LMFDB - Embedded newform 150.2.l.a.137.6

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			137.6
Character	$\chi$	$=$	150.137
Dual form			150.2.l.a.23.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 - 0.156434i) q^{2} +(-1.49368 - 0.876876i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.197931 - 2.22729i) q^{5} +(-1.61247 - 0.632416i) q^{6} +(-1.43195 - 1.43195i) q^{7} +(0.891007 - 0.453990i) q^{8} +(1.46218 + 2.61955i) q^{9} +O(q^{10})$	\(q+(0.987688 - 0.156434i) q^{2} +(-1.49368 - 0.876876i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.197931 - 2.22729i) q^{5} +(-1.61247 - 0.632416i) q^{6} +(-1.43195 - 1.43195i) q^{7} +(0.891007 - 0.453990i) q^{8} +(1.46218 + 2.61955i) q^{9} +(-0.152931 - 2.23083i) q^{10} +(3.22713 - 4.44177i) q^{11} +(-1.69155 - 0.372385i) q^{12} +(-1.00424 + 6.34051i) q^{13} +(-1.63832 - 1.19031i) q^{14} +(-2.24870 + 3.15331i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.101553 + 0.199309i) q^{17} +(1.85396 + 2.35856i) q^{18} +(2.05900 + 0.669009i) q^{19} +(-0.500027 - 2.17944i) q^{20} +(0.883235 + 3.39451i) 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} +(0.112987 - 5.19492i) q^{27} +(-1.80436 - 0.919366i) q^{28} +(2.33841 + 7.19688i) q^{29} +(-1.72773 + 3.46626i) q^{30} +(-0.944961 + 2.90829i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-8.71519 + 3.80480i) q^{33} +(0.131482 + 0.180969i) q^{34} +(-3.47279 + 2.90593i) q^{35} +(2.20010 + 2.03950i) q^{36} +(6.46438 + 1.02386i) q^{37} +(2.13830 + 0.338674i) q^{38} +(7.05986 - 8.59013i) q^{39} +(-0.834811 - 2.07439i) q^{40} +(-0.896615 - 1.23409i) q^{41} +(1.40338 + 3.21455i) q^{42} +(-2.14384 + 2.14384i) q^{43} +(1.69660 - 5.22161i) q^{44} +(6.12391 - 2.73821i) q^{45} +(0.671116 + 2.06548i) q^{46} +(-4.66039 - 2.37459i) q^{47} +(-1.72383 + 0.168558i) 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} +(-0.701069 - 5.14864i) q^{54} +(-9.25436 - 8.06693i) q^{55} +(-1.92596 - 0.625783i) q^{56} +(-2.48885 - 2.80477i) q^{57} +(3.43546 + 6.74246i) q^{58} +(-4.61185 + 3.35071i) q^{59} +(-1.16422 + 3.69386i) q^{60} +(2.55529 + 1.85653i) q^{61} +(-0.478370 + 3.02031i) q^{62} +(1.65729 - 5.84481i) q^{63} +(0.587785 - 0.809017i) q^{64} +(13.9234 + 3.49171i) q^{65} +(-8.01269 + 5.12131i) q^{66} +(2.22498 - 1.13368i) q^{67} +(0.158173 + 0.158173i) q^{68} +(1.37347 - 3.50192i) q^{69} +(-2.97544 + 3.41342i) q^{70} +(5.77333 - 1.87587i) q^{71} +(2.49206 + 1.67022i) q^{72} +(-3.02002 + 0.478324i) q^{73} +6.54496 q^{74} +(6.57824 + 5.63265i) q^{75} +2.16496 q^{76} +(-10.9815 + 1.73929i) q^{77} +(5.62915 - 9.58877i) q^{78} +(-11.0020 + 3.57478i) q^{79} +(-1.14904 - 1.91826i) q^{80} +(-4.72407 + 7.66049i) q^{81} +(-1.07863 - 1.07863i) q^{82} +(-9.31624 + 4.74686i) q^{83} +(1.88897 + 2.95544i) q^{84} +(0.464020 - 0.186739i) q^{85} +(-1.78208 + 2.45282i) q^{86} +(2.81793 - 12.8003i) q^{87} +(0.858876 - 5.42273i) q^{88} +(-7.34358 - 5.33542i) q^{89} +(5.62016 - 3.66248i) q^{90} +(10.5173 - 7.64126i) q^{91} +(0.985966 + 1.93507i) q^{92} +(3.96168 - 3.51545i) q^{93} +(-4.97448 - 1.61631i) q^{94} +(1.89762 - 4.45357i) q^{95} +(-1.67624 + 0.436149i) 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
$3$	−1.49368	−	0.876876i	−0.862378	−	0.506264i
$3$	−1.49368	−	0.876876i	−0.862378	−	0.506264i
$4$	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
$6$	−1.61247	−	0.632416i	−0.658287	−	0.258183i
$7$	−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
$9$	1.46218	+	2.61955i	0.487393	+	0.873183i
$10$	−0.152931	−	2.23083i	−0.0483611	−	0.705451i
$11$	3.22713	−	4.44177i	0.973017	−	1.33924i	0.0325093	−	0.999471i	$-0.489650\pi$
$11$	3.22713	−	4.44177i	0.973017	−	1.33924i	0.940508	−	0.339772i	$-0.110350\pi$
$12$	−1.69155	−	0.372385i	−0.488307	−	0.107498i
$13$	−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
$15$	−2.24870	+	3.15331i	−0.580613	+	0.814180i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	0.101553	+	0.199309i	0.0246303	+	0.0483396i	0.902994	−	0.429654i	$-0.141364\pi$
$17$	0.101553	+	0.199309i	0.0246303	+	0.0483396i	−0.878364	+	0.477993i	$0.841364\pi$
$18$	1.85396	+	2.35856i	0.436984	+	0.555919i
$19$	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
$21$	0.883235	+	3.39451i	0.192738	+	0.740743i
$22$	2.49256	−	4.89192i	0.531415	−	1.04296i
$23$	0.339741	+	2.14504i	0.0708408	+	0.447271i	0.997457	+	0.0712640i	$0.0227033\pi$
$23$	0.339741	+	2.14504i	0.0708408	+	0.447271i	−0.926617	+	0.376007i	$0.877297\pi$
$24$	−1.72897	−	0.103184i	−0.352925	−	0.0210623i
$25$	−4.92165	−	0.881699i	−0.984329	−	0.176340i
$26$			6.41955i			1.25898i
$27$	0.112987	−	5.19492i	0.0217444	−	0.999764i
$28$	−1.80436	−	0.919366i	−0.340992	−	0.173744i
$29$	2.33841	+	7.19688i	0.434231	+	1.33643i	0.893872	+	0.448322i	$0.147978\pi$
$29$	2.33841	+	7.19688i	0.434231	+	1.33643i	−0.459641	+	0.888105i	$0.652022\pi$
$30$	−1.72773	+	3.46626i	−0.315439	+	0.632849i
$31$	−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
$33$	−8.71519	+	3.80480i	−1.51712	+	0.662330i
$34$	0.131482	+	0.180969i	0.0225489	+	0.0310359i
$35$	−3.47279	+	2.90593i	−0.587008	+	0.491193i
$36$	2.20010	+	2.03950i	0.366683	+	0.339917i
$37$	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
$39$	7.05986	−	8.59013i	1.13048	−	1.37552i
$40$	−0.834811	−	2.07439i	−0.131995	−	0.327990i
$41$	−0.896615	−	1.23409i	−0.140028	−	0.192732i	0.733243	−	0.679966i	$-0.238006\pi$
$41$	−0.896615	−	1.23409i	−0.140028	−	0.192732i	−0.873271	+	0.487235i	$0.838006\pi$
$42$	1.40338	+	3.21455i	0.216546	+	0.496016i
$43$	−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
$45$	6.12391	−	2.73821i	0.912898	−	0.408188i
$46$	0.671116	+	2.06548i	0.0989506	+	0.304539i
$47$	−4.66039	−	2.37459i	−0.679788	−	0.346369i	0.0797657	−	0.996814i	$-0.474583\pi$
$47$	−4.66039	−	2.37459i	−0.679788	−	0.346369i	−0.759554	+	0.650444i	$0.774583\pi$
$48$	−1.72383	+	0.168558i	−0.248813	+	0.0243292i
$49$		−	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	$-0.531462\pi$
$53$	5.56485	−	10.9216i	0.764390	−	1.50020i	0.863072	−	0.505082i	$-0.168538\pi$
$54$	−0.701069	−	5.14864i	−0.0954034	−	0.700641i
$55$	−9.25436	−	8.06693i	−1.24786	−	1.08774i
$56$	−1.92596	−	0.625783i	−0.257368	−	0.0836238i
$57$	−2.48885	−	2.80477i	−0.329657	−	0.371501i
$58$	3.43546	+	6.74246i	0.451098	+	0.885329i
$59$	−4.61185	+	3.35071i	−0.600412	+	0.436225i	−0.846025	−	0.533143i	$-0.821011\pi$
$59$	−4.61185	+	3.35071i	−0.600412	+	0.436225i	0.245613	+	0.969368i	$0.421011\pi$
$60$	−1.16422	+	3.69386i	−0.150300	+	0.476875i
$61$	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
$63$	1.65729	−	5.84481i	0.208799	−	0.736377i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	13.9234	+	3.49171i	1.72698	+	0.433094i
$66$	−8.01269	+	5.12131i	−0.986294	+	0.630390i
$67$	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
$69$	1.37347	−	3.50192i	0.165346	−	0.421581i
$70$	−2.97544	+	3.41342i	−0.355633	+	0.407982i
$71$	5.77333	−	1.87587i	0.685168	−	0.222625i	0.0543113	−	0.998524i	$-0.482704\pi$
$71$	5.77333	−	1.87587i	0.685168	−	0.222625i	0.630856	+	0.775900i	$0.282704\pi$
$72$	2.49206	+	1.67022i	0.293692	+	0.196837i
$73$	−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
$75$	6.57824	+	5.63265i	0.759590	+	0.650402i
