LMFDB - Embedded newform 243.2.i.a.61.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			61.3
Character	$\chi$	$=$	243.61
Dual form			243.2.i.a.4.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.34586 + 0.0910299i) q^{2} +(-0.823564 + 1.52373i) q^{3} +(3.50077 - 0.272102i) q^{4} +(-1.67953 + 2.08230i) q^{5} +(1.79326 - 3.64941i) q^{6} +(-3.42025 - 1.55470i) q^{7} +(-3.52404 + 0.411902i) q^{8} +(-1.64349 - 2.50977i) q^{9} +(3.75040 - 5.03765i) q^{10} +(-0.0971655 + 5.00983i) q^{11} +(-2.46850 + 5.55831i) q^{12} +(1.25205 - 0.401453i) q^{13} +(8.16495 + 3.33575i) q^{14} +(-1.78965 - 4.27405i) q^{15} +(1.29109 - 0.201922i) q^{16} +(1.50363 - 5.02247i) q^{17} +(4.08385 + 5.73796i) q^{18} +(3.90336 + 0.925114i) q^{19} +(-5.31307 + 7.74665i) q^{20} +(5.18573 - 3.93114i) q^{21} +(-0.228108 - 11.7612i) q^{22} +(-6.75195 - 4.82601i) q^{23} +(2.27465 - 5.70891i) q^{24} +(-0.456601 - 2.10790i) q^{25} +(-2.90058 + 1.05572i) q^{26} +(5.17772 - 0.437265i) q^{27} +(-12.3966 - 4.51198i) q^{28} +(1.13035 - 8.27560i) q^{29} +(4.58732 + 9.86341i) q^{30} +(1.20173 - 1.17865i) q^{31} +(3.95273 - 0.776291i) q^{32} +(-7.55358 - 4.27397i) q^{33} +(-3.07010 + 11.9189i) q^{34} +(8.98177 - 4.51081i) q^{35} +(-6.43638 - 8.33894i) q^{36} +(-1.35989 + 0.894415i) q^{37} +(-9.24094 - 1.81486i) q^{38} +(-0.419437 + 2.23840i) q^{39} +(5.06105 - 8.02990i) q^{40} +(-0.540280 - 1.02570i) q^{41} +(-11.8071 + 9.69394i) q^{42} +(1.05700 + 3.08919i) q^{43} +(1.02303 + 17.5647i) q^{44} +(7.98638 + 0.793026i) q^{45} +(16.2784 + 10.7065i) q^{46} +(-3.47013 - 3.40347i) q^{47} +(-0.755618 + 2.13356i) q^{48} +(4.67840 + 5.36085i) q^{49} +(1.26300 + 4.90327i) q^{50} +(6.41453 + 6.42744i) q^{51} +(4.27390 - 1.74608i) q^{52} +(-6.34982 + 5.32813i) q^{53} +(-12.1064 + 1.49709i) q^{54} +(-10.2687 - 8.61650i) q^{55} +(12.6935 + 4.07001i) q^{56} +(-4.62429 + 5.18577i) q^{57} +(-1.89830 + 19.5163i) q^{58} +(-0.766536 - 0.422957i) q^{59} +(-7.42812 - 14.4755i) q^{60} +(-8.54229 - 0.663959i) q^{61} +(-2.71180 + 2.87434i) q^{62} +(1.71920 + 11.1392i) q^{63} +(-11.7450 + 2.78361i) q^{64} +(-1.26691 + 3.28139i) q^{65} +(18.1087 + 9.33851i) q^{66} +(-0.810426 - 5.93337i) q^{67} +(3.89724 - 17.9917i) q^{68} +(12.9142 - 6.31361i) q^{69} +(-20.6593 + 11.3993i) q^{70} +(2.44908 + 5.67761i) q^{71} +(6.82549 + 8.16759i) q^{72} +(-3.18566 - 4.27908i) q^{73} +(3.10869 - 2.22196i) q^{74} +(3.58791 + 1.04026i) q^{75} +(13.9165 + 2.17650i) q^{76} +(8.12108 - 16.9838i) q^{77} +(0.780177 - 5.28915i) q^{78} +(-3.67063 - 5.82385i) q^{79} +(-1.74796 + 3.02756i) q^{80} +(-3.59791 + 8.24955i) q^{81} +(1.36079 + 2.35695i) q^{82} +(-6.88942 + 13.0792i) q^{83} +(17.0844 - 15.1731i) q^{84} +(7.93287 + 11.5664i) q^{85} +(-2.76077 - 7.15058i) q^{86} +(11.6788 + 8.53783i) q^{87} +(-1.72114 - 17.6949i) q^{88} +(2.69753 - 6.25358i) q^{89} +(-18.8071 - 1.13333i) q^{90} +(-4.90646 - 0.573482i) q^{91} +(-24.9502 - 15.0575i) q^{92} +(0.806238 + 2.80180i) q^{93} +(8.45024 + 7.66818i) q^{94} +(-8.48219 + 6.57419i) q^{95} +(-2.07247 + 6.66220i) q^{96} +(-4.96329 - 6.15351i) q^{97} +(-11.4629 - 12.1499i) q^{98} +(12.7332 - 7.98971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{80}{81}\right)$

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 $

$2$	−2.34586	+	0.0910299i	−1.65877	+	0.0643679i	−0.851013	−	0.525145i	$-0.824011\pi$
$2$	−2.34586	+	0.0910299i	−1.65877	+	0.0643679i	−0.807759	+	0.589513i	$0.799320\pi$
$3$	−0.823564	+	1.52373i	−0.475485	+	0.879724i
$3$	−0.823564	+	1.52373i	−0.475485	+	0.879724i
$4$	3.50077	−	0.272102i	1.75039	−	0.136051i
$5$	−1.67953	+	2.08230i	−0.751110	+	0.931231i	−0.999297	−	0.0374813i	$-0.988067\pi$
$5$	−1.67953	+	2.08230i	−0.751110	+	0.931231i	0.248187	+	0.968712i	$0.420165\pi$
$6$	1.79326	−	3.64941i	0.732095	−	1.48987i
$7$	−3.42025	−	1.55470i	−1.29273	−	0.587620i	−0.354965	−	0.934880i	$-0.615507\pi$
$7$	−3.42025	−	1.55470i	−1.29273	−	0.587620i	−0.937769	+	0.347260i	$0.887112\pi$
$8$	−3.52404	+	0.411902i	−1.24594	+	0.145629i
$9$	−1.64349	−	2.50977i	−0.547828	−	0.836591i
$10$	3.75040	−	5.03765i	1.18598	−	1.59305i
$11$	−0.0971655	+	5.00983i	−0.0292965	+	1.51052i	0.640490	+	0.767966i	$0.278731\pi$
$11$	−0.0971655	+	5.00983i	−0.0292965	+	1.51052i	−0.669787	+	0.742553i	$0.733615\pi$
$12$	−2.46850	+	5.55831i	−0.712595	+	1.60455i
$13$	1.25205	−	0.401453i	0.347256	−	0.111343i	−0.126580	−	0.991956i	$-0.540400\pi$
$13$	1.25205	−	0.401453i	0.347256	−	0.111343i	0.473835	+	0.880613i	$0.342869\pi$
$14$	8.16495	+	3.33575i	2.18217	+	0.891516i
$15$	−1.78965	−	4.27405i	−0.462084	−	1.10356i
$16$	1.29109	−	0.201922i	0.322772	−	0.0504806i
$17$	1.50363	−	5.02247i	0.364683	−	1.21813i	−0.557108	−	0.830440i	$-0.688089\pi$
$17$	1.50363	−	5.02247i	0.364683	−	1.21813i	0.921791	−	0.387687i	$-0.126726\pi$
$18$	4.08385	+	5.73796i	0.962572	+	1.35245i
$19$	3.90336	+	0.925114i	0.895493	+	0.212236i	0.652497	−	0.757792i	$-0.273722\pi$
$19$	3.90336	+	0.925114i	0.895493	+	0.212236i	0.242996	+	0.970027i	$0.421870\pi$
$20$	−5.31307	+	7.74665i	−1.18804	+	1.73220i
$21$	5.18573	−	3.93114i	1.13162	−	0.857845i
$22$	−0.228108	−	11.7612i	−0.0486328	−	2.50749i
$23$	−6.75195	−	4.82601i	−1.40788	−	1.00629i	−0.995448	−	0.0953034i	$-0.969618\pi$
$23$	−6.75195	−	4.82601i	−1.40788	−	1.00629i	−0.412432	−	0.910989i	$-0.635320\pi$
$24$	2.27465	−	5.70891i	0.464311	−	1.16533i
$25$	−0.456601	−	2.10790i	−0.0913201	−	0.421581i
$26$	−2.90058	+	1.05572i	−0.568851	+	0.207045i
$27$	5.17772	−	0.437265i	0.996453	−	0.0841516i
$28$	−12.3966	−	4.51198i	−2.34273	−	0.852684i
$29$	1.13035	−	8.27560i	0.209900	−	1.53674i	−0.520584	−	0.853811i	$-0.674286\pi$
$29$	1.13035	−	8.27560i	0.209900	−	1.53674i	0.730484	−	0.682930i	$-0.239295\pi$
$30$	4.58732	+	9.86341i	0.837526	+	1.80080i
$31$	1.20173	−	1.17865i	0.215837	−	0.211692i	−0.584253	−	0.811572i	$-0.698612\pi$
$31$	1.20173	−	1.17865i	0.215837	−	0.211692i	0.800090	+	0.599880i	$0.204785\pi$
$32$	3.95273	−	0.776291i	0.698750	−	0.137230i
$33$	−7.55358	−	4.27397i	−1.31491	−	0.744002i
$34$	−3.07010	+	11.9189i	−0.526518	+	2.04407i
$35$	8.98177	−	4.51081i	1.51820	−	0.762466i
$36$	−6.43638	−	8.33894i	−1.07273	−	1.38982i
$37$	−1.35989	+	0.894415i	−0.223565	+	0.147041i	−0.656351	−	0.754456i	$-0.727901\pi$
$37$	−1.35989	+	0.894415i	−0.223565	+	0.147041i	0.432786	+	0.901497i	$0.357531\pi$
$38$	−9.24094	−	1.81486i	−1.49908	−	0.294409i
$39$	−0.419437	+	2.23840i	−0.0671636	+	0.358431i
$40$	5.06105	−	8.02990i	0.800222	−	1.26964i
$41$	−0.540280	−	1.02570i	−0.0843775	−	0.160187i	0.838940	−	0.544223i	$-0.183176\pi$
$41$	−0.540280	−	1.02570i	−0.0843775	−	0.160187i	−0.923318	+	0.384037i	$0.874534\pi$
$42$	−11.8071	+	9.69394i	−1.82188	+	1.49581i
$43$	1.05700	+	3.08919i	0.161191	+	0.471097i	0.996954	−	0.0779925i	$-0.0248510\pi$
$43$	1.05700	+	3.08919i	0.161191	+	0.471097i	−0.835763	+	0.549090i	$0.814974\pi$
$44$	1.02303	+	17.5647i	0.154227	+	2.64798i
$45$	7.98638	+	0.793026i	1.19054	+	0.118217i
$46$	16.2784	+	10.7065i	2.40012	+	1.57859i
$47$	−3.47013	−	3.40347i	−0.506170	−	0.496448i	0.401659	−	0.915789i	$-0.368434\pi$
$47$	−3.47013	−	3.40347i	−0.506170	−	0.496448i	−0.907829	+	0.419342i	$0.862261\pi$
$48$	−0.755618	+	2.13356i	−0.109064	+	0.307953i
$49$	4.67840	+	5.36085i	0.668343	+	0.765836i
$50$	1.26300	+	4.90327i	0.178615	+	0.693428i
$51$	6.41453	+	6.42744i	0.898214	+	0.900022i
$52$	4.27390	−	1.74608i	0.592683	−	0.242138i
$53$	−6.34982	+	5.32813i	−0.872215	+	0.731875i	−0.964563	−	0.263851i	$-0.915007\pi$
$53$	−6.34982	+	5.32813i	−0.872215	+	0.731875i	0.0923483	+	0.995727i	$0.470563\pi$
$54$	−12.1064	+	1.49709i	−1.64747	+	0.203728i
$55$	−10.2687	−	8.61650i	−1.38464	−	1.16185i
$56$	12.6935	+	4.07001i	1.69624	+	0.543878i
$57$	−4.62429	+	5.18577i	−0.612502	+	0.686872i
$58$	−1.89830	+	19.5163i	−0.249260	+	2.56261i
$59$	−0.766536	−	0.422957i	−0.0997944	−	0.0550642i	0.432430	−	0.901667i	$-0.357656\pi$
$59$	−0.766536	−	0.422957i	−0.0997944	−	0.0550642i	−0.532225	+	0.846603i	$0.678644\pi$
$60$	−7.42812	−	14.4755i	−0.958966	−	1.86878i
$61$	−8.54229	−	0.663959i	−1.09373	−	0.0850113i	−0.482069	−	0.876133i	$-0.660115\pi$
$61$	−8.54229	−	0.663959i	−1.09373	−	0.0850113i	−0.611659	+	0.791122i	$0.709497\pi$
$62$	−2.71180	+	2.87434i	−0.344399	+	0.365041i
$63$	1.71920	+	11.1392i	0.216599	+	1.40340i
$64$	−11.7450	+	2.78361i	−1.46812	+	0.347952i
$65$	−1.26691	+	3.28139i	−0.157141	+	0.407006i
$66$	18.1087	+	9.33851i	2.22902	+	1.14949i
$67$	−0.810426	−	5.93337i	−0.0990093	−	0.724876i	−0.971635	−	0.236486i	$-0.924004\pi$
$67$	−0.810426	−	5.93337i	−0.0990093	−	0.724876i	0.872626	−	0.488390i	$-0.162416\pi$
$68$	3.89724	−	17.9917i	0.472609	−	2.18181i
$69$	12.9142	−	6.31361i	1.55468	−	0.760069i
$70$	−20.6593	+	11.3993i	−2.46926	+	1.36248i
$71$	2.44908	+	5.67761i	0.290653	+	0.673808i	0.999502	−	0.0315513i	$-0.0100447\pi$
$71$	2.44908	+	5.67761i	0.290653	+	0.673808i	−0.708850	+	0.705360i	$0.750785\pi$
$72$	6.82549	+	8.16759i	0.804392	+	0.962560i
$73$	−3.18566	−	4.27908i	−0.372853	−	0.500829i	0.575606	−	0.817727i	$-0.304766\pi$
$73$	−3.18566	−	4.27908i	−0.372853	−	0.500829i	−0.948460	+	0.316898i	$0.897359\pi$
$74$	3.10869	−	2.22196i	0.361378	−	0.258298i
$75$	3.58791	+	1.04026i	0.414296	+	0.120119i
$76$	13.9165	+	2.17650i	1.59633	+	0.249662i
$77$	8.12108	−	16.9838i	0.925484	−	1.93548i
