LMFDB - Embedded newform 115.2.j.a.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(4,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 4]))

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

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

chi := DirichletCharacter("115.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.j (of order $22$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	115.9
Dual form			115.2.j.a.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.176688 - 0.601743i) q^{2} +(0.563711 - 0.488459i) q^{3} +(1.35163 - 0.868641i) q^{4} +(-1.82300 - 1.29486i) q^{5} +(-0.393527 - 0.252905i) q^{6} +(0.620531 + 0.283387i) q^{7} +(-1.70945 - 1.48124i) q^{8} +(-0.347766 + 2.41877i) q^{9} +O(q^{10})$	\(q+(-0.176688 - 0.601743i) q^{2} +(0.563711 - 0.488459i) q^{3} +(1.35163 - 0.868641i) q^{4} +(-1.82300 - 1.29486i) q^{5} +(-0.393527 - 0.252905i) q^{6} +(0.620531 + 0.283387i) q^{7} +(-1.70945 - 1.48124i) q^{8} +(-0.347766 + 2.41877i) q^{9} +(-0.457073 + 1.32576i) q^{10} +(0.318051 + 0.0933881i) q^{11} +(0.337635 - 1.14988i) q^{12} +(4.48376 - 2.04767i) q^{13} +(0.0608859 - 0.423471i) q^{14} +(-1.66013 + 0.160532i) q^{15} +(0.745594 - 1.63262i) q^{16} +(-2.80876 + 4.37052i) q^{17} +(1.51692 - 0.218100i) q^{18} +(-3.00018 + 1.92810i) q^{19} +(-3.58879 - 0.166644i) q^{20} +(0.488223 - 0.143355i) q^{21} -0.207885i q^{22} +(4.74694 + 0.683074i) q^{23} -1.68716 q^{24} +(1.64666 + 4.72107i) q^{25} +(-2.02439 - 2.33628i) q^{26} +(2.19521 + 3.41582i) q^{27} +(1.08489 - 0.155984i) q^{28} +(1.41248 + 0.907743i) q^{29} +(0.389924 + 0.970609i) q^{30} +(-5.48185 + 6.32639i) q^{31} +(-5.59195 - 0.804002i) q^{32} +(0.224905 - 0.102711i) q^{33} +(3.12620 + 0.917936i) q^{34} +(-0.764281 - 1.32012i) q^{35} +(1.63099 + 3.57136i) q^{36} +(-5.09981 - 0.733242i) q^{37} +(1.69032 + 1.46467i) q^{38} +(1.52735 - 3.34442i) q^{39} +(1.19831 + 4.91381i) q^{40} +(-0.445398 - 3.09781i) q^{41} +(-0.172526 - 0.268456i) q^{42} +(5.58778 - 4.84184i) q^{43} +(0.511008 - 0.150045i) q^{44} +(3.76595 - 3.95910i) q^{45} +(-0.427690 - 2.97713i) q^{46} -0.330027i q^{47} +(-0.377169 - 1.28452i) q^{48} +(-4.27927 - 4.93855i) q^{49} +(2.54993 - 1.82502i) q^{50} +(0.551487 + 3.83567i) q^{51} +(4.28171 - 6.66247i) q^{52} +(-8.22242 - 3.75505i) q^{53} +(1.66758 - 1.92449i) q^{54} +(-0.458882 - 0.582078i) q^{55} +(-0.640999 - 1.40359i) q^{56} +(-0.749439 + 2.55236i) q^{57} +(0.296661 - 1.01033i) q^{58} +(-0.559864 - 1.22593i) q^{59} +(-2.10444 + 1.65904i) q^{60} +(3.65863 - 4.22228i) q^{61} +(4.77543 + 2.18087i) q^{62} +(-0.901246 + 1.40237i) q^{63} +(-0.00663133 - 0.0461219i) q^{64} +(-10.8253 - 2.07296i) q^{65} +(-0.101543 - 0.117187i) q^{66} +(0.137535 + 0.468400i) q^{67} +8.34713i q^{68} +(3.00955 - 1.93363i) q^{69} +(-0.659332 + 0.693149i) q^{70} +(13.9609 - 4.09929i) q^{71} +(4.17727 - 3.61962i) q^{72} +(-4.09859 - 6.37754i) q^{73} +(0.459850 + 3.19833i) q^{74} +(3.23429 + 1.85699i) q^{75} +(-2.38031 + 5.21216i) q^{76} +(0.170895 + 0.148082i) q^{77} +(-2.28235 - 0.328152i) q^{78} +(4.48603 + 9.82303i) q^{79} +(-3.47324 + 2.01083i) q^{80} +(-4.12801 - 1.21209i) q^{81} +(-1.78539 + 0.815360i) q^{82} +(-3.74104 - 0.537881i) q^{83} +(0.535373 - 0.617854i) q^{84} +(10.7796 - 4.33050i) q^{85} +(-3.90083 - 2.50691i) q^{86} +(1.23962 - 0.178231i) q^{87} +(-0.405360 - 0.630752i) q^{88} +(-9.39014 - 10.8368i) q^{89} +(-3.04776 - 1.56661i) q^{90} +3.36260 q^{91} +(7.00945 - 3.20012i) q^{92} +6.24391i q^{93} +(-0.198592 + 0.0583118i) q^{94} +(7.96596 + 0.369896i) q^{95} +(-3.54497 + 2.27821i) q^{96} +(-7.93510 + 1.14089i) q^{97} +(-2.21564 + 3.44760i) q^{98} +(-0.336491 + 0.736813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.176688	−	0.601743i	−0.124937	−	0.425496i	0.873141	−	0.487468i	$-0.162079\pi$
$2$	−0.176688	−	0.601743i	−0.124937	−	0.425496i	−0.998078	+	0.0619715i	$0.980261\pi$
$3$	0.563711	−	0.488459i	0.325459	−	0.282012i	−0.476770	−	0.879028i	$-0.658193\pi$
$3$	0.563711	−	0.488459i	0.325459	−	0.282012i	0.802229	+	0.597016i	$0.203647\pi$
$4$	1.35163	−	0.868641i	0.675816	−	0.434320i
$5$	−1.82300	−	1.29486i	−0.815271	−	0.579080i
$5$	−1.82300	−	1.29486i	−0.815271	−	0.579080i
$6$	−0.393527	−	0.252905i	−0.160657	−	0.103248i
$7$	0.620531	+	0.283387i	0.234539	+	0.107110i	0.529218	−	0.848486i	$-0.322485\pi$
$7$	0.620531	+	0.283387i	0.234539	+	0.107110i	−0.294679	+	0.955596i	$0.595213\pi$
$8$	−1.70945	−	1.48124i	−0.604381	−	0.523699i
$9$	−0.347766	+	2.41877i	−0.115922	+	0.806255i
$10$	−0.457073	+	1.32576i	−0.144539	+	0.419243i
$11$	0.318051	+	0.0933881i	0.0958959	+	0.0281576i	0.329328	−	0.944215i	$-0.393178\pi$
$11$	0.318051	+	0.0933881i	0.0958959	+	0.0281576i	−0.233433	+	0.972373i	$0.574996\pi$
$12$	0.337635	−	1.14988i	0.0974667	−	0.331941i
$13$	4.48376	−	2.04767i	1.24357	−	0.567920i	0.318576	−	0.947897i	$-0.396795\pi$
$13$	4.48376	−	2.04767i	1.24357	−	0.567920i	0.924996	+	0.379977i	$0.124068\pi$
$14$	0.0608859	−	0.423471i	0.0162725	−	0.113177i
$15$	−1.66013	+	0.160532i	−0.428644	+	0.0414491i
$16$	0.745594	−	1.63262i	0.186399	−	0.408156i
$17$	−2.80876	+	4.37052i	−0.681225	+	1.06001i	0.312690	+	0.949855i	$0.398770\pi$
$17$	−2.80876	+	4.37052i	−0.681225	+	1.06001i	−0.993915	+	0.110151i	$0.964866\pi$
$18$	1.51692	−	0.218100i	0.357542	−	0.0514067i
$19$	−3.00018	+	1.92810i	−0.688289	+	0.442337i	−0.837477	−	0.546472i	$-0.815970\pi$
$19$	−3.00018	+	1.92810i	−0.688289	+	0.442337i	0.149188	+	0.988809i	$0.452334\pi$
$20$	−3.58879	−	0.166644i	−0.802479	−	0.0372628i
$21$	0.488223	−	0.143355i	0.106539	−	0.0312827i
$22$		−	0.207885i		−	0.0443213i
$23$	4.74694	+	0.683074i	0.989805	+	0.142431i
$23$	4.74694	+	0.683074i	0.989805	+	0.142431i
$24$	−1.68716			−0.344390
$25$	1.64666	+	4.72107i	0.329332	+	0.944214i
$26$	−2.02439	−	2.33628i	−0.397016	−	0.458181i
$27$	2.19521	+	3.41582i	0.422469	+	0.657375i
$28$	1.08489	−	0.155984i	0.205025	−	0.0294781i
$29$	1.41248	+	0.907743i	0.262290	+	0.168564i	0.665176	−	0.746687i	$-0.268357\pi$
$29$	1.41248	+	0.907743i	0.262290	+	0.168564i	−0.402886	+	0.915250i	$0.631993\pi$
$30$	0.389924	+	0.970609i	0.0711900	+	0.177208i
$31$	−5.48185	+	6.32639i	−0.984569	+	1.13625i	0.00610251	+	0.999981i	$0.498057\pi$
$31$	−5.48185	+	6.32639i	−0.984569	+	1.13625i	−0.990671	+	0.136272i	$0.956488\pi$
$32$	−5.59195	−	0.804002i	−0.988527	−	0.142129i
$33$	0.224905	−	0.102711i	0.0391509	−	0.0178796i
$34$	3.12620	+	0.917936i	0.536139	+	0.157425i
$35$	−0.764281	−	1.32012i	−0.129187	−	0.223140i
$36$	1.63099	+	3.57136i	0.271831	+	0.595227i
$37$	−5.09981	−	0.733242i	−0.838404	−	0.120544i	−0.290280	−	0.956942i	$-0.593749\pi$
$37$	−5.09981	−	0.733242i	−0.838404	−	0.120544i	−0.548124	+	0.836397i	$0.684658\pi$
$38$	1.69032	+	1.46467i	0.274205	+	0.237600i
$39$	1.52735	−	3.34442i	0.244571	−	0.535537i
$40$	1.19831	+	4.91381i	0.189470	+	0.776941i
$41$	−0.445398	−	3.09781i	−0.0695595	−	0.483797i	−0.994588	−	0.103899i	$-0.966868\pi$
$41$	−0.445398	−	3.09781i	−0.0695595	−	0.483797i	0.925028	−	0.379898i	$-0.124041\pi$
$42$	−0.172526	−	0.268456i	−0.0266213	−	0.0414236i
$43$	5.58778	−	4.84184i	0.852129	−	0.738374i	−0.114809	−	0.993388i	$-0.536625\pi$
$43$	5.58778	−	4.84184i	0.852129	−	0.738374i	0.966937	+	0.255014i	$0.0820800\pi$
$44$	0.511008	−	0.150045i	0.0770373	−	0.0226202i
$45$	3.76595	−	3.95910i	0.561394	−	0.590188i
$46$	−0.427690	−	2.97713i	−0.0630595	−	0.438953i
$47$		−	0.330027i		−	0.0481395i	−0.999710	−	0.0240697i	$-0.992338\pi$
$47$		−	0.330027i		−	0.0481395i	0.999710	−	0.0240697i	$-0.00766237\pi$
$48$	−0.377169	−	1.28452i	−0.0544397	−	0.185404i
$49$	−4.27927	−	4.93855i	−0.611325	−	0.705507i
$50$	2.54993	−	1.82502i	0.360614	−	0.258097i
$51$	0.551487	+	3.83567i	0.0772236	+	0.537102i
$52$	4.28171	−	6.66247i	0.593766	−	0.923918i
$53$	−8.22242	−	3.75505i	−1.12944	−	0.515796i	−0.239052	−	0.971007i	$-0.576837\pi$
$53$	−8.22242	−	3.75505i	−1.12944	−	0.515796i	−0.890384	+	0.455211i	$0.849564\pi$
$54$	1.66758	−	1.92449i	0.226929	−	0.261890i
$55$	−0.458882	−	0.582078i	−0.0618756	−	0.0784874i
$56$	−0.640999	−	1.40359i	−0.0856571	−	0.187563i
$57$	−0.749439	+	2.55236i	−0.0992657	+	0.338068i
$58$	0.296661	−	1.01033i	0.0389535	−	0.132663i
$59$	−0.559864	−	1.22593i	−0.0728881	−	0.159603i	0.869681	−	0.493615i	$-0.164325\pi$
$59$	−0.559864	−	1.22593i	−0.0728881	−	0.159603i	−0.942569	+	0.334012i	$0.891597\pi$
$60$	−2.10444	+	1.65904i	−0.271682	+	0.214181i
$61$	3.65863	−	4.22228i	0.468440	−	0.540608i	−0.471537	−	0.881846i	$-0.656301\pi$
$61$	3.65863	−	4.22228i	0.468440	−	0.540608i	0.939977	+	0.341238i	$0.110846\pi$
$62$	4.77543	+	2.18087i	0.606481	+	0.276971i
$63$	−0.901246	+	1.40237i	−0.113546	+	0.176682i
$64$	−0.00663133	−	0.0461219i	−0.000828917	−	0.00576524i
$65$	−10.8253	−	2.07296i	−1.34272	−	0.257119i
$66$	−0.101543	−	0.117187i	−0.0124991	−	0.0144247i
$67$	0.137535	+	0.468400i	0.0168025	+	0.0572242i	0.967468	−	0.252995i	$-0.0814157\pi$
$67$	0.137535	+	0.468400i	0.0168025	+	0.0572242i	−0.950665	+	0.310219i	$0.899597\pi$
$68$			8.34713i			1.01224i
$69$	3.00955	−	1.93363i	0.362308	−	0.232781i
$70$	−0.659332	+	0.693149i	−0.0788052	+	0.0828471i
$71$	13.9609	−	4.09929i	1.65685	−	0.486496i	0.686287	−	0.727331i	$-0.259240\pi$
$71$	13.9609	−	4.09929i	1.65685	−	0.486496i	0.970566	+	0.240835i	$0.0774214\pi$
$72$	4.17727	−	3.61962i	0.492296	−	0.426577i
$73$	−4.09859	−	6.37754i	−0.479704	−	0.746434i	0.514082	−	0.857741i	$-0.328133\pi$
