LMFDB - Embedded newform 441.2.bb.c.100.4

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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.4
Character	$\chi$	$=$	441.100
Dual form			441.2.bb.c.172.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.06858 + 0.638073i) q^{2} +(2.21941 + 1.51317i) q^{4} +(2.32995 - 0.351184i) q^{5} +(0.990624 - 2.45330i) q^{7} +(0.926114 + 1.16131i) q^{8} +O(q^{10})$	\(q+(2.06858 + 0.638073i) q^{2} +(2.21941 + 1.51317i) q^{4} +(2.32995 - 0.351184i) q^{5} +(0.990624 - 2.45330i) q^{7} +(0.926114 + 1.16131i) q^{8} +(5.04378 + 0.760227i) q^{10} +(-2.76839 + 2.56869i) q^{11} +(-0.814304 - 3.56770i) q^{13} +(3.61457 - 4.44275i) q^{14} +(-0.787989 - 2.00776i) q^{16} +(0.360631 + 4.81229i) q^{17} +(-1.58049 + 2.73749i) q^{19} +(5.70252 + 2.74619i) q^{20} +(-7.36564 + 3.54711i) q^{22} +(-0.496051 + 6.61934i) q^{23} +(0.527486 - 0.162708i) q^{25} +(0.591998 - 7.89966i) q^{26} +(5.91085 - 3.94589i) q^{28} +(-5.84668 - 2.81561i) q^{29} +(1.61421 + 2.79589i) q^{31} +(-0.570924 - 7.61845i) q^{32} +(-2.32459 + 10.1847i) q^{34} +(1.44655 - 6.06396i) q^{35} +(3.09158 - 2.10780i) q^{37} +(-5.01609 + 4.65425i) q^{38} +(2.56563 + 2.38056i) q^{40} +(1.36836 + 1.71587i) q^{41} +(-3.54120 + 4.44052i) q^{43} +(-10.0310 + 1.51194i) q^{44} +(-5.24974 + 13.3761i) q^{46} +(11.1336 + 3.43426i) q^{47} +(-5.03733 - 4.86059i) q^{49} +1.19497 q^{50} +(3.59126 - 9.15037i) q^{52} +(-7.51342 - 5.12256i) q^{53} +(-5.54813 + 6.95714i) q^{55} +(3.76647 - 1.12161i) q^{56} +(-10.2978 - 9.55492i) q^{58} +(5.46159 + 0.823202i) q^{59} +(9.71290 - 6.62214i) q^{61} +(1.55514 + 6.81352i) q^{62} +(2.72023 - 11.9181i) q^{64} +(-3.15021 - 8.02660i) q^{65} +(-6.74180 - 11.6771i) q^{67} +(-6.48141 + 11.2261i) q^{68} +(6.86155 - 11.6208i) q^{70} +(0.622711 - 0.299882i) q^{71} +(-5.47284 + 1.68815i) q^{73} +(7.74012 - 2.38751i) q^{74} +(-7.65004 + 3.68406i) q^{76} +(3.55932 + 9.33628i) q^{77} +(-0.858882 + 1.48763i) q^{79} +(-2.54107 - 4.40127i) q^{80} +(1.73572 + 4.42254i) q^{82} +(1.24668 - 5.46205i) q^{83} +(2.53025 + 11.0858i) q^{85} +(-10.1586 + 6.92604i) q^{86} +(-5.54689 - 0.836058i) q^{88} +(-10.3159 - 9.57177i) q^{89} +(-9.55930 - 1.53652i) q^{91} +(-11.1171 + 13.9404i) q^{92} +(20.8394 + 14.2081i) q^{94} +(-2.72110 + 6.93326i) q^{95} -2.26073 q^{97} +(-7.31871 - 13.2687i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * 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 $

$2$	2.06858	+	0.638073i	1.46271	+	0.451185i	0.921060	−	0.389421i	$-0.127325\pi$
$2$	2.06858	+	0.638073i	1.46271	+	0.451185i	0.541647	+	0.840606i	$0.317801\pi$
$3$		0			0
$3$		0			0
$4$	2.21941	+	1.51317i	1.10971	+	0.756584i
$5$	2.32995	−	0.351184i	1.04199	−	0.157054i	0.394316	−	0.918975i	$-0.370981\pi$
$5$	2.32995	−	0.351184i	1.04199	−	0.157054i	0.647670	+	0.761921i	$0.275743\pi$
$6$		0			0
$7$	0.990624	−	2.45330i	0.374421	−	0.927259i
$7$	0.990624	−	2.45330i	0.374421	−	0.927259i
$8$	0.926114	+	1.16131i	0.327431	+	0.410585i
$9$		0			0
$10$	5.04378	+	0.760227i	1.59498	+	0.240405i
$11$	−2.76839	+	2.56869i	−0.834700	+	0.774489i	−0.976525	−	0.215403i	$-0.930893\pi$
$11$	−2.76839	+	2.56869i	−0.834700	+	0.774489i	0.141825	+	0.989892i	$0.454703\pi$
$12$		0			0
$13$	−0.814304	−	3.56770i	−0.225847	−	0.989502i	−0.952987	−	0.303012i	$-0.902008\pi$
$13$	−0.814304	−	3.56770i	−0.225847	−	0.989502i	0.727139	−	0.686490i	$-0.240849\pi$
$14$	3.61457	−	4.44275i	0.966034	−	1.18738i
$15$		0			0
$16$	−0.787989	−	2.00776i	−0.196997	−	0.501941i
$17$	0.360631	+	4.81229i	0.0874659	+	1.16715i	0.852346	+	0.522978i	$0.175179\pi$
$17$	0.360631	+	4.81229i	0.0874659	+	1.16715i	−0.764880	+	0.644173i	$0.777202\pi$
$18$		0			0
$19$	−1.58049	+	2.73749i	−0.362589	+	0.628023i	−0.988386	−	0.151963i	$-0.951440\pi$
$19$	−1.58049	+	2.73749i	−0.362589	+	0.628023i	0.625797	+	0.779986i	$0.284774\pi$
$20$	5.70252	+	2.74619i	1.27512	+	0.614067i
$21$		0			0
$22$	−7.36564	+	3.54711i	−1.57036	+	0.756246i
$23$	−0.496051	+	6.61934i	−0.103434	+	1.38023i	0.668116	+	0.744057i	$0.267101\pi$
$23$	−0.496051	+	6.61934i	−0.103434	+	1.38023i	−0.771549	+	0.636169i	$0.780518\pi$
$24$		0			0
$25$	0.527486	−	0.162708i	0.105497	−	0.0325416i
$26$	0.591998	−	7.89966i	0.116100	−	1.54925i
$27$		0			0
$28$	5.91085	−	3.94589i	1.11705	−	0.745703i
$29$	−5.84668	−	2.81561i	−1.08570	−	0.522846i	−0.196566	−	0.980491i	$-0.562979\pi$
$29$	−5.84668	−	2.81561i	−1.08570	−	0.522846i	−0.889135	+	0.457645i	$0.848693\pi$
$30$		0			0
$31$	1.61421	+	2.79589i	0.289921	+	0.502157i	0.973791	−	0.227447i	$-0.0730377\pi$
$31$	1.61421	+	2.79589i	0.289921	+	0.502157i	−0.683870	+	0.729604i	$0.739704\pi$
$32$	−0.570924	−	7.61845i	−0.100926	−	1.34676i
$33$		0			0
$34$	−2.32459	+	10.1847i	−0.398665	+	1.74666i
$35$	1.44655	−	6.06396i	0.244511	−	1.02500i
$36$		0			0
$37$	3.09158	−	2.10780i	0.508253	−	0.346521i	−0.281887	−	0.959448i	$-0.590960\pi$
$37$	3.09158	−	2.10780i	0.508253	−	0.346521i	0.790140	+	0.612927i	$0.210008\pi$
$38$	−5.01609	+	4.65425i	−0.813716	+	0.755019i
$39$		0			0
$40$	2.56563	+	2.38056i	0.405662	+	0.376400i
$41$	1.36836	+	1.71587i	0.213702	+	0.267974i	0.877116	−	0.480279i	$-0.159464\pi$
$41$	1.36836	+	1.71587i	0.213702	+	0.267974i	−0.663414	+	0.748253i	$0.730893\pi$
$42$		0			0
$43$	−3.54120	+	4.44052i	−0.540028	+	0.677173i	−0.974726	−	0.223403i	$-0.928284\pi$
$43$	−3.54120	+	4.44052i	−0.540028	+	0.677173i	0.434699	+	0.900576i	$0.356855\pi$
$44$	−10.0310	+	1.51194i	−1.51224	+	0.227933i
$45$		0			0
$46$	−5.24974	+	13.3761i	−0.774031	+	1.97220i
$47$	11.1336	+	3.43426i	1.62400	+	0.500938i	0.967390	−	0.253292i	$-0.0815134\pi$
$47$	11.1336	+	3.43426i	1.62400	+	0.500938i	0.656610	+	0.754230i	$0.271990\pi$
$48$		0			0
$49$	−5.03733	−	4.86059i	−0.719618	−	0.694370i
$50$	1.19497			0.168994
$51$		0			0
$52$	3.59126	−	9.15037i	0.498018	−	1.26893i
$53$	−7.51342	−	5.12256i	−1.03205	−	0.703638i	−0.0760769	−	0.997102i	$-0.524239\pi$
$53$	−7.51342	−	5.12256i	−1.03205	−	0.703638i	−0.955970	+	0.293464i	$0.905192\pi$
$54$		0			0
$55$	−5.54813	+	6.95714i	−0.748110	+	0.938100i
$56$	3.76647	−	1.12161i	0.503315	−	0.149881i
$57$		0			0
$58$	−10.2978	−	9.55492i	−1.35216	−	1.25462i
$59$	5.46159	+	0.823202i	0.711039	+	0.107172i	0.494595	−	0.869123i	$-0.335316\pi$
$59$	5.46159	+	0.823202i	0.711039	+	0.107172i	0.216443	+	0.976295i	$0.430554\pi$
$60$		0			0
$61$	9.71290	−	6.62214i	1.24361	−	0.847879i	0.250854	−	0.968025i	$-0.419289\pi$
$61$	9.71290	−	6.62214i	1.24361	−	0.847879i	0.992756	+	0.120146i	$0.0383364\pi$
$62$	1.55514	+	6.81352i	0.197503	+	0.865317i
$63$		0			0
$64$	2.72023	−	11.9181i	0.340029	−	1.48976i
$65$	−3.15021	−	8.02660i	−0.390735	−	0.995578i
$66$		0			0
$67$	−6.74180	−	11.6771i	−0.823642	−	1.42659i	−0.902953	−	0.429740i	$-0.858605\pi$
$67$	−6.74180	−	11.6771i	−0.823642	−	1.42659i	0.0793105	−	0.996850i	$-0.474728\pi$
$68$	−6.48141	+	11.2261i	−0.785987	+	1.36137i
$69$		0			0
$70$	6.86155	−	11.6208i	0.820112	−	1.38895i
$71$	0.622711	−	0.299882i	0.0739022	−	0.0355894i	−0.396568	−	0.918006i	$-0.629799\pi$
$71$	0.622711	−	0.299882i	0.0739022	−	0.0355894i	0.470470	+	0.882416i	$0.344084\pi$
$72$		0			0
$73$	−5.47284	+	1.68815i	−0.640548	+	0.197583i	−0.597980	−	0.801511i	$-0.704030\pi$
$73$	−5.47284	+	1.68815i	−0.640548	+	0.197583i	−0.0425674	+	0.999094i	$0.513554\pi$
$74$	7.74012	−	2.38751i	0.899770	−	0.277542i
$75$		0			0
$76$	−7.65004	+	3.68406i	−0.877519	+	0.422591i
$77$	3.55932	+	9.33628i	0.405623	+	1.06397i
$78$		0			0
$79$	−0.858882	+	1.48763i	−0.0966318	+	0.167371i	−0.910288	−	0.413974i	$-0.864140\pi$
$79$	−0.858882	+	1.48763i	−0.0966318	+	0.167371i	0.813657	+	0.581346i	$0.197474\pi$
