LMFDB - Embedded newform 429.2.bn.b.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(4,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("429.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bn (of order $30$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	429.49
Dual form			429.2.bn.b.394.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64800 - 1.48387i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.304992 + 2.90181i) q^{4} +(-1.57487 - 0.511707i) q^{5} +(1.64800 - 1.48387i) q^{6} +(1.08496 - 0.114034i) q^{7} +(1.19632 - 1.64659i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-1.64800 - 1.48387i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.304992 + 2.90181i) q^{4} +(-1.57487 - 0.511707i) q^{5} +(1.64800 - 1.48387i) q^{6} +(1.08496 - 0.114034i) q^{7} +(1.19632 - 1.64659i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.83609 + 3.18020i) q^{10} +(0.432504 - 3.28830i) q^{11} -2.91779 q^{12} +(0.269120 + 3.59549i) q^{13} +(-1.95724 - 1.42201i) q^{14} +(0.673523 - 1.51276i) q^{15} +(1.29319 - 0.274876i) q^{16} +(1.40195 + 1.55703i) q^{17} +(1.30348 + 1.79408i) q^{18} +(-2.41021 - 5.41343i) q^{19} +(1.00455 - 4.72604i) q^{20} +1.09094i q^{21} +(-5.59218 + 4.77736i) q^{22} +(-3.01576 - 5.22344i) q^{23} +(1.51252 + 1.36188i) q^{24} +(-1.82670 - 1.32718i) q^{25} +(4.89174 - 6.32473i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.661810 + 3.11357i) q^{28} +(-5.22368 - 2.32573i) q^{29} +(-3.35471 + 1.49361i) q^{30} +(-1.70385 + 0.553614i) q^{31} +(-6.06431 - 3.50123i) q^{32} +(3.22508 + 0.773856i) q^{33} -4.64631i q^{34} +(-1.76703 - 0.375594i) q^{35} +(0.304992 - 2.90181i) q^{36} +(4.17143 - 9.36918i) q^{37} +(-4.06078 + 12.4978i) q^{38} +(-3.60393 - 0.108186i) q^{39} +(-2.72662 + 1.98101i) q^{40} +(-6.39118 - 0.671740i) q^{41} +(1.61881 - 1.79787i) q^{42} +(-3.09684 + 5.36388i) q^{43} +(9.67393 + 0.252135i) q^{44} +(1.43407 + 0.827960i) q^{45} +(-2.78093 + 13.0833i) q^{46} +(5.46084 - 7.51621i) q^{47} +(0.138195 + 1.31484i) q^{48} +(-5.68289 + 1.20794i) q^{49} +(1.04106 + 4.89779i) q^{50} +(-1.69504 + 1.23152i) q^{51} +(-10.3513 + 1.87753i) q^{52} +(0.750218 + 2.30893i) q^{53} +(-1.92051 + 1.10880i) q^{54} +(-2.36379 + 4.95734i) q^{55} +(1.11019 - 1.92291i) q^{56} +(5.63571 - 1.83115i) q^{57} +(5.15757 + 11.5841i) q^{58} +(4.18695 - 0.440066i) q^{59} +(4.59515 + 1.49305i) q^{60} +(-0.614917 - 0.682935i) q^{61} +(3.62944 + 1.61593i) q^{62} +(-1.08496 - 0.114034i) q^{63} +(3.98155 + 12.2539i) q^{64} +(1.41601 - 5.80016i) q^{65} +(-4.16665 - 6.06092i) q^{66} +(1.51000 - 0.871799i) q^{67} +(-4.09061 + 4.54308i) q^{68} +(5.51006 - 2.45324i) q^{69} +(2.35474 + 3.24102i) q^{70} +(-9.42023 + 8.48202i) q^{71} +(-1.51252 + 1.36188i) q^{72} +(-6.18211 - 8.50895i) q^{73} +(-20.7772 + 9.25060i) q^{74} +(1.51085 - 1.67797i) q^{75} +(14.9736 - 8.64502i) q^{76} +(0.0942714 - 3.61701i) q^{77} +(5.77876 + 5.52605i) q^{78} +(-2.25925 - 6.95327i) q^{79} +(-2.17727 - 0.228840i) q^{80} +(0.913545 + 0.406737i) q^{81} +(9.53592 + 10.5907i) q^{82} +(6.70463 + 2.17847i) q^{83} +(-3.16569 + 0.332728i) q^{84} +(-1.41116 - 3.16951i) q^{85} +(13.0629 - 4.24439i) q^{86} +(2.85902 - 4.95196i) q^{87} +(-4.89708 - 4.64602i) q^{88} +(6.51377 - 3.76073i) q^{89} +(-1.13477 - 3.49245i) q^{90} +(0.701994 + 3.87029i) q^{91} +(14.2376 - 10.3443i) q^{92} +(-0.372481 - 1.75238i) q^{93} +(-20.1526 + 4.28356i) q^{94} +(1.02569 + 9.75878i) q^{95} +(4.11594 - 5.66511i) q^{96} +(2.79021 - 13.1269i) q^{97} +(11.1579 + 6.44199i) q^{98} +(-1.10673 + 3.12652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 14 q^{3} - 8 q^{4} + 14 q^{9}+O(q^{10}) $ 112 * q + 14 * q^3 - 8 * q^4 + 14 * q^9	$ 112 q + 14 q^{3} - 8 q^{4} + 14 q^{9} - 40 q^{10} + 15 q^{11} - 104 q^{12} + q^{13} - 6 q^{14} - 6 q^{15} + 32 q^{16} + 8 q^{17} - 12 q^{19} + 42 q^{20} - 9 q^{22} + 8 q^{23} + 30 q^{25} - 57 q^{26} - 28 q^{27} + 18 q^{28} - 10 q^{29} + 10 q^{30} + 30 q^{32} + 30 q^{33} - 12 q^{35} - 8 q^{36} + 30 q^{38} + 4 q^{39} + 20 q^{40} + 72 q^{41} - 12 q^{42} - 108 q^{43} + 6 q^{45} - 18 q^{46} + 2 q^{48} - 40 q^{49} + 111 q^{50} - 26 q^{51} + 13 q^{52} - 46 q^{53} - 38 q^{55} - 100 q^{56} - 12 q^{58} - 18 q^{59} - 46 q^{61} - 9 q^{62} + 52 q^{64} + 24 q^{65} - 32 q^{66} + 48 q^{67} - 8 q^{68} - 7 q^{69} + 18 q^{71} + 32 q^{74} - 216 q^{76} + 4 q^{77} - 26 q^{78} + 108 q^{79} - 66 q^{80} + 14 q^{81} + 39 q^{82} + 27 q^{84} + 6 q^{85} + 60 q^{87} + 28 q^{88} - 120 q^{89} - 20 q^{90} + 47 q^{91} + 78 q^{92} - 6 q^{93} - 50 q^{94} + 60 q^{95} - 69 q^{97} + 72 q^{98}+O(q^{100}) $ 112 * q + 14 * q^3 - 8 * q^4 + 14 * q^9 - 40 * q^10 + 15 * q^11 - 104 * q^12 + q^13 - 6 * q^14 - 6 * q^15 + 32 * q^16 + 8 * q^17 - 12 * q^19 + 42 * q^20 - 9 * q^22 + 8 * q^23 + 30 * q^25 - 57 * q^26 - 28 * q^27 + 18 * q^28 - 10 * q^29 + 10 * q^30 + 30 * q^32 + 30 * q^33 - 12 * q^35 - 8 * q^36 + 30 * q^38 + 4 * q^39 + 20 * q^40 + 72 * q^41 - 12 * q^42 - 108 * q^43 + 6 * q^45 - 18 * q^46 + 2 * q^48 - 40 * q^49 + 111 * q^50 - 26 * q^51 + 13 * q^52 - 46 * q^53 - 38 * q^55 - 100 * q^56 - 12 * q^58 - 18 * q^59 - 46 * q^61 - 9 * q^62 + 52 * q^64 + 24 * q^65 - 32 * q^66 + 48 * q^67 - 8 * q^68 - 7 * q^69 + 18 * q^71 + 32 * q^74 - 216 * q^76 + 4 * q^77 - 26 * q^78 + 108 * q^79 - 66 * q^80 + 14 * q^81 + 39 * q^82 + 27 * q^84 + 6 * q^85 + 60 * q^87 + 28 * q^88 - 120 * q^89 - 20 * q^90 + 47 * q^91 + 78 * q^92 - 6 * q^93 - 50 * q^94 + 60 * q^95 - 69 * q^97 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−1.64800	−	1.48387i	−1.16532	−	1.04925i	−0.997991	−	0.0633527i	$-0.979821\pi$
$2$	−1.64800	−	1.48387i	−1.16532	−	1.04925i	−0.167324	−	0.985902i	$-0.553513\pi$
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$4$	0.304992	+	2.90181i	0.152496	+	1.45090i
$5$	−1.57487	−	0.511707i	−0.704305	−	0.228842i	−0.0650995	−	0.997879i	$-0.520736\pi$
$5$	−1.57487	−	0.511707i	−0.704305	−	0.228842i	−0.639205	+	0.769036i	$0.720736\pi$
$6$	1.64800	−	1.48387i	0.672795	−	0.605787i
$7$	1.08496	−	0.114034i	0.410077	−	0.0431009i	0.102756	−	0.994707i	$-0.467234\pi$
$7$	1.08496	−	0.114034i	0.410077	−	0.0431009i	0.307322	+	0.951606i	$0.400567\pi$
$8$	1.19632	−	1.64659i	0.422963	−	0.582158i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	1.83609	+	3.18020i	0.580623	+	1.00567i
$11$	0.432504	−	3.28830i	0.130405	−	0.991461i
$11$	0.432504	−	3.28830i	0.130405	−	0.991461i
$12$	−2.91779			−0.842293
$13$	0.269120	+	3.59549i	0.0746404	+	0.997211i
$13$	0.269120	+	3.59549i	0.0746404	+	0.997211i
$14$	−1.95724	−	1.42201i	−0.523093	−	0.380049i
$15$	0.673523	−	1.51276i	0.173903	−	0.390592i
$16$	1.29319	−	0.274876i	0.323297	−	0.0687190i
$17$	1.40195	+	1.55703i	0.340024	+	0.377635i	0.888769	−	0.458355i	$-0.151561\pi$
$17$	1.40195	+	1.55703i	0.340024	+	0.377635i	−0.548745	+	0.835990i	$0.684894\pi$
$18$	1.30348	+	1.79408i	0.307233	+	0.422870i
$19$	−2.41021	−	5.41343i	−0.552941	−	1.24193i	−0.946523	−	0.322636i	$-0.895431\pi$
$19$	−2.41021	−	5.41343i	−0.552941	−	1.24193i	0.393582	−	0.919289i	$-0.371236\pi$
$20$	1.00455	−	4.72604i	0.224625	−	1.05678i
$21$			1.09094i			0.238062i
$22$	−5.59218	+	4.77736i	−1.19226	+	1.01854i
$23$	−3.01576	−	5.22344i	−0.628829	−	1.08916i	−0.987787	−	0.155810i	$-0.950201\pi$
$23$	−3.01576	−	5.22344i	−0.628829	−	1.08916i	0.358958	−	0.933354i	$-0.383132\pi$
$24$	1.51252	+	1.36188i	0.308742	+	0.277993i
$25$	−1.82670	−	1.32718i	−0.365341	−	0.265436i
$26$	4.89174	−	6.32473i	0.959348	−	1.24038i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.661810	+	3.11357i	0.125070	+	0.588410i
$29$	−5.22368	−	2.32573i	−0.970014	−	0.431878i	−0.140326	−	0.990105i	$-0.544815\pi$
$29$	−5.22368	−	2.32573i	−0.970014	−	0.431878i	−0.829688	+	0.558227i	$0.811482\pi$
$30$	−3.35471	+	1.49361i	−0.612483	+	0.272695i
$31$	−1.70385	+	0.553614i	−0.306020	+	0.0994320i	−0.458002	−	0.888951i	$-0.651435\pi$
$31$	−1.70385	+	0.553614i	−0.306020	+	0.0994320i	0.151981	+	0.988383i	$0.451435\pi$
$32$	−6.06431	−	3.50123i	−1.07203	−	0.618936i
$33$	3.22508	+	0.773856i	0.561415	+	0.134711i
$34$		−	4.64631i		−	0.796836i
$35$	−1.76703	−	0.375594i	−0.298683	−	0.0634870i
$36$	0.304992	−	2.90181i	0.0508320	−	0.483634i
$37$	4.17143	−	9.36918i	0.685778	−	1.54028i	−0.148483	−	0.988915i	$-0.547439\pi$
$37$	4.17143	−	9.36918i	0.685778	−	1.54028i	0.834262	−	0.551369i	$-0.185894\pi$
$38$	−4.06078	+	12.4978i	−0.658745	+	2.02741i
$39$	−3.60393	−	0.108186i	−0.577090	−	0.0173236i
$40$	−2.72662	+	1.98101i	−0.431117	+	0.313225i
$41$	−6.39118	−	0.671740i	−0.998135	−	0.104908i	−0.408653	−	0.912690i	$-0.634001\pi$
$41$	−6.39118	−	0.671740i	−0.998135	−	0.104908i	−0.589482	+	0.807782i	$0.700668\pi$
$42$	1.61881	−	1.79787i	0.249788	−	0.277418i
$43$	−3.09684	+	5.36388i	−0.472263	+	0.817984i	−0.999496	−	0.0317370i	$-0.989896\pi$
$43$	−3.09684	+	5.36388i	−0.472263	+	0.817984i	0.527233	+	0.849721i	$0.323229\pi$
$44$	9.67393	+	0.252135i	1.45840	+	0.0380108i
$45$	1.43407	+	0.827960i	0.213778	+	0.123425i
$46$	−2.78093	+	13.0833i	−0.410026	+	1.92902i
$47$	5.46084	−	7.51621i	0.796546	−	1.09635i	−0.196716	−	0.980461i	$-0.563028\pi$
$47$	5.46084	−	7.51621i	0.796546	−	1.09635i	0.993262	−	0.115891i	$-0.0369723\pi$
$48$	0.138195	+	1.31484i	0.0199467	+	0.189781i
$49$	−5.68289	+	1.20794i	−0.811842	+	0.172562i
$50$	1.04106	+	4.89779i	0.147228	+	0.692652i
$51$	−1.69504	+	1.23152i	−0.237354	+	0.172447i
$52$	−10.3513	+	1.87753i	−1.43547	+	0.260367i
$53$	0.750218	+	2.30893i	0.103050	+	0.317156i	0.989268	−	0.146113i	$-0.0466763\pi$
$53$	0.750218	+	2.30893i	0.103050	+	0.317156i	−0.886218	+	0.463269i	$0.846676\pi$
$54$	−1.92051	+	1.10880i	−0.261348	+	0.150889i
$55$	−2.36379	+	4.95734i	−0.318733	+	0.668448i
$56$	1.11019	−	1.92291i	0.148356	−	0.256960i
