LMFDB - Embedded newform 847.2.n.h.9.2

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			9.2
Character	$\chi$	$=$	847.9
Dual form			847.2.n.h.753.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.853189 - 0.947563i) q^{2} +(-0.127266 - 0.0566625i) q^{3} +(0.0391138 - 0.372143i) q^{4} +(-1.15917 - 0.246390i) q^{5} +(0.0548908 + 0.168936i) q^{6} +(1.05400 - 2.42674i) q^{7} +(-2.44911 + 1.77938i) q^{8} +(-1.99441 - 2.21501i) q^{9} +O(q^{10})$	\(q+(-0.853189 - 0.947563i) q^{2} +(-0.127266 - 0.0566625i) q^{3} +(0.0391138 - 0.372143i) q^{4} +(-1.15917 - 0.246390i) q^{5} +(0.0548908 + 0.168936i) q^{6} +(1.05400 - 2.42674i) q^{7} +(-2.44911 + 1.77938i) q^{8} +(-1.99441 - 2.21501i) q^{9} +(0.755525 + 1.30861i) q^{10} +(-0.0260644 + 0.0451450i) q^{12} +(-1.39908 + 4.30591i) q^{13} +(-3.19875 + 1.07174i) q^{14} +(0.133562 + 0.0970388i) q^{15} +(3.04360 + 0.646937i) q^{16} +(-4.45339 + 4.94600i) q^{17} +(-0.397257 + 3.77965i) q^{18} +(-0.318279 - 3.02822i) q^{19} +(-0.137032 + 0.421742i) q^{20} +(-0.271644 + 0.249120i) q^{21} +(1.89164 - 3.27641i) q^{23} +(0.412513 - 0.0876823i) q^{24} +(-3.28475 - 1.46247i) q^{25} +(5.27380 - 2.34805i) q^{26} +(0.257460 + 0.792379i) q^{27} +(-0.861870 - 0.487159i) q^{28} +(3.38711 + 2.46088i) q^{29} +(-0.0220037 - 0.209351i) q^{30} +(6.71510 - 1.42734i) q^{31} +(1.04351 + 1.80742i) q^{32} +8.48623 q^{34} +(-1.81970 + 2.55332i) q^{35} +(-0.902311 + 0.655567i) q^{36} +(-3.09928 + 1.37989i) q^{37} +(-2.59788 + 2.88524i) q^{38} +(0.422039 - 0.468722i) q^{39} +(3.27737 - 1.45918i) q^{40} +(-7.57505 + 5.50359i) q^{41} +(0.467820 + 0.0448536i) q^{42} -0.848738 q^{43} +(1.76611 + 3.05899i) q^{45} +(-4.71853 + 1.00295i) q^{46} +(0.571478 + 5.43725i) q^{47} +(-0.350690 - 0.254791i) q^{48} +(-4.77816 - 5.11558i) q^{49} +(1.41674 + 4.36027i) q^{50} +(0.847019 - 0.377117i) q^{51} +(1.54769 + 0.689078i) q^{52} +(-3.85923 + 0.820305i) q^{53} +(0.531167 - 0.920009i) q^{54} +(1.73674 + 7.81883i) q^{56} +(-0.131081 + 0.403424i) q^{57} +(-0.558009 - 5.30910i) q^{58} +(-0.297586 + 2.83134i) q^{59} +(0.0413365 - 0.0459088i) q^{60} +(2.40366 + 0.510915i) q^{61} +(-7.08174 - 5.14519i) q^{62} +(-7.47737 + 2.50528i) q^{63} +(2.74540 - 8.44947i) q^{64} +(2.68271 - 4.64658i) q^{65} +(-0.264856 - 0.458743i) q^{67} +(1.66643 + 1.85076i) q^{68} +(-0.426391 + 0.309791i) q^{69} +(3.97198 - 0.454189i) q^{70} +(1.01414 + 3.12120i) q^{71} +(8.82587 + 1.87600i) q^{72} +(-1.32769 + 12.6322i) q^{73} +(3.95180 + 1.75945i) q^{74} +(0.335171 + 0.372245i) q^{75} -1.13938 q^{76} -0.804222 q^{78} +(3.25624 + 3.61643i) q^{79} +(-3.36866 - 1.49982i) q^{80} +(-0.922538 + 8.77736i) q^{81} +(11.6779 + 2.48222i) q^{82} +(-3.55037 - 10.9269i) q^{83} +(0.0820832 + 0.110835i) q^{84} +(6.38090 - 4.63600i) q^{85} +(0.724134 + 0.804233i) q^{86} +(-0.291625 - 0.505109i) q^{87} +(-0.926864 + 1.60538i) q^{89} +(1.39176 - 4.28339i) q^{90} +(8.97471 + 7.93364i) q^{91} +(-1.14531 - 0.832114i) q^{92} +(-0.935481 - 0.198843i) q^{93} +(4.66456 - 5.18051i) q^{94} +(-0.377183 + 3.58866i) q^{95} +(-0.0303910 - 0.289151i) 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.853189	−	0.947563i	−0.603296	−	0.670028i	0.361700	−	0.932295i	$-0.382197\pi$
$2$	−0.853189	−	0.947563i	−0.603296	−	0.670028i	−0.964995	+	0.262267i	$0.915530\pi$
$3$	−0.127266	−	0.0566625i	−0.0734771	−	0.0327141i	0.369669	−	0.929163i	$-0.379471\pi$
$3$	−0.127266	−	0.0566625i	−0.0734771	−	0.0327141i	−0.443146	+	0.896449i	$0.646138\pi$
$4$	0.0391138	−	0.372143i	0.0195569	−	0.186072i
$5$	−1.15917	−	0.246390i	−0.518398	−	0.110189i	−0.0587200	−	0.998274i	$-0.518702\pi$
$5$	−1.15917	−	0.246390i	−0.518398	−	0.110189i	−0.459678	+	0.888086i	$0.652035\pi$
$6$	0.0548908	+	0.168936i	0.0224091	+	0.0689680i
$7$	1.05400	−	2.42674i	0.398375	−	0.917222i
$7$	1.05400	−	2.42674i	0.398375	−	0.917222i
$8$	−2.44911	+	1.77938i	−0.865891	+	0.629107i
$9$	−1.99441	−	2.21501i	−0.664802	−	0.738337i
$10$	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	$0.883934\pi$
$14$	−3.19875	+	1.07174i	−0.854903	+	0.286434i
$15$	0.133562	+	0.0970388i	0.0344857	+	0.0250553i
$16$	3.04360	+	0.646937i	0.760899	+	0.161734i
$17$	−4.45339	+	4.94600i	−1.08011	+	1.19958i	−0.101287	+	0.994857i	$0.532296\pi$
$17$	−4.45339	+	4.94600i	−1.08011	+	1.19958i	−0.978820	+	0.204723i	$0.934371\pi$
$18$	−0.397257	+	3.77965i	−0.0936344	+	0.890872i
$19$	−0.318279	−	3.02822i	−0.0730182	−	0.694722i	−0.968397	−	0.249416i	$-0.919762\pi$
$19$	−0.318279	−	3.02822i	−0.0730182	−	0.694722i	0.895378	−	0.445306i	$-0.146905\pi$
$20$	−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	−0.598595	−	0.801052i	$-0.704274\pi$
$23$	1.89164	−	3.27641i	0.394434	−	0.683179i	0.993029	+	0.117873i	$0.0376075\pi$
$24$	0.412513	−	0.0876823i	0.0842038	−	0.0178981i
$25$	−3.28475	−	1.46247i	−0.656950	−	0.292493i
$26$	5.27380	−	2.34805i	1.03428	−	0.460490i
$27$	0.257460	+	0.792379i	0.0495481	+	0.152493i
$28$	−0.861870	−	0.487159i	−0.162878	−	0.0920644i
$29$	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	$0.572916\pi$
$30$	−0.0220037	−	0.209351i	−0.00401731	−	0.0382221i
$31$	6.71510	−	1.42734i	1.20607	−	0.256358i	0.439334	−	0.898324i	$-0.355214\pi$
$31$	6.71510	−	1.42734i	1.20607	−	0.256358i	0.766733	+	0.641966i	$0.221881\pi$
$32$	1.04351	+	1.80742i	0.184469	+	0.319510i
$33$		0			0
$34$	8.48623			1.45538
$35$	−1.81970	+	2.55332i	−0.307585	+	0.431590i
$36$	−0.902311	+	0.655567i	−0.150385	+	0.109261i
$37$	−3.09928	+	1.37989i	−0.509518	+	0.226852i	−0.645360	−	0.763878i	$-0.723293\pi$
$37$	−3.09928	+	1.37989i	−0.509518	+	0.226852i	0.135842	+	0.990730i	$0.456626\pi$
$38$	−2.59788	+	2.88524i	−0.421431	+	0.468047i
$39$	0.422039	−	0.468722i	0.0675803	−	0.0750555i
$40$	3.27737	−	1.45918i	0.518197	−	0.230716i
$41$	−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	$0.561015\pi$
$42$	0.467820	+	0.0448536i	0.0721862	+	0.00692106i
$43$	−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
$46$	−4.71853	+	1.00295i	−0.695709	+	0.147878i
$47$	0.571478	+	5.43725i	0.0833586	+	0.793104i	0.953721	+	0.300693i	$0.0972179\pi$
$47$	0.571478	+	5.43725i	0.0833586	+	0.793104i	−0.870362	+	0.492412i	$0.836115\pi$
$48$	−0.350690	−	0.254791i	−0.0506177	−	0.0367759i
$49$	−4.77816	−	5.11558i	−0.682594	−	0.730798i
$50$	1.41674	+	4.36027i	0.200357	+	0.616635i
$51$	0.847019	−	0.377117i	0.118606	−	0.0528069i
$52$	1.54769	+	0.689078i	0.214627	+	0.0955579i
$53$	−3.85923	+	0.820305i	−0.530106	+	0.112677i	−0.465186	−	0.885213i	$-0.654013\pi$
$53$	−3.85923	+	0.820305i	−0.530106	+	0.112677i	−0.0649200	+	0.997890i	$0.520679\pi$
$54$	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
$58$	−0.558009	−	5.30910i	−0.0732701	−	0.697119i
$59$	−0.297586	+	2.83134i	−0.0387424	+	0.368609i	0.957924	+	0.287022i	$0.0926654\pi$
$59$	−0.297586	+	2.83134i	−0.0387424	+	0.368609i	−0.996666	+	0.0815868i	$0.974001\pi$
$60$	0.0413365	−	0.0459088i	0.00533652	−	0.00592680i
$61$	2.40366	+	0.510915i	0.307758	+	0.0654159i	0.359202	−	0.933260i	$-0.383049\pi$
$61$	2.40366	+	0.510915i	0.307758	+	0.0654159i	−0.0514440	+	0.998676i	$0.516382\pi$
$62$	−7.08174	−	5.14519i	−0.899382	−	0.653439i
$63$	−7.47737	+	2.50528i	−0.942060	+	0.315636i
$64$	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	0.849393	−	0.527760i	$-0.176968\pi$
$67$	−0.264856	−	0.458743i	−0.0323573	−	0.0560444i	−0.881751	+	0.471716i	$0.843635\pi$
$68$	1.66643	+	1.85076i	0.202084	+	0.224437i
$69$	−0.426391	+	0.309791i	−0.0513315	+	0.0372945i
$70$	3.97198	−	0.454189i	0.474742	−	0.0542860i
$71$	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	$0.837614\pi$
$72$	8.82587	+	1.87600i	1.04014	+	0.221088i
$73$	−1.32769	+	12.6322i	−0.155395	+	1.47848i	0.587581	+	0.809165i	$0.300080\pi$
$73$	−1.32769	+	12.6322i	−0.155395	+	1.47848i	−0.742976	+	0.669318i	$0.766586\pi$
