LMFDB - Embedded newform 216.2.v.b.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.160171 - 1.40511i) q^{2} +(-1.03533 - 1.38855i) q^{3} +(-1.94869 - 0.450118i) q^{4} +(-1.93709 - 0.705042i) q^{5} +(-2.11691 + 1.23236i) q^{6} +(0.744451 + 0.131267i) q^{7} +(-0.944592 + 2.66604i) q^{8} +(-0.856167 + 2.87524i) q^{9} +O(q^{10})$	\(q+(0.160171 - 1.40511i) q^{2} +(-1.03533 - 1.38855i) q^{3} +(-1.94869 - 0.450118i) q^{4} +(-1.93709 - 0.705042i) q^{5} +(-2.11691 + 1.23236i) q^{6} +(0.744451 + 0.131267i) q^{7} +(-0.944592 + 2.66604i) q^{8} +(-0.856167 + 2.87524i) q^{9} +(-1.30093 + 2.60890i) q^{10} +(-0.949342 - 2.60830i) q^{11} +(1.39253 + 3.17189i) q^{12} +(-0.421307 - 0.502095i) q^{13} +(0.303684 - 1.02501i) q^{14} +(1.02654 + 3.41970i) q^{15} +(3.59479 + 1.75428i) q^{16} +(-3.79256 + 2.18964i) q^{17} +(3.90290 + 1.66354i) q^{18} +(0.155896 - 0.270019i) q^{19} +(3.45743 + 2.24583i) q^{20} +(-0.588484 - 1.16962i) q^{21} +(-3.81701 + 0.916159i) q^{22} +(-1.32831 - 7.53324i) q^{23} +(4.67990 - 1.44862i) q^{24} +(-0.575004 - 0.482485i) q^{25} +(-0.772981 + 0.511564i) q^{26} +(4.87884 - 1.78799i) q^{27} +(-1.39162 - 0.590889i) q^{28} +(-5.89474 - 4.94627i) q^{29} +(4.96950 - 0.894670i) q^{30} +(4.16197 - 0.733867i) q^{31} +(3.04075 - 4.77010i) q^{32} +(-2.63888 + 4.01867i) q^{33} +(2.46923 + 5.67970i) q^{34} +(-1.34952 - 0.779144i) q^{35} +(2.96260 - 5.21757i) q^{36} +(-2.70478 + 1.56160i) q^{37} +(-0.354438 - 0.262301i) q^{38} +(-0.260992 + 1.10484i) q^{39} +(3.70942 - 4.49836i) q^{40} +(4.31331 + 5.14040i) q^{41} +(-1.73770 + 0.639548i) q^{42} +(-3.00565 + 1.09397i) q^{43} +(0.675932 + 5.51008i) q^{44} +(3.68563 - 4.96594i) q^{45} +(-10.7978 + 0.659821i) q^{46} +(1.89499 - 10.7470i) q^{47} +(-1.28589 - 6.80783i) q^{48} +(-6.04087 - 2.19870i) q^{49} +(-0.770046 + 0.730665i) q^{50} +(6.96700 + 2.99917i) q^{51} +(0.594995 + 1.16806i) q^{52} +0.876371 q^{53} +(-1.73088 - 7.14171i) q^{54} +5.72182i q^{55} +(-1.05316 + 1.86074i) q^{56} +(-0.536341 + 0.0630905i) q^{57} +(-7.89425 + 7.49053i) q^{58} +(2.94714 - 8.09720i) q^{59} +(-0.461142 - 7.12601i) q^{60} +(12.1748 + 2.14675i) q^{61} +(-0.364538 - 5.96558i) q^{62} +(-1.01480 + 2.02808i) q^{63} +(-6.21549 - 5.03663i) q^{64} +(0.462111 + 1.26964i) q^{65} +(5.22402 + 4.35160i) q^{66} +(3.32854 - 2.79298i) q^{67} +(8.37613 - 2.55982i) q^{68} +(-9.08507 + 9.64386i) q^{69} +(-1.31094 + 1.77143i) q^{70} +(7.08002 + 12.2629i) q^{71} +(-6.85675 - 4.99850i) q^{72} +(7.17342 - 12.4247i) q^{73} +(1.76100 + 4.05064i) q^{74} +(-0.0746363 + 1.29796i) q^{75} +(-0.425333 + 0.456012i) q^{76} +(-0.364356 - 2.06636i) q^{77} +(1.51063 + 0.543688i) q^{78} +(-7.09014 + 8.44970i) q^{79} +(-5.72657 - 5.93267i) q^{80} +(-7.53396 - 4.92336i) q^{81} +(7.91372 - 5.23734i) q^{82} +(-7.10823 + 8.47125i) q^{83} +(0.620308 + 2.54410i) q^{84} +(8.89031 - 1.56760i) q^{85} +(1.05573 + 4.39851i) q^{86} +(-0.765146 + 13.3062i) q^{87} +(7.85055 - 0.0672036i) q^{88} +(5.55986 + 3.20999i) q^{89} +(-6.38739 - 5.97413i) q^{90} +(-0.247734 - 0.429088i) q^{91} +(-0.802379 + 15.2778i) q^{92} +(-5.32804 - 5.01932i) q^{93} +(-14.7972 - 4.38403i) q^{94} +(-0.492358 + 0.413138i) q^{95} +(-9.77173 + 0.716400i) q^{96} +(1.59192 - 0.579411i) q^{97} +(-4.05700 + 8.13595i) q^{98} +(8.31226 - 0.496445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.160171	−	1.40511i	0.113258	−	0.993566i
$2$	0.160171	−	1.40511i	0.113258	−	0.993566i
$3$	−1.03533	−	1.38855i	−0.597750	−	0.801682i
$3$	−1.03533	−	1.38855i	−0.597750	−	0.801682i
$4$	−1.94869	−	0.450118i	−0.974345	−	0.225059i
$5$	−1.93709	−	0.705042i	−0.866291	−	0.315304i	−0.129627	−	0.991563i	$-0.541378\pi$
$5$	−1.93709	−	0.705042i	−0.866291	−	0.315304i	−0.736664	+	0.676259i	$0.763600\pi$
$6$	−2.11691	+	1.23236i	−0.864224	+	0.503107i
$7$	0.744451	+	0.131267i	0.281376	+	0.0496142i	0.312555	−	0.949900i	$-0.398815\pi$
$7$	0.744451	+	0.131267i	0.281376	+	0.0496142i	−0.0311792	+	0.999514i	$0.509926\pi$
$8$	−0.944592	+	2.66604i	−0.333964	+	0.942586i
$9$	−0.856167	+	2.87524i	−0.285389	+	0.958412i
$10$	−1.30093	+	2.60890i	−0.411390	+	0.825006i
$11$	−0.949342	−	2.60830i	−0.286237	−	0.786431i	−0.996584	−	0.0825793i	$-0.973684\pi$
$11$	−0.949342	−	2.60830i	−0.286237	−	0.786431i	0.710347	−	0.703852i	$-0.248538\pi$
$12$	1.39253	+	3.17189i	0.401989	+	0.915644i
$13$	−0.421307	−	0.502095i	−0.116850	−	0.139256i	0.704449	−	0.709755i	$-0.251194\pi$
$13$	−0.421307	−	0.502095i	−0.116850	−	0.139256i	−0.821298	+	0.570499i	$0.806750\pi$
$14$	0.303684	−	1.02501i	0.0811631	−	0.273946i
$15$	1.02654	+	3.41970i	0.265052	+	0.882964i
$16$	3.59479	+	1.75428i	0.898697	+	0.438571i
$17$	−3.79256	+	2.18964i	−0.919832	+	0.531065i	−0.883581	−	0.468278i	$-0.844875\pi$
$17$	−3.79256	+	2.18964i	−0.919832	+	0.531065i	−0.0362504	+	0.999343i	$0.511541\pi$
$18$	3.90290	+	1.66354i	0.919922	+	0.392101i
$19$	0.155896	−	0.270019i	0.0357649	−	0.0619467i	−0.847589	−	0.530653i	$-0.821947\pi$
$19$	0.155896	−	0.270019i	0.0357649	−	0.0619467i	0.883354	+	0.468707i	$0.155280\pi$
$20$	3.45743	+	2.24583i	0.773104	+	0.502182i
$21$	−0.588484	−	1.16962i	−0.128418	−	0.255231i
$22$	−3.81701	+	0.916159i	−0.813789	+	0.195326i
$23$	−1.32831	−	7.53324i	−0.276973	−	1.57079i	−0.732626	−	0.680632i	$-0.761705\pi$
$23$	−1.32831	−	7.53324i	−0.276973	−	1.57079i	0.455653	−	0.890157i	$-0.349406\pi$
$24$	4.67990	−	1.44862i	0.955281	−	0.295698i
$25$	−0.575004	−	0.482485i	−0.115001	−	0.0964971i
$26$	−0.772981	+	0.511564i	−0.151594	+	0.100326i
$27$	4.87884	−	1.78799i	0.938933	−	0.344100i
$28$	−1.39162	−	0.590889i	−0.262991	−	0.111668i
$29$	−5.89474	−	4.94627i	−1.09463	−	0.918500i	−0.0975734	−	0.995228i	$-0.531108\pi$
$29$	−5.89474	−	4.94627i	−1.09463	−	0.918500i	−0.997052	+	0.0767286i	$0.975553\pi$
$30$	4.96950	−	0.894670i	0.907302	−	0.163344i
$31$	4.16197	−	0.733867i	0.747511	−	0.131806i	0.213099	−	0.977031i	$-0.431644\pi$
$31$	4.16197	−	0.733867i	0.747511	−	0.131806i	0.534412	+	0.845224i	$0.320533\pi$
$32$	3.04075	−	4.77010i	0.537534	−	0.843242i
$33$	−2.63888	+	4.01867i	−0.459369	+	0.699561i
$34$	2.46923	+	5.67970i	0.423469	+	0.974061i
$35$	−1.34952	−	0.779144i	−0.228110	−	0.131699i
$36$	2.96260	−	5.21757i	0.493767	−	0.869594i
$37$	−2.70478	+	1.56160i	−0.444662	+	0.256726i	−0.705573	−	0.708637i	$-0.749310\pi$
$37$	−2.70478	+	1.56160i	−0.444662	+	0.256726i	0.260911	+	0.965363i	$0.415977\pi$
$38$	−0.354438	−	0.262301i	−0.0574974	−	0.0425508i
$39$	−0.260992	+	1.10484i	−0.0417921	+	0.176917i
$40$	3.70942	−	4.49836i	0.586511	−	0.711254i
$41$	4.31331	+	5.14040i	0.673626	+	0.802796i	0.989273	−	0.146081i	$-0.0466660\pi$
$41$	4.31331	+	5.14040i	0.673626	+	0.802796i	−0.315647	+	0.948877i	$0.602222\pi$
$42$	−1.73770	+	0.639548i	−0.268133	+	0.0986844i
$43$	−3.00565	+	1.09397i	−0.458358	+	0.166829i	−0.560871	−	0.827903i	$-0.689534\pi$
$43$	−3.00565	+	1.09397i	−0.458358	+	0.166829i	0.102513	+	0.994732i	$0.467312\pi$
$44$	0.675932	+	5.51008i	0.101901	+	0.830675i
$45$	3.68563	−	4.96594i	0.549421	−	0.740279i
$46$	−10.7978	+	0.659821i	−1.59205	+	0.0972854i
$47$	1.89499	−	10.7470i	0.276412	−	1.56761i	−0.458028	−	0.888938i	$-0.651444\pi$
$47$	1.89499	−	10.7470i	0.276412	−	1.56761i	0.734440	−	0.678673i	$-0.237445\pi$
$48$	−1.28589	−	6.80783i	−0.185602	−	0.982625i
$49$	−6.04087	−	2.19870i	−0.862982	−	0.314100i
$50$	−0.770046	+	0.730665i	−0.108901	+	0.103332i
$51$	6.96700	+	2.99917i	0.975575	+	0.419968i
$52$	0.594995	+	1.16806i	0.0825110	+	0.161981i
$53$	0.876371			0.120379			0.0601894	−	0.998187i	$-0.480830\pi$
$53$	0.876371			0.120379			0.0601894	+	0.998187i	$0.480830\pi$
$54$	−1.73088	−	7.14171i	−0.235544	−	0.971864i
$55$			5.72182i			0.771530i
$56$	−1.05316	+	1.86074i	−0.140735	+	0.248652i
$57$	−0.536341	+	0.0630905i	−0.0710401	+	0.00835654i
$58$	−7.89425	+	7.49053i	−1.03657	+	0.983554i
$59$	2.94714	−	8.09720i	0.383685	−	1.05417i	−0.586107	−	0.810233i	$-0.699340\pi$
$59$	2.94714	−	8.09720i	0.383685	−	1.05417i	0.969792	−	0.243932i	$-0.0784374\pi$
$60$	−0.461142	−	7.12601i	−0.0595331	−	0.919964i
$61$	12.1748	+	2.14675i	1.55883	+	0.274863i	0.885556	−	0.464532i	$-0.153777\pi$
$61$	12.1748	+	2.14675i	1.55883	+	0.274863i	0.673271	+	0.739395i	$0.264889\pi$
$62$	−0.364538	−	5.96558i	−0.0462964	−	0.757630i
$63$	−1.01480	+	2.02808i	−0.127852	+	0.255515i
$64$	−6.21549	−	5.03663i	−0.776936	−	0.629579i
$65$	0.462111	+	1.26964i	0.0573178	+	0.157479i
$66$	5.22402	+	4.35160i	0.643032	+	0.535645i
$67$	3.32854	−	2.79298i	0.406646	−	0.341216i	−0.416410	−	0.909177i	$-0.636712\pi$
$67$	3.32854	−	2.79298i	0.406646	−	0.341216i	0.823056	+	0.567961i	$0.192267\pi$
$68$	8.37613	−	2.55982i	1.01575	−	0.310424i
$69$	−9.08507	+	9.64386i	−1.09371	+	1.16098i
$70$	−1.31094	+	1.77143i	−0.156687	+	0.211726i
$71$	7.08002	+	12.2629i	0.840243	+	1.45534i	0.889689	+	0.456567i	$0.150921\pi$
$71$	7.08002	+	12.2629i	0.840243	+	1.45534i	−0.0494456	+	0.998777i	$0.515745\pi$
$72$	−6.85675	−	4.99850i	−0.808076	−	0.589078i
$73$	7.17342	−	12.4247i	0.839585	−	1.45420i	−0.0506575	−	0.998716i	$-0.516132\pi$
$73$	7.17342	−	12.4247i	0.839585	−	1.45420i	0.890242	−	0.455487i	$-0.150535\pi$
$74$	1.76100	+	4.05064i	0.204712	+	0.470878i
$75$	−0.0746363	+	1.29796i	−0.00861826	+	0.149875i
$76$	−0.425333	+	0.456012i	−0.0487891	+	0.0523082i
$77$	−0.364356	−	2.06636i	−0.0415222	−	0.235484i
$78$	1.51063	+	0.543688i	0.171045	+	0.0615605i
$79$	−7.09014	+	8.44970i	−0.797703	+	0.950666i	−0.999587	−	0.0287437i	$-0.990849\pi$