$80$	−2.54107	−	4.40127i	−0.284100	−	0.492076i
$81$		0			0
$82$	1.73572	+	4.42254i	0.191678	+	0.488387i
$83$	1.24668	−	5.46205i	0.136841	−	0.599538i	−0.859277	−	0.511510i	$-0.829086\pi$
$83$	1.24668	−	5.46205i	0.136841	−	0.599538i	0.996118	−	0.0880279i	$-0.0280565\pi$
$84$		0			0
$85$	2.53025	+	11.0858i	0.274444	+	1.20242i
$86$	−10.1586	+	6.92604i	−1.09543	+	0.746854i
$87$		0			0
$88$	−5.54689	−	0.836058i	−0.591300	−	0.0891241i
$89$	−10.3159	−	9.57177i	−1.09349	−	1.01461i	−0.999819	−	0.0190022i	$-0.993951\pi$
$89$	−10.3159	−	9.57177i	−1.09349	−	1.01461i	−0.0936657	−	0.995604i	$-0.529858\pi$
$90$		0			0
$91$	−9.55930	−	1.53652i	−1.00209	−	0.161071i
$92$	−11.1171	+	13.9404i	−1.15904	+	1.45339i
$93$		0			0
$94$	20.8394	+	14.2081i	2.14942	+	1.46545i
$95$	−2.72110	+	6.93326i	−0.279179	+	0.711338i
$96$		0			0
$97$	−2.26073			−0.229542			−0.114771	−	0.993392i	$-0.536613\pi$
$97$	−2.26073			−0.229542			−0.114771	+	0.993392i	$0.536613\pi$
$98$	−7.31871	−	13.2687i	−0.739301	−	1.34034i
$99$		0			0
$100$	1.41691	+	0.437060i	0.141691	+	0.0437060i
$101$	3.30562	−	8.42259i	0.328922	−	0.838079i	−0.666762	−	0.745270i	$-0.732320\pi$
$101$	3.30562	−	8.42259i	0.328922	−	0.838079i	0.995684	−	0.0928084i	$-0.0295844\pi$
$102$		0			0
$103$	3.44908	−	0.519866i	0.339848	−	0.0512239i	0.0230991	−	0.999733i	$-0.492647\pi$
$103$	3.44908	−	0.519866i	0.339848	−	0.0512239i	0.316749	+	0.948509i	$0.397409\pi$
$104$	3.38907	−	4.24976i	0.332325	−	0.416723i
$105$		0			0
$106$	−12.2735	−	15.3905i	−1.19211	−	1.49486i
$107$	1.62779	+	1.51037i	0.157364	+	0.146013i	0.754925	−	0.655811i	$-0.227673\pi$
$107$	1.62779	+	1.51037i	0.157364	+	0.146013i	−0.597561	+	0.801823i	$0.703864\pi$
$108$		0			0
$109$	10.1361	−	9.40497i	0.970867	−	0.900833i	−0.0242332	−	0.999706i	$-0.507714\pi$
$109$	10.1361	−	9.40497i	0.970867	−	0.900833i	0.995100	+	0.0988735i	$0.0315239\pi$
$110$	−15.9159	+	10.8513i	−1.51752	+	1.03463i
$111$		0			0
$112$	−5.70624	−	0.0557676i	−0.539189	−	0.00526954i
$113$	−2.98913	+	13.0962i	−0.281194	+	1.23199i	0.615071	+	0.788471i	$0.289127\pi$
$113$	−2.98913	+	13.0962i	−0.281194	+	1.23199i	−0.896265	+	0.443519i	$0.853730\pi$
$114$		0			0
$115$	1.16883	+	15.5969i	0.108994	+	1.45442i
$116$	−8.71568	−	15.0960i	−0.809231	−	1.40163i
$117$		0			0
$118$	10.7725	+	5.18775i	0.991687	+	0.477571i
$119$	12.1632	+	3.88243i	1.11500	+	0.355902i
$120$		0			0
$121$	0.243779	−	3.25301i	0.0221618	−	0.295728i
$122$	24.3173	−	7.50090i	2.20159	−	0.679100i
$123$		0			0
$124$	−0.648064	+	8.64781i	−0.0581978	+	0.776596i
$125$	−9.44275	+	4.54739i	−0.844586	+	0.406731i
$126$		0			0
$127$	18.3022	+	8.81389i	1.62406	+	0.782106i	1.00000		0.000730377i	$0.000232486\pi$
$127$	18.3022	+	8.81389i	1.62406	+	0.782106i	0.624061	+	0.781376i	$0.285482\pi$
$128$	5.59182	−	9.68531i	0.494251	−	0.856068i
$129$		0			0
$130$	−1.39491	−	18.6137i	−0.122341	−	1.63253i
$131$	−2.16617	−	5.51930i	−0.189259	−	0.482224i	0.804476	−	0.593985i	$-0.202446\pi$
$131$	−2.16617	−	5.51930i	−0.189259	−	0.482224i	−0.993735	+	0.111761i	$0.964351\pi$
$132$		0			0
$133$	5.15020	+	6.58923i	0.446579	+	0.571359i
$134$	−6.49509	−	28.4569i	−0.561091	−	2.45830i
$135$		0			0
$136$	−5.25457	+	4.87553i	−0.450576	+	0.418073i
$137$	0.332767	+	0.0501565i	0.0284302	+	0.00428516i	0.163242	−	0.986586i	$-0.447805\pi$
$137$	0.332767	+	0.0501565i	0.0284302	+	0.00428516i	−0.134812	+	0.990871i	$0.543043\pi$
$138$		0			0
$139$	8.97964	+	11.2601i	0.761643	+	0.955070i	0.999870	−	0.0161394i	$-0.00513755\pi$
$139$	8.97964	+	11.2601i	0.761643	+	0.955070i	−0.238227	+	0.971210i	$0.576566\pi$
$140$	12.3863	−	11.2695i	1.04683	−	0.952450i
$141$		0			0
$142$	1.47947	−	0.222995i	0.124155	−	0.0187133i
$143$	11.4186	+	7.78508i	0.954873	+	0.651021i
$144$		0			0
$145$	−14.6113	−	4.50698i	−1.21340	−	0.374285i
$146$	−12.3982			−1.02608
$147$		0			0
$148$	10.0510			0.826183
$149$	14.0130	+	4.32243i	1.14799	+	0.354108i	0.809648	−	0.586916i	$-0.199658\pi$
$149$	14.0130	+	4.32243i	1.14799	+	0.354108i	0.338341	+	0.941024i	$0.390134\pi$
$150$		0			0
$151$	−16.4511	−	11.2161i	−1.33877	−	0.912757i	−0.339160	−	0.940729i	$-0.610143\pi$
$151$	−16.4511	−	11.2161i	−1.33877	−	0.912757i	−0.999609	+	0.0279717i	$0.991095\pi$
$152$	−4.64279	+	0.699787i	−0.376580	+	0.0567602i
$153$		0			0
$154$	1.40552	+	21.5840i	0.113260	+	1.73928i
$155$	4.74291	+	5.94742i	0.380959	+	0.477708i
$156$		0			0
$157$	16.9228	+	2.55070i	1.35059	+	0.203568i	0.784167	−	0.620550i	$-0.213090\pi$
$157$	16.9228	+	2.55070i	1.35059	+	0.203568i	0.566419	+	0.824118i	$0.308329\pi$
$158$	−2.72588	+	2.52925i	−0.216859	+	0.201216i
$159$		0			0
$160$	−4.00570	−	17.5501i	−0.316679	−	1.38746i
$161$	15.7478	+	7.77423i	1.24110	+	0.612695i
$162$		0			0
$163$	8.45584	+	21.5451i	0.662313	+	1.68754i	0.724315	+	0.689469i	$0.242156\pi$
$163$	8.45584	+	21.5451i	0.662313	+	1.68754i	−0.0620027	+	0.998076i	$0.519749\pi$
$164$	0.440554	+	5.87879i	0.0344015	+	0.459056i
$165$		0			0
$166$	6.06404	−	10.5032i	0.470660	−	0.815208i
$167$	−5.63854	−	2.71538i	−0.436323	−	0.210122i	0.202810	−	0.979218i	$-0.434993\pi$
$167$	−5.63854	−	2.71538i	−0.436323	−	0.210122i	−0.639133	+	0.769096i	$0.720707\pi$
$168$		0			0
$169$	−0.352799	+	0.169899i	−0.0271384	+	0.0130692i
$170$	−1.83949	+	24.5463i	−0.141082	+	1.88261i
$171$		0			0
$172$	−14.5786	+	4.49691i	−1.11161	+	0.342886i
$173$	0.365794	−	4.88119i	0.0278108	−	0.371110i	−0.965883	−	0.258980i	$-0.916614\pi$
$173$	0.365794	−	4.88119i	0.0278108	−	0.371110i	0.993694	−	0.112130i	$-0.0357673\pi$
$174$		0			0
$175$	0.123370	−	1.45526i	0.00932587	−	0.110008i
$176$	7.33878	+	3.53417i	0.553181	+	0.266398i
$177$		0			0
$178$	−15.2318	−	26.3823i	−1.14167	−	1.97744i
$179$	−0.180063	−	2.40278i	−0.0134586	−	0.179592i	−0.999882	−	0.0153695i	$-0.995108\pi$
$179$	−0.180063	−	2.40278i	−0.0134586	−	0.179592i	0.986423	−	0.164222i	$-0.0525115\pi$
$180$		0			0
$181$	1.74295	−	7.63637i	0.129553	−	0.567607i	−0.867929	−	0.496688i	$-0.834549\pi$
$181$	1.74295	−	7.63637i	0.129553	−	0.567607i	0.997482	−	0.0709196i	$-0.0225934\pi$
$182$	−18.7938	−	9.27794i	−1.39309	−	0.687727i
$183$		0			0
$184$	−8.14650	+	5.55419i	−0.600568	+	0.409460i
$185$	6.46301	−	5.99680i	0.475170	−	0.440893i
$186$		0			0
$187$	−13.3596	−	12.3959i	−0.976953	−	0.906480i
$188$	19.5134	+	24.4690i	1.42316	+	1.78459i
$189$		0			0
$190$	−10.0527	+	12.6057i	−0.729303	+	0.914517i
$191$	−3.05462	+	0.460410i	−0.221024	+	0.0333141i	−0.258621	−	0.965979i	$-0.583268\pi$
$191$	−3.05462	+	0.460410i	−0.221024	+	0.0333141i	0.0375963	+	0.999293i	$0.488030\pi$
$192$		0			0
$193$	−0.231401	+	0.589601i	−0.0166566	+	0.0424404i	−0.938960	−	0.344026i	$-0.888209\pi$
$193$	−0.231401	+	0.589601i	−0.0166566	+	0.0424404i	0.922304	+	0.386466i	$0.126304\pi$
$194$	−4.67650	−	1.44251i	−0.335753	−	0.103566i
$195$		0			0
$196$	−3.82501	−	18.4100i	−0.273215	−	1.31500i
$197$	−12.5847			−0.896624			−0.448312	−	0.893877i	$-0.647975\pi$
$197$	−12.5847			−0.896624			−0.448312	+	0.893877i	$0.647975\pi$
$198$		0			0
$199$	5.77307	−	14.7095i	0.409242	−	1.04273i	−0.566549	−	0.824028i	$-0.691722\pi$
$199$	5.77307	−	14.7095i	0.409242	−	1.04273i	0.975791	−	0.218704i	$-0.0701830\pi$
$200$	0.677467	+	0.461889i	0.0479041	+	0.0326605i
$201$		0			0
$202$	12.2122	−	15.3136i	0.859245	−	1.07746i
$203$	−12.6994	+	11.5544i	−0.891322	+	0.810961i
$204$		0			0
$205$	3.79081	+	3.51736i	0.264762	+	0.245663i
$206$	7.46642	+	1.12538i	0.520210	+	0.0784091i
$207$		0			0
$208$	−6.52144	+	4.44624i	−0.452180	+	0.308291i
$209$	−2.65635	−	11.6382i	−0.183743	−	0.805032i
$210$		0			0
$211$	−3.64883	+	15.9866i	−0.251196	+	1.10056i	0.679186	+	0.733967i	$0.262333\pi$
