LMFDB - Embedded newform 117.2.bc.a.110.6

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			110.6
Character	$\chi$	$=$	117.110
Dual form			117.2.bc.a.50.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104868 + 0.391374i) q^{2} +(0.735256 + 1.56825i) q^{3} +(1.58987 + 0.917915i) q^{4} +(0.537559 - 2.00620i) q^{5} +(-0.690875 + 0.123300i) q^{6} +(-1.39480 - 1.39480i) q^{7} +(-1.09899 + 1.09899i) q^{8} +(-1.91880 + 2.30613i) q^{9} +O(q^{10})$	\(q+(-0.104868 + 0.391374i) q^{2} +(0.735256 + 1.56825i) q^{3} +(1.58987 + 0.917915i) q^{4} +(0.537559 - 2.00620i) q^{5} +(-0.690875 + 0.123300i) q^{6} +(-1.39480 - 1.39480i) q^{7} +(-1.09899 + 1.09899i) q^{8} +(-1.91880 + 2.30613i) q^{9} +(0.728800 + 0.420773i) q^{10} +(-2.68955 - 0.720663i) q^{11} +(-0.270552 + 3.16822i) q^{12} +(3.47606 + 0.957605i) q^{13} +(0.692156 - 0.399616i) q^{14} +(3.54146 - 0.632043i) q^{15} +(1.52096 + 2.63439i) q^{16} +(-2.88941 - 5.00460i) q^{17} +(-0.701336 - 0.992806i) q^{18} +(-4.00984 - 1.07443i) q^{19} +(2.69617 - 2.69617i) q^{20} +(1.16185 - 3.21292i) q^{21} +(0.564096 - 0.977044i) q^{22} +2.93102 q^{23} +(-2.53152 - 0.915445i) 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} +(-0.0236075 + 0.0136298i) q^{29} +(-0.124021 + 1.45231i) q^{30} +(-4.49489 - 1.20440i) q^{31} +(-4.19301 + 1.12351i) q^{32} +(-0.847330 - 4.74775i) q^{33} +(2.26167 - 0.606014i) q^{34} +(-3.54802 + 2.04845i) q^{35} +(-5.16747 + 1.90516i) q^{36} +(6.63559 - 1.77800i) q^{37} +(0.841010 - 1.45667i) q^{38} +(1.05403 + 6.15541i) q^{39} +(1.61401 + 2.79555i) q^{40} +(6.64791 + 6.64791i) q^{41} +(1.13561 + 0.791651i) q^{42} -6.27230i q^{43} +(-3.61454 - 3.61454i) q^{44} +(3.59508 + 5.08917i) q^{45} +(-0.307370 + 1.14712i) q^{46} +(-1.14324 - 4.26664i) q^{47} +(-3.01307 + 4.32220i) q^{48} -3.10909i q^{49} +(-0.196600 + 0.196600i) q^{50} +(5.72399 - 8.21096i) q^{51} +(4.64750 + 4.71320i) q^{52} +8.65927i q^{53} +(1.04130 - 1.82983i) q^{54} +(-2.89158 + 5.00837i) q^{55} +3.06572 q^{56} +(-1.26328 - 7.07840i) q^{57} +(-0.00285867 - 0.0106687i) q^{58} +(3.56328 + 13.2984i) q^{59} +(6.21064 + 2.24589i) q^{60} -9.28187 q^{61} +(0.942743 - 1.63288i) q^{62} +(5.89290 - 0.540244i) q^{63} +4.32500i q^{64} +(3.78973 - 6.45889i) q^{65} +(1.94700 + 0.166265i) q^{66} +(-4.68587 + 4.68587i) q^{67} -10.6089i q^{68} +(2.15505 + 4.59656i) q^{69} +(-0.429635 - 1.60342i) q^{70} +(-2.46714 + 9.20749i) q^{71} +(-0.425668 - 4.64313i) q^{72} +(0.696641 + 0.696641i) q^{73} +2.78345i q^{74} +(-0.101128 + 1.18423i) q^{75} +(-5.38891 - 5.38891i) q^{76} +(2.74619 + 4.75655i) q^{77} +(-2.51960 - 0.232986i) q^{78} +(-6.46914 + 11.2049i) q^{79} +(6.10271 - 1.63522i) q^{80} +(-1.63643 - 8.84998i) q^{81} +(-3.29897 + 1.90466i) q^{82} +(3.21235 - 0.860748i) q^{83} +(4.79638 - 4.04165i) q^{84} +(-11.5934 + 3.10645i) q^{85} +(2.45481 + 0.657764i) q^{86} +(-0.0387325 - 0.0270010i) q^{87} +(3.74777 - 2.16378i) 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} +(-1.41610 - 7.93465i) q^{93} +1.78974 q^{94} +(-4.31105 + 7.46696i) q^{95} +(-4.84489 - 5.74961i) q^{96} +(8.64769 - 8.64769i) q^{97} +(1.21682 + 0.326045i) q^{98} +(6.82264 - 4.81963i) 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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.104868	+	0.391374i	−0.0741530	+	0.276743i	−0.993040	−	0.117778i	$-0.962423\pi$
$2$	−0.104868	+	0.391374i	−0.0741530	+	0.276743i	0.918887	+	0.394521i	$0.129089\pi$
$3$	0.735256	+	1.56825i	0.424500	+	0.905428i
$3$	0.735256	+	1.56825i	0.424500	+	0.905428i
$4$	1.58987	+	0.917915i	0.794937	+	0.458957i
$5$	0.537559	−	2.00620i	0.240404	−	0.897199i	−0.735234	−	0.677813i	$-0.762928\pi$
$5$	0.537559	−	2.00620i	0.240404	−	0.897199i	0.975638	−	0.219386i	$-0.0704054\pi$
$6$	−0.690875	+	0.123300i	−0.282049	+	0.0503372i
$7$	−1.39480	−	1.39480i	−0.527183	−	0.527183i	0.392548	−	0.919731i	$-0.371594\pi$
$7$	−1.39480	−	1.39480i	−0.527183	−	0.527183i	−0.919731	+	0.392548i	$0.871594\pi$
$8$	−1.09899	+	1.09899i	−0.388550	+	0.388550i
$9$	−1.91880	+	2.30613i	−0.639599	+	0.768709i
$10$	0.728800	+	0.420773i	0.230467	+	0.133060i
$11$	−2.68955	−	0.720663i	−0.810930	−	0.217288i	−0.170552	−	0.985349i	$-0.554555\pi$
$11$	−2.68955	−	0.720663i	−0.810930	−	0.217288i	−0.640377	+	0.768061i	$0.721222\pi$
$12$	−0.270552	+	3.16822i	−0.0781016	+	0.914586i
$13$	3.47606	+	0.957605i	0.964086	+	0.265592i
$13$	3.47606	+	0.957605i	0.964086	+	0.265592i
$14$	0.692156	−	0.399616i	0.184986	−	0.106802i
$15$	3.54146	−	0.632043i	0.914400	−	0.163193i
$16$	1.52096	+	2.63439i	0.380241	+	0.658597i
$17$	−2.88941	−	5.00460i	−0.700784	−	1.21379i	−0.968192	−	0.250210i	$-0.919500\pi$
$17$	−2.88941	−	5.00460i	−0.700784	−	1.21379i	0.267408	−	0.963583i	$-0.413833\pi$
$18$	−0.701336	−	0.992806i	−0.165306	−	0.234007i
$19$	−4.00984	−	1.07443i	−0.919920	−	0.246492i	−0.232369	−	0.972628i	$-0.574648\pi$
$19$	−4.00984	−	1.07443i	−0.919920	−	0.246492i	−0.687551	+	0.726136i	$0.741314\pi$
$20$	2.69617	−	2.69617i	0.602882	−	0.602882i
$21$	1.16185	−	3.21292i	0.253537	−	0.701116i
$22$	0.564096	−	0.977044i	0.120266	−	0.208306i
$23$	2.93102			0.611159			0.305580	−	0.952167i	$-0.401150\pi$
$23$	2.93102			0.611159			0.305580	+	0.952167i	$0.401150\pi$
$24$	−2.53152	−	0.915445i	−0.516744	−	0.186864i
$25$	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
$29$	−0.0236075	+	0.0136298i	−0.00438381	+	0.00253099i	−0.502190	−	0.864757i	$-0.667472\pi$
$29$	−0.0236075	+	0.0136298i	−0.00438381	+	0.00253099i	0.497806	+	0.867288i	$0.334139\pi$
$30$	−0.124021	+	1.45231i	−0.0226431	+	0.265155i
$31$	−4.49489	−	1.20440i	−0.807307	−	0.216317i	−0.168517	−	0.985699i	$-0.553898\pi$
$31$	−4.49489	−	1.20440i	−0.807307	−	0.216317i	−0.638790	+	0.769381i	$0.720565\pi$
$32$	−4.19301	+	1.12351i	−0.741227	+	0.198611i
$33$	−0.847330	−	4.74775i	−0.147501	−	0.826477i
$34$	2.26167	−	0.606014i	0.387874	−	0.103930i
$35$	−3.54802	+	2.04845i	−0.599725	+	0.346251i
$36$	−5.16747	+	1.90516i	−0.861246	+	0.317527i
$37$	6.63559	−	1.77800i	1.09088	−	0.292302i	0.331837	−	0.943337i	$-0.392332\pi$
$37$	6.63559	−	1.77800i	1.09088	−	0.292302i	0.759047	+	0.651035i	$0.225665\pi$
$38$	0.841010	−	1.45667i	0.136430	−	0.236303i
$39$	1.05403	+	6.15541i	0.168780	+	0.985654i
$40$	1.61401	+	2.79555i	0.255198	+	0.442016i
$41$	6.64791	+	6.64791i	1.03823	+	1.03823i	0.999240	+	0.0389900i	$0.0124140\pi$
$41$	6.64791	+	6.64791i	1.03823	+	1.03823i	0.0389900	+	0.999240i	$0.487586\pi$
$42$	1.13561	+	0.791651i	0.175228	+	0.122154i
$43$		−	6.27230i		−	0.956516i	−0.878219	−	0.478258i	$-0.841268\pi$
$43$		−	6.27230i		−	0.956516i	0.878219	−	0.478258i	$-0.158732\pi$
$44$	−3.61454	−	3.61454i	−0.544912	−	0.544912i
$45$	3.59508	+	5.08917i	0.535922	+	0.758648i
$46$	−0.307370	+	1.14712i	−0.0453193	+	0.169134i
$47$	−1.14324	−	4.26664i	−0.166759	−	0.622353i	−0.997809	−	0.0661557i	$-0.978927\pi$
$47$	−1.14324	−	4.26664i	−0.166759	−	0.622353i	0.831050	−	0.556197i	$-0.187740\pi$
$48$	−3.01307	+	4.32220i	−0.434899	+	0.623855i
$49$		−	3.10909i		−	0.444156i
$50$	−0.196600	+	0.196600i	−0.0278035	+	0.0278035i
$51$	5.72399	−	8.21096i	0.801519	−	1.14976i
$52$	4.64750	+	4.71320i	0.644492	+	0.653603i
$53$			8.65927i			1.18944i	0.803932	+	0.594721i	$0.202737\pi$
$53$			8.65927i			1.18944i	−0.803932	+	0.594721i	$0.797263\pi$
$54$	1.04130	−	1.82983i	0.141703	−	0.249009i
$55$	−2.89158	+	5.00837i	−0.389901	+	0.675328i
$56$	3.06572			0.409674
$57$	−1.26328	−	7.07840i	−0.167326	−	0.937557i
$58$	−0.00285867	−	0.0106687i	−0.000375362	−	0.00140087i
$59$	3.56328	+	13.2984i	0.463900	+	1.73130i	0.660510	+	0.750817i	$0.270340\pi$
$59$	3.56328	+	13.2984i	0.463900	+	1.73130i	−0.196610	+	0.980482i	$0.562993\pi$
$60$	6.21064	+	2.24589i	0.801790	+	0.289943i
$61$	−9.28187			−1.18842			−0.594211	−	0.804309i	$-0.702535\pi$
$61$	−9.28187			−1.18842			−0.594211	+	0.804309i	$0.702535\pi$
$62$	0.942743	−	1.63288i	0.119729	−	0.207376i
$63$	5.89290	−	0.540244i	0.742436	−	0.0680644i
$64$			4.32500i			0.540625i
$65$	3.78973	−	6.45889i	0.470058	−	0.801127i
$66$	1.94700	+	0.166265i	0.239659	+	0.0204659i
$67$	−4.68587	+	4.68587i	−0.572470	+	0.572470i	−0.932818	−	0.360348i	$-0.882658\pi$
$67$	−4.68587	+	4.68587i	−0.572470	+	0.572470i	0.360348	+	0.932818i	$0.382658\pi$
$68$		−	10.6089i		−	1.28652i
$69$	2.15505	+	4.59656i	0.259437	+	0.553361i
$70$	−0.429635	−	1.60342i	−0.0513512	−	0.191645i
$71$	−2.46714	+	9.20749i	−0.292795	+	1.09273i	0.650157	+	0.759800i	$0.274703\pi$
$71$	−2.46714	+	9.20749i	−0.292795	+	1.09273i	−0.942952	+	0.332928i	$0.891964\pi$
$72$	−0.425668	−	4.64313i	−0.0501655	−	0.547198i
$73$	0.696641	+	0.696641i	0.0815356	+	0.0815356i	0.746698	−	0.665163i	$-0.231638\pi$
$73$	0.696641	+	0.696641i	0.0815356	+	0.0815356i	−0.665163	+	0.746698i	$0.731638\pi$
