LMFDB - Embedded newform 1110.2.l.b.43.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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, 3]))

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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			43.17
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.b.697.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.07828	−	0.825074i	−0.929436	−	0.368984i
$5$	−2.07828	−	0.825074i	−0.929436	−	0.368984i
$6$	−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	$0.122744\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−0.825074	+	2.07828i	−0.260911	+	0.657210i
$11$		−	3.60654i		−	1.08741i	−0.839276	−	0.543706i	$-0.817021\pi$
$11$		−	3.60654i		−	1.08741i	0.839276	−	0.543706i	$-0.182979\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$		−	0.566998i		−	0.157257i	−0.996904	−	0.0786284i	$-0.974946\pi$
$13$		−	0.566998i		−	0.157257i	0.996904	−	0.0786284i	$-0.0250541\pi$
$14$	−1.45633	−	1.45633i	−0.389220	−	0.389220i
$15$	−2.05298	+	0.886151i	−0.530078	+	0.228803i
$16$	1.00000			0.250000
$17$	−3.56279			−0.864104			−0.432052	−	0.901849i	$-0.642210\pi$
$17$	−3.56279			−0.864104			−0.432052	+	0.901849i	$0.642210\pi$
$18$	−1.00000			−0.235702
$19$	−2.60983	+	2.60983i	−0.598736	+	0.598736i	−0.939976	−	0.341240i	$-0.889153\pi$
$19$	−2.60983	+	2.60983i	−0.598736	+	0.598736i	0.341240	+	0.939976i	$0.389153\pi$
$20$	2.07828	+	0.825074i	0.464718	+	0.184492i
$21$		−	2.05956i		−	0.449433i
$22$	−3.60654			−0.768917
$23$		−	2.32324i		−	0.484429i	−0.970223	−	0.242215i	$-0.922126\pi$
$23$		−	2.32324i		−	0.484429i	0.970223	−	0.242215i	$-0.0778738\pi$
$24$	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	$-0.217153\pi$
$29$	0.784491	+	0.784491i	0.145676	+	0.145676i	−0.630507	+	0.776183i	$0.717153\pi$
$30$	0.886151	+	2.05298i	0.161788	+	0.374822i
$31$	−1.50323	+	1.50323i	−0.269988	+	0.269988i	−0.829095	−	0.559107i	$-0.811144\pi$
$31$	−1.50323	+	1.50323i	−0.269988	+	0.269988i	0.559107	+	0.829095i	$0.311144\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.55021	−	2.55021i	−0.443934	−	0.443934i
$34$			3.56279i			0.611014i
$35$	−4.22824	+	1.82508i	−0.714703	+	0.308495i
$36$			1.00000i			0.166667i
$37$	−3.08463	−	5.24262i	−0.507110	−	0.861882i
$37$	−3.08463	−	5.24262i	−0.507110	−	0.861882i
$38$	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	$-0.767878\pi$
$41$		−	8.53277i		−	1.33260i	0.745686	−	0.666298i	$-0.232122\pi$
$42$	−2.05956			−0.317797
$43$			1.13168i			0.172579i	0.996270	+	0.0862897i	$0.0275011\pi$
$43$			1.13168i			0.172579i	−0.996270	+	0.0862897i	$0.972499\pi$
$44$			3.60654i			0.543706i
$45$	−0.825074	+	2.07828i	−0.122995	+	0.309812i
$46$	−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
$50$	3.42947	−	3.63850i	0.485001	−	0.514562i
$51$	−2.51927	+	2.51927i	−0.352769	+	0.352769i
$52$			0.566998i			0.0786284i
$53$	−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
$55$	−2.97566	+	7.49540i	−0.401238	+	1.01068i
$56$	1.45633	+	1.45633i	0.194610	+	0.194610i
$57$			3.69086i			0.488866i
$58$	0.784491	−	0.784491i	0.103009	−	0.103009i
$59$	−5.54174	+	5.54174i	−0.721473	+	0.721473i	−0.968905	−	0.247432i	$-0.920413\pi$
$59$	−5.54174	+	5.54174i	−0.721473	+	0.721473i	0.247432	+	0.968905i	$0.420413\pi$
$60$	2.05298	−	0.886151i	0.265039	−	0.114402i
$61$	−5.08840	+	5.08840i	−0.651503	+	0.651503i	−0.953355	−	0.301852i	$-0.902395\pi$
$61$	−5.08840	+	5.08840i	−0.651503	+	0.651503i	0.301852	+	0.953355i	$0.402395\pi$
$62$	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	0.599385	−	0.800461i	$-0.295412\pi$
$67$	−1.64587	−	1.64587i	−0.201076	−	0.201076i	−0.800461	+	0.599385i	$0.795412\pi$
$68$	3.56279			0.432052
$69$	−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	$0.568102\pi$
$72$	1.00000			0.117851
$73$	−0.352111	+	0.352111i	−0.0412114	+	0.0412114i	−0.727412	−	0.686201i	$-0.759277\pi$
$73$	−0.352111	+	0.352111i	−0.0412114	+	0.0412114i	0.686201	+	0.727412i	$0.259277\pi$
$74$	−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	$-0.743391\pi$
$79$	0.260977	−	0.260977i	0.0293622	−	0.0293622i	0.721635	+	0.692273i	$0.243391\pi$
$80$	−2.07828	−	0.825074i	−0.232359	−	0.0922461i
$81$	−1.00000			−0.111111
$82$	−8.53277			−0.942287
$83$	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
$87$	1.10944			0.118944
$88$	3.60654			0.384458
$89$	−5.23378	−	5.23378i	−0.554780	−	0.554780i	0.373037	−	0.927817i	$-0.378317\pi$
$89$	−5.23378	−	5.23378i	−0.554780	−	0.554780i	−0.927817	+	0.373037i	$0.878317\pi$
$90$	2.07828	+	0.825074i	0.219070	+	0.0869705i
$91$	−0.825735	−	0.825735i	−0.0865606	−	0.0865606i
$92$			2.32324i			0.242215i
$93$			2.12589i			0.220444i
$94$	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
$97$	11.4260			1.16014			0.580068	−	0.814568i	$-0.303026\pi$
$97$	11.4260			1.16014			0.580068	+	0.814568i	$0.303026\pi$
$98$	2.75821			0.278621
$99$	−3.60654			−0.362471
$100$	−3.63850	−	3.42947i	−0.363850	−	0.342947i
$101$		−	2.80173i		−	0.278783i	−0.990237	−	0.139391i	$-0.955485\pi$
$101$		−	2.80173i		−	0.278783i	0.990237	−	0.139391i	$-0.0445146\pi$
$102$	2.51927	+	2.51927i	0.249445	+	0.249445i
$103$	10.2094			1.00596			0.502979	−	0.864298i	$-0.332237\pi$
$103$	10.2094			1.00596			0.502979	+	0.864298i	$0.332237\pi$
$104$	0.566998			0.0555987
$105$	−1.69929	+	4.28035i	−0.165834	+	0.417719i
$106$	−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	$-0.704134\pi$
$109$	2.12012	−	2.12012i	0.203071	−	0.203071i	0.801314	+	0.598243i	$0.204134\pi$
