LMFDB - Embedded newform 225.2.w.a.92.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(2,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			92.20
Character	$\chi$	$=$	225.92
Dual form			225.2.w.a.203.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.995806 - 0.646684i) q^{2} +(1.25867 + 1.18985i) q^{3} +(-0.240044 + 0.539148i) q^{4} +(-1.58674 + 1.57552i) q^{5} +(2.02285 + 0.370893i) q^{6} +(-0.501865 + 0.134474i) q^{7} +(0.481110 + 3.03761i) q^{8} +(0.168525 + 2.99526i) q^{9} +O(q^{10})$	\(q+(0.995806 - 0.646684i) q^{2} +(1.25867 + 1.18985i) q^{3} +(-0.240044 + 0.539148i) q^{4} +(-1.58674 + 1.57552i) q^{5} +(2.02285 + 0.370893i) q^{6} +(-0.501865 + 0.134474i) q^{7} +(0.481110 + 3.03761i) q^{8} +(0.168525 + 2.99526i) q^{9} +(-0.561222 + 2.59503i) q^{10} +(0.757433 - 3.56344i) q^{11} +(-0.943642 + 0.392996i) q^{12} +(2.84186 - 4.37609i) q^{13} +(-0.412798 + 0.458458i) q^{14} +(-3.87182 + 0.0950874i) q^{15} +(1.65366 + 1.83657i) q^{16} +(1.02223 - 0.161905i) q^{17} +(2.10481 + 2.87372i) q^{18} +(2.24416 - 3.08882i) q^{19} +(-0.468551 - 1.23368i) q^{20} +(-0.791689 - 0.427883i) q^{21} +(-1.55016 - 4.03831i) q^{22} +(-2.02516 + 0.106134i) q^{23} +(-3.00873 + 4.39581i) q^{24} +(0.0354827 - 4.99987i) q^{25} -6.19552i q^{26} +(-3.35179 + 3.97058i) q^{27} +(0.0479682 - 0.302860i) q^{28} +(0.344617 + 3.27881i) q^{29} +(-3.79408 + 2.59853i) q^{30} +(0.0878042 - 0.835401i) q^{31} +(-3.10695 - 0.832504i) q^{32} +(5.19331 - 3.58398i) q^{33} +(0.913241 - 0.822286i) q^{34} +(0.584462 - 1.00407i) q^{35} +(-1.65534 - 0.628136i) q^{36} +(7.70548 - 3.92614i) q^{37} +(0.237257 - 4.52713i) q^{38} +(8.78386 - 2.12668i) q^{39} +(-5.54920 - 4.06189i) q^{40} +(0.455626 + 2.14355i) q^{41} +(-1.06507 + 0.0858835i) q^{42} +(1.50348 + 5.61105i) q^{43} +(1.73941 + 1.26375i) q^{44} +(-4.98650 - 4.48719i) q^{45} +(-1.94803 + 1.41532i) q^{46} +(1.69165 + 1.36987i) q^{47} +(-0.103825 + 4.27925i) q^{48} +(-5.82839 + 3.36502i) q^{49} +(-3.19800 - 5.00185i) q^{50} +(1.47930 + 1.01251i) q^{51} +(1.67719 + 2.58264i) q^{52} +(-13.0981 - 2.07453i) q^{53} +(-0.770021 + 6.12147i) q^{54} +(4.41242 + 6.84760i) q^{55} +(-0.649932 - 1.45977i) q^{56} +(6.49990 - 1.21761i) q^{57} +(2.46353 + 3.04220i) q^{58} +(-10.0275 + 2.13140i) q^{59} +(0.878141 - 2.11031i) q^{60} +(-1.04179 - 0.221440i) q^{61} +(-0.452804 - 0.888678i) q^{62} +(-0.487363 - 1.48056i) q^{63} +(-8.33308 + 2.70758i) q^{64} +(2.38531 + 11.4211i) q^{65} +(2.85383 - 6.92738i) q^{66} +(9.43246 - 7.63826i) q^{67} +(-0.158090 + 0.589998i) q^{68} +(-2.67530 - 2.27604i) q^{69} +(-0.0673072 - 1.37782i) q^{70} +(-8.89523 - 12.2432i) q^{71} +(-9.01735 + 1.95296i) q^{72} +(3.03560 + 1.54671i) q^{73} +(5.13419 - 8.89268i) q^{74} +(5.99375 - 6.25100i) q^{75} +(1.12664 + 1.95139i) q^{76} +(0.0990623 + 1.89022i) q^{77} +(7.37173 - 7.79814i) q^{78} +(-9.07699 + 0.954030i) q^{79} +(-5.51748 - 0.308794i) q^{80} +(-8.94320 + 1.00955i) q^{81} +(1.83991 + 1.83991i) q^{82} +(5.10575 + 1.95991i) q^{83} +(0.420733 - 0.324127i) q^{84} +(-1.36693 + 1.86744i) q^{85} +(5.12575 + 4.61524i) q^{86} +(-3.46753 + 4.53700i) q^{87} +(11.1887 + 0.586377i) q^{88} +(3.51917 + 10.8309i) q^{89} +(-7.86737 - 1.24368i) q^{90} +(-0.837761 + 2.57836i) q^{91} +(0.428905 - 1.11734i) q^{92} +(1.10452 - 0.947024i) q^{93} +(2.57043 + 0.270163i) q^{94} +(1.30560 + 8.43688i) q^{95} +(-2.92008 - 4.74465i) q^{96} +(3.87608 - 4.78656i) q^{97} +(-3.62784 + 7.12004i) q^{98} +(10.8011 + 1.66818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	0.995806	−	0.646684i	0.704141	−	0.457274i	−0.142254	−	0.989830i	$-0.545435\pi$
$2$	0.995806	−	0.646684i	0.704141	−	0.457274i	0.846395	+	0.532556i	$0.178768\pi$
$3$	1.25867	+	1.18985i	0.726696	+	0.686959i
$3$	1.25867	+	1.18985i	0.726696	+	0.686959i
$4$	−0.240044	+	0.539148i	−0.120022	+	0.269574i
$5$	−1.58674	+	1.57552i	−0.709611	+	0.704593i
$5$	−1.58674	+	1.57552i	−0.709611	+	0.704593i
$6$	2.02285	+	0.370893i	0.825825	+	0.151416i
$7$	−0.501865	+	0.134474i	−0.189687	+	0.0508265i	−0.352412	−	0.935845i	$-0.614638\pi$
$7$	−0.501865	+	0.134474i	−0.189687	+	0.0508265i	0.162725	+	0.986671i	$0.447972\pi$
$8$	0.481110	+	3.03761i	0.170098	+	1.07396i
$9$	0.168525	+	2.99526i	0.0561749	+	0.998421i
$10$	−0.561222	+	2.59503i	−0.177474	+	0.820620i
$11$	0.757433	−	3.56344i	0.228375	−	1.07442i	−0.703235	−	0.710957i	$-0.748262\pi$
$11$	0.757433	−	3.56344i	0.228375	−	1.07442i	0.931610	−	0.363460i	$-0.118405\pi$
$12$	−0.943642	+	0.392996i	−0.272406	+	0.113448i
$13$	2.84186	−	4.37609i	0.788191	−	1.21371i	−0.184779	−	0.982780i	$-0.559157\pi$
$13$	2.84186	−	4.37609i	0.788191	−	1.21371i	0.972971	−	0.230928i	$-0.0741763\pi$
$14$	−0.412798	+	0.458458i	−0.110325	+	0.122528i
$15$	−3.87182	+	0.0950874i	−0.999699	+	0.0245515i
$16$	1.65366	+	1.83657i	0.413415	+	0.459144i
$17$	1.02223	−	0.161905i	0.247927	−	0.0392678i	−0.0312338	−	0.999512i	$-0.509944\pi$
$17$	1.02223	−	0.161905i	0.247927	−	0.0392678i	0.279161	+	0.960244i	$0.409944\pi$
$18$	2.10481	+	2.87372i	0.496107	+	0.677342i
$19$	2.24416	−	3.08882i	0.514846	−	0.708625i	−0.469881	−	0.882730i	$-0.655703\pi$
$19$	2.24416	−	3.08882i	0.514846	−	0.708625i	0.984727	+	0.174105i	$0.0557032\pi$
$20$	−0.468551	−	1.23368i	−0.104771	−	0.275860i
$21$	−0.791689	−	0.427883i	−0.172761	−	0.0933718i
$22$	−1.55016	−	4.03831i	−0.330496	−	0.860971i
$23$	−2.02516	+	0.106134i	−0.422274	+	0.0221305i	−0.262290	−	0.964989i	$-0.584478\pi$
$23$	−2.02516	+	0.106134i	−0.422274	+	0.0221305i	−0.159984	+	0.987120i	$0.551144\pi$
$24$	−3.00873	+	4.39581i	−0.614154	+	0.897290i
$25$	0.0354827	−	4.99987i	0.00709654	−	0.999975i
$26$		−	6.19552i		−	1.21504i
$27$	−3.35179	+	3.97058i	−0.645052	+	0.764139i
$28$	0.0479682	−	0.302860i	0.00906514	−	0.0572351i
$29$	0.344617	+	3.27881i	0.0639938	+	0.608860i	0.978779	+	0.204919i	$0.0656932\pi$
$29$	0.344617	+	3.27881i	0.0639938	+	0.608860i	−0.914785	+	0.403941i	$0.867640\pi$
$30$	−3.79408	+	2.59853i	−0.692702	+	0.474424i
$31$	0.0878042	−	0.835401i	0.0157701	−	0.150042i	−0.983803	−	0.179252i	$-0.942632\pi$
$31$	0.0878042	−	0.835401i	0.0157701	−	0.150042i	0.999573	+	0.0292094i	$0.00929898\pi$
$32$	−3.10695	−	0.832504i	−0.549236	−	0.147167i
$33$	5.19331	−	3.58398i	0.904040	−	0.623891i
$34$	0.913241	−	0.822286i	0.156620	−	0.141021i
$35$	0.584462	−	1.00407i	0.0987921	−	0.169719i
$36$	−1.65534	−	0.628136i	−0.275891	−	0.104689i
$37$	7.70548	−	3.92614i	1.26677	−	0.645454i	0.314083	−	0.949395i	$-0.398303\pi$
$37$	7.70548	−	3.92614i	1.26677	−	0.645454i	0.952691	+	0.303942i	$0.0983029\pi$
$38$	0.237257	−	4.52713i	0.0384881	−	0.734398i
$39$	8.78386	−	2.12668i	1.40654	−	0.340542i
$40$	−5.54920	−	4.06189i	−0.877406	−	0.642242i
$41$	0.455626	+	2.14355i	0.0711568	+	0.334766i	0.999298	−	0.0374617i	$-0.0119272\pi$
$41$	0.455626	+	2.14355i	0.0711568	+	0.334766i	−0.928141	+	0.372228i	$0.878594\pi$
$42$	−1.06507	+	0.0858835i	−0.164344	+	0.0132521i
$43$	1.50348	+	5.61105i	0.229278	+	0.855677i	0.980645	+	0.195793i	$0.0627281\pi$
$43$	1.50348	+	5.61105i	0.229278	+	0.855677i	−0.751367	+	0.659884i	$0.770605\pi$
$44$	1.73941	+	1.26375i	0.262225	+	0.190518i
$45$	−4.98650	−	4.48719i	−0.743343	−	0.668910i
$46$	−1.94803	+	1.41532i	−0.287221	+	0.208678i
$47$	1.69165	+	1.36987i	0.246753	+	0.199816i	0.744716	−	0.667382i	$-0.232585\pi$
$47$	1.69165	+	1.36987i	0.246753	+	0.199816i	−0.497963	+	0.867198i	$0.665918\pi$
$48$	−0.103825	+	4.27925i	−0.0149858	+	0.617657i
$49$	−5.82839	+	3.36502i	−0.832628	+	0.480718i
$50$	−3.19800	−	5.00185i	−0.452266	−	0.707368i
$51$	1.47930	+	1.01251i	0.207143	+	0.141780i
$52$	1.67719	+	2.58264i	0.232584	+	0.358148i
$53$	−13.0981	−	2.07453i	−1.79916	−	0.284959i	−0.834992	−	0.550262i	$-0.814528\pi$
$53$	−13.0981	−	2.07453i	−1.79916	−	0.284959i	−0.964165	+	0.265303i	$0.914528\pi$
$54$	−0.770021	+	6.12147i	−0.104787	+	0.833027i
$55$	4.41242	+	6.84760i	0.594970	+	0.923330i
$56$	−0.649932	−	1.45977i	−0.0868508	−	0.195070i
$57$	6.49990	−	1.21761i	0.860933	−	0.161277i
$58$	2.46353	+	3.04220i	0.323477	+	0.399460i
$59$	−10.0275	+	2.13140i	−1.30546	+	0.277485i	−0.807580	−	0.589758i	$-0.799223\pi$
$59$	−10.0275	+	2.13140i	−1.30546	+	0.277485i	−0.497885	+	0.867243i	$0.665890\pi$
$60$	0.878141	−	2.11031i	0.113368	−	0.272440i
$61$	−1.04179	−	0.221440i	−0.133388	−	0.0283525i	0.140734	−	0.990047i	$-0.455054\pi$
$61$	−1.04179	−	0.221440i	−0.133388	−	0.0283525i	−0.274122	+	0.961695i	$0.588387\pi$
$62$	−0.452804	−	0.888678i	−0.0575062	−	0.112862i
$63$	−0.487363	−	1.48056i	−0.0614019	−	0.186532i
$64$	−8.33308	+	2.70758i	−1.04163	+	0.338448i
$65$	2.38531	+	11.4211i	0.295861	+	1.41662i
$66$	2.85383	−	6.92738i	0.351282	−	0.852702i
$67$	9.43246	−	7.63826i	1.15236	−	0.933162i	0.153868	−	0.988091i	$-0.450827\pi$
$67$	9.43246	−	7.63826i	1.15236	−	0.933162i	0.998490	+	0.0549297i	$0.0174935\pi$
$68$	−0.158090	+	0.589998i	−0.0191712	+	0.0715478i
$69$	−2.67530	−	2.27604i	−0.322068	−	0.274003i
$70$	−0.0673072	−	1.37782i	−0.00804475	−	0.164681i
$71$	−8.89523	−	12.2432i	−1.05567	−	1.45301i	−0.883788	−	0.467888i	$-0.845015\pi$
$71$	−8.89523	−	12.2432i	−1.05567	−	1.45301i	−0.171882	−	0.985118i	$-0.554985\pi$
$72$	−9.01735	+	1.95296i	−1.06271	+	0.230159i
$73$	3.03560	+	1.54671i	0.355290	+	0.181029i	0.622521	−	0.782603i	$-0.286109\pi$
$73$	3.03560	+	1.54671i	0.355290	+	0.181029i	−0.267231	+	0.963633i	$0.586109\pi$
$74$	5.13419	−	8.89268i	0.596838	−	1.03375i
$75$	5.99375	−	6.25100i	0.692099	−	0.721803i
$76$	1.12664	+	1.95139i	0.129234	+	0.223840i