$79$	−7.09014	+	8.44970i	−0.797703	+	0.950666i	0.201883	+	0.979410i	$0.435294\pi$
$80$	−5.72657	−	5.93267i	−0.640250	−	0.663293i
$81$	−7.53396	−	4.92336i	−0.837106	−	0.547040i
$82$	7.91372	−	5.23734i	0.873924	−	0.578368i
$83$	−7.10823	+	8.47125i	−0.780229	+	0.929841i	−0.998944	−	0.0459479i	$-0.985369\pi$
$83$	−7.10823	+	8.47125i	−0.780229	+	0.929841i	0.218715	+	0.975789i	$0.429814\pi$
$84$	0.620308	+	2.54410i	0.0676811	+	0.277585i
$85$	8.89031	−	1.56760i	0.964289	−	0.170030i
$86$	1.05573	+	4.39851i	0.113842	+	0.474303i
$87$	−0.765146	+	13.3062i	−0.0820322	+	1.42658i
$88$	7.85055	−	0.0672036i	0.836872	−	0.00716393i
$89$	5.55986	+	3.20999i	0.589344	+	0.340258i	0.764838	−	0.644222i	$-0.222819\pi$
$89$	5.55986	+	3.20999i	0.589344	+	0.340258i	−0.175494	+	0.984481i	$0.556152\pi$
$90$	−6.38739	−	5.97413i	−0.673290	−	0.629729i
$91$	−0.247734	−	0.429088i	−0.0259696	−	0.0449807i
$92$	−0.802379	+	15.2778i	−0.0836537	+	1.59283i
$93$	−5.32804	−	5.01932i	−0.552492	−	0.520479i
$94$	−14.7972	−	4.38403i	−1.52622	−	0.452179i
$95$	−0.492358	+	0.413138i	−0.0505149	+	0.0423870i
$96$	−9.77173	+	0.716400i	−0.997323	+	0.0731172i
$97$	1.59192	−	0.579411i	0.161635	−	0.0588303i	−0.259935	−	0.965626i	$-0.583701\pi$
$97$	1.59192	−	0.579411i	0.161635	−	0.0588303i	0.421570	+	0.906796i	$0.361479\pi$
$98$	−4.05700	+	8.13595i	−0.409819	+	0.821855i
$99$	8.31226	−	0.496445i	0.835414	−	0.0498946i
$100$	0.903328	+	1.19903i	0.0903328	+	0.119903i
$101$	−0.0772824	+	0.438290i	−0.00768988	+	0.0436115i	−0.988411	−	0.151800i	$-0.951493\pi$
$101$	−0.0772824	+	0.438290i	−0.00768988	+	0.0436115i	0.980721	+	0.195411i	$0.0626042\pi$
$102$	5.33010	−	9.30905i	0.527758	−	0.921733i
$103$	4.31107	−	11.8446i	0.424782	−	1.16708i	−0.524157	−	0.851621i	$-0.675620\pi$
$103$	4.31107	−	11.8446i	0.424782	−	1.16708i	0.948940	−	0.315458i	$-0.102158\pi$
$104$	1.73657	−	0.648946i	0.170284	−	0.0636344i
$105$	0.315317	+	2.68055i	0.0307718	+	0.261595i
$106$	0.140370	−	1.23140i	0.0136339	−	0.119604i
$107$		−	9.16557i		−	0.886069i	−0.896505	−	0.443034i	$-0.853902\pi$
$107$		−	9.16557i		−	0.886069i	0.896505	−	0.443034i	$-0.146098\pi$
$108$	−10.3122	+	1.28819i	−0.992288	+	0.123956i
$109$			12.6300i			1.20973i	0.796327	+	0.604867i	$0.206774\pi$
$109$			12.6300i			1.20973i	−0.796327	+	0.604867i	$0.793226\pi$
$110$	8.03981	+	0.916473i	0.766566	+	0.0873822i
$111$	4.96872	+	2.13895i	0.471610	+	0.203020i
$112$	2.44586	+	1.77785i	0.231112	+	0.167991i
$113$	−4.39773	+	12.0827i	−0.413703	+	1.13664i	0.541503	+	0.840699i	$0.317856\pi$
$113$	−4.39773	+	12.0827i	−0.413703	+	1.13664i	−0.955206	+	0.295942i	$0.904367\pi$
$114$	0.00274283	+	0.763725i	0.000256889	+	0.0715294i
$115$	−2.73819	+	15.5291i	−0.255338	+	1.44809i
$116$	9.26061	+	12.2921i	0.859826	+	1.14129i
$117$	1.80435	−	0.781481i	0.166812	−	0.0722479i
$118$	−10.9054	−	5.43801i	−1.00393	−	0.500609i
$119$	−3.11080	+	1.13224i	−0.285167	+	0.103792i
$120$	−10.0867	−	0.493427i	−0.920787	−	0.0450435i
$121$	2.52453	−	2.11833i	0.229503	−	0.192576i
$122$	4.96649	−	16.7632i	0.449645	−	1.51767i
$123$	2.67201	−	11.3113i	0.240927	−	1.01991i
$124$	−8.44071	−	0.443298i	−0.757998	−	0.0398094i
$125$	5.92717	+	10.2662i	0.530142	+	0.918233i
$126$	2.68715	+	1.75075i	0.239390	+	0.155969i
$127$	−3.31139	−	1.91183i	−0.293838	−	0.169648i	0.345833	−	0.938296i	$-0.387596\pi$
$127$	−3.31139	−	1.91183i	−0.293838	−	0.169648i	−0.639671	+	0.768648i	$0.720930\pi$
$128$	−8.07259	+	7.92675i	−0.713523	+	0.700632i
$129$	4.63089	+	3.04089i	0.407727	+	0.267736i
$130$	1.85801	−	0.445959i	0.162958	−	0.0391132i
$131$	−13.1264	+	2.31454i	−1.14686	+	0.202222i	−0.714604	−	0.699529i	$-0.753393\pi$
$131$	−13.1264	+	2.31454i	−1.14686	+	0.202222i	−0.432255	+	0.901751i	$0.642282\pi$
$132$	6.95123	−	6.64334i	0.605027	−	0.578228i
$133$	0.151501	−	0.180552i	0.0131368	−	0.0156559i
$134$	−3.39131	−	5.12433i	−0.292965	−	0.442675i
$135$	−10.7113	+	0.0237142i	−0.921886	+	0.00204099i
$136$	−2.25523	−	12.1794i	−0.193384	−	1.04438i
$137$	8.71665	−	10.3881i	0.744714	−	0.887516i	−0.252065	−	0.967710i	$-0.581110\pi$
$137$	8.71665	−	10.3881i	0.744714	−	0.887516i	0.996779	+	0.0801947i	$0.0255542\pi$
$138$	12.0955	+	14.3102i	1.02964	+	1.21817i
$139$	0.183415	+	1.04020i	0.0155571	+	0.0882286i	0.991598	−	0.129360i	$-0.0412921\pi$
$139$	0.183415	+	1.04020i	0.0155571	+	0.0882286i	−0.976041	+	0.217588i	$0.930181\pi$
$140$	2.27908	+	2.12575i	0.192618	+	0.179659i
$141$	−16.8847	+	8.49544i	−1.42195	+	0.715445i
$142$	18.3649	−	7.98405i	1.54114	−	0.670007i
$143$	−0.909646	+	1.57555i	−0.0760685	+	0.131754i
$144$	−8.12171	+	8.83390i	−0.676809	+	0.736158i
$145$	7.93129	+	13.7374i	0.658658	+	1.14083i
$146$	−16.3092	−	12.0696i	−1.34976	−	0.998883i
$147$	3.20131	+	10.6645i	0.264040	+	0.879590i
$148$	5.97368	−	1.82561i	0.491033	−	0.150064i
$149$	−17.2009	+	14.4333i	−1.40915	+	1.18242i	−0.452294	+	0.891869i	$0.649394\pi$
$149$	−17.2009	+	14.4333i	−1.40915	+	1.18242i	−0.956859	+	0.290551i	$0.906161\pi$
$150$	1.81182	+	0.312768i	0.147935	+	0.0255374i
$151$	−6.78428	−	18.6396i	−0.552097	−	1.51687i	−0.830842	−	0.556508i	$-0.812141\pi$
$151$	−6.78428	−	18.6396i	−0.552097	−	1.51687i	0.278746	−	0.960365i	$-0.410081\pi$
$152$	0.572623	+	0.670682i	0.0464459	+	0.0543995i
$153$	−3.04866	−	12.7792i	−0.246469	−	1.03314i
$154$	−2.96184	+	0.180989i	−0.238672	+	0.0145845i
$155$	−8.57950	−	1.51280i	−0.689122	−	0.121511i
$156$	1.00590	−	2.03552i	0.0805367	−	0.162972i
$157$	5.37486	−	14.7673i	0.428960	−	1.17856i	−0.517485	−	0.855693i	$-0.673132\pi$
$157$	5.37486	−	14.7673i	0.428960	−	1.17856i	0.946445	−	0.322866i	$-0.104646\pi$
$158$	10.7372	+	11.3159i	0.854202	+	0.900242i
$159$	−0.907337	−	1.21689i	−0.0719565	−	0.0965055i
$160$	−9.25331	+	7.09624i	−0.731539	+	0.561007i
$161$		−	5.78249i		−	0.455724i
$162$	−8.12461	+	9.79748i	−0.638330	+	0.769763i
$163$	−11.3706			−0.890618			−0.445309	−	0.895377i	$-0.646906\pi$
$163$	−11.3706			−0.890618			−0.445309	+	0.895377i	$0.646906\pi$
$164$	−6.09151	−	11.9585i	−0.475667	−	0.933806i
$165$	7.94506	−	5.92400i	0.618522	−	0.461182i
$166$	10.7645	+	11.3447i	0.835491	+	0.880521i
$167$	10.8721	+	3.95710i	0.841305	+	0.306210i	0.726490	−	0.687177i	$-0.241150\pi$
$167$	10.8721	+	3.95710i	0.841305	+	0.306210i	0.114815	+	0.993387i	$0.463373\pi$
$168$	3.67411	−	0.464110i	0.283464	−	0.0358069i
$169$	2.18283	−	12.3794i	0.167910	−	0.952264i
$170$	−0.778684	−	12.7430i	−0.0597224	−	0.977342i
$171$	0.642896	+	0.679419i	0.0491635	+	0.0519564i
$172$	6.34950	−	0.778906i	0.484145	−	0.0593910i
$173$	6.70079	−	2.43889i	0.509452	−	0.185425i	−0.0744886	−	0.997222i	$-0.523732\pi$
$173$	6.70079	−	2.43889i	0.509452	−	0.185425i	0.583940	+	0.811797i	$0.301510\pi$
$174$	18.5742	+	3.20639i	1.40811	+	0.243076i
$175$	−0.364728	−	0.434665i	−0.0275708	−	0.0328576i
$176$	1.16301	−	11.0417i	0.0876649	−	0.832298i
$177$	−14.2947	+	4.29104i	−1.07445	+	0.322535i
$178$	5.40093	−	7.29809i	0.404817	−	0.547015i
$179$	5.44606	−	3.14429i	0.407058	−	0.235015i	−0.282467	−	0.959277i	$-0.591153\pi$
$179$	5.44606	−	3.14429i	0.407058	−	0.235015i	0.689525	+	0.724262i	$0.257819\pi$
$180$	−9.41741	+	8.01812i	−0.701933	+	0.597635i
$181$	12.3575	+	7.13460i	0.918525	+	0.530311i	0.883164	−	0.469064i	$-0.155409\pi$
$181$	12.3575	+	7.13460i	0.918525	+	0.530311i	0.0353608	+	0.999375i	$0.488742\pi$
$182$	−0.642598	+	0.279367i	−0.0476325	+	0.0207081i
$183$	−9.62414	−	19.1280i	−0.711437	−	1.41398i
$184$	21.3386	+	3.57451i	1.57310	+	0.263516i
$185$	6.34038	−	1.11798i	0.466154	−	0.0821955i
$186$	−7.90612	+	6.68255i	−0.579705	+	0.489988i
$187$	9.31166	+	7.81341i	0.680936	+	0.571373i
$188$	−8.53016	+	20.0896i	−0.622126	+	1.46519i
$189$	3.86676	−	0.690644i	0.281265	−	0.0502370i
$190$	0.501644	+	0.757992i	0.0363931	+	0.0549905i
$191$	−7.59946	−	6.37671i	−0.549878	−	0.461402i	0.325022	−	0.945706i	$-0.394628\pi$
$191$	−7.59946	−	6.37671i	−0.549878	−	0.461402i	−0.874900	+	0.484304i	$0.839073\pi$
$192$	−0.558530	+	13.8451i	−0.0403084	+	0.999187i
$193$	−1.18184	−	6.70255i	−0.0850707	−	0.482460i	−0.997341	−	0.0728719i	$-0.976784\pi$
$193$	−1.18184	−	6.70255i	−0.0850707	−	0.482460i	0.912271	−	0.409588i	$-0.134328\pi$
$194$	−0.559159	−	2.32963i	−0.0401452	−	0.167258i
$195$	1.28452	−	1.95617i	0.0919867	−	0.140084i
$196$	10.7821	+	7.00369i	0.770151	+	0.500263i
$197$	3.08336	−	5.34054i	0.219681	−	0.380498i	−0.735030	−	0.678035i	$-0.762832\pi$
$197$	3.08336	−	5.34054i	0.219681	−	0.380498i	0.954710	+	0.297537i	$0.0961652\pi$
$198$	0.633825	−	11.7592i	0.0450440	−	0.835689i
$199$	2.83677	−	1.63781i	0.201093	−	0.116101i	−0.396072	−	0.918219i	$-0.629627\pi$
$199$	2.83677	−	1.63781i	0.201093	−	0.116101i	0.597165	+	0.802118i	$0.296294\pi$
$200$	1.82947	−	1.07723i	0.129363	−	0.0761715i
$201$	−7.32435	−	1.73019i	−0.516620	−	0.122038i
$202$	0.603469	+	0.178792i	0.0424599	+	0.0125798i
$203$	−3.73906	−	4.45604i	−0.262431	−	0.312753i
$204$	−12.2265	−	8.98044i	−0.856029	−	0.628756i
$205$	−4.73105	−	12.9985i	−0.330431	−	0.907852i
$206$	−15.9524	−	7.95470i	−1.11146	−	0.554230i
$207$	22.7971	+	2.63050i	1.58451	+	0.182832i
$208$	−0.633694	−	2.54401i	−0.0439388	−	0.176396i
$209$	−0.852289	−	0.150282i	−0.0589541	−	0.0103952i
$210$	3.81698	−	0.0137082i	0.263397	−	0.000945958i
$211$	6.00891	+	2.18706i	0.413670	+	0.150564i	0.540467	−	0.841365i	$-0.318247\pi$
$211$	6.00891	+	2.18706i	0.413670	+	0.150564i	−0.126797	+	0.991929i	$0.540470\pi$
