LMFDB - Embedded newform 567.2.bd.a.17.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(17,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 3]))

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

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

chi := DirichletCharacter("567.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bd (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.13
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.313923 - 0.0553531i) q^{2} +(-1.78390 + 0.649287i) q^{4} +(2.68563 - 0.977491i) q^{5} +(-2.48320 - 0.913082i) q^{7} +(-1.07619 + 0.621337i) q^{8} +O(q^{10})$	\(q+(0.313923 - 0.0553531i) q^{2} +(-1.78390 + 0.649287i) q^{4} +(2.68563 - 0.977491i) q^{5} +(-2.48320 - 0.913082i) q^{7} +(-1.07619 + 0.621337i) q^{8} +(0.788975 - 0.455515i) q^{10} +(1.16543 - 3.20200i) q^{11} +(-1.17022 - 3.21516i) q^{13} +(-0.830076 - 0.149185i) q^{14} +(2.60505 - 2.18590i) q^{16} +(-2.33161 - 4.03847i) q^{17} +(4.78098 + 2.76030i) q^{19} +(-4.15623 + 3.48749i) q^{20} +(0.188615 - 1.06969i) q^{22} +(1.35415 + 0.238774i) q^{23} +(2.42692 - 2.03643i) q^{25} +(-0.545329 - 0.944538i) q^{26} +(5.02264 + 0.0165384i) q^{28} +(2.81504 - 7.73427i) q^{29} +(0.756904 + 2.07958i) q^{31} +(2.29434 - 2.73429i) q^{32} +(-0.955489 - 1.13871i) q^{34} +(-7.56149 - 0.0248983i) q^{35} -1.76484 q^{37} +(1.65365 + 0.601880i) q^{38} +(-2.28289 + 2.72064i) q^{40} +(-4.96713 + 1.80789i) q^{41} +(-1.57831 - 8.95103i) q^{43} +6.46875i q^{44} +0.438317 q^{46} +(-2.87974 - 1.04814i) q^{47} +(5.33256 + 4.53473i) q^{49} +(0.649143 - 0.773618i) q^{50} +(4.17513 + 4.97572i) q^{52} +(-1.30996 - 0.756305i) q^{53} -9.73859i q^{55} +(3.23972 - 0.560257i) q^{56} +(0.455592 - 2.58379i) q^{58} +(5.25805 + 4.41203i) q^{59} +(3.36646 - 9.24926i) q^{61} +(0.352721 + 0.610930i) q^{62} +(-2.83176 + 4.90475i) q^{64} +(-6.28558 - 7.49087i) q^{65} +(-1.66553 + 9.44568i) q^{67} +(6.78150 + 5.69035i) q^{68} +(-2.37511 + 0.410736i) q^{70} +(9.64722 + 5.56983i) q^{71} -5.91133i q^{73} +(-0.554024 + 0.0976893i) q^{74} +(-10.3210 - 1.81988i) q^{76} +(-5.81769 + 6.88707i) q^{77} +(1.98492 + 11.2570i) q^{79} +(4.85952 - 8.41694i) q^{80} +(-1.45922 + 0.842484i) q^{82} +(-6.72578 - 2.44798i) q^{83} +(-10.2094 - 8.56673i) q^{85} +(-0.990935 - 2.72257i) q^{86} +(0.735296 + 4.17007i) q^{88} +(-6.12929 + 10.6162i) q^{89} +(-0.0298075 + 9.05240i) q^{91} +(-2.57071 + 0.453286i) q^{92} +(-0.962036 - 0.169633i) q^{94} +(15.5381 + 2.73979i) q^{95} +(-2.47531 + 0.436465i) q^{97} +(1.92503 + 1.12838i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	0.313923	−	0.0553531i	0.221977	−	0.0391406i	−0.0615533	−	0.998104i	$-0.519605\pi$
$2$	0.313923	−	0.0553531i	0.221977	−	0.0391406i	0.283530	+	0.958963i	$0.408494\pi$
$3$		0			0
$3$		0			0
$4$	−1.78390	+	0.649287i	−0.891951	+	0.324644i
$5$	2.68563	−	0.977491i	1.20105	−	0.437147i	0.337461	−	0.941340i	$-0.390432\pi$
$5$	2.68563	−	0.977491i	1.20105	−	0.437147i	0.863591	+	0.504193i	$0.168210\pi$
$6$		0			0
$7$	−2.48320	−	0.913082i	−0.938561	−	0.345112i
$7$	−2.48320	−	0.913082i	−0.938561	−	0.345112i
$8$	−1.07619	+	0.621337i	−0.380489	+	0.219676i
$9$		0			0
$10$	0.788975	−	0.455515i	0.249496	−	0.144047i
$11$	1.16543	−	3.20200i	0.351391	−	0.965439i	−0.630533	−	0.776162i	$-0.717164\pi$
$11$	1.16543	−	3.20200i	0.351391	−	0.965439i	0.981924	−	0.189276i	$-0.0606141\pi$
$12$		0			0
$13$	−1.17022	−	3.21516i	−0.324562	−	0.891726i	−0.989462	−	0.144794i	$-0.953748\pi$
$13$	−1.17022	−	3.21516i	−0.324562	−	0.891726i	0.664900	−	0.746932i	$-0.268474\pi$
$14$	−0.830076	−	0.149185i	−0.221847	−	0.0398713i
$15$		0			0
$16$	2.60505	−	2.18590i	0.651263	−	0.546475i
$17$	−2.33161	−	4.03847i	−0.565499	−	0.979474i	−0.997003	−	0.0773624i	$-0.975350\pi$
$17$	−2.33161	−	4.03847i	−0.565499	−	0.979474i	0.431504	−	0.902111i	$-0.357983\pi$
$18$		0			0
$19$	4.78098	+	2.76030i	1.09683	+	0.633256i	0.935387	−	0.353625i	$-0.115051\pi$
$19$	4.78098	+	2.76030i	1.09683	+	0.633256i	0.161445	+	0.986882i	$0.448385\pi$
$20$	−4.15623	+	3.48749i	−0.929362	+	0.779827i
$21$		0			0
$22$	0.188615	−	1.06969i	0.0402129	−	0.228059i
$23$	1.35415	+	0.238774i	0.282361	+	0.0497878i	0.313035	−	0.949742i	$-0.398654\pi$
$23$	1.35415	+	0.238774i	0.282361	+	0.0497878i	−0.0306742	+	0.999529i	$0.509765\pi$
$24$		0			0
$25$	2.42692	−	2.03643i	0.485383	−	0.407285i
$26$	−0.545329	−	0.944538i	−0.106948	−	0.185239i
$27$		0			0
$28$	5.02264	+	0.0165384i	0.949189	+	0.00312546i
$29$	2.81504	−	7.73427i	0.522741	−	1.43622i	−0.344717	−	0.938707i	$-0.612025\pi$
$29$	2.81504	−	7.73427i	0.522741	−	1.43622i	0.867458	−	0.497511i	$-0.165753\pi$
$30$		0			0
$31$	0.756904	+	2.07958i	0.135944	+	0.373503i	0.988920	−	0.148446i	$-0.0474272\pi$
$31$	0.756904	+	2.07958i	0.135944	+	0.373503i	−0.852977	+	0.521949i	$0.825205\pi$
$32$	2.29434	−	2.73429i	0.405586	−	0.483358i
$33$		0			0
$34$	−0.955489	−	1.13871i	−0.163865	−	0.195287i
$35$	−7.56149	−	0.0248983i	−1.27813	−	0.00420858i
$36$		0			0
$37$	−1.76484			−0.290138			−0.145069	−	0.989422i	$-0.546340\pi$
$37$	−1.76484			−0.290138			−0.145069	+	0.989422i	$0.546340\pi$
$38$	1.65365	+	0.601880i	0.268258	+	0.0976378i
$39$		0			0
$40$	−2.28289	+	2.72064i	−0.360957	+	0.430172i
$41$	−4.96713	+	1.80789i	−0.775735	+	0.282344i	−0.699393	−	0.714737i	$-0.746546\pi$
$41$	−4.96713	+	1.80789i	−0.775735	+	0.282344i	−0.0763420	+	0.997082i	$0.524324\pi$
$42$		0			0
$43$	−1.57831	−	8.95103i	−0.240690	−	1.36502i	−0.830293	−	0.557327i	$-0.811827\pi$
$43$	−1.57831	−	8.95103i	−0.240690	−	1.36502i	0.589603	−	0.807693i	$-0.299284\pi$
$44$			6.46875i			0.975200i
$45$		0			0
$46$	0.438317			0.0646263
$47$	−2.87974	−	1.04814i	−0.420054	−	0.152887i	0.123341	−	0.992364i	$-0.460639\pi$
$47$	−2.87974	−	1.04814i	−0.420054	−	0.152887i	−0.543395	+	0.839477i	$0.682861\pi$
$48$		0			0
$49$	5.33256	+	4.53473i	0.761795	+	0.647818i
$50$	0.649143	−	0.773618i	0.0918027	−	0.109406i
$51$		0			0
$52$	4.17513	+	4.97572i	0.578986	+	0.690009i
$53$	−1.30996	−	0.756305i	−0.179937	−	0.103886i	0.407326	−	0.913283i	$-0.366461\pi$
$53$	−1.30996	−	0.756305i	−0.179937	−	0.103886i	−0.587263	+	0.809396i	$0.699795\pi$
$54$		0			0
$55$		−	9.73859i		−	1.31315i
$56$	3.23972	−	0.560257i	0.432925	−	0.0748675i
$57$		0			0
$58$	0.455592	−	2.58379i	0.0598221	−	0.339268i
$59$	5.25805	+	4.41203i	0.684540	+	0.574397i	0.917329	−	0.398130i	$-0.130341\pi$
$59$	5.25805	+	4.41203i	0.684540	+	0.574397i	−0.232789	+	0.972527i	$0.574785\pi$
$60$		0			0
$61$	3.36646	−	9.24926i	0.431031	−	1.18425i	−0.514150	−	0.857700i	$-0.671893\pi$
$61$	3.36646	−	9.24926i	0.431031	−	1.18425i	0.945181	−	0.326547i	$-0.105885\pi$
$62$	0.352721	+	0.610930i	0.0447956	+	0.0775882i
$63$		0			0
$64$	−2.83176	+	4.90475i	−0.353970	+	0.613094i
$65$	−6.28558	−	7.49087i	−0.779631	−	0.929128i
$66$		0			0
$67$	−1.66553	+	9.44568i	−0.203477	+	1.15397i	0.696342	+	0.717710i	$0.254810\pi$
$67$	−1.66553	+	9.44568i	−0.203477	+	1.15397i	−0.899819	+	0.436264i	$0.856302\pi$
$68$	6.78150	+	5.69035i	0.822377	+	0.690056i
$69$		0			0
$70$	−2.37511	+	0.410736i	−0.283879	+	0.0490924i
$71$	9.64722	+	5.56983i	1.14491	+	0.661017i	0.947643	−	0.319332i	$-0.103459\pi$
$71$	9.64722	+	5.56983i	1.14491	+	0.661017i	0.197272	+	0.980349i	$0.436792\pi$
$72$		0			0
$73$		−	5.91133i		−	0.691869i	−0.938259	−	0.345935i	$-0.887562\pi$
$73$		−	5.91133i		−	0.691869i	0.938259	−	0.345935i	$-0.112438\pi$
$74$	−0.554024	+	0.0976893i	−0.0644040	+	0.0113562i
$75$		0			0
$76$	−10.3210	−	1.81988i	−1.18390	−	0.208754i
$77$	−5.81769	+	6.88707i	−0.662987	+	0.784854i
$78$		0			0
