LMFDB - Embedded newform 1110.2.l.a.697.2

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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			697.2
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.887844 - 2.05225i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.84414 - 1.84414i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.887844 - 2.05225i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.84414 - 1.84414i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-2.05225 + 0.887844i) q^{10} +2.12202i q^{11} +(0.707107 + 0.707107i) q^{12} +5.07258i q^{13} +(-1.84414 + 1.84414i) q^{14} +(-0.823360 + 2.07896i) q^{15} +1.00000 q^{16} -2.93495 q^{17} +1.00000 q^{18} +(-2.28458 - 2.28458i) q^{19} +(0.887844 + 2.05225i) q^{20} +2.60801i q^{21} +2.12202 q^{22} +5.76461i q^{23} +(0.707107 - 0.707107i) q^{24} +(-3.42347 + 3.64416i) q^{25} +5.07258 q^{26} +(0.707107 - 0.707107i) q^{27} +(1.84414 + 1.84414i) q^{28} +(5.76649 - 5.76649i) q^{29} +(2.07896 + 0.823360i) q^{30} +(1.38171 + 1.38171i) q^{31} -1.00000i q^{32} +(1.50049 - 1.50049i) q^{33} +2.93495i q^{34} +(-2.14733 + 5.42195i) q^{35} -1.00000i q^{36} +(-5.46669 - 2.66745i) q^{37} +(-2.28458 + 2.28458i) q^{38} +(3.58685 - 3.58685i) q^{39} +(2.05225 - 0.887844i) q^{40} -6.92685i q^{41} +2.60801 q^{42} +2.00391i q^{43} -2.12202i q^{44} +(2.05225 - 0.887844i) q^{45} +5.76461 q^{46} +(7.27515 + 7.27515i) q^{47} +(-0.707107 - 0.707107i) q^{48} -0.198289i q^{49} +(3.64416 + 3.42347i) q^{50} +(2.07533 + 2.07533i) q^{51} -5.07258i q^{52} +(-0.286733 + 0.286733i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(4.35492 - 1.88402i) q^{55} +(1.84414 - 1.84414i) q^{56} +3.23088i q^{57} +(-5.76649 - 5.76649i) q^{58} +(8.25437 + 8.25437i) q^{59} +(0.823360 - 2.07896i) q^{60} +(2.44633 + 2.44633i) q^{61} +(1.38171 - 1.38171i) q^{62} +(1.84414 - 1.84414i) q^{63} -1.00000 q^{64} +(10.4102 - 4.50366i) q^{65} +(-1.50049 - 1.50049i) q^{66} +(-9.89884 + 9.89884i) q^{67} +2.93495 q^{68} +(4.07619 - 4.07619i) q^{69} +(5.42195 + 2.14733i) q^{70} +1.69758 q^{71} -1.00000 q^{72} +(5.92047 + 5.92047i) q^{73} +(-2.66745 + 5.46669i) q^{74} +(4.99756 - 0.156051i) q^{75} +(2.28458 + 2.28458i) q^{76} +(3.91330 - 3.91330i) q^{77} +(-3.58685 - 3.58685i) q^{78} +(-5.73733 - 5.73733i) q^{79} +(-0.887844 - 2.05225i) q^{80} -1.00000 q^{81} -6.92685 q^{82} +(-7.41007 + 7.41007i) q^{83} -2.60801i q^{84} +(2.60578 + 6.02326i) q^{85} +2.00391 q^{86} -8.15506 q^{87} -2.12202 q^{88} +(-11.9236 + 11.9236i) q^{89} +(-0.887844 - 2.05225i) q^{90} +(9.35455 - 9.35455i) q^{91} -5.76461i q^{92} -1.95403i q^{93} +(7.27515 - 7.27515i) q^{94} +(-2.66018 + 6.71688i) q^{95} +(-0.707107 + 0.707107i) q^{96} -7.94678 q^{97} -0.198289 q^{98} -2.12202 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.887844	−	2.05225i	−0.397056	−	0.917794i
$5$	−0.887844	−	2.05225i	−0.397056	−	0.917794i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−1.84414	−	1.84414i	−0.697020	−	0.697020i	0.266747	−	0.963767i	$-0.414051\pi$
$7$	−1.84414	−	1.84414i	−0.697020	−	0.697020i	−0.963767	+	0.266747i	$0.914051\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	−2.05225	+	0.887844i	−0.648979	+	0.280761i
$11$			2.12202i			0.639813i	0.947449	+	0.319906i	$0.103651\pi$
$11$			2.12202i			0.639813i	−0.947449	+	0.319906i	$0.896349\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$			5.07258i			1.40688i	0.710755	+	0.703440i	$0.248354\pi$
$13$			5.07258i			1.40688i	−0.710755	+	0.703440i	$0.751646\pi$
$14$	−1.84414	+	1.84414i	−0.492867	+	0.492867i
$15$	−0.823360	+	2.07896i	−0.212591	+	0.536785i
$16$	1.00000			0.250000
$17$	−2.93495			−0.711831			−0.355916	−	0.934518i	$-0.615831\pi$
$17$	−2.93495			−0.711831			−0.355916	+	0.934518i	$0.615831\pi$
$18$	1.00000			0.235702
$19$	−2.28458	−	2.28458i	−0.524118	−	0.524118i	0.394694	−	0.918813i	$-0.370851\pi$
$19$	−2.28458	−	2.28458i	−0.524118	−	0.524118i	−0.918813	+	0.394694i	$0.870851\pi$
$20$	0.887844	+	2.05225i	0.198528	+	0.458897i
$21$			2.60801i			0.569114i
$22$	2.12202			0.452416
$23$			5.76461i			1.20200i	0.799248	+	0.601002i	$0.205232\pi$
$23$			5.76461i			1.20200i	−0.799248	+	0.601002i	$0.794768\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	−3.42347	+	3.64416i	−0.684693	+	0.728831i
$26$	5.07258			0.994814
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.84414	+	1.84414i	0.348510	+	0.348510i
$29$	5.76649	−	5.76649i	1.07081	−	1.07081i	0.0735173	−	0.997294i	$-0.476578\pi$
$29$	5.76649	−	5.76649i	1.07081	−	1.07081i	0.997294	−	0.0735173i	$-0.0234224\pi$
$30$	2.07896	+	0.823360i	0.379565	+	0.150324i
$31$	1.38171	+	1.38171i	0.248163	+	0.248163i	0.820216	−	0.572054i	$-0.193853\pi$
$31$	1.38171	+	1.38171i	0.248163	+	0.248163i	−0.572054	+	0.820216i	$0.693853\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.50049	−	1.50049i	0.261203	−	0.261203i
$34$			2.93495i			0.503341i
$35$	−2.14733	+	5.42195i	−0.362965	+	0.916477i
$36$		−	1.00000i		−	0.166667i
$37$	−5.46669	−	2.66745i	−0.898719	−	0.438526i
$37$	−5.46669	−	2.66745i	−0.898719	−	0.438526i
$38$	−2.28458	+	2.28458i	−0.370608	+	0.370608i
$39$	3.58685	−	3.58685i	0.574356	−	0.574356i
$40$	2.05225	−	0.887844i	0.324489	−	0.140380i
$41$		−	6.92685i		−	1.08179i	−0.841089	−	0.540896i	$-0.818085\pi$
$41$		−	6.92685i		−	1.08179i	0.841089	−	0.540896i	$-0.181915\pi$
$42$	2.60801			0.402425
$43$			2.00391i			0.305593i	0.988258	+	0.152797i	$0.0488280\pi$
$43$			2.00391i			0.305593i	−0.988258	+	0.152797i	$0.951172\pi$
$44$		−	2.12202i		−	0.319906i
$45$	2.05225	−	0.887844i	0.305931	−	0.132352i
$46$	5.76461			0.849945
$47$	7.27515	+	7.27515i	1.06119	+	1.06119i	0.998002	+	0.0631877i	$0.0201267\pi$
$47$	7.27515	+	7.27515i	1.06119	+	1.06119i	0.0631877	+	0.998002i	$0.479873\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	0.198289i		−	0.0283271i
$50$	3.64416	+	3.42347i	0.515362	+	0.484151i
$51$	2.07533	+	2.07533i	0.290604	+	0.290604i
$52$		−	5.07258i		−	0.703440i
$53$	−0.286733	+	0.286733i	−0.0393858	+	0.0393858i	−0.726525	−	0.687140i	$-0.758866\pi$
$53$	−0.286733	+	0.286733i	−0.0393858	+	0.0393858i	0.687140	+	0.726525i	$0.258866\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	4.35492	−	1.88402i	0.587217	−	0.254041i
$56$	1.84414	−	1.84414i	0.246434	−	0.246434i
$57$			3.23088i			0.427941i
$58$	−5.76649	−	5.76649i	−0.757178	−	0.757178i
$59$	8.25437	+	8.25437i	1.07463	+	1.07463i	0.996981	+	0.0776460i	$0.0247404\pi$
$59$	8.25437	+	8.25437i	1.07463	+	1.07463i	0.0776460	+	0.996981i	$0.475260\pi$
$60$	0.823360	−	2.07896i	0.106295	−	0.268393i
$61$	2.44633	+	2.44633i	0.313221	+	0.313221i	0.846156	−	0.532935i	$-0.178911\pi$
$61$	2.44633	+	2.44633i	0.313221	+	0.313221i	−0.532935	+	0.846156i	$0.678911\pi$
$62$	1.38171	−	1.38171i	0.175478	−	0.175478i
$63$	1.84414	−	1.84414i	0.232340	−	0.232340i
$64$	−1.00000			−0.125000
$65$	10.4102	−	4.50366i	1.29123	−	0.558610i
$66$	−1.50049	−	1.50049i	−0.184698	−	0.184698i
$67$	−9.89884	+	9.89884i	−1.20934	+	1.20934i	−0.238093	+	0.971242i	$0.576522\pi$
$67$	−9.89884	+	9.89884i	−1.20934	+	1.20934i	−0.971242	+	0.238093i	$0.923478\pi$
$68$	2.93495			0.355916
$69$	4.07619	−	4.07619i	0.490716	−	0.490716i
$70$	5.42195	+	2.14733i	0.648047	+	0.256655i
