LMFDB - Embedded newform 1110.2.o.b.253.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, degree $2$, 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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.4
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.b.487.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.825074 + 2.07828i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.45633 - 1.45633i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.825074 + 2.07828i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.45633 - 1.45633i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-0.825074 + 2.07828i) q^{10} +3.60654i q^{11} +(-0.707107 + 0.707107i) q^{12} -0.566998 q^{13} +(1.45633 - 1.45633i) q^{14} +(-0.886151 - 2.05298i) q^{15} +1.00000 q^{16} +3.56279i q^{17} -1.00000i q^{18} +(2.60983 + 2.60983i) q^{19} +(-0.825074 + 2.07828i) q^{20} +2.05956i q^{21} +3.60654i q^{22} -2.32324 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-3.63850 - 3.42947i) q^{25} -0.566998 q^{26} +(0.707107 + 0.707107i) q^{27} +(1.45633 - 1.45633i) q^{28} +(-0.784491 + 0.784491i) q^{29} +(-0.886151 - 2.05298i) q^{30} +(-1.50323 - 1.50323i) q^{31} +1.00000 q^{32} +(-2.55021 - 2.55021i) q^{33} +3.56279i q^{34} +(1.82508 + 4.22824i) q^{35} -1.00000i q^{36} +(5.24262 + 3.08463i) q^{37} +(2.60983 + 2.60983i) q^{38} +(0.400928 - 0.400928i) q^{39} +(-0.825074 + 2.07828i) q^{40} +8.53277i q^{41} +2.05956i q^{42} +1.13168 q^{43} +3.60654i q^{44} +(2.07828 + 0.825074i) q^{45} -2.32324 q^{46} +(-4.15173 + 4.15173i) q^{47} +(-0.707107 + 0.707107i) q^{48} +2.75821i q^{49} +(-3.63850 - 3.42947i) q^{50} +(-2.51927 - 2.51927i) q^{51} -0.566998 q^{52} +(-4.48711 - 4.48711i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-7.49540 - 2.97566i) q^{55} +(1.45633 - 1.45633i) q^{56} -3.69086 q^{57} +(-0.784491 + 0.784491i) q^{58} +(5.54174 + 5.54174i) q^{59} +(-0.886151 - 2.05298i) q^{60} +(-5.08840 - 5.08840i) q^{61} +(-1.50323 - 1.50323i) q^{62} +(-1.45633 - 1.45633i) q^{63} +1.00000 q^{64} +(0.467815 - 1.17838i) q^{65} +(-2.55021 - 2.55021i) q^{66} +(1.64587 + 1.64587i) q^{67} +3.56279i q^{68} +(1.64278 - 1.64278i) q^{69} +(1.82508 + 4.22824i) q^{70} -3.57811 q^{71} -1.00000i q^{72} +(0.352111 - 0.352111i) q^{73} +(5.24262 + 3.08463i) q^{74} +(4.99781 - 0.147808i) q^{75} +(2.60983 + 2.60983i) q^{76} +(5.25231 + 5.25231i) q^{77} +(0.400928 - 0.400928i) q^{78} +(-0.260977 - 0.260977i) q^{79} +(-0.825074 + 2.07828i) q^{80} -1.00000 q^{81} +8.53277i q^{82} +(2.52897 + 2.52897i) q^{83} +2.05956i q^{84} +(-7.40448 - 2.93957i) q^{85} +1.13168 q^{86} -1.10944i q^{87} +3.60654i q^{88} +(5.23378 - 5.23378i) q^{89} +(2.07828 + 0.825074i) q^{90} +(-0.825735 + 0.825735i) q^{91} -2.32324 q^{92} +2.12589 q^{93} +(-4.15173 + 4.15173i) q^{94} +(-7.57726 + 3.27066i) q^{95} +(-0.707107 + 0.707107i) q^{96} -11.4260i q^{97} +2.75821i q^{98} +3.60654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	−0.825074	+	2.07828i	−0.368984	+	0.929436i
$5$	−0.825074	+	2.07828i	−0.368984	+	0.929436i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	1.45633	−	1.45633i	0.550441	−	0.550441i	−0.376127	−	0.926568i	$-0.622744\pi$
$7$	1.45633	−	1.45633i	0.550441	−	0.550441i	0.926568	+	0.376127i	$0.122744\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−0.825074	+	2.07828i	−0.260911	+	0.657210i
$11$			3.60654i			1.08741i	0.839276	+	0.543706i	$0.182979\pi$
$11$			3.60654i			1.08741i	−0.839276	+	0.543706i	$0.817021\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−0.566998			−0.157257			−0.0786284	−	0.996904i	$-0.525054\pi$
$13$	−0.566998			−0.157257			−0.0786284	+	0.996904i	$0.525054\pi$
$14$	1.45633	−	1.45633i	0.389220	−	0.389220i
$15$	−0.886151	−	2.05298i	−0.228803	−	0.530078i
$16$	1.00000			0.250000
$17$			3.56279i			0.864104i	0.901849	+	0.432052i	$0.142210\pi$
$17$			3.56279i			0.864104i	−0.901849	+	0.432052i	$0.857790\pi$
$18$		−	1.00000i		−	0.235702i
$19$	2.60983	+	2.60983i	0.598736	+	0.598736i	0.939976	−	0.341240i	$-0.110847\pi$
$19$	2.60983	+	2.60983i	0.598736	+	0.598736i	−0.341240	+	0.939976i	$0.610847\pi$
$20$	−0.825074	+	2.07828i	−0.184492	+	0.464718i
$21$			2.05956i			0.449433i
$22$			3.60654i			0.768917i
$23$	−2.32324			−0.484429			−0.242215	−	0.970223i	$-0.577874\pi$
$23$	−2.32324			−0.484429			−0.242215	+	0.970223i	$0.577874\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−3.63850	−	3.42947i	−0.727701	−	0.685895i
$26$	−0.566998			−0.111197
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.45633	−	1.45633i	0.275220	−	0.275220i
$29$	−0.784491	+	0.784491i	−0.145676	+	0.145676i	−0.776183	−	0.630507i	$-0.782847\pi$
$29$	−0.784491	+	0.784491i	−0.145676	+	0.145676i	0.630507	+	0.776183i	$0.282847\pi$
$30$	−0.886151	−	2.05298i	−0.161788	−	0.374822i
$31$	−1.50323	−	1.50323i	−0.269988	−	0.269988i	0.559107	−	0.829095i	$-0.311144\pi$
$31$	−1.50323	−	1.50323i	−0.269988	−	0.269988i	−0.829095	+	0.559107i	$0.811144\pi$
$32$	1.00000			0.176777
$33$	−2.55021	−	2.55021i	−0.443934	−	0.443934i
$34$			3.56279i			0.611014i
$35$	1.82508	+	4.22824i	0.308495	+	0.714703i
$36$		−	1.00000i		−	0.166667i
$37$	5.24262	+	3.08463i	0.861882	+	0.507110i
$37$	5.24262	+	3.08463i	0.861882	+	0.507110i
$38$	2.60983	+	2.60983i	0.423370	+	0.423370i
$39$	0.400928	−	0.400928i	0.0641998	−	0.0641998i
$40$	−0.825074	+	2.07828i	−0.130456	+	0.328605i
$41$			8.53277i			1.33260i	0.745686	+	0.666298i	$0.232122\pi$
$41$			8.53277i			1.33260i	−0.745686	+	0.666298i	$0.767878\pi$
$42$			2.05956i			0.317797i
$43$	1.13168			0.172579			0.0862897	−	0.996270i	$-0.472499\pi$
$43$	1.13168			0.172579			0.0862897	+	0.996270i	$0.472499\pi$
$44$			3.60654i			0.543706i
$45$	2.07828	+	0.825074i	0.309812	+	0.122995i
$46$	−2.32324			−0.342543
$47$	−4.15173	+	4.15173i	−0.605592	+	0.605592i	−0.941791	−	0.336199i	$-0.890859\pi$
$47$	−4.15173	+	4.15173i	−0.605592	+	0.605592i	0.336199	+	0.941791i	$0.390859\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			2.75821i			0.394030i
$50$	−3.63850	−	3.42947i	−0.514562	−	0.485001i
$51$	−2.51927	−	2.51927i	−0.352769	−	0.352769i
$52$	−0.566998			−0.0786284
$53$	−4.48711	−	4.48711i	−0.616352	−	0.616352i	0.328242	−	0.944594i	$-0.393544\pi$
$53$	−4.48711	−	4.48711i	−0.616352	−	0.616352i	−0.944594	+	0.328242i	$0.893544\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−7.49540	−	2.97566i	−1.01068	−	0.401238i
$56$	1.45633	−	1.45633i	0.194610	−	0.194610i
$57$	−3.69086			−0.488866
$58$	−0.784491	+	0.784491i	−0.103009	+	0.103009i
$59$	5.54174	+	5.54174i	0.721473	+	0.721473i	0.968905	−	0.247432i	$-0.0795867\pi$
$59$	5.54174	+	5.54174i	0.721473	+	0.721473i	−0.247432	+	0.968905i	$0.579587\pi$
$60$	−0.886151	−	2.05298i	−0.114402	−	0.265039i
$61$	−5.08840	−	5.08840i	−0.651503	−	0.651503i	0.301852	−	0.953355i	$-0.402395\pi$
$61$	−5.08840	−	5.08840i	−0.651503	−	0.651503i	−0.953355	+	0.301852i	$0.902395\pi$
$62$	−1.50323	−	1.50323i	−0.190910	−	0.190910i
$63$	−1.45633	−	1.45633i	−0.183480	−	0.183480i
$64$	1.00000			0.125000
$65$	0.467815	−	1.17838i	0.0580253	−	0.146160i
$66$	−2.55021	−	2.55021i	−0.313909	−	0.313909i
$67$	1.64587	+	1.64587i	0.201076	+	0.201076i	0.800461	−	0.599385i	$-0.204588\pi$
$67$	1.64587	+	1.64587i	0.201076	+	0.201076i	−0.599385	+	0.800461i	$0.704588\pi$
$68$			3.56279i			0.432052i
$69$	1.64278	−	1.64278i	0.197767	−	0.197767i
$70$	1.82508	+	4.22824i	0.218139	+	0.505372i
$71$	−3.57811			−0.424643			−0.212322	−	0.977200i	$-0.568102\pi$
$71$	−3.57811			−0.424643			−0.212322	+	0.977200i	$0.568102\pi$
$72$		−	1.00000i		−	0.117851i
$73$	0.352111	−	0.352111i	0.0412114	−	0.0412114i	−0.686201	−	0.727412i	$-0.740723\pi$
$73$	0.352111	−	0.352111i	0.0412114	−	0.0412114i	0.727412	+	0.686201i	$0.240723\pi$
$74$	5.24262	+	3.08463i	0.609442	+	0.358581i
$75$	4.99781	−	0.147808i	0.577098	−	0.0170674i
$76$	2.60983	+	2.60983i	0.299368	+	0.299368i
$77$	5.25231	+	5.25231i	0.598556	+	0.598556i
$78$	0.400928	−	0.400928i	0.0453961	−	0.0453961i
$79$	−0.260977	−	0.260977i	−0.0293622	−	0.0293622i	0.692273	−	0.721635i	$-0.256609\pi$
$79$	−0.260977	−	0.260977i	−0.0293622	−	0.0293622i	−0.721635	+	0.692273i	$0.756609\pi$
