LMFDB - Embedded newform 225.2.q.a.106.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.26
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14773 + 0.456515i) q^{2} +(-1.28647 - 1.15974i) q^{3} +(2.57727 + 1.14747i) q^{4} +(0.900133 + 2.04689i) q^{5} +(-2.23356 - 3.07811i) q^{6} +(1.61294 - 2.79370i) q^{7} +(1.45870 + 1.05981i) q^{8} +(0.310005 + 2.98394i) q^{9} +O(q^{10})$	\(q+(2.14773 + 0.456515i) q^{2} +(-1.28647 - 1.15974i) q^{3} +(2.57727 + 1.14747i) q^{4} +(0.900133 + 2.04689i) q^{5} +(-2.23356 - 3.07811i) q^{6} +(1.61294 - 2.79370i) q^{7} +(1.45870 + 1.05981i) q^{8} +(0.310005 + 2.98394i) q^{9} +(0.998810 + 4.80710i) q^{10} +(5.10860 + 1.08587i) q^{11} +(-1.98480 - 4.46515i) q^{12} +(-3.76781 + 0.800873i) q^{13} +(4.73954 - 5.26379i) q^{14} +(1.21587 - 3.67718i) q^{15} +(-1.12637 - 1.25097i) q^{16} +(-3.55929 - 2.58598i) q^{17} +(-0.696404 + 6.55023i) q^{18} +(-2.66915 - 1.93925i) q^{19} +(-0.0288689 + 6.30826i) q^{20} +(-5.31497 + 1.72341i) q^{21} +(10.4762 + 4.66431i) q^{22} +(-5.59186 + 6.21039i) q^{23} +(-0.647472 - 3.05513i) q^{24} +(-3.37952 + 3.68495i) q^{25} -8.45786 q^{26} +(3.06178 - 4.19827i) q^{27} +(7.36268 - 5.34930i) q^{28} +(-0.104794 - 0.997049i) q^{29} +(4.29005 - 7.34255i) q^{30} +(-0.352871 + 3.35734i) q^{31} +(-3.65112 - 6.32393i) q^{32} +(-5.31274 - 7.32159i) q^{33} +(-6.46388 - 7.17886i) q^{34} +(7.17026 + 0.786817i) q^{35} +(-2.62502 + 8.04613i) q^{36} +(-0.878044 + 2.70234i) q^{37} +(-4.84733 - 5.38351i) q^{38} +(5.77597 + 3.33938i) q^{39} +(-0.856288 + 3.93977i) q^{40} +(5.99171 - 1.27358i) q^{41} +(-12.2019 + 1.27507i) q^{42} +(2.26793 - 3.92817i) q^{43} +(11.9202 + 8.66056i) q^{44} +(-5.82875 + 3.32049i) q^{45} +(-14.8450 + 10.7855i) q^{46} +(-0.111400 - 1.05990i) q^{47} +(-0.00174910 + 2.91563i) q^{48} +(-1.70317 - 2.94998i) q^{49} +(-8.94055 + 6.37149i) q^{50} +(1.57986 + 7.45463i) q^{51} +(-10.6296 - 2.25940i) q^{52} +(6.03818 - 4.38700i) q^{53} +(8.49247 - 7.61902i) q^{54} +(2.37577 + 11.4342i) q^{55} +(5.31359 - 2.36576i) q^{56} +(1.18475 + 5.59031i) q^{57} +(0.230098 - 2.18924i) q^{58} +(-3.06903 + 0.652341i) q^{59} +(7.35308 - 8.08190i) q^{60} +(-8.43309 - 1.79251i) q^{61} +(-2.29055 + 7.04959i) q^{62} +(8.83625 + 3.94686i) q^{63} +(-3.91431 - 12.0470i) q^{64} +(-5.03083 - 6.99140i) q^{65} +(-8.06793 - 18.1502i) q^{66} +(-0.364144 + 3.46460i) q^{67} +(-6.20591 - 10.7489i) q^{68} +(14.3962 - 1.50437i) q^{69} +(15.0406 + 4.96321i) q^{70} +(11.0256 - 8.01056i) q^{71} +(-2.71020 + 4.68123i) q^{72} +(-0.320689 - 0.986980i) q^{73} +(-3.11946 + 5.40307i) q^{74} +(8.62123 - 0.821204i) q^{75} +(-4.65388 - 8.06075i) q^{76} +(11.2735 - 12.5205i) q^{77} +(10.8808 + 9.80893i) q^{78} +(0.840501 + 7.99683i) q^{79} +(1.54670 - 3.43160i) q^{80} +(-8.80779 + 1.85008i) q^{81} +13.4500 q^{82} +(5.24545 - 2.33542i) q^{83} +(-15.6757 - 1.65709i) q^{84} +(2.08938 - 9.61320i) q^{85} +(6.66418 - 7.40132i) q^{86} +(-1.02150 + 1.40421i) q^{87} +(6.30112 + 6.99811i) q^{88} +(2.92451 + 9.00073i) q^{89} +(-14.0345 + 4.47062i) q^{90} +(-3.83986 + 11.8179i) q^{91} +(-21.5380 + 9.58932i) q^{92} +(4.34760 - 3.90988i) q^{93} +(0.244603 - 2.32724i) q^{94} +(1.56685 - 7.20905i) q^{95} +(-2.63706 + 12.3699i) q^{96} +(0.199991 + 1.90279i) q^{97} +(-2.31125 - 7.11329i) q^{98} +(-1.65647 + 15.5804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	2.14773	+	0.456515i	1.51868	+	0.322805i	0.890398	−	0.455183i	$-0.150426\pi$
$2$	2.14773	+	0.456515i	1.51868	+	0.322805i	0.628280	+	0.777988i	$0.283759\pi$
$3$	−1.28647	−	1.15974i	−0.742743	−	0.669576i
$3$	−1.28647	−	1.15974i	−0.742743	−	0.669576i
$4$	2.57727	+	1.14747i	1.28863	+	0.573737i
$5$	0.900133	+	2.04689i	0.402552	+	0.915397i
$5$	0.900133	+	2.04689i	0.402552	+	0.915397i
$6$	−2.23356	−	3.07811i	−0.911845	−	1.25663i
$7$	1.61294	−	2.79370i	0.609635	−	1.05592i	−0.381665	−	0.924301i	$-0.624649\pi$
$7$	1.61294	−	2.79370i	0.609635	−	1.05592i	0.991300	−	0.131618i	$-0.0420174\pi$
$8$	1.45870	+	1.05981i	0.515729	+	0.374699i
$9$	0.310005	+	2.98394i	0.103335	+	0.994647i
$10$	0.998810	+	4.80710i	0.315852	+	1.52014i
$11$	5.10860	+	1.08587i	1.54030	+	0.327401i	0.898328	−	0.439325i	$-0.144782\pi$
$11$	5.10860	+	1.08587i	1.54030	+	0.327401i	0.641974	+	0.766726i	$0.278116\pi$
$12$	−1.98480	−	4.46515i	−0.572963	−	1.28898i
$13$	−3.76781	+	0.800873i	−1.04500	+	0.222122i	−0.698264	−	0.715840i	$-0.746044\pi$
$13$	−3.76781	+	0.800873i	−1.04500	+	0.222122i	−0.346738	+	0.937962i	$0.612711\pi$
$14$	4.73954	−	5.26379i	1.26670	−	1.40681i
$15$	1.21587	−	3.67718i	0.313936	−	0.949444i
$16$	−1.12637	−	1.25097i	−0.281594	−	0.312741i
$17$	−3.55929	−	2.58598i	−0.863255	−	0.627192i	0.0655134	−	0.997852i	$-0.479131\pi$
$17$	−3.55929	−	2.58598i	−0.863255	−	0.627192i	−0.928769	+	0.370660i	$0.879131\pi$
$18$	−0.696404	+	6.55023i	−0.164144	+	1.54390i
$19$	−2.66915	−	1.93925i	−0.612345	−	0.444895i	0.237894	−	0.971291i	$-0.423543\pi$
$19$	−2.66915	−	1.93925i	−0.612345	−	0.444895i	−0.850239	+	0.526396i	$0.823543\pi$
$20$	−0.0288689	+	6.30826i	−0.00645528	+	1.41057i
$21$	−5.31497	+	1.72341i	−1.15982	+	0.376080i
$22$	10.4762	+	4.66431i	2.23354	+	0.994434i
$23$	−5.59186	+	6.21039i	−1.16598	+	1.29496i	−0.218249	+	0.975893i	$0.570035\pi$
$23$	−5.59186	+	6.21039i	−1.16598	+	1.29496i	−0.947734	+	0.319062i	$0.896632\pi$
$24$	−0.647472	−	3.05513i	−0.132165	−	0.623626i
$25$	−3.37952	+	3.68495i	−0.675904	+	0.736989i
$26$	−8.45786			−1.65872
$27$	3.06178	−	4.19827i	0.589240	−	0.807958i
$28$	7.36268	−	5.34930i	1.39142	−	1.01092i
$29$	−0.104794	−	0.997049i	−0.0194598	−	0.185147i	0.980474	−	0.196648i	$-0.0630057\pi$
$29$	−0.104794	−	0.997049i	−0.0194598	−	0.185147i	−0.999934	+	0.0115009i	$0.996339\pi$
$30$	4.29005	−	7.34255i	0.783252	−	1.34056i
$31$	−0.352871	+	3.35734i	−0.0633775	+	0.602996i	0.916031	+	0.401107i	$0.131375\pi$
$31$	−0.352871	+	3.35734i	−0.0633775	+	0.602996i	−0.979408	+	0.201889i	$0.935292\pi$
$32$	−3.65112	−	6.32393i	−0.645434	−	1.11792i
$33$	−5.31274	−	7.32159i	−0.924829	−	1.27452i
$34$	−6.46388	−	7.17886i	−1.10855	−	1.23116i
$35$	7.17026	+	0.786817i	1.21200	+	0.132996i
$36$	−2.62502	+	8.04613i	−0.437504	+	1.34102i
$37$	−0.878044	+	2.70234i	−0.144349	+	0.444262i	−0.996927	−	0.0783391i	$-0.975038\pi$
$37$	−0.878044	+	2.70234i	−0.144349	+	0.444262i	0.852577	+	0.522601i	$0.175038\pi$
$38$	−4.84733	−	5.38351i	−0.786341	−	0.873320i
$39$	5.77597	+	3.33938i	0.924896	+	0.534729i
$40$	−0.856288	+	3.93977i	−0.135391	+	0.622933i
$41$	5.99171	−	1.27358i	0.935748	−	0.198899i	0.285290	−	0.958441i	$-0.407910\pi$
$41$	5.99171	−	1.27358i	0.935748	−	0.198899i	0.650458	+	0.759542i	$0.274577\pi$
$42$	−12.2019	+	1.27507i	−1.88279	+	0.196748i
$43$	2.26793	−	3.92817i	0.345856	−	0.599041i	−0.639653	−	0.768664i	$-0.720922\pi$
$43$	2.26793	−	3.92817i	0.345856	−	0.599041i	0.985509	+	0.169624i	$0.0542552\pi$
$44$	11.9202	+	8.66056i	1.79704	+	1.30563i
$45$	−5.82875	+	3.32049i	−0.868899	+	0.494989i
$46$	−14.8450	+	10.7855i	−2.18877	+	1.59023i
$47$	−0.111400	−	1.05990i	−0.0162494	−	0.154603i	0.983388	−	0.181514i	$-0.0580996\pi$
$47$	−0.111400	−	1.05990i	−0.0162494	−	0.154603i	−0.999638	+	0.0269110i	$0.991433\pi$
$48$	−0.00174910	+	2.91563i	−0.000252460	+	0.420835i
$49$	−1.70317	−	2.94998i	−0.243310	−	0.421425i
$50$	−8.94055	+	6.37149i	−1.26438	+	0.901064i
$51$	1.57986	+	7.45463i	0.221224	+	1.04386i
$52$	−10.6296	−	2.25940i	−1.47406	−	0.313322i
$53$	6.03818	−	4.38700i	0.829408	−	0.602600i	−0.0899837	−	0.995943i	$-0.528682\pi$
$53$	6.03818	−	4.38700i	0.829408	−	0.602600i	0.919392	+	0.393343i	$0.128682\pi$
$54$	8.49247	−	7.61902i	1.15568	−	1.03682i
$55$	2.37577	+	11.4342i	0.320349	+	1.54178i
$56$	5.31359	−	2.36576i	0.710059	−	0.316139i
$57$	1.18475	+	5.59031i	0.156924	+	0.740455i
$58$	0.230098	−	2.18924i	0.0302134	−	0.287461i
$59$	−3.06903	+	0.652341i	−0.399553	+	0.0849276i	−0.403306	−	0.915065i	$-0.632139\pi$
$59$	−3.06903	+	0.652341i	−0.399553	+	0.0849276i	0.00375258	+	0.999993i	$0.498806\pi$
$60$	7.35308	−	8.08190i	0.949279	−	1.04337i
$61$	−8.43309	−	1.79251i	−1.07975	−	0.229507i	−0.366498	−	0.930419i	$-0.619443\pi$
$61$	−8.43309	−	1.79251i	−1.07975	−	0.229507i	−0.713248	+	0.700912i	$0.752777\pi$
$62$	−2.29055	+	7.04959i	−0.290900	+	0.895298i
$63$	8.83625	+	3.94686i	1.11326	+	0.497258i
$64$	−3.91431	−	12.0470i	−0.489289	−	1.50588i
$65$	−5.03083	−	6.99140i	−0.623997	−	0.867177i
$66$	−8.06793	−	18.1502i	−0.993094	−	2.23413i
$67$	−0.364144	+	3.46460i	−0.0444873	+	0.423268i	0.949500	+	0.313768i	$0.101592\pi$
$67$	−0.364144	+	3.46460i	−0.0444873	+	0.423268i	−0.993987	+	0.109500i	$0.965075\pi$
$68$	−6.20591	−	10.7489i	−0.752577	−	1.30350i
$69$	14.3962	−	1.50437i	1.73310	−	0.181105i
$70$	15.0406	+	4.96321i	1.79770	+	0.593217i
$71$	11.0256	−	8.01056i	1.30850	−	0.950678i	0.308496	−	0.951226i	$-0.400174\pi$
$71$	11.0256	−	8.01056i	1.30850	−	0.950678i	1.00000		0.000547588i	$0.000174303\pi$
$72$	−2.71020	+	4.68123i	−0.319400	+	0.551688i
$73$	−0.320689	−	0.986980i	−0.0375338	−	0.115517i	0.930534	−	0.366205i	$-0.119343\pi$
$73$	−0.320689	−	0.986980i	−0.0375338	−	0.115517i	−0.968068	+	0.250688i	$0.919343\pi$
$74$	−3.11946	+	5.40307i	−0.362630	+	0.628094i
$75$	8.62123	−	0.821204i	0.995494	−	0.0948245i
$76$	−4.65388	−	8.06075i	−0.533836	−	0.924631i
$77$	11.2735	−	12.5205i	1.28473	−	1.42684i