$110$	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
$113$	−4.98518			−0.468966			−0.234483	−	0.972120i	$-0.575340\pi$
$113$	−4.98518			−0.468966			−0.234483	+	0.972120i	$0.575340\pi$
$114$	3.69086			0.345680
$115$	−1.91685	+	4.82835i	−0.178747	+	0.450246i
$116$	−0.784491	−	0.784491i	−0.0728381	−	0.0728381i
$117$	−0.566998			−0.0524189
$118$	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
$125$	−4.73227	−	10.1294i	−0.423267	−	0.906005i
$126$	−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	$0.0788271\pi$
$128$			1.00000i			0.0883883i
$129$	0.800218	+	0.800218i	0.0704552	+	0.0704552i
$130$	1.17838	+	0.467815i	0.103351	+	0.0410301i
$131$	5.79100	−	5.79100i	0.505962	−	0.505962i	−0.407323	−	0.913284i	$-0.633538\pi$
$131$	5.79100	−	5.79100i	0.505962	−	0.505962i	0.913284	+	0.407323i	$0.133538\pi$
$132$	2.55021	+	2.55021i	0.221967	+	0.221967i
$133$			7.60154i			0.659137i
$134$	−1.64587	+	1.64587i	−0.142182	+	0.142182i
$135$	0.886151	+	2.05298i	0.0762677	+	0.176693i
$136$		−	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	$-0.640723\pi$
$139$	−10.0881			−0.855664			−0.427832	+	0.903858i	$0.640723\pi$
$140$	4.22824	−	1.82508i	0.357352	−	0.154248i
$141$			5.87144i			0.494464i
$142$			3.57811i			0.300268i
$143$	−2.04490			−0.171003
$144$		−	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
$148$	3.08463	+	5.24262i	0.253555	+	0.430941i
$149$		−	8.10303i		−	0.663826i	−0.943310	−	0.331913i	$-0.892306\pi$
$149$		−	8.10303i		−	0.663826i	0.943310	−	0.331913i	$-0.107694\pi$
$150$	−0.147808	−	4.99781i	−0.0120685	−	0.408070i
$151$		−	7.24237i		−	0.589375i	−0.955594	−	0.294688i	$-0.904784\pi$
$151$		−	7.24237i		−	0.589375i	0.955594	−	0.294688i	$-0.0952156\pi$
$152$	−2.60983	−	2.60983i	−0.211685	−	0.211685i
$153$			3.56279i			0.288035i
$154$	−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
$162$			1.00000i			0.0785674i
$163$	−3.48853			−0.273243			−0.136621	−	0.990623i	$-0.543624\pi$
$163$	−3.48853			−0.273243			−0.136621	+	0.990623i	$0.543624\pi$
$164$			8.53277i			0.666298i
$165$	3.19594	+	7.40416i	0.248804	+	0.576413i
$166$	2.52897	−	2.52897i	0.196286	−	0.196286i
$167$	13.0005			1.00601			0.503005	−	0.864284i	$-0.332228\pi$
$167$	13.0005			1.00601			0.503005	+	0.864284i	$0.332228\pi$
$168$	2.05956			0.158899
$169$	12.6785			0.975270
$170$	2.93957	−	7.40448i	0.225455	−	0.567898i
$171$	2.60983	+	2.60983i	0.199579	+	0.199579i
$172$		−	1.13168i		−	0.0862897i
$173$	−12.4447	+	12.4447i	−0.946152	+	0.946152i	−0.998622	−	0.0524705i	$-0.983290\pi$
$173$	−12.4447	+	12.4447i	−0.946152	+	0.946152i	0.0524705	+	0.998622i	$0.483290\pi$
$174$		−	1.10944i		−	0.0841062i
$175$	10.2933	−	0.304419i	0.778101	−	0.0230119i
$176$		−	3.60654i		−	0.271853i
$177$			7.83720i			0.589080i
$178$	−5.23378	+	5.23378i	−0.392289	+	0.392289i
$179$	−6.17102	−	6.17102i	−0.461243	−	0.461243i	0.437819	−	0.899063i	$-0.355751\pi$
$179$	−6.17102	−	6.17102i	−0.461243	−	0.461243i	−0.899063	+	0.437819i	$0.855751\pi$
$180$	0.825074	−	2.07828i	0.0614974	−	0.154906i
$181$	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
$183$			7.19609i			0.531950i
$184$	2.32324			0.171272
$185$	2.08517	+	13.4407i	0.153305	+	0.988179i
$186$	2.12589			0.155878
$187$			12.8493i			0.939637i
$188$	4.15173	−	4.15173i	0.302796	−	0.302796i
$189$	−2.05956			−0.149811
$190$	−3.27066	−	7.57726i	−0.237278	−	0.549713i
$191$	−10.7528	−	10.7528i	−0.778044	−	0.778044i	0.201454	−	0.979498i	$-0.435433\pi$
$191$	−10.7528	−	10.7528i	−0.778044	−	0.778044i	−0.979498	+	0.201454i	$0.935433\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$			6.97010i			0.501719i	0.968024	+	0.250859i	$0.0807131\pi$
$193$			6.97010i			0.501719i	−0.968024	+	0.250859i	$0.919287\pi$
$194$		−	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	$0.0652488\pi$
$198$			3.60654i			0.256306i
$199$	−0.906486	−	0.906486i	−0.0642591	−	0.0642591i	0.674247	−	0.738506i	$-0.264468\pi$
$199$	−0.906486	−	0.906486i	−0.0642591	−	0.0642591i	−0.738506	+	0.674247i	$0.764468\pi$
$200$	−3.42947	+	3.63850i	−0.242500	+	0.257281i
$201$	−2.32762			−0.164178
$202$	−2.80173			−0.197129
$203$	2.28495			0.160372
$204$	2.51927	−	2.51927i	0.176384	−	0.176384i
$205$	−7.04017	+	17.7335i	−0.491707	+	1.23856i
$206$		−	10.2094i		−	0.711320i
$207$	−2.32324			−0.161476
$208$		−	0.566998i		−	0.0393142i
$209$	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
$217$			4.37839i			0.297225i
$218$	−2.12012	−	2.12012i	−0.143593	−	0.143593i
$219$			0.497960i			0.0336490i
$220$	2.97566	−	7.49540i	0.200619	−	0.505340i
$221$			2.02009i			0.135886i
$222$	−1.52593	+	5.88825i	−0.102414	+	0.395194i
$223$	−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
$227$	−14.0497			−0.932514			−0.466257	−	0.884649i	$-0.654398\pi$
$227$	−14.0497			−0.932514			−0.466257	+	0.884649i	$0.654398\pi$
$228$		−	3.69086i		−	0.244433i
$229$		−	17.6048i		−	1.16336i	−0.813418	−	0.581680i	$-0.802396\pi$
$229$		−	17.6048i		−	1.16336i	0.813418	−	0.581680i	$-0.197604\pi$
$230$	4.82835	+	1.91685i	0.318372	+	0.126393i
$231$	−7.42789			−0.488719
$232$	−0.784491	+	0.784491i	−0.0515043	+	0.0515043i
$233$	−2.75919	+	2.75919i	−0.180760	+	0.180760i	−0.791687	−	0.610927i	$-0.790797\pi$
$233$	−2.75919	+	2.75919i	−0.180760	+	0.180760i	0.610927	+	0.791687i	$0.290797\pi$
$234$			0.566998i			0.0370658i
$235$	12.0540	−	5.20298i	0.786313	−	0.339405i
$236$	5.54174	−	5.54174i	0.360737	−	0.360737i
$237$		−	0.369077i		−	0.0239741i
$238$	5.18860	+	5.18860i	0.336327	+	0.336327i
$239$	−1.97901	+	1.97901i	−0.128011	+	0.128011i	−0.768210	−	0.640198i	$-0.778852\pi$
