LMFDB - Embedded newform 117.2.x.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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, 1]))

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

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

chi := DirichletCharacter("117.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.x (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			11.7
Character	$\chi$	$=$	117.11
Dual form			117.2.x.a.32.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.286505 - 0.286505i) q^{2} +(-1.72577 - 0.147373i) q^{3} +1.83583i q^{4} +(2.00620 + 0.537559i) q^{5} +(-0.536665 + 0.452219i) q^{6} +(1.90533 + 0.510531i) q^{7} +(1.09899 + 1.09899i) q^{8} +(2.95656 + 0.508664i) q^{9} +O(q^{10})$	\(q+(0.286505 - 0.286505i) q^{2} +(-1.72577 - 0.147373i) q^{3} +1.83583i q^{4} +(2.00620 + 0.537559i) q^{5} +(-0.536665 + 0.452219i) q^{6} +(1.90533 + 0.510531i) q^{7} +(1.09899 + 1.09899i) q^{8} +(2.95656 + 0.508664i) q^{9} +(0.728800 - 0.420773i) q^{10} +(-1.96889 - 1.96889i) q^{11} +(0.270552 - 3.16822i) q^{12} +(-0.908720 + 3.48916i) q^{13} +(0.692156 - 0.399616i) q^{14} +(-3.38301 - 1.22336i) q^{15} -3.04193 q^{16} +(2.88941 - 5.00460i) q^{17} +(0.992806 - 0.701336i) q^{18} +(-4.00984 + 1.07443i) q^{19} +(-0.986867 + 3.68304i) q^{20} +(-3.21292 - 1.16185i) q^{21} -1.12819 q^{22} +(1.46551 - 2.53833i) q^{23} +(-1.73463 - 2.05856i) q^{24} +(-0.594268 - 0.343101i) q^{25} +(0.739309 + 1.26002i) q^{26} +(-5.02738 - 1.31356i) q^{27} +(-0.937247 + 3.49785i) q^{28} -0.0272596i q^{29} +(-1.31975 + 0.618751i) q^{30} +(1.20440 - 4.49489i) q^{31} +(-3.06950 + 3.06950i) q^{32} +(3.10768 + 3.68801i) q^{33} +(-0.606014 - 2.26167i) q^{34} +(3.54802 + 2.04845i) q^{35} +(-0.933821 + 5.42774i) q^{36} +(6.63559 + 1.77800i) q^{37} +(-0.841010 + 1.45667i) q^{38} +(2.08245 - 5.88756i) q^{39} +(1.61401 + 2.79555i) q^{40} +(-2.43331 - 9.08122i) q^{41} +(-1.25339 + 0.587640i) q^{42} +(5.43197 - 3.13615i) q^{43} +(3.61454 - 3.61454i) q^{44} +(5.65801 + 2.60981i) q^{45} +(-0.307370 - 1.14712i) q^{46} +(-4.26664 + 1.14324i) q^{47} +(5.24967 + 0.448299i) q^{48} +(-2.69255 - 1.55455i) q^{49} +(-0.268561 + 0.0719608i) q^{50} +(-5.72399 + 8.21096i) q^{51} +(-6.40550 - 1.66825i) q^{52} +8.65927i q^{53} +(-1.81671 + 1.06403i) q^{54} +(-2.89158 - 5.00837i) q^{55} +(1.53286 + 2.65499i) q^{56} +(7.07840 - 1.26328i) q^{57} +(-0.00781003 - 0.00781003i) q^{58} +(-9.73507 - 9.73507i) q^{59} +(2.24589 - 6.21064i) q^{60} +(4.64093 + 8.03833i) q^{61} +(-0.942743 - 1.63288i) q^{62} +(5.37353 + 2.47859i) q^{63} -4.32500i q^{64} +(-3.69870 + 6.51145i) q^{65} +(1.94700 + 0.166265i) q^{66} +(6.40101 - 1.71515i) q^{67} +(9.18759 + 5.30446i) q^{68} +(-2.90321 + 4.16460i) q^{69} +(1.60342 - 0.429635i) q^{70} +(2.46714 + 9.20749i) q^{71} +(2.69020 + 3.80823i) q^{72} +(0.696641 - 0.696641i) q^{73} +(2.41054 - 1.39172i) q^{74} +(0.975006 + 0.679692i) q^{75} +(-1.97248 - 7.36138i) q^{76} +(-2.74619 - 4.75655i) q^{77} +(-1.09019 - 2.28345i) q^{78} +(-6.46914 + 11.2049i) q^{79} +(-6.10271 - 1.63522i) q^{80} +(8.48252 + 3.00780i) q^{81} +(-3.29897 - 1.90466i) q^{82} +(0.860748 + 3.21235i) q^{83} +(2.13296 - 5.89836i) q^{84} +(8.48699 - 8.48699i) q^{85} +(0.657764 - 2.45481i) q^{86} +(-0.00401734 + 0.0470438i) q^{87} -4.32756i q^{88} +(-0.569878 + 2.12681i) q^{89} +(2.36877 - 0.873326i) q^{90} +(-3.51273 + 6.18406i) q^{91} +(4.65995 + 2.69042i) q^{92} +(-2.74095 + 7.57966i) q^{93} +(-0.894869 + 1.54996i) q^{94} -8.62210 q^{95} +(5.74961 - 4.84489i) q^{96} +(3.16527 - 11.8130i) q^{97} +(-1.21682 + 0.326045i) q^{98} +(-4.81963 - 6.82264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.286505	−	0.286505i	0.202590	−	0.202590i	−0.598519	−	0.801109i	$-0.704244\pi$
$2$	0.286505	−	0.286505i	0.202590	−	0.202590i	0.801109	+	0.598519i	$0.204244\pi$
$3$	−1.72577	−	0.147373i	−0.996374	−	0.0850859i
$3$	−1.72577	−	0.147373i	−0.996374	−	0.0850859i
$4$			1.83583i			0.917915i
$5$	2.00620	+	0.537559i	0.897199	+	0.240404i	0.677813	−	0.735234i	$-0.262928\pi$
$5$	2.00620	+	0.537559i	0.897199	+	0.240404i	0.219386	+	0.975638i	$0.429595\pi$
$6$	−0.536665	+	0.452219i	−0.219093	+	0.184618i
$7$	1.90533	+	0.510531i	0.720145	+	0.192962i	0.600237	−	0.799823i	$-0.295073\pi$
$7$	1.90533	+	0.510531i	0.720145	+	0.192962i	0.119909	+	0.992785i	$0.461740\pi$
$8$	1.09899	+	1.09899i	0.388550	+	0.388550i
$9$	2.95656	+	0.508664i	0.985521	+	0.169555i
$10$	0.728800	−	0.420773i	0.230467	−	0.133060i
$11$	−1.96889	−	1.96889i	−0.593642	−	0.593642i	0.344971	−	0.938613i	$-0.387889\pi$
$11$	−1.96889	−	1.96889i	−0.593642	−	0.593642i	−0.938613	+	0.344971i	$0.887889\pi$
$12$	0.270552	−	3.16822i	0.0781016	−	0.914586i
$13$	−0.908720	+	3.48916i	−0.252033	+	0.967719i
$13$	−0.908720	+	3.48916i	−0.252033	+	0.967719i
$14$	0.692156	−	0.399616i	0.184986	−	0.106802i
$15$	−3.38301	−	1.22336i	−0.873490	−	0.315871i
$16$	−3.04193			−0.760482
$17$	2.88941	−	5.00460i	0.700784	−	1.21379i	−0.267408	−	0.963583i	$-0.586167\pi$
$17$	2.88941	−	5.00460i	0.700784	−	1.21379i	0.968192	−	0.250210i	$-0.0804996\pi$
$18$	0.992806	−	0.701336i	0.234007	−	0.165306i
$19$	−4.00984	+	1.07443i	−0.919920	+	0.246492i	−0.687551	−	0.726136i	$-0.741314\pi$
$19$	−4.00984	+	1.07443i	−0.919920	+	0.246492i	−0.232369	+	0.972628i	$0.574648\pi$
$20$	−0.986867	+	3.68304i	−0.220670	+	0.823552i
$21$	−3.21292	−	1.16185i	−0.701116	−	0.253537i
$22$	−1.12819			−0.240532
$23$	1.46551	−	2.53833i	0.305580	−	0.529279i	−0.671811	−	0.740723i	$-0.734483\pi$
$23$	1.46551	−	2.53833i	0.305580	−	0.529279i	0.977390	+	0.211444i	$0.0678165\pi$
$24$	−1.73463	−	2.05856i	−0.354081	−	0.420201i
$25$	−0.594268	−	0.343101i	−0.118854	−	0.0686202i
$26$	0.739309	+	1.26002i	0.144991	+	0.247109i
$27$	−5.02738	−	1.31356i	−0.967520	−	0.252794i
$28$	−0.937247	+	3.49785i	−0.177123	+	0.661032i
$29$		−	0.0272596i		−	0.00506199i	−0.999997	−	0.00253099i	$-0.999194\pi$
$29$		−	0.0272596i		−	0.00506199i	0.999997	−	0.00253099i	$-0.000805641\pi$
$30$	−1.31975	+	0.618751i	−0.240952	+	0.112968i
$31$	1.20440	−	4.49489i	0.216317	−	0.807307i	−0.769381	−	0.638790i	$-0.779435\pi$
$31$	1.20440	−	4.49489i	0.216317	−	0.807307i	0.985699	−	0.168517i	$-0.0538979\pi$
$32$	−3.06950	+	3.06950i	−0.542616	+	0.542616i
$33$	3.10768	+	3.68801i	0.540978	+	0.641999i
$34$	−0.606014	−	2.26167i	−0.103930	−	0.387874i
$35$	3.54802	+	2.04845i	0.599725	+	0.346251i
$36$	−0.933821	+	5.42774i	−0.155637	+	0.904624i
$37$	6.63559	+	1.77800i	1.09088	+	0.292302i	0.759047	−	0.651035i	$-0.225665\pi$
$37$	6.63559	+	1.77800i	1.09088	+	0.292302i	0.331837	+	0.943337i	$0.392332\pi$
$38$	−0.841010	+	1.45667i	−0.136430	+	0.236303i
$39$	2.08245	−	5.88756i	0.333459	−	0.942765i
$40$	1.61401	+	2.79555i	0.255198	+	0.442016i
$41$	−2.43331	−	9.08122i	−0.380018	−	1.41825i	−0.845872	−	0.533386i	$-0.820919\pi$
$41$	−2.43331	−	9.08122i	−0.380018	−	1.41825i	0.465854	−	0.884862i	$-0.345747\pi$
$42$	−1.25339	+	0.587640i	−0.193403	+	0.0906749i
$43$	5.43197	−	3.13615i	0.828367	−	0.478258i	−0.0249260	−	0.999689i	$-0.507935\pi$
$43$	5.43197	−	3.13615i	0.828367	−	0.478258i	0.853293	+	0.521431i	$0.174602\pi$
$44$	3.61454	−	3.61454i	0.544912	−	0.544912i
$45$	5.65801	+	2.60981i	0.843446	+	0.389047i
$46$	−0.307370	−	1.14712i	−0.0453193	−	0.169134i
$47$	−4.26664	+	1.14324i	−0.622353	+	0.166759i	−0.556197	−	0.831050i	$-0.687740\pi$
$47$	−4.26664	+	1.14324i	−0.622353	+	0.166759i	−0.0661557	+	0.997809i	$0.521073\pi$
$48$	5.24967	+	0.448299i	0.757724	+	0.0647063i
$49$	−2.69255	−	1.55455i	−0.384650	−	0.222078i
$50$	−0.268561	+	0.0719608i	−0.0379803	+	0.0101768i
$51$	−5.72399	+	8.21096i	−0.801519	+	1.14976i
$52$	−6.40550	−	1.66825i	−0.888283	−	0.231345i
$53$			8.65927i			1.18944i	0.803932	+	0.594721i	$0.202737\pi$
$53$			8.65927i			1.18944i	−0.803932	+	0.594721i	$0.797263\pi$
$54$	−1.81671	+	1.06403i	−0.247223	+	0.144796i
$55$	−2.89158	−	5.00837i	−0.389901	−	0.675328i
$56$	1.53286	+	2.65499i	0.204837	+	0.354788i
$57$	7.07840	−	1.26328i	0.937557	−	0.167326i
$58$	−0.00781003	−	0.00781003i	−0.00102551	−	0.00102551i
$59$	−9.73507	−	9.73507i	−1.26740	−	1.26740i	−0.947427	−	0.319971i	$-0.896327\pi$
$59$	−9.73507	−	9.73507i	−1.26740	−	1.26740i	−0.319971	−	0.947427i	$-0.603673\pi$
$60$	2.24589	−	6.21064i	0.289943	−	0.801790i
$61$	4.64093	+	8.03833i	0.594211	+	1.02920i	0.993658	+	0.112447i	$0.0358688\pi$
$61$	4.64093	+	8.03833i	0.594211	+	1.02920i	−0.399447	+	0.916756i	$0.630798\pi$
$62$	−0.942743	−	1.63288i	−0.119729	−	0.207376i
$63$	5.37353	+	2.47859i	0.677001	+	0.312273i
$64$		−	4.32500i		−	0.540625i
$65$	−3.69870	+	6.51145i	−0.458767	+	0.807646i
$66$	1.94700	+	0.166265i	0.239659	+	0.0204659i
$67$	6.40101	−	1.71515i	0.782008	−	0.209538i	0.154338	−	0.988018i	$-0.450675\pi$
$67$	6.40101	−	1.71515i	0.782008	−	0.209538i	0.627670	+	0.778480i	$0.284009\pi$
$68$	9.18759	+	5.30446i	1.11416	+	0.643260i
$69$	−2.90321	+	4.16460i	−0.349506	+	0.501359i
$70$	1.60342	−	0.429635i	0.191645	−	0.0513512i
$71$	2.46714	+	9.20749i	0.292795	+	1.09273i	0.942952	+	0.332928i	$0.108036\pi$
$71$	2.46714	+	9.20749i	0.292795	+	1.09273i	−0.650157	+	0.759800i	$0.725297\pi$
$72$	2.69020	+	3.80823i	0.317044	+	0.448805i
$73$	0.696641	−	0.696641i	0.0815356	−	0.0815356i	−0.665163	−	0.746698i	$-0.731638\pi$