$77$	0.0990623	+	1.89022i	0.0112892	+	0.215411i
$78$	7.37173	−	7.79814i	0.834684	−	0.882966i
$79$	−9.07699	+	0.954030i	−1.02124	+	0.107337i	−0.600320	−	0.799760i	$-0.704960\pi$
$79$	−9.07699	+	0.954030i	−1.02124	+	0.107337i	−0.420922	+	0.907097i	$0.638293\pi$
$80$	−5.51748	−	0.308794i	−0.616873	−	0.0345242i
$81$	−8.94320	+	1.00955i	−0.993689	+	0.112172i
$82$	1.83991	+	1.83991i	0.203185	+	0.203185i
$83$	5.10575	+	1.95991i	0.560428	+	0.215128i	0.622059	−	0.782971i	$-0.286297\pi$
$83$	5.10575	+	1.95991i	0.560428	+	0.215128i	−0.0616301	+	0.998099i	$0.519630\pi$
$84$	0.420733	−	0.324127i	0.0459057	−	0.0353651i
$85$	−1.36693	+	1.86744i	−0.148264	+	0.202553i
$86$	5.12575	+	4.61524i	0.552723	+	0.497674i
$87$	−3.46753	+	4.53700i	−0.371758	+	0.486417i
$88$	11.1887	+	0.586377i	1.19272	+	0.0625080i
$89$	3.51917	+	10.8309i	0.373031	+	1.14807i	0.944797	+	0.327655i	$0.106258\pi$
$89$	3.51917	+	10.8309i	0.373031	+	1.14807i	−0.571766	+	0.820416i	$0.693742\pi$
$90$	−7.86737	−	1.24368i	−0.829294	−	0.131095i
$91$	−0.837761	+	2.57836i	−0.0878212	+	0.270286i
$92$	0.428905	−	1.11734i	0.0447165	−	0.116490i
$93$	1.10452	−	0.947024i	0.114533	−	0.0982018i
$94$	2.57043	+	0.270163i	0.265120	+	0.0278652i
$95$	1.30560	+	8.43688i	0.133952	+	0.865605i
$96$	−2.92008	−	4.74465i	−0.298030	−	0.484249i
$97$	3.87608	−	4.78656i	0.393557	−	0.486002i	−0.541399	−	0.840765i	$-0.682105\pi$
$97$	3.87608	−	4.78656i	0.393557	−	0.486002i	0.934956	+	0.354764i	$0.115439\pi$
$98$	−3.62784	+	7.12004i	−0.366467	+	0.719232i
$99$	10.8011	+	1.66818i	1.08555	+	0.167659i
$100$	2.68716	+	1.21932i	0.268716	+	0.121932i
$101$	−11.3473	−	6.55139i	−1.12910	−	0.651887i	−0.185393	−	0.982664i	$-0.559356\pi$
$101$	−11.3473	−	6.55139i	−1.12910	−	0.651887i	−0.943709	+	0.330777i	$0.892689\pi$
$102$	2.12787	+	0.0516272i	0.210690	+	0.00511186i
$103$	−0.0319034	+	0.0122466i	−0.00314354	+	0.00120669i	−0.359939	−	0.932976i	$-0.617203\pi$
$103$	−0.0319034	+	0.0122466i	−0.00314354	+	0.00120669i	0.356796	+	0.934182i	$0.383869\pi$
$104$	14.6601	+	6.52709i	1.43754	+	0.640034i
$105$	1.93034	−	0.568381i	0.188382	−	0.0554683i
$106$	−14.3847	+	6.40448i	−1.39716	+	0.622058i
$107$	9.46100	−	9.46100i	0.914629	−	0.914629i	−0.0820027	−	0.996632i	$-0.526132\pi$
$107$	9.46100	−	9.46100i	0.914629	−	0.914629i	0.996632	+	0.0820027i	$0.0261316\pi$
$108$	−1.33615	−	2.76023i	−0.128571	−	0.265603i
$109$	−13.5837	−	4.41363i	−1.30109	−	0.422749i	−0.425128	−	0.905133i	$-0.639771\pi$
$109$	−13.5837	−	4.41363i	−1.30109	−	0.422749i	−0.875960	+	0.482385i	$0.839771\pi$
$110$	8.82214	+	3.96544i	0.841158	+	0.378090i
$111$	14.3702	+	4.22662i	1.36396	+	0.401173i
$112$	−1.07689	−	0.699338i	−0.101756	−	0.0660812i
$113$	4.69796	+	3.05089i	0.441947	+	0.287004i	0.746367	−	0.665534i	$-0.231796\pi$
$113$	4.69796	+	3.05089i	0.441947	+	0.287004i	−0.304421	+	0.952538i	$0.598463\pi$
$114$	5.68523	−	5.41589i	0.532470	−	0.507244i
$115$	3.04618	−	3.35908i	0.284058	−	0.313236i
$116$	−1.85049	−	0.601260i	−0.171814	−	0.0558256i
$117$	13.5865	+	7.77465i	1.25607	+	0.718767i
$118$	−8.60706	+	8.60706i	−0.792344	+	0.792344i
$119$	−0.491249	+	0.218718i	−0.0450328	+	0.0200499i
$120$	−2.15161	−	11.7153i	−0.196414	−	1.06946i
$121$	−2.07540	−	0.924030i	−0.188673	−	0.0840027i
$122$	−1.18062	+	0.453199i	−0.106889	+	0.0410307i
$123$	−1.97701	+	3.24016i	−0.178261	+	0.292155i
$124$	0.429328	+	0.247873i	0.0385548	+	0.0222596i
$125$	7.82109	+	7.98940i	0.699540	+	0.714594i
$126$	−1.44277	−	1.15918i	−0.128532	−	0.103268i
$127$	6.75540	−	13.2582i	0.599445	−	1.17648i	−0.369507	−	0.929228i	$-0.620473\pi$
$127$	6.75540	−	13.2582i	0.599445	−	1.17648i	0.968952	−	0.247249i	$-0.0795267\pi$
$128$	−2.49870	+	3.08563i	−0.220856	+	0.272734i
$129$	−4.78391	+	8.85140i	−0.421200	+	0.779322i
$130$	9.76116	+	9.83067i	0.856110	+	0.862207i
$131$	8.38280	+	0.881068i	0.732409	+	0.0769793i	0.463389	−	0.886155i	$-0.346633\pi$
$131$	8.38280	+	0.881068i	0.732409	+	0.0769793i	0.269020	+	0.963134i	$0.413300\pi$
$132$	0.685673	+	3.66028i	0.0596802	+	0.318587i
$133$	−0.710899	+	1.85195i	−0.0616427	+	0.160585i
$134$	4.45336	−	13.7060i	0.384712	−	1.18402i
$135$	−0.937308	−	11.5811i	−0.0806706	−	0.996741i
$136$	0.983610	+	3.02724i	0.0843438	+	0.259584i
$137$	16.6282	+	0.871447i	1.42064	+	0.0744527i	0.747108	−	0.664703i	$-0.231442\pi$
$137$	16.6282	+	0.871447i	1.42064	+	0.0744527i	0.673535	+	0.739156i	$0.264775\pi$
$138$	−4.13595	−	0.536422i	−0.352076	−	0.0456633i
$139$	4.34871	+	3.91559i	0.368852	+	0.332116i	0.832624	−	0.553839i	$-0.186838\pi$
$139$	4.34871	+	3.91559i	0.368852	+	0.332116i	−0.463772	+	0.885955i	$0.653504\pi$
$140$	0.401048	+	0.556134i	0.0338947	+	0.0470019i
$141$	0.499300	+	3.73703i	0.0420486	+	0.314715i
$142$	−16.7754	−	6.43948i	−1.40776	−	0.540389i
$143$	−13.4414	−	13.4414i	−1.12403	−	1.12403i
$144$	−5.22234	+	5.26265i	−0.435195	+	0.438554i
$145$	−5.71265	−	4.65967i	−0.474409	−	0.386964i
$146$	4.02310	−	0.422845i	0.332954	−	0.0349949i
$147$	−11.3399	−	2.69943i	−0.935301	−	0.222645i
$148$	0.267114	+	5.09685i	0.0219567	+	0.418958i
$149$	−0.125413	−	0.217222i	−0.0102743	−	0.0177955i	0.860843	−	0.508871i	$-0.169937\pi$
$149$	−0.125413	−	0.217222i	−0.0102743	−	0.0177955i	−0.871117	+	0.491076i	$0.836604\pi$
$150$	1.92619	−	10.1008i	0.157273	−	0.824730i
$151$	−8.69231	+	15.0555i	−0.707370	+	1.22520i	0.258459	+	0.966022i	$0.416785\pi$
$151$	−8.69231	+	15.0555i	−0.707370	+	1.22520i	−0.965829	+	0.259179i	$0.916548\pi$
$152$	10.4623	+	5.33082i	0.848606	+	0.432387i
$153$	0.657220	+	3.03456i	0.0531331	+	0.245330i
$154$	1.32102	+	1.81823i	0.106451	+	0.146517i
$155$	1.17687	+	1.46390i	0.0945282	+	0.117583i
$156$	−0.961917	+	5.24630i	−0.0770150	+	0.420040i
$157$	−5.84110	+	21.7993i	−0.466171	+	1.73977i	0.186808	+	0.982396i	$0.440186\pi$
$157$	−5.84110	+	21.7993i	−0.466171	+	1.73977i	−0.652979	+	0.757376i	$0.726481\pi$
$158$	−8.42196	+	6.81997i	−0.670015	+	0.542568i
$159$	−14.0178	−	18.1959i	−1.11169	−	1.44303i
$160$	6.24154	−	3.57409i	0.493437	−	0.282556i
$161$	1.00208	−	0.325596i	0.0789752	−	0.0256606i
$162$	−8.25283	+	6.78874i	−0.648403	+	0.533374i
$163$	−8.28630	−	16.2628i	−0.649033	−	1.27380i	−0.947615	−	0.319416i	$-0.896513\pi$
$163$	−8.28630	−	16.2628i	−0.649033	−	1.27380i	0.298581	−	0.954384i	$-0.403487\pi$
$164$	−1.26506	−	0.268897i	−0.0987848	−	0.0209974i
$165$	−2.59380	+	13.8690i	−0.201927	+	1.07970i
$166$	6.35177	−	1.35011i	0.492993	−	0.104789i
$167$	−4.08308	−	5.04219i	−0.315959	−	0.390176i	0.594282	−	0.804257i	$-0.297436\pi$
$167$	−4.08308	−	5.04219i	−0.315959	−	0.390176i	−0.910240	+	0.414081i	$0.864103\pi$
$168$	0.918853	−	2.61070i	0.0708910	−	0.201420i
$169$	−5.78637	−	12.9964i	−0.445105	−	0.999723i
$170$	−0.153549	+	2.74358i	−0.0117766	+	0.210423i
$171$	9.63004	+	6.20131i	0.736427	+	0.474226i
$172$	−3.38609	−	0.536304i	−0.258187	−	0.0408928i
$173$	11.1040	+	17.0987i	0.844223	+	1.29999i	0.952088	+	0.305824i	$0.0989321\pi$
$173$	11.1040	+	17.0987i	0.844223	+	1.29999i	−0.107865	+	0.994166i	$0.534401\pi$
$174$	−0.518978	+	6.76036i	−0.0393436	+	0.512502i
$175$	0.654547	+	2.51403i	0.0494791	+	0.190043i
$176$	7.79706	−	4.50163i	0.587725	−	0.339323i
$177$	−15.1574	−	9.24841i	−1.13930	−	0.695153i
$178$	10.5086	+	8.50967i	0.787650	+	0.637826i
$179$	12.3568	−	8.97776i	0.923593	−	0.671029i	−0.0208231	−	0.999783i	$-0.506629\pi$
$179$	12.3568	−	8.97776i	0.923593	−	0.671029i	0.944416	+	0.328754i	$0.106629\pi$
$180$	3.61624	−	1.61134i	0.269539	−	0.120102i
$181$	2.74110	+	1.99153i	0.203744	+	0.148029i	0.684979	−	0.728563i	$-0.259811\pi$
$181$	2.74110	+	1.99153i	0.203744	+	0.148029i	−0.481234	+	0.876592i	$0.659811\pi$
$182$	0.833138	+	3.10931i	0.0617563	+	0.230478i
$183$	−1.04780	−	1.51829i	−0.0774554	−	0.112236i
$184$	−1.29672	−	6.10057i	−0.0955951	−	0.449740i
$185$	−6.04089	+	18.3699i	−0.444135	+	1.35058i
$186$	0.487459	−	1.65732i	0.0357422	−	0.121521i
$187$	0.197330	−	3.76529i	0.0144302	−	0.275345i
$188$	−1.14464	+	0.583221i	−0.0834811	+	0.0425358i
$189$	1.14820	−	2.44342i	0.0835196	−	0.177733i
$190$	6.75611	+	7.55718i	0.490140	+	0.548255i
$191$	−2.00337	+	1.80384i	−0.144959	+	0.130521i	−0.738420	−	0.674341i	$-0.764428\pi$
$191$	−2.00337	+	1.80384i	−0.144959	+	0.130521i	0.593461	+	0.804863i	$0.297761\pi$
$192$	−13.7102	−	6.50713i	−0.989452	−	0.469612i
$193$	−20.7419	−	5.55779i	−1.49304	−	0.400058i	−0.582276	−	0.812991i	$-0.697838\pi$
$193$	−20.7419	−	5.55779i	−1.49304	−	0.400058i	−0.910762	+	0.412933i	$0.864504\pi$
$194$	0.764432	−	7.27309i	0.0548830	−	0.522177i
$195$	−10.5871	+	17.2136i	−0.758155	+	1.23269i
$196$	−0.415175	−	3.95012i	−0.0296553	−	0.282152i
$197$	−3.51346	+	22.1831i	−0.250324	+	1.58048i	0.467330	+	0.884083i	$0.345216\pi$
$197$	−3.51346	+	22.1831i	−0.250324	+	1.58048i	−0.717654	+	0.696400i	$0.754784\pi$
$198$	11.8346	−	5.32370i	0.841046	−	0.378339i
$199$		−	20.7252i		−	1.46917i	−0.678517	−	0.734584i	$-0.737377\pi$
$199$		−	20.7252i		−	1.46917i	0.678517	−	0.734584i	$-0.262623\pi$
$200$	15.2047	−	2.29771i	1.07514	−	0.162472i
$201$	20.9608	+	1.60911i	1.47846	+	0.113498i
$202$	−15.5364	+	0.814229i	−1.09314	+	0.0572889i
$203$	−0.613867	−	1.59918i	−0.0430850	−	0.112240i
$204$	−0.900992	+	0.554513i	−0.0630820	+	0.0388237i
$205$	−4.10016	−	2.68341i	−0.286368	−	0.187417i
$206$	−0.0238499	+	0.0328266i	−0.00166170	+	0.00228714i
$207$	−0.659188	−	6.04799i	−0.0458167	−	0.420364i
$208$	12.7365	−	2.01726i	0.883116	−	0.139872i
$209$	−9.30704	−	10.3365i	−0.643781	−	0.714992i
$210$	1.55468	−	1.81432i	0.107283	−	0.125200i
