LMFDB - Embedded newform 441.2.bb.e.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.3
Character	$\chi$	$=$	441.100
Dual form			441.2.bb.e.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.380106 - 0.117247i) q^{2} +(-1.52174 - 1.03751i) q^{4} +(-0.996754 + 0.150237i) q^{5} +(2.64575 - 0.00303574i) q^{7} +(0.952800 + 1.19477i) q^{8} +O(q^{10})$	\(q+(-0.380106 - 0.117247i) q^{2} +(-1.52174 - 1.03751i) q^{4} +(-0.996754 + 0.150237i) q^{5} +(2.64575 - 0.00303574i) q^{7} +(0.952800 + 1.19477i) q^{8} +(0.396487 + 0.0597608i) q^{10} +(-1.00095 + 0.928747i) q^{11} +(-1.26765 - 5.55392i) q^{13} +(-1.00602 - 0.309053i) q^{14} +(1.12367 + 2.86306i) q^{16} +(-0.594210 - 7.92918i) q^{17} +(-1.97740 + 3.42496i) q^{19} +(1.67268 + 0.805519i) q^{20} +(0.489360 - 0.235663i) q^{22} +(0.416919 - 5.56340i) q^{23} +(-3.80692 + 1.17428i) q^{25} +(-0.169342 + 2.25971i) q^{26} +(-4.02930 - 2.74037i) q^{28} +(-8.45611 - 4.07225i) q^{29} +(-2.53729 - 4.39471i) q^{31} +(-0.319828 - 4.26781i) q^{32} +(-0.703810 + 3.08360i) q^{34} +(-2.63671 + 0.400514i) q^{35} +(4.20461 - 2.86666i) q^{37} +(1.15319 - 1.07000i) q^{38} +(-1.12921 - 1.04775i) q^{40} +(4.23188 + 5.30661i) q^{41} +(-0.406277 + 0.509456i) q^{43} +(2.48677 - 0.374821i) q^{44} +(-0.810766 + 2.06580i) q^{46} +(10.4626 + 3.22730i) q^{47} +(6.99998 - 0.0160636i) q^{49} +1.58471 q^{50} +(-3.83320 + 9.76685i) q^{52} +(-6.20346 - 4.22945i) q^{53} +(0.858171 - 1.07611i) q^{55} +(2.52450 + 3.15818i) q^{56} +(2.73676 + 2.53934i) q^{58} +(3.22914 + 0.486714i) q^{59} +(-0.0921568 + 0.0628315i) q^{61} +(0.449171 + 1.96795i) q^{62} +(0.989983 - 4.33740i) q^{64} +(2.09794 + 5.34545i) q^{65} +(-2.03572 - 3.52598i) q^{67} +(-7.32235 + 12.6827i) q^{68} +(1.04919 + 0.156908i) q^{70} +(-1.85333 + 0.892516i) q^{71} +(6.83997 - 2.10985i) q^{73} +(-1.93430 + 0.596654i) q^{74} +(6.56253 - 3.16035i) q^{76} +(-2.64545 + 2.46027i) q^{77} +(-2.75372 + 4.76959i) q^{79} +(-1.55016 - 2.68495i) q^{80} +(-0.986377 - 2.51325i) q^{82} +(0.325178 - 1.42470i) q^{83} +(1.78353 + 7.81417i) q^{85} +(0.214161 - 0.146012i) q^{86} +(-2.06335 - 0.311000i) q^{88} +(4.54981 + 4.22161i) q^{89} +(-3.37074 - 14.6904i) q^{91} +(-6.40651 + 8.03351i) q^{92} +(-3.59852 - 2.45343i) q^{94} +(1.45643 - 3.71092i) q^{95} +4.96295 q^{97} +(-2.66262 - 0.814622i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$1$

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 $

$2$	−0.380106	−	0.117247i	−0.268775	−	0.0829062i	0.157438	−	0.987529i	$-0.449677\pi$
$2$	−0.380106	−	0.117247i	−0.268775	−	0.0829062i	−0.426213	+	0.904623i	$0.640153\pi$
$3$		0			0
$3$		0			0
$4$	−1.52174	−	1.03751i	−0.760872	−	0.518754i
$5$	−0.996754	+	0.150237i	−0.445762	+	0.0671878i	−0.368088	−	0.929791i	$-0.619987\pi$
$5$	−0.996754	+	0.150237i	−0.445762	+	0.0671878i	−0.0776741	+	0.996979i	$0.524749\pi$
$6$		0			0
$7$	2.64575	−	0.00303574i	0.999999	−	0.00114740i
$7$	2.64575	−	0.00303574i	0.999999	−	0.00114740i
$8$	0.952800	+	1.19477i	0.336866	+	0.422416i
$9$		0			0
$10$	0.396487	+	0.0597608i	0.125380	+	0.0188980i
$11$	−1.00095	+	0.928747i	−0.301798	+	0.280028i	−0.816505	−	0.577339i	$-0.804091\pi$
$11$	−1.00095	+	0.928747i	−0.301798	+	0.280028i	0.514707	+	0.857366i	$0.327901\pi$
$12$		0			0
$13$	−1.26765	−	5.55392i	−0.351582	−	1.54038i	−0.773529	−	0.633761i	$-0.781510\pi$
$13$	−1.26765	−	5.55392i	−0.351582	−	1.54038i	0.421947	−	0.906621i	$-0.361347\pi$
$14$	−1.00602	−	0.309053i	−0.268870	−	0.0825978i
$15$		0			0
$16$	1.12367	+	2.86306i	0.280917	+	0.715766i
$17$	−0.594210	−	7.92918i	−0.144117	−	1.92311i	−0.336311	−	0.941751i	$-0.609179\pi$
$17$	−0.594210	−	7.92918i	−0.144117	−	1.92311i	0.192194	−	0.981357i	$-0.438440\pi$
$18$		0			0
$19$	−1.97740	+	3.42496i	−0.453647	+	0.785740i	−0.998609	−	0.0527205i	$-0.983211\pi$
$19$	−1.97740	+	3.42496i	−0.453647	+	0.785740i	0.544962	+	0.838461i	$0.316544\pi$
$20$	1.67268	+	0.805519i	0.374022	+	0.180119i
$21$		0			0
$22$	0.489360	−	0.235663i	0.104332	−	0.0502436i
$23$	0.416919	−	5.56340i	0.0869337	−	1.16005i	−0.767697	−	0.640813i	$-0.778597\pi$
$23$	0.416919	−	5.56340i	0.0869337	−	1.16005i	0.854631	−	0.519236i	$-0.173783\pi$
$24$		0			0
$25$	−3.80692	+	1.17428i	−0.761383	+	0.234856i
$26$	−0.169342	+	2.25971i	−0.0332106	+	0.443165i
$27$		0			0
$28$	−4.02930	−	2.74037i	−0.761467	−	0.517880i
$29$	−8.45611	−	4.07225i	−1.57026	−	0.756197i	−0.572300	−	0.820044i	$-0.693949\pi$
$29$	−8.45611	−	4.07225i	−1.57026	−	0.756197i	−0.997960	+	0.0638471i	$0.979663\pi$
$30$		0			0
$31$	−2.53729	−	4.39471i	−0.455710	−	0.789314i	0.543018	−	0.839721i	$-0.317281\pi$
$31$	−2.53729	−	4.39471i	−0.455710	−	0.789314i	−0.998729	+	0.0504073i	$0.983948\pi$
$32$	−0.319828	−	4.26781i	−0.0565382	−	0.754450i
$33$		0			0
$34$	−0.703810	+	3.08360i	−0.120703	+	0.528832i
$35$	−2.63671	+	0.400514i	−0.445685	+	0.0676993i
$36$		0			0
$37$	4.20461	−	2.86666i	0.691234	−	0.471275i	−0.166051	−	0.986117i	$-0.553102\pi$
$37$	4.20461	−	2.86666i	0.691234	−	0.471275i	0.857285	+	0.514842i	$0.172149\pi$
$38$	1.15319	−	1.07000i	0.187072	−	0.173577i
$39$		0			0
$40$	−1.12921	−	1.04775i	−0.178543	−	0.165664i
$41$	4.23188	+	5.30661i	0.660909	+	0.828753i	0.993442	−	0.114338i	$-0.0364748\pi$
$41$	4.23188	+	5.30661i	0.660909	+	0.828753i	−0.332533	+	0.943092i	$0.607903\pi$
$42$		0			0
$43$	−0.406277	+	0.509456i	−0.0619567	+	0.0776913i	−0.811844	−	0.583874i	$-0.801536\pi$
$43$	−0.406277	+	0.509456i	−0.0619567	+	0.0776913i	0.749887	+	0.661565i	$0.230108\pi$
$44$	2.48677	−	0.374821i	0.374895	−	0.0565064i
$45$		0			0
$46$	−0.810766	+	2.06580i	−0.119541	+	0.304585i
$47$	10.4626	+	3.22730i	1.52613	+	0.470750i	0.940491	−	0.339820i	$-0.110366\pi$
$47$	10.4626	+	3.22730i	1.52613	+	0.470750i	0.585643	+	0.810569i	$0.300842\pi$
$48$		0			0
$49$	6.99998	−	0.0160636i	0.999997	−	0.00229481i
$50$	1.58471			0.224112
$51$		0			0
$52$	−3.83320	+	9.76685i	−0.531570	+	1.35442i
$53$	−6.20346	−	4.22945i	−0.852111	−	0.580959i	0.0565947	−	0.998397i	$-0.481976\pi$
$53$	−6.20346	−	4.22945i	−0.852111	−	0.580959i	−0.908705	+	0.417438i	$0.862928\pi$
$54$		0			0
$55$	0.858171	−	1.07611i	0.115716	−	0.145103i
$56$	2.52450	+	3.15818i	0.337350	+	0.422029i
$57$		0			0
$58$	2.73676	+	2.53934i	0.359354	+	0.333432i
$59$	3.22914	+	0.486714i	0.420398	+	0.0633648i	0.355835	−	0.934549i	$-0.384197\pi$
$59$	3.22914	+	0.486714i	0.420398	+	0.0633648i	0.0645631	+	0.997914i	$0.479435\pi$
$60$		0			0
$61$	−0.0921568	+	0.0628315i	−0.0117995	+	0.00804474i	−0.569205	−	0.822195i	$-0.692749\pi$
$61$	−0.0921568	+	0.0628315i	−0.0117995	+	0.00804474i	0.557406	+	0.830240i	$0.311797\pi$
$62$	0.449171	+	1.96795i	0.0570447	+	0.249929i
$63$		0			0
$64$	0.989983	−	4.33740i	0.123748	−	0.542175i
$65$	2.09794	+	5.34545i	0.260217	+	0.663022i
$66$		0			0
$67$	−2.03572	−	3.52598i	−0.248703	−	0.430767i	0.714463	−	0.699673i	$-0.246671\pi$
$67$	−2.03572	−	3.52598i	−0.248703	−	0.430767i	−0.963166	+	0.268906i	$0.913338\pi$
$68$	−7.32235	+	12.6827i	−0.887965	+	1.53800i
$69$		0			0
$70$	1.04919	+	0.156908i	0.125402	+	0.0187541i
$71$	−1.85333	+	0.892516i	−0.219950	+	0.105922i	−0.540614	−	0.841271i	$-0.681808\pi$
$71$	−1.85333	+	0.892516i	−0.219950	+	0.105922i	0.320664	+	0.947193i	$0.396094\pi$
$72$		0			0
$73$	6.83997	−	2.10985i	0.800558	−	0.246940i	0.132630	−	0.991166i	$-0.457658\pi$
$73$	6.83997	−	2.10985i	0.800558	−	0.246940i	0.667928	+	0.744226i	$0.267181\pi$
$74$	−1.93430	+	0.596654i	−0.224858	+	0.0693596i
$75$		0			0
$76$	6.56253	−	3.16035i	0.752773	−	0.362517i
$77$	−2.64545	+	2.46027i	−0.301477	+	0.280374i
$78$		0			0
$79$	−2.75372	+	4.76959i	−0.309818	+	0.536621i	−0.978322	−	0.207088i	$-0.933602\pi$
$79$	−2.75372	+	4.76959i	−0.309818	+	0.536621i	0.668504	+	0.743708i	$0.266935\pi$
