LMFDB - Embedded newform 414.2.p.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	414.5
Dual form			414.2.p.a.83.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.971812 - 0.235759i) q^{2} +(-0.209960 + 1.71928i) q^{3} +(0.888835 - 0.458227i) q^{4} +(2.11401 + 1.66247i) q^{5} +(0.201293 + 1.72031i) q^{6} +(1.78139 + 1.26852i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.91183 - 0.721960i) q^{9} +O(q^{10})$	\(q+(0.971812 - 0.235759i) q^{2} +(-0.209960 + 1.71928i) q^{3} +(0.888835 - 0.458227i) q^{4} +(2.11401 + 1.66247i) q^{5} +(0.201293 + 1.72031i) q^{6} +(1.78139 + 1.26852i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.91183 - 0.721960i) q^{9} +(2.44636 + 1.11721i) q^{10} +(-0.843505 - 0.804280i) q^{11} +(0.601199 + 1.62436i) q^{12} +(-1.95810 - 2.74977i) q^{13} +(2.03024 + 0.812785i) q^{14} +(-3.30211 + 3.28551i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-0.375565 + 0.241361i) q^{17} +(-2.99996 - 0.0151179i) q^{18} +(-0.413310 + 0.643123i) q^{19} +(2.64079 + 0.508971i) q^{20} +(-2.55496 + 2.79636i) q^{21} +(-1.00934 - 0.582745i) q^{22} +(-0.549609 + 4.76423i) q^{23} +(0.967210 + 1.43684i) q^{24} +(0.526411 + 2.16990i) q^{25} +(-2.55119 - 2.21062i) q^{26} +(1.85262 - 4.85467i) q^{27} +(2.16463 + 0.311227i) q^{28} +(1.81860 - 3.52760i) q^{29} +(-2.43444 + 3.97140i) q^{30} +(2.95568 - 0.569661i) q^{31} +(0.371662 - 0.928368i) q^{32} +(1.55988 - 1.28135i) q^{33} +(-0.308076 + 0.323101i) q^{34} +(1.65698 + 5.64317i) q^{35} +(-2.91896 + 0.692576i) q^{36} +(-0.360632 + 0.0518511i) q^{37} +(-0.250038 + 0.722436i) q^{38} +(5.13874 - 2.78918i) q^{39} +(2.68635 - 0.127966i) q^{40} +(0.889830 - 1.13151i) q^{41} +(-1.82367 + 3.31989i) q^{42} +(0.649086 - 3.36778i) q^{43} +(-1.11828 - 0.328357i) q^{44} +(-4.95540 - 6.36707i) q^{45} +(0.589094 + 4.75951i) q^{46} +(-1.00347 + 0.579352i) q^{47} +(1.27869 + 1.16831i) q^{48} +(-0.725276 - 2.09555i) q^{49} +(1.02314 + 1.98462i) q^{50} +(-0.336113 - 0.696378i) q^{51} +(-3.00044 - 1.54684i) q^{52} +(3.31619 + 7.26144i) q^{53} +(0.655864 - 5.15459i) q^{54} +(-0.446080 - 3.10256i) q^{55} +(2.17699 - 0.207877i) q^{56} +(-1.01893 - 0.845626i) q^{57} +(0.935677 - 3.85691i) q^{58} +(7.00092 - 4.98533i) q^{59} +(-1.42952 + 4.43339i) q^{60} +(-12.0509 - 4.17085i) q^{61} +(2.73806 - 1.25043i) q^{62} +(-4.27129 - 4.97981i) q^{63} +(0.142315 - 0.989821i) q^{64} +(0.431977 - 9.06831i) q^{65} +(1.21382 - 1.61299i) q^{66} +(3.10010 + 3.25130i) q^{67} +(-0.223218 + 0.386624i) q^{68} +(-8.07565 - 1.94523i) q^{69} +(2.94070 + 5.09345i) q^{70} +(-4.13617 + 14.0865i) q^{71} +(-2.67340 + 1.36122i) q^{72} +(-14.0432 - 9.02505i) q^{73} +(-0.338242 + 0.135412i) q^{74} +(-3.84118 + 0.449455i) q^{75} +(-0.0726687 + 0.761021i) q^{76} +(-0.482364 - 2.50274i) q^{77} +(4.33631 - 3.92206i) q^{78} +(-1.62628 - 17.0312i) q^{79} +(2.58045 - 0.757690i) q^{80} +(7.95755 + 4.20445i) q^{81} +(0.597983 - 1.30940i) q^{82} +(3.99567 - 3.14223i) q^{83} +(-0.989572 + 3.65626i) q^{84} +(-1.19520 - 0.114128i) q^{85} +(-0.163195 - 3.42587i) q^{86} +(5.68309 + 3.86734i) q^{87} +(-1.16417 - 0.0554563i) q^{88} +(5.06440 - 5.84463i) q^{89} +(-6.31680 - 5.01931i) q^{90} -7.38229i q^{91} +(1.69459 + 4.48647i) q^{92} +(0.358830 + 5.20125i) q^{93} +(-0.838594 + 0.799598i) q^{94} +(-1.94292 + 0.672450i) q^{95} +(1.51809 + 0.833911i) q^{96} +(-2.45819 - 6.14025i) q^{97} +(-1.19888 - 1.86549i) q^{98} +(1.87549 + 2.95091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{22}\right)$

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 $

$2$	0.971812	−	0.235759i	0.687175	−	0.166707i
$2$	0.971812	−	0.235759i	0.687175	−	0.166707i
$3$	−0.209960	+	1.71928i	−0.121221	+	0.992626i
$3$	−0.209960	+	1.71928i	−0.121221	+	0.992626i
$4$	0.888835	−	0.458227i	0.444418	−	0.229113i
$5$	2.11401	+	1.66247i	0.945412	+	0.743480i	0.966599	−	0.256295i	$-0.0825019\pi$
$5$	2.11401	+	1.66247i	0.945412	+	0.743480i	−0.0211864	+	0.999776i	$0.506744\pi$
$6$	0.201293	+	1.72031i	0.0821777	+	0.702315i
$7$	1.78139	+	1.26852i	0.673302	+	0.479456i	0.864852	−	0.502027i	$-0.167412\pi$
$7$	1.78139	+	1.26852i	0.673302	+	0.479456i	−0.191550	+	0.981483i	$0.561352\pi$
$8$	0.755750	−	0.654861i	0.267198	−	0.231528i
$9$	−2.91183	−	0.721960i	−0.970611	−	0.240653i
$10$	2.44636	+	1.11721i	0.773606	+	0.353294i
$11$	−0.843505	−	0.804280i	−0.254326	−	0.242500i	0.552180	−	0.833725i	$-0.313796\pi$
$11$	−0.843505	−	0.804280i	−0.254326	−	0.242500i	−0.806507	+	0.591225i	$0.798644\pi$
$12$	0.601199	+	1.62436i	0.173551	+	0.468914i
$13$	−1.95810	−	2.74977i	−0.543079	−	0.762648i	0.448270	−	0.893898i	$-0.352040\pi$
$13$	−1.95810	−	2.74977i	−0.543079	−	0.762648i	−0.991349	+	0.131250i	$0.958101\pi$
$14$	2.03024	+	0.812785i	0.542604	+	0.217226i
$15$	−3.30211	+	3.28551i	−0.852601	+	0.848315i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	−0.375565	+	0.241361i	−0.0910880	+	0.0585387i	−0.585392	−	0.810750i	$-0.699059\pi$
$17$	−0.375565	+	0.241361i	−0.0910880	+	0.0585387i	0.494304	+	0.869289i	$0.335423\pi$
$18$	−2.99996	−	0.0151179i	−0.707098	−	0.00356332i
$19$	−0.413310	+	0.643123i	−0.0948199	+	0.147543i	−0.885423	−	0.464787i	$-0.846131\pi$
$19$	−0.413310	+	0.643123i	−0.0948199	+	0.147543i	0.790603	+	0.612329i	$0.209767\pi$
$20$	2.64079	+	0.508971i	0.590499	+	0.113809i
$21$	−2.55496	+	2.79636i	−0.557538	+	0.610216i
$22$	−1.00934	−	0.582745i	−0.215193	−	0.124242i
$23$	−0.549609	+	4.76423i	−0.114601	+	0.993412i
$23$	−0.549609	+	4.76423i	−0.114601	+	0.993412i
$24$	0.967210	+	1.43684i	0.197431	+	0.293293i
$25$	0.526411	+	2.16990i	0.105282	+	0.433979i
$26$	−2.55119	−	2.21062i	−0.500329	−	0.433537i
$27$	1.85262	−	4.85467i	0.356537	−	0.934281i
$28$	2.16463	+	0.311227i	0.409077	+	0.0588164i
$29$	1.81860	−	3.52760i	0.337706	−	0.655059i	−0.657435	−	0.753511i	$-0.728359\pi$
$29$	1.81860	−	3.52760i	0.337706	−	0.655059i	0.995142	+	0.0984520i	$0.0313891\pi$
$30$	−2.43444	+	3.97140i	−0.444466	+	0.725075i
$31$	2.95568	−	0.569661i	0.530856	−	0.102314i	0.0832222	−	0.996531i	$-0.473479\pi$
$31$	2.95568	−	0.569661i	0.530856	−	0.102314i	0.447634	+	0.894217i	$0.352267\pi$
$32$	0.371662	−	0.928368i	0.0657013	−	0.164114i
$33$	1.55988	−	1.28135i	0.271541	−	0.223055i
$34$	−0.308076	+	0.323101i	−0.0528346	+	0.0554113i
$35$	1.65698	+	5.64317i	0.280081	+	0.953870i
$36$	−2.91896	+	0.692576i	−0.486494	+	0.115429i
$37$	−0.360632	+	0.0518511i	−0.0592876	+	0.00852426i	−0.171895	−	0.985115i	$-0.554989\pi$
$37$	−0.360632	+	0.0518511i	−0.0592876	+	0.00852426i	0.112607	+	0.993640i	$0.464080\pi$
$38$	−0.250038	+	0.722436i	−0.0405615	+	0.117195i
$39$	5.13874	−	2.78918i	0.822856	−	0.446626i
$40$	2.68635	−	0.127966i	0.424749	−	0.0202333i
$41$	0.889830	−	1.13151i	0.138968	−	0.176712i	−0.711587	−	0.702598i	$-0.752023\pi$
$41$	0.889830	−	1.13151i	0.138968	−	0.176712i	0.850555	+	0.525885i	$0.176266\pi$
$42$	−1.82367	+	3.31989i	−0.281399	+	0.512271i
$43$	0.649086	−	3.36778i	0.0989847	−	0.513581i	−0.898264	−	0.439456i	$-0.855171\pi$
$43$	0.649086	−	3.36778i	0.0989847	−	0.513581i	0.997249	−	0.0741256i	$-0.0236166\pi$
$44$	−1.11828	−	0.328357i	−0.168587	−	0.0495016i
$45$	−4.95540	−	6.36707i	−0.738707	−	0.949147i
$46$	0.589094	+	4.75951i	0.0868572	+	0.701752i
$47$	−1.00347	+	0.579352i	−0.146371	+	0.0845072i	−0.571397	−	0.820674i	$-0.693598\pi$
$47$	−1.00347	+	0.579352i	−0.146371	+	0.0845072i	0.425026	+	0.905181i	$0.360265\pi$
$48$	1.27869	+	1.16831i	0.184564	+	0.168631i
$49$	−0.725276	−	2.09555i	−0.103611	−	0.299364i
$50$	1.02314	+	1.98462i	0.144695	+	0.280668i
$51$	−0.336113	−	0.696378i	−0.0470653	−	0.0975124i
$52$	−3.00044	−	1.54684i	−0.416087	−	0.214508i
$53$	3.31619	+	7.26144i	0.455514	+	0.997436i	0.988487	+	0.151304i	$0.0483472\pi$
$53$	3.31619	+	7.26144i	0.455514	+	0.997436i	−0.532974	+	0.846132i	$0.678926\pi$
$54$	0.655864	−	5.15459i	0.0892518	−	0.701451i
$55$	−0.446080	−	3.10256i	−0.0601495	−	0.418349i
$56$	2.17699	−	0.207877i	0.290912	−	0.0277788i
$57$	−1.01893	−	0.845626i	−0.134960	−	0.112006i
$58$	0.935677	−	3.85691i	0.122860	−	0.506438i
$59$	7.00092	−	4.98533i	0.911442	−	0.649035i	−0.0250639	−	0.999686i	$-0.507979\pi$
$59$	7.00092	−	4.98533i	0.911442	−	0.649035i	0.936506	+	0.350651i	$0.114040\pi$
$60$	−1.42952	+	4.43339i	−0.184551	+	0.572349i
$61$	−12.0509	−	4.17085i	−1.54296	−	0.534023i	−0.582592	−	0.812765i	$-0.697961\pi$
$61$	−12.0509	−	4.17085i	−1.54296	−	0.534023i	−0.960366	+	0.278742i	$0.910083\pi$
$62$	2.73806	−	1.25043i	0.347734	−	0.158805i
$63$	−4.27129	−	4.97981i	−0.538131	−	0.627397i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	0.431977	−	9.06831i	0.0535801	−	1.12479i
$66$	1.21382	−	1.61299i	0.149411	−	0.198545i
$67$	3.10010	+	3.25130i	0.378738	+	0.397209i	0.885320	−	0.464983i	$-0.153940\pi$
$67$	3.10010	+	3.25130i	0.378738	+	0.397209i	−0.506582	+	0.862192i	$0.669091\pi$
$68$	−0.223218	+	0.386624i	−0.0270691	+	0.0468851i
$69$	−8.07565	−	1.94523i	−0.972194	−	0.234178i
$70$	2.94070	+	5.09345i	0.351481	+	0.608784i
$71$	−4.13617	+	14.0865i	−0.490874	+	1.67176i	0.225657	+	0.974207i	$0.427547\pi$
$71$	−4.13617	+	14.0865i	−0.490874	+	1.67176i	−0.716531	+	0.697555i	$0.754271\pi$
$72$	−2.67340	+	1.36122i	−0.315063	+	0.160422i
$73$	−14.0432	−	9.02505i	−1.64364	−	1.05630i	−0.937357	−	0.348369i	$-0.886736\pi$
$73$	−14.0432	−	9.02505i	−1.64364	−	1.05630i	−0.706280	−	0.707932i	$-0.749628\pi$
$74$	−0.338242	+	0.135412i	−0.0393199	+	0.0157413i
$75$	−3.84118	+	0.449455i	−0.443541	+	0.0518986i