$76$	2.16496			0.248338
$77$	−10.9815	+	1.73929i	−1.25145	+	0.198211i
$78$	5.62915	−	9.58877i	0.637375	−	1.08571i
$79$	−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
$81$	−4.72407	+	7.66049i	−0.524897	+	0.851166i
$82$	−1.07863	−	1.07863i	−0.119115	−	0.119115i
$83$	−9.31624	+	4.74686i	−1.02259	+	0.521036i	−0.883099	−	0.469187i	$-0.844547\pi$
$83$	−9.31624	+	4.74686i	−1.02259	+	0.521036i	−0.139492	+	0.990223i	$0.544547\pi$
$84$	1.88897	+	2.95544i	0.206103	+	0.322465i
$85$	0.464020	−	0.186739i	0.0503301	−	0.0202547i
$86$	−1.78208	+	2.45282i	−0.192166	+	0.264494i
$87$	2.81793	−	12.8003i	0.302113	−	1.37234i
$88$	0.858876	−	5.42273i	0.0915565	−	0.578065i
$89$	−7.34358	−	5.33542i	−0.778418	−	0.565554i	0.126086	−	0.992019i	$-0.459759\pi$
$89$	−7.34358	−	5.33542i	−0.778418	−	0.565554i	−0.904504	+	0.426466i	$0.859759\pi$
$90$	5.62016	−	3.66248i	0.592417	−	0.386060i
$91$	10.5173	−	7.64126i	1.10251	−	0.801022i
$92$	0.985966	+	1.93507i	0.102794	+	0.201745i
$93$	3.96168	−	3.51545i	0.410807	−	0.364535i
$94$	−4.97448	−	1.61631i	−0.513079	−	0.166709i
$95$	1.89762	−	4.45357i	0.194691	−	0.456926i
$96$	−1.67624	+	0.436149i	−0.171080	+	0.0445142i
$97$	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	$0.123448\pi$
$101$			7.60118i			0.756346i	−0.925735	+	0.378173i	$0.876552\pi$
$102$	−0.0377047	−	0.385604i	−0.00373332	−	0.0381804i
$103$	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
$105$	7.73539	−	1.29534i	0.754896	−	0.126413i
$106$	3.78781	−	11.6577i	0.367905	−	1.13230i
$107$	3.60945	−	3.60945i	0.348939	−	0.348939i	−0.510775	−	0.859714i	$-0.670642\pi$
$107$	3.60945	−	3.60945i	0.348939	−	0.348939i	0.859714	+	0.510775i	$0.170642\pi$
$108$	−1.49786	−	4.97558i	−0.144132	−	0.478776i
$109$	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
$111$	−8.75794	−	7.19777i	−0.831266	−	0.683182i
$112$	−2.00015	−	0.316792i	−0.188996	−	0.0299340i
$113$	−13.0078	−	2.06024i	−1.22367	−	0.193811i	−0.489033	−	0.872266i	$-0.662650\pi$
$113$	−13.0078	−	2.06024i	−1.22367	−	0.193811i	−0.734642	+	0.678454i	$0.762650\pi$
$114$	−2.89697	−	2.38090i	−0.271326	−	0.222992i
$115$	4.84487	−	0.332132i	0.451786	−	0.0309715i
$116$	4.44791	+	6.12203i	0.412978	+	0.568416i
$117$	−18.0777	+	6.64031i	−1.67128	+	0.613897i
$118$	−4.03091	+	4.03091i	−0.371075	+	0.371075i
$119$	0.139982	−	0.430819i	0.0128321	−	0.0394931i
$120$	−0.572038	+	3.83051i	−0.0522197	+	0.349676i
$121$	−5.91572	−	18.2067i	−0.537793	−	1.65516i
$122$	2.81426	+	1.43393i	0.254791	+	0.129822i
$123$	0.257120	+	2.62955i	0.0231837	+	0.237099i
$124$			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
$129$	5.08211	−	1.32234i	0.447455	−	0.116425i
$130$	14.2982	+	1.27063i	1.25404	+	0.111441i
$131$	−9.82350	−	3.19185i	−0.858284	−	0.278873i	−0.153372	−	0.988169i	$-0.549013\pi$
$131$	−9.82350	−	3.19185i	−0.858284	−	0.278873i	−0.704911	+	0.709295i	$0.749013\pi$
$132$	−7.11289	+	6.31172i	−0.619098	+	0.549365i
$133$	−1.99039	−	3.90636i	−0.172589	−	0.338724i
$134$	2.02024	−	1.46779i	0.174522	−	0.126797i
$135$	−11.5482	−	1.27989i	−0.993914	−	0.110155i
$136$	0.180969	+	0.131482i	0.0155180	+	0.0112745i
$137$	−2.11029	+	13.3238i	−0.180294	+	1.13833i	0.717057	+	0.697014i	$0.245489\pi$
$137$	−2.11029	+	13.3238i	−0.180294	+	1.13833i	−0.897351	+	0.441317i	$0.854511\pi$
$138$	0.808736	−	3.67366i	0.0688442	−	0.312723i
$139$	−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
$141$	4.87893	+	7.63347i	0.410880	+	0.642854i
$142$	5.40880	−	2.75592i	0.453896	−	0.231272i
$143$	24.9223	+	24.9223i	2.08411	+	2.08411i
$144$	2.72266	+	1.25981i	0.226888	+	0.104984i
$145$	16.4924	−	3.78383i	1.36962	−	0.314230i
$146$	−2.90801	+	0.944871i	−0.240669	+	0.0781981i
$147$	−2.54211	+	4.33028i	−0.209670	+	0.357155i
$148$	6.46438	−	1.02386i	0.531369	−	0.0841605i
$149$	−5.97158			−0.489211			−0.244606	−	0.969623i	$-0.578658\pi$
$149$	−5.97158			−0.489211			−0.244606	+	0.969623i	$0.578658\pi$
$150$	7.37839	+	4.53424i	0.602443	+	0.370219i
$151$	−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
$153$	−0.373612	+	0.557449i	−0.0302047	+	0.0450671i
$154$	−10.5742	+	3.43576i	−0.852091	+	0.276861i
$155$	6.29057	+	2.68034i	0.505271	+	0.215290i
$156$	4.05983	−	10.3513i	0.325046	−	0.828768i
$157$	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
$159$	−17.8890	+	11.4338i	−1.41869	+	0.906757i
$160$	−1.43497	−	1.71489i	−0.113445	−	0.135574i
$161$	2.58509	−	3.55807i	0.203734	−	0.280415i
$162$	−3.46754	+	8.30519i	−0.272436	+	0.652517i
$163$	−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
$165$	6.74939	+	20.1644i	0.525439	+	1.56979i
$166$	−8.45897	+	6.14580i	−0.656544	+	0.477007i
$167$	−4.42748	−	8.68941i	−0.342608	−	0.672407i	0.653838	−	0.756634i	$-0.273158\pi$
$167$	−4.42748	−	8.68941i	−0.342608	−	0.672407i	−0.996447	+	0.0842276i	$0.973158\pi$
$168$	2.32804	+	2.62355i	0.179613	+	0.202411i
$169$	−26.8299	−	8.71756i	−2.06384	−	0.670581i
$170$	0.429095	−	0.257029i	0.0329101	−	0.0197132i
$171$	1.25812	+	6.37185i	0.0962109	+	0.487268i
$172$	−1.37643	+	2.70140i	−0.104952	+	0.205980i
$173$	−2.74408	−	17.3254i	−0.208629	−	1.31723i	−0.840354	−	0.542037i	$-0.817653\pi$
$173$	−2.74408	−	17.3254i	−0.208629	−	1.31723i	0.631726	−	0.775192i	$-0.282347\pi$
$174$	0.780818	−	13.0836i	0.0591937	−	0.991863i
$175$	5.78499	+	8.31008i	0.437304	+	0.628183i
$176$		−	5.49033i		−	0.413849i
$177$	9.82680	−	0.960873i	0.738627	−	0.0722237i
$178$	−8.08781	−	4.12095i	−0.606207	−	0.308878i
$179$	3.59155	+	11.0537i	0.268445	+	0.826190i	0.990880	+	0.134750i	$0.0430232\pi$
$179$	3.59155	+	11.0537i	0.268445	+	0.826190i	−0.722434	+	0.691440i	$0.756977\pi$
$180$	4.97803	−	4.49658i	0.371040	−	0.335155i
$181$	−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
$183$	−2.18885	−	5.01373i	−0.161804	−	0.370626i
$184$	1.27654	+	1.75700i	0.0941076	+	0.129528i
$185$	3.55993	−	14.1954i	0.261731	−	1.04367i
$186$	3.36297	−	4.09191i	0.246585	−	0.300034i
$187$	1.21301	+	0.192122i	0.0887042	+	0.0140494i
$188$	−5.16609	−	0.818228i	−0.376776	−	0.0596754i
$189$	−7.60064	+	7.27706i	−0.552865	+	0.529328i
$190$	1.17756	−	4.69559i	0.0854293	−	0.340654i
$191$	−9.89270	−	13.6161i	−0.715810	−	0.985228i	−0.999653	−	0.0263574i	$-0.991609\pi$
$191$	−9.89270	−	13.6161i	−0.715810	−	0.985228i	0.283842	−	0.958871i	$-0.408391\pi$
$192$	−1.58737	+	0.693000i	−0.114559	+	0.0500130i
$193$	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
$195$	−17.7353	−	17.4246i	−1.27005	−	1.24780i
$196$	−0.895859	−	2.75717i	−0.0639899	−	0.196941i
$197$	15.8178	+	8.05955i	1.12697	+	0.574219i	0.915160	−	0.403091i	$-0.132064\pi$
$197$	15.8178	+	8.05955i	1.12697	+	0.574219i	0.211809	+	0.977311i	$0.432064\pi$
$198$	16.4592	−	0.623483i	1.16970	−	0.0443090i
$199$		−	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
$204$	−0.0975621	−	0.374958i	−0.00683072	−	0.0262523i
$205$	−2.92613	+	1.75276i	−0.204370	+	0.122418i
$206$	8.12095	+	2.63866i	0.565813	+	0.183844i
$207$	−5.12227	+	4.02640i	−0.356022	+	0.279854i
$208$	2.91441	+	5.71986i	0.202078	+	0.396601i
$209$	9.61624	−	6.98661i	0.665169	−	0.483274i
$210$	7.43751	−	2.48948i	0.513237	−	0.171790i
$211$	−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
$213$	−10.2684	−	2.26054i	−0.703581	−	0.154889i
$214$	3.00037	−	4.12966i	0.205101	−	0.282298i
