LMFDB - Embedded newform 117.2.bc.a.41.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(20,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 11]))

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

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

chi := DirichletCharacter("117.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.bc (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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.6
Character	$\chi$	$=$	117.41
Dual form			117.2.bc.a.20.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.724963 + 0.194253i) q^{2} +(1.63234 - 0.579188i) q^{3} +(-1.24421 + 0.718347i) q^{4} +(0.862152 - 0.231013i) q^{5} +(-1.07088 + 0.736978i) q^{6} +(2.34485 + 2.34485i) q^{7} +(1.82389 - 1.82389i) q^{8} +(2.32908 - 1.89087i) q^{9} +O(q^{10})$	\(q+(-0.724963 + 0.194253i) q^{2} +(1.63234 - 0.579188i) q^{3} +(-1.24421 + 0.718347i) q^{4} +(0.862152 - 0.231013i) q^{5} +(-1.07088 + 0.736978i) q^{6} +(2.34485 + 2.34485i) q^{7} +(1.82389 - 1.82389i) q^{8} +(2.32908 - 1.89087i) q^{9} +(-0.580153 + 0.334952i) q^{10} +(-0.447923 - 1.67167i) q^{11} +(-1.61492 + 1.89322i) q^{12} +(-3.32332 + 1.39841i) q^{13} +(-2.15543 - 1.24444i) q^{14} +(1.27353 - 0.876441i) q^{15} +(0.468741 - 0.811883i) q^{16} +(1.04043 - 1.80208i) q^{17} +(-1.32119 + 1.82324i) q^{18} +(0.920617 + 3.43579i) q^{19} +(-0.906755 + 0.906755i) q^{20} +(5.18571 + 2.46949i) q^{21} +(0.649455 + 1.12489i) q^{22} -7.05114 q^{23} +(1.92083 - 4.03358i) q^{24} +(-3.64019 + 2.10166i) q^{25} +(2.13763 - 1.65936i) q^{26} +(2.70669 - 4.43552i) q^{27} +(-4.60192 - 1.23308i) q^{28} +(-7.73359 - 4.46499i) q^{29} +(-0.753009 + 0.882774i) q^{30} +(-0.984980 - 3.67599i) q^{31} +(-1.51729 + 5.66259i) q^{32} +(-1.69938 - 2.46931i) q^{33} +(-0.404215 + 1.50855i) q^{34} +(2.56331 + 1.47993i) q^{35} +(-1.53958 + 4.02573i) q^{36} +(0.351553 - 1.31201i) q^{37} +(-1.33483 - 2.31199i) q^{38} +(-4.61485 + 4.20752i) q^{39} +(1.15113 - 1.99381i) q^{40} +(5.70977 + 5.70977i) q^{41} +(-4.23916 - 0.782948i) q^{42} -7.51496i q^{43} +(1.75815 + 1.75815i) q^{44} +(1.57121 - 2.16826i) q^{45} +(5.11182 - 1.36971i) q^{46} +(1.97394 + 0.528917i) q^{47} +(0.294912 - 1.59676i) q^{48} +3.99667i q^{49} +(2.23075 - 2.23075i) q^{50} +(0.654598 - 3.54422i) q^{51} +(3.13037 - 4.12722i) q^{52} +6.71456i q^{53} +(-1.10064 + 3.74137i) q^{54} +(-0.772356 - 1.33776i) q^{55} +8.55349 q^{56} +(3.49273 + 5.07518i) q^{57} +(6.47390 + 1.73468i) q^{58} +(1.90697 + 0.510971i) q^{59} +(-0.954952 + 2.00532i) q^{60} +0.321743 q^{61} +(1.42815 + 2.47362i) q^{62} +(9.89516 + 1.02755i) q^{63} -2.52494i q^{64} +(-2.54215 + 1.97338i) q^{65} +(1.71166 + 1.46005i) q^{66} +(2.94157 - 2.94157i) q^{67} +2.98957i q^{68} +(-11.5099 + 4.08394i) q^{69} +(-2.14579 - 0.574962i) q^{70} +(2.32908 - 0.624075i) q^{71} +(0.799255 - 7.69671i) q^{72} +(10.7750 + 10.7750i) q^{73} +1.01945i q^{74} +(-4.72477 + 5.53899i) q^{75} +(-3.61354 - 3.61354i) q^{76} +(2.86951 - 4.97014i) q^{77} +(2.52827 - 3.94674i) q^{78} +(2.82917 + 4.90027i) q^{79} +(0.216570 - 0.808252i) q^{80} +(1.84925 - 8.80797i) q^{81} +(-5.24851 - 3.03023i) q^{82} +(2.08171 - 7.76906i) q^{83} +(-8.22609 + 0.652568i) q^{84} +(0.480707 - 1.79402i) q^{85} +(1.45981 + 5.44807i) q^{86} +(-15.2099 - 2.80919i) q^{87} +(-3.86590 - 2.23198i) q^{88} +(-17.9498 - 4.80963i) q^{89} +(-0.717876 + 1.87712i) q^{90} +(-11.0718 - 4.51362i) q^{91} +(8.77313 - 5.06517i) q^{92} +(-3.73692 - 5.42999i) q^{93} -1.53378 q^{94} +(1.58742 + 2.74950i) q^{95} +(0.802975 + 10.1221i) q^{96} +(2.55059 - 2.55059i) q^{97} +(-0.776366 - 2.89744i) q^{98} +(-4.20416 - 3.04650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.724963	+	0.194253i	−0.512626	+	0.137358i	−0.505854	−	0.862619i	$-0.668822\pi$
$2$	−0.724963	+	0.194253i	−0.512626	+	0.137358i	−0.00677241	+	0.999977i	$0.502156\pi$
$3$	1.63234	−	0.579188i	0.942433	−	0.334394i
$3$	1.63234	−	0.579188i	0.942433	−	0.334394i
$4$	−1.24421	+	0.718347i	−0.622107	+	0.359174i
$5$	0.862152	−	0.231013i	0.385566	−	0.103312i	−0.0608287	−	0.998148i	$-0.519374\pi$
$5$	0.862152	−	0.231013i	0.385566	−	0.103312i	0.446395	+	0.894836i	$0.352708\pi$
$6$	−1.07088	+	0.736978i	−0.437184	+	0.300870i
$7$	2.34485	+	2.34485i	0.886271	+	0.886271i	0.994163	−	0.107891i	$-0.0344099\pi$
$7$	2.34485	+	2.34485i	0.886271	+	0.886271i	−0.107891	+	0.994163i	$0.534410\pi$
$8$	1.82389	−	1.82389i	0.644841	−	0.644841i
$9$	2.32908	−	1.89087i	0.776361	−	0.630289i
$10$	−0.580153	+	0.334952i	−0.183461	+	0.105921i
$11$	−0.447923	−	1.67167i	−0.135054	−	0.504028i	−0.999998	−	0.00215928i	$-0.999313\pi$
$11$	−0.447923	−	1.67167i	−0.135054	−	0.504028i	0.864944	−	0.501869i	$-0.167354\pi$
$12$	−1.61492	+	1.89322i	−0.466189	+	0.546526i
$13$	−3.32332	+	1.39841i	−0.921722	+	0.387850i
$13$	−3.32332	+	1.39841i	−0.921722	+	0.387850i
$14$	−2.15543	−	1.24444i	−0.576062	−	0.332589i
$15$	1.27353	−	0.876441i	0.328823	−	0.226296i
$16$	0.468741	−	0.811883i	0.117185	−	0.202971i
$17$	1.04043	−	1.80208i	0.252342	−	0.437069i	−0.711828	−	0.702354i	$-0.752132\pi$
$17$	1.04043	−	1.80208i	0.252342	−	0.437069i	0.964170	+	0.265284i	$0.0854658\pi$
$18$	−1.32119	+	1.82324i	−0.311408	+	0.429742i
$19$	0.920617	+	3.43579i	0.211204	+	0.788224i	0.987468	+	0.157817i	$0.0504456\pi$
$19$	0.920617	+	3.43579i	0.211204	+	0.788224i	−0.776264	+	0.630408i	$0.782888\pi$
$20$	−0.906755	+	0.906755i	−0.202756	+	0.202756i
$21$	5.18571	+	2.46949i	1.13162	+	0.538887i
$22$	0.649455	+	1.12489i	0.138464	+	0.239827i
$23$	−7.05114			−1.47026			−0.735132	−	0.677924i	$-0.762880\pi$
$23$	−7.05114			−1.47026			−0.735132	+	0.677924i	$0.762880\pi$
$24$	1.92083	−	4.03358i	0.392088	−	0.823351i
$25$	−3.64019	+	2.10166i	−0.728037	+	0.420333i
$26$	2.13763	−	1.65936i	0.419225	−	0.325428i
$27$	2.70669	−	4.43552i	0.520903	−	0.853616i
$28$	−4.60192	−	1.23308i	−0.869681	−	0.233030i
$29$	−7.73359	−	4.46499i	−1.43609	−	0.829127i	−0.438516	−	0.898724i	$-0.644496\pi$
$29$	−7.73359	−	4.46499i	−1.43609	−	0.829127i	−0.997575	+	0.0695961i	$0.977829\pi$
$30$	−0.753009	+	0.882774i	−0.137480	+	0.161172i
$31$	−0.984980	−	3.67599i	−0.176908	−	0.660228i	−0.996219	−	0.0868791i	$-0.972311\pi$
$31$	−0.984980	−	3.67599i	−0.176908	−	0.660228i	0.819311	−	0.573349i	$-0.194356\pi$
$32$	−1.51729	+	5.66259i	−0.268221	+	1.00101i
$33$	−1.69938	−	2.46931i	−0.295824	−	0.429852i
$34$	−0.404215	+	1.50855i	−0.0693223	+	0.258714i
$35$	2.56331	+	1.47993i	0.433279	+	0.250154i
$36$	−1.53958	+	4.02573i	−0.256596	+	0.670956i
$37$	0.351553	−	1.31201i	0.0577950	−	0.215694i	−0.930989	−	0.365048i	$-0.881053\pi$
$37$	0.351553	−	1.31201i	0.0577950	−	0.215694i	0.988784	+	0.149354i	$0.0477193\pi$
$38$	−1.33483	−	2.31199i	−0.216537	−	0.375054i
$39$	−4.61485	+	4.20752i	−0.738967	+	0.673742i
$40$	1.15113	−	1.99381i	0.182009	−	0.315249i
$41$	5.70977	+	5.70977i	0.891716	+	0.891716i	0.994685	−	0.102969i	$-0.0328343\pi$
$41$	5.70977	+	5.70977i	0.891716	+	0.891716i	−0.102969	+	0.994685i	$0.532834\pi$
$42$	−4.23916	−	0.782948i	−0.654116	−	0.120811i
$43$		−	7.51496i		−	1.14602i	−0.819548	−	0.573010i	$-0.805775\pi$
$43$		−	7.51496i		−	1.14602i	0.819548	−	0.573010i	$-0.194225\pi$
$44$	1.75815	+	1.75815i	0.265052	+	0.265052i
$45$	1.57121	−	2.16826i	0.234222	−	0.323226i
$46$	5.11182	−	1.36971i	0.753696	−	0.201952i
$47$	1.97394	+	0.528917i	0.287929	+	0.0771504i	0.399893	−	0.916562i	$-0.369047\pi$
$47$	1.97394	+	0.528917i	0.287929	+	0.0771504i	−0.111964	+	0.993712i	$0.535714\pi$
$48$	0.294912	−	1.59676i	0.0425669	−	0.230472i
$49$			3.99667i			0.570953i
$50$	2.23075	−	2.23075i	0.315475	−	0.315475i
$51$	0.654598	−	3.54422i	0.0916620	−	0.496291i
$52$	3.13037	−	4.12722i	0.434104	−	0.572343i
$53$			6.71456i			0.922316i	0.887318	+	0.461158i	$0.152566\pi$
$53$			6.71456i			0.922316i	−0.887318	+	0.461158i	$0.847434\pi$
$54$	−1.10064	+	3.74137i	−0.149778	+	0.509136i
$55$	−0.772356	−	1.33776i	−0.104144	−	0.180384i
$56$	8.55349			1.14301
$57$	3.49273	+	5.07518i	0.462624	+	0.672223i
$58$	6.47390	+	1.73468i	0.850065	+	0.227774i
$59$	1.90697	+	0.510971i	0.248266	+	0.0665228i	0.380806	−	0.924655i	$-0.375647\pi$
$59$	1.90697	+	0.510971i	0.248266	+	0.0665228i	−0.132540	+	0.991178i	$0.542313\pi$
$60$	−0.954952	+	2.00532i	−0.123284	+	0.258885i
$61$	0.321743			0.0411950			0.0205975	−	0.999788i	$-0.493443\pi$
$61$	0.321743			0.0411950			0.0205975	+	0.999788i	$0.493443\pi$
$62$	1.42815	+	2.47362i	0.181375	+	0.314150i
$63$	9.89516	+	1.02755i	1.24667	+	0.129459i
$64$		−	2.52494i		−	0.315618i
$65$	−2.54215	+	1.97338i	−0.315315	+	0.244767i
$66$	1.71166	+	1.46005i	0.210690	+	0.179719i
$67$	2.94157	−	2.94157i	0.359370	−	0.359370i	−0.504210	−	0.863581i	$-0.668216\pi$
$67$	2.94157	−	2.94157i	0.359370	−	0.359370i	0.863581	+	0.504210i	$0.168216\pi$
$68$			2.98957i			0.362539i
$69$	−11.5099	+	4.08394i	−1.38563	+	0.491648i
$70$	−2.14579	−	0.574962i	−0.256471	−	0.0687211i
$71$	2.32908	−	0.624075i	0.276411	−	0.0740641i	−0.117951	−	0.993019i	$-0.537632\pi$
$71$	2.32908	−	0.624075i	0.276411	−	0.0740641i	0.394362	+	0.918955i	$0.370966\pi$
$72$	0.799255	−	7.69671i	0.0941931	−	0.907066i
$73$	10.7750	+	10.7750i	1.26112	+	1.26112i	0.950553	+	0.310564i	$0.100518\pi$