$79$	1.98492	+	11.2570i	0.223321	+	1.26652i	0.865869	+	0.500271i	$0.166766\pi$
$79$	1.98492	+	11.2570i	0.223321	+	1.26652i	−0.642548	+	0.766245i	$0.722123\pi$
$80$	4.85952	−	8.41694i	0.543311	−	0.941042i
$81$		0			0
$82$	−1.45922	+	0.842484i	−0.161144	+	0.0930367i
$83$	−6.72578	−	2.44798i	−0.738250	−	0.268701i	−0.0545974	−	0.998508i	$-0.517388\pi$
$83$	−6.72578	−	2.44798i	−0.738250	−	0.268701i	−0.683653	+	0.729807i	$0.739610\pi$
$84$		0			0
$85$	−10.2094	−	8.56673i	−1.10737	−	0.929192i
$86$	−0.990935	−	2.72257i	−0.106855	−	0.293582i
$87$		0			0
$88$	0.735296	+	4.17007i	0.0783828	+	0.444531i
$89$	−6.12929	+	10.6162i	−0.649703	+	1.12532i	0.333491	+	0.942753i	$0.391773\pi$
$89$	−6.12929	+	10.6162i	−0.649703	+	1.12532i	−0.983194	+	0.182565i	$0.941560\pi$
$90$		0			0
$91$	−0.0298075	+	9.05240i	−0.00312467	+	0.948949i
$92$	−2.57071	+	0.453286i	−0.268015	+	0.0472583i
$93$		0			0
$94$	−0.962036	−	0.169633i	−0.0992265	−	0.0174963i
$95$	15.5381	+	2.73979i	1.59418	+	0.281097i
$96$		0			0
$97$	−2.47531	+	0.436465i	−0.251330	+	0.0443163i	−0.297894	−	0.954599i	$-0.596284\pi$
$97$	−2.47531	+	0.436465i	−0.251330	+	0.0443163i	0.0465636	+	0.998915i	$0.485173\pi$
$98$	1.92503	+	1.12838i	0.194457	+	0.113984i
$99$		0			0
$100$	−3.00716	+	5.20855i	−0.300716	+	0.520855i
$101$	−1.61753	−	9.17347i	−0.160950	−	0.912795i	−0.953142	−	0.302523i	$-0.902171\pi$
$101$	−1.61753	−	9.17347i	−0.160950	−	0.912795i	0.792192	−	0.610272i	$-0.208940\pi$
$102$		0			0
$103$	3.85481	+	10.5910i	0.379825	+	1.04356i	0.971429	+	0.237332i	$0.0762730\pi$
$103$	3.85481	+	10.5910i	0.379825	+	1.04356i	−0.591603	+	0.806229i	$0.701505\pi$
$104$	3.25708	+	2.73301i	0.319383	+	0.267994i
$105$		0			0
$106$	−0.453090	−	0.164911i	−0.0440080	−	0.0160176i
$107$	5.79854	−	3.34779i	0.560566	−	0.323643i	−0.192807	−	0.981237i	$-0.561759\pi$
$107$	5.79854	−	3.34779i	0.560566	−	0.323643i	0.753373	+	0.657594i	$0.228426\pi$
$108$		0			0
$109$	−8.30492	+	14.3845i	−0.795467	+	1.37779i	0.127076	+	0.991893i	$0.459441\pi$
$109$	−8.30492	+	14.3845i	−0.795467	+	1.37779i	−0.922542	+	0.385896i	$0.873892\pi$
$110$	−0.539061	−	3.05717i	−0.0513975	−	0.291490i
$111$		0			0
$112$	−8.46477	+	3.04940i	−0.799846	+	0.288141i
$113$	−10.4246	−	1.83814i	−0.980666	−	0.172918i	−0.339739	−	0.940520i	$-0.610339\pi$
$113$	−10.4246	−	1.83814i	−0.980666	−	0.172918i	−0.640927	+	0.767602i	$0.721450\pi$
$114$		0			0
$115$	3.87016	−	0.682414i	0.360894	−	0.0636354i
$116$			15.6249i			1.45074i
$117$		0			0
$118$	1.89484	+	1.09399i	0.174434	+	0.100710i
$119$	2.10241	+	12.1573i	0.192727	+	1.11446i
$120$		0			0
$121$	−0.468067	−	0.392755i	−0.0425516	−	0.0357050i
$122$	0.544833	−	3.08990i	0.0493269	−	0.279747i
$123$		0			0
$124$	−2.70048	−	3.21831i	−0.242511	−	0.289013i
$125$	−2.61776	+	4.53409i	−0.234139	+	0.405541i
$126$		0			0
$127$	8.48685	+	14.6997i	0.753086	+	1.30438i	0.946320	+	0.323231i	$0.104769\pi$
$127$	8.48685	+	14.6997i	0.753086	+	1.30438i	−0.193234	+	0.981153i	$0.561898\pi$
$128$	−3.05905	+	8.40466i	−0.270384	+	0.742874i
$129$		0			0
$130$	−2.38783	−	2.00363i	−0.209427	−	0.175730i
$131$	2.77758	−	15.7524i	0.242678	−	1.37629i	−0.583146	−	0.812367i	$-0.698179\pi$
$131$	2.77758	−	15.7524i	0.242678	−	1.37629i	0.825824	−	0.563928i	$-0.190710\pi$
$132$		0			0
$133$	−9.35175	−	11.2198i	−0.810900	−	0.972880i
$134$			3.05741i			0.264120i
$135$		0			0
$136$	5.01850	+	2.89743i	0.430333	+	0.248453i
$137$	8.37647	+	9.98269i	0.715650	+	0.852879i	0.994200	−	0.107543i	$-0.0342983\pi$
$137$	8.37647	+	9.98269i	0.715650	+	0.852879i	−0.278550	+	0.960422i	$0.589854\pi$
$138$		0			0
$139$	−2.63292	+	3.13779i	−0.223321	+	0.266144i	−0.866058	−	0.499943i	$-0.833354\pi$
$139$	−2.63292	+	3.13779i	−0.223321	+	0.266144i	0.642737	+	0.766087i	$0.277799\pi$
$140$	13.5051	−	4.86516i	1.14139	−	0.411181i
$141$		0			0
$142$	3.33679	+	1.21449i	0.280017	+	0.101918i
$143$	−11.6588			−0.974954
$144$		0			0
$145$		−	23.5231i		−	1.95349i
$146$	−0.327211	−	1.85570i	−0.0270802	−	0.153579i
$147$		0			0
$148$	3.14830	−	1.14589i	0.258789	−	0.0941913i
$149$	0.958803	−	1.14266i	0.0785482	−	0.0936101i	−0.725339	−	0.688392i	$-0.758317\pi$
$149$	0.958803	−	1.14266i	0.0785482	−	0.0936101i	0.803887	+	0.594782i	$0.202761\pi$
$150$		0			0
$151$	4.56459	+	1.66138i	0.371461	+	0.135201i	0.521004	−	0.853554i	$-0.325558\pi$
$151$	4.56459	+	1.66138i	0.371461	+	0.135201i	−0.149542	+	0.988755i	$0.547780\pi$
$152$	−6.86030			−0.556444
$153$		0			0
$154$	−1.44509	+	2.48404i	−0.116448	+	0.200169i
$155$	4.06553	+	4.84511i	0.326551	+	0.389169i
$156$		0			0
$157$	14.4796	−	17.2561i	1.15560	−	1.37719i	0.242149	−	0.970239i	$-0.422148\pi$
$157$	14.4796	−	17.2561i	1.15560	−	1.37719i	0.913450	−	0.406951i	$-0.133408\pi$
$158$	1.24622	+	3.42397i	0.0991443	+	0.272397i
$159$		0			0
$160$	3.48902	−	9.58599i	0.275831	−	0.757839i
$161$	−3.14462	−	1.82938i	−0.247830	−	0.144175i
$162$		0			0
$163$	−4.81306	−	8.33646i	−0.376988	−	0.652962i	0.613635	−	0.789590i	$-0.289707\pi$
$163$	−4.81306	−	8.33646i	−0.376988	−	0.652962i	−0.990622	+	0.136628i	$0.956374\pi$
$164$	7.68703	−	6.45018i	0.600256	−	0.503675i
$165$		0			0
$166$	−2.24688	−	0.396186i	−0.174392	−	0.0307500i
$167$	−1.75065	+	9.92841i	−0.135469	+	0.768284i	0.839063	+	0.544035i	$0.183104\pi$
$167$	−1.75065	+	9.92841i	−0.135469	+	0.768284i	−0.974532	+	0.224249i	$0.928007\pi$
$168$		0			0
$169$	0.990731	−	0.831322i	0.0762101	−	0.0639479i
$170$	−3.67917	−	2.12417i	−0.282180	−	0.162916i
$171$		0			0
$172$	8.62734	+	14.9430i	0.657828	+	1.13939i
$173$	9.46890	−	7.94535i	0.719907	−	0.604074i	−0.207452	−	0.978245i	$-0.566517\pi$
$173$	9.46890	−	7.94535i	0.719907	−	0.604074i	0.927360	+	0.374171i	$0.122073\pi$
$174$		0			0
$175$	−7.88594	+	2.84088i	−0.596121	+	0.214750i
$176$	−3.96323	−	10.8889i	−0.298740	−	0.820781i
$177$		0			0
$178$	−1.33648	+	3.67196i	−0.100174	+	0.275225i
$179$	13.6692	−	7.89190i	1.02168	−	0.589868i	0.107091	−	0.994249i	$-0.465846\pi$
$179$	13.6692	−	7.89190i	1.02168	−	0.589868i	0.914591	+	0.404381i	$0.132513\pi$
$180$		0			0
$181$	11.3602	−	6.55879i	0.844393	−	0.487511i	−0.0143618	−	0.999897i	$-0.504572\pi$
$181$	11.3602	−	6.55879i	0.844393	−	0.487511i	0.858755	+	0.512386i	$0.171238\pi$
$182$	0.491721	+	2.84341i	0.0364488	+	0.210767i
$183$		0			0
$184$	−1.60568	+	0.584420i	−0.118372	+	0.0430840i
$185$	−4.73971	+	1.72511i	−0.348470	+	0.126833i
$186$		0			0
$187$	−15.6485	+	2.75926i	−1.14433	+	0.201777i
$188$	5.81773			0.424301
$189$		0			0
$190$	5.02943			0.364874
$191$	−17.5029	+	3.08624i	−1.26647	+	0.223313i	−0.766225	−	0.642572i	$-0.777867\pi$
$191$	−17.5029	+	3.08624i	−1.26647	+	0.223313i	−0.500244	+	0.865885i	$0.666756\pi$
$192$		0			0
$193$	12.8024	−	4.65969i	0.921537	−	0.335412i	0.162687	−	0.986678i	$-0.447984\pi$
$193$	12.8024	−	4.65969i	0.921537	−	0.335412i	0.758850	+	0.651266i	$0.225762\pi$
$194$	−0.752899	+	0.274033i	−0.0540550	+	0.0196744i
$195$		0			0
$196$	−12.4571	−	4.62715i	−0.889793	−	0.330510i
$197$	−7.98620	+	4.61083i	−0.568993	+	0.328508i	−0.756747	−	0.653708i	$-0.773213\pi$
$197$	−7.98620	+	4.61083i	−0.568993	+	0.328508i	0.187754	+	0.982216i	$0.439879\pi$
$198$		0			0
$199$	−0.232253	+	0.134091i	−0.0164640	+	0.00950548i	−0.508209	−	0.861234i	$-0.669692\pi$
$199$	−0.232253	+	0.134091i	−0.0164640	+	0.00950548i	0.491745	+	0.870739i	$0.336359\pi$
$200$	−1.34651	+	3.69951i	−0.0952126	+	0.261595i
$201$		0			0
$202$	−1.01556	−	2.79023i	−0.0714546	−	0.196320i
$203$	−14.0523	+	16.6354i	−0.986281	+	1.16757i
$204$		0			0
$205$	−11.5727	+	9.71064i	−0.808272	+	0.678221i
$206$	1.79636	+	3.11138i	0.125158	+	0.216780i
$207$		0			0