$74$	3.95180	+	1.75945i	0.459387	+	0.204532i
$75$	0.335171	+	0.372245i	0.0387022	+	0.0429831i
$76$	−1.13938			−0.130696
$77$		0			0
$78$	−0.804222			−0.0910602
$79$	3.25624	+	3.61643i	0.366356	+	0.406880i	0.897934	−	0.440130i	$-0.145067\pi$
$79$	3.25624	+	3.61643i	0.366356	+	0.406880i	−0.531578	+	0.847009i	$0.678401\pi$
$80$	−3.36866	−	1.49982i	−0.376628	−	0.167685i
$81$	−0.922538	+	8.77736i	−0.102504	+	0.975263i
$82$	11.6779	+	2.48222i	1.28961	+	0.274116i
$83$	−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	$-0.317172\pi$
$84$	0.0820832	+	0.110835i	0.00895601	+	0.0120930i
$85$	6.38090	−	4.63600i	0.692106	−	0.502844i
$86$	0.724134	+	0.804233i	0.0780854	+	0.0867226i
$87$	−0.291625	−	0.505109i	−0.0312655	−	0.0541534i
$88$		0			0
$89$	−0.926864	+	1.60538i	−0.0982474	+	0.170169i	−0.910959	−	0.412496i	$-0.864657\pi$
$89$	−0.926864	+	1.60538i	−0.0982474	+	0.170169i	0.812712	+	0.582666i	$0.197990\pi$
$90$	1.39176	−	4.28339i	0.146704	−	0.451509i
$91$	8.97471	+	7.93364i	0.940806	+	0.831671i
$92$	−1.14531	−	0.832114i	−0.119406	−	0.0867538i
$93$	−0.935481	−	0.198843i	−0.0970049	−	0.0206190i
$94$	4.66456	−	5.18051i	0.481112	−	0.534329i
$95$	−0.377183	+	3.58866i	−0.0386981	+	0.368188i
$96$	−0.0303910	−	0.289151i	−0.00310177	−	0.0295114i
$97$	−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
$101$	−0.0871658	+	0.0185277i	−0.00867332	+	0.00184357i	−0.212246	−	0.977216i	$-0.568078\pi$
$101$	−0.0871658	+	0.0185277i	−0.00867332	+	0.00184357i	0.203573	+	0.979060i	$0.434745\pi$
$102$	−1.08001	−	0.480851i	−0.106937	−	0.0476114i
$103$	−13.3941	+	5.96344i	−1.31976	+	0.587595i	−0.941159	−	0.337965i	$-0.890261\pi$
$103$	−13.3941	+	5.96344i	−1.31976	+	0.587595i	−0.378601	+	0.925560i	$0.623595\pi$
$104$	−4.23537	−	13.0351i	−0.415313	−	1.27820i
$105$	0.376263	−	0.221843i	0.0367195	−	0.0216496i
$106$	4.06994	+	2.95699i	0.395308	+	0.287208i
$107$	−0.521644	−	4.96311i	−0.0504293	−	0.479802i	−0.990368	−	0.138459i	$-0.955785\pi$
$107$	−0.521644	−	4.96311i	−0.0504293	−	0.479802i	0.939939	−	0.341343i	$-0.110882\pi$
$108$	0.304949	−	0.0648189i	0.0293437	−	0.00623720i
$109$	−9.32385	−	16.1494i	−0.893063	−	1.54683i	−0.836184	−	0.548449i	$-0.815219\pi$
$109$	−9.32385	−	16.1494i	−0.893063	−	1.54683i	−0.0568784	−	0.998381i	$-0.518115\pi$
$110$		0			0
$111$	0.472621			0.0448592
$112$	4.77791	−	6.70415i	0.451470	−	0.633483i
$113$	−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	$0.357469\pi$
$114$	0.494106	−	0.219990i	0.0462773	−	0.0206040i
$115$	−3.00001	+	3.33185i	−0.279753	+	0.310697i
$116$	1.04828	−	1.16424i	0.0973307	−	0.108097i
$117$	12.3280	−	5.48877i	1.13972	−	0.507437i
$118$	2.93677	−	2.13369i	0.270352	−	0.196422i
$119$	7.30877	+	16.0203i	0.669994	+	1.46858i
$120$	−0.499778			−0.0456233
$121$		0			0
$122$	−1.56666	−	2.71353i	−0.141838	−	0.245671i
$123$	1.27589	−	0.271200i	0.115043	−	0.0244532i
$124$	−0.268521	−	2.55481i	−0.0241139	−	0.229429i
$125$	8.24097	+	5.98742i	0.737095	+	0.535531i
$126$	8.75352	+	4.94780i	0.779826	+	0.440785i
$127$	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	$0.852172\pi$
$128$	−6.53555	+	2.90982i	−0.577667	+	0.257194i
$129$	0.108016	+	0.0480917i	0.00951024	+	0.00423423i
$130$	−6.69178	+	1.42238i	−0.586908	+	0.124751i
$131$	−2.44042	+	4.22693i	−0.213221	+	0.369309i	−0.952721	−	0.303848i	$-0.901729\pi$
$131$	−2.44042	+	4.22693i	−0.213221	+	0.369309i	0.739500	+	0.673157i	$0.235062\pi$
$132$		0			0
$133$	−7.68418	−	2.41937i	−0.666303	−	0.209786i
$134$	−0.208716	+	0.642362i	−0.0180303	+	0.0554916i
$135$	−0.103206	−	0.981941i	−0.00888257	−	0.0845120i
$136$	2.10603	−	20.0376i	0.180591	−	1.71821i
$137$	−5.51475	+	6.12475i	−0.471157	+	0.523272i	−0.931143	−	0.364653i	$-0.881188\pi$
$137$	−5.51475	+	6.12475i	−0.471157	+	0.523272i	0.459987	+	0.887926i	$0.347854\pi$
$138$	0.657339	+	0.139722i	0.0559564	+	0.0118939i
$139$	−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	$-0.696126\pi$
$140$	0.879026	+	0.777058i	0.0742913	+	0.0656734i
$141$	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
$145$	−3.31991	−	3.68714i	−0.275704	−	0.306200i
$146$	13.1025	−	9.51955i	1.08437	−	0.787844i
$147$	0.318236	+	0.921783i	0.0262476	+	0.0760274i
$148$	0.392291	+	1.20735i	0.0322461	+	0.0992434i
$149$	−7.90827	−	1.68095i	−0.647871	−	0.137709i	−0.127756	−	0.991806i	$-0.540777\pi$
$149$	−7.90827	−	1.68095i	−0.647871	−	0.137709i	−0.520115	+	0.854096i	$0.674111\pi$
$150$	0.0667612	−	0.635190i	0.00545103	−	0.0518631i
$151$	5.39440	+	2.40174i	0.438990	+	0.195451i	0.614317	−	0.789059i	$-0.289432\pi$
$151$	5.39440	+	2.40174i	0.438990	+	0.195451i	−0.175327	+	0.984510i	$0.556098\pi$
$152$	6.16786	+	6.85011i	0.500280	+	0.555617i
$153$	19.8373			1.60375
$154$		0			0
$155$	−8.13565			−0.653471
$156$	−0.157924	−	0.175392i	−0.0126440	−	0.0140426i
$157$	15.2672	+	6.79740i	1.21846	+	0.542491i	0.912313	−	0.409494i	$-0.134295\pi$
$157$	15.2672	+	6.79740i	1.21846	+	0.542491i	0.306143	+	0.951986i	$0.400961\pi$
$158$	0.648597	−	6.17099i	0.0515996	−	0.490938i
$159$	0.537630	+	0.114277i	0.0426368	+	0.00906273i
$160$	−0.764284	−	2.35223i	−0.0604220	−	0.185960i
$161$	−5.95722	−	8.04386i	−0.469495	−	0.633945i
$162$	9.10420	−	6.61459i	0.715294	−	0.519691i
$163$	−16.3333	−	18.1400i	−1.27932	−	1.42083i	−0.857774	−	0.514027i	$-0.828153\pi$
$163$	−16.3333	−	18.1400i	−1.27932	−	1.42083i	−0.421550	−	0.906805i	$-0.638514\pi$
$164$	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	$-0.0453761\pi$
$168$	0.222007	−	1.09348i	0.0171282	−	0.0843638i
$169$	−6.06625	−	4.40739i	−0.466635	−	0.339030i
$170$	−9.83701	−	2.09092i	−0.754464	−	0.160366i
$171$	−6.07277	+	6.74449i	−0.464396	+	0.515764i
$172$	−0.0331974	+	0.315852i	−0.00253128	+	0.0240835i
$173$	−0.289325	−	2.75274i	−0.0219969	−	0.209287i	−1.00000		0.000695231i	$-0.999779\pi$
$173$	−0.289325	−	2.75274i	−0.0219969	−	0.209287i	0.978003	−	0.208592i	$-0.0668880\pi$
$174$	−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
$178$	2.31198	−	0.491427i	0.173291	−	0.0368340i
$179$	−11.3367	−	5.04743i	−0.847345	−	0.377262i	−0.0633215	−	0.997993i	$-0.520169\pi$
$179$	−11.3367	−	5.04743i	−0.847345	−	0.377262i	−0.784024	+	0.620731i	$0.786836\pi$
$180$	1.20746	−	0.537596i	0.0899988	−	0.0400700i
$181$	−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	$-0.305654\pi$
$182$	−0.139509	−	15.2730i	−0.0103411	−	1.13211i
$183$	−0.276955	−	0.201220i	−0.0204731	−	0.0148746i
$184$	1.19716	+	11.3902i	0.0882560	+	0.839699i
$185$	3.93259	−	0.835898i	0.289130	−	0.0614564i
$186$	0.609726	+	1.05608i	0.0447073	+	0.0774353i
$187$		0			0
$188$	2.04579			0.149205
$189$	2.19426	+	0.210381i	0.159609	+	0.0153030i
$190$	3.72228	−	2.70440i	0.270043	−	0.196198i
$191$	−7.88779	+	3.51187i	−0.570741	+	0.254110i	−0.671753	−	0.740775i	$-0.734458\pi$
$191$	−7.88779	+	3.51187i	−0.570741	+	0.254110i	0.101013	+	0.994885i	$0.467792\pi$
$192$	−0.828164	+	0.919770i	−0.0597676	+	0.0663787i
$193$	−4.93423	+	5.48002i	−0.355174	+	0.394460i	−0.894081	−	0.447905i	$-0.852170\pi$
$193$	−4.93423	+	5.48002i	−0.355174	+	0.394460i	0.538908	+	0.842365i	$0.318837\pi$
$194$	1.14745	−	0.510878i	0.0823821	−	0.0366789i
$195$	−0.604705	+	0.439344i	−0.0433038	+	0.0314620i
$196$	−2.09062	+	1.57807i	−0.149330	+	0.112719i
$197$	−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	−0.988988	−	0.147997i	$-0.952717\pi$
$199$	−8.78374	−	15.2139i	−0.622663	−	1.07848i	0.366325	−	0.930487i	$-0.380616\pi$
$200$	10.6470	−	2.26309i	0.752857	−	0.160025i
$201$	0.00771358	+	0.0733899i	0.000544074	+	0.00517652i
$202$	0.0919250	+	0.0667874i	0.00646782	+	0.00469915i
$203$	9.54195	−	5.62587i	0.669713	−	0.394859i
$204$	−0.107211	−	0.329963i	−0.00750630	−	0.0231020i
$205$	10.1368	−	4.51320i	0.707986	−	0.315216i
$206$	17.0784	+	7.60381i	1.18991	+	0.529782i