$78$	0.780177	−	5.28915i	0.0883376	−	0.598878i
$79$	−3.67063	−	5.82385i	−0.412978	−	0.655235i	0.573485	−	0.819216i	$-0.305591\pi$
$79$	−3.67063	−	5.82385i	−0.412978	−	0.655235i	−0.986463	+	0.163981i	$0.947566\pi$
$80$	−1.74796	+	3.02756i	−0.195428	+	0.338492i
$81$	−3.59791	+	8.24955i	−0.399768	+	0.916616i
$82$	1.36079	+	2.35695i	0.150274	+	0.260282i
$83$	−6.88942	+	13.0792i	−0.756213	+	1.43563i	0.139138	+	0.990273i	$0.455567\pi$
$83$	−6.88942	+	13.0792i	−0.756213	+	1.43563i	−0.895351	+	0.445361i	$0.853075\pi$
$84$	17.0844	−	15.1731i	1.86406	−	1.65552i
$85$	7.93287	+	11.5664i	0.860440	+	1.25455i
$86$	−2.76077	−	7.15058i	−0.297702	−	0.771067i
$87$	11.6788	+	8.53783i	1.25210	+	0.915351i
$88$	−1.72114	−	17.6949i	−0.183474	−	1.88628i
$89$	2.69753	−	6.25358i	0.285938	−	0.662878i	−0.713342	−	0.700816i	$-0.752819\pi$
$89$	2.69753	−	6.25358i	0.285938	−	0.662878i	0.999280	+	0.0379374i	$0.0120788\pi$
$90$	−18.8071	−	1.13333i	−1.98244	−	0.119463i
$91$	−4.90646	−	0.573482i	−0.514336	−	0.0601173i
$92$	−24.9502	−	15.0575i	−2.60124	−	1.56986i
$93$	0.806238	+	2.80180i	0.0836029	+	0.290533i
$94$	8.45024	+	7.66818i	0.871575	+	0.790912i
$95$	−8.48219	+	6.57419i	−0.870254	+	0.674498i
$96$	−2.07247	+	6.66220i	−0.211521	+	0.679958i
$97$	−4.96329	−	6.15351i	−0.503946	−	0.624794i	0.460951	−	0.887426i	$-0.347508\pi$
$97$	−4.96329	−	6.15351i	−0.503946	−	0.624794i	−0.964896	+	0.262631i	$0.915410\pi$
$98$	−11.4629	−	12.1499i	−1.15792	−	1.22733i
$99$	12.7332	−	7.98971i	1.27974	−	0.802996i
$100$	−2.17202	−	7.25505i	−0.217202	−	0.725505i
$101$	−1.02382	−	2.14115i	−0.101874	−	0.213052i	0.844919	−	0.534894i	$-0.179649\pi$
$101$	−1.02382	−	2.14115i	−0.101874	−	0.213052i	−0.946793	+	0.321842i	$0.895698\pi$
$102$	−15.6327	−	14.4939i	−1.54786	−	1.43511i
$103$	−5.44892	+	3.28844i	−0.536899	+	0.324020i	−0.759093	−	0.650983i	$-0.774357\pi$
$103$	−5.44892	+	3.28844i	−0.536899	+	0.324020i	0.222194	+	0.975002i	$0.428678\pi$
$104$	−4.24691	+	1.93046i	−0.416444	+	0.189297i
$105$	−0.523813	+	17.4007i	−0.0511189	+	1.69813i
$106$	14.4108	−	13.0771i	1.39970	−	1.27016i
$107$	−1.33160	+	7.55185i	−0.128730	+	0.730065i	0.850292	+	0.526311i	$0.176425\pi$
$107$	−1.33160	+	7.55185i	−0.128730	+	0.730065i	−0.979022	+	0.203754i	$0.934686\pi$
$108$	18.0070	−	2.93963i	1.73273	−	0.282866i
$109$	−2.19234	−	12.4334i	−0.209988	−	1.19090i	−0.889395	−	0.457139i	$-0.848874\pi$
$109$	−2.19234	−	12.4334i	−0.209988	−	1.19090i	0.679407	−	0.733761i	$-0.262237\pi$
$110$	24.8734	+	19.2783i	2.37158	+	1.83812i
$111$	−0.242886	−	2.80871i	−0.0230537	−	0.266591i
$112$	−4.72977	−	1.31662i	−0.446921	−	0.124409i
$113$	4.04254	−	11.8148i	0.380291	−	1.11144i	−0.575603	−	0.817729i	$-0.695233\pi$
$113$	4.04254	−	11.8148i	0.380291	−	1.11144i	0.955894	−	0.293712i	$-0.0948907\pi$
$114$	10.3759	−	12.5860i	0.971788	−	1.17879i
$115$	21.3893	−	5.95412i	1.99456	−	0.555225i
$116$	1.70528	−	29.2786i	0.158331	−	2.71845i
$117$	−3.06528	−	2.48257i	−0.283385	−	0.229514i
$118$	1.83668	+	0.922418i	0.169081	+	0.0849154i
$119$	−12.9512	+	14.8404i	−1.18723	+	1.36042i
$120$	8.06728	+	14.3248i	0.736438	+	1.30767i
$121$	−14.0972	−	0.547035i	−1.28156	−	0.0497305i
$122$	20.0994	+	0.779949i	1.81972	+	0.0706133i
$123$	2.00783	+	0.0214873i	0.181040	+	0.00193745i
$124$	3.88627	−	4.45318i	0.348998	−	0.399907i
$125$	−6.79716	−	3.41366i	−0.607956	−	0.305327i
$126$	−5.04700	−	25.9744i	−0.449623	−	2.31398i
$127$	−0.670753	+	11.5164i	−0.0595197	+	1.02191i	0.827878	+	0.560909i	$0.189548\pi$
$127$	−0.670753	+	11.5164i	−0.0595197	+	1.02191i	−0.887397	+	0.461005i	$0.847489\pi$
$128$	19.5373	−	5.43858i	1.72687	−	0.480707i
$129$	−5.57759	−	0.933571i	−0.491079	−	0.0821964i
$130$	2.67329	−	7.81299i	0.234463	−	0.685245i
$131$	−16.2022	−	4.51018i	−1.41559	−	0.394056i	−0.525870	−	0.850565i	$-0.676260\pi$
$131$	−16.2022	−	4.51018i	−1.41559	−	0.394056i	−0.889719	+	0.456509i	$0.849100\pi$
$132$	−27.6063	−	12.9068i	−2.40282	−	1.12340i
$133$	−11.9122	−	9.23266i	−1.03292	−	0.800573i
$134$	2.44126	+	13.8451i	0.210892	+	1.19603i
$135$	−7.78565	+	11.5159i	−0.670082	+	0.991135i
$136$	−3.23009	+	18.3187i	−0.276978	+	1.57082i
$137$	14.6198	−	13.2667i	1.24905	−	1.13345i	0.263394	−	0.964688i	$-0.415158\pi$
$137$	14.6198	−	13.2667i	1.24905	−	1.13345i	0.985656	−	0.168764i	$-0.0539776\pi$
$138$	−29.7201	+	15.9864i	−2.52994	+	1.36085i
$139$	−3.74781	+	1.70359i	−0.317885	+	0.144496i	−0.566397	−	0.824132i	$-0.691663\pi$
$139$	−3.74781	+	1.70359i	−0.317885	+	0.144496i	0.248513	+	0.968629i	$0.420058\pi$
$140$	30.2157	−	18.2353i	2.55369	−	1.54116i
$141$	8.04383	−	2.48454i	0.677413	−	0.209236i
$142$	−6.26203	−	13.0959i	−0.525498	−	1.09899i
$143$	1.88955	+	6.31155i	0.158012	+	0.527798i
$144$	−2.62866	−	2.90848i	−0.219055	−	0.242373i
$145$	15.3338	+	16.2529i	1.27340	+	1.34973i
$146$	7.86262	+	9.74812i	0.650715	+	0.806760i
$147$	−12.0214	+	2.71360i	−0.991511	+	0.223814i
$148$	−4.51730	+	3.50117i	−0.371320	+	0.287794i
$149$	−0.857376	−	0.778027i	−0.0702390	−	0.0637385i	0.636132	−	0.771580i	$-0.280533\pi$
$149$	−0.857376	−	0.778027i	−0.0702390	−	0.0637385i	−0.706371	+	0.707842i	$0.749669\pi$
$150$	−8.51141	−	2.11369i	−0.694954	−	0.172582i
$151$	−1.80234	−	1.08772i	−0.146672	−	0.0885171i	0.441464	−	0.897279i	$-0.354459\pi$
$151$	−1.80234	−	1.08772i	−0.146672	−	0.0885171i	−0.588136	+	0.808762i	$0.700138\pi$
$152$	−14.1367	−	1.65234i	−1.14664	−	0.134022i
$153$	−15.0764	+	4.48059i	−1.21886	+	0.362234i
$154$	−17.5049	+	40.5808i	−1.41058	+	3.27010i
$155$	0.435948	+	4.48194i	0.0350162	+	0.359998i
$156$	−0.859280	+	7.95026i	−0.0687974	+	0.636530i
$157$	3.72109	+	9.63786i	0.296975	+	0.769185i	0.998406	+	0.0564471i	$0.0179772\pi$
$157$	3.72109	+	9.63786i	0.296975	+	0.769185i	−0.701430	+	0.712738i	$0.747455\pi$
$158$	9.14092	+	13.3278i	0.727213	+	1.06030i
$159$	−2.88913	−	14.0634i	−0.229123	−	1.11530i
$160$	−5.02228	+	9.53456i	−0.397046	+	0.753773i
$161$	15.5904	+	27.0034i	1.22870	+	2.12817i
$162$	7.68923	−	19.6798i	0.604123	−	1.54619i
$163$	−1.77296	+	3.07086i	−0.138869	+	0.240528i	−0.927069	−	0.374891i	$-0.877680\pi$
$163$	−1.77296	+	3.07086i	−0.138869	+	0.240528i	0.788200	+	0.615419i	$0.211013\pi$
$164$	−2.17049	−	3.44371i	−0.169487	−	0.268909i
$165$	21.5862	−	8.55052i	1.68048	−	0.665657i
$166$	14.9710	−	31.3092i	1.16197	−	2.43006i
$167$	−0.724214	−	0.113265i	−0.0560414	−	0.00876471i	0.126436	−	0.991975i	$-0.459646\pi$
$167$	−0.724214	−	0.113265i	−0.0560414	−	0.00876471i	−0.182477	+	0.983210i	$0.558412\pi$
$168$	−16.6555	+	15.9895i	−1.28500	+	1.23362i
$169$	−9.16972	+	6.55412i	−0.705363	+	0.504163i
$170$	−19.6623	−	26.4110i	−1.50803	−	2.02563i
$171$	−4.09329	−	11.3170i	−0.313022	−	0.865430i
$172$	4.54088	+	10.5269i	0.346239	+	0.802672i
$173$	12.3363	−	6.80687i	0.937910	−	0.517517i	0.0609818	−	0.998139i	$-0.480577\pi$
$173$	12.3363	−	6.80687i	0.937910	−	0.517517i	0.876928	+	0.480622i	$0.159589\pi$
$174$	−28.1741	−	18.9654i	−2.13587	−	1.43776i
$175$	−1.71546	+	7.91943i	−0.129676	+	0.598653i
$176$	0.886147	+	6.48774i	0.0667958	+	0.489032i
$177$	1.27576	−	0.819659i	0.0958921	−	0.0616094i
$178$	−5.75876	+	14.9156i	−0.431637	+	1.11797i
$179$	4.87825	−	1.15617i	0.364618	−	0.0864160i	−0.0442231	−	0.999022i	$-0.514081\pi$
$179$	4.87825	−	1.15617i	0.364618	−	0.0864160i	0.408841	+	0.912606i	$0.365933\pi$
$180$	28.1743	+	0.603097i	2.09999	+	0.0449522i
$181$	9.31304	−	9.87124i	0.692233	−	0.733724i	−0.281964	−	0.959425i	$-0.590986\pi$
$181$	9.31304	−	9.87124i	0.692233	−	0.733724i	0.974197	+	0.225701i	$0.0724673\pi$
$182$	11.5620	+	0.898673i	0.857036	+	0.0666141i
$183$	8.04681	−	12.4693i	0.594838	−	0.921757i
$184$	25.7820	+	14.2259i	1.90068	+	1.04875i
$185$	0.421548	−	4.33390i	0.0309928	−	0.318634i
$186$	−2.14637	−	6.49924i	−0.157379	−	0.476547i
$187$	25.0156	+	8.02093i	1.82932	+	0.586548i
$188$	−13.0742	−	10.9706i	−0.953535	−	0.800111i
$189$	−18.3889	−	6.55422i	−1.33760	−	0.476750i
$190$	19.2996	−	16.1943i	1.40014	−	1.17485i
$191$	17.9955	−	7.35196i	1.30211	−	0.531969i	0.382190	−	0.924084i	$-0.375170\pi$
$191$	17.9955	−	7.35196i	1.30211	−	0.531969i	0.919916	+	0.392115i	$0.128256\pi$
$192$	5.43128	−	20.1886i	0.391969	−	1.45699i
$193$	1.01669	+	3.94702i	0.0731827	+	0.284113i	0.994505	−	0.104686i	$-0.0333839\pi$
$193$	1.01669	+	3.94702i	0.0731827	+	0.284113i	−0.921323	+	0.388799i	$0.872890\pi$
$194$	12.2033	+	13.9834i	0.876147	+	1.00395i
$195$	−3.95655	−	4.63286i	−0.283335	−	0.331766i
$196$	17.8367	+	17.4941i	1.27405	+	1.24958i
$197$	6.11072	+	4.01908i	0.435371	+	0.286348i	0.748215	−	0.663457i	$-0.230911\pi$
$197$	6.11072	+	4.01908i	0.435371	+	0.286348i	−0.312844	+	0.949805i	$0.601282\pi$
$198$	−29.1430	+	19.9018i	−2.07110	+	1.41436i
$199$	−1.11616	−	19.1637i	−0.0791223	−	1.35848i	−0.771171	−	0.636628i	$-0.780329\pi$
$199$	−1.11616	−	19.1637i	−0.0791223	−	1.35848i	0.692049	−	0.721851i	$-0.256708\pi$
$200$	2.47733	+	7.24027i	0.175174	+	0.511964i
$201$	9.70827	+	3.65164i	0.684768	+	0.257567i
$202$	2.59665	+	4.92962i	0.182700	+	0.346847i
$203$	−16.7321	+	26.5473i	−1.17436	+	1.86326i
$204$	24.2047	+	20.7556i	1.69467	+	1.45318i
$205$	3.04322	+	0.597669i	0.212548	+	0.0417430i
$206$	12.4831	−	8.21023i	0.869735	−	0.572034i
$207$	−1.01544	+	24.8773i	−0.0705780	+	1.72909i
$208$	1.53544	−	0.771127i	0.106464	−	0.0534680i
$209$	−5.01393	+	19.4653i	−0.346821	+	1.34644i