$211$	−0.644644	+	0.715950i	−0.0443791	+	0.0492880i	−0.764926	−	0.644119i	$-0.777224\pi$
$211$	−0.644644	+	0.715950i	−0.0443791	+	0.0492880i	0.720547	+	0.693407i	$0.243891\pi$
$212$	4.26259	−	6.56382i	0.292756	−	0.450805i
$213$	3.37138	−	25.9942i	0.231003	−	1.78110i
$214$	3.30304	−	15.5396i	0.225791	−	1.06226i
$215$	−11.2259	−	6.53452i	−0.765603	−	0.445651i
$216$	−13.6736	−	8.27113i	−0.930373	−	0.562779i
$217$	0.0682741	+	0.431066i	0.00463475	+	0.0292627i
$218$	−16.3810	+	4.38927i	−1.10946	+	0.297279i
$219$	1.98048	+	5.55871i	0.133828	+	0.375623i
$220$	−4.75105	+	0.735221i	−0.320316	+	0.0495686i
$221$	2.19653	−	4.93348i	0.147754	−	0.331862i
$222$	17.0432	−	5.08409i	1.14387	−	0.341222i
$223$	−1.57747	+	1.02442i	−0.105635	+	0.0686003i	−0.596375	−	0.802706i	$-0.703393\pi$
$223$	−1.57747	+	1.02442i	−0.105635	+	0.0686003i	0.490740	+	0.871306i	$0.336726\pi$
$224$	1.67122			0.111663
$225$	14.9819	−	0.736322i	0.998794	−	0.0490881i
$226$	6.65121			0.442432
$227$	−18.6940	+	12.1400i	−1.24076	+	0.805761i	−0.986877	−	0.161473i	$-0.948375\pi$
$227$	−18.6940	+	12.1400i	−1.24076	+	0.805761i	−0.253886	+	0.967234i	$0.581709\pi$
$228$	−0.903790	+	3.79669i	−0.0598549	+	0.251442i
$229$	−12.0375	+	27.0367i	−0.795461	+	1.78664i	−0.206553	+	0.978435i	$0.566225\pi$
$229$	−12.0375	+	27.0367i	−0.795461	+	1.78664i	−0.588908	+	0.808200i	$0.700442\pi$
$230$	0.861141	−	5.31490i	0.0567820	−	0.350454i
$231$	−2.12439	+	2.49704i	−0.139774	+	0.164293i
$232$	−9.79394	+	2.62428i	−0.643004	+	0.172292i
$233$	−3.52396	−	22.2494i	−0.230862	−	1.45761i	−0.782044	−	0.623223i	$-0.785823\pi$
$233$	−3.52396	−	22.2494i	−0.230862	−	1.45761i	0.551182	−	0.834385i	$-0.314177\pi$
$234$	18.5572	−	1.04410i	1.21312	−	0.0682548i
$235$	−4.84247	+	0.491598i	−0.315888	+	0.0320683i
$236$	1.25789	−	5.91792i	0.0818819	−	0.385224i
$237$	−12.5601	−	9.59942i	−0.815868	−	0.623550i
$238$	−0.347747	+	0.535484i	−0.0225411	+	0.0347103i
$239$	7.85000	−	8.71831i	0.507774	−	0.563940i	−0.433686	−	0.901064i	$-0.642787\pi$
$239$	7.85000	−	8.71831i	0.507774	−	0.563940i	0.941460	+	0.337124i	$0.109454\pi$
$240$	−6.57730	−	6.95364i	−0.424563	−	0.448855i
$241$	12.0744	+	13.4100i	0.777784	+	0.863816i	0.993639	−	0.112609i	$-0.0359208\pi$
$241$	12.0744	+	13.4100i	0.777784	+	0.863816i	−0.215856	+	0.976425i	$0.569254\pi$
$242$	−2.66425	+	0.421976i	−0.171265	+	0.0271257i
$243$	−12.4578	−	9.37035i	−0.799168	−	0.601108i
$244$	0.369465	−	0.508525i	0.0236526	−	0.0325550i
$245$	3.94648	−	14.5222i	0.252131	−	0.927787i
$246$	0.126636	+	4.50507i	0.00807401	+	0.287233i
$247$	−7.13936	−	18.5987i	−0.454267	−	1.18340i
$248$	2.57986	−	0.135205i	0.163821	−	0.00858552i
$249$	4.09448	+	8.54195i	0.259477	+	0.541324i
$250$	12.9549	+	2.89812i	0.819340	+	0.183293i
$251$			14.4353i			0.911146i	0.890199	+	0.455573i	$0.150566\pi$
$251$			14.4353i			0.911146i	−0.890199	+	0.455573i	$0.849434\pi$
$252$	0.915228	+	0.0926382i	0.0576539	+	0.00583566i
$253$	−1.15572	+	7.29691i	−0.0726593	+	0.458753i
$254$	−1.84681	−	17.5712i	−0.115879	−	1.10252i
$255$	−3.94249	+	0.724069i	−0.246888	+	0.0453430i
$256$	1.33895	−	12.7393i	0.0836845	−	0.796205i
$257$	−8.02116	−	2.14926i	−0.500346	−	0.134067i	−0.000185445	−	1.00000i	$-0.500059\pi$
$257$	−8.02116	−	2.14926i	−0.500346	−	0.134067i	−0.500161	+	0.865933i	$0.666726\pi$
$258$	0.960211	+	11.9079i	0.0597802	+	0.741356i
$259$	−3.33915	+	3.00658i	−0.207485	+	0.186820i
$260$	−6.73026	−	1.45554i	−0.417393	−	0.0902687i
$261$	−9.76282	+	1.58478i	−0.604304	+	0.0980953i
$262$	8.91741	−	4.54365i	0.550920	−	0.280708i
$263$	0.496793	−	9.47937i	0.0306336	−	0.584523i	−0.939588	−	0.342306i	$-0.888792\pi$
$263$	0.496793	−	9.47937i	0.0306336	−	0.584523i	0.970222	−	0.242217i	$-0.0778746\pi$
$264$	13.3853	+	14.0510i	0.823807	+	0.864777i
$265$	24.0517	−	17.3445i	1.47748	−	1.06546i
$266$	0.489712	+	2.30391i	0.0300262	+	0.141262i
$267$	−8.45762	+	17.8198i	−0.517598	+	1.09056i
$268$	1.85395	+	6.91902i	0.113248	+	0.422646i
$269$	−5.30936	−	3.85748i	−0.323717	−	0.235195i	0.414043	−	0.910257i	$-0.364116\pi$
$269$	−5.30936	−	3.85748i	−0.323717	−	0.235195i	−0.737760	+	0.675063i	$0.764116\pi$
$270$	−8.42267	−	10.9264i	−0.512588	−	0.664957i
$271$	−17.5001	+	12.7146i	−1.06305	+	0.772354i	−0.974651	−	0.223731i	$-0.928176\pi$
$271$	−17.5001	+	12.7146i	−1.06305	+	0.772354i	−0.0884031	+	0.996085i	$0.528176\pi$
$272$	1.98777	+	1.60967i	0.120526	+	0.0976003i
$273$	−4.12233	+	2.24851i	−0.249495	+	0.136086i
$274$	17.1220	−	9.88539i	1.03438	−	0.597198i
$275$	−17.7899	−	3.91351i	−1.07277	−	0.235993i
$276$	1.86931	−	0.896032i	0.112519	−	0.0539348i
$277$	8.34837	+	12.8554i	0.501605	+	0.772404i	0.995260	−	0.0972541i	$-0.0310060\pi$
$277$	8.34837	+	12.8554i	0.501605	+	0.772404i	−0.493655	+	0.869658i	$0.664339\pi$
$278$	6.86262	+	1.08693i	0.411592	+	0.0651898i
$279$	2.51704	+	0.122211i	0.150691	+	0.00731658i
$280$	3.33117	+	1.29230i	0.199076	+	0.0772295i
$281$	5.10158	+	11.4583i	0.304335	+	0.683546i	0.999372	−	0.0354267i	$-0.0112790\pi$
$281$	5.10158	+	11.4583i	0.304335	+	0.683546i	−0.695038	+	0.718973i	$0.744612\pi$
$282$	2.91388	+	3.39847i	0.173519	+	0.202376i
$283$	5.31409	+	6.56236i	0.315890	+	0.390092i	0.910217	−	0.414132i	$-0.135915\pi$
$283$	5.31409	+	6.56236i	0.315890	+	0.390092i	−0.594327	+	0.804224i	$0.702581\pi$
$284$	8.73617	−	1.85693i	0.518397	−	0.110189i
$285$	−8.39527	+	12.1727i	−0.497293	+	0.721051i
$286$	−22.0774	−	4.69269i	−1.30546	−	0.277485i
$287$	−0.516915	−	1.01450i	−0.0305125	−	0.0598842i
$288$	1.96997	−	9.44642i	0.116082	−	0.556636i
$289$	−15.1492	+	4.92228i	−0.891131	+	0.289546i
$290$	−8.70202	−	0.945849i	−0.511000	−	0.0555422i
$291$	10.5740	−	1.41278i	0.619859	−	0.0828185i
$292$	−1.56259	+	1.26536i	−0.0914435	+	0.0740495i
$293$	−2.79290	+	10.4232i	−0.163163	+	0.608932i	0.835105	+	0.550091i	$0.185407\pi$
$293$	−2.79290	+	10.4232i	−0.163163	+	0.608932i	−0.998267	+	0.0588406i	$0.981260\pi$
$294$	−13.0380	+	4.64523i	−0.760393	+	0.270916i
$295$	12.5529	−	19.1804i	0.730858	−	1.11673i
$296$	15.6333	+	21.5173i	0.908664	+	1.25067i
$297$	11.6102	+	14.9513i	0.673691	+	0.867565i
$298$	−0.265361	−	0.135208i	−0.0153720	−	0.00783241i
$299$	−5.29077	+	9.16388i	−0.305973	+	0.529961i
$300$	1.93145	+	4.73204i	0.111512	+	0.273204i
$301$	−1.50908	−	2.61381i	−0.0869822	−	0.150658i
$302$	1.08031	+	20.6136i	0.0621649	+	1.18618i
$303$	−6.48745	−	21.7477i	−0.372694	−	1.24937i
$304$	9.38393	−	0.986291i	0.538206	−	0.0565677i
$305$	2.00193	−	1.29000i	0.114630	−	0.0738649i
$306$	2.61687	+	2.59682i	0.149596	+	0.148450i
$307$	10.9473	+	10.9473i	0.624795	+	0.624795i	0.946754	−	0.321959i	$-0.104341\pi$
$307$	10.9473	+	10.9473i	0.624795	+	0.624795i	−0.321959	+	0.946754i	$0.604341\pi$
$308$	−1.04289	−	0.400328i	−0.0594241	−	0.0228108i
$309$	−0.0547276	−	0.0225458i	−0.00311334	−	0.00128258i
$310$	2.11861	+	0.696699i	0.120329	+	0.0395699i
$311$	−15.8956	−	14.3125i	−0.901356	−	0.811585i	0.0813633	−	0.996685i	$-0.474073\pi$
$311$	−15.8956	−	14.3125i	−0.901356	−	0.811585i	−0.982720	+	0.185099i	$0.940739\pi$
$312$	10.6860	+	25.6587i	0.604978	+	1.45264i
$313$	14.3033	+	0.749604i	0.808470	+	0.0423701i	0.452092	−	0.891971i	$-0.350678\pi$
$313$	14.3033	+	0.749604i	0.808470	+	0.0423701i	0.356379	+	0.934342i	$0.384011\pi$
$314$	8.28064	+	25.4852i	0.467304	+	1.43821i
$315$	3.10596	+	1.58141i	0.175001	+	0.0891022i
$316$	1.66452	−	5.12285i	0.0936364	−	0.288183i
$317$	−1.24348	+	3.23937i	−0.0698407	+	0.181941i	−0.964058	−	0.265692i	$-0.914400\pi$
$317$	−1.24348	+	3.23937i	−0.0698407	+	0.181941i	0.894217	+	0.447633i	$0.147733\pi$
$318$	−25.7260	−	9.05444i	−1.44264	−	0.507748i
$319$	11.9449	+	1.25546i	0.668784	+	0.0702921i
$320$	8.95658	−	17.4251i	0.500688	−	0.974095i
$321$	23.1655	−	0.651173i	1.29297	−	0.0363449i
$322$	0.787322	−	0.972261i	0.0438757	−	0.0541820i
$323$	1.79395	−	3.52083i	0.0998182	−	0.195904i
$324$	1.60247	−	5.06405i	0.0890259	−	0.281336i
$325$	−21.7790	−	14.3642i	−1.20808	−	0.796785i
$326$	−18.7684	−	10.8360i	−1.03949	−	0.600148i
$327$	−11.8460	−	21.7179i	−0.655084	−	1.20100i
$328$	−6.29206	+	2.41530i	−0.347421	+	0.133362i
$329$	−1.03319	−	0.460007i	−0.0569618	−	0.0253610i
$330$	6.38594	+	15.4882i	0.351534	+	0.852598i
$331$	13.9901	−	6.22880i	0.768966	−	0.342366i	0.0155237	−	0.999879i	$-0.495058\pi$
$331$	13.9901	−	6.22880i	0.768966	−	0.342366i	0.753443	+	0.657514i	$0.228392\pi$
$332$	−2.28229	+	2.28229i	−0.125257	+	0.125257i
$333$	13.0584	+	22.4183i	0.715595	+	1.22852i
$334$	−7.32666	−	2.38058i	−0.400897	−	0.130259i
$335$	−2.93264	+	26.9809i	−0.160227	+	1.47413i
$336$	−0.523343	−	2.16157i	−0.0285507	−	0.117923i
$337$	−18.9241	−	12.2895i	−1.03086	−	0.669450i	−0.0857905	−	0.996313i	$-0.527342\pi$
$337$	−18.9241	−	12.2895i	−1.03086	−	0.669450i	−0.945072	+	0.326864i	$0.894008\pi$
$338$	−14.1667	−	9.19994i	−0.770565	−	0.500411i
$339$	2.28311	+	9.42993i	0.124001	+	0.512164i
$340$	−0.678706	−	1.18525i	−0.0368080	−	0.0642790i
$341$	−2.91040	−	0.945645i	−0.157607	−	0.0512095i
$342$	13.5999	−	0.0522862i	0.735400	−	0.00282731i
$343$	5.04429	−	5.04429i	0.272366	−	0.272366i
$344$	−16.3208	+	7.26650i	−0.879960	+	0.391784i
$345$	7.83094	−	0.603498i	0.421604	−	0.0324912i
$346$	22.1149	+	9.84619i	1.18890	+	0.529334i
$347$	5.72228	−	2.19658i	0.307188	−	0.117919i	−0.199890	−	0.979818i	$-0.564059\pi$
$347$	5.72228	−	2.19658i	0.307188	−	0.117919i	0.507079	+	0.861900i	$0.330725\pi$
$348$	−1.61376	−	2.95859i	−0.0865064	−	0.158597i
$349$	21.5642	+	12.4501i	1.15430	+	0.666437i	0.949932	−	0.312456i	$-0.101152\pi$
