LMFDB - Embedded newform 117.2.x.a.11.2

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			11.2
Character	$\chi$	$=$	117.11
Dual form			117.2.x.a.32.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75651 + 1.75651i) q^{2} +(-1.38793 - 1.03618i) q^{3} -4.17069i q^{4} +(3.52054 + 0.943327i) q^{5} +(4.25797 - 0.617852i) q^{6} +(-1.05231 - 0.281966i) q^{7} +(3.81284 + 3.81284i) q^{8} +(0.852675 + 2.87627i) q^{9} +O(q^{10})$	\(q+(-1.75651 + 1.75651i) q^{2} +(-1.38793 - 1.03618i) q^{3} -4.17069i q^{4} +(3.52054 + 0.943327i) q^{5} +(4.25797 - 0.617852i) q^{6} +(-1.05231 - 0.281966i) q^{7} +(3.81284 + 3.81284i) q^{8} +(0.852675 + 2.87627i) q^{9} +(-7.84085 + 4.52692i) q^{10} +(1.46703 + 1.46703i) q^{11} +(-4.32157 + 5.78860i) q^{12} +(3.60506 + 0.0594429i) q^{13} +(2.34368 - 1.35312i) q^{14} +(-3.90880 - 4.95717i) q^{15} -5.05324 q^{16} +(-2.40801 + 4.17079i) q^{17} +(-6.54995 - 3.55448i) q^{18} +(5.01954 - 1.34498i) q^{19} +(3.93432 - 14.6831i) q^{20} +(1.16837 + 1.48173i) q^{21} -5.15373 q^{22} +(0.496847 - 0.860565i) q^{23} +(-1.34116 - 9.24271i) q^{24} +(7.17423 + 4.14205i) q^{25} +(-6.43675 + 6.22793i) q^{26} +(1.79688 - 4.87558i) q^{27} +(-1.17599 + 4.38887i) q^{28} -3.59614i q^{29} +(15.5732 + 1.84148i) q^{30} +(0.832683 - 3.10761i) q^{31} +(1.25042 - 1.25042i) q^{32} +(-0.516027 - 3.55624i) q^{33} +(-3.09636 - 11.5558i) q^{34} +(-3.43873 - 1.98535i) q^{35} +(11.9960 - 3.55624i) q^{36} +(-3.11289 - 0.834095i) q^{37} +(-6.45441 + 11.1794i) q^{38} +(-4.94196 - 3.81798i) q^{39} +(9.82651 + 17.0200i) q^{40} +(-0.0289477 - 0.108034i) q^{41} +(-4.65493 - 0.550431i) q^{42} +(-7.98646 + 4.61099i) q^{43} +(6.11854 - 6.11854i) q^{44} +(0.288615 + 10.9304i) q^{45} +(0.638875 + 2.38431i) q^{46} +(-7.57174 + 2.02884i) q^{47} +(7.01353 + 5.23606i) q^{48} +(-5.03432 - 2.90657i) q^{49} +(-19.8772 + 5.32608i) q^{50} +(7.66381 - 3.29363i) q^{51} +(0.247918 - 15.0356i) q^{52} -9.48131i q^{53} +(5.40778 + 11.7203i) q^{54} +(3.78086 + 6.54865i) q^{55} +(-2.93721 - 5.08739i) q^{56} +(-8.36038 - 3.33440i) q^{57} +(6.31668 + 6.31668i) q^{58} +(0.399189 + 0.399189i) q^{59} +(-20.6748 + 16.3024i) q^{60} +(4.06219 + 7.03591i) q^{61} +(3.99595 + 6.92119i) q^{62} +(-0.0862689 - 3.26717i) q^{63} -5.71374i q^{64} +(12.6357 + 3.61002i) q^{65} +(7.15300 + 5.34018i) q^{66} +(5.34077 - 1.43106i) q^{67} +(17.3951 + 10.0430i) q^{68} +(-1.58128 + 0.679578i) q^{69} +(9.52747 - 2.55288i) q^{70} +(-0.773983 - 2.88854i) q^{71} +(-7.71565 + 14.2179i) q^{72} +(4.89973 - 4.89973i) q^{73} +(6.93293 - 4.00273i) q^{74} +(-5.66541 - 13.1826i) q^{75} +(-5.60949 - 20.9349i) q^{76} +(-1.13012 - 1.95743i) q^{77} +(15.3870 - 1.97429i) q^{78} +(-5.66155 + 9.80609i) q^{79} +(-17.7902 - 4.76686i) q^{80} +(-7.54589 + 4.90505i) q^{81} +(0.240611 + 0.138917i) q^{82} +(0.638846 + 2.38421i) q^{83} +(6.17983 - 4.87288i) q^{84} +(-12.4119 + 12.4119i) q^{85} +(5.92907 - 22.1276i) q^{86} +(-3.72624 + 4.99118i) q^{87} +11.1871i q^{88} +(0.0437638 - 0.163329i) q^{89} +(-19.7064 - 18.6924i) q^{90} +(-3.77689 - 1.07906i) q^{91} +(-3.58914 - 2.07219i) q^{92} +(-4.37574 + 3.45033i) q^{93} +(9.73618 - 16.8636i) q^{94} +18.9403 q^{95} +(-3.03114 + 0.439833i) q^{96} +(1.80993 - 6.75474i) q^{97} +(13.9483 - 3.73743i) q^{98} +(-2.96869 + 5.47049i) 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 $

$2$	−1.75651	+	1.75651i	−1.24204	+	1.24204i	−0.282891	+	0.959152i	$0.591294\pi$
$2$	−1.75651	+	1.75651i	−1.24204	+	1.24204i	−0.959152	+	0.282891i	$0.908706\pi$
$3$	−1.38793	−	1.03618i	−0.801319	−	0.598237i
$3$	−1.38793	−	1.03618i	−0.801319	−	0.598237i
$4$		−	4.17069i		−	2.08534i
$5$	3.52054	+	0.943327i	1.57443	+	0.421869i	0.937198	−	0.348799i	$-0.113410\pi$
$5$	3.52054	+	0.943327i	1.57443	+	0.421869i	0.637237	+	0.770668i	$0.280077\pi$
$6$	4.25797	−	0.617852i	1.73831	−	0.252237i
$7$	−1.05231	−	0.281966i	−0.397737	−	0.106573i	0.0544057	−	0.998519i	$-0.482674\pi$
$7$	−1.05231	−	0.281966i	−0.397737	−	0.106573i	−0.452143	+	0.891946i	$0.649340\pi$
$8$	3.81284	+	3.81284i	1.34804	+	1.34804i
$9$	0.852675	+	2.87627i	0.284225	+	0.958758i
$10$	−7.84085	+	4.52692i	−2.47950	+	1.43154i
$11$	1.46703	+	1.46703i	0.442327	+	0.442327i	0.892793	−	0.450466i	$-0.148742\pi$
$11$	1.46703	+	1.46703i	0.442327	+	0.442327i	−0.450466	+	0.892793i	$0.648742\pi$
$12$	−4.32157	+	5.78860i	−1.24753	+	1.67103i
$13$	3.60506	+	0.0594429i	0.999864	+	0.0164865i
$13$	3.60506	+	0.0594429i	0.999864	+	0.0164865i
$14$	2.34368	−	1.35312i	0.626375	−	0.361638i
$15$	−3.90880	−	4.95717i	−1.00925	−	1.27994i
$16$	−5.05324			−1.26331
$17$	−2.40801	+	4.17079i	−0.584028	+	1.01157i	0.410968	+	0.911650i	$0.365191\pi$
$17$	−2.40801	+	4.17079i	−0.584028	+	1.01157i	−0.994996	+	0.0999160i	$0.968143\pi$
$18$	−6.54995	−	3.55448i	−1.54384	−	0.837798i
$19$	5.01954	−	1.34498i	1.15156	−	0.308560i	0.367971	−	0.929837i	$-0.380053\pi$
$19$	5.01954	−	1.34498i	1.15156	−	0.308560i	0.783591	+	0.621278i	$0.213386\pi$
$20$	3.93432	−	14.6831i	0.879741	−	3.28324i
$21$	1.16837	+	1.48173i	0.254958	+	0.323340i
$22$	−5.15373			−1.09878
$23$	0.496847	−	0.860565i	0.103600	−	0.179440i	−0.809565	−	0.587030i	$-0.800297\pi$
$23$	0.496847	−	0.860565i	0.103600	−	0.179440i	0.913165	+	0.407589i	$0.133631\pi$
$24$	−1.34116	−	9.24271i	−0.273764	−	1.88666i
$25$	7.17423	+	4.14205i	1.43485	+	0.828409i
$26$	−6.43675	+	6.22793i	−1.26235	+	1.22140i
$27$	1.79688	−	4.87558i	0.345809	−	0.938305i
$28$	−1.17599	+	4.38887i	−0.222242	+	0.829418i
$29$		−	3.59614i		−	0.667787i	−0.942611	−	0.333894i	$-0.891637\pi$
$29$		−	3.59614i		−	0.667787i	0.942611	−	0.333894i	$-0.108363\pi$
$30$	15.5732	+	1.84148i	2.84327	+	0.336207i
$31$	0.832683	−	3.10761i	0.149554	−	0.558144i	−0.849956	−	0.526853i	$-0.823372\pi$
$31$	0.832683	−	3.10761i	0.149554	−	0.558144i	0.999510	−	0.0312904i	$-0.00996168\pi$
$32$	1.25042	−	1.25042i	0.221045	−	0.221045i
$33$	−0.516027	−	3.55624i	−0.0898288	−	0.619062i
$34$	−3.09636	−	11.5558i	−0.531021	−	1.98180i
$35$	−3.43873	−	1.98535i	−0.581251	−	0.335585i
$36$	11.9960	−	3.55624i	1.99934	−	0.592707i
$37$	−3.11289	−	0.834095i	−0.511755	−	0.137124i	−0.00630504	−	0.999980i	$-0.502007\pi$
$37$	−3.11289	−	0.834095i	−0.511755	−	0.137124i	−0.505450	+	0.862856i	$0.668674\pi$
$38$	−6.45441	+	11.1794i	−1.04704	+	1.81353i
$39$	−4.94196	−	3.81798i	−0.791348	−	0.611367i
$40$	9.82651	+	17.0200i	1.55371	+	2.69110i
$41$	−0.0289477	−	0.108034i	−0.00452088	−	0.0168721i	0.963629	−	0.267245i	$-0.0861134\pi$
$41$	−0.0289477	−	0.108034i	−0.00452088	−	0.0168721i	−0.968149	+	0.250373i	$0.919447\pi$
$42$	−4.65493	−	0.550431i	−0.718272	−	0.0849334i
$43$	−7.98646	+	4.61099i	−1.21792	+	0.703169i	−0.964474	−	0.264180i	$-0.914899\pi$
$43$	−7.98646	+	4.61099i	−1.21792	+	0.703169i	−0.253451	+	0.967348i	$0.581566\pi$
$44$	6.11854	−	6.11854i	0.922404	−	0.922404i
$45$	0.288615	+	10.9304i	0.0430242	+	1.62941i
$46$	0.638875	+	2.38431i	0.0941969	+	0.351548i
$47$	−7.57174	+	2.02884i	−1.10445	+	0.295937i	−0.764576	−	0.644534i	$-0.777052\pi$
$47$	−7.57174	+	2.02884i	−1.10445	+	0.295937i	−0.339875	+	0.940470i	$0.610385\pi$
$48$	7.01353	+	5.23606i	1.01232	+	0.755759i
$49$	−5.03432	−	2.90657i	−0.719189	−	0.415224i
$50$	−19.8772	+	5.32608i	−2.81106	+	0.753222i
$51$	7.66381	−	3.29363i	1.07315	−	0.461200i
$52$	0.247918	−	15.0356i	0.0343800	−	2.08506i
$53$		−	9.48131i		−	1.30236i	−0.758924	−	0.651179i	$-0.774275\pi$
$53$		−	9.48131i		−	1.30236i	0.758924	−	0.651179i	$-0.225725\pi$
$54$	5.40778	+	11.7203i	0.735905	+	1.59493i
$55$	3.78086	+	6.54865i	0.509812	+	0.883019i
$56$	−2.93721	−	5.08739i	−0.392501	−	0.679832i
$57$	−8.36038	−	3.33440i	−1.10736	−	0.441651i
$58$	6.31668	+	6.31668i	0.829420	+	0.829420i
$59$	0.399189	+	0.399189i	0.0519700	+	0.0519700i	0.732614	−	0.680644i	$-0.238300\pi$
$59$	0.399189	+	0.399189i	0.0519700	+	0.0519700i	−0.680644	+	0.732614i	$0.738300\pi$
$60$	−20.6748	+	16.3024i	−2.66911	+	2.10463i
$61$	4.06219	+	7.03591i	0.520110	+	0.900856i	0.999727	+	0.0233784i	$0.00744226\pi$
$61$	4.06219	+	7.03591i	0.520110	+	0.900856i	−0.479617	+	0.877478i	$0.659224\pi$
$62$	3.99595	+	6.92119i	0.507486	+	0.878992i
$63$	−0.0862689	−	3.26717i	−0.0108689	−	0.411624i
$64$		−	5.71374i		−	0.714217i
$65$	12.6357	+	3.61002i	1.56727	+	0.447768i
$66$	7.15300	+	5.34018i	0.880473	+	0.657330i
$67$	5.34077	−	1.43106i	0.652479	−	0.174831i	0.0826298	−	0.996580i	$-0.473668\pi$
$67$	5.34077	−	1.43106i	0.652479	−	0.174831i	0.569850	+	0.821749i	$0.307001\pi$
$68$	17.3951	+	10.0430i	2.10946	+	1.21790i
$69$	−1.58128	+	0.679578i	−0.190364	+	0.0818116i
$70$	9.52747	−	2.55288i	1.13875	−	0.305127i
$71$	−0.773983	−	2.88854i	−0.0918549	−	0.342807i	0.904669	−	0.426115i	$-0.140118\pi$
$71$	−0.773983	−	2.88854i	−0.0918549	−	0.342807i	−0.996524	+	0.0833079i	$0.973451\pi$
$72$	−7.71565	+	14.2179i	−0.909298	+	1.67559i
$73$	4.89973	−	4.89973i	0.573470	−	0.573470i	−0.359626	−	0.933096i	$-0.617096\pi$
$73$	4.89973	−	4.89973i	0.573470	−	0.573470i	0.933096	+	0.359626i	$0.117096\pi$
$74$	6.93293	−	4.00273i	0.805937	−	0.465308i
$75$	−5.66541	−	13.1826i	−0.654185	−	1.52220i
