LMFDB - Embedded newform 552.2.bb.a.469.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.5
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36933 - 0.353464i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.75013 + 0.968018i) q^{4} +(-0.708272 + 0.101834i) q^{5} +(-1.26634 + 0.629590i) q^{6} +(-1.58831 + 3.47792i) q^{7} +(-2.05434 - 1.94414i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.36933 - 0.353464i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.75013 + 0.968018i) q^{4} +(-0.708272 + 0.101834i) q^{5} +(-1.26634 + 0.629590i) q^{6} +(-1.58831 + 3.47792i) q^{7} +(-2.05434 - 1.94414i) q^{8} +(0.142315 - 0.989821i) q^{9} +(1.00585 + 0.110904i) q^{10} +(0.408449 - 1.39105i) q^{11} +(1.95657 - 0.414510i) q^{12} +(-5.37158 + 2.45312i) q^{13} +(3.40425 - 4.20101i) q^{14} +(-0.468589 + 0.540781i) q^{15} +(2.12588 + 3.38831i) q^{16} +(-2.62931 - 1.68976i) q^{17} +(-0.544742 + 1.30509i) q^{18} +(-4.06828 - 6.33036i) q^{19} +(-1.33814 - 0.507398i) q^{20} +(1.07719 + 3.66856i) q^{21} +(-1.05099 + 1.76043i) q^{22} +(-4.77745 - 0.419530i) q^{23} +(-2.82571 - 0.123979i) q^{24} +(-4.30619 + 1.26441i) q^{25} +(8.22256 - 1.46047i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(-6.14644 + 4.54929i) q^{28} +(4.55518 - 7.08801i) q^{29} +(0.832800 - 0.574878i) q^{30} +(0.311933 - 0.359990i) q^{31} +(-1.71339 - 5.39113i) q^{32} +(-0.602259 - 1.31876i) q^{33} +(3.00313 + 3.24320i) q^{34} +(0.770788 - 2.62506i) q^{35} +(1.20723 - 1.59455i) q^{36} +(5.60156 + 0.805383i) q^{37} +(3.33325 + 10.1063i) q^{38} +(-2.45312 + 5.37158i) q^{39} +(1.65301 + 1.16778i) q^{40} +(1.28520 + 8.93879i) q^{41} +(-0.178319 - 5.40422i) q^{42} +(-2.10648 + 1.82527i) q^{43} +(2.06140 - 2.03913i) q^{44} +0.715556i q^{45} +(6.39361 + 2.26313i) q^{46} -9.11704 q^{47} +(3.82550 + 1.16855i) q^{48} +(-4.98919 - 5.75783i) q^{49} +(6.34351 - 0.209311i) q^{50} +(-3.09366 + 0.444801i) q^{51} +(-11.7756 - 0.906520i) q^{52} +(4.16104 + 1.90028i) q^{53} +(0.442962 + 1.34305i) q^{54} +(-0.147637 + 1.02684i) q^{55} +(10.0245 - 4.05693i) q^{56} +(-7.22010 - 2.12001i) q^{57} +(-8.74291 + 8.09572i) q^{58} +(-1.26601 + 0.578167i) q^{59} +(-1.34358 + 0.492832i) q^{60} +(-3.93018 - 3.40552i) q^{61} +(-0.554383 + 0.382688i) q^{62} +(3.21648 + 2.06711i) q^{63} +(0.440621 + 7.98786i) q^{64} +(3.55473 - 2.28449i) q^{65} +(0.358555 + 2.01870i) q^{66} +(3.26376 + 11.1154i) q^{67} +(-2.96591 - 5.50251i) q^{68} +(-3.88529 + 2.81150i) q^{69} +(-1.98333 + 3.32213i) q^{70} +(-13.1999 + 3.87584i) q^{71} +(-2.21672 + 1.75675i) q^{72} +(7.18235 - 4.61582i) q^{73} +(-7.38571 - 3.08279i) q^{74} +(-2.42639 + 3.77553i) q^{75} +(-0.992093 - 15.0171i) q^{76} +(4.18922 + 3.62998i) q^{77} +(5.25779 - 6.48838i) q^{78} +(5.49995 + 12.0432i) q^{79} +(-1.85075 - 2.18336i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(1.39968 - 12.6944i) q^{82} +(-11.5494 - 1.66055i) q^{83} +(-1.66602 + 7.46319i) q^{84} +(2.03434 + 0.929053i) q^{85} +(3.52963 - 1.75483i) q^{86} +(-1.19908 - 8.33977i) q^{87} +(-3.54349 + 2.06361i) q^{88} +(-3.74534 - 4.32235i) q^{89} +(0.252923 - 0.979831i) q^{90} -22.5783i q^{91} +(-7.95502 - 5.35888i) q^{92} -0.476335i q^{93} +(12.4842 + 3.22255i) q^{94} +(3.52609 + 4.06933i) q^{95} +(-4.82533 - 2.95231i) q^{96} +(1.61798 + 11.2533i) q^{97} +(4.79665 + 9.64786i) q^{98} +(-1.31876 - 0.602259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.36933	−	0.353464i	−0.968262	−	0.249937i
$2$	−1.36933	−	0.353464i	−0.968262	−	0.249937i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$4$	1.75013	+	0.968018i	0.875063	+	0.484009i
$5$	−0.708272	+	0.101834i	−0.316749	+	0.0455416i	−0.298856	−	0.954298i	$-0.596605\pi$
$5$	−0.708272	+	0.101834i	−0.316749	+	0.0455416i	−0.0178932	+	0.999840i	$0.505696\pi$
$6$	−1.26634	+	0.629590i	−0.516981	+	0.257029i
$7$	−1.58831	+	3.47792i	−0.600327	+	1.31453i	0.328671	+	0.944445i	$0.393399\pi$
$7$	−1.58831	+	3.47792i	−0.600327	+	1.31453i	−0.928997	+	0.370087i	$0.879328\pi$
$8$	−2.05434	−	1.94414i	−0.726319	−	0.687358i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	1.00585	+	0.110904i	0.318079	+	0.0350710i
$11$	0.408449	−	1.39105i	0.123152	−	0.419418i	−0.874719	−	0.484630i	$-0.838954\pi$
$11$	0.408449	−	1.39105i	0.123152	−	0.419418i	0.997871	+	0.0652123i	$0.0207725\pi$
$12$	1.95657	−	0.414510i	0.564814	−	0.119659i
$13$	−5.37158	+	2.45312i	−1.48981	+	0.680373i	−0.983322	−	0.181875i	$-0.941783\pi$
$13$	−5.37158	+	2.45312i	−1.48981	+	0.680373i	−0.506487	+	0.862248i	$0.669056\pi$
$14$	3.40425	−	4.20101i	0.909823	−	1.12277i
$15$	−0.468589	+	0.540781i	−0.120989	+	0.139629i
$16$	2.12588	+	3.38831i	0.531471	+	0.847077i
$17$	−2.62931	−	1.68976i	−0.637702	−	0.409826i	0.181452	−	0.983400i	$-0.441920\pi$
$17$	−2.62931	−	1.68976i	−0.637702	−	0.409826i	−0.819154	+	0.573574i	$0.805557\pi$
$18$	−0.544742	+	1.30509i	−0.128397	+	0.307612i
$19$	−4.06828	−	6.33036i	−0.933326	−	1.45228i	−0.891428	−	0.453162i	$-0.850296\pi$
$19$	−4.06828	−	6.33036i	−0.933326	−	1.45228i	−0.0418984	−	0.999122i	$-0.513341\pi$
$20$	−1.33814	−	0.507398i	−0.299218	−	0.113458i
$21$	1.07719	+	3.66856i	0.235062	+	0.800546i
$22$	−1.05099	+	1.76043i	−0.224072	+	0.375326i
$23$	−4.77745	−	0.419530i	−0.996166	−	0.0874780i
$23$	−4.77745	−	0.419530i	−0.996166	−	0.0874780i
$24$	−2.82571	−	0.123979i	−0.576795	−	0.0253070i
$25$	−4.30619	+	1.26441i	−0.861237	+	0.252882i
$26$	8.22256	−	1.46047i	1.61258	−	0.286421i
$27$	−0.540641	−	0.841254i	−0.104046	−	0.161899i
$28$	−6.14644	+	4.54929i	−1.16157	+	0.859735i
$29$	4.55518	−	7.08801i	0.845877	−	1.31621i	−0.101090	−	0.994877i	$-0.532233\pi$
$29$	4.55518	−	7.08801i	0.845877	−	1.31621i	0.946966	−	0.321332i	$-0.104131\pi$
$30$	0.832800	−	0.574878i	0.152048	−	0.104958i
$31$	0.311933	−	0.359990i	0.0560249	−	0.0646562i	−0.727045	−	0.686589i	$-0.759107\pi$
$31$	0.311933	−	0.359990i	0.0560249	−	0.0646562i	0.783070	+	0.621933i	$0.213652\pi$
$32$	−1.71339	−	5.39113i	−0.302887	−	0.953026i
$33$	−0.602259	−	1.31876i	−0.104840	−	0.229567i
$34$	3.00313	+	3.24320i	0.515032	+	0.556204i
$35$	0.770788	−	2.62506i	0.130287	−	0.443716i
$36$	1.20723	−	1.59455i	0.201206	−	0.265758i
$37$	5.60156	+	0.805383i	0.920891	+	0.132404i	0.586425	−	0.810003i	$-0.300535\pi$
$37$	5.60156	+	0.805383i	0.920891	+	0.132404i	0.334466	+	0.942408i	$0.391444\pi$
$38$	3.33325	+	10.1063i	0.540725	+	1.63946i
$39$	−2.45312	+	5.37158i	−0.392813	+	0.860142i
$40$	1.65301	+	1.16778i	0.261364	+	0.184642i
$41$	1.28520	+	8.93879i	0.200715	+	1.39601i	0.802169	+	0.597097i	$0.203679\pi$
$41$	1.28520	+	8.93879i	0.200715	+	1.39601i	−0.601454	+	0.798908i	$0.705412\pi$
$42$	−0.178319	−	5.40422i	−0.0275151	−	0.833889i
$43$	−2.10648	+	1.82527i	−0.321235	+	0.278351i	−0.800518	−	0.599309i	$-0.795442\pi$
$43$	−2.10648	+	1.82527i	−0.321235	+	0.278351i	0.479283	+	0.877660i	$0.340897\pi$
$44$	2.06140	−	2.03913i	0.310768	−	0.307410i
$45$			0.715556i			0.106669i
$46$	6.39361	+	2.26313i	0.942686	+	0.333680i
$47$	−9.11704			−1.32986			−0.664928	−	0.746907i	$-0.731538\pi$
$47$	−9.11704			−1.32986			−0.664928	+	0.746907i	$0.731538\pi$
$48$	3.82550	+	1.16855i	0.552164	+	0.168666i
$49$	−4.98919	−	5.75783i	−0.712741	−	0.822547i
$50$	6.34351	−	0.209311i	0.897108	−	0.0296011i
$51$	−3.09366	+	0.444801i	−0.433198	+	0.0622845i
$52$	−11.7756	−	0.906520i	−1.63298	−	0.125712i
$53$	4.16104	+	1.90028i	0.571563	+	0.261024i	0.680162	−	0.733062i	$-0.261909\pi$
$53$	4.16104	+	1.90028i	0.571563	+	0.261024i	−0.108599	+	0.994086i	$0.534637\pi$
$54$	0.442962	+	1.34305i	0.0602795	+	0.182766i
$55$	−0.147637	+	1.02684i	−0.0199074	+	0.138459i
$56$	10.0245	−	4.05693i	1.33958	−	0.542130i
$57$	−7.22010	−	2.12001i	−0.956326	−	0.280803i
$58$	−8.74291	+	8.09572i	−1.14800	+	1.06302i
$59$	−1.26601	+	0.578167i	−0.164820	+	0.0752709i	−0.496117	−	0.868256i	$-0.665241\pi$
$59$	−1.26601	+	0.578167i	−0.164820	+	0.0752709i	0.331296	+	0.943527i	$0.392514\pi$
$60$	−1.34358	+	0.492832i	−0.173455	+	0.0636243i
$61$	−3.93018	−	3.40552i	−0.503209	−	0.436033i	0.365900	−	0.930654i	$-0.380761\pi$
$61$	−3.93018	−	3.40552i	−0.503209	−	0.436033i	−0.869108	+	0.494622i	$0.835307\pi$
$62$	−0.554383	+	0.382688i	−0.0704067	+	0.0486014i
$63$	3.21648	+	2.06711i	0.405239	+	0.260431i
$64$	0.440621	+	7.98786i	0.0550776	+	0.998482i
$65$	3.55473	−	2.28449i	0.440910	−	0.283356i
$66$	0.358555	+	2.01870i	0.0441351	+	0.248485i
$67$	3.26376	+	11.1154i	0.398732	+	1.35796i	0.877315	+	0.479914i	$0.159332\pi$
$67$	3.26376	+	11.1154i	0.398732	+	1.35796i	−0.478584	+	0.878042i	$0.658850\pi$
$68$	−2.96591	−	5.50251i	−0.359670	−	0.667277i
$69$	−3.88529	+	2.81150i	−0.467734	+	0.338465i
$70$	−1.98333	+	3.32213i	−0.237053	+	0.397070i
$71$	−13.1999	+	3.87584i	−1.56654	+	0.459978i	−0.945992	−	0.324189i	$-0.894909\pi$
$71$	−13.1999	+	3.87584i	−1.56654	+	0.459978i	−0.620549	+	0.784167i	$0.713090\pi$
$72$	−2.21672	+	1.75675i	−0.261243	+	0.207035i
$73$	7.18235	−	4.61582i	0.840630	−	0.540240i	−0.0480090	−	0.998847i	$-0.515288\pi$
$73$	7.18235	−	4.61582i	0.840630	−	0.540240i	0.888639	+	0.458607i	$0.151651\pi$
$74$	−7.38571	−	3.08279i	−0.858572	−	0.358367i
$75$	−2.42639	+	3.77553i	−0.280175	+	0.435961i
$76$	−0.992093	−	15.0171i	−0.113801	−	1.72258i
$77$	4.18922	+	3.62998i	0.477406	+	0.413675i
$78$	5.25779	−	6.48838i	0.595328	−	0.734664i