$73$	0.696641	−	0.696641i	0.0815356	−	0.0815356i	0.746698	+	0.665163i	$0.231638\pi$
$74$	2.41054	−	1.39172i	0.280219	−	0.161785i
$75$	0.975006	+	0.679692i	0.112584	+	0.0784841i
$76$	−1.97248	−	7.36138i	−0.226259	−	0.844408i
$77$	−2.74619	−	4.75655i	−0.312958	−	0.542059i
$78$	−1.09019	−	2.28345i	−0.123439	−	0.258550i
$79$	−6.46914	+	11.2049i	−0.727835	+	1.26065i	0.229962	+	0.973200i	$0.426140\pi$
$79$	−6.46914	+	11.2049i	−0.727835	+	1.26065i	−0.957796	+	0.287447i	$0.907193\pi$
$80$	−6.10271	−	1.63522i	−0.682304	−	0.182823i
$81$	8.48252	+	3.00780i	0.942502	+	0.334199i
$82$	−3.29897	−	1.90466i	−0.364311	−	0.210335i
$83$	0.860748	+	3.21235i	0.0944793	+	0.352602i	0.996940	−	0.0781706i	$-0.0249079\pi$
$83$	0.860748	+	3.21235i	0.0944793	+	0.352602i	−0.902461	+	0.430772i	$0.858241\pi$
$84$	2.13296	−	5.89836i	0.232725	−	0.643564i
$85$	8.48699	−	8.48699i	0.920543	−	0.920543i
$86$	0.657764	−	2.45481i	0.0709286	−	0.264709i
$87$	−0.00401734	+	0.0470438i	−0.000430704	+	0.00504363i
$88$		−	4.32756i		−	0.461319i
$89$	−0.569878	+	2.12681i	−0.0604069	+	0.225442i	−0.989530	−	0.144330i	$-0.953897\pi$
$89$	−0.569878	+	2.12681i	−0.0604069	+	0.225442i	0.929123	+	0.369771i	$0.120564\pi$
$90$	2.36877	−	0.873326i	0.249691	−	0.0920567i
$91$	−3.51273	+	6.18406i	−0.368234	+	0.648265i
$92$	4.65995	+	2.69042i	0.485833	+	0.280496i
$93$	−2.74095	+	7.57966i	−0.284223	+	0.785974i
$94$	−0.894869	+	1.54996i	−0.0922987	+	0.159866i
$95$	−8.62210			−0.884609
$96$	5.74961	−	4.84489i	0.586817	−	0.494479i
$97$	3.16527	−	11.8130i	0.321385	−	1.19942i	−0.596512	−	0.802605i	$-0.703447\pi$
$97$	3.16527	−	11.8130i	0.321385	−	1.19942i	0.917896	−	0.396820i	$-0.129886\pi$
$98$	−1.21682	+	0.326045i	−0.122917	+	0.0329355i
$99$	−4.81963	−	6.82264i	−0.484391	−	0.685701i
$100$	0.629875	−	1.09098i	0.0629875	−	0.109098i
$101$	−11.7061			−1.16480			−0.582401	−	0.812901i	$-0.697887\pi$
$101$	−11.7061			−1.16480			−0.582401	+	0.812901i	$0.697887\pi$
$102$	0.712530	+	3.99244i	0.0705510	+	0.395310i
$103$	−6.99746	+	4.03998i	−0.689480	+	0.398071i	−0.803417	−	0.595417i	$-0.796987\pi$
$103$	−6.99746	+	4.03998i	−0.689480	+	0.398071i	0.113937	+	0.993488i	$0.463654\pi$
$104$	−4.83320	+	2.83587i	−0.473935	+	0.278079i
$105$	−5.82118	−	4.05804i	−0.568089	−	0.396024i
$106$	2.48093	+	2.48093i	0.240969	+	0.240969i
$107$	−3.06247	+	1.76812i	−0.296060	+	0.170930i	−0.640672	−	0.767815i	$-0.721344\pi$
$107$	−3.06247	+	1.76812i	−0.296060	+	0.170930i	0.344612	+	0.938745i	$0.388011\pi$
$108$	2.41146	−	9.22942i	0.232043	−	0.888101i
$109$	−3.56699	−	3.56699i	−0.341656	−	0.341656i	0.515334	−	0.856990i	$-0.327668\pi$
$109$	−3.56699	−	3.56699i	−0.341656	−	0.341656i	−0.856990	+	0.515334i	$0.827668\pi$
$110$	−2.26338	−	0.606470i	−0.215805	−	0.0578247i
$111$	−11.1895	−	4.04633i	−1.06206	−	0.384060i
$112$	−5.79586	−	1.55300i	−0.547658	−	0.146744i
$113$			14.6710i			1.38014i	0.723745	+	0.690068i	$0.242419\pi$
$113$			14.6710i			1.38014i	−0.723745	+	0.690068i	$0.757581\pi$
$114$	1.66606	−	2.38994i	0.156041	−	0.223838i
$115$	4.30460	−	4.30460i	0.401406	−	0.401406i
$116$	0.0500440			0.00464647
$117$	−4.46150	+	9.85368i	−0.412466	+	0.910973i
$118$	−5.57830			−0.513524
$119$	8.06026	−	8.06026i	0.738883	−	0.738883i
$120$	−2.37342	−	5.06234i	−0.216663	−	0.462126i
$121$		−	3.24697i		−	0.295179i
$122$	3.63268	+	0.973373i	0.328887	+	0.0881250i
$123$	2.86100	+	16.0307i	0.257967	+	1.44544i
$124$	8.25186	+	2.21108i	0.741039	+	0.198561i
$125$	−8.35097	−	8.35097i	−0.746934	−	0.746934i
$126$	2.24967	−	0.829416i	0.200417	−	0.0738902i
$127$	7.25477	−	4.18854i	0.643757	−	0.371673i	−0.142303	−	0.989823i	$-0.545451\pi$
$127$	7.25477	−	4.18854i	0.643757	−	0.371673i	0.786060	+	0.618150i	$0.212118\pi$
$128$	−7.37814	−	7.37814i	−0.652141	−	0.652141i
$129$	−9.83651	+	4.61174i	−0.866056	+	0.406041i
$130$	0.805868	+	2.92526i	0.0706793	+	0.256562i
$131$	16.8917	−	9.75243i	1.47583	−	0.852074i	0.476206	−	0.879333i	$-0.342011\pi$
$131$	16.8917	−	9.75243i	1.47583	−	0.852074i	0.999628	+	0.0272599i	$0.00867816\pi$
$132$	−6.77055	+	5.70518i	−0.589301	+	0.496572i
$133$	−8.18858			−0.710040
$134$	1.34253	−	2.32532i	0.115977	−	0.200877i
$135$	−9.37981	−	5.33777i	−0.807285	−	0.459402i
$136$	8.67540	−	2.32457i	0.743909	−	0.199330i
$137$	1.07858	−	4.02530i	0.0921489	−	0.343904i	−0.904423	−	0.426637i	$-0.859698\pi$
$137$	1.07858	−	4.02530i	0.0921489	−	0.343904i	0.996572	+	0.0827328i	$0.0263648\pi$
$138$	0.361396	+	2.02497i	0.0307640	+	0.172377i
$139$	−5.14086			−0.436042			−0.218021	−	0.975944i	$-0.569960\pi$
$139$	−5.14086			−0.436042			−0.218021	+	0.975944i	$0.569960\pi$
$140$	−3.76060	+	6.51356i	−0.317829	+	0.550496i
$141$	7.53171	−	1.34418i	0.634285	−	0.113201i
$142$	3.34484	+	1.93115i	0.280693	+	0.162058i
$143$	8.65892	−	5.08059i	0.724096	−	0.424860i
$144$	−8.99365	−	1.54732i	−0.749471	−	0.128943i
$145$	0.0146537	−	0.0546882i	0.00121692	−	0.00454161i
$146$		−	0.399182i		−	0.0330366i
$147$	4.41763	+	3.07960i	0.364360	+	0.254001i
$148$	−3.26411	+	12.1818i	−0.268308	+	1.00134i
$149$	0.439177	−	0.439177i	0.0359788	−	0.0359788i	−0.688889	−	0.724867i	$-0.741901\pi$
$149$	0.439177	−	0.439177i	0.0359788	−	0.0359788i	0.724867	+	0.688889i	$0.241901\pi$
$150$	0.474080	−	0.0846090i	0.0387085	−	0.00690830i
$151$	2.54617	+	9.50243i	0.207204	+	0.773297i	0.988766	+	0.149469i	$0.0477566\pi$
$151$	2.54617	+	9.50243i	0.207204	+	0.773297i	−0.781562	+	0.623828i	$0.785577\pi$
$152$	−5.58754	−	3.22597i	−0.453210	−	0.261661i
$153$	11.0884	−	13.3267i	0.896441	−	1.07740i
$154$	−2.14958	−	0.575977i	−0.173218	−	0.0464135i
$155$	4.83254	−	8.37021i	0.388159	−	0.672311i
$156$	10.8086	+	3.82302i	0.865378	+	0.306087i
$157$	8.36636	+	14.4910i	0.667708	+	1.15650i	0.978543	+	0.206040i	$0.0660579\pi$
$157$	8.36636	+	14.4910i	0.667708	+	1.15650i	−0.310835	+	0.950464i	$0.600609\pi$
$158$	1.35681	+	5.06370i	0.107942	+	0.402846i
$159$	1.27614	−	14.9439i	0.101205	−	1.18513i
$160$	−7.80806	+	4.50799i	−0.617281	+	0.356388i
$161$	4.08817	−	4.08817i	0.322193	−	0.322193i
$162$	3.29204	−	1.56854i	0.258647	−	0.123236i
$163$	3.83636	+	14.3175i	0.300487	+	1.12143i	0.936761	+	0.349970i	$0.113808\pi$
$163$	3.83636	+	14.3175i	0.300487	+	1.12143i	−0.636274	+	0.771463i	$0.719525\pi$
$164$	16.6716	−	4.46713i	1.30183	−	0.348824i
$165$	4.25211	+	9.06943i	0.331026	+	0.706054i
$166$	1.16697	+	0.673748i	0.0905741	+	0.0522930i
$167$	1.91163	−	0.512220i	0.147926	−	0.0396368i	−0.184096	−	0.982908i	$-0.558936\pi$
$167$	1.91163	−	0.512220i	0.147926	−	0.0396368i	0.332022	+	0.943272i	$0.392269\pi$
$168$	−2.25409	−	4.80781i	−0.173907	−	0.370930i
$169$	−11.3485	−	6.34133i	−0.872958	−	0.487795i
$170$		−	4.86313i		−	0.372985i
$171$	−12.4019	+	1.13697i	−0.948394	+	0.0869460i
$172$	5.75743	+	9.97217i	0.439000	+	0.760370i
$173$	6.43009	+	11.1372i	0.488871	+	0.846749i	0.999918	−	0.0128037i	$-0.00407567\pi$
$173$	6.43009	+	11.1372i	0.488871	+	0.846749i	−0.511047	+	0.859553i	$0.670742\pi$
$174$	0.0123273	+	0.0146293i	0.000934532	+	0.00110904i
$175$	−0.957111	−	0.957111i	−0.0723508	−	0.0723508i
$176$	5.98921	+	5.98921i	0.451454	+	0.451454i
$177$	15.3658	+	18.2352i	1.15496	+	1.37064i
$178$	0.446070	+	0.772616i	0.0334344	+	0.0579100i
$179$	8.57752	+	14.8567i	0.641114	+	1.11044i	0.985184	+	0.171498i	$0.0548607\pi$
$179$	8.57752	+	14.8567i	0.641114	+	1.11044i	−0.344071	+	0.938944i	$0.611806\pi$
$180$	−4.79116	+	10.3871i	−0.357112	+	0.774212i
$181$			2.95175i			0.219402i	0.993965	+	0.109701i	$0.0349893\pi$
$181$			2.95175i			0.219402i	−0.993965	+	0.109701i	$0.965011\pi$
$182$	0.765349	+	2.77818i	0.0567314	+	0.205932i
$183$	−6.82455	−	14.5563i	−0.504485	−	1.07603i
$184$	4.40017	−	1.17902i	0.324384	−	0.0869186i
$185$	12.3565	+	7.13404i	0.908470	+	0.524505i
$186$	1.38632	+	2.95691i	0.101650	+	0.216811i
$187$	−15.5424	+	4.16457i	−1.13657	+	0.304544i
$188$	−2.09880	−	7.83282i	−0.153070	−	0.571267i
$189$	−8.90819	−	5.06938i	−0.647976	−	0.368743i
$190$	−2.47028	+	2.47028i	−0.179213	+	0.179213i
$191$	3.48168	−	2.01015i	0.251926	−	0.145449i	−0.368720	−	0.929541i	$-0.620204\pi$
$191$	3.48168	−	2.01015i	0.251926	−	0.145449i	0.620646	+	0.784091i	$0.286871\pi$
$192$	−0.637389	+	7.46396i	−0.0459996	+	0.538665i
$193$	−4.10567	−	15.3226i	−0.295533	−	1.10294i	−0.940793	−	0.338981i	$-0.889918\pi$
$193$	−4.10567	−	15.3226i	−0.295533	−	1.10294i	0.645260	−	0.763963i	$-0.276749\pi$
$194$	−2.47761	−	4.29134i	−0.177882	−	0.308101i
$195$	7.34272	−	10.6922i	0.525823	−	0.765683i
$196$	2.85388	−	4.94307i	0.203849	−	0.353076i
$197$	−14.8985	−	3.99204i	−1.06148	−	0.284421i	−0.314489	−	0.949261i	$-0.601833\pi$
$197$	−14.8985	−	3.99204i	−1.06148	−	0.284421i	−0.746986	+	0.664840i	$0.768500\pi$
$198$	−3.33557	−	0.573871i	−0.237049	−	0.0407833i
$199$	10.6715	+	6.16118i	0.756481	+	0.436755i	0.828031	−	0.560682i	$-0.189461\pi$
$199$	10.6715	+	6.16118i	0.756481	+	0.436755i	−0.0715498	+	0.997437i	$0.522794\pi$
$200$	−0.276029	−	1.03016i	−0.0195182	−	0.0728430i
$201$	−11.2994	+	2.01661i	−0.797001	+	0.142241i
$202$	−3.35387	+	3.35387i	−0.235977	+	0.235977i
$203$	0.0139169	−	0.0519385i	0.000976773	−	0.00364537i
$204$	−15.0739	−	10.5083i	−1.05539	−	0.735726i
$205$		−	19.5268i		−	1.36381i
$206$	−0.847332	+	3.16229i	−0.0590364	+	0.220327i