$76$	−0.0726687	+	0.761021i	−0.00833567	+	0.0872950i
$77$	−0.482364	−	2.50274i	−0.0549704	−	0.285214i
$78$	4.33631	−	3.92206i	0.490990	−	0.444086i
$79$	−1.62628	−	17.0312i	−0.182971	−	1.91616i	−0.361764	−	0.932270i	$-0.617825\pi$
$79$	−1.62628	−	17.0312i	−0.182971	−	1.91616i	0.178793	−	0.983887i	$-0.442781\pi$
$80$	2.58045	−	0.757690i	0.288504	−	0.0847123i
$81$	7.95755	+	4.20445i	0.884172	+	0.467161i
$82$	0.597983	−	1.30940i	0.0660362	−	0.144599i
$83$	3.99567	−	3.14223i	0.438582	−	0.344904i	−0.374326	−	0.927297i	$-0.622126\pi$
$83$	3.99567	−	3.14223i	0.438582	−	0.344904i	0.812907	+	0.582393i	$0.197883\pi$
$84$	−0.989572	+	3.65626i	−0.107971	+	0.398930i
$85$	−1.19520	−	0.114128i	−0.129638	−	0.0123789i
$86$	−0.163195	−	3.42587i	−0.0175977	−	0.369422i
$87$	5.68309	+	3.86734i	0.609291	+	0.414623i
$88$	−1.16417	−	0.0554563i	−0.124101	−	0.00591166i
$89$	5.06440	−	5.84463i	0.536825	−	0.619529i	−0.420937	−	0.907090i	$-0.638299\pi$
$89$	5.06440	−	5.84463i	0.536825	−	0.619529i	0.957763	+	0.287560i	$0.0928442\pi$
$90$	−6.31680	−	5.01931i	−0.665850	−	0.529082i
$91$		−	7.38229i		−	0.773875i
$92$	1.69459	+	4.48647i	0.176673	+	0.467746i
$93$	0.358830	+	5.20125i	0.0372090	+	0.539344i
$94$	−0.838594	+	0.799598i	−0.0864944	+	0.0824722i
$95$	−1.94292	+	0.672450i	−0.199339	+	0.0689919i
$96$	1.51809	+	0.833911i	0.154939	+	0.0851107i
$97$	−2.45819	−	6.14025i	−0.249591	−	0.623448i	0.749673	−	0.661808i	$-0.230211\pi$
$97$	−2.45819	−	6.14025i	−0.249591	−	0.623448i	−0.999264	+	0.0383603i	$0.987787\pi$
$98$	−1.19888	−	1.86549i	−0.121105	−	0.188443i
$99$	1.87549	+	2.95091i	0.188494	+	0.296577i
$100$	1.46220	+	1.68747i	0.146220	+	0.168747i
$101$	−4.49833	−	5.72009i	−0.447601	−	0.569171i	0.508928	−	0.860809i	$-0.330042\pi$
$101$	−4.49833	−	5.72009i	−0.447601	−	0.569171i	−0.956529	+	0.291638i	$0.905800\pi$
$102$	−0.490816	−	0.597506i	−0.0485980	−	0.0591619i
$103$	12.3069	+	2.98562i	1.21263	+	0.294182i	0.790563	−	0.612380i	$-0.209788\pi$
$103$	12.3069	+	2.98562i	1.21263	+	0.294182i	0.422072	+	0.906562i	$0.361303\pi$
$104$	−3.28055	−	0.795852i	−0.321684	−	0.0780397i
$105$	−10.0501	+	1.66398i	−0.980787	+	0.162387i
$106$	4.93466	+	6.27493i	0.479297	+	0.609475i
$107$	8.26533	+	9.53870i	0.799040	+	0.922141i	0.998328	−	0.0578001i	$-0.0184086\pi$
$107$	8.26533	+	9.53870i	0.799040	+	0.922141i	−0.199289	+	0.979941i	$0.563863\pi$
$108$	−0.577865	−	5.16392i	−0.0556051	−	0.496898i
$109$	2.95517	+	4.59834i	0.283054	+	0.440441i	0.953445	−	0.301568i	$-0.0975099\pi$
$109$	2.95517	+	4.59834i	0.283054	+	0.440441i	−0.670391	+	0.742008i	$0.733874\pi$
$110$	−1.16496	−	2.90993i	−0.111075	−	0.277451i
$111$	−0.0134280	−	0.630914i	−0.00127453	−	0.0598837i
$112$	2.06661	−	0.715262i	0.195277	−	0.0675859i
$113$	−7.68816	+	7.33064i	−0.723241	+	0.689609i	−0.959382	−	0.282110i	$-0.908966\pi$
$113$	−7.68816	+	7.33064i	−0.723241	+	0.689609i	0.236141	+	0.971719i	$0.424117\pi$
$114$	−1.18957	−	0.581567i	−0.111414	−	0.0544687i
$115$	−9.08229	+	9.15791i	−0.846928	+	0.853980i
$116$		−	3.96879i		−	0.368493i
$117$	3.71644	+	9.42053i	0.343585	+	0.870928i
$118$	5.62824	−	6.49534i	0.518121	−	0.597944i
$119$	−0.975200	−	0.0464545i	−0.0893964	−	0.00425848i
$120$	−0.344016	+	4.64545i	−0.0314042	+	0.424069i
$121$	−0.458767	−	9.63071i	−0.0417061	−	0.875519i
$122$	−12.6945	−	1.21218i	−1.14931	−	0.109745i
$123$	1.75855	+	1.76744i	0.158563	+	0.159364i
$124$	2.36608	−	1.86071i	0.212480	−	0.167096i
$125$	3.09151	−	6.76947i	0.276513	−	0.605480i
$126$	−5.32492	−	3.83245i	−0.474382	−	0.341421i
$127$	1.20105	−	0.352659i	0.106576	−	0.0312934i	−0.228010	−	0.973659i	$-0.573222\pi$
$127$	1.20105	−	0.352659i	0.106576	−	0.0312934i	0.334586	+	0.942365i	$0.391404\pi$
$128$	−0.0950560	−	0.995472i	−0.00840185	−	0.0879881i
$129$	5.65387	+	1.82306i	0.497795	+	0.160511i
$130$	−1.71814	−	8.91453i	−0.150690	−	0.781856i
$131$	−1.56576	+	16.3974i	−0.136801	+	1.43265i	0.622863	+	0.782331i	$0.285969\pi$
$131$	−1.56576	+	16.3974i	−0.136801	+	1.43265i	−0.759665	+	0.650315i	$0.774637\pi$
$132$	0.799330	−	1.85369i	0.0695728	−	0.161343i
$133$	−1.55208	+	0.621360i	−0.134583	+	0.0538787i
$134$	3.77924	+	2.42877i	0.326477	+	0.209814i
$135$	11.9872	−	7.18287i	1.03169	−	0.618203i
$136$	−0.125775	+	0.428352i	−0.0107852	+	0.0367309i
$137$	−0.741116	−	1.28365i	−0.0633178	−	0.109670i	0.832629	−	0.553832i	$-0.186835\pi$
$137$	−0.741116	−	1.28365i	−0.0633178	−	0.109670i	−0.895947	+	0.444162i	$0.853502\pi$
$138$	−8.30661	+	0.0135091i	−0.707106	+	0.00114997i
$139$	−5.80960	+	10.0625i	−0.492764	+	0.853492i	−0.999965	−	0.00833573i	$-0.997347\pi$
$139$	−5.80960	+	10.0625i	−0.492764	+	0.853492i	0.507202	+	0.861827i	$0.330680\pi$
$140$	4.05864	+	4.25658i	0.343017	+	0.359746i
$141$	−0.785380	−	1.84688i	−0.0661409	−	0.155535i
$142$	−0.698560	+	14.6646i	−0.0586219	+	1.23062i
$143$	−0.559916	+	3.89430i	−0.0468226	+	0.325658i
$144$	−2.27712	+	1.95313i	−0.189760	+	0.162761i
$145$	9.70908	−	4.43399i	0.806295	−	0.368223i
$146$	−15.7751	−	5.45982i	−1.30556	−	0.451858i
$147$	3.75511	−	0.806970i	0.309716	−	0.0665578i
$148$	−0.296783	+	0.211338i	−0.0243954	+	0.0173719i
$149$	−1.99911	+	8.24045i	−0.163774	+	0.675084i	0.829422	+	0.558623i	$0.188670\pi$
$149$	−1.99911	+	8.24045i	−0.163774	+	0.675084i	−0.993195	+	0.116461i	$0.962845\pi$
$150$	−3.62694	+	1.34238i	−0.296138	+	0.109605i
$151$	−18.2462	+	1.74230i	−1.48486	+	0.141787i	−0.805751	−	0.592254i	$-0.798238\pi$
$151$	−18.2462	+	1.74230i	−1.48486	+	0.141787i	−0.679105	+	0.734041i	$0.737632\pi$
$152$	0.108797	+	0.756701i	0.00882462	+	0.0613765i
$153$	1.26784	−	0.431661i	0.102499	−	0.0348977i
$154$	−1.05881	−	2.31847i	−0.0853213	−	0.186828i
$155$	7.19538	+	3.70947i	0.577946	+	0.297952i
$156$	3.28942	−	4.83382i	0.263364	−	0.387016i
$157$	4.09632	+	7.94576i	0.326922	+	0.634141i	0.993819	−	0.111009i	$-0.0354082\pi$
$157$	4.09632	+	7.94576i	0.326922	+	0.634141i	−0.666897	+	0.745150i	$0.732378\pi$
$158$	−5.59569	−	16.1677i	−0.445169	−	1.28623i
$159$	−13.1807	+	4.17684i	−1.04530	+	0.331245i
$160$	2.32908	−	1.34470i	0.184130	−	0.106308i
$161$	−7.02260	+	7.78976i	−0.553458	+	0.613919i
$162$	8.72448	+	2.20987i	0.685459	+	0.173624i
$163$	12.0106	+	3.52662i	0.940741	+	0.276226i	0.715927	−	0.698175i	$-0.246004\pi$
$163$	12.0106	+	3.52662i	0.940741	+	0.276226i	0.224814	+	0.974402i	$0.427823\pi$
$164$	0.272424	−	1.41347i	0.0212727	−	0.110373i
$165$	5.42782	−	0.115523i	0.422555	−	0.00899345i
$166$	3.14223	−	3.99567i	0.243884	−	0.310124i
$167$	−19.0648	+	0.908168i	−1.47528	+	0.0702762i	−0.769723	−	0.638378i	$-0.779606\pi$
$167$	−19.0648	+	0.908168i	−1.47528	+	0.0702762i	−0.705556	+	0.708654i	$0.749303\pi$
$168$	−0.0996820	+	3.78649i	−0.00769064	+	0.292134i
$169$	0.524823	−	1.51638i	0.0403710	−	0.116644i
$170$	−1.18842	+	0.170869i	−0.0911476	+	0.0131051i
$171$	1.66780	−	1.57427i	0.127540	−	0.120388i
$172$	−0.966275	−	3.29083i	−0.0736778	−	0.250923i
$173$	−12.5332	+	13.1444i	−0.952878	+	0.999350i	0.0471220	+	0.998889i	$0.484995\pi$
$173$	−12.5332	+	13.1444i	−0.952878	+	0.999350i	−1.00000		0.000460398i	$0.999853\pi$
$174$	6.43465	+	2.41849i	0.487810	+	0.183345i
$175$	−1.81482	+	4.53319i	−0.137187	+	0.342677i
$176$	−1.14443	+	0.220570i	−0.0862645	+	0.0166261i
$177$	7.10126	+	13.0833i	0.533763	+	0.983397i
$178$	3.54372	−	6.87386i	0.265613	−	0.515217i
$179$	18.5771	+	2.67099i	1.38852	+	0.199639i	0.795697	−	0.605694i	$-0.207105\pi$
$179$	18.5771	+	2.67099i	1.38852	+	0.199639i	0.592822	+	0.805333i	$0.298014\pi$
$180$	−7.32209	−	3.38858i	−0.545756	−	0.252570i
$181$	−5.54379	−	4.80372i	−0.412067	−	0.357058i	0.424022	−	0.905652i	$-0.360618\pi$
$181$	−5.54379	−	4.80372i	−0.412067	−	0.357058i	−0.836089	+	0.548594i	$0.815163\pi$
$182$	−1.74044	−	7.17420i	−0.129010	−	0.531787i
$183$	9.70106	−	19.8431i	0.717123	−	1.46685i
$184$	2.70454	+	3.96049i	0.199382	+	0.291971i
$185$	−0.848580	−	0.489928i	−0.0623888	−	0.0360202i
$186$	1.57496	+	4.97003i	0.115481	+	0.364421i
$187$	0.510913	+	0.0984705i	0.0373617	+	0.00720088i
$188$	−0.626443	+	0.974765i	−0.0456881	+	0.0710920i
$189$	9.45848	−	6.29797i	0.688003	−	0.458110i
$190$	−1.72961	+	1.11155i	−0.125479	+	0.0806406i
$191$	10.8114	−	15.1825i	0.782286	−	1.09857i	−0.210373	−	0.977621i	$-0.567468\pi$
$191$	10.8114	−	15.1825i	0.782286	−	1.09857i	0.992659	−	0.120946i	$-0.0385928\pi$
$192$	1.67190	+	0.452502i	0.120659	+	0.0326565i
$193$	5.08543	+	2.03590i	0.366057	+	0.146547i	0.547396	−	0.836873i	$-0.315619\pi$
$193$	5.08543	+	2.03590i	0.366057	+	0.146547i	−0.181339	+	0.983421i	$0.558043\pi$
$194$	−3.83651	−	5.38763i	−0.275446	−	0.386809i
$195$	15.5002	+	2.64667i	1.11000	+	0.189532i
$196$	−1.60489	−	1.53026i	−0.114635	−	0.109304i
$197$	16.1086	+	7.35653i	1.14769	+	0.524131i	0.896165	−	0.443721i	$-0.146342\pi$
$197$	16.1086	+	7.35653i	1.14769	+	0.524131i	0.251522	+	0.967852i	$0.419069\pi$
$198$	2.51832	+	2.42556i	0.178969	+	0.172377i
$199$	−3.99049	+	3.45778i	−0.282878	+	0.245116i	−0.784729	−	0.619839i	$-0.787198\pi$
$199$	−3.99049	+	3.45778i	−0.282878	+	0.245116i	0.501851	+	0.864954i	$0.332653\pi$
$200$	1.81881	+	1.29517i	0.128610	+	0.0915825i
$201$	−6.24078	+	4.64730i	−0.440191	+	0.327795i
$202$	−5.72009	−	4.49833i	−0.402464	−	0.316502i
$203$	7.71447	−	3.97709i	0.541450	−	0.279137i
$204$	−0.617848	−	0.464949i	−0.0432580	−	0.0325529i
$205$	3.76221	−	0.912702i	0.262764	−	0.0637459i
$206$	12.6639			0.882334
$207$	5.03995	−	13.4759i	0.350301	−	0.936637i
$208$	−3.37570			−0.234063
$209$	0.865881	−	0.210060i	0.0598942	−	0.0145302i
