LMFDB - Embedded newform 945.2.bt.c.106.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(106,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 0, 0]))

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

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

chi := DirichletCharacter("945.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bt (of order $9$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			106.14
Character	$\chi$	$=$	945.106
Dual form			945.2.bt.c.526.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.151677 - 0.860201i) q^{2} +(0.910009 - 1.47373i) q^{3} +(1.16245 + 0.423095i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.12968 - 1.00632i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(1.41373 - 2.44866i) q^{8} +(-1.34377 - 2.68222i) q^{9} +O(q^{10})$	\(q+(0.151677 - 0.860201i) q^{2} +(0.910009 - 1.47373i) q^{3} +(1.16245 + 0.423095i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.12968 - 1.00632i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(1.41373 - 2.44866i) q^{8} +(-1.34377 - 2.68222i) q^{9} +(0.436736 + 0.756448i) q^{10} +(2.44012 + 2.04750i) q^{11} +(1.68136 - 1.32811i) q^{12} +(-0.613840 - 3.48126i) q^{13} +(0.151677 + 0.860201i) q^{14} +(0.250189 + 1.71389i) q^{15} +(0.00335878 + 0.00281835i) q^{16} +(-0.965228 - 1.67182i) q^{17} +(-2.51106 + 0.749081i) q^{18} +(2.69683 - 4.67105i) q^{19} +(-1.16245 + 0.423095i) q^{20} +(-0.351083 + 1.69610i) q^{21} +(2.13137 - 1.78844i) q^{22} +(5.92483 + 2.15646i) q^{23} +(-2.32216 - 4.31177i) q^{24} +(0.173648 - 0.984808i) q^{25} -3.08769 q^{26} +(-5.17571 - 0.460487i) q^{27} -1.23705 q^{28} +(0.203447 - 1.15381i) q^{29} +(1.51223 + 0.0447436i) q^{30} +(-8.56695 - 3.11812i) q^{31} +(4.33487 - 3.63738i) q^{32} +(5.23800 - 1.73283i) q^{33} +(-1.58451 + 0.576713i) q^{34} +(0.500000 - 0.866025i) q^{35} +(-0.427223 - 3.68647i) q^{36} +(-3.32569 - 5.76027i) q^{37} +(-3.60899 - 3.02831i) q^{38} +(-5.68904 - 2.26334i) q^{39} +(0.490985 + 2.78451i) q^{40} +(1.43908 + 8.16144i) q^{41} +(1.40573 + 0.559260i) q^{42} +(4.18745 + 3.51368i) q^{43} +(1.97022 + 3.41251i) q^{44} +(2.75348 + 1.19094i) q^{45} +(2.75365 - 4.76946i) q^{46} +(11.1046 - 4.04176i) q^{47} +(0.00721002 - 0.00238522i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-0.820794 - 0.298745i) q^{50} +(-3.34218 - 0.0988876i) q^{51} +(0.759350 - 4.30649i) q^{52} -7.07714 q^{53} +(-1.18115 + 4.38230i) q^{54} -3.18535 q^{55} +(-0.490985 + 2.78451i) q^{56} +(-4.42973 - 8.22510i) q^{57} +(-0.961647 - 0.350011i) q^{58} +(-2.09395 + 1.75703i) q^{59} +(-0.434306 + 2.09815i) q^{60} +(2.36505 - 0.860806i) q^{61} +(-3.98161 + 6.89636i) q^{62} +(2.18010 + 2.06086i) q^{63} +(-2.46700 - 4.27297i) q^{64} +(2.70794 + 2.27223i) q^{65} +(-0.696104 - 4.76856i) q^{66} +(0.338262 + 1.91838i) q^{67} +(-0.414683 - 2.35179i) q^{68} +(8.56969 - 6.76920i) q^{69} +(-0.669118 - 0.561456i) q^{70} +(5.46582 + 9.46707i) q^{71} +(-8.46757 - 0.501511i) q^{72} +(2.52739 - 4.37757i) q^{73} +(-5.45942 + 1.98707i) q^{74} +(-1.29332 - 1.15209i) q^{75} +(5.11122 - 4.28882i) q^{76} +(-2.99325 - 1.08945i) q^{77} +(-2.80982 + 4.55042i) q^{78} +(-2.83689 + 16.0888i) q^{79} -0.00438458 q^{80} +(-5.38857 + 7.20856i) q^{81} +7.23875 q^{82} +(-1.48565 + 8.42555i) q^{83} +(-1.12572 + 1.82308i) q^{84} +(1.81403 + 0.660255i) q^{85} +(3.65761 - 3.06910i) q^{86} +(-1.51526 - 1.34980i) q^{87} +(8.46332 - 3.08040i) q^{88} +(-7.20879 + 12.4860i) q^{89} +(1.44209 - 2.18791i) q^{90} +(1.76748 + 3.06137i) q^{91} +(5.97490 + 5.01353i) q^{92} +(-12.3913 + 9.78788i) q^{93} +(-1.79241 - 10.1653i) q^{94} +(0.936600 + 5.31172i) q^{95} +(-1.41576 - 9.69848i) q^{96} +(-0.974760 - 0.817921i) q^{97} +(-0.436736 - 0.756448i) q^{98} +(2.21289 - 9.29630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 9 q^{8}+O(q^{10}) $ 120 * q + 9 * q^8	$ 120 q + 9 q^{8} - 3 q^{10} - 24 q^{12} + 3 q^{13} + 6 q^{15} - 12 q^{16} + 60 q^{18} - 42 q^{19} + 9 q^{22} + 6 q^{23} - 60 q^{24} - 18 q^{26} - 42 q^{27} + 138 q^{28} - 18 q^{29} + 3 q^{30} - 21 q^{32} + 12 q^{33} + 39 q^{34} + 60 q^{35} + 6 q^{36} - 54 q^{37} - 117 q^{38} - 33 q^{39} - 9 q^{40} + 9 q^{41} + 3 q^{42} + 9 q^{43} + 24 q^{44} + 12 q^{45} - 24 q^{46} - 3 q^{47} + 180 q^{48} + 6 q^{51} + 39 q^{52} - 36 q^{53} - 48 q^{54} + 24 q^{55} + 9 q^{56} - 42 q^{57} - 27 q^{58} + 12 q^{59} + 15 q^{60} + 24 q^{61} - 27 q^{62} + 3 q^{63} - 123 q^{64} + 6 q^{65} - 75 q^{66} - 42 q^{67} - 111 q^{68} + 6 q^{69} + 30 q^{71} + 147 q^{72} - 66 q^{73} - 27 q^{74} - 24 q^{76} - 9 q^{77} - 15 q^{78} - 42 q^{79} - 174 q^{80} - 48 q^{81} + 132 q^{82} + 12 q^{83} - 15 q^{85} + 33 q^{86} + 42 q^{87} + 33 q^{88} + 57 q^{89} - 39 q^{90} - 42 q^{91} - 123 q^{92} - 72 q^{93} + 57 q^{94} - 21 q^{95} - 168 q^{96} + 93 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) $ 120 * q + 9 * q^8 - 3 * q^10 - 24 * q^12 + 3 * q^13 + 6 * q^15 - 12 * q^16 + 60 * q^18 - 42 * q^19 + 9 * q^22 + 6 * q^23 - 60 * q^24 - 18 * q^26 - 42 * q^27 + 138 * q^28 - 18 * q^29 + 3 * q^30 - 21 * q^32 + 12 * q^33 + 39 * q^34 + 60 * q^35 + 6 * q^36 - 54 * q^37 - 117 * q^38 - 33 * q^39 - 9 * q^40 + 9 * q^41 + 3 * q^42 + 9 * q^43 + 24 * q^44 + 12 * q^45 - 24 * q^46 - 3 * q^47 + 180 * q^48 + 6 * q^51 + 39 * q^52 - 36 * q^53 - 48 * q^54 + 24 * q^55 + 9 * q^56 - 42 * q^57 - 27 * q^58 + 12 * q^59 + 15 * q^60 + 24 * q^61 - 27 * q^62 + 3 * q^63 - 123 * q^64 + 6 * q^65 - 75 * q^66 - 42 * q^67 - 111 * q^68 + 6 * q^69 + 30 * q^71 + 147 * q^72 - 66 * q^73 - 27 * q^74 - 24 * q^76 - 9 * q^77 - 15 * q^78 - 42 * q^79 - 174 * q^80 - 48 * q^81 + 132 * q^82 + 12 * q^83 - 15 * q^85 + 33 * q^86 + 42 * q^87 + 33 * q^88 + 57 * q^89 - 39 * q^90 - 42 * q^91 - 123 * q^92 - 72 * q^93 + 57 * q^94 - 21 * q^95 - 168 * q^96 + 93 * q^97 + 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	0.151677	−	0.860201i	0.107252	−	0.608254i	−0.883045	−	0.469287i	$-0.844511\pi$
$2$	0.151677	−	0.860201i	0.107252	−	0.608254i	0.990297	−	0.138967i	$-0.0443781\pi$
$3$	0.910009	−	1.47373i	0.525394	−	0.850859i
$3$	0.910009	−	1.47373i	0.525394	−	0.850859i
$4$	1.16245	+	0.423095i	0.581223	+	0.211548i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	−1.12968	−	1.00632i	−0.461189	−	0.410829i
$7$	−0.939693	+	0.342020i	−0.355170	+	0.129271i
$7$	−0.939693	+	0.342020i	−0.355170	+	0.129271i
$8$	1.41373	−	2.44866i	0.499830	−	0.865732i
$9$	−1.34377	−	2.68222i	−0.447923	−	0.894072i
$10$	0.436736	+	0.756448i	0.138108	+	0.239210i
$11$	2.44012	+	2.04750i	0.735724	+	0.617346i	0.931685	−	0.363266i	$-0.118338\pi$
$11$	2.44012	+	2.04750i	0.735724	+	0.617346i	−0.195962	+	0.980612i	$0.562783\pi$
$12$	1.68136	−	1.32811i	0.485368	−	0.383393i
$13$	−0.613840	−	3.48126i	−0.170249	−	0.965528i	−0.943486	−	0.331411i	$-0.892475\pi$
$13$	−0.613840	−	3.48126i	−0.170249	−	0.965528i	0.773238	−	0.634116i	$-0.218636\pi$
$14$	0.151677	+	0.860201i	0.0405373	+	0.229898i
$15$	0.250189	+	1.71389i	0.0645986	+	0.442523i
$16$	0.00335878	+	0.00281835i	0.000839696	+	0.000704589i
$17$	−0.965228	−	1.67182i	−0.234102	−	0.405477i	0.724909	−	0.688844i	$-0.241882\pi$
$17$	−0.965228	−	1.67182i	−0.234102	−	0.405477i	−0.959011	+	0.283368i	$0.908548\pi$
$18$	−2.51106	+	0.749081i	−0.591864	+	0.176560i
$19$	2.69683	−	4.67105i	0.618695	−	1.07161i	−0.371029	−	0.928621i	$-0.620995\pi$
$19$	2.69683	−	4.67105i	0.618695	−	1.07161i	0.989724	−	0.142991i	$-0.0456719\pi$
$20$	−1.16245	+	0.423095i	−0.259931	+	0.0946070i
$21$	−0.351083	+	1.69610i	−0.0766125	+	0.370118i
$22$	2.13137	−	1.78844i	0.454411	−	0.381296i
$23$	5.92483	+	2.15646i	1.23541	+	0.449653i	0.875448	−	0.483313i	$-0.160567\pi$
$23$	5.92483	+	2.15646i	1.23541	+	0.449653i	0.359964	+	0.932966i	$0.382789\pi$
$24$	−2.32216	−	4.31177i	−0.474008	−	0.880135i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−3.08769			−0.605545
$27$	−5.17571	−	0.460487i	−0.996065	−	0.0886208i
$28$	−1.23705			−0.233780
$29$	0.203447	−	1.15381i	0.0377792	−	0.214256i	−0.960074	−	0.279746i	$-0.909750\pi$
$29$	0.203447	−	1.15381i	0.0377792	−	0.214256i	0.997853	+	0.0654895i	$0.0208609\pi$
$30$	1.51223	+	0.0447436i	0.276095	+	0.00816902i
$31$	−8.56695	−	3.11812i	−1.53867	−	0.560030i	−0.572944	−	0.819594i	$-0.694199\pi$
$31$	−8.56695	−	3.11812i	−1.53867	−	0.560030i	−0.965726	+	0.259564i	$0.916421\pi$
$32$	4.33487	−	3.63738i	0.766303	−	0.643005i
$33$	5.23800	−	1.73283i	0.911819	−	0.301648i
$34$	−1.58451	+	0.576713i	−0.271741	+	0.0989055i
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	−0.427223	−	3.68647i	−0.0712039	−	0.614412i
$37$	−3.32569	−	5.76027i	−0.546740	−	0.946982i	−0.998495	−	0.0548397i	$-0.982535\pi$
$37$	−3.32569	−	5.76027i	−0.546740	−	0.946982i	0.451755	−	0.892142i	$-0.350798\pi$
$38$	−3.60899	−	3.02831i	−0.585456	−	0.491256i
$39$	−5.68904	−	2.26334i	−0.910976	−	0.362425i
$40$	0.490985	+	2.78451i	0.0776315	+	0.440270i
$41$	1.43908	+	8.16144i	0.224747	+	1.27460i	0.863169	+	0.504916i	$0.168476\pi$
$41$	1.43908	+	8.16144i	0.224747	+	1.27460i	−0.638422	+	0.769687i	$0.720412\pi$
$42$	1.40573	+	0.559260i	0.216909	+	0.0862957i
$43$	4.18745	+	3.51368i	0.638580	+	0.535832i	0.903582	−	0.428416i	$-0.140928\pi$
$43$	4.18745	+	3.51368i	0.638580	+	0.535832i	−0.265002	+	0.964248i	$0.585373\pi$
$44$	1.97022	+	3.41251i	0.297021	+	0.514456i
$45$	2.75348	+	1.19094i	0.410465	+	0.177535i
$46$	2.75365	−	4.76946i	0.406003	−	0.703218i
$47$	11.1046	−	4.04176i	1.61978	−	0.589551i	0.636438	−	0.771328i	$-0.280407\pi$
$47$	11.1046	−	4.04176i	1.61978	−	0.589551i	0.983340	+	0.181777i	$0.0581848\pi$
$48$	0.00721002	−	0.00238522i	0.00104068	−	0.000344277i
$49$	0.766044	−	0.642788i	0.109435	−	0.0918268i
$50$	−0.820794	−	0.298745i	−0.116078	−	0.0422489i
$51$	−3.34218	−	0.0988876i	−0.467999	−	0.0138470i
$52$	0.759350	−	4.30649i	0.105303	−	0.597202i
