LMFDB - Embedded newform 546.2.bu.a.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			323.2
Character	$\chi$	$=$	546.323
Dual form			546.2.bu.a.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-1.35787 + 1.07526i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.489109 - 0.489109i) q^{5} +(1.58990 - 0.687181i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.687622 - 2.92013i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.35787 + 1.07526i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.489109 - 0.489109i) q^{5} +(1.58990 - 0.687181i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.687622 - 2.92013i) q^{9} +(-0.599034 + 0.345852i) q^{10} +(-0.247333 + 0.923060i) q^{11} +(-1.71358 + 0.252269i) q^{12} +(2.67710 - 2.41519i) q^{13} -1.00000i q^{14} +(-0.138226 + 1.19007i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.15524 - 2.00093i) q^{17} +(-1.41998 + 2.64266i) q^{18} +(-0.656279 + 0.175849i) q^{19} +(0.668135 - 0.179026i) q^{20} +(-1.39007 - 1.03330i) q^{21} +(0.477811 - 0.827593i) q^{22} +(0.227212 + 0.393543i) q^{23} +(1.72048 + 0.199834i) q^{24} +4.52155i q^{25} +(-3.21098 + 1.64001i) q^{26} +(2.20621 + 4.70454i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(4.11308 - 2.37469i) q^{29} +(0.441528 - 1.11374i) q^{30} +(1.27428 + 1.27428i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.656685 - 1.51934i) q^{33} +(-1.63375 + 1.63375i) q^{34} +(0.599034 + 0.345852i) q^{35} +(2.05556 - 2.18510i) q^{36} +(1.67070 + 0.447663i) q^{37} +0.679430 q^{38} +(-1.03820 + 6.15810i) q^{39} -0.691704 q^{40} +(9.15496 + 2.45307i) q^{41} +(1.07526 + 1.35787i) q^{42} +(0.759424 + 0.438454i) q^{43} +(-0.675726 + 0.675726i) q^{44} +(-1.09194 - 1.76458i) q^{45} +(-0.117614 - 0.438941i) q^{46} +(7.33090 + 7.33090i) q^{47} +(-1.61014 - 0.638319i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(1.17026 - 4.36748i) q^{50} +(0.582861 + 3.95918i) q^{51} +(3.52603 - 0.753063i) q^{52} +10.0392i q^{53} +(-0.913408 - 5.11524i) q^{54} +(0.330504 + 0.572449i) q^{55} +(0.500000 - 0.866025i) q^{56} +(0.702057 - 0.944452i) q^{57} +(-4.58754 + 1.22923i) q^{58} +(11.3752 - 3.04796i) q^{59} +(-0.714740 + 0.961515i) q^{60} +(6.88600 - 11.9269i) q^{61} +(-0.901054 - 1.56067i) q^{62} +(2.99860 - 0.0915937i) q^{63} +1.00000i q^{64} +(0.128104 - 2.49068i) q^{65} +(0.241074 + 1.63754i) q^{66} +(-2.53037 + 9.44348i) q^{67} +(2.00093 - 1.15524i) q^{68} +(-0.731687 - 0.290068i) q^{69} +(-0.489109 - 0.489109i) q^{70} +(-0.951706 - 3.55182i) q^{71} +(-2.55107 + 1.57862i) q^{72} +(-4.44812 + 4.44812i) q^{73} +(-1.49791 - 0.864819i) q^{74} +(-4.86185 - 6.13967i) q^{75} +(-0.656279 - 0.175849i) q^{76} -0.955622 q^{77} +(2.59665 - 5.67956i) q^{78} -3.18127 q^{79} +(0.668135 + 0.179026i) q^{80} +(-8.05435 - 4.01590i) q^{81} +(-8.20812 - 4.73896i) q^{82} +(0.476958 - 0.476958i) q^{83} +(-0.687181 - 1.58990i) q^{84} +(-0.413635 - 1.54371i) q^{85} +(-0.620067 - 0.620067i) q^{86} +(-3.03161 + 7.64715i) q^{87} +(0.827593 - 0.477811i) q^{88} +(0.780848 - 2.91416i) q^{89} +(0.598025 + 1.98707i) q^{90} +(3.02578 + 1.96078i) q^{91} +0.454425i q^{92} +(-3.10050 - 0.360122i) q^{93} +(-5.18373 - 8.97848i) q^{94} +(-0.234982 + 0.407001i) q^{95} +(1.39007 + 1.03330i) q^{96} +(-11.6671 + 3.12620i) q^{97} +(0.965926 - 0.258819i) q^{98} +(2.52538 + 1.35696i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−1.35787	+	1.07526i	−0.783967	+	0.620803i
$3$	−1.35787	+	1.07526i	−0.783967	+	0.620803i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.489109	−	0.489109i	0.218736	−	0.218736i	−0.589230	−	0.807966i	$-0.700569\pi$
$5$	0.489109	−	0.489109i	0.218736	−	0.218736i	0.807966	+	0.589230i	$0.200569\pi$
$6$	1.58990	−	0.687181i	0.649074	−	0.280540i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.687622	−	2.92013i	0.229207	−	0.973378i
$10$	−0.599034	+	0.345852i	−0.189431	+	0.109368i
$11$	−0.247333	+	0.923060i	−0.0745737	+	0.278313i	−0.993136	−	0.116963i	$-0.962684\pi$
$11$	−0.247333	+	0.923060i	−0.0745737	+	0.278313i	0.918563	+	0.395276i	$0.129351\pi$
$12$	−1.71358	+	0.252269i	−0.494668	+	0.0728239i
$13$	2.67710	−	2.41519i	0.742494	−	0.669852i
$13$	2.67710	−	2.41519i	0.742494	−	0.669852i
$14$		−	1.00000i		−	0.267261i
$15$	−0.138226	+	1.19007i	−0.0356898	+	0.307274i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.15524	−	2.00093i	0.280186	−	0.485296i	−0.691244	−	0.722621i	$-0.742937\pi$
$17$	1.15524	−	2.00093i	0.280186	−	0.485296i	0.971430	+	0.237325i	$0.0762705\pi$
$18$	−1.41998	+	2.64266i	−0.334692	+	0.622881i
$19$	−0.656279	+	0.175849i	−0.150561	+	0.0403426i	−0.333312	−	0.942817i	$-0.608166\pi$
$19$	−0.656279	+	0.175849i	−0.150561	+	0.0403426i	0.182751	+	0.983159i	$0.441500\pi$
$20$	0.668135	−	0.179026i	0.149400	−	0.0400315i
$21$	−1.39007	−	1.03330i	−0.303337	−	0.225485i
$22$	0.477811	−	0.827593i	0.101870	−	0.176443i
$23$	0.227212	+	0.393543i	0.0473771	+	0.0820595i	0.888741	−	0.458409i	$-0.151580\pi$
$23$	0.227212	+	0.393543i	0.0473771	+	0.0820595i	−0.841364	+	0.540468i	$0.818247\pi$
$24$	1.72048	+	0.199834i	0.351192	+	0.0407909i
$25$			4.52155i			0.904309i
$26$	−3.21098	+	1.64001i	−0.629724	+	0.321632i
$27$	2.20621	+	4.70454i	0.424585	+	0.905388i
$28$	−0.258819	+	0.965926i	−0.0489122	+	0.182543i
$29$	4.11308	−	2.37469i	0.763779	−	0.440968i	−0.0668719	−	0.997762i	$-0.521302\pi$
$29$	4.11308	−	2.37469i	0.763779	−	0.440968i	0.830651	+	0.556794i	$0.187969\pi$
$30$	0.441528	−	1.11374i	0.0806116	−	0.203340i
$31$	1.27428	+	1.27428i	0.228868	+	0.228868i	0.812220	−	0.583352i	$-0.198259\pi$
$31$	1.27428	+	1.27428i	0.228868	+	0.228868i	−0.583352	+	0.812220i	$0.698259\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−0.656685	−	1.51934i	−0.114314	−	0.264484i
$34$	−1.63375	+	1.63375i	−0.280186	+	0.280186i
$35$	0.599034	+	0.345852i	0.101255	+	0.0584597i
$36$	2.05556	−	2.18510i	0.342594	−	0.364183i
$37$	1.67070	+	0.447663i	0.274662	+	0.0735954i	0.393521	−	0.919316i	$-0.371257\pi$
$37$	1.67070	+	0.447663i	0.274662	+	0.0735954i	−0.118859	+	0.992911i	$0.537924\pi$
$38$	0.679430			0.110218
$39$	−1.03820	+	6.15810i	−0.166244	+	0.986085i
$40$	−0.691704			−0.109368
$41$	9.15496	+	2.45307i	1.42977	+	0.383104i	0.888937	−	0.458029i	$-0.151444\pi$
$41$	9.15496	+	2.45307i	1.42977	+	0.383104i	0.540828	+	0.841133i	$0.318111\pi$
$42$	1.07526	+	1.35787i	0.165917	+	0.209524i
$43$	0.759424	+	0.438454i	0.115811	+	0.0668635i	0.556787	−	0.830656i	$-0.312034\pi$
$43$	0.759424	+	0.438454i	0.115811	+	0.0668635i	−0.440976	+	0.897519i	$0.645367\pi$
$44$	−0.675726	+	0.675726i	−0.101870	+	0.101870i
$45$	−1.09194	−	1.76458i	−0.162777	−	0.263049i
$46$	−0.117614	−	0.438941i	−0.0173412	−	0.0647183i
$47$	7.33090	+	7.33090i	1.06932	+	1.06932i	0.997411	+	0.0719102i	$0.0229095\pi$
$47$	7.33090	+	7.33090i	1.06932	+	1.06932i	0.0719102	+	0.997411i	$0.477091\pi$
$48$	−1.61014	−	0.638319i	−0.232404	−	0.0921334i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	1.17026	−	4.36748i	0.165500	−	0.617655i
$51$	0.582861	+	3.95918i	0.0816169	+	0.554396i
$52$	3.52603	−	0.753063i	0.488973	−	0.104431i
$53$			10.0392i			1.37899i	0.724291	+	0.689495i	$0.242167\pi$
$53$			10.0392i			1.37899i	−0.724291	+	0.689495i	$0.757833\pi$
$54$	−0.913408	−	5.11524i	−0.124299	−	0.696096i
$55$	0.330504	+	0.572449i	0.0445651	+	0.0771891i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	0.702057	−	0.944452i	0.0929897	−	0.125096i
$58$	−4.58754	+	1.22923i	−0.602373	+	0.161405i
$59$	11.3752	−	3.04796i	1.48092	−	0.396811i	0.574259	−	0.818674i	$-0.305290\pi$
$59$	11.3752	−	3.04796i	1.48092	−	0.396811i	0.906660	+	0.421863i	$0.138624\pi$
$60$	−0.714740	+	0.961515i	−0.0922726	+	0.124131i
$61$	6.88600	−	11.9269i	0.881662	−	1.52708i	0.0321692	−	0.999482i	$-0.489758\pi$
$61$	6.88600	−	11.9269i	0.881662	−	1.52708i	0.849493	−	0.527601i	$-0.176908\pi$
$62$	−0.901054	−	1.56067i	−0.114434	−	0.198205i
$63$	2.99860	−	0.0915937i	0.377788	−	0.0115397i
$64$			1.00000i			0.125000i
$65$	0.128104	−	2.49068i	0.0158894	−	0.308931i
$66$	0.241074	+	1.63754i	0.0296742	+	0.201567i
$67$	−2.53037	+	9.44348i	−0.309134	+	1.15370i	0.620194	+	0.784449i	$0.287054\pi$
$67$	−2.53037	+	9.44348i	−0.309134	+	1.15370i	−0.929328	+	0.369256i	$0.879613\pi$
$68$	2.00093	−	1.15524i	0.242648	−	0.140093i
$69$	−0.731687	−	0.290068i	−0.0880848	−	0.0349201i
$70$	−0.489109	−	0.489109i	−0.0584597	−	0.0584597i
$71$	−0.951706	−	3.55182i	−0.112947	−	0.421523i	0.886178	−	0.463344i	$-0.153351\pi$
$71$	−0.951706	−	3.55182i	−0.112947	−	0.421523i	−0.999125	+	0.0418212i	$0.986684\pi$
$72$	−2.55107	+	1.57862i	−0.300646	+	0.186043i
$73$	−4.44812	+	4.44812i	−0.520613	+	0.520613i	−0.917756	−	0.397144i	$-0.870001\pi$
$73$	−4.44812	+	4.44812i	−0.520613	+	0.520613i	0.397144	+	0.917756i	$0.370001\pi$
$74$	−1.49791	−	0.864819i	−0.174129	−	0.100533i
$75$	−4.86185	−	6.13967i	−0.561398	−	0.708948i
$76$	−0.656279	−	0.175849i	−0.0752803	−	0.0201713i
$77$	−0.955622			−0.108903
$78$	2.59665	−	5.67956i	0.294013	−	0.643083i
$79$	−3.18127			−0.357921			−0.178960	−	0.983856i	$-0.557273\pi$
$79$	−3.18127			−0.357921			−0.178960	+	0.983856i	$0.557273\pi$
$80$	0.668135	+	0.179026i	0.0746998	+	0.0200157i