$57$	5.63571	−	1.83115i	0.746468	−	0.242542i
$58$	5.15757	+	11.5841i	0.677222	+	1.52107i
$59$	4.18695	−	0.440066i	0.545094	−	0.0572917i	0.172020	−	0.985093i	$-0.444970\pi$
$59$	4.18695	−	0.440066i	0.545094	−	0.0572917i	0.373074	+	0.927802i	$0.378304\pi$
$60$	4.59515	+	1.49305i	0.593231	+	0.192752i
$61$	−0.614917	−	0.682935i	−0.0787321	−	0.0874408i	0.702492	−	0.711692i	$-0.252071\pi$
$61$	−0.614917	−	0.682935i	−0.0787321	−	0.0874408i	−0.781224	+	0.624251i	$0.785404\pi$
$62$	3.62944	+	1.61593i	0.460940	+	0.205224i
$63$	−1.08496	−	0.114034i	−0.136692	−	0.0143670i
$64$	3.98155	+	12.2539i	0.497693	+	1.53174i
$65$	1.41601	−	5.80016i	0.175635	−	0.719421i
$66$	−4.16665	−	6.06092i	−0.512879	−	0.746048i
$67$	1.51000	−	0.871799i	0.184476	−	0.106507i	−0.404918	−	0.914353i	$-0.632700\pi$
$67$	1.51000	−	0.871799i	0.184476	−	0.106507i	0.589394	+	0.807846i	$0.299367\pi$
$68$	−4.09061	+	4.54308i	−0.496059	+	0.550930i
$69$	5.51006	−	2.45324i	0.663333	−	0.295335i
$70$	2.35474	+	3.24102i	0.281445	+	0.387376i
$71$	−9.42023	+	8.48202i	−1.11798	+	1.00663i	−0.118069	+	0.993005i	$0.537670\pi$
$71$	−9.42023	+	8.48202i	−1.11798	+	1.00663i	−0.999907	+	0.0136246i	$0.995663\pi$
$72$	−1.51252	+	1.36188i	−0.178253	+	0.160499i
$73$	−6.18211	−	8.50895i	−0.723562	−	0.995897i	−0.999398	−	0.0346926i	$-0.988955\pi$
$73$	−6.18211	−	8.50895i	−0.723562	−	0.995897i	0.275836	−	0.961205i	$-0.411045\pi$
$74$	−20.7772	+	9.25060i	−2.41530	+	1.07536i
$75$	1.51085	−	1.67797i	0.174458	−	0.193755i
$76$	14.9736	−	8.64502i	1.71759	−	0.991652i
$77$	0.0942714	−	3.61701i	0.0107432	−	0.412196i
$78$	5.77876	+	5.52605i	0.654315	+	0.625702i
$79$	−2.25925	−	6.95327i	−0.254186	−	0.782304i	−0.993989	−	0.109481i	$-0.965081\pi$
$79$	−2.25925	−	6.95327i	−0.254186	−	0.782304i	0.739803	−	0.672824i	$-0.234919\pi$
$80$	−2.17727	−	0.228840i	−0.243426	−	0.0255851i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	9.53592	+	10.5907i	1.05307	+	1.16955i
$83$	6.70463	+	2.17847i	0.735929	+	0.239118i	0.652915	−	0.757431i	$-0.273546\pi$
$83$	6.70463	+	2.17847i	0.735929	+	0.239118i	0.0830131	+	0.996548i	$0.473546\pi$
$84$	−3.16569	+	0.332728i	−0.345405	+	0.0363036i
$85$	−1.41116	−	3.16951i	−0.153062	−	0.343782i
$86$	13.0629	−	4.24439i	1.40861	−	0.457685i
$87$	2.85902	−	4.95196i	0.306519	−	0.530906i
$88$	−4.89708	−	4.64602i	−0.522031	−	0.495267i
$89$	6.51377	−	3.76073i	0.690458	−	0.398636i	−0.113325	−	0.993558i	$-0.536150\pi$
$89$	6.51377	−	3.76073i	0.690458	−	0.398636i	0.803784	+	0.594922i	$0.202817\pi$
$90$	−1.13477	−	3.49245i	−0.119615	−	0.368137i
$91$	0.701994	+	3.87029i	0.0735890	+	0.405716i
$92$	14.2376	−	10.3443i	1.48438	−	1.07846i
$93$	−0.372481	−	1.75238i	−0.0386244	−	0.181714i
$94$	−20.1526	+	4.28356i	−2.07858	+	0.441816i
$95$	1.02569	+	9.75878i	0.105234	+	1.00123i
$96$	4.11594	−	5.66511i	0.420082	−	0.578193i
$97$	2.79021	−	13.1269i	0.283303	−	1.33283i	−0.574352	−	0.818608i	$-0.694746\pi$
$97$	2.79021	−	13.1269i	0.283303	−	1.33283i	0.857655	−	0.514226i	$-0.171921\pi$
$98$	11.1579	+	6.44199i	1.12711	+	0.650739i
$99$	−1.10673	+	3.12652i	−0.111230	+	0.314227i
$100$	3.29408	−	5.70552i	0.329408	−	0.570552i
$101$	3.93153	−	4.36641i	0.391202	−	0.434474i	−0.515084	−	0.857140i	$-0.672239\pi$
$101$	3.93153	−	4.36641i	0.391202	−	0.434474i	0.906285	+	0.422666i	$0.138906\pi$
$102$	4.62086	+	0.485672i	0.457533	+	0.0480887i
$103$	13.9173	−	10.1115i	1.37131	−	0.996318i	0.373680	−	0.927558i	$-0.378096\pi$
$103$	13.9173	−	10.1115i	1.37131	−	0.996318i	0.997633	−	0.0687601i	$-0.0219043\pi$
$104$	6.24227	+	3.85823i	0.612104	+	0.378330i
$105$	0.558241	−	1.71809i	0.0544788	−	0.167668i
$106$	2.18979	−	4.91836i	0.212692	−	0.477713i
$107$	−1.56600	+	14.8995i	−0.151391	+	1.44038i	0.610159	+	0.792279i	$0.291105\pi$
$107$	−1.56600	+	14.8995i	−0.151391	+	1.44038i	−0.761550	+	0.648106i	$0.775561\pi$
$108$	2.85403	+	0.606643i	0.274629	+	0.0583742i
$109$			1.68110i			0.161020i	0.996754	+	0.0805100i	$0.0256549\pi$
$109$			1.68110i			0.161020i	−0.996754	+	0.0805100i	$0.974345\pi$
$110$	11.2516	−	4.66217i	1.07280	−	0.444521i
$111$	8.88182	+	5.12792i	0.843025	+	0.486721i
$112$	1.37172	−	0.445698i	0.129615	−	0.0421145i
$113$	11.6044	−	5.16662i	1.09165	−	0.486035i	0.219671	−	0.975574i	$-0.429502\pi$
$113$	11.6044	−	5.16662i	1.09165	−	0.486035i	0.871981	+	0.489539i	$0.162835\pi$
$114$	−12.0049	−	5.34491i	−1.12436	−	0.500597i
$115$	2.07656	+	9.76944i	0.193640	+	0.911005i
$116$	5.15565	−	15.8675i	0.478690	−	1.47326i
$117$	0.484306	−	3.57288i	0.0447741	−	0.330313i
$118$	−7.55311	−	5.48766i	−0.695320	−	0.505180i
$119$	1.69862	+	1.52945i	0.155713	+	0.140204i
$120$	−1.68515	−	2.91876i	−0.153832	−	0.266445i
$121$	−10.6259	−	2.84441i	−0.965989	−	0.258582i
$122$			2.03794i			0.184506i
$123$	1.33612	−	6.28596i	0.120474	−	0.566786i
$124$	−2.12614	−	4.77539i	−0.190933	−	0.428843i
$125$	7.06433	+	9.72321i	0.631852	+	0.869670i
$126$	1.61881	+	1.79787i	0.144215	+	0.160167i
$127$	12.9071	−	2.74350i	1.14532	−	0.243446i	0.404106	−	0.914712i	$-0.367583\pi$
$127$	12.9071	−	2.74350i	1.14532	−	0.243446i	0.741216	+	0.671266i	$0.234249\pi$
$128$	5.92533	−	13.3085i	0.523731	−	1.17632i
$129$	−5.01079	−	3.64055i	−0.441175	−	0.320532i
$130$	−10.9403	+	7.45751i	−0.959525	+	0.654067i
$131$	−7.69573			−0.672379			−0.336189	−	0.941794i	$-0.609138\pi$
$131$	−7.69573			−0.672379			−0.336189	+	0.941794i	$0.609138\pi$
$132$	−1.26196	+	9.59458i	−0.109839	+	0.835101i
$133$	−3.23231	−	5.59852i	−0.280277	−	0.485453i
$134$	−3.78212	−	0.803915i	−0.326726	−	0.0694477i
$135$	−0.973325	+	1.33967i	−0.0837705	+	0.115300i
$136$	4.24098	−	0.445745i	0.363661	−	0.0382223i
$137$	−5.28874	+	4.76200i	−0.451848	+	0.406846i	−0.863384	−	0.504548i	$-0.831659\pi$
$137$	−5.28874	+	4.76200i	−0.451848	+	0.406846i	0.411536	+	0.911394i	$0.364992\pi$
$138$	−12.7209	−	4.13327i	−1.08287	−	0.351847i
$139$	1.00678	+	9.57890i	0.0853942	+	0.812472i	0.950467	+	0.310826i	$0.100605\pi$
$139$	1.00678	+	9.57890i	0.0853942	+	0.812472i	−0.865073	+	0.501646i	$0.832728\pi$
$140$	0.550970	−	5.24213i	0.0465655	−	0.443041i
$141$	6.90422	+	6.21659i	0.581440	+	0.523531i
$142$	28.1108			2.35901
$143$	11.9395	+	0.670117i	0.998429	+	0.0560380i
$144$	−1.32208			−0.110173
$145$	7.03654	+	6.33573i	0.584353	+	0.526154i
$146$	−2.43802	+	23.1962i	−0.201772	+	1.91973i
$147$	−0.607295	−	5.77803i	−0.0500888	−	0.476563i
$148$	28.4598	+	9.24715i	2.33938	+	0.760111i
$149$	−15.7920	+	14.2192i	−1.29373	+	1.16488i	−0.317477	+	0.948266i	$0.602836\pi$
$149$	−15.7920	+	14.2192i	−1.29373	+	1.16488i	−0.976257	+	0.216617i	$0.930498\pi$
$150$	−4.97978	+	0.523396i	−0.406597	+	0.0427351i
$151$	6.27805	−	8.64099i	0.510900	−	0.703194i	−0.473170	−	0.880971i	$-0.656890\pi$
$151$	6.27805	−	8.64099i	0.510900	−	0.703194i	0.984071	+	0.177777i	$0.0568905\pi$
$152$	−11.7971	−	2.50755i	−0.956870	−	0.203389i
$153$	−1.04759	−	1.81449i	−0.0846930	−	0.146693i
$154$	−5.52253	+	5.82096i	−0.445018	+	0.469066i
$155$	2.96663			0.238286
$156$	−0.785235	−	10.4909i	−0.0628691	−	0.839944i
$157$	−4.76233	−	3.46004i	−0.380075	−	0.276141i	0.381301	−	0.924451i	$-0.375476\pi$
$157$	−4.76233	−	3.46004i	−0.380075	−	0.276141i	−0.761376	+	0.648310i	$0.775476\pi$
$158$	−6.59449	+	14.8115i	−0.524629	+	1.17834i
$159$	−2.37470	+	0.504759i	−0.188326	+	0.0400300i
$160$	7.75891	+	8.61714i	0.613396	+	0.681245i
$161$	−3.86763	−	5.32334i	−0.304812	−	0.419538i
$162$	−0.901983	−	2.02589i	−0.0708665	−	0.159169i
$163$	−3.26416	+	15.3566i	−0.255668	+	1.20283i	0.643577	+	0.765381i	$0.277450\pi$
$163$	−3.26416	+	15.3566i	−0.255668	+	1.20283i	−0.899246	+	0.437444i	$0.855884\pi$
$164$		−	18.7509i		−	1.46420i
$165$	−4.68310	−	2.86902i	−0.364579	−	0.223353i
$166$	−7.81670	−	13.5389i	−0.606693	−	1.05082i
$167$	−6.85376	−	6.17115i	−0.530360	−	0.477538i	0.359900	−	0.932991i	$-0.382811\pi$
$167$	−6.85376	−	6.17115i	−0.530360	−	0.477538i	−0.890260	+	0.455453i	$0.849477\pi$
$168$	1.79633	+	1.30511i	0.138590	+	0.100692i
$169$	−12.8551	+	1.93524i	−0.988858	+	0.148864i
$170$	−2.37755	+	7.31735i	−0.182350	+	0.561215i
$171$	1.23203	+	5.79624i	0.0942156	+	0.443250i
$172$	−16.5094	−	7.35048i	−1.25883	−	0.560469i
$173$	−9.16785	+	4.08179i	−0.697019	+	0.310333i	−0.724486	−	0.689290i	$-0.757923\pi$
$173$	−9.16785	+	4.08179i	−0.697019	+	0.310333i	0.0274668	+	0.999623i	$0.491256\pi$
$174$	−12.0597	+	3.91845i	−0.914247	+	0.297057i
$175$	−2.13325	−	1.23163i	−0.161259	−	0.0931027i
$176$	−0.344566	−	4.37129i	−0.0259727	−	0.329498i
$177$			4.21001i			0.316444i
$178$	−16.3152	−	3.46789i	−1.22287	−	0.259930i
$179$	0.436694	−	4.15486i	0.0326400	−	0.310549i	−0.966006	−	0.258521i	$-0.916765\pi$
$179$	0.436694	−	4.15486i	0.0326400	−	0.310549i	0.998646	−	0.0520279i	$-0.0165685\pi$
$180$	−1.96520	+	4.41391i	−0.146477	+	0.328993i
$181$	1.36484	−	4.20056i	0.101448	−	0.312225i	−0.887432	−	0.460938i	$-0.847513\pi$
$181$	1.36484	−	4.20056i	0.101448	−	0.312225i	0.988880	+	0.148713i	$0.0475131\pi$
$182$	4.58611	−	7.41992i	0.339945	−	0.550001i
$183$	0.743470	−	0.540162i	0.0549589	−	0.0399300i
$184$	−12.2087	−	1.28319i	−0.900037	−	0.0945977i
$185$	−11.3637	+	12.6207i	−0.835479	+	0.927894i
$186$	−1.98646	+	3.44065i	−0.145654	+	0.252281i
$187$	5.72633	−	3.93663i	0.418751	−	0.287875i
$188$	23.4761	+	13.5539i	1.71217	+	0.988522i
$189$	0.226819	−	1.06710i	0.0164987	−	0.0776201i
$190$	12.7904	−	17.6045i	0.927915	−	1.27717i
$191$	0.0559556	+	0.532382i	0.00404880	+	0.0385218i	0.996360	−	0.0852480i	$-0.0271682\pi$
$191$	0.0559556	+	0.532382i	0.00404880	+	0.0385218i	−0.992311	+	0.123770i	$0.960502\pi$
$192$	−12.6030	+	2.67885i	−0.909543	+	0.193329i
$193$	3.72636	+	17.5312i	0.268230	+	1.26192i	0.881551	+	0.472088i	$0.156500\pi$
$193$	3.72636	+	17.5312i	0.268230	+	1.26192i	−0.613322	+	0.789833i	$0.710167\pi$
