LMFDB - Embedded newform 1110.2.e.d.739.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(739,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1110.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.e (of order $2$, degree $1$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} + \cdots + 64 $ x^16 - 2x^15 + 2x^14 + 8x^13 + 138x^12 - 220x^11 + 196x^10 + 744x^9 + 4241x^8 - 3018x^7 + 658x^6 - 1584x^5 + 16372x^4 - 18840x^3 + 10952x^2 - 1184*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.8
Root			$2.23405 - 2.23405i$ of defining polynomial
Character	$\chi$	$=$	1110.739
Dual form			1110.2.e.d.739.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(2.23405 + 0.0950871i) q^{5} -1.00000i q^{6} -3.20752i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(2.23405 + 0.0950871i) q^{5} -1.00000i q^{6} -3.20752i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(2.23405 + 0.0950871i) q^{10} -3.73314 q^{11} -1.00000i q^{12} -0.424858 q^{13} -3.20752i q^{14} +(0.0950871 - 2.23405i) q^{15} +1.00000 q^{16} +6.90738 q^{17} -1.00000 q^{18} -8.02549i q^{19} +(2.23405 + 0.0950871i) q^{20} -3.20752 q^{21} -3.73314 q^{22} -6.34959 q^{23} -1.00000i q^{24} +(4.98192 + 0.424858i) q^{25} -0.424858 q^{26} +1.00000i q^{27} -3.20752i q^{28} +3.39355i q^{29} +(0.0950871 - 2.23405i) q^{30} +1.20338i q^{31} +1.00000 q^{32} +3.73314i q^{33} +6.90738 q^{34} +(0.304994 - 7.16575i) q^{35} -1.00000 q^{36} +(-5.90637 + 1.45421i) q^{37} -8.02549i q^{38} +0.424858i q^{39} +(2.23405 + 0.0950871i) q^{40} +5.74899 q^{41} -3.20752 q^{42} +9.31001 q^{43} -3.73314 q^{44} +(-2.23405 - 0.0950871i) q^{45} -6.34959 q^{46} -2.04357i q^{47} -1.00000i q^{48} -3.28821 q^{49} +(4.98192 + 0.424858i) q^{50} -6.90738i q^{51} -0.424858 q^{52} +11.8045i q^{53} +1.00000i q^{54} +(-8.34000 - 0.354973i) q^{55} -3.20752i q^{56} -8.02549 q^{57} +3.39355i q^{58} -2.16131i q^{59} +(0.0950871 - 2.23405i) q^{60} -1.45108i q^{61} +1.20338i q^{62} +3.20752i q^{63} +1.00000 q^{64} +(-0.949152 - 0.0403985i) q^{65} +3.73314i q^{66} +11.4940i q^{67} +6.90738 q^{68} +6.34959i q^{69} +(0.304994 - 7.16575i) q^{70} -5.59683 q^{71} -1.00000 q^{72} -12.5062i q^{73} +(-5.90637 + 1.45421i) q^{74} +(0.424858 - 4.98192i) q^{75} -8.02549i q^{76} +11.9741i q^{77} +0.424858i q^{78} +4.50480i q^{79} +(2.23405 + 0.0950871i) q^{80} +1.00000 q^{81} +5.74899 q^{82} +7.00128i q^{83} -3.20752 q^{84} +(15.4314 + 0.656803i) q^{85} +9.31001 q^{86} +3.39355 q^{87} -3.73314 q^{88} -15.9242i q^{89} +(-2.23405 - 0.0950871i) q^{90} +1.36274i q^{91} -6.34959 q^{92} +1.20338 q^{93} -2.04357i q^{94} +(0.763120 - 17.9293i) q^{95} -1.00000i q^{96} -4.43763 q^{97} -3.28821 q^{98} +3.73314 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9	$ 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} - 6 q^{15} + 16 q^{16} + 38 q^{17} - 16 q^{18} + 2 q^{20} + 6 q^{21} + 2 q^{22} + 20 q^{23} - 4 q^{25} - 6 q^{30} + 16 q^{32} + 38 q^{34} + 10 q^{35} - 16 q^{36} + 4 q^{37} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 2 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 18 q^{49} - 4 q^{50} - 20 q^{55} - 16 q^{57} - 6 q^{60} + 16 q^{64} + 12 q^{65} + 38 q^{68} + 10 q^{70} - 24 q^{71} - 16 q^{72} + 4 q^{74} + 2 q^{80} + 16 q^{81} - 6 q^{82} + 6 q^{84} + 2 q^{86} - 2 q^{87} + 2 q^{88} - 2 q^{90} + 20 q^{92} - 22 q^{93} - 16 q^{95} - 38 q^{97} - 18 q^{98} - 2 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 - 6 * q^15 + 16 * q^16 + 38 * q^17 - 16 * q^18 + 2 * q^20 + 6 * q^21 + 2 * q^22 + 20 * q^23 - 4 * q^25 - 6 * q^30 + 16 * q^32 + 38 * q^34 + 10 * q^35 - 16 * q^36 + 4 * q^37 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 2 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 18 * q^49 - 4 * q^50 - 20 * q^55 - 16 * q^57 - 6 * q^60 + 16 * q^64 + 12 * q^65 + 38 * q^68 + 10 * q^70 - 24 * q^71 - 16 * q^72 + 4 * q^74 + 2 * q^80 + 16 * q^81 - 6 * q^82 + 6 * q^84 + 2 * q^86 - 2 * q^87 + 2 * q^88 - 2 * q^90 + 20 * q^92 - 22 * q^93 - 16 * q^95 - 38 * q^97 - 18 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$	2.23405	+	0.0950871i	0.999095	+	0.0425243i
$5$	2.23405	+	0.0950871i	0.999095	+	0.0425243i
$6$		−	1.00000i		−	0.408248i
$7$		−	3.20752i		−	1.21233i	−0.795339	−	0.606165i	$-0.792707\pi$
$7$		−	3.20752i		−	1.21233i	0.795339	−	0.606165i	$-0.207293\pi$
$8$	1.00000			0.353553
$9$	−1.00000			−0.333333
$10$	2.23405	+	0.0950871i	0.706467	+	0.0300692i
$11$	−3.73314			−1.12558			−0.562792	−	0.826599i	$-0.690273\pi$
$11$	−3.73314			−1.12558			−0.562792	+	0.826599i	$0.690273\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−0.424858			−0.117834			−0.0589172	−	0.998263i	$-0.518765\pi$
$13$	−0.424858			−0.117834			−0.0589172	+	0.998263i	$0.518765\pi$
$14$		−	3.20752i		−	0.857247i
$15$	0.0950871	−	2.23405i	0.0245514	−	0.576828i
$16$	1.00000			0.250000
$17$	6.90738			1.67529			0.837643	−	0.546218i	$-0.183933\pi$
$17$	6.90738			1.67529			0.837643	+	0.546218i	$0.183933\pi$
$18$	−1.00000			−0.235702
$19$		−	8.02549i		−	1.84117i	−0.390539	−	0.920586i	$-0.627711\pi$
$19$		−	8.02549i		−	1.84117i	0.390539	−	0.920586i	$-0.372289\pi$
$20$	2.23405	+	0.0950871i	0.499548	+	0.0212621i
$21$	−3.20752			−0.699939
$22$	−3.73314			−0.795907
$23$	−6.34959			−1.32398			−0.661990	−	0.749512i	$-0.730288\pi$
$23$	−6.34959			−1.32398			−0.661990	+	0.749512i	$0.730288\pi$
$24$		−	1.00000i		−	0.204124i
$25$	4.98192	+	0.424858i	0.996383	+	0.0849716i
$26$	−0.424858			−0.0833215
$27$			1.00000i			0.192450i
$28$		−	3.20752i		−	0.606165i
$29$			3.39355i			0.630167i	0.949064	+	0.315084i	$0.102033\pi$
$29$			3.39355i			0.630167i	−0.949064	+	0.315084i	$0.897967\pi$
$30$	0.0950871	−	2.23405i	0.0173605	−	0.407879i
$31$			1.20338i			0.216134i	0.994144	+	0.108067i	$0.0344660\pi$
$31$			1.20338i			0.216134i	−0.994144	+	0.108067i	$0.965534\pi$
$32$	1.00000			0.176777
$33$			3.73314i			0.649856i
$34$	6.90738			1.18461
$35$	0.304994	−	7.16575i	0.0515534	−	1.21123i
$36$	−1.00000			−0.166667
$37$	−5.90637	+	1.45421i	−0.971002	+	0.239071i
$37$	−5.90637	+	1.45421i	−0.971002	+	0.239071i
$38$		−	8.02549i		−	1.30191i
$39$			0.424858i			0.0680317i
$40$	2.23405	+	0.0950871i	0.353234	+	0.0150346i
$41$	5.74899			0.897841			0.448921	−	0.893572i	$-0.351809\pi$
$41$	5.74899			0.897841			0.448921	+	0.893572i	$0.351809\pi$
$42$	−3.20752			−0.494932
$43$	9.31001			1.41976			0.709882	−	0.704321i	$-0.248748\pi$
$43$	9.31001			1.41976			0.709882	+	0.704321i	$0.248748\pi$
$44$	−3.73314			−0.562792
$45$	−2.23405	−	0.0950871i	−0.333032	−	0.0141748i
$46$	−6.34959			−0.936196
$47$		−	2.04357i		−	0.298085i	−0.988831	−	0.149043i	$-0.952381\pi$
$47$		−	2.04357i		−	0.298085i	0.988831	−	0.149043i	$-0.0476191\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.28821			−0.469744
$50$	4.98192	+	0.424858i	0.704549	+	0.0600840i
$51$		−	6.90738i		−	0.967227i
$52$	−0.424858			−0.0589172
$53$			11.8045i			1.62147i	0.585414	+	0.810734i	$0.300932\pi$
$53$			11.8045i			1.62147i	−0.585414	+	0.810734i	$0.699068\pi$
$54$			1.00000i			0.136083i
$55$	−8.34000	−	0.354973i	−1.12456	−	0.0478646i
$56$		−	3.20752i		−	0.428623i
$57$	−8.02549			−1.06300
$58$			3.39355i			0.445596i
$59$		−	2.16131i		−	0.281379i	−0.990054	−	0.140689i	$-0.955068\pi$
$59$		−	2.16131i		−	0.281379i	0.990054	−	0.140689i	$-0.0449318\pi$