$74$			2.78345i			0.323569i
$75$	−0.101128	+	1.18423i	−0.0116772	+	0.136743i
$76$	−5.38891	−	5.38891i	−0.618150	−	0.618150i
$77$	2.74619	+	4.75655i	0.312958	+	0.542059i
$78$	−2.51960	−	0.232986i	−0.285288	−	0.0263805i
$79$	−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
$81$	−1.63643	−	8.84998i	−0.181826	−	0.983331i
$82$	−3.29897	+	1.90466i	−0.364311	+	0.210335i
$83$	3.21235	−	0.860748i	0.352602	−	0.0944793i	−0.0781706	−	0.996940i	$-0.524908\pi$
$83$	3.21235	−	0.860748i	0.352602	−	0.0944793i	0.430772	+	0.902461i	$0.358241\pi$
$84$	4.79638	−	4.04165i	0.523328	−	0.440980i
$85$	−11.5934	+	3.10645i	−1.25748	+	0.336942i
$86$	2.45481	+	0.657764i	0.264709	+	0.0709286i
$87$	−0.0387325	−	0.0270010i	−0.00415256	−	0.00289481i
$88$	3.74777	−	2.16378i	0.399514	−	0.230659i
$89$	0.569878	+	2.12681i	0.0604069	+	0.225442i	0.989530	−	0.144330i	$-0.0461026\pi$
$89$	0.569878	+	2.12681i	0.0604069	+	0.225442i	−0.929123	+	0.369771i	$0.879436\pi$
$90$	−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
$93$	−1.41610	−	7.93465i	−0.146842	−	0.822785i
$94$	1.78974			0.184597
$95$	−4.31105	+	7.46696i	−0.442305	+	0.766094i
$96$	−4.84489	−	5.74961i	−0.494479	−	0.586817i
$97$	8.64769	−	8.64769i	0.878040	−	0.878040i	−0.115292	−	0.993332i	$-0.536780\pi$
$97$	8.64769	−	8.64769i	0.878040	−	0.878040i	0.993332	+	0.115292i	$0.0367803\pi$
$98$	1.21682	+	0.326045i	0.122917	+	0.0329355i
$99$	6.82264	−	4.81963i	0.685701	−	0.484391i
$100$	0.629875	+	1.09098i	0.0629875	+	0.109098i
$101$	−5.85306	−	10.1378i	−0.582401	−	1.00875i	−0.995194	−	0.0979236i	$-0.968780\pi$
$101$	−5.85306	−	10.1378i	−0.582401	−	1.00875i	0.412793	−	0.910825i	$-0.364553\pi$
$102$	2.61329	+	3.10129i	0.258754	+	0.307073i
$103$	6.99746	−	4.03998i	0.689480	−	0.398071i	−0.113937	−	0.993488i	$-0.536346\pi$
$103$	6.99746	−	4.03998i	0.689480	−	0.398071i	0.803417	+	0.595417i	$0.203013\pi$
$104$	−4.87253	+	2.76775i	−0.477791	+	0.271400i
$105$	−5.82118	−	4.05804i	−0.568089	−	0.396024i
$106$	−3.38901	−	0.908082i	−0.329170	−	0.0882007i
$107$	3.06247	+	1.76812i	0.296060	+	0.170930i	0.640672	−	0.767815i	$-0.278656\pi$
$107$	3.06247	+	1.76812i	0.296060	+	0.170930i	−0.344612	+	0.938745i	$0.611989\pi$
$108$	−6.78718	−	6.70310i	−0.653096	−	0.645006i
$109$	−3.56699	+	3.56699i	−0.341656	+	0.341656i	−0.856990	−	0.515334i	$-0.827668\pi$
$109$	−3.56699	+	3.56699i	−0.341656	+	0.341656i	0.515334	+	0.856990i	$0.327668\pi$
$110$	−1.65691	−	1.65691i	−0.157980	−	0.157980i
$111$	7.66720	+	9.09896i	0.727738	+	0.863635i
$112$	1.55300	−	5.79586i	0.146744	−	0.547658i
$113$	−12.7055	−	7.33552i	−1.19523	−	0.690068i	−0.235744	−	0.971815i	$-0.575753\pi$
$113$	−12.7055	−	7.33552i	−1.19523	−	0.690068i	−0.959489	+	0.281748i	$0.909086\pi$
$114$	2.90278	+	0.247884i	0.271870	+	0.0232165i
$115$	1.57559	−	5.88020i	0.146925	−	0.548331i
$116$	−0.0500440			−0.00464647
$117$	−8.87821	+	6.17878i	−0.820791	+	0.571229i
$118$	−5.57830			−0.513524
$119$	−2.95026	+	11.0105i	−0.270450	+	1.00933i
$120$	−3.19740	+	4.58662i	−0.291882	+	0.418699i
$121$	−2.81196	−	1.62349i	−0.255633	−	0.147590i
$122$	0.973373	−	3.63268i	0.0881250	−	0.328887i
$123$	−5.53765	+	15.3135i	−0.499313	+	1.38077i
$124$	−6.04078	−	6.04078i	−0.542478	−	0.542478i
$125$	8.35097	−	8.35097i	0.746934	−	0.746934i
$126$	−0.406541	+	2.36298i	−0.0362176	+	0.210511i
$127$	7.25477	+	4.18854i	0.643757	+	0.371673i	0.786060	−	0.618150i	$-0.212118\pi$
$127$	7.25477	+	4.18854i	0.643757	+	0.371673i	−0.142303	+	0.989823i	$0.545451\pi$
$128$	−10.0787	−	2.70058i	−0.890841	−	0.238700i
$129$	9.83651	−	4.61174i	0.866056	−	0.406041i
$130$	2.13042	+	2.16053i	0.186850	+	0.189491i
$131$	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	$0.00867816\pi$
$132$	3.01088	−	8.32610i	0.262063	−	0.724694i
$133$	4.09429	+	7.09152i	0.355020	+	0.614913i
$134$	−1.34253	−	2.32532i	−0.115977	−	0.200877i
$135$	−5.33777	+	9.37981i	−0.459402	+	0.807285i
$136$	8.67540	+	2.32457i	0.743909	+	0.199330i
$137$	−2.94672	+	2.94672i	−0.251755	+	0.251755i	−0.821690	−	0.569935i	$-0.806969\pi$
$137$	−2.94672	+	2.94672i	−0.251755	+	0.251755i	0.569935	+	0.821690i	$0.306969\pi$
$138$	−2.02497	+	0.361396i	−0.172377	+	0.0307640i
$139$	2.57043	−	4.45212i	0.218021	−	0.377624i	−0.736182	−	0.676784i	$-0.763373\pi$
$139$	2.57043	−	4.45212i	0.218021	−	0.377624i	0.954203	+	0.299160i	$0.0967065\pi$
$140$	−7.52121			−0.635658
$141$	5.85056	−	4.92996i	0.492706	−	0.415177i
$142$	−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
$146$	−0.345702	+	0.199591i	−0.0286105	+	0.0165183i
$147$	4.87582	−	2.28598i	0.402151	−	0.188544i
$148$	12.1818	+	3.26411i	1.00134	+	0.268308i
$149$	0.599927	−	0.160750i	0.0491479	−	0.0131691i	−0.234161	−	0.972198i	$-0.575234\pi$
$149$	0.599927	−	0.160750i	0.0491479	−	0.0131691i	0.283309	+	0.959029i	$0.408568\pi$
$150$	−0.452870	−	0.163766i	−0.0369767	−	0.0133715i
$151$	−9.50243	+	2.54617i	−0.773297	+	0.207204i	−0.623828	−	0.781562i	$-0.714423\pi$
$151$	−9.50243	+	2.54617i	−0.773297	+	0.207204i	−0.149469	+	0.988766i	$0.547757\pi$
$152$	5.58754	−	3.22597i	0.453210	−	0.261661i
$153$	17.0854	+	2.93948i	1.38127	+	0.237642i
$154$	−2.14958	+	0.575977i	−0.173218	+	0.0464135i
$155$	−4.83254	+	8.37021i	−0.388159	+	0.672311i
$156$	−3.97436	+	10.7538i	−0.318203	+	0.860996i
$157$	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	$0.600609\pi$
$158$	−3.70688	−	3.70688i	−0.294904	−	0.294904i
$159$	−13.5799	+	6.36678i	−1.07695	+	0.504918i
$160$			9.01597i			0.712775i
$161$	−4.08817	−	4.08817i	−0.322193	−	0.322193i
$162$	3.63526	+	0.287625i	0.285613	+	0.0225979i
$163$	3.83636	−	14.3175i	0.300487	−	1.12143i	−0.636274	−	0.771463i	$-0.719525\pi$
$163$	3.83636	−	14.3175i	0.300487	−	1.12143i	0.936761	−	0.349970i	$-0.113808\pi$
$164$	4.46713	+	16.6716i	0.348824	+	1.30183i
$165$	−9.98041	−	0.852283i	−0.776974	−	0.0663502i
$166$			1.34750i			0.104586i
$167$	1.39941	−	1.39941i	0.108290	−	0.108290i	−0.650886	−	0.759176i	$-0.725602\pi$
$167$	1.39941	−	1.39941i	0.108290	−	0.108290i	0.759176	+	0.650886i	$0.225602\pi$
$168$	2.25409	+	4.80781i	0.173907	+	0.370930i
$169$	11.1660	+	6.65738i	0.858922	+	0.512107i
$170$		−	4.86313i		−	0.372985i
$171$	10.1718	−	7.18558i	0.777861	−	0.549495i
$172$	5.75743	−	9.97217i	0.439000	−	0.760370i
$173$	12.8602			0.977741			0.488871	−	0.872356i	$-0.337409\pi$
$173$	12.8602			0.977741			0.488871	+	0.872356i	$0.337409\pi$
$174$	0.0146293	−	0.0123273i	0.00110904	−	0.000934532i
$175$	−0.350327	−	1.30744i	−0.0264822	−	0.0988330i
$176$	−2.19220	−	8.18142i	−0.165244	−	0.616697i
$177$	−18.2352	+	15.3658i	−1.37064	+	1.15496i
$178$	−0.892140			−0.0668687
$179$	−8.57752	+	14.8567i	−0.641114	+	1.11044i	0.344071	+	0.938944i	$0.388194\pi$
$179$	−8.57752	+	14.8567i	−0.641114	+	1.11044i	−0.985184	+	0.171498i	$0.945139\pi$
$180$	1.04430	+	11.3911i	0.0778378	+	0.849043i
$181$		−	2.95175i		−	0.219402i	−0.993965	−	0.109701i	$-0.965011\pi$
$181$		−	2.95175i		−	0.219402i	0.993965	−	0.109701i	$-0.0349893\pi$
$182$	2.78865	−	0.726278i	0.206708	−	0.0538353i
$183$	−6.82455	−	14.5563i	−0.504485	−	1.07603i
$184$	−3.22114	+	3.22114i	−0.237466	+	0.237466i
$185$		−	14.2681i		−	1.04901i
$186$	3.25392	+	0.277870i	0.238589	+	0.0203744i
$187$	4.16457	+	15.5424i	0.304544	+	1.13657i
$188$	2.09880	−	7.83282i	0.153070	−	0.571267i
$189$	5.18003	+	8.84431i	0.376792	+	0.643329i
$190$	−2.47028	−	2.47028i	−0.179213	−	0.179213i
$191$			4.02030i			0.290899i	0.989366	+	0.145449i	$0.0464628\pi$
$191$			4.02030i			0.290899i	−0.989366	+	0.145449i	$0.953537\pi$
$192$	−6.78267	+	3.17998i	−0.489497	+	0.229495i
$193$	−11.2169	−	11.2169i	−0.807411	−	0.807411i	0.176830	−	0.984241i	$-0.443416\pi$
$193$	−11.2169	−	11.2169i	−0.807411	−	0.807411i	−0.984241	+	0.176830i	$0.943416\pi$
$194$	2.47761	+	4.29134i	0.177882	+	0.308101i
$195$	12.9156	+	1.19430i	0.924903	+	0.0855253i
$196$	2.85388	−	4.94307i	0.203849	−	0.353076i
$197$	14.8985	−	3.99204i	1.06148	−	0.284421i	0.314489	−	0.949261i	$-0.398167\pi$
$197$	14.8985	−	3.99204i	1.06148	−	0.284421i	0.746986	+	0.664840i	$0.231500\pi$
$198$	1.17080	+	3.17563i	0.0832051	+	0.225682i
$199$	10.6715	−	6.16118i	0.756481	−	0.436755i	−0.0715498	−	0.997437i	$-0.522794\pi$
$199$	10.6715	−	6.16118i	0.756481	−	0.436755i	0.828031	+	0.560682i	$0.189461\pi$
$200$	−1.03016	+	0.276029i	−0.0728430	+	0.0195182i
$201$	−10.7939	−	3.90328i	−0.761343	−	0.275316i
$202$	4.58147	−	1.22760i	0.322351	−	0.0863736i
$203$	0.0519385	+	0.0139169i	0.00364537	+	0.000976773i
$204$	16.6374	−	7.80027i	1.16485	−	0.546128i
$205$	16.9107	−	9.76338i	1.18109	−	0.681904i
$206$	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
$210$	2.19866	−	1.85270i	0.151722	−	0.127848i
