LMFDB - Embedded newform 567.2.bd.a.17.8

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			17.8
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.892534 + 0.157378i) q^{2} +(-1.10754 + 0.403110i) q^{4} +(1.14226 - 0.415747i) q^{5} +(-1.98483 + 1.74942i) q^{7} +(2.49483 - 1.44039i) q^{8} +O(q^{10})$	\(q+(-0.892534 + 0.157378i) q^{2} +(-1.10754 + 0.403110i) q^{4} +(1.14226 - 0.415747i) q^{5} +(-1.98483 + 1.74942i) q^{7} +(2.49483 - 1.44039i) q^{8} +(-0.954073 + 0.550834i) q^{10} +(1.22714 - 3.37155i) q^{11} +(-0.206055 - 0.566132i) q^{13} +(1.49621 - 1.87378i) q^{14} +(-0.194293 + 0.163031i) q^{16} +(3.97470 + 6.88437i) q^{17} +(1.22523 + 0.707386i) q^{19} +(-1.09750 + 0.920911i) q^{20} +(-0.564660 + 3.20235i) q^{22} +(-1.00502 - 0.177213i) q^{23} +(-2.69832 + 2.26416i) q^{25} +(0.273008 + 0.472864i) q^{26} +(1.49306 - 2.73765i) q^{28} +(0.413325 - 1.13560i) q^{29} +(2.83760 + 7.79623i) q^{31} +(-3.55571 + 4.23753i) q^{32} +(-4.63100 - 5.51901i) q^{34} +(-1.53987 + 2.82347i) q^{35} +8.45042 q^{37} +(-1.20488 - 0.438542i) q^{38} +(2.25090 - 2.68252i) q^{40} +(6.73814 - 2.45248i) q^{41} +(1.41438 + 8.02135i) q^{43} +4.22879i q^{44} +0.924908 q^{46} +(0.296592 + 0.107951i) q^{47} +(0.879076 - 6.94458i) q^{49} +(2.05201 - 2.44549i) q^{50} +(0.456428 + 0.543949i) q^{52} +(5.74259 + 3.31549i) q^{53} -4.36136i q^{55} +(-2.43197 + 7.22344i) q^{56} +(-0.190188 + 1.07861i) q^{58} +(0.763827 + 0.640927i) q^{59} +(-4.19127 + 11.5154i) q^{61} +(-3.75960 - 6.51182i) q^{62} +(2.76033 - 4.78103i) q^{64} +(-0.470736 - 0.561001i) q^{65} +(-1.79273 + 10.1671i) q^{67} +(-7.17729 - 6.02246i) q^{68} +(0.930030 - 2.76238i) q^{70} +(0.952881 + 0.550146i) q^{71} -0.933127i q^{73} +(-7.54228 + 1.32991i) q^{74} +(-1.64214 - 0.289554i) q^{76} +(3.46258 + 8.83874i) q^{77} +(-2.33590 - 13.2476i) q^{79} +(-0.154153 + 0.267000i) q^{80} +(-5.62805 + 3.24936i) q^{82} +(-5.66119 - 2.06050i) q^{83} +(7.40228 + 6.21125i) q^{85} +(-2.52476 - 6.93673i) q^{86} +(-1.79484 - 10.1790i) q^{88} +(2.96167 - 5.12977i) q^{89} +(1.39939 + 0.763198i) q^{91} +(1.18454 - 0.208866i) q^{92} +(-0.281708 - 0.0496727i) q^{94} +(1.69362 + 0.298631i) q^{95} +(8.29293 - 1.46227i) q^{97} +(0.308318 + 6.33662i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.892534	+	0.157378i	−0.631117	+	0.111283i	−0.480051	−	0.877241i	$-0.659382\pi$
$2$	−0.892534	+	0.157378i	−0.631117	+	0.111283i	−0.151066	+	0.988524i	$0.548271\pi$
$3$		0			0
$3$		0			0
$4$	−1.10754	+	0.403110i	−0.553768	+	0.201555i
$5$	1.14226	−	0.415747i	0.510832	−	0.185928i	−0.0737273	−	0.997278i	$-0.523489\pi$
$5$	1.14226	−	0.415747i	0.510832	−	0.185928i	0.584560	+	0.811351i	$0.301267\pi$
$6$		0			0
$7$	−1.98483	+	1.74942i	−0.750194	+	0.661218i
$7$	−1.98483	+	1.74942i	−0.750194	+	0.661218i
$8$	2.49483	−	1.44039i	0.882057	−	0.509256i
$9$		0			0
$10$	−0.954073	+	0.550834i	−0.301704	+	0.174189i
$11$	1.22714	−	3.37155i	0.369998	−	1.01656i	−0.605364	−	0.795949i	$-0.706972\pi$
$11$	1.22714	−	3.37155i	0.369998	−	1.01656i	0.975362	−	0.220612i	$-0.0708055\pi$
$12$		0			0
$13$	−0.206055	−	0.566132i	−0.0571495	−	0.157017i	0.907833	−	0.419333i	$-0.137736\pi$
$13$	−0.206055	−	0.566132i	−0.0571495	−	0.157017i	−0.964982	+	0.262316i	$0.915514\pi$
$14$	1.49621	−	1.87378i	0.399878	−	0.500789i
$15$		0			0
$16$	−0.194293	+	0.163031i	−0.0485733	+	0.0407578i
$17$	3.97470	+	6.88437i	0.964005	+	1.66971i	0.712264	+	0.701911i	$0.247670\pi$
$17$	3.97470	+	6.88437i	0.964005	+	1.66971i	0.251741	+	0.967795i	$0.418997\pi$
$18$		0			0
$19$	1.22523	+	0.707386i	0.281087	+	0.162286i	0.633915	−	0.773402i	$-0.281447\pi$
$19$	1.22523	+	0.707386i	0.281087	+	0.162286i	−0.352829	+	0.935688i	$0.614780\pi$
$20$	−1.09750	+	0.920911i	−0.245408	+	0.205922i
$21$		0			0
$22$	−0.564660	+	3.20235i	−0.120386	+	0.682743i
$23$	−1.00502	−	0.177213i	−0.209562	−	0.0369515i	0.0678814	−	0.997693i	$-0.478376\pi$
$23$	−1.00502	−	0.177213i	−0.209562	−	0.0369515i	−0.277444	+	0.960742i	$0.589487\pi$
$24$		0			0
$25$	−2.69832	+	2.26416i	−0.539664	+	0.452832i
$26$	0.273008	+	0.472864i	0.0535413	+	0.0927362i
$27$		0			0
$28$	1.49306	−	2.73765i	0.282162	−	0.517367i
$29$	0.413325	−	1.13560i	0.0767526	−	0.210876i	−0.895382	−	0.445298i	$-0.853098\pi$
$29$	0.413325	−	1.13560i	0.0767526	−	0.210876i	0.972135	+	0.234422i	$0.0753199\pi$
$30$		0			0
$31$	2.83760	+	7.79623i	0.509647	+	1.40024i	0.881602	+	0.471994i	$0.156466\pi$
$31$	2.83760	+	7.79623i	0.509647	+	1.40024i	−0.371954	+	0.928251i	$0.621312\pi$
$32$	−3.55571	+	4.23753i	−0.628567	+	0.749097i
$33$		0			0
$34$	−4.63100	−	5.51901i	−0.794209	−	0.946502i
$35$	−1.53987	+	2.82347i	−0.260285	+	0.477253i
$36$		0			0
$37$	8.45042			1.38924			0.694620	−	0.719377i	$-0.255573\pi$
$37$	8.45042			1.38924			0.694620	+	0.719377i	$0.255573\pi$
$38$	−1.20488	−	0.438542i	−0.195458	−	0.0711409i
$39$		0			0
$40$	2.25090	−	2.68252i	0.355899	−	0.424144i
$41$	6.73814	−	2.45248i	1.05232	−	0.383013i	0.242782	−	0.970081i	$-0.421940\pi$
$41$	6.73814	−	2.45248i	1.05232	−	0.383013i	0.809538	+	0.587067i	$0.199718\pi$
$42$		0			0
$43$	1.41438	+	8.02135i	0.215691	+	1.22324i	0.879703	+	0.475523i	$0.157741\pi$
$43$	1.41438	+	8.02135i	0.215691	+	1.22324i	−0.664012	+	0.747722i	$0.731148\pi$
$44$			4.22879i			0.637515i
$45$		0			0
$46$	0.924908			0.136370
$47$	0.296592	+	0.107951i	0.0432625	+	0.0157462i	0.363561	−	0.931570i	$-0.381561\pi$
$47$	0.296592	+	0.107951i	0.0432625	+	0.0157462i	−0.320298	+	0.947317i	$0.603783\pi$
$48$		0			0
$49$	0.879076	−	6.94458i	0.125582	−	0.992083i
$50$	2.05201	−	2.44549i	0.290198	−	0.345845i
$51$		0			0
$52$	0.456428	+	0.543949i	0.0632951	+	0.0754322i
$53$	5.74259	+	3.31549i	0.788806	+	0.455417i	0.839542	−	0.543295i	$-0.182823\pi$
$53$	5.74259	+	3.31549i	0.788806	+	0.455417i	−0.0507361	+	0.998712i	$0.516157\pi$
$54$		0			0
$55$		−	4.36136i		−	0.588085i
$56$	−2.43197	+	7.22344i	−0.324985	+	0.965273i
$57$		0			0
$58$	−0.190188	+	1.07861i	−0.0249729	+	0.141629i
$59$	0.763827	+	0.640927i	0.0994418	+	0.0834416i	0.691153	−	0.722708i	$-0.257103\pi$
$59$	0.763827	+	0.640927i	0.0994418	+	0.0834416i	−0.591711	+	0.806150i	$0.701547\pi$
$60$		0			0
$61$	−4.19127	+	11.5154i	−0.536637	+	1.47440i	0.314399	+	0.949291i	$0.398197\pi$
$61$	−4.19127	+	11.5154i	−0.536637	+	1.47440i	−0.851036	+	0.525107i	$0.824025\pi$
$62$	−3.75960	−	6.51182i	−0.477470	−	0.827003i
$63$		0			0
$64$	2.76033	−	4.78103i	0.345041	−	0.597629i
$65$	−0.470736	−	0.561001i	−0.0583876	−	0.0695836i
$66$		0			0
$67$	−1.79273	+	10.1671i	−0.219017	+	1.24211i	0.654781	+	0.755818i	$0.272761\pi$
$67$	−1.79273	+	10.1671i	−0.219017	+	1.24211i	−0.873798	+	0.486289i	$0.838350\pi$
$68$	−7.17729	−	6.02246i	−0.870374	−	0.730330i
$69$		0			0
$70$	0.930030	−	2.76238i	0.111160	−	0.330168i
$71$	0.952881	+	0.550146i	0.113086	+	0.0652904i	0.555476	−	0.831532i	$-0.312536\pi$
$71$	0.952881	+	0.550146i	0.113086	+	0.0652904i	−0.442390	+	0.896823i	$0.645869\pi$
$72$		0			0
$73$		−	0.933127i		−	0.109214i	−0.998508	−	0.0546071i	$-0.982609\pi$
$73$		−	0.933127i		−	0.109214i	0.998508	−	0.0546071i	$-0.0173906\pi$
$74$	−7.54228	+	1.32991i	−0.876772	+	0.154599i
$75$		0			0
$76$	−1.64214	−	0.289554i	−0.188366	−	0.0332141i
$77$	3.46258	+	8.83874i	0.394598	+	1.00727i
$78$		0			0
$79$	−2.33590	−	13.2476i	−0.262810	−	1.49047i	−0.775200	−	0.631716i	$-0.782351\pi$
$79$	−2.33590	−	13.2476i	−0.262810	−	1.49047i	0.512390	−	0.858753i	$-0.328760\pi$
$80$	−0.154153	+	0.267000i	−0.0172348	+	0.0298516i
$81$		0			0
$82$	−5.62805	+	3.24936i	−0.621514	+	0.358831i
$83$	−5.66119	−	2.06050i	−0.621396	−	0.226170i	0.0120862	−	0.999927i	$-0.496153\pi$
