.40909i	0.545712	+	0.315067i
$554$	−11.4479	+	11.4479i	−0.486375	+	0.486375i
$555$		0			0
$556$	4.17898	−	2.41274i	0.177228	−	0.102323i
$557$	−5.89341	−	10.2077i	−0.249712	−	0.432513i	0.713734	−	0.700417i	$-0.247003\pi$
$557$	−5.89341	−	10.2077i	−0.249712	−	0.432513i	−0.963446	+	0.267903i	$0.913669\pi$
$558$		0			0
$559$	0.274240	−	0.409894i	0.0115991	−	0.0173367i
$560$	−25.2429	−	7.03416i	−1.06671	−	0.297247i
$561$		0			0
$562$	−26.4666	−	7.09170i	−1.11643	−	0.299145i
$563$	−8.32255	−	31.0602i	−0.350754	−	1.30903i	−0.885745	−	0.464172i	$-0.846352\pi$
$563$	−8.32255	−	31.0602i	−0.350754	−	1.30903i	0.534991	−	0.844858i	$-0.320315\pi$
$564$		0			0
$565$	12.8058	+	0.127612i	0.538744	+	0.00536868i
$566$	8.44250	−	2.26216i	0.354865	−	0.0950858i
$567$		0			0
$568$	19.1111	−	5.12080i	0.801883	−	0.214864i
$569$	−4.64237	−	8.04082i	−0.194618	−	0.337089i	0.752157	−	0.658984i	$-0.229013\pi$
$569$	−4.64237	−	8.04082i	−0.194618	−	0.337089i	−0.946775	+	0.321895i	$0.895680\pi$
$570$		0			0
$571$			31.1596i			1.30399i	0.758223	+	0.651995i	$0.226068\pi$
$571$			31.1596i			1.30399i	−0.758223	+	0.651995i	$0.773932\pi$
$572$	0.362249	−	5.47623i	0.0151464	−	0.228973i
$573$		0			0
$574$	−10.6144	+	39.6134i	−0.443035	+	1.65343i
$575$	14.0567	+	14.6285i	0.586206	+	0.610050i
$576$		0			0
$577$		−	4.57285i		−	0.190370i	−0.995460	−	0.0951852i	$-0.969656\pi$
$577$		−	4.57285i		−	0.190370i	0.995460	−	0.0951852i	$-0.0303443\pi$
$578$	12.8983	−	22.3405i	0.536499	−	0.929243i
$579$		0			0
$580$	−0.910980	+	3.26916i	−0.0378264	+	0.135745i
$581$	4.81009	−	8.33132i	0.199556	−	0.345641i
$582$		0			0
$583$	41.0693	−	23.7114i	1.70092	−	0.982025i
$584$	−17.0365			−0.704975
$585$		0			0
$586$	4.85179			0.200425
$587$	−6.22829	+	3.59590i	−0.257069	+	0.148419i	−0.622997	−	0.782224i	$-0.714085\pi$
$587$	−6.22829	+	3.59590i	−0.257069	+	0.148419i	0.365928	+	0.930643i	$0.380752\pi$
$588$		0			0
$589$	4.60743	−	7.98031i	0.189846	−	0.328823i
$590$	−4.47289	−	7.92870i	−0.184146	−	0.326420i
$591$		0			0
$592$	1.29052	−	2.23524i	0.0530399	−	0.0918677i
$593$		−	28.0561i		−	1.15212i	−0.817406	−	0.576062i	$-0.804589\pi$
$593$		−	28.0561i		−	1.15212i	0.817406	−	0.576062i	$-0.195411\pi$
$594$		0			0
$595$	0.241590	−	0.408980i	0.00990422	−	0.0167665i
$596$	0.113496	−	0.423573i	0.00464898	−	0.0173502i
$597$		0			0
$598$	18.4581	+	12.3494i	0.754808	+	0.505005i
$599$			0.912959i			0.0373025i	0.999826	+	0.0186513i	$0.00593722\pi$
$599$			0.912959i			0.0373025i	−0.999826	+	0.0186513i	$0.994063\pi$
$600$		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	$0.915080\pi$
$602$	0.520445	−	0.139453i	0.0212118	−	0.00568367i
$603$		0			0
$604$	5.79162	−	1.55186i	0.235658	−	0.0631443i
$605$	−21.9054	−	22.3464i	−0.890581	−	0.908509i
$606$		0			0
$607$	−10.0350	−	37.4512i	−0.407309	−	1.52010i	−0.799757	−	0.600324i	$-0.795038\pi$
$607$	−10.0350	−	37.4512i	−0.407309	−	1.52010i	0.392448	−	0.919774i	$-0.371628\pi$
$608$	4.63125	+	1.24094i	0.187822	+	0.0503268i
$609$		0			0
$610$	4.99757	−	17.9344i	0.202346	−	0.726143i
$611$	−5.46530	−	6.23957i	−0.221102	−	0.252426i
$612$		0			0
$613$	−12.3057	−	21.3140i	−0.497021	−	0.860865i	0.502973	−	0.864302i	$-0.332239\pi$