$60$	0.0950871	−	2.23405i	0.0122757	−	0.288414i
$61$		−	1.45108i		−	0.185791i	−0.995676	−	0.0928957i	$-0.970388\pi$
$61$		−	1.45108i		−	0.185791i	0.995676	−	0.0928957i	$-0.0296123\pi$
$62$			1.20338i			0.152829i
$63$			3.20752i			0.404110i
$64$	1.00000			0.125000
$65$	−0.949152	−	0.0403985i	−0.117728	−	0.00501082i
$66$			3.73314i			0.459517i
$67$			11.4940i			1.40422i	0.712069	+	0.702109i	$0.247758\pi$
$67$			11.4940i			1.40422i	−0.712069	+	0.702109i	$0.752242\pi$
$68$	6.90738			0.837643
$69$			6.34959i			0.764401i
$70$	0.304994	−	7.16575i	0.0364538	−	0.856471i
$71$	−5.59683			−0.664222			−0.332111	−	0.943240i	$-0.607761\pi$
$71$	−5.59683			−0.664222			−0.332111	+	0.943240i	$0.607761\pi$
$72$	−1.00000			−0.117851
$73$		−	12.5062i		−	1.46374i	−0.681444	−	0.731870i	$-0.738648\pi$
$73$		−	12.5062i		−	1.46374i	0.681444	−	0.731870i	$-0.261352\pi$
$74$	−5.90637	+	1.45421i	−0.686602	+	0.169049i
$75$	0.424858	−	4.98192i	0.0490584	−	0.575262i
$76$		−	8.02549i		−	0.920586i
$77$			11.9741i			1.36458i
$78$			0.424858i			0.0481057i
$79$			4.50480i			0.506830i	0.967358	+	0.253415i	$0.0815538\pi$
$79$			4.50480i			0.506830i	−0.967358	+	0.253415i	$0.918446\pi$
$80$	2.23405	+	0.0950871i	0.249774	+	0.0106311i
$81$	1.00000			0.111111
$82$	5.74899			0.634870
$83$			7.00128i			0.768491i	0.923231	+	0.384245i	$0.125538\pi$
$83$			7.00128i			0.768491i	−0.923231	+	0.384245i	$0.874462\pi$
$84$	−3.20752			−0.349969
$85$	15.4314	+	0.656803i	1.67377	+	0.0712403i
$86$	9.31001			1.00392
$87$	3.39355			0.363827
$88$	−3.73314			−0.397954
$89$		−	15.9242i		−	1.68796i	−0.536373	−	0.843981i	$-0.680206\pi$
$89$		−	15.9242i		−	1.68796i	0.536373	−	0.843981i	$-0.319794\pi$
$90$	−2.23405	−	0.0950871i	−0.235489	−	0.0100231i
$91$			1.36274i			0.142854i
$92$	−6.34959			−0.661990
$93$	1.20338			0.124785
$94$		−	2.04357i		−	0.210778i
$95$	0.763120	−	17.9293i	0.0782945	−	1.83951i
$96$		−	1.00000i		−	0.102062i
$97$	−4.43763			−0.450573			−0.225286	−	0.974293i	$-0.572332\pi$
$97$	−4.43763			−0.450573			−0.225286	+	0.974293i	$0.572332\pi$
$98$	−3.28821			−0.332159
$99$	3.73314			0.375194
$100$	4.98192	+	0.424858i	0.498192	+	0.0424858i
$101$	13.0171			1.29525			0.647623	−	0.761961i	$-0.275763\pi$
$101$	13.0171			1.29525			0.647623	+	0.761961i	$0.275763\pi$
$102$		−	6.90738i		−	0.683933i
$103$	7.17254			0.706732			0.353366	−	0.935485i	$-0.385037\pi$
$103$	7.17254			0.706732			0.353366	+	0.935485i	$0.385037\pi$
$104$	−0.424858			−0.0416608
$105$	−7.16575	−	0.304994i	−0.699306	−	0.0297644i
$106$			11.8045i			1.14655i
$107$			3.80308i			0.367658i	0.982958	+	0.183829i	$0.0588492\pi$
$107$			3.80308i			0.367658i	−0.982958	+	0.183829i	$0.941151\pi$
$108$			1.00000i			0.0962250i
$109$		−	4.93476i		−	0.472664i	−0.971672	−	0.236332i	$-0.924055\pi$
$109$		−	4.93476i		−	0.472664i	0.971672	−	0.236332i	$-0.0759454\pi$
$110$	−8.34000	−	0.354973i	−0.795187	−	0.0338454i
$111$	1.45421	+	5.90637i	0.138028	+	0.560608i
$112$		−	3.20752i		−	0.303082i
$113$	9.29880			0.874758			0.437379	−	0.899277i	$-0.355907\pi$
$113$	9.29880			0.874758			0.437379	+	0.899277i	$0.355907\pi$
$114$	−8.02549			−0.751656
$115$	−14.1853	−	0.603764i	−1.32278	−	0.0563013i
$116$			3.39355i			0.315084i
$117$	0.424858			0.0392781
$118$		−	2.16131i		−	0.198965i
$119$		−	22.1556i		−	2.03100i
$120$	0.0950871	−	2.23405i	0.00868023	−	0.203940i
$121$	2.93631			0.266937
$122$		−	1.45108i		−	0.131374i
$123$		−	5.74899i		−	0.518369i
$124$			1.20338i			0.108067i
$125$	11.0894	+	1.42287i	0.991869	+	0.127265i
$126$			3.20752i			0.285749i
$127$			14.3747i			1.27555i	0.770222	+	0.637776i	$0.220145\pi$
$127$			14.3747i			1.27555i	−0.770222	+	0.637776i	$0.779855\pi$
$128$	1.00000			0.0883883
$129$		−	9.31001i		−	0.819701i
$130$	−0.949152	−	0.0403985i	−0.0832461	−	0.00354319i
$131$			12.3237i			1.07672i	0.842714	+	0.538362i	$0.180957\pi$
$131$			12.3237i			1.07672i	−0.842714	+	0.538362i	$0.819043\pi$
$132$			3.73314i			0.324928i
$133$	−25.7419			−2.23211
$134$			11.4940i			0.992933i
$135$	−0.0950871	+	2.23405i	−0.00818380	+	0.192276i
$136$	6.90738			0.592303
$137$			17.4773i			1.49319i	0.665280	+	0.746594i	$0.268312\pi$
$137$			17.4773i			1.49319i	−0.665280	+	0.746594i	$0.731688\pi$
$138$			6.34959i			0.540513i
$139$	−0.125741			−0.0106652			−0.00533261	−	0.999986i	$-0.501697\pi$
$139$	−0.125741			−0.0106652			−0.00533261	+	0.999986i	$0.501697\pi$
$140$	0.304994	−	7.16575i	0.0257767	−	0.605617i
$141$	−2.04357			−0.172100
$142$	−5.59683			−0.469676
$143$	1.58605			0.132632
$144$	−1.00000			−0.0833333
$145$	−0.322683	+	7.58136i	−0.0267974	+	0.629597i
$146$		−	12.5062i		−	1.03502i
$147$			3.28821i			0.271207i
$148$	−5.90637	+	1.45421i	−0.485501	+	0.119536i
$149$	2.43147			0.199194			0.0995968	−	0.995028i	$-0.468245\pi$
$149$	2.43147			0.199194			0.0995968	+	0.995028i	$0.468245\pi$
$150$	0.424858	−	4.98192i	0.0346895	−	0.406772i
$151$	−15.1683			−1.23438			−0.617188	−	0.786816i	$-0.711728\pi$
$151$	−15.1683			−1.23438			−0.617188	+	0.786816i	$0.711728\pi$
$152$		−	8.02549i		−	0.650953i
$153$	−6.90738			−0.558429
$154$			11.9741i			0.964902i
$155$	−0.114426	+	2.68841i	−0.00919092	+	0.215938i
$156$			0.424858i			0.0340159i
$157$			19.1941i			1.53185i	0.642928	+	0.765927i	$0.277719\pi$
$157$			19.1941i			1.53185i	−0.642928	+	0.765927i	$0.722281\pi$
$158$			4.50480i			0.358383i
$159$	11.8045			0.936156
$160$	2.23405	+	0.0950871i	0.176617	+	0.00751730i
$161$			20.3665i			1.60510i
$162$	1.00000			0.0785674
$163$	−7.14619			−0.559733			−0.279867	−	0.960039i	$-0.590290\pi$
$163$	−7.14619			−0.559733			−0.279867	+	0.960039i	$0.590290\pi$
$164$	5.74899			0.448921
$165$	−0.354973	+	8.34000i	−0.0276346	+	0.649268i
$166$			7.00128i			0.543405i
$167$	12.6692			0.980373			0.490187	−	0.871618i	$-0.336929\pi$
$167$	12.6692			0.980373			0.490187	+	0.871618i	$0.336929\pi$
$168$	−3.20752			−0.247466
$169$	−12.8195			−0.986115
$170$	15.4314	+	0.656803i	1.18353	+	0.0503745i
$171$			8.02549i			0.613724i
$172$	9.31001			0.709882
$173$		−	19.7245i		−	1.49963i	−0.661649	−	0.749814i	$-0.730143\pi$
$173$		−	19.7245i		−	1.49963i	0.661649	−	0.749814i	$-0.269857\pi$
$174$	3.39355			0.257265
$175$	1.36274	−	15.9796i	0.103014	−	1.20795i
$176$	−3.73314			−0.281396
$177$	−2.16131			−0.162454
$178$		−	15.9242i		−	1.19357i
$179$		−	3.19619i		−	0.238895i	−0.992841	−	0.119447i	$-0.961888\pi$
$179$		−	3.19619i		−	0.238895i	0.992841	−	0.119447i	$-0.0381123\pi$
$180$	−2.23405	−	0.0950871i	−0.166516	−	0.00708738i
$181$	−11.3735			−0.845387			−0.422694	−	0.906273i	$-0.638915\pi$
$181$	−11.3735			−0.845387			−0.422694	+	0.906273i	$0.638915\pi$
$182$			1.36274i			0.101013i
$183$	−1.45108			−0.107267
$184$	−6.34959			−0.468098
$185$	−13.3334	+	2.68716i	−0.980290	+	0.197564i
$186$	1.20338			0.0882361
$187$	−25.7862			−1.88567
$188$		−	2.04357i		−	0.149043i
$189$	3.20752			0.233313
$190$	0.763120	−	17.9293i	0.0553626	−	1.30073i
$191$			12.4830i			0.903235i	0.892212	+	0.451617i	$0.149153\pi$
$191$			12.4830i			0.903235i	−0.892212	+	0.451617i	$0.850847\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	12.1559			0.874999			0.437499	−	0.899219i	$-0.355864\pi$
$193$	12.1559			0.874999			0.437499	+	0.899219i	$0.355864\pi$
$194$	−4.43763			−0.318603