$210$	−9.37449	+	3.98647i	−0.646901	+	0.275092i
$211$	−23.8226	+	12.2814i	−1.64002	+	0.845488i	−0.643206	+	0.765693i	$0.722396\pi$
$211$	−23.8226	+	12.2814i	−1.64002	+	0.845488i	−0.996811	+	0.0797946i	$0.974574\pi$
$212$	6.27493	+	4.93466i	0.430964	+	0.338914i
$213$	−23.3502	−	10.0688i	−1.59993	−	0.689906i
$214$	10.2812	+	7.32119i	0.702807	+	0.500466i
$215$	6.97101	−	6.04042i	0.475419	−	0.411953i
$216$	−1.77902	−	4.88212i	−0.121047	−	0.332186i
$217$	5.98785	+	2.73456i	0.406481	+	0.185634i
$218$	3.95597	+	3.77201i	0.267932	+	0.255473i
$219$	18.4651	−	22.2493i	1.24775	−	1.50347i
$220$	−1.81817	−	2.55326i	−0.122581	−	0.172141i
$221$	1.39908	+	0.560108i	0.0941124	+	0.0376769i
$222$	−0.161793	−	0.609963i	−0.0108588	−	0.0409381i
$223$	1.49790	−	2.10351i	0.100307	−	0.140861i	−0.761372	−	0.648315i	$-0.775474\pi$
$223$	1.49790	−	2.10351i	0.100307	−	0.140861i	0.861679	+	0.507454i	$0.169413\pi$
$224$	1.83973	−	1.18232i	0.122922	−	0.0789972i
$225$	0.0337558	−	6.69842i	0.00225039	−	0.446562i
$226$	−5.74318	+	8.93656i	−0.382030	+	0.594451i
$227$	−7.96702	−	1.53552i	−0.528790	−	0.101916i	−0.0821332	−	0.996621i	$-0.526173\pi$
$227$	−7.96702	−	1.53552i	−0.528790	−	0.101916i	−0.446657	+	0.894705i	$0.647385\pi$
$228$	−1.29315	−	0.284722i	−0.0856408	−	0.0188561i
$229$	17.1879	+	9.92346i	1.13581	+	0.655761i	0.945390	−	0.325942i	$-0.105681\pi$
$229$	17.1879	+	9.92346i	1.13581	+	0.655761i	0.190421	+	0.981703i	$0.439015\pi$
$230$	−6.66721	+	11.0410i	−0.439623	+	0.728022i
$231$	4.40418	−	0.303842i	0.289774	−	0.0199913i
$232$	−0.935677	−	3.85691i	−0.0614302	−	0.253219i
$233$	−7.75745	−	6.72187i	−0.508208	−	0.440364i	0.362631	−	0.931933i	$-0.381878\pi$
$233$	−7.75745	−	6.72187i	−0.508208	−	0.440364i	−0.870839	+	0.491568i	$0.836424\pi$
$234$	5.83265	+	8.27880i	0.381293	+	0.541202i
$235$	−3.08449	−	0.443483i	−0.201210	−	0.0289297i
$236$	3.93826	−	7.63915i	0.256359	−	0.497266i
$237$	29.6228	+	0.779840i	1.92421	+	0.0506560i
$238$	−0.958662	+	0.184767i	−0.0621409	+	0.0119767i
$239$	−9.77946	+	24.4279i	−0.632581	+	1.58011i	0.171234	+	0.985230i	$0.445224\pi$
$239$	−9.77946	+	24.4279i	−0.632581	+	1.58011i	−0.803815	+	0.594880i	$0.797200\pi$
$240$	0.760887	+	4.59560i	0.0491150	+	0.296645i
$241$	−6.19888	+	6.50119i	−0.399305	+	0.418779i	−0.892434	−	0.451177i	$-0.851004\pi$
$241$	−6.19888	+	6.50119i	−0.399305	+	0.418779i	0.493130	+	0.869956i	$0.335853\pi$
$242$	−2.71636	−	9.25108i	−0.174614	−	0.594682i
$243$	−8.89939	+	12.7985i	−0.570896	+	0.821022i
$244$	−12.6225	+	1.81483i	−0.808070	+	0.116183i
$245$	1.95055	−	5.63575i	0.124616	−	0.360055i
$246$	2.12567	+	1.30302i	0.135528	+	0.0830776i
$247$	2.57774	−	0.122793i	0.164018	−	0.00781313i
$248$	1.86071	−	2.36608i	0.118155	−	0.150246i
$249$	4.56343	+	7.52941i	0.289196	+	0.477157i
$250$	1.40841	−	7.30750i	0.0890754	−	0.462167i
$251$	−13.4889	−	3.96070i	−0.851411	−	0.249997i	−0.173221	−	0.984883i	$-0.555417\pi$
$251$	−13.4889	−	3.96070i	−0.851411	−	0.249997i	−0.678191	+	0.734886i	$0.737236\pi$
$252$	−6.07835	−	2.46902i	−0.382900	−	0.155533i
$253$	4.29538	−	3.57662i	0.270048	−	0.224860i
$254$	1.08405	−	0.625876i	0.0680192	−	0.0392709i
$255$	0.447163	−	2.03093i	0.0280024	−	0.127181i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	−8.13157	−	15.7730i	−0.507234	−	0.983896i	−0.993898	−	0.110307i	$-0.964817\pi$
$257$	−8.13157	−	15.7730i	−0.507234	−	0.983896i	0.486664	−	0.873589i	$-0.338214\pi$
$258$	5.92429	+	0.438720i	0.368830	+	0.0273135i
$259$	−0.708200	−	0.365103i	−0.0440054	−	0.0226864i
$260$	−3.77138	−	8.25818i	−0.233891	−	0.512151i
$261$	−7.84226	+	8.95882i	−0.485424	+	0.554537i
$262$	2.34421	+	16.3043i	0.144825	+	1.00728i
$263$	17.1655	−	1.63911i	1.05847	−	0.101072i	0.448727	−	0.893669i	$-0.351878\pi$
$263$	17.1655	−	1.63911i	1.05847	−	0.101072i	0.609746	+	0.792597i	$0.291272\pi$
$264$	0.339774	−	1.98989i	0.0209116	−	0.122469i
$265$	−5.06150	+	20.8638i	−0.310926	+	1.28165i
$266$	−1.36184	+	0.969762i	−0.0834998	+	0.0594599i
$267$	8.98522	+	9.93425i	0.549887	+	0.607966i
$268$	4.24531	+	1.46932i	0.259324	+	0.0897528i
$269$	−8.93372	+	4.07989i	−0.544699	+	0.248756i	−0.668707	−	0.743526i	$-0.733152\pi$
$269$	−8.93372	+	4.07989i	−0.544699	+	0.248756i	0.124009	+	0.992281i	$0.460425\pi$
$270$	9.95587	−	9.80649i	0.605895	−	0.596804i
$271$	0.512276	−	3.56296i	0.0311185	−	0.216434i	−0.968329	−	0.249679i	$-0.919675\pi$
$271$	0.512276	−	3.56296i	0.0311185	−	0.216434i	0.999447	+	0.0332447i	$0.0105841\pi$
$272$	−0.0212423	+	0.445930i	−0.00128800	+	0.0270385i
$273$	12.6922	+	1.54999i	0.768168	+	0.0938095i
$274$	−1.02286	−	1.07274i	−0.0617931	−	0.0648067i
$275$	1.30117	−	2.25370i	0.0784638	−	0.135903i
$276$	−8.06928	+	1.97149i	−0.485713	+	0.118670i
$277$	14.5235	+	25.1555i	0.872635	+	1.51145i	0.859261	+	0.511537i	$0.170924\pi$
$277$	14.5235	+	25.1555i	0.872635	+	1.51145i	0.0133735	+	0.999911i	$0.495743\pi$
$278$	−3.27351	+	11.1485i	−0.196332	+	0.668645i
$279$	−9.01773	−	0.475125i	−0.539877	−	0.0284450i
$280$	4.94776	+	3.17973i	0.295685	+	0.190025i
$281$	−28.1373	+	11.2645i	−1.67853	+	0.671982i	−0.998146	−	0.0608731i	$-0.980612\pi$
$281$	−28.1373	+	11.2645i	−1.67853	+	0.671982i	−0.680385	+	0.732855i	$0.738187\pi$
$282$	−1.19866	−	1.60966i	−0.0713792	−	0.0958539i
$283$	−1.91229	+	20.0264i	−0.113674	+	1.19045i	0.741081	+	0.671415i	$0.234313\pi$
$283$	−1.91229	+	20.0264i	−0.113674	+	1.19045i	−0.854755	+	0.519031i	$0.826293\pi$
$284$	2.77844	+	14.4159i	0.164870	+	0.855426i
$285$	−0.748193	−	3.48160i	−0.0443191	−	0.206232i
$286$	0.373984	+	3.91653i	0.0221141	+	0.231590i
$287$	3.02048	−	0.886892i	0.178293	−	0.0523516i
$288$	−1.75246	+	2.43493i	−0.103265	+	0.143479i
$289$	−6.97926	+	15.2825i	−0.410545	+	0.898968i
$290$	8.39004	−	6.59800i	0.492680	−	0.387448i
$291$	11.0729	−	2.93710i	0.649106	−	0.172176i
$292$	−16.6176	−	1.58679i	−0.972474	−	0.0928600i
$293$	−0.610039	−	12.8063i	−0.0356389	−	0.748152i	−0.943996	−	0.329957i	$-0.892966\pi$
$293$	−0.610039	−	12.8063i	−0.0356389	−	0.748152i	0.908357	−	0.418195i	$-0.137337\pi$
$294$	3.45901	−	1.66952i	0.201733	−	0.0973686i
$295$	23.0880	+	1.09982i	1.34423	+	0.0640337i
$296$	−0.238592	+	0.275350i	−0.0138679	+	0.0160044i
$297$	−5.46721	+	2.60491i	−0.317240	+	0.151152i
$298$			8.47948i			0.491203i
$299$	14.1767	−	7.81755i	0.819861	−	0.452101i
$300$	−3.20822	+	2.15962i	−0.185227	+	0.124686i
$301$	5.42837	−	5.17594i	0.312886	−	0.298336i
$302$	−17.3211	+	5.99490i	−0.996719	+	0.344968i
$303$	10.7789	−	6.53289i	0.619232	−	0.375305i
$304$	0.284129	+	0.709721i	0.0162959	+	0.0407053i
$305$	−18.5417	−	28.8515i	−1.06170	−	1.65203i
$306$	1.13033	−	0.718397i	0.0646167	−	0.0410680i
$307$	4.19741	+	4.84406i	0.239559	+	0.276465i	0.862779	−	0.505581i	$-0.168722\pi$
$307$	4.19741	+	4.84406i	0.239559	+	0.276465i	−0.623221	+	0.782046i	$0.714176\pi$
$308$	−1.57556	−	2.00349i	−0.0897761	−	0.114160i
$309$	−7.71707	+	20.5321i	−0.439009	+	1.16803i
$310$	7.86709	+	1.90854i	0.446821	+	0.108398i
$311$	−3.90094	−	0.946358i	−0.221202	−	0.0536630i	0.123626	−	0.992329i	$-0.460548\pi$
$311$	−3.90094	−	0.946358i	−0.221202	−	0.0536630i	−0.344828	+	0.938666i	$0.612063\pi$
$312$	2.05708	−	5.47308i	0.116459	−	0.309852i
$313$	5.26994	+	6.70128i	0.297875	+	0.378779i	0.911834	−	0.410559i	$-0.134666\pi$
$313$	5.26994	+	6.70128i	0.297875	+	0.378779i	−0.613959	+	0.789338i	$0.710424\pi$
$314$	5.85414	+	6.75604i	0.330368	+	0.381265i
$315$	−0.750722	−	17.6282i	−0.0422984	−	0.993239i
$316$	−9.24963	−	14.3927i	−0.520332	−	0.809653i
$317$	−3.36452	−	8.40416i	−0.188970	−	0.472024i	0.803382	−	0.595464i	$-0.203032\pi$
$317$	−3.36452	−	8.40416i	−0.188970	−	0.472024i	−0.992352	+	0.123440i	$0.960607\pi$
$318$	−11.8244	+	7.16657i	−0.663081	+	0.401881i
$319$	−4.37118	+	1.51288i	−0.244739	+	0.0847050i
$320$	1.94641	−	1.85589i	0.108807	−	0.103748i
$321$	−18.1351	+	12.2077i	−1.01220	+	0.681365i
$322$	−4.98814	+	9.22582i	−0.277978	+	0.514135i
$323$		−	0.341292i		−	0.0189900i
$324$	8.99954	+	0.0907063i	0.499975	+	0.00503924i
$325$	4.93594	−	5.69638i	0.273797	−	0.315978i
$326$	12.5034	+	0.595613i	0.692502	+	0.0329879i
$327$	−8.52629	+	4.11529i	−0.471505	+	0.227576i
$328$	−0.0684934	−	1.43785i	−0.00378191	−	0.0793921i
$329$	−2.52249	−	0.240868i	−0.139069	−	0.0132795i
$330$	5.24758	−	1.39192i	0.288870	−	0.0766228i
$331$	−13.7042	+	10.7771i	−0.753251	+	0.592363i	−0.919209	−	0.393769i	$-0.871171\pi$
$331$	−13.7042	+	10.7771i	−0.753251	+	0.592363i	0.165958	+	0.986133i	$0.446928\pi$
$332$	2.11164	−	4.62384i	0.115891	−	0.253766i
$333$	1.08754	+	0.109380i	0.0595966	+	0.00599399i
$334$	−18.3133	+	5.37727i	−1.00206	+	0.294231i
$335$	1.14845	+	12.0271i	0.0627464	+	0.657111i
$336$	0.795828	+	3.70326i	0.0434160	+	0.202029i
$337$	−4.37930	−	22.7220i	−0.238556	−	1.23775i	−0.881630	−	0.471942i	$-0.843553\pi$
$337$	−4.37930	−	22.7220i	−0.238556	−	1.23775i	0.643074	−	0.765804i	$-0.277659\pi$
$338$	0.152530	−	1.59736i	0.00829652	−	0.0868851i
$339$	−10.9892	−	14.7572i	−0.596852	−	0.801502i
$340$	−1.11464	+	0.446233i	−0.0604496	+	0.0242004i
$341$	−2.95130	−	1.89669i	−0.159822	−	0.102711i
$342$	1.24964	−	1.92310i	0.0675727	−	0.103989i
$343$	5.67908	−	19.3412i	0.306641	−	1.04432i
$344$	−1.71488	−	2.97026i	−0.0924601	−	0.160146i
$345$	−13.8381	−	17.5378i	−0.745017	−	0.944202i
$346$	−9.08095	+	15.7287i	−0.488195	+	0.845579i
$347$	−2.50699	−	2.62926i	−0.134582	−	0.141146i	0.652994	−	0.757363i	$-0.273513\pi$
$347$	−2.50699	−	2.62926i	−0.134582	−	0.141146i	−0.787576	+	0.616217i	$0.788664\pi$