$78$	10.8808	+	9.80893i	1.23201	+	1.11064i
$79$	0.840501	+	7.99683i	0.0945638	+	0.899714i	0.934244	+	0.356634i	$0.116076\pi$
$79$	0.840501	+	7.99683i	0.0945638	+	0.899714i	−0.839681	+	0.543081i	$0.817258\pi$
$80$	1.54670	−	3.43160i	0.172927	−	0.383665i
$81$	−8.80779	+	1.85008i	−0.978644	+	0.205564i
$82$	13.4500			1.48531
$83$	5.24545	−	2.33542i	0.575762	−	0.256346i	−0.0981322	−	0.995173i	$-0.531287\pi$
$83$	5.24545	−	2.33542i	0.575762	−	0.256346i	0.673895	+	0.738827i	$0.264620\pi$
$84$	−15.6757	−	1.65709i	−1.71035	−	0.180803i
$85$	2.08938	−	9.61320i	0.226625	−	1.04270i
$86$	6.66418	−	7.40132i	0.718617	−	0.798105i
$87$	−1.02150	+	1.40421i	−0.109517	+	0.150547i
$88$	6.30112	+	6.99811i	0.671702	+	0.746001i
$89$	2.92451	+	9.00073i	0.309998	+	0.954075i	0.977765	+	0.209705i	$0.0672502\pi$
$89$	2.92451	+	9.00073i	0.309998	+	0.954075i	−0.667767	+	0.744370i	$0.732750\pi$
$90$	−14.0345	+	4.47062i	−1.47936	+	0.471245i
$91$	−3.83986	+	11.8179i	−0.402527	+	1.23885i
$92$	−21.5380	+	9.58932i	−2.24549	+	0.999756i
$93$	4.34760	−	3.90988i	0.450825	−	0.405435i
$94$	0.244603	−	2.32724i	0.0252289	−	0.240037i
$95$	1.56685	−	7.20905i	0.160755	−	0.739632i
$96$	−2.63706	+	12.3699i	−0.269144	+	1.26250i
$97$	0.199991	+	1.90279i	0.0203060	+	0.193199i	0.999972	−	0.00743485i	$-0.00236661\pi$
$97$	0.199991	+	1.90279i	0.0203060	+	0.193199i	−0.979666	+	0.200634i	$0.935700\pi$
$98$	−2.31125	−	7.11329i	−0.233471	−	0.718551i
$99$	−1.65647	+	15.5804i	−0.166481	+	1.56589i
$100$	−12.9383	+	5.61918i	−1.29383	+	0.561918i
$101$	2.15175	−	3.72694i	0.214107	−	0.370844i	−0.738889	−	0.673827i	$-0.764649\pi$
$101$	2.15175	−	3.72694i	0.214107	−	0.370844i	0.952996	+	0.302983i	$0.0979826\pi$
$102$	−0.0100375	+	16.7318i	−0.000993856	+	1.65670i
$103$	0.973725	+	0.433530i	0.0959440	+	0.0427170i	0.454147	−	0.890927i	$-0.349944\pi$
$103$	0.973725	+	0.433530i	0.0959440	+	0.0427170i	−0.358203	+	0.933644i	$0.616611\pi$
$104$	−6.34489	−	2.82493i	−0.622167	−	0.277007i
$105$	−8.31181	−	9.32785i	−0.811150	−	0.910305i
$106$	14.9711	−	6.66558i	1.45413	−	0.647419i
$107$	12.2827			1.18741			0.593706	−	0.804682i	$-0.297664\pi$
$107$	12.2827			1.18741			0.593706	+	0.804682i	$0.297664\pi$
$108$	12.7084	−	7.30675i	1.22287	−	0.703093i
$109$	0.413257	−	1.27187i	0.0395828	−	0.121823i	−0.929313	−	0.369294i	$-0.879599\pi$
$109$	0.413257	−	1.27187i	0.0395828	−	0.121823i	0.968895	+	0.247471i	$0.0795994\pi$
$110$	−0.117348	+	25.6422i	−0.0111887	+	2.44488i
$111$	4.26359	−	2.45818i	0.404682	−	0.233320i
$112$	−5.31160	+	1.12902i	−0.501899	+	0.106682i
$113$	−4.90531	+	1.04266i	−0.461453	+	0.0980848i	−0.432771	−	0.901504i	$-0.642464\pi$
$113$	−4.90531	+	1.04266i	−0.461453	+	0.0980848i	−0.0286816	+	0.999589i	$0.509131\pi$
$114$	−0.00752720	+	12.5474i	−0.000704987	+	1.17517i
$115$	−17.7454	−	5.85575i	−1.65477	−	0.546051i
$116$	0.874005	−	2.68991i	0.0811493	−	0.249752i
$117$	−3.55780	−	10.9946i	−0.328918	−	1.01645i
$118$	−6.88926			−0.634207
$119$	−12.9654	+	5.77256i	−1.18853	+	0.529170i
$120$	5.67070	−	4.07533i	0.517662	−	0.372025i
$121$	14.8697	+	6.62043i	1.35179	+	0.601857i
$122$	−17.2937	−	7.69966i	−1.56570	−	0.697095i
$123$	−9.18517	−	5.31041i	−0.828199	−	0.478824i
$124$	−4.76190	+	8.24785i	−0.427631	+	0.740679i
$125$	−10.5847	−	3.60057i	−0.946725	−	0.322045i
$126$	17.1761	+	12.5107i	1.53017	+	1.11454i
$127$	1.06344	+	3.27294i	0.0943651	+	0.290426i	0.987088	−	0.160181i	$-0.0512077\pi$
$127$	1.06344	+	3.27294i	0.0943651	+	0.290426i	−0.892723	+	0.450607i	$0.851208\pi$
$128$	−1.38068	−	13.1363i	−0.122036	−	1.16109i
$129$	−7.47328	+	2.42326i	−0.657986	+	0.213356i
$130$	−7.61320	−	17.3123i	−0.667722	−	1.51839i
$131$	−0.0776604	+	0.738889i	−0.00678522	+	0.0645571i	−0.997391	−	0.0721949i	$-0.977000\pi$
$131$	−0.0776604	+	0.738889i	−0.00678522	+	0.0645571i	0.990605	+	0.136752i	$0.0436663\pi$
$132$	−5.29102	−	24.9659i	−0.460524	−	2.17300i
$133$	−9.72288	+	4.32890i	−0.843080	+	0.375364i
$134$	−2.36373	+	7.27480i	−0.204195	+	0.628447i
$135$	11.3494	+	2.48813i	0.976802	+	0.214144i
$136$	−2.45131	−	7.54435i	−0.210198	−	0.646922i
$137$	5.36423	+	5.95758i	0.458297	+	0.508991i	0.927358	−	0.374175i	$-0.122074\pi$
$137$	5.36423	+	5.95758i	0.458297	+	0.508991i	−0.469061	+	0.883166i	$0.655408\pi$
$138$	31.6060	+	3.34109i	2.69048	+	0.284413i
$139$	8.44962	−	9.38425i	0.716687	−	0.795962i	−0.269251	−	0.963070i	$-0.586776\pi$
$139$	8.44962	−	9.38425i	0.716687	−	0.795962i	0.985939	+	0.167108i	$0.0534429\pi$
$140$	17.5768	+	10.2555i	1.48551	+	0.866749i
$141$	−1.08590	+	1.49273i	−0.0914491	+	0.125710i
$142$	27.3370	−	12.1712i	2.29407	−	1.02138i
$143$	−20.1179			−1.68234
$144$	3.38362	−	3.74884i	0.281969	−	0.312403i
$145$	1.94652	−	1.11198i	0.161650	−	0.0923448i
$146$	−0.238184	−	2.26617i	−0.0197123	−	0.187550i
$147$	−1.23013	+	5.77029i	−0.101460	+	0.475926i
$148$	−5.36382	+	5.95712i	−0.440903	+	0.489672i
$149$	10.0206	+	17.3561i	0.820917	+	1.42187i	0.905000	+	0.425411i	$0.139870\pi$
$149$	10.0206	+	17.3561i	0.820917	+	1.42187i	−0.0840836	+	0.996459i	$0.526796\pi$
$150$	18.8910	+	2.17199i	1.54244	+	0.177342i
$151$	−5.05712	+	8.75919i	−0.411543	+	0.712813i	−0.995059	−	0.0992889i	$-0.968343\pi$
$151$	−5.05712	+	8.75919i	−0.411543	+	0.712813i	0.583516	+	0.812102i	$0.301677\pi$
$152$	−1.83826	−	5.65759i	−0.149103	−	0.458891i
$153$	6.61300	−	11.4224i	0.534629	−	0.923445i
$154$	29.9282	−	21.7441i	2.41168	−	1.75219i
$155$	−7.18974	+	2.29977i	−0.577494	+	0.184722i
$156$	11.0544	+	15.2343i	0.885058	+	1.21972i
$157$	−2.63111	−	4.55722i	−0.209986	−	0.363706i	0.741724	−	0.670705i	$-0.234008\pi$
$157$	−2.63111	−	4.55722i	−0.209986	−	0.363706i	−0.951710	+	0.306999i	$0.900675\pi$
$158$	−1.84550	+	17.5588i	−0.146820	+	1.39690i
$159$	−12.8557	−	1.35899i	−1.01952	−	0.107775i
$160$	9.65790	−	13.1658i	0.763524	−	1.04085i
$161$	8.33061	+	25.6390i	0.656544	+	2.02063i
$162$	−19.7614	−	0.0474197i	−1.55260	−	0.00372565i
$163$	7.04326	−	21.6769i	0.551670	−	1.69787i	−0.152907	−	0.988241i	$-0.548864\pi$
$163$	7.04326	−	21.6769i	0.551670	−	1.69787i	0.704578	−	0.709627i	$-0.251136\pi$
$164$	16.9036	+	3.59298i	1.31995	+	0.280565i
$165$	10.2043	−	17.4650i	0.794405	−	1.35965i
$166$	12.3320	−	2.62124i	0.957147	−	0.203448i
$167$	−0.733074	+	6.97473i	−0.0567269	+	0.539721i	0.928846	+	0.370467i	$0.120802\pi$
$167$	−0.733074	+	6.97473i	−0.0567269	+	0.539721i	−0.985573	+	0.169254i	$0.945864\pi$
$168$	−9.57945	−	3.11891i	−0.739070	−	0.240629i
$169$	1.67890	−	0.747494i	0.129146	−	0.0574995i
$170$	8.87600	−	19.6928i	0.680758	−	1.51037i
$171$	4.95916	−	8.56577i	0.379236	−	0.655040i
$172$	10.3525	−	7.52156i	0.789373	−	0.573513i
$173$	−4.77800	−	1.01560i	−0.363265	−	0.0772143i	0.0226634	−	0.999743i	$-0.492785\pi$
$173$	−4.77800	−	1.01560i	−0.363265	−	0.0772143i	−0.385928	+	0.922529i	$0.626119\pi$
$174$	−2.83496	+	2.54953i	−0.214918	+	0.193279i
$175$	4.84366	+	15.3850i	0.366146	+	1.16299i
$176$	−4.39582	−	7.61378i	−0.331347	−	0.573910i
$177$	4.70475	+	2.72005i	0.353631	+	0.204452i
$178$	2.17211	+	20.6663i	0.162807	+	1.54900i
$179$	−2.87256	+	2.08704i	−0.214705	+	0.155993i	−0.689940	−	0.723866i	$-0.742363\pi$
$179$	−2.87256	+	2.08704i	−0.214705	+	0.155993i	0.475235	+	0.879859i	$0.342363\pi$
$180$	−18.8324	+	1.86945i	−1.40369	+	0.139341i
$181$	−6.24166	−	4.53483i	−0.463939	−	0.337071i	0.331136	−	0.943583i	$-0.392568\pi$
$181$	−6.24166	−	4.53483i	−0.463939	−	0.337071i	−0.795074	+	0.606512i	$0.792568\pi$
$182$	−13.6421	+	23.6287i	−1.01122	+	1.75148i
$183$	8.77006	+	12.0862i	0.648302	+	0.893437i
$184$	−14.7387	+	3.13281i	−1.08655	+	0.230953i
$185$	−6.32175	+	0.635207i	−0.464784	+	0.0467013i
$186$	11.1224	−	6.41263i	0.815535	−	0.470197i
$187$	−15.3750	−	17.0757i	−1.12433	−	1.24870i
$188$	0.929101	−	2.85948i	0.0677616	−	0.208549i
$189$	−6.79023	−	15.3253i	−0.493917	−	1.11475i
$190$	6.65621	−	14.7678i	0.482892	−	1.07137i
$191$	−13.8479	−	15.3796i	−1.00200	−	1.11283i	−0.993610	−	0.112866i	$-0.963997\pi$
$191$	−13.8479	−	15.3796i	−1.00200	−	1.11283i	−0.00838758	−	0.999965i	$-0.502670\pi$
$192$	−8.93577	+	20.0377i	−0.644884	+	1.44610i
$193$	−7.77957	−	13.4746i	−0.559986	−	0.969924i	−0.997497	−	0.0707108i	$-0.977473\pi$
$193$	−7.77957	−	13.4746i	−0.559986	−	0.969924i	0.437511	−	0.899213i	$-0.355860\pi$
$194$	−0.439123	+	4.17798i	−0.0315272	+	0.299961i
$195$	−1.63620	+	14.8287i	−0.117171	+	1.06190i
$196$	−1.00450	−	9.55722i	−0.0717503	−	0.682659i
$197$	−10.3126	+	7.49255i	−0.734743	+	0.533822i	−0.891060	−	0.453885i	$-0.850038\pi$
$197$	−10.3126	+	7.49255i	−0.734743	+	0.533822i	0.156318	+	0.987707i	$0.450038\pi$
$198$	−10.6703	+	32.7063i	−0.758308	+	2.32434i
$199$	−12.3483			−0.875345			−0.437673	−	0.899134i	$-0.644197\pi$
$199$	−12.3483			−0.875345			−0.437673	+	0.899134i	$0.644197\pi$
$200$	−8.83506	+	1.79359i	−0.624733	+	0.126826i
$201$	4.48649	−	4.03479i	0.316453	−	0.284592i
$202$	6.32279	−	7.02217i	0.444870	−	0.494078i
$203$	−2.95448	−	1.31542i	−0.207364	−	0.0923244i
$204$	−4.48228	+	21.0254i	−0.313822	+	1.47207i
$205$	8.00021	+	11.1180i	0.558759	+	0.776514i
$206$	1.89339	+	1.37563i	0.131919	+	0.0958446i
$207$	−20.2649	−	14.7605i	−1.40851	−	1.02593i
$208$	5.24583	+	3.81132i	0.363733	+	0.264267i
$209$	−11.5299	−	12.8052i	−0.797538	−	0.885755i
$210$	−13.5933	−	23.8282i	−0.938024	−	1.64430i