$207$	−11.0300	+	2.34450i	−0.766637	+	0.162954i
$208$	−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	$0.105829\pi$
$212$	0.154322	+	1.46827i	0.0105989	+	0.100841i
$213$	0.0477895	−	0.454686i	0.00327448	−	0.0311546i
$214$	−4.25780	+	4.72877i	−0.291057	+	0.323252i
$215$	0.983835	+	0.209121i	0.0670970	+	0.0142619i
$216$	−2.04049	−	1.48250i	−0.138838	−	0.100872i
$217$	3.61395	−	17.8002i	0.245331	−	1.20836i
$218$	−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
$222$	−0.403235	−	0.447838i	−0.0270634	−	0.0300569i
$223$	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	$0.0898550\pi$
$224$	5.48601	−	0.627316i	0.366549	−	0.0419143i
$225$	3.31175	+	10.1925i	0.220783	+	0.679501i
$226$	4.76136	+	1.01206i	0.316721	+	0.0673212i
$227$	−0.997106	+	9.48683i	−0.0661803	+	0.629663i	0.910284	+	0.413984i	$0.135863\pi$
$227$	−0.997106	+	9.48683i	−0.0661803	+	0.629663i	−0.976464	+	0.215679i	$0.930804\pi$
$228$	0.145005	+	0.0645602i	0.00960317	+	0.00427561i
$229$	−1.20501	−	1.33830i	−0.0796292	−	0.0884371i	0.702014	−	0.712164i	$-0.252285\pi$
$229$	−1.20501	−	1.33830i	−0.0796292	−	0.0884371i	−0.781643	+	0.623726i	$0.785618\pi$
$230$	5.71671			0.376949
$231$		0			0
$232$	−12.6743			−0.832105
$233$	−13.3515	−	14.8283i	−0.874685	−	0.971436i	0.125101	−	0.992144i	$-0.460075\pi$
$233$	−13.3515	−	14.8283i	−0.874685	−	0.971436i	−0.999786	+	0.0207079i	$0.993408\pi$
$234$	−15.7190	−	6.99857i	−1.02759	−	0.457511i
$235$	0.677242	−	6.44352i	0.0441784	−	0.420329i
$236$	1.04203	+	0.221489i	0.0678301	+	0.0144177i
$237$	−0.209494	−	0.644755i	−0.0136081	−	0.0418814i
$238$	8.94450	−	20.5939i	0.579786	−	1.33490i
$239$	−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	$0.339972\pi$
$240$	0.343732	+	0.381753i	0.0221878	+	0.0246421i
$241$	−1.31079	−	2.27036i	−0.0844356	−	0.146247i	0.820715	−	0.571338i	$-0.193575\pi$
$241$	−1.31079	−	2.27036i	−0.0844356	−	0.146247i	−0.905151	+	0.425091i	$0.860242\pi$
$242$		0			0
$243$	1.86449	−	3.22939i	0.119607	−	0.207166i
$244$	0.284150	−	0.874524i	0.0181908	−	0.0559857i
$245$	4.27829	+	7.10714i	0.273330	+	0.454059i
$246$	−1.34556	−	0.977605i	−0.0857896	−	0.0623298i
$247$	13.4846	+	2.86623i	0.858002	+	0.182374i
$248$	−13.9062	+	15.4444i	−0.883047	+	0.980723i
$249$	−0.167305	+	1.59180i	−0.0106025	+	0.100876i
$250$	−1.35766	−	12.9172i	−0.0858657	−	0.816958i
$251$	−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
$255$	−1.07476	+	0.228447i	−0.0673041	+	0.0143059i
$256$	−7.89912	−	3.51692i	−0.493695	−	0.219807i
$257$	20.8555	−	9.28546i	1.30093	−	0.579211i	0.364872	−	0.931058i	$-0.381113\pi$
$257$	20.8555	−	9.28546i	1.30093	−	0.579211i	0.936058	+	0.351847i	$0.114446\pi$
$258$	−0.0465879	−	0.143383i	−0.00290044	−	0.00892663i
$259$	0.0819861	+	8.97555i	0.00509437	+	0.557714i
$260$	−1.62426	−	1.18010i	−0.100733	−	0.0731865i
$261$	−1.30439	−	12.4105i	−0.0807400	−	0.768190i
$262$	6.08743	−	1.29392i	0.376082	−	0.0799388i
$263$	−3.96286	−	6.86387i	−0.244360	−	0.423244i	0.717591	−	0.696464i	$-0.245245\pi$
$263$	−3.96286	−	6.86387i	−0.244360	−	0.423244i	−0.961952	+	0.273220i	$0.911911\pi$
$264$		0			0
$265$	4.67563			0.287222
$266$	4.26355	+	9.34542i	0.261415	+	0.573005i
$267$	0.208923	−	0.151791i	0.0127859	−	0.00928948i
$268$	−0.181078	+	0.0806210i	−0.0110611	+	0.00492471i
$269$	−7.21769	+	8.01605i	−0.440070	+	0.488747i	−0.921851	−	0.387544i	$-0.873323\pi$
$269$	−7.21769	+	8.01605i	−0.440070	+	0.488747i	0.481781	+	0.876292i	$0.339990\pi$
$270$	−0.842396	+	0.935575i	−0.0512666	+	0.0569373i
$271$	3.02573	−	1.34714i	0.183800	−	0.0818331i	−0.312773	−	0.949828i	$-0.601258\pi$
$271$	3.02573	−	1.34714i	0.183800	−	0.0818331i	0.496573	+	0.867995i	$0.334591\pi$
$272$	−16.7541	+	12.1726i	−1.01587	+	0.738070i
$273$	−0.692637	−	1.51821i	−0.0419203	−	0.0918864i
$274$	10.5087			0.634854
$275$		0			0
$276$	0.0986090	+	0.170796i	0.00593556	+	0.0102807i
$277$	−7.95910	+	1.69176i	−0.478216	+	0.101648i	−0.440712	−	0.897649i	$-0.645274\pi$
$277$	−7.95910	+	1.69176i	−0.478216	+	0.101648i	−0.0375038	+	0.999296i	$0.511941\pi$
$278$	2.97687	+	28.3230i	0.178541	+	1.69870i
$279$	−16.5542	−	12.0273i	−0.991074	−	0.720058i
$280$	−0.0866971	−	9.49130i	−0.00518114	−	0.567213i
$281$	−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	$-0.245036\pi$
$282$	−0.887181	+	0.394998i	−0.0528308	+	0.0235218i
$283$	7.96855	+	3.54783i	0.473681	+	0.210896i	0.629671	−	0.776862i	$-0.283190\pi$
$283$	7.96855	+	3.54783i	0.473681	+	0.210896i	−0.155989	+	0.987759i	$0.549857\pi$
$284$	1.20120	−	0.255323i	0.0712781	−	0.0151506i
$285$	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
$289$	−2.85317	−	27.1461i	−0.167833	−	1.59683i
$290$	−0.661279	+	6.29165i	−0.0388317	+	0.369459i
$291$	0.0918254	−	0.101982i	0.00538290	−	0.00597831i
$292$	4.64905	+	0.988185i	0.272065	+	0.0578292i
$293$	−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	$0.951637\pi$
$294$	0.601932	−	1.08800i	0.0351054	−	0.0634537i
$295$	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
$299$	11.4614	+	12.7292i	0.662830	+	0.736147i
$300$	0.151638	−	0.110172i	0.00875483	−	0.00636076i
$301$	−0.894572	+	2.05967i	−0.0515623	+	0.118717i
$302$	−2.32664	−	7.16067i	−0.133883	−	0.412050i
$303$	0.0121431	+	0.00258109i	0.000697601	+	0.000148280i
$304$	0.990354	−	9.42259i	0.0568007	−	0.540423i
$305$	−2.66038	−	1.18448i	−0.152333	−	0.0678230i
$306$	−16.9250	−	18.7971i	−0.967537	−	1.07456i
$307$	−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
$310$	6.94125	+	7.70904i	0.394236	+	0.437844i
$311$	0.751082	+	0.334403i	0.0425900	+	0.0189623i	0.427921	−	0.903816i	$-0.359246\pi$
$311$	0.751082	+	0.334403i	0.0425900	+	0.0189623i	−0.385331	+	0.922778i	$0.625913\pi$
$312$	−0.199584	+	1.89892i	−0.0112992	+	0.107505i
$313$	−6.24157	−	1.32669i	−0.352794	−	0.0749887i	0.0281058	−	0.999605i	$-0.491052\pi$
$313$	−6.24157	−	1.32669i	−0.352794	−	0.0749887i	−0.380900	+	0.924616i	$0.624386\pi$
$314$	−6.58485	−	20.2661i	−0.371605	−	1.14368i
$315$	9.28485	−	1.06171i	0.523142	−	0.0598204i
$316$	1.47319	−	1.07034i	0.0828736	−	0.0602112i
$317$	5.48498	+	6.09168i	0.308067	+	0.342143i	0.877220	−	0.480089i	$-0.159395\pi$
$317$	5.48498	+	6.09168i	0.308067	+	0.342143i	−0.569153	+	0.822232i	$0.692729\pi$
$318$	−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
$322$	−2.53943	+	12.5078i	−0.141517	+	0.697031i
$323$	16.3950	+	11.9117i	0.912242	+	0.662782i
$324$	3.23035	+	0.686633i	0.179464	+	0.0381463i
$325$	10.8929	−	12.0978i	0.604228	−	0.671063i
$326$	−3.25336	+	30.9537i	−0.180187	+	1.71436i
$327$	0.271545	+	2.58358i	0.0150165	+	0.142872i
$328$	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	−0.367928	−	0.929854i	$-0.619933\pi$
$331$	11.3038	−	19.5788i	0.621313	−	1.07615i	0.989241	−	0.146292i	$-0.0467339\pi$
$332$	−4.20525	+	0.893853i	−0.230793	+	0.0490566i
$333$	9.23768	+	4.11288i	0.506222	+	0.225384i
$334$	−13.2767	+	5.91118i	−0.726471	+	0.323446i
$335$	0.193984	+	0.597021i	0.0105985	+	0.0326187i
$336$	−0.987940	+	0.582483i	−0.0538965	+	0.0317771i
$337$	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	$0.464473\pi$
$338$	0.999383	+	9.50849i	0.0543593	+	0.517194i
$339$	0.520211	−	0.110574i	0.0282540	−	0.00600557i
$340$	−1.47567	−	2.55594i	−0.0800297	−	0.138615i
$341$		0			0
$342$	11.5721			0.625745
$343$	−17.4504	+	6.20353i	−0.942233	+	0.334959i
$344$	2.07865	−	1.51023i	0.112073	−	0.0814261i
$345$	0.570591	−	0.254043i	0.0307196	−	0.0136772i
$346$	−2.36154	+	2.62276i	−0.126957	+	0.141000i
$347$	−4.03031	+	4.47611i	−0.216358	+	0.240290i	−0.841548	−	0.540183i	$-0.818355\pi$
$347$	−4.03031	+	4.47611i	−0.216358	+	0.240290i	0.625189	+	0.780473i	$0.285022\pi$
$348$	−0.199380	+	0.0887695i	−0.0106879	+	0.00475854i
$349$	−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	$0.490038\pi$
$350$	12.0745	+	1.15768i	0.645409	+	0.0618804i