$71$	1.69758			0.201465			0.100733	−	0.994914i	$-0.467881\pi$
$71$	1.69758			0.201465			0.100733	+	0.994914i	$0.467881\pi$
$72$	−1.00000			−0.117851
$73$	5.92047	+	5.92047i	0.692939	+	0.692939i	0.962877	−	0.269939i	$-0.0870035\pi$
$73$	5.92047	+	5.92047i	0.692939	+	0.692939i	−0.269939	+	0.962877i	$0.587003\pi$
$74$	−2.66745	+	5.46669i	−0.310085	+	0.635490i
$75$	4.99756	−	0.156051i	0.577069	−	0.0180192i
$76$	2.28458	+	2.28458i	0.262059	+	0.262059i
$77$	3.91330	−	3.91330i	0.445962	−	0.445962i
$78$	−3.58685	−	3.58685i	−0.406131	−	0.406131i
$79$	−5.73733	−	5.73733i	−0.645500	−	0.645500i	0.306402	−	0.951902i	$-0.400875\pi$
$79$	−5.73733	−	5.73733i	−0.645500	−	0.645500i	−0.951902	+	0.306402i	$0.900875\pi$
$80$	−0.887844	−	2.05225i	−0.0992640	−	0.229449i
$81$	−1.00000			−0.111111
$82$	−6.92685			−0.764943
$83$	−7.41007	+	7.41007i	−0.813360	+	0.813360i	−0.985136	−	0.171776i	$-0.945050\pi$
$83$	−7.41007	+	7.41007i	−0.813360	+	0.813360i	0.171776	+	0.985136i	$0.445050\pi$
$84$		−	2.60801i		−	0.284557i
$85$	2.60578	+	6.02326i	0.282637	+	0.653315i
$86$	2.00391			0.216087
$87$	−8.15506			−0.874314
$88$	−2.12202			−0.226208
$89$	−11.9236	+	11.9236i	−1.26390	+	1.26390i	−0.314714	+	0.949187i	$0.601908\pi$
$89$	−11.9236	+	11.9236i	−1.26390	+	1.26390i	−0.949187	+	0.314714i	$0.898092\pi$
$90$	−0.887844	−	2.05225i	−0.0935870	−	0.216326i
$91$	9.35455	−	9.35455i	0.980623	−	0.980623i
$92$		−	5.76461i		−	0.601002i
$93$		−	1.95403i		−	0.202624i
$94$	7.27515	−	7.27515i	0.750374	−	0.750374i
$95$	−2.66018	+	6.71688i	−0.272929	+	0.689137i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	−7.94678			−0.806874			−0.403437	−	0.915008i	$-0.632184\pi$
$97$	−7.94678			−0.806874			−0.403437	+	0.915008i	$0.632184\pi$
$98$	−0.198289			−0.0200303
$99$	−2.12202			−0.213271
$100$	3.42347	−	3.64416i	0.342347	−	0.364416i
$101$			15.2228i			1.51472i	0.652997	+	0.757360i	$0.273511\pi$
$101$			15.2228i			1.51472i	−0.652997	+	0.757360i	$0.726489\pi$
$102$	2.07533	−	2.07533i	0.205488	−	0.205488i
$103$	−13.4988			−1.33008			−0.665038	−	0.746810i	$-0.731585\pi$
$103$	−13.4988			−1.33008			−0.665038	+	0.746810i	$0.731585\pi$
$104$	−5.07258			−0.497407
$105$	5.35229	−	2.31550i	0.522330	−	0.225970i
$106$	0.286733	+	0.286733i	0.0278500	+	0.0278500i
$107$	2.32171	+	2.32171i	0.224448	+	0.224448i	0.810369	−	0.585920i	$-0.199267\pi$
$107$	2.32171	+	2.32171i	0.224448	+	0.224448i	−0.585920	+	0.810369i	$0.699267\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−5.20603	−	5.20603i	−0.498647	−	0.498647i	0.412369	−	0.911017i	$-0.364701\pi$
$109$	−5.20603	−	5.20603i	−0.498647	−	0.498647i	−0.911017	+	0.412369i	$0.864701\pi$
$110$	−1.88402	−	4.35492i	−0.179634	−	0.415225i
$111$	1.97936	+	5.75171i	0.187873	+	0.545928i
$112$	−1.84414	−	1.84414i	−0.174255	−	0.174255i
$113$	16.6356			1.56494			0.782471	−	0.622687i	$-0.213959\pi$
$113$	16.6356			1.56494			0.782471	+	0.622687i	$0.213959\pi$
$114$	3.23088			0.302600
$115$	11.8304	−	5.11807i	1.10319	−	0.477262i
$116$	−5.76649	+	5.76649i	−0.535406	+	0.535406i
$117$	−5.07258			−0.468960
$118$	8.25437	−	8.25437i	0.759876	−	0.759876i
$119$	5.41247	+	5.41247i	0.496160	+	0.496160i
$120$	−2.07896	−	0.823360i	−0.189782	−	0.0751621i
$121$	6.49703			0.590639
$122$	2.44633	−	2.44633i	0.221481	−	0.221481i
$123$	−4.89802	+	4.89802i	−0.441640	+	0.441640i
$124$	−1.38171	−	1.38171i	−0.124081	−	0.124081i
$125$	10.5182	+	3.79037i	0.940779	+	0.339021i
$126$	−1.84414	−	1.84414i	−0.164289	−	0.164289i
$127$	−6.57279	−	6.57279i	−0.583241	−	0.583241i	0.352552	−	0.935792i	$-0.385314\pi$
$127$	−6.57279	−	6.57279i	−0.583241	−	0.583241i	−0.935792	+	0.352552i	$0.885314\pi$
$128$			1.00000i			0.0883883i
$129$	1.41698	−	1.41698i	0.124758	−	0.124758i
$130$	−4.50366	−	10.4102i	−0.394997	−	0.913035i
$131$	−2.67417	−	2.67417i	−0.233643	−	0.233643i	0.580568	−	0.814212i	$-0.302830\pi$
$131$	−2.67417	−	2.67417i	−0.233643	−	0.233643i	−0.814212	+	0.580568i	$0.802830\pi$
$132$	−1.50049	+	1.50049i	−0.130601	+	0.130601i
$133$			8.42617i			0.730642i
$134$	9.89884	+	9.89884i	0.855129	+	0.855129i
$135$	−2.07896	−	0.823360i	−0.178928	−	0.0708636i
$136$		−	2.93495i		−	0.251670i
$137$	0.925340	+	0.925340i	0.0790571	+	0.0790571i	0.745530	−	0.666472i	$-0.232197\pi$
$137$	0.925340	+	0.925340i	0.0790571	+	0.0790571i	−0.666472	+	0.745530i	$0.732197\pi$
$138$	−4.07619	−	4.07619i	−0.346988	−	0.346988i
$139$	−5.44352			−0.461713			−0.230857	−	0.972988i	$-0.574153\pi$
$139$	−5.44352			−0.461713			−0.230857	+	0.972988i	$0.574153\pi$
$140$	2.14733	−	5.42195i	0.181483	−	0.458238i
$141$		−	10.2886i		−	0.866457i
$142$		−	1.69758i		−	0.142457i
$143$	−10.7641			−0.900140
$144$			1.00000i			0.0833333i
$145$	−16.9540	−	6.71455i	−1.40796	−	0.557613i
$146$	5.92047	−	5.92047i	0.489982	−	0.489982i
$147$	−0.140212	+	0.140212i	−0.0115645	+	0.0115645i
$148$	5.46669	+	2.66745i	0.449359	+	0.219263i
$149$		−	16.9497i		−	1.38858i	−0.719698	−	0.694288i	$-0.755720\pi$
$149$		−	16.9497i		−	1.38858i	0.719698	−	0.694288i	$-0.244280\pi$
$150$	−0.156051	−	4.99756i	−0.0127415	−	0.408049i
$151$		−	1.25999i		−	0.102536i	−0.998685	−	0.0512681i	$-0.983674\pi$
$151$		−	1.25999i		−	0.102536i	0.998685	−	0.0512681i	$-0.0163263\pi$
$152$	2.28458	−	2.28458i	0.185304	−	0.185304i
$153$		−	2.93495i		−	0.237277i
$154$	−3.91330	−	3.91330i	−0.315343	−	0.315343i
$155$	1.60887	−	4.06236i	0.129228	−	0.326297i
$156$	−3.58685	+	3.58685i	−0.287178	+	0.287178i
$157$	4.05205	+	4.05205i	0.323389	+	0.323389i	0.850066	−	0.526677i	$-0.176562\pi$
$157$	4.05205	+	4.05205i	0.323389	+	0.323389i	−0.526677	+	0.850066i	$0.676562\pi$
$158$	−5.73733	+	5.73733i	−0.456437	+	0.456437i
$159$	0.405502			0.0321584
$160$	−2.05225	+	0.887844i	−0.162245	+	0.0701902i
$161$	10.6307	−	10.6307i	0.837820	−	0.837820i
$162$			1.00000i			0.0785674i
$163$	0.200876			0.0157338			0.00786690	−	0.999969i	$-0.497496\pi$
$163$	0.200876			0.0157338			0.00786690	+	0.999969i	$0.497496\pi$
$164$			6.92685i			0.540896i
$165$	−4.41160	−	1.74719i	−0.343442	−	0.136018i
$166$	7.41007	+	7.41007i	0.575133	+	0.575133i
$167$	−7.20812			−0.557781			−0.278891	−	0.960323i	$-0.589967\pi$
$167$	−7.20812			−0.557781			−0.278891	+	0.960323i	$0.589967\pi$
$168$	−2.60801			−0.201212
$169$	−12.7311			−0.979312
$170$	6.02326	−	2.60578i	0.461963	−	0.199854i
$171$	2.28458	−	2.28458i	0.174706	−	0.174706i
$172$		−	2.00391i		−	0.152797i
$173$	−1.14427	−	1.14427i	−0.0869969	−	0.0869969i	0.662269	−	0.749266i	$-0.269594\pi$
$173$	−1.14427	−	1.14427i	−0.0869969	−	0.0869969i	−0.749266	+	0.662269i	$0.769594\pi$
$174$			8.15506i			0.618233i
$175$	13.0337	−	0.406983i	0.985255	−	0.0307650i
$176$			2.12202i			0.159953i
$177$		−	11.6734i		−	0.877429i
$178$	11.9236	+	11.9236i	0.893712	+	0.893712i
$179$	−9.71351	+	9.71351i	−0.726022	+	0.726022i	−0.969825	−	0.243803i	$-0.921605\pi$
$179$	−9.71351	+	9.71351i	−0.726022	+	0.726022i	0.243803	+	0.969825i	$0.421605\pi$
$180$	−2.05225	+	0.887844i	−0.152966	+	0.0661760i
$181$	−1.59280			−0.118392			−0.0591961	−	0.998246i	$-0.518854\pi$
$181$	−1.59280			−0.118392			−0.0591961	+	0.998246i	$0.518854\pi$
$182$	−9.35455	−	9.35455i	−0.693405	−	0.693405i
$183$		−	3.45964i		−	0.255744i
$184$	−5.76461			−0.424972