$211$	−1.81934	+	2.02058i	−0.125248	+	0.139102i	−0.802507	−	0.596643i	$-0.796501\pi$
$211$	−1.81934	+	2.02058i	−0.125248	+	0.139102i	0.677259	+	0.735745i	$0.263168\pi$
$212$	20.5960	−	4.37781i	1.41454	−	0.300669i
$213$	−23.4742	−	2.48148i	−1.60843	−	0.170028i
$214$	26.3799	+	5.60723i	1.80330	+	0.383302i
$215$	10.0820	+	1.10633i	0.687585	+	0.0754510i
$216$	8.91560	−	2.87913i	0.606630	−	0.195900i
$217$	8.81024	+	6.40101i	0.598078	+	0.434529i
$218$	1.46820	−	2.54299i	0.0994388	−	0.172233i
$219$	−0.732084	+	1.64164i	−0.0494696	+	0.110931i
$220$	−6.99741	+	32.1951i	−0.471766	+	2.17059i
$221$	15.4818	+	6.89293i	1.04142	+	0.463669i
$222$	10.2793	−	3.33311i	0.689898	−	0.223704i
$223$	17.1974	+	3.65542i	1.15162	+	0.244785i	0.743881	−	0.668313i	$-0.232983\pi$
$223$	17.1974	+	3.65542i	1.15162	+	0.244785i	0.407741	+	0.913097i	$0.366316\pi$
$224$	−23.5562			−1.57392
$225$	−12.0433	−	8.94193i	−0.802889	−	0.596129i
$226$	−11.0113			−0.732461
$227$	22.7969	+	4.84564i	1.51309	+	0.321616i	0.888331	−	0.459205i	$-0.151866\pi$
$227$	22.7969	+	4.84564i	1.51309	+	0.321616i	0.624755	+	0.780821i	$0.285199\pi$
$228$	−3.36131	+	15.7672i	−0.222608	+	1.04421i
$229$	−21.5190	−	9.58088i	−1.42202	−	0.633122i	−0.455619	−	0.890175i	$-0.650582\pi$
$229$	−21.5190	−	9.58088i	−1.42202	−	0.633122i	−0.966397	+	0.257052i	$0.917249\pi$
$230$	−35.4392	−	20.6776i	−2.33679	−	1.36344i
$231$	−29.0235	+	3.03289i	−1.90960	+	0.199549i
$232$	0.903819	−	1.56546i	0.0593386	−	0.102778i
$233$	−12.4694	−	9.05954i	−0.816897	−	0.593510i	0.0989251	−	0.995095i	$-0.468460\pi$
$233$	−12.4694	−	9.05954i	−0.816897	−	0.593510i	−0.915822	+	0.401585i	$0.868460\pi$
$234$	−2.62198	−	25.2378i	−0.171404	−	1.64984i
$235$	2.06923	−	1.18208i	0.134982	−	0.0771102i
$236$	−8.65824	−	1.84037i	−0.563604	−	0.119798i
$237$	8.19297	−	11.2624i	0.532191	−	0.731574i
$238$	−30.4815	+	6.47903i	−1.97582	+	0.419973i
$239$	16.3356	−	18.1425i	1.05666	−	1.17354i	0.0722970	−	0.997383i	$-0.476967\pi$
$239$	16.3356	−	18.1425i	1.05666	−	1.17354i	0.984362	−	0.176156i	$-0.0563663\pi$
$240$	−5.96955	+	2.62087i	−0.385333	+	0.169177i
$241$	9.25531	+	10.2791i	0.596187	+	0.662132i	0.963420	−	0.267996i	$-0.0863615\pi$
$241$	9.25531	+	10.2791i	0.596187	+	0.662132i	−0.367233	+	0.930129i	$0.619695\pi$
$242$	28.9139	+	21.0072i	1.85866	+	1.35039i
$243$	13.4766	+	7.83469i	0.864522	+	0.502595i
$244$	−19.6775	−	14.2965i	−1.25972	−	0.915240i
$245$	4.50520	−	6.14158i	0.287827	−	0.392371i
$246$	−17.3030	−	15.5985i	−1.10320	−	0.994526i
$247$	11.6099	+	5.16908i	0.738723	+	0.328901i
$248$	−4.07288	+	4.52339i	−0.258628	+	0.287235i
$249$	−9.45659	−	3.07890i	−0.599287	−	0.195118i
$250$	−21.0894	−	12.5651i	−1.33381	−	0.794689i
$251$	−25.5927			−1.61539			−0.807697	−	0.589597i	$-0.799286\pi$
$251$	−25.5927			−1.61539			−0.807697	+	0.589597i	$0.799286\pi$
$252$	18.2445	+	20.3115i	1.14929	+	1.27950i
$253$	−35.3102	+	25.6544i	−2.21994	+	1.61288i
$254$	0.789845	+	7.51487i	0.0495593	+	0.471525i
$255$	−13.8367	+	9.94396i	−0.866490	+	0.622715i
$256$	0.383451	−	3.64829i	0.0239657	−	0.228018i
$257$	10.0340	+	17.3794i	0.625904	+	1.08410i	0.988365	+	0.152098i	$0.0486030\pi$
$257$	10.0340	+	17.3794i	0.625904	+	1.08410i	−0.362462	+	0.931999i	$0.618064\pi$
$258$	−17.1569	+	1.79286i	−1.06814	+	0.111618i
$259$	6.13329	+	6.81171i	0.381104	+	0.423259i
$260$	−4.94334	−	23.7914i	−0.306573	−	1.47548i
$261$	2.94265	−	0.621790i	0.182145	−	0.0384878i
$262$	−0.504108	+	1.55148i	−0.0311439	+	0.0958511i
$263$	15.1483	+	16.8239i	0.934087	+	1.03741i	0.999218	+	0.0395323i	$0.0125868\pi$
$263$	15.1483	+	16.8239i	0.934087	+	1.03741i	−0.0651310	+	0.997877i	$0.520747\pi$
$264$	0.00978472	−	16.3105i	0.000602208	−	1.00384i
$265$	14.4149	+	8.41062i	0.885498	+	0.516660i
$266$	−22.8584	+	4.85870i	−1.40154	+	0.297906i
$267$	6.67621	−	14.9708i	0.408577	−	0.916200i
$268$	−4.91403	+	8.51135i	−0.300172	+	0.519914i
$269$	1.07380	+	0.780162i	0.0654708	+	0.0475673i	0.620039	−	0.784571i	$-0.287117\pi$
$269$	1.07380	+	0.780162i	0.0654708	+	0.0475673i	−0.554568	+	0.832138i	$0.687117\pi$
$270$	23.2397	+	10.5250i	1.41432	+	0.640532i
$271$	19.3662	−	14.0704i	1.17641	−	0.854714i	0.184650	−	0.982804i	$-0.440885\pi$
$271$	19.3662	−	14.0704i	1.17641	−	0.854714i	0.991762	+	0.128091i	$0.0408848\pi$
$272$	0.774128	+	7.36533i	0.0469384	+	0.446589i
$273$	18.6455	−	10.7501i	1.12848	−	0.650626i
$274$	8.80122	+	15.2442i	0.531701	+	0.920933i
$275$	−21.2660	+	15.1552i	−1.28239	+	0.913894i
$276$	38.8290	+	12.6421i	2.33723	+	0.760964i
$277$	−13.8752	−	2.94926i	−0.833680	−	0.177204i	−0.228752	−	0.973485i	$-0.573465\pi$
$277$	−13.8752	−	2.94926i	−0.833680	−	0.177204i	−0.604928	+	0.796281i	$0.706798\pi$
$278$	22.4316	−	16.2975i	1.34536	−	0.977459i
$279$	−10.1275	−	0.0121510i	−0.606317	−	0.000727463i
$280$	9.62540	+	8.74684i	0.575228	+	0.522724i
$281$	13.2772	−	5.91140i	0.792052	−	0.352644i	0.0294948	−	0.999565i	$-0.490610\pi$
$281$	13.2772	−	5.91140i	0.792052	−	0.352644i	0.762557	+	0.646921i	$0.223943\pi$
$282$	−3.01367	+	2.71025i	−0.179462	+	0.161393i
$283$	0.751288	−	7.14803i	0.0446595	−	0.424906i	−0.949235	−	0.314569i	$-0.898140\pi$
$283$	0.751288	−	7.14803i	0.0446595	−	0.424906i	0.993894	−	0.110338i	$-0.0351932\pi$
$284$	37.6078	−	7.99378i	2.23161	−	0.474343i
$285$	−10.3763	+	7.45708i	−0.614640	+	0.441719i
$286$	−43.2079	−	9.18412i	−2.55494	−	0.543068i
$287$	6.10630	−	18.7933i	0.360443	−	1.10933i
$288$	17.7384	−	12.8552i	1.04524	−	0.757499i
$289$	0.727994	+	2.24054i	0.0428232	+	0.131796i
$290$	4.68825	−	1.49962i	0.275303	−	0.0880607i
$291$	1.94946	−	2.67981i	0.114279	−	0.157093i
$292$	0.306031	−	2.91169i	0.0179091	−	0.170394i
$293$	−2.28853	−	3.96384i	−0.133697	−	0.231570i	0.791402	−	0.611296i	$-0.209352\pi$
$293$	−2.28853	−	3.96384i	−0.133697	−	0.231570i	−0.925099	+	0.379726i	$0.876018\pi$
$294$	−5.27622	+	11.8315i	−0.307715	+	0.690026i
$295$	−4.09780	−	5.69476i	−0.238583	−	0.331562i
$296$	−4.14477	+	3.01135i	−0.240910	+	0.175031i
$297$	20.2002	−	18.1226i	1.17213	−	1.05158i
$298$	13.5982	+	41.8509i	0.787721	+	2.42436i
$299$	16.0953	−	27.8779i	0.930817	−	1.61222i
$300$	23.1615	+	7.77617i	1.33723	+	0.448957i
$301$	−7.31609	−	12.6718i	−0.421692	−	0.730392i
$302$	−14.8601	+	16.5038i	−0.855100	+	0.949685i
$303$	−7.09044	+	2.29912i	−0.407335	+	0.132081i
$304$	0.580527	+	5.52334i	0.0332955	+	0.316785i
$305$	−3.92183	−	18.8751i	−0.224563	−	1.08079i
$306$	19.4175	−	21.5133i	1.11002	−	1.22983i
$307$	4.27331			0.243891			0.121945	−	0.992537i	$-0.461087\pi$
$307$	4.27331			0.243891			0.121945	+	0.992537i	$0.461087\pi$
$308$	43.4216	−	19.3326i	2.47418	−	1.10157i
$309$	−0.749885	−	1.68699i	−0.0426594	−	0.0959696i
$310$	−16.4915	+	1.65706i	−0.936656	+	0.0941148i
$311$	0.233840	−	0.259706i	0.0132599	−	0.0147266i	−0.736478	−	0.676461i	$-0.763513\pi$
$311$	0.233840	−	0.259706i	0.0132599	−	0.0147266i	0.749738	+	0.661734i	$0.230179\pi$
$312$	4.88632	+	10.9926i	0.276633	+	0.622333i
$313$	6.46078	+	7.17542i	0.365185	+	0.405579i	0.897533	−	0.440947i	$-0.145357\pi$
$313$	6.46078	+	7.17542i	0.365185	+	0.405579i	−0.532349	+	0.846525i	$0.678690\pi$
$314$	−3.57049	−	10.9889i	−0.201495	−	0.620137i
$315$	−0.124994	+	21.6395i	−0.00704263	+	1.21925i
$316$	−7.00996	+	21.5744i	−0.394341	+	1.21366i
$317$	−1.38073	+	0.614743i	−0.0775498	+	0.0345274i	−0.445145	−	0.895459i	$-0.646848\pi$
$317$	−1.38073	+	0.614743i	−0.0775498	+	0.0345274i	0.367595	+	0.929986i	$0.380181\pi$
$318$	−26.9903	−	8.78757i	−1.51354	−	0.492782i
$319$	0.547312	−	5.20732i	0.0306436	−	0.291554i
$320$	21.1355	−	18.8561i	1.18151	−	1.05409i
$321$	−15.8013	−	14.2447i	−0.881942	−	0.795062i
$322$	6.18736	+	58.8688i	0.344808	+	3.28063i
$323$	4.48543	+	13.8047i	0.249576	+	0.768116i
$324$	−24.8229	−	5.33857i	−1.37905	−	0.296587i
$325$	9.78222	−	16.5907i	0.542620	−	0.920289i
$326$	25.0229	−	43.3409i	1.38589	−	2.40043i
$327$	−2.00669	+	1.15696i	−0.110970	+	0.0639798i
$328$	10.0899	+	4.49230i	0.557120	+	0.248046i
$329$	−3.14073	−	1.39834i	−0.173154	−	0.0770931i
$330$	29.8892	−	32.8517i	1.64535	−	1.80843i
$331$	1.47785	−	0.657983i	0.0812301	−	0.0361660i	−0.365719	−	0.930725i	$-0.619177\pi$
$331$	1.47785	−	0.657983i	0.0812301	−	0.0361660i	0.446950	+	0.894559i	$0.352510\pi$
$332$	16.1987			0.889022
$333$	−8.33582	−	1.78229i	−0.456800	−	0.0976688i
$334$	−4.75852	+	14.6452i	−0.260374	+	0.801350i
$335$	−7.41943	+	2.37324i	−0.405367	+	0.129664i
$336$	8.14257	+	4.70763i	0.444214	+	0.256822i
$337$	8.95098	−	1.90259i	0.487591	−	0.103641i	0.0424451	−	0.999099i	$-0.486485\pi$
$337$	8.95098	−	1.90259i	0.487591	−	0.103641i	0.445146	+	0.895458i	$0.353152\pi$
$338$	3.94707	−	0.838976i	0.214692	−	0.0456343i
$339$	7.51974	+	4.34754i	0.408416	+	0.236126i
$340$	16.4158	−	22.3783i	0.890270	−	1.21363i
$341$	−5.44830	+	16.7682i	−0.295042	+	0.908046i
$342$	14.5614	−	16.1331i	0.787388	−	0.872376i
$343$	11.5927			0.625949
$344$	7.47135	−	3.32646i	0.402828	−	0.179351i
$345$	16.0378	+	28.1133i	0.863444	+	1.51357i
$346$	−9.79824	−	4.36246i	−0.526757	−	0.234527i
$347$	−26.5194	−	11.8072i	−1.42364	−	0.633845i	−0.456878	−	0.889529i	$-0.651033\pi$
$347$	−26.5194	−	11.8072i	−1.42364	−	0.633845i	−0.966760	+	0.255684i	$0.917699\pi$
$348$	−4.24398	+	2.44687i	−0.227501	+	0.131166i
$349$	7.82775	−	13.5581i	0.419010	−	0.725746i	−0.576830	−	0.816864i	$-0.695711\pi$