$215$	4.35063	+	5.19930i	0.296711	+	0.354589i
$216$	−2.25777	−	4.68001i	−0.153622	−	0.318434i
$217$	5.51765	−	2.81138i	0.374562	−	0.190849i
$218$	6.91725	+	6.91725i	0.468495	+	0.468495i
$219$	4.93039	+	1.93372i	0.333165	+	0.130669i
$220$	−11.2942	−	4.81235i	−0.761457	−	0.324448i
$221$	−1.36571	+	0.443745i	−0.0918674	+	0.0298495i
$222$	−9.77609	−	5.73911i	−0.656128	−	0.385184i
$223$	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
$225$	−4.88667	−	14.1817i	−0.325778	−	0.945446i
$226$	−13.1700			−0.876055
$227$	19.7103	−	3.12180i	1.30822	−	0.207201i	0.536896	−	0.843649i	$-0.319597\pi$
$227$	19.7103	−	3.12180i	1.30822	−	0.207201i	0.771320	+	0.636448i	$0.219597\pi$
$228$	−3.23376	−	1.89840i	−0.214161	−	0.125725i
$229$	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
$231$	17.9280	+	7.03142i	1.17957	+	0.462633i
$232$	5.35085	+	5.35085i	0.351300	+	0.351300i
$233$	−4.33449	+	2.20854i	−0.283962	+	0.144686i	−0.590171	−	0.807279i	$-0.700940\pi$
$233$	−4.33449	+	2.20854i	−0.283962	+	0.144686i	0.306208	+	0.951964i	$0.400940\pi$
$234$	−16.8163	+	9.38652i	−1.09932	+	0.613616i
$235$	−6.21134	+	9.91005i	−0.405183	+	0.646460i
$236$	−3.35071	+	4.61185i	−0.218112	+	0.300206i
$237$	19.5682	+	4.30783i	1.27109	+	0.279824i
$238$	0.0708632	−	0.447413i	0.00459338	−	0.0290015i
$239$	−13.5737	−	9.86185i	−0.878008	−	0.637910i	0.0547159	−	0.998502i	$-0.482575\pi$
$239$	−13.5737	−	9.86185i	−0.878008	−	0.637910i	−0.932724	+	0.360592i	$0.882575\pi$
$240$	0.0342279	+	3.87283i	0.00220940	+	0.249990i
$241$	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
$243$	13.7736	−	7.29993i	0.883574	−	0.468291i
$244$	3.00392	+	0.976034i	0.192307	+	0.0624842i
$245$	−6.45705	−	0.573813i	−0.412526	−	0.0366596i
$246$	0.665307	+	2.55696i	0.0424184	+	0.163026i
$247$	−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	$-0.326660\pi$
$252$	−0.229968	−	6.07088i	−0.0144866	−	0.382429i
$253$	10.6241	+	5.41327i	0.667934	+	0.340330i
$254$	3.54883	+	10.9222i	0.222673	+	0.685318i
$255$	−0.856846	−	0.127959i	−0.0536578	−	0.00801312i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−11.8188	+	11.8188i	−0.737238	+	0.737238i	−0.972043	−	0.234805i	$-0.924555\pi$
$257$	−11.8188	+	11.8188i	−0.737238	+	0.737238i	0.234805	+	0.972043i	$0.424555\pi$
$258$	4.81268	−	2.10108i	0.299624	−	0.130807i
$259$	−7.79053	−	10.7227i	−0.484080	−	0.666279i
$260$	14.3209	−	0.981749i	0.888147	−	0.0608855i
$261$	−15.4334	+	16.6487i	−0.955303	+	1.03053i
$262$	−10.2019	−	1.61582i	−0.630274	−	0.0998256i
$263$	7.20902	+	1.14180i	0.444527	+	0.0704062i	0.374686	−	0.927152i	$-0.377751\pi$
$263$	7.20902	+	1.14180i	0.444527	+	0.0704062i	0.0698415	+	0.997558i	$0.477751\pi$
$264$	−6.03795	+	7.34671i	−0.371610	+	0.452159i
$265$	−23.2242	−	14.5563i	−1.42665	−	0.894184i
$266$	−2.57697	−	3.54690i	−0.158004	−	0.217474i
$267$	6.29048	+	14.4088i	0.384971	+	0.881807i
$268$	1.76575	−	1.76575i	0.107860	−	0.107860i
$269$	9.50784	−	29.2621i	0.579703	−	1.78414i	−0.0398701	−	0.999205i	$-0.512694\pi$
$269$	9.50784	−	29.2621i	0.579703	−	1.78414i	0.619573	−	0.784939i	$-0.287306\pi$
$270$	−11.6063	+	0.542410i	−0.706336	+	0.0330100i
$271$	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
$273$	−22.4099	+	2.19126i	−1.35631	+	0.132621i
$274$			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
$279$	−9.00011	+	1.77707i	−0.538822	+	0.106390i
$280$	−1.77501	+	4.16582i	−0.106077	+	0.248955i
$281$	19.6851	+	6.39607i	1.17431	+	0.381558i	0.830251	−	0.557389i	$-0.188197\pi$
$281$	19.6851	+	6.39607i	1.17431	+	0.381558i	0.344062	+	0.938947i	$0.388197\pi$
$282$	6.01300	+	6.77626i	0.358069	+	0.403520i
$283$	−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
$285$	−6.73966	+	4.98825i	−0.399223	+	0.295478i
$286$	28.5141	+	20.7167i	1.68608	+	1.22501i
$287$	−0.483239	+	3.05105i	−0.0285247	+	0.180098i
$288$	2.88622	+	0.818384i	0.170072	+	0.0482238i
$289$	9.96294	−	13.7128i	0.586055	−	0.806636i
$290$	15.6974	−	6.31722i	0.921784	−	0.370960i
$291$	−3.51564	+	2.24702i	−0.206091	+	0.131723i
$292$	−2.72440	+	1.38815i	−0.159433	+	0.0812354i
$293$	−0.153372	−	0.153372i	−0.00896009	−	0.00896009i	0.702613	−	0.711573i	$-0.252017\pi$
$293$	−0.153372	−	0.153372i	−0.00896009	−	0.00896009i	−0.711573	+	0.702613i	$0.752017\pi$
$294$	−1.83341	+	4.67464i	−0.106927	+	0.272630i
$295$	6.55017	+	10.9351i	0.381366	+	0.636669i
$296$	6.22462	−	2.02250i	0.361799	−	0.117556i
$297$	−22.7100	−	17.2666i	−1.31777	−	1.00191i
$298$	−5.89806	+	0.934161i	−0.341666	+	0.0541145i
$299$	−13.9418			−0.806276
$300$	7.99686	+	3.32418i	0.461699	+	0.191922i
$301$	6.13974			0.353889
$302$	−2.98463	+	0.472718i	−0.171746	+	0.0272019i
$303$	6.66529	−	11.3538i	0.382911	−	0.652256i
$304$	2.05900	−	0.669009i	0.118092	−	0.0383703i
$305$	4.64080	−	5.32391i	0.265731	−	0.304846i
$306$	−0.281808	+	0.609032i	−0.0161099	+	0.0348160i
$307$	−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
$309$	−7.96496	−	12.4618i	−0.453111	−	0.708927i
$310$	6.63242	+	1.66328i	0.376696	+	0.0944680i
$311$	−17.8640	+	24.5877i	−1.01298	+	1.39424i	−0.0959647	+	0.995385i	$0.530594\pi$
$311$	−17.8640	+	24.5877i	−1.01298	+	1.39424i	−0.917012	+	0.398859i	$0.869406\pi$
$312$	2.39054	−	10.8590i	0.135338	−	0.614768i
$313$	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
$315$	−12.6901	−	4.84814i	−0.715004	−	0.273162i
$316$	−9.35889	+	6.79963i	−0.526479	+	0.382509i
$317$	4.58149	+	8.99167i	0.257322	+	0.505023i	0.983138	−	0.182866i	$-0.0585376\pi$
$317$	4.58149	+	8.99167i	0.257322	+	0.505023i	−0.725816	+	0.687889i	$0.758538\pi$
$318$	−15.8801	+	14.0915i	−0.890514	+	0.790210i
$319$	39.5132	+	12.8386i	2.21231	+	0.718825i
$320$	−1.68558	−	1.46930i	−0.0942265	−	0.0821363i
$321$	−8.55642	+	2.22634i	−0.477573	+	0.124262i
$322$	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
$327$	−1.64891	−	16.8633i	−0.0911849	−	0.932543i
$328$	−1.35915	−	0.692523i	−0.0750467	−	0.0382382i
$329$	3.27315	+	10.0737i	0.180455	+	0.555382i
$330$	9.82069	+	18.8603i	0.540611	+	1.03822i
$331$	−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
$333$	6.77003	+	18.4308i	0.370995	+	1.01000i
$334$	−5.73229	−	7.88982i	−0.313657	−	0.431712i
$335$	−2.08465	−	5.18006i	−0.113896	−	0.283017i
$336$	2.70980	+	2.22707i	0.147832	+	0.121496i
$337$	−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
$339$	17.6230	+	14.4836i	0.957151	+	0.786642i
$340$	0.383604	−	0.320989i	0.0208038	−	0.0174081i
$341$	9.86844	+	13.5827i	0.534406	+	0.735546i
$342$	2.23941	+	6.09659i	0.121093	+	0.329666i
$343$	−14.1749	+	14.1749i	−0.765374	+	0.765374i
$344$	−0.936894	+	2.88346i	−0.0505139	+	0.155466i
$345$	−7.52794	−	3.75225i	−0.405290	−	0.202014i
$346$	−5.42059	−	16.6829i	−0.291413	−	0.896877i
$347$	22.1485	+	11.2852i	1.18899	+	0.605823i	0.932657	−	0.360765i	$-0.117484\pi$
$347$	22.1485	+	11.2852i	1.18899	+	0.605823i	0.256337	+	0.966587i	$0.417484\pi$
$348$	−1.27552	−	13.0446i	−0.0683749	−	0.699266i
$349$			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	−0.855943	−	0.517070i	$-0.827023\pi$
$353$	1.23037	−	2.41473i	0.0654859	−	0.128523i	0.921429	+	0.388547i	$0.127023\pi$
$354$	9.55550	−	2.48629i	0.507869	−	0.132145i
$355$	−3.03538	−	13.2302i	−0.161101	−	0.702184i
$356$	−8.63290	−	2.80500i	−0.457543	−	0.148665i