$83$	−5.66119	−	2.06050i	−0.621396	−	0.226170i	−0.633482	+	0.773757i	$0.718375\pi$
$84$		0			0
$85$	7.40228	+	6.21125i	0.802890	+	0.673705i
$86$	−2.52476	−	6.93673i	−0.272252	−	0.748007i
$87$		0			0
$88$	−1.79484	−	10.1790i	−0.191330	−	1.08509i
$89$	2.96167	−	5.12977i	0.313937	−	0.543754i	−0.665274	−	0.746599i	$-0.731685\pi$
$89$	2.96167	−	5.12977i	0.313937	−	0.543754i	0.979211	+	0.202845i	$0.0650187\pi$
$90$		0			0
$91$	1.39939	+	0.763198i	0.146696	+	0.0800049i
$92$	1.18454	−	0.208866i	0.123497	−	0.0217758i
$93$		0			0
$94$	−0.281708	−	0.0496727i	−0.0290559	−	0.00512335i
$95$	1.69362	+	0.298631i	0.173762	+	0.0306389i
$96$		0			0
$97$	8.29293	−	1.46227i	0.842019	−	0.148471i	0.264029	−	0.964515i	$-0.414948\pi$
$97$	8.29293	−	1.46227i	0.842019	−	0.148471i	0.577990	+	0.816044i	$0.303837\pi$
$98$	0.308318	+	6.33662i	0.0311448	+	0.640095i
$99$		0			0
$100$	2.07578	−	3.59536i	0.207578	−	0.359536i
$101$	−0.430556	−	2.44180i	−0.0428419	−	0.242968i	0.955865	−	0.293806i	$-0.0949220\pi$
$101$	−0.430556	−	2.44180i	−0.0428419	−	0.242968i	−0.998707	+	0.0508377i	$0.983811\pi$
$102$		0			0
$103$	−3.26796	−	8.97865i	−0.322002	−	0.884693i	−0.990068	−	0.140591i	$-0.955100\pi$
$103$	−3.26796	−	8.97865i	−0.322002	−	0.884693i	0.668066	−	0.744102i	$-0.267122\pi$
$104$	−1.32953	−	1.11561i	−0.130371	−	0.109394i
$105$		0			0
$106$	−5.64724	−	2.05543i	−0.548509	−	0.199641i
$107$	10.6429	−	6.14467i	1.02889	−	0.594028i	0.112221	−	0.993683i	$-0.464203\pi$
$107$	10.6429	−	6.14467i	1.02889	−	0.594028i	0.916666	+	0.399655i	$0.130870\pi$
$108$		0			0
$109$	−4.67103	+	8.09046i	−0.447404	+	0.774926i	−0.998216	−	0.0597033i	$-0.980985\pi$
$109$	−4.67103	+	8.09046i	−0.447404	+	0.774926i	0.550813	+	0.834629i	$0.314318\pi$
$110$	0.686381	+	3.89266i	0.0654438	+	0.371150i
$111$		0			0
$112$	0.100428	−	0.663489i	0.00948960	−	0.0626938i
$113$	−3.90833	−	0.689145i	−0.367665	−	0.0648293i	−0.0132365	−	0.999912i	$-0.504213\pi$
$113$	−3.90833	−	0.689145i	−0.367665	−	0.0648293i	−0.354428	+	0.935083i	$0.615325\pi$
$114$		0			0
$115$	−1.22167	+	0.215414i	−0.113921	+	0.0200874i
$116$			1.42434i			0.132246i
$117$		0			0
$118$	−0.782609	−	0.451839i	−0.0720450	−	0.0415952i
$119$	−19.9327	−	6.71089i	−1.82723	−	0.615186i
$120$		0			0
$121$	−1.43499	−	1.20410i	−0.130454	−	0.109464i
$122$	1.92858	−	10.9375i	0.174605	−	0.990236i
$123$		0			0
$124$	−6.28549	−	7.49075i	−0.564453	−	0.672689i
$125$	−5.17976	+	8.97161i	−0.463292	+	0.802445i
$126$		0			0
$127$	−7.34765	−	12.7265i	−0.651998	−	1.12929i	−0.982637	−	0.185537i	$-0.940598\pi$
$127$	−7.34765	−	12.7265i	−0.651998	−	1.12929i	0.330639	−	0.943757i	$-0.392736\pi$
$128$	2.07265	−	5.69456i	0.183198	−	0.503333i
$129$		0			0
$130$	0.508437	+	0.426629i	0.0445928	+	0.0374178i
$131$	3.07983	−	17.4666i	0.269086	−	1.52606i	−0.488055	−	0.872813i	$-0.662294\pi$
$131$	3.07983	−	17.4666i	0.269086	−	1.52606i	0.757141	−	0.653251i	$-0.226595\pi$
$132$		0			0
$133$	−3.66938	+	0.739398i	−0.318176	+	0.0641139i
$134$		−	9.35660i		−	0.808287i
$135$		0			0
$136$	19.8324	+	11.4503i	1.70062	+	0.981851i
$137$	2.14849	+	2.56047i	0.183558	+	0.218756i	0.849975	−	0.526824i	$-0.176617\pi$
$137$	2.14849	+	2.56047i	0.183558	+	0.218756i	−0.666417	+	0.745580i	$0.732173\pi$
$138$		0			0
$139$	−2.56143	+	3.05259i	−0.217257	+	0.258917i	−0.863655	−	0.504084i	$-0.831830\pi$
$139$	−2.56143	+	3.05259i	−0.217257	+	0.258917i	0.646397	+	0.763001i	$0.276275\pi$
$140$	0.567288	−	3.74783i	0.0479446	−	0.316750i
$141$		0			0
$142$	−0.937059	−	0.341062i	−0.0786363	−	0.0286213i
$143$	−2.16160			−0.180762
$144$		0			0
$145$		−	1.46899i		−	0.121993i
$146$	0.146853	+	0.832847i	0.0121537	+	0.0689269i
$147$		0			0
$148$	−9.35915	+	3.40645i	−0.769317	+	0.280009i
$149$	−9.04723	+	10.7821i	−0.741178	+	0.883302i	−0.996503	−	0.0835536i	$-0.973373\pi$
$149$	−9.04723	+	10.7821i	−0.741178	+	0.883302i	0.255325	+	0.966855i	$0.417817\pi$
$150$		0			0
$151$	−12.4056	−	4.51528i	−1.00956	−	0.367449i	−0.216294	−	0.976328i	$-0.569397\pi$
$151$	−12.4056	−	4.51528i	−1.00956	−	0.367449i	−0.793263	+	0.608880i	$0.791619\pi$
$152$	4.07566			0.330580
$153$		0			0
$154$	−4.48149	−	7.34393i	−0.361129	−	0.591791i
$155$	6.48252	+	7.72557i	0.520689	+	0.620533i
$156$		0			0
$157$	3.21248	−	3.82848i	0.256384	−	0.305546i	−0.622464	−	0.782648i	$-0.713868\pi$
$157$	3.21248	−	3.82848i	0.256384	−	0.305546i	0.878848	+	0.477102i	$0.158313\pi$
$158$	4.16975	+	11.4563i	0.331727	+	0.911413i
$159$		0			0
$160$	−2.29979	+	6.31863i	−0.181815	+	0.499531i
$161$	2.30482	−	1.40647i	0.181645	−	0.110845i
$162$		0			0
$163$	−1.07224	−	1.85718i	−0.0839847	−	0.145466i	0.820973	−	0.570966i	$-0.193431\pi$
$163$	−1.07224	−	1.85718i	−0.0839847	−	0.145466i	−0.904958	+	0.425501i	$0.860098\pi$
$164$	−6.47412	+	5.43243i	−0.505543	+	0.424201i
$165$		0			0
$166$	5.37708	+	0.948123i	0.417342	+	0.0735886i
$167$	2.40447	−	13.6365i	0.186064	−	1.05522i	−0.738517	−	0.674235i	$-0.764474\pi$
$167$	2.40447	−	13.6365i	0.186064	−	1.05522i	0.924581	−	0.380986i	$-0.124415\pi$
$168$		0			0
$169$	9.68053	−	8.12293i	0.744656	−	0.624841i
$170$	−7.58430	−	4.37880i	−0.581689	−	0.335838i
$171$		0			0
$172$	−4.79997	−	8.31379i	−0.365994	−	0.633921i
$173$	2.77181	−	2.32582i	0.210737	−	0.176829i	−0.531310	−	0.847178i	$-0.678300\pi$
$173$	2.77181	−	2.32582i	0.210737	−	0.176829i	0.742046	+	0.670349i	$0.233855\pi$
$174$		0			0
$175$	1.39474	−	9.21445i	0.105432	−	0.696547i
$176$	0.311243	+	0.855133i	0.0234608	+	0.0644581i
$177$		0			0
$178$	−1.83608	+	5.04459i	−0.137620	+	0.378108i
$179$	−21.1818	+	12.2293i	−1.58320	+	0.914063i	−0.588815	+	0.808268i	$0.700405\pi$
$179$	−21.1818	+	12.2293i	−1.58320	+	0.914063i	−0.994388	+	0.105795i	$0.966261\pi$
$180$		0			0
$181$	13.8640	−	8.00438i	1.03050	−	0.594961i	0.113374	−	0.993552i	$-0.463834\pi$
$181$	13.8640	−	8.00438i	1.03050	−	0.594961i	0.917129	+	0.398591i	$0.130501\pi$
$182$	−1.36911	−	0.460948i	−0.101485	−	0.0341677i
$183$		0			0
$184$	−2.76263	+	1.00551i	−0.203664	+	0.0741275i
$185$	9.65254	−	3.51324i	0.709669	−	0.258298i
$186$		0			0
$187$	28.0886	−	4.95277i	2.05404	−	0.362182i
$188$	−0.372003			−0.0271311
$189$		0			0
$190$	−1.55861			−0.113073
$191$	6.32951	−	1.11606i	0.457987	−	0.0807555i	0.0601052	−	0.998192i	$-0.480856\pi$
$191$	6.32951	−	1.11606i	0.457987	−	0.0807555i	0.397882	+	0.917437i	$0.369745\pi$
$192$		0			0
$193$	1.28770	−	0.468686i	0.0926910	−	0.0337368i	−0.295258	−	0.955417i	$-0.595406\pi$
$193$	1.28770	−	0.468686i	0.0926910	−	0.0337368i	0.387949	+	0.921681i	$0.373184\pi$
$194$	−7.17159	+	2.61024i	−0.514890	+	0.187405i
$195$		0			0
$196$	1.82582	+	8.04575i	0.130416	+	0.574696i
$197$	−19.2475	+	11.1125i	−1.37132	+	0.791734i	−0.991095	−	0.133158i	$-0.957488\pi$
$197$	−19.2475	+	11.1125i	−1.37132	+	0.791734i	−0.380229	+	0.924892i	$0.624155\pi$
$198$		0			0
$199$	−11.5230	+	6.65279i	−0.816841	+	0.471603i	−0.849326	−	0.527869i	$-0.822991\pi$
$199$	−11.5230	+	6.65279i	−0.816841	+	0.471603i	0.0324848	+	0.999472i	$0.489658\pi$
$200$	−3.47058	+	9.53534i	−0.245407	+	0.674251i
$201$		0			0
$202$	0.768571	+	2.11163i	0.0540765	+	0.148574i
$203$	1.16626	+	2.97705i	0.0818556	+	0.208948i
$204$		0			0
$205$	6.67707	−	5.60272i	0.466347	−	0.391311i
$206$	4.32981	+	7.49944i	0.301672	+	0.522511i
$207$		0			0
$208$	0.132332	+	0.0764022i	0.00917561	+	0.00529754i
$209$	3.88852	−	3.26286i	0.268975	−	0.225697i
$210$		0			0
$211$	−2.63818	+	14.9619i	−0.181620	+	1.03002i	0.748602	+	0.663019i	$0.230725\pi$
$211$	−2.63818	+	14.9619i	−0.181620	+	1.03002i	−0.930222	+	0.366997i	$0.880386\pi$