$53$	−7.07714			−0.972121			−0.486060	−	0.873925i	$-0.661566\pi$
$53$	−7.07714			−0.972121			−0.486060	+	0.873925i	$0.661566\pi$
$54$	−1.18115	+	4.38230i	−0.160734	+	0.596356i
$55$	−3.18535			−0.429513
$56$	−0.490985	+	2.78451i	−0.0656106	+	0.372096i
$57$	−4.42973	−	8.22510i	−0.586732	−	1.08944i
$58$	−0.961647	−	0.350011i	−0.126270	−	0.0459587i
$59$	−2.09395	+	1.75703i	−0.272609	+	0.228746i	−0.768835	−	0.639447i	$-0.779163\pi$
$59$	−2.09395	+	1.75703i	−0.272609	+	0.228746i	0.496226	+	0.868193i	$0.334719\pi$
$60$	−0.434306	+	2.09815i	−0.0560687	+	0.270870i
$61$	2.36505	−	0.860806i	0.302813	−	0.110215i	−0.186145	−	0.982522i	$-0.559599\pi$
$61$	2.36505	−	0.860806i	0.302813	−	0.110215i	0.488958	+	0.872307i	$0.337377\pi$
$62$	−3.98161	+	6.89636i	−0.505665	+	0.875838i
$63$	2.18010	+	2.06086i	0.274667	+	0.259644i
$64$	−2.46700	−	4.27297i	−0.308375	−	0.534121i
$65$	2.70794	+	2.27223i	0.335878	+	0.281836i
$66$	−0.696104	−	4.76856i	−0.0856845	−	0.586970i
$67$	0.338262	+	1.91838i	0.0413252	+	0.234367i	0.998474	−	0.0552309i	$-0.0175895\pi$
$67$	0.338262	+	1.91838i	0.0413252	+	0.234367i	−0.957148	+	0.289598i	$0.906478\pi$
$68$	−0.414683	−	2.35179i	−0.0502877	−	0.285196i
$69$	8.56969	−	6.76920i	1.03167	−	0.814916i
$70$	−0.669118	−	0.561456i	−0.0799749	−	0.0671069i
$71$	5.46582	+	9.46707i	0.648673	+	1.12353i	0.983440	+	0.181234i	$0.0580091\pi$
$71$	5.46582	+	9.46707i	0.648673	+	1.12353i	−0.334767	+	0.942301i	$0.608658\pi$
$72$	−8.46757	−	0.501511i	−0.997912	−	0.0591036i
$73$	2.52739	−	4.37757i	0.295809	−	0.512356i	−0.679364	−	0.733802i	$-0.737744\pi$
$73$	2.52739	−	4.37757i	0.295809	−	0.512356i	0.975173	+	0.221445i	$0.0710774\pi$
$74$	−5.45942	+	1.98707i	−0.634644	+	0.230992i
$75$	−1.29332	−	1.15209i	−0.149340	−	0.133032i
$76$	5.11122	−	4.28882i	0.586297	−	0.491961i
$77$	−2.99325	−	1.08945i	−0.341113	−	0.124155i
$78$	−2.80982	+	4.55042i	−0.318150	+	0.515234i
$79$	−2.83689	+	16.0888i	−0.319175	+	1.81013i	0.228617	+	0.973516i	$0.426580\pi$
$79$	−2.83689	+	16.0888i	−0.319175	+	1.81013i	−0.547792	+	0.836615i	$0.684531\pi$
$80$	−0.00438458			−0.000490211
$81$	−5.38857	+	7.20856i	−0.598730	+	0.800951i
$82$	7.23875			0.799387
$83$	−1.48565	+	8.42555i	−0.163071	+	0.924824i	0.787959	+	0.615728i	$0.211138\pi$
$83$	−1.48565	+	8.42555i	−0.163071	+	0.924824i	−0.951031	+	0.309097i	$0.899973\pi$
$84$	−1.12572	+	1.82308i	−0.122827	+	0.198914i
$85$	1.81403	+	0.660255i	0.196760	+	0.0716147i
$86$	3.65761	−	3.06910i	0.394411	−	0.330950i
$87$	−1.51526	−	1.34980i	−0.162453	−	0.144714i
$88$	8.46332	−	3.08040i	0.902193	−	0.328371i
$89$	−7.20879	+	12.4860i	−0.764131	+	1.32351i	0.176574	+	0.984287i	$0.443498\pi$
$89$	−7.20879	+	12.4860i	−0.764131	+	1.32351i	−0.940705	+	0.339226i	$0.889835\pi$
$90$	1.44209	−	2.18791i	0.152009	−	0.230626i
$91$	1.76748	+	3.06137i	0.185282	+	0.320919i
$92$	5.97490	+	5.01353i	0.622926	+	0.522697i
$93$	−12.3913	+	9.78788i	−1.28491	+	1.01496i
$94$	−1.79241	−	10.1653i	−0.184873	−	1.04847i
$95$	0.936600	+	5.31172i	0.0960931	+	0.544971i
$96$	−1.41576	−	9.69848i	−0.144496	−	0.989847i
$97$	−0.974760	−	0.817921i	−0.0989719	−	0.0830473i	0.591959	−	0.805968i	$-0.298355\pi$
$97$	−0.974760	−	0.817921i	−0.0989719	−	0.0830473i	−0.690931	+	0.722921i	$0.742799\pi$
$98$	−0.436736	−	0.756448i	−0.0441170	−	0.0764128i
$99$	2.21289	−	9.29630i	0.222404	−	0.934313i
$100$	0.618524	−	1.07132i	0.0618524	−	0.107132i
$101$	2.10599	−	0.766516i	0.209554	−	0.0762712i	−0.235111	−	0.971969i	$-0.575545\pi$
$101$	2.10599	−	0.766516i	0.209554	−	0.0762712i	0.444664	+	0.895697i	$0.353323\pi$
$102$	−0.591995	+	2.85995i	−0.0586162	+	0.283177i
$103$	0.576115	−	0.483418i	0.0567663	−	0.0476326i	−0.613963	−	0.789335i	$-0.710426\pi$
$103$	0.576115	−	0.483418i	0.0567663	−	0.0476326i	0.670729	+	0.741702i	$0.265981\pi$
$104$	−9.39222	−	3.41849i	−0.920983	−	0.335211i
$105$	−0.821284	−	1.52496i	−0.0801492	−	0.148821i
$106$	−1.07344	+	6.08777i	−0.104261	+	0.591296i
$107$	−6.41513			−0.620174			−0.310087	−	0.950708i	$-0.600358\pi$
$107$	−6.41513			−0.620174			−0.310087	+	0.950708i	$0.600358\pi$
$108$	−5.82165	−	2.72511i	−0.560188	−	0.262224i
$109$	−6.49359			−0.621973			−0.310986	−	0.950414i	$-0.600659\pi$
$109$	−6.49359			−0.621973			−0.310986	+	0.950414i	$0.600659\pi$
$110$	−0.483143	+	2.74004i	−0.0460659	+	0.261253i
$111$	−11.5155	−	0.340717i	−1.09300	−	0.0323394i
$112$	−0.00412016	−	0.00149962i	−0.000389318	−	0.000141700i
$113$	8.87757	−	7.44916i	0.835131	−	0.700758i	−0.121332	−	0.992612i	$-0.538716\pi$
$113$	8.87757	−	7.44916i	0.835131	−	0.700758i	0.956463	+	0.291854i	$0.0942720\pi$
$114$	−7.74713	+	2.56290i	−0.725585	+	0.240038i
$115$	−5.92483	+	2.15646i	−0.552493	+	0.201091i
$116$	0.724666	−	1.25516i	0.0672836	−	0.116539i
$117$	−8.51263	+	6.32446i	−0.786993	+	0.584696i
$118$	1.19380	+	2.06772i	0.109898	+	0.190349i
$119$	1.47881	+	1.24087i	0.135563	+	0.113751i
$120$	4.55042	+	1.81035i	0.415395	+	0.165262i
$121$	−0.148216	−	0.840576i	−0.0134742	−	0.0764160i
$122$	−0.381744	−	2.16498i	−0.0345615	−	0.196008i
$123$	13.3373	+	5.30616i	1.20259	+	0.478440i
$124$	−8.63935	−	7.24928i	−0.775837	−	0.651004i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	2.10343	−	1.56274i	0.187388	−	0.139220i
$127$	−7.26339	+	12.5806i	−0.644522	+	1.11634i	0.339890	+	0.940465i	$0.389610\pi$
$127$	−7.26339	+	12.5806i	−0.644522	+	1.11634i	−0.984412	+	0.175879i	$0.943723\pi$
$128$	6.58520	−	2.39682i	0.582055	−	0.211851i
$129$	8.98884	−	2.97369i	0.791423	−	0.261819i
$130$	2.36531	−	1.98473i	0.207451	−	0.174072i
$131$	−13.5343	−	4.92610i	−1.18250	−	0.430395i	−0.325417	−	0.945571i	$-0.605505\pi$
$131$	−13.5343	−	4.92610i	−1.18250	−	0.430395i	−0.857085	+	0.515175i	$0.827727\pi$
$132$	6.82204	+	0.201849i	0.593783	+	0.0175687i
$133$	−0.936600	+	5.31172i	−0.0812135	+	0.460585i
$134$	1.70150			0.146987
$135$	4.26082	−	2.97413i	0.366713	−	0.255972i
$136$	−5.45830			−0.468045
$137$	0.977044	−	5.54109i	0.0834745	−	0.473407i	−0.914201	−	0.405261i	$-0.867181\pi$
$137$	0.977044	−	5.54109i	0.0834745	−	0.473407i	0.997675	−	0.0681460i	$-0.0217084\pi$
$138$	−4.52306	−	8.39838i	−0.385028	−	0.714918i
$139$	15.7239	+	5.72303i	1.33368	+	0.485421i	0.907818	−	0.419365i	$-0.137747\pi$
$139$	15.7239	+	5.72303i	1.33368	+	0.485421i	0.425866	+	0.904786i	$0.359969\pi$
$140$	0.947634	−	0.795159i	0.0800897	−	0.0672032i
$141$	4.14885	−	20.0433i	0.349396	−	1.68795i
$142$	8.97262	−	3.26577i	0.752966	−	0.274057i
$143$	5.63005	−	9.75153i	0.470808	−	0.815464i
$144$	0.00304601	−	0.0127962i	0.000253834	−	0.00106635i
$145$	0.585803	+	1.01464i	0.0486483	+	0.0842613i
$146$	−3.38225	−	2.83804i	−0.279917	−	0.234878i
$147$	−0.250189	−	1.71389i	−0.0206353	−	0.141359i
$148$	−1.42879	−	8.10308i	−0.117446	−	0.666069i
$149$	3.44552	+	19.5405i	0.282268	+	1.60082i	0.714883	+	0.699244i	$0.246480\pi$
$149$	3.44552	+	19.5405i	0.282268	+	1.60082i	−0.432615	+	0.901579i	$0.642409\pi$
$150$	−1.18720	+	0.937770i	−0.0969344	+	0.0765686i
$151$	−9.77707	−	8.20393i	−0.795647	−	0.667627i	0.151490	−	0.988459i	$-0.451593\pi$
$151$	−9.77707	−	8.20393i	−0.795647	−	0.667627i	−0.947136	+	0.320832i	$0.896037\pi$
$152$	−7.62520	−	13.2072i	−0.618486	−	1.07125i
$153$	−3.18715	+	4.83549i	−0.257666	+	0.390926i
$154$	−1.39116	+	2.40955i	−0.112103	+	0.194167i
$155$	8.56695	−	3.11812i	0.688114	−	0.250453i
$156$	−5.65559	−	5.03802i	−0.452809	−	0.403364i
$157$	2.82343	−	2.36914i	0.225335	−	0.189078i	−0.523130	−	0.852253i	$-0.675236\pi$
$157$	2.82343	−	2.36914i	0.225335	−	0.189078i	0.748465	+	0.663175i	$0.230791\pi$
$158$	13.4093	+	4.88059i	1.06679	+	0.388279i
$159$	−6.44026	+	10.4298i	−0.510746	+	0.827138i
$160$	−0.982634	+	5.57280i	−0.0776841	+	0.440568i
$161$	−6.30507			−0.496909
$162$	5.38349	+	5.72863i	0.422967	+	0.450083i
$163$	0.559456			0.0438200			0.0219100	−	0.999760i	$-0.493025\pi$
$163$	0.559456			0.0438200			0.0219100	+	0.999760i	$0.493025\pi$
$164$	−1.78021	+	10.0961i	−0.139011	+	0.788372i
$165$	−2.89870	+	4.69435i	−0.225663	+	0.365455i
$166$	7.02233	+	2.55592i	0.545038	+	0.198378i
$167$	6.28170	−	5.27097i	0.486093	−	0.407880i	−0.366531	−	0.930406i	$-0.619455\pi$
$167$	6.28170	−	5.27097i	0.486093	−	0.407880i	0.852624	+	0.522526i	$0.175010\pi$
$168$	3.65682	+	3.25751i	0.282130	+	0.251322i
$169$	0.473638	−	0.172390i	0.0364337	−	0.0132608i
$170$	0.843098	−	1.46029i	0.0646627	−	0.111999i
$171$	−16.1527	−	0.956679i	−1.23523	−	0.0731591i
$172$	3.38105	+	5.85615i	0.257803	+	0.446528i
$173$	12.1913	+	10.2297i	0.926885	+	0.777749i	0.975256	−	0.221081i	$-0.0709584\pi$
$173$	12.1913	+	10.2297i	0.926885	+	0.777749i	−0.0483707	+	0.998829i	$0.515403\pi$
$174$	−1.39093	+	1.09870i	−0.105446	+	0.0832920i
$175$	0.173648	+	0.984808i	0.0131266	+	0.0744445i
$176$	0.00242524	+	0.0137542i	0.000182810	+	0.00103677i
$177$	0.683881	+	4.68483i	0.0514037	+	0.352134i
$178$	9.64706	+	8.09485i	0.723078	+	0.606734i
$179$	8.14664	+	14.1104i	0.608908	+	1.05466i	0.991421	+	0.130710i	$0.0417256\pi$
$179$	8.14664	+	14.1104i	0.608908	+	1.05466i	−0.382512	+	0.923950i	$0.624941\pi$
$180$	2.69689	+	2.54939i	0.201014	+	0.190020i
$181$	−7.18210	+	12.4398i	−0.533841	+	0.924640i	0.465377	+	0.885113i	$0.345919\pi$
$181$	−7.18210	+	12.4398i	−0.533841	+	0.924640i	−0.999218	+	0.0395279i	$0.987415\pi$
$182$	2.90148	−	1.05605i	0.215072	−	0.0782798i
$183$	0.883615	−	4.26878i	0.0653187	−	0.315558i
$184$	13.6566	−	11.4592i	1.00678	−	0.844785i
$185$	6.25025	+	2.27491i	0.459528	+	0.167254i
$186$	6.54008	+	12.1436i	0.479542	+	0.890410i
$187$	1.06779	−	6.05576i	0.0780848	−	0.442841i
$188$	14.6186			1.06617
$189$	5.02107	−	1.33748i	0.365229	−	0.0972873i
$190$	4.71121			0.341787
$191$	0.554500	−	3.14473i	0.0401222	−	0.227544i	−0.958153	−	0.286258i	$-0.907589\pi$
$191$	0.554500	−	3.14473i	0.0401222	−	0.227544i	0.998275	+	0.0587132i	$0.0186998\pi$