$80$	−0.825074	+	2.07828i	−0.0922461	+	0.232359i
$81$	−1.00000			−0.111111
$82$			8.53277i			0.942287i
$83$	2.52897	+	2.52897i	0.277590	+	0.277590i	0.832146	−	0.554556i	$-0.187112\pi$
$83$	2.52897	+	2.52897i	0.277590	+	0.277590i	−0.554556	+	0.832146i	$0.687112\pi$
$84$			2.05956i			0.224716i
$85$	−7.40448	−	2.93957i	−0.803129	−	0.318841i
$86$	1.13168			0.122032
$87$		−	1.10944i		−	0.118944i
$88$			3.60654i			0.384458i
$89$	5.23378	−	5.23378i	0.554780	−	0.554780i	−0.373037	−	0.927817i	$-0.621683\pi$
$89$	5.23378	−	5.23378i	0.554780	−	0.554780i	0.927817	+	0.373037i	$0.121683\pi$
$90$	2.07828	+	0.825074i	0.219070	+	0.0869705i
$91$	−0.825735	+	0.825735i	−0.0865606	+	0.0865606i
$92$	−2.32324			−0.242215
$93$	2.12589			0.220444
$94$	−4.15173	+	4.15173i	−0.428218	+	0.428218i
$95$	−7.57726	+	3.27066i	−0.777411	+	0.335562i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$		−	11.4260i		−	1.16014i	−0.814568	−	0.580068i	$-0.803026\pi$
$97$		−	11.4260i		−	1.16014i	0.814568	−	0.580068i	$-0.196974\pi$
$98$			2.75821i			0.278621i
$99$	3.60654			0.362471
$100$	−3.63850	−	3.42947i	−0.363850	−	0.342947i
$101$			2.80173i			0.278783i	0.990237	+	0.139391i	$0.0445146\pi$
$101$			2.80173i			0.278783i	−0.990237	+	0.139391i	$0.955485\pi$
$102$	−2.51927	−	2.51927i	−0.249445	−	0.249445i
$103$			10.2094i			1.00596i	0.864298	+	0.502979i	$0.167763\pi$
$103$			10.2094i			1.00596i	−0.864298	+	0.502979i	$0.832237\pi$
$104$	−0.566998			−0.0555987
$105$	−4.28035	−	1.69929i	−0.417719	−	0.165834i
$106$	−4.48711	−	4.48711i	−0.435826	−	0.435826i
$107$	10.7074	−	10.7074i	1.03512	−	1.03512i	0.0357612	−	0.999360i	$-0.488614\pi$
$107$	10.7074	−	10.7074i	1.03512	−	1.03512i	0.999360	−	0.0357612i	$-0.0113856\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	−2.12012	−	2.12012i	−0.203071	−	0.203071i	0.598243	−	0.801314i	$-0.295866\pi$
$109$	−2.12012	−	2.12012i	−0.203071	−	0.203071i	−0.801314	+	0.598243i	$0.795866\pi$
$110$	−7.49540	−	2.97566i	−0.714659	−	0.283718i
$111$	−5.88825	+	1.52593i	−0.558888	+	0.144835i
$112$	1.45633	−	1.45633i	0.137610	−	0.137610i
$113$		−	4.98518i		−	0.468966i	−0.972120	−	0.234483i	$-0.924660\pi$
$113$		−	4.98518i		−	0.468966i	0.972120	−	0.234483i	$-0.0753398\pi$
$114$	−3.69086			−0.345680
$115$	1.91685	−	4.82835i	0.178747	−	0.450246i
$116$	−0.784491	+	0.784491i	−0.0728381	+	0.0728381i
$117$			0.566998i			0.0524189i
$118$	5.54174	+	5.54174i	0.510159	+	0.510159i
$119$	5.18860	+	5.18860i	0.475638	+	0.475638i
$120$	−0.886151	−	2.05298i	−0.0808942	−	0.187411i
$121$	−2.00713			−0.182466
$122$	−5.08840	−	5.08840i	−0.460682	−	0.460682i
$123$	−6.03358	−	6.03358i	−0.544030	−	0.544030i
$124$	−1.50323	−	1.50323i	−0.134994	−	0.134994i
$125$	10.1294	−	4.73227i	0.906005	−	0.423267i
$126$	−1.45633	−	1.45633i	−0.129740	−	0.129740i
$127$	8.16328	−	8.16328i	0.724374	−	0.724374i	−0.245119	−	0.969493i	$-0.578827\pi$
$127$	8.16328	−	8.16328i	0.724374	−	0.724374i	0.969493	+	0.245119i	$0.0788271\pi$
$128$	1.00000			0.0883883
$129$	−0.800218	+	0.800218i	−0.0704552	+	0.0704552i
$130$	0.467815	−	1.17838i	0.0410301	−	0.103351i
$131$	5.79100	+	5.79100i	0.505962	+	0.505962i	0.913284	−	0.407323i	$-0.133538\pi$
$131$	5.79100	+	5.79100i	0.505962	+	0.505962i	−0.407323	+	0.913284i	$0.633538\pi$
$132$	−2.55021	−	2.55021i	−0.221967	−	0.221967i
$133$	7.60154			0.659137
$134$	1.64587	+	1.64587i	0.142182	+	0.142182i
$135$	−2.05298	+	0.886151i	−0.176693	+	0.0762677i
$136$			3.56279i			0.305507i
$137$	11.0100	−	11.0100i	0.940646	−	0.940646i	−0.0576885	−	0.998335i	$-0.518373\pi$
$137$	11.0100	−	11.0100i	0.940646	−	0.940646i	0.998335	+	0.0576885i	$0.0183730\pi$
$138$	1.64278	−	1.64278i	0.139843	−	0.139843i
$139$	10.0881			0.855664			0.427832	−	0.903858i	$-0.359277\pi$
$139$	10.0881			0.855664			0.427832	+	0.903858i	$0.359277\pi$
$140$	1.82508	+	4.22824i	0.154248	+	0.357352i
$141$		−	5.87144i		−	0.494464i
$142$	−3.57811			−0.300268
$143$		−	2.04490i		−	0.171003i
$144$		−	1.00000i		−	0.0833333i
$145$	−0.983129	−	2.27766i	−0.0816444	−	0.189149i
$146$	0.352111	−	0.352111i	0.0291409	−	0.0291409i
$147$	−1.95035	−	1.95035i	−0.160862	−	0.160862i
$148$	5.24262	+	3.08463i	0.430941	+	0.253555i
$149$		−	8.10303i		−	0.663826i	−0.943310	−	0.331913i	$-0.892306\pi$
$149$		−	8.10303i		−	0.663826i	0.943310	−	0.331913i	$-0.107694\pi$
$150$	4.99781	−	0.147808i	0.408070	−	0.0120685i
$151$			7.24237i			0.589375i	0.955594	+	0.294688i	$0.0952156\pi$
$151$			7.24237i			0.589375i	−0.955594	+	0.294688i	$0.904784\pi$
$152$	2.60983	+	2.60983i	0.211685	+	0.211685i
$153$	3.56279			0.288035
$154$	5.25231	+	5.25231i	0.423243	+	0.423243i
$155$	4.36441	−	1.88386i	0.350558	−	0.151315i
$156$	0.400928	−	0.400928i	0.0320999	−	0.0320999i
$157$	11.2460	−	11.2460i	0.897532	−	0.897532i	−0.0976855	−	0.995217i	$-0.531144\pi$
$157$	11.2460	−	11.2460i	0.897532	−	0.897532i	0.995217	+	0.0976855i	$0.0311439\pi$
$158$	−0.260977	−	0.260977i	−0.0207622	−	0.0207622i
$159$	6.34573			0.503249
$160$	−0.825074	+	2.07828i	−0.0652279	+	0.164303i
$161$	−3.38341	+	3.38341i	−0.266650	+	0.266650i
$162$	−1.00000			−0.0785674
$163$		−	3.48853i		−	0.273243i	−0.990623	−	0.136621i	$-0.956376\pi$
$163$		−	3.48853i		−	0.273243i	0.990623	−	0.136621i	$-0.0436244\pi$
$164$			8.53277i			0.666298i
$165$	7.40416	−	3.19594i	0.576413	−	0.248804i
$166$	2.52897	+	2.52897i	0.196286	+	0.196286i
$167$		−	13.0005i		−	1.00601i	−0.864284	−	0.503005i	$-0.832228\pi$
$167$		−	13.0005i		−	1.00601i	0.864284	−	0.503005i	$-0.167772\pi$
$168$			2.05956i			0.158899i
$169$	−12.6785			−0.975270
$170$	−7.40448	−	2.93957i	−0.567898	−	0.225455i
$171$	2.60983	−	2.60983i	0.199579	−	0.199579i
$172$	1.13168			0.0862897
$173$	12.4447	−	12.4447i	0.946152	−	0.946152i	−0.0524705	−	0.998622i	$-0.516710\pi$
$173$	12.4447	−	12.4447i	0.946152	−	0.946152i	0.998622	+	0.0524705i	$0.0167096\pi$
$174$		−	1.10944i		−	0.0841062i
$175$	−10.2933	+	0.304419i	−0.778101	+	0.0230119i
$176$			3.60654i			0.271853i
$177$	−7.83720			−0.589080
$178$	5.23378	−	5.23378i	0.392289	−	0.392289i
$179$	6.17102	−	6.17102i	0.461243	−	0.461243i	−0.437819	−	0.899063i	$-0.644249\pi$
$179$	6.17102	−	6.17102i	0.461243	−	0.461243i	0.899063	+	0.437819i	$0.144249\pi$
$180$	2.07828	+	0.825074i	0.154906	+	0.0614974i
$181$	8.27365			0.614975			0.307488	−	0.951552i	$-0.400512\pi$
$181$	8.27365			0.614975			0.307488	+	0.951552i	$0.400512\pi$
$182$	−0.825735	+	0.825735i	−0.0612076	+	0.0612076i
$183$	7.19609			0.531950
$184$	−2.32324			−0.171272
$185$	−10.7363	+	8.35059i	−0.789347	+	0.613948i
$186$	2.12589			0.155878
$187$	−12.8493			−0.939637
$188$	−4.15173	+	4.15173i	−0.302796	+	0.302796i
$189$	2.05956			0.149811
$190$	−7.57726	+	3.27066i	−0.549713	+	0.237278i
$191$	−10.7528	+	10.7528i	−0.778044	+	0.778044i	−0.979498	−	0.201454i	$-0.935433\pi$
$191$	−10.7528	+	10.7528i	−0.778044	+	0.778044i	0.201454	+	0.979498i	$0.435433\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	6.97010			0.501719			0.250859	−	0.968024i	$-0.419287\pi$
$193$	6.97010			0.501719			0.250859	+	0.968024i	$0.419287\pi$
$194$		−	11.4260i		−	0.820340i
$195$	0.502446	+	1.16404i	0.0359809	+	0.0833584i
$196$			2.75821i			0.197015i
$197$	10.8848	−	10.8848i	0.775511	−	0.775511i	−0.203553	−	0.979064i	$-0.565249\pi$
$197$	10.8848	−	10.8848i	0.775511	−	0.775511i	0.979064	+	0.203553i	$0.0652488\pi$
$198$	3.60654			0.256306
$199$	0.906486	−	0.906486i	0.0642591	−	0.0642591i	−0.674247	−	0.738506i	$-0.735532\pi$
$199$	0.906486	−	0.906486i	0.0642591	−	0.0642591i	0.738506	+	0.674247i	$0.235532\pi$
$200$	−3.63850	−	3.42947i	−0.257281	−	0.242500i
$201$	−2.32762			−0.164178
$202$			2.80173i			0.197129i
$203$			2.28495i			0.160372i
$204$	−2.51927	−	2.51927i	−0.176384	−	0.176384i
$205$	−17.7335	−	7.04017i	−1.23856	−	0.491707i
$206$			10.2094i			0.711320i
$207$			2.32324i			0.161476i
$208$	−0.566998			−0.0393142
$209$	−9.41246	+	9.41246i	−0.651073	+	0.651073i
$210$	−4.28035	−	1.69929i	−0.295372	−	0.117262i
$211$	−14.3134			−0.985375			−0.492687	−	0.870206i	$-0.663985\pi$
$211$	−14.3134			−0.985375			−0.492687	+	0.870206i	$0.663985\pi$
$212$	−4.48711	−	4.48711i	−0.308176	−	0.308176i
$213$	2.53010	−	2.53010i	0.173360	−	0.173360i