$73$	10.7750	+	10.7750i	1.26112	+	1.26112i	0.310564	+	0.950553i	$0.399482\pi$
$74$			1.01945i			0.118509i
$75$	−4.72477	+	5.53899i	−0.545570	+	0.639587i
$76$	−3.61354	−	3.61354i	−0.414501	−	0.414501i
$77$	2.86951	−	4.97014i	0.327011	−	0.566400i
$78$	2.52827	−	3.94674i	0.286270	−	0.446880i
$79$	2.82917	+	4.90027i	0.318307	+	0.551324i	0.980135	−	0.198332i	$-0.0635524\pi$
$79$	2.82917	+	4.90027i	0.318307	+	0.551324i	−0.661828	+	0.749656i	$0.730219\pi$
$80$	0.216570	−	0.808252i	0.0242133	−	0.0903653i
$81$	1.84925	−	8.80797i	0.205472	−	0.978663i
$82$	−5.24851	−	3.03023i	−0.579601	−	0.334633i
$83$	2.08171	−	7.76906i	0.228498	−	0.852765i	−0.752475	−	0.658620i	$-0.771140\pi$
$83$	2.08171	−	7.76906i	0.228498	−	0.852765i	0.980973	−	0.194144i	$-0.0621930\pi$
$84$	−8.22609	+	0.652568i	−0.897540	+	0.0712010i
$85$	0.480707	−	1.79402i	0.0521400	−	0.194589i
$86$	1.45981	+	5.44807i	0.157415	+	0.587480i
$87$	−15.2099	−	2.80919i	−1.63068	−	0.301176i
$88$	−3.86590	−	2.23198i	−0.412106	−	0.237930i
$89$	−17.9498	−	4.80963i	−1.90267	−	0.509820i	−0.996150	−	0.0876684i	$-0.972058\pi$
$89$	−17.9498	−	4.80963i	−1.90267	−	0.509820i	−0.906525	−	0.422152i	$-0.861275\pi$
$90$	−0.717876	+	1.87712i	−0.0756707	+	0.197866i
$91$	−11.0718	−	4.51362i	−1.16064	−	0.473155i
$92$	8.77313	−	5.06517i	0.914662	−	0.528080i
$93$	−3.73692	−	5.42999i	−0.387500	−	0.563064i
$94$	−1.53378			−0.158197
$95$	1.58742	+	2.74950i	0.162866	+	0.282093i
$96$	0.802975	+	10.1221i	0.0819533	+	1.03308i
$97$	2.55059	−	2.55059i	0.258973	−	0.258973i	−0.565663	−	0.824636i	$-0.691380\pi$
$97$	2.55059	−	2.55059i	0.258973	−	0.258973i	0.824636	+	0.565663i	$0.191380\pi$
$98$	−0.776366	−	2.89744i	−0.0784248	−	0.292685i
$99$	−4.20416	−	3.04650i	−0.422534	−	0.306185i
$100$	3.01945	−	5.22984i	0.301945	−	0.522984i
$101$	−5.79207	+	10.0322i	−0.576333	+	0.998238i	0.419563	+	0.907726i	$0.362183\pi$
$101$	−5.79207	+	10.0322i	−0.576333	+	0.998238i	−0.995895	+	0.0905114i	$0.971150\pi$
$102$	0.213918	+	2.69659i	0.0211810	+	0.267002i
$103$	4.16671	+	2.40565i	0.410558	+	0.237036i	0.691029	−	0.722827i	$-0.257158\pi$
$103$	4.16671	+	2.40565i	0.410558	+	0.237036i	−0.280472	+	0.959862i	$0.590491\pi$
$104$	−3.51081	+	8.61190i	−0.344263	+	0.844467i
$105$	5.04136	+	0.931110i	0.491986	+	0.0908671i
$106$	−1.30433	−	4.86781i	−0.126687	−	0.472803i
$107$	10.1799	−	5.87734i	0.984123	−	0.568184i	0.0806108	−	0.996746i	$-0.474313\pi$
$107$	10.1799	−	5.87734i	0.984123	−	0.568184i	0.903512	+	0.428562i	$0.140980\pi$
$108$	−0.181460	+	7.46308i	−0.0174610	+	0.718135i
$109$	−10.7029	+	10.7029i	−1.02516	+	1.02516i	−0.0254811	+	0.999675i	$0.508112\pi$
$109$	−10.7029	+	10.7029i	−1.02516	+	1.02516i	−0.999675	+	0.0254811i	$0.991888\pi$
$110$	0.819793	+	0.819793i	0.0781642	+	0.0781642i
$111$	−0.186048	−	2.34527i	−0.0176589	−	0.222603i
$112$	3.00287	−	0.804618i	0.283745	−	0.0760292i
$113$	−1.63143	+	0.941905i	−0.153472	+	0.0886070i	−0.574769	−	0.818316i	$-0.694908\pi$
$113$	−1.63143	+	0.941905i	−0.153472	+	0.0886070i	0.421297	+	0.906923i	$0.361575\pi$
$114$	−3.51797	−	3.00084i	−0.329488	−	0.281054i
$115$	−6.07916	+	1.62891i	−0.566885	+	0.151896i
$116$	12.8297			1.19120
$117$	−5.09606	+	9.54097i	−0.471131	+	0.882063i
$118$	−1.48174			−0.136405
$119$	6.66529	−	1.78596i	0.611006	−	0.163718i
$120$	0.724241	−	3.92130i	0.0661139	−	0.357964i
$121$	6.93243	−	4.00244i	0.630221	−	0.363858i
$122$	−0.233252	+	0.0624996i	−0.0211176	+	0.00565845i
$123$	12.6273	+	6.01326i	1.13857	+	0.542198i
$124$	3.86617	+	3.86617i	0.347192	+	0.347192i
$125$	−5.80858	+	5.80858i	−0.519535	+	0.519535i
$126$	−7.37323	+	1.17723i	−0.656859	+	0.104876i
$127$	16.5495	−	9.55486i	1.46853	−	0.847857i	0.469153	−	0.883117i	$-0.344559\pi$
$127$	16.5495	−	9.55486i	1.46853	−	0.847857i	0.999378	+	0.0352603i	$0.0112260\pi$
$128$	−2.54410	−	9.49469i	−0.224868	−	0.839220i
$129$	−4.35258	−	12.2670i	−0.383223	−	1.08005i
$130$	1.45963	−	1.92445i	0.128018	−	0.168785i
$131$	−5.36729	−	3.09881i	−0.468942	−	0.270744i	0.246854	−	0.969053i	$-0.420603\pi$
$131$	−5.36729	−	3.09881i	−0.468942	−	0.270744i	−0.715797	+	0.698309i	$0.753936\pi$
$132$	3.88821	+	1.85161i	0.338425	+	0.161162i
$133$	−5.89771	+	10.2151i	−0.511397	+	0.885765i
$134$	−1.56112	+	2.70394i	−0.134860	+	0.233585i
$135$	1.30892	−	4.44937i	0.112654	−	0.382941i
$136$	−1.38916	−	5.18443i	−0.119120	−	0.444561i
$137$	−16.0834	+	16.0834i	−1.37410	+	1.37410i	−0.519819	+	0.854276i	$0.674001\pi$
$137$	−16.0834	+	16.0834i	−1.37410	+	1.37410i	−0.854276	+	0.519819i	$0.825999\pi$
$138$	7.55091	−	5.19653i	0.642776	−	0.442358i
$139$	−2.13566	−	3.69907i	−0.181144	−	0.313751i	0.761126	−	0.648604i	$-0.224647\pi$
$139$	−2.13566	−	3.69907i	−0.181144	−	0.313751i	−0.942271	+	0.334853i	$0.891313\pi$
$140$	−4.25241			−0.359394
$141$	3.52849	−	0.279912i	0.297153	−	0.0235729i
$142$	−1.56727	+	0.904862i	−0.131522	+	0.0759344i
$143$	3.82628	+	4.92911i	0.319970	+	0.412193i
$144$	−0.443427	−	2.77727i	−0.0369522	−	0.231439i
$145$	−7.69900	−	2.06294i	−0.639367	−	0.171318i
$146$	−9.90453	−	5.71839i	−0.819705	−	0.473257i
$147$	2.31483	+	6.52394i	0.190924	+	0.538085i
$148$	0.505075	+	1.88496i	0.0415169	+	0.154943i
$149$	1.84262	−	6.87676i	0.150953	−	0.563366i	−0.848464	−	0.529252i	$-0.822472\pi$
$149$	1.84262	−	6.87676i	0.150953	−	0.563366i	0.999418	−	0.0341138i	$-0.0108609\pi$
$150$	2.34932	−	4.93336i	0.191821	−	0.402807i
$151$	−2.15839	+	8.05524i	−0.175648	+	0.655526i	0.820793	+	0.571226i	$0.193532\pi$
$151$	−2.15839	+	8.05524i	−0.175648	+	0.655526i	−0.996440	+	0.0842999i	$0.973135\pi$
$152$	7.94559	+	4.58739i	0.644473	+	0.372087i
$153$	−0.984245	−	6.16452i	−0.0795715	−	0.498372i
$154$	−1.11482	+	4.16058i	−0.0898350	+	0.335269i
$155$	−1.69840	−	2.94172i	−0.136419	−	0.236285i
$156$	2.71940	−	8.55011i	0.217726	−	0.684557i
$157$	−5.99642	+	10.3861i	−0.478566	+	0.828901i	−0.999698	−	0.0245753i	$-0.992177\pi$
$157$	−5.99642	+	10.3861i	−0.478566	+	0.828901i	0.521132	+	0.853476i	$0.325510\pi$
$158$	−3.00294	−	3.00294i	−0.238901	−	0.238901i
$159$	3.88900	+	10.9605i	0.308417	+	0.869221i
$160$			5.23253i			0.413668i
$161$	−16.5339	−	16.5339i	−1.30305	−	1.30305i
$162$	0.370342	+	6.74467i	0.0290968	+	0.529911i
$163$	4.92857	−	1.32061i	0.386035	−	0.103438i	−0.0605813	−	0.998163i	$-0.519295\pi$
$163$	4.92857	−	1.32061i	0.386035	−	0.103438i	0.446617	+	0.894725i	$0.352629\pi$
$164$	−11.2058	−	3.00258i	−0.875023	−	0.234462i
$165$	−2.03556	−	1.73634i	−0.158468	−	0.135174i
$166$			6.03665i			0.468535i
$167$	15.2466	−	15.2466i	1.17982	−	1.17982i	0.200028	−	0.979790i	$-0.435897\pi$
$167$	15.2466	−	15.2466i	1.17982	−	1.17982i	0.979790	−	0.200028i	$-0.0641033\pi$
$168$	13.9622	−	4.95408i	1.07721	−	0.382216i
$169$	9.08888	−	9.29475i	0.699144	−	0.714981i
$170$			1.39398i			0.106913i
$171$	8.64082	+	6.26147i	0.660780	+	0.478827i
$172$	5.39835	+	9.35022i	0.411621	+	0.712948i
$173$	20.6094			1.56690			0.783451	−	0.621454i	$-0.213458\pi$
$173$	20.6094			1.56690			0.783451	+	0.621454i	$0.213458\pi$
$174$	11.5723	−	0.918022i	0.877296	−	0.0695950i
$175$	−13.4638	−	3.60761i	−1.01777	−	0.272710i
$176$	−1.56716	−	0.419920i	−0.118129	−	0.0316526i
$177$	3.40878	−	0.270415i	0.256219	−	0.0203256i
$178$	13.9472			1.04539
$179$	1.16791	+	2.02287i	0.0872933	+	0.151196i	0.906366	−	0.422493i	$-0.138845\pi$
$179$	1.16791	+	2.02287i	0.0872933	+	0.151196i	−0.819073	+	0.573690i	$0.805512\pi$
$180$	−0.397354	+	3.82646i	−0.0296170	+	0.285207i
$181$			3.23247i			0.240267i	0.992758	+	0.120134i	$0.0383323\pi$
$181$			3.23247i			0.240267i	−0.992758	+	0.120134i	$0.961668\pi$
$182$	8.90340	+	1.12148i	0.659964	+	0.0831294i
$183$	0.525195	−	0.186350i	0.0388235	−	0.0137754i
$184$	−12.8605	+	12.8605i	−0.948088	+	0.948088i
$185$		−	1.21237i		−	0.0891352i
$186$	3.76392	+	3.21063i	0.275984	+	0.235415i
$187$	−3.47853	−	0.932069i	−0.254375	−	0.0681596i
$188$	−2.83596	+	0.759892i	−0.206833	+	0.0554208i
$189$	16.7474	−	4.05385i	1.21820	−	0.294874i
$190$	−1.68492	−	1.68492i	−0.122237	−	0.122237i
$191$			24.6994i			1.78718i	0.448880	+	0.893592i	$0.351823\pi$
$191$			24.6994i			1.78718i	−0.448880	+	0.893592i	$0.648177\pi$
$192$	−1.46242	−	4.12157i	−0.105541	−	0.297449i
$193$	7.82705	+	7.82705i	0.563403	+	0.563403i	0.930273	−	0.366869i	$-0.119570\pi$
$193$	7.82705	+	7.82705i	0.563403	+	0.563403i	−0.366869	+	0.930273i	$0.619570\pi$
$194$	−1.35362	+	2.34454i	−0.0971843	+	0.168328i
$195$	−3.00671	+	4.69361i	−0.215315	+	0.336116i
$196$	−2.87100	−	4.97272i	−0.205071	−	0.355194i
$197$	0.112445	−	0.419649i	0.00801134	−	0.0298987i	−0.961804	−	0.273737i	$-0.911740\pi$
$197$	0.112445	−	0.419649i	0.00801134	−	0.0298987i	0.969816	+	0.243839i	$0.0784067\pi$
$198$	3.63965	+	1.39193i	0.258659	+	0.0989199i
$199$	−8.95125	−	5.16801i	−0.634537	−	0.366350i	0.147970	−	0.988992i	$-0.452726\pi$
$199$	−8.95125	−	5.16801i	−0.634537	−	0.366350i	−0.782507	+	0.622642i	$0.786059\pi$
$200$	−2.80609	+	10.4725i	−0.198421	+	0.740516i
$201$	3.09793	−	6.50538i	0.218511	−	0.458854i
$202$	2.25026	−	8.39807i	0.158328	−	0.590886i
$203$	−7.66438	−	28.6039i	−0.537934	−	2.00760i
$204$	1.73152	+	4.88000i	0.121231	+	0.341669i
$205$	6.24172	+	3.60366i	0.435940	+	0.251690i
$206$	−3.48801	−	0.934610i	−0.243021	−	0.0651173i
