LMFDB - Embedded newform 225.2.q.a.61.10

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			61.10
Character	$\chi$	$=$	225.61
Dual form			225.2.q.a.166.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0944267 - 0.898410i) q^{2} +(1.34957 - 1.08566i) q^{3} +(1.15807 - 0.246156i) q^{4} +(-0.280458 - 2.21841i) q^{5} +(-1.10280 - 1.10995i) q^{6} +(-1.53265 + 2.65463i) q^{7} +(-0.888808 - 2.73547i) q^{8} +(0.642678 - 2.93035i) q^{9} +O(q^{10})$	\(q+(-0.0944267 - 0.898410i) q^{2} +(1.34957 - 1.08566i) q^{3} +(1.15807 - 0.246156i) q^{4} +(-0.280458 - 2.21841i) q^{5} +(-1.10280 - 1.10995i) q^{6} +(-1.53265 + 2.65463i) q^{7} +(-0.888808 - 2.73547i) q^{8} +(0.642678 - 2.93035i) q^{9} +(-1.96656 + 0.461443i) q^{10} +(0.137323 + 1.30654i) q^{11} +(1.29566 - 1.58948i) q^{12} +(-0.522291 + 4.96927i) q^{13} +(2.52967 + 1.12628i) q^{14} +(-2.78694 - 2.68942i) q^{15} +(-0.210472 + 0.0937080i) q^{16} +(1.36059 + 4.18745i) q^{17} +(-2.69334 - 0.300684i) q^{18} +(-1.05356 - 3.24253i) q^{19} +(-0.870865 - 2.50004i) q^{20} +(0.813610 + 5.24655i) q^{21} +(1.16084 - 0.246745i) q^{22} +(5.20744 + 2.31850i) q^{23} +(-4.16930 - 2.72676i) q^{24} +(-4.84269 + 1.24434i) q^{25} +4.51376 q^{26} +(-2.31403 - 4.65245i) q^{27} +(-1.12147 + 3.45152i) q^{28} +(-4.40263 - 4.88961i) q^{29} +(-2.15304 + 2.75777i) q^{30} +(3.64850 - 4.05207i) q^{31} +(-2.77218 - 4.80156i) q^{32} +(1.60379 + 1.61418i) q^{33} +(3.63357 - 1.61777i) q^{34} +(6.31890 + 2.65554i) q^{35} +(0.0229438 - 3.55176i) q^{36} +(5.90992 + 4.29381i) q^{37} +(-2.81363 + 1.25271i) q^{38} +(4.69008 + 7.27341i) q^{39} +(-5.81912 + 2.73892i) q^{40} +(-0.166456 + 1.58372i) q^{41} +(4.63672 - 1.22637i) q^{42} +(-2.24167 + 3.88268i) q^{43} +(0.480642 + 1.47926i) q^{44} +(-6.68097 - 0.603882i) q^{45} +(1.59124 - 4.89734i) q^{46} +(-4.44418 - 4.93576i) q^{47} +(-0.182311 + 0.354967i) q^{48} +(-1.19804 - 2.07507i) q^{49} +(1.57521 + 4.23322i) q^{50} +(6.38236 + 4.17412i) q^{51} +(0.618363 + 5.88333i) q^{52} +(-2.18021 + 6.70999i) q^{53} +(-3.96130 + 2.51826i) q^{54} +(2.85993 - 0.671068i) q^{55} +(8.62389 + 1.83306i) q^{56} +(-4.94214 - 3.23221i) q^{57} +(-3.97715 + 4.41707i) q^{58} +(0.368583 - 3.50683i) q^{59} +(-3.88949 - 2.42852i) q^{60} +(1.28168 + 12.1944i) q^{61} +(-3.98493 - 2.89522i) q^{62} +(6.79400 + 6.19728i) q^{63} +(-4.42478 + 3.21479i) q^{64} +(11.1704 - 0.235015i) q^{65} +(1.29876 - 1.59328i) q^{66} +(3.68929 - 4.09737i) q^{67} +(2.60642 + 4.51446i) q^{68} +(9.54491 - 2.52454i) q^{69} +(1.78909 - 5.92772i) q^{70} +(-2.00148 + 6.15992i) q^{71} +(-8.58710 + 0.846495i) q^{72} +(5.08449 - 3.69410i) q^{73} +(3.29954 - 5.71498i) q^{74} +(-5.18461 + 6.93685i) q^{75} +(-2.01827 - 3.49574i) q^{76} +(-3.67885 - 1.63793i) q^{77} +(6.09163 - 4.90041i) q^{78} +(1.88852 + 2.09741i) q^{79} +(0.266911 + 0.440631i) q^{80} +(-8.17393 - 3.76654i) q^{81} +1.43855 q^{82} +(-11.8007 - 2.50831i) q^{83} +(2.23369 + 5.87561i) q^{84} +(8.90790 - 4.19274i) q^{85} +(3.69991 + 1.64731i) q^{86} +(-11.2501 - 1.81911i) q^{87} +(3.45195 - 1.53691i) q^{88} +(5.99213 - 4.35354i) q^{89} +(0.0883282 + 6.05927i) q^{90} +(-12.3911 - 9.00265i) q^{91} +(6.60130 + 1.40315i) q^{92} +(0.524729 - 9.42958i) q^{93} +(-4.01469 + 4.45876i) q^{94} +(-6.89777 + 3.24662i) q^{95} +(-8.95412 - 3.47039i) q^{96} +(-11.3905 - 12.6505i) q^{97} +(-1.75113 + 1.27227i) q^{98} +(3.91688 + 0.437280i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.0944267	−	0.898410i	−0.0667697	−	0.635272i	−0.975819	−	0.218582i	$-0.929857\pi$
$2$	−0.0944267	−	0.898410i	−0.0667697	−	0.635272i	0.909049	−	0.416690i	$-0.136810\pi$
$3$	1.34957	−	1.08566i	0.779175	−	0.626807i
$3$	1.34957	−	1.08566i	0.779175	−	0.626807i
$4$	1.15807	−	0.246156i	0.579036	−	0.123078i
$5$	−0.280458	−	2.21841i	−0.125425	−	0.992103i
$5$	−0.280458	−	2.21841i	−0.125425	−	0.992103i
$6$	−1.10280	−	1.10995i	−0.450218	−	0.453136i
$7$	−1.53265	+	2.65463i	−0.579288	+	1.00336i	0.416273	+	0.909239i	$0.363336\pi$
$7$	−1.53265	+	2.65463i	−0.579288	+	1.00336i	−0.995561	+	0.0941164i	$0.969997\pi$
$8$	−0.888808	−	2.73547i	−0.314241	−	0.967134i
$9$	0.642678	−	2.93035i	0.214226	−	0.976784i
$10$	−1.96656	+	0.461443i	−0.621880	+	0.145921i
$11$	0.137323	+	1.30654i	0.0414044	+	0.393937i	0.995524	+	0.0945105i	$0.0301286\pi$
$11$	0.137323	+	1.30654i	0.0414044	+	0.393937i	−0.954119	+	0.299426i	$0.903205\pi$
$12$	1.29566	−	1.58948i	0.374024	−	0.458843i
$13$	−0.522291	+	4.96927i	−0.144858	+	1.37823i	0.644646	+	0.764481i	$0.277005\pi$
$13$	−0.522291	+	4.96927i	−0.144858	+	1.37823i	−0.789504	+	0.613746i	$0.789662\pi$
$14$	2.52967	+	1.12628i	0.676082	+	0.301011i
$15$	−2.78694	−	2.68942i	−0.719585	−	0.694404i
$16$	−0.210472	+	0.0937080i	−0.0526179	+	0.0234270i
$17$	1.36059	+	4.18745i	0.329991	+	1.01561i	0.969137	+	0.246522i	$0.0792877\pi$
$17$	1.36059	+	4.18745i	0.329991	+	1.01561i	−0.639147	+	0.769085i	$0.720712\pi$
$18$	−2.69334	−	0.300684i	−0.634827	−	0.0708720i
$19$	−1.05356	−	3.24253i	−0.241703	−	0.743887i	−0.996161	−	0.0875381i	$-0.972100\pi$
$19$	−1.05356	−	3.24253i	−0.241703	−	0.743887i	0.754458	−	0.656349i	$-0.227900\pi$
$20$	−0.870865	−	2.50004i	−0.194731	−	0.559026i
$21$	0.813610	+	5.24655i	0.177544	+	1.14489i
$22$	1.16084	−	0.246745i	0.247492	−	0.0526061i
$23$	5.20744	+	2.31850i	1.08583	+	0.483441i	0.870031	−	0.492998i	$-0.164099\pi$
$23$	5.20744	+	2.31850i	1.08583	+	0.483441i	0.215796	+	0.976439i	$0.430766\pi$
$24$	−4.16930	−	2.72676i	−0.851055	−	0.556598i
$25$	−4.84269	+	1.24434i	−0.968537	+	0.248868i
$26$	4.51376			0.885221
$27$	−2.31403	−	4.65245i	−0.445336	−	0.895364i
$28$	−1.12147	+	3.45152i	−0.211937	+	0.652277i
$29$	−4.40263	−	4.88961i	−0.817547	−	0.907978i	0.179579	−	0.983744i	$-0.442527\pi$
$29$	−4.40263	−	4.88961i	−0.817547	−	0.907978i	−0.997126	+	0.0757657i	$0.975860\pi$
$30$	−2.15304	+	2.75777i	−0.393089	+	0.503497i
$31$	3.64850	−	4.05207i	0.655290	−	0.727773i	−0.320314	−	0.947311i	$-0.603788\pi$
$31$	3.64850	−	4.05207i	0.655290	−	0.727773i	0.975604	+	0.219538i	$0.0704552\pi$
$32$	−2.77218	−	4.80156i	−0.490057	−	0.848803i
$33$	1.60379	+	1.61418i	0.279184	+	0.280993i
$34$	3.63357	−	1.61777i	0.623153	−	0.277445i
$35$	6.31890	+	2.65554i	1.06809	+	0.448868i
$36$	0.0229438	−	3.55176i	0.00382396	−	0.591959i
$37$	5.90992	+	4.29381i	0.971584	+	0.705897i	0.955812	−	0.293978i	$-0.0949793\pi$
$37$	5.90992	+	4.29381i	0.971584	+	0.705897i	0.0157722	+	0.999876i	$0.494979\pi$
$38$	−2.81363	+	1.25271i	−0.456432	+	0.203216i
$39$	4.69008	+	7.27341i	0.751013	+	1.16468i
$40$	−5.81912	+	2.73892i	−0.920083	+	0.433062i
$41$	−0.166456	+	1.58372i	−0.0259961	+	0.247336i	0.973805	+	0.227385i	$0.0730176\pi$
$41$	−0.166456	+	1.58372i	−0.0259961	+	0.247336i	−0.999801	+	0.0199508i	$0.993649\pi$
$42$	4.63672	−	1.22637i	0.715462	−	0.189233i
$43$	−2.24167	+	3.88268i	−0.341851	+	0.592103i	−0.984776	−	0.173826i	$-0.944387\pi$
$43$	−2.24167	+	3.88268i	−0.341851	+	0.592103i	0.642926	+	0.765929i	$0.277720\pi$
$44$	0.480642	+	1.47926i	0.0724595	+	0.223008i
$45$	−6.68097	−	0.603882i	−0.995940	−	0.0900214i
$46$	1.59124	−	4.89734i	0.234616	−	0.722074i
$47$	−4.44418	−	4.93576i	−0.648250	−	0.719955i	0.326014	−	0.945365i	$-0.394294\pi$
$47$	−4.44418	−	4.93576i	−0.648250	−	0.719955i	−0.974264	+	0.225410i	$0.927628\pi$
$48$	−0.182311	+	0.354967i	−0.0263143	+	0.0512350i
$49$	−1.19804	−	2.07507i	−0.171149	−	0.296438i
$50$	1.57521	+	4.23322i	0.222768	+	0.598667i
$51$	6.38236	+	4.17412i	0.893710	+	0.584494i
$52$	0.618363	+	5.88333i	0.0857516	+	0.815872i
$53$	−2.18021	+	6.70999i	−0.299475	+	0.921688i	0.682207	+	0.731159i	$0.261020\pi$
$53$	−2.18021	+	6.70999i	−0.299475	+	0.921688i	−0.981682	+	0.190529i	$0.938980\pi$
$54$	−3.96130	+	2.51826i	−0.539064	+	0.342692i
$55$	2.85993	−	0.671068i	0.385633	−	0.0904868i
$56$	8.62389	+	1.83306i	1.15242	+	0.244954i
$57$	−4.94214	−	3.23221i	−0.654603	−	0.428116i
$58$	−3.97715	+	4.41707i	−0.522225	+	0.579990i
$59$	0.368583	−	3.50683i	0.0479854	−	0.456550i	−0.943976	−	0.330013i	$-0.892947\pi$
$59$	0.368583	−	3.50683i	0.0479854	−	0.456550i	0.991962	−	0.126537i	$-0.0403864\pi$
$60$	−3.88949	−	2.42852i	−0.502131	−	0.313520i
$61$	1.28168	+	12.1944i	0.164103	+	1.56133i	0.698196	+	0.715907i	$0.253986\pi$
$61$	1.28168	+	12.1944i	0.164103	+	1.56133i	−0.534093	+	0.845426i	$0.679347\pi$
$62$	−3.98493	−	2.89522i	−0.506087	−	0.367694i
$63$	6.79400	+	6.19728i	0.855964	+	0.780784i
$64$	−4.42478	+	3.21479i	−0.553097	+	0.401848i
$65$	11.1704	−	0.235015i	1.38551	−	0.0291501i
$66$	1.29876	−	1.59328i	0.159866	−	0.196119i
$67$	3.68929	−	4.09737i	0.450719	−	0.500574i	−0.474370	−	0.880326i	$-0.657324\pi$
$67$	3.68929	−	4.09737i	0.450719	−	0.500574i	0.925088	+	0.379752i	$0.123991\pi$
$68$	2.60642	+	4.51446i	0.316075	+	0.547458i
$69$	9.54491	−	2.52454i	1.14907	−	0.303919i
$70$	1.78909	−	5.92772i	0.213837	−	0.708498i
$71$	−2.00148	+	6.15992i	−0.237532	+	0.731048i	0.759244	+	0.650807i	$0.225569\pi$
$71$	−2.00148	+	6.15992i	−0.237532	+	0.731048i	−0.996775	+	0.0802415i	$0.974431\pi$
$72$	−8.58710	+	0.846495i	−1.01200	+	0.0997604i
$73$	5.08449	−	3.69410i	0.595094	−	0.432361i	−0.249040	−	0.968493i	$-0.580115\pi$
$73$	5.08449	−	3.69410i	0.595094	−	0.432361i	0.844134	+	0.536132i	$0.180115\pi$
$74$	3.29954	−	5.71498i	0.383564	−	0.664352i
$75$	−5.18461	+	6.93685i	−0.598667	+	0.800998i
$76$	−2.01827	−	3.49574i	−0.231511	−	0.400989i