$613$	−12.3057	−	21.3140i	−0.497021	−	0.860865i	−0.999994	+	0.00343656i	$0.998906\pi$
$614$	−31.9122	+	18.4245i	−1.28787	+	0.743553i
$615$		0			0
$616$	−23.6110	+	23.6110i	−0.951316	+	0.951316i
$617$	13.3501	+	7.70769i	0.537455	+	0.310300i	0.744047	−	0.668127i	$-0.232904\pi$
$617$	13.3501	+	7.70769i	0.537455	+	0.310300i	−0.206592	+	0.978427i	$0.566237\pi$
$618$		0			0
$619$	−20.7915	+	20.7915i	−0.835683	+	0.835683i	−0.988287	−	0.152604i	$-0.951234\pi$
$619$	−20.7915	+	20.7915i	−0.835683	+	0.835683i	0.152604	+	0.988287i	$0.451234\pi$
$620$	−0.0222700	+	2.23478i	−0.000894385	+	0.0897510i
$621$		0			0
$622$	12.8316	+	22.2249i	0.514498	+	0.891137i
$623$	−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
$628$	−0.506664	−	1.89090i	−0.0202181	−	0.0754549i
$629$	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	$0.335952\pi$
$632$	−14.6984			−0.584670
$633$		0			0
$634$	−9.06908	−	15.7081i	−0.360179	−	0.623849i
$635$	0.926277	−	1.56806i	0.0367582	−	0.0622267i
$636$		0			0
$637$	0.309512	−	0.909991i	0.0122633	−	0.0360551i
$638$	26.7512	+	26.7512i	1.05909	+	1.05909i
$639$		0			0
$640$	28.5670	−	7.35020i	1.12921	−	0.290542i
$641$	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
$643$	−13.9057	+	24.0854i	−0.548387	+	0.949834i	0.449999	+	0.893029i	$0.351424\pi$
$643$	−13.9057	+	24.0854i	−0.548387	+	0.949834i	−0.998385	+	0.0568044i	$0.981909\pi$
$644$	0.829680	+	3.09641i	0.0326940	+	0.122016i
$645$		0			0
$646$	−0.174424	+	0.302111i	−0.00686261	+	0.0118864i
$647$	4.76862	−	17.7967i	0.187474	−	0.699662i	−0.806613	−	0.591079i	$-0.798702\pi$
$647$	4.76862	−	17.7967i	0.187474	−	0.699662i	0.994087	−	0.108583i	$-0.0346313\pi$
$648$		0			0
$649$	−13.4076			−0.526296
$650$	17.6180	+	20.9417i	0.691037	+	0.821402i
$651$		0			0
$652$	3.46357	−	1.99970i	0.135644	−	0.0783141i
$653$	−1.90911	+	7.12491i	−0.0747094	+	0.278819i	−0.993167	−	0.116700i	$-0.962769\pi$
$653$	−1.90911	+	7.12491i	−0.0747094	+	0.278819i	0.918458	+	0.395519i	$0.129435\pi$
$654$		0			0
$655$	34.6929	+	9.66746i	1.35556	+	0.377739i
$656$	−12.1694	−	45.4167i	−0.475134	−	1.77322i
$657$		0			0
$658$		−	9.06214i		−	0.353279i
$659$	12.0786	+	6.97358i	0.470515	+	0.271652i	0.716455	−	0.697633i	$-0.245763\pi$
$659$	12.0786	+	6.97358i	0.470515	+	0.271652i	−0.245940	+	0.969285i	$0.579097\pi$
$660$		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
$665$	8.28396	−	14.0236i	0.321238	−	0.543813i
$666$		0			0
$667$	−19.5369	+	5.23490i	−0.756472	+	0.202696i
$668$	1.00022			0.0386996
$669$		0			0
$670$	38.2678	−	37.5126i	1.47841	−	1.44924i
$671$	−19.3893	−	19.3893i	−0.748515	−	0.748515i
$672$		0			0
$673$	−32.4730	−	8.70112i	−1.25174	−	0.335404i	−0.428734	−	0.903431i	$-0.641040\pi$
$673$	−32.4730	−	8.70112i	−1.25174	−	0.335404i	−0.823010	+	0.568027i	$0.807707\pi$
$674$	−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	−0.999483	−	0.0321566i	$-0.989762\pi$
$677$	−25.1691	+	25.1691i	−0.967326	+	0.967326i	0.0321566	+	0.999483i	$0.489762\pi$
$678$		0			0
$679$	−12.0673	+	6.96707i	−0.463101	+	0.267372i
$680$	−0.00469500	+	0.471141i	−0.000180045	+	0.0180674i
$681$		0			0
$682$	21.5760	+	12.4569i	0.826187	+	0.477000i
$683$	−26.6361	−	15.3784i	−1.01920	−	0.588437i	−0.105329	−	0.994437i	$-0.533590\pi$