$210$	−0.355194	−	40.8672i	−0.0245107	−	2.82011i
$211$	−19.0277	+	3.73693i	−1.30992	+	0.257261i	−0.798462	−	0.602045i	$-0.794353\pi$
$211$	−19.0277	+	3.73693i	−1.30992	+	0.257261i	−0.511462	+	0.859306i	$0.670896\pi$
$212$	−20.7795	+	20.3804i	−1.42714	+	1.39973i
$213$	−10.6681	−	0.944143i	−0.730966	−	0.0646916i
$214$	2.43629	−	17.8368i	0.166541	−	1.21930i
$215$	−8.20787	−	2.98742i	−0.559772	−	0.203740i
$216$	−18.0664	+	3.67365i	−1.22926	+	0.249960i
$217$	−5.94267	+	2.16295i	−0.403414	+	0.146831i
$218$	6.27472	+	28.9673i	0.424978	+	1.96192i
$219$	9.14374	−	1.32998i	0.617877	−	0.0898714i
$220$	−38.2931	−	27.3703i	−2.58172	−	1.84530i
$221$	−0.133670	−	6.89200i	−0.00899163	−	0.463606i
$222$	0.825452	+	6.56672i	0.0554007	+	0.440730i
$223$	−5.22800	+	7.62261i	−0.350093	+	0.510448i	−0.959234	−	0.282614i	$-0.908798\pi$
$223$	−5.22800	+	7.62261i	−0.350093	+	0.510448i	0.609141	+	0.793062i	$0.291514\pi$
$224$	−14.7262	−	3.49018i	−0.983937	−	0.233197i
$225$	−4.53994	+	4.61027i	−0.302663	+	0.307351i
$226$	−8.40773	+	28.0838i	−0.559274	+	1.86811i
$227$	−8.80735	+	1.37744i	−0.584564	+	0.0914242i	−0.439884	−	0.898054i	$-0.644981\pi$
$227$	−8.80735	+	1.37744i	−0.584564	+	0.0914242i	−0.144680	+	0.989479i	$0.546215\pi$
$228$	−14.7775	+	19.4125i	−0.978666	+	1.28562i
$229$	−6.85729	−	2.80151i	−0.453142	−	0.185129i	0.140126	−	0.990134i	$-0.455249\pi$
$229$	−6.85729	−	2.80151i	−0.453142	−	0.185129i	−0.593269	+	0.805005i	$0.702163\pi$
$230$	−49.6343	+	15.9146i	−3.27279	+	1.04938i
$231$	19.1904	+	26.3616i	1.26264	+	1.73446i
$232$	−0.574657	+	29.6292i	−0.0377281	+	1.94525i
$233$	10.6270	−	14.2745i	0.696195	−	0.935153i	−0.303649	−	0.952784i	$-0.598205\pi$
$233$	10.6270	−	14.2745i	0.696195	−	0.935153i	0.999845	+	0.0176311i	$0.00561245\pi$
$234$	7.41669	+	5.54473i	0.484844	+	0.362470i
$235$	12.9152	−	1.50957i	0.842497	−	0.0984738i
$236$	−2.79855	−	1.27210i	−0.182170	−	0.0828066i
$237$	11.8970	−	0.796724i	0.772791	−	0.0517528i
$238$	29.0307	−	35.9924i	1.88178	−	2.33304i
$239$	2.45450	−	0.190779i	0.158769	−	0.0123405i	0.00213791	−	0.999998i	$-0.499319\pi$
$239$	2.45450	−	0.190779i	0.158769	−	0.0123405i	0.156631	+	0.987657i	$0.449937\pi$
$240$	−3.17362	−	5.15681i	−0.204856	−	0.332870i
$241$	6.76935	−	0.262682i	0.436052	−	0.0169208i	0.180185	−	0.983633i	$-0.442330\pi$
$241$	6.76935	−	0.262682i	0.436052	−	0.0169208i	0.255867	+	0.966712i	$0.417639\pi$
$242$	33.1198			2.12902
$243$	−9.60694	−	12.2763i	−0.616286	−	0.787523i
$244$	−30.0853			−1.92601
$245$	−19.0204	+	0.738078i	−1.21517	+	0.0471541i
$246$	−4.71205	+	0.132367i	−0.300429	+	0.00843940i
$247$	5.25858	−	0.408730i	0.334596	−	0.0260068i
$248$	−3.74947	+	4.64861i	−0.238091	+	0.295187i
$249$	−14.2553	−	21.2692i	−0.903394	−	1.34788i
$250$	16.2559	+	7.38921i	1.02811	+	0.467335i
$251$	−16.0195	+	1.87241i	−1.01114	+	0.118185i	−0.605499	−	0.795846i	$-0.707026\pi$
$251$	−16.0195	+	1.87241i	−1.01114	+	0.118185i	−0.405643	+	0.914032i	$0.632952\pi$
$252$	9.04952	+	38.5279i	0.570066	+	2.42703i
$253$	24.8335	−	33.3572i	1.56127	−	2.09715i
$254$	0.525155	−	27.0768i	0.0329511	−	1.69895i
$255$	−24.1573	+	2.56185i	−1.51279	+	0.160429i
$256$	−22.3487	+	7.16582i	−1.39679	+	0.447864i
$257$	−26.8426	−	10.9664i	−1.67440	−	0.684066i	−0.675803	−	0.737082i	$-0.736203\pi$
$257$	−26.8426	−	10.9664i	−1.67440	−	0.684066i	−0.998594	+	0.0530162i	$0.983116\pi$
$258$	13.1692	+	1.68230i	0.819879	+	0.104735i
$259$	6.04171	−	0.944907i	0.375414	−	0.0587137i
$260$	−3.54230	+	11.8321i	−0.219684	+	0.733797i
$261$	−22.6276	+	10.7639i	−1.40061	+	0.666270i
$262$	38.4185	+	9.10535i	2.37350	+	0.562531i
$263$	7.10576	−	10.3605i	0.438160	−	0.638853i	−0.541220	−	0.840881i	$-0.682037\pi$
$263$	7.10576	−	10.3605i	0.438160	−	0.638853i	0.979380	+	0.202028i	$0.0647532\pi$
$264$	28.3796	+	11.9503i	1.74664	+	0.735490i
$265$	−0.430006	−	22.1710i	−0.0264150	−	1.36195i
$266$	28.7848	+	20.5741i	1.76491	+	1.26148i
$267$	7.30716	+	9.26053i	0.447191	+	0.566735i
$268$	−4.45159	−	20.5508i	−0.271924	−	1.25534i
$269$	−21.5566	+	7.84595i	−1.31433	+	0.478376i	−0.901636	−	0.432495i	$-0.857633\pi$
$269$	−21.5566	+	7.84595i	−1.31433	+	0.478376i	−0.412691	+	0.910871i	$0.635411\pi$
$270$	17.2157	−	27.7235i	1.04771	−	1.68720i
$271$	−0.912109	−	0.331981i	−0.0554067	−	0.0201664i	0.314168	−	0.949367i	$-0.398274\pi$
$271$	−0.912109	−	0.331981i	−0.0554067	−	0.0201664i	−0.369575	+	0.929201i	$0.620497\pi$
$272$	0.927166	−	6.78806i	0.0562177	−	0.411586i
$273$	4.91461	−	7.00380i	0.297446	−	0.423889i
$274$	−33.0882	+	32.4527i	−1.99893	+	1.96054i
$275$	10.6046	−	2.08267i	0.639481	−	0.125590i
$276$	43.4917	−	25.6165i	2.61789	−	1.54193i
$277$	1.19026	−	4.62089i	0.0715160	−	0.277642i	−0.922630	−	0.385686i	$-0.873965\pi$
$277$	1.19026	−	4.62089i	0.0715160	−	0.277642i	0.994146	+	0.108044i	$0.0344587\pi$
$278$	8.63674	−	4.33753i	0.517997	−	0.260148i
$279$	−4.93317	−	1.07898i	−0.295341	−	0.0645967i
$280$	−29.7941	+	19.5959i	−1.78054	+	1.17108i
$281$	24.9723	+	4.90441i	1.48973	+	0.292573i	0.870315	−	0.492495i	$-0.163915\pi$
$281$	24.9723	+	4.90441i	1.48973	+	0.292573i	0.619410	+	0.785068i	$0.287372\pi$
$282$	−18.6435	+	6.56061i	−1.11021	+	0.390679i
$283$	−0.661960	+	1.05027i	−0.0393495	+	0.0624322i	−0.865085	−	0.501625i	$-0.832736\pi$
$283$	−0.661960	+	1.05027i	−0.0393495	+	0.0624322i	0.825736	+	0.564057i	$0.190760\pi$
$284$	10.1186	+	19.2096i	0.600426	+	1.13988i
$285$	−3.03165	−	18.3388i	−0.179579	−	1.08630i
$286$	−5.00716	−	14.6340i	−0.296080	−	0.865326i
$287$	0.253248	+	4.34811i	0.0149488	+	0.256661i
$288$	−8.44457	−	8.64463i	−0.497601	−	0.509390i
$289$	−8.76098	−	5.76219i	−0.515352	−	0.338952i
$290$	−37.4504	−	36.7311i	−2.19916	−	2.15692i
$291$	13.4639	−	2.49488i	0.789265	−	0.146253i
$292$	−12.3166	−	14.1133i	−0.720775	−	0.825916i
$293$	6.69307	+	25.9841i	0.391013	+	1.51801i	0.796916	+	0.604090i	$0.206463\pi$
$293$	6.69307	+	25.9841i	0.391013	+	1.51801i	−0.405903	+	0.913916i	$0.633043\pi$
$294$	27.9535	−	7.46002i	1.63028	−	0.435077i
$295$	2.16814	−	0.885784i	0.126234	−	0.0515723i
$296$	4.42391	−	3.71210i	0.257134	−	0.215761i
$297$	1.68752	+	25.9820i	0.0979201	+	1.50763i
$298$	2.08210	+	1.74709i	0.120613	+	0.101206i
$299$	−10.3912	−	3.33180i	−0.600938	−	0.192683i
$300$	12.8435	+	2.66543i	0.741520	+	0.153889i
$301$	1.18755	−	12.2091i	0.0684495	−	0.703722i
$302$	4.32704	+	2.38756i	0.248993	+	0.137389i
$303$	4.10571	+	0.203343i	0.235867	+	0.0116817i
$304$	5.22638	+	0.406227i	0.299754	+	0.0232987i
$305$	15.7296	−	16.6724i	0.900676	−	0.954660i
$306$	34.9593	−	11.8832i	1.99849	−	0.679319i
$307$	13.7894	−	3.26814i	0.787001	−	0.186523i	0.182584	−	0.983190i	$-0.441554\pi$
$307$	13.7894	−	3.26814i	0.787001	−	0.186523i	0.604418	+	0.796668i	$0.293406\pi$
$308$	23.8087	−	61.6662i	1.35663	−	3.51376i
$309$	−0.523151	−	11.0109i	−0.0297610	−	0.626389i
$310$	−1.43066	−	10.4743i	−0.0812562	−	0.594901i
$311$	−0.315220	+	1.45522i	−0.0178745	+	0.0825178i	−0.985400	−	0.170256i	$-0.945540\pi$
$311$	−0.315220	+	1.45522i	−0.0178745	+	0.0825178i	0.967525	+	0.252774i	$0.0813429\pi$
$312$	0.556112	−	8.06099i	0.0314837	−	0.456363i
$313$	−3.90907	+	2.15693i	−0.220954	+	0.121917i	−0.589728	−	0.807602i	$-0.700765\pi$
$313$	−3.90907	+	2.15693i	−0.220954	+	0.121917i	0.368775	+	0.929519i	$0.379777\pi$
$314$	−9.60647	−	22.2703i	−0.542125	−	1.25679i
$315$	−26.0825	−	15.1287i	−1.46958	−	0.852407i
$316$	−14.4347	−	19.3892i	−0.812017	−	1.09073i
$317$	−26.8081	+	19.1613i	−1.50569	+	1.07621i	−0.532441	+	0.846467i	$0.678725\pi$
$317$	−26.8081	+	19.1613i	−1.50569	+	1.07621i	−0.973253	+	0.229738i	$0.926213\pi$
$318$	8.05769	+	32.7278i	0.451853	+	1.83529i
$319$	41.3495	+	6.46694i	2.31513	+	0.362079i
$320$	13.9298	−	29.1317i	0.778699	−	1.62851i
$321$	−10.4103	−	8.24842i	−0.581047	−	0.460382i
$322$	−39.0310	−	61.9269i	−2.17511	−	3.45105i
$323$	10.5156	−	18.2135i	0.585101	−	1.01343i
$324$	−10.3508	+	29.8588i	−0.575042	+	1.65882i
$325$	−1.41791	−	2.45589i	−0.0786515	−	0.136228i
$326$	3.87957	−	7.36519i	0.214870	−	0.407920i
$327$	20.7506	+	6.89915i	1.14751	+	0.381524i
$328$	2.32645	+	3.39205i	0.128457	+	0.187295i
$329$	6.57734	+	17.0357i	0.362620	+	0.939210i
$330$	−49.8597	+	22.0233i	−2.74469	+	1.21234i
$331$	−1.33303	−	13.7047i	−0.0732697	−	0.753278i	−0.957922	−	0.287028i	$-0.907333\pi$
$331$	−1.33303	−	13.7047i	−0.0732697	−	0.753278i	0.884653	−	0.466251i	$-0.154396\pi$
$332$	−20.5594	+	47.6621i	−1.12834	+	2.61580i
$333$	4.47974	+	1.94306i	0.245488	+	0.106479i
$334$	1.70921	+	0.199778i	0.0935240	+	0.0109314i
$335$	13.7162	+	8.27775i	0.749394	+	0.452262i
$336$	5.90144	−	6.12256i	0.321950	−	0.334013i
$337$	15.3879	+	13.9638i	0.838233	+	0.760656i	0.973143	−	0.230202i	$-0.0739388\pi$
$337$	15.3879	+	13.9638i	0.838233	+	0.760656i	−0.134910	+	0.990858i	$0.543075\pi$
$338$	20.9142	−	16.2097i	1.13758	−	0.881694i
$339$	14.6732	+	15.8900i	0.796939	+	0.863024i
$340$	30.9184	+	38.3328i	1.67679	+	2.07889i
$341$	5.78806	+	6.13499i	0.313441	+	0.332228i
$342$	10.6325	+	26.1754i	0.574938	+	1.41540i
$343$	−0.124136	−	0.414643i	−0.00670272	−	0.0223886i
$344$	−4.99735	−	10.4511i	−0.269439	−	0.563484i
$345$	−8.54301	+	37.4951i	−0.459940	+	2.01867i
$346$	−28.3195	+	17.0909i	−1.52247	+	0.918813i
$347$	−16.5976	+	7.54454i	−0.891006	+	0.405012i	−0.806378	−	0.591401i	$-0.798575\pi$