$212$	−7.69664	−	1.35713i	−0.528608	−	0.0932078i
$213$		0			0
$214$	−8.53210	+	7.15928i	−0.583242	+	0.489398i
$215$	4.95044	+	8.57441i	0.337617	+	0.584770i
$216$		0			0
$217$	−19.2710	−	10.5100i	−1.30820	−	0.713467i
$218$	2.89579	−	7.95612i	0.196128	−	0.538857i
$219$		0			0
$220$	1.75811	+	4.83036i	0.118532	+	0.325663i
$221$	3.07846	−	3.66877i	0.207080	−	0.246788i
$222$		0			0
$223$	4.53645	+	5.40633i	0.303783	+	0.362035i	0.896242	−	0.443566i	$-0.146287\pi$
$223$	4.53645	+	5.40633i	0.303783	+	0.362035i	−0.592458	+	0.805601i	$0.701842\pi$
$224$	−0.355741	−	14.6312i	−0.0237689	−	0.977588i
$225$		0			0
$226$	3.59677			0.239254
$227$	16.1249	+	5.86897i	1.07024	+	0.389537i	0.816268	−	0.577673i	$-0.196039\pi$
$227$	16.1249	+	5.86897i	1.07024	+	0.389537i	0.253976	+	0.967210i	$0.418261\pi$
$228$		0			0
$229$	5.74182	−	6.84283i	0.379430	−	0.452187i	−0.542204	−	0.840247i	$-0.682410\pi$
$229$	5.74182	−	6.84283i	0.379430	−	0.452187i	0.921634	+	0.388060i	$0.126855\pi$
$230$	1.05648	−	0.384528i	0.0696623	−	0.0253550i
$231$		0			0
$232$	−0.604535	−	3.42849i	−0.0396897	−	0.225091i
$233$		−	8.54612i		−	0.559875i	−0.960018	−	0.279937i	$-0.909686\pi$
$233$		−	8.54612i		−	0.559875i	0.960018	−	0.279937i	$-0.0903137\pi$
$234$		0			0
$235$	0.383665			0.0250275
$236$	−1.10433	−	0.401944i	−0.0718858	−	0.0261643i
$237$		0			0
$238$	18.8468	+	2.85273i	1.22165	+	0.184915i
$239$	−8.54791	+	10.1870i	−0.552919	+	0.658943i	−0.968032	−	0.250827i	$-0.919297\pi$
$239$	−8.54791	+	10.1870i	−0.552919	+	0.658943i	0.415113	+	0.909770i	$0.363742\pi$
$240$		0			0
$241$	8.98273	+	10.7052i	0.578629	+	0.689583i	0.973378	−	0.229206i	$-0.0736130\pi$
$241$	8.98273	+	10.7052i	0.578629	+	0.689583i	−0.394749	+	0.918789i	$0.629169\pi$
$242$	1.47027	+	0.848864i	0.0945128	+	0.0545670i
$243$		0			0
$244$		−	14.4433i		−	0.924637i
$245$	−1.88306	−	8.29797i	−0.120304	−	0.530138i
$246$		0			0
$247$	0.148009	−	0.839402i	0.00941761	−	0.0534099i
$248$	18.3090	+	15.3631i	1.16262	+	0.975555i
$249$		0			0
$250$	3.21118	−	8.82264i	0.203093	−	0.557993i
$251$	−12.8062	−	22.1810i	−0.808322	−	1.40005i	−0.914025	−	0.405657i	$-0.867043\pi$
$251$	−12.8062	−	22.1810i	−0.808322	−	1.40005i	0.105704	−	0.994398i	$-0.466291\pi$
$252$		0			0
$253$	−1.83079	+	3.17103i	−0.115101	+	0.199361i
$254$	8.56089	+	10.2025i	0.537158	+	0.640160i
$255$		0			0
$256$	−2.87102	+	16.2824i	−0.179439	+	1.01765i
$257$	9.14993	+	7.67771i	0.570757	+	0.478922i	0.881897	−	0.471442i	$-0.156266\pi$
$257$	9.14993	+	7.67771i	0.570757	+	0.478922i	−0.311140	+	0.950364i	$0.600711\pi$
$258$		0			0
$259$	−16.7726	+	14.7833i	−1.04220	+	0.918590i
$260$	0.747503	+	0.431571i	0.0463582	+	0.0267649i
$261$		0			0
$262$			16.0742i			0.993069i
$263$	14.0094	−	2.47023i	0.863854	−	0.152321i	0.275872	−	0.961195i	$-0.411034\pi$
$263$	14.0094	−	2.47023i	0.863854	−	0.152321i	0.587982	+	0.808874i	$0.299922\pi$
$264$		0			0
$265$	7.93792	+	1.39967i	0.487622	+	0.0859810i
$266$	3.15868	−	1.23742i	0.193671	−	0.0758709i
$267$		0			0
$268$	−2.11294	−	11.9831i	−0.129068	−	0.731984i
$269$	15.2108	−	26.3459i	0.927421	−	1.60634i	0.139801	−	0.990180i	$-0.455354\pi$
$269$	15.2108	−	26.3459i	0.927421	−	1.60634i	0.787620	−	0.616161i	$-0.211313\pi$
$270$		0			0
$271$	−11.2849	+	6.51534i	−0.685509	+	0.395779i	−0.801927	−	0.597421i	$-0.796192\pi$
$271$	−11.2849	+	6.51534i	−0.685509	+	0.395779i	0.116418	+	0.993200i	$0.462859\pi$
$272$	−1.89463	−	0.689587i	−0.114879	−	0.0418124i
$273$		0			0
$274$	−2.32056	−	1.94718i	−0.140190	−	0.117634i
$275$	4.32250	+	11.8760i	0.260657	+	0.716148i
$276$		0			0
$277$	3.11459	+	17.6637i	0.187138	+	1.06131i	0.923178	+	0.384373i	$0.125582\pi$
$277$	3.11459	+	17.6637i	0.187138	+	1.06131i	−0.736040	+	0.676938i	$0.763307\pi$
$278$	1.80575	−	3.12765i	0.108302	−	0.187584i
$279$		0			0
$280$	0.225197	+	9.26210i	0.0134581	+	0.553516i
$281$	9.46609	−	1.66913i	0.564700	−	0.0995718i	0.115992	−	0.993250i	$-0.462995\pi$
$281$	9.46609	−	1.66913i	0.564700	−	0.0995718i	0.448708	+	0.893678i	$0.351884\pi$
$282$		0			0
$283$	−13.1374	−	2.31648i	−0.780939	−	0.137701i	−0.231054	−	0.972941i	$-0.574217\pi$
$283$	−13.1374	−	2.31648i	−0.780939	−	0.137701i	−0.549885	+	0.835240i	$0.685328\pi$
$284$	−1.27712	−	0.225191i	−0.0757832	−	0.0133626i
$285$		0			0
$286$	1.92930	−	0.340188i	0.114082	−	0.0201158i
$287$	−9.08362	+	16.6556i	−0.536189	+	0.983147i
$288$		0			0
$289$	−23.0964	+	40.0042i	−1.35861	+	2.35319i
$290$	0.231186	+	1.31112i	0.0135757	+	0.0769916i
$291$		0			0
$292$	0.376153	+	1.03347i	0.0220127	+	0.0604794i
$293$	1.25235	+	1.05085i	0.0731631	+	0.0613911i	0.678636	−	0.734475i	$-0.262571\pi$
$293$	1.25235	+	1.05085i	0.0731631	+	0.0613911i	−0.605473	+	0.795866i	$0.707016\pi$
$294$		0			0
$295$	1.13895	+	0.414544i	0.0663122	+	0.0241357i
$296$	21.0824	−	12.1719i	1.22539	−	0.707479i
$297$		0			0
$298$	6.37810	−	11.0472i	0.369473	−	0.639947i
$299$	0.106765	+	0.605493i	0.00617436	+	0.0350165i
$300$		0			0
$301$	−16.8400	−	13.4467i	−0.970641	−	0.775052i
$302$	11.7831	+	2.07767i	0.678039	+	0.119556i
$303$		0			0
$304$	−0.353380	+	0.0623104i	−0.0202677	+	0.00357375i
$305$			14.8961i			0.852946i
$306$		0			0
$307$	9.99990	+	5.77344i	0.570724	+	0.329508i	0.757439	−	0.652906i	$-0.226451\pi$
$307$	9.99990	+	5.77344i	0.570724	+	0.329508i	−0.186714	+	0.982414i	$0.559784\pi$
$308$	−7.39792	−	8.39342i	−0.421536	−	0.478260i
$309$		0			0
$310$	−7.00170	−	5.87513i	−0.397670	−	0.333685i
$311$	−4.17791	+	23.6941i	−0.236908	+	1.34357i	0.601651	+	0.798759i	$0.294510\pi$
$311$	−4.17791	+	23.6941i	−0.236908	+	1.34357i	−0.838559	+	0.544811i	$0.816601\pi$
$312$		0			0
$313$	20.8975	+	24.9047i	1.18120	+	1.40770i	0.892960	+	0.450136i	$0.148624\pi$
$313$	20.8975	+	24.9047i	1.18120	+	1.40770i	0.288236	+	0.957559i	$0.406931\pi$
$314$	−2.26473	+	3.92262i	−0.127806	+	0.221366i
$315$		0			0
$316$	7.92734	+	13.7305i	0.445947	+	0.772404i
$317$	−1.72725	+	4.74558i	−0.0970120	+	0.266538i	−0.978700	−	0.205294i	$-0.934185\pi$
$317$	−1.72725	+	4.74558i	−0.0970120	+	0.266538i	0.881688	+	0.471832i	$0.156407\pi$
$318$		0			0
$319$	−3.32153	−	2.78709i	−0.185970	−	0.156047i
$320$	1.16530	−	6.60877i	0.0651425	−	0.369441i
$321$		0			0
$322$	−1.83578	+	1.61805i	−0.102304	+	0.0901704i
$323$			11.2466i			0.625776i
$324$		0			0
$325$	1.83782	+	1.06106i	0.101944	+	0.0588572i
$326$	1.24929	+	1.48885i	0.0691920	+	0.0824598i
$327$		0			0
$328$	13.2780	−	15.8241i	0.733155	−	0.873740i
$329$	−0.777536	+	0.304600i	−0.0428669	+	0.0167932i
$330$		0			0
$331$	−11.5066	−	4.18808i	−0.632463	−	0.230198i	0.00584016	−	0.999983i	$-0.498141\pi$
$331$	−11.5066	−	4.18808i	−0.632463	−	0.230198i	−0.638303	+	0.769785i	$0.720363\pi$
$332$	7.10058			0.389695
$333$		0			0
$334$			12.5494i			0.686673i
$335$	2.17918	+	12.3587i	0.119061	+	0.675230i
$336$		0			0
$337$	16.9278	−	6.16122i	0.922116	−	0.335623i	0.163036	−	0.986620i	$-0.447871\pi$
$337$	16.9278	−	6.16122i	0.922116	−	0.335623i	0.759080	+	0.650997i	$0.225649\pi$
$338$	−7.36183	+	8.77349i	−0.400431	+	0.477215i
$339$		0			0
$340$	−10.7021	−	3.89525i	−0.580404	−	0.211250i
$341$	29.7675			1.61200
$342$		0			0
$343$	10.4042	+	15.3217i	0.561772	+	0.827292i
$344$	15.0825	+	17.9747i	0.813196	+	0.969130i
$345$		0			0
$346$	−2.10790	+	2.51210i	−0.113321	+	0.135051i
$347$	−3.91300	−	10.7509i	−0.210061	−	0.577137i	0.789257	−	0.614063i	$-0.210466\pi$
$347$	−3.91300	−	10.7509i	−0.210061	−	0.577137i	−0.999318	+	0.0369254i	$0.988244\pi$
$348$		0			0
$349$	−2.98735	+	8.20768i	−0.159909	+	0.439347i	−0.993610	−	0.112870i	$-0.963996\pi$
