LMFDB - Embedded newform 847.2.n.h.130.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			130.4
Character	$\chi$	$=$	847.130
Dual form			847.2.n.h.632.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24721 - 0.265102i) q^{2} +(0.0145619 + 0.138547i) q^{3} +(-0.341843 + 0.152198i) q^{4} +(0.792967 - 0.880679i) q^{5} +(0.0548908 + 0.168936i) q^{6} +(-1.98226 + 1.75232i) q^{7} +(-2.44911 + 1.77938i) q^{8} +(2.91546 - 0.619700i) q^{9} +O(q^{10})$	\(q+(1.24721 - 0.265102i) q^{2} +(0.0145619 + 0.138547i) q^{3} +(-0.341843 + 0.152198i) q^{4} +(0.792967 - 0.880679i) q^{5} +(0.0548908 + 0.168936i) q^{6} +(-1.98226 + 1.75232i) q^{7} +(-2.44911 + 1.77938i) q^{8} +(2.91546 - 0.619700i) q^{9} +(0.755525 - 1.30861i) q^{10} +(-0.0260644 - 0.0451450i) q^{12} +(-1.39908 + 4.30591i) q^{13} +(-2.00775 + 2.71101i) q^{14} +(0.133562 + 0.0970388i) q^{15} +(-2.08206 + 2.31236i) q^{16} +(6.51006 + 1.38375i) q^{17} +(3.47190 - 1.54579i) q^{18} +(2.78166 + 1.23847i) q^{19} +(-0.137032 + 0.421742i) q^{20} +(-0.271644 - 0.249120i) q^{21} +(1.89164 + 3.27641i) q^{23} +(-0.282192 - 0.313405i) q^{24} +(0.375843 + 3.57591i) q^{25} +(-0.603431 + 5.74127i) q^{26} +(0.257460 + 0.792379i) q^{27} +(0.410923 - 0.900715i) q^{28} +(3.38711 + 2.46088i) q^{29} +(0.192305 + 0.0856198i) q^{30} +(-4.59366 - 5.10178i) q^{31} +(1.04351 - 1.80742i) q^{32} +8.48623 q^{34} +(-0.0286387 + 3.13527i) q^{35} +(-0.902311 + 0.655567i) q^{36} +(0.354621 - 3.37400i) q^{37} +(3.79763 + 0.807210i) q^{38} +(-0.616944 - 0.131136i) q^{39} +(-0.374998 + 3.56787i) q^{40} +(-7.57505 + 5.50359i) q^{41} +(-0.404839 - 0.238691i) q^{42} -0.848738 q^{43} +(1.76611 - 3.05899i) q^{45} +(3.22785 + 3.58489i) q^{46} +(-4.99454 - 2.22371i) q^{47} +(-0.350690 - 0.254791i) q^{48} +(0.858747 - 6.94713i) q^{49} +(1.41674 + 4.36027i) q^{50} +(-0.0969164 + 0.922098i) q^{51} +(-0.177088 - 1.68488i) q^{52} +(2.64002 + 2.93204i) q^{53} +(0.531167 + 0.920009i) q^{54} +(1.73674 - 7.81883i) q^{56} +(-0.131081 + 0.403424i) q^{57} +(4.87682 + 2.17130i) q^{58} +(2.60081 - 1.15795i) q^{59} +(-0.0604264 - 0.0128440i) q^{60} +(-1.64430 + 1.82618i) q^{61} +(-7.08174 - 5.14519i) q^{62} +(-4.69330 + 6.33723i) q^{63} +(2.74540 - 8.44947i) q^{64} +(2.68271 + 4.64658i) q^{65} +(-0.264856 + 0.458743i) q^{67} +(-2.43602 + 0.517792i) q^{68} +(-0.426391 + 0.309791i) q^{69} +(0.795449 + 3.91793i) q^{70} +(1.01414 + 3.12120i) q^{71} +(-6.03760 + 6.70543i) q^{72} +(11.6036 - 5.16627i) q^{73} +(-0.452167 - 4.30208i) q^{74} +(-0.489959 + 0.104144i) q^{75} -1.13938 q^{76} -0.804222 q^{78} +(-4.76004 + 1.01178i) q^{79} +(0.385444 + 3.66726i) q^{80} +(8.06269 - 3.58974i) q^{81} +(-7.98864 + 8.87229i) q^{82} +(-3.55037 - 10.9269i) q^{83} +(0.130775 + 0.0438160i) q^{84} +(6.38090 - 4.63600i) q^{85} +(-1.05855 + 0.225002i) q^{86} +(-0.291625 + 0.505109i) q^{87} +(-0.926864 - 1.60538i) q^{89} +(1.39176 - 4.28339i) q^{90} +(-4.77200 - 10.9871i) q^{91} +(-1.14531 - 0.832114i) q^{92} +(0.639943 - 0.710729i) q^{93} +(-6.81873 - 1.44937i) q^{94} +(3.29646 - 1.46768i) q^{95} +(0.265608 + 0.118256i) q^{96} +(-0.304405 + 0.936862i) q^{97} +(-0.770662 - 8.89217i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9} - 14 q^{10} - 18 q^{12} + 4 q^{13} + 22 q^{14} + 16 q^{15} + 20 q^{16} + 12 q^{17} + 41 q^{18} + 24 q^{19} + 40 q^{20} + 2 q^{21} - 14 q^{23} + 7 q^{24} - 29 q^{25} - 5 q^{26} + 4 q^{27} + 24 q^{28} + 30 q^{29} - 6 q^{30} + 3 q^{31} + 30 q^{32} + 48 q^{34} - 6 q^{35} - 46 q^{36} - 11 q^{37} + 12 q^{38} + 32 q^{39} + 20 q^{40} - 10 q^{41} + 45 q^{42} + 72 q^{43} - 16 q^{45} + 17 q^{46} + 3 q^{47} - 62 q^{48} + 35 q^{49} - 6 q^{50} - 28 q^{51} - 2 q^{52} - 42 q^{53} - 34 q^{54} + 24 q^{56} + 36 q^{57} + 8 q^{58} - 9 q^{59} + 27 q^{60} + 20 q^{61} - 128 q^{62} + 36 q^{63} - 36 q^{64} + 40 q^{65} - 38 q^{67} + 33 q^{68} + 106 q^{69} - 18 q^{70} - 50 q^{71} - 42 q^{72} + 14 q^{73} + q^{74} - 16 q^{75} + 96 q^{76} - 100 q^{78} - 11 q^{79} - 18 q^{80} + 12 q^{81} - 24 q^{82} - 104 q^{83} + 44 q^{84} - 32 q^{85} + 2 q^{86} - 48 q^{87} - 10 q^{89} - 42 q^{90} - 14 q^{91} + 80 q^{92} - 13 q^{93} + 18 q^{94} + 8 q^{95} - 7 q^{96} + 46 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9 - 14 * q^10 - 18 * q^12 + 4 * q^13 + 22 * q^14 + 16 * q^15 + 20 * q^16 + 12 * q^17 + 41 * q^18 + 24 * q^19 + 40 * q^20 + 2 * q^21 - 14 * q^23 + 7 * q^24 - 29 * q^25 - 5 * q^26 + 4 * q^27 + 24 * q^28 + 30 * q^29 - 6 * q^30 + 3 * q^31 + 30 * q^32 + 48 * q^34 - 6 * q^35 - 46 * q^36 - 11 * q^37 + 12 * q^38 + 32 * q^39 + 20 * q^40 - 10 * q^41 + 45 * q^42 + 72 * q^43 - 16 * q^45 + 17 * q^46 + 3 * q^47 - 62 * q^48 + 35 * q^49 - 6 * q^50 - 28 * q^51 - 2 * q^52 - 42 * q^53 - 34 * q^54 + 24 * q^56 + 36 * q^57 + 8 * q^58 - 9 * q^59 + 27 * q^60 + 20 * q^61 - 128 * q^62 + 36 * q^63 - 36 * q^64 + 40 * q^65 - 38 * q^67 + 33 * q^68 + 106 * q^69 - 18 * q^70 - 50 * q^71 - 42 * q^72 + 14 * q^73 + q^74 - 16 * q^75 + 96 * q^76 - 100 * q^78 - 11 * q^79 - 18 * q^80 + 12 * q^81 - 24 * q^82 - 104 * q^83 + 44 * q^84 - 32 * q^85 + 2 * q^86 - 48 * q^87 - 10 * q^89 - 42 * q^90 - 14 * q^91 + 80 * q^92 - 13 * q^93 + 18 * q^94 + 8 * q^95 - 7 * q^96 + 46 * q^97 - 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.24721	−	0.265102i	0.881909	−	0.187456i	0.255368	−	0.966844i	$-0.417803\pi$
$2$	1.24721	−	0.265102i	0.881909	−	0.187456i	0.626541	+	0.779388i	$0.284470\pi$
$3$	0.0145619	+	0.138547i	0.00840730	+	0.0799901i	0.997921	−	0.0644488i	$-0.0205289\pi$
$3$	0.0145619	+	0.138547i	0.00840730	+	0.0799901i	−0.989514	+	0.144439i	$0.953862\pi$
$4$	−0.341843	+	0.152198i	−0.170921	+	0.0760991i
$5$	0.792967	−	0.880679i	0.354626	−	0.393852i	−0.539266	−	0.842136i	$-0.681298\pi$
$5$	0.792967	−	0.880679i	0.354626	−	0.393852i	0.893891	+	0.448284i	$0.147965\pi$
$6$	0.0548908	+	0.168936i	0.0224091	+	0.0689680i
$7$	−1.98226	+	1.75232i	−0.749226	+	0.662315i
$7$	−1.98226	+	1.75232i	−0.749226	+	0.662315i
$8$	−2.44911	+	1.77938i	−0.865891	+	0.629107i
$9$	2.91546	−	0.619700i	0.971820	−	0.206567i
$10$	0.755525	−	1.30861i	0.238918	−	0.413818i
$11$		0			0
$11$		0			0
$12$	−0.0260644	−	0.0451450i	−0.00752416	−	0.0130322i
$13$	−1.39908	+	4.30591i	−0.388034	+	1.19425i	0.546221	+	0.837641i	$0.316066\pi$
$13$	−1.39908	+	4.30591i	−0.388034	+	1.19425i	−0.934255	+	0.356605i	$0.883934\pi$
$14$	−2.00775	+	2.71101i	−0.536594	+	0.724548i
$15$	0.133562	+	0.0970388i	0.0344857	+	0.0250553i
$16$	−2.08206	+	2.31236i	−0.520515	+	0.578091i
$17$	6.51006	+	1.38375i	1.57892	+	0.335610i	0.912215	−	0.409712i	$-0.134371\pi$
$17$	6.51006	+	1.38375i	1.57892	+	0.335610i	0.666705	+	0.745322i	$0.267704\pi$
$18$	3.47190	−	1.54579i	0.818335	−	0.364346i
$19$	2.78166	+	1.23847i	0.638156	+	0.284125i	0.700198	−	0.713948i	$-0.253095\pi$
$19$	2.78166	+	1.23847i	0.638156	+	0.284125i	−0.0620428	+	0.998073i	$0.519762\pi$
$20$	−0.137032	+	0.421742i	−0.0306413	+	0.0943043i
$21$	−0.271644	−	0.249120i	−0.0592776	−	0.0543624i
$22$		0			0
$23$	1.89164	+	3.27641i	0.394434	+	0.683179i	0.993029	−	0.117873i	$-0.0376075\pi$
$23$	1.89164	+	3.27641i	0.394434	+	0.683179i	−0.598595	+	0.801052i	$0.704274\pi$
$24$	−0.282192	−	0.313405i	−0.0576021	−	0.0639736i
$25$	0.375843	+	3.57591i	0.0751687	+	0.715182i
$26$	−0.603431	+	5.74127i	−0.118343	+	1.12596i
$27$	0.257460	+	0.792379i	0.0495481	+	0.152493i
$28$	0.410923	−	0.900715i	0.0776571	−	0.170219i
$29$	3.38711	+	2.46088i	0.628971	+	0.456974i	0.856043	−	0.516904i	$-0.172916\pi$
$29$	3.38711	+	2.46088i	0.628971	+	0.456974i	−0.227073	+	0.973878i	$0.572916\pi$
$30$	0.192305	+	0.0856198i	0.0351100	+	0.0156320i
$31$	−4.59366	−	5.10178i	−0.825046	−	0.916306i	0.172592	−	0.984993i	$-0.444786\pi$
$31$	−4.59366	−	5.10178i	−0.825046	−	0.916306i	−0.997638	+	0.0686871i	$0.978119\pi$
$32$	1.04351	−	1.80742i	0.184469	−	0.319510i
$33$		0			0
$34$	8.48623			1.45538
$35$	−0.0286387	+	3.13527i	−0.00484083	+	0.529957i
$36$	−0.902311	+	0.655567i	−0.150385	+	0.109261i
$37$	0.354621	−	3.37400i	0.0582994	−	0.554681i	−0.925919	−	0.377722i	$-0.876707\pi$
$37$	0.354621	−	3.37400i	0.0582994	−	0.554681i	0.984218	−	0.176959i	$-0.0566260\pi$
$38$	3.79763	+	0.807210i	0.616056	+	0.130947i
$39$	−0.616944	−	0.131136i	−0.0987901	−	0.0209985i
$40$	−0.374998	+	3.56787i	−0.0592924	+	0.564130i
$41$	−7.57505	+	5.50359i	−1.18302	+	0.859517i	−0.992509	−	0.122168i	$-0.961015\pi$
$41$	−7.57505	+	5.50359i	−1.18302	+	0.859517i	−0.190514	+	0.981684i	$0.561015\pi$
$42$	−0.404839	−	0.238691i	−0.0624680	−	0.0368307i
$43$	−0.848738			−0.129431			−0.0647157	−	0.997904i	$-0.520614\pi$
$43$	−0.848738			−0.129431			−0.0647157	+	0.997904i	$0.520614\pi$
$44$		0			0
$45$	1.76611	−	3.05899i	0.263276	−	0.456007i
$46$	3.22785	+	3.58489i	0.475920	+	0.528563i
$47$	−4.99454	−	2.22371i	−0.728528	−	0.324362i	0.00874021	−	0.999962i	$-0.497218\pi$
$47$	−4.99454	−	2.22371i	−0.728528	−	0.324362i	−0.737268	+	0.675600i	$0.763885\pi$
$48$	−0.350690	−	0.254791i	−0.0506177	−	0.0367759i
$49$	0.858747	−	6.94713i	0.122678	−	0.992447i
$50$	1.41674	+	4.36027i	0.200357	+	0.616635i
$51$	−0.0969164	+	0.922098i	−0.0135710	+	0.129120i
$52$	−0.177088	−	1.68488i	−0.0245577	−	0.233651i
$53$	2.64002	+	2.93204i	0.362635	+	0.402746i	0.896658	−	0.442723i	$-0.145987\pi$
$53$	2.64002	+	2.93204i	0.362635	+	0.402746i	−0.534024	+	0.845469i	$0.679321\pi$
$54$	0.531167	+	0.920009i	0.0722827	+	0.125197i
$55$		0			0
$56$	1.73674	−	7.81883i	0.232081	−	1.04484i
$57$	−0.131081	+	0.403424i	−0.0173620	+	0.0534349i
$58$	4.87682	+	2.17130i	0.640357	+	0.285105i
$59$	2.60081	−	1.15795i	0.338596	−	0.150753i	−0.230393	−	0.973098i	$-0.574001\pi$
$59$	2.60081	−	1.15795i	0.338596	−	0.150753i	0.568989	+	0.822345i	$0.307335\pi$
$60$	−0.0604264	−	0.0128440i	−0.00780102	−	0.00165816i