$683$	−26.6361	−	15.3784i	−1.01920	−	0.588437i	−0.913873	+	0.406001i	$0.866923\pi$
$684$		0			0
$685$	−30.7186	+	30.1124i	−1.17370	+	1.15054i
$686$	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	$0.847044\pi$
$692$	1.24638	+	0.333966i	0.0473802	+	0.0126955i
$693$		0			0
$694$	−26.4382	−	26.4382i	−1.00358	−	1.00358i
$695$	24.8085	+	25.3080i	0.941042	+	0.959986i
$696$		0			0
$697$	0.852297			0.0322831
$698$	−39.9534	+	10.7055i	−1.51226	+	0.405208i
$699$		0			0
$700$	−0.0787222	+	3.94947i	−0.00297542	+	0.149276i
$701$			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
$707$		−	6.51526i		−	0.245032i
$708$		0			0
$709$	−8.24828	−	30.7830i	−0.309771	−	1.15608i	−0.928760	−	0.370680i	$-0.879125\pi$
$709$	−8.24828	−	30.7830i	−0.309771	−	1.15608i	0.618990	−	0.785399i	$-0.287542\pi$
$710$	−12.8206	−	22.7259i	−0.481147	−	0.852887i
$711$		0			0
$712$	11.9196	−	44.4844i	0.446705	−	1.66712i
$713$	−11.5352	+	6.65983i	−0.431996	+	0.249413i
$714$		0			0
$715$	39.6131	−	7.44524i	1.48145	−	0.278436i
$716$	4.25084			0.158861
$717$		0			0
$718$	6.18186	−	23.0710i	0.230705	−	0.861002i
$719$	−15.4818	+	26.8152i	−0.577372	+	1.00004i	0.418407	+	0.908260i	$0.362589\pi$
$719$	−15.4818	+	26.8152i	−0.577372	+	1.00004i	−0.995779	+	0.0917785i	$0.970745\pi$
$720$		0			0
$721$	4.48053	+	16.7216i	0.166864	+	0.622744i
$722$	8.44057	−	14.6195i	0.314126	−	0.544081i
$723$		0			0
$724$	−2.28019	−	1.31647i	−0.0847427	−	0.0489262i
$725$	−24.9193	−	0.496701i	−0.925481	−	0.0184470i
$726$		0			0
$727$	16.2588	+	16.2588i	0.603007	+	0.603007i	0.941109	−	0.338103i	$-0.109785\pi$
$727$	16.2588	+	16.2588i	0.603007	+	0.603007i	−0.338103	+	0.941109i	$0.609785\pi$
$728$	−4.68379	−	23.6215i	−0.173593	−	0.875470i
$729$		0			0
$730$	5.59852	+	21.7590i	0.207211	+	0.805336i
$731$	−0.00559879	−	0.00969739i	−0.000207079	−	0.000358671i
$732$		0			0
$733$	31.2515			1.15430			0.577150	−	0.816638i	$-0.304165\pi$
$733$	31.2515			1.15430			0.577150	+	0.816638i	$0.304165\pi$
$734$	16.0980	−	4.31344i	0.594187	−	0.159212i
$735$		0			0
$736$	−4.90054	−	4.90054i	−0.180636	−	0.180636i
$737$	−20.4273	−	76.2357i	−0.752449	−	2.80818i
$738$		0			0
$739$	−26.3668	−	7.06496i	−0.969918	−	0.259889i	−0.261125	−	0.965305i	$-0.584093\pi$
$739$	−26.3668	−	7.06496i	−0.969918	−	0.259889i	−0.708793	+	0.705416i	$0.750760\pi$
$740$	−0.374801	−	0.104441i	−0.0137780	−	0.00383934i
$741$		0			0
$742$	−26.4213	+	26.4213i	−0.969956	+	0.969956i
$743$	16.4830	+	28.5494i	0.604703	+	1.04738i	0.992098	+	0.125463i	$0.0400415\pi$
$743$	16.4830	+	28.5494i	0.604703	+	1.04738i	−0.387395	+	0.921914i	$0.626625\pi$
$744$		0			0
$745$	3.22041	+	0.0320919i	0.117987	+	0.00117576i
$746$	11.3566	−	11.3566i	0.415794	−	0.415794i
$747$		0			0
$748$	−0.107916	−	0.0623052i	−0.00394579	−	0.00227810i
$749$	−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	$0.142161\pi$
$752$	5.19487	+	8.99777i	0.189437	+	0.328115i
$753$		0			0
$754$	−26.7630	+	5.30672i	−0.974653	+	0.193259i
$755$	21.6367	+	38.3535i	0.787440	+	1.39583i
$756$		0			0
$757$	−49.3561	−	13.2249i	−1.79388	−	0.480668i	−0.800882	−	0.598822i	$-0.795636\pi$
$757$	−49.3561	−	13.2249i	−1.79388	−	0.480668i	−0.992995	+	0.118154i	$0.962302\pi$