$185$	−0.620706	+	13.5873i	−0.0456352	+	0.998958i
$186$	−1.95403			−0.143277
$187$		−	6.22803i		−	0.455439i
$188$	−7.27515	−	7.27515i	−0.530595	−	0.530595i
$189$	−2.60801			−0.189705
$190$	6.71688	+	2.66018i	0.487294	+	0.192990i
$191$	−14.2911	+	14.2911i	−1.03407	+	1.03407i	−0.0346716	+	0.999399i	$0.511039\pi$
$191$	−14.2911	+	14.2911i	−1.03407	+	1.03407i	−0.999399	+	0.0346716i	$0.988961\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$		−	11.4610i		−	0.824978i	−0.910963	−	0.412489i	$-0.864660\pi$
$193$		−	11.4610i		−	0.824978i	0.910963	−	0.412489i	$-0.135340\pi$
$194$			7.94678i			0.570546i
$195$	−10.5457	−	4.17656i	−0.755193	−	0.299090i
$196$			0.198289i			0.0141635i
$197$	3.61811	+	3.61811i	0.257780	+	0.257780i	0.824151	−	0.566371i	$-0.191653\pi$
$197$	3.61811	+	3.61811i	0.257780	+	0.257780i	−0.566371	+	0.824151i	$0.691653\pi$
$198$			2.12202i			0.150805i
$199$	−14.1563	+	14.1563i	−1.00351	+	1.00351i	−0.00351772	+	0.999994i	$0.501120\pi$
$199$	−14.1563	+	14.1563i	−1.00351	+	1.00351i	−0.999994	+	0.00351772i	$0.998880\pi$
$200$	−3.64416	−	3.42347i	−0.257681	−	0.242076i
$201$	13.9991			0.987418
$202$	15.2228			1.07107
$203$	−21.2685			−1.49275
$204$	−2.07533	−	2.07533i	−0.145302	−	0.145302i
$205$	−14.2156	+	6.14996i	−0.992863	+	0.429532i
$206$			13.4988i			0.940505i
$207$	−5.76461			−0.400668
$208$			5.07258i			0.351720i
$209$	4.84792	−	4.84792i	0.335338	−	0.335338i
$210$	−2.31550	−	5.35229i	−0.159785	−	0.369343i
$211$	8.13385			0.559957			0.279979	−	0.960006i	$-0.409673\pi$
$211$	8.13385			0.559957			0.279979	+	0.960006i	$0.409673\pi$
$212$	0.286733	−	0.286733i	0.0196929	−	0.0196929i
$213$	−1.20037	−	1.20037i	−0.0822478	−	0.0822478i
$214$	2.32171	−	2.32171i	0.158709	−	0.158709i
$215$	4.11252	−	1.77916i	0.280472	−	0.121338i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$		−	5.09614i		−	0.345949i
$218$	−5.20603	+	5.20603i	−0.352597	+	0.352597i
$219$		−	8.37281i		−	0.565782i
$220$	−4.35492	+	1.88402i	−0.293608	+	0.127021i
$221$		−	14.8878i		−	1.00146i
$222$	5.75171	−	1.97936i	0.386029	−	0.132846i
$223$	−18.5142	+	18.5142i	−1.23980	+	1.23980i	−0.279721	+	0.960081i	$0.590242\pi$
$223$	−18.5142	+	18.5142i	−1.23980	+	1.23980i	−0.960081	+	0.279721i	$0.909758\pi$
$224$	−1.84414	+	1.84414i	−0.123217	+	0.123217i
$225$	−3.64416	−	3.42347i	−0.242944	−	0.228231i
$226$		−	16.6356i		−	1.10658i
$227$	8.71126			0.578187			0.289093	−	0.957301i	$-0.406646\pi$
$227$	8.71126			0.578187			0.289093	+	0.957301i	$0.406646\pi$
$228$		−	3.23088i		−	0.213970i
$229$		−	18.0323i		−	1.19160i	−0.803131	−	0.595802i	$-0.796834\pi$
$229$		−	18.0323i		−	1.19160i	0.803131	−	0.595802i	$-0.203166\pi$
$230$	−5.11807	−	11.8304i	−0.337476	−	0.780075i
$231$	−5.53425			−0.364127
$232$	5.76649	+	5.76649i	0.378589	+	0.378589i
$233$	−15.7454	−	15.7454i	−1.03151	−	1.03151i	−0.999487	−	0.0320280i	$-0.989803\pi$
$233$	−15.7454	−	15.7454i	−1.03151	−	1.03151i	−0.0320280	−	0.999487i	$-0.510197\pi$
$234$			5.07258i			0.331605i
$235$	8.47123	−	21.3896i	0.552602	−	1.39531i
$236$	−8.25437	−	8.25437i	−0.537314	−	0.537314i
$237$			8.11381i			0.527048i
$238$	5.41247	−	5.41247i	0.350838	−	0.350838i
$239$	10.3297	+	10.3297i	0.668170	+	0.668170i	0.957292	−	0.289122i	$-0.0933635\pi$
$239$	10.3297	+	10.3297i	0.668170	+	0.668170i	−0.289122	+	0.957292i	$0.593363\pi$
$240$	−0.823360	+	2.07896i	−0.0531477	+	0.134196i
$241$	−6.49380	+	6.49380i	−0.418303	+	0.418303i	−0.884618	−	0.466316i	$-0.845581\pi$
$241$	−6.49380	+	6.49380i	−0.418303	+	0.418303i	0.466316	+	0.884618i	$0.345581\pi$
$242$		−	6.49703i		−	0.417645i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−2.44633	−	2.44633i	−0.156610	−	0.156610i
$245$	−0.406940	+	0.176050i	−0.0259984	+	0.0112474i
$246$	4.89802	+	4.89802i	0.312287	+	0.312287i
$247$	11.5887	−	11.5887i	0.737372	−	0.737372i
$248$	−1.38171	+	1.38171i	−0.0877388	+	0.0877388i
$249$	10.4794			0.664106
$250$	3.79037	−	10.5182i	0.239724	−	0.665231i
$251$	−2.81874	−	2.81874i	−0.177917	−	0.177917i	0.612530	−	0.790447i	$-0.290152\pi$
$251$	−2.81874	−	2.81874i	−0.177917	−	0.177917i	−0.790447	+	0.612530i	$0.790152\pi$
$252$	−1.84414	+	1.84414i	−0.116170	+	0.116170i
$253$	−12.2326			−0.769057
$254$	−6.57279	+	6.57279i	−0.412413	+	0.412413i
$255$	2.41652	−	6.10166i	0.151329	−	0.382101i
$256$	1.00000			0.0625000
$257$	−11.1961			−0.698394			−0.349197	−	0.937049i	$-0.613546\pi$
$257$	−11.1961			−0.698394			−0.349197	+	0.937049i	$0.613546\pi$
$258$	−1.41698	−	1.41698i	−0.0882172	−	0.0882172i
$259$	5.16220	+	15.0005i	0.320763	+	0.932086i
$260$	−10.4102	+	4.50366i	−0.645613	+	0.279305i
$261$	5.76649	+	5.76649i	0.356937	+	0.356937i
$262$	−2.67417	+	2.67417i	−0.165211	+	0.165211i
$263$	2.56637	+	2.56637i	0.158249	+	0.158249i	0.781790	−	0.623541i	$-0.214307\pi$
$263$	2.56637	+	2.56637i	0.158249	+	0.158249i	−0.623541	+	0.781790i	$0.714307\pi$
$264$	1.50049	+	1.50049i	0.0923490	+	0.0923490i
$265$	0.843022	+	0.333874i	0.0517864	+	0.0205097i
$266$	8.42617			0.516642
$267$	16.8625			1.03197
$268$	9.89884	−	9.89884i	0.604668	−	0.604668i
$269$			32.1166i			1.95819i	0.203414	+	0.979093i	$0.434796\pi$
$269$			32.1166i			1.95819i	−0.203414	+	0.979093i	$0.565204\pi$
$270$	−0.823360	+	2.07896i	−0.0501081	+	0.126522i
$271$	15.5594			0.945166			0.472583	−	0.881286i	$-0.343322\pi$
$271$	15.5594			0.945166			0.472583	+	0.881286i	$0.343322\pi$
$272$	−2.93495			−0.177958
$273$	−13.2293			−0.800675
$274$	0.925340	−	0.925340i	0.0559018	−	0.0559018i
$275$	−7.73297	−	7.26466i	−0.466316	−	0.438076i
$276$	−4.07619	+	4.07619i	−0.245358	+	0.245358i
$277$			14.4437i			0.867838i	0.900952	+	0.433919i	$0.142870\pi$
$277$			14.4437i			0.867838i	−0.900952	+	0.433919i	$0.857130\pi$
$278$			5.44352i			0.326481i
$279$	−1.38171	+	1.38171i	−0.0827209	+	0.0827209i
$280$	−5.42195	−	2.14733i	−0.324023	−	0.128328i
$281$	10.1736	−	10.1736i	0.606908	−	0.606908i	−0.335229	−	0.942137i	$-0.608814\pi$
$281$	10.1736	−	10.1736i	0.606908	−	0.606908i	0.942137	+	0.335229i	$0.108814\pi$
$282$	−10.2886			−0.612678
$283$	−11.7533			−0.698659			−0.349330	−	0.937000i	$-0.613591\pi$
$283$	−11.7533			−0.698659			−0.349330	+	0.937000i	$0.613591\pi$
$284$	−1.69758			−0.100733
$285$	6.63058	−	2.86852i	0.392762	−	0.169916i
$286$			10.7641i			0.636495i
$287$	−12.7741	+	12.7741i	−0.754031	+	0.754031i
$288$	1.00000			0.0589256
$289$	−8.38604			−0.493296
$290$	−6.71455	+	16.9540i	−0.394292	+	0.995576i
$291$	5.61922	+	5.61922i	0.329405	+	0.329405i
$292$	−5.92047	−	5.92047i	−0.346469	−	0.346469i
$293$	−14.2767	+	14.2767i	−0.834051	+	0.834051i	−0.988068	−	0.154017i	$-0.950779\pi$
$293$	−14.2767	+	14.2767i	−0.834051	+	0.834051i	0.154017	+	0.988068i	$0.450779\pi$
$294$	0.140212	+	0.140212i	0.00817732	+	0.00817732i
$295$	9.61144	−	24.2686i	0.559600	−	1.41297i
$296$	2.66745	−	5.46669i	0.155042	−	0.317745i
$297$	1.50049	+	1.50049i	0.0870675	+	0.0870675i
$298$	−16.9497			−0.981871
$299$	−29.2414			−1.69107
$300$	−4.99756	+	0.156051i	−0.288535	+	0.00900961i
$301$	3.69549	−	3.69549i	0.213005	−	0.213005i
$302$	−1.25999			−0.0725041
$303$	10.7641	−	10.7641i	0.618382	−	0.618382i
$304$	−2.28458	−	2.28458i	−0.131030	−	0.131030i
$305$	2.84853	−	7.19245i	0.163106	−	0.411839i
$306$	−2.93495			−0.167780