$61$	−1.64430	+	1.82618i	−0.210531	+	0.233818i	−0.839157	−	0.543890i	$-0.816951\pi$
$61$	−1.64430	+	1.82618i	−0.210531	+	0.233818i	0.628626	+	0.777708i	$0.283618\pi$
$62$	−7.08174	−	5.14519i	−0.899382	−	0.653439i
$63$	−4.69330	+	6.33723i	−0.591300	+	0.798416i
$64$	2.74540	−	8.44947i	0.343175	−	1.05618i
$65$	2.68271	+	4.64658i	0.332749	+	0.576338i
$66$		0			0
$67$	−0.264856	+	0.458743i	−0.0323573	+	0.0560444i	−0.881751	−	0.471716i	$-0.843635\pi$
$67$	−0.264856	+	0.458743i	−0.0323573	+	0.0560444i	0.849393	+	0.527760i	$0.176968\pi$
$68$	−2.43602	+	0.517792i	−0.295411	+	0.0627915i
$69$	−0.426391	+	0.309791i	−0.0513315	+	0.0372945i
$70$	0.795449	+	3.91793i	0.0950743	+	0.468282i
$71$	1.01414	+	3.12120i	0.120356	+	0.370418i	0.993026	−	0.117892i	$-0.0376136\pi$
$71$	1.01414	+	3.12120i	0.120356	+	0.370418i	−0.872670	+	0.488310i	$0.837614\pi$
$72$	−6.03760	+	6.70543i	−0.711538	+	0.790242i
$73$	11.6036	−	5.16627i	1.35810	−	0.604666i	0.406967	−	0.913443i	$-0.366586\pi$
$73$	11.6036	−	5.16627i	1.35810	−	0.604666i	0.951134	+	0.308777i	$0.0999198\pi$
$74$	−0.452167	−	4.30208i	−0.0525634	−	0.500107i
$75$	−0.489959	+	0.104144i	−0.0565755	+	0.0120255i
$76$	−1.13938			−0.130696
$77$		0			0
$78$	−0.804222			−0.0910602
$79$	−4.76004	+	1.01178i	−0.535546	+	0.113834i	−0.467742	−	0.883865i	$-0.654933\pi$
$79$	−4.76004	+	1.01178i	−0.535546	+	0.113834i	−0.0678038	+	0.997699i	$0.521599\pi$
$80$	0.385444	+	3.66726i	0.0430940	+	0.410012i
$81$	8.06269	−	3.58974i	0.895854	−	0.398860i
$82$	−7.98864	+	8.87229i	−0.882198	+	0.979780i
$83$	−3.55037	−	10.9269i	−0.389704	−	1.19938i	−0.933010	−	0.359850i	$-0.882828\pi$
$83$	−3.55037	−	10.9269i	−0.389704	−	1.19938i	0.543306	−	0.839535i	$-0.317172\pi$
$84$	0.130775	+	0.0438160i	0.0142687	+	0.00478072i
$85$	6.38090	−	4.63600i	0.692106	−	0.502844i
$86$	−1.05855	+	0.225002i	−0.114147	+	0.0242626i
$87$	−0.291625	+	0.505109i	−0.0312655	+	0.0541534i
$88$		0			0
$89$	−0.926864	−	1.60538i	−0.0982474	−	0.170169i	0.812712	−	0.582666i	$-0.197990\pi$
$89$	−0.926864	−	1.60538i	−0.0982474	−	0.170169i	−0.910959	+	0.412496i	$0.864657\pi$
$90$	1.39176	−	4.28339i	0.146704	−	0.451509i
$91$	−4.77200	−	10.9871i	−0.500242	−	1.15176i
$92$	−1.14531	−	0.832114i	−0.119406	−	0.0867538i
$93$	0.639943	−	0.710729i	0.0663590	−	0.0736992i
$94$	−6.81873	−	1.44937i	−0.703299	−	0.149491i
$95$	3.29646	−	1.46768i	0.338209	−	0.150581i
$96$	0.265608	+	0.118256i	0.0271085	+	0.0120695i
$97$	−0.304405	+	0.936862i	−0.0309076	+	0.0951239i	−0.965320	−	0.261068i	$-0.915925\pi$
$97$	−0.304405	+	0.936862i	−0.0309076	+	0.0951239i	0.934413	+	0.356192i	$0.115925\pi$
$98$	−0.770662	−	8.89217i	−0.0778486	−	0.898244i
$99$		0			0
$100$	−0.672726	−	1.16520i	−0.0672726	−	0.116520i
$101$	0.0596283	+	0.0662240i	0.00593324	+	0.00658953i	0.746104	−	0.665829i	$-0.231922\pi$
$101$	0.0596283	+	0.0662240i	0.00593324	+	0.00658953i	−0.740171	+	0.672419i	$0.765255\pi$
$102$	0.123575	+	1.17574i	0.0122358	+	0.116416i
$103$	1.53256	−	14.5813i	0.151008	−	1.43674i	−0.612258	−	0.790658i	$-0.709739\pi$
$103$	1.53256	−	14.5813i	0.151008	−	1.43674i	0.763266	−	0.646085i	$-0.223595\pi$
$104$	−4.23537	−	13.0351i	−0.415313	−	1.27820i
$105$	−0.434799	+	0.0416876i	−0.0424321	+	0.00406829i
$106$	4.06994	+	2.95699i	0.395308	+	0.287208i
$107$	4.55901	+	2.02980i	0.440736	+	0.196228i	0.615093	−	0.788454i	$-0.289118\pi$
$107$	4.55901	+	2.02980i	0.440736	+	0.196228i	−0.174358	+	0.984682i	$0.555785\pi$
$108$	−0.208609	−	0.231684i	−0.0200734	−	0.0222938i
$109$	−9.32385	+	16.1494i	−0.893063	+	1.54683i	−0.0568784	+	0.998381i	$0.518115\pi$
$109$	−9.32385	+	16.1494i	−0.893063	+	1.54683i	−0.836184	+	0.548449i	$0.815219\pi$
$110$		0			0
$111$	0.472621			0.0448592
$112$	0.0751956	−	8.23216i	0.00710532	−	0.777866i
$113$	−3.08852	+	2.24394i	−0.290543	+	0.211092i	−0.723503	−	0.690321i	$-0.757469\pi$
$113$	−3.08852	+	2.24394i	−0.290543	+	0.211092i	0.432960	+	0.901413i	$0.357469\pi$
$114$	−0.0565360	+	0.537904i	−0.00529508	+	0.0503793i
$115$	4.38547	+	0.932161i	0.408947	+	0.0869245i
$116$	−1.53240	−	0.325722i	−0.142280	−	0.0302425i
$117$	−1.41057	+	13.4207i	−0.130408	+	1.24075i
$118$	2.93677	−	2.13369i	0.270352	−	0.196422i
$119$	−15.3294	+	8.66473i	−1.40525	+	0.794295i
$120$	−0.499778			−0.0456233
$121$		0			0
$122$	−1.56666	+	2.71353i	−0.141838	+	0.245671i
$123$	−0.872813	−	0.969357i	−0.0786989	−	0.0874040i
$124$	2.34679	+	1.04486i	0.210748	+	0.0938310i
$125$	8.24097	+	5.98742i	0.737095	+	0.535531i
$126$	−4.17351	+	9.14805i	−0.371806	+	0.814973i
$127$	1.04258	+	3.20872i	0.0925137	+	0.284728i	0.986598	−	0.163171i	$-0.0521723\pi$
$127$	1.04258	+	3.20872i	0.0925137	+	0.284728i	−0.894084	+	0.447899i	$0.852172\pi$
$128$	0.747802	−	7.11486i	0.0660970	−	0.628871i
$129$	−0.0123592	−	0.117590i	−0.00108817	−	0.0103532i
$130$	4.57771	+	5.08406i	0.401492	+	0.445902i
$131$	−2.44042	−	4.22693i	−0.213221	−	0.369309i	0.739500	−	0.673157i	$-0.235062\pi$
$131$	−2.44042	−	4.22693i	−0.213221	−	0.369309i	−0.952721	+	0.303848i	$0.901729\pi$
$132$		0			0
$133$	−7.68418	+	2.41937i	−0.666303	+	0.209786i
$134$	−0.208716	+	0.642362i	−0.0180303	+	0.0554916i
$135$	0.901989	+	0.401591i	0.0776308	+	0.0345635i
$136$	−18.4061	+	8.19491i	−1.57831	+	0.702708i
$137$	8.06156	+	1.71354i	0.688746	+	0.146397i	0.538973	−	0.842323i	$-0.318812\pi$
$137$	8.06156	+	1.71354i	0.688746	+	0.146397i	0.149773	+	0.988720i	$0.452146\pi$
$138$	−0.449672	+	0.499411i	−0.0382786	+	0.0425127i
$139$	−18.0696	−	13.1283i	−1.53264	−	1.11353i	−0.954747	−	0.297419i	$-0.903874\pi$
$139$	−18.0696	−	13.1283i	−1.53264	−	1.11353i	−0.577895	−	0.816111i	$-0.696126\pi$
$140$	−0.467392	−	1.07613i	−0.0395019	−	0.0909494i
$141$	0.235358	−	0.724359i	0.0198208	−	0.0610020i
$142$	2.09228	+	3.62393i	0.175580	+	0.304114i
$143$		0			0
$144$	−4.63720	+	8.03186i	−0.386433	+	0.669322i
$145$	4.85311	−	1.03156i	0.403029	−	0.0856665i
$146$	13.1025	−	9.51955i	1.08437	−	0.787844i
$147$	0.975008	+	0.0178137i	0.0804173	+	0.00146925i
$148$	0.392291	+	1.20735i	0.0322461	+	0.0992434i
$149$	5.40988	−	6.00828i	0.443195	−	0.492218i	−0.479612	−	0.877481i	$-0.659223\pi$
$149$	5.40988	−	6.00828i	0.443195	−	0.492218i	0.922807	+	0.385263i	$0.125889\pi$
$150$	−0.583471	+	0.259778i	−0.0476402	+	0.0212108i
$151$	−0.617230	−	5.87255i	−0.0502295	−	0.477902i	−0.990504	−	0.137484i	$-0.956098\pi$
$151$	−0.617230	−	5.87255i	−0.0502295	−	0.477902i	0.940274	−	0.340417i	$-0.110568\pi$
$152$	−9.01630	+	1.91647i	−0.731318	+	0.155446i
$153$	19.8373			1.60375
$154$		0			0
$155$	−8.13565			−0.653471
$156$	0.230856	−	0.0490700i	0.0184833	−	0.00392875i
$157$	−1.74688	−	16.6205i	−0.139416	−	1.32646i	−0.810789	−	0.585339i	$-0.800961\pi$
$157$	−1.74688	−	16.6205i	−0.139416	−	1.32646i	0.671372	−	0.741120i	$-0.265705\pi$
$158$	−5.66853	+	2.52379i	−0.450964	+	0.200782i
$159$	−0.367781	+	0.408463i	−0.0291670	+	0.0323932i
$160$	−0.764284	−	2.35223i	−0.0604220	−	0.185960i
$161$	−9.49105	−	3.17996i	−0.747999	−	0.250616i
$162$	9.10420	−	6.61459i	0.715294	−	0.519691i
$163$	23.8763	−	5.07507i	1.87014	−	0.397510i	0.874048	−	0.485840i	$-0.161486\pi$
$163$	23.8763	−	5.07507i	1.87014	−	0.397510i	0.996091	+	0.0883299i	$0.0281530\pi$
$164$	1.75184	−	3.03427i	0.136795	−	0.236937i
$165$		0			0
$166$	−7.32480	−	12.6869i	−0.568515	−	0.984696i
$167$	3.52216	−	10.8401i	0.272553	−	0.838832i	−0.717304	−	0.696761i	$-0.754624\pi$
$167$	3.52216	−	10.8401i	0.272553	−	0.838832i	0.989856	−	0.142071i	$-0.0453761\pi$
$168$	1.10857	+	0.126763i	0.0855277	+	0.00977995i
$169$	−6.06625	−	4.40739i	−0.466635	−	0.339030i
$170$	6.72930	−	7.47364i	0.516114	−	0.573202i
$171$	8.87729	+	1.88693i	0.678863	+	0.144297i
$172$	0.290135	−	0.129176i	0.0221226	−	0.00984961i
$173$	2.52860	+	1.12581i	0.192246	+	0.0855935i	0.500602	−	0.865678i	$-0.333112\pi$
$173$	2.52860	+	1.12581i	0.192246	+	0.0855935i	−0.308356	+	0.951271i	$0.599779\pi$
$174$	−0.229811	+	0.707286i	−0.0174219	+	0.0536192i
$175$	−7.01116	−	6.42980i	−0.529994	−	0.486048i
$176$		0			0
$177$	0.198304	+	0.343472i	0.0149054	+	0.0258169i
$178$	−1.58158	−	1.75652i	−0.118544	−	0.131657i
$179$	1.29715	+	12.3416i	0.0969538	+	0.922454i	0.929580	+	0.368619i	$0.120169\pi$
$179$	1.29715	+	12.3416i	0.0969538	+	0.922454i	−0.832627	+	0.553835i	$0.813164\pi$
$180$	−0.138158	+	1.31449i	−0.0102977	+	0.0979763i
$181$	−5.00602	−	15.4069i	−0.372095	−	1.14519i	−0.945418	−	0.325860i	$-0.894346\pi$
$181$	−5.00602	−	15.4069i	−0.372095	−	1.14519i	0.573323	−	0.819329i	$-0.305654\pi$
$182$	−8.86438	−	12.4381i	−0.657071	−	0.921975i
$183$	−0.276955	−	0.201220i	−0.0204731	−	0.0148746i
$184$	−10.4628	−	4.65835i	−0.771329	−	0.343418i
$185$	−2.69020	−	2.98777i	−0.197788	−	0.219666i
$186$	0.609726	−	1.05608i	0.0447073	−	0.0774353i
$187$		0			0
$188$	2.04579			0.149205
$189$	−1.89886	−	1.11955i	−0.138121	−	0.0814356i
$190$	3.72228	−	2.70440i	0.270043	−	0.196198i
$191$	0.902526	−	8.58696i	0.0653045	−	0.621331i	−0.912102	−	0.409963i	$-0.865542\pi$
$191$	0.902526	−	8.58696i	0.0653045	−	0.621331i	0.977407	−	0.211368i	$-0.0677918\pi$
$192$	1.21063	+	0.257326i	0.0873694	+	0.0185709i
$193$	7.21295	+	1.53316i	0.519199	+	0.110359i	0.460055	−	0.887890i	$-0.347830\pi$
$193$	7.21295	+	1.53316i	0.519199	+	0.110359i	0.0591439	+	0.998249i	$0.481163\pi$
$194$	−0.131292	+	1.24916i	−0.00942622	+	0.0896844i
$195$	−0.604705	+	0.439344i	−0.0433038	+	0.0314620i
$196$	0.763783	+	2.50552i	0.0545559	+	0.178966i
$197$	−9.94302			−0.708411			−0.354205	−	0.935168i	$-0.615249\pi$
$197$	−9.94302			−0.708411			−0.354205	+	0.935168i	$0.615249\pi$
$198$		0			0
$199$	−8.78374	+	15.2139i	−0.622663	+	1.07848i	0.366325	+	0.930487i	$0.380616\pi$
$199$	−8.78374	+	15.2139i	−0.622663	+	1.07848i	−0.988988	+	0.147997i	$0.952717\pi$