$73$	−4.09859	−	6.37754i	−0.479704	−	0.746434i	−0.993786	+	0.111307i	$0.964496\pi$
$74$	0.459850	+	3.19833i	0.0534565	+	0.371798i
$75$	3.23429	+	1.85699i	0.373463	+	0.214427i
$76$	−2.38031	+	5.21216i	−0.273041	+	0.597876i
$77$	0.170895	+	0.148082i	0.0194753	+	0.0168755i
$78$	−2.28235	−	0.328152i	−0.258425	−	0.0371559i
$79$	4.48603	+	9.82303i	0.504717	+	1.10518i	0.974907	+	0.222612i	$0.0714582\pi$
$79$	4.48603	+	9.82303i	0.504717	+	1.10518i	−0.470190	+	0.882565i	$0.655815\pi$
$80$	−3.47324	+	2.01083i	−0.388320	+	0.224818i
$81$	−4.12801	−	1.21209i	−0.458668	−	0.134677i
$82$	−1.78539	+	0.815360i	−0.197163	+	0.0900415i
$83$	−3.74104	−	0.537881i	−0.410633	−	0.0590401i	−0.0660968	−	0.997813i	$-0.521055\pi$
$83$	−3.74104	−	0.537881i	−0.410633	−	0.0590401i	−0.344536	+	0.938773i	$0.611964\pi$
$84$	0.535373	−	0.617854i	0.0584140	−	0.0674134i
$85$	10.7796	−	4.33050i	1.16921	−	0.469708i
$86$	−3.90083	−	2.50691i	−0.420638	−	0.270328i
$87$	1.23962	−	0.178231i	0.132902	−	0.0191084i
$88$	−0.405360	−	0.630752i	−0.0432115	−	0.0672384i
$89$	−9.39014	−	10.8368i	−0.995353	−	1.14870i	−0.988879	−	0.148720i	$-0.952485\pi$
$89$	−9.39014	−	10.8368i	−0.995353	−	1.14870i	−0.00647382	−	0.999979i	$-0.502061\pi$
$90$	−3.04776	−	1.56661i	−0.321262	−	0.165135i
$91$	3.36260			0.352496
$92$	7.00945	−	3.20012i	0.730786	−	0.333635i
$93$			6.24391i			0.647464i
$94$	−0.198592	+	0.0583118i	−0.0204832	+	0.00601440i
$95$	7.96596	+	0.369896i	0.817290	+	0.0379506i
$96$	−3.54497	+	2.27821i	−0.361807	+	0.232519i
$97$	−7.93510	+	1.14089i	−0.805687	+	0.115840i	−0.532839	−	0.846217i	$-0.678875\pi$
$97$	−7.93510	+	1.14089i	−0.805687	+	0.115840i	−0.272848	+	0.962057i	$0.587966\pi$
$98$	−2.21564	+	3.44760i	−0.223813	+	0.348260i
$99$	−0.336491	+	0.736813i	−0.0338186	+	0.0740525i
$100$	6.32659	+	4.95079i	0.632659	+	0.495079i
$101$	−1.33265	+	9.26880i	−0.132604	+	0.922281i	0.809538	+	0.587067i	$0.199718\pi$
$101$	−1.33265	+	9.26880i	−0.132604	+	0.922281i	−0.942142	+	0.335213i	$0.891192\pi$
$102$	2.21065	−	1.00957i	0.218887	−	0.0999623i
$103$	−5.41741	+	18.4500i	−0.533794	+	1.81793i	0.0403576	+	0.999185i	$0.487150\pi$
$103$	−5.41741	+	18.4500i	−0.533794	+	1.81793i	−0.574151	+	0.818749i	$0.694668\pi$
$104$	−10.6978	−	3.14117i	−1.04901	−	0.308017i
$105$	−1.07566	−	0.370845i	−0.104973	−	0.0361908i
$106$	−0.806776	+	5.61125i	−0.0783610	+	0.545013i
$107$	3.02873	+	2.62441i	0.292799	+	0.253712i	0.788856	−	0.614578i	$-0.210674\pi$
$107$	3.02873	+	2.62441i	0.292799	+	0.253712i	−0.496057	+	0.868290i	$0.665219\pi$
$108$	5.93424	+	2.71008i	0.571022	+	0.260777i
$109$	4.33801	+	2.78787i	0.415506	+	0.267030i	0.731648	−	0.681682i	$-0.238751\pi$
$109$	4.33801	+	2.78787i	0.415506	+	0.267030i	−0.316142	+	0.948712i	$0.602388\pi$
$110$	−0.269183	+	0.378975i	−0.0256656	+	0.0361338i
$111$	−3.23298	+	2.07771i	−0.306861	+	0.197207i
$112$	0.925328	−	0.801802i	0.0874353	−	0.0757631i
$113$	−1.24377	−	4.23590i	−0.117004	−	0.398480i	0.880077	−	0.474832i	$-0.157491\pi$
$113$	−1.24377	−	4.23590i	−0.117004	−	0.398480i	−0.997081	+	0.0763517i	$0.975673\pi$
$114$	1.66828			0.156249
$115$	−7.76918	−	7.39188i	−0.724480	−	0.689296i
$116$	2.69765			0.250470
$117$	3.39352	+	11.5573i	0.313731	+	1.06847i
$118$	−0.638774	+	0.553501i	−0.0588039	+	0.0509539i
$119$	−2.98147	+	1.91608i	−0.273311	+	0.175646i
$120$	3.07569	+	2.18464i	0.280771	+	0.199429i
$121$	−9.16135	−	5.88764i	−0.832850	−	0.535240i
$122$	−3.18716	−	1.45553i	−0.288552	−	0.131777i
$123$	−1.76423	−	1.52871i	−0.159075	−	0.137839i
$124$	−1.91408	+	13.3127i	−0.171889	+	1.19552i
$125$	3.11127	−	10.7387i	0.278281	−	0.960500i
$126$	1.00310	+	0.294538i	0.0893635	+	0.0262395i
$127$	3.92240	−	13.3585i	0.348056	−	1.18537i	−0.580525	−	0.814243i	$-0.697153\pi$
$127$	3.92240	−	13.3585i	0.348056	−	1.18537i	0.928581	−	0.371129i	$-0.121029\pi$
$128$	−10.3044	+	4.70588i	−0.910792	+	0.415945i
$129$	0.784857	−	5.45880i	0.0691028	−	0.480620i
$130$	0.665316	+	6.88034i	0.0583521	+	0.603446i
$131$	3.15052	−	6.89868i	0.275263	−	0.602741i	−0.720626	−	0.693324i	$-0.756146\pi$
$131$	3.15052	−	6.89868i	0.275263	−	0.602741i	0.995889	+	0.0905827i	$0.0288730\pi$
$132$	0.214770	−	0.334188i	0.0186933	−	0.0290874i
$133$	−2.40810	+	0.346233i	−0.208809	+	0.0300222i
$134$	0.257556	−	0.165521i	0.0222494	−	0.0142988i
$135$	0.421141	−	9.06954i	0.0362460	−	0.780582i
$136$	11.2752	−	3.31071i	0.966843	−	0.283891i
$137$			10.7067i			0.914738i	0.889277	+	0.457369i	$0.151208\pi$
$137$			10.7067i			0.914738i	−0.889277	+	0.457369i	$0.848792\pi$
$138$	−1.69530	−	1.46933i	−0.144313	−	0.125078i
$139$	−2.70899			−0.229774			−0.114887	−	0.993379i	$-0.536651\pi$
$139$	−2.70899			−0.229774			−0.114887	+	0.993379i	$0.536651\pi$
$140$	−2.17973	−	1.12043i	−0.184221	−	0.0946932i
$141$	−0.161205	−	0.186040i	−0.0135759	−	0.0156674i
$142$	−4.93343	−	7.67657i	−0.414004	−	0.644204i
$143$	1.61729	−	0.232531i	0.135245	−	0.0194453i
$144$	3.68964	+	2.37119i	0.307470	+	0.197599i
$145$	−1.39954	−	3.48378i	−0.116226	−	0.289312i
$146$	−3.11347	+	3.59313i	−0.257672	+	0.297370i
$147$	−4.82455	−	0.693666i	−0.397922	−	0.0572126i
$148$	−7.52999	+	3.43883i	−0.618961	+	0.282670i
$149$	20.8446	+	6.12051i	1.70765	+	0.501412i	0.982355	−	0.187024i	$-0.0598843\pi$
$149$	20.8446	+	6.12051i	1.70765	+	0.501412i	0.725297	+	0.688436i	$0.241702\pi$
$150$	0.545974	−	2.27432i	0.0445786	−	0.185697i
$151$	−1.55851	−	3.41266i	−0.126830	−	0.277718i	0.835556	−	0.549405i	$-0.185146\pi$
$151$	−1.55851	−	3.41266i	−0.126830	−	0.277718i	−0.962386	+	0.271687i	$0.912418\pi$
$152$	7.98464	+	1.14802i	0.647640	+	0.0931165i
$153$	−9.59447	−	8.31365i	−0.775667	−	0.672119i
$154$	0.0589120	−	0.128999i	0.00474726	−	0.0103951i
$155$	18.1852	−	4.43477i	1.46067	−	0.356209i
$156$	−0.840692	−	5.84714i	−0.0673093	−	0.468146i
$157$	−7.15764	−	11.1375i	−0.571242	−	0.888869i	0.428652	−	0.903470i	$-0.358989\pi$
$157$	−7.15764	−	11.1375i	−0.571242	−	0.888869i	−0.999893	+	0.0146006i	$0.995352\pi$
$158$	5.11831	−	4.43504i	0.407191	−	0.352833i
$159$	−6.46926	+	1.89954i	−0.513045	+	0.150644i
$160$	9.15306	+	8.70651i	0.723613	+	0.688310i
$161$	2.75205	+	1.76909i	0.216892	+	0.139424i
$162$			2.69816i			0.211988i
$163$	4.49707	+	15.3156i	0.352238	+	1.19961i	0.925024	+	0.379907i	$0.124044\pi$
$163$	4.49707	+	15.3156i	0.352238	+	1.19961i	−0.572787	+	0.819704i	$0.694138\pi$
$164$	−3.29290	−	3.80021i	−0.257132	−	0.296746i
$165$	−0.542998	−	0.103979i	−0.0422723	−	0.00809479i
$166$	0.337330	+	2.34618i	0.0261819	+	0.182099i
$167$	−5.69144	+	8.85605i	−0.440417	+	0.685302i	−0.988517	−	0.151111i	$-0.951715\pi$
$167$	−5.69144	+	8.85605i	−0.440417	+	0.685302i	0.548100	+	0.836413i	$0.315351\pi$
$168$	−1.04694	−	0.478119i	−0.0807728	−	0.0368877i
$169$	7.39801	−	8.53776i	0.569077	−	0.656750i
$170$	−4.51047	−	5.72140i	−0.345937	−	0.438811i
$171$	−3.62026	−	7.92726i	−0.276848	−	0.606213i
$172$	3.34680	−	11.3982i	0.255191	−	0.869101i
$173$	2.09003	−	7.11798i	0.158902	−	0.541170i	−0.841098	−	0.540883i	$-0.818090\pi$
$173$	2.09003	−	7.11798i	0.158902	−	0.541170i	1.00000		0.000287607i	$-9.15482e-5\pi$
$174$	−0.326275	−	0.714443i	−0.0247349	−	0.0541618i
$175$	−0.316085	+	3.39621i	−0.0238938	+	0.256730i
$176$	0.389604	−	0.449627i	0.0293675	−	0.0338919i
$177$	−0.914418	−	0.417601i	−0.0687319	−	0.0313888i
$178$	−4.86185	+	7.56518i	−0.364411	+	0.567034i
$179$	2.25969	+	15.7165i	0.168897	+	1.17471i	0.881169	+	0.472802i	$0.156757\pi$
$179$	2.25969	+	15.7165i	0.168897	+	1.17471i	−0.712272	+	0.701904i	$0.752334\pi$
$180$	1.65113	−	8.62250i	0.123068	−	0.642683i
$181$	0.777285	+	0.897034i	0.0577751	+	0.0666760i	0.783901	−	0.620885i	$-0.213227\pi$
$181$	0.777285	+	0.897034i	0.0577751	+	0.0666760i	−0.726126	+	0.687561i	$0.758681\pi$
$182$	−0.594129	−	2.02342i	−0.0440398	−	0.149986i
$183$		−	4.16724i		−	0.308051i
$184$	−7.10283	−	8.19905i	−0.523628	−	0.604442i
$185$	8.34751	+	7.94026i	0.613721	+	0.583779i
$186$	3.75723	−	1.10322i	0.275493	−	0.0808922i
$187$	−1.30148	+	1.12774i	−0.0951738	+	0.0824686i
$188$	−0.286675	−	0.446075i	−0.0209079	−	0.0325334i
$189$	0.394199	+	2.74172i	0.0286738	+	0.199431i
$190$	−1.18490	−	4.85881i	−0.0859620	−	0.352495i
$191$	0.0820154	−	0.179589i	0.00593443	−	0.0129946i	−0.906642	−	0.421902i	$-0.861363\pi$
$191$	0.0820154	−	0.179589i	0.00593443	−	0.0129946i	0.912576	+	0.408907i	$0.134090\pi$
$192$	−0.0262668	−	0.0227603i	−0.00189564	−	0.00164258i
$193$	−3.40744	−	0.489915i	−0.245273	−	0.0352649i	0.0185820	−	0.999827i	$-0.494085\pi$
$193$	−3.40744	−	0.489915i	−0.245273	−	0.0352649i	−0.263855	+	0.964562i	$0.584994\pi$
$194$	2.08856	+	4.57331i	0.149950	+	0.328344i
$195$	−7.11493	+	4.11918i	−0.509510	+	0.294981i
$196$	−10.0738	−	2.95794i	−0.719559	−	0.211282i
$197$	21.3447	−	9.74780i	1.52075	−	0.694502i	0.532368	−	0.846513i	$-0.321302\pi$
$197$	21.3447	−	9.74780i	1.52075	−	0.694502i	0.988379	+	0.152011i	$0.0485750\pi$
$198$	0.502825	+	0.0722954i	0.0357343	+	0.00513781i
$199$	13.4152	−	15.4820i	0.950981	−	1.09749i	−0.0441598	−	0.999024i	$-0.514061\pi$
$199$	13.4152	−	15.4820i	0.950981	−	1.09749i	0.995140	−	0.0984657i	$-0.0313935\pi$
$200$	4.17818	−	10.5095i	0.295442	−	0.743136i
$201$	0.306324	+	0.196862i	0.0216064	+	0.0138856i
$202$	5.81290	−	0.835769i	0.408994	−	0.0588045i
$203$	0.619242	+	0.963559i	0.0434623	+	0.0676286i
$204$	4.07723	+	4.70537i	0.285463	+	0.329442i
$205$	−3.19928	+	6.22404i	−0.223447	+	0.434706i