$79$	5.49995	+	12.0432i	0.618793	+	1.35497i	0.916394	+	0.400277i	$0.131086\pi$
$79$	5.49995	+	12.0432i	0.618793	+	1.35497i	−0.297601	+	0.954690i	$0.596187\pi$
$80$	−1.85075	−	2.18336i	−0.206920	−	0.244107i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	1.39968	−	12.6944i	0.154568	−	1.40186i
$83$	−11.5494	−	1.66055i	−1.26771	−	0.182269i	−0.524546	−	0.851382i	$-0.675765\pi$
$83$	−11.5494	−	1.66055i	−1.26771	−	0.182269i	−0.743161	+	0.669113i	$0.766674\pi$
$84$	−1.66602	+	7.46319i	−0.181778	+	0.814301i
$85$	2.03434	+	0.929053i	0.220655	+	0.100770i
$86$	3.52963	−	1.75483i	0.380610	−	0.189229i
$87$	−1.19908	−	8.33977i	−0.128555	−	0.894117i
$88$	−3.54349	+	2.06361i	−0.377738	+	0.219981i
$89$	−3.74534	−	4.32235i	−0.397005	−	0.458168i	0.521690	−	0.853135i	$-0.325302\pi$
$89$	−3.74534	−	4.32235i	−0.397005	−	0.458168i	−0.918696	+	0.394966i	$0.870756\pi$
$90$	0.252923	−	0.979831i	0.0266605	−	0.103283i
$91$		−	22.5783i		−	2.36685i
$92$	−7.95502	−	5.35888i	−0.829368	−	0.558702i
$93$		−	0.476335i		−	0.0493937i
$94$	12.4842	+	3.22255i	1.28765	+	0.332380i
$95$	3.52609	+	4.06933i	0.361770	+	0.417504i
$96$	−4.82533	−	2.95231i	−0.492483	−	0.301319i
$97$	1.61798	+	11.2533i	0.164281	+	1.14260i	0.890449	+	0.455083i	$0.150391\pi$
$97$	1.61798	+	11.2533i	0.164281	+	1.14260i	−0.726168	+	0.687518i	$0.758700\pi$
$98$	4.79665	+	9.64786i	0.484535	+	0.974581i
$99$	−1.31876	−	0.602259i	−0.132541	−	0.0605293i
$100$	−8.76034	−	1.95559i	−0.876034	−	0.195559i
$101$	−0.132610	−	0.0190665i	−0.0131952	−	0.00189719i	0.135714	−	0.990748i	$-0.456667\pi$
$101$	−0.132610	−	0.0190665i	−0.0131952	−	0.00189719i	−0.148909	+	0.988851i	$0.547576\pi$
$102$	4.39345	+	0.484418i	0.435017	+	0.0479645i
$103$	14.5733	+	4.27911i	1.43595	+	0.421634i	0.904871	−	0.425687i	$-0.139967\pi$
$103$	14.5733	+	4.27911i	1.43595	+	0.421634i	0.531082	+	0.847321i	$0.321786\pi$
$104$	15.8043	+	5.40358i	1.54974	+	0.529865i
$105$	−1.13653	−	2.48865i	−0.110914	−	0.242867i
$106$	−5.02615	−	4.07289i	−0.488183	−	0.395594i
$107$	−1.72355	−	1.49346i	−0.166622	−	0.144378i	0.567559	−	0.823333i	$-0.307888\pi$
$107$	−1.72355	−	1.49346i	−0.166622	−	0.144378i	−0.734180	+	0.678954i	$0.762433\pi$
$108$	−0.131841	−	1.99565i	−0.0126864	−	0.192031i
$109$	−0.459352	+	0.714766i	−0.0439980	+	0.0684622i	−0.862556	−	0.505962i	$-0.831138\pi$
$109$	−0.459352	+	0.714766i	−0.0439980	+	0.0684622i	0.818558	+	0.574424i	$0.194774\pi$
$110$	0.565114	−	1.35389i	0.0538815	−	0.129089i
$111$	4.76079	−	3.05958i	0.451875	−	0.290402i
$112$	−15.1608	+	2.01196i	−1.43257	+	0.190112i
$113$	9.29057	−	2.72796i	0.873984	−	0.256625i	0.186175	−	0.982517i	$-0.440391\pi$
$113$	9.29057	−	2.72796i	0.873984	−	0.256625i	0.687809	+	0.725892i	$0.258573\pi$
$114$	9.13735	+	5.45504i	0.855791	+	0.510912i
$115$	3.42646	−	0.189366i	0.319519	−	0.0176585i
$116$	14.8335	−	7.99540i	1.37725	−	0.742355i
$117$	1.66369	+	5.66602i	0.153809	+	0.523824i
$118$	1.93795	−	0.344212i	0.178402	−	0.0316873i
$119$	10.0530	−	6.46068i	0.921558	−	0.592250i
$120$	2.01400	−	0.199943i	0.183852	−	0.0182522i
$121$	7.48560	+	4.81070i	0.680509	+	0.437336i
$122$	4.17799	+	6.05246i	0.378257	+	0.547964i
$123$	6.82496	+	5.91386i	0.615386	+	0.533235i
$124$	0.894400	−	0.328071i	0.0803195	−	0.0294617i
$125$	6.17565	−	2.82033i	0.552367	−	0.252258i
$126$	−3.67378	−	3.96746i	−0.327286	−	0.353450i
$127$	−16.1877	−	4.75314i	−1.43643	−	0.421773i	−0.531397	−	0.847123i	$-0.678333\pi$
$127$	−16.1877	−	4.75314i	−1.43643	−	0.421773i	−0.905029	+	0.425350i	$0.860151\pi$
$128$	2.22007	−	11.0938i	0.196228	−	0.980558i
$129$	−0.396670	+	2.75890i	−0.0349248	+	0.242907i
$130$	−5.67508	+	1.87174i	−0.497738	+	0.164163i
$131$	−4.95676	−	2.26368i	−0.433074	−	0.197778i	0.186936	−	0.982372i	$-0.440144\pi$
$131$	−4.95676	−	2.26368i	−0.433074	−	0.197778i	−0.620010	+	0.784594i	$0.712872\pi$
$132$	0.222557	−	2.89100i	0.0193711	−	0.251629i
$133$	28.4782	−	4.09455i	2.46937	−	0.355042i
$134$	−0.540286	−	16.3742i	−0.0466736	−	1.41452i
$135$	0.468589	+	0.540781i	0.0403297	+	0.0465430i
$136$	2.11637	+	8.58309i	0.181477	+	0.735994i
$137$	22.2078			1.89734			0.948671	−	0.316265i	$-0.102429\pi$
$137$	22.2078			1.89734			0.948671	+	0.316265i	$0.102429\pi$
$138$	6.31400	−	2.47656i	0.537484	−	0.210819i
$139$		−	19.7869i		−	1.67831i	−0.543895	−	0.839153i	$-0.683051\pi$
$139$		−	19.7869i		−	1.67831i	0.543895	−	0.839153i	$-0.316949\pi$
$140$	3.89008	−	3.84805i	0.328772	−	0.325220i
$141$	−6.89020	+	5.97039i	−0.580259	+	0.502798i
$142$	19.4450	−	0.641610i	1.63179	−	0.0538427i
$143$	1.21839	+	8.47412i	0.101887	+	0.708641i
$144$	3.65636	−	1.62204i	0.304697	−	0.135170i
$145$	−2.50451	+	5.48411i	−0.207988	+	0.455431i
$146$	−11.4665	+	3.78187i	−0.948977	+	0.312990i
$147$	−7.54115	−	1.08425i	−0.621984	−	0.0894278i
$148$	9.02382	+	6.83194i	0.741753	+	0.561582i
$149$	−2.82573	+	9.62354i	−0.231492	+	0.788391i	0.759032	+	0.651053i	$0.225673\pi$
$149$	−2.82573	+	9.62354i	−0.231492	+	0.788391i	−0.990524	+	0.137337i	$0.956146\pi$
$150$	4.65704	−	4.31230i	0.380245	−	0.352098i
$151$	−3.44502	−	7.54354i	−0.280352	−	0.613884i	0.716105	−	0.697993i	$-0.245923\pi$
$151$	−3.44502	−	7.54354i	−0.280352	−	0.613884i	−0.996457	+	0.0841081i	$0.973196\pi$
$152$	−3.94950	+	20.9140i	−0.320347	+	1.69635i
$153$	−2.04675	+	2.36207i	−0.165470	+	0.190962i
$154$	−4.45336	−	6.45138i	−0.358862	−	0.519867i
$155$	−0.184274	+	0.286737i	−0.0148013	+	0.0230312i
$156$	−9.49306	+	7.02628i	−0.760053	+	0.562553i
$157$	−0.664966	−	1.03471i	−0.0530700	−	0.0825786i	0.813705	−	0.581279i	$-0.197447\pi$
$157$	−0.664966	−	1.03471i	−0.0530700	−	0.0825786i	−0.866775	+	0.498700i	$0.833811\pi$
$158$	−3.27440	−	18.4352i	−0.260497	−	1.46662i
$159$	4.38913	−	1.28876i	0.348080	−	0.102206i
$160$	1.76255	+	3.64391i	0.139342	+	0.288076i
$161$	9.04718	−	15.9493i	0.713018	−	1.25698i
$162$	1.21428	+	0.724931i	0.0954028	+	0.0569560i
$163$	−1.47331	−	5.01765i	−0.115399	−	0.393012i	0.881456	−	0.472267i	$-0.156564\pi$
$163$	−1.47331	−	5.01765i	−0.115399	−	0.393012i	−0.996854	+	0.0792546i	$0.974746\pi$
$164$	−6.40364	+	16.8881i	−0.500041	+	1.31874i
$165$	0.560859	+	0.872713i	0.0436628	+	0.0679406i
$166$	15.2279	+	6.35612i	1.18192	+	0.493331i
$167$	−14.8745	−	9.55923i	−1.15102	−	0.739715i	−0.181178	−	0.983450i	$-0.557991\pi$
$167$	−14.8745	−	9.55923i	−1.15102	−	0.739715i	−0.969842	+	0.243735i	$0.921627\pi$
$168$	4.91930	−	9.63068i	0.379532	−	0.743023i
$169$	14.3229	−	16.5295i	1.10176	−	1.27150i
$170$	−2.45730	−	1.99125i	−0.188466	−	0.152722i
$171$	−6.84490	+	3.12596i	−0.523443	+	0.239048i
$172$	−5.45350	+	1.15535i	−0.415825	+	0.0880946i
$173$	2.40566	−	8.19292i	0.182899	−	0.622897i	−0.816089	−	0.577926i	$-0.803862\pi$
$173$	2.40566	−	8.19292i	0.182899	−	0.622897i	0.998988	−	0.0449708i	$-0.0143195\pi$
$174$	−1.30588	+	11.8437i	−0.0989983	+	0.897870i
$175$	2.44206	−	16.9849i	0.184602	−	1.28394i
$176$	5.58162	−	1.57326i	0.420731	−	0.118589i
$177$	−0.578167	+	1.26601i	−0.0434577	+	0.0951591i
$178$	3.60081	+	7.24257i	0.269892	+	0.542853i
$179$	−0.201507	+	0.0289723i	−0.0150613	+	0.00216549i	−0.149841	−	0.988710i	$-0.547876\pi$
$179$	−0.201507	+	0.0289723i	−0.0150613	+	0.00216549i	0.134780	+	0.990876i	$0.456967\pi$
$180$	−0.692671	+	1.25231i	−0.0516286	+	0.0933419i
$181$	−5.75664	+	4.98816i	−0.427888	+	0.370767i	−0.842017	−	0.539451i	$-0.818632\pi$
$181$	−5.75664	+	4.98816i	−0.427888	+	0.370767i	0.414129	+	0.910218i	$0.364086\pi$
$182$	−7.98061	+	30.9171i	−0.591562	+	2.29173i
$183$	−5.20038			−0.384423
$184$	8.99887	+	10.1499i	0.663406	+	0.748260i
$185$	−4.04945			−0.297721
$186$	−0.168367	+	0.652260i	−0.0123453	+	0.0478260i
$187$	−3.42448	+	2.96733i	−0.250423	+	0.216992i
$188$	−15.9560	−	8.82546i	−1.16371	−	0.643663i
$189$	3.78452	−	0.544132i	0.275284	−	0.0395798i
$190$	−3.39002	−	6.81860i	−0.245938	−	0.494673i
$191$	0.862579	−	1.88878i	0.0624140	−	0.136668i	−0.875855	−	0.482575i	$-0.839702\pi$
$191$	0.862579	−	1.88878i	0.0624140	−	0.136668i	0.938269	+	0.345907i	$0.112429\pi$
$192$	5.56393	+	5.74827i	0.401542	+	0.414846i
$193$	−0.687034	+	4.77842i	−0.0494538	+	0.343959i	0.950040	+	0.312130i	$0.101042\pi$
$193$	−0.687034	+	4.77842i	−0.0494538	+	0.343959i	−0.999493	+	0.0318290i	$0.989867\pi$
$194$	1.76209	−	15.9814i	0.126511	−	1.14740i
$195$	1.19047	−	4.05435i	0.0852510	−	0.290338i
$196$	−3.15802	−	14.9065i	−0.225573	−	1.06475i
$197$	−19.8941	+	9.08532i	−1.41739	+	0.647302i	−0.969119	−	0.246594i	$-0.920689\pi$
$197$	−19.8941	+	9.08532i	−1.41739	+	0.647302i	−0.448275	+	0.893896i	$0.647961\pi$
$198$	1.59294	+	1.29083i	0.113206	+	0.0917351i
$199$	6.64117	−	7.66431i	0.470780	−	0.543309i	−0.469849	−	0.882747i	$-0.655691\pi$
$199$	6.64117	−	7.66431i	0.470780	−	0.543309i	0.940628	+	0.339438i	$0.110237\pi$
$200$	11.3046	+	5.77431i	0.799353	+	0.408305i
$201$	9.74559	+	6.26311i	0.687401	+	0.441766i
$202$	0.174848	+	0.0729813i	0.0123023	+	0.00513495i
$203$	17.4165	+	27.1006i	1.22240	+	1.90209i
$204$	−5.84486	−	2.21626i	−0.409222	−	0.155169i
$205$	−1.82055	−	6.20022i	−0.127153	−	0.433042i
$206$	−18.4432	−	11.0107i	−1.28500	−	0.767149i
$207$	−1.09516	+	4.66911i	−0.0761189	+	0.324526i
$208$	−19.7313	−	12.9855i	−1.36812	−	0.900384i
$209$	−10.4675	+	3.07355i	−0.724055	+	0.212602i
$210$	0.676632	+	3.80950i	0.0466921	+	0.262881i
$211$	−5.74585	−	8.94071i	−0.395560	−	0.615504i	0.585161	−	0.810917i	$-0.301032\pi$