$80$	−1.55016	−	2.68495i	−0.173313	−	0.300187i
$81$		0			0
$82$	−0.986377	−	2.51325i	−0.108927	−	0.277542i
$83$	0.325178	−	1.42470i	0.0356930	−	0.156381i	−0.953941	−	0.299995i	$-0.903015\pi$
$83$	0.325178	−	1.42470i	0.0356930	−	0.156381i	0.989634	+	0.143614i	$0.0458722\pi$
$84$		0			0
$85$	1.78353	+	7.81417i	0.193451	+	0.847566i
$86$	0.214161	−	0.146012i	0.0230935	−	0.0157449i
$87$		0			0
$88$	−2.06335	−	0.311000i	−0.219954	−	0.0331527i
$89$	4.54981	+	4.22161i	0.482279	+	0.447490i	0.883458	−	0.468510i	$-0.155209\pi$
$89$	4.54981	+	4.22161i	0.482279	+	0.447490i	−0.401179	+	0.916000i	$0.631399\pi$
$90$		0			0
$91$	−3.37074	−	14.6904i	−0.353349	−	1.53998i
$92$	−6.40651	+	8.03351i	−0.667925	+	0.837552i
$93$		0			0
$94$	−3.59852	−	2.45343i	−0.371159	−	0.253052i
$95$	1.45643	−	3.71092i	0.149427	−	0.380733i
$96$		0			0
$97$	4.96295			0.503912			0.251956	−	0.967739i	$-0.418926\pi$
$97$	4.96295			0.503912			0.251956	+	0.967739i	$0.418926\pi$
$98$	−2.66262	−	0.814622i	−0.268965	−	0.0822892i
$99$		0			0
$100$	7.01147	+	2.16275i	0.701147	+	0.216275i
$101$	1.86183	−	4.74387i	0.185259	−	0.472033i	−0.807827	−	0.589420i	$-0.799357\pi$
$101$	1.86183	−	4.74387i	0.185259	−	0.472033i	0.993086	+	0.117387i	$0.0374518\pi$
$102$		0			0
$103$	−7.18152	+	1.08244i	−0.707616	+	0.106656i	−0.492983	−	0.870039i	$-0.664094\pi$
$103$	−7.18152	+	1.08244i	−0.707616	+	0.106656i	−0.214633	+	0.976695i	$0.568856\pi$
$104$	5.42787	−	6.80633i	0.532246	−	0.667416i
$105$		0			0
$106$	1.86208	+	2.33497i	0.180861	+	0.226793i
$107$	6.63311	+	6.15463i	0.641247	+	0.594991i	0.932287	−	0.361721i	$-0.117811\pi$
$107$	6.63311	+	6.15463i	0.641247	+	0.594991i	−0.291039	+	0.956711i	$0.594001\pi$
$108$		0			0
$109$	−2.98074	+	2.76572i	−0.285503	+	0.264908i	−0.809903	−	0.586564i	$-0.800480\pi$
$109$	−2.98074	+	2.76572i	−0.285503	+	0.264908i	0.524400	+	0.851472i	$0.324290\pi$
$110$	−0.452367	+	0.308418i	−0.0431315	+	0.0294065i
$111$		0			0
$112$	2.98164	+	7.57154i	0.281738	+	0.715443i
$113$	−2.81671	+	12.3408i	−0.264974	+	1.16093i	0.650806	+	0.759244i	$0.274431\pi$
$113$	−2.81671	+	12.3408i	−0.264974	+	1.16093i	−0.915780	+	0.401681i	$0.868426\pi$
$114$		0			0
$115$	0.420260	+	5.60798i	0.0391894	+	0.522947i
$116$	8.64304	+	14.9702i	0.802487	+	1.38995i
$117$		0			0
$118$	−1.17035	−	0.563610i	−0.107739	−	0.0518845i
$119$	−1.59620	−	20.9768i	−0.146323	−	1.92294i
$120$		0			0
$121$	−0.682699	+	9.10998i	−0.0620635	+	0.828180i
$122$	0.0423961	−	0.0130775i	0.00383837	−	0.00118398i
$123$		0			0
$124$	−0.698444	+	9.32008i	−0.0627221	+	0.836968i
$125$	8.15908	−	3.92921i	0.729771	−	0.351439i
$126$		0			0
$127$	−4.57770	−	2.20450i	−0.406205	−	0.195618i	0.219613	−	0.975587i	$-0.429521\pi$
$127$	−4.57770	−	2.20450i	−0.406205	−	0.195618i	−0.625818	+	0.779969i	$0.715235\pi$
$128$	−5.16463	+	8.94539i	−0.456493	+	0.790669i
$129$		0			0
$130$	−0.170699	−	2.27781i	−0.0149713	−	0.199778i
$131$	−2.28244	−	5.81557i	−0.199418	−	0.508109i	0.795826	−	0.605526i	$-0.207037\pi$
$131$	−2.28244	−	5.81557i	−0.199418	−	0.508109i	−0.995244	+	0.0974169i	$0.968942\pi$
$132$		0			0
$133$	−5.22132	+	9.06760i	−0.452745	+	0.786260i
$134$	0.360380	+	1.57893i	0.0311321	+	0.136399i
$135$		0			0
$136$	8.90741	−	8.26486i	0.763804	−	0.708706i
$137$	−4.49565	−	0.677611i	−0.384090	−	0.0578922i	−0.0458405	−	0.998949i	$-0.514597\pi$
$137$	−4.49565	−	0.677611i	−0.384090	−	0.0578922i	−0.338249	+	0.941057i	$0.609835\pi$
$138$		0			0
$139$	−1.42918	−	1.79214i	−0.121222	−	0.152007i	0.717518	−	0.696540i	$-0.245278\pi$
$139$	−1.42918	−	1.79214i	−0.121222	−	0.152007i	−0.838739	+	0.544533i	$0.816707\pi$
$140$	4.42793	+	2.12612i	0.374228	+	0.179690i
$141$		0			0
$142$	0.809106	−	0.121953i	0.0678987	−	0.0102341i
$143$	6.42704	+	4.38188i	0.537456	+	0.366432i
$144$		0			0
$145$	9.04046	+	2.78861i	0.750770	+	0.231582i
$146$	−2.84729			−0.235643
$147$		0			0
$148$	−9.37252			−0.770416
$149$	8.08088	+	2.49262i	0.662011	+	0.204203i	0.607512	−	0.794310i	$-0.292168\pi$
$149$	8.08088	+	2.49262i	0.662011	+	0.204203i	0.0544991	+	0.998514i	$0.482644\pi$
$150$		0			0
$151$	10.1861	+	6.94477i	0.828934	+	0.565158i	0.901785	−	0.432185i	$-0.142257\pi$
$151$	10.1861	+	6.94477i	0.828934	+	0.565158i	−0.0728507	+	0.997343i	$0.523210\pi$
$152$	−5.97612	+	0.900756i	−0.484728	+	0.0730609i
$153$		0			0
$154$	1.29401	−	0.624992i	0.104274	−	0.0503633i
$155$	3.18930	+	3.99925i	0.256171	+	0.321228i
$156$		0			0
$157$	0.626460	+	0.0944237i	0.0499970	+	0.00753583i	0.173993	−	0.984747i	$-0.444333\pi$
$157$	0.626460	+	0.0944237i	0.0499970	+	0.00753583i	−0.123996	+	0.992283i	$0.539571\pi$
$158$	1.60593	−	1.49008i	0.127761	−	0.118545i
$159$		0			0
$160$	0.959972	+	4.20591i	0.0758924	+	0.332506i
$161$	1.08617	−	14.7206i	0.0856026	−	1.16015i
$162$		0			0
$163$	−6.96803	−	17.7542i	−0.545778	−	1.39062i	−0.891816	−	0.452399i	$-0.850568\pi$
$163$	−6.96803	−	17.7542i	−0.545778	−	1.39062i	0.346038	−	0.938221i	$-0.387527\pi$
$164$	−0.934191	−	12.4659i	−0.0729480	−	0.973424i
$165$		0			0
$166$	−0.290644	+	0.503410i	−0.0225584	+	0.0390722i
$167$	11.3682	+	5.47462i	0.879694	+	0.423638i	0.818513	−	0.574488i	$-0.194799\pi$
$167$	11.3682	+	5.47462i	0.879694	+	0.423638i	0.0611814	+	0.998127i	$0.480513\pi$
$168$		0			0
$169$	−17.5266	+	8.44035i	−1.34820	+	0.649257i
$170$	0.238257	−	3.17933i	0.0182735	−	0.243843i
$171$		0			0
$172$	1.14681	−	0.353745i	0.0874438	−	0.0269728i
$173$	−0.229875	+	3.06747i	−0.0174771	+	0.233215i	0.981624	+	0.190825i	$0.0611163\pi$
$173$	−0.229875	+	3.06747i	−0.0174771	+	0.233215i	−0.999101	+	0.0423902i	$0.986503\pi$
$174$		0			0
$175$	−10.0686	+	3.11840i	−0.761113	+	0.235729i
$176$	−3.78380	−	1.82218i	−0.285215	−	0.137352i
$177$		0			0
$178$	−1.23444	−	2.13811i	−0.0925251	−	0.160258i
$179$	−0.725492	−	9.68102i	−0.0542258	−	0.723593i	−0.956370	−	0.292158i	$-0.905627\pi$
$179$	−0.725492	−	9.68102i	−0.0542258	−	0.723593i	0.902144	−	0.431435i	$-0.141992\pi$
$180$		0			0
$181$	−0.786784	+	3.44713i	−0.0584812	+	0.256223i	−0.995715	−	0.0924799i	$-0.970521\pi$
$181$	−0.786784	+	3.44713i	−0.0584812	+	0.256223i	0.937233	+	0.348703i	$0.113378\pi$
$182$	−0.441176	+	5.97913i	−0.0327021	+	0.443203i
$183$		0			0
$184$	7.04424	−	4.80268i	0.519308	−	0.354058i
$185$	−3.76029	+	3.48904i	−0.276462	+	0.256519i
$186$		0			0
$187$	7.95897	+	7.38485i	0.582018	+	0.540034i
$188$	−12.5731	−	15.7662i	−0.916989	−	1.14987i
$189$		0			0
$190$	−0.988693	+	1.23978i	−0.0717273	+	0.0899432i
$191$	20.4764	−	3.08632i	1.48162	−	0.223318i	0.642088	−	0.766631i	$-0.278068\pi$
$191$	20.4764	−	3.08632i	1.48162	−	0.223318i	0.839531	+	0.543313i	$0.182830\pi$
$192$		0			0
$193$	9.43715	−	24.0455i	0.679301	−	1.73083i	−0.00325269	−	0.999995i	$-0.501035\pi$
$193$	9.43715	−	24.0455i	0.679301	−	1.73083i	0.682554	−	0.730836i	$-0.260869\pi$
$194$	−1.88645	−	0.581892i	−0.135439	−	0.0417774i
$195$		0			0
$196$	−10.6688	−	7.23809i	−0.762060	−	0.517006i
$197$	−10.3126			−0.734741			−0.367370	−	0.930075i	$-0.619742\pi$
$197$	−10.3126			−0.734741			−0.367370	+	0.930075i	$0.619742\pi$
$198$		0			0
$199$	5.10580	−	13.0094i	0.361941	−	0.922210i	−0.627675	−	0.778475i	$-0.715993\pi$
$199$	5.10580	−	13.0094i	0.361941	−	0.922210i	0.989616	−	0.143735i	$-0.0459113\pi$
$200$	−5.03023	−	3.42955i	−0.355691	−	0.242506i
$201$		0			0
$202$	−1.26390	+	1.58488i	−0.0889275	+	0.111512i
$203$	−22.3851	−	10.7485i	−1.57113	−	0.754395i
$204$		0			0
$205$	−5.01539	−	4.65360i	−0.350290	−	0.325022i
$206$	2.85665	+	0.430571i	0.199032	+	0.0299993i
$207$		0			0
$208$	14.4768	−	9.87013i	1.00379	−	0.684370i
$209$	−1.20164	−	5.26473i	−0.0831192	−	0.364169i
$210$		0			0