$76$	−5.60949	−	20.9349i	−0.643453	−	2.40140i
$77$	−1.13012	−	1.95743i	−0.128790	−	0.223070i
$78$	15.3870	−	1.97429i	1.74223	−	0.223544i
$79$	−5.66155	+	9.80609i	−0.636974	+	1.10327i	0.349119	+	0.937078i	$0.386481\pi$
$79$	−5.66155	+	9.80609i	−0.636974	+	1.10327i	−0.986093	+	0.166193i	$0.946853\pi$
$80$	−17.7902	−	4.76686i	−1.98900	−	0.532951i
$81$	−7.54589	+	4.90505i	−0.838432	+	0.545006i
$82$	0.240611	+	0.138917i	0.0265710	+	0.0153408i
$83$	0.638846	+	2.38421i	0.0701225	+	0.261701i	0.992083	−	0.125583i	$-0.0400801\pi$
$83$	0.638846	+	2.38421i	0.0701225	+	0.261701i	−0.921961	+	0.387284i	$0.873413\pi$
$84$	6.17983	−	4.87288i	0.674275	−	0.531675i
$85$	−12.4119	+	12.4119i	−1.34626	+	1.34626i
$86$	5.92907	−	22.1276i	0.639348	−	2.38608i
$87$	−3.72624	+	4.99118i	−0.399495	+	0.535111i
$88$			11.1871i			1.19255i
$89$	0.0437638	−	0.163329i	0.00463895	−	0.0173128i	−0.963568	−	0.267465i	$-0.913814\pi$
$89$	0.0437638	−	0.163329i	0.00463895	−	0.0173128i	0.968207	+	0.250152i	$0.0804807\pi$
$90$	−19.7064	−	18.6924i	−2.07723	−	1.97036i
$91$	−3.77689	−	1.07906i	−0.395926	−	0.113116i
$92$	−3.58914	−	2.07219i	−0.374194	−	0.216041i
$93$	−4.37574	+	3.45033i	−0.453743	+	0.357783i
$94$	9.73618	−	16.8636i	1.00421	−	1.73934i
$95$	18.9403			1.94323
$96$	−3.03114	+	0.439833i	−0.309364	+	0.0448903i
$97$	1.80993	−	6.75474i	0.183770	−	0.685840i	−0.811120	−	0.584879i	$-0.801142\pi$
$97$	1.80993	−	6.75474i	0.183770	−	0.685840i	0.994890	−	0.100960i	$-0.0321915\pi$
$98$	13.9483	−	3.73743i	1.40899	−	0.377537i
$99$	−2.96869	+	5.47049i	−0.298364	+	0.549805i
$100$	17.2752	−	29.9215i	1.72752	−	2.99215i
$101$	−15.4071			−1.53306			−0.766530	−	0.642208i	$-0.778018\pi$
$101$	−15.4071			−1.53306			−0.766530	+	0.642208i	$0.778018\pi$
$102$	−7.67630	+	19.2469i	−0.760066	+	1.90573i
$103$	−4.45016	+	2.56930i	−0.438487	+	0.253161i	−0.702956	−	0.711234i	$-0.748137\pi$
$103$	−4.45016	+	2.56930i	−0.438487	+	0.253161i	0.264468	+	0.964394i	$0.414803\pi$
$104$	13.5189	+	13.9722i	1.32563	+	1.37008i
$105$	2.71552	+	6.31865i	0.265008	+	0.616637i
$106$	16.6541	+	16.6541i	1.61758	+	1.61758i
$107$	−4.70507	+	2.71647i	−0.454856	+	0.262611i	−0.709879	−	0.704324i	$-0.751250\pi$
$107$	−4.70507	+	2.71647i	−0.454856	+	0.262611i	0.255023	+	0.966935i	$0.417917\pi$
$108$	−20.3345	−	7.49421i	−1.95669	−	0.721131i
$109$	−1.46605	−	1.46605i	−0.140422	−	0.140422i	0.633401	−	0.773824i	$-0.281658\pi$
$109$	−1.46605	−	1.46605i	−0.140422	−	0.140422i	−0.773824	+	0.633401i	$0.781658\pi$
$110$	−18.1439	−	4.86165i	−1.72996	−	0.463540i
$111$	3.45618	+	4.38316i	0.328047	+	0.416031i
$112$	5.31760	+	1.42485i	0.502466	+	0.134635i
$113$		−	5.01207i		−	0.471496i	−0.971814	−	0.235748i	$-0.924246\pi$
$113$		−	5.01207i		−	0.471496i	0.971814	−	0.235748i	$-0.0757539\pi$
$114$	20.5420	−	8.82822i	1.92394	−	0.826839i
$115$	2.56097	−	2.56097i	0.238811	−	0.238811i
$116$	−14.9984			−1.39256
$117$	2.90297	+	10.4198i	0.268380	+	0.963313i
$118$	−1.40236			−0.129098
$119$	3.71000	−	3.71000i	0.340095	−	0.340095i
$120$	3.99728	−	33.8045i	0.364900	−	3.08592i
$121$		−	6.69562i		−	0.608693i
$122$	−19.4940	−	5.22339i	−1.76490	−	0.472904i
$123$	−0.0717654	+	0.179939i	−0.00647087	+	0.0162245i
$124$	−12.9609	−	3.47286i	−1.16392	−	0.311872i
$125$	8.46382	+	8.46382i	0.757027	+	0.757027i
$126$	5.89036	+	5.58729i	0.524755	+	0.497755i
$127$	11.1449	−	6.43453i	0.988953	−	0.570972i	0.0839916	−	0.996466i	$-0.473233\pi$
$127$	11.1449	−	6.43453i	0.988953	−	0.570972i	0.904961	+	0.425494i	$0.139900\pi$
$128$	12.5371	+	12.5371i	1.10813	+	1.10813i
$129$	15.8624	+	1.87568i	1.39661	+	0.165144i
$130$	−28.5358	+	15.8537i	−2.50276	+	1.39046i
$131$	−11.9519	+	6.90042i	−1.04424	+	0.602893i	−0.921032	−	0.389488i	$-0.872652\pi$
$131$	−11.9519	+	6.90042i	−1.04424	+	0.602893i	−0.123209	+	0.992381i	$0.539319\pi$
$132$	−14.8320	+	2.15219i	−1.29096	+	0.187324i
$133$	−5.66137			−0.490903
$134$	−6.86748	+	11.8948i	−0.593260	+	1.02756i
$135$	10.9252	−	15.4696i	0.940295	−	1.33141i
$136$	−25.0839	+	6.72121i	−2.15093	+	0.576339i
$137$	1.92441	−	7.18198i	0.164413	−	0.613598i	−0.833701	−	0.552216i	$-0.813782\pi$
$137$	1.92441	−	7.18198i	0.164413	−	0.613598i	0.998114	−	0.0613822i	$-0.0195508\pi$
$138$	1.58386	−	3.97124i	0.134827	−	0.338054i
$139$	−13.3087			−1.12883			−0.564416	−	0.825491i	$-0.690899\pi$
$139$	−13.3087			−1.12883			−0.564416	+	0.825491i	$0.690899\pi$
$140$	−8.28027	+	14.3418i	−0.699811	+	1.21211i
$141$	12.6112	+	5.02978i	1.06206	+	0.423584i
$142$	6.43328	+	3.71426i	0.539869	+	0.311694i
$143$	5.20154	+	5.37595i	0.434975	+	0.449560i
$144$	−4.30878	−	14.5345i	−0.359065	−	1.21121i
$145$	3.39234	−	12.6604i	0.281718	−	1.05139i
$146$			17.2129i			1.42455i
$147$	3.97555	+	9.25054i	0.327897	+	0.762972i
$148$	−3.47875	+	12.9829i	−0.285951	+	1.06719i
$149$	−4.64616	+	4.64616i	−0.380628	+	0.380628i	−0.871328	−	0.490700i	$-0.836741\pi$
$149$	−4.64616	+	4.64616i	−0.380628	+	0.380628i	0.490700	+	0.871328i	$0.336741\pi$
$150$	33.1069	+	13.2041i	2.70316	+	1.07811i
$151$	−0.774476	−	2.89038i	−0.0630260	−	0.235216i	0.927226	−	0.374501i	$-0.122186\pi$
$151$	−0.774476	−	2.89038i	−0.0630260	−	0.235216i	−0.990252	+	0.139285i	$0.955519\pi$
$152$	24.2669	+	14.0105i	1.96830	+	1.13640i
$153$	−14.0496	−	3.36976i	−1.13584	−	0.272429i
$154$	5.42334	+	1.45318i	0.437025	+	0.117101i
$155$	5.86299	−	10.1550i	0.470927	−	0.815669i
$156$	−15.9236	+	20.6114i	−1.27491	+	1.65023i
$157$	6.59432	+	11.4217i	0.526284	+	0.911551i	0.999531	+	0.0306210i	$0.00974851\pi$
$157$	6.59432	+	11.4217i	0.526284	+	0.911551i	−0.473247	+	0.880930i	$0.656918\pi$
$158$	−7.27995	−	27.1691i	−0.579161	−	2.16146i
$159$	−9.82431	+	13.1594i	−0.779119	+	1.04360i
$160$	5.58170	−	3.22260i	0.441272	−	0.254769i
$161$	−0.765489	+	0.765489i	−0.0603290	+	0.0603290i
$162$	4.63867	−	21.8703i	0.364448	−	1.71829i
$163$	−1.71629	−	6.40529i	−0.134430	−	0.501701i	−1.00000		0.000911896i	$-0.999710\pi$
$163$	−1.71629	−	6.40529i	−0.134430	−	0.501701i	0.865569	−	0.500790i	$-0.166957\pi$
$164$	−0.450577	+	0.120732i	−0.0351842	+	0.00942758i
$165$	1.53800	−	13.0067i	0.119733	−	1.01257i
$166$	−5.31003	−	3.06575i	−0.412139	−	0.237948i
$167$	19.0223	−	5.09701i	1.47199	−	0.394418i	0.568377	−	0.822768i	$-0.307572\pi$
$167$	19.0223	−	5.09701i	1.47199	−	0.394418i	0.903613	+	0.428350i	$0.140905\pi$
$168$	−1.19481	+	10.1044i	−0.0921818	+	0.779571i
$169$	12.9929	+	0.428590i	0.999456	+	0.0329685i
$170$		−	43.6034i		−	3.34423i
$171$	8.14857	+	13.2907i	0.623137	+	1.01637i
$172$	19.2310	+	33.3090i	1.46635	+	2.53979i
$173$	−12.0119	−	20.8052i	−0.913246	−	1.58179i	−0.809449	−	0.587190i	$-0.800234\pi$
$173$	−12.0119	−	20.8052i	−0.913246	−	1.58179i	−0.103797	−	0.994598i	$-0.533099\pi$
$174$	−2.22188	−	15.3123i	−0.168441	−	1.16082i
$175$	−6.38162	−	6.38162i	−0.482405	−	0.482405i
$176$	−7.41328	−	7.41328i	−0.558797	−	0.558797i
$177$	−0.140414	−	0.967676i	−0.0105542	−	0.0727350i
$178$	0.210017	+	0.363761i	0.0157415	+	0.0272650i
$179$	−3.40509	−	5.89778i	−0.254508	−	0.440821i	0.710254	−	0.703946i	$-0.248580\pi$
$179$	−3.40509	−	5.89778i	−0.254508	−	0.440821i	−0.964762	+	0.263125i	$0.915247\pi$
$180$	45.5872	−	1.20372i	3.39787	−	0.0897202i
$181$			13.5743i			1.00897i	0.863422	+	0.504483i	$0.168317\pi$
$181$			13.5743i			1.00897i	−0.863422	+	0.504483i	$0.831683\pi$
$182$	8.52955	−	4.73878i	0.632252	−	0.351262i
$183$	1.65244	−	13.9745i	0.122152	−	1.03302i
$184$	5.17559	−	1.38680i	0.381550	−	0.102236i
$185$	−10.1722	−	5.87294i	−0.747877	−	0.431787i
$186$	1.62549	−	13.7466i	0.119187	−	1.00795i
$187$	−9.65132	+	2.58606i	−0.705774	+	0.189112i
$188$	8.46166	+	31.5793i	0.617130	+	2.30316i
$189$	−3.26563	+	4.62397i	−0.237539	+	0.336344i
$190$	−33.2688	+	33.2688i	−2.41358	+	2.41358i
$191$	11.3188	−	6.53489i	0.818997	−	0.472848i	−0.0310737	−	0.999517i	$-0.509893\pi$
$191$	11.3188	−	6.53489i	0.818997	−	0.472848i	0.850070	+	0.526669i	$0.176559\pi$
$192$	−5.92044	+	7.93024i	−0.427271	+	0.572316i
$193$	4.12391	+	15.3906i	0.296846	+	1.10784i	0.939741	+	0.341888i	$0.111066\pi$
$193$	4.12391	+	15.3906i	0.296846	+	1.10784i	−0.642895	+	0.765954i	$0.722267\pi$
$194$	8.68563	+	15.0440i	0.623592	+	1.08009i
$195$	−13.7968	−	18.1033i	−0.988009	−	1.29640i
$196$	−12.1224	+	20.9966i	−0.865884	+	1.49975i
$197$	21.1610	+	5.67007i	1.50766	+	0.403976i	0.915657	−	0.401961i	$-0.131671\pi$
$197$	21.1610	+	5.67007i	1.50766	+	0.403976i	0.592002	+	0.805937i	$0.298338\pi$
$198$	−4.39446	−	14.8235i	−0.312301	−	1.05346i
$199$	−5.60410	−	3.23553i	−0.397264	−	0.229360i	0.288039	−	0.957619i	$-0.406997\pi$
$199$	−5.60410	−	3.23553i	−0.397264	−	0.229360i	−0.685303	+	0.728258i	$0.740330\pi$
$200$	11.5612	+	43.1472i	0.817504	+	3.05097i
$201$	−8.89542	−	3.54779i	−0.627435	−	0.250242i
$202$	27.0627	−	27.0627i	1.90413	−	1.90413i
$203$	−1.01399	+	3.78427i	−0.0711683	+	0.265604i
$204$	−13.7367	−	31.9634i	−0.961760	−	2.23788i
$205$		−	0.407647i		−	0.0284713i
$206$	3.30376	−	12.3298i	0.230184	−	0.859057i
$207$	2.89887	+	0.695286i	0.201485	+	0.0483257i
$208$	−18.2173	−	0.300379i	−1.26314	−	0.0208276i
$209$	9.33696	+	5.39070i	0.645851	+	0.372882i