$200$	−7.28339	−	8.08903i	−0.515014	−	0.571981i
$201$	−0.0674143	−	0.0300148i	−0.00475504	−	0.00211708i
$202$	0.0919250	+	0.0667874i	0.00646782	+	0.00469915i
$203$	−11.0264	+	1.05719i	−0.773902	+	0.0742000i
$204$	−0.107211	−	0.329963i	−0.00750630	−	0.0231020i
$205$	−1.15986	+	11.0353i	−0.0810083	+	0.770742i
$206$	−1.95412	−	18.5923i	−0.136150	−	1.29538i
$207$	7.54539	+	8.38000i	0.524441	+	0.582450i
$208$	−7.04388	−	12.2004i	−0.488405	−	0.845942i
$209$		0			0
$210$	−0.531233	+	0.167259i	−0.0366586	+	0.0115420i
$211$	−0.164385	+	0.505926i	−0.0113167	+	0.0348294i	−0.956555	−	0.291550i	$-0.905829\pi$
$211$	−0.164385	+	0.505926i	−0.0113167	+	0.0348294i	0.945239	+	0.326380i	$0.105829\pi$
$212$	−1.34872	−	0.600490i	−0.0926306	−	0.0412418i
$213$	−0.417665	+	0.185956i	−0.0286179	+	0.0127415i
$214$	6.22413	+	1.32298i	0.425473	+	0.0904371i
$215$	−0.673021	+	0.747466i	−0.0458997	+	0.0509768i
$216$	−2.04049	−	1.48250i	−0.138838	−	0.100872i
$217$	18.0458	+	2.06351i	1.22503	+	0.140080i
$218$	−7.34754	+	22.6134i	−0.497638	+	1.53157i
$219$	0.884741	+	1.53242i	0.0597852	+	0.103551i
$220$		0			0
$221$	−15.0664	+	26.0958i	−1.01348	+	1.75539i
$222$	0.589456	−	0.125293i	0.0395617	−	0.00840910i
$223$	14.8180	−	10.7659i	0.992287	−	0.720939i	0.0318661	−	0.999492i	$-0.489855\pi$
$223$	14.8180	−	10.7659i	0.992287	−	0.720939i	0.960421	+	0.278554i	$0.0898550\pi$
$224$	1.09866	+	5.41136i	0.0734071	+	0.361561i
$225$	3.31175	+	10.1925i	0.220783	+	0.679501i
$226$	−3.25715	+	3.61743i	−0.216662	+	0.240628i
$227$	8.71439	−	3.87990i	0.578394	−	0.257518i	−0.0966212	−	0.995321i	$-0.530804\pi$
$227$	8.71439	−	3.87990i	0.578394	−	0.257518i	0.675016	+	0.737803i	$0.264137\pi$
$228$	−0.0165915	−	0.157858i	−0.00109880	−	0.0104544i
$229$	1.76150	−	0.374419i	0.116403	−	0.0247423i	−0.149342	−	0.988786i	$-0.547715\pi$
$229$	1.76150	−	0.374419i	0.116403	−	0.0247423i	0.265745	+	0.964043i	$0.414382\pi$
$230$	5.71671			0.376949
$231$		0			0
$232$	−12.6743			−0.832105
$233$	19.5175	−	4.14856i	1.27863	−	0.271781i	0.481959	−	0.876194i	$-0.339925\pi$
$233$	19.5175	−	4.14856i	1.27863	−	0.271781i	0.796672	+	0.604412i	$0.206592\pi$
$234$	1.79858	+	17.1124i	0.117577	+	1.11867i
$235$	−5.91888	+	2.63525i	−0.386105	+	0.171905i
$236$	−0.712828	+	0.791676i	−0.0464012	+	0.0515337i
$237$	−0.209494	−	0.644755i	−0.0136081	−	0.0418814i
$238$	−16.8220	+	14.8706i	−1.09041	+	0.963917i
$239$	−3.13293	+	2.27621i	−0.202653	+	0.147236i	−0.684483	−	0.729029i	$-0.739972\pi$
$239$	−3.13293	+	2.27621i	−0.202653	+	0.147236i	0.481831	+	0.876264i	$0.339972\pi$
$240$	−0.502474	+	0.106804i	−0.0324346	+	0.00689418i
$241$	−1.31079	+	2.27036i	−0.0844356	+	0.146247i	−0.905151	−	0.425091i	$-0.860242\pi$
$241$	−1.31079	+	2.27036i	−0.0844356	+	0.146247i	0.820715	+	0.571338i	$0.193575\pi$
$242$		0			0
$243$	1.86449	+	3.22939i	0.119607	+	0.207166i
$244$	0.284150	−	0.874524i	0.0181908	−	0.0559857i
$245$	−5.43723	−	6.26512i	−0.347372	−	0.400264i
$246$	−1.34556	−	0.977605i	−0.0857896	−	0.0623298i
$247$	−9.22451	+	10.2449i	−0.586941	+	0.651864i
$248$	20.3284	+	4.32093i	1.29085	+	0.274379i
$249$	1.46219	−	0.651009i	0.0926626	−	0.0412560i
$250$	11.8655	+	5.28285i	0.750439	+	0.334117i
$251$	−2.94543	+	9.06510i	−0.185914	+	0.572184i	−0.999963	−	0.00861205i	$-0.997259\pi$
$251$	−2.94543	+	9.06510i	−0.185914	+	0.572184i	0.814049	+	0.580796i	$0.197259\pi$
$252$	0.639855	−	2.88065i	0.0403071	−	0.181464i
$253$		0			0
$254$	2.15095	+	3.72555i	0.134963	+	0.233762i
$255$	0.735221	+	0.816546i	0.0460413	+	0.0511341i
$256$	0.903823	+	8.59930i	0.0564889	+	0.537456i
$257$	−2.38630	+	22.7041i	−0.148853	+	1.41624i	0.623884	+	0.781517i	$0.285554\pi$
$257$	−2.38630	+	22.7041i	−0.148853	+	1.41624i	−0.772737	+	0.634726i	$0.781113\pi$
$258$	−0.0465879	−	0.143383i	−0.00290044	−	0.00892663i
$259$	5.20937	+	7.30956i	0.323694	+	0.454194i
$260$	−1.62426	−	1.18010i	−0.100733	−	0.0731865i
$261$	11.4000	+	5.07560i	0.705642	+	0.314172i
$262$	−4.16428	−	4.62490i	−0.257270	−	0.285728i
$263$	−3.96286	+	6.86387i	−0.244360	+	0.423244i	−0.961952	−	0.273220i	$-0.911911\pi$
$263$	−3.96286	+	6.86387i	−0.244360	+	0.423244i	0.717591	+	0.696464i	$0.245245\pi$
$264$		0			0
$265$	4.67563			0.287222
$266$	−8.94239	+	5.05455i	−0.548293	+	0.309914i
$267$	0.208923	−	0.151791i	0.0127859	−	0.00928948i
$268$	0.0207190	−	0.197129i	0.00126562	−	0.0120415i
$269$	10.5509	+	2.24267i	0.643303	+	0.136738i	0.518000	−	0.855380i	$-0.326677\pi$
$269$	10.5509	+	2.24267i	0.643303	+	0.136738i	0.125302	+	0.992119i	$0.460010\pi$
$270$	1.23143	+	0.261749i	0.0749424	+	0.0159295i
$271$	−0.346206	+	3.29393i	−0.0210305	+	0.200092i	−0.999992	−	0.00395214i	$-0.998742\pi$
$271$	−0.346206	+	3.29393i	−0.0210305	+	0.200092i	0.978962	+	0.204044i	$0.0654087\pi$
$272$	−16.7541	+	12.1726i	−1.01587	+	0.738070i
$273$	1.45274	−	0.821139i	0.0879237	−	0.0496976i
$274$	10.5087			0.634854
$275$		0			0
$276$	0.0986090	−	0.170796i	0.00593556	−	0.0102807i
$277$	5.44465	+	6.04690i	0.327138	+	0.363323i	0.884168	−	0.467169i	$-0.154726\pi$
$277$	5.44465	+	6.04690i	0.327138	+	0.363323i	−0.557031	+	0.830492i	$0.688059\pi$
$278$	−26.0169	−	11.5835i	−1.56039	−	0.694730i
$279$	−16.5542	−	12.0273i	−0.991074	−	0.720058i
$280$	−5.50870	−	7.72958i	−0.329208	−	0.461931i
$281$	−4.55889	−	14.0308i	−0.271961	−	0.837009i	−0.990008	−	0.141014i	$-0.954964\pi$
$281$	−4.55889	−	14.0308i	−0.271961	−	0.837009i	0.718047	−	0.695995i	$-0.245036\pi$
$282$	0.101512	−	0.965820i	0.00604494	−	0.0575138i
$283$	−0.911767	−	8.67488i	−0.0541989	−	0.515668i	−0.987618	−	0.156880i	$-0.949857\pi$
$283$	−0.911767	−	8.67488i	−0.0541989	−	0.515668i	0.933419	−	0.358789i	$-0.116810\pi$
$284$	−0.821716	−	0.912608i	−0.0487599	−	0.0541533i
$285$	0.251345	+	0.435342i	0.0148884	+	0.0257874i
$286$		0			0
$287$	5.37169	−	24.1835i	0.317081	−	1.42751i
$288$	1.92227	−	5.91613i	0.113271	−	0.348611i
$289$	24.9358	+	11.1021i	1.46681	+	0.653066i
$290$	5.77937	−	2.57314i	0.339376	−	0.151100i
$291$	−0.134232	−	0.0285319i	−0.00786882	−	0.00167257i
$292$	−3.18032	+	3.53210i	−0.186114	+	0.206700i
$293$	−19.6847	−	14.3018i	−1.14999	−	0.835518i	−0.161512	−	0.986871i	$-0.551637\pi$
$293$	−19.6847	−	14.3018i	−1.14999	−	0.835518i	−0.988480	+	0.151352i	$0.951637\pi$
$294$	1.22076	−	0.236259i	0.0711962	−	0.0137789i
$295$	1.04257	−	3.20869i	0.0607007	−	0.186817i
$296$	5.13512	+	8.89429i	0.298473	+	0.516970i
$297$		0			0
$298$	5.15444	−	8.92775i	0.298589	−	0.517171i
$299$	−16.7545	+	3.56128i	−0.968937	+	0.205954i
$300$	0.151638	−	0.110172i	0.00875483	−	0.00636076i
$301$	1.68242	−	1.48726i	0.0969733	−	0.0857243i
$302$	−2.32664	−	7.16067i	−0.133883	−	0.412050i
$303$	−0.00830683	+	0.00922567i	−0.000477215	+	0.000530001i
$304$	−8.65538	+	3.85362i	−0.496420	+	0.221020i
$305$	0.304402	+	2.89620i	0.0174300	+	0.165836i
$306$	24.7413	−	5.25892i	1.41436	−	0.300632i
$307$	−9.84856			−0.562087			−0.281044	−	0.959695i	$-0.590681\pi$
$307$	−9.84856			−0.562087			−0.281044	+	0.959695i	$0.590681\pi$
$308$		0			0
$309$	2.04252			0.116195
$310$	−10.1468	+	2.15678i	−0.576302	+	0.122497i
$311$	−0.0859393	−	0.817658i	−0.00487317	−	0.0463651i	0.991815	−	0.127683i	$-0.0407539\pi$
$311$	−0.0859393	−	0.817658i	−0.00487317	−	0.0463651i	−0.996688	+	0.0813175i	$0.974087\pi$
$312$	1.74430	−	0.776614i	0.0987518	−	0.0439671i
$313$	4.26973	−	4.74201i	0.241339	−	0.268034i	−0.610291	−	0.792177i	$-0.708948\pi$
$313$	4.26973	−	4.74201i	0.241339	−	0.268034i	0.851630	+	0.524143i	$0.175614\pi$
$314$	−6.58485	−	20.2661i	−0.371605	−	1.14368i
$315$	1.85943	+	9.15850i	0.104767	+	0.516023i
$316$	1.47319	−	1.07034i	0.0828736	−	0.0602112i
$317$	−8.01804	+	1.70429i	−0.450338	+	0.0957223i	−0.427497	−	0.904017i	$-0.640605\pi$
$317$	−8.01804	+	1.70429i	−0.450338	+	0.0957223i	−0.0228411	+	0.999739i	$0.507271\pi$
$318$	−0.350415	+	0.606937i	−0.0196503	+	0.0340354i
$319$		0			0
$320$	−5.26426	−	9.11796i	−0.294281	−	0.509710i
$321$	−0.214835	+	0.661194i	−0.0119909	+	0.0369042i
$322$	−12.6803	−	1.44998i	−0.706647	−	0.0808039i
$323$	16.3950	+	11.9117i	0.912242	+	0.662782i
$324$	−2.20982	+	2.45425i	−0.122768	+	0.136347i
$325$	−15.9234	−	3.38462i	−0.883271	−	0.187745i
$326$	28.4333	−	12.6593i	1.57478	−	0.701136i
$327$	−2.37322	−	1.05663i	−0.131239	−	0.0584315i
$328$	8.75912	−	26.9578i	0.483642	−	1.48850i
$329$	13.7971	−	4.34404i	0.760661	−	0.239495i
$330$		0			0
$331$	11.3038	+	19.5788i	0.621313	+	1.07615i	0.989241	+	0.146292i	$0.0467339\pi$
$331$	11.3038	+	19.5788i	0.621313	+	1.07615i	−0.367928	+	0.929854i	$0.619933\pi$
$332$	2.87672	+	3.19493i	0.157881	+	0.175344i
$333$	−1.05698	−	10.0565i	−0.0579222	−	0.551093i
$334$	1.51913	−	14.4536i	0.0831233	−	0.790865i
$335$	0.193984	+	0.597021i	0.0105985	+	0.0326187i
$336$	1.14164	−	0.109457i	0.0622813	−	0.00597139i
$337$	20.0270	+	14.5504i	1.09094	+	0.792613i	0.979557	−	0.201165i	$-0.0644727\pi$
$337$	20.0270	+	14.5504i	1.09094	+	0.792613i	0.111381	+	0.993778i	$0.464473\pi$
$338$	−8.73429	−	3.88876i	−0.475083	−	0.211520i
$339$	−0.355866	−	0.395229i	−0.0193280	−	0.0214659i
$340$	−1.47567	+	2.55594i	−0.0800297	+	0.138615i
$341$		0			0
$342$	11.5721			0.625745
$343$	10.4713	+	15.2758i	0.565398	+	0.824818i
$344$	2.07865	−	1.51023i	0.112073	−	0.0814261i
$345$	−0.0652874	+	0.621168i	−0.00351495	+	0.0334425i
$346$	3.45215	+	0.733777i	0.185589	+	0.0394481i
$347$	5.89158	+	1.25230i	0.316277	+	0.0672267i	0.363315	−	0.931666i	$-0.381645\pi$
$347$	5.89158	+	1.25230i	0.316277	+	0.0672267i	−0.0470381	+	0.998893i	$0.514978\pi$
$348$	0.0228131	−	0.217052i	0.00122291	−	0.0116352i
$349$	−16.9933	+	12.3463i	−0.909630	+	0.660885i	−0.940921	−	0.338626i	$-0.890038\pi$
$349$	−16.9933	+	12.3463i	−0.909630	+	0.660885i	0.0312916	+	0.999510i	$0.490038\pi$
