LMFDB - Embedded newform 150.2.l.a.137.1

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			137.1
Character	$\chi$	$=$	150.137
Dual form			150.2.l.a.23.1

$q$-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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{9}{20}\right)$

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	0.382663	−	0.923888i	$-0.375007\pi$
$7$	−1.43195	−	1.43195i	−0.541225	−	0.541225i	−0.923888	+	0.382663i	$0.875007\pi$
$8$	−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	−0.0325093	+	0.999471i	$0.510350\pi$
$11$	−3.22713	+	4.44177i	−0.973017	+	1.33924i	−0.940508	+	0.339772i	$0.889650\pi$
$12$	−1.72383	−	0.168558i	−0.497627	−	0.0486584i
$13$	−1.00424	+	6.34051i	−0.278526	+	1.75854i	0.310638	+	0.950528i	$0.399457\pi$
$13$	−1.00424	+	6.34051i	−0.278526	+	1.75854i	−0.589164	+	0.808014i	$0.700543\pi$
$14$	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	0.878364	−	0.477993i	$-0.158636\pi$
$17$	−0.101553	−	0.199309i	−0.0246303	−	0.0483396i	−0.902994	+	0.429654i	$0.858636\pi$
$18$	−2.35856	−	1.85396i	−0.555919	−	0.436984i
$19$	2.05900	+	0.669009i	0.472366	+	0.153481i	0.535520	−	0.844523i	$-0.320116\pi$
$19$	2.05900	+	0.669009i	0.472366	+	0.153481i	−0.0631534	+	0.998004i	$0.520116\pi$
$20$	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	−0.997457	−	0.0712640i	$-0.977297\pi$
$23$	−0.339741	−	2.14504i	−0.0708408	−	0.447271i	0.926617	−	0.376007i	$-0.122703\pi$
$24$	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	−0.893872	−	0.448322i	$-0.852022\pi$
$29$	−2.33841	−	7.19688i	−0.434231	−	1.33643i	0.459641	−	0.888105i	$-0.347978\pi$
$30$	−1.30321	+	3.64714i	−0.237932	+	0.665874i
$31$	−0.944961	+	2.90829i	−0.169720	+	0.522344i	−0.999353	−	0.0359646i	$-0.988550\pi$
$31$	−0.944961	+	2.90829i	−0.169720	+	0.522344i	0.829633	+	0.558309i	$0.188550\pi$
$32$	−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	0.663235	−	0.748411i	$-0.269183\pi$
$37$	6.46438	+	1.02386i	1.06274	+	0.168321i	0.399502	+	0.916732i	$0.369183\pi$
$38$	−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	0.873271	−	0.487235i	$-0.161994\pi$
$41$	0.896615	+	1.23409i	0.140028	+	0.192732i	−0.733243	+	0.679966i	$0.761994\pi$
$42$	−1.77574	−	3.02482i	−0.274003	−	0.466741i
$43$	−2.14384	+	2.14384i	−0.326933	+	0.326933i	−0.851419	−	0.524486i	$-0.824258\pi$
$43$	−2.14384	+	2.14384i	−0.326933	+	0.326933i	0.524486	+	0.851419i	$0.324258\pi$
$44$	−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	0.759554	−	0.650444i	$-0.225417\pi$
$47$	4.66039	+	2.37459i	0.679788	+	0.346369i	−0.0797657	+	0.996814i	$0.525417\pi$
$48$	−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	0.0986812	+	0.995119i	$0.468538\pi$
$53$	−5.56485	+	10.9216i	−0.764390	+	1.50020i	−0.863072	+	0.505082i	$0.831462\pi$
$54$	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	−0.245613	−	0.969368i	$-0.578989\pi$
$59$	4.61185	−	3.35071i	0.600412	−	0.436225i	0.846025	+	0.533143i	$0.178989\pi$
$60$	0.716626	−	3.80611i	0.0925160	−	0.491366i
$61$	2.55529	+	1.85653i	0.327171	+	0.237704i	0.739229	−	0.673454i	$-0.235190\pi$
$61$	2.55529	+	1.85653i	0.327171	+	0.237704i	−0.412058	+	0.911158i	$0.635190\pi$
$62$	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	−0.312766	−	0.949830i	$-0.601255\pi$
$67$	2.22498	−	1.13368i	0.271824	−	0.138501i	0.584590	+	0.811329i	$0.301255\pi$
$68$	−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	−0.630856	−	0.775900i	$-0.717296\pi$
$71$	−5.77333	+	1.87587i	−0.685168	+	0.222625i	−0.0543113	+	0.998524i	$0.517296\pi$
$72$	−2.81603	−	1.03439i	−0.331873	−	0.121904i
$73$	−3.02002	+	0.478324i	−0.353467	+	0.0559836i	−0.330643	−	0.943756i	$-0.607266\pi$
$73$	−3.02002	+	0.478324i	−0.353467	+	0.0559836i	−0.0228237	+	0.999740i	$0.507266\pi$
$74$	−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	−0.853543	−	0.521022i	$-0.825551\pi$
$79$	−11.0020	+	3.57478i	−1.23783	+	0.402194i	−0.384282	+	0.923216i	$0.625551\pi$