$307$	−16.2628	+	16.2628i	−0.928166	+	0.928166i	−0.997587	−	0.0694214i	$-0.977885\pi$
$307$	−16.2628	+	16.2628i	−0.928166	+	0.928166i	0.0694214	+	0.997587i	$0.477885\pi$
$308$	−3.91330	+	3.91330i	−0.222981	+	0.222981i
$309$	9.54509	+	9.54509i	0.543001	+	0.543001i
$310$	−4.06236	−	1.60887i	−0.230727	−	0.0913779i
$311$	11.0741	+	11.0741i	0.627952	+	0.627952i	0.947552	−	0.319600i	$-0.103549\pi$
$311$	11.0741	+	11.0741i	0.627952	+	0.627952i	−0.319600	+	0.947552i	$0.603549\pi$
$312$	3.58685	+	3.58685i	0.203066	+	0.203066i
$313$		−	4.41462i		−	0.249529i	−0.992186	−	0.124764i	$-0.960182\pi$
$313$		−	4.41462i		−	0.249529i	0.992186	−	0.124764i	$-0.0398175\pi$
$314$	4.05205	−	4.05205i	0.228671	−	0.228671i
$315$	−5.42195	−	2.14733i	−0.305492	−	0.120988i
$316$	5.73733	+	5.73733i	0.322750	+	0.322750i
$317$	−1.75051	+	1.75051i	−0.0983187	+	0.0983187i	−0.754555	−	0.656237i	$-0.772147\pi$
$317$	−1.75051	+	1.75051i	−0.0983187	+	0.0983187i	0.656237	+	0.754555i	$0.272147\pi$
$318$		−	0.405502i		−	0.0227394i
$319$	12.2366	+	12.2366i	0.685119	+	0.685119i
$320$	0.887844	+	2.05225i	0.0496320	+	0.114724i
$321$		−	3.28340i		−	0.183261i
$322$	−10.6307	−	10.6307i	−0.592428	−	0.592428i
$323$	6.70514	+	6.70514i	0.373084	+	0.373084i
$324$	1.00000			0.0555556
$325$	−18.4853	−	17.3658i	−1.02538	−	0.963281i
$326$		−	0.200876i		−	0.0111255i
$327$			7.36244i			0.407144i
$328$	6.92685			0.382471
$329$		−	26.8328i		−	1.47934i
$330$	−1.74719	+	4.41160i	−0.0961794	+	0.242850i
$331$	−17.0019	+	17.0019i	−0.934511	+	0.934511i	−0.997984	−	0.0634724i	$-0.979783\pi$
$331$	−17.0019	+	17.0019i	−0.934511	+	0.934511i	0.0634724	+	0.997984i	$0.479783\pi$
$332$	7.41007	−	7.41007i	0.406680	−	0.406680i
$333$	2.66745	−	5.46669i	0.146175	−	0.299573i
$334$			7.20812i			0.394411i
$335$	29.1035	+	11.5263i	1.59009	+	0.629748i
$336$			2.60801i			0.142279i
$337$	16.7264	−	16.7264i	0.911145	−	0.911145i	−0.0852173	−	0.996362i	$-0.527158\pi$
$337$	16.7264	−	16.7264i	0.911145	−	0.911145i	0.996362	+	0.0852173i	$0.0271584\pi$
$338$			12.7311i			0.692478i
$339$	−11.7631	−	11.7631i	−0.638885	−	0.638885i
$340$	−2.60578	−	6.02326i	−0.141318	−	0.326657i
$341$	−2.93202	+	2.93202i	−0.158778	+	0.158778i
$342$	−2.28458	−	2.28458i	−0.123536	−	0.123536i
$343$	−13.2747	+	13.2747i	−0.716764	+	0.716764i
$344$	−2.00391			−0.108044
$345$	−11.9844	−	4.74635i	−0.645218	−	0.255535i
$346$	−1.14427	+	1.14427i	−0.0615161	+	0.0615161i
$347$		−	27.1062i		−	1.45514i	−0.686036	−	0.727568i	$-0.740651\pi$
$347$		−	27.1062i		−	1.45514i	0.686036	−	0.727568i	$-0.259349\pi$
$348$	8.15506			0.437157
$349$			1.86734i			0.0999566i	0.998750	+	0.0499783i	$0.0159152\pi$
$349$			1.86734i			0.0999566i	−0.998750	+	0.0499783i	$0.984085\pi$
$350$	−0.406983	−	13.0337i	−0.0217541	−	0.696680i
$351$	3.58685	+	3.58685i	0.191452	+	0.191452i
$352$	2.12202			0.113104
$353$	15.2302			0.810619			0.405310	−	0.914179i	$-0.367164\pi$
$353$	15.2302			0.810619			0.405310	+	0.914179i	$0.367164\pi$
$354$	−11.6734			−0.620436
$355$	−1.50718	−	3.48385i	−0.0799929	−	0.184904i
$356$	11.9236	−	11.9236i	0.631950	−	0.631950i
$357$		−	7.65439i		−	0.405113i
$358$	9.71351	+	9.71351i	0.513375	+	0.513375i
$359$			18.9718i			1.00129i	0.865651	+	0.500647i	$0.166905\pi$
$359$			18.9718i			1.00129i	−0.865651	+	0.500647i	$0.833095\pi$
$360$	0.887844	+	2.05225i	0.0467935	+	0.108163i
$361$		−	8.56139i		−	0.450600i
$362$			1.59280i			0.0837159i
$363$	−4.59410	−	4.59410i	−0.241128	−	0.241128i
$364$	−9.35455	+	9.35455i	−0.490312	+	0.490312i
$365$	6.89384	−	17.4067i	0.360840	−	0.911111i
$366$	−3.45964			−0.180838
$367$	−23.8239	−	23.8239i	−1.24360	−	1.24360i	−0.958497	−	0.285103i	$-0.907972\pi$
$367$	−23.8239	−	23.8239i	−1.24360	−	1.24360i	−0.285103	−	0.958497i	$-0.592028\pi$
$368$			5.76461i			0.300501i
$369$	6.92685			0.360598
$370$	13.5873	+	0.620706i	0.706370	+	0.0322690i
$371$	1.05755			0.0549054
$372$			1.95403i			0.101312i
$373$	−2.47846	−	2.47846i	−0.128330	−	0.128330i	0.640025	−	0.768354i	$-0.278924\pi$
$373$	−2.47846	−	2.47846i	−0.128330	−	0.128330i	−0.768354	+	0.640025i	$0.778924\pi$
$374$	−6.22803			−0.322044
$375$	−4.75731	−	10.1177i	−0.245667	−	0.522476i
$376$	−7.27515	+	7.27515i	−0.375187	+	0.375187i
$377$	29.2510	+	29.2510i	1.50650	+	1.50650i
$378$			2.60801i			0.134142i
$379$			31.6861i			1.62761i	0.581139	+	0.813804i	$0.302607\pi$
$379$			31.6861i			1.62761i	−0.581139	+	0.813804i	$0.697393\pi$
$380$	2.66018	−	6.71688i	0.136464	−	0.344569i
$381$			9.29533i			0.476214i
$382$	14.2911	+	14.2911i	0.731198	+	0.731198i
$383$		−	12.7864i		−	0.653357i	−0.945136	−	0.326678i	$-0.894071\pi$
$383$		−	12.7864i		−	0.653357i	0.945136	−	0.326678i	$-0.105929\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−11.5055	−	4.55668i	−0.586374	−	0.232230i
$386$	−11.4610			−0.583347
$387$	−2.00391			−0.101864
$388$	7.94678			0.403437
$389$	15.4731	+	15.4731i	0.784518	+	0.784518i	0.980590	−	0.196071i	$-0.0628184\pi$
$389$	15.4731	+	15.4731i	0.784518	+	0.784518i	−0.196071	+	0.980590i	$0.562818\pi$
$390$	−4.17656	+	10.5457i	−0.211488	+	0.534002i
$391$		−	16.9189i		−	0.855623i
$392$	0.198289			0.0100151
$393$			3.78185i			0.190769i
$394$	3.61811	−	3.61811i	0.182278	−	0.182278i
$395$	−6.68059	+	16.8683i	−0.336137	+	0.848736i
$396$	2.12202			0.106635
$397$	−11.7358	+	11.7358i	−0.589002	+	0.589002i	−0.937361	−	0.348359i	$-0.886739\pi$
$397$	−11.7358	+	11.7358i	−0.589002	+	0.589002i	0.348359	+	0.937361i	$0.386739\pi$
$398$	14.1563	+	14.1563i	0.709590	+	0.709590i
$399$	5.95820	−	5.95820i	0.298283	−	0.298283i
$400$	−3.42347	+	3.64416i	−0.171173	+	0.182208i
$401$	−11.6604	−	11.6604i	−0.582291	−	0.582291i	0.353241	−	0.935532i	$-0.385079\pi$
$401$	−11.6604	−	11.6604i	−0.582291	−	0.582291i	−0.935532	+	0.353241i	$0.885079\pi$
$402$		−	13.9991i		−	0.698210i
$403$	−7.00884	+	7.00884i	−0.349135	+	0.349135i
$404$		−	15.2228i		−	0.757360i
$405$	0.887844	+	2.05225i	0.0441173	+	0.101977i
$406$			21.2685i			1.05554i
$407$	5.66038	−	11.6004i	0.280575	−	0.575012i
$408$	−2.07533	+	2.07533i	−0.102744	+	0.102744i
$409$	22.9972	−	22.9972i	1.13714	−	1.13714i	0.148176	−	0.988961i	$-0.452660\pi$
$409$	22.9972	−	22.9972i	1.13714	−	1.13714i	0.988961	−	0.148176i	$-0.0473403\pi$
$410$	6.14996	+	14.2156i	0.303725	+	0.702060i
$411$		−	1.30863i		−	0.0645499i
$412$	13.4988			0.665038
$413$		−	30.4444i		−	1.49807i
$414$			5.76461i			0.283315i
$415$	21.7863	+	8.62833i	1.06945	+	0.423548i
$416$	5.07258			0.248704
$417$	3.84915	+	3.84915i	0.188494	+	0.188494i
$418$	−4.84792	−	4.84792i	−0.237120	−	0.237120i
$419$		−	24.2039i		−	1.18244i	−0.806512	−	0.591218i	$-0.798647\pi$
$419$		−	24.2039i		−	1.18244i	0.806512	−	0.591218i	$-0.201353\pi$
$420$	−5.35229	+	2.31550i	−0.261165	+	0.112985i
$421$	−9.91998	−	9.91998i	−0.483470	−	0.483470i	0.422768	−	0.906238i	$-0.361059\pi$
$421$	−9.91998	−	9.91998i	−0.483470	−	0.483470i	−0.906238	+	0.422768i	$0.861059\pi$
$422$		−	8.13385i		−	0.395949i
$423$	−7.27515	+	7.27515i	−0.353730	+	0.353730i
$424$	−0.286733	−	0.286733i	−0.0139250	−	0.0139250i
$425$	10.0477	−	10.6954i	0.487386	−	0.518805i
$426$	−1.20037	+	1.20037i	−0.0581580	+	0.0581580i
$427$		−	9.02276i		−	0.436642i
$428$	−2.32171	−	2.32171i	−0.112224	−	0.112224i