$81$	−8.05435	−	4.01590i	−0.894928	−	0.446211i
$82$	−8.20812	−	4.73896i	−0.906435	−	0.523330i
$83$	0.476958	−	0.476958i	0.0523529	−	0.0523529i	−0.680446	−	0.732799i	$-0.738214\pi$
$83$	0.476958	−	0.476958i	0.0523529	−	0.0523529i	0.732799	+	0.680446i	$0.238214\pi$
$84$	−0.687181	−	1.58990i	−0.0749776	−	0.173472i
$85$	−0.413635	−	1.54371i	−0.0448650	−	0.167439i
$86$	−0.620067	−	0.620067i	−0.0668635	−	0.0668635i
$87$	−3.03161	+	7.64715i	−0.325023	+	0.819860i
$88$	0.827593	−	0.477811i	0.0882217	−	0.0509348i
$89$	0.780848	−	2.91416i	0.0827697	−	0.308901i	−0.912113	−	0.409939i	$-0.865550\pi$
$89$	0.780848	−	2.91416i	0.0827697	−	0.308901i	0.994883	+	0.101039i	$0.0322165\pi$
$90$	0.598025	+	1.98707i	0.0630374	+	0.209456i
$91$	3.02578	+	1.96078i	0.317188	+	0.205546i
$92$			0.454425i			0.0473771i
$93$	−3.10050	−	0.360122i	−0.321507	−	0.0373429i
$94$	−5.18373	−	8.97848i	−0.534661	−	0.926059i
$95$	−0.234982	+	0.407001i	−0.0241087	+	0.0417574i
$96$	1.39007	+	1.03330i	0.141873	+	0.105461i
$97$	−11.6671	+	3.12620i	−1.18462	+	0.317417i	−0.796756	−	0.604301i	$-0.793452\pi$
$97$	−11.6671	+	3.12620i	−1.18462	+	0.317417i	−0.387860	+	0.921718i	$0.626786\pi$
$98$	0.965926	−	0.258819i	0.0975732	−	0.0261447i
$99$	2.52538	+	1.35696i	0.253811	+	0.136380i
$100$	−2.26077	+	3.91577i	−0.226077	+	0.391577i
$101$	−6.62431	−	11.4736i	−0.659143	−	1.14167i	−0.980838	−	0.194826i	$-0.937586\pi$
$101$	−6.62431	−	11.4736i	−0.659143	−	1.14167i	0.321695	−	0.946843i	$-0.395748\pi$
$102$	0.461711	−	3.97513i	0.0457162	−	0.393597i
$103$		−	14.5464i		−	1.43330i	−0.697435	−	0.716649i	$-0.745675\pi$
$103$		−	14.5464i		−	1.43330i	0.697435	−	0.716649i	$-0.254325\pi$
$104$	−3.60079	−	0.185201i	−0.353087	−	0.0181604i
$105$	−1.18529	+	0.174496i	−0.115673	+	0.0170290i
$106$	2.59834	−	9.69712i	0.252373	−	0.941867i
$107$	1.64456	−	0.949487i	0.158986	−	0.0917903i	−0.418396	−	0.908265i	$-0.637408\pi$
$107$	1.64456	−	0.949487i	0.158986	−	0.0917903i	0.577382	+	0.816474i	$0.304074\pi$
$108$	−0.441637	+	5.17735i	−0.0424965	+	0.498191i
$109$	5.65529	+	5.65529i	0.541679	+	0.541679i	0.924021	−	0.382342i	$-0.124882\pi$
$109$	5.65529	+	5.65529i	0.541679	+	0.541679i	−0.382342	+	0.924021i	$0.624882\pi$
$110$	−0.171081	−	0.638484i	−0.0163120	−	0.0608771i
$111$	−2.74995	+	1.18857i	−0.261014	+	0.112814i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	−11.7563	−	6.78749i	−1.10594	−	0.638514i	−0.168164	−	0.985759i	$-0.553784\pi$
$113$	−11.7563	−	6.78749i	−1.10594	−	0.638514i	−0.937774	+	0.347245i	$0.887117\pi$
$114$	−0.922577	+	0.730565i	−0.0864073	+	0.0684237i
$115$	0.303617	+	0.0813540i	0.0283124	+	0.00758630i
$116$	4.74937			0.440968
$117$	−5.21183	−	9.47823i	−0.481834	−	0.876262i
$118$	−11.7764			−1.08411
$119$	2.23175	+	0.597994i	0.204584	+	0.0548181i
$120$	0.939245	−	0.743764i	0.0857409	−	0.0678960i
$121$	8.73541	+	5.04339i	0.794129	+	0.458490i
$122$	−9.73827	+	9.73827i	−0.881662	+	0.881662i
$123$	−15.0689	+	6.51304i	−1.35872	+	0.587261i
$124$	0.466420	+	1.74070i	0.0418857	+	0.156320i
$125$	4.65707	+	4.65707i	0.416541	+	0.416541i
$126$	−2.92013	−	0.687622i	−0.260146	−	0.0612583i
$127$	−7.37225	+	4.25637i	−0.654181	+	0.377692i	−0.790056	−	0.613034i	$-0.789949\pi$
$127$	−7.37225	+	4.25637i	−0.654181	+	0.377692i	0.135875	+	0.990726i	$0.456615\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−1.50265	+	0.221217i	−0.132301	+	0.0194770i
$130$	−0.768375	+	2.37266i	−0.0673910	+	0.208096i
$131$			3.60145i			0.314660i	0.987546	+	0.157330i	$0.0502886\pi$
$131$			3.60145i			0.314660i	−0.987546	+	0.157330i	$0.949711\pi$
$132$	0.190966	−	1.64413i	0.0166214	−	0.143103i
$133$	−0.339715	−	0.588403i	−0.0294570	−	0.0510210i
$134$	4.88830	−	8.46679i	0.422285	−	0.731419i
$135$	3.38010	+	1.22195i	0.290913	+	0.105169i
$136$	−2.23175	+	0.597994i	−0.191371	+	0.0512776i
$137$	−4.13009	+	1.10665i	−0.352857	+	0.0945478i	−0.430894	−	0.902403i	$-0.641802\pi$
$137$	−4.13009	+	1.10665i	−0.352857	+	0.0945478i	0.0780364	+	0.996951i	$0.475135\pi$
$138$	0.631680	+	0.469559i	0.0537722	+	0.0399715i
$139$	8.79259	−	15.2292i	0.745778	−	1.29173i	−0.204052	−	0.978960i	$-0.565411\pi$
$139$	8.79259	−	15.2292i	0.745778	−	1.29173i	0.949830	−	0.312766i	$-0.101255\pi$
$140$	0.345852	+	0.599034i	0.0292298	+	0.0506276i
$141$	−17.8370	−	2.07177i	−1.50215	−	0.174474i
$142$			3.67711i			0.308576i
$143$	1.56723	+	3.06848i	0.131058	+	0.256599i
$144$	2.87272	−	0.864568i	0.239393	−	0.0720473i
$145$	0.850262	−	3.17322i	0.0706104	−	0.263522i
$146$	5.44781	−	3.14529i	0.450864	−	0.260306i
$147$	0.638319	−	1.61014i	0.0526477	−	0.132802i
$148$	1.22304	+	1.22304i	0.100533	+	0.100533i
$149$	−3.20516	−	11.9618i	−0.262577	−	0.979949i	−0.963717	−	0.266926i	$-0.913992\pi$
$149$	−3.20516	−	11.9618i	−0.262577	−	0.979949i	0.701140	−	0.713023i	$-0.252675\pi$
$150$	3.10712	+	7.18881i	0.253695	+	0.586963i
$151$	−6.54217	+	6.54217i	−0.532394	+	0.532394i	−0.921284	−	0.388890i	$-0.872859\pi$
$151$	−6.54217	+	6.54217i	−0.532394	+	0.532394i	0.388890	+	0.921284i	$0.372859\pi$
$152$	0.588403	+	0.339715i	0.0477258	+	0.0275545i
$153$	−5.04861	−	4.74933i	−0.408156	−	0.383960i
$154$	0.923060	+	0.247333i	0.0743823	+	0.0199307i
$155$	1.24653			0.100123
$156$	−3.97815	+	4.81397i	−0.318507	+	0.385426i
$157$	−0.344590			−0.0275013			−0.0137506	−	0.999905i	$-0.504377\pi$
$157$	−0.344590			−0.0275013			−0.0137506	+	0.999905i	$0.504377\pi$
$158$	3.07287	+	0.823373i	0.244465	+	0.0655041i
$159$	−10.7948	−	13.6319i	−0.856081	−	1.08108i
$160$	−0.599034	−	0.345852i	−0.0473578	−	0.0273420i
$161$	−0.321327	+	0.321327i	−0.0253241	+	0.0253241i
$162$	6.74051	+	5.96368i	0.529585	+	0.468551i
$163$	2.09998	+	7.83722i	0.164483	+	0.613858i	0.998106	+	0.0615241i	$0.0195961\pi$
$163$	2.09998	+	7.83722i	0.164483	+	0.613858i	−0.833623	+	0.552334i	$0.813737\pi$
$164$	6.70190	+	6.70190i	0.523330	+	0.523330i
$165$	−1.06431	−	0.421934i	−0.0828568	−	0.0328475i
$166$	−0.584151	+	0.337260i	−0.0453389	+	0.0261765i
$167$	−4.79071	+	17.8792i	−0.370716	+	1.38353i	0.488788	+	0.872403i	$0.337439\pi$
$167$	−4.79071	+	17.8792i	−0.370716	+	1.38353i	−0.859504	+	0.511129i	$0.829227\pi$
$168$	0.252269	+	1.71358i	0.0194630	+	0.132206i
$169$	1.33374	−	12.9314i	0.102595	−	0.994723i
$170$			1.59816i			0.122574i
$171$	0.0622315	+	2.03734i	0.00475896	+	0.155799i
$172$	0.438454	+	0.759424i	0.0334318	+	0.0579055i
$173$	5.44635	−	9.43336i	0.414079	−	0.717205i	−0.581253	−	0.813723i	$-0.697437\pi$
$173$	5.44635	−	9.43336i	0.414079	−	0.717205i	0.995331	+	0.0965181i	$0.0307706\pi$
$174$	4.90754	−	6.60194i	0.372040	−	0.500492i
$175$	−4.36748	+	1.17026i	−0.330150	+	0.0884635i
$176$	−0.923060	+	0.247333i	−0.0695782	+	0.0186434i
$177$	−12.1686	+	16.3700i	−0.914649	+	1.23045i
$178$	−1.50848	+	2.61277i	−0.113066	+	0.195835i
$179$	1.11063	+	1.92368i	0.0830127	+	0.143782i	0.904543	−	0.426383i	$-0.140212\pi$
$179$	1.11063	+	1.92368i	0.0830127	+	0.143782i	−0.821530	+	0.570165i	$0.806879\pi$
$180$	−0.0633558	−	2.07415i	−0.00472226	−	0.154598i
$181$		−	6.51249i		−	0.484069i	−0.970268	−	0.242035i	$-0.922185\pi$
$181$		−	6.51249i		−	0.484069i	0.970268	−	0.242035i	$-0.0778148\pi$
$182$	−2.41519	−	2.67710i	−0.179026	−	0.198440i
$183$	3.47425	+	23.5994i	0.256824	+	1.74452i
$184$	0.117614	−	0.438941i	0.00867060	−	0.0323591i
$185$	1.03611	−	0.598199i	0.0761764	−	0.0439805i
$186$	2.90164	+	1.15032i	0.212759	+	0.0843455i
$187$	1.56125	+	1.56125i	0.114170	+	0.114170i
$188$	2.68329	+	10.0142i	0.195699	+	0.730360i
$189$	−3.97322	+	3.34866i	−0.289010	+	0.243579i
$190$	0.332315	−	0.332315i	0.0241087	−	0.0241087i
$191$	0.590207	+	0.340756i	0.0427059	+	0.0246563i	0.521201	−	0.853434i	$-0.325484\pi$
$191$	0.590207	+	0.340756i	0.0427059	+	0.0246563i	−0.478495	+	0.878090i	$0.658818\pi$
$192$	−1.07526	−	1.35787i	−0.0776004	−	0.0979958i
$193$	12.6264	+	3.38324i	0.908869	+	0.243531i	0.682821	−	0.730585i	$-0.260753\pi$
$193$	12.6264	+	3.38324i	0.908869	+	0.243531i	0.226048	+	0.974116i	$0.427419\pi$
$194$	12.0787			0.867199
$195$	2.50419	+	3.51977i	0.179329	+	0.252056i
$196$	−1.00000			−0.0714286
$197$	−3.46619	−	0.928764i	−0.246956	−	0.0661717i	0.133218	−	0.991087i	$-0.457469\pi$
$197$	−3.46619	−	0.928764i	−0.246956	−	0.0661717i	−0.380174	+	0.924915i	$0.624136\pi$
$198$	−2.08813	−	1.96434i	−0.148397	−	0.139600i
$199$	8.29160	+	4.78716i	0.587776	+	0.339353i	0.764218	−	0.644958i	$-0.223125\pi$
$199$	8.29160	+	4.78716i	0.587776	+	0.339353i	−0.176442	+	0.984311i	$0.556459\pi$
$200$	3.19722	−	3.19722i	0.226077	−	0.226077i
$201$	−6.71830	−	15.5438i	−0.473872	−	1.09638i
$202$	3.42899	+	12.7972i	0.241263	+	0.900406i
$203$	3.35831	+	3.35831i	0.235707	+	0.235707i
$204$	−1.47482	+	3.72018i	−0.103258	+	0.260465i
$205$	5.67759	−	3.27796i	0.396540	−	0.228942i
$206$	−3.76488	+	14.0507i	−0.262312	+	0.978960i
$207$	1.30544	−	0.392881i	0.0907340	−	0.0273071i
$208$	3.43016	+	1.11084i	0.237839	+	0.0770232i
$209$		−	0.649278i		−	0.0449115i
$210$	1.19007	+	0.138226i	0.0821224	+	0.00953850i
$211$	−10.7025	−	18.5373i	−0.736792	−	1.27616i	−0.953932	−	0.300022i	$-0.903006\pi$
$211$	−10.7025	−	18.5373i	−0.736792	−	1.27616i	0.217140	−	0.976140i	$-0.430327\pi$
$212$	−5.01960	+	8.69420i	−0.344747	+	0.597120i