$207$	5.62403	−	6.75929i	0.390897	−	0.469803i
$208$	2.76426	−	10.6138i	0.191667	−	0.735933i
$209$	10.0104	+	5.77948i	0.692431	+	0.399775i
$210$	−2.83045	+	0.505150i	−0.195319	+	0.0348586i
$211$	−11.4740	+	19.8736i	−0.789903	+	1.36815i	0.136122	+	0.990692i	$0.456536\pi$
$211$	−11.4740	+	19.8736i	−0.789903	+	1.36815i	−0.926026	+	0.377461i	$0.876797\pi$
$212$	−15.8969			−1.09181
$213$	−2.90078	−	16.2536i	−0.198758	−	1.11368i
$214$	−0.370839	+	1.38399i	−0.0253500	+	0.0946075i
$215$	12.5835	−	3.37173i	0.858185	−	0.229950i
$216$	−4.08144	−	6.96860i	−0.277707	−	0.474153i
$217$	4.58956	−	7.94935i	0.311560	−	0.539637i
$218$	−2.04392			−0.138432
$219$	−1.30491	+	1.09958i	−0.0881775	+	0.0743024i
$220$	9.19451	−	5.30845i	0.619894	−	0.357896i
$221$	14.8362	+	14.6294i	0.997989	+	0.984078i
$222$	−4.36514	+	2.04655i	−0.292969	+	0.137355i
$223$	14.8498	+	14.8498i	0.994414	+	0.994414i	0.999984	−	0.00557092i	$-0.00177329\pi$
$223$	14.8498	+	14.8498i	0.994414	+	0.994414i	−0.00557092	+	0.999984i	$0.501773\pi$
$224$	−7.41547	+	4.28132i	−0.495467	+	0.286058i
$225$	−1.58247	−	1.31668i	−0.105498	−	0.0877788i
$226$	4.20333	+	4.20333i	0.279601	+	0.279601i
$227$	−27.7434	−	7.43381i	−1.84139	−	0.493399i	−0.842424	−	0.538816i	$-0.818872\pi$
$227$	−27.7434	−	7.43381i	−1.84139	−	0.493399i	−0.998968	+	0.0454160i	$0.985539\pi$
$228$	2.31917	+	12.9947i	0.153591	+	0.860598i
$229$	7.21566	+	1.93343i	0.476824	+	0.127765i	0.489223	−	0.872159i	$-0.337280\pi$
$229$	7.21566	+	1.93343i	0.476824	+	0.127765i	−0.0123994	+	0.999923i	$0.503947\pi$
$230$		−	2.46658i		−	0.162642i
$231$	4.03831	+	8.61342i	0.265701	+	0.566721i
$232$	0.0299579	−	0.0299579i	0.00196683	−	0.00196683i
$233$	6.28380			0.411666			0.205833	−	0.978587i	$-0.434010\pi$
$233$	6.28380			0.411666			0.205833	+	0.978587i	$0.434010\pi$
$234$	1.54489	+	4.10137i	0.100993	+	0.268115i
$235$	−9.17428			−0.598464
$236$	17.8719	−	17.8719i	1.16336	−	1.16336i
$237$	12.8155	−	18.3837i	0.832459	−	1.19415i
$238$		−	4.61861i		−	0.299380i
$239$	4.67278	+	1.25207i	0.302257	+	0.0809894i	0.406760	−	0.913535i	$-0.366659\pi$
$239$	4.67278	+	1.25207i	0.302257	+	0.0809894i	−0.104503	+	0.994525i	$0.533325\pi$
$240$	10.2909	+	3.72138i	0.664274	+	0.240214i
$241$	−9.07485	−	2.43160i	−0.584563	−	0.156633i	−0.0455956	−	0.998960i	$-0.514519\pi$
$241$	−9.07485	−	2.43160i	−0.584563	−	0.156633i	−0.538967	+	0.842327i	$0.681185\pi$
$242$	−0.930274	−	0.930274i	−0.0598003	−	0.0598003i
$243$	−14.1956	−	6.44086i	−0.910649	−	0.413181i
$244$	−14.7570	+	8.51996i	−0.944721	+	0.545435i
$245$	−4.56613	−	4.56613i	−0.291720	−	0.291720i
$246$	5.41257	+	3.77319i	0.345093	+	0.240570i
$247$	−0.105048	−	14.9673i	−0.00668404	−	0.952348i
$248$	6.26345	−	3.61620i	0.397729	−	0.229629i
$249$	−1.01204	−	5.67063i	−0.0641353	−	0.359362i
$250$	−4.78520			−0.302642
$251$	1.72591	−	2.98936i	0.108938	−	0.188687i	−0.806402	−	0.591368i	$-0.798588\pi$
$251$	1.72591	−	2.98936i	0.108938	−	0.188687i	0.915340	+	0.402681i	$0.131922\pi$
$252$	−4.55026	+	9.86488i	−0.286640	+	0.621429i
$253$	−7.88311	+	2.11227i	−0.495607	+	0.132798i
$254$	0.878490	−	3.27857i	0.0551214	−	0.205716i
$255$	−15.8973	+	13.3958i	−0.995530	+	0.838879i
$256$	4.42225			0.276391
$257$	−7.37423	+	12.7725i	−0.459992	+	0.796730i	−0.998960	−	0.0455966i	$-0.985481\pi$
$257$	−7.37423	+	12.7725i	−0.459992	+	0.796730i	0.538968	+	0.842326i	$0.318814\pi$
$258$	−1.49692	+	4.13950i	−0.0931944	+	0.257714i
$259$	11.7352	+	6.77534i	0.729192	+	0.420999i
$260$	−11.9539	−	6.79018i	−0.741350	−	0.421109i
$261$	0.0138660	−	0.0805948i	0.000858284	−	0.00498869i
$262$	2.04544	−	7.63368i	0.126368	−	0.471611i
$263$		−	10.9010i		−	0.672187i	−0.941829	−	0.336094i	$-0.890894\pi$
$263$		−	10.9010i		−	0.672187i	0.941829	−	0.336094i	$-0.109106\pi$
$264$	−0.637766	+	7.46836i	−0.0392518	+	0.459646i
$265$	−4.65487	+	17.3722i	−0.285946	+	1.06717i
$266$	−2.34607	+	2.34607i	−0.143847	+	0.143847i
$267$	1.29691	−	3.58640i	0.0793697	−	0.219484i
$268$	3.14872	+	11.7512i	0.192338	+	0.717817i
$269$	−26.4194	−	15.2532i	−1.61082	−	0.930006i	−0.989181	−	0.146701i	$-0.953135\pi$
$269$	−26.4194	−	15.2532i	−1.61082	−	0.930006i	−0.621637	−	0.783306i	$-0.713532\pi$
$270$	−4.21666	+	1.15807i	−0.256618	+	0.0704777i
$271$	−0.434695	−	0.116476i	−0.0264059	−	0.00707543i	0.245592	−	0.969373i	$-0.421018\pi$
$271$	−0.434695	−	0.116476i	−0.0264059	−	0.00707543i	−0.271998	+	0.962298i	$0.587684\pi$
$272$	−8.78937	+	15.2236i	−0.532934	+	0.923068i
$273$	6.97353	−	10.1546i	0.422057	−	0.614583i
$274$	−0.844251	−	1.46229i	−0.0510031	−	0.0883400i
$275$	0.494520	+	1.84557i	0.0298207	+	0.111292i
$276$	−7.64550	−	5.32980i	−0.460205	−	0.320816i
$277$	19.2306	−	11.1028i	1.15545	−	0.667102i	0.205244	−	0.978711i	$-0.434201\pi$
$277$	19.2306	−	11.1028i	1.15545	−	0.667102i	0.950211	+	0.311609i	$0.100868\pi$
$278$	−1.47289	+	1.47289i	−0.0883378	+	0.0883378i
$279$	5.84729	−	12.6768i	0.350068	−	0.758940i
$280$	1.64801	+	6.15044i	0.0984871	+	0.367559i
$281$	−14.4025	+	3.85914i	−0.859182	+	0.230217i	−0.661404	−	0.750030i	$-0.730039\pi$
$281$	−14.4025	+	3.85914i	−0.859182	+	0.230217i	−0.197778	+	0.980247i	$0.563372\pi$
$282$	1.77276	−	2.54299i	0.105566	−	0.151433i
$283$	−11.3008	−	6.52451i	−0.671762	−	0.387842i	0.124982	−	0.992159i	$-0.460113\pi$
$283$	−11.3008	−	6.52451i	−0.671762	−	0.387842i	−0.796744	+	0.604317i	$0.793446\pi$
$284$	−16.9034	+	4.52924i	−1.00303	+	0.268761i
$285$	14.8798	+	1.27067i	0.881401	+	0.0752678i
$286$	1.02521	−	3.93644i	0.0606220	−	0.232767i
$287$		−	18.5450i		−	1.09467i
$288$	−10.6365	+	7.51382i	−0.626762	+	0.442756i
$289$	−8.19733	−	14.1982i	−0.482196	−	0.835188i
$290$	−0.0114701	−	0.0198668i	−0.000673548	−	0.00116662i
$291$	−7.20345	+	19.9200i	−0.422274	+	1.16773i
$292$	1.27891	+	1.27891i	0.0748427	+	0.0748427i
$293$	−14.5729	−	14.5729i	−0.851360	−	0.851360i	0.138940	−	0.990301i	$-0.455630\pi$
$293$	−14.5729	−	14.5729i	−0.851360	−	0.851360i	−0.990301	+	0.138940i	$0.955630\pi$
$294$	2.14800	−	0.383352i	0.125274	−	0.0223576i
$295$	−14.2973	−	24.7637i	−0.832421	−	1.44180i
$296$	5.33842	+	9.24641i	0.310289	+	0.537437i
$297$	7.31210	+	12.4846i	0.424291	+	0.724429i
$298$		−	0.251653i		−	0.0145779i
$299$	7.52492	+	7.42003i	0.435177	+	0.429111i
$300$	−1.24780	+	1.78995i	−0.0720417	+	0.103343i
$301$	11.9508	−	3.20220i	0.688831	−	0.184572i
$302$	3.45199	+	1.99301i	0.198640	+	0.114685i
$303$	20.2021	+	1.72517i	1.16058	+	0.0991083i
$304$	12.1976	−	3.26835i	0.699583	−	0.187453i
$305$	4.98955	+	18.6213i	0.285701	+	1.06625i
$306$	−0.641284	−	6.99504i	−0.0366598	−	0.399880i
$307$	6.08464	−	6.08464i	0.347269	−	0.347269i	−0.511822	−	0.859091i	$-0.671029\pi$
$307$	6.08464	−	6.08464i	0.347269	−	0.347269i	0.859091	+	0.511822i	$0.171029\pi$
$308$	8.73221	−	5.04154i	0.497564	−	0.287269i
$309$	12.6714	−	5.94084i	0.720850	−	0.337963i
$310$	−1.01356	−	3.78266i	−0.0575664	−	0.214841i
$311$	0.349663	+	0.605634i	0.0198276	+	0.0343423i	0.875769	−	0.482731i	$-0.160355\pi$
$311$	0.349663	+	0.605634i	0.0198276	+	0.0343423i	−0.855941	+	0.517073i	$0.827022\pi$
$312$	8.75893	−	4.18177i	0.495877	−	0.236746i
$313$	−10.7052	+	18.5420i	−0.605094	+	1.04805i	0.386943	+	0.922104i	$0.373531\pi$
$313$	−10.7052	+	18.5420i	−0.605094	+	1.04805i	−0.992037	+	0.125949i	$0.959802\pi$
$314$	6.54874	+	1.75473i	0.369567	+	0.0990251i
$315$	9.44797	+	7.86112i	0.532333	+	0.442924i
$316$	−20.5702	−	11.8762i	−1.15717	−	0.668090i
$317$	6.48972	+	24.2200i	0.364499	+	1.36033i	0.868099	+	0.496392i	$0.165342\pi$
$317$	6.48972	+	24.2200i	0.364499	+	1.36033i	−0.503600	+	0.863937i	$0.667991\pi$
$318$	−3.91589	−	4.64713i	−0.219592	−	0.260598i
$319$	−0.0536711	+	0.0536711i	−0.00300501	+	0.00300501i
$320$	2.32494	−	8.67681i	0.129968	−	0.485048i
$321$	5.54569	−	2.60004i	0.309530	−	0.145120i
$322$		−	2.34256i		−	0.130546i
$323$	−6.20895	+	23.1721i	−0.345475	+	1.28933i
$324$	−5.52180	+	15.5725i	−0.306767	+	0.865137i
$325$	1.73716	−	1.76171i	0.0963601	−	0.0977223i
$326$	5.20118	+	3.00290i	0.288067	+	0.166315i
$327$	5.63013	+	6.68149i	0.311347	+	0.369487i
$328$	7.30596	−	12.6543i	0.403404	−	0.698716i
$329$	−8.71299			−0.480363
$330$	3.81669	+	1.38019i	0.210102	+	0.0759769i
$331$	2.70198	−	10.0839i	0.148514	−	0.554263i	−0.851059	−	0.525069i	$-0.824039\pi$
$331$	2.70198	−	10.0839i	0.148514	−	0.554263i	0.999574	−	0.0291938i	$-0.00929401\pi$
$332$	−5.89733	+	1.58019i	−0.323658	+	0.0867240i
$333$	18.7141	+	8.63206i	1.02553	+	0.473034i
$334$	0.400939	−	0.694446i	0.0219384	−	0.0379984i
$335$	13.7637			0.751991
$336$	9.77346	+	3.53427i	0.533186	+	0.192810i
$337$	11.9865	−	6.92043i	0.652948	−	0.376980i	−0.136637	−	0.990621i	$-0.543629\pi$
$337$	11.9865	−	6.92043i	0.652948	−	0.376980i	0.789585	+	0.613641i	$0.210296\pi$
$338$	−5.06822	+	1.43457i	−0.275675	+	0.0780302i
$339$	2.16212	−	25.3188i	0.117430	−	1.37513i
$340$	15.5807	+	15.5807i	0.844980	+	0.844980i
$341$	−11.2213	+	6.47860i	−0.607666	+	0.350836i
$342$	−3.22745	+	3.87895i	−0.174521	+	0.209749i
$343$	−14.1001	−	14.1001i	−0.761335	−	0.761335i
$344$	9.41623	+	2.52307i	0.507689	+	0.136035i
$345$	−8.06314	+	6.79437i	−0.434105	+	0.365797i
$346$	5.03313	+	1.34862i	0.270583	+	0.0725025i
$347$			4.08070i			0.219063i	0.993983	+	0.109532i	$0.0349351\pi$