$206$	12.0594			0.840215
$207$	−3.30302	+	11.2442i	−0.229576	+	0.781524i
$208$		−	8.84702i		−	0.613431i
$209$	−1.13427	+	0.333052i	−0.0784592	+	0.0230377i
$210$	−0.0330982	+	0.712792i	−0.00228399	+	0.0491873i
$211$	−8.87705	+	5.70494i	−0.611122	+	0.392744i	−0.809278	−	0.587427i	$-0.800141\pi$
$211$	−8.87705	+	5.70494i	−0.611122	+	0.392744i	0.198156	+	0.980171i	$0.436505\pi$
$212$	−14.3755	+	2.06688i	−0.987311	+	0.141954i
$213$	5.86758	−	9.13013i	0.402040	−	0.625586i
$214$	1.04408	−	2.28622i	0.0713720	−	0.156283i
$215$	−16.4560	+	1.59127i	−1.12229	+	0.108524i
$216$	1.30706	−	9.09081i	0.0889342	−	0.618551i
$217$	−5.19447	+	2.37224i	−0.352624	+	0.161038i
$218$	0.911108	−	3.10295i	0.0617080	−	0.210158i
$219$	−5.42559	−	1.59310i	−0.366627	−	0.107651i
$220$	−1.12586	−	0.388152i	−0.0759052	−	0.0261692i
$221$	−3.64446	+	25.3478i	−0.245153	+	1.70508i
$222$	1.82147	+	1.57832i	0.122249	+	0.105930i
$223$	7.12981	+	3.25608i	0.477447	+	0.218043i	0.639578	−	0.768726i	$-0.279109\pi$
$223$	7.12981	+	3.25608i	0.477447	+	0.218043i	−0.162130	+	0.986769i	$0.551836\pi$
$224$	−3.24214	−	2.08359i	−0.216624	−	0.139216i
$225$	−11.9918	+	2.34106i	−0.799454	+	0.156071i
$226$	−2.32916	+	1.49686i	−0.154934	+	0.0995698i
$227$	12.1118	−	10.4949i	0.803888	−	0.696573i	−0.152618	−	0.988285i	$-0.548770\pi$
$227$	12.1118	−	10.4949i	0.803888	−	0.696573i	0.956506	+	0.291712i	$0.0942250\pi$
$228$	1.20411	+	4.10084i	0.0797444	+	0.271585i
$229$	−23.6597			−1.56348			−0.781738	−	0.623607i	$-0.785666\pi$
$229$	−23.6597			−1.56348			−0.781738	+	0.623607i	$0.785666\pi$
$230$	−3.07529	+	5.98110i	−0.202779	+	0.394382i
$231$	0.168667			0.0110975
$232$	−1.06996	−	3.64396i	−0.0702465	−	0.239238i
$233$	5.33235	−	4.62051i	0.349334	−	0.302699i	−0.462464	−	0.886638i	$-0.653035\pi$
$233$	5.33235	−	4.62051i	0.349334	−	0.302699i	0.811798	+	0.583939i	$0.198489\pi$
$234$	6.35492	−	4.08406i	0.415434	−	0.266983i
$235$	−0.427340	+	0.601640i	−0.0278766	+	0.0392467i
$236$	−1.82162	−	1.17069i	−0.118578	−	0.0762052i
$237$	7.32697	+	3.34611i	0.475938	+	0.217353i
$238$	1.67977	+	1.45553i	0.108884	+	0.0943481i
$239$	−2.20794	+	15.3566i	−0.142820	+	0.993334i	0.784784	+	0.619769i	$0.212774\pi$
$239$	−2.20794	+	15.3566i	−0.142820	+	0.993334i	−0.927604	+	0.373565i	$0.878135\pi$
$240$	−0.975697	+	2.83006i	−0.0629810	+	0.182680i
$241$	5.22796	+	1.53507i	0.336762	+	0.0988824i	0.445742	−	0.895162i	$-0.352940\pi$
$241$	5.22796	+	1.53507i	0.336762	+	0.0988824i	−0.108979	+	0.994044i	$0.534758\pi$
$242$	−1.92415	+	6.55305i	−0.123689	+	0.421246i
$243$	−13.9994	+	6.39333i	−0.898065	+	0.410133i
$244$	1.27747	−	8.88501i	0.0817817	−	0.568804i
$245$	1.40638	+	14.5440i	0.0898504	+	0.929185i
$246$	−0.608175	+	1.33172i	−0.0387758	+	0.0849071i
$247$	−9.50400	+	14.7885i	−0.604725	+	0.940971i
$248$	18.7419	−	2.69467i	1.19011	−	0.171112i
$249$	−2.37160	+	1.52413i	−0.150294	+	0.0965881i
$250$	−7.01167	+	0.0252127i	−0.443457	+	0.00159459i
$251$	−10.0309	+	2.94534i	−0.633145	+	0.185908i	−0.582529	−	0.812810i	$-0.697937\pi$
$251$	−10.0309	+	2.94534i	−0.633145	+	0.185908i	−0.0506162	+	0.998718i	$0.516119\pi$
$252$			2.67834i			0.168720i
$253$	1.44598	+	0.660560i	0.0909077	+	0.0415290i
$254$	−8.73140			−0.547856
$255$	3.96131	−	7.70654i	0.248067	−	0.482602i
$256$	4.59137	+	5.29872i	0.286960	+	0.331170i
$257$	14.8085	+	23.0424i	0.923726	+	1.43735i	0.899146	+	0.437649i	$0.144189\pi$
$257$	14.8085	+	23.0424i	0.923726	+	1.43735i	0.0245804	+	0.999698i	$0.492175\pi$
$258$	−3.42347	+	0.492220i	−0.213136	+	0.0306443i
$259$	−2.95680	−	1.90022i	−0.183727	−	0.118074i
$260$	−16.4325	+	6.60146i	−1.01910	+	0.409405i
$261$	−2.68683	+	3.10076i	−0.166310	+	0.191932i
$262$	−4.70789	−	0.676893i	−0.290855	−	0.0418186i
$263$	11.7496	−	5.36587i	0.724513	−	0.330874i	−0.0187952	−	0.999823i	$-0.505983\pi$
$263$	11.7496	−	5.36587i	0.724513	−	0.330874i	0.743308	+	0.668950i	$0.233256\pi$
$264$	−0.536602	−	0.157561i	−0.0330256	−	0.00969719i
$265$	10.1272	+	17.4924i	0.622109	+	1.07455i
$266$	0.633826	+	1.38788i	0.0388623	+	0.0850967i
$267$	−10.5867	−	1.52213i	−0.647893	−	0.0931529i
$268$	0.592768	+	0.513636i	0.0362090	+	0.0313753i
$269$	−7.21770	+	15.8046i	−0.440071	+	0.963621i	0.551514	+	0.834166i	$0.314050\pi$
$269$	−7.21770	+	15.8046i	−0.440071	+	0.963621i	−0.991585	+	0.129456i	$0.958677\pi$
$270$	−5.53194	+	1.34906i	−0.336663	+	0.0821010i
$271$	−2.26606	−	15.7608i	−0.137653	−	0.957401i	−0.935194	−	0.354135i	$-0.884775\pi$
$271$	−2.26606	−	15.7608i	−0.137653	−	0.957401i	0.797541	−	0.603265i	$-0.206134\pi$
$272$	5.04121	+	7.84428i	0.305669	+	0.475629i
$273$	1.89553	−	1.64249i	0.114723	−	0.0994079i
$274$	6.44270	−	1.89175i	0.389218	−	0.114285i
$275$	0.0828301	+	1.65532i	0.00499484	+	0.0998194i
$276$	2.38818	−	5.22777i	0.143752	−	0.314675i
$277$		−	11.2072i		−	0.673373i	−0.941617	−	0.336686i	$-0.890694\pi$
$277$		−	11.2072i		−	0.673373i	0.941617	−	0.336686i	$-0.109306\pi$
$278$	0.478646	+	1.63012i	0.0287073	+	0.0977679i
$279$	−13.3957	−	15.4594i	−0.801977	−	0.925530i
$280$	−0.648917	+	3.38876i	−0.0387802	+	0.202517i
$281$	−2.18825	−	15.2196i	−0.130540	−	0.907927i	−0.944852	−	0.327499i	$-0.893794\pi$
$281$	−2.18825	−	15.2196i	−0.130540	−	0.907927i	0.814311	−	0.580428i	$-0.197115\pi$
$282$	−0.0834655	+	0.129875i	−0.00497030	+	0.00773393i
$283$	27.1954	+	12.4197i	1.61660	+	0.738276i	0.998843	−	0.0480939i	$-0.0153147\pi$
$283$	27.1954	+	12.4197i	1.61660	+	0.738276i	0.617756	+	0.786370i	$0.288042\pi$
$284$	15.3092	−	17.6677i	0.908432	−	1.04839i
$285$	4.67118	−	3.68253i	0.276697	−	0.218134i
$286$	−0.425679	−	0.932108i	−0.0251710	−	0.0551167i
$287$	0.601496	−	2.04851i	0.0355052	−	0.120920i
$288$	3.88938	−	13.2460i	0.229184	−	0.780529i
$289$	−4.15024	−	9.08775i	−0.244131	−	0.534573i
$290$	−1.84906	+	1.45770i	−0.108580	+	0.0855993i
$291$	−3.91582	+	4.51910i	−0.229550	+	0.264914i
$292$	−11.0796	−	5.05987i	−0.648383	−	0.296107i
$293$	4.52495	−	7.04095i	0.264350	−	0.411337i	−0.683550	−	0.729903i	$-0.739565\pi$
$293$	4.52495	−	7.04095i	0.264350	−	0.411337i	0.947901	+	0.318566i	$0.103201\pi$
$294$	0.435030	+	3.02570i	0.0253715	+	0.176462i
$295$	−0.566780	+	2.95982i	−0.0329992	+	0.172327i
$296$	7.63174	+	8.80750i	0.443586	+	0.511926i
$297$	0.379192	+	1.29141i	0.0220030	+	0.0749352i
$298$		−	13.6245i		−	0.789245i
$299$	22.6828	−	6.65740i	1.31178	−	0.385007i
$300$	5.98463	−	0.299463i	0.345523	−	0.0172895i
$301$	4.83951	−	1.42101i	0.278944	−	0.0819055i
$302$	−1.77817	+	1.54080i	−0.102322	+	0.0886629i
$303$	3.77620	+	5.87587i	0.216937	+	0.337560i
$304$	0.910943	+	6.33575i	0.0522462	+	0.363380i
$305$	−12.1370	+	2.95980i	−0.694960	+	0.169478i
$306$	−3.30746	+	7.24232i	−0.189075	+	0.414016i
$307$	−21.5761	−	18.6958i	−1.23141	−	1.06703i	−0.995452	−	0.0952648i	$-0.969630\pi$
$307$	−21.5761	−	18.6958i	−1.23141	−	1.06703i	−0.235963	−	0.971762i	$-0.575824\pi$
$308$	0.359617	+	0.0517051i	0.0204911	+	0.00294617i
$309$	5.95821	+	13.0467i	0.338951	+	0.742199i
$310$	−5.88170	−	10.1593i	−0.334058	−	0.577007i
$311$	16.0356	+	4.70847i	0.909293	+	0.266993i	0.702743	−	0.711443i	$-0.251958\pi$
$311$	16.0356	+	4.70847i	0.909293	+	0.266993i	0.206550	+	0.978436i	$0.433776\pi$
$312$	−7.56483	+	3.45474i	−0.428274	+	0.195586i
$313$	3.53958	+	0.508914i	0.200069	+	0.0287655i	0.241621	−	0.970371i	$-0.422321\pi$
$313$	3.53958	+	0.508914i	0.200069	+	0.0287655i	−0.0415519	+	0.999136i	$0.513230\pi$
$314$	−5.43724	+	6.27491i	−0.306841	+	0.354114i
$315$	3.45884	−	1.38952i	0.194884	−	0.0782908i
$316$	14.5961	+	9.38037i	0.821097	+	0.527687i
$317$	−18.8698	+	2.71307i	−1.05984	+	0.152381i	−0.650120	−	0.759832i	$-0.725281\pi$
$317$	−18.8698	+	2.71307i	−1.05984	+	0.152381i	−0.409716	+	0.912213i	$0.634372\pi$
$318$	2.28607	+	3.55720i	0.128197	+	0.199478i
$319$	0.364466	+	0.420616i	0.0204062	+	0.0235500i
$320$	−0.0476326	+	0.0926670i	−0.00266275	+	0.00518024i
$321$	2.98925			0.166844
$322$	0.578284	−	1.96860i	0.0322265	−	0.109706i
$323$		−	18.5279i		−	1.03092i
$324$	−6.63242	+	1.94745i	−0.368468	+	0.108192i
$325$	17.0504	+	17.7963i	0.945787	+	0.987164i
$326$	8.42149	−	5.41216i	0.466423	−	0.299752i
$327$	3.80715	−	0.547385i	0.210536	−	0.0302705i
$328$	−3.82723	+	5.95529i	−0.211323	+	0.328826i
$329$	0.0935255	−	0.204792i	0.00515623	−	0.0112906i
$330$	0.0333722	+	0.345117i	0.00183708	+	0.0189981i
$331$	2.89685	−	20.1481i	0.159226	−	1.10744i	−0.740839	−	0.671682i	$-0.765572\pi$
$331$	2.89685	−	20.1481i	0.159226	−	1.10744i	0.900065	−	0.435756i	$-0.143519\pi$
$332$	−5.52373	+	2.52260i	−0.303154	+	0.138446i
$333$	3.54708	−	12.0803i	0.194379	−	0.661994i
$334$	6.33467	+	1.86003i	0.346618	+	0.101776i
$335$	0.355788	−	1.03198i	0.0194388	−	0.0563832i
$336$	0.129971	−	0.903969i	0.00709051	−	0.0493156i
$337$	4.69760	+	4.07049i	0.255894	+	0.221734i	0.773355	−	0.633973i	$-0.218577\pi$
$337$	4.69760	+	4.07049i	0.255894	+	0.221734i	−0.517461	+	0.855707i	$0.673123\pi$
$338$	−6.44467	−	2.94318i	−0.350544	−	0.160088i
$339$	−2.77019	−	1.78029i	−0.150456	−	0.0966922i
$340$	10.8084	−	15.2168i	0.586167	−	0.825248i
$341$	−2.33431	+	1.50017i	−0.126410	+	0.0812389i
$342$	−4.13052	+	3.57912i	−0.223353	+	0.193536i
$343$	−2.60124	−	8.85903i	−0.140454	−	0.478342i
$344$	−16.7240			−0.901696
$345$	−7.99020	−	0.371960i	−0.430178	−	0.0200257i
$346$	−4.65248			−0.250119
$347$	−5.20278	−	17.7190i	−0.279300	−	0.951207i	−0.972973	−	0.230918i	$-0.925827\pi$