$211$	22.9480			1.57981			0.789903	−	0.613231i	$-0.210131\pi$
$211$	22.9480			1.57981			0.789903	+	0.613231i	$0.210131\pi$
$212$	−7.94847	+	13.7672i	−0.545903	+	0.945532i
$213$	−16.2536	+	2.90078i	−1.11368	+	0.198758i
$214$	−1.01315	+	1.01315i	−0.0692575	+	0.0692575i
$215$	−12.5835	−	3.37173i	−0.858185	−	0.229950i
$216$	6.96860	−	4.08144i	0.474153	−	0.277707i
$217$	4.58956	+	7.94935i	0.311560	+	0.539637i
$218$	−1.02196	−	1.77009i	−0.0692160	−	0.119886i
$219$	−0.580295	+	1.60471i	−0.0392127	+	0.108437i
$220$	−9.19451	+	5.30845i	−0.619894	+	0.357896i
$221$	−5.25132	−	20.1632i	−0.353242	−	1.35632i
$222$	−4.36514	+	2.04655i	−0.292969	+	0.137355i
$223$	−20.2852	−	5.43539i	−1.35839	−	0.363981i	−0.495168	−	0.868797i	$-0.664893\pi$
$223$	−20.2852	−	5.43539i	−1.35839	−	0.363981i	−0.863227	+	0.504817i	$0.831560\pi$
$224$	7.41547	+	4.28132i	0.495467	+	0.286058i
$225$	−1.93151	+	0.712116i	−0.128768	+	0.0474744i
$226$	4.20333	−	4.20333i	0.279601	−	0.279601i
$227$	−20.3096	−	20.3096i	−1.34799	−	1.34799i	−0.887840	−	0.460153i	$-0.847795\pi$
$227$	−20.3096	−	20.3096i	−1.34799	−	1.34799i	−0.460153	−	0.887840i	$-0.652205\pi$
$228$	4.48891	−	12.4134i	0.297285	−	0.822095i
$229$	−1.93343	+	7.21566i	−0.127765	+	0.476824i	−0.999923	−	0.0123994i	$-0.996053\pi$
$229$	−1.93343	+	7.21566i	−0.127765	+	0.476824i	0.872159	+	0.489223i	$0.162720\pi$
$230$	2.13612	+	1.23329i	0.140852	+	0.0813209i
$231$	−5.44029	+	7.80399i	−0.357945	+	0.513465i
$232$	0.0109654	−	0.0409233i	0.000719912	−	0.00268675i
$233$	−6.28380			−0.411666			−0.205833	−	0.978587i	$-0.565990\pi$
$233$	−6.28380			−0.411666			−0.205833	+	0.978587i	$0.565990\pi$
$234$	−1.48717	−	4.12266i	−0.0972193	−	0.269506i
$235$	−9.17428			−0.598464
$236$	−6.54158	+	24.4135i	−0.425821	+	1.58918i
$237$	−22.3285	−	1.90675i	−1.45039	−	0.123857i
$238$	−3.99984	−	2.30931i	−0.259271	−	0.149690i
$239$	1.25207	−	4.67278i	0.0809894	−	0.302257i	−0.913535	−	0.406760i	$-0.866659\pi$
$239$	1.25207	−	4.67278i	0.0809894	−	0.302257i	0.994525	+	0.104503i	$0.0333252\pi$
$240$	7.05148	+	8.36825i	0.455171	+	0.540168i
$241$	6.64325	+	6.64325i	0.427929	+	0.427929i	0.887923	−	0.459993i	$-0.152148\pi$
$241$	6.64325	+	6.64325i	0.427929	+	0.427929i	−0.459993	+	0.887923i	$0.652148\pi$
$242$	0.930274	−	0.930274i	0.0598003	−	0.0598003i
$243$	12.6758	−	9.07333i	0.813150	−	0.582054i
$244$	−14.7570	−	8.51996i	−0.944721	−	0.545435i
$245$	−6.23745	−	1.67132i	−0.398496	−	0.106777i
$246$	−5.41257	−	3.77319i	−0.345093	−	0.240570i
$247$	−12.9096	−	7.57464i	−0.821416	−	0.481963i
$248$	6.26345	−	3.61620i	0.397729	−	0.229629i
$249$	3.71177	+	4.40489i	0.235224	+	0.279149i
$250$	2.39260	+	4.14410i	0.151321	+	0.262096i
$251$	−1.72591	−	2.98936i	−0.108938	−	0.188687i	0.806402	−	0.591368i	$-0.201412\pi$
$251$	−1.72591	−	2.98936i	−0.108938	−	0.188687i	−0.915340	+	0.402681i	$0.868078\pi$
$252$	9.86488	+	4.55026i	0.621429	+	0.286640i
$253$	−7.88311	−	2.11227i	−0.495607	−	0.132798i
$254$	−2.40008	+	2.40008i	−0.150594	+	0.150594i
$255$	−13.3958	−	15.8973i	−0.838879	−	0.995530i
$256$	−2.21113	+	3.82978i	−0.138195	+	0.239361i
$257$	−14.7485			−0.919984			−0.459992	−	0.887923i	$-0.652148\pi$
$257$	−14.7485			−0.919984			−0.459992	+	0.887923i	$0.652148\pi$
$258$	0.773377	+	4.33337i	0.0481483	+	0.269784i
$259$	−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
$263$	−9.44058	+	5.45052i	−0.582131	+	0.336094i	−0.761980	−	0.647601i	$-0.775773\pi$
$263$	−9.44058	+	5.45052i	−0.582131	+	0.336094i	0.179849	+	0.983694i	$0.442439\pi$
$264$	6.14891	+	4.28650i	0.378439	+	0.263816i
$265$	17.3722	+	4.65487i	1.06717	+	0.285946i
$266$	−3.20479	+	0.858722i	−0.196499	+	0.0526516i
$267$	−2.91636	+	2.45746i	−0.178478	+	0.150394i
$268$	−11.7512	+	3.14872i	−0.717817	+	0.192338i
$269$	26.4194	−	15.2532i	1.61082	−	0.930006i	0.621637	−	0.783306i	$-0.286468\pi$
$269$	26.4194	−	15.2532i	1.61082	−	0.930006i	0.989181	−	0.146701i	$-0.0468654\pi$
$270$	−3.11125	−	3.07270i	−0.189344	−	0.186999i
$271$	−0.434695	+	0.116476i	−0.0264059	+	0.00707543i	−0.271998	−	0.962298i	$-0.587684\pi$
$271$	−0.434695	+	0.116476i	−0.0264059	+	0.00707543i	0.245592	+	0.969373i	$0.421018\pi$
$272$	8.78937	−	15.2236i	0.532934	−	0.923068i
$273$	7.11537	−	10.0557i	0.430642	−	0.608598i
$274$	−0.844251	−	1.46229i	−0.0510031	−	0.0883400i
$275$	−1.35105	−	1.35105i	−0.0814716	−	0.0814716i
$276$	−0.792992	+	9.28610i	−0.0477325	+	0.558958i
$277$		−	22.2056i		−	1.33420i	−0.744966	−	0.667102i	$-0.767534\pi$
$277$		−	22.2056i		−	1.33420i	0.744966	−	0.667102i	$-0.232466\pi$
$278$	1.47289	+	1.47289i	0.0883378	+	0.0883378i
$279$	11.4023	−	8.05479i	0.682638	−	0.482227i
$280$	1.64801	−	6.15044i	0.0984871	−	0.367559i
$281$	−3.85914	−	14.4025i	−0.230217	−	0.859182i	−0.980247	−	0.197778i	$-0.936628\pi$
$281$	−3.85914	−	14.4025i	−0.230217	−	0.859182i	0.750030	−	0.661404i	$-0.230039\pi$
$282$	1.31592	+	2.80675i	0.0783616	+	0.167140i
$283$		−	13.0490i		−	0.775683i	−0.921726	−	0.387842i	$-0.873221\pi$
$283$		−	13.0490i		−	0.775683i	0.921726	−	0.387842i	$-0.126779\pi$
$284$	−12.3741	+	12.3741i	−0.734269	+	0.734269i
$285$	−14.8798	−	1.27067i	−0.881401	−	0.0752678i
$286$	2.89646	−	2.85608i	0.171271	−	0.168884i
$287$		−	18.5450i		−	1.09467i
$288$	5.45458	−	11.8254i	0.321414	−	0.696819i
$289$	−8.19733	+	14.1982i	−0.482196	+	0.835188i
$290$	−0.0229402			−0.00134710
$291$	19.9200	+	7.20345i	1.16773	+	0.422274i
$292$	0.468115	+	1.74703i	0.0273943	+	0.102237i
$293$	5.33407	+	19.9070i	0.311620	+	1.16298i	0.927096	+	0.374825i	$0.122297\pi$
$293$	5.33407	+	19.9070i	0.311620	+	1.16298i	−0.615476	+	0.788155i	$0.711036\pi$
$294$	0.383352	+	2.14800i	0.0223576	+	0.125274i
$295$	28.5946			1.66484
$296$	−5.33842	+	9.24641i	−0.310289	+	0.537437i
$297$	12.5748	+	7.15592i	0.729662	+	0.415228i
$298$			0.251653i			0.0145779i
$299$	10.1884	+	2.80676i	0.589210	+	0.162319i
$300$	−1.24780	+	1.78995i	−0.0720417	+	0.103343i
$301$	−8.74857	+	8.74857i	−0.504259	+	0.504259i
$302$		−	3.98601i		−	0.229369i
$303$	11.5951	−	16.6329i	0.666120	−	0.955536i
$304$	−3.26835	−	12.1976i	−0.187453	−	0.699583i
$305$	−4.98955	+	18.6213i	−0.285701	+	1.06625i
$306$	−2.94215	+	6.37852i	−0.168192	+	0.364636i
$307$	6.08464	+	6.08464i	0.347269	+	0.347269i	0.859091	−	0.511822i	$-0.171029\pi$
$307$	6.08464	+	6.08464i	0.347269	+	0.347269i	−0.511822	+	0.859091i	$0.671029\pi$
$308$			10.0831i			0.574537i
$309$	11.4806	+	8.00332i	0.653109	+	0.455293i
$310$	−2.76910	−	2.76910i	−0.157274	−	0.157274i
$311$	−0.349663	−	0.605634i	−0.0198276	−	0.0343423i	0.855941	−	0.517073i	$-0.172978\pi$
$311$	−0.349663	−	0.605634i	−0.0198276	−	0.0343423i	−0.875769	+	0.482731i	$0.839645\pi$
$312$	−7.92307	−	5.60633i	−0.448555	−	0.317396i
$313$	−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
$315$	2.08395	−	12.1127i	0.117417	−	0.682476i
$316$	−20.5702	+	11.8762i	−1.15717	+	0.668090i
$317$	24.2200	−	6.48972i	1.36033	−	0.364499i	0.496392	−	0.868099i	$-0.334658\pi$
$317$	24.2200	−	6.48972i	1.36033	−	0.364499i	0.863937	+	0.503600i	$0.167991\pi$
$318$	−1.06769	−	5.98247i	−0.0598732	−	0.335481i
$319$	0.0733161	−	0.0196450i	0.00410491	−	0.00109991i
$320$	8.67681	+	2.32494i	0.485048	+	0.129968i
$321$	−0.521146	+	6.10273i	−0.0290875	+	0.340621i
$322$	2.02872	−	1.17128i	0.113056	−	0.0652730i
$323$	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
$327$	−8.21658	−	2.97127i	−0.454378	−	0.164312i
$328$	−14.6119			−0.806808
$329$	−4.35650	+	7.54567i	−0.240181	+	0.416006i
$330$	1.38019	−	3.81669i	0.0759769	−	0.210102i
$331$	7.38195	−	7.38195i	0.405749	−	0.405749i	−0.474504	−	0.880253i	$-0.657373\pi$
$331$	7.38195	−	7.38195i	0.405749	−	0.405749i	0.880253	+	0.474504i	$0.157373\pi$
$332$	5.89733	+	1.58019i	0.323658	+	0.0867240i
$333$	−8.63206	+	18.7141i	−0.473034	+	1.02553i
$334$	0.400939	+	0.694446i	0.0219384	+	0.0379984i
$335$	6.88184	+	11.9197i	0.375995	+	0.651243i
$336$	10.2312	−	1.82596i	0.558158	−	0.0996143i
$337$	−11.9865	+	6.92043i	−0.652948	+	0.376980i	−0.789585	−	0.613641i	$-0.789704\pi$
$337$	−11.9865	+	6.92043i	−0.652948	+	0.376980i	0.136637	+	0.990621i	$0.456371\pi$
$338$	−3.77648	+	3.67192i	−0.205414	+	0.199726i
$339$	2.16212	−	25.3188i	0.117430	−	1.37513i
$340$	−21.2836	−	5.70292i	−1.15426	−	0.309284i
$341$	11.2213	+	6.47860i	0.607666	+	0.350836i
$342$	1.74554	+	4.73453i	0.0943880	+	0.256014i
$343$	−14.1001	+	14.1001i	−0.761335	+	0.761335i
$344$	6.89316	+	6.89316i	0.371654	+	0.371654i
$345$	10.3801	−	1.85253i	0.558844	−	0.0997368i
$346$	−1.34862	+	5.03313i	−0.0725025	+	0.270583i
$347$	−3.53399	−	2.04035i	−0.189715	−	0.109532i	0.402134	−	0.915581i	$-0.368268\pi$
$347$	−3.53399	−	2.04035i	−0.189715	−	0.109532i	−0.591849	+	0.806049i	$0.701602\pi$
$348$	−0.0367952	−	0.0784814i	−0.00197243	−	0.00420704i