$429$	7.61138	+	7.61138i	0.367481	+	0.367481i
$430$	−1.77916	−	4.11252i	−0.0857986	−	0.198324i
$431$	18.4635	+	18.4635i	0.889356	+	0.889356i	0.994461	−	0.105105i	$-0.0335180\pi$
$431$	18.4635	+	18.4635i	0.889356	+	0.889356i	−0.105105	+	0.994461i	$0.533518\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	20.6095	−	20.6095i	0.990427	−	0.990427i	−0.00952737	−	0.999955i	$-0.503033\pi$
$433$	20.6095	−	20.6095i	0.990427	−	0.990427i	0.999955	+	0.00952737i	$0.00303270\pi$
$434$	−5.09614			−0.244623
$435$	7.24042	+	16.7362i	0.347151	+	0.802440i
$436$	5.20603	+	5.20603i	0.249324	+	0.249324i
$437$	13.1697	−	13.1697i	0.629992	−	0.629992i
$438$	−8.37281			−0.400068
$439$	6.00049	−	6.00049i	0.286388	−	0.286388i	−0.549262	−	0.835650i	$-0.685091\pi$
$439$	6.00049	−	6.00049i	0.286388	−	0.286388i	0.835650	+	0.549262i	$0.185091\pi$
$440$	1.88402	+	4.35492i	0.0898172	+	0.207612i
$441$	0.198289			0.00944235
$442$	−14.8878			−0.708140
$443$	−19.3252	−	19.3252i	−0.918168	−	0.918168i	0.0787279	−	0.996896i	$-0.474914\pi$
$443$	−19.3252	−	19.3252i	−0.918168	−	0.918168i	−0.996896	+	0.0787279i	$0.974914\pi$
$444$	−1.97936	−	5.75171i	−0.0939364	−	0.272964i
$445$	35.0565	+	13.8839i	1.66184	+	0.658162i
$446$	18.5142	+	18.5142i	0.876673	+	0.876673i
$447$	−11.9853	+	11.9853i	−0.566884	+	0.566884i
$448$	1.84414	+	1.84414i	0.0871275	+	0.0871275i
$449$	−23.5893	−	23.5893i	−1.11325	−	1.11325i	−0.992709	−	0.120538i	$-0.961538\pi$
$449$	−23.5893	−	23.5893i	−1.11325	−	1.11325i	−0.120538	−	0.992709i	$-0.538462\pi$
$450$	−3.42347	+	3.64416i	−0.161384	+	0.171787i
$451$	14.6989			0.692145
$452$	−16.6356			−0.782471
$453$	−0.890945	+	0.890945i	−0.0418603	+	0.0418603i
$454$		−	8.71126i		−	0.408840i
$455$	−27.5033	−	10.8925i	−1.28937	−	0.510648i
$456$	−3.23088			−0.151300
$457$	−10.5479			−0.493409			−0.246704	−	0.969091i	$-0.579348\pi$
$457$	−10.5479			−0.493409			−0.246704	+	0.969091i	$0.579348\pi$
$458$	−18.0323			−0.842592
$459$	−2.07533	+	2.07533i	−0.0968679	+	0.0968679i
$460$	−11.8304	+	5.11807i	−0.551596	+	0.238631i
$461$	−26.9418	+	26.9418i	−1.25481	+	1.25481i	−0.301265	+	0.953541i	$0.597409\pi$
$461$	−26.9418	+	26.9418i	−1.25481	+	1.25481i	−0.953541	+	0.301265i	$0.902591\pi$
$462$			5.53425i			0.257476i
$463$			16.5851i			0.770773i	0.922755	+	0.385387i	$0.125932\pi$
$463$			16.5851i			0.770773i	−0.922755	+	0.385387i	$0.874068\pi$
$464$	5.76649	−	5.76649i	0.267703	−	0.267703i
$465$	−4.01017	+	1.73488i	−0.185967	+	0.0804530i
$466$	−15.7454	+	15.7454i	−0.729391	+	0.729391i
$467$	34.4641			1.59481			0.797403	−	0.603447i	$-0.206207\pi$
$467$	34.4641			1.59481			0.797403	+	0.603447i	$0.206207\pi$
$468$	5.07258			0.234480
$469$	36.5097			1.68586
$470$	−21.3896	−	8.47123i	−0.986630	−	0.390749i
$471$		−	5.73047i		−	0.264046i
$472$	−8.25437	+	8.25437i	−0.379938	+	0.379938i
$473$	−4.25233			−0.195523
$474$	8.11381			0.372680
$475$	16.1465	−	0.504183i	0.740854	−	0.0231335i
$476$	−5.41247	−	5.41247i	−0.248080	−	0.248080i
$477$	−0.286733	−	0.286733i	−0.0131286	−	0.0131286i
$478$	10.3297	−	10.3297i	0.472467	−	0.472467i
$479$	15.9403	+	15.9403i	0.728333	+	0.728333i	0.970288	−	0.241954i	$-0.0777885\pi$
$479$	15.9403	+	15.9403i	0.728333	+	0.728333i	−0.241954	+	0.970288i	$0.577788\pi$
$480$	2.07896	+	0.823360i	0.0948911	+	0.0375811i
$481$	13.5308	−	27.7302i	0.616953	−	1.26439i
$482$	6.49380	+	6.49380i	0.295785	+	0.295785i
$483$	−15.0341			−0.684077
$484$	−6.49703			−0.295320
$485$	7.05550	+	16.3088i	0.320374	+	0.740544i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	5.52466			0.250346			0.125173	−	0.992135i	$-0.460051\pi$
$487$	5.52466			0.250346			0.125173	+	0.992135i	$0.460051\pi$
$488$	−2.44633	+	2.44633i	−0.110740	+	0.110740i
$489$	−0.142041	−	0.142041i	−0.00642329	−	0.00642329i
$490$	0.176050	+	0.406940i	0.00795313	+	0.0183837i
$491$	30.9165			1.39524			0.697621	−	0.716467i	$-0.254242\pi$
$491$	30.9165			1.39524			0.697621	+	0.716467i	$0.254242\pi$
$492$	4.89802	−	4.89802i	0.220820	−	0.220820i
$493$	−16.9244	+	16.9244i	−0.762237	+	0.762237i
$494$	−11.5887	−	11.5887i	−0.521401	−	0.521401i
$495$	1.88402	+	4.35492i	0.0846805	+	0.195739i
$496$	1.38171	+	1.38171i	0.0620407	+	0.0620407i
$497$	−3.13057	−	3.13057i	−0.140425	−	0.140425i
$498$		−	10.4794i		−	0.469594i
$499$	15.3419	−	15.3419i	0.686798	−	0.686798i	−0.274725	−	0.961523i	$-0.588587\pi$
$499$	15.3419	−	15.3419i	0.686798	−	0.686798i	0.961523	+	0.274725i	$0.0885867\pi$
$500$	−10.5182	−	3.79037i	−0.470389	−	0.169511i
$501$	5.09691	+	5.09691i	0.227713	+	0.227713i
$502$	−2.81874	+	2.81874i	−0.125806	+	0.125806i
$503$		−	6.97745i		−	0.311109i	−0.987827	−	0.155555i	$-0.950284\pi$
$503$		−	6.97745i		−	0.311109i	0.987827	−	0.155555i	$-0.0497164\pi$
$504$	1.84414	+	1.84414i	0.0821446	+	0.0821446i
$505$	31.2409	−	13.5154i	1.39020	−	0.601429i
$506$			12.2326i			0.543806i
$507$	9.00221	+	9.00221i	0.399802	+	0.399802i
$508$	6.57279	+	6.57279i	0.291620	+	0.291620i
$509$	−15.9733			−0.708002			−0.354001	−	0.935245i	$-0.615179\pi$
$509$	−15.9733			−0.708002			−0.354001	+	0.935245i	$0.615179\pi$
$510$	−6.10166	−	2.41652i	−0.270186	−	0.107006i
$511$		−	21.8364i		−	0.965984i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.23088			−0.142647
$514$			11.1961i			0.493839i
$515$	11.9848	+	27.7029i	0.528114	+	1.22074i
$516$	−1.41698	+	1.41698i	−0.0623790	+	0.0623790i
$517$	−15.4380	+	15.4380i	−0.678963	+	0.678963i
$518$	15.0005	−	5.16220i	0.659084	−	0.226814i
$519$			1.61824i			0.0710327i
$520$	4.50366	+	10.4102i	0.197498	+	0.456518i
$521$		−	38.5368i		−	1.68833i	−0.536084	−	0.844165i	$-0.680097\pi$
$521$		−	38.5368i		−	1.68833i	0.536084	−	0.844165i	$-0.319903\pi$
$522$	5.76649	−	5.76649i	0.252393	−	0.252393i
$523$			14.7060i			0.643047i	0.946902	+	0.321523i	$0.104195\pi$
$523$			14.7060i			0.643047i	−0.946902	+	0.321523i	$0.895805\pi$
$524$	2.67417	+	2.67417i	0.116822	+	0.116822i
$525$	−9.50399	−	8.92843i	−0.414788	−	0.389669i
$526$	2.56637	−	2.56637i	0.111899	−	0.111899i
$527$	−4.05526	−	4.05526i	−0.176650	−	0.176650i
$528$	1.50049	−	1.50049i	0.0653006	−	0.0653006i
$529$	−10.2307			−0.444812
$530$	0.333874	−	0.843022i	0.0145026	−	0.0366185i
$531$	−8.25437	+	8.25437i	−0.358209	+	0.358209i
$532$		−	8.42617i		−	0.365321i
$533$	35.1370			1.52195
$534$		−	16.8625i		−	0.729713i
$535$	2.70342	−	6.82606i	0.116879	−	0.295116i
$536$	−9.89884	−	9.89884i	−0.427565	−	0.427565i
$537$	13.7370			0.592794
$538$	32.1166			1.38465
$539$	0.420774			0.0181240
$540$	2.07896	+	0.823360i	0.0894642	+	0.0354318i
$541$	−24.9509	+	24.9509i	−1.07272	+	1.07272i	−0.0755841	+	0.997139i	$0.524082\pi$
$541$	−24.9509	+	24.9509i	−1.07272	+	1.07272i	−0.997139	+	0.0755841i	$0.975918\pi$
$542$		−	15.5594i		−	0.668333i
$543$	1.12628	+	1.12628i	0.0483334	+	0.0483334i
$544$			2.93495i			0.125835i
$545$	−6.06194	+	15.3062i	−0.259665	+	0.655646i
$546$			13.2293i			0.566163i
$547$			36.4914i			1.56026i	0.625617	+	0.780131i	$0.284847\pi$
$547$			36.4914i			1.56026i	−0.625617	+	0.780131i	$0.715153\pi$
$548$	−0.925340	−	0.925340i	−0.0395286	−	0.0395286i
$549$	−2.44633	+	2.44633i	−0.104407	+	0.104407i
$550$	−7.26466	+	7.73297i	−0.309766	+	0.329735i
$551$	−26.3480			−1.12246
$552$	4.07619	+	4.07619i	0.173494	+	0.173494i