$212$	−1.70778	−	0.394471i	−0.117290	−	0.0270924i
$213$	9.69759	−	22.5272i	0.664468	−	1.54354i
$214$	−12.8787	−	1.46806i	−0.880368	−	0.100355i
$215$	6.59350			0.449673
$216$	0.158343	+	14.6961i	0.0107739	+	0.999942i
$217$	3.19471			0.216871
$218$	17.7466	+	2.02296i	1.20195	+	0.137012i
$219$	−24.6793	+	2.90306i	−1.66767	+	0.196170i
$220$	2.57550	−	11.1501i	0.173640	−	0.751737i
$221$	2.69724	+	0.981715i	0.181436	+	0.0660373i
$222$	3.80131	−	6.63902i	0.255127	−	0.445582i
$223$	−16.3621	−	2.88507i	−1.09568	−	0.193199i	−0.403543	−	0.914961i	$-0.632221\pi$
$223$	−16.3621	−	2.88507i	−1.09568	−	0.193199i	−0.692141	+	0.721762i	$0.743333\pi$
$224$	2.88984	−	3.15195i	0.193086	−	0.210599i
$225$	1.87956	−	1.24018i	0.125304	−	0.0826789i
$226$	16.2731	+	8.11461i	1.08247	+	0.539776i
$227$	0.151200	+	0.415419i	0.0100355	+	0.0275724i	0.944609	−	0.328197i	$-0.106441\pi$
$227$	0.151200	+	0.415419i	0.0100355	+	0.0275724i	−0.934574	+	0.355770i	$0.884219\pi$
$228$	1.07356	+	0.118473i	0.0710983	+	0.00784607i
$229$	−6.21678	−	7.40887i	−0.410817	−	0.489592i	0.520470	−	0.853880i	$-0.325757\pi$
$229$	−6.21678	−	7.40887i	−0.410817	−	0.489592i	−0.931286	+	0.364288i	$0.881312\pi$
$230$	21.3815	+	6.33478i	1.40985	+	0.417703i
$231$	−2.49203	+	2.64531i	−0.163964	+	0.174048i
$232$	18.7551	−	11.0434i	1.23133	−	0.725033i
$233$	1.49279	−	0.861864i	0.0977961	−	0.0564626i	−0.450304	−	0.892875i	$-0.648685\pi$
$233$	1.49279	−	0.861864i	0.0977961	−	0.0564626i	0.548100	+	0.836413i	$0.315351\pi$
$234$	−0.809065	−	2.66049i	−0.0528902	−	0.173921i
$235$	−11.2478	+	19.4818i	−0.733728	+	1.27085i
$236$	−9.38776	+	14.4524i	−0.611091	+	0.940769i
$237$	19.0735	+	1.09678i	1.23896	+	0.0712438i
$238$	1.09266	+	4.55238i	0.0708269	+	0.295087i
$239$	−1.11054	−	6.29821i	−0.0718351	−	0.407397i	−0.999428	−	0.0338057i	$-0.989237\pi$
$239$	−1.11054	−	6.29821i	−0.0718351	−	0.407397i	0.927593	−	0.373592i	$-0.121874\pi$
$240$	−2.30892	+	14.0939i	−0.149040	+	0.909760i
$241$	−13.9890	−	11.7382i	−0.901114	−	0.756124i	0.0692941	−	0.997596i	$-0.477925\pi$
$241$	−13.9890	−	11.7382i	−0.901114	−	0.756124i	−0.970408	+	0.241472i	$0.922370\pi$
$242$	−2.57214	−	3.88655i	−0.165343	−	0.249837i
$243$	0.963804	+	15.5586i	0.0618281	+	0.998087i
$244$	−22.7587	−	9.66347i	−1.45698	−	0.618640i
$245$	10.1515	+	8.51813i	0.648557	+	0.544204i
$246$	−15.4657	−	5.56623i	−0.986056	−	0.354890i
$247$	−0.201255	+	0.0354867i	−0.0128056	+	0.00225797i
$248$	−1.97485	+	11.7892i	−0.125403	+	0.748612i
$249$	19.1222	+	1.09958i	1.21182	+	0.0696832i
$250$	15.3745	−	6.68400i	0.972368	−	0.422733i
$251$	22.9769	+	13.2657i	1.45029	+	0.837325i	0.998497	−	0.0547989i	$-0.0174518\pi$
$251$	22.9769	+	13.2657i	1.45029	+	0.837325i	0.451791	+	0.892124i	$0.350785\pi$
$252$	2.89040	−	3.49533i	0.182078	−	0.220185i
$253$	−18.3879	+	10.6163i	−1.15604	+	0.667438i
$254$	−3.21673	+	4.34666i	−0.201836	+	0.272734i
$255$	−11.3811	−	10.7217i	−0.712714	−	0.671418i
$256$	9.84498	+	12.6125i	0.615312	+	0.788284i
$257$	14.9145	+	17.7744i	0.930341	+	1.10874i	0.993848	+	0.110755i	$0.0353270\pi$
$257$	14.9145	+	17.7744i	0.930341	+	1.10874i	−0.0635070	+	0.997981i	$0.520229\pi$
$258$	5.01453	−	6.01986i	0.312191	−	0.374780i
$259$	−2.21856	+	0.807489i	−0.137855	+	0.0501749i
$260$	−0.329023	−	2.68214i	−0.0204051	−	0.166339i
$261$	19.2686	−	12.7139i	1.19270	−	0.786972i
$262$	1.14972	+	18.8148i	0.0710297	+	1.16238i
$263$	2.19804	−	12.4657i	0.135537	−	0.768669i	−0.838947	−	0.544213i	$-0.816828\pi$
$263$	2.19804	−	12.4657i	0.135537	−	0.768669i	0.974484	−	0.224456i	$-0.0720606\pi$
$264$	−8.22126	−	10.8313i	−0.505984	−	0.666623i
$265$	−1.69761	−	0.617878i	−0.104283	−	0.0379559i
$266$	−0.229430	−	0.241796i	−0.0140673	−	0.0148255i
$267$	−1.29907	−	11.0436i	−0.0795019	−	0.675856i
$268$	−7.74346	+	3.94441i	−0.473007	+	0.240943i
$269$	1.20091			0.0732208			0.0366104	−	0.999330i	$-0.488344\pi$
$269$	1.20091			0.0732208			0.0366104	+	0.999330i	$0.488344\pi$
$270$	−1.68233	+	15.0545i	−0.102383	+	0.916185i
$271$			5.81199i			0.353053i	0.984296	+	0.176527i	$0.0564862\pi$
$271$			5.81199i			0.353053i	−0.984296	+	0.176527i	$0.943514\pi$
$272$	−17.4747	+	1.21805i	−1.05956	+	0.0738553i
$273$	−0.339325	+	0.788242i	−0.0205369	+	0.0477066i
$274$	−13.2003	−	13.9118i	−0.797460	−	0.840441i
$275$	−0.712590	+	1.95782i	−0.0429708	+	0.118061i
$276$	22.0449	−	14.7035i	1.32694	−	0.885049i
$277$	−14.3435	−	2.52915i	−0.861817	−	0.151962i	−0.274766	−	0.961511i	$-0.588600\pi$
$277$	−14.3435	−	2.52915i	−0.861817	−	0.151962i	−0.587051	+	0.809550i	$0.699711\pi$
$278$	1.49098	−	0.0911090i	0.0894229	−	0.00546436i
$279$	−1.45330	+	12.5949i	−0.0870067	+	0.754040i
$280$	3.35197	−	2.86189i	0.200318	−	0.171030i
$281$	−3.34759	−	9.19743i	−0.199701	−	0.548673i	0.798905	−	0.601457i	$-0.205413\pi$
$281$	−3.34759	−	9.19743i	−0.199701	−	0.548673i	−0.998606	+	0.0527839i	$0.983191\pi$
$282$	9.23261	+	25.0857i	0.549794	+	1.49383i
$283$	−1.06126	+	0.890502i	−0.0630853	+	0.0529348i	−0.673785	−	0.738927i	$-0.735333\pi$
$283$	−1.06126	+	0.890502i	−0.0630853	+	0.0529348i	0.610700	+	0.791862i	$0.290888\pi$
$284$	−8.27698	−	27.0835i	−0.491148	−	1.60711i
$285$	1.08342	+	0.255931i	0.0641762	+	0.0151600i
$286$	2.06813	+	1.53052i	0.122291	+	0.0905013i
$287$	2.53628	+	4.39297i	0.149712	+	0.259309i
$288$	11.1118	+	12.8269i	0.654767	+	0.755831i
$289$	1.08903	−	1.88625i	0.0640603	−	0.110956i
$290$	20.5730	−	8.94402i	1.20809	−	0.525211i
$291$	−2.45271	−	1.61058i	−0.143781	−	0.0944140i
$292$	−19.5714	+	20.9830i	−1.14533	+	1.22794i
$293$	−0.541790	−	3.07264i	−0.0316517	−	0.179506i	0.964883	−	0.262678i	$-0.0846058\pi$
$293$	−0.541790	−	3.07264i	−0.0316517	−	0.179506i	−0.996535	+	0.0831727i	$0.973495\pi$
$294$	15.4975	−	2.79006i	0.903835	−	0.162720i
$295$	−11.4177	+	13.6071i	−0.664766	+	0.792237i
$296$	−1.60838	−	8.68611i	−0.0934851	−	0.504870i
$297$	−9.29531	−	11.0280i	−0.539368	−	0.639912i
$298$	17.5253	+	26.4810i	1.01521	+	1.53401i
$299$	−3.22277	+	3.84075i	−0.186378	+	0.222116i
$300$	0.729678	−	2.49572i	0.0421280	−	0.144091i
$301$	−2.38116	+	0.419863i	−0.137248	+	0.0242005i
$302$	−27.2775	+	6.54714i	−1.56964	+	0.376746i
$303$	0.688603	−	0.346466i	0.0395592	−	0.0199039i
$304$	1.03410	−	0.697177i	0.0593098	−	0.0399858i
$305$	−22.0702	−	12.7422i	−1.26373	−	0.729617i
$306$	−18.4446	+	2.23684i	−1.05440	+	0.127872i
$307$	−13.5864	−	23.5323i	−0.775415	−	1.34306i	−0.934561	−	0.355803i	$-0.884207\pi$
$307$	−13.5864	−	23.5323i	−0.775415	−	1.34306i	0.159146	−	0.987255i	$-0.449126\pi$
$308$	−0.220092	+	4.19071i	−0.0125409	+	0.238788i
$309$	−20.9102	+	6.27693i	−1.18954	+	0.357082i
$310$	−3.49984	+	11.8129i	−0.198778	+	0.670925i
$311$	−15.0893	+	12.6614i	−0.855634	+	0.717962i	−0.961023	−	0.276469i	$-0.910836\pi$
$311$	−15.0893	+	12.6614i	−0.855634	+	0.717962i	0.105389	+	0.994431i	$0.466391\pi$
$312$	−2.69902	−	1.73944i	−0.152802	−	0.0984764i
$313$	12.9477	−	4.71256i	0.731845	−	0.266370i	0.0508993	−	0.998704i	$-0.483791\pi$
$313$	12.9477	−	4.71256i	0.731845	−	0.266370i	0.680946	+	0.732334i	$0.261569\pi$
$314$	−19.8888	−	9.91758i	−1.12239	−	0.559682i
$315$	3.39563	−	3.21310i	0.191322	−	0.181038i
$316$	17.6199	−	13.2745i	0.991195	−	0.746746i
$317$	−1.93237	+	10.9590i	−0.108533	+	0.615521i	0.881217	+	0.472711i	$0.156725\pi$
$317$	−1.93237	+	10.9590i	−0.108533	+	0.615521i	−0.989750	+	0.142809i	$0.954386\pi$
$318$	−1.85520	+	1.08000i	−0.104034	+	0.0605634i
$319$	−7.30522	+	20.0709i	−0.409014	+	1.12376i
$320$	8.48890	+	14.1386i	0.474544	+	0.790370i
$321$	−12.7269	+	9.48942i	−0.710346	+	0.529648i
$322$	−8.12506	−	0.926190i	−0.452792	−	0.0516145i
$323$			1.36542i			0.0759740i
$324$	12.4653	+	12.9853i	0.692514	+	0.721405i
$325$			0.491981i			0.0272902i
$326$	−1.82125	+	15.9771i	−0.100870	+	0.884887i
$327$	17.5374	−	13.0763i	0.969822	−	0.723119i
$328$	−17.7788	+	6.64385i	−0.981671	+	0.366845i
$329$	2.82145	−	7.75186i	0.155551	−	0.427374i
$330$	−7.05132	−	12.1126i	−0.388162	−	0.666775i
$331$	−3.55339	+	20.1523i	−0.195312	+	1.10767i	0.716661	+	0.697421i	$0.245669\pi$
$331$	−3.55339	+	20.1523i	−0.195312	+	1.10767i	−0.911973	+	0.410249i	$0.865442\pi$
$332$	17.6648	−	13.3083i	0.969482	−	0.730388i
$333$	−2.17424	−	9.11386i	−0.119147	−	0.499436i
$334$	7.30158	−	14.6427i	0.399524	−	0.801211i
$335$	−8.41683	+	3.06348i	−0.459860	+	0.167376i
$336$	−0.0636392	−	5.23688i	−0.00347181	−	0.285695i
$337$	−27.2025	+	22.8256i	−1.48181	+	1.24339i	−0.577591	+	0.816326i	$0.696007\pi$
$337$	−27.2025	+	22.8256i	−1.48181	+	1.24339i	−0.904222	+	0.427062i	$0.859548\pi$
$338$	−17.0449	−	5.04995i	−0.927119	−	0.274681i
$339$	21.3305	−	6.40310i	1.15852	−	0.347769i
$340$	−18.0301	−	0.946922i	−0.977817	−	0.0513541i
$341$	−5.86527	−	10.1590i	−0.317622	−	0.550138i
$342$	1.05763	−	0.794519i	0.0571903	−	0.0429627i
$343$	−8.79113	−	5.07556i	−0.474676	−	0.274054i
$344$	−0.0774416	−	9.04653i	−0.00417537	−	0.487756i
$345$	24.3979	−	12.2756i	1.31354	−	0.660898i
$346$	−2.35364	−	9.80601i	−0.126532	−	0.527175i
$347$	11.0057	−	1.94061i	0.590818	−	0.104177i	0.129757	−	0.991546i	$-0.458580\pi$
$347$	11.0057	−	1.94061i	0.590818	−	0.104177i	0.461061	+	0.887369i	$0.347469\pi$
$348$	7.48040	−	25.5853i	0.400992	−	1.37151i
$349$	−18.9269	+	22.5561i	−1.01313	+	1.20740i	−0.0350059	+	0.999387i	$0.511145\pi$
$349$	−18.9269	+	22.5561i	−1.01313	+	1.20740i	−0.978125	+	0.208016i	$0.933299\pi$
$350$	−0.669173	+	0.442863i	−0.0357688	+	0.0236720i