$211$	−3.64883	+	15.9866i	−0.251196	+	1.10056i	−0.930381	+	0.366593i	$0.880524\pi$
$212$	−8.92406	−	22.7381i	−0.612907	−	1.56166i
$213$		0			0
$214$	2.40349	+	4.16296i	0.164299	+	0.284574i
$215$	−6.69139	+	11.5898i	−0.456349	+	0.790419i
$216$		0			0
$217$	8.45823	−	1.19046i	0.574182	−	0.0808135i
$218$	26.9685	−	12.9873i	1.82654	−	0.879614i
$219$		0			0
$220$	−22.8409	+	7.04549i	−1.53993	+	0.475007i
$221$	16.8751	−	5.20529i	1.13514	−	0.350146i
$222$		0			0
$223$	−15.4604	+	7.44536i	−1.03531	+	0.498578i	−0.872774	−	0.488125i	$-0.837681\pi$
$223$	−15.4604	+	7.44536i	−1.03531	+	0.498578i	−0.162534	+	0.986703i	$0.551967\pi$
$224$	−19.2559	−	6.14637i	−1.28659	−	0.410672i
$225$		0			0
$226$	−14.5396	+	25.1833i	−0.967160	+	1.67517i
$227$	−0.778078	−	1.34767i	−0.0516429	−	0.0894480i	0.839048	−	0.544057i	$-0.183112\pi$
$227$	−0.778078	−	1.34767i	−0.0516429	−	0.0894480i	−0.890691	+	0.454609i	$0.849779\pi$
$228$		0			0
$229$	10.4245	+	26.5611i	0.688869	+	1.75521i	0.654814	+	0.755790i	$0.272747\pi$
$229$	10.4245	+	26.5611i	0.688869	+	1.75521i	0.0340551	+	0.999420i	$0.489158\pi$
$230$	−7.53416	+	33.0093i	−0.496788	+	2.17657i
$231$		0			0
$232$	−2.14489	−	9.39738i	−0.140819	−	0.616968i
$233$	8.54244	−	5.82414i	0.559634	−	0.381552i	−0.250215	−	0.968190i	$-0.580501\pi$
$233$	8.54244	−	5.82414i	0.559634	−	0.381552i	0.809849	+	0.586638i	$0.199549\pi$
$234$		0			0
$235$	27.1468	+	4.09172i	1.77086	+	0.266914i
$236$	10.8759	+	10.0913i	0.707959	+	0.656890i
$237$		0			0
$238$	22.6833	+	15.7921i	1.47034	+	1.02365i
$239$	−4.07948	+	5.11551i	−0.263880	+	0.330895i	−0.896065	−	0.443922i	$-0.853587\pi$
$239$	−4.07948	+	5.11551i	−0.263880	+	0.330895i	0.632185	+	0.774817i	$0.282158\pi$
$240$		0			0
$241$	−12.0684	−	8.22807i	−0.777392	−	0.530017i	0.108396	−	0.994108i	$-0.465429\pi$
$241$	−12.0684	−	8.22807i	−0.777392	−	0.530017i	−0.885787	+	0.464091i	$0.846381\pi$
$242$	2.57993	−	6.57356i	0.165844	−	0.422565i
$243$		0			0
$244$	31.5773			2.02153
$245$	−13.4437	−	9.55591i	−0.858886	−	0.610505i
$246$		0			0
$247$	11.0535	+	3.40956i	0.703320	+	0.216945i
$248$	−1.75196	+	4.46391i	−0.111249	+	0.283459i
$249$		0			0
$250$	−22.4347	+	3.38148i	−1.41889	+	0.213864i
$251$	−4.35204	+	5.45728i	−0.274698	+	0.344461i	−0.899974	−	0.435943i	$-0.856415\pi$
$251$	−4.35204	+	5.45728i	−0.274698	+	0.344461i	0.625276	+	0.780404i	$0.284986\pi$
$252$		0			0
$253$	−15.6297	−	19.5991i	−0.982634	−	1.23218i
$254$	32.2357	+	29.9104i	2.02265	+	1.87674i
$255$		0			0
$256$	−0.175483	+	0.162824i	−0.0109677	+	0.0101765i
$257$	−19.8290	+	13.5192i	−1.23690	+	0.843304i	−0.991999	−	0.126244i	$-0.959708\pi$
$257$	−19.8290	+	13.5192i	−1.23690	+	0.843304i	−0.244900	+	0.969548i	$0.578755\pi$
$258$		0			0
$259$	−2.10848	−	9.67261i	−0.131014	−	0.601027i
$260$	5.15400	−	22.5811i	0.319637	−	1.40042i
$261$		0			0
$262$	−0.959174	−	12.7993i	−0.0592580	−	0.790743i
$263$	−11.1795	−	19.3634i	−0.689355	−	1.19400i	−0.972047	−	0.234787i	$-0.924561\pi$
$263$	−11.1795	−	19.3634i	−0.689355	−	1.19400i	0.282691	−	0.959211i	$-0.408773\pi$
$264$		0			0
$265$	−19.3049	−	9.29673i	−1.18589	−	0.571094i
$266$	6.44919	+	16.9166i	0.395425	+	1.03722i
$267$		0			0
$268$	2.70666	−	36.1179i	0.165336	−	2.20625i
$269$	1.10178	−	0.339853i	0.0671765	−	0.0207212i	−0.260985	−	0.965343i	$-0.584047\pi$
$269$	1.10178	−	0.339853i	0.0671765	−	0.0207212i	0.328161	+	0.944622i	$0.393571\pi$
$270$		0			0
$271$	0.956147	−	12.7589i	0.0580818	−	0.775047i	−0.889785	−	0.456380i	$-0.849146\pi$
$271$	0.956147	−	12.7589i	0.0580818	−	0.775047i	0.947867	−	0.318667i	$-0.103235\pi$
$272$	9.37776	−	4.51609i	0.568610	−	0.273828i
$273$		0			0
$274$	0.656351	+	0.316082i	0.0396516	+	0.0190952i
$275$	−1.04234	+	1.80539i	−0.0628555	+	0.108869i
$276$		0			0
$277$	0.0729498	+	0.973448i	0.00438313	+	0.0584888i	0.998966	−	0.0454535i	$-0.0144733\pi$
$277$	0.0729498	+	0.973448i	0.00438313	+	0.0584888i	−0.994583	+	0.103942i	$0.966854\pi$
$278$	11.3903	+	29.0221i	0.683147	+	1.74063i
$279$		0			0
$280$	8.38180	−	3.93602i	0.500908	−	0.235222i
$281$	0.239885	+	1.05101i	0.0143104	+	0.0626977i	0.981579	−	0.191057i	$-0.0611915\pi$
$281$	0.239885	+	1.05101i	0.0143104	+	0.0626977i	−0.967269	+	0.253755i	$0.918334\pi$
$282$		0			0
$283$	−2.68174	+	2.48829i	−0.159413	+	0.147914i	−0.755847	−	0.654749i	$-0.772774\pi$
$283$	−2.68174	+	2.48829i	−0.159413	+	0.147914i	0.596434	+	0.802662i	$0.296584\pi$
$284$	1.83582	+	0.276706i	0.108936	+	0.0164195i
$285$		0			0
$286$	18.6529	+	23.3900i	1.10297	+	1.38308i
$287$	5.56508	−	1.65722i	0.328496	−	0.0978223i
$288$		0			0
$289$	−6.21793	+	0.937202i	−0.365761	+	0.0551295i
$290$	−27.3488	−	18.6461i	−1.60598	−	1.09494i
$291$		0			0
$292$	−14.7009	−	4.53464i	−0.860307	−	0.265370i
$293$	14.6955			0.858520			0.429260	−	0.903181i	$-0.358774\pi$
$293$	14.6955			0.858520			0.429260	+	0.903181i	$0.358774\pi$
$294$		0			0
$295$	13.0143			0.757724
$296$	5.31097	+	1.63822i	0.308694	+	0.0952195i
$297$		0			0
$298$	26.2290	+	17.8826i	1.51940	+	1.03591i
$299$	24.0197	−	3.62039i	1.38910	−	0.209373i
$300$		0			0
$301$	7.38592	+	13.0865i	0.425718	+	0.754293i
$302$	−26.8736	−	33.6985i	−1.54640	−	1.93913i
$303$		0			0
$304$	6.74164	+	1.01614i	0.386659	+	0.0582795i
$305$	20.3050	−	18.8403i	1.16266	−	1.07879i
$306$		0			0
$307$	−1.33142	−	5.83332i	−0.0759879	−	0.332925i	0.922618	−	0.385716i	$-0.126045\pi$
$307$	−1.33142	−	5.83332i	−0.0759879	−	0.332925i	−0.998606	+	0.0527909i	$0.983188\pi$
$308$	−6.22777	+	26.1069i	−0.354860	+	1.48758i
$309$		0			0
$310$	6.01620	+	15.3290i	0.341697	+	0.870630i
$311$	2.33695	+	31.1845i	0.132516	+	1.76831i	0.527437	+	0.849594i	$0.323153\pi$
$311$	2.33695	+	31.1845i	0.132516	+	1.76831i	−0.394921	+	0.918715i	$0.629228\pi$
$312$		0			0
$313$	4.58928	−	7.94887i	0.259402	−	0.449297i	−0.706680	−	0.707533i	$-0.749808\pi$
$313$	4.58928	−	7.94887i	0.259402	−	0.449297i	0.966082	+	0.258236i	$0.0831413\pi$
$314$	33.3786	+	16.0743i	1.88366	+	0.907125i
$315$		0			0
$316$	−4.15724	+	2.00202i	−0.233863	+	0.112623i
$317$	2.00730	−	26.7856i	0.112741	−	1.50443i	−0.598295	−	0.801276i	$-0.704155\pi$
$317$	2.00730	−	26.7856i	0.112741	−	1.50443i	0.711037	−	0.703155i	$-0.248226\pi$
$318$		0			0
$319$	23.4183	−	7.22359i	1.31117	−	0.404443i
$320$	2.15256	−	28.7239i	0.120332	−	1.60572i
$321$		0			0
$322$	27.6151	+	26.1299i	1.53893	+	1.45616i
$323$	−13.7436	−	6.61855i	−0.764712	−	0.368266i
$324$		0			0
$325$	−1.01003	−	1.74942i	−0.0560263	−	0.0970403i
$326$	3.74423	+	49.9633i	0.207374	+	2.76721i
$327$		0			0
$328$	−0.725401	+	3.17819i	−0.0400535	+	0.175486i
$329$	19.4544	−	23.9119i	1.07256	−	1.31831i
$330$		0			0
$331$	−12.6596	+	8.63118i	−0.695835	+	0.474412i	−0.858861	−	0.512210i	$-0.828827\pi$
$331$	−12.6596	+	8.63118i	−0.695835	+	0.474412i	0.163025	+	0.986622i	$0.447875\pi$
$332$	11.0319	−	10.2361i	0.605454	−	0.561779i
$333$		0			0
$334$	−9.93116	−	9.21477i	−0.543409	−	0.504210i
$335$	−19.8089	−	24.8396i	−1.08228	−	1.35713i
$336$		0			0
$337$	−5.95614	+	7.46876i	−0.324452	+	0.406850i	−0.917129	−	0.398590i	$-0.869500\pi$
$337$	−5.95614	+	7.46876i	−0.324452	+	0.406850i	0.592677	+	0.805440i	$0.298071\pi$
$338$	−0.838202	+	0.126339i	−0.0455922	+	0.00687192i
$339$		0			0
$340$	−11.1590	+	28.4325i	−0.605179	+	1.54197i
$341$	−11.6505	−	3.59372i	−0.630912	−	0.194611i
$342$		0			0
$343$	−16.9146	+	7.54305i	−0.913301	+	0.407286i
$344$	−8.43638			−0.454859
$345$		0			0
$346$	3.87123	−	9.86372i	0.208118	−	0.530277i
$347$	12.2083	+	8.32350i	0.655378	+	0.446829i	0.844811	−	0.535065i	$-0.179713\pi$
$347$	12.2083	+	8.32350i	0.655378	+	0.446829i	−0.189433	+	0.981894i	$0.560665\pi$