$347$	−16.5976	+	7.54454i	−0.891006	+	0.405012i	−0.0846283	+	0.996413i	$0.526970\pi$
$348$	43.2081	+	26.7112i	2.31620	+	1.43187i
$349$	−25.3716	+	23.0235i	−1.35811	+	1.23242i	−0.410954	+	0.911656i	$0.634804\pi$
$349$	−25.3716	+	23.0235i	−1.35811	+	1.23242i	−0.947159	+	0.320766i	$0.896060\pi$
$350$	3.30331	−	18.7340i	0.176569	−	1.00138i
$351$	6.30721	−	2.62609i	0.336654	−	0.140170i
$352$	3.50501	+	19.8779i	0.186818	+	1.05950i
$353$	−18.3306	−	14.2073i	−0.975637	−	0.756176i	−0.00581337	−	0.999983i	$-0.501850\pi$
$353$	−18.3306	−	14.2073i	−0.975637	−	0.756176i	−0.969824	+	0.243807i	$0.921604\pi$
$354$	−2.91814	+	2.03894i	−0.155097	+	0.108368i
$355$	−15.9358	−	4.43603i	−0.845783	−	0.235440i
$356$	7.74184	−	22.6264i	0.410316	−	1.19920i
$357$	−11.9466	−	31.9561i	−0.632282	−	1.69130i
$358$	−11.3384	+	3.15627i	−0.599255	+	0.166814i
$359$	0.264846	−	4.54723i	0.0139780	−	0.239993i	−0.984081	−	0.177720i	$-0.943128\pi$
$359$	0.264846	−	4.54723i	0.0139780	−	0.239993i	0.998059	−	0.0622735i	$-0.0198351\pi$
$360$	−28.4710	+	0.494944i	−1.50055	+	0.0260858i
$361$	−2.59862	−	1.30507i	−0.136769	−	0.0686881i
$362$	−20.9485	+	24.0043i	−1.10103	+	1.26164i
$363$	12.4435	−	21.0297i	0.653113	−	1.10378i
$364$	−17.3324	−	0.672577i	−0.908466	−	0.0352526i
$365$	14.2607	+	0.553381i	0.746441	+	0.0289653i
$366$	−17.7416	+	29.9837i	−0.927368	+	1.56727i
$367$	22.5278	−	25.8140i	1.17594	−	1.34748i	0.250716	−	0.968061i	$-0.419334\pi$
$367$	22.5278	−	25.8140i	1.17594	−	1.34748i	0.925225	−	0.379418i	$-0.123876\pi$
$368$	−9.69184	−	4.86742i	−0.505222	−	0.253732i
$369$	−1.68632	+	3.04169i	−0.0877863	+	0.158344i
$370$	−0.594378	+	10.2051i	−0.0309002	+	0.530536i
$371$	30.0016	−	8.35152i	1.55761	−	0.433589i
$372$	3.58483	+	9.58910i	0.185865	+	0.497171i
$373$	−1.11119	+	3.24758i	−0.0575353	+	0.168153i	−0.971173	−	0.238377i	$-0.923385\pi$
$373$	−1.11119	+	3.24758i	−0.0575353	+	0.168153i	0.913637	+	0.406530i	$0.133261\pi$
$374$	−59.4131	−	16.5388i	−3.07218	−	0.855200i
$375$	10.7994	−	7.54564i	0.557677	−	0.389655i
$376$	13.6308	+	10.5646i	0.702953	+	0.544830i
$377$	−1.90702	−	10.8152i	−0.0982164	−	0.557013i
$378$	43.7344	+	13.7013i	2.24946	+	0.704720i
$379$	−4.79436	+	27.1902i	−0.246270	+	1.39666i	0.571256	+	0.820772i	$0.306456\pi$
$379$	−4.79436	+	27.1902i	−0.246270	+	1.39666i	−0.817526	+	0.575892i	$0.804655\pi$
$380$	−27.9054	+	25.3228i	−1.43152	+	1.29903i
$381$	−16.9954	−	10.5065i	−0.870701	−	0.538265i
$382$	−41.5455	+	18.8848i	−2.12565	+	0.966229i
$383$	−21.9264	+	13.2326i	−1.12039	+	0.676156i	−0.950938	−	0.309383i	$-0.899878\pi$
$383$	−21.9264	+	13.2326i	−1.12039	+	0.676156i	−0.169448	+	0.985539i	$0.554199\pi$
$384$	−7.80330	+	34.2485i	−0.398211	+	1.74774i
$385$	21.7257	+	45.4354i	1.10724	+	2.31560i
$386$	−2.74430	−	9.16659i	−0.139681	−	0.466567i
$387$	6.01601	−	7.72986i	0.305811	−	0.392931i
$388$	−19.0497	−	20.1915i	−0.967103	−	1.02507i
$389$	−3.29685	−	4.08746i	−0.167157	−	0.207242i	0.687858	−	0.725845i	$-0.258551\pi$
$389$	−3.29685	−	4.08746i	−0.167157	−	0.207242i	−0.855015	+	0.518603i	$0.826452\pi$
$390$	9.70323	+	10.5079i	0.491342	+	0.532086i
$391$	−34.3909	+	26.6549i	−1.73922	+	1.34800i
$392$	−18.6950	−	16.9648i	−0.944241	−	0.856853i
$393$	20.2158	−	20.9732i	1.01975	−	1.05796i
$394$	−14.7007	−	8.87193i	−0.740612	−	0.446962i
$395$	18.2919	+	2.13802i	0.920367	+	0.107575i
$396$	42.4021	−	31.4349i	2.13078	−	1.57966i
$397$	0.790827	−	1.83334i	0.0396905	−	0.0920129i	−0.897218	−	0.441589i	$-0.854415\pi$
$397$	0.790827	−	1.83334i	0.0396905	−	0.0920129i	0.936908	+	0.349576i	$0.113674\pi$
$398$	4.36282	+	44.8537i	0.218688	+	2.24831i
$399$	23.8785	−	10.5473i	1.19542	−	0.528024i
$400$	−1.01514	−	2.62929i	−0.0507572	−	0.131464i
$401$	17.5256	+	25.5529i	0.875186	+	1.27605i	0.960098	+	0.279665i	$0.0902233\pi$
$401$	17.5256	+	25.5529i	0.875186	+	1.27605i	−0.0849113	+	0.996389i	$0.527061\pi$
$402$	−23.1066	−	7.68248i	−1.15245	−	0.383167i
$403$	1.03145	−	1.95816i	0.0513803	−	0.0975431i
$404$	−4.16678	−	7.21708i	−0.207305	−	0.359063i
$405$	−11.1352	−	21.3473i	−0.553311	−	1.06076i
$406$	36.8345	−	63.7993i	1.82807	−	3.16631i
$407$	−4.34873	−	6.89973i	−0.215558	−	0.342007i
$408$	−25.2526	−	20.0084i	−1.25019	−	0.990564i
$409$	−4.38003	+	9.16006i	−0.216579	+	0.452936i	−0.981570	−	0.191105i	$-0.938793\pi$
$409$	−4.38003	+	9.16006i	−0.216579	+	0.452936i	0.764991	+	0.644041i	$0.222743\pi$
$410$	−7.19336	−	1.12502i	−0.355255	−	0.0555608i
$411$	8.17455	+	33.2025i	0.403221	+	1.63776i
$412$	−18.1807	+	12.9947i	−0.895696	+	0.640205i
$413$	1.96418	+	2.63835i	0.0966508	+	0.129825i
$414$	0.117495	−	58.4511i	0.00577457	−	2.87272i
$415$	−15.6638	−	36.3129i	−0.768908	−	1.78253i
$416$	4.63736	−	2.55879i	0.227365	−	0.125455i
$417$	0.490757	−	7.11364i	0.0240325	−	0.348357i
$418$	9.99004	−	46.1192i	0.488629	−	2.25576i
$419$	−0.720539	−	5.27528i	−0.0352006	−	0.257714i	0.964785	−	0.263039i	$-0.0847248\pi$
$419$	−0.720539	−	5.27528i	−0.0352006	−	0.257714i	−0.999986	+	0.00532487i	$0.998305\pi$
$420$	2.90101	+	61.0584i	0.141555	+	2.97934i
$421$	9.47444	−	24.5394i	0.461756	−	1.19598i	−0.485139	−	0.874437i	$-0.661231\pi$
$421$	9.47444	−	24.5394i	0.461756	−	1.19598i	0.946896	−	0.321541i	$-0.104201\pi$
$422$	44.2962	−	10.4984i	2.15631	−	0.511054i
$423$	−2.83885	+	14.3028i	−0.138029	+	0.695425i
$424$	20.1824	−	21.3921i	0.980143	−	1.03889i
$425$	−11.2734	−	0.876240i	−0.546842	−	0.0425039i
$426$	25.1118	+	1.24371i	1.21667	+	0.0602579i
$427$	28.1845	+	15.5516i	1.36395	+	0.752593i
$428$	−2.60674	+	26.7996i	−0.126002	+	1.29541i
$429$	−11.1732	−	2.31880i	−0.539449	−	0.111953i
$430$	19.5264	+	6.26090i	0.941648	+	0.301927i
$431$	11.5532	+	9.69428i	0.556498	+	0.466957i	0.877134	−	0.480245i	$-0.159452\pi$
$431$	11.5532	+	9.69428i	0.556498	+	0.466957i	−0.320637	+	0.947202i	$0.603897\pi$
$432$	6.59660	−	1.61004i	0.317379	−	0.0774633i
$433$	−13.4701	+	11.3028i	−0.647332	+	0.543176i	−0.906260	−	0.422720i	$-0.861075\pi$
$433$	−13.4701	+	11.3028i	−0.647332	+	0.543176i	0.258928	+	0.965897i	$0.416631\pi$
$434$	13.7437	−	5.61494i	0.659721	−	0.269526i
$435$	−37.3933	+	9.97923i	−1.79287	+	0.478468i
$436$	−11.0580	−	42.9298i	−0.529583	−	2.05597i
$437$	−21.8907	−	25.0840i	−1.04718	−	1.19993i
$438$	−21.3288	+	3.95229i	−1.01913	+	0.188848i
$439$	−28.6071	−	28.0576i	−1.36534	−	1.33912i	−0.887599	−	0.460618i	$-0.847628\pi$
$439$	−28.6071	−	28.0576i	−1.36534	−	1.33912i	−0.477743	−	0.878500i	$-0.658545\pi$
$440$	39.7367	+	26.1352i	1.89437	+	1.24595i
$441$	5.76563	−	20.5522i	0.274554	−	0.978676i
$442$	0.940950	+	16.1555i	0.0447564	+	0.768438i
$443$	6.93071	+	20.2558i	0.329288	+	0.962381i	0.979293	+	0.202450i	$0.0648904\pi$
$443$	6.93071	+	20.2558i	0.329288	+	0.962381i	−0.650005	+	0.759930i	$0.725233\pi$
$444$	−1.61454	−	9.76656i	−0.0766228	−	0.463501i
$445$	8.49121	+	16.1202i	0.402522	+	0.764169i
$446$	11.5703	−	18.3575i	0.547868	−	0.869251i
$447$	1.89160	−	0.665651i	0.0894698	−	0.0314842i
$448$	44.4985	+	8.73922i	2.10236	+	0.412889i
$449$	−17.5593	+	11.5489i	−0.828673	+	0.545027i	−0.891512	−	0.452997i	$-0.850355\pi$
$449$	−17.5593	+	11.5489i	−0.828673	+	0.545027i	0.0628393	+	0.998024i	$0.479984\pi$
$450$	10.2304	−	11.2283i	0.482265	−	0.529307i
$451$	5.19105	−	2.60704i	0.244437	−	0.122761i
$452$	10.9372	−	42.4608i	0.514443	−	1.99719i
$453$	3.14172	−	1.85047i	0.147611	−	0.0869424i
$454$	20.5354	−	4.03302i	0.963773	−	0.189279i
$455$	9.43472	−	9.25351i	0.442306	−	0.433811i
$456$	14.1602	−	20.1796i	0.663111	−	0.944997i
$457$	−1.49995	+	10.9816i	−0.0701646	+	0.513696i	0.921847	+	0.387553i	$0.126680\pi$
$457$	−1.49995	+	10.9816i	−0.0701646	+	0.513696i	−0.992012	+	0.126143i	$0.959740\pi$
$458$	16.3412	+	5.94772i	0.763576	+	0.277919i
$459$	5.58922	−	26.6624i	0.260882	−	1.24450i
$460$	73.2590	−	26.6641i	3.41572	−	1.24322i
$461$	4.61358	+	21.2986i	0.214876	+	0.991977i	0.949564	+	0.313572i	$0.101526\pi$
$461$	4.61358	+	21.2986i	0.214876	+	0.991977i	−0.734689	+	0.678405i	$0.762672\pi$
$462$	−47.4177	−	60.0935i	−2.20607	−	2.79580i
$463$	−2.97330	−	2.12519i	−0.138181	−	0.0987658i	0.510301	−	0.859996i	$-0.329534\pi$
$463$	−2.97330	−	2.12519i	−0.138181	−	0.0987658i	−0.648482	+	0.761230i	$0.724596\pi$
$464$	−0.211653	−	10.9128i	−0.00982574	−	0.506612i
$465$	−7.18829	−	3.02690i	−0.333349	−	0.140369i
$466$	−23.6299	+	34.4533i	−1.09464	+	1.59602i
$467$	0.198980	+	0.0471592i	0.00920771	+	0.00218227i	0.235217	−	0.971943i	$-0.424420\pi$
$467$	0.198980	+	0.0471592i	0.00920771	+	0.00218227i	−0.226009	+	0.974125i	$0.572568\pi$
$468$	−11.4063	−	7.85685i	−0.527259	−	0.363183i
$469$	−6.45272	+	21.5536i	−0.297959	+	0.995252i
$470$	−30.1599	+	4.71692i	−1.39117	+	0.217575i
$471$	−17.7500	−	2.26747i	−0.817878	−	0.104480i
$472$	2.87552	+	1.17478i	0.132357	+	0.0540736i
$473$	−15.5790	+	4.99521i	−0.716324	+	0.229680i
$474$	−27.8360	+	2.95198i	−1.27855	+	0.135589i
$475$	0.167773	−	8.65032i	0.00769794	−	0.396904i
$476$	−41.3011	+	55.4770i	−1.89303	+	2.54278i
$477$	23.8082	+	7.17990i	1.09010	+	0.328745i
$478$	−5.74055	+	0.670974i	−0.262566	+	0.0306896i
$479$	1.35293	+	0.614982i	0.0618169	+	0.0280992i	0.444481	−	0.895788i	$-0.353388\pi$
$479$	1.35293	+	0.614982i	0.0618169	+	0.0280992i	−0.382664	+	0.923888i	$0.624993\pi$
$480$	−10.3919	−	15.5049i	−0.474323	−	0.707698i
$481$	−1.34358	+	1.66578i	−0.0612621	+	0.0759531i
$482$	−15.8560	+	1.23243i	−0.722222	+	0.0561355i