$349$	21.5642	+	12.4501i	1.15430	+	0.666437i	0.204371	+	0.978893i	$0.434485\pi$
$350$	2.27759	+	2.08020i	0.121742	+	0.111192i
$351$	7.85028	+	25.9516i	0.419017	+	1.38519i
$352$	−5.31988	+	10.4409i	−0.283551	+	0.556500i
$353$	7.53592	−	9.30608i	0.401096	−	0.495313i	−0.536081	−	0.844167i	$-0.680096\pi$
$353$	7.53592	−	9.30608i	0.401096	−	0.495313i	0.937177	+	0.348854i	$0.113429\pi$
$354$	−21.0746	+	0.592399i	−1.12010	+	0.0314856i
$355$	33.4039	+	5.41222i	1.77289	+	0.287251i
$356$	−6.68421	−	0.702539i	−0.354262	−	0.0372345i
$357$	−0.878565	−	0.309217i	−0.0464986	−	0.0163655i
$358$	6.49923	−	16.9311i	0.343495	−	0.894834i
$359$	−0.491484	+	1.51263i	−0.0259395	+	0.0798336i	−0.963188	−	0.268828i	$-0.913364\pi$
$359$	−0.491484	+	1.51263i	−0.0259395	+	0.0798336i	0.937249	+	0.348662i	$0.113364\pi$
$360$	11.2313	−	17.3058i	0.591939	−	0.912098i
$361$	1.36675	+	4.20643i	0.0719343	+	0.221391i
$362$	4.01749	+	0.210548i	0.211155	+	0.0110661i
$363$	−1.51280	−	3.63247i	−0.0794017	−	0.190655i
$364$	−1.18902	−	1.07060i	−0.0623216	−	0.0561146i
$365$	−7.25358	+	2.32841i	−0.379670	+	0.121874i
$366$	−2.02526	−	0.834332i	−0.105862	−	0.0436113i
$367$	11.4258	+	4.38596i	0.596423	+	0.228945i	0.637805	−	0.770198i	$-0.279843\pi$
$367$	11.4258	+	4.38596i	0.596423	+	0.228945i	−0.0413820	+	0.999143i	$0.513176\pi$
$368$	−3.54384	−	3.54384i	−0.184736	−	0.184736i
$369$	−6.34371	+	1.72596i	−0.330241	+	0.0898499i
$370$	5.86396	+	22.1994i	0.304853	+	1.15409i
$371$	6.85243	−	0.720219i	0.355760	−	0.0373919i
$372$	0.245454	+	0.822826i	0.0127262	+	0.0426616i
$373$	0.301720	+	5.75716i	0.0156225	+	0.298095i	0.995255	+	0.0972975i	$0.0310198\pi$
$373$	0.301720	+	5.75716i	0.0156225	+	0.298095i	−0.979633	+	0.200797i	$0.935647\pi$
$374$	−2.23845	−	3.87711i	−0.115747	−	0.200480i
$375$	0.338042	+	19.3620i	0.0174564	+	0.999848i
$376$	−3.34726	+	5.79763i	−0.172622	+	0.298990i
$377$	15.3277	+	7.80986i	0.789418	+	0.402228i
$378$	−0.436735	−	3.17570i	−0.0224632	−	0.163340i
$379$	18.9029	+	26.0177i	0.970979	+	1.33644i	0.941551	+	0.336871i	$0.109369\pi$
$379$	18.9029	+	26.0177i	0.970979	+	1.33644i	0.0294286	+	0.999567i	$0.490631\pi$
$380$	−4.86213	−	1.32131i	−0.249422	−	0.0677819i
$381$	24.2781	−	8.64989i	1.24381	−	0.443148i
$382$	−0.828450	+	3.09182i	−0.0423872	+	0.158191i
$383$	18.2564	−	14.7838i	0.932859	−	0.755414i	−0.0369405	−	0.999317i	$-0.511761\pi$
$383$	18.2564	−	14.7838i	0.932859	−	0.755414i	0.969800	+	0.243903i	$0.0784279\pi$
$384$	−6.81648	+	0.910741i	−0.347852	+	0.0464760i
$385$	−3.13526	−	2.84321i	−0.159788	−	0.144904i
$386$	−24.2491	+	7.87900i	−1.23425	+	0.401031i
$387$	−16.5532	+	5.44891i	−0.841446	+	0.276984i
$388$	1.65024	+	3.23877i	0.0837781	+	0.164424i
$389$	−3.09586	−	0.658045i	−0.156966	−	0.0333642i	0.128758	−	0.991676i	$-0.458901\pi$
$389$	−3.09586	−	0.658045i	−0.156966	−	0.0333642i	−0.285725	+	0.958312i	$0.592234\pi$
$390$	0.589116	+	23.9879i	0.0298310	+	1.21468i
$391$	−2.05299	+	0.436377i	−0.103824	+	0.0220685i
$392$	−13.0257	−	16.0854i	−0.657898	−	0.812436i
$393$	9.50289	+	11.0832i	0.479357	+	0.559075i
$394$	10.8467	+	24.3622i	0.546451	+	1.22735i
$395$	12.8997	−	15.8148i	0.649056	−	0.795727i
$396$	−3.49214	+	5.42295i	−0.175487	+	0.272514i
$397$	14.5612	+	2.30626i	0.730804	+	0.115748i	0.510737	−	0.859737i	$-0.329372\pi$
$397$	14.5612	+	2.30626i	0.730804	+	0.115748i	0.220067	+	0.975485i	$0.429372\pi$
$398$	−13.4026	−	20.6382i	−0.671813	−	1.03450i
$399$	−3.09833	+	1.48515i	−0.155111	+	0.0743504i
$400$	9.24132	−	8.20292i	0.462066	−	0.410146i
$401$	−11.9028	+	6.87210i	−0.594399	+	0.343176i	−0.766835	−	0.641844i	$-0.778169\pi$
$401$	−11.9028	+	6.87210i	−0.594399	+	0.343176i	0.172436	+	0.985021i	$0.444836\pi$
$402$	21.9134	−	11.9526i	1.09294	−	0.596143i
$403$	−3.40626	−	2.75833i	−0.169678	−	0.137402i
$404$	6.25603	−	4.54527i	0.311249	−	0.226136i
$405$	12.6000	−	15.6921i	0.626097	−	0.779745i
$406$	−1.64545	−	1.19549i	−0.0816626	−	0.0593313i
$407$	−8.15418	−	30.4318i	−0.404188	−	1.50845i
$408$	−2.36391	+	4.98066i	−0.117031	+	0.246579i
$409$	1.87611	+	8.82638i	0.0927674	+	0.436436i	0.999879	+	0.0155465i	$0.00494880\pi$
$409$	1.87611	+	8.82638i	0.0927674	+	0.436436i	−0.907112	+	0.420890i	$0.861718\pi$
$410$	−5.81828	−	0.0206451i	−0.287344	−	0.00101959i
$411$	19.8926	+	20.8819i	0.981230	+	1.03003i
$412$	0.00105551	−	0.0201404i	5.20014e−5	−	0.000992246i
$413$	4.74581	−	2.41811i	0.233526	−	0.118988i
$414$	−4.56756	−	5.59634i	−0.224483	−	0.275045i
$415$	−11.1894	+	4.93433i	−0.549264	+	0.242217i
$416$	−12.4726	+	11.2304i	−0.611521	+	0.550616i
$417$	0.814648	+	10.1028i	0.0398935	+	0.494734i
$418$	−15.9525	−	4.27445i	−0.780260	−	0.209070i
$419$	2.59078	−	24.6496i	0.126568	−	1.20421i	−0.728259	−	0.685302i	$-0.759670\pi$
$419$	2.59078	−	24.6496i	0.126568	−	1.20421i	0.854827	−	0.518913i	$-0.173663\pi$
$420$	−0.156926	+	1.17718i	−0.00765721	+	0.0574404i
$421$	−1.99467	−	18.9780i	−0.0972144	−	0.924934i	−0.929061	−	0.369927i	$-0.879383\pi$
$421$	−1.99467	−	18.9780i	−0.0972144	−	0.924934i	0.831846	−	0.555006i	$-0.187284\pi$
$422$	−0.178947	+	1.12983i	−0.00871101	+	0.0549992i
$423$	−3.81804	+	5.29780i	−0.185640	+	0.257588i
$424$		−	40.7848i		−	1.98069i
$425$	−0.773235	−	5.11677i	−0.0375074	−	0.248200i
$426$	−13.4528	−	28.0654i	−0.651790	−	1.35977i
$427$	0.552617	−	0.0289614i	0.0267430	−	0.00140154i
$428$	2.82982	+	7.37194i	0.136785	+	0.356336i
$429$	−0.925132	−	32.9116i	−0.0446658	−	1.58899i
$430$	−15.4046	+	0.752522i	−0.742877	+	0.0362898i
$431$	4.15662	−	5.72109i	0.200217	−	0.275575i	−0.697088	−	0.716985i	$-0.745522\pi$
$431$	4.15662	−	5.72109i	0.200217	−	0.275575i	0.897306	+	0.441410i	$0.145522\pi$
$432$	−12.8350	+	0.410176i	−0.617523	+	0.0197346i
$433$	−19.0459	+	3.01658i	−0.915289	+	0.144968i	−0.596273	−	0.802782i	$-0.703352\pi$
$433$	−19.0459	+	3.01658i	−0.915289	+	0.144968i	−0.319016	+	0.947749i	$0.603352\pi$
$434$	0.346751	+	0.385106i	0.0166446	+	0.0184857i
$435$	−1.64607	−	12.6622i	−0.0789229	−	0.607105i
$436$	5.64030	−	6.26419i	0.270121	−	0.300000i
$437$	−4.21695	+	6.49353i	−0.201724	+	0.310628i
$438$	5.56690	+	4.25465i	0.265997	+	0.203295i
$439$	5.98920	−	28.1770i	0.285849	−	1.34481i	−0.567458	−	0.823403i	$-0.692073\pi$
$439$	5.98920	−	28.1770i	0.285849	−	1.34481i	0.853306	−	0.521410i	$-0.174594\pi$
$440$	−18.6775	+	16.6976i	−0.890413	+	0.796029i
$441$	−11.0614	−	16.8905i	−0.526731	−	0.804309i
$442$	−1.00309	−	6.33325i	−0.0477120	−	0.301242i
$443$	10.6292	−	2.84808i	0.505007	−	0.135316i	0.00268407	−	0.999996i	$-0.499146\pi$
$443$	10.6292	−	2.84808i	0.505007	−	0.135316i	0.502323	+	0.864680i	$0.332479\pi$
$444$	−5.72826	+	6.73310i	−0.271851	+	0.319539i
$445$	−22.6483	−	11.6413i	−1.07363	−	0.551849i
$446$	−0.908377	+	2.04025i	−0.0430129	+	0.0966086i
$447$	0.100607	−	0.422635i	0.00475854	−	0.0199899i
$448$	3.81798	−	2.47943i	0.180383	−	0.117142i
$449$	−10.1447			−0.478756			−0.239378	−	0.970926i	$-0.576944\pi$
$449$	−10.1447			−0.478756			−0.239378	+	0.970926i	$0.576944\pi$
$450$	14.4429	−	10.4218i	0.680845	−	0.491288i
$451$	7.98352			0.375929
$452$	−2.77260	+	1.80055i	−0.130412	+	0.0846906i
$453$	−28.8546	+	8.60748i	−1.35571	+	0.404415i
$454$	−10.7648	+	24.1782i	−0.505218	+	1.13474i
$455$	−2.73295	−	5.41110i	−0.128123	−	0.253676i
$456$	6.82580	+	19.1583i	0.319647	+	0.897171i
$457$	−16.1787	+	4.33508i	−0.756809	+	0.202786i	−0.616536	−	0.787327i	$-0.711465\pi$
$457$	−16.1787	+	4.33508i	−0.756809	+	0.202786i	−0.140273	+	0.990113i	$0.544798\pi$
$458$	5.49717	+	34.7078i	0.256866	+	1.62179i
$459$	−2.78344	+	4.60152i	−0.129920	+	0.214781i
$460$	1.07982	+	2.44867i	0.0503470	+	0.114170i
$461$	3.40393	−	16.0142i	0.158537	−	0.745857i	−0.824998	−	0.565136i	$-0.808824\pi$
$461$	3.40393	−	16.0142i	0.158537	−	0.745857i	0.983534	−	0.180721i	$-0.0578430\pi$
$462$	−0.500681	+	3.86038i	−0.0232938	+	0.179601i
$463$	−15.4980	+	23.8648i	−0.720253	+	1.10909i	0.269037	+	0.963130i	$0.413295\pi$
$463$	−15.4980	+	23.8648i	−0.720253	+	1.10909i	−0.989290	+	0.145963i	$0.953372\pi$
$464$	−5.45190	+	6.05495i	−0.253098	+	0.281094i
$465$	−0.260525	+	3.24287i	−0.0120816	+	0.150384i
$466$	−17.8975	−	19.8772i	−0.829087	−	0.920794i
$467$	14.3112	−	2.26668i	0.662245	−	0.104889i	0.183741	−	0.982975i	$-0.441179\pi$
$467$	14.3112	−	2.26668i	0.662245	−	0.104889i	0.478504	+	0.878085i	$0.341179\pi$
$468$	−7.45304	+	5.45885i	−0.344517	+	0.252336i
$469$	−3.70667	+	5.10180i	−0.171158	+	0.235579i
$470$	−4.50425	+	3.62108i	−0.207766	+	0.167028i
$471$	−33.2899	+	20.4882i	−1.53392	+	0.944046i
$472$	−11.2987	−	29.4341i	−0.520064	−	1.35481i
$473$	21.1334	−	1.10756i	0.971716	−	0.0509255i
$474$	−18.7152	−	1.43673i	−0.859619	−	0.0659911i
$475$	−15.3641	−	11.3301i	−0.704953	−	0.519862i
$476$		−	0.317358i		−	0.0145461i
$477$	4.00641	−	39.5817i	0.183441	−	1.81232i
$478$	2.17909	−	13.7582i	0.0996691	−	0.629286i
$479$	0.522567	+	4.97189i	0.0238767	+	0.227171i	0.999953	+	0.00974125i	$0.00310079\pi$
$479$	0.522567	+	4.97189i	0.0238767	+	0.227171i	−0.976076	+	0.217430i	$0.930233\pi$
$480$	12.1087	+	2.92787i	0.552684	+	0.133638i
$481$	4.71681	−	44.8774i	0.215068	−	2.04623i
$482$	20.6959	+	5.54544i	0.942670	+	0.252588i
$483$	1.64871	+	0.782506i	0.0750188	+	0.0356053i
$484$	0.996378	−	0.897143i	0.0452899	−	0.0407792i
$485$	1.39099	+	13.7019i	0.0631615	+	0.622170i
$486$	−18.4652	−	1.27480i	−0.837598	−	0.0578259i
$487$	5.12953	−	2.61363i	0.232441	−	0.118435i	−0.333891	−	0.942612i	$-0.608362\pi$
$487$	5.12953	−	2.61363i	0.232441	−	0.118435i	0.566332	+	0.824177i	$0.308362\pi$