$350$	−10.4489	−	6.16063i	−0.558519	−	0.329299i
$351$	−3.77212			−0.201341
$352$		0			0
$353$	13.5755	−	23.5134i	0.722549	−	1.25149i	−0.237426	−	0.971406i	$-0.576304\pi$
$353$	13.5755	−	23.5134i	0.722549	−	1.25149i	0.959975	−	0.280086i	$-0.0903629\pi$
$354$	0.338381	+	0.375810i	0.0179847	+	0.0199741i
$355$	3.55295	+	1.58188i	0.188571	+	0.0839573i
$356$	0.561177	+	0.407719i	0.0297423	+	0.0216090i
$357$	−1.42370	−	1.99767i	−0.0753501	−	0.105728i
$358$	4.88960	+	15.0487i	0.258424	+	0.795346i
$359$	3.62500	−	34.4896i	0.191320	−	1.82029i	−0.305225	−	0.952280i	$-0.598732\pi$
$359$	3.62500	−	34.4896i	0.191320	−	1.82029i	0.496545	−	0.868011i	$-0.334602\pi$
$360$	1.11772	+	10.6344i	0.0589089	+	0.560480i
$361$	−6.50969	−	7.22974i	−0.342615	−	0.380513i
$362$	−10.3280	−	17.8886i	−0.542826	−	0.940202i
$363$		0			0
$364$	3.30349	+	3.02957i	0.173150	+	0.158792i
$365$	4.65147	−	14.3157i	0.243469	−	0.749320i
$366$	−0.398765	−	0.177541i	−0.0208438	−	0.00928024i
$367$	27.2139	−	12.1164i	1.42056	−	0.632472i	0.454486	−	0.890754i	$-0.349823\pi$
$367$	27.2139	−	12.1164i	1.42056	−	0.632472i	0.966070	+	0.258282i	$0.0831563\pi$
$368$	−11.5148	−	2.44754i	−0.600249	−	0.127587i
$369$	−18.6742	+	20.7398i	−0.972138	+	1.07967i
$370$	−4.14731	−	3.01320i	−0.215608	−	0.156649i
$371$	−10.3711	−	1.18592i	−0.538440	−	0.0615698i
$372$	−0.110588	+	0.340356i	−0.00573373	+	0.0176466i
$373$	0.00623341	+	0.0107966i	0.000322754	+	0.000559025i	0.866187	−	0.499720i	$-0.166564\pi$
$373$	0.00623341	+	0.0107966i	0.000322754	+	0.000559025i	−0.865864	+	0.500279i	$0.833231\pi$
$374$		0			0
$375$	−0.709534	+	1.22895i	−0.0366402	+	0.0634627i
$376$	16.1890	−	3.44108i	0.834884	−	0.177460i
$377$	−15.3352	+	11.1416i	−0.789801	+	0.573824i
$378$	−2.66506	−	0.892926i	−0.137076	−	0.0459271i
$379$	6.82987	+	21.0202i	0.350827	+	1.07973i	0.958390	+	0.285462i	$0.0921471\pi$
$379$	6.82987	+	21.0202i	0.350827	+	1.07973i	−0.607563	+	0.794271i	$0.707853\pi$
$380$	−0.903492	+	1.00343i	−0.0463482	+	0.0514748i
$381$	−0.429377	+	0.191171i	−0.0219976	+	0.00979398i
$382$	−1.15079	−	10.9490i	−0.0588793	−	0.560199i
$383$	−27.3919	+	5.82232i	−1.39966	+	0.297507i	−0.845087	−	0.534629i	$-0.820451\pi$
$383$	−27.3919	+	5.82232i	−1.39966	+	0.297507i	−0.554572	+	0.832136i	$0.687118\pi$
$384$	0.996632			0.0508592
$385$		0			0
$386$	9.40249			0.478574
$387$	−2.47446	+	0.525963i	−0.125784	+	0.0267362i
$388$	−0.0385301	−	0.366589i	−0.00195607	−	0.0186107i
$389$	1.55921	−	0.694203i	0.0790549	−	0.0351975i	−0.366828	−	0.930289i	$-0.619556\pi$
$389$	1.55921	−	0.694203i	0.0790549	−	0.0351975i	0.445883	+	0.895091i	$0.352890\pi$
$390$	−0.637721	+	0.708261i	−0.0322923	+	0.0358642i
$391$	7.78091	+	23.9472i	0.393498	+	1.21106i
$392$	10.2584	+	18.5423i	0.518129	+	0.936528i
$393$	0.550092	−	0.399665i	0.0277485	−	0.0201604i
$394$	−12.4010	+	2.63592i	−0.624754	+	0.132796i
$395$	−2.88350	+	4.99437i	−0.145085	+	0.251294i
$396$		0			0
$397$	−6.61778	−	11.4623i	−0.332137	−	0.575278i	0.650794	−	0.759255i	$-0.274436\pi$
$397$	−6.61778	−	11.4623i	−0.332137	−	0.575278i	−0.982931	+	0.183976i	$0.941103\pi$
$398$	−6.92192	+	21.3035i	−0.346964	+	1.06785i
$399$	−0.447092	−	1.02939i	−0.0223826	−	0.0515339i
$400$	−9.05134	−	6.57618i	−0.452567	−	0.328809i
$401$	15.8514	−	17.6048i	0.791581	−	0.879140i	−0.203411	−	0.979094i	$-0.565203\pi$
$401$	15.8514	−	17.6048i	0.791581	−	0.879140i	0.994992	+	0.0999533i	$0.0318693\pi$
$402$	−0.0920366	−	0.0195630i	−0.00459037	−	0.000975713i
$403$	28.3947	−	12.6421i	1.41444	−	0.629749i
$404$	−0.0304627	−	0.0135629i	−0.00151557	−	0.000674777i
$405$	3.23204	−	9.94718i	0.160601	−	0.494280i
$406$	−13.4720	+	4.24166i	−0.668602	+	0.210510i
$407$		0			0
$408$	−1.40341	−	2.43077i	−0.0694790	−	0.120341i
$409$	−7.36604	−	8.18082i	−0.364227	−	0.404515i	0.532978	−	0.846129i	$-0.321073\pi$
$409$	−7.36604	−	8.18082i	−0.364227	−	0.404515i	−0.897205	+	0.441614i	$0.854406\pi$
$410$	1.47891	+	14.0709i	0.0730380	+	0.694910i
$411$	−0.120014	+	1.14186i	−0.00591985	+	0.0563236i
$412$	1.69536	+	5.21778i	0.0835243	+	0.257061i
$413$	−3.12638	+	6.85282i	−0.153839	+	0.337205i
$414$	11.6322	+	8.45130i	0.571692	+	0.415359i
$415$	−12.4384	−	5.53795i	−0.610579	−	0.271847i
$416$	6.32264	+	7.02200i	0.309993	+	0.344282i
$417$	1.55576	−	2.69466i	0.0761860	−	0.131958i
$418$		0			0
$419$	26.6021			1.29960			0.649799	−	0.760106i	$-0.274853\pi$
$419$	26.6021			1.29960			0.649799	+	0.760106i	$0.274853\pi$
$420$	0.142288	−	0.0804262i	0.00694295	−	0.00392440i
$421$	−24.1625	+	17.5551i	−1.17761	+	0.855584i	−0.991900	−	0.127021i	$-0.959458\pi$
$421$	−24.1625	+	17.5551i	−1.17761	+	0.855584i	−0.185710	+	0.982605i	$0.559458\pi$
$422$	−0.0709005	+	0.674574i	−0.00345138	+	0.0328377i
$423$	−15.9394	−	3.38802i	−0.775000	−	0.164731i
$424$	−11.6829	−	2.48328i	−0.567372	−	0.120599i
$425$	−2.50142	+	23.7995i	−0.121337	+	1.15444i
$426$	−0.471617	+	0.342650i	−0.0228499	+	0.0166014i
$427$	0.0593853	−	6.50130i	0.00287386	−	0.314620i
$428$	−1.86739			−0.0902639
$429$		0			0
$430$	−0.641243	+	1.11066i	−0.0309235	+	0.0535610i
$431$	−0.678140	−	0.753150i	−0.0326648	−	0.0362780i	0.726591	−	0.687070i	$-0.241104\pi$
$431$	−0.678140	−	0.753150i	−0.0326648	−	0.0362780i	−0.759256	+	0.650792i	$0.774437\pi$
$432$	−2.36832	−	1.05444i	−0.113946	−	0.0507319i
$433$	10.5268	+	7.64814i	0.505884	+	0.367546i	0.811260	−	0.584686i	$-0.198782\pi$
$433$	10.5268	+	7.64814i	0.505884	+	0.367546i	−0.305376	+	0.952232i	$0.598782\pi$
$434$	23.0539	−	2.21036i	1.10662	−	0.106101i
$435$	0.213590	+	0.657362i	0.0102409	+	0.0315181i
$436$	0.729383	−	6.93962i	0.0349311	−	0.332347i
$437$	1.20414	+	11.4566i	0.0576017	+	0.548043i
$438$	1.50970	+	1.67669i	0.0721364	+	0.0801156i
$439$	14.6142	+	25.3126i	0.697499	+	1.20810i	0.969331	+	0.245759i	$0.0790370\pi$
$439$	14.6142	+	25.3126i	0.697499	+	1.20810i	−0.271832	+	0.962345i	$0.587630\pi$
$440$		0			0
$441$	−1.80149	−	20.7862i	−0.0857853	−	0.989820i
$442$	−11.8729	+	36.5410i	−0.564735	+	1.73808i
$443$	−19.0504	−	8.48180i	−0.905113	−	0.402982i	−0.0992354	−	0.995064i	$-0.531640\pi$
$443$	−19.0504	−	8.48180i	−0.905113	−	0.402982i	−0.805878	+	0.592082i	$0.798306\pi$
$444$	−0.161562	+	0.0719320i	−0.00766739	+	0.00341374i
$445$	−2.14879	−	0.456740i	−0.101863	−	0.0216515i
$446$	15.6271	−	17.3556i	0.739963	−	0.821812i
$447$	0.911207	+	0.662031i	0.0430986	+	0.0313130i
$448$	9.36407	+	21.5599i	0.442411	+	1.01861i
$449$	8.69837	−	26.7708i	0.410501	−	1.26339i	−0.505712	−	0.862702i	$-0.668770\pi$
$449$	8.69837	−	26.7708i	0.410501	−	1.26339i	0.916213	−	0.400691i	$-0.131230\pi$
$450$	6.83250	+	11.8342i	0.322087	+	0.557871i
$451$		0			0
$452$	0.714264	−	1.23714i	0.0335961	−	0.0581902i
$453$	0.804636	−	0.171031i	0.0378051	−	0.00803572i
$454$	9.84009	−	7.14924i	0.461818	−	0.335531i
$455$	−13.4601	−	4.50980i	−0.631021	−	0.211423i
$456$	−0.396816	−	1.22127i	−0.0185826	−	0.0571913i
$457$	9.56086	−	10.6184i	0.447238	−	0.496709i	−0.476798	−	0.879013i	$-0.658203\pi$
$457$	9.56086	−	10.6184i	0.447238	−	0.496709i	0.924036	+	0.382304i	$0.124869\pi$
$458$	2.09770	−	0.933957i	0.0980191	−	0.0436409i
$459$	0.579618	+	5.51469i	0.0270542	+	0.257404i
$460$	−1.64101	+	0.348808i	−0.0765127	+	0.0162633i
$461$	21.8340			1.01691			0.508456	−	0.861088i	$-0.330217\pi$
$461$	21.8340			1.01691			0.508456	+	0.861088i	$0.330217\pi$
$462$		0			0
$463$	23.2851			1.08215			0.541074	−	0.840975i	$-0.318018\pi$
$463$	23.2851			1.08215			0.541074	+	0.840975i	$0.318018\pi$
$464$	−12.7426	+	2.70853i	−0.591562	+	0.125740i
$465$	−0.118470	−	1.12717i	−0.00549393	−	0.0522712i
$466$	23.2425	−	10.3482i	1.07669	−	0.479373i
$467$	−12.5711	+	13.9616i	−0.581722	+	0.646068i	−0.960124	−	0.279574i	$-0.909807\pi$
$467$	−12.5711	+	13.9616i	−0.581722	+	0.646068i	0.378402	+	0.925641i	$0.376474\pi$
$468$	−1.56041	−	4.80246i	−0.0721302	−	0.221994i
$469$	−0.278851	−	1.37346i	−0.0128762	−	0.0634206i
$470$	−6.68346	+	4.85582i	−0.308285	+	0.223982i
$471$	2.27728	−	0.484051i	0.104931	−	0.0223039i
$472$	−4.30922	+	7.46378i	−0.198348	+	0.343549i
$473$		0			0
$474$	−0.432208	−	0.748607i	−0.0198520	−	0.0343846i
$475$	−3.38320	+	10.4124i	−0.155232	+	0.477755i
$476$	3.92150	−	5.29509i	0.179742	−	0.242700i
$477$	9.51385	+	6.91222i	0.435609	+	0.316489i
$478$	−3.30399	+	3.66945i	−0.151121	+	0.167837i
$479$	−27.8884	−	5.92786i	−1.27425	−	0.270851i	−0.479370	−	0.877613i	$-0.659135\pi$
$479$	−27.8884	−	5.92786i	−1.27425	−	0.270851i	−0.794884	+	0.606762i	$0.792468\pi$
$480$	0.314764	−	0.140142i	0.0143670	−	0.00639658i
$481$	14.0320	+	6.24744i	0.639804	+	0.284859i
$482$	−1.03295	+	3.17911i	−0.0470498	+	0.144804i
$483$	0.302367	−	1.36126i	0.0137582	−	0.0619396i
$484$		0			0
$485$	0.583691	+	1.01098i	0.0265041	+	0.0459064i
$486$	3.18153	+	3.53344i	0.144317	+	0.160280i
$487$	2.56663	+	24.4199i	0.116305	+	1.10657i	0.884560	+	0.466426i	$0.154459\pi$
$487$	2.56663	+	24.4199i	0.116305	+	1.10657i	−0.768255	+	0.640144i	$0.778875\pi$
$488$	0.777597	−	7.39834i	0.0352002	−	0.334907i
$489$	1.05082	+	3.23409i	0.0475197	+	0.146251i
$490$	−8.44225	−	6.37249i	−0.381382	−	0.287880i
$491$	−18.4358	−	13.3944i	−0.831995	−	0.604480i	0.0881280	−	0.996109i	$-0.471912\pi$
$491$	−18.4358	−	13.3944i	−0.831995	−	0.604480i	−0.920123	+	0.391629i	$0.871912\pi$
$492$	0.445899	+	0.198527i	0.0201027	+	0.00895029i
$493$	18.6450	+	20.7074i	0.839730	+	0.932614i
$494$	−8.78894	+	15.2229i	−0.395433	+	0.684911i
$495$		0			0
$496$	21.3615			0.959158
$497$	−7.47963	−	4.40995i	−0.335507	−	0.197813i
$498$	1.65107	−	1.19957i	0.0739863	−	0.0537542i
$499$	−3.53356	+	33.6196i	−0.158184	+	1.50502i	0.571141	+	0.820852i	$0.306501\pi$
$499$	−3.53356	+	33.6196i	−0.158184	+	1.50502i	−0.729325	+	0.684167i	$0.760166\pi$
$500$	−3.72839	−	0.792493i	−0.166739	−	0.0354414i