$349$	−2.98735	+	8.20768i	−0.159909	+	0.439347i	0.833701	+	0.552217i	$0.186218\pi$
$350$	0.205299	+	8.44371i	0.0109737	+	0.451335i
$351$		0			0
$352$	9.92369	+	17.1883i	0.528934	+	0.916141i
$353$	17.0490	−	14.3058i	0.907428	−	0.761422i	−0.0642000	−	0.997937i	$-0.520450\pi$
$353$	17.0490	−	14.3058i	0.907428	−	0.761422i	0.971628	+	0.236515i	$0.0760051\pi$
$354$		0			0
$355$	1.31716	+	0.232250i	0.0699074	+	0.0123266i
$356$	−1.21230	+	6.87529i	−0.0642517	+	0.364389i
$357$		0			0
$358$	16.9809	−	14.2486i	0.897466	−	0.753063i
$359$	−22.7063	−	13.1095i	−1.19839	−	0.691891i	−0.238195	−	0.971217i	$-0.576556\pi$
$359$	−22.7063	−	13.1095i	−1.19839	−	0.691891i	−0.960196	+	0.279326i	$0.909889\pi$
$360$		0			0
$361$	−8.49921	−	14.7211i	−0.447327	−	0.774793i
$362$	−11.1144	+	9.32606i	−0.584158	+	0.490167i
$363$		0			0
$364$	−1.85752	−	0.281163i	−0.0973607	−	0.0147369i
$365$	−0.387945	−	1.06587i	−0.0203060	−	0.0557902i
$366$		0			0
$367$	6.11382	−	16.7976i	0.319139	−	0.876827i	−0.671584	−	0.740929i	$-0.734386\pi$
$367$	6.11382	−	16.7976i	0.319139	−	0.876827i	0.990723	−	0.135898i	$-0.0433921\pi$
$368$	0.224161	−	0.129419i	0.0116852	−	0.00674644i
$369$		0			0
$370$	−8.06231	+	4.65478i	−0.419140	+	0.241990i
$371$	−17.1982	+	3.46552i	−0.892887	+	0.179921i
$372$		0			0
$373$	−10.0649	+	3.66333i	−0.521141	+	0.189680i	−0.589179	−	0.808003i	$-0.700549\pi$
$373$	−10.0649	+	3.66333i	−0.521141	+	0.189680i	0.0680373	+	0.997683i	$0.478326\pi$
$374$	−24.2905	+	8.84103i	−1.25603	+	0.457159i
$375$		0			0
$376$	0.895441	−	0.157890i	0.0461788	−	0.00814258i
$377$	−0.728069			−0.0374974
$378$		0			0
$379$	13.1823			0.677127			0.338564	−	0.940944i	$-0.390059\pi$
$379$	13.1823			0.677127			0.338564	+	0.940944i	$0.390059\pi$
$380$	−1.99613	+	0.351971i	−0.102399	+	0.0180557i
$381$		0			0
$382$	−5.47366	+	1.99225i	−0.280057	+	0.101932i
$383$	−14.9561	+	5.44356i	−0.764219	+	0.278153i	−0.694576	−	0.719419i	$-0.744408\pi$
$383$	−14.9561	+	5.44356i	−0.764219	+	0.278153i	−0.0696426	+	0.997572i	$0.522186\pi$
$384$		0			0
$385$	7.62984	+	8.65654i	0.388852	+	0.441178i
$386$	−1.07556	+	0.620974i	−0.0547445	+	0.0316067i
$387$		0			0
$388$	−8.59527	+	4.96248i	−0.436359	+	0.251932i
$389$	8.53902	−	23.4608i	0.432945	−	1.18951i	−0.511051	−	0.859551i	$-0.670743\pi$
$389$	8.53902	−	23.4608i	0.432945	−	1.18951i	0.943996	−	0.329957i	$-0.107034\pi$
$390$		0			0
$391$	−2.77467	−	7.62333i	−0.140321	−	0.385529i
$392$	−7.80978	−	18.5918i	−0.394454	−	0.939028i
$393$		0			0
$394$	15.4301	−	12.9474i	0.777359	−	0.652281i
$395$	−8.17584	−	14.1610i	−0.411371	−	0.712516i
$396$		0			0
$397$	−18.6785	−	10.7840i	−0.937446	−	0.541235i	−0.0482875	−	0.998833i	$-0.515376\pi$
$397$	−18.6785	−	10.7840i	−0.937446	−	0.541235i	−0.889159	+	0.457599i	$0.848710\pi$
$398$	9.23763	−	7.75129i	0.463041	−	0.388537i
$399$		0			0
$400$	0.155136	−	0.879821i	0.00775681	−	0.0439911i
$401$	−9.32277	−	1.64386i	−0.465557	−	0.0820903i	−0.0640509	−	0.997947i	$-0.520402\pi$
$401$	−9.32277	−	1.64386i	−0.465557	−	0.0820903i	−0.401506	+	0.915856i	$0.631513\pi$
$402$		0			0
$403$	3.82900	−	3.21291i	0.190736	−	0.160046i
$404$	1.46117	+	2.53083i	0.0726961	+	0.125913i
$405$		0			0
$406$	−1.50945	−	2.47357i	−0.0749128	−	0.122761i
$407$	10.3699	−	28.4910i	0.514016	−	1.41225i
$408$		0			0
$409$	−4.45219	−	12.2323i	−0.220146	−	0.604847i	0.779625	−	0.626247i	$-0.215410\pi$
$409$	−4.45219	−	12.2323i	−0.220146	−	0.604847i	−0.999771	+	0.0213999i	$0.993188\pi$
$410$	−5.07776	+	6.05144i	−0.250773	+	0.298859i
$411$		0			0
$412$	7.23878	+	8.62684i	0.356629	+	0.425014i
$413$	−2.63731	+	0.0641233i	−0.129774	+	0.00315530i
$414$		0			0
$415$	−7.32317			−0.359480
$416$	3.13168	+	1.13984i	0.153543	+	0.0558851i
$417$		0			0
$418$	−2.95714	+	3.52418i	−0.144638	+	0.172373i
$419$	11.0177	−	4.01012i	0.538251	−	0.195907i	−0.0585680	−	0.998283i	$-0.518653\pi$
$419$	11.0177	−	4.01012i	0.538251	−	0.195907i	0.596819	+	0.802376i	$0.296431\pi$
$420$		0			0
$421$	−2.93922	−	16.6692i	−0.143249	−	0.812405i	−0.968756	−	0.248014i	$-0.920222\pi$
$421$	−2.93922	−	16.6692i	−0.143249	−	0.812405i	0.825508	−	0.564391i	$-0.190889\pi$
$422$		−	13.7691i		−	0.670272i
$423$		0			0
$424$	19.1024			0.927696
$425$	−26.3123	−	9.57690i	−1.27633	−	0.464548i
$426$		0			0
$427$	−11.8263	−	30.1884i	−0.572316	−	1.46092i
$428$	−9.31041	+	11.0957i	−0.450036	+	0.536332i
$429$		0			0
$430$	−5.76785	−	6.87386i	−0.278151	−	0.331487i
$431$	1.64280	+	0.948469i	0.0791307	+	0.0456861i	0.539043	−	0.842278i	$-0.318786\pi$
$431$	1.64280	+	0.948469i	0.0791307	+	0.0456861i	−0.459913	+	0.887964i	$0.652119\pi$
$432$		0			0
$433$		−	8.59518i		−	0.413058i	−0.978440	−	0.206529i	$-0.933783\pi$
$433$		−	8.59518i		−	0.413058i	0.978440	−	0.206529i	$-0.0662168\pi$
$434$	18.8541	+	6.34773i	0.905024	+	0.304701i
$435$		0			0
$436$	1.91199	−	10.8434i	0.0915676	−	0.519306i
$437$	−1.10603	−	0.928067i	−0.0529085	−	0.0443955i
$438$		0			0
$439$	5.95017	−	16.3480i	0.283986	−	0.780246i	−0.712891	−	0.701275i	$-0.752614\pi$
$439$	5.95017	−	16.3480i	0.283986	−	0.780246i	0.996877	−	0.0789705i	$-0.0251633\pi$
$440$	−6.28207	−	10.8809i	−0.299486	−	0.518725i
$441$		0			0
$442$	−2.17025	+	3.75898i	−0.103228	+	0.178796i
$443$	19.6774	+	23.4506i	0.934901	+	1.11417i	0.993264	+	0.115876i	$0.0369676\pi$
$443$	19.6774	+	23.4506i	0.934901	+	1.11417i	−0.0583624	+	0.998295i	$0.518588\pi$
$444$		0			0
$445$	1.25030	−	7.09081i	0.0592700	−	0.336137i
$446$	−4.89977	−	4.11140i	−0.232011	−	0.194680i
$447$		0			0
$448$	2.88524	+	14.3185i	0.136315	+	0.676485i
$449$	−23.7529	−	13.7137i	−1.12097	−	0.647191i	−0.179320	−	0.983791i	$-0.557390\pi$
$449$	−23.7529	−	13.7137i	−1.12097	−	0.647191i	−0.941648	+	0.336600i	$0.890723\pi$
$450$		0			0
$451$		−	25.7275i		−	1.21146i
$452$	4.60642	−	0.812237i	0.216668	−	0.0382044i
$453$		0			0
$454$	−15.3156	−	2.70056i	−0.718798	−	0.126743i
$455$	1.91575	+	0.289977i	0.0898120	+	0.0135943i
$456$		0			0
$457$	3.98175	+	22.5816i	0.186259	+	1.05632i	0.924328	+	0.381600i	$0.124627\pi$
$457$	3.98175	+	22.5816i	0.186259	+	1.05632i	−0.738069	+	0.674725i	$0.764262\pi$
$458$	−4.04785	+	7.01109i	−0.189144	+	0.327607i
$459$		0			0
$460$	1.26621	−	0.731047i	0.0590374	−	0.0340852i
$461$	−28.3324	−	10.3121i	−1.31957	−	0.480284i	−0.416250	−	0.909250i	$-0.636656\pi$
$461$	−28.3324	−	10.3121i	−1.31957	−	0.480284i	−0.903321	+	0.428966i	$0.858878\pi$
$462$		0			0
$463$	−22.9581	−	19.2641i	−1.06695	−	0.895279i	−0.0721787	−	0.997392i	$-0.522995\pi$
$463$	−22.9581	−	19.2641i	−1.06695	−	0.895279i	−0.994773	+	0.102113i	$0.967440\pi$
$464$	0.104832	+	0.288025i	0.00486672	+	0.0133712i
$465$		0			0
$466$	1.34497	+	7.62769i	0.0623045	+	0.353346i
$467$	1.17552	−	2.03607i	0.0543967	−	0.0942179i	−0.837545	−	0.546369i	$-0.816010\pi$
$467$	1.17552	−	2.03607i	0.0543967	−	0.0942179i	0.891942	+	0.452151i	$0.149343\pi$
$468$		0			0
$469$	−14.2282	−	23.3161i	−0.656998	−	1.07664i
$470$	−0.342434	+	0.0603803i	−0.0157953	+	0.00278514i
$471$		0			0
$472$	2.82881	+	0.498795i	0.130207	+	0.0229589i
$473$	28.7800	+	5.07470i	1.32331	+	0.233335i
$474$		0			0
$475$	−4.90769	+	0.865359i	−0.225180	+	0.0397054i
$476$	24.7815	−	0.602533i	1.13586	−	0.0276171i
$477$		0			0
$478$	6.02609	−	10.4375i	0.275627	−	0.477400i
$479$	−3.25239	−	18.4452i	−0.148606	−	0.842784i	−0.964401	−	0.264444i	$-0.914812\pi$
$479$	−3.25239	−	18.4452i	−0.148606	−	0.842784i	0.815796	−	0.578340i	$-0.196299\pi$
$480$		0			0
$481$	−1.74125	−	4.78405i	−0.0793943	−	0.218134i
$482$	−9.70215	−	8.14107i	−0.441921	−	0.370816i
$483$		0			0
$484$	2.07469	+	0.755125i	0.0943040	+	0.0343239i