$351$	−3.77212			−0.201341
$352$		0			0
$353$	13.5755	+	23.5134i	0.722549	+	1.25149i	0.959975	+	0.280086i	$0.0903629\pi$
$353$	13.5755	+	23.5134i	0.722549	+	1.25149i	−0.237426	+	0.971406i	$0.576304\pi$
$354$	−0.494651	+	0.105141i	−0.0262904	+	0.00558820i
$355$	−0.406531	−	3.86788i	−0.0215764	−	0.205286i
$356$	0.561177	+	0.407719i	0.0297423	+	0.0216090i
$357$	−0.0224064	−	2.45298i	−0.00118587	−	0.129825i
$358$	4.88960	+	15.0487i	0.258424	+	0.795346i
$359$	−31.6814	+	14.1055i	−1.67208	+	0.744457i	−0.672086	+	0.740473i	$0.734602\pi$
$359$	−31.6814	+	14.1055i	−1.67208	+	0.744457i	−0.999992	+	0.00398451i	$0.998732\pi$
$360$	−9.76849	−	4.34921i	−0.514845	−	0.229224i
$361$	9.51598	−	2.02268i	0.500841	−	0.106457i
$362$	−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
$366$	0.0456269	+	0.434111i	0.00238496	+	0.0226913i
$367$	−3.11384	+	29.6262i	−0.162541	+	1.54647i	0.544172	+	0.838973i	$0.316844\pi$
$367$	−3.11384	+	29.6262i	−0.162541	+	1.54647i	−0.706713	+	0.707500i	$0.749823\pi$
$368$	7.87701	−	8.74831i	0.410618	−	0.456037i
$369$	27.2982	+	5.80242i	1.42109	+	0.302062i
$370$	−4.14731	−	3.01320i	−0.215608	−	0.156649i
$371$	−2.07697	+	10.2300i	−0.107831	+	0.531113i
$372$	−0.110588	+	0.340356i	−0.00573373	+	0.0176466i
$373$	0.00623341	−	0.0107966i	0.000322754	−	0.000559025i	−0.865864	−	0.500279i	$-0.833231\pi$
$373$	0.00623341	−	0.0107966i	0.000322754	−	0.000559025i	0.866187	+	0.499720i	$0.166564\pi$
$374$		0			0
$375$	−0.709534	−	1.22895i	−0.0366402	−	0.0634627i
$376$	−11.0746	−	12.2995i	−0.571127	−	0.634300i
$377$	−15.3352	+	11.1416i	−0.789801	+	0.573824i
$378$	−1.67277	−	2.25870i	−0.0860381	−	0.116175i
$379$	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	$0.707853\pi$
$380$	1.32074	+	0.280732i	0.0677526	+	0.0144013i
$381$	0.0491296	−	0.467437i	0.00251698	−	0.0239475i
$382$	10.0575	+	4.47789i	0.514586	+	0.229109i
$383$	18.7382	+	20.8109i	0.957478	+	1.06339i	0.997937	+	0.0642058i	$0.0204514\pi$
$383$	18.7382	+	20.8109i	0.957478	+	1.06339i	−0.0404587	+	0.999181i	$0.512882\pi$
$384$	0.996632			0.0508592
$385$		0			0
$386$	9.40249			0.478574
$387$	1.69273	+	1.87997i	0.0860462	+	0.0955640i
$388$	0.336741	+	0.149927i	0.0170954	+	0.00761137i
$389$	−0.178405	+	1.69741i	−0.00904551	+	0.0860623i	−0.998113	−	0.0613994i	$-0.980444\pi$
$389$	−0.178405	+	1.69741i	−0.00904551	+	0.0860623i	0.989068	+	0.147462i	$0.0471103\pi$
$390$	0.932233	+	0.198152i	0.0472055	+	0.0100338i
$391$	7.78091	+	23.9472i	0.393498	+	1.21106i
$392$	20.8048	+	4.02645i	1.05080	+	0.203367i
$393$	0.550092	−	0.399665i	0.0277485	−	0.0201604i
$394$	8.48328	+	9.42164i	0.427381	+	0.474655i
$395$	−2.88350	−	4.99437i	−0.145085	−	0.251294i
$396$		0			0
$397$	−6.61778	+	11.4623i	−0.332137	+	0.575278i	−0.982931	−	0.183976i	$-0.941103\pi$
$397$	−6.61778	+	11.4623i	−0.332137	+	0.575278i	0.650794	+	0.759255i	$0.274436\pi$
$398$	−6.92192	+	21.3035i	−0.346964	+	1.06785i
$399$	0.840848	+	0.743309i	0.0420951	+	0.0372120i
$400$	−9.05134	−	6.57618i	−0.452567	−	0.328809i
$401$	−23.1719	−	4.92534i	−1.15715	−	0.245960i	−0.410934	−	0.911665i	$-0.634797\pi$
$401$	−23.1719	−	4.92534i	−1.15715	−	0.245960i	−0.746214	+	0.665706i	$0.768131\pi$
$402$	0.0629603	−	0.0699245i	0.00314018	−	0.00348752i
$403$	−3.24894	+	30.9116i	−0.161841	+	1.53982i
$404$	0.00348556	+	0.0331629i	0.000173413	+	0.00164991i
$405$	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
$409$	10.7678	−	2.28877i	0.532434	−	0.113172i	0.0661540	−	0.997809i	$-0.478927\pi$
$409$	10.7678	−	2.28877i	0.532434	−	0.113172i	0.466280	+	0.884637i	$0.345594\pi$
$410$	−12.9252	−	5.75466i	−0.638329	−	0.284202i
$411$	1.04888	−	0.466993i	0.0517376	−	0.0230351i
$412$	1.69536	+	5.21778i	0.0835243	+	0.257061i
$413$	6.55728	+	3.70640i	0.322663	+	0.182380i
$414$	11.6322	+	8.45130i	0.571692	+	0.415359i
$415$	1.42321	+	13.5410i	0.0698628	+	0.664700i
$416$	−9.24255	+	1.96456i	−0.453153	+	0.0963207i
$417$	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	$0.274853\pi$
$420$	−0.0678401	−	0.148701i	−0.00331026	−	0.00725587i
$421$	−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	$0.559458\pi$
$422$	0.619648	−	0.275885i	0.0301640	−	0.0134299i
$423$	10.9038	−	12.1099i	0.530162	−	0.588804i
$424$	7.99204	−	8.87606i	0.388128	−	0.431060i
$425$	21.8616	−	9.73343i	1.06045	−	0.472141i
$426$	−0.471617	+	0.342650i	−0.0228499	+	0.0166014i
$427$	3.77333	−	5.29457i	0.182604	−	0.256222i
$428$	−1.86739			−0.0902639
$429$		0			0
$430$	−0.641243	−	1.11066i	−0.0309235	−	0.0535610i
$431$	0.991317	−	0.210711i	0.0477501	−	0.0101496i	−0.183975	−	0.982931i	$-0.558896\pi$
$431$	0.991317	−	0.210711i	0.0477501	−	0.0101496i	0.231725	+	0.972781i	$0.425563\pi$
$432$	0.270984	+	2.57824i	0.0130377	+	0.124046i
$433$	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	$0.598782\pi$
$434$	−19.9502	+	11.7625i	−0.957641	+	0.564619i
$435$	0.213590	+	0.657362i	0.0102409	+	0.0315181i
$436$	−6.37458	+	2.83814i	−0.305287	+	0.135922i
$437$	−10.5238	−	4.68548i	−0.503420	−	0.224137i
$438$	−2.20691	+	0.469093i	−0.105450	+	0.0224142i
$439$	14.6142	−	25.3126i	0.697499	−	1.20810i	−0.271832	−	0.962345i	$-0.587630\pi$
$439$	14.6142	−	25.3126i	0.697499	−	1.20810i	0.969331	−	0.245759i	$-0.0790370\pi$
$440$		0			0
$441$	−1.80149	+	20.7862i	−0.0857853	+	0.989820i
$442$	−11.8729	+	36.5410i	−0.564735	+	1.73808i
$443$	2.17976	+	20.7391i	0.103564	+	0.985342i	0.915697	+	0.401870i	$0.131640\pi$
$443$	2.17976	+	20.7391i	0.103564	+	0.985342i	−0.812133	+	0.583472i	$0.801694\pi$
$444$	0.0184860	−	0.175883i	0.000877307	−	0.00834702i
$445$	1.46994	−	1.63254i	0.0696821	−	0.0773898i
$446$	−22.8439	−	4.85563i	−1.08169	−	0.229921i
$447$	0.911207	+	0.662031i	0.0430986	+	0.0313130i
$448$	−17.6110	−	15.5681i	−0.832043	−	0.735525i
$449$	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
$453$	−0.550435	−	0.611320i	−0.0258617	−	0.0287223i
$454$	9.84009	−	7.14924i	0.461818	−	0.335531i
$455$	−8.44848	−	11.4077i	−0.396071	−	0.534803i
$456$	−0.396816	−	1.22127i	−0.0185826	−	0.0571913i
$457$	−13.9763	−	2.97074i	−0.653781	−	0.138966i	−0.130933	−	0.991391i	$-0.541797\pi$
$457$	−13.9763	−	2.97074i	−0.653781	−	0.138966i	−0.522848	+	0.852426i	$0.675131\pi$
$458$	−0.240020	+	2.28364i	−0.0112154	+	0.106708i
$459$	−5.06567	−	2.25538i	−0.236445	−	0.105272i
$460$	1.12258	+	1.24676i	0.0523408	+	0.0581303i
$461$	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	$0.318018\pi$
$464$	8.71697	+	9.68117i	0.404675	+	0.449437i
$465$	1.03539	+	0.460986i	0.0480152	+	0.0213777i
$466$	−2.65943	+	25.3027i	−0.123195	+	1.17213i
$467$	18.3767	+	3.90609i	0.850372	+	0.180752i	0.612428	−	0.790527i	$-0.290193\pi$
$467$	18.3767	+	3.90609i	0.850372	+	0.180752i	0.237944	+	0.971279i	$0.423526\pi$
$468$	−1.56041	−	4.80246i	−0.0721302	−	0.221994i
$469$	−1.39241	+	0.159220i	−0.0642955	+	0.00735209i
$470$	−6.68346	+	4.85582i	−0.308285	+	0.223982i
$471$	−1.55784	−	1.73016i	−0.0717815	−	0.0797214i
$472$	−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
$476$	6.24774	−	2.09329i	0.286364	−	0.0959460i
$477$	9.51385	+	6.91222i	0.435609	+	0.316489i
$478$	4.82983	+	1.02661i	0.220911	+	0.0469562i
$479$	19.0779	−	21.1881i	0.871691	−	0.968111i	−0.128029	−	0.991770i	$-0.540865\pi$
$479$	19.0779	−	21.1881i	0.871691	−	0.968111i	0.999720	+	0.0236599i	$0.00753187\pi$
$480$	−0.0360155	+	0.342665i	−0.00164388	+	0.0156404i
$481$	−1.60555	−	15.2758i	−0.0732068	−	0.696516i
$482$	−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
$486$	−4.65081	+	0.988561i	−0.210965	+	0.0448420i
$487$	−22.4315	−	9.98716i	−1.01647	−	0.452562i	−0.170253	−	0.985400i	$-0.554459\pi$
$487$	−22.4315	−	9.98716i	−1.01647	−	0.452562i	−0.846217	+	0.532839i	$0.821125\pi$
$488$	−6.79595	+	3.02575i	−0.307638	+	0.136969i
$489$	1.05082	+	3.23409i	0.0475197	+	0.146251i