$351$	−2.95323	−	1.69634i	−0.157632	−	0.0905441i
$352$	−15.3285	−	3.40272i	−0.817014	−	0.181366i
$353$	1.05874	−	1.26175i	0.0563508	−	0.0671563i	−0.737133	−	0.675748i	$-0.763821\pi$
$353$	1.05874	−	1.26175i	0.0563508	−	0.0671563i	0.793484	+	0.608592i	$0.208265\pi$
$354$	3.73980	+	20.7730i	0.198768	+	1.10407i
$355$	−5.06871	−	28.7461i	−0.269019	−	1.52568i
$356$	−9.38957	−	8.75787i	−0.497646	−	0.464166i
$357$	4.79290	+	3.14727i	0.253667	+	0.166571i
$358$	−3.54578	−	8.15597i	−0.187400	−	0.431056i
$359$	−5.17384	+	8.96135i	−0.273065	+	0.472962i	−0.969645	−	0.244517i	$-0.921371\pi$
$359$	−5.17384	+	8.96135i	−0.273065	+	0.472962i	0.696580	+	0.717479i	$0.254704\pi$
$360$	9.75797	+	14.5168i	0.514290	+	0.765103i
$361$	9.45139	+	16.3703i	0.497442	+	0.861594i
$362$	12.0042	−	16.2209i	0.630929	−	0.852553i
$363$	−5.55515	−	1.31227i	−0.291570	−	0.0688761i
$364$	0.289617	+	0.947670i	0.0151800	+	0.0496714i
$365$	−22.6555	+	19.0102i	−1.18584	+	0.995039i
$366$	−28.4186	+	10.4592i	−1.48546	+	0.546714i
$367$	−2.26512	−	6.22336i	−0.118238	−	0.324857i	0.866429	−	0.499300i	$-0.166410\pi$
$367$	−2.26512	−	6.22336i	−0.118238	−	0.324857i	−0.984667	+	0.174444i	$0.944187\pi$
$368$	8.44043	−	29.4106i	0.439988	−	1.53314i
$369$	−18.4728	+	8.00074i	−0.961654	+	0.416502i
$370$	−0.555341	−	9.08802i	−0.0288708	−	0.472464i
$371$	0.652415	+	0.115038i	0.0338717	+	0.00597249i
$372$	8.12341	+	12.1793i	0.421179	+	0.631470i
$373$	−3.26986	+	8.98387i	−0.169307	+	0.465167i	−0.995108	−	0.0987948i	$-0.968501\pi$
$373$	−3.26986	+	8.98387i	−0.169307	+	0.465167i	0.825801	+	0.563962i	$0.190723\pi$
$374$	12.4702	−	11.8325i	0.644819	−	0.611842i
$375$	8.11852	−	18.8591i	0.419239	−	0.973880i
$376$	26.8619	+	15.2036i	1.38530	+	0.784068i
$377$			5.04362i			0.259759i
$378$	−0.351089	−	5.54386i	−0.0180581	−	0.285145i
$379$	32.8619			1.68800			0.844000	−	0.536343i	$-0.180194\pi$
$379$	32.8619			1.68800			0.844000	+	0.536343i	$0.180194\pi$
$380$	1.14541	−	0.583458i	0.0587585	−	0.0299308i
$381$	0.773712	+	6.57743i	0.0396384	+	0.336972i
$382$	−10.1772	+	9.65674i	−0.520712	+	0.494082i
$383$	17.7062	+	6.44453i	0.904744	+	0.329300i	0.752152	−	0.658989i	$-0.229016\pi$
$383$	17.7062	+	6.44453i	0.904744	+	0.329300i	0.152592	+	0.988289i	$0.451238\pi$
$384$	19.3645	+	3.00240i	0.988193	+	0.153215i
$385$	−0.751085	+	4.25961i	−0.0382788	+	0.217090i
$386$	−9.60714	+	0.587063i	−0.488991	+	0.0298807i
$387$	−0.572076	−	9.57858i	−0.0290802	−	0.486907i
$388$	−3.36296	+	0.412541i	−0.170728	+	0.0209436i
$389$	32.5922	−	11.8626i	1.65249	−	0.601458i	0.663335	−	0.748323i	$-0.269140\pi$
$389$	32.5922	−	11.8626i	1.65249	−	0.601458i	0.989157	+	0.146865i	$0.0469182\pi$
$390$	−2.54289	−	2.11823i	−0.128764	−	0.107261i
$391$	21.5328	+	25.6618i	1.08896	+	1.29777i
$392$	11.5680	−	14.0283i	0.584271	−	0.708537i
$393$	16.8041	+	15.8304i	0.847654	+	0.798538i
$394$	−7.01020	−	5.18788i	−0.353169	−	0.261362i
$395$	19.6916	−	11.3690i	0.990792	−	0.572034i
$396$	−16.4215	−	2.77408i	−0.825210	−	0.139403i
$397$	7.71976	+	4.45700i	0.387444	+	0.223691i	0.681052	−	0.732235i	$-0.261523\pi$
$397$	7.71976	+	4.45700i	0.387444	+	0.223691i	−0.293608	+	0.955926i	$0.594856\pi$
$398$	−1.84694	−	4.24831i	−0.0925786	−	0.212948i
$399$	−0.407561	−	0.0234359i	−0.0204036	−	0.00117326i
$400$	−1.22060	−	2.74315i	−0.0610300	−	0.137158i
$401$	−5.23648	+	0.923333i	−0.261497	+	0.0461090i	−0.302860	−	0.953035i	$-0.597941\pi$
$401$	−5.23648	+	0.923333i	−0.261497	+	0.0461090i	0.0413623	+	0.999144i	$0.486830\pi$
$402$	−3.60427	+	10.0144i	−0.179765	+	0.499474i
$403$	−2.12194	−	1.78052i	−0.105701	−	0.0886939i
$404$	0.347882	−	0.819305i	0.0173078	−	0.0407620i
$405$	11.1227	+	14.8487i	0.552694	+	0.737839i
$406$	−6.86013	+	4.54008i	−0.340463	+	0.225320i
$407$	6.64088	+	5.57236i	0.329176	+	0.276212i
$408$	−14.5769	+	15.7413i	−0.721663	+	0.779309i
$409$	5.33255	+	30.2424i	0.263678	+	1.49539i	0.772774	+	0.634681i	$0.218869\pi$
$409$	5.33255	+	30.2424i	0.263678	+	1.49539i	−0.509096	+	0.860710i	$0.670020\pi$
$410$	−19.0221	+	4.56569i	−0.939434	+	0.225483i
$411$	−23.4491	−	1.34839i	−1.15666	−	0.0665112i
$412$	−13.7324	+	21.1409i	−0.676546	+	1.04154i
$413$	3.25689	−	5.64110i	0.160261	−	0.277581i
$414$	7.34759	−	31.6112i	0.361115	−	1.55361i
$415$	19.7418	−	11.3980i	0.969089	−	0.559504i
$416$	−3.67613	+	0.482934i	−0.180237	+	0.0236778i
$417$	1.25448	−	1.33164i	0.0614320	−	0.0652105i
$418$	−0.347675	+	1.17349i	−0.0170053	+	0.0573974i
$419$	−6.31758	−	7.52899i	−0.308634	−	0.367815i	0.589324	−	0.807897i	$-0.299394\pi$
$419$	−6.31758	−	7.52899i	−0.308634	−	0.367815i	−0.897958	+	0.440081i	$0.854950\pi$
$420$	0.592110	−	5.36549i	0.0288920	−	0.261809i
$421$	−5.77588	−	15.8691i	−0.281499	−	0.773413i	−0.997184	−	0.0749895i	$-0.976108\pi$
$421$	−5.77588	−	15.8691i	−0.281499	−	0.773413i	0.715685	−	0.698423i	$-0.246115\pi$
$422$	4.03553	−	8.09289i	0.196446	−	0.393956i
$423$	29.2777	+	14.6498i	1.42353	+	0.712296i
$424$	−0.827813	+	2.33644i	−0.0402022	+	0.113467i
$425$	3.23721	+	0.570807i	0.157028	+	0.0276882i
$426$	−30.1001	−	17.2344i	−1.45835	−	0.835011i
$427$	8.78177	+	3.19630i	0.424979	+	0.154680i
$428$	−4.12559	+	17.8609i	−0.199418	+	0.863337i
$429$	3.12953	−	0.368131i	0.151095	−	0.0177735i
$430$	1.05609	−	9.26462i	0.0509292	−	0.446780i
$431$	4.98460			0.240100			0.120050	−	0.992768i	$-0.461695\pi$
$431$	4.98460			0.240100			0.120050	+	0.992768i	$0.461695\pi$
$432$	20.6750	+	2.13140i	0.994728	+	0.102547i
$433$	1.51448			0.0727813			0.0363907	−	0.999338i	$-0.488414\pi$
$433$	1.51448			0.0727813			0.0363907	+	0.999338i	$0.488414\pi$
$434$	0.511702	−	4.48893i	0.0245625	−	0.215476i
$435$	10.8636	−	25.2358i	0.520869	−	1.20996i
$436$	5.68499	−	24.6119i	0.272262	−	1.17870i
$437$	−2.24120	−	0.815730i	−0.107211	−	0.0390216i
$438$	0.126209	+	35.1422i	0.00603049	+	1.67916i
$439$	11.1514	+	1.96629i	0.532227	+	0.0938460i	0.433302	−	0.901249i	$-0.357348\pi$
$439$	11.1514	+	1.96629i	0.532227	+	0.0938460i	0.0989253	+	0.995095i	$0.468460\pi$
$440$	−15.2546	−	5.40479i	−0.727233	−	0.257663i
$441$	11.4938	−	15.4865i	0.547322	−	0.737451i
$442$	1.81144	−	3.63269i	0.0861615	−	0.172789i
$443$	1.11491	+	3.06318i	0.0529709	+	0.145536i	0.963356	−	0.268225i	$-0.0864370\pi$
$443$	1.11491	+	3.06318i	0.0529709	+	0.145536i	−0.910385	+	0.413761i	$0.864215\pi$
$444$	−8.71971	−	6.40466i	−0.413819	−	0.303952i
$445$	−8.50676	−	10.1380i	−0.403259	−	0.480585i
$446$	−6.67459	+	22.5284i	−0.316051	+	1.06675i
$447$	37.8501	+	8.94114i	1.79025	+	0.422901i
$448$	−3.96598	−	4.56541i	−0.187375	−	0.215695i
$449$	−19.0431	+	10.9945i	−0.898698	+	0.518864i	−0.876778	−	0.480896i	$-0.840311\pi$
$449$	−19.0431	+	10.9945i	−0.898698	+	0.518864i	−0.0219208	+	0.999760i	$0.506978\pi$
$450$	−1.44155	−	2.83963i	−0.0679552	−	0.133862i
$451$	9.31288	−	16.1304i	0.438527	−	0.759550i
$452$	14.0084	−	21.5659i	0.658901	−	1.01437i
$453$	−18.8582	+	28.7186i	−0.886034	+	1.34932i
$454$	0.607929	−	0.145915i	0.0285315	−	0.00684814i
$455$	0.177357	+	1.00584i	0.00831464	+	0.0471547i
$456$	0.338422	−	1.48950i	0.0158481	−	0.0697521i
$457$	−0.610943	−	0.512642i	−0.0285787	−	0.0239804i	0.628386	−	0.777901i	$-0.283716\pi$
$457$	−0.610943	−	0.512642i	−0.0285787	−	0.0239804i	−0.656965	+	0.753921i	$0.728160\pi$
$458$	−11.4061	+	7.54860i	−0.532970	+	0.352723i
$459$	−14.5882	+	17.4640i	−0.680921	+	0.815148i
$460$	12.3258	−	29.0288i	0.574693	−	1.35347i
$461$	2.30805	+	1.93668i	0.107496	+	0.0902002i	0.694952	−	0.719056i	$-0.255426\pi$
$461$	2.30805	+	1.93668i	0.107496	+	0.0902002i	−0.587455	+	0.809257i	$0.699870\pi$
$462$	3.31780	+	3.92529i	0.154358	+	0.182621i
$463$	9.53305	−	1.68093i	0.443038	−	0.0781196i	0.0523209	−	0.998630i	$-0.483338\pi$
$463$	9.53305	−	1.68093i	0.443038	−	0.0781196i	0.390717	+	0.920511i	$0.372227\pi$
$464$	−12.5132	−	28.1218i	−0.580909	−	1.30552i
$465$	6.78204	+	13.4793i	0.314510	+	0.625090i
$466$	−0.971914	−	2.23559i	−0.0450231	−	0.103562i
$467$	4.68978	+	2.70765i	0.217017	+	0.125295i	0.604568	−	0.796553i	$-0.293346\pi$
$467$	4.68978	+	2.70765i	0.217017	+	0.125295i	−0.387551	+	0.921848i	$0.626679\pi$
$468$	−3.86788	+	0.710694i	−0.178793	+	0.0328518i
$469$	2.84456	−	1.64231i	0.131349	−	0.0758346i
$470$	25.5726	+	18.9249i	1.17958	+	0.872941i
$471$	−26.0700	+	7.82580i	−1.20124	+	0.360594i
$472$	18.8036	+	15.5057i	0.865505	+	0.713709i
$473$	5.70679	+	6.80109i	0.262398	+	0.312714i
$474$	4.59614	−	26.6248i	0.211108	−	1.22292i
$475$	−0.219921	+	0.0800447i	−0.0100907	+	0.00367270i
$476$	6.57163	−	0.806155i	0.301210	−	0.0369500i
$477$	−0.750320	+	2.51977i	−0.0343548	+	0.115372i
$478$	−9.02758	+	0.551648i	−0.412912	+	0.0252318i
$479$	−2.45737	+	13.9364i	−0.112280	+	0.636772i	0.875781	+	0.482709i	$0.160347\pi$
$479$	−2.45737	+	13.9364i	−0.112280	+	0.636772i	−0.988061	+	0.154063i	$0.950764\pi$
$480$	19.4338	+	5.50175i	0.887027	+	0.251119i
$481$	1.92361	+	0.700138i	0.0877093	+	0.0319236i
$482$	−18.7342	+	17.7761i	−0.853318	+	0.809678i
$483$	−8.02930	+	5.98681i	−0.365346	+	0.272409i
$484$	−5.87303	+	2.99164i	−0.266956	+	0.135983i
$485$	−3.49219			−0.158572
$486$	22.0160	+	1.13780i	0.998667	+	0.0516114i
$487$		−	19.4173i		−	0.879884i	−0.898026	−	0.439942i	$-0.854999\pi$
$487$		−	19.4173i		−	0.879884i	0.898026	−	0.439942i	$-0.145001\pi$
$488$	−17.2236	+	30.4307i	−0.779674	+	1.37753i
$489$	11.7724	+	15.7888i	0.532367	+	0.713993i
$490$	13.5949	−	12.8997i	0.614156	−	0.582748i