$195$	−0.0403985	+	0.949152i	−0.00289300	+	0.0679702i
$196$	−3.28821			−0.234872
$197$			8.89921i			0.634042i	0.948418	+	0.317021i	$0.102683\pi$
$197$			8.89921i			0.634042i	−0.948418	+	0.317021i	$0.897317\pi$
$198$	3.73314			0.265302
$199$		−	10.3470i		−	0.733481i	−0.930323	−	0.366740i	$-0.880474\pi$
$199$		−	10.3470i		−	0.733481i	0.930323	−	0.366740i	$-0.119526\pi$
$200$	4.98192	+	0.424858i	0.352275	+	0.0300420i
$201$	11.4940			0.810726
$202$	13.0171			0.915878
$203$	10.8849			0.763971
$204$		−	6.90738i		−	0.483613i
$205$	12.8435	+	0.546655i	0.897029	+	0.0381800i
$206$	7.17254			0.499735
$207$	6.34959			0.441327
$208$	−0.424858			−0.0294586
$209$			29.9602i			2.07239i
$210$	−7.16575	−	0.304994i	−0.494484	−	0.0210466i
$211$	5.52374			0.380270			0.190135	−	0.981758i	$-0.439107\pi$
$211$	5.52374			0.380270			0.190135	+	0.981758i	$0.439107\pi$
$212$			11.8045i			0.810734i
$213$			5.59683i			0.383489i
$214$			3.80308i			0.259973i
$215$	20.7990	+	0.885263i	1.41848	+	0.0603744i
$216$			1.00000i			0.0680414i
$217$	3.85987			0.262025
$218$		−	4.93476i		−	0.334224i
$219$	−12.5062			−0.845091
$220$	−8.34000	−	0.354973i	−0.562282	−	0.0239323i
$221$	−2.93466			−0.197406
$222$	1.45421	+	5.90637i	0.0976005	+	0.396410i
$223$			3.24704i			0.217438i	0.994073	+	0.108719i	$0.0346748\pi$
$223$			3.24704i			0.217438i	−0.994073	+	0.108719i	$0.965325\pi$
$224$		−	3.20752i		−	0.214312i
$225$	−4.98192	−	0.424858i	−0.332128	−	0.0283239i
$226$	9.29880			0.618547
$227$	3.24282			0.215234			0.107617	−	0.994192i	$-0.465678\pi$
$227$	3.24282			0.215234			0.107617	+	0.994192i	$0.465678\pi$
$228$	−8.02549			−0.531501
$229$	−23.2392			−1.53569			−0.767845	−	0.640636i	$-0.778671\pi$
$229$	−23.2392			−1.53569			−0.767845	+	0.640636i	$0.778671\pi$
$230$	−14.1853	−	0.603764i	−0.935349	−	0.0398110i
$231$	11.9741			0.787839
$232$			3.39355i			0.222798i
$233$			23.5036i			1.53977i	0.638181	+	0.769886i	$0.279687\pi$
$233$			23.5036i			1.53977i	−0.638181	+	0.769886i	$0.720313\pi$
$234$	0.424858			0.0277738
$235$	0.194317	−	4.56543i	0.0126759	−	0.297815i
$236$		−	2.16131i		−	0.140689i
$237$	4.50480			0.292618
$238$		−	22.1556i		−	1.43613i
$239$			6.75627i			0.437027i	0.975834	+	0.218514i	$0.0701208\pi$
$239$			6.75627i			0.437027i	−0.975834	+	0.218514i	$0.929879\pi$
$240$	0.0950871	−	2.23405i	0.00613785	−	0.144207i
$241$			27.0533i			1.74266i	0.490699	+	0.871329i	$0.336741\pi$
$241$			27.0533i			1.74266i	−0.490699	+	0.871329i	$0.663259\pi$
$242$	2.93631			0.188753
$243$		−	1.00000i		−	0.0641500i
$244$		−	1.45108i		−	0.0928957i
$245$	−7.34600	−	0.312666i	−0.469319	−	0.0199755i
$246$		−	5.74899i		−	0.366542i
$247$			3.40969i			0.216953i
$248$			1.20338i			0.0764147i
$249$	7.00128			0.443688
$250$	11.0894	+	1.42287i	0.701357	+	0.0899901i
$251$			12.9375i			0.816609i	0.912846	+	0.408305i	$0.133880\pi$
$251$			12.9375i			0.816609i	−0.912846	+	0.408305i	$0.866120\pi$
$252$			3.20752i			0.202055i
$253$	23.7039			1.49025
$254$			14.3747i			0.901951i
$255$	0.656803	−	15.4314i	0.0411306	−	0.966352i
$256$	1.00000			0.0625000
$257$	14.5960			0.910473			0.455237	−	0.890370i	$-0.349555\pi$
$257$	14.5960			0.910473			0.455237	+	0.890370i	$0.349555\pi$
$258$		−	9.31001i		−	0.579616i
$259$	4.66443	+	18.9448i	0.289833	+	1.17717i
$260$	−0.949152	−	0.0403985i	−0.0588639	−	0.00250541i
$261$		−	3.39355i		−	0.210056i
$262$			12.3237i			0.761358i
$263$			12.2500i			0.755370i	0.925934	+	0.377685i	$0.123280\pi$
$263$			12.2500i			0.755370i	−0.925934	+	0.377685i	$0.876720\pi$
$264$			3.73314i			0.229759i
$265$	−1.12245	+	26.3717i	−0.0689518	+	1.62000i
$266$	−25.7419			−1.57834
$267$	−15.9242			−0.974545
$268$			11.4940i			0.702109i
$269$	14.1886			0.865094			0.432547	−	0.901611i	$-0.357615\pi$
$269$	14.1886			0.865094			0.432547	+	0.901611i	$0.357615\pi$
$270$	−0.0950871	+	2.23405i	−0.00578682	+	0.135960i
$271$	−8.82413			−0.536028			−0.268014	−	0.963415i	$-0.586367\pi$
$271$	−8.82413			−0.536028			−0.268014	+	0.963415i	$0.586367\pi$
$272$	6.90738			0.418821
$273$	1.36274			0.0824769
$274$			17.4773i			1.05584i
$275$	−18.5982	−	1.58605i	−1.12151	−	0.0956426i
$276$			6.34959i			0.382200i
$277$	−12.6061			−0.757426			−0.378713	−	0.925514i	$-0.623633\pi$
$277$	−12.6061			−0.757426			−0.378713	+	0.925514i	$0.623633\pi$
$278$	−0.125741			−0.00754145
$279$		−	1.20338i		−	0.0720445i
$280$	0.304994	−	7.16575i	0.0182269	−	0.428236i
$281$		−	15.8731i		−	0.946908i	−0.880819	−	0.473454i	$-0.843007\pi$
$281$		−	15.8731i		−	0.946908i	0.880819	−	0.473454i	$-0.156993\pi$
$282$	−2.04357			−0.121693
$283$	29.1588			1.73331			0.866656	−	0.498906i	$-0.166265\pi$
$283$	29.1588			1.73331			0.866656	+	0.498906i	$0.166265\pi$
$284$	−5.59683			−0.332111
$285$	−17.9293	−	0.763120i	−1.06204	−	0.0452034i
$286$	1.58605			0.0937853
$287$		−	18.4400i		−	1.08848i
$288$	−1.00000			−0.0589256
$289$	30.7119			1.80658
$290$	−0.322683	+	7.58136i	−0.0189486	+	0.445193i
$291$			4.43763i			0.260138i
$292$		−	12.5062i		−	0.731870i
$293$		−	28.4275i		−	1.66075i	−0.557204	−	0.830376i	$-0.688126\pi$
$293$		−	28.4275i		−	1.66075i	0.557204	−	0.830376i	$-0.311874\pi$
$294$			3.28821i			0.191772i
$295$	0.205513	−	4.82846i	0.0119654	−	0.281124i
$296$	−5.90637	+	1.45421i	−0.343301	+	0.0845245i
$297$		−	3.73314i		−	0.216619i
$298$	2.43147			0.140851
$299$	2.69767			0.156010
$300$	0.424858	−	4.98192i	0.0245292	−	0.287631i
$301$		−	29.8621i		−	1.72122i
$302$	−15.1683			−0.872835
$303$		−	13.0171i		−	0.747811i
$304$		−	8.02549i		−	0.460293i
$305$	0.137979	−	3.24177i	0.00790064	−	0.185623i
$306$	−6.90738			−0.394869
$307$		−	20.6139i		−	1.17650i	−0.808680	−	0.588249i	$-0.799818\pi$
$307$		−	20.6139i		−	1.17650i	0.808680	−	0.588249i	$-0.200182\pi$
$308$			11.9741i			0.682289i
$309$		−	7.17254i		−	0.408032i
$310$	−0.114426	+	2.68841i	−0.00649896	+	0.152691i
$311$			15.0056i			0.850887i	0.904985	+	0.425443i	$0.139882\pi$
$311$			15.0056i			0.850887i	−0.904985	+	0.425443i	$0.860118\pi$
$312$			0.424858i			0.0240528i
$313$	−28.8720			−1.63194			−0.815972	−	0.578092i	$-0.803798\pi$
$313$	−28.8720			−1.63194			−0.815972	+	0.578092i	$0.803798\pi$
$314$			19.1941i			1.08318i
$315$	−0.304994	+	7.16575i	−0.0171845	+	0.403744i
$316$			4.50480i			0.253415i
$317$			14.7214i			0.826837i	0.910541	+	0.413419i	$0.135665\pi$
$317$			14.7214i			0.826837i	−0.910541	+	0.413419i	$0.864335\pi$
$318$	11.8045			0.661962
$319$		−	12.6686i		−	0.709306i
$320$	2.23405	+	0.0950871i	0.124887	+	0.00531553i
$321$	3.80308			0.212267
$322$			20.3665i			1.13498i
$323$		−	55.4351i		−	3.08449i
$324$	1.00000			0.0555556
$325$	−2.11661	−	0.180504i	−0.117408	−	0.0100126i
$326$	−7.14619			−0.395791
$327$	−4.93476			−0.272893
$328$	5.74899			0.317435
$329$	−6.55479			−0.361378
$330$	−0.354973	+	8.34000i	−0.0195406	+	0.459102i
$331$			8.15238i			0.448095i	0.974578	+	0.224048i	$0.0719271\pi$
$331$			8.15238i			0.448095i	−0.974578	+	0.224048i	$0.928073\pi$
$332$			7.00128i			0.384245i
$333$	5.90637	−	1.45421i	0.323667	−	0.0796904i
$334$	12.6692			0.693228
$335$	−1.09293	+	25.6782i	−0.0597134	+	1.40295i
$336$	−3.20752			−0.174985
$337$		−	28.0034i		−	1.52544i	−0.646726	−	0.762722i	$-0.723862\pi$
$337$		−	28.0034i		−	1.52544i	0.646726	−	0.762722i	$-0.276138\pi$
$338$	−12.8195			−0.697289
$339$		−	9.29880i		−	0.505042i