$501$	1.55315	+	0.330132i	0.0693897	+	0.0147492i
$502$	−1.27038	+	12.0869i	−0.0567001	+	0.539465i
$503$	6.41293	−	4.65927i	0.285938	−	0.207746i	−0.435565	−	0.900157i	$-0.643451\pi$
$503$	6.41293	−	4.65927i	0.285938	−	0.207746i	0.721503	+	0.692411i	$0.243451\pi$
$504$	0.218053	−	23.8717i	0.00971287	−	1.06333i
$505$	0.105605			0.00469938
$506$		0			0
$507$	0.522295	−	0.904641i	0.0231959	−	0.0401765i
$508$	−0.844759	−	0.938200i	−0.0374801	−	0.0416259i
$509$	32.2003	+	14.3365i	1.42725	+	0.635454i	0.967564	−	0.252625i	$-0.0812939\pi$
$509$	32.2003	+	14.3365i	1.42725	+	0.635454i	0.459690	+	0.888080i	$0.347961\pi$
$510$	1.13344	+	0.823493i	0.0501896	+	0.0364649i
$511$	−13.9485	+	30.5742i	−0.617045	+	1.35252i
$512$	7.82840	+	24.0933i	0.345969	+	1.06478i
$513$	−0.265176	+	2.52298i	−0.0117078	+	0.111392i
$514$	3.04270	+	28.9494i	0.134208	+	1.27690i
$515$	−11.6262	−	12.9122i	−0.512312	−	0.568980i
$516$	0.0221219	+	0.0383163i	0.000973862	+	0.00168678i
$517$		0			0
$518$	8.43495	+	7.73553i	0.370610	+	0.339880i
$519$	−0.119156	+	0.366724i	−0.00523037	+	0.0160974i
$520$	−14.8383	−	6.60643i	−0.650702	−	0.289711i
$521$	−8.28606	+	3.68919i	−0.363019	+	0.161626i	−0.580137	−	0.814519i	$-0.697001\pi$
$521$	−8.28606	+	3.68919i	−0.363019	+	0.161626i	0.217118	+	0.976145i	$0.430334\pi$
$522$	15.5637	+	3.30817i	0.681205	+	0.144795i
$523$	7.36043	−	8.17459i	0.321849	−	0.357450i	−0.560409	−	0.828216i	$-0.689356\pi$
$523$	7.36043	−	8.17459i	0.321849	−	0.357450i	0.882258	+	0.470766i	$0.156023\pi$
$524$	1.47757	+	1.07352i	0.0645480	+	0.0468969i
$525$	0.788734	−	1.06501i	0.0344232	−	0.0464806i
$526$	−3.12288	+	9.61124i	−0.136164	+	0.419070i
$527$	−22.8454	−	39.5694i	−0.995160	−	1.72367i
$528$		0			0
$529$	4.34342	−	7.52302i	0.188844	−	0.327088i
$530$	5.83149	−	1.23952i	0.253304	−	0.0538413i
$531$	6.86496	−	4.98769i	0.297914	−	0.216447i
$532$	2.25856	−	1.99656i	0.0979208	−	0.0865619i
$533$	−13.0999	−	40.3174i	−0.567421	−	1.74634i
$534$	0.220330	−	0.244701i	0.00953462	−	0.0105893i
$535$	5.40274	−	2.40546i	0.233581	−	0.103997i
$536$	−0.167619	−	1.59479i	−0.00724005	−	0.0688845i
$537$	−1.69100	+	0.359433i	−0.0729721	+	0.0155107i
$538$	13.7538			0.592967
$539$		0			0
$540$	−0.369460			−0.0158990
$541$	15.4191	−	3.27744i	0.662920	−	0.140908i	0.135849	−	0.990729i	$-0.456624\pi$
$541$	15.4191	−	3.27744i	0.662920	−	0.140908i	0.527071	+	0.849821i	$0.323290\pi$
$542$	0.441438	+	4.20000i	0.0189614	+	0.180405i
$543$	2.06169	−	0.917923i	0.0884755	−	0.0393918i
$544$	9.29436	−	10.3224i	0.398492	−	0.442571i
$545$	6.82891	+	21.0172i	0.292519	+	0.900279i
$546$	1.59418	−	1.40925i	0.0682246	−	0.0603105i
$547$	−7.87927	+	5.72463i	−0.336893	+	0.244767i	−0.743350	−	0.668903i	$-0.766764\pi$
$547$	−7.87927	+	5.72463i	−0.336893	+	0.244767i	0.406457	+	0.913670i	$0.366764\pi$
$548$	−3.01658	+	0.641194i	−0.128862	+	0.0273905i
$549$	−3.66220	+	6.34312i	−0.156299	+	0.270718i
$550$		0			0
$551$	6.37404	+	11.0402i	0.271543	+	0.470327i
$552$	0.493041	−	1.51743i	0.0209852	−	0.0645859i
$553$	7.66270	−	10.3467i	0.325851	−	0.439987i
$554$	8.39366	+	6.09835i	0.356612	+	0.259094i
$555$	0.374773	−	0.416227i	0.0159082	−	0.0176679i
$556$	8.17506	+	1.73766i	0.346700	+	0.0736933i
$557$	−21.4884	+	9.56726i	−0.910494	+	0.405378i	−0.807883	−	0.589344i	$-0.799386\pi$
$557$	−21.4884	+	9.56726i	−0.910494	+	0.405378i	−0.102611	+	0.994722i	$0.532720\pi$
$558$	−23.8350	−	10.6120i	−1.00902	−	0.449243i
$559$	1.18745	−	3.65459i	0.0502238	−	0.154573i
$560$	−7.19026	−	6.59405i	−0.303844	−	0.278650i
$561$		0			0
$562$	−9.40549	−	16.2908i	−0.396747	−	0.687185i
$563$	18.4093	+	20.4456i	0.775858	+	0.861678i	0.993439	−	0.114365i	$-0.0364832\pi$
$563$	18.4093	+	20.4456i	0.775858	+	0.861678i	−0.217581	+	0.976042i	$0.569817\pi$
$564$	0.0297905	+	0.283438i	0.00125441	+	0.0119349i
$565$	−0.472902	+	4.49936i	−0.0198951	+	0.189290i
$566$	−3.43689	−	10.5777i	−0.144463	−	0.444613i
$567$	−9.69201	+	21.2442i	−0.407026	+	0.892174i
$568$	−8.03754	−	5.83962i	−0.337248	−	0.245025i
$569$	−25.6268	−	11.4098i	−1.07433	−	0.478322i	−0.208172	−	0.978092i	$-0.566751\pi$
$569$	−25.6268	−	11.4098i	−1.07433	−	0.478322i	−0.866158	+	0.499770i	$0.833418\pi$
$570$	0.428889	+	0.476330i	0.0179642	+	0.0199513i
$571$	20.4952	−	35.4988i	0.857699	−	1.48558i	−0.0164198	−	0.999865i	$-0.505227\pi$
$571$	20.4952	−	35.4988i	0.857699	−	1.48558i	0.874119	−	0.485713i	$-0.161440\pi$
$572$		0			0
$573$	1.20284			0.0502494
$574$	0.288517	−	31.5859i	0.0120425	−	1.31837i
$575$	−11.0052	+	7.99575i	−0.458949	+	0.333446i
$576$	2.76796	−	26.3354i	0.115332	−	1.09731i
$577$	−20.8505	−	4.43191i	−0.868017	−	0.184503i	−0.247684	−	0.968841i	$-0.579669\pi$
$577$	−20.8505	−	4.43191i	−0.868017	−	0.184503i	−0.620334	+	0.784338i	$0.713003\pi$
$578$	34.0433	+	7.23612i	1.41601	+	0.300983i
$579$	−0.107381	+	1.02166i	−0.00446258	+	0.0424586i
$580$	−1.50200	+	1.09127i	−0.0623671	+	0.0453124i
$581$	26.1852	+	15.4387i	1.08635	+	0.640503i
$582$	−0.174979			−0.00725312
$583$		0			0
$584$	−19.2258	+	33.3000i	−0.795568	+	1.37796i
$585$	10.7008	+	11.8845i	0.442424	+	0.491362i
$586$	−28.3423	−	12.6188i	−1.17081	−	0.521279i
$587$	−33.2927	−	24.1886i	−1.37414	−	0.998369i	−0.997401	−	0.0720478i	$-0.977047\pi$
$587$	−33.2927	−	24.1886i	−1.37414	−	0.998369i	−0.376735	−	0.926321i	$-0.622953\pi$
$588$	−0.336010	+	0.142305i	−0.0138568	+	0.00586856i
$589$	−6.45957	−	19.8805i	−0.266162	−	0.819162i
$590$	0.449667	−	4.27830i	0.0185125	−	0.176135i
$591$	−0.144789	−	1.37758i	−0.00595582	−	0.0566659i
$592$	7.06356	+	7.84488i	0.290311	+	0.322423i
$593$	−7.97036	−	13.8051i	−0.327304	−	0.566907i	0.654672	−	0.755913i	$-0.272807\pi$
$593$	−7.97036	−	13.8051i	−0.327304	−	0.566907i	−0.981976	+	0.189006i	$0.939473\pi$
$594$		0			0
$595$	−4.52489	+	20.3712i	−0.185502	+	0.835136i
$596$	−0.934879	+	2.87726i	−0.0382941	+	0.117857i
$597$	−2.23575	−	0.995418i	−0.0915030	−	0.0407397i
$598$	−19.9522	+	8.88331i	−0.815907	+	0.363265i
$599$	33.4812	+	7.11664i	1.36800	+	0.290778i	0.832627	−	0.553835i	$-0.186836\pi$
$599$	33.4812	+	7.11664i	1.36800	+	0.290778i	0.535377	+	0.844613i	$0.320169\pi$
$600$	1.01465	−	1.12688i	0.0414229	−	0.0460048i
$601$	23.5251	+	17.0920i	0.959610	+	0.697198i	0.953060	−	0.302781i	$-0.0979150\pi$
$601$	23.5251	+	17.0920i	0.959610	+	0.697198i	0.00655012	+	0.999979i	$0.497915\pi$
$602$	1.70406	−	2.30094i	0.0694522	−	0.0937793i
$603$	−0.487892	+	1.50158i	−0.0198685	+	0.0611490i
$604$	1.10479	+	1.91355i	0.0449531	+	0.0778611i
$605$		0			0
$606$	−0.00791460	+	0.0137085i	−0.000321508	+	0.000556869i
$607$	−22.2443	+	4.72817i	−0.902868	+	0.191910i	−0.635879	−	0.771789i	$-0.719362\pi$
$607$	−22.2443	+	4.72817i	−0.902868	+	0.191910i	−0.266989	+	0.963700i	$0.586029\pi$
$608$	5.14114	−	3.73526i	0.208501	−	0.151485i
$609$	−0.307035	−	1.51228i	−0.0124417	−	0.0612807i
$610$	1.14744	+	3.53146i	0.0464585	+	0.142985i
$611$	16.5628	−	18.3949i	0.670061	−	0.744178i
$612$	−6.78124	+	3.01920i	−0.274115	+	0.122044i
$613$	−3.25966	−	31.0136i	−0.131656	−	1.25263i	−0.838360	−	0.545117i	$-0.816485\pi$
$613$	−3.25966	−	31.0136i	−0.131656	−	1.25263i	0.706704	−	0.707509i	$-0.250181\pi$
$614$	−12.2832	+	2.61088i	−0.495710	+	0.105366i
$615$	−1.54580			−0.0623328
$616$		0			0
$617$	−45.1880			−1.81920			−0.909600	−	0.415484i	$-0.863612\pi$
$617$	−45.1880			−1.81920			−0.909600	+	0.415484i	$0.863612\pi$
$618$	2.54744	−	0.541476i	0.102473	−	0.0217814i
$619$	2.60160	+	24.7526i	0.104567	+	0.994889i	0.913459	+	0.406931i	$0.133401\pi$
$619$	2.60160	+	24.7526i	0.104567	+	0.994889i	−0.808892	+	0.587958i	$0.799932\pi$
$620$	2.78111	−	1.23823i	0.111692	−	0.0497285i
$621$	−2.10914	+	2.34244i	−0.0846369	+	0.0939988i
$622$	−0.323947	−	0.997007i	−0.0129891	−	0.0399763i
$623$	4.65042	+	1.55812i	0.186315	+	0.0624246i
$624$	1.58775	−	1.15357i	0.0635608	−	0.0461797i
$625$	−5.77737	+	1.22802i	−0.231095	+	0.0491207i
$626$	4.06812	−	7.04619i	0.162595	−	0.281622i
$627$		0			0
$628$	3.12677	+	5.41572i	0.124772	+	0.216111i
$629$	6.97739	−	21.4742i	0.278207	−	0.856232i
$630$	4.74704	+	10.9296i	0.189127	+	0.435446i
$631$	−9.63326	−	6.99897i	−0.383494	−	0.278625i	0.379290	−	0.925278i	$-0.376168\pi$
$631$	−9.63326	−	6.99897i	−0.383494	−	0.278625i	−0.762784	+	0.646653i	$0.776168\pi$
$632$	9.85752	−	10.9479i	0.392111	−	0.435483i
$633$	−0.0724882	−	0.0154079i	−0.00288115	−	0.000612407i
$634$	−9.54835	+	4.25120i	−0.379214	+	0.168837i
$635$	3.65258	+	1.62623i	0.144948	+	0.0645352i
$636$	0.0635561	−	0.195606i	0.00252016	−	0.00775626i
$637$	28.7123	+	13.4172i	1.13762	+	0.531611i
$638$		0			0
$639$	4.89089	+	8.47127i	0.193481	+	0.335118i
$640$	−5.67293	−	6.30042i	−0.224242	−	0.249046i
$641$	−1.28735	−	12.2483i	−0.0508472	−	0.483779i	−0.990081	−	0.140500i	$-0.955129\pi$
$641$	−1.28735	−	12.2483i	−0.0508472	−	0.483779i	0.939233	−	0.343279i	$-0.111538\pi$
$642$	−0.0926598	+	0.881600i	−0.00365699	+	0.0347940i
$643$	6.67201	+	20.5343i	0.263118	+	0.809795i	0.992121	+	0.125284i	$0.0399843\pi$
$643$	6.67201	+	20.5343i	0.263118	+	0.809795i	−0.729002	+	0.684511i	$0.760016\pi$
$644$	3.72843	−	0.357474i	0.146921	−	0.0140864i
$645$	−0.113360	−	0.0823605i	−0.00446353	−	0.00324294i
$646$	23.6058	+	10.5100i	0.928757	+	0.413509i
$647$	7.80534	+	8.66871i	0.306860	+	0.340802i	0.876775	−	0.480902i	$-0.159691\pi$
$647$	7.80534	+	8.66871i	0.306860	+	0.340802i	−0.569915	+	0.821704i	$0.693024\pi$
$648$	−13.3589	+	23.1383i	−0.524787	+	0.908957i
$649$		0			0
$650$	−20.7571			−0.814159
$651$	−0.0231122	+	2.53024i	−0.000905837	+	0.0991679i
$652$	−7.38953	+	5.36881i	−0.289396	+	0.210259i
$653$	−3.53706	+	33.6529i	−0.138416	+	1.31694i	0.676105	+	0.736805i	$0.263667\pi$
$653$	−3.53706	+	33.6529i	−0.138416	+	1.31694i	−0.814521	+	0.580134i	$0.803000\pi$