$207$	−16.4227	+	13.3328i	−1.14146	+	0.926692i
$208$	−0.422426	+	3.35364i	−0.0292900	+	0.232533i
$209$	5.33115	−	3.07794i	0.368763	−	0.212906i
$210$	−3.83567	+	0.304280i	−0.264686	+	0.0209973i
$211$	−9.66942			−0.665671			−0.332835	−	0.942985i	$-0.608005\pi$
$211$	−9.66942			−0.665671			−0.332835	+	0.942985i	$0.608005\pi$
$212$	−4.82339	−	8.35435i	−0.331272	−	0.573779i
$213$	3.44040	−	2.36768i	0.235732	−	0.162231i
$214$	−6.23832	+	6.23832i	−0.426443	+	0.426443i
$215$	−1.73605	−	6.47904i	−0.118398	−	0.441867i
$216$	−3.15319	−	13.0266i	−0.214547	−	0.886347i
$217$	6.31003	−	10.9293i	0.428353	−	0.741929i
$218$	5.68016	−	9.83832i	0.384709	−	0.666335i
$219$	23.8292	+	11.3477i	1.61023	+	0.766807i
$220$	1.92195	+	1.10964i	0.129578	+	0.0748119i
$221$	−0.937631	+	7.44385i	−0.0630719	+	0.500728i
$222$	0.590455	+	1.66409i	0.0396287	+	0.111687i
$223$	−1.48425	−	5.53929i	−0.0993926	−	0.370938i	0.898256	−	0.439472i	$-0.144835\pi$
$223$	−1.48425	−	5.53929i	−0.0993926	−	0.370938i	−0.997649	+	0.0685340i	$0.978168\pi$
$224$	−16.8358	+	9.72013i	−1.12489	+	0.649453i
$225$	−4.50433	+	11.7781i	−0.300289	+	0.785204i
$226$	0.999756	−	0.999756i	0.0665028	−	0.0665028i
$227$	1.96276	+	1.96276i	0.130273	+	0.130273i	0.769237	−	0.638964i	$-0.220637\pi$
$227$	1.96276	+	1.96276i	0.130273	+	0.130273i	−0.638964	+	0.769237i	$0.720637\pi$
$228$	−7.99145	−	3.80561i	−0.529246	−	0.252033i
$229$	7.20699	−	1.93111i	0.476251	−	0.127611i	−0.0127053	−	0.999919i	$-0.504044\pi$
$229$	7.20699	−	1.93111i	0.476251	−	0.127611i	0.488956	+	0.872308i	$0.337378\pi$
$230$	4.09074	−	2.36179i	0.269736	−	0.155732i
$231$	1.80538	−	9.77496i	0.118785	−	0.643145i
$232$	−22.2488	+	5.96155i	−1.46071	+	0.391395i
$233$	−11.7795			−0.771703			−0.385851	−	0.922561i	$-0.626092\pi$
$233$	−11.7795			−0.771703			−0.385851	+	0.922561i	$0.626092\pi$
$234$	1.84109	−	7.90677i	0.120356	−	0.516882i
$235$	1.82403			0.118986
$236$	−2.73974	+	0.734110i	−0.178342	+	0.0477865i
$237$	7.45636	+	6.36030i	0.484343	+	0.413146i
$238$	−4.48515	+	2.58951i	−0.290729	+	0.167853i
$239$	5.68254	−	1.52263i	0.367573	−	0.0984909i	−0.0703044	−	0.997526i	$-0.522397\pi$
$239$	5.68254	−	1.52263i	0.367573	−	0.0984909i	0.437877	+	0.899035i	$0.355730\pi$
$240$	−0.114613	−	1.44478i	−0.00739823	−	0.0932601i
$241$	14.2986	+	14.2986i	0.921052	+	0.921052i	0.997104	−	0.0760521i	$-0.0242315\pi$
$241$	14.2986	+	14.2986i	0.921052	+	0.921052i	−0.0760521	+	0.997104i	$0.524232\pi$
$242$	−4.24826	+	4.24826i	−0.273089	+	0.273089i
$243$	−2.08287	−	15.4487i	−0.133616	−	0.991033i
$244$	−0.400317	+	0.231123i	−0.0256277	+	0.0147962i
$245$	0.923283	+	3.44574i	0.0589864	+	0.220140i
$246$	−10.3224	−	1.90649i	−0.658134	−	0.121554i
$247$	−7.86416	−	10.1308i	−0.500385	−	0.644609i
$248$	−8.50109	−	4.90811i	−0.539820	−	0.311665i
$249$	−1.10168	−	13.8875i	−0.0698161	−	0.880082i
$250$	3.08267	−	5.33934i	0.194965	−	0.337690i
$251$	5.68718	−	9.85049i	0.358972	−	0.621757i	−0.628818	−	0.777553i	$-0.716461\pi$
$251$	5.68718	−	9.85049i	0.358972	−	0.621757i	0.987789	+	0.155795i	$0.0497941\pi$
$252$	−13.0498	+	5.82967i	−0.822062	+	0.367235i
$253$	3.15837	+	11.7872i	0.198565	+	0.741055i
$254$	−10.1417	+	10.1417i	−0.636348	+	0.636348i
$255$	−0.254399	−	3.20688i	−0.0159311	−	0.200823i
$256$	6.21369	+	10.7624i	0.388356	+	0.672652i
$257$	7.04976			0.439752			0.219876	−	0.975528i	$-0.429435\pi$
$257$	7.04976			0.439752			0.219876	+	0.975528i	$0.429435\pi$
$258$	5.53836	+	8.04761i	0.344803	+	0.501022i
$259$	3.90082	−	2.25214i	0.242385	−	0.139941i
$260$	1.74541	−	4.28145i	0.108246	−	0.265524i
$261$	−26.4549	+	4.22386i	−1.63751	+	0.261450i
$262$	4.49304	+	1.20391i	0.277581	+	0.0743776i
$263$	14.1534	+	8.17149i	0.872738	+	0.503876i	0.868257	−	0.496114i	$-0.165240\pi$
$263$	14.1534	+	8.17149i	0.872738	+	0.503876i	0.00448113	+	0.999990i	$0.498574\pi$
$264$	−7.60321	−	1.40427i	−0.467945	−	0.0864268i
$265$	1.55115	+	5.78898i	0.0952865	+	0.355614i
$266$	2.29130	−	8.55124i	0.140489	−	0.524310i
$267$	−32.0859	+	2.54534i	−1.96363	+	0.155773i
$268$	−1.54688	+	5.77302i	−0.0944905	+	0.352643i
$269$	−15.1323	−	8.73666i	−0.922635	−	0.532683i	−0.0381600	−	0.999272i	$-0.512150\pi$
$269$	−15.1323	−	8.73666i	−0.922635	−	0.532683i	−0.884475	+	0.466588i	$0.845483\pi$
$270$	−0.0846113	+	3.47989i	−0.00514928	+	0.211779i
$271$	−4.92749	+	18.3896i	−0.299324	+	1.11709i	0.638399	+	0.769706i	$0.279597\pi$
$271$	−4.92749	+	18.3896i	−0.299324	+	1.11709i	−0.937723	+	0.347385i	$0.887070\pi$
$272$	−0.975387	−	1.68942i	−0.0591415	−	0.102436i
$273$	−20.6871	−	0.955127i	−1.25204	−	0.0578069i
$274$	8.53560	−	14.7841i	0.515654	−	0.893140i
$275$	5.14382	+	5.14382i	0.310184	+	0.310184i
$276$	11.3871	−	13.3494i	0.685421	−	0.803539i
$277$		−	24.7288i		−	1.48581i	−0.669397	−	0.742904i	$-0.733448\pi$
$277$		−	24.7288i		−	1.48581i	0.669397	−	0.742904i	$-0.266552\pi$
$278$	2.26683	+	2.26683i	0.135956	+	0.135956i
$279$	−9.24491	−	6.69923i	−0.553478	−	0.401072i
$280$	7.37441	−	1.97597i	0.440706	−	0.118087i
$281$	9.18553	+	2.46126i	0.547963	+	0.146826i	0.522170	−	0.852841i	$-0.325122\pi$
$281$	9.18553	+	2.46126i	0.547963	+	0.146826i	0.0257923	+	0.999667i	$0.491789\pi$
$282$	−2.50365	+	0.888347i	−0.149090	+	0.0529003i
$283$		−	9.96084i		−	0.592110i	−0.955171	−	0.296055i	$-0.904329\pi$
$283$		−	9.96084i		−	0.592110i	0.955171	−	0.296055i	$-0.0956712\pi$
$284$	−2.44957	+	2.44957i	−0.145355	+	0.145355i
$285$	4.18370	+	3.56871i	0.247821	+	0.211392i
$286$	−3.73141	−	2.83016i	−0.220643	−	0.167351i
$287$			26.7771i			1.58060i
$288$	7.17332	+	16.0576i	0.422692	+	0.946205i
$289$	6.33500	+	10.9725i	0.372647	+	0.645443i
$290$	5.98222			0.351288
$291$	2.68616	−	5.64070i	0.157465	−	0.330664i
$292$	−21.1466	−	5.66621i	−1.23751	−	0.331590i
$293$	19.0311	+	5.09937i	1.11181	+	0.297909i	0.767565	−	0.640971i	$-0.221468\pi$
$293$	19.0311	+	5.09937i	1.11181	+	0.297909i	0.344245	+	0.938880i	$0.388135\pi$
$294$	−2.94546	−	4.27995i	−0.171783	−	0.249612i
$295$	1.76214			0.102596
$296$	−1.75177	−	3.03416i	−0.101820	−	0.176357i
$297$	−8.62712	−	2.53793i	−0.500596	−	0.147266i
$298$			5.34333i			0.309531i
$299$	23.4332	−	9.86042i	1.35518	−	0.570243i
$300$	1.89971	−	10.2857i	0.109680	−	0.593846i
$301$	17.6215	−	17.6215i	1.01569	−	1.01569i
$302$		−	6.25902i		−	0.360166i
$303$	−3.64413	+	19.7306i	−0.209350	+	1.13350i
$304$	3.22099	+	0.863062i	0.184736	+	0.0495000i
$305$	0.277392	−	0.0743268i	0.0158834	−	0.00425594i
$306$	1.91102	+	4.27786i	0.109246	+	0.244549i
$307$	−23.5691	−	23.5691i	−1.34516	−	1.34516i	−0.890840	−	0.454318i	$-0.849883\pi$
$307$	−23.5691	−	23.5691i	−1.34516	−	1.34516i	−0.454318	−	0.890840i	$-0.650117\pi$
$308$			8.24522i			0.469815i
$309$	8.19481	+	1.51353i	0.466187	+	0.0861020i
$310$	1.80272	+	1.80272i	0.102388	+	0.102388i
$311$	−14.1990	+	24.5934i	−0.805153	+	1.39457i	0.111035	+	0.993817i	$0.464583\pi$
$311$	−14.1990	+	24.5934i	−0.805153	+	1.39457i	−0.916188	+	0.400749i	$0.868750\pi$
$312$	−0.742922	+	16.0910i	−0.0420597	+	0.910973i
$313$	−11.9559	−	20.7083i	−0.675790	−	1.17050i	−0.976237	−	0.216704i	$-0.930469\pi$
$313$	−11.9559	−	20.7083i	−0.675790	−	1.17050i	0.300448	−	0.953798i	$-0.402864\pi$
$314$	2.32965	−	8.69436i	0.131470	−	0.490651i
$315$	8.76851	−	1.40001i	0.494050	−	0.0788814i
$316$	−7.04019	−	4.06466i	−0.396042	−	0.228655i
$317$	4.06219	−	15.1603i	0.228155	−	0.851487i	−0.752960	−	0.658066i	$-0.771375\pi$
$317$	4.06219	−	15.1603i	0.228155	−	0.851487i	0.981116	−	0.193422i	$-0.0619585\pi$
$318$	−4.94848	−	7.19048i	−0.277497	−	0.403222i
$319$	−3.99994	+	14.9280i	−0.223954	+	0.835807i
$320$	−0.583294	−	2.17688i	−0.0326071	−	0.121692i
$321$	13.2129	−	15.4899i	0.737473	−	0.864561i
$322$	15.1982	+	8.77470i	0.846964	+	0.488995i
$323$	7.14942	+	1.91568i	0.397805	+	0.106591i
$324$	4.02632	+	12.2874i	0.223685	+	0.682633i
$325$	9.15850	−	12.0750i	0.508022	−	0.669800i
$326$	−3.31650	+	1.91478i	−0.183684	+	0.106050i
$327$	−11.2719	+	23.6699i	−0.623335	+	1.30895i
$328$	20.8279			1.15003
$329$	3.38838	+	5.86884i	0.186807	+	0.323560i
$330$	1.81300	+	0.863369i	0.0998023	+	0.0475269i
$331$	12.3776	−	12.3776i	0.680335	−	0.680335i	−0.279741	−	0.960076i	$-0.590248\pi$
$331$	12.3776	−	12.3776i	0.680335	−	0.680335i	0.960076	+	0.279741i	$0.0902484\pi$
$332$	2.99079	+	11.1618i	0.164141	+	0.612581i
$333$	−1.66205	−	3.72053i	−0.0910797	−	0.203884i
$334$	−8.09152	+	14.0149i	−0.442748	+	0.766863i
$335$	1.85654	−	3.21563i	0.101434	−	0.175688i
$336$	4.43569	−	3.05264i	0.241987	−	0.166535i
$337$	2.23792	+	1.29206i	0.121907	+	0.0703831i	0.559714	−	0.828686i	$-0.310911\pi$
$337$	2.23792	+	1.29206i	0.121907	+	0.0703831i	−0.437807	+	0.899069i	$0.644245\pi$
$338$	−4.78356	+	8.50389i	−0.260191	+	0.462551i
$339$	−2.11751	+	2.48242i	−0.115007	+	0.134826i
$340$	0.690630	+	2.57747i	0.0374547	+	0.139783i
$341$	−5.70386	+	3.29313i	−0.308881	+	0.178333i
$342$	−7.48058	−	2.86083i	−0.404503	−	0.154696i
$343$	7.04236	−	7.04236i	0.380252	−	0.380252i
$344$	−13.7064	−	13.7064i	−0.739002	−	0.739002i
$345$	−8.97983	+	6.17991i	−0.483458	+	0.332715i
$346$	−14.9410	+	4.00344i	−0.803235	+	0.215226i
$347$	0.00943108	−	0.00544504i	0.000506287	−	0.000292305i	−0.499747	−	0.866172i	$-0.666574\pi$