$340$	15.4314	+	0.656803i	0.836885	+	0.0356201i
$341$		−	4.49238i		−	0.243276i
$342$			8.02549i			0.433969i
$343$		−	11.9057i		−	0.642846i
$344$	9.31001			0.501962
$345$	−0.603764	+	14.1853i	−0.0325056	+	0.763709i
$346$		−	19.7245i		−	1.06040i
$347$	−6.82853			−0.366575			−0.183287	−	0.983059i	$-0.558674\pi$
$347$	−6.82853			−0.366575			−0.183287	+	0.983059i	$0.558674\pi$
$348$	3.39355			0.181914
$349$	−5.65418			−0.302662			−0.151331	−	0.988483i	$-0.548356\pi$
$349$	−5.65418			−0.302662			−0.151331	+	0.988483i	$0.548356\pi$
$350$	1.36274	−	15.9796i	0.0728416	−	0.854146i
$351$		−	0.424858i		−	0.0226772i
$352$	−3.73314			−0.198977
$353$	−12.7850			−0.680476			−0.340238	−	0.940339i	$-0.610508\pi$
$353$	−12.7850			−0.680476			−0.340238	+	0.940339i	$0.610508\pi$
$354$	−2.16131			−0.114872
$355$	−12.5036	−	0.532187i	−0.663621	−	0.0282456i
$356$		−	15.9242i		−	0.843981i
$357$	−22.1556			−1.17260
$358$		−	3.19619i		−	0.168924i
$359$	11.3292			0.597933			0.298966	−	0.954264i	$-0.403358\pi$
$359$	11.3292			0.597933			0.298966	+	0.954264i	$0.403358\pi$
$360$	−2.23405	−	0.0950871i	−0.117745	−	0.00501153i
$361$	−45.4084			−2.38992
$362$	−11.3735			−0.597779
$363$		−	2.93631i		−	0.154116i
$364$			1.36274i			0.0714271i
$365$	1.18918	−	27.9394i	0.0622445	−	1.46242i
$366$	−1.45108			−0.0758490
$367$		−	10.0590i		−	0.525075i	−0.964922	−	0.262538i	$-0.915441\pi$
$367$		−	10.0590i		−	0.525075i	0.964922	−	0.262538i	$-0.0845594\pi$
$368$	−6.34959			−0.330995
$369$	−5.74899			−0.299280
$370$	−13.3334	+	2.68716i	−0.693170	+	0.139699i
$371$	37.8631			1.96576
$372$	1.20338			0.0623924
$373$			9.39169i			0.486283i	0.969991	+	0.243142i	$0.0781780\pi$
$373$			9.39169i			0.486283i	−0.969991	+	0.243142i	$0.921822\pi$
$374$	−25.7862			−1.33337
$375$	1.42287	−	11.0894i	0.0734766	−	0.572656i
$376$		−	2.04357i		−	0.105389i
$377$		−	1.44178i		−	0.0742554i
$378$	3.20752			0.164977
$379$	−10.7371			−0.551526			−0.275763	−	0.961226i	$-0.588930\pi$
$379$	−10.7371			−0.551526			−0.275763	+	0.961226i	$0.588930\pi$
$380$	0.763120	−	17.9293i	0.0391473	−	0.919754i
$381$	14.3747			0.736440
$382$			12.4830i			0.638683i
$383$	11.2412			0.574399			0.287199	−	0.957871i	$-0.407276\pi$
$383$	11.2412			0.574399			0.287199	+	0.957871i	$0.407276\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−1.13859	+	26.7507i	−0.0580277	+	1.36334i
$386$	12.1559			0.618717
$387$	−9.31001			−0.473255
$388$	−4.43763			−0.225286
$389$			7.80757i			0.395860i	0.980216	+	0.197930i	$0.0634218\pi$
$389$			7.80757i			0.395860i	−0.980216	+	0.197930i	$0.936578\pi$
$390$	−0.0403985	+	0.949152i	−0.00204566	+	0.0480622i
$391$	−43.8590			−2.21805
$392$	−3.28821			−0.166079
$393$	12.3237			0.621646
$394$			8.89921i			0.448336i
$395$	−0.428349	+	10.0639i	−0.0215526	+	0.506371i
$396$	3.73314			0.187597
$397$			33.1348i			1.66299i	0.555534	+	0.831494i	$0.312514\pi$
$397$			33.1348i			1.66299i	−0.555534	+	0.831494i	$0.687486\pi$
$398$		−	10.3470i		−	0.518649i
$399$			25.7419i			1.28871i
$400$	4.98192	+	0.424858i	0.249096	+	0.0212429i
$401$		−	33.2206i		−	1.65896i	−0.558540	−	0.829478i	$-0.688638\pi$
$401$		−	33.2206i		−	1.65896i	0.558540	−	0.829478i	$-0.311362\pi$
$402$	11.4940			0.573270
$403$		−	0.511266i		−	0.0254680i
$404$	13.0171			0.647623
$405$	2.23405	+	0.0950871i	0.111011	+	0.00472492i
$406$	10.8849			0.540209
$407$	22.0493	−	5.42878i	1.09294	−	0.269095i
$408$		−	6.90738i		−	0.341966i
$409$		−	18.4622i		−	0.912899i	−0.889749	−	0.456449i	$-0.849121\pi$
$409$		−	18.4622i		−	0.912899i	0.889749	−	0.456449i	$-0.150879\pi$
$410$	12.8435	+	0.546655i	0.634295	+	0.0269974i
$411$	17.4773			0.862092
$412$	7.17254			0.353366
$413$	−6.93245			−0.341124
$414$	6.34959			0.312065
$415$	−0.665732	+	15.6412i	−0.0326795	+	0.767796i
$416$	−0.424858			−0.0208304
$417$			0.125741i			0.00615757i
$418$			29.9602i			1.46540i
$419$	0.759460			0.0371021			0.0185510	−	0.999828i	$-0.494095\pi$
$419$	0.759460			0.0371021			0.0185510	+	0.999828i	$0.494095\pi$
$420$	−7.16575	−	0.304994i	−0.349653	−	0.0148822i
$421$		−	27.6679i		−	1.34845i	−0.738525	−	0.674227i	$-0.764477\pi$
$421$		−	27.6679i		−	1.34845i	0.738525	−	0.674227i	$-0.235523\pi$
$422$	5.52374			0.268891
$423$			2.04357i			0.0993617i
$424$			11.8045i			0.573276i
$425$	34.4120	+	2.93466i	1.66923	+	0.142352i
$426$			5.59683i			0.271168i
$427$	−4.65437			−0.225241
$428$			3.80308i			0.183829i
$429$		−	1.58605i		−	0.0765754i
$430$	20.7990	+	0.885263i	1.00302	+	0.0426911i
$431$			4.94514i			0.238199i	0.992882	+	0.119100i	$0.0380008\pi$
$431$			4.94514i			0.238199i	−0.992882	+	0.119100i	$0.961999\pi$
$432$			1.00000i			0.0481125i
$433$		−	3.83656i		−	0.184373i	−0.995742	−	0.0921867i	$-0.970614\pi$
$433$		−	3.83656i		−	0.184373i	0.995742	−	0.0921867i	$-0.0293857\pi$
$434$	3.85987			0.185280
$435$	7.58136	+	0.322683i	0.363498	+	0.0154715i
$436$		−	4.93476i		−	0.236332i
$437$			50.9585i			2.43768i
$438$	−12.5062			−0.597569
$439$		−	27.6321i		−	1.31881i	−0.751789	−	0.659404i	$-0.770809\pi$
$439$		−	27.6321i		−	1.31881i	0.751789	−	0.659404i	$-0.229191\pi$
$440$	−8.34000	−	0.354973i	−0.397594	−	0.0169227i
$441$	3.28821			0.156581
$442$	−2.93466			−0.139587
$443$		−	17.7327i		−	0.842504i	−0.906944	−	0.421252i	$-0.861591\pi$
$443$		−	17.7327i		−	0.842504i	0.906944	−	0.421252i	$-0.138409\pi$
$444$	1.45421	+	5.90637i	0.0690139	+	0.280304i
$445$	1.51419	−	35.5754i	0.0717793	−	1.68643i
$446$			3.24704i			0.153752i
$447$		−	2.43147i		−	0.115004i
$448$		−	3.20752i		−	0.151541i
$449$		−	25.3794i		−	1.19773i	−0.800850	−	0.598864i	$-0.795619\pi$
$449$		−	25.3794i		−	1.19773i	0.800850	−	0.598864i	$-0.204381\pi$
$450$	−4.98192	−	0.424858i	−0.234850	−	0.0200280i
$451$	−21.4618			−1.01059
$452$	9.29880			0.437379
$453$			15.1683i			0.712667i
$454$	3.24282			0.152193
$455$	−0.129579	+	3.04443i	−0.00607477	+	0.142725i
$456$	−8.02549			−0.375828
$457$	−41.8627			−1.95826			−0.979128	−	0.203243i	$-0.934852\pi$
$457$	−41.8627			−1.95826			−0.979128	+	0.203243i	$0.934852\pi$
$458$	−23.2392			−1.08590
$459$			6.90738i			0.322409i
$460$	−14.1853	−	0.603764i	−0.661392	−	0.0281506i
$461$		−	9.86731i		−	0.459567i	−0.973242	−	0.229783i	$-0.926198\pi$
$461$		−	9.86731i		−	0.459567i	0.973242	−	0.229783i	$-0.0738017\pi$
$462$	11.9741			0.557087
$463$	2.13573			0.0992558			0.0496279	−	0.998768i	$-0.484196\pi$
$463$	2.13573			0.0992558			0.0496279	+	0.998768i	$0.484196\pi$
$464$			3.39355i			0.157542i
$465$	2.68841	+	0.114426i	0.124672	+	0.00530638i
$466$			23.5036i			1.08878i
$467$	23.1295			1.07031			0.535154	−	0.844755i	$-0.320254\pi$
$467$	23.1295			1.07031			0.535154	+	0.844755i	$0.320254\pi$
$468$	0.424858			0.0196391
$469$	36.8674			1.70238
$470$	0.194317	−	4.56543i	0.00896318	−	0.210587i
$471$	19.1941			0.884416
$472$		−	2.16131i		−	0.0994823i
$473$	−34.7556			−1.59806
$474$	4.50480			0.206912
$475$	3.40969	−	39.9823i	0.156447	−	1.83451i
$476$		−	22.1556i		−	1.01550i
$477$		−	11.8045i		−	0.540490i
$478$			6.75627i			0.309025i
$479$		−	42.3018i		−	1.93282i	−0.257006	−	0.966410i	$-0.582736\pi$
$479$		−	42.3018i		−	1.93282i	0.257006	−	0.966410i	$-0.417264\pi$
$480$	0.0950871	−	2.23405i	0.00434011	−	0.101970i
$481$	2.50937	−	0.617834i	0.114417	−	0.0281708i
$482$			27.0533i			1.23225i