$349$	7.82775	−	13.5581i	0.419010	−	0.725746i	0.995840	+	0.0911179i	$0.0290440\pi$
$350$	3.37942	+	35.2540i	0.180638	+	1.88441i
$351$	−8.17393	+	18.2704i	−0.436292	+	0.975201i
$352$	−11.7852	−	36.2711i	−0.628153	−	1.93326i
$353$	3.56260	+	33.8959i	0.189618	+	1.80410i	0.513597	+	0.858032i	$0.328313\pi$
$353$	3.56260	+	33.8959i	0.189618	+	1.80410i	−0.323979	+	0.946064i	$0.605021\pi$
$354$	8.86281	+	7.98975i	0.471053	+	0.424650i
$355$	26.3212	+	15.3576i	1.39699	+	0.815097i
$356$	−2.79084	+	26.5531i	−0.147914	+	1.40731i
$357$	23.3742	+	7.61025i	1.23710	+	0.402777i
$358$	−7.12227	+	3.17104i	−0.376423	+	0.167595i
$359$	−5.81490	+	17.8964i	−0.306898	+	0.944536i	0.672064	+	0.740494i	$0.265408\pi$
$359$	−5.81490	+	17.8964i	−0.306898	+	0.944536i	−0.978962	+	0.204043i	$0.934592\pi$
$360$	−12.0215	−	1.33376i	−0.633589	−	0.0702953i
$361$	−2.50765	−	7.71776i	−0.131982	−	0.406198i
$362$	−11.3352	−	12.5890i	−0.595765	−	0.661665i
$363$	−11.4515	−	25.7620i	−0.601046	−	1.35215i
$364$	−23.4571	+	26.0517i	−1.22948	+	1.36548i
$365$	1.73158	−	1.54483i	0.0906349	−	0.0808600i
$366$	13.3182	+	29.9616i	0.696155	+	1.56612i
$367$	−8.82813	+	3.93054i	−0.460824	+	0.205172i	−0.623999	−	0.781425i	$-0.714493\pi$
$367$	−8.82813	+	3.93054i	−0.460824	+	0.205172i	0.163175	+	0.986597i	$0.447827\pi$
$368$	14.0675			0.733320
$369$	5.65774	+	17.4841i	0.294530	+	0.910186i
$370$	−13.8674	−	1.52172i	−0.720933	−	0.0791104i
$371$	−2.51670	−	23.9448i	−0.130661	−	1.24315i
$372$	15.6914	−	5.08804i	0.813561	−	0.263803i
$373$	−10.1373	+	11.2587i	−0.524892	+	0.582951i	−0.946044	−	0.324039i	$-0.894959\pi$
$373$	−10.1373	+	11.2587i	−0.524892	+	0.582951i	0.421152	+	0.906990i	$0.361626\pi$
$374$	−25.2261	−	43.6929i	−1.30441	−	2.25931i
$375$	9.44117	+	16.9075i	0.487540	+	0.873101i
$376$	0.960794	−	1.66414i	0.0495492	−	0.0858217i
$377$	1.19335	+	3.67276i	0.0614608	+	0.189157i
$378$	−7.58739	−	36.0145i	−0.390253	−	1.85238i
$379$	18.3810	−	13.3546i	0.944168	−	0.685978i	−0.00525227	−	0.999986i	$-0.501672\pi$
$379$	18.3810	−	13.3546i	0.944168	−	0.685978i	0.949420	+	0.314008i	$0.101672\pi$
$380$	12.3104	−	16.7817i	0.631508	−	0.860884i
$381$	2.42767	−	5.44385i	0.124373	−	0.278897i
$382$	−22.7205	−	39.3531i	−1.16248	−	2.01348i
$383$	−2.07829	+	19.7736i	−0.106196	+	1.01039i	0.803555	+	0.595231i	$0.202939\pi$
$383$	−2.07829	+	19.7736i	−0.106196	+	1.01039i	−0.909751	+	0.415155i	$0.863727\pi$
$384$	−13.4584	+	18.5006i	−0.686798	+	0.944105i
$385$	35.7756	+	11.8055i	1.82330	+	0.601663i
$386$	−10.5571	−	32.4914i	−0.537342	−	1.65377i
$387$	12.4245	+	5.54961i	0.631573	+	0.282103i
$388$	−1.66797	+	5.13347i	−0.0846782	+	0.260613i
$389$	−22.2828	−	4.73636i	−1.12978	−	0.240143i	−0.395156	−	0.918614i	$-0.629309\pi$
$389$	−22.2828	−	4.73636i	−1.12978	−	0.240143i	−0.734627	+	0.678471i	$0.762643\pi$
$390$	−10.2836	+	31.1011i	−0.520733	+	1.57487i
$391$	35.9630	−	7.64417i	1.81873	−	0.386582i
$392$	0.641995	−	6.10818i	0.0324257	−	0.308510i
$393$	0.956827	−	0.860492i	0.0482655	−	0.0434061i
$394$	−25.5692	+	11.3841i	−1.28816	+	0.573525i
$395$	−15.6121	+	8.91863i	−0.785529	+	0.448745i
$396$	−22.1472	+	38.2541i	−1.11294	+	1.92234i
$397$	−27.7854	+	20.1873i	−1.39451	+	1.01317i	−0.399158	+	0.916882i	$0.630697\pi$
$397$	−27.7854	+	20.1873i	−1.39451	+	1.01317i	−0.995353	+	0.0962893i	$0.969303\pi$
$398$	−26.5208	−	5.63717i	−1.32937	−	0.282566i
$399$	17.5286	+	5.70701i	0.877527	+	0.285708i
$400$	8.41635	+	0.0770342i	0.420817	+	0.00385171i
$401$	8.47125	+	14.6726i	0.423034	+	0.732716i	0.996235	−	0.0866987i	$-0.0276317\pi$
$401$	8.47125	+	14.6726i	0.423034	+	0.732716i	−0.573201	+	0.819415i	$0.694298\pi$
$402$	11.4777	−	6.61750i	0.572458	−	0.330051i
$403$	−1.35925	−	12.9324i	−0.0677092	−	0.644210i
$404$	9.82219	−	7.13624i	0.488672	−	0.355041i
$405$	−11.7151	−	16.3633i	−0.582127	−	0.813098i
$406$	−5.74493	−	4.17394i	−0.285116	−	0.207149i
$407$	−7.41996	+	12.8517i	−0.367794	+	0.637037i
$408$	−5.59595	+	12.5484i	−0.277041	+	0.621241i
$409$	−17.6749	+	3.75692i	−0.873969	+	0.185768i	−0.622995	−	0.782226i	$-0.714084\pi$
$409$	−17.6749	+	3.75692i	−0.873969	+	0.185768i	−0.250974	+	0.967994i	$0.580751\pi$
$410$	12.1068	+	27.5307i	0.597912	+	1.35964i
$411$	0.00832987	−	13.8854i	0.000410882	−	0.684914i
$412$	2.01209	+	2.23465i	0.0991283	+	0.110093i
$413$	−3.12772	+	9.62612i	−0.153905	+	0.473671i
$414$	−36.7853	−	40.9529i	−1.80790	−	2.01273i
$415$	9.50195	+	8.63466i	0.466433	+	0.423859i
$416$	18.8214	+	20.9033i	0.922795	+	1.02487i
$417$	−21.7535	+	2.27319i	−1.06527	+	0.111319i
$418$	−18.9173	−	32.7658i	−0.925276	−	1.60263i
$419$	0.560784	−	5.33551i	0.0273961	−	0.260657i	−0.972247	−	0.233955i	$-0.924833\pi$
$419$	0.560784	−	5.33551i	0.0273961	−	0.260657i	0.999643	−	0.0267013i	$-0.00850028\pi$
$420$	−10.7183	−	33.5780i	−0.523000	−	1.63844i
$421$	−2.61154	−	24.8472i	−0.127279	−	1.21098i	−0.852599	−	0.522565i	$-0.824975\pi$
$421$	−2.61154	−	24.8472i	−0.127279	−	1.21098i	0.725321	−	0.688411i	$-0.241691\pi$
$422$	−4.82987	+	3.50911i	−0.235115	+	0.170821i
$423$	3.12815	−	0.660987i	0.152096	−	0.0321383i
$424$	13.4573			0.653544
$425$	21.5579	−	4.37644i	1.04571	−	0.212289i
$426$	−49.2836	−	16.0459i	−2.38780	−	0.777427i
$427$	−18.6098	+	20.6683i	−0.900592	+	1.00021i
$428$	31.6557	+	14.0940i	1.53014	+	0.681261i
$429$	25.8810	+	23.3315i	1.24955	+	1.12646i
$430$	21.1484	+	6.97868i	1.01986	+	0.336542i
$431$	22.8037	+	16.5678i	1.09841	+	0.798044i	0.980800	−	0.195016i	$-0.0624757\pi$
$431$	22.8037	+	16.5678i	1.09841	+	0.798044i	0.117613	+	0.993059i	$0.462476\pi$
$432$	−8.70061	+	0.898642i	−0.418608	+	0.0432359i
$433$	−16.8101	−	12.2132i	−0.807840	−	0.586930i	0.105363	−	0.994434i	$-0.466399\pi$
$433$	−16.8101	−	12.2132i	−0.807840	−	0.586930i	−0.913204	+	0.407503i	$0.866399\pi$
$434$	15.9999	+	17.7697i	0.768020	+	0.852972i
$435$	−3.79375	−	0.826933i	−0.181896	−	0.0396484i
$436$	2.52452	−	2.80376i	0.120902	−	0.134276i
$437$	26.9690	−	5.73244i	1.29010	−	0.274220i
$438$	−2.32175	+	3.19159i	−0.110938	+	0.152500i
$439$	−22.2979	−	4.73956i	−1.06422	−	0.226207i	−0.357654	−	0.933854i	$-0.616423\pi$
$439$	−22.2979	−	4.73956i	−1.06422	−	0.226207i	−0.706566	+	0.707647i	$0.749757\pi$
$440$	−8.65251	+	19.1969i	−0.412492	+	0.915178i
$441$	8.27456	−	5.99667i	0.394027	−	0.285556i
$442$	30.1040	+	21.8718i	1.43190	+	1.04034i
$443$	0.774060	−	1.34071i	0.0367767	−	0.0636991i	−0.847051	−	0.531511i	$-0.821624\pi$
$443$	0.774060	−	1.34071i	0.0367767	−	0.0636991i	0.883828	+	0.467812i	$0.154958\pi$
$444$	13.8091	−	1.44302i	0.655351	−	0.0684827i
$445$	−15.7910	+	14.0880i	−0.748567	+	0.667836i
$446$	35.2667	+	15.7017i	1.66992	+	0.743498i
$447$	7.23745	−	33.9494i	0.342320	−	1.60575i
$448$	−39.9693	−	8.49574i	−1.88837	−	0.401386i
$449$	−9.38310			−0.442816			−0.221408	−	0.975181i	$-0.571065\pi$
$449$	−9.38310			−0.442816			−0.221408	+	0.975181i	$0.571065\pi$
$450$	−21.7838	−	24.7029i	−1.02690	−	1.16450i
$451$	31.9922			1.50646
$452$	−13.8387	−	2.94151i	−0.650919	−	0.138357i
$453$	16.6642	−	5.40348i	0.782953	−	0.253878i
$454$	46.7497	+	20.8143i	2.19407	+	0.976863i
$455$	−27.6463	+	2.77789i	−1.29608	+	0.130229i
$456$	−4.19646	+	9.41021i	−0.196517	+	0.440674i
$457$	−11.1738	+	19.3536i	−0.522688	+	0.905323i	0.476963	+	0.878923i	$0.341737\pi$
$457$	−11.1738	+	19.3536i	−0.522688	+	0.905323i	−0.999651	+	0.0263993i	$0.991596\pi$
$458$	−41.8433	−	30.4009i	−1.95521	−	1.42054i
$459$	−21.7544	+	7.02518i	−1.01541	+	0.327907i
$460$	−39.0153	−	35.4542i	−1.81910	−	1.65306i
$461$	22.8998	+	4.86750i	1.06655	+	0.226702i	0.707570	−	0.706643i	$-0.249791\pi$
$461$	22.8998	+	4.86750i	1.06655	+	0.226702i	0.358980	+	0.933345i	$0.383125\pi$
$462$	−63.7192	−	6.73581i	−2.96449	−	0.313378i
$463$	28.4839	−	6.05443i	1.32376	−	0.281373i	0.508795	−	0.860888i	$-0.330091\pi$
$463$	28.4839	−	6.05443i	1.32376	−	0.281373i	0.814962	+	0.579514i	$0.196758\pi$
$464$	−1.12924	+	1.25414i	−0.0524235	+	0.0582222i
$465$	11.9165	+	5.37965i	0.552615	+	0.249475i
$466$	−22.6451	−	25.1500i	−1.04902	−	1.16505i
$467$	−22.3500	−	16.2382i	−1.03423	−	0.751415i	−0.0650824	−	0.997880i	$-0.520731\pi$
$467$	−22.3500	−	16.2382i	−1.03423	−	0.751415i	−0.969152	+	0.246465i	$0.920731\pi$
$468$	3.44666	−	32.4186i	0.159322	−	1.49855i
$469$	9.09170	+	6.60551i	0.419816	+	0.305014i
$470$	4.98379	−	1.59415i	0.229885	−	0.0735328i
$471$	−1.90035	+	8.91414i	−0.0875634	+	0.410742i
$472$	−5.16815	−	2.30101i	−0.237884	−	0.105913i
$473$	15.8514	−	17.6048i	0.728850	−	0.809470i
$474$	22.7378	−	20.4485i	1.04438	−	0.939232i
$475$	16.1665	−	3.28194i	0.741770	−	0.150586i
$476$	−40.0391			−1.83519
$477$	14.9624	+	16.6576i	0.685081	+	0.762698i
$478$	43.3668	−	31.5078i	1.98355	−	1.44113i
$479$	0.559570	+	5.32396i	0.0255674	+	0.243258i	0.999840	+	0.0178851i	$0.00569331\pi$
$479$	0.559570	+	5.32396i	0.0255674	+	0.243258i	−0.974273	+	0.225373i	$0.927640\pi$
$480$	−27.6935	+	5.73678i	−1.26403	+	0.261847i
$481$	1.14407	−	10.8851i	0.0521651	−	0.496318i
$482$	15.1854	+	26.3019i	0.691676	+	1.19802i
$483$	19.0175	−	42.6451i	0.865325	−	1.94042i
$484$	30.7265	+	34.1252i	1.39666	+	1.55115i
$485$	−3.71478	+	2.12212i	−0.168679	+	0.0963605i
$486$	25.3674	+	22.9791i	1.15069	+	1.04235i
$487$	−10.3850	+	31.9619i	−0.470591	+	1.44833i	0.381221	+	0.924484i	$0.375504\pi$
$487$	−10.3850	+	31.9619i	−0.470591	+	1.44833i	−0.851812	+	0.523848i	$0.824496\pi$