$208$	−10.0765	−	5.81768i	−0.698680	−	0.403383i
$209$	14.4104	−	12.0917i	0.996787	−	0.836404i
$210$		0			0
$211$	−2.27165	+	12.8832i	−0.156387	+	0.886914i	0.801120	+	0.598503i	$0.204238\pi$
$211$	−2.27165	+	12.8832i	−0.156387	+	0.886914i	−0.957507	+	0.288410i	$0.906873\pi$
$212$	2.82789	+	0.498634i	0.194221	+	0.0342463i
$213$		0			0
$214$	1.63499	−	1.37192i	0.111765	−	0.0937822i
$215$	−12.9883	−	22.4964i	−0.885795	−	1.53424i
$216$		0			0
$217$	0.0192796	−	5.85512i	0.00130878	−	0.397471i
$218$	−1.81088	+	4.97534i	−0.122648	+	0.336973i
$219$		0			0
$220$	6.32314	+	17.3727i	0.426306	+	1.17127i
$221$	−10.2558	+	12.2224i	−0.689882	+	0.822170i
$222$		0			0
$223$	9.50475	+	11.3273i	0.636485	+	0.758534i	0.983811	−	0.179211i	$-0.0573545\pi$
$223$	9.50475	+	11.3273i	0.636485	+	0.758534i	−0.347325	+	0.937745i	$0.612910\pi$
$224$	−8.19393	+	4.69486i	−0.547480	+	0.313689i
$225$		0			0
$226$	−3.37428			−0.224454
$227$	8.61703	+	3.13634i	0.571933	+	0.208166i	0.611764	−	0.791040i	$-0.290460\pi$
$227$	8.61703	+	3.13634i	0.571933	+	0.208166i	−0.0398319	+	0.999206i	$0.512682\pi$
$228$		0			0
$229$	8.22374	−	9.80068i	0.543440	−	0.647647i	−0.422515	−	0.906356i	$-0.638853\pi$
$229$	8.22374	−	9.80068i	0.543440	−	0.647647i	0.965955	+	0.258709i	$0.0832971\pi$
$230$	1.17716	−	0.428451i	0.0776196	−	0.0282512i
$231$		0			0
$232$	1.77607	+	10.0726i	0.116605	+	0.661299i
$233$			17.0668i			1.11808i	0.829140	+	0.559042i	$0.188831\pi$
$233$			17.0668i			1.11808i	−0.829140	+	0.559042i	$0.811169\pi$
$234$		0			0
$235$	−8.75849			−0.571341
$236$	−12.2445	−	4.45664i	−0.797050	−	0.290103i
$237$		0			0
$238$	1.33294	+	3.70008i	0.0864015	+	0.239841i
$239$	4.33839	−	5.17029i	0.280627	−	0.334438i	−0.607257	−	0.794505i	$-0.707730\pi$
$239$	4.33839	−	5.17029i	0.280627	−	0.334438i	0.887884	+	0.460067i	$0.152175\pi$
$240$		0			0
$241$	−1.80490	−	2.15100i	−0.116264	−	0.138558i	0.704773	−	0.709432i	$-0.251049\pi$
$241$	−1.80490	−	2.15100i	−0.116264	−	0.138558i	−0.821037	+	0.570875i	$0.806604\pi$
$242$	−0.168677	−	0.0973859i	−0.0108430	−	0.00626021i
$243$		0			0
$244$			18.6856i			1.19622i
$245$	18.7540	+	6.96609i	1.19815	+	0.445047i
$246$		0			0
$247$	3.28000	−	18.6018i	0.208701	−	1.18360i
$248$	−2.10669	−	1.76772i	−0.133775	−	0.112250i
$249$		0			0
$250$	−0.570798	+	1.56826i	−0.0361005	+	0.0991852i
$251$	−11.4184	−	19.7772i	−0.720720	−	1.24832i	−0.960712	−	0.277549i	$-0.910478\pi$
$251$	−11.4184	−	19.7772i	−0.720720	−	1.24832i	0.239992	−	0.970775i	$-0.422855\pi$
$252$		0			0
$253$	2.34273	−	4.05772i	0.147286	−	0.255107i
$254$	3.47789	+	4.14479i	0.218222	+	0.260067i
$255$		0			0
$256$	1.47184	−	8.34721i	0.0919899	−	0.521701i
$257$	9.59035	+	8.04726i	0.598229	+	0.501974i	0.890876	−	0.454247i	$-0.150092\pi$
$257$	9.59035	+	8.04726i	0.598229	+	0.501974i	−0.292647	+	0.956221i	$0.594536\pi$
$258$		0			0
$259$	4.38245	+	1.61144i	0.272312	+	0.100130i
$260$	16.0766	+	9.28182i	0.997027	+	0.575634i
$261$		0			0
$262$		−	5.09880i		−	0.315005i
$263$	12.5268	−	2.20881i	0.772435	−	0.136201i	0.226480	−	0.974016i	$-0.427278\pi$
$263$	12.5268	−	2.20881i	0.772435	−	0.136201i	0.545955	+	0.837815i	$0.316167\pi$
$264$		0			0
$265$	−4.25735	−	0.750685i	−0.261527	−	0.0461142i
$266$	−3.55678	−	3.00451i	−0.218080	−	0.184218i
$267$		0			0
$268$	−3.16182	−	17.9316i	−0.193139	−	1.09534i
$269$	9.79421	−	16.9641i	0.597163	−	1.03432i	−0.396074	−	0.918218i	$-0.629628\pi$
$269$	9.79421	−	16.9641i	0.597163	−	1.03432i	0.993238	−	0.116099i	$-0.0370389\pi$
$270$		0			0
$271$	16.1584	−	9.32907i	0.981555	−	0.566701i	0.0788154	−	0.996889i	$-0.474886\pi$
$271$	16.1584	−	9.32907i	0.981555	−	0.566701i	0.902739	+	0.430188i	$0.141553\pi$
$272$	−14.9017	−	5.42376i	−0.903546	−	0.328864i
$273$		0			0
$274$	3.18214	+	2.67013i	0.192240	+	0.161309i
$275$	−3.69222	−	10.1443i	−0.222649	−	0.611724i
$276$		0			0
$277$	−0.463675	−	2.62963i	−0.0278595	−	0.157999i	0.967704	−	0.252088i	$-0.0811173\pi$
$277$	−0.463675	−	2.62963i	−0.0278595	−	0.157999i	−0.995564	+	0.0940890i	$0.970006\pi$
$278$	−0.652848	+	1.13077i	−0.0391552	+	0.0678188i
$279$		0			0
$280$	8.15305	−	4.67144i	0.487238	−	0.279172i
$281$	−17.0926	+	3.01388i	−1.01966	+	0.179793i	−0.658396	−	0.752672i	$-0.728765\pi$
$281$	−17.0926	+	3.01388i	−1.01966	+	0.179793i	−0.361261	+	0.932465i	$0.617654\pi$
$282$		0			0
$283$	1.07644	+	0.189805i	0.0639875	+	0.0112827i	0.205550	−	0.978647i	$-0.434102\pi$
$283$	1.07644	+	0.189805i	0.0639875	+	0.0112827i	−0.141563	+	0.989929i	$0.545213\pi$
$284$	−20.8261	−	3.67221i	−1.23580	−	0.217905i
$285$		0			0
$286$	−3.65995	+	0.645349i	−0.216418	+	0.0381603i
$287$	13.9851	+	0.0460498i	0.825516	+	0.00271823i
$288$		0			0
$289$	−2.37284	+	4.10988i	−0.139579	+	0.241758i
$290$	−1.30208	−	7.38444i	−0.0764606	−	0.433629i
$291$		0			0
$292$	3.83815	+	10.5452i	0.224611	+	0.617113i
$293$	−16.1311	−	13.5356i	−0.942391	−	0.790760i	0.0356088	−	0.999366i	$-0.488663\pi$
$293$	−16.1311	−	13.5356i	−0.942391	−	0.790760i	−0.978000	+	0.208606i	$0.933107\pi$
$294$		0			0
$295$	18.4339	+	6.70940i	1.07326	+	0.390636i
$296$	1.89930	−	1.09656i	0.110394	−	0.0637362i
$297$		0			0
$298$	0.237741	−	0.411779i	0.0137720	−	0.0238537i
$299$	−0.816966	−	4.63324i	−0.0472464	−	0.267947i
$300$		0			0
$301$	−4.25377	+	23.6683i	−0.245183	+	1.36422i
$302$	1.52489	+	0.268880i	0.0877478	+	0.0154723i
$303$		0			0
$304$	18.4884	−	3.26001i	1.06039	−	0.186974i
$305$		−	28.1308i		−	1.61077i
$306$		0			0
$307$	−19.7567	−	11.4065i	−1.12757	−	0.651004i	−0.184249	−	0.982880i	$-0.558985\pi$
$307$	−19.7567	−	11.4065i	−1.12757	−	0.651004i	−0.943323	+	0.331876i	$0.892318\pi$
$308$	5.90650	−	16.0632i	0.336554	−	0.915285i
$309$		0			0
$310$	1.54446	+	1.29595i	0.0877193	+	0.0736052i
$311$	3.90921	−	22.1702i	0.221671	−	1.25716i	−0.647277	−	0.762255i	$-0.724092\pi$
$311$	3.90921	−	22.1702i	0.221671	−	1.25716i	0.868948	−	0.494903i	$-0.164796\pi$
$312$		0			0
$313$	−0.907448	−	1.08145i	−0.0512920	−	0.0611274i	0.739788	−	0.672839i	$-0.234926\pi$
$313$	−0.907448	−	1.08145i	−0.0512920	−	0.0611274i	−0.791080	+	0.611712i	$0.790481\pi$
$314$	3.59031	−	6.21859i	0.202613	−	0.350935i
$315$		0			0
$316$	−10.8500	−	18.7927i	−0.610358	−	1.05717i
$317$	2.34444	−	6.44131i	0.131677	−	0.361780i	−0.856279	−	0.516513i	$-0.827230\pi$
$317$	2.34444	−	6.44131i	0.131677	−	0.361780i	0.987956	+	0.154733i	$0.0494519\pi$
$318$		0			0
$319$	−21.4844	−	18.0275i	−1.20289	−	1.00935i
$320$	−2.81072	+	15.9404i	−0.157124	+	0.891095i
$321$		0			0
$322$	−1.08843	−	0.400219i	−0.0606558	−	0.0223034i
$323$		−	25.7438i		−	1.43242i
$324$		0			0
$325$	−9.38747	−	5.41986i	−0.520723	−	0.300640i
$326$	−1.97238	−	2.35059i	−0.109240	−	0.130187i
$327$		0			0
$328$	4.22225	−	5.03188i	0.233135	−	0.277839i
$329$	6.19394	+	5.23219i	0.341483	+	0.288460i
$330$		0			0
$331$	−2.79664	−	1.01790i	−0.153717	−	0.0559486i	0.264015	−	0.964518i	$-0.414953\pi$
$331$	−2.79664	−	1.01790i	−0.153717	−	0.0559486i	−0.417733	+	0.908570i	$0.637175\pi$
$332$	13.5876			0.745715
$333$		0			0
$334$			3.21366i			0.175844i
$335$	4.76007	+	26.9957i	0.260070	+	1.47493i
$336$		0			0
$337$	23.6884	−	8.62186i	1.29039	−	0.469663i	0.396534	−	0.918020i	$-0.370213\pi$
$337$	23.6884	−	8.62186i	1.29039	−	0.469663i	0.893854	+	0.448357i	$0.147991\pi$
$338$	0.264997	−	0.315811i	0.0144139	−	0.0171779i
$339$		0			0
$340$	23.7749	+	8.65335i	1.28937	+	0.469294i
$341$	7.54092			0.408364
$342$		0			0
$343$	−9.10124	−	16.1297i	−0.491421	−	0.870922i
$344$	7.26016	+	8.65232i	0.391442	+	0.466502i
$345$		0			0
$346$	2.53271	−	3.01836i	0.136159	−	0.162268i