$214$	10.7074	−	10.7074i	0.731941	−	0.731941i
$215$	−0.933719	+	2.35195i	−0.0636791	+	0.160401i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−4.37839			−0.297225
$218$	−2.12012	−	2.12012i	−0.143593	−	0.143593i
$219$			0.497960i			0.0336490i
$220$	−7.49540	−	2.97566i	−0.505340	−	0.200619i
$221$		−	2.02009i		−	0.135886i
$222$	−5.88825	+	1.52593i	−0.395194	+	0.102414i
$223$	−9.69983	−	9.69983i	−0.649549	−	0.649549i	0.303335	−	0.952884i	$-0.401900\pi$
$223$	−9.69983	−	9.69983i	−0.649549	−	0.649549i	−0.952884	+	0.303335i	$0.901900\pi$
$224$	1.45633	−	1.45633i	0.0973051	−	0.0973051i
$225$	−3.42947	+	3.63850i	−0.228632	+	0.242567i
$226$		−	4.98518i		−	0.331609i
$227$			14.0497i			0.932514i	0.884649	+	0.466257i	$0.154398\pi$
$227$			14.0497i			0.932514i	−0.884649	+	0.466257i	$0.845602\pi$
$228$	−3.69086			−0.244433
$229$		−	17.6048i		−	1.16336i	−0.813418	−	0.581680i	$-0.802396\pi$
$229$		−	17.6048i		−	1.16336i	0.813418	−	0.581680i	$-0.197604\pi$
$230$	1.91685	−	4.82835i	0.126393	−	0.318372i
$231$	−7.42789			−0.488719
$232$	−0.784491	+	0.784491i	−0.0515043	+	0.0515043i
$233$	2.75919	−	2.75919i	0.180760	−	0.180760i	−0.610927	−	0.791687i	$-0.709203\pi$
$233$	2.75919	−	2.75919i	0.180760	−	0.180760i	0.791687	+	0.610927i	$0.209203\pi$
$234$			0.566998i			0.0370658i
$235$	−5.20298	−	12.0540i	−0.339405	−	0.786313i
$236$	5.54174	+	5.54174i	0.360737	+	0.360737i
$237$	0.369077			0.0239741
$238$	5.18860	+	5.18860i	0.336327	+	0.336327i
$239$	1.97901	+	1.97901i	0.128011	+	0.128011i	0.768210	−	0.640198i	$-0.221148\pi$
$239$	1.97901	+	1.97901i	0.128011	+	0.128011i	−0.640198	+	0.768210i	$0.721148\pi$
$240$	−0.886151	−	2.05298i	−0.0572008	−	0.132519i
$241$	−5.52310	+	5.52310i	−0.355774	+	0.355774i	−0.862253	−	0.506478i	$-0.830947\pi$
$241$	−5.52310	+	5.52310i	−0.355774	+	0.355774i	0.506478	+	0.862253i	$0.330947\pi$
$242$	−2.00713			−0.129023
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−5.08840	−	5.08840i	−0.325752	−	0.325752i
$245$	−5.73234	−	2.27573i	−0.366225	−	0.145391i
$246$	−6.03358	−	6.03358i	−0.384687	−	0.384687i
$247$	−1.47977	−	1.47977i	−0.0941553	−	0.0941553i
$248$	−1.50323	−	1.50323i	−0.0954552	−	0.0954552i
$249$	−3.57650			−0.226651
$250$	10.1294	−	4.73227i	0.640642	−	0.299295i
$251$	12.9548	+	12.9548i	0.817701	+	0.817701i	0.985774	−	0.168073i	$-0.0537546\pi$
$251$	12.9548	+	12.9548i	0.817701	+	0.817701i	−0.168073	+	0.985774i	$0.553755\pi$
$252$	−1.45633	−	1.45633i	−0.0917401	−	0.0917401i
$253$		−	8.37886i		−	0.526775i
$254$	8.16328	−	8.16328i	0.512210	−	0.512210i
$255$	7.31435	−	3.15717i	0.458042	−	0.197710i
$256$	1.00000			0.0625000
$257$		−	15.9569i		−	0.995367i	−0.867359	−	0.497683i	$-0.834184\pi$
$257$		−	15.9569i		−	0.995367i	0.867359	−	0.497683i	$-0.165816\pi$
$258$	−0.800218	+	0.800218i	−0.0498194	+	0.0498194i
$259$	12.1272	−	3.14275i	0.753549	−	0.195281i
$260$	0.467815	−	1.17838i	0.0290127	−	0.0730800i
$261$	0.784491	+	0.784491i	0.0485588	+	0.0485588i
$262$	5.79100	+	5.79100i	0.357769	+	0.357769i
$263$	−18.7568	+	18.7568i	−1.15659	+	1.15659i	−0.171388	+	0.985204i	$0.554825\pi$
$263$	−18.7568	+	18.7568i	−1.15659	+	1.15659i	−0.985204	+	0.171388i	$0.945175\pi$
$264$	−2.55021	−	2.55021i	−0.156954	−	0.156954i
$265$	13.0277	−	5.62327i	0.800283	−	0.345435i
$266$	7.60154			0.466081
$267$			7.40169i			0.452976i
$268$	1.64587	+	1.64587i	0.100538	+	0.100538i
$269$			23.7613i			1.44875i	0.689404	+	0.724377i	$0.257873\pi$
$269$			23.7613i			1.44875i	−0.689404	+	0.724377i	$0.742127\pi$
$270$	−2.05298	+	0.886151i	−0.124941	+	0.0539294i
$271$	−21.4180			−1.30105			−0.650525	−	0.759485i	$-0.725451\pi$
$271$	−21.4180			−1.30105			−0.650525	+	0.759485i	$0.725451\pi$
$272$			3.56279i			0.216026i
$273$		−	1.16777i		−	0.0706764i
$274$	11.0100	−	11.0100i	0.665137	−	0.665137i
$275$	12.3685	−	13.1224i	0.745850	−	0.791311i
$276$	1.64278	−	1.64278i	0.0988837	−	0.0988837i
$277$	13.2073			0.793550			0.396775	−	0.917916i	$-0.370129\pi$
$277$	13.2073			0.793550			0.396775	+	0.917916i	$0.370129\pi$
$278$	10.0881			0.605046
$279$	−1.50323	+	1.50323i	−0.0899960	+	0.0899960i
$280$	1.82508	+	4.22824i	0.109069	+	0.252686i
$281$	3.11380	−	3.11380i	0.185754	−	0.185754i	−0.608104	−	0.793857i	$-0.708070\pi$
$281$	3.11380	−	3.11380i	0.185754	−	0.185754i	0.793857	+	0.608104i	$0.208070\pi$
$282$		−	5.87144i		−	0.349639i
$283$			2.74240i			0.163019i	0.996673	+	0.0815094i	$0.0259741\pi$
$283$			2.74240i			0.163019i	−0.996673	+	0.0815094i	$0.974026\pi$
$284$	−3.57811			−0.212322
$285$	3.04523	−	7.67064i	0.180384	−	0.454369i
$286$		−	2.04490i		−	0.120917i
$287$	12.4265	+	12.4265i	0.733515	+	0.733515i
$288$		−	1.00000i		−	0.0589256i
$289$	4.30652			0.253325
$290$	−0.983129	−	2.27766i	−0.0577313	−	0.133749i
$291$	8.07942	+	8.07942i	0.473624	+	0.473624i
$292$	0.352111	−	0.352111i	0.0206057	−	0.0206057i
$293$	−14.1737	−	14.1737i	−0.828037	−	0.828037i	0.159208	−	0.987245i	$-0.449106\pi$
$293$	−14.1737	−	14.1737i	−0.828037	−	0.828037i	−0.987245	+	0.159208i	$0.949106\pi$
$294$	−1.95035	−	1.95035i	−0.113747	−	0.113747i
$295$	−16.0896	+	6.94495i	−0.936775	+	0.404350i
$296$	5.24262	+	3.08463i	0.304721	+	0.179290i
$297$	−2.55021	+	2.55021i	−0.147978	+	0.147978i
$298$		−	8.10303i		−	0.469396i
$299$	1.31727			0.0761798
$300$	4.99781	−	0.147808i	0.288549	−	0.00853370i
$301$	1.64810	−	1.64810i	0.0949947	−	0.0949947i
$302$			7.24237i			0.416751i
$303$	−1.98112	−	1.98112i	−0.113813	−	0.113813i
$304$	2.60983	+	2.60983i	0.149684	+	0.149684i
$305$	14.7734	−	6.37682i	0.845925	−	0.365136i
$306$	3.56279			0.203671
$307$	−10.5206	−	10.5206i	−0.600445	−	0.600445i	0.339986	−	0.940431i	$-0.389578\pi$
$307$	−10.5206	−	10.5206i	−0.600445	−	0.600445i	−0.940431	+	0.339986i	$0.889578\pi$
$308$	5.25231	+	5.25231i	0.299278	+	0.299278i
$309$	−7.21911	−	7.21911i	−0.410681	−	0.410681i
$310$	4.36441	−	1.88386i	0.247882	−	0.106996i
$311$	23.6104	+	23.6104i	1.33882	+	1.33882i	0.897201	+	0.441622i	$0.145597\pi$
$311$	23.6104	+	23.6104i	1.33882	+	1.33882i	0.441622	+	0.897201i	$0.354403\pi$
$312$	0.400928	−	0.400928i	0.0226981	−	0.0226981i
$313$	31.5356			1.78250			0.891250	−	0.453512i	$-0.149829\pi$
$313$	31.5356			1.78250			0.891250	+	0.453512i	$0.149829\pi$
$314$	11.2460	−	11.2460i	0.634651	−	0.634651i
$315$	4.22824	−	1.82508i	0.238234	−	0.102832i
$316$	−0.260977	−	0.260977i	−0.0146811	−	0.0146811i
$317$	−16.4324	−	16.4324i	−0.922933	−	0.922933i	0.0743023	−	0.997236i	$-0.476327\pi$
$317$	−16.4324	−	16.4324i	−0.922933	−	0.922933i	−0.997236	+	0.0743023i	$0.976327\pi$
$318$	6.34573			0.355851
$319$	−2.82930	−	2.82930i	−0.158410	−	0.158410i
$320$	−0.825074	+	2.07828i	−0.0461231	+	0.116179i
$321$			15.1425i			0.845173i
$322$	−3.38341	+	3.38341i	−0.188550	+	0.188550i
$323$	−9.29828	+	9.29828i	−0.517370	+	0.517370i
$324$	−1.00000			−0.0555556
$325$	2.06302	+	1.94450i	0.114436	+	0.107862i
$326$		−	3.48853i		−	0.193212i
$327$	2.99831			0.165807
$328$			8.53277i			0.471144i
$329$			12.0926i			0.666685i
$330$	7.40416	−	3.19594i	0.407586	−	0.175931i
$331$	−13.7264	+	13.7264i	−0.754470	+	0.754470i	−0.975310	−	0.220840i	$-0.929120\pi$
$331$	−13.7264	+	13.7264i	−0.754470	+	0.754470i	0.220840	+	0.975310i	$0.429120\pi$
$332$	2.52897	+	2.52897i	0.138795	+	0.138795i
$333$	3.08463	−	5.24262i	0.169037	−	0.287294i
$334$		−	13.0005i		−	0.711356i
$335$	−4.77856	+	2.06262i	−0.261081	+	0.112693i
$336$			2.05956i			0.112358i
$337$	−17.9668	−	17.9668i	−0.978715	−	0.978715i	0.0210635	−	0.999778i	$-0.493295\pi$
$337$	−17.9668	−	17.9668i	−0.978715	−	0.978715i	−0.999778	+	0.0210635i	$0.993295\pi$
$338$	−12.6785			−0.689620
$339$	3.52506	+	3.52506i	0.191455	+	0.191455i
$340$	−7.40448	−	2.93957i	−0.401564	−	0.159420i
$341$	5.42146	−	5.42146i	0.293588	−	0.293588i
$342$	2.60983	−	2.60983i	0.141123	−	0.141123i
$343$	14.2112	+	14.2112i	0.767331	+	0.767331i
$344$	1.13168			0.0610160
$345$	2.05874	+	4.76957i	0.110839	+	0.256785i
$346$	12.4447	−	12.4447i	0.669030	−	0.669030i
$347$	−1.20902			−0.0649038			−0.0324519	−	0.999473i	$-0.510332\pi$
$347$	−1.20902			−0.0649038			−0.0324519	+	0.999473i	$0.510332\pi$
$348$		−	1.10944i		−	0.0594721i