$347$	−5.20278	−	17.7190i	−0.279300	−	0.951207i	0.693674	−	0.720290i	$-0.255991\pi$
$348$	1.52069	−	1.31769i	0.0815178	−	0.0706355i
$349$	−11.2395	+	7.22316i	−0.601634	+	0.386647i	−0.805712	−	0.592308i	$-0.798217\pi$
$349$	−11.2395	+	7.22316i	−0.601634	+	0.386647i	0.204077	+	0.978955i	$0.434581\pi$
$350$	2.09949	−	0.409867i	0.112223	−	0.0219083i
$351$	16.8373	+	10.8207i	0.898707	+	0.577564i
$352$	−1.70344	−	0.777935i	−0.0907937	−	0.0414641i
$353$	−2.35141	−	2.03751i	−0.125153	−	0.108446i	0.590036	−	0.807377i	$-0.299114\pi$
$353$	−2.35141	−	2.03751i	−0.125153	−	0.108446i	−0.715188	+	0.698932i	$0.753659\pi$
$354$	−0.0897219	+	0.624029i	−0.00476866	+	0.0331668i
$355$	−30.7587	−	10.6044i	−1.63250	−	0.562825i
$356$	−22.1053	−	6.49070i	−1.17158	−	0.344006i
$357$	−0.744766	+	2.53644i	−0.0394172	+	0.134243i
$358$	9.05802	−	4.13666i	0.478731	−	0.218629i
$359$	4.58962	−	31.9215i	0.242231	−	1.68475i	−0.398642	−	0.917107i	$-0.630518\pi$
$359$	4.58962	−	31.9215i	0.242231	−	1.68475i	0.640873	−	0.767647i	$-0.278573\pi$
$360$	−12.3021	+	1.18959i	−0.648376	+	0.0626968i
$361$	−2.60936	+	5.71370i	−0.137335	+	0.300721i
$362$	0.402447	−	0.626220i	0.0211522	−	0.0329134i
$363$	−8.04023	+	1.15601i	−0.422003	+	0.0606748i
$364$	4.54499	−	2.92089i	0.238222	−	0.153096i
$365$	−0.786294	+	16.9334i	−0.0411565	+	0.886333i
$366$	−2.50761	+	0.736299i	−0.131075	+	0.0384870i
$367$		−	16.6172i		−	0.867410i	−0.901055	−	0.433705i	$-0.857206\pi$
$367$		−	16.6172i		−	0.867410i	0.901055	−	0.433705i	$-0.142794\pi$
$368$	4.65449	−	7.24066i	0.242632	−	0.377446i
$369$	7.64777			0.398127
$370$	3.30309	−	6.42600i	0.171719	−	0.334072i
$371$	−4.03813	−	4.66025i	−0.209649	−	0.241948i
$372$	5.42372	+	8.43947i	0.281207	+	0.437566i
$373$	23.6461	−	3.39980i	1.22435	−	0.176035i	0.500342	−	0.865828i	$-0.333208\pi$
$373$	23.6461	−	3.39980i	1.22435	−	0.176035i	0.724007	+	0.689793i	$0.242298\pi$
$374$	0.908566	+	0.583900i	0.0469808	+	0.0301928i
$375$	−3.49156	−	7.57326i	−0.180303	−	0.391081i
$376$	−0.488851	+	0.564164i	−0.0252106	+	0.0290946i
$377$	8.19196	+	1.17783i	0.421907	+	0.0606611i
$378$	1.58016	−	0.721634i	0.0812746	−	0.0371168i
$379$	29.7006	+	8.72087i	1.52561	+	0.447961i	0.933705	−	0.358043i	$-0.116556\pi$
$379$	29.7006	+	8.72087i	1.52561	+	0.447961i	0.591910	+	0.806004i	$0.298374\pi$
$380$	11.0883	−	6.41959i	0.568820	−	0.329318i
$381$	−4.31395	−	9.44624i	−0.221011	−	0.483946i
$382$	−0.122557	−	0.0176211i	−0.00627058	−	0.000901573i
$383$	−1.81837	−	1.57563i	−0.0929146	−	0.0805109i	0.607165	−	0.794576i	$-0.292307\pi$
$383$	−1.81837	−	1.57563i	−0.0929146	−	0.0805109i	−0.700080	+	0.714065i	$0.746852\pi$
$384$	−3.51010	+	7.68605i	−0.179124	+	0.392227i
$385$	−0.119797	−	0.491239i	−0.00610541	−	0.0250358i
$386$	0.307249	+	2.13696i	0.0156386	+	0.108769i
$387$	9.76804	+	15.1994i	0.496537	+	0.772627i
$388$	−9.73430	+	8.43482i	−0.494184	+	0.428213i
$389$	9.99300	−	2.93421i	0.506665	−	0.148770i	−0.0184026	−	0.999831i	$-0.505858\pi$
$389$	9.99300	−	2.93421i	0.506665	−	0.148770i	0.525068	+	0.851060i	$0.324040\pi$
$390$	3.73581	+	3.55355i	0.189170	+	0.179941i
$391$	−16.3184	+	18.8280i	−0.825257	+	0.952172i
$392$			14.7808i			0.746545i
$393$	−1.59374	−	5.42777i	−0.0803933	−	0.273795i
$394$	−9.63701	−	11.1217i	−0.485506	−	0.560303i
$395$	4.54144	−	23.7162i	0.228505	−	1.19329i
$396$	0.185214	+	1.28819i	0.00930733	+	0.0647339i
$397$	17.7532	−	27.6246i	0.891009	−	1.38644i	−0.0311036	−	0.999516i	$-0.509902\pi$
$397$	17.7532	−	27.6246i	0.891009	−	1.38644i	0.922113	−	0.386921i	$-0.126461\pi$
$398$	−11.6865	−	5.33704i	−0.585791	−	0.267522i
$399$	−1.18835	+	1.37143i	−0.0594922	+	0.0686576i
$400$	8.93547	+	0.831623i	0.446774	+	0.0415812i
$401$	−3.76143	−	8.23638i	−0.187837	−	0.411305i	0.792161	−	0.610312i	$-0.208956\pi$
$401$	−3.76143	−	8.23638i	−0.187837	−	0.411305i	−0.979998	+	0.199007i	$0.936229\pi$
$402$	0.0643369	−	0.219111i	0.00320883	−	0.0109283i
$403$	−11.6250	+	39.5910i	−0.579081	+	1.97217i
$404$	6.25000	+	13.6856i	0.310949	+	0.680884i
$405$	5.95587	+	7.55485i	0.295949	+	0.375403i
$406$	0.470403	−	0.542874i	0.0233457	−	0.0269424i
$407$	−1.55352	−	0.709470i	−0.0770052	−	0.0351671i
$408$	4.73883	−	7.37377i	0.234607	−	0.365056i
$409$	2.84706	+	19.8018i	0.140778	+	0.979135i	0.930663	+	0.365879i	$0.119231\pi$
$409$	2.84706	+	19.8018i	0.140778	+	0.979135i	−0.789884	+	0.613256i	$0.789859\pi$
$410$	4.31055	+	0.825432i	0.212883	+	0.0407652i
$411$	5.22980	+	6.03551i	0.257967	+	0.297710i
$412$	8.70409	+	29.6434i	0.428820	+	1.46043i
$413$		−	0.919386i		−	0.0452400i
$414$	7.34970		0.000861232i	0.361218		4.23273e-5i
$415$	6.12344	+	5.82469i	0.300588	+	0.285923i
$416$	−26.7193	+	7.84550i	−1.31002	+	0.384657i
$417$	−1.52709	+	1.32323i	−0.0747819	+	0.0647989i
$418$	0.400823	+	0.623694i	0.0196049	+	0.0305058i
$419$	−1.15949	−	8.06441i	−0.0566447	−	0.393972i	−0.998344	−	0.0575181i	$-0.981681\pi$
$419$	−1.15949	−	8.06441i	−0.0566447	−	0.393972i	0.941700	−	0.336454i	$-0.109228\pi$
$420$	−1.77602	+	0.433113i	−0.0866610	+	0.0211337i
$421$	7.93751	−	17.3807i	0.386851	−	0.847085i	−0.611585	−	0.791178i	$-0.709468\pi$
$421$	7.93751	−	17.3807i	0.386851	−	0.847085i	0.998436	−	0.0559063i	$-0.0178048\pi$
$422$	5.00137	+	4.33371i	0.243463	+	0.210962i
$423$	0.798259	+	0.114772i	0.0388127	+	0.00558042i
$424$	8.49363	+	18.5985i	0.412487	+	0.903221i
$425$	−25.2586	−	6.06360i	−1.22522	−	0.294128i
$426$	−6.53072	−	1.91759i	−0.316414	−	0.0929076i
$427$	3.46683	−	1.58325i	0.167772	−	0.0766188i
$428$	6.37340	+	0.916357i	0.308070	+	0.0442938i
$429$	0.798103	−	0.921060i	0.0385328	−	0.0444692i
$430$	3.86511	+	9.62115i	0.186392	+	0.463973i
$431$	−6.57609	−	4.22620i	−0.316759	−	0.203569i	0.372593	−	0.927995i	$-0.378469\pi$
$431$	−6.57609	−	4.22620i	−0.316759	−	0.203569i	−0.689353	+	0.724426i	$0.742105\pi$
$432$	7.21348	−	1.03714i	0.347059	−	0.0498995i
$433$	−9.12617	−	14.2006i	−0.438576	−	0.682437i	0.549658	−	0.835390i	$-0.314758\pi$
$433$	−9.12617	−	14.2006i	−0.438576	−	0.682437i	−0.988233	+	0.152953i	$0.951122\pi$
$434$	2.34528	+	2.70659i	0.112577	+	0.129921i
$435$	−2.49062	−	1.28023i	−0.119416	−	0.0613821i
$436$	8.28505			0.396782
$437$	−15.5587	+	7.10322i	−0.744274	+	0.339793i
$438$			3.54629i			0.169448i
$439$	−30.7525	+	9.02974i	−1.46773	+	0.430966i	−0.915362	−	0.402631i	$-0.868096\pi$
$439$	−30.7525	+	9.02974i	−1.46773	+	0.430966i	−0.552373	+	0.833597i	$0.686277\pi$
$440$	−0.0777663	+	1.67475i	−0.00370736	+	0.0798405i
$441$	13.4334	−	8.63310i	0.639684	−	0.411100i
$442$	15.8968	−	2.28561i	0.756132	−	0.108715i
$443$	−16.8843	+	26.2725i	−0.802198	+	1.24824i	0.162974	+	0.986630i	$0.447891\pi$
$443$	−16.8843	+	26.2725i	−0.802198	+	1.24824i	−0.965172	+	0.261614i	$0.915745\pi$
$444$	−2.56501	+	5.61659i	−0.121730	+	0.266552i
$445$	3.08607	+	31.9144i	0.146294	+	1.51289i
$446$	0.699571	−	4.86562i	0.0331256	−	0.230394i
$447$	14.7399	−	6.73150i	0.697174	−	0.318389i
$448$	0.00895541	−	0.0304993i	0.000423103	−	0.00144096i
$449$	−13.2496	−	3.89045i	−0.625289	−	0.183601i	−0.0462880	−	0.998928i	$-0.514739\pi$
$449$	−13.2496	−	3.89045i	−0.625289	−	0.183601i	−0.579001	+	0.815327i	$0.696557\pi$
$450$	3.52752	+	6.80235i	0.166289	+	0.320666i
$451$	0.147640	−	1.02686i	0.00695208	−	0.0483528i
$452$	−5.36060	−	4.64498i	−0.252141	−	0.218482i
$453$	−2.54549	−	1.16249i	−0.119598	−	0.0546184i
$454$	−8.45525	−	5.43386i	−0.396825	−	0.255024i
$455$	−6.13001	−	4.35410i	−0.287379	−	0.204123i
$456$	5.06179	−	3.25301i	0.237040	−	0.152336i
$457$	−12.0486	+	10.4402i	−0.563609	+	0.488370i	−0.889436	−	0.457060i	$-0.848903\pi$
$457$	−12.0486	+	10.4402i	−0.563609	+	0.488370i	0.325827	+	0.945429i	$0.394357\pi$
$458$	4.18037	+	14.2370i	0.195336	+	0.665253i
$459$	−21.0947			−0.984618
$460$	−16.9220	−	3.24246i	−0.788990	−	0.151181i
$461$	11.5522			0.538040			0.269020	−	0.963135i	$-0.413300\pi$
$461$	11.5522			0.538040			0.269020	+	0.963135i	$0.413300\pi$
$462$	−0.0298014	−	0.101494i	−0.00138649	−	0.00472194i
$463$	−27.8930	+	24.1695i	−1.29630	+	1.12325i	−0.311371	+	0.950288i	$0.600788\pi$
$463$	−27.8930	+	24.1695i	−1.29630	+	1.12325i	−0.984929	+	0.172961i	$0.944666\pi$
$464$	2.53513	−	1.62923i	0.117691	−	0.0756352i
$465$	8.08501	−	11.3827i	0.374933	−	0.527858i
$466$	−3.72252	−	2.39232i	−0.172442	−	0.110822i
$467$	16.5556	+	7.56068i	0.766101	+	0.349867i	0.759837	−	0.650114i	$-0.225279\pi$
$467$	16.5556	+	7.56068i	0.766101	+	0.349867i	0.00626403	+	0.999980i	$0.498006\pi$
$468$	14.6259	+	12.6734i	0.676083	+	0.585829i
$469$	−0.0473940	+	0.329632i	−0.00218845	+	0.0152210i
$470$	0.437538	+	0.150847i	0.0201821	+	0.00695803i
$471$	−9.47505	−	2.78212i	−0.436587	−	0.128194i
$472$	−0.858845	+	2.92496i	−0.0395316	+	0.134632i
$473$	2.22937	−	1.01812i	0.102506	−	0.0468131i
$474$	0.718915	−	5.00017i	0.0330209	−	0.229665i
$475$	−14.0430	−	10.9891i	−0.644336	−	0.504216i
$476$	−2.36547	+	5.17965i	−0.108421	+	0.237409i
$477$	11.9421	−	18.5822i	0.546790	−	0.850821i
$478$	9.63082	−	1.38470i	0.440504	−	0.0633348i
$479$	18.1099	−	11.6385i	0.827463	−	0.531778i	−0.0570081	−	0.998374i	$-0.518156\pi$
$479$	18.1099	−	11.6385i	0.827463	−	0.531778i	0.884471	+	0.466596i	$0.154520\pi$
$480$	9.41245	+	0.437064i	0.429618	+	0.0199491i
$481$	−24.3678	+	7.15503i	−1.11108	+	0.326241i
$482$		−	3.41711i		−	0.155645i
$483$	2.41549	−	0.347006i	0.109908	−	0.0157893i
$484$	−17.4970			−0.795319
$485$	15.9430	+	8.19501i	0.723934	+	0.372116i