$347$			4.08070i			0.219063i	−0.993983	+	0.109532i	$0.965065\pi$
$348$	−0.0863645	−	0.00737515i	−0.00462962	−	0.000395349i
$349$	−4.92767	+	4.92767i	−0.263772	+	0.263772i	−0.826585	−	0.562812i	$-0.809719\pi$
$349$	−4.92767	+	4.92767i	−0.263772	+	0.263772i	0.562812	+	0.826585i	$0.309719\pi$
$350$	−0.548435			−0.0293151
$351$	9.15168	−	16.3477i	0.488481	−	0.872575i
$352$	12.0870			0.644239
$353$	7.23489	−	7.23489i	0.385074	−	0.385074i	−0.487852	−	0.872926i	$-0.662219\pi$
$353$	7.23489	−	7.23489i	0.385074	−	0.385074i	0.872926	+	0.487852i	$0.162219\pi$
$354$	9.62686	+	0.822092i	0.511662	+	0.0436937i
$355$			19.7983i			1.05078i
$356$	−3.90446	−	1.04620i	−0.206936	−	0.0554484i
$357$	−15.0980	+	12.7223i	−0.799072	+	0.673335i
$358$	6.71403	+	1.79902i	0.354847	+	0.0950811i
$359$	13.1160	+	13.1160i	0.692237	+	0.692237i	0.962724	−	0.270486i	$-0.0871845\pi$
$359$	13.1160	+	13.1160i	0.692237	+	0.692237i	−0.270486	+	0.962724i	$0.587184\pi$
$360$	3.34993	+	9.08621i	0.176557	+	0.478885i
$361$	−1.53007	+	0.883389i	−0.0805302	+	0.0464941i
$362$	0.845692	+	0.845692i	0.0444486	+	0.0444486i
$363$	−0.478516	+	5.60352i	−0.0251156	+	0.294109i
$364$	−11.3529	−	6.44877i	−0.595052	−	0.338007i
$365$	1.77208	−	1.02311i	0.0927551	−	0.0535522i
$366$	−6.12571	−	2.21518i	−0.320196	−	0.115789i
$367$	−0.345131			−0.0180157			−0.00900784	−	0.999959i	$-0.502867\pi$
$367$	−0.345131			−0.0180157			−0.00900784	+	0.999959i	$0.502867\pi$
$368$	−4.45797	+	7.72143i	−0.232388	+	0.402507i
$369$	−2.57493	−	28.0869i	−0.134045	−	1.46215i
$370$	5.58415	−	1.49627i	0.290306	−	0.0777873i
$371$	−4.42082	+	16.4987i	−0.229518	+	0.856571i
$372$	−13.9150	−	5.03192i	−0.721457	−	0.260893i
$373$	1.14621			0.0593486			0.0296743	−	0.999560i	$-0.490553\pi$
$373$	1.14621			0.0593486			0.0296743	+	0.999560i	$0.490553\pi$
$374$	−3.25981	+	5.64615i	−0.168561	+	0.291956i
$375$	13.1812	+	15.6426i	0.680672	+	0.807779i
$376$	−5.94538	−	3.43257i	−0.306609	−	0.177021i
$377$	0.0951132	+	0.0247714i	0.00489858	+	0.00127579i
$378$	−4.00465	+	1.09984i	−0.205977	+	0.0565696i
$379$	−4.88833	+	18.2435i	−0.251097	+	0.937105i	0.719124	+	0.694882i	$0.244543\pi$
$379$	−4.88833	+	18.2435i	−0.251097	+	0.937105i	−0.970221	+	0.242223i	$0.922123\pi$
$380$		−	15.8287i		−	0.811996i
$381$	−13.1373	+	6.15930i	−0.673047	+	0.315551i
$382$	0.421602	−	1.57344i	0.0215710	−	0.0805042i
$383$	21.4489	−	21.4489i	1.09599	−	1.09599i	0.101112	−	0.994875i	$-0.467760\pi$
$383$	21.4489	−	21.4489i	1.09599	−	1.09599i	0.994875	−	0.101112i	$-0.0322399\pi$
$384$	11.6456	+	13.8203i	0.594288	+	0.705264i
$385$	−2.95248	−	11.0188i	−0.150472	−	0.561571i
$386$	−5.56630	−	3.21370i	−0.283317	−	0.163573i
$387$	17.6552	−	6.50917i	0.897464	−	0.330880i
$388$	21.6866	+	5.81090i	1.10097	+	0.295004i
$389$	1.94710	−	3.37247i	0.0987217	−	0.170991i	−0.812434	−	0.583053i	$-0.801858\pi$
$389$	1.94710	−	3.37247i	0.0987217	−	0.170991i	0.911156	+	0.412062i	$0.135191\pi$
$390$	−0.959638	−	5.16709i	−0.0485931	−	0.261646i
$391$	−8.46890	−	14.6686i	−0.428290	−	0.741821i
$392$	−1.25065	−	4.66750i	−0.0631675	−	0.235744i
$393$	−30.5884	+	14.3411i	−1.54298	+	0.723411i
$394$	−5.41224	+	3.12476i	−0.272665	+	0.157423i
$395$	−19.0016	+	19.0016i	−0.956077	+	0.956077i
$396$	12.5252	−	8.84803i	0.629415	−	0.444630i
$397$	−6.68334	−	24.9426i	−0.335427	−	1.25183i	−0.903405	−	0.428788i	$-0.858941\pi$
$397$	−6.68334	−	24.9426i	−0.335427	−	1.25183i	0.567978	−	0.823044i	$-0.307726\pi$
$398$	4.82265	−	1.29222i	0.241737	−	0.0647733i
$399$	14.1316	+	1.20678i	0.707465	+	0.0604144i
$400$	1.80772	+	1.04369i	0.0903861	+	0.0521844i
$401$	−7.98552	+	2.13971i	−0.398778	+	0.106852i	−0.452634	−	0.891697i	$-0.649515\pi$
$401$	−7.98552	+	2.13971i	−0.398778	+	0.106852i	0.0538559	+	0.998549i	$0.482849\pi$
$402$	−2.65958	+	3.81512i	−0.132648	+	0.190281i
$403$	14.5889	+	8.28695i	0.726727	+	0.412803i
$404$		−	21.4904i		−	1.06919i
$405$	15.4007	+	10.5941i	0.765269	+	0.526424i
$406$	−0.0108934	−	0.0188679i	−0.000540630	−	0.000936398i
$407$	−9.56404	−	16.5654i	−0.474072	−	0.821117i
$408$	−15.3143	+	2.73314i	−0.758171	+	0.135311i
$409$	−16.7829	−	16.7829i	−0.829860	−	0.829860i	0.157637	−	0.987497i	$-0.449612\pi$
$409$	−16.7829	−	16.7829i	−0.829860	−	0.829860i	−0.987497	+	0.157637i	$0.949612\pi$
$410$	−5.59452	−	5.59452i	−0.276294	−	0.276294i
$411$	−2.45459	+	6.78778i	−0.121076	+	0.334817i
$412$	−7.41672	−	12.8461i	−0.365396	−	0.632884i
$413$	−13.5784	−	23.5185i	−0.668151	−	1.15727i
$414$	−0.325260	−	3.54789i	−0.0159856	−	0.174369i
$415$			6.90732i			0.339067i
$416$	−7.92066	−	13.4993i	−0.388342	−	0.661857i
$417$	8.87195	+	0.757626i	0.434461	+	0.0371011i
$418$	4.52387	−	1.21217i	0.221270	−	0.0592891i
$419$	32.2951	+	18.6456i	1.57772	+	0.910896i	0.995177	+	0.0980943i	$0.0312747\pi$
$419$	32.2951	+	18.6456i	1.57772	+	0.910896i	0.582541	+	0.812801i	$0.302059\pi$
$420$	7.44986	−	10.6867i	0.363516	−	0.521457i
$421$	−23.8978	+	6.40339i	−1.16471	+	0.312082i	−0.788844	−	0.614594i	$-0.789320\pi$
$421$	−23.8978	+	6.40339i	−1.16471	+	0.312082i	−0.375862	+	0.926676i	$0.622653\pi$
$422$	2.40652	+	8.98125i	0.117147	+	0.437200i
$423$	−13.1961	+	1.20978i	−0.641616	+	0.0588215i
$424$	−9.51641	+	9.51641i	−0.462158	+	0.462158i
$425$	−3.43416	+	1.98272i	−0.166581	+	0.0961758i
$426$	−5.48783	−	3.82565i	−0.265886	−	0.185353i
$427$	4.73868	+	17.6850i	0.229321	+	0.855836i
$428$	−3.24596	−	5.62217i	−0.156899	−	0.271758i
$429$	−15.6921	+	7.49184i	−0.757619	+	0.361709i
$430$	2.63921	−	4.57125i	0.127274	−	0.220445i
$431$	−4.14613	−	1.11095i	−0.199712	−	0.0535127i	0.157576	−	0.987507i	$-0.449632\pi$
$431$	−4.14613	−	1.11095i	−0.199712	−	0.0535127i	−0.357288	+	0.933994i	$0.616299\pi$
$432$	15.2929	+	3.99574i	0.735782	+	0.192245i
$433$	6.59375	+	3.80690i	0.316875	+	0.182948i	0.649999	−	0.759935i	$-0.274769\pi$
$433$	6.59375	+	3.80690i	0.316875	+	0.182948i	−0.333124	+	0.942883i	$0.608103\pi$
$434$	−0.962598	−	3.59247i	−0.0462062	−	0.172444i
$435$	−0.0333484	+	0.0922197i	−0.00159893	+	0.00442160i
$436$	6.54839	−	6.54839i	0.313611	−	0.313611i
$437$	−3.14918	+	11.7529i	−0.150646	+	0.562218i
$438$	−0.0588288	+	0.688897i	−0.00281095	+	0.0329168i
$439$			26.6268i			1.27083i	0.772171	+	0.635415i	$0.219171\pi$
$439$			26.6268i			1.27083i	−0.772171	+	0.635415i	$0.780829\pi$
$440$	2.32632	−	8.68193i	0.110903	−	0.413895i
$441$	−7.16996	−	5.96572i	−0.341427	−	0.284082i
$442$	8.44204	−	0.0592503i	0.401547	−	0.00281825i
$443$	−6.42528	−	3.70964i	−0.305274	−	0.176250i	0.339535	−	0.940593i	$-0.389730\pi$
$443$	−6.42528	−	3.70964i	−0.305274	−	0.176250i	−0.644810	+	0.764343i	$0.723063\pi$
$444$	7.42837	−	20.5420i	0.352535	−	0.974878i
$445$	−2.28657	+	3.96046i	−0.108394	+	0.187744i
$446$	8.50907			0.402916
$447$	−0.822641	+	0.693195i	−0.0389096	+	0.0327870i
$448$	2.20804	−	8.24054i	0.104320	−	0.389329i
$449$	31.9954	−	8.57315i	1.50996	−	0.404592i	0.593536	−	0.804807i	$-0.297731\pi$
$449$	31.9954	−	8.57315i	1.50996	−	0.404592i	0.916421	+	0.400216i	$0.131065\pi$
$450$	−0.830622	+	0.0761490i	−0.0391559	+	0.00358970i
$451$	−13.0890	+	22.6708i	−0.616336	+	1.06753i
$452$	−26.9335			−1.26685
$453$	−2.99370	−	16.7742i	−0.140656	−	0.788123i
$454$	−10.0784	+	5.81880i	−0.473005	+	0.273090i
$455$	−10.3715	+	10.5181i	−0.486224	+	0.493098i
$456$	9.16739	+	6.39073i	0.429302	+	0.299274i
$457$	−11.8366	−	11.8366i	−0.553694	−	0.553694i	0.373811	−	0.927505i	$-0.378051\pi$
$457$	−11.8366	−	11.8366i	−0.553694	−	0.553694i	−0.927505	+	0.373811i	$0.878051\pi$
$458$	2.62126	−	1.51339i	0.122484	−	0.0707159i
$459$	−21.1000	+	21.3646i	−0.984862	+	0.997216i
$460$	7.90252	+	7.90252i	0.368457	+	0.368457i
$461$	−34.7327	−	9.30659i	−1.61766	−	0.433451i	−0.667348	−	0.744746i	$-0.732571\pi$
$461$	−34.7327	−	9.30659i	−1.61766	−	0.433451i	−0.950313	+	0.311295i	$0.899237\pi$
$462$	3.62479	+	1.31079i	0.168640	+	0.0609836i
$463$	5.87537	+	1.57430i	0.273052	+	0.0731639i	0.392746	−	0.919647i	$-0.371525\pi$
$463$	5.87537	+	1.57430i	0.273052	+	0.0731639i	−0.119695	+	0.992811i	$0.538192\pi$
$464$			0.0829218i			0.00384955i
$465$	−9.57340	+	13.7329i	−0.443956	+	0.636846i
$466$	1.80034	−	1.80034i	0.0833993	−	0.0833993i
$467$	23.2541			1.07607			0.538036	−	0.842922i	$-0.319167\pi$
$467$	23.2541			1.07607			0.538036	+	0.842922i	$0.319167\pi$
$468$	−18.0897	−	8.19055i	−0.836196	−	0.378608i
$469$	13.0716			0.603593
$470$	−2.62848	+	2.62848i	−0.121243	+	0.121243i
$471$	−12.3028	−	26.2410i	−0.566884	−	1.20912i
$472$		−	21.3974i		−	0.984896i
$473$	−16.8696	−	4.52021i	−0.775667	−	0.207839i
$474$	−1.59530	−	8.93874i	−0.0732743	−	0.410570i
$475$	2.75156	+	0.737278i	0.126250	+	0.0338286i
$476$	14.7973	+	14.7973i	0.678231	+	0.678231i
$477$	−4.40466	+	25.6017i	−0.201676	+	1.17222i
$478$	1.69750	−	0.980051i	0.0776418	−	0.0448265i
$479$	9.59779	+	9.59779i	0.438534	+	0.438534i	0.891519	−	0.452984i	$-0.149641\pi$
$479$	9.59779	+	9.59779i	0.438534	+	0.438534i	−0.452984	+	0.891519i	$0.649641\pi$
$480$	14.1393	−	6.62905i	0.645366	−	0.302573i
$481$	−12.2336	+	21.5369i	−0.557805	+	0.981999i
$482$	−3.29666	+	1.90333i	−0.150159	+	0.0866942i
$483$	−7.65772	+	6.45275i	−0.348438	+	0.293610i
$484$	5.96088			0.270949
$485$	12.7003	−	21.9976i	0.576692	−	0.998860i
$486$	−5.91246	+	2.22178i	−0.268195	+	0.100782i