$483$	−53.9855	+	1.51651i	−2.45642	+	0.0690038i
$484$	−49.4999	+	1.92082i	−2.25000	+	0.0873101i
$485$	21.1494			0.960347
$486$	23.6540	+	27.9238i	1.07297	+	1.26665i
$487$	−36.1433			−1.63781			−0.818904	−	0.573931i	$-0.805418\pi$
$487$	−36.1433			−1.63781			−0.818904	+	0.573931i	$0.805418\pi$
$488$	30.3769	−	1.17876i	1.37510	−	0.0533600i
$489$	−3.21900	−	5.23056i	−0.145568	−	0.236534i
$490$	44.5520	−	3.46285i	2.01265	−	0.156436i
$491$	23.5142	−	29.1530i	1.06118	−	1.31566i	0.114521	−	0.993421i	$-0.463467\pi$
$491$	23.5142	−	29.1530i	1.06118	−	1.31566i	0.946659	−	0.322236i	$-0.104435\pi$
$492$	7.03482	−	0.471112i	0.317154	−	0.0212394i
$493$	−39.8643	−	18.1206i	−1.79540	−	0.816109i
$494$	−12.2987	+	1.43751i	−0.553344	+	0.0646766i
$495$	−4.74892	+	39.9333i	−0.213448	+	1.79487i
$496$	1.31354	−	1.76440i	0.0589799	−	0.0792237i
$497$	0.450476	−	23.2264i	0.0202066	−	1.04185i
$498$	35.3771	+	48.5968i	1.58528	+	2.17768i
$499$	35.2774	−	11.3113i	1.57923	−	0.506361i	0.618961	−	0.785422i	$-0.287554\pi$
$499$	35.2774	−	11.3113i	1.57923	−	0.506361i	0.960274	+	0.279061i	$0.0900230\pi$
$500$	−24.7242	−	10.1009i	−1.10570	−	0.451727i
$501$	0.769021	−	1.01022i	0.0343573	−	0.0451334i
$502$	37.4090	−	5.85066i	1.66964	−	0.261128i
$503$	−5.72878	+	19.1355i	−0.255434	+	0.853209i	0.730043	+	0.683401i	$0.239500\pi$
$503$	−5.72878	+	19.1355i	−0.255434	+	0.853209i	−0.985477	+	0.169808i	$0.945685\pi$
$504$	−10.6468	−	38.5468i	−0.474246	−	1.71701i
$505$	6.17805	+	1.46422i	0.274919	+	0.0651571i
$506$	−55.2194	+	80.5118i	−2.45480	+	3.57919i
$507$	−2.43484	−	19.3699i	−0.108135	−	0.860247i
$508$	0.785472	+	40.4987i	0.0348497	+	1.79684i
$509$	−9.18850	−	6.56754i	−0.407273	−	0.291101i	0.359345	−	0.933205i	$-0.383000\pi$
$509$	−9.18850	−	6.56754i	−0.407273	−	0.291101i	−0.766618	+	0.642104i	$0.778062\pi$
$510$	56.4363	−	8.20876i	2.49904	−	0.363490i
$511$	4.24309	+	19.5883i	0.187703	+	0.866534i
$512$	13.6603	−	4.97196i	0.603708	−	0.219732i
$513$	20.6150	+	3.08318i	0.910176	+	0.136126i
$514$	63.9672	+	23.2822i	2.82147	+	1.02693i
$515$	2.30414	−	16.8693i	0.101533	−	0.743351i
$516$	−19.7799	−	1.75055i	−0.870761	−	0.0770637i
$517$	17.3880	−	17.0540i	0.764723	−	0.750035i
$518$	−14.0870	+	2.76659i	−0.618946	+	0.121557i
$519$	0.212097	+	24.4030i	0.00931001	+	1.07117i
$520$	3.11305	−	12.0856i	0.136516	−	0.529988i
$521$	−19.9496	+	10.0191i	−0.874008	+	0.438944i	−0.828479	−	0.560019i	$-0.810794\pi$
$521$	−19.9496	+	10.0191i	−0.874008	+	0.438944i	−0.0455290	+	0.998963i	$0.514497\pi$
$522$	52.1012	−	27.3104i	2.28041	−	1.19534i
$523$	7.76402	−	5.10648i	0.339497	−	0.223291i	−0.368299	−	0.929707i	$-0.620060\pi$
$523$	7.76402	−	5.10648i	0.339497	−	0.223291i	0.707796	+	0.706417i	$0.249689\pi$
$524$	−57.9473	−	11.3805i	−2.53144	−	0.497158i
$525$	−10.6543	−	9.13605i	−0.464990	−	0.398730i
$526$	−15.7260	+	24.9510i	−0.685686	+	1.08791i
$527$	−4.11277	−	7.80791i	−0.179155	−	0.340118i
$528$	−10.6153	−	3.99282i	−0.461974	−	0.173765i
$529$	14.8527	+	43.4085i	0.645768	+	1.88733i
$530$	3.02695	+	51.9708i	0.131483	+	2.25747i
$531$	0.198266	+	2.61895i	0.00860400	+	0.113653i
$532$	−44.2142	−	29.0801i	−1.91693	−	1.26078i
$533$	−1.08822	−	1.06732i	−0.0471362	−	0.0462309i
$534$	−17.9845	−	21.0587i	−0.778267	−	0.911299i
$535$	−13.4887	−	15.4564i	−0.583169	−	0.668237i
$536$	5.29994	+	20.5756i	0.228922	+	0.888732i
$537$	−2.25587	+	8.38530i	−0.0973480	+	0.361852i
$538$	49.8544	−	20.3678i	2.14938	−	0.878117i
$539$	−27.3115	+	22.9171i	−1.17639	+	0.987108i
$540$	−24.1223	+	42.4332i	−1.03806	+	1.82603i
$541$	−7.54610	−	6.33193i	−0.324432	−	0.272231i	0.465995	−	0.884788i	$-0.345697\pi$
$541$	−7.54610	−	6.33193i	−0.324432	−	0.272231i	−0.790427	+	0.612557i	$0.790141\pi$
$542$	2.16990	+	0.695750i	0.0932051	+	0.0298850i
$543$	7.37119	+	22.3201i	0.316328	+	0.957848i
$544$	2.04454	−	21.0197i	0.0876589	−	0.901212i
$545$	29.5721	+	16.3172i	1.26673	+	0.698951i
$546$	−10.8914	+	16.8773i	−0.466110	+	0.722281i
$547$	−19.9661	−	1.55189i	−0.853689	−	0.0663540i	−0.356814	−	0.934176i	$-0.616137\pi$
$547$	−19.9661	−	1.55189i	−0.853689	−	0.0663540i	−0.496876	+	0.867822i	$0.665520\pi$
$548$	47.5705	−	50.4218i	2.03211	−	2.15391i
$549$	12.3727	+	22.5304i	0.528056	+	0.961574i
$550$	−24.6873	+	5.85099i	−1.05267	+	0.249487i
$551$	12.0680	−	31.2570i	0.514115	−	1.33159i
$552$	−42.9095	+	27.5688i	−1.82635	+	1.17341i
$553$	3.50017	+	25.6258i	0.148842	+	1.08972i
$554$	−2.37155	+	10.9483i	−0.100757	+	0.465148i
$555$	6.25650	+	4.21156i	0.265574	+	0.178771i
$556$	−12.6567	+	6.98365i	−0.536762	+	0.296173i
$557$	3.01207	+	6.98277i	0.127626	+	0.295869i	0.970034	−	0.242971i	$-0.0781219\pi$
$557$	3.01207	+	6.98277i	0.127626	+	0.295869i	−0.842408	+	0.538840i	$0.818863\pi$
$558$	11.6707	+	2.08206i	0.494061	+	0.0881407i
$559$	2.56358	+	3.44348i	0.108428	+	0.145644i
$560$	10.6854	−	7.63747i	0.451541	−	0.322742i
$561$	−32.8236	+	31.5112i	−1.38581	+	1.33040i
$562$	−59.0280	−	9.23181i	−2.48995	−	0.389420i
$563$	11.6596	−	24.3840i	0.491393	−	1.02766i	−0.495845	−	0.868411i	$-0.665142\pi$
$563$	11.6596	−	24.3840i	0.491393	−	1.02766i	0.987238	−	0.159250i	$-0.0509077\pi$
$564$	27.4836	−	10.8866i	1.15727	−	0.458407i
$565$	17.8123	+	28.2611i	0.749368	+	1.18895i
$566$	1.45726	−	2.52404i	0.0612531	−	0.106094i
$567$	25.1313	−	22.6219i	1.05542	−	0.950029i
$568$	−10.9693	−	18.9994i	−0.460261	−	0.797196i
$569$	12.3369	−	23.4211i	0.517191	−	0.981862i	−0.477469	−	0.878649i	$-0.658446\pi$
$569$	12.3369	−	23.4211i	0.517191	−	0.981862i	0.994659	−	0.103213i	$-0.0329124\pi$
$570$	8.78119	+	42.7442i	0.367804	+	1.79036i
$571$	−5.32167	−	7.75919i	−0.222705	−	0.324712i	0.697183	−	0.716893i	$-0.254437\pi$
$571$	−5.32167	−	7.75919i	−0.222705	−	0.324712i	−0.919888	+	0.392181i	$0.871721\pi$
$572$	8.33228	+	21.5811i	0.348390	+	0.902353i
$573$	−3.61804	+	33.4750i	−0.151146	+	1.39844i
$574$	−0.989892	−	10.1770i	−0.0413173	−	0.424779i
$575$	−7.08981	+	16.4360i	−0.295665	+	0.685429i
$576$	26.2889	+	24.9024i	1.09537	+	1.03760i
$577$	8.38739	+	0.980345i	0.349172	+	0.0408123i	0.288871	−	0.957368i	$-0.406720\pi$
$577$	8.38739	+	0.980345i	0.349172	+	0.0408123i	0.0603004	+	0.998180i	$0.480794\pi$
$578$	21.0765	+	12.7198i	0.876669	+	0.529072i
$579$	−6.85148	−	1.70147i	−0.284738	−	0.0707106i
$580$	58.1025	+	52.7253i	2.41258	+	2.18930i
$581$	43.8978	−	34.0234i	1.82119	−	1.41153i
$582$	−31.3572	+	7.07825i	−1.29980	+	0.293403i
$583$	−26.0760	−	32.3292i	−1.07996	−	1.33894i
$584$	12.9890	+	13.7675i	0.537487	+	0.569703i
$585$	10.3177	−	2.21325i	0.426584	−	0.0915065i
$586$	−18.0663	−	60.3457i	−0.746312	−	2.49286i
$587$	−5.11890	−	10.7053i	−0.211280	−	0.441854i	0.769059	−	0.639178i	$-0.220725\pi$
$587$	−5.11890	−	10.7053i	−0.211280	−	0.441854i	−0.980338	+	0.197324i	$0.936775\pi$
$588$	−41.3459	+	12.7707i	−1.70508	+	0.526656i
$589$	5.78118	−	3.48896i	0.238209	−	0.143760i
$590$	−5.00552	+	2.27529i	−0.206074	+	0.0936721i
$591$	−11.1565	+	6.00109i	−0.458919	+	0.246852i
$592$	−1.57514	+	1.42936i	−0.0647377	+	0.0587463i
$593$	1.02900	−	5.83577i	0.0422561	−	0.239646i	−0.956363	−	0.292181i	$-0.905619\pi$
$593$	1.02900	−	5.83577i	0.0422561	−	0.239646i	0.998619	+	0.0525350i	$0.0167301\pi$
$594$	−6.32383	−	60.7964i	−0.259470	−	2.49451i
$595$	−9.15017	−	51.8932i	−0.375120	−	2.12741i
$596$	−3.21318	−	2.49040i	−0.131617	−	0.102011i
$597$	30.1195	+	14.0818i	1.23271	+	0.576330i
$598$	24.6795	+	6.87001i	1.00922	+	0.280936i
$599$	−12.1892	+	35.6242i	−0.498036	+	1.45557i	0.355572	+	0.934649i	$0.384286\pi$
$599$	−12.1892	+	35.6242i	−0.498036	+	1.45557i	−0.853608	+	0.520916i	$0.825590\pi$
$600$	−13.0724	−	2.18805i	−0.533679	−	0.0893268i
$601$	15.2395	−	4.24221i	0.621634	−	0.173044i	0.0569851	−	0.998375i	$-0.481851\pi$
$601$	15.2395	−	4.24221i	0.621634	−	0.173044i	0.564648	+	0.825331i	$0.309012\pi$
$602$	−1.67444	+	28.7490i	−0.0682449	+	1.17172i
$603$	−13.5595	+	11.7854i	−0.552185	+	0.479938i
$604$	−6.60554	−	3.31743i	−0.268776	−	0.134984i
$605$	24.8158	−	28.4358i	1.00891	−	1.15608i
$606$	−9.64991	−	0.103271i	−0.392001	−	0.00419509i
$607$	−18.9167	−	0.734056i	−0.767807	−	0.0297944i	−0.348104	−	0.937456i	$-0.613174\pi$
$607$	−18.9167	−	0.734056i	−0.767807	−	0.0297944i	−0.419703	+	0.907662i	$0.637866\pi$
$608$	16.1471	+	0.626581i	0.654851	+	0.0254112i
$609$	−26.6709	−	47.3586i	−1.08076	−	1.91907i
$610$	−35.3818	+	40.5430i	−1.43257	+	1.64154i
$611$	−5.71110	−	2.86822i	−0.231046	−	0.116036i
$612$	−51.5600	+	19.7878i	−2.08419	+	0.799876i
$613$	−0.383457	+	6.58370i	−0.0154877	+	0.265913i	0.981671	+	0.190584i	$0.0610380\pi$
$613$	−0.383457	+	6.58370i	−0.0154877	+	0.265913i	−0.997159	+	0.0753298i	$0.975999\pi$
$614$	−32.0504	+	8.92184i	−1.29345	+	0.360056i
$615$	−3.41697	+	4.14481i	−0.137785	+	0.167135i
$616$	−21.6234	+	63.1968i	−0.871231	+	2.54627i
$617$	10.6517	+	2.96511i	0.428822	+	0.119371i	0.475857	−	0.879522i	$-0.342138\pi$
$617$	10.6517	+	2.96511i	0.428822	+	0.119371i	−0.0470353	+	0.998893i	$0.514977\pi$
$618$	2.22956	+	25.7824i	0.0896860	+	1.03712i
$619$	33.3293	+	25.8321i	1.33962	+	1.03828i	0.995035	+	0.0995254i	$0.0317325\pi$
$619$	33.3293	+	25.8321i	1.33962	+	1.03828i	0.344582	+	0.938756i	$0.388021\pi$
$620$	2.74570	+	15.5716i	0.110270	+	0.625372i
$621$	−37.0700	−	22.0353i	−1.48757	−	0.884247i
$622$	0.606993	−	3.44243i	0.0243382	−	0.138029i