$348$		0			0
$349$	21.1658	−	26.5411i	1.13298	−	1.42071i	0.239909	−	0.970795i	$-0.422882\pi$
$349$	21.1658	−	26.5411i	1.13298	−	1.42071i	0.893071	−	0.449916i	$-0.148546\pi$
$350$	1.18376	−	2.93161i	0.0632748	−	0.156701i
$351$		0			0
$352$	21.1500	+	19.6243i	1.12730	+	1.04598i
$353$	−7.87113	−	1.18638i	−0.418938	−	0.0631448i	−0.0638093	−	0.997962i	$-0.520325\pi$
$353$	−7.87113	−	1.18638i	−0.418938	−	0.0631448i	−0.355129	+	0.934817i	$0.615563\pi$
$354$		0			0
$355$	1.34557	−	0.917396i	0.0714156	−	0.0486903i
$356$	−8.41155	−	36.8534i	−0.445811	−	1.95323i
$357$		0			0
$358$	1.16067	−	5.08523i	0.0613433	−	0.268763i
$359$	6.02182	+	15.3433i	0.317820	+	0.809791i	0.997114	+	0.0759247i	$0.0241909\pi$
$359$	6.02182	+	15.3433i	0.317820	+	0.809791i	−0.679294	+	0.733866i	$0.737714\pi$
$360$		0			0
$361$	4.50411	+	7.80134i	0.237058	+	0.410597i
$362$	8.47800	−	14.6843i	0.445594	−	0.771791i
$363$		0			0
$364$	−18.8910	−	17.8750i	−0.990157	−	0.936904i
$365$	−12.1586	+	5.85528i	−0.636411	+	0.306479i
$366$		0			0
$367$	−13.1509	+	4.05651i	−0.686470	+	0.211748i	−0.618319	−	0.785927i	$-0.712186\pi$
$367$	−13.1509	+	4.05651i	−0.686470	+	0.211748i	−0.0681509	+	0.997675i	$0.521710\pi$
$368$	13.6809	−	4.22001i	0.713168	−	0.219983i
$369$		0			0
$370$	17.1957	−	8.28099i	0.893960	−	0.430508i
$371$	−20.0101	+	13.3581i	−1.03887	+	0.693518i
$372$		0			0
$373$	0.833024	−	1.44284i	0.0431324	−	0.0747075i	−0.843653	−	0.536888i	$-0.819600\pi$
$373$	0.833024	−	1.44284i	0.0431324	−	0.0747075i	0.886786	+	0.462181i	$0.152933\pi$
$374$	−19.7260	−	34.1664i	−1.02001	−	1.76670i
$375$		0			0
$376$	6.32273	+	16.1101i	0.326070	+	0.830813i
$377$	−5.28428	+	23.1520i	−0.272154	+	1.19239i
$378$		0			0
$379$	−8.56033	−	37.5052i	−0.439714	−	1.92651i	−0.370256	−	0.928930i	$-0.620730\pi$
$379$	−8.56033	−	37.5052i	−0.439714	−	1.92651i	−0.0694585	−	0.997585i	$-0.522127\pi$
$380$	−16.5304	+	11.2703i	−0.847994	+	0.578152i
$381$		0			0
$382$	−6.61250	−	0.996674i	−0.338325	−	0.0509943i
$383$	−11.0575	−	10.2598i	−0.565010	−	0.524253i	0.345129	−	0.938555i	$-0.387835\pi$
$383$	−11.0575	−	10.2598i	−0.565010	−	0.524253i	−0.910139	+	0.414302i	$0.864026\pi$
$384$		0			0
$385$	11.5718	+	20.5031i	0.589754	+	1.04494i
$386$	−0.854881	+	1.07199i	−0.0435123	+	0.0545627i
$387$		0			0
$388$	−5.01749	−	3.42087i	−0.254724	−	0.173668i
$389$	−12.8976	+	32.8627i	−0.653936	+	1.66620i	0.0883247	+	0.996092i	$0.471849\pi$
$389$	−12.8976	+	32.8627i	−0.653936	+	1.66620i	−0.742261	+	0.670111i	$0.766247\pi$
$390$		0			0
$391$	−32.0330			−1.61998
$392$	0.979511	−	10.3514i	0.0494728	−	0.522823i
$393$		0			0
$394$	−26.0325	−	8.02996i	−1.31150	−	0.404544i
$395$	−1.47872	+	3.76773i	−0.0744027	+	0.189575i
$396$		0			0
$397$	3.08559	−	0.465078i	0.154862	−	0.0233416i	−0.0711539	−	0.997465i	$-0.522668\pi$
$397$	3.08559	−	0.465078i	0.154862	−	0.0233416i	0.226015	+	0.974124i	$0.427430\pi$
$398$	21.3278	−	26.7442i	1.06907	−	1.34057i
$399$		0			0
$400$	−0.742333	−	0.930856i	−0.0371166	−	0.0465428i
$401$	−22.1135	−	20.5183i	−1.10429	−	1.02464i	−0.999546	−	0.0301366i	$-0.990406\pi$
$401$	−22.1135	−	20.5183i	−1.10429	−	1.02464i	−0.104748	−	0.994499i	$-0.533404\pi$
$402$		0			0
$403$	8.66046	−	8.03573i	0.431408	−	0.400288i
$404$	20.0813	−	13.6912i	0.999084	−	0.681164i
$405$		0			0
$406$	−33.6423	+	15.7981i	−1.66964	+	0.784047i
$407$	−3.14440	+	13.7765i	−0.155862	+	0.682877i
$408$		0			0
$409$	0.520814	+	6.94978i	0.0257526	+	0.343644i	0.995166	+	0.0982097i	$0.0313116\pi$
$409$	0.520814	+	6.94978i	0.0257526	+	0.343644i	−0.969413	+	0.245435i	$0.921069\pi$
$410$	5.59726	+	9.69475i	0.276429	+	0.478789i
$411$		0			0
$412$	8.44158	+	4.06525i	0.415887	+	0.200281i
$413$	7.42994	−	12.5834i	0.365604	−	0.619189i
$414$		0			0
$415$	0.986515	−	13.1641i	0.0484261	−	0.646202i
$416$	−26.7154	+	8.24062i	−1.30983	+	0.404030i
$417$		0			0
$418$	1.93116	−	25.7695i	0.0944561	−	1.26043i
$419$	0.699385	−	0.336806i	0.0341672	−	0.0164541i	−0.416722	−	0.909034i	$-0.636821\pi$
$419$	0.699385	−	0.336806i	0.0341672	−	0.0164541i	0.450889	+	0.892580i	$0.351107\pi$
$420$		0			0
$421$	2.60941	+	1.25662i	0.127175	+	0.0612441i	0.496389	−	0.868100i	$-0.334659\pi$
$421$	2.60941	+	1.25662i	0.127175	+	0.0612441i	−0.369214	+	0.929344i	$0.620373\pi$
$422$	−17.7485	+	30.7413i	−0.863982	+	1.49646i
$423$		0			0
$424$	−1.00940	−	13.4695i	−0.0490207	−	0.654136i
$425$	0.973226	+	2.47974i	0.0472084	+	0.120285i
$426$		0			0
$427$	−6.62425	−	30.3887i	−0.320570	−	1.47061i
$428$	1.32729	+	5.81524i	0.0641570	+	0.281090i
$429$		0			0
$430$	−21.2368	+	19.7049i	−1.02413	+	0.950254i
$431$	−13.5941	−	2.04898i	−0.654806	−	0.0986961i	−0.186767	−	0.982404i	$-0.559801\pi$
$431$	−13.5941	−	2.04898i	−0.654806	−	0.0986961i	−0.468039	+	0.883708i	$0.655039\pi$
$432$		0			0
$433$	−6.46716	−	8.10956i	−0.310792	−	0.389721i	0.601763	−	0.798675i	$-0.294465\pi$
$433$	−6.46716	−	8.10956i	−0.310792	−	0.389721i	−0.912555	+	0.408954i	$0.865894\pi$
$434$	18.2561	+	2.93441i	0.876322	+	0.140856i
$435$		0			0
$436$	36.7276	−	5.53579i	1.75893	−	0.265116i
$437$	−17.3363	−	11.8197i	−0.829310	−	0.565414i
$438$		0			0
$439$	22.0973	+	6.81612i	1.05465	+	0.325316i	0.773135	−	0.634242i	$-0.218688\pi$
$439$	22.0973	+	6.81612i	1.05465	+	0.325316i	0.281513	+	0.959558i	$0.409164\pi$
$440$	−13.2176			−0.630124
$441$		0			0
$442$	38.2289			1.81836
$443$	−0.566661	−	0.174792i	−0.0269229	−	0.00830461i	0.281264	−	0.959630i	$-0.409246\pi$
$443$	−0.566661	−	0.174792i	−0.0269229	−	0.00830461i	−0.308187	+	0.951326i	$0.599722\pi$
$444$		0			0
$445$	−27.3971	−	18.6790i	−1.29875	−	0.885469i
$446$	−36.7318	+	5.53643i	−1.73930	+	0.262158i
$447$		0			0
$448$	−26.5439	−	18.4799i	−1.25408	−	0.873093i
$449$	3.27437	+	4.10593i	0.154527	+	0.193771i	0.853069	−	0.521799i	$-0.174739\pi$
$449$	3.27437	+	4.10593i	0.154527	+	0.193771i	−0.698542	+	0.715569i	$0.746167\pi$
$450$		0			0
$451$	−8.19570	−	1.23530i	−0.385921	−	0.0581682i
$452$	−26.4509	+	24.5429i	−1.24415	+	1.15440i
$453$		0			0
$454$	−0.749605	−	3.28424i	−0.0351807	−	0.154137i
$455$	−22.8123	−	0.222947i	−1.06946	−	0.0104519i
$456$		0			0
$457$	1.63194	+	4.15812i	0.0763391	+	0.194509i	0.963949	−	0.266087i	$-0.0857309\pi$
$457$	1.63194	+	4.15812i	0.0763391	+	0.194509i	−0.887610	+	0.460596i	$0.847636\pi$
$458$	4.61594	+	61.5954i	0.215689	+	2.87817i
$459$		0			0
$460$	−21.0067	+	36.3847i	−0.979442	+	1.69644i
$461$	−6.92874	−	3.33671i	−0.322704	−	0.155406i	0.265517	−	0.964106i	$-0.414457\pi$
$461$	−6.92874	−	3.33671i	−0.322704	−	0.155406i	−0.588221	+	0.808700i	$0.700172\pi$
$462$		0			0
$463$	−30.0709	+	14.4814i	−1.39751	+	0.673006i	−0.972655	−	0.232254i	$-0.925390\pi$
$463$	−30.0709	+	14.4814i	−1.39751	+	0.673006i	−0.424857	+	0.905261i	$0.639676\pi$
$464$	−1.04596	+	13.9574i	−0.0485577	+	0.647957i
$465$		0			0
$466$	21.3869	−	6.59700i	0.990731	−	0.305600i
$467$	−0.926085	+	12.3578i	−0.0428541	+	0.571849i	0.933907	+	0.357517i	$0.116376\pi$
$467$	−0.926085	+	12.3578i	−0.0428541	+	0.571849i	−0.976761	+	0.214332i	$0.931243\pi$
$468$		0			0
$469$	−35.3261	+	4.97198i	−1.63121	+	0.229585i
$470$	53.5445	+	25.7857i	2.46982	+	1.18940i
$471$		0			0
$472$	4.10206	+	7.10498i	0.188813	+	0.327033i
$473$	−1.60291	−	21.3893i	−0.0737018	−	0.983482i
$474$		0			0
$475$	−0.388275	+	1.70115i	−0.0178153	+	0.0780539i
$476$	21.1204	+	27.0217i	0.968052	+	1.23854i
$477$		0			0
$478$	−11.7028	+	7.97884i	−0.535274	+	0.364944i
$479$	8.00248	−	7.42522i	0.365643	−	0.339267i	−0.475859	−	0.879522i	$-0.657863\pi$
$479$	8.00248	−	7.42522i	0.365643	−	0.339267i	0.841501	+	0.540255i	$0.181672\pi$
$480$		0			0
$481$	−10.0375	−	9.31344i	−0.457671	−	0.424656i