$488$	0.171431	−	3.27109i	0.00776030	−	0.148075i
$489$	8.92048	−	30.3290i	0.403398	−	1.37152i
$490$	−5.46131	−	17.0134i	−0.246717	−	0.768586i
$491$	−1.17754	−	5.53987i	−0.0531415	−	0.250011i	0.943556	−	0.331212i	$-0.107458\pi$
$491$	−1.17754	−	5.53987i	−0.0531415	−	0.250011i	−0.996698	+	0.0812014i	$0.974124\pi$
$492$	−1.27236	−	1.84369i	−0.0573622	−	0.0831198i
$493$	0.883135	+	3.29590i	0.0397744	+	0.148440i
$494$	−19.1369	−	13.9037i	−0.861008	−	0.625559i
$495$	−19.7668	+	14.3703i	−0.888450	+	0.645899i
$496$	1.67947	−	1.22021i	0.0754106	−	0.0547890i
$497$	6.11061	+	4.94827i	0.274098	+	0.221960i
$498$	9.60124	+	5.85829i	0.430242	+	0.262516i
$499$	7.79783	−	4.50208i	0.349079	−	0.201541i	−0.315201	−	0.949025i	$-0.602072\pi$
$499$	7.79783	−	4.50208i	0.349079	−	0.201541i	0.664279	+	0.747484i	$0.268738\pi$
$500$	−6.18488	+	2.29892i	−0.276596	+	0.102811i
$501$	0.860162	−	11.2047i	0.0384292	−	0.500590i
$502$	9.33505	+	14.3747i	0.416644	+	0.641575i
$503$	27.7817	+	4.40020i	1.23873	+	0.196195i	0.741218	−	0.671264i	$-0.234248\pi$
$503$	27.7817	+	4.40020i	1.23873	+	0.196195i	0.497509	+	0.867459i	$0.334248\pi$
$504$	4.26287	−	2.19273i	0.189883	−	0.0976717i
$505$	28.3271	−	7.48259i	1.26054	−	0.332971i
$506$	3.56793	+	8.01369i	0.158614	+	0.356252i
$507$	8.18058	−	23.2431i	0.363312	−	1.03226i
$508$	5.52656	+	6.82473i	0.245201	+	0.302798i
$509$	4.06044	−	0.863074i	0.179976	−	0.0382551i	−0.117042	−	0.993127i	$-0.537341\pi$
$509$	4.06044	−	0.863074i	0.179976	−	0.0382551i	0.297018	+	0.954872i	$0.404008\pi$
$510$	−3.45771	+	3.27058i	−0.153110	+	0.144824i
$511$	−1.73145	−	0.368032i	−0.0765950	−	0.0162808i
$512$	−10.5101	−	20.6272i	−0.464483	−	0.911600i
$513$	4.74247	+	19.2637i	0.209385	+	0.850514i
$514$	−9.37741	+	3.04690i	−0.413620	+	0.134393i
$515$	0.0313277	−	0.0696966i	0.00138046	−	0.00307120i
$516$	−3.62387	−	4.70396i	−0.159532	−	0.207080i
$517$	6.16277	−	4.99051i	0.271038	−	0.219483i
$518$	−1.38083	+	5.15334i	−0.0606704	+	0.226425i
$519$	−6.36849	+	34.7338i	−0.279546	+	1.52464i
$520$	−33.5453	+	12.7404i	−1.47106	+	0.558705i
$521$	−2.57762	−	3.54779i	−0.112928	−	0.155432i	0.748812	−	0.662783i	$-0.230625\pi$
$521$	−2.57762	−	3.54779i	−0.112928	−	0.155432i	−0.861739	+	0.507351i	$0.830625\pi$
$522$	−8.69703	+	7.89159i	−0.380658	+	0.345406i
$523$	6.22141	+	3.16996i	0.272043	+	0.138613i	0.584691	−	0.811256i	$-0.301216\pi$
$523$	6.22141	+	3.16996i	0.272043	+	0.138613i	−0.312648	+	0.949869i	$0.601216\pi$
$524$	−2.48727	+	4.30808i	−0.108657	+	0.188199i
$525$	−2.16745	+	3.94316i	−0.0945955	+	0.172094i
$526$	−5.63545	−	9.76088i	−0.245717	−	0.425595i
$527$	−0.0454998	−	0.868188i	−0.00198200	−	0.0378189i
$528$	15.1702	+	3.61122i	0.660199	+	0.157158i
$529$	−18.7840	+	1.97428i	−0.816696	+	0.0858382i
$530$	12.7344	−	32.8256i	0.553146	−	1.42585i
$531$	−8.07399	−	29.6757i	−0.350381	−	1.28782i
$532$	−0.827831	−	0.827831i	−0.0358910	−	0.0358910i
$533$	10.6752	+	4.09782i	0.462394	+	0.177496i
$534$	3.10166	+	23.2145i	0.134222	+	1.00459i
$535$	−0.106159	+	29.9181i	−0.00458965	+	1.29347i
$536$	27.7401	+	24.9773i	1.19819	+	1.07885i
$537$	26.2354	+	3.40266i	1.13214	+	0.146836i
$538$	−7.78166	−	0.407819i	−0.335491	−	0.0175823i
$539$	7.57645	+	23.3179i	0.326341	+	1.00437i
$540$	6.46892	+	2.27463i	0.278378	+	0.0978843i
$541$	−1.97652	+	6.08311i	−0.0849774	+	0.261533i	−0.984512	−	0.175315i	$-0.943906\pi$
$541$	−1.97652	+	6.08311i	−0.0849774	+	0.261533i	0.899535	+	0.436849i	$0.143906\pi$
$542$	−9.20438	+	23.9782i	−0.395362	+	1.02995i
$543$	1.08054	+	5.76818i	0.0463705	+	0.247536i
$544$	−3.31080	−	0.347979i	−0.141950	−	0.0149195i
$545$	28.5076	−	14.3982i	1.22113	−	0.616750i
$546$	−2.65096	+	4.90492i	−0.113451	+	0.209911i
$547$	−14.0670	+	17.3713i	−0.601463	+	0.742745i	−0.983401	−	0.181443i	$-0.941923\pi$
$547$	−14.0670	+	17.3713i	−0.601463	+	0.742745i	0.381939	+	0.924188i	$0.375257\pi$
$548$	−4.46134	+	8.75588i	−0.190579	+	0.374033i
$549$	0.487703	−	3.15776i	0.0208146	−	0.134770i
$550$	−20.2461	+	7.60733i	−0.863295	+	0.324378i
$551$	10.9010	+	6.29372i	0.464400	+	0.268122i
$552$	5.62660	−	9.22153i	0.239484	−	0.392494i
$553$	4.42713	−	1.69942i	0.188261	−	0.0722665i
$554$	16.6267	+	7.40269i	0.706401	+	0.314510i
$555$	−29.4609	+	15.9340i	−1.25055	+	0.676360i
$556$	−3.15497	+	1.40468i	−0.133800	+	0.0595718i
$557$	12.9165	−	12.9165i	0.547288	−	0.547288i	−0.378367	−	0.925656i	$-0.623514\pi$
$557$	12.9165	−	12.9165i	0.547288	−	0.547288i	0.925656	+	0.378367i	$0.123514\pi$
$558$	2.58552	−	1.50603i	0.109454	−	0.0637554i
$559$	28.8271	+	9.36650i	1.21926	+	0.396161i
$560$	2.81056	−	0.586987i	0.118768	−	0.0248047i
$561$	4.72850	−	4.50448i	0.199637	−	0.190179i
$562$	12.4901	+	8.11116i	0.526863	+	0.342149i
$563$	−1.28460	−	0.834227i	−0.0541393	−	0.0351585i	0.517286	−	0.855813i	$-0.326942\pi$
$563$	−1.28460	−	0.834227i	−0.0541393	−	0.0351585i	−0.571425	+	0.820654i	$0.693609\pi$
$564$	−2.13467	−	0.627857i	−0.0898858	−	0.0264375i
$565$	−12.2612	+	2.56075i	−0.515831	+	0.107732i
$566$	9.53558	+	3.09830i	0.400810	+	0.130231i
$567$	4.35252	−	1.70929i	0.182789	−	0.0717834i
$568$	32.9106	−	32.9106i	1.38090	−	1.38090i
$569$	−19.6977	+	8.76996i	−0.825769	+	0.367656i	−0.775709	−	0.631090i	$-0.782608\pi$
$569$	−19.6977	+	8.76996i	−0.825769	+	0.367656i	−0.0500595	+	0.998746i	$0.515941\pi$
$570$	−0.488142	+	17.5508i	−0.0204460	+	0.735121i
$571$	−27.0104	−	12.0258i	−1.13035	−	0.503263i	−0.245618	−	0.969367i	$-0.578991\pi$
$571$	−27.0104	−	12.0258i	−1.13035	−	0.503263i	−0.884730	+	0.466103i	$0.845657\pi$
$572$	10.4734	−	4.02038i	0.437917	−	0.168101i
$573$	−4.66788	−	0.113254i	−0.195004	−	0.00473126i
$574$	−1.17081	−	0.675967i	−0.0488686	−	0.0282143i
$575$	0.458798	+	10.1293i	0.0191332	+	0.422421i
$576$	−9.51425	−	24.5035i	−0.396427	−	1.02098i
$577$	8.18599	−	16.0659i	0.340787	−	0.668832i	−0.655475	−	0.755217i	$-0.727531\pi$
$577$	8.18599	−	16.0659i	0.340787	−	0.668832i	0.996262	+	0.0863848i	$0.0275314\pi$
$578$	−11.9025	+	14.6984i	−0.495080	+	0.611372i
$579$	−19.4944	−	31.6752i	−0.810161	−	1.31638i
$580$	3.88354	−	1.96144i	0.161255	−	0.0814442i
$581$	−2.82595	−	0.297020i	−0.117240	−	0.0123225i
$582$	9.61604	−	8.24489i	0.398598	−	0.341762i
$583$	−17.3134	+	45.1029i	−0.717046	+	1.86797i
$584$	−3.23785	+	9.96509i	−0.133983	+	0.412358i
$585$	−33.8073	+	9.06937i	−1.39776	+	0.374972i
$586$	3.95935	+	12.1856i	0.163559	+	0.503384i
$587$	−4.06898	−	0.213246i	−0.167945	−	0.00880161i	−0.0318218	−	0.999494i	$-0.510131\pi$
$587$	−4.06898	−	0.213246i	−0.167945	−	0.00880161i	−0.136123	+	0.990692i	$0.543464\pi$
$588$	4.17748	−	5.46592i	0.172276	−	0.225411i
$589$	−2.38336	−	2.14599i	−0.0982046	−	0.0884238i
$590$	0.0965772	−	27.2177i	0.00397602	−	1.12054i
$591$	−30.8169	+	23.7409i	−1.26764	+	0.976569i
$592$	19.9529	+	7.65920i	0.820059	+	0.314791i
$593$	20.3883	+	20.3883i	0.837248	+	0.837248i	0.988496	−	0.151247i	$-0.0483290\pi$
$593$	20.3883	+	20.3883i	0.837248	+	0.837248i	−0.151247	+	0.988496i	$0.548329\pi$
$594$	21.2303	+	7.38053i	0.871088	+	0.302827i
$595$	0.434890	−	1.12102i	0.0178288	−	0.0459574i
$596$	0.147220	−	0.0154734i	0.00603035	−	0.000633816i
$597$	24.6598	−	26.0863i	1.00926	−	1.06764i
$598$	0.657555	+	12.5469i	0.0268894	+	0.513081i
$599$	−17.8913	−	30.9886i	−0.731018	−	1.26616i	−0.956449	−	0.291901i	$-0.905712\pi$
$599$	−17.8913	−	30.9886i	−0.731018	−	1.26616i	0.225431	−	0.974259i	$-0.427621\pi$
$600$	21.8717	+	15.1992i	0.892909	+	0.620506i
$601$	7.24440	−	12.5477i	0.295505	−	0.511830i	−0.679597	−	0.733586i	$-0.737845\pi$
$601$	7.24440	−	12.5477i	0.295505	−	0.511830i	0.975102	+	0.221756i	$0.0711787\pi$
$602$	−3.19306	−	1.62695i	−0.130140	−	0.0663094i
$603$	24.4682	+	26.9655i	0.996422	+	1.09812i
$604$	−6.03062	−	8.30044i	−0.245383	−	0.337740i
$605$	4.74895	−	1.80364i	0.193072	−	0.0733286i
$606$	−20.5241	−	17.4611i	−0.833735	−	0.709309i
$607$	0.471143	−	1.75833i	0.0191231	−	0.0713684i	−0.955705	−	0.294327i	$-0.904905\pi$
$607$	0.471143	−	1.75833i	0.0191231	−	0.0713684i	0.974828	+	0.222958i	$0.0715713\pi$
$608$	−9.54395	+	7.72854i	−0.387058	+	0.313434i
$609$	1.13012	−	2.74325i	0.0457948	−	0.111162i
$610$	1.15932	−	2.57920i	0.0469394	−	0.104429i
$611$	10.8021	−	3.50982i	0.437007	−	0.141992i
$612$	−1.79384	−	0.374091i	−0.0725118	−	0.0151217i
$613$	−7.51388	−	14.7468i	−0.303483	−	0.595619i	0.688022	−	0.725690i	$-0.258479\pi$
$613$	−7.51388	−	14.7468i	−0.303483	−	0.595619i	−0.991505	+	0.130071i	$0.958479\pi$
$614$	17.9808	+	3.82194i	0.725646	+	0.154241i
$615$	−1.96792	−	8.25611i	−0.0793543	−	0.332918i
$616$	−5.69409	+	1.21032i	−0.229421	+	0.0487650i
$617$	−11.5221	−	14.2286i	−0.463863	−	0.572823i	0.490512	−	0.871434i	$-0.336810\pi$
$617$	−11.5221	−	14.2286i	−0.463863	−	0.572823i	−0.954375	+	0.298612i	$0.903476\pi$
$618$	−0.0690780	+	0.0129403i	−0.00277873	+	0.000520533i
$619$	−1.36804	−	3.07266i	−0.0549861	−	0.123501i	0.883963	−	0.467557i	$-0.154866\pi$
$619$	−1.36804	−	3.07266i	−0.0549861	−	0.123501i	−0.938949	+	0.344056i	$0.888199\pi$
$620$	−1.07176	+	0.283105i	−0.0430429	+	0.0113698i
$621$	6.36648	−	8.39679i	0.255478	−	0.336951i
$622$	−25.0846	−	3.97300i	−1.00580	−	0.159303i
$623$	−3.22262	−	4.96240i	−0.129112	−	0.198815i
$624$	18.4313	+	12.6154i	0.737844	+	0.505020i
$625$	−24.9975	−	0.354818i	−0.999899	−	0.0141927i
$626$	14.7281	−	8.50325i	0.588652	−	0.339858i
$627$	0.584342	−	24.0843i	0.0233364	−	0.961833i
$628$	−10.3509	−	8.38202i	−0.413047	−	0.334479i
$629$	7.24112	−	5.26098i	0.288722	−	0.209769i