$348$	6.82345	+	0.833287i	0.365775	+	0.0446689i
$349$	0.372392	−	7.81747i	0.0199337	−	0.418460i	−0.966741	−	0.255756i	$-0.917676\pi$
$349$	0.372392	−	7.81747i	0.0199337	−	0.418460i	0.986675	−	0.162703i	$-0.0520214\pi$
$350$	−0.694919	+	4.83327i	−0.0371450	+	0.258349i
$351$	−16.9768	+	4.41166i	−0.906155	+	0.235477i
$352$	−1.06017	+	0.484162i	−0.0565071	+	0.0258059i
$353$	−14.8223	−	5.13004i	−0.788910	−	0.273044i	−0.0972425	−	0.995261i	$-0.531002\pi$
$353$	−14.8223	−	5.13004i	−0.788910	−	0.273044i	−0.691667	+	0.722216i	$0.743123\pi$
$354$	9.98558	+	11.0403i	0.530728	+	0.586784i
$355$	−32.1623	+	22.9027i	−1.70700	+	1.21555i
$356$	1.82325	−	7.51556i	0.0966323	−	0.398324i
$357$	0.284621	−	1.66689i	0.0150638	−	0.0882210i
$358$	18.6832	−	1.78403i	0.987437	−	0.0942888i
$359$	−2.99385	−	20.8227i	−0.158010	−	1.09898i	−0.902295	−	0.431119i	$-0.858119\pi$
$359$	−2.99385	−	20.8227i	−0.158010	−	1.09898i	0.744285	−	0.667862i	$-0.232790\pi$
$360$	−7.91458	−	1.56682i	−0.417135	−	0.0825785i
$361$	7.65010	+	16.7514i	0.402637	+	0.881652i
$362$	−6.52004	−	3.36131i	−0.342686	−	0.176667i
$363$	16.6542	+	1.23332i	0.874118	+	0.0647323i
$364$	−3.38276	−	6.56164i	−0.177305	−	0.343924i
$365$	−14.6836	−	42.4255i	−0.768575	−	2.22065i
$366$	4.74941	−	21.5709i	0.248256	−	1.12753i
$367$	22.2648	−	12.8546i	1.16221	−	0.671005i	0.210381	−	0.977620i	$-0.432530\pi$
$367$	22.2648	−	12.8546i	1.16221	−	0.671005i	0.951834	+	0.306615i	$0.0991963\pi$
$368$	3.56203	+	3.21123i	0.185683	+	0.167397i
$369$	−3.40794	+	2.65235i	−0.177410	+	0.138076i
$370$	−0.940164	−	0.276057i	−0.0488768	−	0.0143515i
$371$	−3.30387	+	17.1421i	−0.171528	+	0.889974i
$372$	2.70229	+	4.45863i	0.140107	+	0.231169i
$373$	15.6797	−	19.9384i	0.811864	−	1.03237i	−0.186886	−	0.982382i	$-0.559840\pi$
$373$	15.6797	−	19.9384i	0.811864	−	1.03237i	0.998750	−	0.0499871i	$-0.0159180\pi$
$374$	0.519727	−	0.0247576i	0.0268744	−	0.00128019i
$375$	10.9895	+	6.73649i	0.567496	+	0.347871i
$376$	−0.378975	+	1.09498i	−0.0195442	+	0.0564691i
$377$	−13.2611	+	1.90666i	−0.682981	+	0.0981978i
$378$	7.70706	−	8.35036i	0.396408	−	0.429496i
$379$	−4.16185	−	14.1739i	−0.213780	−	0.728067i	−0.994643	−	0.103365i	$-0.967039\pi$
$379$	−4.16185	−	14.1739i	−0.213780	−	0.728067i	0.780864	−	0.624701i	$-0.214779\pi$
$380$	−1.41880	+	1.48799i	−0.0727828	+	0.0763324i
$381$	0.354147	+	2.13898i	0.0181435	+	0.109583i
$382$	6.92724	−	17.3034i	0.354429	−	0.885320i
$383$	10.9442	−	2.10932i	0.559221	−	0.107781i	0.0981941	−	0.995167i	$-0.468693\pi$
$383$	10.9442	−	2.10932i	0.559221	−	0.107781i	0.461027	+	0.887386i	$0.347481\pi$
$384$	1.73145	+	0.0455816i	0.0883577	+	0.00232608i
$385$	3.14102	−	6.09272i	0.160081	−	0.310514i
$386$	5.42206	+	0.779574i	0.275976	+	0.0396793i
$387$	−4.32143	+	9.33780i	−0.219671	+	0.474667i
$388$	−4.99855	−	4.33127i	−0.253763	−	0.219887i
$389$	0.135108	+	0.556921i	0.00685022	+	0.0282370i	0.975134	−	0.221616i	$-0.0711330\pi$
$389$	0.135108	+	0.556921i	0.00685022	+	0.0282370i	−0.968284	+	0.249853i	$0.919618\pi$
$390$	15.6873	−	1.08226i	0.794357	−	0.0548022i
$391$	−0.943487	−	1.92194i	−0.0477142	−	0.0971965i
$392$	−1.92042	−	1.10875i	−0.0969958	−	0.0560006i
$393$	−27.8629	−	6.13477i	−1.40550	−	0.309458i
$394$	17.3888	+	3.35143i	0.876037	+	0.168842i
$395$	24.8759	−	38.7076i	1.25164	−	1.94759i
$396$	3.01918	+	1.76347i	0.151720	+	0.0886178i
$397$	−5.80485	+	3.73055i	−0.291337	+	0.187231i	−0.678143	−	0.734930i	$-0.737215\pi$
$397$	−5.80485	+	3.73055i	−0.291337	+	0.187231i	0.386805	+	0.922161i	$0.373578\pi$
$398$	−3.06280	+	4.30110i	−0.153524	+	0.215595i
$399$	−0.742415	−	2.79892i	−0.0371672	−	0.140121i
$400$	2.07289	+	0.829861i	0.103645	+	0.0414931i
$401$	16.5472	+	23.2373i	0.826327	+	1.16041i	0.984910	+	0.173068i	$0.0553681\pi$
$401$	16.5472	+	23.2373i	0.826327	+	1.16041i	−0.158583	+	0.987346i	$0.550692\pi$
$402$	−4.96922	+	5.98762i	−0.247842	+	0.298635i
$403$	−7.35396	−	7.01198i	−0.366327	−	0.349292i
$404$	−6.61938	−	3.02297i	−0.329326	−	0.150398i
$405$	9.83252	+	22.1174i	0.488582	+	1.09902i
$406$	6.55938	−	5.68374i	0.325537	−	0.282079i
$407$	0.345898	+	0.246313i	0.0171455	+	0.0122093i
$408$	−0.710048	−	0.306180i	−0.0351526	−	0.0151582i
$409$	−4.29071	−	3.37425i	−0.212162	−	0.166846i	0.506423	−	0.862285i	$-0.330967\pi$
$409$	−4.29071	−	3.37425i	−0.212162	−	0.166846i	−0.718585	+	0.695439i	$0.755210\pi$
$410$	3.44098	−	1.77395i	0.169938	−	0.0876091i
$411$	2.36256	−	1.00467i	0.116536	−	0.0495567i
$412$	12.3069	−	2.98562i	0.606317	−	0.147091i
$413$	18.7954			0.924859
$414$	1.72083	−	14.2842i	0.0845743	−	0.702031i
$415$	13.6707			0.671070
$416$	−3.28055	+	0.795852i	−0.160842	+	0.0390199i
$417$	−16.0805	−	12.1010i	−0.787465	−	0.592591i
$418$	0.791949	−	0.408278i	0.0387355	−	0.0199695i
$419$	−29.8966	−	23.5109i	−1.46054	−	1.14858i	−0.958984	−	0.283460i	$-0.908518\pi$
$419$	−29.8966	−	23.5109i	−1.46054	−	1.14858i	−0.501559	−	0.865123i	$-0.667240\pi$
$420$	−8.17039	+	6.08421i	−0.398674	+	0.296879i
$421$	23.3879	+	16.6544i	1.13986	+	0.811688i	0.984363	−	0.176149i	$-0.0563641\pi$
$421$	23.3879	+	16.6544i	1.13986	+	0.811688i	0.155493	+	0.987837i	$0.450304\pi$
$422$	−20.2557	+	17.5516i	−0.986030	+	0.854400i
$423$	3.34020	−	0.962515i	0.162406	−	0.0467991i
$424$	7.26144	+	3.31619i	0.352647	+	0.161048i
$425$	−0.721431	−	0.687883i	−0.0349945	−	0.0333672i
$426$	−25.0658	−	4.28000i	−1.21444	−	0.207366i
$427$	−16.1765	−	22.7167i	−0.782836	−	1.09934i
$428$	11.7174	+	4.69094i	0.566382	+	0.226745i
$429$	−6.57783	−	1.78030i	−0.317581	−	0.0859537i
$430$	5.35043	−	7.51363i	0.258021	−	0.362339i
$431$	−15.3142	+	9.84187i	−0.737661	+	0.474066i	−0.854740	−	0.519056i	$-0.826283\pi$
$431$	−15.3142	+	9.84187i	−0.737661	+	0.474066i	0.117079	+	0.993123i	$0.462647\pi$
$432$	−2.87987	−	4.32508i	−0.138558	−	0.208091i
$433$	−14.4850	+	22.5391i	−0.696104	+	1.08316i	0.295687	+	0.955285i	$0.404451\pi$
$433$	−14.4850	+	22.5391i	−0.696104	+	1.08316i	−0.991791	+	0.127873i	$0.959185\pi$
$434$	6.46375	+	1.24579i	0.310270	+	0.0597997i
$435$	5.58474	+	17.6236i	0.267768	+	0.844985i
$436$	4.73374	+	2.73303i	0.226705	+	0.130888i
$437$	−2.83683	−	2.32257i	−0.135704	−	0.111104i
$438$	12.6991	−	25.9755i	0.606787	−	1.24116i
$439$	3.06416	+	12.6307i	0.146245	+	0.602828i	0.997009	+	0.0772815i	$0.0246240\pi$
$439$	3.06416	+	12.6307i	0.146245	+	0.602828i	−0.850765	+	0.525547i	$0.823861\pi$
$440$	−2.36887	−	2.05264i	−0.112931	−	0.0978556i
$441$	0.598983	+	6.62551i	0.0285230	+	0.315500i
$442$	1.49169	+	0.214473i	0.0709527	+	0.0102015i
$443$	7.27694	−	14.1153i	0.345738	−	0.670638i	−0.650289	−	0.759687i	$-0.725352\pi$
$443$	7.27694	−	14.1153i	0.345738	−	0.670638i	0.996027	+	0.0890487i	$0.0283827\pi$
$444$	−0.301037	−	0.554625i	−0.0142866	−	0.0263214i
$445$	20.4227	−	3.93615i	0.968129	−	0.186592i
$446$	0.959758	−	2.39736i	0.0454459	−	0.113518i
$447$	−13.7479	−	5.16720i	−0.650253	−	0.244400i
$448$	1.50913	−	1.58273i	0.0712996	−	0.0747768i
$449$	−3.55579	−	12.1099i	−0.167808	−	0.571501i	−0.999859	−	0.0168020i	$-0.994652\pi$
$449$	−3.55579	−	12.1099i	−0.167808	−	0.571501i	0.832051	−	0.554699i	$-0.187167\pi$
$450$	−1.54641	−	6.51756i	−0.0728984	−	0.307241i
$451$	−1.66063	+	0.238762i	−0.0781959	+	0.0112429i
$452$	−3.47441	+	10.0387i	−0.163423	+	0.472179i
$453$	0.835476	−	31.7361i	0.0392541	−	1.49109i
$454$	−8.10446	+	0.386063i	−0.380361	+	0.0181188i
$455$	12.2729	−	15.6062i	0.575361	−	0.731630i
$456$	−1.32382	+	0.0281756i	−0.0619937	+	0.00131944i
$457$	5.75953	−	29.8833i	0.269420	−	1.39788i	−0.554976	−	0.831867i	$-0.687272\pi$
$457$	5.75953	−	29.8833i	0.269420	−	1.39788i	0.824395	−	0.566015i	$-0.191515\pi$
$458$	19.0430	+	5.59152i	0.889820	+	0.261275i
$459$	0.475950	+	2.27040i	0.0222154	+	0.105973i
$460$	−3.87626	+	12.3016i	−0.180732	+	0.573566i
$461$	1.84211	−	1.06354i	0.0857958	−	0.0495342i	−0.456488	−	0.889729i	$-0.650893\pi$
$461$	1.84211	−	1.06354i	0.0857958	−	0.0495342i	0.542284	+	0.840195i	$0.317560\pi$
$462$	4.20840	−	1.33360i	0.195793	−	0.0620448i
$463$	−1.00031	−	2.89020i	−0.0464883	−	0.134319i	0.919367	−	0.393401i	$-0.128701\pi$
$463$	−1.00031	−	2.89020i	−0.0464883	−	0.134319i	−0.965855	+	0.259081i	$0.916580\pi$
$464$	−1.81860	−	3.52760i	−0.0844266	−	0.163765i
$465$	−7.88836	+	11.5920i	−0.365814	+	0.537567i
$466$	−9.12352	−	4.70350i	−0.422639	−	0.217886i
$467$	10.7536	+	23.5470i	0.497616	+	1.08963i	0.977237	+	0.212151i	$0.0680468\pi$
$467$	10.7536	+	23.5470i	0.497616	+	1.08963i	−0.479621	+	0.877476i	$0.659226\pi$
$468$	7.62004	+	6.67033i	0.352237	+	0.308336i
$469$	1.39815	+	9.72437i	0.0645607	+	0.449030i
$470$	−3.10210	+	0.296215i	−0.143089	+	0.0136634i
$471$	−14.5210	+	5.37443i	−0.669094	+	0.247641i
$472$	2.02624	−	8.35229i	0.0932655	−	0.384445i
$473$	−3.25615	+	2.31869i	−0.149718	+	0.106614i
$474$	28.9716	−	6.22598i	1.33071	−	0.285969i
$475$	−1.61308	−	0.558293i	−0.0740133	−	0.0256162i
$476$	−0.888079	+	0.405572i	−0.0407050	+	0.0185894i
$477$	−4.41372	−	23.5383i	−0.202091	−	1.07774i
$478$	−3.74469	+	26.0449i	−0.171278	+	1.19127i
$479$	1.24840	−	26.2072i	0.0570410	−	1.19744i	−0.771024	−	0.636806i	$-0.780255\pi$
$479$	1.24840	−	26.2072i	0.0570410	−	1.19744i	0.828065	−	0.560632i	$-0.189442\pi$
$480$	1.82289	+	4.28667i	0.0832033	+	0.195659i
$481$	0.848732	+	0.890125i	0.0386989	+	0.0405862i
$482$	−4.49142	+	7.77938i	−0.204579	+	0.354341i
$483$	−11.9183	−	13.7093i	−0.542301	−	0.623797i
$484$	−4.82082	−	8.34990i	−0.219128	−	0.379541i
$485$	5.01138	−	17.0672i	0.227555	−	0.774982i