$488$	−10.4017	−	11.5522i	−0.470861	−	0.522944i
$489$	−34.2005	+	19.7183i	−1.54660	+	0.891694i
$490$	12.4797	−	11.1338i	0.563775	−	0.502973i
$491$	−18.0180	+	3.82984i	−0.813139	+	0.172838i	−0.595670	−	0.803229i	$-0.703113\pi$
$491$	−18.0180	+	3.82984i	−0.813139	+	0.172838i	−0.217469	+	0.976067i	$0.569780\pi$
$492$	−17.5791	−	24.2261i	−0.792526	−	1.09220i
$493$	−2.20535	+	3.81978i	−0.0993241	+	0.172034i
$494$	22.5753	+	16.4019i	1.01571	+	0.737958i
$495$	−33.3824	+	10.6338i	−1.50043	+	0.477955i
$496$	4.59738	−	3.34019i	0.206429	−	0.149979i
$497$	−4.59544	−	43.7227i	−0.206134	−	1.96123i
$498$	−18.9047	−	10.9297i	−0.847139	−	0.489774i
$499$	−4.11042	−	7.11946i	−0.184008	−	0.318711i	0.759234	−	0.650818i	$-0.225574\pi$
$499$	−4.11042	−	7.11946i	−0.184008	−	0.318711i	−0.943242	+	0.332107i	$0.892241\pi$
$500$	−23.1480	−	21.4253i	−1.03521	−	0.958168i
$501$	9.03195	−	8.12260i	0.403518	−	0.362891i
$502$	−54.9663	−	11.6834i	−2.45326	−	0.521457i
$503$	−7.60211	+	5.52326i	−0.338961	+	0.246270i	−0.744223	−	0.667931i	$-0.767180\pi$
$503$	−7.60211	+	5.52326i	−0.338961	+	0.246270i	0.405262	+	0.914201i	$0.367180\pi$
$504$	8.70654	+	15.1220i	0.387820	+	0.673589i
$505$	9.56549	+	1.04965i	0.425659	+	0.0467090i
$506$	−87.5486	+	38.9792i	−3.89201	+	1.73284i
$507$	−3.02675	−	0.985458i	−0.134423	−	0.0437657i
$508$	−1.01483	+	9.65550i	−0.0450260	+	0.428393i
$509$	26.8468	−	5.70646i	1.18996	−	0.252934i	0.429956	−	0.902850i	$-0.358529\pi$
$509$	26.8468	−	5.70646i	1.18996	−	0.252934i	0.760007	+	0.649915i	$0.225196\pi$
$510$	−34.2572	+	15.0403i	−1.51693	+	0.665996i
$511$	−3.27458	−	0.696033i	−0.144859	−	0.0307907i
$512$	−5.67432	+	17.4638i	−0.250772	+	0.771797i
$513$	−16.3139	+	5.26826i	−0.720275	+	0.232599i
$514$	13.6164	+	41.9070i	0.600594	+	1.84844i
$515$	−0.0109070	+	2.38334i	−0.000480622	+	0.105023i
$516$	−22.0413	−	2.33000i	−0.970313	−	0.102573i
$517$	0.581813	−	5.53558i	0.0255881	−	0.243455i
$518$	10.0630	+	17.4297i	0.442144	+	0.765817i
$519$	4.96892	+	6.84777i	0.218112	+	0.300584i
$520$	0.0710714	−	15.5301i	0.00311669	−	0.681040i
$521$	9.78838	−	7.11167i	0.428837	−	0.311568i	−0.352347	−	0.935869i	$-0.614616\pi$
$521$	9.78838	−	7.11167i	0.428837	−	0.311568i	0.781184	+	0.624301i	$0.214616\pi$
$522$	6.60388	+	0.00792338i	0.289044	+	0.000346797i
$523$	5.88343	+	18.1073i	0.257264	+	0.791778i	0.993375	+	0.114917i	$0.0366603\pi$
$523$	5.88343	+	18.1073i	0.257264	+	0.791778i	−0.736111	+	0.676861i	$0.763340\pi$
$524$	−1.04801	+	1.81520i	−0.0457824	+	0.0792974i
$525$	11.6114	−	25.4097i	0.506761	−	1.10897i
$526$	24.8542	+	43.0488i	1.08370	+	1.87702i
$527$	9.93798	−	11.0372i	0.432905	−	0.480790i
$528$	−3.17492	+	14.8929i	−0.138171	+	0.648130i
$529$	−4.89588	−	46.5812i	−0.212864	−	2.02527i
$530$	27.1197	+	24.6444i	1.17801	+	1.07048i
$531$	−2.89796	−	8.95556i	−0.125761	−	0.388638i
$532$	−30.0257			−1.30178
$533$	−21.5557	+	9.59720i	−0.933679	+	0.415701i
$534$	21.1731	−	29.1056i	0.916251	−	1.25952i
$535$	11.0560	+	25.1413i	0.477994	+	1.08695i
$536$	−4.20299	+	4.66790i	−0.181542	+	0.201622i
$537$	6.11588	+	0.646515i	0.263920	+	0.0278992i
$538$	1.95008	+	2.16579i	0.0840741	+	0.0933737i
$539$	−5.49754	−	16.9197i	−0.236796	−	0.728782i
$540$	26.3954	+	19.4357i	1.13588	+	0.836380i
$541$	−5.46686	+	16.8253i	−0.235039	+	0.723374i	0.762078	+	0.647485i	$0.224179\pi$
$541$	−5.46686	+	16.8253i	−0.235039	+	0.723374i	−0.997116	+	0.0758887i	$0.975821\pi$
$542$	48.0168	−	21.3784i	2.06250	−	0.918283i
$543$	2.77048	+	13.0726i	0.118893	+	0.561000i
$544$	−3.35813	+	31.9505i	−0.143979	+	1.36986i
$545$	2.97537	−	0.298964i	0.127451	−	0.0128062i
$546$	44.9533	−	14.5764i	1.92382	−	0.623812i
$547$	−3.24401	−	30.8647i	−0.138704	−	1.31968i	−0.813452	−	0.581632i	$-0.802414\pi$
$547$	−3.24401	−	30.8647i	−0.138704	−	1.31968i	0.674748	−	0.738048i	$-0.264252\pi$
$548$	6.98889	+	21.5096i	0.298551	+	0.918844i
$549$	2.73443	−	25.7195i	0.116703	−	1.09768i
$550$	−52.5923	+	22.8412i	−2.24254	+	0.973950i
$551$	−1.65382	+	2.86450i	−0.0704550	+	0.122032i
$552$	22.5941	+	13.0628i	0.961669	+	0.555989i
$553$	23.6964	+	10.5503i	1.00767	+	0.448646i
$554$	−28.4539	−	12.6685i	−1.20889	−	0.538232i
$555$	8.86941	+	6.51441i	0.376486	+	0.276522i
$556$	32.5451	−	14.4900i	1.38022	−	0.614513i
$557$	−7.31303			−0.309863			−0.154931	−	0.987925i	$-0.549516\pi$
$557$	−7.31303			−0.309863			−0.154931	+	0.987925i	$0.549516\pi$
$558$	−21.7456	−	4.64945i	−0.920566	−	0.196827i
$559$	−5.39917	+	16.6169i	−0.228360	+	0.702821i
$560$	−7.09212	−	9.85600i	−0.299697	−	0.416492i
$561$	−0.0238751	+	39.7983i	−0.00100801	+	1.68029i
$562$	31.2146	−	6.63486i	1.31671	−	0.279875i
$563$	37.2243	−	7.91227i	1.56882	−	0.333462i	0.660199	−	0.751091i	$-0.270472\pi$
$563$	37.2243	−	7.91227i	1.56882	−	0.333462i	0.908618	+	0.417629i	$0.137139\pi$
$564$	−4.51151	+	2.60111i	−0.189969	+	0.109527i
$565$	−6.54964	−	9.10211i	−0.275545	−	0.382928i
$566$	4.87675	−	15.0091i	0.204985	−	0.630879i
$567$	−9.03791	+	27.5904i	−0.379557	+	1.15869i
$568$	24.5727			1.03105
$569$	−27.8581	+	12.4032i	−1.16787	+	0.519971i	−0.896734	−	0.442569i	$-0.854067\pi$
$569$	−27.8581	+	12.4032i	−1.16787	+	0.519971i	−0.271140	+	0.962540i	$0.587401\pi$
$570$	−25.6898	+	11.2789i	−1.07603	+	0.472420i
$571$	−30.4237	−	13.5455i	−1.27319	−	0.566861i	−0.344873	−	0.938649i	$-0.612078\pi$
$571$	−30.4237	−	13.5455i	−1.27319	−	0.566861i	−0.928317	+	0.371789i	$0.878745\pi$
$572$	−51.8492	−	23.0847i	−2.16792	−	0.965221i
$573$	−0.0215037	+	35.8454i	−0.000898332	+	1.49746i
$574$	21.6941	−	37.5753i	0.905495	−	1.56836i
$575$	−3.98715	−	41.5938i	−0.166276	−	1.73458i
$576$	34.7341	−	15.4147i	1.44726	−	0.642280i
$577$	−3.04250	−	9.36386i	−0.126661	−	0.389823i	0.867539	−	0.497369i	$-0.165701\pi$
$577$	−3.04250	−	9.36386i	−0.126661	−	0.389823i	−0.994200	+	0.107546i	$0.965701\pi$
$578$	0.540700	+	5.14442i	0.0224902	+	0.213980i
$579$	−5.61887	+	26.3570i	−0.233512	+	1.09536i
$580$	6.29267	−	0.632285i	0.261289	−	0.0262542i
$581$	1.93614	−	18.4211i	0.0803244	−	0.764236i
$582$	5.41029	−	4.86557i	0.224264	−	0.201684i
$583$	35.6104	−	15.8548i	1.47483	−	0.656637i
$584$	0.578221	−	1.77958i	0.0239269	−	0.0736395i
$585$	19.3023	−	17.1791i	0.798053	−	0.710267i
$586$	−3.10559	−	9.55803i	−0.128291	−	0.394839i
$587$	1.66599	+	1.85027i	0.0687628	+	0.0763688i	0.776545	−	0.630062i	$-0.216971\pi$
$587$	1.66599	+	1.85027i	0.0687628	+	0.0763688i	−0.707782	+	0.706431i	$0.750304\pi$
$588$	−9.79163	+	13.4600i	−0.403800	+	0.555083i
$589$	7.45259	−	8.27695i	0.307079	−	0.341046i
$590$	−6.20125	−	14.1016i	−0.255301	−	0.580552i
$591$	21.9563	+	2.32101i	0.903160	+	0.0954737i
$592$	4.36954	−	1.94545i	0.179587	−	0.0799573i
$593$	31.8245			1.30687			0.653437	−	0.756981i	$-0.273326\pi$
$593$	31.8245			1.30687			0.653437	+	0.756981i	$0.273326\pi$
$594$	51.6579	−	29.7009i	2.11955	−	1.21864i
$595$	−23.4864	−	21.3426i	−0.962847	−	0.874963i
$596$	5.90998	+	56.2297i	0.242082	+	2.30326i
$597$	15.8857	+	14.3208i	0.650157	+	0.586110i
$598$	47.2952	−	52.5266i	1.93404	−	2.14797i
$599$	12.7051	+	22.0059i	0.519118	+	0.899139i	0.999753	+	0.0222180i	$0.00707278\pi$
$599$	12.7051	+	22.0059i	0.519118	+	0.899139i	−0.480635	+	0.876921i	$0.659594\pi$
$600$	13.4461	+	7.93897i	0.548936	+	0.324107i
$601$	−19.1020	+	33.0856i	−0.779186	+	1.34959i	0.153226	+	0.988191i	$0.451034\pi$
$601$	−19.1020	+	33.0856i	−0.779186	+	1.34959i	−0.932412	+	0.361398i	$0.882300\pi$
$602$	−9.92813	−	30.5556i	−0.404640	−	1.24535i
$603$	−10.4510	−	0.0125392i	−0.425599	−	0.000510637i
$604$	−23.0845	+	16.7719i	−0.939294	+	0.682437i
$605$	−0.166561	+	36.3960i	−0.00677167	+	1.47971i
$606$	−16.2780	+	1.70101i	−0.661247	+	0.0690988i
$607$	−9.75568	−	16.8973i	−0.395971	−	0.685842i	0.597254	−	0.802052i	$-0.296259\pi$
$607$	−9.75568	−	16.8973i	−0.395971	−	0.685842i	−0.993225	+	0.116211i	$0.962925\pi$
$608$	−2.51830	+	23.9600i	−0.102130	+	0.971706i
$609$	2.27530	+	5.11868i	0.0922000	+	0.207419i
$610$	0.193713	−	42.3291i	0.00784322	−	1.71385i
$611$	1.26858	+	3.90429i	0.0513213	+	0.157951i
$612$	30.1503	−	21.8503i	1.21876	−	0.883245i
$613$	4.69881	−	14.4615i	0.189783	−	0.584093i	−0.810215	−	0.586133i	$-0.800649\pi$
$613$	4.69881	−	14.4615i	0.189783	−	0.584093i	0.999998	+	0.00204035i	$0.000649464\pi$
$614$	9.17793	+	1.95083i	0.370391	+	0.0787291i
$615$	2.60195	−	23.5811i	0.104921	−	0.950883i
$616$	29.7140	−	6.31590i	1.19721	−	0.254475i
$617$	−3.57995	+	34.0610i	−0.144124	+	1.37124i	0.648352	+	0.761340i	$0.275458\pi$
$617$	−3.57995	+	34.0610i	−0.144124	+	1.37124i	−0.792476	+	0.609903i	$0.791208\pi$
$618$	−0.840416	−	3.96554i	−0.0338065	−	0.159518i
$619$	29.2892	−	13.0404i	1.17723	−	0.524138i	0.277563	−	0.960707i	$-0.410473\pi$
$619$	29.2892	−	13.0404i	1.17723	−	0.524138i	0.899671	+	0.436569i	$0.143807\pi$
$620$	−21.1688	−	2.32292i	−0.850159	−	0.0932909i
$621$	8.95184	+	42.4910i	0.359225	+	1.70510i
$622$	0.620787	−	0.451028i	0.0248913	−	0.0180846i
$623$	29.8624	+	6.34745i	1.19641	+	0.254305i
$624$	−2.32846	−	10.9869i	−0.0932129	−	0.439830i
$625$	−2.15767	−	24.9067i	−0.0863069	−	0.996269i
$626$	10.6003	+	18.3603i	0.423675	+	0.733827i
$627$	−0.0179042	+	29.8452i	−0.000715025	+	1.19190i
$628$	−1.55179	−	14.7643i	−0.0619233	−	0.589160i
$629$	10.1134	−	7.34782i	0.403248	−	0.292977i
$630$	−10.1472	+	46.4189i	−0.404275	+	1.84937i