$357$	−0.586863	+	0.520760i	−0.0310601	+	0.0275616i
$358$	5.27651	+	10.3557i	0.278872	+	0.547317i
$359$	3.19128	−	2.31860i	0.168429	−	0.122371i	−0.500377	−	0.865807i	$-0.666805\pi$
$359$	3.19128	−	2.31860i	0.168429	−	0.122371i	0.668807	+	0.743436i	$0.266805\pi$
$360$	4.21332	−	5.21996i	0.222061	−	0.275116i
$361$	−11.5794	−	8.41294i	−0.609443	−	0.442787i
$362$	−0.618655	+	3.90603i	−0.0325158	+	0.205297i
$363$	−7.12882	+	32.3824i	−0.374166	+	1.69964i
$364$	7.64126	−	10.5173i	0.400511	−	0.551256i
$365$	0.467612	+	6.82114i	0.0244759	+	0.357035i
$366$	−2.94622	−	4.60960i	−0.154002	−	0.240947i
$367$	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
$369$	1.92173	−	4.15318i	0.100042	−	0.216206i
$370$	1.29545	−	14.5775i	0.0673471	−	0.757849i
$371$	−23.6077	+	7.67062i	−1.22565	+	0.398239i
$372$	2.68145	−	4.56762i	0.139027	−	0.236820i
$373$	−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
$375$	13.8476	−	13.5368i	0.715086	−	0.699036i
$376$	−5.23048			−0.269742
$377$	−47.9802	+	7.59932i	−2.47111	+	0.391385i
$378$	−6.36868	+	8.37647i	−0.327570	+	0.430839i
$379$	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
$381$	7.26283	−	18.5180i	0.372086	−	0.948705i
$382$	−11.9009	−	11.9009i	−0.608905	−	0.608905i
$383$	21.2826	−	10.8440i	1.08749	−	0.554104i	0.184093	−	0.982909i	$-0.441065\pi$
$383$	21.2826	−	10.8440i	1.08749	−	0.554104i	0.903397	+	0.428805i	$0.141065\pi$
$384$	−1.45942	+	0.932788i	−0.0744757	+	0.0476011i
$385$	1.70034	+	24.8031i	0.0866573	+	1.26409i
$386$	9.22037	−	12.6908i	0.469304	−	0.645942i
$387$	−8.75058	−	2.48122i	−0.444817	−	0.126128i
$388$	0.376840	−	2.37927i	0.0191311	−	0.120789i
$389$	−14.6439	−	10.6394i	−0.742476	−	0.539440i	0.151010	−	0.988532i	$-0.451748\pi$
$389$	−14.6439	−	10.6394i	−0.742476	−	0.539440i	−0.893486	+	0.449092i	$0.851748\pi$
$390$	−20.2428	−	14.4357i	−1.02503	−	0.730978i
$391$	−0.393024	+	0.285549i	−0.0198761	+	0.0144408i
$392$	−1.31615	−	2.58308i	−0.0664754	−	0.130465i
$393$	11.8743	+	13.3816i	0.598982	+	0.675013i
$394$	16.8838	+	5.48588i	0.850594	+	0.276375i
$395$	5.78443	+	25.2123i	0.291046	+	1.26857i
$396$	16.1590	−	3.19059i	0.812020	−	0.160333i
$397$	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	$0.00669086\pi$
$401$			0.841787i			0.0420368i	−0.999779	+	0.0210184i	$0.993309\pi$
$402$	−4.30466	+	0.420913i	−0.214697	+	0.0209933i
$403$	−17.4911	−	8.91216i	−0.871293	−	0.443946i
$404$	2.34889	+	7.22915i	0.116862	+	0.359664i
$405$	16.1271	+	12.0381i	0.801362	+	0.598179i
$406$	4.73546	−	14.5742i	0.235017	−	0.723307i
$407$	25.4091	−	25.4091i	1.25948	−	1.25948i
$408$	−0.155017	−	0.355079i	−0.00767450	−	0.0175790i
$409$	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
$411$	14.8354	−	18.0511i	0.731779	−	0.890396i
$412$	8.43375	+	1.33577i	0.415501	+	0.0658089i
$413$	11.4020	+	1.80589i	0.561054	+	0.0888622i
$414$	−4.42934	+	4.77812i	−0.217690	+	0.234832i
$415$	8.72867	+	21.6895i	0.428474	+	1.06470i
$416$	3.77332	+	5.19352i	0.185002	+	0.254633i
$417$	18.0792	−	7.89285i	0.885343	−	0.386515i
$418$	8.40490	−	8.40490i	0.411097	−	0.411097i
$419$	−0.0964938	+	0.296977i	−0.00471403	+	0.0145083i	−0.953386	−	0.301754i	$-0.902428\pi$
$419$	−0.0964938	+	0.296977i	−0.00471403	+	0.0145083i	0.948672	+	0.316262i	$0.102428\pi$
$420$	6.95651	−	3.62231i	0.339443	−	0.176751i
$421$	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
$423$	−0.593975	−	15.6802i	−0.0288800	−	0.762398i
$424$		−	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
$429$	−15.3722	−	59.0797i	−0.742179	−	2.85240i
$430$	5.11042	+	4.45470i	0.246446	+	0.214824i
$431$	−23.0434	−	7.48726i	−1.10996	−	0.360648i	−0.304033	−	0.952661i	$-0.598333\pi$
$431$	−23.0434	−	7.48726i	−1.10996	−	0.360648i	−0.805928	+	0.592013i	$0.798333\pi$
$432$	−2.96209	−	4.26919i	−0.142514	−	0.205402i
$433$	−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
$435$	−27.9523	−	8.80992i	−1.34021	−	0.422403i
$436$	7.91418	+	5.74999i	0.379021	+	0.275375i
$437$	−0.735524	+	4.64392i	−0.0351849	+	0.222149i
$438$	5.17219	+	1.13863i	0.247137	+	0.0544058i
$439$	−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
$441$	7.59423	−	4.23894i	0.361630	−	0.201854i
$442$	−1.27948	+	0.651925i	−0.0608585	+	0.0310089i
$443$	−16.9801	−	16.9801i	−0.806749	−	0.806749i	0.177391	−	0.984140i	$-0.443234\pi$
$443$	−16.9801	−	16.9801i	−0.806749	−	0.806749i	−0.984140	+	0.177391i	$0.943234\pi$
$444$	−10.5535	−	4.13914i	−0.500848	−	0.196435i
$445$	−13.3371	+	15.3002i	−0.632237	+	0.725301i
$446$	5.16436	−	1.67800i	0.244539	−	0.0794557i
$447$	8.91965	+	5.23633i	0.421885	+	0.247670i
$448$	−2.00015	+	0.316792i	−0.0944980	+	0.0149670i
$449$	6.98488			0.329637			0.164818	−	0.986324i	$-0.447296\pi$
$449$	6.98488			0.329637			0.164818	+	0.986324i	$0.447296\pi$
$450$	−7.04502	−	13.2426i	−0.332105	−	0.624264i
$451$	−8.37502			−0.394364
$452$	−13.0078	+	2.06024i	−0.611837	+	0.0969055i
$453$	4.51366	+	2.64977i	0.212070	+	0.124497i
$454$	18.9792	−	6.16673i	0.890739	−	0.289419i
$455$	−14.9376	−	24.9375i	−0.700286	−	1.16909i
$456$	−3.49092	−	1.36915i	−0.163477	−	0.0641165i
$457$	−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
$459$	1.04687	−	0.505042i	0.0488637	−	0.0235733i
$460$	4.50511	−	1.81302i	0.210052	−	0.0845326i
$461$	1.73628	−	2.38979i	0.0808667	−	0.111303i	−0.766667	−	0.642045i	$-0.778086\pi$
$461$	1.73628	−	2.38979i	0.0808667	−	0.111303i	0.847534	+	0.530741i	$0.178086\pi$
$462$	18.8072	+	4.14030i	0.874990	+	0.192624i
$463$	−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
$465$	−7.04579	−	9.51963i	−0.326741	−	0.441462i
$466$	−3.93564	+	2.85941i	−0.182315	+	0.132460i
$467$	−2.07783	−	4.07796i	−0.0961504	−	0.188706i	0.837922	−	0.545791i	$-0.183771\pi$
$467$	−2.07783	−	4.07796i	−0.0961504	−	0.188706i	−0.934072	+	0.357085i	$0.883771\pi$
$468$	−15.1409	+	11.9016i	−0.699889	+	0.550152i
$469$	−4.80942	−	1.56267i	−0.222078	−	0.0721576i
$470$	−4.58459	+	10.7597i	−0.211471	+	0.496308i
$471$	−2.71948	−	10.4517i	−0.125307	−	0.481588i
$472$	−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
$477$	36.7465	−	1.39198i	1.68251	−	0.0637343i
$478$	−14.9493	−	7.61704i	−0.683765	−	0.348395i
$479$	8.54601	+	26.3019i	0.390477	+	1.20176i	0.932428	+	0.361355i	$0.117686\pi$
$479$	8.54601	+	26.3019i	0.390477	+	1.20176i	−0.541951	+	0.840410i	$0.682314\pi$
$480$	0.639651	+	3.81980i	0.0291959	+	0.174349i
$481$	−12.9836	+	39.9593i	−0.591999	+	1.82199i
$482$	12.0274	−	12.0274i	0.547835	−	0.547835i
$483$	−6.98129	+	3.04783i	−0.317660	+	0.138681i
$484$	−11.2524	−	15.4876i	−0.511472	−	0.703980i
$485$	−4.56413	−	2.86067i	−0.207247	−	0.129896i
$486$	12.4620	−	9.36471i	0.565289	−	0.424792i
$487$	−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
$489$	6.30240	−	7.66848i	0.285004	−	0.346781i
$490$	−6.46731	+	0.443356i	−0.292164	+	0.0200288i
$491$	4.84555	+	6.66933i	0.218677	+	0.300982i	0.904235	−	0.427035i	$-0.140442\pi$
$491$	4.84555	+	6.66933i	0.218677	+	0.300982i	−0.685558	+	0.728018i	$0.740442\pi$
$492$	1.05711	+	2.42140i	0.0476583	+	0.109165i
$493$	−1.19693	+	1.19693i	−0.0539071	+	0.0539071i
$494$	−4.29473	+	13.2178i	−0.193229	+	0.594698i
$495$	7.60018	−	36.0375i	0.341603	−	1.61977i
$496$	0.944961	+	2.90829i	0.0424300	+	0.130586i