$211$	−1.25847	+	5.51370i	−0.0866364	+	0.379579i	−0.999595	−	0.0284745i	$-0.990935\pi$
$211$	−1.25847	+	5.51370i	−0.0866364	+	0.379579i	0.912958	+	0.408053i	$0.133792\pi$
$212$	5.05199	+	12.8723i	0.346972	+	0.884071i
$213$		0			0
$214$	−1.79967	−	3.11712i	−0.123023	−	0.213082i
$215$	0.328420	−	0.568840i	0.0223981	−	0.0387946i
$216$		0			0
$217$	−6.72637	−	11.6196i	−0.456616	−	0.788790i
$218$	1.45727	−	0.701785i	0.0986988	−	0.0475309i
$219$		0			0
$220$	−2.42239	+	0.747209i	−0.163318	+	0.0503768i
$221$	−43.2848	+	13.3516i	−2.91165	+	0.898125i
$222$		0			0
$223$	6.54971	−	3.15417i	0.438601	−	0.211219i	−0.201534	−	0.979482i	$-0.564593\pi$
$223$	6.54971	−	3.15417i	0.438601	−	0.211219i	0.640135	+	0.768262i	$0.278878\pi$
$224$	−0.859142	−	11.2906i	−0.0574038	−	0.754384i
$225$		0			0
$226$	2.51757	−	4.36056i	0.167466	−	0.290060i
$227$	12.3789	+	21.4410i	0.821619	+	1.42309i	0.904476	+	0.426525i	$0.140262\pi$
$227$	12.3789	+	21.4410i	0.821619	+	1.42309i	−0.0828563	+	0.996562i	$0.526404\pi$
$228$		0			0
$229$	3.91641	+	9.97884i	0.258803	+	0.659420i	0.999929	−	0.0119465i	$-0.00380279\pi$
$229$	3.91641	+	9.97884i	0.258803	+	0.659420i	−0.741125	+	0.671367i	$0.765708\pi$
$230$	0.497776	−	2.18090i	0.0328224	−	0.143804i
$231$		0			0
$232$	−3.19157	−	13.9832i	−0.209537	−	0.918040i
$233$	−24.7796	+	16.8944i	−1.62336	+	1.10679i	−0.706406	+	0.707807i	$0.749685\pi$
$233$	−24.7796	+	16.8944i	−1.62336	+	1.10679i	−0.916958	+	0.398984i	$0.869363\pi$
$234$		0			0
$235$	−10.9135	−	1.64495i	−0.711921	−	0.107305i
$236$	−4.40895	−	4.09091i	−0.286998	−	0.266296i
$237$		0			0
$238$	−1.85275	+	8.16056i	−0.120096	+	0.528970i
$239$	7.40228	−	9.28217i	0.478814	−	0.600413i	−0.482491	−	0.875901i	$-0.660268\pi$
$239$	7.40228	−	9.28217i	0.478814	−	0.600413i	0.961305	+	0.275488i	$0.0888393\pi$
$240$		0			0
$241$	−14.7941	−	10.0865i	−0.952975	−	0.649727i	−0.0162775	−	0.999868i	$-0.505182\pi$
$241$	−14.7941	−	10.0865i	−0.952975	−	0.649727i	−0.936697	+	0.350140i	$0.886134\pi$
$242$	1.32762	−	3.38271i	0.0853424	−	0.217449i
$243$		0			0
$244$	0.205427			0.0131511
$245$	−6.97485	+	1.06766i	−0.445607	+	0.0682106i
$246$		0			0
$247$	21.5286	+	6.64070i	1.36983	+	0.422538i
$248$	2.83316	−	7.21877i	0.179906	−	0.458392i
$249$		0			0
$250$	−3.56200	+	0.536885i	−0.225281	+	0.0339556i
$251$	5.65700	−	7.09366i	0.357067	−	0.447748i	−0.570560	−	0.821256i	$-0.693274\pi$
$251$	5.65700	−	7.09366i	0.357067	−	0.447748i	0.927627	+	0.373508i	$0.121845\pi$
$252$		0			0
$253$	4.74967	+	5.95590i	0.298610	+	0.374444i
$254$	1.48154	+	1.37467i	0.0929600	+	0.0862543i
$255$		0			0
$256$	−3.51069	+	3.25744i	−0.219418	+	0.203590i
$257$	19.8528	−	13.5354i	1.23838	−	0.844314i	0.246212	−	0.969216i	$-0.420814\pi$
$257$	19.8528	−	13.5354i	1.23838	−	0.844314i	0.992169	+	0.124902i	$0.0398616\pi$
$258$		0			0
$259$	11.1156	−	7.59722i	0.690693	−	0.472068i
$260$	2.35343	−	10.3110i	0.145953	−	0.639463i
$261$		0			0
$262$	0.185711	+	2.47814i	0.0114733	+	0.153100i
$263$	−5.42343	−	9.39366i	−0.334423	−	0.579238i	0.648951	−	0.760831i	$-0.275208\pi$
$263$	−5.42343	−	9.39366i	−0.334423	−	0.579238i	−0.983374	+	0.181592i	$0.941875\pi$
$264$		0			0
$265$	6.81874	+	3.28373i	0.418872	+	0.201718i
$266$	3.04780	−	2.83446i	0.186873	−	0.173792i
$267$		0			0
$268$	−0.560377	+	7.47772i	−0.0342305	+	0.456774i
$269$	−17.5711	+	5.41995i	−1.07133	+	0.330460i	−0.779752	−	0.626088i	$-0.784655\pi$
$269$	−17.5711	+	5.41995i	−1.07133	+	0.330460i	−0.291574	+	0.956548i	$0.594179\pi$
$270$		0			0
$271$	0.829511	−	11.0691i	0.0503892	−	0.672397i	−0.913627	−	0.406553i	$-0.866730\pi$
$271$	0.829511	−	11.0691i	0.0503892	−	0.672397i	0.964016	−	0.265844i	$-0.0856505\pi$
$272$	22.0340	−	10.6110i	1.33601	−	0.643388i
$273$		0			0
$274$	1.62938	+	0.784666i	0.0984342	+	0.0474034i
$275$	2.71993	−	4.71106i	0.164018	−	0.284087i
$276$		0			0
$277$	2.32241	+	30.9904i	0.139540	+	1.86203i	0.427016	+	0.904244i	$0.359565\pi$
$277$	2.32241	+	30.9904i	0.139540	+	1.86203i	−0.287476	+	0.957788i	$0.592816\pi$
$278$	0.333118	+	0.848770i	0.0199791	+	0.0509058i
$279$		0			0
$280$	−2.99078	−	2.76866i	−0.178733	−	0.165459i
$281$	0.779955	+	3.41721i	0.0465282	+	0.203853i	0.992849	−	0.119375i	$-0.0380890\pi$
$281$	0.779955	+	3.41721i	0.0465282	+	0.203853i	−0.946321	+	0.323228i	$0.895232\pi$
$282$		0			0
$283$	13.8112	−	12.8149i	0.820988	−	0.761765i	−0.153034	−	0.988221i	$-0.548904\pi$
$283$	13.8112	−	12.8149i	0.820988	−	0.761765i	0.974022	+	0.226456i	$0.0727138\pi$
$284$	3.74629	+	0.564662i	0.222301	+	0.0335065i
$285$		0			0
$286$	−1.92919	−	2.41913i	−0.114076	−	0.143046i
$287$	11.2126	+	14.0271i	0.661859	+	0.827994i
$288$		0			0
$289$	−45.7086	+	6.88947i	−2.68874	+	0.405263i
$290$	−3.10938	−	2.11994i	−0.182589	−	0.124487i
$291$		0			0
$292$	−12.5977	−	3.88587i	−0.737223	−	0.227403i
$293$	−15.1796			−0.886800			−0.443400	−	0.896324i	$-0.646228\pi$
$293$	−15.1796			−0.886800			−0.443400	+	0.896324i	$0.646228\pi$
$294$		0			0
$295$	−3.29178			−0.191655
$296$	7.43116	+	2.29221i	0.431927	+	0.133232i
$297$		0			0
$298$	−2.77934	−	1.89492i	−0.161003	−	0.109770i
$299$	−31.4272	+	4.73689i	−1.81748	+	0.273941i
$300$		0			0
$301$	−1.07336	+	1.34913i	−0.0618675	+	0.0777623i
$302$	−3.05755	−	3.83404i	−0.175942	−	0.220624i
$303$		0			0
$304$	−12.0278	−	1.81290i	−0.689843	−	0.103977i
$305$	0.0824181	−	0.0764728i	0.00471925	−	0.00437882i
$306$		0			0
$307$	3.37078	+	14.7683i	0.192381	+	0.842874i	0.975323	+	0.220781i	$0.0708605\pi$
$307$	3.37078	+	14.7683i	0.192381	+	0.842874i	−0.782943	+	0.622093i	$0.786282\pi$
$308$	6.57824	−	0.999231i	0.374830	−	0.0569365i
$309$		0			0
$310$	−0.743370	−	1.89408i	−0.0422206	−	0.107576i
$311$	−1.31048	−	17.4871i	−0.0743103	−	0.991603i	−0.902370	−	0.430962i	$-0.858174\pi$
$311$	−1.31048	−	17.4871i	−0.0743103	−	0.991603i	0.828059	−	0.560640i	$-0.189445\pi$
$312$		0			0
$313$	−2.61668	+	4.53221i	−0.147903	+	0.256176i	−0.930452	−	0.366413i	$-0.880586\pi$
$313$	−2.61668	+	4.53221i	−0.147903	+	0.256176i	0.782549	+	0.622589i	$0.213919\pi$
$314$	−0.227050	−	0.109342i	−0.0128132	−	0.00617051i
$315$		0			0
$316$	9.13895	−	4.40109i	0.514106	−	0.247580i
$317$	1.03999	−	13.8777i	0.0584115	−	0.779447i	−0.888689	−	0.458510i	$-0.848383\pi$
$317$	1.03999	−	13.8777i	0.0584115	−	0.779447i	0.947101	−	0.320937i	$-0.103998\pi$
$318$		0			0
$319$	12.2462	−	3.77746i	0.685658	−	0.211497i
$320$	−0.335134	+	4.47205i	−0.0187346	+	0.249995i
$321$		0			0
$322$	−2.13881	+	5.46804i	−0.119191	+	0.304722i
$323$	28.3321	+	13.6440i	1.57644	+	0.759174i
$324$		0			0
$325$	11.3477	+	19.6548i	0.629456	+	1.09025i
$326$	0.566954	+	7.56547i	0.0314007	+	0.419013i
$327$		0			0
$328$	−2.30806	+	10.1123i	−0.127441	+	0.558357i
$329$	27.6913	+	8.50686i	1.52667	+	0.468998i
$330$		0			0
$331$	−16.9929	+	11.5855i	−0.934012	+	0.636799i	−0.931712	−	0.363199i	$-0.881685\pi$
$331$	−16.9929	+	11.5855i	−0.934012	+	0.636799i	−0.00230028	+	0.999997i	$0.500732\pi$
$332$	−1.97297	+	1.83065i	−0.108281	+	0.100470i
$333$		0			0
$334$	−3.67922	−	3.41382i	−0.201318	−	0.186796i
$335$	2.55885	+	3.20869i	0.139805	+	0.175310i
$336$		0			0
$337$	10.8161	−	13.5630i	0.589193	−	0.738825i	−0.394457	−	0.918914i	$-0.629067\pi$
$337$	10.8161	−	13.5630i	0.589193	−	0.738825i	0.983650	+	0.180090i	$0.0576388\pi$
$338$	7.65155	−	1.15329i	0.416190	−	0.0627305i
$339$		0			0
$340$	5.39318	−	13.7416i	0.292486	−	0.745243i
$341$	6.62128	+	2.04239i	0.358562	+	0.110602i
$342$		0			0
$343$	18.5201	−	0.0637505i	0.999994	−	0.00344220i
$344$	−0.995785			−0.0536891
$345$		0			0
$346$	0.447028	−	1.13901i	0.0240324	−	0.0612336i
$347$	16.0754	+	10.9600i	0.862970	+	0.588363i	0.911888	−	0.410440i	$-0.134625\pi$
$347$	16.0754	+	10.9600i	0.862970	+	0.588363i	−0.0489174	+	0.998803i	$0.515577\pi$