$491$	8.52216	−	23.4144i	0.384600	−	1.05668i	−0.584797	−	0.811180i	$-0.698826\pi$
$491$	8.52216	−	23.4144i	0.384600	−	1.05668i	0.969397	−	0.245499i	$-0.0789520\pi$
$492$	−10.2983	+	20.8395i	−0.464285	+	0.939517i
$493$	33.1867	+	5.85171i	1.49465	+	0.263548i
$494$	0.0176275	+	0.288471i	0.000793101	+	0.0129789i
$495$	−16.4516	−	4.89883i	−0.739444	−	0.220186i
$496$	16.2488	+	4.66317i	0.729592	+	0.209383i
$497$	3.66101	+	10.0585i	0.164219	+	0.451187i
$498$	4.60787	−	26.6927i	0.206483	−	1.19613i
$499$	26.2739	−	22.0464i	1.17618	−	0.986934i	0.176185	−	0.984357i	$-0.443624\pi$
$499$	26.2739	−	22.0464i	1.17618	−	0.986934i	0.999997	−	0.00257701i	$-0.000820288\pi$
$500$	−6.92923	−	22.6735i	−0.309885	−	1.01399i
$501$	−5.76155	−	19.1934i	−0.257407	−	0.857496i
$502$	22.3201	−	30.1604i	0.996194	−	1.34612i
$503$	−5.33340	−	9.23771i	−0.237804	−	0.411889i	0.722280	−	0.691601i	$-0.243094\pi$
$503$	−5.33340	−	9.23771i	−0.237804	−	0.411889i	−0.960084	+	0.279712i	$0.909761\pi$
$504$	−4.44838	−	4.62120i	−0.198146	−	0.205844i
$505$	0.458715	−	0.794518i	0.0204126	−	0.0353556i
$506$	11.9718	+	27.5375i	0.532213	+	1.22419i
$507$	−19.4495	+	9.78587i	−0.863781	+	0.434606i
$508$	5.59232	+	5.21608i	0.248119	+	0.231426i
$509$	−6.89823	−	39.1218i	−0.305759	−	1.73404i	−0.619911	−	0.784672i	$-0.712831\pi$
$509$	−6.89823	−	39.1218i	−0.305759	−	1.73404i	0.314152	−	0.949373i	$-0.398280\pi$
$510$	−16.8881	+	14.2745i	−0.747819	+	0.632085i
$511$	6.97121	−	8.30796i	0.308388	−	0.367522i
$512$	19.2989	−	11.8132i	0.852901	−	0.522073i
$513$	0.277797	−	1.59612i	0.0122650	−	0.0704705i
$514$	27.3639	−	18.1096i	1.20697	−	0.798781i
$515$	−16.7018	+	19.9045i	−0.735970	+	0.877095i
$516$	−7.65541	−	8.01020i	−0.337011	−	0.352630i
$517$	−29.8304	+	5.25990i	−1.31194	+	0.231330i
$518$	0.779265	+	3.24666i	0.0342389	+	0.142650i
$519$	−10.3241	−	6.77935i	−0.453177	−	0.297580i
$520$	−3.82141	+	0.0327127i	−0.167580	+	0.00143455i
$521$	−15.1484	−	8.74596i	−0.663665	−	0.383167i	0.130007	−	0.991513i	$-0.458500\pi$
$521$	−15.1484	−	8.74596i	−0.663665	−	0.383167i	−0.793672	+	0.608346i	$0.791833\pi$
$522$	−14.7782	−	29.1110i	−0.646826	−	1.27415i
$523$	−19.3217	−	33.4661i	−0.844878	−	1.46337i	−0.885727	−	0.464206i	$-0.846340\pi$
$523$	−19.3217	−	33.4661i	−0.844878	−	1.46337i	0.0408499	−	0.999165i	$-0.486993\pi$
$524$	26.6211	+	1.39812i	1.16295	+	0.0610770i
$525$	−0.225942	+	0.956468i	−0.00986090	+	0.0417437i
$526$	−17.1637	−	5.08515i	−0.748373	−	0.221723i
$527$	−14.1776	+	11.8964i	−0.617587	+	0.518217i
$528$	−16.5361	+	9.81693i	−0.719640	+	0.427227i
$529$	−33.3724	+	12.1465i	−1.45097	+	0.528111i
$530$	−1.14010	+	2.28636i	−0.0495226	+	0.0993133i
$531$	20.7581	+	15.4063i	0.900825	+	0.668575i
$532$	−0.376499	+	0.283647i	−0.0163233	+	0.0122976i
$533$	0.763739	−	4.33138i	0.0330812	−	0.187613i
$534$	−15.7256	+	0.0564764i	−0.680512	+	0.00244397i
$535$	−6.46211	+	17.7545i	−0.279381	+	0.767594i
$536$	4.30206	+	11.5122i	0.185821	+	0.497252i
$537$	−10.0045	−	4.30677i	−0.431726	−	0.185851i
$538$	0.192352	−	1.68742i	0.00829287	−	0.0727497i
$539$			17.8437i			0.768583i
$540$	20.8838	+	4.77516i	0.898694	+	0.205490i
$541$		−	34.6309i		−	1.48890i	−0.667679	−	0.744449i	$-0.732712\pi$
$541$		−	34.6309i		−	1.48890i	0.667679	−	0.744449i	$-0.267288\pi$
$542$	8.16651	+	0.930915i	0.350782	+	0.0399862i
$543$	−2.88735	−	24.5457i	−0.123908	−	1.05336i
$544$	−1.08745	+	24.7490i	−0.0466239	+	1.06111i
$545$	8.90467	−	24.4654i	0.381434	−	1.04798i
$546$	1.05322	+	0.603044i	0.0450736	+	0.0258079i
$547$	5.81585	−	32.9833i	0.248668	−	1.41027i	−0.563150	−	0.826355i	$-0.690411\pi$
$547$	5.81585	−	32.9833i	0.248668	−	1.41027i	0.811818	−	0.583910i	$-0.198478\pi$
$548$	−21.6619	+	16.3197i	−0.925352	+	0.697142i
$549$	−16.5961	+	33.1675i	−0.708305	+	1.41556i
$550$	2.63683	+	1.31486i	0.112435	+	0.0560657i
$551$	−2.25455	+	0.820590i	−0.0960472	+	0.0349583i
$552$	−17.1292	−	33.3306i	−0.729066	−	1.41865i
$553$	−6.38743	+	5.35969i	−0.271621	+	0.227917i
$554$	−5.85116	+	19.7491i	−0.248592	+	0.839061i
$555$	−8.11679	−	7.64648i	−0.344538	−	0.324575i
$556$	0.110793	−	2.10959i	0.00469869	−	0.0894664i
$557$	−13.2023	−	22.8671i	−0.559401	−	0.968911i	−0.997547	−	0.0700066i	$-0.977698\pi$
$557$	−13.2023	−	22.8671i	−0.559401	−	0.968911i	0.438146	−	0.898904i	$-0.355635\pi$
$558$	17.4646	+	4.05940i	0.739334	+	0.171848i
$559$	1.81558	+	1.04823i	0.0767908	+	0.0443352i
$560$	−3.48439	−	5.16829i	−0.147242	−	0.218400i
$561$	1.20867	−	21.0192i	0.0510300	−	0.887433i
$562$	−13.4596	+	3.23058i	−0.567760	+	0.136274i
$563$	−20.5566	+	3.62468i	−0.866356	+	0.152762i	−0.589126	−	0.808041i	$-0.700528\pi$
$563$	−20.5566	+	3.62468i	−0.866356	+	0.152762i	−0.277231	+	0.960803i	$0.589417\pi$
$564$	36.7271	−	8.95486i	1.54649	−	0.377067i
$565$	17.0376	−	20.3046i	0.716775	−	0.854220i
$566$	1.08127	+	1.63382i	0.0454493	+	0.0686747i
$567$	−4.96238	−	4.65416i	−0.208401	−	0.195456i
$568$	−39.3812	+	7.29209i	−1.65240	+	0.305969i
$569$	20.8581	−	24.8577i	0.874418	−	1.04209i	−0.124339	−	0.992240i	$-0.539681\pi$
$569$	20.8581	−	24.8577i	0.874418	−	1.04209i	0.998757	−	0.0498506i	$-0.0158745\pi$
$570$	0.533145	−	1.48133i	0.0223310	−	0.0620463i
$571$	2.23408	+	12.6701i	0.0934935	+	0.530228i	0.995199	+	0.0978764i	$0.0312050\pi$
$571$	2.23408	+	12.6701i	0.0934935	+	0.530228i	−0.901705	+	0.432352i	$0.857684\pi$
$572$	2.48181	−	2.66082i	0.103769	−	0.111254i
$573$	−0.986421	+	17.1543i	−0.0412083	+	0.716631i
$574$	6.57886	−	2.86014i	0.274596	−	0.119380i
$575$	−2.87089	+	4.97253i	−0.119725	+	0.207369i
$576$	19.8030	−	13.5588i	0.825125	−	0.564950i
$577$	16.5679	+	28.6964i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$577$	16.5679	+	28.6964i	0.689730	+	1.19465i	−0.282195	+	0.959357i	$0.591062\pi$
$578$	−2.47596	−	1.83233i	−0.102986	−	0.0762148i
$579$	−8.08325	+	8.58042i	−0.335929	+	0.356590i
$580$	−9.27217	−	30.3399i	−0.385006	−	1.25980i
$581$	−6.40372	+	5.37336i	−0.265671	+	0.222924i
$582$	−2.65591	+	3.18837i	−0.110091	+	0.132162i
$583$	−0.831976	−	2.28583i	−0.0344569	−	0.0946696i
$584$	26.3488	+	30.8609i	1.09032	+	1.27703i
$585$	−4.04616	+	0.241655i	−0.167288	+	0.00999118i
$586$	−4.40419	+	0.269126i	−0.181935	+	0.0111175i
$587$	27.2988	+	4.81352i	1.12674	+	0.198675i	0.705799	−	0.708412i	$-0.250588\pi$
$587$	27.2988	+	4.81352i	1.12674	+	0.198675i	0.420943	+	0.907087i	$0.361699\pi$
$588$	−1.43809	−	22.2227i	−0.0593057	−	0.916449i
$589$	0.450675	−	1.23822i	0.0185697	−	0.0510199i
$590$	17.2908	+	18.2227i	0.711849	+	0.750216i
$591$	−10.6079	+	1.24783i	−0.436353	+	0.0513287i
$592$	−12.4626	+	0.868689i	−0.512209	+	0.0357029i
$593$		−	3.09941i		−	0.127277i	−0.997973	−	0.0636387i	$-0.979729\pi$
$593$		−	3.09941i		−	0.127277i	0.997973	−	0.0636387i	$-0.0202705\pi$
$594$	−16.9845	+	11.2946i	−0.696882	+	0.463423i
$595$	6.82417			0.279764
$596$	40.0159	−	20.3835i	1.63912	−	0.834942i
$597$	−5.21118	−	2.24333i	−0.213280	−	0.0918132i
$598$	4.88049	+	5.14354i	0.199578	+	0.210335i
$599$	2.99899	+	1.09154i	0.122535	+	0.0445992i	0.402560	−	0.915394i	$-0.368120\pi$
$599$	2.99899	+	1.09154i	0.122535	+	0.0445992i	−0.280025	+	0.959993i	$0.590343\pi$
$600$	−3.38990	−	1.42502i	−0.138392	−	0.0581763i
$601$	1.48624	−	8.42889i	0.0606251	−	0.343822i	−0.939375	−	0.342893i	$-0.888593\pi$
$601$	1.48624	−	8.42889i	0.0606251	−	0.343822i	1.00000		0.000928888i	$-0.000295674\pi$
$602$	0.208561	+	3.41305i	0.00850032	+	0.139106i
$603$	5.18068	+	11.9616i	0.210973	+	0.487113i
$604$	4.83040	+	39.3766i	0.196546	+	1.60221i
$605$	−6.38374	+	2.32349i	−0.259536	+	0.0944634i
$606$	−0.376529	−	1.02306i	−0.0152955	−	0.0415589i
$607$	−2.15954	−	2.57364i	−0.0876531	−	0.104461i	0.720435	−	0.693522i	$-0.243942\pi$
$607$	−2.15954	−	2.57364i	−0.0876531	−	0.104461i	−0.808088	+	0.589061i	$0.799498\pi$
$608$	−0.813979	−	1.56470i	−0.0330112	−	0.0634569i
$609$	−2.31628	+	9.80538i	−0.0938602	+	0.397334i
$610$	−21.4393	+	28.9701i	−0.868050	+	1.17297i
$611$	−6.19438	+	3.57633i	−0.250598	+	0.144683i
$612$	0.188729	+	26.2750i	0.00762892	+	1.06210i
$613$	6.39597	+	3.69272i	0.258331	+	0.149147i	0.623573	−	0.781765i	$-0.285680\pi$
$613$	6.39597	+	3.69272i	0.258331	+	0.149147i	−0.365242	+	0.930913i	$0.619014\pi$
$614$	−35.2417	+	15.3212i	−1.42224	+	0.618313i
$615$	−13.1509	+	20.0271i	−0.530294	+	0.807570i
$616$	5.85317	+	0.980487i	0.235831	+	0.0395049i
$617$	−45.9169	+	8.09638i	−1.84854	+	0.325948i	−0.984215	−	0.176979i	$-0.943367\pi$
$617$	−45.9169	+	8.09638i	−1.84854	+	0.325948i	−0.864329	+	0.502928i	$0.832256\pi$
$618$	5.47057	+	30.3866i	0.220059	+	1.22233i
$619$	12.0986	+	10.1519i	0.486284	+	0.408041i	0.852692	−	0.522414i	$-0.174968\pi$
$619$	12.0986	+	10.1519i	0.486284	+	0.408041i	−0.366408	+	0.930454i	$0.619413\pi$
$620$	16.0378	+	6.80976i	0.644095	+	0.273487i
$621$	−19.9500	−	34.3785i	−0.800567	−	1.37956i
$622$	15.3738	+	23.2301i	0.616435	+	0.931443i
$623$	3.71768	+	3.11950i	0.148946	+	0.124980i
$624$	−2.87642	+	3.51382i	−0.115149	+	0.140666i
$625$	−3.59165	−	20.3693i	−0.143666	−	0.814771i
$626$	−4.54784	−	18.9478i	−0.181768	−	0.757304i
$627$	0.673730	+	1.33904i	0.0269062	+	0.0534761i
$628$	−17.1210	+	26.3576i	−0.683201	+	1.05178i
$629$	6.83869	−	11.8450i	0.272676	−	0.472289i
$630$	−3.97089	−	5.28590i	−0.158204	−	0.210595i
$631$	36.1614	−	20.8778i	1.43956	−	0.831132i	0.441744	−	0.897141i	$-0.354360\pi$
$631$	36.1614	−	20.8778i	1.43956	−	0.831132i	0.997819	+	0.0660087i	$0.0210265\pi$