$210$	−15.8687	−	6.32894i	−1.09504	−	0.436738i
$211$	−3.86928	+	6.70180i	−0.266372	+	0.461371i	−0.967922	−	0.251250i	$-0.919158\pi$
$211$	−3.86928	+	6.70180i	−0.266372	+	0.461371i	0.701550	+	0.712620i	$0.252492\pi$
$212$	−39.5436			−2.71586
$213$	−1.91881	+	4.81107i	−0.131475	+	0.329649i
$214$	3.49300	−	13.0360i	0.238776	−	0.891126i
$215$	−32.4664	+	8.69933i	−2.21419	+	0.593290i
$216$	25.4410	−	11.7386i	1.73104	−	0.798709i
$217$	−1.75249	+	3.03539i	−0.118966	+	0.206056i
$218$	5.15028			0.348821
$219$	−11.8775	+	1.72348i	−0.802604	+	0.116462i
$220$	27.3123	−	15.7688i	1.84140	−	1.06313i
$221$	−8.92894	+	14.8928i	−0.600625	+	1.00180i
$222$	−13.7699	−	1.62825i	−0.924177	−	0.109281i
$223$	−13.6034	−	13.6034i	−0.910949	−	0.910949i	0.0853980	−	0.996347i	$-0.472784\pi$
$223$	−13.6034	−	13.6034i	−0.910949	−	0.910949i	−0.996347	+	0.0853980i	$0.972784\pi$
$224$	−1.66841	+	0.963255i	−0.111475	+	0.0643602i
$225$	−5.79636	+	24.1669i	−0.386424	+	1.61112i
$226$	8.80377	+	8.80377i	0.585618	+	0.585618i
$227$	13.2663	+	3.55471i	0.880518	+	0.235934i	0.670631	−	0.741792i	$-0.266024\pi$
$227$	13.2663	+	3.55471i	0.880518	+	0.235934i	0.209887	+	0.977726i	$0.432690\pi$
$228$	−13.9067	+	34.8685i	−0.920995	+	2.30922i
$229$	−3.36174	−	0.900776i	−0.222150	−	0.0595249i	0.146027	−	0.989281i	$-0.453351\pi$
$229$	−3.36174	−	0.900776i	−0.222150	−	0.0595249i	−0.368177	+	0.929756i	$0.620018\pi$
$230$			8.99675i			0.593228i
$231$	−0.459718	+	3.88778i	−0.0302472	+	0.255797i
$232$	13.7115	−	13.7115i	0.900205	−	0.900205i
$233$	−15.4604			−1.01284			−0.506422	−	0.862286i	$-0.669032\pi$
$233$	−15.4604			−1.01284			−0.506422	+	0.862286i	$0.669032\pi$
$234$	−23.4017	−	13.2035i	−1.52982	−	0.863137i
$235$	−28.5705			−1.86373
$236$	1.66489	−	1.66489i	0.108375	−	0.108375i
$237$	18.0187	−	7.74376i	1.17044	−	0.503011i
$238$			13.0333i			0.844826i
$239$	17.0284	+	4.56275i	1.10148	+	0.295139i	0.763365	−	0.645967i	$-0.223546\pi$
$239$	17.0284	+	4.56275i	1.10148	+	0.295139i	0.338110	+	0.941107i	$0.390212\pi$
$240$	19.7521	+	25.0498i	1.27499	+	1.61696i
$241$	2.35683	+	0.631510i	0.151816	+	0.0406791i	0.333927	−	0.942599i	$-0.391626\pi$
$241$	2.35683	+	0.631510i	0.151816	+	0.0406791i	−0.182110	+	0.983278i	$0.558293\pi$
$242$	11.7610	+	11.7610i	0.756023	+	0.756023i
$243$	15.5556	+	1.01103i	0.997895	+	0.0648574i
$244$	29.3446	−	16.9421i	1.87859	−	1.08461i
$245$	−14.9817	−	14.9817i	−0.957146	−	0.957146i
$246$	−0.190008	−	0.442122i	−0.0121145	−	0.0281887i
$247$	18.1757	−	4.55036i	1.15649	−	0.289533i
$248$	15.0237	−	8.67395i	0.954007	−	0.550796i
$249$	1.58379	−	3.97106i	0.100369	−	0.251656i
$250$	−29.7336			−1.88052
$251$	11.2944	−	19.5625i	0.712896	−	1.23477i	−0.250869	−	0.968021i	$-0.580716\pi$
$251$	11.2944	−	19.5625i	0.712896	−	1.23477i	0.963765	−	0.266752i	$-0.0859504\pi$
$252$	−13.6263	+	0.359801i	−0.858377	+	0.0226653i
$253$	1.99137	−	0.533586i	0.125196	−	0.0335462i
$254$	−8.27389	+	30.8786i	−0.519150	+	1.93749i
$255$	30.0878	−	4.36588i	1.88417	−	0.273402i
$256$	−32.6157			−2.03848
$257$	−4.46450	+	7.73274i	−0.278488	+	0.482355i	−0.971009	−	0.239042i	$-0.923167\pi$
$257$	−4.46450	+	7.73274i	−0.278488	+	0.482355i	0.692521	+	0.721397i	$0.256500\pi$
$258$	−31.1572	+	24.5679i	−1.93976	+	1.52953i
$259$	3.04054	+	1.75546i	0.188930	+	0.109079i
$260$	15.0563	−	52.6995i	0.933750	−	3.26829i
$261$	10.3435	−	3.06634i	0.640246	−	0.189802i
$262$	8.87296	−	33.1143i	0.548173	−	2.04581i
$263$			17.1384i			1.05680i	0.848996	+	0.528399i	$0.177207\pi$
$263$			17.1384i			1.05680i	−0.848996	+	0.528399i	$0.822793\pi$
$264$	11.5918	−	15.5269i	0.713429	−	0.955615i
$265$	8.94397	−	33.3794i	0.549424	−	2.05048i
$266$	9.94427	−	9.94427i	0.609722	−	0.609722i
$267$	−0.229978	+	0.181341i	−0.0140744	+	0.0110979i
$268$	−5.96848	−	22.2747i	−0.364583	−	1.36064i
$269$	−13.5579	−	7.82768i	−0.826643	−	0.477262i	0.0260591	−	0.999660i	$-0.491704\pi$
$269$	−13.5579	−	7.82768i	−0.826643	−	0.477262i	−0.852702	+	0.522398i	$0.825038\pi$
$270$	7.98228	+	46.3630i	0.485786	+	2.82156i
$271$	−4.96831	−	1.33125i	−0.301803	−	0.0808679i	0.104740	−	0.994500i	$-0.466599\pi$
$271$	−4.96831	−	1.33125i	−0.301803	−	0.0808679i	−0.406543	+	0.913632i	$0.633266\pi$
$272$	12.1683	−	21.0760i	0.737809	−	1.27792i
$273$	4.12395	+	5.41118i	0.249593	+	0.327500i
$274$	9.23500	+	15.9955i	0.557907	+	0.966323i
$275$	4.44832	+	16.6014i	0.268244	+	1.00110i
$276$	2.83431	+	6.59504i	0.170605	+	0.396975i
$277$	23.2754	−	13.4380i	1.39848	−	0.807413i	0.404247	−	0.914650i	$-0.367534\pi$
$277$	23.2754	−	13.4380i	1.39848	−	0.807413i	0.994234	+	0.107237i	$0.0342003\pi$
$278$	23.3770	−	23.3770i	1.40206	−	1.40206i
$279$	9.64835	−	0.254763i	0.577632	−	0.0152523i
$280$	−5.54149	−	20.6811i	−0.331168	−	1.23593i
$281$	−8.35114	+	2.23768i	−0.498187	+	0.133489i	−0.499159	−	0.866511i	$-0.666358\pi$
$281$	−8.35114	+	2.23768i	−0.498187	+	0.133489i	0.000971269		1.00000i	$0.499691\pi$
$282$	−30.9867	+	13.3170i	−1.84523	+	0.793013i
$283$	−3.30997	−	1.91101i	−0.196757	−	0.113598i	0.398385	−	0.917218i	$-0.369571\pi$
$283$	−3.30997	−	1.91101i	−0.196757	−	0.113598i	−0.595142	+	0.803621i	$0.702904\pi$
$284$	−12.0472	+	3.22804i	−0.714871	+	0.191549i
$285$	−26.2877	−	19.6255i	−1.55715	−	1.16251i
$286$	−18.5795	−	0.306353i	−1.09863	−	0.0181150i
$287$			0.121848i			0.00719248i
$288$	4.66274	+	2.53034i	0.274755	+	0.149102i
$289$	−3.09700	−	5.36417i	−0.182177	−	0.315539i
$290$	16.2794	+	28.1968i	0.955962	+	1.65577i
$291$	−9.51115	+	7.49967i	−0.557553	+	0.439638i
$292$	−20.4352	−	20.4352i	−1.19588	−	1.19588i
$293$	−18.7059	−	18.7059i	−1.09281	−	1.09281i	−0.995227	−	0.0975857i	$-0.968888\pi$
$293$	−18.7059	−	18.7059i	−1.09281	−	1.09281i	−0.0975857	−	0.995227i	$-0.531112\pi$
$294$	−23.2318	−	9.26561i	−1.35491	−	0.540381i
$295$	1.02880	+	1.78193i	0.0598989	+	0.103748i
$296$	−8.68867	−	15.0492i	−0.505018	−	0.874718i
$297$	9.78871	−	4.51655i	0.567999	−	0.262077i
$298$		−	16.3221i		−	0.945513i
$299$	1.84232	−	3.07285i	0.106544	−	0.177708i
$300$	−54.9806	+	23.6286i	−3.17431	+	1.36420i
$301$	9.70440	−	2.60029i	0.559352	−	0.149878i
$302$	6.43738	+	3.71662i	0.370429	+	0.213868i
$303$	21.3839	+	15.9644i	1.22847	+	0.917133i
$304$	−25.3650	+	6.79652i	−1.45478	+	0.389807i
$305$	7.66394	+	28.6022i	0.438836	+	1.63776i
$306$	30.5973	−	18.7593i	1.74913	−	1.07240i
$307$	−13.6470	+	13.6470i	−0.778874	+	0.778874i	−0.979639	−	0.200765i	$-0.935657\pi$
$307$	−13.6470	+	13.6470i	−0.778874	+	0.778874i	0.200765	+	0.979639i	$0.435657\pi$
$308$	−8.16384	+	4.71339i	−0.465178	+	0.268571i
$309$	8.83874	+	1.04515i	0.502818	+	0.0594567i
$310$	7.53897	+	28.1358i	0.428185	+	1.59801i
$311$	−9.51140	−	16.4742i	−0.539342	−	0.934167i	−0.998940	−	0.0460402i	$-0.985340\pi$
$311$	−9.51140	−	16.4742i	−0.539342	−	0.934167i	0.459598	−	0.888127i	$-0.347994\pi$
$312$	−4.28556	−	33.4003i	−0.242622	−	1.89092i
$313$	16.0084	−	27.7274i	0.904848	−	1.56724i	0.0837269	−	0.996489i	$-0.473318\pi$
$313$	16.0084	−	27.7274i	0.904848	−	1.56724i	0.821121	−	0.570754i	$-0.193349\pi$
$314$	−31.6454	−	8.47936i	−1.78585	−	0.478518i
$315$	2.77829	−	11.5836i	0.156539	−	0.652661i
$316$	40.8981	+	23.6125i	2.30070	+	1.32831i
$317$	−1.69818	−	6.33771i	−0.0953795	−	0.355961i	0.901697	−	0.432368i	$-0.142322\pi$
$317$	−1.69818	−	6.33771i	−0.0953795	−	0.355961i	−0.997077	+	0.0764069i	$0.975655\pi$
$318$	−5.85805	−	40.3711i	−0.328503	−	2.26390i
$319$	5.27566	−	5.27566i	0.295380	−	0.295380i
$320$	5.38992	−	20.1155i	0.301306	−	1.12449i
$321$	9.34503	+	1.10502i	0.521589	+	0.0616763i
$322$		−	2.68919i		−	0.149862i
$323$	−6.47745	+	24.1742i	−0.360415	+	1.34509i
$324$	20.4574	+	31.4715i	1.13652	+	1.74842i
$325$	25.6173	+	15.3588i	1.42099	+	0.851952i
$326$	14.2657	+	8.23630i	0.790103	+	0.456166i
$327$	0.515682	+	3.55386i	0.0285173	+	0.196529i
$328$	0.301545	−	0.522291i	0.0166500	−	0.0288387i
$329$	8.53990			0.470820
$330$	20.1449	+	25.5479i	1.10894	+	1.40637i
$331$	−8.61586	+	32.1548i	−0.473570	+	1.76739i	0.153211	+	0.988193i	$0.451039\pi$
$331$	−8.61586	+	32.1548i	−0.473570	+	1.76739i	−0.626782	+	0.779195i	$0.715628\pi$
$332$	9.94377	−	2.66443i	0.545735	−	0.146229i
$333$	−0.255195	−	9.66472i	−0.0139846	−	0.529624i
$334$	−24.4600	+	42.3659i	−1.33839	+	2.31816i
$335$	20.1524			1.10104
$336$	−5.90404	−	7.48755i	−0.322092	−	0.408479i
$337$	−1.39905	+	0.807743i	−0.0762112	+	0.0440006i	−0.537621	−	0.843186i	$-0.680677\pi$
$337$	−1.39905	+	0.807743i	−0.0762112	+	0.0440006i	0.461410	+	0.887187i	$0.347344\pi$
$338$	−23.5751	+	22.0694i	−1.28232	+	1.20042i
$339$	−5.19339	+	6.95638i	−0.282066	+	0.377818i
$340$	51.7662	+	51.7662i	2.80742	+	2.80742i
$341$	5.78055	−	3.33740i	0.313034	−	0.180730i
$342$	−37.6584	−	9.03228i	−2.03633	−	0.488410i
$343$	9.87055	+	9.87055i	0.532960	+	0.532960i
$344$	−48.0321	−	12.8701i	−2.58971	−	0.693912i
$345$	−6.20804	+	0.900817i	−0.334230	+	0.0484983i
$346$	57.6436	+	15.4456i	3.09894	+	0.830359i
$347$			21.4397i			1.15094i	0.817822	+	0.575471i	$0.195181\pi$
$347$			21.4397i			1.15094i	−0.817822	+	0.575471i	$0.804819\pi$
$348$	20.8166	+	15.5410i	1.11589	+	0.833084i