$213$	5.11143	+	3.79957i	0.350229	+	0.260342i
$214$	−1.83427	+	0.491490i	−0.125388	+	0.0335976i
$215$	0.585892	−	0.156989i	0.0399575	−	0.0107066i
$216$	1.76659	−	4.88663i	0.120201	−	0.332493i
$217$	−0.901054	+	1.56067i	−0.0611675	+	0.105945i
$218$	−3.99889	−	6.92629i	−0.270839	−	0.469107i
$219$	1.25707	−	10.8229i	0.0849451	−	0.731341i
$220$			0.661008i			0.0445651i
$221$	−1.73993	−	8.14680i	−0.117040	−	0.548013i
$222$	2.96387	−	0.436335i	0.198922	−	0.0292849i
$223$	5.63645	−	21.0355i	0.377445	−	1.40864i	−0.472295	−	0.881440i	$-0.656574\pi$
$223$	5.63645	−	21.0355i	0.377445	−	1.40864i	0.849740	−	0.527202i	$-0.176759\pi$
$224$	0.866025	−	0.500000i	0.0578638	−	0.0334077i
$225$	13.2035	+	3.10912i	0.880234	+	0.207274i
$226$	9.59897	+	9.59897i	0.638514	+	0.638514i
$227$	−5.82374	−	21.7345i	−0.386535	−	1.44257i	−0.835733	−	0.549136i	$-0.814957\pi$
$227$	−5.82374	−	21.7345i	−0.386535	−	1.44257i	0.449198	−	0.893432i	$-0.351710\pi$
$228$	1.08023	−	0.466891i	0.0715397	−	0.0309206i
$229$	9.41590	−	9.41590i	0.622220	−	0.622220i	−0.323879	−	0.946099i	$-0.604987\pi$
$229$	9.41590	−	9.41590i	0.622220	−	0.622220i	0.946099	+	0.323879i	$0.104987\pi$
$230$	−0.272216	−	0.157164i	−0.0179494	−	0.0103631i
$231$	1.29761	−	1.02754i	0.0853765	−	0.0676074i
$232$	−4.58754	−	1.22923i	−0.301187	−	0.0807027i
$233$	−6.19134			−0.405608			−0.202804	−	0.979219i	$-0.565005\pi$
$233$	−6.19134			−0.405608			−0.202804	+	0.979219i	$0.565005\pi$
$234$	2.58110	+	10.5042i	0.168732	+	0.686680i
$235$	7.17121			0.467798
$236$	11.3752	+	3.04796i	0.740459	+	0.198405i
$237$	4.31975	−	3.42070i	0.280598	−	0.222198i
$238$	−2.00093	−	1.15524i	−0.129701	−	0.0748829i
$239$	−10.4405	+	10.4405i	−0.675342	+	0.675342i	−0.958942	−	0.283601i	$-0.908471\pi$
$239$	−10.4405	+	10.4405i	−0.675342	+	0.675342i	0.283601	+	0.958942i	$0.408471\pi$
$240$	−1.09974	+	0.475326i	−0.0709880	+	0.0306822i
$241$	3.14908	+	11.7525i	0.202850	+	0.757046i	0.990094	+	0.140405i	$0.0448403\pi$
$241$	3.14908	+	11.7525i	0.202850	+	0.757046i	−0.787244	+	0.616641i	$0.788493\pi$
$242$	−7.13244	−	7.13244i	−0.458490	−	0.458490i
$243$	15.2549	−	3.20747i	0.978603	−	0.205759i
$244$	11.9269	−	6.88600i	0.763542	−	0.440831i
$245$	−0.179026	+	0.668135i	−0.0114376	+	0.0426856i
$246$	16.2412	−	2.39099i	1.03550	−	0.152444i
$247$	−1.33222	+	2.05580i	−0.0847668	+	0.130808i
$248$		−	1.80211i		−	0.114434i
$249$	−0.134792	+	1.16050i	−0.00854210	+	0.0735438i
$250$	−3.29305	−	5.70372i	−0.208271	−	0.360735i
$251$	−3.51417	+	6.08672i	−0.221812	+	0.384190i	−0.955358	−	0.295450i	$-0.904531\pi$
$251$	−3.51417	+	6.08672i	−0.221812	+	0.384190i	0.733546	+	0.679640i	$0.237864\pi$
$252$	2.64266	+	1.41998i	0.166472	+	0.0894502i
$253$	−0.419461	+	0.112394i	−0.0263713	+	0.00706617i
$254$	8.22267	−	2.20326i	0.515936	−	0.138245i
$255$	2.22155	+	1.65139i	0.139119	+	0.103414i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.65180	+	2.86099i	0.103036	+	0.178464i	0.912934	−	0.408107i	$-0.133811\pi$
$257$	1.65180	+	2.86099i	0.103036	+	0.178464i	−0.809898	+	0.586571i	$0.800478\pi$
$258$	1.50870	+	0.175236i	0.0939279	+	0.0109097i
$259$			1.72964i			0.107474i
$260$	1.35628	−	2.09294i	0.0841131	−	0.129799i
$261$	−4.10615	−	13.6436i	−0.254165	−	0.844519i
$262$	0.932123	−	3.47873i	0.0575868	−	0.214917i
$263$	8.77075	−	5.06379i	0.540828	−	0.312247i	−0.204587	−	0.978848i	$-0.565585\pi$
$263$	8.77075	−	5.06379i	0.540828	−	0.312247i	0.745414	+	0.666601i	$0.232252\pi$
$264$	−0.609991	+	1.53868i	−0.0375424	+	0.0946995i
$265$	4.91026	+	4.91026i	0.301635	+	0.301635i
$266$	0.175849	+	0.656279i	0.0107820	+	0.0402390i
$267$	2.07320	+	4.79667i	0.126878	+	0.293552i
$268$	−6.91311	+	6.91311i	−0.422285	+	0.422285i
$269$	−2.87311	−	1.65879i	−0.175177	−	0.101138i	0.409848	−	0.912154i	$-0.365582\pi$
$269$	−2.87311	−	1.65879i	−0.175177	−	0.101138i	−0.585025	+	0.811016i	$0.698915\pi$
$270$	−2.94867	−	2.05515i	−0.179450	−	0.125073i
$271$	10.8523	+	2.90785i	0.659228	+	0.176640i	0.572897	−	0.819627i	$-0.305819\pi$
$271$	10.8523	+	2.90785i	0.659228	+	0.176640i	0.0863303	+	0.996267i	$0.472486\pi$
$272$	2.31047			0.140093
$273$	−6.21697	+	0.591013i	−0.376268	+	0.0357697i
$274$	4.27578			0.258310
$275$	−4.17366	−	1.11833i	−0.251681	−	0.0674377i
$276$	−0.488626	−	0.617050i	−0.0294118	−	0.0371420i
$277$	24.9930	+	14.4297i	1.50168	+	0.866997i	0.999998	+	0.00194697i	$0.000619740\pi$
$277$	24.9930	+	14.4297i	1.50168	+	0.866997i	0.501685	+	0.865050i	$0.332714\pi$
$278$	−12.4346	+	12.4346i	−0.745778	+	0.745778i
$279$	4.59730	−	2.84485i	0.275233	−	0.170317i
$280$	−0.179026	−	0.668135i	−0.0106989	−	0.0399287i
$281$	−14.0821	−	14.0821i	−0.840066	−	0.840066i	0.148802	−	0.988867i	$-0.452458\pi$
$281$	−14.0821	−	14.0821i	−0.840066	−	0.840066i	−0.988867	+	0.148802i	$0.952458\pi$
$282$	16.6930	+	6.61774i	0.994056	+	0.394081i
$283$	−0.407336	+	0.235175i	−0.0242136	+	0.0139797i	−0.512058	−	0.858951i	$-0.671117\pi$
$283$	−0.407336	+	0.235175i	−0.0242136	+	0.0139797i	0.487844	+	0.872931i	$0.337783\pi$
$284$	0.951706	−	3.55182i	0.0564734	−	0.210762i
$285$	−0.118558	−	0.805322i	−0.00702275	−	0.0477032i
$286$	−0.719643	−	3.36955i	−0.0425534	−	0.199246i
$287$			9.47792i			0.559464i
$288$	−2.99860	+	0.0915937i	−0.176694	+	0.00539721i
$289$	5.83086	+	10.0993i	0.342992	+	0.594079i
$290$	−1.64258	+	2.84503i	−0.0964556	+	0.167066i
$291$	12.4810	−	16.7902i	0.731646	−	0.984258i
$292$	−6.07624	+	1.62812i	−0.355585	+	0.0952787i
$293$	−20.9122	+	5.60342i	−1.22171	+	0.327355i	−0.811345	−	0.584568i	$-0.801264\pi$
$293$	−20.9122	+	5.60342i	−1.22171	+	0.327355i	−0.410361	+	0.911923i	$0.634597\pi$
$294$	−1.03330	+	1.39007i	−0.0602635	+	0.0810703i
$295$	4.07290	−	7.05447i	0.237133	−	0.410727i
$296$	−0.864819	−	1.49791i	−0.0502666	−	0.0870643i
$297$	−4.88823	+	0.872873i	−0.283644	+	0.0506492i
$298$			12.3838i			0.717373i
$299$	1.55875	+	0.504795i	0.0901449	+	0.0291930i
$300$	−1.14065	−	7.74803i	−0.0658553	−	0.447333i
$301$	−0.226960	+	0.847027i	−0.0130818	+	0.0488218i
$302$	8.01249	−	4.62601i	0.461067	−	0.266197i
$303$	21.3321	+	8.45684i	1.22550	+	0.485833i
$304$	−0.480429	−	0.480429i	−0.0275545	−	0.0275545i
$305$	−2.46555	−	9.20155i	−0.141177	−	0.526879i
$306$	3.64737	+	5.89417i	0.208506	+	0.336947i
$307$	−12.1224	+	12.1224i	−0.691861	+	0.691861i	−0.962641	−	0.270780i	$-0.912718\pi$
$307$	−12.1224	+	12.1224i	−0.691861	+	0.691861i	0.270780	+	0.962641i	$0.412718\pi$
$308$	−0.827593	−	0.477811i	−0.0471565	−	0.0272258i
$309$	15.6412	+	19.7521i	0.889795	+	1.12366i
$310$	−1.20405	−	0.322625i	−0.0683855	−	0.0183238i
$311$	−16.1442			−0.915452			−0.457726	−	0.889093i	$-0.651336\pi$
$311$	−16.1442			−0.915452			−0.457726	+	0.889093i	$0.651336\pi$
$312$	5.08855	−	3.62032i	0.288082	−	0.204960i
$313$	4.95586			0.280122			0.140061	−	0.990143i	$-0.455270\pi$
$313$	4.95586			0.280122			0.140061	+	0.990143i	$0.455270\pi$
$314$	0.332848	+	0.0891865i	0.0187837	+	0.00503308i
$315$	1.42184	−	1.51144i	0.0801118	−	0.0851601i
$316$	−2.75506	−	1.59064i	−0.154984	−	0.0894802i
$317$	−2.01058	+	2.01058i	−0.112925	+	0.112925i	−0.761312	−	0.648386i	$-0.775444\pi$
$317$	−2.01058	+	2.01058i	−0.112925	+	0.112925i	0.648386	+	0.761312i	$0.275444\pi$
$318$	6.89874	+	15.9613i	0.386862	+	0.895066i
$319$	1.17468	+	4.38395i	0.0657693	+	0.245454i
$320$	0.489109	+	0.489109i	0.0273420	+	0.0273420i
$321$	−1.21215	+	3.05761i	−0.0676556	+	0.170659i
$322$	0.393543	−	0.227212i	0.0219313	−	0.0126620i
$323$	−0.406295	+	1.51631i	−0.0226069	+	0.0843700i
$324$	−4.96732	−	7.50504i	−0.275962	−	0.416947i
$325$	10.9204	+	12.1046i	0.605754	+	0.671444i
$326$		−	8.11369i		−	0.449375i
$327$	−13.7601	−	1.59823i	−0.760933	−	0.0883823i
$328$	−4.73896	−	8.20812i	−0.261665	−	0.453217i
$329$	−5.18373	+	8.97848i	−0.285788	+	0.495000i
$330$	0.918844	+	0.683021i	0.0505807	+	0.0375991i
$331$	−16.0182	+	4.29205i	−0.880438	+	0.235913i	−0.670596	−	0.741823i	$-0.733962\pi$
$331$	−16.0182	+	4.29205i	−0.880438	+	0.235913i	−0.209842	+	0.977735i	$0.567295\pi$
$332$	0.651536	−	0.174579i	0.0357577	−	0.00958125i
$333$	2.45605	−	4.57085i	0.134591	−	0.250481i
$334$	9.25494	−	16.0300i	0.506408	−	0.877124i
$335$	3.38126	+	5.85652i	0.184738	+	0.319976i
$336$	0.199834	−	1.72048i	0.0109018	−	0.0938601i
$337$			16.5753i			0.902916i	0.892292	+	0.451458i	$0.149096\pi$
$337$			16.5753i			0.902916i	−0.892292	+	0.451458i	$0.850904\pi$
$338$	−4.63519	+	12.1456i	−0.252121	+	0.660632i
$339$	23.2618	−	3.42455i	1.26341	−	0.185996i
$340$	0.413635	−	1.54371i	0.0224325	−	0.0837193i
$341$	−1.49141	+	0.861067i	−0.0807644	+	0.0466294i
$342$	0.467191	−	1.98402i	0.0252628	−	0.107284i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−0.226960	−	0.847027i	−0.0122369	−	0.0456686i
$345$	−0.499749	+	0.216000i	−0.0269056	+	0.0116290i
$346$	−7.70231	+	7.70231i	−0.414079	+	0.414079i
$347$	−12.7078	−	7.33688i	−0.682193	−	0.393864i	0.118488	−	0.992956i	$-0.462195\pi$
$347$	−12.7078	−	7.33688i	−0.682193	−	0.393864i	−0.800681	+	0.599091i	$0.795529\pi$
$348$	−6.44903	+	5.10682i	−0.345704	+	0.273754i
$349$	−13.4718	−	3.60976i	−0.721129	−	0.193226i	−0.120454	−	0.992719i	$-0.538435\pi$
$349$	−13.4718	−	3.60976i	−0.721129	−	0.193226i	−0.600676	+	0.799493i	$0.705102\pi$