$490$	3.08427	−	10.1177i	0.139333	−	0.457070i
$491$	−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	$0.871912\pi$
$492$	−0.0510200	−	0.485423i	−0.00230016	−	0.0218846i
$493$	−27.2556	+	5.79337i	−1.22753	+	0.260920i
$494$	−8.78894	−	15.2229i	−0.395433	−	0.684911i
$495$		0			0
$496$	21.3615			0.959158
$497$	8.64325	+	0.828696i	0.387703	+	0.0371721i
$498$	1.65107	−	1.19957i	0.0739863	−	0.0537542i
$499$	30.8822	−	13.7496i	1.38248	−	0.615518i	0.425308	−	0.905049i	$-0.360166\pi$
$499$	30.8822	−	13.7496i	1.38248	−	0.615518i	0.957169	+	0.289530i	$0.0934992\pi$
$500$	2.55051	−	2.83263i	0.114062	−	0.126679i
$501$	−1.06248	+	1.18000i	−0.0474680	+	0.0527186i
$502$	11.1028	−	4.94327i	0.495540	−	0.220629i
$503$	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	$0.243451\pi$
$504$	13.8550	−	19.4408i	0.617153	−	0.865963i
$505$	0.105605			0.00469938
$506$		0			0
$507$	0.522295	+	0.904641i	0.0231959	+	0.0401765i
$508$	1.23488	−	0.262483i	0.0547891	−	0.0116458i
$509$	−3.68438	−	35.0545i	−0.163307	−	1.55377i	−0.702562	−	0.711623i	$-0.747961\pi$
$509$	−3.68438	−	35.0545i	−0.163307	−	1.55377i	0.539255	−	0.842143i	$-0.318706\pi$
$510$	1.13344	+	0.823493i	0.0501896	+	0.0364649i
$511$	29.2556	+	16.5363i	1.29419	+	0.731523i
$512$	7.82840	+	24.0933i	0.345969	+	1.06478i
$513$	2.31756	−	1.03184i	0.102323	−	0.0455570i
$514$	−26.5922	−	11.8396i	−1.17293	−	0.522223i
$515$	16.9954	−	3.61249i	0.748907	−	0.159185i
$516$	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
$520$	1.69781	+	16.1535i	0.0744537	+	0.708380i
$521$	0.948096	−	9.02053i	0.0415368	−	0.395197i	−0.953926	−	0.300043i	$-0.902999\pi$
$521$	0.948096	−	9.02053i	0.0415368	−	0.395197i	0.995463	−	0.0951539i	$-0.0303343\pi$
$522$	−10.6468	+	11.8245i	−0.465999	+	0.517544i
$523$	−10.7596	−	2.28703i	−0.470485	−	0.100005i	−0.0334332	−	0.999441i	$-0.510644\pi$
$523$	−10.7596	−	2.28703i	−0.470485	−	0.100005i	−0.437052	+	0.899436i	$0.643977\pi$
$524$	1.47757	+	1.07352i	0.0645480	+	0.0468969i
$525$	1.25661	−	0.421026i	0.0548431	−	0.0183751i
$526$	−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
$530$	−3.98920	−	4.43045i	−0.173280	−	0.192447i
$531$	6.86496	−	4.98769i	0.297914	−	0.216447i
$532$	−1.20091	+	2.76499i	−0.0520661	+	0.119877i
$533$	−13.0999	−	40.3174i	−0.567421	−	1.74634i
$534$	−0.322083	−	0.0684608i	−0.0139379	−	0.00296259i
$535$	−0.618185	+	5.88164i	−0.0267265	+	0.254285i
$536$	1.46494	+	0.652233i	0.0632758	+	0.0281722i
$537$	1.15678	+	1.28473i	0.0499187	+	0.0554403i
$538$	13.7538			0.592967
$539$		0			0
$540$	−0.369460			−0.0158990
$541$	−10.5479	−	11.7146i	−0.453490	−	0.503652i	0.472432	−	0.881367i	$-0.343376\pi$
$541$	−10.5479	−	11.7146i	−0.453490	−	0.503652i	−0.925922	+	0.377716i	$0.876710\pi$
$542$	−3.85802	−	1.71770i	−0.165716	−	0.0737817i
$543$	−0.235900	+	2.24444i	−0.0101234	+	0.0963180i
$544$	−13.5867	−	2.88794i	−0.582524	−	0.123819i
$545$	6.82891	+	21.0172i	0.292519	+	0.900279i
$546$	−0.847652	+	1.95164i	−0.0362761	+	0.0835225i
$547$	−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	$0.366764\pi$
$548$	2.06358	+	2.29184i	0.0881518	+	0.0979025i
$549$	−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
$553$	12.2082	−	4.09035i	0.519146	−	0.173939i
$554$	8.39366	+	6.09835i	0.356612	+	0.259094i
$555$	−0.547849	−	0.116449i	−0.0232549	−	0.00494298i
$556$	−5.59239	+	6.21098i	−0.237170	+	0.263404i
$557$	2.45872	−	23.3932i	0.104179	−	0.991200i	−0.810148	−	0.586225i	$-0.800614\pi$
$557$	2.45872	−	23.3932i	0.104179	−	0.991200i	0.914328	−	0.404975i	$-0.132720\pi$
$558$	2.72722	+	25.9477i	0.115452	+	1.09846i
$559$	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
$563$	−26.9110	+	5.72011i	−1.13416	+	0.241074i	−0.736487	−	0.676452i	$-0.763517\pi$
$563$	−26.9110	+	5.72011i	−1.13416	+	0.241074i	−0.397677	+	0.917526i	$0.630183\pi$
$564$	−0.260360	−	0.115920i	−0.0109631	−	0.00488109i
$565$	4.13301	−	1.84014i	0.173877	−	0.0774151i
$566$	−3.43689	−	10.5777i	−0.144463	−	0.444613i
$567$	20.3280	+	11.4901i	0.853698	+	0.482540i
$568$	−8.03754	−	5.83962i	−0.337248	−	0.245025i
$569$	2.93223	+	27.8983i	0.122926	+	1.16956i	0.865893	+	0.500230i	$0.166751\pi$
$569$	2.93223	+	27.8983i	0.122926	+	1.16956i	−0.742967	+	0.669328i	$0.766582\pi$
$570$	−0.626959	+	0.133264i	−0.0262604	+	0.00558182i
$571$	20.4952	+	35.4988i	0.857699	+	1.48558i	0.874119	+	0.485713i	$0.161440\pi$
$571$	20.4952	+	35.4988i	0.857699	+	1.48558i	−0.0164198	+	0.999865i	$0.505227\pi$
$572$		0			0
$573$	1.20284			0.0502494
$574$	18.3323	−	25.7231i	0.765175	−	1.07366i
$575$	−11.0052	+	7.99575i	−0.458949	+	0.333446i
$576$	−24.1911	+	10.7706i	−1.00796	+	0.448774i
$577$	14.2634	−	15.8411i	0.593793	−	0.659474i	−0.369090	−	0.929394i	$-0.620331\pi$
$577$	14.2634	−	15.8411i	0.593793	−	0.659474i	0.962883	+	0.269920i	$0.0869973\pi$
$578$	−23.2883	+	25.8643i	−0.968666	+	1.07581i
$579$	0.938471	−	0.417834i	0.0390015	−	0.0173646i
$580$	−1.50200	+	1.09127i	−0.0623671	+	0.0453124i
$581$	−30.2589	−	2.90116i	−1.25535	−	0.120360i
$582$	−0.174979			−0.00725312
$583$		0			0
$584$	−19.2258	−	33.3000i	−0.795568	−	1.37796i
$585$	−15.6426	+	3.32495i	−0.646744	+	0.137470i
$586$	3.24295	+	30.8546i	0.133965	+	1.27459i
$587$	−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	$-0.622953\pi$
$588$	0.355483	−	0.0823749i	0.0146599	−	0.00339708i
$589$	−6.45957	−	19.8805i	−0.266162	−	0.819162i
$590$	−3.92995	+	1.74972i	−0.161793	+	0.0720350i
$591$	1.26541	+	0.563397i	0.0520520	+	0.0231750i
$592$	−10.3256	+	2.19478i	−0.424382	+	0.0902051i
$593$	−7.97036	+	13.8051i	−0.327304	+	0.566907i	−0.981976	−	0.189006i	$-0.939473\pi$
$593$	−7.97036	+	13.8051i	−0.327304	+	0.566907i	0.654672	+	0.755913i	$0.272807\pi$
$594$		0			0
$595$	−4.52489	−	20.3712i	−0.185502	−	0.835136i
$596$	−0.934879	+	2.87726i	−0.0382941	+	0.117857i
$597$	0.255815	+	2.43392i	0.0104698	+	0.0996138i
$598$	2.28295	−	21.7208i	0.0933567	−	0.888229i
$599$	−22.9038	+	25.4372i	−0.935823	+	1.03934i	0.0633216	+	0.997993i	$0.479831\pi$
$599$	−22.9038	+	25.4372i	−0.935823	+	1.03934i	−0.999145	+	0.0413439i	$0.986836\pi$
$600$	−1.48323	−	0.315271i	−0.0605528	−	0.0128709i
$601$	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	$0.497915\pi$
$602$	2.71490	−	0.909625i	0.110651	−	0.0370735i
$603$	−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
$607$	15.2169	+	16.9000i	0.617633	+	0.685951i	0.968083	−	0.250631i	$-0.0806379\pi$
$607$	15.2169	+	16.9000i	0.617633	+	0.685951i	−0.350450	+	0.936582i	$0.613971\pi$
$608$	5.14114	−	3.73526i	0.208501	−	0.151485i
$609$	−1.53314	+	0.175312i	−0.0621261	+	0.00710402i
$610$	1.14744	+	3.53146i	0.0464585	+	0.142985i
$611$	−24.2119	−	5.14639i	−0.979507	−	0.208201i
$612$	0.775914	−	7.38233i	0.0313645	−	0.298413i
$613$	28.4884	+	12.6838i	1.15063	+	0.512295i	0.891265	−	0.453483i	$-0.149819\pi$
$613$	28.4884	+	12.6838i	1.15063	+	0.512295i	0.259369	+	0.965778i	$0.416485\pi$
$614$	8.40269	+	9.33213i	0.339105	+	0.376614i
$615$	−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	$0.863612\pi$
$618$	−1.74265	−	1.93541i	−0.0700998	−	0.0778537i
$619$	−22.7371	−	10.1232i	−0.913883	−	0.406887i	−0.104740	−	0.994500i	$-0.533401\pi$
$619$	−22.7371	−	10.1232i	−0.913883	−	0.406887i	−0.809142	+	0.587613i	$0.800068\pi$
$620$	−0.318217	+	3.02763i	−0.0127799	+	0.121592i
$621$	3.08318	+	0.655350i	0.123724	+	0.0262983i
$622$	−0.323947	−	0.997007i	−0.0129891	−	0.0399763i
$623$	2.91892	+	3.94133i	0.116944	+	0.157906i
$624$	1.58775	−	1.15357i	0.0635608	−	0.0461797i
$625$	3.95218	+	4.38934i	0.158087	+	0.175574i
$626$	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
$630$	−8.92777	−	7.89214i	−0.355691	−	0.314430i
$631$	−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	$0.776168\pi$
$632$	−14.4099	−	3.06292i	−0.573195	−	0.121836i
$633$	0.0495877	−	0.0550727i	0.00197093	−	0.00218894i