$349$	−0.362566	+	0.362566i	−0.0194077	+	0.0194077i	−0.716744	−	0.697336i	$-0.754368\pi$
$349$	−0.362566	+	0.362566i	−0.0194077	+	0.0194077i	0.697336	+	0.716744i	$0.254368\pi$
$350$	22.4188			1.19834
$351$	6.76767	−	17.4699i	0.361232	−	0.932476i
$352$	3.66881			0.195548
$353$	−24.4203	+	24.4203i	−1.29976	+	1.29976i	−0.371211	+	0.928549i	$0.621057\pi$
$353$	−24.4203	+	24.4203i	−1.29976	+	1.29976i	−0.928549	+	0.371211i	$0.878943\pi$
$354$	1.94638	+	1.45310i	0.103449	+	0.0772312i
$355$		−	10.8994i		−	0.578478i
$356$	−0.681192	−	0.182525i	−0.0361031	−	0.00967380i
$357$	−8.99342	+	1.30499i	−0.475982	+	0.0690673i
$358$	16.3406	+	4.37846i	0.863629	+	0.231409i
$359$	−2.81379	−	2.81379i	−0.148506	−	0.148506i	0.628944	−	0.777450i	$-0.283487\pi$
$359$	−2.81379	−	2.81379i	−0.148506	−	0.148506i	−0.777450	+	0.628944i	$0.783487\pi$
$360$	−40.5754	+	42.7763i	−2.13851	+	2.25451i
$361$	6.93231	−	4.00237i	0.364858	−	0.210651i
$362$	−23.8434	−	23.8434i	−1.25318	−	1.25318i
$363$	−6.93785	+	9.29303i	−0.364143	+	0.487758i
$364$	−4.50041	+	15.7522i	−0.235886	+	0.825641i
$365$	21.8718	−	12.6277i	1.14482	−	0.660963i
$366$	21.6438	+	27.4489i	1.13134	+	1.43478i
$367$	−3.42145			−0.178598			−0.0892992	−	0.996005i	$-0.528463\pi$
$367$	−3.42145			−0.178598			−0.0892992	+	0.996005i	$0.528463\pi$
$368$	−2.51069	+	4.34864i	−0.130879	+	0.226689i
$369$	0.286053	−	0.175380i	0.0148913	−	0.00912991i
$370$	28.1836	−	7.55176i	1.46519	−	0.392598i
$371$	−2.67341	+	9.97731i	−0.138797	+	0.517996i
$372$	14.3902	+	18.2498i	0.746099	+	0.946210i
$373$	3.18074			0.164692			0.0823462	−	0.996604i	$-0.473759\pi$
$373$	3.18074			0.164692			0.0823462	+	0.996604i	$0.473759\pi$
$374$	12.4102	−	21.4951i	0.641717	−	1.11149i
$375$	−2.97714	−	20.5172i	−0.153739	−	1.05950i
$376$	−36.6055	−	21.1342i	−1.88778	−	1.08991i
$377$	0.213765	−	12.9643i	0.0110095	−	0.667696i
$378$	−2.38595	−	13.8582i	−0.122720	−	0.712789i
$379$	1.52519	−	5.69207i	0.0783436	−	0.292382i	−0.915627	−	0.402029i	$-0.868305\pi$
$379$	1.52519	−	5.69207i	0.0783436	−	0.292382i	0.993971	+	0.109647i	$0.0349719\pi$
$380$		−	78.9939i		−	4.05230i
$381$	−22.1356	−	2.61747i	−1.13404	−	0.134097i
$382$	−8.40294	+	31.3602i	−0.429932	+	1.60453i
$383$	−5.41465	+	5.41465i	−0.276676	+	0.276676i	−0.831781	−	0.555105i	$-0.812678\pi$
$383$	−5.41465	+	5.41465i	−0.276676	+	0.276676i	0.555105	+	0.831781i	$0.312678\pi$
$384$	−4.40991	−	30.3912i	−0.225042	−	1.55089i
$385$	−2.13215	−	7.95730i	−0.108665	−	0.405542i
$386$	−34.2776	−	19.7902i	−1.74468	−	1.00729i
$387$	−20.0723	−	19.0396i	−1.02033	−	0.967836i
$388$	−28.1719	−	7.54863i	−1.43021	−	0.383224i
$389$	2.78690	−	4.82705i	0.141301	−	0.244741i	−0.786686	−	0.617354i	$-0.788205\pi$
$389$	2.78690	−	4.82705i	0.141301	−	0.244741i	0.927987	+	0.372613i	$0.121538\pi$
$390$	56.0329	+	7.56438i	2.83734	+	0.383037i
$391$	2.39282	+	4.14449i	0.121010	+	0.209596i
$392$	−8.11279	−	30.2773i	−0.409758	−	1.52924i
$393$	23.7384	+	2.80699i	1.19744	+	0.141594i
$394$	−47.1292	+	27.2100i	−2.37433	+	1.37082i
$395$	−29.1821	+	29.1821i	−1.46831	+	1.46831i
$396$	22.8157	+	12.3815i	1.14653	+	0.622191i
$397$	7.60801	+	28.3935i	0.381835	+	1.42503i	0.843096	+	0.537763i	$0.180731\pi$
$397$	7.60801	+	28.3935i	0.381835	+	1.42503i	−0.461261	+	0.887265i	$0.652603\pi$
$398$	15.5269	−	4.16043i	0.778294	−	0.208543i
$399$	7.85755	+	5.86618i	0.393370	+	0.293676i
$400$	−36.2532	−	20.9308i	−1.81266	−	1.04654i
$401$	−6.64370	+	1.78018i	−0.331771	+	0.0888977i	−0.420859	−	0.907126i	$-0.638271\pi$
$401$	−6.64370	+	1.78018i	−0.331771	+	0.0888977i	0.0890883	+	0.996024i	$0.471605\pi$
$402$	21.8567	−	9.39320i	1.09011	−	0.468490i
$403$	3.18660	−	11.1536i	0.158736	−	0.555602i
$404$			64.2580i			3.19696i
$405$	−31.1927	+	10.1502i	−1.54998	+	0.504368i
$406$	−4.86603	−	8.42821i	−0.241497	−	0.418285i
$407$	−3.34306	−	5.79036i	−0.165709	−	0.287017i
$408$	41.7790	+	16.6628i	2.06837	+	0.824933i
$409$	−8.74255	−	8.74255i	−0.432291	−	0.432291i	0.457116	−	0.889407i	$-0.348882\pi$
$409$	−8.74255	−	8.74255i	−0.432291	−	0.432291i	−0.889407	+	0.457116i	$0.848882\pi$
$410$	0.716038	+	0.716038i	0.0353626	+	0.0353626i
$411$	−10.1127	+	7.97403i	−0.498824	+	0.393330i
$412$	10.7157	+	18.5602i	0.527927	+	0.914396i
$413$	−0.307514	−	0.532630i	−0.0151318	−	0.0262090i
$414$	−6.31318	+	3.87062i	−0.310276	+	0.190231i
$415$			8.99634i			0.441613i
$416$	4.58216	−	4.43350i	0.224659	−	0.217370i
$417$	18.4715	+	13.7902i	0.904554	+	0.675309i
$418$	−25.8694	+	6.93167i	−1.26531	+	0.339039i
$419$	16.9909	+	9.80972i	0.830062	+	0.479236i	0.853874	−	0.520480i	$-0.174247\pi$
$419$	16.9909	+	9.80972i	0.830062	+	0.479236i	−0.0238122	+	0.999716i	$0.507580\pi$
$420$	26.3531	−	11.3256i	1.28590	−	0.552633i
$421$	−23.7926	+	6.37520i	−1.15958	+	0.310708i	−0.786798	−	0.617211i	$-0.788263\pi$
$421$	−23.7926	+	6.37520i	−1.15958	+	0.310708i	−0.372782	+	0.927919i	$0.621596\pi$
$422$	−4.97535	−	18.5683i	−0.242196	−	0.903888i
$423$	−12.2917	−	20.0484i	−0.597645	−	0.974788i
$424$	36.1507	−	36.1507i	1.75563	−	1.75563i
$425$	−34.5512	+	19.9482i	−1.67598	+	0.967628i
$426$	−5.08029	−	11.8211i	−0.246141	−	0.572736i
$427$	−2.29080	−	8.54938i	−0.110860	−	0.413734i
$428$	11.3296	+	19.6234i	0.547635	+	0.948531i
$429$	−1.64892	−	12.8511i	−0.0796105	−	0.620459i
$430$	41.7471	−	72.3081i	2.01322	−	3.48701i
$431$	29.0239	+	7.77693i	1.39803	+	0.374601i	0.877637	−	0.479325i	$-0.159119\pi$
$431$	29.0239	+	7.77693i	1.39803	+	0.374601i	0.520394	+	0.853926i	$0.325785\pi$
$432$	−9.08006	+	24.6375i	−0.436865	+	1.18537i
$433$	−9.14810	−	5.28166i	−0.439629	−	0.253820i	0.263811	−	0.964574i	$-0.415020\pi$
$433$	−9.14810	−	5.28166i	−0.439629	−	0.253820i	−0.703440	+	0.710754i	$0.748354\pi$
$434$	−2.25345	−	8.40998i	−0.108169	−	0.403692i
$435$	−17.8267	+	14.0566i	−0.854725	+	0.673963i
$436$	−6.11444	+	6.11444i	−0.292829	+	0.292829i
$437$	1.33650	−	4.98789i	0.0639335	−	0.238603i
$438$	17.8356	−	23.8902i	0.852218	−	1.14152i
$439$		−	17.3209i		−	0.826681i	−0.910577	−	0.413341i	$-0.864362\pi$
$439$		−	17.3209i		−	0.826681i	0.910577	−	0.413341i	$-0.135638\pi$
$440$	−10.5531	+	39.3848i	−0.503100	+	1.87760i
$441$	4.06744	−	16.9584i	0.193687	−	0.807545i
$442$	−10.4756	−	41.8433i	−0.498276	−	1.99028i
$443$	−12.5928	−	7.27044i	−0.598300	−	0.345429i	0.170072	−	0.985432i	$-0.445600\pi$
$443$	−12.5928	−	7.27044i	−0.598300	−	0.345429i	−0.768373	+	0.640003i	$0.778933\pi$
$444$	18.2808	−	14.4147i	0.867568	−	0.684089i
$445$	0.308145	−	0.533722i	0.0146075	−	0.0253009i
$446$	47.7890			2.26288
$447$	11.2628	−	1.63428i	0.532710	−	0.0772988i
$448$	−1.61108	+	6.01264i	−0.0761165	+	0.284071i
$449$	6.25020	−	1.67474i	0.294965	−	0.0790357i	−0.108302	−	0.994118i	$-0.534541\pi$
$449$	6.25020	−	1.67474i	0.294965	−	0.0790357i	0.403267	+	0.915082i	$0.367875\pi$
$450$	−32.2681	−	52.6309i	−1.52113	−	2.48104i
$451$	0.116023	−	0.200957i	0.00546330	−	0.00946271i
$452$	−20.9038			−0.983230
$453$	−1.92003	+	4.81413i	−0.0902110	+	0.226188i
$454$	−29.5464	+	17.0586i	−1.38668	+	0.800601i
$455$	−12.2788	−	7.36172i	−0.575639	−	0.345123i
$456$	−19.1633	−	44.5903i	−0.897403	−	2.08813i
$457$	−21.7644	−	21.7644i	−1.01810	−	1.01810i	−0.999833	−	0.0182637i	$-0.994186\pi$
$457$	−21.7644	−	21.7644i	−1.01810	−	1.01810i	−0.0182637	−	0.999833i	$-0.505814\pi$
$458$	7.48717	−	4.32272i	0.349853	−	0.201987i
$459$	16.0081	+	19.2348i	0.747195	+	0.897805i
$460$	−10.6810	−	10.6810i	−0.498003	−	0.498003i
$461$	21.9630	+	5.88496i	1.02292	+	0.274090i	0.731017	−	0.682359i	$-0.239046\pi$
$461$	21.9630	+	5.88496i	1.02292	+	0.274090i	0.291900	+	0.956449i	$0.405713\pi$
$462$	−6.02144	−	7.63644i	−0.280143	−	0.355279i
$463$	37.7738	+	10.1215i	1.75550	+	0.470384i	0.985786	−	0.168008i	$-0.0537334\pi$
$463$	37.7738	+	10.1215i	1.75550	+	0.470384i	0.769712	+	0.638392i	$0.220400\pi$
$464$			18.1722i			0.843623i
$465$	−18.6598	+	8.01929i	−0.865326	+	0.371886i
$466$	27.1564	−	27.1564i	1.25800	−	1.25800i
$467$	3.00565			0.139085			0.0695425	−	0.997579i	$-0.477846\pi$
$467$	3.00565			0.139085			0.0695425	+	0.997579i	$0.477846\pi$
$468$	43.4578	−	12.1074i	2.00884	−	0.559664i
$469$	−6.02368			−0.278148
$470$	50.1845	−	50.1845i	2.31484	−	2.31484i
$471$	2.68247	−	22.6854i	0.123602	−	1.04529i
$472$			3.04409i			0.140116i
$473$	−18.4809	−	4.95194i	−0.849752	−	0.227690i
$474$	−18.0480	+	45.2520i	−0.828972	+	2.07850i
$475$	41.5823	+	11.1419i	1.90793	+	0.511228i
$476$	−15.4732	−	15.4732i	−0.709215	−	0.709215i
$477$	27.2708	−	8.08448i	1.24865	−	0.370163i
$478$	−37.9251	+	21.8961i	−1.73466	+	1.00150i
$479$	11.8027	+	11.8027i	0.539277	+	0.539277i	0.923317	−	0.384039i	$-0.125467\pi$
$479$	11.8027	+	11.8027i	0.539277	+	0.539277i	−0.384039	+	0.923317i	$0.625467\pi$
$480$	−11.0862	−	1.31090i	−0.506012	−	0.0598343i
$481$	−11.1726	−	3.19200i	−0.509425	−	0.145543i
$482$	−5.24905	+	3.03054i	−0.239088	+	0.138037i
$483$	1.85562	−	0.269260i	0.0844338	−	0.0122518i
$484$	−27.9253			−1.26933
$485$	12.7438	−	22.0730i	0.578668	−	1.00228i
$486$	−29.0996	+	25.5478i	−1.31998	+	1.15887i
$487$	31.8259	−	8.52772i	1.44217	−	0.386428i	0.548876	−	0.835904i	$-0.315056\pi$