$630$	4.11560	−	0.433800i	0.163969	−	0.0172830i
$631$	35.4540	+	25.7589i	1.41140	+	1.02544i	0.993117	+	0.117130i	$0.0373693\pi$
$631$	35.4540	+	25.7589i	1.41140	+	1.02544i	0.418287	+	0.908315i	$0.362631\pi$
$632$	−7.26500	−	27.1133i	−0.288986	−	1.07851i
$633$	−1.66327	+	0.134120i	−0.0661090	+	0.00533078i
$634$	0.856586	+	4.02992i	0.0340194	+	0.160049i
$635$	10.1695	+	31.6806i	0.403565	+	1.25721i
$636$	13.1752	−	3.18988i	0.522429	−	0.126487i
$637$	−1.83786	+	35.0685i	−0.0728187	+	1.38946i
$638$	12.7067	−	6.47436i	0.503061	−	0.256323i
$639$	35.1727	−	28.7068i	1.39141	−	1.13563i
$640$	−0.896693	−	8.83284i	−0.0354449	−	0.349149i
$641$	5.84428	−	5.26222i	0.230835	−	0.207845i	−0.545594	−	0.838050i	$-0.683696\pi$
$641$	5.84428	−	5.26222i	0.230835	−	0.207845i	0.776429	+	0.630205i	$0.217029\pi$
$642$	22.6472	−	15.6292i	0.893814	−	0.616834i
$643$	6.97039	+	1.86771i	0.274885	+	0.0736553i	0.393628	−	0.919270i	$-0.371220\pi$
$643$	6.97039	+	1.86771i	0.274885	+	0.0736553i	−0.118743	+	0.992925i	$0.537886\pi$
$644$	−0.0649995	+	0.618429i	−0.00256134	+	0.0243695i
$645$	−6.35473	−	21.5820i	−0.250217	−	0.849790i
$646$	−0.490436	−	4.66618i	−0.0192959	−	0.183589i
$647$	−4.82885	+	30.4881i	−0.189842	+	1.19861i	0.690165	+	0.723652i	$0.257538\pi$
$647$	−4.82885	+	30.4881i	−0.189842	+	1.19861i	−0.880007	+	0.474961i	$0.842462\pi$
$648$	−7.36928	−	26.6802i	−0.289493	−	1.04810i
$649$			37.3467i			1.46598i
$650$	−30.9768	−	0.219834i	−1.21501	−	0.00862259i
$651$	−0.426968	+	0.623807i	−0.0167342	+	0.0244489i
$652$	10.7571	−	0.563758i	0.421282	−	0.0220785i
$653$	4.76328	+	12.4088i	0.186401	+	0.485592i	0.994656	−	0.103240i	$-0.0329211\pi$
$653$	4.76328	+	12.4088i	0.186401	+	0.485592i	−0.808255	+	0.588833i	$0.799588\pi$
$654$	−25.8409	−	13.9662i	−1.01046	−	0.546122i
$655$	−14.6895	+	11.8092i	−0.573965	+	0.461425i
$656$	−3.18334	+	4.38149i	−0.124289	+	0.171069i
$657$	−4.12124	+	9.35307i	−0.160785	+	0.364898i
$658$	−1.32634	+	0.210071i	−0.0517061	+	0.00818944i
$659$	21.3480	+	23.7094i	0.831601	+	0.923586i	0.998047	−	0.0624645i	$-0.0198960\pi$
$659$	21.3480	+	23.7094i	0.831601	+	0.923586i	−0.166447	+	0.986050i	$0.553229\pi$
$660$	−6.85483	−	4.72762i	−0.266824	−	0.184022i
$661$	−13.9762	+	15.5222i	−0.543612	+	0.603742i	−0.950877	−	0.309568i	$-0.899816\pi$
$661$	−13.9762	+	15.5222i	−0.543612	+	0.603742i	0.407266	+	0.913310i	$0.366482\pi$
$662$	9.90337	−	15.2499i	0.384906	−	0.592702i
$663$	8.63481	−	3.59612i	0.335348	−	0.139662i
$664$	−3.49702	+	16.4522i	−0.135711	+	0.638469i
$665$	−1.78978	−	4.05860i	−0.0694046	−	0.157386i
$666$	27.5012	+	13.8796i	1.06565	+	0.537824i
$667$	−1.04590	−	6.60353i	−0.0404973	−	0.255690i
$668$	3.69861	−	0.991040i	0.143104	−	0.0383445i
$669$	−3.20443	−	0.587536i	−0.123890	−	0.0227155i
$670$	14.5278	+	28.7643i	0.561258	+	1.11126i
$671$	−1.57817	+	3.54464i	−0.0609248	+	0.136839i
$672$	2.10352	+	1.98850i	0.0811451	+	0.0767079i
$673$	−3.58198	+	2.32617i	−0.138075	+	0.0896672i	−0.611828	−	0.790991i	$-0.709566\pi$
$673$	−3.58198	+	2.32617i	−0.138075	+	0.0896672i	0.473753	+	0.880658i	$0.342899\pi$
$674$	−26.7921			−1.03199
$675$	19.7335	+	16.8994i	0.759542	+	0.650459i
$676$	8.39598			0.322922
$677$	0.318278	−	0.206692i	0.0122324	−	0.00794381i	−0.538508	−	0.842620i	$-0.681012\pi$
$677$	0.318278	−	0.206692i	0.0122324	−	0.00794381i	0.550741	+	0.834676i	$0.314345\pi$
$678$	8.37171	+	7.91393i	0.321514	+	0.303933i
$679$	−1.30160	+	2.92344i	−0.0499508	+	0.112191i
$680$	−6.33020	−	3.25374i	−0.242752	−	0.124775i
$681$	−37.9744	−	6.96266i	−1.45518	−	0.266810i
$682$	−3.50972	+	0.940427i	−0.134394	+	0.0360108i
$683$	−1.95353	−	12.3341i	−0.0747497	−	0.471951i	−0.996460	−	0.0840713i	$-0.973208\pi$
$683$	−1.95353	−	12.3341i	−0.0747497	−	0.471951i	0.921710	−	0.387880i	$-0.126792\pi$
$684$	−5.65506	+	3.70343i	−0.216227	+	0.141604i
$685$	−27.7576	+	24.8153i	−1.06056	+	0.948143i
$686$	1.76107	−	8.28519i	0.0672381	−	0.316330i
$687$	−47.3209	+	19.7076i	−1.80540	+	0.751892i
$688$	−7.81888	+	12.0400i	−0.298092	+	0.459021i
$689$	−46.3012	+	51.4227i	−1.76394	+	1.95905i
$690$	7.40782	−	5.66511i	0.282011	−	0.215667i
$691$	17.1043	+	18.9962i	0.650676	+	0.722649i	0.974729	−	0.223390i	$-0.0717122\pi$
$691$	17.1043	+	18.9962i	0.650676	+	0.722649i	−0.324053	+	0.946039i	$0.605046\pi$
$692$	−11.8842	+	1.88227i	−0.451769	+	0.0715532i
$693$	−5.64502	+	0.615266i	−0.214436	+	0.0233720i
$694$	4.27779	−	5.88787i	0.162383	−	0.223501i
$695$	−13.0694	+	0.638443i	−0.495749	+	0.0242175i
$696$	−15.4499	−	8.35019i	−0.585626	−	0.316513i
$697$	0.812807	+	2.11743i	0.0307873	+	0.0802035i
$698$	29.5250	−	1.54734i	1.11754	−	0.0585676i
$699$	22.0379	−	32.1978i	0.833550	−	1.21783i
$700$	−1.51256	−	0.250581i	−0.0571693	−	0.00947109i
$701$			2.53613i			0.0957882i	0.998852	+	0.0478941i	$0.0152510\pi$
$701$			2.53613i			0.0957882i	−0.998852	+	0.0478941i	$0.984749\pi$
$702$	24.5998	+	20.7661i	0.928460	+	0.783765i
$703$	5.16520	−	32.6118i	0.194809	−	1.22998i
$704$	3.33656	+	31.7452i	0.125751	+	1.19644i
$705$	−6.68002	−	5.14304i	−0.251584	−	0.193698i
$706$	1.48622	−	14.1404i	0.0559345	−	0.532181i
$707$	6.57582	+	1.76199i	0.247309	+	0.0662663i
$708$	8.62471	−	5.95204i	0.324136	−	0.223691i
$709$	31.8410	−	28.6698i	1.19581	−	1.07672i	0.200532	−	0.979687i	$-0.435733\pi$
$709$	31.8410	−	28.6698i	1.19581	−	1.07672i	0.995282	−	0.0970287i	$-0.0309339\pi$
$710$	36.7638	−	16.2122i	1.37972	−	0.608434i
$711$	−4.38727	−	27.0272i	−0.164535	−	1.01360i
$712$	−31.2069	+	15.9007i	−1.16953	+	0.595904i
$713$	−0.0891528	+	1.70114i	−0.00333880	+	0.0637081i
$714$	−1.07485	+	0.260234i	−0.0402251	+	0.00973900i
$715$	42.5052	+	0.150822i	1.58960	+	0.00564042i
$716$	1.87416	+	8.81722i	0.0700406	+	0.329515i
$717$	20.2541	−	1.63321i	0.756401	−	0.0609933i
$718$	0.488772	+	1.82412i	0.0182408	+	0.0680756i
$719$	−19.7220	−	14.3289i	−0.735508	−	0.534378i	0.155793	−	0.987790i	$-0.450207\pi$
$719$	−19.7220	−	14.3289i	−0.735508	−	0.534378i	−0.891301	+	0.453412i	$0.850207\pi$
$720$	−0.00491166	−	16.5784i	−0.000183047	−	0.617839i
$721$	0.0143644	−	0.0104363i	0.000534957	−	0.000388669i
$722$	4.08125	+	3.30493i	0.151888	+	0.122997i
$723$	−0.758094	+	31.2456i	−0.0281938	+	1.16204i
$724$	−1.73171	+	0.999805i	−0.0643586	+	0.0371575i
$725$	16.4059	−	1.60670i	0.609299	−	0.0596713i
$726$	−3.85552	−	2.63893i	−0.143092	−	0.0979397i
$727$	1.97225	+	3.03699i	0.0731466	+	0.112636i	0.873351	−	0.487092i	$-0.161942\pi$
$727$	1.97225	+	3.03699i	0.0731466	+	0.112636i	−0.800204	+	0.599728i	$0.795276\pi$
$728$	−8.23511	−	1.30431i	−0.305213	−	0.0483411i
$729$	−4.53102	−	26.6171i	−0.167816	−	0.985818i
$730$	−5.71741	+	7.00941i	−0.211611	+	0.259430i
$731$	2.44536	+	5.49237i	0.0904449	+	0.203142i
$732$	1.07010	−	0.200461i	0.0395522	−	0.00740923i
$733$	−16.1433	−	19.9354i	−0.596268	−	0.736329i	0.386271	−	0.922385i	$-0.373763\pi$
$733$	−16.1433	−	19.9354i	−0.596268	−	0.736329i	−0.982539	+	0.186056i	$0.940429\pi$
$734$	14.2142	−	3.02133i	0.524656	−	0.111519i
$735$	22.2465	−	13.5830i	0.820574	−	0.501015i
$736$	6.38041	+	1.35620i	0.235185	+	0.0499901i
$737$	−20.0740	−	39.3975i	−0.739436	−	1.45122i
$738$	−5.20096	+	5.82110i	−0.191450	+	0.214278i
$739$	−29.9562	+	9.73335i	−1.10196	+	0.358047i	−0.802855	−	0.596175i	$-0.796687\pi$
$739$	−29.9562	+	9.73335i	−1.10196	+	0.358047i	−0.299101	+	0.954222i	$0.596687\pi$
$740$	−8.45402	−	7.66652i	−0.310776	−	0.281827i
$741$	13.1435	−	31.9044i	0.482837	−	1.17204i
$742$	6.35793	−	5.14855i	0.233407	−	0.189009i
$743$	2.34408	−	8.74824i	0.0859961	−	0.320942i	−0.909505	−	0.415693i	$-0.863539\pi$
$743$	2.34408	−	8.74824i	0.0859961	−	0.320942i	0.995501	+	0.0947515i	$0.0302056\pi$
$744$	3.40808	+	2.89946i	0.124946	+	0.106300i
$745$	0.541236	+	0.147084i	0.0198293	+	0.00538874i
$746$	4.02352	+	5.53790i	0.147311	+	0.202757i
$747$	−5.01001	+	15.6233i	−0.183307	+	0.571628i
$748$	1.98268	+	1.01023i	0.0724940	+	0.0369375i
$749$	−3.47588	+	6.02041i	−0.127006	+	0.219981i
$750$	12.8577	+	19.0621i	0.469497	+	0.696051i
$751$	10.7556	+	18.6292i	0.392476	+	0.679788i	0.992775	−	0.119987i	$-0.0382853\pi$
$751$	10.7556	+	18.6292i	0.392476	+	0.679788i	−0.600300	+	0.799775i	$0.704952\pi$
$752$	0.281542	+	5.37215i	0.0102668	+	0.195902i
$753$	−17.1758	+	18.1693i	−0.625920	+	0.662126i
$754$	20.3139	−	2.13508i	0.739790	−	0.0777551i
$755$	−9.92783	−	37.5841i	−0.361311	−	1.36783i
$756$	1.04175	+	1.20558i	0.0378880	+	0.0438466i
$757$	16.0153	+	16.0153i	0.582086	+	0.582086i	0.935476	−	0.353390i	$-0.114971\pi$
$757$	16.0153	+	16.0153i	0.582086	+	0.582086i	−0.353390	+	0.935476i	$0.614971\pi$
$758$	35.6489	+	13.6843i	1.29483	+	0.497037i
$759$	−10.1369	+	7.80931i	−0.367946	+	0.283460i
$760$	−24.9998	+	8.02496i	−0.906837	+	0.291096i
$761$	−10.9434	−	9.85349i	−0.396698	−	0.357189i	0.446507	−	0.894780i	$-0.352668\pi$
$761$	−10.9434	−	9.85349i	−0.396698	−	0.357189i	−0.843206	+	0.537591i	$0.819334\pi$
$762$	18.5826	−	24.3139i	0.673175	−	0.880799i
$763$	7.41073	+	0.388380i	0.268286	+	0.0140603i
$764$	−0.491641	−	1.51311i	−0.0177869	−	0.0547425i
$765$	−5.82385	−	3.77960i	−0.210562	−	0.136652i
$766$	8.61943	−	26.5279i	0.311433	−	0.958491i
$767$	−19.1695	+	49.9382i	−0.692170	+	1.80316i
$768$	16.8431	−	14.4415i	0.607773	−	0.521111i
$769$	29.9321	+	3.14599i	1.07938	+	0.113447i	0.627488	−	0.778626i	$-0.284083\pi$
$769$	29.9321	+	3.14599i	1.07938	+	0.113447i	0.451890	+	0.892074i	$0.350750\pi$
$770$	−4.96077	−	0.803764i	−0.178774	−	0.0289656i
$771$	−7.53873	−	12.2492i	−0.271501	−	0.441143i
$772$	7.97546	−	9.84887i	0.287043	−	0.354469i