$239$	−1.97901	+	1.97901i	−0.128011	+	0.128011i	0.640198	+	0.768210i	$0.278852\pi$
$240$	−2.05298	+	0.886151i	−0.132519	+	0.0572008i
$241$	−5.52310	−	5.52310i	−0.355774	−	0.355774i	0.506478	−	0.862253i	$-0.330947\pi$
$241$	−5.52310	−	5.52310i	−0.355774	−	0.355774i	−0.862253	+	0.506478i	$0.830947\pi$
$242$			2.00713i			0.129023i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	5.08840	−	5.08840i	0.325752	−	0.325752i
$245$	2.27573	−	5.73234i	0.145391	−	0.366225i
$246$	−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	−0.168073	−	0.985774i	$-0.553755\pi$
$251$	12.9548	−	12.9548i	0.817701	−	0.817701i	0.985774	+	0.168073i	$0.0537546\pi$
$252$	1.45633	+	1.45633i	0.0917401	+	0.0917401i
$253$	−8.37886			−0.526775
$254$	−8.16328	−	8.16328i	−0.512210	−	0.512210i
$255$	7.31435	−	3.15717i	0.458042	−	0.197710i
$256$	1.00000			0.0625000
$257$	15.9569			0.995367			0.497683	−	0.867359i	$-0.334184\pi$
$257$	15.9569			0.995367			0.497683	+	0.867359i	$0.334184\pi$
$258$	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	$-0.445175\pi$
$263$	18.7568	−	18.7568i	1.15659	−	1.15659i	0.985204	−	0.171388i	$-0.0548252\pi$
$264$	2.55021	−	2.55021i	0.156954	−	0.156954i
$265$	5.62327	+	13.0277i	0.345435	+	0.800283i
$266$	7.60154			0.466081
$267$	−7.40169			−0.452976
$268$	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	$0.725451\pi$
$272$	−3.56279			−0.216026
$273$	−1.16777			−0.0706764
$274$	−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
$277$		−	13.2073i		−	0.793550i	−0.917916	−	0.396775i	$-0.870129\pi$
$277$		−	13.2073i		−	0.793550i	0.917916	−	0.396775i	$-0.129871\pi$
$278$			10.0881i			0.605046i
$279$	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	0.793857	−	0.608104i	$-0.208070\pi$
$281$	3.11380	+	3.11380i	0.185754	+	0.185754i	−0.608104	+	0.793857i	$0.708070\pi$
$282$	5.87144			0.349639
$283$	2.74240			0.163019			0.0815094	−	0.996673i	$-0.474026\pi$
$283$	2.74240			0.163019			0.0815094	+	0.996673i	$0.474026\pi$
$284$	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
$288$	−1.00000			−0.0589256
$289$	−4.30652			−0.253325
$290$	−2.27766	+	0.983129i	−0.133749	+	0.0577313i
$291$	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
$298$	−8.10303			−0.469396
$299$	−1.31727			−0.0761798
$300$	−4.99781	+	0.147808i	−0.288549	+	0.00853370i
$301$	1.64810	+	1.64810i	0.0949947	+	0.0949947i
$302$	−7.24237			−0.416751
$303$	−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	0.940431	−	0.339986i	$-0.110422\pi$
$307$	10.5206	+	10.5206i	0.600445	+	0.600445i	−0.339986	+	0.940431i	$0.610422\pi$
$308$	5.25231	+	5.25231i	0.299278	+	0.299278i
$309$	7.21911	−	7.21911i	0.410681	−	0.410681i
$310$	−1.88386	−	4.36441i	−0.106996	−	0.247882i
$311$	23.6104	−	23.6104i	1.33882	−	1.33882i	0.441622	−	0.897201i	$-0.354403\pi$
$311$	23.6104	−	23.6104i	1.33882	−	1.33882i	0.897201	−	0.441622i	$-0.145597\pi$
$312$	0.400928	−	0.400928i	0.0226981	−	0.0226981i
$313$			31.5356i			1.78250i	0.453512	+	0.891250i	$0.350171\pi$
$313$			31.5356i			1.78250i	−0.453512	+	0.891250i	$0.649829\pi$
$314$	−11.2460	−	11.2460i	−0.634651	−	0.634651i
$315$	1.82508	+	4.22824i	0.102832	+	0.238234i
$316$	−0.260977	+	0.260977i	−0.0146811	+	0.0146811i
$317$	16.4324	+	16.4324i	0.922933	+	0.922933i	0.997236	−	0.0743023i	$-0.0236730\pi$
$317$	16.4324	+	16.4324i	0.922933	+	0.922933i	−0.0743023	+	0.997236i	$0.523673\pi$
$318$			6.34573i			0.355851i
$319$	2.82930	−	2.82930i	0.158410	−	0.158410i
$320$	2.07828	+	0.825074i	0.116179	+	0.0461231i
$321$		−	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
$325$	1.94450	−	2.06302i	0.107862	−	0.114436i
$326$			3.48853i			0.193212i
$327$		−	2.99831i		−	0.165807i
$328$	8.53277			0.471144
$329$			12.0926i			0.666685i
$330$	7.40416	−	3.19594i	0.407586	−	0.175931i
$331$	−13.7264	−	13.7264i	−0.754470	−	0.754470i	0.220840	−	0.975310i	$-0.429120\pi$
$331$	−13.7264	−	13.7264i	−0.754470	−	0.754470i	−0.975310	+	0.220840i	$0.929120\pi$
$332$	−2.52897	−	2.52897i	−0.138795	−	0.138795i
$333$	−5.24262	+	3.08463i	−0.287294	+	0.169037i
$334$		−	13.0005i		−	0.711356i
$335$	2.06262	+	4.77856i	0.112693	+	0.261081i
$336$		−	2.05956i		−	0.112358i
$337$	17.9668	+	17.9668i	0.978715	+	0.978715i	0.999778	−	0.0210635i	$-0.00670521\pi$
$337$	17.9668	+	17.9668i	0.978715	+	0.978715i	−0.0210635	+	0.999778i	$0.506705\pi$
$338$		−	12.6785i		−	0.689620i
$339$	−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
$347$			1.20902i			0.0649038i	0.999473	+	0.0324519i	$0.0103316\pi$
$347$			1.20902i			0.0649038i	−0.999473	+	0.0324519i	$0.989668\pi$
$348$	−1.10944			−0.0594721
$349$		−	26.9158i		−	1.44077i	−0.693575	−	0.720384i	$-0.743966\pi$
$349$		−	26.9158i		−	1.44077i	0.693575	−	0.720384i	$-0.256034\pi$
$350$	−0.304419	−	10.2933i	−0.0162719	−	0.550200i
$351$	−0.400928	+	0.400928i	−0.0213999	+	0.0213999i
$352$	−3.60654			−0.192229
$353$	13.0238			0.693186			0.346593	−	0.938016i	$-0.387338\pi$
$353$	13.0238			0.693186			0.346593	+	0.938016i	$0.387338\pi$
$354$	7.83720			0.416543
$355$	7.43631	+	2.95220i	0.394678	+	0.156687i
$356$	5.23378	+	5.23378i	0.277390	+	0.277390i
$357$			7.33778i			0.388357i
$358$	−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
$362$		−	8.27365i		−	0.434853i
$363$	−1.41925	+	1.41925i	−0.0744915	+	0.0744915i
$364$	0.825735	+	0.825735i	0.0432803	+	0.0432803i
$365$	1.02230	−	0.441268i	0.0535098	−	0.0230970i
$366$	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	$0.252603\pi$
$368$		−	2.32324i		−	0.121107i
