LMFDB - Embedded newform 150.2.l.a.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			23.1
Character	$\chi$	$=$	150.23
Dual form			150.2.l.a.137.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 - 0.156434i) q^{2} +(-1.58737 + 0.693000i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-0.197931 - 2.22729i) q^{5} +(1.67624 - 0.436149i) q^{6} +(-1.43195 + 1.43195i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(2.03950 - 2.20010i) q^{9} +O(q^{10})$	\(q+(-0.987688 - 0.156434i) q^{2} +(-1.58737 + 0.693000i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-0.197931 - 2.22729i) q^{5} +(1.67624 - 0.436149i) q^{6} +(-1.43195 + 1.43195i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(2.03950 - 2.20010i) q^{9} +(-0.152931 + 2.23083i) q^{10} +(-3.22713 - 4.44177i) q^{11} +(-1.72383 + 0.168558i) q^{12} +(-1.00424 - 6.34051i) q^{13} +(1.63832 - 1.19031i) q^{14} +(1.85770 + 3.39837i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-0.101553 + 0.199309i) q^{17} +(-2.35856 + 1.85396i) q^{18} +(2.05900 - 0.669009i) q^{19} +(0.500027 - 2.17944i) q^{20} +(1.28069 - 3.26537i) q^{21} +(2.49256 + 4.89192i) q^{22} +(-0.339741 + 2.14504i) q^{23} +(1.72897 + 0.103184i) q^{24} +(-4.92165 + 0.881699i) q^{25} +6.41955i q^{26} +(-1.71278 + 4.90575i) q^{27} +(-1.80436 + 0.919366i) q^{28} +(-2.33841 + 7.19688i) q^{29} +(-1.30321 - 3.64714i) q^{30} +(-0.944961 - 2.90829i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.20081 + 4.81433i) q^{33} +(0.131482 - 0.180969i) q^{34} +(3.47279 + 2.90593i) q^{35} +(2.61955 - 1.46218i) q^{36} +(6.46438 - 1.02386i) q^{37} +(-2.13830 + 0.338674i) q^{38} +(5.98808 + 9.36882i) q^{39} +(-0.834811 + 2.07439i) q^{40} +(0.896615 - 1.23409i) q^{41} +(-1.77574 + 3.02482i) q^{42} +(-2.14384 - 2.14384i) q^{43} +(-1.69660 - 5.22161i) q^{44} +(-5.30394 - 4.10709i) q^{45} +(0.671116 - 2.06548i) q^{46} +(4.66039 - 2.37459i) q^{47} +(-1.69155 - 0.372385i) q^{48} +2.89906i q^{49} +(4.99898 - 0.100928i) q^{50} +(0.0230812 - 0.386754i) q^{51} +(1.00424 - 6.34051i) q^{52} +(-5.56485 - 10.9216i) q^{53} +(2.45912 - 4.57742i) q^{54} +(-9.25436 + 8.06693i) q^{55} +(1.92596 - 0.625783i) q^{56} +(-2.80477 + 2.48885i) q^{57} +(3.43546 - 6.74246i) q^{58} +(4.61185 + 3.35071i) q^{59} +(0.716626 + 3.80611i) q^{60} +(2.55529 - 1.85653i) q^{61} +(0.478370 + 3.02031i) q^{62} +(0.229968 + 6.07088i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-13.9234 + 3.49171i) q^{65} +(-7.34671 - 6.03795i) q^{66} +(2.22498 + 1.13368i) q^{67} +(-0.158173 + 0.158173i) q^{68} +(-0.947217 - 3.64041i) q^{69} +(-2.97544 - 3.41342i) q^{70} +(-5.77333 - 1.87587i) q^{71} +(-2.81603 + 1.03439i) q^{72} +(-3.02002 - 0.478324i) q^{73} -6.54496 q^{74} +(7.20147 - 4.81029i) q^{75} +2.16496 q^{76} +(10.9815 + 1.73929i) q^{77} +(-4.44875 - 10.1902i) q^{78} +(-11.0020 - 3.57478i) q^{79} +(1.14904 - 1.91826i) q^{80} +(-0.680873 - 8.97421i) q^{81} +(-1.07863 + 1.07863i) q^{82} +(9.31624 + 4.74686i) q^{83} +(2.22707 - 2.70980i) q^{84} +(0.464020 + 0.186739i) q^{85} +(1.78208 + 2.45282i) q^{86} +(-1.27552 - 13.0446i) q^{87} +(0.858876 + 5.42273i) q^{88} +(7.34358 - 5.33542i) q^{89} +(4.59615 + 4.88625i) q^{90} +(10.5173 + 7.64126i) q^{91} +(-0.985966 + 1.93507i) q^{92} +(3.51545 + 3.96168i) q^{93} +(-4.97448 + 1.61631i) q^{94} +(-1.89762 - 4.45357i) q^{95} +(1.61247 + 0.632416i) q^{96} +(1.09363 + 2.14637i) q^{97} +(0.453513 - 2.86337i) q^{98} +(-16.3541 - 1.95898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$3$	−1.58737	+	0.693000i	−0.916470	+	0.400104i
$3$	−1.58737	+	0.693000i	−0.916470	+	0.400104i
$4$	0.951057	+	0.309017i	0.475528	+	0.154508i
$5$	−0.197931	−	2.22729i	−0.0885173	−	0.996075i
$5$	−0.197931	−	2.22729i	−0.0885173	−	0.996075i
$6$	1.67624	−	0.436149i	0.684321	−	0.178057i
$7$	−1.43195	+	1.43195i	−0.541225	+	0.541225i	−0.923888	−	0.382663i	$-0.875007\pi$
$7$	−1.43195	+	1.43195i	−0.541225	+	0.541225i	0.382663	+	0.923888i	$0.375007\pi$
$8$	−0.891007	−	0.453990i	−0.315018	−	0.160510i
$9$	2.03950	−	2.20010i	0.679834	−	0.733366i
$10$	−0.152931	+	2.23083i	−0.0483611	+	0.705451i
$11$	−3.22713	−	4.44177i	−0.973017	−	1.33924i	−0.940508	−	0.339772i	$-0.889650\pi$
$11$	−3.22713	−	4.44177i	−0.973017	−	1.33924i	−0.0325093	−	0.999471i	$-0.510350\pi$
$12$	−1.72383	+	0.168558i	−0.497627	+	0.0486584i
$13$	−1.00424	−	6.34051i	−0.278526	−	1.75854i	−0.589164	−	0.808014i	$-0.700543\pi$
$13$	−1.00424	−	6.34051i	−0.278526	−	1.75854i	0.310638	−	0.950528i	$-0.399457\pi$
$14$	1.63832	−	1.19031i	0.437860	−	0.318124i
$15$	1.85770	+	3.39837i	0.479657	+	0.877456i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−0.101553	+	0.199309i	−0.0246303	+	0.0483396i	−0.902994	−	0.429654i	$-0.858636\pi$
$17$	−0.101553	+	0.199309i	−0.0246303	+	0.0483396i	0.878364	+	0.477993i	$0.158636\pi$
$18$	−2.35856	+	1.85396i	−0.555919	+	0.436984i
$19$	2.05900	−	0.669009i	0.472366	−	0.153481i	−0.0631534	−	0.998004i	$-0.520116\pi$
$19$	2.05900	−	0.669009i	0.472366	−	0.153481i	0.535520	+	0.844523i	$0.320116\pi$
$20$	0.500027	−	2.17944i	0.111810	−	0.487338i
$21$	1.28069	−	3.26537i	0.279470	−	0.712562i
$22$	2.49256	+	4.89192i	0.531415	+	1.04296i
$23$	−0.339741	+	2.14504i	−0.0708408	+	0.447271i	0.926617	+	0.376007i	$0.122703\pi$
$23$	−0.339741	+	2.14504i	−0.0708408	+	0.447271i	−0.997457	+	0.0712640i	$0.977297\pi$
$24$	1.72897	+	0.103184i	0.352925	+	0.0210623i
$25$	−4.92165	+	0.881699i	−0.984329	+	0.176340i
$26$			6.41955i			1.25898i
$27$	−1.71278	+	4.90575i	−0.329624	+	0.944112i
$28$	−1.80436	+	0.919366i	−0.340992	+	0.173744i
$29$	−2.33841	+	7.19688i	−0.434231	+	1.33643i	0.459641	+	0.888105i	$0.347978\pi$
$29$	−2.33841	+	7.19688i	−0.434231	+	1.33643i	−0.893872	+	0.448322i	$0.852022\pi$
$30$	−1.30321	−	3.64714i	−0.237932	−	0.665874i
$31$	−0.944961	−	2.90829i	−0.169720	−	0.522344i	0.829633	−	0.558309i	$-0.188550\pi$
$31$	−0.944961	−	2.90829i	−0.169720	−	0.522344i	−0.999353	+	0.0359646i	$0.988550\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	8.20081	+	4.81433i	1.42758	+	0.838068i
$34$	0.131482	−	0.180969i	0.0225489	−	0.0310359i
$35$	3.47279	+	2.90593i	0.587008	+	0.491193i
$36$	2.61955	−	1.46218i	0.436591	−	0.243696i
$37$	6.46438	−	1.02386i	1.06274	−	0.168321i	0.399502	−	0.916732i	$-0.369183\pi$
$37$	6.46438	−	1.02386i	1.06274	−	0.168321i	0.663235	+	0.748411i	$0.269183\pi$
$38$	−2.13830	+	0.338674i	−0.346879	+	0.0549402i
$39$	5.98808	+	9.36882i	0.958860	+	1.50021i
$40$	−0.834811	+	2.07439i	−0.131995	+	0.327990i
$41$	0.896615	−	1.23409i	0.140028	−	0.192732i	−0.733243	−	0.679966i	$-0.761994\pi$
$41$	0.896615	−	1.23409i	0.140028	−	0.192732i	0.873271	+	0.487235i	$0.161994\pi$
$42$	−1.77574	+	3.02482i	−0.274003	+	0.466741i
$43$	−2.14384	−	2.14384i	−0.326933	−	0.326933i	0.524486	−	0.851419i	$-0.324258\pi$
$43$	−2.14384	−	2.14384i	−0.326933	−	0.326933i	−0.851419	+	0.524486i	$0.824258\pi$
$44$	−1.69660	−	5.22161i	−0.255773	−	0.787187i
$45$	−5.30394	−	4.10709i	−0.790665	−	0.612249i
$46$	0.671116	−	2.06548i	0.0989506	−	0.304539i
$47$	4.66039	−	2.37459i	0.679788	−	0.346369i	−0.0797657	−	0.996814i	$-0.525417\pi$
$47$	4.66039	−	2.37459i	0.679788	−	0.346369i	0.759554	+	0.650444i	$0.225417\pi$
$48$	−1.69155	−	0.372385i	−0.244154	−	0.0537491i
$49$			2.89906i			0.414151i
$50$	4.99898	−	0.100928i	0.706963	−	0.0142734i
$51$	0.0230812	−	0.386754i	0.00323202	−	0.0541564i
$52$	1.00424	−	6.34051i	0.139263	−	0.879271i
$53$	−5.56485	−	10.9216i	−0.764390	−	1.50020i	−0.863072	−	0.505082i	$-0.831462\pi$
$53$	−5.56485	−	10.9216i	−0.764390	−	1.50020i	0.0986812	−	0.995119i	$-0.468538\pi$
$54$	2.45912	−	4.57742i	0.334644	−	0.622907i
$55$	−9.25436	+	8.06693i	−1.24786	+	1.08774i
$56$	1.92596	−	0.625783i	0.257368	−	0.0836238i
$57$	−2.80477	+	2.48885i	−0.371501	+	0.329657i
$58$	3.43546	−	6.74246i	0.451098	−	0.885329i
$59$	4.61185	+	3.35071i	0.600412	+	0.436225i	0.846025	−	0.533143i	$-0.178989\pi$
$59$	4.61185	+	3.35071i	0.600412	+	0.436225i	−0.245613	+	0.969368i	$0.578989\pi$
$60$	0.716626	+	3.80611i	0.0925160	+	0.491366i
$61$	2.55529	−	1.85653i	0.327171	−	0.237704i	−0.412058	−	0.911158i	$-0.635190\pi$
$61$	2.55529	−	1.85653i	0.327171	−	0.237704i	0.739229	+	0.673454i	$0.235190\pi$
$62$	0.478370	+	3.02031i	0.0607530	+	0.383580i
$63$	0.229968	+	6.07088i	0.0289733	+	0.764859i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	−13.9234	+	3.49171i	−1.72698	+	0.433094i
$66$	−7.34671	−	6.03795i	−0.904318	−	0.743220i
$67$	2.22498	+	1.13368i	0.271824	+	0.138501i	0.584590	−	0.811329i	$-0.301255\pi$
$67$	2.22498	+	1.13368i	0.271824	+	0.138501i	−0.312766	+	0.949830i	$0.601255\pi$
$68$	−0.158173	+	0.158173i	−0.0191813	+	0.0191813i
$69$	−0.947217	−	3.64041i	−0.114032	−	0.438254i
$70$	−2.97544	−	3.41342i	−0.355633	−	0.407982i
$71$	−5.77333	−	1.87587i	−0.685168	−	0.222625i	−0.0543113	−	0.998524i	$-0.517296\pi$
$71$	−5.77333	−	1.87587i	−0.685168	−	0.222625i	−0.630856	+	0.775900i	$0.717296\pi$
$72$	−2.81603	+	1.03439i	−0.331873	+	0.121904i
$73$	−3.02002	−	0.478324i	−0.353467	−	0.0559836i	−0.0228237	−	0.999740i	$-0.507266\pi$
$73$	−3.02002	−	0.478324i	−0.353467	−	0.0559836i	−0.330643	+	0.943756i	$0.607266\pi$
$74$	−6.54496			−0.760836
$75$	7.20147	−	4.81029i	0.831554	−	0.555444i
$76$	2.16496			0.248338
$77$	10.9815	+	1.73929i	1.25145	+	0.198211i
$78$	−4.44875	−	10.1902i	−0.503722	−	1.15381i
$79$	−11.0020	−	3.57478i	−1.23783	−	0.402194i	−0.384282	−	0.923216i	$-0.625551\pi$