$634$	1.09253	−	10.3947i	0.0433899	−	0.412827i
$635$	−0.417931	−	3.97635i	−0.0165851	−	0.157797i
$636$	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
$640$	8.29279	−	1.76269i	0.327801	−	0.0696763i
$641$	11.2510	+	5.00928i	0.444389	+	0.197855i	0.616717	−	0.787185i	$-0.288462\pi$
$641$	11.2510	+	5.00928i	0.444389	+	0.197855i	−0.172328	+	0.985040i	$0.555129\pi$
$642$	0.809817	−	0.360554i	0.0319609	−	0.0142299i
$643$	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	$0.760016\pi$
$644$	−3.22648	+	1.90231i	−0.127141	+	0.0749616i
$645$	−0.113360	−	0.0823605i	−0.00446353	−	0.00324294i
$646$	−2.70099	−	25.6982i	−0.106269	−	1.01108i
$647$	−11.4100	+	2.42527i	−0.448573	+	0.0953472i	−0.426659	−	0.904413i	$-0.640309\pi$
$647$	−11.4100	+	2.42527i	−0.448573	+	0.0953472i	−0.0219144	+	0.999760i	$0.506976\pi$
$648$	−13.3589	−	23.1383i	−0.524787	−	0.908957i
$649$		0			0
$650$	−20.7571			−0.814159
$651$	−1.46854	+	2.06059i	−0.0575566	+	0.0807609i
$652$	−7.38953	+	5.36881i	−0.289396	+	0.210259i
$653$	30.9128	−	13.7633i	1.20971	−	0.538598i	0.300040	−	0.953927i	$-0.403000\pi$
$653$	30.9128	−	13.7633i	1.20971	−	0.538598i	0.909671	+	0.415329i	$0.136333\pi$
$654$	2.21643	−	2.46159i	0.0866691	−	0.0962558i
$655$	3.87035	−	4.29846i	0.151227	−	0.167955i
$656$	−26.6159	+	11.8501i	−1.03917	+	0.462670i
$657$	30.6284	−	22.2528i	1.19493	−	0.868165i
$658$	−7.65532	−	16.7799i	−0.298436	−	0.654151i
$659$	−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	0.999967	−	0.00814061i	$-0.00259127\pi$
$661$	12.6733	+	21.9508i	0.492933	+	0.853786i	−0.507033	+	0.861926i	$0.669258\pi$
$662$	−28.1964	+	5.99333i	−1.09588	+	0.232937i
$663$	0.438790	+	4.17480i	0.0170412	+	0.162136i
$664$	28.1384	+	20.4437i	1.09198	+	0.793371i
$665$	8.31119	+	4.69778i	0.322294	+	0.182172i
$666$	−3.98428	−	12.2623i	−0.154388	−	0.475156i
$667$	14.4700	−	6.44248i	0.560282	−	0.249454i
$668$	−3.89630	−	1.73475i	−0.150753	−	0.0671194i
$669$	−2.49585	+	0.530510i	−0.0964952	+	0.0205107i
$670$	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	$-0.0361292\pi$
$674$	−3.29934	−	31.3911i	−0.127086	−	1.20914i
$675$	0.313137	−	2.97930i	0.0120526	−	0.114673i
$676$	−1.87746	+	2.08513i	−0.0722099	+	0.0801972i
$677$	−26.7041	−	5.67614i	−1.02632	−	0.218152i	−0.336160	−	0.941805i	$-0.609128\pi$
$677$	−26.7041	−	5.67614i	−1.02632	−	0.218152i	−0.690164	+	0.723653i	$0.742462\pi$
$678$	−0.548614	−	0.398592i	−0.0210694	−	0.0153078i
$679$	1.95268	+	1.72617i	0.0749369	+	0.0662442i
$680$	−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	0.886494	−	0.462740i	$-0.153134\pi$
$683$	1.11077	+	1.92391i	0.0425024	+	0.0736162i	−0.843992	+	0.536356i	$0.819800\pi$
$684$	2.27239	+	2.52374i	0.0868870	+	0.0964978i
$685$	7.90163	−	5.74087i	0.301906	−	0.219347i
$686$	20.7667	+	11.2426i	0.792877	+	0.429243i
$687$	0.0775254	+	0.238599i	0.00295778	+	0.00910310i
$688$	−2.58322	−	0.549080i	−0.0984842	−	0.0209335i
$689$	1.86720	−	17.7652i	0.0711345	−	0.676799i
$690$	−0.727544	−	0.323923i	−0.0276971	−	0.0123316i
$691$	0.655611	+	0.728130i	0.0249406	+	0.0276994i	0.755486	−	0.655165i	$-0.227401\pi$
$691$	0.655611	+	0.728130i	0.0249406	+	0.0276994i	−0.730545	+	0.682864i	$0.760734\pi$
$692$	−1.03573			−0.0393726
$693$		0			0
$694$	7.68002			0.291529
$695$	17.7111	+	19.6702i	0.671820	+	0.746132i
$696$	1.61300	+	0.718155i	0.0611407	+	0.0272216i
$697$	6.51392	−	61.9758i	0.246732	−	2.34750i
$698$	26.1974	+	5.56843i	0.991587	+	0.210768i
$699$	0.858981	+	2.64367i	0.0324897	+	0.0999929i
$700$	2.11858	+	2.86065i	0.0800746	+	0.108123i
$701$	−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	$0.371139\pi$
$702$	3.21833	+	3.57432i	0.121468	+	0.134904i
$703$	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
$707$	−0.0469111	+	0.231057i	−0.00176427	+	0.00868980i
$708$	−0.120064	−	0.0872319i	−0.00451229	−	0.00327837i
$709$	−31.4219	−	6.67893i	−1.18007	−	0.250833i	−0.424212	−	0.905563i	$-0.639449\pi$
$709$	−31.4219	−	6.67893i	−1.18007	−	0.250833i	−0.755862	+	0.654731i	$0.772782\pi$
$710$	−3.31821	+	3.68525i	−0.124530	+	0.138305i
$711$	1.51615	−	14.4252i	0.0568602	−	0.540989i
$712$	−0.586585	−	5.58098i	−0.0219832	−	0.209156i
$713$	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
$717$	0.527692	−	0.112164i	0.0197070	−	0.00418885i
$718$	40.3960	+	17.9855i	1.50757	+	0.671211i
$719$	14.5687	−	6.48641i	0.543321	−	0.241902i	−0.116676	−	0.993170i	$-0.537224\pi$
$719$	14.5687	−	6.48641i	0.543321	−	0.241902i	0.659997	+	0.751268i	$0.270557\pi$
$720$	3.39635	+	10.4529i	0.126574	+	0.389556i
$721$	0.354318	+	38.7895i	0.0131955	+	1.44460i
$722$	−10.0356	−	7.29126i	−0.373485	−	0.271352i
$723$	0.0381752	+	0.363213i	0.00141975	+	0.0135080i
$724$	−5.92940	+	1.26033i	−0.220364	+	0.0468399i
$725$	−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	$0.848243\pi$
$728$	−36.0970	−	3.46090i	−1.33784	−	0.128270i
$729$	21.0002	−	15.2575i	0.777784	−	0.565093i
$730$	−17.5336	+	7.80648i	−0.648949	+	0.288931i
$731$	3.77977	−	4.19786i	0.139800	−	0.155263i
$732$	−0.0857154	+	0.0951966i	−0.00316813	+	0.00351857i
$733$	−20.8391	+	9.27818i	−0.769711	+	0.342697i	−0.753738	−	0.657175i	$-0.771751\pi$
$733$	−20.8391	+	9.27818i	−0.769711	+	0.342697i	−0.0159730	+	0.999872i	$0.505085\pi$
$734$	30.7293	−	22.3262i	1.13424	−	0.824074i
$735$	−0.141773	−	1.14692i	−0.00522936	−	0.0423047i
$736$	7.89580			0.291043
$737$		0			0
$738$	−17.7924	−	30.8174i	−0.654948	−	1.13440i
$739$	42.4972	−	9.03306i	1.56329	−	0.332287i	0.656648	−	0.754197i	$-0.271974\pi$
$739$	42.4972	−	9.03306i	1.56329	−	0.332287i	0.906638	+	0.421910i	$0.138640\pi$
$740$	−0.157255	−	1.49618i	−0.00578081	−	0.0550008i
$741$	−1.55372	−	1.12884i	−0.0570773	−	0.0414691i
$742$	11.4656	−	6.76003i	0.420914	−	0.248169i
$743$	−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	$-0.342256\pi$
$744$	2.64491	−	1.17759i	0.0969672	−	0.0431726i
$745$	8.75289	+	3.89704i	0.320681	+	0.142776i
$746$	−0.0155487	+	0.00330498i	−0.000569279	+	0.000121004i
$747$	−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
$751$	−0.202951	−	1.93095i	−0.00740580	−	0.0704614i	0.990195	−	0.139694i	$-0.0446118\pi$
$751$	−0.202951	−	1.93095i	−0.00740580	−	0.0704614i	−0.997601	+	0.0692321i	$0.977945\pi$
$752$	−1.77821	+	16.9185i	−0.0648445	+	0.616955i
$753$	0.888505	−	0.986785i	0.0323789	−	0.0359604i
$754$	23.6412	+	5.02509i	0.860962	+	0.183003i
$755$	−5.66128	−	4.11316i	−0.206035	−	0.149693i
$756$	0.164118	−	0.808352i	0.00596892	−	0.0293995i
$757$	−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
$761$	9.02503	+	10.0233i	0.327157	+	0.363345i	0.884175	−	0.467156i	$-0.154721\pi$
$761$	9.02503	+	10.0233i	0.327157	+	0.363345i	−0.557018	+	0.830500i	$0.688055\pi$
$762$	−0.484842	+	0.352258i	−0.0175640	+	0.0127610i
$763$	−49.0177	+	5.60510i	−1.77456	+	0.202918i
$764$	0.998398	+	3.07275i	0.0361208	+	0.111168i
$765$	−22.9949	−	4.88772i	−0.831382	−	0.176716i
$766$	3.73238	−	35.5113i	0.134857	−	1.28307i
$767$	−11.7752	−	5.24264i	−0.425177	−	0.189301i
$768$	0.806013	+	0.895168i	0.0290845	+	0.0323016i
$769$	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
$772$	1.84636	+	2.05059i	0.0664518	+	0.0738022i
$773$	16.2722	+	7.24485i	0.585271	+	0.260579i	0.677939	−	0.735118i	$-0.262873\pi$
$773$	16.2722	+	7.24485i	0.585271	+	0.260579i	−0.0926689	+	0.995697i	$0.529540\pi$
$774$	0.337167	−	3.20793i	0.0121192	−	0.115307i
$775$	−24.1449	−	5.13215i	−0.867309	−	0.184352i
$776$	−0.921514	−	2.83613i	−0.0330804	−	0.101811i
$777$	0.498143	−	1.14693i	0.0178708	−	0.0411458i
$778$	1.76062	−	1.27917i	0.0631213	−	0.0458603i
$779$	19.0771	+	21.1872i	0.683507	+	0.759112i
$780$	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
$784$	−11.2333	−	18.6609i	−0.401190	−	0.666462i
$785$	−16.0225	−	11.6410i	−0.571869	−	0.415487i