$369$	−8.53277			−0.444199
$370$	13.4407	−	2.08517i	0.698748	−	0.108403i
$371$	−13.0694			−0.678530
$372$		−	2.12589i		−	0.110222i
$373$	2.85523	−	2.85523i	0.147838	−	0.147838i	−0.629314	−	0.777152i	$-0.716664\pi$
$373$	2.85523	−	2.85523i	0.147838	−	0.147838i	0.777152	+	0.629314i	$0.216664\pi$
$374$	12.8493			0.664424
$375$	−10.5088	−	3.81638i	−0.542673	−	0.197077i
$376$	−4.15173	−	4.15173i	−0.214109	−	0.214109i
$377$	0.444804	−	0.444804i	0.0229086	−	0.0229086i
$378$			2.05956i			0.105932i
$379$		−	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
$383$		−	26.5555i		−	1.35692i	−0.734636	−	0.678461i	$-0.762647\pi$
$383$		−	26.5555i		−	1.35692i	0.734636	−	0.678461i	$-0.237353\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	6.58223	+	15.2493i	0.335462	+	0.777177i
$386$	6.97010			0.354769
$387$	1.13168			0.0575265
$388$	−11.4260			−0.580068
$389$	−5.00317	+	5.00317i	−0.253671	+	0.253671i	−0.822474	−	0.568803i	$-0.807407\pi$
$389$	−5.00317	+	5.00317i	−0.253671	+	0.253671i	0.568803	+	0.822474i	$0.307407\pi$
$390$	1.16404	−	0.502446i	0.0589433	−	0.0254423i
$391$			8.27723i			0.418597i
$392$	−2.75821			−0.139311
$393$		−	8.18971i		−	0.413116i
$394$	−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	0.329219	−	0.944254i	$-0.393215\pi$
$397$	−12.2545	−	12.2545i	−0.615035	−	0.615035i	−0.944254	+	0.329219i	$0.893215\pi$
$398$	−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	−0.930740	−	0.365681i	$-0.880836\pi$
$401$	−11.3153	+	11.3153i	−0.565059	+	0.565059i	0.365681	+	0.930740i	$0.380836\pi$
$402$			2.32762i			0.116091i
$403$	0.852327	+	0.852327i	0.0424575	+	0.0424575i
$404$			2.80173i			0.139391i
$405$	2.07828	+	0.825074i	0.103271	+	0.0409983i
$406$		−	2.28495i		−	0.113400i
$407$	−18.9077	+	11.1248i	−0.937221	+	0.551437i
$408$	−2.51927	−	2.51927i	−0.124723	−	0.124723i
$409$	20.6313	+	20.6313i	1.02015	+	1.02015i	0.999793	+	0.0203618i	$0.00648181\pi$
$409$	20.6313	+	20.6313i	1.02015	+	1.02015i	0.0203618	+	0.999793i	$0.493518\pi$
$410$	17.7335	+	7.04017i	0.875795	+	0.347689i
$411$		−	15.5705i		−	0.768034i
$412$	−10.2094			−0.502979
$413$			16.1412i			0.794256i
$414$			2.32324i			0.114181i
$415$	−3.16932	−	7.34249i	−0.155576	−	0.360429i
$416$	−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	$0.697084\pi$
$420$	1.69929	−	4.28035i	0.0829169	−	0.208859i
$421$	18.2239	−	18.2239i	0.888180	−	0.888180i	−0.106169	−	0.994348i	$-0.533858\pi$
$421$	18.2239	−	18.2239i	0.888180	−	0.888180i	0.994348	+	0.106169i	$0.0338583\pi$
$422$			14.3134i			0.696765i
$423$	4.15173	+	4.15173i	0.201864	+	0.201864i
$424$	4.48711	−	4.48711i	0.217913	−	0.217913i
$425$	−12.9632	−	12.2185i	−0.628809	−	0.592684i
$426$	2.53010	+	2.53010i	0.122584	+	0.122584i
$427$			14.8208i			0.717228i
$428$	−10.7074	+	10.7074i	−0.517561	+	0.517561i
$429$	−1.44596	+	1.44596i	−0.0698117	+	0.0698117i
$430$	−2.35195	−	0.933719i	−0.113421	−	0.0450279i
$431$	−7.25652	+	7.25652i	−0.349534	+	0.349534i	−0.859936	−	0.510402i	$-0.829497\pi$
$431$	−7.25652	+	7.25652i	−0.349534	+	0.349534i	0.510402	+	0.859936i	$0.329497\pi$
$432$	−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
$438$	0.497960			0.0237934
$439$	−16.0555	−	16.0555i	−0.766287	−	0.766287i	0.211164	−	0.977451i	$-0.432275\pi$
$439$	−16.0555	−	16.0555i	−0.766287	−	0.766287i	−0.977451	+	0.211164i	$0.932275\pi$
$440$	−7.49540	−	2.97566i	−0.357329	−	0.141859i
$441$	2.75821			0.131343
$442$	2.02009			0.0960861
$443$	−0.486475	+	0.486475i	−0.0231131	+	0.0231131i	−0.718569	−	0.695456i	$-0.755203\pi$
$443$	−0.486475	+	0.486475i	−0.0231131	+	0.0231131i	0.695456	+	0.718569i	$0.255203\pi$
$444$	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	−0.122716	+	0.992442i	$0.539160\pi$
$449$	−23.6298	+	23.6298i	−1.11516	+	1.11516i	−0.992442	+	0.122716i	$0.960840\pi$
$450$	−3.63850	−	3.42947i	−0.171521	−	0.161667i
$451$	−30.7738			−1.44908
$452$	4.98518			0.234483
$453$	−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
$457$	25.3719			1.18685			0.593423	−	0.804890i	$-0.297776\pi$
$457$	25.3719			1.18685			0.593423	+	0.804890i	$0.297776\pi$
$458$	−17.6048			−0.822620
$459$	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	0.964158	−	0.265328i	$-0.0854803\pi$
$461$	15.0045	+	15.0045i	0.698830	+	0.698830i	−0.265328	+	0.964158i	$0.585480\pi$
$462$			7.42789i			0.345577i
$463$		−	30.1885i		−	1.40298i	−0.712681	−	0.701488i	$-0.752519\pi$
$463$		−	30.1885i		−	1.40298i	0.712681	−	0.701488i	$-0.247481\pi$
$464$	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
$467$	−4.43185			−0.205082			−0.102541	−	0.994729i	$-0.532697\pi$
$467$	−4.43185			−0.205082			−0.102541	+	0.994729i	$0.532697\pi$
$468$	0.566998			0.0262095
$469$	−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
$473$	4.08144			0.187665
$474$	−0.369077			−0.0169523
$475$	−18.4462	+	0.545538i	−0.846371	+	0.0250310i
$476$	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	$-0.837258\pi$
$479$	−8.37886	+	8.37886i	−0.382840	+	0.382840i	0.489284	+	0.872124i	$0.337258\pi$
$480$	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
$483$	−4.78486			−0.217719
$484$	2.00713			0.0912331
$485$	−23.7465	−	9.42732i	−1.07827	−	0.428072i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−9.23525			−0.418489			−0.209245	−	0.977863i	$-0.567100\pi$
$487$	−9.23525			−0.418489			−0.209245	+	0.977863i	$0.567100\pi$
$488$	−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
$495$	7.49540	+	2.97566i	0.336893	+	0.133746i
$496$	−1.50323	+	1.50323i	−0.0674970	+	0.0674970i