$192$	−8.54220	−	0.252744i	−0.616480	−	0.0182402i
$193$	16.3263	+	5.94230i	1.17520	+	0.427736i	0.854503	−	0.519447i	$-0.173862\pi$
$193$	16.3263	+	5.94230i	1.17520	+	0.427736i	0.320693	+	0.947183i	$0.396084\pi$
$194$	−0.851425	+	0.714430i	−0.0611288	+	0.0512931i
$195$	5.81291	−	1.92302i	0.416271	−	0.137711i
$196$	1.16245	−	0.423095i	0.0830318	−	0.0302211i
$197$	−4.97459	+	8.61623i	−0.354425	+	0.613881i	−0.987019	−	0.160602i	$-0.948657\pi$
$197$	−4.97459	+	8.61623i	−0.354425	+	0.613881i	0.632595	+	0.774483i	$0.281990\pi$
$198$	−7.66104	−	3.31357i	−0.544447	−	0.235485i
$199$	−5.29138	−	9.16494i	−0.375096	−	0.649686i	0.615245	−	0.788336i	$-0.289057\pi$
$199$	−5.29138	−	9.16494i	−0.375096	−	0.649686i	−0.990341	+	0.138650i	$0.955724\pi$
$200$	−2.16597	−	1.81746i	−0.153157	−	0.128514i
$201$	3.13499	+	1.24723i	0.221125	+	0.0879730i
$202$	−0.339929	−	1.92783i	−0.0239173	−	0.135642i
$203$	0.203447	+	1.15381i	0.0142792	+	0.0809813i
$204$	−3.84327	−	1.52901i	−0.269082	−	0.107052i
$205$	−6.34847	−	5.32700i	−0.443397	−	0.372054i
$206$	−0.328453	−	0.568898i	−0.0228844	−	0.0396370i
$207$	−2.17750	−	18.7894i	−0.151347	−	1.30596i
$208$	0.00774967	−	0.0134228i	0.000537343	−	0.000930705i
$209$	16.1446	−	5.87615i	1.11674	−	0.406462i
$210$	−1.43634	+	0.475170i	−0.0991168	+	0.0327898i
$211$	14.0901	−	11.8230i	0.970002	−	0.813928i	−0.0125490	−	0.999921i	$-0.503995\pi$
$211$	14.0901	−	11.8230i	0.970002	−	0.813928i	0.982551	+	0.185993i	$0.0595501\pi$
$212$	−8.22679	−	2.99431i	−0.565018	−	0.205650i
$213$	18.9259	+	0.559973i	1.29678	+	0.0383687i
$214$	−0.973025	+	5.51830i	−0.0665146	+	0.377223i
$215$	−5.46632			−0.372800
$216$	−8.44465	+	12.0225i	−0.574586	+	0.818030i
$217$	9.11676			0.618886
$218$	−0.984925	+	5.58579i	−0.0667076	+	0.378317i
$219$	−4.15142	−	7.70833i	−0.280527	−	0.520881i
$220$	−3.70279	−	1.34771i	−0.249642	−	0.0908624i
$221$	−5.22755	+	4.38644i	−0.351643	+	0.295064i
$222$	−2.03972	+	9.85396i	−0.136897	+	0.661354i
$223$	6.20658	−	2.25901i	0.415623	−	0.151274i	−0.125740	−	0.992063i	$-0.540131\pi$
$223$	6.20658	−	2.25901i	0.415623	−	0.151274i	0.541363	+	0.840789i	$0.317908\pi$
$224$	−2.82938	+	4.90064i	−0.189046	+	0.327437i
$225$	−2.87481	+	0.857591i	−0.191654	+	0.0571728i
$226$	−5.06126	−	8.76636i	−0.336670	−	0.583129i
$227$	−13.8394	−	11.6126i	−0.918551	−	0.770756i	0.0551751	−	0.998477i	$-0.482428\pi$
$227$	−13.8394	−	11.6126i	−0.918551	−	0.770756i	−0.973727	+	0.227721i	$0.926873\pi$
$228$	−1.66932	−	11.4354i	−0.110553	−	0.757330i
$229$	−0.317957	−	1.80322i	−0.0210112	−	0.119160i	0.972498	−	0.232910i	$-0.0748249\pi$
$229$	−0.317957	−	1.80322i	−0.0210112	−	0.119160i	−0.993509	+	0.113750i	$0.963714\pi$
$230$	0.956332	+	5.42363i	0.0630586	+	0.357623i
$231$	−4.32945	+	3.41983i	−0.284857	+	0.225009i
$232$	−2.53766	−	2.12935i	−0.166605	−	0.139799i
$233$	5.90191	+	10.2224i	0.386647	+	0.669692i	0.991996	−	0.126268i	$-0.0403000\pi$
$233$	5.90191	+	10.2224i	0.386647	+	0.669692i	−0.605349	+	0.795960i	$0.706967\pi$
$234$	4.14914	+	8.28185i	0.271238	+	0.541401i
$235$	−5.90865	+	10.2341i	−0.385438	+	0.667598i
$236$	−3.17749	+	1.15651i	−0.206837	+	0.0752826i
$237$	21.1290	+	18.8218i	1.37247	+	1.22260i
$238$	1.29170	−	1.08387i	0.0837286	−	0.0702566i
$239$	1.70859	+	0.621875i	0.110519	+	0.0402257i	0.396688	−	0.917954i	$-0.370160\pi$
$239$	1.70859	+	0.621875i	0.110519	+	0.0402257i	−0.286169	+	0.958179i	$0.592382\pi$
$240$	−0.00399001	+	0.00646170i	−0.000257554	+	0.000417101i
$241$	−3.96221	+	22.4708i	−0.255228	+	1.44747i	0.540258	+	0.841499i	$0.318327\pi$
$241$	−3.96221	+	22.4708i	−0.255228	+	1.44747i	−0.795486	+	0.605972i	$0.792784\pi$
$242$	−0.745546			−0.0479255
$243$	5.71982	+	14.5012i	0.366927	+	0.930250i
$244$	3.11344			0.199318
$245$	−0.173648	+	0.984808i	−0.0110940	+	0.0629171i
$246$	6.58733	−	10.6680i	0.419993	−	0.680166i
$247$	−17.9166	−	6.52109i	−1.14000	−	0.414927i
$248$	−19.7466	+	16.5694i	−1.25391	+	1.05216i
$249$	11.0650	+	9.85677i	0.701218	+	0.624648i
$250$	0.820794	−	0.298745i	0.0519116	−	0.0188943i
$251$	2.61791	−	4.53435i	0.165241	−	0.286206i	−0.771500	−	0.636230i	$-0.780493\pi$
$251$	2.61791	−	4.53435i	0.165241	−	0.286206i	0.936741	+	0.350024i	$0.113826\pi$
$252$	1.66231	+	3.31803i	0.104715	+	0.209016i
$253$	10.0419	+	17.3931i	0.631330	+	1.09350i
$254$	9.72013	+	8.15616i	0.609895	+	0.511763i
$255$	2.62383	−	2.07256i	0.164310	−	0.129789i
$256$	−2.77648	−	15.7462i	−0.173530	−	0.984139i
$257$	1.48473	+	8.42030i	0.0926147	+	0.525244i	0.995452	+	0.0952622i	$0.0303690\pi$
$257$	1.48473	+	8.42030i	0.0926147	+	0.525244i	−0.902837	+	0.429982i	$0.858520\pi$
$258$	−1.19457	−	8.18325i	−0.0743708	−	0.509467i
$259$	5.09525	+	4.27543i	0.316604	+	0.265662i
$260$	2.18646	+	3.78706i	0.135598	+	0.234863i
$261$	−3.36814	+	1.00476i	−0.208483	+	0.0621930i
$262$	−6.29028	+	10.8951i	−0.388615	+	0.673101i
$263$	−3.97908	+	1.44827i	−0.245360	+	0.0893039i	−0.461773	−	0.886998i	$-0.652787\pi$
$263$	−3.97908	+	1.44827i	−0.245360	+	0.0893039i	0.216413	+	0.976302i	$0.430564\pi$
$264$	3.16202	−	15.2758i	0.194609	−	0.940163i
$265$	5.42141	−	4.54910i	0.333034	−	0.279449i
$266$	4.42709	+	1.61133i	0.271442	+	0.0987969i
$267$	11.8409	+	21.9862i	0.724654	+	1.34553i
$268$	−0.418446	+	2.37313i	−0.0255607	+	0.144962i
$269$	−23.9197			−1.45841			−0.729206	−	0.684294i	$-0.760110\pi$
$269$	−23.9197			−1.45841			−0.729206	+	0.684294i	$0.760110\pi$
$270$	−1.91208	−	4.11627i	−0.116366	−	0.250508i
$271$	−2.67962			−0.162775			−0.0813875	−	0.996683i	$-0.525935\pi$
$271$	−2.67962			−0.162775			−0.0813875	+	0.996683i	$0.525935\pi$
$272$	0.00146980	−	0.00833565i	8.91197e−5	−	0.000505423i
$273$	6.12006	+	0.181078i	0.370403	+	0.0109594i
$274$	−4.61826	−	1.68091i	−0.278999	−	0.101547i
$275$	2.44012	−	2.04750i	0.147145	−	0.123469i
$276$	12.8258	−	4.24303i	0.772023	−	0.255401i
$277$	−16.4378	+	5.98285i	−0.987649	+	0.359475i	−0.784809	−	0.619737i	$-0.787239\pi$
$277$	−16.4378	+	5.98285i	−0.987649	+	0.359475i	−0.202840	+	0.979212i	$0.565017\pi$
$278$	7.30791	−	12.6577i	0.438299	−	0.759156i
$279$	3.14854	+	27.1685i	0.188498	+	1.62653i
$280$	−1.41373	−	2.44866i	−0.0844868	−	0.146335i
$281$	23.3688	+	19.6087i	1.39406	+	1.16976i	0.963663	+	0.267122i	$0.0860726\pi$
$281$	23.3688	+	19.6087i	1.39406	+	1.16976i	0.430402	+	0.902637i	$0.358372\pi$
$282$	−16.6120	−	6.60895i	−0.989229	−	0.393557i
$283$	1.75487	+	9.95239i	0.104316	+	0.591608i	0.991491	+	0.130174i	$0.0415537\pi$
$283$	1.75487	+	9.95239i	0.104316	+	0.591608i	−0.887175	+	0.461434i	$0.847335\pi$
$284$	2.34824	+	13.3175i	0.139342	+	0.790249i
$285$	8.68036	+	3.45342i	0.514180	+	0.204563i
$286$	−7.53433	−	6.32205i	−0.445514	−	0.373831i
$287$	−4.14367	−	7.17705i	−0.244593	−	0.423648i
$288$	−15.5813	−	6.73925i	−0.918137	−	0.397114i
$289$	6.63667	−	11.4951i	0.390392	−	0.676180i
$290$	0.961647	−	0.350011i	0.0564699	−	0.0205534i
$291$	−2.09244	+	0.692220i	−0.122661	+	0.0405786i
$292$	4.79009	−	4.01936i	0.280319	−	0.235215i
$293$	−19.6060	−	7.13599i	−1.14539	−	0.416889i	−0.301534	−	0.953455i	$-0.597499\pi$
$293$	−19.6060	−	7.13599i	−1.14539	−	0.416889i	−0.843858	+	0.536566i	$0.819721\pi$
$294$	−1.51223	−	0.0447436i	−0.0881953	−	0.00260950i
$295$	0.474660	−	2.69193i	0.0276358	−	0.156730i
$296$	−18.8066			−1.09311
$297$	−11.6865	−	11.7209i	−0.678119	−	0.680117i
$298$	17.3314			1.00398
$299$	3.87030	−	21.9496i	0.223825	−	1.26938i
$300$	−1.01597	−	1.88644i	−0.0586570	−	0.108914i
$301$	−5.13666	−	1.86959i	−0.296072	−	0.107762i
$302$	−8.53999	+	7.16590i	−0.491421	+	0.412351i
$303$	0.786827	−	3.80120i	0.0452020	−	0.218373i
$304$	0.0222227	−	0.00808842i	0.00127456	−	0.000463903i
$305$	−1.25841	+	2.17964i	−0.0720566	+	0.124806i
$306$	3.67608	+	3.47502i	0.210147	+	0.198654i
$307$	−12.0820	−	20.9266i	−0.689554	−	1.19434i	−0.971982	−	0.235054i	$-0.924473\pi$
$307$	−12.0820	−	20.9266i	−0.689554	−	1.19434i	0.282428	−	0.959288i	$-0.408860\pi$
$308$	−3.01855	−	2.53286i	−0.171998	−	0.144323i
$309$	−0.188158	−	1.28895i	−0.0107040	−	0.0733260i
$310$	−1.38280	−	7.84225i	−0.0785378	−	0.445410i
$311$	−5.36392	−	30.4203i	−0.304160	−	1.72498i	−0.627431	−	0.778672i	$-0.715894\pi$
$311$	−5.36392	−	30.4203i	−0.304160	−	1.72498i	0.323271	−	0.946306i	$-0.395218\pi$
$312$	−13.5849	+	10.7308i	−0.769096	+	0.607510i
$313$	19.6280	+	16.4699i	1.10944	+	0.930933i	0.998024	−	0.0628408i	$-0.0200160\pi$
$313$	19.6280	+	16.4699i	1.10944	+	0.930933i	0.111419	+	0.993774i	$0.464460\pi$
$314$	−1.60969	−	2.78806i	−0.0908401	−	0.157340i
$315$	−2.99475	−	0.177371i	−0.168735	−	0.00999372i
$316$	−10.1048	+	17.5021i	−0.568441	+	0.984568i
$317$	−3.40869	+	1.24066i	−0.191451	+	0.0696826i	−0.435967	−	0.899963i	$-0.643593\pi$
$317$	−3.40869	+	1.24066i	−0.191451	+	0.0696826i	0.244515	+	0.969645i	$0.421371\pi$
$318$	7.99490	+	7.12188i	0.448332	+	0.399375i
$319$	2.85886	−	2.39887i	0.160065	−	0.134311i
$320$	4.63644	+	1.68753i	0.259185	+	0.0943356i
$321$	−5.83782	+	9.45418i	−0.325835	+	0.527681i
$322$	−0.956332	+	5.42363i	−0.0532943	+	0.302247i
$323$	−10.4122			−0.579352
$324$	−9.31383	+	6.09967i	−0.517435	+	0.338870i
$325$	−3.53496			−0.196084
$326$	0.0848565	−	0.481245i	0.00469976	−	0.0266537i
$327$	−5.90922	+	9.56980i	−0.326781	+	0.529211i
$328$	22.0191	+	8.01428i	1.21580	+	0.442515i
$329$	−9.05258	+	7.59602i	−0.499085	+	0.418782i
$330$	3.59842	+	3.20549i	0.198087	+	0.176456i
$331$	26.7702	−	9.74355i	1.47142	−	0.535554i	0.522936	−	0.852372i	$-0.324837\pi$
$331$	26.7702	−	9.74355i	1.47142	−	0.535554i	0.948486	+	0.316818i	$0.102615\pi$
$332$	−5.29180	+	9.16567i	−0.290425	+	0.503031i
$333$	−10.9813	+	16.6607i	−0.601773	+	0.913000i
$334$	−3.58131	−	6.20301i	−0.195961	−	0.339414i
$335$	−1.49223	−	1.25213i	−0.0815294	−	0.0684113i
$336$	−0.00595941	+	0.00470734i	−0.000325113	+	0.000256807i