$211$	−5.74585	−	8.94071i	−0.395560	−	0.615504i	−0.980721	+	0.195413i	$0.937395\pi$
$212$	5.44284	+	7.35370i	0.373816	+	0.505054i
$213$	−7.43769	+	11.5733i	−0.509622	+	0.792988i
$214$	1.83222	+	2.65425i	0.125248	+	0.181441i
$215$	1.30608	−	1.50730i	0.0890742	−	0.102797i
$216$	−0.524857	+	2.77930i	−0.0357120	+	0.189108i
$217$	0.756570	+	1.65666i	0.0513593	+	0.112461i
$218$	0.881649	−	0.816386i	0.0597128	−	0.0552926i
$219$	2.40534	−	8.19184i	0.162538	−	0.553553i
$220$	−1.25238	+	1.65418i	−0.0844354	+	0.111525i
$221$	18.2687	+	2.62665i	1.22889	+	0.176687i
$222$	−7.60055	+	2.50680i	−0.510115	+	0.168245i
$223$	2.97243	−	6.50872i	0.199049	−	0.435856i	−0.783616	−	0.621245i	$-0.786627\pi$
$223$	2.97243	−	6.50872i	0.199049	−	0.435856i	0.982665	+	0.185389i	$0.0593545\pi$
$224$	21.4713	+	2.60378i	1.43461	+	0.173972i
$225$	0.638706	+	4.44230i	0.0425804	+	0.296153i
$226$	−13.6861	+	0.451588i	−0.910385	+	0.0300392i
$227$	−9.07896	+	7.86697i	−0.602592	+	0.522149i	−0.901865	−	0.432019i	$-0.857801\pi$
$227$	−9.07896	+	7.86697i	−0.602592	+	0.522149i	0.299273	+	0.954168i	$0.403256\pi$
$228$	−10.5839	−	10.6995i	−0.700934	−	0.708590i
$229$			16.1553i			1.06757i	0.845619	+	0.533787i	$0.179231\pi$
$229$			16.1553i			1.06757i	−0.845619	+	0.533787i	$0.820769\pi$
$230$	−4.75888	−	0.951825i	−0.313791	−	0.0627615i
$231$	5.54314			0.364712
$232$	−23.1380	+	5.70524i	−1.51908	+	0.374567i
$233$	−1.26783	−	1.46316i	−0.0830586	−	0.0958547i	0.712699	−	0.701470i	$-0.247473\pi$
$233$	−1.26783	−	1.46316i	−0.0830586	−	0.0958547i	−0.795758	+	0.605615i	$0.792927\pi$
$234$	−0.275409	−	8.34671i	−0.0180041	−	0.545641i
$235$	6.45735	−	0.928426i	0.421231	−	0.0605638i
$236$	−2.77535	−	0.213654i	−0.180660	−	0.0139077i
$237$	12.0432	+	5.49995i	0.782291	+	0.357260i
$238$	−16.0495	+	5.29342i	−1.04034	+	0.343121i
$239$	−1.51652	+	10.5476i	−0.0980956	+	0.682270i	0.880131	+	0.474731i	$0.157455\pi$
$239$	−1.51652	+	10.5476i	−0.0980956	+	0.682270i	−0.978227	+	0.207539i	$0.933455\pi$
$240$	−2.82850	−	0.438088i	−0.182579	−	0.0282784i
$241$	−20.6858	−	6.07391i	−1.33249	−	0.391255i	−0.463507	−	0.886093i	$-0.653409\pi$
$241$	−20.6858	−	6.07391i	−1.33249	−	0.391255i	−0.868985	+	0.494838i	$0.835227\pi$
$242$	−8.54984	−	9.23333i	−0.549604	−	0.593541i
$243$	−0.909632	+	0.415415i	−0.0583529	+	0.0266489i
$244$	−3.58171	−	9.76459i	−0.229295	−	0.625114i
$245$	4.12005	+	3.57004i	0.263220	+	0.228082i
$246$	−7.25528	−	10.5104i	−0.462580	−	0.670119i
$247$	37.3822	+	24.0241i	2.37857	+	1.52862i
$248$	−1.34069	+	0.133099i	−0.0851338	+	0.00845182i
$249$	−9.81585	+	6.30826i	−0.622054	+	0.399770i
$250$	−9.45339	+	1.67908i	−0.597885	+	0.106195i
$251$	2.28812	+	7.79262i	0.144425	+	0.491866i	0.999652	−	0.0263880i	$-0.00840054\pi$
$251$	2.28812	+	7.79262i	0.144425	+	0.491866i	−0.855227	+	0.518254i	$0.826582\pi$
$252$	3.62825	+	6.73131i	0.228558	+	0.424033i
$253$	−2.53493	+	6.47431i	−0.159370	+	0.407037i
$254$	20.4862	+	12.2304i	1.28542	+	0.767402i
$255$	2.14585	−	0.630080i	0.134379	−	0.0394571i
$256$	−6.96125	+	14.4063i	−0.435078	+	0.900393i
$257$	6.62270	−	4.25615i	0.413113	−	0.265492i	−0.317534	−	0.948247i	$-0.602855\pi$
$257$	6.62270	−	4.25615i	0.413113	−	0.265492i	0.730647	+	0.682755i	$0.239218\pi$
$258$	1.51834	−	3.63763i	0.0945279	−	0.226469i
$259$	−11.6981	+	18.2026i	−0.726885	+	1.13106i
$260$	8.43265	−	0.557097i	0.522971	−	0.0345497i
$261$	−6.36759	−	5.51755i	−0.394144	−	0.341528i
$262$	5.98731	+	4.85176i	0.369897	+	0.299743i
$263$	4.70803	+	10.3091i	0.290309	+	0.635689i	0.997449	−	0.0713854i	$-0.0227420\pi$
$263$	4.70803	+	10.3091i	0.290309	+	0.635689i	−0.707140	+	0.707074i	$0.750015\pi$
$264$	−1.32662	+	3.88007i	−0.0816478	+	0.238802i
$265$	−3.14066	−	0.922182i	−0.192929	−	0.0566492i
$266$	−40.4433	−	4.45924i	−2.47974	−	0.273414i
$267$	−5.66108	−	0.813940i	−0.346452	−	0.0498123i
$268$	−5.04786	+	22.6126i	−0.308347	+	1.38129i
$269$	−21.9914	−	10.0431i	−1.34084	−	0.612341i	−0.389654	−	0.920961i	$-0.627405\pi$
$269$	−21.9914	−	10.0431i	−1.34084	−	0.612341i	−0.951185	+	0.308621i	$0.900133\pi$
$270$	−0.450506	−	0.906137i	−0.0274169	−	0.0551457i
$271$	1.05589	+	7.34389i	0.0641409	+	0.446110i	0.996432	+	0.0844005i	$0.0268975\pi$
$271$	1.05589	+	7.34389i	0.0641409	+	0.446110i	−0.932291	+	0.361709i	$0.882193\pi$
$272$	0.135804	−	12.5011i	0.00823433	−	0.757993i
$273$	−14.7856	−	17.0635i	−0.894867	−	1.03273i
$274$	−30.4098	−	7.84967i	−1.83712	−	0.474216i
$275$			6.50657i			0.392361i
$276$	−9.52133	+	1.15946i	−0.573117	+	0.0697911i
$277$		−	16.7084i		−	1.00391i	−0.864893	−	0.501957i	$-0.832614\pi$
$277$		−	16.7084i		−	1.00391i	0.864893	−	0.501957i	$-0.167386\pi$
$278$	−6.99398	+	27.0948i	−0.419471	+	1.62504i
$279$	−0.311933	−	0.359990i	−0.0186750	−	0.0215521i
$280$	−6.68695	+	3.89425i	−0.399622	+	0.232726i
$281$	1.07110	+	7.44965i	0.0638964	+	0.444409i	0.996506	+	0.0835220i	$0.0266169\pi$
$281$	1.07110	+	7.44965i	0.0638964	+	0.444409i	−0.932610	+	0.360887i	$0.882474\pi$
$282$	11.5453	−	5.73999i	0.687511	−	0.341812i
$283$	8.69836	+	3.97241i	0.517064	+	0.236135i	0.656815	−	0.754051i	$-0.271903\pi$
$283$	8.69836	+	3.97241i	0.517064	+	0.236135i	−0.139751	+	0.990187i	$0.544630\pi$
$284$	−26.8534	−	5.99454i	−1.59346	−	0.355710i
$285$	5.32969	+	0.766293i	0.315703	+	0.0453913i
$286$	1.32691	−	12.0345i	0.0784621	−	0.711616i
$287$	−33.1298	−	9.72777i	−1.95559	−	0.574212i
$288$	−5.58010	+	0.928710i	−0.328810	+	0.0547248i
$289$	−3.00405	−	6.57796i	−0.176709	−	0.386939i
$290$	5.36794	−	6.62430i	0.315216	−	0.388992i
$291$	8.59214	+	7.44513i	0.503680	+	0.436442i
$292$	17.0382	−	1.12562i	0.997086	−	0.0658717i
$293$	5.52159	−	8.59176i	0.322575	−	0.501936i	−0.641659	−	0.766990i	$-0.721754\pi$
$293$	5.52159	−	8.59176i	0.322575	−	0.501936i	0.964233	+	0.265054i	$0.0853899\pi$
$294$	9.94308	+	4.15023i	0.579892	+	0.242046i
$295$	0.837802	−	0.538423i	0.0487787	−	0.0313482i
$296$	−9.94173	−	12.5448i	−0.577852	−	0.729150i
$297$	−1.39105	+	0.408449i	−0.0807170	+	0.0237006i
$298$	7.27092	−	12.1790i	0.421193	−	0.705510i
$299$	26.6916	−	9.46611i	1.54362	−	0.547439i
$300$	−7.90126	+	4.25887i	−0.456179	+	0.245886i
$301$	−3.00241	−	10.2253i	−0.173056	−	0.589375i
$302$	2.05099	+	11.5473i	0.118021	+	0.664471i
$303$	−0.112706	+	0.0724318i	−0.00647480	+	0.00416110i
$304$	12.8005	−	27.2422i	0.734161	−	1.56245i
$305$	3.13044	+	2.01181i	0.179248	+	0.115196i
$306$	3.63758	−	2.51100i	0.207946	−	0.143544i
$307$	−17.5689	−	15.2236i	−1.00271	−	0.868855i	−0.0113403	−	0.999936i	$-0.503610\pi$
$307$	−17.5689	−	15.2236i	−1.00271	−	0.868855i	−0.991372	+	0.131081i	$0.958155\pi$
$308$	3.81778	+	10.4082i	0.217538	+	0.593061i
$309$	13.8160	−	6.30956i	0.785965	−	0.358938i
$310$	0.353683	−	0.327502i	0.0200879	−	0.0186009i
$311$	−1.47956	−	0.434439i	−0.0838983	−	0.0246348i	0.239514	−	0.970893i	$-0.423012\pi$
$311$	−1.47956	−	0.434439i	−0.0838983	−	0.0246348i	−0.323412	+	0.946258i	$0.604830\pi$
$312$	15.4827	−	6.26584i	0.876533	−	0.354733i
$313$	2.42168	−	16.8432i	0.136881	−	0.952032i	−0.799405	−	0.600793i	$-0.794852\pi$
$313$	2.42168	−	16.8432i	0.136881	−	0.952032i	0.936286	−	0.351239i	$-0.114239\pi$
$314$	0.544825	+	1.65190i	0.0307463	+	0.0932219i
$315$	−2.48865	−	1.13653i	−0.140219	−	0.0640361i
$316$	−2.03244	+	26.4012i	−0.114334	+	1.48518i
$317$	−29.2576	+	4.20661i	−1.64327	+	0.236267i	−0.900996	−	0.433828i	$-0.857162\pi$
$317$	−29.2576	+	4.20661i	−1.64327	+	0.236267i	−0.742275	+	0.670095i	$0.766253\pi$
$318$	−6.46569	+	0.213343i	−0.362578	+	0.0119637i
$319$	−7.99922	−	9.23159i	−0.447870	−	0.516870i
$320$	−1.12552	−	5.61271i	−0.0629183	−	0.313760i
$321$	−2.28058			−0.127290
$322$	−18.0261	+	18.6419i	−1.00455	+	1.03887i
$323$			23.5189i			1.30863i
$324$	−1.40651	−	1.42187i	−0.0781395	−	0.0789930i
$325$	20.0293	−	17.3555i	1.11102	−	0.962708i
$326$	0.243894	+	7.39158i	0.0135080	+	0.409381i
$327$	0.120917	+	0.840996i	0.00668672	+	0.0465072i
$328$	14.7380	−	20.8619i	0.813772	−	1.15191i
$329$	14.4807	−	31.7084i	0.798348	−	1.74814i
$330$	−0.459527	−	1.39328i	−0.0252962	−	0.0766973i
$331$	27.6918	+	3.98148i	1.52208	+	0.218842i	0.852038	−	0.523481i	$-0.175367\pi$
$331$	27.6918	+	3.98148i	1.52208	+	0.218842i	0.670043	+	0.742323i	$0.266276\pi$
$332$	−18.6054	−	14.0862i	−1.02110	−	0.773078i
$333$	1.59437	−	5.42993i	0.0873710	−	0.297558i
$334$	16.9892	+	18.3473i	0.929606	+	1.00392i
$335$	−3.44355	−	7.54033i	−0.188141	−	0.411972i
$336$	−10.1402	+	11.4488i	−0.553196	+	0.624582i
$337$	−3.56218	+	4.11097i	−0.194044	+	0.223939i	−0.844431	−	0.535664i	$-0.820061\pi$
$337$	−3.56218	+	4.11097i	−0.194044	+	0.223939i	0.650387	+	0.759603i	$0.274607\pi$
$338$	−25.4554	+	17.5717i	−1.38459	+	0.955776i
$339$	5.23491	−	8.14569i	0.284322	−	0.442413i
$340$	2.66102	+	3.59524i	0.144314	+	0.194979i
$341$	−0.373356	−	0.580953i	−0.0202183	−	0.0314604i
$342$	10.4778	−	1.86104i	0.566577	−	0.100634i
$343$	2.26974	−	0.666455i	0.122554	−	0.0359852i
$344$	7.87601	+	0.345562i	0.424646	+	0.0186314i
$345$	2.46553	−	2.38696i	0.132740	−	0.128510i
$346$	−6.19005	+	10.3685i	−0.332779	+	0.557414i
$347$	3.14945	+	10.7260i	0.169071	+	0.575804i	0.999817	+	0.0191514i	$0.00609645\pi$
$347$	3.14945	+	10.7260i	0.169071	+	0.575804i	−0.830745	+	0.556653i	$0.812085\pi$
$348$	5.97451	−	15.7564i	0.320267	−	0.844630i