$79$	−11.0020	−	3.57478i	−1.23783	−	0.402194i	−0.853543	+	0.521022i	$0.825551\pi$
$80$	1.14904	−	1.91826i	0.128466	−	0.214468i
$81$	−0.680873	−	8.97421i	−0.0756526	−	0.997134i
$82$	−1.07863	+	1.07863i	−0.119115	+	0.119115i
$83$	9.31624	+	4.74686i	1.02259	+	0.521036i	0.883099	−	0.469187i	$-0.155453\pi$
$83$	9.31624	+	4.74686i	1.02259	+	0.521036i	0.139492	+	0.990223i	$0.455453\pi$
$84$	2.22707	−	2.70980i	0.242993	−	0.295663i
$85$	0.464020	+	0.186739i	0.0503301	+	0.0202547i
$86$	1.78208	+	2.45282i	0.192166	+	0.264494i
$87$	−1.27552	−	13.0446i	−0.136750	−	1.39853i
$88$	0.858876	+	5.42273i	0.0915565	+	0.578065i
$89$	7.34358	−	5.33542i	0.778418	−	0.565554i	−0.126086	−	0.992019i	$-0.540241\pi$
$89$	7.34358	−	5.33542i	0.778418	−	0.565554i	0.904504	+	0.426466i	$0.140241\pi$
$90$	4.59615	+	4.88625i	0.484477	+	0.515056i
$91$	10.5173	+	7.64126i	1.10251	+	0.801022i
$92$	−0.985966	+	1.93507i	−0.102794	+	0.201745i
$93$	3.51545	+	3.96168i	0.364535	+	0.410807i
$94$	−4.97448	+	1.61631i	−0.513079	+	0.166709i
$95$	−1.89762	−	4.45357i	−0.194691	−	0.456926i
$96$	1.61247	+	0.632416i	0.164572	+	0.0645457i
$97$	1.09363	+	2.14637i	0.111041	+	0.217931i	0.939839	−	0.341617i	$-0.110975\pi$
$97$	1.09363	+	2.14637i	0.111041	+	0.217931i	−0.828798	+	0.559548i	$0.810975\pi$
$98$	0.453513	−	2.86337i	0.0458117	−	0.289244i
$99$	−16.3541	−	1.95898i	−1.64365	−	0.196884i
$100$	−4.95322	−	0.682327i	−0.495322	−	0.0682327i
$101$			7.60118i			0.756346i	0.925735	+	0.378173i	$0.123448\pi$
$101$			7.60118i			0.756346i	−0.925735	+	0.378173i	$0.876552\pi$
$102$	−0.0832988	+	0.378382i	−0.00824781	+	0.0374654i
$103$	7.60819	−	3.87657i	0.749657	−	0.381970i	−0.0370356	−	0.999314i	$-0.511791\pi$
$103$	7.60819	−	3.87657i	0.749657	−	0.381970i	0.786693	+	0.617344i	$0.211791\pi$
$104$	−1.98375	+	6.10535i	−0.194523	+	0.598679i
$105$	−7.52642	−	2.20616i	−0.734503	−	0.215299i
$106$	3.78781	+	11.6577i	0.367905	+	1.13230i
$107$	−3.60945	−	3.60945i	−0.348939	−	0.348939i	0.510775	−	0.859714i	$-0.329358\pi$
$107$	−3.60945	−	3.60945i	−0.348939	−	0.348939i	−0.859714	+	0.510775i	$0.829358\pi$
$108$	−3.14491	+	4.13637i	−0.302619	+	0.398022i
$109$	5.74999	−	7.91418i	0.550749	−	0.758041i	−0.439365	−	0.898309i	$-0.644796\pi$
$109$	5.74999	−	7.91418i	0.550749	−	0.758041i	0.990114	+	0.140268i	$0.0447964\pi$
$110$	10.4024	−	6.51991i	0.991827	−	0.621649i
$111$	−9.55184	+	6.10506i	−0.906620	+	0.579466i
$112$	−2.00015	+	0.316792i	−0.188996	+	0.0299340i
$113$	13.0078	−	2.06024i	1.22367	−	0.193811i	0.489033	−	0.872266i	$-0.337350\pi$
$113$	13.0078	−	2.06024i	1.22367	−	0.193811i	0.734642	+	0.678454i	$0.237350\pi$
$114$	3.15958	−	2.01945i	0.295922	−	0.189139i
$115$	4.84487	+	0.332132i	0.451786	+	0.0309715i
$116$	−4.44791	+	6.12203i	−0.412978	+	0.568416i
$117$	−15.9979	−	10.7221i	−1.47901	−	0.991255i
$118$	−4.03091	−	4.03091i	−0.371075	−	0.371075i
$119$	−0.139982	−	0.430819i	−0.0128321	−	0.0394931i
$120$	−0.112397	−	3.87135i	−0.0102604	−	0.353404i
$121$	−5.91572	+	18.2067i	−0.537793	+	1.65516i
$122$	−2.81426	+	1.43393i	−0.254791	+	0.129822i
$123$	−0.568041	+	2.58031i	−0.0512185	+	0.232658i
$124$		−	3.05796i		−	0.274613i
$125$	2.93794	+	10.7874i	0.262778	+	0.964856i
$126$	0.722558	−	6.03211i	0.0643706	−	0.537383i
$127$	1.79653	−	11.3429i	0.159417	−	1.00652i	−0.770150	−	0.637863i	$-0.779819\pi$
$127$	1.79653	−	11.3429i	0.159417	−	1.00652i	0.929567	−	0.368654i	$-0.120181\pi$
$128$	−0.453990	−	0.891007i	−0.0401275	−	0.0787546i
$129$	4.88876	+	1.91739i	0.430432	+	0.168817i
$130$	14.2982	−	1.27063i	1.25404	−	0.111441i
$131$	9.82350	−	3.19185i	0.858284	−	0.278873i	0.153372	−	0.988169i	$-0.450987\pi$
$131$	9.82350	−	3.19185i	0.858284	−	0.278873i	0.704911	+	0.709295i	$0.250987\pi$
$132$	6.31172	+	7.11289i	0.549365	+	0.619098i
$133$	−1.99039	+	3.90636i	−0.172589	+	0.338724i
$134$	−2.02024	−	1.46779i	−0.174522	−	0.126797i
$135$	11.2655	+	2.84385i	0.969584	+	0.244760i
$136$	0.180969	−	0.131482i	0.0155180	−	0.0112745i
$137$	2.11029	+	13.3238i	0.180294	+	1.13833i	0.897351	+	0.441317i	$0.145489\pi$
$137$	2.11029	+	13.3238i	0.180294	+	1.13833i	−0.717057	+	0.697014i	$0.754511\pi$
$138$	0.366069	+	3.74377i	0.0311619	+	0.318691i
$139$	−6.69452	−	9.21421i	−0.567822	−	0.781539i	0.424473	−	0.905441i	$-0.360459\pi$
$139$	−6.69452	−	9.21421i	−0.567822	−	0.781539i	−0.992295	+	0.123901i	$0.960459\pi$
$140$	2.40483	+	3.83686i	0.203246	+	0.324274i
$141$	−5.75219	+	6.99901i	−0.484422	+	0.589423i
$142$	5.40880	+	2.75592i	0.453896	+	0.231272i
$143$	−24.9223	+	24.9223i	−2.08411	+	2.08411i
$144$	2.94318	−	0.581129i	0.245265	−	0.0484274i
$145$	16.4924	+	3.78383i	1.36962	+	0.314230i
$146$	2.90801	+	0.944871i	0.240669	+	0.0781981i
$147$	−2.00905	−	4.60189i	−0.165704	−	0.379557i
$148$	6.46438	+	1.02386i	0.531369	+	0.0841605i
$149$	5.97158			0.489211			0.244606	−	0.969623i	$-0.421342\pi$
$149$	5.97158			0.489211			0.244606	+	0.969623i	$0.421342\pi$
$150$	−7.86530	+	3.62451i	−0.642199	+	0.295940i
$151$	−3.02183			−0.245913			−0.122956	−	0.992412i	$-0.539238\pi$
$151$	−3.02183			−0.245913			−0.122956	+	0.992412i	$0.539238\pi$
$152$	−2.13830	−	0.338674i	−0.173439	−	0.0274701i
$153$	0.231382	+	0.629918i	0.0187062	+	0.0509259i
$154$	−10.5742	−	3.43576i	−0.852091	−	0.276861i
$155$	−6.29057	+	2.68034i	−0.505271	+	0.215290i
$156$	2.79988	+	10.7607i	0.224170	+	0.861545i
$157$	4.40896	−	4.40896i	0.351873	−	0.351873i	−0.508933	−	0.860806i	$-0.669960\pi$
$157$	4.40896	−	4.40896i	0.351873	−	0.351873i	0.860806	+	0.508933i	$0.169960\pi$
$158$	10.3074	+	5.25186i	0.820010	+	0.417816i
$159$	16.4022	+	13.4802i	1.30078	+	1.06905i
$160$	−1.43497	+	1.71489i	−0.113445	+	0.135574i
$161$	−2.58509	−	3.55807i	−0.203734	−	0.280415i
$162$	−0.731385	+	8.97023i	−0.0574630	+	0.704768i
$163$	−0.896493	−	5.66023i	−0.0702187	−	0.443344i	−0.997601	−	0.0692282i	$-0.977946\pi$
$163$	−0.896493	−	5.66023i	−0.0702187	−	0.443344i	0.927382	−	0.374116i	$-0.122054\pi$
$164$	1.23409	−	0.896615i	0.0963659	−	0.0700139i
$165$	9.09973	−	19.2185i	0.708413	−	1.49616i
$166$	−8.45897	−	6.14580i	−0.656544	−	0.477007i
$167$	4.42748	−	8.68941i	0.342608	−	0.672407i	−0.653838	−	0.756634i	$-0.726842\pi$
$167$	4.42748	−	8.68941i	0.342608	−	0.672407i	0.996447	+	0.0842276i	$0.0268423\pi$
$168$	−2.62355	+	2.32804i	−0.202411	+	0.179613i
$169$	−26.8299	+	8.71756i	−2.06384	+	0.670581i
$170$	−0.429095	−	0.257029i	−0.0329101	−	0.0197132i
$171$	2.72744	−	5.89444i	0.208573	−	0.450759i
$172$	−1.37643	−	2.70140i	−0.104952	−	0.205980i
$173$	2.74408	−	17.3254i	0.208629	−	1.31723i	−0.631726	−	0.775192i	$-0.717653\pi$
$173$	2.74408	−	17.3254i	0.208629	−	1.31723i	0.840354	−	0.542037i	$-0.182347\pi$
$174$	−0.780818	+	13.0836i	−0.0591937	+	0.991863i
$175$	5.78499	−	8.31008i	0.437304	−	0.628183i
$176$		−	5.49033i		−	0.413849i
$177$	−9.64277	−	2.12280i	−0.724795	−	0.159560i
$178$	−8.08781	+	4.12095i	−0.606207	+	0.308878i
$179$	−3.59155	+	11.0537i	−0.268445	+	0.826190i	0.722434	+	0.691440i	$0.243023\pi$
$179$	−3.59155	+	11.0537i	−0.268445	+	0.826190i	−0.990880	+	0.134750i	$0.956977\pi$
$180$	−3.77519	−	5.54509i	−0.281386	−	0.413306i
$181$	−1.22208	−	3.76116i	−0.0908362	−	0.279565i	0.895310	−	0.445444i	$-0.146954\pi$
$181$	−1.22208	−	3.76116i	−0.0908362	−	0.279565i	−0.986146	+	0.165879i	$0.946954\pi$
$182$	−9.19245	−	9.19245i	−0.681390	−	0.681390i
$183$	−2.76962	+	4.71782i	−0.204736	+	0.348751i
$184$	1.27654	−	1.75700i	0.0941076	−	0.129528i
$185$	−3.55993	−	14.1954i	−0.261731	−	1.04367i
$186$	−2.85243	−	4.46284i	−0.209150	−	0.327232i
$187$	1.21301	−	0.192122i	0.0887042	−	0.0140494i
$188$	5.16609	−	0.818228i	0.376776	−	0.0596754i
$189$	−4.57217	−	9.47738i	−0.332576	−	0.689378i
$190$	1.17756	+	4.69559i	0.0854293	+	0.340654i
$191$	9.89270	−	13.6161i	0.715810	−	0.985228i	−0.283842	−	0.958871i	$-0.591609\pi$
$191$	9.89270	−	13.6161i	0.715810	−	0.985228i	0.999653	−	0.0263574i	$-0.00839078\pi$
$192$	−1.49368	−	0.876876i	−0.107797	−	0.0632830i
$193$	11.0921	+	11.0921i	0.798428	+	0.798428i	0.982848	−	0.184419i	$-0.0590404\pi$
$193$	11.0921	+	11.0921i	0.798428	+	0.798428i	−0.184419	+	0.982848i	$0.559040\pi$
$194$	−0.744401	−	2.29103i	−0.0534449	−	0.164486i
$195$	19.6819	−	15.1916i	1.40945	−	1.08789i
$196$	−0.895859	+	2.75717i	−0.0639899	+	0.196941i
$197$	−15.8178	+	8.05955i	−1.12697	+	0.574219i	−0.915160	−	0.403091i	$-0.867936\pi$
$197$	−15.8178	+	8.05955i	−1.12697	+	0.574219i	−0.211809	+	0.977311i	$0.567936\pi$
$198$	15.8463	+	4.49320i	1.12615	+	0.319318i
$199$			2.78155i			0.197179i	0.995128	+	0.0985894i	$0.0314330\pi$
$199$			2.78155i			0.197179i	−0.995128	+	0.0985894i	$0.968567\pi$
$200$	4.78550	+	1.44878i	0.338386	+	0.102444i
$201$	−4.31751	−	0.257666i	−0.304533	−	0.0181743i
$202$	1.18909	−	7.50760i	0.0836639	−	0.528233i
$203$	−6.95707	−	13.6540i	−0.488290	−	0.958324i
$204$	0.141465	−	0.360693i	0.00990455	−	0.0252535i
$205$	−2.92613	−	1.75276i	−0.204370	−	0.122418i
$206$	−8.12095	+	2.63866i	−0.565813	+	0.183844i
$207$	4.02640	+	5.12227i	0.279854	+	0.356022i
$208$	2.91441	−	5.71986i	0.202078	−	0.396601i
$209$	−9.61624	−	6.98661i	−0.665169	−	0.483274i
$210$	7.08864	+	3.35639i	0.489162	+	0.231613i
$211$	−11.4724	+	8.33520i	−0.789794	+	0.573819i	−0.907902	−	0.419182i	$-0.862317\pi$
$211$	−11.4724	+	8.33520i	−0.789794	+	0.573819i	0.118108	+	0.993001i	$0.462317\pi$
$212$	−1.91752	−	12.1067i	−0.131695	−	0.831493i
$213$	10.4644	−	1.02322i	0.717009	−	0.0701097i