$482$	−19.7143	−	24.7209i	−0.897961	−	1.12601i
$483$		0			0
$484$	5.46340	−	6.85089i	0.248336	−	0.311404i
$485$	−5.26739	+	0.793932i	−0.239180	+	0.0360506i
$486$		0			0
$487$	1.79986	−	4.58597i	0.0815594	−	0.207810i	−0.884277	−	0.466963i	$-0.845348\pi$
$487$	1.79986	−	4.58597i	0.0815594	−	0.207810i	0.965836	+	0.259153i	$0.0834434\pi$
$488$	16.6856	+	5.14683i	0.755322	+	0.232986i
$489$		0			0
$490$	−21.7120	−	28.3452i	−0.980848	−	1.28051i
$491$	21.8251			0.984954			0.492477	−	0.870326i	$-0.336092\pi$
$491$	21.8251			0.984954			0.492477	+	0.870326i	$0.336092\pi$
$492$		0			0
$493$	11.4410	−	29.1513i	0.515278	−	1.31291i
$494$	20.6896	+	14.1059i	0.930868	+	0.634655i
$495$		0			0
$496$	4.34151	−	5.44409i	0.194940	−	0.244447i
$497$	−0.118827	−	1.82476i	−0.00533010	−	0.0818519i
$498$		0			0
$499$	16.4276	+	15.2426i	0.735400	+	0.682351i	0.956117	−	0.292987i	$-0.0946492\pi$
$499$	16.4276	+	15.2426i	0.735400	+	0.682351i	−0.220717	+	0.975338i	$0.570840\pi$
$500$	−27.8383	−	4.19595i	−1.24497	−	0.187649i
$501$		0			0
$502$	−12.4847	+	8.51191i	−0.557218	+	0.379905i
$503$	−4.71613	−	20.6627i	−0.210282	−	0.921305i	−0.964375	−	0.264538i	$-0.914781\pi$
$503$	−4.71613	−	20.6627i	−0.210282	−	0.921305i	0.754093	−	0.656767i	$-0.228077\pi$
$504$		0			0
$505$	4.74407	−	20.7851i	0.211108	−	0.924925i
$506$	−19.8258	−	50.5152i	−0.881362	−	2.24567i
$507$		0			0
$508$	27.2833	+	47.2560i	1.21050	+	2.09665i
$509$	−2.04832	+	3.54779i	−0.0907900	+	0.157253i	−0.907844	−	0.419309i	$-0.862273\pi$
$509$	−2.04832	+	3.54779i	−0.0907900	+	0.157253i	0.817054	+	0.576561i	$0.195606\pi$
$510$		0			0
$511$	−1.28000	+	15.0988i	−0.0566239	+	0.667933i
$512$	−20.6191	+	9.92964i	−0.911244	+	0.438832i
$513$		0			0
$514$	−49.6441	+	15.3132i	−2.18971	+	0.675436i
$515$	7.85364	−	2.42253i	0.346073	−	0.106749i
$516$		0			0
$517$	−39.6436	+	19.0914i	−1.74352	+	0.839637i
$518$	1.81028	−	21.3539i	0.0795389	−	0.938238i
$519$		0			0
$520$	6.40392	−	11.0919i	0.280831	−	0.486413i
$521$	7.41589	+	12.8447i	0.324896	+	0.562736i	0.981491	−	0.191507i	$-0.0613374\pi$
$521$	7.41589	+	12.8447i	0.324896	+	0.562736i	−0.656595	+	0.754243i	$0.728004\pi$
$522$		0			0
$523$	0.763939	+	1.94648i	0.0334047	+	0.0851138i	0.946603	−	0.322402i	$-0.104490\pi$
$523$	0.763939	+	1.94648i	0.0334047	+	0.0851138i	−0.913198	+	0.407516i	$0.866395\pi$
$524$	3.54402	−	15.5274i	0.154821	−	0.678316i
$525$		0			0
$526$	−10.7704	−	47.1881i	−0.469610	−	2.05750i
$527$	−12.8725	+	8.77633i	−0.560735	+	0.382303i
$528$		0			0
$529$	−20.8264	−	3.13908i	−0.905497	−	0.136482i
$530$	−34.0017	−	31.5489i	−1.47694	−	1.37040i
$531$		0			0
$532$	1.45979	+	22.4173i	0.0632900	+	0.971914i
$533$	5.00746	−	6.27915i	0.216897	−	0.271980i
$534$		0			0
$535$	4.32308	+	2.94743i	0.186903	+	0.127428i
$536$	7.31711	−	18.6437i	0.316051	−	0.805285i
$537$		0			0
$538$	2.49597			0.107609
$539$	26.4306	+	0.516667i	1.13845	+	0.0222544i
$540$		0			0
$541$	5.26699	+	1.62465i	0.226446	+	0.0698493i	0.405902	−	0.913917i	$-0.366958\pi$
$541$	5.26699	+	1.62465i	0.226446	+	0.0698493i	−0.179456	+	0.983766i	$0.557434\pi$
$542$	10.1190	−	25.7827i	0.434647	−	1.10746i
$543$		0			0
$544$	36.4563	−	5.49490i	1.56305	−	0.235592i
$545$	20.3139	−	25.4728i	0.870151	−	1.09113i
$546$		0			0
$547$	−6.15673	−	7.72030i	−0.263243	−	0.330096i	0.632590	−	0.774487i	$-0.281992\pi$
$547$	−6.15673	−	7.72030i	−0.263243	−	0.330096i	−0.895833	+	0.444390i	$0.853420\pi$
$548$	0.662651	+	0.614850i	0.0283070	+	0.0262651i
$549$		0			0
$550$	−3.30813	+	3.06950i	−0.141059	+	0.130884i
$551$	16.9483	−	11.5552i	0.722022	−	0.492267i
$552$		0			0
$553$	2.79876	+	3.58077i	0.119016	+	0.152270i
$554$	−0.470228	+	2.06020i	−0.0199781	+	0.0875296i
$555$		0			0
$556$	2.89106	+	38.5785i	0.122608	+	1.63609i
$557$	−21.1022	−	36.5502i	−0.894131	−	1.54868i	−0.834877	−	0.550437i	$-0.814461\pi$
$557$	−21.1022	−	36.5502i	−0.894131	−	1.54868i	−0.0592538	−	0.998243i	$-0.518872\pi$
$558$		0			0
$559$	18.7261	+	9.01800i	0.792028	+	0.381421i
$560$	−13.3149	+	1.87400i	−0.562655	+	0.0791911i
$561$		0			0
$562$	−0.174396	+	2.32715i	−0.00735645	+	0.0981651i
$563$	−0.932212	+	0.287549i	−0.0392880	+	0.0121188i	−0.314337	−	0.949311i	$-0.601782\pi$
$563$	−0.932212	+	0.287549i	−0.0392880	+	0.0121188i	0.275049	+	0.961430i	$0.411306\pi$
$564$		0			0
$565$	−2.36535	+	31.5633i	−0.0995108	+	1.32788i
$566$	−7.13511	+	3.43609i	−0.299911	+	0.144429i
$567$		0			0
$568$	0.924957	+	0.445436i	0.0388103	+	0.0186901i
$569$	10.9500	−	18.9659i	0.459047	−	0.795092i	−0.539864	−	0.841752i	$-0.681524\pi$
$569$	10.9500	−	18.9659i	0.459047	−	0.795092i	0.998911	+	0.0466601i	$0.0148578\pi$
$570$		0			0
$571$	2.51062	+	33.5019i	0.105066	+	1.40201i	0.761763	+	0.647856i	$0.224334\pi$
$571$	2.51062	+	33.5019i	0.105066	+	1.40201i	−0.656697	+	0.754155i	$0.728047\pi$
$572$	13.5625	+	34.5566i	0.567075	+	1.44488i
$573$		0			0
$574$	12.5692	+	0.122840i	0.524630	+	0.00512725i
$575$	0.815359	+	3.57232i	0.0340028	+	0.148976i
$576$		0			0
$577$	32.6690	−	30.3124i	1.36003	−	1.26192i	0.426003	−	0.904722i	$-0.359921\pi$
$577$	32.6690	−	30.3124i	1.36003	−	1.26192i	0.934027	−	0.357202i	$-0.116269\pi$
$578$	−13.4603	−	2.02881i	−0.559874	−	0.0843875i
$579$		0			0
$580$	−25.6086	−	32.1122i	−1.06334	−	1.33339i
$581$	−12.1650	−	8.46931i	−0.504691	−	0.351366i
$582$		0			0
$583$	33.9583	−	5.11839i	1.40641	−	0.211982i
$584$	−7.02894	−	4.79225i	−0.290860	−	0.198305i
$585$		0			0
$586$	30.3988	+	9.37679i	1.25576	+	0.387352i
$587$	9.00545			0.371695			0.185847	−	0.982579i	$-0.440497\pi$
$587$	9.00545			0.371695			0.185847	+	0.982579i	$0.440497\pi$
$588$		0			0
$589$	−10.2050			−0.420488
$590$	26.9212	+	8.30410i	1.10833	+	0.341874i
$591$		0			0
$592$	−6.66811	−	4.54624i	−0.274058	−	0.186849i
$593$	17.0226	−	2.56575i	0.699036	−	0.105363i	0.210097	−	0.977681i	$-0.432622\pi$
$593$	17.0226	−	2.56575i	0.699036	−	0.105363i	0.488939	+	0.872318i	$0.337384\pi$
$594$		0			0
$595$	29.7032	+	4.77436i	1.21771	+	0.195730i
$596$	24.5600	+	30.7973i	1.00602	+	1.26151i
$597$		0			0
$598$	51.9968	+	7.83726i	2.12631	+	0.320489i
$599$	−9.08028	+	8.42527i	−0.371010	+	0.344247i	−0.843539	−	0.537068i	$-0.819532\pi$
$599$	−9.08028	+	8.42527i	−0.371010	+	0.344247i	0.472529	+	0.881315i	$0.343341\pi$
$600$		0			0
$601$	1.83143	+	8.02401i	0.0747055	+	0.327306i	0.998447	−	0.0557105i	$-0.0177424\pi$
$601$	1.83143	+	8.02401i	0.0747055	+	0.327306i	−0.923741	+	0.383017i	$0.874885\pi$
$602$	6.92824	+	31.7832i	0.282374	+	1.29539i
$603$		0			0
$604$	−19.5397	−	49.7865i	−0.795061	−	2.02578i
$605$	−0.574410	−	7.66497i	−0.0233531	−	0.311625i
$606$		0			0
$607$	10.7963	−	18.6998i	0.438209	−	0.759000i	−0.559342	−	0.828937i	$-0.688946\pi$
$607$	10.7963	−	18.6998i	0.438209	−	0.759000i	0.997551	+	0.0699364i	$0.0222796\pi$
$608$	21.7578	+	10.4780i	0.882394	+	0.424938i
$609$		0			0
$610$	54.0240	−	26.0166i	2.18737	−	1.05338i
$611$	3.18627	−	42.5178i	0.128903	−	1.72009i
$612$		0			0
$613$	−30.9579	+	9.54925i	−1.25038	+	0.385691i	−0.848105	−	0.529829i	$-0.822256\pi$
$613$	−30.9579	+	9.54925i	−1.25038	+	0.385691i	−0.402274	+	0.915519i	$0.631780\pi$
$614$	0.967937	−	12.9162i	0.0390628	−	0.521256i
$615$		0			0
$616$	−7.54598	+	12.7799i	−0.304036	+	0.514918i
$617$	13.0925	+	6.30501i	0.527084	+	0.253830i	0.678449	−	0.734648i	$-0.262653\pi$
$617$	13.0925	+	6.30501i	0.527084	+	0.253830i	−0.151365	+	0.988478i	$0.548367\pi$
$618$		0			0
$619$	12.3152	+	21.3305i	0.494988	+	0.857344i	0.999983	−	0.00577766i	$-0.00183910\pi$
$619$	12.3152	+	21.3305i	0.494988	+	0.857344i	−0.504995	+	0.863122i	$0.668506\pi$
$620$	1.52701	+	20.3766i	0.0613263	+	0.818343i