$194$	−24.0769	+	17.4929i	−1.72862	+	1.25592i
$195$	5.62037	+	2.01454i	0.402483	+	0.144264i
$196$	−5.23843	−	16.1222i	−0.374174	−	1.15159i
$197$	−10.5714	+	6.10341i	−0.753182	+	0.434850i	−0.826842	−	0.562434i	$-0.809865\pi$
$197$	−10.5714	+	6.10341i	−0.753182	+	0.434850i	0.0736606	+	0.997283i	$0.476532\pi$
$198$	6.46325	−	3.51028i	0.459323	−	0.249465i
$199$	−8.57341	+	14.8496i	−0.607753	+	1.05266i	0.383857	+	0.923392i	$0.374595\pi$
$199$	−8.57341	+	14.8496i	−0.607753	+	1.05266i	−0.991610	+	0.129266i	$0.958738\pi$
$200$	−4.37064	+	1.42011i	−0.309051	+	0.100417i
$201$	0.709185	+	1.59286i	0.0500220	+	0.112351i
$202$	−12.9584	+	1.36198i	−0.911747	+	0.0958285i
$203$	−5.93272	−	1.92766i	−0.416395	−	0.135295i
$204$	−4.09061	−	4.54308i	−0.286400	−	0.318079i
$205$	9.72157	+	4.32832i	0.678984	+	0.302303i
$206$	−37.9400	−	3.98765i	−2.64340	−	0.277833i
$207$	1.86384	+	5.73631i	0.129546	+	0.398701i
$208$	1.33634	+	4.57568i	0.0926583	+	0.317266i
$209$	−18.8434	+	5.58418i	−1.30343	+	0.386266i
$210$	−3.46941	+	2.00306i	−0.239412	+	0.138224i
$211$	4.50782	−	5.00644i	0.310331	−	0.344657i	−0.567723	−	0.823220i	$-0.692175\pi$
$211$	4.50782	−	5.00644i	0.310331	−	0.344657i	0.878053	+	0.478563i	$0.158842\pi$
$212$	−6.47126	+	2.88119i	−0.444448	+	0.197881i
$213$	−7.45087	−	10.2552i	−0.510525	−	0.702677i
$214$	24.6896	−	22.2306i	1.68775	−	1.51966i
$215$	7.62186	−	6.86275i	0.519806	−	0.468036i
$216$	−1.19632	−	1.64659i	−0.0813992	−	0.112036i
$217$	−1.78548	+	0.794947i	−0.121206	+	0.0539646i
$218$	2.49453	−	2.77046i	0.168951	−	0.187639i
$219$	9.10854	−	5.25882i	0.615498	−	0.355358i
$220$	−15.1062	−	5.34730i	−1.01846	−	0.360515i
$221$	−5.22099	+	5.45975i	−0.351202	+	0.367262i
$222$	−7.02811	−	21.6303i	−0.471696	−	1.45173i
$223$	−6.86534	−	0.721577i	−0.459737	−	0.0483204i	−0.128171	−	0.991752i	$-0.540911\pi$
$223$	−6.86534	−	0.721577i	−0.459737	−	0.0483204i	−0.331567	+	0.943432i	$0.607577\pi$
$224$	−6.97881	−	3.10716i	−0.466291	−	0.207606i
$225$	1.51085	+	1.67797i	0.100723	+	0.111865i
$226$	−26.7908	−	8.70484i	−1.78209	−	0.579038i
$227$	14.1378	−	1.48594i	0.938356	−	0.0986252i	0.377012	−	0.926208i	$-0.376951\pi$
$227$	14.1378	−	1.48594i	0.938356	−	0.0986252i	0.561343	+	0.827583i	$0.310285\pi$
$228$	7.03250	+	15.7952i	0.465738	+	1.04607i
$229$	8.86373	−	2.88000i	0.585732	−	0.190316i	−0.00113477	−	0.999999i	$-0.500361\pi$
$229$	8.86373	−	2.88000i	0.585732	−	0.190316i	0.586867	+	0.809683i	$0.300361\pi$
$230$	11.0744	−	19.1814i	0.730225	−	1.26479i
$231$	3.58734	+	0.471835i	0.236030	+	0.0310445i
$232$	−10.0787	+	5.81896i	−0.661701	+	0.382033i
$233$	1.98272	+	6.10220i	0.129893	+	0.399768i	0.994761	−	0.102231i	$-0.0325980\pi$
$233$	1.98272	+	6.10220i	0.129893	+	0.399768i	−0.864868	+	0.501999i	$0.832598\pi$
$234$	−6.09982	+	5.16947i	−0.398758	+	0.337939i
$235$	−12.4462	+	9.04272i	−0.811903	+	0.589882i
$236$	2.55397	+	12.0155i	0.166249	+	0.782142i
$237$	7.15134	−	1.52006i	0.464529	−	0.0987387i
$238$	−0.529838	−	5.04107i	−0.0343443	−	0.326764i
$239$	12.1151	−	16.6749i	0.783658	−	1.07861i	−0.211211	−	0.977440i	$-0.567741\pi$
$239$	12.1151	−	16.6749i	0.783658	−	1.07861i	0.994869	−	0.101172i	$-0.0322593\pi$
$240$	0.455172	−	2.14142i	0.0293813	−	0.138228i
$241$	1.49038	+	0.860469i	0.0960035	+	0.0554277i	0.547233	−	0.836980i	$-0.315681\pi$
$241$	1.49038	+	0.860469i	0.0960035	+	0.0554277i	−0.451230	+	0.892408i	$0.649014\pi$
$242$	13.2908	+	20.4550i	0.854363	+	1.31490i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.79420	−	1.99266i	0.114862	−	0.127567i
$245$	9.56794	+	1.00563i	0.611273	+	0.0642474i
$246$	−11.5295	+	8.37665i	−0.735093	+	0.534076i
$247$	18.8153	−	10.1228i	1.19719	−	0.644096i
$248$	−1.12677	+	3.46784i	−0.0715500	+	0.220208i
$249$	−2.86736	+	6.44019i	−0.181711	+	0.408130i
$250$	2.78594	−	26.5064i	0.176198	−	1.67641i
$251$	7.08565	+	1.50610i	0.447242	+	0.0950642i	0.426026	−	0.904711i	$-0.359913\pi$
$251$	7.08565	+	1.50610i	0.447242	+	0.0950642i	0.0212155	+	0.999775i	$0.493246\pi$
$252$		−	3.18313i		−	0.200518i
$253$	−18.4806	+	7.65756i	−1.16187	+	0.481427i
$254$	−25.3420	−	14.6312i	−1.59010	−	0.918044i
$255$	3.29966	−	1.07212i	0.206632	−	0.0671390i
$256$	−5.97184	+	2.65884i	−0.373240	+	0.166177i
$257$	−0.231639	−	0.103133i	−0.0144493	−	0.00643323i	0.399499	−	0.916734i	$-0.369184\pi$
$257$	−0.231639	−	0.103133i	−0.0144493	−	0.00643323i	−0.413949	+	0.910300i	$0.635851\pi$
$258$	2.85570	+	13.4350i	0.177788	+	0.836426i
$259$	3.45744	−	10.6409i	0.214835	−	0.661193i
$260$	17.2628	+	2.33999i	1.07059	+	0.145120i
$261$	4.62599	+	3.36098i	0.286341	+	0.208039i
$262$	12.6826	+	11.4195i	0.783533	+	0.705496i
$263$	6.65968	+	11.5349i	0.410654	+	0.711273i	0.994961	−	0.100259i	$-0.0319672\pi$
$263$	6.65968	+	11.5349i	0.410654	+	0.711273i	−0.584308	+	0.811532i	$0.698634\pi$
$264$	5.13245	−	4.38462i	0.315881	−	0.269854i
$265$		−	4.02017i		−	0.246957i
$266$	−2.98062	+	14.0227i	−0.182753	+	0.859787i
$267$	3.05925	+	6.87119i	0.187223	+	0.420510i
$268$	2.99033	+	4.11583i	0.182663	+	0.251415i
$269$	−3.62708	−	4.02828i	−0.221147	−	0.245609i	0.622354	−	0.782736i	$-0.286176\pi$
$269$	−3.62708	−	4.02828i	−0.221147	−	0.245609i	−0.843501	+	0.537127i	$0.819510\pi$
$270$	3.59194	−	0.763490i	0.218598	−	0.0464645i
$271$	3.41067	−	7.66050i	0.207184	−	0.465342i	−0.779827	−	0.625995i	$-0.784693\pi$
$271$	3.41067	−	7.66050i	0.207184	−	0.465342i	0.987011	+	0.160653i	$0.0513598\pi$
$272$	2.24098	+	1.62817i	0.135880	+	0.0987223i
$273$	−3.92246	+	0.293593i	−0.237398	+	0.0177691i
$274$	15.7821			0.953430
$275$	−5.15422	+	5.43275i	−0.310811	+	0.327607i
$276$	8.79935	+	15.2409i	0.529658	+	0.917395i
$277$	−13.0984	−	2.78416i	−0.787009	−	0.167284i	−0.203159	−	0.979146i	$-0.565121\pi$
$277$	−13.0984	−	2.78416i	−0.787009	−	0.167284i	−0.583850	+	0.811862i	$0.698454\pi$
$278$	12.5547	−	17.2800i	0.752979	−	1.03639i
$279$	1.78172	−	0.187266i	0.106669	−	0.0112113i
$280$	−2.73238	+	2.46025i	−0.163291	+	0.147028i
$281$	17.7685	+	5.77332i	1.05998	+	0.344407i	0.786576	−	0.617493i	$-0.211852\pi$
$281$	17.7685	+	5.77332i	1.05998	+	0.344407i	0.273400	+	0.961900i	$0.411852\pi$
$282$	−2.15358	−	20.4899i	−0.128244	−	1.22016i
$283$	−1.37221	+	13.0557i	−0.0815693	+	0.776080i	0.874911	+	0.484284i	$0.160920\pi$
$283$	−1.37221	+	13.0557i	−0.0815693	+	0.776080i	−0.956480	+	0.291797i	$0.905747\pi$
$284$	−27.4863	−	24.7487i	−1.63101	−	1.46857i
$285$	−9.81254			−0.581244
$286$	−18.6819	−	18.8210i	−1.10469	−	1.11291i
$287$	−7.01080			−0.413834
$288$	5.20384	+	4.68556i	0.306639	+	0.276099i
$289$	1.31812	−	12.5411i	0.0775367	−	0.737712i
$290$	−2.19485	−	20.8826i	−0.128886	−	1.22627i
$291$	12.7633	+	4.14706i	0.748199	+	0.243105i
$292$	22.8058	−	20.5345i	1.33461	−	1.20169i
$293$	−9.05665	+	0.951893i	−0.529095	+	0.0556102i	−0.365310	−	0.930886i	$-0.619037\pi$
$293$	−9.05665	+	0.951893i	−0.529095	+	0.0556102i	−0.163785	+	0.986496i	$0.552370\pi$
$294$	−7.57301	+	10.4234i	−0.441667	+	0.607903i
$295$	−6.81910	−	1.44944i	−0.397023	−	0.0843899i
$296$	−10.4369	−	18.0772i	−0.606630	−	1.05071i
$297$	−2.99371	−	1.42748i	−0.173713	−	0.0828306i
$298$	47.1248			2.72987
$299$	17.9693	−	12.2489i	1.03919	−	0.708370i
$300$	5.32994	+	3.87243i	0.307724	+	0.223575i
$301$	−2.74829	+	6.17275i	−0.158409	+	0.355792i
$302$	−23.1684	+	4.92459i	−1.33319	+	0.283378i
$303$	3.93153	+	4.36641i	0.225861	+	0.250844i
$304$	−4.60488	−	6.33808i	−0.264108	−	0.363514i
$305$	0.618954	+	1.39019i	0.0354412	+	0.0796022i
$306$	−0.966022	+	4.54478i	−0.0552238	+	0.259808i
$307$			31.9368i			1.82273i	0.411597	+	0.911366i	$0.364971\pi$
$307$			31.9368i			1.82273i	−0.411597	+	0.911366i	$0.635029\pi$
$308$	10.5246	−	0.829601i	0.599695	−	0.0472709i
$309$	8.60137	+	14.8980i	0.489315	+	0.847518i
$310$	−4.88903	−	4.40210i	−0.277678	−	0.250022i
$311$	5.61946	+	4.08278i	0.318650	+	0.231513i	0.735599	−	0.677417i	$-0.236901\pi$
$311$	5.61946	+	4.08278i	0.318650	+	0.231513i	−0.416949	+	0.908930i	$0.636901\pi$
$312$	−4.48959	+	5.80477i	−0.254173	+	0.328631i
$313$	8.39276	−	25.8303i	0.474387	−	1.46001i	−0.372396	−	0.928074i	$-0.621464\pi$
$313$	8.39276	−	25.8303i	0.474387	−	1.46001i	0.846783	−	0.531939i	$-0.178536\pi$
$314$	2.71410	+	12.7688i	0.153165	+	0.720587i
$315$	1.65033	+	0.734773i	0.0929853	+	0.0413997i
$316$	19.4880	−	8.67661i	1.09629	−	0.488098i
$317$	−30.2194	+	9.81889i	−1.69729	+	0.551484i	−0.988138	−	0.153569i	$-0.950923\pi$
$317$	−30.2194	+	9.81889i	−1.69729	+	0.551484i	−0.709155	+	0.705053i	$0.750923\pi$
$318$	4.66252	+	2.69191i	0.261461	+	0.150955i
$319$	−9.90698	+	16.1712i	−0.554685	+	0.905412i
$320$		−	21.3358i		−	1.19271i
$321$	−14.6541	−	3.11483i	−0.817915	−	0.173853i
$322$	−1.52527	+	14.5120i	−0.0849999	+	0.808720i
$323$	5.04985	−	11.3422i	0.280981	−	0.631094i
$324$	−0.901647	+	2.77498i	−0.0500915	+	0.154166i
$325$	4.28026	−	6.92508i	0.237426	−	0.384134i
$326$	28.1666	−	20.4642i	1.56000	−	1.13341i
$327$	−1.67189	−	0.175723i	−0.0924557	−	0.00971748i
$328$	−8.75198	+	9.72006i	−0.483247	+	0.536700i
$329$	5.06771	−	8.77753i	0.279392	−	0.483921i
$330$	3.46052	+	11.6773i	0.190496	+	0.642813i
$331$	−24.5150	−	14.1537i	−1.34746	−	0.777959i	−0.359574	−	0.933117i	$-0.617078\pi$
$331$	−24.5150	−	14.1537i	−1.34746	−	0.777959i	−0.987890	+	0.155158i	$0.950411\pi$
$332$	−4.27663	+	20.1199i	−0.234710	+	1.10423i
$333$	−6.02823	+	8.29715i	−0.330345	+	0.454681i
$334$	2.13784	+	20.3402i	0.116977	+	1.11297i
$335$	−2.82416	+	0.600294i	−0.154300	+	0.0327976i
$336$	0.299873	+	1.41079i	0.0163594	+	0.0769650i
$337$	10.9719	−	7.97159i	0.597680	−	0.434240i	−0.247375	−	0.968920i	$-0.579568\pi$
$337$	10.9719	−	7.97159i	0.597680	−	0.434240i	0.845055	+	0.534680i	$0.179568\pi$
$338$	24.0570	+	15.8861i	1.30853	+	0.864090i
$339$	3.92533	+	12.0809i	0.213195	+	0.656145i