$347$	−0.787258	−	2.16297i	−0.0422622	−	0.116114i	0.916766	−	0.399424i	$-0.130790\pi$
$347$	−0.787258	−	2.16297i	−0.0422622	−	0.116114i	−0.959029	+	0.283310i	$0.908568\pi$
$348$		0			0
$349$	−2.39148	+	6.57053i	−0.128013	+	0.351712i	−0.987097	−	0.160121i	$-0.948811\pi$
$349$	−2.39148	+	6.57053i	−0.128013	+	0.351712i	0.859084	+	0.511834i	$0.171034\pi$
$350$	−2.31833	+	1.32833i	−0.123920	+	0.0710022i
$351$		0			0
$352$	−6.08129	−	10.5331i	−0.324134	−	0.561416i
$353$	−16.9198	+	14.1974i	−0.900550	+	0.755651i	−0.970298	−	0.241914i	$-0.922225\pi$
$353$	−16.9198	+	14.1974i	−0.900550	+	0.755651i	0.0697482	+	0.997565i	$0.477780\pi$
$354$		0			0
$355$	31.3534	+	5.52844i	1.66406	+	0.293419i
$356$	4.04106	−	22.9180i	0.214176	−	1.21465i
$357$		0			0
$358$	3.85423	−	3.23408i	0.203702	−	0.170926i
$359$	28.2380	+	16.3032i	1.49035	+	0.860451i	0.999939	−	0.0110424i	$-0.00351496\pi$
$359$	28.2380	+	16.3032i	1.49035	+	0.860451i	0.490407	+	0.871494i	$0.336848\pi$
$360$		0			0
$361$	5.73852	+	9.93941i	0.302027	+	0.523127i
$362$	3.20317	−	2.68777i	0.168355	−	0.141266i
$363$		0			0
$364$	−5.82443	−	16.1679i	−0.305283	−	0.847431i
$365$	−5.77827	−	15.8757i	−0.302449	−	0.830971i
$366$		0			0
$367$	−1.45484	+	3.99714i	−0.0759420	+	0.208649i	−0.971855	−	0.235581i	$-0.924301\pi$
$367$	−1.45484	+	3.99714i	−0.0759420	+	0.208649i	0.895913	+	0.444230i	$0.146523\pi$
$368$	4.04958	−	2.33803i	0.211099	−	0.121878i
$369$		0			0
$370$	−1.39241	+	0.803911i	−0.0723882	+	0.0417933i
$371$	2.56232	+	3.07415i	0.133029	+	0.159602i
$372$		0			0
$373$	22.9007	−	8.33516i	1.18575	−	0.431578i	0.327521	−	0.944844i	$-0.393787\pi$
$373$	22.9007	−	8.33516i	1.18575	−	0.431578i	0.858230	+	0.513266i	$0.171564\pi$
$374$	−4.75970	+	1.73239i	−0.246118	+	0.0895797i
$375$		0			0
$376$	3.75039	−	0.661295i	0.193412	−	0.0341037i
$377$	−28.1612			−1.45037
$378$		0			0
$379$	−17.8518			−0.916987			−0.458493	−	0.888698i	$-0.651611\pi$
$379$	−17.8518			−0.916987			−0.458493	+	0.888698i	$0.651611\pi$
$380$	−29.4974	+	5.20119i	−1.51319	+	0.266815i
$381$		0			0
$382$	−5.32375	+	1.93769i	−0.272387	+	0.0991406i
$383$	−25.7206	+	9.36155i	−1.31426	+	0.478353i	−0.901616	−	0.432538i	$-0.857618\pi$
$383$	−25.7206	+	9.36155i	−1.31426	+	0.478353i	−0.412648	+	0.910891i	$0.635396\pi$
$384$		0			0
$385$	−8.89213	+	24.1829i	−0.453185	+	1.23247i
$386$	3.76104	−	2.17144i	0.191432	−	0.110523i
$387$		0			0
$388$	4.13233	−	2.38580i	0.209787	−	0.121121i
$389$	−5.57461	+	15.3161i	−0.282644	+	0.776558i	0.714401	+	0.699736i	$0.246699\pi$
$389$	−5.57461	+	15.3161i	−0.282644	+	0.776558i	−0.997045	+	0.0768211i	$0.975523\pi$
$390$		0			0
$391$	−2.19308	−	6.02544i	−0.110909	−	0.304720i
$392$	−8.55643	−	1.56690i	−0.432165	−	0.0791403i
$393$		0			0
$394$	−2.25183	+	1.88951i	−0.113446	+	0.0951921i
$395$	16.3344	+	28.2920i	0.821874	+	1.42353i
$396$		0			0
$397$	3.94601	+	2.27823i	0.198045	+	0.114341i	0.595743	−	0.803175i	$-0.296858\pi$
$397$	3.94601	+	2.27823i	0.198045	+	0.114341i	−0.397698	+	0.917516i	$0.630191\pi$
$398$	−0.0654872	+	0.0549503i	−0.00328258	+	0.00275441i
$399$		0			0
$400$	1.87083	−	10.6100i	0.0935414	−	0.530499i
$401$	37.1238	+	6.54593i	1.85388	+	0.326888i	0.985587	−	0.169170i	$-0.0541088\pi$
$401$	37.1238	+	6.54593i	1.85388	+	0.326888i	0.868289	+	0.496059i	$0.165220\pi$
$402$		0			0
$403$	5.80043	−	4.86714i	0.288940	−	0.242449i
$404$	8.84173	+	15.3143i	0.439893	+	0.761916i
$405$		0			0
$406$	−3.49053	+	6.00007i	−0.173232	+	0.297778i
$407$	−2.05680	+	5.65101i	−0.101952	+	0.280110i
$408$		0			0
$409$	−0.342534	−	0.941105i	−0.0169372	−	0.0465347i	0.930936	−	0.365183i	$-0.118993\pi$
$409$	−0.342534	−	0.941105i	−0.0169372	−	0.0465347i	−0.947873	+	0.318648i	$0.896771\pi$
$410$	−3.09542	+	3.68898i	−0.152872	+	0.182186i
$411$		0			0
$412$	−13.7532	−	16.3904i	−0.677571	−	0.807498i
$413$	−9.02825	−	15.7570i	−0.444251	−	0.775350i
$414$		0			0
$415$	−20.4559			−1.00414
$416$	−11.4761	−	4.17695i	−0.562661	−	0.204792i
$417$		0			0
$418$	3.85444	−	4.59354i	0.188527	−	0.224677i
$419$	−2.20646	+	0.803084i	−0.107792	+	0.0392332i	−0.395353	−	0.918529i	$-0.629378\pi$
$419$	−2.20646	+	0.803084i	−0.107792	+	0.0392332i	0.287561	+	0.957762i	$0.407156\pi$
$420$		0			0
$421$	1.14047	+	6.46793i	0.0555831	+	0.315228i	0.999905	−	0.0137960i	$-0.00439155\pi$
$421$	1.14047	+	6.46793i	0.0555831	+	0.315228i	−0.944322	+	0.329024i	$0.893280\pi$
$422$			4.17007i			0.202996i
$423$		0			0
$424$	1.87968			0.0912853
$425$	−13.8827	−	5.05288i	−0.673409	−	0.245101i
$426$		0			0
$427$	−16.8049	+	19.8939i	−0.813247	+	0.962734i
$428$	−8.17035	+	9.73704i	−0.394929	+	0.470658i
$429$		0			0
$430$	−5.32258	−	6.34320i	−0.256677	−	0.305896i
$431$	13.3456	+	7.70506i	0.642833	+	0.371140i	0.785705	−	0.618602i	$-0.212300\pi$
$431$	13.3456	+	7.70506i	0.642833	+	0.371140i	−0.142872	+	0.989741i	$0.545634\pi$
$432$		0			0
$433$			9.87188i			0.474412i	0.971459	+	0.237206i	$0.0762317\pi$
$433$			9.87188i			0.474412i	−0.971459	+	0.237206i	$0.923768\pi$
$434$	−0.318047	−	1.83912i	−0.0152667	−	0.0882808i
$435$		0			0
$436$	5.47546	−	31.0529i	0.262227	−	1.48716i
$437$	5.81510	+	4.87945i	0.278174	+	0.233416i
$438$		0			0
$439$	−12.0752	+	33.1763i	−0.576317	+	1.58342i	0.218021	+	0.975944i	$0.430040\pi$
$439$	−12.0752	+	33.1763i	−0.576317	+	1.58342i	−0.794339	+	0.607475i	$0.792182\pi$
$440$	6.05094	+	10.4805i	0.288467	+	0.499640i
$441$		0			0
$442$	−2.54299	+	4.40460i	−0.120958	+	0.209505i
$443$	−2.86061	−	3.40914i	−0.135912	−	0.161973i	0.693796	−	0.720172i	$-0.255937\pi$
$443$	−2.86061	−	3.40914i	−0.135912	−	0.161973i	−0.829707	+	0.558199i	$0.811493\pi$
$444$		0			0
$445$	−6.08375	+	34.5026i	−0.288397	+	1.63558i
$446$	3.61076	+	3.02979i	0.170975	+	0.143465i
$447$		0			0
$448$	11.5103	−	9.59385i	0.543809	−	0.453267i
$449$	−4.96216	−	2.86491i	−0.234179	−	0.135203i	0.378319	−	0.925675i	$-0.376502\pi$
$449$	−4.96216	−	2.86491i	−0.234179	−	0.135203i	−0.612498	+	0.790472i	$0.709835\pi$
$450$		0			0
$451$			18.0117i			0.848138i
$452$	19.7900	−	3.48951i	0.930843	−	0.164133i
$453$		0			0
$454$	2.87869	+	0.507591i	0.135104	+	0.0238224i
$455$	8.76859	+	24.3406i	0.411078	+	1.14110i
$456$		0			0
$457$	7.09654	+	40.2465i	0.331962	+	1.88265i	0.455384	+	0.890295i	$0.349502\pi$
$457$	7.09654	+	40.2465i	0.331962	+	1.88265i	−0.123422	+	0.992354i	$0.539387\pi$
$458$	2.03913	−	3.53187i	0.0952821	−	0.165033i
$459$		0			0
$460$	−6.46090	+	3.73020i	−0.301241	+	0.173922i
$461$	25.5016	+	9.28183i	1.18773	+	0.432298i	0.858925	−	0.512101i	$-0.171133\pi$
$461$	25.5016	+	9.28183i	1.18773	+	0.432298i	0.328803	+	0.944399i	$0.393355\pi$
$462$		0			0
$463$	−9.76642	−	8.19500i	−0.453884	−	0.380854i	0.386991	−	0.922084i	$-0.373515\pi$
$463$	−9.76642	−	8.19500i	−0.453884	−	0.380854i	−0.840875	+	0.541230i	$0.817959\pi$
$464$	−9.57299	−	26.3016i	−0.444415	−	1.22102i
$465$		0			0
$466$	0.944701	+	5.35766i	0.0437624	+	0.248189i
$467$	−11.2722	+	19.5239i	−0.521613	+	0.903460i	0.478071	+	0.878321i	$0.341336\pi$
$467$	−11.2722	+	19.5239i	−0.521613	+	0.903460i	−0.999684	+	0.0251391i	$0.991997\pi$
$468$		0			0
$469$	12.7605	−	21.9347i	0.589226	−	1.01285i
$470$	−2.74949	+	0.484810i	−0.126825	+	0.0223626i
$471$		0			0
$472$	−8.40000	−	1.48115i	−0.386641	−	0.0681753i
$473$	−30.5006	−	5.37808i	−1.40242	−	0.247284i
$474$		0			0
$475$	17.2242	−	3.03709i	0.790300	−	0.139351i
$476$	−11.6441	−	20.3223i	−0.533704	−	0.931473i
$477$		0			0
$478$	1.07573	−	1.86322i	0.0492027	−	0.0852215i
$479$	5.66597	+	32.1333i	0.258885	+	1.46821i	0.785901	+	0.618353i	$0.212200\pi$
$479$	5.66597	+	32.1333i	0.258885	+	1.46821i	−0.527016	+	0.849856i	$0.676689\pi$