$621$		0			0
$622$	−15.0638	+	65.9987i	−0.604003	+	2.64631i
$623$	−33.7016	+	15.8260i	−1.35023	+	0.634054i
$624$		0			0
$625$	−22.6847	+	15.4661i	−0.907387	+	0.618646i
$626$	14.5653	−	13.5146i	0.582145	−	0.540152i
$627$		0			0
$628$	33.6990	+	31.2681i	1.34474	+	1.24773i
$629$	11.2583	+	14.1174i	0.448897	+	0.562899i
$630$		0			0
$631$	−18.5002	+	23.1985i	−0.736481	+	0.923518i	−0.999144	−	0.0413694i	$-0.986828\pi$
$631$	−18.5002	+	23.1985i	−0.736481	+	0.923518i	0.262663	+	0.964888i	$0.415399\pi$
$632$	−2.52302	+	0.380284i	−0.100360	+	0.0151269i
$633$		0			0
$634$	21.2434	−	54.1274i	0.843685	−	2.14967i
$635$	45.7386	+	14.1085i	1.81508	+	0.559879i
$636$		0			0
$637$	−13.2392	+	21.9297i	−0.524556	+	0.868885i
$638$	53.0518			2.10034
$639$		0			0
$640$	9.62734	−	24.5301i	0.380554	−	0.969636i
$641$	14.3078	+	9.75491i	0.565125	+	0.385296i	0.811917	−	0.583773i	$-0.198424\pi$
$641$	14.3078	+	9.75491i	0.565125	+	0.385296i	−0.246792	+	0.969069i	$0.579376\pi$
$642$		0			0
$643$	6.28946	−	7.88674i	0.248032	−	0.311022i	−0.642193	−	0.766543i	$-0.721975\pi$
$643$	6.28946	−	7.88674i	0.248032	−	0.311022i	0.890225	+	0.455520i	$0.150547\pi$
$644$	23.1871	+	41.0833i	0.913700	+	1.61891i
$645$		0			0
$646$	−24.2065	−	22.4604i	−0.952393	−	0.883692i
$647$	13.3727	+	2.01560i	0.525734	+	0.0792416i	0.406546	−	0.913630i	$-0.366733\pi$
$647$	13.3727	+	2.01560i	0.525734	+	0.0792416i	0.119187	+	0.992872i	$0.461971\pi$
$648$		0			0
$649$	−17.2344	+	11.7502i	−0.676507	+	0.461235i
$650$	−0.973067	−	4.26329i	−0.0381668	−	0.167220i
$651$		0			0
$652$	−13.8344	+	60.6126i	−0.541798	+	2.37377i
$653$	0.675086	+	1.72009i	0.0264181	+	0.0673123i	0.943474	−	0.331446i	$-0.107536\pi$
$653$	0.675086	+	1.72009i	0.0264181	+	0.0673123i	−0.917056	+	0.398758i	$0.869441\pi$
$654$		0			0
$655$	−6.98536	−	12.0990i	−0.272940	−	0.472747i
$656$	2.36681	−	4.09944i	0.0924085	−	0.160056i
$657$		0			0
$658$	55.5006	−	37.0504i	2.16364	−	1.44438i
$659$	−38.1355	+	18.3651i	−1.48555	+	0.715402i	−0.988345	−	0.152232i	$-0.951354\pi$
$659$	−38.1355	+	18.3651i	−1.48555	+	0.715402i	−0.497203	+	0.867634i	$0.665639\pi$
$660$		0			0
$661$	0.334947	−	0.103318i	0.0130279	−	0.00401859i	−0.288234	−	0.957560i	$-0.593068\pi$
$661$	0.334947	−	0.103318i	0.0130279	−	0.00401859i	0.301262	+	0.953541i	$0.402592\pi$
$662$	−31.6947	+	9.77653i	−1.23185	+	0.379976i
$663$		0			0
$664$	7.49770	−	3.61070i	0.290967	−	0.140122i
$665$	14.3138	+	13.5439i	0.555064	+	0.525211i
$666$		0			0
$667$	21.5377	−	37.3044i	0.833944	−	1.44443i
$668$	−8.40541	−	14.5586i	−0.325215	−	0.563289i
$669$		0			0
$670$	−25.1269	−	64.0222i	−0.970735	−	2.47339i
$671$	−9.87885	+	43.2821i	−0.381369	+	1.67089i
$672$		0			0
$673$	5.01549	+	21.9743i	0.193333	+	0.847047i	0.974796	+	0.223096i	$0.0716164\pi$
$673$	5.01549	+	21.9743i	0.193333	+	0.847047i	−0.781463	+	0.623951i	$0.785526\pi$
$674$	−17.0864	+	11.6493i	−0.658142	+	0.448714i
$675$		0			0
$676$	−1.04009	−	0.156769i	−0.0400036	−	0.00602957i
$677$	−1.13458	−	1.05274i	−0.0436056	−	0.0404601i	0.658069	−	0.752958i	$-0.271373\pi$
$677$	−1.13458	−	1.05274i	−0.0436056	−	0.0404601i	−0.701675	+	0.712498i	$0.747564\pi$
$678$		0			0
$679$	−2.23953	+	5.54624i	−0.0859454	+	0.212845i
$680$	−10.5307	+	13.2051i	−0.403834	+	0.506392i
$681$		0			0
$682$	−21.8070	−	14.8678i	−0.835034	−	0.569317i
$683$	11.0922	−	28.2626i	0.424433	−	1.08144i	−0.545510	−	0.838104i	$-0.683664\pi$
$683$	11.0922	−	28.2626i	0.424433	−	1.08144i	0.969943	−	0.243333i	$-0.0782407\pi$
$684$		0			0
$685$	0.792945			0.0302969
$686$	−39.8021	+	4.81068i	−1.51965	+	0.183672i
$687$		0			0
$688$	11.7059	+	3.61081i	0.446285	+	0.137661i
$689$	−12.1576	+	30.9769i	−0.463166	+	1.18013i
$690$		0			0
$691$	2.74499	−	0.413741i	0.104425	−	0.0157395i	−0.0966221	−	0.995321i	$-0.530804\pi$
$691$	2.74499	−	0.413741i	0.104425	−	0.0157395i	0.201047	+	0.979582i	$0.435566\pi$
$692$	8.19791	−	10.2798i	0.311638	−	0.390781i
$693$		0			0
$694$	19.9429	+	25.0076i	0.757023	+	0.949277i
$695$	24.8765	+	23.0820i	0.943620	+	0.875551i
$696$		0			0
$697$	−7.76380	+	7.20375i	−0.294075	+	0.272862i
$698$	60.7183	−	41.3970i	2.29822	−	1.56690i
$699$		0			0
$700$	2.47587	−	3.04315i	0.0935790	−	0.115020i
$701$	2.86234	−	12.5407i	0.108109	−	0.473657i	−0.891671	−	0.452684i	$-0.850467\pi$
$701$	2.86234	−	12.5407i	0.108109	−	0.473657i	0.999780	−	0.0209728i	$-0.00667635\pi$
$702$		0			0
$703$	0.883878	+	11.7945i	0.0333361	+	0.444839i
$704$	23.0832	+	39.9814i	0.869983	+	1.50685i
$705$		0			0
$706$	−15.5251	−	7.47648i	−0.584294	−	0.281381i
$707$	−17.3885	−	16.4533i	−0.653961	−	0.618790i
$708$		0			0
$709$	1.49816	−	19.9915i	0.0562645	−	0.750798i	−0.895713	−	0.444632i	$-0.853335\pi$
$709$	1.49816	−	19.9915i	0.0562645	−	0.750798i	0.951978	−	0.306166i	$-0.0990464\pi$
$710$	3.36879	−	1.03913i	0.126428	−	0.0389980i
$711$		0			0
$712$	1.56208	−	20.8445i	0.0585415	−	0.781182i
$713$	−19.3077	+	9.29809i	−0.723079	+	0.348216i
$714$		0			0
$715$	29.3388	+	14.1288i	1.09721	+	0.528389i
$716$	3.23617	−	5.60521i	0.120941	−	0.209477i
$717$		0			0
$718$	2.66645	+	35.5813i	0.0995110	+	1.32788i
$719$	2.89840	+	7.38501i	0.108092	+	0.275414i	0.974678	−	0.223614i	$-0.0717855\pi$
$719$	2.89840	+	7.38501i	0.108092	+	0.275414i	−0.866586	+	0.499028i	$0.833690\pi$
$720$		0			0
$721$	2.14136	−	8.97662i	0.0797484	−	0.334307i
$722$	4.33928	+	19.0116i	0.161491	+	0.707540i
$723$		0			0
$724$	15.4234	−	14.3109i	0.573208	−	0.531859i
$725$	−3.54217	−	0.533896i	−0.131553	−	0.0198284i
$726$		0			0
$727$	15.6061	+	19.5694i	0.578796	+	0.725788i	0.981907	−	0.189363i	$-0.0606424\pi$
$727$	15.6061	+	19.5694i	0.578796	+	0.725788i	−0.403111	+	0.915151i	$0.632071\pi$
$728$	−7.06862	−	12.5243i	−0.261981	−	0.464181i
$729$		0			0
$730$	−28.8872	+	4.35404i	−1.06916	+	0.161150i
$731$	−22.6461	−	15.4399i	−0.837598	−	0.571064i
$732$		0			0
$733$	22.4294	+	6.91856i	0.828450	+	0.255543i	0.679847	−	0.733354i	$-0.262046\pi$
$733$	22.4294	+	6.91856i	0.828450	+	0.255543i	0.148603	+	0.988897i	$0.452522\pi$
$734$	−29.7920			−1.09964
$735$		0			0
$736$	50.7123			1.86928
$737$	48.6589	+	15.0093i	1.79237	+	0.552874i
$738$		0			0
$739$	5.55121	+	3.78475i	0.204205	+	0.139224i	0.661105	−	0.750294i	$-0.270088\pi$
$739$	5.55121	+	3.78475i	0.204205	+	0.139224i	−0.456900	+	0.889518i	$0.651040\pi$
$740$	23.4183	−	3.52973i	0.860872	−	0.129756i
$741$		0			0
$742$	−49.9160	+	14.8644i	−1.83247	+	0.545689i
$743$	−1.97850	−	2.48096i	−0.0725842	−	0.0910178i	0.744214	−	0.667942i	$-0.232824\pi$
$743$	−1.97850	−	2.48096i	−0.0725842	−	0.0910178i	−0.816798	+	0.576924i	$0.804253\pi$
$744$		0			0
$745$	34.1676	+	5.14993i	1.25180	+	0.188679i
$746$	2.64382	−	2.45310i	0.0967969	−	0.0898144i
$747$		0			0
$748$	−10.8934	−	47.7270i	−0.398302	−	1.74507i
$749$	5.31790	−	2.49724i	0.194312	−	0.0912471i
$750$		0			0
$751$	−14.2088	−	36.2033i	−0.518485	−	1.32108i	−0.915150	−	0.403114i	$-0.867928\pi$
$751$	−14.2088	−	36.2033i	−0.518485	−	1.32108i	0.396665	−	0.917964i	$-0.370168\pi$
$752$	−1.87797	−	25.0598i	−0.0684825	−	0.913836i
$753$		0			0
$754$	−25.7036	+	44.5199i	−0.936070	+	1.62132i
$755$	−42.2691	−	20.3557i	−1.53833	−	0.740821i
$756$		0			0
$757$	24.6810	−	11.8858i	0.897047	−	0.431995i	0.0722255	−	0.997388i	$-0.476990\pi$
$757$	24.6810	−	11.8858i	0.897047	−	0.431995i	0.824821	+	0.565393i	$0.191276\pi$
$758$	6.22334	−	83.0447i	0.226042	−	3.01632i
$759$		0			0
$760$	−10.5717	+	3.26094i	−0.383476	+	0.118287i
$761$	−0.191179	+	2.55110i	−0.00693022	+	0.0924774i	−0.999596	−	0.0284110i	$-0.990955\pi$
$761$	−0.191179	+	2.55110i	−0.00693022	+	0.0924774i	0.992666	+	0.120888i	$0.0385743\pi$
$762$		0			0