$350$	4.52155			0.241687
$351$	17.2686	+	7.26611i	0.921728	+	0.387836i
$352$	0.955622			0.0509348
$353$	−9.52698	−	2.55275i	−0.507070	−	0.135869i	−0.00379078	−	0.999993i	$-0.501207\pi$
$353$	−9.52698	−	2.55275i	−0.507070	−	0.135869i	−0.503279	+	0.864124i	$0.667873\pi$
$354$	15.9909	−	12.6627i	0.849904	−	0.673017i
$355$	−2.20271	−	1.27174i	−0.116908	−	0.0674968i
$356$	2.13332	−	2.13332i	0.113066	−	0.113066i
$357$	−3.67342	+	1.58771i	−0.194418	+	0.0840307i
$358$	−0.574907	−	2.14558i	−0.0303848	−	0.113397i
$359$	25.7702	+	25.7702i	1.36010	+	1.36010i	0.873782	+	0.486318i	$0.161660\pi$
$359$	25.7702	+	25.7702i	1.36010	+	1.36010i	0.486318	+	0.873782i	$0.338340\pi$
$360$	−0.475631	+	2.01987i	−0.0250680	+	0.106456i
$361$	−16.0547	+	9.26919i	−0.844984	+	0.487852i
$362$	−1.68556	+	6.29058i	−0.0885909	+	0.330626i
$363$	−17.2845	+	2.54459i	−0.907202	+	0.133556i
$364$	1.64001	+	3.21098i	0.0859597	+	0.168301i
$365$			4.35123i			0.227754i
$366$	2.75211	−	23.6945i	0.143855	−	1.23853i
$367$	−12.2275	−	21.1787i	−0.638271	−	1.10552i	−0.985812	−	0.167853i	$-0.946317\pi$
$367$	−12.2275	−	21.1787i	−0.638271	−	1.10552i	0.347541	−	0.937665i	$-0.387017\pi$
$368$	−0.227212	+	0.393543i	−0.0118443	+	0.0205149i
$369$	13.4584	−	25.0469i	0.700618	−	1.30389i
$370$	−1.15563	+	0.309651i	−0.0600784	+	0.0160980i
$371$	−9.69712	+	2.59834i	−0.503449	+	0.134899i
$372$	−2.50505	−	1.86212i	−0.129881	−	0.0965466i
$373$	17.1444	−	29.6949i	0.887703	−	1.53755i	0.0451184	−	0.998982i	$-0.485633\pi$
$373$	17.1444	−	29.6949i	0.887703	−	1.53755i	0.842584	−	0.538565i	$-0.181033\pi$
$374$	−1.10397	−	1.91213i	−0.0570849	−	0.0988739i
$375$	−11.3313	−	1.31613i	−0.585144	−	0.0679644i
$376$		−	10.3675i		−	0.534661i
$377$	5.27581	−	16.2911i	0.271718	−	0.839035i
$378$	4.70454	−	2.20621i	0.241975	−	0.113475i
$379$	3.05664	−	11.4075i	0.157009	−	0.585966i	−0.841916	−	0.539609i	$-0.818572\pi$
$379$	3.05664	−	11.4075i	0.157009	−	0.585966i	0.998925	−	0.0463569i	$-0.0147611\pi$
$380$	−0.407001	+	0.234982i	−0.0208787	+	0.0120543i
$381$	5.43384	−	13.7067i	0.278384	−	0.702215i
$382$	−0.481902	−	0.481902i	−0.0246563	−	0.0246563i
$383$	5.32445	+	19.8711i	0.272067	+	1.01537i	0.957782	+	0.287496i	$0.0928230\pi$
$383$	5.32445	+	19.8711i	0.272067	+	1.01537i	−0.685715	+	0.727870i	$0.740510\pi$
$384$	0.687181	+	1.58990i	0.0350676	+	0.0811343i
$385$	−0.467403	+	0.467403i	−0.0238211	+	0.0238211i
$386$	−11.3205	−	6.53591i	−0.576200	−	0.332669i
$387$	1.80254	−	1.91613i	0.0916282	−	0.0974022i
$388$	−11.6671	−	3.12620i	−0.592308	−	0.158709i
$389$	−1.98079			−0.100430			−0.0502151	−	0.998738i	$-0.515991\pi$
$389$	−1.98079			−0.100430			−0.0502151	+	0.998738i	$0.515991\pi$
$390$	−1.50788	−	4.04797i	−0.0763543	−	0.204977i
$391$	1.04994			0.0530975
$392$	0.965926	+	0.258819i	0.0487866	+	0.0130723i
$393$	−3.87250	−	4.89030i	−0.195342	−	0.246683i
$394$	3.10771	+	1.79423i	0.156564	+	0.0903922i
$395$	−1.55599	+	1.55599i	−0.0782902	+	0.0782902i
$396$	1.50857	+	2.43786i	0.0758083	+	0.122507i
$397$	8.96772	+	33.4680i	0.450077	+	1.67971i	0.702171	+	0.712008i	$0.252214\pi$
$397$	8.96772	+	33.4680i	0.450077	+	1.67971i	−0.252094	+	0.967703i	$0.581119\pi$
$398$	−6.77006	−	6.77006i	−0.339353	−	0.339353i
$399$	1.09398	+	0.433693i	0.0547673	+	0.0217118i
$400$	−3.91577	+	2.26077i	−0.195789	+	0.113039i
$401$	−6.92912	+	25.8598i	−0.346024	+	1.29138i	0.545388	+	0.838183i	$0.316382\pi$
$401$	−6.92912	+	25.8598i	−0.346024	+	1.29138i	−0.891412	+	0.453194i	$0.850284\pi$
$402$	2.46634	+	16.7530i	0.123010	+	0.835564i
$403$	6.48901	+	0.333752i	0.323241	+	0.0166254i
$404$		−	13.2486i		−	0.659143i
$405$	−5.90367	+	1.97524i	−0.293355	+	0.0981506i
$406$	−2.37469	−	4.11308i	−0.117854	−	0.204129i
$407$	−0.826440	+	1.43144i	−0.0409651	+	0.0709536i
$408$	2.38742	−	3.21171i	0.118195	−	0.159003i
$409$	−15.2615	+	4.08931i	−0.754633	+	0.202203i	−0.615572	−	0.788081i	$-0.711075\pi$
$409$	−15.2615	+	4.08931i	−0.754633	+	0.202203i	−0.139061	+	0.990284i	$0.544408\pi$
$410$	−6.33253	+	1.69680i	−0.312741	+	0.0837988i
$411$	4.41818	−	5.94362i	0.217933	−	0.293177i
$412$	7.27319	−	12.5975i	0.358324	−	0.620636i
$413$	5.88821	+	10.1987i	0.289740	+	0.501844i
$414$	−1.36264	+	0.0416224i	−0.0669700	+	0.00204563i
$415$		−	0.466568i		−	0.0229029i
$416$	−3.02578	−	1.96078i	−0.148351	−	0.0961354i
$417$	4.43620	+	30.1336i	0.217242	+	1.47565i
$418$	−0.168045	+	0.627154i	−0.00821937	+	0.0306751i
$419$	−1.43075	+	0.826043i	−0.0698966	+	0.0403548i	−0.534541	−	0.845143i	$-0.679515\pi$
$419$	−1.43075	+	0.826043i	−0.0698966	+	0.0403548i	0.464644	+	0.885497i	$0.346182\pi$
$420$	−1.11374	−	0.441528i	−0.0543450	−	0.0215444i
$421$	5.05280	+	5.05280i	0.246259	+	0.246259i	0.819433	−	0.573175i	$-0.194288\pi$
$421$	5.05280	+	5.05280i	0.246259	+	0.246259i	−0.573175	+	0.819433i	$0.694288\pi$
$422$	5.54004	+	20.6757i	0.269685	+	1.00648i
$423$	26.4481	−	16.3663i	1.28595	−	0.795757i
$424$	7.09878	−	7.09878i	0.344747	−	0.344747i
$425$	9.04729	+	5.22345i	0.438858	+	0.253375i
$426$	−3.95386	−	4.99304i	−0.191565	−	0.241914i
$427$	13.3027	+	3.56446i	0.643764	+	0.172496i
$428$	1.89897			0.0917903
$429$	−5.42751	−	2.48142i	−0.262043	−	0.119804i
$430$	−0.606560			−0.0292509
$431$	−8.60327	−	2.30524i	−0.414405	−	0.111039i	0.0455917	−	0.998960i	$-0.485483\pi$
$431$	−8.60327	−	2.30524i	−0.414405	−	0.111039i	−0.459997	+	0.887921i	$0.652149\pi$
$432$	−2.97114	+	4.26290i	−0.142949	+	0.205099i
$433$	−11.2117	−	6.47306i	−0.538798	−	0.311075i	0.205794	−	0.978595i	$-0.434022\pi$
$433$	−11.2117	−	6.47306i	−0.538798	−	0.311075i	−0.744592	+	0.667520i	$0.767356\pi$
$434$	1.27428	−	1.27428i	0.0611675	−	0.0611675i
$435$	2.25750	+	5.22308i	0.108239	+	0.250427i
$436$	2.06998	+	7.72527i	0.0991340	+	0.369973i
$437$	−0.218319	−	0.218319i	−0.0104436	−	0.0104436i
$438$	−4.01540	+	10.1287i	−0.191863	+	0.483969i
$439$	−35.4886	+	20.4894i	−1.69378	+	0.977904i	−0.742363	+	0.669998i	$0.766295\pi$
$439$	−35.4886	+	20.4894i	−1.69378	+	0.977904i	−0.951417	+	0.307906i	$0.900372\pi$
$440$	0.171081	−	0.638484i	0.00815598	−	0.0304385i
$441$	0.864568	+	2.87272i	0.0411699	+	0.136796i
$442$	−0.427902	+	8.31953i	−0.0203532	+	0.395720i
$443$		−	37.6638i		−	1.78946i	−0.446607	−	0.894730i	$-0.647368\pi$
$443$		−	37.6638i		−	1.78946i	0.446607	−	0.894730i	$-0.352632\pi$
$444$	−2.97581	−	0.345640i	−0.141226	−	0.0164034i
$445$	−1.04342	−	1.80726i	−0.0494630	−	0.0856725i
$446$	−10.8888	+	18.8599i	−0.515599	+	0.893043i
$447$	17.2143	+	12.7962i	0.814207	+	0.605239i
$448$	−0.965926	+	0.258819i	−0.0456357	+	0.0122281i
$449$	−24.8854	+	6.66802i	−1.17441	+	0.314683i	−0.792709	−	0.609601i	$-0.791330\pi$
$449$	−24.8854	+	6.66802i	−1.17441	+	0.314683i	−0.381705	+	0.924284i	$0.624663\pi$
$450$	−11.9489	−	6.42050i	−0.563277	−	0.302665i
$451$	−4.52865	+	7.84385i	−0.213246	+	0.369353i
$452$	−6.78749	−	11.7563i	−0.319257	−	0.552969i
$453$	1.84887	−	15.9180i	0.0868675	−	0.747891i
$454$			22.5012i			1.05603i
$455$	2.43897	−	0.520897i	0.114341	−	0.0244200i
$456$	−1.16426	+	0.171399i	−0.0545214	+	0.00802651i
$457$	3.53106	−	13.1781i	0.165176	−	0.616446i	−0.832841	−	0.553512i	$-0.813287\pi$
$457$	3.53106	−	13.1781i	0.165176	−	0.616446i	0.998018	−	0.0629344i	$-0.0200459\pi$
$458$	−11.5321	+	6.65805i	−0.538858	+	0.311110i
$459$	11.9621	+	1.02039i	0.558344	+	0.0476277i
$460$	0.222263	+	0.222263i	0.0103631	+	0.0103631i
$461$	−3.32582	−	12.4121i	−0.154899	−	0.578090i	−0.999114	−	0.0420857i	$-0.986600\pi$
$461$	−3.32582	−	12.4121i	−0.154899	−	0.578090i	0.844215	−	0.536004i	$-0.180067\pi$
$462$	−1.51934	+	0.656685i	−0.0706862	+	0.0305517i
$463$	2.61340	−	2.61340i	0.121455	−	0.121455i	−0.643767	−	0.765222i	$-0.722629\pi$
$463$	2.61340	−	2.61340i	0.121455	−	0.121455i	0.765222	+	0.643767i	$0.222629\pi$
$464$	4.11308	+	2.37469i	0.190945	+	0.110242i
$465$	−1.69262	+	1.34034i	−0.0784934	+	0.0621569i
$466$	5.98038	+	1.60244i	0.277036	+	0.0742314i
$467$	−26.4925			−1.22593			−0.612963	−	0.790111i	$-0.710023\pi$
$467$	−26.4925			−1.22593			−0.612963	+	0.790111i	$0.710023\pi$
$468$	0.225534	−	10.8143i	0.0104253	−	0.499891i
$469$	−9.77661			−0.451442
$470$	−6.92686	−	1.85605i	−0.319512	−	0.0856130i
$471$	0.467908	−	0.370525i	0.0215601	−	0.0170729i
$472$	−10.1987	−	5.88821i	−0.469432	−	0.271027i
$473$	−0.592549	+	0.592549i	−0.0272454	+	0.0272454i
$474$	−5.05790	+	2.18611i	−0.232317	+	0.100411i
$475$	−0.795111	−	2.96739i	−0.0364822	−	0.136153i
$476$	1.63375	+	1.63375i	0.0748829	+	0.0748829i
$477$	29.3158	+	6.90318i	1.34228	+	0.316075i
$478$	12.7870	−	7.38257i	0.584863	−	0.337671i
$479$	3.48343	−	13.0003i	0.159162	−	0.594001i	−0.839551	−	0.543281i	$-0.817182\pi$
$479$	3.48343	−	13.0003i	0.159162	−	0.594001i	0.998713	−	0.0507198i	$-0.0161516\pi$
$480$	1.18529	−	0.174496i	0.0541009	−	0.00796461i
$481$	5.55383	−	2.83662i	0.253233	−	0.129339i
$482$		−	12.1671i		−	0.554196i
$483$	0.0908095	−	0.781831i	0.00413197	−	0.0355745i
$484$	5.04339	+	8.73541i	0.229245	+	0.397064i
$485$	−4.17744	+	7.23554i	−0.189688	+	0.328549i
$486$	−15.5653	−	0.850080i	−0.706055	−	0.0385604i
$487$	−37.8914	+	10.1530i	−1.71702	+	0.460075i	−0.977129	−	0.212649i	$-0.931791\pi$