$654$	−3.24001	−	0.688686i	−0.126694	−	0.0269297i
$655$	−5.65775	−	1.20259i	−0.221066	−	0.0469891i
$656$	3.04540	−	28.9751i	0.118903	−	1.13129i
$657$	30.6284	−	22.2528i	1.19493	−	0.868165i
$658$	16.0563	−	9.07558i	0.625939	−	0.353803i
$659$	−27.2313			−1.06078			−0.530390	−	0.847754i	$-0.677955\pi$
$659$	−27.2313			−1.06078			−0.530390	+	0.847754i	$0.677955\pi$
$660$		0			0
$661$	12.6733	−	21.9508i	0.492933	−	0.853786i	−0.507033	−	0.861926i	$-0.669258\pi$
$661$	12.6733	−	21.9508i	0.492933	−	0.853786i	0.999967	+	0.00814061i	$0.00259127\pi$
$662$	19.2886	+	21.4221i	0.749671	+	0.832595i
$663$	−3.83488	−	1.70740i	−0.148934	−	0.0663099i
$664$	28.1384	+	20.4437i	1.09198	+	0.793371i
$665$	−3.96261	+	8.68578i	−0.153663	+	0.336820i
$666$	−3.98428	−	12.2623i	−0.154388	−	0.475156i
$667$	−1.65567	+	15.7527i	−0.0641079	+	0.609946i
$668$	0.445818	+	4.24167i	0.0172492	+	0.164115i
$669$	1.70736	+	1.89622i	0.0660104	+	0.0733120i
$670$	0.400210	+	0.693184i	0.0154615	+	0.0267800i
$671$		0			0
$672$	−0.733728	+	0.231015i	−0.0283042	+	0.00891160i
$673$	6.64968	−	20.4656i	0.256326	−	0.788892i	−0.737239	−	0.675632i	$-0.763871\pi$
$673$	6.64968	−	20.4656i	0.256326	−	0.788892i	0.993565	−	0.113260i	$-0.0361292\pi$
$674$	28.8351	+	12.8382i	1.11069	+	0.494510i
$675$	−2.73671	+	1.21846i	−0.105336	+	0.0468987i
$676$	2.74450	+	0.583362i	0.105558	+	0.0224370i
$677$	18.2678	−	20.2884i	0.702087	−	0.779747i	−0.281620	−	0.959526i	$-0.590872\pi$
$677$	18.2678	−	20.2884i	0.702087	−	0.779747i	0.983707	+	0.179780i	$0.0575384\pi$
$678$	−0.548614	−	0.398592i	−0.0210694	−	0.0153078i
$679$	−1.03827	−	2.39052i	−0.0398452	−	0.0917399i
$680$	−7.37832	+	22.7081i	−0.282946	+	0.870817i
$681$	0.664446	+	1.15085i	0.0254616	+	0.0441008i
$682$		0			0
$683$	1.11077	−	1.92391i	0.0425024	−	0.0736162i	−0.843992	−	0.536356i	$-0.819800\pi$
$683$	1.11077	−	1.92391i	0.0425024	−	0.0736162i	0.886494	+	0.462740i	$0.153134\pi$
$684$	−3.32182	+	0.706075i	−0.127013	+	0.0269975i
$685$	7.90163	−	5.74087i	0.301906	−	0.219347i
$686$	17.1096	+	16.2762i	0.653247	+	0.621427i
$687$	0.0775254	+	0.238599i	0.00295778	+	0.00910310i
$688$	1.76713	−	1.96259i	0.0673710	−	0.0748231i
$689$	−16.3187	+	7.26555i	−0.621693	+	0.276795i
$690$	0.0832460	+	0.792033i	0.00316912	+	0.0301522i
$691$	−0.958385	+	0.203711i	−0.0364587	+	0.00774953i	−0.226105	−	0.974103i	$-0.572599\pi$
$691$	−0.958385	+	0.203711i	−0.0364587	+	0.00774953i	0.189646	+	0.981852i	$0.439266\pi$
$692$	−1.03573			−0.0393726
$693$		0			0
$694$	7.68002			0.291529
$695$	−25.8904	+	5.50318i	−0.982080	+	0.208747i
$696$	−0.184561	−	1.75598i	−0.00699576	−	0.0665602i
$697$	−56.9296	+	25.3467i	−2.15636	+	0.960074i
$698$	−17.9211	+	19.9034i	−0.678324	+	0.753355i
$699$	0.858981	+	2.64367i	0.0324897	+	0.0999929i
$700$	3.37532	+	1.13090i	0.127575	+	0.0427438i
$701$	−9.49475	+	6.89834i	−0.358612	+	0.260547i	−0.752473	−	0.658623i	$-0.771139\pi$
$701$	−9.49475	+	6.89834i	−0.358612	+	0.260547i	0.393861	+	0.919170i	$0.371139\pi$
$702$	−4.70462	+	0.999998i	−0.177564	+	0.0377425i
$703$	5.16504	−	8.94611i	0.194803	−	0.337409i
$704$		0			0
$705$	−0.451296	−	0.781668i	−0.0169968	−	0.0294393i
$706$	10.6980	−	32.9250i	0.402623	−	1.23915i
$707$	−0.234245	−	0.0267855i	−0.00880968	−	0.00100737i
$708$	−0.120064	−	0.0872319i	−0.00451229	−	0.00327837i
$709$	21.4951	−	23.8727i	0.807264	−	0.896558i	−0.189082	−	0.981961i	$-0.560551\pi$
$709$	21.4951	−	23.8727i	0.807264	−	0.896558i	0.996346	+	0.0854034i	$0.0272179\pi$
$710$	4.85063	+	1.03103i	0.182041	+	0.0386940i
$711$	−13.2507	+	5.89959i	−0.496940	+	0.221252i
$712$	5.12657	+	2.28249i	0.192126	+	0.0855401i
$713$	8.02598	−	24.7014i	0.300575	−	0.925076i
$714$	−2.30523	−	2.11409i	−0.0862712	−	0.0791177i
$715$		0			0
$716$	−2.32179	−	4.02146i	−0.0867693	−	0.150289i
$717$	−0.360983	−	0.400912i	−0.0134812	−	0.0149723i
$718$	−4.62214	−	43.9767i	−0.172497	−	1.64120i
$719$	−1.66696	+	15.8601i	−0.0621672	+	0.591481i	0.918449	+	0.395540i	$0.129443\pi$
$719$	−1.66696	+	15.8601i	−0.0621672	+	0.591481i	−0.980616	+	0.195941i	$0.937224\pi$
$720$	3.39635	+	10.4529i	0.126574	+	0.389556i
$721$	22.5132	+	31.5896i	0.838437	+	1.17646i
$722$	−10.0356	−	7.29126i	−0.373485	−	0.271352i
$723$	−0.333639	−	0.148546i	−0.0124082	−	0.00552448i
$724$	4.05618	+	4.50484i	0.150747	+	0.167421i
$725$	−7.52687	+	13.0369i	−0.279541	+	0.484179i
$726$		0			0
$727$	−47.9125			−1.77697			−0.888487	−	0.458901i	$-0.848243\pi$
$727$	−47.9125			−1.77697			−0.888487	+	0.458901i	$0.848243\pi$
$728$	31.2374	+	18.4174i	1.15773	+	0.682593i
$729$	21.0002	−	15.2575i	0.777784	−	0.565093i
$730$	2.00621	−	19.0878i	0.0742532	−	0.706472i
$731$	−5.52533	−	1.17445i	−0.204362	−	0.0434384i
$732$	0.125300	+	0.0266334i	0.00463123	+	0.000984399i
$733$	2.38443	−	22.6863i	0.0880708	−	0.837938i	−0.857928	−	0.513769i	$-0.828249\pi$
$733$	2.38443	−	22.6863i	0.0880708	−	0.837938i	0.945999	−	0.324169i	$-0.105085\pi$
$734$	30.7293	−	22.3262i	1.13424	−	0.824074i
$735$	0.788837	−	0.844543i	0.0290967	−	0.0311514i
$736$	7.89580			0.291043
$737$		0			0
$738$	−17.7924	+	30.8174i	−0.654948	+	1.13440i
$739$	−29.0715	−	32.2871i	−1.06941	−	1.18770i	−0.981478	−	0.191575i	$-0.938640\pi$
$739$	−29.0715	−	32.2871i	−1.06941	−	1.18770i	−0.0879336	−	0.996126i	$-0.528026\pi$
$740$	1.37436	+	0.611904i	0.0505225	+	0.0224941i
$741$	−1.55372	−	1.12884i	−0.0570773	−	0.0414691i
$742$	−13.2493	+	1.27031i	−0.486397	+	0.0466347i
$743$	−11.6189	−	35.7593i	−0.426256	−	1.31188i	−0.901787	−	0.432181i	$-0.857744\pi$
$743$	−11.6189	−	35.7593i	−0.426256	−	1.31188i	0.475531	−	0.879699i	$-0.342256\pi$
$744$	−0.302633	+	2.87936i	−0.0110950	+	0.105562i
$745$	−1.00151	−	9.52874i	−0.0366925	−	0.349106i
$746$	0.0106365	+	0.0118131i	0.000389432	+	0.000432508i
$747$	−17.1224	−	29.6568i	−0.626475	−	1.08509i
$748$		0			0
$749$	−12.5940	+	3.96524i	−0.460175	+	0.144887i
$750$	−0.559139	+	1.72085i	−0.0204169	+	0.0628367i
$751$	1.77373	+	0.789715i	0.0647243	+	0.0288171i	0.438843	−	0.898564i	$-0.355388\pi$
$751$	1.77373	+	0.789715i	0.0647243	+	0.0288171i	−0.374119	+	0.927381i	$0.622055\pi$
$752$	15.5410	−	6.91928i	0.566721	−	0.252320i
$753$	−1.29883	−	0.276075i	−0.0473321	−	0.0100607i
$754$	−16.1725	+	17.9613i	−0.588966	+	0.654113i
$755$	−5.66128	−	4.11316i	−0.206035	−	0.149693i
$756$	0.819504	+	0.0937089i	0.0298051	+	0.00340816i
$757$	−13.5212	+	41.6140i	−0.491436	+	1.51249i	0.331001	+	0.943630i	$0.392614\pi$
$757$	−13.5212	+	41.6140i	−0.491436	+	1.51249i	−0.822438	+	0.568855i	$0.807386\pi$
$758$	14.0908	+	24.4059i	0.511799	+	0.886462i
$759$		0			0
$760$	−5.46183	+	9.46016i	−0.198121	+	0.343156i
$761$	−13.1930	+	2.80425i	−0.478244	+	0.101654i	−0.440726	−	0.897642i	$-0.645279\pi$
$761$	−13.1930	+	2.80425i	−0.478244	+	0.101654i	−0.0375189	+	0.999296i	$0.511945\pi$
$762$	−0.484842	+	0.352258i	−0.0175640	+	0.0127610i
$763$	−9.81655	−	48.3507i	−0.355383	−	1.75041i
$764$	0.998398	+	3.07275i	0.0361208	+	0.111168i
$765$	15.7303	−	17.4703i	0.568731	−	0.631640i
$766$	−32.6198	+	14.5233i	−1.17860	+	0.524748i
$767$	1.34732	+	12.8189i	0.0486490	+	0.462864i
$768$	−1.17824	+	0.250444i	−0.0425162	+	0.00903711i
$769$	1.99208			0.0718362			0.0359181	−	0.999355i	$-0.488564\pi$
$769$	1.99208			0.0718362			0.0359181	+	0.999355i	$0.488564\pi$
$770$		0			0
$771$	−3.18033			−0.114537
$772$	−2.69904	+	0.573698i	−0.0971404	+	0.0206478i
$773$	−1.86188	−	17.7146i	−0.0669670	−	0.637149i	−0.975600	−	0.219554i	$-0.929540\pi$
$773$	−1.86188	−	17.7146i	−0.0669670	−	0.637149i	0.908633	−	0.417595i	$-0.137127\pi$
$774$	−2.94673	+	1.31197i	−0.105918	+	0.0471578i
$775$	16.5170	−	18.3440i	0.593308	−	0.658936i
$776$	−0.921514	−	2.83613i	−0.0330804	−	0.101811i
$777$	−0.936859	+	0.828183i	−0.0336096	+	0.0297109i
$778$	1.76062	−	1.27917i	0.0631213	−	0.0458603i
$779$	−27.8872	+	5.92761i	−0.999163	+	0.212379i
$780$	0.139847	−	0.242221i	0.00500731	−	0.00867291i
$781$		0			0
$782$	16.0529	+	27.8044i	0.574049	+	0.994283i
$783$	−1.07791	+	3.31745i	−0.0385212	+	0.118556i
$784$	14.2763	+	16.4501i	0.509869	+	0.587503i
$785$	−16.0225	−	11.6410i	−0.571869	−	0.415487i
$786$	0.580127	−	0.644296i	0.0206924	−	0.0229813i
$787$	−32.4566	−	6.89887i	−1.15695	−	0.245918i	−0.410822	−	0.911716i	$-0.634758\pi$
$787$	−32.4566	−	6.89887i	−1.15695	−	0.245918i	−0.746133	+	0.665797i	$0.768092\pi$
$788$	3.39895	−	1.51331i	0.121083	−	0.0539094i
$789$	−1.00867	−	0.449091i	−0.0359098	−	0.0159881i
$790$	−2.27231	+	6.99344i	−0.0808451	+	0.248816i
$791$	2.19016	−	9.86016i	0.0778731	−	0.350587i
$792$		0			0
$793$	−5.56286	−	9.63516i	−0.197543	−	0.342155i
$794$	−11.2924	−	12.5415i	−0.400754	−	0.445082i
$795$	0.0680859	+	0.647794i	0.00241476	+	0.0229749i
$796$	0.687132	−	6.53762i	0.0243547	−	0.231720i
$797$	−2.95511	−	9.09488i	−0.104675	−	0.322157i	0.884979	−	0.465631i	$-0.154173\pi$
$797$	−2.95511	−	9.09488i	−0.104675	−	0.322157i	−0.989654	+	0.143474i	$0.954173\pi$
$798$	−0.830511	−	1.16534i	−0.0293998	−	0.0412525i
$799$	−29.4376	−	21.3877i	−1.04143	−	0.756642i
$800$	6.85537	+	3.05221i	0.242374	+	0.107912i
$801$	−3.69709	−	4.10603i	−0.130630	−	0.145079i
$802$	15.1029	−	26.1591i	0.533303	−	0.923708i
$803$		0			0
$804$	0.0276133			0.000973845
$805$	−10.3266	+	5.83696i	−0.363965	+	0.205726i
$806$	32.0626	−	23.2949i	1.12936	−	0.820526i
$807$	−0.157074	+	1.49446i	−0.00552926	+	0.0526074i
$808$	−0.263874	−	0.0560882i	−0.00928305	−	0.00197317i
$809$	−20.1862	−	4.29070i	−0.709708	−	0.150853i	−0.161106	−	0.986937i	$-0.551506\pi$
$809$	−20.1862	−	4.29070i	−0.709708	−	0.150853i	−0.548601	+	0.836084i	$0.684840\pi$
$810$	1.39400	−	13.2630i	0.0489802	−	0.466015i
$811$	−9.38639	+	6.81961i	−0.329601	+	0.239469i	−0.740261	−	0.672319i	$-0.765298\pi$