$77$	−3.67885	−	1.63793i	−0.419244	−	0.186659i
$78$	6.09163	−	4.90041i	0.689741	−	0.554862i
$79$	1.88852	+	2.09741i	0.212475	+	0.235977i	0.839956	−	0.542655i	$-0.182581\pi$
$79$	1.88852	+	2.09741i	0.212475	+	0.235977i	−0.627481	+	0.778632i	$0.715914\pi$
$80$	0.266911	+	0.440631i	0.0298416	+	0.0492641i
$81$	−8.17393	−	3.76654i	−0.908215	−	0.418505i
$82$	1.43855			0.158861
$83$	−11.8007	−	2.50831i	−1.29529	−	0.275323i	−0.491838	−	0.870687i	$-0.663675\pi$
$83$	−11.8007	−	2.50831i	−1.29529	−	0.275323i	−0.803456	+	0.595364i	$0.797008\pi$
$84$	2.23369	+	5.87561i	0.243715	+	0.641081i
$85$	8.90790	−	4.19274i	0.966198	−	0.454767i
$86$	3.69991	+	1.64731i	0.398971	+	0.177634i
$87$	−11.2501	−	1.81911i	−1.20614	−	0.195029i
$88$	3.45195	−	1.53691i	0.367979	−	0.163835i
$89$	5.99213	−	4.35354i	0.635164	−	0.461474i	−0.223021	−	0.974814i	$-0.571592\pi$
$89$	5.99213	−	4.35354i	0.635164	−	0.461474i	0.858185	+	0.513340i	$0.171592\pi$
$90$	0.0883282	+	6.05927i	0.00931061	+	0.638703i
$91$	−12.3911	−	9.00265i	−1.29894	−	0.943734i
$92$	6.60130	+	1.40315i	0.688233	+	0.146288i
$93$	0.524729	−	9.42958i	0.0544118	−	0.977802i
$94$	−4.01469	+	4.45876i	−0.414083	+	0.459886i
$95$	−6.89777	+	3.24662i	−0.707697	+	0.333096i
$96$	−8.95412	−	3.47039i	−0.913876	−	0.354195i
$97$	−11.3905	−	12.6505i	−1.15653	−	1.28446i	−0.952171	−	0.305564i	$-0.901155\pi$
$97$	−11.3905	−	12.6505i	−1.15653	−	1.28446i	−0.204361	−	0.978896i	$-0.565512\pi$
$98$	−1.75113	+	1.27227i	−0.176891	+	0.128519i
$99$	3.91688	+	0.437280i	0.393661	+	0.0439483i
$100$	−5.30188	+	2.63309i	−0.530188	+	0.263309i
$101$	−6.32691	+	10.9585i	−0.629551	+	1.09042i	0.358090	+	0.933687i	$0.383428\pi$
$101$	−6.32691	+	10.9585i	−0.629551	+	1.09042i	−0.987642	+	0.156728i	$0.949905\pi$
$102$	3.14741	−	6.12813i	0.311640	−	0.606775i
$103$	−18.1574	+	3.85947i	−1.78910	+	0.380285i	−0.978651	−	0.205527i	$-0.934109\pi$
$103$	−18.1574	+	3.85947i	−1.78910	+	0.380285i	−0.810447	+	0.585812i	$0.800776\pi$
$104$	14.0575	−	2.98801i	1.37845	−	0.292999i
$105$	11.4108	−	3.27636i	1.11358	−	0.319740i
$106$	6.23419	+	1.32512i	0.605518	+	0.128707i
$107$	−12.3221			−1.19122			−0.595611	−	0.803273i	$-0.703090\pi$
$107$	−12.3221			−1.19122			−0.595611	+	0.803273i	$0.703090\pi$
$108$	−3.82504	−	4.81825i	−0.368065	−	0.463637i
$109$	−0.372310	−	0.270499i	−0.0356608	−	0.0259091i	0.569812	−	0.821775i	$-0.307016\pi$
$109$	−0.372310	−	0.270499i	−0.0356608	−	0.0259091i	−0.605473	+	0.795866i	$0.707016\pi$
$110$	−0.872948	−	2.50602i	−0.0832323	−	0.238940i
$111$	12.6375	−	0.621379i	1.19950	−	0.0589787i
$112$	0.0738196	−	0.702346i	0.00697529	−	0.0663655i
$113$	1.23627	−	11.7623i	0.116298	−	1.10650i	−0.768280	−	0.640113i	$-0.778887\pi$
$113$	1.23627	−	11.7623i	0.116298	−	1.10650i	0.884579	−	0.466391i	$-0.154446\pi$
$114$	−2.43718	+	4.74527i	−0.228262	+	0.444436i
$115$	3.68292	−	12.2025i	0.343434	−	1.13789i
$116$	−6.30216	−	4.57879i	−0.585141	−	0.425130i
$117$	14.2260	+	4.72414i	1.31520	+	0.436746i
$118$	−3.18537			−0.293237
$119$	−13.2014	−	2.80605i	−1.21017	−	0.257231i
$120$	−4.87976	+	10.0140i	−0.445459	+	0.914146i
$121$	9.07143	−	1.92819i	0.824676	−	0.175290i
$122$	10.8345	−	2.30295i	0.980913	−	0.208499i
$123$	1.49474	+	2.31806i	0.134776	+	0.209012i
$124$	3.22778	−	5.59068i	0.289863	−	0.502058i
$125$	4.11863	+	10.3941i	0.368382	+	0.929675i
$126$	4.92616	−	6.68898i	0.438857	−	0.595902i
$127$	14.1647	−	10.2913i	1.25691	−	0.913201i	0.258311	−	0.966062i	$-0.416834\pi$
$127$	14.1647	−	10.2913i	1.25691	−	0.913201i	0.998602	+	0.0528609i	$0.0168340\pi$
$128$	−4.11379	−	4.56882i	−0.363611	−	0.403831i
$129$	1.18999	+	7.67364i	0.104773	+	0.675626i
$130$	−1.26592	−	10.0134i	−0.111028	−	0.878230i
$131$	−3.51142	+	3.89983i	−0.306794	+	0.340730i	−0.876751	−	0.480945i	$-0.840293\pi$
$131$	−3.51142	+	3.89983i	−0.306794	+	0.340730i	0.569956	+	0.821675i	$0.306960\pi$
$132$	2.25464	+	1.47456i	0.196241	+	0.128344i
$133$	10.2225	+	2.17285i	0.886399	+	0.188410i
$134$	−4.02949	−	2.92759i	−0.348095	−	0.252906i
$135$	−9.67204	+	6.43829i	−0.832437	+	0.554120i
$136$	10.2453	−	7.44368i	0.878531	−	0.638290i
$137$	−1.66112	+	0.739580i	−0.141919	+	0.0631866i	−0.476468	−	0.879192i	$-0.658083\pi$
$137$	−1.66112	+	0.739580i	−0.141919	+	0.0631866i	0.334548	+	0.942379i	$0.391416\pi$
$138$	−3.16936	−	8.33686i	−0.269794	−	0.709681i
$139$	−9.38142	−	4.17688i	−0.795721	−	0.354278i	−0.0317235	−	0.999497i	$-0.510100\pi$
$139$	−9.38142	−	4.17688i	−0.795721	−	0.354278i	−0.763998	+	0.645219i	$0.776766\pi$
$140$	7.97142	+	1.51987i	0.673708	+	0.128452i
$141$	−11.3563	−	1.83628i	−0.956373	−	0.154643i
$142$	5.72313	+	1.21649i	0.480274	+	0.102085i
$143$	−6.56427			−0.548932
$144$	0.139332	+	0.676980i	0.0116110	+	0.0564150i
$145$	−9.61241	+	11.1382i	−0.798267	+	0.924974i
$146$	−3.79892	−	4.21913i	−0.314401	−	0.349178i
$147$	−3.86966	−	1.49978i	−0.319164	−	0.123700i
$148$	7.90105	+	3.51777i	0.649462	+	0.289159i
$149$	−3.40851	−	5.90371i	−0.279236	−	0.483651i	0.691959	−	0.721937i	$-0.256748\pi$
$149$	−3.40851	−	5.90371i	−0.279236	−	0.483651i	−0.971195	+	0.238286i	$0.923415\pi$
$150$	6.72169	+	4.00288i	0.548824	+	0.326834i
$151$	9.80375	−	16.9806i	0.797818	−	1.38186i	−0.123216	−	0.992380i	$-0.539321\pi$
$151$	9.80375	−	16.9806i	0.797818	−	1.38186i	0.921034	−	0.389482i	$-0.127346\pi$
$152$	−7.93342	+	5.76397i	−0.643485	+	0.467519i
$153$	13.1451	−	1.29581i	1.06272	−	0.104760i
$154$	−1.12415	+	3.45978i	−0.0905866	+	0.278797i
$155$	−10.0124	−	6.95743i	−0.804215	−	0.558834i
$156$	7.22183	+	7.26864i	0.578210	+	0.581957i
$157$	7.62958	+	13.2148i	0.608907	+	1.05466i	0.991421	+	0.130708i	$0.0417251\pi$
$157$	7.62958	+	13.2148i	0.608907	+	1.05466i	−0.382514	+	0.923950i	$0.624942\pi$
$158$	1.70601	−	1.89471i	0.135723	−	0.150735i
$159$	4.34244	+	11.4226i	0.344378	+	0.905868i
$160$	−9.87434	+	7.49647i	−0.780635	+	0.592648i
$161$	−14.1360	+	10.2704i	−1.11407	+	0.809419i
$162$	−2.61206	+	7.69920i	−0.205223	+	0.604906i
$163$	−0.570284	−	0.414336i	−0.0446681	−	0.0324533i	0.565227	−	0.824935i	$-0.308789\pi$
$163$	−0.570284	−	0.414336i	−0.0446681	−	0.0324533i	−0.609895	+	0.792482i	$0.708789\pi$
$164$	0.197075	+	1.87504i	0.0153889	+	0.146416i
$165$	3.13112	−	4.01057i	0.243757	−	0.312222i
$166$	−1.13919	+	10.8387i	−0.0884186	+	0.841247i
$167$	−3.02187	+	3.35613i	−0.233839	+	0.259705i	−0.848632	−	0.528984i	$-0.822573\pi$
$167$	−3.02187	+	3.35613i	−0.233839	+	0.259705i	0.614792	+	0.788689i	$0.289240\pi$
$168$	13.6286	−	6.88878i	1.05147	−	0.531481i
$169$	−11.7049	−	2.48796i	−0.900379	−	0.191381i
$170$	−4.60794	−	7.60704i	−0.353413	−	0.583433i
$171$	−10.1788	+	1.00340i	−0.778396	+	0.0767323i
$172$	−1.64027	+	5.04822i	−0.125069	+	0.384923i
$173$	0.455293	+	4.33182i	0.0346153	+	0.329342i	0.998102	+	0.0615856i	$0.0196157\pi$
$173$	0.455293	+	4.33182i	0.0346153	+	0.329342i	−0.963487	+	0.267757i	$0.913718\pi$
$174$	−0.571995	+	10.2790i	−0.0433629	+	0.779248i
$175$	4.11888	−	14.7627i	0.311358	−	1.11595i
$176$	−0.151336	−	0.262122i	−0.0114074	−	0.0197582i
$177$	−3.30980	−	5.13287i	−0.248780	−	0.385810i
$178$	−4.47708	−	4.97230i	−0.335571	−	0.372689i
$179$	−0.115016	+	0.353983i	−0.00859671	+	0.0264579i	−0.955263	−	0.295758i	$-0.904428\pi$
$179$	−0.115016	+	0.353983i	−0.00859671	+	0.0264579i	0.946666	+	0.322216i	$0.104428\pi$
$180$	−7.88569	+	0.945220i	−0.587764	+	0.0704525i
$181$	1.51210	+	4.65376i	0.112393	+	0.345912i	0.991394	−	0.130908i	$-0.0417894\pi$
$181$	1.51210	+	4.65376i	0.112393	+	0.345912i	−0.879001	+	0.476820i	$0.841789\pi$
$182$	−6.91802	+	11.9824i	−0.512797	+	0.888191i
$183$	14.9687	+	15.0657i	1.10652	+	1.11369i
$184$	1.71378	−	16.3055i	0.126341	−	1.20206i
$185$	7.86794	−	14.3149i	0.578462	−	1.05245i
$186$	−8.52118	+	0.418983i	−0.624803	+	0.0307213i
$187$	−5.28424	+	2.35269i	−0.386422	+	0.172046i
$188$	−6.36165	−	4.62201i	−0.463971	−	0.337094i
$189$	15.8971	+	0.987677i	1.15635	+	0.0718429i
$190$	3.56813	+	5.89046i	0.258859	+	0.427339i
$191$	3.83399	−	1.70700i	0.277418	−	0.123514i	−0.263312	−	0.964711i	$-0.584815\pi$
$191$	3.83399	−	1.70700i	0.277418	−	0.123514i	0.540730	+	0.841196i	$0.318148\pi$
$192$	−2.48137	+	9.14239i	−0.179078	+	0.659795i
$193$	1.47540	+	2.55547i	0.106202	+	0.183946i	0.914228	−	0.405199i	$-0.132798\pi$
$193$	1.47540	+	2.55547i	0.106202	+	0.183946i	−0.808027	+	0.589146i	$0.799464\pi$
$194$	−10.2897	+	11.4279i	−0.738759	+	0.820475i
$195$	14.8200	−	12.4444i	1.06128	−	0.891162i
$196$	−1.89821	−	2.10817i	−0.135586	−	0.150584i
$197$	−2.11764	+	6.51743i	−0.150876	+	0.464348i	−0.997720	−	0.0674935i	$-0.978500\pi$
$197$	−2.11764	+	6.51743i	−0.150876	+	0.464348i	0.846844	+	0.531842i	$0.178500\pi$
$198$	0.0229987	−	3.56025i	0.00163444	−	0.253016i
$199$	9.62725			0.682458			0.341229	−	0.939980i	$-0.389157\pi$
$199$	9.62725			0.682458			0.341229	+	0.939980i	$0.389157\pi$
$200$	7.70808	+	12.1410i	0.545043	+	0.858501i
$201$	0.530596	−	9.53501i	0.0374253	−	0.672548i
$202$	10.4427	+	4.64938i	0.734745	+	0.327129i
$203$	19.7278	−	4.19327i	1.38462	−	0.294310i
$204$	8.41872	+	3.26288i	0.589428	+	0.228447i
$205$	3.56003	−	0.0749002i	0.248643	−	0.00523126i
$206$	5.18192	+	15.9483i	0.361042	+	1.11117i
$207$	10.1407	−	13.7696i	0.704830	−	0.957052i
$208$	−0.355733	−	1.09483i	−0.0246656	−	0.0759130i
$209$	4.09181	−	1.82179i	0.283037	−	0.126016i
$210$	−4.02100	−	9.94221i	−0.277475	−	0.686078i