$497$	−5.21090	+	5.21090i	−0.233741	+	0.233741i
$498$		−	3.57650i		−	0.160267i
$499$	−3.77024	−	3.77024i	−0.168779	−	0.168779i	0.617664	−	0.786442i	$-0.288079\pi$
$499$	−3.77024	−	3.77024i	−0.168779	−	0.168779i	−0.786442	+	0.617664i	$0.788079\pi$
$500$	4.73227	+	10.1294i	0.211633	+	0.453003i
$501$	9.19275	−	9.19275i	0.410702	−	0.410702i
$502$	−12.9548	−	12.9548i	−0.578202	−	0.578202i
$503$			36.6383i			1.63362i	0.576906	+	0.816810i	$0.304260\pi$
$503$			36.6383i			1.63362i	−0.576906	+	0.816810i	$0.695740\pi$
$504$	1.45633	−	1.45633i	0.0648701	−	0.0648701i
$505$	−2.31164	+	5.82279i	−0.102867	+	0.259111i
$506$			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	$-0.722725\pi$
$509$	−29.0584			−1.28799			−0.643996	+	0.765029i	$0.722725\pi$
$510$	−3.15717	−	7.31435i	−0.139802	−	0.323885i
$511$			1.02558i			0.0453689i
$512$		−	1.00000i		−	0.0441942i
$513$	3.69086			0.162955
$514$		−	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
$518$	−3.14275	+	12.1272i	−0.138084	+	0.532839i
$519$			17.5994i			0.772530i
$520$	−1.17838	−	0.467815i	−0.0516754	−	0.0205151i
$521$			20.4068i			0.894036i	0.894525	+	0.447018i	$0.147514\pi$
$521$			20.4068i			0.894036i	−0.894525	+	0.447018i	$0.852486\pi$
$522$	−0.784491	−	0.784491i	−0.0343362	−	0.0343362i
$523$			7.81649i			0.341791i	0.985289	+	0.170896i	$0.0546661\pi$
$523$			7.81649i			0.341791i	−0.985289	+	0.170896i	$0.945334\pi$
$524$	−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
$532$		−	7.60154i		−	0.329569i
$533$	−4.83806			−0.209560
$534$			7.40169i			0.320302i
$535$	−31.0873	+	13.4186i	−1.34402	+	0.580135i
$536$	1.64587	−	1.64587i	0.0710910	−	0.0710910i
$537$	−8.72713			−0.376604
$538$	23.7613			1.02442
$539$	9.94759			0.428473
$540$	−0.886151	−	2.05298i	−0.0381339	−	0.0883463i
$541$	−12.4935	−	12.4935i	−0.537139	−	0.537139i	0.385548	−	0.922688i	$-0.374012\pi$
$541$	−12.4935	−	12.4935i	−0.537139	−	0.537139i	−0.922688	+	0.385548i	$0.874012\pi$
$542$			21.4180i			0.919982i
$543$	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
$547$		−	35.8153i		−	1.53135i	−0.643227	−	0.765675i	$-0.722405\pi$
$547$		−	35.8153i		−	1.53135i	0.643227	−	0.765675i	$-0.277595\pi$
$548$	−11.0100	+	11.0100i	−0.470323	+	0.470323i
$549$	5.08840	+	5.08840i	0.217168	+	0.217168i
$550$	−13.1224	−	12.3685i	−0.559542	−	0.527396i
$551$	−4.09478			−0.174443
$552$	1.64278	−	1.64278i	0.0699214	−	0.0699214i
$553$		−	0.760137i		−	0.0323243i
$554$	−13.2073			−0.561124
$555$	10.9784	+	8.02956i	0.466009	+	0.340836i
$556$	10.0881			0.427832
$557$			27.7893i			1.17747i	0.808327	+	0.588734i	$0.200374\pi$
$557$			27.7893i			1.17747i	−0.808327	+	0.588734i	$0.799626\pi$
$558$	1.50323	−	1.50323i	0.0636368	−	0.0636368i
$559$	0.641659			0.0271393
$560$	−4.22824	+	1.82508i	−0.178676	+	0.0771238i
$561$	9.08586	+	9.08586i	0.383605	+	0.383605i
$562$	3.11380	−	3.11380i	0.131348	−	0.131348i
$563$		−	4.47346i		−	0.188534i	−0.995547	−	0.0942669i	$-0.969949\pi$
$563$		−	4.47346i		−	0.188534i	0.995547	−	0.0942669i	$-0.0300507\pi$
$564$		−	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
$568$		−	3.57811i		−	0.150134i
$569$	21.9727	+	21.9727i	0.921144	+	0.921144i	0.997110	−	0.0759661i	$-0.0242041\pi$
$569$	21.9727	+	21.9727i	0.921144	+	0.921144i	−0.0759661	+	0.997110i	$0.524204\pi$
$570$	−7.67064	−	3.04523i	−0.321288	−	0.127551i
$571$	11.4199			0.477906			0.238953	−	0.971031i	$-0.423196\pi$
$571$	11.4199			0.477906			0.238953	+	0.971031i	$0.423196\pi$
$572$	2.04490			0.0855015
$573$	−15.2067			−0.635270
$574$	−12.4265	+	12.4265i	−0.518673	+	0.518673i
$575$	7.96749	−	8.45313i	0.332267	−	0.352520i
$576$			1.00000i			0.0416667i
$577$	−10.5104			−0.437555			−0.218778	−	0.975775i	$-0.570207\pi$
$577$	−10.5104			−0.437555			−0.218778	+	0.975775i	$0.570207\pi$
$578$			4.30652i			0.179128i
$579$	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
$587$			28.8278i			1.18985i	0.803781	+	0.594925i	$0.202818\pi$
$587$			28.8278i			1.18985i	−0.803781	+	0.594925i	$0.797182\pi$
$588$	−1.95035	−	1.95035i	−0.0804310	−	0.0804310i
$589$		−	7.84635i		−	0.323303i
$590$	−6.94495	−	16.0896i	−0.285919	−	0.662400i
$591$		−	15.3935i		−	0.633202i
$592$	−3.08463	−	5.24262i	−0.126777	−	0.215470i
$593$	−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
$597$	−1.28197			−0.0524673
$598$			1.31727i			0.0538673i
$599$		−	18.9390i		−	0.773826i	−0.922116	−	0.386913i	$-0.873541\pi$
$599$		−	18.9390i		−	0.773826i	0.922116	−	0.386913i	$-0.126459\pi$
$600$	0.147808	+	4.99781i	0.00603423	+	0.204035i
$601$	−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
$605$	4.17138	+	1.65603i	0.169591	+	0.0673272i
$606$	−1.98112	+	1.98112i	−0.0804777	+	0.0804777i
$607$			26.8510i			1.08985i	0.838485	+	0.544925i	$0.183442\pi$
$607$			26.8510i			1.08985i	−0.838485	+	0.544925i	$0.816558\pi$
$608$	2.60983	+	2.60983i	0.105843	+	0.105843i
$609$	1.61571	−	1.61571i	0.0654717	−	0.0654717i
$610$	−6.37682	−	14.7734i	−0.258190	−	0.598159i
$611$	2.35402	+	2.35402i	0.0952335	+	0.0952335i
$612$		−	3.56279i		−	0.144017i
$613$	−2.19500	+	2.19500i	−0.0886554	+	0.0886554i	−0.750044	−	0.661388i	$-0.769968\pi$
$613$	−2.19500	+	2.19500i	−0.0886554	+	0.0886554i	0.661388	+	0.750044i	$0.269968\pi$
$614$	10.5206	−	10.5206i	0.424579	−	0.424579i
$615$	7.56133	+	17.5176i	0.304902	+	0.706379i
$616$	5.25231	−	5.25231i	0.211622	−	0.211622i
$617$	20.4982	+	20.4982i	0.825228	+	0.825228i	0.986852	−	0.161625i	$-0.0516734\pi$
$617$	20.4982	+	20.4982i	0.825228	+	0.825228i	−0.161625	+	0.986852i	$0.551673\pi$
$618$	−7.21911	−	7.21911i	−0.290395	−	0.290395i