$485$	8.86472	−	5.11805i	0.402526	−	0.232398i
$486$		0			0
$487$	0.370050	−	0.640946i	0.0167686	−	0.0290440i	−0.857519	−	0.514452i	$-0.827995\pi$
$487$	0.370050	−	0.640946i	0.0167686	−	0.0290440i	0.874288	+	0.485408i	$0.161329\pi$
$488$	6.13021	+	34.7661i	0.277502	+	1.57379i
$489$		0			0
$490$	2.98661	+	7.10986i	0.134921	+	0.321191i
$491$	−13.6257	−	2.40259i	−0.614921	−	0.108427i	−0.142492	−	0.989796i	$-0.545512\pi$
$491$	−13.6257	−	2.40259i	−0.614921	−	0.108427i	−0.472429	+	0.881369i	$0.656623\pi$
$492$		0			0
$493$	9.46075	−	1.66819i	0.426091	−	0.0751313i
$494$			0.772488i			0.0347559i
$495$		0			0
$496$	−1.82236	−	1.05214i	−0.0818262	−	0.0472424i
$497$	−2.85374	+	0.575042i	−0.128008	+	0.0257942i
$498$		0			0
$499$	1.83412	+	1.53901i	0.0821066	+	0.0688956i	0.682917	−	0.730496i	$-0.260711\pi$
$499$	1.83412	+	1.53901i	0.0821066	+	0.0688956i	−0.600811	+	0.799391i	$0.705155\pi$
$500$	2.12023	−	12.0244i	0.0948195	−	0.537748i
$501$		0			0
$502$	14.9208	+	17.7819i	0.665947	+	0.793645i
$503$	0.926534	−	1.60480i	0.0413121	−	0.0715547i	−0.844630	−	0.535350i	$-0.820180\pi$
$503$	0.926534	−	1.60480i	0.0413121	−	0.0715547i	0.885942	+	0.463796i	$0.153513\pi$
$504$		0			0
$505$	−1.50698	−	2.61016i	−0.0670596	−	0.116151i
$506$	1.13500	−	3.11837i	0.0504567	−	0.138629i
$507$		0			0
$508$	13.2680	+	11.1332i	0.588671	+	0.493954i
$509$	0.923884	−	5.23961i	0.0409505	−	0.232242i	−0.957463	−	0.288558i	$-0.906824\pi$
$509$	0.923884	−	5.23961i	0.0409505	−	0.232242i	0.998413	+	0.0563160i	$0.0179354\pi$
$510$		0			0
$511$	1.63243	+	1.85210i	0.0722144	+	0.0819319i
$512$		−	2.86433i		−	0.126587i
$513$		0			0
$514$	−9.37492	−	5.41261i	−0.413510	−	0.238740i
$515$	−7.46570	−	8.89728i	−0.328978	−	0.392061i
$516$		0			0
$517$	0.727924	−	0.867506i	0.0320140	−	0.0381529i
$518$	12.6436	−	15.8342i	0.555526	−	0.695716i
$519$		0			0
$520$	−1.98247	−	0.721560i	−0.0869371	−	0.0316425i
$521$	−24.4240			−1.07004			−0.535018	−	0.844841i	$-0.679695\pi$
$521$	−24.4240			−1.07004			−0.535018	+	0.844841i	$0.679695\pi$
$522$		0			0
$523$			30.7392i			1.34413i	0.740492	+	0.672065i	$0.234593\pi$
$523$			30.7392i			1.34413i	−0.740492	+	0.672065i	$0.765407\pi$
$524$	3.62994	+	20.5864i	0.158575	+	0.899322i
$525$		0			0
$526$	−12.1151	+	4.40952i	−0.528242	+	0.192264i
$527$	−42.3936	+	50.5227i	−1.84669	+	2.20080i
$528$		0			0
$529$	−20.6343	−	7.51026i	−0.897142	−	0.326533i
$530$	−7.30513			−0.317315
$531$		0			0
$532$	3.76592	−	2.29808i	0.163273	−	0.0996342i
$533$	−2.77686	−	3.30933i	−0.120279	−	0.143343i
$534$		0			0
$535$	9.60227	−	11.4435i	0.415142	−	0.494747i
$536$	10.1720	+	27.9474i	0.439365	+	1.20715i
$537$		0			0
$538$	−9.42992	+	25.9085i	−0.406553	+	1.11699i
$539$	−22.3353	−	11.4859i	−0.962048	−	0.494731i
$540$		0			0
$541$	14.3316	+	24.8231i	0.616166	+	1.06723i	0.990179	+	0.139807i	$0.0446481\pi$
$541$	14.3316	+	24.8231i	0.616166	+	1.06723i	−0.374013	+	0.927423i	$0.622019\pi$
$542$	9.04679	−	7.59115i	0.388593	−	0.326068i
$543$		0			0
$544$	−43.3056	−	7.63595i	−1.85671	−	0.327389i
$545$	−1.97193	+	11.1833i	−0.0844680	+	0.479042i
$546$		0			0
$547$	−28.4534	+	23.8752i	−1.21658	+	1.02083i	−0.217582	+	0.976042i	$0.569817\pi$
$547$	−28.4534	+	23.8752i	−1.21658	+	1.02083i	−0.998996	+	0.0447884i	$0.985739\pi$
$548$	−3.41169	−	1.96974i	−0.145740	−	0.0841430i
$549$		0			0
$550$	−5.72699	−	9.91944i	−0.244200	−	0.422966i
$551$	1.30973	−	1.09899i	0.0557962	−	0.0468186i
$552$		0			0
$553$	27.8119	+	22.2077i	1.18268	+	0.944366i
$554$	−5.55975	−	15.2753i	−0.236211	−	0.648985i
$555$		0			0
$556$	1.60634	−	4.41339i	0.0681242	−	0.187170i
$557$	−20.8533	+	12.0396i	−0.883581	+	0.510136i	−0.871837	−	0.489795i	$-0.837071\pi$
$557$	−20.8533	+	12.0396i	−0.883581	+	0.510136i	−0.0117433	+	0.999931i	$0.503738\pi$
$558$		0			0
$559$	4.24971	−	2.45357i	0.179743	−	0.103775i
$560$	−0.161129	−	0.799627i	−0.00680893	−	0.0337904i
$561$		0			0
$562$	−8.18612	+	2.97950i	−0.345311	+	0.125683i
$563$	−5.49200	+	1.99893i	−0.231460	+	0.0842447i	−0.455147	−	0.890417i	$-0.650413\pi$
$563$	−5.49200	+	1.99893i	−0.231460	+	0.0842447i	0.223686	+	0.974661i	$0.428191\pi$
$564$		0			0
$565$	−4.75083	+	0.837699i	−0.199869	+	0.0352423i
$566$	12.0902			0.508187
$567$		0			0
$568$	3.16971			0.132998
$569$	14.3012	−	2.52168i	0.599536	−	0.105714i	0.134360	−	0.990933i	$-0.457102\pi$
$569$	14.3012	−	2.52168i	0.599536	−	0.105714i	0.465176	+	0.885218i	$0.345991\pi$
$570$		0			0
$571$	37.5999	−	13.6852i	1.57351	−	0.572710i	0.599728	−	0.800204i	$-0.295276\pi$
$571$	37.5999	−	13.6852i	1.57351	−	0.572710i	0.973779	+	0.227494i	$0.0730533\pi$
$572$	2.39406	−	0.871365i	0.100101	−	0.0364336i
$573$		0			0
$574$	5.48622	−	16.2952i	0.228991	−	0.680149i
$575$	3.11312	−	1.79736i	0.129826	−	0.0749550i
$576$		0			0
$577$	10.4145	−	6.01282i	0.433561	−	0.250317i	−0.267301	−	0.963613i	$-0.586132\pi$
$577$	10.4145	−	6.01282i	0.433561	−	0.250317i	0.700863	+	0.713296i	$0.252799\pi$
$578$	14.3186	−	39.3399i	0.595573	−	1.63632i
$579$		0			0
$580$	0.592164	+	1.62696i	0.0245883	+	0.0675557i
$581$	14.8412	−	5.81404i	0.615715	−	0.241207i
$582$		0			0
$583$	18.2253	−	15.2929i	0.754816	−	0.633366i
$584$	−1.34407	−	2.32800i	−0.0556180	−	0.0963332i
$585$		0			0
$586$	−1.28314	−	0.740824i	−0.0530062	−	0.0306032i
$587$	13.0785	−	10.9742i	0.539807	−	0.452952i	−0.331665	−	0.943397i	$-0.607610\pi$
$587$	13.0785	−	10.9742i	0.539807	−	0.452952i	0.871472	+	0.490445i	$0.163166\pi$
$588$		0			0
$589$	−2.03824	+	11.5594i	−0.0839843	+	0.476299i
$590$	−1.08179	−	0.190749i	−0.0445366	−	0.00785301i
$591$		0			0
$592$	−1.64186	+	1.37768i	−0.0674800	+	0.0566224i
$593$	8.82192	+	15.2800i	0.362273	+	0.627475i	0.988335	−	0.152299i	$-0.0486675\pi$
$593$	8.82192	+	15.2800i	0.362273	+	0.627475i	−0.626062	+	0.779774i	$0.715334\pi$
$594$		0			0
$595$	−25.5583	+	0.621421i	−1.04779	+	0.0254758i
$596$	5.67378	−	15.5886i	0.232407	−	0.638533i
$597$		0			0
$598$	−0.190582	−	0.523620i	−0.00779348	−	0.0214124i
$599$	−9.65598	+	11.5076i	−0.394533	+	0.470186i	−0.926345	−	0.376677i	$-0.877067\pi$
$599$	−9.65598	+	11.5076i	−0.394533	+	0.470186i	0.531812	+	0.846862i	$0.321511\pi$
$600$		0			0
$601$	−4.19281	−	4.99680i	−0.171028	−	0.203824i	0.673721	−	0.738986i	$-0.264695\pi$
$601$	−4.19281	−	4.99680i	−0.171028	−	0.203824i	−0.844749	+	0.535162i	$0.820251\pi$
$602$	17.1465	+	9.35135i	0.698838	+	0.381132i
$603$		0			0
$604$	15.5599			0.633122
$605$	−2.13973	−	0.778797i	−0.0869923	−	0.0316626i
$606$		0			0
$607$	20.8219	−	24.8146i	0.845136	−	1.00719i	−0.154679	−	0.987965i	$-0.549434\pi$
$607$	20.8219	−	24.8146i	0.845136	−	1.00719i	0.999815	−	0.0192294i	$-0.00612128\pi$
$608$	−7.35413	+	2.67669i	−0.298250	+	0.108554i
$609$		0			0
$610$	−2.34431	−	13.2952i	−0.0949183	−	0.538308i
$611$		−	0.190154i		−	0.00769283i
$612$		0			0
$613$	3.85405			0.155663			0.0778317	−	0.996967i	$-0.475200\pi$
$613$	3.85405			0.155663			0.0778317	+	0.996967i	$0.475200\pi$
$614$	−9.83386	−	3.57923i	−0.396862	−	0.144446i
$615$		0			0
$616$	21.3698	+	17.0637i	0.861015	+	0.687516i
$617$	20.8477	−	24.8453i	0.839295	−	1.00023i	−0.160617	−	0.987017i	$-0.551348\pi$
$617$	20.8477	−	24.8453i	0.839295	−	1.00023i	0.999913	−	0.0132165i	$-0.00420707\pi$
$618$		0			0
$619$	−12.0752	−	14.3907i	−0.485344	−	0.578410i	0.466683	−	0.884425i	$-0.345449\pi$
$619$	−12.0752	−	14.3907i	−0.485344	−	0.578410i	−0.952027	+	0.306015i	$0.901004\pi$
$620$	−10.2939	−	5.94318i	−0.413413	−	0.238684i
$621$		0			0
$622$		−	21.8053i		−	0.874313i
$623$	3.09570	+	15.3629i	0.124026	+	0.615502i
$624$		0			0
$625$	0.871603	−	4.94311i	0.0348641	−	0.197724i