$480$		0			0
$481$	2.06526	+	5.67424i	0.0941676	+	0.258723i
$482$	−0.685664	−	0.575340i	−0.0312311	−	0.0262060i
$483$		0			0
$484$	1.09000	+	0.396726i	0.0495453	+	0.0180330i
$485$	−6.22115	+	3.59178i	−0.282488	+	0.163094i
$486$		0			0
$487$	3.41485	−	5.91469i	0.154741	−	0.268020i	−0.778223	−	0.627988i	$-0.783879\pi$
$487$	3.41485	−	5.91469i	0.154741	−	0.268020i	0.932965	+	0.359967i	$0.117212\pi$
$488$	2.12397	+	12.0456i	0.0961476	+	0.545280i
$489$		0			0
$490$	6.27290	+	1.14873i	0.283381	+	0.0518942i
$491$	2.93823	+	0.518089i	0.132601	+	0.0233810i	0.239554	−	0.970883i	$-0.422999\pi$
$491$	2.93823	+	0.518089i	0.132601	+	0.0233810i	−0.106954	+	0.994264i	$0.534110\pi$
$492$		0			0
$493$	−37.7982	+	6.66485i	−1.70235	+	0.300170i
$494$		−	6.02109i		−	0.270902i
$495$		0			0
$496$	6.51752	+	3.76289i	0.292645	+	0.168959i
$497$	−18.8703	−	22.6397i	−0.846447	−	1.01553i
$498$		0			0
$499$	23.4393	+	19.6679i	1.04929	+	0.880457i	0.993019	−	0.117958i	$-0.0376349\pi$
$499$	23.4393	+	19.6679i	1.04929	+	0.880457i	0.0562697	+	0.998416i	$0.482079\pi$
$500$	1.72589	−	9.78804i	0.0771844	−	0.437734i
$501$		0			0
$502$	−4.67921	−	5.57647i	−0.208843	−	0.248890i
$503$	4.53519	−	7.85518i	0.202214	−	0.350245i	−0.747027	−	0.664793i	$-0.768520\pi$
$503$	4.53519	−	7.85518i	0.202214	−	0.350245i	0.949242	+	0.314548i	$0.101853\pi$
$504$		0			0
$505$	−13.3111	−	23.0555i	−0.592335	−	1.02595i
$506$	0.510829	−	1.40349i	0.0227091	−	0.0623928i
$507$		0			0
$508$	−24.6840	−	20.7123i	−1.09518	−	0.918962i
$509$	1.29588	−	7.34928i	0.0574387	−	0.325751i	−0.942526	−	0.334132i	$-0.891557\pi$
$509$	1.29588	−	7.34928i	0.0574387	−	0.325751i	0.999965	+	0.00838120i	$0.00266785\pi$
$510$		0			0
$511$	−5.39753	+	14.6790i	−0.238773	+	0.649362i
$512$		−	20.5900i		−	0.909956i
$513$		0			0
$514$	3.45607	+	1.99536i	0.152441	+	0.0880117i
$515$	20.7052	+	24.6755i	0.912380	+	1.08733i
$516$		0			0
$517$	−6.71229	+	7.99940i	−0.295206	+	0.351813i
$518$	1.46495	+	0.263287i	0.0643662	+	0.0115682i
$519$		0			0
$520$	11.4188	+	4.15611i	0.500748	+	0.182257i
$521$	−15.7598			−0.690450			−0.345225	−	0.938520i	$-0.612197\pi$
$521$	−15.7598			−0.690450			−0.345225	+	0.938520i	$0.612197\pi$
$522$		0			0
$523$		−	5.63241i		−	0.246288i	−0.992389	−	0.123144i	$-0.960702\pi$
$523$		−	5.63241i		−	0.246288i	0.992389	−	0.123144i	$-0.0392977\pi$
$524$	5.27292	+	29.9042i	0.230348	+	1.30637i
$525$		0			0
$526$	3.81019	−	1.38679i	0.166132	−	0.0604671i
$527$	6.63351	−	7.90550i	0.288960	−	0.344369i
$528$		0			0
$529$	−19.8362	−	7.21979i	−0.862444	−	0.313904i
$530$	−1.37803			−0.0598579
$531$		0			0
$532$	23.9675	+	13.9431i	1.03912	+	0.604508i
$533$	11.6253	+	13.8545i	0.503548	+	0.600105i
$534$		0			0
$535$	12.3003	−	14.6590i	0.531789	−	0.633762i
$536$	−4.07653	−	11.2002i	−0.176079	−	0.483774i
$537$		0			0
$538$	2.13561	−	5.86755i	0.0920729	−	0.252968i
$539$	20.7349	−	11.7899i	0.893117	−	0.507829i
$540$		0			0
$541$	−0.446747	−	0.773788i	−0.0192071	−	0.0332677i	0.856262	−	0.516542i	$-0.172781\pi$
$541$	−0.446747	−	0.773788i	−0.0192071	−	0.0332677i	−0.875469	+	0.483274i	$0.839448\pi$
$542$	4.55611	−	3.82303i	0.195702	−	0.164213i
$543$		0			0
$544$	−16.3919	−	2.89033i	−0.702795	−	0.123922i
$545$	−8.24321	+	46.7496i	−0.353100	+	2.00253i
$546$		0			0
$547$	4.87449	−	4.09018i	0.208418	−	0.174884i	−0.532603	−	0.846365i	$-0.678786\pi$
$547$	4.87449	−	4.09018i	0.208418	−	0.174884i	0.741021	+	0.671481i	$0.234342\pi$
$548$	−21.4244	−	12.3694i	−0.915207	−	0.528395i
$549$		0			0
$550$	−1.72059	−	2.98015i	−0.0733663	−	0.127074i
$551$	34.8076	−	29.2070i	1.48285	−	1.24426i
$552$		0			0
$553$	5.34965	−	29.7659i	0.227490	−	1.26577i
$554$	−0.291117	−	0.799836i	−0.0123684	−	0.0339818i
$555$		0			0
$556$	2.65954	−	7.30703i	0.112790	−	0.309887i
$557$	14.9657	−	8.64047i	0.634119	−	0.366109i	−0.148227	−	0.988953i	$-0.547357\pi$
$557$	14.9657	−	8.64047i	0.634119	−	0.366109i	0.782345	+	0.622845i	$0.214023\pi$
$558$		0			0
$559$	−26.9320	+	15.5492i	−1.13910	+	0.657662i
$560$	−19.7525	+	16.4638i	−0.834696	+	0.695722i
$561$		0			0
$562$	−5.19892	+	1.89225i	−0.219303	+	0.0798199i
$563$	1.75211	−	0.637716i	0.0738426	−	0.0268765i	−0.304835	−	0.952405i	$-0.598601\pi$
$563$	1.75211	−	0.637716i	0.0738426	−	0.0268765i	0.378677	+	0.925529i	$0.376379\pi$
$564$		0			0
$565$	−29.7935	+	5.25340i	−1.25342	+	0.221012i
$566$	0.348424			0.0146454
$567$		0			0
$568$	−13.8429			−0.580837
$569$	25.3007	−	4.46119i	1.06066	−	0.187023i	0.384010	−	0.923329i	$-0.374543\pi$
$569$	25.3007	−	4.46119i	1.06066	−	0.187023i	0.676648	+	0.736306i	$0.263432\pi$
$570$		0			0
$571$	2.05601	−	0.748326i	0.0860413	−	0.0313165i	−0.298641	−	0.954366i	$-0.596533\pi$
$571$	2.05601	−	0.748326i	0.0860413	−	0.0313165i	0.384682	+	0.923049i	$0.374311\pi$
$572$	20.7981	−	7.56988i	0.869611	−	0.316513i
$573$		0			0
$574$	4.39280	−	0.759664i	0.183352	−	0.0317078i
$575$	3.77267	−	2.17815i	0.157331	−	0.0908351i
$576$		0			0
$577$	12.3597	−	7.13589i	0.514542	−	0.297071i	−0.220157	−	0.975464i	$-0.570657\pi$
$577$	12.3597	−	7.13589i	0.514542	−	0.297071i	0.734699	+	0.678394i	$0.237324\pi$
$578$	−0.517395	+	1.42153i	−0.0215208	+	0.0591279i
$579$		0			0
$580$	15.2732	+	41.9629i	0.634187	+	1.74241i
$581$	14.4662	+	12.2200i	0.600161	+	0.506972i
$582$		0			0
$583$	−3.94835	+	3.31306i	−0.163524	+	0.137213i
$584$	3.67293	+	6.36170i	0.151987	+	0.263249i
$585$		0			0
$586$	−5.81318	−	3.35624i	−0.240140	−	0.138645i
$587$	20.9075	−	17.5435i	0.862947	−	0.724098i	−0.0996541	−	0.995022i	$-0.531774\pi$
$587$	20.9075	−	17.5435i	0.862947	−	0.724098i	0.962601	+	0.270924i	$0.0873292\pi$
$588$		0			0
$589$	−2.12151	+	12.0317i	−0.0874154	+	0.495757i
$590$	6.15822	+	1.08586i	0.253530	+	0.0447042i
$591$		0			0
$592$	−4.59750	+	3.85776i	−0.188956	+	0.158553i
$593$	9.81715	+	17.0038i	0.403142	+	0.698262i	0.994103	−	0.108438i	$-0.0345848\pi$
$593$	9.81715	+	17.0038i	0.403142	+	0.698262i	−0.590961	+	0.806700i	$0.701251\pi$
$594$		0			0
$595$	17.5299	+	30.5949i	0.718657	+	1.25427i
$596$	−0.968498	+	2.66093i	−0.0396712	+	0.108996i
$597$		0			0
$598$	−0.512929	−	1.40926i	−0.0209752	−	0.0576290i
$599$	−12.4046	+	14.7832i	−0.506837	+	0.604025i	−0.957416	−	0.288712i	$-0.906773\pi$
$599$	−12.4046	+	14.7832i	−0.506837	+	0.604025i	0.450579	+	0.892737i	$0.351218\pi$
$600$		0			0
$601$	−13.5997	−	16.2075i	−0.554743	−	0.661116i	0.413683	−	0.910421i	$-0.364242\pi$
$601$	−13.5997	−	16.2075i	−0.554743	−	0.661116i	−0.968425	+	0.249305i	$0.919798\pi$
$602$	−0.0252407	+	7.66549i	−0.00102873	+	0.312422i
$603$		0			0
$604$	−9.22150			−0.375217
$605$	−1.64097	−	0.597265i	−0.0667150	−	0.0242823i
$606$		0			0
$607$	−9.60228	+	11.4436i	−0.389745	+	0.464480i	−0.924865	−	0.380296i	$-0.875822\pi$
$607$	−9.60228	+	11.4436i	−0.389745	+	0.464480i	0.535120	+	0.844776i	$0.320266\pi$
$608$	18.5167	−	6.73951i	0.750949	−	0.273323i
$609$		0			0
$610$	−1.55713	−	8.83091i	−0.0630463	−	0.357553i
$611$			10.4854i			0.424194i
$612$		0			0
$613$	5.58886			0.225732			0.112866	−	0.993610i	$-0.463997\pi$
$613$	5.58886			0.225732			0.112866	+	0.993610i	$0.463997\pi$
$614$	−6.83346	−	2.48717i	−0.275776	−	0.100374i
$615$		0			0
$616$	1.98173	−	11.0265i	0.0798462	−	0.444271i
$617$	−4.78146	+	5.69832i	−0.192494	+	0.229406i	−0.853655	−	0.520838i	$-0.825619\pi$
$617$	−4.78146	+	5.69832i	−0.192494	+	0.229406i	0.661161	+	0.750244i	$0.270064\pi$
$618$		0			0
$619$	9.85761	+	11.7478i	0.396211	+	0.472185i	0.926861	−	0.375406i	$-0.122497\pi$
$619$	9.85761	+	11.7478i	0.396211	+	0.472185i	−0.530650	+	0.847591i	$0.678052\pi$
$620$	−10.3984	−	6.00351i	−0.417609	−	0.241107i