$631$	−20.5908	−	14.9601i	−0.819706	−	0.595551i	0.0969226	−	0.995292i	$-0.469100\pi$
$631$	−20.5908	−	14.9601i	−0.819706	−	0.595551i	−0.916628	+	0.399741i	$0.869100\pi$
$632$	−7.24908	+	12.5558i	−0.288353	+	0.499442i
$633$	4.68386	−	0.489453i	0.186167	−	0.0194540i
$634$	−3.24609	+	0.689978i	−0.128919	+	0.0274025i
$635$	−5.74210	+	5.12282i	−0.227868	+	0.203293i
$636$	−31.5732	−	18.2541i	−1.25196	−	0.723820i
$637$	8.77978	+	9.75093i	0.347867	+	0.386346i
$638$	3.55270	−	10.9341i	0.140653	−	0.432885i
$639$	27.3210	+	30.4164i	1.08080	+	1.20325i
$640$	25.6457	−	14.6505i	1.01373	−	0.579111i
$641$	−8.76523	−	9.73477i	−0.346206	−	0.384500i	0.544744	−	0.838602i	$-0.316627\pi$
$641$	−8.76523	−	9.73477i	−0.346206	−	0.384500i	−0.890950	+	0.454102i	$0.849960\pi$
$642$	−27.4340	−	37.8074i	−1.08274	−	1.49214i
$643$	−10.3859	−	17.9890i	−0.409581	−	0.709415i	0.585262	−	0.810845i	$-0.300992\pi$
$643$	−10.3859	−	17.9890i	−0.409581	−	0.709415i	−0.994843	+	0.101429i	$0.967658\pi$
$644$	−7.94983	+	75.6376i	−0.313267	+	2.98054i
$645$	−11.6871	−	13.1157i	−0.460179	−	0.516431i
$646$	3.33144	+	31.6966i	0.131074	+	1.24708i
$647$	−20.2863	+	14.7388i	−0.797535	+	0.579443i	−0.910190	−	0.414191i	$-0.864065\pi$
$647$	−20.2863	+	14.7388i	−0.797535	+	0.579443i	0.112655	+	0.993634i	$0.464065\pi$
$648$	−14.8087	−	6.63587i	−0.581740	−	0.260682i
$649$	−16.3868			−0.643238
$650$	28.5835	−	31.1668i	1.12114	−	1.22246i
$651$	−3.91059	−	18.4523i	−0.153268	−	0.723202i
$652$	43.0260	−	47.7853i	1.68503	−	1.87141i
$653$	−32.4180	−	14.4334i	−1.26862	−	0.564824i	−0.341600	−	0.939845i	$-0.610969\pi$
$653$	−32.4180	−	14.4334i	−1.26862	−	0.564824i	−0.927016	+	0.375021i	$0.877635\pi$
$654$	−4.83800	+	1.56875i	−0.189181	+	0.0613431i
$655$	−1.58233	+	0.506136i	−0.0618268	+	0.0197764i
$656$	−8.34212	−	6.06090i	−0.325705	−	0.236638i
$657$	2.84567	−	1.26289i	0.111020	−	0.0492699i
$658$	−6.10709	−	4.43706i	−0.238079	−	0.172975i
$659$	−11.8938	−	13.2094i	−0.463317	−	0.514566i	0.465528	−	0.885033i	$-0.345864\pi$
$659$	−11.8938	−	13.2094i	−0.463317	−	0.514566i	−0.928846	+	0.370467i	$0.879198\pi$
$660$	46.3399	−	33.3028i	1.80378	−	1.29631i
$661$	−17.0651	+	18.9527i	−0.663756	+	0.737175i	−0.977174	−	0.212440i	$-0.931859\pi$
$661$	−17.0651	+	18.9527i	−0.663756	+	0.737175i	0.313419	+	0.949615i	$0.398526\pi$
$662$	3.47442	−	0.738510i	0.135037	−	0.0287030i
$663$	−11.9228	−	26.8224i	−0.463044	−	1.04169i
$664$	10.1267	+	2.15249i	0.392990	+	0.0835327i
$665$	−17.6127	−	16.0051i	−0.682990	−	0.620650i
$666$	−17.0895	−	7.63331i	−0.662204	−	0.295785i
$667$	6.77806	+	4.92455i	0.262447	+	0.190679i
$668$	−9.89264	+	17.1346i	−0.382758	+	0.662956i
$669$	−17.8846	−	24.6471i	−0.691457	−	0.952911i
$670$	−17.0184	+	1.71000i	−0.657478	+	0.0660631i
$671$	−41.1349	−	18.3144i	−1.58799	−	0.707021i
$672$	30.3044	+	27.3191i	1.16902	+	1.05386i
$673$	−28.1699	−	5.98769i	−1.08587	−	0.230808i	−0.369992	−	0.929035i	$-0.620639\pi$
$673$	−28.1699	−	5.98769i	−1.08587	−	0.230808i	−0.715877	+	0.698227i	$0.753973\pi$
$674$	20.0929			0.773949
$675$	5.12305	+	25.4707i	0.197186	+	0.980366i
$676$	5.18470			0.199411
$677$	−43.7518	−	9.29974i	−1.68152	−	0.357418i	−0.734503	−	0.678605i	$-0.762585\pi$
$677$	−43.7518	−	9.29974i	−1.68152	−	0.357418i	−0.947016	+	0.321187i	$0.895918\pi$
$678$	14.1657	+	12.7702i	0.544030	+	0.490438i
$679$	5.63839	+	2.51037i	0.216381	+	0.0963392i
$680$	13.2359	−	11.8085i	0.507575	−	0.452834i
$681$	−23.7079	−	32.6723i	−0.908488	−	1.25200i
$682$	−19.3564	+	33.5263i	−0.741196	+	1.28379i
$683$	−14.3100	−	10.3968i	−0.547556	−	0.397823i	0.279328	−	0.960196i	$-0.409888\pi$
$683$	−14.3100	−	10.3968i	−0.547556	−	0.397823i	−0.826884	+	0.562373i	$0.809888\pi$
$684$	22.6101	−	16.3858i	0.864517	−	0.626525i
$685$	−7.36600	+	16.3426i	−0.281440	+	0.624419i
$686$	24.8981	+	5.29226i	0.950614	+	0.202059i
$687$	16.5722	+	37.2820i	0.632269	+	1.42240i
$688$	−7.46855	+	1.58749i	−0.284736	+	0.0605224i
$689$	−19.2373	+	21.3652i	−0.732883	+	0.813948i
$690$	21.6107	+	67.7014i	0.822706	+	2.57735i
$691$	5.97372	+	6.63449i	0.227251	+	0.252388i	0.845977	−	0.533219i	$-0.179018\pi$
$691$	5.97372	+	6.63449i	0.227251	+	0.252388i	−0.618726	+	0.785607i	$0.712351\pi$
$692$	−11.1488	−	8.10009i	−0.423814	−	0.307919i
$693$	40.8551	+	29.7580i	1.55196	+	1.13041i
$694$	−51.5666	−	37.4653i	−1.95744	−	1.42216i
$695$	26.8143	+	8.84837i	1.01713	+	0.335638i
$696$	−2.97826	+	0.965721i	−0.112891	+	0.0366056i
$697$	−24.6197	−	10.9614i	−0.932538	−	0.415193i
$698$	23.0014	−	25.5456i	0.870615	−	0.966916i
$699$	5.53477	+	26.1161i	0.209344	+	0.987801i
$700$	−5.17044	+	45.2092i	−0.195424	+	1.70875i
$701$	26.5540			1.00293			0.501466	−	0.865177i	$-0.332794\pi$
$701$	26.5540			1.00293			0.501466	+	0.865177i	$0.332794\pi$
$702$	−25.8961	+	35.5084i	−0.977387	+	1.34018i
$703$	7.58415	−	5.51021i	0.286042	−	0.207821i
$704$	−6.91522	−	65.7939i	−0.260627	−	2.47970i
$705$	−4.03290	−	0.879062i	−0.151888	−	0.0331074i
$706$	−7.82246	+	74.4257i	−0.294402	+	2.80105i
$707$	−6.94129	−	12.0227i	−0.261054	−	0.452159i
$708$	9.00421	+	12.4089i	0.338399	+	0.466354i
$709$	31.7202	+	35.2289i	1.19128	+	1.32305i	0.934239	+	0.356647i	$0.116080\pi$
$709$	31.7202	+	35.2289i	1.19128	+	1.32305i	0.257038	+	0.966401i	$0.417253\pi$
$710$	49.5200	+	45.0001i	1.85845	+	1.68882i
$711$	−23.6015	+	4.98707i	−0.885126	+	0.187030i
$712$	−5.27306	+	16.2288i	−0.197616	+	0.608200i
$713$	−18.8772	−	20.9652i	−0.706956	−	0.785154i
$714$	46.7274	+	27.0155i	1.74873	+	1.01103i
$715$	−18.1088	−	41.1791i	−0.677230	−	1.54001i
$716$	−9.79818	+	2.08267i	−0.366175	+	0.0778329i
$717$	−42.0557	+	4.39473i	−1.57060	+	0.164124i
$718$	−20.6588	+	35.7821i	−0.770981	+	1.33538i
$719$	1.45972	+	1.06055i	0.0544382	+	0.0395517i	0.614672	−	0.788783i	$-0.289289\pi$
$719$	1.45972	+	1.06055i	0.0544382	+	0.0395517i	−0.560233	+	0.828335i	$0.689289\pi$
$720$	10.7192	+	3.55145i	0.399480	+	0.132355i
$721$	2.78172	−	2.02104i	0.103597	−	0.0752673i
$722$	−1.86250	−	17.7205i	−0.0693150	−	0.659488i
$723$	0.0143721	−	23.9574i	0.000534506	−	0.890987i
$724$	−10.8828	−	18.8496i	−0.404457	−	0.700540i
$725$	4.02823	+	2.98339i	0.149605	+	0.110800i
$726$	−12.8340	−	60.5577i	−0.476313	−	2.24751i
$727$	−10.3950	−	2.20952i	−0.385529	−	0.0819466i	0.0110701	−	0.999939i	$-0.496476\pi$
$727$	−10.3950	−	2.20952i	−0.385529	−	0.0819466i	−0.396599	+	0.917992i	$0.629810\pi$
$728$	−18.1259	+	13.1693i	−0.671792	+	0.488085i
$729$	−8.25098	−	25.7084i	−0.305592	−	0.952163i
$730$	4.42421	−	2.52739i	0.163747	−	0.0935430i
$731$	−18.2304	+	8.11669i	−0.674275	+	0.300207i
$732$	8.73421	+	41.2128i	0.322826	+	1.52327i
$733$	−3.84916	+	36.6223i	−0.142172	+	1.35268i	0.658051	+	0.752974i	$0.271381\pi$
$733$	−3.84916	+	36.6223i	−0.142172	+	1.35268i	−0.800223	+	0.599703i	$0.795285\pi$
$734$	−20.7548	+	4.41157i	−0.766074	+	0.162834i
$735$	−12.9184	+	2.67608i	−0.476504	+	0.0987089i
$736$	59.6907	+	12.6876i	2.20023	+	0.467673i
$737$	−5.62236	+	17.3039i	−0.207102	+	0.637396i
$738$	4.16958	+	40.1340i	0.153484	+	1.47735i
$739$	−11.1267	−	34.2443i	−0.409301	−	1.25970i	−0.917250	−	0.398311i	$-0.869596\pi$
$739$	−11.1267	−	34.2443i	−0.409301	−	1.25970i	0.507950	−	0.861387i	$-0.330404\pi$
$740$	−17.0217	−	5.61694i	−0.625731	−	0.206483i
$741$	−8.94105	−	20.1144i	−0.328458	−	0.738920i
$742$	5.52597	−	52.5761i	0.202865	−	1.93013i
$743$	−23.3121	−	40.3777i	−0.855238	−	1.48132i	−0.876424	−	0.481540i	$-0.840078\pi$
$743$	−23.3121	−	40.3777i	−0.855238	−	1.48132i	0.0211862	−	0.999776i	$-0.493256\pi$
$744$	10.4856	−	1.09572i	0.384420	−	0.0401710i
$745$	−26.5063	+	36.1338i	−0.971114	+	1.32384i
$746$	−26.9121	+	19.5528i	−0.985321	+	0.715877i
$747$	8.59488	+	14.9281i	0.314470	+	0.546191i
$748$	−20.0316	−	61.6509i	−0.732427	−	2.25418i
$749$	19.8113	−	34.3141i	0.723888	−	1.25381i
$750$	12.5586	+	40.6229i	0.458575	+	1.48334i
$751$	−16.8588	−	29.2004i	−0.615188	−	1.06554i	−0.990352	−	0.138578i	$-0.955747\pi$
$751$	−16.8588	−	29.2004i	−0.615188	−	1.06554i	0.375164	−	0.926959i	$-0.377586\pi$
$752$	−1.20042	+	1.33320i	−0.0437749	+	0.0486169i
$753$	32.9242	+	29.6808i	1.19982	+	1.08163i
$754$	0.886334	+	8.43291i	0.0322784	+	0.307108i
$755$	−22.4812	−	2.46694i	−0.818174	−	0.0897810i
$756$	0.0851064	−	47.2889i	0.00309529	−	1.71988i
$757$	22.9933			0.835707			0.417853	−	0.908514i	$-0.362783\pi$
$757$	22.9933			0.835707			0.417853	+	0.908514i	$0.362783\pi$
$758$	45.5741	−	20.2909i	1.65532	−	0.736998i
$759$	75.1780	+	7.94712i	2.72879	+	0.288462i
$760$	9.92578	−	8.85530i	0.360046	−	0.321215i
$761$	21.6319	−	24.0246i	0.784154	−	0.870892i	−0.210128	−	0.977674i	$-0.567388\pi$
$761$	21.6319	−	24.0246i	0.784154	−	0.870892i	0.994282	+	0.106782i	$0.0340548\pi$
$762$	7.69919	−	10.5837i	0.278912	−	0.383406i
$763$	−2.88667	−	3.20598i	−0.104505	−	0.116064i
$764$	−18.0420	−	55.5275i	−0.652736	−	2.00891i
$765$	29.3329	+	3.25443i	1.06053	+	0.117664i
$766$	−13.4906	+	41.5197i	−0.487435	+	1.50017i
$767$	11.0411	−	4.91580i	0.398670	−	0.177499i
$768$	−4.72437	+	4.24871i	−0.170476	+	0.153312i
$769$	0.702199	−	6.68098i	0.0253219	−	0.240922i	−0.974539	−	0.224220i	$-0.928017\pi$
$769$	0.702199	−	6.68098i	0.0253219	−	0.240922i	0.999861	−	0.0167023i	$-0.00531674\pi$
$770$	71.4472	+	41.6872i	2.57478	+	1.50230i
$771$	7.24715	−	33.9949i	0.261000	−	1.22430i
$772$	−4.58828	−	43.6545i	−0.165136	−	1.57116i