$347$	0.00943108	−	0.00544504i	0.000506287	−	0.000292305i	0.500253	+	0.865879i	$0.333240\pi$
$348$	20.9424	−	7.43078i	1.12263	−	0.398332i
$349$	−10.5425	+	2.82485i	−0.564325	+	0.151211i	−0.529693	−	0.848190i	$-0.677693\pi$
$349$	−10.5425	+	2.82485i	−0.564325	+	0.151211i	−0.0346326	+	0.999400i	$0.511026\pi$
$350$	10.4615			0.559193
$351$	−2.79250	+	18.5257i	−0.149053	+	0.988829i
$352$	10.1456			0.540763
$353$	−4.27775	+	1.14622i	−0.227682	+	0.0610071i	−0.370856	−	0.928690i	$-0.620936\pi$
$353$	−4.27775	+	1.14622i	−0.227682	+	0.0610071i	0.143174	+	0.989697i	$0.454269\pi$
$354$	−2.41871	+	0.858207i	−0.128553	+	0.0456132i
$355$	1.86385	−	1.07610i	0.0989230	−	0.0571132i
$356$	25.7884	−	6.90998i	1.36678	−	0.366228i
$357$	9.84562	−	6.77575i	0.521085	−	0.358611i
$358$	−1.23964	−	1.23964i	−0.0655168	−	0.0655168i
$359$	−12.7394	+	12.7394i	−0.672359	+	0.672359i	−0.958259	−	0.285900i	$-0.907707\pi$
$359$	−12.7394	+	12.7394i	−0.672359	+	0.672359i	0.285900	+	0.958259i	$0.407707\pi$
$360$	−1.08896	−	6.82037i	−0.0573933	−	0.359465i
$361$	5.49736	−	3.17390i	0.289335	−	0.167047i
$362$	−0.627917	−	2.34342i	−0.0330026	−	0.123167i
$363$	8.99793	−	10.5485i	0.472269	−	0.553654i
$364$	17.0180	−	2.33747i	0.891985	−	0.122517i
$365$	11.7788	+	6.80051i	0.616532	+	0.355955i
$366$	−0.344548	+	0.237117i	−0.0180098	+	0.0123943i
$367$	5.44622	−	9.43313i	0.284290	−	0.492405i	−0.688146	−	0.725572i	$-0.741575\pi$
$367$	5.44622	−	9.43313i	0.284290	−	0.492405i	0.972437	+	0.233166i	$0.0749087\pi$
$368$	−3.30516	+	5.72470i	−0.172293	+	0.298421i
$369$	24.0949	+	2.50211i	1.25433	+	0.130254i
$370$	0.235507	+	0.878923i	0.0122434	+	0.0456930i
$371$	−15.7447	+	15.7447i	−0.817422	+	0.817422i
$372$	8.55014	+	4.07167i	0.443304	+	0.211106i
$373$	−3.53750	−	6.12713i	−0.183165	−	0.317251i	0.759792	−	0.650166i	$-0.225301\pi$
$373$	−3.53750	−	6.12713i	−0.183165	−	0.317251i	−0.942957	+	0.332916i	$0.891968\pi$
$374$	2.70286			0.139762
$375$	−6.11733	+	12.8459i	−0.315898	+	0.663357i
$376$	4.56493	−	2.63557i	0.235419	−	0.135919i
$377$	31.9451	+	4.02382i	1.64525	+	0.207237i
$378$	−11.3538	+	6.19213i	−0.583976	+	0.318489i
$379$	−6.12940	−	1.64237i	−0.314846	−	0.0843627i	0.0979357	−	0.995193i	$-0.468776\pi$
$379$	−6.12940	−	1.64237i	−0.314846	−	0.0843627i	−0.412782	+	0.910830i	$0.635443\pi$
$380$	−3.95019	−	2.28065i	−0.202641	−	0.116995i
$381$	21.4804	−	25.1821i	1.10047	−	1.29012i
$382$	−4.79793	−	17.9061i	−0.245484	−	0.916157i
$383$	−3.94973	+	14.7406i	−0.201822	+	0.753210i	0.788573	+	0.614941i	$0.210820\pi$
$383$	−3.94973	+	14.7406i	−0.201822	+	0.753210i	−0.990395	+	0.138268i	$0.955846\pi$
$384$	−9.65205	−	14.0251i	−0.492554	−	0.715714i
$385$	1.32579	−	4.94791i	0.0675685	−	0.252169i
$386$	−7.19475	−	4.15389i	−0.366203	−	0.211427i
$387$	−14.2098	−	17.5030i	−0.722324	−	0.889725i
$388$	−1.34127	+	5.00568i	−0.0680926	+	0.254125i
$389$	−3.87977	−	6.71995i	−0.196712	−	0.340715i	0.750748	−	0.660588i	$-0.229693\pi$
$389$	−3.87977	−	6.71995i	−0.196712	−	0.340715i	−0.947460	+	0.319873i	$0.896360\pi$
$390$	1.26800	−	3.98675i	0.0642078	−	0.201877i
$391$	−7.33624	+	12.7067i	−0.371010	+	0.642608i
$392$	7.28948	+	7.28948i	0.368174	+	0.368174i
$393$	−10.5560	−	1.94964i	−0.532482	−	0.0983464i
$394$			0.326072i			0.0164273i
$395$	3.57120	+	3.57120i	0.179687	+	0.179687i
$396$	7.41932	+	0.770450i	0.372835	+	0.0387165i
$397$	−11.5751	+	3.10154i	−0.580938	+	0.155662i	−0.537308	−	0.843386i	$-0.680559\pi$
$397$	−11.5751	+	3.10154i	−0.580938	+	0.155662i	−0.0436297	+	0.999048i	$0.513892\pi$
$398$	7.49322	+	2.00780i	0.375601	+	0.100642i
$399$	−3.71060	+	20.0905i	−0.185762	+	1.00578i
$400$			3.94054i			0.197027i
$401$	−8.65209	+	8.65209i	−0.432065	+	0.432065i	−0.889330	−	0.457265i	$-0.848829\pi$
$401$	−8.65209	+	8.65209i	−0.432065	+	0.432065i	0.457265	+	0.889330i	$0.348829\pi$
$402$	−0.982193	+	5.31794i	−0.0489873	+	0.265235i
$403$	8.41396	+	10.8391i	0.419129	+	0.539933i
$404$		−	16.6429i		−	0.828014i
$405$	−0.440424	−	8.02101i	−0.0218848	−	0.398567i
$406$	11.1128	+	19.2479i	0.551518	+	0.955257i
$407$	−2.35073			−0.116521
$408$	−5.27035	−	7.65817i	−0.260921	−	0.379136i
$409$	22.5777	+	6.04968i	1.11640	+	0.299138i	0.769425	−	0.638738i	$-0.220543\pi$
$409$	22.5777	+	6.04968i	1.11640	+	0.299138i	0.346972	+	0.937875i	$0.387210\pi$
$410$	−5.22503	−	1.40004i	−0.258046	−	0.0691432i
$411$	−16.9383	+	35.5689i	−0.835503	+	1.75448i
$412$	−6.91237			−0.340548
$413$	3.27341	+	5.66972i	0.161074	+	0.278989i
$414$	9.31590	−	12.8559i	0.457852	−	0.631834i
$415$		−	7.17901i		−	0.352404i
$416$	−2.87622	−	20.9404i	−0.141018	−	1.02669i
$417$	−5.62859	−	4.80121i	−0.275633	−	0.235116i
$418$	−3.26698	+	3.26698i	−0.159793	+	0.159793i
$419$		−	2.37785i		−	0.116166i	−0.998312	−	0.0580829i	$-0.981501\pi$
$419$		−	2.37785i		−	0.116166i	0.998312	−	0.0580829i	$-0.0184988\pi$
$420$	−6.94139	+	2.46295i	−0.338705	+	0.120180i
$421$	−24.8463	−	6.65755i	−1.21094	−	0.324469i	−0.403807	−	0.914844i	$-0.632313\pi$
$421$	−24.8463	−	6.65755i	−1.21094	−	0.324469i	−0.807129	+	0.590375i	$0.798980\pi$
$422$	7.00997	−	1.87832i	0.341240	−	0.0914350i
$423$	5.59759	−	2.50058i	0.272164	−	0.121582i
$424$	12.2466	+	12.2466i	0.594748	+	0.594748i
$425$			8.74656i			0.424271i
$426$	−2.03423	+	2.38479i	−0.0985588	+	0.115543i
$427$	0.754440	+	0.754440i	0.0365099	+	0.0365099i
$428$	−8.44394	+	14.6253i	−0.408153	+	0.706942i
$429$	9.10068	+	5.82986i	0.439385	+	0.281469i
$430$	2.51715	+	4.35983i	0.121388	+	0.210250i
$431$	1.60462	−	5.98851i	0.0772917	−	0.288456i	−0.916452	−	0.400146i	$-0.868959\pi$
$431$	1.60462	−	5.98851i	0.0772917	−	0.288456i	0.993743	+	0.111689i	$0.0356262\pi$
$432$	−2.33239	−	4.27662i	−0.112217	−	0.205759i
$433$	−28.2304	−	16.2988i	−1.35666	−	0.783271i	−0.367492	−	0.930027i	$-0.619783\pi$
$433$	−28.2304	−	16.2988i	−1.35666	−	0.783271i	−0.989173	+	0.146756i	$0.953117\pi$
$434$	−2.45149	+	9.14908i	−0.117675	+	0.439170i
$435$	−13.7622	+	1.09175i	−0.659849	+	0.0523452i
$436$	5.62832	−	21.0052i	0.269548	−	1.00597i
$437$	−6.49140	−	24.2263i	−0.310526	−	1.15890i
$438$	−19.4796	−	3.59777i	−0.930772	−	0.171908i
$439$	−26.2432	−	15.1515i	−1.25252	−	0.723144i	−0.280912	−	0.959734i	$-0.590637\pi$
$439$	−26.2432	−	15.1515i	−1.25252	−	0.723144i	−0.971610	+	0.236590i	$0.923970\pi$
$440$	−3.84861	−	1.03123i	−0.183475	−	0.0491621i
$441$	7.55718	+	9.30858i	0.359865	+	0.443266i
$442$	−0.766244	−	5.57865i	−0.0364465	−	0.265349i
$443$	−16.8525	+	9.72980i	−0.800687	+	0.462277i	−0.843711	−	0.536797i	$-0.819634\pi$
$443$	−16.8525	+	9.72980i	−0.800687	+	0.462277i	0.0430245	+	0.999074i	$0.486301\pi$
$444$	1.91620	+	2.78437i	0.0909390	+	0.132141i
$445$	−16.5865			−0.786278
$446$	2.15205	+	3.72746i	0.101902	+	0.176500i
$447$	−0.975149	−	12.2925i	−0.0461229	−	0.581413i
$448$	5.92062	−	5.92062i	0.279723	−	0.279723i
$449$	−9.27489	−	34.6143i	−0.437709	−	1.63355i	−0.734499	−	0.678609i	$-0.762583\pi$
$449$	−9.27489	−	34.6143i	−0.437709	−	1.63355i	0.296790	−	0.954943i	$-0.404084\pi$
$450$	0.977546	−	9.41363i	0.0460820	−	0.443763i
$451$	6.98732	−	12.1024i	0.329020	−	0.569879i
$452$	1.35323	−	2.34386i	0.0636506	−	0.110246i
$453$	1.14226	+	14.3990i	0.0536681	+	0.676525i
$454$	−1.80420	−	1.04166i	−0.0846753	−	0.0488873i
$455$	−10.5883	−	1.33370i	−0.496385	−	0.0625249i
$456$	15.6269	+	2.88620i	0.731796	+	0.135159i
$457$	7.52282	+	28.0755i	0.351903	+	1.31332i	0.884338	+	0.466848i	$0.154610\pi$
$457$	7.52282	+	28.0755i	0.351903	+	1.31332i	−0.532435	+	0.846471i	$0.678723\pi$
$458$	−4.84967	+	2.79996i	−0.226610	+	0.130834i
$459$	−5.17704	−	9.49255i	−0.241644	−	0.443074i
$460$	6.39366	−	6.39366i	0.298106	−	0.298106i
$461$	−3.23659	−	3.23659i	−0.150743	−	0.150743i	0.627707	−	0.778450i	$-0.283994\pi$
$461$	−3.23659	−	3.23659i	−0.150743	−	0.150743i	−0.778450	+	0.627707i	$0.783994\pi$
$462$	0.589984	+	7.43718i	0.0274486	+	0.346009i
$463$	−9.91166	+	2.65582i	−0.460634	+	0.123426i	−0.481671	−	0.876352i	$-0.659970\pi$
$463$	−9.91166	+	2.65582i	−0.460634	+	0.123426i	0.0210370	+	0.999779i	$0.493303\pi$
$464$	−7.25010	+	4.18584i	−0.336577	+	0.194323i
$465$	−4.47619	−	3.81820i	−0.207578	−	0.177065i
$466$	8.53972	−	2.28821i	0.395595	−	0.105999i
$467$	17.4482			0.807406			0.403703	−	0.914890i	$-0.367723\pi$
$467$	17.4482			0.807406			0.403703	+	0.914890i	$0.367723\pi$
$468$	−0.513138	−	15.5318i	−0.0237198	−	0.717956i
$469$	13.7951			0.636999
$470$	−1.32235	+	0.354323i	−0.0609955	+	0.0163437i
$471$	−3.77270	+	20.4267i	−0.173837	+	0.941214i
$472$	4.41005	−	2.54615i	0.202989	−	0.117196i
$473$	−12.5626	+	3.36613i	−0.577627	+	0.154775i
$474$	−6.64109	−	3.16256i	−0.305035	−	0.145261i
$475$	−10.5721	−	10.5721i	−0.485081	−	0.485081i
$476$	−7.01010	+	7.01010i	−0.321308	+	0.321308i
$477$	12.6963	+	15.6388i	0.581326	+	0.716050i
$478$	−3.82385	+	2.20770i	−0.174899	+	0.100978i
$479$	−1.47435	−	5.50234i	−0.0673646	−	0.251408i	0.924029	−	0.382322i	$-0.124876\pi$
$479$	−1.47435	−	5.50234i	−0.0673646	−	0.251408i	−0.991394	+	0.130914i	$0.958209\pi$
$480$	3.03062	+	8.54128i	0.138328	+	0.389854i
$481$	0.666417	+	4.85186i	0.0303860	+	0.221226i
$482$	−13.1435	−	7.58839i	−0.598669	−	0.345642i
$483$	−36.5652	−	17.4127i	−1.66377	−	0.792307i
$484$	−5.75028	+	9.95978i	−0.261376	+	0.452717i