$486$	6.32067	+	7.29444i	0.286712	+	0.330883i
$487$	−16.0245	−	24.9345i	−0.726137	−	1.12989i	−0.986401	−	0.164354i	$-0.947446\pi$
$487$	−16.0245	−	24.9345i	−0.726137	−	1.12989i	0.260264	−	0.965538i	$-0.416190\pi$
$488$	−12.5085	+	1.79845i	−0.566232	+	0.0814118i
$489$	10.0161	+	6.43695i	0.452943	+	0.291089i
$490$	8.50328	−	3.41603i	0.384139	−	0.154321i
$491$	5.36441	−	6.19086i	0.242093	−	0.279390i	−0.621680	−	0.783271i	$-0.713550\pi$
$491$	5.36441	−	6.19086i	0.242093	−	0.279390i	0.863773	+	0.503881i	$0.168095\pi$
$492$	−3.71249	−	0.533775i	−0.167372	−	0.0240644i
$493$	−7.93461	+	3.62362i	−0.357357	+	0.163199i
$494$	10.5781	+	3.10602i	0.475932	+	0.139746i
$495$	1.56749	−	0.907500i	0.0704536	−	0.0407891i
$496$	6.24138	+	13.6667i	0.280246	+	0.613653i
$497$	9.82485	+	1.41260i	0.440705	+	0.0633638i
$498$	1.33617	+	1.15780i	0.0598752	+	0.0518821i
$499$	−17.6070	+	38.5539i	−0.788197	+	1.72591i	−0.106456	+	0.994317i	$0.533950\pi$
$499$	−17.6070	+	38.5539i	−0.788197	+	1.72591i	−0.681741	+	0.731593i	$0.738777\pi$
$500$	−5.12279	−	17.2174i	−0.229098	−	0.769984i
$501$	1.11749	+	7.77229i	0.0499256	+	0.347240i
$502$	3.54467	+	5.51562i	0.158207	+	0.246174i
$503$	−29.9957	+	25.9914i	−1.33744	+	1.15890i	−0.363630	+	0.931543i	$0.618463\pi$
$503$	−29.9957	+	25.9914i	−1.33744	+	1.15890i	−0.973812	+	0.227356i	$0.926992\pi$
$504$	3.61788	−	1.06230i	0.161153	−	0.0473188i
$505$	14.4313	−	15.1714i	0.642182	−	0.675120i
$506$	0.142001	−	0.986818i	0.00631272	−	0.0438694i
$507$		−	8.42645i		−	0.374232i
$508$	−6.30206	−	21.4629i	−0.279609	−	0.952260i
$509$	1.56358	+	1.80446i	0.0693043	+	0.0799815i	0.789343	−	0.613953i	$-0.210421\pi$
$509$	1.56358	+	1.80446i	0.0693043	+	0.0799815i	−0.720039	+	0.693934i	$0.755876\pi$
$510$	−5.33727	−	1.02204i	−0.236338	−	0.0452567i
$511$	−0.735993	−	5.11895i	−0.0325584	−	0.226449i
$512$	−9.87168	+	15.3606i	−0.436271	+	0.678850i
$513$	−13.1721	−	6.01549i	−0.581562	−	0.265590i
$514$	11.2491	−	12.9822i	0.496178	−	0.572620i
$515$	33.7662	−	26.6196i	1.48792	−	1.17300i
$516$	−3.68090	−	8.06004i	−0.162042	−	0.354824i
$517$	0.0308206	−	0.104965i	0.00135549	−	0.00461637i
$518$	−0.621014	+	2.11498i	−0.0272858	+	0.0929268i
$519$	−2.29867	−	5.03338i	−0.100900	−	0.220941i
$520$	15.4348	+	19.5786i	0.676860	+	0.858578i
$521$	−16.7682	+	19.3515i	−0.734627	+	0.847804i	−0.992984	−	0.118245i	$-0.962273\pi$
$521$	−16.7682	+	19.3515i	−0.734627	+	0.847804i	0.258358	+	0.966049i	$0.416819\pi$
$522$	2.34059	+	1.06891i	0.102445	+	0.0467850i
$523$	13.4485	−	20.9263i	0.588063	−	0.915045i	−0.411929	−	0.911216i	$-0.635145\pi$
$523$	13.4485	−	20.9263i	0.588063	−	0.915045i	0.999993	−	0.00382875i	$-0.00121873\pi$
$524$	−1.73413	−	12.0611i	−0.0757559	−	0.526894i
$525$	1.48073	+	2.06888i	0.0646243	+	0.0902932i
$526$	−5.30489	−	6.12217i	−0.231304	−	0.266939i
$527$	−12.2524	−	41.7278i	−0.533723	−	1.81769i
$528$		−	0.443765i		−	0.0193124i
$529$	22.0668	+	6.48502i	0.959427	+	0.281957i
$530$	8.73655	−	9.18465i	0.379492	−	0.398956i
$531$	3.15994	−	0.927842i	0.137130	−	0.0402649i
$532$	−2.95412	+	2.55976i	−0.128077	+	0.110980i
$533$	−8.34034	−	12.9778i	−0.361260	−	0.562132i
$534$	0.954600	+	6.63939i	0.0413096	+	0.287314i
$535$	−2.12313	−	8.70610i	−0.0917909	−	0.376398i
$536$	0.458707	−	1.00443i	0.0198131	−	0.0433847i
$537$	8.95066	+	7.75579i	0.386250	+	0.334687i
$538$	10.7856	+	1.55073i	0.464999	+	0.0668567i
$539$	−0.899825	−	1.97034i	−0.0387582	−	0.0848686i
$540$	−7.30894	−	12.6245i	−0.314527	−	0.543272i
$541$	39.2602	+	11.5278i	1.68793	+	0.495621i	0.977992	−	0.208643i	$-0.0669047\pi$
$541$	39.2602	+	11.5278i	1.68793	+	0.495621i	0.709938	+	0.704264i	$0.248723\pi$
$542$	−9.08357	+	4.14833i	−0.390173	+	0.178186i
$543$	0.876328	+	0.125997i	0.0376068	+	0.00540705i
$544$	19.2204	−	22.1815i	0.824067	−	0.951024i
$545$	−4.29829	−	10.6994i	−0.184118	−	0.458313i
$546$	−1.32327	−	0.850416i	−0.0566309	−	0.0363944i
$547$	4.26943	−	0.613851i	0.182547	−	0.0262464i	−0.0504348	−	0.998727i	$-0.516061\pi$
$547$	4.26943	−	0.613851i	0.182547	−	0.0262464i	0.232982	+	0.972481i	$0.425152\pi$
$548$	9.30031	+	14.4716i	0.397289	+	0.618194i
$549$	8.94037	+	10.3177i	0.381566	+	0.440350i
$550$	0.981441	−	0.342317i	0.0418488	−	0.0145964i
$551$	−5.98790			−0.255093
$552$	−8.00884	−	1.15246i	−0.340879	−	0.0490518i
$553$			7.36677i			0.313267i
$554$	−6.74383	+	1.98017i	−0.286518	+	0.0841292i
$555$	8.58407	+	0.398598i	0.364374	+	0.0169195i
$556$	−3.66156	+	2.35314i	−0.155285	+	0.0997954i
$557$	7.21472	−	1.03732i	0.305697	−	0.0439527i	0.0122409	−	0.999925i	$-0.496103\pi$
$557$	7.21472	−	1.03732i	0.305697	−	0.0439527i	0.293457	+	0.955972i	$0.405194\pi$
$558$	−6.93574	+	10.7922i	−0.293613	+	0.456871i
$559$	15.1398	−	33.1516i	0.640346	−	1.40216i
$560$	−2.72510	+	0.263512i	−0.115156	+	0.0111354i
$561$	−0.182806	+	1.27144i	−0.00771806	+	0.0536803i
$562$	−8.77167	+	4.00589i	−0.370010	+	0.168978i
$563$	−1.75632	+	5.98146i	−0.0740199	+	0.252089i	−0.988188	−	0.153247i	$-0.951027\pi$
$563$	−1.75632	+	5.98146i	−0.0740199	+	0.252089i	0.914168	+	0.405335i	$0.132845\pi$
$564$	−0.379491	−	0.111429i	−0.0159795	−	0.00469200i
$565$	−3.21751	+	9.33256i	−0.135362	+	0.392624i
$566$	2.66839	−	18.5590i	0.112161	−	0.780095i
$567$	−2.21807	−	1.92196i	−0.0931500	−	0.0807149i
$568$	−29.9374	−	13.6720i	−1.25615	−	0.573663i
$569$	−27.0577	−	17.3890i	−1.13432	−	0.728983i	−0.167862	−	0.985810i	$-0.553686\pi$
$569$	−27.0577	−	17.3890i	−1.13432	−	0.728983i	−0.966457	+	0.256828i	$0.917323\pi$
$570$	−3.04127	−	2.16019i	−0.127385	−	0.0904805i
$571$	13.4126	−	8.61978i	0.561302	−	0.360727i	−0.229017	−	0.973422i	$-0.573551\pi$
$571$	13.4126	−	8.61978i	0.561302	−	0.360727i	0.790319	+	0.612696i	$0.209915\pi$
$572$	1.98400	−	1.71914i	0.0829550	−	0.0718809i
$573$	−0.0414886	−	0.141297i	−0.00173321	−	0.00590278i
$574$	−1.33895			−0.0558868
$575$	4.59176	+	23.5354i	0.191490	+	0.981495i
$576$	0.113864			0.00474434
$577$	0.368166	+	1.25386i	0.0153270	+	0.0521989i	0.966801	−	0.255529i	$-0.0822496\pi$
$577$	0.368166	+	1.25386i	0.0153270	+	0.0521989i	−0.951474	+	0.307728i	$0.900431\pi$
$578$	−4.73519	+	4.10307i	−0.196958	+	0.170665i
$579$	−2.16011	+	1.38822i	−0.0897712	+	0.0576925i
$580$	−4.91781	−	3.49308i	−0.204201	−	0.145042i
$581$	−2.16900	−	1.39393i	−0.0899854	−	0.0578301i
$582$	3.41121	+	1.55785i	0.141399	+	0.0645749i
$583$	−2.26447	−	1.96217i	−0.0937847	−	0.0812649i
$584$	−2.44036	+	16.9731i	−0.100983	+	0.702351i
$585$	8.77869	−	25.4631i	0.362954	−	1.05277i
$586$	−5.03635	−	1.47880i	−0.208049	−	0.0610888i
$587$	−3.11097	+	10.5950i	−0.128403	+	0.437302i	−0.998449	−	0.0556688i	$-0.982271\pi$
$587$	−3.11097	+	10.5950i	−0.128403	+	0.437302i	0.870046	+	0.492971i	$0.164089\pi$
$588$	−7.12356	+	3.25322i	−0.293771	+	0.134161i
$589$	4.24863	−	29.5499i	0.175062	−	1.21758i
$590$	1.88119	−	0.181908i	0.0774475	−	0.00748903i
$591$	7.27085	−	15.9209i	0.299083	−	0.654900i
$592$	−4.99950	+	7.77937i	−0.205478	+	0.319730i
$593$	−37.7303	+	5.42480i	−1.54940	+	0.222770i	−0.863282	−	0.504723i	$-0.831595\pi$
$593$	−37.7303	+	5.42480i	−1.54940	+	0.222770i	−0.686116	+	0.727492i	$0.740686\pi$
$594$	0.710098	−	0.456352i	0.0291357	−	0.0187244i
$595$	7.91628	+	0.367589i	0.324536	+	0.0150697i
$596$	33.4907	−	9.83375i	1.37183	−	0.402806i
$597$		−	15.2802i		−	0.625375i
$598$	−8.01382	−	12.4730i	−0.327710	−	0.510057i
$599$	−32.5001			−1.32792			−0.663959	−	0.747769i	$-0.731125\pi$
$599$	−32.5001			−1.32792			−0.663959	+	0.747769i	$0.731125\pi$
$600$	−2.77818	−	7.96520i	−0.113419	−	0.325178i
$601$	29.3475	+	33.8688i	1.19711	+	1.38154i	0.905141	+	0.425110i	$0.139765\pi$
$601$	29.3475	+	33.8688i	1.19711	+	1.38154i	0.291968	+	0.956428i	$0.405690\pi$
$602$	−1.71016	−	2.66106i	−0.0697010	−	0.108457i
$603$	−1.18078	+	0.169771i	−0.0480851	+	0.00691359i
$604$	−5.07091	−	3.25887i	−0.206332	−	0.132602i
$605$	9.07746	+	22.5959i	0.369051	+	0.918653i
$606$	2.86856	−	3.31049i	0.116527	−	0.134480i
$607$	34.3933	+	4.94501i	1.39598	+	0.200712i	0.798898	−	0.601467i	$-0.205417\pi$
$607$	34.3933	+	4.94501i	1.39598	+	0.200712i	0.597084	+	0.802179i	$0.296326\pi$
$608$	18.3271	−	8.36970i	0.743261	−	0.339436i
$609$	0.819732	+	0.240695i	0.0332172	+	0.00975346i
$610$	3.92549	+	6.78037i	0.158939	+	0.274529i
$611$	−0.675786	−	1.47977i	−0.0273394	−	0.0598649i
$612$	−20.1898	−	2.90285i	−0.816123	−	0.117341i
$613$	21.1859	+	18.3577i	0.855691	+	0.741461i	0.967662	−	0.252251i	$-0.0811707\pi$
$613$	21.1859	+	18.3577i	0.855691	+	0.741461i	−0.111970	+	0.993712i	$0.535716\pi$
$614$	−7.43784	+	16.2866i	−0.300167	+	0.657274i
$615$	1.23672	+	5.07128i	0.0498692	+	0.204494i
$616$	−0.0727914	−	0.506275i	−0.00293285	−	0.0203984i
$617$	7.15357	+	11.1312i	0.287992	+	0.448124i	0.954862	−	0.297050i	$-0.0960028\pi$
$617$	7.15357	+	11.1312i	0.287992	+	0.448124i	−0.666870	+	0.745174i	$0.732366\pi$
$618$	6.79799	−	5.89050i	0.273455	−	0.236951i
$619$	9.59908	−	2.81854i	0.385820	−	0.113287i	−0.0830698	−	0.996544i	$-0.526472\pi$
$619$	9.59908	−	2.81854i	0.385820	−	0.113287i	0.468889	+	0.883257i	$0.344654\pi$
$620$	20.7275	−	21.7906i	0.832436	−	0.875131i
$621$	8.08728	+	17.7142i	0.324531	+	0.710845i
$622$		−	10.4812i		−	0.420258i
$623$	−2.75587	−	9.38562i	−0.110411	−	0.376027i
$624$	−4.32140	−	4.98717i	−0.172995	−	0.199646i
$625$	−19.5770	+	15.5480i	−0.783080	+	0.621921i
$626$	−0.319164	−	2.21983i	−0.0127564	−	0.0887224i
$627$	−0.476719	+	0.741790i	−0.0190383	+	0.0296242i