$340$	8.76692	−	5.06158i	0.475453	−	0.274503i
$341$	1.08353	+	5.84221i	0.0586764	+	0.316374i
$342$	6.57048	−	11.3804i	0.355291	−	0.615382i
$343$	−13.2908	+	4.31844i	−0.717635	+	0.233174i
$344$	5.12731	+	11.5161i	0.276446	+	0.620909i
$345$	−9.93299	+	1.04400i	−0.534774	+	0.0562070i
$346$	21.1655	+	6.87709i	1.13786	+	0.369715i
$347$	2.64001	+	2.93203i	0.141723	+	0.157400i	0.809828	−	0.586668i	$-0.199561\pi$
$347$	2.64001	+	2.93203i	0.141723	+	0.157400i	−0.668104	+	0.744068i	$0.732894\pi$
$348$	15.2416	+	6.78600i	0.817036	+	0.363768i
$349$	−29.2473	−	3.07402i	−1.56557	−	0.164548i	−0.718311	−	0.695723i	$-0.755084\pi$
$349$	−29.2473	−	3.07402i	−1.56557	−	0.164548i	−0.847263	+	0.531174i	$0.821751\pi$
$350$	1.68802	+	5.19520i	0.0902287	+	0.277695i
$351$	3.50268	+	0.855121i	0.186959	+	0.0456430i
$352$	−14.1359	+	18.4270i	−0.753448	+	0.982162i
$353$	19.4578	−	11.2339i	1.03563	−	0.597923i	0.117039	−	0.993127i	$-0.462660\pi$
$353$	19.4578	−	11.2339i	1.03563	−	0.597923i	0.918593	+	0.395205i	$0.129326\pi$
$354$	6.24711	−	6.93812i	0.332030	−	0.368757i
$355$	19.1760	−	8.53769i	1.01776	−	0.453134i
$356$	12.8995	+	17.7547i	0.683675	+	0.940997i
$357$	−1.69862	+	1.52945i	−0.0899007	+	0.0809469i
$358$	−6.88495	+	6.19924i	−0.363881	+	0.327640i
$359$	−13.0983	−	18.0283i	−0.691302	−	0.951496i	−1.00000		0.000335512i	$-0.999893\pi$
$359$	−13.0983	−	18.0283i	−0.691302	−	0.951496i	0.308698	−	0.951160i	$-0.400107\pi$
$360$	3.07892	−	1.37082i	0.162273	−	0.0722486i
$361$	−10.7826	+	11.9753i	−0.567504	+	0.630277i
$362$	−8.48235	+	4.89729i	−0.445823	+	0.257396i
$363$	3.93953	−	10.2703i	0.206772	−	0.539054i
$364$	−11.0167	+	3.21746i	−0.577433	+	0.168641i
$365$	5.38195	+	16.5639i	0.281704	+	0.866997i
$366$	−2.02677	−	0.213022i	−0.105941	−	0.0111349i
$367$	4.45625	+	1.98405i	0.232614	+	0.103567i	0.519734	−	0.854328i	$-0.326031\pi$
$367$	4.45625	+	1.98405i	0.232614	+	0.103567i	−0.287120	+	0.957895i	$0.592698\pi$
$368$	−5.33575	−	5.92595i	−0.278145	−	0.308911i
$369$	6.11186	+	1.98586i	0.318171	+	0.103380i
$370$	37.4550	−	3.93668i	1.94719	−	0.204658i
$371$	1.07726	+	2.41955i	0.0559283	+	0.125617i
$372$	4.97147	−	1.61533i	0.257759	−	0.0837509i
$373$	5.35412	−	9.27360i	0.277226	−	0.480169i	−0.693469	−	0.720487i	$-0.743918\pi$
$373$	5.35412	−	9.27360i	0.277226	−	0.480169i	0.970694	+	0.240318i	$0.0772517\pi$
$374$	−15.2785	−	2.00955i	−0.790031	−	0.103911i
$375$	−10.4084	+	6.00927i	−0.537486	+	0.310318i
$376$	−5.84322	−	17.9836i	−0.301341	−	0.927432i
$377$	6.95637	−	19.4076i	0.358271	−	0.999544i
$378$	−1.95724	+	1.42201i	−0.100669	+	0.0731406i
$379$	−5.16187	−	24.2847i	−0.265148	−	1.24742i	−0.886071	−	0.463550i	$-0.846575\pi$
$379$	−5.16187	−	24.2847i	−0.265148	−	1.24742i	0.620923	−	0.783871i	$-0.286758\pi$
$380$	−28.0053	+	5.95270i	−1.43664	+	0.305367i
$381$	1.37930	+	13.1232i	0.0706639	+	0.672322i
$382$	0.697770	−	0.960398i	0.0357010	−	0.0491383i
$383$	7.45453	−	35.0708i	0.380909	−	1.79204i	−0.201878	−	0.979411i	$-0.564705\pi$
$383$	7.45453	−	35.0708i	0.380909	−	1.79204i	0.582787	−	0.812625i	$-0.301962\pi$
$384$	12.6162	+	7.28399i	0.643820	+	0.371710i
$385$	−1.99931	+	5.64809i	−0.101894	+	0.287853i
$386$	19.8729	−	34.4209i	1.01150	−	1.75198i
$387$	4.14438	−	4.60280i	0.210670	−	0.233973i
$388$	38.9427	+	4.09304i	1.97702	+	0.207793i
$389$	16.0778	−	11.6812i	0.815175	−	0.592259i	−0.100151	−	0.994972i	$-0.531933\pi$
$389$	16.0778	−	11.6812i	0.815175	−	0.592259i	0.915326	+	0.402713i	$0.131933\pi$
$390$	−6.27309	−	11.6599i	−0.317650	−	0.590420i
$391$	3.90510	−	12.0187i	0.197489	−	0.607809i
$392$	−4.80958	+	10.8025i	−0.242920	+	0.545608i
$393$	0.804422	−	7.65357i	0.0405777	−	0.386071i
$394$	26.4784	+	5.62816i	1.33396	+	0.283542i
$395$			12.1066i			0.609149i
$396$	−9.41011	−	2.25795i	−0.472876	−	0.113466i
$397$	−27.0561	−	15.6208i	−1.35791	−	0.783988i	−0.368565	−	0.929602i	$-0.620151\pi$
$397$	−27.0561	−	15.6208i	−1.35791	−	0.783988i	−0.989341	+	0.145614i	$0.953484\pi$
$398$	36.1639	−	11.7504i	1.81273	−	0.588992i
$399$	5.90572	−	2.62939i	0.295656	−	0.131634i
$400$	−2.72709	−	1.21418i	−0.136354	−	0.0607088i
$401$	2.88718	+	13.5831i	0.144179	+	0.678307i	0.989557	+	0.144140i	$0.0460415\pi$
$401$	2.88718	+	13.5831i	0.144179	+	0.678307i	−0.845379	+	0.534168i	$0.820625\pi$
$402$	1.19485	−	3.67737i	0.0595937	−	0.183411i
$403$	−2.44905	−	5.97719i	−0.121996	−	0.297745i
$404$	13.8696	+	10.0768i	0.690036	+	0.501341i
$405$	−1.23059	−	1.10803i	−0.0611484	−	0.0550583i
$406$	6.91675	+	11.9802i	0.343273	+	0.594566i
$407$	−29.0045	−	17.7691i	−1.43770	−	0.880783i
$408$			4.26434i			0.211116i
$409$	−3.74522	+	17.6199i	−0.185189	+	0.871246i	0.783194	+	0.621778i	$0.213589\pi$
$409$	−3.74522	+	17.6199i	−0.185189	+	0.871246i	−0.968383	+	0.249468i	$0.919744\pi$
$410$	−9.59852	−	21.5586i	−0.474037	−	1.06471i
$411$	−4.18309	−	5.75753i	−0.206337	−	0.283998i
$412$	33.5863	+	37.3014i	1.65468	+	1.83771i
$413$	4.49250	−	0.954910i	0.221061	−	0.0469881i
$414$	5.44032	−	12.2192i	0.267377	−	0.600539i
$415$	−9.44420	−	6.86161i	−0.463598	−	0.336823i
$416$	10.9566	−	22.7464i	0.537193	−	1.11524i
$417$	−9.63167			−0.471665
$418$	39.3402	+	18.7584i	1.92419	+	0.917504i
$419$	13.1898	+	22.8455i	0.644366	+	1.11607i	0.984448	+	0.175678i	$0.0562119\pi$
$419$	13.1898	+	22.8455i	0.644366	+	1.11607i	−0.340082	+	0.940396i	$0.610455\pi$
$420$	5.15582	+	1.09590i	0.251578	+	0.0534746i
$421$	18.4931	−	25.4535i	0.901297	−	1.24053i	−0.0687549	−	0.997634i	$-0.521903\pi$
$421$	18.4931	−	25.4535i	0.901297	−	1.24053i	0.970052	−	0.242896i	$-0.0780974\pi$
$422$	−14.8578	+	1.56162i	−0.723267	+	0.0760184i
$423$	−6.90422	+	6.21659i	−0.335695	+	0.302261i
$424$	4.69937	+	1.52692i	0.228222	+	0.0741537i
$425$	−0.494502	−	4.70488i	−0.0239869	−	0.228220i
$426$	−2.93838	+	27.9568i	−0.142365	+	1.35451i
$427$	−0.745040	−	0.670837i	−0.0360550	−	0.0324641i
$428$	−43.7130			−2.11295
$429$	−1.91446	+	11.8040i	−0.0924310	+	0.569903i
$430$	−22.7443			−1.09683
$431$	−12.3546	−	11.1241i	−0.595099	−	0.535829i	0.315604	−	0.948891i	$-0.397793\pi$
$431$	−12.3546	−	11.1241i	−0.595099	−	0.535829i	−0.910703	+	0.413061i	$0.864459\pi$
$432$	0.138195	−	1.31484i	0.00664891	−	0.0632602i
$433$	2.66717	+	25.3764i	0.128176	+	1.21951i	0.849754	+	0.527180i	$0.176751\pi$
$433$	2.66717	+	25.3764i	0.128176	+	1.21951i	−0.721578	+	0.692334i	$0.756583\pi$
$434$	4.12208	+	1.33935i	0.197866	+	0.0642906i
$435$	−7.03654	+	6.33573i	−0.337376	+	0.303775i
$436$	−4.87822	+	0.512722i	−0.233624	+	0.0245549i
$437$	−21.0081	+	28.9152i	−1.00495	+	1.38320i
$438$	−22.8143	−	4.84934i	−1.09011	−	0.231710i
$439$	9.15931	+	15.8644i	0.437150	+	0.757166i	0.997468	−	0.0711114i	$-0.0226546\pi$
$439$	9.15931	+	15.8644i	0.437150	+	0.757166i	−0.560318	+	0.828277i	$0.689321\pi$
$440$	5.33488	+	9.82276i	0.254331	+	0.468282i
$441$	5.80985			0.276660
$442$	16.7058	−	1.25041i	0.794613	−	0.0594761i
$443$	7.75299	+	5.63288i	0.368356	+	0.267626i	0.756529	−	0.653960i	$-0.226894\pi$
$443$	7.75299	+	5.63288i	0.368356	+	0.267626i	−0.388173	+	0.921586i	$0.626894\pi$
$444$	−12.1714	+	27.3373i	−0.577627	+	1.29737i
$445$	−12.1827	+	2.58952i	−0.577518	+	0.122755i
$446$	10.2434	+	11.3764i	0.485039	+	0.538690i
$447$	−12.4906	−	17.1918i	−0.590785	−	0.813146i
$448$	5.71720	+	12.8410i	0.270112	+	0.606682i
$449$	3.25151	−	15.2972i	0.153448	−	0.721917i	−0.832386	−	0.554196i	$-0.813026\pi$
$449$	3.25151	−	15.2972i	0.153448	−	0.721917i	0.985834	−	0.167721i	$-0.0536409\pi$
$450$		−	5.00721i		−	0.236042i
$451$	−4.97310	+	20.7256i	−0.234174	+	0.975931i
$452$	18.5318	+	32.0980i	0.871663	+	1.50976i
$453$	7.93742	+	7.14689i	0.372933	+	0.335790i
$454$	−25.5040	−	18.5298i	−1.19696	−	0.869645i
$455$	0.874903	−	6.45443i	0.0410161	−	0.302588i
$456$	3.72694	−	11.4704i	0.174530	−	0.537149i
$457$	2.53180	+	11.9112i	0.118432	+	0.557181i	0.996852	+	0.0792899i	$0.0252653\pi$
$457$	2.53180	+	11.9112i	0.118432	+	0.557181i	−0.878419	+	0.477891i	$0.841401\pi$
$458$	−18.8810	−	8.40637i	−0.882252	−	0.392804i
$459$	1.91405	−	0.852190i	0.0893402	−	0.0397768i
$460$	−27.7157	+	9.00538i	−1.29225	+	0.419878i
$461$	−28.0054	−	16.1689i	−1.30434	−	0.753062i	−0.323196	−	0.946332i	$-0.604757\pi$
$461$	−28.0054	−	16.1689i	−1.30434	−	0.753062i	−0.981146	+	0.193270i	$0.938091\pi$
$462$	−5.21181	−	6.10073i	−0.242475	−	0.283832i
$463$			26.8231i			1.24658i	0.781993	+	0.623288i	$0.214203\pi$
$463$			26.8231i			1.24658i	−0.781993	+	0.623288i	$0.785797\pi$
$464$	−7.39450	−	1.57175i	−0.343281	−	0.0729667i
$465$	−0.310098	+	2.95038i	−0.0143804	+	0.136821i
$466$	5.78733	−	12.9986i	0.268093	−	0.602147i
$467$	−6.16705	+	18.9802i	−0.285377	+	0.878300i	0.700908	+	0.713251i	$0.252778\pi$
$467$	−6.16705	+	18.9802i	−0.285377	+	0.878300i	−0.986285	+	0.165049i	$0.947222\pi$
$468$	10.5155	+	0.315664i	0.486079	+	0.0145916i
$469$	1.53888	−	1.11806i	0.0710588	−	0.0516272i
$470$	33.9297	+	3.56615i	1.56506	+	0.164494i
$471$	3.93888	−	4.37457i	0.181494	−	0.201570i
$472$	4.28432	−	7.42066i	0.197202	−	0.341563i
$473$	16.2987	+	12.5032i	0.749413	+	0.574899i
$474$	−14.0410	−	8.10658i	−0.644925	−	0.372348i
$475$	−2.78184	+	13.0875i	−0.127639	+	0.600496i
$476$	−3.92009	+	5.39554i	−0.179677	+	0.247304i
$477$	−0.253769	−	2.41446i	−0.0116193	−	0.110550i
$478$	−44.7091	+	9.50322i	−2.04495	+	0.434667i
$479$	−1.47723	−	6.94983i	−0.0674964	−	0.317546i	0.931427	−	0.363927i	$-0.118564\pi$
$479$	−1.47723	−	6.94983i	−0.0674964	−	0.317546i	−0.998924	+	0.0463815i	$0.985231\pi$
$480$	−9.38096	+	6.81567i	−0.428180	+	0.311091i
$481$	34.8094	+	12.4769i	1.58717	+	0.568898i
$482$	−1.17932	−	3.62958i	−0.0537167	−	0.165323i
$483$	5.69846	−	3.29001i	0.259289	−	0.149700i
$484$	5.01311	−	31.7018i	0.227869	−	1.44099i
$485$	−11.1113	+	19.2454i	−0.504540	+	0.873889i