$485$	1.60977	−	2.78821i	0.0730961	−	0.126606i
$486$	4.51096	+	10.7951i	0.204621	+	0.489676i
$487$	0.694702	+	2.59266i	0.0314800	+	0.117485i	0.979878	−	0.199598i	$-0.0639635\pi$
$487$	0.694702	+	2.59266i	0.0314800	+	0.117485i	−0.948398	+	0.317082i	$0.897297\pi$
$488$	0.586823	−	0.586823i	0.0265642	−	0.0265642i
$489$	7.28023	−	5.01025i	0.329224	−	0.226571i
$490$	−1.33869	−	2.31868i	−0.0604759	−	0.104747i
$491$	12.8561			0.580190			0.290095	−	0.956998i	$-0.406313\pi$
$491$	12.8561			0.580190			0.290095	+	0.956998i	$0.406313\pi$
$492$	−20.0307	+	1.58902i	−0.903054	+	0.0716384i
$493$	−16.0926	+	9.29105i	−0.724773	+	0.418448i
$494$	7.66917	+	5.81683i	0.345052	+	0.261711i
$495$	−4.32841	−	1.65533i	−0.194547	−	0.0744016i
$496$	−3.44618	−	0.923400i	−0.154738	−	0.0414619i
$497$	6.92471	+	3.99799i	0.310616	+	0.179334i
$498$	3.49636	+	9.85389i	0.156676	+	0.441563i
$499$	9.97973	+	37.2449i	0.446754	+	1.66731i	0.711264	+	0.702925i	$0.248123\pi$
$499$	9.97973	+	37.2449i	0.446754	+	1.66731i	−0.264510	+	0.964383i	$0.585210\pi$
$500$	3.05454	−	11.3997i	0.136603	−	0.509810i
$501$	16.0570	−	33.7183i	0.717375	−	1.50642i
$502$	−2.20951	+	8.24599i	−0.0986151	+	0.368037i
$503$	−6.93258	−	4.00252i	−0.309108	−	0.178464i	0.337419	−	0.941355i	$-0.390446\pi$
$503$	−6.93258	−	4.00252i	−0.309108	−	0.178464i	−0.646527	+	0.762891i	$0.723779\pi$
$504$	19.9218	−	16.1735i	0.887387	−	0.720426i
$505$	−2.67609	+	9.98730i	−0.119084	+	0.444429i
$506$	−4.57940	−	7.93176i	−0.203579	−	0.352610i
$507$	9.45275	−	20.4364i	0.419811	−	0.907611i
$508$	−13.7274	+	23.7766i	−0.609056	+	1.05492i
$509$	−18.5650	−	18.5650i	−0.822881	−	0.822881i	0.163639	−	0.986520i	$-0.447677\pi$
$509$	−18.5650	−	18.5650i	−0.822881	−	0.822881i	−0.986520	+	0.163639i	$0.947677\pi$
$510$	0.807377	+	2.27545i	0.0357512	+	0.100759i
$511$			50.5315i			2.23538i
$512$	7.30587	+	7.30587i	0.322877	+	0.322877i
$513$	17.7313	+	5.21621i	0.782858	+	0.230301i
$514$	−5.11081	+	1.36944i	−0.225428	+	0.0604033i
$515$	4.14807	+	1.11147i	0.182786	+	0.0489773i
$516$	14.2275	+	12.1361i	0.626331	+	0.534262i
$517$		−	3.53670i		−	0.155544i
$518$	−2.39046	+	2.39046i	−0.105031	+	0.105031i
$519$	33.6416	−	11.9367i	1.47670	−	0.523963i
$520$	−1.03739	+	8.23581i	−0.0454924	+	0.361164i
$521$		−	8.94139i		−	0.391729i	−0.980631	−	0.195865i	$-0.937249\pi$
$521$		−	8.94139i		−	0.391729i	0.980631	−	0.195865i	$-0.0627513\pi$
$522$	18.3583	−	8.20108i	0.803520	−	0.358951i
$523$	−13.5085	−	23.3975i	−0.590687	−	1.02310i	−0.994140	−	0.108100i	$-0.965523\pi$
$523$	−13.5085	−	23.3975i	−0.590687	−	1.02310i	0.403453	−	0.915000i	$-0.367810\pi$
$524$	8.90408			0.388977
$525$	−24.0670	+	1.90921i	−1.05037	+	0.0833249i
$526$	−11.8481	−	3.17468i	−0.516600	−	0.138422i
$527$	−7.64925	−	2.04961i	−0.333207	−	0.0892825i
$528$	−2.80136	+	0.222229i	−0.121913	+	0.00967128i
$529$	26.7186			1.16168
$530$	−2.24905	−	3.89548i	−0.0976927	−	0.169209i
$531$	5.40767	−	2.41573i	0.234673	−	0.104834i
$532$		−	16.9464i		−	0.734721i
$533$	−26.9600	−	10.9907i	−1.16777	−	0.476062i
$534$	22.7666	−	8.07807i	0.985209	−	0.349572i
$535$	7.41884	−	7.41884i	0.320744	−	0.320744i
$536$		−	10.7302i		−	0.463474i
$537$	3.07804	+	2.62558i	0.132827	+	0.113302i
$538$	12.6675	+	3.39425i	0.546135	+	0.146336i
$539$	6.68113	−	1.79020i	0.287776	−	0.0771095i
$540$	1.56762	+	6.47623i	0.0674597	+	0.278693i
$541$	3.92558	+	3.92558i	0.168774	+	0.168774i	0.786440	−	0.617666i	$-0.211922\pi$
$541$	3.92558	+	3.92558i	0.168774	+	0.168774i	−0.617666	+	0.786440i	$0.711922\pi$
$542$		−	14.2890i		−	0.613764i
$543$	1.87221	+	5.27649i	0.0803441	+	0.226436i
$544$	8.62583	+	8.62583i	0.369829	+	0.369829i
$545$	−6.75505	+	11.7001i	−0.289355	+	0.501177i
$546$	15.1829	−	3.32611i	0.649770	−	0.142344i
$547$	17.8852	+	30.9781i	0.764717	+	1.32453i	0.940396	+	0.340081i	$0.110455\pi$
$547$	17.8852	+	30.9781i	0.764717	+	1.32453i	−0.175679	+	0.984448i	$0.556212\pi$
$548$	8.45771	−	31.5646i	0.361296	−	1.34837i
$549$	0.749366	−	0.608373i	0.0319822	−	0.0259647i
$550$	−4.72828	−	2.72987i	−0.201614	−	0.116402i
$551$	8.22109	−	30.6815i	0.350230	−	1.30708i
$552$	−13.5441	+	28.4414i	−0.576474	+	1.21054i
$553$	−4.85642	+	18.1244i	−0.206516	+	0.770728i
$554$	4.80365	+	17.9274i	0.204087	+	0.761664i
$555$	−0.702190	−	1.97900i	−0.0298063	−	0.0840040i
$556$	5.31444	+	3.06829i	0.225383	+	0.130125i
$557$	14.0461	+	3.76365i	0.595154	+	0.159471i	0.543807	−	0.839210i	$-0.316982\pi$
$557$	14.0461	+	3.76365i	0.595154	+	0.159471i	0.0513461	+	0.998681i	$0.483649\pi$
$558$	8.00356	+	3.06084i	0.338818	+	0.129575i
$559$	10.5090	+	24.9746i	0.444485	+	1.05631i
$560$	2.40306	−	1.38741i	0.101548	−	0.0586286i
$561$	−6.21799	+	0.493267i	−0.262524	+	0.0208258i
$562$	−7.13727			−0.301068
$563$	5.44609	+	9.43290i	0.229525	+	0.397550i	0.957668	−	0.287877i	$-0.0929493\pi$
$563$	5.44609	+	9.43290i	0.229525	+	0.397550i	−0.728142	+	0.685426i	$0.759616\pi$
$564$	−4.18913	+	2.88296i	−0.176394	+	0.121394i
$565$	−1.18895	+	1.18895i	−0.0500194	+	0.0500194i
$566$	1.93492	+	7.22124i	0.0813309	+	0.303531i
$567$	24.9896	−	16.3172i	1.04946	−	0.685257i
$568$	3.10974	−	5.38622i	0.130482	−	0.226001i
$569$	−11.8936	+	20.6003i	−0.498606	+	0.863610i	−0.999999	−	0.00160919i	$-0.999488\pi$
$569$	−11.8936	+	20.6003i	−0.498606	+	0.863610i	0.501393	+	0.865220i	$0.332821\pi$
$570$	−3.72626	−	1.77448i	−0.156076	−	0.0743249i
$571$	−5.32696	−	3.07552i	−0.222926	−	0.128706i	0.384378	−	0.923176i	$-0.374416\pi$
$571$	−5.32696	−	3.07552i	−0.222926	−	0.128706i	−0.607304	+	0.794469i	$0.707749\pi$
$572$	−8.30153	−	3.38428i	−0.347104	−	0.141504i
$573$	14.3056	+	40.3178i	0.597625	+	1.68430i
$574$	−5.20154	−	19.4124i	−0.217108	−	0.810259i
$575$	25.6675	−	14.8191i	1.07041	−	0.618000i
$576$	−4.77433	−	5.88079i	−0.198930	−	0.245033i
$577$	−8.01421	+	8.01421i	−0.333636	+	0.333636i	−0.853965	−	0.520330i	$-0.825809\pi$
$577$	−8.01421	+	8.01421i	−0.333636	+	0.333636i	0.520330	+	0.853965i	$0.325809\pi$
$578$	−6.72409	−	6.72409i	−0.279685	−	0.279685i
$579$	17.3098	+	8.24309i	0.719369	+	0.342571i
$580$	11.0611	−	2.96382i	0.459288	−	0.123066i
$581$	23.0986	−	13.3360i	0.958292	−	0.553270i
$582$	−0.851642	+	4.61109i	−0.0353017	+	0.191136i
$583$	11.2245	−	3.00761i	0.464873	−	0.124562i
$584$	39.3047			1.62644
$585$	−2.18949	+	9.40303i	−0.0905244	+	0.388767i
$586$	−14.7874			−0.610863
$587$	−9.10458	+	2.43957i	−0.375786	+	0.100692i	−0.441768	−	0.897129i	$-0.645649\pi$
$587$	−9.10458	+	2.43957i	−0.375786	+	0.100692i	0.0659820	+	0.997821i	$0.478982\pi$
$588$	−7.56659	−	6.45433i	−0.312041	−	0.266172i
$589$	11.7232	−	6.76837i	0.483044	−	0.278886i
$590$	−1.27749	+	0.342301i	−0.0525933	+	0.0140923i
$591$	−0.0595077	−	0.750137i	−0.00244782	−	0.0308565i
$592$	−0.900415	−	0.900415i	−0.0370068	−	0.0370068i
$593$	−17.4989	+	17.4989i	−0.718593	+	0.718593i	−0.968317	−	0.249724i	$-0.919660\pi$
$593$	−17.4989	+	17.4989i	−0.718593	+	0.718593i	0.249724	+	0.968317i	$0.419660\pi$
$594$	6.74734	+	0.164057i	0.276847	+	0.00673135i
$595$	5.33391	−	3.07954i	0.218669	−	0.126249i
$596$	2.64729	+	9.87981i	0.108437	+	0.404693i
$597$	−17.6048	−	3.25150i	−0.720515	−	0.133075i
$598$	−15.0728	+	11.7004i	−0.616371	+	0.478465i
$599$	−22.0827	−	12.7495i	−0.902275	−	0.520929i	−0.0243375	−	0.999704i	$-0.507748\pi$
$599$	−22.0827	−	12.7495i	−0.902275	−	0.520929i	−0.877938	+	0.478775i	$0.841081\pi$
$600$	1.48503	+	18.7199i	0.0606263	+	0.764238i
$601$	−6.76828	+	11.7230i	−0.276084	+	0.478191i	−0.970408	−	0.241471i	$-0.922370\pi$
$601$	−6.76828	+	11.7230i	−0.276084	+	0.478191i	0.694324	+	0.719662i	$0.255703\pi$
$602$	−9.35189	+	16.1979i	−0.381154	+	0.660179i
$603$	1.28904	−	12.4133i	0.0524939	−	0.505508i
$604$	−3.10095	−	11.5729i	−0.126176	−	0.470895i
$605$	5.05219	−	5.05219i	0.205401	−	0.205401i
$606$	−1.19088	−	15.0119i	−0.0483760	−	0.609815i
$607$	−14.8399	−	25.7035i	−0.602334	−	1.04327i	−0.992467	−	0.122515i	$-0.960904\pi$
$607$	−14.8399	−	25.7035i	−0.602334	−	1.04327i	0.390133	−	0.920759i	$-0.372429\pi$
$608$	−20.8523			−0.845673
$609$	−29.0779	−	42.2522i	−1.17830	−	1.71214i
$610$	−0.186660	+	0.107768i	−0.00755765	+	0.00436341i
$611$	−7.29969	+	1.00263i	−0.295314	+	0.0405622i
$612$	5.65288	+	6.96296i	0.228504	+	0.281461i
$613$	31.3638	+	8.40390i	1.26677	+	0.339430i	0.828793	−	0.559555i	$-0.189028\pi$
$613$	31.3638	+	8.40390i	1.26677	+	0.339430i	0.437979	+	0.898985i	$0.355695\pi$
$614$	21.6651	+	12.5083i	0.874331	+	0.504795i
$615$	12.2758	+	2.26727i	0.495009	+	0.0914252i
$616$	−3.83131	−	14.2986i	−0.154368	−	0.576108i
$617$	−12.2195	+	45.6038i	−0.491939	+	1.83594i	0.0546012	+	0.998508i	$0.482611\pi$
$617$	−12.2195	+	45.6038i	−0.491939	+	1.83594i	−0.546540	+	0.837433i	$0.684055\pi$
$618$	−6.23494	+	0.494612i	−0.250806	+	0.0198962i
$619$	2.80945	−	10.4850i	0.112921	−	0.421429i	−0.886202	−	0.463300i	$-0.846665\pi$
$619$	2.80945	−	10.4850i	0.112921	−	0.421429i	0.999123	+	0.0418712i	$0.0133319\pi$
$620$	4.22636	+	2.44009i	0.169735	+	0.0979964i
$621$	−19.0853	+	31.2755i	−0.765865	+	1.25504i
$622$	5.51641	−	20.5875i	0.221188	−	0.825485i
$623$	−30.8118	−	53.3675i	−1.23445	−	2.13812i
$624$	1.25284	+	5.71895i	0.0501539	+	0.228941i
$625$	6.84229	−	11.8512i	0.273692	−	0.474048i