$80$	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	0.139492	−	0.990223i	$-0.455453\pi$
$83$	9.31624	−	4.74686i	1.02259	−	0.521036i	0.883099	+	0.469187i	$0.155453\pi$
$84$	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	0.904504	−	0.426466i	$-0.140241\pi$
$89$	7.34358	+	5.33542i	0.778418	+	0.565554i	−0.126086	+	0.992019i	$0.540241\pi$
$90$	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	−0.828798	−	0.559548i	$-0.810975\pi$
$97$	1.09363	−	2.14637i	0.111041	−	0.217931i	0.939839	+	0.341617i	$0.110975\pi$
$98$	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	$-0.876552\pi$
$101$		−	7.60118i		−	0.756346i	0.925735	−	0.378173i	$-0.123448\pi$
$102$	−0.0832988	−	0.378382i	−0.00824781	−	0.0374654i
$103$	7.60819	+	3.87657i	0.749657	+	0.381970i	0.786693	−	0.617344i	$-0.211791\pi$
$103$	7.60819	+	3.87657i	0.749657	+	0.381970i	−0.0370356	+	0.999314i	$0.511791\pi$
$104$	−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	−0.859714	−	0.510775i	$-0.829358\pi$
$107$	−3.60945	+	3.60945i	−0.348939	+	0.348939i	0.510775	+	0.859714i	$0.329358\pi$
$108$	−3.14491	−	4.13637i	−0.302619	−	0.398022i
$109$	5.74999	+	7.91418i	0.550749	+	0.758041i	0.990114	−	0.140268i	$-0.0447964\pi$
$109$	5.74999	+	7.91418i	0.550749	+	0.758041i	−0.439365	+	0.898309i	$0.644796\pi$
$110$	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	0.734642	−	0.678454i	$-0.237350\pi$
$113$	13.0078	+	2.06024i	1.22367	+	0.193811i	0.489033	+	0.872266i	$0.337350\pi$
$114$	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	0.929567	+	0.368654i	$0.120181\pi$
$127$	1.79653	+	11.3429i	0.159417	+	1.00652i	−0.770150	+	0.637863i	$0.779819\pi$
$128$	−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	0.704911	−	0.709295i	$-0.250987\pi$
$131$	9.82350	+	3.19185i	0.858284	+	0.278873i	0.153372	+	0.988169i	$0.450987\pi$
$132$	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	−0.717057	−	0.697014i	$-0.754511\pi$
$137$	2.11029	−	13.3238i	0.180294	−	1.13833i	0.897351	−	0.441317i	$-0.145489\pi$
$138$	0.366069	−	3.74377i	0.0311619	−	0.318691i
$139$	−6.69452	+	9.21421i	−0.567822	+	0.781539i	−0.992295	−	0.123901i	$-0.960459\pi$
$139$	−6.69452	+	9.21421i	−0.567822	+	0.781539i	0.424473	+	0.905441i	$0.360459\pi$
$140$	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	0.860806	−	0.508933i	$-0.169960\pi$
$157$	4.40896	+	4.40896i	0.351873	+	0.351873i	−0.508933	+	0.860806i	$0.669960\pi$
$158$	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	0.927382	+	0.374116i	$0.122054\pi$
$163$	−0.896493	+	5.66023i	−0.0702187	+	0.443344i	−0.997601	+	0.0692282i	$0.977946\pi$
$164$	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	0.996447	−	0.0842276i	$-0.0268423\pi$
$167$	4.42748	+	8.68941i	0.342608	+	0.672407i	−0.653838	+	0.756634i	$0.726842\pi$
$168$	−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	0.840354	+	0.542037i	$0.182347\pi$
$173$	2.74408	+	17.3254i	0.208629	+	1.31723i	−0.631726	+	0.775192i	$0.717653\pi$
$174$	−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	−0.990880	−	0.134750i	$-0.956977\pi$
$179$	−3.59155	−	11.0537i	−0.268445	−	0.826190i	0.722434	−	0.691440i	$-0.243023\pi$
$180$	−3.77519	+	5.54509i	−0.281386	+	0.413306i
$181$	−1.22208	+	3.76116i	−0.0908362	+	0.279565i	−0.986146	−	0.165879i	$-0.946954\pi$
$181$	−1.22208	+	3.76116i	−0.0908362	+	0.279565i	0.895310	+	0.445444i	$0.146954\pi$
$182$	−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	0.999653	+	0.0263574i	$0.00839078\pi$
$191$	9.89270	+	13.6161i	0.715810	+	0.985228i	−0.283842	+	0.958871i	$0.591609\pi$
$192$	−1.49368	+	0.876876i	−0.107797	+	0.0632830i
$193$	11.0921	−	11.0921i	0.798428	−	0.798428i	−0.184419	−	0.982848i	$-0.559040\pi$
$193$	11.0921	−	11.0921i	0.798428	−	0.798428i	0.982848	+	0.184419i	$0.0590404\pi$
$194$	−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	−0.211809	−	0.977311i	$-0.567936\pi$