$214$	3.00037	+	4.12966i	0.205101	+	0.282298i
$215$	−4.35063	+	5.19930i	−0.296711	+	0.354589i
$216$	3.75326	−	3.59347i	0.255377	−	0.244505i
$217$	5.51765	+	2.81138i	0.374562	+	0.190849i
$218$	−6.91725	+	6.91725i	−0.468495	+	0.468495i
$219$	5.12538	−	1.33360i	0.346341	−	0.0901162i
$220$	−11.2942	+	4.81235i	−0.761457	+	0.324448i
$221$	1.36571	+	0.443745i	0.0918674	+	0.0298495i
$222$	10.3893	−	4.53566i	0.697283	−	0.304413i
$223$	5.36327	+	0.849459i	0.359151	+	0.0568840i	0.333403	−	0.942784i	$-0.391803\pi$
$223$	5.36327	+	0.849459i	0.359151	+	0.0568840i	0.0257485	+	0.999668i	$0.491803\pi$
$224$	2.02508			0.135306
$225$	−8.09788	+	12.6263i	−0.539859	+	0.841756i
$226$	−13.1700			−0.876055
$227$	−19.7103	−	3.12180i	−1.30822	−	0.207201i	−0.536896	−	0.843649i	$-0.680403\pi$
$227$	−19.7103	−	3.12180i	−1.30822	−	0.207201i	−0.771320	+	0.636448i	$0.780403\pi$
$228$	−3.43659	+	1.50032i	−0.227594	+	0.0993609i
$229$	10.9433	+	3.55568i	0.723151	+	0.234966i	0.647389	−	0.762160i	$-0.275861\pi$
$229$	10.9433	+	3.55568i	0.723151	+	0.234966i	0.0757621	+	0.997126i	$0.475861\pi$
$230$	−4.73326	−	1.08595i	−0.312102	−	0.0716052i
$231$	−18.6370	+	4.84925i	−1.22622	+	0.319057i
$232$	5.35085	−	5.35085i	0.351300	−	0.351300i
$233$	4.33449	+	2.20854i	0.283962	+	0.144686i	0.590171	−	0.807279i	$-0.299060\pi$
$233$	4.33449	+	2.20854i	0.283962	+	0.144686i	−0.306208	+	0.951964i	$0.599060\pi$
$234$	14.1236	+	13.0927i	0.923292	+	0.855895i
$235$	−6.21134	−	9.91005i	−0.405183	−	0.646460i
$236$	3.35071	+	4.61185i	0.218112	+	0.300206i
$237$	19.9416	−	1.94991i	1.29535	−	0.126660i
$238$	0.0708632	+	0.447413i	0.00459338	+	0.0290015i
$239$	13.5737	−	9.86185i	0.878008	−	0.637910i	−0.0547159	−	0.998502i	$-0.517425\pi$
$239$	13.5737	−	9.86185i	0.878008	−	0.637910i	0.932724	+	0.360592i	$0.117425\pi$
$240$	−0.494600	+	3.84127i	−0.0319263	+	0.247953i
$241$	13.7609	+	9.99786i	0.886416	+	0.644019i	0.934941	−	0.354803i	$-0.115452\pi$
$241$	13.7609	+	9.99786i	0.886416	+	0.644019i	−0.0485253	+	0.998822i	$0.515452\pi$
$242$	8.69105	−	17.0571i	0.558682	−	1.09648i
$243$	7.29993	+	13.7736i	0.468291	+	0.883574i
$244$	3.00392	−	0.976034i	0.192307	−	0.0624842i
$245$	6.45705	−	0.573813i	0.412526	−	0.0366596i
$246$	0.964696	−	2.45968i	0.0615068	−	0.156823i
$247$	−6.30958	−	12.3833i	−0.401469	−	0.787928i
$248$	−0.478370	+	3.02031i	−0.0303765	+	0.191790i
$249$	−18.0779	−	1.07888i	−1.14564	−	0.0683711i
$250$	−1.21425	−	11.1142i	−0.0767959	−	0.702924i
$251$		−	27.1027i		−	1.71071i	−0.518046	−	0.855353i	$-0.673340\pi$
$251$		−	27.1027i		−	1.71071i	0.518046	−	0.855353i	$-0.326660\pi$
$252$	−1.65729	+	5.84481i	−0.104400	+	0.368189i
$253$	10.6241	−	5.41327i	0.667934	−	0.340330i
$254$	−3.54883	+	10.9222i	−0.222673	+	0.685318i
$255$	−0.865983	+	0.0251420i	−0.0542300	+	0.00157445i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	11.8188	+	11.8188i	0.737238	+	0.737238i	0.972043	−	0.234805i	$-0.0754451\pi$
$257$	11.8188	+	11.8188i	0.737238	+	0.737238i	−0.234805	+	0.972043i	$0.575445\pi$
$258$	−4.52863	−	2.65856i	−0.281940	−	0.165515i
$259$	−7.79053	+	10.7227i	−0.484080	+	0.666279i
$260$	−14.3209	−	0.981749i	−0.888147	−	0.0608855i
$261$	11.0647	+	19.8228i	0.684885	+	1.22700i
$262$	−10.2019	+	1.61582i	−0.630274	+	0.0998256i
$263$	−7.20902	+	1.14180i	−0.444527	+	0.0704062i	−0.374686	−	0.927152i	$-0.622249\pi$
$263$	−7.20902	+	1.14180i	−0.444527	+	0.0704062i	−0.0698415	+	0.997558i	$0.522249\pi$
$264$	−5.12131	−	8.01269i	−0.315195	−	0.493147i
$265$	−23.2242	+	14.5563i	−1.42665	+	0.894184i
$266$	2.57697	−	3.54690i	0.158004	−	0.217474i
$267$	−7.95954	+	13.5584i	−0.487116	+	0.829761i
$268$	1.76575	+	1.76575i	0.107860	+	0.107860i
$269$	−9.50784	−	29.2621i	−0.579703	−	1.78414i	−0.619573	−	0.784939i	$-0.712694\pi$
$269$	−9.50784	−	29.2621i	−0.579703	−	1.78414i	0.0398701	−	0.999205i	$-0.487306\pi$
$270$	−10.6820	−	4.57116i	−0.650084	−	0.278192i
$271$	4.91027	−	15.1123i	0.298278	−	0.918004i	−0.683823	−	0.729648i	$-0.739684\pi$
$271$	4.91027	−	15.1123i	0.298278	−	0.918004i	0.982101	−	0.188356i	$-0.0603160\pi$
$272$	−0.199309	+	0.101553i	−0.0120849	+	0.00615756i
$273$	−21.9903	−	4.84103i	−1.33091	−	0.292993i
$274$		−	13.4899i		−	0.814956i
$275$	19.7991	+	19.0155i	1.19393	+	1.14667i
$276$	0.224092	−	3.75495i	0.0134888	−	0.226021i
$277$	−1.50370	+	9.49399i	−0.0903486	+	0.570438i	0.900436	+	0.434989i	$0.143248\pi$
$277$	−1.50370	+	9.49399i	−0.0903486	+	0.570438i	−0.990784	+	0.135449i	$0.956752\pi$
$278$	5.17068	+	10.1480i	0.310117	+	0.608638i
$279$	−8.32578	−	3.85245i	−0.498451	−	0.230640i
$280$	−1.77501	−	4.16582i	−0.106077	−	0.248955i
$281$	−19.6851	+	6.39607i	−1.17431	+	0.381558i	−0.830251	−	0.557389i	$-0.811803\pi$
$281$	−19.6851	+	6.39607i	−1.17431	+	0.381558i	−0.344062	+	0.938947i	$0.611803\pi$
$282$	6.77626	−	6.01300i	0.403520	−	0.358069i
$283$	−5.53912	+	10.8711i	−0.329267	+	0.646222i	−0.994990	−	0.0999766i	$-0.968123\pi$
$283$	−5.53912	+	10.8711i	−0.329267	+	0.646222i	0.665723	+	0.746199i	$0.268123\pi$
$284$	−4.91108	−	3.56811i	−0.291419	−	0.211728i
$285$	6.09855	+	5.75442i	0.361247	+	0.340863i
$286$	28.5141	−	20.7167i	1.68608	−	1.22501i
$287$	0.483239	+	3.05105i	0.0285247	+	0.180098i
$288$	−2.99785	+	0.113560i	−0.176650	+	0.00669160i
$289$	9.96294	+	13.7128i	0.586055	+	0.806636i
$290$	−15.6974	−	6.31722i	−0.921784	−	0.370960i
$291$	−3.22344	−	2.64921i	−0.188961	−	0.155299i
$292$	−2.72440	−	1.38815i	−0.159433	−	0.0812354i
$293$	0.153372	−	0.153372i	0.00896009	−	0.00896009i	−0.702613	−	0.711573i	$-0.747983\pi$
$293$	0.153372	−	0.153372i	0.00896009	−	0.00896009i	0.711573	+	0.702613i	$0.247983\pi$
$294$	1.26442	+	4.85951i	0.0737425	+	0.283413i
$295$	6.55017	−	10.9351i	0.381366	−	0.636669i
$296$	−6.22462	−	2.02250i	−0.361799	−	0.117556i
$297$	27.3176	−	8.22375i	1.58513	−	0.477191i
$298$	−5.89806	−	0.934161i	−0.341666	−	0.0541145i
$299$	13.9418			0.806276
$300$	8.33546	−	2.34948i	0.481248	−	0.135647i
$301$	6.13974			0.353889
$302$	2.98463	+	0.472718i	0.171746	+	0.0272019i
$303$	−5.26762	−	12.0659i	−0.302617	−	0.693168i
$304$	2.05900	+	0.669009i	0.118092	+	0.0383703i
$305$	−4.64080	−	5.32391i	−0.265731	−	0.304846i
$306$	−0.129993	−	0.658359i	−0.00743119	−	0.0376359i
$307$	−4.76351	+	4.76351i	−0.271868	+	0.271868i	−0.829852	−	0.557984i	$-0.811575\pi$
$307$	−4.76351	+	4.76351i	−0.271868	+	0.271868i	0.557984	+	0.829852i	$0.311575\pi$
$308$	9.90651	+	5.04762i	0.564476	+	0.287615i
$309$	−9.39057	+	11.4260i	−0.534211	+	0.650004i
$310$	6.63242	−	1.66328i	0.376696	−	0.0944680i
$311$	17.8640	+	24.5877i	1.01298	+	1.39424i	0.917012	+	0.398859i	$0.130594\pi$
$311$	17.8640	+	24.5877i	1.01298	+	1.39424i	0.0959647	+	0.995385i	$0.469406\pi$
$312$	−1.08206	−	11.0662i	−0.0612598	−	0.626501i
$313$	1.36617	+	8.62568i	0.0772206	+	0.487552i	0.995742	+	0.0921812i	$0.0293839\pi$
$313$	1.36617	+	8.62568i	0.0772206	+	0.487552i	−0.918522	+	0.395371i	$0.870616\pi$
$314$	−5.04439	+	3.66496i	−0.284671	+	0.206826i
$315$	13.4761	−	1.71382i	0.759292	−	0.0965628i
$316$	−9.35889	−	6.79963i	−0.526479	−	0.382509i
$317$	−4.58149	+	8.99167i	−0.257322	+	0.505023i	−0.983138	−	0.182866i	$-0.941462\pi$
$317$	−4.58149	+	8.99167i	−0.257322	+	0.505023i	0.725816	+	0.687889i	$0.241462\pi$
$318$	−14.0915	−	15.8801i	−0.790210	−	0.890514i
$319$	39.5132	−	12.8386i	2.21231	−	0.718825i
$320$	1.68558	−	1.46930i	0.0942265	−	0.0821363i
$321$	8.23090	+	3.22819i	0.459404	+	0.180180i
$322$	1.99666	+	3.91866i	0.111269	+	0.218378i
$323$	−0.0757580	+	0.478317i	−0.00421529	+	0.0266143i
$324$	2.12563	−	8.74538i	0.118091	−	0.485854i
$325$	10.5329	+	30.3203i	0.584262	+	1.68187i
$326$			5.73079i			0.317399i
$327$	−3.64284	+	16.5475i	−0.201450	+	0.915079i
$328$	−1.35915	+	0.692523i	−0.0750467	+	0.0382382i
$329$	−3.27315	+	10.0737i	−0.180455	+	0.555382i
$330$	−11.9941	+	17.5584i	−0.660255	+	0.966556i
$331$	−7.78449	−	23.9582i	−0.427874	−	1.31686i	−0.900215	−	0.435445i	$-0.856591\pi$
$331$	−7.78449	−	23.9582i	−0.427874	−	1.31686i	0.472341	−	0.881416i	$-0.343409\pi$
$332$	7.39341	+	7.39341i	0.405766	+	0.405766i
$333$	10.9315	−	16.3104i	0.599043	−	0.893806i
$334$	−5.73229	+	7.88982i	−0.313657	+	0.431712i
$335$	2.08465	−	5.18006i	0.113896	−	0.283017i
$336$	2.95544	−	1.88897i	0.161232	−	0.103052i
$337$	−29.9840	+	4.74900i	−1.63333	+	0.258694i	−0.904649	−	0.426157i	$-0.859867\pi$
$337$	−29.9840	+	4.74900i	−1.63333	+	0.258694i	−0.728683	+	0.684852i	$0.759867\pi$
$338$	27.8633	−	4.41311i	1.51556	−	0.240042i
$339$	−19.2205	+	12.2848i	−1.04392	+	0.667219i
$340$	0.383604	+	0.320989i	0.0208038	+	0.0174081i
$341$	−9.86844	+	13.5827i	−0.534406	+	0.735546i
$342$	−3.61596	+	5.39521i	−0.195528	+	0.291739i
$343$	−14.1749	−	14.1749i	−0.765374	−	0.765374i
$344$	0.936894	+	2.88346i	0.0505139	+	0.155466i
$345$	−7.92078	+	2.83028i	−0.426440	+	0.152377i
$346$	−5.42059	+	16.6829i	−0.291413	+	0.896877i
$347$	−22.1485	+	11.2852i	−1.18899	+	0.605823i	−0.932657	−	0.360765i	$-0.882516\pi$
$347$	−22.1485	+	11.2852i	−1.18899	+	0.605823i	−0.256337	+	0.966587i	$0.582516\pi$
$348$	2.81793	−	12.8003i	0.151057	−	0.686170i
$349$		−	7.66380i		−	0.410234i	−0.978737	−	0.205117i	$-0.934243\pi$
$349$		−	7.66380i		−	0.410234i	0.978737	−	0.205117i	$-0.0657575\pi$
$350$	−7.01375	+	7.30280i	−0.374901	+	0.390351i
$351$	32.8250	+	5.93334i	1.75207	+	0.316698i
$352$	−0.858876	+	5.42273i	−0.0457783	+	0.289033i