$211$	−5.67978	−	2.52880i	−0.391012	−	0.174090i	0.201807	−	0.979425i	$-0.435319\pi$
$211$	−5.67978	−	2.52880i	−0.391012	−	0.174090i	−0.592819	+	0.805336i	$0.701985\pi$
$212$	−0.873134	+	8.30732i	−0.0599671	+	0.570549i
$213$	3.98645	+	10.4862i	0.273147	+	0.718501i
$214$	1.16353	+	11.0703i	0.0795376	+	0.756749i
$215$	9.24207	+	3.88400i	0.630304	+	0.264887i
$216$	−10.6699	+	10.4651i	−0.725994	+	0.712059i
$217$	5.16487	+	15.8958i	0.350614	+	1.07908i
$218$	−0.207863	+	0.360029i	−0.0140783	+	0.0243842i
$219$	2.85133	−	10.5055i	0.192675	−	0.709894i
$220$	3.14682	−	1.48113i	0.212158	−	0.0998580i
$221$	−21.5192	+	4.57405i	−1.44754	+	0.307684i
$222$	−1.75157	−	11.2949i	−0.117557	−	0.758067i
$223$	−1.63494	−	15.5554i	−0.109484	−	1.04167i	−0.901976	−	0.431787i	$-0.857883\pi$
$223$	−1.63494	−	15.5554i	−0.109484	−	1.04167i	0.792492	−	0.609883i	$-0.208783\pi$
$224$	16.9951			1.13554
$225$	0.534074	+	14.9905i	0.0356049	+	0.999366i
$226$	−10.6841			−0.710696
$227$	0.350039	+	3.33040i	0.0232329	+	0.221046i	0.999978	+	0.00664221i	$0.00211430\pi$
$227$	0.350039	+	3.33040i	0.0232329	+	0.221046i	−0.976745	+	0.214404i	$0.931219\pi$
$228$	−6.51898	−	2.52659i	−0.431730	−	0.167328i
$229$	−23.1383	+	4.91819i	−1.52902	+	0.325003i	−0.894204	−	0.447660i	$-0.852258\pi$
$229$	−23.1383	+	4.91819i	−1.52902	+	0.325003i	−0.634816	+	0.772663i	$0.718924\pi$
$230$	−11.3106	−	2.15653i	−0.745798	−	0.142197i
$231$	−6.74310	+	1.78349i	−0.443664	+	0.117345i
$232$	−9.46229	+	16.3892i	−0.621230	+	1.07600i
$233$	−6.81754	−	20.9822i	−0.446632	−	1.37459i	−0.880684	−	0.473704i	$-0.842917\pi$
$233$	−6.81754	−	20.9822i	−0.446632	−	1.37459i	0.434053	−	0.900888i	$-0.357083\pi$
$234$	2.90089	−	13.2269i	0.189637	−	0.864669i
$235$	−9.70314	+	11.2433i	−0.632963	+	0.733431i
$236$	−0.436381	−	4.15189i	−0.0284060	−	0.270265i
$237$	4.82576	+	0.780311i	0.313467	+	0.0506867i
$238$	−1.27442	+	12.1253i	−0.0826082	+	0.785965i
$239$	−13.2172	−	5.88467i	−0.854949	−	0.380648i	−0.0680145	−	0.997684i	$-0.521666\pi$
$239$	−13.2172	−	5.88467i	−0.854949	−	0.380648i	−0.786935	+	0.617037i	$0.788333\pi$
$240$	0.838592	+	0.304887i	0.0541309	+	0.0196804i
$241$	8.13902	−	3.62373i	0.524281	−	0.233425i	−0.127491	−	0.991840i	$-0.540693\pi$
$241$	8.13902	−	3.62373i	0.524281	−	0.233425i	0.651772	+	0.758415i	$0.274026\pi$
$242$	−2.58889	−	7.96779i	−0.166420	−	0.512189i
$243$	−15.1205	+	3.79091i	−0.969979	+	0.243187i
$244$	4.48600	+	13.8065i	0.287187	+	0.883870i
$245$	−4.26735	+	3.23971i	−0.272631	+	0.206978i
$246$	1.94142	−	1.56178i	0.123781	−	0.0995754i
$247$	16.6633	−	3.54188i	1.06026	−	0.225365i
$248$	−14.3271	−	6.37884i	−0.909773	−	0.405057i
$249$	−18.6490	+	9.42641i	−1.18183	+	0.597374i
$250$	8.94923	−	4.68170i	0.565999	−	0.296096i
$251$	12.4010			0.782742			0.391371	−	0.920233i	$-0.372001\pi$
$251$	12.4010			0.782742			0.391371	+	0.920233i	$0.372001\pi$
$252$	9.39344	+	5.50451i	0.591731	+	0.346752i
$253$	−2.31412	+	7.12212i	−0.145487	+	0.447764i
$254$	−10.5833	−	11.7539i	−0.664054	−	0.737507i
$255$	7.46994	−	15.3294i	0.467786	−	0.959962i
$256$	−11.0356	+	12.2563i	−0.689726	+	0.766018i
$257$	15.6534	+	27.1124i	0.976431	+	1.69123i	0.675130	+	0.737699i	$0.264088\pi$
$257$	15.6534	+	27.1124i	0.976431	+	1.69123i	0.301301	+	0.953529i	$0.402579\pi$
$258$	6.78170	−	1.79369i	0.422210	−	0.111671i
$259$	−20.4563	+	9.10773i	−1.27109	+	0.565927i
$260$	12.8782	−	3.02181i	0.798673	−	0.187405i
$261$	−17.1578	+	9.75880i	−1.06204	+	0.604055i
$262$	3.83522	+	2.78645i	0.236940	+	0.172147i
$263$	23.3849	−	10.4116i	1.44197	−	0.642008i	0.471205	−	0.882024i	$-0.343819\pi$
$263$	23.3849	−	10.4116i	1.44197	−	0.642008i	0.970769	+	0.240016i	$0.0771525\pi$
$264$	2.99008	−	5.82181i	0.184027	−	0.358308i
$265$	15.4970	+	2.95472i	0.951971	+	0.181507i
$266$	0.986837	−	9.38912i	0.0605068	−	0.575684i
$267$	3.36033	−	12.3808i	0.205649	−	0.757694i
$268$	3.26387	−	5.65319i	0.199373	−	0.345324i
$269$	0.317149	+	0.976085i	0.0193369	+	0.0595129i	0.960259	−	0.279109i	$-0.0900392\pi$
$269$	0.317149	+	0.976085i	0.0193369	+	0.0595129i	−0.940922	+	0.338622i	$0.890039\pi$
$270$	6.69752	+	8.08151i	0.407598	+	0.491825i
$271$	6.14011	−	18.8973i	0.372985	−	1.14793i	−0.571843	−	0.820363i	$-0.693771\pi$
$271$	6.14011	−	18.8973i	0.372985	−	1.14793i	0.944828	−	0.327567i	$-0.106229\pi$
$272$	−0.678763	−	0.753843i	−0.0411560	−	0.0457084i
$273$	−26.4965	+	1.30282i	−1.60364	+	0.0788502i
$274$	0.821301	+	1.42253i	0.0496166	+	0.0859384i
$275$	−2.29080	−	6.15629i	−0.138140	−	0.371238i
$276$	10.4323	−	5.27313i	0.627948	−	0.317405i
$277$	−1.89213	−	18.0024i	−0.113687	−	1.08166i	−0.891456	−	0.453108i	$-0.850315\pi$
$277$	−1.89213	−	18.0024i	−0.113687	−	1.08166i	0.777769	−	0.628550i	$-0.216351\pi$
$278$	−2.86669	+	8.82276i	−0.171933	+	0.529154i
$279$	−9.52918	−	13.2956i	−0.570497	−	0.795984i
$280$	1.64785	−	19.6454i	0.0984778	−	1.17404i
$281$	25.1370	+	5.34304i	1.49955	+	0.318739i	0.883298	−	0.468812i	$-0.155318\pi$
$281$	25.1370	+	5.34304i	1.49955	+	0.318739i	0.616250	+	0.787551i	$0.288651\pi$
$282$	−0.577394	+	10.3760i	−0.0343833	+	0.617882i
$283$	5.88858	−	6.53993i	0.350040	−	0.388758i	−0.542253	−	0.840215i	$-0.682429\pi$
$283$	5.88858	−	6.53993i	0.350040	−	0.388758i	0.892293	+	0.451457i	$0.149095\pi$
$284$	−0.801557	+	7.62631i	−0.0475637	+	0.452538i
$285$	−5.78430	+	11.8702i	−0.342632	+	0.703130i
$286$	0.619842	+	5.89741i	0.0366520	+	0.348721i
$287$	−3.94908	−	2.86917i	−0.233107	−	0.169362i
$288$	−15.8519	+	5.03761i	−0.934080	+	0.296844i
$289$	−1.93028	+	1.40243i	−0.113546	+	0.0824960i
$290$	10.9143	+	7.58414i	0.640910	+	0.445356i
$291$	−29.1064	−	4.70642i	−1.70625	−	0.275895i
$292$	4.97888	−	5.52961i	0.291367	−	0.323596i
$293$	−3.17339	−	5.49647i	−0.185391	−	0.321107i	0.758317	−	0.651886i	$-0.226022\pi$
$293$	−3.17339	−	5.49647i	−0.185391	−	0.321107i	−0.943708	+	0.330779i	$0.892689\pi$
$294$	−0.982019	+	3.61816i	−0.0572725	+	0.211015i
$295$	−7.88296	+	0.165851i	−0.458964	+	0.00965622i
$296$	6.49279	−	19.9828i	0.377386	−	1.16147i
$297$	5.76084	−	3.66226i	0.334278	−	0.212506i
$298$	−4.98210	+	3.61971i	−0.288605	+	0.209684i
$299$	−14.2411	+	24.6662i	−0.823582	+	1.42649i
$300$	−4.29661	+	9.30959i	−0.248065	+	0.537489i
$301$	−6.87138	−	11.9016i	−0.396060	−	0.685996i
$302$	−16.1813	−	7.20436i	−0.931127	−	0.414565i
$303$	3.35865	+	21.6582i	0.192949	+	1.24423i
$304$	0.525596	+	0.583733i	0.0301450	+	0.0334794i
$305$	26.6927	−	6.26331i	1.52842	−	0.358636i
$306$	−2.40542	−	11.6874i	−0.137509	−	0.668122i
$307$	−25.8730			−1.47665			−0.738325	−	0.674445i	$-0.764383\pi$
$307$	−25.8730			−1.47665			−0.738325	+	0.674445i	$0.764383\pi$
$308$	−4.66356	−	0.991270i	−0.265731	−	0.0564828i
$309$	−20.3146	+	24.9214i	−1.15566	+	1.41773i
$310$	−5.30519	+	9.65220i	−0.301314	+	0.548208i
$311$	3.06338	+	1.36391i	0.173709	+	0.0773400i	0.491748	−	0.870737i	$-0.336358\pi$
$311$	3.06338	+	1.36391i	0.173709	+	0.0773400i	−0.318040	+	0.948077i	$0.603025\pi$
$312$	15.7276	−	19.2942i	0.890400	−	1.09232i
$313$	−8.10590	+	3.60898i	−0.458173	+	0.203992i	−0.622827	−	0.782360i	$-0.714016\pi$
$313$	−8.10590	+	3.60898i	−0.458173	+	0.203992i	0.164654	+	0.986351i	$0.447349\pi$
$314$	11.1519	−	8.10232i	0.629338	−	0.457241i
$315$	11.8427	−	16.8100i	0.667259	−	0.947134i
$316$	2.70333	+	1.96408i	0.152074	+	0.110488i
$317$	31.2503	+	6.64245i	1.75519	+	0.373077i	0.969414	−	0.245432i	$-0.0789298\pi$
$317$	31.2503	+	6.64245i	1.75519	+	0.373077i	0.785777	+	0.618509i	$0.212263\pi$
$318$	9.85210	−	4.97988i	0.552478	−	0.279258i
$319$	5.78389	−	6.42366i	0.323836	−	0.359656i
$320$	8.37268	+	8.91435i	0.468047	+	0.498328i
$321$	−16.6295	+	13.3776i	−0.928170	+	0.746666i
$322$	10.5618	+	11.7301i	0.588587	+	0.653692i
$323$	12.1445	−	8.82347i	0.675736	−	0.490951i
$324$	−10.3932	−	2.34987i	−0.577397	−	0.130548i
$325$	−3.65418	−	24.7145i	−0.202697	−	1.37091i
$326$	−0.318393	+	0.551473i	−0.0176342	+	0.0305433i
$327$	−0.796129	+	0.0391453i	−0.0440260	+	0.00216474i
$328$	4.48017	−	0.952290i	0.247376	−	0.0525814i
$329$	19.9140	−	4.23285i	1.09789	−	0.233365i
$330$	−3.89880	−	2.43432i	−0.214622	−	0.134005i
$331$	12.0676	+	2.56505i	0.663297	+	0.140988i	0.527245	−	0.849713i	$-0.323225\pi$
$331$	12.0676	+	2.56505i	0.663297	+	0.140988i	0.136052	+	0.990702i	$0.456558\pi$
$332$	−14.2835			−0.783908
$333$	16.3805	−	14.5586i	0.897648	−	0.797807i
$334$	3.30052	+	2.39797i	0.180596	+	0.131211i
$335$	−10.1243	−	7.03522i	−0.553152	−	0.384375i
$336$	−0.662886	−	1.02801i	−0.0361634	−	0.0560825i
$337$	0.748779	−	7.12416i	0.0407886	−	0.388078i	−0.955015	−	0.296558i	$-0.904161\pi$
$337$	0.748779	−	7.12416i	0.0407886	−	0.388078i	0.995803	−	0.0915192i	$-0.0291723\pi$
$338$	−1.12995	+	10.7507i	−0.0614611	+	0.584763i
$339$	−11.1014	−	17.2162i	−0.602948	−	0.935057i
$340$	9.28392	−	7.04823i	0.503491	−	0.382244i
$341$	5.79521	+	4.21047i	0.313828	+	0.228010i
$342$	1.86262	+	9.05003i	0.100719	+	0.489369i
$343$	−14.1124			−0.761998
$344$	12.6134	+	2.68105i	0.680067	+	0.144553i
$345$	−8.27741	−	20.4665i	−0.445641	−	1.10188i
$346$	3.84876	−	0.818079i	0.206911	−	0.0439802i
$347$	−0.310983	+	0.0661014i	−0.0166944	+	0.00354851i	−0.216251	−	0.976338i	$-0.569383\pi$
$347$	−0.310983	+	0.0661014i	−0.0166944	+	0.00354851i	0.199557	+	0.979886i	$0.436050\pi$
$348$	−13.4762	+	0.662620i	−0.722401	+	0.0355202i
$349$	−7.13603	+	12.3600i	−0.381983	+	0.661614i	−0.991346	−	0.131278i	$-0.958092\pi$