$349$	9.84647	+	15.3214i	0.527069	+	0.820136i	0.998077	−	0.0619936i	$-0.0197458\pi$
$349$	9.84647	+	15.3214i	0.527069	+	0.820136i	−0.471007	+	0.882129i	$0.656109\pi$
$350$	−9.34752	+	22.3947i	−0.499646	+	1.19705i
$351$	4.96779	+	3.19261i	0.265161	+	0.170409i
$352$	−8.19917	+	0.181406i	−0.437017	+	0.00966896i
$353$	−7.13423	+	8.23334i	−0.379717	+	0.438216i	−0.913149	−	0.407627i	$-0.866357\pi$
$353$	−7.13423	+	8.23334i	−0.379717	+	0.438216i	0.533432	+	0.845843i	$0.320902\pi$
$354$	1.23919	−	1.52922i	0.0658622	−	0.0812773i
$355$	8.95444	−	4.08936i	0.475252	−	0.217040i
$356$	−2.37070	−	11.1902i	−0.125647	−	0.593080i
$357$	3.36672	−	11.4660i	0.178186	−	0.606844i
$358$	0.286169	+	0.0315528i	0.0151245	+	0.00166762i
$359$	−0.185539	+	1.29046i	−0.00979240	+	0.0681076i	−0.994132	−	0.108177i	$-0.965499\pi$
$359$	−0.185539	+	1.29046i	−0.00979240	+	0.0681076i	0.984339	+	0.176284i	$0.0564078\pi$
$360$	1.39114	−	1.46999i	0.0733196	−	0.0774755i
$361$	−15.6297	+	34.2243i	−0.822616	+	1.80128i
$362$	9.64588	−	4.79567i	0.506976	−	0.252055i
$363$	8.80758	−	1.26634i	0.462278	−	0.0664655i
$364$	21.8562	−	39.5148i	1.14558	−	2.07114i
$365$	−4.61701	+	4.00066i	−0.241665	+	0.209404i
$366$	7.12103	+	1.83815i	0.372222	+	0.0960815i
$367$	−26.5583			−1.38633			−0.693167	−	0.720777i	$-0.743785\pi$
$367$	−26.5583			−1.38633			−0.693167	+	0.720777i	$0.743785\pi$
$368$	−8.73479	−	17.0793i	−0.455333	−	0.890321i
$369$	9.03071			0.470120
$370$	5.54503	+	1.43134i	0.288272	+	0.0744116i
$371$	−13.2181	+	11.4535i	−0.686249	+	0.594638i
$372$	0.461101	−	0.833647i	0.0239070	−	0.0432226i
$373$	−5.67492	+	0.815931i	−0.293836	+	0.0422473i	−0.287657	−	0.957734i	$-0.592876\pi$
$373$	−5.67492	+	0.815931i	−0.293836	+	0.0422473i	−0.00617973	+	0.999981i	$0.501967\pi$
$374$	5.73808	−	2.85282i	0.296709	−	0.147516i
$375$	2.82033	−	6.17565i	0.145641	−	0.318909i
$376$	18.7295	+	17.7248i	0.965900	+	0.914088i
$377$	−7.08082	+	49.2482i	−0.364681	+	2.53641i
$378$	−5.37459	−	0.592597i	−0.276439	−	0.0304799i
$379$	−5.30399	+	18.0637i	−0.272448	+	0.927872i	0.703651	+	0.710546i	$0.251552\pi$
$379$	−5.30399	+	18.0637i	−0.272448	+	0.927872i	−0.976099	+	0.217327i	$0.930266\pi$
$380$	2.23192	+	10.5352i	0.114495	+	0.540442i
$381$	−15.3465	+	7.00851i	−0.786224	+	0.359057i
$382$	−1.84877	+	2.28148i	−0.0945914	+	0.116731i
$383$	7.31662	−	8.44382i	0.373862	−	0.431459i	−0.537374	−	0.843344i	$-0.680584\pi$
$383$	7.31662	−	8.44382i	0.373862	−	0.431459i	0.911236	+	0.411884i	$0.135129\pi$
$384$	−5.58705	−	9.83793i	−0.285113	−	0.502040i
$385$	−3.33677	−	2.14441i	−0.170057	−	0.109289i
$386$	2.62978	−	6.30039i	0.133852	−	0.320682i
$387$	1.50691	+	2.34480i	0.0766006	+	0.119193i
$388$	−8.06174	+	21.2610i	−0.409273	+	1.07936i
$389$	−7.90748	−	26.9304i	−0.400925	−	1.36543i	−0.874651	−	0.484753i	$-0.838909\pi$
$389$	−7.90748	−	26.9304i	−0.400925	−	1.36543i	0.473726	−	0.880672i	$-0.342909\pi$
$390$	−3.06321	+	5.13096i	−0.155112	+	0.259816i
$391$	11.8525	+	9.17579i	0.599406	+	0.464040i
$392$	−0.944556	+	21.5282i	−0.0477073	+	1.08734i
$393$	−5.22846	+	1.53522i	−0.263741	+	0.0774414i
$394$	30.4529	−	5.40895i	1.53419	−	0.272499i
$395$	−5.12187	−	7.96979i	−0.257709	−	0.401004i
$396$	−1.72500	−	2.33062i	−0.0866848	−	0.117118i
$397$	1.12288	−	1.74724i	0.0563558	−	0.0876914i	−0.811932	−	0.583752i	$-0.801584\pi$
$397$	1.12288	−	1.74724i	0.0563558	−	0.0876914i	0.868288	+	0.496060i	$0.165221\pi$
$398$	−11.8030	+	8.14756i	−0.591631	+	0.408400i
$399$	18.8410	−	21.7437i	0.943232	−	1.08855i
$400$	−13.4387	−	11.9027i	−0.671933	−	0.595135i
$401$	10.0368	+	21.9776i	0.501215	+	1.09751i	0.976072	+	0.217446i	$0.0697725\pi$
$401$	10.0368	+	21.9776i	0.501215	+	1.09751i	−0.474857	+	0.880063i	$0.657500\pi$
$402$	−11.1311	−	12.0210i	−0.555171	−	0.599552i
$403$	−0.792476	+	2.69893i	−0.0394761	+	0.134443i
$404$	−0.213628	−	0.161738i	−0.0106284	−	0.00804676i
$405$	0.708272	+	0.101834i	0.0351943	+	0.00506018i
$406$	−14.2698	−	43.2657i	−0.708199	−	2.14724i
$407$	3.40828	−	7.46310i	0.168942	−	0.369932i
$408$	7.22017	+	5.10074i	0.357452	+	0.252524i
$409$	−1.74400	−	12.1298i	−0.0862354	−	0.599780i	−0.986416	−	0.164264i	$-0.947475\pi$
$409$	−1.74400	−	12.1298i	−0.0862354	−	0.599780i	0.900181	−	0.435516i	$-0.143434\pi$
$410$	0.301375	+	9.13365i	0.0148839	+	0.451079i
$411$	16.7835	−	14.5430i	0.827871	−	0.717355i
$412$	21.3629	+	21.5962i	1.05247	+	1.06397i
$413$		−	5.32140i		−	0.261849i
$414$	3.15000	−	6.00645i	0.154814	−	0.295201i
$415$	8.34919			0.409846
$416$	22.4287	+	24.7558i	1.09966	+	1.21375i
$417$	−12.9577	−	14.9540i	−0.634541	−	0.732299i
$418$	15.4199	−	0.508797i	0.754212	−	0.0248861i
$419$	1.15065	−	0.165438i	0.0562129	−	0.00808220i	−0.114151	−	0.993463i	$-0.536415\pi$
$419$	1.15065	−	0.165438i	0.0562129	−	0.00808220i	0.170364	+	0.985381i	$0.445506\pi$
$420$	0.419990	−	5.45563i	0.0204934	−	0.266207i
$421$	−17.2221	−	7.86506i	−0.839353	−	0.383320i	−0.0511170	−	0.998693i	$-0.516278\pi$
$421$	−17.2221	−	7.86506i	−0.839353	−	0.383320i	−0.788236	+	0.615373i	$0.789005\pi$
$422$	4.70774	+	14.2737i	0.229169	+	0.694834i
$423$	−1.29749	+	9.02424i	−0.0630861	+	0.438774i
$424$	−4.85377	−	11.9935i	−0.235720	−	0.582455i
$425$	13.4588	+	3.95187i	0.652850	+	0.191694i
$426$	14.2754	−	13.2187i	0.691645	−	0.640446i
$427$	18.0865	−	8.25984i	0.875268	−	0.399722i
$428$	−1.57073	−	4.28217i	−0.0759239	−	0.206987i
$429$	6.47017	+	5.60643i	0.312383	+	0.270681i
$430$	−2.32124	+	1.60234i	−0.111940	+	0.0772716i
$431$	−2.81702	−	1.81039i	−0.135691	−	0.0872033i	0.471034	−	0.882115i	$-0.343881\pi$
$431$	−2.81702	−	1.81039i	−0.135691	−	0.0872033i	−0.606725	+	0.794912i	$0.707517\pi$
$432$	1.70109	−	3.62026i	0.0818436	−	0.174180i
$433$	21.7134	−	13.9544i	1.04348	−	0.670604i	0.0976346	−	0.995222i	$-0.468872\pi$
$433$	21.7134	−	13.9544i	1.04348	−	0.670604i	0.945845	+	0.324619i	$0.105236\pi$
$434$	−0.450425	−	2.53593i	−0.0216211	−	0.121729i
$435$	1.69855	+	5.78472i	0.0814391	+	0.277356i
$436$	−1.49583	+	0.806270i	−0.0716373	+	0.0386133i
$437$	16.7802	+	31.9497i	0.802706	+	1.52836i
$438$	−6.18923	+	10.3671i	−0.295733	+	0.495360i
$439$	0.381882	−	0.112131i	0.0182262	−	0.00535170i	−0.272607	−	0.962126i	$-0.587886\pi$
$439$	0.381882	−	0.112131i	0.0182262	−	0.00535170i	0.290833	+	0.956774i	$0.406068\pi$
$440$	2.29961	−	1.82244i	0.109630	−	0.0868816i
$441$	−6.40926	+	4.11898i	−0.305203	+	0.196142i
$442$	−24.0875	−	10.0541i	−1.14573	−	0.478224i
$443$	4.32278	−	6.72637i	0.205381	−	0.319579i	−0.723248	−	0.690588i	$-0.757352\pi$
$443$	4.32278	−	6.72637i	0.205381	−	0.319579i	0.928629	+	0.371009i	$0.120988\pi$
$444$	11.2937	−	0.746111i	0.535976	−	0.0354088i
$445$	3.09288	+	2.68000i	0.146617	+	0.127044i
$446$	−6.37084	+	7.86193i	−0.301668	+	0.372273i
$447$	4.16654	+	9.12344i	0.197070	+	0.431524i
$448$	−28.4810	−	11.1548i	−1.34560	−	0.527014i
$449$	2.86601	+	0.841537i	0.135255	+	0.0397146i	0.348660	−	0.937249i	$-0.386637\pi$
$449$	2.86601	+	0.841537i	0.135255	+	0.0397146i	−0.213404	+	0.976964i	$0.568455\pi$
$450$	0.695595	−	6.30873i	0.0327906	−	0.297396i
$451$	12.9593	+	1.86326i	0.610228	+	0.0877375i
$452$	18.9004	+	4.21917i	0.889000	+	0.198453i
$453$	−7.54354	−	3.44502i	−0.354426	−	0.161861i
$454$	15.2128	−	7.56338i	0.713971	−	0.354967i
$455$	2.29924	+	15.9916i	0.107790	+	0.749696i
$456$	10.7109	+	18.3921i	0.501585	+	0.861291i
$457$	16.7543	+	19.3355i	0.783735	+	0.904478i	0.997373	−	0.0724348i	$-0.0230769\pi$
$457$	16.7543	+	19.3355i	0.783735	+	0.904478i	−0.213638	+	0.976913i	$0.568531\pi$
$458$	5.71033	−	22.1219i	0.266826	−	1.03369i
$459$			3.12547i			0.145884i
$460$	6.18004	+	2.98546i	0.288146	+	0.139198i
$461$			13.5694i			0.631988i	0.948761	+	0.315994i	$0.102338\pi$
$461$			13.5694i			0.631988i	−0.948761	+	0.315994i	$0.897662\pi$
$462$	−7.59038	−	1.95930i	−0.353136	−	0.0911549i
$463$	−0.789187	−	0.910771i	−0.0366766	−	0.0423271i	0.737115	−	0.675767i	$-0.236188\pi$
$463$	−0.789187	−	0.910771i	−0.0366766	−	0.0423271i	−0.773792	+	0.633440i	$0.781642\pi$
$464$	33.7001	+	0.366096i	1.56449	+	0.0169956i
$465$	0.0485072	+	0.337375i	0.00224947	+	0.0156454i
$466$	1.21891	+	2.45168i	0.0564648	+	0.113572i
$467$	−32.8795	−	15.0156i	−1.52148	−	0.694837i	−0.532991	−	0.846121i	$-0.678932\pi$
$467$	−32.8795	−	15.0156i	−1.52148	−	0.694837i	−0.988490	+	0.151284i	$0.951659\pi$
$468$	−2.57314	+	11.5267i	−0.118943	+	0.532824i
$469$	−43.8422	−	6.30356i	−2.02445	−	0.291071i
$470$	−9.17040	−	1.01112i	−0.422999	−	0.0466395i
$471$	−1.18014	−	0.346519i	−0.0543778	−	0.0159668i
$472$	3.72485	+	1.27355i	0.171450	+	0.0586199i
$473$	1.67866	+	3.67575i	0.0771848	+	0.169011i
$474$	−14.5471	−	11.7881i	−0.668170	−	0.541445i
$475$	25.5229	+	22.1157i	1.17107	+	1.01474i
$476$	23.8481	−	1.57551i	1.09308	−	0.0722132i
$477$	2.47312	−	3.84825i	0.113236	−	0.176199i
$478$	5.80483	−	13.9072i	0.265507	−	0.636098i
$479$	18.2903	−	11.7545i	0.835707	−	0.537076i	−0.0513798	−	0.998679i	$-0.516362\pi$
$479$	18.2903	−	11.7545i	0.835707	−	0.537076i	0.887087	+	0.461603i	$0.152726\pi$
$480$	3.71830	+	1.59966i	0.169716	+	0.0730141i
$481$	−32.0650	+	9.41512i	−1.46204	+	0.429293i
$482$	26.1788	+	15.6289i	1.19241	+	0.711877i
$483$	−3.60714	−	17.9783i	−0.164130	−	0.818040i
$484$	8.44389	+	15.6655i	0.383813	+	0.712069i
$485$	−2.29194	−	7.80564i	−0.104072	−	0.354436i
$486$	1.39242	−	0.247318i	0.0631615	−	0.0112186i