$786$	−0.848040	−	0.180256i	−0.0302486	−	0.00642953i
$787$	22.2029	−	24.6588i	0.791449	−	0.878993i	−0.203531	−	0.979068i	$-0.565242\pi$
$787$	22.2029	−	24.6588i	0.791449	−	0.878993i	0.994980	+	0.100076i	$0.0319085\pi$
$788$	−0.388910	+	3.70023i	−0.0138543	+	0.131815i
$789$	0.115413	+	1.09808i	0.00410882	+	0.0390928i
$790$	−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
$794$	16.5075	−	3.50878i	0.585829	−	0.124522i
$795$	−0.595049	−	0.264933i	−0.0211042	−	0.00939621i
$796$	−6.00532	+	2.67374i	−0.212853	+	0.0947682i
$797$	−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	$0.954173\pi$
$798$	−0.0130707	−	1.43094i	−0.000462699	−	0.0506547i
$799$	−29.4376	−	21.3877i	−1.04143	−	0.756642i
$800$	−0.784396	−	7.46303i	−0.0277326	−	0.263858i
$801$	5.40447	−	1.14876i	0.190957	−	0.0405893i
$802$	15.1029	+	26.1591i	0.533303	+	0.923708i
$803$		0			0
$804$	0.0276133			0.000973845
$805$	4.92352	+	10.7920i	0.173531	+	0.380369i
$806$	32.0626	−	23.2949i	1.12936	−	0.820526i
$807$	1.37278	−	0.611199i	0.0483240	−	0.0215152i
$808$	0.180511	−	0.200478i	0.00635035	−	0.00705277i
$809$	13.8089	−	15.3364i	0.485496	−	0.539198i	−0.449769	−	0.893145i	$-0.648494\pi$
$809$	13.8089	−	15.3364i	0.485496	−	0.539198i	0.935266	+	0.353946i	$0.115160\pi$
$810$	−12.1831	+	5.42427i	−0.428071	+	0.190590i
$811$	−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	$0.365298\pi$
$812$	−1.72041	−	3.77102i	−0.0603745	−	0.132337i
$813$	−0.461406			−0.0161822
$814$		0			0
$815$	14.4636	+	25.0517i	0.506639	+	0.877524i
$816$	2.82195	−	0.599825i	0.0987882	−	0.0209981i
$817$	0.270136	+	2.57017i	0.00945085	+	0.0899188i
$818$	−11.3557	−	8.25043i	−0.397044	−	0.288469i
$819$	−0.326116	−	35.7020i	−0.0113954	−	1.24753i
$820$	−1.28307	−	3.94888i	−0.0448067	−	0.137901i
$821$	13.4119	−	5.97134i	0.468077	−	0.208401i	−0.159124	−	0.987259i	$-0.550867\pi$
$821$	13.4119	−	5.97134i	0.468077	−	0.208401i	0.627201	+	0.778857i	$0.284200\pi$
$822$	−1.33740	−	0.595450i	−0.0466472	−	0.0207687i
$823$	−21.4681	+	4.56319i	−0.748332	+	0.159063i	−0.566265	−	0.824223i	$-0.691612\pi$
$823$	−21.4681	+	4.56319i	−0.748332	+	0.159063i	−0.182067	+	0.983286i	$0.558279\pi$
$824$	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	$-0.0908166\pi$
$828$	0.441063	+	4.19644i	0.0153280	+	0.145836i
$829$	−3.56734	+	33.9409i	−0.123899	+	1.17882i	0.739094	+	0.673602i	$0.235254\pi$
$829$	−3.56734	+	33.9409i	−0.123899	+	1.17882i	−0.862993	+	0.505216i	$0.831413\pi$
$830$	11.6166	−	12.9016i	0.403220	−	0.447821i
$831$	1.10878	+	0.235679i	0.0384632	+	0.00817561i
$832$	32.5417	+	23.6429i	1.12818	+	0.819670i
$833$	46.5807	−	0.851042i	1.61392	−	0.0294869i
$834$	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
$838$	−22.6966	−	25.2071i	−0.784042	−	0.870767i
$839$	−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	$0.473460\pi$
$840$	−0.526767	+	1.21283i	−0.0181752	+	0.0418467i
$841$	−3.54490	−	10.9101i	−0.122238	−	0.376210i
$842$	37.2498	+	7.91768i	1.28371	+	0.272861i
$843$	−0.214830	+	2.04397i	−0.00739912	+	0.0703979i
$844$	0.181847	+	0.0809636i	0.00625944	+	0.00278688i
$845$	5.94591	+	6.60360i	0.204545	+	0.227171i
$846$	−20.7779			−0.714360
$847$		0			0
$848$	−12.2766			−0.421581
$849$	−0.813097	−	0.903036i	−0.0279054	−	0.0309921i
$850$	−27.8752	−	12.4108i	−0.956110	−	0.425688i
$851$	−1.34163	+	12.7648i	−0.0459905	+	0.437570i
$852$	−0.167339	−	0.0355691i	−0.00573295	−	0.00121858i
$853$	−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	$0.914967\pi$
$854$	−8.23630	+	0.941807i	−0.281840	+	0.0322280i
$855$	8.70117	−	6.32177i	0.297574	−	0.216200i
$856$	10.1088	+	11.2270i	0.345513	+	0.383731i
$857$	−11.7477	−	20.3476i	−0.401294	−	0.695062i	0.592588	−	0.805506i	$-0.298106\pi$
$857$	−11.7477	−	20.3476i	−0.401294	−	0.695062i	−0.993882	+	0.110443i	$0.964773\pi$
$858$		0			0
$859$	−2.56165	+	4.43691i	−0.0874025	+	0.151386i	−0.906412	−	0.422394i	$-0.861190\pi$
$859$	−2.56165	+	4.43691i	−0.0874025	+	0.151386i	0.819010	+	0.573779i	$0.194523\pi$
$860$	0.116304	−	0.357948i	0.00396595	−	0.0122059i
$861$	0.686663	−	3.38211i	0.0234014	−	0.115262i
$862$	−1.04544	−	0.759559i	−0.0356079	−	0.0258707i
$863$	41.0966	+	8.73535i	1.39894	+	0.297355i	0.844807	−	0.535071i	$-0.179715\pi$
$863$	41.0966	+	8.73535i	1.39894	+	0.297355i	0.554137	+	0.832426i	$0.313048\pi$
$864$	−1.16350	+	1.29220i	−0.0395830	+	0.0439614i
$865$	−0.342870	+	3.26219i	−0.0116579	+	0.110918i
$866$	−1.73423	−	16.5001i	−0.0589315	−	0.560696i
$867$	−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
$871$	2.34586	−	0.498628i	0.0794865	−	0.0168954i
$872$	51.5710	+	22.9609i	1.74642	+	0.777554i
$873$	2.68227	−	1.19422i	0.0907810	−	0.0404183i
$874$	4.53898	+	13.9695i	0.153533	+	0.472527i
$875$	23.2159	−	13.6880i	0.784841	−	0.462738i
$876$	−0.535673	−	0.389189i	−0.0180987	−	0.0131495i
$877$	0.347929	+	3.31032i	0.0117487	+	0.111782i	0.998825	−	0.0484724i	$-0.0154353\pi$
$877$	0.347929	+	3.31032i	0.0117487	+	0.111782i	−0.987076	+	0.160254i	$0.948769\pi$
$878$	−36.4539	+	7.74852i	−1.23026	+	0.261500i
$879$	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	$0.669587\pi$
$882$	21.2333	−	16.0276i	0.714961	−	0.539676i
$883$	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	$0.188181\pi$
$884$	−10.3007	+	4.58615i	−0.346449	+	0.154249i
$885$	−0.314496	+	0.349283i	−0.0105717	+	0.0117410i
$886$	17.7918	−	19.7598i	0.597727	−	0.663844i
$887$	−11.4367	+	5.09193i	−0.384005	+	0.170970i	−0.589654	−	0.807656i	$-0.700736\pi$
$887$	−11.4367	+	5.09193i	−0.384005	+	0.170970i	0.205649	+	0.978626i	$0.434069\pi$
$888$	−1.15750	+	0.840973i	−0.0388431	+	0.0282212i
$889$	8.88562	+	0.851934i	0.298014	+	0.0285729i
$890$	−2.80107			−0.0938922
$891$		0			0
$892$	−3.42687	−	5.93552i	−0.114740	−	0.198736i
$893$	16.2833	−	3.46112i	0.544900	−	0.115822i
$894$	−0.150117	−	1.42826i	−0.00502065	−	0.0477683i
$895$	11.8976	+	8.64410i	0.397692	+	0.288940i
$896$	0.172887	+	18.9271i	0.00577575	+	0.632309i
$897$	−0.737381	−	2.26942i	−0.0246204	−	0.0757739i
$898$	−32.7884	+	14.5983i	−1.09416	+	0.487152i
$899$	26.2573	+	11.6905i	0.875730	+	0.389900i
$900$	3.92261	−	0.833777i	0.130754	−	0.0277926i
$901$	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
$905$	2.00673	+	19.0928i	0.0667060	+	0.634665i
$906$	−0.109639	+	1.04314i	−0.00364250	+	0.0346561i
$907$	10.9356	−	12.1452i	0.363110	−	0.403275i	−0.533712	−	0.845666i	$-0.679203\pi$
$907$	10.9356	−	12.1452i	0.363110	−	0.403275i	0.896822	+	0.442392i	$0.145870\pi$
$908$	3.49146	+	0.742133i	0.115868	+	0.0246285i
$909$	0.214883	+	0.156122i	0.00712722	+	0.00517823i
$910$	−3.60140	+	17.7384i	−0.119385	+	0.588023i
$911$	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
$915$	0.271461	+	0.301488i	0.00897421	+	0.00996687i
$916$	−0.545171	+	0.396090i	−0.0180130	+	0.0130872i
$917$	7.68547	+	10.3775i	0.253797	+	0.342694i
$918$	2.18486	+	6.72431i	0.0721112	+	0.221935i
$919$	3.26152	+	0.693258i	0.107588	+	0.0228685i	0.261391	−	0.965233i	$-0.415819\pi$
$919$	3.26152	+	0.693258i	0.107588	+	0.0228685i	−0.153803	+	0.988102i	$0.549152\pi$
$920$	1.41872	−	13.4982i	0.0467739	−	0.445024i
$921$	1.25339	+	0.558044i	0.0413005	+	0.0183882i
$922$	−18.6285	−	20.6891i	−0.613499	−	0.681359i
$923$	−14.8585			−0.489072
$924$		0			0
$925$	12.1984			0.401081
$926$	−19.8666	−	22.0640i	−0.652856	−	0.725070i
$927$	39.9223	+	17.7746i	1.31122	+	0.583794i
$928$	−0.913345	+	8.68990i	−0.0299820	+	0.285260i
$929$	−30.0999	−	6.39793i	−0.987545	−	0.209909i	−0.314296	−	0.949325i	$-0.601769\pi$
$929$	−30.0999	−	6.39793i	−0.987545	−	0.209909i	−0.673249	+	0.739416i	$0.735102\pi$
$930$	−0.446572	−	1.37441i	−0.0146437	−	0.0450686i
$931$	−13.9703	+	16.0975i	−0.457859	+	0.527574i
$932$	−6.04049	+	4.38868i	−0.197863	+	0.143756i
$933$	−0.0766392	−	0.0851164i	−0.00250905	−	0.00278659i