$349$	−7.13603	+	12.3600i	−0.381983	+	0.661614i	0.609363	+	0.792892i	$0.291425\pi$
$350$	−13.6519	−	2.30645i	−0.729723	−	0.123285i
$351$	24.3279	−	9.06912i	1.29852	−	0.484074i
$352$	5.89274	−	4.28133i	0.314084	−	0.228196i
$353$	−9.97502	−	11.0784i	−0.530917	−	0.589643i	0.416703	−	0.909043i	$-0.363185\pi$
$353$	−9.97502	−	11.0784i	−0.530917	−	0.589643i	−0.947620	+	0.319400i	$0.896519\pi$
$354$	−4.29888	+	3.45824i	−0.228483	+	0.183803i
$355$	14.2266	+	2.71250i	0.755068	+	0.143965i
$356$	5.86767	−	6.51670i	0.310986	−	0.345385i
$357$	−20.8627	+	10.5453i	−1.10417	+	0.558118i
$358$	0.328882	+	0.0699061i	0.0173820	+	0.00369465i
$359$	12.3016	+	8.93763i	0.649253	+	0.471710i	0.863017	−	0.505175i	$-0.168572\pi$
$359$	12.3016	+	8.93763i	0.649253	+	0.471710i	−0.213763	+	0.976885i	$0.568572\pi$
$360$	4.28620	+	18.8123i	0.225902	+	0.991496i
$361$	5.96733	−	4.33552i	0.314070	−	0.228185i
$362$	4.03820	−	1.79792i	0.212243	−	0.0944968i
$363$	10.1492	−	12.4507i	0.532693	−	0.653494i
$364$	−16.5658	−	7.37557i	−0.868284	−	0.386585i
$365$	−9.62101	−	10.2434i	−0.503587	−	0.536166i
$366$	12.1217	−	14.8706i	0.633613	−	0.777301i
$367$	−8.24408	−	1.75233i	−0.430337	−	0.0914710i	−0.0123497	−	0.999924i	$-0.503931\pi$
$367$	−8.24408	−	1.75233i	−0.430337	−	0.0914710i	−0.417988	+	0.908453i	$0.637264\pi$
$368$	−1.31328			−0.0684595
$369$	4.53389	+	1.50560i	0.236025	+	0.0783783i
$370$	−13.6035	−	5.71693i	−0.707215	−	0.297209i
$371$	−14.4710	−	16.0717i	−0.751299	−	0.834402i
$372$	−1.71347	−	11.0493i	−0.0888394	−	0.572879i
$373$	29.5017	+	13.1350i	1.52754	+	0.680104i	0.986927	−	0.161168i	$-0.0515260\pi$
$373$	29.5017	+	13.1350i	1.52754	+	0.680104i	0.540612	+	0.841272i	$0.318193\pi$
$374$	2.61266	+	4.52525i	0.135097	+	0.233995i
$375$	16.8428	+	9.55610i	0.869760	+	0.493475i
$376$	−9.55160	+	16.5439i	−0.492586	+	0.853184i
$377$	26.5972	−	19.3240i	1.36983	−	0.995238i
$378$	−0.613774	−	14.3754i	−0.0315691	−	0.739391i
$379$	5.98776	−	18.4284i	0.307571	−	0.946605i	−0.671135	−	0.741335i	$-0.734193\pi$
$379$	5.98776	−	18.4284i	0.307571	−	0.946605i	0.978705	−	0.205270i	$-0.0658072\pi$
$380$	−7.18894	+	5.45775i	−0.368785	+	0.279977i
$381$	7.94342	−	29.2668i	0.406954	−	1.49938i
$382$	−1.89562	−	3.28331i	−0.0969883	−	0.167989i
$383$	−17.6891	+	19.6458i	−0.903873	+	1.00385i	0.0960915	+	0.995373i	$0.469366\pi$
$383$	−17.6891	+	19.6458i	−0.903873	+	1.00385i	−0.999964	+	0.00847965i	$0.997301\pi$
$384$	−10.5120	−	1.69977i	−0.536440	−	0.0867408i
$385$	−2.60184	+	8.62057i	−0.132602	+	0.439345i
$386$	2.15654	−	1.56682i	0.109765	−	0.0797489i
$387$	9.93695	+	9.06418i	0.505123	+	0.460758i
$388$	−16.3050	−	11.8463i	−0.827762	−	0.601405i
$389$	−1.10391	−	10.5030i	−0.0559707	−	0.532525i	−0.986201	−	0.165550i	$-0.947060\pi$
$389$	−1.10391	−	10.5030i	−0.0559707	−	0.532525i	0.930231	−	0.366975i	$-0.119607\pi$
$390$	−12.5796	−	12.1394i	−0.636991	−	0.614701i
$391$	−2.62345	+	24.9604i	−0.132673	+	1.26230i
$392$	−4.61145	+	5.12154i	−0.232914	+	0.258677i
$393$	−0.505014	+	9.07531i	−0.0254746	+	0.457789i
$394$	6.05529	+	1.28709i	0.305061	+	0.0648427i
$395$	4.12326	−	4.77774i	0.207464	−	0.240394i
$396$	4.64367	−	0.457761i	0.233353	−	0.0230033i
$397$	−0.814060	+	2.50542i	−0.0408565	+	0.125743i	−0.969404	−	0.245469i	$-0.921058\pi$
$397$	−0.814060	+	2.50542i	−0.0408565	+	0.125743i	0.928548	+	0.371213i	$0.121058\pi$
$398$	−0.909069	−	8.64922i	−0.0455675	−	0.433546i
$399$	16.1549	−	8.16571i	0.808756	−	0.408797i
$400$	0.902644	−	0.715697i	0.0451322	−	0.0357849i
$401$	3.74794	+	6.49163i	0.187163	+	0.324177i	0.944303	−	0.329076i	$-0.106737\pi$
$401$	3.74794	+	6.49163i	0.187163	+	0.324177i	−0.757140	+	0.653253i	$0.773404\pi$
$402$	−8.61645	+	0.423667i	−0.429750	+	0.0211306i
$403$	18.2302	+	20.2467i	0.908113	+	1.00856i
$404$	−4.62951	+	14.2482i	−0.230327	+	0.708873i
$405$	−6.06330	+	19.1895i	−0.301288	+	0.953533i
$406$	−5.63011	−	17.3277i	−0.279417	−	0.859959i
$407$	−4.79846	+	8.31118i	−0.237851	+	0.411970i
$408$	5.74549	−	21.1688i	0.284444	−	1.04801i
$409$	−3.44852	+	32.8104i	−0.170518	+	1.62237i	0.490111	+	0.871660i	$0.336956\pi$
$409$	−3.44852	+	32.8104i	−0.170518	+	1.62237i	−0.660629	+	0.750712i	$0.729710\pi$
$410$	−0.403453	−	3.19129i	−0.0199251	−	0.157607i
$411$	−1.43887	+	2.80153i	−0.0709742	+	0.138190i
$412$	−20.0775	+	8.93908i	−0.989148	+	0.440397i
$413$	8.74443	+	6.35320i	0.430285	+	0.312620i
$414$	−13.3283	−	7.81032i	−0.655049	−	0.383856i
$415$	−2.25487	+	26.8822i	−0.110687	+	1.31960i
$416$	25.3081	−	11.2679i	1.24083	−	0.552454i
$417$	−17.1956	+	4.54806i	−0.842070	+	0.222719i
$418$	−2.02309	−	3.50410i	−0.0989527	−	0.171391i
$419$	12.1266	−	13.4680i	0.592424	−	0.657954i	−0.370150	−	0.928972i	$-0.620694\pi$
$419$	12.1266	−	13.4680i	0.592424	−	0.657954i	0.962574	+	0.271018i	$0.0873603\pi$
$420$	12.4080	−	6.60309i	0.605451	−	0.322198i
$421$	16.1076	+	17.8893i	0.785036	+	0.871870i	0.994369	−	0.105974i	$-0.0337960\pi$
$421$	16.1076	+	17.8893i	0.785036	+	0.871870i	−0.209333	+	0.977844i	$0.567129\pi$
$422$	−1.73558	+	5.34155i	−0.0844865	+	0.260023i
$423$	−17.3197	+	9.85091i	−0.842113	+	0.478968i
$424$	20.2928			0.985503
$425$	−11.7995	−	18.5855i	−0.572361	−	0.901529i
$426$	9.04445	−	4.57164i	0.438205	−	0.221497i
$427$	−34.3360	−	15.2874i	−1.66163	−	0.739807i
$428$	−14.2699	+	3.03315i	−0.689760	+	0.146613i
$429$	−8.85895	+	7.12658i	−0.427714	+	0.344074i
$430$	2.61673	−	8.66991i	0.126190	−	0.418100i
$431$	−5.44510	−	16.7583i	−0.262281	−	0.807218i	−0.992307	−	0.123799i	$-0.960492\pi$
$431$	−5.44510	−	16.7583i	−0.262281	−	0.807218i	0.730026	−	0.683419i	$-0.239508\pi$
$432$	0.923010	+	0.762365i	0.0444083	+	0.0366793i
$433$	0.572909	+	1.76323i	0.0275322	+	0.0847355i	0.963878	−	0.266342i	$-0.0858152\pi$
$433$	0.572909	+	1.76323i	0.0275322	+	0.0847355i	−0.936346	+	0.351078i	$0.885815\pi$
$434$	13.7933	−	6.14115i	0.662098	−	0.294785i
$435$	−0.880347	+	25.4675i	−0.0422094	+	1.22108i
$436$	−0.497746	−	0.221611i	−0.0238377	−	0.0106132i
$437$	2.03145	−	19.3279i	0.0971774	−	0.924581i
$438$	−9.70746	−	1.56967i	−0.463841	−	0.0750016i
$439$	1.00546	+	9.56630i	0.0479879	+	0.456574i	0.991960	+	0.126550i	$0.0403904\pi$
$439$	1.00546	+	9.56630i	0.0479879	+	0.456574i	−0.943972	+	0.330025i	$0.892943\pi$
$440$	−4.37761	−	7.22680i	−0.208695	−	0.344524i
$441$	−6.85063	+	2.17708i	−0.326221	+	0.103671i
$442$	6.14136	+	18.9011i	0.292114	+	0.899036i
$443$	−18.6090	+	32.2317i	−0.884138	+	1.53137i	−0.0374398	+	0.999299i	$0.511920\pi$
$443$	−18.6090	+	32.2317i	−0.884138	+	1.53137i	−0.846698	+	0.532073i	$0.821413\pi$
$444$	14.4821	−	3.83039i	0.687292	−	0.181782i
$445$	−11.3385	−	12.0720i	−0.537495	−	0.572268i
$446$	−13.8208	+	2.93770i	−0.654433	+	0.139104i
$447$	−11.0095	−	4.26698i	−0.520729	−	0.201821i
$448$	−1.75243	−	16.6733i	−0.0827947	−	0.787739i
$449$	−27.8383			−1.31377			−0.656885	−	0.753991i	$-0.728126\pi$
$449$	−27.8383			−1.31377			−0.656885	+	0.753991i	$0.728126\pi$
$450$	13.4172	−	1.89532i	0.632491	−	0.0893462i
$451$	−2.09206			−0.0985111
$452$	−1.46367	−	13.9259i	−0.0688453	−	0.655019i
$453$	−5.20433	−	33.5601i	−0.244521	−	1.57679i
$454$	2.95901	−	0.628957i	0.138873	−	0.0295184i
$455$	−16.4964	+	30.0134i	−0.773362	+	1.40705i
$456$	−4.44899	+	16.3919i	−0.208343	+	0.767620i
$457$	4.49089	−	7.77846i	0.210075	−	0.363861i	−0.741663	−	0.670773i	$-0.765962\pi$
$457$	4.49089	−	7.77846i	0.210075	−	0.363861i	0.951738	+	0.306912i	$0.0992958\pi$
$458$	6.60342	+	20.3232i	0.308558	+	0.949643i
$459$	16.3335	−	16.0200i	0.762381	−	0.747748i
$460$	1.26137	−	15.0379i	0.0588119	−	0.701147i
$461$	1.22076	+	11.6148i	0.0568566	+	0.540954i	0.985463	+	0.169889i	$0.0543408\pi$
$461$	1.22076	+	11.6148i	0.0568566	+	0.540954i	−0.928607	+	0.371066i	$0.878992\pi$
$462$	2.23903	+	5.88966i	0.104169	+	0.274012i
$463$	−2.84599	+	27.0778i	−0.132265	+	1.25841i	0.704045	+	0.710155i	$0.251375\pi$
$463$	−2.84599	+	27.0778i	−0.132265	+	1.25841i	−0.836310	+	0.548257i	$0.815291\pi$
$464$	1.38482	+	0.616563i	0.0642888	+	0.0286232i
$465$	−21.0658	+	1.48054i	−0.976905	+	0.0686583i
$466$	−18.2069	+	8.10622i	−0.843417	+	0.375514i
$467$	−1.51920	−	4.67562i	−0.0703002	−	0.216362i	0.909734	−	0.415192i	$-0.136286\pi$
$467$	−1.51920	−	4.67562i	−0.0703002	−	0.216362i	−0.980034	+	0.198830i	$0.936286\pi$
$468$	17.6377	+	1.96907i	0.815301	+	0.0910201i
$469$	5.22261	+	16.0736i	0.241158	+	0.742208i
$470$	11.0173	+	7.65573i	0.508191	+	0.353132i
$471$	24.6435	+	9.55118i	1.13551	+	0.440095i
$472$	−9.92042	+	2.10865i	−0.456624	+	0.0970585i
$473$	−5.38071	−	2.39565i	−0.247405	−	0.110152i
$474$	0.245359	−	4.40919i	0.0112697	−	0.202521i
$475$	9.13688	+	14.3916i	0.419229	+	0.660330i
$476$	−15.9789			−0.732394
$477$	18.2615	+	10.7011i	0.836135	+	0.489971i
$478$	−4.03879	+	12.4301i	−0.184730	+	0.568541i
$479$	23.2878	+	25.8637i	1.06405	+	1.18174i	0.982728	+	0.185054i	$0.0592460\pi$
$479$	23.2878	+	25.8637i	1.06405	+	1.18174i	0.0813171	+	0.996688i	$0.474087\pi$
$480$	−5.18749	+	20.8372i	−0.236775	+	0.951084i
$481$	−24.4238	+	27.1253i	−1.11363	+	1.23681i
$482$	−4.02413	−	6.97000i	−0.183294	−	0.317475i
$483$	−7.92731	+	29.2074i	−0.360705	+	1.32898i
$484$	10.0307	−	4.46597i	0.455942	−	0.202999i
$485$	−24.8693	+	28.8168i	−1.12926	+	1.30850i
$486$	4.83357	+	13.2264i	0.219255	+	0.599963i
$487$	10.2778	+	7.46726i	0.465732	+	0.338374i	0.795775	−	0.605592i	$-0.207064\pi$