$348$		0			0
$349$	5.27482	−	6.61442i	0.282355	−	0.354062i	−0.620348	−	0.784327i	$-0.713008\pi$
$349$	5.27482	−	6.61442i	0.282355	−	0.354062i	0.902703	+	0.430265i	$0.141580\pi$
$350$	4.19275	−	0.00481078i	0.224112	−	0.000257147i
$351$		0			0
$352$	4.28385	+	3.97483i	0.228330	+	0.211859i
$353$	14.7637	+	2.22526i	0.785790	+	0.118439i	0.529668	−	0.848205i	$-0.322317\pi$
$353$	14.7637	+	2.22526i	0.785790	+	0.118439i	0.256123	+	0.966644i	$0.417555\pi$
$354$		0			0
$355$	1.71323	−	1.16806i	0.0909286	−	0.0619940i
$356$	−2.54370	−	11.1447i	−0.134816	−	0.590667i
$357$		0			0
$358$	−0.859308	+	3.76487i	−0.0454158	+	0.198980i
$359$	−7.10880	−	18.1129i	−0.375188	−	0.955964i	−0.986380	−	0.164481i	$-0.947405\pi$
$359$	−7.10880	−	18.1129i	−0.375188	−	0.955964i	0.611192	−	0.791482i	$-0.290690\pi$
$360$		0			0
$361$	1.67975	+	2.90942i	0.0884081	+	0.153127i
$362$	0.703227	−	1.21802i	0.0369608	−	0.0640179i
$363$		0			0
$364$	−10.1120	+	25.8523i	−0.530015	+	1.35503i
$365$	−6.50080	+	3.13062i	−0.340267	+	0.163864i
$366$		0			0
$367$	32.7692	−	10.1080i	1.71054	−	0.527632i	0.723810	−	0.689999i	$-0.242389\pi$
$367$	32.7692	−	10.1080i	1.71054	−	0.527632i	0.986730	+	0.162367i	$0.0519130\pi$
$368$	16.3968	−	5.05776i	0.854744	−	0.263654i
$369$		0			0
$370$	1.83839	−	0.885320i	0.0955732	−	0.0460256i
$371$	−16.4256	−	11.1712i	−0.852777	−	0.579981i
$372$		0			0
$373$	14.9819	−	25.9493i	0.775731	−	1.34361i	−0.158652	−	0.987335i	$-0.550715\pi$
$373$	14.9819	−	25.9493i	0.775731	−	1.34361i	0.934383	−	0.356271i	$-0.115952\pi$
$374$	−2.15940	−	3.74019i	−0.111660	−	0.193401i
$375$		0			0
$376$	6.11292	+	15.5755i	0.315250	+	0.803243i
$377$	−11.8976	+	52.1268i	−0.612757	+	2.68466i
$378$		0			0
$379$	3.91090	+	17.1348i	0.200890	+	0.880154i	0.970397	+	0.241516i	$0.0776447\pi$
$379$	3.91090	+	17.1348i	0.200890	+	0.880154i	−0.769507	+	0.638638i	$0.779498\pi$
$380$	−6.06643	+	4.13602i	−0.311201	+	0.212173i
$381$		0			0
$382$	−8.14505	−	1.22767i	−0.416737	−	0.0628130i
$383$	1.59085	+	1.47609i	0.0812885	+	0.0754247i	0.719771	−	0.694212i	$-0.244247\pi$
$383$	1.59085	+	1.47609i	0.0812885	+	0.0754247i	−0.638482	+	0.769637i	$0.720437\pi$
$384$		0			0
$385$	2.26724	−	2.84973i	0.115549	−	0.145236i
$386$	−6.40638	+	8.03334i	−0.326076	+	0.408886i
$387$		0			0
$388$	−7.55234	−	5.14910i	−0.383412	−	0.261406i
$389$	−3.91342	+	9.97122i	−0.198418	+	0.505561i	−0.995104	−	0.0988324i	$-0.968489\pi$
$389$	−3.91342	+	9.97122i	−0.198418	+	0.505561i	0.796686	+	0.604393i	$0.206584\pi$
$390$		0			0
$391$	−44.3609			−2.24343
$392$	6.68877	+	8.34809i	0.337834	+	0.421642i
$393$		0			0
$394$	3.91987	+	1.20912i	0.197480	+	0.0609146i
$395$	2.02822	−	5.16782i	0.102051	−	0.260021i
$396$		0			0
$397$	−0.141604	+	0.0213434i	−0.00710690	+	0.00107119i	−0.152595	−	0.988289i	$-0.548763\pi$
$397$	−0.141604	+	0.0213434i	−0.00710690	+	0.00107119i	0.145488	+	0.989360i	$0.453525\pi$
$398$	−3.46606	+	4.34630i	−0.173738	+	0.217860i
$399$		0			0
$400$	−7.63975	−	9.57994i	−0.381987	−	0.478997i
$401$	4.01812	+	3.72827i	0.200655	+	0.186181i	0.774100	−	0.633063i	$-0.218203\pi$
$401$	4.01812	+	3.72827i	0.200655	+	0.186181i	−0.573445	+	0.819244i	$0.694393\pi$
$402$		0			0
$403$	−21.1915	+	19.6629i	−1.05562	+	0.979476i
$404$	−7.75503	+	5.28729i	−0.385827	+	0.263053i
$405$		0			0
$406$	7.24848	+	6.71015i	0.359736	+	0.333019i
$407$	−1.54621	+	6.77440i	−0.0766429	+	0.335795i
$408$		0			0
$409$	−0.268348	−	3.58086i	−0.0132690	−	0.177062i	−0.999901	−	0.0140960i	$-0.995513\pi$
$409$	−0.268348	−	3.58086i	−0.0132690	−	0.177062i	0.986632	−	0.162966i	$-0.0521061\pi$
$410$	1.36076	+	2.35690i	0.0672030	+	0.116399i
$411$		0			0
$412$	12.0515	+	5.80368i	0.593733	+	0.285927i
$413$	8.54497	+	1.27792i	0.420471	+	0.0628824i
$414$		0			0
$415$	−0.110081	+	1.46893i	−0.00540366	+	0.0721069i
$416$	−23.2977	+	7.18638i	−1.14226	+	0.352341i
$417$		0			0
$418$	−0.160524	+	2.14204i	−0.00785148	+	0.104771i
$419$	−25.6645	+	12.3594i	−1.25379	+	0.603796i	−0.938527	−	0.345207i	$-0.887809\pi$
$419$	−25.6645	+	12.3594i	−1.25379	+	0.603796i	−0.315268	+	0.949003i	$0.602094\pi$
$420$		0			0
$421$	−0.0411916	−	0.0198368i	−0.00200755	−	0.000966787i	0.432880	−	0.901452i	$-0.357497\pi$
$421$	−0.0411916	−	0.0198368i	−0.00200755	−	0.000966787i	−0.434887	+	0.900485i	$0.643212\pi$
$422$	1.12482	−	1.94824i	0.0547552	−	0.0948387i
$423$		0			0
$424$	−0.857425	−	11.4415i	−0.0416403	−	0.555651i
$425$	11.5732	+	29.4879i	0.561381	+	1.43038i
$426$		0			0
$427$	−0.243633	+	0.166516i	−0.0117902	+	0.00805828i
$428$	−3.70843	−	16.2477i	−0.179254	−	0.785361i
$429$		0			0
$430$	−0.191529	+	0.177713i	−0.00923636	+	0.00857009i
$431$	−7.07224	−	1.06597i	−0.340658	−	0.0513459i	−0.0235143	−	0.999723i	$-0.507486\pi$
$431$	−7.07224	−	1.06597i	−0.340658	−	0.0513459i	−0.317143	+	0.948378i	$0.602724\pi$
$432$		0			0
$433$	6.03880	+	7.57242i	0.290206	+	0.363907i	0.905467	−	0.424416i	$-0.139521\pi$
$433$	6.03880	+	7.57242i	0.290206	+	0.363907i	−0.615261	+	0.788324i	$0.710949\pi$
$434$	1.19437	+	5.20533i	0.0573315	+	0.249864i
$435$		0			0
$436$	7.40539	−	1.11618i	0.354654	−	0.0534555i
$437$	18.2300	+	12.4290i	0.872060	+	0.594560i
$438$		0			0
$439$	12.7903	+	3.94527i	0.610446	+	0.188298i	0.584537	−	0.811367i	$-0.301276\pi$
$439$	12.7903	+	3.94527i	0.610446	+	0.188298i	0.0259083	+	0.999664i	$0.491752\pi$
$440$	2.10338			0.100274
$441$		0			0
$442$	18.0182			0.857040
$443$	−20.5617	−	6.34243i	−0.976914	−	0.301338i	−0.235120	−	0.971966i	$-0.575548\pi$
$443$	−20.5617	−	6.34243i	−0.976914	−	0.301338i	−0.741794	+	0.670628i	$0.766025\pi$
$444$		0			0
$445$	−5.16929	−	3.52436i	−0.245048	−	0.167071i
$446$	−2.85940	+	0.430985i	−0.135397	+	0.0204077i
$447$		0			0
$448$	2.60608	−	11.4787i	0.123126	−	0.542316i
$449$	−2.87263	−	3.60216i	−0.135568	−	0.169996i	0.709414	−	0.704792i	$-0.248960\pi$
$449$	−2.87263	−	3.60216i	−0.135568	−	0.169996i	−0.844981	+	0.534796i	$0.820388\pi$
$450$		0			0
$451$	−9.16440	−	1.38131i	−0.431535	−	0.0650434i
$452$	17.0900	−	15.8572i	0.803845	−	0.745859i
$453$		0			0
$454$	−2.19142	−	9.60123i	−0.102848	−	0.450608i
$455$	5.56684	+	14.1364i	0.260977	+	0.662723i
$456$		0			0
$457$	−6.17651	−	15.7375i	−0.288925	−	0.736169i	−0.999471	−	0.0325182i	$-0.989647\pi$
$457$	−6.17651	−	15.7375i	−0.288925	−	0.736169i	0.710546	−	0.703651i	$-0.248448\pi$
$458$	−0.318658	−	4.25220i	−0.0148899	−	0.198692i
$459$		0			0
$460$	5.17879	−	8.96993i	0.241462	−	0.418225i
$461$	26.1377	+	12.5873i	1.21735	+	0.586247i	0.928574	−	0.371148i	$-0.121036\pi$
$461$	26.1377	+	12.5873i	1.21735	+	0.586247i	0.288781	+	0.957395i	$0.406750\pi$
$462$		0			0
$463$	13.6146	−	6.55643i	0.632723	−	0.304703i	−0.0898947	−	0.995951i	$-0.528653\pi$
$463$	13.6146	−	6.55643i	0.632723	−	0.304703i	0.722618	+	0.691248i	$0.242939\pi$
$464$	2.15723	−	28.7862i	0.100147	−	1.33637i
$465$		0			0
$466$	11.3997	−	3.51634i	0.528080	−	0.162891i
$467$	1.52638	−	20.3681i	0.0706324	−	0.942523i	−0.843506	−	0.537120i	$-0.819512\pi$
$467$	1.52638	−	20.3681i	0.0706324	−	0.942523i	0.914138	−	0.405403i	$-0.132869\pi$
$468$		0			0
$469$	−5.39672	−	9.32268i	−0.249197	−	0.430481i
$470$	3.95544	+	1.90484i	0.182451	+	0.0878636i
$471$		0			0
$472$	2.49521	+	4.32183i	0.114851	+	0.198928i
$473$	−0.0664916	−	0.887269i	−0.00305729	−	0.0407967i
$474$		0			0
$475$	3.50595	−	15.3606i	0.160864	−	0.704791i
$476$	−19.3346	+	33.5774i	−0.886199	+	1.53902i
$477$		0			0
$478$	−3.90196	+	2.66031i	−0.178471	+	0.121680i
$479$	1.30910	−	1.21467i	0.0598143	−	0.0554996i	−0.649699	−	0.760191i	$-0.725105\pi$
$479$	1.30910	−	1.21467i	0.0598143	−	0.0554996i	0.709514	+	0.704692i	$0.248915\pi$
$480$		0			0
$481$	−21.2512	−	19.7182i	−0.968969	−	0.899072i