$349$		−	26.9158i		−	1.44077i	−0.693575	−	0.720384i	$-0.743966\pi$
$349$		−	26.9158i		−	1.44077i	0.693575	−	0.720384i	$-0.256034\pi$
$350$	−10.2933	+	0.304419i	−0.550200	+	0.0162719i
$351$	−0.400928	−	0.400928i	−0.0213999	−	0.0213999i
$352$			3.60654i			0.192229i
$353$			13.0238i			0.693186i	0.938016	+	0.346593i	$0.112662\pi$
$353$			13.0238i			0.693186i	−0.938016	+	0.346593i	$0.887338\pi$
$354$	−7.83720			−0.416543
$355$	2.95220	−	7.43631i	0.156687	−	0.394678i
$356$	5.23378	−	5.23378i	0.277390	−	0.277390i
$357$	−7.33778			−0.388357
$358$	6.17102	−	6.17102i	0.326148	−	0.326148i
$359$			6.68890i			0.353027i	0.984298	+	0.176513i	$0.0564819\pi$
$359$			6.68890i			0.353027i	−0.984298	+	0.176513i	$0.943518\pi$
$360$	2.07828	+	0.825074i	0.109535	+	0.0434852i
$361$		−	5.37757i		−	0.283030i
$362$	8.27365			0.434853
$363$	1.41925	−	1.41925i	0.0744915	−	0.0744915i
$364$	−0.825735	+	0.825735i	−0.0432803	+	0.0432803i
$365$	0.441268	+	1.02230i	0.0230970	+	0.0535098i
$366$	7.19609			0.376145
$367$	−0.221534	+	0.221534i	−0.0115640	+	0.0115640i	−0.712865	−	0.701301i	$-0.752603\pi$
$367$	−0.221534	+	0.221534i	−0.0115640	+	0.0115640i	0.701301	+	0.712865i	$0.252603\pi$
$368$	−2.32324			−0.121107
$369$	8.53277			0.444199
$370$	−10.7363	+	8.35059i	−0.558152	+	0.434127i
$371$	−13.0694			−0.678530
$372$	2.12589			0.110222
$373$	−2.85523	+	2.85523i	−0.147838	+	0.147838i	−0.777152	−	0.629314i	$-0.783336\pi$
$373$	−2.85523	+	2.85523i	−0.147838	+	0.147838i	0.629314	+	0.777152i	$0.283336\pi$
$374$	−12.8493			−0.664424
$375$	−3.81638	+	10.5088i	−0.197077	+	0.542673i
$376$	−4.15173	+	4.15173i	−0.214109	+	0.214109i
$377$	0.444804	−	0.444804i	0.0229086	−	0.0229086i
$378$	2.05956			0.105932
$379$		−	15.3156i		−	0.786711i	−0.919386	−	0.393355i	$-0.871314\pi$
$379$		−	15.3156i		−	0.786711i	0.919386	−	0.393355i	$-0.128686\pi$
$380$	−7.57726	+	3.27066i	−0.388705	+	0.167781i
$381$			11.5446i			0.591449i
$382$	−10.7528	+	10.7528i	−0.550160	+	0.550160i
$383$	−26.5555			−1.35692			−0.678461	−	0.734636i	$-0.737353\pi$
$383$	−26.5555			−1.35692			−0.678461	+	0.734636i	$0.737353\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−15.2493	+	6.58223i	−0.777177	+	0.335462i
$386$	6.97010			0.354769
$387$		−	1.13168i		−	0.0575265i
$388$		−	11.4260i		−	0.580068i
$389$	5.00317	+	5.00317i	0.253671	+	0.253671i	0.822474	−	0.568803i	$-0.192593\pi$
$389$	5.00317	+	5.00317i	0.253671	+	0.253671i	−0.568803	+	0.822474i	$0.692593\pi$
$390$	0.502446	+	1.16404i	0.0254423	+	0.0589433i
$391$		−	8.27723i		−	0.418597i
$392$			2.75821i			0.139311i
$393$	−8.18971			−0.413116
$394$	10.8848	−	10.8848i	0.548369	−	0.548369i
$395$	0.757709	−	0.327058i	0.0381245	−	0.0164561i
$396$	3.60654			0.181235
$397$	12.2545	+	12.2545i	0.615035	+	0.615035i	0.944254	−	0.329219i	$-0.106785\pi$
$397$	12.2545	+	12.2545i	0.615035	+	0.615035i	−0.329219	+	0.944254i	$0.606785\pi$
$398$	0.906486	−	0.906486i	0.0454381	−	0.0454381i
$399$	−5.37510	+	5.37510i	−0.269092	+	0.269092i
$400$	−3.63850	−	3.42947i	−0.181925	−	0.171474i
$401$	−11.3153	−	11.3153i	−0.565059	−	0.565059i	0.365681	−	0.930740i	$-0.380836\pi$
$401$	−11.3153	−	11.3153i	−0.565059	−	0.565059i	−0.930740	+	0.365681i	$0.880836\pi$
$402$	−2.32762			−0.116091
$403$	0.852327	+	0.852327i	0.0424575	+	0.0424575i
$404$			2.80173i			0.139391i
$405$	0.825074	−	2.07828i	0.0409983	−	0.103271i
$406$			2.28495i			0.113400i
$407$	−11.1248	+	18.9077i	−0.551437	+	0.937221i
$408$	−2.51927	−	2.51927i	−0.124723	−	0.124723i
$409$	−20.6313	+	20.6313i	−1.02015	+	1.02015i	−0.0203618	+	0.999793i	$0.506482\pi$
$409$	−20.6313	+	20.6313i	−1.02015	+	1.02015i	−0.999793	+	0.0203618i	$0.993518\pi$
$410$	−17.7335	−	7.04017i	−0.875795	−	0.347689i
$411$			15.5705i			0.768034i
$412$			10.2094i			0.502979i
$413$	16.1412			0.794256
$414$			2.32324i			0.114181i
$415$	−7.34249	+	3.16932i	−0.360429	+	0.155576i
$416$	−0.566998			−0.0277993
$417$	−7.13339	+	7.13339i	−0.349324	+	0.349324i
$418$	−9.41246	+	9.41246i	−0.460378	+	0.460378i
$419$			33.3394i			1.62873i	0.580350	+	0.814367i	$0.302916\pi$
$419$			33.3394i			1.62873i	−0.580350	+	0.814367i	$0.697084\pi$
$420$	−4.28035	−	1.69929i	−0.208859	−	0.0829169i
$421$	18.2239	+	18.2239i	0.888180	+	0.888180i	0.994348	−	0.106169i	$-0.0338583\pi$
$421$	18.2239	+	18.2239i	0.888180	+	0.888180i	−0.106169	+	0.994348i	$0.533858\pi$
$422$	−14.3134			−0.696765
$423$	4.15173	+	4.15173i	0.201864	+	0.201864i
$424$	−4.48711	−	4.48711i	−0.217913	−	0.217913i
$425$	12.2185	−	12.9632i	0.592684	−	0.628809i
$426$	2.53010	−	2.53010i	0.122584	−	0.122584i
$427$	−14.8208			−0.717228
$428$	10.7074	−	10.7074i	0.517561	−	0.517561i
$429$	1.44596	+	1.44596i	0.0698117	+	0.0698117i
$430$	−0.933719	+	2.35195i	−0.0450279	+	0.113421i
$431$	−7.25652	−	7.25652i	−0.349534	−	0.349534i	0.510402	−	0.859936i	$-0.329497\pi$
$431$	−7.25652	−	7.25652i	−0.349534	−	0.349534i	−0.859936	+	0.510402i	$0.829497\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	28.6180	+	28.6180i	1.37529	+	1.37529i	0.852393	+	0.522901i	$0.175150\pi$
$433$	28.6180	+	28.6180i	1.37529	+	1.37529i	0.522901	+	0.852393i	$0.324850\pi$
$434$	−4.37839			−0.210170
$435$	2.30572	+	0.915368i	0.110551	+	0.0438886i
$436$	−2.12012	−	2.12012i	−0.101535	−	0.101535i
$437$	−6.06327	−	6.06327i	−0.290045	−	0.290045i
$438$			0.497960i			0.0237934i
$439$	16.0555	−	16.0555i	0.766287	−	0.766287i	−0.211164	−	0.977451i	$-0.567725\pi$
$439$	16.0555	−	16.0555i	0.766287	−	0.766287i	0.977451	+	0.211164i	$0.0677254\pi$
$440$	−7.49540	−	2.97566i	−0.357329	−	0.141859i
$441$	2.75821			0.131343
$442$		−	2.02009i		−	0.0960861i
$443$	0.486475	−	0.486475i	0.0231131	−	0.0231131i	−0.695456	−	0.718569i	$-0.744797\pi$
$443$	0.486475	−	0.486475i	0.0231131	−	0.0231131i	0.718569	+	0.695456i	$0.244797\pi$
$444$	−5.88825	+	1.52593i	−0.279444	+	0.0724175i
$445$	6.55901	+	15.1955i	0.310927	+	0.720337i
$446$	−9.69983	−	9.69983i	−0.459300	−	0.459300i
$447$	5.72971	+	5.72971i	0.271006	+	0.271006i
$448$	1.45633	−	1.45633i	0.0688051	−	0.0688051i
$449$	23.6298	+	23.6298i	1.11516	+	1.11516i	0.992442	+	0.122716i	$0.0391604\pi$
$449$	23.6298	+	23.6298i	1.11516	+	1.11516i	0.122716	+	0.992442i	$0.460840\pi$
$450$	−3.42947	+	3.63850i	−0.161667	+	0.171521i
$451$	−30.7738			−1.44908
$452$		−	4.98518i		−	0.234483i
$453$	−5.12113	−	5.12113i	−0.240612	−	0.240612i
$454$			14.0497i			0.659387i
$455$	−1.03482	−	2.39740i	−0.0485130	−	0.112392i
$456$	−3.69086			−0.172840
$457$		−	25.3719i		−	1.18685i	−0.804890	−	0.593423i	$-0.797776\pi$
$457$		−	25.3719i		−	1.18685i	0.804890	−	0.593423i	$-0.202224\pi$
$458$		−	17.6048i		−	0.822620i
$459$	−2.51927	+	2.51927i	−0.117590	+	0.117590i
$460$	1.91685	−	4.82835i	0.0893735	−	0.225123i
$461$	15.0045	−	15.0045i	0.698830	−	0.698830i	−0.265328	−	0.964158i	$-0.585480\pi$
$461$	15.0045	−	15.0045i	0.698830	−	0.698830i	0.964158	+	0.265328i	$0.0854803\pi$
$462$	−7.42789			−0.345577
$463$	−30.1885			−1.40298			−0.701488	−	0.712681i	$-0.747481\pi$
$463$	−30.1885			−1.40298			−0.701488	+	0.712681i	$0.747481\pi$
$464$	−0.784491	+	0.784491i	−0.0364191	+	0.0364191i
$465$	−1.75401	+	4.41819i	−0.0813405	+	0.204889i
$466$	2.75919	−	2.75919i	0.127817	−	0.127817i
$467$			4.43185i			0.205082i	0.994729	+	0.102541i	$0.0326972\pi$
$467$			4.43185i			0.205082i	−0.994729	+	0.102541i	$0.967303\pi$
$468$			0.566998i			0.0262095i
$469$	4.79387			0.221360
$470$	−5.20298	−	12.0540i	−0.239996	−	0.556007i
$471$			15.9043i			0.732832i
$472$	5.54174	+	5.54174i	0.255079	+	0.255079i
$473$			4.08144i			0.187665i
$474$	0.369077			0.0169523
$475$	−0.545538	−	18.4462i	−0.0250310	−	0.846371i
$476$	5.18860	+	5.18860i	0.237819	+	0.237819i
$477$	−4.48711	+	4.48711i	−0.205451	+	0.205451i
$478$	1.97901	+	1.97901i	0.0905177	+	0.0905177i
$479$	8.37886	+	8.37886i	0.382840	+	0.382840i	0.872124	−	0.489284i	$-0.162742\pi$
$479$	8.37886	+	8.37886i	0.382840	+	0.382840i	−0.489284	+	0.872124i	$0.662742\pi$
$480$	−0.886151	−	2.05298i	−0.0404471	−	0.0937054i
$481$	−2.97255	−	1.74898i	−0.135537	−	0.0797465i
$482$	−5.52310	+	5.52310i	−0.251570	+	0.251570i
$483$		−	4.78486i		−	0.217719i
$484$	−2.00713			−0.0912331