$632$	−15.8299	−	26.8841i	−0.629680	−	1.06939i
$633$	−3.18437	−	10.6080i	−0.126567	−	0.421632i
$634$	15.0892	+	4.47053i	0.599268	+	0.177547i
$635$	5.06652	+	6.03805i	0.201059	+	0.239613i
$636$	1.22037	+	2.77975i	0.0483910	+	0.110224i
$637$	1.44111	+	3.95942i	0.0570988	+	0.156878i
$638$	27.0319	+	13.4795i	1.07020	+	0.533657i
$639$	−41.3205	+	9.85758i	−1.63462	+	0.389960i
$640$	21.2260	−	9.66328i	0.839031	−	0.381975i
$641$	−20.1746	−	3.55732i	−0.796848	−	0.140506i	−0.239621	−	0.970866i	$-0.577023\pi$
$641$	−20.1746	−	3.55732i	−0.796848	−	0.140506i	−0.557226	+	0.830361i	$0.688134\pi$
$642$	11.2952	+	19.4027i	0.445787	+	0.765762i
$643$	−16.7499	−	6.09648i	−0.660553	−	0.240422i	−0.0100781	−	0.999949i	$-0.503208\pi$
$643$	−16.7499	−	6.09648i	−0.660553	−	0.240422i	−0.650475	+	0.759527i	$0.725430\pi$
$644$	−2.60280	+	11.2683i	−0.102565	+	0.444032i
$645$	−6.82648	−	9.15544i	−0.268792	−	0.360495i
$646$	1.91857	+	0.218701i	0.0754852	+	0.00860469i
$647$	−26.7567			−1.05192			−0.525958	−	0.850511i	$-0.676293\pi$
$647$	−26.7567			−1.05192			−0.525958	+	0.850511i	$0.676293\pi$
$648$	20.2424	−	15.4352i	0.795196	−	0.606353i
$649$	−23.9177			−0.938853
$650$	0.691289	+	0.0788013i	0.0271146	+	0.00309084i
$651$	−3.30759	−	4.43603i	−0.129635	−	0.173862i
$652$	22.1579	+	5.11814i	0.867769	+	0.200442i
$653$	43.1647	+	15.7107i	1.68916	+	0.614806i	0.994520	−	0.104547i	$-0.0333393\pi$
$653$	43.1647	+	15.7107i	1.68916	+	0.614806i	0.694645	+	0.719353i	$0.255561\pi$
$654$	−15.5646	−	26.7365i	−0.608625	−	1.04548i
$655$	27.0588	+	4.77120i	1.05728	+	0.186426i
$656$	6.48771	+	26.0454i	0.253302	+	1.01690i
$657$	29.5824	+	31.2629i	1.15412	+	1.21968i
$658$	−10.4403	−	5.20608i	−0.407007	−	0.202954i
$659$	13.8775	+	38.1282i	0.540592	+	1.48526i	0.846074	+	0.533066i	$0.178960\pi$
$659$	13.8775	+	38.1282i	0.540592	+	1.48526i	−0.305482	+	0.952198i	$0.598818\pi$
$660$	−18.1490	+	7.96781i	−0.706447	+	0.310147i
$661$	16.6703	+	19.8669i	0.648400	+	0.772733i	0.985672	−	0.168675i	$-0.0539487\pi$
$661$	16.6703	+	19.8669i	0.648400	+	0.772733i	−0.337272	+	0.941407i	$0.609504\pi$
$662$	27.7471	+	8.22075i	1.07842	+	0.319508i
$663$	−1.42938	−	4.76167i	−0.0555125	−	0.184928i
$664$	−15.8703	−	26.9527i	−0.615887	−	1.04597i
$665$	−0.420768	+	0.242930i	−0.0163167	+	0.00942043i
$666$	−13.1543	+	1.59527i	−0.509717	+	0.0618154i
$667$	−29.4314	+	50.9767i	−1.13959	+	1.97382i
$668$	−19.4051	−	12.6049i	−0.750806	−	0.487698i
$669$	12.9341	+	25.7066i	0.500062	+	0.993875i
$670$	2.95640	+	12.3173i	0.114216	+	0.475858i
$671$	−5.95872	−	33.7936i	−0.230034	−	1.30459i
$672$	−7.36861	−	0.749379i	−0.284250	−	0.0289079i
$673$	7.67968	+	6.44402i	0.296030	+	0.248399i	0.778690	−	0.627409i	$-0.215885\pi$
$673$	7.67968	+	6.44402i	0.296030	+	0.248399i	−0.482660	+	0.875808i	$0.660329\pi$
$674$	27.7155	+	41.8786i	1.06756	+	1.61310i
$675$	−3.66803	−	1.32587i	−0.141183	−	0.0510326i
$676$	−9.82586	+	23.1411i	−0.377918	+	0.890044i
$677$	11.4265	+	9.58797i	0.439156	+	0.368496i	0.835394	−	0.549652i	$-0.185240\pi$
$677$	11.4265	+	9.58797i	0.439156	+	0.368496i	−0.396237	+	0.918148i	$0.629684\pi$
$678$	−5.58054	−	30.9974i	−0.214319	−	1.19045i
$679$	1.26116	−	0.222377i	0.0483990	−	0.00853404i
$680$	−4.21844	+	25.1826i	−0.161770	+	0.965709i
$681$	0.420290	−	0.640048i	0.0161055	−	0.0245267i
$682$	−15.2139	+	6.61420i	−0.582572	+	0.253271i
$683$	−11.0184	−	6.36145i	−0.421605	−	0.243414i	0.274158	−	0.961685i	$-0.411601\pi$
$683$	−11.0184	−	6.36145i	−0.421605	−	0.243414i	−0.695764	+	0.718270i	$0.744934\pi$
$684$	−0.946987	−	1.61336i	−0.0362090	−	0.0616882i
$685$	−24.2090	+	13.9770i	−0.924977	+	0.534035i
$686$	−8.53983	+	11.5396i	−0.326052	+	0.440583i
$687$	−3.85118	+	16.3030i	−0.146932	+	0.621998i
$688$	−12.7238	−	1.34018i	−0.485091	−	0.0510940i
$689$	−0.369221	−	0.440021i	−0.0140662	−	0.0167635i
$690$	−13.3408	−	36.2480i	−0.507876	−	1.37994i
$691$	18.7595	−	6.82789i	0.713644	−	0.259745i	0.0404189	−	0.999183i	$-0.487131\pi$
$691$	18.7595	−	6.82789i	0.713644	−	0.259745i	0.673225	+	0.739438i	$0.264909\pi$
$692$	−14.1556	+	1.73649i	−0.538113	+	0.0660114i
$693$	6.25323	+	0.721544i	0.237541	+	0.0274092i
$694$	−0.963969	−	15.7751i	−0.0365918	−	0.598815i
$695$	0.378093	−	2.14427i	0.0143419	−	0.0813369i
$696$	−34.7521	−	14.6088i	−1.31727	−	0.553747i
$697$	−27.6141	−	10.0507i	−1.04596	−	0.380698i
$698$	28.6624	+	30.2072i	1.08489	+	1.14336i
$699$	−2.74228	−	1.18051i	−0.103723	−	0.0446508i
$700$	0.515090	+	1.01120i	0.0194686	+	0.0382197i
$701$	23.1054			0.872679			0.436340	−	0.899782i	$-0.356275\pi$
$701$	23.1054			0.872679			0.436340	+	0.899782i	$0.356275\pi$
$702$	−2.85658	+	3.87792i	−0.107815	+	0.146363i
$703$			0.973789i			0.0367272i
$704$	−7.23640	+	20.9933i	−0.272732	+	0.791216i
$705$	38.6968	−	4.55196i	1.45741	−	0.171437i
$706$	−1.60333	−	1.68974i	−0.0603419	−	0.0635942i
$707$	−0.115066	+	0.316141i	−0.00432749	+	0.0118897i
$708$	29.7874	−	1.92762i	1.11948	−	0.0724442i
$709$	2.25096	+	0.396904i	0.0845364	+	0.0149061i	0.215756	−	0.976447i	$-0.430778\pi$
$709$	2.25096	+	0.396904i	0.0845364	+	0.0149061i	−0.131220	+	0.991353i	$0.541889\pi$
$710$	−41.2034	+	2.51781i	−1.54634	+	0.0944918i
$711$	−18.2245	−	27.6202i	−0.683474	−	1.03584i
$712$	−13.8097	+	11.7907i	−0.517542	+	0.441874i
$713$	−11.0568	−	30.3783i	−0.414080	−	1.13768i
$714$	5.18996	−	6.23046i	0.194229	−	0.233169i
$715$	2.87289	−	2.41064i	0.107440	−	0.0901530i
$716$	−12.0280	+	3.67587i	−0.449507	+	0.137374i
$717$	−7.59562	+	8.06280i	−0.283664	+	0.301111i
$718$	11.7630	+	8.70519i	0.438992	+	0.324875i
$719$	−9.89692	−	17.1420i	−0.369093	−	0.639287i	0.620331	−	0.784340i	$-0.286998\pi$
$719$	−9.89692	−	17.1420i	−0.369093	−	0.639287i	−0.989424	+	0.145053i	$0.953665\pi$
$720$	21.9607	−	11.3859i	0.818428	−	0.424327i
$721$	4.76417	−	8.25179i	0.177427	−	0.307313i
$722$	24.5160	−	10.6582i	0.912390	−	0.396658i
$723$	−1.81580	+	31.5775i	−0.0675303	+	1.17438i
$724$	−20.8695	−	19.4655i	−0.775609	−	0.723428i
$725$	1.00299	+	5.68825i	0.0372502	+	0.211256i
$726$	−2.73366	+	7.59543i	−0.101456	+	0.281893i
$727$	−11.5970	+	13.8207i	−0.430107	+	0.512582i	−0.936953	−	0.349455i	$-0.886367\pi$
$727$	−11.5970	+	13.8207i	−0.430107	+	0.512582i	0.506846	+	0.862037i	$0.330811\pi$
$728$	1.37797	−	0.255155i	0.0510710	−	0.00945666i
$729$	20.6062	−	17.4467i	0.763191	−	0.646173i
$730$	23.0827	+	34.8784i	0.854330	+	1.29091i
$731$	9.00374	−	10.7302i	0.333015	−	0.396872i
$732$	10.1446	+	41.6066i	0.374955	+	1.53782i
$733$	6.13198	−	1.08123i	0.226490	−	0.0399362i	−0.0592514	−	0.998243i	$-0.518871\pi$
$733$	6.13198	−	1.08123i	0.226490	−	0.0399362i	0.285741	+	0.958307i	$0.407760\pi$
$734$	−9.10734	+	2.18594i	−0.336158	+	0.0806846i
$735$	1.31768	−	22.9150i	0.0486034	−	0.845234i
$736$	−39.9734	−	16.5705i	−1.47344	−	0.610797i
$737$	−10.4448	−	6.03032i	−0.384740	−	0.222130i
$738$	8.28313	+	27.2378i	0.304906	+	1.00264i
$739$	−17.2254	−	29.8353i	−0.633647	−	1.09751i	−0.986800	−	0.161944i	$-0.948224\pi$
$739$	−17.2254	−	29.8353i	−0.633647	−	1.09751i	0.353153	−	0.935566i	$-0.385110\pi$
$740$	−12.8587	−	0.675325i	−0.472694	−	0.0248254i
$741$	0.257642	+	0.242713i	0.00946470	+	0.00891629i
$742$	0.266140	−	0.898291i	0.00977031	−	0.0329773i
$743$	20.9598	−	17.5873i	0.768939	−	0.645217i	−0.171498	−	0.985185i	$-0.554861\pi$
$743$	20.9598	−	17.5873i	0.768939	−	0.645217i	0.940437	+	0.339968i	$0.110416\pi$
$744$	18.4145	−	9.46353i	0.675109	−	0.346950i
$745$	43.4957	−	15.8311i	1.59356	−	0.580008i
$746$	12.0996	+	6.03349i	0.442998	+	0.220902i
$747$	−18.2710	−	27.6906i	−0.668502	−	1.01315i
$748$	−14.6286	−	19.4173i	−0.534874	−	0.709966i
$749$	1.20313	−	6.82331i	0.0439616	−	0.249318i
$750$	−25.1988	−	14.4281i	−0.920131	−	0.526841i
$751$	7.78513	−	21.3895i	0.284084	−	0.780513i	−0.712781	−	0.701387i	$-0.752565\pi$
$751$	7.78513	−	21.3895i	0.284084	−	0.780513i	0.996865	−	0.0791265i	$-0.0252131\pi$
$752$	25.6653	−	35.3088i	0.935919	−	1.28758i
$753$	−5.36859	−	45.6391i	−0.195642	−	1.66318i
$754$	7.08686	+	0.807844i	0.258088	+	0.0294199i
$755$			40.8898i			1.48813i
$756$	−7.84599	−	0.394648i	−0.285356	−	0.0143532i
$757$		−	21.1725i		−	0.769529i	−0.923015	−	0.384765i	$-0.874283\pi$
$757$		−	21.1725i		−	0.769529i	0.923015	−	0.384765i	$-0.125717\pi$
$758$	5.26353	−	46.1747i	0.191180	−	1.67714i
$759$	33.7789	+	14.5412i	1.22610	+	0.527813i
$760$	−0.636362	−	1.70289i	−0.0230833	−	0.0617704i
$761$	−7.32872	+	20.1355i	−0.265666	+	0.729911i	0.733094	+	0.680127i	$0.238076\pi$
$761$	−7.32872	+	20.1355i	−0.265666	+	0.729911i	−0.998760	+	0.0497840i	$0.984147\pi$
$762$	9.36596	−	0.0336367i	0.339293	−	0.00121853i
$763$	−1.65790	+	9.40240i	−0.0600199	+	0.340390i
$764$	11.9387	+	15.8469i	0.431928	+	0.573320i
$765$	−3.10437	+	26.9039i	−0.112239	+	0.972711i
$766$	11.8913	−	23.8470i	0.429651	−	0.861627i
$767$	−5.30721	+	1.93167i	−0.191632	+	0.0697485i
$768$	7.32036	−	26.7285i	0.264151	−	0.964481i
$769$	23.3889	−	19.6256i	0.843426	−	0.707719i	−0.114905	−	0.993376i	$-0.536656\pi$
$769$	23.3889	−	19.6256i	0.843426	−	0.707719i	0.958332	+	0.285658i	$0.0922120\pi$
$770$	5.86494	+	1.73763i	0.211358	+	0.0626198i
$771$	9.23924	−	39.1120i	0.332743	−	1.40859i
$772$	−0.713900	+	13.5932i	−0.0256938	+	0.489228i
$773$	−19.2878	−	33.4074i	−0.693734	−	1.20158i	−0.970606	−	0.240675i	$-0.922631\pi$
$773$	−19.2878	−	33.4074i	−0.693734	−	1.20158i	0.276872	−	0.960907i	$-0.410702\pi$