$349$	−1.80365	+	6.73133i	−0.0965474	+	0.360320i	−0.997250	−	0.0741174i	$-0.976386\pi$
$349$	−1.80365	+	6.73133i	−0.0965474	+	0.360320i	0.900702	+	0.434437i	$0.143053\pi$
$350$	0.548435			0.0293151
$351$	−16.2176	−	9.38024i	−0.865632	−	0.500680i
$352$	12.0870			0.644239
$353$	−2.64815	+	9.88304i	−0.140947	+	0.526021i	0.858955	+	0.512050i	$0.171114\pi$
$353$	−2.64815	+	9.88304i	−0.140947	+	0.526021i	−0.999902	+	0.0139710i	$0.995553\pi$
$354$	−4.10148	−	8.74815i	−0.217991	−	0.464959i
$355$	17.1458	+	9.89913i	0.910005	+	0.525391i
$356$	−1.04620	+	3.90446i	−0.0554484	+	0.206936i
$357$	−19.4364	+	3.46881i	−1.02868	+	0.183589i
$358$	−4.91501	−	4.91501i	−0.259766	−	0.259766i
$359$	−13.1160	+	13.1160i	−0.692237	+	0.692237i	−0.962724	−	0.270486i	$-0.912816\pi$
$359$	−13.1160	+	13.1160i	−0.692237	+	0.692237i	0.270486	+	0.962724i	$0.412816\pi$
$360$	−9.54386	−	1.64198i	−0.503005	−	0.0865400i
$361$	−1.53007	−	0.883389i	−0.0805302	−	0.0464941i
$362$	1.15524	+	0.309545i	0.0607179	+	0.0162693i
$363$	0.478516	−	5.60352i	0.0251156	−	0.294109i
$364$	0.0916352	−	13.0563i	0.00480299	−	0.684334i
$365$	1.77208	−	1.02311i	0.0927551	−	0.0535522i
$366$	6.41261	−	1.14446i	0.335193	−	0.0598218i
$367$	0.172565	+	0.298892i	0.00900784	+	0.0156020i	0.870494	−	0.492179i	$-0.163799\pi$
$367$	0.172565	+	0.298892i	0.00900784	+	0.0156020i	−0.861486	+	0.507781i	$0.830466\pi$
$368$	4.45797	+	7.72143i	0.232388	+	0.402507i
$369$	−28.0869	+	2.57493i	−1.46215	+	0.134045i
$370$	5.58415	+	1.49627i	0.290306	+	0.0777873i
$371$	12.0779	−	12.0779i	0.627054	−	0.627054i
$372$	5.03192	−	13.9150i	0.260893	−	0.721457i
$373$	−0.573106	+	0.992649i	−0.0296743	+	0.0513974i	−0.880481	−	0.474081i	$-0.842780\pi$
$373$	−0.573106	+	0.992649i	−0.0296743	+	0.0513974i	0.850807	+	0.525479i	$0.176114\pi$
$374$	−6.51961			−0.337121
$375$	19.2365	+	6.95629i	0.993368	+	0.359221i
$376$	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	−0.970221	−	0.242223i	$-0.922123\pi$
$379$	−4.88833	−	18.2435i	−0.251097	−	0.937105i	0.719124	−	0.694882i	$-0.244543\pi$
$380$	−13.7081	+	7.91435i	−0.703209	+	0.405998i
$381$	−1.23456	+	14.4569i	−0.0632483	+	0.740651i
$382$	−1.57344	−	0.421602i	−0.0805042	−	0.0215710i
$383$	29.2997	−	7.85084i	1.49715	−	0.401159i	0.585003	−	0.811031i	$-0.301093\pi$
$383$	29.2997	−	7.85084i	1.49715	−	0.401159i	0.912143	+	0.409872i	$0.134427\pi$
$384$	−3.17525	−	17.7915i	−0.162037	−	0.907921i
$385$	11.0188	−	2.95248i	0.561571	−	0.150472i
$386$	5.56630	−	3.21370i	0.283317	−	0.163573i
$387$	14.4647	+	12.0353i	0.735282	+	0.611787i
$388$	21.6866	−	5.81090i	1.10097	−	0.295004i
$389$	−1.94710	+	3.37247i	−0.0987217	+	0.170991i	−0.911156	−	0.412062i	$-0.864809\pi$
$389$	−1.94710	+	3.37247i	−0.0987217	+	0.170991i	0.812434	+	0.583053i	$0.198142\pi$
$390$	−1.82185	+	4.92957i	−0.0922529	+	0.249618i
$391$	−8.46890	−	14.6686i	−0.428290	−	0.741821i
$392$	3.41685	+	3.41685i	0.172577	+	0.172577i
$393$	27.7139	+	19.3198i	1.39798	+	0.974556i
$394$			6.24952i			0.314846i
$395$	19.0016	+	19.0016i	0.956077	+	0.956077i
$396$	15.2712	−	1.40001i	0.767404	−	0.0703534i
$397$	−6.68334	+	24.9426i	−0.335427	+	1.25183i	0.567978	+	0.823044i	$0.307726\pi$
$397$	−6.68334	+	24.9426i	−0.335427	+	1.25183i	−0.903405	+	0.428788i	$0.858941\pi$
$398$	1.29222	+	4.82265i	0.0647733	+	0.241737i
$399$	−8.11090	+	11.6349i	−0.406053	+	0.582476i
$400$			2.08738i			0.104369i
$401$	−5.84581	+	5.84581i	−0.291926	+	0.291926i	−0.837841	−	0.545915i	$-0.816182\pi$
$401$	−5.84581	+	5.84581i	−0.291926	+	0.291926i	0.545915	+	0.837841i	$0.316182\pi$
$402$	2.65958	−	3.81512i	0.132648	−	0.190281i
$403$	−14.4712	−	8.49091i	−0.720861	−	0.422962i
$404$		−	21.4904i		−	1.06919i
$405$	−18.6345	−	1.47438i	−0.925955	−	0.0732623i
$406$	−0.0108934	+	0.0188679i	−0.000540630	+	0.000936398i
$407$	−19.1281			−0.948144
$408$	2.73314	+	15.3143i	0.135311	+	0.758171i
$409$	−6.14296	−	22.9258i	−0.303750	−	1.13361i	−0.934016	−	0.357231i	$-0.883721\pi$
$409$	−6.14296	−	22.9258i	−0.303750	−	1.13361i	0.630266	−	0.776379i	$-0.282946\pi$
$410$	2.04774	+	7.64226i	0.101131	+	0.377424i
$411$	−6.78778	−	2.45459i	−0.334817	−	0.121076i
$412$	14.8334			0.730791
$413$	13.5784	−	23.5185i	0.668151	−	1.15727i
$414$	−2.05563	−	2.90993i	−0.101029	−	0.143015i
$415$		−	6.90732i		−	0.339067i
$416$	−15.6511	−	0.109847i	−0.767356	−	0.00538568i
$417$	8.87195	+	0.757626i	0.434461	+	0.0371011i
$418$	−3.31171	+	3.31171i	−0.161981	+	0.161981i
$419$		−	37.2911i		−	1.82179i	−0.412636	−	0.910896i	$-0.635392\pi$
$419$		−	37.2911i		−	1.82179i	0.412636	−	0.910896i	$-0.364608\pi$
$420$	−5.53001	−	11.7951i	−0.269837	−	0.575543i
$421$	6.40339	+	23.8978i	0.312082	+	1.16471i	0.926676	+	0.375862i	$0.122653\pi$
$421$	6.40339	+	23.8978i	0.312082	+	1.16471i	−0.614594	+	0.788844i	$0.710680\pi$
$422$	−2.40652	+	8.98125i	−0.117147	+	0.437200i
$423$	12.0330	+	5.55035i	0.585067	+	0.269867i
$424$	−9.51641	−	9.51641i	−0.462158	−	0.462158i
$425$		−	3.96543i		−	0.192352i
$426$	0.569198	−	6.66542i	0.0275777	−	0.322941i
$427$	12.9463	+	12.9463i	0.626516	+	0.626516i
$428$	3.24596	+	5.62217i	0.156899	+	0.271758i
$429$	1.60110	−	17.3149i	0.0773017	−	0.835970i
$430$	2.63921	−	4.57125i	0.127274	−	0.220445i
$431$	4.14613	−	1.11095i	0.199712	−	0.0535127i	−0.157576	−	0.987507i	$-0.550368\pi$
$431$	4.14613	−	1.11095i	0.199712	−	0.0535127i	0.357288	+	0.933994i	$0.383701\pi$
$432$	−4.18605	−	15.2419i	−0.201402	−	0.733328i
$433$	6.59375	−	3.80690i	0.316875	−	0.182948i	−0.333124	−	0.942883i	$-0.608103\pi$
$433$	6.59375	−	3.80690i	0.316875	−	0.182948i	0.649999	+	0.759935i	$0.274769\pi$
$434$	−3.59247	+	0.962598i	−0.172444	+	0.0462062i
$435$	−0.0749904	+	0.0631904i	−0.00359552	+	0.00302975i
$436$	−8.94527	+	2.39688i	−0.428401	+	0.114790i
$437$	−11.7529	−	3.14918i	−0.562218	−	0.150646i
$438$	−0.567188	−	0.395396i	−0.0271013	−	0.0188927i
$439$	−23.0595	+	13.3134i	−1.10057	+	0.635415i	−0.936371	−	0.351013i	$-0.885837\pi$
$439$	−23.0595	+	13.3134i	−1.10057	+	0.635415i	−0.164200	+	0.986427i	$0.552504\pi$
$440$	−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	$0.723063\pi$
$444$	3.83782	+	21.5040i	0.182135	+	1.02054i
$445$	4.57315			0.216788
$446$	4.25454	−	7.36907i	0.201458	−	0.348936i
$447$	0.693195	+	0.822641i	0.0327870	+	0.0389096i
$448$	6.03249	−	6.03249i	0.285008	−	0.285008i
$449$	−31.9954	−	8.57315i	−1.50996	−	0.404592i	−0.593536	−	0.804807i	$-0.702269\pi$
$449$	−31.9954	−	8.57315i	−1.50996	−	0.404592i	−0.916421	+	0.400216i	$0.868935\pi$
$450$	−0.0761490	−	0.830622i	−0.00358970	−	0.0391559i
$451$	−13.0890	−	22.6708i	−0.616336	−	1.06753i
$452$	−13.4668	−	23.3251i	−0.633423	−	1.09712i
$453$	−10.9797	−	13.0301i	−0.515873	−	0.612206i
$454$	10.0784	−	5.81880i	0.473005	−	0.273090i
$455$	−14.2947	+	3.72293i	−0.670148	+	0.174534i
$456$	9.16739	+	6.39073i	0.429302	+	0.299274i
$457$	16.1691	+	4.33251i	0.756360	+	0.202666i	0.616337	−	0.787482i	$-0.288616\pi$
$457$	16.1691	+	4.33251i	0.756360	+	0.202666i	0.140023	+	0.990148i	$0.455282\pi$
$458$	−2.62126	−	1.51339i	−0.122484	−	0.0707159i
$459$	7.95233	+	28.9554i	0.371183	+	1.35152i
$460$	7.90252	−	7.90252i	0.368457	−	0.368457i
$461$	−25.4261	−	25.4261i	−1.18421	−	1.18421i	−0.978643	−	0.205567i	$-0.934096\pi$
$461$	−25.4261	−	25.4261i	−1.18421	−	1.18421i	−0.205567	−	0.978643i	$-0.565904\pi$
$462$	−2.48376	−	2.94757i	−0.115555	−	0.137134i
$463$	−1.57430	+	5.87537i	−0.0731639	+	0.273052i	−0.992811	−	0.119695i	$-0.961808\pi$
$463$	−1.57430	+	5.87537i	−0.0731639	+	0.273052i	0.919647	+	0.392746i	$0.128475\pi$
$464$	−0.0718124	−	0.0414609i	−0.00333381	−	0.00192477i
$465$	−16.6797	−	1.42437i	−0.773503	−	0.0660538i
$466$	0.658971	−	2.45931i	0.0305262	−	0.113926i
$467$	−23.2541			−1.07607			−0.538036	−	0.842922i	$-0.680833\pi$
$467$	−23.2541			−1.07607			−0.538036	+	0.842922i	$0.680833\pi$
$468$	−19.7868	+	1.67405i	−0.914647	+	0.0773829i
$469$	13.0716			0.603593
$470$	0.962090	−	3.59057i	0.0443779	−	0.165621i
$471$	−16.5740	+	23.7751i	−0.763689	+	1.09550i
$472$	−18.5307	−	10.6987i	−0.852945	−	0.492448i
$473$	−4.52021	+	16.8696i	−0.207839	+	0.775667i
$474$	3.08780	−	8.53882i	0.141827	−	0.392201i
$475$	−2.01428	−	2.01428i	−0.0924216	−	0.0924216i
$476$	−14.7973	+	14.7973i	−0.678231	+	0.678231i
$477$	−19.9694	−	16.6154i	−0.914334	−	0.760766i
$478$	1.69750	+	0.980051i	0.0776418	+	0.0448265i
$479$	13.1108	+	3.51304i	0.599049	+	0.160515i	0.545586	−	0.838055i	$-0.316307\pi$
$479$	13.1108	+	3.51304i	0.599049	+	0.160515i	0.0534635	+	0.998570i	$0.482974\pi$
$480$	−14.1393	+	6.62905i	−0.645366	+	0.302573i
$481$	24.7683	+	0.173836i	1.12934	+	0.00792625i
$482$	−3.29666	+	1.90333i	−0.150159	+	0.0866942i
$483$	3.40541	−	9.41711i	0.154951	−	0.428493i