$353$	−1.23037	−	2.41473i	−0.0654859	−	0.128523i	0.855943	−	0.517070i	$-0.172977\pi$
$353$	−1.23037	−	2.41473i	−0.0654859	−	0.128523i	−0.921429	+	0.388547i	$0.872977\pi$
$354$	9.19197	+	3.60513i	0.488548	+	0.191610i
$355$	−3.03538	+	13.2302i	−0.161101	+	0.702184i
$356$	8.63290	−	2.80500i	0.457543	−	0.148665i
$357$	0.520760	+	0.586863i	0.0275616	+	0.0310601i
$358$	5.27651	−	10.3557i	0.278872	−	0.547317i
$359$	−3.19128	−	2.31860i	−0.168429	−	0.122371i	0.500377	−	0.865807i	$-0.333195\pi$
$359$	−3.19128	−	2.31860i	−0.168429	−	0.122371i	−0.668807	+	0.743436i	$0.733195\pi$
$360$	2.86126	+	6.06739i	0.150802	+	0.319779i
$361$	−11.5794	+	8.41294i	−0.609443	+	0.442787i
$362$	0.618655	+	3.90603i	0.0325158	+	0.205297i
$363$	−3.22681	−	33.0005i	−0.169364	−	1.73207i
$364$	7.64126	+	10.5173i	0.400511	+	0.551256i
$365$	−0.467612	+	6.82114i	−0.0244759	+	0.357035i
$366$	3.47355	−	4.22647i	0.181566	−	0.220921i
$367$	25.0999	+	12.7890i	1.31020	+	0.667581i	0.962820	−	0.270143i	$-0.0870709\pi$
$367$	25.0999	+	12.7890i	1.31020	+	0.667581i	0.347381	+	0.937724i	$0.387071\pi$
$368$	−1.53568	+	1.53568i	−0.0800527	+	0.0800527i
$369$	−0.886462	−	4.48956i	−0.0461474	−	0.233717i
$370$	1.29545	+	14.5775i	0.0673471	+	0.757849i
$371$	23.6077	+	7.67062i	1.22565	+	0.398239i
$372$	2.11917	+	4.85412i	0.109874	+	0.251674i
$373$	−25.8075	−	4.08750i	−1.33626	−	0.211643i	−0.552919	−	0.833235i	$-0.686486\pi$
$373$	−25.8075	−	4.08750i	−1.33626	−	0.211643i	−0.783341	+	0.621592i	$0.786486\pi$
$374$	−1.22813			−0.0635052
$375$	−12.1393	−	15.0877i	−0.626871	−	0.779123i
$376$	−5.23048			−0.269742
$377$	47.9802	+	7.59932i	2.47111	+	0.391385i
$378$	3.03329	+	10.0759i	0.156016	+	0.518250i
$379$	20.6572	+	6.71194i	1.06109	+	0.344769i	0.787012	−	0.616938i	$-0.211627\pi$
$379$	20.6572	+	6.71194i	1.06109	+	0.344769i	0.274079	+	0.961707i	$0.411627\pi$
$380$	−0.428512	−	4.82199i	−0.0219822	−	0.247363i
$381$	5.00884	+	19.2503i	0.256611	+	0.986225i
$382$	−11.9009	+	11.9009i	−0.608905	+	0.608905i
$383$	−21.2826	−	10.8440i	−1.08749	−	0.554104i	−0.184093	−	0.982909i	$-0.558935\pi$
$383$	−21.2826	−	10.8440i	−1.08749	−	0.554104i	−0.903397	+	0.428805i	$0.858935\pi$
$384$	1.33812	+	1.09974i	0.0682856	+	0.0561210i
$385$	1.70034	−	24.8031i	0.0866573	−	1.26409i
$386$	−9.22037	−	12.6908i	−0.469304	−	0.645942i
$387$	−9.08904	+	0.344298i	−0.462022	+	0.0175016i
$388$	0.376840	+	2.37927i	0.0191311	+	0.120789i
$389$	14.6439	−	10.6394i	0.742476	−	0.539440i	−0.151010	−	0.988532i	$-0.548252\pi$
$389$	14.6439	−	10.6394i	0.742476	−	0.539440i	0.893486	+	0.449092i	$0.148252\pi$
$390$	−21.8160	+	11.9256i	−1.10470	+	0.603877i
$391$	−0.393024	−	0.285549i	−0.0198761	−	0.0144408i
$392$	1.31615	−	2.58308i	0.0664754	−	0.130465i
$393$	−13.3816	+	11.8743i	−0.675013	+	0.598982i
$394$	16.8838	−	5.48588i	0.850594	−	0.276375i
$395$	−5.78443	+	25.2123i	−0.291046	+	1.26857i
$396$	−14.9483	−	6.91678i	−0.751180	−	0.347581i
$397$	6.38543	+	12.5321i	0.320476	+	0.628969i	0.993900	−	0.110287i	$-0.0351771\pi$
$397$	6.38543	+	12.5321i	0.320476	+	0.628969i	−0.673424	+	0.739257i	$0.735177\pi$
$398$	0.435130	−	2.74730i	0.0218111	−	0.137710i
$399$	0.452380	−	7.58019i	0.0226473	−	0.379484i
$400$	−4.49995	−	2.17956i	−0.224997	−	0.108978i
$401$			0.841787i			0.0420368i	0.999779	+	0.0210184i	$0.00669086\pi$
$401$			0.841787i			0.0420368i	−0.999779	+	0.0210184i	$0.993309\pi$
$402$	4.22404	+	0.929900i	0.210676	+	0.0463792i
$403$	−17.4911	+	8.91216i	−0.871293	+	0.443946i
$404$	−2.34889	+	7.22915i	−0.116862	+	0.359664i
$405$	−19.8534	+	3.29277i	−0.986524	+	0.163619i
$406$	4.73546	+	14.5742i	0.235017	+	0.723307i
$407$	−25.4091	−	25.4091i	−1.25948	−	1.25948i
$408$	−0.196148	+	0.334122i	−0.00971079	+	0.0165415i
$409$	8.95042	−	12.3192i	0.442570	−	0.609145i	−0.528211	−	0.849113i	$-0.677137\pi$
$409$	8.95042	−	12.3192i	0.442570	−	0.609145i	0.970781	+	0.239968i	$0.0771371\pi$
$410$	2.61592	+	2.18893i	0.129191	+	0.108103i
$411$	−12.5832	−	19.6875i	−0.620685	−	0.971110i
$412$	8.43375	−	1.33577i	0.415501	−	0.0658089i
$413$	−11.4020	+	1.80589i	−0.561054	+	0.0888622i
$414$	−3.17552	−	5.68907i	−0.156068	−	0.279603i
$415$	8.72867	−	21.6895i	0.428474	−	1.06470i
$416$	−3.77332	+	5.19352i	−0.185002	+	0.254633i
$417$	17.0121	+	9.98708i	0.833088	+	0.489069i
$418$	8.40490	+	8.40490i	0.411097	+	0.411097i
$419$	0.0964938	+	0.296977i	0.00471403	+	0.0145083i	0.953386	−	0.301754i	$-0.0975721\pi$
$419$	0.0964938	+	0.296977i	0.00471403	+	0.0145083i	−0.948672	+	0.316262i	$0.897572\pi$
$420$	−6.47631	−	4.42397i	−0.316012	−	0.215868i
$421$	11.7686	−	36.2199i	0.573565	−	1.76525i	−0.0674500	−	0.997723i	$-0.521486\pi$
$421$	11.7686	−	36.2199i	0.573565	−	1.76525i	0.641015	−	0.767528i	$-0.278514\pi$
$422$	12.6351	−	6.43790i	0.615067	−	0.313392i
$423$	4.28055	−	15.0963i	0.208127	−	0.734008i
$424$			12.2576i			0.595283i
$425$	0.324078	−	1.07047i	0.0157201	−	0.0519254i
$426$	−10.4956	−	0.626372i	−0.508515	−	0.0303478i
$427$	−1.00059	+	6.31749i	−0.0484220	+	0.305725i
$428$	−2.31741	−	4.54817i	−0.112016	−	0.219844i
$429$	22.2898	−	56.8321i	1.07616	−	2.74388i
$430$	5.11042	−	4.45470i	0.246446	−	0.214824i
$431$	23.0434	−	7.48726i	1.10996	−	0.360648i	0.304033	−	0.952661i	$-0.401667\pi$
$431$	23.0434	−	7.48726i	1.10996	−	0.360648i	0.805928	+	0.592013i	$0.201667\pi$
$432$	−4.26919	+	2.96209i	−0.205402	+	0.142514i
$433$	−2.46001	+	4.82804i	−0.118220	+	0.232021i	−0.942532	−	0.334116i	$-0.891562\pi$
$433$	−2.46001	+	4.82804i	−0.118220	+	0.232021i	0.824312	+	0.566136i	$0.191562\pi$
$434$	−5.00992	−	3.63992i	−0.240484	−	0.174722i
$435$	−28.8017	+	5.42288i	−1.38094	+	0.260007i
$436$	7.91418	−	5.74999i	0.379021	−	0.275375i
$437$	0.735524	+	4.64392i	0.0351849	+	0.222149i
$438$	−5.27090	+	0.515393i	−0.251853	+	0.0246264i
$439$	−15.7160	−	21.6312i	−0.750083	−	1.03240i	−0.997975	−	0.0636130i	$-0.979738\pi$
$439$	−15.7160	−	21.6312i	−0.750083	−	1.03240i	0.247892	−	0.968788i	$-0.420262\pi$
$440$	11.9080	−	2.98629i	0.567692	−	0.142366i
$441$	6.37822	+	5.91263i	0.303725	+	0.281554i
$442$	−1.27948	−	0.651925i	−0.0608585	−	0.0310089i
$443$	16.9801	−	16.9801i	0.806749	−	0.806749i	−0.177391	−	0.984140i	$-0.556766\pi$
$443$	16.9801	−	16.9801i	0.806749	−	0.806749i	0.984140	+	0.177391i	$0.0567659\pi$
$444$	−10.9709	+	2.85457i	−0.520656	+	0.135472i
$445$	−13.3371	−	15.3002i	−0.632237	−	0.725301i
$446$	−5.16436	−	1.67800i	−0.244539	−	0.0794557i
$447$	−9.47912	+	4.13831i	−0.448347	+	0.195735i
$448$	−2.00015	−	0.316792i	−0.0944980	−	0.0149670i
$449$	−6.98488			−0.329637			−0.164818	−	0.986324i	$-0.552704\pi$
$449$	−6.98488			−0.329637			−0.164818	+	0.986324i	$0.552704\pi$
$450$	9.97337	−	11.2041i	0.470149	−	0.528166i
$451$	−8.37502			−0.394364
$452$	13.0078	+	2.06024i	0.611837	+	0.0969055i
$453$	4.79677	−	2.09413i	0.225372	−	0.0983908i
$454$	18.9792	+	6.16673i	0.890739	+	0.289419i
$455$	14.9376	−	24.9375i	0.700286	−	1.16909i
$456$	3.62899	−	0.944244i	0.169943	−	0.0442183i
$457$	−4.53549	+	4.53549i	−0.212161	+	0.212161i	−0.805185	−	0.593024i	$-0.797934\pi$
$457$	−4.53549	+	4.53549i	−0.212161	+	0.212161i	0.593024	+	0.805185i	$0.297934\pi$
$458$	−10.2523	−	5.22381i	−0.479058	−	0.244092i
$459$	−0.803824	−	0.839567i	−0.0375193	−	0.0391876i
$460$	4.50511	+	1.81302i	0.210052	+	0.0845326i
$461$	−1.73628	−	2.38979i	−0.0808667	−	0.111303i	0.766667	−	0.642045i	$-0.221914\pi$
$461$	−1.73628	−	2.38979i	−0.0808667	−	0.111303i	−0.847534	+	0.530741i	$0.821914\pi$
$462$	19.1661	−	1.87408i	0.891689	−	0.0871901i
$463$	−4.47610	−	28.2610i	−0.208022	−	1.31340i	−0.841761	−	0.539851i	$-0.818481\pi$
$463$	−4.47610	−	28.2610i	−0.208022	−	1.31340i	0.633739	−	0.773547i	$-0.281519\pi$
$464$	−6.12203	+	4.44791i	−0.284208	+	0.206489i
$465$	8.12800	−	8.61407i	0.376927	−	0.399468i
$466$	−3.93564	−	2.85941i	−0.182315	−	0.132460i
$467$	2.07783	−	4.07796i	0.0961504	−	0.188706i	−0.837922	−	0.545791i	$-0.816229\pi$
$467$	2.07783	−	4.07796i	0.0961504	−	0.188706i	0.934072	+	0.357085i	$0.116229\pi$
$468$	−11.9016	−	15.1409i	−0.550152	−	0.699889i
$469$	−4.80942	+	1.56267i	−0.222078	+	0.0721576i
$470$	4.58459	+	10.7597i	0.211471	+	0.496308i
$471$	−3.94325	+	10.0541i	−0.181695	+	0.463267i
$472$	−2.58800	−	5.07924i	−0.119122	−	0.233791i
$473$	−2.60399	+	16.4409i	−0.119731	+	0.755955i
$474$	−20.0012	−	1.19365i	−0.918684	−	0.0548264i
$475$	−9.54379	+	5.10804i	−0.437899	+	0.234373i
$476$		−	0.452990i		−	0.0207628i
$477$	−35.3782	−	10.0314i	−1.61986	−	0.459309i
$478$	−14.9493	+	7.61704i	−0.683765	+	0.348395i
$479$	−8.54601	+	26.3019i	−0.390477	+	1.20176i	0.541951	+	0.840410i	$0.317686\pi$
$479$	−8.54601	+	26.3019i	−0.390477	+	1.20176i	−0.932428	+	0.361355i	$0.882314\pi$
$480$	1.08942	−	3.71661i	0.0497249	−	0.169639i
$481$	−12.9836	−	39.9593i	−0.591999	−	1.82199i
$482$	−12.0274	−	12.0274i	−0.547835	−	0.547835i
$483$	6.56924	+	3.85651i	0.298911	+	0.175477i
$484$	−11.2524	+	15.4876i	−0.511472	+	0.703980i
$485$	4.56413	−	2.86067i	0.207247	−	0.129896i
$486$	−5.05540	−	14.7459i	−0.229317	−	0.668890i
$487$	−29.8920	+	4.73443i	−1.35454	+	0.214538i	−0.791133	−	0.611644i	$-0.790509\pi$
$487$	−29.8920	+	4.73443i	−1.35454	+	0.214538i	−0.563404	+	0.826182i	$0.690509\pi$
$488$	−3.11963	+	0.494100i	−0.141219	+	0.0223669i
$489$	5.34561	+	8.36363i	0.241737	+	0.378216i
$490$	−6.46731	−	0.443356i	−0.292164	−	0.0200288i
$491$	−4.84555	+	6.66933i	−0.218677	+	0.300982i	−0.904235	−	0.427035i	$-0.859558\pi$