$623$	−18.9487	+	17.1950i	−0.759162	+	0.688903i
$624$	−0.0895462	+	2.97466i	−0.00358472	+	0.119082i
$625$	28.3416	−	12.8828i	1.13366	−	0.515314i
$626$	8.97377	−	5.41570i	0.358664	−	0.216455i
$627$	−25.5305	−	23.6708i	−1.01959	−	0.945319i
$628$	15.6492	+	32.7274i	0.624469	+	1.30597i
$629$	2.44740	+	8.17488i	0.0975841	+	0.325954i
$630$	62.5630	+	33.1155i	2.49257	+	1.31936i
$631$	−21.9881	−	23.3060i	−0.875332	−	0.927797i	0.122576	−	0.992459i	$-0.460885\pi$
$631$	−21.9881	−	23.3060i	−0.875332	−	0.927797i	−0.997907	+	0.0646618i	$0.979403\pi$
$632$	15.3343	+	19.0116i	0.609966	+	0.756240i
$633$	9.97651	−	32.0707i	0.396531	−	1.27470i
$634$	61.1437	−	47.3900i	2.42833	−	1.88210i
$635$	−22.8540	−	20.7389i	−0.906932	−	0.822997i
$636$	−13.9409	−	48.4468i	−0.552792	−	1.92104i
$637$	8.00971	+	4.83388i	0.317356	+	0.191525i
$638$	−97.5887	−	11.4065i	−3.86357	−	0.451587i
$639$	10.2245	−	15.4777i	0.404474	−	0.612289i
$640$	−21.4888	+	49.8167i	−0.849420	+	1.96918i
$641$	0.815813	+	8.38729i	0.0322227	+	0.331278i	0.997534	+	0.0701781i	$0.0223568\pi$
$641$	0.815813	+	8.38729i	0.0322227	+	0.331278i	−0.965312	+	0.261100i	$0.915915\pi$
$642$	25.1719	+	18.4020i	0.993457	+	0.726268i
$643$	−9.49188	−	24.5846i	−0.374323	−	0.969521i	−0.984206	−	0.177029i	$-0.943351\pi$
$643$	−9.49188	−	24.5846i	−0.374323	−	0.969521i	0.609883	−	0.792492i	$-0.291217\pi$
$644$	61.9262	+	90.2905i	2.44023	+	3.55795i
$645$	11.3117	−	10.0462i	0.445399	−	0.395570i
$646$	−23.0100	+	43.6835i	−0.905317	+	1.71870i
$647$	9.89409	+	17.1371i	0.388977	+	0.673728i	0.992312	−	0.123760i	$-0.0394953\pi$
$647$	9.89409	+	17.1371i	0.388977	+	0.673728i	−0.603335	+	0.797488i	$0.706162\pi$
$648$	9.28120	−	30.5537i	0.364600	−	1.20026i
$649$	2.19342	−	3.79911i	0.0860992	−	0.149128i
$650$	3.54977	+	5.63210i	0.139233	+	0.220909i
$651$	1.59841	−	10.8363i	0.0626468	−	0.424709i
$652$	−5.37115	+	11.2328i	−0.210350	+	0.439910i
$653$	−2.54280	−	0.397687i	−0.0995075	−	0.0155627i	0.104569	−	0.994518i	$-0.466654\pi$
$653$	−2.54280	−	0.397687i	−0.0995075	−	0.0155627i	−0.204077	+	0.978955i	$0.565419\pi$
$654$	−49.3059	−	14.2955i	−1.92801	−	0.558998i
$655$	36.6036	−	26.1627i	1.43022	−	1.02226i
$656$	−0.904659	−	1.21517i	−0.0353210	−	0.0474443i
$657$	−5.50394	+	15.0279i	−0.214729	+	0.586294i
$658$	−16.9803	−	39.3647i	−0.661959	−	1.53459i
$659$	9.39373	−	5.18324i	0.365928	−	0.201910i	−0.289483	−	0.957183i	$-0.593483\pi$
$659$	9.39373	−	5.18324i	0.365928	−	0.201910i	0.655411	+	0.755273i	$0.272496\pi$
$660$	73.2416	−	35.8071i	2.85093	−	1.39379i
$661$	−5.19195	+	23.9687i	−0.201943	+	0.932274i	0.758038	+	0.652210i	$0.226158\pi$
$661$	−5.19195	+	23.9687i	−0.201943	+	0.932274i	−0.959981	+	0.280064i	$0.909644\pi$
$662$	4.37462	+	32.0279i	0.170025	+	1.24480i
$663$	10.6116	+	5.47233i	0.412121	+	0.212528i
$664$	18.8913	−	48.9296i	0.733123	−	1.89884i
$665$	39.2321	−	9.29818i	1.52136	−	0.360568i
$666$	−10.6857	−	4.15035i	−0.414063	−	0.160823i
$667$	−47.5702	+	50.4214i	−1.84192	+	1.95233i
$668$	−2.56613	−	0.199455i	−0.0992864	−	0.00771715i
$669$	−7.30918	−	14.2438i	−0.282589	−	0.550695i
$670$	−32.9297	−	18.1698i	−1.27218	−	0.701962i
$671$	4.15634	−	42.7309i	0.160454	−	1.64961i
$672$	17.4461	−	19.5644i	0.672997	−	0.754711i
$673$	21.7329	+	6.96837i	0.837741	+	0.268611i	0.693071	−	0.720869i	$-0.256257\pi$
$673$	21.7329	+	6.96837i	0.837741	+	0.268611i	0.144670	+	0.989480i	$0.453788\pi$
$674$	−37.3690	−	31.3563i	−1.43940	−	1.20780i
$675$	−3.28586	−	10.7145i	−0.126473	−	0.412400i
$676$	−30.3177	+	25.4396i	−1.16607	+	0.978445i
$677$	18.1828	−	7.42848i	0.698821	−	0.285500i	−0.000814814	−	1.00000i	$-0.500259\pi$
$677$	18.1828	−	7.42848i	0.698821	−	0.285500i	0.699635	+	0.714500i	$0.253346\pi$
$678$	−35.8677	−	35.9399i	−1.37749	−	1.38026i
$679$	7.40886	+	28.7630i	0.284326	+	1.10382i
$680$	−32.7200	−	37.4929i	−1.25475	−	1.43779i
$681$	5.15456	−	14.5544i	0.197523	−	0.557726i
$682$	−14.1364	−	13.8649i	−0.541312	−	0.530915i
$683$	−10.2842	−	6.76404i	−0.393515	−	0.258819i	0.337296	−	0.941399i	$-0.390488\pi$
$683$	−10.2842	−	6.76404i	−0.393515	−	0.258819i	−0.730811	+	0.682580i	$0.760858\pi$
$684$	−17.4090	−	38.5043i	−0.665652	−	1.47225i
$685$	3.07086	+	52.7246i	0.117331	+	2.01450i
$686$	0.328950	+	0.961393i	0.0125594	+	0.0367062i
$687$	9.91615	−	8.14141i	0.378325	−	0.310614i
$688$	1.98845	+	3.77498i	0.0758090	+	0.143920i
$689$	−5.81128	+	9.22023i	−0.221392	+	0.351263i
$690$	16.6275	−	88.7357i	0.632998	−	3.37811i
$691$	−40.2354	−	7.90198i	−1.53063	−	0.300605i	−0.644702	−	0.764434i	$-0.723019\pi$
$691$	−40.2354	−	7.90198i	−1.53063	−	0.300605i	−0.885925	+	0.463828i	$0.846476\pi$
$692$	41.3343	−	27.1860i	1.57130	−	1.03346i
$693$	−55.9724	+	7.53057i	−2.12621	+	0.286063i
$694$	38.2488	−	19.2093i	1.45191	−	0.729174i
$695$	2.74720	−	10.6653i	0.104207	−	0.404557i
$696$	−44.6735	−	25.2771i	−1.69334	−	0.958127i
$697$	−5.96390	+	1.17127i	−0.225899	+	0.0443651i
$698$	57.4224	−	56.3195i	2.17347	−	2.13172i
$699$	12.9984	+	27.9485i	0.491646	+	1.05711i
$700$	−3.85054	+	28.1909i	−0.145537	+	1.06552i
$701$	7.29576	+	2.65544i	0.275557	+	0.100295i	0.476102	−	0.879390i	$-0.342049\pi$
$701$	7.29576	+	2.65544i	0.275557	+	0.100295i	−0.200545	+	0.979684i	$0.564271\pi$
$702$	−14.5568	+	6.73457i	−0.549410	+	0.254180i
$703$	−6.13558	+	2.23317i	−0.231408	+	0.0842256i
$704$	−12.8042	−	59.1108i	−0.482577	−	2.22782i
$705$	−8.33634	+	20.9225i	−0.313965	+	0.787988i
$706$	44.2941	+	31.6596i	1.66703	+	1.19152i
$707$	0.172906	+	8.91500i	0.00650280	+	0.335283i
$708$	4.24312	−	3.21658i	0.159466	−	0.120886i
$709$	13.5111	−	19.6997i	0.507422	−	0.739839i	−0.483343	−	0.875431i	$-0.660578\pi$
$709$	13.5111	−	19.6997i	0.507422	−	0.739839i	0.990765	+	0.135592i	$0.0432937\pi$
$710$	37.7869	+	8.95565i	1.41812	+	0.336100i
$711$	−8.58392	+	18.7839i	−0.321922	+	0.704450i
$712$	−6.93036	+	23.1490i	−0.259726	+	0.867546i
$713$	−13.8022	+	2.15863i	−0.516897	+	0.0808412i
$714$	30.9340	+	73.8770i	1.15768	+	2.76478i
$715$	−16.3161	−	6.66585i	−0.610187	−	0.249289i
$716$	16.7631	−	5.37486i	0.626465	−	0.200868i
$717$	−1.73074	+	3.89711i	−0.0646358	+	0.145540i
$718$	−0.207357	+	10.6913i	−0.00773848	+	0.398994i
$719$	24.1724	−	32.4691i	0.901477	−	1.21089i	−0.0754129	−	0.997152i	$-0.524027\pi$
$719$	24.1724	−	32.4691i	0.901477	−	1.21089i	0.976890	−	0.213742i	$-0.0685651\pi$
$720$	10.4712	−	0.588763i	0.390240	−	0.0219419i
$721$	23.7492	−	2.77589i	0.884467	−	0.103379i
$722$	6.21478	+	2.82497i	0.231290	+	0.105134i
$723$	−5.17474	+	10.5310i	−0.192451	+	0.391651i
$724$	29.9168	−	37.0911i	1.11185	−	1.37848i
$725$	−17.9603	+	1.39598i	−0.667028	+	0.0518455i
$726$	−27.2763	+	50.4655i	−1.01232	+	1.87295i
$727$	40.2196	−	1.56070i	1.49166	−	0.0578833i	0.720025	−	0.693948i	$-0.244130\pi$
$727$	40.2196	−	1.56070i	1.49166	−	0.0578833i	0.771636	+	0.636064i	$0.219439\pi$
$728$	17.5268			0.649586
$729$	26.6176	−	4.52807i	0.985837	−	0.167706i
$730$	−33.5040			−1.24004
$731$	17.1047	−	0.663740i	0.632640	−	0.0245493i
$732$	24.7771	−	45.8417i	0.915789	−	1.69436i
$733$	2.13086	−	0.165623i	0.0787051	−	0.00611744i	−0.0380795	−	0.999275i	$-0.512124\pi$
$733$	2.13086	−	0.165623i	0.0787051	−	0.00611744i	0.116785	+	0.993157i	$0.462741\pi$
$734$	−50.4971	+	62.6066i	−1.86388	+	2.31085i
$735$	14.5399	−	29.5898i	0.536312	−	1.09143i
$736$	−30.4350	−	13.8344i	−1.12185	−	0.509943i
$737$	29.8039	−	3.48357i	1.09784	−	0.128319i
$738$	3.67898	−	7.28888i	0.135425	−	0.268308i
$739$	−11.6500	+	15.6487i	−0.428553	+	0.575646i	−0.962982	−	0.269567i	$-0.913119\pi$
$739$	−11.6500	+	15.6487i	−0.428553	+	0.575646i	0.534429	+	0.845213i	$0.320527\pi$
$740$	0.296485	−	15.2867i	0.0108990	−	0.561950i
$741$	−3.70799	+	8.34926i	−0.136216	+	0.306718i
$742$	−69.6193	+	22.3225i	−2.55580	+	0.819485i
$743$	−40.3575	−	16.4879i	−1.48057	−	0.604881i	−0.513208	−	0.858264i	$-0.671543\pi$
$743$	−40.3575	−	16.4879i	−1.48057	−	0.604881i	−0.967366	+	0.253383i	$0.918457\pi$
$744$	−3.99528	−	9.54158i	−0.146474	−	0.349811i
$745$	3.06007	−	0.478587i	0.112112	−	0.0175341i
$746$	2.31107	−	7.71951i	0.0846143	−	0.282631i
$747$	44.1486	−	4.20467i	1.61531	−	0.153841i
$748$	89.7564	+	21.2727i	3.28182	+	0.777805i
$749$	16.2952	−	23.7590i	0.595415	−	0.868136i
$750$	−24.6469	+	18.6841i	−0.899978	+	0.682245i
$751$	0.476076	+	24.5463i	0.0173722	+	0.895708i	0.902582	+	0.430517i	$0.141669\pi$
$751$	0.476076	+	24.5463i	0.0173722	+	0.895708i	−0.885210	+	0.465191i	$0.845986\pi$
$752$	−5.16747	−	3.69349i	−0.188438	−	0.134688i
$753$	10.3400	−	25.9514i	0.376812	−	0.945721i
$754$	5.45810	+	25.1974i	0.198772	+	0.917635i
$755$	5.29203	−	1.92614i	0.192597	−	0.0700995i
$756$	−66.1589	−	17.9412i	−2.40617	−	0.652515i
$757$	10.0509	+	3.65824i	0.365307	+	0.132961i	0.518151	−	0.855289i	$-0.326621\pi$
$757$	10.0509	+	3.65824i	0.365307	+	0.132961i	−0.152843	+	0.988250i	$0.548843\pi$
$758$	8.77176	−	64.2206i	0.318605	−	2.33260i
$759$	30.3753	+	65.3113i	1.10255	+	2.37065i
$760$	27.1837	−	26.6616i	0.986056	−	0.967117i
$761$	−7.65998	+	1.50437i	−0.277674	+	0.0545334i	−0.329610	−	0.944117i	$-0.606917\pi$
$761$	−7.65998	+	1.50437i	−0.277674	+	0.0545334i	0.0519366	+	0.998650i	$0.483461\pi$
$762$	40.8252	+	23.0997i	1.47894	+	0.836814i
$763$	−11.8318	+	45.9337i	−0.428338	+	1.66291i
$764$	60.9975	−	30.6341i	2.20681	−	1.10830i
$765$	15.9915	−	38.9189i	0.578173	−	1.40712i