$619$	−38.1723			−1.53428			−0.767138	−	0.641482i	$-0.778320\pi$
$619$	−38.1723			−1.53428			−0.767138	+	0.641482i	$0.778320\pi$
$620$	−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
$623$	−15.2442			−0.610747
$624$	−0.400928	−	0.400928i	−0.0160500	−	0.0160500i
$625$	1.47743	+	24.9563i	0.0590973	+	0.998252i
$626$	31.5356			1.26042
$627$	13.3112			0.531599
$628$	−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	−0.991981	−	0.126387i	$-0.959662\pi$
$631$	−21.7435	+	21.7435i	−0.865594	+	0.865594i	0.126387	+	0.991981i	$0.459662\pi$
$632$	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
$635$	−23.7009	+	10.2303i	−0.940541	+	0.405976i
$636$	6.34573			0.251625
$637$	1.56390			0.0619639
$638$	−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	$0.555741\pi$
$642$	−15.1425			−0.597628
$643$	44.2809			1.74627			0.873134	−	0.487480i	$-0.162084\pi$
$643$	44.2809			1.74627			0.873134	+	0.487480i	$0.162084\pi$
$644$	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
$647$		−	31.8355i		−	1.25158i	−0.779991	−	0.625791i	$-0.784776\pi$
$647$		−	31.8355i		−	1.25158i	0.779991	−	0.625791i	$-0.215224\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	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
$652$	3.48853			0.136621
$653$	−29.8088			−1.16651			−0.583254	−	0.812290i	$-0.698221\pi$
$653$	−29.8088			−1.16651			−0.583254	+	0.812290i	$0.698221\pi$
$654$	−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
$658$	12.0926			0.471418
$659$	40.0379			1.55965			0.779827	−	0.625995i	$-0.215307\pi$
$659$	40.0379			1.55965			0.779827	+	0.625995i	$0.215307\pi$
$660$	−3.19594	−	7.40416i	−0.124402	−	0.288207i
$661$	20.8346	−	20.8346i	0.810373	−	0.810373i	−0.174316	−	0.984690i	$-0.555772\pi$
$661$	20.8346	−	20.8346i	0.810373	−	0.810373i	0.984690	+	0.174316i	$0.0557716\pi$
$662$	−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
$668$	−13.0005			−0.503005
$669$	−13.7176			−0.530354
$670$	4.77856	−	2.06262i	0.184612	−	0.0796860i
$671$	18.3515	+	18.3515i	0.708453	+	0.708453i
$672$	−2.05956			−0.0794493
$673$	−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	0.785059	−	0.619420i	$-0.212632\pi$
$677$	4.30980	+	4.30980i	0.165639	+	0.165639i	−0.619420	+	0.785059i	$0.712632\pi$
$678$	3.52506	+	3.52506i	0.135379	+	0.135379i
$679$	16.6400	−	16.6400i	0.638586	−	0.638586i
$680$	−2.93957	+	7.40448i	−0.112727	+	0.283949i
$681$	−9.93466	+	9.93466i	−0.380697	+	0.380697i
$682$	5.42146	−	5.42146i	0.207598	−	0.207598i
$683$			36.6278i			1.40152i	0.713395	+	0.700762i	$0.247157\pi$
$683$			36.6278i			1.40152i	−0.713395	+	0.700762i	$0.752843\pi$
$684$	−2.60983	−	2.60983i	−0.0997894	−	0.0997894i
$685$	−31.9659	+	13.7978i	−1.22135	+	0.527186i
$686$	14.2112	−	14.2112i	0.542585	−	0.542585i
$687$	−12.4485	−	12.4485i	−0.474940	−	0.474940i
$688$			1.13168i			0.0431448i
$689$	−2.54418	+	2.54418i	−0.0969255	+	0.0969255i
$690$	4.76957	−	2.05874i	0.181575	−	0.0783750i
$691$		−	31.0649i		−	1.18177i	−0.806757	−	0.590883i	$-0.798780\pi$
$691$		−	31.0649i		−	1.18177i	0.806757	−	0.590883i	$-0.201220\pi$
$692$	12.4447	−	12.4447i	0.473076	−	0.473076i
$693$	−5.25231	+	5.25231i	−0.199519	+	0.199519i
$694$	1.20902			0.0458939
$695$	20.9660	+	8.32346i	0.795285	+	0.315727i
$696$			1.10944i			0.0420531i
$697$			30.4005i			1.15150i
$698$	−26.9158			−1.01878
$699$			3.90208i			0.147590i
$700$	−10.2933	+	0.304419i	−0.389050	+	0.0115060i
$701$	−11.6605	−	11.6605i	−0.440411	−	0.440411i	0.451739	−	0.892150i	$-0.350804\pi$
$701$	−11.6605	−	11.6605i	−0.440411	−	0.440411i	−0.892150	+	0.451739i	$0.850804\pi$
$702$	0.400928	+	0.400928i	0.0151320	+	0.0151320i
$703$	21.7327	+	5.63200i	0.819664	+	0.212415i
$704$			3.60654i			0.135927i
$705$	4.84437	−	12.2025i	0.182450	−	0.459573i
$706$		−	13.0238i		−	0.490157i
$707$	−4.08025	−	4.08025i	−0.153453	−	0.153453i
$708$		−	7.83720i		−	0.294540i
$709$	−12.6150	+	12.6150i	−0.473768	+	0.473768i	−0.903132	−	0.429364i	$-0.858738\pi$
$709$	−12.6150	+	12.6150i	−0.473768	+	0.473768i	0.429364	+	0.903132i	$0.358738\pi$
$710$	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
$717$			2.79874i			0.104521i
$718$	6.68890			0.249628
$719$			15.6860i			0.584988i	0.956267	+	0.292494i	$0.0944852\pi$
$719$			15.6860i			0.584988i	−0.956267	+	0.292494i	$0.905515\pi$
$720$	−0.825074	+	2.07828i	−0.0307487	+	0.0774530i
$721$	14.8682	−	14.8682i	0.553721	−	0.553721i
$722$	5.37757			0.200133
$723$	−7.81085			−0.290488
$724$	−8.27365			−0.307488
$725$	0.163984	+	5.54476i	0.00609020	+	0.205927i
$726$	1.41925	+	1.41925i	0.0526735	+	0.0526735i
$727$		−	44.2369i		−	1.64065i	−0.571894	−	0.820327i	$-0.693791\pi$
$727$		−	44.2369i		−	1.64065i	0.571894	−	0.820327i	$-0.306209\pi$
$728$	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
$732$		−	7.19609i		−	0.265975i
$733$	27.8801	−	27.8801i	1.02977	−	1.02977i	0.0302314	−	0.999543i	$-0.490376\pi$
$733$	27.8801	−	27.8801i	1.02977	−	1.02977i	0.999543	−	0.0302314i	$-0.00962443\pi$
$734$	0.221534	+	0.221534i	0.00817696	+	0.00817696i
$735$	−2.44419	−	5.66256i	−0.0901553	−	0.208867i
$736$	−2.32324			−0.0856358
$737$	−5.93591	+	5.93591i	−0.218652	+	0.218652i
$738$			8.53277i			0.314096i
$739$	−44.3607			−1.63183			−0.815917	−	0.578169i	$-0.803768\pi$
$739$	−44.3607			−1.63183			−0.815917	+	0.578169i	$0.803768\pi$
$740$	−2.08517	−	13.4407i	−0.0766524	−	0.494089i
$741$	2.09271			0.0768775
$742$			13.0694i			0.479793i
$743$	7.56548	−	7.56548i	0.277551	−	0.277551i	−0.554580	−	0.832131i	$-0.687121\pi$