$763$	−13.0321	−	34.1838i	−0.471793	−	1.23754i
$764$	−7.47613	−	3.60032i	−0.270477	−	0.130255i
$765$		0			0
$766$	−16.3267	−	28.2788i	−0.589909	−	1.02175i
$767$	−1.51046	−	20.1557i	−0.0545395	−	0.727779i
$768$		0			0
$769$	4.34030	−	19.0161i	0.156515	−	0.685739i	−0.834390	−	0.551175i	$-0.814180\pi$
$769$	4.34030	−	19.0161i	0.156515	−	0.685739i	0.990905	−	0.134563i	$-0.0429632\pi$
$770$	10.8547	+	49.7960i	0.391178	+	1.79452i
$771$		0			0
$772$	−1.40574	+	0.958418i	−0.0505937	+	0.0344942i
$773$	−27.3523	+	25.3793i	−0.983796	+	0.912829i	−0.996200	−	0.0870942i	$-0.972242\pi$
$773$	−27.3523	+	25.3793i	−0.983796	+	0.912829i	0.0124045	+	0.999923i	$0.496051\pi$
$774$		0			0
$775$	1.30639	+	1.21215i	0.0469269	+	0.0435418i
$776$	−2.09369	−	2.62541i	−0.0751592	−	0.0942466i
$777$		0			0
$778$	−47.6486	+	59.7494i	−1.70828	+	2.14212i
$779$	−6.85987	+	1.03396i	−0.245780	+	0.0370454i
$780$		0			0
$781$	−0.953602	+	2.42974i	−0.0341226	+	0.0869429i
$782$	−66.2629	−	20.4394i	−2.36956	−	0.730911i
$783$		0			0
$784$	−5.78955	+	13.9439i	−0.206770	+	0.497995i
$785$	40.3251			1.43926
$786$		0			0
$787$	−1.48397	+	3.78108i	−0.0528977	+	0.134781i	−0.954880	−	0.296992i	$-0.904017\pi$
$787$	−1.48397	+	3.78108i	−0.0528977	+	0.134781i	0.901982	+	0.431773i	$0.142112\pi$
$788$	−27.9307	−	19.0428i	−0.994988	−	0.678372i
$789$		0			0
$790$	−5.46294	+	6.85032i	−0.194363	+	0.243723i
$791$	29.1678	+	20.3067i	1.03709	+	0.722022i
$792$		0			0
$793$	−31.5351	−	29.2603i	−1.11984	−	1.03906i
$794$	6.67955	+	1.00678i	0.237048	+	0.0357293i
$795$		0			0
$796$	35.0708	−	23.9109i	1.24305	−	0.847499i
$797$	6.72402	+	29.4599i	0.238177	+	1.04352i	0.942648	+	0.333789i	$0.108327\pi$
$797$	6.72402	+	29.4599i	0.238177	+	1.04352i	−0.704471	+	0.709733i	$0.748816\pi$
$798$		0			0
$799$	−12.5115	+	54.8165i	−0.442625	+	1.93927i
$800$	−1.54074	−	3.92574i	−0.0544733	−	0.138796i
$801$		0			0
$802$	−32.6513	−	56.5538i	−1.15296	−	1.99698i
$803$	10.8146	−	18.7315i	0.381640	−	0.661019i
$804$		0			0
$805$	39.4218	+	12.5832i	1.38944	+	0.443500i
$806$	23.0422	−	11.0966i	0.811628	−	0.390859i
$807$		0			0
$808$	12.8426	−	3.96142i	0.451802	−	0.139362i
$809$	−1.85627	+	0.572585i	−0.0652631	+	0.0201310i	−0.327215	−	0.944950i	$-0.606110\pi$
$809$	−1.85627	+	0.572585i	−0.0652631	+	0.0201310i	0.261952	+	0.965081i	$0.415634\pi$
$810$		0			0
$811$	−7.08977	+	3.41425i	−0.248956	+	0.119891i	−0.554201	−	0.832383i	$-0.686976\pi$
$811$	−7.08977	+	3.41425i	−0.248956	+	0.119891i	0.305245	+	0.952274i	$0.401262\pi$
$812$	−45.6689	+	6.42769i	−1.60267	+	0.225568i
$813$		0			0
$814$	−15.2949	+	26.4915i	−0.536085	+	0.928527i
$815$	27.2680	+	47.2296i	0.955157	+	1.65438i
$816$		0			0
$817$	−6.55905	−	16.7122i	−0.229472	−	0.584685i
$818$	−3.35712	+	14.7085i	−0.117379	+	0.514270i
$819$		0			0
$820$	3.09101	+	13.5426i	0.107943	+	0.472928i
$821$	31.0062	−	21.1397i	1.08212	−	0.737780i	0.115328	−	0.993327i	$-0.463208\pi$
$821$	31.0062	−	21.1397i	1.08212	−	0.737780i	0.966797	+	0.255547i	$0.0822557\pi$
$822$		0			0
$823$	42.2134	+	6.36265i	1.47147	+	0.221788i	0.835314	−	0.549774i	$-0.185286\pi$
$823$	42.2134	+	6.36265i	1.47147	+	0.221788i	0.636154	+	0.771562i	$0.280524\pi$
$824$	3.79797	+	3.52400i	0.132309	+	0.122764i
$825$		0			0
$826$	23.3986	−	21.2890i	0.814140	−	0.740738i
$827$	2.73275	−	3.42676i	0.0950271	−	0.119160i	−0.732044	−	0.681257i	$-0.761434\pi$
$827$	2.73275	−	3.42676i	0.0950271	−	0.119160i	0.827072	+	0.562097i	$0.190005\pi$
$828$		0			0
$829$	32.2152	+	21.9640i	1.11888	+	0.762840i	0.973986	−	0.226607i	$-0.0727632\pi$
$829$	32.2152	+	21.9640i	1.11888	+	0.762840i	0.144895	+	0.989447i	$0.453716\pi$
$830$	10.4404	−	26.6016i	0.362390	−	0.923355i
$831$		0			0
$832$	−44.7353			−1.55092
$833$	21.5739	−	25.9940i	0.747492	−	0.900637i
$834$		0			0
$835$	−14.0911	−	4.34654i	−0.487644	−	0.150418i
$836$	11.7151	−	29.8495i	0.405174	−	1.03237i
$837$		0			0
$838$	1.66164	−	0.250452i	0.0574004	−	0.00865172i
$839$	−21.7619	+	27.2886i	−0.751304	+	0.942106i	−0.999647	−	0.0265666i	$-0.991543\pi$
$839$	−21.7619	+	27.2886i	−0.751304	+	0.942106i	0.248343	+	0.968672i	$0.420114\pi$
$840$		0			0
$841$	8.17476	+	10.2508i	0.281888	+	0.353477i
$842$	4.59595	+	4.26442i	0.158387	+	0.146961i
$843$		0			0
$844$	−32.2886	+	29.9594i	−1.11142	+	1.03125i
$845$	−0.762340	+	0.519755i	−0.0262253	+	0.0178801i
$846$		0			0
$847$	−7.73910	−	3.82057i	−0.265919	−	0.131276i
$848$	−4.36440	+	19.1217i	−0.149874	+	0.656641i
$849$		0			0
$850$	0.430942	+	5.75053i	0.0147812	+	0.197241i
$851$	12.4187	+	21.5098i	0.425707	+	0.737346i
$852$		0			0
$853$	−30.4926	−	14.6845i	−1.04405	−	0.502786i	−0.168390	−	0.985720i	$-0.553857\pi$
$853$	−30.4926	−	14.6845i	−1.04405	−	0.502786i	−0.875657	+	0.482934i	$0.839571\pi$
$854$	5.68739	−	67.0882i	0.194618	−	2.29571i
$855$		0			0
$856$	−0.246487	+	3.28914i	−0.00842474	+	0.112420i
$857$	−35.1052	+	10.8285i	−1.19917	+	0.369896i	−0.829096	−	0.559106i	$-0.811144\pi$
$857$	−35.1052	+	10.8285i	−1.19917	+	0.369896i	−0.370076	+	0.929002i	$0.620668\pi$
$858$		0			0
$859$	1.26295	−	16.8528i	0.0430911	−	0.575011i	−0.933314	−	0.359062i	$-0.883097\pi$
$859$	1.26295	−	16.8528i	0.0430911	−	0.575011i	0.976405	−	0.215949i	$-0.0692844\pi$
$860$	−32.3883	+	15.5974i	−1.10443	+	0.531866i
$861$		0			0
$862$	−26.8131	−	12.9125i	−0.913259	−	0.439802i
$863$	−9.62243	+	16.6665i	−0.327551	+	0.567336i	−0.982025	−	0.188749i	$-0.939557\pi$
$863$	−9.62243	+	16.6665i	−0.327551	+	0.567336i	0.654474	+	0.756084i	$0.272890\pi$
$864$		0			0
$865$	−0.861910	−	11.5014i	−0.0293058	−	0.391059i
$866$	−8.20335	−	20.9018i	−0.278761	−	0.710272i
$867$		0			0
$868$	20.5737	+	10.1566i	0.698315	+	0.344738i
$869$	−1.44353	−	6.32453i	−0.0489685	−	0.214545i
$870$		0			0
$871$	−36.1707	+	33.5615i	−1.22560	+	1.13719i
$872$	20.3093	+	3.06114i	0.687760	+	0.103663i
$873$		0			0
$874$	−28.3198	−	35.5119i	−0.957931	−	1.20121i
$875$	1.80188	+	27.6706i	0.0609147	+	0.935438i
$876$		0			0
$877$	1.63035	−	0.245736i	0.0550531	−	0.00829792i	−0.121458	−	0.992597i	$-0.538757\pi$
$877$	1.63035	−	0.245736i	0.0550531	−	0.00829792i	0.176511	+	0.984299i	$0.443519\pi$
$878$	41.3609	+	28.1994i	1.39586	+	0.951683i
$879$		0			0
$880$	18.3402	+	5.65719i	0.618246	+	0.190704i
$881$	−32.1716			−1.08389			−0.541944	−	0.840414i	$-0.682312\pi$
$881$	−32.1716			−1.08389			−0.541944	+	0.840414i	$0.682312\pi$
$882$		0			0
$883$	−56.6986			−1.90806			−0.954030	−	0.299711i	$-0.903110\pi$
$883$	−56.6986			−1.90806			−0.954030	+	0.299711i	$0.903110\pi$
$884$	45.3293	+	13.9822i	1.52459	+	0.470274i
$885$		0			0
$886$	−1.06065	−	0.723142i	−0.0356334	−	0.0242944i
$887$	−39.5759	+	5.96511i	−1.32883	+	0.200289i	−0.774799	−	0.632208i	$-0.782149\pi$
$887$	−39.5759	+	5.96511i	−1.32883	+	0.200289i	−0.554030	+	0.832496i	$0.686911\pi$
$888$		0			0
$889$	39.7537	−	36.1696i	1.33330	−	1.21309i
$890$	−44.7545	−	56.1203i	−1.50017	−	1.88116i
$891$		0			0
$892$	−45.5791	−	6.86995i	−1.52610	−	0.230023i
$893$	−26.9977	+	25.0502i	−0.903445	+	0.838275i
$894$		0			0
$895$	−1.26336	−	5.53512i	−0.0422293	−	0.185019i
$896$	−18.2215	−	23.3129i	−0.608739	−	0.778829i
$897$		0			0
$898$	4.15342	+	10.5827i	0.138601	+	0.353150i
$899$	−1.56562	−	20.8917i	−0.0522162	−	0.696777i
$900$		0			0
$901$	21.9417	−	38.0041i	0.730983	−	1.26610i
$902$	−16.1653	−	7.78478i	−0.538244	−	0.259205i
$903$		0			0
$904$	−17.9771	+	8.65730i	−0.597908	+	0.287937i
$905$	1.37923	−	18.4045i	0.0458470	−	0.611786i
$906$		0			0
$907$	−27.7572	+	8.56197i	−0.921664	+	0.284296i	−0.719046	−	0.694962i	$-0.755421\pi$
$907$	−27.7572	+	8.56197i	−0.921664	+	0.284296i	−0.202618	+	0.979258i	$0.564945\pi$