$626$	12.6903	+	12.6903i	0.507205	+	0.507205i
$627$	6.91955	−	8.11199i	0.276340	−	0.323962i
$628$		−	17.2300i		−	0.687554i
$629$	−1.99859	−	1.99859i	−0.0796891	−	0.0796891i
$630$	−6.08489	+	2.71826i	−0.242428	+	0.108298i
$631$	−20.6714	+	5.53890i	−0.822917	+	0.220500i	−0.645622	−	0.763658i	$-0.723402\pi$
$631$	−20.6714	+	5.53890i	−0.822917	+	0.220500i	−0.177296	+	0.984158i	$0.556735\pi$
$632$	14.0976	+	3.77745i	0.560774	+	0.150259i
$633$	−15.7838	+	5.60042i	−0.627350	+	0.222597i
$634$			11.7797i			0.467834i
$635$	12.0609	−	12.0609i	0.478622	−	0.478622i
$636$	−12.7122	−	10.8435i	−0.504070	−	0.429973i
$637$	−5.58900	−	13.2822i	−0.221444	−	0.526260i
$638$		−	11.5992i		−	0.459218i
$639$	4.24457	−	5.85750i	0.167913	−	0.231719i
$640$	−4.38680	−	7.59815i	−0.173403	−	0.300343i
$641$	−31.4401			−1.24181			−0.620904	−	0.783887i	$-0.713234\pi$
$641$	−31.4401			−1.24181			−0.620904	+	0.783887i	$0.713234\pi$
$642$	−6.56991	+	13.7962i	−0.259294	+	0.544494i
$643$	12.1175	+	3.24688i	0.477868	+	0.128044i	0.489710	−	0.871885i	$-0.337103\pi$
$643$	12.1175	+	3.24688i	0.477868	+	0.128044i	−0.0118416	+	0.999930i	$0.503769\pi$
$644$	32.4488	+	8.69463i	1.27866	+	0.342616i
$645$	−6.58642	−	9.57051i	−0.259340	−	0.376838i
$646$	−5.55519			−0.218566
$647$	13.7408	+	23.7997i	0.540205	+	0.935662i	0.998892	+	0.0470643i	$0.0149866\pi$
$647$	13.7408	+	23.7997i	0.540205	+	0.935662i	−0.458687	+	0.888598i	$0.651680\pi$
$648$	−12.6919	−	19.4375i	−0.498586	−	0.763579i
$649$		−	3.41671i		−	0.134117i
$650$	−4.29397	+	10.5330i	−0.168423	+	0.413137i
$651$	3.97001	−	21.4951i	0.155597	−	0.842457i
$652$	−5.18354	+	5.18354i	−0.203003	+	0.203003i
$653$			1.56462i			0.0612282i	0.999531	+	0.0306141i	$0.00974629\pi$
$653$			1.56462i			0.0612282i	−0.999531	+	0.0306141i	$0.990254\pi$
$654$	3.57372	−	19.3494i	0.139743	−	0.756621i
$655$	−5.34329	−	1.43173i	−0.208780	−	0.0559423i
$656$	7.31206	−	1.95926i	0.285488	−	0.0764963i
$657$	45.4699	+	4.72176i	1.77395	+	0.184213i
$658$	−3.59649	−	3.59649i	−0.140206	−	0.140206i
$659$		−	1.47083i		−	0.0572955i	−0.999590	−	0.0286477i	$-0.990880\pi$
$659$		−	1.47083i		−	0.0572955i	0.999590	−	0.0286477i	$-0.00912010\pi$
$660$	3.77997	+	0.698140i	0.147135	+	0.0271750i
$661$	−14.5257	−	14.5257i	−0.564985	−	0.564985i	0.365734	−	0.930719i	$-0.380818\pi$
$661$	−14.5257	−	14.5257i	−0.564985	−	0.564985i	−0.930719	+	0.365734i	$0.880818\pi$
$662$	−6.56892	+	11.3777i	−0.255308	+	0.442207i
$663$	2.78086	+	12.6940i	0.108000	+	0.492993i
$664$	−10.3731	−	17.9667i	−0.402553	−	0.697243i
$665$	−2.72490	+	10.1695i	−0.105667	+	0.394354i
$666$	1.92765	+	2.37439i	0.0746948	+	0.0920056i
$667$	54.5306	+	31.4833i	2.11143	+	1.21904i
$668$	−8.01769	+	29.9224i	−0.310214	+	1.15773i
$669$	−5.63109	−	8.18236i	−0.217711	−	0.316348i
$670$	−0.721279	+	2.69185i	−0.0278654	+	0.103995i
$671$	−0.144116	−	0.537849i	−0.00556354	−	0.0207634i
$672$	−21.8519	+	25.6176i	−0.842957	+	0.988222i
$673$	−16.7885	−	9.69285i	−0.647149	−	0.373632i	0.140214	−	0.990121i	$-0.455221\pi$
$673$	−16.7885	−	9.69285i	−0.647149	−	0.373632i	−0.787363	+	0.616489i	$0.788554\pi$
$674$	−1.87339	−	0.501974i	−0.0721604	−	0.0193353i
$675$	−0.530896	+	21.8347i	−0.0204342	+	0.840417i
$676$	−4.63165	+	18.0936i	−0.178140	+	0.695909i
$677$	38.9340	−	22.4785i	1.49635	−	0.863920i	0.496362	−	0.868115i	$-0.334669\pi$
$677$	38.9340	−	22.4785i	1.49635	−	0.863920i	0.999991	+	0.00419533i	$0.00133542\pi$
$678$	1.05290	−	2.21099i	0.0404363	−	0.0849126i
$679$	11.9615			0.459040
$680$	−2.39534	−	4.14885i	−0.0918571	−	0.159101i
$681$	4.34070	+	2.06709i	0.166336	+	0.0792110i
$682$	3.49539	−	3.49539i	0.133845	−	0.133845i
$683$	−2.74805	−	10.2559i	−0.105151	−	0.392429i	0.893211	−	0.449638i	$-0.148447\pi$
$683$	−2.74805	−	10.2559i	−0.105151	−	0.392429i	−0.998362	+	0.0572080i	$0.981780\pi$
$684$	−15.2489	−	1.58351i	−0.583058	−	0.0605469i
$685$	−10.1509	+	17.5818i	−0.387844	+	0.671766i
$686$	−3.73745	+	6.47345i	−0.142696	+	0.247158i
$687$	10.6458	−	7.32643i	0.406162	−	0.279521i
$688$	−6.10127	−	3.52257i	−0.232609	−	0.134297i
$689$	−9.38974	−	22.3146i	−0.357721	−	0.850119i
$690$	5.30957	−	6.22456i	0.202132	−	0.236965i
$691$	−3.56157	−	13.2920i	−0.135488	−	0.505650i	−0.999995	−	0.00302891i	$-0.999036\pi$
$691$	−3.56157	−	13.2920i	−0.135488	−	0.505650i	0.864507	−	0.502621i	$-0.167631\pi$
$692$	−25.6425	+	14.8047i	−0.974781	+	0.562790i
$693$	−2.71454	−	17.0017i	−0.103117	−	0.645842i
$694$	−0.00577947	+	0.00577947i	−0.000219386	+	0.000219386i
$695$	−2.69580	−	2.69580i	−0.102258	−	0.102258i
$696$	−32.8648	+	22.6175i	−1.24574	+	0.857316i
$697$	16.2301	−	4.34884i	0.614759	−	0.164724i
$698$	7.09416	−	4.09582i	0.268518	−	0.155029i
$699$	−19.2282	+	6.82257i	−0.727278	+	0.258053i
$700$	19.3434	−	5.18304i	0.731111	−	0.195900i
$701$	6.62924			0.250383			0.125191	−	0.992133i	$-0.460045\pi$
$701$	6.62924			0.250383			0.125191	+	0.992133i	$0.460045\pi$
$702$	−1.57422	−	13.9729i	−0.0594151	−	0.527373i
$703$	4.83145			0.182222
$704$	−4.22087	+	1.13098i	−0.159080	+	0.0426254i
$705$	2.97744	−	1.05646i	0.112137	−	0.0397884i
$706$	2.87855	−	1.66193i	0.108336	−	0.0625477i
$707$	−37.1055	+	9.94239i	−1.39550	+	0.373922i
$708$	−4.04700	+	2.78514i	−0.152095	+	0.104672i
$709$	14.6235	+	14.6235i	0.549196	+	0.549196i	0.926208	−	0.377013i	$-0.123049\pi$
$709$	14.6235	+	14.6235i	0.549196	+	0.549196i	−0.377013	+	0.926208i	$0.623049\pi$
$710$	−1.14219	+	1.14219i	−0.0428656	+	0.0428656i
$711$	15.8551	+	6.06354i	0.594614	+	0.227401i
$712$	−41.5106	+	23.9662i	−1.55568	+	0.898170i
$713$	6.94523	+	25.9200i	0.260101	+	0.970710i
$714$	−5.82150	+	6.82471i	−0.217864	+	0.255408i
$715$	4.43753	+	3.36573i	0.165954	+	0.125871i
$716$	−2.90625	−	1.67792i	−0.108612	−	0.0627069i
$717$	8.39396	−	5.77672i	0.313478	−	0.215735i
$718$	6.76091	−	11.7102i	0.252315	−	0.437022i
$719$	−8.60336	+	14.9014i	−0.320851	+	0.555730i	−0.980664	−	0.195700i	$-0.937302\pi$
$719$	−8.60336	+	14.9014i	−0.320851	+	0.555730i	0.659813	+	0.751430i	$0.270636\pi$
$720$	−1.02389	−	2.29199i	−0.0381580	−	0.0854175i
$721$	4.12942	+	15.4112i	0.153788	+	0.573943i
$722$	−3.36884	+	3.36884i	−0.125375	+	0.125375i
$723$	31.6217	+	15.0586i	1.17602	+	0.560035i
$724$	−2.32203	−	4.02188i	−0.0862977	−	0.149472i
$725$	37.5356			1.39404
$726$	−4.47408	+	9.39517i	−0.166049	+	0.348687i
$727$	9.73598	−	5.62107i	0.361088	−	0.208474i	−0.308470	−	0.951234i	$-0.599817\pi$
$727$	9.73598	−	5.62107i	0.361088	−	0.208474i	0.669558	+	0.742760i	$0.266484\pi$
$728$	−28.4260	+	11.9613i	−1.05354	+	0.443316i
$729$	−12.3476	−	24.0112i	−0.457320	−	0.889302i
$730$	−9.86024	−	2.64204i	−0.364944	−	0.0977864i
$731$	−13.5426	−	7.81882i	−0.500891	−	0.289189i
$732$	−0.519591	+	0.609131i	−0.0192046	+	0.0225141i
$733$	−1.81736	−	6.78249i	−0.0671258	−	0.250517i	0.924207	−	0.381892i	$-0.124727\pi$
$733$	−1.81736	−	6.78249i	−0.0671258	−	0.250517i	−0.991333	+	0.131375i	$0.958061\pi$
$734$	−2.11589	+	7.89661i	−0.0780990	+	0.291469i
$735$	3.50285	+	5.08987i	0.129204	+	0.187743i
$736$	10.6986	−	39.9277i	0.394356	−	1.47176i
$737$	−6.23495	−	3.59975i	−0.229667	−	0.132598i
$738$	−17.9540	+	2.86658i	−0.660894	+	0.105520i
$739$	7.57418	−	28.2672i	0.278621	−	1.03983i	−0.674755	−	0.738042i	$-0.735751\pi$
$739$	7.57418	−	28.2672i	0.278621	−	1.03983i	0.953376	−	0.301785i	$-0.0975826\pi$
$740$	0.870903	+	1.50845i	0.0320150	+	0.0554516i
$741$	−18.7047	−	11.9821i	−0.687133	−	0.440175i
$742$	8.35584	−	14.4727i	0.306753	−	0.531311i
$743$	26.7178	+	26.7178i	0.980182	+	0.980182i	0.999807	−	0.0196250i	$-0.00624723\pi$
$743$	26.7178	+	26.7178i	0.980182	+	0.980182i	−0.0196250	+	0.999807i	$0.506247\pi$
$744$	−16.7194	−	3.08798i	−0.612963	−	0.113211i
$745$		−	6.35448i		−	0.232810i
$746$	3.75477	+	3.75477i	0.137472	+	0.137472i
$747$	−9.84177	−	22.0310i	−0.360092	−	0.806072i
$748$	4.99758	−	1.33910i	0.182730	−	0.0489623i
$749$	37.6518	+	10.0888i	1.37577	+	0.368635i
$750$	1.93949	−	10.5011i	0.0708201	−	0.383445i
$751$			1.61030i			0.0587606i	0.999568	+	0.0293803i	$0.00935339\pi$
$751$			1.61030i			0.0587606i	−0.999568	+	0.0293803i	$0.990647\pi$
$752$	1.35469	−	1.35469i	0.0494003	−	0.0494003i
$753$	3.57814	−	19.3733i	0.130395	−	0.706003i
$754$	−23.9406	+	3.28831i	−0.871866	+	0.119753i
$755$			7.44346i			0.270895i
$756$	−17.9253	+	17.0743i	−0.651938	+	0.620987i
$757$	−23.8109	−	41.2417i	−0.865422	−	1.49896i	−0.866627	−	0.498956i	$-0.833717\pi$
$757$	−23.8109	−	41.2417i	−0.865422	−	1.49896i	0.00120524	−	0.999999i	$-0.499616\pi$
$758$	4.76262			0.172986
$759$	11.9825	+	17.4115i	0.434939	+	0.631996i
$760$	7.91006	+	2.11949i	0.286928	+	0.0768821i
$761$	27.4425	+	7.35320i	0.994790	+	0.266553i	0.719261	−	0.694740i	$-0.244480\pi$
$761$	27.4425	+	7.35320i	0.994790	+	0.266553i	0.275529	+	0.961293i	$0.411147\pi$
$762$	−10.6808	+	22.4287i	−0.386924	+	0.812506i
$763$	−50.1937			−1.81713
$764$	−17.7427	−	30.7313i	−0.641910	−	1.11182i
$765$	−2.27265	−	5.08738i	−0.0821680	−	0.183935i
$766$		−	11.4536i		−	0.413837i
$767$	−7.05202	+	0.968615i	−0.254634	+	0.0349747i
$768$	16.3763	+	13.9691i	0.590930	+	0.504065i
$769$	−5.08356	+	5.08356i	−0.183318	+	0.183318i	−0.792800	−	0.609482i	$-0.791377\pi$