$774$	−13.5506	−	0.730384i	−0.487067	−	0.0262531i
$775$	−2.74723	−	1.58611i	−0.0986833	−	0.0569748i
$776$	0.0410163	+	4.79142i	0.00147240	+	0.172002i
$777$	3.41819	+	2.24457i	0.122627	+	0.0805234i
$778$	−11.4480	−	47.6958i	−0.410429	−	1.70998i
$779$	2.06043	−	0.363310i	0.0738227	−	0.0130169i
$780$	−3.38365	+	3.23378i	−0.121154	+	0.115788i
$781$	25.2640	−	30.1085i	0.904019	−	1.07737i
$782$	39.5066	−	26.1457i	1.41275	−	0.934969i
$783$	−37.6034	−	13.5923i	−1.34384	−	0.485750i
$784$	−17.8585	−	18.5012i	−0.637804	−	0.660759i
$785$	−20.8231	+	24.8160i	−0.743209	+	0.885722i
$786$	24.9351	−	21.0761i	0.889404	−	0.751758i
$787$	0.641604	+	3.63872i	0.0228707	+	0.129706i	0.994105	−	0.108418i	$-0.0345785\pi$
$787$	0.641604	+	3.63872i	0.0228707	+	0.129706i	−0.971235	+	0.238124i	$0.923467\pi$
$788$	−8.41240	+	9.01918i	−0.299679	+	0.321295i
$789$	−19.5850	+	9.85408i	−0.697246	+	0.350815i
$790$	−12.8206	−	29.4899i	−0.456138	−	1.04920i
$791$	−4.85994	+	8.41767i	−0.172800	+	0.299298i
$792$	−6.52816	+	22.6297i	−0.231968	+	0.804112i
$793$	−4.05147	−	7.01736i	−0.143872	−	0.249194i
$794$	7.49908	−	10.1333i	0.266133	−	0.359616i
$795$	0.899632	+	2.99693i	0.0319067	+	0.106290i
$796$	−6.26518	+	1.91470i	−0.222064	+	0.0678647i
$797$	20.3153	−	17.0465i	0.719604	−	0.603820i	−0.207672	−	0.978199i	$-0.566589\pi$
$797$	20.3153	−	17.0465i	0.719604	−	0.603820i	0.927276	+	0.374379i	$0.122144\pi$
$798$	−0.0982098	+	0.568916i	−0.00347659	+	0.0201394i
$799$	16.3452	+	44.9080i	0.578251	+	1.58873i
$800$	−4.04994	+	1.27571i	−0.143187	+	0.0451031i
$801$	−13.9896	+	13.2376i	−0.494300	+	0.467729i
$802$	0.458653	+	7.50574i	0.0161956	+	0.265037i
$803$	−39.2174	−	6.91508i	−1.38395	−	0.244028i
$804$	13.4941	+	6.66844i	0.475900	+	0.235178i
$805$	−4.07690	+	11.2012i	−0.143692	+	0.394790i
$806$	−2.84170	+	2.69638i	−0.100095	+	0.0949758i
$807$	−1.24334	−	1.66753i	−0.0437678	−	0.0586998i
$808$	−1.09550	−	0.620043i	−0.0385394	−	0.0218130i
$809$			3.27098i			0.115001i	0.998345	+	0.0575007i	$0.0183131\pi$
$809$			3.27098i			0.115001i	−0.998345	+	0.0575007i	$0.981687\pi$
$810$	22.6457	−	13.2504i	0.795689	−	0.465571i
$811$	−1.75903			−0.0617677			−0.0308839	−	0.999523i	$-0.509832\pi$
$811$	−1.75903			−0.0617677			−0.0308839	+	0.999523i	$0.509832\pi$
$812$	5.28053	+	10.3665i	0.185310	+	0.363791i
$813$	8.07027	−	6.01735i	0.283037	−	0.211038i
$814$	8.89348	−	8.43866i	0.311716	−	0.295775i
$815$	22.0259	+	8.01678i	0.771534	+	0.280816i
$816$	19.7835	+	23.0035i	0.692560	+	0.805283i
$817$	−0.173176	+	0.982130i	−0.00605866	+	0.0343604i
$818$	43.3482	−	2.64887i	1.51563	−	0.0926157i
$819$	1.44583	−	0.344923i	0.0505214	−	0.0120526i
$820$	3.36851	+	27.4595i	0.117633	+	0.958928i
$821$	−46.0142	+	16.7478i	−1.60591	+	0.584502i	−0.980625	−	0.195897i	$-0.937238\pi$
$821$	−46.0142	+	16.7478i	−1.60591	+	0.584502i	−0.625282	+	0.780399i	$0.715016\pi$
$822$	−5.65052	+	32.7327i	−0.197085	+	1.14168i
$823$	−11.6513	−	13.8855i	−0.406139	−	0.484017i	0.523743	−	0.851876i	$-0.324535\pi$
$823$	−11.6513	−	13.8855i	−0.406139	−	0.484017i	−0.929882	+	0.367859i	$0.880091\pi$
$824$	27.5058	+	22.6817i	0.958211	+	0.790156i
$825$	3.45631	−	1.03753i	0.120333	−	0.0361222i
$826$	−7.40473	−	5.47985i	−0.257644	−	0.190668i
$827$	11.2394	−	6.48908i	0.390833	−	0.225648i	−0.291688	−	0.956514i	$-0.594217\pi$
$827$	11.2394	−	6.48908i	0.390833	−	0.225648i	0.682521	+	0.730866i	$0.260884\pi$
$828$	−43.2404	−	15.3874i	−1.50271	−	0.534750i
$829$	−4.97254	−	2.87090i	−0.172703	−	0.0997104i	0.411157	−	0.911565i	$-0.365125\pi$
$829$	−4.97254	−	2.87090i	−0.172703	−	0.0997104i	−0.583860	+	0.811854i	$0.698458\pi$
$830$	−12.8533	−	29.5652i	−0.446146	−	1.02622i
$831$	11.3385	+	22.5352i	0.393327	+	0.781739i
$832$	0.0897660	+	5.24273i	0.00311208	+	0.181759i
$833$	27.7247	−	4.88862i	0.960605	−	0.169381i
$834$	−1.67017	−	1.97597i	−0.0578332	−	0.0684224i
$835$	−18.2702	−	15.3305i	−0.632266	−	0.530534i
$836$	1.59320	+	0.676483i	0.0551021	+	0.0233967i
$837$	18.9934	−	11.0220i	0.656509	−	0.380976i
$838$	−11.5910	+	7.67098i	−0.400404	+	0.264990i
$839$	−25.0821	−	21.0464i	−0.865930	−	0.726602i	0.0973069	−	0.995254i	$-0.468977\pi$
$839$	−25.0821	−	21.0464i	−0.865930	−	0.726602i	−0.963237	+	0.268653i	$0.913422\pi$
$840$	−7.44429	−	1.69138i	−0.256852	−	0.0583582i
$841$	5.24653	+	29.7545i	0.180915	+	1.02602i
$842$	−23.2230	+	5.57399i	−0.800318	+	0.192092i
$843$	−9.30526	+	14.1707i	−0.320490	+	0.488066i
$844$	−10.7251	−	6.96663i	−0.369172	−	0.239801i
$845$	−12.9563	+	22.4410i	−0.445712	+	0.771995i
$846$	25.2740	−	38.7921i	0.868939	−	1.33370i
$847$	2.15745	−	1.24561i	0.0741310	−	0.0427996i
$848$	3.15037	+	1.53740i	0.108184	+	0.0527946i
$849$	2.33527	+	0.551649i	0.0801462	+	0.0189325i
$850$	1.32056	−	4.45722i	0.0452947	−	0.152881i
$851$	15.3567	+	18.3014i	0.526422	+	0.627365i
$852$	−29.0375	+	39.5335i	−0.994809	+	1.35440i
$853$	17.3146	+	47.5715i	0.592842	+	1.62882i	0.765206	+	0.643785i	$0.222637\pi$
$853$	17.3146	+	47.5715i	0.592842	+	1.62882i	−0.172364	+	0.985033i	$0.555141\pi$
$854$	5.89776	−	11.8274i	0.201817	−	0.404726i
$855$	−0.766327	−	1.76936i	−0.0262078	−	0.0605109i
$856$	24.4357	+	8.65772i	0.835196	+	0.295915i
$857$	43.9658	+	7.75236i	1.50184	+	0.264816i	0.863269	−	0.504744i	$-0.168413\pi$
$857$	43.9658	+	7.75236i	1.50184	+	0.264816i	0.638575	+	0.769559i	$0.279524\pi$
$858$	−0.0160043	−	4.45631i	−0.000546378	−	0.152136i
$859$	21.2132	+	7.72099i	0.723786	+	0.263437i	0.677532	−	0.735493i	$-0.263049\pi$
$859$	21.2132	+	7.72099i	0.723786	+	0.263437i	0.0462539	+	0.998930i	$0.485272\pi$
$860$	−12.8487	−	2.96786i	−0.438137	−	0.101203i
$861$	3.47398	−	8.06995i	0.118393	−	0.275023i
$862$	0.798391	−	7.00393i	0.0271933	−	0.238555i
$863$	−5.45202			−0.185589			−0.0927945	−	0.995685i	$-0.529580\pi$
$863$	−5.45202			−0.185589			−0.0927945	+	0.995685i	$0.529580\pi$
$864$	6.30642	−	28.7094i	0.214549	−	0.976713i
$865$	−14.6995			−0.499799
$866$	0.242577	−	2.12802i	0.00824310	−	0.0723130i
$867$	−3.74666	+	0.440725i	−0.127243	+	0.0149678i
$868$	−6.22550	−	1.43800i	−0.211307	−	0.0488088i
$869$	28.7703	+	10.4715i	0.975966	+	0.355222i
$870$	−33.7192	−	19.3066i	−1.14319	−	0.654556i
$871$	−2.80468	−	0.494540i	−0.0950328	−	0.0167568i
$872$	−33.6720	−	11.9302i	−1.14028	−	0.404007i
$873$	0.302995	+	5.07321i	0.0102548	+	0.171702i
$874$	−1.50517	+	3.01848i	−0.0509131	+	0.102102i
$875$	3.06488	+	8.42069i	0.103612	+	0.284671i
$876$	49.3990	+	5.45144i	1.66904	+	0.184187i
$877$	−17.8965	−	21.3282i	−0.604322	−	0.720203i	0.373968	−	0.927442i	$-0.377997\pi$
$877$	−17.8965	−	21.3282i	−0.604322	−	0.720203i	−0.978291	+	0.207238i	$0.933553\pi$
$878$	4.54900	−	15.3540i	0.153521	−	0.518174i
$879$	−3.70560	+	3.93351i	−0.124987	+	0.132674i
$880$	−10.0377	+	20.5687i	−0.338370	+	0.693372i
$881$	15.7703	−	9.10498i	0.531315	−	0.306755i	−0.210237	−	0.977650i	$-0.567424\pi$
$881$	15.7703	−	9.10498i	0.531315	−	0.306755i	0.741552	+	0.670896i	$0.234090\pi$
$882$	−19.9193	−	18.6305i	−0.670717	−	0.627323i
$883$	−9.43348	+	16.3393i	−0.317462	+	0.549860i	−0.979958	−	0.199206i	$-0.936164\pi$
$883$	−9.43348	+	16.3393i	−0.317462	+	0.549860i	0.662496	+	0.749065i	$0.269497\pi$
$884$	−4.81420	−	3.12714i	−0.161919	−	0.105177i
$885$	30.7154	+	1.76622i	1.03249	+	0.0593710i
$886$	4.48270	−	1.07594i	0.150599	−	0.0361468i
$887$	−4.50791	−	25.5656i	−0.151361	−	0.858409i	−0.962038	−	0.272916i	$-0.912012\pi$
$887$	−4.50791	−	25.5656i	−0.151361	−	0.858409i	0.810677	−	0.585493i	$-0.199099\pi$
$888$	−10.3959	+	11.2263i	−0.348864	+	0.376731i
$889$	−2.21421	−	1.85794i	−0.0742621	−	0.0623133i
$890$	−15.6075	+	10.3291i	−0.523165	+	0.346234i
$891$	−5.68929	+	24.3247i	−0.190598	+	0.814910i
$892$	30.5860	+	12.9870i	1.02409	+	0.434836i
$893$	−2.60648	−	2.18709i	−0.0872224	−	0.0731883i
$894$	18.6258	−	51.7516i	0.622941	−	1.73083i
$895$	−12.7663	+	2.25105i	−0.426732	+	0.0752444i
$896$	−7.05016	+	4.84141i	−0.235529	+	0.161740i
$897$	8.66973	+	0.498535i	0.289474	+	0.0166456i
$898$	12.3984	+	28.5187i	0.413740	+	0.951682i
$899$	−28.1636	−	16.2603i	−0.939309	−	0.542310i
$900$	−4.22091	+	1.57071i	−0.140697	+	0.0523569i
$901$	−3.32369	+	1.91893i	−0.110728	+	0.0639290i
$902$	−21.1734	−	15.6693i	−0.704996	−	0.521730i
$903$	3.04830	+	2.87167i	0.101441	+	0.0955634i
$904$	−28.0587	−	23.1377i	−0.933220	−	0.769548i
$905$	−18.9073	−	22.5329i	−0.628501	−	0.749018i
$906$	37.3324	+	31.0978i	1.24028	+	1.03315i
$907$	6.38033	−	2.32225i	0.211855	−	0.0771090i	−0.233912	−	0.972258i	$-0.575153\pi$
$907$	6.38033	−	2.32225i	0.211855	−	0.0771090i	0.445768	+	0.895149i	$0.352931\pi$
$908$	−0.107655	−	0.877582i	−0.00357264	−	0.0291236i
$909$	−1.19402	−	0.597454i	−0.0396032	−	0.0198163i
$910$	1.44173	−	0.0880998i	0.0477930	−	0.00292048i
$911$	−7.60529	+	43.1317i	−0.251974	+	1.42902i	0.551747	+	0.834012i	$0.313962\pi$
$911$	−7.60529	+	43.1317i	−0.251974	+	1.42902i	−0.803721	+	0.595006i	$0.797150\pi$
$912$	−2.03871	−	0.714096i	−0.0675084	−	0.0236461i
$913$	28.8437	+	10.4982i	0.954587	+	0.347441i
$914$	−0.818176	+	0.776334i	−0.0270629	+	0.0256788i
$915$	5.15673	+	43.8381i	0.170476	+	1.44924i
$916$	8.77971	+	17.2359i	0.290090	+	0.569490i
$917$	−10.0758			−0.332732
$918$	22.2023	+	23.2954i	0.732783	+	0.768862i
$919$			53.5416i			1.76617i	0.469209	+	0.883087i	$0.344539\pi$
$919$			53.5416i			1.76617i	−0.469209	+	0.883087i	$0.655461\pi$
$920$	−38.8145	−	21.9687i	−1.27968	−	0.724288i
$921$	−18.6094	+	43.2292i	−0.613201	+	1.42445i