$487$	16.9260	−	4.53531i	0.766990	−	0.205514i	0.145949	−	0.989292i	$-0.453377\pi$
$487$	16.9260	−	4.53531i	0.766990	−	0.205514i	0.621041	+	0.783778i	$0.286710\pi$
$488$	−3.73369	+	13.9343i	−0.169016	+	0.630777i
$489$	−4.51066	−	25.2741i	−0.203979	−	1.14293i
$490$	−2.61644			−0.118199
$491$	16.5414	−	28.6505i	0.746502	−	1.29298i	−0.202988	−	0.979181i	$-0.565065\pi$
$491$	16.5414	−	28.6505i	0.746502	−	1.29298i	0.949490	−	0.313798i	$-0.101602\pi$
$492$	−29.4296	+	5.25230i	−1.32679	+	0.236792i
$493$	−0.136423	−	0.0787641i	−0.00614420	−	0.00354736i
$494$	−4.31832	−	4.25812i	−0.194290	−	0.191582i
$495$	−6.00157	−	16.2784i	−0.269750	−	0.731660i
$496$	−3.66371	+	13.6731i	−0.164505	+	0.613942i
$497$			18.8028i			0.843421i
$498$	−1.91462	−	1.33471i	−0.0857962	−	0.0598099i
$499$	3.32151	−	12.3960i	0.148691	−	0.554923i	−0.850872	−	0.525373i	$-0.823926\pi$
$499$	3.32151	−	12.3960i	0.148691	−	0.554923i	0.999563	−	0.0295500i	$-0.00940744\pi$
$500$	15.3310	−	15.3310i	0.685622	−	0.685622i
$501$	−3.37452	+	0.602250i	−0.150762	+	0.0269066i
$502$	−0.361986	−	1.35095i	−0.0161562	−	0.0602959i
$503$	15.5398	+	8.97189i	0.692884	+	0.400037i	0.804691	−	0.593693i	$-0.202331\pi$
$503$	15.5398	+	8.97189i	0.692884	+	0.400037i	−0.111808	+	0.993730i	$0.535664\pi$
$504$	3.18150	+	8.62936i	0.141715	+	0.384382i
$505$	−23.4848	−	6.29273i	−1.04506	−	0.280023i
$506$	−1.65338	+	2.86373i	−0.0735015	+	0.127308i
$507$	18.6503	+	12.6161i	0.828288	+	0.560303i
$508$	7.68945	+	13.3185i	0.341164	+	0.590914i
$509$	−1.19026	−	4.44211i	−0.0527574	−	0.196893i	0.934517	−	0.355918i	$-0.115832\pi$
$509$	−1.19026	−	4.44211i	−0.0527574	−	0.196893i	−0.987275	+	0.159025i	$0.949165\pi$
$510$	−0.716695	+	8.39265i	−0.0317358	+	0.371633i
$511$	1.68298	−	0.971671i	0.0744508	−	0.0429842i
$512$	16.0233	−	16.0233i	0.708135	−	0.708135i
$513$	21.5703	−	0.134440i	0.952353	−	0.00593569i
$514$	1.54665	+	5.77216i	0.0682196	+	0.254599i
$515$	−16.2100	+	4.34346i	−0.714298	+	0.191396i
$516$	−8.46637	−	18.0582i	−0.372711	−	0.794966i
$517$	10.6514	+	6.14961i	0.468450	+	0.270460i
$518$	5.30338	−	1.42104i	0.233017	−	0.0624367i
$519$	−9.45552	−	20.1679i	−0.415051	−	0.885274i
$520$	−11.2208	+	3.09117i	−0.492065	+	0.135557i
$521$			21.6812i			0.949869i	0.880021	+	0.474934i	$0.157528\pi$
$521$			21.6812i			0.949869i	−0.880021	+	0.474934i	$0.842472\pi$
$522$	−0.0191182	−	0.0270635i	−0.000836779	−	0.00118454i
$523$	2.49525	+	4.32190i	0.109110	+	0.188983i	0.915410	−	0.402523i	$-0.131867\pi$
$523$	2.49525	+	4.32190i	0.109110	+	0.188983i	−0.806300	+	0.591507i	$0.798533\pi$
$524$	17.9038	+	31.0103i	0.782131	+	1.35469i
$525$	1.51070	+	1.79281i	0.0659324	+	0.0782445i
$526$	−3.12321	−	3.12321i	−0.136178	−	0.136178i
$527$	−19.0151	−	19.0151i	−0.828312	−	0.828312i
$528$	−9.45335	−	11.2187i	−0.411404	−	0.488229i
$529$	7.20457	+	12.4787i	0.313242	+	0.542551i
$530$	3.64358	+	6.31087i	0.158267	+	0.274127i
$531$	−23.8305	−	33.7342i	−1.03415	−	1.46394i
$532$		−	15.0328i		−	0.651756i
$533$	33.8970	−	0.237906i	1.46824	−	0.0103048i
$534$	−0.655951	−	1.39910i	−0.0283858	−	0.0605448i
$535$	−7.09438	+	1.90093i	−0.306717	+	0.0821846i
$536$	8.91954	+	5.14970i	0.385265	+	0.222433i
$537$	−12.6133	−	26.9033i	−0.544306	−	1.16096i
$538$	−11.9394	+	3.19916i	−0.514745	+	0.137926i
$539$	2.24061	+	8.36206i	0.0965097	+	0.360179i
$540$	9.79923	−	17.2197i	0.421692	−	0.741019i
$541$	22.5983	−	22.5983i	0.971577	−	0.971577i	−0.0280298	−	0.999607i	$-0.508923\pi$
$541$	22.5983	−	22.5983i	0.971577	−	0.971577i	0.999607	+	0.0280298i	$0.00892333\pi$
$542$	−0.157914	+	0.0911714i	−0.00678297	+	0.00391615i
$543$	0.435009	−	5.09404i	0.0186680	−	0.218606i
$544$	6.49258	+	24.2306i	0.278367	+	1.03888i
$545$	−5.23862	−	9.07356i	−0.224398	−	0.388669i
$546$	−0.911387	−	4.90729i	−0.0390038	−	0.210013i
$547$	−1.65957	+	2.87445i	−0.0709580	+	0.122903i	−0.899321	−	0.437288i	$-0.855939\pi$
$547$	−1.65957	+	2.87445i	−0.0709580	+	0.122903i	0.828363	+	0.560191i	$0.189272\pi$
$548$	7.38976	+	1.98008i	0.315675	+	0.0845848i
$549$	9.63240	+	26.1265i	0.411101	+	1.11505i
$550$	0.670449	+	0.387084i	0.0285881	+	0.0165053i
$551$	0.0292887	+	0.109307i	0.00124774	+	0.00465662i
$552$	−7.76743	+	1.38625i	−0.330604	+	0.0590028i
$553$	−18.0462	+	18.0462i	−0.767404	+	0.767404i
$554$	2.32866	−	8.69068i	0.0989353	−	0.369232i
$555$	−20.2731	−	14.1327i	−0.860547	−	0.599901i
$556$		−	9.43775i		−	0.400250i
$557$	6.06419	−	22.6319i	0.256948	−	0.958944i	−0.710048	−	0.704153i	$-0.751327\pi$
$557$	6.06419	−	22.6319i	0.256948	−	0.958944i	0.966996	−	0.254790i	$-0.0820065\pi$
$558$	−1.95669	−	5.30725i	−0.0828334	−	0.224674i
$559$	6.00638	+	21.8029i	0.254043	+	0.922163i
$560$	−10.7928	−	6.23124i	−0.456080	−	0.263318i
$561$	27.4363	−	4.89656i	1.15836	−	0.206733i
$562$	−3.02073	+	5.23206i	−0.127422	+	0.220701i
$563$	6.03464			0.254330			0.127165	−	0.991882i	$-0.459412\pi$
$563$	6.03464			0.254330			0.127165	+	0.991882i	$0.459412\pi$
$564$	2.46769	+	13.8269i	0.103909	+	0.582219i
$565$	−7.88655	+	29.4330i	−0.331790	+	1.23826i
$566$	−5.10704	+	1.36843i	−0.214665	+	0.0575193i
$567$	14.6264	+	10.0614i	0.614251	+	0.422540i
$568$	−7.40754	+	12.8302i	−0.310814	+	0.538345i
$569$	11.1365			0.466865			0.233433	−	0.972373i	$-0.425004\pi$
$569$	11.1365			0.466865			0.233433	+	0.972373i	$0.425004\pi$
$570$	4.62718	−	3.89908i	0.193811	−	0.163314i
$571$	8.38390	−	4.84045i	0.350855	−	0.202566i	−0.314207	−	0.949355i	$-0.601738\pi$
$571$	8.38390	−	4.84045i	0.350855	−	0.202566i	0.665062	+	0.746788i	$0.268405\pi$
$572$	9.32710	+	15.8963i	0.389986	+	0.664658i
$573$	−6.30482	+	2.95595i	−0.263388	+	0.123487i
$574$	−5.31323	−	5.31323i	−0.221770	−	0.221770i
$575$	−1.74181	+	1.00563i	−0.0726385	+	0.0419379i
$576$	2.19997	−	12.7871i	0.0916656	−	0.532797i
$577$	12.2885	+	12.2885i	0.511579	+	0.511579i	0.915010	−	0.403431i	$-0.132183\pi$
$577$	12.2885	+	12.2885i	0.511579	+	0.511579i	−0.403431	+	0.915010i	$0.632183\pi$
$578$	−6.41644	−	1.71928i	−0.266889	−	0.0715126i
$579$	4.82731	+	27.0483i	0.200616	+	1.12409i
$580$	0.100398	+	0.0269016i	0.00416881	+	0.00111703i
$581$			6.56002i			0.272155i
$582$	3.64335	+	7.77101i	0.151022	+	0.322119i
$583$	17.0491	−	17.0491i	0.706102	−	0.706102i
$584$	1.53120			0.0633613
$585$	−14.2476	+	17.3701i	−0.589065	+	0.718166i
$586$	−8.35045			−0.344954
$587$	−23.1920	+	23.1920i	−0.957237	+	0.957237i	−0.999122	−	0.0418854i	$-0.986664\pi$
$587$	−23.1920	+	23.1920i	−0.957237	+	0.957237i	0.0418854	+	0.999122i	$0.486664\pi$
$588$	−5.65362	+	8.11001i	−0.233151	+	0.334451i
$589$			19.3179i			0.795979i
$590$	−11.1912	−	2.99867i	−0.460733	−	0.123453i
$591$	25.1231	+	9.08499i	1.03343	+	0.373707i
$592$	−20.1850	−	5.40855i	−0.829598	−	0.222290i
$593$	19.9618	+	19.9618i	0.819732	+	0.819732i	0.986069	−	0.166337i	$-0.0531939\pi$
$593$	19.9618	+	19.9618i	0.819732	+	0.819732i	−0.166337	+	0.986069i	$0.553194\pi$
$594$	5.67186	+	1.48194i	0.232719	+	0.0608049i
$595$	20.5033	−	11.8376i	0.840555	−	0.485295i
$596$	0.806254	+	0.806254i	0.0330255	+	0.0330255i
$597$	−17.5085	−	12.2055i	−0.716576	−	0.499537i
$598$	4.28181	−	0.0300518i	0.175096	−	0.00122891i
$599$	−19.7475	+	11.4012i	−0.806859	+	0.465840i	−0.845864	−	0.533399i	$-0.820915\pi$
$599$	−19.7475	+	11.4012i	−0.806859	+	0.465840i	0.0390047	+	0.999239i	$0.487581\pi$
$600$	0.324546	+	1.81849i	0.0132495	+	0.0742395i
$601$	27.8966			1.13793			0.568963	−	0.822363i	$-0.307345\pi$
$601$	27.8966			1.13793			0.568963	+	0.822363i	$0.307345\pi$
$602$	2.50651	−	4.34140i	0.102158	−	0.176942i
$603$	19.7974	−	1.81497i	0.806213	−	0.0739113i
$604$	−17.4448	+	4.67433i	−0.709821	+	0.190196i
$605$	1.74544	−	6.51406i	0.0709622	−	0.264834i
$606$	6.28227	−	5.29373i	0.255200	−	0.215043i
$607$	10.9754			0.445476			0.222738	−	0.974878i	$-0.428501\pi$
$607$	10.9754			0.445476			0.222738	+	0.974878i	$0.428501\pi$
$608$	9.01023	−	15.6062i	0.365413	−	0.632914i
$609$	−0.0316717	+	0.0875829i	−0.00128340	+	0.00354904i
$610$	6.76462	+	3.90556i	0.273892	+	0.158131i
$611$	−0.111775	−	15.9259i	−0.00452195	−	0.644291i
$612$	24.4655	+	20.3564i	0.988959	+	0.822857i
$613$	6.13904	−	22.9112i	0.247953	−	0.925375i	−0.723923	−	0.689881i	$-0.757663\pi$
$613$	6.13904	−	22.9112i	0.247953	−	0.925375i	0.971876	−	0.235493i	$-0.0756706\pi$
$614$		−	3.48657i		−	0.140706i
$615$	−2.87772	+	33.6987i	−0.116041	+	1.35886i
$616$	2.20935	−	8.24540i	0.0890172	−	0.332217i
$617$	5.02190	−	5.02190i	0.202174	−	0.202174i	−0.598757	−	0.800931i	$-0.704338\pi$
$617$	5.02190	−	5.02190i	0.202174	−	0.202174i	0.800931	+	0.598757i	$0.204338\pi$
$618$	1.92834	−	5.33250i	0.0775690	−	0.214505i
$619$	−2.12877	−	7.94467i	−0.0855624	−	0.319323i	0.909858	−	0.414920i	$-0.136191\pi$
$619$	−2.12877	−	7.94467i	−0.0855624	−	0.319323i	−0.995420	+	0.0955973i	$0.969524\pi$
$620$	15.3663	+	8.87172i	0.617124	+	0.356297i
$621$	−10.7019	+	10.8362i	−0.429453	+	0.434840i
$622$	0.273697	+	0.0733370i	0.0109743	+	0.00294055i
$623$	−2.17160	+	3.76133i	−0.0870035	+	0.150694i
$624$	−6.33466	+	17.9095i	−0.253589	+	0.716956i
$625$	−10.5491	−	18.2715i	−0.421962	−	0.730860i
$626$	2.24527	+	8.37946i	0.0897391	+	0.334911i
$627$	−16.4238	−	11.4493i	−0.655905	−	0.457242i
$628$	−26.6029	+	15.3592i	−1.06157	+	0.612899i