$769$	−5.08356	+	5.08356i	−0.183318	+	0.183318i	0.609482	+	0.792800i	$0.291377\pi$
$770$			3.84459i			0.138549i
$771$	11.5076	−	4.08314i	0.414437	−	0.147051i
$772$	−15.3611	−	4.11598i	−0.552857	−	0.148138i
$773$	16.2573	−	4.35613i	0.584734	−	0.156679i	0.0456886	−	0.998956i	$-0.485452\pi$
$773$	16.2573	−	4.35613i	0.584734	−	0.156679i	0.539045	+	0.842277i	$0.318785\pi$
$774$	13.7016	+	9.92870i	0.492493	+	0.356880i
$775$	11.3112	+	11.3112i	0.406311	+	0.406311i
$776$		−	9.30396i		−	0.333993i
$777$	5.06306	−	5.93557i	0.181636	−	0.212938i
$778$	4.11806	+	4.11806i	0.147640	+	0.147640i
$779$	−14.3611	+	24.8741i	−0.514538	+	0.891206i
$780$	0.369348	−	7.99972i	0.0132248	−	0.286436i
$781$	−2.08650	−	3.61392i	−0.0746608	−	0.129316i
$782$	2.85018	−	10.6370i	0.101922	−	0.380379i
$783$	−40.7370	+	22.2171i	−1.45582	+	0.793975i
$784$	3.24483	+	1.87340i	0.115887	+	0.0669073i
$785$	−2.77050	+	10.3396i	−0.0988834	+	0.369038i
$786$	8.03147	−	0.637129i	0.286473	−	0.0227256i
$787$	8.07920	−	30.1520i	0.287992	−	1.07480i	−0.658633	−	0.752465i	$-0.728865\pi$
$787$	8.07920	−	30.1520i	0.287992	−	1.07480i	0.946625	−	0.322337i	$-0.104469\pi$
$788$	0.161549	+	0.602907i	0.00575493	+	0.0214777i
$789$	27.8361	+	5.14116i	0.990991	+	0.183030i
$790$	−3.28271	−	1.89527i	−0.116794	−	0.0674308i
$791$	−6.03409	−	1.61683i	−0.214547	−	0.0574878i
$792$	−13.2244	+	2.11144i	−0.469908	+	0.0750268i
$793$	−1.06925	+	0.449930i	−0.0379703	+	0.0159775i
$794$	7.78904	−	4.49700i	0.276423	−	0.159593i
$795$	5.88492	+	8.55118i	0.208717	+	0.303279i
$796$	14.8497			0.526334
$797$	−12.0072	−	20.7970i	−0.425315	−	0.736667i	0.571135	−	0.820856i	$-0.306503\pi$
$797$	−12.0072	−	20.7970i	−0.425315	−	0.736667i	−0.996450	+	0.0841890i	$0.973170\pi$
$798$	−1.21260	−	15.2856i	−0.0429254	−	0.541106i
$799$	3.00691	−	3.00691i	0.106377	−	0.106377i
$800$	−6.37765	−	23.8017i	−0.225484	−	0.841518i
$801$	−50.9009	+	22.7386i	−1.79850	+	0.803431i
$802$	4.59175	−	7.95314i	0.162140	−	0.280835i
$803$	13.1859	−	22.8386i	0.465319	−	0.805957i
$804$	0.818634	+	10.3195i	0.0288710	+	0.363940i
$805$	−18.0743	−	10.4352i	−0.637035	−	0.367792i
$806$	−8.20533	−	6.22349i	−0.289021	−	0.219213i
$807$	−29.7613	−	5.49674i	−1.04765	−	0.193495i
$808$	7.73345	+	28.8616i	0.272062	+	1.01535i
$809$	−9.87219	+	5.69971i	−0.347088	+	0.200391i	−0.663402	−	0.748263i	$-0.730888\pi$
$809$	−9.87219	+	5.69971i	−0.347088	+	0.200391i	0.316314	+	0.948655i	$0.397555\pi$
$810$	1.87740	+	5.72938i	0.0659650	+	0.201310i
$811$	−17.0695	+	17.0695i	−0.599392	+	0.599392i	−0.940151	−	0.340759i	$-0.889316\pi$
$811$	−17.0695	+	17.0695i	−0.599392	+	0.599392i	0.340759	+	0.940151i	$0.389316\pi$
$812$	30.0836	+	30.0836i	1.05573	+	1.05573i
$813$	2.60771	+	32.8721i	0.0914565	+	1.15288i
$814$	1.70419	−	0.456636i	0.0597318	−	0.0160051i
$815$	3.94410	−	2.27713i	0.138156	−	0.0797643i
$816$	−2.57066	−	2.19278i	−0.0899910	−	0.0767626i
$817$	25.8198	−	6.91840i	0.903322	−	0.242044i
$818$	−17.5432			−0.613383
$819$	−34.3217	+	10.4227i	−1.19930	+	0.364197i
$820$	−10.3547			−0.361602
$821$	−48.8865	+	13.0991i	−1.70615	+	0.457162i	−0.974476	−	0.224493i	$-0.927928\pi$
$821$	−48.8865	+	13.0991i	−1.70615	+	0.457162i	−0.731674	+	0.681654i	$0.761261\pi$
$822$	5.37025	−	29.0764i	0.187309	−	1.01416i
$823$	−10.0930	+	5.82722i	−0.351821	+	0.203124i	−0.665487	−	0.746409i	$-0.731776\pi$
$823$	−10.0930	+	5.82722i	−0.351821	+	0.203124i	0.313666	+	0.949533i	$0.398443\pi$
$824$	11.9872	−	3.21197i	0.417595	−	0.111894i
$825$	11.3757	+	5.41723i	0.396051	+	0.188604i
$826$	−3.47446	−	3.47446i	−0.120892	−	0.120892i
$827$	19.7531	−	19.7531i	0.686883	−	0.686883i	−0.274659	−	0.961542i	$-0.588565\pi$
$827$	19.7531	−	19.7531i	0.686883	−	0.686883i	0.961542	+	0.274659i	$0.0885649\pi$
$828$	10.8558	−	28.3860i	0.377264	−	0.986482i
$829$	−0.903024	+	0.521361i	−0.0313633	+	0.0181076i	−0.515600	−	0.856830i	$-0.672431\pi$
$829$	−0.903024	+	0.521361i	−0.0313633	+	0.0181076i	0.484236	+	0.874937i	$0.339097\pi$
$830$	1.39455	+	5.20452i	0.0484054	+	0.180651i
$831$	−14.3226	−	40.3658i	−0.496846	−	1.40028i
$832$	3.53091	+	8.39118i	0.122412	+	0.290912i
$833$	7.20234	+	4.15827i	0.249546	+	0.144076i
$834$	5.01317	+	2.38732i	0.173592	+	0.0826662i
$835$	9.62274	−	16.6671i	0.333009	−	0.576788i
$836$	−4.42206	+	7.65924i	−0.152940	+	0.264900i
$837$	−18.9710	−	5.58088i	−0.655733	−	0.192904i
$838$	0.461906	+	1.72386i	0.0159563	+	0.0595496i
$839$	39.1889	−	39.1889i	1.35295	−	1.35295i	0.470606	−	0.882344i	$-0.344035\pi$
$839$	39.1889	−	39.1889i	1.35295	−	1.35295i	0.882344	−	0.470606i	$-0.155965\pi$
$840$	10.8931	−	7.49663i	0.375848	−	0.258658i
$841$	25.3722	+	43.9460i	0.874905	+	1.51538i
$842$	19.3059			0.665326
$843$	16.4195	−	1.30254i	0.565516	−	0.0448619i
$844$	12.0308	−	6.94601i	0.414118	−	0.239091i
$845$	5.68879	−	10.1131i	0.195700	−	0.347903i
$846$	−3.57230	+	2.90017i	−0.122818	+	0.0997100i
$847$	25.6407	+	6.87039i	0.881023	+	0.236069i
$848$	5.45144	+	3.14739i	0.187203	+	0.108082i
$849$	−5.76920	−	16.2595i	−0.197998	−	0.558024i
$850$	−1.69905	−	6.34093i	−0.0582768	−	0.217492i
$851$	−2.47885	+	9.25120i	−0.0849740	+	0.317127i
$852$	−2.57978	+	5.41730i	−0.0883817	+	0.185594i
$853$	−4.30591	+	16.0699i	−0.147431	+	0.550222i	0.852204	+	0.523210i	$0.175266\pi$
$853$	−4.30591	+	16.0699i	−0.147431	+	0.550222i	−0.999635	+	0.0270114i	$0.991401\pi$
$854$	−0.693493	−	0.400389i	−0.0237309	−	0.0137010i
$855$	8.89618	+	3.40220i	0.304243	+	0.116353i
$856$	7.84729	−	29.2865i	0.268215	−	1.00099i
$857$	−1.09346	−	1.89393i	−0.0373519	−	0.0646953i	0.846745	−	0.531999i	$-0.178559\pi$
$857$	−1.09346	−	1.89393i	−0.0373519	−	0.0646953i	−0.884097	+	0.467303i	$0.845226\pi$
$858$	−7.73013	−	2.45860i	−0.263902	−	0.0839351i
$859$	9.26248	−	16.0431i	0.316032	−	0.547383i	−0.663624	−	0.748066i	$-0.730983\pi$
$859$	9.26248	−	16.0431i	0.316032	−	0.547383i	0.979656	+	0.200683i	$0.0643160\pi$
$860$	6.81423	+	6.81423i	0.232363	+	0.232363i
$861$	15.5090	+	43.7094i	0.528545	+	1.48961i
$862$			4.65315i			0.158487i
$863$	33.1737	+	33.1737i	1.12925	+	1.12925i	0.990300	+	0.138946i	$0.0443715\pi$
$863$	33.1737	+	33.1737i	1.12925	+	1.12925i	0.138946	+	0.990300i	$0.455629\pi$
$864$	21.0097	+	22.0568i	0.714764	+	0.750389i
$865$	17.7684	−	4.76103i	0.604144	−	0.161880i
$866$	23.6321	+	6.33219i	0.803050	+	0.215177i
$867$	16.6960	+	14.2418i	0.567027	+	0.483676i
$868$			18.1312i			0.615412i
$869$	6.92439	−	6.92439i	0.234894	−	0.234894i
$870$	9.76503	−	3.46483i	0.331066	−	0.117469i
$871$	−5.66225	+	13.8893i	−0.191858	+	0.470622i
$872$			39.0419i			1.32213i
$873$	1.11771	−	10.7633i	0.0378286	−	0.364284i
$874$	9.41205	+	16.3022i	0.318367	+	0.551429i
$875$	−27.2405			−0.920898
$876$	−37.8002	+	2.99866i	−1.27715	+	0.101315i
$877$	−20.8693	−	5.59190i	−0.704705	−	0.188825i	−0.111368	−	0.993779i	$-0.535523\pi$
$877$	−20.8693	−	5.59190i	−0.704705	−	0.188825i	−0.593337	+	0.804954i	$0.702190\pi$
$878$	21.9686	+	5.88647i	0.741405	+	0.198659i
$879$	34.0188	−	2.69868i	1.14743	−	0.0910242i
$880$	−1.44814			−0.0488168
$881$	−1.99749	−	3.45976i	−0.0672973	−	0.116562i	0.830413	−	0.557148i	$-0.188104\pi$
$881$	−1.99749	−	3.45976i	−0.0672973	−	0.116562i	−0.897711	+	0.440585i	$0.854771\pi$
$882$	−7.28689	−	5.28037i	−0.245362	−	0.177799i
$883$			23.3078i			0.784371i	0.919886	+	0.392186i	$0.128281\pi$
$883$			23.3078i			0.784371i	−0.919886	+	0.392186i	$0.871719\pi$
$884$	−4.18066	−	9.93529i	−0.140611	−	0.334160i
$885$	2.87642	−	1.02061i	0.0966897	−	0.0343075i
$886$	10.3274	−	10.3274i	0.346956	−	0.346956i
$887$		−	20.4985i		−	0.688273i	−0.938920	−	0.344136i	$-0.888172\pi$
$887$		−	20.4985i		−	0.688273i	0.938920	−	0.344136i	$-0.111828\pi$
$888$	−4.61684	−	3.93818i	−0.154931	−	0.132157i
$889$	61.2109	+	16.4014i	2.05295	+	0.550086i
$890$	12.0246	−	3.22199i	0.403066	−	0.108001i
$891$	−15.5524	+	0.853961i	−0.521023	+	0.0286088i
$892$	5.82586	+	5.82586i	0.195064	+	0.195064i
$893$			7.26899i			0.243247i
$894$	3.09479	+	8.72214i	0.103505	+	0.291712i
$895$	1.47422	+	1.47422i	0.0492778	+	0.0492778i
$896$	16.2981	−	28.2292i	0.544482	−	0.943071i
$897$	32.5399	−	29.6678i	1.08648	−	0.990579i
$898$	13.4479	+	23.2924i	0.448762	+	0.777279i
$899$	−8.79584	+	32.8265i	−0.293358	+	1.09483i
$900$	−2.85638	−	17.8901i	−0.0952128	−	0.596337i
$901$	12.1002	+	6.98606i	0.403116	+	0.232739i
$902$	−2.71462	+	10.1311i	−0.0903869	+	0.337328i
$903$	18.5581	−	38.9704i	0.617576	−	1.29686i
$904$	−1.25761	+	4.69347i	−0.0418275	+	0.156102i
$905$	0.746742	+	2.78688i	0.0248225	+	0.0926390i
$906$	−3.62515	−	10.2169i	−0.120438	−	0.339433i
$907$	17.0708	+	9.85585i	0.566828	+	0.327258i	0.755881	−	0.654709i	$-0.227209\pi$
$907$	17.0708	+	9.85585i	0.566828	+	0.327258i	−0.189054	+	0.981967i	$0.560542\pi$
$908$	−3.85204	−	1.03215i	−0.127834	−	0.0342531i
$909$	5.47928	+	34.3178i	0.181736	+	1.13825i
$910$	7.93516	−	1.08992i	0.263048	−	0.0361304i
$911$	19.5647	−	11.2957i	0.648208	−	0.374243i	−0.139561	−	0.990213i	$-0.544569\pi$
$911$	19.5647	−	11.2957i	0.648208	−	0.374243i	0.787769	+	0.615970i	$0.211236\pi$
$912$	5.75763	−	0.456748i	0.190654	−	0.0151244i
$913$	−13.9198			−0.460677
$914$	−10.9075	−	18.8924i	−0.360789	−	0.624905i
$915$	0.409749	−	0.281989i	0.0135459	−	0.00932226i
$916$	−7.57983	+	7.57983i	−0.250445	+	0.250445i