$487$	10.2778	+	7.46726i	0.465732	+	0.338374i	−0.330044	+	0.943966i	$0.607064\pi$
$488$	32.2182	−	14.3445i	1.45845	−	0.649344i
$489$	−1.21947	+	0.0599606i	−0.0551462	+	0.00271151i
$490$	3.31354	+	3.52791i	0.149691	+	0.159375i
$491$	−1.18773	+	11.3005i	−0.0536013	+	0.509982i	0.934476	+	0.356025i	$0.115868\pi$
$491$	−1.18773	+	11.3005i	−0.0536013	+	0.509982i	−0.988078	+	0.153957i	$0.950798\pi$
$492$	2.30162	+	2.31654i	0.103765	+	0.104438i
$493$	14.4849	−	25.0885i	0.652366	−	1.12993i
$494$	−4.75552	−	14.6360i	−0.213961	−	0.658504i
$495$	−0.128454	−	8.81188i	−0.00577358	−	0.396065i
$496$	−0.388194	+	1.19474i	−0.0174304	+	0.0536454i
$497$	−13.2847	−	14.7542i	−0.595902	−	0.661816i
$498$	10.2297	+	15.8644i	0.458406	+	0.710899i
$499$	−9.68467	−	16.7743i	−0.433545	−	0.750923i	0.563630	−	0.826027i	$-0.309404\pi$
$499$	−9.68467	−	16.7743i	−0.433545	−	0.750923i	−0.997176	+	0.0751046i	$0.976071\pi$
$500$	7.32823	+	11.0233i	0.327728	+	0.492975i
$501$	−0.434607	+	7.81005i	−0.0194168	+	0.348927i
$502$	−1.17098	−	11.1411i	−0.0522634	−	0.497253i
$503$	5.93488	−	18.2657i	0.264623	−	0.814427i	−0.727157	−	0.686471i	$-0.759159\pi$
$503$	5.93488	−	18.2657i	0.264623	−	0.814427i	0.991780	−	0.127955i	$-0.0408413\pi$
$504$	10.9139	−	24.0930i	0.486144	−	1.07319i
$505$	26.0850	+	10.9623i	1.16077	+	0.487815i
$506$	6.61709	+	1.40651i	0.294166	+	0.0625268i
$507$	−18.4977	+	9.34991i	−0.821511	+	0.415244i
$508$	13.8705	−	15.4047i	0.615403	−	0.683474i
$509$	1.50625	−	14.3310i	0.0667632	−	0.635209i	−0.909063	−	0.416659i	$-0.863201\pi$
$509$	1.50625	−	14.3310i	0.0667632	−	0.635209i	0.975826	−	0.218550i	$-0.0701326\pi$
$510$	−14.4774	−	5.26356i	−0.641071	−	0.233074i
$511$	2.01371	+	19.1592i	0.0890814	+	0.847553i
$512$	2.10561	+	1.52982i	0.0930558	+	0.0676090i
$513$	−12.6477	+	12.4049i	−0.558410	+	0.547692i
$514$	22.8800	−	16.6233i	1.00919	−	0.733222i
$515$	13.6543	+	39.1981i	0.601679	+	1.72727i
$516$	3.26700	+	8.59370i	0.143822	+	0.378316i
$517$	5.83849	−	6.48430i	0.256776	−	0.285179i
$518$	10.1141	+	17.5181i	0.444388	+	0.769703i
$519$	5.31734	+	5.35180i	0.233405	+	0.234918i
$520$	−10.5712	−	30.3473i	−0.463577	−	1.33082i
$521$	4.65920	−	14.3396i	0.204123	−	0.628227i	−0.795625	−	0.605790i	$-0.792857\pi$
$521$	4.65920	−	14.3396i	0.204123	−	0.628227i	0.999748	−	0.0224375i	$-0.00714269\pi$
$522$	10.3875	+	14.4932i	0.454651	+	0.634350i
$523$	12.9615	−	9.41708i	0.566767	−	0.411780i	−0.267162	−	0.963652i	$-0.586086\pi$
$523$	12.9615	−	9.41708i	0.566767	−	0.411780i	0.833929	+	0.551871i	$0.186086\pi$
$524$	−3.10651	+	5.38064i	−0.135709	+	0.235054i
$525$	−10.4686	−	24.3950i	−0.456885	−	1.06468i
$526$	−11.5621	−	20.0261i	−0.504130	−	0.873178i
$527$	21.9319	+	9.76473i	0.955370	+	0.425358i
$528$	−0.488814	−	0.189452i	−0.0212729	−	0.00824483i
$529$	6.35198	+	7.05459i	0.276173	+	0.306721i
$530$	1.19123	−	14.2016i	0.0517436	−	0.616879i
$531$	−10.0394	−	3.33384i	−0.435671	−	0.144676i
$532$	12.3732			0.536446
$533$	−7.78301	−	1.65433i	−0.337119	−	0.0716569i
$534$	−11.4404	−	1.84987i	−0.495073	−	0.0800518i
$535$	3.45583	+	27.3355i	0.149409	+	1.18182i
$536$	−14.4873	−	6.45017i	−0.625756	−	0.278605i
$537$	0.229084	+	0.602594i	0.00988569	+	0.0260038i
$538$	0.846977	−	0.377098i	0.0365158	−	0.0162579i
$539$	2.54664	−	1.85024i	0.109692	−	0.0796956i
$540$	−9.61610	+	9.83683i	−0.413811	+	0.423310i
$541$	12.8369	+	9.32652i	0.551900	+	0.400979i	0.828485	−	0.560011i	$-0.189203\pi$
$541$	12.8369	+	9.32652i	0.551900	+	0.400979i	−0.276586	+	0.960989i	$0.589203\pi$
$542$	−17.5573	−	3.73192i	−0.754152	−	0.160300i
$543$	7.09310	+	4.63895i	0.304394	+	0.199076i
$544$	16.3345	−	18.1413i	0.700336	−	0.777802i
$545$	−0.495660	+	0.901800i	−0.0212318	+	0.0386288i
$546$	3.67244	+	23.6817i	0.157166	+	1.01348i
$547$	−10.5774	−	11.7474i	−0.452258	−	0.502283i	0.473294	−	0.880905i	$-0.343065\pi$
$547$	−10.5774	−	11.7474i	−0.452258	−	0.502283i	−0.925552	+	0.378621i	$0.876398\pi$
$548$	−1.74165	+	1.26538i	−0.0743996	+	0.0540545i
$549$	36.5576	+	4.08128i	1.56024	+	0.174185i
$550$	−5.31456	+	2.63939i	−0.226614	+	0.112544i
$551$	−11.2163	+	19.4271i	−0.477829	+	0.827624i
$552$	−15.3894	−	23.8660i	−0.655016	−	1.01580i
$553$	−8.46228	+	1.79871i	−0.359853	+	0.0764891i
$554$	−15.9948	+	3.39981i	−0.679556	+	0.144444i
$555$	−4.92275	−	27.8608i	−0.208959	−	1.18263i
$556$	−11.8925	−	2.52783i	−0.504355	−	0.107204i
$557$	32.3933			1.37255			0.686273	−	0.727344i	$-0.259245\pi$
$557$	32.3933			1.37255			0.686273	+	0.727344i	$0.259245\pi$
$558$	−11.0451	+	9.81656i	−0.467574	+	0.415568i
$559$	−18.1233	−	13.1673i	−0.766533	−	0.556919i
$560$	−1.57880	+	0.0332166i	−0.0667163	+	0.00140366i
$561$	−4.57722	+	8.91202i	−0.193250	+	0.376266i
$562$	2.42663	−	23.0879i	0.102361	−	0.973902i
$563$	1.93555	−	18.4155i	0.0815737	−	0.776122i	−0.874900	−	0.484304i	$-0.839073\pi$
$563$	1.93555	−	18.4155i	0.0815737	−	0.776122i	0.956474	−	0.291819i	$-0.0942604\pi$
$564$	−13.6034	+	0.668874i	−0.572807	+	0.0281647i
$565$	−26.4403	+	0.556283i	−1.11235	+	0.0234030i
$566$	−6.43157	−	4.67281i	−0.270339	−	0.196413i
$567$	22.5266	−	15.9260i	0.946027	−	0.668828i
$568$	18.6292			0.781664
$569$	9.47432	+	2.01383i	0.397184	+	0.0844241i	0.402174	−	0.915563i	$-0.368255\pi$
$569$	9.47432	+	2.01383i	0.397184	+	0.0844241i	−0.00498942	+	0.999988i	$0.501588\pi$
$570$	11.2105	+	4.07580i	0.469556	+	0.170717i
$571$	29.3236	−	6.23292i	1.22715	−	0.260840i	0.451657	−	0.892191i	$-0.350833\pi$
$571$	29.3236	−	6.23292i	1.22715	−	0.260840i	0.775497	+	0.631352i	$0.217500\pi$
$572$	−7.60190	+	1.61583i	−0.317851	+	0.0675614i
$573$	3.32101	−	6.46614i	0.138737	−	0.270127i
$574$	−2.20480	+	3.81882i	−0.0920264	+	0.159394i
$575$	−28.1030	−	4.74794i	−1.17198	−	0.198003i
$576$	6.57676	+	15.0322i	0.274032	+	0.626343i
$577$	−26.5530	+	19.2919i	−1.10542	+	0.803131i	−0.981936	−	0.189216i	$-0.939405\pi$
$577$	−26.5530	+	19.2919i	−1.10542	+	0.803131i	−0.123480	+	0.992347i	$0.539405\pi$
$578$	1.44223	+	1.60176i	0.0599888	+	0.0666243i
$579$	4.76553	+	1.84700i	0.198048	+	0.0767585i
$580$	−8.39014	+	15.2649i	−0.348382	+	0.633842i
$581$	24.7450	−	27.4821i	1.02660	−	1.14015i
$582$	−1.47987	+	26.5939i	−0.0613427	+	1.10235i
$583$	−9.06627	−	1.92709i	−0.375486	−	0.0798121i
$584$	−14.6242	−	10.6251i	−0.605155	−	0.439671i
$585$	6.49026	−	32.8841i	0.268339	−	1.35959i
$586$	−4.63843	+	3.37002i	−0.191612	+	0.139214i
$587$	−0.932458	+	0.415157i	−0.0384867	+	0.0171354i	−0.425890	−	0.904775i	$-0.640039\pi$
$587$	−0.932458	+	0.415157i	−0.0384867	+	0.0171354i	0.387403	+	0.921910i	$0.373372\pi$
$588$	−4.85052	−	0.784315i	−0.200032	−	0.0323446i
$589$	−16.9829	−	7.56125i	−0.699766	−	0.311556i
$590$	0.893364	+	7.06646i	0.0367792	+	0.290922i
$591$	4.21782	+	11.0948i	0.173498	+	0.456378i
$592$	−1.64623	−	0.349918i	−0.0676598	−	0.0143815i
$593$	4.83840			0.198689			0.0993446	−	0.995053i	$-0.468325\pi$
$593$	4.83840			0.198689			0.0993446	+	0.995053i	$0.468325\pi$
$594$	−3.83419	−	4.82978i	−0.157319	−	0.198168i
$595$	−2.52253	+	30.0732i	−0.103413	+	1.23288i
$596$	−5.40053	−	5.99790i	−0.221214	−	0.245683i
$597$	12.9927	−	10.4519i	0.531754	−	0.427769i
$598$	23.5051	+	10.4652i	0.961196	+	0.427952i
$599$	−4.41032	−	7.63890i	−0.180201	−	0.312117i	0.761748	−	0.647874i	$-0.224341\pi$
$599$	−4.41032	−	7.63890i	−0.180201	−	0.312117i	−0.941949	+	0.335756i	$0.891008\pi$
$600$	23.5836	+	8.01682i	0.962798	+	0.327285i
$601$	5.73110	−	9.92656i	0.233777	−	0.404913i	−0.725140	−	0.688602i	$-0.758225\pi$
$601$	5.73110	−	9.92656i	0.233777	−	0.404913i	0.958916	+	0.283689i	$0.0915582\pi$
$602$	−10.0437	+	7.29714i	−0.409349	+	0.297409i
$603$	−9.63572	−	13.4442i	−0.392397	−	0.547491i
$604$	7.17358	−	22.0780i	0.291889	−	0.898341i
$605$	−6.82168	−	19.5834i	−0.277341	−	0.796178i
$606$	19.1408	−	5.06255i	0.777541	−	0.205652i
$607$	−18.0174	−	31.2070i	−0.731302	−	1.26665i	−0.956327	−	0.292299i	$-0.905580\pi$
$607$	−18.0174	−	31.2070i	−0.731302	−	1.26665i	0.225025	−	0.974353i	$-0.427754\pi$
$608$	−12.6485	+	14.0476i	−0.512965	+	0.569705i
$609$	22.0716	−	27.0768i	0.894385	−	1.09721i
$610$	−8.14753	−	23.3896i	−0.329884	−	0.947016i
$611$	26.8483	−	19.5064i	1.08617	−	0.789145i
$612$	14.9040	−	4.73640i	0.602460	−	0.191457i
$613$	−15.2951	−	11.1125i	−0.617761	−	0.448830i	0.234378	−	0.972146i	$-0.424695\pi$
$613$	−15.2951	−	11.1125i	−0.617761	−	0.448830i	−0.852139	+	0.523316i	$0.824695\pi$
$614$	2.44310	+	23.2445i	0.0985955	+	0.938073i
$615$	4.72319	−	3.96607i	0.190458	−	0.159927i
$616$	−1.21071	+	11.5192i	−0.0487811	+	0.464121i
$617$	−16.6953	+	18.5420i	−0.672126	+	0.746472i	−0.978682	−	0.205381i	$-0.934157\pi$
$617$	−16.6953	+	18.5420i	−0.672126	+	0.746472i	0.306556	+	0.951853i	$0.400823\pi$
$618$	24.3078	+	15.8976i	0.977805	+	0.639493i
$619$	13.0334	+	2.77034i	0.523857	+	0.111349i	0.462247	−	0.886751i	$-0.347043\pi$
$619$	13.0334	+	2.77034i	0.523857	+	0.111349i	0.0616097	+	0.998100i	$0.480377\pi$
$620$	−13.3077	−	5.59259i	−0.534450	−	0.224604i
$621$	−1.26348	−	29.5924i	−0.0507018	−	1.18750i
$622$	0.936081	−	2.88096i	0.0375334	−	0.115516i
$623$	2.37318	+	22.5793i	0.0950796	+	0.904622i
$624$	−1.66870	−	1.09135i	−0.0668017	−	0.0436889i
$625$	21.9032	−	12.0519i	0.876129	−	0.482077i
$626$	4.00776	+	6.94164i	0.160182	+	0.277444i
$627$	3.54434	−	6.90096i	0.141547	−	0.275598i
$628$	12.0885	+	13.4256i	0.482384	+	0.535742i
$629$	−9.93916	+	30.5896i	−0.396300	+	1.21969i