$482$	4.44073	+	5.56850i	0.202270	+	0.253638i
$483$		0			0
$484$	10.4906	−	13.1548i	0.476844	−	0.597943i
$485$	−4.94685	+	0.745617i	−0.224625	+	0.0338567i
$486$		0			0
$487$	−5.04193	+	12.8466i	−0.228472	+	0.582136i	−0.998433	−	0.0559540i	$-0.982180\pi$
$487$	−5.04193	+	12.8466i	−0.228472	+	0.582136i	0.769962	+	0.638090i	$0.220275\pi$
$488$	−0.162876	−	0.0502407i	−0.00737307	−	0.00227429i
$489$		0			0
$490$	2.77636	+	0.411955i	0.125423	+	0.0186102i
$491$	1.39136			0.0627913			0.0313956	−	0.999507i	$-0.490005\pi$
$491$	1.39136			0.0627913			0.0313956	+	0.999507i	$0.490005\pi$
$492$		0			0
$493$	−27.2649	+	69.4697i	−1.22795	+	3.12876i
$494$	−7.40455	−	5.04834i	−0.333147	−	0.227136i
$495$		0			0
$496$	9.73126	−	12.2026i	0.436947	−	0.547914i
$497$	−4.90074	+	2.36700i	−0.219828	+	0.106175i
$498$		0			0
$499$	27.3747	+	25.4000i	1.22546	+	1.13706i	0.986104	+	0.166127i	$0.0531262\pi$
$499$	27.3747	+	25.4000i	1.22546	+	1.13706i	0.239354	+	0.970932i	$0.423064\pi$
$500$	−16.4926	−	2.48586i	−0.737572	−	0.111171i
$501$		0			0
$502$	−2.98197	+	2.03307i	−0.133092	+	0.0907405i
$503$	−1.34751	−	5.90385i	−0.0600827	−	0.263240i	0.935961	−	0.352104i	$-0.114533\pi$
$503$	−1.34751	−	5.90385i	−0.0600827	−	0.263240i	−0.996044	+	0.0888640i	$0.971676\pi$
$504$		0			0
$505$	−1.14309	+	5.00819i	−0.0508667	+	0.222861i
$506$	−1.10707	−	2.82076i	−0.0492151	−	0.125398i
$507$		0			0
$508$	4.67890	+	8.10409i	0.207592	+	0.359561i
$509$	7.16090	−	12.4030i	0.317401	−	0.549755i	−0.662544	−	0.749023i	$-0.730523\pi$
$509$	7.16090	−	12.4030i	0.317401	−	0.549755i	0.979945	+	0.199268i	$0.0638564\pi$
$510$		0			0
$511$	18.0905	−	5.60291i	0.800274	−	0.247858i
$512$	20.3290	−	9.78994i	0.898424	−	0.432658i
$513$		0			0
$514$	−9.13313	+	2.81720i	−0.402845	+	0.124261i
$515$	6.99559	−	2.15785i	0.308262	−	0.0950864i
$516$		0			0
$517$	−13.4699	+	6.48678i	−0.592407	+	0.285288i
$518$	−5.11587	+	1.58447i	−0.224779	+	0.0696176i
$519$		0			0
$520$	−4.38769	+	7.59970i	−0.192413	+	0.333269i
$521$	−1.04267	−	1.80596i	−0.0456804	−	0.0791207i	0.842281	−	0.539038i	$-0.181212\pi$
$521$	−1.04267	−	1.80596i	−0.0456804	−	0.0791207i	−0.887962	+	0.459918i	$0.847879\pi$
$522$		0			0
$523$	−12.9190	−	32.9170i	−0.564907	−	1.43936i	−0.872866	−	0.487960i	$-0.837741\pi$
$523$	−12.9190	−	32.9170i	−0.564907	−	1.43936i	0.307959	−	0.951400i	$-0.400354\pi$
$524$	−2.56041	+	11.2179i	−0.111852	+	0.490055i
$525$		0			0
$526$	0.960099	+	4.20647i	0.0418623	+	0.183411i
$527$	−33.3388	+	22.7300i	−1.45226	+	0.990134i
$528$		0			0
$529$	−8.03448	−	1.21100i	−0.349325	−	0.0526523i
$530$	−2.20684	−	2.04764i	−0.0958588	−	0.0889440i
$531$		0			0
$532$	17.3532	−	8.38141i	0.752357	−	0.363380i
$533$	24.1080	−	30.2305i	1.04423	−	1.30943i
$534$		0			0
$535$	−7.53624	−	5.13812i	−0.325820	−	0.222140i
$536$	2.27311	−	5.79178i	0.0981833	−	0.250167i
$537$		0			0
$538$	7.31433			0.315343
$539$	−6.99172	+	6.51729i	−0.301155	+	0.280720i
$540$		0			0
$541$	10.1158	+	3.12030i	0.434910	+	0.134152i	0.504477	−	0.863425i	$-0.331685\pi$
$541$	10.1158	+	3.12030i	0.434910	+	0.134152i	−0.0695665	+	0.997577i	$0.522162\pi$
$542$	−1.61312	+	4.11015i	−0.0692893	+	0.176546i
$543$		0			0
$544$	−33.6502	+	5.07195i	−1.44274	+	0.217458i
$545$	2.55556	−	3.20456i	0.109468	−	0.137268i
$546$		0			0
$547$	0.686842	+	0.861272i	0.0293672	+	0.0368253i	0.796298	−	0.604904i	$-0.206789\pi$
$547$	0.686842	+	0.861272i	0.0293672	+	0.0368253i	−0.766931	+	0.641730i	$0.778217\pi$
$548$	6.13821	+	5.69543i	0.262211	+	0.243297i
$549$		0			0
$550$	−1.58622	+	1.47180i	−0.0676366	+	0.0627576i
$551$	30.6684	−	20.9094i	1.30652	−	0.890769i
$552$		0			0
$553$	−7.27119	+	12.6275i	−0.309202	+	0.536976i
$554$	2.75077	−	12.0519i	0.116869	−	0.512037i
$555$		0			0
$556$	0.315493	+	4.20996i	0.0133799	+	0.178542i
$557$	19.2070	+	33.2675i	0.813826	+	1.40959i	0.910168	+	0.414240i	$0.135953\pi$
$557$	19.2070	+	33.2675i	0.813826	+	1.40959i	−0.0963414	+	0.995348i	$0.530714\pi$
$558$		0			0
$559$	3.34450	+	1.61062i	0.141457	+	0.0681221i
$560$	−4.10948	−	7.09901i	−0.173657	−	0.299988i
$561$		0			0
$562$	0.104192	−	1.39035i	0.00439508	−	0.0586483i
$563$	2.87966	−	0.888257i	0.121363	−	0.0374356i	−0.233479	−	0.972362i	$-0.575011\pi$
$563$	2.87966	−	0.888257i	0.121363	−	0.0374356i	0.354842	+	0.934926i	$0.384535\pi$
$564$		0			0
$565$	0.953526	−	12.7239i	0.0401151	−	0.535299i
$566$	−6.75221	+	3.25169i	−0.283816	+	0.136679i
$567$		0			0
$568$	−2.83221	−	1.36392i	−0.118837	−	0.0572288i
$569$	−7.49635	+	12.9841i	−0.314263	+	0.544320i	−0.979281	−	0.202508i	$-0.935091\pi$
$569$	−7.49635	+	12.9841i	−0.314263	+	0.544320i	0.665017	+	0.746828i	$0.268424\pi$
$570$		0			0
$571$	−0.977645	−	13.0458i	−0.0409132	−	0.545948i	−0.979571	−	0.201098i	$-0.935549\pi$
$571$	−0.977645	−	13.0458i	−0.0409132	−	0.545948i	0.938658	−	0.344850i	$-0.112070\pi$
$572$	−5.23408	−	13.3362i	−0.218848	−	0.557615i
$573$		0			0
$574$	−2.61734	−	6.64643i	−0.109246	−	0.277417i
$575$	4.94580	+	21.6690i	0.206254	+	0.903659i
$576$		0			0
$577$	−23.4625	+	21.7700i	−0.976755	+	0.906296i	−0.995617	−	0.0935257i	$-0.970186\pi$
$577$	−23.4625	+	21.7700i	−0.976755	+	0.906296i	0.0188617	+	0.999822i	$0.493996\pi$
$578$	18.1819	+	2.74048i	0.756267	+	0.113989i
$579$		0			0
$580$	−10.8641	−	13.6231i	−0.451106	−	0.565669i
$581$	0.856015	−	3.77038i	0.0355135	−	0.156422i
$582$		0			0
$583$	10.1374	−	1.52797i	0.419850	−	0.0632822i
$584$	9.03792	+	6.16195i	0.373992	+	0.254983i
$585$		0			0
$586$	5.76984	+	1.77976i	0.238350	+	0.0735212i
$587$	−29.2589			−1.20765			−0.603823	−	0.797119i	$-0.706356\pi$
$587$	−29.2589			−1.20765			−0.603823	+	0.797119i	$0.706356\pi$
$588$		0			0
$589$	20.0690			0.826927
$590$	1.25122	+	0.385952i	0.0515121	+	0.0158894i
$591$		0			0
$592$	12.9320	+	8.81689i	0.531502	+	0.362372i
$593$	17.3139	−	2.60966i	0.710999	−	0.107166i	0.216422	−	0.976300i	$-0.430561\pi$
$593$	17.3139	−	2.60966i	0.710999	−	0.107166i	0.494577	+	0.869134i	$0.335323\pi$
$594$		0			0
$595$	4.74250	+	20.6689i	0.194424	+	0.847343i
$596$	−9.71091	−	12.1771i	−0.397775	−	0.498793i
$597$		0			0
$598$	12.5011	+	1.88423i	0.511206	+	0.0770519i
$599$	22.2846	−	20.6771i	0.910524	−	0.844843i	−0.0778376	−	0.996966i	$-0.524802\pi$
$599$	22.2846	−	20.6771i	0.910524	−	0.844843i	0.988362	+	0.152123i	$0.0486111\pi$
$600$		0			0
$601$	−1.25465	−	5.49697i	−0.0511781	−	0.224226i	0.942871	−	0.333158i	$-0.108114\pi$
$601$	−1.25465	−	5.49697i	−0.0511781	−	0.224226i	−0.994049	+	0.108932i	$0.965257\pi$
$602$	0.566172	−	0.386962i	0.0230755	−	0.0157714i
$603$		0			0
$604$	−8.29540	−	21.1363i	−0.337535	−	0.860025i
$605$	−0.688169	−	9.18298i	−0.0279781	−	0.373341i
$606$		0			0
$607$	−3.14210	+	5.44228i	−0.127534	+	0.220895i	−0.922721	−	0.385469i	$-0.874040\pi$
$607$	−3.14210	+	5.44228i	−0.127534	+	0.220895i	0.795187	+	0.606365i	$0.207373\pi$
$608$	15.2495	+	7.34378i	0.618450	+	0.297830i
$609$		0			0
$610$	−0.0402938	+	0.0194045i	−0.00163145	+	0.000785665i
$611$	4.66123	−	62.1998i	0.188573	−	2.51633i
$612$		0			0
$613$	−26.8309	+	8.27625i	−1.08369	+	0.334274i	−0.784633	−	0.619960i	$-0.787149\pi$
$613$	−26.8309	+	8.27625i	−1.08369	+	0.334274i	−0.299058	+	0.954235i	$0.596672\pi$
$614$	0.450293	−	6.00875i	0.0181724	−	0.242493i
$615$		0			0
$616$	−5.46005	−	0.816564i	−0.219992	−	0.0329003i
$617$	−17.3508	−	8.35568i	−0.698515	−	0.336387i	0.0507000	−	0.998714i	$-0.483855\pi$
$617$	−17.3508	−	8.35568i	−0.698515	−	0.336387i	−0.749215	+	0.662327i	$0.769569\pi$
$618$		0			0
$619$	−8.88783	−	15.3942i	−0.357232	−	0.618744i	0.630265	−	0.776380i	$-0.282946\pi$
$619$	−8.88783	−	15.3942i	−0.357232	−	0.618744i	−0.987497	+	0.157636i	$0.949613\pi$
$620$	−0.704040	−	9.39476i	−0.0282749	−	0.377303i