$486$	2.10907	−	0.685279i	0.0956694	−	0.0310849i
$487$	1.65585	+	3.71911i	0.0750339	+	0.168529i	0.947168	−	0.320738i	$-0.103931\pi$
$487$	1.65585	+	3.71911i	0.0750339	+	0.168529i	−0.872134	+	0.489267i	$0.837264\pi$
$488$	−1.86015	+	0.195510i	−0.0842051	+	0.00885032i
$489$	−14.9313	−	4.85148i	−0.675218	−	0.219392i
$490$	−14.2758	−	15.8549i	−0.644914	−	0.716250i
$491$	24.2016	+	10.7752i	1.09220	+	0.486280i	0.872165	−	0.489212i	$-0.162715\pi$
$491$	24.2016	+	10.7752i	1.09220	+	0.486280i	0.220037	+	0.975491i	$0.429382\pi$
$492$	18.6481	+	1.96000i	0.840723	+	0.0883635i
$493$	−3.70214	−	11.3940i	−0.166736	−	0.513160i
$494$	−46.0286	−	11.2371i	−2.07092	−	0.505581i
$495$	3.34282	−	4.35756i	0.150249	−	0.195858i
$496$	−2.05122	+	1.18428i	−0.0921027	+	0.0531755i
$497$	−9.25336	+	10.2769i	−0.415070	+	0.460982i
$498$	14.2818	−	6.35868i	0.639984	−	0.284939i
$499$	19.5351	+	26.8878i	0.874512	+	1.20366i	0.977911	+	0.209023i	$0.0670283\pi$
$499$	19.5351	+	26.8878i	0.874512	+	1.20366i	−0.103398	+	0.994640i	$0.532972\pi$
$500$	−26.0603	+	23.4648i	−1.16545	+	1.04938i
$501$	6.85376	−	6.17115i	0.306203	−	0.275707i
$502$	−9.44232	−	12.9962i	−0.421431	−	0.580051i
$503$	17.6453	−	7.85621i	0.786767	−	0.350291i	0.0262883	−	0.999654i	$-0.491631\pi$
$503$	17.6453	−	7.85621i	0.786767	−	0.350291i	0.760478	+	0.649363i	$0.224965\pi$
$504$	−1.48573	+	1.65007i	−0.0661797	+	0.0735000i
$505$	−8.42598	+	4.86474i	−0.374951	+	0.216478i
$506$	41.8189	+	14.8031i	1.85908	+	0.658078i
$507$	−0.580906	−	12.9870i	−0.0257989	−	0.576774i
$508$	11.8977	+	36.6172i	0.527874	+	1.62463i
$509$	24.4639	+	2.57126i	1.08434	+	0.113969i	0.629802	−	0.776756i	$-0.283136\pi$
$509$	24.4639	+	2.57126i	1.08434	+	0.113969i	0.454542	+	0.890725i	$0.349803\pi$
$510$	−7.02874	−	3.12940i	−0.311238	−	0.138572i
$511$	−7.67767	−	8.52692i	−0.339640	−	0.377209i
$512$	−13.9230	−	4.52385i	−0.615314	−	0.199928i
$513$	−5.89327	+	0.619408i	−0.260194	+	0.0273475i
$514$	0.228708	+	0.513686i	0.0100879	+	0.0226577i
$515$	−27.0921	+	8.80277i	−1.19382	+	0.387896i
$516$	9.03592	−	15.6507i	0.397784	−	0.688982i
$517$	−22.3537	−	21.2077i	−0.983116	−	0.932714i
$518$	−21.4876	+	12.4059i	−0.944110	+	0.545082i
$519$	−3.10113	−	9.54429i	−0.136124	−	0.418948i
$520$	−7.85649	−	9.27043i	−0.344530	−	0.406535i
$521$	−8.89769	+	6.46455i	−0.389815	+	0.283217i	−0.765380	−	0.643579i	$-0.777449\pi$
$521$	−8.89769	+	6.46455i	−0.389815	+	0.283217i	0.375565	+	0.926796i	$0.377449\pi$
$522$	−2.63640	−	12.4033i	−0.115392	−	0.542876i
$523$	15.8602	−	3.37120i	0.693520	−	0.147412i	0.152351	−	0.988326i	$-0.451316\pi$
$523$	15.8602	−	3.37120i	0.693520	−	0.147412i	0.541168	+	0.840914i	$0.317982\pi$
$524$	−2.34714	−	22.3315i	−0.102535	−	0.975556i
$525$	1.44787	−	1.99282i	0.0631903	−	0.0869739i
$526$	6.14112	−	28.8917i	0.267765	−	1.25974i
$527$	−3.25071	−	1.87680i	−0.141603	−	0.0817547i
$528$	4.38336	+	0.114245i	0.190761	+	0.00497188i
$529$	−6.68958	+	11.5867i	−0.290851	+	0.503769i
$530$	−5.96540	+	6.62525i	−0.259121	+	0.287783i
$531$	−4.18695	−	0.440066i	−0.181698	−	0.0190972i
$532$	15.2600	−	11.0870i	0.661604	−	0.480684i
$533$	0.695245	−	23.1602i	0.0301144	−	1.00318i
$534$	5.15429	−	15.8633i	0.223048	−	0.686471i
$535$	10.0904	−	22.6634i	0.436246	−	0.979825i
$536$	0.370945	−	3.52930i	0.0160224	−	0.152443i
$537$	4.08645	+	0.868603i	0.176344	+	0.0374830i
$538$			12.0208i			0.518251i
$539$	1.51419	+	19.2095i	0.0652207	+	0.827412i
$540$	−4.18431	−	2.41581i	−0.180064	−	0.103960i
$541$	−30.4489	+	9.89343i	−1.30910	+	0.425352i	−0.878738	−	0.477305i	$-0.841614\pi$
$541$	−30.4489	+	9.89343i	−1.30910	+	0.425352i	−0.430361	+	0.902657i	$0.641614\pi$
$542$	−16.9880	+	7.56354i	−0.729697	+	0.324882i
$543$	4.03488	+	1.79645i	0.173153	+	0.0770928i
$544$	−3.05037	−	14.3509i	−0.130784	−	0.615288i
$545$	0.860230	−	2.64752i	0.0368482	−	0.113407i
$546$	6.89989	+	5.33658i	0.295288	+	0.228385i
$547$	25.3786	+	18.4386i	1.08511	+	0.788378i	0.978567	−	0.205930i	$-0.0660221\pi$
$547$	25.3786	+	18.4386i	1.08511	+	0.788378i	0.106542	+	0.994308i	$0.466022\pi$
$548$	−15.4314	−	13.8945i	−0.659198	−	0.593545i
$549$	0.459490	+	0.795859i	0.0196105	+	0.0339665i
$550$	16.5557	−	1.30500i	0.705937	−	0.0556454i
$551$			33.8835i			1.44349i
$552$	2.55231	−	12.0077i	0.108634	−	0.511081i
$553$	−3.24412	−	7.28641i	−0.137954	−	0.309850i
$554$	17.4550	+	24.0247i	0.741590	+	1.02071i
$555$	−11.3637	−	12.6207i	−0.482364	−	0.535720i
$556$	−27.4891	+	5.84298i	−1.16580	+	0.247798i
$557$	9.15462	−	20.5616i	0.387894	−	0.871224i	−0.609052	−	0.793130i	$-0.708450\pi$
$557$	9.15462	−	20.5616i	0.387894	−	0.871224i	0.996946	−	0.0780935i	$-0.0248833\pi$
$558$	−3.21416	−	2.33522i	−0.136066	−	0.0988579i
$559$	−20.1192	−	9.69113i	−0.850952	−	0.409891i
$560$	−2.38835			−0.100926
$561$	3.31650	+	6.10645i	0.140023	+	0.257815i
$562$	−20.7156	−	35.8805i	−0.873836	−	1.51353i
$563$	29.8524	+	6.34533i	1.25813	+	0.267424i	0.788277	−	0.615321i	$-0.210974\pi$
$563$	29.8524	+	6.34533i	1.25813	+	0.267424i	0.469853	+	0.882745i	$0.344307\pi$
$564$	−15.9336	+	21.9307i	−0.670926	+	0.923450i
$565$	−20.9193	+	2.19871i	−0.880081	+	0.0925003i
$566$	21.6344	−	19.4797i	0.909360	−	0.818791i
$567$	1.03754	+	0.337119i	0.0435728	+	0.0141577i
$568$	2.69681	+	25.6585i	0.113156	+	1.07661i
$569$	4.23874	−	40.3289i	0.177697	−	1.69067i	−0.435058	−	0.900402i	$-0.643272\pi$
$569$	4.23874	−	40.3289i	0.177697	−	1.69067i	0.612755	−	0.790273i	$-0.290061\pi$
$570$	16.1711	+	14.5605i	0.677333	+	0.609873i
$571$	−33.5411			−1.40365			−0.701826	−	0.712348i	$-0.747632\pi$
$571$	−33.5411			−1.40365			−0.701826	+	0.712348i	$0.747632\pi$
$572$	1.69689	+	34.8504i	0.0709507	+	1.45717i
$573$	−0.535314			−0.0223631
$574$	11.5538	+	10.4031i	0.482247	+	0.434217i
$575$	−1.42355	+	13.5441i	−0.0593660	+	0.564830i
$576$	−1.34680	−	12.8140i	−0.0561168	−	0.533915i
$577$	−19.9905	−	6.49531i	−0.832216	−	0.270403i	−0.138238	−	0.990399i	$-0.544144\pi$
$577$	−19.9905	−	6.49531i	−0.832216	−	0.270403i	−0.693979	+	0.719996i	$0.744144\pi$
$578$	−20.7816	+	18.7119i	−0.864402	+	0.778311i
$579$	−17.8246	+	1.87345i	−0.740767	+	0.0778577i
$580$	−16.2390	+	22.3510i	−0.674287	+	0.928076i
$581$	7.52269	+	1.59900i	0.312094	+	0.0663376i
$582$	−14.8803	−	25.7735i	−0.616809	−	1.06835i
$583$	7.91694	−	1.46832i	0.327886	−	0.0608117i
$584$	−21.4066			−0.885810
$585$	−2.59099	+	5.37900i	−0.107124	+	0.222394i
$586$	16.3379	+	11.8702i	0.674912	+	0.490352i
$587$	8.53730	−	19.1751i	0.352372	−	0.791441i	−0.647204	−	0.762317i	$-0.724062\pi$
$587$	8.53730	−	19.1751i	0.352372	−	0.791441i	0.999576	−	0.0291235i	$-0.00927162\pi$
$588$	16.5815	−	3.52450i	0.683809	−	0.145348i
$589$	7.10359	+	7.88933i	0.292698	+	0.325074i
$590$	9.08712	+	12.5073i	0.374111	+	0.514919i
$591$	−4.96496	−	11.1515i	−0.204231	−	0.458711i
$592$	2.81909	−	13.2628i	0.115864	−	0.545096i
$593$			9.87010i			0.405316i	0.979250	+	0.202658i	$0.0649580\pi$
$593$			9.87010i			0.405316i	−0.979250	+	0.202658i	$0.935042\pi$
$594$	2.81546	+	6.79477i	0.115520	+	0.278793i
$595$	−1.89249	−	3.27788i	−0.0775844	−	0.134380i
$596$	−46.0778	−	41.4887i	−1.88742	−	1.69944i
$597$	−13.8721	−	10.0786i	−0.567746	−	0.412491i
$598$	−47.7892	−	6.47786i	−1.95424	−	0.264899i
$599$	12.8189	−	39.4524i	0.523765	−	1.61198i	−0.242981	−	0.970031i	$-0.578125\pi$
$599$	12.8189	−	39.4524i	0.523765	−	1.61198i	0.766746	−	0.641951i	$-0.221875\pi$
$600$	−0.955472	−	4.49514i	−0.0390070	−	0.183513i
$601$	−8.60693	−	3.83205i	−0.351084	−	0.156313i	0.223615	−	0.974678i	$-0.428214\pi$
$601$	−8.60693	−	3.83205i	−0.351084	−	0.156313i	−0.574699	+	0.818365i	$0.694881\pi$
$602$	13.6888	−	6.09462i	0.557912	−	0.248398i
$603$	−1.65826	+	0.538801i	−0.0675295	+	0.0219417i
$604$	26.9892	+	15.5823i	1.09818	+	0.634033i
$605$	15.2789	+	9.91692i	0.621176	+	0.403180i
$606$		−	13.0297i		−	0.529297i
$607$	17.9312	+	3.81139i	0.727804	+	0.154700i	0.556890	−	0.830586i	$-0.311995\pi$
$607$	17.9312	+	3.81139i	0.727804	+	0.154700i	0.170914	+	0.985286i	$0.445328\pi$
$608$	−4.33738	+	41.2674i	−0.175904	+	1.67361i
$609$	2.53723	−	5.69872i	0.102814	−	0.230924i
$610$	1.04283	−	3.20949i	0.0422228	−	0.129949i
$611$	28.4941	+	17.6117i	1.15275	+	0.712492i
$612$	4.94578	−	3.59332i	0.199921	−	0.145251i
$613$	44.6391	+	4.69176i	1.80296	+	0.189498i	0.945624	−	0.325263i	$-0.105453\pi$
$613$	44.6391	+	4.69176i	1.80296	+	0.189498i	0.857334	+	0.514761i	$0.172119\pi$
$614$	47.3901	−	52.6321i	1.91251	−	2.12406i
$615$	−5.32079	+	9.21588i	−0.214555	+	0.371620i
$616$	−5.84296	−	4.48232i	−0.235419	−	0.180598i
$617$	34.9793	+	20.1953i	1.40821	+	0.813032i	0.995216	−	0.0977009i	$-0.0311488\pi$
$617$	34.9793	+	20.1953i	1.40821	+	0.813032i	0.412996	+	0.910733i	$0.364482\pi$
$618$	7.93162	−	37.3153i	0.319056	−	1.50104i
$619$	−5.83816	+	8.03554i	−0.234656	+	0.322976i	−0.910064	−	0.414468i	$-0.863968\pi$
$619$	−5.83816	+	8.03554i	−0.234656	+	0.322976i	0.675408	+	0.737444i	$0.263968\pi$
$620$	0.904800	+	8.60860i	0.0363376	+	0.345730i
$621$	−5.89971	+	1.25402i	−0.236747	+	0.0503222i
$622$	−3.20259	−	15.0670i	−0.128412	−	0.604131i
$623$	6.63835	−	4.82304i	0.265960	−	0.193231i
$624$	−4.69030	+	0.850728i	−0.187762	+	0.0340564i
$625$	−2.66128	−	8.19058i	−0.106451	−	0.327623i
$626$	−52.1601	+	30.1146i	−2.08474	+	1.20362i
$627$	−3.58392	−	19.3239i	−0.143128	−	0.771722i
$628$	8.58788	−	14.8746i	0.342694	−	0.593563i
$629$	20.4362	−	6.64014i	0.814846	−	0.264760i
$630$	−1.62944	−	3.65978i	−0.0649184	−	0.145809i
$631$	12.4279	−	1.30623i	0.494747	−	0.0520000i	0.146130	−	0.989265i	$-0.453318\pi$
$631$	12.4279	−	1.30623i	0.494747	−	0.0520000i	0.348617	+	0.937265i	$0.386651\pi$
$632$	−14.1520	−	4.59826i	−0.562936	−	0.182909i
$633$	4.50782	+	5.00644i	0.179170	+	0.198988i
$634$	64.3718	+	28.6601i	2.55653	+	1.13824i