$497$	−10.9532	−	5.58095i	−0.491320	−	0.250340i
$498$	18.0241	−	1.76242i	0.807680	−	0.0789757i
$499$		−	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	$0.473411\pi$
$503$	−17.3097	+	33.9723i	−0.771804	+	1.51475i	−0.855237	+	0.518236i	$0.826589\pi$
$504$	−1.17683	−	5.96016i	−0.0524203	−	0.265487i
$505$	16.9300	+	1.50451i	0.753377	+	0.0669497i
$506$	11.3402	+	3.68464i	0.504132	+	0.163802i
$507$	32.4311	+	36.5477i	1.44032	+	1.62314i
$508$	5.21374	+	10.2325i	0.231322	+	0.453996i
$509$	5.62616	−	4.08765i	0.249375	−	0.181182i	−0.456075	−	0.889942i	$-0.650745\pi$
$509$	5.62616	−	4.08765i	0.249375	−	0.181182i	0.705450	+	0.708760i	$0.250745\pi$
$510$	−0.866314	+	0.00765643i	−0.0383610	+	0.000339032i
$511$	5.00944	+	3.63957i	0.221605	+	0.161005i
$512$	0.156434	−	0.987688i	0.00691349	−	0.0436501i
$513$	3.70809	−	10.6207i	0.163716	−	0.468917i
$514$	−9.82444	+	13.5222i	−0.433337	+	0.596438i
$515$	10.1401	−	16.1784i	0.446828	−	0.712904i
$516$	4.42475	−	2.82808i	0.194789	−	0.124499i
$517$	−25.5871	+	13.0373i	−1.12532	+	0.573379i
$518$	−9.37203	−	9.37203i	−0.411783	−	0.411783i
$519$	−11.0935	+	28.2849i	−0.486950	+	1.24157i
$520$	13.9910	−	3.20995i	0.613548	−	0.140766i
$521$	20.6631	−	6.71385i	0.905267	−	0.294139i	0.180858	−	0.983509i	$-0.442113\pi$
$521$	20.6631	−	6.71385i	0.905267	−	0.294139i	0.724409	+	0.689370i	$0.242113\pi$
$522$	−12.6390	+	18.8580i	−0.553192	+	0.825394i
$523$	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
$525$	−1.35403	−	17.4853i	−0.0590949	−	0.763123i
$526$	7.29888			0.318246
$527$	−0.675613	+	0.107007i	−0.0294302	+	0.00466128i
$528$	−4.81433	+	8.20081i	−0.209517	+	0.356894i
$529$	17.3885	−	5.64988i	0.756023	−	0.245647i
$530$	−25.2154	−	10.7440i	−1.09528	−	0.466689i
$531$	−15.5207	−	7.18164i	−0.673541	−	0.311657i
$532$	−3.10010	−	3.10010i	−0.134407	−	0.134407i
$533$	8.72515	−	4.44569i	0.377928	−	0.192564i
$534$	8.46707	+	13.2474i	0.366406	+	0.573271i
$535$	−7.32488	−	8.75372i	−0.316682	−	0.378456i
$536$	1.46779	−	2.02024i	0.0633987	−	0.0872609i
$537$	4.32805	−	19.6600i	0.186769	−	0.848392i
$538$	4.81318	−	30.3892i	0.207511	−	1.31017i
$539$	−12.8769	−	9.35565i	−0.554649	−	0.402976i
$540$	−11.3785	+	2.35135i	−0.489654	+	0.101186i
$541$	−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
$543$	5.12347	−	4.54638i	0.219869	−	0.195104i
$544$	0.212742	+	0.0691240i	0.00912123	+	0.00296367i
$545$	18.7653	−	11.2404i	0.803816	−	0.481487i
$546$	−21.7912	+	5.66997i	−0.932579	+	0.242652i
$547$	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
$552$	−0.366069	−	3.74377i	−0.0155809	−	0.159346i
$553$	20.8732	+	10.6354i	0.887619	+	0.452265i
$554$	−2.97037	−	9.14187i	−0.126199	−	0.388401i
$555$	−17.7650	+	18.0818i	−0.754082	+	0.767530i
$556$	−3.51952	+	10.8320i	−0.149261	+	0.459377i
$557$	−3.60663	+	3.60663i	−0.152818	+	0.152818i	−0.779375	−	0.626557i	$-0.784463\pi$
$557$	−3.60663	+	3.60663i	−0.152818	+	0.152818i	0.626557	+	0.779375i	$0.284463\pi$
$558$	−8.61131	+	3.16312i	−0.364546	+	0.133905i
$559$	−11.4401	−	15.7460i	−0.483866	−	0.665985i
$560$	−1.10148	+	4.39220i	−0.0465460	+	0.185604i
$561$	−1.64339	−	1.35063i	−0.0693839	−	0.0570236i
$562$	20.4433	+	3.23790i	0.862349	+	0.136583i
$563$	25.1492	+	3.98324i	1.05991	+	0.167874i	0.661965	−	0.749534i	$-0.269723\pi$
$563$	25.1492	+	3.98324i	1.05991	+	0.167874i	0.397948	+	0.917408i	$0.369723\pi$
$564$	6.99901	+	5.75219i	0.294712	+	0.242211i
$565$	−7.16341	+	28.5645i	−0.301367	+	1.20172i
$566$	−7.17155	−	9.87079i	−0.301443	−	0.414900i
$567$	17.7340	−	4.20480i	0.744759	−	0.176585i
$568$	4.29245	−	4.29245i	0.180107	−	0.180107i
$569$	−9.49637	+	29.2268i	−0.398108	+	1.22525i	0.528406	+	0.848992i	$0.322790\pi$
$569$	−9.49637	+	29.2268i	−0.398108	+	1.22525i	−0.926514	+	0.376260i	$0.877210\pi$
$570$	−5.87635	+	5.98115i	−0.246133	+	0.250523i
$571$	−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
$573$	2.83690	+	29.0128i	0.118513	+	1.21203i
$574$			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
$579$	−26.2945	+	6.84170i	−1.09276	+	0.284332i
$580$	14.5159	−	8.69506i	0.602741	−	0.361043i
$581$	20.1376	+	6.54311i	0.835449	+	0.271454i
$582$	−3.12085	+	2.76933i	−0.129363	+	0.114792i
$583$	−30.5528	−	59.9633i	−1.26537	−	2.48343i
$584$	−2.47370	+	1.79725i	−0.102363	+	0.0743708i
$585$	11.2118	+	41.5785i	0.463550	+	1.71906i
$586$	−0.175477	−	0.127491i	−0.00724887	−	0.00526661i
$587$	−3.88731	+	24.5435i	−0.160447	+	1.01302i	0.767701	+	0.640808i	$0.221400\pi$
$587$	−3.88731	+	24.5435i	−0.160447	+	1.01302i	−0.928148	+	0.372212i	$0.878600\pi$
$588$	−1.07957	+	4.90389i	−0.0445205	+	0.202233i
$589$	−3.89134	+	5.35598i	−0.160340	+	0.220689i
$590$	8.18016	+	9.77584i	0.336772	+	0.402465i
$591$	−16.5595	−	25.9086i	−0.681167	−	1.06574i
$592$	5.83160	−	2.97135i	0.239677	−	0.122122i
$593$	−25.7915	−	25.7915i	−1.05913	−	1.05913i	−0.998138	−	0.0609902i	$-0.980574\pi$
$593$	−25.7915	−	25.7915i	−1.05913	−	1.05913i	−0.0609902	−	0.998138i	$-0.519426\pi$
$594$	−25.1315	−	13.5014i	−1.03116	−	0.553968i
$595$	−0.931852	−	0.397052i	−0.0382022	−	0.0162775i
$596$	−5.67931	+	1.84532i	−0.232634	+	0.0755873i
$597$	−2.43907	+	4.15475i	−0.0998246	+	0.170043i
$598$	−13.7702	+	2.18098i	−0.563104	+	0.0891870i
$599$	−36.9040			−1.50786			−0.753929	−	0.656956i	$-0.771844\pi$
$599$	−36.9040			−1.50786			−0.753929	+	0.656956i	$0.771844\pi$
$600$	8.41843	+	2.03227i	0.343681	+	0.0829671i
$601$	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
$603$	6.22305	+	4.17079i	0.253422	+	0.169848i
$604$	−2.87393	+	0.933797i	−0.116939	+	0.0379956i
$605$	−41.7226	+	9.57237i	−1.69626	+	0.389172i
$606$	4.80711	−	12.2567i	0.195276	−	0.497893i
$607$	−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
$609$	−22.3645	+	14.2943i	−0.906256	+	0.579234i
$610$	3.75082	−	5.98434i	0.151866	−	0.242299i
$611$	19.7363	−	27.1646i	0.798444	−	1.09896i
$612$	−0.183064	+	0.645618i	−0.00739994	+	0.0260976i
$613$	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
$615$	5.90767	−	0.0522116i	0.238220	−	0.00210538i
$616$	−8.99493	+	6.53520i	−0.362416	+	0.263311i
$617$	−11.4572	−	22.4860i	−0.461250	−	0.905254i	−0.998102	−	0.0615777i	$-0.980387\pi$
$617$	−11.4572	−	22.4860i	−0.461250	−	0.905254i	0.536852	−	0.843676i	$-0.319613\pi$
$618$	−9.81635	−	11.0624i	−0.394872	−	0.444994i
$619$	−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
$621$	11.1817	−	1.52256i	0.448706	−	0.0610984i
$622$	−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
$627$	−20.4900	+	2.00353i	−0.818292	+	0.0800133i
$628$	5.55561	+	2.83072i	0.221693	+	0.112958i
$629$	0.452414	+	1.39239i	0.0180389	+	0.0555181i
$630$	−13.2923	−	2.80329i	−0.529576	−	0.111686i
$631$	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
$633$	9.82723	+	22.5100i	0.390597	+	0.894694i
$634$	5.93169	+	8.16427i	0.235577	+	0.324245i
$635$	25.6194	−	1.75630i	1.01668	−	0.0696966i
$636$	−13.4802	+	16.4022i	−0.534526	+	0.650388i
$637$	18.3815	+	2.91135i	0.728303	+	0.115352i
$638$	41.0351	+	6.49933i	1.62460	+	0.257311i
$639$	13.3556	+	12.3807i	0.528338	+	0.489771i
$640$	−1.89467	−	1.18753i	−0.0748935	−	0.0469411i
$641$	−10.4719	−	14.4133i	−0.413614	−	0.569291i	0.550481	−	0.834847i	$-0.314444\pi$
$641$	−10.4719	−	14.4133i	−0.413614	−	0.569291i	−0.964095	+	0.265557i	$0.914444\pi$