$630$	−16.2205	−	9.05227i	−0.646240	−	0.360651i
$631$	12.8766	+	39.6300i	0.512608	+	1.57764i	0.787593	+	0.616195i	$0.211327\pi$
$631$	12.8766	+	39.6300i	0.512608	+	1.57764i	−0.274986	+	0.961448i	$0.588673\pi$
$632$	4.05887	−	7.03017i	0.161453	−	0.279645i
$633$	−10.4107	+	2.75352i	−0.413787	+	0.109443i
$634$	3.01678	−	28.7028i	0.119812	−	1.13993i
$635$	−26.8028	−	28.5368i	−1.06364	−	1.13245i
$636$	7.84058	+	12.1592i	0.310899	+	0.482145i
$637$	10.9373	−	4.86960i	0.433351	−	0.192940i
$638$	−6.31724	−	4.58974i	−0.250102	−	0.181710i
$639$	16.7644	+	9.82389i	0.663191	+	0.388627i
$640$	−8.98178	+	10.4074i	−0.355036	+	0.411390i
$641$	−12.1065	+	5.39016i	−0.478178	+	0.212899i	−0.631649	−	0.775255i	$-0.717622\pi$
$641$	−12.1065	+	5.39016i	−0.478178	+	0.212899i	0.153471	+	0.988153i	$0.450955\pi$
$642$	13.5889	+	13.6769i	0.536310	+	0.539785i
$643$	−18.9481	−	32.8190i	−0.747239	−	1.29426i	−0.949141	−	0.314851i	$-0.898046\pi$
$643$	−18.9481	−	32.8190i	−0.747239	−	1.29426i	0.201902	−	0.979406i	$-0.435288\pi$
$644$	−13.8423	+	15.3735i	−0.545465	+	0.605800i
$645$	16.6895	−	4.79202i	0.657150	−	0.188686i
$646$	−9.07386	−	10.0775i	−0.357006	−	0.396495i
$647$	2.22129	−	6.83642i	0.0873278	−	0.268767i	−0.897851	−	0.440300i	$-0.854872\pi$
$647$	2.22129	−	6.83642i	0.0873278	−	0.268767i	0.985178	+	0.171533i	$0.0548720\pi$
$648$	−3.03821	+	25.7073i	−0.119352	+	1.00988i
$649$	4.63243			0.181839
$650$	−21.8587	+	5.61666i	−0.857369	+	0.220303i
$651$	24.2278	+	15.8452i	0.949563	+	0.621023i
$652$	−0.762421	−	0.339452i	−0.0298587	−	0.0132940i
$653$	38.6307	−	8.21121i	1.51174	−	0.321330i	0.623906	−	0.781499i	$-0.285545\pi$
$653$	38.6307	−	8.21121i	1.51174	−	0.321330i	0.887831	+	0.460170i	$0.152211\pi$
$654$	0.110344	+	0.711553i	0.00431480	+	0.0278239i
$655$	9.63623	+	6.69603i	0.376518	+	0.261636i
$656$	−0.113373	−	0.348927i	−0.00442648	−	0.0136233i
$657$	−7.55732	−	17.2735i	−0.294839	−	0.673902i
$658$	−5.68325	−	17.4912i	−0.221556	−	0.681879i
$659$	−6.34938	+	2.82693i	−0.247337	+	0.110121i	−0.526661	−	0.850075i	$-0.676556\pi$
$659$	−6.34938	+	2.82693i	−0.247337	+	0.110121i	0.279324	+	0.960197i	$0.409890\pi$
$660$	2.63884	−	5.41527i	0.102717	−	0.210789i
$661$	−29.7431	−	13.2425i	−1.15687	−	0.515073i	−0.263619	−	0.964627i	$-0.584916\pi$
$661$	−29.7431	−	13.2425i	−1.15687	−	0.515073i	−0.893253	+	0.449554i	$0.851583\pi$
$662$	1.16496	−	11.0839i	0.0452776	−	0.430788i
$663$	−24.0758	+	29.5356i	−0.935027	+	1.14707i
$664$	3.62713	+	34.5098i	0.140760	+	1.33924i
$665$	1.95330	−	23.2870i	0.0757458	−	0.903030i
$666$	−14.6264	−	13.3417i	−0.566760	−	0.516981i
$667$	−11.5898	−	35.6698i	−0.448760	−	1.38114i
$668$	−2.67341	+	4.63048i	−0.103437	+	0.179159i
$669$	−19.0944	−	19.2182i	−0.738233	−	0.743017i
$670$	−5.36450	+	9.76012i	−0.207249	+	0.377066i
$671$	−15.7565	+	3.34914i	−0.608272	+	0.129292i
$672$	22.9361	−	18.4510i	0.884780	−	0.711762i
$673$	0.797260	+	7.58542i	0.0307321	+	0.292397i	0.999083	+	0.0428054i	$0.0136296\pi$
$673$	0.797260	+	7.58542i	0.0307321	+	0.292397i	−0.968351	+	0.249591i	$0.919704\pi$
$674$	−6.47112			−0.249258
$675$	16.9954	+	19.6509i	0.654152	+	0.756363i
$676$	−14.1676			−0.544906
$677$	0.602100	+	5.72860i	0.0231406	+	0.220168i	0.999981	+	0.00619777i	$0.00197282\pi$
$677$	0.602100	+	5.72860i	0.0231406	+	0.220168i	−0.976840	+	0.213970i	$0.931361\pi$
$678$	−14.4189	+	11.5993i	−0.553756	+	0.445469i
$679$	51.0400	−	10.8489i	1.95874	−	0.416342i
$680$	−19.3865	−	20.6407i	−0.743439	−	0.791536i
$681$	4.08809	+	4.11458i	0.156656	+	0.157671i
$682$	3.23550	−	5.60406i	0.123894	−	0.214590i
$683$	7.75429	+	23.8652i	0.296709	+	0.913178i	0.982642	+	0.185513i	$0.0593946\pi$
$683$	7.75429	+	23.8652i	0.296709	+	0.913178i	−0.685932	+	0.727665i	$0.740605\pi$
$684$	−11.5408	+	3.66760i	−0.441275	+	0.140234i
$685$	2.10657	+	3.47763i	0.0804878	+	0.132874i
$686$	1.33259	+	12.6787i	0.0508784	+	0.484076i
$687$	−25.8872	+	31.7578i	−0.987659	+	1.21164i
$688$	0.107969	−	1.02726i	0.00411628	−	0.0391638i
$689$	−32.2050	−	14.3386i	−1.22691	−	0.546257i
$690$	−17.6057	+	9.36909i	−0.670237	+	0.356675i
$691$	31.0761	−	13.8360i	1.18219	−	0.526345i	0.280974	−	0.959715i	$-0.409342\pi$
$691$	31.0761	−	13.8360i	1.18219	−	0.526345i	0.901216	+	0.433370i	$0.142676\pi$
$692$	1.59356	+	4.90449i	0.0605782	+	0.186441i
$693$	−7.16403	+	9.72767i	−0.272139	+	0.369523i
$694$	0.0887512	+	0.273148i	0.00336895	+	0.0103686i
$695$	−6.63493	+	21.9833i	−0.251677	+	0.833873i
$696$	5.02307	+	32.3912i	0.190399	+	1.22778i
$697$	−6.85824	+	1.45776i	−0.259775	+	0.0552168i
$698$	11.7781	+	5.24397i	0.445809	+	0.198487i
$699$	−31.9803	−	20.9154i	−1.20961	−	0.791095i
$700$	1.13604	−	18.1101i	0.0429384	−	0.684499i
$701$	−43.0578			−1.62627			−0.813135	−	0.582076i	$-0.802241\pi$
$701$	−43.0578			−1.62627			−0.813135	+	0.582076i	$0.802241\pi$
$702$	−10.4450	−	21.0000i	−0.394220	−	0.792594i
$703$	7.69632	−	23.6868i	0.290272	−	0.893366i
$704$	−4.80787	−	5.33968i	−0.181204	−	0.201247i
$705$	−0.888657	+	25.7079i	−0.0334688	+	0.968217i
$706$	−9.01102	+	10.0077i	−0.339134	+	0.376647i
$707$	−19.3939	−	33.5912i	−0.729383	−	1.26333i
$708$	−5.09647	−	5.12950i	−0.191537	−	0.192778i
$709$	3.13740	−	1.39686i	0.117828	−	0.0524602i	−0.346976	−	0.937874i	$-0.612792\pi$
$709$	3.13740	−	1.39686i	0.117828	−	0.0524602i	0.464804	+	0.885414i	$0.346125\pi$
$710$	1.09357	−	13.0374i	0.0410410	−	0.489285i
$711$	7.35985	−	4.18606i	0.276016	−	0.156989i
$712$	−17.2348	−	12.5218i	−0.645902	−	0.469275i
$713$	28.3941	−	12.6419i	1.06337	−	0.473441i
$714$	11.4440	+	17.7475i	0.428282	+	0.664183i
$715$	1.84100	+	14.5622i	0.0688496	+	0.544597i
$716$	−0.0460619	+	0.438250i	−0.00172141	+	0.0163782i
$717$	−24.2263	+	6.40762i	−0.904747	+	0.239297i
$718$	6.86806	−	11.8958i	0.256314	−	0.443948i
$719$	−3.21496	−	9.89464i	−0.119898	−	0.369008i	0.873039	−	0.487650i	$-0.162146\pi$
$719$	−3.21496	−	9.89464i	−0.119898	−	0.369008i	−0.992937	+	0.118642i	$0.962146\pi$
$720$	1.46274	−	0.498960i	0.0545132	−	0.0185952i
$721$	17.5835	−	54.1163i	0.654842	−	2.01540i
$722$	−4.45855	−	4.95172i	−0.165930	−	0.184284i
$723$	7.05004	−	13.7267i	0.262194	−	0.510501i
$724$	2.89667	+	5.01718i	0.107654	+	0.186462i
$725$	27.4049	+	18.2005i	1.01779	+	0.675949i
$726$	−12.1442	−	7.94243i	−0.450714	−	0.294771i
$727$	2.55736	+	24.3317i	0.0948472	+	0.902411i	0.933701	+	0.358054i	$0.116560\pi$
$727$	2.55736	+	24.3317i	0.0948472	+	0.902411i	−0.838854	+	0.544357i	$0.816774\pi$
$728$	−13.6132	+	41.8970i	−0.504538	+	1.55281i
$729$	−16.2905	+	21.5318i	−0.603352	+	0.797475i
$730$	−8.29433	+	9.61086i	−0.306987	+	0.355714i
$731$	−19.3085	−	4.10415i	−0.714151	−	0.151798i
$732$	21.0433	+	13.7625i	0.777785	+	0.508678i
$733$	−16.0105	+	17.7815i	−0.591362	+	0.656774i	−0.962334	−	0.271870i	$-0.912358\pi$
$733$	−16.0105	+	17.7815i	−0.591362	+	0.656774i	0.370972	+	0.928644i	$0.379025\pi$
$734$	−0.795852	+	7.57203i	−0.0293754	+	0.279489i
$735$	−2.24185	+	9.00512i	−0.0826920	+	0.332159i
$736$	−3.30354	−	31.4311i	−0.121770	−	1.15857i
$737$	5.86001	+	4.25755i	0.215856	+	0.156829i
$738$	0.924524	−	4.21546i	0.0340322	−	0.155173i
$739$	34.3422	−	24.9510i	1.26330	−	0.917839i	0.264382	−	0.964418i	$-0.414832\pi$
$739$	34.3422	−	24.9510i	1.26330	−	0.917839i	0.998915	+	0.0465793i	$0.0148320\pi$
$740$	5.58795	−	18.5144i	0.205417	−	0.680601i
$741$	18.6429	−	22.8707i	0.684865	−	0.840175i
$742$	−13.0725	+	14.5185i	−0.479908	+	0.532992i
$743$	−6.21697	−	10.7681i	−0.228079	−	0.395044i	0.729160	−	0.684343i	$-0.239911\pi$
$743$	−6.21697	−	10.7681i	−0.228079	−	0.395044i	−0.957239	+	0.289300i	$0.906578\pi$
$744$	−26.2607	+	6.94571i	−0.962764	+	0.254642i
$745$	−12.1409	+	9.21722i	−0.444809	+	0.337693i
$746$	9.01486	−	27.7449i	0.330058	−	1.01581i
$747$	−14.9343	+	32.9681i	−0.546417	+	1.20624i
$748$	−5.54040	+	4.02533i	−0.202577	+	0.147181i
$749$	18.8855	−	32.7106i	0.690060	−	1.19522i
$750$	6.99488	−	16.0341i	0.255417	−	0.585483i
$751$	−21.2022	−	36.7234i	−0.773681	−	1.34005i	−0.935533	−	0.353240i	$-0.885080\pi$
$751$	−21.2022	−	36.7234i	−0.773681	−	1.34005i	0.161852	−	0.986815i	$-0.448253\pi$
$752$	1.39789	+	0.622383i	0.0509760	+	0.0226960i
$753$	16.7360	−	13.4632i	0.609892	−	0.490628i
$754$	−19.8724	−	22.0705i	−0.723709	−	0.803761i
$755$	−40.4195	−	16.9864i	−1.47102	−	0.618198i
$756$	18.6531	−	2.76937i	0.678408	−	0.100721i
$757$	28.4481			1.03397			0.516983	−	0.855996i	$-0.327055\pi$
$757$	28.4481			1.03397			0.516983	+	0.855996i	$0.327055\pi$
$758$	−17.1217	−	3.63933i	−0.621888	−	0.132186i
$759$	4.60915	+	12.1241i	0.167301	+	0.440078i
$760$	15.0118	+	15.9830i	0.544536	+	0.579765i
$761$	25.0079	+	11.1342i	0.906535	+	0.403615i	0.806408	−	0.591359i	$-0.201409\pi$
$761$	25.0079	+	11.1342i	0.906535	+	0.403615i	0.100127	+	0.994975i	$0.468075\pi$
$762$	−27.0437	−	4.37288i	−0.979689	−	0.158413i
$763$	1.28870	−	0.573764i	0.0466539	−	0.0207717i
$764$	4.01985	−	2.92059i	0.145433	−	0.105663i
$765$	−6.56130	−	28.7979i	−0.237224	−	1.04119i
$766$	19.3203	+	14.0370i	0.698070	+	0.507178i
$767$	17.2339	+	3.66317i	0.622279	+	0.132269i
$768$	−1.58715	+	28.5216i	−0.0572712	+	1.02919i
$769$	15.6273	−	17.3558i	0.563533	−	0.625867i	−0.392279	−	0.919846i	$-0.628313\pi$
$769$	15.6273	−	17.3558i	0.563533	−	0.625867i	0.955812	+	0.293979i	$0.0949797\pi$
$770$	7.99048	+	1.52350i	0.287957	+	0.0549033i
$771$	50.5603	+	19.5959i	1.82088	+	0.705728i
$772$	2.33766	+	2.59623i	0.0841342	+	0.0934405i