$337$	1.35121	+	7.66310i	0.0736052	+	0.417436i	0.999239	+	0.0390144i	$0.0124218\pi$
$337$	1.35121	+	7.66310i	0.0736052	+	0.417436i	−0.925633	+	0.378421i	$0.876467\pi$
$338$	−0.0764504	−	0.433572i	−0.00415835	−	0.0235832i
$339$	−2.89940	−	19.8620i	−0.157474	−	1.07875i
$340$	1.82936	+	1.53502i	0.0992112	+	0.0832481i
$341$	−14.5200	−	25.1494i	−0.786304	−	1.36192i
$342$	−3.27292	+	13.7494i	−0.176979	+	0.743485i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	14.5238	−	5.28621i	0.783068	−	0.285014i
$345$	−2.21360	+	10.6940i	−0.119176	+	0.575746i
$346$	10.6487	−	8.93534i	0.572479	−	0.480367i
$347$	11.1437	+	4.05599i	0.598228	+	0.217737i	0.623344	−	0.781947i	$-0.285774\pi$
$347$	11.1437	+	4.05599i	0.598228	+	0.217737i	−0.0251167	+	0.999685i	$0.507996\pi$
$348$	−1.19031	−	2.21017i	−0.0638075	−	0.118477i
$349$	6.05793	−	34.3562i	0.324273	−	1.83905i	−0.190460	−	0.981695i	$-0.560998\pi$
$349$	6.05793	−	34.3562i	0.324273	−	1.83905i	0.514733	−	0.857351i	$-0.327891\pi$
$350$	0.873471			0.0466890
$351$	1.57398	+	18.3006i	0.0840129	+	0.976816i
$352$	18.0252			0.960744
$353$	3.29239	−	18.6721i	0.175236	−	0.993814i	−0.762635	−	0.646830i	$-0.776095\pi$
$353$	3.29239	−	18.6721i	0.175236	−	0.993814i	0.937871	−	0.346985i	$-0.112794\pi$
$354$	4.13363	+	0.122305i	0.219700	+	0.00650042i
$355$	−10.2724	−	3.73884i	−0.545201	−	0.198437i
$356$	−13.6626	+	11.4643i	−0.724116	+	0.607606i
$357$	3.17445	−	1.05017i	0.168010	−	0.0555809i
$358$	13.3734	−	4.86753i	0.706808	−	0.257257i
$359$	2.64865	−	4.58759i	0.139790	−	0.242124i	−0.787627	−	0.616152i	$-0.788691\pi$
$359$	2.64865	−	4.58759i	0.139790	−	0.242124i	0.927417	+	0.374029i	$0.122024\pi$
$360$	6.80890	−	5.05867i	0.358860	−	0.266615i
$361$	−5.04580	−	8.73957i	−0.265568	−	0.459978i
$362$	9.61134	+	8.06487i	0.505161	+	0.423880i
$363$	−1.37366	−	0.546501i	−0.0720986	−	0.0286839i
$364$	0.759350	+	4.30649i	0.0398007	+	0.225721i
$365$	0.877755	+	4.97799i	0.0459438	+	0.260560i
$366$	−3.53799	−	1.40756i	−0.184934	−	0.0735744i
$367$	−2.31755	−	1.94466i	−0.120975	−	0.101510i	0.580293	−	0.814408i	$-0.302938\pi$
$367$	−2.31755	−	1.94466i	−0.120975	−	0.101510i	−0.701268	+	0.712897i	$0.747383\pi$
$368$	0.0138225	+	0.0239413i	0.000720550	+	0.00124803i
$369$	19.9570	−	14.8270i	1.03892	−	0.771863i
$370$	2.90489	−	5.03143i	0.151018	−	0.261571i
$371$	6.65034	−	2.42053i	0.345268	−	0.125667i
$372$	−18.5454	+	6.13518i	−0.961533	+	0.318094i
$373$	1.33609	−	1.12112i	0.0691804	−	0.0580492i	−0.607542	−	0.794288i	$-0.707844\pi$
$373$	1.33609	−	1.12112i	0.0691804	−	0.0580492i	0.676722	+	0.736238i	$0.263400\pi$
$374$	−5.04721	−	1.83703i	−0.260985	−	0.0949908i
$375$	1.73129	+	0.0512250i	0.0894036	+	0.00264525i
$376$	5.80212	−	32.9054i	0.299221	−	1.69697i
$377$	−4.14158			−0.213302
$378$	−0.388922	−	4.52199i	−0.0200040	−	0.232586i
$379$	−19.2620			−0.989422			−0.494711	−	0.869057i	$-0.664726\pi$
$379$	−19.2620			−0.989422			−0.494711	+	0.869057i	$0.664726\pi$
$380$	−1.15862	+	6.57085i	−0.0594359	+	0.337078i
$381$	11.9306	+	22.1527i	0.611224	+	1.13492i
$382$	−2.62099	−	0.953964i	−0.134102	−	0.0488090i
$383$	−3.58191	+	3.00558i	−0.183027	+	0.153578i	−0.729698	−	0.683770i	$-0.760339\pi$
$383$	−3.58191	+	3.00558i	−0.183027	+	0.153578i	0.546671	+	0.837348i	$0.315895\pi$
$384$	2.46033	−	11.8859i	0.125553	−	0.606552i
$385$	2.99325	−	1.08945i	0.152550	−	0.0555237i
$386$	7.58790	−	13.1426i	0.386214	−	0.668942i
$387$	3.79751	−	15.9532i	0.193038	−	0.810948i
$388$	−0.787047	−	1.36321i	−0.0399562	−	0.0692063i
$389$	−8.55008	−	7.17437i	−0.433506	−	0.363755i	0.399767	−	0.916617i	$-0.369091\pi$
$389$	−8.55008	−	7.17437i	−0.433506	−	0.363755i	−0.833273	+	0.552862i	$0.813536\pi$
$390$	−0.772506	−	5.29195i	−0.0391174	−	0.267968i
$391$	−2.11358	−	11.9867i	−0.106889	−	0.606195i
$392$	−0.490985	−	2.78451i	−0.0247985	−	0.140639i
$393$	−19.5761	+	15.4632i	−0.987485	+	0.780015i
$394$	6.65717	+	5.58603i	0.335383	+	0.281420i
$395$	−8.16850	−	14.1482i	−0.411002	−	0.711876i
$396$	6.50559	−	9.87017i	0.326918	−	0.495995i
$397$	−14.1916	+	24.5805i	−0.712255	+	1.23366i	0.251754	+	0.967791i	$0.418993\pi$
$397$	−14.1916	+	24.5805i	−0.712255	+	1.23366i	−0.964009	+	0.265871i	$0.914341\pi$
$398$	−8.68627	+	3.16155i	−0.435404	+	0.158474i
$399$	6.97573	+	6.21401i	0.349224	+	0.311090i
$400$	0.00335878	−	0.00281835i	0.000167939	−	0.000140918i
$401$	−12.9321	−	4.70690i	−0.645798	−	0.235051i	−0.00170536	−	0.999999i	$-0.500543\pi$
$401$	−12.9321	−	4.70690i	−0.645798	−	0.235051i	−0.644093	+	0.764947i	$0.722765\pi$
$402$	1.54838	−	2.50755i	0.0772260	−	0.125065i
$403$	−5.59623	+	31.7378i	−0.278768	+	1.58097i
$404$	2.77240			0.137932
$405$	−0.505683	−	8.98578i	−0.0251276	−	0.446507i
$406$	1.02336			0.0507887
$407$	3.67908	−	20.8651i	0.182365	−	1.03424i
$408$	−4.96710	+	8.04407i	−0.245908	+	0.398241i
$409$	−17.6158	−	6.41164i	−0.871046	−	0.317035i	−0.132456	−	0.991189i	$-0.542286\pi$
$409$	−17.6158	−	6.41164i	−0.871046	−	0.317035i	−0.738591	+	0.674154i	$0.764508\pi$
$410$	−5.54521	+	4.65298i	−0.273858	+	0.229794i
$411$	−7.27696	−	6.48234i	−0.358946	−	0.319750i
$412$	0.874234	−	0.318195i	0.0430704	−	0.0156763i
$413$	1.36673	−	2.36724i	0.0672523	−	0.116484i
$414$	−16.4930	−	0.976834i	−0.810586	−	0.0480088i
$415$	−4.27776	−	7.40930i	−0.209987	−	0.363708i
$416$	−15.3236	−	12.8580i	−0.751301	−	0.630416i
$417$	22.7431	−	17.9648i	1.11373	−	0.879740i
$418$	−2.60591	−	14.7789i	−0.127459	−	0.722858i
$419$	6.49415	+	36.8301i	0.317260	+	1.79927i	0.559259	+	0.828993i	$0.311086\pi$
$419$	6.49415	+	36.8301i	0.317260	+	1.79927i	−0.241999	+	0.970277i	$0.577803\pi$
$420$	−0.309496	−	2.12016i	−0.0151019	−	0.103453i
$421$	23.7006	+	19.8871i	1.15510	+	0.969240i	0.999826	−	0.0186321i	$-0.00593113\pi$
$421$	23.7006	+	19.8871i	1.15510	+	0.969240i	0.155269	+	0.987872i	$0.450376\pi$
$422$	−8.03301	−	13.9136i	−0.391041	−	0.677303i
$423$	−25.7629	−	24.3539i	−1.25264	−	1.18413i
$424$	−10.0052	+	17.3295i	−0.485895	+	0.841596i
$425$	−1.81403	+	0.660255i	−0.0879936	+	0.0320270i
$426$	3.35230	−	16.1951i	0.162420	−	0.784656i
$427$	−1.92800	+	1.61779i	−0.0933026	+	0.0782902i
$428$	−7.45723	−	2.71421i	−0.360459	−	0.131196i
$429$	−9.24774	−	17.1712i	−0.446485	−	0.829031i
$430$	−0.829114	+	4.70214i	−0.0399834	+	0.226757i
$431$	13.4075			0.645817			0.322908	−	0.946430i	$-0.395339\pi$
$431$	13.4075			0.645817			0.322908	+	0.946430i	$0.395339\pi$
$432$	−0.0160863	−	0.0161337i	−0.000773951	−	0.000776231i
$433$	33.0550			1.58852			0.794262	−	0.607576i	$-0.207858\pi$
$433$	33.0550			1.58852			0.794262	+	0.607576i	$0.207858\pi$
$434$	1.38280	−	7.84225i	0.0663765	−	0.376440i
$435$	2.02839	+	0.0600155i	0.0972540	+	0.00287752i
$436$	−7.54844	−	2.74741i	−0.361505	−	0.131577i
$437$	26.0512	−	21.8595i	1.24620	−	1.04568i
$438$	−7.26039	+	2.40188i	−0.346915	+	0.114766i
$439$	−15.3656	+	5.59262i	−0.733361	+	0.266921i	−0.681587	−	0.731737i	$-0.738710\pi$
$439$	−15.3656	+	5.59262i	−0.733361	+	0.266921i	−0.0517739	+	0.998659i	$0.516488\pi$
$440$	−4.50324	+	7.79984i	−0.214683	+	0.371843i
$441$	−2.75348	−	1.19094i	−0.131118	−	0.0567114i
$442$	2.98032	+	5.16207i	0.141759	+	0.245535i
$443$	−7.88333	−	6.61490i	−0.374548	−	0.314283i	0.436009	−	0.899942i	$-0.356391\pi$
$443$	−7.88333	−	6.61490i	−0.374548	−	0.314283i	−0.810558	+	0.585659i	$0.800836\pi$
$444$	−13.2420	−	5.26822i	−0.628436	−	0.250018i
$445$	−2.50359	−	14.1986i	−0.118681	−	0.673076i
$446$	−1.00181	−	5.68154i	−0.0474370	−	0.269029i
$447$	31.9329	+	12.7043i	1.51038	+	0.600892i
$448$	3.77966	+	3.17151i	0.178572	+	0.149840i
$449$	4.81862	+	8.34610i	0.227405	+	0.393877i	0.957038	−	0.289962i	$-0.0936426\pi$
$449$	4.81862	+	8.34610i	0.227405	+	0.393877i	−0.729633	+	0.683838i	$0.760309\pi$
$450$	0.301659	+	2.60299i	0.0142204	+	0.122706i
$451$	−13.1990	+	22.8614i	−0.621519	+	1.07650i
$452$	13.4714	−	4.90318i	0.633641	−	0.230626i
$453$	−20.9876	+	6.94312i	−0.986084	+	0.326216i
$454$	−12.0883	+	10.1433i	−0.567332	+	0.476048i
$455$	−3.32178	−	1.20903i	−0.155727	−	0.0566801i
$456$	−26.4029	−	0.781202i	−1.23643	−	0.0365831i
$457$	4.03053	−	22.8583i	0.188540	−	1.06926i	−0.732782	−	0.680464i	$-0.761778\pi$
$457$	4.03053	−	22.8583i	0.188540	−	1.06926i	0.921322	−	0.388801i	$-0.127111\pi$
$458$	−1.59936			−0.0747333
$459$	4.22588	+	9.09734i	0.197247	+	0.424628i
$460$	−7.79967			−0.363662
$461$	2.29999	−	13.0439i	0.107121	−	0.607515i	−0.883231	−	0.468939i	$-0.844636\pi$
$461$	2.29999	−	13.0439i	0.107121	−	0.607515i	0.990352	−	0.138576i	$-0.0442525\pi$
$462$	2.28507	+	4.24290i	0.106311	+	0.197398i
$463$	−33.4693	−	12.1818i	−1.55545	−	0.566138i	−0.585763	−	0.810483i	$-0.699205\pi$
$463$	−33.4693	−	12.1818i	−1.55545	−	0.566138i	−0.969688	+	0.244345i	$0.921427\pi$
$464$	0.00393517	−	0.00330200i	0.000182686	−	0.000153292i
$465$	3.20074	−	15.4629i	0.148431	−	0.717075i
$466$	9.68850	−	3.52633i	0.448811	−	0.163354i
$467$	5.78442	−	10.0189i	0.267671	−	0.463620i	−0.700589	−	0.713565i	$-0.747079\pi$
$467$	5.78442	−	10.0189i	0.267671	−	0.463620i	0.968260	+	0.249945i	$0.0804126\pi$
$468$	−12.5713	+	3.75018i	−0.581109	+	0.173352i
$469$	−0.973986	−	1.68699i	−0.0449745	−	0.0778981i
$470$	7.90717	+	6.63490i	0.364731	+	0.306045i
$471$	−0.922130	−	6.31692i	−0.0424895	−	0.291068i
$472$	1.34209	+	7.61135i	0.0617745	+	0.350341i
$473$	3.02359	+	17.1476i	0.139025	+	0.788449i
$474$	19.3953	−	15.3203i	0.890854	−	0.703687i
$475$	−4.13178	−	3.46698i	−0.189579	−	0.159076i
$476$	1.19403	+	2.06813i	0.0547284	+	0.0947924i
$477$	9.51004	+	18.9824i	0.435435	+	0.869146i
$478$	0.794090	−	1.37540i	0.0363208	−	0.0629095i
$479$	1.84557	−	0.671733i	0.0843263	−	0.0306923i	−0.299513	−	0.954092i	$-0.596824\pi$
$479$	1.84557	−	0.671733i	0.0843263	−	0.0306923i	0.383839	+	0.923400i	$0.374602\pi$
$480$	7.31860	+	6.51943i	0.334047	+	0.297570i
$481$	−18.0115	+	15.1135i	−0.821255	+	0.689115i