$487$	−37.8914	+	10.1530i	−1.71702	+	0.460075i	−0.739894	+	0.672723i	$0.765124\pi$
$488$	−13.3027	+	3.56446i	−0.602186	+	0.161355i
$489$	−11.2786	−	8.38390i	−0.510034	−	0.379133i
$490$	0.345852	−	0.599034i	0.0156240	−	0.0270616i
$491$	8.73726	+	15.1334i	0.394307	+	0.682960i	0.993012	−	0.118009i	$-0.0376513\pi$
$491$	8.73726	+	15.1334i	0.394307	+	0.682960i	−0.598705	+	0.800969i	$0.704318\pi$
$492$	−16.3066	−	1.89401i	−0.735159	−	0.0853885i
$493$		−	10.9733i		−	0.494212i
$494$	1.81890	−	1.64095i	0.0818363	−	0.0738298i
$495$	1.89889	−	0.571486i	0.0853488	−	0.0256864i
$496$	−0.466420	+	1.74070i	−0.0209429	+	0.0781598i
$497$	3.18447	−	1.83856i	0.142843	−	0.0824705i
$498$	0.430559	−	1.08607i	0.0192938	−	0.0486680i
$499$	−24.8719	−	24.8719i	−1.11342	−	1.11342i	−0.992685	−	0.120736i	$-0.961475\pi$
$499$	−24.8719	−	24.8719i	−1.11342	−	1.11342i	−0.120736	−	0.992685i	$-0.538525\pi$
$500$	1.70461	+	6.36168i	0.0762323	+	0.284503i
$501$	−12.7196	−	29.4289i	−0.568271	−	1.31478i
$502$	4.96979	−	4.96979i	0.221812	−	0.221812i
$503$	2.94409	+	1.69977i	0.131271	+	0.0757891i	0.564197	−	0.825640i	$-0.309186\pi$
$503$	2.94409	+	1.69977i	0.131271	+	0.0757891i	−0.432927	+	0.901429i	$0.642519\pi$
$504$	−2.18510	−	2.05556i	−0.0973320	−	0.0915621i
$505$	−8.85186	−	2.37185i	−0.393903	−	0.105546i
$506$	0.434258			0.0193051
$507$	12.0936	+	18.9933i	0.537096	+	0.843521i
$508$	−8.51274			−0.377692
$509$	13.5551	+	3.63207i	0.600817	+	0.160989i	0.546392	−	0.837529i	$-0.316001\pi$
$509$	13.5551	+	3.63207i	0.600817	+	0.160989i	0.0544250	+	0.998518i	$0.482667\pi$
$510$	−1.71845	−	2.17010i	−0.0760940	−	0.0960936i
$511$	−5.44781	−	3.14529i	−0.240997	−	0.139140i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.27518	−	2.69953i	−0.100451	−	0.119187i
$514$	−0.855032	−	3.19102i	−0.0377138	−	0.140750i
$515$	−7.11476	−	7.11476i	−0.313514	−	0.313514i
$516$	−1.41194	−	0.559746i	−0.0621573	−	0.0246415i
$517$	−8.58003	+	4.95368i	−0.377349	+	0.217863i
$518$	0.447663	−	1.67070i	0.0196692	−	0.0734064i
$519$	2.74790	+	18.6655i	0.120619	+	0.819326i
$520$	−1.85176	+	1.67060i	−0.0812052	+	0.0732605i
$521$		−	36.5045i		−	1.59929i	−0.600473	−	0.799645i	$-0.705021\pi$
$521$		−	36.5045i		−	1.59929i	0.600473	−	0.799645i	$-0.294979\pi$
$522$	0.435013	+	14.2415i	0.0190400	+	0.623332i
$523$	−6.98395	−	12.0965i	−0.305387	−	0.528945i	0.671961	−	0.740587i	$-0.265452\pi$
$523$	−6.98395	−	12.0965i	−0.305387	−	0.528945i	−0.977347	+	0.211642i	$0.932119\pi$
$524$	−1.80072	+	3.11895i	−0.0786650	+	0.136252i
$525$	4.67213	−	6.28525i	0.203908	−	0.274311i
$526$	−9.78250	+	2.62121i	−0.426537	+	0.114290i
$527$	4.02185	−	1.07765i	0.175194	−	0.0469432i
$528$	0.987447	−	1.32838i	0.0429731	−	0.0578102i
$529$	11.3967	−	19.7397i	0.495511	−	0.858250i
$530$	−3.47208	−	6.01382i	−0.150817	−	0.261223i
$531$	−1.07865	−	35.3128i	−0.0468093	−	1.53244i
$532$		−	0.679430i		−	0.0294570i
$533$	30.4334	−	15.5438i	1.31822	−	0.673279i
$534$	−0.761088	−	5.16981i	−0.0329355	−	0.223720i
$535$	0.339966	−	1.26877i	0.0146980	−	0.0548537i
$536$	8.46679	−	4.88830i	0.365710	−	0.211143i
$537$	−3.57655	−	1.41788i	−0.154340	−	0.0611860i
$538$	2.34589	+	2.34589i	0.101138	+	0.101138i
$539$	−0.247333	−	0.923060i	−0.0106534	−	0.0397590i
$540$	2.31628	+	2.74830i	0.0996768	+	0.118268i
$541$	−31.4285	+	31.4285i	−1.35122	+	1.35122i	−0.466917	+	0.884301i	$0.654635\pi$
$541$	−31.4285	+	31.4285i	−1.35122	+	1.35122i	−0.884301	+	0.466917i	$0.845365\pi$
$542$	−9.72987	−	5.61754i	−0.417934	−	0.241294i
$543$	7.00263	+	8.84311i	0.300512	+	0.379494i
$544$	−2.23175	−	0.597994i	−0.0956853	−	0.0256388i
$545$	5.53210			0.236969
$546$	6.15810	+	1.03820i	0.263542	+	0.0444307i
$547$	−19.0132			−0.812944			−0.406472	−	0.913663i	$-0.633241\pi$
$547$	−19.0132			−0.812944			−0.406472	+	0.913663i	$0.633241\pi$
$548$	−4.13009	−	1.10665i	−0.176429	−	0.0472739i
$549$	−30.0932	−	28.3092i	−1.28434	−	1.20821i
$550$	3.74200	+	2.16044i	0.159559	+	0.0921216i
$551$	−2.28174	+	2.28174i	−0.0972053	+	0.0972053i
$552$	0.312272	+	0.722490i	0.0132912	+	0.0307512i
$553$	−0.823373	−	3.07287i	−0.0350134	−	0.130672i
$554$	−20.4067	−	20.4067i	−0.866997	−	0.866997i
$555$	−0.763683	+	1.92637i	−0.0324166	+	0.0817697i
$556$	15.2292	−	8.79259i	0.645863	−	0.372889i
$557$	−9.57033	+	35.7170i	−0.405508	+	1.51338i	0.397609	+	0.917555i	$0.369840\pi$
$557$	−9.57033	+	35.7170i	−0.405508	+	1.51338i	−0.803117	+	0.595822i	$0.796826\pi$
$558$	−5.17695	+	1.55804i	−0.219158	+	0.0659573i
$559$	3.09200	−	0.660366i	0.130778	−	0.0279305i
$560$			0.691704i			0.0292298i
$561$	−3.79872	−	0.441221i	−0.160382	−	0.0186284i
$562$	9.95752	+	17.2469i	0.420033	+	0.727518i
$563$	17.6157	−	30.5113i	0.742414	−	1.28590i	−0.208979	−	0.977920i	$-0.567014\pi$
$563$	17.6157	−	30.5113i	0.742414	−	1.28590i	0.951393	−	0.307979i	$-0.0996526\pi$
$564$	−14.4114	−	10.7127i	−0.606831	−	0.451087i
$565$	−9.06993	+	2.43028i	−0.381575	+	0.102243i
$566$	0.454324	−	0.121736i	0.0190967	−	0.00511694i
$567$	1.79444	−	8.81930i	0.0753594	−	0.370376i
$568$	−1.83856	+	3.18447i	−0.0771441	+	0.133617i
$569$	10.5121	+	18.2075i	0.440690	+	0.763298i	0.997741	−	0.0671807i	$-0.0214004\pi$
$569$	10.5121	+	18.2075i	0.440690	+	0.763298i	−0.557051	+	0.830479i	$0.688067\pi$
$570$	−0.0939149	+	0.808566i	−0.00393366	+	0.0338671i
$571$		−	26.4973i		−	1.10888i	−0.832225	−	0.554439i	$-0.812933\pi$
$571$		−	26.4973i		−	1.10888i	0.832225	−	0.554439i	$-0.187067\pi$
$572$	−0.176982	+	3.44099i	−0.00739999	+	0.143875i
$573$	−1.16783	+	0.171925i	−0.0487867	+	0.00718226i
$574$	2.45307	−	9.15496i	0.102389	−	0.382121i
$575$	−1.77942	+	1.02735i	−0.0742071	+	0.0428435i
$576$	2.92013	+	0.687622i	0.121672	+	0.0286509i
$577$	−2.94218	−	2.94218i	−0.122484	−	0.122484i	0.643208	−	0.765692i	$-0.277603\pi$
$577$	−2.94218	−	2.94218i	−0.122484	−	0.122484i	−0.765692	+	0.643208i	$0.777603\pi$
$578$	−3.01827	−	11.2644i	−0.125544	−	0.468535i
$579$	−20.7829	+	8.98271i	−0.863708	+	0.373309i
$580$	2.32296	−	2.32296i	0.0964556	−	0.0964556i
$581$	0.584151	+	0.337260i	0.0242347	+	0.0139919i
$582$	−16.4013	+	12.9878i	−0.679855	+	0.538360i
$583$	−9.26678	−	2.48303i	−0.383791	−	0.102836i
$584$	6.29059			0.260306
$585$	−7.18504	−	2.08673i	−0.297065	−	0.0862757i
$586$	21.6499			0.894351
$587$	36.5825	+	9.80224i	1.50992	+	0.404582i	0.916409	−	0.400244i	$-0.131075\pi$
$587$	36.5825	+	9.80224i	1.50992	+	0.404582i	0.593511	+	0.804826i	$0.297741\pi$
$588$	1.35787	−	1.07526i	0.0559976	−	0.0443431i
$589$	−1.06037	−	0.612203i	−0.0436916	−	0.0252254i
$590$	−5.75995	+	5.75995i	−0.237133	+	0.237133i
$591$	5.70531	−	2.46593i	0.234685	−	0.101435i
$592$	0.447663	+	1.67070i	0.0183988	+	0.0686654i
$593$	24.3689	+	24.3689i	1.00071	+	1.00071i	1.00000		0.000709316i	$0.000225782\pi$
$593$	24.3689	+	24.3689i	1.00071	+	1.00071i	0.000709316		1.00000i	$0.499774\pi$
$594$	4.94759	+	0.422038i	0.203002	+	0.0173164i
$595$	1.38405	−	0.799082i	0.0567405	−	0.0327592i
$596$	3.20516	−	11.9618i	0.131288	−	0.489975i
$597$	−16.4064	+	2.41531i	−0.671468	+	0.0988519i
$598$	−1.37499	−	0.891029i	−0.0562274	−	0.0364369i
$599$			20.6846i			0.845148i	0.906328	+	0.422574i	$0.138873\pi$
$599$			20.6846i			0.845148i	−0.906328	+	0.422574i	$0.861127\pi$
$600$	−0.903558	+	7.77925i	−0.0368876	+	0.317586i
$601$	14.7216	+	25.4985i	0.600506	+	1.04011i	0.992744	+	0.120243i	$0.0383675\pi$
$601$	14.7216	+	25.4985i	0.600506	+	1.04011i	−0.392238	+	0.919864i	$0.628299\pi$
$602$	0.438454	−	0.759424i	0.0178700	−	0.0309518i
$603$	25.8363	+	13.8826i	1.05213	+	0.565342i
$604$	−8.93677	+	2.39460i	−0.363632	+	0.0974349i
$605$	6.73934	−	1.80580i	0.273993	−	0.0734162i
$606$	−18.4165	−	13.6898i	−0.748117	−	0.556112i
$607$	−18.5803	+	32.1820i	−0.754151	+	1.30623i	0.191645	+	0.981464i	$0.438618\pi$
$607$	−18.5803	+	32.1820i	−0.754151	+	1.30623i	−0.945795	+	0.324763i	$0.894716\pi$
$608$	0.339715	+	0.588403i	0.0137773	+	0.0238629i
$609$	−8.17122	−	0.949086i	−0.331114	−	0.0384589i
$610$			9.52615i			0.385703i
$611$	37.3310	+	1.92006i	1.51025	+	0.0776774i
$612$	−1.99756	−	6.63734i	−0.0807466	−	0.268299i
$613$	4.52043	−	16.8705i	0.182579	−	0.681393i	−0.812557	−	0.582881i	$-0.801925\pi$
$613$	4.52043	−	16.8705i	0.182579	−	0.681393i	0.995136	−	0.0985114i	$-0.0314081\pi$
$614$	14.8468	−	8.57182i	0.599169	−	0.345931i
$615$	−4.18476	+	10.5559i	−0.168746	+	0.425656i
$616$	0.675726	+	0.675726i	0.0272258	+	0.0272258i
$617$	−2.26152	−	8.44012i	−0.0910455	−	0.339786i	0.905345	−	0.424677i	$-0.139612\pi$
$617$	−2.26152	−	8.44012i	−0.0910455	−	0.339786i	−0.996390	+	0.0848911i	$0.972946\pi$
$618$	−9.99599	−	23.1273i	−0.402098	−	0.930316i
$619$	27.9324	−	27.9324i	1.12270	−	1.12270i	0.131363	−	0.991334i	$-0.458065\pi$
$619$	27.9324	−	27.9324i	1.12270	−	1.12270i	0.991334	−	0.131363i	$-0.0419352\pi$
$620$	1.07952	+	0.623263i	0.0433547	+	0.0250308i
$621$	−1.35016	+	1.93717i	−0.0541801	+	0.0777358i
$622$	15.5941	+	4.17842i	0.625266	+	0.167539i
$623$	3.01696			0.120872
$624$	−5.85217	+	2.17994i	−0.234274	+	0.0872676i
$625$	−18.0521			−0.722084
$626$	−4.78700	−	1.28267i	−0.191327	−	0.0512659i
$627$	0.698144	+	0.881635i	0.0278812	+	0.0352091i
$628$	−0.298424	−	0.172295i	−0.0119084	−	0.00687532i