$197$	−15.8178	−	8.05955i	−1.12697	−	0.574219i	−0.915160	+	0.403091i	$0.867936\pi$
$198$	15.8463	−	4.49320i	1.12615	−	0.319318i
$199$		−	2.78155i		−	0.197179i	−0.995128	−	0.0985894i	$-0.968567\pi$
$199$		−	2.78155i		−	0.197179i	0.995128	−	0.0985894i	$-0.0314330\pi$
$200$	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	0.118108	−	0.993001i	$-0.462317\pi$
$211$	−11.4724	−	8.33520i	−0.789794	−	0.573819i	−0.907902	+	0.419182i	$0.862317\pi$
$212$	−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	0.0257485	−	0.999668i	$-0.491803\pi$
$223$	5.36327	−	0.849459i	0.359151	−	0.0568840i	0.333403	+	0.942784i	$0.391803\pi$
$224$	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	−0.771320	−	0.636448i	$-0.780403\pi$
$227$	−19.7103	+	3.12180i	−1.30822	+	0.207201i	−0.536896	+	0.843649i	$0.680403\pi$
$228$	−3.43659	−	1.50032i	−0.227594	−	0.0993609i
$229$	10.9433	−	3.55568i	0.723151	−	0.234966i	0.0757621	−	0.997126i	$-0.475861\pi$
$229$	10.9433	−	3.55568i	0.723151	−	0.234966i	0.647389	+	0.762160i	$0.275861\pi$
$230$	−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	−0.306208	−	0.951964i	$-0.599060\pi$
$233$	4.33449	−	2.20854i	0.283962	−	0.144686i	0.590171	+	0.807279i	$0.299060\pi$
$234$	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	0.932724	−	0.360592i	$-0.117425\pi$
$239$	13.5737	+	9.86185i	0.878008	+	0.637910i	−0.0547159	+	0.998502i	$0.517425\pi$
$240$	−0.494600	−	3.84127i	−0.0319263	−	0.247953i
$241$	13.7609	−	9.99786i	0.886416	−	0.644019i	−0.0485253	−	0.998822i	$-0.515452\pi$
$241$	13.7609	−	9.99786i	0.886416	−	0.644019i	0.934941	+	0.354803i	$0.115452\pi$
$242$	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	$0.326660\pi$
$251$			27.1027i			1.71071i	−0.518046	+	0.855353i	$0.673340\pi$
$252$	−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	−0.234805	−	0.972043i	$-0.575445\pi$
$257$	11.8188	−	11.8188i	0.737238	−	0.737238i	0.972043	+	0.234805i	$0.0754451\pi$
$258$	−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	−0.0698415	−	0.997558i	$-0.522249\pi$
$263$	−7.20902	−	1.14180i	−0.444527	−	0.0704062i	−0.374686	+	0.927152i	$0.622249\pi$
$264$	−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	0.0398701	+	0.999205i	$0.487306\pi$
$269$	−9.50784	+	29.2621i	−0.579703	+	1.78414i	−0.619573	+	0.784939i	$0.712694\pi$
$270$	−10.6820	+	4.57116i	−0.650084	+	0.278192i
$271$	4.91027	+	15.1123i	0.298278	+	0.918004i	0.982101	+	0.188356i	$0.0603160\pi$
$271$	4.91027	+	15.1123i	0.298278	+	0.918004i	−0.683823	+	0.729648i	$0.739684\pi$
$272$	−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	−0.990784	−	0.135449i	$-0.956752\pi$
$277$	−1.50370	−	9.49399i	−0.0903486	−	0.570438i	0.900436	−	0.434989i	$-0.143248\pi$
$278$	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	−0.344062	−	0.938947i	$-0.611803\pi$
$281$	−19.6851	−	6.39607i	−1.17431	−	0.381558i	−0.830251	+	0.557389i	$0.811803\pi$
$282$	6.77626	+	6.01300i	0.403520	+	0.358069i
$283$	−5.53912	−	10.8711i	−0.329267	−	0.646222i	0.665723	−	0.746199i	$-0.268123\pi$
$283$	−5.53912	−	10.8711i	−0.329267	−	0.646222i	−0.994990	+	0.0999766i	$0.968123\pi$
$284$	−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	0.711573	−	0.702613i	$-0.247983\pi$
$293$	0.153372	+	0.153372i	0.00896009	+	0.00896009i	−0.702613	+	0.711573i	$0.747983\pi$
$294$	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	0.557984	−	0.829852i	$-0.311575\pi$
$307$	−4.76351	−	4.76351i	−0.271868	−	0.271868i	−0.829852	+	0.557984i	$0.811575\pi$
$308$	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	0.0959647	−	0.995385i	$-0.469406\pi$
$311$	17.8640	−	24.5877i	1.01298	−	1.39424i	0.917012	−	0.398859i	$-0.130594\pi$
$312$	−1.08206	+	11.0662i	−0.0612598	+	0.626501i
$313$	1.36617	−	8.62568i	0.0772206	−	0.487552i	−0.918522	−	0.395371i	$-0.870616\pi$
$313$	1.36617	−	8.62568i	0.0772206	−	0.487552i	0.995742	−	0.0921812i	$-0.0293839\pi$
$314$	−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	0.725816	−	0.687889i	$-0.241462\pi$