$621$		0			0
$622$	−1.55219	+	6.80060i	−0.0622372	+	0.272679i
$623$	12.0505	+	11.1555i	0.482793	+	0.446936i
$624$		0			0
$625$	8.91601	−	6.07883i	0.356641	−	0.243153i
$626$	1.52600	−	1.41592i	0.0609913	−	0.0565917i
$627$		0			0
$628$	−0.855347	−	0.793646i	−0.0341321	−	0.0316699i
$629$	−25.2286	−	31.6357i	−1.00593	−	1.26140i
$630$		0			0
$631$	−10.9711	+	13.7573i	−0.436752	+	0.547670i	−0.950684	−	0.310161i	$-0.899617\pi$
$631$	−10.9711	+	13.7573i	−0.436752	+	0.547670i	0.513932	+	0.857831i	$0.328189\pi$
$632$	−8.32233	+	1.25439i	−0.331044	+	0.0498969i
$633$		0			0
$634$	−2.02242	+	5.15305i	−0.0803206	+	0.204654i
$635$	4.89404	+	1.50961i	0.194214	+	0.0599071i
$636$		0			0
$637$	−8.96272	−	38.8570i	−0.355116	−	1.53957i
$638$	−5.09776			−0.201822
$639$		0			0
$640$	3.80394	−	9.69227i	0.150364	−	0.383121i
$641$	−0.935184	−	0.637597i	−0.0369375	−	0.0251836i	0.544711	−	0.838624i	$-0.316640\pi$
$641$	−0.935184	−	0.637597i	−0.0369375	−	0.0251836i	−0.581648	+	0.813441i	$0.697592\pi$
$642$		0			0
$643$	−3.09397	+	3.87972i	−0.122014	+	0.153001i	−0.839087	−	0.543997i	$-0.816910\pi$
$643$	−3.09397	+	3.87972i	−0.122014	+	0.153001i	0.717073	+	0.696998i	$0.245482\pi$
$644$	−16.9256	+	21.2741i	−0.666964	+	0.838317i
$645$		0			0
$646$	−9.16948	−	8.50803i	−0.360768	−	0.334744i
$647$	−1.08809	−	0.164004i	−0.0427774	−	0.00644765i	0.127619	−	0.991823i	$-0.459267\pi$
$647$	−1.08809	−	0.164004i	−0.0427774	−	0.00644765i	−0.170396	+	0.985376i	$0.554505\pi$
$648$		0			0
$649$	−3.68425	+	2.51188i	−0.144619	+	0.0985997i
$650$	−2.00885	−	8.80137i	−0.0787938	−	0.345218i
$651$		0			0
$652$	−7.81661	+	34.2468i	−0.306122	+	1.34121i
$653$	−14.4254	−	36.7552i	−0.564508	−	1.43834i	−0.873286	−	0.487209i	$-0.838015\pi$
$653$	−14.4254	−	36.7552i	−0.564508	−	1.43834i	0.308777	−	0.951134i	$-0.400080\pi$
$654$		0			0
$655$	3.14875	+	5.45379i	0.123032	+	0.213097i
$656$	−10.4379	+	18.0790i	−0.407532	+	0.705867i
$657$		0			0
$658$	−9.52823	−	6.48024i	−0.371449	−	0.252626i
$659$	−27.8454	+	13.4096i	−1.08470	+	0.522365i	−0.888817	−	0.458262i	$-0.848472\pi$
$659$	−27.8454	+	13.4096i	−1.08470	+	0.522365i	−0.195884	+	0.980627i	$0.562758\pi$
$660$		0			0
$661$	16.0825	−	4.96079i	0.625536	−	0.192952i	0.0342490	−	0.999413i	$-0.489096\pi$
$661$	16.0825	−	4.96079i	0.625536	−	0.192952i	0.591287	+	0.806461i	$0.298620\pi$
$662$	7.81745	−	2.41137i	0.303834	−	0.0937204i
$663$		0			0
$664$	2.01202	−	0.968939i	0.0780816	−	0.0376021i
$665$	3.84209	−	9.82260i	0.148990	−	0.380904i
$666$		0			0
$667$	−26.1810	+	45.3469i	−1.01373	+	1.75584i
$668$	−11.6195	−	20.1255i	−0.449571	−	0.778679i
$669$		0			0
$670$	−0.596423	−	1.51966i	−0.0230418	−	0.0587096i
$671$	0.0338900	−	0.148482i	0.00130831	−	0.00573207i
$672$		0			0
$673$	−5.81855	−	25.4927i	−0.224289	−	0.982672i	−0.954209	−	0.299140i	$-0.903300\pi$
$673$	−5.81855	−	25.4927i	−0.224289	−	0.982672i	0.729921	−	0.683532i	$-0.239557\pi$
$674$	−5.70150	+	3.88722i	−0.219614	+	0.149730i
$675$		0			0
$676$	35.4279	+	5.33989i	1.36261	+	0.205380i
$677$	−31.1247	−	28.8795i	−1.19622	−	1.10993i	−0.991364	−	0.131137i	$-0.958137\pi$
$677$	−31.1247	−	28.8795i	−1.19622	−	1.10993i	−0.204856	−	0.978792i	$-0.565672\pi$
$678$		0			0
$679$	13.1307	−	0.0150663i	0.503911	−	0.000578190i
$680$	−7.63681	+	9.57626i	−0.292858	+	0.367233i
$681$		0			0
$682$	−2.27732	−	1.55265i	−0.0872031	−	0.0594541i
$683$	−1.74948	+	4.45761i	−0.0669421	+	0.170566i	−0.960430	−	0.278522i	$-0.910156\pi$
$683$	−1.74948	+	4.45761i	−0.0669421	+	0.170566i	0.893488	+	0.449087i	$0.148251\pi$
$684$		0			0
$685$	4.58287			0.175102
$686$	−7.04709	−	2.14720i	−0.269059	−	0.0819806i
$687$		0			0
$688$	−1.91513	−	0.590738i	−0.0730135	−	0.0225217i
$689$	−15.6262	+	39.8150i	−0.595312	+	1.51683i
$690$		0			0
$691$	42.1121	−	6.34738i	1.60202	−	0.241466i	0.713619	−	0.700534i	$-0.247055\pi$
$691$	42.1121	−	6.34738i	1.60202	−	0.241466i	0.888401	+	0.459069i	$0.151817\pi$
$692$	3.53233	−	4.42940i	0.134279	−	0.168381i
$693$		0			0
$694$	−4.82531	−	6.05075i	−0.183166	−	0.229683i
$695$	1.69379	+	1.57161i	0.0642491	+	0.0596144i
$696$		0			0
$697$	39.5624	−	36.7086i	1.49853	−	1.39044i
$698$	−2.78051	+	1.89572i	−0.105244	+	0.0717541i
$699$		0			0
$700$	18.5572	+	5.70082i	0.701395	+	0.215471i
$701$	4.15804	−	18.2176i	0.157047	−	0.688068i	−0.833685	−	0.552240i	$-0.813773\pi$
$701$	4.15804	−	18.2176i	0.157047	−	0.688068i	0.990732	−	0.135828i	$-0.0433695\pi$
$702$		0			0
$703$	1.50398	+	20.0692i	0.0567235	+	0.756923i
$704$	3.03742	+	5.26097i	0.114477	+	0.198280i
$705$		0			0
$706$	−5.35085	−	2.57683i	−0.201382	−	0.0969804i
$707$	4.91154	−	12.5567i	0.184717	−	0.472245i
$708$		0			0
$709$	3.90476	−	52.1054i	0.146646	−	1.95686i	−0.119268	−	0.992862i	$-0.538055\pi$
$709$	3.90476	−	52.1054i	0.146646	−	1.95686i	0.265914	−	0.963997i	$-0.414326\pi$
$710$	−0.788158	+	0.243115i	−0.0295791	+	0.00912393i
$711$		0			0
$712$	−0.708805	+	9.45835i	−0.0265636	+	0.354467i
$713$	−25.5074	+	12.2837i	−0.955259	+	0.460028i
$714$		0			0
$715$	−7.06450	−	3.40209i	−0.264197	−	0.127231i
$716$	−8.94011	+	15.4847i	−0.334108	+	0.578692i
$717$		0			0
$718$	0.578408	+	7.71831i	0.0215860	+	0.288045i
$719$	−4.20535	−	10.7150i	−0.156833	−	0.399604i	0.830762	−	0.556628i	$-0.187905\pi$
$719$	−4.20535	−	10.7150i	−0.156833	−	0.399604i	−0.987595	+	0.157024i	$0.949810\pi$
$720$		0			0
$721$	−18.9972	+	2.88567i	−0.707493	+	0.107468i
$722$	−0.297363	−	1.30283i	−0.0110667	−	0.0484865i
$723$		0			0
$724$	4.77370	−	4.42935i	0.177413	−	0.164615i
$725$	36.9736	+	5.57288i	1.37317	+	0.206972i
$726$		0			0
$727$	−23.5336	−	29.5103i	−0.872815	−	1.09447i	−0.994790	−	0.101942i	$-0.967494\pi$
$727$	−23.5336	−	29.5103i	−0.872815	−	1.09447i	0.121976	−	0.992533i	$-0.461077\pi$
$728$	14.3401	−	18.0243i	0.531480	−	0.668026i
$729$		0			0
$730$	2.83805	−	0.427767i	0.105041	−	0.0158324i
$731$	4.28098	+	2.91872i	0.158338	+	0.107953i
$732$		0			0
$733$	−10.3408	−	3.18970i	−0.381945	−	0.117814i	0.0978366	−	0.995202i	$-0.468808\pi$
$733$	−10.3408	−	3.18970i	−0.381945	−	0.117814i	−0.479781	+	0.877388i	$0.659284\pi$
$734$	−13.6409			−0.503495
$735$		0			0
$736$	−23.8769			−0.880114
$737$	5.31240	+	1.63866i	0.195685	+	0.0603608i
$738$		0			0
$739$	3.98669	+	2.71808i	0.146653	+	0.0999862i	0.634424	−	0.772986i	$-0.281237\pi$
$739$	3.98669	+	2.71808i	0.146653	+	0.0999862i	−0.487771	+	0.872972i	$0.662190\pi$
$740$	9.34210	−	1.40809i	0.343422	−	0.0517626i
$741$		0			0
$742$	4.93369	+	6.17211i	0.181121	+	0.226585i
$743$	26.2741	+	32.9467i	0.963905	+	1.20870i	0.977959	+	0.208797i	$0.0669548\pi$
$743$	26.2741	+	32.9467i	0.963905	+	1.20870i	−0.0140543	+	0.999901i	$0.504474\pi$
$744$		0			0
$745$	−8.42913	−	1.27049i	−0.308820	−	0.0465471i
$746$	−8.73717	+	8.10691i	−0.319891	+	0.296815i
$747$		0			0
$748$	−4.44969	−	19.4953i	−0.162697	−	0.712820i
$749$	17.5682	+	16.2635i	0.641930	+	0.594254i
$750$		0			0
$751$	−1.01302	−	2.58112i	−0.0369655	−	0.0941865i	0.911199	−	0.411966i	$-0.135158\pi$
$751$	−1.01302	−	2.58112i	−0.0369655	−	0.0941865i	−0.948164	+	0.317780i	$0.897063\pi$
$752$	2.51659	+	33.5816i	0.0917707	+	1.22460i
$753$		0			0
$754$	10.6341	−	18.4187i	0.387269	−	0.670770i
$755$	−11.1964	−	5.39191i	−0.407479	−	0.196232i
$756$		0			0
$757$	31.0570	−	14.9563i	1.12879	−	0.543595i	0.226190	−	0.974083i	$-0.427373\pi$
$757$	31.0570	−	14.9563i	1.12879	−	0.543595i	0.902596	+	0.430488i	$0.141659\pi$
$758$	0.522447	−	6.97157i	0.0189761	−	0.253219i
$759$		0			0
$760$	5.82140	−	1.79566i	0.211164	−	0.0651356i
$761$	1.51238	−	20.1813i	0.0548236	−	0.731571i	−0.900282	−	0.435306i	$-0.856640\pi$
$761$	1.51238	−	20.1813i	0.0548236	−	0.731571i	0.955106	−	0.296264i	$-0.0957409\pi$
$762$		0			0