$491$	−4.84555	+	6.66933i	−0.218677	+	0.300982i	0.685558	+	0.728018i	$0.259558\pi$
$492$	−1.33760	+	2.27848i	−0.0603036	+	0.102722i
$493$	−1.19693	−	1.19693i	−0.0539071	−	0.0539071i
$494$	4.29473	+	13.2178i	0.193229	+	0.594698i
$495$	−1.12623	+	36.8130i	−0.0506205	+	1.65462i
$496$	0.944961	−	2.90829i	0.0424300	−	0.130586i
$497$	10.9532	−	5.58095i	0.491320	−	0.250340i
$498$	17.6866	+	3.89361i	0.792555	+	0.174477i
$499$			38.0463i			1.70318i	0.524205	+	0.851592i	$0.324363\pi$
$499$			38.0463i			1.70318i	−0.524205	+	0.851592i	$0.675637\pi$
$500$	−0.539345	+	11.1673i	−0.0241203	+	0.499418i
$501$	−1.00629	+	16.8616i	−0.0449576	+	0.753320i
$502$	−4.23979	+	26.7690i	−0.189231	+	1.19476i
$503$	17.3097	+	33.9723i	0.771804	+	1.51475i	0.855237	+	0.518236i	$0.173411\pi$
$503$	17.3097	+	33.9723i	0.771804	+	1.51475i	−0.0834338	+	0.996513i	$0.526589\pi$
$504$	2.55122	−	5.51360i	0.113640	−	0.245595i
$505$	16.9300	−	1.50451i	0.753377	−	0.0669497i
$506$	−11.3402	+	3.68464i	−0.504132	+	0.163802i
$507$	36.5477	−	32.4311i	1.62314	−	1.44032i
$508$	5.21374	−	10.2325i	0.231322	−	0.453996i
$509$	−5.62616	−	4.08765i	−0.249375	−	0.181182i	0.456075	−	0.889942i	$-0.349255\pi$
$509$	−5.62616	−	4.08765i	−0.249375	−	0.181182i	−0.705450	+	0.708760i	$0.749255\pi$
$510$	0.859254	+	0.110637i	0.0380484	+	0.00489909i
$511$	5.00944	−	3.63957i	0.221605	−	0.161005i
$512$	−0.156434	−	0.987688i	−0.00691349	−	0.0436501i
$513$	−0.244613	+	11.2468i	−0.0107999	+	0.496558i
$514$	−9.82444	−	13.5222i	−0.433337	−	0.596438i
$515$	−10.1401	−	16.1784i	−0.446828	−	0.712904i
$516$	4.05698	+	3.33426i	0.178599	+	0.146783i
$517$	−25.5871	−	13.0373i	−1.12532	−	0.573379i
$518$	9.37203	−	9.37203i	0.411783	−	0.411783i
$519$	7.65067	+	29.4036i	0.335827	+	1.29067i
$520$	13.9910	+	3.20995i	0.613548	+	0.140766i
$521$	−20.6631	−	6.71385i	−0.905267	−	0.294139i	−0.180858	−	0.983509i	$-0.557887\pi$
$521$	−20.6631	−	6.71385i	−0.905267	−	0.294139i	−0.724409	+	0.689370i	$0.757887\pi$
$522$	−7.82747	−	21.3096i	−0.342599	−	0.932696i
$523$	42.4737	+	6.72718i	1.85725	+	0.294159i	0.981909	−	0.189354i	$-0.0606393\pi$
$523$	42.4737	+	6.72718i	1.85725	+	0.294159i	0.875337	+	0.483513i	$0.160639\pi$
$524$	10.3290			0.451226
$525$	−3.42404	+	17.2002i	−0.149437	+	0.750678i
$526$	7.29888			0.318246
$527$	0.675613	+	0.107007i	0.0294302	+	0.00466128i
$528$	3.80480	+	8.71519i	0.165583	+	0.379280i
$529$	17.3885	+	5.64988i	0.756023	+	0.245647i
$530$	25.2154	−	10.7440i	1.09528	−	0.466689i
$531$	16.7778	−	3.31276i	0.728093	−	0.143762i
$532$	−3.10010	+	3.10010i	−0.134407	+	0.134407i
$533$	−8.72515	−	4.44569i	−0.377928	−	0.192564i
$534$	9.98255	−	12.1463i	0.431987	−	0.525623i
$535$	−7.32488	+	8.75372i	−0.316682	+	0.378456i
$536$	−1.46779	−	2.02024i	−0.0633987	−	0.0872609i
$537$	−1.95906	−	20.0352i	−0.0845398	−	0.864584i
$538$	4.81318	+	30.3892i	0.207511	+	1.31017i
$539$	12.8769	−	9.35565i	0.554649	−	0.402976i
$540$	9.83537	+	6.18591i	0.423247	+	0.266199i
$541$	−8.60979	−	6.25538i	−0.370164	−	0.268940i	0.387115	−	0.922031i	$-0.373472\pi$
$541$	−8.60979	−	6.25538i	−0.370164	−	0.268940i	−0.757279	+	0.653092i	$0.773472\pi$
$542$	−7.21390	+	14.1581i	−0.309863	+	0.608141i
$543$	4.54638	+	5.12347i	0.195104	+	0.219869i
$544$	0.212742	−	0.0691240i	0.00912123	−	0.00296367i
$545$	−18.7653	−	11.2404i	−0.803816	−	0.481487i
$546$	20.9622	+	8.22147i	0.897100	+	0.351846i
$547$	6.48863	+	12.7347i	0.277434	+	0.544495i	0.987112	−	0.160031i	$-0.0511596\pi$
$547$	6.48863	+	12.7347i	0.277434	+	0.544495i	−0.709678	+	0.704526i	$0.751160\pi$
$548$	−2.11029	+	13.3238i	−0.0901470	+	0.569166i
$549$	1.12697	−	9.40828i	0.0480980	−	0.401536i
$550$	−16.5807	−	21.8786i	−0.707002	−	0.932907i
$551$			16.3828i			0.697929i
$552$	−0.808736	+	3.67366i	−0.0344221	+	0.156361i
$553$	20.8732	−	10.6354i	0.887619	−	0.452265i
$554$	2.97037	−	9.14187i	0.126199	−	0.388401i
$555$	15.4883	+	20.0663i	0.657443	+	0.851769i
$556$	−3.51952	−	10.8320i	−0.149261	−	0.459377i
$557$	3.60663	+	3.60663i	0.152818	+	0.152818i	0.779375	−	0.626557i	$-0.215537\pi$
$557$	3.60663	+	3.60663i	0.152818	+	0.152818i	−0.626557	+	0.779375i	$0.715537\pi$
$558$	7.62062	+	5.10746i	0.322606	+	0.216216i
$559$	−11.4401	+	15.7460i	−0.483866	+	0.665985i
$560$	1.10148	+	4.39220i	0.0465460	+	0.185604i
$561$	−1.79236	+	1.14559i	−0.0756735	+	0.0483667i
$562$	20.4433	−	3.23790i	0.862349	−	0.136583i
$563$	−25.1492	+	3.98324i	−1.05991	+	0.167874i	−0.661965	−	0.749534i	$-0.730277\pi$
$563$	−25.1492	+	3.98324i	−1.05991	+	0.167874i	−0.397948	+	0.917408i	$0.630277\pi$
$564$	−7.63347	+	4.87893i	−0.321427	+	0.205440i
$565$	−7.16341	−	28.5645i	−0.301367	−	1.20172i
$566$	7.17155	−	9.87079i	0.301443	−	0.414900i
$567$	13.8256	+	11.8756i	0.580619	+	0.498729i
$568$	4.29245	+	4.29245i	0.180107	+	0.180107i
$569$	9.49637	+	29.2268i	0.398108	+	1.22525i	0.926514	+	0.376260i	$0.122790\pi$
$569$	9.49637	+	29.2268i	0.398108	+	1.22525i	−0.528406	+	0.848992i	$0.677210\pi$
$570$	−5.12327	−	6.63760i	−0.214590	−	0.278018i
$571$	−6.95564	+	21.4073i	−0.291085	+	0.895866i	0.693424	+	0.720530i	$0.256101\pi$
$571$	−6.95564	+	21.4073i	−0.291085	+	0.895866i	−0.984509	+	0.175336i	$0.943899\pi$
$572$	−31.4039	+	16.0011i	−1.31306	+	0.669039i
$573$	−6.26741	+	28.4695i	−0.261825	+	1.18933i
$574$		−	3.08908i		−	0.128936i
$575$	−0.219194	−	10.8567i	−0.00914101	−	0.452754i
$576$	2.97871	+	0.356805i	0.124113	+	0.0148669i
$577$	6.51823	−	41.1545i	0.271358	−	1.71328i	−0.355943	−	0.934508i	$-0.615840\pi$
$577$	6.51823	−	41.1545i	0.271358	−	1.71328i	0.627301	−	0.778777i	$-0.284160\pi$
$578$	−7.69512	−	15.1025i	−0.320075	−	0.628182i
$579$	−25.2942	−	9.92048i	−1.05119	−	0.412281i
$580$	14.5159	+	8.69506i	0.602741	+	0.361043i
$581$	−20.1376	+	6.54311i	−0.835449	+	0.271454i
$582$	2.76933	+	3.12085i	0.114792	+	0.129363i
$583$	−30.5528	+	59.9633i	−1.26537	+	2.48343i
$584$	2.47370	+	1.79725i	0.102363	+	0.0743708i
$585$	−20.7147	+	37.7542i	−0.856446	+	1.56094i
$586$	−0.175477	+	0.127491i	−0.00724887	+	0.00526661i
$587$	3.88731	+	24.5435i	0.160447	+	1.01302i	0.928148	+	0.372212i	$0.121400\pi$
$587$	3.88731	+	24.5435i	0.160447	+	1.01302i	−0.767701	+	0.640808i	$0.778600\pi$
$588$	−0.488659	−	4.99748i	−0.0201519	−	0.206093i
$589$	−3.89134	−	5.35598i	−0.160340	−	0.220689i
$590$	−8.18016	+	9.77584i	−0.336772	+	0.402465i
$591$	19.5234	−	23.7552i	0.803086	−	0.977160i
$592$	5.83160	+	2.97135i	0.239677	+	0.122122i
$593$	25.7915	−	25.7915i	1.05913	−	1.05913i	0.0609902	−	0.998138i	$-0.480574\pi$
$593$	25.7915	−	25.7915i	1.05913	−	1.05913i	0.998138	−	0.0609902i	$-0.0194258\pi$
$594$	−28.2677	+	3.84910i	−1.15984	+	0.157930i
$595$	−0.931852	+	0.397052i	−0.0382022	+	0.0162775i
$596$	5.67931	+	1.84532i	0.232634	+	0.0755873i
$597$	−1.92761	−	4.41535i	−0.0788920	−	0.180708i
$598$	−13.7702	−	2.18098i	−0.563104	−	0.0891870i
$599$	36.9040			1.50786			0.753929	−	0.656956i	$-0.228156\pi$
$599$	36.9040			1.50786			0.753929	+	0.656956i	$0.228156\pi$
$600$	−8.60038	+	1.01660i	−0.351109	+	0.0415025i
$601$	20.4696			0.834972			0.417486	−	0.908683i	$-0.362911\pi$
$601$	20.4696			0.834972			0.417486	+	0.908683i	$0.362911\pi$
$602$	−6.06415	−	0.960467i	−0.247156	−	0.0391457i
$603$	7.03205	−	2.58302i	0.286367	−	0.105189i
$604$	−2.87393	−	0.933797i	−0.116939	−	0.0379956i
$605$	41.7226	+	9.57237i	1.69626	+	0.389172i
$606$	3.31525	+	12.7414i	0.134673	+	0.517584i
$607$	−4.57545	+	4.57545i	−0.185712	+	0.185712i	−0.793839	−	0.608128i	$-0.791921\pi$
$607$	−4.57545	+	4.57545i	−0.185712	+	0.185712i	0.608128	+	0.793839i	$0.291921\pi$
$608$	−1.92899	−	0.982870i	−0.0782309	−	0.0398607i
$609$	20.5057	+	16.8528i	0.830933	+	0.682908i
$610$	3.75082	+	5.98434i	0.151866	+	0.242299i
$611$	−19.7363	−	27.1646i	−0.798444	−	1.09896i
$612$	0.0254023	+	0.670589i	0.00102683	+	0.0271070i
$613$	4.60648	+	29.0842i	0.186054	+	1.17470i	0.887098	+	0.461581i	$0.152718\pi$
$613$	4.60648	+	29.0842i	0.186054	+	1.17470i	−0.701044	+	0.713118i	$0.747282\pi$
$614$	5.45004	−	3.95968i	0.219946	−	0.159800i
$615$	5.85953	+	0.754469i	0.236279	+	0.0304231i
$616$	−8.99493	−	6.53520i	−0.362416	−	0.263311i
$617$	11.4572	−	22.4860i	0.461250	−	0.905254i	−0.536852	−	0.843676i	$-0.680387\pi$
$617$	11.4572	−	22.4860i	0.461250	−	0.905254i	0.998102	−	0.0615777i	$-0.0196132\pi$
$618$	11.0624	−	9.81635i	0.444994	−	0.394872i
$619$	−2.83846	+	0.922271i	−0.114087	+	0.0370692i	−0.365504	−	0.930810i	$-0.619103\pi$
$619$	−2.83846	+	0.922271i	−0.114087	+	0.0370692i	0.251417	+	0.967879i	$0.419103\pi$
$620$	−6.81096	+	0.605264i	−0.273535	+	0.0243080i
$621$	−9.94112	−	5.34065i	−0.398924	−	0.214313i
$622$	−13.7977	−	27.0796i	−0.553239	−	1.08579i
$623$	−2.87557	+	18.1557i	−0.115207	+	0.727391i
$624$	−0.662395	+	11.0992i	−0.0265170	+	0.444325i
$625$	23.4452	−	8.67882i	0.937809	−	0.347153i
$626$		−	8.73320i		−	0.349049i
$627$	20.1063	+	4.42629i	0.802967	+	0.176769i
$628$	5.55561	−	2.83072i	0.221693	−	0.112958i
$629$	−0.452414	+	1.39239i	−0.0180389	+	0.0555181i
$630$	−13.5783	−	0.415405i	−0.540972	−	0.0165502i
$631$	9.27752	+	28.5533i	0.369332	+	1.13669i	0.947223	+	0.320574i	$0.103876\pi$
$631$	9.27752	+	28.5533i	0.369332	+	1.13669i	−0.577891	+	0.816114i	$0.696124\pi$
$632$	8.17997	+	8.17997i	0.325382	+	0.325382i
$633$	12.4347	−	21.1815i	0.494235	−	0.841887i
$634$	5.93169	−	8.16427i	0.235577	−	0.324245i
$635$	−25.6194	−	1.75630i	−1.01668	−	0.0696966i
$636$	11.4338	+	17.8890i	0.453378	+	0.709346i