$317$	−4.58149	−	8.99167i	−0.257322	−	0.505023i	−0.983138	+	0.182866i	$0.941462\pi$
$318$	−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	0.472341	+	0.881416i	$0.343409\pi$
$331$	−7.78449	+	23.9582i	−0.427874	+	1.31686i	−0.900215	+	0.435445i	$0.856591\pi$
$332$	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	−0.728683	−	0.684852i	$-0.759867\pi$
$337$	−29.9840	−	4.74900i	−1.63333	−	0.258694i	−0.904649	+	0.426157i	$0.859867\pi$
$338$	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	−0.256337	−	0.966587i	$-0.582516\pi$
$347$	−22.1485	−	11.2852i	−1.18899	−	0.605823i	−0.932657	+	0.360765i	$0.882516\pi$
$348$	2.81793	+	12.8003i	0.151057	+	0.686170i
$349$			7.66380i			0.410234i	0.978737	+	0.205117i	$0.0657575\pi$
$349$			7.66380i			0.410234i	−0.978737	+	0.205117i	$0.934243\pi$
$350$	−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	−0.921429	−	0.388547i	$-0.872977\pi$
$353$	−1.23037	+	2.41473i	−0.0654859	+	0.128523i	0.855943	+	0.517070i	$0.172977\pi$
$354$	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	−0.668807	−	0.743436i	$-0.733195\pi$
$359$	−3.19128	+	2.31860i	−0.168429	+	0.122371i	0.500377	+	0.865807i	$0.333195\pi$
$360$	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	0.347381	−	0.937724i	$-0.387071\pi$
$367$	25.0999	−	12.7890i	1.31020	−	0.667581i	0.962820	+	0.270143i	$0.0870709\pi$
$368$	−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	−0.783341	−	0.621592i	$-0.786486\pi$
$373$	−25.8075	+	4.08750i	−1.33626	+	0.211643i	−0.552919	+	0.833235i	$0.686486\pi$
$374$	−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	0.274079	−	0.961707i	$-0.411627\pi$
$379$	20.6572	−	6.71194i	1.06109	−	0.344769i	0.787012	+	0.616938i	$0.211627\pi$
$380$	−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	−0.903397	−	0.428805i	$-0.858935\pi$
$383$	−21.2826	+	10.8440i	−1.08749	+	0.554104i	−0.184093	+	0.982909i	$0.558935\pi$
$384$	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	0.893486	−	0.449092i	$-0.148252\pi$
$389$	14.6439	+	10.6394i	0.742476	+	0.539440i	−0.151010	+	0.988532i	$0.548252\pi$
$390$	−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	−0.673424	−	0.739257i	$-0.735177\pi$
$397$	6.38543	−	12.5321i	0.320476	−	0.628969i	0.993900	+	0.110287i	$0.0351771\pi$
$398$	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	$-0.993309\pi$
$401$		−	0.841787i		−	0.0420368i	0.999779	−	0.0210184i	$-0.00669086\pi$
$402$	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	0.970781	−	0.239968i	$-0.0771371\pi$
$409$	8.95042	+	12.3192i	0.442570	+	0.609145i	−0.528211	+	0.849113i	$0.677137\pi$
$410$	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	−0.948672	−	0.316262i	$-0.897572\pi$
$419$	0.0964938	−	0.296977i	0.00471403	−	0.0145083i	0.953386	+	0.301754i	$0.0975721\pi$
$420$	−6.47631	+	4.42397i	−0.316012	+	0.215868i
$421$	11.7686	+	36.2199i	0.573565	+	1.76525i	0.641015	+	0.767528i	$0.278514\pi$
$421$	11.7686	+	36.2199i	0.573565	+	1.76525i	−0.0674500	+	0.997723i	$0.521486\pi$
$422$	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	0.805928	−	0.592013i	$-0.201667\pi$
$431$	23.0434	+	7.48726i	1.10996	+	0.360648i	0.304033	+	0.952661i	$0.401667\pi$
$432$	−4.26919	−	2.96209i	−0.205402	−	0.142514i
$433$	−2.46001	−	4.82804i	−0.118220	−	0.232021i	0.824312	−	0.566136i	$-0.191562\pi$
$433$	−2.46001	−	4.82804i	−0.118220	−	0.232021i	−0.942532	+	0.334116i	$0.891562\pi$
$434$	−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	0.247892	+	0.968788i	$0.420262\pi$
$439$	−15.7160	+	21.6312i	−0.750083	+	1.03240i	−0.997975	+	0.0636130i	$0.979738\pi$
$440$	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	0.984140	−	0.177391i	$-0.0567659\pi$
$443$	16.9801	+	16.9801i	0.806749	+	0.806749i	−0.177391	+	0.984140i	$0.556766\pi$
$444$	−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	0.593024	−	0.805185i	$-0.297934\pi$
$457$	−4.53549	−	4.53549i	−0.212161	−	0.212161i	−0.805185	+	0.593024i	$0.797934\pi$