$743$	7.56548	−	7.56548i	0.277551	−	0.277551i	0.832131	+	0.554580i	$0.187121\pi$
$744$	−2.12589			−0.0779388
$745$	−6.68560	+	16.8404i	−0.244942	+	0.616984i
$746$	−2.85523	−	2.85523i	−0.104537	−	0.104537i
$747$	2.52897	−	2.52897i	0.0925300	−	0.0925300i
$748$		−	12.8493i		−	0.469819i
$749$		−	31.1869i		−	1.13955i
$750$	−3.81638	+	10.5088i	−0.139355	+	0.383728i
$751$			5.20586i			0.189964i	0.995479	+	0.0949822i	$0.0302794\pi$
$751$			5.20586i			0.189964i	−0.995479	+	0.0949822i	$0.969721\pi$
$752$	−4.15173	+	4.15173i	−0.151398	+	0.151398i
$753$		−	18.3209i		−	0.667650i
$754$	−0.444804	−	0.444804i	−0.0161988	−	0.0161988i
$755$	−5.97549	+	15.0517i	−0.217470	+	0.547786i
$756$	2.05956			0.0749055
$757$	−27.0653			−0.983705			−0.491853	−	0.870678i	$-0.663680\pi$
$757$	−27.0653			−0.983705			−0.491853	+	0.870678i	$0.663680\pi$
$758$	−15.3156			−0.556289
$759$	−5.92475	+	5.92475i	−0.215055	+	0.215055i
$760$	3.27066	+	7.57726i	0.118639	+	0.274856i
$761$		−	1.85691i		−	0.0673130i	−0.999433	−	0.0336565i	$-0.989285\pi$
$761$		−	1.85691i		−	0.0673130i	0.999433	−	0.0336565i	$-0.0107152\pi$
$762$	−11.5446			−0.418217
$763$		−	6.17519i		−	0.223557i
$764$	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	$-0.0760189\pi$
$769$	20.3839	+	20.3839i	0.735061	+	0.735061i	−0.236557	+	0.971618i	$0.576019\pi$
$770$	15.2493	−	6.58223i	0.549547	−	0.237207i
$771$	11.2833	−	11.2833i	0.406357	−	0.406357i
$772$		−	6.97010i		−	0.250859i
$773$	−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
$775$	−10.6248	+	0.314223i	−0.381654	+	0.0112872i
$776$			11.4260i			0.410170i
$777$	−10.7975	+	6.35298i	−0.387358	+	0.227912i
$778$	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
$782$	8.27723			0.295993
$783$		−	1.10944i		−	0.0396481i
$784$			2.75821i			0.0985075i
$785$	−32.6513	+	14.0936i	−1.16537	+	0.503023i
$786$	−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
$790$	0.327058	+	0.757709i	0.0116362	+	0.0269581i
$791$	−7.26007	+	7.26007i	−0.258138	+	0.258138i
$792$		−	3.60654i		−	0.128153i
$793$	2.88511	+	2.88511i	0.102453	+	0.102453i
$794$	−12.2545	+	12.2545i	−0.434895	+	0.434895i
$795$	13.1882	+	5.23570i	0.467738	+	0.185691i
$796$	0.906486	+	0.906486i	0.0321296	+	0.0321296i
$797$			39.8958i			1.41318i	0.707622	+	0.706591i	$0.249768\pi$
$797$			39.8958i			1.41318i	−0.707622	+	0.706591i	$0.750232\pi$
$798$	5.37510	−	5.37510i	0.190277	−	0.190277i
$799$	14.7918	−	14.7918i	0.523295	−	0.523295i
$800$	3.42947	−	3.63850i	0.121250	−	0.128641i
$801$	−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
$808$	2.80173			0.0985646
$809$	3.79166	+	3.79166i	0.133308	+	0.133308i	0.770612	−	0.637305i	$-0.219951\pi$
$809$	3.79166	+	3.79166i	0.133308	+	0.133308i	−0.637305	+	0.770612i	$0.719951\pi$
$810$	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	$0.310666\pi$
$812$	−2.28495			−0.0801862
$813$	−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
$820$	7.04017	−	17.7335i	0.245854	−	0.619281i
$821$	−41.6214			−1.45260			−0.726298	−	0.687380i	$-0.758761\pi$
$821$	−41.6214			−1.45260			−0.726298	+	0.687380i	$0.758761\pi$
$822$	−15.5705			−0.543082
$823$	−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
$827$	44.3537			1.54233			0.771165	−	0.636635i	$-0.219674\pi$
$827$	44.3537			1.54233			0.771165	+	0.636635i	$0.219674\pi$
$828$	2.32324			0.0807382
$829$	15.9798	+	15.9798i	0.555003	+	0.555003i	0.927880	−	0.372878i	$-0.121629\pi$
$829$	15.9798	+	15.9798i	0.555003	+	0.555003i	−0.372878	+	0.927880i	$0.621629\pi$
$830$	−7.34249	+	3.16932i	−0.254861	+	0.110009i
$831$	−9.33897	−	9.33897i	−0.323965	−	0.323965i
$832$			0.566998i			0.0196571i
$833$		−	9.82693i		−	0.340483i
$834$	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
$837$	2.12589			0.0734814
$838$	33.3394			1.15169
$839$	16.0448			0.553926			0.276963	−	0.960881i	$-0.410672\pi$
$839$	16.0448			0.553926			0.276963	+	0.960881i	$0.410672\pi$
$840$	−4.28035	−	1.69929i	−0.147686	−	0.0586311i
$841$		−	27.7691i		−	0.957557i
$842$	−18.2239	−	18.2239i	−0.628038	−	0.628038i
$843$	4.40357			0.151667
$844$	14.3134			0.492687
$845$	−26.3495	−	10.4607i	−0.906451	−	0.359860i
$846$	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
$853$	−9.09546			−0.311423			−0.155711	−	0.987803i	$-0.549767\pi$
$853$	−9.09546			−0.311423			−0.155711	+	0.987803i	$0.549767\pi$
$854$	14.8208			0.507157
$855$	−3.27066	−	7.57726i	−0.111854	−	0.259137i
$856$	10.7074	+	10.7074i	0.365971	+	0.365971i
$857$	4.89927			0.167356			0.0836779	−	0.996493i	$-0.473333\pi$
$857$	4.89927			0.167356			0.0836779	+	0.996493i	$0.473333\pi$
$858$	1.44596	+	1.44596i	0.0493643	+	0.0493643i
$859$	17.1060	−	17.1060i	0.583648	−	0.583648i	−0.352256	−	0.935904i	$-0.614585\pi$
$859$	17.1060	−	17.1060i	0.583648	−	0.583648i	0.935904	+	0.352256i	$0.114585\pi$
$860$	−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
$865$	36.1313	−	15.5958i	1.22850	−	0.530272i
$866$	28.6180	−	28.6180i	0.972480	−	0.972480i
$867$	−3.04517	+	3.04517i	−0.103419	+	0.103419i
$868$		−	4.37839i		−	0.148612i
$869$	−0.941224	−	0.941224i	−0.0319288	−	0.0319288i
$870$	−0.915368	+	2.30572i	−0.0310339	+	0.0781713i
$871$	−0.933207	+	0.933207i	−0.0316205	+	0.0316205i
$872$	2.12012	+	2.12012i	0.0717964	+	0.0717964i
$873$		−	11.4260i		−	0.386712i
$874$	6.06327	−	6.06327i	0.205093	−	0.205093i
$875$	−21.6435	−	7.86007i	−0.731685	−	0.265719i
$876$		−	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
$880$	−2.97566	+	7.49540i	−0.100310	+	0.252670i
$881$			47.7941i			1.61022i	0.593123	+	0.805112i	$0.297895\pi$