$483$	20.3665			0.926706
$484$	2.93631			0.133469
$485$	−9.91386	−	0.421961i	−0.450165	−	0.0191603i
$486$		−	1.00000i		−	0.0453609i
$487$	10.2364			0.463858			0.231929	−	0.972733i	$-0.425496\pi$
$487$	10.2364			0.463858			0.231929	+	0.972733i	$0.425496\pi$
$488$		−	1.45108i		−	0.0656872i
$489$			7.14619i			0.323162i
$490$	−7.34600	−	0.312666i	−0.331859	−	0.0141248i
$491$	−30.2449			−1.36494			−0.682468	−	0.730916i	$-0.739093\pi$
$491$	−30.2449			−1.36494			−0.682468	+	0.730916i	$0.739093\pi$
$492$		−	5.74899i		−	0.259184i
$493$			23.4406i			1.05571i
$494$			3.40969i			0.153409i
$495$	8.34000	+	0.354973i	0.374855	+	0.0159549i
$496$			1.20338i			0.0540334i
$497$			17.9520i			0.805256i
$498$	7.00128			0.313735
$499$			5.43439i			0.243277i	0.992574	+	0.121638i	$0.0388148\pi$
$499$			5.43439i			0.243277i	−0.992574	+	0.121638i	$0.961185\pi$
$500$	11.0894	+	1.42287i	0.495934	+	0.0636326i
$501$		−	12.6692i		−	0.566019i
$502$			12.9375i			0.577430i
$503$	1.52679			0.0680760			0.0340380	−	0.999421i	$-0.489163\pi$
$503$	1.52679			0.0680760			0.0340380	+	0.999421i	$0.489163\pi$
$504$			3.20752i			0.142874i
$505$	29.0807	+	1.23776i	1.29407	+	0.0550794i
$506$	23.7039			1.05377
$507$			12.8195i			0.569334i
$508$			14.3747i			0.637776i
$509$	10.8171			0.479459			0.239729	−	0.970840i	$-0.422941\pi$
$509$	10.8171			0.479459			0.239729	+	0.970840i	$0.422941\pi$
$510$	0.656803	−	15.4314i	0.0290837	−	0.683314i
$511$	−40.1139			−1.77454
$512$	1.00000			0.0441942
$513$	8.02549			0.354334
$514$	14.5960			0.643802
$515$	16.0238	+	0.682016i	0.706092	+	0.0300532i
$516$		−	9.31001i		−	0.409850i
$517$			7.62892i			0.335520i
$518$	4.66443	+	18.9448i	0.204943	+	0.832388i
$519$	−19.7245			−0.865811
$520$	−0.949152	−	0.0403985i	−0.0416231	−	0.00177159i
$521$	−39.8552			−1.74609			−0.873044	−	0.487642i	$-0.837857\pi$
$521$	−39.8552			−1.74609			−0.873044	+	0.487642i	$0.837857\pi$
$522$		−	3.39355i		−	0.148532i
$523$	17.5477			0.767309			0.383654	−	0.923477i	$-0.374665\pi$
$523$	17.5477			0.767309			0.383654	+	0.923477i	$0.374665\pi$
$524$			12.3237i			0.538362i
$525$	−15.9796	−	1.36274i	−0.697408	−	0.0594749i
$526$			12.2500i			0.534127i
$527$			8.31221i			0.362085i
$528$			3.73314i			0.162464i
$529$	17.3173			0.752925
$530$	−1.12245	+	26.3717i	−0.0487563	+	1.14551i
$531$			2.16131i			0.0937928i
$532$	−25.7419			−1.11605
$533$	−2.44250			−0.105797
$534$	−15.9242			−0.689107
$535$	−0.361624	+	8.49625i	−0.0156344	+	0.367325i
$536$			11.4940i			0.496466i
$537$	−3.19619			−0.137926
$538$	14.1886			0.611714
$539$	12.2753			0.528736
$540$	−0.0950871	+	2.23405i	−0.00409190	+	0.0961380i
$541$		−	23.3560i		−	1.00415i	−0.864824	−	0.502076i	$-0.832570\pi$
$541$		−	23.3560i		−	1.00415i	0.864824	−	0.502076i	$-0.167430\pi$
$542$	−8.82413			−0.379029
$543$			11.3735i			0.488085i
$544$	6.90738			0.296152
$545$	0.469232	−	11.0245i	0.0200997	−	0.472237i
$546$	1.36274			0.0583200
$547$	15.6858			0.670675			0.335337	−	0.942098i	$-0.391150\pi$
$547$	15.6858			0.670675			0.335337	+	0.942098i	$0.391150\pi$
$548$			17.4773i			0.746594i
$549$			1.45108i			0.0619305i
$550$	−18.5982	−	1.58605i	−0.793029	−	0.0676295i
$551$	27.2349			1.16025
$552$			6.34959i			0.270256i
$553$	14.4493			0.614445
$554$	−12.6061			−0.535581
$555$	2.68716	+	13.3334i	0.114064	+	0.565971i
$556$	−0.125741			−0.00533261
$557$	−39.5638			−1.67637			−0.838186	−	0.545384i	$-0.816384\pi$
$557$	−39.5638			−1.67637			−0.838186	+	0.545384i	$0.816384\pi$
$558$		−	1.20338i		−	0.0509432i
$559$	−3.95543			−0.167297
$560$	0.304994	−	7.16575i	0.0128884	−	0.302808i
$561$			25.7862i			1.08869i
$562$		−	15.8731i		−	0.669565i
$563$	−32.4565			−1.36788			−0.683939	−	0.729540i	$-0.739734\pi$
$563$	−32.4565			−1.36788			−0.683939	+	0.729540i	$0.739734\pi$
$564$	−2.04357			−0.0860498
$565$	20.7739	+	0.884197i	0.873967	+	0.0371984i
$566$	29.1588			1.22564
$567$		−	3.20752i		−	0.134703i
$568$	−5.59683			−0.234838
$569$			3.24636i			0.136094i	0.997682	+	0.0680472i	$0.0216769\pi$
$569$			3.24636i			0.136094i	−0.997682	+	0.0680472i	$0.978323\pi$
$570$	−17.9293	−	0.763120i	−0.750976	−	0.0319636i
$571$	28.9822			1.21287			0.606433	−	0.795134i	$-0.292600\pi$
$571$	28.9822			1.21287			0.606433	+	0.795134i	$0.292600\pi$
$572$	1.58605			0.0663162
$573$	12.4830			0.521483
$574$		−	18.4400i		−	0.769671i
$575$	−31.6331	−	2.69767i	−1.31919	−	0.112501i
$576$	−1.00000			−0.0416667
$577$	14.3774			0.598538			0.299269	−	0.954169i	$-0.403257\pi$
$577$	14.3774			0.598538			0.299269	+	0.954169i	$0.403257\pi$
$578$	30.7119			1.27745
$579$		−	12.1559i		−	0.505181i
$580$	−0.322683	+	7.58136i	−0.0133987	+	0.314799i
$581$	22.4568			0.931664
$582$			4.43763i			0.183946i
$583$		−	44.0677i		−	1.82510i
$584$		−	12.5062i		−	0.517510i
$585$	0.949152	+	0.0403985i	0.0392426	+	0.00167027i
$586$		−	28.4275i		−	1.17433i
$587$	−11.8386			−0.488632			−0.244316	−	0.969696i	$-0.578563\pi$
$587$	−11.8386			−0.488632			−0.244316	+	0.969696i	$0.578563\pi$
$588$			3.28821i			0.135603i
$589$	9.65771			0.397939
$590$	0.205513	−	4.82846i	0.00846082	−	0.198785i
$591$	8.89921			0.366064
$592$	−5.90637	+	1.45421i	−0.242751	+	0.0597678i
$593$		−	1.69514i		−	0.0696112i	−0.999394	−	0.0348056i	$-0.988919\pi$
$593$		−	1.69514i		−	0.0696112i	0.999394	−	0.0348056i	$-0.0110812\pi$
$594$		−	3.73314i		−	0.153172i
$595$	2.10671	−	49.4966i	0.0863667	−	2.02916i
$596$	2.43147			0.0995968
$597$	−10.3470			−0.423475
$598$	2.69767			0.110316
$599$	44.7372			1.82791			0.913956	−	0.405813i	$-0.133012\pi$
$599$	44.7372			1.82791			0.913956	+	0.405813i	$0.133012\pi$
$600$	0.424858	−	4.98192i	0.0173448	−	0.203386i
$601$	6.63433			0.270620			0.135310	−	0.990803i	$-0.456797\pi$
$601$	6.63433			0.270620			0.135310	+	0.990803i	$0.456797\pi$
$602$		−	29.8621i		−	1.21709i
$603$		−	11.4940i		−	0.468073i
$604$	−15.1683			−0.617188
$605$	6.55985	+	0.279205i	0.266696	+	0.0113513i
$606$		−	13.0171i		−	0.528782i
$607$	29.4488			1.19529			0.597645	−	0.801760i	$-0.296103\pi$
$607$	29.4488			1.19529			0.597645	+	0.801760i	$0.296103\pi$
$608$		−	8.02549i		−	0.325476i
$609$		−	10.8849i		−	0.441079i
$610$	0.137979	−	3.24177i	0.00558660	−	0.131256i
$611$			0.868226i			0.0351247i
$612$	−6.90738			−0.279214
$613$			47.2277i			1.90751i	0.300590	+	0.953754i	$0.402817\pi$
$613$			47.2277i			1.90751i	−0.300590	+	0.953754i	$0.597183\pi$
$614$		−	20.6139i		−	0.831910i
$615$	0.546655	−	12.8435i	0.0220433	−	0.517900i
$616$			11.9741i			0.482451i
$617$		−	39.6156i		−	1.59487i	−0.603408	−	0.797433i	$-0.706191\pi$
$617$		−	39.6156i		−	1.59487i	0.603408	−	0.797433i	$-0.293809\pi$
$618$		−	7.17254i		−	0.288522i
$619$	−21.3347			−0.857512			−0.428756	−	0.903420i	$-0.641048\pi$
$619$	−21.3347			−0.857512			−0.428756	+	0.903420i	$0.641048\pi$
$620$	−0.114426	+	2.68841i	−0.00459546	+	0.107969i
$621$		−	6.34959i		−	0.254800i
$622$			15.0056i			0.601668i
$623$	−51.0772			−2.04637
$624$			0.424858i			0.0170079i
$625$	24.6390	+	4.23321i	0.985560	+	0.169329i
$626$	−28.8720			−1.15396
$627$	29.9602			1.19650
$628$			19.1941i			0.765927i
$629$	−40.7976	+	10.0448i	−1.62671	+	0.400513i
$630$	−0.304994	+	7.16575i	−0.0121513	+	0.285490i
$631$		−	13.9231i		−	0.554269i	−0.960831	−	0.277134i	$-0.910615\pi$
$631$		−	13.9231i		−	0.554269i	0.960831	−	0.277134i	$-0.0893847\pi$