$766$	50.2316	−	33.0378i	1.81494	−	1.19371i
$767$	−1.12954	−	0.221834i	−0.0407852	−	0.00800995i
$768$	7.48682	−	39.9548i	0.270158	−	1.44174i
$769$	−12.6389	+	20.0529i	−0.455770	+	0.723128i	−0.992715	−	0.120490i	$-0.961554\pi$
$769$	−12.6389	+	20.0529i	−0.455770	+	0.723128i	0.536945	+	0.843617i	$0.319578\pi$
$770$	−55.1013	−	104.607i	−1.98571	−	3.76978i
$771$	38.8164	−	31.8693i	1.39794	−	1.14774i
$772$	4.63318	+	13.5410i	0.166752	+	0.487350i
$773$	−2.73590	−	46.9735i	−0.0984034	−	1.68952i	−0.581178	−	0.813776i	$-0.697408\pi$
$773$	−2.73590	−	46.9735i	−0.0984034	−	1.68952i	0.482775	−	0.875744i	$-0.339629\pi$
$774$	−13.4090	+	18.6808i	−0.481978	+	0.671467i
$775$	−3.03319	−	1.99496i	−0.108955	−	0.0716611i
$776$	20.0255	+	19.6409i	0.718873	+	0.705066i
$777$	−3.53596	+	9.98411i	−0.126852	+	0.358178i
$778$	8.10602	+	9.28847i	0.290615	+	0.333008i
$779$	−1.16002	−	4.50348i	−0.0415621	−	0.161354i
$780$	−15.1116	−	15.1420i	−0.541082	−	0.542171i
$781$	−28.6818	+	11.7178i	−1.02632	+	0.419296i
$782$	78.2497	−	65.6593i	2.79820	−	2.34797i
$783$	2.23399	−	43.3430i	0.0798364	−	1.54895i
$784$	7.12270	+	5.97665i	0.254382	+	0.213452i
$785$	−26.3186	−	8.43871i	−0.939350	−	0.301190i
$786$	−45.5142	+	51.0405i	−1.62344	+	1.82055i
$787$	3.62570	−	37.2754i	0.129242	−	1.32872i	−0.676493	−	0.736449i	$-0.736501\pi$
$787$	3.62570	−	37.2754i	0.129242	−	1.32872i	0.805735	−	0.592276i	$-0.201770\pi$
$788$	22.4858	+	12.4072i	0.801024	+	0.441987i
$789$	9.93445	+	19.3597i	0.353676	+	0.689225i
$790$	−43.1049	−	3.35038i	−1.53360	−	0.119201i
$791$	−32.1949	+	34.1246i	−1.14472	+	1.21333i
$792$	−41.5814	+	33.4009i	−1.47753	+	1.18685i
$793$	−10.9619	+	2.59802i	−0.389268	+	0.0922583i
$794$	−1.68828	+	4.37275i	−0.0599148	+	0.155183i
$795$	34.1367	+	17.6040i	1.21070	+	0.624350i
$796$	−9.12188	−	66.7840i	−0.323317	−	2.36710i
$797$	−0.850810	+	3.92778i	−0.0301372	+	0.139129i	−0.989924	−	0.141602i	$-0.954775\pi$
$797$	−0.850810	+	3.92778i	−0.0301372	+	0.139129i	0.959786	+	0.280731i	$0.0905770\pi$
$798$	−55.0555	+	26.9160i	−1.94894	+	0.952818i
$799$	−22.3116	+	12.3110i	−0.789328	+	0.435533i
$800$	−3.44116	−	7.97751i	−0.121664	−	0.282048i
$801$	−20.1284	+	3.50748i	−0.711203	+	0.123931i
$802$	−43.4386	−	58.3482i	−1.53387	−	2.06035i
$803$	21.7470	−	15.5438i	0.767435	−	0.548529i
$804$	34.9800	+	10.1419i	1.23365	+	0.357678i
$805$	−82.4137	−	12.8893i	−2.90470	−	0.454287i
$806$	−2.24139	+	4.68747i	−0.0789495	+	0.165109i
$807$	5.79813	−	39.3080i	0.204104	−	1.38371i
$808$	4.48994	+	7.12378i	0.157956	+	0.250614i
$809$	−2.98824	+	5.17579i	−0.105061	+	0.181971i	−0.913763	−	0.406247i	$-0.866837\pi$
$809$	−2.98824	+	5.17579i	−0.105061	+	0.181971i	0.808702	+	0.588218i	$0.200170\pi$
$810$	28.0648	+	49.0641i	0.986096	+	1.72394i
$811$	−8.92235	−	15.4540i	−0.313306	−	0.542662i	0.665770	−	0.746157i	$-0.268103\pi$
$811$	−8.92235	−	15.4540i	−0.313306	−	0.542662i	−0.979076	+	0.203495i	$0.934770\pi$
$812$	−51.3518	+	97.4889i	−1.80209	+	3.42119i
$813$	1.25703	−	1.11640i	0.0440859	−	0.0391538i
$814$	10.8296	+	15.7899i	0.379576	+	0.553436i
$815$	−3.41669	−	8.84944i	−0.119681	−	0.309982i
$816$	9.57956	+	7.00315i	0.335352	+	0.245159i
$817$	1.26799	+	13.0361i	0.0443614	+	0.456075i
$818$	9.44109	−	21.8869i	0.330100	−	0.765258i
$819$	6.62438	+	13.2566i	0.231474	+	0.463223i
$820$	10.8162	+	1.26424i	0.377720	+	0.0441491i
$821$	−7.12833	−	4.30197i	−0.248780	−	0.150140i	0.386827	−	0.922152i	$-0.373571\pi$
$821$	−7.12833	−	4.30197i	−0.248780	−	0.150140i	−0.635607	+	0.772013i	$0.719250\pi$
$822$	−22.1988	−	77.1442i	−0.774270	−	2.69071i
$823$	18.1378	+	16.4592i	0.632244	+	0.573731i	0.923825	−	0.382815i	$-0.125045\pi$
$823$	18.1378	+	16.4592i	0.632244	+	0.573731i	−0.291581	+	0.956546i	$0.594181\pi$
$824$	17.8477	−	13.8330i	0.621755	−	0.481897i
$825$	−5.56013	+	17.8737i	−0.193579	+	0.622283i
$826$	−4.84785	−	6.01039i	−0.168678	−	0.209128i
$827$	−0.328048	−	0.347710i	−0.0114073	−	0.0120911i	0.721645	−	0.692263i	$-0.243386\pi$
$827$	−0.328048	−	0.347710i	−0.0114073	−	0.0120911i	−0.733052	+	0.680172i	$0.761905\pi$
$828$	3.21434	+	87.3662i	0.111706	+	3.03618i
$829$	−7.28401	−	24.3303i	−0.252984	−	0.845026i	−0.986275	−	0.165111i	$-0.947202\pi$
$829$	−7.28401	−	24.3303i	−0.252984	−	0.845026i	0.733291	−	0.679915i	$-0.237983\pi$
$830$	40.0507	+	83.7589i	1.39018	+	2.90731i
$831$	6.06071	+	5.61923i	0.210244	+	0.194929i
$832$	−13.5878	+	8.20027i	−0.471072	+	0.284293i
$833$	33.9593	−	15.4364i	1.17662	−	0.534839i
$834$	−0.503691	+	16.7323i	−0.0174414	+	0.579391i
$835$	1.45219	−	1.31779i	0.0502552	−	0.0456042i
$836$	−12.2561	+	69.5078i	−0.423886	+	2.40398i
$837$	5.70685	−	6.62819i	0.197258	−	0.229104i
$838$	2.17049	+	12.3095i	0.0749783	+	0.425223i
$839$	−28.0105	−	21.7098i	−0.967029	−	0.749504i	0.00108901	−	0.999999i	$-0.499653\pi$
$839$	−28.0105	−	21.7098i	−0.967029	−	0.749504i	−0.968118	+	0.250496i	$0.919406\pi$
$840$	−5.32144	−	61.5366i	−0.183607	−	2.12321i
$841$	−39.2702	−	10.9316i	−1.35414	−	0.376952i
$842$	−19.9919	+	58.4284i	−0.688965	+	2.01358i
$843$	−28.0393	+	34.0119i	−0.965725	+	1.17143i
$844$	−65.5950	+	18.2596i	−2.25787	+	0.628522i
$845$	1.75324	−	30.1019i	0.0603132	−	1.03554i
$846$	5.35755	−	33.8107i	0.184196	−	1.16244i
$847$	47.3655	+	23.7878i	1.62750	+	0.817360i
$848$	−7.12230	+	8.16125i	−0.244581	+	0.280259i
$849$	−1.05516	−	1.87361i	−0.0362130	−	0.0643022i
$850$	26.5256	+	1.02931i	0.909821	+	0.0353052i
$851$	13.4984	+	0.523798i	0.462718	+	0.0179556i
$852$	−37.6035	−	0.402423i	−1.28827	−	0.0137868i
$853$	14.1060	−	16.1637i	0.482981	−	0.553434i	−0.459290	−	0.888286i	$-0.651896\pi$
$853$	14.1060	−	16.1637i	0.482981	−	0.553434i	0.942271	+	0.334852i	$0.108686\pi$
$854$	−67.5325	−	33.9161i	−2.31092	−	1.16059i
$855$	30.4401	+	10.4838i	1.04103	+	0.358538i
$856$	1.58198	−	27.1615i	0.0540710	−	0.928363i
$857$	−13.8915	+	3.86696i	−0.474524	+	0.132093i	−0.497174	−	0.867651i	$-0.665629\pi$
$857$	−13.8915	+	3.86696i	−0.474524	+	0.132093i	0.0226505	+	0.999743i	$0.492790\pi$
$858$	26.4219	+	4.42247i	0.902029	+	0.150981i
$859$	1.85575	−	5.42364i	0.0633175	−	0.185052i	−0.909954	−	0.414708i	$-0.863884\pi$
$859$	1.85575	−	5.42364i	0.0633175	−	0.185052i	0.973272	+	0.229656i	$0.0737601\pi$
$860$	−29.5468	−	8.22491i	−1.00754	−	0.280467i
$861$	−6.83389	−	3.19506i	−0.232898	−	0.108887i
$862$	−27.9846	−	21.6897i	−0.953159	−	0.738754i
$863$	−4.51423	−	25.6015i	−0.153666	−	0.871485i	−0.959995	−	0.280017i	$-0.909660\pi$
$863$	−4.51423	−	25.6015i	−0.153666	−	0.871485i	0.806329	−	0.591468i	$-0.201451\pi$
$864$	20.1267	−	5.74781i	0.684724	−	0.195544i
$865$	−6.54528	+	37.1201i	−0.222546	+	1.26212i
$866$	30.5701	−	27.7408i	1.03881	−	0.942672i
$867$	15.9952	−	8.60381i	0.543227	−	0.292201i
$868$	−20.2154	+	9.18902i	−0.686155	+	0.311895i
$869$	29.5332	−	17.8234i	1.00184	−	0.604616i
$870$	86.8109	−	26.8138i	2.94317	−	0.909072i
$871$	−3.39666	−	7.10351i	−0.115091	−	0.240693i
$872$	12.8472	+	42.9127i	0.435062	+	1.45321i
$873$	−7.28682	+	22.5699i	−0.246622	+	0.763876i
$874$	53.6359	+	56.8507i	1.81426	+	1.92300i
$875$	17.9408	+	22.2431i	0.606509	+	0.751954i
$876$	31.6483	−	7.14397i	1.06930	−	0.241372i
$877$	−20.4550	+	15.8538i	−0.690715	+	0.535344i	−0.896385	−	0.443277i	$-0.853816\pi$
$877$	−20.4550	+	15.8538i	−0.690715	+	0.535344i	0.205670	+	0.978621i	$0.434063\pi$
$878$	69.6622	+	63.2151i	2.35099	+	2.13341i
$879$	−45.1048	−	11.2011i	−1.52135	−	0.377805i
$880$	−14.9977	−	9.05116i	−0.505573	−	0.305115i
$881$	−47.5521	−	5.55805i	−1.60207	−	0.187255i	−0.732396	−	0.680879i	$-0.761598\pi$
$881$	−47.5521	−	5.55805i	−1.60207	−	0.187255i	−0.869676	+	0.493624i	$0.835672\pi$
$882$	−11.6545	+	48.7374i	−0.392427	+	1.64107i
$883$	−10.3967	+	24.1023i	−0.349877	+	0.811107i	0.648862	+	0.760906i	$0.275245\pi$
$883$	−10.3967	+	24.1023i	−0.349877	+	0.811107i	−0.998739	+	0.0502004i	$0.984014\pi$
$884$	−2.34327	−	24.0910i	−0.0788128	−	0.810267i
$885$	−0.435912	+	4.03316i	−0.0146530	+	0.135573i
$886$	−18.1023	−	46.8862i	−0.608160	−	1.57517i
$887$	13.5490	+	19.7549i	0.454930	+	0.663305i	0.982512	−	0.186200i	$-0.0596172\pi$
$887$	13.5490	+	19.7549i	0.454930	+	0.663305i	−0.527582	+	0.849504i	$0.676901\pi$
$888$	2.01285	+	9.79797i	0.0675469	+	0.328798i
$889$	20.1986	−	38.3461i	0.677440	−	1.28609i
$890$	−21.3866	−	37.0426i	−0.716880	−	1.24167i
$891$	−40.9792	−	18.8265i	−1.37286	−	0.630711i
$892$	−16.2279	+	28.1076i	−0.543351	+	0.941111i
$893$	−10.3966	−	16.4953i	−0.347907	−	0.551993i
$894$	−4.37684	+	1.73372i	−0.146383	+	0.0579841i
$895$	−5.78571	+	12.0998i	−0.193395	+	0.404451i
$896$	−75.2778	−	11.7732i	−2.51485	−	0.393316i
$897$	13.6346	−	13.0894i	0.455244	−	0.437041i
$898$	40.1402	−	28.6905i	1.33950	−	0.957414i
$899$	−8.39566	−	11.2773i	−0.280011	−	0.376120i
$900$	−14.6388	+	17.3748i	−0.487961	+	0.579161i
$901$	17.2126	+	39.9033i	0.573435	+	1.32937i
$902$	−11.9401	+	6.58829i	−0.397563	+	0.219366i
$903$	17.6253	+	11.8645i	0.586535	+	0.394826i
$904$	−9.37957	+	43.3009i	−0.311960	+	1.44017i
$905$	4.91328	+	35.9716i	0.163323	+	1.19574i
$906$	−7.20158	+	4.62692i	−0.239256	+	0.153719i
$907$	3.28174	−	8.49991i	0.108968	−	0.282235i	−0.867664	−	0.497150i	$-0.834380\pi$
$907$	3.28174	−	8.49991i	0.108968	−	0.282235i	0.976633	+	0.214916i	$0.0689476\pi$
$908$	−30.4577	+	7.21861i	−1.01077	+	0.239558i
$909$	−3.69115	+	6.08851i	−0.122428	+	0.201943i