$758$	−3.85120	−	14.3729i	−0.139882	−	0.522046i
$759$		0			0
$760$	−0.160988	+	16.1551i	−0.00583967	+	0.586007i
$761$	−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
$763$	−5.61932	+	1.50569i	−0.203433	+	0.0545097i
$764$	−2.57470	−	4.45951i	−0.0931494	−	0.161339i
$765$		0			0
$766$		−	39.5553i		−	1.42919i
$767$	5.37693	−	8.03664i	0.194150	−	0.290186i
$768$		0			0
$769$	7.82422	−	29.2004i	0.282148	−	1.05299i	−0.668750	−	0.743488i	$-0.733170\pi$
$769$	7.82422	−	29.2004i	0.282148	−	1.05299i	0.950898	−	0.309505i	$-0.100163\pi$
$770$	37.9151	+	22.3970i	1.36636	+	0.807130i
$771$		0			0
$772$		−	2.60488i		−	0.0937517i
$773$	3.59641	−	6.22916i	0.129354	−	0.224047i	−0.794073	−	0.607823i	$-0.792043\pi$
$773$	3.59641	−	6.22916i	0.129354	−	0.224047i	0.923426	+	0.383776i	$0.125376\pi$
$774$		0			0
$775$	−15.9358	+	3.93136i	−0.572432	+	0.141219i
$776$	6.91074	−	11.9698i	0.248081	−	0.429689i
$777$		0			0
$778$	−42.7119	+	24.6597i	−1.53130	+	0.884094i
$779$	29.2247			1.04708
$780$		0			0
$781$	−38.4300			−1.37513
$782$	0.436687	−	0.252122i	0.0156159	−	0.00901585i
$783$		0			0
$784$	−0.601981	+	1.04266i	−0.0214993	+	0.0372379i
$785$	12.5219	−	7.06412i	0.446927	−	0.252129i
$786$		0			0
$787$	−3.58943	+	6.21708i	−0.127949	+	0.221615i	−0.922882	−	0.385083i	$-0.874173\pi$
$787$	−3.58943	+	6.21708i	−0.127949	+	0.221615i	0.794933	+	0.606698i	$0.207506\pi$
$788$		−	2.33124i		−	0.0830470i
$789$		0			0
$790$	4.83017	+	18.7727i	0.171850	+	0.667904i
$791$	−3.84642	+	14.3550i	−0.136763	+	0.510407i
$792$		0			0
$793$	19.3979	−	3.84631i	0.688838	−	0.136586i
$794$		−	36.7145i		−	1.30295i
$795$		0			0
$796$	−2.33336	−	4.04150i	−0.0827037	−	0.143247i
$797$	38.0553	−	10.1969i	1.34799	−	0.361192i	0.488596	−	0.872510i	$-0.337509\pi$
$797$	38.0553	−	10.1969i	1.34799	−	0.361192i	0.859391	+	0.511318i	$0.170843\pi$
$798$		0			0
$799$	−0.181915	+	0.0487439i	−0.00643568	+	0.00172443i
$800$	−4.12188	−	7.47969i	−0.145730	−	0.264447i
$801$		0			0
$802$	12.9022	+	48.1515i	0.455591	+	1.70029i
$803$	31.9634	+	8.56456i	1.12796	+	0.302237i
$804$		0			0
$805$	−20.5051	+	11.5677i	−0.722711	+	0.407710i
$806$	−16.1195	+	7.93716i	−0.567784	+	0.279575i
$807$		0			0
$808$	3.23129	+	5.59676i	0.113676	+	0.196893i
$809$	−24.2062	+	13.9754i	−0.851043	+	0.491350i	−0.861003	−	0.508600i	$-0.830163\pi$
$809$	−24.2062	+	13.9754i	−0.851043	+	0.491350i	0.00995956	+	0.999950i	$0.496830\pi$
$810$		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	$0.446167\pi$
$812$	−3.41066	−	1.96915i	−0.119691	−	0.0691035i
$813$		0			0
$814$	−3.06696	+	3.06696i	−0.107497	+	0.107497i
$815$	20.5615	+	20.9754i	0.720238	+	0.734737i
$816$		0			0
$817$	−0.191979	−	0.332517i	−0.00671648	−	0.0116333i
$818$	−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
$823$	−10.5653	−	39.4302i	−0.368283	−	1.37445i	−0.862915	−	0.505348i	$-0.831364\pi$
$823$	−10.5653	−	39.4302i	−0.368283	−	1.37445i	0.494633	−	0.869102i	$-0.335303\pi$
$824$	−12.1421	−	12.1421i	−0.422989	−	0.422989i
$825$		0			0
$826$	10.2042	−	2.73420i	0.355049	−	0.0951350i
$827$	−31.8649			−1.10805			−0.554026	−	0.832499i	$-0.686909\pi$
$827$	−31.8649			−1.10805			−0.554026	+	0.832499i	$0.686909\pi$
$828$		0			0