$632$			4.50480i			0.179191i
$633$		−	5.52374i		−	0.219549i
$634$			14.7214i			0.584662i
$635$	−1.36685	+	32.1138i	−0.0542419	+	1.27440i
$636$	11.8045			0.468078
$637$	1.39702			0.0553520
$638$		−	12.6686i		−	0.501555i
$639$	5.59683			0.221407
$640$	2.23405	+	0.0950871i	0.0883084	+	0.00375865i
$641$	25.1770			0.994431			0.497216	−	0.867627i	$-0.334356\pi$
$641$	25.1770			0.994431			0.497216	+	0.867627i	$0.334356\pi$
$642$	3.80308			0.150096
$643$	6.70070			0.264250			0.132125	−	0.991233i	$-0.457820\pi$
$643$	6.70070			0.264250			0.132125	+	0.991233i	$0.457820\pi$
$644$			20.3665i			0.802551i
$645$	0.885263	−	20.7990i	0.0348572	−	0.818959i
$646$		−	55.4351i		−	2.18106i
$647$	−2.02361			−0.0795562			−0.0397781	−	0.999209i	$-0.512665\pi$
$647$	−2.02361			−0.0795562			−0.0397781	+	0.999209i	$0.512665\pi$
$648$	1.00000			0.0392837
$649$			8.06846i			0.316715i
$650$	−2.11661	−	0.180504i	−0.0830202	−	0.00707996i
$651$		−	3.85987i		−	0.151280i
$652$	−7.14619			−0.279867
$653$	−17.8433			−0.698262			−0.349131	−	0.937074i	$-0.613523\pi$
$653$	−17.8433			−0.698262			−0.349131	+	0.937074i	$0.613523\pi$
$654$	−4.93476			−0.192964
$655$	−1.17182	+	27.5316i	−0.0457869	+	1.07575i
$656$	5.74899			0.224460
$657$			12.5062i			0.487913i
$658$	−6.55479			−0.255532
$659$	−28.2166			−1.09916			−0.549582	−	0.835440i	$-0.685213\pi$
$659$	−28.2166			−1.09916			−0.549582	+	0.835440i	$0.685213\pi$
$660$	−0.354973	+	8.34000i	−0.0138173	+	0.324634i
$661$		−	14.9551i		−	0.581687i	−0.956771	−	0.290843i	$-0.906064\pi$
$661$		−	14.9551i		−	0.581687i	0.956771	−	0.290843i	$-0.0939358\pi$
$662$			8.15238i			0.316851i
$663$			2.93466i			0.113973i
$664$			7.00128i			0.271703i
$665$	−57.5086	−	2.44773i	−2.23009	−	0.0949188i
$666$	5.90637	−	1.45421i	0.228867	−	0.0563496i
$667$		−	21.5477i		−	0.834329i
$668$	12.6692			0.490187
$669$	3.24704			0.125538
$670$	−1.09293	+	25.6782i	−0.0422237	+	0.992035i
$671$			5.41707i			0.209124i
$672$	−3.20752			−0.123733
$673$		−	26.7443i		−	1.03092i	−0.856915	−	0.515458i	$-0.827622\pi$
$673$		−	26.7443i		−	1.03092i	0.856915	−	0.515458i	$-0.172378\pi$
$674$		−	28.0034i		−	1.07865i
$675$	−0.424858	+	4.98192i	−0.0163528	+	0.191754i
$676$	−12.8195			−0.493058
$677$		−	23.3020i		−	0.895569i	−0.894141	−	0.447785i	$-0.852213\pi$
$677$		−	23.3020i		−	0.895569i	0.894141	−	0.447785i	$-0.147787\pi$
$678$		−	9.29880i		−	0.357118i
$679$			14.2338i			0.546243i
$680$	15.4314	+	0.656803i	0.591767	+	0.0251872i
$681$		−	3.24282i		−	0.124265i
$682$		−	4.49238i		−	0.172022i
$683$	0.507613			0.0194233			0.00971163	−	0.999953i	$-0.496909\pi$
$683$	0.507613			0.0194233			0.00971163	+	0.999953i	$0.496909\pi$
$684$			8.02549i			0.306862i
$685$	−1.66187	+	39.0451i	−0.0634967	+	1.49184i
$686$		−	11.9057i		−	0.454560i
$687$			23.2392i			0.886631i
$688$	9.31001			0.354941
$689$		−	5.01522i		−	0.191065i
$690$	−0.603764	+	14.1853i	−0.0229849	+	0.540024i
$691$	−25.1513			−0.956801			−0.478401	−	0.878142i	$-0.658783\pi$
$691$	−25.1513			−0.956801			−0.478401	+	0.878142i	$0.658783\pi$
$692$		−	19.7245i		−	0.749814i
$693$		−	11.9741i		−	0.454859i
$694$	−6.82853			−0.259208
$695$	−0.280911	−	0.0119564i	−0.0106556	−	0.000453531i
$696$	3.39355			0.128632
$697$	39.7105			1.50414
$698$	−5.65418			−0.214014
$699$	23.5036			0.888988
$700$	1.36274	−	15.9796i	0.0515068	−	0.603973i
$701$			13.4801i			0.509136i	0.967055	+	0.254568i	$0.0819332\pi$
$701$			13.4801i			0.509136i	−0.967055	+	0.254568i	$0.918067\pi$
$702$		−	0.424858i		−	0.0160352i
$703$	11.6708	+	47.4015i	0.440172	+	1.78778i
$704$	−3.73314			−0.140698
$705$	−4.56543	−	0.194317i	−0.171944	−	0.00731841i
$706$	−12.7850			−0.481169
$707$		−	41.7525i		−	1.57027i
$708$	−2.16131			−0.0812270
$709$		−	16.0914i		−	0.604326i	−0.953256	−	0.302163i	$-0.902291\pi$
$709$		−	16.0914i		−	0.604326i	0.953256	−	0.302163i	$-0.0977086\pi$
$710$	−12.5036	−	0.532187i	−0.469251	−	0.0199726i
$711$		−	4.50480i		−	0.168943i
$712$		−	15.9242i		−	0.596785i
$713$		−	7.64097i		−	0.286157i
$714$	−22.1556			−0.829152
$715$	3.54331	+	0.150813i	0.132512	+	0.00564010i
$716$		−	3.19619i		−	0.119447i
$717$	6.75627			0.252318
$718$	11.3292			0.422802
$719$	−32.6719			−1.21845			−0.609227	−	0.792996i	$-0.708520\pi$
$719$	−32.6719			−1.21845			−0.609227	+	0.792996i	$0.708520\pi$
$720$	−2.23405	−	0.0950871i	−0.0832580	−	0.00354369i
$721$		−	23.0061i		−	0.856792i
$722$	−45.4084			−1.68993
$723$	27.0533			1.00612
$724$	−11.3735			−0.422694
$725$	−1.44178	+	16.9064i	−0.0535463	+	0.627888i
$726$		−	2.93631i		−	0.108977i
$727$	−31.3272			−1.16186			−0.580931	−	0.813953i	$-0.697311\pi$
$727$	−31.3272			−1.16186			−0.580931	+	0.813953i	$0.697311\pi$
$728$			1.36274i			0.0505066i
$729$	−1.00000			−0.0370370
$730$	1.18918	−	27.9394i	0.0440135	−	1.03408i
$731$	64.3078			2.37851
$732$	−1.45108			−0.0536334
$733$			28.4514i			1.05088i	0.850831	+	0.525439i	$0.176099\pi$
$733$			28.4514i			1.05088i	−0.850831	+	0.525439i	$0.823901\pi$
$734$		−	10.0590i		−	0.371284i
$735$	−0.312666	+	7.34600i	−0.0115329	+	0.270961i
$736$	−6.34959			−0.234049
$737$		−	42.9088i		−	1.58057i
$738$	−5.74899			−0.211623
$739$	15.5668			0.572635			0.286318	−	0.958135i	$-0.407569\pi$
$739$	15.5668			0.572635			0.286318	+	0.958135i	$0.407569\pi$
$740$	−13.3334	+	2.68716i	−0.490145	+	0.0987820i
$741$	3.40969			0.125258
$742$	37.8631			1.39000
$743$		−	50.7985i		−	1.86362i	−0.362950	−	0.931809i	$-0.618230\pi$
$743$		−	50.7985i		−	1.86362i	0.362950	−	0.931809i	$-0.381770\pi$
$744$	1.20338			0.0441181
$745$	5.43201	+	0.231201i	0.199013	+	0.00847056i
$746$			9.39169i			0.343854i
$747$		−	7.00128i		−	0.256164i
$748$	−25.7862			−0.942837
$749$	12.1985			0.445722
$750$	1.42287	−	11.0894i	0.0519558	−	0.404929i
$751$	−33.5086			−1.22275			−0.611373	−	0.791342i	$-0.709383\pi$
$751$	−33.5086			−1.22275			−0.611373	+	0.791342i	$0.709383\pi$
$752$		−	2.04357i		−	0.0745213i
$753$	12.9375			0.471470
$754$		−	1.44178i		−	0.0525065i
$755$	−33.8866	−	1.44231i	−1.23326	−	0.0524909i
$756$	3.20752			0.116656
$757$	26.5221			0.963964			0.481982	−	0.876181i	$-0.339917\pi$
$757$	26.5221			0.963964			0.481982	+	0.876181i	$0.339917\pi$
$758$	−10.7371			−0.389988
$759$		−	23.7039i		−	0.860396i
$760$	0.763120	−	17.9293i	0.0276813	−	0.650364i
$761$	31.0909			1.12704			0.563521	−	0.826102i	$-0.309446\pi$
$761$	31.0909			1.12704			0.563521	+	0.826102i	$0.309446\pi$
$762$	14.3747			0.520742
$763$	−15.8284			−0.573025
$764$			12.4830i			0.451617i
$765$	−15.4314	−	0.656803i	−0.557924	−	0.0237468i
$766$	11.2412			0.406161
$767$			0.918249i			0.0331561i
$768$		−	1.00000i		−	0.0360844i
$769$			6.61015i			0.238368i	0.992872	+	0.119184i	$0.0380278\pi$
$769$			6.61015i			0.238368i	−0.992872	+	0.119184i	$0.961972\pi$
$770$	−1.13859	+	26.7507i	−0.0410318	+	0.964030i
$771$		−	14.5960i		−	0.525662i
$772$	12.1559			0.437499
$773$			35.7529i			1.28594i	0.765890	+	0.642971i	$0.222298\pi$
$773$			35.7529i			1.28594i	−0.765890	+	0.642971i	$0.777702\pi$
$774$	−9.31001			−0.334642
$775$	−0.511266	+	5.99514i	−0.0183652	+	0.215352i
$776$	−4.43763			−0.159302
$777$	18.9448	−	4.66443i	0.679642	−	0.167335i
$778$			7.80757i			0.279915i
$779$		−	46.1384i		−	1.65308i
$780$	−0.0403985	+	0.949152i	−0.00144650	+	0.0339851i
$781$	20.8937			0.747637