$910$	−21.2902	+	22.5662i	−0.705762	+	0.748064i
$911$	1.48968	+	0.115787i	0.0493553	+	0.00383620i	0.102146	−	0.994769i	$-0.467429\pi$
$911$	1.48968	+	0.115787i	0.0493553	+	0.00383620i	−0.0527910	+	0.998606i	$0.516812\pi$
$912$	−4.92324	+	7.62902i	−0.163025	+	0.252622i
$913$	−64.8554	−	35.7857i	−2.14640	−	1.18433i
$914$	2.51901	−	25.8977i	0.0833216	−	0.856621i
$915$	12.4499	+	37.6985i	0.411580	+	1.24627i
$916$	−24.7681	−	7.94157i	−0.818361	−	0.262397i
$917$	48.4035	+	40.6154i	1.59842	+	1.34124i
$918$	−10.6844	+	63.0550i	−0.352639	+	2.08113i
$919$	10.9040	−	9.14956i	0.359690	−	0.301816i	−0.444977	−	0.895542i	$-0.646788\pi$
$919$	10.9040	−	9.14956i	0.359690	−	0.301816i	0.804667	+	0.593726i	$0.202344\pi$
$920$	−72.9243	+	29.7929i	−2.40424	+	0.982242i
$921$	−6.37668	+	23.7028i	−0.210119	+	0.781032i
$922$	−12.7616	−	49.5436i	−0.420281	−	1.63163i
$923$	5.34566	+	6.12545i	0.175955	+	0.201622i
$924$	74.3544	+	87.0641i	2.44608	+	2.86420i
$925$	2.50627	+	2.45813i	0.0824055	+	0.0808228i
$926$	7.16839	+	4.71473i	0.235568	+	0.154935i
$927$	17.2085	+	8.27105i	0.565200	+	0.271657i
$928$	−1.95632	−	33.5887i	−0.0642193	−	1.10260i
$929$	12.2990	+	35.9452i	0.403518	+	1.17932i	0.941688	+	0.336488i	$0.109239\pi$
$929$	12.2990	+	35.9452i	0.403518	+	1.17932i	−0.538170	+	0.842836i	$0.680884\pi$
$930$	17.1382	+	6.44632i	0.561985	+	0.211383i
$931$	13.3021	+	25.2534i	0.435958	+	0.827647i
$932$	33.3185	−	52.8633i	1.09138	−	1.73160i
$933$	−1.95775	−	1.67877i	−0.0640939	−	0.0549606i
$934$	−0.471072	−	0.0925156i	−0.0154140	−	0.00302720i
$935$	−58.7165	+	38.6184i	−1.92023	+	1.26296i
$936$	11.8247	+	7.48610i	0.386504	+	0.244691i
$937$	50.3589	−	25.2912i	1.64515	−	0.826227i	0.647197	−	0.762323i	$-0.275941\pi$
$937$	50.3589	−	25.2912i	1.64515	−	0.826227i	0.997956	−	0.0639035i	$-0.0203550\pi$
$938$	13.1751	−	51.1490i	0.430183	−	1.67007i
$939$	−0.0672083	−	7.73272i	−0.00219326	−	0.252348i
$940$	44.8025	−	8.79893i	1.46130	−	0.286989i
$941$	−25.9276	+	25.4296i	−0.845217	+	0.828983i	−0.986968	−	0.160920i	$-0.948554\pi$
$941$	−25.9276	+	25.4296i	−0.845217	+	0.828983i	0.141751	+	0.989902i	$0.454727\pi$
$942$	41.8454	+	3.70338i	1.36340	+	0.120663i
$943$	−1.30207	+	9.53284i	−0.0424012	+	0.310432i
$944$	−1.07507	−	0.391293i	−0.0349905	−	0.0127355i
$945$	44.5327	−	27.2831i	1.44865	−	0.887521i
$946$	36.0914	−	13.1362i	1.17343	−	0.427095i
$947$	9.16157	+	42.2945i	0.297711	+	1.37439i	0.843799	+	0.536660i	$0.180314\pi$
$947$	9.16157	+	42.2945i	0.297711	+	1.37439i	−0.546088	+	0.837728i	$0.683883\pi$
$948$	41.4318	−	6.02633i	1.34564	−	0.195726i
$949$	−5.70644	−	4.07872i	−0.185239	−	0.132401i
$950$	0.393867	+	20.3077i	0.0127787	+	0.658868i
$951$	−7.11837	−	56.6288i	−0.230829	−	1.83631i
$952$	39.5278	−	57.6329i	1.28110	−	1.86789i
$953$	33.3265	+	7.89854i	1.07955	+	0.255859i	0.731656	−	0.681674i	$-0.238748\pi$
$953$	33.3265	+	7.89854i	1.07955	+	0.255859i	0.347897	+	0.937533i	$0.386896\pi$
$954$	−56.5043	−	14.6757i	−1.82939	−	0.475145i
$955$	−14.9150	+	49.8197i	−0.482640	+	1.61213i
$956$	8.54074	−	1.33575i	0.276227	−	0.0432012i
$957$	−43.9078	+	57.6794i	−1.41934	+	1.86451i
$958$	−3.22976	−	1.31950i	−0.104349	−	0.0426312i
$959$	−70.6290	+	22.6463i	−2.28073	+	0.731286i
$960$	32.9167	+	45.2170i	1.06238	+	1.45937i
$961$	−0.546188	+	28.1613i	−0.0176190	+	0.908430i
$962$	3.00022	−	4.02999i	0.0967309	−	0.129932i
$963$	21.1419	−	9.06936i	0.681288	−	0.292256i
$964$	23.6265	−	2.76154i	0.760958	−	0.0889432i
$965$	−9.92641	−	4.51211i	−0.319543	−	0.145250i
$966$	126.504	−	8.47182i	4.07021	−	0.272576i
$967$	30.4267	−	37.7232i	0.978456	−	1.21309i	0.00142449	−	0.999999i	$-0.499547\pi$
$967$	30.4267	−	37.7232i	0.978456	−	1.21309i	0.977031	−	0.213096i	$-0.0683547\pi$
$968$	49.9044	−	3.87888i	1.60399	−	0.124672i
$969$	19.0921	+	31.0228i	0.613328	+	0.996596i
$970$	−49.6136	+	1.92523i	−1.59300	+	0.0618155i
$971$	−50.4526			−1.61910			−0.809550	−	0.587051i	$-0.800289\pi$
$971$	−50.4526			−1.61910			−0.809550	+	0.587051i	$0.800289\pi$
$972$	−36.9721	−	40.3623i	−1.18588	−	1.29462i
$973$	15.4670			0.495849
$974$	84.7869	−	3.29012i	2.71675	−	0.105422i
$975$	4.90984	−	0.137923i	0.157241	−	0.00441707i
$976$	−11.1629	+	0.867650i	−0.357316	+	0.0277728i
$977$	−33.5892	+	41.6440i	−1.07461	+	1.33231i	−0.134704	+	0.990886i	$0.543008\pi$
$977$	−33.5892	+	41.6440i	−1.07461	+	1.33231i	−0.939909	+	0.341425i	$0.889090\pi$
$978$	8.02746	+	11.9771i	0.256690	+	0.382986i
$979$	31.0673	+	14.1218i	0.992914	+	0.451335i
$980$	−66.3853	+	7.75933i	−2.12060	+	0.247863i
$981$	−27.6018	+	25.9363i	−0.881259	+	0.828083i
$982$	−52.5071	+	70.5293i	−1.67557	+	2.25068i
$983$	−0.872081	+	44.9642i	−0.0278151	+	1.43414i	0.682825	+	0.730582i	$0.260751\pi$
$983$	−0.872081	+	44.9642i	−0.0278151	+	1.43414i	−0.710641	+	0.703555i	$0.751595\pi$
$984$	−7.08454	+	0.751308i	−0.225847	+	0.0239508i
$985$	−18.6321	+	5.97413i	−0.593667	+	0.190352i
$986$	95.1655	+	38.8794i	3.03069	+	1.23817i
$987$	−31.3747	−	4.00795i	−0.998666	−	0.127574i
$988$	18.2979	−	2.86174i	0.582133	−	0.0910440i
$989$	7.77166	−	25.9592i	0.247124	−	0.825453i
$990$	7.50516	−	94.1101i	0.238530	−	2.99102i
$991$	−14.1620	−	3.35645i	−0.449870	−	0.106621i	−0.000565375	−	1.00000i	$-0.500180\pi$
$991$	−14.1620	−	3.35645i	−0.449870	−	0.106621i	−0.449304	+	0.893379i	$0.648328\pi$
$992$	3.83514	−	5.59178i	0.121766	−	0.177539i
$993$	21.9800	+	9.25553i	0.697516	+	0.293715i
$994$	1.05755	+	54.5269i	0.0335434	+	1.72949i
$995$	41.7791	+	29.8619i	1.32449	+	0.946686i
$996$	−55.6920	−	70.5797i	−1.76467	−	2.23640i
$997$	5.84240	+	26.9715i	0.185031	+	0.854197i	0.971588	+	0.236679i	$0.0760591\pi$
$997$	5.84240	+	26.9715i	0.185031	+	0.854197i	−0.786557	+	0.617518i	$0.788138\pi$
$998$	−81.7261	+	29.7459i	−2.58700	+	0.941589i
$999$	−6.65004	+	5.22566i	−0.210398	+	0.165333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.61.3	yes	1404
3.2	odd	2		729.2.i.a.262.24		1404
243.4	even	81	inner	243.2.i.a.4.3	✓	1404
243.239	odd	162		729.2.i.a.64.24		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.4.3	✓	1404	243.4	even	81	inner
243.2.i.a.61.3	yes	1404	1.1	even	1	trivial
729.2.i.a.64.24		1404	243.239	odd	162
729.2.i.a.262.24		1404	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.34586 + 0.0910299i) q^{2} +(-0.823564 + 1.52373i) q^{3} +(3.50077 - 0.272102i) q^{4} +(-1.67953 + 2.08230i) q^{5} +(1.79326 - 3.64941i) q^{6} +(-3.42025 - 1.55470i) q^{7} +(-3.52404 + 0.411902i) q^{8} +(-1.64349 - 2.50977i) q^{9} +(3.75040 - 5.03765i) q^{10} +(-0.0971655 + 5.00983i) q^{11} +(-2.46850 + 5.55831i) q^{12} +(1.25205 - 0.401453i) q^{13} +(8.16495 + 3.33575i) q^{14} +(-1.78965 - 4.27405i) q^{15} +(1.29109 - 0.201922i) q^{16} +(1.50363 - 5.02247i) q^{17} +(4.08385 + 5.73796i) q^{18} +(3.90336 + 0.925114i) q^{19} +(-5.31307 + 7.74665i) q^{20} +(5.18573 - 3.93114i) q^{21} +(-0.228108 - 11.7612i) q^{22} +(-6.75195 - 4.82601i) q^{23} +(2.27465 - 5.70891i) q^{24} +(-0.456601 - 2.10790i) q^{25} +(-2.90058 + 1.05572i) q^{26} +(5.17772 - 0.437265i) q^{27} +(-12.3966 - 4.51198i) q^{28} +(1.13035 - 8.27560i) q^{29} +(4.58732 + 9.86341i) q^{30} +(1.20173 - 1.17865i) q^{31} +(3.95273 - 0.776291i) q^{32} +(-7.55358 - 4.27397i) q^{33} +(-3.07010 + 11.9189i) q^{34} +(8.98177 - 4.51081i) q^{35} +(-6.43638 - 8.33894i) q^{36} +(-1.35989 + 0.894415i) q^{37} +(-9.24094 - 1.81486i) q^{38} +(-0.419437 + 2.23840i) q^{39} +(5.06105 - 8.02990i) q^{40} +(-0.540280 - 1.02570i) q^{41} +(-11.8071 + 9.69394i) q^{42} +(1.05700 + 3.08919i) q^{43} +(1.02303 + 17.5647i) q^{44} +(7.98638 + 0.793026i) q^{45} +(16.2784 + 10.7065i) q^{46} +(-3.47013 - 3.40347i) q^{47} +(-0.755618 + 2.13356i) q^{48} +(4.67840 + 5.36085i) q^{49} +(1.26300 + 4.90327i) q^{50} +(6.41453 + 6.42744i) q^{51} +(4.27390 - 1.74608i) q^{52} +(-6.34982 + 5.32813i) q^{53} +(-12.1064 + 1.49709i) q^{54} +(-10.2687 - 8.61650i) q^{55} +(12.6935 + 4.07001i) q^{56} +(-4.62429 + 5.18577i) q^{57} +(-1.89830 + 19.5163i) q^{58} +(-0.766536 - 0.422957i) q^{59} +(-7.42812 - 14.4755i) q^{60} +(-8.54229 - 0.663959i) q^{61} +(-2.71180 + 2.87434i) q^{62} +(1.71920 + 11.1392i) q^{63} +(-11.7450 + 2.78361i) q^{64} +(-1.26691 + 3.28139i) q^{65} +(18.1087 + 9.33851i) q^{66} +(-0.810426 - 5.93337i) q^{67} +(3.89724 - 17.9917i) q^{68} +(12.9142 - 6.31361i) q^{69} +(-20.6593 + 11.3993i) q^{70} +(2.44908 + 5.67761i) q^{71} +(6.82549 + 8.16759i) q^{72} +(-3.18566 - 4.27908i) q^{73} +(3.10869 - 2.22196i) q^{74} +(3.58791 + 1.04026i) q^{75} +(13.9165 + 2.17650i) q^{76} +(8.12108 - 16.9838i) q^{77} +(0.780177 - 5.28915i) q^{78} +(-3.67063 - 5.82385i) q^{79} +(-1.74796 + 3.02756i) q^{80} +(-3.59791 + 8.24955i) q^{81} +(1.36079 + 2.35695i) q^{82} +(-6.88942 + 13.0792i) q^{83} +(17.0844 - 15.1731i) q^{84} +(7.93287 + 11.5664i) q^{85} +(-2.76077 - 7.15058i) q^{86} +(11.6788 + 8.53783i) q^{87} +(-1.72114 - 17.6949i) q^{88} +(2.69753 - 6.25358i) q^{89} +(-18.8071 - 1.13333i) q^{90} +(-4.90646 - 0.573482i) q^{91} +(-24.9502 - 15.0575i) q^{92} +(0.806238 + 2.80180i) q^{93} +(8.45024 + 7.66818i) q^{94} +(-8.48219 + 6.57419i) q^{95} +(-2.07247 + 6.66220i) q^{96} +(-4.96329 - 6.15351i) q^{97} +(-11.4629 - 12.1499i) q^{98} +(12.7332 - 7.98971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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