$635$	−21.7310	−	2.28402i	−0.862367	−	0.0906384i
$636$	−2.18898	−	6.73698i	−0.0867986	−	0.267139i
$637$	−5.87251	−	20.1077i	−0.232677	−	0.796697i
$638$	40.3227	−	11.9495i	1.59639	−	0.473085i
$639$	10.9779	−	6.33809i	0.434279	−	0.250731i
$640$	−16.1417	+	17.9272i	−0.638057	+	0.708634i
$641$	−29.5172	+	13.1419i	−1.16586	+	0.519074i	−0.896099	−	0.443853i	$-0.853611\pi$
$641$	−29.5172	+	13.1419i	−1.16586	+	0.519074i	−0.269760	+	0.962928i	$0.586944\pi$
$642$	19.5281	+	26.8781i	0.770712	+	1.06079i
$643$	−11.6791	+	10.5159i	−0.460578	+	0.414706i	−0.866481	−	0.499210i	$-0.833624\pi$
$643$	−11.6791	+	10.5159i	−0.460578	+	0.414706i	0.405903	+	0.913916i	$0.366957\pi$
$644$	14.2677	−	12.8467i	0.562227	−	0.506231i
$645$	6.02846	+	8.29746i	0.237370	+	0.326712i
$646$	−25.1525	+	11.1986i	−0.989610	+	0.440603i
$647$	27.7034	−	30.7677i	1.08913	−	1.20960i	0.112733	−	0.993625i	$-0.464040\pi$
$647$	27.7034	−	30.7677i	1.08913	−	1.20960i	0.976398	−	0.215977i	$-0.0692938\pi$
$648$	1.76262	−	1.01765i	0.0692423	−	0.0399771i
$649$	0.363800	−	13.9583i	0.0142804	−	0.547911i
$650$	−17.3298	+	5.06121i	−0.679731	+	0.198517i
$651$	−0.603959	−	1.85879i	−0.0236710	−	0.0728519i
$652$	−45.5575	−	4.78829i	−1.78417	−	0.187524i
$653$	14.7306	+	6.55848i	0.576452	+	0.256653i	0.674188	−	0.738559i	$-0.264494\pi$
$653$	14.7306	+	6.55848i	0.576452	+	0.256653i	−0.0977364	+	0.995212i	$0.531160\pi$
$654$	2.49453	+	2.77046i	0.0975439	+	0.108333i
$655$	12.1198	+	3.93796i	0.473559	+	0.153869i
$656$	−8.44966	+	0.888095i	−0.329904	+	0.0346743i
$657$	4.27791	+	9.60834i	0.166897	+	0.374857i
$658$	−21.3763	+	6.94559i	−0.833336	+	0.270767i
$659$	15.2573	−	26.4264i	0.594340	−	1.02943i	−0.399300	−	0.916820i	$-0.630747\pi$
$659$	15.2573	−	26.4264i	0.594340	−	1.02943i	0.993640	−	0.112606i	$-0.0359199\pi$
$660$	6.89703	−	14.4645i	0.268467	−	0.563030i
$661$	19.5449	−	11.2843i	0.760210	−	0.438907i	−0.0691612	−	0.997605i	$-0.522032\pi$
$661$	19.5449	−	11.2843i	0.760210	−	0.438907i	0.829371	+	0.558698i	$0.188699\pi$
$662$	19.3985	+	59.7024i	0.753944	+	2.32040i
$663$	−4.88410	−	5.76309i	−0.189683	−	0.223820i
$664$	11.6079	−	8.43365i	0.450475	−	0.327289i
$665$	2.22567	+	10.4710i	0.0863077	+	0.406046i
$666$	22.2465	−	4.72863i	0.862033	−	0.183231i
$667$	3.60502	+	34.2995i	0.139587	+	1.32808i
$668$	15.8172	−	21.7704i	0.611984	−	0.842324i
$669$	1.43525	−	6.75231i	0.0554899	−	0.261059i
$670$	5.54499	+	3.20140i	0.214222	+	0.123681i
$671$	−2.51165	+	1.72666i	−0.0969612	+	0.0666571i
$672$	3.81963	−	6.61579i	0.147345	−	0.255210i
$673$	7.65666	−	8.50358i	0.295143	−	0.327789i	−0.577275	−	0.816549i	$-0.695884\pi$
$673$	7.65666	−	8.50358i	0.295143	−	0.327789i	0.872418	+	0.488760i	$0.162551\pi$
$674$	−29.9106	−	3.14373i	−1.15211	−	0.121092i
$675$	−1.82670	+	1.32718i	−0.0703099	+	0.0510831i
$676$	−9.53640	−	36.7129i	−0.366785	−	1.41204i
$677$	2.92328	−	8.99694i	0.112351	−	0.345781i	−0.879034	−	0.476758i	$-0.841812\pi$
$677$	2.92328	−	8.99694i	0.112351	−	0.345781i	0.991385	+	0.130978i	$0.0418117\pi$
$678$	11.4576	−	25.7341i	0.440025	−	0.988312i
$679$	1.53036	−	14.5604i	0.0587297	−	0.558776i
$680$	−6.90709	−	1.46815i	−0.264875	−	0.0563009i
$681$			14.2156i			0.544744i
$682$	6.88342	−	11.2358i	0.263580	−	0.430241i
$683$	−7.28490	−	4.20594i	−0.278749	−	0.160936i	0.354108	−	0.935205i	$-0.384785\pi$
$683$	−7.28490	−	4.20594i	−0.278749	−	0.160936i	−0.632857	+	0.774269i	$0.718118\pi$
$684$	−16.4438	+	5.34292i	−0.628745	+	0.204292i
$685$	10.7658	−	4.79326i	0.411342	−	0.183141i
$686$	28.3113	+	12.6050i	1.08093	+	0.481261i
$687$	1.93771	+	9.11622i	0.0739283	+	0.347805i
$688$	−2.53040	+	7.78776i	−0.0964704	+	0.296906i
$689$	−8.09985	+	3.31878i	−0.308580	+	0.126435i
$690$	17.9188	+	13.0187i	0.682156	+	0.495615i
$691$	−16.3715	−	14.7410i	−0.622802	−	0.560773i	0.296151	−	0.955141i	$-0.404297\pi$
$691$	−16.3715	−	14.7410i	−0.622802	−	0.560773i	−0.918953	+	0.394368i	$0.870964\pi$
$692$	−14.6407	−	25.3584i	−0.556555	−	0.963982i
$693$	−0.844229	+	3.51837i	−0.0320696	+	0.133652i
$694$		−	8.74944i		−	0.332124i
$695$	3.31604	−	15.6007i	0.125784	−	0.591770i
$696$	−4.73357	−	10.6318i	−0.179425	−	0.402996i
$697$	−7.91423	−	10.8930i	−0.299773	−	0.412602i
$698$	43.6383	+	48.4652i	1.65173	+	1.83444i
$699$	−6.27602	+	1.33401i	−0.237381	+	0.0504569i
$700$	2.92333	−	6.56592i	0.110492	−	0.248168i
$701$	−33.2228	−	24.1378i	−1.25481	−	0.911671i	−0.256316	−	0.966593i	$-0.582509\pi$
$701$	−33.2228	−	24.1378i	−1.25481	−	0.911671i	−0.998491	+	0.0549223i	$0.982509\pi$
$702$	−4.50355	−	6.60677i	−0.169975	−	0.249356i
$703$	−60.7734			−2.29211
$704$	42.0167	−	7.79266i	1.58356	−	0.293697i
$705$	−7.69220	−	13.3233i	−0.289705	−	0.501783i
$706$	−48.7362	−	10.3592i	−1.83421	−	0.389874i
$707$	3.76764	−	5.18572i	0.141697	−	0.195029i
$708$	−12.2166	+	1.28402i	−0.459129	+	0.0482564i
$709$	2.93341	−	2.64125i	0.110166	−	0.0991943i	−0.612207	−	0.790698i	$-0.709718\pi$
$709$	2.93341	−	2.64125i	0.110166	−	0.0991943i	0.722373	+	0.691503i	$0.243051\pi$
$710$	−44.2709	−	14.3845i	−1.66146	−	0.539841i
$711$	0.764218	+	7.27105i	0.0286604	+	0.272686i
$712$	1.60016	−	15.2246i	0.0599687	−	0.570564i
$713$	8.03016	+	7.23039i	0.300732	+	0.270780i
$714$	5.06884			0.189697
$715$	−18.4602	−	7.16486i	−0.690374	−	0.267951i
$716$	12.1898			0.455554
$717$	15.3172	+	13.7917i	0.572032	+	0.515060i
$718$	−5.16554	+	49.1469i	−0.192776	+	1.83414i
$719$	−1.05172	−	10.0064i	−0.0392225	−	0.373177i	−0.996473	−	0.0839164i	$-0.973257\pi$
$719$	−1.05172	−	10.0064i	−0.0392225	−	0.373177i	0.957250	−	0.289261i	$-0.0934095\pi$
$720$	2.08211	+	0.676518i	0.0775956	+	0.0252123i
$721$	13.9467	−	12.5577i	0.519402	−	0.467672i
$722$	35.5395	−	3.73535i	1.32264	−	0.139015i
$723$	−1.01154	+	1.39227i	−0.0376196	+	0.0517790i
$724$	12.6055	+	2.67938i	0.468479	+	0.0995782i
$725$	6.45546	+	11.1812i	0.239750	+	0.415259i
$726$	−21.7322	+	11.0798i	−0.806559	+	0.411211i
$727$	−24.2547			−0.899559			−0.449779	−	0.893140i	$-0.648497\pi$
$727$	−24.2547			−0.899559			−0.449779	+	0.893140i	$0.648497\pi$
$728$	7.21259	+	3.47420i	0.267317	+	0.128762i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	15.7093	−	35.2836i	0.581426	−	1.30590i
$731$	−12.6933	+	2.69805i	−0.469480	+	0.0997911i
$732$	1.79420	+	1.99266i	0.0663155	+	0.0736508i
$733$	−26.6647	−	36.7008i	−0.984883	−	1.35558i	−0.934157	−	0.356863i	$-0.883846\pi$
$733$	−26.6647	−	36.7008i	−0.984883	−	1.35558i	−0.0507262	−	0.998713i	$-0.516154\pi$
$734$	−4.39985	−	9.88222i	−0.162401	−	0.364759i
$735$	−2.00024	+	9.41041i	−0.0737801	+	0.347108i
$736$			42.2354i			1.55682i
$737$	−2.21366	−	5.34239i	−0.0815411	−	0.196790i
$738$	−7.12561	−	12.3419i	−0.262297	−	0.454312i
$739$	17.2412	+	15.5241i	0.634229	+	0.571063i	0.922266	−	0.386557i	$-0.126336\pi$
$739$	17.2412	+	15.5241i	0.634229	+	0.571063i	−0.288036	+	0.957619i	$0.593002\pi$
$740$	−40.0887	−	29.1262i	−1.47369	−	1.07070i
$741$	8.10058	+	19.7703i	0.297582	+	0.726282i
$742$	1.81498	−	5.58594i	0.0666301	−	0.205066i
$743$	−3.45131	−	16.2371i	−0.126616	−	0.595682i	−0.995007	−	0.0998022i	$-0.968179\pi$
$743$	−3.45131	−	16.2371i	−0.126616	−	0.595682i	0.868391	−	0.495880i	$-0.165154\pi$
$744$	−3.33107	−	1.48309i	−0.122123	−	0.0543726i
$745$	32.1465	−	14.3126i	1.17776	−	0.524371i
$746$	−22.5844	+	7.33813i	−0.826875	+	0.268668i
$747$	−6.10519	−	3.52483i	−0.223377	−	0.128967i
$748$	13.1698	+	15.4161i	0.481537	+	0.563667i
$749$			16.3439i			0.597194i
$750$	26.0700	+	5.54135i	0.951943	+	0.202342i
$751$	−3.57057	+	33.9718i	−0.130292	+	1.23965i	0.712602	+	0.701568i	$0.247516\pi$
$751$	−3.57057	+	33.9718i	−0.130292	+	1.23965i	−0.842895	+	0.538079i	$0.819150\pi$
$752$	4.99588	−	11.2209i	0.182181	−	0.409186i
$753$	−2.23850	+	6.88940i	−0.0815755	+	0.251064i
$754$	−40.2625	+	21.6615i	−1.46627	+	0.788866i
$755$	−14.3088	+	10.3959i	−0.520750	+	0.378347i
$756$	3.16569	+	0.332728i	0.115135	+	0.0121012i
$757$	−26.8835	+	29.8571i	−0.977096	+	1.08517i	0.0192545	+	0.999815i	$0.493871\pi$
$757$	−26.8835	+	29.8571i	−0.977096	+	1.08517i	−0.996350	+	0.0853601i	$0.972796\pi$
$758$	−27.5286	+	47.6809i	−0.999882	+	1.73185i
$759$	−5.68387	−	19.1798i	−0.206311	−	0.696182i
$760$	17.2958	+	9.98573i	0.627384	+	0.362220i
$761$	1.26872	−	5.96887i	0.0459911	−	0.216371i	−0.949151	−	0.314822i	$-0.898055\pi$
$761$	1.26872	−	5.96887i	0.0459911	−	0.216371i	0.995142	+	0.0984505i	$0.0313886\pi$
$762$	17.2000	−	23.6738i	0.623091	−	0.857611i
$763$	0.191703	+	1.82393i	0.00694010	+	0.0660307i
$764$	−1.52780	+	0.324744i	−0.0552740	+	0.0117488i
$765$	0.721342	+	3.39365i	0.0260802	+	0.122698i
$766$	−64.3257	+	46.7353i	−2.32418	+	1.68862i
$767$	2.70904	+	14.9357i	0.0978179	+	0.539297i
$768$	−2.02004	−	6.21705i	−0.0728920	−	0.224339i
$769$	21.5265	−	12.4283i	0.776266	−	0.448177i	−0.0588396	−	0.998267i	$-0.518740\pi$
$769$	21.5265	−	12.4283i	0.776266	−	0.448177i	0.835105	+	0.550090i	$0.185407\pi$
$770$	11.6759	−	6.34135i	0.420770	−	0.228526i
$771$	0.126780	−	0.219590i	0.00456589	−	0.00790835i
$772$	−49.7355	+	16.1601i	−1.79002	+	0.581613i
$773$	−11.8336	−	26.5788i	−0.425627	−	0.955973i	−0.991334	−	0.131367i	$-0.958063\pi$
$773$	−11.8336	−	26.5788i	−0.425627	−	0.955973i	0.565707	−	0.824606i	$-0.308603\pi$
$774$	−13.6599	+	1.43571i	−0.490995	+	0.0516057i
$775$	3.84717	+	1.25002i	0.138195	+	0.0449021i
$776$	−18.2767	−	20.2983i	−0.656094	−	0.728666i
$777$	10.2212	+	4.55077i	0.366684	+	0.163258i
$778$	−43.8296	−	4.60667i	−1.57137	−	0.165157i
$779$	11.7677	+	36.2172i	0.421621	+	1.29762i
$780$	−4.13162	+	16.9236i	−0.147936	+	0.605963i
$781$	23.8172	+	34.6451i	0.852245	+	1.23970i
$782$	−24.2697	+	14.0121i	−0.867884	+	0.501073i
$783$	−3.82611	+	4.24933i	−0.136734	+	0.151859i
$784$	−7.01703	+	3.12418i	−0.250608	+	0.111578i