$782$	−43.8590			−1.56840
$783$	−3.39355			−0.121276
$784$	−3.28821			−0.117436
$785$	−1.82511	+	42.8804i	−0.0651409	+	1.53047i
$786$	12.3237			0.439570
$787$			21.9895i			0.783840i	0.919999	+	0.391920i	$0.128189\pi$
$787$			21.9895i			0.783840i	−0.919999	+	0.391920i	$0.871811\pi$
$788$			8.89921i			0.317021i
$789$	12.2500			0.436113
$790$	−0.428349	+	10.0639i	−0.0152400	+	0.358059i
$791$		−	29.8261i		−	1.06050i
$792$	3.73314			0.132651
$793$			0.616502i			0.0218926i
$794$			33.1348i			1.17591i
$795$	26.3717	+	1.12245i	0.935309	+	0.0398093i
$796$		−	10.3470i		−	0.366740i
$797$	16.6230			0.588817			0.294409	−	0.955680i	$-0.404877\pi$
$797$	16.6230			0.588817			0.294409	+	0.955680i	$0.404877\pi$
$798$			25.7419i			0.911255i
$799$		−	14.1157i		−	0.499378i
$800$	4.98192	+	0.424858i	0.176137	+	0.0150210i
$801$			15.9242i			0.562654i
$802$		−	33.2206i		−	1.17306i
$803$			46.6874i			1.64756i
$804$	11.4940			0.405363
$805$	−1.93659	+	45.4996i	−0.0682557	+	1.60365i
$806$		−	0.511266i		−	0.0180086i
$807$		−	14.1886i		−	0.499462i
$808$	13.0171			0.457939
$809$			37.6802i			1.32476i	0.749166	+	0.662382i	$0.230454\pi$
$809$			37.6802i			1.32476i	−0.749166	+	0.662382i	$0.769546\pi$
$810$	2.23405	+	0.0950871i	0.0784964	+	0.00334102i
$811$	9.23902			0.324426			0.162213	−	0.986756i	$-0.448137\pi$
$811$	9.23902			0.324426			0.162213	+	0.986756i	$0.448137\pi$
$812$	10.8849			0.381985
$813$			8.82413i			0.309476i
$814$	22.0493	−	5.42878i	0.772828	−	0.190279i
$815$	−15.9649	−	0.679511i	−0.559227	−	0.0238022i
$816$		−	6.90738i		−	0.241807i
$817$		−	74.7174i		−	2.61403i
$818$		−	18.4622i		−	0.645517i
$819$		−	1.36274i		−	0.0476181i
$820$	12.8435	+	0.546655i	0.448514	+	0.0190900i
$821$	−2.02441			−0.0706525			−0.0353262	−	0.999376i	$-0.511247\pi$
$821$	−2.02441			−0.0706525			−0.0353262	+	0.999376i	$0.511247\pi$
$822$	17.4773			0.609591
$823$		−	21.4801i		−	0.748748i	−0.927278	−	0.374374i	$-0.877858\pi$
$823$		−	21.4801i		−	0.748748i	0.927278	−	0.374374i	$-0.122142\pi$
$824$	7.17254			0.249867
$825$	−1.58605	+	18.5982i	−0.0552193	+	0.647505i
$826$	−6.93245			−0.241211
$827$	−46.1615			−1.60519			−0.802597	−	0.596522i	$-0.796549\pi$
$827$	−46.1615			−1.60519			−0.802597	+	0.596522i	$0.796549\pi$
$828$	6.34959			0.220663
$829$			7.43600i			0.258263i	0.991627	+	0.129131i	$0.0412189\pi$
$829$			7.43600i			0.258263i	−0.991627	+	0.129131i	$0.958781\pi$
$830$	−0.665732	+	15.6412i	−0.0231079	+	0.542913i
$831$			12.6061i			0.437300i
$832$	−0.424858			−0.0147293
$833$	−22.7129			−0.786955
$834$			0.125741i			0.00435406i
$835$	28.3036	+	1.20468i	0.979486	+	0.0416896i
$836$			29.9602i			1.03620i
$837$	−1.20338			−0.0415949
$838$	0.759460			0.0262351
$839$	−31.3881			−1.08364			−0.541819	−	0.840495i	$-0.682264\pi$
$839$	−31.3881			−1.08364			−0.541819	+	0.840495i	$0.682264\pi$
$840$	−7.16575	−	0.304994i	−0.247242	−	0.0105233i
$841$	17.4838			0.602889
$842$		−	27.6679i		−	0.953500i
$843$	−15.8731			−0.546698
$844$	5.52374			0.190135
$845$	−28.6393	−	1.21897i	−0.985223	−	0.0419338i
$846$			2.04357i			0.0702593i
$847$		−	9.41828i		−	0.323616i
$848$			11.8045i			0.405367i
$849$		−	29.1588i		−	1.00073i
$850$	34.4120	+	2.93466i	1.18032	+	0.100658i
$851$	37.5030	−	9.23366i	1.28559	−	0.316526i
$852$			5.59683i			0.191744i
$853$	−29.1070			−0.996605			−0.498302	−	0.867003i	$-0.666043\pi$
$853$	−29.1070			−0.996605			−0.498302	+	0.867003i	$0.666043\pi$
$854$	−4.65437			−0.159269
$855$	−0.763120	+	17.9293i	−0.0260982	+	0.613169i
$856$			3.80308i			0.129987i
$857$	26.4364			0.903050			0.451525	−	0.892259i	$-0.350880\pi$
$857$	26.4364			0.903050			0.451525	+	0.892259i	$0.350880\pi$
$858$		−	1.58605i		−	0.0541470i
$859$			3.12912i			0.106764i	0.998574	+	0.0533821i	$0.0170001\pi$
$859$			3.12912i			0.106764i	−0.998574	+	0.0533821i	$0.983000\pi$
$860$	20.7990	+	0.885263i	0.709240	+	0.0301872i
$861$	−18.4400			−0.628434
$862$			4.94514i			0.168432i
$863$			40.9780i			1.39491i	0.716631	+	0.697453i	$0.245683\pi$
$863$			40.9780i			1.39491i	−0.716631	+	0.697453i	$0.754317\pi$
$864$			1.00000i			0.0340207i
$865$	1.87555	−	44.0655i	0.0637706	−	1.49827i
$866$		−	3.83656i		−	0.130372i
$867$		−	30.7119i		−	1.04303i
$868$	3.85987			0.131013
$869$		−	16.8170i		−	0.570479i
$870$	7.58136	+	0.322683i	0.257032	+	0.0109400i
$871$		−	4.88333i		−	0.165465i
$872$		−	4.93476i		−	0.167112i
$873$	4.43763			0.150191
$874$			50.9585i			1.72370i
$875$	4.56388	−	35.5696i	0.154287	−	1.20247i
$876$	−12.5062			−0.422545
$877$			52.0228i			1.75669i	0.478030	+	0.878343i	$0.341351\pi$
$877$			52.0228i			1.75669i	−0.478030	+	0.878343i	$0.658649\pi$
$878$		−	27.6321i		−	0.932538i
$879$	−28.4275			−0.958836
$880$	−8.34000	−	0.354973i	−0.281141	−	0.0119661i
$881$	−12.4748			−0.420288			−0.210144	−	0.977670i	$-0.567393\pi$
$881$	−12.4748			−0.420288			−0.210144	+	0.977670i	$0.567393\pi$
$882$	3.28821			0.110720
$883$	−5.68269			−0.191238			−0.0956189	−	0.995418i	$-0.530483\pi$
$883$	−5.68269			−0.191238			−0.0956189	+	0.995418i	$0.530483\pi$
$884$	−2.93466			−0.0987032
$885$	−4.82846	−	0.205513i	−0.162307	−	0.00690823i
$886$		−	17.7327i		−	0.595740i
$887$			45.8573i			1.53974i	0.638203	+	0.769868i	$0.279678\pi$
$887$			45.8573i			1.53974i	−0.638203	+	0.769868i	$0.720322\pi$
$888$	1.45421	+	5.90637i	0.0488002	+	0.198205i
$889$	46.1073			1.54639
$890$	1.51419	−	35.5754i	0.0507556	−	1.19249i
$891$	−3.73314			−0.125065
$892$			3.24704i			0.108719i
$893$	−16.4006			−0.548826
$894$		−	2.43147i		−	0.0813204i
$895$	0.303917	−	7.14044i	0.0101588	−	0.238678i
$896$		−	3.20752i		−	0.107156i
$897$		−	2.69767i		−	0.0900727i
$898$		−	25.3794i		−	0.846922i
$899$	−4.08374			−0.136200
$900$	−4.98192	−	0.424858i	−0.166064	−	0.0141619i
$901$			81.5380i			2.71642i
$902$	−21.4618			−0.714598
$903$	−29.8621			−0.993748
$904$	9.29880			0.309274
$905$	−25.4090	−	1.08148i	−0.844623	−	0.0359495i
$906$			15.1683i			0.503932i
$907$	56.7099			1.88302			0.941510	−	0.336985i	$-0.109407\pi$
$907$	56.7099			1.88302			0.941510	+	0.336985i	$0.109407\pi$
$908$	3.24282			0.107617
$909$	−13.0171			−0.431749
$910$	−0.129579	+	3.04443i	−0.00429551	+	0.100922i
$911$			36.6773i			1.21517i	0.794254	+	0.607586i	$0.207862\pi$
$911$			36.6773i			1.21517i	−0.794254	+	0.607586i	$0.792138\pi$
$912$	−8.02549			−0.265750
$913$		−	26.1367i		−	0.865000i
$914$	−41.8627			−1.38470
$915$	−3.24177	−	0.137979i	−0.107170	−	0.00456144i
$916$	−23.2392			−0.767845
$917$	39.5284			1.30534
$918$			6.90738i			0.227978i
$919$		−	9.37210i		−	0.309157i	−0.987981	−	0.154578i	$-0.950598\pi$
$919$		−	9.37210i		−	0.309157i	0.987981	−	0.154578i	$-0.0494019\pi$
$920$	−14.1853	−	0.603764i	−0.467674	−	0.0199055i
$921$	−20.6139			−0.679251
$922$		−	9.86731i		−	0.324963i
$923$	2.37786			0.0782682
$924$	11.9741			0.393920
$925$	−30.0429	+	4.73540i	−0.987805	+	0.155699i
$926$	2.13573			0.0701844
$927$	−7.17254			−0.235577
$928$			3.39355i			0.111399i
$929$	−50.0310			−1.64146			−0.820732	−	0.571314i	$-0.806434\pi$
$929$	−50.0310			−1.64146			−0.820732	+	0.571314i	$0.806434\pi$
$930$	2.68841	+	0.114426i	0.0881563	+	0.00375218i
$931$			26.3894i			0.864879i
$932$			23.5036i			0.769886i
$933$	15.0056			0.491260
$934$	23.1295			0.756822
$935$	−57.6075	−	2.45194i	−1.88397	−	0.0801869i