$484$	−2.98044	−	5.16228i	−0.135475	−	0.234649i
$485$	−12.7003	−	21.9976i	−0.576692	−	0.998860i
$486$	2.22178	+	5.91246i	0.100782	+	0.268195i
$487$	16.9260	+	4.53531i	0.766990	+	0.205514i	0.621041	−	0.783778i	$-0.286710\pi$
$487$	16.9260	+	4.53531i	0.766990	+	0.205514i	0.145949	+	0.989292i	$0.453377\pi$
$488$	10.2006	−	10.2006i	0.461761	−	0.461761i
$489$	25.2741	−	4.51066i	1.14293	−	0.203979i
$490$	1.30822	−	2.26591i	0.0590994	−	0.102363i
$491$	33.0828			1.49300			0.746502	−	0.665383i	$-0.231732\pi$
$491$	33.0828			1.49300			0.746502	+	0.665383i	$0.231732\pi$
$492$	−22.8606	+	19.2634i	−1.03064	+	0.868463i
$493$	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
$497$	16.2837	−	9.40140i	0.730424	−	0.421711i
$498$	−2.11321	+	0.990754i	−0.0946950	+	0.0443967i
$499$	−12.3960	−	3.32151i	−0.554923	−	0.148691i	−0.0295500	−	0.999563i	$-0.509407\pi$
$499$	−12.3960	−	3.32151i	−0.554923	−	0.148691i	−0.525373	+	0.850872i	$0.676074\pi$
$500$	20.9425	−	5.61152i	0.936577	−	0.250955i
$501$	3.22355	+	1.16570i	0.144017	+	0.0520795i
$502$	1.35095	−	0.361986i	0.0602959	−	0.0161562i
$503$	−15.5398	+	8.97189i	−0.692884	+	0.400037i	−0.804691	−	0.593693i	$-0.797669\pi$
$503$	−15.5398	+	8.97189i	−0.692884	+	0.400037i	0.111808	+	0.993730i	$0.464336\pi$
$504$	−5.88249	+	7.06994i	−0.262027	+	0.314920i
$505$	−23.4848	+	6.29273i	−1.04506	+	0.280023i
$506$	1.65338	−	2.86373i	0.0735015	−	0.127308i
$507$	−2.23057	+	22.4059i	−0.0990629	+	0.995081i
$508$	7.68945	+	13.3185i	0.341164	+	0.590914i
$509$	3.25185	+	3.25185i	0.144136	+	0.144136i	0.775493	−	0.631357i	$-0.217502\pi$
$509$	3.25185	+	3.25185i	0.144136	+	0.144136i	−0.631357	+	0.775493i	$0.717502\pi$
$510$	7.62659	−	3.57565i	0.337711	−	0.158332i
$511$		−	1.94334i		−	0.0859684i
$512$	−16.0233	−	16.0233i	−0.708135	−	0.708135i
$513$	18.7477	+	10.6687i	0.827730	+	0.471036i
$514$	1.54665	−	5.77216i	0.0682196	−	0.254599i
$515$	−4.34346	−	16.2100i	−0.191396	−	0.714298i
$516$	19.8720	+	1.69698i	0.874816	+	0.0747055i
$517$			12.2992i			0.540919i
$518$	3.88234	−	3.88234i	0.170580	−	0.170580i
$519$	9.45552	+	20.1679i	0.415051	+	0.885274i
$520$	2.93337	+	11.2631i	0.128637	+	0.493919i
$521$			21.6812i			0.949869i	0.880021	+	0.474934i	$0.157528\pi$
$521$			21.6812i			0.949869i	−0.880021	+	0.474934i	$0.842472\pi$
$522$	0.0300886	+	0.0138786i	0.00131694	+	0.000607451i
$523$	2.49525	−	4.32190i	0.109110	−	0.188983i	−0.806300	−	0.591507i	$-0.798533\pi$
$523$	2.49525	−	4.32190i	0.109110	−	0.188983i	0.915410	+	0.402523i	$0.131867\pi$
$524$	35.8076			1.56426
$525$	1.79281	−	1.51070i	0.0782445	−	0.0659324i
$526$	−1.14317	−	4.26638i	−0.0498447	−	0.186023i
$527$	6.96002	+	25.9751i	0.303183	+	1.13150i
$528$	11.2187	−	9.45335i	0.488229	−	0.411404i
$529$	−14.4091			−0.626484
$530$	−3.64358	+	6.31087i	−0.158267	+	0.274127i
$531$	−37.5049	−	17.2995i	−1.62757	−	0.750733i
$532$			15.0328i			0.651756i
$533$	16.7425	+	29.4746i	0.725197	+	1.27669i
$534$	−0.655951	−	1.39910i	−0.0283858	−	0.0605448i
$535$	5.19345	−	5.19345i	0.224532	−	0.224532i
$536$		−	10.2994i		−	0.444866i
$537$	−29.6056	−	2.52819i	−1.27758	−	0.109100i
$538$	3.19916	+	11.9394i	0.137926	+	0.514745i
$539$	−2.24061	+	8.36206i	−0.0965097	+	0.360179i
$540$	−17.0962	+	10.0131i	−0.735705	+	0.430896i
$541$	22.5983	+	22.5983i	0.971577	+	0.971577i	0.999607	−	0.0280298i	$-0.00892333\pi$
$541$	22.5983	+	22.5983i	0.971577	+	0.971577i	−0.0280298	+	0.999607i	$0.508923\pi$
$542$		−	0.182343i		−	0.00783230i
$543$	4.62907	−	2.17029i	0.198652	−	0.0931361i
$544$	17.7381	+	17.7381i	0.760513	+	0.760513i
$545$	5.23862	+	9.07356i	0.224398	+	0.388669i
$546$	3.18935	+	3.83929i	0.136492	+	0.164306i
$547$	−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
$549$	17.8100	−	21.4052i	0.760113	−	0.913550i
$550$	0.670449	−	0.387084i	0.0285881	−	0.0165053i
$551$	0.109307	−	0.0292887i	0.00465662	−	0.00124774i
$552$	−7.41992	−	2.68318i	−0.315813	−	0.114204i
$553$	24.6516	−	6.60538i	1.04829	−	0.280890i
$554$	8.69068	+	2.32866i	0.369232	+	0.0989353i
$555$	22.3759	−	10.4907i	0.949803	−	0.445305i
$556$	8.17333	−	4.71888i	0.346626	−	0.200125i
$557$	−6.06419	−	22.6319i	−0.256948	−	0.958944i	−0.966996	−	0.254790i	$-0.917994\pi$
$557$	−6.06419	−	22.6319i	−0.256948	−	0.958944i	0.710048	−	0.704153i	$-0.248673\pi$
$558$	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
$561$	−21.3123	+	17.9587i	−0.899806	+	0.758218i
$562$	6.04146			0.254844
$563$	3.01732	−	5.22615i	0.127165	−	0.220256i	−0.795412	−	0.606069i	$-0.792746\pi$
$563$	3.01732	−	5.22615i	0.127165	−	0.220256i	0.922577	+	0.385813i	$0.126079\pi$
$564$	13.8269	−	2.46769i	0.582219	−	0.103909i
$565$	−21.5465	+	21.5465i	−0.906466	+	0.906466i
$566$	5.10704	+	1.36843i	0.214665	+	0.0575193i
$567$	−10.0614	+	14.6264i	−0.422540	+	0.614251i
$568$	−7.40754	−	12.8302i	−0.310814	−	0.538345i
$569$	5.56824	+	9.64447i	0.233433	+	0.404317i	0.958816	−	0.284028i	$-0.0916708\pi$
$569$	5.56824	+	9.64447i	0.233433	+	0.404317i	−0.725383	+	0.688345i	$0.758338\pi$
$570$	2.05772	−	5.69029i	0.0861884	−	0.238340i
$571$	−8.38390	+	4.84045i	−0.350855	+	0.202566i	−0.665062	−	0.746788i	$-0.731595\pi$
$571$	−8.38390	+	4.84045i	−0.350855	+	0.202566i	0.314207	+	0.949355i	$0.398262\pi$
$572$	−9.10306	−	16.0257i	−0.380618	−	0.670066i
$573$	−6.30482	+	2.95595i	−0.263388	+	0.123487i
$574$	7.25800	+	1.94478i	0.302943	+	0.0811734i
$575$	1.74181	+	1.00563i	0.0726385	+	0.0419379i
$576$	−9.97400	−	8.29880i	−0.415583	−	0.345783i
$577$	12.2885	−	12.2885i	0.511579	−	0.511579i	−0.403431	−	0.915010i	$-0.632183\pi$
$577$	12.2885	−	12.2885i	0.511579	−	0.511579i	0.915010	+	0.403431i	$0.132183\pi$
$578$	−4.69716	−	4.69716i	−0.195376	−	0.195376i
$579$	9.34359	−	25.8382i	0.388306	−	1.07380i
$580$	−0.0269016	+	0.100398i	−0.00111703	+	0.00416881i
$581$	−5.68114	−	3.28001i	−0.235693	−	0.136078i
$582$	−4.90821	+	7.04074i	−0.203452	+	0.291848i
$583$	6.24041	−	23.2895i	0.258451	−	0.964554i
$584$	−1.53120			−0.0633613
$585$	7.62329	+	21.1329i	0.315184	+	0.873738i
$586$	−8.35045			−0.344954
$587$	8.48887	−	31.6809i	0.350373	−	1.30761i	−0.535835	−	0.844323i	$-0.680003\pi$
$587$	8.48887	−	31.6809i	0.350373	−	1.30761i	0.886208	−	0.463287i	$-0.153330\pi$
$588$	9.85028	+	0.841171i	0.406219	+	0.0346893i
$589$	16.7298	+	9.65893i	0.689338	+	0.397989i
$590$	−2.99867	+	11.1912i	−0.123453	+	0.460733i
$591$	17.2147	+	20.4294i	0.708119	+	0.840352i
$592$	14.7764	+	14.7764i	0.607308	+	0.607308i
$593$	−19.9618	+	19.9618i	−0.819732	+	0.819732i	−0.986069	−	0.166337i	$-0.946806\pi$
$593$	−19.9618	+	19.9618i	−0.819732	+	0.819732i	0.166337	+	0.986069i	$0.446806\pi$
$594$	−4.11933	+	4.17100i	−0.169018	+	0.171138i
$595$	20.5033	+	11.8376i	0.840555	+	0.485295i
$596$	1.10136	+	0.295109i	0.0451136	+	0.0120882i
$597$	17.5085	+	12.2055i	0.716576	+	0.499537i
$598$	−2.16693	+	3.69313i	−0.0886123	+	0.151023i
$599$	−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	$0.487581\pi$
$600$	−1.19031	−	1.41259i	−0.0485942	−	0.0576686i
$601$	−13.9483	−	24.1592i	−0.568963	−	0.985473i	−0.996669	−	0.0815548i	$-0.974011\pi$
$601$	−13.9483	−	24.1592i	−0.568963	−	0.985473i	0.427706	−	0.903918i	$-0.359322\pi$
$602$	−2.50651	−	4.34140i	−0.102158	−	0.176942i
$603$	−1.81497	−	19.7974i	−0.0739113	−	0.806213i
$604$	−17.4448	−	4.67433i	−0.709821	−	0.190196i
$605$	−4.76863	+	4.76863i	−0.193872	+	0.193872i
$606$	5.29373	+	6.28227i	0.215043	+	0.255200i
$607$	−5.48768	+	9.50494i	−0.222738	+	0.385794i	−0.955638	−	0.294542i	$-0.904833\pi$
$607$	−5.48768	+	9.50494i	−0.222738	+	0.385794i	0.732900	+	0.680336i	$0.238166\pi$
$608$	18.0205			0.730826
$609$	0.0163630	+	0.0916848i	0.000663061	+	0.00371526i
$610$	−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	0.971876	+	0.235493i	$0.0756706\pi$
$613$	6.13904	+	22.9112i	0.247953	+	0.925375i	−0.723923	+	0.689881i	$0.757663\pi$
$614$	−3.01945	+	1.74328i	−0.121855	+	0.0703532i
$615$	27.7451	+	19.3415i	1.11879	+	0.779926i
$616$	−8.24540	−	2.20935i	−0.332217	−	0.0890172i
$617$	6.86004	−	1.83814i	0.276175	−	0.0740008i	−0.118073	−	0.993005i	$-0.537672\pi$
$617$	6.86004	−	1.83814i	0.276175	−	0.0740008i	0.394248	+	0.919004i	$0.371005\pi$
$618$	−4.33624	+	3.65391i	−0.174429	+	0.146982i
$619$	7.94467	−	2.12877i	0.319323	−	0.0855624i	−0.0955973	−	0.995420i	$-0.530476\pi$
$619$	7.94467	−	2.12877i	0.319323	−	0.0855624i	0.414920	+	0.909858i	$0.363809\pi$
$620$	−15.3663	+	8.87172i	−0.617124	+	0.356297i
$621$	−14.7353	−	3.85005i	−0.591309	−	0.154497i
$622$	0.273697	−	0.0733370i	0.0109743	−	0.00294055i
$623$	2.17160	−	3.76133i	0.0870035	−	0.150694i
$624$	−14.6126	+	12.1389i	−0.584971	+	0.485944i
$625$	−10.5491	−	18.2715i	−0.421962	−	0.730860i
$626$	−6.13419	−	6.13419i	−0.245172	−	0.245172i