$485$	23.7465	+	9.42732i	1.07827	+	0.428072i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$			9.23525i			0.418489i	0.977863	+	0.209245i	$0.0671005\pi$
$487$			9.23525i			0.418489i	−0.977863	+	0.209245i	$0.932900\pi$
$488$	−5.08840	−	5.08840i	−0.230341	−	0.230341i
$489$	2.46676	+	2.46676i	0.111551	+	0.111551i
$490$	−5.73234	−	2.27573i	−0.258961	−	0.102807i
$491$	−29.1580			−1.31588			−0.657941	−	0.753069i	$-0.728572\pi$
$491$	−29.1580			−1.31588			−0.657941	+	0.753069i	$0.728572\pi$
$492$	−6.03358	−	6.03358i	−0.272015	−	0.272015i
$493$	−2.79498	−	2.79498i	−0.125879	−	0.125879i
$494$	−1.47977	−	1.47977i	−0.0665779	−	0.0665779i
$495$	−2.97566	+	7.49540i	−0.133746	+	0.336893i
$496$	−1.50323	−	1.50323i	−0.0674970	−	0.0674970i
$497$	−5.21090	+	5.21090i	−0.233741	+	0.233741i
$498$	−3.57650			−0.160267
$499$	3.77024	−	3.77024i	0.168779	−	0.168779i	−0.617664	−	0.786442i	$-0.711921\pi$
$499$	3.77024	−	3.77024i	0.168779	−	0.168779i	0.786442	+	0.617664i	$0.211921\pi$
$500$	10.1294	−	4.73227i	0.453003	−	0.211633i
$501$	9.19275	+	9.19275i	0.410702	+	0.410702i
$502$	12.9548	+	12.9548i	0.578202	+	0.578202i
$503$	36.6383			1.63362			0.816810	−	0.576906i	$-0.195740\pi$
$503$	36.6383			1.63362			0.816810	+	0.576906i	$0.195740\pi$
$504$	−1.45633	−	1.45633i	−0.0648701	−	0.0648701i
$505$	−5.82279	−	2.31164i	−0.259111	−	0.102867i
$506$		−	8.37886i		−	0.372486i
$507$	8.96506	−	8.96506i	0.398152	−	0.398152i
$508$	8.16328	−	8.16328i	0.362187	−	0.362187i
$509$	29.0584			1.28799			0.643996	−	0.765029i	$-0.277275\pi$
$509$	29.0584			1.28799			0.643996	+	0.765029i	$0.277275\pi$
$510$	7.31435	−	3.15717i	0.323885	−	0.139802i
$511$		−	1.02558i		−	0.0453689i
$512$	1.00000			0.0441942
$513$			3.69086i			0.162955i
$514$		−	15.9569i		−	0.703831i
$515$	−21.2179	−	8.42348i	−0.934974	−	0.371183i
$516$	−0.800218	+	0.800218i	−0.0352276	+	0.0352276i
$517$	−14.9734	−	14.9734i	−0.658529	−	0.658529i
$518$	12.1272	−	3.14275i	0.532839	−	0.138084i
$519$			17.5994i			0.772530i
$520$	0.467815	−	1.17838i	0.0205151	−	0.0516754i
$521$		−	20.4068i		−	0.894036i	−0.894525	−	0.447018i	$-0.852486\pi$
$521$		−	20.4068i		−	0.894036i	0.894525	−	0.447018i	$-0.147514\pi$
$522$	0.784491	+	0.784491i	0.0343362	+	0.0343362i
$523$	7.81649			0.341791			0.170896	−	0.985289i	$-0.445334\pi$
$523$	7.81649			0.341791			0.170896	+	0.985289i	$0.445334\pi$
$524$	5.79100	+	5.79100i	0.252981	+	0.252981i
$525$	7.06321	−	7.49372i	0.308264	−	0.327053i
$526$	−18.7568	+	18.7568i	−0.817834	+	0.817834i
$527$	5.35569	−	5.35569i	0.233298	−	0.233298i
$528$	−2.55021	−	2.55021i	−0.110984	−	0.110984i
$529$	−17.6025			−0.765328
$530$	13.0277	−	5.62327i	0.565886	−	0.244259i
$531$	5.54174	−	5.54174i	0.240491	−	0.240491i
$532$	7.60154			0.329569
$533$		−	4.83806i		−	0.209560i
$534$			7.40169i			0.320302i
$535$	13.4186	+	31.0873i	0.580135	+	1.34402i
$536$	1.64587	+	1.64587i	0.0710910	+	0.0710910i
$537$			8.72713i			0.376604i
$538$			23.7613i			1.02442i
$539$	−9.94759			−0.428473
$540$	−2.05298	+	0.886151i	−0.0883463	+	0.0381339i
$541$	−12.4935	+	12.4935i	−0.537139	+	0.537139i	−0.922688	−	0.385548i	$-0.874012\pi$
$541$	−12.4935	+	12.4935i	−0.537139	+	0.537139i	0.385548	+	0.922688i	$0.374012\pi$
$542$	−21.4180			−0.919982
$543$	−5.85035	+	5.85035i	−0.251063	+	0.251063i
$544$			3.56279i			0.152753i
$545$	6.15547	−	2.65695i	0.263671	−	0.113811i
$546$		−	1.16777i		−	0.0499758i
$547$	35.8153			1.53135			0.765675	−	0.643227i	$-0.222405\pi$
$547$	35.8153			1.53135			0.765675	+	0.643227i	$0.222405\pi$
$548$	11.0100	−	11.0100i	0.470323	−	0.470323i
$549$	−5.08840	+	5.08840i	−0.217168	+	0.217168i
$550$	12.3685	−	13.1224i	0.527396	−	0.559542i
$551$	−4.09478			−0.174443
$552$	1.64278	−	1.64278i	0.0699214	−	0.0699214i
$553$	−0.760137			−0.0323243
$554$	13.2073			0.561124
$555$	1.68693	−	13.4965i	0.0716063	−	0.572893i
$556$	10.0881			0.427832
$557$	−27.7893			−1.17747			−0.588734	−	0.808327i	$-0.700374\pi$
$557$	−27.7893			−1.17747			−0.588734	+	0.808327i	$0.700374\pi$
$558$	−1.50323	+	1.50323i	−0.0636368	+	0.0636368i
$559$	−0.641659			−0.0271393
$560$	1.82508	+	4.22824i	0.0771238	+	0.178676i
$561$	9.08586	−	9.08586i	0.383605	−	0.383605i
$562$	3.11380	−	3.11380i	0.131348	−	0.131348i
$563$	−4.47346			−0.188534			−0.0942669	−	0.995547i	$-0.530051\pi$
$563$	−4.47346			−0.188534			−0.0942669	+	0.995547i	$0.530051\pi$
$564$		−	5.87144i		−	0.247232i
$565$	10.3606	+	4.11315i	0.435874	+	0.173041i
$566$			2.74240i			0.115272i
$567$	−1.45633	+	1.45633i	−0.0611601	+	0.0611601i
$568$	−3.57811			−0.150134
$569$	−21.9727	+	21.9727i	−0.921144	+	0.921144i	−0.997110	−	0.0759661i	$-0.975796\pi$
$569$	−21.9727	+	21.9727i	−0.921144	+	0.921144i	0.0759661	+	0.997110i	$0.475796\pi$
$570$	3.04523	−	7.67064i	0.127551	−	0.321288i
$571$	11.4199			0.477906			0.238953	−	0.971031i	$-0.423196\pi$
$571$	11.4199			0.477906			0.238953	+	0.971031i	$0.423196\pi$
$572$		−	2.04490i		−	0.0855015i
$573$		−	15.2067i		−	0.635270i
$574$	12.4265	+	12.4265i	0.518673	+	0.518673i
$575$	8.45313	+	7.96749i	0.352520	+	0.332267i
$576$		−	1.00000i		−	0.0416667i
$577$			10.5104i			0.437555i	0.975775	+	0.218778i	$0.0702069\pi$
$577$			10.5104i			0.437555i	−0.975775	+	0.218778i	$0.929793\pi$
$578$	4.30652			0.179128
$579$	−4.92860	+	4.92860i	−0.204826	+	0.204826i
$580$	−0.983129	−	2.27766i	−0.0408222	−	0.0945745i
$581$	7.36601			0.305594
$582$	8.07942	+	8.07942i	0.334903	+	0.334903i
$583$	16.1829	−	16.1829i	0.670229	−	0.670229i
$584$	0.352111	−	0.352111i	0.0145704	−	0.0145704i
$585$	−1.17838	−	0.467815i	−0.0487200	−	0.0193418i
$586$	−14.1737	−	14.1737i	−0.585511	−	0.585511i
$587$	−28.8278			−1.18985			−0.594925	−	0.803781i	$-0.702818\pi$
$587$	−28.8278			−1.18985			−0.594925	+	0.803781i	$0.702818\pi$
$588$	−1.95035	−	1.95035i	−0.0804310	−	0.0804310i
$589$		−	7.84635i		−	0.323303i
$590$	−16.0896	+	6.94495i	−0.662400	+	0.285919i
$591$			15.3935i			0.633202i
$592$	5.24262	+	3.08463i	0.215470	+	0.126777i
$593$	−28.5378	−	28.5378i	−1.17191	−	1.17191i	−0.981755	−	0.190150i	$-0.939103\pi$
$593$	−28.5378	−	28.5378i	−1.17191	−	1.17191i	−0.190150	−	0.981755i	$-0.560897\pi$
$594$	−2.55021	+	2.55021i	−0.104636	+	0.104636i
$595$	−15.0643	+	6.50239i	−0.617578	+	0.266572i
$596$		−	8.10303i		−	0.331913i
$597$			1.28197i			0.0524673i
$598$	1.31727			0.0538673
$599$		−	18.9390i		−	0.773826i	−0.922116	−	0.386913i	$-0.873541\pi$
$599$		−	18.9390i		−	0.773826i	0.922116	−	0.386913i	$-0.126459\pi$
$600$	4.99781	−	0.147808i	0.204035	−	0.00603423i
$601$	−0.127289			−0.00519224			−0.00259612	−	0.999997i	$-0.500826\pi$
$601$	−0.127289			−0.00519224			−0.00259612	+	0.999997i	$0.500826\pi$
$602$	1.64810	−	1.64810i	0.0671714	−	0.0671714i
$603$	1.64587	−	1.64587i	0.0670252	−	0.0670252i
$604$			7.24237i			0.294688i
$605$	1.65603	−	4.17138i	0.0673272	−	0.169591i
$606$	−1.98112	−	1.98112i	−0.0804777	−	0.0804777i
$607$	−26.8510			−1.08985			−0.544925	−	0.838485i	$-0.683442\pi$
$607$	−26.8510			−1.08985			−0.544925	+	0.838485i	$0.683442\pi$
$608$	2.60983	+	2.60983i	0.105843	+	0.105843i
$609$	−1.61571	−	1.61571i	−0.0654717	−	0.0654717i
$610$	14.7734	−	6.37682i	0.598159	−	0.258190i
$611$	2.35402	−	2.35402i	0.0952335	−	0.0952335i
$612$	3.56279			0.144017
$613$	2.19500	−	2.19500i	0.0886554	−	0.0886554i	−0.661388	−	0.750044i	$-0.730032\pi$
$613$	2.19500	−	2.19500i	0.0886554	−	0.0886554i	0.750044	+	0.661388i	$0.230032\pi$
$614$	−10.5206	−	10.5206i	−0.424579	−	0.424579i
$615$	17.5176	−	7.56133i	0.706379	−	0.304902i
$616$	5.25231	+	5.25231i	0.211622	+	0.211622i
$617$	−20.4982	−	20.4982i	−0.825228	−	0.825228i	0.161625	−	0.986852i	$-0.448327\pi$
$617$	−20.4982	−	20.4982i	−0.825228	−	0.825228i	−0.986852	+	0.161625i	$0.948327\pi$
$618$	−7.21911	−	7.21911i	−0.290395	−	0.290395i
$619$	38.1723			1.53428			0.767138	−	0.641482i	$-0.221680\pi$
$619$	38.1723			1.53428			0.767138	+	0.641482i	$0.221680\pi$
$620$	4.36441	−	1.88386i	0.175279	−	0.0756575i
$621$	−1.64278	−	1.64278i	−0.0659225	−	0.0659225i
$622$	23.6104	+	23.6104i	0.946691	+	0.946691i
$623$		−	15.2442i		−	0.610747i
$624$	0.400928	−	0.400928i	0.0160500	−	0.0160500i
$625$	1.47743	+	24.9563i	0.0590973	+	0.998252i
$626$	31.5356			1.26042