$486$	−5.63118	+	14.5358i	−0.255435	+	0.659358i
$487$	−25.6653	−	16.4941i	−1.16301	−	0.747420i	−0.190821	−	0.981625i	$-0.561115\pi$
$487$	−25.6653	−	16.4941i	−1.16301	−	0.747420i	−0.972187	+	0.234205i	$0.924751\pi$
$488$	−11.8388	+	4.73953i	−0.535916	+	0.214549i
$489$	−8.58499	+	19.9091i	−0.388226	+	0.900319i
$490$	0.566891	−	5.93675i	0.0256095	−	0.268195i
$491$	5.06081	+	26.2580i	0.228391	+	1.18501i	0.897218	+	0.441588i	$0.145585\pi$
$491$	5.06081	+	26.2580i	0.228391	+	1.18501i	−0.668827	+	0.743419i	$0.733203\pi$
$492$	2.37295	+	0.765145i	0.106981	+	0.0344954i
$493$	0.168421	+	1.76379i	0.00758530	+	0.0794369i
$494$	2.47613	−	0.727057i	0.111406	−	0.0327119i
$495$	−0.941009	+	9.35618i	−0.0422952	+	0.420529i
$496$	1.25043	−	2.73806i	0.0561460	−	0.122943i
$497$	−25.2372	+	19.8467i	−1.13204	+	0.890248i
$498$	6.20992	+	6.24129i	0.278273	+	0.279679i
$499$	−21.1809	−	2.02253i	−0.948186	−	0.0905408i	−0.390510	−	0.920599i	$-0.627701\pi$
$499$	−21.1809	−	2.02253i	−0.948186	−	0.0905408i	−0.557677	+	0.830058i	$0.688307\pi$
$500$	−0.354104	−	7.43356i	−0.0158360	−	0.332439i
$501$	2.44145	−	32.9684i	0.109076	−	1.47292i
$502$	−14.0424	−	0.668923i	−0.626744	−	0.0298555i
$503$	−27.1325	+	31.3126i	−1.20978	+	1.39616i	−0.315336	+	0.948980i	$0.602117\pi$
$503$	−27.1325	+	31.3126i	−1.20978	+	1.39616i	−0.894444	+	0.447181i	$0.852428\pi$
$504$	−6.48911	−	0.966394i	−0.289048	−	0.0430466i
$505$		−	19.5707i		−	0.870883i
$506$	3.33108	−	4.48847i	0.148085	−	0.199537i
$507$	2.49688	+	1.22069i	0.110890	+	0.0542130i
$508$	0.905935	−	0.863807i	0.0401944	−	0.0383252i
$509$	40.9632	−	14.1775i	1.81566	−	0.628407i	0.817003	−	0.576634i	$-0.195634\pi$
$509$	40.9632	−	14.1775i	1.81566	−	0.628407i	0.998659	−	0.0517729i	$-0.0164872\pi$
$510$	−0.0442505	−	2.07910i	−0.00195945	−	0.0920641i
$511$	−13.5680	−	33.8913i	−0.600214	−	1.49926i
$512$	−0.540641	−	0.841254i	−0.0238932	−	0.0371785i
$513$	2.35644	+	3.19795i	0.104040	+	0.141193i
$514$	−11.6210	−	13.4113i	−0.512580	−	0.591549i
$515$	21.0533	+	26.7715i	0.927721	+	1.17969i
$516$	5.86073	−	0.970352i	0.258004	−	0.0427174i
$517$	1.31239	+	0.318383i	0.0577189	+	0.0140025i
$518$	−0.774313	−	0.187846i	−0.0340214	−	0.00825350i
$519$	−19.9674	−	24.3078i	−0.876472	−	1.06699i
$520$	−5.61201	−	7.13626i	−0.246103	−	0.312946i
$521$	5.25785	+	6.06789i	0.230351	+	0.265839i	0.859144	−	0.511733i	$-0.170996\pi$
$521$	5.25785	+	6.06789i	0.230351	+	0.265839i	−0.628794	+	0.777572i	$0.716451\pi$
$522$	−5.50907	+	10.5552i	−0.241126	+	0.461987i
$523$	4.83421	+	7.52217i	0.211385	+	0.328922i	0.930714	−	0.365748i	$-0.119187\pi$
$523$	4.83421	+	7.52217i	0.211385	+	0.328922i	−0.719329	+	0.694670i	$0.755550\pi$
$524$	6.12201	+	15.2920i	0.267441	+	0.668036i
$525$	−7.41278	−	4.07196i	−0.323520	−	0.177715i
$526$	16.2952	−	5.63984i	0.710506	−	0.245909i
$527$	−0.972558	+	0.927332i	−0.0423653	+	0.0403952i
$528$	−0.138938	−	2.01390i	−0.00604649	−	0.0876438i
$529$	−22.3959	−	5.23693i	−0.973733	−	0.227693i
$530$			21.4690i			0.932553i
$531$	−23.9847	+	9.46208i	−1.04085	+	0.410619i
$532$	−1.09482	+	1.26349i	−0.0474665	+	0.0547793i
$533$	−4.85376	−	0.231213i	−0.210240	−	0.0100150i
$534$	11.0740	+	7.53587i	0.479220	+	0.326109i
$535$	1.61513	+	33.9057i	0.0698282	+	1.46587i
$536$	4.47205	+	0.427029i	0.193163	+	0.0184448i
$537$	−8.49263	+	31.3784i	−0.366484	+	1.35408i
$538$	−7.72002	+	6.07109i	−0.332834	+	0.261743i
$539$	−1.07363	+	2.35093i	−0.0462447	+	0.101262i
$540$	7.36327	−	11.8772i	0.316864	−	0.511115i
$541$	4.72010	−	1.38595i	0.202933	−	0.0595864i	−0.178686	−	0.983906i	$-0.557185\pi$
$541$	4.72010	−	1.38595i	0.202933	−	0.0595864i	0.381619	+	0.924320i	$0.375367\pi$
$542$	−0.342163	−	3.58330i	−0.0146972	−	0.153916i
$543$	9.42291	−	8.52273i	0.404376	−	0.365745i
$544$	0.0844885	+	0.438368i	0.00362241	+	0.0187949i
$545$	−1.39736	+	14.6338i	−0.0598563	+	0.626843i
$546$	12.6999	−	1.48601i	0.543504	−	0.0635953i
$547$	−15.2066	+	6.08782i	−0.650189	+	0.260296i	−0.673224	−	0.739438i	$-0.735091\pi$
$547$	−15.2066	+	6.08782i	−0.650189	+	0.260296i	0.0230357	+	0.999735i	$0.492667\pi$
$548$	−1.24693	−	0.801355i	−0.0532663	−	0.0342322i
$549$	32.0790	+	20.8451i	1.36910	+	0.889646i
$550$	0.733167	−	2.49694i	0.0312623	−	0.106470i
$551$	1.51703	+	2.62758i	0.0646278	+	0.111939i
$552$	−7.37702	+	3.81832i	−0.313987	+	0.162518i
$553$	18.7074	−	32.4021i	0.795518	−	1.37788i
$554$	20.0448	+	21.0224i	0.851621	+	0.893154i
$555$	1.02049	−	1.35608i	0.0433174	−	0.0575623i
$556$	−0.552864	+	11.6060i	−0.0234466	+	0.492206i
$557$	−4.37033	+	30.3963i	−0.185177	+	1.28793i	0.659112	+	0.752045i	$0.270932\pi$
$557$	−4.37033	+	30.3963i	−0.185177	+	1.28793i	−0.844289	+	0.535889i	$0.819977\pi$
$558$	−8.87555	+	1.66428i	−0.375732	+	0.0704545i
$559$	−10.5316	+	4.80961i	−0.445438	+	0.203425i
$560$	5.55794	+	1.92362i	0.234866	+	0.0812878i
$561$	−0.276570	+	0.857727i	−0.0116768	+	0.0362133i
$562$	−24.6884	+	17.5806i	−1.04142	+	0.741591i
$563$	−4.74418	+	19.5558i	−0.199944	+	0.824179i	0.780142	+	0.625603i	$0.215147\pi$
$563$	−4.74418	+	19.5558i	−0.199944	+	0.824179i	−0.980085	+	0.198576i	$0.936368\pi$
$564$	−1.54436	−	1.28169i	−0.0650294	−	0.0539690i
$565$	−28.4398	+	2.71567i	−1.19647	+	0.114249i
$566$	2.86302	+	19.9127i	0.120342	+	0.836995i
$567$	8.84205	+	17.5841i	0.371331	+	0.738462i
$568$	6.09880	+	13.3545i	0.255900	+	0.560342i
$569$	25.8750	+	13.3395i	1.08474	+	0.559222i	0.905397	−	0.424565i	$-0.139573\pi$
$569$	25.8750	+	13.3395i	1.08474	+	0.559222i	0.179341	+	0.983787i	$0.442603\pi$
$570$	−1.54792	−	3.20707i	−0.0648353	−	0.134329i
$571$	−15.4401	−	29.9496i	−0.646148	−	1.25335i	−0.953396	−	0.301723i	$-0.902438\pi$
$571$	−15.4401	−	29.9496i	−0.646148	−	1.25335i	0.307247	−	0.951630i	$-0.400592\pi$
$572$	1.28680	+	3.71796i	0.0538038	+	0.155456i
$573$	23.8330	+	21.7755i	0.995637	+	0.909686i
$574$	2.72624	−	1.57400i	0.113791	−	0.0656973i
$575$	−10.6272	+	1.31535i	−0.443186	+	0.0548539i
$576$	−1.12901	+	2.77945i	−0.0470420	+	0.115810i
$577$	44.4052	+	13.0385i	1.84861	+	0.542802i	0.999903	+	0.0139443i	$0.00443875\pi$
$577$	44.4052	+	13.0385i	1.84861	+	0.542802i	0.848711	+	0.528858i	$0.177379\pi$
$578$	−3.17955	+	16.4971i	−0.132252	+	0.686188i
$579$	−4.56801	+	8.31581i	−0.189840	+	0.345593i
$580$	6.59800	−	8.39004i	0.273967	−	0.348378i
$581$	11.1038	−	0.528940i	0.460664	−	0.0219441i
$582$	10.0683	−	5.46485i	0.417346	−	0.226525i
$583$	3.04301	−	8.79221i	0.126029	−	0.364136i
$584$	−16.5233	+	2.37570i	−0.683740	+	0.0983070i
$585$	−7.80480	+	26.0935i	−0.322689	+	1.07884i
$586$	−3.61204	−	12.3015i	−0.149212	−	0.508170i
$587$	4.76831	−	5.00086i	0.196809	−	0.206407i	−0.617933	−	0.786230i	$-0.712030\pi$
$587$	4.76831	−	5.00086i	0.196809	−	0.206407i	0.814742	+	0.579823i	$0.196878\pi$
$588$	2.96790	−	2.43795i	0.122394	−	0.100540i
$589$	−0.855252	+	2.13632i	−0.0352400	+	0.0880253i
$590$	22.6965	−	4.37438i	0.934398	−	0.180090i
$591$	−16.0301	+	26.1505i	−0.659389	+	1.07569i
$592$	−0.166951	+	0.323839i	−0.00686162	+	0.0133097i
$593$	25.9252	+	3.72748i	1.06462	+	0.153069i	0.652293	−	0.757967i	$-0.273807\pi$
$593$	25.9252	+	3.72748i	1.06462	+	0.153069i	0.412327	+	0.911036i	$0.364716\pi$
$594$	−4.69896	+	3.82043i	−0.192801	+	0.156754i
$595$	−1.98435	−	1.71945i	−0.0813504	−	0.0704905i
$596$	1.99911	+	8.24045i	0.0818868	+	0.337542i
$597$	−5.10704	−	7.58676i	−0.209017	−	0.310505i
$598$	11.9340	−	10.9395i	0.488019	−	0.447348i
$599$	27.2557	+	15.7361i	1.11364	+	0.642960i	0.939770	−	0.341809i	$-0.111039\pi$
$599$	27.2557	+	15.7361i	1.11364	+	0.642960i	0.173870	+	0.984769i	$0.444373\pi$
$600$	−2.60864	+	2.85511i	−0.106497	+	0.116560i
$601$	−6.98946	−	1.34711i	−0.285106	−	0.0549497i	0.0446932	−	0.999001i	$-0.485769\pi$
$601$	−6.98946	−	1.34711i	−0.285106	−	0.0549497i	−0.329799	+	0.944051i	$0.606981\pi$
$602$	4.05508	−	6.30983i	0.165273	−	0.257169i
$603$	−6.67968	−	11.7054i	−0.272018	−	0.476680i
$604$	−15.4195	+	9.90952i	−0.627411	+	0.403213i
$605$	15.0410	−	21.1221i	0.611502	−	0.858734i
$606$	8.93488	−	8.88996i	0.362954	−	0.361130i
$607$	13.1791	+	5.27610i	0.534921	+	0.214150i	0.623365	−	0.781931i	$-0.285765\pi$
$607$	13.1791	+	5.27610i	0.534921	+	0.214150i	−0.0884436	+	0.996081i	$0.528189\pi$
$608$	0.443443	+	0.622729i	0.0179840	+	0.0252550i
$609$	5.21799	+	14.0984i	0.211444	+	0.571294i
$610$	−24.8211	−	23.6668i	−1.00498	−	0.958242i
$611$	3.55797	+	1.62487i	0.143940	+	0.0657353i
$612$	0.929100	−	0.964632i	0.0375566	−	0.0389929i
$613$	26.9417	−	23.3451i	1.08816	−	0.942899i	0.0895738	−	0.995980i	$-0.471450\pi$
$613$	26.9417	−	23.3451i	1.08816	−	0.942899i	0.998590	+	0.0530807i	$0.0169041\pi$
$614$	5.22112	+	3.71794i	0.210707	+	0.150044i
$615$	0.779275	+	6.65992i	0.0314234	+	0.268554i
$616$	−2.00349	−	1.57556i	−0.0807230	−	0.0634813i
$617$	−24.8194	+	12.7953i	−0.999193	+	0.515120i	−0.878588	−	0.477581i	$-0.841514\pi$
$617$	−24.8194	+	12.7953i	−0.999193	+	0.515120i	−0.120605	+	0.992701i	$0.538484\pi$
$618$	−2.65891	+	21.7727i	−0.106957	+	0.875827i
$619$	−6.08477	+	1.47615i	−0.244567	+	0.0593314i	−0.356169	−	0.934422i	$-0.615917\pi$
$619$	−6.08477	+	1.47615i	−0.244567	+	0.0593314i	0.111601	+	0.993753i	$0.464402\pi$
$620$	8.09528			0.325114
$621$	22.1106	+	11.4945i	0.887266	+	0.461257i
$622$	−4.01409			−0.160950
$623$	16.4357	−	3.98726i	0.658482	−	0.159746i
$624$	0.708763	−	5.80377i	0.0283732	−	0.232337i
$625$	27.7127	−	14.2869i	1.10851	−	0.571475i
$626$	6.70128	+	5.26994i	0.267837	+	0.210629i
$627$	0.179352	+	1.53279i	0.00716262	+	0.0612139i