$829$	27.6391	+	47.8724i	0.959946	+	1.66268i	0.722620	+	0.691246i	$0.242938\pi$
$829$	27.6391	+	47.8724i	0.959946	+	1.66268i	0.237326	+	0.971430i	$0.423729\pi$
$830$	12.1875	−	3.13582i	0.423035	−	0.108846i
$831$		0			0
$832$	15.2983	+	17.4656i	0.530373	+	0.605510i
$833$	−0.0154318	−	0.0154318i	−0.000534681	−	0.000534681i
$834$		0			0
$835$	1.83044	+	7.11413i	0.0633452	+	0.246195i
$836$	−3.70036	−	2.13640i	−0.127980	−	0.0738890i
$837$		0			0
$838$	−1.68488	+	2.91830i	−0.0582032	+	0.100811i
$839$	−1.00953	−	3.76762i	−0.0348528	−	0.130073i	0.946307	−	0.323268i	$-0.104782\pi$
$839$	−1.00953	−	3.76762i	−0.0348528	−	0.130073i	−0.981160	+	0.193195i	$0.938115\pi$
$840$		0			0
$841$	−2.07559	+	3.59503i	−0.0715721	+	0.123966i
$842$	−13.6019	+	50.7629i	−0.468751	+	1.74940i
$843$		0			0
$844$	−6.03930			−0.207881
$845$	−11.4235	+	26.7302i	−0.392980	+	0.919547i
$846$		0			0
$847$	31.4485	−	18.1568i	1.08058	−	0.623876i
$848$	11.0876	−	41.3796i	0.380751	−	1.42098i
$849$		0			0
$850$	0.603284	−	0.148830i	0.0206925	−	0.00510482i
$851$	−0.600167	−	2.23986i	−0.0205735	−	0.0767812i
$852$		0			0
$853$		−	53.5726i		−	1.83429i	−0.398554	−	0.917145i	$-0.630488\pi$
$853$		−	53.5726i		−	1.83429i	0.398554	−	0.917145i	$-0.369512\pi$
$854$	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	$-0.0989554\pi$
$857$	18.9164	+	18.9164i	0.646171	+	0.646171i	−0.305894	+	0.952066i	$0.598955\pi$
$858$		0			0
$859$		−	18.1203i		−	0.618258i	−0.951020	−	0.309129i	$-0.899963\pi$
$859$		−	18.1203i		−	0.618258i	0.951020	−	0.309129i	$-0.100037\pi$
$860$	0.0801778	+	0.0473622i	0.00273404	+	0.00161504i
$861$		0			0
$862$	2.42312	−	0.649274i	0.0825320	−	0.0221144i
$863$	−21.4967			−0.731757			−0.365879	−	0.930663i	$-0.619232\pi$
$863$	−21.4967			−0.731757			−0.365879	+	0.930663i	$0.619232\pi$
$864$		0			0
$865$	−0.0944315	+	9.47615i	−0.00321077	+	0.322199i
$866$	15.9037	+	15.9037i	0.540431	+	0.540431i
$867$		0			0
$868$	−2.50515	−	0.671252i	−0.0850303	−	0.0227838i
$869$	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
$875$	−28.2350	+	6.66780i	−0.954518	+	0.225413i
$876$		0			0
$877$	−18.4889	−	10.6745i	−0.624324	−	0.360454i	0.154226	−	0.988036i	$-0.450711\pi$
$877$	−18.4889	−	10.6745i	−0.624324	−	0.360454i	−0.778551	+	0.627582i	$0.784045\pi$
$878$	−28.7551	−	16.6018i	−0.970437	−	0.560282i
$879$		0			0
$880$	−50.4848	−	0.503090i	−1.70184	−	0.0169591i
$881$	−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	−0.101082	+	0.994878i	$0.532230\pi$
$883$	−32.5668	+	32.5668i	−1.09596	+	1.09596i	−0.994878	+	0.101082i	$0.967770\pi$
$884$	0.0806241	−	0.0396990i	0.00271168	−	0.00133522i
$885$		0			0
$886$	−12.7526	−	3.41705i	−0.428432	−	0.114798i
$887$	15.4358	+	4.13600i	0.518282	+	0.138873i	0.508472	−	0.861079i	$-0.330211\pi$
$887$	15.4358	+	4.13600i	0.518282	+	0.138873i	0.00981024	+	0.999952i	$0.496877\pi$
$888$		0			0
$889$	1.49444	+	1.49444i	0.0501219	+	0.0501219i
$890$	−60.7325	−	0.605210i	−2.03576	−	0.0202867i
$891$		0			0
$892$	5.77663			0.193416
$893$	−6.23773	+	1.67139i	−0.208738	+	0.0559311i
$894$		0			0
$895$	7.77924	+	30.2345i	0.260031	+	1.01063i
$896$			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
$902$			79.0135i			2.63086i
$903$		0			0
$904$	−3.81532	−	14.2390i	−0.126896	−	0.473581i