$811$	−9.38639	+	6.81961i	−0.329601	+	0.239469i	0.410660	+	0.911788i	$0.365298\pi$
$812$	3.60839	−	2.03959i	0.126630	−	0.0715755i
$813$	−0.461406			−0.0161822
$814$		0			0
$815$	14.4636	−	25.0517i	0.506639	−	0.877524i
$816$	−1.93044	−	2.14397i	−0.0675789	−	0.0750540i
$817$	−2.36090	−	1.05114i	−0.0825974	−	0.0367747i
$818$	−11.3557	−	8.25043i	−0.397044	−	0.288469i
$819$	−20.7213	−	29.0752i	−0.724060	−	1.01597i
$820$	−1.28307	−	3.94888i	−0.0448067	−	0.137901i
$821$	−1.53459	+	14.6007i	−0.0535577	+	0.509567i	0.934553	+	0.355824i	$0.115800\pi$
$821$	−1.53459	+	14.6007i	−0.0535577	+	0.509567i	−0.988111	+	0.153743i	$0.950867\pi$
$822$	0.153026	+	1.45595i	0.00533741	+	0.0507820i
$823$	14.6859	+	16.3104i	0.511919	+	0.568543i	0.942584	−	0.333968i	$-0.108388\pi$
$823$	14.6859	+	16.3104i	0.511919	+	0.568543i	−0.430666	+	0.902512i	$0.641721\pi$
$824$	22.1924	+	38.4383i	0.773108	+	1.33906i
$825$		0			0
$826$	−2.08255	+	9.37570i	−0.0724612	+	0.326222i
$827$	10.0277	−	30.8620i	0.348697	−	1.07318i	−0.610878	−	0.791725i	$-0.709183\pi$
$827$	10.0277	−	30.8620i	0.348697	−	1.07318i	0.959575	−	0.281454i	$-0.0908166\pi$
$828$	−3.85475	−	1.71625i	−0.133962	−	0.0596437i
$829$	31.1774	−	13.8811i	1.08284	−	0.482109i	0.213809	−	0.976875i	$-0.431413\pi$
$829$	31.1774	−	13.8811i	1.08284	−	0.482109i	0.869026	+	0.494766i	$0.164746\pi$
$830$	−16.9814	−	3.60951i	−0.589434	−	0.125288i
$831$	−0.758495	+	0.842394i	−0.0263119	+	0.0292223i
$832$	32.5417	+	23.6429i	1.12818	+	0.819670i
$833$	15.2036	−	44.0379i	0.526774	−	1.52582i
$834$	1.22600	−	3.77324i	0.0424529	−	0.130656i
$835$	−6.75369	−	11.6977i	−0.233721	−	0.404817i
$836$		0			0
$837$	2.85986	−	4.95342i	0.0988512	−	0.171215i
$838$	33.1783	−	7.05227i	1.14613	−	0.243617i
$839$	−24.2944	+	17.6509i	−0.838735	+	0.609376i	−0.922017	−	0.387150i	$-0.873460\pi$
$839$	−24.2944	+	17.6509i	−0.838735	+	0.609376i	0.0832822	+	0.996526i	$0.473460\pi$
$840$	0.990693	−	0.875771i	0.0341821	−	0.0302170i
$841$	−3.54490	−	10.9101i	−0.122238	−	0.376210i
$842$	−25.4818	+	28.3004i	−0.878161	+	0.975297i
$843$	1.87754	−	0.835935i	0.0646660	−	0.0287911i
$844$	−0.0208071	−	0.197966i	−0.000716209	−	0.00681428i
$845$	−8.69184	+	1.84751i	−0.299008	+	0.0635562i
$846$	−20.7779			−0.714360
$847$		0			0
$848$	−12.2766			−0.421581
$849$	1.18860	−	0.252645i	0.0407927	−	0.00867075i
$850$	3.18949	+	30.3460i	0.109399	+	1.04086i
$851$	11.7254	−	5.22049i	0.401942	−	0.178956i
$852$	0.114473	−	0.127136i	0.00392179	−	0.00435559i
$853$	−0.848431	−	2.61120i	−0.0290497	−	0.0894058i	0.935480	−	0.353378i	$-0.114967\pi$
$853$	−0.848431	−	2.61120i	−0.0290497	−	0.0894058i	−0.964530	+	0.263973i	$0.914967\pi$
$854$	−1.64944	−	8.12422i	−0.0564428	−	0.278005i
$855$	8.70117	−	6.32177i	0.297574	−	0.216200i
$856$	−14.7773	+	3.14101i	−0.505077	+	0.107358i
$857$	−11.7477	+	20.3476i	−0.401294	+	0.695062i	−0.993882	−	0.110443i	$-0.964773\pi$
$857$	−11.7477	+	20.3476i	−0.401294	+	0.695062i	0.592588	+	0.805506i	$0.298106\pi$
$858$		0			0
$859$	−2.56165	−	4.43691i	−0.0874025	−	0.151386i	0.819010	−	0.573779i	$-0.194523\pi$
$859$	−2.56165	−	4.43691i	−0.0874025	−	0.151386i	−0.906412	+	0.422394i	$0.861190\pi$
$860$	0.116304	−	0.357948i	0.00396595	−	0.0122059i
$861$	3.42877	+	0.392074i	0.116852	+	0.0133619i
$862$	−1.04544	−	0.759559i	−0.0356079	−	0.0258707i
$863$	−28.1133	+	31.2230i	−0.956989	+	1.06284i	0.0409816	+	0.999160i	$0.486952\pi$
$863$	−28.1133	+	31.2230i	−0.956989	+	1.06284i	−0.997970	+	0.0636836i	$0.979715\pi$
$864$	1.70082	+	0.361521i	0.0578632	+	0.0122992i
$865$	2.99657	−	1.33416i	0.101887	−	0.0453628i
$866$	15.1566	+	6.74816i	0.515042	+	0.229312i
$867$	−1.17505	+	3.61644i	−0.0399069	+	0.122821i
$868$	−6.48288	+	2.04114i	−0.220043	+	0.0692809i
$869$		0			0
$870$	0.440659	+	0.763244i	0.0149397	+	0.0258764i
$871$	−1.60476	−	1.78226i	−0.0543751	−	0.0603896i
$872$	−5.90079	−	56.1423i	−0.199826	−	1.90122i
$873$	−0.306907	+	2.92002i	−0.0103872	+	0.0988278i
$874$	4.53898	+	13.9695i	0.153533	+	0.472527i
$875$	−26.8277	+	2.57218i	−0.906940	+	0.0869555i
$876$	−0.535673	−	0.389189i	−0.0180987	−	0.0131495i
$877$	−3.04079	−	1.35385i	−0.102680	−	0.0457162i	0.354754	−	0.934960i	$-0.384565\pi$
$877$	−3.04079	−	1.35385i	−0.102680	−	0.0457162i	−0.457434	+	0.889244i	$0.651231\pi$
$878$	24.9374	+	27.6958i	0.841596	+	0.934687i
$879$	1.69482	−	2.93551i	0.0571649	−	0.0990125i
$880$		0			0
$881$	−30.1520			−1.01585			−0.507923	−	0.861403i	$-0.669587\pi$
$881$	−30.1520			−1.01585			−0.507923	+	0.861403i	$0.669587\pi$
$882$	−7.75731	−	25.4472i	−0.261202	−	0.856851i
$883$	16.5449	−	12.0206i	0.556781	−	0.404525i	−0.273498	−	0.961872i	$-0.588181\pi$
$883$	16.5449	−	12.0206i	0.556781	−	0.404525i	0.830279	+	0.557347i	$0.188181\pi$
$884$	1.17861	−	11.2137i	0.0396409	−	0.377158i
$885$	0.459737	+	0.0977200i	0.0154539	+	0.00328482i
$886$	−26.0084	−	5.52826i	−0.873769	−	0.185725i
$887$	1.30859	−	12.4504i	0.0439381	−	0.418043i	−0.950339	−	0.311215i	$-0.899264\pi$
$887$	1.30859	−	12.4504i	0.0439381	−	0.418043i	0.994278	−	0.106828i	$-0.0340694\pi$
$888$	−1.15750	+	0.840973i	−0.0388431	+	0.0282212i
$889$	−7.68937	−	4.53361i	−0.257893	−	0.152052i
$890$	−2.80107			−0.0938922
$891$		0			0
$892$	−3.42687	+	5.93552i	−0.114740	+	0.198736i
$893$	−11.1391	−	12.3712i	−0.372755	−	0.413986i
$894$	1.31197	+	0.584127i	0.0438789	+	0.0195361i
$895$	11.8976	+	8.64410i	0.397692	+	0.288940i
$896$	10.9852	+	15.4139i	0.366989	+	0.514943i
$897$	−0.737381	−	2.26942i	−0.0246204	−	0.0757739i
$898$	3.75167	−	35.6947i	0.125195	−	1.19115i
$899$	−3.00438	−	28.5847i	−0.100202	−	0.953354i
$900$	−2.68338	−	2.98019i	−0.0894459	−	0.0993398i
$901$	13.1294	+	22.7409i	0.437405	+	0.757608i
$902$		0			0
$903$	0.230555	+	0.211437i	0.00767238	+	0.00703620i
$904$	3.57129	−	10.9913i	0.118779	−	0.365565i
$905$	−17.5382	−	7.80850i	−0.582989	−	0.259563i
$906$	0.958208	−	0.426622i	0.0318343	−	0.0141736i
$907$	−15.9858	−	3.39790i	−0.530801	−	0.112825i	−0.0652884	−	0.997866i	$-0.520797\pi$
$907$	−15.9858	−	3.39790i	−0.530801	−	0.112825i	−0.465513	+	0.885041i	$0.654130\pi$
$908$	−2.38844	+	2.65263i	−0.0792630	+	0.0880305i
$909$	0.214883	+	0.156122i	0.00712722	+	0.00517823i
$910$	−17.9831	−	2.05634i	−0.596135	−	0.0681671i
$911$	11.5866	−	35.6599i	0.383881	−	1.18147i	−0.553407	−	0.832911i	$-0.686673\pi$
$911$	11.5866	−	35.6599i	0.383881	−	1.18147i	0.937289	−	0.348554i	$-0.113327\pi$
$912$	−0.659946	−	1.14306i	−0.0218530	−	0.0378505i
$913$		0			0
$914$	9.10942	−	15.7780i	0.301313	−	0.521889i
$915$	−0.396826	+	0.0843480i	−0.0131187	+	0.00278846i
$916$	−0.545171	+	0.396090i	−0.0180130	+	0.0130872i
$917$	12.2445	+	4.10250i	0.404349	+	0.135477i
$918$	2.18486	+	6.72431i	0.0721112	+	0.221935i
$919$	−2.23114	+	2.47793i	−0.0735985	+	0.0817395i	−0.778819	−	0.627248i	$-0.784181\pi$
$919$	−2.23114	+	2.47793i	−0.0735985	+	0.0817395i	0.705221	+	0.708988i	$0.250848\pi$
$920$	−12.3992	+	5.52047i	−0.408789	+	0.182004i
$921$	−0.143413	−	1.36449i	−0.00472563	−	0.0449614i
$922$	27.2316	−	5.78825i	0.896824	−	0.190626i
$923$	−14.8585			−0.489072
$924$		0			0
$925$	12.1984			0.401081
$926$	29.0413	−	6.17292i	0.954356	−	0.202855i
$927$	−4.56794	−	43.4610i	−0.150031	−	1.42745i
$928$	7.98234	−	3.55397i	0.262033	−	0.116665i
$929$	20.5907	−	22.8683i	0.675559	−	0.750285i	−0.303728	−	0.952759i	$-0.598231\pi$
$929$	20.5907	−	22.8683i	0.675559	−	0.750285i	0.979288	+	0.202474i	$0.0648981\pi$
$930$	−0.446572	−	1.37441i	−0.0146437	−	0.0450686i
$931$	10.9926	−	18.2610i	0.360267	−	0.598479i
$932$	−6.04049	+	4.38868i	−0.197863	+	0.143756i
$933$	0.112033	−	0.0238133i	0.00366778	−	0.000779611i
$934$	−11.9775	+	20.7457i	−0.391917	+	0.678820i
$935$		0			0
$936$	−20.4259	−	35.3788i	−0.667643	−	1.15639i
$937$	−6.97232	+	21.4586i	−0.227776	+	0.701022i	0.770222	+	0.637776i	$0.220145\pi$
$937$	−6.97232	+	21.4586i	−0.227776	+	0.701022i	−0.997998	+	0.0632461i	$0.979855\pi$
$938$	−0.711894	−	1.63907i	−0.0232441	−	0.0535175i
$939$	0.719167	+	0.522505i	0.0234691	+	0.0170513i
$940$	1.62224	−	1.80168i	0.0529117	−	0.0587644i
$941$	−44.1427	−	9.38282i	−1.43901	−	0.305871i	−0.578658	−	0.815570i	$-0.696423\pi$
$941$	−44.1427	−	9.38282i	−1.43901	−	0.305871i	−0.860353	+	0.509699i	$0.829757\pi$
$942$	2.71192	−	1.20742i	0.0883591	−	0.0393400i
$943$	−32.3613	−	14.4082i	−1.05383	−	0.469195i
$944$	−2.73743	+	8.42494i	−0.0890958	+	0.274209i
$945$	−2.49170	+	0.784513i	−0.0810549	+	0.0255202i
$946$		0			0
$947$	−14.7713	−	25.5846i	−0.480002	−	0.831388i	0.519735	−	0.854328i	$-0.326031\pi$
$947$	−14.7713	−	25.5846i	−0.480002	−	0.831388i	−0.999737	+	0.0229397i	$0.992697\pi$
$948$	0.169744	+	0.188520i	0.00551304	+	0.00612285i
$949$	6.01114	+	57.1922i	0.195130	+	1.85654i
$950$	−1.45920	+	13.8834i	−0.0473427	+	0.450436i
$951$	−0.352881	−	1.08606i	−0.0114430	−	0.0352178i
$952$	22.1256	−	48.4978i	0.717095	−	1.57182i
$953$	38.5292	+	27.9931i	1.24808	+	0.906785i	0.998109	−	0.0614674i	$-0.0195780\pi$
$953$	38.5292	+	27.9931i	1.24808	+	0.906785i	0.249974	+	0.968253i	$0.419578\pi$
$954$	13.6982	+	6.09883i	0.443496	+	0.197457i
$955$	−6.84668	−	7.60401i	−0.221553	−	0.246060i
$956$	0.724535	−	1.25493i	0.0234331	−	0.0405874i
$957$		0			0
$958$	−36.3541			−1.17455
$959$	−18.9828	+	10.7298i	−0.612987	+	0.346482i
$960$	1.18661	−	0.862121i	0.0382976	−	0.0278248i
$961$	−1.68603	+	16.0415i	−0.0543880	+	0.517467i
$962$	19.1570	+	4.07195i	0.617647	+	0.131285i
$963$	14.5495	+	3.09258i	0.468850	+	0.0996571i
$964$	0.102540	−	0.975606i	0.00330260	−	0.0314222i
$965$	7.06985	−	5.13655i	0.227586	−	0.165351i
$966$	0.0162403	−	1.77793i	0.000522524	−	0.0572041i
$967$	24.2423			0.779580			0.389790	−	0.920904i	$-0.372548\pi$
$967$	24.2423			0.779580			0.389790	+	0.920904i	$0.372548\pi$