$629$	2.82580	−	2.82580i	0.112672	−	0.112672i
$630$	−1.76458	+	1.09194i	−0.0703027	+	0.0435040i
$631$	0.387029	+	1.44441i	0.0154074	+	0.0575011i	0.973202	−	0.229954i	$-0.0738575\pi$
$631$	0.387029	+	1.44441i	0.0154074	+	0.0575011i	−0.957794	+	0.287455i	$0.907191\pi$
$632$	2.24950	+	2.24950i	0.0894802	+	0.0894802i
$633$	34.4651	+	13.6633i	1.36987	+	0.543066i
$634$	2.46245	−	1.42170i	0.0977963	−	0.0564627i
$635$	−1.52400	+	5.68766i	−0.0604782	+	0.225708i
$636$	−2.53258	−	17.2030i	−0.100423	−	0.682142i
$637$	−1.11084	+	3.43016i	−0.0440132	+	0.135908i
$638$		−	4.53860i		−	0.179685i
$639$	−11.0262	+	0.336800i	−0.436189	+	0.0133236i
$640$	−0.345852	−	0.599034i	−0.0136710	−	0.0236789i
$641$	3.68067	−	6.37511i	0.145378	−	0.251802i	−0.784136	−	0.620589i	$-0.786894\pi$
$641$	3.68067	−	6.37511i	0.145378	−	0.251802i	0.929514	+	0.368787i	$0.120227\pi$
$642$	1.96222	−	2.63970i	0.0774425	−	0.104181i
$643$	−9.91929	+	2.65787i	−0.391179	+	0.104816i	−0.449047	−	0.893508i	$-0.648236\pi$
$643$	−9.91929	+	2.65787i	−0.391179	+	0.104816i	0.0578682	+	0.998324i	$0.481570\pi$
$644$	−0.438941	+	0.117614i	−0.0172967	+	0.00463463i
$645$	−0.626761	+	0.843159i	−0.0246787	+	0.0331994i
$646$	0.784902	−	1.35949i	0.0308816	−	0.0534884i
$647$	−3.54406	−	6.13848i	−0.139331	−	0.241329i	0.787912	−	0.615787i	$-0.211162\pi$
$647$	−3.54406	−	6.13848i	−0.139331	−	0.241329i	−0.927244	+	0.374459i	$0.877829\pi$
$648$	2.85562	+	8.53495i	0.112179	+	0.335285i
$649$			11.2538i			0.441750i
$650$	−7.41537	−	14.5186i	−0.290855	−	0.569466i
$651$	−0.454616	−	3.08806i	−0.0178178	−	0.121031i
$652$	−2.09998	+	7.83722i	−0.0822414	+	0.306929i
$653$	−17.8645	+	10.3141i	−0.699092	+	0.403621i	−0.807009	−	0.590539i	$-0.798915\pi$
$653$	−17.8645	+	10.3141i	−0.699092	+	0.403621i	0.107917	+	0.994160i	$0.465582\pi$
$654$	12.8776	+	5.10514i	0.503552	+	0.199627i
$655$	1.76150	+	1.76150i	0.0688275	+	0.0688275i
$656$	2.45307	+	9.15496i	0.0957761	+	0.357441i
$657$	9.93047	+	16.0477i	0.387424	+	0.626081i
$658$	7.33090	−	7.33090i	0.285788	−	0.285788i
$659$	−40.1163	−	23.1612i	−1.56271	−	0.902231i	−0.996981	−	0.0776400i	$-0.975262\pi$
$659$	−40.1163	−	23.1612i	−1.56271	−	0.902231i	−0.565729	−	0.824591i	$-0.691405\pi$
$660$	−0.710756	−	0.897562i	−0.0276662	−	0.0349376i
$661$	14.0298	+	3.75929i	0.545698	+	0.146219i	0.521128	−	0.853479i	$-0.325512\pi$
$661$	14.0298	+	3.75929i	0.545698	+	0.146219i	0.0245703	+	0.999698i	$0.492178\pi$
$662$	16.5832			0.644525
$663$	11.1225	+	9.19141i	0.431964	+	0.356965i
$664$	−0.674520			−0.0261765
$665$	−0.453951	−	0.121636i	−0.0176035	−	0.00471683i
$666$	−3.55538	+	3.77943i	−0.137768	+	0.146450i
$667$	1.86908	+	1.07912i	0.0723712	+	0.0417835i
$668$	−13.0885	+	13.0885i	−0.506408	+	0.506408i
$669$	14.9651	+	34.6242i	0.578585	+	1.33865i
$670$	−1.75027	−	6.53210i	−0.0676188	−	0.252357i
$671$	9.30610	+	9.30610i	0.359258	+	0.359258i
$672$	−0.638319	+	1.61014i	−0.0246237	+	0.0621125i
$673$	15.0031	−	8.66207i	0.578329	−	0.333898i	−0.182140	−	0.983273i	$-0.558302\pi$
$673$	15.0031	−	8.66207i	0.578329	−	0.333898i	0.760469	+	0.649374i	$0.224969\pi$
$674$	4.29001	−	16.0106i	0.165245	−	0.616703i
$675$	−21.2718	+	9.97546i	−0.818751	+	0.383956i
$676$	7.62075	−	10.5321i	0.293106	−	0.405079i
$677$		−	36.1386i		−	1.38892i	−0.719532	−	0.694460i	$-0.755643\pi$
$677$		−	36.1386i		−	1.38892i	0.719532	−	0.694460i	$-0.244357\pi$
$678$	−23.3556	−	2.71274i	−0.896965	−	0.104182i
$679$	−6.03935	−	10.4605i	−0.231769	−	0.401435i
$680$	−0.799082	+	1.38405i	−0.0306434	+	0.0530759i
$681$	31.2782	+	23.2506i	1.19858	+	0.890964i
$682$	1.66345	−	0.445721i	0.0636969	−	0.0170675i
$683$	9.12410	−	2.44479i	0.349124	−	0.0935475i	−0.0799956	−	0.996795i	$-0.525491\pi$
$683$	9.12410	−	2.44479i	0.349124	−	0.0935475i	0.429119	+	0.903248i	$0.358824\pi$
$684$	−0.964775	+	1.79550i	−0.0368891	+	0.0686528i
$685$	−1.47879	+	2.56134i	−0.0565016	+	0.0978637i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	−2.66101	+	22.9101i	−0.101524	+	0.874076i
$688$			0.876907i			0.0334318i
$689$	24.2465	+	26.8759i	0.923720	+	1.02389i
$690$	0.538626	−	0.0792952i	0.0205051	−	0.00301872i
$691$	−8.04837	+	30.0369i	−0.306174	+	1.14266i	0.625756	+	0.780019i	$0.284791\pi$
$691$	−8.04837	+	30.0369i	−0.306174	+	1.14266i	−0.931930	+	0.362639i	$0.881876\pi$
$692$	9.43336	−	5.44635i	0.358603	−	0.207039i
$693$	−0.657107	+	2.79054i	−0.0249614	+	0.106004i
$694$	10.3759	+	10.3759i	0.393864	+	0.393864i
$695$	−3.14821	−	11.7493i	−0.119418	−	0.445676i
$696$	7.55103	−	3.26368i	0.286221	−	0.123709i
$697$	15.4846	−	15.4846i	0.586519	−	0.586519i
$698$	12.0785	+	6.97352i	0.457178	+	0.263952i
$699$	8.40704	−	6.65731i	0.317983	−	0.251803i
$700$	−4.36748	−	1.17026i	−0.165075	−	0.0442317i
$701$	46.7837			1.76700			0.883498	−	0.468434i	$-0.155182\pi$
$701$	46.7837			1.76700			0.883498	+	0.468434i	$0.155182\pi$
$702$	−14.7996	−	11.4880i	−0.558573	−	0.433585i
$703$	−1.17517			−0.0443223
$704$	−0.923060	−	0.247333i	−0.0347891	−	0.00932172i
$705$	−9.73758	+	7.71093i	−0.366738	+	0.290411i
$706$	8.54166	+	4.93153i	0.321470	+	0.185601i
$707$	9.36819	−	9.36819i	0.352327	−	0.352327i
$708$	−18.7233	+	8.09253i	−0.703666	+	0.304136i
$709$	−4.08957	−	15.2625i	−0.153587	−	0.573194i	−0.999222	−	0.0394332i	$-0.987445\pi$
$709$	−4.08957	−	15.2625i	−0.153587	−	0.573194i	0.845635	−	0.533761i	$-0.179222\pi$
$710$	1.79851	+	1.79851i	0.0674968	+	0.0674968i
$711$	−2.18751	+	9.28973i	−0.0820382	+	0.348392i
$712$	−2.61277	+	1.50848i	−0.0979176	+	0.0565328i
$713$	−0.211953	+	0.791018i	−0.00793769	+	0.0296239i
$714$	3.95918	−	0.582861i	0.148169	−	0.0218130i
$715$	2.26736	+	0.734276i	0.0847946	+	0.0274604i
$716$			2.22127i			0.0830127i
$717$	2.95058	−	25.4032i	0.110191	−	0.948700i
$718$	−18.2223	−	31.5619i	−0.680050	−	1.17788i
$719$	−21.5484	+	37.3229i	−0.803619	+	1.39191i	0.113600	+	0.993527i	$0.463762\pi$
$719$	−21.5484	+	37.3229i	−0.803619	+	1.39191i	−0.917219	+	0.398383i	$0.869571\pi$
$720$	0.982205	−	1.82794i	0.0366046	−	0.0681233i
$721$	14.0507	−	3.76488i	0.523276	−	0.140211i
$722$	17.9067	−	4.79808i	0.666418	−	0.178566i
$723$	−16.9131	−	12.5723i	−0.629004	−	0.467569i
$724$	3.25624	−	5.63998i	0.121017	−	0.209608i
$725$	10.7372	+	18.5975i	0.398771	+	0.690692i
$726$	17.3542	+	2.01568i	0.644073	+	0.0748090i
$727$			12.7998i			0.474720i	0.971422	+	0.237360i	$0.0762821\pi$
$727$			12.7998i			0.474720i	−0.971422	+	0.237360i	$0.923718\pi$
$728$	−0.753063	−	3.52603i	−0.0279104	−	0.130683i
$729$	−17.2653	+	20.7584i	−0.639456	+	0.768828i
$730$	1.12618	−	4.20296i	0.0416818	−	0.155559i
$731$	1.75463	−	1.01303i	0.0648973	−	0.0374685i
$732$	−8.79093	+	22.1748i	−0.324922	+	0.819606i
$733$	22.4620	+	22.4620i	0.829652	+	0.829652i	0.987468	−	0.157817i	$-0.0504455\pi$
$733$	22.4620	+	22.4620i	0.829652	+	0.829652i	−0.157817	+	0.987468i	$0.550445\pi$
$734$	6.32943	+	23.6217i	0.233623	+	0.871894i
$735$	−0.475326	−	1.09974i	−0.0175327	−	0.0405646i
$736$	0.321327	−	0.321327i	0.0118443	−	0.0118443i
$737$	−8.09105	−	4.67137i	−0.298038	−	0.172072i
$738$	−19.4825	+	20.7102i	−0.717160	+	0.762352i
$739$	14.0152	+	3.75536i	0.515558	+	0.138143i	0.507211	−	0.861822i	$-0.330676\pi$
$739$	14.0152	+	3.75536i	0.515558	+	0.138143i	0.00834668	+	0.999965i	$0.497343\pi$
$740$	1.19640			0.0439805
$741$	−0.401551	−	4.22399i	−0.0147514	−	0.155172i
$742$	10.0392			0.368551
$743$	−21.7841	−	5.83703i	−0.799180	−	0.214140i	−0.163956	−	0.986468i	$-0.552426\pi$
$743$	−21.7841	−	5.83703i	−0.799180	−	0.214140i	−0.635224	+	0.772328i	$0.719092\pi$
$744$	1.93774	+	2.44703i	0.0710409	+	0.0897124i
$745$	−7.41830	−	4.28296i	−0.271785	−	0.156915i
$746$	−24.2458	+	24.2458i	−0.887703	+	0.887703i
$747$	−1.06481	−	1.72075i	−0.0389595	−	0.0629588i
$748$	0.571456	+	2.13270i	0.0208945	+	0.0779794i
$749$	1.34278	+	1.34278i	0.0490640	+	0.0490640i
$750$	10.6045	+	4.20403i	0.387223	+	0.153509i
$751$	35.4118	−	20.4450i	1.29220	−	0.746049i	0.313152	−	0.949703i	$-0.398615\pi$
$751$	35.4118	−	20.4450i	1.29220	−	0.746049i	0.979043	+	0.203654i	$0.0652817\pi$
$752$	−2.68329	+	10.0142i	−0.0978497	+	0.365180i
$753$	−1.77303	−	12.0436i	−0.0646130	−	0.438894i
$754$	−9.31249	+	14.3705i	−0.339141	+	0.523344i
$755$			6.39967i			0.232908i
$756$	−5.11524	+	0.913408i	−0.186039	+	0.0332203i
$757$	23.2232	+	40.2237i	0.844061	+	1.46196i	0.886435	+	0.462854i	$0.153175\pi$
$757$	23.2232	+	40.2237i	0.844061	+	1.46196i	−0.0423740	+	0.999102i	$0.513492\pi$
$758$	−5.90497	+	10.2277i	−0.214478	+	0.371487i
$759$	0.448720	−	0.603647i	0.0162875	−	0.0219110i
$760$	0.453951	−	0.121636i	0.0164665	−	0.00441219i
$761$	18.6904	−	5.00807i	0.677526	−	0.181543i	0.0963833	−	0.995344i	$-0.469273\pi$
$761$	18.6904	−	5.00807i	0.677526	−	0.181543i	0.581143	+	0.813802i	$0.302606\pi$
$762$	−8.79624	+	11.8333i	−0.318654	+	0.428674i
$763$	−3.99889	+	6.92629i	−0.144770	+	0.250748i
$764$	0.340756	+	0.590207i	0.0123281	+	0.0213529i
$765$	−4.79226	+	0.146382i	−0.173264	+	0.00529245i
$766$		−	20.5721i		−	0.743300i
$767$	23.0910	−	35.6328i	0.833769	−	1.28663i
$768$	−0.252269	−	1.71358i	−0.00910299	−	0.0618335i
$769$	11.2085	−	41.8307i	0.404189	−	1.50846i	−0.401357	−	0.915922i	$-0.631461\pi$