$621$		0			0
$622$		−	7.17613i		−	0.287737i
$623$	24.9137	−	20.7657i	0.998148	−	0.831960i
$624$		0			0
$625$	−5.34899	+	30.3356i	−0.213960	+	1.21343i
$626$	−0.344731	−	0.289263i	−0.0137782	−	0.0115613i
$627$		0			0
$628$	−14.6260	+	40.1847i	−0.583642	+	1.60354i
$629$	4.11492	+	7.12725i	0.164073	+	0.284182i
$630$		0			0
$631$	−12.0123	+	20.8060i	−0.478203	+	0.828272i	−0.999688	−	0.0249886i	$-0.992045\pi$
$631$	−12.0123	+	20.8060i	−0.478203	+	0.828272i	0.521485	+	0.853261i	$0.325378\pi$
$632$	−9.13056	−	10.8814i	−0.363194	−	0.432838i
$633$		0			0
$634$	0.379429	−	2.15185i	0.0150690	−	0.0854608i
$635$	37.1614	+	31.1821i	1.47470	+	1.23742i
$636$		0			0
$637$	8.33960	−	22.4517i	0.330427	−	0.889569i
$638$	−7.74232	−	4.47003i	−0.306521	−	0.176970i
$639$		0			0
$640$			25.5620i			1.01043i
$641$	−44.3011	+	7.81149i	−1.74979	+	0.308535i	−0.954615	−	0.297844i	$-0.903732\pi$
$641$	−44.3011	+	7.81149i	−1.74979	+	0.308535i	−0.795176	+	0.606379i	$0.792621\pi$
$642$		0			0
$643$	−5.46038	−	0.962813i	−0.215337	−	0.0379696i	0.0649390	−	0.997889i	$-0.479315\pi$
$643$	−5.46038	−	0.962813i	−0.215337	−	0.0379696i	−0.280276	+	0.959920i	$0.590426\pi$
$644$	6.79747	+	1.22167i	0.267858	+	0.0481405i
$645$		0			0
$646$	−1.42500	−	8.08158i	−0.0560659	−	0.317965i
$647$	−17.8595	+	30.9335i	−0.702127	+	1.21612i	0.265591	+	0.964086i	$0.414433\pi$
$647$	−17.8595	+	30.9335i	−0.702127	+	1.21612i	−0.967718	+	0.252035i	$0.918900\pi$
$648$		0			0
$649$	20.2552	−	11.6943i	0.795086	−	0.459043i
$650$	−3.24695	−	1.18179i	−0.127356	−	0.0463538i
$651$		0			0
$652$	13.9988	+	11.7464i	0.548235	+	0.460023i
$653$	−9.10992	−	25.0293i	−0.356499	−	0.979472i	−0.980235	−	0.197837i	$-0.936608\pi$
$653$	−9.10992	−	25.0293i	−0.356499	−	0.979472i	0.623736	−	0.781635i	$-0.285614\pi$
$654$		0			0
$655$	−7.93829	−	45.0203i	−0.310175	−	1.75909i
$656$	−8.98777	+	15.5673i	−0.350914	+	0.607800i
$657$		0			0
$658$	2.23404	+	1.29965i	0.0870919	+	0.0506656i
$659$	−27.7440	+	4.89202i	−1.08075	+	0.190566i	−0.685549	−	0.728027i	$-0.740438\pi$
$659$	−27.7440	+	4.89202i	−1.08075	+	0.190566i	−0.395205	+	0.918593i	$0.629327\pi$
$660$		0			0
$661$	−32.7012	−	5.76611i	−1.27193	−	0.224276i	−0.503380	−	0.864065i	$-0.667910\pi$
$661$	−32.7012	−	5.76611i	−1.27193	−	0.224276i	−0.768550	+	0.639790i	$0.779021\pi$
$662$	−0.934275	−	0.164738i	−0.0363116	−	0.00640272i
$663$		0			0
$664$	8.75922	−	1.54449i	0.339924	−	0.0599377i
$665$	−36.0826	−	20.9910i	−1.39922	−	0.813997i
$666$		0			0
$667$	5.65875	−	9.80124i	0.219108	−	0.379505i
$668$	−3.32341	−	18.8480i	−0.128587	−	0.729250i
$669$		0			0
$670$	2.98859	+	8.21108i	0.115459	+	0.317222i
$671$	−25.6927	−	21.5588i	−0.991857	−	0.832267i
$672$		0			0
$673$	2.51415	+	0.915077i	0.0969135	+	0.0352736i	0.390022	−	0.920806i	$-0.372467\pi$
$673$	2.51415	+	0.915077i	0.0969135	+	0.0352736i	−0.293108	+	0.956079i	$0.594690\pi$
$674$	6.95908	−	4.01783i	0.268054	−	0.154761i
$675$		0			0
$676$	−1.22760	+	2.12627i	−0.0472154	+	0.0817795i
$677$	−6.89486	−	39.1027i	−0.264991	−	1.50284i	−0.769060	−	0.639176i	$-0.779275\pi$
$677$	−6.89486	−	39.1027i	−0.264991	−	1.50284i	0.504069	−	0.863663i	$-0.331836\pi$
$678$		0			0
$679$	6.54523	+	1.17634i	0.251183	+	0.0451436i
$680$	16.3101	+	2.87591i	0.625463	+	0.110286i
$681$		0			0
$682$	2.36727	−	0.417413i	0.0906474	−	0.0159836i
$683$		−	19.6212i		−	0.750783i	−0.926866	−	0.375392i	$-0.877508\pi$
$683$		−	19.6212i		−	0.750783i	0.926866	−	0.375392i	$-0.122492\pi$
$684$		0			0
$685$	32.2541	+	18.6219i	1.23237	+	0.711507i
$686$	−3.74992	−	4.55971i	−0.143173	−	0.174090i
$687$		0			0
$688$	−23.6776	−	19.8679i	−0.902701	−	0.757456i
$689$	−0.898699	+	5.09677i	−0.0342377	+	0.194172i
$690$		0			0
$691$	−3.58492	−	4.27234i	−0.136377	−	0.162527i	0.693534	−	0.720424i	$-0.256053\pi$
$691$	−3.58492	−	4.27234i	−0.136377	−	0.162527i	−0.829910	+	0.557897i	$0.811608\pi$
$692$	−11.7328	+	20.3218i	−0.446013	+	0.772517i
$693$		0			0
$694$	−0.366866	−	0.635430i	−0.0139260	−	0.0241206i
$695$	−4.00390	+	11.0006i	−0.151876	+	0.417277i
$696$		0			0
$697$	18.8825	+	15.8443i	0.715227	+	0.600146i
$698$	−0.387041	+	2.19502i	−0.0146497	+	0.0830826i
$699$		0			0
$700$	12.2232	−	10.1881i	0.461994	−	0.385073i
$701$			46.9342i			1.77268i	0.463033	+	0.886341i	$0.346761\pi$
$701$			46.9342i			1.77268i	−0.463033	+	0.886341i	$0.653239\pi$
$702$		0			0
$703$	−8.43766	−	4.87149i	−0.318232	−	0.183732i
$704$	12.4048	+	14.7834i	0.467523	+	0.557172i
$705$		0			0
$706$	−4.52564	+	5.39345i	−0.170325	+	0.202985i
$707$	−4.35948	+	24.2565i	−0.163955	+	0.912260i
$708$		0			0
$709$	16.3092	+	5.93606i	0.612505	+	0.222934i	0.629599	−	0.776920i	$-0.283219\pi$
$709$	16.3092	+	5.93606i	0.612505	+	0.222934i	−0.0170941	+	0.999854i	$0.505441\pi$
$710$	10.1486			0.380869
$711$		0			0
$712$		−	15.2334i		−	0.570896i
$713$	0.528416	+	2.99680i	0.0197893	+	0.112231i
$714$		0			0
$715$	−31.3111	+	11.3963i	−1.17097	+	0.426198i
$716$	−19.2603	+	22.9536i	−0.719793	+	0.857816i
$717$		0			0
$718$	9.76700	+	3.55490i	0.364501	+	0.132668i
$719$	−26.6722			−0.994706			−0.497353	−	0.867548i	$-0.665695\pi$
$719$	−26.6722			−0.994706			−0.497353	+	0.867548i	$0.665695\pi$
$720$		0			0
$721$	0.0981882	−	29.8193i	0.00365672	−	1.11053i
$722$	2.35163	+	2.80257i	0.0875187	+	0.104301i
$723$		0			0
$724$	−16.0069	+	19.0762i	−0.594890	+	0.708962i
$725$	−8.91838	−	24.5031i	−0.331220	−	0.910021i
$726$		0			0
$727$	11.6117	−	31.9029i	0.430654	−	1.18321i	−0.514758	−	0.857336i	$-0.672118\pi$
$727$	11.6117	−	31.9029i	0.430654	−	1.18321i	0.945412	−	0.325878i	$-0.105660\pi$
$728$	−5.59251	−	9.76059i	−0.207272	−	0.361752i
$729$		0			0
$730$	−2.69270	−	4.66390i	−0.0996614	−	0.172619i
$731$	−32.4685	+	27.2443i	−1.20089	+	1.00767i
$732$		0			0
$733$	15.0444	+	2.65274i	0.555679	+	0.0979811i	0.444433	−	0.895812i	$-0.353405\pi$
$733$	15.0444	+	2.65274i	0.555679	+	0.0979811i	0.111245	+	0.993793i	$0.464516\pi$
$734$	−0.235454	+	1.33532i	−0.00869076	+	0.0492877i
$735$		0			0
$736$	3.75977	−	3.15482i	0.138587	−	0.116288i
$737$	28.3040	+	16.3413i	1.04259	+	0.601940i
$738$		0			0
$739$	15.5321	+	26.9024i	0.571359	+	0.989622i	0.996427	+	0.0844608i	$0.0269168\pi$
$739$	15.5321	+	26.9024i	0.571359	+	0.989622i	−0.425068	+	0.905161i	$0.639750\pi$
$740$	7.33508	−	6.15486i	0.269643	−	0.226257i
$741$		0			0
$742$	0.974535	+	0.823216i	0.0357763	+	0.0302212i
$743$	10.8218	+	29.7328i	0.397015	+	1.09079i	0.963731	+	0.266876i	$0.0859915\pi$
$743$	10.8218	+	29.7328i	0.397015	+	1.09079i	−0.566716	+	0.823913i	$0.691786\pi$
$744$		0			0
$745$	1.45806	−	4.00598i	0.0534191	−	0.146768i
$746$	6.72767	−	3.88422i	0.246317	−	0.142211i
$747$		0			0
$748$	26.1239	−	15.0826i	0.955183	−	0.551475i
$749$	−17.4557	+	3.01869i	−0.637819	+	0.110300i
$750$		0			0
$751$	19.7899	−	7.20294i	0.722145	−	0.262839i	0.0453087	−	0.998973i	$-0.485573\pi$
$751$	19.7899	−	7.20294i	0.722145	−	0.262839i	0.676836	+	0.736134i	$0.263351\pi$
$752$	−9.79302	+	3.56437i	−0.357115	+	0.129979i
$753$		0			0
$754$	−8.84044	+	1.55881i	−0.321950	+	0.0567685i
$755$	13.8828			0.505247
$756$		0			0
$757$	−13.1053			−0.476322			−0.238161	−	0.971226i	$-0.576545\pi$
$757$	−13.1053			−0.476322			−0.238161	+	0.971226i	$0.576545\pi$
$758$	−5.60410	+	0.988154i	−0.203550	+	0.0358914i
$759$		0			0
$760$	−18.4243	+	6.70588i	−0.668318	+	0.243248i
$761$	9.52482	−	3.46675i	0.345274	−	0.125670i	−0.163561	−	0.986533i	$-0.552298\pi$
$761$	9.52482	−	3.46675i	0.345274	−	0.125670i	0.508836	+	0.860864i	$0.330076\pi$
$762$		0			0
$763$	33.7570	−	28.1366i	1.22209	−	1.01861i
$764$	29.2197	−	16.8700i	1.05713	−	0.610335i