$881$			47.7941i			1.61022i	−0.593123	+	0.805112i	$0.702105\pi$
$882$		−	2.75821i		−	0.0928738i
$883$	13.3347			0.448747			0.224374	−	0.974503i	$-0.427966\pi$
$883$	13.3347			0.448747			0.224374	+	0.974503i	$0.427966\pi$
$884$		−	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	$-0.965954\pi$
$887$	−32.7918	−	32.7918i	−1.10104	−	1.10104i	−0.106755	−	0.994285i	$-0.534046\pi$
$888$	1.52593	−	5.88825i	0.0512069	−	0.197597i
$889$		−	23.7768i		−	0.797450i
$890$	15.1955	−	6.55901i	0.509356	−	0.219859i
$891$			3.60654i			0.120824i
$892$	9.69983	+	9.69983i	0.324774	+	0.324774i
$893$		−	21.6706i		−	0.725180i
$894$	−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
$902$			30.7738i			1.02466i
$903$	2.33076			0.0775629
$904$		−	4.98518i		−	0.165805i
$905$	−17.1950	−	6.82637i	−0.571580	−	0.226916i
$906$	−5.12113	+	5.12113i	−0.170138	+	0.170138i
$907$	−4.02073			−0.133506			−0.0667530	−	0.997770i	$-0.521264\pi$
$907$	−4.02073			−0.133506			−0.0667530	+	0.997770i	$0.521264\pi$
$908$	14.0497			0.466257
$909$	−2.80173			−0.0929276
$910$	2.39740	−	1.03482i	0.0794731	−	0.0343038i
$911$	30.6544	+	30.6544i	1.01563	+	1.01563i	0.999876	+	0.0157497i	$0.00501349\pi$
$911$	30.6544	+	30.6544i	1.01563	+	1.01563i	0.0157497	+	0.999876i	$0.494987\pi$
$912$			3.69086i			0.122216i
$913$	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
$917$		−	16.8672i		−	0.557004i
$918$	2.51927	−	2.51927i	0.0831484	−	0.0831484i
$919$	−30.5298	−	30.5298i	−1.00708	−	1.00708i	−0.999975	−	0.00711010i	$-0.997737\pi$
$919$	−30.5298	−	30.5298i	−1.00708	−	1.00708i	−0.00711010	−	0.999975i	$-0.502263\pi$
$920$	−4.82835	−	1.91685i	−0.159186	−	0.0631966i
$921$	14.8784			0.490261
$922$	15.0045	−	15.0045i	0.494148	−	0.494148i
$923$			2.02878i			0.0667780i
$924$	7.42789			0.244360
$925$	6.75599	−	29.6539i	0.222136	−	0.975016i
$926$	−30.1885			−0.992054
$927$		−	10.2094i		−	0.335320i
$928$	0.784491	−	0.784491i	0.0257522	−	0.0257522i
$929$	41.1786			1.35103			0.675513	−	0.737348i	$-0.263922\pi$
$929$	41.1786			1.35103			0.675513	+	0.737348i	$0.263922\pi$
$930$	−4.41819	−	1.75401i	−0.144878	−	0.0575164i
$931$	−7.19846	−	7.19846i	−0.235920	−	0.235920i
$932$	2.75919	−	2.75919i	0.0903802	−	0.0903802i
$933$		−	33.3902i		−	1.09314i
$934$			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	$-0.167844\pi$
$938$			4.79387i			0.156525i
$939$	22.2991	+	22.2991i	0.727703	+	0.727703i
$940$	−12.0540	+	5.20298i	−0.393157	+	0.169702i
$941$	11.0609			0.360576			0.180288	−	0.983614i	$-0.442297\pi$
$941$	11.0609			0.360576			0.180288	+	0.983614i	$0.442297\pi$
$942$	−15.9043			−0.518190
$943$	−19.8237			−0.645548
$944$	−5.54174	+	5.54174i	−0.180368	+	0.180368i
$945$	4.28035	+	1.69929i	0.139240	+	0.0552779i
$946$		−	4.08144i		−	0.132699i
$947$	−31.1637			−1.01268			−0.506341	−	0.862333i	$-0.669002\pi$
$947$	−31.1637			−1.01268			−0.506341	+	0.862333i	$0.669002\pi$
$948$			0.369077i			0.0119871i
$949$	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	−0.676919	−	0.736058i	$-0.736685\pi$
$953$	1.82567	−	1.82567i	0.0591394	−	0.0591394i	0.736058	+	0.676919i	$0.236685\pi$
$954$	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
$957$		−	4.00123i		−	0.129341i
$958$	8.37886	+	8.37886i	0.270709	+	0.270709i
$959$		−	32.0683i		−	1.03554i
$960$	2.05298	−	0.886151i	0.0662597	−	0.0286004i
$961$			26.4806i			0.854213i
$962$	1.74898	+	2.97255i	0.0563893	+	0.0958390i
$963$	−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
$967$	27.6923			0.890524			0.445262	−	0.895400i	$-0.353111\pi$
$967$	27.6923			0.890524			0.445262	+	0.895400i	$0.353111\pi$
$968$		−	2.00713i		−	0.0645116i
$969$		−	13.1498i		−	0.422431i
$970$	−9.42732	+	23.7465i	−0.302693	+	0.762454i
$971$	−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
$975$	−0.0838068	−	2.83375i	−0.00268396	−	0.0907526i
$976$	−5.08840	+	5.08840i	−0.162876	+	0.162876i
$977$		−	17.9170i		−	0.573215i	−0.958048	−	0.286607i	$-0.907472\pi$
$977$		−	17.9170i		−	0.573215i	0.958048	−	0.286607i	$-0.0925275\pi$
$978$	2.46676	+	2.46676i	0.0788784	+	0.0788784i
$979$	−18.8759	+	18.8759i	−0.603275	+	0.603275i
$980$	−2.27573	+	5.73234i	−0.0726955	+	0.183113i
$981$	−2.12012	−	2.12012i	−0.0676903	−	0.0676903i
$982$			29.1580i			0.930469i
$983$	−3.29763	+	3.29763i	−0.105178	+	0.105178i	−0.757738	−	0.652559i	$-0.773695\pi$
$983$	−3.29763	+	3.29763i	−0.105178	+	0.105178i	0.652559	+	0.757738i	$0.273695\pi$
$984$	6.03358	−	6.03358i	0.192344	−	0.192344i
$985$	−31.6025	+	13.6409i	−1.00694	+	0.434636i
$986$	−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	−0.781032	−	0.624491i	$-0.785307\pi$
$991$	−4.92794	+	4.92794i	−0.156541	+	0.156541i	0.624491	+	0.781032i	$0.285307\pi$
$992$	1.50323	+	1.50323i	0.0477276	+	0.0477276i
$993$	−19.4120			−0.616022
$994$	5.21090	+	5.21090i	0.165280	+	0.165280i
$995$	1.13601	+	2.63185i	0.0360141	+	0.0834353i
$996$	−3.57650			−0.113326
$997$	−39.1924			−1.24124			−0.620618	−	0.784113i	$-0.713118\pi$
$997$	−39.1924			−1.24124			−0.620618	+	0.784113i	$0.713118\pi$
$998$	−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.l.b.43.17	✓	40
5.2	odd	4		1110.2.o.b.487.4	yes	40
37.31	odd	4		1110.2.o.b.253.4	yes	40
185.142	even	4	inner	1110.2.l.b.697.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.17	✓	40	1.1	even	1	trivial
1110.2.l.b.697.17	yes	40	185.142	even	4	inner
1110.2.o.b.253.4	yes	40	37.31	odd	4
1110.2.o.b.487.4	yes	40	5.2	odd	4

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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