$458$	−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	−0.847534	−	0.530741i	$-0.821914\pi$
$461$	−1.73628	+	2.38979i	−0.0808667	+	0.111303i	0.766667	+	0.642045i	$0.221914\pi$
$462$	19.1661	+	1.87408i	0.891689	+	0.0871901i
$463$	−4.47610	+	28.2610i	−0.208022	+	1.31340i	0.633739	+	0.773547i	$0.281519\pi$
$463$	−4.47610	+	28.2610i	−0.208022	+	1.31340i	−0.841761	+	0.539851i	$0.818481\pi$
$464$	−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	0.934072	−	0.357085i	$-0.116229\pi$
$467$	2.07783	+	4.07796i	0.0961504	+	0.188706i	−0.837922	+	0.545791i	$0.816229\pi$
$468$	−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	−0.932428	−	0.361355i	$-0.882314\pi$
$479$	−8.54601	−	26.3019i	−0.390477	−	1.20176i	0.541951	−	0.840410i	$-0.317686\pi$
$480$	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	−0.563404	−	0.826182i	$-0.690509\pi$
$487$	−29.8920	−	4.73443i	−1.35454	−	0.214538i	−0.791133	+	0.611644i	$0.790509\pi$
$488$	−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	0.685558	−	0.728018i	$-0.259558\pi$
$491$	−4.84555	−	6.66933i	−0.218677	−	0.300982i	−0.904235	+	0.427035i	$0.859558\pi$
$492$	−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	$-0.675637\pi$
$499$		−	38.0463i		−	1.70318i	0.524205	−	0.851592i	$-0.324363\pi$
$500$	−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	−0.0834338	−	0.996513i	$-0.526589\pi$
$503$	17.3097	−	33.9723i	0.771804	−	1.51475i	0.855237	−	0.518236i	$-0.173411\pi$
$504$	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	−0.705450	−	0.708760i	$-0.749255\pi$
$509$	−5.62616	+	4.08765i	−0.249375	+	0.181182i	0.456075	+	0.889942i	$0.349255\pi$
$510$	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	−0.724409	−	0.689370i	$-0.757887\pi$
$521$	−20.6631	+	6.71385i	−0.905267	+	0.294139i	−0.180858	+	0.983509i	$0.557887\pi$
$522$	−7.82747	+	21.3096i	−0.342599	+	0.932696i
$523$	42.4737	−	6.72718i	1.85725	−	0.294159i	0.875337	−	0.483513i	$-0.160639\pi$
$523$	42.4737	−	6.72718i	1.85725	−	0.294159i	0.981909	+	0.189354i	$0.0606393\pi$
$524$	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	−0.757279	−	0.653092i	$-0.773472\pi$
$541$	−8.60979	+	6.25538i	−0.370164	+	0.268940i	0.387115	+	0.922031i	$0.373472\pi$
$542$	−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	−0.709678	−	0.704526i	$-0.751160\pi$
$547$	6.48863	−	12.7347i	0.277434	−	0.544495i	0.987112	+	0.160031i	$0.0511596\pi$
$548$	−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	−0.626557	−	0.779375i	$-0.715537\pi$
$557$	3.60663	−	3.60663i	0.152818	−	0.152818i	0.779375	+	0.626557i	$0.215537\pi$
$558$	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	−0.397948	−	0.917408i	$-0.630277\pi$
$563$	−25.1492	−	3.98324i	−1.05991	−	0.167874i	−0.661965	+	0.749534i	$0.730277\pi$
$564$	−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	−0.528406	−	0.848992i	$-0.677210\pi$
$569$	9.49637	−	29.2268i	0.398108	−	1.22525i	0.926514	−	0.376260i	$-0.122790\pi$
$570$	−5.12327	+	6.63760i	−0.214590	+	0.278018i
$571$	−6.95564	−	21.4073i	−0.291085	−	0.895866i	−0.984509	−	0.175336i	$-0.943899\pi$
$571$	−6.95564	−	21.4073i	−0.291085	−	0.895866i	0.693424	−	0.720530i	$-0.256101\pi$
$572$	−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	0.627301	+	0.778777i	$0.284160\pi$
$577$	6.51823	+	41.1545i	0.271358	+	1.71328i	−0.355943	+	0.934508i	$0.615840\pi$
$578$	−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	−0.767701	−	0.640808i	$-0.778600\pi$
$587$	3.88731	−	24.5435i	0.160447	−	1.01302i	0.928148	−	0.372212i	$-0.121400\pi$
$588$	−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	0.998138	+	0.0609902i	$0.0194258\pi$
$593$	25.7915	+	25.7915i	1.05913	+	1.05913i	0.0609902	+	0.998138i	$0.480574\pi$
$594$	−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	0.608128	−	0.793839i	$-0.291921\pi$
$607$	−4.57545	−	4.57545i	−0.185712	−	0.185712i	−0.793839	+	0.608128i	$0.791921\pi$