$917$	−5.31926	−	19.8518i	−0.175658	−	0.655563i
$918$	5.59712	+	5.87608i	0.184732	+	0.193940i
$919$	−17.1487	+	29.7024i	−0.565682	+	0.979790i	0.431304	+	0.902207i	$0.358054\pi$
$919$	−17.1487	+	29.7024i	−0.565682	+	0.979790i	−0.996986	+	0.0775834i	$0.975280\pi$
$920$	−8.11676	+	14.0586i	−0.267602	+	0.463500i
$921$	−52.1237	−	24.8219i	−1.71753	−	0.817908i
$922$	2.97512	+	1.71769i	0.0979804	+	0.0565690i
$923$	−6.86756	+	5.33102i	−0.226048	+	0.175473i
$924$	4.77554	+	13.4590i	0.157104	+	0.442769i
$925$	1.47769	+	5.51482i	0.0485862	+	0.181326i
$926$	6.66968	−	3.85074i	0.219179	−	0.126543i
$927$	14.2534	−	2.27573i	0.468142	−	0.0747449i
$928$	37.0175	−	37.0175i	1.21516	−	1.21516i
$929$	−26.7700	−	26.7700i	−0.878296	−	0.878296i	0.115063	−	0.993358i	$-0.463293\pi$
$929$	−26.7700	−	26.7700i	−0.878296	−	0.878296i	−0.993358	+	0.115063i	$0.963293\pi$
$930$	3.98677	+	1.89854i	0.130731	+	0.0622556i
$931$	−13.7317	+	3.67941i	−0.450039	+	0.120588i
$932$	14.6563	−	8.46180i	0.480082	−	0.277175i
$933$	−8.93344	+	48.3688i	−0.292468	+	1.58352i
$934$	−12.6493	+	3.38937i	−0.413897	+	0.110903i
$935$	−3.21434			−0.105120
$936$	8.10701	+	26.6963i	0.264986	+	0.872596i
$937$	−15.2063			−0.496770			−0.248385	−	0.968661i	$-0.579900\pi$
$937$	−15.2063			−0.496770			−0.248385	+	0.968661i	$0.579900\pi$
$938$	−10.0009	+	2.67975i	−0.326542	+	0.0874968i
$939$	−31.5102	−	26.8783i	−1.02830	−	0.877140i
$940$	−2.26948	+	1.31029i	−0.0740223	+	0.0427368i
$941$	−17.9820	+	4.81825i	−0.586195	+	0.157071i	−0.539714	−	0.841849i	$-0.681468\pi$
$941$	−17.9820	+	4.81825i	−0.586195	+	0.157071i	−0.0464816	+	0.998919i	$0.514801\pi$
$942$	−1.23289	−	15.5415i	−0.0401697	−	0.506368i
$943$	−40.2604	−	40.2604i	−1.31106	−	1.31106i
$944$	1.30872	−	1.30872i	0.0425953	−	0.0425953i
$945$	13.5023	−	7.36391i	0.439231	−	0.239548i
$946$	8.45350	−	4.88063i	0.274847	−	0.158683i
$947$	8.20537	+	30.6228i	0.266639	+	0.995109i	0.961240	+	0.275714i	$0.0889142\pi$
$947$	8.20537	+	30.6228i	0.266639	+	0.995109i	−0.694601	+	0.719395i	$0.744419\pi$
$948$	−13.8462	−	2.55732i	−0.449704	−	0.0830577i
$949$	−50.8766	−	20.7408i	−1.65152	−	0.673275i
$950$	9.71804	+	5.61071i	0.315295	+	0.182036i
$951$	−2.14978	−	27.0996i	−0.0697115	−	0.878764i
$952$	8.89934	−	15.4141i	0.288429	−	0.499574i
$953$	−3.04156	+	5.26813i	−0.0985257	+	0.170651i	−0.911075	−	0.412242i	$-0.864746\pi$
$953$	−3.04156	+	5.26813i	−0.0985257	+	0.170651i	0.812549	+	0.582893i	$0.198079\pi$
$954$	−12.2423	−	8.87122i	−0.396358	−	0.287216i
$955$	5.70588	+	21.2946i	0.184638	+	0.689078i
$956$	−5.97652	+	5.97652i	−0.193294	+	0.193294i
$957$	2.11684	+	26.6843i	0.0684278	+	0.862581i
$958$	2.13769	+	3.70259i	0.0690657	+	0.119625i
$959$	−75.4263			−2.43564
$960$	−2.21296	−	3.21558i	−0.0714230	−	0.103782i
$961$	14.3040	−	8.25844i	0.461421	−	0.266401i
$962$	−1.42562	−	3.38796i	−0.0459637	−	0.109232i
$963$	12.5964	−	32.9375i	0.405915	−	1.06140i
$964$	−28.0618	−	7.51914i	−0.903810	−	0.242175i
$965$	8.55626	+	4.93996i	0.275436	+	0.159023i
$966$	29.8909	+	5.52068i	0.961724	+	0.177625i
$967$	4.30859	+	16.0799i	0.138555	+	0.517094i	0.999958	+	0.00917177i	$0.00291951\pi$
$967$	4.30859	+	16.0799i	0.138555	+	0.517094i	−0.861403	+	0.507922i	$0.830414\pi$
$968$	5.34397	−	19.9440i	0.171762	−	0.641023i
$969$	12.7798	−	1.01381i	0.410548	−	0.0325684i
$970$	−0.625408	+	2.33405i	−0.0200806	+	0.0749419i
$971$	−44.7254	−	25.8222i	−1.43531	−	0.828675i	−0.437788	−	0.899078i	$-0.644238\pi$
$971$	−44.7254	−	25.8222i	−1.43531	−	0.828675i	−0.997519	+	0.0704032i	$0.977571\pi$
$972$	13.6891	+	17.7252i	0.439077	+	0.568537i
$973$	3.66597	−	13.6816i	0.117526	−	0.438612i
$974$	−1.00727	−	1.74464i	−0.0322749	−	0.0559018i
$975$	7.95612	−	25.0150i	0.254800	−	0.801121i
$976$	0.150814	−	0.261218i	0.00482744	−	0.00836137i
$977$	−13.8335	−	13.8335i	−0.442574	−	0.442574i	0.450302	−	0.892876i	$-0.351316\pi$
$977$	−13.8335	−	13.8335i	−0.442574	−	0.442574i	−0.892876	+	0.450302i	$0.851316\pi$
$978$	−4.30464	+	5.04645i	−0.137647	+	0.161368i
$979$			32.1605i			1.02785i
$980$	−3.62400	−	3.62400i	−0.115764	−	0.115764i
$981$	−4.69019	+	45.1659i	−0.149746	+	1.44204i
$982$	−9.32022	+	2.49735i	−0.297420	+	0.0796935i
$983$	27.8597	+	7.46499i	0.888587	+	0.238096i	0.674108	−	0.738633i	$-0.264528\pi$
$983$	27.8597	+	7.46499i	0.888587	+	0.238096i	0.214479	+	0.976729i	$0.431195\pi$
$984$	33.9983	−	12.0633i	1.08383	−	0.384564i
$985$		−	0.387777i		−	0.0123556i
$986$	9.86169	−	9.86169i	0.314060	−	0.314060i
$987$	8.93015	+	7.61745i	0.284250	+	0.242466i
$988$	17.0622	+	6.95571i	0.542819	+	0.221291i
$989$			52.9891i			1.68495i
$990$	3.45949	+	0.359246i	0.109950	+	0.0114176i
$991$	−16.9576	−	29.3715i	−0.538677	−	0.933015i	−0.998976	−	0.0452515i	$-0.985591\pi$
$991$	−16.9576	−	29.3715i	−0.538677	−	0.933015i	0.460299	−	0.887764i	$-0.347742\pi$
$992$	22.3101			0.708348
$993$	13.0355	−	27.3735i	0.413670	−	0.868671i
$994$	−5.79678	−	1.55324i	−0.183863	−	0.0492659i
$995$	−8.91122	−	2.38775i	−0.282505	−	0.0756969i
$996$	11.3467	+	16.4876i	0.359535	+	0.522429i
$997$	−44.9427			−1.42335			−0.711675	−	0.702508i	$-0.752063\pi$
$997$	−44.9427			−1.42335			−0.711675	+	0.702508i	$0.752063\pi$
$998$	−14.4699	−	25.0625i	−0.458035	−	0.793341i
$999$	−4.86792	−	5.11054i	−0.154014	−	0.161690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.bc.a.41.6	yes	48
3.2	odd	2		351.2.bf.a.314.7		48
9.2	odd	6		117.2.x.a.2.6	✓	48
9.7	even	3		351.2.ba.a.197.7		48
13.7	odd	12		117.2.x.a.59.6	yes	48
39.20	even	12		351.2.ba.a.98.7		48
117.7	odd	12		351.2.bf.a.332.7		48
117.20	even	12	inner	117.2.bc.a.20.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.2.6	✓	48	9.2	odd	6
117.2.x.a.59.6	yes	48	13.7	odd	12
117.2.bc.a.20.6	yes	48	117.20	even	12	inner
117.2.bc.a.41.6	yes	48	1.1	even	1	trivial
351.2.ba.a.98.7		48	39.20	even	12
351.2.ba.a.197.7		48	9.7	even	3
351.2.bf.a.314.7		48	3.2	odd	2
351.2.bf.a.332.7		48	117.7	odd	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.724963 + 0.194253i) q^{2} +(1.63234 - 0.579188i) q^{3} +(-1.24421 + 0.718347i) q^{4} +(0.862152 - 0.231013i) q^{5} +(-1.07088 + 0.736978i) q^{6} +(2.34485 + 2.34485i) q^{7} +(1.82389 - 1.82389i) q^{8} +(2.32908 - 1.89087i) q^{9} +O(q^{10})\)	\(q+(-0.724963 + 0.194253i) q^{2} +(1.63234 - 0.579188i) q^{3} +(-1.24421 + 0.718347i) q^{4} +(0.862152 - 0.231013i) q^{5} +(-1.07088 + 0.736978i) q^{6} +(2.34485 + 2.34485i) q^{7} +(1.82389 - 1.82389i) q^{8} +(2.32908 - 1.89087i) q^{9} +(-0.580153 + 0.334952i) q^{10} +(-0.447923 - 1.67167i) q^{11} +(-1.61492 + 1.89322i) q^{12} +(-3.32332 + 1.39841i) q^{13} +(-2.15543 - 1.24444i) q^{14} +(1.27353 - 0.876441i) q^{15} +(0.468741 - 0.811883i) q^{16} +(1.04043 - 1.80208i) q^{17} +(-1.32119 + 1.82324i) q^{18} +(0.920617 + 3.43579i) q^{19} +(-0.906755 + 0.906755i) q^{20} +(5.18571 + 2.46949i) q^{21} +(0.649455 + 1.12489i) q^{22} -7.05114 q^{23} +(1.92083 - 4.03358i) q^{24} +(-3.64019 + 2.10166i) q^{25} +(2.13763 - 1.65936i) q^{26} +(2.70669 - 4.43552i) q^{27} +(-4.60192 - 1.23308i) q^{28} +(-7.73359 - 4.46499i) q^{29} +(-0.753009 + 0.882774i) q^{30} +(-0.984980 - 3.67599i) q^{31} +(-1.51729 + 5.66259i) q^{32} +(-1.69938 - 2.46931i) q^{33} +(-0.404215 + 1.50855i) q^{34} +(2.56331 + 1.47993i) q^{35} +(-1.53958 + 4.02573i) q^{36} +(0.351553 - 1.31201i) q^{37} +(-1.33483 - 2.31199i) q^{38} +(-4.61485 + 4.20752i) q^{39} +(1.15113 - 1.99381i) q^{40} +(5.70977 + 5.70977i) q^{41} +(-4.23916 - 0.782948i) q^{42} -7.51496i q^{43} +(1.75815 + 1.75815i) q^{44} +(1.57121 - 2.16826i) q^{45} +(5.11182 - 1.36971i) q^{46} +(1.97394 + 0.528917i) q^{47} +(0.294912 - 1.59676i) q^{48} +3.99667i q^{49} +(2.23075 - 2.23075i) q^{50} +(0.654598 - 3.54422i) q^{51} +(3.13037 - 4.12722i) q^{52} +6.71456i q^{53} +(-1.10064 + 3.74137i) q^{54} +(-0.772356 - 1.33776i) q^{55} +8.55349 q^{56} +(3.49273 + 5.07518i) q^{57} +(6.47390 + 1.73468i) q^{58} +(1.90697 + 0.510971i) q^{59} +(-0.954952 + 2.00532i) q^{60} +0.321743 q^{61} +(1.42815 + 2.47362i) q^{62} +(9.89516 + 1.02755i) q^{63} -2.52494i q^{64} +(-2.54215 + 1.97338i) q^{65} +(1.71166 + 1.46005i) q^{66} +(2.94157 - 2.94157i) q^{67} +2.98957i q^{68} +(-11.5099 + 4.08394i) q^{69} +(-2.14579 - 0.574962i) q^{70} +(2.32908 - 0.624075i) q^{71} +(0.799255 - 7.69671i) q^{72} +(10.7750 + 10.7750i) q^{73} +1.01945i q^{74} +(-4.72477 + 5.53899i) q^{75} +(-3.61354 - 3.61354i) q^{76} +(2.86951 - 4.97014i) q^{77} +(2.52827 - 3.94674i) q^{78} +(2.82917 + 4.90027i) q^{79} +(0.216570 - 0.808252i) q^{80} +(1.84925 - 8.80797i) q^{81} +(-5.24851 - 3.03023i) q^{82} +(2.08171 - 7.76906i) q^{83} +(-8.22609 + 0.652568i) q^{84} +(0.480707 - 1.79402i) q^{85} +(1.45981 + 5.44807i) q^{86} +(-15.2099 - 2.80919i) q^{87} +(-3.86590 - 2.23198i) q^{88} +(-17.9498 - 4.80963i) q^{89} +(-0.717876 + 1.87712i) q^{90} +(-11.0718 - 4.51362i) q^{91} +(8.77313 - 5.06517i) q^{92} +(-3.73692 - 5.42999i) q^{93} -1.53378 q^{94} +(1.58742 + 2.74950i) q^{95} +(0.802975 + 10.1221i) q^{96} +(2.55059 - 2.55059i) q^{97} +(-0.776366 - 2.89744i) q^{98} +(-4.20416 - 3.04650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Introduction

L-functions

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