$487$	31.8259	−	8.52772i	1.44217	−	0.386428i	0.893292	+	0.449476i	$0.148389\pi$
$488$	−11.3383	+	42.3153i	−0.513263	+	1.91552i
$489$	−4.25493	+	10.6685i	−0.192415	+	0.482444i
$490$	52.6311			2.37763
$491$	−4.14967	+	7.18745i	−0.187272	+	0.324365i	−0.944340	−	0.328972i	$-0.893298\pi$
$491$	−4.14967	+	7.18745i	−0.187272	+	0.324365i	0.757068	+	0.653337i	$0.226631\pi$
$492$	0.750468	+	0.299311i	0.0338337	+	0.0134940i
$493$	14.9988	+	8.65954i	0.675510	+	0.390006i
$494$	−23.9331	+	39.9186i	−1.07680	+	1.79602i
$495$	−15.6118	+	16.4587i	−0.701700	+	0.739762i
$496$	−4.20775	+	15.7035i	−0.188934	+	0.705109i
$497$			3.25789i			0.146136i
$498$	4.19327	+	9.75717i	0.187905	+	0.437229i
$499$	−8.30646	+	31.0001i	−0.371848	+	1.38776i	0.486048	+	0.873932i	$0.338438\pi$
$499$	−8.30646	+	31.0001i	−0.371848	+	1.38776i	−0.857896	+	0.513823i	$0.828229\pi$
$500$	35.2999	−	35.2999i	1.57866	−	1.57866i
$501$	−31.6829	−	12.6362i	−1.41549	−	0.564544i
$502$	14.5230	+	54.2006i	0.648193	+	2.41909i
$503$	−4.86486	−	2.80873i	−0.216914	−	0.125235i	0.387607	−	0.921825i	$-0.373302\pi$
$503$	−4.86486	−	2.80873i	−0.216914	−	0.125235i	−0.604520	+	0.796590i	$0.706635\pi$
$504$	12.1282	−	12.7861i	0.540235	−	0.569538i
$505$	−54.2412	−	14.5339i	−2.41370	−	0.646750i
$506$	−2.56062	+	4.43512i	−0.113833	+	0.197165i
$507$	−17.5891	−	14.0578i	−0.781161	−	0.624330i
$508$	−26.8364	−	46.4820i	−1.19067	−	2.06231i
$509$	−2.43684	−	9.09443i	−0.108011	−	0.403103i	0.890658	−	0.454674i	$-0.150244\pi$
$509$	−2.43684	−	9.09443i	−0.108011	−	0.403103i	−0.998669	+	0.0515702i	$0.983577\pi$
$510$	−45.1809	+	60.5183i	−2.00064	+	2.67980i
$511$	−6.53761	+	3.77449i	−0.289207	+	0.166974i
$512$	32.2158	−	32.2158i	1.42375	−	1.42375i
$513$	2.46194	−	26.8899i	0.108697	−	1.18722i
$514$	−5.74071	−	21.4246i	−0.253212	−	0.945000i
$515$	−18.0907	+	4.84738i	−0.797170	+	0.213601i
$516$	7.82287	−	66.1571i	0.344383	−	2.91241i
$517$	−14.0844	−	8.13162i	−0.619430	−	0.357628i
$518$	−8.42425	+	2.25727i	−0.370140	+	0.0991788i
$519$	−4.88625	+	41.3225i	−0.214483	+	1.81386i
$520$	34.4135	+	61.9423i	1.50913	+	2.71635i
$521$			4.93419i			0.216171i	0.994142	+	0.108085i	$0.0344720\pi$
$521$			4.93419i			0.216171i	−0.994142	+	0.108085i	$0.965528\pi$
$522$	−12.7824	+	23.5546i	−0.559471	+	1.03096i
$523$	−22.2619	−	38.5588i	−0.973447	−	1.68606i	−0.684969	−	0.728572i	$-0.740184\pi$
$523$	−22.2619	−	38.5588i	−0.973447	−	1.68606i	−0.288478	−	0.957487i	$-0.593149\pi$
$524$	28.7795	+	49.8475i	1.25724	+	2.17760i
$525$	2.24473	+	15.4697i	0.0979680	+	0.675153i
$526$	−30.1038	−	30.1038i	−1.31259	−	1.31259i
$527$	10.9561	+	10.9561i	0.477255	+	0.477255i
$528$	2.60761	+	17.9706i	0.113482	+	0.782068i
$529$	11.0063	+	19.0634i	0.478534	+	0.828845i
$530$	42.9211	+	74.3415i	1.86437	+	3.22919i
$531$	−0.807799	+	1.48856i	−0.0350555	+	0.0645979i
$532$			23.6118i			1.02370i
$533$	−0.0979365	−	0.391191i	−0.00424210	−	0.0169444i
$534$	0.0854320	−	0.722488i	0.00369700	−	0.0312651i
$535$	−19.1269	+	5.12504i	−0.826929	+	0.221575i
$536$	25.8199	+	14.9071i	1.11525	+	0.643890i
$537$	−1.38514	+	11.7140i	−0.0597732	+	0.505495i
$538$	37.5642	−	10.0653i	1.61951	−	0.433945i
$539$	−3.12149	−	11.6495i	−0.134452	−	0.501782i
$540$	−64.5190	−	45.5658i	−2.77645	−	1.96084i
$541$	−6.30577	+	6.30577i	−0.271106	+	0.271106i	−0.829545	−	0.558439i	$-0.811400\pi$
$541$	−6.30577	+	6.30577i	−0.271106	+	0.271106i	0.558439	+	0.829545i	$0.311400\pi$
$542$	11.0653	−	6.38854i	0.475294	−	0.274411i
$543$	14.0653	−	18.8401i	0.603601	−	0.808504i
$544$	2.20422	+	8.22625i	0.0945050	+	0.352697i
$545$	−3.77833	−	6.54426i	−0.161846	−	0.280325i
$546$	−16.7486	−	2.26104i	−0.716774	−	0.0967636i
$547$	−19.7484	+	34.2052i	−0.844381	+	1.46251i	0.0417768	+	0.999127i	$0.486698\pi$
$547$	−19.7484	+	34.2052i	−0.844381	+	1.46251i	−0.886158	+	0.463384i	$0.846635\pi$
$548$	−29.9538	−	8.02609i	−1.27956	−	0.342858i
$549$	−16.7735	+	17.6833i	−0.715875	+	0.754705i
$550$	−36.9741	−	21.3470i	−1.57658	−	0.910239i
$551$	−4.83675	−	18.0510i	−0.206052	−	0.768998i
$552$	−8.62030	−	3.43806i	−0.366905	−	0.146334i
$553$	8.72271	−	8.72271i	0.370927	−	0.370927i
$554$	−17.2794	+	64.4876i	−0.734131	+	2.73982i
$555$	8.03289	+	18.6914i	0.340977	+	0.793407i
$556$			55.5065i			2.35400i
$557$	7.83663	−	29.2467i	0.332049	−	1.23922i	−0.574985	−	0.818164i	$-0.694992\pi$
$557$	7.83663	−	29.2467i	0.332049	−	1.23922i	0.907034	−	0.421058i	$-0.138341\pi$
$558$	−16.5000	+	17.3950i	−0.698500	+	0.736388i
$559$	−29.0658	+	16.1481i	−1.22935	+	0.682994i
$560$	17.3767	+	10.0325i	0.734301	+	0.423949i
$561$	16.0749	+	6.41121i	0.678684	+	0.270682i
$562$	10.7384	−	18.5994i	0.452971	−	0.784569i
$563$	−40.4140			−1.70325			−0.851623	−	0.524155i	$-0.824381\pi$
$563$	−40.4140			−1.70325			−0.851623	+	0.524155i	$0.824381\pi$
$564$	20.9776	−	52.5975i	0.883317	−	2.21476i
$565$	4.72802	−	17.6452i	0.198909	−	0.742339i
$566$	9.17073	−	2.45729i	0.385475	−	0.103288i
$567$	9.32370	−	3.03396i	0.391559	−	0.127415i
$568$	8.06248	−	13.9646i	0.338294	−	0.585943i
$569$	31.7435			1.33076			0.665378	−	0.746506i	$-0.268270\pi$
$569$	31.7435			1.33076			0.665378	+	0.746506i	$0.268270\pi$
$570$	80.6471	−	11.7023i	3.37793	−	0.490154i
$571$	0.748124	−	0.431930i	0.0313080	−	0.0180757i	−0.484264	−	0.874922i	$-0.660913\pi$
$571$	0.748124	−	0.431930i	0.0313080	−	0.0180757i	0.515572	+	0.856846i	$0.327579\pi$
$572$	22.4214	−	21.6940i	0.937486	−	0.907071i
$573$	−22.4809	−	2.65830i	−0.939153	−	0.111052i
$574$	−0.214028	−	0.214028i	−0.00893337	−	0.00893337i
$575$	7.12900	−	4.11593i	0.297300	−	0.171646i
$576$	16.4343	−	4.87196i	0.684761	−	0.202998i
$577$	31.3663	+	31.3663i	1.30579	+	1.30579i	0.924421	+	0.381374i	$0.124549\pi$
$577$	31.3663	+	31.3663i	1.30579	+	1.30579i	0.381374	+	0.924421i	$0.375451\pi$
$578$	14.8622	+	3.98231i	0.618185	+	0.165642i
$579$	10.2237	−	25.6342i	0.424884	−	1.06532i
$580$	−52.8025	−	14.1484i	−2.19250	−	0.587479i
$581$		−	2.68906i		−	0.111561i
$582$	3.53319	−	29.8797i	0.146455	−	1.23856i
$583$	13.9094	−	13.9094i	0.576068	−	0.576068i
$584$	37.3638			1.54612
$585$	0.390742	+	39.4219i	0.0161552	+	1.62989i
$586$	65.7145			2.71464
$587$	6.54632	−	6.54632i	0.270195	−	0.270195i	−0.558983	−	0.829179i	$-0.688808\pi$
$587$	6.54632	−	6.54632i	0.270195	−	0.270195i	0.829179	+	0.558983i	$0.188808\pi$
$588$	38.5811	−	16.5807i	1.59106	−	0.683779i
$589$		−	16.7187i		−	0.688883i
$590$	−4.93708	−	1.32289i	−0.203257	−	0.0544624i
$591$	−23.4947	−	29.7962i	−0.966443	−	1.22565i
$592$	15.7302	+	4.21489i	0.646506	+	0.173231i
$593$	−17.5563	−	17.5563i	−0.720952	−	0.720952i	0.247847	−	0.968799i	$-0.420277\pi$
$593$	−17.5563	−	17.5563i	−0.720952	−	0.720952i	−0.968799	+	0.247847i	$0.920277\pi$
$594$	−9.26062	+	25.1274i	−0.379968	+	1.03099i
$595$	16.5610	−	9.56148i	0.678933	−	0.391982i
$596$	19.3777	+	19.3777i	0.793740	+	0.793740i
$597$	4.42549	+	10.2975i	0.181123	+	0.421449i
$598$	2.16145	+	8.63357i	0.0883884	+	0.353053i
$599$	8.11974	−	4.68793i	0.331764	−	0.191544i	−0.324860	−	0.945762i	$-0.605317\pi$
$599$	8.11974	−	4.68793i	0.331764	−	0.191544i	0.656624	+	0.754218i	$0.271984\pi$
$600$	28.6619	−	71.8646i	1.17012	−	2.93386i
$601$	−19.1966			−0.783047			−0.391523	−	0.920168i	$-0.628052\pi$
$601$	−19.1966			−0.783047			−0.391523	+	0.920168i	$0.628052\pi$
$602$	−12.4785	+	21.6134i	−0.508585	+	0.880895i
$603$	8.67005	+	14.1413i	0.353072	+	0.575878i
$604$	−12.0549	+	3.23010i	−0.490506	+	0.131431i
$605$	6.31616	−	23.5722i	0.256789	−	0.958348i
$606$	−65.6028	+	9.51928i	−2.66493	+	0.386694i
$607$	−0.813780			−0.0330303			−0.0165152	−	0.999864i	$-0.505257\pi$
$607$	−0.813780			−0.0330303			−0.0165152	+	0.999864i	$0.505257\pi$
$608$	4.59473	−	7.95831i	0.186341	−	0.322752i
$609$	5.32852	−	4.20161i	0.215922	−	0.170258i
$610$	−63.7020	−	36.7784i	−2.57922	−	1.48911i
$611$	−27.4172	+	6.86401i	−1.10918	+	0.277688i
$612$	−14.0542	+	58.5964i	−0.568107	+	2.36862i
$613$	4.63944	−	17.3146i	0.187385	−	0.699331i	−0.806722	−	0.590931i	$-0.798761\pi$
$613$	4.63944	−	17.3146i	0.187385	−	0.699331i	0.994107	−	0.108400i	$-0.0345727\pi$
$614$		−	47.9422i		−	1.93479i
$615$	−0.422394	+	0.565784i	−0.0170326	+	0.0228146i
$616$	3.15439	−	11.7724i	0.127094	−	0.474322i
$617$	−6.22635	+	6.22635i	−0.250663	+	0.250663i	−0.821243	−	0.570579i	$-0.806719\pi$
$617$	−6.22635	+	6.22635i	−0.250663	+	0.250663i	0.570579	+	0.821243i	$0.306719\pi$
$618$	−17.3612	+	13.6895i	−0.698370	+	0.550674i
$619$	−10.8658	−	40.5517i	−0.436734	−	1.62991i	−0.736883	−	0.676020i	$-0.763703\pi$
$619$	−10.8658	−	40.5517i	−0.436734	−	1.62991i	0.300150	−	0.953892i	$-0.402963\pi$
$620$	−42.3533	−	24.4527i	−1.70095	−	0.982044i
$621$	−3.30297	−	3.96874i	−0.132544	−	0.159260i
$622$	45.6441	+	12.2303i	1.83016	+	0.490390i
$623$	−0.0921064	+	0.159533i	−0.00369017	+	0.00639155i
$624$	24.9730	+	19.2932i	0.999718	+	0.772346i
$625$	1.10286	+	1.91021i	0.0441144	+	0.0764084i
$626$	20.5845	+	76.8225i	0.822723	+	3.07044i
$627$	−7.37330	−	17.1566i	−0.294461	−	0.685170i
$628$	47.6363	−	27.5028i	1.90090	−	1.09748i
$629$	10.9747	−	10.9747i	0.437590	−	0.437590i
$630$	15.4666	+	25.2268i	0.616205	+	1.00506i