$553$			21.1609i			0.899852i
$554$	14.4437			0.613654
$555$	10.0466	−	9.16877i	0.426453	−	0.389192i
$556$	5.44352			0.230857
$557$		−	32.6303i		−	1.38259i	−0.722572	−	0.691296i	$-0.757040\pi$
$557$		−	32.6303i		−	1.38259i	0.722572	−	0.691296i	$-0.242960\pi$
$558$	1.38171	+	1.38171i	0.0584925	+	0.0584925i
$559$	−10.1650			−0.429933
$560$	−2.14733	+	5.42195i	−0.0907413	+	0.229119i
$561$	−4.40388	+	4.40388i	−0.185932	+	0.185932i
$562$	−10.1736	−	10.1736i	−0.429149	−	0.429149i
$563$		−	20.4470i		−	0.861738i	−0.902415	−	0.430869i	$-0.858207\pi$
$563$		−	20.4470i		−	0.861738i	0.902415	−	0.430869i	$-0.141793\pi$
$564$			10.2886i			0.433229i
$565$	−14.7698	−	34.1404i	−0.621369	−	1.43630i
$566$			11.7533i			0.494027i
$567$	1.84414	+	1.84414i	0.0774466	+	0.0774466i
$568$			1.69758i			0.0712287i
$569$	11.2342	−	11.2342i	0.470964	−	0.470964i	−0.431263	−	0.902226i	$-0.641932\pi$
$569$	11.2342	−	11.2342i	0.470964	−	0.470964i	0.902226	+	0.431263i	$0.141932\pi$
$570$	−2.86852	−	6.63058i	−0.120149	−	0.277725i
$571$	26.4113			1.10528			0.552639	−	0.833421i	$-0.313621\pi$
$571$	26.4113			1.10528			0.552639	+	0.833421i	$0.313621\pi$
$572$	10.7641			0.450070
$573$	20.2107			0.844315
$574$	12.7741	+	12.7741i	0.533180	+	0.533180i
$575$	−21.0071	−	19.7349i	−0.876058	−	0.823004i
$576$		−	1.00000i		−	0.0416667i
$577$	−7.95386			−0.331123			−0.165562	−	0.986199i	$-0.552944\pi$
$577$	−7.95386			−0.331123			−0.165562	+	0.986199i	$0.552944\pi$
$578$			8.38604i			0.348813i
$579$	−8.10412	+	8.10412i	−0.336796	+	0.336796i
$580$	16.9540	+	6.71455i	0.703978	+	0.278806i
$581$	27.3304			1.13386
$582$	5.61922	−	5.61922i	0.232924	−	0.232924i
$583$	−0.608453	−	0.608453i	−0.0251995	−	0.0251995i
$584$	−5.92047	+	5.92047i	−0.244991	+	0.244991i
$585$	4.50366	+	10.4102i	0.186203	+	0.430409i
$586$	14.2767	+	14.2767i	0.589763	+	0.589763i
$587$		−	12.8759i		−	0.531445i	−0.964050	−	0.265723i	$-0.914389\pi$
$587$		−	12.8759i		−	0.531445i	0.964050	−	0.265723i	$-0.0856105\pi$
$588$	0.140212	−	0.140212i	0.00578224	−	0.00578224i
$589$		−	6.31326i		−	0.260133i
$590$	−24.2686	−	9.61144i	−0.999123	−	0.395697i
$591$		−	5.11678i		−	0.210476i
$592$	−5.46669	−	2.66745i	−0.224680	−	0.109631i
$593$	17.6097	−	17.6097i	0.723143	−	0.723143i	−0.246102	−	0.969244i	$-0.579150\pi$
$593$	17.6097	−	17.6097i	0.723143	−	0.723143i	0.969244	+	0.246102i	$0.0791497\pi$
$594$	1.50049	−	1.50049i	0.0615660	−	0.0615660i
$595$	6.30232	−	15.9132i	0.258370	−	0.652377i
$596$			16.9497i			0.694288i
$597$	20.0200			0.819364
$598$			29.2414i			1.19577i
$599$		−	28.1341i		−	1.14953i	−0.818320	−	0.574763i	$-0.805094\pi$
$599$		−	28.1341i		−	1.14953i	0.818320	−	0.574763i	$-0.194906\pi$
$600$	0.156051	+	4.99756i	0.00637076	+	0.204025i
$601$	−14.8826			−0.607072			−0.303536	−	0.952820i	$-0.598167\pi$
$601$	−14.8826			−0.607072			−0.303536	+	0.952820i	$0.598167\pi$
$602$	−3.69549	−	3.69549i	−0.150617	−	0.150617i
$603$	−9.89884	−	9.89884i	−0.403112	−	0.403112i
$604$			1.25999i			0.0512681i
$605$	−5.76835	−	13.3335i	−0.234517	−	0.542086i
$606$	−10.7641	−	10.7641i	−0.437262	−	0.437262i
$607$			5.21022i			0.211476i	0.994394	+	0.105738i	$0.0337205\pi$
$607$			5.21022i			0.211476i	−0.994394	+	0.105738i	$0.966279\pi$
$608$	−2.28458	+	2.28458i	−0.0926519	+	0.0926519i
$609$	15.0391	+	15.0391i	0.609414	+	0.609414i
$610$	−7.19245	−	2.84853i	−0.291214	−	0.115333i
$611$	−36.9038	+	36.9038i	−1.49297	+	1.49297i
$612$			2.93495i			0.118639i
$613$	15.0091	+	15.0091i	0.606211	+	0.606211i	0.941954	−	0.335743i	$-0.108987\pi$
$613$	15.0091	+	15.0091i	0.606211	+	0.606211i	−0.335743	+	0.941954i	$0.608987\pi$
$614$	16.2628	+	16.2628i	0.656312	+	0.656312i
$615$	14.4007	+	5.70329i	0.580690	+	0.229979i
$616$	3.91330	+	3.91330i	0.157671	+	0.157671i
$617$	−6.06777	+	6.06777i	−0.244279	+	0.244279i	−0.818618	−	0.574339i	$-0.805259\pi$
$617$	−6.06777	+	6.06777i	−0.244279	+	0.244279i	0.574339	+	0.818618i	$0.305259\pi$
$618$	9.54509	−	9.54509i	0.383960	−	0.383960i
$619$	−20.1898			−0.811495			−0.405747	−	0.913985i	$-0.632989\pi$
$619$	−20.1898			−0.811495			−0.405747	+	0.913985i	$0.632989\pi$
$620$	−1.60887	+	4.06236i	−0.0646139	+	0.163148i
$621$	4.07619	+	4.07619i	0.163572	+	0.163572i
$622$	11.0741	−	11.0741i	0.444029	−	0.444029i
$623$	43.9776			1.76193
$624$	3.58685	−	3.58685i	0.143589	−	0.143589i
$625$	−1.55975	−	24.9513i	−0.0623900	−	0.998052i
$626$	−4.41462			−0.176444
$627$	−6.85600			−0.273802
$628$	−4.05205	−	4.05205i	−0.161695	−	0.161695i
$629$	16.0445	+	7.82884i	0.639736	+	0.312156i
$630$	−2.14733	+	5.42195i	−0.0855517	+	0.216016i
$631$	1.59016	+	1.59016i	0.0633034	+	0.0633034i	0.738050	−	0.674746i	$-0.235747\pi$
$631$	1.59016	+	1.59016i	0.0633034	+	0.0633034i	−0.674746	+	0.738050i	$0.735747\pi$
$632$	5.73733	−	5.73733i	0.228219	−	0.228219i
$633$	−5.75150	−	5.75150i	−0.228602	−	0.228602i
$634$	1.75051	+	1.75051i	0.0695218	+	0.0695218i
$635$	−7.65340	+	19.3246i	−0.303716	+	0.766874i
$636$	−0.405502			−0.0160792
$637$	1.00584			0.0398528
$638$	12.2366	−	12.2366i	0.484452	−	0.484452i
$639$			1.69758i			0.0671550i
$640$	2.05225	−	0.887844i	0.0811223	−	0.0350951i
$641$	−27.0270			−1.06750			−0.533752	−	0.845641i	$-0.679218\pi$
$641$	−27.0270			−1.06750			−0.533752	+	0.845641i	$0.679218\pi$
$642$	−3.28340			−0.129585
$643$	18.0452			0.711635			0.355817	−	0.934556i	$-0.384203\pi$
$643$	18.0452			0.711635			0.355817	+	0.934556i	$0.384203\pi$
$644$	−10.6307	+	10.6307i	−0.418910	+	0.418910i
$645$	−4.16605	−	1.64994i	−0.164038	−	0.0649663i
$646$	6.70514	−	6.70514i	0.263810	−	0.263810i
$647$		−	2.13093i		−	0.0837754i	−0.999122	−	0.0418877i	$-0.986663\pi$
$647$		−	2.13093i		−	0.0837754i	0.999122	−	0.0418877i	$-0.0133372\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−17.5159	+	17.5159i	−0.687560	+	0.687560i
$650$	−17.3658	+	18.4853i	−0.681143	+	0.725052i
$651$	−3.60352	+	3.60352i	−0.141233	+	0.141233i
$652$	−0.200876			−0.00786690
$653$	12.1928			0.477142			0.238571	−	0.971125i	$-0.423321\pi$
$653$	12.1928			0.477142			0.238571	+	0.971125i	$0.423321\pi$
$654$	7.36244			0.287894
$655$	−3.11382	+	7.86231i	−0.121667	+	0.307206i
$656$		−	6.92685i		−	0.270448i
$657$	−5.92047	+	5.92047i	−0.230980	+	0.230980i
$658$	−26.8328			−1.04605
$659$	−19.4303			−0.756898			−0.378449	−	0.925622i	$-0.623543\pi$
$659$	−19.4303			−0.756898			−0.378449	+	0.925622i	$0.623543\pi$
$660$	4.41160	+	1.74719i	0.171721	+	0.0680091i
$661$	25.0660	+	25.0660i	0.974956	+	0.974956i	0.999694	−	0.0247380i	$-0.00787514\pi$
$661$	25.0660	+	25.0660i	0.974956	+	0.974956i	−0.0247380	+	0.999694i	$0.507875\pi$
$662$	17.0019	+	17.0019i	0.660799	+	0.660799i
$663$	−10.5273	+	10.5273i	−0.408845	+	0.408845i
$664$	−7.41007	−	7.41007i	−0.287566	−	0.287566i
$665$	17.2926	−	7.48113i	0.670579	−	0.290106i
$666$	−5.46669	−	2.66745i	−0.211830	−	0.103362i
$667$	33.2416	+	33.2416i	1.28712	+	1.28712i
$668$	7.20812			0.278891
$669$	26.1830			1.01229
$670$	11.5263	−	29.1035i	0.445299	−	1.12437i
$671$	−5.19117	+	5.19117i	−0.200403	+	0.200403i
$672$	2.60801			0.100606
$673$	25.0421	−	25.0421i	0.965303	−	0.965303i	−0.0341149	−	0.999418i	$-0.510861\pi$
$673$	25.0421	−	25.0421i	0.965303	−	0.965303i	0.999418	+	0.0341149i	$0.0108612\pi$