$769$	11.2085	−	41.8307i	0.404189	−	1.50846i	0.805546	−	0.592533i	$-0.201872\pi$
$770$	0.572449	−	0.330504i	0.0206296	−	0.0119105i
$771$	−5.31924	−	2.10874i	−0.191568	−	0.0759446i
$772$	9.24318	+	9.24318i	0.332669	+	0.332669i
$773$	−8.99619	−	33.5742i	−0.323571	−	1.20758i	−0.915741	−	0.401769i	$-0.868396\pi$
$773$	−8.99619	−	33.5742i	−0.323571	−	1.20758i	0.592171	−	0.805813i	$-0.298271\pi$
$774$	−2.23705	+	1.38431i	−0.0804091	+	0.0497578i
$775$	−5.76173	+	5.76173i	−0.206967	+	0.206967i
$776$	10.4605	+	6.03935i	0.375508	+	0.216800i
$777$	−1.85981	−	2.34862i	−0.0667205	−	0.0842564i
$778$	1.91330	+	0.512667i	0.0685951	+	0.0183800i
$779$	−6.43958			−0.230722
$780$	0.408806	+	4.30030i	0.0146376	+	0.153976i
$781$	3.51393			0.125738
$782$	−1.01416	−	0.271743i	−0.0362663	−	0.00971753i
$783$	20.2461	+	14.1111i	0.723536	+	0.504288i
$784$	−0.866025	−	0.500000i	−0.0309295	−	0.0178571i
$785$	−0.168542	+	0.168542i	−0.00601552	+	0.00601552i
$786$	2.47485	+	5.72594i	0.0882748	+	0.204238i
$787$	9.54632	+	35.6274i	0.340290	+	1.26998i	0.898020	+	0.439955i	$0.145006\pi$
$787$	9.54632	+	35.6274i	0.340290	+	1.26998i	−0.557730	+	0.830022i	$0.688328\pi$
$788$	−2.53743	−	2.53743i	−0.0903922	−	0.0903922i
$789$	−6.46463	+	16.3068i	−0.230147	+	0.580539i
$790$	1.90569	−	1.10025i	0.0678013	−	0.0391451i
$791$	3.51347	−	13.1124i	0.124924	−	0.466224i
$792$	−0.826200	−	2.74523i	−0.0293577	−	0.0975476i
$793$	−10.3712	−	48.5605i	−0.368292	−	1.72443i
$794$		−	34.6486i		−	1.22963i
$795$	−11.9473	−	1.38768i	−0.423727	−	0.0492159i
$796$	4.78716	+	8.29160i	0.169676	+	0.293888i
$797$	−11.3862	+	19.7214i	−0.403319	+	0.698569i	−0.994124	−	0.108245i	$-0.965477\pi$
$797$	−11.3862	+	19.7214i	−0.403319	+	0.698569i	0.590805	+	0.806814i	$0.298810\pi$
$798$	−0.944452	−	0.702057i	−0.0334332	−	0.0248525i
$799$	23.1375	−	6.19968i	0.818547	−	0.219329i
$800$	4.36748	−	1.17026i	0.154414	−	0.0413750i
$801$	−7.97282	−	4.28402i	−0.281706	−	0.151369i
$802$	13.3860	−	23.1853i	0.472677	−	0.818700i
$803$	−3.00571	−	5.20604i	−0.106069	−	0.183717i
$804$	1.95370	−	16.8205i	0.0689016	−	0.593213i
$805$			0.314328i			0.0110786i
$806$	−6.18153	−	2.00186i	−0.217735	−	0.0705125i
$807$	5.68495	−	0.836925i	0.200120	−	0.0294611i
$808$	−3.42899	+	12.7972i	−0.120632	+	0.450203i
$809$	−40.1870	+	23.2020i	−1.41290	+	0.815739i	−0.995661	−	0.0930572i	$-0.970336\pi$
$809$	−40.1870	+	23.2020i	−1.41290	+	0.815739i	−0.417240	+	0.908796i	$0.637003\pi$
$810$	6.21373	−	0.379957i	0.218328	−	0.0133503i
$811$	2.87161	+	2.87161i	0.100836	+	0.100836i	0.755725	−	0.654889i	$-0.227285\pi$
$811$	2.87161	+	2.87161i	0.100836	+	0.100836i	−0.654889	+	0.755725i	$0.727285\pi$
$812$	1.22923	+	4.58754i	0.0431374	+	0.160991i
$813$	−17.8627	+	7.72054i	−0.626471	+	0.270771i
$814$	1.16876	−	1.16876i	0.0409651	−	0.0409651i
$815$	4.86037	+	2.80614i	0.170251	+	0.0982946i
$816$	−3.13732	+	2.48436i	−0.109828	+	0.0869701i
$817$	−0.575495	−	0.154204i	−0.0201340	−	0.00539490i
$818$	15.7999			0.552429
$819$	7.80634	−	7.48739i	0.272776	−	0.261631i
$820$	6.55592			0.228942
$821$	51.3684	+	13.7641i	1.79277	+	0.480371i	0.992812	−	0.119684i	$-0.0381880\pi$
$821$	51.3684	+	13.7641i	1.79277	+	0.480371i	0.799959	+	0.600055i	$0.204855\pi$
$822$	−5.80596	+	4.59759i	−0.202506	+	0.160359i
$823$	−37.6529	−	21.7389i	−1.31250	−	0.757770i	−0.329988	−	0.943985i	$-0.607045\pi$
$823$	−37.6529	−	21.7389i	−1.31250	−	0.757770i	−0.982509	+	0.186215i	$0.940378\pi$
$824$	−10.2858	+	10.2858i	−0.358324	+	0.358324i
$825$	6.86978	−	2.96923i	0.239175	−	0.103375i
$826$	−3.04796	−	11.3752i	−0.106052	−	0.395792i
$827$	−32.1295	−	32.1295i	−1.11725	−	1.11725i	−0.992143	−	0.125110i	$-0.960072\pi$
$827$	−32.1295	−	32.1295i	−1.11725	−	1.11725i	−0.125110	−	0.992143i	$-0.539928\pi$
$828$	1.32698	+	0.312473i	0.0461158	+	0.0108592i
$829$	−4.15563	+	2.39926i	−0.144331	+	0.0833296i	−0.570427	−	0.821349i	$-0.693222\pi$
$829$	−4.15563	+	2.39926i	−0.144331	+	0.0833296i	0.426095	+	0.904678i	$0.359889\pi$
$830$	−0.120757	+	0.450670i	−0.00419153	+	0.0156430i
$831$	−49.4530	+	7.28035i	−1.71550	+	0.252552i
$832$	2.41519	+	2.67710i	0.0837316	+	0.0928118i
$833$			2.31047i			0.0800531i
$834$	3.51412	−	30.2550i	0.121684	−	1.04765i
$835$	6.40168	+	11.0880i	0.221539	+	0.383717i
$836$	0.324639	−	0.562291i	0.0112279	−	0.0194472i
$837$	−3.18358	+	8.80624i	−0.110041	+	0.304388i
$838$	1.59579	−	0.427591i	0.0551257	−	0.0147709i
$839$	−24.4967	+	6.56388i	−0.845721	+	0.226610i	−0.655560	−	0.755143i	$-0.727567\pi$
$839$	−24.4967	+	6.56388i	−0.845721	+	0.226610i	−0.190160	+	0.981753i	$0.560901\pi$
$840$	0.961515	+	0.714740i	0.0331754	+	0.0246609i
$841$	−3.22174	+	5.58022i	−0.111094	+	0.192421i
$842$	−3.57287	−	6.18839i	−0.123129	−	0.213266i
$843$	34.2635	+	3.97970i	1.18010	+	0.137068i
$844$		−	21.4051i		−	0.736792i
$845$	−5.67252	−	6.97721i	−0.195141	−	0.240023i
$846$	−29.7828	+	8.96337i	−1.02395	+	0.308167i
$847$	−2.61065	+	9.74309i	−0.0897031	+	0.334776i
$848$	−8.69420	+	5.01960i	−0.298560	+	0.172374i
$849$	0.300234	−	0.757331i	0.0103040	−	0.0259915i
$850$	−7.38708	−	7.38708i	−0.253375	−	0.253375i
$851$	0.203429	+	0.759208i	0.00697346	+	0.0260253i
$852$	2.52684	+	5.84624i	0.0865681	+	0.200289i
$853$	−21.0210	+	21.0210i	−0.719744	+	0.719744i	−0.968553	−	0.248809i	$-0.919961\pi$
$853$	−21.0210	+	21.0210i	−0.719744	+	0.719744i	0.248809	+	0.968553i	$0.419961\pi$
$854$	−11.9269	−	6.88600i	−0.408130	−	0.235634i
$855$	1.02692	+	0.966042i	0.0351199	+	0.0330380i
$856$	−1.83427	−	0.491490i	−0.0626940	−	0.0167988i
$857$	−21.7425			−0.742709			−0.371354	−	0.928491i	$-0.621107\pi$
$857$	−21.7425			−0.742709			−0.371354	+	0.928491i	$0.621107\pi$
$858$	4.60033	+	3.80161i	0.157053	+	0.129785i
$859$	16.4693			0.561924			0.280962	−	0.959719i	$-0.409346\pi$
$859$	16.4693			0.561924			0.280962	+	0.959719i	$0.409346\pi$
$860$	0.585892	+	0.156989i	0.0199788	+	0.00535329i
$861$	−10.1912	−	12.8698i	−0.347317	−	0.438601i
$862$	7.71348	+	4.45338i	0.262722	+	0.151683i
$863$	1.78788	−	1.78788i	0.0608601	−	0.0608601i	−0.676022	−	0.736882i	$-0.736297\pi$
$863$	1.78788	−	1.78788i	0.0608601	−	0.0608601i	0.736882	+	0.676022i	$0.236297\pi$
$864$	3.97322	−	3.34866i	0.135172	−	0.113924i
$865$	−1.95008	−	7.27780i	−0.0663047	−	0.247453i
$866$	9.15428	+	9.15428i	0.311075	+	0.311075i
$867$	−18.7770	−	7.44389i	−0.637700	−	0.252808i
$868$	−1.56067	+	0.901054i	−0.0529726	+	0.0305838i
$869$	0.786833	−	2.93650i	0.0266915	−	0.0996140i
$870$	−0.828745	−	5.62939i	−0.0280971	−	0.190854i
$871$	16.0337	+	31.3925i	0.543282	+	1.06369i
$872$		−	7.99779i		−	0.270839i
$873$	1.10633	+	36.2192i	0.0374437	+	1.22583i
$874$	0.154375	+	0.267385i	0.00522181	+	0.00904443i
$875$	−3.29305	+	5.70372i	−0.111325	+	0.192821i
$876$	6.50008	−	8.74433i	0.219618	−	0.295444i
$877$	36.5170	−	9.78470i	1.23309	−	0.330406i	0.417309	−	0.908765i	$-0.362973\pi$
$877$	36.5170	−	9.78470i	1.23309	−	0.330406i	0.815782	+	0.578359i	$0.196307\pi$
$878$	39.5824	−	10.6061i	1.33584	−	0.357938i
$879$	22.3710	−	30.0948i	0.754554	−	1.01507i
$880$	−0.330504	+	0.572449i	−0.0111413	+	0.0192973i
$881$	22.7343	+	39.3770i	0.765938	+	1.32664i	0.939749	+	0.341865i	$0.111058\pi$
$881$	22.7343	+	39.3770i	0.765938	+	1.32664i	−0.173811	+	0.984779i	$0.555608\pi$
$882$	−0.0915937	−	2.99860i	−0.00308412	−	0.100968i
$883$		−	18.6998i		−	0.629298i	−0.949208	−	0.314649i	$-0.898113\pi$
$883$		−	18.6998i		−	0.629298i	0.949208	−	0.314649i	$-0.101887\pi$
$884$	2.56657	−	7.92530i	0.0863232	−	0.266557i
$885$	2.05494	+	13.9585i	0.0690759	+	0.469210i
$886$	−9.74811	+	36.3804i	−0.327494	+	1.22222i
$887$	−4.77023	+	2.75409i	−0.160169	+	0.0924734i	−0.577942	−	0.816078i	$-0.696144\pi$
$887$	−4.77023	+	2.75409i	−0.160169	+	0.0924734i	0.417773	+	0.908551i	$0.362811\pi$
$888$	2.78496	+	1.10406i	0.0934571	+	0.0370498i
$889$	−6.01942	−	6.01942i	−0.201885	−	0.201885i
$890$	0.540116	+	2.01574i	0.0181047	+	0.0675678i
$891$	5.69902	−	6.44138i	0.190924	−	0.215794i
$892$	15.3991	−	15.3991i	0.515599	−	0.515599i
$893$	−6.10024	−	3.52198i	−0.204137	−	0.117858i
$894$	−13.3158	−	16.8156i	−0.445347	−	0.562396i
$895$	1.48411	+	0.397666i	0.0496083	+	0.0132925i
$896$	1.00000			0.0334077
$897$	−2.65937	+	0.990621i	−0.0887937	+	0.0330759i
$898$	25.7632			0.859731
$899$	8.26724	+	2.21520i	0.275728	+	0.0738811i
$900$	9.88002	+	9.29433i	0.329334	+	0.309811i
$901$	20.0877	+	11.5976i	0.669219	+	0.386374i
$902$	6.40448	−	6.40448i	0.213246	−	0.213246i
$903$	−0.602594	−	1.39419i	−0.0200531	−	0.0463959i
$904$	3.51347	+	13.1124i	0.116856	+	0.436113i
$905$	−3.18532	−	3.18532i	−0.105883	−	0.105883i
$906$	−5.90574	+	14.8971i	−0.196205	+	0.494921i
$907$	−21.9185	+	12.6546i	−0.727791	+	0.420190i	−0.817613	−	0.575768i	$-0.804703\pi$
$907$	−21.9185	+	12.6546i	−0.727791	+	0.420190i	0.0898227	+	0.995958i	$0.471370\pi$
$908$	5.82374	−	21.7345i	0.193268	−	0.721284i
$909$	−38.0596	+	11.4543i	−1.26236	+	0.379916i
$910$	−2.49068	−	0.128104i	−0.0825653	−	0.00424661i
$911$			29.1233i			0.964898i	0.875924	+	0.482449i	$0.160253\pi$
$911$			29.1233i			0.964898i	−0.875924	+	0.482449i	$0.839747\pi$
$912$	1.16895	+	0.135773i	0.0387077	+	0.00449590i
$913$	0.322293	+	0.558228i	0.0106663	+	0.0184746i