$631$	10.1974	+	38.0571i	0.405951	+	1.51503i	0.802295	+	0.596928i	$0.203612\pi$
$631$	10.1974	+	38.0571i	0.405951	+	1.51503i	−0.396344	+	0.918102i	$0.629721\pi$
$632$	−58.9756	+	15.8025i	−2.34592	+	0.628589i
$633$	12.3145	−	5.29233i	0.489458	−	0.210351i
$634$	14.1152	+	8.14939i	0.560585	+	0.323654i
$635$	45.3061	−	12.1397i	1.79792	−	0.481750i
$636$	54.8835	+	40.9741i	2.17627	+	1.62473i
$637$	−17.9763	−	10.7776i	−0.712245	−	0.427024i
$638$			18.5336i			0.733751i
$639$	7.64829	−	4.68918i	0.302562	−	0.185501i
$640$	32.3108	+	55.9640i	1.27720	+	2.21217i
$641$	2.03145	+	3.51858i	0.0802375	+	0.138976i	0.903352	−	0.428900i	$-0.141099\pi$
$641$	2.03145	+	3.51858i	0.0802375	+	0.138976i	−0.823114	+	0.567876i	$0.807765\pi$
$642$	−18.3557	+	14.4737i	−0.724441	+	0.571231i
$643$	32.8246	+	32.8246i	1.29447	+	1.29447i	0.931990	+	0.362484i	$0.118071\pi$
$643$	32.8246	+	32.8246i	1.29447	+	1.29447i	0.362484	+	0.931990i	$0.381929\pi$
$644$	3.19261	+	3.19261i	0.125807	+	0.125807i
$645$	54.0749	+	21.5669i	2.12920	+	0.849194i
$646$	−31.0846	−	53.8400i	−1.22301	−	2.11831i
$647$	10.2129	+	17.6893i	0.401511	+	0.695438i	0.993909	−	0.110208i	$-0.0351518\pi$
$647$	10.2129	+	17.6893i	0.401511	+	0.695438i	−0.592397	+	0.805646i	$0.701818\pi$
$648$	−47.4735	−	10.0691i	−1.86493	−	0.395551i
$649$			1.17125i			0.0459755i
$650$	−71.9752	+	18.0193i	−2.82310	+	0.706775i
$651$	5.57752	−	2.39702i	0.218600	−	0.0939465i
$652$	−26.7145	+	7.15812i	−1.04622	+	0.280334i
$653$	18.9516	+	10.9417i	0.741635	+	0.428183i	0.822663	−	0.568529i	$-0.192487\pi$
$653$	18.9516	+	10.9417i	0.741635	+	0.428183i	−0.0810287	+	0.996712i	$0.525821\pi$
$654$	−7.14821	−	5.33660i	−0.279517	−	0.208678i
$655$	−48.5865	+	13.0187i	−1.89843	+	0.508683i
$656$	0.146280	+	0.545924i	0.00571127	+	0.0213148i
$657$	18.2708	+	9.91509i	0.712814	+	0.386824i
$658$	−15.0005	+	15.0005i	−0.584779	+	0.584779i
$659$	37.6542	−	21.7397i	1.46680	−	0.846858i	0.467491	−	0.883998i	$-0.345158\pi$
$659$	37.6542	−	21.7397i	1.46680	−	0.846858i	0.999310	+	0.0371399i	$0.0118247\pi$
$660$	−54.2468	−	6.41451i	−2.11155	−	0.249685i
$661$	8.54938	+	31.9067i	0.332532	+	1.24103i	0.906520	+	0.422164i	$0.138729\pi$
$661$	8.54938	+	31.9067i	0.332532	+	1.24103i	−0.573987	+	0.818864i	$0.694604\pi$
$662$	−41.3465	−	71.6143i	−1.60698	−	2.78337i
$663$	27.8243	−	11.4182i	1.08061	−	0.443445i
$664$	−6.65478	+	11.5264i	−0.258255	+	0.447312i
$665$	−19.9311	−	5.34052i	−0.772894	−	0.207096i
$666$	17.4245	+	16.5280i	0.675185	+	0.640446i
$667$	−3.09471	−	1.78673i	−0.119828	−	0.0691826i
$668$	−21.2580	−	79.3360i	−0.822498	−	3.06960i
$669$	4.78497	+	32.9760i	0.184998	+	1.27492i
$670$	−35.3979	+	35.3979i	−1.36754	+	1.36754i
$671$	−4.36256	+	16.2813i	−0.168415	+	0.628532i
$672$	3.31373	+	0.391838i	0.127830	+	0.0151155i
$673$			18.8483i			0.726548i	0.931682	+	0.363274i	$0.118341\pi$
$673$			18.8483i			0.726548i	−0.931682	+	0.363274i	$0.881659\pi$
$674$	1.03864	−	3.87627i	0.0400070	−	0.149308i
$675$	33.0861	−	27.5358i	1.27348	−	1.05985i
$676$	1.78752	−	54.1894i	0.0687506	−	2.08421i
$677$	37.0180	+	21.3723i	1.42272	+	0.821406i	0.996530	−	0.0832299i	$-0.0265236\pi$
$677$	37.0180	+	21.3723i	1.42272	+	0.821406i	0.426186	+	0.904636i	$0.359857\pi$
$678$	−3.09672	−	21.3412i	−0.118929	−	0.819605i
$679$	−3.80922	+	6.59776i	−0.146184	+	0.253199i
$680$	−94.6493			−3.62963
$681$	−14.7294	−	18.6799i	−0.564431	−	0.715817i
$682$	−4.29142	+	16.0158i	−0.164327	+	0.613277i
$683$	22.6396	−	6.06625i	0.866279	−	0.232119i	0.201801	−	0.979427i	$-0.435321\pi$
$683$	22.6396	−	6.06625i	0.866279	−	0.232119i	0.664478	+	0.747308i	$0.268654\pi$
$684$	55.4314	−	33.9851i	2.11947	−	1.29945i
$685$	13.5499	−	23.4691i	0.517715	−	0.896709i
$686$	−34.6755			−1.32392
$687$	3.73248	+	4.73357i	0.142403	+	0.180597i
$688$	40.3575	−	23.3004i	1.53862	−	0.888321i
$689$	0.563596	−	34.1807i	0.0214713	−	1.30218i
$690$	9.32222	−	12.4868i	0.354891	−	0.475365i
$691$	−2.90103	−	2.90103i	−0.110360	−	0.110360i	0.649770	−	0.760131i	$-0.274865\pi$
$691$	−2.90103	−	2.90103i	−0.110360	−	0.110360i	−0.760131	+	0.649770i	$0.774865\pi$
$692$	−86.7719	+	50.0978i	−3.29857	+	1.90443i
$693$	4.66648	−	4.91960i	0.177265	−	0.186880i
$694$	−37.6591	−	37.6591i	−1.42952	−	1.42952i
$695$	−46.8540	−	12.5545i	−1.77727	−	0.476219i
$696$	−33.2381	+	4.82301i	−1.25989	+	0.182816i
$697$	0.520295	+	0.139413i	0.0197076	+	0.00528063i
$698$		−	1.27370i		−	0.0482104i
$699$	21.4579	+	16.0197i	0.811611	+	0.605921i
$700$	−26.6157	+	26.6157i	−1.00598	+	1.00598i
$701$	14.4149			0.544443			0.272221	−	0.962235i	$-0.412242\pi$
$701$	14.4149			0.544443			0.272221	+	0.962235i	$0.412242\pi$
$702$	18.7987	+	42.5737i	0.709510	+	1.60684i
$703$	−16.7471			−0.631629
$704$	8.38224	−	8.38224i	0.315918	−	0.315918i
$705$	39.6537	+	29.6041i	1.49345	+	1.11495i
$706$		−	85.7891i		−	3.22871i
$707$	16.2131	+	4.34427i	0.609755	+	0.163383i
$708$	−4.03587	+	0.585624i	−0.151677	+	0.0220091i
$709$	3.04405	+	0.815650i	0.114322	+	0.0306324i	0.315526	−	0.948917i	$-0.397819\pi$
$709$	3.04405	+	0.815650i	0.114322	+	0.0306324i	−0.201205	+	0.979549i	$0.564486\pi$
$710$	19.1449	+	19.1449i	0.718495	+	0.718495i
$711$	−33.0325	−	7.92275i	−1.23881	−	0.297126i
$712$	0.789610	−	0.455882i	0.0295919	−	0.0170849i
$713$	−2.26059	−	2.26059i	−0.0846596	−	0.0846596i
$714$	13.5048	−	18.0893i	0.505406	−	0.676975i
$715$	13.2410	+	23.8330i	0.495184	+	0.891304i
$716$	−24.5978	+	14.2015i	−0.919263	+	0.530737i
$717$	−18.9063	−	23.9772i	−0.706070	−	0.895444i
$718$	9.88493			0.368902
$719$	13.5806	−	23.5222i	0.506469	−	0.877230i	−0.493503	−	0.869744i	$-0.664284\pi$
$719$	13.5806	−	23.5222i	0.506469	−	0.877230i	0.999972	−	0.00748603i	$-0.00238290\pi$
$720$	−1.45844	−	55.2340i	−0.0543530	−	2.05845i
$721$	5.40742	−	1.44891i	0.201383	−	0.0539604i
$722$	−5.14648	+	19.2069i	−0.191532	+	0.714807i
$723$	−2.61674	−	3.31858i	−0.0973177	−	0.123419i
$724$	56.6139			2.10404
$725$	14.8954	−	25.7996i	0.553201	−	0.958172i
$726$	−4.13690	−	28.5098i	−0.153535	−	1.05810i
$727$	15.8046	+	9.12479i	0.586160	+	0.338420i	0.763578	−	0.645716i	$-0.223441\pi$
$727$	15.8046	+	9.12479i	0.586160	+	0.338420i	−0.177417	+	0.984136i	$0.556774\pi$
$728$	−10.2864	−	18.5150i	−0.381240	−	0.686210i
$729$	−20.5425	−	17.5216i	−0.760832	−	0.648949i
$730$	−16.2374	+	60.5988i	−0.600973	+	2.24286i
$731$		−	44.4132i		−	1.64268i
$732$	−58.2831	−	6.89180i	−2.15421	−	0.254728i
$733$	−5.19367	+	19.3830i	−0.191833	+	0.715929i	0.801231	+	0.598354i	$0.204179\pi$
$733$	−5.19367	+	19.3830i	−0.191833	+	0.715929i	−0.993064	+	0.117574i	$0.962488\pi$
$734$	6.00983	−	6.00983i	0.221827	−	0.221827i
$735$	5.26980	+	36.3172i	0.194379	+	1.33958i
$736$	−0.454799	−	1.69733i	−0.0167641	−	0.0625645i
$737$	9.93450	+	5.73569i	0.365942	+	0.211277i
$738$	−0.194400	+	0.810514i	−0.00715595	+	0.0298354i
$739$	15.0974	+	4.04534i	0.555368	+	0.148810i	0.525577	−	0.850746i	$-0.323849\pi$
$739$	15.0974	+	4.04534i	0.555368	+	0.148810i	0.0297903	+	0.999556i	$0.490516\pi$
$740$	−24.4942	+	42.4252i	−0.900424	+	1.55958i
$741$	−29.9415	−	12.5177i	−1.09993	−	0.459848i
$742$	−12.8294	−	22.2212i	−0.470982	−	0.815765i
$743$	4.96951	+	18.5465i	0.182314	+	0.680404i	0.995190	+	0.0979670i	$0.0312340\pi$
$743$	4.96951	+	18.5465i	0.182314	+	0.680404i	−0.812876	+	0.582437i	$0.802099\pi$
$744$	−29.8395	−	3.52843i	−1.09397	−	0.129359i
$745$	−20.7398	+	11.9742i	−0.759849	+	0.438699i
$746$	−5.58701	+	5.58701i	−0.204555	+	0.204555i
$747$	−6.31290	+	3.87045i	−0.230977	+	0.141612i
$748$	10.7857	+	40.2526i	0.394363	+	1.47178i
$749$	5.71716	−	1.53191i	0.208900	−	0.0559747i
$750$	41.2681	+	30.8093i	1.50690	+	1.12500i
$751$	8.86872	+	5.12036i	0.323624	+	0.186844i	0.653007	−	0.757352i	$-0.273507\pi$
$751$	8.86872	+	5.12036i	0.323624	+	0.186844i	−0.329383	+	0.944196i	$0.606841\pi$
$752$	38.2618	−	10.2522i	1.39527	−	0.373860i
$753$	−35.9460	+	15.4483i	−1.30994	+	0.562966i
$754$	22.3965	+	23.1475i	0.815633	+	0.842982i
$755$		−	10.9063i		−	0.396921i
$756$	19.2851	+	13.6199i	0.701394	+	0.495351i
$757$	7.56191	+	13.0976i	0.274842	+	0.476041i	0.970095	−	0.242724i	$-0.0780410\pi$
$757$	7.56191	+	13.0976i	0.274842	+	0.476041i	−0.695253	+	0.718765i	$0.744708\pi$
$758$	7.31920	+	12.6772i	0.265845	+	0.460457i
$759$	−3.31676	−	1.32283i	−0.120391	−	0.0480158i
$760$	72.2162	+	72.2162i	2.61956	+	2.61956i
$761$	−15.0366	−	15.0366i	−0.545077	−	0.545077i	0.379936	−	0.925013i	$-0.375946\pi$
$761$	−15.0366	−	15.0366i	−0.545077	−	0.545077i	−0.925013	+	0.379936i	$0.875946\pi$
$762$	43.4792	−	34.2840i	1.57509	−	1.24198i
$763$	1.12937	+	1.95612i	0.0408859	+	0.0708164i
$764$	−27.2550	−	47.2070i	−0.986050	−	1.70789i
$765$	−46.2834	−	25.1167i	−1.67338	−	0.908097i
$766$		−	19.0218i		−	0.687287i
$767$	1.41537	+	1.46283i	0.0511062	+	0.0528198i
$768$	45.2682	+	33.7956i	1.63347	+	1.21949i
$769$	10.8225	−	2.89988i	0.390269	−	0.104572i	−0.0583479	−	0.998296i	$-0.518583\pi$
$769$	10.8225	−	2.89988i	0.390269	−	0.104572i	0.448617	+	0.893724i	$0.351917\pi$
$770$	17.7223	+	10.2320i	0.638667	+	0.368734i
$771$	14.2089	−	6.10646i	0.511720	−	0.219919i