$487$	14.7498	−	9.47915i	0.668379	−	0.429541i	−0.161962	−	0.986797i	$-0.551782\pi$
$487$	14.7498	−	9.47915i	0.668379	−	0.429541i	0.830341	+	0.557256i	$0.188146\pi$
$488$	1.45311	+	14.6369i	0.0657791	+	0.662583i
$489$	−4.39932	−	2.82727i	−0.198944	−	0.127854i
$490$	−4.37982	−	6.34485i	−0.197860	−	0.286631i
$491$	12.0227	+	10.4177i	0.542575	+	0.470144i	0.882502	−	0.470308i	$-0.155857\pi$
$491$	12.0227	+	10.4177i	0.542575	+	0.470144i	−0.339928	+	0.940452i	$0.610403\pi$
$492$	6.21981	+	16.9567i	0.280411	+	0.764466i
$493$	−23.9540	+	10.9394i	−1.07883	+	0.492687i
$494$	−42.6969	−	46.1102i	−1.92102	−	2.07459i
$495$	0.995374	+	0.292268i	0.0447387	+	0.0131365i
$496$	1.88289	+	0.291629i	0.0845443	+	0.0130945i
$497$	7.48572	−	52.0644i	0.335781	−	2.33541i
$498$	15.6709	−	5.16854i	0.702229	−	0.231608i
$499$	−23.0525	−	10.5277i	−1.03197	−	0.471285i	−0.173870	−	0.984769i	$-0.555627\pi$
$499$	−23.0525	−	10.5277i	−1.03197	−	0.471285i	−0.858099	+	0.513484i	$0.828355\pi$
$500$	13.5383	+	1.04222i	0.605451	+	0.0466093i
$501$	−17.5013	+	2.51631i	−0.781901	+	0.112420i
$502$	−0.378777	−	11.4794i	−0.0169056	−	0.512352i
$503$	−4.31600	−	4.98093i	−0.192441	−	0.222089i	0.651326	−	0.758798i	$-0.274213\pi$
$503$	−4.31600	−	4.98093i	−0.192441	−	0.222089i	−0.843768	+	0.536709i	$0.819667\pi$
$504$	−2.58900	−	10.4998i	−0.115323	−	0.467700i
$505$	0.0958658			0.00426597
$506$	5.75960	−	7.96946i	0.256045	−	0.354286i
$507$		−	21.8717i		−	0.971356i
$508$	−23.7294	−	23.9886i	−1.05282	−	1.06432i
$509$	18.3485	−	15.8990i	0.813281	−	0.704712i	−0.145345	−	0.989381i	$-0.546429\pi$
$509$	18.3485	−	15.8990i	0.813281	−	0.704712i	0.958626	+	0.284669i	$0.0918837\pi$
$510$	−3.16109	+	0.104304i	−0.139976	+	0.00461865i
$511$	4.64563	+	32.3110i	0.205510	+	1.42936i
$512$	14.6243	−	17.2664i	0.646311	−	0.763074i
$513$	−3.12596	+	6.84490i	−0.138015	+	0.302210i
$514$	−10.5731	+	3.48719i	−0.466358	+	0.153813i
$515$	−10.7576	−	1.54672i	−0.474038	−	0.0681564i
$516$	−3.36488	+	4.44443i	−0.148131	+	0.195655i
$517$	−3.72385	+	12.6823i	−0.163775	+	0.557765i
$518$	22.4525	−	20.7905i	0.986508	−	0.913483i
$519$	−3.54715	−	7.76717i	−0.155703	−	0.340941i
$520$	−11.7440	−	2.21779i	−0.515008	−	0.0972566i
$521$	12.2136	−	14.0953i	0.535089	−	0.617526i	−0.422255	−	0.906477i	$-0.638761\pi$
$521$	12.2136	−	14.0953i	0.535089	−	0.617526i	0.957344	+	0.288952i	$0.0933067\pi$
$522$	6.76907	+	9.80606i	0.296274	+	0.429199i
$523$	1.58325	−	2.46358i	0.0692307	−	0.107725i	−0.804912	−	0.593394i	$-0.797788\pi$
$523$	1.58325	−	2.46358i	0.0692307	−	0.107725i	0.874143	+	0.485669i	$0.161424\pi$
$524$	−6.48368	−	8.75995i	−0.283241	−	0.382680i
$525$	−9.27714	−	14.4355i	−0.404888	−	0.630017i
$526$	−2.80293	−	15.7807i	−0.122213	−	0.688072i
$527$	−1.42847	+	0.419435i	−0.0622249	+	0.0182709i
$528$	3.18804	−	4.84418i	0.138742	−	0.210816i
$529$	22.6480	+	4.00856i	0.984695	+	0.174285i
$530$	3.97464	+	2.37288i	0.172648	+	0.103071i
$531$	0.392110	+	1.33541i	0.0170161	+	0.0579516i
$532$	53.8041	+	20.4014i	2.33270	+	0.884515i
$533$	−28.8315	−	44.8627i	−1.24883	−	1.94322i
$534$	7.46418	+	3.11554i	0.323007	+	0.134823i
$535$	1.37283	+	0.882262i	0.0593524	+	0.0381435i
$536$	14.9050	−	29.1799i	0.643796	−	1.26038i
$537$	−0.133316	+	0.153854i	−0.00575300	+	0.00663931i
$538$	26.5636	+	21.5255i	1.14524	+	0.928031i
$539$	−10.0473	+	4.58843i	−0.432766	+	0.197638i
$540$	0.296605	+	1.40004i	0.0127638	+	0.0602480i
$541$	−2.88361	+	9.82067i	−0.123976	+	0.422224i	−0.997968	−	0.0637167i	$-0.979705\pi$
$541$	−2.88361	+	9.82067i	−0.123976	+	0.422224i	0.873992	+	0.485940i	$0.161523\pi$
$542$	1.14994	−	10.4294i	0.0493941	−	0.447982i
$543$	−1.08403	+	7.53960i	−0.0465202	+	0.323555i
$544$	−4.60467	+	17.0702i	−0.197423	+	0.731878i
$545$	0.252559	−	0.553027i	0.0108184	−	0.0236891i
$546$	14.2151	+	28.5918i	0.608348	+	1.22362i
$547$	2.07438	−	0.298250i	0.0886940	−	0.0127523i	−0.0978249	−	0.995204i	$-0.531189\pi$
$547$	2.07438	−	0.298250i	0.0886940	−	0.0127523i	0.186519	+	0.982451i	$0.440279\pi$
$548$	38.8665	+	21.4976i	1.66029	+	0.918331i
$549$	−3.93018	+	3.40552i	−0.167736	+	0.145344i
$550$	2.29984	−	8.90964i	0.0980655	−	0.379908i
$551$	−63.4014			−2.70099
$552$	13.4477	+	1.77777i	0.572370	+	0.0756669i
$553$	−50.6210			−2.15262
$554$	−5.90584	+	22.8794i	−0.250915	+	0.972051i
$555$	−3.06037	+	2.65182i	−0.129905	+	0.112564i
$556$	19.1541	−	34.6296i	0.812315	−	1.46862i
$557$	17.7144	−	2.54695i	0.750583	−	0.107918i	0.243603	−	0.969875i	$-0.421671\pi$
$557$	17.7144	−	2.54695i	0.750583	−	0.107918i	0.506981	+	0.861957i	$0.330762\pi$
$558$	0.299896	+	0.603202i	0.0126956	+	0.0255356i
$559$	6.83750	−	14.9720i	0.289195	−	0.633250i
$560$	10.5331	−	2.96891i	0.445106	−	0.125459i
$561$	−0.644862	+	4.48511i	−0.0272261	+	0.189362i
$562$	1.16650	−	10.5796i	0.0492058	−	0.446274i
$563$	−8.45934	+	28.8099i	−0.356519	+	1.21419i	0.564749	+	0.825263i	$0.308973\pi$
$563$	−8.45934	+	28.8099i	−0.356519	+	1.21419i	−0.921268	+	0.388929i	$0.872845\pi$
$564$	−17.8382	+	3.77910i	−0.751122	+	0.159129i
$565$	−6.30246	+	2.87824i	−0.265146	+	0.121088i
$566$	−10.5068	−	8.51410i	−0.441635	−	0.357874i
$567$	2.50382	−	2.88956i	0.105151	−	0.121350i
$568$	34.6523	+	17.7002i	1.45398	+	0.742684i
$569$	8.61612	+	5.53724i	0.361207	+	0.232133i	0.708638	−	0.705572i	$-0.249310\pi$
$569$	8.61612	+	5.53724i	0.361207	+	0.232133i	−0.347432	+	0.937705i	$0.612946\pi$
$570$	−7.02724	−	2.93316i	−0.294339	−	0.122857i
$571$	−8.89724	−	13.8444i	−0.372338	−	0.579369i	0.603635	−	0.797261i	$-0.293718\pi$
$571$	−8.89724	−	13.8444i	−0.372338	−	0.579369i	−0.975973	+	0.217892i	$0.930082\pi$
$572$	−6.07076	+	16.0102i	−0.253831	+	0.669420i
$573$	−0.584997	−	1.99232i	−0.0244386	−	0.0832302i
$574$	41.9271	+	25.0307i	1.75000	+	1.04476i
$575$	21.1030	−	4.23408i	0.880057	−	0.176573i
$576$	7.96926	+	0.700655i	0.332052	+	0.0291939i
$577$	−33.8648	+	9.94361i	−1.40981	+	0.413958i	−0.896041	−	0.443970i	$-0.853570\pi$
$577$	−33.8648	+	9.94361i	−1.40981	+	0.413958i	−0.513770	+	0.857928i	$0.671751\pi$
$578$	1.78846	+	10.0692i	0.0743903	+	0.418824i
$579$	2.60998	+	4.06120i	0.108467	+	0.168778i
$580$	−9.69193	+	7.17348i	−0.402435	+	0.297862i
$581$	24.1193	−	37.5303i	1.00064	−	1.55702i
$582$	−9.13389	−	13.2319i	−0.378612	−	0.548478i
$583$	4.34297	−	5.01205i	0.179867	−	0.207578i
$584$	−23.7288	−	4.48106i	−0.981904	−	0.185428i
$585$	−1.75534	−	3.84367i	−0.0725745	−	0.158916i
$586$	−10.5977	+	9.81326i	−0.437789	+	0.405382i
$587$	−2.43599	+	8.29623i	−0.100544	+	0.342422i	−0.994366	−	0.106000i	$-0.966196\pi$
$587$	−2.43599	+	8.29623i	−0.100544	+	0.342422i	0.893822	+	0.448422i	$0.148014\pi$
$588$	−12.1484	−	9.19755i	−0.500991	−	0.379301i
$589$	−3.54790	−	0.510111i	−0.146189	−	0.0210187i
$590$	−1.33754	+	0.441145i	−0.0550657	+	0.0181617i
$591$	−9.08532	+	19.8941i	−0.373720	+	0.818332i
$592$	9.17938	+	20.6920i	0.377270	+	0.850435i
$593$	5.73637	+	39.8973i	0.235564	+	1.63839i	0.673362	+	0.739313i	$0.264850\pi$
$593$	5.73637	+	39.8973i	0.235564	+	1.63839i	−0.437797	+	0.899074i	$0.644241\pi$
$594$	2.04918	−	0.0676150i	0.0840788	−	0.00277428i
$595$	−6.46235	+	5.59966i	−0.264931	+	0.229564i
$596$	−14.2611	+	14.1070i	−0.584159	+	0.577847i
$597$		−	10.1413i		−	0.415057i
$598$	−39.8955	+	3.52769i	−1.63145	+	0.144258i
$599$	−13.7874			−0.563338			−0.281669	−	0.959512i	$-0.590888\pi$
$599$	−13.7874			−0.563338			−0.281669	+	0.959512i	$0.590888\pi$
$600$	12.3248	−	3.03898i	0.503157	−	0.124066i
$601$	9.63910	+	11.1241i	0.393187	+	0.453762i	0.917484	−	0.397774i	$-0.130217\pi$
$601$	9.63910	+	11.1241i	0.393187	+	0.453762i	−0.524296	+	0.851536i	$0.675672\pi$
$602$	0.497021	+	15.0630i	0.0202571	+	0.613922i
$603$	11.4667	−	1.64866i	0.466960	−	0.0671387i
$604$	1.27306	−	16.5370i	0.0518002	−	0.672880i
$605$	−5.79173	−	2.64500i	−0.235467	−	0.107534i
$606$	0.179934	−	0.0593454i	0.00730931	−	0.00241074i
$607$	0.0211358	−	0.147003i	0.000857877	−	0.00596667i	−0.989388	−	0.145298i	$-0.953586\pi$
$607$	0.0211358	−	0.147003i	0.000857877	−	0.00596667i	0.990246	+	0.139331i	$0.0444952\pi$
$608$	−27.1573	+	32.7790i	−1.10137	+	1.32936i
$609$	30.9096	+	9.07588i	1.25252	+	0.367773i
$610$	−3.57550	−	3.86133i	−0.144768	−	0.156341i
$611$	48.9729	−	22.3652i	1.98123	−	0.904799i
$612$	−5.86859	+	2.15264i	−0.237224	+	0.0870151i
$613$	−18.2342	−	15.8000i	−0.736471	−	0.638156i	0.203631	−	0.979048i	$-0.434726\pi$
$613$	−18.2342	−	15.8000i	−0.736471	−	0.638156i	−0.940103	+	0.340892i	$0.889271\pi$
$614$	18.6767	+	27.0561i	0.753729	+	1.09189i
$615$	−5.43616	−	3.49361i	−0.219207	−	0.140876i
$616$	−1.54888	−	15.6017i	−0.0624063	−	0.628609i
$617$	−38.5389	+	24.7674i	−1.55152	+	0.997100i	−0.566616	+	0.823982i	$0.691748\pi$
$617$	−38.5389	+	24.7674i	−1.55152	+	0.997100i	−0.984901	+	0.173118i	$0.944616\pi$
$618$	−21.1489	+	3.75640i	−0.850732	+	0.151105i
$619$	9.95818	+	33.9145i	0.400253	+	1.36314i	0.875472	+	0.483269i	$0.160551\pi$
$619$	9.95818	+	33.9145i	0.400253	+	1.36314i	−0.475218	+	0.879868i	$0.657631\pi$
$620$	−0.600070	+	0.323444i	−0.0240994	+	0.0129898i
$621$	2.22995	+	4.24586i	0.0894849	+	0.170380i
$622$	1.87245	+	1.11786i	0.0750784	+	0.0448222i
$623$	20.9816	−	6.16075i	0.840610	−	0.246825i
$624$	−23.4156	+	3.10743i	−0.937375	+	0.124397i
$625$	14.7908	−	9.50548i	0.591632	−	0.380219i
$626$	−9.26953	+	22.2079i	−0.370485	+	0.887604i
$627$	−5.89809	+	9.17761i	−0.235547	+	0.366518i