$968$		0			0
$969$	−1.41158	+	2.44493i	−0.0453465	+	0.0785425i
$970$	0.995998	+	1.10617i	0.0319796	+	0.0355169i
$971$	17.8718	+	7.95706i	0.573535	+	0.255354i	0.672945	−	0.739692i	$-0.265029\pi$
$971$	17.8718	+	7.95706i	0.573535	+	0.255354i	−0.0994104	+	0.995047i	$0.531696\pi$
$972$	−1.12887	−	0.820172i	−0.0362085	−	0.0263070i
$973$	58.8237	−	5.63989i	1.88580	−	0.180807i
$974$	9.67488	+	29.7762i	0.310003	+	0.954092i
$975$	0.237055	−	2.25542i	0.00759182	−	0.0722314i
$976$	−0.799257	−	7.60443i	−0.0255836	−	0.243412i
$977$	−23.3403	−	25.9220i	−0.746722	−	0.829319i	0.243341	−	0.969941i	$-0.421757\pi$
$977$	−23.3403	−	25.9220i	−0.746722	−	0.829319i	−0.990063	+	0.140621i	$0.955090\pi$
$978$	2.16796	+	3.75501i	0.0693236	+	0.120072i
$979$		0			0
$980$	2.81222	+	1.31415i	0.0898329	+	0.0419790i
$981$	−17.1755	+	52.8608i	−0.548372	+	1.68772i
$982$	−26.5441	−	11.8182i	−0.847057	−	0.377134i
$983$	15.0663	−	6.70797i	0.480541	−	0.213951i	−0.152146	−	0.988358i	$-0.548618\pi$
$983$	15.0663	−	6.70797i	0.480541	−	0.213951i	0.632688	+	0.774407i	$0.281952\pi$
$984$	3.86247	+	0.820993i	0.123131	+	0.0261723i
$985$	−7.88449	+	8.75661i	−0.251221	+	0.279009i
$986$	28.7438	+	20.8836i	0.915389	+	0.665069i
$987$	0.802766	+	1.84829i	0.0255523	+	0.0588319i
$988$	1.59408	−	4.90608i	0.0507145	−	0.156083i
$989$	−1.60551	−	2.78082i	−0.0510521	−	0.0884248i
$990$		0			0
$991$	4.68799	−	8.11983i	0.148919	−	0.257935i	−0.781909	−	0.623392i	$-0.785754\pi$
$991$	4.68799	−	8.11983i	0.148919	−	0.257935i	0.930828	+	0.365457i	$0.119087\pi$
$992$	−14.0146	+	2.97890i	−0.444964	+	0.0945800i
$993$	−2.54797	+	1.85121i	−0.0808575	+	0.0587464i
$994$	−10.4977	−	3.51725i	−0.332968	−	0.111560i
$995$	6.43333	+	19.7998i	0.203950	+	0.627695i
$996$	−0.400757	+	0.445085i	−0.0126985	+	0.0141031i
$997$	5.87601	−	2.61617i	0.186095	−	0.0828549i	−0.311574	−	0.950222i	$-0.600856\pi$
$997$	5.87601	−	2.61617i	0.186095	−	0.0828549i	0.497669	+	0.867367i	$0.334189\pi$
$998$	4.50554	+	42.8674i	0.142620	+	1.35694i
$999$	2.76478	−	0.587673i	0.0874739	−	0.0185932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.h.130.4		40
7.2	even	3	inner	847.2.n.h.9.2		40
11.2	odd	10		77.2.m.b.25.4	yes	40
11.3	even	5		847.2.n.j.81.4		40
11.4	even	5		847.2.e.h.606.8		20
11.5	even	5	inner	847.2.n.h.753.2		40
11.6	odd	10		847.2.n.i.753.4		40
11.7	odd	10		847.2.e.i.606.3		20
11.8	odd	10		77.2.m.b.4.2	✓	40
11.9	even	5		847.2.n.j.487.2		40
11.10	odd	2		847.2.n.i.130.2		40
33.2	even	10		693.2.by.b.487.2		40
33.8	even	10		693.2.by.b.235.4		40
77.2	odd	30		77.2.m.b.58.2	yes	40
77.4	even	15		5929.2.a.by.1.3		10
77.9	even	15		847.2.n.j.366.4		40
77.13	even	10		539.2.q.h.410.4		40
77.16	even	15	inner	847.2.n.h.632.4		40
77.18	odd	30		5929.2.a.bw.1.8		10
77.19	even	30		539.2.q.h.422.4		40
77.24	even	30		539.2.f.g.344.2		20
77.30	odd	30		77.2.m.b.37.4	yes	40
77.37	even	15		847.2.e.h.485.8		20
77.41	even	10		539.2.q.h.312.2		40
77.46	odd	30		539.2.f.h.344.2		20
77.51	odd	30		847.2.e.i.485.3		20
77.52	even	30		539.2.f.g.246.2		20
77.58	even	15		847.2.n.j.807.2		40
77.59	odd	30		5929.2.a.bz.1.3		10
77.65	odd	6		847.2.n.i.9.4		40
77.68	even	30		539.2.q.h.520.2		40
77.72	odd	30		847.2.n.i.632.2		40
77.73	even	30		5929.2.a.bx.1.8		10
77.74	odd	30		539.2.f.h.246.2		20
231.2	even	30		693.2.by.b.289.4		40
231.107	even	30		693.2.by.b.37.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.4.2	✓	40	11.8	odd	10
77.2.m.b.25.4	yes	40	11.2	odd	10
77.2.m.b.37.4	yes	40	77.30	odd	30
77.2.m.b.58.2	yes	40	77.2	odd	30
539.2.f.g.246.2		20	77.52	even	30
539.2.f.g.344.2		20	77.24	even	30
539.2.f.h.246.2		20	77.74	odd	30
539.2.f.h.344.2		20	77.46	odd	30
539.2.q.h.312.2		40	77.41	even	10
539.2.q.h.410.4		40	77.13	even	10
539.2.q.h.422.4		40	77.19	even	30
539.2.q.h.520.2		40	77.68	even	30
693.2.by.b.37.2		40	231.107	even	30
693.2.by.b.235.4		40	33.8	even	10
693.2.by.b.289.4		40	231.2	even	30
693.2.by.b.487.2		40	33.2	even	10
847.2.e.h.485.8		20	77.37	even	15
847.2.e.h.606.8		20	11.4	even	5
847.2.e.i.485.3		20	77.51	odd	30
847.2.e.i.606.3		20	11.7	odd	10
847.2.n.h.9.2		40	7.2	even	3	inner
847.2.n.h.130.4		40	1.1	even	1	trivial
847.2.n.h.632.4		40	77.16	even	15	inner
847.2.n.h.753.2		40	11.5	even	5	inner
847.2.n.i.9.4		40	77.65	odd	6
847.2.n.i.130.2		40	11.10	odd	2
847.2.n.i.632.2		40	77.72	odd	30
847.2.n.i.753.4		40	11.6	odd	10
847.2.n.j.81.4		40	11.3	even	5
847.2.n.j.366.4		40	77.9	even	15
847.2.n.j.487.2		40	11.9	even	5
847.2.n.j.807.2		40	77.58	even	15
5929.2.a.bw.1.8		10	77.18	odd	30
5929.2.a.bx.1.8		10	77.73	even	30
5929.2.a.by.1.3		10	77.4	even	15
5929.2.a.bz.1.3		10	77.59	odd	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24721 - 0.265102i) q^{2} +(0.0145619 + 0.138547i) q^{3} +(-0.341843 + 0.152198i) q^{4} +(0.792967 - 0.880679i) q^{5} +(0.0548908 + 0.168936i) q^{6} +(-1.98226 + 1.75232i) q^{7} +(-2.44911 + 1.77938i) q^{8} +(2.91546 - 0.619700i) q^{9} +O(q^{10})\)	\(q+(1.24721 - 0.265102i) q^{2} +(0.0145619 + 0.138547i) q^{3} +(-0.341843 + 0.152198i) q^{4} +(0.792967 - 0.880679i) q^{5} +(0.0548908 + 0.168936i) q^{6} +(-1.98226 + 1.75232i) q^{7} +(-2.44911 + 1.77938i) q^{8} +(2.91546 - 0.619700i) q^{9} +(0.755525 - 1.30861i) q^{10} +(-0.0260644 - 0.0451450i) q^{12} +(-1.39908 + 4.30591i) q^{13} +(-2.00775 + 2.71101i) q^{14} +(0.133562 + 0.0970388i) q^{15} +(-2.08206 + 2.31236i) q^{16} +(6.51006 + 1.38375i) q^{17} +(3.47190 - 1.54579i) q^{18} +(2.78166 + 1.23847i) q^{19} +(-0.137032 + 0.421742i) q^{20} +(-0.271644 - 0.249120i) q^{21} +(1.89164 + 3.27641i) q^{23} +(-0.282192 - 0.313405i) q^{24} +(0.375843 + 3.57591i) q^{25} +(-0.603431 + 5.74127i) q^{26} +(0.257460 + 0.792379i) q^{27} +(0.410923 - 0.900715i) q^{28} +(3.38711 + 2.46088i) q^{29} +(0.192305 + 0.0856198i) q^{30} +(-4.59366 - 5.10178i) q^{31} +(1.04351 - 1.80742i) q^{32} +8.48623 q^{34} +(-0.0286387 + 3.13527i) q^{35} +(-0.902311 + 0.655567i) q^{36} +(0.354621 - 3.37400i) q^{37} +(3.79763 + 0.807210i) q^{38} +(-0.616944 - 0.131136i) q^{39} +(-0.374998 + 3.56787i) q^{40} +(-7.57505 + 5.50359i) q^{41} +(-0.404839 - 0.238691i) q^{42} -0.848738 q^{43} +(1.76611 - 3.05899i) q^{45} +(3.22785 + 3.58489i) q^{46} +(-4.99454 - 2.22371i) q^{47} +(-0.350690 - 0.254791i) q^{48} +(0.858747 - 6.94713i) q^{49} +(1.41674 + 4.36027i) q^{50} +(-0.0969164 + 0.922098i) q^{51} +(-0.177088 - 1.68488i) q^{52} +(2.64002 + 2.93204i) q^{53} +(0.531167 + 0.920009i) q^{54} +(1.73674 - 7.81883i) q^{56} +(-0.131081 + 0.403424i) q^{57} +(4.87682 + 2.17130i) q^{58} +(2.60081 - 1.15795i) q^{59} +(-0.0604264 - 0.0128440i) q^{60} +(-1.64430 + 1.82618i) q^{61} +(-7.08174 - 5.14519i) q^{62} +(-4.69330 + 6.33723i) q^{63} +(2.74540 - 8.44947i) q^{64} +(2.68271 + 4.64658i) q^{65} +(-0.264856 + 0.458743i) q^{67} +(-2.43602 + 0.517792i) q^{68} +(-0.426391 + 0.309791i) q^{69} +(0.795449 + 3.91793i) q^{70} +(1.01414 + 3.12120i) q^{71} +(-6.03760 + 6.70543i) q^{72} +(11.6036 - 5.16627i) q^{73} +(-0.452167 - 4.30208i) q^{74} +(-0.489959 + 0.104144i) q^{75} -1.13938 q^{76} -0.804222 q^{78} +(-4.76004 + 1.01178i) q^{79} +(0.385444 + 3.66726i) q^{80} +(8.06269 - 3.58974i) q^{81} +(-7.98864 + 8.87229i) q^{82} +(-3.55037 - 10.9269i) q^{83} +(0.130775 + 0.0438160i) q^{84} +(6.38090 - 4.63600i) q^{85} +(-1.05855 + 0.225002i) q^{86} +(-0.291625 + 0.505109i) q^{87} +(-0.926864 - 1.60538i) q^{89} +(1.39176 - 4.28339i) q^{90} +(-4.77200 - 10.9871i) q^{91} +(-1.14531 - 0.832114i) q^{92} +(0.639943 - 0.710729i) q^{93} +(-6.81873 - 1.44937i) q^{94} +(3.29646 - 1.46768i) q^{95} +(0.265608 + 0.118256i) q^{96} +(-0.304405 + 0.936862i) q^{97} +(-0.770662 - 8.89217i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9} - 14 q^{10} - 18 q^{12} + 4 q^{13} + 22 q^{14} + 16 q^{15} + 20 q^{16} + 12 q^{17} + 41 q^{18} + 24 q^{19} + 40 q^{20} + 2 q^{21} - 14 q^{23} + 7 q^{24} - 29 q^{25} - 5 q^{26} + 4 q^{27} + 24 q^{28} + 30 q^{29} - 6 q^{30} + 3 q^{31} + 30 q^{32} + 48 q^{34} - 6 q^{35} - 46 q^{36} - 11 q^{37} + 12 q^{38} + 32 q^{39} + 20 q^{40} - 10 q^{41} + 45 q^{42} + 72 q^{43} - 16 q^{45} + 17 q^{46} + 3 q^{47} - 62 q^{48} + 35 q^{49} - 6 q^{50} - 28 q^{51} - 2 q^{52} - 42 q^{53} - 34 q^{54} + 24 q^{56} + 36 q^{57} + 8 q^{58} - 9 q^{59} + 27 q^{60} + 20 q^{61} - 128 q^{62} + 36 q^{63} - 36 q^{64} + 40 q^{65} - 38 q^{67} + 33 q^{68} + 106 q^{69} - 18 q^{70} - 50 q^{71} - 42 q^{72} + 14 q^{73} + q^{74} - 16 q^{75} + 96 q^{76} - 100 q^{78} - 11 q^{79} - 18 q^{80} + 12 q^{81} - 24 q^{82} - 104 q^{83} + 44 q^{84} - 32 q^{85} + 2 q^{86} - 48 q^{87} - 10 q^{89} - 42 q^{90} - 14 q^{91} + 80 q^{92} - 13 q^{93} + 18 q^{94} + 8 q^{95} - 7 q^{96} + 46 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9 - 14 * q^10 - 18 * q^12 + 4 * q^13 + 22 * q^14 + 16 * q^15 + 20 * q^16 + 12 * q^17 + 41 * q^18 + 24 * q^19 + 40 * q^20 + 2 * q^21 - 14 * q^23 + 7 * q^24 - 29 * q^25 - 5 * q^26 + 4 * q^27 + 24 * q^28 + 30 * q^29 - 6 * q^30 + 3 * q^31 + 30 * q^32 + 48 * q^34 - 6 * q^35 - 46 * q^36 - 11 * q^37 + 12 * q^38 + 32 * q^39 + 20 * q^40 - 10 * q^41 + 45 * q^42 + 72 * q^43 - 16 * q^45 + 17 * q^46 + 3 * q^47 - 62 * q^48 + 35 * q^49 - 6 * q^50 - 28 * q^51 - 2 * q^52 - 42 * q^53 - 34 * q^54 + 24 * q^56 + 36 * q^57 + 8 * q^58 - 9 * q^59 + 27 * q^60 + 20 * q^61 - 128 * q^62 + 36 * q^63 - 36 * q^64 + 40 * q^65 - 38 * q^67 + 33 * q^68 + 106 * q^69 - 18 * q^70 - 50 * q^71 - 42 * q^72 + 14 * q^73 + q^74 - 16 * q^75 + 96 * q^76 - 100 * q^78 - 11 * q^79 - 18 * q^80 + 12 * q^81 - 24 * q^82 - 104 * q^83 + 44 * q^84 - 32 * q^85 + 2 * q^86 - 48 * q^87 - 10 * q^89 - 42 * q^90 - 14 * q^91 + 80 * q^92 - 13 * q^93 + 18 * q^94 + 8 * q^95 - 7 * q^96 + 46 * q^97 - 116 * q^98

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