$628$	−19.3490	−	8.83638i	−0.772108	−	0.352610i
$629$	17.5288	−	20.2293i	0.698919	−	0.806596i
$630$	−1.44727	−	1.83582i	−0.0576607	−	0.0731409i
$631$	7.02551	+	15.3837i	0.279681	+	0.612416i	0.996384	−	0.0849623i	$-0.0270770\pi$
$631$	7.02551	+	15.3837i	0.279681	+	0.612416i	−0.716703	+	0.697378i	$0.754350\pi$
$632$	6.88168	−	23.4368i	0.273738	−	0.932267i
$633$	−2.21747	+	7.55201i	−0.0881365	+	0.300165i
$634$	4.96664	+	10.8754i	0.197250	+	0.431918i
$635$	−24.4479	+	19.2735i	−0.970185	+	0.764846i
$636$	−7.09403	+	8.18694i	−0.281296	+	0.324633i
$637$	−29.2997	−	13.3807i	−1.16090	−	0.530164i
$638$	0.188706	−	0.293633i	0.00747095	−	0.0116250i
$639$	5.06009	+	35.1937i	0.200174	+	1.39224i
$640$	24.8785	+	4.76401i	0.983407	+	0.188314i
$641$	−19.5982	−	22.6175i	−0.774081	−	0.893338i	0.222586	−	0.974913i	$-0.428550\pi$
$641$	−19.5982	−	22.6175i	−0.774081	−	0.893338i	−0.996667	+	0.0815755i	$0.974005\pi$
$642$	−0.528163	−	1.79876i	−0.0208449	−	0.0709914i
$643$			24.1238i			0.951351i	0.879621	+	0.475675i	$0.157796\pi$
$643$			24.1238i			0.951351i	−0.879621	+	0.475675i	$0.842204\pi$
$644$	5.25645		0.000615947i	0.207133		2.42717e-5i
$645$	−8.49919	+	8.93511i	−0.334655	+	0.351820i
$646$	−11.1490	+	3.27366i	−0.438653	+	0.128800i
$647$	−6.22567	+	5.39457i	−0.244756	+	0.212082i	−0.768596	−	0.639734i	$-0.779044\pi$
$647$	−6.22567	+	5.39457i	−0.244756	+	0.212082i	0.523840	+	0.851817i	$0.324499\pi$
$648$	5.26120	+	8.18659i	0.206680	+	0.321600i
$649$	−0.0635777	−	0.442193i	−0.00249564	−	0.0173576i
$650$	7.69623	−	13.4044i	0.301871	−	0.525762i
$651$	−1.76944	+	3.87454i	−0.0693500	+	0.151855i
$652$	19.3822	+	16.7947i	0.759064	+	0.657732i
$653$	10.0445	+	1.44418i	0.393070	+	0.0565150i	0.336016	−	0.941856i	$-0.390920\pi$
$653$	10.0445	+	1.44418i	0.393070	+	0.0565150i	0.0570539	+	0.998371i	$0.481829\pi$
$654$	−1.00206	−	2.19421i	−0.0391837	−	0.0858003i
$655$	−14.6763	+	8.49681i	−0.573449	+	0.331998i
$656$	−5.38965	−	1.58254i	−0.210430	−	0.0617879i
$657$	16.8511	−	7.69565i	0.657425	−	0.300236i
$658$	−0.139757	−	0.0200940i	−0.00544830	−	0.000783347i
$659$	14.7008	−	16.9656i	0.572661	−	0.660885i	−0.393350	−	0.919389i	$-0.628684\pi$
$659$	14.7008	−	16.9656i	0.572661	−	0.660885i	0.966010	+	0.258503i	$0.0832293\pi$
$660$	−0.824254	+	0.331128i	−0.0320840	+	0.0128891i
$661$	−9.98338	−	6.41593i	−0.388309	−	0.249551i	0.331891	−	0.943318i	$-0.392313\pi$
$661$	−9.98338	−	6.41593i	−0.388309	−	0.249551i	−0.720200	+	0.693767i	$0.755950\pi$
$662$	−12.6358	+	1.81675i	−0.491104	+	0.0706101i
$663$	10.3269	+	16.0690i	0.401064	+	0.624068i
$664$	5.59838	+	6.46087i	0.217259	+	0.250730i
$665$	4.83830	+	2.48698i	0.187621	+	0.0964410i
$666$	−7.89593			−0.305961
$667$	6.08487	+	5.27382i	0.235607	+	0.204203i
$668$			16.9139i			0.654420i
$669$	5.60961	−	1.64713i	0.216880	−	0.0636818i
$670$	−0.683851	−	0.0317544i	−0.0264195	−	0.00122678i
$671$	1.55794	−	1.00123i	0.0601436	−	0.0386520i
$672$	−2.84538	+	0.409104i	−0.109763	+	0.0157815i
$673$	18.8100	−	29.2690i	0.725074	−	1.12824i	−0.261545	−	0.965191i	$-0.584232\pi$
$673$	18.8100	−	29.2690i	0.725074	−	1.12824i	0.986619	−	0.163045i	$-0.0521316\pi$
$674$	1.61938	−	3.54595i	0.0623762	−	0.136585i
$675$	−12.5115	+	15.9885i	−0.481570	+	0.615396i
$676$	2.58314	−	17.9661i	0.0993514	−	0.691004i
$677$	8.27158	−	3.77751i	0.317903	−	0.145181i	−0.250072	−	0.968227i	$-0.580454\pi$
$677$	8.27158	−	3.77751i	0.317903	−	0.145181i	0.567975	+	0.823046i	$0.307727\pi$
$678$	−0.581820	+	1.98150i	−0.0223447	+	0.0760989i
$679$	−5.24729	−	1.54074i	−0.201372	−	0.0591283i
$680$	−24.8417	−	8.56445i	−0.952634	−	0.328432i
$681$	1.70122	−	11.8322i	0.0651907	−	0.453412i
$682$	1.31516	+	1.13960i	0.0503602	+	0.0436374i
$683$	−0.872401	−	0.398412i	−0.0333815	−	0.0152448i	0.398654	−	0.917101i	$-0.369477\pi$
$683$	−0.872401	−	0.398412i	−0.0333815	−	0.0152448i	−0.432036	+	0.901856i	$0.642205\pi$
$684$	−11.7792	−	7.57003i	−0.450389	−	0.289447i
$685$	13.8638	−	19.5184i	0.529707	−	0.745759i
$686$	−4.87125	+	3.13056i	−0.185985	+	0.119525i
$687$	−13.3372	+	11.5568i	−0.508847	+	0.440918i
$688$	−3.73868	−	12.7328i	−0.142536	−	0.485433i
$689$	−44.5565			−1.69747
$690$	1.18795	+	4.87377i	0.0452243	+	0.185541i
$691$	−1.18099			−0.0449269			−0.0224634	−	0.999748i	$-0.507151\pi$
$691$	−1.18099			−0.0449269			−0.0224634	+	0.999748i	$0.507151\pi$
$692$	−3.35802	−	11.4364i	−0.127653	−	0.434746i
$693$	−0.417606	+	0.361858i	−0.0158635	+	0.0137458i
$694$	−9.74303	+	6.26147i	−0.369840	+	0.237682i
$695$	4.93850	+	3.50777i	0.187328	+	0.133057i
$696$	−2.38307	−	1.53151i	−0.0903301	−	0.0580516i
$697$	14.7901	+	6.75439i	0.560214	+	0.255841i
$698$	6.33236	+	5.48702i	0.239683	+	0.207687i
$699$	0.748979	−	5.20926i	0.0283290	−	0.197032i
$700$	2.52286	+	4.86499i	0.0953551	+	0.183879i
$701$	−50.2799	−	14.7635i	−1.89905	−	0.557610i	−0.990032	−	0.140846i	$-0.955018\pi$
$701$	−50.2799	−	14.7635i	−1.89905	−	0.557610i	−0.909015	−	0.416764i	$-0.863164\pi$
$702$	3.53632	−	12.0436i	0.133470	−	0.454556i
$703$	16.7141	−	7.63309i	0.630385	−	0.287887i
$704$	0.00219814	−	0.0152884i	8.28455e−5	−	0.000576203i
$705$	0.0529799	+	0.547889i	0.00199534	+	0.0206347i
$706$	−0.810590	+	1.77494i	−0.0305070	+	0.0668009i
$707$	−3.45361	+	5.37392i	−0.129886	+	0.202107i
$708$	−1.59870	+	0.229858i	−0.0600828	+	0.00863861i
$709$	−23.0765	+	14.8304i	−0.866658	+	0.556967i	−0.896729	−	0.442581i	$-0.854063\pi$
$709$	−23.0765	+	14.8304i	−0.866658	+	0.556967i	0.0300710	+	0.999548i	$0.490427\pi$
$710$	−0.946454	+	20.3825i	−0.0355198	+	0.764942i
$711$	−25.3197	+	7.43453i	−0.949562	+	0.278817i
$712$			32.4340i			1.21552i
$713$	−30.3434	+	26.2865i	−1.13637	+	0.984436i
$714$	1.65787			0.0620444
$715$	−3.24942	−	1.67027i	−0.121521	−	0.0624644i
$716$	16.7062	+	19.2800i	0.624342	+	0.720529i
$717$	6.25641	+	9.73516i	0.233650	+	0.363566i
$718$	−20.0195	+	2.87837i	−0.747120	+	0.107420i
$719$	30.4388	+	19.5618i	1.13518	+	0.729533i	0.966634	−	0.256161i	$-0.0824579\pi$
$719$	30.4388	+	19.5618i	1.13518	+	0.729533i	0.168542	+	0.985695i	$0.446094\pi$
$720$	−3.65585	−	9.10025i	−0.136246	−	0.339146i
$721$	−8.59017	+	9.91358i	−0.319915	+	0.369201i
$722$	3.89922	+	0.560623i	0.145114	+	0.0208642i
$723$	3.69688	−	1.68831i	0.137488	−	0.0627888i
$724$	1.82980	+	0.537279i	0.0680041	+	0.0199678i
$725$	−1.95965	+	8.16314i	−0.0727795	+	0.303171i
$726$	2.11623	+	4.63390i	0.0785407	+	0.171980i
$727$	47.8701	+	6.88269i	1.77541	+	0.255265i	0.950659	−	0.310238i	$-0.100409\pi$
$727$	47.8701	+	6.88269i	1.77541	+	0.255265i	0.824746	+	0.565503i	$0.191318\pi$
$728$	−5.74818	−	4.98082i	−0.213042	−	0.184602i
$729$	0.592928	−	1.29833i	0.0219603	−	0.0480864i
$730$	10.3285	−	2.51877i	0.382274	−	0.0932239i
$731$	5.46661	+	38.0211i	0.202190	+	1.40626i
$732$	−3.61983	−	5.63257i	−0.133793	−	0.208186i
$733$	22.5514	−	19.5409i	0.832954	−	0.721759i	−0.129974	−	0.991517i	$-0.541489\pi$
$733$	22.5514	−	19.5409i	0.832954	−	0.721759i	0.962928	+	0.269759i	$0.0869439\pi$
$734$	−9.99927	+	2.93605i	−0.369080	+	0.108372i
$735$	7.89696	+	7.51168i	0.291284	+	0.277073i
$736$	−25.9955	−	7.63626i	−0.958205	−	0.281476i
$737$			0.161819i			0.00596068i
$738$	−1.35127	−	4.60199i	−0.0497408	−	0.169402i
$739$	−16.9295	−	19.5377i	−0.622763	−	0.718707i	0.353466	−	0.935447i	$-0.385003\pi$
$739$	−16.9295	−	19.5377i	−0.622763	−	0.718707i	−0.976229	+	0.216740i	$0.930458\pi$
$740$	18.1800	+	3.48131i	0.668310	+	0.127976i
$741$	1.86606	+	12.9788i	0.0685516	+	0.476787i
$742$	−2.09079	+	3.25333i	−0.0767551	+	0.119433i
$743$	33.8272	+	15.4483i	1.24100	+	0.566745i	0.924258	−	0.381768i	$-0.124685\pi$
$743$	33.8272	+	15.4483i	1.24100	+	0.566745i	0.316740	+	0.948512i	$0.397412\pi$
$744$	9.24876	−	10.6736i	0.339076	−	0.391314i
$745$	−30.0744	−	38.1485i	−1.10184	−	1.39765i
$746$	−6.22378	−	13.6282i	−0.227869	−	0.498963i
$747$	2.60201	−	8.86164i	0.0952027	−	0.324231i
$748$	−0.779523	+	2.65481i	−0.0285022	+	0.0970695i
$749$	1.13570	+	2.48683i	0.0414975	+	0.0908669i
$750$	−3.94024	+	3.43912i	−0.143877	+	0.125579i
$751$	−6.11771	+	7.06022i	−0.223239	+	0.257631i	−0.856310	−	0.516463i	$-0.827249\pi$
$751$	−6.11771	+	7.06022i	−0.223239	+	0.257631i	0.633071	+	0.774094i	$0.281794\pi$
$752$	−0.538811	−	0.246067i	−0.0196484	−	0.00897312i
$753$	−4.21586	+	6.56000i	−0.153634	+	0.239060i
$754$	−0.738670	−	5.13756i	−0.0269008	−	0.187099i
$755$	−1.57776	+	8.23934i	−0.0574206	+	0.299860i
$756$	2.91438	+	3.36337i	0.105995	+	0.122325i
$757$	4.40593	+	15.0052i	0.160136	+	0.545374i	0.999997	+	0.00257145i	$0.000818519\pi$
$757$	4.40593	+	15.0052i	0.160136	+	0.545374i	−0.839861	+	0.542802i	$0.817363\pi$
$758$		−	19.4130i		−	0.705111i
$759$	1.13777	−	0.333934i	0.0412984	−	0.0121210i
$760$	−13.0695	−	12.4318i	−0.474080	−	0.450950i
$761$	5.35844	−	1.57338i	0.194243	−	0.0570350i	−0.183164	−	0.983082i	$-0.558634\pi$
$761$	5.35844	−	1.57338i	0.194243	−	0.0570350i	0.377407	+	0.926047i	$0.376816\pi$
$762$	−4.92199	+	4.26492i	−0.178305	+	0.154502i
$763$	1.90182	+	2.95930i	0.0688507	+	0.107134i
$764$	−0.0451435	−	0.313980i	−0.00163323	−	0.0113594i
$765$	6.72568	+	27.5793i	0.243167	+	0.997132i
$766$	−0.626840	+	1.37259i	−0.0226486	+	0.0495936i
$767$	−5.02059	−	4.35037i	−0.181283	−	0.157083i
$768$	5.17641	+	0.744255i	0.186788	+	0.0268560i
$769$	19.5148	+	42.7314i	0.703720	+	1.54093i	0.835401	+	0.549640i	$0.185235\pi$
$769$	19.5148	+	42.7314i	0.703720	+	1.54093i	−0.131681	+	0.991292i	$0.542037\pi$