$772$	64.1895	−	17.1995i	2.31023	−	0.619025i
$773$	9.63935	+	35.9745i	0.346703	+	1.29391i	0.890610	+	0.454768i	$0.150278\pi$
$773$	9.63935	+	35.9745i	0.346703	+	1.29391i	−0.543907	+	0.839146i	$0.683055\pi$
$774$	68.7006	−	1.81403i	2.46939	−	0.0652039i
$775$	18.8457	−	18.8457i	0.676959	−	0.676959i
$776$	32.6557	−	18.8538i	1.17227	−	0.676811i
$777$	−2.40108	−	5.58699i	−0.0861384	−	0.200432i
$778$	3.58356	+	13.3740i	0.128477	+	0.479481i
$779$	−0.290608	−	0.503349i	−0.0104121	−	0.0180343i
$780$	−75.5030	+	57.5421i	−2.70344	+	2.06034i
$781$	3.10213	−	5.37305i	0.111003	−	0.192263i
$782$	−11.4829	−	3.07683i	−0.410627	−	0.110027i
$783$	−17.5333	−	6.46183i	−0.626588	−	0.230927i
$784$	25.4397	+	14.6876i	0.908559	+	0.524557i
$785$	12.4412	+	46.4312i	0.444045	+	1.65720i
$786$	−46.6273	+	36.7663i	−1.66314	+	1.31141i
$787$	−12.6075	+	12.6075i	−0.449410	+	0.449410i	−0.895158	−	0.445748i	$-0.852938\pi$
$787$	−12.6075	+	12.6075i	−0.449410	+	0.449410i	0.445748	+	0.895158i	$0.352938\pi$
$788$	23.6481	−	88.2559i	0.842428	−	3.14398i
$789$	17.7584	−	23.7868i	0.632215	−	0.846832i
$790$		−	102.517i		−	3.64741i
$791$	−1.41323	+	5.27426i	−0.0502488	+	0.187531i
$792$	−32.1772	+	9.53899i	−1.14337	+	0.338953i
$793$	14.2262	+	25.6064i	0.505187	+	0.909309i
$794$	−63.2371	−	36.5100i	−2.24420	−	1.29569i
$795$	−47.0005	+	37.0605i	−1.66694	+	1.31440i
$796$	−13.4944	+	23.3729i	−0.478295	+	0.828431i
$797$	−30.6646			−1.08619			−0.543097	−	0.839670i	$-0.682748\pi$
$797$	−30.6646			−1.08619			−0.543097	+	0.839670i	$0.682748\pi$
$798$	−24.1059	+	3.49789i	−0.853341	+	0.123824i
$799$	9.77093	−	36.4656i	0.345671	−	1.29006i
$800$	14.1501	−	3.79150i	0.500281	−	0.134050i
$801$	0.507094	−	0.0133897i	0.0179173	−	0.000473103i
$802$	8.54286	−	14.7967i	0.301659	−	0.522488i
$803$	14.3761			0.507323
$804$	−14.7967	+	37.1000i	−0.521839	+	1.30842i
$805$	−3.41704	+	1.97283i	−0.120435	+	0.0695332i
$806$	13.9942	+	25.1888i	0.492926	+	0.887239i
$807$	10.7066	+	24.9127i	0.376889	+	0.876968i
$808$	−58.7447	−	58.7447i	−2.06663	−	2.06663i
$809$	16.2110	−	9.35943i	0.569949	−	0.329060i	−0.187180	−	0.982326i	$-0.559935\pi$
$809$	16.2110	−	9.35943i	0.569949	−	0.329060i	0.757129	+	0.653266i	$0.226602\pi$
$810$	36.9614	−	72.6194i	1.29869	−	2.55159i
$811$	−19.1799	−	19.1799i	−0.673497	−	0.673497i	0.285024	−	0.958521i	$-0.407999\pi$
$811$	−19.1799	−	19.1799i	−0.673497	−	0.673497i	−0.958521	+	0.285024i	$0.907999\pi$
$812$	15.7830	+	4.22904i	0.553875	+	0.148410i
$813$	5.51623	+	6.99573i	0.193463	+	0.245351i
$814$	16.0430	+	4.29870i	0.562306	+	0.150669i
$815$		−	24.1691i		−	0.846608i
$816$	−38.7271	+	16.6435i	−1.35572	+	0.582639i
$817$	−33.8867	+	33.8867i	−1.18554	+	1.18554i
$818$	30.7128			1.07385
$819$	−0.116795	−	11.7835i	−0.00408115	−	0.411747i
$820$	−1.70017			−0.0593724
$821$	4.05037	−	4.05037i	0.141359	−	0.141359i	−0.632886	−	0.774245i	$-0.718130\pi$
$821$	4.05037	−	4.05037i	0.141359	−	0.141359i	0.774245	+	0.632886i	$0.218130\pi$
$822$	3.75666	−	31.7697i	0.131029	−	1.10809i
$823$			4.55481i			0.158771i	0.996844	+	0.0793853i	$0.0252958\pi$
$823$			4.55481i			0.158771i	−0.996844	+	0.0793853i	$0.974704\pi$
$824$	−26.7641	−	7.17141i	−0.932371	−	0.249828i
$825$	11.0280	−	27.6507i	0.383946	−	0.962674i
$826$	1.47573	+	0.395420i	0.0513471	+	0.0137584i
$827$	−30.1308	−	30.1308i	−1.04775	−	1.04775i	−0.998801	−	0.0489483i	$-0.984413\pi$
$827$	−30.1308	−	30.1308i	−1.04775	−	1.04775i	−0.0489483	−	0.998801i	$-0.515587\pi$
$828$	2.89982	−	12.0903i	0.100776	−	0.420166i
$829$	−41.6833	+	24.0659i	−1.44772	+	0.835843i	−0.998346	−	0.0575000i	$-0.981687\pi$
$829$	−41.6833	+	24.0659i	−1.44772	+	0.835843i	−0.449376	+	0.893343i	$0.648354\pi$
$830$	−15.8022	−	15.8022i	−0.548503	−	0.548503i
$831$	−46.2286	−	5.46639i	−1.60365	−	0.189627i
$832$	0.339641	−	20.5984i	0.0117749	−	0.714120i
$833$	24.2454	−	13.9981i	0.840052	−	0.485004i
$834$	−56.6682	+	8.22282i	−1.96226	+	0.284733i
$835$	71.7770			2.48394
$836$	22.4829	−	38.9415i	0.777588	−	1.34682i
$837$	−13.6552	−	9.64381i	−0.471992	−	0.333339i
$838$	−47.0757	+	12.6139i	−1.62620	+	0.435740i
$839$	−11.7866	+	43.9883i	−0.406920	+	1.51864i	0.393568	+	0.919295i	$0.371240\pi$
$839$	−11.7866	+	43.9883i	−0.406920	+	1.51864i	−0.800488	+	0.599349i	$0.795426\pi$
$840$	−13.7381	+	34.4459i	−0.474011	+	1.18849i
$841$	16.0678			0.554060
$842$	30.5939	−	52.9902i	1.05433	−	1.82616i
$843$	13.9094	+	5.54752i	0.479065	+	0.191067i
$844$	27.9511	+	16.1376i	0.962116	+	0.555478i
$845$	45.3379	+	13.7655i	1.55967	+	0.473546i
$846$	56.8060	+	13.6248i	1.95303	+	0.468429i
$847$	−1.88794	+	7.04589i	−0.0648704	+	0.242100i
$848$			47.9114i			1.64528i
$849$	2.61385	+	6.08206i	0.0897070	+	0.208736i
$850$	25.6505	−	95.7290i	0.879805	−	3.28348i
$851$	−2.26442	+	2.26442i	−0.0776234	+	0.0776234i
$852$	20.0655	+	8.00276i	0.687431	+	0.274170i
$853$	−1.38029	−	5.15130i	−0.0472602	−	0.176377i	0.938262	−	0.345927i	$-0.112435\pi$
$853$	−1.38029	−	5.15130i	−0.0472602	−	0.176377i	−0.985522	+	0.169549i	$0.945769\pi$
$854$	19.0409	+	10.9933i	0.651567	+	0.376183i
$855$	16.1499	+	54.4774i	0.552315	+	1.86309i
$856$	−28.2972	−	7.58220i	−0.967177	−	0.259154i
$857$	−13.2475	+	22.9453i	−0.452525	+	0.783797i	−0.998542	−	0.0539773i	$-0.982810\pi$
$857$	−13.2475	+	22.9453i	−0.452525	+	0.783797i	0.546017	+	0.837774i	$0.316143\pi$
$858$	25.4696	+	19.6769i	0.869516	+	0.671757i
$859$	−10.2070	−	17.6790i	−0.348257	−	0.603199i	0.637683	−	0.770299i	$-0.279893\pi$
$859$	−10.2070	−	17.6790i	−0.348257	−	0.603199i	−0.985940	+	0.167100i	$0.946560\pi$
$860$	36.2822	+	135.407i	1.23721	+	4.61734i
$861$	0.126256	−	0.169116i	0.00430281	−	0.00576347i
$862$	−64.6411	+	37.3206i	−2.20169	+	1.27114i
$863$	5.37905	−	5.37905i	0.183105	−	0.183105i	−0.609602	−	0.792707i	$-0.708671\pi$
$863$	5.37905	−	5.37905i	0.183105	−	0.183105i	0.792707	+	0.609602i	$0.208671\pi$
$864$	−3.84966	−	8.34335i	−0.130968	−	0.283847i
$865$	−22.6623	−	84.5767i	−0.770540	−	2.87569i
$866$	25.3461	−	6.79146i	0.861294	−	0.230783i
$867$	−1.25982	+	10.6541i	−0.0427856	+	0.361833i
$868$	12.6597	+	7.30907i	0.429697	+	0.248086i
$869$	−22.6915	+	6.08018i	−0.769758	+	0.206256i
$870$	6.62224	−	56.0035i	0.224515	−	1.89870i
$871$	19.3389	−	4.84157i	0.655273	−	0.164050i
$872$		−	11.1796i		−	0.378590i
$873$	20.9717	−	0.553755i	0.709786	−	0.0187418i
$874$	6.41371	+	11.1089i	0.216947	+	0.375763i
$875$	−6.52007	−	11.2931i	−0.220419	−	0.381776i
$876$	7.18807	+	49.5371i	0.242863	+	1.67370i
$877$	−26.5969	−	26.5969i	−0.898112	−	0.898112i	0.0971570	−	0.995269i	$-0.469025\pi$
$877$	−26.5969	−	26.5969i	−0.898112	−	0.898112i	−0.995269	+	0.0971570i	$0.969025\pi$
$878$	30.4244	+	30.4244i	1.02677	+	1.02677i
$879$	6.57979	+	45.3451i	0.221931	+	1.52945i
$880$	−19.1056	−	33.0919i	−0.644051	−	1.11553i
$881$	22.2493	+	38.5369i	0.749598	+	1.29834i	0.948016	+	0.318224i	$0.103086\pi$
$881$	22.2493	+	38.5369i	0.749598	+	1.29834i	−0.198418	+	0.980117i	$0.563580\pi$
$882$	22.6432	+	36.9322i	0.762437	+	1.24357i
$883$		−	37.8402i		−	1.27342i	−0.771102	−	0.636712i	$-0.780294\pi$
$883$		−	37.8402i		−	1.27342i	0.771102	−	0.636712i	$-0.219706\pi$
$884$	62.1133	+	37.2398i	2.08910	+	1.25251i
$885$	0.418500	−	3.53920i	0.0140677	−	0.118969i
$886$	34.8900	−	9.34875i	1.17215	−	0.314077i
$887$	−37.7583	−	21.7998i	−1.26780	−	0.731965i	−0.293229	−	0.956042i	$-0.594730\pi$
$887$	−37.7583	−	21.7998i	−1.26780	−	0.731965i	−0.974571	+	0.224078i	$0.928063\pi$
$888$	−3.53442	+	29.8902i	−0.118607	+	1.00305i
$889$	−13.5423	+	3.62864i	−0.454193	+	0.121701i
$890$	0.396230	+	1.47875i	0.0132817	+	0.0495678i
$891$	−18.2660	−	3.87420i	−0.611932	−	0.129790i
$892$	−56.7354	+	56.7354i	−1.89964	+	1.89964i
$893$	−35.2779	+	20.3677i	−1.18053	+	0.681579i
$894$	−16.9126	+	22.6538i	−0.565641	+	0.757658i
$895$	−6.42422	−	23.9755i	−0.214738	−	0.801413i
$896$	−9.65791	−	16.7280i	−0.322648	−	0.558843i
$897$	−5.74102	+	2.35592i	−0.191687	+	0.0786620i
$898$	−8.03687	+	13.9203i	−0.268194	+	0.464525i
$899$	−11.1754	−	2.99445i	−0.372721	−	0.0998704i
$900$	100.792	+	24.1748i	3.35975	+	0.805827i
$901$	39.5446	+	22.8311i	1.31742	+	0.760613i
$902$	0.149189	+	0.556780i	0.00496744	+	0.0185388i
$903$	−16.1633	−	6.44647i	−0.537882	−	0.214525i
$904$	19.1102	−	19.1102i	0.635596	−	0.635596i
$905$	−12.8050	+	47.7887i	−0.425651	+	1.58855i
$906$	−5.08352	−	11.8287i	−0.168889	−	0.392981i
$907$		−	9.10149i		−	0.302210i	−0.988518	−	0.151105i	$-0.951717\pi$
$907$		−	9.10149i		−	0.302210i	0.988518	−	0.151105i	$-0.0482832\pi$
$908$	14.8256	−	55.3297i	0.492003	−	1.83618i
$909$	−13.1372	−	44.3149i	−0.435734	−	1.46983i
$910$	34.4989	−	8.63694i	1.14363	−	0.286312i
$911$	−11.3340	−	6.54367i	−0.375511	−	0.216802i	0.300352	−	0.953828i	$-0.402896\pi$
$911$	−11.3340	−	6.54367i	−0.375511	−	0.216802i	−0.675863	+	0.737027i	$0.736229\pi$
$912$	42.2471	+	16.8495i	1.39894	+	0.557943i
$913$	−2.56050	+	4.43492i	−0.0847402	+	0.146774i
$914$	76.4591			2.52904
$915$	19.0000	−	47.6389i	0.628120	−	1.57489i
$916$	−3.75685	+	14.0208i	−0.124130	+	0.463259i
$917$	14.5228	−	3.89138i	0.479585	−	0.128505i