$674$	−16.7264	−	16.7264i	−0.644277	−	0.644277i
$675$	0.156051	+	4.99756i	0.00600641	+	0.192356i
$676$	12.7311			0.489656
$677$	−4.04562	+	4.04562i	−0.155486	+	0.155486i	−0.780563	−	0.625077i	$-0.785068\pi$
$677$	−4.04562	+	4.04562i	−0.155486	+	0.155486i	0.625077	+	0.780563i	$0.285068\pi$
$678$	−11.7631	+	11.7631i	−0.451760	+	0.451760i
$679$	14.6550	+	14.6550i	0.562407	+	0.562407i
$680$	−6.02326	+	2.60578i	−0.230982	+	0.0999272i
$681$	−6.15979	−	6.15979i	−0.236044	−	0.236044i
$682$	2.93202	+	2.93202i	0.112273	+	0.112273i
$683$		−	49.4497i		−	1.89214i	−0.323961	−	0.946070i	$-0.605015\pi$
$683$		−	49.4497i		−	1.89214i	0.323961	−	0.946070i	$-0.394985\pi$
$684$	−2.28458	+	2.28458i	−0.0873531	+	0.0873531i
$685$	1.07747	−	2.72059i	0.0411681	−	0.103948i
$686$	13.2747	+	13.2747i	0.506829	+	0.506829i
$687$	−12.7507	+	12.7507i	−0.486471	+	0.486471i
$688$			2.00391i			0.0763983i
$689$	−1.45448	−	1.45448i	−0.0554111	−	0.0554111i
$690$	−4.74635	+	11.9844i	−0.180690	+	0.456238i
$691$		−	9.04475i		−	0.344078i	−0.985090	−	0.172039i	$-0.944964\pi$
$691$		−	9.04475i		−	0.344078i	0.985090	−	0.172039i	$-0.0550356\pi$
$692$	1.14427	+	1.14427i	0.0434985	+	0.0434985i
$693$	3.91330	+	3.91330i	0.148654	+	0.148654i
$694$	−27.1062			−1.02894
$695$	4.83299	+	11.1715i	0.183326	+	0.423758i
$696$		−	8.15506i		−	0.309117i
$697$			20.3300i			0.770054i
$698$	1.86734			0.0706800
$699$			22.2673i			0.842228i
$700$	−13.0337	+	0.406983i	−0.492627	+	0.0153825i
$701$	−6.79801	+	6.79801i	−0.256757	+	0.256757i	−0.823734	−	0.566977i	$-0.808113\pi$
$701$	−6.79801	+	6.79801i	−0.256757	+	0.256757i	0.566977	+	0.823734i	$0.308113\pi$
$702$	3.58685	−	3.58685i	0.135377	−	0.135377i
$703$	6.39509	+	18.5831i	0.241195	+	0.700875i
$704$		−	2.12202i		−	0.0799766i
$705$	−21.1148	+	9.13468i	−0.795230	+	0.344032i
$706$		−	15.2302i		−	0.573194i
$707$	28.0729	−	28.0729i	1.05579	−	1.05579i
$708$			11.6734i			0.438715i
$709$	12.7014	+	12.7014i	0.477012	+	0.477012i	0.904175	−	0.427163i	$-0.140487\pi$
$709$	12.7014	+	12.7014i	0.477012	+	0.477012i	−0.427163	+	0.904175i	$0.640487\pi$
$710$	−3.48385	+	1.50718i	−0.130747	+	0.0565635i
$711$	5.73733	−	5.73733i	0.215167	−	0.215167i
$712$	−11.9236	−	11.9236i	−0.446856	−	0.446856i
$713$	−7.96502	+	7.96502i	−0.298292	+	0.298292i
$714$	−7.65439			−0.286458
$715$	9.55685	+	22.0907i	0.357406	+	0.826144i
$716$	9.71351	−	9.71351i	0.363011	−	0.363011i
$717$		−	14.6083i		−	0.545558i
$718$	18.9718			0.708022
$719$		−	25.0596i		−	0.934567i	−0.884108	−	0.467283i	$-0.845233\pi$
$719$		−	25.0596i		−	0.934567i	0.884108	−	0.467283i	$-0.154767\pi$
$720$	2.05225	−	0.887844i	0.0764829	−	0.0330880i
$721$	24.8937	+	24.8937i	0.927089	+	0.927089i
$722$	−8.56139			−0.318622
$723$	9.18363			0.341543
$724$	1.59280			0.0591961
$725$	1.27261	+	40.7554i	0.0472634	+	1.51362i
$726$	−4.59410	+	4.59410i	−0.170503	+	0.170503i
$727$			28.9528i			1.07380i	0.843646	+	0.536899i	$0.180404\pi$
$727$			28.9528i			1.07380i	−0.843646	+	0.536899i	$0.819596\pi$
$728$	9.35455	+	9.35455i	0.346703	+	0.346703i
$729$		−	1.00000i		−	0.0370370i
$730$	−17.4067	−	6.89384i	−0.644253	−	0.255152i
$731$		−	5.88138i		−	0.217531i
$732$			3.45964i			0.127872i
$733$	12.6845	+	12.6845i	0.468513	+	0.468513i	0.901433	−	0.432920i	$-0.142517\pi$
$733$	12.6845	+	12.6845i	0.468513	+	0.468513i	−0.432920	+	0.901433i	$0.642517\pi$
$734$	−23.8239	+	23.8239i	−0.879358	+	0.879358i
$735$	0.412236	+	0.163264i	0.0152055	+	0.00602207i
$736$	5.76461			0.212486
$737$	−21.0055	−	21.0055i	−0.773748	−	0.773748i
$738$		−	6.92685i		−	0.254981i
$739$	−5.09966			−0.187594			−0.0937970	−	0.995591i	$-0.529900\pi$
$739$	−5.09966			−0.187594			−0.0937970	+	0.995591i	$0.529900\pi$
$740$	0.620706	−	13.5873i	0.0228176	−	0.499479i
$741$	−16.3889			−0.602062
$742$		−	1.05755i		−	0.0388240i
$743$	−5.46112	−	5.46112i	−0.200349	−	0.200349i	0.599801	−	0.800150i	$-0.295247\pi$
$743$	−5.46112	−	5.46112i	−0.200349	−	0.200349i	−0.800150	+	0.599801i	$0.795247\pi$
$744$	1.95403			0.0716384
$745$	−34.7851	+	15.0487i	−1.27443	+	0.551342i
$746$	−2.47846	+	2.47846i	−0.0907429	+	0.0907429i
$747$	−7.41007	−	7.41007i	−0.271120	−	0.271120i
$748$			6.22803i			0.227719i
$749$		−	8.56313i		−	0.312890i
$750$	−10.1177	+	4.75731i	−0.369446	+	0.173712i
$751$		−	50.1472i		−	1.82990i	−0.403569	−	0.914949i	$-0.632230\pi$
$751$		−	50.1472i		−	1.82990i	0.403569	−	0.914949i	$-0.367770\pi$
$752$	7.27515	+	7.27515i	0.265297	+	0.265297i
$753$			3.98630i			0.145269i
$754$	29.2510	−	29.2510i	1.06526	−	1.06526i
$755$	−2.58581	+	1.11867i	−0.0941072	+	0.0407126i
$756$	2.60801			0.0948524
$757$	−38.6619			−1.40519			−0.702596	−	0.711589i	$-0.747976\pi$
$757$	−38.6619			−1.40519			−0.702596	+	0.711589i	$0.747976\pi$
$758$	31.6861			1.15089
$759$	8.64976	+	8.64976i	0.313966	+	0.313966i
$760$	−6.71688	−	2.66018i	−0.243647	−	0.0964949i
$761$			2.58952i			0.0938702i	0.998898	+	0.0469351i	$0.0149454\pi$
$761$			2.58952i			0.0938702i	−0.998898	+	0.0469351i	$0.985055\pi$
$762$	9.29533			0.336734
$763$			19.2013i			0.695134i
$764$	14.2911	−	14.2911i	0.517035	−	0.517035i
$765$	−6.02326	+	2.60578i	−0.217772	+	0.0942122i
$766$	−12.7864			−0.461993
$767$	−41.8709	+	41.8709i	−1.51187	+	1.51187i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	0.970999	−	0.970999i	0.0350151	−	0.0350151i	−0.689382	−	0.724398i	$-0.742118\pi$
$769$	0.970999	−	0.970999i	0.0350151	−	0.0350151i	0.724398	+	0.689382i	$0.242118\pi$
$770$	−4.55668	+	11.5055i	−0.164211	+	0.414629i
$771$	7.91684	+	7.91684i	0.285118	+	0.285118i
$772$			11.4610i			0.412489i
$773$	33.8554	−	33.8554i	1.21769	−	1.21769i	0.249255	−	0.968438i	$-0.419814\pi$
$773$	33.8554	−	33.8554i	1.21769	−	1.21769i	0.968438	−	0.249255i	$-0.0801859\pi$
$774$			2.00391i			0.0720290i
$775$	−9.76541	+	0.304929i	−0.350784	+	0.0109534i
$776$		−	7.94678i		−	0.285273i
$777$	6.95673	−	14.2572i	0.249571	−	0.511473i
$778$	15.4731	−	15.4731i	0.554738	−	0.554738i
$779$	−15.8249	+	15.8249i	−0.566988	+	0.566988i
$780$	10.5457	+	4.17656i	0.377596	+	0.149545i
$781$			3.60229i			0.128900i
$782$	−16.9189			−0.605017
$783$		−	8.15506i		−	0.291438i
$784$		−	0.198289i		−	0.00708176i
$785$	4.71824	−	11.9134i	0.168401	−	0.425208i
$786$	3.78185			0.134894
$787$	29.0495	+	29.0495i	1.03550	+	1.03550i	0.999346	+	0.0361558i	$0.0115112\pi$
$787$	29.0495	+	29.0495i	1.03550	+	1.03550i	0.0361558	+	0.999346i	$0.488489\pi$
$788$	−3.61811	−	3.61811i	−0.128890	−	0.128890i
$789$		−	3.62939i		−	0.129210i
$790$	16.8683	+	6.68059i	0.600147	+	0.237685i
$791$	−30.6783	−	30.6783i	−1.09080	−	1.09080i
$792$		−	2.12202i		−	0.0754027i
$793$	−12.4092	+	12.4092i	−0.440664	+	0.440664i
$794$	11.7358	+	11.7358i	0.416487	+	0.416487i
$795$	−0.360022	−	0.832191i	−0.0127687	−	0.0295148i
$796$	14.1563	−	14.1563i	0.501756	−	0.501756i
$797$			46.2735i			1.63909i	0.573014	+	0.819546i	$0.305774\pi$
$797$			46.2735i			1.63909i	−0.573014	+	0.819546i	$0.694226\pi$
$798$	−5.95820	−	5.95820i	−0.210918	−	0.210918i
$799$	−21.3522	−	21.3522i	−0.755388	−	0.755388i
$800$	3.64416	+	3.42347i	0.128840	+	0.121038i
$801$	−11.9236	−	11.9236i	−0.421300	−	0.421300i
$802$	−11.6604	+	11.6604i	−0.411742	+	0.411742i
$803$	−12.5634	+	12.5634i	−0.443351	+	0.443351i
$804$	−13.9991			−0.493709