$773$	7.40797	+	22.7994i	0.266446	+	0.820037i	0.991357	+	0.131194i	$0.0418811\pi$
$773$	7.40797	+	22.7994i	0.266446	+	0.820037i	−0.724910	+	0.688843i	$0.758119\pi$
$774$	24.1510	+	17.5911i	0.868091	+	0.632298i
$775$	−11.1791	−	12.6465i	−0.401565	−	0.454276i
$776$	−1.72486	+	2.98755i	−0.0619190	+	0.107247i
$777$	0.00952411	−	15.8761i	0.000341675	−	0.569551i
$778$	−45.6953	−	20.3449i	−1.63826	−	0.729399i
$779$	−18.4626	−	8.22007i	−0.661490	−	0.294515i
$780$	−21.2324	+	36.3400i	−0.760243	+	1.30118i
$781$	65.0237	−	28.9504i	2.32673	−	1.03593i
$782$	80.7286			2.88685
$783$	−4.50674	−	2.61279i	−0.161058	−	0.0933736i
$784$	−1.77191	+	5.45339i	−0.0632826	+	0.194764i
$785$	6.95979	−	9.48771i	0.248405	−	0.338631i
$786$	2.44784	−	1.41130i	0.0873115	−	0.0503395i
$787$	−20.5075	+	4.35900i	−0.731013	+	0.155382i	−0.558357	−	0.829601i	$-0.688568\pi$
$787$	−20.5075	+	4.35900i	−0.731013	+	0.155382i	−0.172656	+	0.984982i	$0.555235\pi$
$788$	−35.1758	+	7.47685i	−1.25309	+	0.266352i
$789$	0.0235232	−	39.2116i	0.000837447	−	1.39597i
$790$	−37.6021	+	12.0277i	−1.33782	+	0.427926i
$791$	−4.99912	+	15.3857i	−0.177748	+	0.547053i
$792$	−18.9285	+	20.9716i	−0.672597	+	0.745194i
$793$	33.2098			1.17932
$794$	−68.8915	+	30.6725i	−2.44487	+	1.08853i
$795$	−8.79015	−	27.5375i	−0.311755	−	0.976654i
$796$	−31.8248	−	14.1693i	−1.12800	−	0.502218i
$797$	44.9022	+	19.9918i	1.59052	+	0.708144i	0.995428	−	0.0955149i	$-0.0304497\pi$
$797$	44.9022	+	19.9918i	1.59052	+	0.708144i	0.595090	+	0.803659i	$0.297116\pi$
$798$	35.0414	+	20.2592i	1.24045	+	0.717168i
$799$	−2.34438	+	4.06058i	−0.0829381	+	0.143653i
$800$	35.6424	+	7.91767i	1.26015	+	0.279932i
$801$	−25.9510	+	11.5168i	−0.916934	+	0.406928i
$802$	11.4957	+	35.3802i	0.405928	+	1.24932i
$803$	−0.566545	−	5.39032i	−0.0199929	−	0.190220i
$804$	16.1927	−	5.25059i	0.571073	−	0.185174i
$805$	−44.9815	+	40.1303i	−1.58539	+	1.41441i
$806$	2.98453	−	28.3959i	0.105126	−	1.00020i
$807$	−0.476627	−	2.24898i	−0.0167780	−	0.0791680i
$808$	7.08861	−	3.15605i	0.249376	−	0.111029i
$809$	16.4483	−	50.6225i	0.578290	−	1.77979i	−0.0464034	−	0.998923i	$-0.514776\pi$
$809$	16.4483	−	50.6225i	0.578290	−	1.77979i	0.624693	−	0.780870i	$-0.285224\pi$
$810$	−17.6908	−	40.4921i	−0.621592	−	1.42275i
$811$	15.8173	+	48.6807i	0.555421	+	1.70941i	0.694830	+	0.719174i	$0.255480\pi$
$811$	15.8173	+	48.6807i	0.555421	+	1.70941i	−0.139409	+	0.990235i	$0.544520\pi$
$812$	−6.10508	−	6.78038i	−0.214246	−	0.237945i
$813$	−41.2320	−	4.35867i	−1.44607	−	0.152865i
$814$	−21.8031	+	24.2148i	−0.764199	+	0.848729i
$815$	50.7101	−	5.09533i	1.77630	−	0.178482i
$816$	7.54598	−	10.3731i	0.264162	−	0.363130i
$817$	−13.6712	+	6.08679i	−0.478294	+	0.212950i
$818$	−39.6762			−1.38724
$819$	−36.4542	−	7.79431i	−1.27381	−	0.272355i
$820$	7.86109	+	37.8341i	0.274521	+	1.32122i
$821$	2.78882	+	26.5339i	0.0973306	+	0.926039i	0.928828	+	0.370511i	$0.120817\pi$
$821$	2.78882	+	26.5339i	0.0973306	+	0.926039i	−0.831498	+	0.555528i	$0.812516\pi$
$822$	6.35677	−	29.8183i	0.221718	−	1.04003i
$823$	−10.6629	+	11.8423i	−0.371684	+	0.412797i	−0.899750	−	0.436407i	$-0.856251\pi$
$823$	−10.6629	+	11.8423i	−0.371684	+	0.412797i	0.528065	+	0.849204i	$0.322918\pi$
$824$	0.960916	+	1.66436i	0.0334751	+	0.0579806i
$825$	44.9342	+	5.16630i	1.56441	+	0.179868i
$826$	−11.1120	+	19.2465i	−0.386635	+	0.669672i
$827$	−9.54798	−	29.3857i	−0.332016	−	1.02184i	−0.968173	−	0.250280i	$-0.919477\pi$
$827$	−9.54798	−	29.3857i	−0.332016	−	1.02184i	0.636158	−	0.771559i	$-0.280523\pi$
$828$	−35.2908	−	61.2952i	−1.22644	−	2.13016i
$829$	−4.17800	+	3.03549i	−0.145108	+	0.105427i	−0.657971	−	0.753044i	$-0.728585\pi$
$829$	−4.17800	+	3.03549i	−0.145108	+	0.105427i	0.512863	+	0.858471i	$0.328585\pi$
$830$	16.4658	+	22.8827i	0.571537	+	0.794272i
$831$	14.4296	+	19.8858i	0.500558	+	0.689829i
$832$	24.3965	+	42.2560i	0.845797	+	1.46496i
$833$	−1.56649	+	14.9042i	−0.0542758	+	0.516400i
$834$	−47.7584	−	5.04858i	−1.65374	−	0.174818i
$835$	−14.9364	+	4.77766i	−0.516894	+	0.165338i
$836$	−15.0219	−	46.2327i	−0.519543	−	1.59899i
$837$	13.0146	+	11.7609i	0.449851	+	0.406516i
$838$	3.64016	−	11.2032i	0.125747	−	0.387010i
$839$	26.5095	+	5.63477i	0.915210	+	0.194534i	0.641361	−	0.767239i	$-0.278370\pi$
$839$	26.5095	+	5.63477i	0.915210	+	0.194534i	0.273848	+	0.961773i	$0.411703\pi$
$840$	−2.23872	−	22.4155i	−0.0772431	−	0.773409i
$841$	27.3832	−	5.82047i	0.944247	−	0.200706i
$842$	5.73420	−	54.5573i	0.197614	−	1.88017i
$843$	−23.9364	−	7.79329i	−0.824414	−	0.268415i
$844$	−7.00747	+	3.11993i	−0.241207	+	0.107392i
$845$	3.04127	+	2.76368i	0.104623	+	0.0950734i
$846$	7.02018	+	0.00842286i	0.241359	+	0.000289584i
$847$	42.4795	−	30.8632i	1.45961	−	1.06047i
$848$	−12.2892	−	2.61216i	−0.422014	−	0.0897019i
$849$	−9.25637	+	8.32442i	−0.317678	+	0.285693i
$850$	48.2985	+	0.442073i	1.65663	+	0.0151630i
$851$	−11.8727	−	20.5641i	−0.406990	−	0.704928i
$852$	−57.6519	−	33.3315i	−1.97512	−	1.14192i
$853$	−1.77868	−	16.9230i	−0.0609009	−	0.579433i	−0.981838	−	0.189722i	$-0.939241\pi$
$853$	−1.77868	−	16.9230i	−0.0609009	−	0.579433i	0.920937	−	0.389712i	$-0.127425\pi$
$854$	−49.4043	+	35.8944i	−1.69058	+	1.22828i
$855$	21.9971	+	2.44053i	0.752285	+	0.0834643i
$856$	17.9168	+	13.0173i	0.612383	+	0.444922i
$857$	8.21483	−	14.2285i	0.280613	−	0.486036i	−0.690923	−	0.722929i	$-0.742796\pi$
$857$	8.21483	−	14.2285i	0.280613	−	0.486036i	0.971536	+	0.236892i	$0.0761289\pi$
$858$	44.9344	+	61.9250i	1.53404	+	2.11408i
$859$	−33.0745	+	7.03021i	−1.12849	+	0.239868i	−0.734077	−	0.679066i	$-0.762385\pi$
$859$	−33.0745	+	7.03021i	−1.12849	+	0.239868i	−0.394412	+	0.918934i	$0.629052\pi$
$860$	24.7145	+	14.4201i	0.842756	+	0.491721i
$861$	−29.6509	+	17.0952i	−1.01050	+	0.582604i
$862$	41.4127	+	45.9935i	1.41052	+	1.56654i
$863$	−5.06350	+	15.5839i	−0.172364	+	0.530481i	−0.999503	−	0.0315159i	$-0.989967\pi$
$863$	−5.06350	+	15.5839i	−0.172364	+	0.530481i	0.827140	+	0.561996i	$0.189967\pi$
$864$	−37.7285	−	4.03409i	−1.28355	−	0.137243i
$865$	−2.22202	−	10.6942i	−0.0755511	−	0.363614i
$866$	−30.5280	−	33.9048i	−1.03739	−	1.15213i
$867$	1.66190	−	3.72667i	0.0564410	−	0.126564i
$868$	15.3613	+	26.6066i	0.521398	+	0.903088i
$869$	−4.38971	+	41.7653i	−0.148911	+	1.41679i
$870$	−7.77045	−	3.50794i	−0.263443	−	0.118930i
$871$	−1.40268	−	13.3456i	−0.0475279	−	0.452198i
$872$	1.95076	−	1.41731i	0.0660612	−	0.0479963i
$873$	−5.61580	+	1.18664i	−0.190066	+	0.0401615i
$874$	60.5392			2.04777
$875$	−27.1314	+	23.7630i	−0.917210	+	0.803335i
$876$	−3.77051	+	3.39089i	−0.127394	+	0.114567i
$877$	−19.6794	+	21.8562i	−0.664527	+	0.738032i	−0.977315	−	0.211791i	$-0.932070\pi$
$877$	−19.6794	+	21.8562i	−0.664527	+	0.738032i	0.312788	+	0.949823i	$0.398737\pi$
$878$	−45.7263	−	20.3586i	−1.54319	−	0.687071i
$879$	−1.65291	+	7.75346i	−0.0557513	+	0.261518i
$880$	11.6278	−	15.8512i	0.391972	−	0.534343i
$881$	−8.48509	−	6.16478i	−0.285870	−	0.207697i	0.435604	−	0.900139i	$-0.356535\pi$
$881$	−8.48509	−	6.16478i	−0.285870	−	0.207697i	−0.721474	+	0.692442i	$0.756535\pi$
$882$	20.5091	−	9.10179i	0.690579	−	0.306473i
$883$	9.01475	+	6.54960i	0.303370	+	0.220411i	0.729047	−	0.684464i	$-0.239964\pi$
$883$	9.01475	+	6.54960i	0.303370	+	0.220411i	−0.425676	+	0.904876i	$0.639964\pi$
$884$	31.9912	+	35.5298i	1.07598	+	1.19500i
$885$	−1.33275	+	12.0785i	−0.0447999	+	0.406015i
$886$	2.27453	−	2.52612i	0.0764144	−	0.0848667i
$887$	16.6369	−	3.53628i	0.558611	−	0.118737i	0.0800504	−	0.996791i	$-0.474492\pi$
$887$	16.6369	−	3.53628i	0.558611	−	0.118737i	0.478561	+	0.878054i	$0.341159\pi$
$888$	8.82451	+	0.932846i	0.296131	+	0.0313043i
$889$	10.8589	+	2.30812i	0.364195	+	0.0774120i
$890$	−40.3464	+	23.0484i	−1.35241	+	0.772586i
$891$	−47.0045	−	0.112793i	−1.57471	−	0.00377870i
$892$	40.1278	+	29.1545i	1.34358	+	0.976165i
$893$	−1.75807	+	3.04507i	−0.0588317	+	0.101899i
$894$	31.0425	−	69.6102i	1.03822	−	2.32811i
$895$	−6.85763	−	4.00121i	−0.229225	−	0.133746i
$896$	−38.9257	−	17.3308i	−1.30042	−	0.578983i
$897$	−53.0373	+	17.1977i	−1.77086	+	0.574214i
$898$	−20.1524	−	4.28353i	−0.672494	−	0.142943i
$899$	3.38441			0.112876
$900$	−20.7782	−	36.8651i	−0.692608	−	1.22884i
$901$	−32.8363			−1.09394
$902$	68.7108	+	14.6049i	2.28782	+	0.486291i
$903$	−5.28412	+	24.7867i	−0.175844	+	0.824849i
$904$	−8.26041	−	3.67777i	−0.274737	−	0.122321i
$905$	3.66398	−	16.8579i	0.121795	−	0.560377i
$906$	38.2571	−	3.99778i	1.27101	−	0.132817i
$907$	23.8660	−	41.3371i	0.792457	−	1.37258i	−0.131984	−	0.991252i	$-0.542135\pi$
$907$	23.8660	−	41.3371i	0.792457	−	1.37258i	0.924441	−	0.381324i	$-0.124532\pi$
$908$	53.1935	+	38.6474i	1.76529	+	1.28256i
$909$	11.7880	+	5.26532i	0.390984	+	0.174640i
$910$	−60.6451	−	6.65479i	−2.01037	−	0.220604i
$911$	−26.7962	−	5.69571i	−0.887799	−	0.188707i	−0.258630	−	0.965976i	$-0.583271\pi$
$911$	−26.7962	−	5.69571i	−0.887799	−	0.188707i	−0.629168	+	0.777269i	$0.716604\pi$
$912$	5.65881	−	7.77887i	0.187382	−	0.257584i
$913$	29.3329	−	6.23489i	0.970776	−	0.206345i
$914$	−32.8336	+	36.4654i	−1.08604	+	1.20617i
$915$	−16.8449	+	28.8305i	−0.556875	+	0.953108i
$916$	−44.4664	−	49.3850i	−1.46921	−	1.63173i
$917$	1.93897	+	1.40875i	0.0640305	+	0.0465209i
$918$	−49.9298	+	5.15700i	−1.64793	+	0.170206i