$934$	−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	$0.979855\pi$
$938$	1.33886	+	1.18355i	0.0437153	+	0.0386443i
$939$	0.719167	+	0.522505i	0.0234691	+	0.0170513i
$940$	−2.37143	−	0.504062i	−0.0773474	−	0.0164407i
$941$	30.1971	−	33.5373i	0.984397	−	1.09328i	−0.0112362	−	0.999937i	$-0.503577\pi$
$941$	30.1971	−	33.5373i	0.984397	−	1.09328i	0.995634	−	0.0933472i	$-0.0297567\pi$
$942$	−0.310299	+	2.95230i	−0.0101101	+	0.0961912i
$943$	3.70280	+	35.2298i	0.120580	+	1.14724i
$944$	−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	−0.999737	−	0.0229397i	$-0.992697\pi$
$947$	−14.7713	+	25.5846i	−0.480002	+	0.831388i	0.519735	+	0.854328i	$0.326031\pi$
$948$	−0.248136	+	0.0527428i	−0.00805907	+	0.00171301i
$949$	−52.5355	−	23.3903i	−1.70537	−	0.759281i
$950$	12.7529	−	5.67797i	0.413760	−	0.184218i
$951$	−0.352881	−	1.08606i	−0.0114430	−	0.0352178i
$952$	−46.4063	−	26.2304i	−1.50404	−	0.850134i
$953$	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	$0.419578\pi$
$954$	−1.56736	−	14.9124i	−0.0507450	−	0.482807i
$955$	10.0086	−	2.12740i	0.323871	−	0.0688409i
$956$	0.724535	+	1.25493i	0.0234331	+	0.0405874i
$957$		0			0
$958$	−36.3541			−1.17455
$959$	9.05063	+	19.8384i	0.292260	+	0.640614i
$960$	1.18661	−	0.862121i	0.0382976	−	0.0278248i
$961$	14.7354	−	6.56060i	0.475334	−	0.211632i
$962$	−13.1049	+	14.5545i	−0.422520	+	0.469256i
$963$	−9.95299	+	11.0539i	−0.320731	+	0.356207i
$964$	−0.896170	+	0.399001i	−0.0288637	+	0.0128509i
$965$	7.06985	−	5.13655i	0.227586	−	0.165351i
$966$	1.03191	−	1.44793i	0.0332010	−	0.0465862i
$967$	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
$970$	−1.45597	+	0.309476i	−0.0467484	+	0.00993667i
$971$	−2.04491	−	19.4560i	−0.0656242	−	0.624373i	−0.977065	−	0.212941i	$-0.931696\pi$
$971$	−2.04491	−	19.4560i	−0.0656242	−	0.624373i	0.911441	−	0.411431i	$-0.134971\pi$
$972$	−1.12887	−	0.820172i	−0.0362085	−	0.0263070i
$973$	−50.9044	+	30.0130i	−1.63192	+	0.962171i
$974$	9.67488	+	29.7762i	0.310003	+	0.954092i
$975$	−2.07178	+	0.922417i	−0.0663501	+	0.0295410i
$976$	6.98526	+	3.11004i	0.223593	+	0.0995498i
$977$	34.1193	−	7.25228i	1.09157	−	0.232021i	0.373250	−	0.927731i	$-0.378243\pi$
$977$	34.1193	−	7.25228i	1.09157	−	0.232021i	0.718323	+	0.695710i	$0.244910\pi$
$978$	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
$982$	3.03720	+	28.8970i	0.0969208	+	0.922140i
$983$	−1.72390	+	16.4018i	−0.0549839	+	0.523137i	0.932016	+	0.362417i	$0.118048\pi$
$983$	−1.72390	+	16.4018i	−0.0549839	+	0.523137i	−0.987000	+	0.160720i	$0.948618\pi$
$984$	−2.64224	+	2.93450i	−0.0842314	+	0.0935485i
$985$	11.5257	+	2.44986i	0.367239	+	0.0780591i
$986$	28.7438	+	20.8836i	0.915389	+	0.665069i
$987$	−1.50976	−	1.33463i	−0.0480563	−	0.0424818i
$988$	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	0.930828	−	0.365457i	$-0.119087\pi$
$991$	4.68799	+	8.11983i	0.148919	+	0.257935i	−0.781909	+	0.623392i	$0.785754\pi$
$992$	9.58710	+	10.6476i	0.304391	+	0.338060i
$993$	−2.54797	+	1.85121i	−0.0808575	+	0.0587464i
$994$	−6.58909	−	8.89705i	−0.208993	−	0.282197i
$995$	6.43333	+	19.7998i	0.203950	+	0.627695i
$996$	0.585834	+	0.124523i	0.0185628	+	0.00394565i
$997$	−0.672337	+	6.39686i	−0.0212931	+	0.202590i	−0.999996	−	0.00268963i	$-0.999144\pi$
$997$	−0.672337	+	6.39686i	−0.0212931	+	0.202590i	0.978703	+	0.205280i	$0.0658105\pi$
$998$	−39.3770	−	17.5318i	−1.24646	−	0.554958i
$999$	−1.89133	−	2.10054i	−0.0598391	−	0.0664581i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.4.2	✓	40	77.74	odd	30
77.2.m.b.25.4	yes	40	77.46	odd	30
77.2.m.b.37.4	yes	40	11.8	odd	10
77.2.m.b.58.2	yes	40	11.2	odd	10
539.2.f.g.246.2		20	77.19	even	30
539.2.f.g.344.2		20	77.68	even	30
539.2.f.h.246.2		20	77.30	odd	30
539.2.f.h.344.2		20	77.2	odd	30
539.2.q.h.312.2		40	77.52	even	30
539.2.q.h.410.4		40	77.24	even	30
539.2.q.h.422.4		40	77.41	even	10
539.2.q.h.520.2		40	77.13	even	10
693.2.by.b.37.2		40	33.8	even	10
693.2.by.b.235.4		40	231.74	even	30
693.2.by.b.289.4		40	33.2	even	10
693.2.by.b.487.2		40	231.200	even	30
847.2.e.h.485.8		20	11.4	even	5
847.2.e.h.606.8		20	77.4	even	15
847.2.e.i.485.3		20	11.7	odd	10
847.2.e.i.606.3		20	77.18	odd	30
847.2.n.h.9.2		40	1.1	even	1	trivial
847.2.n.h.130.4		40	7.4	even	3	inner
847.2.n.h.632.4		40	11.5	even	5	inner
847.2.n.h.753.2		40	77.60	even	15	inner
847.2.n.i.9.4		40	11.10	odd	2
847.2.n.i.130.2		40	77.32	odd	6
847.2.n.i.632.2		40	11.6	odd	10
847.2.n.i.753.4		40	77.39	odd	30
847.2.n.j.81.4		40	77.25	even	15
847.2.n.j.366.4		40	11.9	even	5
847.2.n.j.487.2		40	77.53	even	15
847.2.n.j.807.2		40	11.3	even	5
5929.2.a.bw.1.8		10	77.51	odd	30
5929.2.a.bx.1.8		10	77.40	even	30
5929.2.a.by.1.3		10	77.37	even	15
5929.2.a.bz.1.3		10	77.26	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)

\(f(q)\)	\(=\)	\(q+(-0.853189 - 0.947563i) q^{2} +(-0.127266 - 0.0566625i) q^{3} +(0.0391138 - 0.372143i) q^{4} +(-1.15917 - 0.246390i) q^{5} +(0.0548908 + 0.168936i) q^{6} +(1.05400 - 2.42674i) q^{7} +(-2.44911 + 1.77938i) q^{8} +(-1.99441 - 2.21501i) q^{9} +O(q^{10})\)	\(q+(-0.853189 - 0.947563i) q^{2} +(-0.127266 - 0.0566625i) q^{3} +(0.0391138 - 0.372143i) q^{4} +(-1.15917 - 0.246390i) q^{5} +(0.0548908 + 0.168936i) q^{6} +(1.05400 - 2.42674i) q^{7} +(-2.44911 + 1.77938i) q^{8} +(-1.99441 - 2.21501i) q^{9} +(0.755525 + 1.30861i) q^{10} +(-0.0260644 + 0.0451450i) q^{12} +(-1.39908 + 4.30591i) q^{13} +(-3.19875 + 1.07174i) q^{14} +(0.133562 + 0.0970388i) q^{15} +(3.04360 + 0.646937i) q^{16} +(-4.45339 + 4.94600i) q^{17} +(-0.397257 + 3.77965i) q^{18} +(-0.318279 - 3.02822i) q^{19} +(-0.137032 + 0.421742i) q^{20} +(-0.271644 + 0.249120i) q^{21} +(1.89164 - 3.27641i) q^{23} +(0.412513 - 0.0876823i) q^{24} +(-3.28475 - 1.46247i) q^{25} +(5.27380 - 2.34805i) q^{26} +(0.257460 + 0.792379i) q^{27} +(-0.861870 - 0.487159i) q^{28} +(3.38711 + 2.46088i) q^{29} +(-0.0220037 - 0.209351i) q^{30} +(6.71510 - 1.42734i) q^{31} +(1.04351 + 1.80742i) q^{32} +8.48623 q^{34} +(-1.81970 + 2.55332i) q^{35} +(-0.902311 + 0.655567i) q^{36} +(-3.09928 + 1.37989i) q^{37} +(-2.59788 + 2.88524i) q^{38} +(0.422039 - 0.468722i) q^{39} +(3.27737 - 1.45918i) q^{40} +(-7.57505 + 5.50359i) q^{41} +(0.467820 + 0.0448536i) q^{42} -0.848738 q^{43} +(1.76611 + 3.05899i) q^{45} +(-4.71853 + 1.00295i) q^{46} +(0.571478 + 5.43725i) q^{47} +(-0.350690 - 0.254791i) q^{48} +(-4.77816 - 5.11558i) q^{49} +(1.41674 + 4.36027i) q^{50} +(0.847019 - 0.377117i) q^{51} +(1.54769 + 0.689078i) q^{52} +(-3.85923 + 0.820305i) q^{53} +(0.531167 - 0.920009i) q^{54} +(1.73674 + 7.81883i) q^{56} +(-0.131081 + 0.403424i) q^{57} +(-0.558009 - 5.30910i) q^{58} +(-0.297586 + 2.83134i) q^{59} +(0.0413365 - 0.0459088i) q^{60} +(2.40366 + 0.510915i) q^{61} +(-7.08174 - 5.14519i) q^{62} +(-7.47737 + 2.50528i) q^{63} +(2.74540 - 8.44947i) q^{64} +(2.68271 - 4.64658i) q^{65} +(-0.264856 - 0.458743i) q^{67} +(1.66643 + 1.85076i) q^{68} +(-0.426391 + 0.309791i) q^{69} +(3.97198 - 0.454189i) q^{70} +(1.01414 + 3.12120i) q^{71} +(8.82587 + 1.87600i) q^{72} +(-1.32769 + 12.6322i) q^{73} +(3.95180 + 1.75945i) q^{74} +(0.335171 + 0.372245i) q^{75} -1.13938 q^{76} -0.804222 q^{78} +(3.25624 + 3.61643i) q^{79} +(-3.36866 - 1.49982i) q^{80} +(-0.922538 + 8.77736i) q^{81} +(11.6779 + 2.48222i) q^{82} +(-3.55037 - 10.9269i) q^{83} +(0.0820832 + 0.110835i) q^{84} +(6.38090 - 4.63600i) q^{85} +(0.724134 + 0.804233i) q^{86} +(-0.291625 - 0.505109i) q^{87} +(-0.926864 + 1.60538i) q^{89} +(1.39176 - 4.28339i) q^{90} +(8.97471 + 7.93364i) q^{91} +(-1.14531 - 0.832114i) q^{92} +(-0.935481 - 0.198843i) q^{93} +(4.66456 - 5.18051i) q^{94} +(-0.377183 + 3.58866i) q^{95} +(-0.0303910 - 0.289151i) 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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