$629$	28.0711	−	28.0711i	1.11927	−	1.11927i
$630$	4.95915	−	0.454640i	0.197577	−	0.0181133i
$631$	−2.37087	−	8.84821i	−0.0943828	−	0.352242i	0.902542	−	0.430601i	$-0.141698\pi$
$631$	−2.37087	−	8.84821i	−0.0943828	−	0.352242i	−0.996925	+	0.0783596i	$0.975032\pi$
$632$	−19.4235	+	5.20451i	−0.772625	+	0.207024i
$633$	22.7303	−	32.6062i	0.903450	−	1.29598i
$634$	8.79849	+	5.07981i	0.349433	+	0.201745i
$635$	16.8061	−	4.50318i	0.666930	−	0.178703i
$636$	27.4345	+	2.34278i	1.08785	+	0.0928974i
$637$	7.87083	−	7.98210i	0.311854	−	0.316262i
$638$			0.0307541i			0.00121757i
$639$	2.61073	+	28.4774i	0.103279	+	1.12655i
$640$	−10.8358	−	18.7682i	−0.428323	−	0.741877i
$641$	−6.30605	−	10.9224i	−0.249074	−	0.431409i	0.714195	−	0.699947i	$-0.246793\pi$
$641$	−6.30605	−	10.9224i	−0.249074	−	0.431409i	−0.963269	+	0.268538i	$0.913460\pi$
$642$	0.843945	−	2.33379i	0.0333078	−	0.0921075i
$643$	16.4044	+	16.4044i	0.646926	+	0.646926i	0.952249	−	0.305323i	$-0.0987644\pi$
$643$	16.4044	+	16.4044i	0.646926	+	0.646926i	−0.305323	+	0.952249i	$0.598764\pi$
$644$	7.50518	+	7.50518i	0.295745	+	0.295745i
$645$	−22.2131	+	3.96436i	−0.874639	+	0.156097i
$646$	4.86004	+	8.41783i	0.191216	+	0.331195i
$647$	−6.02571	−	10.4368i	−0.236895	−	0.410314i	0.722927	−	0.690925i	$-0.242796\pi$
$647$	−6.02571	−	10.4368i	−0.236895	−	0.410314i	−0.959822	+	0.280610i	$0.909463\pi$
$648$	6.01664	+	12.6277i	0.236356	+	0.496063i
$649$			38.3345i			1.50476i
$650$	−0.00703565	−	1.00244i	−0.000275961	−	0.0393191i
$651$	−9.09205	+	13.0424i	−0.356345	+	0.511171i
$652$	−26.2845	+	7.04291i	−1.02938	+	0.275822i
$653$	−38.2976	−	22.1111i	−1.49870	−	0.865275i	−0.498702	−	0.866774i	$-0.666190\pi$
$653$	−38.2976	−	22.1111i	−1.49870	−	0.865275i	−0.999999	+	0.00149827i	$0.999523\pi$
$654$	3.52734	+	0.301220i	0.137930	+	0.0117786i
$655$	39.1306	−	10.4850i	1.52896	−	0.409683i
$656$	7.40194	+	27.6244i	0.288997	+	1.07855i
$657$	2.41402	−	1.70531i	0.0941798	−	0.0665303i
$658$	−2.49632	+	2.49632i	−0.0973166	+	0.0973166i
$659$	15.5471	−	8.97611i	0.605628	−	0.349660i	−0.165624	−	0.986189i	$-0.552964\pi$
$659$	15.5471	−	8.97611i	0.605628	−	0.349660i	0.771252	+	0.636529i	$0.219631\pi$
$660$	−16.6499	+	7.80614i	−0.648098	+	0.303854i
$661$	−2.88002	−	10.7484i	−0.112020	−	0.418063i	0.887027	−	0.461718i	$-0.152767\pi$
$661$	−2.88002	−	10.7484i	−0.112020	−	0.418063i	−0.999047	+	0.0436543i	$0.986100\pi$
$662$	−2.11497	−	3.66323i	−0.0822006	−	0.142376i
$663$	−23.4478	−	27.4334i	−0.910639	−	1.06542i
$664$	−2.58438	+	4.47628i	−0.100293	+	0.173713i
$665$	−16.4279	−	4.40185i	−0.637047	−	0.170696i
$666$	7.83483	−	2.88857i	0.303593	−	0.111930i
$667$	−0.0691941	−	0.0399492i	−0.00267920	−	0.00154684i
$668$	0.940348	+	3.50943i	0.0363832	+	0.135784i
$669$	−23.4388	−	27.8157i	−0.906197	−	1.07542i
$670$	3.94337	−	3.94337i	0.152346	−	0.152346i
$671$	6.68909	−	24.9640i	0.258230	−	0.963726i
$672$	13.4283	−	6.29574i	0.518010	−	0.242863i
$673$			7.43737i			0.286690i	0.989673	+	0.143345i	$0.0457858\pi$
$673$			7.43737i			0.286690i	−0.989673	+	0.143345i	$0.954214\pi$
$674$	1.45147	−	5.41695i	0.0559084	−	0.208653i
$675$	2.53693	+	2.50550i	0.0976465	+	0.0964369i
$676$	11.6416	−	20.8338i	0.447754	−	0.801301i
$677$	20.4211	+	11.7901i	0.784847	+	0.453131i	0.838145	−	0.545447i	$-0.183640\pi$
$677$	20.4211	+	11.7901i	0.784847	+	0.453131i	−0.0532985	+	0.998579i	$0.516973\pi$
$678$	−6.63452	−	7.87344i	−0.254797	−	0.302378i
$679$	12.0618	−	20.8916i	0.462888	−	0.801745i
$680$	18.6541			0.715354
$681$	46.7831	+	16.9177i	1.79273	+	0.648287i
$682$	−1.35880	+	5.07111i	−0.0520311	+	0.194183i
$683$	−16.0795	+	4.30850i	−0.615266	+	0.164860i	−0.552975	−	0.833198i	$-0.686507\pi$
$683$	−16.0795	+	4.30850i	−0.615266	+	0.164860i	−0.0622913	+	0.998058i	$0.519841\pi$
$684$	−2.08728	−	22.7677i	−0.0798090	−	0.870545i
$685$	4.32767	−	7.49574i	0.165352	−	0.286398i
$686$	−8.07952			−0.308477
$687$	−12.1676	−	4.40005i	−0.464224	−	0.167872i
$688$	−16.5237	+	9.53994i	−0.629958	+	0.363707i
$689$	−30.2136	−	7.86885i	−1.15104	−	0.299779i
$690$	−0.363508	+	4.25676i	−0.0138385	+	0.162052i
$691$	−35.4408	−	35.4408i	−1.34823	−	1.34823i	−0.887581	−	0.460651i	$-0.847616\pi$
$691$	−35.4408	−	35.4408i	−1.34823	−	1.34823i	−0.460651	−	0.887581i	$-0.652384\pi$
$692$	−20.4461	+	11.8045i	−0.777243	+	0.448742i
$693$	−5.69981	−	15.4599i	−0.216518	−	0.587274i
$694$	1.16914	+	1.16914i	0.0443800	+	0.0443800i
$695$	−10.3136	−	2.76352i	−0.391217	−	0.104826i
$696$	−0.0561155	+	0.0472855i	−0.00212705	+	0.00179235i
$697$	−52.4786	−	14.0616i	−1.98777	−	0.532621i
$698$			2.82361i			0.106875i
$699$	−10.8444	−	0.926064i	−0.410173	−	0.0350269i
$700$	1.75709	−	1.75709i	0.0664119	−	0.0664119i
$701$	−29.7762			−1.12463			−0.562317	−	0.826922i	$-0.690090\pi$
$701$	−29.7762			−1.12463			−0.562317	+	0.826922i	$0.690090\pi$
$702$	−2.06169	−	7.30570i	−0.0778135	−	0.275736i
$703$	−28.5180			−1.07558
$704$	−8.51544	+	8.51544i	−0.320938	+	0.320938i
$705$	15.8327	+	1.35204i	0.596293	+	0.0509208i
$706$		−	4.14567i		−	0.156024i
$707$	−22.3040	−	5.97633i	−0.838827	−	0.224763i
$708$	−33.4767	+	28.2090i	−1.25813	+	1.06016i
$709$	36.6562	+	9.82199i	1.37665	+	0.368873i	0.869904	−	0.493222i	$-0.164181\pi$
$709$	36.6562	+	9.82199i	1.37665	+	0.368873i	0.506748	+	0.862094i	$0.330848\pi$
$710$	5.67231	+	5.67231i	0.212878	+	0.212878i
$711$	−24.8259	+	29.8373i	−0.931045	+	1.11899i
$712$	−2.96362	+	1.71105i	−0.111066	+	0.0641242i
$713$	−9.64448	−	9.64448i	−0.361189	−	0.361189i
$714$	−0.680660	+	7.97066i	−0.0254731	+	0.298295i
$715$	20.1026	−	5.53799i	0.751796	−	0.207109i
$716$	−27.2744	+	15.7469i	−1.01929	+	0.588488i
$717$	−7.87961	−	2.84942i	−0.294270	−	0.106414i
$718$	7.51562			0.280481
$719$	−2.07633	+	3.59631i	−0.0774340	+	0.134120i	−0.902142	−	0.431439i	$-0.858006\pi$
$719$	−2.07633	+	3.59631i	−0.0774340	+	0.134120i	0.824708	+	0.565559i	$0.191339\pi$
$720$	−17.2113	−	7.93885i	−0.641426	−	0.295863i
$721$	−15.3950	+	4.12507i	−0.573339	+	0.153626i
$722$	−0.185279	+	0.691470i	−0.00689536	+	0.0257338i
$723$	15.3028	+	5.53377i	0.569115	+	0.205803i
$724$	−5.41891			−0.201392
$725$	−0.00935280	+	0.0161995i	−0.000347354	+	0.000601635i
$726$	1.46834	+	1.74254i	0.0544953	+	0.0646716i
$727$	−17.8851	−	10.3260i	−0.663323	−	0.382970i	0.130219	−	0.991485i	$-0.458432\pi$
$727$	−17.8851	−	10.3260i	−0.663323	−	0.382970i	−0.793542	+	0.608516i	$0.791765\pi$
$728$	−10.6566	+	2.93575i	−0.394961	+	0.108806i
$729$	23.5491	+	13.2075i	0.872191	+	0.489166i
$730$	0.214584	−	0.800839i	0.00794212	−	0.0296404i
$731$		−	36.2464i		−	1.34062i
$732$	26.7228	−	12.5287i	0.987703	−	0.463074i
$733$	11.0400	−	41.2018i	0.407771	−	1.52182i	−0.391117	−	0.920341i	$-0.627911\pi$
$733$	11.0400	−	41.2018i	0.407771	−	1.52182i	0.798888	−	0.601480i	$-0.205422\pi$
$734$	−0.0988818	+	0.0988818i	−0.00364979	+	0.00364979i
$735$	7.20717	+	8.55302i	0.265840	+	0.315483i
$736$	3.29304	+	12.2898i	0.121383	+	0.453008i
$737$	−15.9798	−	9.22594i	−0.588623	−	0.339842i
$738$	−8.78478	−	7.30932i	−0.323372	−	0.269060i
$739$	−18.5262	−	4.96408i	−0.681497	−	0.182607i	−0.0985688	−	0.995130i	$-0.531426\pi$
$739$	−18.5262	−	4.96408i	−0.681497	−	0.182607i	−0.582928	+	0.812524i	$0.698093\pi$
$740$	−13.0969	+	22.6845i	−0.481451	+	0.833898i
$741$	−2.02449	+	25.8456i	−0.0743716	+	0.949463i
$742$	3.46038	+	5.99356i	0.127035	+	0.220031i
$743$	3.81128	+	14.2239i	0.139822	+	0.521824i	0.999931	+	0.0117137i	$0.00372866\pi$
$743$	3.81128	+	14.2239i	0.139822	+	0.521824i	−0.860109	+	0.510110i	$0.829605\pi$
$744$	−11.3422	+	5.31767i	−0.415825	+	0.194955i
$745$	1.11716	−	0.644992i	0.0409296	−	0.0236307i
$746$	0.328396	−	0.328396i	0.0120234	−	0.0120234i
$747$	0.910844	+	9.93535i	0.0333260	+	0.363516i
$748$	−7.64545	−	28.5332i	−0.279545	−	1.04328i
$749$	−6.73768	+	1.80536i	−0.246189	+	0.0659662i
$750$	8.25815	+	0.705210i	0.301545	+	0.0257506i
$751$	5.72719	+	3.30659i	0.208988	+	0.120659i	0.600841	−	0.799369i	$-0.294832\pi$
$751$	5.72719	+	3.30659i	0.208988	+	0.120659i	−0.391853	+	0.920028i	$0.628166\pi$
$752$	12.9788	−	3.47766i	0.473288	−	0.126817i
$753$	−3.41908	+	4.90460i	−0.124598	+	0.178734i
$754$	0.0343476	−	0.0201533i	0.00125086	−	0.000733940i
$755$			20.4325i			0.743614i
$756$	9.30652	−	16.3539i	0.338475	−	0.594786i
$757$	−0.157058	−	0.272032i	−0.00570837	−	0.00988718i	0.863157	−	0.504935i	$-0.168484\pi$
$757$	−0.157058	−	0.272032i	−0.00570837	−	0.00988718i	−0.868865	+	0.495048i	$0.835150\pi$
$758$	3.82633	+	6.62739i	0.138978	+	0.240718i
$759$	13.9157	−	2.48354i	0.505109	−	0.0901467i
$760$	−9.47557	−	9.47557i	−0.343715	−	0.343715i
$761$	19.6502	+	19.6502i	0.712321	+	0.712321i	0.967020	−	0.254699i	$-0.0819766\pi$
$761$	19.6502	+	19.6502i	0.712321	+	0.712321i	−0.254699	+	0.967020i	$0.581977\pi$
$762$	−1.99925	+	5.52859i	−0.0724250	+	0.200280i
$763$	−4.97522	−	8.61734i	−0.180115	−	0.311969i
$764$	3.69029	+	6.39178i	0.133510	+	0.231246i
$765$	29.4093	−	20.7753i	1.06330	−	0.751132i
$766$		−	12.2904i		−	0.444072i
$767$	42.8137	−	25.1208i	1.54591	−	0.907058i
$768$	−7.63179	−	0.651721i	−0.275388	−	0.0235170i
$769$	26.8812	−	7.20278i	0.969359	−	0.259739i	0.260802	−	0.965392i	$-0.416013\pi$
$769$	26.8812	−	7.20278i	0.969359	−	0.259739i	0.708557	+	0.705653i	$0.249346\pi$