$637$	18.3815	−	2.91135i	0.728303	−	0.115352i
$638$	−41.0351	+	6.49933i	−1.62460	+	0.257311i
$639$	−15.9018	+	8.87606i	−0.629065	+	0.351131i
$640$	−1.89467	+	1.18753i	−0.0748935	+	0.0469411i
$641$	10.4719	−	14.4133i	0.413614	−	0.569291i	−0.550481	−	0.834847i	$-0.685556\pi$
$641$	10.4719	−	14.4133i	0.413614	−	0.569291i	0.964095	+	0.265557i	$0.0855558\pi$
$642$	−7.62456	−	4.47604i	−0.300917	−	0.176655i
$643$	10.8997	+	10.8997i	0.429840	+	0.429840i	0.888574	−	0.458734i	$-0.151697\pi$
$643$	10.8997	+	10.8997i	0.429840	+	0.429840i	−0.458734	+	0.888574i	$0.651697\pi$
$644$	−1.35906	−	4.18276i	−0.0535545	−	0.164824i
$645$	3.30296	−	11.2682i	0.130054	−	0.443685i
$646$	0.149651	−	0.460577i	0.00588792	−	0.0181212i
$647$	1.92749	−	0.982107i	0.0757776	−	0.0386106i	−0.415691	−	0.909506i	$-0.636460\pi$
$647$	1.92749	−	0.982107i	0.0757776	−	0.0386106i	0.491469	+	0.870895i	$0.336460\pi$
$648$	−3.46754	+	8.30519i	−0.136218	+	0.326259i
$649$		−	31.2980i		−	1.22855i
$650$	−5.66011	−	31.5948i	−0.222008	−	1.23925i
$651$	−10.7069	−	0.638977i	−0.419635	−	0.0250435i
$652$	0.896493	−	5.66023i	0.0351094	−	0.221672i
$653$	−2.89362	−	5.67905i	−0.113236	−	0.222238i	0.827432	−	0.561565i	$-0.189801\pi$
$653$	−2.89362	−	5.67905i	−0.113236	−	0.222238i	−0.940668	+	0.339327i	$0.889801\pi$
$654$	6.18659	−	15.7739i	0.241915	−	0.616808i
$655$	−9.05355	−	21.2480i	−0.353752	−	0.830229i
$656$	1.45075	−	0.471379i	0.0566424	−	0.0184042i
$657$	−7.21170	+	5.66880i	−0.281355	+	0.221161i
$658$	4.80873	−	9.43766i	0.187464	−	0.367918i
$659$	−27.9601	−	20.3142i	−1.08917	−	0.791330i	−0.109913	−	0.993941i	$-0.535057\pi$
$659$	−27.9601	−	20.3142i	−1.08917	−	0.791330i	−0.979259	+	0.202611i	$0.935057\pi$
$660$	14.5932	−	15.4659i	0.568039	−	0.602009i
$661$	−33.8226	+	24.5736i	−1.31555	+	0.955801i	−0.315572	+	0.948902i	$0.602196\pi$
$661$	−33.8226	+	24.5736i	−1.31555	+	0.955801i	−0.999976	+	0.00689972i	$0.997804\pi$
$662$	3.94076	+	24.8810i	0.153162	+	0.967027i
$663$	−2.47540	+	0.242047i	−0.0961366	+	0.00940032i
$664$	−6.14580	−	8.45897i	−0.238503	−	0.328272i
$665$	9.09455	+	3.65999i	0.352672	+	0.141928i
$666$	−13.3484	+	14.3996i	−0.517242	+	0.557971i
$667$	−14.6431	−	7.46104i	−0.566984	−	0.288893i
$668$	6.89596	−	6.89596i	0.266813	−	0.266813i
$669$	−9.10219	+	2.36834i	−0.351911	+	0.0915654i
$670$	−2.86932	+	4.79017i	−0.110852	+	0.185060i
$671$	−16.4925	−	5.35875i	−0.636687	−	0.206872i
$672$	−3.21455	+	1.40338i	−0.124004	+	0.0541366i
$673$	−5.89775	−	0.934113i	−0.227342	−	0.0360074i	0.0417241	−	0.999129i	$-0.486715\pi$
$673$	−5.89775	−	0.934113i	−0.227342	−	0.0360074i	−0.269066	+	0.963122i	$0.586715\pi$
$674$	30.3577			1.16934
$675$	4.10429	−	25.6545i	0.157974	−	0.987443i
$676$	−28.2106			−1.08502
$677$	−21.6557	−	3.42993i	−0.832297	−	0.131823i	−0.274277	−	0.961651i	$-0.588439\pi$
$677$	−21.6557	−	3.42993i	−0.832297	−	0.131823i	−0.558020	+	0.829828i	$0.688439\pi$
$678$	20.9057	−	9.12681i	0.802877	−	0.350513i
$679$	−4.63951	−	1.50747i	−0.178048	−	0.0578514i
$680$	−0.328667	−	0.377046i	−0.0126038	−	0.0144591i
$681$	33.4509	−	8.70376i	1.28184	−	0.333529i
$682$	11.8717	−	11.8717i	0.454593	−	0.454593i
$683$	11.0839	+	5.64753i	0.424114	+	0.216097i	0.653002	−	0.757356i	$-0.273509\pi$
$683$	11.0839	+	5.64753i	0.424114	+	0.216097i	−0.228888	+	0.973453i	$0.573509\pi$
$684$	4.41543	−	4.76312i	0.168828	−	0.182123i
$685$	29.2584	−	7.33742i	1.11790	−	0.280348i
$686$	11.7830	+	16.2179i	0.449875	+	0.619200i
$687$	−19.8351	+	1.93950i	−0.756757	+	0.0739964i
$688$	−0.474286	−	2.99453i	−0.0180820	−	0.114165i
$689$	−63.6603	+	46.2519i	−2.42526	+	1.76206i
$690$	8.26601	−	1.55635i	0.314682	−	0.0592493i
$691$	6.87945	+	4.99821i	0.261706	+	0.190141i	0.710899	−	0.703294i	$-0.248288\pi$
$691$	6.87945	+	4.99821i	0.261706	+	0.190141i	−0.449193	+	0.893435i	$0.648288\pi$
$692$	7.96363	−	15.6295i	0.302732	−	0.594145i
$693$	26.2233	−	20.6130i	0.996141	−	0.783023i
$694$	23.6412	−	7.68150i	0.897408	−	0.291586i
$695$	−19.1977	+	16.7344i	−0.728209	+	0.634772i
$696$	−4.78565	+	12.2019i	−0.181400	+	0.462513i
$697$	0.154911	+	0.304029i	0.00586765	+	0.0115159i
$698$	−1.19888	+	7.56945i	−0.0453784	+	0.286508i
$699$	−8.41097	−	0.501961i	−0.318132	−	0.0189859i
$700$	8.06981	−	6.11570i	0.305010	−	0.231152i
$701$			19.8483i			0.749660i	0.927093	+	0.374830i	$0.122299\pi$
$701$			19.8483i			0.749660i	−0.927093	+	0.374830i	$0.877701\pi$
$702$	−31.4927	−	10.9953i	−1.18862	−	0.414989i
$703$	12.6252	−	6.43284i	0.476167	−	0.242619i
$704$	1.69660	−	5.22161i	0.0639432	−	0.196797i
$705$	16.7274	+	11.4265i	0.629989	+	0.430346i
$706$	0.837472	+	2.57747i	0.0315187	+	0.0970045i
$707$	−10.8845	−	10.8845i	−0.409353	−	0.409353i
$708$	−8.51483	−	4.99868i	−0.320007	−	0.187862i
$709$	2.74291	−	3.77529i	0.103012	−	0.141784i	−0.754399	−	0.656416i	$-0.772072\pi$
$709$	2.74291	−	3.77529i	0.103012	−	0.141784i	0.857411	+	0.514632i	$0.172072\pi$
$710$	5.06767	−	12.5924i	0.190186	−	0.472586i
$711$	−30.3035	+	16.9148i	−1.13647	+	0.634355i
$712$	−8.96541	+	1.41998i	−0.335993	+	0.0532160i
$713$	6.55944	−	1.03891i	0.245653	−	0.0389076i
$714$	−0.422544	−	0.661102i	−0.0158133	−	0.0247411i
$715$	60.4420	+	50.5763i	2.26040	+	1.89145i
$716$	−6.83154	+	9.40281i	−0.255307	+	0.351399i
$717$	−14.7122	+	25.0610i	−0.549437	+	0.935920i
$718$	2.78928	+	2.78928i	0.104095	+	0.104095i
$719$	−5.35309	−	16.4751i	−0.199637	−	0.614418i	−0.999891	−	0.0147577i	$-0.995302\pi$
$719$	−5.35309	−	16.4751i	−0.199637	−	0.614418i	0.800255	−	0.599660i	$-0.204698\pi$
$720$	−1.87689	−	6.44029i	−0.0699475	−	0.240015i
$721$	−5.34349	+	16.4456i	−0.199002	+	0.612465i
$722$	12.7529	−	6.49795i	0.474615	−	0.241829i
$723$	−28.7721	−	6.33403i	−1.07005	−	0.235565i
$724$		−	3.95472i		−	0.146976i
$725$	5.16334	−	37.4823i	0.191761	−	1.39206i
$726$	−1.97532	+	33.0989i	−0.0733111	+	1.22842i
$727$	−0.833437	+	5.26211i	−0.0309105	+	0.195161i	−0.998311	−	0.0580887i	$-0.981499\pi$
$727$	−0.833437	+	5.26211i	−0.0309105	+	0.195161i	0.967401	+	0.253250i	$0.0814994\pi$
$728$	−5.90192	−	11.5832i	−0.218740	−	0.429301i
$729$	−21.1328	−	16.8049i	−0.782696	−	0.622404i
$730$	1.52892	−	6.66401i	0.0565877	−	0.246646i
$731$	0.645002	−	0.209574i	0.0238563	−	0.00775137i
$732$	−4.09195	+	3.63105i	−0.151243	+	0.134207i
$733$	7.56657	−	14.8502i	0.279478	−	0.548506i	−0.708010	−	0.706202i	$-0.750407\pi$
$733$	7.56657	−	14.8502i	0.279478	−	0.548506i	0.987488	+	0.157697i	$0.0504068\pi$
$734$	−22.7902	−	16.5580i	−0.841201	−	0.611168i
$735$	−9.85209	+	5.38559i	−0.363400	+	0.198651i
$736$	1.75700	−	1.27654i	0.0647640	−	0.0470538i
$737$	−2.14474	−	13.5414i	−0.0790026	−	0.498803i
$738$	0.173226	+	4.57296i	0.00637655	+	0.168333i
$739$	4.33206	+	5.96257i	0.159357	+	0.219337i	0.881228	−	0.472691i	$-0.156717\pi$
$739$	4.33206	+	5.96257i	0.159357	+	0.219337i	−0.721871	+	0.692028i	$0.756717\pi$
$740$	1.00093	−	14.6007i	0.0367948	−	0.536732i
$741$	18.5973	+	15.2843i	0.683187	+	0.561482i
$742$	−22.1171	−	11.2692i	−0.811946	−	0.413707i
$743$	24.6348	−	24.6348i	0.903763	−	0.903763i	−0.0919959	−	0.995759i	$-0.529325\pi$
$743$	24.6348	−	24.6348i	0.903763	−	0.903763i	0.995759	+	0.0919959i	$0.0293247\pi$
$744$	−1.33372	−	5.12587i	−0.0488967	−	0.187923i
$745$	−1.18196	−	13.3004i	−0.0433037	−	0.487291i
$746$	24.8503	+	8.07436i	0.909835	+	0.295623i
$747$	29.4441	−	10.8154i	1.07730	−	0.395716i
$748$	1.21301	+	0.192122i	0.0443521	+	0.00702468i
$749$	10.3371			0.377709
$750$	9.62962	+	16.8009i	0.351624	+	0.613482i
$751$	−16.0915			−0.587188			−0.293594	−	0.955930i	$-0.594851\pi$
$751$	−16.0915			−0.587188			−0.293594	+	0.955930i	$0.594851\pi$
$752$	5.16609	+	0.818228i	0.188388	+	0.0298377i
$753$	18.7822	+	43.0220i	0.684460	+	1.56781i
$754$	−46.2007	−	15.0115i	−1.68253	−	0.546687i
$755$	0.598113	+	6.73049i	0.0217676	+	0.244948i
$756$	−1.41972	−	10.4264i	−0.0516347	−	0.379204i
$757$	−5.11239	+	5.11239i	−0.185813	+	0.185813i	−0.793883	−	0.608070i	$-0.791944\pi$
$757$	−5.11239	+	5.11239i	−0.185813	+	0.185813i	0.608070	+	0.793883i	$0.291944\pi$
$758$	−19.3529	−	9.86081i	−0.702930	−	0.358161i
$759$	−13.1131	+	15.9554i	−0.475975	+	0.579145i
$760$	−0.331089	+	4.82966i	−0.0120099	+	0.175190i
$761$	−17.3299	−	23.8525i	−0.628208	−	0.864654i	0.369711	−	0.929147i	$-0.379457\pi$
$761$	−17.3299	−	23.8525i	−0.628208	−	0.864654i	−0.997918	+	0.0644935i	$0.979457\pi$
$762$	−1.93576	−	19.7969i	−0.0701251	−	0.717166i
$763$	3.09901	+	19.5664i	0.112192	+	0.708350i
$764$	13.6161	−	9.89270i	0.492614	−	0.357905i
$765$	1.35721	−	0.640036i	0.0490702	−	0.0231406i
$766$	19.3242	+	14.0399i	0.698212	+	0.507281i
$767$	16.6138	−	32.6064i	0.599890	−	1.17735i
$768$	−1.14961	−	1.29553i	−0.0414829	−	0.0467485i
$769$	−44.5425	+	14.4727i	−1.60624	+	0.521900i	−0.968641	−	0.248466i	$-0.920074\pi$
$769$	−44.5425	+	14.4727i	−1.60624	+	0.521900i	−0.637602	+	0.770366i	$0.720074\pi$
$770$	−5.55947	+	24.2318i	−0.200350	+	0.873253i
$771$	−26.9513	−	10.5704i	−0.970628	−	0.380684i
$772$	7.12158	+	13.9769i	0.256311	+	0.503039i
$773$	5.89531	−	37.2215i	0.212039	−	1.33876i	−0.620242	−	0.784411i	$-0.712966\pi$
$773$	5.89531	−	37.2215i	0.212039	−	1.33876i	0.832281	−	0.554353i	$-0.187034\pi$
$774$	9.03100	+	1.08178i	0.324613	+	0.0388838i
$775$	7.21500	+	13.4804i	0.259170	+	0.484231i
$776$		−	2.40893i		−	0.0864756i
$777$	4.93561	−	22.4198i	0.177064	−	0.804307i
$778$	−16.1280	+	8.21763i	−0.578217	+	0.294616i