$608$	−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	−0.701044	−	0.713118i	$-0.747282\pi$
$613$	4.60648	−	29.0842i	0.186054	−	1.17470i	0.887098	−	0.461581i	$-0.152718\pi$
$614$	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	0.998102	+	0.0615777i	$0.0196132\pi$
$617$	11.4572	+	22.4860i	0.461250	+	0.905254i	−0.536852	+	0.843676i	$0.680387\pi$
$618$	11.0624	+	9.81635i	0.444994	+	0.394872i
$619$	−2.83846	−	0.922271i	−0.114087	−	0.0370692i	0.251417	−	0.967879i	$-0.419103\pi$
$619$	−2.83846	−	0.922271i	−0.114087	−	0.0370692i	−0.365504	+	0.930810i	$0.619103\pi$
$620$	−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	−0.577891	−	0.816114i	$-0.696124\pi$
$631$	9.27752	−	28.5533i	0.369332	−	1.13669i	0.947223	−	0.320574i	$-0.103876\pi$
$632$	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	0.964095	−	0.265557i	$-0.0855558\pi$
$641$	10.4719	+	14.4133i	0.413614	+	0.569291i	−0.550481	+	0.834847i	$0.685556\pi$
$642$	−7.62456	+	4.47604i	−0.300917	+	0.176655i
$643$	10.8997	−	10.8997i	0.429840	−	0.429840i	−0.458734	−	0.888574i	$-0.651697\pi$
$643$	10.8997	−	10.8997i	0.429840	−	0.429840i	0.888574	+	0.458734i	$0.151697\pi$
$644$	−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	0.491469	−	0.870895i	$-0.336460\pi$
$647$	1.92749	+	0.982107i	0.0757776	+	0.0386106i	−0.415691	+	0.909506i	$0.636460\pi$
$648$	−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	−0.940668	−	0.339327i	$-0.889801\pi$
$653$	−2.89362	+	5.67905i	−0.113236	+	0.222238i	0.827432	+	0.561565i	$0.189801\pi$
$654$	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	−0.979259	−	0.202611i	$-0.935057\pi$
$659$	−27.9601	+	20.3142i	−1.08917	+	0.791330i	−0.109913	+	0.993941i	$0.535057\pi$
$660$	14.5932	+	15.4659i	0.568039	+	0.602009i
$661$	−33.8226	−	24.5736i	−1.31555	−	0.955801i	−0.999976	−	0.00689972i	$-0.997804\pi$
$661$	−33.8226	−	24.5736i	−1.31555	−	0.955801i	−0.315572	−	0.948902i	$-0.602196\pi$
$662$	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	−0.269066	−	0.963122i	$-0.586715\pi$
$673$	−5.89775	+	0.934113i	−0.227342	+	0.0360074i	0.0417241	+	0.999129i	$0.486715\pi$
$674$	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	−0.558020	−	0.829828i	$-0.688439\pi$
$677$	−21.6557	+	3.42993i	−0.832297	+	0.131823i	−0.274277	+	0.961651i	$0.588439\pi$
$678$	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	−0.228888	−	0.973453i	$-0.573509\pi$
$683$	11.0839	−	5.64753i	0.424114	−	0.216097i	0.653002	+	0.757356i	$0.273509\pi$
$684$	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	−0.449193	−	0.893435i	$-0.648288\pi$
$691$	6.87945	−	4.99821i	0.261706	−	0.190141i	0.710899	+	0.703294i	$0.248288\pi$
$692$	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	$-0.877701\pi$
$701$		−	19.8483i		−	0.749660i	0.927093	−	0.374830i	$-0.122299\pi$
$702$	−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	0.857411	−	0.514632i	$-0.172072\pi$
$709$	2.74291	+	3.77529i	0.103012	+	0.141784i	−0.754399	+	0.656416i	$0.772072\pi$
$710$	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	0.800255	+	0.599660i	$0.204698\pi$
$719$	−5.35309	+	16.4751i	−0.199637	+	0.614418i	−0.999891	+	0.0147577i	$0.995302\pi$
$720$	−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	0.967401	−	0.253250i	$-0.0814994\pi$
$727$	−0.833437	−	5.26211i	−0.0309105	−	0.195161i	−0.998311	+	0.0580887i	$0.981499\pi$
$728$	−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	0.987488	−	0.157697i	$-0.0504068\pi$
$733$	7.56657	+	14.8502i	0.279478	+	0.548506i	−0.708010	+	0.706202i	$0.750407\pi$
$734$	−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	−0.721871	−	0.692028i	$-0.756717\pi$
$739$	4.33206	−	5.96257i	0.159357	−	0.219337i	0.881228	+	0.472691i	$0.156717\pi$
$740$	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	0.995759	−	0.0919959i	$-0.0293247\pi$
$743$	24.6348	+	24.6348i	0.903763	+	0.903763i	−0.0919959	+	0.995759i	$0.529325\pi$