$628$	7.28192	+	5.18543i	0.290580	+	0.206921i
$629$	0.122926	−	0.106516i	0.00490139	−	0.00424708i
$630$	−4.88558	−	16.9543i	−0.194646	−	0.675477i
$631$	28.5725	+	13.0486i	1.13745	+	0.519457i	0.892934	−	0.450187i	$-0.148643\pi$
$631$	28.5725	+	13.0486i	1.13745	+	0.519457i	0.244519	+	0.969645i	$0.421370\pi$
$632$	−12.3821	−	11.8063i	−0.492534	−	0.469630i
$633$	−16.1134	−	43.5363i	−0.640449	−	1.73041i
$634$	−5.25103	−	7.37404i	−0.208545	−	0.292861i
$635$	3.12531	+	1.25118i	0.124024	+	0.0496517i
$636$	−9.80154	+	9.75227i	−0.388656	+	0.386703i
$637$	−4.34210	+	6.09763i	−0.172040	+	0.241597i
$638$	−3.89129	+	2.50078i	−0.154058	+	0.0990068i
$639$	22.2137	−	38.0314i	0.878762	−	1.50450i
$640$	1.45400	−	2.26246i	0.0574742	−	0.0894316i
$641$	−3.56555	−	0.687204i	−0.140831	−	0.0271429i	0.118349	−	0.992972i	$-0.462240\pi$
$641$	−3.56555	−	0.687204i	−0.140831	−	0.0271429i	−0.259179	+	0.965829i	$0.583452\pi$
$642$	−14.7458	+	16.1390i	−0.581970	+	0.636957i
$643$	−9.16015	−	5.28861i	−0.361241	−	0.208563i	0.308384	−	0.951262i	$-0.400212\pi$
$643$	−9.16015	−	5.28861i	−0.361241	−	0.208563i	−0.669625	+	0.742699i	$0.733545\pi$
$644$	−2.67246	+	10.1418i	−0.105310	+	0.399641i
$645$	8.92152	+	13.2534i	0.351285	+	0.521850i
$646$	−0.0804626	−	0.331672i	−0.00316576	−	0.0130494i
$647$	−4.80022	−	4.15942i	−0.188716	−	0.163524i	0.555378	−	0.831598i	$-0.312573\pi$
$647$	−4.80022	−	4.15942i	−0.188716	−	0.163524i	−0.744095	+	0.668074i	$0.767119\pi$
$648$	8.76724	−	2.03357i	0.344410	−	0.0798863i
$649$	−9.91492	−	1.42555i	−0.389195	−	0.0559577i
$650$	3.45383	−	6.69950i	0.135470	−	0.262776i
$651$	−5.95867	+	9.72062i	−0.233539	+	0.380981i
$652$	12.2914	−	2.36898i	0.481369	−	0.0927763i
$653$	15.4229	−	38.5245i	0.603543	−	1.50758i	−0.240141	−	0.970738i	$-0.577194\pi$
$653$	15.4229	−	38.5245i	0.603543	−	1.50758i	0.843684	−	0.536840i	$-0.180382\pi$
$654$	−7.31573	+	6.00944i	−0.286067	+	0.234988i
$655$	−30.5702	+	32.0611i	−1.19448	+	1.25273i
$656$	−0.405549	−	1.38117i	−0.0158340	−	0.0539258i
$657$	34.3759	+	36.4181i	1.34113	+	1.42080i
$658$	−2.50817	+	0.360620i	−0.0977786	+	0.0140584i
$659$	−5.25560	+	15.1851i	−0.204729	+	0.591526i	−0.999889	−	0.0148735i	$-0.995265\pi$
$659$	−5.25560	+	15.1851i	−0.204729	+	0.591526i	0.795160	+	0.606399i	$0.207387\pi$
$660$	4.77150	−	2.58985i	0.185730	−	0.100810i
$661$	39.2889	−	1.87156i	1.52816	−	0.0727952i	0.733433	−	0.679762i	$-0.237917\pi$
$661$	39.2889	−	1.87156i	1.52816	−	0.0727952i	0.794727	+	0.606967i	$0.207614\pi$
$662$	−10.7771	+	13.7042i	−0.418864	+	0.532629i
$663$	−1.25673	+	2.28781i	−0.0488074	+	0.0888512i
$664$	0.962003	−	4.99134i	0.0373329	−	0.193702i
$665$	−4.31410	−	1.26674i	−0.167294	−	0.0491219i
$666$	1.08267	−	0.150099i	0.0419525	−	0.00581623i
$667$	15.8068	+	10.6031i	0.612041	+	0.410552i
$668$	−16.5293	+	9.54321i	−0.639539	+	0.369238i
$669$	3.30202	+	3.01696i	0.127663	+	0.116643i
$670$	3.95157	+	11.4173i	0.152663	+	0.441089i
$671$	6.81045	+	13.2104i	0.262914	+	0.509983i
$672$	1.64647	+	3.41125i	0.0635140	+	0.131592i
$673$	14.1576	+	7.29878i	0.545737	+	0.281347i	0.708968	−	0.705241i	$-0.249161\pi$
$673$	14.1576	+	7.29878i	0.545737	+	0.281347i	−0.163231	+	0.986588i	$0.552191\pi$
$674$	−9.61277	−	21.0490i	−0.370270	−	0.810778i
$675$	11.5094	+	1.46444i	0.442996	+	0.0563662i
$676$	−0.228363	−	1.58830i	−0.00878318	−	0.0610883i
$677$	19.5182	−	1.86376i	0.750144	−	0.0716301i	0.287021	−	0.957924i	$-0.407335\pi$
$677$	19.5182	−	1.86376i	0.750144	−	0.0716301i	0.463123	+	0.886294i	$0.346729\pi$
$678$	−14.1586	−	11.7504i	−0.543757	−	0.451273i
$679$	3.41005	−	14.0564i	0.130866	−	0.539437i
$680$	−0.978013	+	0.696440i	−0.0375051	+	0.0267073i
$681$	4.31274	−	13.3751i	0.165264	−	0.512536i
$682$	−3.31527	−	1.14743i	−0.126948	−	0.0439372i
$683$	0.967224	−	0.441716i	0.0370098	−	0.0169018i	−0.396824	−	0.917895i	$-0.629888\pi$
$683$	0.967224	−	0.441716i	0.0370098	−	0.0169018i	0.433834	+	0.900993i	$0.357160\pi$
$684$	0.761025	−	2.16350i	0.0290985	−	0.0827235i
$685$	0.567310	−	3.94573i	0.0216758	−	0.150759i
$686$	0.959141	−	20.1349i	0.0366202	−	0.768752i
$687$	−20.6700	+	27.4673i	−0.788608	+	1.04794i
$688$	−2.36680	−	2.48223i	−0.0902336	−	0.0946343i
$689$	13.4738	−	23.3374i	0.513312	−	0.889083i
$690$	−17.5827	−	13.7810i	−0.669361	−	0.524632i
$691$	7.23602	+	12.5331i	0.275271	+	0.476783i	0.970203	−	0.242292i	$-0.0778991\pi$
$691$	7.23602	+	12.5331i	0.275271	+	0.476783i	−0.694932	+	0.719075i	$0.744566\pi$
$692$	−5.11680	+	17.4262i	−0.194512	+	0.662446i
$693$	−0.402315	+	7.63581i	−0.0152827	+	0.290060i
$694$	−3.05620	−	1.96410i	−0.116012	−	0.0745561i
$695$	−29.0102	+	11.6139i	−1.10042	+	0.440541i
$696$	6.82756	−	0.798891i	0.258798	−	0.0302819i
$697$	−0.0610865	+	0.639727i	−0.00231382	+	0.0242314i
$698$	−1.48114	−	7.68490i	−0.0560621	−	0.290878i
$699$	13.1855	−	11.9259i	0.498722	−	0.451079i
$700$	0.464156	+	4.86086i	0.0175434	+	0.183723i
$701$	−7.51307	+	2.20604i	−0.283765	+	0.0833209i	−0.420518	−	0.907284i	$-0.638152\pi$
$701$	−7.51307	+	2.20604i	−0.283765	+	0.0833209i	0.136753	+	0.990605i	$0.456333\pi$
$702$	−15.4582	+	8.28974i	−0.583431	+	0.312876i
$703$	0.115706	−	0.253362i	0.00436395	−	0.00955571i
$704$	−0.916137	+	0.720458i	−0.0345282	+	0.0271533i
$705$	1.41009	−	5.20999i	0.0531071	−	0.196220i
$706$	−15.6139	−	1.49095i	−0.587637	−	0.0561125i
$707$	−0.757217	−	15.8959i	−0.0284781	−	0.597828i
$708$	12.3069	+	8.37487i	0.462523	+	0.314747i
$709$	45.1487	+	2.15070i	1.69560	+	0.0807711i	0.872958	−	0.487796i	$-0.162199\pi$
$709$	45.1487	+	2.15070i	1.69560	+	0.0807711i	0.822637	+	0.568567i	$0.192502\pi$
$710$	−25.8562	+	29.8397i	−0.970367	+	1.11986i
$711$	−7.56036	+	50.7660i	−0.283536	+	1.90388i
$712$		−	7.73355i		−	0.289827i
$713$	1.08953	+	14.3947i	0.0408032	+	0.539084i
$714$	−0.116385	−	1.68700i	−0.00435560	−	0.0631344i
$715$	−7.65784	+	7.30173i	−0.286387	+	0.273069i
$716$	17.7359	−	6.13846i	0.662823	−	0.229405i
$717$	−39.9451	−	21.9425i	−1.49178	−	0.819457i
$718$	−7.81860	−	19.5299i	−0.291788	−	0.728850i
$719$	−7.61248	−	11.8452i	−0.283897	−	0.441753i	0.669791	−	0.742550i	$-0.266384\pi$
$719$	−7.61248	−	11.8452i	−0.283897	−	0.441753i	−0.953688	+	0.300797i	$0.902747\pi$
$720$	−8.06087	+	0.343283i	−0.300411	+	0.0127934i
$721$	18.1360	+	20.9301i	0.675422	+	0.779478i
$722$	11.3837	+	14.4756i	0.423659	+	0.538727i
$723$	−9.87584	−	12.0226i	−0.367287	−	0.447125i
$724$	−7.12871	−	1.72941i	−0.264936	−	0.0642729i
$725$	8.61186	+	2.08921i	0.319836	+	0.0775915i
$726$	16.4755	−	2.72782i	0.611463	−	0.101239i
$727$	−14.3160	−	18.2043i	−0.530951	−	0.675160i	0.444397	−	0.895830i	$-0.353418\pi$
$727$	−14.3160	−	18.2043i	−0.530951	−	0.675160i	−0.975348	+	0.220670i	$0.929176\pi$
$728$	−4.83437	−	5.57916i	−0.179174	−	0.206778i
$729$	−20.1356	−	17.9877i	−0.745763	−	0.666211i
$730$	−24.2719	−	37.7678i	−0.898343	−	1.39785i
$731$	0.569077	+	1.42149i	0.0210481	+	0.0525755i
$732$	−0.469994	−	22.0825i	−0.0173715	−	0.816194i
$733$	20.6113	−	7.13366i	0.761298	−	0.263488i	0.0812877	−	0.996691i	$-0.474097\pi$
$733$	20.6113	−	7.13366i	0.761298	−	0.263488i	0.680010	+	0.733203i	$0.261976\pi$
$734$	18.6066	−	17.7414i	0.686783	−	0.654846i
$735$	9.27989	+	4.53683i	0.342294	+	0.167343i
$736$	4.21869	+	2.28093i	0.155503	+	0.0840761i
$737$		−	5.23584i		−	0.192865i
$738$	−2.68656	+	3.38104i	−0.0988937	+	0.124458i
$739$	7.14300	−	8.24346i	0.262759	−	0.303241i	−0.609004	−	0.793167i	$-0.708431\pi$
$739$	7.14300	−	8.24346i	0.262759	−	0.303241i	0.871764	+	0.489926i	$0.162976\pi$
$740$	−0.978745	−	0.0466234i	−0.0359794	−	0.00171391i
$741$	−0.330108	+	4.45764i	−0.0121268	+	0.163755i
$742$	0.830665	+	17.4378i	0.0304947	+	0.640162i
$743$	6.83459	+	0.652625i	0.250737	+	0.0239425i	0.219668	−	0.975575i	$-0.429503\pi$
$743$	6.83459	+	0.652625i	0.250737	+	0.0239425i	0.0310693	+	0.999517i	$0.490109\pi$
$744$	3.67728	+	3.69586i	0.134816	+	0.135497i
$745$	−17.9257	+	14.0969i	−0.656745	+	0.516470i
$746$	10.5371	−	23.0729i	0.385789	−	0.844761i
$747$	−13.9033	+	6.26493i	−0.508694	+	0.229222i
$748$	0.499240	−	0.146590i	0.0182540	−	0.00535986i
$749$	2.62372	+	27.4769i	0.0958688	+	1.00398i
$750$	12.2679	+	3.95573i	0.447961	+	0.144443i
$751$	8.87333	+	46.0392i	0.323792	+	1.67999i	0.670412	+	0.741989i	$0.266117\pi$
$751$	8.87333	+	46.0392i	0.323792	+	1.67999i	−0.346620	+	0.938006i	$0.612671\pi$
$752$	−0.110142	+	1.15346i	−0.00401646	+	0.0420623i
$753$	9.64167	−	22.3596i	0.351362	−	0.814828i
$754$	−12.4378	+	4.97933i	−0.452957	+	0.181336i
$755$	−41.4692	−	26.6506i	−1.50922	−	0.969915i
$756$	5.52114	−	9.93198i	0.200802	−	0.361223i
$757$	12.1384	−	41.3395i	0.441177	−	1.50251i	−0.376273	−	0.926509i	$-0.622795\pi$
$757$	12.1384	−	41.3395i	0.441177	−	1.50251i	0.817449	−	0.576000i	$-0.195387\pi$
$758$	−7.38617	−	12.7932i	−0.268278	−	0.464670i
$759$	5.24734	+	8.13590i	0.190466	+	0.295314i
$760$	−1.02800	+	1.78054i	−0.0372894	+	0.0645871i
$761$	−8.50049	−	8.91505i	−0.308142	−	0.323170i	0.551394	−	0.834245i	$-0.314096\pi$
$761$	−8.50049	−	8.91505i	−0.308142	−	0.323170i	−0.859536	+	0.511074i	$0.829248\pi$
$762$	0.848447	+	1.99519i	0.0307360	+	0.0722781i
$763$	−0.568778	+	11.9401i	−0.0205911	+	0.432261i
$764$	2.65254	−	18.4488i	0.0959655	−	0.667455i
$765$	3.39784	+	1.19521i	0.122849	+	0.0432130i
$766$	10.1384	−	4.63004i	0.366314	−	0.167290i
$767$	−27.4170	−	9.48912i	−0.989971	−	0.342632i
$768$	1.69339	−	0.363908i	0.0611050	−	0.0131314i
$769$	−5.27492	+	3.75625i	−0.190218	+	0.135454i	−0.671199	−	0.741277i	$-0.734220\pi$