$642$	−8.10280	+	3.53745i	−0.319792	+	0.139612i
$643$	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
$645$	−1.93933	−	11.5811i	−0.0763609	−	0.456004i
$646$	0.149651	+	0.460577i	0.00588792	+	0.0181212i
$647$	−1.92749	−	0.982107i	−0.0757776	−	0.0386106i	0.415691	−	0.909506i	$-0.363540\pi$
$647$	−1.92749	−	0.982107i	−0.0757776	−	0.0386106i	−0.491469	+	0.870895i	$0.663540\pi$
$648$	−0.731385	+	8.97023i	−0.0287315	+	0.352384i
$649$			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	$-0.810199\pi$
$653$	2.89362	−	5.67905i	0.113236	−	0.222238i	0.940668	+	0.339327i	$0.110199\pi$
$654$	−4.26661	−	16.3977i	−0.166838	−	0.641202i
$655$	−9.05355	+	21.2480i	−0.353752	+	0.830229i
$656$	−1.45075	−	0.471379i	−0.0566424	−	0.0184042i
$657$	−5.66880	−	7.21170i	−0.221161	−	0.281355i
$658$	4.80873	+	9.43766i	0.187464	+	0.367918i
$659$	27.9601	−	20.3142i	1.08917	−	0.791330i	0.109913	−	0.993941i	$-0.464943\pi$
$659$	27.9601	−	20.3142i	1.08917	−	0.791330i	0.979259	+	0.202611i	$0.0649427\pi$
$660$	12.6502	+	17.0918i	0.492407	+	0.665296i
$661$	−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
$663$	2.42904	+	0.534741i	0.0943362	+	0.0207676i
$664$	−6.14580	+	8.45897i	−0.238503	+	0.328272i
$665$	−9.09455	+	3.65999i	−0.352672	+	0.141928i
$666$	9.56989	+	17.1448i	0.370826	+	0.664349i
$667$	−14.6431	+	7.46104i	−0.566984	+	0.288893i
$668$	−6.89596	−	6.89596i	−0.266813	−	0.266813i
$669$	−8.75590	−	3.43410i	−0.338523	−	0.132770i
$670$	−2.86932	−	4.79017i	−0.110852	−	0.185060i
$671$	16.4925	−	5.35875i	0.636687	−	0.206872i
$672$	3.02482	+	1.77574i	0.116685	+	0.0685007i
$673$	−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
$675$	−5.13644	+	25.4680i	−0.197702	+	0.980262i
$676$	−28.2106			−1.08502
$677$	21.6557	−	3.42993i	0.832297	−	0.131823i	0.274277	−	0.961651i	$-0.411561\pi$
$677$	21.6557	−	3.42993i	0.832297	−	0.131823i	0.558020	+	0.829828i	$0.311561\pi$
$678$	19.6718	+	11.5484i	0.755490	+	0.443515i
$679$	−4.63951	+	1.50747i	−0.178048	+	0.0578514i
$680$	0.328667	−	0.377046i	0.0126038	−	0.0144591i
$681$	−32.1783	−	12.6205i	−1.23308	−	0.483617i
$682$	11.8717	+	11.8717i	0.454593	+	0.454593i
$683$	−11.0839	+	5.64753i	−0.424114	+	0.216097i	−0.653002	−	0.757356i	$-0.726491\pi$
$683$	−11.0839	+	5.64753i	−0.424114	+	0.216097i	0.228888	+	0.973453i	$0.426491\pi$
$684$	3.16555	+	5.67121i	0.121038	+	0.216844i
$685$	29.2584	+	7.33742i	1.11790	+	0.280348i
$686$	−11.7830	+	16.2179i	−0.449875	+	0.619200i
$687$	−19.4637	−	4.28482i	−0.742585	−	0.163476i
$688$	−0.474286	+	2.99453i	−0.0180820	+	0.114165i
$689$	63.6603	+	46.2519i	2.42526	+	1.76206i
$690$	−8.02224	−	2.52842i	−0.305401	−	0.0962554i
$691$	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
$693$	−20.6130	−	26.2233i	−0.783023	−	0.996141i
$694$	23.6412	+	7.68150i	0.897408	+	0.291586i
$695$	19.1977	+	16.7344i	0.728209	+	0.634772i
$696$	−3.30044	−	12.6845i	−0.125103	−	0.480805i
$697$	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	$0.877701\pi$
$702$	33.3491	+	0.725327i	1.25868	+	0.0273757i
$703$	12.6252	+	6.43284i	0.476167	+	0.242619i
$704$	−1.69660	−	5.22161i	−0.0639432	−	0.196797i
$705$	17.9676	−	9.35590i	0.676701	−	0.352364i
$706$	0.837472	−	2.57747i	0.0315187	−	0.0970045i
$707$	10.8845	−	10.8845i	0.409353	−	0.409353i
$708$	9.04891	−	3.95049i	0.340079	−	0.148469i
$709$	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
$711$	−25.4512	−	23.5934i	−0.954496	−	0.884821i
$712$	−8.96541	−	1.41998i	−0.335993	−	0.0532160i
$713$	−6.55944	−	1.03891i	−0.245653	−	0.0389076i
$714$	−0.498173	+	0.606155i	−0.0186436	+	0.0226848i
$715$	60.4420	−	50.5763i	2.26040	−	1.89145i
$716$	6.83154	+	9.40281i	0.255307	+	0.351399i
$717$	11.6271	+	26.6329i	0.434224	+	0.994624i
$718$	2.78928	−	2.78928i	0.104095	−	0.104095i
$719$	5.35309	−	16.4751i	0.199637	−	0.614418i	−0.800255	−	0.599660i	$-0.795302\pi$
$719$	5.35309	−	16.4751i	0.199637	−	0.614418i	0.999891	−	0.0147577i	$-0.00469769\pi$
$720$	3.34487	−	5.81480i	0.124656	−	0.216705i
$721$	−5.34349	−	16.4456i	−0.199002	−	0.612465i
$722$	−12.7529	−	6.49795i	−0.474615	−	0.241829i
$723$	−29.3213	+	2.86706i	−1.09047	+	0.106627i
$724$			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
$729$	−26.9745	−	1.17392i	−0.999054	−	0.0434785i
$730$	1.52892	+	6.66401i	0.0565877	+	0.246646i
$731$	−0.645002	−	0.209574i	−0.0238563	−	0.00775137i
$732$	−3.63105	−	4.09195i	−0.134207	−	0.151243i
$733$	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
$735$	9.14162	+	6.51912i	0.337194	+	0.240461i
$736$	1.75700	+	1.27654i	0.0647640	+	0.0470538i
$737$	2.14474	−	13.5414i	0.0790026	−	0.498803i
$738$	1.24837	−	4.40267i	0.0459533	−	0.162065i
$739$	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
$741$	20.2831	−	12.9639i	0.745118	−	0.476242i
$742$	−22.1171	+	11.2692i	−0.811946	+	0.413707i
$743$	−24.6348	−	24.6348i	−0.903763	−	0.903763i	0.0919959	−	0.995759i	$-0.470675\pi$
$743$	−24.6348	−	24.6348i	−0.903763	−	0.903763i	−0.995759	+	0.0919959i	$0.970675\pi$
$744$	1.93390	−	4.93086i	0.0709003	−	0.180774i
$745$	−1.18196	+	13.3004i	−0.0433037	+	0.487291i
$746$	−24.8503	+	8.07436i	−0.909835	+	0.295623i
$747$	−26.0566	−	17.4636i	−0.953363	−	0.638959i
$748$	1.21301	−	0.192122i	0.0443521	−	0.00702468i
$749$	−10.3371			−0.377709
$750$	11.5595	−	15.5364i	0.422093	−	0.567308i
$751$	−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
$753$	−23.7657	+	40.4828i	−0.866069	+	1.47528i
$754$	−46.2007	+	15.0115i	−1.68253	+	0.546687i
$755$	−0.598113	+	6.73049i	−0.0217676	+	0.244948i
$756$	−4.97991	+	9.26962i	−0.181117	+	0.337133i
$757$	−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
$759$	−11.1223	−	17.4018i	−0.403715	−	0.631644i
$760$	−0.331089	−	4.82966i	−0.0120099	−	0.175190i
$761$	17.3299	−	23.8525i	0.628208	−	0.864654i	−0.369711	−	0.929147i	$-0.620543\pi$
$761$	17.3299	−	23.8525i	0.628208	−	0.864654i	0.997918	+	0.0644935i	$0.0205432\pi$
$762$	4.27656	−	19.4261i	0.154923	−	0.703735i
$763$	3.09901	−	19.5664i	0.112192	−	0.708350i
$764$	−13.6161	−	9.89270i	−0.492614	−	0.357905i
$765$	1.16765	+	0.942478i	0.0422165	+	0.0340754i
$766$	19.3242	−	14.0399i	0.698212	−	0.507281i
$767$	−16.6138	−	32.6064i	−0.599890	−	1.17735i
$768$	−1.29553	+	1.14961i	−0.0467485	+	0.0414829i
$769$	−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
$771$	28.0172	−	7.28994i	1.00901	−	0.262541i
$772$	7.12158	−	13.9769i	0.256311	−	0.503039i
$773$	−5.89531	−	37.2215i	−0.212039	−	1.33876i	−0.832281	−	0.554353i	$-0.812966\pi$
$773$	−5.89531	−	37.2215i	−0.212039	−	1.33876i	0.620242	−	0.784411i	$-0.287034\pi$
$774$	−9.03100	−	1.08178i	−0.324613	−	0.0388838i
$775$	7.21500	−	13.4804i	0.259170	−	0.484231i
$776$		−	2.40893i		−	0.0864756i
$777$	2.23407	+	22.8477i	0.0801468	+	0.819657i
$778$	−16.1280	−	8.21763i	−0.578217	−	0.294616i
$779$	−1.02051	−	3.14082i	−0.0365637	−	0.112532i
$780$	−22.2518	−	11.0913i	−0.796743	−	0.397131i
$781$	10.2991	−	31.6974i	0.368532	−	1.13422i
$782$	−0.343516	+	0.343516i	−0.0122841	+	0.0122841i
$783$	37.6514	−	11.3347i	1.34555	−	0.405069i
$784$	−1.70402	−	2.34539i	−0.0608580	−	0.0837639i
$785$	10.6927	−	8.94736i	0.381639	−	0.319345i
$786$	13.8215	+	11.3593i	0.492997	+	0.405173i
$787$	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