$770$	−4.00285	−	2.31105i	−0.144253	−	0.0832844i
$771$	14.6086	−	20.9557i	0.526115	−	0.754702i
$772$	28.1297	−	7.53732i	1.01241	−	0.271274i
$773$	7.98648	+	29.8060i	0.287254	+	1.07205i	0.947177	+	0.320713i	$0.103922\pi$
$773$	7.98648	+	29.8060i	0.287254	+	1.07205i	−0.659923	+	0.751333i	$0.729411\pi$
$774$	3.19340	−	6.92322i	0.114784	−	0.248850i
$775$	−2.25794	+	2.25794i	−0.0811076	+	0.0811076i
$776$	16.4609	−	9.50368i	0.590911	−	0.341162i
$777$	−19.2538	−	13.4221i	−0.690727	−	0.481516i
$778$	−0.408377	−	1.52408i	−0.0146410	−	0.0546411i
$779$	19.5143	+	33.7998i	0.699173	+	1.21100i
$780$	19.6290	+	13.4800i	0.702831	+	0.482661i
$781$	13.2710	−	22.9860i	0.474873	−	0.822504i
$782$	−6.62900	−	1.77624i	−0.237053	−	0.0635181i
$783$	−0.0358070	+	0.137045i	−0.00127964	+	0.00489757i
$784$	8.19055	+	4.72882i	0.292520	+	0.168886i
$785$	8.99482	+	33.5691i	0.321039	+	1.19813i
$786$	−4.65496	+	12.8725i	−0.166037	+	0.459148i
$787$	18.0297	−	18.0297i	0.642689	−	0.642689i	−0.308527	−	0.951216i	$-0.599836\pi$
$787$	18.0297	−	18.0297i	0.642689	−	0.642689i	0.951216	+	0.308527i	$0.0998360\pi$
$788$	7.32871	−	27.3511i	0.261075	−	0.974344i
$789$	−1.60652	+	18.8127i	−0.0571937	+	0.669750i
$790$			10.8881i			0.387383i
$791$	−7.49001	+	27.9531i	−0.266314	+	0.993898i
$792$	2.20127	−	12.7947i	0.0782188	−	0.454639i
$793$	−32.2643	+	8.88836i	−1.14574	+	0.315635i
$794$	−9.06099	−	5.23137i	−0.321563	−	0.185654i
$795$	10.5934	−	29.2944i	0.375710	−	1.03897i
$796$	−11.3109	+	19.5910i	−0.400903	+	0.694385i
$797$	−7.39914			−0.262091			−0.131046	−	0.991376i	$-0.541833\pi$
$797$	−7.39914			−0.262091			−0.131046	+	0.991376i	$0.541833\pi$
$798$	4.39453	−	3.70303i	0.155565	−	0.131086i
$799$	−6.60658	+	24.6561i	−0.233724	+	0.872270i
$800$	2.87725	−	0.770958i	0.101726	−	0.0272575i
$801$	−2.76671	+	5.99818i	−0.0977570	+	0.211935i
$802$	−1.67485	+	2.90093i	−0.0591412	+	0.102436i
$803$	−2.74321			−0.0968059
$804$	−3.70215	−	20.7438i	−0.130565	−	0.731579i
$805$	10.3993	−	6.00404i	0.366527	−	0.211615i
$806$	6.55406	−	1.80555i	0.230857	−	0.0635978i
$807$	43.3458	+	30.2171i	1.52585	+	1.06369i
$808$	−12.8649	−	12.8649i	−0.452584	−	0.452584i
$809$	−32.2345	+	18.6106i	−1.13331	+	0.654315i	−0.944764	−	0.327751i	$-0.893709\pi$
$809$	−32.2345	+	18.6106i	−1.13331	+	0.654315i	−0.188542	+	0.982065i	$0.560376\pi$
$810$	7.44766	−	1.37713i	0.261684	−	0.0483875i
$811$	−6.98393	−	6.98393i	−0.245239	−	0.245239i	0.573775	−	0.819013i	$-0.305479\pi$
$811$	−6.98393	−	6.98393i	−0.245239	−	0.245239i	−0.819013	+	0.573775i	$0.805479\pi$
$812$	0.0953502	+	0.0255490i	0.00334614	+	0.000896594i
$813$	0.733018	+	0.265074i	0.0257081	+	0.00929654i
$814$	−7.48622	−	2.00593i	−0.262392	−	0.0703077i
$815$			30.7860i			1.07839i
$816$	17.4120	−	24.9772i	0.609541	−	0.874375i
$817$	−18.4117	+	18.4117i	−0.644145	+	0.644145i
$818$	−9.61677			−0.336242
$819$	−13.5312	+	16.4967i	−0.472819	+	0.576443i
$820$	35.8478			1.25186
$821$	9.83790	−	9.83790i	0.343345	−	0.343345i	−0.514278	−	0.857623i	$-0.671940\pi$
$821$	9.83790	−	9.83790i	0.343345	−	0.343345i	0.857623	+	0.514278i	$0.171940\pi$
$822$	1.24148	+	2.64799i	0.0433017	+	0.0923592i
$823$		−	16.2167i		−	0.565280i	−0.959226	−	0.282640i	$-0.908790\pi$
$823$		−	16.2167i		−	0.565280i	0.959226	−	0.282640i	$-0.0912101\pi$
$824$	−12.1300	−	3.25022i	−0.422568	−	0.113227i
$825$	−0.581440	−	3.25791i	−0.0202431	−	0.113426i
$826$	−10.6285	−	2.84789i	−0.369812	−	0.0990909i
$827$	−39.0484	−	39.0484i	−1.35784	−	1.35784i	−0.876570	−	0.481274i	$-0.840174\pi$
$827$	−39.0484	−	39.0484i	−1.35784	−	1.35784i	−0.481274	−	0.876570i	$-0.659826\pi$
$828$	12.4089	+	10.3248i	0.431239	+	0.358810i
$829$	−21.0986	+	12.1813i	−0.732784	+	0.423073i	−0.819440	−	0.573165i	$-0.805715\pi$
$829$	−21.0986	+	12.1813i	−0.732784	+	0.423073i	0.0866559	+	0.996238i	$0.472382\pi$
$830$	1.97898	+	1.97898i	0.0686915	+	0.0686915i
$831$	−34.8238	+	16.3268i	−1.20803	+	0.566370i
$832$	15.0906	+	3.93021i	0.523173	+	0.136256i
$833$	−15.5598	+	8.98343i	−0.539114	+	0.311257i
$834$	2.75892	−	2.32480i	0.0955337	−	0.0805011i
$835$	4.11046			0.142248
$836$	−10.6101	+	18.3773i	−0.366960	+	0.635593i
$837$	−11.9593	+	21.0155i	−0.413374	+	0.726402i
$838$	14.5948	−	3.91066i	0.504168	−	0.135091i
$839$	−4.59066	+	17.1326i	−0.158487	+	0.591482i	0.840294	+	0.542131i	$0.182382\pi$
$839$	−4.59066	+	17.1326i	−0.158487	+	0.591482i	−0.998781	+	0.0493516i	$0.984285\pi$
$840$	−1.93767	−	10.8571i	−0.0668559	−	0.374606i
$841$	28.9993			0.999974
$842$	−5.01223	+	8.68144i	−0.172733	+	0.299182i
$843$	25.4242	−	4.53745i	0.875654	−	0.156278i
$844$	−36.4845	−	21.0643i	−1.25585	−	0.725064i
$845$	−19.3584	−	18.8224i	−0.665949	−	0.647511i
$846$	−3.43415	+	4.12736i	−0.118068	+	0.141902i
$847$	1.65768	−	6.18654i	0.0569585	−	0.212572i
$848$		−	26.3409i		−	0.904549i
$849$	18.5410	+	12.9252i	0.636326	+	0.443593i
$850$	−0.415848	+	1.55196i	−0.0142635	+	0.0532320i
$851$	14.2377	−	14.2377i	0.488061	−	0.488061i
$852$	29.8388	−	5.32533i	1.02226	−	0.182443i
$853$	−1.66744	−	6.22299i	−0.0570922	−	0.213071i	0.931487	−	0.363775i	$-0.118512\pi$
$853$	−1.66744	−	6.22299i	−0.0570922	−	0.213071i	−0.988579	+	0.150705i	$0.951846\pi$
$854$	6.42450	+	3.70918i	0.219842	+	0.126926i
$855$	−25.4918	−	4.38576i	−0.871801	−	0.149990i
$856$	−5.30874	−	1.42247i	−0.181449	−	0.0486191i
$857$	19.0536	−	33.0018i	0.650858	−	1.12732i	−0.332057	−	0.943259i	$-0.607743\pi$
$857$	19.0536	−	33.0018i	0.650858	−	1.12732i	0.982915	−	0.184060i	$-0.0589240\pi$
$858$	−2.34940	+	6.64231i	−0.0802074	+	0.226765i
$859$	−11.6865	−	20.2416i	−0.398738	−	0.690634i	0.594832	−	0.803850i	$-0.297218\pi$
$859$	−11.6865	−	20.2416i	−0.398738	−	0.690634i	−0.993570	+	0.113215i	$0.963885\pi$
$860$	6.18992	+	23.1011i	0.211074	+	0.787741i
$861$	−2.73303	+	32.0043i	−0.0931414	+	1.09070i
$862$	−1.50618	+	0.869594i	−0.0513007	+	0.0296185i
$863$	8.96522	−	8.96522i	0.305180	−	0.305180i	−0.537857	−	0.843036i	$-0.680766\pi$
$863$	8.96522	−	8.96522i	0.305180	−	0.305180i	0.843036	+	0.537857i	$0.180766\pi$
$864$	19.4635	−	11.3996i	0.662162	−	0.387822i
$865$	6.91311	+	25.8001i	0.235053	+	0.877228i
$866$	2.97984	−	0.798446i	0.101259	−	0.0271323i
$867$	12.0543	+	25.7109i	0.409385	+	0.873187i
$868$	14.5937	+	8.42565i	0.495341	+	0.285985i
$869$	34.7981	−	9.32413i	1.18045	−	0.316299i
$870$	0.0168669	+	0.0359759i	0.000571843	+	0.00121970i
$871$	0.167691	+	23.8927i	0.00568199	+	0.809574i
$872$		−	7.84015i		−	0.265501i
$873$	15.3672	−	33.3157i	0.520100	−	1.12757i
$874$	2.46501	+	4.26953i	0.0833803	+	0.144419i
$875$	−11.6479	−	20.1748i	−0.393771	−	0.682031i
$876$	−2.01863	−	2.39559i	−0.0682033	−	0.0809394i
$877$	25.8481	+	25.8481i	0.872828	+	0.872828i	0.992780	−	0.119951i	$-0.0382738\pi$
$877$	25.8481	+	25.8481i	0.872828	+	0.872828i	−0.119951	+	0.992780i	$0.538274\pi$
$878$	7.62873	+	7.62873i	0.257457	+	0.257457i
$879$	23.0019	+	27.2972i	0.775834	+	0.920712i
$880$	8.79599	+	15.2351i	0.296513	+	0.513575i
$881$	1.20714	+	2.09083i	0.0406696	+	0.0704418i	0.885644	−	0.464365i	$-0.153718\pi$
$881$	1.20714	+	2.09083i	0.0406696	+	0.0704418i	−0.844974	+	0.534807i	$0.820384\pi$
$882$	−3.76344	+	0.345021i	−0.126722	+	0.0116175i
$883$		−	4.43328i		−	0.149192i	−0.997214	−	0.0745958i	$-0.976233\pi$
$883$		−	4.43328i		−	0.149192i	0.997214	−	0.0745958i	$-0.0237667\pi$
$884$	−26.8570	+	27.2367i	−0.903300	+	0.916069i
$885$	21.0244	+	44.8434i	0.706726	+	1.50739i
$886$	−2.90371	+	0.778047i	−0.0975520	+	0.0261390i
$887$	−14.4537	−	8.34486i	−0.485309	−	0.280193i	0.237318	−	0.971432i	$-0.423732\pi$
$887$	−14.4537	−	8.34486i	−0.485309	−	0.280193i	−0.722626	+	0.691239i	$0.757065\pi$
$888$	−7.85021	−	16.7439i	−0.263436	−	0.561889i
$889$	15.9611	−	4.27676i	0.535318	−	0.143438i
$890$	0.479578	+	1.78981i	0.0160755	+	0.0599945i
$891$	−10.7791	−	22.6231i	−0.361114	−	0.757903i
$892$	−27.2616	+	27.2616i	−0.912787	+	0.912787i
$893$	15.8802	−	9.16843i	0.531410	−	0.306810i
$894$	−0.0370869	+	0.434295i	−0.00124037	+	0.0145250i
$895$	9.22185	+	34.4164i	0.308252	+	1.15041i
$896$	−10.2910	−	17.8245i	−0.343798	−	0.595475i
$897$	−11.8928	−	13.9142i	−0.397088	−	0.464582i
$898$	6.71061	−	11.6231i	0.223936	−	0.387868i
$899$	−0.122529	−	0.0328316i	−0.00408658	−	0.00109499i
$900$	2.41720	−	2.90514i	0.0805735	−	0.0968380i
$901$	43.3362	+	25.0201i	1.44374	+	0.833542i
$902$	2.74524	+	10.2454i	0.0914064	+	0.341133i
$903$	−21.0962	+	3.76503i	−0.702037	+	0.125293i
$904$	−16.1233	+	16.1233i	−0.536252	+	0.536252i
$905$	−1.58674	+	5.92179i	−0.0527450	+	0.196847i
$906$	−5.66362	−	3.94820i	−0.188161	−	0.131170i
$907$		−	6.54162i		−	0.217211i	−0.994085	−	0.108606i	$-0.965361\pi$
$907$		−	6.54162i		−	0.217211i	0.994085	−	0.108606i	$-0.0346385\pi$
$908$	13.6472	−	50.9321i	0.452899	−	1.69024i
$909$	−34.6099	−	5.95449i	−1.14794	−	0.197498i
$910$	0.0420056	+	5.98500i	0.00139247	+	0.198401i
$911$	−11.6758	−	6.74101i	−0.386835	−	0.223340i	0.293953	−	0.955820i	$-0.405029\pi$
$911$	−11.6758	−	6.74101i	−0.386835	−	0.223340i	−0.680788	+	0.732480i	$0.738363\pi$
$912$	−21.5320	+	3.84281i	−0.712996	+	0.127248i
$913$	4.63005	−	8.01947i	0.153232	−	0.265406i
$914$	−6.78251			−0.224346
$915$	−5.86654	−	32.8713i	−0.193942	−	1.08669i
$916$	−3.54945	+	13.2467i	−0.117277	+	0.437684i