$769$	−5.27492	+	3.75625i	−0.190218	+	0.135454i	0.480980	+	0.876731i	$0.340281\pi$
$770$	1.61606	−	6.66150i	0.0582389	−	0.240064i
$771$	28.8256	−	10.6687i	1.03813	−	0.384225i
$772$	5.45301	−	0.520699i	0.196258	−	0.0187404i
$773$	0.319543	+	2.22247i	0.0114931	+	0.0799366i	0.994761	−	0.102230i	$-0.0325979\pi$
$773$	0.319543	+	2.22247i	0.0114931	+	0.0799366i	−0.983268	+	0.182167i	$0.941689\pi$
$774$	−1.99815	+	10.0934i	−0.0718219	+	0.362800i
$775$	2.79201	+	6.11365i	0.100292	+	0.219609i
$776$	−5.87878	−	3.03072i	−0.211036	−	0.108797i
$777$	0.776407	−	1.14094i	0.0278534	−	0.0409309i
$778$	0.262598	+	0.509369i	0.00941460	+	0.0182618i
$779$	0.359925	+	1.03994i	0.0128957	+	0.0372595i
$780$	14.9899	−	4.75017i	0.536726	−	0.170083i
$781$	14.8184	−	8.55540i	0.530244	−	0.306136i
$782$	−1.37001	−	1.64532i	−0.0489913	−	0.0588367i
$783$	−13.7561	−	15.3640i	−0.491605	−	0.549065i
$784$	−2.12768	−	0.624745i	−0.0759887	−	0.0223123i
$785$	−4.54996	+	23.6074i	−0.162395	+	0.842585i
$786$	−28.5238	+	0.607087i	−1.01741	+	0.0216541i
$787$	26.9724	−	34.2982i	0.961462	−	1.22260i	−0.0134280	−	0.999910i	$-0.504274\pi$
$787$	26.9724	−	34.2982i	0.961462	−	1.22260i	0.974890	−	0.222688i	$-0.0714832\pi$
$788$	17.6888	−	0.842622i	0.630138	−	0.0300172i
$789$	−0.785992	+	29.8565i	−0.0279821	+	1.06292i
$790$	15.0490	−	43.4812i	0.535420	−	1.54699i
$791$	−22.9947	+	3.30613i	−0.817596	+	0.117553i
$792$	3.34983	+	1.00196i	0.119031	+	0.0356032i
$793$	12.1280	+	41.3041i	0.430677	+	1.46675i
$794$	−4.76171	+	4.99394i	−0.168987	+	0.177228i
$795$	−34.8080	−	13.0827i	−1.23451	−	0.463996i
$796$	−1.96244	+	4.90195i	−0.0695570	+	0.173745i
$797$	−36.2266	+	6.98210i	−1.28321	+	0.247319i	−0.784869	−	0.619661i	$-0.787270\pi$
$797$	−36.2266	+	6.98210i	−1.28321	+	0.247319i	−0.498343	+	0.866980i	$0.666058\pi$
$798$	−1.38136	−	2.54499i	−0.0488995	−	0.0900918i
$799$	0.237035	−	0.459783i	0.00838568	−	0.0162660i
$800$	2.21011	+	0.317766i	0.0781392	+	0.0112347i
$801$	−18.9663	+	13.3623i	−0.670140	+	0.472134i
$802$	21.5591	+	18.6811i	0.761280	+	0.659653i
$803$	4.58688	+	18.9074i	0.161867	+	0.667227i
$804$	−3.41751	+	6.99037i	−0.120526	+	0.246532i
$805$	−27.7961	+	4.79272i	−0.979683	+	0.168921i
$806$	−8.79980	−	5.08057i	−0.309960	−	0.178955i
$807$	−5.13875	−	16.2162i	−0.180892	−	0.570836i
$808$	−7.14548	−	1.37718i	−0.251377	−	0.0484490i
$809$	25.2429	−	39.2787i	0.887493	−	1.38097i	−0.0368159	−	0.999322i	$-0.511722\pi$
$809$	25.2429	−	39.2787i	0.887493	−	1.38097i	0.924309	−	0.381644i	$-0.124642\pi$
$810$	14.7697	+	19.1759i	0.518956	+	0.673772i
$811$	4.96353	−	3.18986i	0.174293	−	0.112011i	−0.450586	−	0.892733i	$-0.648785\pi$
$811$	4.96353	−	3.18986i	0.174293	−	0.112011i	0.624879	+	0.780722i	$0.285148\pi$
$812$	5.03449	−	7.06995i	0.176676	−	0.248107i
$813$	6.01815	+	1.62882i	0.211066	+	0.0571253i
$814$	0.394218	+	0.157821i	0.0138173	+	0.00553163i
$815$	19.5275	+	27.4225i	0.684019	+	0.960570i
$816$	−0.762217	−	0.130149i	−0.0266829	−	0.00455612i
$817$	1.89762	+	1.80938i	0.0663894	+	0.0633022i
$818$	−4.96527	−	2.26756i	−0.173607	−	0.0792835i
$819$	−5.32972	+	21.4960i	−0.186235	+	0.751131i
$820$	2.92576	−	2.53519i	0.102172	−	0.0885326i
$821$	10.0566	+	7.16124i	0.350976	+	0.249929i	0.741924	−	0.670484i	$-0.233913\pi$
$821$	10.0566	+	7.16124i	0.350976	+	0.249929i	−0.390948	+	0.920413i	$0.627853\pi$
$822$	2.05910	−	1.53334i	0.0718194	−	0.0534815i
$823$	−10.8073	−	8.49893i	−0.376718	−	0.296254i	0.411790	−	0.911279i	$-0.364904\pi$
$823$	−10.8073	−	8.49893i	−0.376718	−	0.296254i	−0.788508	+	0.615024i	$0.789146\pi$
$824$	11.2561	−	5.80292i	0.392125	−	0.202154i
$825$	3.60154	+	2.71027i	0.125390	+	0.0943594i
$826$	18.2656	−	4.43117i	0.635540	−	0.154180i
$827$	22.2029			0.772069			0.386035	−	0.922484i	$-0.373845\pi$
$827$	22.2029			0.772069			0.386035	+	0.922484i	$0.373845\pi$
$828$	−1.69531	−	14.2873i	−0.0589160	−	0.496517i
$829$	−40.3572			−1.40166			−0.700831	−	0.713327i	$-0.747187\pi$
$829$	−40.3572			−1.40166			−0.700831	+	0.713327i	$0.747187\pi$
$830$	13.2854	−	3.22300i	0.461142	−	0.111872i
$831$	−46.2987	+	19.6883i	−1.60608	+	0.682981i
$832$	−3.00044	+	1.54684i	−0.104022	+	0.0536269i
$833$	0.778173	+	0.611962i	0.0269621	+	0.0212032i
$834$	−18.4801	−	7.96881i	−0.639915	−	0.275937i
$835$	−41.8129	−	29.7748i	−1.44700	−	1.03040i
$836$	0.673370	−	0.583479i	0.0232890	−	0.0201800i
$837$	2.71023	−	15.4042i	0.0936794	−	0.532448i
$838$	−34.5967	−	15.7998i	−1.19512	−	0.545795i
$839$	−9.99077	−	9.52618i	−0.344920	−	0.328880i	0.497740	−	0.867326i	$-0.334163\pi$
$839$	−9.99077	−	9.52618i	−0.344920	−	0.328880i	−0.842660	+	0.538446i	$0.819012\pi$
$840$	−6.50567	+	7.83895i	−0.224467	+	0.270470i
$841$	7.68501	+	10.7921i	0.265000	+	0.372141i
$842$	26.6551	+	10.6711i	0.918594	+	0.367750i
$843$	−13.4591	−	50.7409i	−0.463554	−	1.74761i
$844$	−15.5467	+	21.8323i	−0.535140	+	0.751499i
$845$	3.63041	−	2.33312i	0.124890	−	0.0802619i
$846$	3.01912	−	1.72287i	0.103800	−	0.0592333i
$847$	11.3995	−	17.7380i	0.391692	−	0.609485i
$848$	7.83857	+	1.51076i	0.269178	+	0.0518798i
$849$	−34.0295	−	7.49251i	−1.16789	−	0.257142i
$850$	−0.863269	−	0.498409i	−0.0296099	−	0.0170953i
$851$	−0.0488240	−	1.74663i	−0.00167366	−	0.0598738i
$852$	−25.3683	+	1.75014i	−0.869104	+	0.0599589i
$853$	3.85608	+	15.8950i	0.132030	+	0.544234i	0.998951	+	0.0457892i	$0.0145803\pi$
$853$	3.85608	+	15.8950i	0.132030	+	0.544234i	−0.866921	+	0.498445i	$0.833905\pi$
$854$	−21.0762	−	18.2626i	−0.721212	−	0.624934i
$855$	6.14293	−	0.555355i	0.210084	−	0.0189927i
$856$	12.4930	+	1.79623i	0.427003	+	0.0613938i
$857$	12.0546	−	23.3826i	0.411776	−	0.798735i	−0.588174	−	0.808735i	$-0.700153\pi$
$857$	12.0546	−	23.3826i	0.411776	−	0.798735i	0.999950	+	0.00999994i	$0.00318313\pi$
$858$	−6.81213	−	0.179334i	−0.232562	−	0.00612236i
$859$	−19.4932	+	3.75701i	−0.665100	+	0.128188i	−0.510618	−	0.859808i	$-0.670583\pi$
$859$	−19.4932	+	3.75701i	−0.665100	+	0.128188i	−0.154483	+	0.987995i	$0.549371\pi$
$860$	3.42820	−	8.56324i	0.116901	−	0.292004i
$861$	0.890634	+	5.37925i	0.0303527	+	0.183324i
$862$	−12.5623	+	13.1749i	−0.427872	+	0.448739i
$863$	−2.41304	−	8.21806i	−0.0821409	−	0.279746i	0.908173	−	0.418596i	$-0.137478\pi$
$863$	−2.41304	−	8.21806i	−0.0821409	−	0.279746i	−0.990313	+	0.138850i	$0.955659\pi$
$864$	−3.81837	−	3.52421i	−0.129904	−	0.119896i
$865$	−48.3473	+	6.95130i	−1.64386	+	0.236351i
$866$	−8.76288	+	25.3187i	−0.297775	+	0.860364i
$867$	−24.8094	−	15.2080i	−0.842572	−	0.516491i
$868$	6.57526	−	0.313218i	0.223179	−	0.0106313i
$869$	−12.3261	+	15.6739i	−0.418133	+	0.531699i
$870$	9.58223	+	15.8101i	0.324868	+	0.536014i
$871$	2.86999	−	14.8909i	0.0972459	−	0.504560i
$872$	5.24464	+	1.53996i	0.177606	+	0.0521498i
$873$	2.72482	+	19.6541i	0.0922210	+	0.665191i
$874$	−3.30443	−	1.58830i	−0.111774	−	0.0537249i
$875$	14.0944	−	8.13741i	0.476478	−	0.275095i
$876$	6.21718	−	28.2372i	0.210059	−	0.954046i
$877$	−10.3662	−	29.9511i	−0.350041	−	1.01138i	−0.973335	−	0.229390i	$-0.926327\pi$
$877$	−10.3662	−	29.9511i	−0.350041	−	1.01138i	0.623293	−	0.781988i	$-0.285794\pi$
$878$	5.95558	+	11.5522i	0.200991	+	0.389868i
$879$	22.1457	+	1.63998i	0.746955	+	0.0553153i
$880$	−2.78602	−	1.43629i	−0.0939167	−	0.0484174i
$881$	−2.31325	−	5.06530i	−0.0779353	−	0.170654i	0.866653	−	0.498911i	$-0.166266\pi$
$881$	−2.31325	−	5.06530i	−0.0779353	−	0.170654i	−0.944589	+	0.328256i	$0.893539\pi$
$882$	2.14412	+	6.29753i	0.0721963	+	0.212049i
$883$	−2.58692	−	17.9924i	−0.0870568	−	0.605493i	−0.985914	−	0.167252i	$-0.946511\pi$
$883$	−2.58692	−	17.9924i	−0.0870568	−	0.605493i	0.898857	−	0.438241i	$-0.144398\pi$
$884$	1.50021	−	0.143253i	0.0504575	−	0.00481811i
$885$	−6.73844	+	39.4637i	−0.226510	+	1.32656i
$886$	3.74401	−	15.4330i	0.125782	−	0.518482i
$887$	15.8479	−	11.2852i	0.532120	−	0.378921i	−0.282183	−	0.959360i	$-0.591059\pi$
$887$	15.8479	−	11.2852i	0.532120	−	0.378921i	0.814303	+	0.580440i	$0.197119\pi$
$888$	−0.423309	−	0.468019i	−0.0142053	−	0.0157057i
$889$	2.58689	+	0.895330i	0.0867614	+	0.0300284i
$890$	18.9190	−	8.64004i	0.634168	−	0.289615i
$891$	−3.33067	−	9.94658i	−0.111582	−	0.333223i
$892$	0.367505	−	2.55605i	0.0123050	−	0.0855830i
$893$	0.0421485	−	0.884806i	0.00141045	−	0.0296089i
$894$	−14.5786	−	1.78035i	−0.487581	−	0.0595439i
$895$	34.8317	+	36.5305i	1.16430	+	1.22108i
$896$	1.09345	−	1.89390i	0.0365294	−	0.0632709i
$897$	10.4640	+	26.0151i	0.349383	+	0.868619i
$898$	−6.31057	−	10.9302i	−0.210586	−	0.364746i
$899$	3.36568	−	11.4625i	0.112252	−	0.382294i
$900$	−3.03939	−	5.96926i	−0.101313	−	0.198975i
$901$	−2.99808	−	1.92675i	−0.0998804	−	0.0641892i
$902$	−1.55753	+	0.623540i	−0.0518600	+	0.0207616i
$903$	7.75914	+	10.4196i	0.258208	+	0.346743i
$904$	−1.00977	+	10.5748i	−0.0335845	+	0.351713i
$905$	−3.73355	−	19.3715i	−0.124107	−	0.643930i
$906$	−6.67015	−	31.0385i	−0.221601	−	1.03119i
$907$	0.525082	+	5.49891i	0.0174351	+	0.182588i	0.999994	−	0.00336130i	$-0.00106994\pi$
$907$	0.525082	+	5.49891i	0.0174351	+	0.182588i	−0.982559	+	0.185950i	$0.940464\pi$
$908$	−7.78499	+	2.28588i	−0.258354	+	0.0758595i
$909$	8.96872	+	19.9036i	0.297474	+	0.660160i
$910$	8.24760	−	18.0597i	0.273405	−	0.598674i
$911$	−19.5414	+	15.3675i	−0.647434	+	0.509148i	−0.887022	−	0.461727i	$-0.847230\pi$
$911$	−19.5414	+	15.3675i	−0.647434	+	0.509148i	0.239588	+	0.970875i	$0.422988\pi$
$912$	−1.27986	+	0.339484i	−0.0423805	+	0.0112414i
$913$	−5.89760	−	0.563152i	−0.195182	−	0.0186376i