$918$	−61.9047	−	5.66776i	−2.04316	−	0.187064i
$919$	−17.1982	+	29.7882i	−0.567317	+	0.982622i	0.429513	+	0.903061i	$0.358685\pi$
$919$	−17.1982	+	29.7882i	−0.567317	+	0.982622i	−0.996830	+	0.0795615i	$0.974648\pi$
$920$	19.5291			0.643855
$921$	33.0817	−	4.80031i	1.09008	−	0.158176i
$922$	−48.9152	+	28.2412i	−1.61094	+	0.930075i
$923$	−2.61855	−	10.4594i	−0.0861907	−	0.344275i
$924$	16.2147	+	1.91734i	0.533425	+	0.0630758i
$925$	−18.8777	−	18.8777i	−0.620696	−	0.620696i
$926$	−84.1287	+	48.5717i	−2.76464	+	1.59617i
$927$	−11.1846	−	10.6091i	−0.367349	−	0.348448i
$928$	−4.49668	−	4.49668i	−0.147611	−	0.147611i
$929$	−36.1275	−	9.68033i	−1.18530	−	0.317601i	−0.388276	−	0.921543i	$-0.626929\pi$
$929$	−36.1275	−	9.68033i	−1.18530	−	0.317601i	−0.797028	+	0.603942i	$0.793596\pi$
$930$	18.6902	−	46.8621i	0.612874	−	1.53667i
$931$	−29.1792	−	7.81855i	−0.956311	−	0.256243i
$932$			64.4804i			2.11213i
$933$	−3.86910	+	32.7205i	−0.126668	+	1.07122i
$934$	−5.27947	+	5.27947i	−0.172750	+	0.172750i
$935$	−36.4174			−1.19098
$936$	−28.6606	+	50.7977i	−0.936799	+	1.66037i
$937$	−24.1148			−0.787796			−0.393898	−	0.919154i	$-0.628874\pi$
$937$	−24.1148			−0.787796			−0.393898	+	0.919154i	$0.628874\pi$
$938$	10.5807	−	10.5807i	0.345471	−	0.345471i
$939$	−50.9489	+	21.8960i	−1.66265	+	0.714548i
$940$			119.159i			3.88652i
$941$	25.0567	+	6.71393i	0.816826	+	0.218868i	0.642958	−	0.765901i	$-0.277707\pi$
$941$	25.0567	+	6.71393i	0.816826	+	0.218868i	0.173868	+	0.984769i	$0.444373\pi$
$942$	35.1353	+	44.5589i	1.14477	+	1.45181i
$943$	−0.107353	−	0.0287652i	−0.00349590	−	0.000936724i
$944$	−2.01720	−	2.01720i	−0.0656543	−	0.0656543i
$945$	−15.8587	+	13.1983i	−0.515883	+	0.429342i
$946$	41.1601	−	23.7638i	1.33823	−	0.772627i
$947$	−5.62821	−	5.62821i	−0.182892	−	0.182892i	0.609723	−	0.792615i	$-0.291281\pi$
$947$	−5.62821	−	5.62821i	−0.182892	−	0.182892i	−0.792615	+	0.609723i	$0.791281\pi$
$948$	−32.2968	−	75.1501i	−1.04895	−	2.44076i
$949$	17.9551	−	17.3726i	0.582847	−	0.563938i
$950$	−92.6109	+	53.4689i	−3.00470	+	1.73476i
$951$	−4.21003	+	10.5559i	−0.136520	+	0.342298i
$952$	28.2913			0.916926
$953$	8.56006	−	14.8265i	0.277288	−	0.480276i	−0.693422	−	0.720532i	$-0.743898\pi$
$953$	8.56006	−	14.8265i	0.277288	−	0.480276i	0.970710	+	0.240255i	$0.0772312\pi$
$954$	−33.7011	+	62.1021i	−1.09111	+	2.01063i
$955$	46.0127	−	12.3291i	1.48894	−	0.398959i
$956$	19.0298	−	71.0201i	0.615467	−	2.29695i
$957$	−12.7887	+	1.85571i	−0.413402	+	0.0599865i
$958$	−41.4631			−1.33961
$959$	−4.05015	+	7.01507i	−0.130786	+	0.226528i
$960$	−28.3240	+	22.3339i	−0.914153	+	0.720822i
$961$	17.8829	+	10.3247i	0.576867	+	0.333054i
$962$	25.2316	−	14.0180i	0.813499	−	0.451958i
$963$	−11.8252	−	11.2168i	−0.381062	−	0.361456i
$964$	2.63383	−	9.82958i	0.0848299	−	0.316589i
$965$			58.0736i			1.86946i
$966$	−2.78647	+	3.73239i	−0.0896532	+	0.120088i
$967$	15.7940	−	58.9441i	0.507902	−	1.89552i	0.0674879	−	0.997720i	$-0.478502\pi$
$967$	15.7940	−	58.9441i	0.507902	−	1.89552i	0.440414	−	0.897795i	$-0.354832\pi$
$968$	25.5293	−	25.5293i	0.820544	−	0.820544i
$969$	34.0389	−	26.8402i	1.09349	−	0.862231i
$970$	16.3868	+	61.1563i	0.526148	+	1.96361i
$971$	11.7550	+	6.78673i	0.377235	+	0.217797i	0.676614	−	0.736338i	$-0.263446\pi$
$971$	11.7550	+	6.78673i	0.377235	+	0.217797i	−0.299380	+	0.954134i	$0.596780\pi$
$972$	4.21667	−	64.8777i	0.135250	−	2.08095i
$973$	14.0049	+	3.75261i	0.448978	+	0.120303i
$974$	−40.9236	+	70.8817i	−1.31128	+	2.27120i
$975$	−19.6405	−	47.8609i	−0.629001	−	1.53278i
$976$	−20.5272	−	35.5542i	−0.657060	−	1.13806i
$977$	−6.09948	−	22.7636i	−0.195140	−	0.728271i	−0.992231	−	0.124412i	$-0.960296\pi$
$977$	−6.09948	−	22.7636i	−0.195140	−	0.728271i	0.797091	−	0.603859i	$-0.206371\pi$
$978$	−11.2655	−	26.2131i	−0.360229	−	0.838204i
$979$	0.303812	−	0.175406i	0.00970986	−	0.00560599i
$980$	−62.4840	+	62.4840i	−1.99598	+	1.99598i
$981$	2.96670	−	5.46683i	0.0947194	−	0.174542i
$982$	−5.33589	−	19.9138i	−0.170275	−	0.635475i
$983$	44.5280	−	11.9312i	1.42022	−	0.380547i	0.534659	−	0.845068i	$-0.320440\pi$
$983$	44.5280	−	11.9312i	1.42022	−	0.380547i	0.885562	+	0.464521i	$0.153773\pi$
$984$	−0.959707	+	0.412447i	−0.0305944	+	0.0131483i
$985$	69.1495	+	39.9235i	2.20329	+	1.27207i
$986$	−41.5562	+	11.1349i	−1.32342	+	0.354609i
$987$	−11.8528	−	8.84885i	−0.377277	−	0.281662i
$988$	−18.9781	−	75.8051i	−0.603775	−	2.41168i
$989$			9.16382i			0.291393i
$990$	−1.48745	−	56.3323i	−0.0472741	−	1.79036i
$991$	−14.6503	−	25.3750i	−0.465381	−	0.806064i	0.533838	−	0.845587i	$-0.320749\pi$
$991$	−14.6503	−	25.3750i	−0.465381	−	0.806064i	−0.999219	+	0.0395234i	$0.987416\pi$
$992$	−2.84461	−	4.92702i	−0.0903166	−	0.156433i
$993$	45.2762	−	35.7009i	1.43680	−	1.13294i
$994$	−5.72253	−	5.72253i	−0.181508	−	0.181508i
$995$	−16.6773	−	16.6773i	−0.528706	−	0.528706i
$996$	−16.5620	−	6.60548i	−0.524788	−	0.209303i
$997$	26.0669	+	45.1492i	0.825548	+	1.42989i	0.901500	+	0.432780i	$0.142467\pi$
$997$	26.0669	+	45.1492i	0.825548	+	1.42989i	−0.0759518	+	0.997111i	$0.524200\pi$
$998$	−39.8617	−	69.0426i	−1.26180	−	2.18550i
$999$	−9.66017	+	13.6783i	−0.305634	+	0.432764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.11.2	✓	48
3.2	odd	2		351.2.ba.a.89.11		48
9.4	even	3		351.2.bf.a.206.2		48
9.5	odd	6		117.2.bc.a.50.11	yes	48
13.6	odd	12		117.2.bc.a.110.11	yes	48
39.32	even	12		351.2.bf.a.305.2		48
117.32	even	12	inner	117.2.x.a.32.2	yes	48
117.58	odd	12		351.2.ba.a.71.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.2	✓	48	1.1	even	1	trivial
117.2.x.a.32.2	yes	48	117.32	even	12	inner
117.2.bc.a.50.11	yes	48	9.5	odd	6
117.2.bc.a.110.11	yes	48	13.6	odd	12
351.2.ba.a.71.11		48	117.58	odd	12
351.2.ba.a.89.11		48	3.2	odd	2
351.2.bf.a.206.2		48	9.4	even	3
351.2.bf.a.305.2		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)

\(f(q)\)	\(=\)	\(q+(-1.75651 + 1.75651i) q^{2} +(-1.38793 - 1.03618i) q^{3} -4.17069i q^{4} +(3.52054 + 0.943327i) q^{5} +(4.25797 - 0.617852i) q^{6} +(-1.05231 - 0.281966i) q^{7} +(3.81284 + 3.81284i) q^{8} +(0.852675 + 2.87627i) q^{9} +O(q^{10})\)	\(q+(-1.75651 + 1.75651i) q^{2} +(-1.38793 - 1.03618i) q^{3} -4.17069i q^{4} +(3.52054 + 0.943327i) q^{5} +(4.25797 - 0.617852i) q^{6} +(-1.05231 - 0.281966i) q^{7} +(3.81284 + 3.81284i) q^{8} +(0.852675 + 2.87627i) q^{9} +(-7.84085 + 4.52692i) q^{10} +(1.46703 + 1.46703i) q^{11} +(-4.32157 + 5.78860i) q^{12} +(3.60506 + 0.0594429i) q^{13} +(2.34368 - 1.35312i) q^{14} +(-3.90880 - 4.95717i) q^{15} -5.05324 q^{16} +(-2.40801 + 4.17079i) q^{17} +(-6.54995 - 3.55448i) q^{18} +(5.01954 - 1.34498i) q^{19} +(3.93432 - 14.6831i) q^{20} +(1.16837 + 1.48173i) q^{21} -5.15373 q^{22} +(0.496847 - 0.860565i) q^{23} +(-1.34116 - 9.24271i) q^{24} +(7.17423 + 4.14205i) q^{25} +(-6.43675 + 6.22793i) q^{26} +(1.79688 - 4.87558i) q^{27} +(-1.17599 + 4.38887i) q^{28} -3.59614i q^{29} +(15.5732 + 1.84148i) q^{30} +(0.832683 - 3.10761i) q^{31} +(1.25042 - 1.25042i) q^{32} +(-0.516027 - 3.55624i) q^{33} +(-3.09636 - 11.5558i) q^{34} +(-3.43873 - 1.98535i) q^{35} +(11.9960 - 3.55624i) q^{36} +(-3.11289 - 0.834095i) q^{37} +(-6.45441 + 11.1794i) q^{38} +(-4.94196 - 3.81798i) q^{39} +(9.82651 + 17.0200i) q^{40} +(-0.0289477 - 0.108034i) q^{41} +(-4.65493 - 0.550431i) q^{42} +(-7.98646 + 4.61099i) q^{43} +(6.11854 - 6.11854i) q^{44} +(0.288615 + 10.9304i) q^{45} +(0.638875 + 2.38431i) q^{46} +(-7.57174 + 2.02884i) q^{47} +(7.01353 + 5.23606i) q^{48} +(-5.03432 - 2.90657i) q^{49} +(-19.8772 + 5.32608i) q^{50} +(7.66381 - 3.29363i) q^{51} +(0.247918 - 15.0356i) q^{52} -9.48131i q^{53} +(5.40778 + 11.7203i) q^{54} +(3.78086 + 6.54865i) q^{55} +(-2.93721 - 5.08739i) q^{56} +(-8.36038 - 3.33440i) q^{57} +(6.31668 + 6.31668i) q^{58} +(0.399189 + 0.399189i) q^{59} +(-20.6748 + 16.3024i) q^{60} +(4.06219 + 7.03591i) q^{61} +(3.99595 + 6.92119i) q^{62} +(-0.0862689 - 3.26717i) q^{63} -5.71374i q^{64} +(12.6357 + 3.61002i) q^{65} +(7.15300 + 5.34018i) q^{66} +(5.34077 - 1.43106i) q^{67} +(17.3951 + 10.0430i) q^{68} +(-1.58128 + 0.679578i) q^{69} +(9.52747 - 2.55288i) q^{70} +(-0.773983 - 2.88854i) q^{71} +(-7.71565 + 14.2179i) q^{72} +(4.89973 - 4.89973i) q^{73} +(6.93293 - 4.00273i) q^{74} +(-5.66541 - 13.1826i) q^{75} +(-5.60949 - 20.9349i) q^{76} +(-1.13012 - 1.95743i) q^{77} +(15.3870 - 1.97429i) q^{78} +(-5.66155 + 9.80609i) q^{79} +(-17.7902 - 4.76686i) q^{80} +(-7.54589 + 4.90505i) q^{81} +(0.240611 + 0.138917i) q^{82} +(0.638846 + 2.38421i) q^{83} +(6.17983 - 4.87288i) q^{84} +(-12.4119 + 12.4119i) q^{85} +(5.92907 - 22.1276i) q^{86} +(-3.72624 + 4.99118i) q^{87} +11.1871i q^{88} +(0.0437638 - 0.163329i) q^{89} +(-19.7064 - 18.6924i) q^{90} +(-3.77689 - 1.07906i) q^{91} +(-3.58914 - 2.07219i) q^{92} +(-4.37574 + 3.45033i) q^{93} +(9.73618 - 16.8636i) q^{94} +18.9403 q^{95} +(-3.03114 + 0.439833i) q^{96} +(1.80993 - 6.75474i) q^{97} +(13.9483 - 3.73743i) q^{98} +(-2.96869 + 5.47049i) 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

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