$917$	37.1631	−	9.95782i	1.22723	−	0.328836i
$918$	0.0758286	+	12.1663i	0.00250272	+	0.401549i
$919$	24.5247	−	42.4781i	0.808996	−	1.40122i	−0.104564	−	0.994518i	$-0.533345\pi$
$919$	24.5247	−	42.4781i	0.808996	−	1.40122i	0.913560	−	0.406704i	$-0.133322\pi$
$920$	9.46139			0.311933
$921$	−11.3974	+	9.60398i	−0.375557	+	0.316462i
$922$	−12.6175	+	7.28470i	−0.415534	+	0.239909i
$923$	−34.3683	+	0.241214i	−1.13125	+	0.00793964i
$924$	−15.8128	+	7.41365i	−0.520202	+	0.243891i
$925$	−3.33329	−	3.33329i	−0.109598	−	0.109598i
$926$	2.13437	−	1.23228i	0.0701397	−	0.0404952i
$927$	−22.7434	+	8.38511i	−0.746992	+	0.275403i
$928$	0.0836734	+	0.0836734i	0.00274671	+	0.00274671i
$929$	39.3652	+	10.5479i	1.29153	+	0.346065i	0.838242	−	0.545299i	$-0.183584\pi$
$929$	39.3652	+	10.5479i	1.29153	+	0.346065i	0.453289	+	0.891364i	$0.350250\pi$
$930$	1.19171	+	6.67737i	0.0390777	+	0.218960i
$931$	12.4670	+	3.34051i	0.408588	+	0.109481i
$932$			11.5360i			0.377874i
$933$	−0.514183	−	1.09672i	−0.0168336	−	0.0359048i
$934$	6.66242	−	6.66242i	0.218001	−	0.218001i
$935$	−33.4198			−1.09295
$936$	−15.7322	+	5.92593i	−0.514222	+	0.193695i
$937$	18.3170			0.598390			0.299195	−	0.954192i	$-0.403282\pi$
$937$	18.3170			0.598390			0.299195	+	0.954192i	$0.403282\pi$
$938$	3.74510	−	3.74510i	0.122282	−	0.122282i
$939$	21.2073	−	30.4215i	0.692074	−	0.992767i
$940$		−	16.8424i		−	0.549339i
$941$	−2.71294	−	0.726930i	−0.0884393	−	0.0236972i	0.214328	−	0.976762i	$-0.431244\pi$
$941$	−2.71294	−	0.726930i	−0.0884393	−	0.0236972i	−0.302767	+	0.953064i	$0.597911\pi$
$942$	−11.0430	−	3.99337i	−0.359801	−	0.130111i
$943$	−26.6172	−	7.13206i	−0.866775	−	0.232252i
$944$	29.6134	+	29.6134i	0.963834	+	0.963834i
$945$	−15.1465	−	14.9589i	−0.492716	−	0.486612i
$946$	−6.12831	+	3.53818i	−0.199248	+	0.115036i
$947$	30.8700	+	30.8700i	1.00314	+	1.00314i	0.999995	+	0.00314473i	$0.00100100\pi$
$947$	30.8700	+	30.8700i	1.00314	+	1.00314i	0.00314473	+	0.999995i	$0.498999\pi$
$948$	33.7493	+	23.5271i	1.09612	+	0.764126i
$949$	1.79764	+	3.06374i	0.0583538	+	0.0994532i
$950$	0.999570	−	0.577102i	0.0324303	−	0.0187237i
$951$	−7.63039	−	42.7545i	−0.247432	−	1.38641i
$952$	17.7162			0.574186
$953$	9.07394	−	15.7165i	0.293934	−	0.509108i	−0.680803	−	0.732467i	$-0.738369\pi$
$953$	9.07394	−	15.7165i	0.293934	−	0.509108i	0.974736	+	0.223359i	$0.0717021\pi$
$954$	6.07305	+	8.59697i	0.196622	+	0.278337i
$955$	8.06552	−	2.16115i	0.260994	−	0.0699331i
$956$	−2.29858	+	8.57842i	−0.0743414	+	0.277446i
$957$	0.100534	−	0.0847143i	0.00324979	−	0.00273842i
$958$	5.49964			0.177685
$959$	4.11007	−	7.11886i	0.132721	−	0.229880i
$960$	−5.29104	+	14.6315i	−0.170768	+	0.472231i
$961$	8.09330	+	4.67267i	0.261074	+	0.150731i
$962$	2.66545	+	9.67544i	0.0859374	+	0.311949i
$963$	−9.95376	+	3.66978i	−0.320755	+	0.118257i
$964$	4.46400	−	16.6599i	0.143776	−	0.536579i
$965$		−	32.9472i		−	1.06061i
$966$	−0.345231	+	4.04273i	−0.0111076	+	0.130073i
$967$	−4.76393	+	17.7792i	−0.153198	+	0.571742i	0.846055	+	0.533095i	$0.178971\pi$
$967$	−4.76393	+	17.7792i	−0.153198	+	0.571742i	−0.999253	+	0.0386464i	$0.987695\pi$
$968$	3.56837	−	3.56837i	0.114692	−	0.114692i
$969$	14.1302	−	39.0747i	0.453926	−	1.25526i
$970$	−2.66372	−	9.94115i	−0.0855270	−	0.319191i
$971$	−9.07902	−	5.24177i	−0.291360	−	0.168217i	0.347195	−	0.937793i	$-0.387134\pi$
$971$	−9.07902	−	5.24177i	−0.291360	−	0.168217i	−0.638555	+	0.769576i	$0.720467\pi$
$972$	11.8243	−	26.0607i	0.379265	−	0.835898i
$973$	−9.79502	−	2.62457i	−0.314014	−	0.0841398i
$974$	3.55000	−	6.14878i	0.113749	−	0.197020i
$975$	−3.25756	+	2.78430i	−0.104325	+	0.0891690i
$976$	−14.1174	−	24.4520i	−0.451887	−	0.782690i
$977$	14.8955	+	55.5906i	0.476548	+	1.77850i	0.615429	+	0.788192i	$0.288983\pi$
$977$	14.8955	+	55.5906i	0.476548	+	1.77850i	−0.138881	+	0.990309i	$0.544351\pi$
$978$	−8.53349	−	5.94883i	−0.272871	−	0.190223i
$979$	5.30948	−	3.06543i	0.169692	−	0.0979715i
$980$	8.38264	−	8.38264i	0.267774	−	0.267774i
$981$	−8.73163	−	12.3604i	−0.278780	−	0.394638i
$982$	−3.46933	−	12.9477i	−0.110711	−	0.413178i
$983$	−42.2268	+	11.3146i	−1.34682	+	0.360881i	−0.858962	−	0.512040i	$-0.828890\pi$
$983$	−42.2268	+	11.3146i	−1.34682	+	0.360881i	−0.487863	+	0.872920i	$0.662223\pi$
$984$	−14.4733	+	20.7617i	−0.461392	+	0.661859i
$985$	−27.7434	−	16.0177i	−0.883978	−	0.510365i
$986$	−0.0616524	+	0.0165197i	−0.00196341	+	0.000526095i
$987$	15.0366	+	1.28406i	0.478621	+	0.0408721i
$988$	27.4775	−	0.192850i	0.874174	−	0.00613538i
$989$		−	18.3842i		−	0.584584i
$990$	−6.38333	−	2.94437i	−0.202875	−	0.0935781i
$991$	16.9722	+	29.3967i	0.539140	+	0.933818i	0.998951	+	0.0458007i	$0.0145839\pi$
$991$	16.9722	+	29.3967i	0.539140	+	0.933818i	−0.459811	+	0.888017i	$0.652083\pi$
$992$	10.1002	+	17.4940i	0.320680	+	0.555435i
$993$	−6.14910	+	17.0044i	−0.195136	+	0.539617i
$994$	5.38710	+	5.38710i	0.170869	+	0.170869i
$995$	18.0971	+	18.0971i	0.573717	+	0.573717i
$996$	10.4103	−	1.85793i	0.329863	−	0.0588707i
$997$	20.0818	+	34.7827i	0.635997	+	1.10158i	0.986303	+	0.164943i	$0.0527442\pi$
$997$	20.0818	+	34.7827i	0.635997	+	1.10158i	−0.350306	+	0.936635i	$0.613923\pi$
$998$	−2.59990	−	4.50316i	−0.0822984	−	0.142545i
$999$	−31.0241	−	17.6549i	−0.981560	−	0.558576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.11.7	✓	48
3.2	odd	2		351.2.ba.a.89.6		48
9.4	even	3		351.2.bf.a.206.7		48
9.5	odd	6		117.2.bc.a.50.6	yes	48
13.6	odd	12		117.2.bc.a.110.6	yes	48
39.32	even	12		351.2.bf.a.305.7		48
117.32	even	12	inner	117.2.x.a.32.7	yes	48
117.58	odd	12		351.2.ba.a.71.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.7	✓	48	1.1	even	1	trivial
117.2.x.a.32.7	yes	48	117.32	even	12	inner
117.2.bc.a.50.6	yes	48	9.5	odd	6
117.2.bc.a.110.6	yes	48	13.6	odd	12
351.2.ba.a.71.6		48	117.58	odd	12
351.2.ba.a.89.6		48	3.2	odd	2
351.2.bf.a.206.7		48	9.4	even	3
351.2.bf.a.305.7		48	39.32	even	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.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.286505 - 0.286505i) q^{2} +(-1.72577 - 0.147373i) q^{3} +1.83583i q^{4} +(2.00620 + 0.537559i) q^{5} +(-0.536665 + 0.452219i) q^{6} +(1.90533 + 0.510531i) q^{7} +(1.09899 + 1.09899i) q^{8} +(2.95656 + 0.508664i) q^{9} +O(q^{10})\)	\(q+(0.286505 - 0.286505i) q^{2} +(-1.72577 - 0.147373i) q^{3} +1.83583i q^{4} +(2.00620 + 0.537559i) q^{5} +(-0.536665 + 0.452219i) q^{6} +(1.90533 + 0.510531i) q^{7} +(1.09899 + 1.09899i) q^{8} +(2.95656 + 0.508664i) q^{9} +(0.728800 - 0.420773i) q^{10} +(-1.96889 - 1.96889i) q^{11} +(0.270552 - 3.16822i) q^{12} +(-0.908720 + 3.48916i) q^{13} +(0.692156 - 0.399616i) q^{14} +(-3.38301 - 1.22336i) q^{15} -3.04193 q^{16} +(2.88941 - 5.00460i) q^{17} +(0.992806 - 0.701336i) q^{18} +(-4.00984 + 1.07443i) q^{19} +(-0.986867 + 3.68304i) q^{20} +(-3.21292 - 1.16185i) q^{21} -1.12819 q^{22} +(1.46551 - 2.53833i) q^{23} +(-1.73463 - 2.05856i) q^{24} +(-0.594268 - 0.343101i) q^{25} +(0.739309 + 1.26002i) q^{26} +(-5.02738 - 1.31356i) q^{27} +(-0.937247 + 3.49785i) q^{28} -0.0272596i q^{29} +(-1.31975 + 0.618751i) q^{30} +(1.20440 - 4.49489i) q^{31} +(-3.06950 + 3.06950i) q^{32} +(3.10768 + 3.68801i) q^{33} +(-0.606014 - 2.26167i) q^{34} +(3.54802 + 2.04845i) q^{35} +(-0.933821 + 5.42774i) q^{36} +(6.63559 + 1.77800i) q^{37} +(-0.841010 + 1.45667i) q^{38} +(2.08245 - 5.88756i) q^{39} +(1.61401 + 2.79555i) q^{40} +(-2.43331 - 9.08122i) q^{41} +(-1.25339 + 0.587640i) q^{42} +(5.43197 - 3.13615i) q^{43} +(3.61454 - 3.61454i) q^{44} +(5.65801 + 2.60981i) q^{45} +(-0.307370 - 1.14712i) q^{46} +(-4.26664 + 1.14324i) q^{47} +(5.24967 + 0.448299i) q^{48} +(-2.69255 - 1.55455i) q^{49} +(-0.268561 + 0.0719608i) q^{50} +(-5.72399 + 8.21096i) q^{51} +(-6.40550 - 1.66825i) q^{52} +8.65927i q^{53} +(-1.81671 + 1.06403i) q^{54} +(-2.89158 - 5.00837i) q^{55} +(1.53286 + 2.65499i) q^{56} +(7.07840 - 1.26328i) q^{57} +(-0.00781003 - 0.00781003i) q^{58} +(-9.73507 - 9.73507i) q^{59} +(2.24589 - 6.21064i) q^{60} +(4.64093 + 8.03833i) q^{61} +(-0.942743 - 1.63288i) q^{62} +(5.37353 + 2.47859i) q^{63} -4.32500i q^{64} +(-3.69870 + 6.51145i) q^{65} +(1.94700 + 0.166265i) q^{66} +(6.40101 - 1.71515i) q^{67} +(9.18759 + 5.30446i) q^{68} +(-2.90321 + 4.16460i) q^{69} +(1.60342 - 0.429635i) q^{70} +(2.46714 + 9.20749i) q^{71} +(2.69020 + 3.80823i) q^{72} +(0.696641 - 0.696641i) q^{73} +(2.41054 - 1.39172i) q^{74} +(0.975006 + 0.679692i) q^{75} +(-1.97248 - 7.36138i) q^{76} +(-2.74619 - 4.75655i) q^{77} +(-1.09019 - 2.28345i) q^{78} +(-6.46914 + 11.2049i) q^{79} +(-6.10271 - 1.63522i) q^{80} +(8.48252 + 3.00780i) q^{81} +(-3.29897 - 1.90466i) q^{82} +(0.860748 + 3.21235i) q^{83} +(2.13296 - 5.89836i) q^{84} +(8.48699 - 8.48699i) q^{85} +(0.657764 - 2.45481i) q^{86} +(-0.00401734 + 0.0470438i) q^{87} -4.32756i q^{88} +(-0.569878 + 2.12681i) q^{89} +(2.36877 - 0.873326i) q^{90} +(-3.51273 + 6.18406i) q^{91} +(4.65995 + 2.69042i) q^{92} +(-2.74095 + 7.57966i) q^{93} +(-0.894869 + 1.54996i) q^{94} -8.62210 q^{95} +(5.74961 - 4.84489i) q^{96} +(3.16527 - 11.8130i) q^{97} +(-1.21682 + 0.326045i) q^{98} +(-4.81963 - 6.82264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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