$785$	5.72954	+	7.88603i	0.204496	+	0.281465i
$786$	−12.6826	+	11.4195i	−0.452373	+	0.407319i
$787$	3.63733	−	3.27507i	0.129657	−	0.116743i	−0.601751	−	0.798684i	$-0.705530\pi$
$787$	3.63733	−	3.27507i	0.129657	−	0.116743i	0.731408	+	0.681940i	$0.238863\pi$
$788$	−20.9351	−	28.8147i	−0.745782	−	1.02648i
$789$	−12.1678	+	5.41747i	−0.433187	+	0.192867i
$790$	17.9646	−	19.9517i	0.639152	−	0.709851i
$791$	12.0012	−	6.92890i	0.426714	−	0.246363i
$792$	3.82411	+	5.56265i	0.135884	+	0.197660i
$793$	2.29000	−	2.39472i	0.0813203	−	0.0850391i
$794$	21.4093	+	65.8910i	0.759787	+	2.33838i
$795$	3.99814	+	0.420222i	0.141800	+	0.0149037i
$796$	−45.7054	−	20.3494i	−1.61999	−	0.721264i
$797$	22.8207	+	25.3449i	0.808350	+	0.897764i	0.996433	−	0.0843891i	$-0.0268939\pi$
$797$	22.8207	+	25.3449i	0.808350	+	0.897764i	−0.188082	+	0.982153i	$0.560227\pi$
$798$	−13.6343	−	4.43006i	−0.482650	−	0.156823i
$799$	19.3588	−	2.03469i	0.684865	−	0.0719823i
$800$	6.43094	+	14.4441i	0.227368	+	0.510677i
$801$	−7.15333	+	2.32426i	−0.252750	+	0.0821236i
$802$	15.3975	−	26.6692i	0.543704	−	0.941722i
$803$	−30.6538	+	16.6485i	−1.08175	+	0.587513i
$804$	−4.40586	+	2.54373i	−0.155383	+	0.0897103i
$805$	3.36704	+	10.3627i	0.118673	+	0.365237i
$806$	−4.83332	+	13.4845i	−0.170246	+	0.474972i
$807$	4.38535	−	3.18614i	0.154372	−	0.112158i
$808$	−2.48633	−	11.6972i	−0.0874686	−	0.411508i
$809$	0.685882	−	0.145789i	0.0241143	−	0.00512566i	−0.195839	−	0.980636i	$-0.562743\pi$
$809$	0.685882	−	0.145789i	0.0241143	−	0.00512566i	0.219953	+	0.975510i	$0.429410\pi$
$810$	0.383848	+	3.65207i	0.0134870	+	0.128320i
$811$	13.5135	−	18.5997i	0.474522	−	0.653123i	−0.502919	−	0.864334i	$-0.667741\pi$
$811$	13.5135	−	18.5997i	0.474522	−	0.653123i	0.977441	+	0.211210i	$0.0677405\pi$
$812$	3.78425	−	17.8035i	0.132801	−	0.624781i
$813$	7.26202	+	4.19273i	0.254690	+	0.147045i
$814$	21.4326	+	72.3226i	0.751211	+	2.53491i
$815$	12.9987	−	22.5145i	0.455326	−	0.788647i
$816$	−1.85350	+	2.05852i	−0.0648854	+	0.0720625i
$817$	36.5010	+	3.83641i	1.27701	+	0.134219i
$818$	32.3177	−	23.4802i	1.12996	−	0.820966i
$819$	0.118024	−	3.93167i	0.00412410	−	0.137383i
$820$	−9.59495	+	29.5302i	−0.335070	+	1.03124i
$821$	−0.398029	+	0.893987i	−0.0138913	+	0.0312004i	−0.920358	−	0.391077i	$-0.872103\pi$
$821$	−0.398029	+	0.893987i	−0.0138913	+	0.0312004i	0.906467	+	0.422278i	$0.138769\pi$
$822$	−1.64968	+	15.6956i	−0.0575390	+	0.547447i
$823$	38.2420	+	8.12858i	1.33303	+	0.283344i	0.818687	−	0.574240i	$-0.194702\pi$
$823$	38.2420	+	8.12858i	1.33303	+	0.283344i	0.514344	+	0.857584i	$0.328036\pi$
$824$		−	35.0127i		−	1.21973i
$825$	−4.86423	−	5.69386i	−0.169351	−	0.198235i
$826$	−8.82062	−	5.09259i	−0.306909	−	0.177194i
$827$	−11.0474	+	3.58951i	−0.384155	+	0.124819i	−0.494727	−	0.869049i	$-0.664732\pi$
$827$	−11.0474	+	3.58951i	−0.384155	+	0.124819i	0.110572	+	0.993868i	$0.464732\pi$
$828$	−16.0772	+	7.15803i	−0.558721	+	0.248759i
$829$	−34.2830	−	15.2638i	−1.19070	−	0.530132i	−0.286845	−	0.957977i	$-0.592606\pi$
$829$	−34.2830	−	15.2638i	−1.19070	−	0.530132i	−0.903852	+	0.427845i	$0.859273\pi$
$830$	5.38234	+	25.3219i	0.186824	+	0.878937i
$831$	4.13807	−	12.7357i	0.143548	−	0.441795i
$832$	−42.9874	+	17.6134i	−1.49032	+	0.610635i
$833$	−9.84795	−	7.15496i	−0.341211	−	0.247905i
$834$	15.8730	+	14.2921i	0.549638	+	0.494896i
$835$	7.63598	+	13.2259i	0.264254	+	0.457701i
$836$	−21.9513	−	52.9768i	−0.759202	−	1.83224i
$837$			1.79153i			0.0619244i
$838$	12.1628	−	57.2214i	0.420157	−	1.97668i
$839$	−6.09766	−	13.6956i	−0.210515	−	0.472824i	0.777168	−	0.629293i	$-0.216655\pi$
$839$	−6.09766	−	13.6956i	−0.210515	−	0.472824i	−0.987683	+	0.156469i	$0.949989\pi$
$840$	−2.16116	−	2.97458i	−0.0745671	−	0.102633i
$841$	2.47306	+	2.74661i	0.0852778	+	0.0947106i
$842$	−68.2464	+	14.5062i	−2.35193	+	0.499918i
$843$	−7.59900	+	17.0676i	−0.261724	+	0.587841i
$844$	15.9026	+	11.5539i	0.547389	+	0.397701i
$845$	21.2355	+	3.53032i	0.730523	+	0.121447i
$846$	20.6028			0.708339
$847$	−11.8530	−	1.87436i	−0.407275	−	0.0644038i
$848$	1.60484	+	2.77967i	0.0551106	+	0.0954543i
$849$	−12.8407	−	2.72938i	−0.440693	−	0.0936722i
$850$	−6.16648	+	8.48744i	−0.211509	+	0.291117i
$851$	−61.5194	+	6.46595i	−2.10886	+	0.221650i
$852$	27.4863	−	24.7487i	0.941664	−	0.847878i
$853$	15.2977	+	4.97051i	0.523782	+	0.170187i	0.558961	−	0.829194i	$-0.311200\pi$
$853$	15.2977	+	4.97051i	0.523782	+	0.170187i	−0.0351792	+	0.999381i	$0.511200\pi$
$854$	0.232394	+	2.21109i	0.00795237	+	0.0756618i
$855$	1.02569	−	9.75878i	0.0350778	−	0.333743i
$856$	22.6599	+	20.4031i	0.774499	+	0.697362i
$857$	28.1822			0.962686			0.481343	−	0.876532i	$-0.340149\pi$
$857$	28.1822			0.962686			0.481343	+	0.876532i	$0.340149\pi$
$858$	20.6707	−	16.6123i	0.705685	−	0.567133i
$859$	39.0998			1.33407			0.667033	−	0.745028i	$-0.267564\pi$
$859$	39.0998			1.33407			0.667033	+	0.745028i	$0.267564\pi$
$860$	22.2390	+	20.0241i	0.758343	+	0.682815i
$861$	0.732828	−	6.97239i	0.0249747	−	0.237618i
$862$	3.85366	+	36.6652i	0.131256	+	1.24882i
$863$	0.128747	+	0.0418324i	0.00438259	+	0.00142399i	0.311207	−	0.950342i	$-0.399267\pi$
$863$	0.128747	+	0.0418324i	0.00438259	+	0.00142399i	−0.306825	+	0.951766i	$0.599267\pi$
$864$	−5.20384	+	4.68556i	−0.177038	+	0.159406i
$865$	16.5269	−	1.73705i	0.561931	−	0.0590613i
$866$	33.2598	−	45.7782i	1.13021	−	1.55561i
$867$	12.3346	+	2.62180i	0.418906	+	0.0890412i
$868$	−2.85134	−	4.93867i	−0.0967808	−	0.167629i
$869$	−23.8416	+	4.42180i	−0.808771	+	0.149999i
$870$	20.9977			0.711887
$871$	3.54092	+	5.19458i	0.119979	+	0.176011i
$872$	2.76808	+	2.01113i	0.0937391	+	0.0681055i
$873$	−5.45847	+	12.2599i	−0.184741	+	0.414935i
$874$	77.5279	−	16.4791i	2.62242	−	0.557412i
$875$	8.77331	+	9.74375i	0.296592	+	0.329399i
$876$	18.0381	+	24.8273i	0.609451	+	0.838838i
$877$	18.2611	+	41.0152i	0.616635	+	1.38498i	0.904153	+	0.427210i	$0.140503\pi$
$877$	18.2611	+	41.0152i	0.616635	+	1.38498i	−0.287518	+	0.957775i	$0.592830\pi$
$878$	8.44611	−	39.7358i	0.285042	−	1.34102i
$879$		−	9.10654i		−	0.307156i
$880$	−1.69417	+	7.06054i	−0.0571105	+	0.238011i
$881$	−11.5841	−	20.0643i	−0.390279	−	0.675983i	0.602207	−	0.798340i	$-0.294288\pi$
$881$	−11.5841	−	20.0643i	−0.390279	−	0.675983i	−0.992486	+	0.122357i	$0.960955\pi$
$882$	−9.57466	−	8.62107i	−0.322396	−	0.290286i
$883$	−28.9627	−	21.0426i	−0.974672	−	0.708141i	−0.0181608	−	0.999835i	$-0.505781\pi$
$883$	−28.9627	−	21.0426i	−0.974672	−	0.708141i	−0.956512	+	0.291694i	$0.905781\pi$
$884$	−17.4355	−	13.4851i	−0.586419	−	0.453554i
$885$	2.15429	−	6.63023i	0.0724158	−	0.222873i
$886$	−4.41851	−	20.7874i	−0.148443	−	0.698368i
$887$	−19.2132	−	8.55425i	−0.645115	−	0.287224i	0.0579820	−	0.998318i	$-0.481533\pi$
$887$	−19.2132	−	8.55425i	−0.645115	−	0.287224i	−0.703097	+	0.711094i	$0.748200\pi$
$888$	19.0691	−	8.49011i	0.639917	−	0.284909i
$889$	13.6909	−	4.44844i	0.459178	−	0.149196i
$890$	23.9197	+	13.8101i	0.801792	+	0.462915i
$891$	1.73259	−	2.82810i	0.0580438	−	0.0947449i
$892$		−	20.1420i		−	0.674403i
$893$	−53.8502	−	11.4462i	−1.80203	−	0.383033i
$894$	−4.92588	+	46.8667i	−0.164746	+	1.56746i
$895$	−2.81381	+	6.31992i	−0.0940553	+	0.211252i
$896$	4.91114	−	15.1149i	0.164070	−	0.504955i
$897$	10.3035	+	19.1512i	0.344023	+	0.639439i
$898$	−28.0575	+	20.3850i	−0.936291	+	0.680255i
$899$	10.1879	+	1.07079i	0.339786	+	0.0357130i
$900$	−4.40835	+	4.89596i	−0.146945	+	0.163199i
$901$	−2.54330	+	4.40513i	−0.0847297	+	0.146756i
$902$	38.9498	−	26.7765i	1.29689	−	0.891560i
$903$	−5.85166	−	3.37846i	−0.194731	−	0.112428i
$904$	5.37528	−	25.2887i	0.178779	−	0.841089i
$905$	−4.29891	+	5.91694i	−0.142901	+	0.196686i
$906$	−2.47586	−	23.5562i	−0.0822549	−	0.782603i
$907$	−30.4842	+	6.47962i	−1.01221	+	0.215152i	−0.684023	−	0.729460i	$-0.739771\pi$
$907$	−30.4842	+	6.47962i	−1.01221	+	0.215152i	−0.328188	+	0.944612i	$0.606438\pi$
$908$	8.62381	+	40.5718i	0.286191	+	1.34642i
$909$	−4.75344	+	3.45358i	−0.157662	+	0.114548i
$910$	−11.0194	+	9.33868i	−0.365289	+	0.309574i
$911$	13.7673	+	42.3715i	0.456132	+	1.40383i	0.869801	+	0.493403i	$0.164247\pi$
$911$	13.7673	+	42.3715i	0.456132	+	1.40383i	−0.413669	+	0.910428i	$0.635753\pi$
$912$	6.78470	−	3.91715i	0.224664	−	0.129710i
$913$	10.0632	−	21.1047i	0.333044	−	0.698462i
$914$	13.5022	−	23.3865i	0.446613	−	0.773557i
$915$	−1.44728	+	0.470248i	−0.0478455	+	0.0155459i
$916$	11.0606	+	24.8425i	0.365452	+	0.820818i
$917$	−8.34958	+	0.877576i	−0.275727	+	0.0289801i
$918$	−4.41890	−	1.43579i	−0.145846	−	0.0473881i
$919$	5.04349	+	5.60137i	0.166369	+	0.184772i	0.820565	−	0.571554i	$-0.193659\pi$
$919$	5.04349	+	5.60137i	0.166369	+	0.184772i	−0.654195	+	0.756326i	$0.726992\pi$
$920$	18.5705	+	8.26813i	0.612252	+	0.272592i
$921$	−31.7619	−	3.33831i	−1.04659	−	0.110001i
$922$	22.1605	+	68.2029i	0.729816	+	2.24614i
$923$	−33.0322	−	31.5877i	−1.08727	−	1.03972i
$924$	−0.275064	+	10.5537i	−0.00904895	+	0.347190i
$925$	−20.0545	+	11.5785i	−0.659389	+	0.380699i
$926$	39.8020	−	44.2046i	1.30797	−	1.45265i
$927$	−15.7155	+	6.99699i	−0.516164	+	0.229811i
$928$	23.5351	+	32.3933i	0.772577	+	1.06336i
$929$	−22.0496	+	19.8536i	−0.723426	+	0.651375i	−0.946233	−	0.323487i	$-0.895145\pi$
$929$	−22.0496	+	19.8536i	−0.723426	+	0.651375i	0.222807	+	0.974863i	$0.428478\pi$
$930$	4.88903	−	4.40210i	0.160317	−	0.144350i
$931$	20.2361	+	27.8525i	0.663210	+	0.912830i
$932$	−17.1027	+	7.61460i	−0.560217	+	0.249425i
$933$	−4.64781	+	5.16191i	−0.152162	+	0.168993i
$934$	38.3275	−	22.1284i	1.25411	−	0.724064i
$935$	−11.0327	+	3.26949i	−0.360806	+	0.106924i
$936$	−5.30369	−	5.07176i	−0.173356	−	0.165776i
$937$	−13.5378	−	41.6650i	−0.442260	−	1.36114i	−0.885461	−	0.464714i	$-0.846157\pi$