$773$	1.17568	−	0.854182i	0.0422863	−	0.0307228i	−0.566441	−	0.824102i	$-0.691680\pi$
$773$	1.17568	−	0.854182i	0.0422863	−	0.0307228i	0.608728	+	0.793379i	$0.291680\pi$
$774$	7.20503	−	9.78335i	0.258980	−	0.351655i
$775$	−12.6264	+	24.1629i	−0.453553	+	0.867956i
$776$	−24.4810	+	42.4023i	−0.878815	+	1.52215i
$777$	−17.7193	+	34.5002i	−0.635676	+	1.23769i
$778$	−9.33179	+	1.98353i	−0.334561	+	0.0711131i
$779$	5.31064	−	1.12881i	0.190273	−	0.0404438i
$780$	14.0994	−	18.0595i	0.504839	−	0.646635i
$781$	−8.32304	−	1.76912i	−0.297822	−	0.0633039i
$782$	22.6724			0.810764
$783$	−12.5608	+	31.7977i	−0.448887	+	1.13636i
$784$	0.446604	+	0.324477i	0.0159501	+	0.0115885i
$785$	27.1761	−	20.6317i	0.969957	−	0.736379i
$786$	8.20103	−	0.403241i	0.292521	−	0.0143831i
$787$	0.757863	−	7.21059i	0.0270149	−	0.257030i	−0.972676	−	0.232167i	$-0.925418\pi$
$787$	0.757863	−	7.21059i	0.0270149	−	0.257030i	0.999691	−	0.0248628i	$-0.00791488\pi$
$788$	−0.848078	+	8.06893i	−0.0302115	+	0.287444i
$789$	20.2560	−	39.4393i	0.721134	−	1.40408i
$790$	−4.68171	−	3.25323i	−0.166568	−	0.115745i
$791$	29.3298	+	21.3093i	1.04285	+	0.757673i
$792$	−2.28519	−	11.1032i	−0.0812006	−	0.394533i
$793$	−61.2666			−2.17564
$794$	2.32776	+	0.494781i	0.0826092	+	0.0175591i
$795$	24.1221	−	12.8369i	0.855522	−	0.455276i
$796$	11.1491	−	2.36980i	0.395168	−	0.0839955i
$797$	4.18917	−	0.890435i	0.148388	−	0.0315408i	−0.133119	−	0.991100i	$-0.542499\pi$
$797$	4.18917	−	0.890435i	0.148388	−	0.0315408i	0.281507	+	0.959559i	$0.409166\pi$
$798$	−8.86161	−	13.7426i	−0.313697	−	0.486484i
$799$	14.6216	−	25.3253i	0.517275	−	0.895946i
$800$	19.3996	+	19.8029i	0.685879	+	0.700138i
$801$	−8.90639	−	20.3570i	−0.314692	−	0.719278i
$802$	5.47824	−	3.98017i	0.193443	−	0.140545i
$803$	5.52470	+	6.13581i	0.194963	+	0.216528i
$804$	−1.73263	−	11.1728i	−0.0611052	−	0.394036i
$805$	26.7484	+	28.4789i	0.942759	+	1.00375i
$806$	16.4684	−	18.2900i	0.580076	−	0.644240i
$807$	1.48771	+	0.972978i	0.0523700	+	0.0342504i
$808$	35.6001	+	7.56704i	1.25241	+	0.266208i
$809$	20.0966	+	14.6011i	0.706560	+	0.513346i	0.882062	−	0.471133i	$-0.156155\pi$
$809$	20.0966	+	14.6011i	0.706560	+	0.513346i	−0.175502	+	0.984479i	$0.556155\pi$
$810$	17.8126	+	3.63532i	0.625869	+	0.127732i
$811$	−18.6705	+	13.5649i	−0.655610	+	0.476329i	−0.865178	−	0.501465i	$-0.832794\pi$
$811$	−18.6705	+	13.5649i	−0.655610	+	0.476329i	0.209567	+	0.977794i	$0.432794\pi$
$812$	21.8140	−	9.71222i	0.765521	−	0.340832i
$813$	−12.2296	−	32.1693i	−0.428910	−	1.12823i
$814$	7.91995	+	3.52619i	0.277594	+	0.123593i
$815$	−0.759225	+	1.38133i	−0.0265945	+	0.0483858i
$816$	−1.73446	−	0.280456i	−0.0607181	−	0.00981794i
$817$	14.9514	+	3.17802i	0.523084	+	0.111185i
$818$	29.8029			1.04203
$819$	−34.3444	+	30.5244i	−1.20009	+	1.06661i
$820$	4.10433	−	0.963062i	0.143330	−	0.0336316i
$821$	−26.0440	−	28.9248i	−0.908943	−	1.00948i	−0.999907	−	0.0136294i	$-0.995661\pi$
$821$	−26.0440	−	28.9248i	−0.908943	−	1.00948i	0.0909640	−	0.995854i	$-0.471005\pi$
$822$	2.65279	+	1.02816i	0.0925268	+	0.0358610i
$823$	−29.9969	−	13.3555i	−1.04563	−	0.465543i	−0.189268	−	0.981925i	$-0.560612\pi$
$823$	−29.9969	−	13.3555i	−1.04563	−	0.465543i	−0.856358	+	0.516382i	$0.827278\pi$
$824$	26.6959	+	46.2386i	0.929994	+	1.61080i
$825$	−9.77524	−	5.82131i	−0.340330	−	0.202672i
$826$	4.88207	−	8.45599i	0.169869	−	0.294221i
$827$	3.02903	−	2.20072i	0.105330	−	0.0765264i	−0.533874	−	0.845564i	$-0.679264\pi$
$827$	3.02903	−	2.20072i	0.105330	−	0.0765264i	0.639203	+	0.769038i	$0.279264\pi$
$828$	8.35423	−	18.4424i	0.290330	−	0.640917i
$829$	−8.58235	+	26.4138i	−0.298077	+	0.917388i	0.684093	+	0.729395i	$0.260198\pi$
$829$	−8.58235	+	26.4138i	−0.298077	+	0.917388i	−0.982170	+	0.187993i	$0.939802\pi$
$830$	24.3642	−	0.512603i	0.845693	−	0.0177927i
$831$	−22.0980	−	22.2413i	−0.766573	−	0.771541i
$832$	−13.6641	−	23.6670i	−0.473718	−	0.820504i
$833$	7.05921	−	7.84005i	0.244587	−	0.271642i
$834$	5.70974	+	15.0192i	0.197712	+	0.520072i
$835$	8.29277	+	5.76249i	0.286983	+	0.199419i
$836$	4.29017	−	3.11699i	0.148379	−	0.107803i
$837$	−27.2948	−	7.59782i	−0.943445	−	0.262619i
$838$	−13.2448	−	9.62294i	−0.457535	−	0.332419i
$839$	2.25286	+	21.4346i	0.0777774	+	0.740003i	0.962021	+	0.272976i	$0.0880081\pi$
$839$	2.25286	+	21.4346i	0.0777774	+	0.740003i	−0.884243	+	0.467027i	$0.845325\pi$
$840$	−19.1044	−	28.3019i	−0.659164	−	0.976508i
$841$	−1.49386	+	14.2131i	−0.0515123	+	0.490107i
$842$	14.5509	−	16.1604i	0.501458	−	0.556925i
$843$	39.7249	−	20.0795i	1.36820	−	0.691574i
$844$	−7.20007	−	1.53042i	−0.247837	−	0.0526793i
$845$	−2.23657	+	26.6641i	−0.0769404	+	0.917272i
$846$	10.4856	+	14.6300i	0.360502	+	0.502990i
$847$	−8.78471	+	27.0365i	−0.301846	+	0.928987i
$848$	−0.169908	−	1.61657i	−0.00583466	−	0.0555131i
$849$	0.846898	−	15.2191i	0.0290655	−	0.522318i
$850$	−15.5832	+	12.3558i	−0.534499	+	0.423799i
$851$	20.8203	+	36.0619i	0.713712	+	1.23619i
$852$	7.19783	+	11.1625i	0.246594	+	0.382419i
$853$	−30.9670	−	34.3923i	−1.06029	−	1.17757i	−0.983572	−	0.180519i	$-0.942222\pi$
$853$	−30.9670	−	34.3923i	−1.06029	−	1.17757i	−0.0767185	−	0.997053i	$-0.524444\pi$
$854$	−10.4921	+	32.2913i	−0.359032	+	1.10499i
$855$	5.08070	+	22.2994i	0.173756	+	0.762625i
$856$	10.9520	+	33.7067i	0.374331	+	1.15207i
$857$	11.5451	−	19.9968i	0.394375	−	0.683077i	−0.598646	−	0.801013i	$-0.704295\pi$
$857$	11.5451	−	19.9968i	0.394375	−	0.683077i	0.993021	+	0.117936i	$0.0376279\pi$
$858$	7.23911	+	7.28602i	0.247139	+	0.248741i
$859$	−4.37235	+	41.6001i	−0.149183	+	1.41938i	0.622127	+	0.782916i	$0.286269\pi$
$859$	−4.37235	+	41.6001i	−0.149183	+	1.41938i	−0.771309	+	0.636460i	$0.780398\pi$
$860$	11.6590	+	2.22297i	0.397570	+	0.0758026i
$861$	−8.44451	+	0.415213i	−0.287788	+	0.0141504i
$862$	−14.5416	+	6.47436i	−0.495290	+	0.220517i
$863$	8.30540	+	6.03422i	0.282719	+	0.205407i	0.720102	−	0.693868i	$-0.244095\pi$
$863$	8.30540	+	6.03422i	0.282719	+	0.205407i	−0.437383	+	0.899275i	$0.644095\pi$
$864$	−15.9241	+	24.0084i	−0.541748	+	0.816781i
$865$	9.48207	−	2.22492i	0.322400	−	0.0756496i
$866$	1.53001	−	0.681203i	0.0519917	−	0.0231482i
$867$	−1.08248	+	3.98831i	−0.0367631	+	0.135450i
$868$	9.89413	+	17.1371i	0.335829	+	0.581672i
$869$	−2.48101	+	2.75544i	−0.0841626	+	0.0934721i
$870$	22.9634	−	1.61390i	0.778533	−	0.0547164i
$871$	18.4341	+	20.4731i	0.624615	+	0.693705i
$872$	−0.409030	+	1.25886i	−0.0138515	+	0.0426305i
$873$	−44.3907	+	25.2481i	−1.50240	+	0.854518i
$874$	−17.5562			−0.593849
$875$	−33.9049	−	4.99706i	−1.14619	−	0.168931i
$876$	0.716065	−	12.8680i	0.0241936	−	0.434768i
$877$	13.9396	+	6.20630i	0.470706	+	0.209572i	0.628360	−	0.777922i	$-0.283726\pi$
$877$	13.9396	+	6.20630i	0.470706	+	0.209572i	−0.157654	+	0.987494i	$0.550393\pi$
$878$	8.49951	−	1.80663i	0.286845	−	0.0609707i
$879$	−10.2500	−	3.97264i	−0.345724	−	0.133994i
$880$	−0.539050	+	0.409239i	−0.0181714	+	0.0137955i
$881$	7.88976	+	24.2822i	0.265813	+	0.818088i	0.991505	+	0.130068i	$0.0415196\pi$
$881$	7.88976	+	24.2822i	0.265813	+	0.818088i	−0.725692	+	0.688019i	$0.758480\pi$
$882$	2.60279	+	5.94910i	0.0876406	+	0.200317i
$883$	−7.07144	−	21.7636i	−0.237973	−	0.732405i	−0.996713	−	0.0810118i	$-0.974185\pi$
$883$	−7.07144	−	21.7636i	−0.237973	−	0.732405i	0.758740	−	0.651393i	$-0.225815\pi$
$884$	−23.7949	+	10.5942i	−0.800307	+	0.356320i
$885$	−10.4585	+	8.78205i	−0.351560	+	0.295205i
$886$	30.7144	+	13.6749i	1.03187	+	0.459418i
$887$	−3.04382	+	28.9600i	−0.102202	+	0.972382i	0.816477	+	0.577377i	$0.195924\pi$
$887$	−3.04382	+	28.9600i	−0.102202	+	0.972382i	−0.918679	+	0.395005i	$0.870743\pi$
$888$	−12.9320	−	34.0171i	−0.433971	−	1.14154i
$889$	5.60993	+	53.3749i	0.188151	+	1.79014i
$890$	−9.77496	+	11.3265i	−0.327657	+	0.379665i
$891$	3.79867	−	11.1968i	0.127260	−	0.375107i
$892$	−5.72244	−	17.6119i	−0.191602	−	0.589689i
$893$	−11.3221	+	19.6105i	−0.378881	+	0.656240i
$894$	−2.79391	+	10.2939i	−0.0934424	+	0.344280i
$895$	0.817537	+	0.155875i	0.0273272	+	0.00521034i
$896$	18.4335	−	3.91817i	0.615821	−	0.130897i
$897$	7.55988	+	48.7498i	0.252417	+	1.62771i
$898$	2.62868	+	25.0102i	0.0877201	+	0.834601i
$899$	−35.8760			−1.19653
$900$	4.30849	+	17.2286i	0.143616	+	0.574287i
$901$	−31.0641			−1.03490
$902$	0.197546	+	1.87952i	0.00657756	+	0.0625813i
$903$	−22.1945	−	8.60202i	−0.738587	−	0.286257i
$904$	−33.2742	+	7.07265i	−1.10668	+	0.235233i
$905$	9.89988	−	4.65964i	0.329083	−	0.154892i
$906$	−29.6593	+	7.84459i	−0.985363	+	0.260619i
$907$	6.18003	−	10.7041i	0.205204	−	0.355425i	−0.744993	−	0.667072i	$-0.767547\pi$
$907$	6.18003	−	10.7041i	0.205204	−	0.355425i	0.950198	+	0.311647i	$0.100881\pi$
$908$	1.22517	+	3.77068i	0.0406586	+	0.125134i
$909$	28.0462	+	25.5829i	0.930234	+	0.848531i
$910$	28.5220	+	11.9864i	0.945495	+	0.397347i
$911$	−5.66581	−	53.9066i	−0.187717	−	1.78601i	−0.531602	−	0.846994i	$-0.678410\pi$
$911$	−5.66581	−	53.9066i	−0.187717	−	1.78601i	0.343885	−	0.939012i	$-0.388257\pi$
$912$	1.34306	+	0.217170i	0.0444733	+	0.00719120i
$913$	1.65671	−	15.7625i	0.0548290	−	0.521663i
$914$	−7.41230	−	3.30017i	−0.245177	−	0.109160i
$915$	29.2238	−	37.4320i	0.966110	−	1.23746i
$916$	−25.5851	+	11.3912i	−0.845357	+	0.376377i
$917$	−4.97082	−	15.2986i	−0.164151	−	0.505204i
$918$	−15.9348	−	13.1614i	−0.525927	−	0.434392i