$627$	−1.70348	+	19.9481i	−0.0680305	+	0.796651i
$628$			30.7184i			1.22580i
$629$	−28.0711	−	28.0711i	−1.11927	−	1.11927i
$630$	4.52207	+	2.08584i	0.180163	+	0.0831020i
$631$	−2.37087	+	8.84821i	−0.0943828	+	0.352242i	−0.996925	−	0.0783596i	$-0.975032\pi$
$631$	−2.37087	+	8.84821i	−0.0943828	+	0.352242i	0.902542	+	0.430601i	$0.141698\pi$
$632$	−5.20451	−	19.4235i	−0.207024	−	0.772625i
$633$	16.8727	+	35.9882i	0.670628	+	1.43040i
$634$			10.1596i			0.403490i
$635$	12.3029	−	12.3029i	0.488226	−	0.488226i
$636$	−27.4345	−	2.34278i	−1.08785	−	0.0928974i
$637$	2.97728	−	10.8074i	0.117964	−	0.428204i
$638$			0.0307541i			0.00121757i
$639$	−16.4997	−	23.3568i	−0.652717	−	0.923982i
$640$	−10.8358	+	18.7682i	−0.428323	+	0.741877i
$641$	−12.6121			−0.498148			−0.249074	−	0.968484i	$-0.580126\pi$
$641$	−12.6121			−0.498148			−0.249074	+	0.968484i	$0.580126\pi$
$642$	−2.33379	−	0.843945i	−0.0921075	−	0.0333078i
$643$	6.00442	+	22.4088i	0.236791	+	0.883717i	0.977333	+	0.211707i	$0.0679023\pi$
$643$	6.00442	+	22.4088i	0.236791	+	0.883717i	−0.740542	+	0.672010i	$0.765431\pi$
$644$	−2.74709	−	10.2523i	−0.108250	−	0.403996i
$645$	−3.96436	−	22.2131i	−0.156097	−	0.874639i
$646$	−9.72007			−0.382431
$647$	6.02571	−	10.4368i	0.236895	−	0.410314i	−0.722927	−	0.690925i	$-0.757204\pi$
$647$	6.02571	−	10.4368i	0.236895	−	0.410314i	0.959822	+	0.280610i	$0.0905369\pi$
$648$	11.5244	+	7.92758i	0.452722	+	0.311425i
$649$		−	38.3345i		−	1.50476i
$650$	−0.871661	+	0.495129i	−0.0341893	+	0.0194206i
$651$	−9.09205	+	13.0424i	−0.356345	+	0.511171i
$652$	19.2416	−	19.2416i	0.753559	−	0.753559i
$653$			44.2223i			1.73055i	0.501297	+	0.865275i	$0.332856\pi$
$653$			44.2223i			1.73055i	−0.501297	+	0.865275i	$0.667144\pi$
$654$	2.02454	−	2.90416i	0.0791656	−	0.113562i
$655$	−10.4850	−	39.1306i	−0.409683	−	1.52896i
$656$	−7.40194	+	27.6244i	−0.288997	+	1.07855i
$657$	−2.94325	+	0.269829i	−0.114827	+	0.0105270i
$658$	−2.49632	−	2.49632i	−0.0973166	−	0.0973166i
$659$			17.9522i			0.699319i	0.936877	+	0.349660i	$0.113703\pi$
$659$			17.9522i			0.699319i	−0.936877	+	0.349660i	$0.886297\pi$
$660$	−15.0853	−	10.5162i	−0.587194	−	0.409342i
$661$	−7.86836	−	7.86836i	−0.306044	−	0.306044i	0.537329	−	0.843373i	$-0.319433\pi$
$661$	−7.86836	−	7.86836i	−0.306044	−	0.306044i	−0.843373	+	0.537329i	$0.819433\pi$
$662$	2.11497	+	3.66323i	0.0822006	+	0.142376i
$663$	27.7598	−	23.0605i	1.07810	−	0.895595i
$664$	−2.58438	+	4.47628i	−0.100293	+	0.173713i
$665$	16.4279	−	4.40185i	0.637047	−	0.170696i
$666$	−6.41899	−	5.34088i	−0.248731	−	0.206955i
$667$	−0.0691941	+	0.0399492i	−0.00267920	+	0.00154684i
$668$	3.50943	−	0.940348i	0.135784	−	0.0363832i
$669$	−6.39074	−	35.8085i	−0.247080	−	1.38444i
$670$	−5.38674	+	1.44337i	−0.208108	+	0.0557624i
$671$	24.9640	+	6.68909i	0.963726	+	0.258230i
$672$	−1.26190	+	14.7772i	−0.0486790	+	0.570041i
$673$	−6.44095	+	3.71869i	−0.248281	+	0.143345i	−0.618977	−	0.785409i	$-0.712452\pi$
$673$	−6.44095	+	3.71869i	−0.248281	+	0.143345i	0.370696	+	0.928754i	$0.379119\pi$
$674$	−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	$0.516973\pi$
$678$	9.68238	+	3.50134i	0.371850	+	0.134468i
$679$	−24.1235			−0.925775
$680$	9.32707	−	16.1550i	0.357677	−	0.619515i
$681$	16.9177	−	46.7831i	0.648287	−	1.79273i
$682$	−3.71231	+	3.71231i	−0.142152	+	0.142152i
$683$	16.0795	+	4.30850i	0.615266	+	0.164860i	0.552975	−	0.833198i	$-0.313493\pi$
$683$	16.0795	+	4.30850i	0.615266	+	0.164860i	0.0622913	+	0.998058i	$0.480159\pi$
$684$	22.7677	−	2.08728i	0.870545	−	0.0798090i
$685$	4.32767	+	7.49574i	0.165352	+	0.286398i
$686$	−4.03976	−	6.99707i	−0.154239	−	0.267149i
$687$	−12.7375	+	2.27326i	−0.485966	+	0.0867303i
$688$	16.5237	−	9.53994i	0.629958	−	0.363707i
$689$	−8.29216	+	30.1001i	−0.315906	+	1.14672i
$690$	−0.363508	+	4.25676i	−0.0138385	+	0.162052i
$691$	48.4131	+	12.9722i	1.84172	+	0.493487i	0.998993	−	0.0448552i	$-0.0142826\pi$
$691$	48.4131	+	12.9722i	1.84172	+	0.493487i	0.842726	+	0.538342i	$0.180949\pi$
$692$	20.4461	+	11.8045i	0.777243	+	0.448742i
$693$	−16.2386	−	2.79378i	−0.616853	−	0.106127i
$694$	1.16914	−	1.16914i	0.0443800	−	0.0443800i
$695$	−7.55007	−	7.55007i	−0.286391	−	0.286391i
$696$	0.0722402	−	0.0128927i	0.00273826	−	0.000488697i
$697$	14.0616	−	52.4786i	0.532621	−	1.98777i
$698$	−2.44532	−	1.41180i	−0.0925566	−	0.0534376i
$699$	−4.62020	−	9.85455i	−0.174752	−	0.372733i
$700$	0.643141	−	2.40023i	0.0243084	−	0.0907203i
$701$	29.7762			1.12463			0.562317	−	0.826922i	$-0.309910\pi$
$701$	29.7762			1.12463			0.562317	+	0.826922i	$0.309910\pi$
$702$	5.37189	−	5.36346i	0.202749	−	0.202431i
$703$	−28.5180			−1.07558
$704$	3.11687	−	11.6323i	0.117471	−	0.438409i
$705$	−6.74544	−	14.3875i	−0.254048	−	0.541866i
$706$	−3.59025	−	2.07283i	−0.135121	−	0.0780122i
$707$	−5.97633	+	22.3040i	−0.224763	+	0.838827i
$708$	−43.0962	+	7.69137i	−1.61965	+	0.289059i
$709$	−26.8342	−	26.8342i	−1.00778	−	1.00778i	−0.999970	−	0.00780933i	$-0.997514\pi$
$709$	−26.8342	−	26.8342i	−1.00778	−	1.00778i	−0.00780933	−	0.999970i	$-0.502486\pi$
$710$	−5.67231	+	5.67231i	−0.212878	+	0.212878i
$711$	−13.4269	−	36.4185i	−0.503548	−	1.36580i
$712$	−2.96362	−	1.71105i	−0.111066	−	0.0641242i
$713$	−13.1746	−	3.53013i	−0.493393	−	0.132204i
$714$	0.680660	−	7.97066i	0.0254731	−	0.298295i
$715$	−14.8474	+	14.6404i	−0.555260	+	0.547520i
$716$	−27.2744	+	15.7469i	−1.01929	+	0.588488i
$717$	8.24866	−	1.47214i	0.308052	−	0.0549780i
$718$	−3.75781	−	6.50872i	−0.140240	−	0.242903i
$719$	2.07633	+	3.59631i	0.0774340	+	0.134120i	0.902142	−	0.431439i	$-0.141994\pi$
$719$	2.07633	+	3.59631i	0.0774340	+	0.134120i	−0.824708	+	0.565559i	$0.808661\pi$
$720$	−7.93885	+	17.2113i	−0.295863	+	0.641426i
$721$	−15.3950	−	4.12507i	−0.573339	−	0.153626i
$722$	0.506191	−	0.506191i	0.0188385	−	0.0188385i
$723$	−5.53377	+	15.3028i	−0.205803	+	0.569115i
$724$	2.70945	−	4.69291i	0.100696	−	0.174411i
$725$	−0.0187056			−0.000694709
$726$	2.14289	+	0.774910i	0.0795301	+	0.0287596i
$727$	17.8851	+	10.3260i	0.663323	+	0.382970i	0.793542	−	0.608516i	$-0.208235\pi$
$727$	17.8851	+	10.3260i	0.663323	+	0.382970i	−0.130219	+	0.991485i	$0.541568\pi$
$728$	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
$731$	−31.3903	+	18.1232i	−1.16101	+	0.670311i
$732$	2.51123	−	29.4070i	0.0928176	−	1.08691i
$733$	−41.2018	−	11.0400i	−1.52182	−	0.407771i	−0.601480	−	0.798888i	$-0.705422\pi$
$733$	−41.2018	−	11.0400i	−1.52182	−	0.407771i	−0.920341	+	0.391117i	$0.872089\pi$
$734$	−0.135075	+	0.0361933i	−0.00498571	+	0.00133592i
$735$	−1.96508	−	11.0107i	−0.0724831	−	0.406136i
$736$	−12.2898	+	3.29304i	−0.453008	+	0.121383i
$737$	15.9798	−	9.22594i	0.588623	−	0.339842i
$738$	1.93767	−	11.2625i	0.0713265	−	0.414579i
$739$	−18.5262	+	4.96408i	−0.681497	+	0.182607i	−0.582928	−	0.812524i	$-0.698093\pi$
$739$	−18.5262	+	4.96408i	−0.681497	+	0.182607i	−0.0985688	+	0.995130i	$0.531426\pi$
$740$	13.0969	−	22.6845i	0.481451	−	0.833898i
$741$	2.38707	−	25.8147i	0.0876912	−	0.948326i
$742$	3.46038	+	5.99356i	0.127035	+	0.220031i
$743$	−10.4126	−	10.4126i	−0.382001	−	0.382001i	0.489821	−	0.871823i	$-0.337062\pi$
$743$	−10.4126	−	10.4126i	−0.382001	−	0.382001i	−0.871823	+	0.489821i	$0.837062\pi$
$744$	10.2763	+	7.16380i	0.376749	+	0.262638i
$745$		−	1.28998i		−	0.0472614i
$746$	−0.328396	−	0.328396i	−0.0120234	−	0.0120234i
$747$	−4.17886	+	9.05969i	−0.152897	+	0.331477i
$748$	−7.64545	+	28.5332i	−0.279545	+	1.04328i
$749$	−1.80536	−	6.73768i	−0.0659662	−	0.246189i
$750$	−4.73980	+	6.79916i	−0.173073	+	0.248270i
$751$			6.61319i			0.241319i	0.992694	+	0.120659i	$0.0385009\pi$
$751$			6.61319i			0.241319i	−0.992694	+	0.120659i	$0.961499\pi$
$752$	9.50114	−	9.50114i	0.346471	−	0.346471i
$753$	3.41908	−	4.90460i	0.124598	−	0.178734i
$754$	0.000279494	−	0.0398225i	1.01786e−5	−	0.00145025i
$755$			20.4325i			0.743614i
$756$	0.117275	+	18.8162i	0.00426524	+	0.684338i
$757$	−0.157058	+	0.272032i	−0.00570837	+	0.00988718i	−0.868865	−	0.495048i	$-0.835150\pi$
$757$	−0.157058	+	0.272032i	−0.00570837	+	0.00988718i	0.863157	+	0.504935i	$0.168484\pi$
$758$	7.65265			0.277957
$759$	−2.48354	−	13.9157i	−0.0901467	−	0.505109i
$760$	−3.46830	−	12.9439i	−0.125808	−	0.469523i
$761$	−7.19249	−	26.8427i	−0.260727	−	0.973048i	−0.964814	−	0.262934i	$-0.915310\pi$
$761$	−7.19249	−	26.8427i	−0.260727	−	0.973048i	0.704086	−	0.710114i	$-0.251357\pi$
$762$	−5.52859	−	1.99925i	−0.200280	−	0.0724250i
$763$	9.95045			0.360230
$764$	−3.69029	+	6.39178i	−0.133510	+	0.231246i
$765$	15.0816	−	32.6966i	0.545276	−	1.18215i
$766$			12.2904i			0.444072i
$767$	−0.348384	+	49.6381i	−0.0125794	+	1.79233i
$768$	−7.63179	−	0.651721i	−0.275388	−	0.0235170i