$765$		0			0
$766$	−7.55611	+	4.36252i	−0.273013	+	0.157624i
$767$	8.03230	−	22.0685i	0.290029	−	0.796849i
$768$		0			0
$769$	−7.15123	−	19.6478i	−0.257880	−	0.708519i	−0.999298	−	0.0374752i	$-0.988068\pi$
$769$	−7.15123	−	19.6478i	−0.257880	−	0.708519i	0.741418	−	0.671044i	$-0.234154\pi$
$770$	−1.45285	+	8.08377i	−0.0523570	+	0.291319i
$771$		0			0
$772$	−19.8127	+	16.6249i	−0.713076	+	0.598342i
$773$	−10.5944	−	18.3500i	−0.381054	−	0.660005i	0.610159	−	0.792279i	$-0.291105\pi$
$773$	−10.5944	−	18.3500i	−0.381054	−	0.660005i	−0.991213	+	0.132274i	$0.957772\pi$
$774$		0			0
$775$	6.07185	+	3.50558i	0.218107	+	0.125924i
$776$	2.39271	−	2.00772i	0.0858932	−	0.0720730i
$777$		0			0
$778$	−0.902204	+	5.11665i	−0.0323456	+	0.183441i
$779$	−28.7381	−	5.06729i	−1.02965	−	0.181555i
$780$		0			0
$781$	29.0777	−	24.3991i	1.04048	−	0.873069i
$782$	−1.02199	−	1.77013i	−0.0365462	−	0.0632998i
$783$		0			0
$784$	23.8041	+	0.156764i	0.850145	+	0.00559873i
$785$	22.0192	−	60.4974i	0.785900	−	2.15924i
$786$		0			0
$787$	−7.46006	−	20.4964i	−0.265923	−	0.730616i	−0.998740	−	0.0501905i	$-0.984017\pi$
$787$	−7.46006	−	20.4964i	−0.265923	−	0.730616i	0.732817	−	0.680426i	$-0.238205\pi$
$788$	11.2528	−	13.4106i	0.400866	−	0.477733i
$789$		0			0
$790$	6.69381	+	7.97737i	0.238155	+	0.283822i
$791$	24.2081	+	14.0830i	0.860739	+	0.500734i
$792$		0			0
$793$	−33.6774			−1.19592
$794$	1.36485	+	0.496765i	0.0484368	+	0.0176295i
$795$		0			0
$796$	0.327253	−	0.390005i	0.0115992	−	0.0138233i
$797$	14.4170	−	5.24735i	0.510676	−	0.185871i	−0.0738137	−	0.997272i	$-0.523517\pi$
$797$	14.4170	−	5.24735i	0.510676	−	0.185871i	0.584490	+	0.811401i	$0.301295\pi$
$798$		0			0
$799$	2.48156	+	14.0736i	0.0877913	+	0.497889i
$800$		−	11.3081i		−	0.399803i
$801$		0			0
$802$	12.0164			0.424313
$803$	−18.9281	−	6.88926i	−0.667957	−	0.243117i
$804$		0			0
$805$	−10.2335	−	1.83920i	−0.360683	−	0.0648234i
$806$	1.55148	−	1.84898i	0.0546485	−	0.0651275i
$807$		0			0
$808$	7.44058	+	8.86734i	0.261759	+	0.311952i
$809$	−11.6471	−	6.72444i	−0.409489	−	0.236419i	0.281081	−	0.959684i	$-0.409307\pi$
$809$	−11.6471	−	6.72444i	−0.409489	−	0.236419i	−0.690570	+	0.723265i	$0.742640\pi$
$810$		0			0
$811$		−	3.07886i		−	0.108113i	−0.998538	−	0.0540566i	$-0.982785\pi$
$811$		−	3.07886i		−	0.108113i	0.998538	−	0.0540566i	$-0.0172152\pi$
$812$	14.2669	−	38.7999i	0.500668	−	1.36161i
$813$		0			0
$814$	−0.332876	+	1.88783i	−0.0116673	+	0.0661685i
$815$	−21.0749	−	17.6840i	−0.738223	−	0.619442i
$816$		0			0
$817$	17.1617	−	47.1513i	0.600411	−	1.64962i
$818$	−0.159623	−	0.276474i	−0.00558107	−	0.00966670i
$819$		0			0
$820$	14.3395	−	24.8368i	0.500759	−	0.867340i
$821$	2.90182	+	3.45825i	0.101274	+	0.120694i	0.814301	−	0.580443i	$-0.197121\pi$
$821$	2.90182	+	3.45825i	0.101274	+	0.120694i	−0.713027	+	0.701137i	$0.752676\pi$
$822$		0			0
$823$	5.31672	−	30.1526i	0.185329	−	1.05105i	−0.740202	−	0.672384i	$-0.765270\pi$
$823$	5.31672	−	30.1526i	0.185329	−	1.05105i	0.925532	−	0.378670i	$-0.123619\pi$
$824$	−10.7291	−	9.00275i	−0.373765	−	0.313626i
$825$		0			0
$826$	−3.70637	−	4.44674i	−0.128961	−	0.154722i
$827$	−12.8966	−	7.44587i	−0.448459	−	0.258918i	0.258720	−	0.965952i	$-0.416699\pi$
$827$	−12.8966	−	7.44587i	−0.448459	−	0.258918i	−0.707179	+	0.707034i	$0.750033\pi$
$828$		0			0
$829$			25.2709i			0.877695i	0.898561	+	0.438848i	$0.144613\pi$
$829$			25.2709i			0.877695i	−0.898561	+	0.438848i	$0.855387\pi$
$830$	−6.42157	+	1.13230i	−0.222896	+	0.0393026i
$831$		0			0
$832$	19.0834	+	3.36491i	0.661597	+	0.116657i
$833$	5.87990	−	32.1086i	0.203727	−	1.11250i
$834$		0			0
$835$	5.00334	+	28.3753i	0.173148	+	0.981969i
$836$	−17.8557	+	30.9270i	−0.617552	+	1.06963i
$837$		0			0
$838$	−0.648204	+	0.374241i	−0.0223918	+	0.0129279i
$839$	−16.6975	−	6.07738i	−0.576460	−	0.209814i	0.0373037	−	0.999304i	$-0.488123\pi$
$839$	−16.6975	−	6.07738i	−0.576460	−	0.209814i	−0.613764	+	0.789490i	$0.710345\pi$
$840$		0			0
$841$	−29.6792	−	24.9038i	−1.02342	−	0.858751i
$842$	0.716040	+	1.96730i	0.0246764	+	0.0677978i
$843$		0			0
$844$	−4.31247	−	24.4572i	−0.148441	−	0.841853i
$845$	1.84813	−	3.20106i	0.0635776	−	0.110120i
$846$		0			0
$847$	0.803687	+	1.40267i	0.0276150	+	0.0481964i
$848$	−5.06571	+	0.893222i	−0.173957	+	0.0306734i
$849$		0			0
$850$	−4.63779	−	0.817767i	−0.159075	−	0.0280492i
$851$	−2.38986	−	0.421397i	−0.0819235	−	0.0144453i
$852$		0			0
$853$	−13.7587	+	2.42603i	−0.471089	+	0.0830656i	−0.404152	−	0.914692i	$-0.632433\pi$
$853$	−13.7587	+	2.42603i	−0.471089	+	0.0830656i	−0.0669361	+	0.997757i	$0.521322\pi$
$854$	−4.17426	+	7.17537i	−0.142840	+	0.245536i
$855$		0			0
$856$	−4.16021	+	7.20569i	−0.142193	+	0.246286i
$857$	−3.71073	−	21.0446i	−0.126756	−	0.718869i	−0.980249	−	0.197765i	$-0.936632\pi$
$857$	−3.71073	−	21.0446i	−0.126756	−	0.718869i	0.853493	−	0.521104i	$-0.174480\pi$
$858$		0			0
$859$	−4.24094	−	11.6519i	−0.144699	−	0.397557i	0.846078	−	0.533059i	$-0.178958\pi$
$859$	−4.24094	−	11.6519i	−0.144699	−	0.397557i	−0.990777	+	0.135502i	$0.956735\pi$
$860$	37.7765	+	31.6982i	1.28817	+	1.08090i
$861$		0			0
$862$	4.61598	+	1.68008i	0.157221	+	0.0572237i
$863$	9.03144	−	5.21430i	0.307434	−	0.177497i	−0.338344	−	0.941023i	$-0.609867\pi$
$863$	9.03144	−	5.21430i	0.307434	−	0.177497i	0.645778	+	0.763526i	$0.276533\pi$
$864$		0			0
$865$	17.6635	−	30.5941i	0.600577	−	1.04023i
$866$	0.546439	+	3.09901i	0.0185688	+	0.105309i
$867$		0			0
$868$	3.76726	+	10.4575i	0.127869	+	0.354950i
$869$	38.3583	+	6.76360i	1.30122	+	0.229440i
$870$		0			0
$871$	32.3184	−	5.69861i	1.09507	−	0.193090i
$872$		−	20.6406i		−	0.698979i
$873$		0			0
$874$	2.09559	+	1.20989i	0.0708843	+	0.0409250i
$875$	10.6404	−	8.86882i	0.359711	−	0.299821i
$876$		0			0
$877$	31.4881	+	26.4217i	1.06328	+	0.892197i	0.994427	−	0.105430i	$-0.0336218\pi$
$877$	31.4881	+	26.4217i	1.06328	+	0.892197i	0.0688523	+	0.997627i	$0.478066\pi$
$878$	−1.95427	+	11.0832i	−0.0659534	+	0.374040i
$879$		0			0
$880$	−21.2876	−	25.3695i	−0.717604	−	0.855207i
$881$	14.4200	−	24.9761i	0.485821	−	0.841467i	−0.514046	−	0.857762i	$-0.671854\pi$
$881$	14.4200	−	24.9761i	0.485821	−	0.841467i	0.999867	+	0.0162958i	$0.00518736\pi$
$882$		0			0
$883$	24.3484	+	42.1726i	0.819388	+	1.41922i	0.906134	+	0.422991i	$0.139020\pi$
$883$	24.3484	+	42.1726i	0.819388	+	1.41922i	−0.0867455	+	0.996231i	$0.527647\pi$
$884$	10.3595	−	28.4626i	0.348429	−	0.957301i
$885$		0			0
$886$	−1.08672	−	0.911864i	−0.0365090	−	0.0306347i
$887$	1.38081	−	7.83099i	0.0463632	−	0.262939i	−0.952811	−	0.303563i	$-0.901824\pi$
$887$	1.38081	−	7.83099i	0.0463632	−	0.262939i	0.999174	+	0.0406244i	$0.0129347\pi$
$888$		0			0
$889$	−7.65256	−	44.2514i	−0.256659	−	1.48414i
$890$			11.1679i			0.374350i
$891$		0			0
$892$	−24.3102	−	14.0355i	−0.813967	−	0.469944i
$893$	−10.8748	−	12.9601i	−0.363912	−	0.433693i
$894$		0			0
$895$	28.9961	−	34.5562i	0.969233	−	1.15509i
$896$	15.2704	−	18.0773i	0.510147	−	0.603920i
$897$		0			0
$898$	−1.71632	−	0.624689i	−0.0572743	−	0.0208461i
$899$	18.2147			0.607495
$900$		0			0
$901$			7.05364i			0.234991i
$902$	0.997004	+	5.65429i	0.0331966	+	0.188267i
$903$		0			0
$904$	12.3609	−	4.49902i	0.411119	−	0.149635i
$905$	24.0981	−	28.7189i	0.801046	−	0.954650i
$906$		0			0
$907$	−40.7073	−	14.8163i	−1.35167	−	0.491966i	−0.438198	−	0.898878i	$-0.644383\pi$
$907$	−40.7073	−	14.8163i	−1.35167	−	0.491966i	−0.913467	+	0.406913i	$0.866605\pi$
$908$	−17.4083			−0.577716
$909$		0			0
$910$	4.09999	+	7.15570i	0.135913	+	0.237209i