$482$	18.7284	+	6.81659i	0.853057	+	0.310487i
$483$	−5.73767	+	9.29198i	−0.261073	+	0.422800i
$484$	0.183351	−	1.03983i	0.00833412	−	0.0472652i
$485$	1.27246			0.0577794
$486$	13.3415	−	2.72071i	0.605182	−	0.123414i
$487$	−38.6049			−1.74935			−0.874677	−	0.484707i	$-0.838926\pi$
$487$	−38.6049			−1.74935			−0.874677	+	0.484707i	$0.838926\pi$
$488$	1.23572	−	7.00814i	0.0559386	−	0.317244i
$489$	0.509110	−	0.824488i	0.0230228	−	0.0372846i
$490$	0.820794	+	0.298745i	0.0370797	+	0.0134959i
$491$	−8.38976	+	7.03985i	−0.378625	+	0.317704i	−0.812162	−	0.583432i	$-0.801710\pi$
$491$	−8.38976	+	7.03985i	−0.378625	+	0.317704i	0.433538	+	0.901135i	$0.357265\pi$
$492$	13.2589	+	11.8111i	0.597758	+	0.532485i
$493$	−2.12533	+	0.773558i	−0.0957202	+	0.0348393i
$494$	−8.32697	+	14.4227i	−0.374648	+	0.648910i
$495$	4.28037	+	8.54380i	0.192388	+	0.384015i
$496$	−0.0199866	−	0.0346178i	−0.000897425	−	0.00155438i
$497$	−8.37412	−	7.02672i	−0.375631	−	0.315191i
$498$	10.1571	−	8.02312i	0.455151	−	0.359524i
$499$	−6.62608	−	37.5784i	−0.296624	−	1.68224i	−0.660527	−	0.750803i	$-0.729667\pi$
$499$	−6.62608	−	37.5784i	−0.296624	−	1.68224i	0.363902	−	0.931437i	$-0.381444\pi$
$500$	0.214811	+	1.21825i	0.00960665	+	0.0544820i
$501$	−2.05160	−	14.0542i	−0.0916585	−	0.627894i
$502$	−3.50338	−	2.93969i	−0.156364	−	0.131205i
$503$	−0.168367	−	0.291620i	−0.00750710	−	0.0130027i	0.862247	−	0.506487i	$-0.169056\pi$
$503$	−0.168367	−	0.291620i	−0.00750710	−	0.0130027i	−0.869755	+	0.493485i	$0.835723\pi$
$504$	8.12844	−	2.42481i	0.362069	−	0.108010i
$505$	−1.12057	+	1.94089i	−0.0498648	+	0.0863684i
$506$	16.4847	−	5.99994i	0.732835	−	0.266730i
$507$	0.176958	−	0.854892i	0.00785898	−	0.0379671i
$508$	−13.7661	+	11.5511i	−0.610771	+	0.512498i
$509$	−11.8765	−	4.32269i	−0.526416	−	0.191600i	0.0651211	−	0.997877i	$-0.479257\pi$
$509$	−11.8765	−	4.32269i	−0.526416	−	0.191600i	−0.591538	+	0.806277i	$0.701479\pi$
$510$	−1.38485	−	2.57138i	−0.0613221	−	0.113862i
$511$	−0.877755	+	4.97799i	−0.0388296	+	0.220214i
$512$	0.0496059			0.00219229
$513$	−16.1090	+	22.9341i	−0.711228	+	1.01257i
$514$	7.46835			0.329415
$515$	−0.130595	+	0.740639i	−0.00575469	+	0.0326365i
$516$	11.7072	+	0.346389i	0.515380	+	0.0152489i
$517$	35.3722	+	12.8744i	1.55567	+	0.566216i
$518$	4.45056	−	3.73446i	0.195546	−	0.164083i
$519$	26.1700	−	8.65755i	1.14873	−	0.380024i
$520$	9.39222	−	3.41849i	0.411876	−	0.149911i
$521$	11.9893	−	20.7660i	0.525259	−	0.909776i	−0.474308	−	0.880359i	$-0.657302\pi$
$521$	11.9893	−	20.7660i	0.525259	−	0.909776i	0.999567	−	0.0294167i	$-0.00936498\pi$
$522$	0.353426	+	3.04968i	0.0154690	+	0.133481i
$523$	−13.1970	−	22.8579i	−0.577065	−	0.999507i	−0.995814	−	0.0914044i	$-0.970864\pi$
$523$	−13.1970	−	22.8579i	−0.577065	−	0.999507i	0.418748	−	0.908102i	$-0.362469\pi$
$524$	−13.6487	−	11.4526i	−0.596247	−	0.500311i
$525$	1.60936	+	0.640273i	0.0702384	+	0.0279438i
$526$	0.642267	+	3.64247i	0.0280042	+	0.158819i
$527$	3.05612	+	17.3321i	0.133127	+	0.754999i
$528$	0.0224771	+	0.00894233i	0.000978188	+	0.000389165i
$529$	12.8342	+	10.7692i	0.558009	+	0.468225i
$530$	−3.09084	−	5.35349i	−0.134258	−	0.232541i
$531$	7.52652	+	3.25538i	0.326623	+	0.141272i
$532$	−3.33611	+	5.77831i	−0.144639	+	0.250522i
$533$	27.5287	−	10.0196i	1.19240	−	0.433999i
$534$	20.7085	−	6.85080i	0.896146	−	0.296463i
$535$	4.91427	−	4.12356i	0.212463	−	0.178277i
$536$	5.17566	+	1.88379i	0.223555	+	0.0813672i
$537$	28.2084	+	0.834623i	1.21728	+	0.0360166i
$538$	−3.62807	+	20.5758i	−0.156417	+	0.887085i
$539$	3.18535			0.137203
$540$	6.21131	−	1.65453i	0.267292	−	0.0711995i
$541$	−26.9602			−1.15911			−0.579555	−	0.814933i	$-0.696774\pi$
$541$	−26.9602			−1.15911			−0.579555	+	0.814933i	$0.696774\pi$
$542$	−0.406435	+	2.30501i	−0.0174579	+	0.0990086i
$543$	11.7971	+	21.9048i	0.506262	+	0.940024i
$544$	−10.2652	−	3.73623i	−0.440117	−	0.160189i
$545$	4.97438	−	4.17400i	0.213079	−	0.178794i
$546$	1.08403	−	5.23702i	0.0463924	−	0.224124i
$547$	−40.8517	+	14.8688i	−1.74669	+	0.635744i	−0.999581	−	0.0289534i	$-0.990783\pi$
$547$	−40.8517	+	14.8688i	−1.74669	+	0.635744i	−0.747112	+	0.664698i	$0.768560\pi$
$548$	3.48017	−	6.02783i	0.148665	−	0.257496i
$549$	−5.48694	−	5.18684i	−0.234177	−	0.221369i
$550$	−1.39116	−	2.40955i	−0.0593191	−	0.102744i
$551$	−4.84082	−	4.06193i	−0.206226	−	0.173044i
$552$	−4.46022	−	30.5541i	−0.189839	−	1.30047i
$553$	−2.83689	−	16.0888i	−0.120637	−	0.684165i
$554$	2.65323	+	15.0472i	0.112725	+	0.639296i
$555$	9.04039	−	7.14101i	0.383743	−	0.303119i
$556$	15.8568	+	13.3054i	0.672477	+	0.564275i
$557$	−19.1966	−	33.2495i	−0.813387	−	1.40883i	−0.910480	−	0.413553i	$-0.864288\pi$
$557$	−19.1966	−	33.2495i	−0.813387	−	1.40883i	0.0970929	−	0.995275i	$-0.469046\pi$
$558$	23.8479	+	1.41245i	1.00956	+	0.0597936i
$559$	9.66162	−	16.7344i	0.408643	−	0.707791i
$560$	0.00412016	−	0.00149962i	0.000174109	−	6.33703e-5i
$561$	−7.95286	−	7.08443i	−0.335770	−	0.299105i
$562$	20.4120	−	17.1277i	0.861026	−	0.722487i
$563$	23.8817	+	8.69222i	1.00649	+	0.366333i	0.792085	−	0.610411i	$-0.208996\pi$
$563$	23.8817	+	8.69222i	1.00649	+	0.366333i	0.214408	+	0.976744i	$0.431218\pi$
$564$	13.3030	−	21.5439i	0.560159	−	0.907160i
$565$	−2.01238	+	11.4128i	−0.0846615	+	0.480139i
$566$	8.82723			0.371036
$567$	2.59813	−	8.61683i	0.109111	−	0.361873i
$568$	30.9088			1.29691
$569$	−5.05483	+	28.6674i	−0.211910	+	1.20180i	0.674280	+	0.738476i	$0.264454\pi$
$569$	−5.05483	+	28.6674i	−0.211910	+	1.20180i	−0.886189	+	0.463323i	$0.846657\pi$
$570$	4.28724	−	6.94306i	0.179573	−	0.290813i
$571$	39.4978	+	14.3760i	1.65293	+	0.601618i	0.989229	−	0.146377i	$-0.0467613\pi$
$571$	39.4978	+	14.3760i	1.65293	+	0.601618i	0.663704	+	0.747995i	$0.268983\pi$
$572$	10.6704	−	8.95357i	0.446154	−	0.374368i
$573$	−4.12988	−	3.67891i	−0.172528	−	0.153689i
$574$	−6.80220	+	2.47580i	−0.283919	+	0.103338i
$575$	3.15253	−	5.46035i	0.131470	−	0.227712i
$576$	−8.14595	+	12.3589i	−0.339415	+	0.514955i
$577$	−14.1202	−	24.4568i	−0.587830	−	1.01815i	−0.994516	−	0.104583i	$-0.966649\pi$
$577$	−14.1202	−	24.4568i	−0.587830	−	1.01815i	0.406686	−	0.913568i	$-0.366684\pi$
$578$	−8.88143	−	7.45240i	−0.369419	−	0.309979i
$579$	23.6145	−	18.6531i	0.981384	−	0.775196i
$580$	0.251674	+	1.42731i	0.0104502	+	0.0592660i
$581$	−1.48565	−	8.42555i	−0.0616352	−	0.349551i
$582$	0.278074	+	1.90491i	0.0115266	+	0.0789611i
$583$	−17.2691	−	14.4905i	−0.715212	−	0.600134i
$584$	−7.14613	−	12.3775i	−0.295709	−	0.512183i
$585$	2.45577	−	10.3166i	0.101534	−	0.426540i
$586$	−9.11215	+	15.7827i	−0.376419	+	0.651978i
$587$	17.0587	−	6.20886i	0.704088	−	0.256267i	0.0349328	−	0.999390i	$-0.488878\pi$
$587$	17.0587	−	6.20886i	0.704088	−	0.256267i	0.669155	+	0.743123i	$0.266656\pi$
$588$	0.434306	−	2.09815i	0.0179105	−	0.0865263i
$589$	−37.6685	+	31.6076i	−1.55210	+	1.30237i
$590$	−2.24361	−	0.816606i	−0.0923678	−	0.0336191i
$591$	8.17110	+	15.1721i	0.336114	+	0.624095i
$592$	0.00506419	−	0.0287205i	0.000208137	−	0.00118040i
$593$	−20.7415			−0.851752			−0.425876	−	0.904781i	$-0.640034\pi$
$593$	−20.7415			−0.851752			−0.425876	+	0.904781i	$0.640034\pi$
$594$	−11.8549	+	8.27495i	−0.486413	+	0.339525i
$595$	−1.93046			−0.0791409
$596$	−4.26228	+	24.1726i	−0.174590	+	0.990147i
$597$	−18.3219	−	0.542102i	−0.749864	−	0.0221868i
$598$	−18.2940	−	6.65848i	−0.748098	−	0.272285i
$599$	10.9822	−	9.21517i	0.448721	−	0.376521i	−0.390240	−	0.920713i	$-0.627608\pi$
$599$	10.9822	−	9.21517i	0.448721	−	0.376521i	0.838961	+	0.544192i	$0.183164\pi$
$600$	−4.64950	+	1.53815i	−0.189815	+	0.0627946i
$601$	−36.5443	+	13.3010i	−1.49067	+	0.542560i	−0.953626	−	0.300993i	$-0.902682\pi$
$601$	−36.5443	+	13.3010i	−1.49067	+	0.542560i	−0.537046	+	0.843553i	$0.680460\pi$
$602$	−2.38734	+	4.13499i	−0.0973006	+	0.168530i
$603$	4.69096	−	3.48515i	0.191031	−	0.141926i
$604$	−7.89426	−	13.6733i	−0.321213	−	0.556357i
$605$	0.653852	+	0.548647i	0.0265829	+	0.0223057i
$606$	−3.15045	−	1.25338i	−0.127978	−	0.0509152i
$607$	6.73144	+	38.1759i	0.273221	+	1.54951i	0.744558	+	0.667558i	$0.232660\pi$
$607$	6.73144	+	38.1759i	0.273221	+	1.54951i	−0.471337	+	0.881953i	$0.656228\pi$
$608$	−5.30000	−	30.0578i	−0.214943	−	1.21900i
$609$	1.88554	+	0.750147i	0.0764059	+	0.0303975i
$610$	1.68406	+	1.41309i	0.0681854	+	0.0572143i
$611$	−20.8869	−	36.1771i	−0.844993	−	1.46357i
$612$	−5.75076	+	4.27253i	−0.232461	+	0.172707i
$613$	−18.0932	+	31.3383i	−0.730778	+	1.26574i	0.225774	+	0.974180i	$0.427509\pi$
$613$	−18.0932	+	31.3383i	−0.730778	+	1.26574i	−0.956551	+	0.291564i	$0.905824\pi$
$614$	−19.8336	+	7.21884i	−0.800419	+	0.291329i
$615$	−13.6277	+	4.50833i	−0.549523	+	0.181793i
$616$	−6.89936	+	5.78925i	−0.277983	+	0.233256i
$617$	−30.9229	−	11.2550i	−1.24491	−	0.453111i	−0.366232	−	0.930524i	$-0.619352\pi$
$617$	−30.9229	−	11.2550i	−1.24491	−	0.453111i	−0.878679	+	0.477413i	$0.841575\pi$
$618$	−1.13730	−	0.0336500i	−0.0457488	−	0.00135360i
$619$	−7.02452	+	39.8380i	−0.282339	+	1.60122i	0.432299	+	0.901730i	$0.357703\pi$
$619$	−7.02452	+	39.8380i	−0.282339	+	1.60122i	−0.714638	+	0.699494i	$0.753409\pi$
$620$	11.2779			0.452930
$621$	−29.6721	−	13.8895i	−1.19070	−	0.557367i
$622$	−26.9812			−1.08185
$623$	2.50359	−	14.1986i	0.100304	−	0.568853i
$624$	−0.0127294	−	0.0236358i	−0.000509582	−	0.000946190i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	17.1445	−	14.3860i	0.685233	−	0.574979i
$627$	6.03185	−	29.1401i	0.240889	−	1.16374i
$628$	4.28446	−	1.55942i	0.170969	−	0.0622275i
$629$	−6.42010	+	11.1199i	−0.255986	+	0.443381i
$630$	−0.606809	+	2.54919i	−0.0241758	+	0.101562i
$631$	−7.70513	−	13.3457i	−0.306737	−	0.531283i	0.670910	−	0.741539i	$-0.265904\pi$
$631$	−7.70513	−	13.3457i	−0.306737	−	0.531283i	−0.977646	+	0.210256i	$0.932570\pi$