$627$		−	13.3112i		−	0.531599i
$628$	11.2460	−	11.2460i	0.448766	−	0.448766i
$629$	−10.9899	+	18.6784i	−0.438195	+	0.744755i
$630$	4.22824	−	1.82508i	0.168457	−	0.0727130i
$631$	−21.7435	−	21.7435i	−0.865594	−	0.865594i	0.126387	−	0.991981i	$-0.459662\pi$
$631$	−21.7435	−	21.7435i	−0.865594	−	0.865594i	−0.991981	+	0.126387i	$0.959662\pi$
$632$	−0.260977	−	0.260977i	−0.0103811	−	0.0103811i
$633$	10.1211	−	10.1211i	0.402278	−	0.402278i
$634$	−16.4324	−	16.4324i	−0.652613	−	0.652613i
$635$	10.2303	+	23.7009i	0.405976	+	0.940541i
$636$	6.34573			0.251625
$637$		−	1.56390i		−	0.0619639i
$638$	−2.82930	−	2.82930i	−0.112013	−	0.112013i
$639$			3.57811i			0.141548i
$640$	−0.825074	+	2.07828i	−0.0326139	+	0.0821513i
$641$	−8.82193			−0.348445			−0.174223	−	0.984706i	$-0.555741\pi$
$641$	−8.82193			−0.348445			−0.174223	+	0.984706i	$0.555741\pi$
$642$			15.1425i			0.597628i
$643$			44.2809i			1.74627i	0.487480	+	0.873134i	$0.337916\pi$
$643$			44.2809i			1.74627i	−0.487480	+	0.873134i	$0.662084\pi$
$644$	−3.38341	+	3.38341i	−0.133325	+	0.133325i
$645$	−1.00284	−	2.32332i	−0.0394867	−	0.0914805i
$646$	−9.29828	+	9.29828i	−0.365836	+	0.365836i
$647$	31.8355			1.25158			0.625791	−	0.779991i	$-0.284776\pi$
$647$	31.8355			1.25158			0.625791	+	0.779991i	$0.284776\pi$
$648$	−1.00000			−0.0392837
$649$	−19.9865	+	19.9865i	−0.784539	+	0.784539i
$650$	2.06302	+	1.94450i	0.0809184	+	0.0762697i
$651$	3.09599	−	3.09599i	0.121341	−	0.121341i
$652$		−	3.48853i		−	0.136621i
$653$		−	29.8088i		−	1.16651i	−0.812290	−	0.583254i	$-0.801779\pi$
$653$		−	29.8088i		−	1.16651i	0.812290	−	0.583254i	$-0.198221\pi$
$654$	2.99831			0.117243
$655$	−16.8133	+	7.25732i	−0.656951	+	0.283567i
$656$			8.53277i			0.333149i
$657$	−0.352111	−	0.352111i	−0.0137371	−	0.0137371i
$658$			12.0926i			0.471418i
$659$	−40.0379			−1.55965			−0.779827	−	0.625995i	$-0.784693\pi$
$659$	−40.0379			−1.55965			−0.779827	+	0.625995i	$0.784693\pi$
$660$	7.40416	−	3.19594i	0.288207	−	0.124402i
$661$	20.8346	+	20.8346i	0.810373	+	0.810373i	0.984690	−	0.174316i	$-0.0557716\pi$
$661$	20.8346	+	20.8346i	0.810373	+	0.810373i	−0.174316	+	0.984690i	$0.555772\pi$
$662$	−13.7264	+	13.7264i	−0.533491	+	0.533491i
$663$	1.42842	+	1.42842i	0.0554753	+	0.0554753i
$664$	2.52897	+	2.52897i	0.0981429	+	0.0981429i
$665$	−6.27184	+	15.7981i	−0.243211	+	0.612626i
$666$	3.08463	−	5.24262i	0.119527	−	0.203147i
$667$	1.82256	−	1.82256i	0.0705699	−	0.0705699i
$668$		−	13.0005i		−	0.503005i
$669$	13.7176			0.530354
$670$	−4.77856	+	2.06262i	−0.184612	+	0.0796860i
$671$	18.3515	−	18.3515i	0.708453	−	0.708453i
$672$			2.05956i			0.0794493i
$673$	−16.7404	−	16.7404i	−0.645295	−	0.645295i	0.306557	−	0.951852i	$-0.400823\pi$
$673$	−16.7404	−	16.7404i	−0.645295	−	0.645295i	−0.951852	+	0.306557i	$0.900823\pi$
$674$	−17.9668	−	17.9668i	−0.692056	−	0.692056i
$675$	−0.147808	−	4.99781i	−0.00568913	−	0.192366i
$676$	−12.6785			−0.487635
$677$	−4.30980	−	4.30980i	−0.165639	−	0.165639i	0.619420	−	0.785059i	$-0.287368\pi$
$677$	−4.30980	−	4.30980i	−0.165639	−	0.165639i	−0.785059	+	0.619420i	$0.787368\pi$
$678$	3.52506	+	3.52506i	0.135379	+	0.135379i
$679$	−16.6400	−	16.6400i	−0.638586	−	0.638586i
$680$	−7.40448	−	2.93957i	−0.283949	−	0.112727i
$681$	−9.93466	−	9.93466i	−0.380697	−	0.380697i
$682$	5.42146	−	5.42146i	0.207598	−	0.207598i
$683$	36.6278			1.40152			0.700762	−	0.713395i	$-0.252843\pi$
$683$	36.6278			1.40152			0.700762	+	0.713395i	$0.252843\pi$
$684$	2.60983	−	2.60983i	0.0997894	−	0.0997894i
$685$	13.7978	+	31.9659i	0.527186	+	1.22135i
$686$	14.2112	+	14.2112i	0.542585	+	0.542585i
$687$	12.4485	+	12.4485i	0.474940	+	0.474940i
$688$	1.13168			0.0431448
$689$	2.54418	+	2.54418i	0.0969255	+	0.0969255i
$690$	2.05874	+	4.76957i	0.0783750	+	0.181575i
$691$			31.0649i			1.18177i	0.806757	+	0.590883i	$0.201220\pi$
$691$			31.0649i			1.18177i	−0.806757	+	0.590883i	$0.798780\pi$
$692$	12.4447	−	12.4447i	0.473076	−	0.473076i
$693$	5.25231	−	5.25231i	0.199519	−	0.199519i
$694$	−1.20902			−0.0458939
$695$	−8.32346	+	20.9660i	−0.315727	+	0.795285i
$696$		−	1.10944i		−	0.0420531i
$697$	−30.4005			−1.15150
$698$		−	26.9158i		−	1.01878i
$699$			3.90208i			0.147590i
$700$	−10.2933	+	0.304419i	−0.389050	+	0.0115060i
$701$	−11.6605	+	11.6605i	−0.440411	+	0.440411i	−0.892150	−	0.451739i	$-0.850804\pi$
$701$	−11.6605	+	11.6605i	−0.440411	+	0.440411i	0.451739	+	0.892150i	$0.350804\pi$
$702$	−0.400928	−	0.400928i	−0.0151320	−	0.0151320i
$703$	5.63200	+	21.7327i	0.212415	+	0.819664i
$704$			3.60654i			0.135927i
$705$	12.2025	+	4.84437i	0.459573	+	0.182450i
$706$			13.0238i			0.490157i
$707$	4.08025	+	4.08025i	0.153453	+	0.153453i
$708$	−7.83720			−0.294540
$709$	12.6150	+	12.6150i	0.473768	+	0.473768i	0.903132	−	0.429364i	$-0.141262\pi$
$709$	12.6150	+	12.6150i	0.473768	+	0.473768i	−0.429364	+	0.903132i	$0.641262\pi$
$710$	2.95220	−	7.43631i	0.110794	−	0.279080i
$711$	−0.260977	+	0.260977i	−0.00978740	+	0.00978740i
$712$	5.23378	−	5.23378i	0.196144	−	0.196144i
$713$	3.49237	+	3.49237i	0.130790	+	0.130790i
$714$	−7.33778			−0.274610
$715$	4.24988	+	1.68719i	0.158936	+	0.0630975i
$716$	6.17102	−	6.17102i	0.230622	−	0.230622i
$717$	−2.79874			−0.104521
$718$			6.68890i			0.249628i
$719$			15.6860i			0.584988i	0.956267	+	0.292494i	$0.0944852\pi$
$719$			15.6860i			0.584988i	−0.956267	+	0.292494i	$0.905515\pi$
$720$	2.07828	+	0.825074i	0.0774530	+	0.0307487i
$721$	14.8682	+	14.8682i	0.553721	+	0.553721i
$722$		−	5.37757i		−	0.200133i
$723$		−	7.81085i		−	0.290488i
$724$	8.27365			0.307488
$725$	5.54476	−	0.163984i	0.205927	−	0.00609020i
$726$	1.41925	−	1.41925i	0.0526735	−	0.0526735i
$727$	44.2369			1.64065			0.820327	−	0.571894i	$-0.193791\pi$
$727$	44.2369			1.64065			0.820327	+	0.571894i	$0.193791\pi$
$728$	−0.825735	+	0.825735i	−0.0306038	+	0.0306038i
$729$			1.00000i			0.0370370i
$730$	0.441268	+	1.02230i	0.0163320	+	0.0378371i
$731$			4.03193i			0.149126i
$732$	7.19609			0.265975
$733$	−27.8801	+	27.8801i	−1.02977	+	1.02977i	−0.0302314	+	0.999543i	$0.509624\pi$
$733$	−27.8801	+	27.8801i	−1.02977	+	1.02977i	−0.999543	+	0.0302314i	$0.990376\pi$
$734$	−0.221534	+	0.221534i	−0.00817696	+	0.00817696i
$735$	5.66256	−	2.44419i	0.208867	−	0.0901553i
$736$	−2.32324			−0.0856358
$737$	−5.93591	+	5.93591i	−0.218652	+	0.218652i
$738$	8.53277			0.314096
$739$	44.3607			1.63183			0.815917	−	0.578169i	$-0.196232\pi$
$739$	44.3607			1.63183			0.815917	+	0.578169i	$0.196232\pi$
$740$	−10.7363	+	8.35059i	−0.394673	+	0.306974i
$741$	2.09271			0.0768775
$742$	−13.0694			−0.479793
$743$	−7.56548	+	7.56548i	−0.277551	+	0.277551i	−0.832131	−	0.554580i	$-0.812879\pi$
$743$	−7.56548	+	7.56548i	−0.277551	+	0.277551i	0.554580	+	0.832131i	$0.312879\pi$
$744$	2.12589			0.0779388
$745$	16.8404	+	6.68560i	0.616984	+	0.244942i
$746$	−2.85523	+	2.85523i	−0.104537	+	0.104537i
$747$	2.52897	−	2.52897i	0.0925300	−	0.0925300i
$748$	−12.8493			−0.469819
$749$		−	31.1869i		−	1.13955i
$750$	−3.81638	+	10.5088i	−0.139355	+	0.383728i
$751$		−	5.20586i		−	0.189964i	−0.995479	−	0.0949822i	$-0.969721\pi$
$751$		−	5.20586i		−	0.189964i	0.995479	−	0.0949822i	$-0.0302794\pi$
$752$	−4.15173	+	4.15173i	−0.151398	+	0.151398i
$753$	−18.3209			−0.667650
$754$	0.444804	−	0.444804i	0.0161988	−	0.0161988i
$755$	−15.0517	−	5.97549i	−0.547786	−	0.217470i
$756$	2.05956			0.0749055
$757$			27.0653i			0.983705i	0.870678	+	0.491853i	$0.163680\pi$
$757$			27.0653i			0.983705i	−0.870678	+	0.491853i	$0.836320\pi$
$758$		−	15.3156i		−	0.556289i
$759$	5.92475	+	5.92475i	0.215055	+	0.215055i
$760$	−7.57726	+	3.27066i	−0.274856	+	0.118639i
$761$			1.85691i			0.0673130i	0.999433	+	0.0336565i	$0.0107152\pi$
$761$			1.85691i			0.0673130i	−0.999433	+	0.0336565i	$0.989285\pi$
$762$			11.5446i			0.418217i
$763$	−6.17519			−0.223557
$764$	−10.7528	+	10.7528i	−0.389022	+	0.389022i
$765$	−2.93957	+	7.40448i	−0.106280	+	0.267710i
$766$	−26.5555			−0.959489
$767$	−3.14215	−	3.14215i	−0.113457	−	0.113457i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−20.3839	+	20.3839i	−0.735061	+	0.735061i	−0.971618	−	0.236557i	$-0.923981\pi$