$905$	5.19065	−	18.6273i	0.172543	−	0.619192i
$906$		0			0
$907$	1.35973	−	5.07458i	0.0451491	−	0.168499i	−0.939670	−	0.342082i	$-0.888868\pi$
$907$	1.35973	−	5.07458i	0.0451491	−	0.168499i	0.984819	+	0.173583i	$0.0555346\pi$
$908$	−7.10833	+	4.10399i	−0.235898	+	0.136196i
$909$		0			0
$910$	−28.6301	+	13.7446i	−0.949080	+	0.455630i
$911$	−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
$913$	4.79714	−	17.9032i	0.158762	−	0.592508i
$914$	−22.7981	+	39.4874i	−0.754093	+	1.30613i
$915$		0			0
$916$	1.24593	+	4.64987i	0.0411666	+	0.153636i
$917$	−20.8969	+	36.1945i	−0.690076	+	1.19525i
$918$		0			0
$919$	45.6207	+	26.3391i	1.50489	+	0.868847i	0.999984	+	0.00567026i	$0.00180491\pi$
$919$	45.6207	+	26.3391i	1.50489	+	0.868847i	0.504903	+	0.863176i	$0.331528\pi$
$920$	11.8773	−	20.1066i	0.391582	−	0.662896i
$921$		0			0
$922$	2.82041	+	2.82041i	0.0928851	+	0.0928851i
$923$	15.4118	−	23.0352i	0.507284	−	0.758214i
$924$		0			0
$925$	0.0569454	−	2.85694i	0.00187235	−	0.0939355i
$926$	−19.0876	−	33.0606i	−0.627256	−	1.08644i
$927$		0			0
$928$	8.51438			0.279498
$929$	8.04841	−	2.15657i	0.264060	−	0.0707546i	−0.124360	−	0.992237i	$-0.539688\pi$
$929$	8.04841	−	2.15657i	0.264060	−	0.0707546i	0.388420	+	0.921483i	$0.373021\pi$
$930$		0			0
$931$	−0.529147	−	0.529147i	−0.0173421	−	0.0173421i
$932$	0.753121	+	2.81069i	0.0246693	+	0.0920671i
$933$		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	−0.386947	−	0.922102i	$-0.626470\pi$
$937$	16.3814	−	16.3814i	0.535156	−	0.535156i	0.922102	+	0.386947i	$0.126470\pi$
$938$	31.0933	+	53.8551i	1.01523	+	1.75843i
$939$		0			0
$940$	1.11846	−	1.09639i	0.0364802	−	0.0357603i
$941$	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
$943$	−36.5835	−	21.1215i	−1.19132	−	0.687810i
$944$	−8.56432	+	8.56432i	−0.278745	+	0.278745i
$945$		0			0
$946$	0.899011	−	0.519044i	0.0292294	−	0.0168756i
$947$	−16.7208	−	28.9613i	−0.543353	−	0.941114i	−0.998709	−	0.0508048i	$-0.983821\pi$
$947$	−16.7208	−	28.9613i	−0.543353	−	0.941114i	0.455356	−	0.890309i	$-0.349512\pi$
$948$		0			0
$949$	−17.9521	+	15.7244i	−0.582749	+	0.510436i
$950$	20.6862	−	5.10327i	0.671149	−	0.165572i
$951$		0			0
$952$	−0.528140	−	0.141515i	−0.0171171	−	0.00458652i
$953$	−3.88895	−	14.5138i	−0.125975	−	0.470147i	0.873897	−	0.486111i	$-0.161585\pi$
$953$	−3.88895	−	14.5138i	−0.125975	−	0.470147i	−0.999873	+	0.0159642i	$0.994918\pi$
$954$		0			0
$955$	27.0068	−	26.4739i	0.873921	−	0.856675i
$956$	−0.826681	+	0.221508i	−0.0267368	+	0.00716409i
$957$		0			0
$958$	3.35726	−	0.899575i	0.108468	−	0.0290640i
$959$	−24.9594	−	43.2310i	−0.805982	−	1.39600i
$960$		0			0
$961$			20.2237i			0.652378i
$962$	−0.608402	−	3.06831i	−0.0196157	−	0.0989264i
$963$		0			0
$964$	−0.216305	+	0.807262i	−0.00696672	+	0.0260002i
$965$	18.5274	−	4.76706i	0.596420	−	0.153457i
$966$		0			0
$967$		−	7.49252i		−	0.240943i	−0.992717	−	0.120472i	$-0.961559\pi$
$967$		−	7.49252i		−	0.240943i	0.992717	−	0.120472i	$-0.0384407\pi$
$968$	−18.0100	+	31.1943i	−0.578864	+	1.00262i
$969$		0			0
$970$	−17.5588	−	4.89290i	−0.563778	−	0.157101i
$971$	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
$973$	−35.6165	+	20.5632i	−1.14181	+	0.659225i