$919$	−0.890312	−	2.74010i	−0.0293687	−	0.0903875i	0.935298	−	0.353862i	$-0.115132\pi$
$919$	−0.890312	−	2.74010i	−0.0293687	−	0.0903875i	−0.964666	+	0.263474i	$0.915132\pi$
$920$	−36.6529	+	0.771148i	−1.20841	+	0.0254240i
$921$	−34.9174	+	28.0893i	−1.15057	+	0.925574i
$922$	10.3196	−	2.19349i	0.339857	−	0.0722388i
$923$	−29.5649	−	13.1632i	−0.973142	−	0.433271i
$924$	−7.36998	+	3.72526i	−0.242455	+	0.122552i
$925$	−33.9628	−	13.4396i	−1.11669	−	0.441891i
$926$	24.5957			0.808265
$927$	−0.359735	+	55.6879i	−0.0118152	+	1.82903i
$928$	−11.2729	+	34.6943i	−0.370050	+	1.13890i
$929$	−33.8463	−	37.5901i	−1.11046	−	1.23329i	−0.969974	−	0.243209i	$-0.921800\pi$
$929$	−33.8463	−	37.5901i	−1.11046	−	1.23329i	−0.140487	−	0.990083i	$-0.544867\pi$
$930$	3.31931	+	18.7860i	0.108844	+	0.616016i
$931$	−5.46625	+	6.07089i	−0.179149	+	0.198965i
$932$	−13.0601	−	22.6207i	−0.427798	−	0.740967i
$933$	5.61499	−	1.48511i	0.183827	−	0.0486204i
$934$	−4.05717	+	1.80637i	−0.132755	+	0.0591061i
$935$	6.70125	+	11.0628i	0.219154	+	0.361791i
$936$	0.278508	−	43.1137i	0.00910332	−	1.40922i
$937$	41.9653	+	30.4896i	1.37095	+	0.996051i	0.997663	+	0.0683333i	$0.0217681\pi$
$937$	41.9653	+	30.4896i	1.37095	+	0.996051i	0.373283	+	0.927717i	$0.378232\pi$
$938$	13.9475	−	6.20982i	0.455401	−	0.202758i
$939$	−7.02135	+	13.6708i	−0.229133	+	0.446131i
$940$	−8.46933	+	15.4090i	−0.276239	+	0.502587i
$941$	3.50844	−	33.3806i	0.114372	−	1.08818i	−0.775306	−	0.631586i	$-0.782404\pi$
$941$	3.50844	−	33.3806i	0.114372	−	1.08818i	0.889678	−	0.456589i	$-0.150929\pi$
$942$	6.25387	−	23.0418i	0.203762	−	0.750743i
$943$	−4.53867	+	7.86121i	−0.147800	+	0.255996i
$944$	0.251042	+	0.772628i	0.00817072	+	0.0251469i
$945$	−2.26741	−	35.5434i	−0.0737587	−	1.15623i
$946$	−1.64419	+	5.06029i	−0.0534572	+	0.164524i
$947$	10.8600	+	12.0613i	0.352903	+	0.391939i	0.893292	−	0.449477i	$-0.148390\pi$
$947$	10.8600	+	12.0613i	0.352903	+	0.391939i	−0.540389	+	0.841415i	$0.681723\pi$
$948$	5.78065	−	0.284232i	0.187747	−	0.00923144i
$949$	15.7014	+	27.1956i	0.509688	+	0.882806i
$950$	12.0667	−	9.56760i	0.391497	−	0.310414i
$951$	49.3859	−	24.9628i	1.60145	−	0.809474i
$952$	4.05767	+	38.6062i	0.131510	+	1.25123i
$953$	0.829618	−	2.55330i	0.0268740	−	0.0827096i	−0.936720	−	0.350080i	$-0.886155\pi$
$953$	0.829618	−	2.55330i	0.0268740	−	0.0827096i	0.963594	+	0.267370i	$0.0861546\pi$
$954$	7.88964	−	17.4167i	0.255436	−	0.563888i
$955$	−4.86211	−	8.02662i	−0.157334	−	0.259735i
$956$	−16.7550	−	3.56139i	−0.541895	−	0.115183i
$957$	0.831842	−	14.9485i	0.0268896	−	0.483217i
$958$	21.0372	−	23.3642i	0.679681	−	0.754862i
$959$	0.582613	−	5.54319i	0.0188135	−	0.178999i
$960$	20.9775	+	2.94064i	0.677046	+	0.0949089i
$961$	0.132668	+	1.26225i	0.00427962	+	0.0407179i
$962$	26.6759	+	19.3812i	0.860066	+	0.624875i
$963$	−7.91914	+	36.1081i	−0.255191	+	1.16357i
$964$	8.53357	−	6.20000i	0.274848	−	0.199689i
$965$	5.25528	−	3.98974i	0.169174	−	0.128434i
$966$	26.9888	+	4.36401i	0.868351	+	0.140410i
$967$	−2.74701	+	3.05086i	−0.0883378	+	0.0981091i	−0.785693	−	0.618617i	$-0.787693\pi$
$967$	−2.74701	+	3.05086i	−0.0883378	+	0.0981091i	0.697355	+	0.716726i	$0.254360\pi$
$968$	−13.3373	−	23.1008i	−0.428676	−	0.742489i
$969$	6.81050	−	25.0927i	0.218785	−	0.806093i
$970$	28.2376	+	19.6218i	0.906655	+	0.630018i
$971$	−0.954719	+	2.93832i	−0.0306384	+	0.0942953i	−0.965206	−	0.261489i	$-0.915786\pi$
$971$	−0.954719	+	2.93832i	−0.0306384	+	0.0942953i	0.934568	+	0.355785i	$0.115786\pi$
$972$	−16.5774	+	8.11214i	−0.531722	+	0.260197i
$973$	25.4665	−	18.5025i	0.816419	−	0.593163i
$974$	5.73816	−	9.93878i	0.183862	−	0.318459i
$975$	−31.7632	−	29.3868i	−1.01724	−	0.941130i
$976$	−1.41247	−	2.44647i	−0.0452121	−	0.0783096i
$977$	23.4886	+	10.4578i	0.751468	+	0.334575i	0.746476	−	0.665413i	$-0.231744\pi$
$977$	23.4886	+	10.4578i	0.751468	+	0.334575i	0.00499195	+	0.999988i	$0.498411\pi$
$978$	0.169019	+	1.08992i	0.00540464	+	0.0348517i
$979$	6.51093	+	7.23112i	0.208090	+	0.231108i
$980$	−4.14442	+	4.80225i	−0.132389	+	0.153402i
$981$	−1.03193	+	0.917155i	−0.0329471	+	0.0292825i
$982$	10.2646			0.327556
$983$	39.6591	+	8.42980i	1.26493	+	0.268869i	0.791066	−	0.611730i	$-0.209526\pi$
$983$	39.6591	+	8.42980i	1.26493	+	0.268869i	0.473862	+	0.880599i	$0.342860\pi$
$984$	5.01244	−	6.14913i	0.159791	−	0.196027i
$985$	15.0523	+	2.86993i	0.479605	+	0.0914437i
$986$	−23.9075	−	10.6443i	−0.761371	−	0.338984i
$987$	22.2799	−	27.3324i	0.709177	−	0.870000i
$988$	18.4254	−	8.20351i	0.586190	−	0.260988i
$989$	−20.6753	+	15.0215i	−0.657437	+	0.477656i
$990$	−7.90455	+	0.947481i	−0.251223	+	0.0301129i
$991$	−4.89581	−	3.55701i	−0.155520	−	0.112992i	0.507304	−	0.861767i	$-0.330642\pi$
$991$	−4.89581	−	3.55701i	−0.155520	−	0.112992i	−0.662824	+	0.748775i	$0.730642\pi$
$992$	−29.5705	−	6.28541i	−0.938865	−	0.199562i
$993$	19.0709	−	9.63965i	0.605197	−	0.305905i
$994$	−12.0009	+	13.3283i	−0.380645	+	0.422749i
$995$	−2.70004	−	21.3572i	−0.0855970	−	0.677069i
$996$	−19.2766	+	15.5070i	−0.610801	+	0.491359i
$997$	−20.6365	−	22.9192i	−0.653565	−	0.725857i	0.321714	−	0.946837i	$-0.395741\pi$
$997$	−20.6365	−	22.9192i	−0.653565	−	0.725857i	−0.975278	+	0.220980i	$0.929074\pi$
$998$	−14.1557	+	10.2847i	−0.448092	+	0.325558i
$999$	6.30096	−	37.4316i	0.199354	−	1.18428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.61.10	yes	224
3.2	odd	2		675.2.r.a.586.19		224
9.4	even	3	inner	225.2.q.a.211.19	yes	224
9.5	odd	6		675.2.r.a.361.10		224
25.16	even	5	inner	225.2.q.a.16.19	✓	224
75.41	odd	10		675.2.r.a.316.10		224
225.41	odd	30		675.2.r.a.91.19		224
225.166	even	15	inner	225.2.q.a.166.10	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.19	✓	224	25.16	even	5	inner
225.2.q.a.61.10	yes	224	1.1	even	1	trivial
225.2.q.a.166.10	yes	224	225.166	even	15	inner
225.2.q.a.211.19	yes	224	9.4	even	3	inner
675.2.r.a.91.19		224	225.41	odd	30
675.2.r.a.316.10		224	75.41	odd	10
675.2.r.a.361.10		224	9.5	odd	6
675.2.r.a.586.19		224	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.0944267 - 0.898410i) q^{2} +(1.34957 - 1.08566i) q^{3} +(1.15807 - 0.246156i) q^{4} +(-0.280458 - 2.21841i) q^{5} +(-1.10280 - 1.10995i) q^{6} +(-1.53265 + 2.65463i) q^{7} +(-0.888808 - 2.73547i) q^{8} +(0.642678 - 2.93035i) q^{9} +O(q^{10})\)	\(q+(-0.0944267 - 0.898410i) q^{2} +(1.34957 - 1.08566i) q^{3} +(1.15807 - 0.246156i) q^{4} +(-0.280458 - 2.21841i) q^{5} +(-1.10280 - 1.10995i) q^{6} +(-1.53265 + 2.65463i) q^{7} +(-0.888808 - 2.73547i) q^{8} +(0.642678 - 2.93035i) q^{9} +(-1.96656 + 0.461443i) q^{10} +(0.137323 + 1.30654i) q^{11} +(1.29566 - 1.58948i) q^{12} +(-0.522291 + 4.96927i) q^{13} +(2.52967 + 1.12628i) q^{14} +(-2.78694 - 2.68942i) q^{15} +(-0.210472 + 0.0937080i) q^{16} +(1.36059 + 4.18745i) q^{17} +(-2.69334 - 0.300684i) q^{18} +(-1.05356 - 3.24253i) q^{19} +(-0.870865 - 2.50004i) q^{20} +(0.813610 + 5.24655i) q^{21} +(1.16084 - 0.246745i) q^{22} +(5.20744 + 2.31850i) q^{23} +(-4.16930 - 2.72676i) q^{24} +(-4.84269 + 1.24434i) q^{25} +4.51376 q^{26} +(-2.31403 - 4.65245i) q^{27} +(-1.12147 + 3.45152i) q^{28} +(-4.40263 - 4.88961i) q^{29} +(-2.15304 + 2.75777i) q^{30} +(3.64850 - 4.05207i) q^{31} +(-2.77218 - 4.80156i) q^{32} +(1.60379 + 1.61418i) q^{33} +(3.63357 - 1.61777i) q^{34} +(6.31890 + 2.65554i) q^{35} +(0.0229438 - 3.55176i) q^{36} +(5.90992 + 4.29381i) q^{37} +(-2.81363 + 1.25271i) q^{38} +(4.69008 + 7.27341i) q^{39} +(-5.81912 + 2.73892i) q^{40} +(-0.166456 + 1.58372i) q^{41} +(4.63672 - 1.22637i) q^{42} +(-2.24167 + 3.88268i) q^{43} +(0.480642 + 1.47926i) q^{44} +(-6.68097 - 0.603882i) q^{45} +(1.59124 - 4.89734i) q^{46} +(-4.44418 - 4.93576i) q^{47} +(-0.182311 + 0.354967i) q^{48} +(-1.19804 - 2.07507i) q^{49} +(1.57521 + 4.23322i) q^{50} +(6.38236 + 4.17412i) q^{51} +(0.618363 + 5.88333i) q^{52} +(-2.18021 + 6.70999i) q^{53} +(-3.96130 + 2.51826i) q^{54} +(2.85993 - 0.671068i) q^{55} +(8.62389 + 1.83306i) q^{56} +(-4.94214 - 3.23221i) q^{57} +(-3.97715 + 4.41707i) q^{58} +(0.368583 - 3.50683i) q^{59} +(-3.88949 - 2.42852i) q^{60} +(1.28168 + 12.1944i) q^{61} +(-3.98493 - 2.89522i) q^{62} +(6.79400 + 6.19728i) q^{63} +(-4.42478 + 3.21479i) q^{64} +(11.1704 - 0.235015i) q^{65} +(1.29876 - 1.59328i) q^{66} +(3.68929 - 4.09737i) q^{67} +(2.60642 + 4.51446i) q^{68} +(9.54491 - 2.52454i) q^{69} +(1.78909 - 5.92772i) q^{70} +(-2.00148 + 6.15992i) q^{71} +(-8.58710 + 0.846495i) q^{72} +(5.08449 - 3.69410i) q^{73} +(3.29954 - 5.71498i) q^{74} +(-5.18461 + 6.93685i) q^{75} +(-2.01827 - 3.49574i) q^{76} +(-3.67885 - 1.63793i) q^{77} +(6.09163 - 4.90041i) q^{78} +(1.88852 + 2.09741i) q^{79} +(0.266911 + 0.440631i) q^{80} +(-8.17393 - 3.76654i) q^{81} +1.43855 q^{82} +(-11.8007 - 2.50831i) q^{83} +(2.23369 + 5.87561i) q^{84} +(8.90790 - 4.19274i) q^{85} +(3.69991 + 1.64731i) q^{86} +(-11.2501 - 1.81911i) q^{87} +(3.45195 - 1.53691i) q^{88} +(5.99213 - 4.35354i) q^{89} +(0.0883282 + 6.05927i) q^{90} +(-12.3911 - 9.00265i) q^{91} +(6.60130 + 1.40315i) q^{92} +(0.524729 - 9.42958i) q^{93} +(-4.01469 + 4.45876i) q^{94} +(-6.89777 + 3.24662i) q^{95} +(-8.95412 - 3.47039i) q^{96} +(-11.3905 - 12.6505i) q^{97} +(-1.75113 + 1.27227i) q^{98} +(3.91688 + 0.437280i) 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

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