$628$	−0.162159	−	2.45457i	−0.00647085	−	0.0979478i
$629$	−13.3674	−	11.5829i	−0.532991	−	0.461840i
$630$	3.00606	+	2.43593i	0.119764	+	0.0970497i
$631$	−9.35822	−	20.4916i	−0.372545	−	0.815759i	−0.999331	−	0.0365682i	$-0.988357\pi$
$631$	−9.35822	−	20.4916i	−0.372545	−	0.815759i	0.626786	−	0.779191i	$-0.284370\pi$
$632$	12.1150	−	35.4335i	0.481907	−	1.40947i
$633$	−10.1973	−	2.99421i	−0.405308	−	0.119009i
$634$	41.5502	+	4.58128i	1.65017	+	0.181946i
$635$	11.9493	+	1.71805i	0.474195	+	0.0681789i
$636$	8.92907	+	1.99325i	0.354061	+	0.0790376i
$637$	40.9245	+	18.6896i	1.62149	+	0.740508i
$638$	7.69053	+	15.4685i	0.304471	+	0.612405i
$639$	1.95785	+	13.6171i	0.0774514	+	0.538686i
$640$	−0.442689	+	8.08347i	−0.0174988	+	0.319527i
$641$	−3.94380	−	4.55139i	−0.155771	−	0.179769i	0.672500	−	0.740097i	$-0.265221\pi$
$641$	−3.94380	−	4.55139i	−0.155771	−	0.179769i	−0.828271	+	0.560328i	$0.810675\pi$
$642$	3.12286	+	0.806103i	0.123250	+	0.0318144i
$643$		−	11.1761i		−	0.440743i	−0.975416	−	0.220372i	$-0.929273\pi$
$643$		−	11.1761i		−	0.440743i	0.975416	−	0.220372i	$-0.0707270\pi$
$644$	31.2729	−	19.1554i	1.23232	−	0.754827i
$645$		−	1.99444i		−	0.0785312i
$646$	8.31308	−	32.2051i	0.327074	−	1.26709i
$647$	−21.9453	−	25.3262i	−0.862757	−	0.995675i	−0.999987	−	0.00513556i	$-0.998365\pi$
$647$	−21.9453	−	25.3262i	−0.862757	−	0.995675i	0.137230	−	0.990539i	$-0.456180\pi$
$648$	1.42340	+	2.44417i	0.0559163	+	0.0960159i
$649$	0.287159	+	1.99724i	0.0112720	+	0.0783984i
$650$	−33.5612	+	16.6857i	−1.31638	+	0.654468i
$651$	1.65666	+	0.756570i	0.0649295	+	0.0296523i
$652$	2.27869	−	10.2077i	0.0892403	−	0.399765i
$653$	4.12173	+	0.592615i	0.161296	+	0.0231908i	0.222490	−	0.974935i	$-0.428582\pi$
$653$	4.12173	+	0.592615i	0.161296	+	0.0231908i	−0.0611938	+	0.998126i	$0.519491\pi$
$654$	0.131687	−	1.19434i	0.00514936	−	0.0467024i
$655$	3.74126	+	1.09853i	0.146183	+	0.0429232i
$656$	−27.5552	+	23.3575i	−1.07585	+	0.911957i
$657$	−3.54668	−	7.76614i	−0.138369	−	0.302986i
$658$	−31.0367	+	38.3008i	−1.20994	+	1.49312i
$659$	−3.63113	−	3.14640i	−0.141449	−	0.122566i	0.581262	−	0.813716i	$-0.302559\pi$
$659$	−3.63113	−	3.14640i	−0.141449	−	0.122566i	−0.722711	+	0.691150i	$0.757104\pi$
$660$	0.136771	+	2.07028i	0.00532382	+	0.0805855i
$661$	1.69224	−	2.63318i	0.0658205	−	0.102419i	−0.806783	−	0.590848i	$-0.798793\pi$
$661$	1.69224	−	2.63318i	0.0658205	−	0.102419i	0.872604	+	0.488429i	$0.162430\pi$
$662$	−36.5119	−	15.2400i	−1.41908	−	0.592321i
$663$	15.5267	−	9.97839i	0.603006	−	0.387529i
$664$	20.4980	+	25.8649i	0.795475	+	1.00375i
$665$	−19.7534	+	5.80011i	−0.766003	+	0.224919i
$666$	−4.10251	+	6.87181i	−0.158969	+	0.266277i
$667$	−24.7358	+	31.9515i	−0.957773	+	1.23717i
$668$	−16.7787	−	31.1286i	−0.649186	−	1.20440i
$669$	−2.01589	−	6.86549i	−0.0779388	−	0.265435i
$670$	2.05012	+	11.5424i	0.0792031	+	0.445921i
$671$	−6.34254	+	4.07610i	−0.244851	+	0.157356i
$672$	17.9321	−	12.0929i	0.691745	−	0.466495i
$673$	−40.0916	−	25.7653i	−1.54542	−	0.993181i	−0.986463	−	0.163983i	$-0.947566\pi$
$673$	−40.0916	−	25.7653i	−1.54542	−	0.993181i	−0.558956	−	0.829197i	$-0.688798\pi$
$674$	6.33088	−	4.37017i	0.243856	−	0.168333i
$675$	3.39179	+	2.93900i	0.130550	+	0.113122i
$676$	41.0678	−	15.0639i	1.57953	−	0.579381i
$677$	−7.16768	+	3.27337i	−0.275476	+	0.125806i	−0.548363	−	0.836240i	$-0.684749\pi$
$677$	−7.16768	+	3.27337i	−0.275476	+	0.125806i	0.272887	+	0.962046i	$0.412022\pi$
$678$	−10.0475	+	9.30377i	−0.385873	+	0.357309i
$679$	−41.7080	−	12.2466i	−1.60061	−	0.469981i
$680$	−2.37302	−	5.86364i	−0.0910011	−	0.224860i
$681$	−1.70966	+	11.8909i	−0.0655141	+	0.455661i
$682$	0.305901	+	0.927484i	0.0117136	+	0.0355152i
$683$	−9.29577	−	4.24524i	−0.355693	−	0.162439i	0.229551	−	0.973297i	$-0.426274\pi$
$683$	−9.29577	−	4.24524i	−0.355693	−	0.162439i	−0.585244	+	0.810857i	$0.699001\pi$
$684$	−15.0054	−	1.15516i	−0.573747	−	0.0441687i
$685$	−15.7292	+	2.26151i	−0.600981	+	0.0864080i
$686$	−3.34359	+	0.110326i	−0.127659	+	0.00421225i
$687$	10.5795	+	12.2094i	0.403632	+	0.465817i
$688$	−10.6627	−	3.25707i	−0.406512	−	0.124175i
$689$	−27.0130			−1.02911
$690$	−4.21983	+	2.39706i	−0.160646	+	0.0912546i
$691$		−	11.3134i		−	0.430382i	−0.976572	−	0.215191i	$-0.930963\pi$
$691$		−	11.3134i		−	0.430382i	0.976572	−	0.215191i	$-0.0690375\pi$
$692$	12.1411	−	12.0099i	0.461536	−	0.456549i
$693$	4.18922	−	3.62998i	0.159135	−	0.137892i
$694$	−0.521363	−	15.8007i	−0.0197907	−	0.599787i
$695$	2.01499	+	14.0145i	0.0764328	+	0.531602i
$696$	−13.7504	+	19.4639i	−0.521207	+	0.737777i
$697$	11.7252	−	25.6746i	0.444123	−	0.972493i
$698$	−8.06749	−	24.4604i	−0.305359	−	0.925840i
$699$	−1.91633	−	0.275527i	−0.0724822	−	0.0104214i
$700$	20.7156	−	27.3617i	0.782975	−	1.03418i
$701$	3.99746	−	13.6141i	0.150982	−	0.514197i	−0.848915	−	0.528529i	$-0.822744\pi$
$701$	3.99746	−	13.6141i	0.150982	−	0.514197i	0.999897	+	0.0143318i	$0.00456211\pi$
$702$	−5.67407	−	6.12767i	−0.214154	−	0.231274i
$703$	−17.6903	−	38.7364i	−0.667204	−	1.46097i
$704$	11.2915	+	2.64971i	0.425564	+	0.0998647i
$705$	4.27215	−	4.93032i	0.160898	−	0.185687i
$706$	12.6793	−	8.75246i	0.477192	−	0.329403i
$707$	0.276939	−	0.430925i	0.0104154	−	0.0162066i
$708$	−2.23739	+	1.65600i	−0.0840861	+	0.0622363i
$709$	11.4675	+	17.8438i	0.430671	+	0.670137i	0.986981	−	0.160838i	$-0.0514196\pi$
$709$	11.4675	+	17.8438i	0.430671	+	0.670137i	−0.556310	+	0.830975i	$0.687783\pi$
$710$	−13.7070	+	2.43460i	−0.514415	+	0.0913689i
$711$	12.7034	−	3.73004i	0.476413	−	0.139887i
$712$	−0.709070	+	16.1611i	−0.0265735	+	0.605661i
$713$	−1.64127	+	1.58897i	−0.0614661	+	0.0595073i
$714$	−8.66296	+	14.5107i	−0.324203	+	0.543049i
$715$	−1.72591	−	5.87791i	−0.0645454	−	0.219821i
$716$	−0.380707	−	0.144357i	−0.0142277	−	0.00539487i
$717$	5.76112	+	8.96448i	0.215153	+	0.334785i
$718$	0.710195	−	1.70148i	0.0265042	−	0.0634986i
$719$	37.1006	+	23.8431i	1.38362	+	0.889199i	0.999420	−	0.0340509i	$-0.0108408\pi$
$719$	37.1006	+	23.8431i	1.38362	+	0.889199i	0.384200	+	0.923250i	$0.374477\pi$
$720$	−2.42452	+	1.52119i	−0.0903566	+	0.0566913i
$721$	−38.0295	+	43.8883i	−1.41629	+	1.63449i
$722$	33.4993	−	41.3398i	1.24671	−	1.53851i
$723$	−19.6109	+	8.95599i	−0.729337	+	0.333077i
$724$	−14.9035	+	3.15737i	−0.553883	+	0.117343i
$725$	−10.6533	+	36.2819i	−0.395655	+	1.34748i
$726$	−12.5081	−	1.37913i	−0.464218	−	0.0511843i
$727$	−3.22664	+	22.4418i	−0.119669	+	0.832319i	0.838251	+	0.545285i	$0.183578\pi$
$727$	−3.22664	+	22.4418i	−0.119669	+	0.832319i	−0.957920	+	0.287034i	$0.907331\pi$
$728$	−43.8954	+	46.3834i	−1.62687	+	1.71909i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	7.73630	−	3.84628i	0.286333	−	0.142357i
$731$	8.62285	−	1.23978i	0.318927	−	0.0458549i
$732$	−9.10132	−	5.03406i	−0.336394	−	0.186064i
$733$	5.35278	−	4.63821i	0.197709	−	0.171316i	−0.550380	−	0.834914i	$-0.685517\pi$
$733$	5.35278	−	4.63821i	0.197709	−	0.171316i	0.748089	+	0.663598i	$0.230972\pi$
$734$	36.3671	+	9.38743i	1.34234	+	0.346496i
$735$	5.45160			0.201085
$736$	5.92388	+	26.4747i	0.218357	+	0.975869i
$737$	16.7951			0.618655
$738$	−12.3660	−	3.19203i	−0.455200	−	0.117500i
$739$	−33.0204	+	28.6123i	−1.21467	+	1.05252i	−0.217603	+	0.976037i	$0.569824\pi$
$739$	−33.0204	+	28.6123i	−1.21467	+	1.05252i	−0.997071	+	0.0764839i	$0.975631\pi$
$740$	−7.08704	−	3.91994i	−0.260525	−	0.144100i
$741$	43.9840	−	6.32395i	1.61579	−	0.232316i
$742$	22.1483	−	11.0115i	0.813091	−	0.404246i
$743$	17.3858	−	38.0696i	0.637824	−	1.39664i	−0.263995	−	0.964524i	$-0.585040\pi$
$743$	17.3858	−	38.0696i	0.637824	−	1.39664i	0.901818	−	0.432115i	$-0.142233\pi$
$744$	−0.926064	+	0.978554i	−0.0339511	+	0.0358755i
$745$	1.02138	−	7.10384i	0.0374204	−	0.260265i
$746$	8.05924	+	0.888604i	0.295070	+	0.0325341i
$747$	−3.28729	+	11.1955i	−0.120276	+	0.409621i
$748$	−8.86569	+	1.87824i	−0.324162	+	0.0686753i
$749$	7.93168	−	3.62228i	0.289817	−	0.132355i
$750$	−6.04483	+	7.45962i	−0.220726	+	0.272387i
$751$	−12.1120	+	13.9780i	−0.441973	+	0.510064i	−0.932405	−	0.361415i	$-0.882294\pi$
$751$	−12.1120	+	13.9780i	−0.441973	+	0.510064i	0.490432	+	0.871480i	$0.336839\pi$
$752$	−19.3818	−	30.8913i	−0.706780	−	1.12649i
$753$	6.83232	+	4.39087i	0.248984	+	0.160012i
$754$	27.1035	−	64.9342i	0.987050	−	2.36476i
$755$	3.20820	+	4.99206i	0.116758	+	0.181680i
$756$	7.15012	+	2.71119i	0.260047	+	0.0986049i
$757$	−2.35614	−	8.02429i	−0.0856355	−	0.291648i	0.905529	−	0.424284i	$-0.139474\pi$
$757$	−2.35614	−	8.02429i	−0.0856355	−	0.291648i	−0.991165	+	0.132636i	$0.957656\pi$
$758$	13.6478	−	22.8604i	0.495711	−	0.830329i
$759$	2.32400	+	6.55299i	0.0843559	+	0.237858i
$760$	0.667562	−	15.2150i	0.0242150	−	0.551906i
$761$	6.64698	−	1.95173i	0.240953	−	0.0707502i	−0.159026	−	0.987274i	$-0.550835\pi$
$761$	6.64698	−	1.95173i	0.240953	−	0.0707502i	0.399979	+	0.916524i	$0.369017\pi$
$762$	23.4917	−	4.17252i	0.851013	−	0.151154i
$763$	−1.75631	−	2.73287i	−0.0635826	−	0.0989364i
$764$	3.33800	−	2.47062i	0.120765	−	0.0893839i
$765$	1.20911	−	1.88142i	0.0437156	−	0.0680228i
$766$	−13.0034	+	8.97622i	−0.469834	+	0.324324i
$767$	5.38216	−	6.21134i	0.194339	−	0.224279i
$768$	4.17315	+	15.4462i	0.150586	+	0.557366i
$769$	10.2955	+	22.5440i	0.371266	+	0.812958i	0.999393	+	0.0348474i	$0.0110945\pi$