$911$	32.8056	+	39.0962i	1.08690	+	1.29531i	0.952551	+	0.304379i	$0.0984490\pi$
$911$	32.8056	+	39.0962i	1.08690	+	1.29531i	0.134346	+	0.990934i	$0.457107\pi$
$912$		0			0
$913$	−15.6769	+	18.6830i	−0.518829	+	0.618316i
$914$	4.45553	+	12.2415i	0.147376	+	0.404912i
$915$		0			0
$916$	−8.30690	+	22.8230i	−0.274468	+	0.754094i
$917$	−21.2805	+	36.5802i	−0.702745	+	1.20799i
$918$		0			0
$919$	19.5951	+	33.9398i	0.646384	+	1.11957i	0.983980	+	0.178279i	$0.0570529\pi$
$919$	19.5951	+	33.9398i	0.646384	+	1.11957i	−0.337596	+	0.941291i	$0.609614\pi$
$920$	−3.74101	+	3.13908i	−0.123337	+	0.103492i
$921$		0			0
$922$	8.51932	+	1.50219i	0.280569	+	0.0494719i
$923$	6.61849	−	37.5353i	0.217850	−	1.23549i
$924$		0			0
$925$	−4.28312	+	3.59396i	−0.140828	+	0.118169i
$926$	−3.51952	−	2.03200i	−0.115659	−	0.0667756i
$927$		0			0
$928$	−14.6891	−	25.4422i	−0.482192	−	0.835181i
$929$	23.4335	−	19.6630i	0.768828	−	0.645123i	−0.171581	−	0.985170i	$-0.554887\pi$
$929$	23.4335	−	19.6630i	0.768828	−	0.645123i	0.940409	+	0.340047i	$0.110443\pi$
$930$		0			0
$931$	12.9777	+	36.3999i	0.425326	+	1.19296i
$932$	−11.0813	−	30.4455i	−0.362979	−	0.997275i
$933$		0			0
$934$	−2.45788	+	6.75297i	−0.0804242	+	0.220964i
$935$	−39.3290	+	22.7066i	−1.28620	+	0.742586i
$936$		0			0
$937$	−4.39414	+	2.53696i	−0.143550	+	0.0828787i	−0.570055	−	0.821607i	$-0.693078\pi$
$937$	−4.39414	+	2.53696i	−0.143550	+	0.0828787i	0.426505	+	0.904485i	$0.359745\pi$
$938$	2.79166	−	7.59216i	0.0911511	−	0.247893i
$939$		0			0
$940$	15.6243	−	5.68677i	0.509608	−	0.185482i
$941$	13.6748	−	4.97722i	0.445785	−	0.162253i	−0.109367	−	0.994001i	$-0.534882\pi$
$941$	13.6748	−	4.97722i	0.445785	−	0.162253i	0.555152	+	0.831749i	$0.312660\pi$
$942$		0			0
$943$	−7.15793	+	1.26214i	−0.233094	+	0.0411008i
$944$	23.3417			0.759709
$945$		0			0
$946$	−9.87254			−0.320984
$947$	−53.6444	+	9.45896i	−1.74321	+	0.307375i	−0.952437	−	0.304735i	$-0.901432\pi$
$947$	−53.6444	+	9.45896i	−1.74321	+	0.307375i	−0.790772	+	0.612110i	$0.790321\pi$
$948$		0			0
$949$	−19.0059	+	6.91758i	−0.616958	+	0.224554i
$950$	5.23896	−	1.90683i	0.169974	−	0.0618656i
$951$		0			0
$952$	−9.81635	−	11.7772i	−0.318150	−	0.381702i
$953$	−19.6055	+	11.3192i	−0.635084	+	0.366666i	−0.782718	−	0.622376i	$-0.786167\pi$
$953$	−19.6055	+	11.3192i	−0.635084	+	0.366666i	0.147634	+	0.989042i	$0.452834\pi$
$954$		0			0
$955$	−43.9897	+	25.3975i	−1.42347	+	0.821843i
$956$	−4.38225	+	12.0401i	−0.141732	+	0.389406i
$957$		0			0
$958$	3.55736	+	9.77376i	0.114933	+	0.315776i
$959$	−11.6854	−	32.4374i	−0.377343	−	1.04746i
$960$		0			0
$961$	19.9956	−	16.7783i	0.645021	−	0.541237i
$962$	0.962419	+	1.66696i	0.0310296	+	0.0537449i
$963$		0			0
$964$	4.61638	+	2.66527i	0.148683	+	0.0858424i
$965$	29.8277	−	25.0284i	0.960189	−	0.805694i
$966$		0			0
$967$	5.14316	−	29.1683i	0.165393	−	0.937990i	−0.783265	−	0.621687i	$-0.786447\pi$
$967$	5.14316	−	29.1683i	0.165393	−	0.937990i	0.948658	−	0.316303i	$-0.102441\pi$
$968$	0.747761	+	0.131850i	0.0240339	+	0.00423783i
$969$		0			0
$970$	−1.75415	+	1.47190i	−0.0563222	+	0.0472600i
$971$	−7.12855	−	12.3470i	−0.228766	−	0.396234i	0.728677	−	0.684858i	$-0.240136\pi$
$971$	−7.12855	−	12.3470i	−0.228766	−	0.396234i	−0.957443	+	0.288623i	$0.906802\pi$
$972$		0			0
$973$	9.40313	−	5.38769i	0.301450	−	0.172722i
$974$	0.744603	−	2.04578i	0.0238586	−	0.0655510i
$975$		0			0
$976$	−11.4482	−	31.4535i	−0.366447	−	1.00680i
$977$	−12.8962	+	15.3691i	−0.412587	+	0.491702i	−0.931815	−	0.362934i	$-0.881775\pi$
$977$	−12.8962	+	15.3691i	−0.412587	+	0.491702i	0.519228	+	0.854636i	$0.326220\pi$
$978$		0			0
$979$	26.8499	+	31.9985i	0.858126	+	1.02268i
$980$	−37.9782	−	0.250110i	−1.21317	−	0.00798947i
$981$		0			0
$982$	0.951057			0.0303494
$983$	15.7312	+	5.72570i	0.501748	+	0.182621i	0.580480	−	0.814274i	$-0.302865\pi$
$983$	15.7312	+	5.72570i	0.501748	+	0.182621i	−0.0787320	+	0.996896i	$0.525087\pi$
$984$		0			0
$985$	−16.9410	+	20.1894i	−0.539784	+	0.643289i
$986$	−11.4968	+	4.18450i	−0.366133	+	0.133262i
$987$		0			0
$988$	6.22671	+	35.3134i	0.198098	+	1.12347i
$989$		−	12.4979i		−	0.397411i
$990$		0			0
$991$	22.1202			0.702671			0.351335	−	0.936250i	$-0.385728\pi$
$991$	22.1202			0.702671			0.351335	+	0.936250i	$0.385728\pi$
$992$	7.42276	+	2.70166i	0.235673	+	0.0857779i
$993$		0			0
$994$	−7.17699	−	6.06260i	−0.227640	−	0.192294i
$995$	−0.492673	+	0.587145i	−0.0156188	+	0.0186138i
$996$		0			0
$997$	−28.6879	−	34.1890i	−0.908556	−	1.08277i	−0.996241	−	0.0866267i	$-0.972391\pi$
$997$	−28.6879	−	34.1890i	−0.908556	−	1.08277i	0.0876848	−	0.996148i	$-0.472053\pi$
$998$	8.44683	+	4.87678i	0.267380	+	0.154372i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.13		132
3.2	odd	2		189.2.bd.a.185.10	yes	132
7.5	odd	6		567.2.ba.a.341.10		132
21.5	even	6		189.2.ba.a.131.13	yes	132
27.7	even	9		189.2.ba.a.101.13	✓	132
27.20	odd	18		567.2.ba.a.143.10		132
189.47	even	18	inner	567.2.bd.a.467.13		132
189.61	odd	18		189.2.bd.a.47.10	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.13	✓	132	27.7	even	9
189.2.ba.a.131.13	yes	132	21.5	even	6
189.2.bd.a.47.10	yes	132	189.61	odd	18
189.2.bd.a.185.10	yes	132	3.2	odd	2
567.2.ba.a.143.10		132	27.20	odd	18
567.2.ba.a.341.10		132	7.5	odd	6
567.2.bd.a.17.13		132	1.1	even	1	trivial
567.2.bd.a.467.13		132	189.47	even	18	inner

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.313923 - 0.0553531i) q^{2} +(-1.78390 + 0.649287i) q^{4} +(2.68563 - 0.977491i) q^{5} +(-2.48320 - 0.913082i) q^{7} +(-1.07619 + 0.621337i) q^{8} +O(q^{10})\)	\(q+(0.313923 - 0.0553531i) q^{2} +(-1.78390 + 0.649287i) q^{4} +(2.68563 - 0.977491i) q^{5} +(-2.48320 - 0.913082i) q^{7} +(-1.07619 + 0.621337i) q^{8} +(0.788975 - 0.455515i) q^{10} +(1.16543 - 3.20200i) q^{11} +(-1.17022 - 3.21516i) q^{13} +(-0.830076 - 0.149185i) q^{14} +(2.60505 - 2.18590i) q^{16} +(-2.33161 - 4.03847i) q^{17} +(4.78098 + 2.76030i) q^{19} +(-4.15623 + 3.48749i) q^{20} +(0.188615 - 1.06969i) q^{22} +(1.35415 + 0.238774i) q^{23} +(2.42692 - 2.03643i) q^{25} +(-0.545329 - 0.944538i) q^{26} +(5.02264 + 0.0165384i) q^{28} +(2.81504 - 7.73427i) q^{29} +(0.756904 + 2.07958i) q^{31} +(2.29434 - 2.73429i) q^{32} +(-0.955489 - 1.13871i) q^{34} +(-7.56149 - 0.0248983i) q^{35} -1.76484 q^{37} +(1.65365 + 0.601880i) q^{38} +(-2.28289 + 2.72064i) q^{40} +(-4.96713 + 1.80789i) q^{41} +(-1.57831 - 8.95103i) q^{43} +6.46875i q^{44} +0.438317 q^{46} +(-2.87974 - 1.04814i) q^{47} +(5.33256 + 4.53473i) q^{49} +(0.649143 - 0.773618i) q^{50} +(4.17513 + 4.97572i) q^{52} +(-1.30996 - 0.756305i) q^{53} -9.73859i q^{55} +(3.23972 - 0.560257i) q^{56} +(0.455592 - 2.58379i) q^{58} +(5.25805 + 4.41203i) q^{59} +(3.36646 - 9.24926i) q^{61} +(0.352721 + 0.610930i) q^{62} +(-2.83176 + 4.90475i) q^{64} +(-6.28558 - 7.49087i) q^{65} +(-1.66553 + 9.44568i) q^{67} +(6.78150 + 5.69035i) q^{68} +(-2.37511 + 0.410736i) q^{70} +(9.64722 + 5.56983i) q^{71} -5.91133i q^{73} +(-0.554024 + 0.0976893i) q^{74} +(-10.3210 - 1.81988i) q^{76} +(-5.81769 + 6.88707i) q^{77} +(1.98492 + 11.2570i) q^{79} +(4.85952 - 8.41694i) q^{80} +(-1.45922 + 0.842484i) q^{82} +(-6.72578 - 2.44798i) q^{83} +(-10.2094 - 8.56673i) q^{85} +(-0.990935 - 2.72257i) q^{86} +(0.735296 + 4.17007i) q^{88} +(-6.12929 + 10.6162i) q^{89} +(-0.0298075 + 9.05240i) q^{91} +(-2.57071 + 0.453286i) q^{92} +(-0.962036 - 0.169633i) q^{94} +(15.5381 + 2.73979i) q^{95} +(-2.47531 + 0.436465i) q^{97} +(1.92503 + 1.12838i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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