$937$	−13.5378	−	41.6650i	−0.442260	−	1.36114i	0.443201	−	0.896422i	$-0.353843\pi$
$938$	−4.19513	−	0.440926i	−0.136976	−	0.0143968i
$939$	24.8115	+	11.0468i	0.809692	+	0.360498i
$940$	−30.0362	−	33.3586i	−0.979673	−	1.08804i
$941$	−16.7191	−	5.43235i	−0.545026	−	0.177090i	0.0235466	−	0.999723i	$-0.492504\pi$
$941$	−16.7191	−	5.43235i	−0.545026	−	0.177090i	−0.568573	+	0.822633i	$0.692504\pi$
$942$	−12.9826	+	1.36452i	−0.422995	+	0.0444586i
$943$	15.7655	+	35.4098i	0.513394	+	1.15310i
$944$	5.29356	−	1.71998i	0.172291	−	0.0559806i
$945$	−0.903253	+	1.56448i	−0.0293828	+	0.0508926i
$946$	−8.30710	−	44.7905i	−0.270087	−	1.45626i
$947$	−5.64107	+	3.25687i	−0.183310	+	0.105834i	−0.588847	−	0.808245i	$-0.700418\pi$
$947$	−5.64107	+	3.25687i	−0.183310	+	0.105834i	0.405537	+	0.914079i	$0.367085\pi$
$948$	6.59203	+	20.2882i	0.214099	+	0.658930i
$949$	28.9301	−	24.5177i	0.939112	−	0.795877i
$950$	24.0047	−	17.4404i	0.778814	−	0.565841i
$951$	−6.60631	−	31.0803i	−0.214224	−	1.00785i
$952$	4.55047	−	0.967233i	0.147482	−	0.0313482i
$953$	2.28947	+	21.7828i	0.0741631	+	0.705615i	0.966921	+	0.255077i	$0.0821009\pi$
$953$	2.28947	+	21.7828i	0.0741631	+	0.705615i	−0.892758	+	0.450537i	$0.851232\pi$
$954$	−3.16452	+	4.35559i	−0.102455	+	0.141018i
$955$	0.184301	−	0.867066i	0.00596383	−	0.0280576i
$956$	52.0825	+	30.0698i	1.68447	+	0.972528i
$957$	−15.0470	−	11.5431i	−0.486401	−	0.373134i
$958$	−7.87816	+	13.6454i	−0.254532	+	0.440862i
$959$	−5.19506	+	5.76969i	−0.167757	+	0.186313i
$960$	21.2189	+	2.23020i	0.684837	+	0.0719793i
$961$	−22.4829	+	16.3348i	−0.725255	+	0.526929i
$962$	−38.8520	−	72.2147i	−1.25264	−	2.32830i
$963$	4.62955	−	14.2483i	0.149185	−	0.459144i
$964$	−2.04236	+	4.58722i	−0.0657800	+	0.147744i
$965$	3.10227	−	29.5162i	0.0998657	−	0.950159i
$966$	−14.2730	−	3.03383i	−0.459227	−	0.0976117i
$967$		−	28.0179i		−	0.900994i	−0.892778	−	0.450497i	$-0.851247\pi$
$967$		−	28.0179i		−	0.900994i	0.892778	−	0.450497i	$-0.148753\pi$
$968$	−17.3955	+	14.0937i	−0.559113	+	0.452988i
$969$	10.7522	+	6.20776i	0.345409	+	0.199422i
$970$	46.8692	−	15.2287i	1.50488	−	0.488965i
$971$	56.1376	−	24.9941i	1.80154	−	0.802098i	0.832990	−	0.553288i	$-0.186627\pi$
$971$	56.1376	−	24.9941i	1.80154	−	0.802098i	0.968552	−	0.248811i	$-0.0800397\pi$
$972$	−2.66553	−	1.18677i	−0.0854970	−	0.0380657i
$973$	2.18464	+	10.2779i	0.0700365	+	0.329496i
$974$	2.78982	−	8.58618i	0.0893916	−	0.275119i
$975$	6.43973	+	4.98068i	0.206236	+	0.159509i
$976$	−0.982927	−	0.714138i	−0.0314627	−	0.0228590i
$977$	−28.7879	−	25.9208i	−0.921007	−	0.829278i	0.0646729	−	0.997907i	$-0.479400\pi$
$977$	−28.7879	−	25.9208i	−0.921007	−	0.829278i	−0.985680	+	0.168628i	$0.946066\pi$
$978$	17.4079	+	30.1514i	0.556644	+	0.964136i
$979$	−9.54918	−	23.0458i	−0.305193	−	0.736546i
$980$			28.0710i			0.896696i
$981$	0.349520	−	1.64436i	0.0111593	−	0.0525004i
$982$	−23.8953	−	53.6697i	−0.762529	−	1.71267i
$983$	−17.0369	−	23.4493i	−0.543393	−	0.747917i	0.445704	−	0.895180i	$-0.352953\pi$
$983$	−17.0369	−	23.4493i	−0.543393	−	0.747917i	−0.989097	+	0.147264i	$0.952953\pi$
$984$	−8.75198	−	9.72006i	−0.279003	−	0.309864i
$985$	19.7718	−	4.20262i	0.629982	−	0.133907i
$986$	−10.8061	+	24.2709i	−0.344136	+	0.772942i
$987$	8.19972	+	5.95745i	0.261000	+	0.189628i
$988$	35.1128	+	51.5110i	1.11709	+	1.63878i
$989$	37.3572			1.18789
$990$	−11.9750	+	2.22096i	−0.380592	+	0.0705867i
$991$	28.3444	+	49.0940i	0.900391	+	1.55952i	0.826988	+	0.562220i	$0.190052\pi$
$991$	28.3444	+	49.0940i	0.900391	+	1.55952i	0.0734026	+	0.997302i	$0.476614\pi$
$992$	12.2710	+	2.60828i	0.389604	+	0.0828130i
$993$	16.6387	−	22.9012i	0.528013	−	0.726747i
$994$	30.4992	−	3.20559i	0.967375	−	0.101675i
$995$	21.1007	−	18.9991i	0.668936	−	0.602313i
$996$	−19.5627	−	6.35631i	−0.619868	−	0.201407i
$997$	1.14858	+	10.9280i	0.0363758	+	0.346093i	0.997539	+	0.0701124i	$0.0223358\pi$
$997$	1.14858	+	10.9280i	0.0363758	+	0.346093i	−0.961163	+	0.275980i	$0.910998\pi$
$998$	7.70401	−	73.2988i	0.243866	−	2.32023i
$999$	−7.62158	−	6.86250i	−0.241136	−	0.217120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bn.b.49.2	✓	112
11.9	even	5	inner	429.2.bn.b.361.13	yes	112
13.4	even	6	inner	429.2.bn.b.82.13	yes	112
143.108	even	30	inner	429.2.bn.b.394.2	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bn.b.49.2	✓	112	1.1	even	1	trivial
429.2.bn.b.82.13	yes	112	13.4	even	6	inner
429.2.bn.b.361.13	yes	112	11.9	even	5	inner
429.2.bn.b.394.2	yes	112	143.108	even	30	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64800 - 1.48387i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.304992 + 2.90181i) q^{4} +(-1.57487 - 0.511707i) q^{5} +(1.64800 - 1.48387i) q^{6} +(1.08496 - 0.114034i) q^{7} +(1.19632 - 1.64659i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-1.64800 - 1.48387i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.304992 + 2.90181i) q^{4} +(-1.57487 - 0.511707i) q^{5} +(1.64800 - 1.48387i) q^{6} +(1.08496 - 0.114034i) q^{7} +(1.19632 - 1.64659i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.83609 + 3.18020i) q^{10} +(0.432504 - 3.28830i) q^{11} -2.91779 q^{12} +(0.269120 + 3.59549i) q^{13} +(-1.95724 - 1.42201i) q^{14} +(0.673523 - 1.51276i) q^{15} +(1.29319 - 0.274876i) q^{16} +(1.40195 + 1.55703i) q^{17} +(1.30348 + 1.79408i) q^{18} +(-2.41021 - 5.41343i) q^{19} +(1.00455 - 4.72604i) q^{20} +1.09094i q^{21} +(-5.59218 + 4.77736i) q^{22} +(-3.01576 - 5.22344i) q^{23} +(1.51252 + 1.36188i) q^{24} +(-1.82670 - 1.32718i) q^{25} +(4.89174 - 6.32473i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.661810 + 3.11357i) q^{28} +(-5.22368 - 2.32573i) q^{29} +(-3.35471 + 1.49361i) q^{30} +(-1.70385 + 0.553614i) q^{31} +(-6.06431 - 3.50123i) q^{32} +(3.22508 + 0.773856i) q^{33} -4.64631i q^{34} +(-1.76703 - 0.375594i) q^{35} +(0.304992 - 2.90181i) q^{36} +(4.17143 - 9.36918i) q^{37} +(-4.06078 + 12.4978i) q^{38} +(-3.60393 - 0.108186i) q^{39} +(-2.72662 + 1.98101i) q^{40} +(-6.39118 - 0.671740i) q^{41} +(1.61881 - 1.79787i) q^{42} +(-3.09684 + 5.36388i) q^{43} +(9.67393 + 0.252135i) q^{44} +(1.43407 + 0.827960i) q^{45} +(-2.78093 + 13.0833i) q^{46} +(5.46084 - 7.51621i) q^{47} +(0.138195 + 1.31484i) q^{48} +(-5.68289 + 1.20794i) q^{49} +(1.04106 + 4.89779i) q^{50} +(-1.69504 + 1.23152i) q^{51} +(-10.3513 + 1.87753i) q^{52} +(0.750218 + 2.30893i) q^{53} +(-1.92051 + 1.10880i) q^{54} +(-2.36379 + 4.95734i) q^{55} +(1.11019 - 1.92291i) q^{56} +(5.63571 - 1.83115i) q^{57} +(5.15757 + 11.5841i) q^{58} +(4.18695 - 0.440066i) q^{59} +(4.59515 + 1.49305i) q^{60} +(-0.614917 - 0.682935i) q^{61} +(3.62944 + 1.61593i) q^{62} +(-1.08496 - 0.114034i) q^{63} +(3.98155 + 12.2539i) q^{64} +(1.41601 - 5.80016i) q^{65} +(-4.16665 - 6.06092i) q^{66} +(1.51000 - 0.871799i) q^{67} +(-4.09061 + 4.54308i) q^{68} +(5.51006 - 2.45324i) q^{69} +(2.35474 + 3.24102i) q^{70} +(-9.42023 + 8.48202i) q^{71} +(-1.51252 + 1.36188i) q^{72} +(-6.18211 - 8.50895i) q^{73} +(-20.7772 + 9.25060i) q^{74} +(1.51085 - 1.67797i) q^{75} +(14.9736 - 8.64502i) q^{76} +(0.0942714 - 3.61701i) q^{77} +(5.77876 + 5.52605i) q^{78} +(-2.25925 - 6.95327i) q^{79} +(-2.17727 - 0.228840i) q^{80} +(0.913545 + 0.406737i) q^{81} +(9.53592 + 10.5907i) q^{82} +(6.70463 + 2.17847i) q^{83} +(-3.16569 + 0.332728i) q^{84} +(-1.41116 - 3.16951i) q^{85} +(13.0629 - 4.24439i) q^{86} +(2.85902 - 4.95196i) q^{87} +(-4.89708 - 4.64602i) q^{88} +(6.51377 - 3.76073i) q^{89} +(-1.13477 - 3.49245i) q^{90} +(0.701994 + 3.87029i) q^{91} +(14.2376 - 10.3443i) q^{92} +(-0.372481 - 1.75238i) q^{93} +(-20.1526 + 4.28356i) q^{94} +(1.02569 + 9.75878i) q^{95} +(4.11594 - 5.66511i) q^{96} +(2.79021 - 13.1269i) q^{97} +(11.1579 + 6.44199i) q^{98} +(-1.10673 + 3.12652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 14 q^{3} - 8 q^{4} + 14 q^{9}+O(q^{10}) \) 112 * q + 14 * q^3 - 8 * q^4 + 14 * q^9	\( 112 q + 14 q^{3} - 8 q^{4} + 14 q^{9} - 40 q^{10} + 15 q^{11} - 104 q^{12} + q^{13} - 6 q^{14} - 6 q^{15} + 32 q^{16} + 8 q^{17} - 12 q^{19} + 42 q^{20} - 9 q^{22} + 8 q^{23} + 30 q^{25} - 57 q^{26} - 28 q^{27} + 18 q^{28} - 10 q^{29} + 10 q^{30} + 30 q^{32} + 30 q^{33} - 12 q^{35} - 8 q^{36} + 30 q^{38} + 4 q^{39} + 20 q^{40} + 72 q^{41} - 12 q^{42} - 108 q^{43} + 6 q^{45} - 18 q^{46} + 2 q^{48} - 40 q^{49} + 111 q^{50} - 26 q^{51} + 13 q^{52} - 46 q^{53} - 38 q^{55} - 100 q^{56} - 12 q^{58} - 18 q^{59} - 46 q^{61} - 9 q^{62} + 52 q^{64} + 24 q^{65} - 32 q^{66} + 48 q^{67} - 8 q^{68} - 7 q^{69} + 18 q^{71} + 32 q^{74} - 216 q^{76} + 4 q^{77} - 26 q^{78} + 108 q^{79} - 66 q^{80} + 14 q^{81} + 39 q^{82} + 27 q^{84} + 6 q^{85} + 60 q^{87} + 28 q^{88} - 120 q^{89} - 20 q^{90} + 47 q^{91} + 78 q^{92} - 6 q^{93} - 50 q^{94} + 60 q^{95} - 69 q^{97} + 72 q^{98}+O(q^{100}) \) 112 * q + 14 * q^3 - 8 * q^4 + 14 * q^9 - 40 * q^10 + 15 * q^11 - 104 * q^12 + q^13 - 6 * q^14 - 6 * q^15 + 32 * q^16 + 8 * q^17 - 12 * q^19 + 42 * q^20 - 9 * q^22 + 8 * q^23 + 30 * q^25 - 57 * q^26 - 28 * q^27 + 18 * q^28 - 10 * q^29 + 10 * q^30 + 30 * q^32 + 30 * q^33 - 12 * q^35 - 8 * q^36 + 30 * q^38 + 4 * q^39 + 20 * q^40 + 72 * q^41 - 12 * q^42 - 108 * q^43 + 6 * q^45 - 18 * q^46 + 2 * q^48 - 40 * q^49 + 111 * q^50 - 26 * q^51 + 13 * q^52 - 46 * q^53 - 38 * q^55 - 100 * q^56 - 12 * q^58 - 18 * q^59 - 46 * q^61 - 9 * q^62 + 52 * q^64 + 24 * q^65 - 32 * q^66 + 48 * q^67 - 8 * q^68 - 7 * q^69 + 18 * q^71 + 32 * q^74 - 216 * q^76 + 4 * q^77 - 26 * q^78 + 108 * q^79 - 66 * q^80 + 14 * q^81 + 39 * q^82 + 27 * q^84 + 6 * q^85 + 60 * q^87 + 28 * q^88 - 120 * q^89 - 20 * q^90 + 47 * q^91 + 78 * q^92 - 6 * q^93 - 50 * q^94 + 60 * q^95 - 69 * q^97 + 72 * q^98

Introduction

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