$779$	1.02051	−	3.14082i	0.0365637	−	0.112532i
$780$	23.4130	−	8.36601i	0.838320	−	0.299551i
$781$	10.2991	+	31.6974i	0.368532	+	1.13422i
$782$	0.343516	+	0.343516i	0.0122841	+	0.0122841i
$783$	−31.3009	−	23.7983i	−1.11860	−	0.850481i
$784$	−1.70402	+	2.34539i	−0.0608580	+	0.0837639i
$785$	−10.6927	−	8.94736i	−0.381639	−	0.319345i
$786$	15.0744	−	9.63481i	0.537686	−	0.343662i
$787$	6.11175	−	0.968005i	0.217860	−	0.0345057i	−0.0465501	−	0.998916i	$-0.514823\pi$
$787$	6.11175	−	0.968005i	0.217860	−	0.0345057i	0.264410	+	0.964410i	$0.414823\pi$
$788$	−17.5341	+	2.77713i	−0.624627	+	0.0989313i
$789$	10.6521	−	6.80831i	0.379226	−	0.242382i
$790$	9.65728	−	23.9970i	0.343591	−	0.853775i
$791$	−15.6764	+	21.5767i	−0.557388	+	0.767179i
$792$	13.6822	+	9.17005i	0.486177	+	0.325844i
$793$	−14.3375	−	14.3375i	−0.509138	−	0.509138i
$794$	−4.34636	−	13.3767i	−0.154247	−	0.474722i
$795$	26.7779	−	39.2006i	0.949715	−	1.39030i
$796$	−0.859546	+	2.64541i	−0.0304658	+	0.0937641i
$797$	10.7200	−	5.46214i	0.379724	−	0.193479i	−0.253702	−	0.967282i	$-0.581648\pi$
$797$	10.7200	−	5.46214i	0.379724	−	0.193479i	0.633426	+	0.773804i	$0.281648\pi$
$798$	−1.63261	+	7.41609i	−0.0577939	+	0.262527i
$799$			1.17001i			0.0413919i
$800$	4.10358	+	2.85667i	0.145084	+	0.100999i
$801$	3.23878	−	27.0382i	0.114437	−	0.955348i
$802$	0.131684	−	0.831423i	0.00464994	−	0.0293586i
$803$	7.62141	+	14.9579i	0.268954	+	0.527851i
$804$	−4.02657	−	1.57924i	−0.142006	−	0.0556954i
$805$	−7.41319	+	6.46200i	−0.261280	+	0.227755i
$806$	18.6699	−	6.06622i	0.657620	−	0.213674i
$807$	35.3712	+	39.8610i	1.24512	+	1.40317i
$808$	3.45086	−	6.77270i	0.121401	−	0.238263i
$809$	−31.1568	−	22.6367i	−1.09542	−	0.795866i	−0.115110	−	0.993353i	$-0.536722\pi$
$809$	−31.1568	−	22.6367i	−1.09542	−	0.795866i	−0.980305	+	0.197487i	$0.936722\pi$
$810$	20.1241	−	0.146478i	0.707088	−	0.00514672i
$811$	12.9742	−	9.42631i	0.455586	−	0.331002i	−0.336211	−	0.941787i	$-0.609146\pi$
$811$	12.9742	−	9.42631i	0.455586	−	0.331002i	0.791797	+	0.610784i	$0.209146\pi$
$812$	−2.39724	−	15.1356i	−0.0841267	−	0.531155i
$813$	2.67838	+	27.3916i	0.0939347	+	0.960665i
$814$	21.1214	+	29.0712i	0.740306	+	1.01894i
$815$	−12.4295	+	3.11708i	−0.435388	+	0.109187i
$816$	0.246002	−	0.299324i	0.00861178	−	0.0104784i
$817$	−5.84842	−	2.97992i	−0.204610	−	0.104254i
$818$	−10.7674	+	10.7674i	−0.376472	+	0.376472i
$819$	38.2616	−	7.55473i	1.33697	−	0.263984i
$820$	−2.24129	−	2.57120i	−0.0782691	−	0.0897902i
$821$	5.82793	+	1.89361i	0.203396	+	0.0660875i	0.408943	−	0.912560i	$-0.365897\pi$
$821$	5.82793	+	1.89361i	0.203396	+	0.0660875i	−0.205547	+	0.978647i	$0.565897\pi$
$822$	9.34852	+	21.4135i	0.326067	+	0.746882i
$823$	19.7116	+	3.12202i	0.687105	+	0.108827i	0.490218	−	0.871600i	$-0.336917\pi$
$823$	19.7116	+	3.12202i	0.687105	+	0.108827i	0.196886	+	0.980426i	$0.436917\pi$
$824$	−8.53887			−0.297466
$825$	−44.6063	−	16.4638i	−1.55299	−	0.573196i
$826$	11.5441			0.401670
$827$	16.3031	+	2.58216i	0.566914	+	0.0897904i	0.433311	−	0.901244i	$-0.357345\pi$
$827$	16.3031	+	2.58216i	0.566914	+	0.0897904i	0.133603	+	0.991035i	$0.457345\pi$
$828$	2.24646	+	6.11579i	0.0780699	+	0.212538i
$829$	6.29526	+	2.04545i	0.218643	+	0.0710415i	0.416290	−	0.909232i	$-0.363330\pi$
$829$	6.29526	+	2.04545i	0.218643	+	0.0710415i	−0.197647	+	0.980273i	$0.563330\pi$
$830$	−12.0142	+	20.0570i	−0.417019	+	0.696190i
$831$	−4.19241	−	16.1126i	−0.145433	−	0.558938i
$832$	4.53931	−	4.53931i	0.157372	−	0.157372i
$833$	−0.577809	−	0.294409i	−0.0200199	−	0.0102007i
$834$	−15.2404	−	12.5254i	−0.527731	−	0.433719i
$835$	−20.2302	−	8.14137i	−0.700094	−	0.281744i
$836$	−6.98661	−	9.61624i	−0.241637	−	0.332585i
$837$	15.8859	+	0.345510i	0.549096	+	0.0119426i
$838$	−0.0488483	−	0.308416i	−0.00168744	−	0.0106541i
$839$	−7.33822	+	5.33153i	−0.253343	+	0.184065i	−0.707207	−	0.707006i	$-0.750045\pi$
$839$	−7.33822	+	5.33153i	−0.253343	+	0.184065i	0.453864	+	0.891071i	$0.350045\pi$
$840$	5.70451	+	5.38262i	0.196824	+	0.185718i
$841$	−22.8654	−	16.6127i	−0.788462	−	0.572851i
$842$	−17.2897	+	33.9330i	−0.595843	+	1.16941i
$843$	26.8151	−	23.7947i	0.923560	−	0.819534i
$844$	−13.4866	+	4.38208i	−0.464229	+	0.150837i
$845$	24.7270	+	58.0325i	0.850634	+	1.99638i
$846$	−6.58943	+	14.2408i	−0.226549	+	0.489610i
$847$	−17.6001	−	34.5421i	−0.604745	−	1.18688i
$848$	1.91752	−	12.1067i	0.0658477	−	0.415746i
$849$	1.25894	−	21.0952i	0.0432069	−	0.723984i
$850$	−0.487546	+	1.00659i	−0.0167227	+	0.0345259i
$851$			14.2142i			0.487256i
$852$	10.2684	+	2.26054i	0.351790	+	0.0774447i
$853$	−10.6218	+	5.41209i	−0.363684	+	0.185306i	−0.626277	−	0.779600i	$-0.715422\pi$
$853$	−10.6218	+	5.41209i	−0.363684	+	0.185306i	0.262593	+	0.964907i	$0.415422\pi$
$854$	1.97655	−	6.08318i	0.0676360	−	0.208162i
$855$	−13.6685	−	4.90811i	−0.467452	−	0.167854i
$856$	1.57739	+	4.85470i	0.0539140	+	0.165930i
$857$	7.62449	+	7.62449i	0.260448	+	0.260448i	0.825236	−	0.564788i	$-0.191042\pi$
$857$	7.62449	+	7.62449i	0.260448	+	0.260448i	−0.564788	+	0.825236i	$0.691042\pi$
$858$	−30.9058	+	52.6455i	−1.05511	+	1.79729i
$859$	19.5703	−	26.9362i	0.667730	−	0.919051i	−0.331976	−	0.943288i	$-0.607715\pi$
$859$	19.5703	−	26.9362i	0.667730	−	0.919051i	0.999706	+	0.0242364i	$0.00771544\pi$
$860$	−5.74437	+	3.60041i	−0.195881	+	0.122773i
$861$	−2.88146	−	4.50827i	−0.0981998	−	0.153641i
$862$	−23.9310	+	3.79029i	−0.815092	+	0.129098i
$863$	23.7530	−	3.76211i	0.808562	−	0.128064i	0.261552	−	0.965189i	$-0.415766\pi$
$863$	23.7530	−	3.76211i	0.808562	−	0.128064i	0.547010	+	0.837126i	$0.315766\pi$
$864$	4.68001	−	2.25777i	0.159217	−	0.0768110i
$865$	−39.1319	−	2.68263i	−1.33053	−	0.0912121i
$866$	3.18499	−	4.38377i	0.108230	−	0.148966i
$867$	−25.3179	−	14.8630i	−0.859840	−	0.504774i
$868$	4.37883	+	4.37883i	0.148627	+	0.148627i
$869$	19.6267	+	60.4048i	0.665790	+	2.04909i
$870$	29.2955	−	0.850532i	0.993209	−	0.0288358i
$871$	4.95372	−	15.2460i	0.167850	−	0.516590i
$872$	−8.71624	+	4.44115i	−0.295169	+	0.150396i
$873$	6.95270	+	1.97143i	0.235313	+	0.0667229i
$874$		−	4.70180i		−	0.159041i
$875$	−19.6540	−	11.2400i	−0.664426	−	0.379982i
$876$	5.28663	+	0.315502i	0.178619	+	0.0106598i
$877$	2.17218	−	13.7146i	0.0733494	−	0.463110i	−0.923487	−	0.383630i	$-0.874674\pi$
$877$	2.17218	−	13.7146i	0.0733494	−	0.463110i	0.996836	−	0.0794802i	$-0.0253261\pi$
$878$	12.1386	+	23.8234i	0.409659	+	0.804001i
$879$	−0.137172	+	0.349746i	−0.00462669	+	0.0117966i
$880$	−12.2286	+	1.08670i	−0.412224	+	0.0366328i
$881$	27.0334	−	8.78367i	0.910777	−	0.295930i	0.184099	−	0.982908i	$-0.441063\pi$
$881$	27.0334	−	8.78367i	0.910777	−	0.295930i	0.726678	+	0.686978i	$0.241063\pi$
$882$	−5.37475	−	6.83761i	−0.180977	−	0.230234i
$883$	7.99886	−	15.6986i	0.269183	−	0.528301i	−0.716359	−	0.697732i	$-0.754193\pi$
$883$	7.99886	−	15.6986i	0.269183	−	0.528301i	0.985542	+	0.169430i	$0.0541928\pi$
$884$	1.16174	+	0.844053i	0.0390735	+	0.0283886i
$885$	−2.81950	+	21.8974i	−0.0947764	+	0.736073i
$886$	−19.4273	+	14.1148i	−0.652674	+	0.474195i
$887$	−1.55300	−	9.80527i	−0.0521447	−	0.329229i	−0.999946	−	0.0103679i	$-0.996700\pi$
$887$	−1.55300	−	9.80527i	−0.0521447	−	0.329229i	0.947802	−	0.318861i	$-0.103300\pi$
$888$	11.2824	−	1.10320i	0.378612	−	0.0370210i
$889$	13.6698	+	18.8149i	0.458471	+	0.631032i
$890$	10.7794	+	17.1982i	0.361325	+	0.576487i
$891$	−37.6641	+	31.9852i	−1.26179	+	1.07155i
$892$	4.83828	+	2.46523i	0.161998	+	0.0825419i
$893$	8.00712	−	8.00712i	0.267948	−	0.267948i
$894$	10.0098	−	2.60450i	0.334778	−	0.0871074i
$895$	25.3306	+	5.81157i	0.846709	+	0.194259i
$896$	1.92596	+	0.625783i	0.0643419	+	0.0209060i
$897$	−22.1309	+	9.66169i	−0.738928	+	0.322594i
$898$	6.89889	+	1.09268i	0.230219	+	0.0364631i
$899$	23.1403			0.771773
$900$	−11.6033	+	9.50598i	−0.386776	+	0.316866i
$901$	2.74191			0.0913462
$902$	8.27191	+	1.31014i	0.275424	+	0.0436229i
$903$	−9.74605	+	4.25484i	−0.324328	+	0.141592i
$904$	−12.5254	−	4.06975i	−0.416589	−	0.135358i
$905$	−8.13532	+	3.46637i	−0.270427	+	0.115226i
$906$	−5.06531	+	1.31797i	−0.168284	+	0.0437865i
$907$	16.5638	−	16.5638i	0.549992	−	0.549992i	−0.376446	−	0.926438i	$-0.622854\pi$
$907$	16.5638	−	16.5638i	0.549992	−	0.549992i	0.926438	+	0.376446i	$0.122854\pi$
$908$	−17.7809	−	9.05981i	−0.590079	−	0.300660i
$909$	16.7234	+	15.5026i	0.554679	+	0.514189i
$910$	−18.6548	+	22.2937i	−0.618400	+	0.739030i
$911$	25.0445	+	34.4709i	0.829763	+	1.14207i	0.987967	+	0.154664i	$0.0494295\pi$
$911$	25.0445	+	34.4709i	0.829763	+	1.14207i	−0.158205	+	0.987406i	$0.550571\pi$
$912$	−3.73202	+	0.364920i	−0.123579	+	0.0120837i
$913$	−8.98029	−	56.6993i	−0.297204	−	1.87647i
$914$	5.18916	−	3.77014i	0.171642	−	0.124705i
$915$	11.0561	+	5.23495i	0.365505	+	0.173062i
$916$	9.30889	+	6.76331i	0.307574	+	0.223466i
$917$	−9.49617	+	18.6373i	−0.313591	+	0.615458i
$918$	0.662590	+	0.954976i	0.0218687	+	0.0315189i
$919$	6.21323	−	2.01880i	0.204955	−	0.0665940i	−0.204740	−	0.978816i	$-0.565635\pi$
$919$	6.21323	−	2.01880i	0.204955	−	0.0665940i	0.409696	+	0.912222i	$0.365635\pi$
$920$	−4.16602	−	2.49546i	−0.137350	−	0.0822727i
$921$	4.26035	−	10.8626i	0.140383	−	0.357934i
$922$	1.34106	+	2.63198i	0.0441655	+	0.0866796i
$923$	−6.09617	+	38.4897i	−0.200658	+	1.26690i
$924$	−19.2233	−	1.14723i	−0.632401	−	0.0377412i
$925$	−30.9126	+	10.7387i	−1.01640	+	0.353086i
$926$			28.6132i			0.940289i