$773$	−7.24319	+	14.2156i	−0.260519	+	0.511298i	−0.983803	−	0.179253i	$-0.942632\pi$
$773$	−7.24319	+	14.2156i	−0.260519	+	0.511298i	0.723284	+	0.690551i	$0.242632\pi$
$774$	−12.9600	+	16.1307i	−0.465839	+	0.579807i
$775$	−4.17378	−	0.468652i	−0.149927	−	0.0168345i
$776$	16.4045	+	9.47115i	0.588888	+	0.339995i
$777$	−7.78028	−	0.188768i	−0.279116	−	0.00677202i
$778$	−3.50842	+	1.34676i	−0.125783	+	0.0482836i
$779$	7.64355	+	3.40313i	0.273859	+	0.121930i
$780$	−6.73934	−	9.84003i	−0.241307	−	0.352330i
$781$	−50.3656	+	22.4242i	−1.80222	+	0.802401i
$782$	−1.76218	+	1.76218i	−0.0630156	+	0.0630156i
$783$	−14.1739	−	9.62155i	−0.506533	−	0.343846i
$784$	−15.8183	−	5.13967i	−0.564939	−	0.183560i
$785$	−25.0769	−	43.7925i	−0.895032	−	1.56302i
$786$	16.6304	+	4.89139i	0.593186	+	0.174470i
$787$	28.9044	+	18.7708i	1.03033	+	0.669105i	0.944940	−	0.327242i	$-0.106119\pi$
$787$	28.9044	+	18.7708i	1.03033	+	0.669105i	0.0853913	+	0.996347i	$0.472786\pi$
$788$	−11.1166	−	7.21921i	−0.396013	−	0.257174i
$789$	11.9043	−	11.3403i	0.423805	−	0.403727i
$790$	2.61847	−	24.0905i	0.0931609	−	0.857101i
$791$	−2.76801	−	0.899380i	−0.0984190	−	0.0319783i
$792$	0.129224	+	33.6120i	0.00459179	+	1.19435i
$793$	−3.92967	+	3.92967i	−0.139547	+	0.139547i
$794$	15.9915	−	7.11988i	0.567518	−	0.252675i
$795$	50.9105	+	6.78673i	1.80561	+	0.240701i
$796$	11.1739	+	4.97496i	0.396050	+	0.176333i
$797$	−6.34369	+	2.43511i	−0.224705	+	0.0862561i	−0.468116	−	0.883667i	$-0.655067\pi$
$797$	−6.34369	+	2.43511i	−0.224705	+	0.0862561i	0.243411	+	0.969923i	$0.421734\pi$
$798$	−2.12492	+	3.48256i	−0.0752213	+	0.123281i
$799$	1.95105	+	1.12644i	0.0690231	+	0.0398505i
$800$	−4.27266	+	15.5048i	−0.151061	+	0.548178i
$801$	−31.8483	+	12.3661i	−1.12530	+	0.436935i
$802$	−7.40883	+	14.5406i	−0.261615	+	0.513448i
$803$	7.81089	−	9.64564i	0.275640	−	0.340387i
$804$	−5.89906	+	10.9147i	−0.208044	+	0.384932i
$805$	−1.07706	+	2.09544i	−0.0379614	+	0.0738544i
$806$	−5.17574	−	0.543992i	−0.182308	−	0.0191613i
$807$	−2.09295	−	11.1726i	−0.0736753	−	0.393296i
$808$	14.4412	−	37.6207i	0.508041	−	1.32349i
$809$	−12.8231	+	39.4654i	−0.450836	+	1.38753i	0.425120	+	0.905137i	$0.360232\pi$
$809$	−12.8231	+	39.4654i	−0.450836	+	1.38753i	−0.875955	+	0.482392i	$0.839768\pi$
$810$	2.39930	−	23.7744i	0.0843029	−	0.835349i
$811$	−3.67505	−	11.3106i	−0.129048	−	0.397170i	0.865568	−	0.500791i	$-0.166957\pi$
$811$	−3.67505	−	11.3106i	−0.129048	−	0.397170i	−0.994617	+	0.103620i	$0.966957\pi$
$812$	1.00955	+	0.0529083i	0.0354283	+	0.00185672i
$813$	−37.1553	−	4.81894i	−1.30309	−	0.169008i
$814$	−27.7997	−	25.0310i	−0.974381	−	0.877336i
$815$	38.7705	+	12.7496i	1.35807	+	0.446598i
$816$	0.586701	+	4.39119i	0.0205386	+	0.153722i
$817$	20.7056	+	7.94813i	0.724397	+	0.278070i
$818$	7.57611	+	7.57611i	0.264893	+	0.264893i
$819$	−7.86406	−	2.07480i	−0.274792	−	0.0724993i
$820$	2.43098	−	1.56646i	0.0848934	−	0.0547031i
$821$	29.6130	−	3.11245i	1.03350	−	0.108625i	0.427441	−	0.904043i	$-0.359415\pi$
$821$	29.6130	−	3.11245i	1.03350	−	0.108625i	0.606061	+	0.795418i	$0.292749\pi$
$822$	33.3131	+	7.93008i	1.16193	+	0.276593i
$823$	−2.86402	−	54.6488i	−0.0998336	−	1.90494i	−0.350021	−	0.936742i	$-0.613826\pi$
$823$	−2.86402	−	54.6488i	−0.0998336	−	1.90494i	0.250188	−	0.968197i	$-0.419508\pi$
$824$	−0.0525493	−	0.0910181i	−0.00183064	−	0.00317077i
$825$	−17.7352	−	26.0931i	−0.617460	−	0.908445i
$826$	3.16215	−	5.47701i	0.110025	−	0.190570i
$827$	−28.9400	−	14.7457i	−1.00634	−	0.512758i	−0.128502	−	0.991709i	$-0.541017\pi$
$827$	−28.9400	−	14.7457i	−1.00634	−	0.512758i	−0.877841	+	0.478951i	$0.841017\pi$
$828$	3.41900	+	1.09639i	0.118818	+	0.0381020i
$829$	6.13705	+	8.44692i	0.213148	+	0.293374i	0.902182	−	0.431356i	$-0.141965\pi$
$829$	6.13705	+	8.44692i	0.213148	+	0.293374i	−0.689033	+	0.724730i	$0.741965\pi$
$830$	−7.95148	+	12.1496i	−0.276000	+	0.421719i
$831$	−4.78804	+	26.1140i	−0.166095	+	0.905885i
$832$	−11.8329	+	44.1609i	−0.410231	+	1.53100i
$833$	−5.41314	+	4.38348i	−0.187554	+	0.151878i
$834$	7.34452	+	9.53356i	0.254320	+	0.330120i
$835$	14.4229	+	1.56766i	0.499123	+	0.0542513i
$836$	7.80702	−	2.53665i	0.270011	−	0.0877320i
$837$	3.02272	+	3.14872i	0.104481	+	0.108836i
$838$	−13.3606	−	26.2217i	−0.461535	−	0.905813i
$839$	31.0962	+	6.60971i	1.07356	+	0.228192i	0.710589	−	0.703608i	$-0.248429\pi$
$839$	31.0962	+	6.60971i	1.07356	+	0.228192i	0.362972	+	0.931800i	$0.381762\pi$
$840$	2.65522	+	5.59017i	0.0916139	+	0.192879i
$841$	17.7344	−	3.76957i	0.611532	−	0.129985i
$842$	−14.2591	−	17.6085i	−0.491401	−	0.606830i
$843$	−7.21244	+	20.4924i	−0.248410	+	0.705796i
$844$	−0.231260	−	0.519419i	−0.00796030	−	0.0178791i
$845$	29.6575	+	11.5054i	1.02025	+	0.395797i
$846$	−0.376029	+	7.74464i	−0.0129281	+	0.266266i
$847$	1.16583	+	0.184650i	0.0400584	+	0.00634463i
$848$	−17.8497	−	27.4861i	−0.612961	−	0.943878i
$849$	−1.11949	+	14.5828i	−0.0384209	+	0.500482i
$850$	−4.07892	−	4.59527i	−0.139906	−	0.157616i
$851$	−15.1881	+	8.76886i	−0.520642	+	0.300593i
$852$	13.2055	+	8.05744i	0.452412	+	0.276043i
$853$	−6.90378	−	5.59057i	−0.236381	−	0.191417i	0.503810	−	0.863815i	$-0.331931\pi$
$853$	−6.90378	−	5.59057i	−0.236381	−	0.191417i	−0.740190	+	0.672397i	$0.765265\pi$
$854$	0.531570	−	0.386208i	0.0181900	−	0.0132158i
$855$	−25.0506	+	5.33244i	−0.856714	+	0.182365i
$856$	33.2906	+	24.1870i	1.13785	+	0.826695i
$857$	−8.63726	−	32.2347i	−0.295043	−	1.10112i	−0.941183	−	0.337897i	$-0.890284\pi$
$857$	−8.63726	−	32.2347i	−0.295043	−	1.10112i	0.646140	−	0.763219i	$-0.276382\pi$
$858$	−22.2046	−	32.1753i	−0.758054	−	1.09845i
$859$	3.96216	+	18.6405i	0.135187	+	0.636005i	0.992605	+	0.121385i	$0.0387336\pi$
$859$	3.96216	+	18.6405i	0.135187	+	0.636005i	−0.857418	+	0.514620i	$0.827933\pi$
$860$	6.21780	−	4.48387i	0.212025	−	0.152899i
$861$	0.556476	−	1.89198i	0.0189647	−	0.0644785i
$862$	0.439445	−	8.38511i	0.0149676	−	0.285598i
$863$	6.96061	−	3.54661i	0.236942	−	0.120728i	−0.331489	−	0.943459i	$-0.607551\pi$
$863$	6.96061	−	3.54661i	0.236942	−	0.120728i	0.568430	+	0.822731i	$0.307551\pi$
$864$	13.7194	−	9.54601i	0.466742	−	0.324762i
$865$	−44.5585	−	9.63658i	−1.51503	−	0.327654i
$866$	−17.0153	+	15.3206i	−0.578202	+	0.520616i
$867$	−24.9247	−	11.8297i	−0.846487	−	0.401758i
$868$	−0.248797	−	0.0666650i	−0.00844473	−	0.00226276i
$869$	−3.47558	+	33.0679i	−0.117901	+	1.12175i
$870$	−9.82759	−	11.5446i	−0.333187	−	0.391398i
$871$	−6.61990	−	62.9842i	−0.224307	−	2.13414i
$872$	6.87159	−	43.3855i	0.232701	−	1.46922i
$873$	14.9902	+	10.8032i	0.507342	+	0.365634i
$874$			9.19333i			0.310969i
$875$	−4.99950	−	2.95786i	−0.169014	−	0.0999941i
$876$	−3.47237	−	0.266566i	−0.117321	−	0.00900644i
$877$	−26.6685	+	1.39764i	−0.900531	+	0.0471948i	−0.496980	−	0.867762i	$-0.665558\pi$
$877$	−26.6685	+	1.39764i	−0.900531	+	0.0471948i	−0.403551	+	0.914957i	$0.632224\pi$
$878$	−12.2575	−	31.9319i	−0.413671	−	1.07765i
$879$	−15.9174	+	9.79634i	−0.536881	+	0.330422i
$880$	−5.27949	+	19.4273i	−0.177972	+	0.654895i
$881$	3.19056	−	4.39144i	0.107493	−	0.147951i	−0.751881	−	0.659298i	$-0.770853\pi$
$881$	3.19056	−	4.39144i	0.107493	−	0.147951i	0.859374	+	0.511347i	$0.170853\pi$
$882$	−21.9378	−	9.66643i	−0.738683	−	0.325486i
$883$	−10.5487	+	1.67075i	−0.354993	+	0.0562253i	−0.331384	−	0.943496i	$-0.607516\pi$
$883$	−10.5487	+	1.67075i	−0.354993	+	0.0562253i	−0.0236087	+	0.999721i	$0.507516\pi$
$884$	2.13261	+	2.36851i	0.0717276	+	0.0796616i
$885$	38.6218	−	9.20589i	1.29826	−	0.309452i
$886$	8.74278	−	9.70984i	0.293719	−	0.326208i
$887$	−10.6522	+	16.4030i	−0.357666	+	0.550758i	−0.971004	−	0.239063i	$-0.923160\pi$
$887$	−10.6522	+	16.4030i	−0.357666	+	0.550758i	0.613338	+	0.789821i	$0.289826\pi$
$888$	−5.92516	+	45.6845i	−0.198835	+	1.53307i
$889$	−1.60741	+	7.56227i	−0.0539108	+	0.253630i
$890$	−30.0815	+	3.05381i	−1.00833	+	0.102364i
$891$	−3.17640	+	32.6332i	−0.106413	+	1.09325i
$892$	−0.173652	−	1.09640i	−0.00581431	−	0.0367101i
$893$	8.02763	−	2.15100i	0.268635	−	0.0719804i
$894$	−0.173126	−	0.485923i	−0.00579021	−	0.0162517i
$895$	−5.46243	+	33.7138i	−0.182589	+	1.12693i
$896$	0.839070	−	1.88458i	0.0280314	−	0.0629595i
$897$	−17.5630	+	5.23914i	−0.586411	+	0.174930i
$898$	−10.1021	+	6.56039i	−0.337112	+	0.218923i
$899$	2.76938			0.0923640
$900$	−3.19934	+	8.25423i	−0.106645	+	0.275141i
$901$	−13.7251			−0.457250
$902$	7.95004	−	5.16281i	0.264707	−	0.171903i
$903$	1.21059	−	5.08552i	0.0402859	−	0.169235i
$904$	−7.00717	+	15.7384i	−0.233055	+	0.523450i
$905$	−7.48710	+	1.15862i	−0.248880	+	0.0385139i
$906$	−23.1672	+	27.2312i	−0.769680	+	0.904695i
$907$	−2.05800	+	0.551439i	−0.0683347	+	0.0183102i	−0.292824	−	0.956166i	$-0.594595\pi$
$907$	−2.05800	+	0.551439i	−0.0683347	+	0.0183102i	0.224490	+	0.974476i	$0.427928\pi$
$908$	−2.05788	−	12.9930i	−0.0682933	−	0.431187i
$909$	17.7108	−	35.0923i	0.587431	−	1.16394i
$910$	−6.22076	−	3.62105i	−0.206216	−	0.120037i
$911$	−3.55092	+	16.7058i	−0.117647	+	0.553487i	0.879358	+	0.476160i	$0.157972\pi$
$911$	−3.55092	+	16.7058i	−0.117647	+	0.553487i	−0.997006	+	0.0773269i	$0.975361\pi$
$912$	12.9849	+	9.92403i	0.429972	+	0.328618i
$913$	10.8513	−	16.7095i	0.359125	−	0.553004i
$914$	−13.3074	+	14.7794i	−0.440171	+	0.488859i
$915$	4.05468	+	0.758313i	0.134044	+	0.0250690i
$916$	−11.6873	−	12.9800i	−0.386158	−	0.428872i
$917$	−4.32552	+	0.685095i	−0.142841	+	0.0226238i
$918$	0.203961	+	6.38223i	0.00673172	+	0.210645i