$770$	−0.274433	+	0.158883i	−0.00988987	+	0.00572574i
$771$	19.6030	+	5.75595i	0.705983	+	0.207295i
$772$	−5.03116	+	2.29765i	−0.181075	+	0.0826943i
$773$	−2.21219	−	0.318064i	−0.0795668	−	0.0114400i	0.102416	−	0.994742i	$-0.467343\pi$
$773$	−2.21219	−	0.318064i	−0.0795668	−	0.0114400i	−0.181983	+	0.983302i	$0.558252\pi$
$774$	7.42021	−	8.56338i	0.266714	−	0.307804i
$775$	−38.8941	−	15.4628i	−1.39712	−	0.555439i
$776$	15.2546	+	9.80352i	0.547607	+	0.351926i
$777$	−2.59496	+	0.373099i	−0.0930937	+	0.0133848i
$778$	−3.53128	−	5.49478i	−0.126603	−	0.196997i
$779$	7.30917	+	8.43523i	0.261878	+	0.302223i
$780$	−6.03867	+	11.7479i	−0.216219	+	0.420643i
$781$	4.82309			0.172584
$782$	14.2129	+	6.49281i	0.508251	+	0.232182i
$783$			6.81745i			0.243636i
$784$	−11.2534	+	3.30429i	−0.401907	+	0.118010i
$785$	−1.37316	+	29.5718i	−0.0490100	+	1.05546i
$786$	−2.98453	+	1.91804i	−0.106454	+	0.0684142i
$787$	−26.1936	+	3.76607i	−0.933700	+	0.134246i	−0.592341	−	0.805687i	$-0.701796\pi$
$787$	−26.1936	+	3.76607i	−0.933700	+	0.134246i	−0.341359	+	0.939933i	$0.610887\pi$
$788$	20.3828	−	31.7163i	0.726108	−	1.12985i
$789$	4.00239	−	8.76400i	0.142489	−	0.312007i
$790$	−15.0735	+	1.45757i	−0.536289	+	0.0518582i
$791$	0.428600	−	2.98098i	0.0152392	−	0.105991i
$792$	1.66661	−	0.761116i	0.0592205	−	0.0270451i
$793$	7.75860	−	26.4234i	0.275516	−	0.938322i
$794$	−19.7597	−	5.80196i	−0.701244	−	0.205904i
$795$	14.2531	+	4.91393i	0.505506	+	0.174279i
$796$	4.68415	−	32.5790i	0.166025	−	1.15473i
$797$	−30.1610	−	26.1347i	−1.06836	−	0.925737i	−0.0709348	−	0.997481i	$-0.522598\pi$
$797$	−30.1610	−	26.1347i	−1.06836	−	0.925737i	−0.997423	+	0.0717435i	$0.977144\pi$
$798$	1.03522	+	0.472768i	0.0366463	+	0.0167358i
$799$	1.44239	+	0.926969i	0.0510281	+	0.0327938i
$800$	−5.41231	−	27.7239i	−0.191354	−	0.980189i
$801$	29.4773	−	18.9439i	1.04153	−	0.669349i
$802$	−4.29158	+	3.71868i	−0.151541	+	0.131311i
$803$	−0.707974	−	2.41114i	−0.0249839	−	0.0850873i
$804$	0.585040			0.0206328
$805$	−2.72626	−	6.78857i	−0.0960879	−	0.239266i
$806$	25.8776			0.911500
$807$	3.65117	+	12.4348i	0.128527	+	0.437724i
$808$	16.0075	−	13.8705i	0.563140	−	0.487964i
$809$	−0.752013	+	0.483289i	−0.0264394	+	0.0169915i	−0.553794	−	0.832654i	$-0.686820\pi$
$809$	−0.752013	+	0.483289i	−0.0264394	+	0.0169915i	0.527354	+	0.849645i	$0.323184\pi$
$810$	3.49375	−	4.91875i	0.122758	−	0.172827i
$811$	−6.28784	−	4.04095i	−0.220796	−	0.141897i	0.425567	−	0.904927i	$-0.360075\pi$
$811$	−6.28784	−	4.04095i	−0.220796	−	0.141897i	−0.646363	+	0.763030i	$0.723711\pi$
$812$	1.67397	+	0.764478i	0.0587450	+	0.0268279i
$813$	−8.97590	−	7.77766i	−0.314799	−	0.272775i
$814$	−0.152430	+	1.06018i	−0.00534268	+	0.0371591i
$815$	11.6335	−	33.7435i	0.407502	−	1.18198i
$816$	6.67340	+	1.95949i	0.233616	+	0.0685957i
$817$	−7.42881	+	25.3002i	−0.259901	+	0.885142i
$818$	11.4125	−	5.21193i	0.399030	−	0.182231i
$819$	−1.16940	+	8.13333i	−0.0408620	+	0.284202i
$820$	1.08221	+	11.1916i	0.0377924	+	0.390829i
$821$	6.02859	−	13.2008i	0.210399	−	0.460710i	−0.774782	−	0.632229i	$-0.782140\pi$
$821$	6.02859	−	13.2008i	0.210399	−	0.460710i	0.985181	+	0.171519i	$0.0548675\pi$
$822$	2.70778	−	4.21339i	0.0944448	−	0.146959i
$823$	24.1518	−	3.47250i	0.841877	−	0.121044i	0.292134	−	0.956377i	$-0.405635\pi$
$823$	24.1518	−	3.47250i	0.841877	−	0.121044i	0.549743	+	0.835334i	$0.314726\pi$
$824$	36.5898	−	23.5148i	1.27466	−	0.819177i
$825$	0.855246	+	0.892662i	0.0297759	+	0.0310785i
$826$	−0.553234	+	0.162444i	−0.0192495	+	0.00565216i
$827$		−	18.2026i		−	0.632965i	−0.948598	−	0.316483i	$-0.897498\pi$
$827$		−	18.2026i		−	0.632965i	0.948598	−	0.316483i	$-0.102502\pi$
$828$	5.30268	+	18.0671i	0.184281	+	0.627876i
$829$	−1.17628			−0.0408540			−0.0204270	−	0.999791i	$-0.506503\pi$
$829$	−1.17628			−0.0408540			−0.0204270	+	0.999791i	$0.506503\pi$
$830$	2.42303	−	4.71389i	0.0841046	−	0.163621i
$831$	−5.47423	−	6.31760i	−0.189899	−	0.219155i
$832$	−0.124176	−	0.193221i	−0.00430502	−	0.00669874i
$833$	33.6035	−	4.83145i	1.16429	−	0.167400i
$834$	1.06606	+	0.685117i	0.0369147	+	0.0237237i
$835$	21.8429	−	8.77496i	0.755904	−	0.303670i
$836$	−1.24381	+	1.43544i	−0.0430182	+	0.0496457i
$837$	−33.6436	−	4.83722i	−1.16289	−	0.167199i
$838$	−4.64784	+	2.12260i	−0.160557	+	0.0733239i
$839$	40.4730	+	11.8840i	1.39728	+	0.410280i	0.891751	−	0.452527i	$-0.149477\pi$
$839$	40.4730	+	11.8840i	1.39728	+	0.410280i	0.505534	+	0.862807i	$0.331296\pi$
$840$	1.28946	+	2.22725i	0.0444908	+	0.0768474i
$841$	−10.8759	−	23.8150i	−0.375033	−	0.821207i
$842$	−11.8612	−	1.70538i	−0.408764	−	0.0587713i
$843$	−8.66770	−	7.51060i	−0.298531	−	0.258679i
$844$	−7.04296	+	15.4219i	−0.242429	+	0.530845i
$845$	−24.5418	+	5.98493i	−0.844263	+	0.205888i
$846$	−0.0719791	−	0.500625i	−0.00247469	−	0.0172119i
$847$	−4.01642	−	6.24967i	−0.138006	−	0.214741i
$848$	−12.2612	+	10.6244i	−0.421050	+	0.364842i
$849$	21.3969	−	6.28269i	0.734339	−	0.215621i
$850$	0.814159	+	16.2705i	0.0279254	+	0.558075i
$851$	−23.7076	−	6.96420i	−0.812687	−	0.238730i
$852$		−	17.4374i		−	0.597395i
$853$	−4.49011	−	15.2919i	−0.153738	−	0.523585i	0.846219	−	0.532835i	$-0.178874\pi$
$853$	−4.49011	−	15.2919i	−0.153738	−	0.523585i	−0.999957	+	0.00925078i	$0.997055\pi$
$854$	−1.56526	−	1.80640i	−0.0535620	−	0.0618138i
$855$	−3.66498	+	19.1391i	−0.125340	+	0.654545i
$856$	−1.29006	−	8.97259i	−0.0440935	−	0.306677i
$857$	−3.65657	+	5.68973i	−0.124906	+	0.194358i	−0.898075	−	0.439843i	$-0.855034\pi$
$857$	−3.65657	+	5.68973i	−0.124906	+	0.194358i	0.773169	+	0.634200i	$0.218671\pi$
$858$	−0.695256	−	0.317513i	−0.0237357	−	0.0108397i
$859$	2.18077	−	2.51674i	0.0744068	−	0.0858700i	−0.717326	−	0.696738i	$-0.754634\pi$
$859$	2.18077	−	2.51674i	0.0744068	−	0.0858700i	0.791732	+	0.610868i	$0.209179\pi$
$860$	−20.8603	+	16.4452i	−0.711329	+	0.560777i
$861$	−0.661541	−	1.44857i	−0.0225453	−	0.0493672i
$862$	−1.38117	+	4.70383i	−0.0470428	+	0.160213i
$863$	10.9615	−	37.3315i	0.373135	−	1.27078i	−0.532394	−	0.846496i	$-0.678708\pi$
$863$	10.9615	−	37.3315i	0.373135	−	1.27078i	0.905529	−	0.424284i	$-0.139474\pi$
$864$	−9.52921	−	20.8661i	−0.324190	−	0.709878i
$865$	−13.0269	+	10.2698i	−0.442929	+	0.349183i
$866$	−6.93263	+	8.00068i	−0.235580	+	0.271874i
$867$	−6.77852	−	3.09565i	−0.230211	−	0.105134i
$868$	−4.96039	+	7.71852i	−0.168367	+	0.261984i
$869$	0.509430	+	3.54316i	0.0172812	+	0.120194i
$870$	−0.330306	+	1.72491i	−0.0111984	+	0.0584800i
$871$	1.57580	+	1.81857i	0.0533939	+	0.0616199i
$872$	−3.28608	−	11.1914i	−0.111281	−	0.378988i
$873$		−	19.5899i		−	0.663018i
$874$	7.02335	+	8.10729i	0.237568	+	0.274233i
$875$	4.97385	−	5.78201i	0.168147	−	0.195468i
$876$	−8.71722	+	2.55961i	−0.294528	+	0.0864811i
$877$	−24.4763	+	21.2088i	−0.826505	+	0.716171i	−0.961538	−	0.274670i	$-0.911431\pi$
$877$	−24.4763	+	21.2088i	−0.826505	+	0.716171i	0.135034	+	0.990841i	$0.456886\pi$
$878$	10.8672	+	16.9096i	0.366749	+	0.570672i
$879$	−0.888451	−	6.17931i	−0.0299667	−	0.208423i
$880$	−1.29245	+	0.315187i	−0.0435686	+	0.0106249i
$881$	1.57762	−	3.45451i	0.0531515	−	0.116385i	−0.881193	−	0.472757i	$-0.843259\pi$
$881$	1.57762	−	3.45451i	0.0531515	−	0.116385i	0.934344	+	0.356371i	$0.115986\pi$
$882$	−7.56842	−	6.55807i	−0.254842	−	0.220822i
$883$	8.25337	+	1.18666i	0.277748	+	0.0399342i	0.279781	−	0.960064i	$-0.409738\pi$
$883$	8.25337	+	1.18666i	0.277748	+	0.0399342i	−0.00203308	+	0.999998i	$0.500647\pi$
$884$	17.0921	+	37.4266i	0.574871	+	1.25879i
$885$	1.12625	+	1.94533i	0.0378584	+	0.0653916i
$886$	18.7925	+	5.51799i	0.631348	+	0.185380i
$887$	−11.1324	+	5.08398i	−0.373788	+	0.170703i	−0.593446	−	0.804874i	$-0.702233\pi$
$887$	−11.1324	+	5.08398i	−0.373788	+	0.170703i	0.219658	+	0.975577i	$0.429506\pi$
$888$	8.60420	+	1.23710i	0.288738	+	0.0415143i
$889$	6.21958	−	7.17778i	0.208598	−	0.240735i
$890$	18.6590	−	7.49591i	0.625452	−	0.251263i
$891$	−1.19972	−	0.771013i	−0.0401921	−	0.0258299i
$892$	12.4652	−	1.79223i	0.417367	−	0.0600083i
$893$	0.636326	+	0.990143i	0.0212938	+	0.0331339i
$894$	−6.65499	−	7.68027i	−0.222576	−	0.256867i
$895$	16.2313	−	31.5771i	0.542552	−	1.05551i
$896$	−7.72781			−0.258168
$897$	9.53471	−	14.8325i	0.318355	−	0.495242i
$898$			8.66027i			0.288997i
$899$	−13.4857	+	3.95976i	−0.449774	+	0.132065i
$900$	−14.1750	+	13.5808i	−0.472499	+	0.452694i
$901$	39.5063	−	25.3892i	1.31615	−	0.845836i
$902$	−0.643989	+	0.0925917i	−0.0214425	+	0.00308297i
$903$	2.03398	−	3.16494i	0.0676866	−	0.105322i
$904$	−4.14824	+	9.08337i	−0.137968	+	0.302108i
$905$	−0.255454	−	2.64177i	−0.00849159	−	0.0878154i
$906$	−0.249761	+	1.73713i	−0.00829777	+	0.0577122i
$907$	−5.61456	+	2.56409i	−0.186429	+	0.0851391i	−0.506442	−	0.862274i	$-0.669040\pi$
$907$	−5.61456	+	2.56409i	−0.186429	+	0.0851391i	0.320014	+	0.947413i	$0.396312\pi$
$908$	7.25436	−	24.7061i	0.240744	−	0.819900i
$909$	−21.9556	−	6.44675i	−0.728222	−	0.213825i
$910$	−1.53695	+	4.45801i	−0.0509494	+	0.147782i
$911$	−3.96194	+	27.5559i	−0.131265	+	0.912967i	0.812644	+	0.582761i	$0.198028\pi$
$911$	−3.96194	+	27.5559i	−0.131265	+	0.912967i	−0.943909	+	0.330207i	$0.892882\pi$
$912$	3.60826	+	3.12657i	0.119481	+	0.103531i
$913$	−1.13961	−	0.520442i	−0.0377155	−	0.0172241i
$914$	8.41112	+	5.40550i	0.278215	+	0.178798i
$915$	−5.39600	+	7.59688i	−0.178386	+	0.251145i
$916$	−31.9792	+	20.5518i	−1.05662	+	0.679049i