$632$	35.3854	+	29.6919i	1.40755	+	1.18108i
$633$	−4.60181	−	31.5240i	−0.182905	−	1.25297i
$634$	0.550201	+	3.12034i	0.0218513	+	0.123925i
$635$	−2.52255	−	14.3061i	−0.100104	−	0.567720i
$636$	−11.8993	+	9.39924i	−0.471836	+	0.372704i
$637$	−2.70794	−	2.27223i	−0.107292	−	0.0900291i
$638$	−1.62989	−	2.82305i	−0.0645278	−	0.111765i
$639$	18.0480	−	27.3821i	0.713966	−	1.08322i
$640$	−3.50391	+	6.06896i	−0.138504	+	0.239897i
$641$	−5.82180	+	2.11896i	−0.229947	+	0.0836940i	−0.454424	−	0.890785i	$-0.650155\pi$
$641$	−5.82180	+	2.11896i	−0.229947	+	0.0836940i	0.224477	+	0.974479i	$0.427933\pi$
$642$	7.24703	+	6.45568i	0.286017	+	0.254785i
$643$	21.1557	−	17.7517i	0.834298	−	0.700059i	−0.121975	−	0.992533i	$-0.538923\pi$
$643$	21.1557	−	17.7517i	0.834298	−	0.700059i	0.956273	+	0.292474i	$0.0944785\pi$
$644$	−7.32929	−	2.66764i	−0.288815	−	0.105120i
$645$	−4.97440	+	8.05589i	−0.195867	+	0.317200i
$646$	−1.57929	+	8.95661i	−0.0621364	+	0.352393i
$647$	−31.4659			−1.23705			−0.618525	−	0.785765i	$-0.712270\pi$
$647$	−31.4659			−1.23705			−0.618525	+	0.785765i	$0.712270\pi$
$648$	10.0333	+	23.3858i	0.394145	+	0.918679i
$649$	−8.70702			−0.341780
$650$	−0.536171	+	3.04078i	−0.0210304	+	0.119269i
$651$	8.29633	−	13.4357i	0.325159	−	0.526585i
$652$	0.650337	+	0.236703i	0.0254692	+	0.00927002i
$653$	−1.32183	+	1.10915i	−0.0517271	+	0.0434042i	−0.668285	−	0.743906i	$-0.732971\pi$
$653$	−1.32183	+	1.10915i	−0.0517271	+	0.0434042i	0.616558	+	0.787310i	$0.288527\pi$
$654$	7.33566	+	6.53463i	0.286847	+	0.255524i
$655$	13.5343	−	4.92610i	0.528831	−	0.192479i
$656$	−0.0181683	+	0.0314684i	−0.000709352	+	0.00122863i
$657$	−15.1378	−	0.896573i	−0.590583	−	0.0349786i
$658$	5.16104	+	8.93918i	0.201198	+	0.348486i
$659$	−18.0407	−	15.1379i	−0.702764	−	0.589689i	0.219794	−	0.975546i	$-0.429461\pi$
$659$	−18.0407	−	15.1379i	−0.702764	−	0.589689i	−0.922559	+	0.385857i	$0.873906\pi$
$660$	−5.35573	+	4.23050i	−0.208472	+	0.164672i
$661$	7.90954	+	44.8572i	0.307646	+	1.74474i	0.610783	+	0.791798i	$0.290855\pi$
$661$	7.90954	+	44.8572i	0.307646	+	1.74474i	−0.303138	+	0.952947i	$0.598034\pi$
$662$	−4.32100	−	24.5056i	−0.167940	−	0.952438i
$663$	1.70731	+	11.6957i	0.0663065	+	0.454224i
$664$	18.5310	+	15.5493i	0.719142	+	0.603431i
$665$	−2.69683	−	4.67105i	−0.104579	−	0.181135i
$666$	12.6659	+	11.9732i	0.490795	+	0.463951i
$667$	3.69353	−	6.39737i	0.143014	−	0.247707i
$668$	9.53226	−	3.46946i	0.368814	−	0.134237i
$669$	2.31887	−	11.2025i	0.0896525	−	0.433115i
$670$	−1.30342	+	1.09370i	−0.0503556	+	0.0422534i
$671$	7.53350	+	2.74197i	0.290828	+	0.105853i
$672$	4.64746	+	8.62937i	0.179280	+	0.332885i
$673$	−0.949905	+	5.38718i	−0.0366161	+	0.207660i	−0.997627	−	0.0688501i	$-0.978067\pi$
$673$	−0.949905	+	5.38718i	−0.0366161	+	0.207660i	0.961011	+	0.276511i	$0.0891781\pi$
$674$	6.79675			0.261801
$675$	−1.35224	+	5.01711i	−0.0520479	+	0.193109i
$676$	0.623516			0.0239814
$677$	−5.42738	+	30.7802i	−0.208591	+	1.18298i	0.683097	+	0.730328i	$0.260633\pi$
$677$	−5.42738	+	30.7802i	−0.208591	+	1.18298i	−0.891688	+	0.452651i	$0.850478\pi$
$678$	−17.5250	−	0.518526i	−0.673045	−	0.0199139i
$679$	1.19572	+	0.435207i	0.0458875	+	0.0167017i
$680$	4.18130	−	3.50853i	0.160346	−	0.134546i
$681$	−29.7078	+	9.82794i	−1.13841	+	0.376607i
$682$	−23.8359	+	8.67557i	−0.912725	+	0.332205i
$683$	20.7921	−	36.0130i	0.795587	−	1.37800i	−0.126878	−	0.991918i	$-0.540496\pi$
$683$	20.7921	−	36.0130i	0.795587	−	1.37800i	0.922466	−	0.386079i	$-0.126171\pi$
$684$	−18.3718	−	7.94621i	−0.702465	−	0.303831i
$685$	2.81329	+	4.87275i	0.107490	+	0.186178i
$686$	0.669118	+	0.561456i	0.0255470	+	0.0214365i
$687$	−2.94681	−	1.17237i	−0.112428	−	0.0447286i
$688$	0.00416192	+	0.0236034i	0.000158672	+	0.000899872i
$689$	4.34423	+	24.6374i	0.165502	+	0.938609i
$690$	8.86324	+	3.52617i	0.337418	+	0.134239i
$691$	9.24740	+	7.75949i	0.351788	+	0.295185i	0.801507	−	0.597985i	$-0.204032\pi$
$691$	9.24740	+	7.75949i	0.351788	+	0.295185i	−0.449720	+	0.893170i	$0.648476\pi$
$692$	9.84354	+	17.0495i	0.374195	+	0.648125i
$693$	1.10008	+	9.49252i	0.0417887	+	0.360591i
$694$	5.17921	−	8.97066i	0.196600	−	0.340522i
$695$	−15.7239	+	5.72303i	−0.596441	+	0.217087i
$696$	−5.44738	+	1.80210i	−0.206482	+	0.0683085i
$697$	12.2554	−	10.2835i	0.464208	−	0.389517i
$698$	−28.6344	−	10.4221i	−1.08383	−	0.394481i
$699$	20.4359	+	0.604650i	0.772955	+	0.0228700i
$700$	−0.214811	+	1.21825i	−0.00811910	+	0.0460457i
$701$	0.303524			0.0114640			0.00573198	−	0.999984i	$-0.498175\pi$
$701$	0.303524			0.0114640			0.00573198	+	0.999984i	$0.498175\pi$
$702$	15.9810	+	1.42184i	0.603163	+	0.0536639i
$703$	−35.8753			−1.35306
$704$	2.72914	−	15.4777i	0.102859	−	0.583340i
$705$	9.70537	+	18.0209i	0.365525	+	0.678706i
$706$	−15.5624	−	5.66424i	−0.585697	−	0.213176i
$707$	−1.71682	+	1.44058i	−0.0645675	+	0.0541786i
$708$	−1.18716	+	5.73521i	−0.0446161	+	0.215542i
$709$	15.1185	−	5.50270i	0.567788	−	0.206658i	−0.0421440	−	0.999112i	$-0.513419\pi$
$709$	15.1185	−	5.50270i	0.567788	−	0.206658i	0.609932	+	0.792453i	$0.291197\pi$
$710$	−4.77423	+	8.26921i	−0.179174	+	0.310338i
$711$	46.9658	−	14.0105i	1.76135	−	0.525433i
$712$	20.3826	+	35.3038i	0.763872	+	1.32306i
$713$	−44.0336	−	36.9486i	−1.64907	−	1.38374i
$714$	−0.421868	−	2.88995i	−0.0157880	−	0.108154i
$715$	1.95530	+	11.0890i	0.0731239	+	0.414706i
$716$	3.49998	+	19.8494i	0.130800	+	0.741805i
$717$	2.47131	−	1.95209i	0.0922926	−	0.0729020i
$718$	−3.54451	−	2.97420i	−0.132280	−	0.110996i
$719$	−15.1191	−	26.1870i	−0.563847	−	0.976611i	−0.997156	−	0.0753660i	$-0.975988\pi$
$719$	−15.1191	−	26.1870i	−0.563847	−	0.976611i	0.433309	−	0.901245i	$-0.357346\pi$
$720$	0.00589186	+	0.0117604i	0.000219577	+	0.000438284i
$721$	−0.376032	+	0.651307i	−0.0140042	+	0.0242559i
$722$	−8.28312	+	3.01481i	−0.308266	+	0.112200i
$723$	29.5103	+	26.2878i	1.09750	+	0.977656i
$724$	−13.6120	+	11.4218i	−0.505886	+	0.424489i
$725$	−1.10095	−	0.400713i	−0.0408882	−	0.0148821i
$726$	−0.678453	+	1.09873i	−0.0251798	+	0.0407779i
$727$	1.52295	−	8.63709i	0.0564832	−	0.320332i	−0.943454	−	0.331502i	$-0.892445\pi$
$727$	1.52295	−	8.63709i	0.0564832	−	0.320332i	0.999938	+	0.0111702i	$0.00355566\pi$
$728$	9.99500			0.370439
$729$	26.5759	+	4.76670i	0.984293	+	0.176544i
$730$	4.41521			0.163414
$731$	1.83242	−	10.3922i	0.0677745	−	0.384368i
$732$	2.83326	−	4.58837i	0.104720	−	0.169591i
$733$	1.35539	+	0.493323i	0.0500626	+	0.0182213i	0.366930	−	0.930249i	$-0.380409\pi$
$733$	1.35539	+	0.493323i	0.0500626	+	0.0182213i	−0.316867	+	0.948470i	$0.602631\pi$
$734$	−2.02432	+	1.69860i	−0.0747189	+	0.0626966i
$735$	1.29332	+	1.15209i	0.0477049	+	0.0424956i
$736$	33.5272	−	12.2029i	1.23583	−	0.449805i
$737$	−3.10249	+	5.37366i	−0.114282	+	0.197941i
$738$	−9.72721	−	19.4159i	−0.358063	−	0.714709i
$739$	−19.7728	−	34.2476i	−0.727356	−	1.25982i	−0.957997	−	0.286778i	$-0.907416\pi$
$739$	−19.7728	−	34.2476i	−0.727356	−	1.25982i	0.230641	−	0.973039i	$-0.425918\pi$
$740$	6.30307	+	5.28891i	0.231706	+	0.194424i
$741$	−25.9146	+	20.4699i	−0.951995	+	0.751982i
$742$	−1.07344	−	6.08777i	−0.0394071	−	0.223489i
$743$	5.22799	+	29.6494i	0.191796	+	1.08773i	0.916908	+	0.399099i	$0.130677\pi$
$743$	5.22799	+	29.6494i	0.191796	+	1.08773i	−0.725111	+	0.688632i	$0.758212\pi$
$744$	6.44921	+	44.1794i	0.236440	+	1.61970i
$745$	−15.1998	−	12.7542i	−0.556879	−	0.467277i
$746$	−0.761731	−	1.31936i	−0.0278890	−	0.0483051i
$747$	24.5955	−	7.33715i	0.899903	−	0.268452i
$748$	3.80341	−	6.58771i	0.139067	−	0.240870i
$749$	6.02825	−	2.19410i	0.220267	−	0.0801708i
$750$	0.306661	−	1.48149i	0.0111977	−	0.0540964i
$751$	15.8572	−	13.3057i	0.578636	−	0.485533i	−0.305863	−	0.952076i	$-0.598945\pi$
$751$	15.8572	−	13.3057i	0.578636	−	0.485533i	0.884499	+	0.466542i	$0.154500\pi$
$752$	0.0486892	+	0.0177214i	0.00177551	+	0.000646234i
$753$	−4.30010	−	7.98440i	−0.156704	−	0.290968i
$754$	−0.628181	+	3.56259i	−0.0228770	+	0.129742i
$755$	12.7631			0.464495
$756$	6.40260	+	0.569645i	0.232860	+	0.0207178i
$757$	−12.9914			−0.472181			−0.236091	−	0.971731i	$-0.575866\pi$
$757$	−12.9914			−0.472181			−0.236091	+	0.971731i	$0.575866\pi$
$758$	−2.92160	+	16.5692i	−0.106117	+	0.601820i
$759$	34.7710	+	1.02880i	1.26211	+	0.0373429i
$760$	14.3307	+	5.21595i	0.519829	+	0.189202i
$761$	−23.6845	+	19.8736i	−0.858561	+	0.720418i	−0.961657	−	0.274253i	$-0.911569\pi$
$761$	−23.6845	+	19.8736i	−0.858561	+	0.720418i	0.103097	+	0.994671i	$0.467125\pi$
$762$	20.8654	−	6.90269i	0.755873	−	0.250058i
$763$	6.10197	−	2.22094i	0.220906	−	0.0804033i
$764$	1.97510	−	3.42097i	0.0714565	−	0.123766i
$765$	−0.666696	−	5.75286i	−0.0241044	−	0.207995i
$766$	2.04211	+	3.53704i	0.0737845	+	0.127798i
$767$	7.40203	+	6.21104i	0.267272	+	0.224268i
$768$	−25.7323	−	10.2374i	−0.928535	−	0.369411i
$769$	−2.27973	−	12.9290i	−0.0822091	−	0.466231i	−0.997924	−	0.0644024i	$-0.979486\pi$
$769$	−2.27973	−	12.9290i	−0.0822091	−	0.466231i	0.915715	−	0.401829i	$-0.131625\pi$
$770$	−0.483143	−	2.74004i	−0.0174113	−	0.0987443i
$771$	13.7604	+	5.47446i	0.495568	+	0.197158i
$772$	16.4643	+	13.8152i	0.592564	+	0.497220i
$773$	−9.49347	−	16.4432i	−0.341456	−	0.591420i	0.643247	−	0.765659i	$-0.277587\pi$
$773$	−9.49347	−	16.4432i	−0.341456	−	0.591420i	−0.984703	+	0.174239i	$0.944253\pi$
$774$	−13.1470	−	5.68635i	−0.472558	−	0.204392i
$775$	−4.55838	+	7.89535i	−0.163742	+	0.283609i
$776$	−3.38086	+	1.23053i	−0.121366	+	0.0441736i
$777$	10.9376	−	3.61836i	0.392383	−	0.129808i
$778$	−7.46825	+	6.26660i	−0.267750	+	0.224669i
$779$	42.0034	+	15.2880i	1.50493	+	0.547749i
$780$	7.57081	+	0.224003i	0.271078	+	0.00802059i
$781$	−6.04662	+	34.2921i	−0.216365	+	1.22707i
$782$	−10.6316			−0.380185
$783$	−1.58430	+	5.87808i	−0.0566181	+	0.210065i