$927$	6.98808	−	24.6450i	0.229519	−	0.809449i
$928$	6.74246	−	3.43546i	0.221332	−	0.112774i
$929$	−8.15479	+	25.0979i	−0.267550	+	0.823434i	0.723545	+	0.690277i	$0.242511\pi$
$929$	−8.15479	+	25.0979i	−0.267550	+	0.823434i	−0.991095	+	0.133157i	$0.957489\pi$
$930$	−9.37547	+	7.23652i	−0.307434	+	0.237295i
$931$	1.93950	+	5.96916i	0.0635644	+	0.195631i
$932$	3.43987	+	3.43987i	0.112677	+	0.112677i
$933$	−45.3962	−	26.6501i	−1.48621	−	0.872486i
$934$	−2.69018	+	3.70271i	−0.0880254	+	0.121157i
$935$	−0.668004	−	2.66370i	−0.0218461	−	0.0871124i
$936$	9.38652	+	16.8163i	0.306808	+	0.549659i
$937$	43.6912	−	6.92001i	1.42733	−	0.226067i	0.605521	−	0.795829i	$-0.292965\pi$
$937$	43.6912	−	6.92001i	1.42733	−	0.226067i	0.821809	+	0.569763i	$0.192965\pi$
$938$	4.99466	−	0.791077i	0.163081	−	0.0258296i
$939$	−8.14622	−	12.7454i	−0.265842	−	0.415930i
$940$	−2.84496	−	11.3444i	−0.0927923	−	0.370014i
$941$	−3.24570	+	4.46733i	−0.105807	+	0.145631i	−0.858637	−	0.512584i	$-0.828688\pi$
$941$	−3.24570	+	4.46733i	−0.105807	+	0.145631i	0.752830	+	0.658215i	$0.228688\pi$
$942$	5.46750	−	9.31342i	0.178141	−	0.303448i
$943$	2.34254	+	2.34254i	0.0762837	+	0.0762837i
$944$	1.76157	+	5.42156i	0.0573342	+	0.176457i
$945$	−20.2039	+	12.0594i	−0.657233	+	0.392293i
$946$	5.14385	−	15.8312i	0.167241	−	0.514715i
$947$	−3.30825	+	1.68564i	−0.107504	+	0.0547759i	−0.506916	−	0.861996i	$-0.669214\pi$
$947$	−3.30825	+	1.68564i	−0.107504	+	0.0547759i	0.399412	+	0.916772i	$0.369214\pi$
$948$	19.5682	+	4.30783i	0.635545	+	0.139912i
$949$			19.6288i			0.637179i
$950$	10.2254	−	3.55217i	0.331755	−	0.115248i
$951$	1.04129	−	17.4481i	0.0337662	−	0.565794i
$952$	−0.0708632	+	0.447413i	−0.00229669	+	0.0145007i
$953$	19.8647	+	38.9868i	0.643482	+	1.26290i	0.950359	+	0.311156i	$0.100716\pi$
$953$	19.8647	+	38.9868i	0.643482	+	1.26290i	−0.306877	+	0.951749i	$0.599284\pi$
$954$	33.3733	+	15.4423i	1.08050	+	0.499963i
$955$	−32.2851	−	19.3389i	−1.04472	−	0.625791i
$956$	15.9568	−	5.18468i	0.516080	−	0.167685i
$957$	−53.8250	+	47.7623i	−1.73991	+	1.54394i
$958$	12.5553	−	24.6412i	0.405644	−	0.796121i
$959$	−22.1008	−	16.0572i	−0.713673	−	0.518514i
$960$	−1.65741	+	3.50043i	−0.0534927	+	0.112976i
$961$	17.5143	−	12.7249i	0.564978	−	0.410481i
$962$	6.57270	+	41.4984i	0.211912	+	1.33796i
$963$	−15.3026	+	0.579672i	−0.493120	+	0.0186797i
$964$	9.99786	+	13.7609i	0.322009	+	0.443208i
$965$	22.5099	−	26.9009i	0.724620	−	0.865969i
$966$	−5.88507	−	4.83669i	−0.189349	−	0.155618i
$967$	22.3283	+	11.3768i	0.718028	+	0.365854i	0.774520	−	0.632549i	$-0.217991\pi$
$967$	22.3283	+	11.3768i	0.718028	+	0.365854i	−0.0564917	+	0.998403i	$0.517991\pi$
$968$	13.5366	−	13.5366i	0.435084	−	0.435084i
$969$	−0.211218	−	0.811768i	−0.00678530	−	0.0260777i
$970$	−4.95545	+	2.11146i	−0.159110	+	0.0677950i
$971$	26.2601	+	8.53244i	0.842728	+	0.273819i	0.698397	−	0.715711i	$-0.253897\pi$
$971$	26.2601	+	8.53244i	0.842728	+	0.273819i	0.144331	+	0.989529i	$0.453897\pi$
$972$	2.68638	+	15.3552i	0.0861657	+	0.492520i
$973$	22.7804	+	3.60807i	0.730308	+	0.115669i
$974$	30.2646			0.969741
$975$	−37.7317	−	40.8303i	−1.20838	−	1.30762i
$976$	3.15851			0.101102
$977$	−9.20136	−	1.45735i	−0.294378	−	0.0466248i	0.00749885	−	0.999972i	$-0.497613\pi$
$977$	−9.20136	−	1.45735i	−0.294378	−	0.0466248i	−0.301876	+	0.953347i	$0.597613\pi$
$978$	−3.97144	−	9.09689i	−0.126993	−	0.290887i
$979$	−47.3974	−	15.4004i	−1.51483	−	0.492197i
$980$	6.31834	+	1.44961i	0.201832	+	0.0463061i
$981$	−5.68488	−	28.7915i	−0.181504	−	0.919243i
$982$	5.82921	−	5.82921i	0.186017	−	0.186017i
$983$	41.2314	+	21.0084i	1.31508	+	0.670065i	0.963905	−	0.266245i	$-0.0857832\pi$
$983$	41.2314	+	21.0084i	1.31508	+	0.670065i	0.351172	+	0.936311i	$0.385783\pi$
$984$	1.67756	−	2.04119i	0.0534788	−	0.0650706i
$985$	21.0818	+	33.6355i	0.671722	+	1.07172i
$986$	0.994954	+	1.36944i	0.0316858	+	0.0436118i
$987$	−1.78538	−	18.2590i	−0.0568294	−	0.581191i
$988$	−2.17413	−	13.7269i	−0.0691684	−	0.436712i
$989$	5.32698	−	3.87028i	0.169388	−	0.123068i
$990$	6.87119	−	36.1836i	0.218381	−	1.14999i
$991$	−18.5452	−	13.4739i	−0.589107	−	0.428011i	0.252889	−	0.967495i	$-0.418619\pi$
$991$	−18.5452	−	13.4739i	−0.589107	−	0.428011i	−0.841996	+	0.539484i	$0.818619\pi$
$992$	−1.38828	+	2.72466i	−0.0440781	+	0.0865081i
$993$	28.9599	+	32.6359i	0.919015	+	1.03567i
$994$	−11.6914	+	3.79878i	−0.370830	+	0.120490i
$995$	6.19532	−	0.550554i	0.196405	−	0.0174537i
$996$	−16.8597	−	6.61246i	−0.534221	−	0.209524i
$997$	21.8872	+	42.9560i	0.693173	+	1.36043i	0.922087	+	0.386983i	$0.126483\pi$
$997$	21.8872	+	42.9560i	0.693173	+	1.36043i	−0.228914	+	0.973447i	$0.573517\pi$
$998$	5.95175	−	37.5779i	0.188399	−	1.18951i
$999$	−6.04925	+	33.4663i	−0.191390	+	1.05883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.23.1	✓	80
3.2	odd	2	inner	150.2.l.a.23.6	yes	80
5.2	odd	4		750.2.l.c.407.9		80
5.3	odd	4		750.2.l.a.407.2		80
5.4	even	2		750.2.l.b.593.10		80
15.2	even	4		750.2.l.c.407.4		80
15.8	even	4		750.2.l.a.407.7		80
15.14	odd	2		750.2.l.b.593.5		80
25.9	even	10		750.2.l.a.293.7		80
25.12	odd	20	inner	150.2.l.a.137.6	yes	80
25.13	odd	20		750.2.l.b.707.5		80
25.16	even	5		750.2.l.c.293.4		80
75.38	even	20		750.2.l.b.707.10		80
75.41	odd	10		750.2.l.c.293.9		80
75.59	odd	10		750.2.l.a.293.2		80
75.62	even	20	inner	150.2.l.a.137.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.23.1	✓	80	1.1	even	1	trivial
150.2.l.a.23.6	yes	80	3.2	odd	2	inner
150.2.l.a.137.1	yes	80	75.62	even	20	inner
150.2.l.a.137.6	yes	80	25.12	odd	20	inner
750.2.l.a.293.2		80	75.59	odd	10
750.2.l.a.293.7		80	25.9	even	10
750.2.l.a.407.2		80	5.3	odd	4
750.2.l.a.407.7		80	15.8	even	4
750.2.l.b.593.5		80	15.14	odd	2
750.2.l.b.593.10		80	5.4	even	2
750.2.l.b.707.5		80	25.13	odd	20
750.2.l.b.707.10		80	75.38	even	20
750.2.l.c.293.4		80	25.16	even	5
750.2.l.c.293.9		80	75.41	odd	10
750.2.l.c.407.4		80	15.2	even	4
750.2.l.c.407.9		80	5.2	odd	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 - 0.156434i) q^{2} +(-1.58737 + 0.693000i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-0.197931 - 2.22729i) q^{5} +(1.67624 - 0.436149i) q^{6} +(-1.43195 + 1.43195i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(2.03950 - 2.20010i) q^{9} +O(q^{10})\)	\(q+(-0.987688 - 0.156434i) q^{2} +(-1.58737 + 0.693000i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-0.197931 - 2.22729i) q^{5} +(1.67624 - 0.436149i) q^{6} +(-1.43195 + 1.43195i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(2.03950 - 2.20010i) q^{9} +(-0.152931 + 2.23083i) q^{10} +(-3.22713 - 4.44177i) q^{11} +(-1.72383 + 0.168558i) q^{12} +(-1.00424 - 6.34051i) q^{13} +(1.63832 - 1.19031i) q^{14} +(1.85770 + 3.39837i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-0.101553 + 0.199309i) q^{17} +(-2.35856 + 1.85396i) q^{18} +(2.05900 - 0.669009i) q^{19} +(0.500027 - 2.17944i) q^{20} +(1.28069 - 3.26537i) q^{21} +(2.49256 + 4.89192i) q^{22} +(-0.339741 + 2.14504i) q^{23} +(1.72897 + 0.103184i) q^{24} +(-4.92165 + 0.881699i) q^{25} +6.41955i q^{26} +(-1.71278 + 4.90575i) q^{27} +(-1.80436 + 0.919366i) q^{28} +(-2.33841 + 7.19688i) q^{29} +(-1.30321 - 3.64714i) q^{30} +(-0.944961 - 2.90829i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.20081 + 4.81433i) q^{33} +(0.131482 - 0.180969i) q^{34} +(3.47279 + 2.90593i) q^{35} +(2.61955 - 1.46218i) q^{36} +(6.46438 - 1.02386i) q^{37} +(-2.13830 + 0.338674i) q^{38} +(5.98808 + 9.36882i) q^{39} +(-0.834811 + 2.07439i) q^{40} +(0.896615 - 1.23409i) q^{41} +(-1.77574 + 3.02482i) q^{42} +(-2.14384 - 2.14384i) q^{43} +(-1.69660 - 5.22161i) q^{44} +(-5.30394 - 4.10709i) q^{45} +(0.671116 - 2.06548i) q^{46} +(4.66039 - 2.37459i) q^{47} +(-1.69155 - 0.372385i) q^{48} +2.89906i q^{49} +(4.99898 - 0.100928i) q^{50} +(0.0230812 - 0.386754i) q^{51} +(1.00424 - 6.34051i) q^{52} +(-5.56485 - 10.9216i) q^{53} +(2.45912 - 4.57742i) q^{54} +(-9.25436 + 8.06693i) q^{55} +(1.92596 - 0.625783i) q^{56} +(-2.80477 + 2.48885i) q^{57} +(3.43546 - 6.74246i) q^{58} +(4.61185 + 3.35071i) q^{59} +(0.716626 + 3.80611i) q^{60} +(2.55529 - 1.85653i) q^{61} +(0.478370 + 3.02031i) q^{62} +(0.229968 + 6.07088i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-13.9234 + 3.49171i) q^{65} +(-7.34671 - 6.03795i) q^{66} +(2.22498 + 1.13368i) q^{67} +(-0.158173 + 0.158173i) q^{68} +(-0.947217 - 3.64041i) q^{69} +(-2.97544 - 3.41342i) q^{70} +(-5.77333 - 1.87587i) q^{71} +(-2.81603 + 1.03439i) q^{72} +(-3.02002 - 0.478324i) q^{73} -6.54496 q^{74} +(7.20147 - 4.81029i) q^{75} +2.16496 q^{76} +(10.9815 + 1.73929i) q^{77} +(-4.44875 - 10.1902i) q^{78} +(-11.0020 - 3.57478i) q^{79} +(1.14904 - 1.91826i) q^{80} +(-0.680873 - 8.97421i) q^{81} +(-1.07863 + 1.07863i) q^{82} +(9.31624 + 4.74686i) q^{83} +(2.22707 - 2.70980i) q^{84} +(0.464020 + 0.186739i) q^{85} +(1.78208 + 2.45282i) q^{86} +(-1.27552 - 13.0446i) q^{87} +(0.858876 + 5.42273i) q^{88} +(7.34358 - 5.33542i) q^{89} +(4.59615 + 4.88625i) q^{90} +(10.5173 + 7.64126i) q^{91} +(-0.985966 + 1.93507i) q^{92} +(3.51545 + 3.96168i) q^{93} +(-4.97448 + 1.61631i) q^{94} +(-1.89762 - 4.45357i) q^{95} +(1.61247 + 0.632416i) q^{96} +(1.09363 + 2.14637i) q^{97} +(0.453513 - 2.86337i) q^{98} +(-16.3541 - 1.95898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

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