$769$	−20.3839	+	20.3839i	−0.735061	+	0.735061i	0.236557	+	0.971618i	$0.423981\pi$
$770$	−15.2493	+	6.58223i	−0.549547	+	0.237207i
$771$	11.2833	+	11.2833i	0.406357	+	0.406357i
$772$	6.97010			0.250859
$773$	−29.3204	−	29.3204i	−1.05458	−	1.05458i	−0.998422	−	0.0561599i	$-0.982114\pi$
$773$	−29.3204	−	29.3204i	−1.05458	−	1.05458i	−0.0561599	−	0.998422i	$-0.517886\pi$
$774$		−	1.13168i		−	0.0406774i
$775$	0.314223	+	10.6248i	0.0112872	+	0.381654i
$776$		−	11.4260i		−	0.410170i
$777$	−6.35298	+	10.7975i	−0.227912	+	0.387358i
$778$	5.00317	+	5.00317i	0.179373	+	0.179373i
$779$	−22.2691	+	22.2691i	−0.797873	+	0.797873i
$780$	0.502446	+	1.16404i	0.0179904	+	0.0416792i
$781$		−	12.9046i		−	0.461762i
$782$		−	8.27723i		−	0.295993i
$783$	−1.10944			−0.0396481
$784$			2.75821i			0.0985075i
$785$	14.0936	+	32.6513i	0.503023	+	1.16537i
$786$	−8.18971			−0.292117
$787$	26.3563	−	26.3563i	0.939502	−	0.939502i	−0.0587699	−	0.998272i	$-0.518718\pi$
$787$	26.3563	−	26.3563i	0.939502	−	0.939502i	0.998272	+	0.0587699i	$0.0187178\pi$
$788$	10.8848	−	10.8848i	0.387756	−	0.387756i
$789$		−	26.5261i		−	0.944353i
$790$	0.757709	−	0.327058i	0.0269581	−	0.0116362i
$791$	−7.26007	−	7.26007i	−0.258138	−	0.258138i
$792$	3.60654			0.128153
$793$	2.88511	+	2.88511i	0.102453	+	0.102453i
$794$	12.2545	+	12.2545i	0.434895	+	0.434895i
$795$	−5.23570	+	13.1882i	−0.185691	+	0.467738i
$796$	0.906486	−	0.906486i	0.0321296	−	0.0321296i
$797$	−39.8958			−1.41318			−0.706591	−	0.707622i	$-0.749768\pi$
$797$	−39.8958			−1.41318			−0.706591	+	0.707622i	$0.749768\pi$
$798$	−5.37510	+	5.37510i	−0.190277	+	0.190277i
$799$	−14.7918	−	14.7918i	−0.523295	−	0.523295i
$800$	−3.63850	−	3.42947i	−0.128641	−	0.121250i
$801$	−5.23378	−	5.23378i	−0.184927	−	0.184927i
$802$	−11.3153	−	11.3153i	−0.399557	−	0.399557i
$803$	1.26990	+	1.26990i	0.0448138	+	0.0448138i
$804$	−2.32762			−0.0820888
$805$	−4.24011	−	9.82323i	−0.149444	−	0.346223i
$806$	0.852327	+	0.852327i	0.0300220	+	0.0300220i
$807$	−16.8018	−	16.8018i	−0.591451	−	0.591451i
$808$			2.80173i			0.0985646i
$809$	−3.79166	+	3.79166i	−0.133308	+	0.133308i	−0.770612	−	0.637305i	$-0.780049\pi$
$809$	−3.79166	+	3.79166i	−0.133308	+	0.133308i	0.637305	+	0.770612i	$0.280049\pi$
$810$	0.825074	−	2.07828i	0.0289902	−	0.0730234i
$811$	31.9155			1.12070			0.560352	−	0.828255i	$-0.310666\pi$
$811$	31.9155			1.12070			0.560352	+	0.828255i	$0.310666\pi$
$812$			2.28495i			0.0801862i
$813$	15.1448	−	15.1448i	0.531152	−	0.531152i
$814$	−11.1248	+	18.9077i	−0.389925	+	0.662715i
$815$	7.25014	+	2.87830i	0.253961	+	0.100822i
$816$	−2.51927	−	2.51927i	−0.0881922	−	0.0881922i
$817$	2.95349	+	2.95349i	0.103330	+	0.103330i
$818$	−20.6313	+	20.6313i	−0.721358	+	0.721358i
$819$	0.825735	+	0.825735i	0.0288535	+	0.0288535i
$820$	−17.7335	−	7.04017i	−0.619281	−	0.245854i
$821$	−41.6214			−1.45260			−0.726298	−	0.687380i	$-0.758761\pi$
$821$	−41.6214			−1.45260			−0.726298	+	0.687380i	$0.758761\pi$
$822$			15.5705i			0.543082i
$823$	−12.1965	−	12.1965i	−0.425142	−	0.425142i	0.461828	−	0.886970i	$-0.347194\pi$
$823$	−12.1965	−	12.1965i	−0.425142	−	0.425142i	−0.886970	+	0.461828i	$0.847194\pi$
$824$			10.2094i			0.355660i
$825$	0.533075	+	18.0248i	0.0185593	+	0.627544i
$826$	16.1412			0.561624
$827$		−	44.3537i		−	1.54233i	−0.636635	−	0.771165i	$-0.719674\pi$
$827$		−	44.3537i		−	1.54233i	0.636635	−	0.771165i	$-0.280326\pi$
$828$			2.32324i			0.0807382i
$829$	−15.9798	+	15.9798i	−0.555003	+	0.555003i	−0.927880	−	0.372878i	$-0.878371\pi$
$829$	−15.9798	+	15.9798i	−0.555003	+	0.555003i	0.372878	+	0.927880i	$0.378371\pi$
$830$	−7.34249	+	3.16932i	−0.254861	+	0.110009i
$831$	−9.33897	+	9.33897i	−0.323965	+	0.323965i
$832$	−0.566998			−0.0196571
$833$	−9.82693			−0.340483
$834$	−7.13339	+	7.13339i	−0.247009	+	0.247009i
$835$	27.0187	+	10.7264i	0.935021	+	0.371202i
$836$	−9.41246	+	9.41246i	−0.325537	+	0.325537i
$837$		−	2.12589i		−	0.0734814i
$838$			33.3394i			1.15169i
$839$	−16.0448			−0.553926			−0.276963	−	0.960881i	$-0.589328\pi$
$839$	−16.0448			−0.553926			−0.276963	+	0.960881i	$0.589328\pi$
$840$	−4.28035	−	1.69929i	−0.147686	−	0.0586311i
$841$			27.7691i			0.957557i
$842$	18.2239	+	18.2239i	0.628038	+	0.628038i
$843$			4.40357i			0.151667i
$844$	−14.3134			−0.492687
$845$	10.4607	−	26.3495i	0.359860	−	0.906451i
$846$	4.15173	+	4.15173i	0.142739	+	0.142739i
$847$	−2.92304	+	2.92304i	−0.100437	+	0.100437i
$848$	−4.48711	−	4.48711i	−0.154088	−	0.154088i
$849$	−1.93917	−	1.93917i	−0.0665522	−	0.0665522i
$850$	12.2185	−	12.9632i	0.419091	−	0.444635i
$851$	−12.1799	−	7.16634i	−0.417521	−	0.245659i
$852$	2.53010	−	2.53010i	0.0866799	−	0.0866799i
$853$		−	9.09546i		−	0.311423i	−0.987803	−	0.155711i	$-0.950233\pi$
$853$		−	9.09546i		−	0.311423i	0.987803	−	0.155711i	$-0.0497670\pi$
$854$	−14.8208			−0.507157
$855$	3.27066	+	7.57726i	0.111854	+	0.259137i
$856$	10.7074	−	10.7074i	0.365971	−	0.365971i
$857$		−	4.89927i		−	0.167356i	−0.996493	−	0.0836779i	$-0.973333\pi$
$857$		−	4.89927i		−	0.167356i	0.996493	−	0.0836779i	$-0.0266667\pi$
$858$	1.44596	+	1.44596i	0.0493643	+	0.0493643i
$859$	−17.1060	−	17.1060i	−0.583648	−	0.583648i	0.352256	−	0.935904i	$-0.385415\pi$
$859$	−17.1060	−	17.1060i	−0.583648	−	0.583648i	−0.935904	+	0.352256i	$0.885415\pi$
$860$	−0.933719	+	2.35195i	−0.0318396	+	0.0802007i
$861$	−17.5738			−0.598912
$862$	−7.25652	−	7.25652i	−0.247158	−	0.247158i
$863$	1.19926	+	1.19926i	0.0408233	+	0.0408233i	0.727224	−	0.686400i	$-0.240810\pi$
$863$	1.19926	+	1.19926i	0.0408233	+	0.0408233i	−0.686400	+	0.727224i	$0.740810\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	15.5958	+	36.1313i	0.530272	+	1.22850i
$866$	28.6180	+	28.6180i	0.972480	+	0.972480i
$867$	−3.04517	+	3.04517i	−0.103419	+	0.103419i
$868$	−4.37839			−0.148612
$869$	0.941224	−	0.941224i	0.0319288	−	0.0319288i
$870$	2.30572	+	0.915368i	0.0781713	+	0.0310339i
$871$	−0.933207	−	0.933207i	−0.0316205	−	0.0316205i
$872$	−2.12012	−	2.12012i	−0.0717964	−	0.0717964i
$873$	−11.4260			−0.386712
$874$	−6.06327	−	6.06327i	−0.205093	−	0.205093i
$875$	7.86007	−	21.6435i	0.265719	−	0.731685i
$876$			0.497960i			0.0168245i
$877$	8.67517	−	8.67517i	0.292940	−	0.292940i	−0.545301	−	0.838240i	$-0.683585\pi$
$877$	8.67517	−	8.67517i	0.292940	−	0.292940i	0.838240	+	0.545301i	$0.183585\pi$
$878$	16.0555	−	16.0555i	0.541847	−	0.541847i
$879$	20.0447			0.676090
$880$	−7.49540	−	2.97566i	−0.252670	−	0.100310i
$881$		−	47.7941i		−	1.61022i	−0.593123	−	0.805112i	$-0.702105\pi$
$881$		−	47.7941i		−	1.61022i	0.593123	−	0.805112i	$-0.297895\pi$
$882$	2.75821			0.0928738
$883$			13.3347i			0.448747i	0.974503	+	0.224374i	$0.0720336\pi$
$883$			13.3347i			0.448747i	−0.974503	+	0.224374i	$0.927966\pi$
$884$		−	2.02009i		−	0.0679431i
$885$	6.46628	−	16.2879i	0.217361	−	0.547512i
$886$	0.486475	−	0.486475i	0.0163435	−	0.0163435i
$887$	32.7918	+	32.7918i	1.10104	+	1.10104i	0.994285	+	0.106755i	$0.0340461\pi$
$887$	32.7918	+	32.7918i	1.10104	+	1.10104i	0.106755	+	0.994285i	$0.465954\pi$
$888$	−5.88825	+	1.52593i	−0.197597	+	0.0512069i
$889$		−	23.7768i		−	0.797450i
$890$	6.55901	+	15.1955i	0.219859	+	0.509356i
$891$		−	3.60654i		−	0.120824i
$892$	−9.69983	−	9.69983i	−0.324774	−	0.324774i
$893$	−21.6706			−0.725180
$894$	5.72971	+	5.72971i	0.191630	+	0.191630i
$895$	7.73356	+	17.9167i	0.258504	+	0.598888i
$896$	1.45633	−	1.45633i	0.0486525	−	0.0486525i
$897$	−0.931452	+	0.931452i	−0.0311003	+	0.0311003i
$898$	23.6298	+	23.6298i	0.788536	+	0.788536i
$899$	2.35854			0.0786617
$900$	−3.42947	+	3.63850i	−0.114316	+	0.121283i
$901$	15.9866	−	15.9866i	0.532592	−	0.532592i
$902$	−30.7738			−1.02466
$903$			2.33076i			0.0775629i
$904$		−	4.98518i		−	0.165805i
$905$	−6.82637	+	17.1950i	−0.226916	+	0.571580i
$906$	−5.12113	−	5.12113i	−0.170138	−	0.170138i
$907$			4.02073i			0.133506i	0.997770	+	0.0667530i	$0.0212640\pi$
$907$			4.02073i			0.133506i	−0.997770	+	0.0667530i	$0.978736\pi$
$908$			14.0497i			0.466257i
$909$	2.80173			0.0929276
$910$	−1.03482	−	2.39740i	−0.0343038	−	0.0794731i
$911$	30.6544	−	30.6544i	1.01563	−	1.01563i	0.0157497	−	0.999876i	$-0.494987\pi$