$914$	−6.82149	+	11.8152i	−0.225635	+	0.390811i
$915$	13.2420	+	9.84340i	0.437766	+	0.325413i
$916$	12.8624	−	3.44646i	0.424984	−	0.113874i
$917$	−3.47873	+	0.932123i	−0.114878	+	0.0307814i
$918$	−11.2904	−	4.08165i	−0.372640	−	0.134714i
$919$	14.1865	−	24.5718i	0.467970	−	0.810547i	−0.531360	−	0.847146i	$-0.678319\pi$
$919$	14.1865	−	24.5718i	0.467970	−	0.810547i	0.999330	+	0.0365986i	$0.0116523\pi$
$920$	−0.157164	−	0.272216i	−0.00518154	−	0.00897468i
$921$	3.42588	−	29.4954i	0.112887	−	0.971906i
$922$			12.8500i			0.423191i
$923$	−11.1261	−	7.21002i	−0.366221	−	0.237321i
$924$	1.63754	−	0.241074i	0.0538709	−	0.00793075i
$925$	−2.02413	+	7.55415i	−0.0665530	+	0.248379i
$926$	−3.20075	+	1.84796i	−0.105183	+	0.0607276i
$927$	−42.4774	−	10.0024i	−1.39514	−	0.328522i
$928$	−3.35831	−	3.35831i	−0.110242	−	0.110242i
$929$	−3.79036	−	14.1458i	−0.124358	−	0.464109i	0.875458	−	0.483294i	$-0.160560\pi$
$929$	−3.79036	−	14.1458i	−0.124358	−	0.464109i	−0.999816	+	0.0191845i	$0.993893\pi$
$930$	1.98185	−	0.856589i	0.0649875	−	0.0280886i
$931$	0.480429	−	0.480429i	0.0157454	−	0.0157454i
$932$	−5.36186	−	3.09567i	−0.175633	−	0.101402i
$933$	21.9217	−	17.3592i	0.717684	−	0.568315i
$934$	25.5898	+	6.85676i	0.837324	+	0.224360i
$935$	1.52724			0.0499461
$936$	−3.01680	+	10.3874i	−0.0986071	+	0.339524i
$937$	6.65662			0.217462			0.108731	−	0.994071i	$-0.465321\pi$
$937$	6.65662			0.217462			0.108731	+	0.994071i	$0.465321\pi$
$938$	9.44348	+	2.53037i	0.308341	+	0.0826196i
$939$	−6.72942	+	5.32885i	−0.219606	+	0.173901i
$940$	6.21045	+	3.58561i	0.202563	+	0.116950i
$941$	−34.5361	+	34.5361i	−1.12585	+	1.12585i	−0.135001	+	0.990845i	$0.543104\pi$
$941$	−34.5361	+	34.5361i	−1.12585	+	1.12585i	−0.990845	+	0.135001i	$0.956896\pi$
$942$	−0.547864	+	0.236796i	−0.0178504	+	0.00771522i
$943$	1.11473	+	4.16024i	0.0363007	+	0.135476i
$944$	8.32719	+	8.32719i	0.271027	+	0.271027i
$945$	−0.305482	+	3.58120i	−0.00993733	+	0.116496i
$946$	0.725722	−	0.418996i	0.0235952	−	0.0136227i
$947$	12.6072	−	47.0506i	0.409678	−	1.52894i	−0.385583	−	0.922673i	$-0.626000\pi$
$947$	12.6072	−	47.0506i	0.409678	−	1.52894i	0.795261	−	0.606267i	$-0.207334\pi$
$948$	5.45137	−	0.802537i	0.177052	−	0.0260652i
$949$	−1.16502	+	22.6511i	−0.0378182	+	0.735286i
$950$			3.07207i			0.0996712i
$951$	0.568206	−	4.89201i	0.0184253	−	0.158634i
$952$	−1.15524	−	2.00093i	−0.0374414	−	0.0648505i
$953$	26.8481	−	46.5022i	0.869694	−	1.50635i	0.00738436	−	0.999973i	$-0.497649\pi$
$953$	26.8481	−	46.5022i	0.869694	−	1.50635i	0.862310	−	0.506381i	$-0.169017\pi$
$954$	−26.5302	−	14.2554i	−0.858947	−	0.461537i
$955$	0.455342	−	0.122009i	0.0147345	−	0.00394811i
$956$	−14.2620	+	3.82150i	−0.461267	+	0.123596i
$957$	−6.30896	−	4.68975i	−0.203940	−	0.151598i
$958$	−6.72947	+	11.6558i	−0.217419	+	0.376582i
$959$	−2.13789	−	3.70294i	−0.0690361	−	0.119574i
$960$	−1.19007	−	0.138226i	−0.0384092	−	0.00446123i
$961$		−	27.7524i		−	0.895239i
$962$	−6.09876	+	1.30253i	−0.196632	+	0.0419951i
$963$	−1.64179	−	5.45522i	−0.0529060	−	0.175792i
$964$	−3.14908	+	11.7525i	−0.101425	+	0.378523i
$965$	7.83046	−	4.52092i	0.252071	−	0.145534i
$966$	−0.290068	+	0.731687i	−0.00933278	+	0.0235416i
$967$	−14.8869	−	14.8869i	−0.478729	−	0.478729i	0.425996	−	0.904725i	$-0.359924\pi$
$967$	−14.8869	−	14.8869i	−0.478729	−	0.478729i	−0.904725	+	0.425996i	$0.859924\pi$
$968$	−2.61065	−	9.74309i	−0.0839096	−	0.313155i
$969$	−1.07874	−	2.49583i	−0.0346541	−	0.0801776i
$970$	5.90779	−	5.90779i	0.189688	−	0.189688i
$971$	−43.4280	−	25.0732i	−1.39367	−	0.804637i	−0.399952	−	0.916536i	$-0.630973\pi$
$971$	−43.4280	−	25.0732i	−1.39367	−	0.804637i	−0.993720	+	0.111899i	$0.964307\pi$
$972$	14.8149	+	4.84970i	0.475187	+	0.155554i
$973$	16.9860	+	4.55138i	0.544546	+	0.145911i
$974$	39.2281			1.25695
$975$	−27.8441	−	4.69425i	−0.891725	−	0.150336i
$976$	13.7720			0.440831
$977$	31.4033	+	8.41450i	1.00468	+	0.269204i	0.723406	−	0.690423i	$-0.242576\pi$
$977$	31.4033	+	8.41450i	1.00468	+	0.269204i	0.281276	+	0.959627i	$0.409242\pi$
$978$	8.72434	+	11.0173i	0.278974	+	0.352295i
$979$	2.49682	+	1.44154i	0.0797986	+	0.0460718i
$980$	−0.489109	+	0.489109i	−0.0156240	+	0.0156240i
$981$	20.4029	−	12.6255i	0.651414	−	0.403101i
$982$	−4.52274	−	16.8791i	−0.144326	−	0.538633i
$983$	15.5750	+	15.5750i	0.496766	+	0.496766i	0.910430	−	0.413664i	$-0.135751\pi$
$983$	15.5750	+	15.5750i	0.496766	+	0.496766i	−0.413664	+	0.910430i	$0.635751\pi$
$984$	15.2608	+	6.04993i	0.486495	+	0.192865i
$985$	−2.14961	+	1.24108i	−0.0684924	+	0.0395441i
$986$	−2.84010	+	10.5994i	−0.0904471	+	0.337553i
$987$	−2.61539	−	17.7655i	−0.0832488	−	0.565481i
$988$	−2.18163	+	1.11427i	−0.0694070	+	0.0354496i
$989$			0.398488i			0.0126712i
$990$	−1.98210	+	0.0605441i	−0.0629952	+	0.00192422i
$991$	−16.1345	−	27.9458i	−0.512530	−	0.887729i	−0.999894	−	0.0145299i	$-0.995375\pi$
$991$	−16.1345	−	27.9458i	−0.512530	−	0.887729i	0.487364	−	0.873199i	$-0.337959\pi$
$992$	0.901054	−	1.56067i	0.0286085	−	0.0495514i
$993$	17.1355	−	23.0518i	0.543779	−	0.731526i
$994$	−3.55182	+	0.951706i	−0.112657	+	0.0301863i
$995$	6.39694	−	1.71405i	0.202797	−	0.0543392i
$996$	−0.696984	+	0.937627i	−0.0220848	+	0.0297099i
$997$	−22.2803	+	38.5906i	−0.705625	+	1.22218i	0.260841	+	0.965382i	$0.416000\pi$
$997$	−22.2803	+	38.5906i	−0.705625	+	1.22218i	−0.966466	+	0.256796i	$0.917333\pi$
$998$	17.5871	+	30.4618i	0.556710	+	0.964251i
$999$	1.57987	+	8.84751i	0.0499847	+	0.279923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.323.2	yes	56
3.2	odd	2		546.2.bu.b.323.14	yes	56
13.6	odd	12		546.2.bu.b.71.14	yes	56
39.32	even	12	inner	546.2.bu.a.71.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.2	✓	56	39.32	even	12	inner
546.2.bu.a.323.2	yes	56	1.1	even	1	trivial
546.2.bu.b.71.14	yes	56	13.6	odd	12
546.2.bu.b.323.14	yes	56	3.2	odd	2

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.35787 + 1.07526i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.489109 - 0.489109i) q^{5} +(1.58990 - 0.687181i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.687622 - 2.92013i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.35787 + 1.07526i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.489109 - 0.489109i) q^{5} +(1.58990 - 0.687181i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.687622 - 2.92013i) q^{9} +(-0.599034 + 0.345852i) q^{10} +(-0.247333 + 0.923060i) q^{11} +(-1.71358 + 0.252269i) q^{12} +(2.67710 - 2.41519i) q^{13} -1.00000i q^{14} +(-0.138226 + 1.19007i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.15524 - 2.00093i) q^{17} +(-1.41998 + 2.64266i) q^{18} +(-0.656279 + 0.175849i) q^{19} +(0.668135 - 0.179026i) q^{20} +(-1.39007 - 1.03330i) q^{21} +(0.477811 - 0.827593i) q^{22} +(0.227212 + 0.393543i) q^{23} +(1.72048 + 0.199834i) q^{24} +4.52155i q^{25} +(-3.21098 + 1.64001i) q^{26} +(2.20621 + 4.70454i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(4.11308 - 2.37469i) q^{29} +(0.441528 - 1.11374i) q^{30} +(1.27428 + 1.27428i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.656685 - 1.51934i) q^{33} +(-1.63375 + 1.63375i) q^{34} +(0.599034 + 0.345852i) q^{35} +(2.05556 - 2.18510i) q^{36} +(1.67070 + 0.447663i) q^{37} +0.679430 q^{38} +(-1.03820 + 6.15810i) q^{39} -0.691704 q^{40} +(9.15496 + 2.45307i) q^{41} +(1.07526 + 1.35787i) q^{42} +(0.759424 + 0.438454i) q^{43} +(-0.675726 + 0.675726i) q^{44} +(-1.09194 - 1.76458i) q^{45} +(-0.117614 - 0.438941i) q^{46} +(7.33090 + 7.33090i) q^{47} +(-1.61014 - 0.638319i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(1.17026 - 4.36748i) q^{50} +(0.582861 + 3.95918i) q^{51} +(3.52603 - 0.753063i) q^{52} +10.0392i q^{53} +(-0.913408 - 5.11524i) q^{54} +(0.330504 + 0.572449i) q^{55} +(0.500000 - 0.866025i) q^{56} +(0.702057 - 0.944452i) q^{57} +(-4.58754 + 1.22923i) q^{58} +(11.3752 - 3.04796i) q^{59} +(-0.714740 + 0.961515i) q^{60} +(6.88600 - 11.9269i) q^{61} +(-0.901054 - 1.56067i) q^{62} +(2.99860 - 0.0915937i) q^{63} +1.00000i q^{64} +(0.128104 - 2.49068i) q^{65} +(0.241074 + 1.63754i) q^{66} +(-2.53037 + 9.44348i) q^{67} +(2.00093 - 1.15524i) q^{68} +(-0.731687 - 0.290068i) q^{69} +(-0.489109 - 0.489109i) q^{70} +(-0.951706 - 3.55182i) q^{71} +(-2.55107 + 1.57862i) q^{72} +(-4.44812 + 4.44812i) q^{73} +(-1.49791 - 0.864819i) q^{74} +(-4.86185 - 6.13967i) q^{75} +(-0.656279 - 0.175849i) q^{76} -0.955622 q^{77} +(2.59665 - 5.67956i) q^{78} -3.18127 q^{79} +(0.668135 + 0.179026i) q^{80} +(-8.05435 - 4.01590i) q^{81} +(-8.20812 - 4.73896i) q^{82} +(0.476958 - 0.476958i) q^{83} +(-0.687181 - 1.58990i) q^{84} +(-0.413635 - 1.54371i) q^{85} +(-0.620067 - 0.620067i) q^{86} +(-3.03161 + 7.64715i) q^{87} +(0.827593 - 0.477811i) q^{88} +(0.780848 - 2.91416i) q^{89} +(0.598025 + 1.98707i) q^{90} +(3.02578 + 1.96078i) q^{91} +0.454425i q^{92} +(-3.10050 - 0.360122i) q^{93} +(-5.18373 - 8.97848i) q^{94} +(-0.234982 + 0.407001i) q^{95} +(1.39007 + 1.03330i) q^{96} +(-11.6671 + 3.12620i) q^{97} +(0.965926 - 0.258819i) q^{98} +(2.52538 + 1.35696i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

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