$789$	−9.76677	−	8.02689i	−0.347706	−	0.285765i
$790$	9.65728	+	23.9970i	0.343591	+	0.853775i
$791$	15.6764	+	21.5767i	0.557388	+	0.767179i
$792$	15.4609	−	5.67913i	0.549381	−	0.201799i
$793$	−14.3375	+	14.3375i	−0.509138	+	0.509138i
$794$	4.34636	−	13.3767i	0.154247	−	0.474722i
$795$	21.9255	+	42.1071i	0.777619	+	1.49339i
$796$	−0.859546	−	2.64541i	−0.0304658	−	0.0937641i
$797$	−10.7200	−	5.46214i	−0.379724	−	0.193479i	0.253702	−	0.967282i	$-0.418352\pi$
$797$	−10.7200	−	5.46214i	−0.379724	−	0.193479i	−0.633426	+	0.773804i	$0.718352\pi$
$798$	0.738992	+	7.55763i	0.0261600	+	0.267537i
$799$		−	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
$804$	−4.18582	+	1.08913i	−0.147622	+	0.0384106i
$805$	−7.41319	−	6.46200i	−0.261280	−	0.227755i
$806$	−18.6699	−	6.06622i	−0.657620	−	0.213674i
$807$	−39.8610	+	35.3712i	−1.40317	+	1.24512i
$808$	3.45086	+	6.77270i	0.121401	+	0.238263i
$809$	31.1568	−	22.6367i	1.09542	−	0.795866i	0.115110	−	0.993353i	$-0.463278\pi$
$809$	31.1568	−	22.6367i	1.09542	−	0.795866i	0.980305	+	0.197487i	$0.0632781\pi$
$810$	17.8117	+	9.36708i	0.625841	+	0.329126i
$811$	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
$813$	5.91718	−	26.8786i	0.207525	−	0.942674i
$814$	21.1214	−	29.0712i	0.740306	−	1.01894i
$815$	12.4295	+	3.11708i	0.435388	+	0.109187i
$816$	−0.208655	−	0.326458i	−0.00730440	−	0.0114283i
$817$	−5.84842	+	2.97992i	−0.204610	+	0.104254i
$818$	10.7674	+	10.7674i	0.376472	+	0.376472i
$819$	35.3948	+	16.3777i	1.23679	+	0.572282i
$820$	−2.24129	+	2.57120i	−0.0782691	+	0.0897902i
$821$	−5.82793	+	1.89361i	−0.203396	+	0.0660875i	−0.408943	−	0.912560i	$-0.634103\pi$
$821$	−5.82793	+	1.89361i	−0.203396	+	0.0660875i	0.205547	+	0.978647i	$0.434103\pi$
$822$	11.8290	−	20.1497i	0.412583	−	0.702800i
$823$	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
$825$	46.2478	−	11.0417i	1.61014	−	0.384423i
$826$	11.5441			0.401670
$827$	−16.3031	+	2.58216i	−0.566914	+	0.0897904i	−0.433311	−	0.901244i	$-0.642655\pi$
$827$	−16.3031	+	2.58216i	−0.566914	+	0.0897904i	−0.133603	+	0.991035i	$0.542655\pi$
$828$	−3.62734	+	5.41220i	−0.126059	+	0.188087i
$829$	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
$831$	−6.07900	+	15.4996i	−0.210878	+	0.537674i
$832$	4.53931	+	4.53931i	0.157372	+	0.157372i
$833$	0.577809	−	0.294409i	0.0200199	−	0.0102007i
$834$	16.6219	−	10.6239i	0.575570	−	0.367875i
$835$	−20.2302	+	8.14137i	−0.700094	+	0.281744i
$836$	6.98661	−	9.61624i	0.241637	−	0.332585i
$837$	15.0016	+	5.23760i	0.518530	+	0.181038i
$838$	−0.0488483	+	0.308416i	−0.00168744	+	0.0106541i
$839$	7.33822	+	5.33153i	0.253343	+	0.184065i	0.707207	−	0.707006i	$-0.249955\pi$
$839$	7.33822	+	5.33153i	0.253343	+	0.184065i	−0.453864	+	0.891071i	$0.649955\pi$
$840$	6.30421	−	4.66595i	0.217516	−	0.160991i
$841$	−22.8654	+	16.6127i	−0.788462	+	0.572851i
$842$	17.2897	+	33.9330i	0.595843	+	1.16941i
$843$	−23.7947	−	26.8151i	−0.819534	−	0.923560i
$844$	−13.4866	−	4.38208i	−0.464229	−	0.150837i
$845$	−24.7270	+	58.0325i	−0.850634	+	1.99638i
$846$	−3.03959	−	15.3942i	−0.104503	−	0.529265i
$847$	−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
$852$	−10.4644	+	1.02322i	−0.358504	+	0.0350549i
$853$	−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
$855$	14.4410	−	1.54101i	0.493871	−	0.0527015i
$856$	1.57739	−	4.85470i	0.0539140	−	0.165930i
$857$	−7.62449	+	7.62449i	−0.260448	+	0.260448i	−0.825236	−	0.564788i	$-0.808958\pi$
$857$	−7.62449	+	7.62449i	−0.260448	+	0.260448i	0.564788	+	0.825236i	$0.308958\pi$
$858$	−24.4251	−	55.9476i	−0.833859	−	1.91002i
$859$	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
$861$	3.39720	−	4.13356i	0.115776	−	0.140871i
$862$	−23.9310	−	3.79029i	−0.815092	−	0.129098i
$863$	−23.7530	−	3.76211i	−0.808562	−	0.128064i	−0.261552	−	0.965189i	$-0.584234\pi$
$863$	−23.7530	−	3.76211i	−0.808562	−	0.128064i	−0.547010	+	0.837126i	$0.684234\pi$
$864$	−3.59347	−	3.75326i	−0.122252	−	0.127688i
$865$	−39.1319	+	2.68263i	−1.33053	+	0.0912121i
$866$	−3.18499	−	4.38377i	−0.108230	−	0.148966i
$867$	−26.9059	+	11.7463i	−0.913772	+	0.398926i
$868$	4.37883	−	4.37883i	0.148627	−	0.148627i
$869$	−19.6267	+	60.4048i	−0.665790	+	2.04909i
$870$	−28.9864	−	4.32875i	−0.982730	−	0.146758i
$871$	4.95372	+	15.2460i	0.167850	+	0.516590i
$872$	8.71624	+	4.44115i	0.295169	+	0.150396i
$873$	7.22161	−	0.273559i	0.244415	−	0.00925856i
$874$			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
$879$	0.0946011	+	0.363578i	0.00319081	+	0.0122632i
$880$	−12.2286	−	1.08670i	−0.412224	−	0.0366328i
$881$	−27.0334	−	8.78367i	−0.910777	−	0.295930i	−0.184099	−	0.982908i	$-0.558937\pi$
$881$	−27.0334	−	8.78367i	−0.910777	−	0.295930i	−0.726678	+	0.686978i	$0.758937\pi$
$882$	6.83761	−	5.37475i	0.230234	−	0.180977i
$883$	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
$885$	−0.195118	−	22.0773i	−0.00655882	−	0.742121i
$886$	−19.4273	−	14.1148i	−0.652674	−	0.474195i
$887$	1.55300	−	9.80527i	0.0521447	−	0.329229i	−0.947802	−	0.318861i	$-0.896700\pi$
$887$	1.55300	−	9.80527i	0.0521447	−	0.329229i	0.999946	−	0.0103679i	$-0.00330025\pi$
$888$	−11.0711	−	2.43724i	−0.371522	−	0.0817885i
$889$	13.6698	−	18.8149i	0.458471	−	0.631032i
$890$	−10.7794	+	17.1982i	−0.361325	+	0.576487i
$891$	18.7809	+	45.7047i	0.629185	+	1.53116i
$892$	4.83828	−	2.46523i	0.161998	−	0.0825419i
$893$	−8.00712	−	8.00712i	−0.267948	−	0.267948i
$894$	9.62898	+	3.77653i	0.322041	+	0.126306i
$895$	25.3306	−	5.81157i	0.846709	−	0.194259i
$896$	−1.92596	+	0.625783i	−0.0643419	+	0.0209060i
$897$	20.8247	+	12.2252i	0.695315	+	0.408189i
$898$	6.89889	−	1.09268i	0.230219	−	0.0364631i
$899$	−23.1403			−0.771773
$900$	−9.02989	−	11.9775i	−0.300996	−	0.399251i
$901$	2.74191			0.0913462
$902$	−8.27191	+	1.31014i	−0.275424	+	0.0436229i
$903$	−9.17082	−	5.38379i	−0.305186	−	0.179161i
$904$	−12.5254	+	4.06975i	−0.416589	+	0.135358i
$905$	8.13532	+	3.46637i	0.270427	+	0.115226i
$906$	4.87260	+	1.91105i	0.161881	+	0.0634905i
$907$	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
$909$	−19.9117	+	11.1143i	−0.660428	+	0.368638i
$910$	−18.6548	−	22.2937i	−0.618400	−	0.739030i
$911$	−25.0445	+	34.4709i	−0.829763	+	1.14207i	0.158205	+	0.987406i	$0.449429\pi$
$911$	−25.0445	+	34.4709i	−0.829763	+	1.14207i	−0.987967	+	0.154664i	$0.950571\pi$
$912$	−3.66213	−	0.806197i	−0.121265	−	0.0266959i
$913$	−8.98029	+	56.6993i	−0.297204	+	1.87647i
$914$	−5.18916	−	3.77014i	−0.171642	−	0.124705i
$915$	−11.6003	+	3.88283i	−0.383494	+	0.128363i
$916$	9.30889	−	6.76331i	0.307574	−	0.223466i
$917$	9.49617	+	18.6373i	0.313591	+	0.615458i
$918$	0.954976	−	0.662590i	0.0315189	−	0.0218687i
$919$	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
$921$	2.93817	+	11.2922i	0.0968159	+	0.372090i
$922$	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
$927$	0.969677	+	25.5983i	0.0318484	+	0.840757i
$928$	6.74246	+	3.43546i	0.221332	+	0.112774i
$929$	8.15479	+	25.0979i	0.267550	+	0.823434i	0.991095	+	0.133157i	$0.0425114\pi$
$929$	8.15479	+	25.0979i	0.267550	+	0.823434i	−0.723545	+	0.690277i	$0.757489\pi$
$930$	−8.44825	−	8.30022i	−0.277029	−	0.272175i
$931$	1.93950	−	5.96916i	0.0635644	−	0.195631i
$932$	−3.43987	+	3.43987i	−0.112677	+	0.112677i
$933$	48.2436	−	21.0618i	1.57943	−	0.689531i