$769$	−19.6784	+	19.6784i	−0.709620	+	0.709620i	−0.966455	−	0.256835i	$-0.917320\pi$
$769$	−19.6784	+	19.6784i	−0.709620	+	0.709620i	0.256835	+	0.966455i	$0.417320\pi$
$770$			4.62209i			0.166569i
$771$	−10.8439	−	23.1292i	−0.390534	−	0.832979i
$772$	−7.53732	−	28.1297i	−0.271274	−	1.01241i
$773$	−7.98648	+	29.8060i	−0.287254	+	1.07205i	0.659923	+	0.751333i	$0.270589\pi$
$773$	−7.98648	+	29.8060i	−0.287254	+	1.07205i	−0.947177	+	0.320713i	$0.896078\pi$
$774$	−6.22717	+	4.39899i	−0.223831	+	0.158118i
$775$	−2.25794	−	2.25794i	−0.0811076	−	0.0811076i
$776$			19.0074i			0.682325i
$777$	1.99701	−	23.3854i	0.0716422	−	0.838945i
$778$	−1.11571	−	1.11571i	−0.0400000	−	0.0400000i
$779$	−19.5143	−	33.7998i	−0.699173	−	1.21100i
$780$	19.4379	+	13.7542i	0.695987	+	0.492478i
$781$	13.2710	−	22.9860i	0.474873	−	0.822504i
$782$	6.62900	−	1.77624i	0.237053	−	0.0635181i
$783$	0.136588	−	0.0375125i	0.00488124	−	0.00134059i
$784$	8.19055	−	4.72882i	0.292520	−	0.168886i
$785$	33.5691	−	8.99482i	1.19813	−	0.321039i
$786$	−10.4676	+	8.82047i	−0.373366	+	0.314616i
$787$	−24.6290	+	6.59932i	−0.877929	+	0.235240i	−0.669513	−	0.742800i	$-0.733497\pi$
$787$	−24.6290	+	6.59932i	−0.877929	+	0.235240i	−0.208416	+	0.978040i	$0.566831\pi$
$788$	27.3511	+	7.32871i	0.974344	+	0.261075i
$789$	−15.4890	−	10.7976i	−0.551423	−	0.384406i
$790$	−9.42941	+	5.44407i	−0.335483	+	0.193691i
$791$	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
$795$	5.47303	+	30.6664i	0.194108	+	1.08763i
$796$	22.6218			0.801807
$797$	−3.69957	+	6.40785i	−0.131046	+	0.226978i	−0.924080	−	0.382199i	$-0.875167\pi$
$797$	−3.69957	+	6.40785i	−0.131046	+	0.226978i	0.793034	+	0.609177i	$0.208500\pi$
$798$	−3.70303	−	4.39453i	−0.131086	−	0.155565i
$799$	−18.0495	+	18.0495i	−0.638546	+	0.638546i
$800$	−2.87725	−	0.770958i	−0.101726	−	0.0272575i
$801$	−5.99818	−	2.76671i	−0.211935	−	0.0977570i
$802$	−1.67485	−	2.90093i	−0.0591412	−	0.102436i
$803$	−1.37161	−	2.37569i	−0.0484029	−	0.0838364i
$804$	−13.5781	−	16.1136i	−0.478862	−	0.568284i
$805$	−10.3993	+	6.00404i	−0.366527	+	0.211615i
$806$	4.84069	−	4.77321i	0.170506	−	0.168129i
$807$	43.3458	+	30.2171i	1.52585	+	1.06369i
$808$	17.5737	+	4.70886i	0.618241	+	0.165657i
$809$	32.2345	+	18.6106i	1.13331	+	0.654315i	0.944764	−	0.327751i	$-0.106291\pi$
$809$	32.2345	+	18.6106i	1.13331	+	0.654315i	0.188542	+	0.982065i	$0.439624\pi$
$810$	2.53120	−	7.13843i	0.0889372	−	0.250819i
$811$	−6.98393	+	6.98393i	−0.245239	+	0.245239i	−0.819013	−	0.573775i	$-0.805479\pi$
$811$	−6.98393	+	6.98393i	−0.245239	+	0.245239i	0.573775	+	0.819013i	$0.305479\pi$
$812$	0.0698012	+	0.0698012i	0.00244954	+	0.00244954i
$813$	−0.502276	−	0.596070i	−0.0176156	−	0.0209051i
$814$	2.00593	−	7.48622i	0.0703077	−	0.262392i
$815$	−26.6615	−	15.3930i	−0.933910	−	0.539193i
$816$	30.3368	+	2.59063i	1.06200	+	0.0906903i
$817$	−6.73916	+	25.1509i	−0.235773	+	0.879919i
$818$	9.61677			0.336242
$819$	21.0014	+	3.76515i	0.733849	+	0.131565i
$820$	35.8478			1.25186
$821$	−3.60092	+	13.4388i	−0.125673	+	0.469018i	−0.999863	−	0.0165663i	$-0.994727\pi$
$821$	−3.60092	+	13.4388i	−0.125673	+	0.469018i	0.874190	+	0.485585i	$0.161393\pi$
$822$	1.67249	−	2.39915i	0.0583346	−	0.0836800i
$823$	−14.0441	−	8.10836i	−0.489546	−	0.282640i	0.234840	−	0.972034i	$-0.424543\pi$
$823$	−14.0441	−	8.10836i	−0.489546	−	0.282640i	−0.724386	+	0.689394i	$0.757877\pi$
$824$	−3.25022	+	12.1300i	−0.113227	+	0.422568i
$825$	1.12542	−	3.11216i	0.0391819	−	0.108351i
$826$	7.78059	+	7.78059i	0.270721	+	0.270721i
$827$	39.0484	−	39.0484i	1.35784	−	1.35784i	0.481274	−	0.876570i	$-0.340174\pi$
$827$	39.0484	−	39.0484i	1.35784	−	1.35784i	0.876570	−	0.481274i	$-0.159826\pi$
$828$	−15.1460	+	5.58405i	−0.526358	+	0.194059i
$829$	−21.0986	−	12.1813i	−0.732784	−	0.423073i	0.0866559	−	0.996238i	$-0.472382\pi$
$829$	−21.0986	−	12.1813i	−0.732784	−	0.423073i	−0.819440	+	0.573165i	$0.805715\pi$
$830$	2.70334	+	0.724358i	0.0938344	+	0.0251428i
$831$	34.8238	−	16.3268i	1.20803	−	0.566370i
$832$	−4.14164	+	15.0340i	−0.143586	+	0.521209i
$833$	−15.5598	+	8.98343i	−0.539114	+	0.311257i
$834$	−1.22690	+	3.39280i	−0.0424841	+	0.117483i
$835$	−2.05523	−	3.55976i	−0.0711241	−	0.123191i
$836$	10.6101	+	18.3773i	0.366960	+	0.635593i
$837$	21.0155	+	11.9593i	0.726402	+	0.413374i
$838$	14.5948	+	3.91066i	0.504168	+	0.135091i
$839$	12.5419	−	12.5419i	0.432995	−	0.432995i	−0.456651	−	0.889646i	$-0.650951\pi$
$839$	12.5419	−	12.5419i	0.432995	−	0.432995i	0.889646	+	0.456651i	$0.150951\pi$
$840$	10.8571	−	1.93767i	0.374606	−	0.0668559i
$841$	−14.4996	+	25.1141i	−0.499987	+	0.866003i
$842$	−10.0245			−0.345466
$843$	19.7492	−	16.6416i	0.680200	−	0.573168i
$844$	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
$848$	−22.8119	+	13.1704i	−0.783363	+	0.452275i
$849$	20.4641	−	9.59437i	0.702325	−	0.329278i
$850$	1.55196	+	0.415848i	0.0532320	+	0.0142635i
$851$	19.4490	−	5.21135i	0.666704	−	0.178643i
$852$	−28.5038	−	10.3075i	−0.976525	−	0.353130i
$853$	6.22299	−	1.66744i	0.213071	−	0.0570922i	−0.150705	−	0.988579i	$-0.548154\pi$
$853$	6.22299	−	1.66744i	0.213071	−	0.0570922i	0.363775	+	0.931487i	$0.381488\pi$
$854$	−6.42450	+	3.70918i	−0.219842	+	0.126926i
$855$	−8.94772	−	24.2694i	−0.306005	−	0.829996i
$856$	−5.30874	+	1.42247i	−0.181449	+	0.0486191i
$857$	−19.0536	+	33.0018i	−0.650858	+	1.12732i	0.332057	+	0.943259i	$0.392257\pi$
$857$	−19.0536	+	33.0018i	−0.650858	+	1.12732i	−0.982915	+	0.184060i	$0.941076\pi$
$858$	6.60868	+	2.44241i	0.225616	+	0.0833824i
$859$	−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	$0.963885\pi$
$860$	−16.9112	−	16.9112i	−0.576666	−	0.576666i
$861$	29.0831	−	13.6353i	0.991148	−	0.464689i
$862$			1.73919i			0.0592370i
$863$	−8.96522	−	8.96522i	−0.305180	−	0.305180i	0.537857	−	0.843036i	$-0.319234\pi$
$863$	−8.96522	−	8.96522i	−0.305180	−	0.305180i	−0.843036	+	0.537857i	$0.819234\pi$
$864$	22.5557	−	0.140582i	0.767360	−	0.00478269i
$865$	6.91311	−	25.8001i	0.235053	−	0.877228i
$866$	0.798446	+	2.97984i	0.0271323	+	0.101259i
$867$	−28.2934	−	2.41613i	−0.960895	−	0.0820562i
$868$			16.8513i			0.571971i
$869$	25.4740	−	25.4740i	0.864146	−	0.864146i
$870$	−0.0168669	−	0.0359759i	−0.000571843	−	0.00121970i
$871$	−20.7756	+	11.8011i	−0.703953	+	0.399866i
$872$		−	7.84015i		−	0.265501i
$873$	3.34950	+	36.5358i	0.113363	+	1.23655i
$874$	2.46501	−	4.26953i	0.0833803	−	0.144419i
$875$	−23.2958			−0.787542
$876$	−2.39559	+	2.01863i	−0.0809394	+	0.0682033i
$877$	9.46106	+	35.3092i	0.319477	+	1.19231i	0.919748	+	0.392509i	$0.128393\pi$
$877$	9.46106	+	35.3092i	0.319477	+	1.19231i	−0.600271	+	0.799797i	$0.704941\pi$
$878$	−2.79231	−	10.4210i	−0.0942358	−	0.351693i
$879$	−27.2972	+	23.0019i	−0.920712	+	0.775834i
$880$	−17.5920			−0.593025
$881$	−1.20714	+	2.09083i	−0.0406696	+	0.0704418i	−0.885644	−	0.464365i	$-0.846282\pi$
$881$	−1.20714	+	2.09083i	−0.0406696	+	0.0704418i	0.844974	+	0.534807i	$0.179616\pi$
$882$	−3.08672	+	2.18052i	−0.103935	+	0.0734218i
$883$			4.43328i			0.149192i	0.997214	+	0.0745958i	$0.0237667\pi$
$883$			4.43328i			0.149192i	−0.997214	+	0.0745958i	$0.976233\pi$
$884$	10.1591	−	36.8772i	0.341689	−	1.24031i
$885$	21.0244	+	44.8434i	0.706726	+	1.50739i
$886$	2.12566	−	2.12566i	0.0714130	−	0.0714130i
$887$			16.6897i			0.560386i	0.959944	+	0.280193i	$0.0903985\pi$
$887$			16.6897i			0.560386i	−0.959944	+	0.280193i	$0.909602\pi$
$888$	−18.4258	−	1.57348i	−0.618328	−	0.0528025i
$889$	−4.27676	−	15.9611i	−0.143438	−	0.535318i
$890$	−0.479578	+	1.78981i	−0.0160755	+	0.0599945i
$891$	−1.97658	+	24.9818i	−0.0662179	+	0.836921i
$892$	−27.2616	−	27.2616i	−0.912787	−	0.912787i
$893$			18.3369i			0.613620i
$894$	−0.394654	+	0.185029i	−0.0131992	+	0.00618831i
$895$	25.1946	+	25.1946i	0.842161	+	0.842161i
$896$	10.2910	+	17.8245i	0.343798	+	0.595475i
$897$	3.08939	+	18.0416i	0.103152	+	0.602391i
$898$	6.71061	−	11.6231i	0.223936	−	0.387868i
$899$	0.122529	−	0.0328316i	0.00408658	−	0.00109499i
$900$	−3.72453	−	0.640790i	−0.124151	−	0.0213597i
$901$	43.3362	−	25.0201i	1.44374	−	0.833542i
$902$	10.2454	−	2.74524i	0.341133	−	0.0914064i
$903$	−20.1524	−	7.28748i	−0.670628	−	0.242512i
$904$	22.0248	−	5.90152i	0.732533	−	0.196282i
$905$	−5.92179	−	1.58674i	−0.196847	−	0.0527450i
$906$	6.25105	−	2.93074i	0.207677	−	0.0973673i
$907$	5.66521	−	3.27081i	0.188110	−	0.108606i	−0.402987	−	0.915206i	$-0.632028\pi$
$907$	5.66521	−	3.27081i	0.188110	−	0.108606i	0.591098	+	0.806600i	$0.298695\pi$
$908$	−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	$0.738363\pi$
$912$	16.7258	−	14.0940i	0.553848	−	0.466698i
$913$	−9.26009			−0.306464
$914$	−3.39126	+	5.87383i	−0.112173	+	0.194289i