$626$	−22.5712	−	18.9395i	−0.902125	−	0.756973i
$627$		0			0
$628$	−2.01464	+	5.53517i	−0.0803928	+	0.220877i
$629$	33.5878	+	58.1758i	1.33923	+	2.31962i
$630$		0			0
$631$	3.17557	−	5.50025i	0.126417	−	0.218961i	−0.795869	−	0.605469i	$-0.792985\pi$
$631$	3.17557	−	5.50025i	0.126417	−	0.218961i	0.922286	+	0.386508i	$0.126319\pi$
$632$	−24.9094	−	29.6859i	−0.990843	−	1.18084i
$633$		0			0
$634$	0.794779	−	4.50742i	0.0315647	−	0.179012i
$635$	−13.6839	−	11.4822i	−0.543029	−	0.455655i
$636$		0			0
$637$	−4.11269	+	0.933295i	−0.162951	+	0.0369785i
$638$	3.40320	+	1.96484i	0.134734	+	0.0777888i
$639$		0			0
$640$		−	7.36635i		−	0.291180i
$641$	−29.8979	+	5.27182i	−1.18090	+	0.208224i	−0.729425	−	0.684061i	$-0.760212\pi$
$641$	−29.8979	+	5.27182i	−1.18090	+	0.208224i	−0.451473	+	0.892285i	$0.649101\pi$
$642$		0			0
$643$	3.55310	+	0.626507i	0.140121	+	0.0247070i	0.243268	−	0.969959i	$-0.421780\pi$
$643$	3.55310	+	0.626507i	0.140121	+	0.0247070i	−0.103148	+	0.994666i	$0.532892\pi$
$644$	−1.98571	+	2.48681i	−0.0782479	+	0.0979942i
$645$		0			0
$646$	−1.76996	−	10.0379i	−0.0696382	−	0.394938i
$647$	−4.12557	+	7.14569i	−0.162193	+	0.280926i	−0.935655	−	0.352917i	$-0.885190\pi$
$647$	−4.12557	+	7.14569i	−0.162193	+	0.280926i	0.773462	+	0.633843i	$0.218523\pi$
$648$		0			0
$649$	3.09824	−	1.78877i	0.121617	−	0.0702155i
$650$	−1.80730	−	0.657804i	−0.0708882	−	0.0258012i
$651$		0			0
$652$	1.93620	+	1.62466i	0.0758274	+	0.0636268i
$653$	−13.5899	−	37.3379i	−0.531814	−	1.46115i	−0.856910	−	0.515466i	$-0.827619\pi$
$653$	−13.5899	−	37.3379i	−0.531814	−	1.46115i	0.325096	−	0.945681i	$-0.394603\pi$
$654$		0			0
$655$	−3.74373	−	21.2318i	−0.146280	−	0.829594i
$656$	−0.909343	+	1.57503i	−0.0355039	+	0.0614945i
$657$		0			0
$658$	0.646040	−	0.394233i	0.0251852	−	0.0153688i
$659$	−28.1991	+	4.97227i	−1.09848	+	0.193692i	−0.693375	−	0.720577i	$-0.743877\pi$
$659$	−28.1991	+	4.97227i	−1.09848	+	0.193692i	−0.405107	+	0.914269i	$0.632766\pi$
$660$		0			0
$661$	−0.279751	−	0.0493277i	−0.0108811	−	0.00191862i	0.168205	−	0.985752i	$-0.446203\pi$
$661$	−0.279751	−	0.0493277i	−0.0108811	−	0.00191862i	−0.179086	+	0.983833i	$0.557314\pi$
$662$	10.9292	+	1.92711i	0.424775	+	0.0748992i
$663$		0			0
$664$	−17.0917	+	3.01372i	−0.663285	+	0.116955i
$665$	−3.88397	+	2.37012i	−0.150614	+	0.0919092i
$666$		0			0
$667$	−0.616645	+	1.06806i	−0.0238766	+	0.0413555i
$668$	2.83395	+	16.0721i	0.109649	+	0.621850i
$669$		0			0
$670$	−3.88998	−	10.6876i	−0.150283	−	0.412899i
$671$	33.6815	+	28.2622i	1.30026	+	1.09105i
$672$		0			0
$673$	−4.12151	−	1.50011i	−0.158873	−	0.0578249i	0.261360	−	0.965241i	$-0.415829\pi$
$673$	−4.12151	−	1.50011i	−0.158873	−	0.0578249i	−0.420232	+	0.907417i	$0.638051\pi$
$674$	−14.1390	+	8.16315i	−0.544614	+	0.314433i
$675$		0			0
$676$	−7.44711	+	12.8988i	−0.286427	+	0.496106i
$677$	8.81436	+	49.9887i	0.338763	+	1.92122i	0.386345	+	0.922354i	$0.373737\pi$
$677$	8.81436	+	49.9887i	0.338763	+	1.92122i	−0.0475818	+	0.998867i	$0.515151\pi$
$678$		0			0
$679$	−13.9019	+	17.4101i	−0.533506	+	0.668140i
$680$	27.4141	+	4.83385i	1.05128	+	0.185370i
$681$		0			0
$682$	−26.5685	+	4.68475i	−1.01736	+	0.179388i
$683$		−	40.5678i		−	1.55229i	−0.630557	−	0.776143i	$-0.717174\pi$
$683$		−	40.5678i		−	1.55229i	0.630557	−	0.776143i	$-0.282826\pi$
$684$		0			0
$685$	3.51864	+	2.03149i	0.134440	+	0.0776191i
$686$	−11.6974	−	12.0377i	−0.446607	−	0.459602i
$687$		0			0
$688$	−1.58254	−	1.32791i	−0.0603336	−	0.0506259i
$689$	0.693713	−	3.93424i	0.0264284	−	0.149883i
$690$		0			0
$691$	2.07608	+	2.47418i	0.0789780	+	0.0941223i	0.804086	−	0.594512i	$-0.202655\pi$
$691$	2.07608	+	2.47418i	0.0789780	+	0.0941223i	−0.725109	+	0.688635i	$0.758210\pi$
$692$	−2.13232	+	3.69328i	−0.0810585	+	0.140397i
$693$		0			0
$694$	5.18443	+	8.97970i	0.196798	+	0.340865i
$695$	−1.65670	+	4.55175i	−0.0628422	+	0.172658i
$696$		0			0
$697$	43.6658	+	36.6400i	1.65396	+	1.38784i
$698$	1.37460	−	7.79577i	0.0520296	−	0.295074i
$699$		0			0
$700$	2.16972	+	10.7676i	0.0820076	+	0.406976i
$701$		−	6.55534i		−	0.247592i	−0.992308	−	0.123796i	$-0.960493\pi$
$701$		−	6.55534i		−	0.247592i	0.992308	−	0.123796i	$-0.0395068\pi$
$702$		0			0
$703$	10.3537	+	5.97771i	0.390497	+	0.225454i
$704$	−12.7322	−	15.1736i	−0.479862	−	0.571877i
$705$		0			0
$706$	−12.9654	+	15.4516i	−0.487959	+	0.581527i
$707$	5.12631	+	4.09333i	0.192795	+	0.153946i
$708$		0			0
$709$	9.22465	+	3.35750i	0.346439	+	0.126094i	0.509379	−	0.860543i	$-0.329875\pi$
$709$	9.22465	+	3.35750i	0.346439	+	0.126094i	−0.162939	+	0.986636i	$0.552098\pi$
$710$	−1.21216			−0.0454915
$711$		0			0
$712$		−	17.0639i		−	0.639496i
$713$	−1.47026	−	8.33826i	−0.0550617	−	0.312270i
$714$		0			0
$715$	−2.46911	+	0.898681i	−0.0923393	+	0.0336088i
$716$	18.5299	−	22.0830i	0.692494	−	0.825282i
$717$		0			0
$718$	22.3292	+	8.12718i	0.833320	+	0.303304i
$719$	11.8461			0.441784			0.220892	−	0.975298i	$-0.429103\pi$
$719$	11.8461			0.441784			0.220892	+	0.975298i	$0.429103\pi$
$720$		0			0
$721$	22.1938	+	12.1040i	0.826539	+	0.450778i
$722$	9.90260	+	11.8015i	0.368537	+	0.439205i
$723$		0			0
$724$	−12.1282	+	14.4539i	−0.450742	+	0.537174i
$725$	1.45590	+	4.00005i	0.0540707	+	0.148558i
$726$		0			0
$727$	15.4099	−	42.3383i	0.571521	−	1.57024i	−0.230580	−	0.973053i	$-0.574062\pi$
$727$	15.4099	−	42.3383i	0.571521	−	1.57024i	0.802101	−	0.597188i	$-0.203716\pi$
$728$	4.59054	−	0.111614i	0.170137	−	0.00413668i
$729$		0			0
$730$	0.513998	+	0.890271i	0.0190239	+	0.0329504i
$731$	−49.6002	+	41.6196i	−1.83453	+	1.53935i
$732$		0			0
$733$	4.22098	+	0.744273i	0.155906	+	0.0274904i	0.251056	−	0.967973i	$-0.419222\pi$
$733$	4.22098	+	0.744273i	0.155906	+	0.0274904i	−0.0951505	+	0.995463i	$0.530333\pi$
$734$	−2.81322	+	15.9546i	−0.103838	+	0.588895i
$735$		0			0
$736$	4.32452	−	3.62871i	0.159404	−	0.133756i
$737$	32.0789	+	18.5208i	1.18164	+	0.682221i
$738$		0			0
$739$	−6.26410	−	10.8497i	−0.230429	−	0.399114i	0.727506	−	0.686102i	$-0.240679\pi$
$739$	−6.26410	−	10.8497i	−0.230429	−	0.399114i	−0.957934	+	0.286988i	$0.907346\pi$
$740$	−9.27432	+	7.78208i	−0.340931	+	0.286075i
$741$		0			0
$742$	14.8046	−	5.79971i	0.543494	−	0.212914i
$743$	5.70379	+	15.6710i	0.209252	+	0.574914i	0.999271	−	0.0381673i	$-0.0121520\pi$
$743$	5.70379	+	15.6710i	0.209252	+	0.574914i	−0.790020	+	0.613081i	$0.789930\pi$
$744$		0			0
$745$	−5.85164	+	16.0772i	−0.214387	+	0.589025i
$746$	8.40674	−	4.85363i	0.307793	−	0.177704i
$747$		0			0
$748$	−29.1126	+	16.8082i	−1.06446	+	0.614567i
$749$	−10.3747	+	30.8150i	−0.379083	+	1.12595i
$750$		0			0
$751$	−47.2397	+	17.1939i	−1.72380	+	0.627413i	−0.998159	−	0.0606582i	$-0.980680\pi$
$751$	−47.2397	+	17.1939i	−1.72380	+	0.627413i	−0.725644	+	0.688071i	$0.758458\pi$
$752$	−0.0752253	+	0.0273798i	−0.00274318	+	0.000998437i
$753$		0			0
$754$	0.649826	−	0.114582i	0.0236653	−	0.00417282i
$755$	−16.0476			−0.584033
$756$		0			0
$757$	8.96036			0.325670			0.162835	−	0.986653i	$-0.447936\pi$
$757$	8.96036			0.325670			0.162835	+	0.986653i	$0.447936\pi$
$758$	−11.7656	+	2.07459i	−0.427346	+	0.0753527i
$759$		0			0
$760$	4.65545	−	1.69444i	0.168871	−	0.0614639i
$761$	26.8181	−	9.76100i	0.972156	−	0.353836i	0.193370	−	0.981126i	$-0.438058\pi$
$761$	26.8181	−	9.76100i	0.972156	−	0.353836i	0.778786	+	0.627290i	$0.215836\pi$
$762$		0			0
$763$	−4.88241	−	24.2297i	−0.176755	−	0.877176i
$764$	−6.56027	+	3.78757i	−0.237342	+	0.137030i
$765$		0			0
$766$	12.4921	−	7.21231i	0.451358	−	0.260591i
$767$	0.205459	−	0.564494i	0.00741869	−	0.0203827i