$784$	0.00438458			0.000156592
$785$	−0.640021	+	3.62974i	−0.0228433	+	0.129551i
$786$	10.3322	+	19.1848i	0.368538	+	0.684299i
$787$	5.46078	+	1.98756i	0.194656	+	0.0708489i	0.437509	−	0.899214i	$-0.355861\pi$
$787$	5.46078	+	1.98756i	0.194656	+	0.0708489i	−0.242853	+	0.970063i	$0.578083\pi$
$788$	−9.42817	+	7.91117i	−0.335865	+	0.281824i
$789$	−1.48664	+	7.18202i	−0.0529258	+	0.255687i
$790$	−13.4093	+	4.88059i	−0.477082	+	0.173644i
$791$	−5.79442	+	10.0362i	−0.206026	+	0.356847i
$792$	−19.6350	−	18.5611i	−0.697700	−	0.659541i
$793$	−4.44845	−	7.70494i	−0.157969	−	0.273611i
$794$	18.9917	+	15.9359i	0.673989	+	0.565544i
$795$	−1.77062	−	12.1294i	−0.0627976	−	0.430186i
$796$	−2.27330	−	12.8925i	−0.0805748	−	0.456963i
$797$	0.714079	+	4.04974i	0.0252940	+	0.143449i	0.994839	−	0.101462i	$-0.0323522\pi$
$797$	0.714079	+	4.04974i	0.0252940	+	0.143449i	−0.969545	+	0.244912i	$0.921241\pi$
$798$	6.40335	−	5.05802i	0.226676	−	0.179052i
$799$	−17.4756	−	14.6638i	−0.618243	−	0.518767i
$800$	−2.82938	−	4.90064i	−0.100034	−	0.173264i
$801$	43.1771	+	2.55726i	1.52559	+	0.0903564i
$802$	−6.01038	+	10.4103i	−0.212234	+	0.367600i
$803$	15.1302	−	5.50696i	0.533935	−	0.194336i
$804$	3.11656	+	2.77624i	0.109913	+	0.0979105i
$805$	4.82996	−	4.05282i	0.170234	−	0.142843i
$806$	26.4521	+	9.62777i	0.931735	+	0.339124i
$807$	−21.7672	+	35.2513i	−0.766241	+	1.24090i
$808$	1.10037	−	6.24049i	0.0387108	−	0.219540i
$809$	20.9585			0.736862			0.368431	−	0.929655i	$-0.379895\pi$
$809$	20.9585			0.736862			0.368431	+	0.929655i	$0.379895\pi$
$810$	−7.80628	−	0.927944i	−0.274285	−	0.0326046i
$811$	21.5855			0.757971			0.378985	−	0.925403i	$-0.376273\pi$
$811$	21.5855			0.757971			0.378985	+	0.925403i	$0.376273\pi$
$812$	−0.251674	+	1.42731i	−0.00883202	+	0.0500889i
$813$	−2.43847	+	3.94903i	−0.0855210	+	0.138499i
$814$	−17.3902	−	6.32950i	−0.609525	−	0.221849i
$815$	−0.428568	+	0.359612i	−0.0150121	+	0.0125966i
$816$	−0.0109470	−	0.00975160i	−0.000383221	−	0.000341374i
$817$	27.7054	−	10.0840i	0.969290	−	0.352793i
$818$	−8.18721	+	14.1807i	−0.286259	+	0.495815i
$819$	5.83617	−	8.85454i	0.203932	−	0.309403i
$820$	−5.12592	−	8.87836i	−0.179005	−	0.310046i
$821$	20.8417	+	17.4883i	0.727381	+	0.610345i	0.929416	−	0.369033i	$-0.120311\pi$
$821$	20.8417	+	17.4883i	0.727381	+	0.610345i	−0.202035	+	0.979378i	$0.564755\pi$
$822$	−6.67986	+	5.27643i	−0.232987	+	0.184037i
$823$	6.84084	+	38.7963i	0.238457	+	1.35236i	0.835210	+	0.549931i	$0.185346\pi$
$823$	6.84084	+	38.7963i	0.238457	+	1.35236i	−0.596753	+	0.802425i	$0.703543\pi$
$824$	−0.369252	−	2.09413i	−0.0128635	−	0.0729526i
$825$	−0.796940	−	5.45933i	−0.0277459	−	0.190069i
$826$	−1.82900	−	1.53472i	−0.0636392	−	0.0533996i
$827$	−1.46826	−	2.54311i	−0.0510566	−	0.0884325i	0.839368	−	0.543564i	$-0.182926\pi$
$827$	−1.46826	−	2.54311i	−0.0510566	−	0.0884325i	−0.890424	+	0.455132i	$0.849592\pi$
$828$	5.41851	−	22.7630i	0.188306	−	0.791069i
$829$	12.1224	−	20.9967i	0.421029	−	0.729244i	−0.575011	−	0.818145i	$-0.695002\pi$
$829$	12.1224	−	20.9967i	0.421029	−	0.729244i	0.996040	+	0.0889017i	$0.0283357\pi$
$830$	−7.02233	+	2.55592i	−0.243749	+	0.0887172i
$831$	−6.14138	+	29.6693i	−0.213042	+	1.02922i
$832$	−13.3610	+	11.2112i	−0.463208	+	0.388678i
$833$	−1.81403	−	0.660255i	−0.0628526	−	0.0228765i
$834$	−12.0037	−	22.2885i	−0.415656	−	0.771787i
$835$	−1.42395	+	8.07560i	−0.0492777	+	0.279468i
$836$	21.2534			0.735063
$837$	42.9042	+	20.0834i	1.48299	+	0.694185i
$838$	32.6663			1.12844
$839$	3.33702	−	18.9252i	0.115207	−	0.653369i	−0.871441	−	0.490500i	$-0.836814\pi$
$839$	3.33702	−	18.9252i	0.115207	−	0.653369i	0.986648	−	0.162869i	$-0.0520748\pi$
$840$	−4.89518	−	0.144837i	−0.168900	−	0.00499735i
$841$	25.9612	+	9.44911i	0.895214	+	0.325831i
$842$	20.7018	−	17.3708i	0.713430	−	0.598639i
$843$	50.1638	−	16.5952i	1.72773	−	0.571569i
$844$	21.3812	−	7.78213i	0.735972	−	0.267872i
$845$	−0.252018	+	0.436507i	−0.00866967	+	0.0150163i
$846$	−24.8569	+	18.4674i	−0.854596	+	0.634922i
$847$	0.426772	+	0.739191i	0.0146641	+	0.0253989i
$848$	−0.0237706	−	0.0199459i	−0.000816286	−	0.000684945i
$849$	16.2641	+	6.47055i	0.558182	+	0.222069i
$850$	0.292805	+	1.66058i	0.0100431	+	0.0569574i
$851$	−7.28235	−	41.3003i	−0.249636	−	1.41576i
$852$	21.7634	+	8.65838i	0.745600	+	0.296631i
$853$	4.30058	+	3.60862i	0.147249	+	0.123557i	0.713437	−	0.700720i	$-0.247138\pi$
$853$	4.30058	+	3.60862i	0.147249	+	0.123557i	−0.566187	+	0.824277i	$0.691582\pi$
$854$	1.09919	+	1.90385i	0.0376135	+	0.0651484i
$855$	12.9886	−	9.64988i	0.444201	−	0.330019i
$856$	−9.06928	+	15.7085i	−0.309982	+	0.536904i
$857$	−3.64833	+	1.32788i	−0.124624	+	0.0453596i	−0.403580	−	0.914945i	$-0.632234\pi$
$857$	−3.64833	+	1.32788i	−0.124624	+	0.0453596i	0.278955	+	0.960304i	$0.410012\pi$
$858$	−16.1733	+	5.35045i	−0.552148	+	0.182661i
$859$	−28.9482	+	24.2905i	−0.987701	+	0.828780i	−0.985233	−	0.171217i	$-0.945230\pi$
$859$	−28.9482	+	24.2905i	−0.987701	+	0.828780i	−0.00246789	+	0.999997i	$0.500786\pi$
$860$	−6.35430	−	2.31278i	−0.216680	−	0.0788650i
$861$	−14.3478	−	0.424519i	−0.488972	−	0.0144676i
$862$	2.03360	−	11.5331i	0.0692649	−	0.392821i
$863$	17.5107			0.596072			0.298036	−	0.954555i	$-0.403668\pi$
$863$	17.5107			0.596072			0.298036	+	0.954555i	$0.403668\pi$
$864$	−24.1110	+	16.8299i	−0.820272	+	0.572564i
$865$	−15.9146			−0.541112
$866$	5.01368	−	28.4340i	0.170372	−	0.966226i
$867$	−10.9012	−	20.2413i	−0.370224	−	0.687430i
$868$	10.5977	+	3.85726i	0.359711	+	0.130924i
$869$	−39.8642	+	33.4501i	−1.35230	+	1.13472i
$870$	0.359285	−	1.73572i	0.0121809	−	0.0588465i
$871$	6.47073	−	2.35515i	0.219252	−	0.0798013i
$872$	−9.18020	+	15.9006i	−0.310881	+	0.538462i
$873$	−0.883990	+	3.71362i	−0.0299185	+	0.125687i
$874$	−14.8522	−	25.7248i	−0.502385	−	0.870156i
$875$	−0.766044	−	0.642788i	−0.0258970	−	0.0217302i
$876$	−1.56444	−	10.7170i	−0.0528574	−	0.362092i
$877$	−4.12060	−	23.3691i	−0.139143	−	0.789119i	−0.971885	−	0.235457i	$-0.924341\pi$
$877$	−4.12060	−	23.3691i	−0.139143	−	0.789119i	0.832742	−	0.553661i	$-0.186770\pi$
$878$	2.48018	+	14.0658i	0.0837019	+	0.474697i
$879$	−28.3581	+	22.4001i	−0.956496	+	0.755537i
$880$	−0.0106989	−	0.00897745i	−0.000360660	−	0.000302630i
$881$	26.9751	+	46.7222i	0.908814	+	1.57411i	0.815714	+	0.578455i	$0.196344\pi$
$881$	26.9751	+	46.7222i	0.908814	+	1.57411i	0.0930993	+	0.995657i	$0.470323\pi$
$882$	−1.44209	+	2.18791i	−0.0485576	+	0.0736708i
$883$	−5.80567	+	10.0557i	−0.195376	+	0.338402i	−0.947024	−	0.321163i	$-0.895926\pi$
$883$	−5.80567	+	10.0557i	−0.195376	+	0.338402i	0.751647	+	0.659565i	$0.229260\pi$
$884$	−7.93263	+	2.88724i	−0.266803	+	0.0971084i
$885$	−3.53524	−	3.14920i	−0.118836	−	0.105859i
$886$	−6.88586	+	5.77792i	−0.231335	+	0.194113i
$887$	−5.25125	−	1.91130i	−0.176320	−	0.0641752i	0.252352	−	0.967636i	$-0.418796\pi$
$887$	−5.25125	−	1.91130i	−0.176320	−	0.0641752i	−0.428672	+	0.903460i	$0.641018\pi$
$888$	−17.1141	+	27.7158i	−0.574313	+	0.930082i
$889$	2.52255	−	14.3061i	0.0846036	−	0.479811i
$890$	−12.5933			−0.422130
$891$	−27.9083	+	6.55661i	−0.934964	+	0.219655i
$892$	8.17058			0.273571
$893$	11.0681	−	62.7702i	0.370379	−	2.10053i
$894$	15.7717	−	25.5418i	0.527485	−	0.854246i
$895$	−15.3107	−	5.57263i	−0.511779	−	0.186272i
$896$	−5.36831	+	4.50454i	−0.179343	+	0.150486i
$897$	−28.8258	−	25.6781i	−0.962464	−	0.857366i
$898$	7.91019	−	2.87908i	0.263967	−	0.0960760i
$899$	−5.34062	+	9.25023i	−0.178120	+	0.308513i
$900$	−3.70465	−	0.219416i	−0.123488	−	0.00731388i
$901$	6.83106	+	11.8317i	0.227575	+	0.394172i
$902$	17.6634	+	14.8214i	0.588128	+	0.493498i
$903$	−7.42969	+	5.86872i	−0.247244	+	0.195299i
$904$	−5.68994	−	32.2693i	−0.189245	−	1.07326i
$905$	−2.49432	−	14.1460i	−0.0829139	−	0.470228i
$906$	2.78915	+	19.1067i	0.0926633	+	0.634777i
$907$	−27.8970	−	23.4084i	−0.926305	−	0.777263i	0.0488450	−	0.998806i	$-0.484446\pi$
$907$	−27.8970	−	23.4084i	−0.926305	−	0.777263i	−0.975150	+	0.221544i	$0.928890\pi$
$908$	−11.1743	−	19.3544i	−0.370831	−	0.642298i
$909$	−4.88592	−	4.61869i	−0.162056	−	0.153192i
$910$	−1.54384	+	2.67402i	−0.0511779	+	0.0886428i
$911$	26.9086	−	9.79391i	0.891520	−	0.324487i	0.144671	−	0.989480i	$-0.453788\pi$
$911$	26.9086	−	9.79391i	0.891520	−	0.324487i	0.746849	+	0.664993i	$0.231566\pi$
$912$	0.00830274	−	0.0401109i	0.000274931	−	0.00132820i
$913$	−20.8765	+	17.5175i	−0.690912	+	0.579744i
$914$	−19.0514	−	6.93413i	−0.630163	−	0.229361i
$915$	2.06703	+	3.83806i	0.0683340	+	0.126882i
$916$	0.393328	−	2.23068i	0.0129959	−	0.0737036i
$917$	14.4030			0.475627
$918$	8.46651	−	2.25525i	0.279437	−	0.0744345i
$919$	51.4263			1.69640			0.848199	−	0.529677i	$-0.177687\pi$
$919$	51.4263			1.69640			0.848199	+	0.529677i	$0.177687\pi$
$920$	−3.09569	+	17.5565i	−0.102062	+	0.578822i
$921$	−41.8348	−	1.23780i	−1.37850	−	0.0407868i
$922$	−10.8715	−	3.95691i	−0.358035	−	0.130314i
$923$	29.6022	−	24.8392i	0.974368	−	0.817592i
$924$	−6.47966	+	2.14360i	−0.213165	+	0.0705193i
$925$	−6.25025	+	2.27491i	−0.205507	+	0.0747985i
$926$	−15.5553	+	26.9426i	−0.511180	+	0.885390i
$927$	−2.07080	−	0.895663i	−0.0680139	−	0.0294174i
$928$	−3.31492	−	5.74161i	−0.108818	−	0.188478i
$929$	20.1475	+	16.9058i	0.661018	+	0.554660i	0.910392	−	0.413747i	$-0.135780\pi$
$929$	20.1475	+	16.9058i	0.661018	+	0.554660i	−0.249374	+	0.968407i	$0.580225\pi$
$930$	−12.8157	−	5.09864i	−0.420244	−	0.167191i
$931$	−0.936600	−	5.31172i	−0.0306958	−	0.174085i
$932$	2.53559	+	14.3800i	0.0830560	+	0.471034i
$933$	−49.7126	−	19.7778i	−1.62752	−	0.647495i
$934$	−7.74092	−	6.49540i	−0.253291	−	0.212536i
$935$	3.07459	+	5.32534i	0.100550	+	0.174157i
$936$	3.45184	+	29.7856i	0.112827	+	0.973574i
$937$	−7.58117	+	13.1310i	−0.247666	+	0.428970i	−0.962878	−	0.269938i	$-0.912997\pi$