$763$	−7.87790	+	7.32646i	−0.285199	+	0.265236i
$764$	−34.3619	−	16.5478i	−1.24317	−	0.598679i
$765$		0			0
$766$	−0.431623	−	0.747593i	−0.0155952	−	0.0270116i
$767$	−1.39023	−	18.5514i	−0.0501984	−	0.669851i
$768$		0			0
$769$	−6.29534	+	27.5817i	−0.227016	+	0.994621i	0.725042	+	0.688704i	$0.241820\pi$
$769$	−6.29534	+	27.5817i	−0.227016	+	0.994621i	−0.952058	+	0.305917i	$0.901037\pi$
$770$	−1.19591	+	0.817371i	−0.0430977	+	0.0294560i
$771$		0			0
$772$	−39.3083	+	26.7999i	−1.41474	+	0.964550i
$773$	−19.6942	+	18.2736i	−0.708352	+	0.657255i	−0.949692	−	0.313186i	$-0.898604\pi$
$773$	−19.6942	+	18.2736i	−0.708352	+	0.657255i	0.241340	+	0.970441i	$0.422413\pi$
$774$		0			0
$775$	14.8199	+	13.7508i	0.532345	+	0.493944i
$776$	4.72870	+	5.92960i	0.169750	+	0.212860i
$777$		0			0
$778$	2.65661	−	3.33128i	0.0952441	−	0.119432i
$779$	−26.5431	+	4.00072i	−0.951004	+	0.143341i
$780$		0			0
$781$	1.02617	−	2.61464i	0.0367193	−	0.0935592i
$782$	16.8618	+	5.20119i	0.602978	+	0.185994i
$783$		0			0
$784$	7.91165	+	20.0233i	0.282559	+	0.715119i
$785$	−0.638613			−0.0227931
$786$		0			0
$787$	8.86710	−	22.5930i	0.316078	−	0.805353i	−0.681233	−	0.732067i	$-0.738556\pi$
$787$	8.86710	−	22.5930i	0.316078	−	0.805353i	0.997311	−	0.0732866i	$-0.0233488\pi$
$788$	15.6931	+	10.6994i	0.559044	+	0.381150i
$789$		0			0
$790$	−1.37685	+	1.72652i	−0.0489861	+	0.0614267i
$791$	−7.41484	+	32.6592i	−0.263641	+	1.16123i
$792$		0			0
$793$	0.465784	+	0.432184i	0.0165405	+	0.0153473i
$794$	0.0563270	+	0.00848992i	0.00199897	+	0.000301296i
$795$		0			0
$796$	−21.2670	+	14.4996i	−0.753791	+	0.513926i
$797$	−5.23766	−	22.9477i	−0.185527	−	0.812849i	−0.978937	−	0.204161i	$-0.934553\pi$
$797$	−5.23766	−	22.9477i	−0.185527	−	0.812849i	0.793410	−	0.608688i	$-0.208304\pi$
$798$		0			0
$799$	19.3728	−	84.8778i	0.685361	−	3.00276i
$800$	6.22916	+	15.8716i	0.220234	+	0.561147i
$801$		0			0
$802$	−1.09018	−	1.88825i	−0.0384957	−	0.0666765i
$803$	−4.88696	+	8.46446i	−0.172457	+	0.298704i
$804$		0			0
$805$	1.12893	+	14.8360i	0.0397894	+	0.522901i
$806$	10.3604	−	4.98932i	0.364931	−	0.175741i
$807$		0			0
$808$	7.44180	−	2.29549i	0.261802	−	0.0807551i
$809$	31.6351	−	9.75813i	1.11223	−	0.343077i	0.316417	−	0.948620i	$-0.397520\pi$
$809$	31.6351	−	9.75813i	1.11223	−	0.343077i	0.795813	+	0.605543i	$0.207044\pi$
$810$		0			0
$811$	−21.1430	+	10.1819i	−0.742431	+	0.357536i	−0.766560	−	0.642173i	$-0.778033\pi$
$811$	−21.1430	+	10.1819i	−0.742431	+	0.357536i	0.0241288	+	0.999709i	$0.492319\pi$
$812$	22.9128	+	39.5811i	0.804081	+	1.38903i
$813$		0			0
$814$	1.38200	−	2.39370i	0.0484392	−	0.0838992i
$815$	9.61275	+	16.6498i	0.336720	+	0.583216i
$816$		0			0
$817$	−0.941493	−	2.39888i	−0.0329387	−	0.0839263i
$818$	−0.317845	+	1.39257i	−0.0111132	+	0.0486900i
$819$		0			0
$820$	2.80399	+	12.2851i	0.0979197	+	0.429014i
$821$	−4.31123	+	2.93935i	−0.150463	+	0.102584i	−0.636212	−	0.771515i	$-0.719499\pi$
$821$	−4.31123	+	2.93935i	−0.150463	+	0.102584i	0.485749	+	0.874099i	$0.338547\pi$
$822$		0			0
$823$	−21.4715	−	3.23631i	−0.748449	−	0.112811i	−0.236268	−	0.971688i	$-0.575924\pi$
$823$	−21.4715	−	3.23631i	−0.748449	−	0.112811i	−0.512181	+	0.858877i	$0.671162\pi$
$824$	−8.13582	−	7.54894i	−0.283425	−	0.262980i
$825$		0			0
$826$	−3.09816	−	1.48762i	−0.107799	−	0.0517609i
$827$	5.84177	−	7.32535i	0.203138	−	0.254727i	−0.669819	−	0.742525i	$-0.733628\pi$
$827$	5.84177	−	7.32535i	0.203138	−	0.254727i	0.872957	+	0.487797i	$0.162200\pi$
$828$		0			0
$829$	28.2068	+	19.2311i	0.979663	+	0.667923i	0.943483	−	0.331422i	$-0.107528\pi$
$829$	28.2068	+	19.2311i	0.979663	+	0.667923i	0.0361805	+	0.999345i	$0.488481\pi$
$830$	0.214070	−	0.545442i	0.00743048	−	0.0189326i
$831$		0			0
$832$	−25.3445			−0.878664
$833$	−4.28683	−	55.4945i	−0.148530	−	1.92277i
$834$		0			0
$835$	−12.1537	−	3.74893i	−0.420598	−	0.129737i
$836$	−3.63361	+	9.25828i	−0.125671	+	0.320204i
$837$		0			0
$838$	11.2043	−	1.68878i	0.387048	−	0.0583380i
$839$	16.6247	−	20.8467i	0.573948	−	0.719708i	−0.407120	−	0.913375i	$-0.633467\pi$
$839$	16.6247	−	20.8467i	0.573948	−	0.719708i	0.981067	+	0.193667i	$0.0620382\pi$
$840$		0			0
$841$	36.8414	+	46.1976i	1.27039	+	1.59302i
$842$	0.0133313	+	0.0123697i	0.000459429	+	0.000426287i
$843$		0			0
$844$	7.63557	−	7.08477i	0.262827	−	0.243868i
$845$	16.2016	−	11.0461i	0.557353	−	0.379997i
$846$		0			0
$847$	−1.77859	+	24.1048i	−0.0611132	+	0.828251i
$848$	5.13853	−	22.5134i	0.176458	−	0.773113i
$849$		0			0
$850$	−0.941651	−	12.5655i	−0.0322984	−	0.430992i
$851$	−14.1954	−	24.5871i	−0.486611	−	0.842835i
$852$		0			0
$853$	49.9659	+	24.0623i	1.71080	+	0.823878i	0.991640	+	0.129034i	$0.0411878\pi$
$853$	49.9659	+	24.0623i	1.71080	+	0.823878i	0.719161	+	0.694844i	$0.244527\pi$
$854$	0.112130	−	0.0347284i	0.00383701	−	0.00118838i
$855$		0			0
$856$	−1.03336	+	13.7892i	−0.0353194	+	0.471305i
$857$	20.5020	−	6.32402i	0.700334	−	0.216025i	0.0759155	−	0.997114i	$-0.475812\pi$
$857$	20.5020	−	6.32402i	0.700334	−	0.216025i	0.624419	+	0.781090i	$0.285336\pi$
$858$		0			0
$859$	3.04723	−	40.6625i	0.103970	−	1.38739i	−0.664398	−	0.747379i	$-0.731312\pi$
$859$	3.04723	−	40.6625i	0.103970	−	1.38739i	0.768369	−	0.640008i	$-0.221069\pi$
$860$	−1.08995	+	0.524891i	−0.0371669	+	0.0178986i
$861$		0			0
$862$	2.56322	+	1.23438i	0.0873035	+	0.0420432i
$863$	−8.51832	+	14.7542i	−0.289967	+	0.502238i	−0.973802	−	0.227399i	$-0.926978\pi$
$863$	−8.51832	+	14.7542i	−0.289967	+	0.502238i	0.683834	+	0.729637i	$0.260311\pi$
$864$		0			0
$865$	−0.231717	−	3.09205i	−0.00787861	−	0.105133i
$866$	−1.40754	−	3.58635i	−0.0478301	−	0.121869i
$867$		0			0
$868$	−1.81961	+	24.6607i	−0.0617617	+	0.837040i
$869$	−1.67340	−	7.33164i	−0.0567662	−	0.248709i
$870$		0			0
$871$	−17.0024	+	15.7760i	−0.576106	+	0.534548i
$872$	−6.14447	−	0.926129i	−0.208078	−	0.0313627i
$873$		0			0
$874$	−5.47207	−	6.86176i	−0.185095	−	0.232102i
$875$	21.5750	−	10.4205i	0.729367	−	0.352276i
$876$		0			0
$877$	−9.84241	+	1.48351i	−0.332355	+	0.0500944i	−0.313100	−	0.949720i	$-0.601367\pi$
$877$	−9.84241	+	1.48351i	−0.332355	+	0.0500944i	−0.0192548	+	0.999815i	$0.506129\pi$
$878$	−4.39908	−	2.99924i	−0.148462	−	0.101220i
$879$		0			0
$880$	4.04528	+	1.24780i	0.136366	+	0.0420634i
$881$	−20.5389			−0.691973			−0.345986	−	0.938240i	$-0.612456\pi$
$881$	−20.5389			−0.691973			−0.345986	+	0.938240i	$0.612456\pi$
$882$		0			0
$883$	−46.0187			−1.54865			−0.774326	−	0.632787i	$-0.781911\pi$
$883$	−46.0187			−1.54865			−0.774326	+	0.632787i	$0.781911\pi$
$884$	79.7208	+	24.5906i	2.68130	+	0.827071i
$885$		0			0
$886$	7.07197	+	4.82159i	0.237588	+	0.161984i
$887$	−30.3587	+	4.57583i	−1.01934	+	0.153641i	−0.637391	−	0.770540i	$-0.719986\pi$
$887$	−30.3587	+	4.57583i	−1.01934	+	0.153641i	−0.381953	+	0.924182i	$0.624748\pi$
$888$		0			0
$889$	−12.1181	−	5.81867i	−0.406429	−	0.195152i
$890$	1.55166	+	1.94571i	0.0520116	+	0.0652205i
$891$		0			0
$892$	−13.2395	−	1.99553i	−0.443290	−	0.0668152i
$893$	−31.7422	+	29.4525i	−1.06221	+	0.985590i
$894$		0			0
$895$	2.17758	+	9.54060i	0.0727885	+	0.318907i
$896$	−13.6371	+	23.6829i	−0.455585	+	0.791192i
$897$		0			0
$898$	0.669559	+	1.70601i	0.0223435	+	0.0569302i
$899$	3.55923	+	47.4946i	0.118707	+	1.58403i
$900$		0			0
$901$	−29.8499	+	51.7015i	−0.994444	+	1.72243i
$902$	3.32149	+	1.59954i	0.110593	+	0.0532590i
$903$		0			0
$904$	−17.4282	+	8.39299i	−0.579654	+	0.279147i
$905$	0.266346	−	3.55414i	0.00885364	−	0.118144i
$906$		0			0
$907$	36.9726	−	11.4045i	1.22765	−	0.378681i	0.387928	−	0.921690i	$-0.373191\pi$
$907$	36.9726	−	11.4045i	1.22765	−	0.378681i	0.839727	+	0.543008i	$0.182715\pi$