$917$	3.90999	−	3.38803i	0.129119	−	0.111883i
$918$	3.72718	+	12.6936i	0.123015	+	0.418951i
$919$	−10.1186			−0.333783			−0.166892	−	0.985975i	$-0.553373\pi$
$919$	−10.1186			−0.333783			−0.166892	+	0.985975i	$0.553373\pi$
$920$	2.33183	+	24.1441i	0.0768781	+	0.796006i
$921$	−21.2948			−0.701689
$922$	−2.04113	−	6.95146i	−0.0672211	−	0.228934i
$923$	54.2033	−	46.9675i	1.78412	−	1.54595i
$924$	0.227976	−	0.146511i	0.00749986	−	0.00481987i
$925$	−4.93598	−	25.2840i	−0.162294	−	0.831332i
$926$	19.4722	+	12.5140i	0.639895	+	0.411235i
$927$	−42.7423	−	19.5197i	−1.40384	−	0.641112i
$928$	−7.16867	−	6.21169i	−0.235323	−	0.203909i
$929$	−3.82221	+	26.5841i	−0.125403	+	0.872195i	0.825874	+	0.563855i	$0.190682\pi$
$929$	−3.82221	+	26.5841i	−0.125403	+	0.872195i	−0.951276	+	0.308340i	$0.900227\pi$
$930$	−8.27795	−	2.85392i	−0.271445	−	0.0935838i
$931$	22.3606	+	6.56567i	0.732840	+	0.215181i
$932$	3.19381	−	10.8771i	0.104617	−	0.356292i
$933$	11.3393	−	5.17849i	0.371233	−	0.169536i
$934$	1.62442	−	11.2981i	0.0531526	−	0.369684i
$935$	3.83287	−	0.370632i	0.125348	−	0.0121209i
$936$	11.3181	−	24.7832i	0.369944	−	0.810064i
$937$	4.52925	−	7.04765i	0.147964	−	0.230237i	−0.759358	−	0.650673i	$-0.774487\pi$
$937$	4.52925	−	7.04765i	0.147964	−	0.230237i	0.907322	+	0.420437i	$0.138123\pi$
$938$	0.206728	−	0.0297230i	0.00674990	−	0.000970489i
$939$	2.24388	−	1.44206i	0.0732263	−	0.0470597i
$940$	−0.0549972	+	1.18440i	−0.00179381	+	0.0386309i
$941$	17.3245	−	5.08692i	0.564761	−	0.165829i	0.0131254	−	0.999914i	$-0.495822\pi$
$941$	17.3245	−	5.08692i	0.564761	−	0.165829i	0.551636	+	0.834085i	$0.314004\pi$
$942$			6.19311i			0.201782i
$943$	0.00175878	−	15.0094i	5.72739e−5	−	0.488772i
$944$	−2.41891			−0.0787290
$945$	2.83152	−	5.50858i	0.0921094	−	0.179194i
$946$	−1.00655	−	1.16162i	−0.0327257	−	0.0377674i
$947$	1.44406	+	2.24700i	0.0469256	+	0.0730177i	0.863924	−	0.503623i	$-0.168000\pi$
$947$	1.44406	+	2.24700i	0.0469256	+	0.0730177i	−0.816998	+	0.576640i	$0.804363\pi$
$948$	12.8099	−	1.84179i	0.416047	−	0.0598185i
$949$	−31.4362	−	20.2028i	−1.02046	−	0.655811i
$950$	−4.13142	+	10.3919i	−0.134041	+	0.337158i
$951$	−9.31191	+	10.7465i	−0.301959	+	0.348480i
$952$	7.93484	+	1.14086i	0.257170	+	0.0369754i
$953$	−43.3185	+	19.7829i	−1.40322	+	0.640831i	−0.966005	−	0.258524i	$-0.916764\pi$
$953$	−43.3185	+	19.7829i	−1.40322	+	0.640831i	−0.437219	+	0.899355i	$0.644037\pi$
$954$	−13.2917	−	3.90280i	−0.430336	−	0.126358i
$955$	−0.382057	+	0.221192i	−0.0123631	+	0.00715759i
$956$	10.3550	+	22.6743i	0.334905	+	0.733340i
$957$	0.410907	+	0.0590796i	0.0132827	+	0.00190977i
$958$	−10.2032	−	8.84112i	−0.329650	−	0.285644i
$959$	−3.03415	+	6.64386i	−0.0979778	+	0.214541i
$960$	0.0184129	+	0.0755040i	0.000594274	+	0.00243688i
$961$	−5.56079	−	38.6762i	−0.179380	−	1.24762i
$962$	8.61097	+	13.3989i	0.277629	+	0.431999i
$963$	−7.40113	+	6.41312i	−0.238498	+	0.206660i
$964$	8.39969	−	2.46637i	0.270536	−	0.0794365i
$965$	5.57738	+	5.30528i	0.179542	+	0.170783i
$966$	−0.635595	−	1.39219i	−0.0204499	−	0.0447930i
$967$			45.2970i			1.45665i	0.685230	+	0.728327i	$0.259702\pi$
$967$			45.2970i			1.45665i	−0.685230	+	0.728327i	$0.740298\pi$
$968$	6.93981	+	23.6348i	0.223054	+	0.759652i
$969$	−9.05012	−	10.4444i	−0.290732	−	0.335522i
$970$	2.11436	−	11.0415i	0.0678880	−	0.354522i
$971$	1.61600	+	11.2395i	0.0518600	+	0.360694i	0.999183	+	0.0404143i	$0.0128678\pi$
$971$	1.61600	+	11.2395i	0.0518600	+	0.360694i	−0.947323	+	0.320280i	$0.896223\pi$
$972$	−13.3686	+	20.8019i	−0.428797	+	0.667222i
$973$	−1.68101	−	0.767693i	−0.0538908	−	0.0246111i
$974$	−12.1729	+	14.0482i	−0.390044	+	0.450134i
$975$	18.3043	+	1.70358i	0.586206	+	0.0545582i
$976$	−4.16555	−	9.12128i	−0.133336	−	0.291965i
$977$	−8.77534	+	29.8860i	−0.280748	+	0.956139i	0.691537	+	0.722341i	$0.256934\pi$
$977$	−8.77534	+	29.8860i	−0.280748	+	0.956139i	−0.972285	+	0.233799i	$0.924884\pi$
$978$	2.10367	−	7.16444i	0.0672680	−	0.229094i
$979$	−1.97451	−	4.32358i	−0.0631057	−	0.138182i
$980$	14.5345	+	18.4365i	0.464286	+	0.588934i
$981$	−8.25182	+	9.52311i	−0.263460	+	0.304049i
$982$	−4.67313	−	2.13415i	−0.149126	−	0.0681034i
$983$	−18.9900	+	29.5490i	−0.605687	+	0.942467i	0.394040	+	0.919093i	$0.371077\pi$
$983$	−18.9900	+	29.5490i	−0.605687	+	0.942467i	−0.999727	+	0.0233737i	$0.992559\pi$
$984$	0.751458	+	5.22650i	0.0239556	+	0.166615i
$985$	−51.5335	−	9.86821i	−1.64199	−	0.314427i
$986$	3.58243	+	4.13435i	0.114088	+	0.131664i
$987$	−0.0473112	−	0.161127i	−0.00150593	−	0.00512873i
$988$			28.2442i			0.898567i
$989$	29.8322	−	19.1670i	0.948608	−	0.609476i
$990$	−0.823039	−	0.782884i	−0.0261579	−	0.0248817i
$991$	1.91867	−	0.563371i	0.0609484	−	0.0178961i	−0.251116	−	0.967957i	$-0.580798\pi$
$991$	1.91867	−	0.563371i	0.0609484	−	0.0178961i	0.312065	+	0.950061i	$0.398979\pi$
$992$	35.7407	−	30.9695i	1.13477	−	0.983282i
$993$	−8.20850	−	12.7727i	−0.260489	−	0.405329i
$994$	−0.885907	−	6.16162i	−0.0280993	−	0.195435i
$995$	−44.5030	+	10.8528i	−1.41084	+	0.344057i
$996$	−1.88160	+	4.12013i	−0.0596209	+	0.130551i
$997$	−7.37038	−	6.38647i	−0.233422	−	0.202262i	0.530294	−	0.847814i	$-0.322082\pi$
$997$	−7.37038	−	6.38647i	−0.233422	−	0.202262i	−0.763716	+	0.645553i	$0.776627\pi$
$998$	26.3105	+	3.78288i	0.832844	+	0.119745i
$999$	−8.69055	−	19.0297i	−0.274957	−	0.602072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.j.a.9.5	✓	100
5.2	odd	4		575.2.k.g.101.6		100
5.3	odd	4		575.2.k.g.101.5		100
5.4	even	2	inner	115.2.j.a.9.6	yes	100
23.18	even	11	inner	115.2.j.a.64.6	yes	100
115.18	odd	44		575.2.k.g.501.5		100
115.64	even	22	inner	115.2.j.a.64.5	yes	100
115.87	odd	44		575.2.k.g.501.6		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.9.5	✓	100	1.1	even	1	trivial
115.2.j.a.9.6	yes	100	5.4	even	2	inner
115.2.j.a.64.5	yes	100	115.64	even	22	inner
115.2.j.a.64.6	yes	100	23.18	even	11	inner
575.2.k.g.101.5		100	5.3	odd	4
575.2.k.g.101.6		100	5.2	odd	4
575.2.k.g.501.5		100	115.18	odd	44
575.2.k.g.501.6		100	115.87	odd	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.176688 - 0.601743i) q^{2} +(0.563711 - 0.488459i) q^{3} +(1.35163 - 0.868641i) q^{4} +(-1.82300 - 1.29486i) q^{5} +(-0.393527 - 0.252905i) q^{6} +(0.620531 + 0.283387i) q^{7} +(-1.70945 - 1.48124i) q^{8} +(-0.347766 + 2.41877i) q^{9} +O(q^{10})\)	\(q+(-0.176688 - 0.601743i) q^{2} +(0.563711 - 0.488459i) q^{3} +(1.35163 - 0.868641i) q^{4} +(-1.82300 - 1.29486i) q^{5} +(-0.393527 - 0.252905i) q^{6} +(0.620531 + 0.283387i) q^{7} +(-1.70945 - 1.48124i) q^{8} +(-0.347766 + 2.41877i) q^{9} +(-0.457073 + 1.32576i) q^{10} +(0.318051 + 0.0933881i) q^{11} +(0.337635 - 1.14988i) q^{12} +(4.48376 - 2.04767i) q^{13} +(0.0608859 - 0.423471i) q^{14} +(-1.66013 + 0.160532i) q^{15} +(0.745594 - 1.63262i) q^{16} +(-2.80876 + 4.37052i) q^{17} +(1.51692 - 0.218100i) q^{18} +(-3.00018 + 1.92810i) q^{19} +(-3.58879 - 0.166644i) q^{20} +(0.488223 - 0.143355i) q^{21} -0.207885i q^{22} +(4.74694 + 0.683074i) q^{23} -1.68716 q^{24} +(1.64666 + 4.72107i) q^{25} +(-2.02439 - 2.33628i) q^{26} +(2.19521 + 3.41582i) q^{27} +(1.08489 - 0.155984i) q^{28} +(1.41248 + 0.907743i) q^{29} +(0.389924 + 0.970609i) q^{30} +(-5.48185 + 6.32639i) q^{31} +(-5.59195 - 0.804002i) q^{32} +(0.224905 - 0.102711i) q^{33} +(3.12620 + 0.917936i) q^{34} +(-0.764281 - 1.32012i) q^{35} +(1.63099 + 3.57136i) q^{36} +(-5.09981 - 0.733242i) q^{37} +(1.69032 + 1.46467i) q^{38} +(1.52735 - 3.34442i) q^{39} +(1.19831 + 4.91381i) q^{40} +(-0.445398 - 3.09781i) q^{41} +(-0.172526 - 0.268456i) q^{42} +(5.58778 - 4.84184i) q^{43} +(0.511008 - 0.150045i) q^{44} +(3.76595 - 3.95910i) q^{45} +(-0.427690 - 2.97713i) q^{46} -0.330027i q^{47} +(-0.377169 - 1.28452i) q^{48} +(-4.27927 - 4.93855i) q^{49} +(2.54993 - 1.82502i) q^{50} +(0.551487 + 3.83567i) q^{51} +(4.28171 - 6.66247i) q^{52} +(-8.22242 - 3.75505i) q^{53} +(1.66758 - 1.92449i) q^{54} +(-0.458882 - 0.582078i) q^{55} +(-0.640999 - 1.40359i) q^{56} +(-0.749439 + 2.55236i) q^{57} +(0.296661 - 1.01033i) q^{58} +(-0.559864 - 1.22593i) q^{59} +(-2.10444 + 1.65904i) q^{60} +(3.65863 - 4.22228i) q^{61} +(4.77543 + 2.18087i) q^{62} +(-0.901246 + 1.40237i) q^{63} +(-0.00663133 - 0.0461219i) q^{64} +(-10.8253 - 2.07296i) q^{65} +(-0.101543 - 0.117187i) q^{66} +(0.137535 + 0.468400i) q^{67} +8.34713i q^{68} +(3.00955 - 1.93363i) q^{69} +(-0.659332 + 0.693149i) q^{70} +(13.9609 - 4.09929i) q^{71} +(4.17727 - 3.61962i) q^{72} +(-4.09859 - 6.37754i) q^{73} +(0.459850 + 3.19833i) q^{74} +(3.23429 + 1.85699i) q^{75} +(-2.38031 + 5.21216i) q^{76} +(0.170895 + 0.148082i) q^{77} +(-2.28235 - 0.328152i) q^{78} +(4.48603 + 9.82303i) q^{79} +(-3.47324 + 2.01083i) q^{80} +(-4.12801 - 1.21209i) q^{81} +(-1.78539 + 0.815360i) q^{82} +(-3.74104 - 0.537881i) q^{83} +(0.535373 - 0.617854i) q^{84} +(10.7796 - 4.33050i) q^{85} +(-3.90083 - 2.50691i) q^{86} +(1.23962 - 0.178231i) q^{87} +(-0.405360 - 0.630752i) q^{88} +(-9.39014 - 10.8368i) q^{89} +(-3.04776 - 1.56661i) q^{90} +3.36260 q^{91} +(7.00945 - 3.20012i) q^{92} +6.24391i q^{93} +(-0.198592 + 0.0583118i) q^{94} +(7.96596 + 0.369896i) q^{95} +(-3.54497 + 2.27821i) q^{96} +(-7.93510 + 1.14089i) q^{97} +(-2.21564 + 3.44760i) q^{98} +(-0.336491 + 0.736813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

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