$769$	10.2955	+	22.5440i	0.371266	+	0.812958i	−0.628127	+	0.778111i	$0.716178\pi$
$770$	3.81116	+	4.11583i	0.137345	+	0.148324i
$771$	2.21792	−	7.55353i	0.0798764	−	0.272034i
$772$	−5.82800	+	7.69778i	−0.209754	+	0.277049i
$773$	7.26933	+	1.04517i	0.261460	+	0.0375922i	0.271798	−	0.962354i	$-0.412382\pi$
$773$	7.26933	+	1.04517i	0.261460	+	0.0375922i	−0.0103384	+	0.999947i	$0.503291\pi$
$774$	−1.23465	−	3.74344i	−0.0443787	−	0.134555i
$775$	−0.888067	+	1.94460i	−0.0319003	+	0.0698520i
$776$	18.5542	−	26.2637i	0.666056	−	0.942812i
$777$	3.07934	+	21.4172i	0.110471	+	0.768340i
$778$	1.30901	+	39.6716i	0.0469303	+	1.42230i
$779$	51.3572	−	44.5013i	1.84006	−	1.59442i
$780$	6.00815	−	5.94324i	0.215126	−	0.212802i
$781$			19.9448i			0.713682i
$782$	−12.9867	−	16.7541i	−0.464402	−	0.599126i
$783$	−8.42553			−0.301104
$784$	8.90287	−	29.1454i	0.317959	−	1.04091i
$785$	0.576345	+	0.665138i	0.0205706	+	0.0237398i
$786$	7.70213	−	0.254141i	0.274726	−	0.00906490i
$787$	−29.7909	+	4.28328i	−1.06193	+	0.152683i	−0.651072	−	0.759016i	$-0.725680\pi$
$787$	−29.7909	+	4.28328i	−1.06193	+	0.152683i	−0.410859	+	0.911699i	$0.634771\pi$
$788$	−43.6119	−	3.35737i	−1.55361	−	0.119601i
$789$	10.3091	+	4.70803i	0.367015	+	0.167610i
$790$	4.19650	+	12.7237i	0.149305	+	0.452688i
$791$	−5.26872	+	36.6448i	−0.187334	+	1.30294i
$792$	1.53831	+	3.80111i	0.0546615	+	0.135067i
$793$	29.4655	+	8.65184i	1.04635	+	0.307236i
$794$	−2.15518	+	1.99565i	−0.0764845	+	0.0708229i
$795$	−2.97746	+	1.35976i	−0.105599	+	0.0482257i
$796$	19.0421	−	6.98475i	0.674928	−	0.247568i
$797$	−23.0252	−	19.9515i	−0.815596	−	0.706718i	0.143546	−	0.989644i	$-0.454150\pi$
$797$	−23.0252	−	19.9515i	−0.815596	−	0.706718i	−0.959142	+	0.282926i	$0.908695\pi$
$798$	−33.4852	+	23.1147i	−1.18536	+	0.818251i
$799$	23.9715	+	15.4056i	0.848052	+	0.545010i
$800$	14.1948	+	21.0488i	0.501861	+	0.744187i
$801$	−4.81138	+	3.09208i	−0.170002	+	0.109253i
$802$	−5.97543	−	33.6422i	−0.211000	−	1.18795i
$803$	−3.48721	−	11.8763i	−0.123061	−	0.419107i
$804$	10.9932	+	20.3951i	0.387701	+	0.719281i
$805$	−4.78369	+	12.2177i	−0.168603	+	0.430618i
$806$	2.03914	−	3.41561i	0.0718255	−	0.120310i
$807$	−23.1968	+	6.81121i	−0.816567	+	0.239766i
$808$	0.235359	+	0.296982i	0.00827989	+	0.0104478i
$809$	31.3598	−	20.1537i	1.10255	−	0.708568i	0.142895	−	0.989738i	$-0.454359\pi$
$809$	31.3598	−	20.1537i	1.10255	−	0.708568i	0.959658	+	0.281170i	$0.0907225\pi$
$810$	−0.933863	−	0.389793i	−0.0328126	−	0.0136959i
$811$	8.27577	−	12.8773i	0.290601	−	0.452185i	−0.665002	−	0.746842i	$-0.731569\pi$
$811$	8.27577	−	12.8773i	0.290601	−	0.452185i	0.955603	+	0.294657i	$0.0952055\pi$
$812$	4.24720	+	64.2889i	0.149047	+	2.25610i
$813$	5.60721	+	4.85868i	0.196654	+	0.170401i
$814$	−7.30500	+	9.01474i	−0.256040	+	0.315966i
$815$	1.55448	+	3.40383i	0.0544509	+	0.119231i
$816$	−8.08387	−	9.53666i	−0.282992	−	0.333850i
$817$	20.1244	+	5.90904i	0.704062	+	0.206731i
$818$	−1.89934	+	17.2261i	−0.0664088	+	0.602298i
$819$	−22.3485	−	3.21322i	−0.780919	−	0.112279i
$820$	2.81574	−	12.6135i	0.0983297	−	0.440482i
$821$	−12.2929	−	5.61400i	−0.429026	−	0.195930i	0.189185	−	0.981941i	$-0.439415\pi$
$821$	−12.2929	−	5.61400i	−0.429026	−	0.195930i	−0.618212	+	0.786012i	$0.712143\pi$
$822$	−28.1226	+	13.9818i	−0.980890	+	0.487672i
$823$	3.34264	+	23.2486i	0.116517	+	0.810395i	0.961343	+	0.275354i	$0.0887950\pi$
$823$	3.34264	+	23.2486i	0.116517	+	0.810395i	−0.844826	+	0.535042i	$0.820296\pi$
$824$	−21.6193	−	37.1234i	−0.753146	−	1.29325i
$825$	4.26090	+	4.91734i	0.148345	+	0.171200i
$826$	−1.88092	+	7.28674i	−0.0654457	+	0.253538i
$827$		−	48.8451i		−	1.69851i	−0.527982	−	0.849256i	$-0.677051\pi$
$827$		−	48.8451i		−	1.69851i	0.527982	−	0.849256i	$-0.322949\pi$
$828$	−6.43646	+	7.11140i	−0.223682	+	0.247138i
$829$		−	33.7473i		−	1.17209i	−0.810278	−	0.586046i	$-0.800684\pi$
$829$		−	33.7473i		−	1.17209i	0.810278	−	0.586046i	$-0.199316\pi$
$830$	−11.4328	−	2.95114i	−0.396838	−	0.102436i
$831$	−10.9417	−	12.6274i	−0.379564	−	0.438040i
$832$	−21.9620	−	41.8265i	−0.761395	−	1.45007i
$833$	3.38880	+	23.5696i	0.117415	+	0.816639i
$834$	12.4577	+	25.0570i	0.431373	+	0.867653i
$835$	11.5086	+	5.25581i	0.398272	+	0.181885i
$836$	−21.2948	−	4.75367i	−0.736495	−	0.164409i
$837$	−0.471487	−	0.0677896i	−0.0162970	−	0.00234315i
$838$	−1.63409	−	0.180174i	−0.0564489	−	0.00622400i
$839$	33.6798	+	9.88928i	1.16276	+	0.341416i	0.805503	−	0.592592i	$-0.201895\pi$
$839$	33.6798	+	9.88928i	1.16276	+	0.341416i	0.357253	+	0.934008i	$0.383713\pi$
$840$	−2.50347	+	7.32210i	−0.0863780	+	0.252636i
$841$	−17.4431	−	38.1950i	−0.601486	−	1.31707i
$842$	20.8027	+	16.8573i	0.716908	+	0.580939i
$843$	5.68797	+	4.92865i	0.195904	+	0.169752i
$844$	−1.40119	−	21.2095i	−0.0482308	−	0.730060i
$845$	−8.46125	+	13.1660i	−0.291076	+	0.452923i
$846$	4.96644	−	11.8985i	0.170750	−	0.409080i
$847$	−28.6207	+	18.3934i	−0.983420	+	0.632006i
$848$	2.40714	+	18.1387i	0.0826615	+	0.622884i
$849$	9.17516	−	2.69407i	0.314891	−	0.0924603i
$850$	−17.0327	−	10.1686i	−0.584218	−	0.348781i
$851$	−26.4233	−	6.19770i	−0.905779	−	0.212454i
$852$	−24.2200	+	13.0549i	−0.829765	+	0.447252i
$853$	3.34683	+	11.3983i	0.114593	+	0.390269i	0.996738	−	0.0807104i	$-0.0257189\pi$
$853$	3.34683	+	11.3983i	0.114593	+	0.390269i	−0.882144	+	0.470979i	$0.843901\pi$
$854$	−27.6860	+	4.91750i	−0.947394	+	0.168273i
$855$	4.52972	−	2.91108i	0.154913	−	0.0995567i
$856$	0.637248	+	6.41890i	0.0217807	+	0.219393i
$857$	−17.9645	−	11.5451i	−0.613656	−	0.394373i	0.196571	−	0.980490i	$-0.437019\pi$
$857$	−17.9645	−	11.5451i	−0.613656	−	0.394373i	−0.810226	+	0.586117i	$0.800656\pi$
$858$	−6.87812	−	9.96403i	−0.234815	−	0.340166i
$859$	30.8322	+	26.7162i	1.05198	+	0.911547i	0.996217	−	0.0868974i	$-0.0276952\pi$
$859$	30.8322	+	26.7162i	1.05198	+	0.911547i	0.0557636	+	0.998444i	$0.482241\pi$
$860$	3.74491	−	1.37365i	0.127700	−	0.0468412i
$861$	−31.4081	+	14.3436i	−1.07039	+	0.488829i
$862$	3.21752	+	3.47473i	0.109589	+	0.118350i
$863$	2.90071	+	0.851725i	0.0987413	+	0.0289931i	0.330730	−	0.943725i	$-0.392705\pi$
$863$	2.90071	+	0.851725i	0.0987413	+	0.0289931i	−0.231989	+	0.972718i	$0.574523\pi$
$864$	−3.60898	+	4.35606i	−0.122780	+	0.148196i
$865$	−0.869542	+	6.04780i	−0.0295653	+	0.205631i
$866$	−34.6652	+	11.4332i	−1.17797	+	0.388516i
$867$	−6.57796	−	3.00405i	−0.223399	−	0.102023i
$868$	−0.279581	+	3.63173i	−0.00948960	+	0.123269i
$869$	18.9992	−	2.73167i	0.644503	−	0.0926655i
$870$	−0.281179	−	8.52156i	−0.00953285	−	0.288908i
$871$	−44.7988	−	51.7006i	−1.51795	−	1.75181i
$872$	2.33327	−	0.575326i	0.0790146	−	0.0194830i
$873$	11.3690			0.384784
$874$	−11.6845	−	49.6809i	−0.395235	−	1.68048i
$875$			25.9580i			0.877541i
$876$	12.1395	−	12.0083i	0.410156	−	0.405724i
$877$	25.4976	−	22.0938i	0.860993	−	0.746055i	−0.107735	−	0.994180i	$-0.534360\pi$
$877$	25.4976	−	22.0938i	0.860993	−	0.746055i	0.968728	+	0.248125i	$0.0798144\pi$
$878$	−0.562556	+	0.0185622i	−0.0189854	+	0.000626444i
$879$	−1.45347	−	10.1091i	−0.0490242	−	0.340971i
$880$	−3.79310	+	1.68270i	−0.127865	+	0.0567237i
$881$	−1.55258	+	3.39969i	−0.0523079	+	0.114538i	−0.933981	−	0.357322i	$-0.883690\pi$
$881$	−1.55258	+	3.39969i	−0.0523079	+	0.114538i	0.881673	+	0.471860i	$0.156417\pi$
$882$	10.2323	−	3.37480i	0.344539	−	0.113635i
$883$	−6.13076	−	0.881470i	−0.206316	−	0.0296638i	0.0383816	−	0.999263i	$-0.487780\pi$
$883$	−6.13076	−	0.881470i	−0.206316	−	0.0296638i	−0.244698	+	0.969599i	$0.578689\pi$
$884$	29.4299	+	22.2814i	0.989836	+	0.749405i
$885$	0.280577	−	0.955557i	0.00943148	−	0.0321207i
$886$	−8.29683	+	7.68267i	−0.278738	+	0.258104i
$887$	17.3746	+	38.0450i	0.583381	+	1.27743i	0.939360	+	0.342933i	$0.111420\pi$
$887$	17.3746	+	38.0450i	0.583381	+	1.27743i	−0.355979	+	0.934494i	$0.615852\pi$
$888$	−15.7285	−	2.97025i	−0.527815	−	0.0996752i
$889$	42.2422	−	48.7501i	1.41676	−	1.63503i
$890$	−3.28789	−	4.76303i	−0.110210	−	0.159657i
$891$	−0.783809	+	1.21963i	−0.0262586	+	0.0408591i
$892$	11.5027	−	8.51371i	0.385139	−	0.285060i
$893$	37.0906	+	57.7141i	1.24119	+	1.93133i
$894$	−2.48055	−	13.9657i	−0.0829620	−	0.467083i
$895$	0.139771	−	0.0410405i	0.00467203	−	0.00137183i
$896$	35.0571	+	25.3416i	1.17117	+	0.846603i
$897$	13.9732	−	24.6333i	0.466551	−	0.822482i
$898$	−3.62706	−	2.16537i	−0.121037	−	0.0722595i
$899$	−1.13070	−	3.85081i	−0.0377109	−	0.128432i
$900$	−3.18241	+	8.39286i	−0.106080	+	0.279762i
$901$	−7.72966	−	12.0276i	−0.257512	−	0.400697i
$902$	−17.0869	−	7.13205i	−0.568932	−	0.237471i
$903$	−8.96520	−	5.76158i	−0.298343	−	0.191733i
$904$	−24.3895	−	12.4580i	−0.811184	−	0.414348i
$905$	3.56931	−	4.11920i	0.118648	−	0.136927i
$906$	9.11190	+	7.38374i	0.302723	+	0.245308i
$907$	39.1812	−	17.8935i	1.30099	−	0.594143i	0.360120	−	0.932906i	$-0.382736\pi$
$907$	39.1812	−	17.8935i	1.30099	−	0.594143i	0.940872	+	0.338763i	$0.110008\pi$
$908$	−23.5047	+	4.97958i	−0.780031	+	0.165253i
$909$	−0.0377448	+	0.128547i	−0.00125192	+	0.00426364i
$910$	2.50403	−	22.7104i	0.0830078	−	0.752843i
$911$	1.32850	−	9.23989i	0.0440150	−	0.306131i	−0.955907	−	0.293669i	$-0.905124\pi$
$911$	1.32850	−	9.23989i	0.0440150	−	0.306131i	0.999922	−	0.0124628i	$-0.00396712\pi$
$912$	−8.16583	−	28.9708i	−0.270398	−	0.959320i