$937$	−7.58117	+	13.1310i	−0.247666	+	0.428970i	0.715212	+	0.698908i	$0.246330\pi$
$938$	−1.59888	+	0.581946i	−0.0522054	+	0.0190012i
$939$	42.1339	−	13.9387i	1.37499	−	0.454873i
$940$	−11.1985	+	9.39664i	−0.365254	+	0.306485i
$941$	−12.1175	−	4.41042i	−0.395020	−	0.143775i	0.136870	−	0.990589i	$-0.456296\pi$
$941$	−12.1175	−	4.41042i	−0.395020	−	0.143775i	−0.531890	+	0.846814i	$0.678518\pi$
$942$	−5.57369	−	0.164913i	−0.181601	−	0.00537315i
$943$	−9.07351	+	51.4584i	−0.295474	+	1.67572i
$944$	−0.0119851			−0.000390081
$945$	−2.98665	+	4.25205i	−0.0971557	+	0.138319i
$946$	15.2090			0.494488
$947$	9.39030	−	53.2551i	0.305144	−	1.73056i	−0.317683	−	0.948197i	$-0.602905\pi$
$947$	9.39030	−	53.2551i	0.305144	−	1.73056i	0.622827	−	0.782360i	$-0.285984\pi$
$948$	16.5979	+	30.8188i	0.539074	+	1.00095i
$949$	−16.7909	−	6.11138i	−0.545055	−	0.198384i
$950$	−3.60899	+	3.02831i	−0.117091	+	0.0982512i
$951$	−1.27354	+	6.15251i	−0.0412973	+	0.199509i
$952$	5.12912	−	1.86685i	0.166236	−	0.0605049i
$953$	7.77872	−	13.4731i	0.251977	−	0.436438i	−0.712093	−	0.702085i	$-0.752252\pi$
$953$	7.77872	−	13.4731i	0.251977	−	0.436438i	0.964070	+	0.265648i	$0.0855858\pi$
$954$	17.7712	−	5.30136i	0.575363	−	0.171638i
$955$	1.59662	+	2.76543i	0.0516654	+	0.0894871i
$956$	1.72303	+	1.44579i	0.0557266	+	0.0467602i
$957$	−0.933699	−	6.39618i	−0.0301822	−	0.206759i
$958$	−0.297895	−	1.68945i	−0.00962456	−	0.0545836i
$959$	0.977044	+	5.54109i	0.0315504	+	0.178931i
$960$	6.70617	−	5.29721i	0.216441	−	0.170967i
$961$	39.9227	+	33.4991i	1.28783	+	1.08062i
$962$	10.2687	+	17.7859i	0.331076	+	0.573441i
$963$	8.62045	+	17.2068i	0.277790	+	0.554480i
$964$	−14.1131	+	24.4447i	−0.454554	+	0.787310i
$965$	−16.3263	+	5.94230i	−0.525564	+	0.191290i
$966$	7.12270	+	6.34492i	0.229169	+	0.204145i
$967$	33.4331	−	28.0537i	1.07513	−	0.902145i	0.0796271	−	0.996825i	$-0.474627\pi$
$967$	33.4331	−	28.0537i	1.07513	−	0.902145i	0.995508	+	0.0946794i	$0.0301826\pi$
$968$	−2.26782	−	0.825420i	−0.0728906	−	0.0265300i
$969$	−9.47521	+	15.3448i	−0.304388	+	0.492947i
$970$	0.193002	−	1.09457i	0.00619693	−	0.0351446i
$971$	39.6133			1.27125			0.635626	−	0.771998i	$-0.280742\pi$
$971$	39.6133			1.27125			0.635626	+	0.771998i	$0.280742\pi$
$972$	0.513609	+	19.2768i	0.0164740	+	0.618305i
$973$	−16.7330			−0.536436
$974$	−5.85546	+	33.2080i	−0.187621	+	1.06405i
$975$	−3.21685	+	5.20959i	−0.103022	+	0.166840i
$976$	0.0103697	+	0.00377428i	0.000331927	+	0.000120812i
$977$	23.3558	−	19.5978i	0.747218	−	0.626991i	−0.187547	−	0.982256i	$-0.560054\pi$
$977$	23.3558	−	19.5978i	0.747218	−	0.626991i	0.934766	+	0.355265i	$0.115609\pi$
$978$	−0.632006	−	0.562993i	−0.0202093	−	0.0180025i
$979$	−43.1554	+	15.7073i	−1.37925	+	0.502007i
$980$	−0.618524	+	1.07132i	−0.0197580	+	0.0342219i
$981$	8.72587	+	17.4172i	0.278596	+	0.556089i
$982$	4.78315	+	8.28466i	0.152637	+	0.264374i
$983$	−13.9674	−	11.7200i	−0.445489	−	0.373810i	0.392269	−	0.919850i	$-0.371690\pi$
$983$	−13.9674	−	11.7200i	−0.445489	−	0.373810i	−0.837759	+	0.546040i	$0.816135\pi$
$984$	31.8484	−	25.1571i	1.01529	−	0.801980i
$985$	−1.72766	−	9.79802i	−0.0550477	−	0.312191i
$986$	0.343052	+	1.94554i	0.0109250	+	0.0619588i
$987$	2.95656	+	20.2535i	0.0941084	+	0.644677i
$988$	−18.0680	−	15.1608i	−0.574819	−	0.482330i
$989$	17.2328	+	29.8480i	0.547970	+	0.949112i
$990$	7.99862	−	2.38609i	0.254213	−	0.0758348i
$991$	−0.660141	+	1.14340i	−0.0209701	+	0.0363212i	−0.876320	−	0.481729i	$-0.840009\pi$
$991$	−0.660141	+	1.14340i	−0.0209701	+	0.0363212i	0.855350	+	0.518051i	$0.173342\pi$
$992$	−48.4784	+	17.6447i	−1.53919	+	0.560219i
$993$	10.0017	−	48.3188i	0.317395	−	1.53335i
$994$	−7.31455	+	6.13764i	−0.232003	+	0.194674i
$995$	9.94455	+	3.61952i	0.315263	+	0.114746i
$996$	8.69215	+	16.1395i	0.275421	+	0.511400i
$997$	5.33704	−	30.2679i	0.169026	−	0.958594i	−0.775790	−	0.630991i	$-0.782648\pi$
$997$	5.33704	−	30.2679i	0.169026	−	0.958594i	0.944816	−	0.327602i	$-0.106241\pi$
$998$	−33.3300			−1.05504
$999$	14.5603	+	31.3449i	0.460667	+	0.991708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bt.c.106.14	✓	120
27.13	even	9	inner	945.2.bt.c.526.14	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.bt.c.106.14	✓	120	1.1	even	1	trivial
945.2.bt.c.526.14	yes	120	27.13	even	9	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bt (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.151677 - 0.860201i) q^{2} +(0.910009 - 1.47373i) q^{3} +(1.16245 + 0.423095i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.12968 - 1.00632i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(1.41373 - 2.44866i) q^{8} +(-1.34377 - 2.68222i) q^{9} +O(q^{10})\)	\(q+(0.151677 - 0.860201i) q^{2} +(0.910009 - 1.47373i) q^{3} +(1.16245 + 0.423095i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.12968 - 1.00632i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(1.41373 - 2.44866i) q^{8} +(-1.34377 - 2.68222i) q^{9} +(0.436736 + 0.756448i) q^{10} +(2.44012 + 2.04750i) q^{11} +(1.68136 - 1.32811i) q^{12} +(-0.613840 - 3.48126i) q^{13} +(0.151677 + 0.860201i) q^{14} +(0.250189 + 1.71389i) q^{15} +(0.00335878 + 0.00281835i) q^{16} +(-0.965228 - 1.67182i) q^{17} +(-2.51106 + 0.749081i) q^{18} +(2.69683 - 4.67105i) q^{19} +(-1.16245 + 0.423095i) q^{20} +(-0.351083 + 1.69610i) q^{21} +(2.13137 - 1.78844i) q^{22} +(5.92483 + 2.15646i) q^{23} +(-2.32216 - 4.31177i) q^{24} +(0.173648 - 0.984808i) q^{25} -3.08769 q^{26} +(-5.17571 - 0.460487i) q^{27} -1.23705 q^{28} +(0.203447 - 1.15381i) q^{29} +(1.51223 + 0.0447436i) q^{30} +(-8.56695 - 3.11812i) q^{31} +(4.33487 - 3.63738i) q^{32} +(5.23800 - 1.73283i) q^{33} +(-1.58451 + 0.576713i) q^{34} +(0.500000 - 0.866025i) q^{35} +(-0.427223 - 3.68647i) q^{36} +(-3.32569 - 5.76027i) q^{37} +(-3.60899 - 3.02831i) q^{38} +(-5.68904 - 2.26334i) q^{39} +(0.490985 + 2.78451i) q^{40} +(1.43908 + 8.16144i) q^{41} +(1.40573 + 0.559260i) q^{42} +(4.18745 + 3.51368i) q^{43} +(1.97022 + 3.41251i) q^{44} +(2.75348 + 1.19094i) q^{45} +(2.75365 - 4.76946i) q^{46} +(11.1046 - 4.04176i) q^{47} +(0.00721002 - 0.00238522i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-0.820794 - 0.298745i) q^{50} +(-3.34218 - 0.0988876i) q^{51} +(0.759350 - 4.30649i) q^{52} -7.07714 q^{53} +(-1.18115 + 4.38230i) q^{54} -3.18535 q^{55} +(-0.490985 + 2.78451i) q^{56} +(-4.42973 - 8.22510i) q^{57} +(-0.961647 - 0.350011i) q^{58} +(-2.09395 + 1.75703i) q^{59} +(-0.434306 + 2.09815i) q^{60} +(2.36505 - 0.860806i) q^{61} +(-3.98161 + 6.89636i) q^{62} +(2.18010 + 2.06086i) q^{63} +(-2.46700 - 4.27297i) q^{64} +(2.70794 + 2.27223i) q^{65} +(-0.696104 - 4.76856i) q^{66} +(0.338262 + 1.91838i) q^{67} +(-0.414683 - 2.35179i) q^{68} +(8.56969 - 6.76920i) q^{69} +(-0.669118 - 0.561456i) q^{70} +(5.46582 + 9.46707i) q^{71} +(-8.46757 - 0.501511i) q^{72} +(2.52739 - 4.37757i) q^{73} +(-5.45942 + 1.98707i) q^{74} +(-1.29332 - 1.15209i) q^{75} +(5.11122 - 4.28882i) q^{76} +(-2.99325 - 1.08945i) q^{77} +(-2.80982 + 4.55042i) q^{78} +(-2.83689 + 16.0888i) q^{79} -0.00438458 q^{80} +(-5.38857 + 7.20856i) q^{81} +7.23875 q^{82} +(-1.48565 + 8.42555i) q^{83} +(-1.12572 + 1.82308i) q^{84} +(1.81403 + 0.660255i) q^{85} +(3.65761 - 3.06910i) q^{86} +(-1.51526 - 1.34980i) q^{87} +(8.46332 - 3.08040i) q^{88} +(-7.20879 + 12.4860i) q^{89} +(1.44209 - 2.18791i) q^{90} +(1.76748 + 3.06137i) q^{91} +(5.97490 + 5.01353i) q^{92} +(-12.3913 + 9.78788i) q^{93} +(-1.79241 - 10.1653i) q^{94} +(0.936600 + 5.31172i) q^{95} +(-1.41576 - 9.69848i) q^{96} +(-0.974760 - 0.817921i) q^{97} +(-0.436736 - 0.756448i) q^{98} +(2.21289 - 9.29630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 9 q^{8}+O(q^{10}) \) 120 * q + 9 * q^8	\( 120 q + 9 q^{8} - 3 q^{10} - 24 q^{12} + 3 q^{13} + 6 q^{15} - 12 q^{16} + 60 q^{18} - 42 q^{19} + 9 q^{22} + 6 q^{23} - 60 q^{24} - 18 q^{26} - 42 q^{27} + 138 q^{28} - 18 q^{29} + 3 q^{30} - 21 q^{32} + 12 q^{33} + 39 q^{34} + 60 q^{35} + 6 q^{36} - 54 q^{37} - 117 q^{38} - 33 q^{39} - 9 q^{40} + 9 q^{41} + 3 q^{42} + 9 q^{43} + 24 q^{44} + 12 q^{45} - 24 q^{46} - 3 q^{47} + 180 q^{48} + 6 q^{51} + 39 q^{52} - 36 q^{53} - 48 q^{54} + 24 q^{55} + 9 q^{56} - 42 q^{57} - 27 q^{58} + 12 q^{59} + 15 q^{60} + 24 q^{61} - 27 q^{62} + 3 q^{63} - 123 q^{64} + 6 q^{65} - 75 q^{66} - 42 q^{67} - 111 q^{68} + 6 q^{69} + 30 q^{71} + 147 q^{72} - 66 q^{73} - 27 q^{74} - 24 q^{76} - 9 q^{77} - 15 q^{78} - 42 q^{79} - 174 q^{80} - 48 q^{81} + 132 q^{82} + 12 q^{83} - 15 q^{85} + 33 q^{86} + 42 q^{87} + 33 q^{88} + 57 q^{89} - 39 q^{90} - 42 q^{91} - 123 q^{92} - 72 q^{93} + 57 q^{94} - 21 q^{95} - 168 q^{96} + 93 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) \) 120 * q + 9 * q^8 - 3 * q^10 - 24 * q^12 + 3 * q^13 + 6 * q^15 - 12 * q^16 + 60 * q^18 - 42 * q^19 + 9 * q^22 + 6 * q^23 - 60 * q^24 - 18 * q^26 - 42 * q^27 + 138 * q^28 - 18 * q^29 + 3 * q^30 - 21 * q^32 + 12 * q^33 + 39 * q^34 + 60 * q^35 + 6 * q^36 - 54 * q^37 - 117 * q^38 - 33 * q^39 - 9 * q^40 + 9 * q^41 + 3 * q^42 + 9 * q^43 + 24 * q^44 + 12 * q^45 - 24 * q^46 - 3 * q^47 + 180 * q^48 + 6 * q^51 + 39 * q^52 - 36 * q^53 - 48 * q^54 + 24 * q^55 + 9 * q^56 - 42 * q^57 - 27 * q^58 + 12 * q^59 + 15 * q^60 + 24 * q^61 - 27 * q^62 + 3 * q^63 - 123 * q^64 + 6 * q^65 - 75 * q^66 - 42 * q^67 - 111 * q^68 + 6 * q^69 + 30 * q^71 + 147 * q^72 - 66 * q^73 - 27 * q^74 - 24 * q^76 - 9 * q^77 - 15 * q^78 - 42 * q^79 - 174 * q^80 - 48 * q^81 + 132 * q^82 + 12 * q^83 - 15 * q^85 + 33 * q^86 + 42 * q^87 + 33 * q^88 + 57 * q^89 - 39 * q^90 - 42 * q^91 - 123 * q^92 - 72 * q^93 + 57 * q^94 - 21 * q^95 - 168 * q^96 + 93 * q^97 + 3 * q^98 + 51 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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