$908$	0.312378	−	4.16840i	0.0103666	−	0.138333i
$909$		0			0
$910$	−47.0468	−	15.0171i	−1.55959	−	0.497812i
$911$	−3.39064	−	1.63285i	−0.112337	−	0.0540986i	0.376871	−	0.926266i	$-0.377000\pi$
$911$	−3.39064	−	1.63285i	−0.112337	−	0.0540986i	−0.489208	+	0.872167i	$0.662714\pi$
$912$		0			0
$913$	10.5790	+	18.3234i	0.350114	+	0.606416i
$914$	0.722621	+	9.64271i	0.0239022	+	0.318953i
$915$		0			0
$916$	−17.0553	+	74.7241i	−0.563523	+	2.46895i
$917$	−15.6863	−	0.153304i	−0.518009	−	0.00506254i
$918$		0			0
$919$	−0.452101	+	0.308237i	−0.0149134	+	0.0101678i	−0.570754	−	0.821121i	$-0.693349\pi$
$919$	−0.452101	+	0.308237i	−0.0149134	+	0.0101678i	0.555840	+	0.831289i	$0.312397\pi$
$920$	−17.0304	+	15.8019i	−0.561476	+	0.520974i
$921$		0			0
$922$	−12.2036	−	11.3233i	−0.401904	−	0.372913i
$923$	−1.57696	−	1.97745i	−0.0519064	−	0.0650886i
$924$		0			0
$925$	1.28781	−	1.61486i	0.0423430	−	0.0530964i
$926$	−71.4442	+	10.7685i	−2.34780	+	0.353874i
$927$		0			0
$928$	−18.1126	+	46.1501i	−0.594575	+	1.51495i
$929$	46.0597	+	14.2075i	1.51117	+	0.466134i	0.936030	−	0.351921i	$-0.114472\pi$
$929$	46.0597	+	14.2075i	1.51117	+	0.466134i	0.575140	+	0.818055i	$0.304948\pi$
$930$		0			0
$931$	21.2672	−	6.10752i	0.697006	−	0.200166i
$932$	27.7721			0.909705
$933$		0			0
$934$	−9.80082	+	24.9721i	−0.320693	+	0.817112i
$935$	−35.4806	−	24.1902i	−1.16034	−	0.791105i
$936$		0			0
$937$	−6.00647	+	7.53188i	−0.196223	+	0.246056i	−0.870202	−	0.492694i	$-0.836012\pi$
$937$	−6.00647	+	7.53188i	−0.196223	+	0.246056i	0.673980	+	0.738750i	$0.264584\pi$
$938$	−76.2473	−	12.2557i	−2.48956	−	0.400162i
$939$		0			0
$940$	54.0584	+	50.1589i	1.76319	+	1.63600i
$941$	20.8448	+	3.14185i	0.679521	+	0.102421i	0.479729	−	0.877417i	$-0.340735\pi$
$941$	20.8448	+	3.14185i	0.679521	+	0.102421i	0.199793	+	0.979838i	$0.435973\pi$
$942$		0			0
$943$	−12.0367	+	8.20649i	−0.391969	+	0.267240i
$944$	−2.65088	−	11.6143i	−0.0862787	−	0.378012i
$945$		0			0
$946$	10.3322	−	45.2683i	0.335929	−	1.47180i
$947$	11.2554	+	28.6782i	0.365751	+	0.931917i	0.988734	+	0.149682i	$0.0478251\pi$
$947$	11.2554	+	28.6782i	0.365751	+	0.931917i	−0.622983	+	0.782235i	$0.714080\pi$
$948$		0			0
$949$	10.4794	+	18.1508i	0.340175	+	0.589200i
$950$	−1.88863	+	3.27121i	−0.0612754	+	0.106132i
$951$		0			0
$952$	6.75582	+	17.7208i	0.218957	+	0.574336i
$953$	−30.5517	+	14.7129i	−0.989668	+	0.476599i	−0.857420	−	0.514618i	$-0.827934\pi$
$953$	−30.5517	+	14.7129i	−0.989668	+	0.476599i	−0.132248	+	0.991217i	$0.542220\pi$
$954$		0			0
$955$	−6.95543	+	2.14547i	−0.225072	+	0.0694257i
$956$	−16.7947	+	5.18047i	−0.543179	+	0.167548i
$957$		0			0
$958$	21.2916	−	10.2535i	0.687900	−	0.331275i
$959$	0.452695	−	0.766689i	0.0146183	−	0.0247577i
$960$		0			0
$961$	10.2886	−	17.8205i	0.331892	−	0.574854i
$962$	−14.8207	−	25.6703i	−0.477840	−	0.827643i
$963$		0			0
$964$	−14.3342	−	36.5229i	−0.461673	−	1.17632i
$965$	−0.332096	+	1.45501i	−0.0106905	+	0.0468383i
$966$		0			0
$967$	−4.25791	−	18.6551i	−0.136925	−	0.599908i	−0.996100	−	0.0882269i	$-0.971880\pi$
$967$	−4.25791	−	18.6551i	−0.136925	−	0.599908i	0.859175	−	0.511681i	$-0.170977\pi$
$968$	4.00352	−	2.72955i	0.128678	−	0.0877312i
$969$		0			0
$970$	−11.4026	−	1.71867i	−0.366116	−	0.0551831i
$971$	33.7597	+	31.3244i	1.08340	+	1.00525i	0.999962	+	0.00873585i	$0.00278074\pi$
$971$	33.7597	+	31.3244i	1.08340	+	1.00525i	0.0834387	+	0.996513i	$0.473410\pi$
$972$		0			0
$973$	36.5198	−	10.8752i	1.17077	−	0.348642i
$974$	6.64933	−	8.33800i	0.213058	−	0.267167i
$975$		0			0
$976$	−20.9494	−	14.2830i	−0.670573	−	0.457189i
$977$	−10.2461	+	26.1066i	−0.327802	+	0.835225i	0.668040	+	0.744125i	$0.267133\pi$
$977$	−10.2461	+	26.1066i	−0.327802	+	0.835225i	−0.995842	+	0.0910995i	$0.970962\pi$
$978$		0			0
$979$	53.1454			1.69853
$980$	−15.3774	−	41.5511i	−0.491212	−	1.32730i
$981$		0			0
$982$	45.1470	+	13.9260i	1.44070	+	0.444397i
$983$	5.33136	−	13.5841i	0.170044	−	0.433265i	−0.820294	−	0.571943i	$-0.806190\pi$
$983$	5.33136	−	13.5841i	0.170044	−	0.433265i	0.990338	+	0.138678i	$0.0442852\pi$
$984$		0			0
$985$	−29.3218	+	4.41955i	−0.934270	+	0.140819i
$986$	42.2673	−	53.0016i	1.34607	−	1.68791i
$987$		0			0
$988$	19.3731	+	24.2931i	0.616340	+	0.772866i
$989$	−27.6367	−	25.6431i	−0.878796	−	0.815403i
$990$		0			0
$991$	8.55383	−	7.93679i	0.271721	−	0.252121i	−0.532528	−	0.846412i	$-0.678758\pi$
$991$	8.55383	−	7.93679i	0.271721	−	0.252121i	0.804250	+	0.594292i	$0.202568\pi$
$992$	20.3788	−	13.8940i	0.647027	−	0.441136i
$993$		0			0
$994$	0.918530	−	3.85049i	0.0291340	−	0.122130i
$995$	8.28523	−	36.3000i	0.262659	−	1.15079i
$996$		0			0
$997$	−2.04425	−	27.2786i	−0.0647421	−	0.863923i	−0.931162	−	0.364606i	$-0.881204\pi$
$997$	−2.04425	−	27.2786i	−0.0647421	−	0.863923i	0.866420	−	0.499316i	$-0.166415\pi$
$998$	24.2559	+	42.0125i	0.767808	+	1.32988i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.100.4		48
3.2	odd	2		147.2.m.a.100.1	yes	48
49.25	even	21	inner	441.2.bb.c.172.4		48
147.5	even	42		7203.2.a.k.1.5		24
147.44	odd	42		7203.2.a.i.1.5		24
147.74	odd	42		147.2.m.a.25.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.25.1	✓	48	147.74	odd	42
147.2.m.a.100.1	yes	48	3.2	odd	2
441.2.bb.c.100.4		48	1.1	even	1	trivial
441.2.bb.c.172.4		48	49.25	even	21	inner
7203.2.a.i.1.5		24	147.44	odd	42
7203.2.a.k.1.5		24	147.5	even	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)

\(f(q)\)	\(=\)	\(q+(2.06858 + 0.638073i) q^{2} +(2.21941 + 1.51317i) q^{4} +(2.32995 - 0.351184i) q^{5} +(0.990624 - 2.45330i) q^{7} +(0.926114 + 1.16131i) q^{8} +O(q^{10})\)	\(q+(2.06858 + 0.638073i) q^{2} +(2.21941 + 1.51317i) q^{4} +(2.32995 - 0.351184i) q^{5} +(0.990624 - 2.45330i) q^{7} +(0.926114 + 1.16131i) q^{8} +(5.04378 + 0.760227i) q^{10} +(-2.76839 + 2.56869i) q^{11} +(-0.814304 - 3.56770i) q^{13} +(3.61457 - 4.44275i) q^{14} +(-0.787989 - 2.00776i) q^{16} +(0.360631 + 4.81229i) q^{17} +(-1.58049 + 2.73749i) q^{19} +(5.70252 + 2.74619i) q^{20} +(-7.36564 + 3.54711i) q^{22} +(-0.496051 + 6.61934i) q^{23} +(0.527486 - 0.162708i) q^{25} +(0.591998 - 7.89966i) q^{26} +(5.91085 - 3.94589i) q^{28} +(-5.84668 - 2.81561i) q^{29} +(1.61421 + 2.79589i) q^{31} +(-0.570924 - 7.61845i) q^{32} +(-2.32459 + 10.1847i) q^{34} +(1.44655 - 6.06396i) q^{35} +(3.09158 - 2.10780i) q^{37} +(-5.01609 + 4.65425i) q^{38} +(2.56563 + 2.38056i) q^{40} +(1.36836 + 1.71587i) q^{41} +(-3.54120 + 4.44052i) q^{43} +(-10.0310 + 1.51194i) q^{44} +(-5.24974 + 13.3761i) q^{46} +(11.1336 + 3.43426i) q^{47} +(-5.03733 - 4.86059i) q^{49} +1.19497 q^{50} +(3.59126 - 9.15037i) q^{52} +(-7.51342 - 5.12256i) q^{53} +(-5.54813 + 6.95714i) q^{55} +(3.76647 - 1.12161i) q^{56} +(-10.2978 - 9.55492i) q^{58} +(5.46159 + 0.823202i) q^{59} +(9.71290 - 6.62214i) q^{61} +(1.55514 + 6.81352i) q^{62} +(2.72023 - 11.9181i) q^{64} +(-3.15021 - 8.02660i) q^{65} +(-6.74180 - 11.6771i) q^{67} +(-6.48141 + 11.2261i) q^{68} +(6.86155 - 11.6208i) q^{70} +(0.622711 - 0.299882i) q^{71} +(-5.47284 + 1.68815i) q^{73} +(7.74012 - 2.38751i) q^{74} +(-7.65004 + 3.68406i) q^{76} +(3.55932 + 9.33628i) q^{77} +(-0.858882 + 1.48763i) q^{79} +(-2.54107 - 4.40127i) q^{80} +(1.73572 + 4.42254i) q^{82} +(1.24668 - 5.46205i) q^{83} +(2.53025 + 11.0858i) q^{85} +(-10.1586 + 6.92604i) q^{86} +(-5.54689 - 0.836058i) q^{88} +(-10.3159 - 9.57177i) q^{89} +(-9.55930 - 1.53652i) q^{91} +(-11.1171 + 13.9404i) q^{92} +(20.8394 + 14.2081i) q^{94} +(-2.72110 + 6.93326i) q^{95} -2.26073 q^{97} +(-7.31871 - 13.2687i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

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