$744$	−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	0.608070	−	0.793883i	$-0.291944\pi$
$757$	−5.11239	−	5.11239i	−0.185813	−	0.185813i	−0.793883	+	0.608070i	$0.791944\pi$
$758$	−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	−0.997918	−	0.0644935i	$-0.979457\pi$
$761$	−17.3299	+	23.8525i	−0.628208	+	0.864654i	0.369711	+	0.929147i	$0.379457\pi$
$762$	−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	−0.637602	−	0.770366i	$-0.720074\pi$
$769$	−44.5425	−	14.4727i	−1.60624	−	0.521900i	−0.968641	+	0.248466i	$0.920074\pi$
$770$	−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	0.832281	+	0.554353i	$0.187034\pi$
$773$	5.89531	+	37.2215i	0.212039	+	1.33876i	−0.620242	+	0.784411i	$0.712966\pi$
$774$	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	0.264410	−	0.964410i	$-0.414823\pi$
$787$	6.11175	+	0.968005i	0.217860	+	0.0345057i	−0.0465501	+	0.998916i	$0.514823\pi$
$788$	−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	0.633426	−	0.773804i	$-0.281648\pi$
$797$	10.7200	+	5.46214i	0.379724	+	0.193479i	−0.253702	+	0.967282i	$0.581648\pi$
$798$	−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	−0.980305	−	0.197487i	$-0.936722\pi$
$809$	−31.1568	+	22.6367i	−1.09542	+	0.795866i	−0.115110	+	0.993353i	$0.536722\pi$
$810$	20.1241	+	0.146478i	0.707088	+	0.00514672i
$811$	12.9742	+	9.42631i	0.455586	+	0.331002i	0.791797	−	0.610784i	$-0.209146\pi$
$811$	12.9742	+	9.42631i	0.455586	+	0.331002i	−0.336211	+	0.941787i	$0.609146\pi$
$812$	−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	−0.205547	−	0.978647i	$-0.565897\pi$
$821$	5.82793	−	1.89361i	0.203396	−	0.0660875i	0.408943	+	0.912560i	$0.365897\pi$
$822$	9.34852	−	21.4135i	0.326067	−	0.746882i
$823$	19.7116	−	3.12202i	0.687105	−	0.108827i	0.196886	−	0.980426i	$-0.436917\pi$
$823$	19.7116	−	3.12202i	0.687105	−	0.108827i	0.490218	+	0.871600i	$0.336917\pi$
$824$	−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	0.133603	−	0.991035i	$-0.457345\pi$
$827$	16.3031	−	2.58216i	0.566914	−	0.0897904i	0.433311	+	0.901244i	$0.357345\pi$
$828$	2.24646	−	6.11579i	0.0780699	−	0.212538i
$829$	6.29526	−	2.04545i	0.218643	−	0.0710415i	−0.197647	−	0.980273i	$-0.563330\pi$
$829$	6.29526	−	2.04545i	0.218643	−	0.0710415i	0.416290	+	0.909232i	$0.363330\pi$
$830$	−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	0.453864	−	0.891071i	$-0.350045\pi$
$839$	−7.33822	−	5.33153i	−0.253343	−	0.184065i	−0.707207	+	0.707006i	$0.750045\pi$
$840$	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	0.262593	−	0.964907i	$-0.415422\pi$
$853$	−10.6218	−	5.41209i	−0.363684	−	0.185306i	−0.626277	+	0.779600i	$0.715422\pi$
$854$	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	−0.564788	−	0.825236i	$-0.691042\pi$
$857$	7.62449	−	7.62449i	0.260448	−	0.260448i	0.825236	+	0.564788i	$0.191042\pi$
$858$	−30.9058	−	52.6455i	−1.05511	−	1.79729i
$859$	19.5703	+	26.9362i	0.667730	+	0.919051i	0.999706	−	0.0242364i	$-0.00771544\pi$
$859$	19.5703	+	26.9362i	0.667730	+	0.919051i	−0.331976	+	0.943288i	$0.607715\pi$
$860$	−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	0.547010	−	0.837126i	$-0.315766\pi$
$863$	23.7530	+	3.76211i	0.808562	+	0.128064i	0.261552	+	0.965189i	$0.415766\pi$
$864$	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	0.996836	+	0.0794802i	$0.0253261\pi$
$877$	2.17218	+	13.7146i	0.0733494	+	0.463110i	−0.923487	+	0.383630i	$0.874674\pi$
$878$	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	0.726678	−	0.686978i	$-0.241063\pi$
$881$	27.0334	+	8.78367i	0.910777	+	0.295930i	0.184099	+	0.982908i	$0.441063\pi$
$882$	−5.37475	+	6.83761i	−0.180977	+	0.230234i
$883$	7.99886	+	15.6986i	0.269183	+	0.528301i	0.985542	−	0.169430i	$-0.0541928\pi$
$883$	7.99886	+	15.6986i	0.269183	+	0.528301i	−0.716359	+	0.697732i	$0.754193\pi$
$884$	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	0.947802	+	0.318861i	$0.103300\pi$