$914$	−1.44807	−	30.3988i	−0.0478980	−	1.00550i
$915$	53.4967	−	25.8207i	1.76855	−	0.853606i
$916$	19.8244	+	0.944355i	0.655018	+	0.0312024i
$917$	−23.5896	+	27.2239i	−0.778999	+	0.899012i
$918$	0.997799	+	2.09419i	0.0329323	+	0.0691185i
$919$		−	42.7953i		−	1.41169i	−0.708369	−	0.705843i	$-0.750568\pi$
$919$		−	42.7953i		−	1.41169i	0.708369	−	0.705843i	$-0.249432\pi$
$920$	−0.866778	+	12.8687i	−0.0285768	+	0.424269i
$921$	−9.20958	+	6.19945i	−0.303466	+	0.204279i
$922$	1.53945	−	1.46786i	0.0506990	−	0.0483414i
$923$	46.8337	−	16.2093i	1.54155	−	0.533535i
$924$	3.77537	−	2.28818i	0.124200	−	0.0752755i
$925$	−0.302352	−	0.755239i	−0.00994128	−	0.0248321i
$926$	−1.65350	−	2.57290i	−0.0543375	−	0.0845508i
$927$	−33.6801	−	17.5787i	−1.10620	−	0.577361i
$928$	−2.59900	−	2.99941i	−0.0853165	−	0.0984605i
$929$	−18.6369	−	23.6988i	−0.611458	−	0.777532i	0.377455	−	0.926028i	$-0.376799\pi$
$929$	−18.6369	−	23.6988i	−0.611458	−	0.777532i	−0.988913	+	0.148496i	$0.952557\pi$
$930$	−4.93308	+	13.1250i	−0.161762	+	0.430386i
$931$	1.64746	+	0.399670i	0.0539933	+	0.0130986i
$932$	−9.97524	−	2.41997i	−0.326750	−	0.0792687i
$933$	2.44609	−	6.50810i	0.0800815	−	0.213066i
$934$	16.0019	+	20.3480i	0.523597	+	0.665808i
$935$	0.916370	+	1.05755i	0.0299685	+	0.0345855i
$936$	8.97783	+	4.68581i	0.293450	+	0.153161i
$937$	−2.90884	−	4.52625i	−0.0950277	−	0.147866i	0.790485	−	0.612482i	$-0.209829\pi$
$937$	−2.90884	−	4.52625i	−0.0950277	−	0.147866i	−0.885512	+	0.464616i	$0.846192\pi$
$938$	3.65135	+	9.12063i	0.119221	+	0.297799i
$939$	−12.6278	+	7.65350i	−0.412094	+	0.249762i
$940$	−2.94482	+	1.01921i	−0.0960496	+	0.0332431i
$941$	17.9664	−	17.1310i	0.585689	−	0.558454i	−0.338219	−	0.941067i	$-0.609824\pi$
$941$	17.9664	−	17.1310i	0.585689	−	0.558454i	0.923908	+	0.382614i	$0.124976\pi$
$942$	−12.8446	+	8.64640i	−0.418501	+	0.281715i
$943$	4.90172	+	4.86124i	0.159622	+	0.158304i
$944$		−	8.59456i		−	0.279729i
$945$	30.4655	+	2.41053i	0.991042	+	0.0784145i
$946$	−2.61771	+	3.02100i	−0.0851090	+	0.0982211i
$947$	6.61368	+	0.315049i	0.214916	+	0.0102377i	0.154764	−	0.987952i	$-0.450538\pi$
$947$	6.61368	+	0.315049i	0.214916	+	0.0102377i	0.0601521	+	0.998189i	$0.480841\pi$
$948$	26.6871	−	12.8808i	0.866757	−	0.418349i
$949$	2.68131	+	56.2876i	0.0870389	+	1.82717i
$950$	−1.69923	−	0.162257i	−0.0551304	−	0.00526432i
$951$	15.1555	−	4.02000i	0.491451	−	0.130357i
$952$	−0.767428	+	0.603512i	−0.0248725	+	0.0195599i
$953$	6.43132	−	14.0826i	0.208331	−	0.456181i	−0.776405	−	0.630234i	$-0.782959\pi$
$953$	6.43132	−	14.0826i	0.208331	−	0.456181i	0.984736	+	0.174053i	$0.0556863\pi$
$954$	−9.83866	−	21.8342i	−0.318538	−	0.706908i
$955$	48.0959	−	14.1222i	1.55635	−	0.456984i
$956$	2.50119	+	26.1936i	0.0808941	+	0.847161i
$957$	−1.68329	−	7.83292i	−0.0544130	−	0.253202i
$958$	−4.96537	−	25.7628i	−0.160424	−	0.832358i
$959$	0.308122	−	3.22680i	0.00994979	−	0.104199i
$960$	2.78213	+	3.73608i	0.0897929	+	0.120581i
$961$	−20.3679	+	8.15406i	−0.657028	+	0.263034i
$962$	1.03466	+	0.664937i	0.0333589	+	0.0214384i
$963$	−17.1807	−	33.7423i	−0.553641	−	1.08733i
$964$	−2.53076	+	8.61898i	−0.0815103	+	0.277599i
$965$	7.36600	+	12.7583i	0.237120	+	0.410704i
$966$	−14.8144	−	10.5130i	−0.476647	−	0.338252i
$967$	15.4018	−	26.6767i	0.495289	−	0.857866i	−0.504696	−	0.863297i	$-0.668395\pi$
$967$	15.4018	−	26.6767i	0.495289	−	0.857866i	0.999985	+	0.00543102i	$0.00172876\pi$
$968$	−6.65349	−	6.97798i	−0.213851	−	0.224281i
$969$	0.586776	+	0.0716577i	0.0188500	+	0.00230198i
$970$	0.846374	−	17.7676i	0.0271754	−	0.570483i
$971$	−3.35037	+	23.3024i	−0.107519	+	0.747808i	0.862724	+	0.505674i	$0.168756\pi$
$971$	−3.35037	+	23.3024i	−0.107519	+	0.747808i	−0.970243	+	0.242134i	$0.922153\pi$
$972$	−2.04549	+	15.4537i	−0.0656093	+	0.495677i
$973$	−23.1137	+	10.5557i	−0.740990	+	0.338399i
$974$	−28.8305	−	9.97834i	−0.923789	−	0.319727i
$975$	8.75731	+	9.68227i	0.280458	+	0.310081i
$976$	−10.3877	+	7.39703i	−0.332501	+	0.236773i
$977$	−7.06042	+	29.1035i	−0.225883	+	0.931102i	0.740100	+	0.672497i	$0.234778\pi$
$977$	−7.06042	+	29.1035i	−0.225883	+	0.931102i	−0.965983	+	0.258605i	$0.916737\pi$
$978$	−3.64925	+	21.3718i	−0.116690	+	0.683396i
$979$	−8.97257	+	0.856776i	−0.286765	+	0.0273827i
$980$	−0.848731	−	5.90305i	−0.0271117	−	0.188566i
$981$	−5.28515	−	15.5231i	−0.168742	−	0.495614i
$982$	11.1087	+	24.3247i	0.354493	+	0.776232i
$983$	1.15626	+	0.596093i	0.0368790	+	0.0190124i	0.476567	−	0.879138i	$-0.341881\pi$
$983$	1.15626	+	0.596093i	0.0368790	+	0.0190124i	−0.439688	+	0.898150i	$0.644911\pi$
$984$	2.48645	+	0.184133i	0.0792651	+	0.00586993i
$985$	21.8235	+	42.3318i	0.695356	+	1.34880i
$986$	0.579502	+	1.67436i	0.0184551	+	0.0533225i
$987$	0.943741	−	4.28628i	0.0300396	−	0.136434i
$988$	2.23492	−	1.29033i	0.0711023	−	0.0410509i
$989$	15.6881	+	4.94336i	0.498854	+	0.157190i
$990$	1.29132	+	9.31430i	0.0410408	+	0.296028i
$991$	−5.35200	−	1.57149i	−0.170012	−	0.0499200i	0.195619	−	0.980680i	$-0.437328\pi$
$991$	−5.35200	−	1.57149i	−0.170012	−	0.0499200i	−0.365631	+	0.930760i	$0.619147\pi$
$992$	0.569661	−	2.95568i	0.0180868	−	0.0938430i
$993$	−15.6515	−	25.8241i	−0.496686	−	0.819503i
$994$	−19.8467	+	25.2372i	−0.629500	+	0.800475i
$995$	−14.1844	+	0.675686i	−0.449675	+	0.0214207i
$996$	7.50631	+	4.60132i	0.237847	+	0.145798i
$997$	15.2892	−	44.1752i	0.484214	−	1.39904i	−0.393263	−	0.919426i	$-0.628654\pi$
$997$	15.2892	−	44.1752i	0.484214	−	1.39904i	0.877477	−	0.479618i	$-0.159225\pi$
$998$	−21.0607	+	3.02807i	−0.666663	+	0.0958517i
$999$	−0.416394	+	1.84681i	−0.0131741	+	0.0584305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.5.18	✓	480
9.2	odd	6	inner	414.2.p.a.281.13	yes	480
23.14	odd	22	inner	414.2.p.a.221.13	yes	480
207.83	even	66	inner	414.2.p.a.83.18	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.5.18	✓	480	1.1	even	1	trivial
414.2.p.a.83.18	yes	480	207.83	even	66	inner
414.2.p.a.221.13	yes	480	23.14	odd	22	inner
414.2.p.a.281.13	yes	480	9.2	odd	6	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.971812 - 0.235759i) q^{2} +(-0.209960 + 1.71928i) q^{3} +(0.888835 - 0.458227i) q^{4} +(2.11401 + 1.66247i) q^{5} +(0.201293 + 1.72031i) q^{6} +(1.78139 + 1.26852i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.91183 - 0.721960i) q^{9} +O(q^{10})\)	\(q+(0.971812 - 0.235759i) q^{2} +(-0.209960 + 1.71928i) q^{3} +(0.888835 - 0.458227i) q^{4} +(2.11401 + 1.66247i) q^{5} +(0.201293 + 1.72031i) q^{6} +(1.78139 + 1.26852i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.91183 - 0.721960i) q^{9} +(2.44636 + 1.11721i) q^{10} +(-0.843505 - 0.804280i) q^{11} +(0.601199 + 1.62436i) q^{12} +(-1.95810 - 2.74977i) q^{13} +(2.03024 + 0.812785i) q^{14} +(-3.30211 + 3.28551i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-0.375565 + 0.241361i) q^{17} +(-2.99996 - 0.0151179i) q^{18} +(-0.413310 + 0.643123i) q^{19} +(2.64079 + 0.508971i) q^{20} +(-2.55496 + 2.79636i) q^{21} +(-1.00934 - 0.582745i) q^{22} +(-0.549609 + 4.76423i) q^{23} +(0.967210 + 1.43684i) q^{24} +(0.526411 + 2.16990i) q^{25} +(-2.55119 - 2.21062i) q^{26} +(1.85262 - 4.85467i) q^{27} +(2.16463 + 0.311227i) q^{28} +(1.81860 - 3.52760i) q^{29} +(-2.43444 + 3.97140i) q^{30} +(2.95568 - 0.569661i) q^{31} +(0.371662 - 0.928368i) q^{32} +(1.55988 - 1.28135i) q^{33} +(-0.308076 + 0.323101i) q^{34} +(1.65698 + 5.64317i) q^{35} +(-2.91896 + 0.692576i) q^{36} +(-0.360632 + 0.0518511i) q^{37} +(-0.250038 + 0.722436i) q^{38} +(5.13874 - 2.78918i) q^{39} +(2.68635 - 0.127966i) q^{40} +(0.889830 - 1.13151i) q^{41} +(-1.82367 + 3.31989i) q^{42} +(0.649086 - 3.36778i) q^{43} +(-1.11828 - 0.328357i) q^{44} +(-4.95540 - 6.36707i) q^{45} +(0.589094 + 4.75951i) q^{46} +(-1.00347 + 0.579352i) q^{47} +(1.27869 + 1.16831i) q^{48} +(-0.725276 - 2.09555i) q^{49} +(1.02314 + 1.98462i) q^{50} +(-0.336113 - 0.696378i) q^{51} +(-3.00044 - 1.54684i) q^{52} +(3.31619 + 7.26144i) q^{53} +(0.655864 - 5.15459i) q^{54} +(-0.446080 - 3.10256i) q^{55} +(2.17699 - 0.207877i) q^{56} +(-1.01893 - 0.845626i) q^{57} +(0.935677 - 3.85691i) q^{58} +(7.00092 - 4.98533i) q^{59} +(-1.42952 + 4.43339i) q^{60} +(-12.0509 - 4.17085i) q^{61} +(2.73806 - 1.25043i) q^{62} +(-4.27129 - 4.97981i) q^{63} +(0.142315 - 0.989821i) q^{64} +(0.431977 - 9.06831i) q^{65} +(1.21382 - 1.61299i) q^{66} +(3.10010 + 3.25130i) q^{67} +(-0.223218 + 0.386624i) q^{68} +(-8.07565 - 1.94523i) q^{69} +(2.94070 + 5.09345i) q^{70} +(-4.13617 + 14.0865i) q^{71} +(-2.67340 + 1.36122i) q^{72} +(-14.0432 - 9.02505i) q^{73} +(-0.338242 + 0.135412i) q^{74} +(-3.84118 + 0.449455i) q^{75} +(-0.0726687 + 0.761021i) q^{76} +(-0.482364 - 2.50274i) q^{77} +(4.33631 - 3.92206i) q^{78} +(-1.62628 - 17.0312i) q^{79} +(2.58045 - 0.757690i) q^{80} +(7.95755 + 4.20445i) q^{81} +(0.597983 - 1.30940i) q^{82} +(3.99567 - 3.14223i) q^{83} +(-0.989572 + 3.65626i) q^{84} +(-1.19520 - 0.114128i) q^{85} +(-0.163195 - 3.42587i) q^{86} +(5.68309 + 3.86734i) q^{87} +(-1.16417 - 0.0554563i) q^{88} +(5.06440 - 5.84463i) q^{89} +(-6.31680 - 5.01931i) q^{90} -7.38229i q^{91} +(1.69459 + 4.48647i) q^{92} +(0.358830 + 5.20125i) q^{93} +(-0.838594 + 0.799598i) q^{94} +(-1.94292 + 0.672450i) q^{95} +(1.51809 + 0.833911i) q^{96} +(-2.45819 - 6.14025i) q^{97} +(-1.19888 - 1.86549i) q^{98} +(1.87549 + 2.95091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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