$974$	8.45010			0.270759
$975$		0			0
$976$	−24.7704			−0.792880
$977$	33.6679	−	19.4382i	1.07713	−	0.621883i	0.147011	−	0.989135i	$-0.453035\pi$
$977$	33.6679	−	19.4382i	1.07713	−	0.621883i	0.930122	+	0.367252i	$0.119701\pi$
$978$		0			0
$979$	−44.7263	+	77.4683i	−1.42946	+	2.47590i
$980$	0.174832	+	0.0487183i	0.00558479	+	0.00155625i
$981$		0			0
$982$	4.63761	−	8.03257i	0.147992	−	0.256330i
$983$		−	0.207440i		−	0.00661630i	−0.999995	−	0.00330815i	$-0.998947\pi$
$983$		−	0.207440i		−	0.00661630i	0.999995	−	0.00330815i	$-0.00105302\pi$
$984$		0			0
$985$	16.5812	−	4.26628i	0.528319	−	0.135935i
$986$	−0.160336	+	0.598381i	−0.00510613	+	0.0190563i
$987$		0			0
$988$	2.76455	−	1.36125i	0.0879519	−	0.0433072i
$989$			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	$0.700621\pi$
$992$	5.41599	−	1.45121i	0.171958	−	0.0460760i
$993$		0			0
$994$	29.2480	−	7.83698i	0.927691	−	0.248574i
$995$	24.4753	−	23.9924i	0.775921	−	0.760609i
$996$		0			0
$997$	−8.96942	−	33.4743i	−0.284064	−	1.06014i	−0.949520	−	0.313706i	$-0.898429\pi$
$997$	−8.96942	−	33.4743i	−0.284064	−	1.06014i	0.665456	−	0.746437i	$-0.268237\pi$
$998$	12.9137	+	3.46020i	0.408774	+	0.109531i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.dp.a.28.1		20
3.2	odd	2		65.2.t.a.28.5	yes	20
5.2	odd	4		585.2.cf.a.262.1		20
13.7	odd	12		585.2.cf.a.163.1		20
15.2	even	4		65.2.o.a.2.5	✓	20
15.8	even	4		325.2.s.b.132.1		20
15.14	odd	2		325.2.x.b.93.1		20
39.2	even	12		845.2.k.d.268.9		20
39.5	even	4		845.2.o.f.258.1		20
39.8	even	4		845.2.o.e.258.5		20
39.11	even	12		845.2.k.e.268.2		20
39.17	odd	6		845.2.t.e.188.5		20
39.20	even	12		65.2.o.a.33.5	yes	20
39.23	odd	6		845.2.f.d.408.2		20
39.29	odd	6		845.2.f.e.408.9		20
39.32	even	12		845.2.o.g.488.1		20
39.35	odd	6		845.2.t.f.188.1		20
39.38	odd	2		845.2.t.g.418.1		20
65.7	even	12	inner	585.2.dp.a.397.1		20
195.2	odd	12		845.2.f.d.437.9		20
195.17	even	12		845.2.o.f.357.1		20
195.32	odd	12		845.2.t.g.657.1		20
195.47	odd	4		845.2.t.f.427.1		20
195.59	even	12		325.2.s.b.293.1		20
195.62	even	12		845.2.k.d.577.9		20
195.77	even	4		845.2.o.g.587.1		20
195.98	odd	12		325.2.x.b.7.1		20
195.107	even	12		845.2.k.e.577.2		20
195.122	odd	4		845.2.t.e.427.5		20
195.137	odd	12		65.2.t.a.7.5	yes	20
195.152	even	12		845.2.o.e.357.5		20
195.167	odd	12		845.2.f.e.437.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.5	✓	20	15.2	even	4
65.2.o.a.33.5	yes	20	39.20	even	12
65.2.t.a.7.5	yes	20	195.137	odd	12
65.2.t.a.28.5	yes	20	3.2	odd	2
325.2.s.b.132.1		20	15.8	even	4
325.2.s.b.293.1		20	195.59	even	12
325.2.x.b.7.1		20	195.98	odd	12
325.2.x.b.93.1		20	15.14	odd	2
585.2.cf.a.163.1		20	13.7	odd	12
585.2.cf.a.262.1		20	5.2	odd	4
585.2.dp.a.28.1		20	1.1	even	1	trivial
585.2.dp.a.397.1		20	65.7	even	12	inner
845.2.f.d.408.2		20	39.23	odd	6
845.2.f.d.437.9		20	195.2	odd	12
845.2.f.e.408.9		20	39.29	odd	6
845.2.f.e.437.2		20	195.167	odd	12
845.2.k.d.268.9		20	39.2	even	12
845.2.k.d.577.9		20	195.62	even	12
845.2.k.e.268.2		20	39.11	even	12
845.2.k.e.577.2		20	195.107	even	12
845.2.o.e.258.5		20	39.8	even	4
845.2.o.e.357.5		20	195.152	even	12
845.2.o.f.258.1		20	39.5	even	4
845.2.o.f.357.1		20	195.17	even	12
845.2.o.g.488.1		20	39.32	even	12