$768$		0			0
$769$	0.460020	+	1.26389i	0.0165887	+	0.0455772i	0.947711	−	0.319131i	$-0.103391\pi$
$769$	0.460020	+	1.26389i	0.0165887	+	0.0455772i	−0.931122	+	0.364708i	$0.881169\pi$
$770$	−8.17223	−	6.52549i	−0.294507	−	0.235162i
$771$		0			0
$772$	−1.23725	+	1.03817i	−0.0445295	+	0.0373647i
$773$	−8.35543	−	14.4720i	−0.300524	−	0.520523i	0.675731	−	0.737148i	$-0.263828\pi$
$773$	−8.35543	−	14.4720i	−0.300524	−	0.520523i	−0.976255	+	0.216626i	$0.930495\pi$
$774$		0			0
$775$	−25.3086	−	14.6120i	−0.909113	−	0.524877i
$776$	18.5832	−	15.5932i	0.667100	−	0.559763i
$777$		0			0
$778$	−3.92916	+	22.2834i	−0.140867	+	0.798897i
$779$	9.99061	+	1.76161i	0.357951	+	0.0631164i
$780$		0			0
$781$	3.02417	−	2.53758i	0.108213	−	0.0908018i
$782$	3.67623	+	6.36741i	0.131462	+	0.227698i
$783$		0			0
$784$	0.961386	+	1.49260i	0.0343352	+	0.0533072i
$785$	2.07779	−	5.70869i	0.0741596	−	0.203752i
$786$		0			0
$787$	4.47731	+	12.3013i	0.159599	+	0.438495i	0.993557	−	0.113333i	$-0.0361528\pi$
$787$	4.47731	+	12.3013i	0.159599	+	0.438495i	−0.833958	+	0.551828i	$0.813931\pi$
$788$	16.8377	−	20.0664i	0.599818	−	0.714835i
$789$		0			0
$790$	9.52584	+	11.3524i	0.338914	+	0.403902i
$791$	8.96297	−	5.46947i	0.318686	−	0.194472i
$792$		0			0
$793$	7.38288			0.262174
$794$	18.3683	+	6.68553i	0.651868	+	0.237261i
$795$		0			0
$796$	10.0803	−	12.0132i	0.357287	−	0.425798i
$797$	28.9247	−	10.5277i	1.02457	−	0.372912i	0.225557	−	0.974230i	$-0.427580\pi$
$797$	28.9247	−	10.5277i	1.02457	−	0.372912i	0.799010	+	0.601318i	$0.205358\pi$
$798$		0			0
$799$	0.435691	+	2.47093i	0.0154136	+	0.0874151i
$800$		−	19.4849i		−	0.688896i
$801$		0			0
$802$	8.57959			0.302956
$803$	−3.14609	−	1.14508i	−0.111023	−	0.0404091i
$804$		0			0
$805$	2.04796	−	2.56477i	0.0721810	−	0.0903963i
$806$	−2.91187	+	3.47023i	−0.102566	+	0.122234i
$807$		0			0
$808$	−4.59132	−	5.47172i	−0.161522	−	0.192495i
$809$	−48.9190	−	28.2434i	−1.71990	−	0.992985i	−0.919069	−	0.394097i	$-0.871058\pi$
$809$	−48.9190	−	28.2434i	−1.71990	−	0.992985i	−0.800832	−	0.598889i	$-0.795609\pi$
$810$		0			0
$811$			0.658409i			0.0231199i	0.999933	+	0.0115599i	$0.00367972\pi$
$811$			0.658409i			0.0231199i	−0.999933	+	0.0115599i	$0.996320\pi$
$812$	−2.49176	−	2.82706i	−0.0874436	−	0.0992104i
$813$		0			0
$814$	−4.77162	+	27.0612i	−0.167245	+	0.948494i
$815$	−1.99690	−	1.67559i	−0.0699482	−	0.0586935i
$816$		0			0
$817$	−3.94125	+	10.8285i	−0.137887	+	0.378841i
$818$	5.89881	+	10.2170i	0.206247	+	0.357231i
$819$		0			0
$820$	−5.13658	+	8.89682i	−0.179377	+	0.310690i
$821$	26.7252	+	31.8499i	0.932718	+	1.11157i	0.993547	+	0.113421i	$0.0361810\pi$
$821$	26.7252	+	31.8499i	0.932718	+	1.11157i	−0.0608295	+	0.998148i	$0.519375\pi$
$822$		0			0
$823$	−5.29377	+	30.0224i	−0.184529	+	1.04652i	0.742030	+	0.670367i	$0.233863\pi$
$823$	−5.29377	+	30.0224i	−0.184529	+	1.04652i	−0.926559	+	0.376150i	$0.877248\pi$
$824$	−21.0858	−	17.6931i	−0.734559	−	0.616369i
$825$		0			0
$826$	2.34380	−	0.472287i	0.0815512	−	0.0164330i
$827$	36.1773	+	20.8870i	1.25801	+	0.726311i	0.972687	−	0.232121i	$-0.0745666\pi$
$827$	36.1773	+	20.8870i	1.25801	+	0.726311i	0.285321	+	0.958432i	$0.407900\pi$
$828$		0			0
$829$		−	43.6190i		−	1.51495i	−0.652864	−	0.757475i	$-0.726433\pi$
$829$		−	43.6190i		−	1.51495i	0.652864	−	0.757475i	$-0.273567\pi$
$830$	6.53618	−	1.15250i	0.226874	−	0.0400040i
$831$		0			0
$832$	−3.27548	−	0.577555i	−0.113557	−	0.0200231i
$833$	51.3032	−	21.5507i	1.77755	−	0.746688i
$834$		0			0
$835$	−2.92279	−	16.5760i	−0.101147	−	0.573635i
$836$	−2.99139	+	5.18124i	−0.103459	+	0.179197i
$837$		0			0
$838$	−9.20258	+	5.31311i	−0.317898	+	0.183538i
$839$	−8.50951	−	3.09721i	−0.293781	−	0.106928i	0.190925	−	0.981605i	$-0.438851\pi$
$839$	−8.50951	−	3.09721i	−0.293781	−	0.106928i	−0.484706	+	0.874677i	$0.661073\pi$
$840$		0			0
$841$	21.0965	+	17.7021i	0.727467	+	0.610417i
$842$	5.24671	+	14.4152i	0.180814	+	0.496781i
$843$		0			0
$844$	−3.10940	−	17.6343i	−0.107030	−	0.606997i
$845$	7.68056	−	13.3031i	0.264219	−	0.457641i
$846$		0			0
$847$	4.95468	−	0.120467i	0.170245	−	0.00413931i
$848$	−1.65628	+	0.292046i	−0.0568767	+	0.0100289i
$849$		0			0
$850$	24.9918	+	4.40673i	0.857212	+	0.151150i
$851$	−8.49288	−	1.49752i	−0.291132	−	0.0513344i
$852$		0			0
$853$	−49.6962	+	8.76279i	−1.70157	+	0.300032i	−0.938241	−	0.345982i	$-0.887546\pi$
$853$	−49.6962	+	8.76279i	−1.70157	+	0.300032i	−0.763325	+	0.646014i	$0.776435\pi$
$854$	15.3064	+	25.0830i	0.523773	+	0.858321i
$855$		0			0
$856$	17.7015	−	30.6599i	0.605025	−	1.04793i
$857$	−2.67909	−	15.1938i	−0.0915158	−	0.519012i	−0.995759	−	0.0919951i	$-0.970676\pi$
$857$	−2.67909	−	15.1938i	−0.0915158	−	0.519012i	0.904244	−	0.427017i	$-0.140436\pi$
$858$		0			0
$859$	−1.57769	−	4.33468i	−0.0538303	−	0.147897i	0.909863	−	0.414908i	$-0.136186\pi$
$859$	−1.57769	−	4.33468i	−0.0538303	−	0.147897i	−0.963694	+	0.267011i	$0.913964\pi$
$860$	−8.93923	−	7.50090i	−0.304825	−	0.255779i
$861$		0			0
$862$	−1.61552	−	0.588001i	−0.0550248	−	0.0200274i
$863$	−27.5293	+	15.8941i	−0.937108	+	0.541040i	−0.889053	−	0.457805i	$-0.848636\pi$
$863$	−27.5293	+	15.8941i	−0.937108	+	0.541040i	−0.0480557	+	0.998845i	$0.515302\pi$
$864$		0			0
$865$	2.19916	−	3.80906i	0.0747737	−	0.129512i
$866$	1.35269	+	7.67149i	0.0459663	+	0.260688i
$867$		0			0
$868$	25.5801	+	3.87190i	0.868244	+	0.131421i
$869$	−47.5314	−	8.38106i	−1.61239	−	0.284308i
$870$		0			0
$871$	6.12532	−	1.08006i	0.207548	−	0.0365964i
$872$			26.9125i			0.911372i
$873$		0			0
$874$	1.13322	+	0.654267i	0.0383319	+	0.0221309i
$875$	−5.41416	−	26.8687i	−0.183032	−	0.908327i
$876$		0			0
$877$	−14.8121	−	12.4288i	−0.500167	−	0.419690i	0.357486	−	0.933919i	$-0.383634\pi$
$877$	−14.8121	−	12.4288i	−0.500167	−	0.419690i	−0.857653	+	0.514228i	$0.828078\pi$
$878$	−2.73792	+	15.5275i	−0.0924004	+	0.524029i
$879$		0			0
$880$	0.711038	+	0.847382i	0.0239691	+	0.0285652i
$881$	0.310834	−	0.538380i	0.0104723	−	0.0181385i	−0.860742	−	0.509042i	$-0.830000\pi$
$881$	0.310834	−	0.538380i	0.0104723	−	0.0181385i	0.871214	+	0.490903i	$0.163333\pi$
$882$		0			0
$883$	−1.97025	−	3.41257i	−0.0663041	−	0.114842i	0.830968	−	0.556321i	$-0.187787\pi$
$883$	−1.97025	−	3.41257i	−0.0663041	−	0.114842i	−0.897272	+	0.441479i	$0.854454\pi$
$884$	−1.93059	+	5.30425i	−0.0649328	+	0.178401i
$885$		0			0
$886$	−21.2533	−	17.8337i	−0.714020	−	0.599134i
$887$	8.69367	−	49.3042i	0.291905	−	1.65547i	−0.387618	−	0.921820i	$-0.626702\pi$
$887$	8.69367	−	49.3042i	0.291905	−	1.65547i	0.679523	−	0.733654i	$-0.262187\pi$
$888$		0			0
$889$	36.8478	+	12.4058i	1.23583	+	0.416077i
$890$			6.52556i			0.218737i
$891$		0			0
$892$	−7.20364	−	4.15902i	−0.241196	−	0.139254i
$893$	0.287031	+	0.342070i	0.00960512	+	0.0114469i
$894$		0			0
$895$	−19.1107	+	22.7753i	−0.638802	+	0.761294i
$896$	5.84831	+	14.9286i	0.195378	+	0.498731i
$897$		0			0
$898$	23.3585	+	8.50179i	0.779482	+	0.283708i
$899$	10.0263			0.334395
$900$		0			0
$901$			52.7122i			1.75610i
$902$	4.04894	+	22.9627i	0.134815	+	0.764574i
$903$		0			0
$904$	−10.7433	+	3.91024i	−0.357316	+	0.130053i
$905$	12.5084	−	14.9070i	0.415794	−	0.495524i
$906$		0			0
$907$	21.0519	+	7.66226i	0.699016	+	0.254421i	0.666991	−	0.745066i	$-0.267582\pi$
$907$	21.0519	+	7.66226i	0.699016	+	0.254421i	0.0320254	+	0.999487i	$0.489804\pi$
$908$	−20.2247			−0.671181
$909$		0			0
$910$	−1.75551	+	0.0426833i	−0.0581946	+	0.00141494i
$911$	24.0775	+	28.6944i	0.797723	+	0.950689i	0.999587	−	0.0287243i	$-0.00914450\pi$