$915$	−32.8713	+	5.86654i	−1.08669	+	0.193942i
$916$	−9.69727	+	9.69727i	−0.320407	+	0.320407i
$917$	−37.1631	−	9.95782i	−1.22723	−	0.328836i
$918$	−12.1663	+	0.0758286i	−0.401549	+	0.00250272i
$919$	24.5247	+	42.4781i	0.808996	+	1.40122i	0.913560	+	0.406704i	$0.133322\pi$
$919$	24.5247	+	42.4781i	0.808996	+	1.40122i	−0.104564	+	0.994518i	$0.533345\pi$
$920$	4.73070	+	8.19381i	0.155966	+	0.270142i
$921$	−5.06845	+	14.0160i	−0.167011	+	0.461843i
$922$	12.6175	−	7.28470i	0.415534	−	0.239909i
$923$	−17.3931	+	29.6432i	−0.572499	+	0.975719i
$924$	−15.8128	+	7.41365i	−0.520202	+	0.243891i
$925$	4.55335	+	1.22007i	0.149713	+	0.0401156i
$926$	−2.13437	−	1.23228i	−0.0701397	−	0.0404952i
$927$	−4.10999	+	23.8889i	−0.134990	+	0.784615i
$928$	0.0836734	−	0.0836734i	0.00274671	−	0.00274671i
$929$	28.8173	+	28.8173i	0.945466	+	0.945466i	0.998588	−	0.0531218i	$-0.0169172\pi$
$929$	28.8173	+	28.8173i	0.945466	+	0.945466i	−0.0531218	+	0.998588i	$0.516917\pi$
$930$	2.30663	−	6.37863i	0.0756375	−	0.209163i
$931$	−3.34051	+	12.4670i	−0.109481	+	0.408588i
$932$	−9.99046	−	5.76799i	−0.327248	−	0.188937i
$933$	0.692692	−	0.993653i	0.0226777	−	0.0325307i
$934$	2.43862	−	9.10104i	0.0797939	−	0.297795i
$935$	33.4198			1.09295
$936$	2.96663	−	16.5474i	0.0969675	−	0.540869i
$937$	18.3170			0.598390			0.299195	−	0.954192i	$-0.403282\pi$
$937$	18.3170			0.598390			0.299195	+	0.954192i	$0.403282\pi$
$938$	−1.37080	+	5.11590i	−0.0447582	+	0.167040i
$939$	−36.9494	−	3.15532i	−1.20580	−	0.102970i
$940$	−14.5859	−	8.42120i	−0.475741	−	0.274669i
$941$	−0.726930	+	2.71294i	−0.0236972	+	0.0884393i	−0.976762	−	0.214328i	$-0.931244\pi$
$941$	−0.726930	+	2.71294i	−0.0236972	+	0.0884393i	0.953064	+	0.302767i	$0.0979105\pi$
$942$	−7.56685	−	8.97987i	−0.246541	−	0.292580i
$943$	19.4851	+	19.4851i	0.634524	+	0.634524i
$944$	−29.6134	+	29.6134i	−0.963834	+	0.963834i
$945$	20.5280	−	5.63782i	0.667776	−	0.183398i
$946$	−6.12831	−	3.53818i	−0.199248	−	0.115036i
$947$	42.1692	+	11.2992i	1.37031	+	0.367175i	0.867593	−	0.497274i	$-0.165666\pi$
$947$	42.1692	+	11.2992i	1.37031	+	0.367175i	0.502721	+	0.864449i	$0.332332\pi$
$948$	−33.7493	−	23.5271i	−1.09612	−	0.764126i
$949$	1.75446	+	3.08867i	0.0569521	+	0.100263i
$950$	0.999570	−	0.577102i	0.0324303	−	0.0187237i
$951$	27.9854	+	33.2113i	0.907488	+	1.07695i
$952$	−8.85811	−	15.3427i	−0.287093	−	0.497260i
$953$	−9.07394	−	15.7165i	−0.293934	−	0.509108i	0.680803	−	0.732467i	$-0.261631\pi$
$953$	−9.07394	−	15.7165i	−0.293934	−	0.509108i	−0.974736	+	0.223359i	$0.928298\pi$
$954$	8.59697	−	6.07305i	0.278337	−	0.196622i
$955$	8.06552	+	2.16115i	0.260994	+	0.0699331i
$956$	6.27984	−	6.27984i	0.203104	−	0.203104i
$957$	0.0847143	+	0.100534i	0.00273842	+	0.00324979i
$958$	−2.74982	+	4.76283i	−0.0888426	+	0.153880i
$959$	8.22015			0.265442
$960$	2.73359	+	15.3168i	0.0882262	+	0.494348i
$961$	−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
$965$	−28.5331	+	16.4736i	−0.918513	+	0.530304i
$966$	3.32849	+	2.32034i	0.107092	+	0.0746558i
$967$	17.7792	+	4.76393i	0.571742	+	0.153198i	0.533095	−	0.846055i	$-0.321029\pi$
$967$	17.7792	+	4.76393i	0.571742	+	0.153198i	0.0386464	+	0.999253i	$0.487695\pi$
$968$	4.87449	−	1.30612i	0.156672	−	0.0419801i
$969$	−31.7744	+	26.7746i	−1.02074	+	0.860124i
$970$	9.94115	−	2.66372i	0.319191	−	0.0855270i
$971$	9.07902	−	5.24177i	0.291360	−	0.168217i	−0.347195	−	0.937793i	$-0.612866\pi$
$971$	9.07902	−	5.24177i	0.291360	−	0.168217i	0.638555	+	0.769576i	$0.279533\pi$
$972$	28.4814	−	2.79020i	0.913541	−	0.0894957i
$973$	−9.79502	+	2.62457i	−0.314014	+	0.0841398i
$974$	−3.55000	+	6.14878i	−0.113749	+	0.197020i
$975$	−1.48555	+	4.01960i	−0.0475756	+	0.128730i
$976$	−14.1174	−	24.4520i	−0.451887	−	0.782690i
$977$	−40.6952	−	40.6952i	−1.30195	−	1.30195i	−0.927073	−	0.374880i	$-0.877684\pi$
$977$	−40.6952	−	40.6952i	−1.30195	−	1.30195i	−0.374880	−	0.927073i	$-0.622316\pi$
$978$	−0.885094	+	10.3646i	−0.0283022	+	0.331424i
$979$		−	6.13085i		−	0.195943i
$980$	−8.38264	−	8.38264i	−0.267774	−	0.267774i
$981$	−1.38160	−	15.0703i	−0.0441110	−	0.481157i
$982$	−3.46933	+	12.9477i	−0.110711	+	0.413178i
$983$	−11.3146	−	42.2268i	−0.360881	−	1.34682i	−0.872920	−	0.487863i	$-0.837777\pi$
$983$	−11.3146	−	42.2268i	−0.360881	−	1.34682i	0.512040	−	0.858962i	$-0.328890\pi$
$984$	−10.7435	−	22.9151i	−0.342490	−	0.730507i
$985$		−	32.0353i		−	1.02073i
$986$	−0.0451327	+	0.0451327i	−0.00143732	+	0.00143732i
$987$	−15.0366	−	1.28406i	−0.478621	−	0.0408721i
$988$	−13.5717	−	23.8926i	−0.431774	−	0.760125i
$989$		−	18.3842i		−	0.584584i
$990$	7.00031	−	0.641768i	0.222484	−	0.0203967i
$991$	16.9722	−	29.3967i	0.539140	−	0.933818i	−0.459811	−	0.888017i	$-0.652083\pi$
$991$	16.9722	−	29.3967i	0.539140	−	0.933818i	0.998951	−	0.0458007i	$-0.0145839\pi$
$992$	20.2003			0.641361
$993$	17.0044	+	6.14910i	0.539617	+	0.195136i
$994$	1.97182	+	7.35892i	0.0625422	+	0.233411i
$995$	−6.62400	−	24.7211i	−0.209995	−	0.783711i
$996$	1.85793	+	10.4103i	0.0588707	+	0.329863i
$997$	−40.1636			−1.27199			−0.635997	−	0.771692i	$-0.719411\pi$
$997$	−40.1636			−1.27199			−0.635997	+	0.771692i	$0.719411\pi$
$998$	2.59990	−	4.50316i	0.0822984	−	0.142545i
$999$	−35.6951	+	0.222476i	−1.12934	+	0.00703882i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.7	✓	48	13.11	odd	12
117.2.x.a.32.7	yes	48	9.5	odd	6
117.2.bc.a.50.6	yes	48	117.50	even	12	inner
117.2.bc.a.110.6	yes	48	1.1	even	1	trivial
351.2.ba.a.71.6		48	9.4	even	3
351.2.ba.a.89.6		48	39.11	even	12
351.2.bf.a.206.7		48	117.76	odd	12
351.2.bf.a.305.7		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.104868 + 0.391374i) q^{2} +(0.735256 + 1.56825i) q^{3} +(1.58987 + 0.917915i) q^{4} +(0.537559 - 2.00620i) q^{5} +(-0.690875 + 0.123300i) q^{6} +(-1.39480 - 1.39480i) q^{7} +(-1.09899 + 1.09899i) q^{8} +(-1.91880 + 2.30613i) q^{9} +O(q^{10})\)	\(q+(-0.104868 + 0.391374i) q^{2} +(0.735256 + 1.56825i) q^{3} +(1.58987 + 0.917915i) q^{4} +(0.537559 - 2.00620i) q^{5} +(-0.690875 + 0.123300i) q^{6} +(-1.39480 - 1.39480i) q^{7} +(-1.09899 + 1.09899i) q^{8} +(-1.91880 + 2.30613i) q^{9} +(0.728800 + 0.420773i) q^{10} +(-2.68955 - 0.720663i) q^{11} +(-0.270552 + 3.16822i) q^{12} +(3.47606 + 0.957605i) q^{13} +(0.692156 - 0.399616i) q^{14} +(3.54146 - 0.632043i) q^{15} +(1.52096 + 2.63439i) q^{16} +(-2.88941 - 5.00460i) q^{17} +(-0.701336 - 0.992806i) q^{18} +(-4.00984 - 1.07443i) q^{19} +(2.69617 - 2.69617i) q^{20} +(1.16185 - 3.21292i) q^{21} +(0.564096 - 0.977044i) q^{22} +2.93102 q^{23} +(-2.53152 - 0.915445i) 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} +(-0.0236075 + 0.0136298i) q^{29} +(-0.124021 + 1.45231i) q^{30} +(-4.49489 - 1.20440i) q^{31} +(-4.19301 + 1.12351i) q^{32} +(-0.847330 - 4.74775i) q^{33} +(2.26167 - 0.606014i) q^{34} +(-3.54802 + 2.04845i) q^{35} +(-5.16747 + 1.90516i) q^{36} +(6.63559 - 1.77800i) q^{37} +(0.841010 - 1.45667i) q^{38} +(1.05403 + 6.15541i) q^{39} +(1.61401 + 2.79555i) q^{40} +(6.64791 + 6.64791i) q^{41} +(1.13561 + 0.791651i) q^{42} -6.27230i q^{43} +(-3.61454 - 3.61454i) q^{44} +(3.59508 + 5.08917i) q^{45} +(-0.307370 + 1.14712i) q^{46} +(-1.14324 - 4.26664i) q^{47} +(-3.01307 + 4.32220i) q^{48} -3.10909i q^{49} +(-0.196600 + 0.196600i) q^{50} +(5.72399 - 8.21096i) q^{51} +(4.64750 + 4.71320i) q^{52} +8.65927i q^{53} +(1.04130 - 1.82983i) q^{54} +(-2.89158 + 5.00837i) q^{55} +3.06572 q^{56} +(-1.26328 - 7.07840i) q^{57} +(-0.00285867 - 0.0106687i) q^{58} +(3.56328 + 13.2984i) q^{59} +(6.21064 + 2.24589i) q^{60} -9.28187 q^{61} +(0.942743 - 1.63288i) q^{62} +(5.89290 - 0.540244i) q^{63} +4.32500i q^{64} +(3.78973 - 6.45889i) q^{65} +(1.94700 + 0.166265i) q^{66} +(-4.68587 + 4.68587i) q^{67} -10.6089i q^{68} +(2.15505 + 4.59656i) q^{69} +(-0.429635 - 1.60342i) q^{70} +(-2.46714 + 9.20749i) q^{71} +(-0.425668 - 4.64313i) q^{72} +(0.696641 + 0.696641i) q^{73} +2.78345i q^{74} +(-0.101128 + 1.18423i) q^{75} +(-5.38891 - 5.38891i) q^{76} +(2.74619 + 4.75655i) q^{77} +(-2.51960 - 0.232986i) q^{78} +(-6.46914 + 11.2049i) q^{79} +(6.10271 - 1.63522i) q^{80} +(-1.63643 - 8.84998i) q^{81} +(-3.29897 + 1.90466i) q^{82} +(3.21235 - 0.860748i) q^{83} +(4.79638 - 4.04165i) q^{84} +(-11.5934 + 3.10645i) q^{85} +(2.45481 + 0.657764i) q^{86} +(-0.0387325 - 0.0270010i) q^{87} +(3.74777 - 2.16378i) 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} +(-1.41610 - 7.93465i) q^{93} +1.78974 q^{94} +(-4.31105 + 7.46696i) q^{95} +(-4.84489 - 5.74961i) q^{96} +(8.64769 - 8.64769i) q^{97} +(1.21682 + 0.326045i) q^{98} +(6.82264 - 4.81963i) 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

Modular forms

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