$934$	−2.69018	−	3.70271i	−0.0880254	−	0.121157i
$935$	0.668004	−	2.66370i	0.0218461	−	0.0871124i
$936$	−13.0927	+	14.1236i	−0.427947	+	0.461646i
$937$	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
$939$	−9.60427	+	11.6861i	−0.313424	+	0.381360i
$940$	−2.84496	+	11.3444i	−0.0927923	+	0.370014i
$941$	3.24570	+	4.46733i	0.105807	+	0.145631i	0.858637	−	0.512584i	$-0.171312\pi$
$941$	3.24570	+	4.46733i	0.105807	+	0.145631i	−0.752830	+	0.658215i	$0.771312\pi$
$942$	−4.32100	−	9.89759i	−0.140786	−	0.322481i
$943$	2.34254	−	2.34254i	0.0762837	−	0.0762837i
$944$	−1.76157	+	5.42156i	−0.0573342	+	0.176457i
$945$	14.7037	+	18.3692i	0.478312	+	0.597550i
$946$	5.14385	+	15.8312i	0.167241	+	0.514715i
$947$	3.30825	+	1.68564i	0.107504	+	0.0547759i	0.506916	−	0.861996i	$-0.330786\pi$
$947$	3.30825	+	1.68564i	0.107504	+	0.0547759i	−0.399412	+	0.916772i	$0.630786\pi$
$948$	19.9416	−	1.94991i	0.647674	−	0.0633302i
$949$		−	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	$0.400716\pi$
$953$	−19.8647	+	38.9868i	−0.643482	+	1.26290i	−0.950359	+	0.311156i	$0.899284\pi$
$954$	36.0764	−	7.12326i	1.16802	−	0.230624i
$955$	−32.2851	+	19.3389i	−1.04472	+	0.625791i
$956$	−15.9568	−	5.18468i	−0.516080	−	0.167685i
$957$	−47.7623	−	53.8250i	−1.54394	−	1.73991i
$958$	12.5553	+	24.6412i	0.405644	+	0.796121i
$959$	22.1008	−	16.0572i	0.713673	−	0.518514i
$960$	1.22932	+	3.67271i	0.0396762	+	0.118536i
$961$	17.5143	+	12.7249i	0.564978	+	0.410481i
$962$	−6.57270	+	41.4984i	−0.211912	+	1.33796i
$963$	14.7328	+	4.17747i	0.474758	+	0.134617i
$964$	9.99786	−	13.7609i	0.322009	−	0.443208i
$965$	−22.5099	−	26.9009i	−0.724620	−	0.865969i
$966$	−6.41855	+	4.10242i	−0.206514	+	0.131993i
$967$	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
$969$	0.306266	−	0.780885i	0.00983869	−	0.0250856i
$970$	−4.95545	−	2.11146i	−0.159110	−	0.0677950i
$971$	−26.2601	+	8.53244i	−0.842728	+	0.273819i	−0.698397	−	0.715711i	$-0.746103\pi$
$971$	−26.2601	+	8.53244i	−0.842728	+	0.273819i	−0.144331	+	0.989529i	$0.546103\pi$
$972$	10.8436	−	11.1989i	0.347810	−	0.359205i
$973$	22.7804	−	3.60807i	0.730308	−	0.115669i
$974$	−30.2646			−0.969741
$975$	−42.3200	+	36.0529i	−1.35533	+	1.15462i
$976$	3.15851			0.101102
$977$	9.20136	−	1.45735i	0.294378	−	0.0466248i	−0.00749885	−	0.999972i	$-0.502387\pi$
$977$	9.20136	−	1.45735i	0.294378	−	0.0466248i	0.301876	+	0.953347i	$0.402387\pi$
$978$	5.02519	−	8.55998i	0.160688	−	0.273718i
$979$	−47.3974	+	15.4004i	−1.51483	+	0.492197i
$980$	−6.31834	+	1.44961i	−0.201832	+	0.0463061i
$981$	−12.3241	+	26.6343i	−0.393477	+	0.850368i
$982$	5.82921	+	5.82921i	0.186017	+	0.186017i
$983$	−41.2314	+	21.0084i	−1.31508	+	0.670065i	−0.963905	−	0.266245i	$-0.914217\pi$
$983$	−41.2314	+	21.0084i	−1.31508	+	0.670065i	−0.351172	+	0.936311i	$0.614217\pi$
$984$	1.42289	+	2.22622i	0.0453600	+	0.0709692i
$985$	21.0818	−	33.6355i	0.671722	−	1.07172i
$986$	−0.994954	+	1.36944i	−0.0316858	+	0.0436118i
$987$	3.94435	−	17.9171i	0.125550	−	0.570307i
$988$	−2.17413	+	13.7269i	−0.0691684	+	0.436712i
$989$	−5.32698	−	3.87028i	−0.169388	−	0.123068i
$990$	1.86910	−	36.7828i	0.0594039	−	1.16903i
$991$	−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
$993$	32.6359	−	28.9599i	1.03567	−	0.919015i
$994$	−11.6914	−	3.79878i	−0.370830	−	0.120490i
$995$	−6.19532	−	0.550554i	−0.196405	−	0.0174537i
$996$	17.5265	−	4.56031i	0.555349	−	0.144499i
$997$	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.137.6	yes	80
3.2	odd	2	inner	150.2.l.a.137.1	yes	80
5.2	odd	4		750.2.l.a.293.7		80
5.3	odd	4		750.2.l.c.293.4		80
5.4	even	2		750.2.l.b.707.5		80
15.2	even	4		750.2.l.a.293.2		80
15.8	even	4		750.2.l.c.293.9		80
15.14	odd	2		750.2.l.b.707.10		80
25.2	odd	20		750.2.l.b.593.10		80
25.11	even	5		750.2.l.c.407.9		80
25.14	even	10		750.2.l.a.407.2		80
25.23	odd	20	inner	150.2.l.a.23.1	✓	80
75.2	even	20		750.2.l.b.593.5		80
75.11	odd	10		750.2.l.c.407.4		80
75.14	odd	10		750.2.l.a.407.7		80
75.23	even	20	inner	150.2.l.a.23.6	yes	80

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

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)

\(f(q)\)	\(=\)	\(q+(0.987688 - 0.156434i) q^{2} +(-1.49368 - 0.876876i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.197931 - 2.22729i) q^{5} +(-1.61247 - 0.632416i) q^{6} +(-1.43195 - 1.43195i) q^{7} +(0.891007 - 0.453990i) q^{8} +(1.46218 + 2.61955i) q^{9} +O(q^{10})\)	\(q+(0.987688 - 0.156434i) q^{2} +(-1.49368 - 0.876876i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.197931 - 2.22729i) q^{5} +(-1.61247 - 0.632416i) q^{6} +(-1.43195 - 1.43195i) q^{7} +(0.891007 - 0.453990i) q^{8} +(1.46218 + 2.61955i) q^{9} +(-0.152931 - 2.23083i) q^{10} +(3.22713 - 4.44177i) q^{11} +(-1.69155 - 0.372385i) q^{12} +(-1.00424 + 6.34051i) q^{13} +(-1.63832 - 1.19031i) q^{14} +(-2.24870 + 3.15331i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.101553 + 0.199309i) q^{17} +(1.85396 + 2.35856i) q^{18} +(2.05900 + 0.669009i) q^{19} +(-0.500027 - 2.17944i) q^{20} +(0.883235 + 3.39451i) 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} +(0.112987 - 5.19492i) q^{27} +(-1.80436 - 0.919366i) q^{28} +(2.33841 + 7.19688i) q^{29} +(-1.72773 + 3.46626i) q^{30} +(-0.944961 + 2.90829i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-8.71519 + 3.80480i) q^{33} +(0.131482 + 0.180969i) q^{34} +(-3.47279 + 2.90593i) q^{35} +(2.20010 + 2.03950i) q^{36} +(6.46438 + 1.02386i) q^{37} +(2.13830 + 0.338674i) q^{38} +(7.05986 - 8.59013i) q^{39} +(-0.834811 - 2.07439i) q^{40} +(-0.896615 - 1.23409i) q^{41} +(1.40338 + 3.21455i) q^{42} +(-2.14384 + 2.14384i) q^{43} +(1.69660 - 5.22161i) q^{44} +(6.12391 - 2.73821i) q^{45} +(0.671116 + 2.06548i) q^{46} +(-4.66039 - 2.37459i) q^{47} +(-1.72383 + 0.168558i) 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} +(-0.701069 - 5.14864i) q^{54} +(-9.25436 - 8.06693i) q^{55} +(-1.92596 - 0.625783i) q^{56} +(-2.48885 - 2.80477i) q^{57} +(3.43546 + 6.74246i) q^{58} +(-4.61185 + 3.35071i) q^{59} +(-1.16422 + 3.69386i) q^{60} +(2.55529 + 1.85653i) q^{61} +(-0.478370 + 3.02031i) q^{62} +(1.65729 - 5.84481i) q^{63} +(0.587785 - 0.809017i) q^{64} +(13.9234 + 3.49171i) q^{65} +(-8.01269 + 5.12131i) q^{66} +(2.22498 - 1.13368i) q^{67} +(0.158173 + 0.158173i) q^{68} +(1.37347 - 3.50192i) q^{69} +(-2.97544 + 3.41342i) q^{70} +(5.77333 - 1.87587i) q^{71} +(2.49206 + 1.67022i) q^{72} +(-3.02002 + 0.478324i) q^{73} +6.54496 q^{74} +(6.57824 + 5.63265i) q^{75} +2.16496 q^{76} +(-10.9815 + 1.73929i) q^{77} +(5.62915 - 9.58877i) q^{78} +(-11.0020 + 3.57478i) q^{79} +(-1.14904 - 1.91826i) q^{80} +(-4.72407 + 7.66049i) q^{81} +(-1.07863 - 1.07863i) q^{82} +(-9.31624 + 4.74686i) q^{83} +(1.88897 + 2.95544i) q^{84} +(0.464020 - 0.186739i) q^{85} +(-1.78208 + 2.45282i) q^{86} +(2.81793 - 12.8003i) q^{87} +(0.858876 - 5.42273i) q^{88} +(-7.34358 - 5.33542i) q^{89} +(5.62016 - 3.66248i) q^{90} +(10.5173 - 7.64126i) q^{91} +(0.985966 + 1.93507i) q^{92} +(3.96168 - 3.51545i) q^{93} +(-4.97448 - 1.61631i) q^{94} +(1.89762 - 4.45357i) q^{95} +(-1.67624 + 0.436149i) 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

Modular forms

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