$936$	0.424858			0.0138869
$937$		−	32.5441i		−	1.06317i	−0.847005	−	0.531585i	$-0.821597\pi$
$937$		−	32.5441i		−	1.06317i	0.847005	−	0.531585i	$-0.178403\pi$
$938$	36.8674			1.20376
$939$			28.8720i			0.942203i
$940$	0.194317	−	4.56543i	0.00633793	−	0.148908i
$941$	−23.1571			−0.754900			−0.377450	−	0.926030i	$-0.623199\pi$
$941$	−23.1571			−0.754900			−0.377450	+	0.926030i	$0.623199\pi$
$942$	19.1941			0.625376
$943$	−36.5037			−1.18872
$944$		−	2.16131i		−	0.0703446i
$945$	7.16575	+	0.304994i	0.233102	+	0.00992146i
$946$	−34.7556			−1.13000
$947$	−18.7484			−0.609242			−0.304621	−	0.952474i	$-0.598530\pi$
$947$	−18.7484			−0.609242			−0.304621	+	0.952474i	$0.598530\pi$
$948$	4.50480			0.146309
$949$			5.31336i			0.172479i
$950$	3.40969	−	39.9823i	0.110625	−	1.29720i
$951$	14.7214			0.477375
$952$		−	22.1556i		−	0.718067i
$953$			17.1259i			0.554763i	0.960760	+	0.277382i	$0.0894666\pi$
$953$			17.1259i			0.554763i	−0.960760	+	0.277382i	$0.910533\pi$
$954$		−	11.8045i		−	0.382184i
$955$	−1.18697	+	27.8875i	−0.0384094	+	0.902418i
$956$			6.75627i			0.218514i
$957$	−12.6686			−0.409518
$958$		−	42.3018i		−	1.36671i
$959$	56.0589			1.81024
$960$	0.0950871	−	2.23405i	0.00306892	−	0.0721035i
$961$	29.5519			0.953286
$962$	2.50937	−	0.617834i	0.0809053	−	0.0199198i
$963$		−	3.80308i		−	0.122553i
$964$			27.0533i			0.871329i
$965$	27.1568	+	1.15587i	0.874207	+	0.0372087i
$966$	20.3665			0.655280
$967$	22.1462			0.712175			0.356087	−	0.934453i	$-0.384111\pi$
$967$	22.1462			0.712175			0.356087	+	0.934453i	$0.384111\pi$
$968$	2.93631			0.0943766
$969$	−55.4351			−1.78083
$970$	−9.91386	−	0.421961i	−0.318315	−	0.0135484i
$971$	−7.32119			−0.234948			−0.117474	−	0.993076i	$-0.537480\pi$
$971$	−7.32119			−0.234948			−0.117474	+	0.993076i	$0.537480\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			0.403318i			0.0129298i
$974$	10.2364			0.327997
$975$	−0.180504	+	2.11661i	−0.00578076	+	0.0677857i
$976$		−	1.45108i		−	0.0464479i
$977$	−51.6787			−1.65335			−0.826675	−	0.562680i	$-0.809770\pi$
$977$	−51.6787			−1.65335			−0.826675	+	0.562680i	$0.809770\pi$
$978$			7.14619i			0.228510i
$979$			59.4472i			1.89994i
$980$	−7.34600	−	0.312666i	−0.234659	−	0.00998775i
$981$			4.93476i			0.157555i
$982$	−30.2449			−0.965155
$983$		−	37.3050i		−	1.18985i	−0.803783	−	0.594923i	$-0.797183\pi$
$983$		−	37.3050i		−	1.18985i	0.803783	−	0.594923i	$-0.202817\pi$
$984$		−	5.74899i		−	0.183271i
$985$	−0.846200	+	19.8812i	−0.0269622	+	0.633469i
$986$			23.4406i			0.746500i
$987$			6.55479i			0.208641i
$988$			3.40969i			0.108477i
$989$	−59.1147			−1.87974
$990$	8.34000	+	0.354973i	0.265062	+	0.0112818i
$991$			25.2376i			0.801699i	0.916144	+	0.400850i	$0.131285\pi$
$991$			25.2376i			0.801699i	−0.916144	+	0.400850i	$0.868715\pi$
$992$			1.20338i			0.0382074i
$993$	8.15238			0.258708
$994$			17.9520i			0.569402i
$995$	0.983869	−	23.1157i	0.0311907	−	0.732817i
$996$	7.00128			0.221844
$997$	−45.6991			−1.44731			−0.723653	−	0.690164i	$-0.757538\pi$
$997$	−45.6991			−1.44731			−0.723653	+	0.690164i	$0.757538\pi$
$998$			5.43439i			0.172023i
$999$	−1.45421	−	5.90637i	−0.0460093	−	0.186869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.e.d.739.8	yes	16
3.2	odd	2		3330.2.e.e.739.1		16
5.4	even	2		1110.2.e.c.739.9	yes	16
15.14	odd	2		3330.2.e.f.739.15		16
37.36	even	2		1110.2.e.c.739.1	✓	16
111.110	odd	2		3330.2.e.f.739.16		16
185.184	even	2	inner	1110.2.e.d.739.16	yes	16
555.554	odd	2		3330.2.e.e.739.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.e.c.739.1	✓	16	37.36	even	2
1110.2.e.c.739.9	yes	16	5.4	even	2
1110.2.e.d.739.8	yes	16	1.1	even	1	trivial
1110.2.e.d.739.16	yes	16	185.184	even	2	inner
3330.2.e.e.739.1		16	3.2	odd	2
3330.2.e.e.739.2		16	555.554	odd	2
3330.2.e.f.739.15		16	15.14	odd	2
3330.2.e.f.739.16		16	111.110	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(2.23405 + 0.0950871i) q^{5} -1.00000i q^{6} -3.20752i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(2.23405 + 0.0950871i) q^{5} -1.00000i q^{6} -3.20752i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(2.23405 + 0.0950871i) q^{10} -3.73314 q^{11} -1.00000i q^{12} -0.424858 q^{13} -3.20752i q^{14} +(0.0950871 - 2.23405i) q^{15} +1.00000 q^{16} +6.90738 q^{17} -1.00000 q^{18} -8.02549i q^{19} +(2.23405 + 0.0950871i) q^{20} -3.20752 q^{21} -3.73314 q^{22} -6.34959 q^{23} -1.00000i q^{24} +(4.98192 + 0.424858i) q^{25} -0.424858 q^{26} +1.00000i q^{27} -3.20752i q^{28} +3.39355i q^{29} +(0.0950871 - 2.23405i) q^{30} +1.20338i q^{31} +1.00000 q^{32} +3.73314i q^{33} +6.90738 q^{34} +(0.304994 - 7.16575i) q^{35} -1.00000 q^{36} +(-5.90637 + 1.45421i) q^{37} -8.02549i q^{38} +0.424858i q^{39} +(2.23405 + 0.0950871i) q^{40} +5.74899 q^{41} -3.20752 q^{42} +9.31001 q^{43} -3.73314 q^{44} +(-2.23405 - 0.0950871i) q^{45} -6.34959 q^{46} -2.04357i q^{47} -1.00000i q^{48} -3.28821 q^{49} +(4.98192 + 0.424858i) q^{50} -6.90738i q^{51} -0.424858 q^{52} +11.8045i q^{53} +1.00000i q^{54} +(-8.34000 - 0.354973i) q^{55} -3.20752i q^{56} -8.02549 q^{57} +3.39355i q^{58} -2.16131i q^{59} +(0.0950871 - 2.23405i) q^{60} -1.45108i q^{61} +1.20338i q^{62} +3.20752i q^{63} +1.00000 q^{64} +(-0.949152 - 0.0403985i) q^{65} +3.73314i q^{66} +11.4940i q^{67} +6.90738 q^{68} +6.34959i q^{69} +(0.304994 - 7.16575i) q^{70} -5.59683 q^{71} -1.00000 q^{72} -12.5062i q^{73} +(-5.90637 + 1.45421i) q^{74} +(0.424858 - 4.98192i) q^{75} -8.02549i q^{76} +11.9741i q^{77} +0.424858i q^{78} +4.50480i q^{79} +(2.23405 + 0.0950871i) q^{80} +1.00000 q^{81} +5.74899 q^{82} +7.00128i q^{83} -3.20752 q^{84} +(15.4314 + 0.656803i) q^{85} +9.31001 q^{86} +3.39355 q^{87} -3.73314 q^{88} -15.9242i q^{89} +(-2.23405 - 0.0950871i) q^{90} +1.36274i q^{91} -6.34959 q^{92} +1.20338 q^{93} -2.04357i q^{94} +(0.763120 - 17.9293i) q^{95} -1.00000i q^{96} -4.43763 q^{97} -3.28821 q^{98} +3.73314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} - 6 q^{15} + 16 q^{16} + 38 q^{17} - 16 q^{18} + 2 q^{20} + 6 q^{21} + 2 q^{22} + 20 q^{23} - 4 q^{25} - 6 q^{30} + 16 q^{32} + 38 q^{34} + 10 q^{35} - 16 q^{36} + 4 q^{37} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 2 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 18 q^{49} - 4 q^{50} - 20 q^{55} - 16 q^{57} - 6 q^{60} + 16 q^{64} + 12 q^{65} + 38 q^{68} + 10 q^{70} - 24 q^{71} - 16 q^{72} + 4 q^{74} + 2 q^{80} + 16 q^{81} - 6 q^{82} + 6 q^{84} + 2 q^{86} - 2 q^{87} + 2 q^{88} - 2 q^{90} + 20 q^{92} - 22 q^{93} - 16 q^{95} - 38 q^{97} - 18 q^{98} - 2 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 - 6 * q^15 + 16 * q^16 + 38 * q^17 - 16 * q^18 + 2 * q^20 + 6 * q^21 + 2 * q^22 + 20 * q^23 - 4 * q^25 - 6 * q^30 + 16 * q^32 + 38 * q^34 + 10 * q^35 - 16 * q^36 + 4 * q^37 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 2 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 18 * q^49 - 4 * q^50 - 20 * q^55 - 16 * q^57 - 6 * q^60 + 16 * q^64 + 12 * q^65 + 38 * q^68 + 10 * q^70 - 24 * q^71 - 16 * q^72 + 4 * q^74 + 2 * q^80 + 16 * q^81 - 6 * q^82 + 6 * q^84 + 2 * q^86 - 2 * q^87 + 2 * q^88 - 2 * q^90 + 20 * q^92 - 22 * q^93 - 16 * q^95 - 38 * q^97 - 18 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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