$913$	−7.02724	+	15.3875i	−0.232568	+	0.509252i
$914$	−16.1078	−	32.3988i	−0.532798	−	1.07166i
$915$	3.68328	−	0.529576i	0.121766	−	0.0175073i
$916$	−15.6386	+	28.2738i	−0.516715	+	0.934194i
$917$	15.7458	−	13.6438i	0.519972	−	0.450558i
$918$	1.10474	−	4.27980i	0.0364619	−	0.141254i
$919$	9.85595			0.325118			0.162559	−	0.986699i	$-0.448025\pi$
$919$	9.85595			0.325118			0.162559	+	0.986699i	$0.448025\pi$
$920$	−7.40726	−	6.27249i	−0.244210	−	0.206798i
$921$	−23.2470			−0.766016
$922$	4.79628	−	18.5809i	0.157957	−	0.611930i
$923$	61.3965	−	53.2004i	2.02089	−	1.75111i
$924$	9.70119	+	5.36586i	0.319146	+	0.176524i
$925$	−25.1397	+	3.61454i	−0.826589	+	0.118845i
$926$	0.758733	+	1.52609i	0.0249335	+	0.0501506i
$927$	6.30956	−	13.8160i	0.207233	−	0.453777i
$928$	−46.0172	−	12.4131i	−1.51059	−	0.407480i
$929$	−0.0902499	+	0.627702i	−0.00296100	+	0.0205942i	−0.991248	−	0.132010i	$-0.957857\pi$
$929$	−0.0902499	+	0.627702i	−0.00296100	+	0.0205942i	0.988287	+	0.152604i	$0.0487660\pi$
$930$	0.0528277	−	0.479123i	0.00173229	−	0.0157111i
$931$	−16.1517	+	55.0078i	−0.529352	+	1.80281i
$932$	−0.802506	−	3.78800i	−0.0262869	−	0.124080i
$933$	−1.40268	+	0.640580i	−0.0459215	+	0.0209717i
$934$	39.7154	+	32.1830i	1.29953	+	1.05306i
$935$	2.12329	−	2.45040i	0.0694389	−	0.0801368i
$936$	7.59776	−	14.8744i	0.248341	−	0.486185i
$937$	−42.7108	−	27.4486i	−1.39530	−	0.896705i	−0.395537	−	0.918450i	$-0.629442\pi$
$937$	−42.7108	−	27.4486i	−1.39530	−	0.896705i	−0.999764	+	0.0217447i	$0.993078\pi$
$938$	57.8064	+	24.1283i	1.88744	+	0.787817i
$939$	−9.19974	−	14.3151i	−0.300222	−	0.467155i
$940$	12.1999	+	4.62596i	0.397917	+	0.150882i
$941$	−3.45367	−	11.7621i	−0.112586	−	0.383434i	0.883851	−	0.467768i	$-0.154942\pi$
$941$	−3.45367	−	11.7621i	−0.112586	−	0.383434i	−0.996438	+	0.0843341i	$0.973124\pi$
$942$	1.49351	+	0.891635i	0.0486613	+	0.0290510i
$943$	−2.38991	−	43.2438i	−0.0778261	−	1.40821i
$944$	−4.65040	−	3.06051i	−0.151357	−	0.0996112i
$945$	−2.62506	+	0.770788i	−0.0853933	+	0.0250737i
$946$	−0.999390	−	5.62665i	−0.0324930	−	0.182938i
$947$	10.2553	+	15.9576i	0.333253	+	0.518552i	0.966929	−	0.255047i	$-0.0820909\pi$
$947$	10.2553	+	15.9576i	0.333253	+	0.518552i	−0.633676	+	0.773599i	$0.718455\pi$
$948$	15.7531	+	21.2837i	0.511636	+	0.691261i
$949$	−27.2574	+	42.4134i	−0.884814	+	1.37680i
$950$	−27.1322	−	39.3052i	−0.880284	−	1.27523i
$951$	−19.3567	+	22.3388i	−0.627683	+	0.724385i
$952$	−33.2128	−	6.27206i	−1.07643	−	0.203279i
$953$	−16.0552	−	35.1560i	−0.520078	−	1.13881i	−0.969410	−	0.245448i	$-0.921065\pi$
$953$	−16.0552	−	35.1560i	−0.520078	−	1.13881i	0.449331	−	0.893365i	$-0.351662\pi$
$954$	−4.74673	+	4.39536i	−0.153681	+	0.142305i
$955$	−0.418598	+	1.42561i	−0.0135455	+	0.0461318i
$956$	−12.8644	+	16.9917i	−0.416065	+	0.549550i
$957$	−12.0908	−	1.73840i	−0.390840	−	0.0561943i
$958$	−29.2003	+	9.63078i	−0.943418	+	0.311156i
$959$	−35.2730	+	77.2371i	−1.13902	+	2.49412i
$960$	−4.52615	−	3.50474i	−0.146081	−	0.113115i
$961$	4.37947	+	30.4599i	0.141273	+	0.982577i
$962$	47.2354	−	1.55859i	1.52293	−	0.0502509i
$963$	−1.72355	+	1.49346i	−0.0555405	+	0.0481261i
$964$	−30.3232	−	30.6544i	−0.976644	−	0.987311i
$965$		−	3.45439i		−	0.111201i
$966$	−1.41532	+	25.8932i	−0.0455373	+	0.833100i
$967$	−12.8613			−0.413592			−0.206796	−	0.978384i	$-0.566304\pi$
$967$	−12.8613			−0.413592			−0.206796	+	0.978384i	$0.566304\pi$
$968$	−6.02527	−	24.4359i	−0.193659	−	0.785399i
$969$	15.4016	+	17.7744i	0.494770	+	0.570995i
$970$	0.379410	+	11.4986i	0.0121821	+	0.369198i
$971$	−35.4895	+	5.10262i	−1.13891	+	0.163751i	−0.685860	−	0.727733i	$-0.740574\pi$
$971$	−35.4895	+	5.10262i	−1.13891	+	0.163751i	−0.453052	+	0.891484i	$0.649665\pi$
$972$	−1.99410	−	0.153511i	−0.0639608	−	0.00492388i
$973$	68.8175	+	31.4279i	2.20619	+	1.00753i
$974$	−23.5479	+	7.76653i	−0.754524	+	0.248856i
$975$	3.77170	−	26.2328i	0.120791	−	0.840121i
$976$	3.18385	−	20.5564i	0.101913	−	0.657995i
$977$	4.82289	+	1.41613i	0.154298	+	0.0453060i	0.357969	−	0.933733i	$-0.383469\pi$
$977$	4.82289	+	1.41613i	0.154298	+	0.0453060i	−0.203671	+	0.979039i	$0.565287\pi$
$978$	5.02477	+	5.42646i	0.160675	+	0.173519i
$979$	−7.54240	+	3.44450i	−0.241056	+	0.110087i
$980$	3.75474	+	10.2363i	0.119941	+	0.326987i
$981$	0.642118	+	0.556399i	0.0205013	+	0.0177644i
$982$	−12.7807	−	18.5148i	−0.407848	−	0.590832i
$983$	−23.3362	−	14.9972i	−0.744308	−	0.478338i	0.112707	−	0.993628i	$-0.464048\pi$
$983$	−23.3362	−	14.9972i	−0.744308	−	0.478338i	−0.857016	+	0.515290i	$0.827684\pi$
$984$	−2.52339	−	25.4178i	−0.0804429	−	0.810289i
$985$	13.1652	−	8.46077i	0.419479	−	0.269583i
$986$	36.6676	−	6.51279i	1.16773	−	0.207410i
$987$	−9.82076	−	33.4464i	−0.312598	−	1.06461i
$988$	42.1678	+	78.2318i	1.34154	+	2.48889i
$989$	10.8293	−	7.83641i	0.344353	−	0.249183i
$990$	−1.25969	−	0.752041i	−0.0400355	−	0.0239014i
$991$	41.5334	−	12.1953i	1.31935	−	0.387397i	0.455093	−	0.890444i	$-0.349606\pi$
$991$	41.5334	−	12.1953i	1.31935	−	0.387397i	0.864259	+	0.503047i	$0.167788\pi$
$992$	−2.47522	−	1.06487i	−0.0785882	−	0.0338097i
$993$	23.5354	−	15.1253i	0.746873	−	0.479986i
$994$	−28.6533	+	68.6473i	−0.908828	+	2.17736i
$995$	−3.92326	+	6.10472i	−0.124376	+	0.193533i
$996$	−23.2855	+	1.53834i	−0.737829	+	0.0487441i
$997$	28.9973	+	25.1263i	0.918354	+	0.795758i	0.979307	−	0.202382i	$-0.0648683\pi$
$997$	28.9973	+	25.1263i	0.918354	+	0.795758i	−0.0609525	+	0.998141i	$0.519414\pi$
$998$	27.8452	+	22.5641i	0.881426	+	0.714255i
$999$	−2.35090	−	5.14776i	−0.0743793	−	0.162868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.5	yes	480
8.5	even	2	inner	552.2.bb.a.469.13	yes	480
23.18	even	11	inner	552.2.bb.a.133.13	yes	480
184.133	even	22	inner	552.2.bb.a.133.5	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.5	✓	480	184.133	even	22	inner
552.2.bb.a.133.13	yes	480	23.18	even	11	inner
552.2.bb.a.469.5	yes	480	1.1	even	1	trivial
552.2.bb.a.469.13	yes	480	8.5	even	2	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36933 - 0.353464i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.75013 + 0.968018i) q^{4} +(-0.708272 + 0.101834i) q^{5} +(-1.26634 + 0.629590i) q^{6} +(-1.58831 + 3.47792i) q^{7} +(-2.05434 - 1.94414i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.36933 - 0.353464i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.75013 + 0.968018i) q^{4} +(-0.708272 + 0.101834i) q^{5} +(-1.26634 + 0.629590i) q^{6} +(-1.58831 + 3.47792i) q^{7} +(-2.05434 - 1.94414i) q^{8} +(0.142315 - 0.989821i) q^{9} +(1.00585 + 0.110904i) q^{10} +(0.408449 - 1.39105i) q^{11} +(1.95657 - 0.414510i) q^{12} +(-5.37158 + 2.45312i) q^{13} +(3.40425 - 4.20101i) q^{14} +(-0.468589 + 0.540781i) q^{15} +(2.12588 + 3.38831i) q^{16} +(-2.62931 - 1.68976i) q^{17} +(-0.544742 + 1.30509i) q^{18} +(-4.06828 - 6.33036i) q^{19} +(-1.33814 - 0.507398i) q^{20} +(1.07719 + 3.66856i) q^{21} +(-1.05099 + 1.76043i) q^{22} +(-4.77745 - 0.419530i) q^{23} +(-2.82571 - 0.123979i) q^{24} +(-4.30619 + 1.26441i) q^{25} +(8.22256 - 1.46047i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(-6.14644 + 4.54929i) q^{28} +(4.55518 - 7.08801i) q^{29} +(0.832800 - 0.574878i) q^{30} +(0.311933 - 0.359990i) q^{31} +(-1.71339 - 5.39113i) q^{32} +(-0.602259 - 1.31876i) q^{33} +(3.00313 + 3.24320i) q^{34} +(0.770788 - 2.62506i) q^{35} +(1.20723 - 1.59455i) q^{36} +(5.60156 + 0.805383i) q^{37} +(3.33325 + 10.1063i) q^{38} +(-2.45312 + 5.37158i) q^{39} +(1.65301 + 1.16778i) q^{40} +(1.28520 + 8.93879i) q^{41} +(-0.178319 - 5.40422i) q^{42} +(-2.10648 + 1.82527i) q^{43} +(2.06140 - 2.03913i) q^{44} +0.715556i q^{45} +(6.39361 + 2.26313i) q^{46} -9.11704 q^{47} +(3.82550 + 1.16855i) q^{48} +(-4.98919 - 5.75783i) q^{49} +(6.34351 - 0.209311i) q^{50} +(-3.09366 + 0.444801i) q^{51} +(-11.7756 - 0.906520i) q^{52} +(4.16104 + 1.90028i) q^{53} +(0.442962 + 1.34305i) q^{54} +(-0.147637 + 1.02684i) q^{55} +(10.0245 - 4.05693i) q^{56} +(-7.22010 - 2.12001i) q^{57} +(-8.74291 + 8.09572i) q^{58} +(-1.26601 + 0.578167i) q^{59} +(-1.34358 + 0.492832i) q^{60} +(-3.93018 - 3.40552i) q^{61} +(-0.554383 + 0.382688i) q^{62} +(3.21648 + 2.06711i) q^{63} +(0.440621 + 7.98786i) q^{64} +(3.55473 - 2.28449i) q^{65} +(0.358555 + 2.01870i) q^{66} +(3.26376 + 11.1154i) q^{67} +(-2.96591 - 5.50251i) q^{68} +(-3.88529 + 2.81150i) q^{69} +(-1.98333 + 3.32213i) q^{70} +(-13.1999 + 3.87584i) q^{71} +(-2.21672 + 1.75675i) q^{72} +(7.18235 - 4.61582i) q^{73} +(-7.38571 - 3.08279i) q^{74} +(-2.42639 + 3.77553i) q^{75} +(-0.992093 - 15.0171i) q^{76} +(4.18922 + 3.62998i) q^{77} +(5.25779 - 6.48838i) q^{78} +(5.49995 + 12.0432i) q^{79} +(-1.85075 - 2.18336i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(1.39968 - 12.6944i) q^{82} +(-11.5494 - 1.66055i) q^{83} +(-1.66602 + 7.46319i) q^{84} +(2.03434 + 0.929053i) q^{85} +(3.52963 - 1.75483i) q^{86} +(-1.19908 - 8.33977i) q^{87} +(-3.54349 + 2.06361i) q^{88} +(-3.74534 - 4.32235i) q^{89} +(0.252923 - 0.979831i) q^{90} -22.5783i q^{91} +(-7.95502 - 5.35888i) q^{92} -0.476335i q^{93} +(12.4842 + 3.22255i) q^{94} +(3.52609 + 4.06933i) q^{95} +(-4.82533 - 2.95231i) q^{96} +(1.61798 + 11.2533i) q^{97} +(4.79665 + 9.64786i) q^{98} +(-1.31876 - 0.602259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more