$919$	−9.31331	+	12.8187i	−0.307218	+	0.422849i	−0.934511	−	0.355934i	$-0.884163\pi$
$919$	−9.31331	+	12.8187i	−0.307218	+	0.422849i	0.627293	+	0.778783i	$0.284163\pi$
$920$	11.6691	+	7.63701i	0.384719	+	0.251785i
$921$	0.753470	+	26.8047i	0.0248277	+	0.883245i
$922$	−6.96649	−	18.1483i	−0.229429	−	0.597683i
$923$	−78.8565	+	4.13270i	−2.59559	+	0.136029i
$924$	−0.836329	−	1.74476i	−0.0275132	−	0.0573984i
$925$	−19.3568	−	38.6658i	−0.636448	−	1.27132i
$926$			33.7870i			1.11031i
$927$	−0.0420582	−	0.0934953i	−0.00138137	−	0.00307079i
$928$	1.65892	−	10.4740i	0.0544566	−	0.343826i
$929$	−4.37661	−	41.6407i	−0.143592	−	1.36619i	−0.794608	−	0.607122i	$-0.792324\pi$
$929$	−4.37661	−	41.6407i	−0.143592	−	1.36619i	0.651017	−	0.759064i	$-0.274343\pi$
$930$	1.83768	+	3.39774i	0.0602598	+	0.111416i
$931$	−2.68589	+	25.5545i	−0.0880265	+	0.837516i
$932$	12.8417	+	3.44091i	0.420642	+	0.112711i
$933$	−2.97774	−	36.9281i	−0.0974868	−	1.20897i
$934$	12.7854	−	11.5120i	0.418350	−	0.376684i
$935$	5.61917	+	6.28543i	0.183767	+	0.205556i
$936$	−17.0798	+	45.0108i	−0.558270	+	1.47122i
$937$	51.3677	−	26.1732i	1.67811	−	0.855040i	0.686301	−	0.727317i	$-0.259233\pi$
$937$	51.3677	−	26.1732i	1.67811	−	0.855040i	0.991810	−	0.127723i	$-0.0407668\pi$
$938$	−0.391876	+	7.47744i	−0.0127952	+	0.244147i
$939$	17.1113	+	17.9623i	0.558406	+	0.586176i
$940$	0.897363	−	2.72881i	0.0292688	−	0.0890041i
$941$	−8.96309	−	42.1680i	−0.292188	−	1.37464i	−0.842058	−	0.539388i	$-0.818656\pi$
$941$	−8.96309	−	42.1680i	−0.292188	−	1.37464i	0.549869	−	0.835251i	$-0.314678\pi$
$942$	−19.9009	+	41.9303i	−0.648405	+	1.36616i
$943$	−1.15022	−	4.29267i	−0.0374562	−	0.139789i
$944$	−20.4965	−	14.8916i	−0.667104	−	0.484679i
$945$	2.02776	+	5.68610i	0.0659630	+	0.184969i
$946$	20.3285	−	14.7696i	0.660938	−	0.480200i
$947$	−11.9721	−	9.69480i	−0.389040	−	0.315039i	0.414768	−	0.909927i	$-0.363863\pi$
$947$	−11.9721	−	9.69480i	−0.389040	−	0.315039i	−0.803808	+	0.594889i	$0.797196\pi$
$948$	8.19050	−	4.46749i	0.266015	−	0.145097i
$949$	15.3953	−	8.88849i	0.499753	−	0.288533i
$950$	−22.6267	−	1.34689i	−0.734106	−	0.0436989i
$951$	−5.41949	+	2.59777i	−0.175739	+	0.0842383i
$952$	−0.900725	−	1.38700i	−0.0291927	−	0.0449528i
$953$	8.02759	+	1.27145i	0.260039	+	0.0411862i	0.285093	−	0.958500i	$-0.407976\pi$
$953$	8.02759	+	1.27145i	0.260039	+	0.0411862i	−0.0250535	+	0.999686i	$0.507976\pi$
$954$	−21.6073	−	42.0066i	−0.699561	−	1.36001i
$955$	0.336838	−	6.01857i	0.0108998	−	0.194756i
$956$	2.81611	+	6.32509i	0.0910796	+	0.204568i
$957$	13.5409	+	15.7928i	0.437715	+	0.510508i
$958$	3.73562	+	4.61310i	0.120692	+	0.149043i
$959$	−8.46230	+	1.79872i	−0.273262	+	0.0580836i
$960$	32.0067	−	11.2756i	1.03301	−	0.363919i
$961$	29.6324	+	6.29856i	0.955884	+	0.203179i
$962$	−24.3245	−	47.7395i	−0.784253	−	1.53918i
$963$	29.9326	+	26.7438i	0.964564	+	0.861806i
$964$	−10.1284	+	3.29092i	−0.326214	+	0.105993i
$965$	41.6685	−	23.8606i	1.34136	−	0.768099i
$966$	2.14783	−	0.286968i	0.0691051	−	0.00923304i
$967$	18.1568	−	14.7031i	0.583883	−	0.472819i	−0.291286	−	0.956636i	$-0.594083\pi$
$967$	18.1568	−	14.7031i	0.583883	−	0.472819i	0.875169	+	0.483817i	$0.160750\pi$
$968$	1.80834	−	6.74882i	0.0581223	−	0.216915i
$969$	6.44726	−	2.29705i	0.207116	−	0.0737919i
$970$	10.2459	+	12.7449i	0.328977	+	0.409213i
$971$	−22.7096	−	31.2571i	−0.728786	−	1.00309i	−0.999186	−	0.0403401i	$-0.987156\pi$
$971$	−22.7096	−	31.2571i	−0.728786	−	1.00309i	0.270400	−	0.962748i	$-0.412844\pi$
$972$	8.04243	−	4.46730i	0.257961	−	0.143289i
$973$	−2.70901	−	1.38031i	−0.0868469	−	0.0442507i
$974$	3.41782	−	5.91985i	0.109514	−	0.189684i
$975$	−10.3215	−	43.9937i	−0.330552	−	1.40892i
$976$	−1.31608	−	2.27951i	−0.0421266	−	0.0729655i
$977$	0.945873	+	18.0483i	0.0302612	+	0.577417i	0.971116	+	0.238608i	$0.0766910\pi$
$977$	0.945873	+	18.0483i	0.0302612	+	0.577417i	−0.940855	+	0.338810i	$0.889976\pi$
$978$	−10.7302	−	35.9705i	−0.343114	−	1.15021i
$979$	41.2607	−	4.33668i	1.31870	−	0.138601i
$980$	6.88227	+	5.61370i	0.219846	+	0.179323i
$981$	10.9308	−	41.4307i	0.348993	−	1.32278i
$982$	−4.75514	−	4.75514i	−0.151743	−	0.151743i
$983$	−52.7467	−	20.2476i	−1.68236	−	0.645797i	−0.685731	−	0.727855i	$-0.740517\pi$
$983$	−52.7467	−	20.2476i	−1.68236	−	0.645797i	−0.996628	+	0.0820584i	$0.973851\pi$
$984$	−10.7935	−	4.44652i	−0.344084	−	0.141750i
$985$	−29.3750	−	40.7344i	−0.935965	−	1.29791i
$986$	3.01084	+	2.71097i	0.0958846	+	0.0863349i
$987$	−0.753116	−	1.80834i	−0.0239719	−	0.0575602i
$988$	11.7412	+	0.615330i	0.373537	+	0.0195763i
$989$	−3.64030	−	11.2037i	−0.115755	−	0.356257i
$990$	−10.3908	+	27.0929i	−0.330241	+	0.861069i
$991$	3.60066	−	11.0817i	0.114379	−	0.352021i	−0.877438	−	0.479690i	$-0.840749\pi$
$991$	3.60066	−	11.0817i	0.114379	−	0.352021i	0.991817	+	0.127668i	$0.0407493\pi$
$992$	−0.968278	+	2.52245i	−0.0307428	+	0.0800878i
$993$	25.0203	+	8.80607i	0.793996	+	0.279452i
$994$	9.28494	+	0.975887i	0.294501	+	0.0309533i
$995$	32.6529	+	32.8855i	1.03517	+	1.04254i
$996$	−5.58824	+	0.157083i	−0.177070	+	0.00497737i
$997$	−12.4171	+	15.3338i	−0.393253	+	0.485627i	−0.934866	−	0.355001i	$-0.884480\pi$
$997$	−12.4171	+	15.3338i	−0.393253	+	0.485627i	0.541613	+	0.840628i	$0.317814\pi$
$998$	4.85370	−	9.52593i	0.153641	−	0.301538i
$999$	−10.2381	+	43.7548i	−0.323919	+	1.38434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.w.a.92.20	✓	448
3.2	odd	2		675.2.bd.a.467.9		448
9.4	even	3		675.2.bd.a.17.20		448
9.5	odd	6	inner	225.2.w.a.167.9	yes	448
25.3	odd	20	inner	225.2.w.a.128.9	yes	448
75.53	even	20		675.2.bd.a.278.20		448
225.103	odd	60		675.2.bd.a.503.9		448
225.203	even	60	inner	225.2.w.a.203.20	yes	448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.92.20	✓	448	1.1	even	1	trivial
225.2.w.a.128.9	yes	448	25.3	odd	20	inner
225.2.w.a.167.9	yes	448	9.5	odd	6	inner
225.2.w.a.203.20	yes	448	225.203	even	60	inner
675.2.bd.a.17.20		448	9.4	even	3
675.2.bd.a.278.20		448	75.53	even	20
675.2.bd.a.467.9		448	3.2	odd	2
675.2.bd.a.503.9		448	225.103	odd	60

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.995806 - 0.646684i) q^{2} +(1.25867 + 1.18985i) q^{3} +(-0.240044 + 0.539148i) q^{4} +(-1.58674 + 1.57552i) q^{5} +(2.02285 + 0.370893i) q^{6} +(-0.501865 + 0.134474i) q^{7} +(0.481110 + 3.03761i) q^{8} +(0.168525 + 2.99526i) q^{9} +O(q^{10})\)	\(q+(0.995806 - 0.646684i) q^{2} +(1.25867 + 1.18985i) q^{3} +(-0.240044 + 0.539148i) q^{4} +(-1.58674 + 1.57552i) q^{5} +(2.02285 + 0.370893i) q^{6} +(-0.501865 + 0.134474i) q^{7} +(0.481110 + 3.03761i) q^{8} +(0.168525 + 2.99526i) q^{9} +(-0.561222 + 2.59503i) q^{10} +(0.757433 - 3.56344i) q^{11} +(-0.943642 + 0.392996i) q^{12} +(2.84186 - 4.37609i) q^{13} +(-0.412798 + 0.458458i) q^{14} +(-3.87182 + 0.0950874i) q^{15} +(1.65366 + 1.83657i) q^{16} +(1.02223 - 0.161905i) q^{17} +(2.10481 + 2.87372i) q^{18} +(2.24416 - 3.08882i) q^{19} +(-0.468551 - 1.23368i) q^{20} +(-0.791689 - 0.427883i) q^{21} +(-1.55016 - 4.03831i) q^{22} +(-2.02516 + 0.106134i) q^{23} +(-3.00873 + 4.39581i) q^{24} +(0.0354827 - 4.99987i) q^{25} -6.19552i q^{26} +(-3.35179 + 3.97058i) q^{27} +(0.0479682 - 0.302860i) q^{28} +(0.344617 + 3.27881i) q^{29} +(-3.79408 + 2.59853i) q^{30} +(0.0878042 - 0.835401i) q^{31} +(-3.10695 - 0.832504i) q^{32} +(5.19331 - 3.58398i) q^{33} +(0.913241 - 0.822286i) q^{34} +(0.584462 - 1.00407i) q^{35} +(-1.65534 - 0.628136i) q^{36} +(7.70548 - 3.92614i) q^{37} +(0.237257 - 4.52713i) q^{38} +(8.78386 - 2.12668i) q^{39} +(-5.54920 - 4.06189i) q^{40} +(0.455626 + 2.14355i) q^{41} +(-1.06507 + 0.0858835i) q^{42} +(1.50348 + 5.61105i) q^{43} +(1.73941 + 1.26375i) q^{44} +(-4.98650 - 4.48719i) q^{45} +(-1.94803 + 1.41532i) q^{46} +(1.69165 + 1.36987i) q^{47} +(-0.103825 + 4.27925i) q^{48} +(-5.82839 + 3.36502i) q^{49} +(-3.19800 - 5.00185i) q^{50} +(1.47930 + 1.01251i) q^{51} +(1.67719 + 2.58264i) q^{52} +(-13.0981 - 2.07453i) q^{53} +(-0.770021 + 6.12147i) q^{54} +(4.41242 + 6.84760i) q^{55} +(-0.649932 - 1.45977i) q^{56} +(6.49990 - 1.21761i) q^{57} +(2.46353 + 3.04220i) q^{58} +(-10.0275 + 2.13140i) q^{59} +(0.878141 - 2.11031i) q^{60} +(-1.04179 - 0.221440i) q^{61} +(-0.452804 - 0.888678i) q^{62} +(-0.487363 - 1.48056i) q^{63} +(-8.33308 + 2.70758i) q^{64} +(2.38531 + 11.4211i) q^{65} +(2.85383 - 6.92738i) q^{66} +(9.43246 - 7.63826i) q^{67} +(-0.158090 + 0.589998i) q^{68} +(-2.67530 - 2.27604i) q^{69} +(-0.0673072 - 1.37782i) q^{70} +(-8.89523 - 12.2432i) q^{71} +(-9.01735 + 1.95296i) q^{72} +(3.03560 + 1.54671i) q^{73} +(5.13419 - 8.89268i) q^{74} +(5.99375 - 6.25100i) q^{75} +(1.12664 + 1.95139i) q^{76} +(0.0990623 + 1.89022i) q^{77} +(7.37173 - 7.79814i) q^{78} +(-9.07699 + 0.954030i) q^{79} +(-5.51748 - 0.308794i) q^{80} +(-8.94320 + 1.00955i) q^{81} +(1.83991 + 1.83991i) q^{82} +(5.10575 + 1.95991i) q^{83} +(0.420733 - 0.324127i) q^{84} +(-1.36693 + 1.86744i) q^{85} +(5.12575 + 4.61524i) q^{86} +(-3.46753 + 4.53700i) q^{87} +(11.1887 + 0.586377i) q^{88} +(3.51917 + 10.8309i) q^{89} +(-7.86737 - 1.24368i) q^{90} +(-0.837761 + 2.57836i) q^{91} +(0.428905 - 1.11734i) q^{92} +(1.10452 - 0.947024i) q^{93} +(2.57043 + 0.270163i) q^{94} +(1.30560 + 8.43688i) q^{95} +(-2.92008 - 4.74465i) q^{96} +(3.87608 - 4.78656i) q^{97} +(-3.62784 + 7.12004i) q^{98} +(10.8011 + 1.66818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Introduction

L-functions

Modular forms

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