$911$	24.0775	+	28.6944i	0.797723	+	0.950689i	−0.201864	+	0.979413i	$0.564700\pi$
$912$		0			0
$913$	−13.8942	+	16.5584i	−0.459830	+	0.548005i
$914$	−7.10770	−	19.5282i	−0.235102	−	0.645937i
$915$		0			0
$916$	−3.60086	+	9.89327i	−0.118976	+	0.326883i
$917$	24.4434	+	40.0561i	0.807193	+	1.32277i
$918$		0			0
$919$	6.76771	+	11.7220i	0.223246	+	0.386674i	0.955792	−	0.294044i	$-0.0950012\pi$
$919$	6.76771	+	11.7220i	0.223246	+	0.386674i	−0.732546	+	0.680718i	$0.761668\pi$
$920$	−2.73759	+	2.29711i	−0.0902556	+	0.0757334i
$921$		0			0
$922$	26.9105	+	4.74505i	0.886250	+	0.156270i
$923$	0.115109	−	0.652818i	0.00378887	−	0.0214878i
$924$		0			0
$925$	−22.8019	+	19.1331i	−0.749722	+	0.629092i
$926$	23.5226	+	13.5808i	0.773000	+	0.446292i
$927$		0			0
$928$	3.34248	+	5.78935i	0.109722	+	0.190045i
$929$	28.4979	−	23.9126i	0.934986	−	0.784547i	−0.0417195	−	0.999129i	$-0.513284\pi$
$929$	28.4979	−	23.9126i	0.934986	−	0.784547i	0.976706	+	0.214583i	$0.0688391\pi$
$930$		0			0
$931$	5.98957	−	7.88686i	0.196300	−	0.258481i
$932$	3.44503	+	9.46514i	0.112846	+	0.310041i
$933$		0			0
$934$	−0.728762	+	2.00226i	−0.0238458	+	0.0655159i
$935$	30.0252	−	17.3351i	0.981930	−	0.566917i
$936$		0			0
$937$	−42.3336	+	24.4413i	−1.38298	+	0.798463i	−0.992511	−	0.122153i	$-0.961020\pi$
$937$	−42.3336	+	24.4413i	−1.38298	+	0.798463i	−0.390468	+	0.920617i	$0.627687\pi$
$938$	16.3686	+	18.5712i	0.534454	+	0.606372i
$939$		0			0
$940$	−0.424923	+	0.154659i	−0.0138595	+	0.00504443i
$941$	−30.0578	+	10.9401i	−0.979856	+	0.356638i	−0.781784	−	0.623549i	$-0.785690\pi$
$941$	−30.0578	+	10.9401i	−0.979856	+	0.356638i	−0.198072	+	0.980188i	$0.563468\pi$
$942$		0			0
$943$	−7.20661	+	1.27072i	−0.234679	+	0.0413803i
$944$	−0.252898			−0.00823112
$945$		0			0
$946$	−26.4858			−0.861128
$947$	34.1040	−	6.01346i	1.10823	−	0.195411i	0.410564	−	0.911832i	$-0.365332\pi$
$947$	34.1040	−	6.01346i	1.10823	−	0.195411i	0.697669	+	0.716421i	$0.254221\pi$
$948$		0			0
$949$	−0.528273	+	0.192276i	−0.0171485	+	0.00624154i
$950$	4.24409	−	1.54472i	0.137697	−	0.0501174i
$951$		0			0
$952$	−59.3952	+	11.9684i	−1.92501	+	0.387898i
$953$	43.1385	−	24.9060i	1.39739	−	0.806786i	0.403275	−	0.915079i	$-0.367872\pi$
$953$	43.1385	−	24.9060i	1.39739	−	0.806786i	0.994119	+	0.108293i	$0.0345386\pi$
$954$		0			0
$955$	6.76592	−	3.90631i	0.218940	−	0.126405i
$956$	5.36064	−	14.7282i	0.173376	−	0.476345i
$957$		0			0
$958$	5.80574	+	15.9511i	0.187575	+	0.515358i
$959$	−8.74372	−	1.32349i	−0.282349	−	0.0427376i
$960$		0			0
$961$	−28.9819	+	24.3187i	−0.934901	+	0.784475i
$962$	2.30703	+	3.99589i	0.0743816	+	0.128833i
$963$		0			0
$964$	−14.2641	−	8.23537i	−0.459415	−	0.265243i
$965$	1.27603	−	1.07072i	0.0410770	−	0.0344677i
$966$		0			0
$967$	−0.0919287	+	0.521354i	−0.00295623	+	0.0167656i	−0.986250	−	0.165259i	$-0.947154\pi$
$967$	−0.0919287	+	0.521354i	−0.00295623	+	0.0167656i	0.983294	+	0.182025i	$0.0582651\pi$
$968$	−5.31444	−	0.937079i	−0.170813	−	0.0301189i
$969$		0			0
$970$	−7.10659	+	5.96314i	−0.228179	+	0.191465i
$971$	−9.94776	−	17.2300i	−0.319239	−	0.552938i	0.661091	−	0.750306i	$-0.270094\pi$
$971$	−9.94776	−	17.2300i	−0.319239	−	0.552938i	−0.980329	+	0.197368i	$0.936761\pi$
$972$		0			0
$973$	−0.256265	−	10.5399i	−0.00821547	−	0.337893i
$974$	−0.229412	+	0.630304i	−0.00735083	+	0.0201962i
$975$		0			0
$976$	−1.06304	−	2.92068i	−0.0340271	−	0.0934886i
$977$	31.6302	−	37.6954i	1.01194	−	1.20598i	0.0335032	−	0.999439i	$-0.489334\pi$
$977$	31.6302	−	37.6954i	1.01194	−	1.20598i	0.978437	−	0.206545i	$-0.0662219\pi$
$978$		0			0
$979$	−13.6609	−	16.2804i	−0.436603	−	0.520324i
$980$	5.43056	+	8.43122i	0.173473	+	0.269325i
$981$		0			0
$982$	12.5395			0.400153
$983$	−25.6891	−	9.35008i	−0.819356	−	0.298221i	−0.101873	−	0.994797i	$-0.532484\pi$
$983$	−25.6891	−	9.35008i	−0.819356	−	0.298221i	−0.717483	+	0.696576i	$0.754706\pi$
$984$		0			0
$985$	−17.3655	+	20.6954i	−0.553311	+	0.659411i
$986$	−8.18150	+	2.97782i	−0.260552	+	0.0948332i
$987$		0			0
$988$	0.174446	+	0.989333i	0.00554987	+	0.0314749i
$989$		−	8.31230i		−	0.264316i
$990$		0			0
$991$	44.3720			1.40952			0.704761	−	0.709445i	$-0.251054\pi$
$991$	44.3720			1.40952			0.704761	+	0.709445i	$0.251054\pi$
$992$	−43.1265	−	15.6968i	−1.36927	−	0.498372i
$993$		0			0
$994$	2.45656	−	0.962360i	0.0779174	−	0.0305242i
$995$	−10.3963	+	12.3898i	−0.329585	+	0.392784i
$996$		0			0
$997$	−16.9190	−	20.1633i	−0.535830	−	0.638577i	0.428418	−	0.903581i	$-0.359071\pi$
$997$	−16.9190	−	20.1633i	−0.535830	−	0.638577i	−0.964247	+	0.265004i	$0.914627\pi$
$998$	−1.87922	−	1.08497i	−0.0594857	−	0.0343441i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.8		132
3.2	odd	2		189.2.bd.a.185.15	yes	132
7.5	odd	6		567.2.ba.a.341.15		132
21.5	even	6		189.2.ba.a.131.8	yes	132
27.7	even	9		189.2.ba.a.101.8	✓	132
27.20	odd	18		567.2.ba.a.143.15		132
189.47	even	18	inner	567.2.bd.a.467.8		132
189.61	odd	18		189.2.bd.a.47.15	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.8	✓	132	27.7	even	9
189.2.ba.a.131.8	yes	132	21.5	even	6
189.2.bd.a.47.15	yes	132	189.61	odd	18
189.2.bd.a.185.15	yes	132	3.2	odd	2
567.2.ba.a.143.15		132	27.20	odd	18
567.2.ba.a.341.15		132	7.5	odd	6
567.2.bd.a.17.8		132	1.1	even	1	trivial
567.2.bd.a.467.8		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)

\(f(q)\)	\(=\)	\(q+(-0.892534 + 0.157378i) q^{2} +(-1.10754 + 0.403110i) q^{4} +(1.14226 - 0.415747i) q^{5} +(-1.98483 + 1.74942i) q^{7} +(2.49483 - 1.44039i) q^{8} +O(q^{10})\)	\(q+(-0.892534 + 0.157378i) q^{2} +(-1.10754 + 0.403110i) q^{4} +(1.14226 - 0.415747i) q^{5} +(-1.98483 + 1.74942i) q^{7} +(2.49483 - 1.44039i) q^{8} +(-0.954073 + 0.550834i) q^{10} +(1.22714 - 3.37155i) q^{11} +(-0.206055 - 0.566132i) q^{13} +(1.49621 - 1.87378i) q^{14} +(-0.194293 + 0.163031i) q^{16} +(3.97470 + 6.88437i) q^{17} +(1.22523 + 0.707386i) q^{19} +(-1.09750 + 0.920911i) q^{20} +(-0.564660 + 3.20235i) q^{22} +(-1.00502 - 0.177213i) q^{23} +(-2.69832 + 2.26416i) q^{25} +(0.273008 + 0.472864i) q^{26} +(1.49306 - 2.73765i) q^{28} +(0.413325 - 1.13560i) q^{29} +(2.83760 + 7.79623i) q^{31} +(-3.55571 + 4.23753i) q^{32} +(-4.63100 - 5.51901i) q^{34} +(-1.53987 + 2.82347i) q^{35} +8.45042 q^{37} +(-1.20488 - 0.438542i) q^{38} +(2.25090 - 2.68252i) q^{40} +(6.73814 - 2.45248i) q^{41} +(1.41438 + 8.02135i) q^{43} +4.22879i q^{44} +0.924908 q^{46} +(0.296592 + 0.107951i) q^{47} +(0.879076 - 6.94458i) q^{49} +(2.05201 - 2.44549i) q^{50} +(0.456428 + 0.543949i) q^{52} +(5.74259 + 3.31549i) q^{53} -4.36136i q^{55} +(-2.43197 + 7.22344i) q^{56} +(-0.190188 + 1.07861i) q^{58} +(0.763827 + 0.640927i) q^{59} +(-4.19127 + 11.5154i) q^{61} +(-3.75960 - 6.51182i) q^{62} +(2.76033 - 4.78103i) q^{64} +(-0.470736 - 0.561001i) q^{65} +(-1.79273 + 10.1671i) q^{67} +(-7.17729 - 6.02246i) q^{68} +(0.930030 - 2.76238i) q^{70} +(0.952881 + 0.550146i) q^{71} -0.933127i q^{73} +(-7.54228 + 1.32991i) q^{74} +(-1.64214 - 0.289554i) q^{76} +(3.46258 + 8.83874i) q^{77} +(-2.33590 - 13.2476i) q^{79} +(-0.154153 + 0.267000i) q^{80} +(-5.62805 + 3.24936i) q^{82} +(-5.66119 - 2.06050i) q^{83} +(7.40228 + 6.21125i) q^{85} +(-2.52476 - 6.93673i) q^{86} +(-1.79484 - 10.1790i) q^{88} +(2.96167 - 5.12977i) q^{89} +(1.39939 + 0.763198i) q^{91} +(1.18454 - 0.208866i) q^{92} +(-0.281708 - 0.0496727i) q^{94} +(1.69362 + 0.298631i) q^{95} +(8.29293 - 1.46227i) q^{97} +(0.308318 + 6.33662i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 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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