$908$	3.40757	−	45.4709i	0.113084	−	1.50900i
$909$		0			0
$910$	−0.458541	−	6.02601i	−0.0152005	−	0.199760i
$911$	24.2426	+	11.6746i	0.803194	+	0.386798i	0.789994	−	0.613115i	$-0.210084\pi$
$911$	24.2426	+	11.6746i	0.803194	+	0.386798i	0.0132004	+	0.999913i	$0.495798\pi$
$912$		0			0
$913$	0.997698	+	1.72806i	0.0330190	+	0.0571905i
$914$	0.502552	+	6.70609i	0.0166229	+	0.221818i
$915$		0			0
$916$	4.39335	−	19.2485i	0.145160	−	0.635990i
$917$	−6.05643	−	15.3796i	−0.200001	−	0.507880i
$918$		0			0
$919$	24.6678	−	16.8182i	0.813714	−	0.554781i	−0.0834326	−	0.996513i	$-0.526588\pi$
$919$	24.6678	−	16.8182i	0.813714	−	0.554781i	0.897147	+	0.441732i	$0.145636\pi$
$920$	−6.29984	+	5.84540i	−0.207700	+	0.192717i
$921$		0			0
$922$	−8.45927	−	7.84906i	−0.278591	−	0.258495i
$923$	7.30634	+	9.16186i	0.240491	+	0.301566i
$924$		0			0
$925$	−12.6404	+	15.8505i	−0.415612	+	0.521161i
$926$	−5.94370	+	0.895869i	−0.195322	+	0.0294401i
$927$		0			0
$928$	−14.6751	+	37.3915i	−0.481733	+	1.22744i
$929$	−1.77568	−	0.547724i	−0.0582581	−	0.0179702i	0.265489	−	0.964114i	$-0.414467\pi$
$929$	−1.77568	−	0.547724i	−0.0582581	−	0.0179702i	−0.323747	+	0.946144i	$0.604943\pi$
$930$		0			0
$931$	−13.7868	+	24.0064i	−0.451843	+	0.786779i
$932$	55.2363			1.80932
$933$		0			0
$934$	−2.96829	+	7.56307i	−0.0971253	+	0.247471i
$935$	−9.04262	−	6.16515i	−0.295725	−	0.201622i
$936$		0			0
$937$	−6.17885	+	7.74803i	−0.201854	+	0.253117i	−0.872447	−	0.488708i	$-0.837468\pi$
$937$	−6.17885	+	7.74803i	−0.201854	+	0.253117i	0.670593	+	0.741825i	$0.266040\pi$
$938$	0.958268	+	4.17635i	0.0312886	+	0.136363i
$939$		0			0
$940$	14.9010	+	13.8261i	0.486016	+	0.450957i
$941$	7.71531	+	1.16290i	0.251512	+	0.0379093i	0.273588	−	0.961847i	$-0.411790\pi$
$941$	7.71531	+	1.16290i	0.251512	+	0.0379093i	−0.0220762	+	0.999756i	$0.507028\pi$
$942$		0			0
$943$	31.2871	−	21.3312i	1.01885	−	0.694640i
$944$	2.23499	+	9.79213i	0.0727427	+	0.318707i
$945$		0			0
$946$	−0.0787559	+	0.345052i	−0.00256058	+	0.0112186i
$947$	−2.57368	−	6.55763i	−0.0836333	−	0.213094i	0.882939	−	0.469487i	$-0.155561\pi$
$947$	−2.57368	−	6.55763i	−0.0836333	−	0.213094i	−0.966573	+	0.256393i	$0.917466\pi$
$948$		0			0
$949$	−20.3886	−	35.3141i	−0.661843	−	1.14635i
$950$	−3.13361	+	5.42758i	−0.101668	+	0.176094i
$951$		0			0
$952$	23.5417	−	21.8938i	0.762990	−	0.709582i
$953$	33.9873	−	16.3674i	1.10096	−	0.530193i	0.206997	−	0.978341i	$-0.433631\pi$
$953$	33.9873	−	16.3674i	1.10096	−	0.530193i	0.893959	+	0.448149i	$0.147917\pi$
$954$		0			0
$955$	−19.9462	+	6.15260i	−0.645445	+	0.199094i
$956$	−20.8947	+	6.44516i	−0.675783	+	0.208451i
$957$		0			0
$958$	−0.640013	+	0.308214i	−0.0206779	+	0.00995794i
$959$	−11.8964	−	1.77914i	−0.384156	−	0.0574515i
$960$		0			0
$961$	2.62434	−	4.54549i	0.0846561	−	0.146629i
$962$	5.76579	+	9.98663i	0.185896	+	0.321982i
$963$		0			0
$964$	12.0481	+	30.6981i	0.388043	+	0.988718i
$965$	−5.79401	+	25.3852i	−0.186516	+	0.817179i
$966$		0			0
$967$	8.74956	+	38.3343i	0.281367	+	1.23275i	0.896042	+	0.443969i	$0.146430\pi$
$967$	8.74956	+	38.3343i	0.281367	+	1.23275i	−0.614675	+	0.788780i	$0.710713\pi$
$968$	−11.5348	+	7.86432i	−0.370744	+	0.252769i
$969$		0			0
$970$	1.96775	+	0.296590i	0.0631805	+	0.00952293i
$971$	−16.4568	−	15.2697i	−0.528124	−	0.490028i	0.370448	−	0.928853i	$-0.379204\pi$
$971$	−16.4568	−	15.2697i	−0.528124	−	0.490028i	−0.898572	+	0.438825i	$0.855395\pi$
$972$		0			0
$973$	−3.78670	−	4.73721i	−0.121396	−	0.151868i
$974$	3.42270	−	4.29192i	0.109670	−	0.137522i
$975$		0			0
$976$	−0.283444	−	0.193249i	−0.00907283	−	0.00618575i
$977$	−14.8655	+	37.8766i	−0.475588	+	1.21178i	0.468905	+	0.883249i	$0.344649\pi$
$977$	−14.8655	+	37.8766i	−0.475588	+	1.21178i	−0.944493	+	0.328531i	$0.893447\pi$
$978$		0			0
$979$	−8.47495			−0.270861
$980$	11.7216	+	5.61175i	0.374434	+	0.179261i
$981$		0			0
$982$	−0.528865	−	0.163133i	−0.0168767	−	0.00520579i
$983$	12.7054	−	32.3729i	0.405240	−	1.03253i	−0.571973	−	0.820273i	$-0.693822\pi$
$983$	12.7054	−	32.3729i	0.405240	−	1.03253i	0.977213	−	0.212262i	$-0.0680831\pi$
$984$		0			0
$985$	10.2791	−	1.54933i	0.327520	−	0.0493656i
$986$	18.5087	−	23.2091i	0.589436	−	0.739129i
$987$		0			0
$988$	−25.8713	−	32.4416i	−0.823075	−	1.03210i
$989$	2.66492	+	2.47269i	0.0847396	+	0.0786268i
$990$		0			0
$991$	−5.90508	+	5.47911i	−0.187581	+	0.174050i	−0.768373	−	0.640002i	$-0.778933\pi$
$991$	−5.90508	+	5.47911i	−0.187581	+	0.174050i	0.580792	+	0.814052i	$0.302743\pi$
$992$	−17.9443	+	12.2342i	−0.569732	+	0.388437i
$993$		0			0
$994$	2.14032	−	0.325114i	0.0678869	−	0.0103120i
$995$	−3.13475	+	13.7342i	−0.0993782	+	0.435404i
$996$		0			0
$997$	−1.37466	−	18.3435i	−0.0435358	−	0.580944i	−0.975729	−	0.218983i	$-0.929726\pi$
$997$	−1.37466	−	18.3435i	−0.0435358	−	0.580944i	0.932193	−	0.361962i	$-0.117893\pi$
$998$	−7.42720	−	12.8643i	−0.235104	−	0.407212i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.100.3		60
3.2	odd	2		147.2.m.b.100.3	yes	60
49.25	even	21	inner	441.2.bb.e.172.3		60
147.5	even	42		7203.2.a.m.1.17		30
147.44	odd	42		7203.2.a.n.1.17		30
147.74	odd	42		147.2.m.b.25.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.25.3	✓	60	147.74	odd	42
147.2.m.b.100.3	yes	60	3.2	odd	2
441.2.bb.e.100.3		60	1.1	even	1	trivial
441.2.bb.e.172.3		60	49.25	even	21	inner
7203.2.a.m.1.17		30	147.5	even	42
7203.2.a.n.1.17		30	147.44	odd	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.380106 - 0.117247i) q^{2} +(-1.52174 - 1.03751i) q^{4} +(-0.996754 + 0.150237i) q^{5} +(2.64575 - 0.00303574i) q^{7} +(0.952800 + 1.19477i) q^{8} +O(q^{10})\)	\(q+(-0.380106 - 0.117247i) q^{2} +(-1.52174 - 1.03751i) q^{4} +(-0.996754 + 0.150237i) q^{5} +(2.64575 - 0.00303574i) q^{7} +(0.952800 + 1.19477i) q^{8} +(0.396487 + 0.0597608i) q^{10} +(-1.00095 + 0.928747i) q^{11} +(-1.26765 - 5.55392i) q^{13} +(-1.00602 - 0.309053i) q^{14} +(1.12367 + 2.86306i) q^{16} +(-0.594210 - 7.92918i) q^{17} +(-1.97740 + 3.42496i) q^{19} +(1.67268 + 0.805519i) q^{20} +(0.489360 - 0.235663i) q^{22} +(0.416919 - 5.56340i) q^{23} +(-3.80692 + 1.17428i) q^{25} +(-0.169342 + 2.25971i) q^{26} +(-4.02930 - 2.74037i) q^{28} +(-8.45611 - 4.07225i) q^{29} +(-2.53729 - 4.39471i) q^{31} +(-0.319828 - 4.26781i) q^{32} +(-0.703810 + 3.08360i) q^{34} +(-2.63671 + 0.400514i) q^{35} +(4.20461 - 2.86666i) q^{37} +(1.15319 - 1.07000i) q^{38} +(-1.12921 - 1.04775i) q^{40} +(4.23188 + 5.30661i) q^{41} +(-0.406277 + 0.509456i) q^{43} +(2.48677 - 0.374821i) q^{44} +(-0.810766 + 2.06580i) q^{46} +(10.4626 + 3.22730i) q^{47} +(6.99998 - 0.0160636i) q^{49} +1.58471 q^{50} +(-3.83320 + 9.76685i) q^{52} +(-6.20346 - 4.22945i) q^{53} +(0.858171 - 1.07611i) q^{55} +(2.52450 + 3.15818i) q^{56} +(2.73676 + 2.53934i) q^{58} +(3.22914 + 0.486714i) q^{59} +(-0.0921568 + 0.0628315i) q^{61} +(0.449171 + 1.96795i) q^{62} +(0.989983 - 4.33740i) q^{64} +(2.09794 + 5.34545i) q^{65} +(-2.03572 - 3.52598i) q^{67} +(-7.32235 + 12.6827i) q^{68} +(1.04919 + 0.156908i) q^{70} +(-1.85333 + 0.892516i) q^{71} +(6.83997 - 2.10985i) q^{73} +(-1.93430 + 0.596654i) q^{74} +(6.56253 - 3.16035i) q^{76} +(-2.64545 + 2.46027i) q^{77} +(-2.75372 + 4.76959i) q^{79} +(-1.55016 - 2.68495i) q^{80} +(-0.986377 - 2.51325i) q^{82} +(0.325178 - 1.42470i) q^{83} +(1.78353 + 7.81417i) q^{85} +(0.214161 - 0.146012i) q^{86} +(-2.06335 - 0.311000i) q^{88} +(4.54981 + 4.22161i) q^{89} +(-3.37074 - 14.6904i) q^{91} +(-6.40651 + 8.03351i) q^{92} +(-3.59852 - 2.45343i) q^{94} +(1.45643 - 3.71092i) q^{95} +4.96295 q^{97} +(-2.66262 - 0.814622i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Introduction

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