$922$	3.09094	−	2.93287i	0.101795	−	0.0965888i
$923$	3.17430	−	8.72131i	0.104483	−	0.287065i
$924$	6.04690	−	4.03317i	0.198928	−	0.132682i
$925$	2.30871	+	0.407087i	0.0759098	+	0.0133849i
$926$	−0.834980	−	13.6643i	−0.0274392	−	0.449035i
$927$	30.3649	+	22.5363i	0.997314	+	0.740188i
$928$	−41.5186	+	13.0781i	−1.36292	+	0.429310i
$929$	−6.19598	−	17.0233i	−0.203284	−	0.558517i	0.795597	−	0.605827i	$-0.207157\pi$
$929$	−6.19598	−	17.0233i	−0.203284	−	0.558517i	−0.998880	+	0.0473097i	$0.984935\pi$
$930$	20.0263	−	7.37054i	0.656688	−	0.241689i
$931$	−1.53544	+	1.28838i	−0.0503219	+	0.0422251i
$932$	−3.29693	+	1.00757i	−0.107995	+	0.0330041i
$933$	33.2035	+	7.84349i	1.08703	+	0.256784i
$934$	4.55572	−	6.15599i	0.149068	−	0.201430i
$935$	−12.5287	−	21.7004i	−0.409733	−	0.709678i
$936$	0.379082	+	5.54864i	0.0123907	+	0.181363i
$937$	18.2222	−	31.5618i	0.595294	−	1.03108i	−0.398212	−	0.917294i	$-0.630369\pi$
$937$	18.2222	−	31.5618i	0.595294	−	1.03108i	0.993505	−	0.113785i	$-0.0362976\pi$
$938$	−1.85201	−	4.25998i	−0.0604703	−	0.139093i
$939$	−19.9488	−	13.0995i	−0.651004	−	0.427484i
$940$	30.6877	−	32.9012i	1.00092	−	1.07312i
$941$	−1.27775	−	7.24648i	−0.0416535	−	0.236229i	0.956872	−	0.290509i	$-0.0938246\pi$
$941$	−1.27775	−	7.24648i	−0.0416535	−	0.236229i	−0.998526	+	0.0542804i	$0.982714\pi$
$942$	6.82048	+	37.8847i	0.222223	+	1.23435i
$943$	32.9944	−	39.3213i	1.07445	−	1.28048i
$944$	24.7991	−	23.9376i	0.807142	−	0.779102i
$945$	−7.97718	−	1.38839i	−0.259498	−	0.0451643i
$946$	10.4704	−	6.92935i	0.340421	−	0.225293i
$947$	8.67174	−	10.3346i	0.281794	−	0.335829i	−0.606518	−	0.795070i	$-0.707434\pi$
$947$	8.67174	−	10.3346i	0.281794	−	0.335829i	0.888312	+	0.459241i	$0.151879\pi$
$948$	−36.6747	−	10.7226i	−1.19114	−	0.348255i
$949$	−9.26060	+	1.63289i	−0.300612	+	0.0530059i
$950$	0.0772468	+	0.321835i	0.00250622	+	0.0104417i
$951$	17.2179	−	8.66305i	0.558328	−	0.280919i
$952$	−0.0801509	−	9.36302i	−0.00259770	−	0.303457i
$953$	33.5466	+	19.3681i	1.08668	+	0.627395i	0.932690	−	0.360678i	$-0.117455\pi$
$953$	33.5466	+	19.3681i	1.08668	+	0.627395i	0.153989	+	0.988073i	$0.450788\pi$
$954$	3.42039	+	1.45788i	0.110739	+	0.0472006i
$955$	10.2250	+	17.7102i	0.330872	+	0.573087i
$956$	−0.670833	+	12.7731i	−0.0216963	+	0.413113i
$957$	35.4329	−	10.6364i	1.14538	−	0.343827i
$958$	19.1887	+	5.68510i	0.619958	+	0.183677i
$959$	7.85273	−	6.58922i	0.253578	−	0.212777i
$960$	10.8433	−	26.4255i	0.349967	−	0.852878i
$961$	−12.3471	+	4.49396i	−0.398292	+	0.144967i
$962$	1.29188	−	2.59076i	0.0416520	−	0.0835293i
$963$	26.3532	+	7.84726i	0.849219	+	0.252874i
$964$	21.9767	+	29.1708i	0.707823	+	0.939530i
$965$	−2.43625	+	13.8167i	−0.0784256	+	0.444774i
$966$	7.12608	+	12.2410i	0.229278	+	0.393848i
$967$	−5.65523	+	15.5376i	−0.181860	+	0.499656i	−0.996804	−	0.0798834i	$-0.974545\pi$
$967$	−5.65523	+	15.5376i	−0.181860	+	0.499656i	0.814944	+	0.579539i	$0.196767\pi$
$968$	3.26290	+	8.73145i	0.104873	+	0.280639i
$969$	1.89596	−	1.41367i	0.0609070	−	0.0454135i
$970$	−0.559350	+	4.90693i	−0.0179596	+	0.157552i
$971$		−	54.1911i		−	1.73907i	−0.493868	−	0.869537i	$-0.664417\pi$
$971$		−	54.1911i		−	1.73907i	0.493868	−	0.869537i	$-0.335583\pi$
$972$	5.12507	−	30.7528i	0.164387	−	0.986396i
$973$			0.798454i			0.0255972i
$974$	−27.2836	−	3.11011i	−0.874223	−	0.0996542i
$975$	0.683142	−	0.509364i	0.0218781	−	0.0163127i
$976$	39.9999	+	29.0752i	1.28037	+	0.930675i
$977$	6.10992	−	16.7869i	0.195474	−	0.537060i	−0.802771	−	0.596288i	$-0.796642\pi$
$977$	6.10992	−	16.7869i	0.195474	−	0.537060i	0.998244	+	0.0592281i	$0.0188639\pi$
$978$	24.0706	−	14.0127i	0.769693	−	0.448076i
$979$	3.09439	−	17.5491i	0.0988971	−	0.560873i
$980$	−15.9480	−	21.1686i	−0.509440	−	0.676206i
$981$	−36.3142	−	10.8134i	−1.15942	−	0.345245i
$982$	−31.5350	−	15.7249i	−1.00632	−	0.501803i
$983$	5.24850	−	1.91030i	0.167401	−	0.0609291i	−0.256960	−	0.966422i	$-0.582721\pi$
$983$	5.24850	−	1.91030i	0.167401	−	0.0609291i	0.424361	+	0.905493i	$0.360499\pi$
$984$	27.6324	+	17.8082i	0.880887	+	0.567706i
$985$	−9.73805	+	8.17119i	−0.310280	+	0.260356i
$986$	13.5379	−	45.6938i	0.431134	−	1.45519i
$987$	−13.6850	+	4.10803i	−0.435599	+	0.130760i
$988$	0.408157	+	0.0214360i	0.0129852	+	0.000681972i
$989$	12.2336	+	21.1892i	0.389005	+	0.673777i
$990$	−9.51849	+	22.3317i	−0.302518	+	0.709748i
$991$	−32.6527	−	18.8521i	−1.03725	−	0.598855i	−0.118195	−	0.992990i	$-0.537711\pi$
$991$	−32.6527	−	18.8521i	−1.03725	−	0.598855i	−0.919053	+	0.394135i	$0.871044\pi$
$992$	9.15488	−	22.0845i	0.290668	−	0.701184i
$993$	31.6615	−	15.9303i	1.00475	−	0.505532i
$994$	14.7198	−	3.53304i	0.466883	−	0.112061i
$995$	−6.64978	+	1.17254i	−0.210812	+	0.0371719i
$996$	−36.7683	−	10.7500i	−1.16505	−	0.340627i
$997$	−16.6660	+	19.8617i	−0.527817	+	0.629028i	−0.962411	−	0.271599i	$-0.912448\pi$
$997$	−16.6660	+	19.8617i	−0.527817	+	0.629028i	0.434594	+	0.900627i	$0.356892\pi$
$998$	−26.7694	−	40.4491i	−0.847371	−	1.28039i
$999$	−10.4040	+	12.4549i	−0.329169	+	0.394057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.19	✓	192
3.2	odd	2		648.2.v.b.35.14		192
4.3	odd	2		864.2.bh.b.335.19		192
8.3	odd	2	inner	216.2.v.b.11.29	yes	192
8.5	even	2		864.2.bh.b.335.20		192
24.11	even	2		648.2.v.b.35.4		192
27.5	odd	18	inner	216.2.v.b.59.29	yes	192
27.22	even	9		648.2.v.b.611.4		192
108.59	even	18		864.2.bh.b.815.20		192
216.5	odd	18		864.2.bh.b.815.19		192
216.59	even	18	inner	216.2.v.b.59.19	yes	192
216.211	odd	18		648.2.v.b.611.14		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.19	✓	192	1.1	even	1	trivial
216.2.v.b.11.29	yes	192	8.3	odd	2	inner
216.2.v.b.59.19	yes	192	216.59	even	18	inner
216.2.v.b.59.29	yes	192	27.5	odd	18	inner
648.2.v.b.35.4		192	24.11	even	2
648.2.v.b.35.14		192	3.2	odd	2
648.2.v.b.611.4		192	27.22	even	9
648.2.v.b.611.14		192	216.211	odd	18
864.2.bh.b.335.19		192	4.3	odd	2
864.2.bh.b.335.20		192	8.5	even	2
864.2.bh.b.815.19		192	216.5	odd	18
864.2.bh.b.815.20		192	108.59	even	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.160171 - 1.40511i) q^{2} +(-1.03533 - 1.38855i) q^{3} +(-1.94869 - 0.450118i) q^{4} +(-1.93709 - 0.705042i) q^{5} +(-2.11691 + 1.23236i) q^{6} +(0.744451 + 0.131267i) q^{7} +(-0.944592 + 2.66604i) q^{8} +(-0.856167 + 2.87524i) q^{9} +O(q^{10})\)	\(q+(0.160171 - 1.40511i) q^{2} +(-1.03533 - 1.38855i) q^{3} +(-1.94869 - 0.450118i) q^{4} +(-1.93709 - 0.705042i) q^{5} +(-2.11691 + 1.23236i) q^{6} +(0.744451 + 0.131267i) q^{7} +(-0.944592 + 2.66604i) q^{8} +(-0.856167 + 2.87524i) q^{9} +(-1.30093 + 2.60890i) q^{10} +(-0.949342 - 2.60830i) q^{11} +(1.39253 + 3.17189i) q^{12} +(-0.421307 - 0.502095i) q^{13} +(0.303684 - 1.02501i) q^{14} +(1.02654 + 3.41970i) q^{15} +(3.59479 + 1.75428i) q^{16} +(-3.79256 + 2.18964i) q^{17} +(3.90290 + 1.66354i) q^{18} +(0.155896 - 0.270019i) q^{19} +(3.45743 + 2.24583i) q^{20} +(-0.588484 - 1.16962i) q^{21} +(-3.81701 + 0.916159i) q^{22} +(-1.32831 - 7.53324i) q^{23} +(4.67990 - 1.44862i) q^{24} +(-0.575004 - 0.482485i) q^{25} +(-0.772981 + 0.511564i) q^{26} +(4.87884 - 1.78799i) q^{27} +(-1.39162 - 0.590889i) q^{28} +(-5.89474 - 4.94627i) q^{29} +(4.96950 - 0.894670i) q^{30} +(4.16197 - 0.733867i) q^{31} +(3.04075 - 4.77010i) q^{32} +(-2.63888 + 4.01867i) q^{33} +(2.46923 + 5.67970i) q^{34} +(-1.34952 - 0.779144i) q^{35} +(2.96260 - 5.21757i) q^{36} +(-2.70478 + 1.56160i) q^{37} +(-0.354438 - 0.262301i) q^{38} +(-0.260992 + 1.10484i) q^{39} +(3.70942 - 4.49836i) q^{40} +(4.31331 + 5.14040i) q^{41} +(-1.73770 + 0.639548i) q^{42} +(-3.00565 + 1.09397i) q^{43} +(0.675932 + 5.51008i) q^{44} +(3.68563 - 4.96594i) q^{45} +(-10.7978 + 0.659821i) q^{46} +(1.89499 - 10.7470i) q^{47} +(-1.28589 - 6.80783i) q^{48} +(-6.04087 - 2.19870i) q^{49} +(-0.770046 + 0.730665i) q^{50} +(6.96700 + 2.99917i) q^{51} +(0.594995 + 1.16806i) q^{52} +0.876371 q^{53} +(-1.73088 - 7.14171i) q^{54} +5.72182i q^{55} +(-1.05316 + 1.86074i) q^{56} +(-0.536341 + 0.0630905i) q^{57} +(-7.89425 + 7.49053i) q^{58} +(2.94714 - 8.09720i) q^{59} +(-0.461142 - 7.12601i) q^{60} +(12.1748 + 2.14675i) q^{61} +(-0.364538 - 5.96558i) q^{62} +(-1.01480 + 2.02808i) q^{63} +(-6.21549 - 5.03663i) q^{64} +(0.462111 + 1.26964i) q^{65} +(5.22402 + 4.35160i) q^{66} +(3.32854 - 2.79298i) q^{67} +(8.37613 - 2.55982i) q^{68} +(-9.08507 + 9.64386i) q^{69} +(-1.31094 + 1.77143i) q^{70} +(7.08002 + 12.2629i) q^{71} +(-6.85675 - 4.99850i) q^{72} +(7.17342 - 12.4247i) q^{73} +(1.76100 + 4.05064i) q^{74} +(-0.0746363 + 1.29796i) q^{75} +(-0.425333 + 0.456012i) q^{76} +(-0.364356 - 2.06636i) q^{77} +(1.51063 + 0.543688i) q^{78} +(-7.09014 + 8.44970i) q^{79} +(-5.72657 - 5.93267i) q^{80} +(-7.53396 - 4.92336i) q^{81} +(7.91372 - 5.23734i) q^{82} +(-7.10823 + 8.47125i) q^{83} +(0.620308 + 2.54410i) q^{84} +(8.89031 - 1.56760i) q^{85} +(1.05573 + 4.39851i) q^{86} +(-0.765146 + 13.3062i) q^{87} +(7.85055 - 0.0672036i) q^{88} +(5.55986 + 3.20999i) q^{89} +(-6.38739 - 5.97413i) q^{90} +(-0.247734 - 0.429088i) q^{91} +(-0.802379 + 15.2778i) q^{92} +(-5.32804 - 5.01932i) q^{93} +(-14.7972 - 4.38403i) q^{94} +(-0.492358 + 0.413138i) q^{95} +(-9.77173 + 0.716400i) q^{96} +(1.59192 - 0.579411i) q^{97} +(-4.05700 + 8.13595i) q^{98} +(8.31226 - 0.496445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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