$919$	−26.2312	−	19.0581i	−0.865287	−	0.628668i	0.0640314	−	0.997948i	$-0.479604\pi$
$919$	−26.2312	−	19.0581i	−0.865287	−	0.628668i	−0.929318	+	0.369280i	$0.879604\pi$
$920$	−19.6793	−	27.3485i	−0.648807	−	0.901655i
$921$	−5.49748	−	4.95593i	−0.181148	−	0.163303i
$922$	46.9606	+	20.9082i	1.54657	+	0.688575i
$923$	−35.1269	+	39.0123i	−1.15621	+	1.28411i
$924$	−78.2814	−	25.4871i	−2.57527	−	0.838463i
$925$	−6.99062	−	12.3682i	−0.229850	−	0.406663i
$926$	63.9397			2.10119
$927$	−0.991768	+	3.03993i	−0.0325739	+	0.0998445i
$928$	−5.92266	+	4.30306i	−0.194421	+	0.141255i
$929$	2.86275	+	27.2373i	0.0939239	+	0.893626i	0.935462	+	0.353428i	$0.114984\pi$
$929$	2.86275	+	27.2373i	0.0939239	+	0.893626i	−0.841538	+	0.540198i	$0.818349\pi$
$930$	23.1376	+	16.9941i	0.758712	+	0.557259i
$931$	−1.17473	+	11.1768i	−0.0385002	+	0.366305i
$932$	−21.7414	−	37.6571i	−0.712162	−	1.23350i
$933$	−0.602020	+	0.0629097i	−0.0197092	+	0.00205957i
$934$	−40.5889	−	45.0785i	−1.32811	−	1.47501i
$935$	21.1125	−	46.8413i	0.690451	−	1.53187i
$936$	6.46246	−	19.8085i	0.211232	−	0.647461i
$937$	−1.04032	+	3.20177i	−0.0339857	+	0.104597i	−0.966610	−	0.256251i	$-0.917513\pi$
$937$	−1.04032	+	3.20177i	−0.0339857	+	0.104597i	0.932625	+	0.360848i	$0.117513\pi$
$938$	16.5111	+	18.3374i	0.539105	+	0.598737i
$939$	0.0100326	−	16.7238i	0.000327403	−	0.545760i
$940$	6.68935	−	0.672143i	0.218183	−	0.0219229i
$941$	36.8080	−	7.82379i	1.19991	−	0.255048i	0.435744	−	0.900071i	$-0.356485\pi$
$941$	36.8080	−	7.82379i	1.19991	−	0.255048i	0.764164	+	0.645022i	$0.223152\pi$
$942$	−8.15088	+	18.2777i	−0.265570	+	0.595518i
$943$	−25.5954	+	44.3325i	−0.833501	+	1.44367i
$944$	4.27293	+	3.10446i	0.139072	+	0.101042i
$945$	25.2570	−	27.6936i	0.821612	−	0.900874i
$946$	42.0815	−	30.5740i	1.36819	−	0.994047i
$947$	−4.47082	−	42.5370i	−0.145282	−	1.38227i	−0.787770	−	0.615970i	$-0.788764\pi$
$947$	−4.47082	−	42.5370i	−0.145282	−	1.38227i	0.642488	−	0.766296i	$-0.277902\pi$
$948$	34.0388	−	19.6251i	1.10553	−	0.637394i
$949$	1.99874	+	3.46192i	0.0648819	+	0.112379i
$950$	36.2196	+	0.331515i	1.17512	+	0.0107558i
$951$	2.48921	+	0.810446i	0.0807183	+	0.0262805i
$952$	−25.0304	−	5.32039i	−0.811242	−	0.172435i
$953$	−18.7757	+	13.6414i	−0.608205	+	0.441887i	−0.848782	−	0.528743i	$-0.822663\pi$
$953$	−18.7757	+	13.6414i	−0.608205	+	0.441887i	0.240577	+	0.970630i	$0.422663\pi$
$954$	24.5308	+	42.6066i	0.794215	+	1.37944i
$955$	19.0155	−	42.1888i	0.615327	−	1.36520i
$956$	62.9191	−	28.0134i	2.03495	−	0.906018i
$957$	−6.74324	+	6.06432i	−0.217978	+	0.196032i
$958$	−1.22866	+	11.6899i	−0.0396961	+	0.377684i
$959$	25.2959	−	5.37681i	0.816847	−	0.173626i
$960$	−49.0584	−	0.253940i	−1.58335	−	0.00819588i
$961$	19.1754	+	4.07585i	0.618560	+	0.131479i
$962$	7.42637	−	22.8560i	0.239436	−	0.736908i
$963$	3.80770	+	36.6508i	0.122701	+	1.18105i
$964$	12.0585	+	37.1121i	0.388377	+	1.19530i
$965$	20.5784	−	28.0529i	0.662442	−	0.903054i
$966$	60.3126	−	82.9086i	1.94053	−	2.66754i
$967$	−1.27712	+	12.1510i	−0.0410693	+	0.390749i	0.954608	+	0.297866i	$0.0962748\pi$
$967$	−1.27712	+	12.1510i	−0.0410693	+	0.390749i	−0.995677	+	0.0928827i	$0.970392\pi$
$968$	14.6741	+	25.4163i	0.471644	+	0.816911i
$969$	10.2395	−	22.9613i	0.328941	−	0.737623i
$970$	−8.94714	+	2.86190i	−0.287275	+	0.0918901i
$971$	5.88273	−	4.27405i	0.188786	−	0.137161i	−0.489378	−	0.872072i	$-0.662776\pi$
$971$	5.88273	−	4.27405i	0.188786	−	0.137161i	0.678164	+	0.734911i	$0.262776\pi$
$972$	25.7426	+	35.6561i	0.825694	+	1.14367i
$973$	−12.5880	−	38.7420i	−0.403554	−	1.24201i
$974$	−36.8954	+	63.9047i	−1.18221	+	2.04764i
$975$	−31.8255	+	9.99865i	−1.01923	+	0.320213i
$976$	7.25645	+	12.5685i	0.232273	+	0.402309i
$977$	−20.3190	+	22.5666i	−0.650063	+	0.721968i	−0.974612	−	0.223901i	$-0.928121\pi$
$977$	−20.3190	+	22.5666i	−0.650063	+	0.721968i	0.324549	+	0.945869i	$0.394787\pi$
$978$	−82.4554	+	26.7367i	−2.63663	+	0.854945i
$979$	5.16659	+	49.1568i	0.165125	+	1.57106i
$980$	18.6584	−	10.6589i	0.596021	−	0.340486i
$981$	3.92331	+	0.838846i	0.125262	+	0.0267823i
$982$	−40.4462			−1.29069
$983$	−55.2950	+	24.6189i	−1.76364	+	0.785222i	−0.775559	+	0.631275i	$0.782532\pi$
$983$	−55.2950	+	24.6189i	−1.76364	+	0.785222i	−0.988079	+	0.153947i	$0.950801\pi$
$984$	−7.77041	−	17.4808i	−0.247712	−	0.557269i
$985$	−24.6191	−	14.3645i	−0.784431	−	0.457690i
$986$	−6.48030	+	7.19711i	−0.206375	+	0.229203i
$987$	2.41874	+	5.44135i	0.0769892	+	0.173200i
$988$	23.9905	+	26.6442i	0.763241	+	0.847665i
$989$	11.7135	+	36.0505i	0.372468	+	1.14634i
$990$	−76.5510	+	7.59905i	−2.43295	+	0.241514i
$991$	4.33999	−	13.3571i	0.137864	−	0.424303i	−0.858160	−	0.513382i	$-0.828392\pi$
$991$	4.33999	−	13.3571i	0.137864	−	0.424303i	0.996025	+	0.0890792i	$0.0283924\pi$
$992$	22.5200	−	10.0265i	0.715010	−	0.318343i
$993$	−2.66430	−	0.867451i	−0.0845490	−	0.0275277i
$994$	10.0903	−	96.0027i	0.320045	−	3.04502i
$995$	−11.1151	−	25.2755i	−0.352372	−	0.801289i
$996$	−20.8392	−	18.7863i	−0.660315	−	0.595268i
$997$	2.94793	+	28.0477i	0.0933620	+	0.888280i	0.936520	+	0.350614i	$0.114027\pi$
$997$	2.94793	+	28.0477i	0.0933620	+	0.888280i	−0.843158	+	0.537666i	$0.819306\pi$
$998$	−5.57796	−	17.1672i	−0.176567	−	0.543418i
$999$	8.65678	+	11.9602i	0.273888	+	0.378405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.26	yes	224
3.2	odd	2		675.2.r.a.181.3		224
9.4	even	3	inner	225.2.q.a.31.3	✓	224
9.5	odd	6		675.2.r.a.631.26		224
25.21	even	5	inner	225.2.q.a.196.3	yes	224
75.71	odd	10		675.2.r.a.46.26		224
225.121	even	15	inner	225.2.q.a.121.26	yes	224
225.221	odd	30		675.2.r.a.496.3		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.3	✓	224	9.4	even	3	inner
225.2.q.a.106.26	yes	224	1.1	even	1	trivial
225.2.q.a.121.26	yes	224	225.121	even	15	inner
225.2.q.a.196.3	yes	224	25.21	even	5	inner
675.2.r.a.46.26		224	75.71	odd	10
675.2.r.a.181.3		224	3.2	odd	2
675.2.r.a.496.3		224	225.221	odd	30
675.2.r.a.631.26		224	9.5	odd	6

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.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.14773 + 0.456515i) q^{2} +(-1.28647 - 1.15974i) q^{3} +(2.57727 + 1.14747i) q^{4} +(0.900133 + 2.04689i) q^{5} +(-2.23356 - 3.07811i) q^{6} +(1.61294 - 2.79370i) q^{7} +(1.45870 + 1.05981i) q^{8} +(0.310005 + 2.98394i) q^{9} +O(q^{10})\)	\(q+(2.14773 + 0.456515i) q^{2} +(-1.28647 - 1.15974i) q^{3} +(2.57727 + 1.14747i) q^{4} +(0.900133 + 2.04689i) q^{5} +(-2.23356 - 3.07811i) q^{6} +(1.61294 - 2.79370i) q^{7} +(1.45870 + 1.05981i) q^{8} +(0.310005 + 2.98394i) q^{9} +(0.998810 + 4.80710i) q^{10} +(5.10860 + 1.08587i) q^{11} +(-1.98480 - 4.46515i) q^{12} +(-3.76781 + 0.800873i) q^{13} +(4.73954 - 5.26379i) q^{14} +(1.21587 - 3.67718i) q^{15} +(-1.12637 - 1.25097i) q^{16} +(-3.55929 - 2.58598i) q^{17} +(-0.696404 + 6.55023i) q^{18} +(-2.66915 - 1.93925i) q^{19} +(-0.0288689 + 6.30826i) q^{20} +(-5.31497 + 1.72341i) q^{21} +(10.4762 + 4.66431i) q^{22} +(-5.59186 + 6.21039i) q^{23} +(-0.647472 - 3.05513i) q^{24} +(-3.37952 + 3.68495i) q^{25} -8.45786 q^{26} +(3.06178 - 4.19827i) q^{27} +(7.36268 - 5.34930i) q^{28} +(-0.104794 - 0.997049i) q^{29} +(4.29005 - 7.34255i) q^{30} +(-0.352871 + 3.35734i) q^{31} +(-3.65112 - 6.32393i) q^{32} +(-5.31274 - 7.32159i) q^{33} +(-6.46388 - 7.17886i) q^{34} +(7.17026 + 0.786817i) q^{35} +(-2.62502 + 8.04613i) q^{36} +(-0.878044 + 2.70234i) q^{37} +(-4.84733 - 5.38351i) q^{38} +(5.77597 + 3.33938i) q^{39} +(-0.856288 + 3.93977i) q^{40} +(5.99171 - 1.27358i) q^{41} +(-12.2019 + 1.27507i) q^{42} +(2.26793 - 3.92817i) q^{43} +(11.9202 + 8.66056i) q^{44} +(-5.82875 + 3.32049i) q^{45} +(-14.8450 + 10.7855i) q^{46} +(-0.111400 - 1.05990i) q^{47} +(-0.00174910 + 2.91563i) q^{48} +(-1.70317 - 2.94998i) q^{49} +(-8.94055 + 6.37149i) q^{50} +(1.57986 + 7.45463i) q^{51} +(-10.6296 - 2.25940i) q^{52} +(6.03818 - 4.38700i) q^{53} +(8.49247 - 7.61902i) q^{54} +(2.37577 + 11.4342i) q^{55} +(5.31359 - 2.36576i) q^{56} +(1.18475 + 5.59031i) q^{57} +(0.230098 - 2.18924i) q^{58} +(-3.06903 + 0.652341i) q^{59} +(7.35308 - 8.08190i) q^{60} +(-8.43309 - 1.79251i) q^{61} +(-2.29055 + 7.04959i) q^{62} +(8.83625 + 3.94686i) q^{63} +(-3.91431 - 12.0470i) q^{64} +(-5.03083 - 6.99140i) q^{65} +(-8.06793 - 18.1502i) q^{66} +(-0.364144 + 3.46460i) q^{67} +(-6.20591 - 10.7489i) q^{68} +(14.3962 - 1.50437i) q^{69} +(15.0406 + 4.96321i) q^{70} +(11.0256 - 8.01056i) q^{71} +(-2.71020 + 4.68123i) q^{72} +(-0.320689 - 0.986980i) q^{73} +(-3.11946 + 5.40307i) q^{74} +(8.62123 - 0.821204i) q^{75} +(-4.65388 - 8.06075i) q^{76} +(11.2735 - 12.5205i) q^{77} +(10.8808 + 9.80893i) q^{78} +(0.840501 + 7.99683i) q^{79} +(1.54670 - 3.43160i) q^{80} +(-8.80779 + 1.85008i) q^{81} +13.4500 q^{82} +(5.24545 - 2.33542i) q^{83} +(-15.6757 - 1.65709i) q^{84} +(2.08938 - 9.61320i) q^{85} +(6.66418 - 7.40132i) q^{86} +(-1.02150 + 1.40421i) q^{87} +(6.30112 + 6.99811i) q^{88} +(2.92451 + 9.00073i) q^{89} +(-14.0345 + 4.47062i) q^{90} +(-3.83986 + 11.8179i) q^{91} +(-21.5380 + 9.58932i) q^{92} +(4.34760 - 3.90988i) q^{93} +(0.244603 - 2.32724i) q^{94} +(1.56685 - 7.20905i) q^{95} +(-2.63706 + 12.3699i) q^{96} +(0.199991 + 1.90279i) q^{97} +(-2.31125 - 7.11329i) q^{98} +(-1.65647 + 15.5804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more