$911$	30.6544	−	30.6544i	1.01563	−	1.01563i	0.999876	−	0.0157497i	$-0.00501349\pi$
$912$	−3.69086			−0.122216
$913$	−9.12082	+	9.12082i	−0.301855	+	0.301855i
$914$		−	25.3719i		−	0.839227i
$915$	−5.93731	+	14.9555i	−0.196281	+	0.494413i
$916$		−	17.6048i		−	0.581680i
$917$	16.8672			0.557004
$918$	−2.51927	+	2.51927i	−0.0831484	+	0.0831484i
$919$	30.5298	−	30.5298i	1.00708	−	1.00708i	0.00711010	−	0.999975i	$-0.497737\pi$
$919$	30.5298	−	30.5298i	1.00708	−	1.00708i	0.999975	−	0.00711010i	$-0.00226324\pi$
$920$	1.91685	−	4.82835i	0.0631966	−	0.159186i
$921$	14.8784			0.490261
$922$	15.0045	−	15.0045i	0.494148	−	0.494148i
$923$	2.02878			0.0667780
$924$	−7.42789			−0.244360
$925$	−8.49666	−	29.2029i	−0.279368	−	0.960184i
$926$	−30.1885			−0.992054
$927$	10.2094			0.335320
$928$	−0.784491	+	0.784491i	−0.0257522	+	0.0257522i
$929$	−41.1786			−1.35103			−0.675513	−	0.737348i	$-0.736078\pi$
$929$	−41.1786			−1.35103			−0.675513	+	0.737348i	$0.736078\pi$
$930$	−1.75401	+	4.41819i	−0.0575164	+	0.144878i
$931$	−7.19846	+	7.19846i	−0.235920	+	0.235920i
$932$	2.75919	−	2.75919i	0.0903802	−	0.0903802i
$933$	−33.3902			−1.09314
$934$			4.43185i			0.145015i
$935$	10.6017	−	26.7046i	0.346712	−	0.873332i
$936$			0.566998i			0.0185329i
$937$	41.8558	−	41.8558i	1.36737	−	1.36737i	0.503200	−	0.864170i	$-0.332156\pi$
$937$	41.8558	−	41.8558i	1.36737	−	1.36737i	0.864170	−	0.503200i	$-0.167844\pi$
$938$	4.79387			0.156525
$939$	−22.2991	+	22.2991i	−0.727703	+	0.727703i
$940$	−5.20298	−	12.0540i	−0.169702	−	0.393157i
$941$	11.0609			0.360576			0.180288	−	0.983614i	$-0.442297\pi$
$941$	11.0609			0.360576			0.180288	+	0.983614i	$0.442297\pi$
$942$			15.9043i			0.518190i
$943$		−	19.8237i		−	0.645548i
$944$	5.54174	+	5.54174i	0.180368	+	0.180368i
$945$	−1.69929	+	4.28035i	−0.0552779	+	0.139240i
$946$			4.08144i			0.132699i
$947$			31.1637i			1.01268i	0.862333	+	0.506341i	$0.169002\pi$
$947$			31.1637i			1.01268i	−0.862333	+	0.506341i	$0.830998\pi$
$948$	0.369077			0.0119871
$949$	−0.199646	+	0.199646i	−0.00648078	+	0.00648078i
$950$	−0.545538	−	18.4462i	−0.0176996	−	0.598474i
$951$	23.2389			0.753572
$952$	5.18860	+	5.18860i	0.168163	+	0.168163i
$953$	−1.82567	+	1.82567i	−0.0591394	+	0.0591394i	−0.736058	−	0.676919i	$-0.763315\pi$
$953$	−1.82567	+	1.82567i	−0.0591394	+	0.0591394i	0.676919	+	0.736058i	$0.263315\pi$
$954$	−4.48711	+	4.48711i	−0.145275	+	0.145275i
$955$	−13.4755	−	31.2191i	−0.436055	−	1.01023i
$956$	1.97901	+	1.97901i	0.0640057	+	0.0640057i
$957$	4.00123			0.129341
$958$	8.37886	+	8.37886i	0.270709	+	0.270709i
$959$		−	32.0683i		−	1.03554i
$960$	−0.886151	−	2.05298i	−0.0286004	−	0.0662597i
$961$		−	26.4806i		−	0.854213i
$962$	−2.97255	−	1.74898i	−0.0958390	−	0.0563893i
$963$	−10.7074	−	10.7074i	−0.345041	−	0.345041i
$964$	−5.52310	+	5.52310i	−0.177887	+	0.177887i
$965$	−5.75085	+	14.4858i	−0.185126	+	0.466315i
$966$		−	4.78486i		−	0.153950i
$967$		−	27.6923i		−	0.890524i	−0.895400	−	0.445262i	$-0.853111\pi$
$967$		−	27.6923i		−	0.890524i	0.895400	−	0.445262i	$-0.146889\pi$
$968$	−2.00713			−0.0645116
$969$		−	13.1498i		−	0.422431i
$970$	23.7465	+	9.42732i	0.762454	+	0.302693i
$971$	−37.8952			−1.21611			−0.608057	−	0.793894i	$-0.708051\pi$
$971$	−37.8952			−1.21611			−0.608057	+	0.793894i	$0.708051\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	14.6916	−	14.6916i	0.470993	−	0.470993i
$974$			9.23525i			0.295917i
$975$	−2.83375	+	0.0838068i	−0.0907526	+	0.00268396i
$976$	−5.08840	−	5.08840i	−0.162876	−	0.162876i
$977$	17.9170			0.573215			0.286607	−	0.958048i	$-0.407472\pi$
$977$	17.9170			0.573215			0.286607	+	0.958048i	$0.407472\pi$
$978$	2.46676	+	2.46676i	0.0788784	+	0.0788784i
$979$	18.8759	+	18.8759i	0.603275	+	0.603275i
$980$	−5.73234	−	2.27573i	−0.183113	−	0.0726955i
$981$	−2.12012	+	2.12012i	−0.0676903	+	0.0676903i
$982$	−29.1580			−0.930469
$983$	3.29763	−	3.29763i	0.105178	−	0.105178i	−0.652559	−	0.757738i	$-0.726305\pi$
$983$	3.29763	−	3.29763i	0.105178	−	0.105178i	0.757738	+	0.652559i	$0.226305\pi$
$984$	−6.03358	−	6.03358i	−0.192344	−	0.192344i
$985$	13.6409	+	31.6025i	0.434636	+	1.00694i
$986$	−2.79498	−	2.79498i	−0.0890102	−	0.0890102i
$987$	−8.55074	−	8.55074i	−0.272173	−	0.272173i
$988$	−1.47977	−	1.47977i	−0.0470777	−	0.0470777i
$989$	−2.62916			−0.0836025
$990$	−2.97566	+	7.49540i	−0.0945728	+	0.238220i
$991$	−4.92794	−	4.92794i	−0.156541	−	0.156541i	0.624491	−	0.781032i	$-0.285307\pi$
$991$	−4.92794	−	4.92794i	−0.156541	−	0.156541i	−0.781032	+	0.624491i	$0.785307\pi$
$992$	−1.50323	−	1.50323i	−0.0477276	−	0.0477276i
$993$		−	19.4120i		−	0.616022i
$994$	−5.21090	+	5.21090i	−0.165280	+	0.165280i
$995$	1.13601	+	2.63185i	0.0360141	+	0.0834353i
$996$	−3.57650			−0.113326
$997$			39.1924i			1.24124i	0.784113	+	0.620618i	$0.213118\pi$
$997$			39.1924i			1.24124i	−0.784113	+	0.620618i	$0.786882\pi$
$998$	3.77024	−	3.77024i	0.119345	−	0.119345i
$999$	1.52593	+	5.88825i	0.0482783	+	0.186296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.b.253.4	yes	40
5.2	odd	4		1110.2.l.b.697.17	yes	40
37.6	odd	4		1110.2.l.b.43.17	✓	40
185.117	even	4	inner	1110.2.o.b.487.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.17	✓	40	37.6	odd	4
1110.2.l.b.697.17	yes	40	5.2	odd	4
1110.2.o.b.253.4	yes	40	1.1	even	1	trivial
1110.2.o.b.487.4	yes	40	185.117	even	4	inner

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.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.825074 + 2.07828i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.45633 - 1.45633i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.825074 + 2.07828i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.45633 - 1.45633i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-0.825074 + 2.07828i) q^{10} +3.60654i q^{11} +(-0.707107 + 0.707107i) q^{12} -0.566998 q^{13} +(1.45633 - 1.45633i) q^{14} +(-0.886151 - 2.05298i) q^{15} +1.00000 q^{16} +3.56279i q^{17} -1.00000i q^{18} +(2.60983 + 2.60983i) q^{19} +(-0.825074 + 2.07828i) q^{20} +2.05956i q^{21} +3.60654i q^{22} -2.32324 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-3.63850 - 3.42947i) q^{25} -0.566998 q^{26} +(0.707107 + 0.707107i) q^{27} +(1.45633 - 1.45633i) q^{28} +(-0.784491 + 0.784491i) q^{29} +(-0.886151 - 2.05298i) q^{30} +(-1.50323 - 1.50323i) q^{31} +1.00000 q^{32} +(-2.55021 - 2.55021i) q^{33} +3.56279i q^{34} +(1.82508 + 4.22824i) q^{35} -1.00000i q^{36} +(5.24262 + 3.08463i) q^{37} +(2.60983 + 2.60983i) q^{38} +(0.400928 - 0.400928i) q^{39} +(-0.825074 + 2.07828i) q^{40} +8.53277i q^{41} +2.05956i q^{42} +1.13168 q^{43} +3.60654i q^{44} +(2.07828 + 0.825074i) q^{45} -2.32324 q^{46} +(-4.15173 + 4.15173i) q^{47} +(-0.707107 + 0.707107i) q^{48} +2.75821i q^{49} +(-3.63850 - 3.42947i) q^{50} +(-2.51927 - 2.51927i) q^{51} -0.566998 q^{52} +(-4.48711 - 4.48711i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-7.49540 - 2.97566i) q^{55} +(1.45633 - 1.45633i) q^{56} -3.69086 q^{57} +(-0.784491 + 0.784491i) q^{58} +(5.54174 + 5.54174i) q^{59} +(-0.886151 - 2.05298i) q^{60} +(-5.08840 - 5.08840i) q^{61} +(-1.50323 - 1.50323i) q^{62} +(-1.45633 - 1.45633i) q^{63} +1.00000 q^{64} +(0.467815 - 1.17838i) q^{65} +(-2.55021 - 2.55021i) q^{66} +(1.64587 + 1.64587i) q^{67} +3.56279i q^{68} +(1.64278 - 1.64278i) q^{69} +(1.82508 + 4.22824i) q^{70} -3.57811 q^{71} -1.00000i q^{72} +(0.352111 - 0.352111i) q^{73} +(5.24262 + 3.08463i) q^{74} +(4.99781 - 0.147808i) q^{75} +(2.60983 + 2.60983i) q^{76} +(5.25231 + 5.25231i) q^{77} +(0.400928 - 0.400928i) q^{78} +(-0.260977 - 0.260977i) q^{79} +(-0.825074 + 2.07828i) q^{80} -1.00000 q^{81} +8.53277i q^{82} +(2.52897 + 2.52897i) q^{83} +2.05956i q^{84} +(-7.40448 - 2.93957i) q^{85} +1.13168 q^{86} -1.10944i q^{87} +3.60654i q^{88} +(5.23378 - 5.23378i) q^{89} +(2.07828 + 0.825074i) q^{90} +(-0.825735 + 0.825735i) q^{91} -2.32324 q^{92} +2.12589 q^{93} +(-4.15173 + 4.15173i) q^{94} +(-7.57726 + 3.27066i) q^{95} +(-0.707107 + 0.707107i) q^{96} -11.4260i q^{97} +2.75821i q^{98} +3.60654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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