845.2.o.g.587.1		20	195.77	even	4
845.2.t.e.188.5		20	39.17	odd	6
845.2.t.e.427.5		20	195.122	odd	4
845.2.t.f.188.1		20	39.35	odd	6
845.2.t.f.427.1		20	195.47	odd	4
845.2.t.g.418.1		20	39.38	odd	2
845.2.t.g.657.1		20	195.32	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.31467 + 0.759023i) q^{2} +(0.152233 - 0.263675i) q^{4} +(2.15400 + 0.600231i) q^{5} +(-1.29744 + 2.24723i) q^{7} -2.57390i q^{8} +(-3.28738 + 0.845834i) q^{10} +(-1.29395 + 4.82908i) q^{11} +(-2.37567 - 2.71223i) q^{13} -3.93915i q^{14} +(2.25812 + 3.91117i) q^{16} +(-0.0790751 + 0.0211881i) q^{17} +(-2.71143 + 0.726525i) q^{19} +(0.486175 - 0.476581i) q^{20} +(-1.96427 - 7.33077i) q^{22} +(3.91925 + 1.05016i) q^{23} +(4.27945 + 2.58580i) q^{25} +(5.18186 + 1.76249i) q^{26} +(0.395026 + 0.684205i) q^{28} +(-4.31701 + 2.49243i) q^{29} +(-2.32124 + 2.32124i) q^{31} +(-1.47921 - 0.854024i) q^{32} +(0.0878751 - 0.0878751i) q^{34} +(-4.14355 + 4.06178i) q^{35} +(-0.285750 - 0.494934i) q^{37} +(3.01318 - 3.01318i) q^{38} +(1.54493 - 5.54419i) q^{40} +(-10.0563 - 2.69458i) q^{41} +(0.0354017 + 0.132121i) q^{43} +(1.07633 + 1.07633i) q^{44} +(-5.94960 + 1.59419i) q^{46} +2.30053 q^{47} +(0.133293 + 0.230870i) q^{49} +(-7.58873 - 0.151261i) q^{50} +(-1.07680 + 0.213514i) q^{52} +(-6.70735 - 6.70735i) q^{53} +(-5.68573 + 9.62518i) q^{55} +(5.78416 + 3.33948i) q^{56} +(3.78362 - 6.55343i) q^{58} +(0.694109 + 2.59045i) q^{59} +(-2.74237 + 4.74992i) q^{61} +(1.28978 - 4.81352i) q^{62} -6.43957 q^{64} +(-3.48923 - 7.26810i) q^{65} +(-13.6718 + 7.89339i) q^{67} +(-0.00645104 + 0.0240756i) q^{68} +(2.36440 - 8.48494i) q^{70} +(1.98951 + 7.42495i) q^{71} -6.61894i q^{73} +(0.751333 + 0.433783i) q^{74} +(-0.221202 + 0.825536i) q^{76} +(-9.17326 - 9.17326i) q^{77} -5.71054i q^{79} +(2.51638 + 9.78006i) q^{80} +(15.2660 - 4.09050i) q^{82} -3.70736 q^{83} +(-0.183046 - 0.00182408i) q^{85} +(-0.146824 - 0.146824i) q^{86} +(12.4296 + 3.33050i) q^{88} +(17.2829 + 4.63094i) q^{89} +(9.17731 - 1.81973i) q^{91} +(0.873538 - 0.873538i) q^{92} +(-3.02443 + 1.74616i) q^{94} +(-6.27651 - 0.0625465i) q^{95} +(4.65043 + 2.68493i) q^{97} +(-0.350471 - 0.202345i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 6 q^{4} - 2 q^{7} - 2 q^{10} + 16 q^{11} - 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 16 q^{22} + 10 q^{23} + 18 q^{25} + 24 q^{26} + 18 q^{28} - 48 q^{32} + 2 q^{34} - 40 q^{35} - 4 q^{37}+ \cdots + 30 q^{98}+O(q^{100}) \) 20 * q + 6 * q^2 + 6 * q^4 - 2 * q^7 - 2 * q^10 + 16 * q^11 - 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 16 * q^22 + 10 * q^23 + 18 * q^25 + 24 * q^26 + 18 * q^28 - 48 * q^32 + 2 * q^34 - 40 * q^35 - 4 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 + 10 * q^43 + 36 * q^44 + 4 * q^46 + 40 * q^47 + 18 * q^49 - 36 * q^50 - 30 * q^52 + 10 * q^53 - 10 * q^55 + 16 * q^59 - 16 * q^61 + 44 * q^62 + 20 * q^64 + 14 * q^65 + 18 * q^67 - 22 * q^68 - 12 * q^70 + 16 * q^71 - 18 * q^74 - 64 * q^76 + 28 * q^77 + 2 * q^80 + 56 * q^82 - 48 * q^83 - 26 * q^85 - 60 * q^86 + 82 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^94 + 26 * q^95 + 66 * q^97 + 30 * q^98

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