$887$	−1.55300	+	9.80527i	−0.0521447	+	0.329229i	−0.999946	+	0.0103679i	$0.996700\pi$
$888$	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	0.926438	−	0.376446i	$-0.122854\pi$
$907$	16.5638	+	16.5638i	0.549992	+	0.549992i	−0.376446	+	0.926438i	$0.622854\pi$
$908$	−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	−0.158205	−	0.987406i	$-0.550571\pi$
$911$	25.0445	−	34.4709i	0.829763	−	1.14207i	0.987967	−	0.154664i	$-0.0494295\pi$
$912$	−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	0.409696	−	0.912222i	$-0.365635\pi$
$919$	6.21323	+	2.01880i	0.204955	+	0.0665940i	−0.204740	+	0.978816i	$0.565635\pi$
$920$	−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	−0.991095	−	0.133157i	$-0.957489\pi$
$929$	−8.15479	−	25.0979i	−0.267550	−	0.823434i	0.723545	−	0.690277i	$-0.242511\pi$
$930$	−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	0.821809	−	0.569763i	$-0.192965\pi$
$937$	43.6912	+	6.92001i	1.42733	+	0.226067i	0.605521	+	0.795829i	$0.292965\pi$
$938$	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	0.752830	−	0.658215i	$-0.228688\pi$
$941$	−3.24570	−	4.46733i	−0.105807	−	0.145631i	−0.858637	+	0.512584i	$0.828688\pi$
$942$	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	0.399412	−	0.916772i	$-0.369214\pi$
$947$	−3.30825	−	1.68564i	−0.107504	−	0.0547759i	−0.506916	+	0.861996i	$0.669214\pi$
$948$	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	−0.306877	−	0.951749i	$-0.599284\pi$
$953$	19.8647	−	38.9868i	0.643482	−	1.26290i	0.950359	−	0.311156i	$-0.100716\pi$
$954$	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	−0.0564917	−	0.998403i	$-0.517991\pi$
$967$	22.3283	−	11.3768i	0.718028	−	0.365854i	0.774520	+	0.632549i	$0.217991\pi$
$968$	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	0.144331	−	0.989529i	$-0.453897\pi$
$971$	26.2601	−	8.53244i	0.842728	−	0.273819i	0.698397	+	0.715711i	$0.253897\pi$
$972$	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	−0.301876	−	0.953347i	$-0.597613\pi$
$977$	−9.20136	+	1.45735i	−0.294378	+	0.0466248i	0.00749885	+	0.999972i	$0.497613\pi$
$978$	−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	0.351172	−	0.936311i	$-0.385783\pi$
$983$	41.2314	−	21.0084i	1.31508	−	0.670065i	0.963905	+	0.266245i	$0.0857832\pi$
$984$	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	−0.841996	−	0.539484i	$-0.818619\pi$
$991$	−18.5452	+	13.4739i	−0.589107	+	0.428011i	0.252889	+	0.967495i	$0.418619\pi$
$992$	−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	−0.228914	−	0.973447i	$-0.573517\pi$
$997$	21.8872	−	42.9560i	0.693173	−	1.36043i	0.922087	−	0.386983i	$-0.126483\pi$
$998$	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.137.1	yes	80
3.2	odd	2	inner	150.2.l.a.137.6	yes	80
5.2	odd	4		750.2.l.a.293.2		80
5.3	odd	4		750.2.l.c.293.9		80
5.4	even	2		750.2.l.b.707.10		80
15.2	even	4		750.2.l.a.293.7		80
15.8	even	4		750.2.l.c.293.4		80
15.14	odd	2		750.2.l.b.707.5		80
25.2	odd	20		750.2.l.b.593.5		80
25.11	even	5		750.2.l.c.407.4		80
25.14	even	10		750.2.l.a.407.7		80
25.23	odd	20	inner	150.2.l.a.23.6	yes	80
75.2	even	20		750.2.l.b.593.10		80
75.11	odd	10		750.2.l.c.407.9		80
75.14	odd	10		750.2.l.a.407.2		80
75.23	even	20	inner	150.2.l.a.23.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.23.1	✓	80	75.23	even	20	inner
150.2.l.a.23.6	yes	80	25.23	odd	20	inner
150.2.l.a.137.1	yes	80	1.1	even	1	trivial
150.2.l.a.137.6	yes	80	3.2	odd	2	inner
750.2.l.a.293.2		80	5.2	odd	4
750.2.l.a.293.7		80	15.2	even	4
750.2.l.a.407.2		80	75.14	odd	10
750.2.l.a.407.7		80	25.14	even	10
750.2.l.b.593.5		80	25.2	odd	20
750.2.l.b.593.10		80	75.2	even	20
750.2.l.b.707.5		80	15.14	odd	2
750.2.l.b.707.10		80	5.4	even	2
750.2.l.c.293.4		80	15.8	even	4
750.2.l.c.293.9		80	5.3	odd	4
750.2.l.c.407.4		80	25.11	even	5
750.2.l.c.407.9		80	75.11	odd	10

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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