$805$	−31.2554	−	12.3785i	−1.10161	−	0.436285i
$806$	7.00884	+	7.00884i	0.246876	+	0.246876i
$807$	22.7099	−	22.7099i	0.799426	−	0.799426i
$808$	−15.2228			−0.535535
$809$	−5.77592	+	5.77592i	−0.203070	+	0.203070i	−0.801314	−	0.598244i	$-0.795865\pi$
$809$	−5.77592	+	5.77592i	−0.203070	+	0.203070i	0.598244	+	0.801314i	$0.295865\pi$
$810$	2.05225	−	0.887844i	0.0721087	−	0.0311957i
$811$	−48.8974			−1.71702			−0.858510	−	0.512797i	$-0.828609\pi$
$811$	−48.8974			−1.71702			−0.858510	+	0.512797i	$0.828609\pi$
$812$	21.2685			0.746377
$813$	−11.0022	−	11.0022i	−0.385862	−	0.385862i
$814$	−11.6004	−	5.66038i	−0.406595	−	0.198396i
$815$	−0.178346	−	0.412247i	−0.00624719	−	0.0144404i
$816$	2.07533	+	2.07533i	0.0726510	+	0.0726510i
$817$	4.57809	−	4.57809i	0.160167	−	0.160167i
$818$	−22.9972	−	22.9972i	−0.804077	−	0.804077i
$819$	9.35455	+	9.35455i	0.326874	+	0.326874i
$820$	14.2156	−	6.14996i	0.496432	−	0.214766i
$821$	11.8926			0.415053			0.207527	−	0.978229i	$-0.433459\pi$
$821$	11.8926			0.415053			0.207527	+	0.978229i	$0.433459\pi$
$822$	−1.30863			−0.0456437
$823$	−4.60009	+	4.60009i	−0.160349	+	0.160349i	−0.782721	−	0.622372i	$-0.786169\pi$
$823$	−4.60009	+	4.60009i	−0.160349	+	0.160349i	0.622372	+	0.782721i	$0.286169\pi$
$824$		−	13.4988i		−	0.470253i
$825$	0.331144	+	10.6049i	0.0115289	+	0.369216i
$826$	−30.4444			−1.05930
$827$	1.44766			0.0503400			0.0251700	−	0.999683i	$-0.491987\pi$
$827$	1.44766			0.0503400			0.0251700	+	0.999683i	$0.491987\pi$
$828$	5.76461			0.200334
$829$	−17.0831	+	17.0831i	−0.593320	+	0.593320i	−0.938527	−	0.345207i	$-0.887809\pi$
$829$	−17.0831	+	17.0831i	−0.593320	+	0.593320i	0.345207	+	0.938527i	$0.387809\pi$
$830$	8.62833	−	21.7863i	0.299494	−	0.756213i
$831$	10.2132	−	10.2132i	0.354293	−	0.354293i
$832$		−	5.07258i		−	0.175860i
$833$			0.581970i			0.0201641i
$834$	3.84915	−	3.84915i	0.133285	−	0.133285i
$835$	6.39969	+	14.7929i	0.221470	+	0.511929i
$836$	−4.84792	+	4.84792i	−0.167669	+	0.167669i
$837$	1.95403			0.0675413
$838$	−24.2039			−0.836109
$839$	−24.1753			−0.834624			−0.417312	−	0.908763i	$-0.637028\pi$
$839$	−24.1753			−0.834624			−0.417312	+	0.908763i	$0.637028\pi$
$840$	2.31550	+	5.35229i	0.0798925	+	0.184671i
$841$		−	37.5049i		−	1.29327i
$842$	−9.91998	+	9.91998i	−0.341865	+	0.341865i
$843$	−14.3877			−0.495538
$844$	−8.13385			−0.279979
$845$	11.3032	+	26.1273i	0.388841	+	0.898807i
$846$	7.27515	+	7.27515i	0.250125	+	0.250125i
$847$	−11.9814	−	11.9814i	−0.411687	−	0.411687i
$848$	−0.286733	+	0.286733i	−0.00984645	+	0.00984645i
$849$	8.31082	+	8.31082i	0.285226	+	0.285226i
$850$	−10.6954	−	10.0477i	−0.366850	−	0.344634i
$851$	15.3768	−	31.5133i	0.527110	−	1.08026i
$852$	1.20037	+	1.20037i	0.0411239	+	0.0411239i
$853$	−51.8584			−1.77560			−0.887799	−	0.460232i	$-0.847766\pi$
$853$	−51.8584			−1.77560			−0.887799	+	0.460232i	$0.847766\pi$
$854$	−9.02276			−0.308753
$855$	−6.71688	−	2.66018i	−0.229712	−	0.0909762i
$856$	−2.32171	+	2.32171i	−0.0793545	+	0.0793545i
$857$	50.1319			1.71247			0.856236	−	0.516585i	$-0.172797\pi$
$857$	50.1319			1.71247			0.856236	+	0.516585i	$0.172797\pi$
$858$	7.61138	−	7.61138i	0.259848	−	0.259848i
$859$	22.7307	+	22.7307i	0.775560	+	0.775560i	0.979072	−	0.203512i	$-0.0652357\pi$
$859$	22.7307	+	22.7307i	0.775560	+	0.775560i	−0.203512	+	0.979072i	$0.565236\pi$
$860$	−4.11252	+	1.77916i	−0.140236	+	0.0606688i
$861$	18.0653			0.615664
$862$	18.4635	−	18.4635i	0.628869	−	0.628869i
$863$	16.0282	−	16.0282i	0.545605	−	0.545605i	−0.379562	−	0.925167i	$-0.623925\pi$
$863$	16.0282	−	16.0282i	0.545605	−	0.545605i	0.925167	+	0.379562i	$0.123925\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−1.33239	+	3.36425i	−0.0453027	+	0.114388i
$866$	−20.6095	−	20.6095i	−0.700338	−	0.700338i
$867$	5.92983	+	5.92983i	0.201387	+	0.201387i
$868$			5.09614i			0.172974i
$869$	12.1747	−	12.1747i	0.412999	−	0.412999i
$870$	16.7362	−	7.24042i	0.567411	−	0.245473i
$871$	−50.2126	−	50.2126i	−1.70139	−	1.70139i
$872$	5.20603	−	5.20603i	0.176298	−	0.176298i
$873$		−	7.94678i		−	0.268958i
$874$	−13.1697	−	13.1697i	−0.445472	−	0.445472i
$875$	−12.4071	−	26.3871i	−0.419437	−	0.892046i
$876$			8.37281i			0.282891i
$877$	37.8142	+	37.8142i	1.27689	+	1.27689i	0.942396	+	0.334498i	$0.108567\pi$
$877$	37.8142	+	37.8142i	1.27689	+	1.27689i	0.334498	+	0.942396i	$0.391433\pi$
$878$	−6.00049	−	6.00049i	−0.202507	−	0.202507i
$879$	20.1902			0.681000
$880$	4.35492	−	1.88402i	0.146804	−	0.0635104i
$881$		−	44.7156i		−	1.50651i	−0.657731	−	0.753253i	$-0.728484\pi$
$881$		−	44.7156i		−	1.50651i	0.657731	−	0.753253i	$-0.271516\pi$
$882$		−	0.198289i		−	0.00667675i
$883$	19.8417			0.667727			0.333863	−	0.942621i	$-0.391648\pi$
$883$	19.8417			0.667727			0.333863	+	0.942621i	$0.391648\pi$
$884$			14.8878i			0.500731i
$885$	−23.9568	+	10.3642i	−0.805300	+	0.348388i
$886$	−19.3252	+	19.3252i	−0.649243	+	0.649243i
$887$	−19.6978	+	19.6978i	−0.661387	+	0.661387i	−0.955707	−	0.294320i	$-0.904907\pi$
$887$	−19.6978	+	19.6978i	−0.661387	+	0.661387i	0.294320	+	0.955707i	$0.404907\pi$
$888$	−5.75171	+	1.97936i	−0.193015	+	0.0664231i
$889$			24.2423i			0.813060i
$890$	13.8839	−	35.0565i	0.465391	−	1.17510i
$891$		−	2.12202i		−	0.0710903i
$892$	18.5142	−	18.5142i	0.619901	−	0.619901i
$893$		−	33.2413i		−	1.11238i
$894$	11.9853	+	11.9853i	0.400847	+	0.400847i
$895$	28.5586	+	11.3105i	0.954610	+	0.378068i
$896$	1.84414	−	1.84414i	0.0616084	−	0.0616084i
$897$	20.6768	+	20.6768i	0.690378	+	0.690378i
$898$	−23.5893	+	23.5893i	−0.787184	+	0.787184i
$899$	15.9353			0.531471
$900$	3.64416	+	3.42347i	0.121472	+	0.114116i
$901$	0.841548	−	0.841548i	0.0280360	−	0.0280360i
$902$		−	14.6989i		−	0.489420i
$903$	−5.22621			−0.173917
$904$			16.6356i			0.553291i
$905$	1.41416	+	3.26883i	0.0470083	+	0.108660i
$906$	0.890945	+	0.890945i	0.0295997	+	0.0295997i
$907$	−53.6798			−1.78241			−0.891204	−	0.453603i	$-0.850138\pi$
$907$	−53.6798			−1.78241			−0.891204	+	0.453603i	$0.850138\pi$
$908$	−8.71126			−0.289093
$909$	−15.2228			−0.504907
$910$	−10.8925	+	27.5033i	−0.361083	+	0.911724i
$911$	6.84880	−	6.84880i	0.226911	−	0.226911i	−0.584490	−	0.811401i	$-0.698705\pi$
$911$	6.84880	−	6.84880i	0.226911	−	0.226911i	0.811401	+	0.584490i	$0.198705\pi$
$912$			3.23088i			0.106985i
$913$	−15.7243	−	15.7243i	−0.520399	−	0.520399i
$914$			10.5479i			0.348893i
$915$	−7.10004	+	3.07162i	−0.234720	+	0.101545i
$916$			18.0323i			0.595802i
$917$			9.86309i			0.325708i
$918$	2.07533	+	2.07533i	0.0684960	+	0.0684960i
$919$	18.9548	−	18.9548i	0.625261	−	0.625261i	−0.321611	−	0.946872i	$-0.604224\pi$
$919$	18.9548	−	18.9548i	0.625261	−	0.625261i	0.946872	+	0.321611i	$0.104224\pi$
$920$	5.11807	+	11.8304i	0.168738	+	0.390037i
$921$	22.9990			0.757844
$922$	26.9418	+	26.9418i	0.887281	+	0.887281i
$923$			8.61108i			0.283437i
$924$	5.53425			0.182063
$925$	28.4356	−	10.7896i	0.934958	−	0.354758i
$926$	16.5851			0.545019
$927$		−	13.4988i		−	0.443359i
$928$	−5.76649	−	5.76649i	−0.189294	−	0.189294i
$929$	43.3213			1.42133			0.710663	−	0.703532i	$-0.248395\pi$
$929$	43.3213			1.42133			0.710663	+	0.703532i	$0.248395\pi$
$930$	1.73488	+	4.01017i	0.0568889	+	0.131499i
$931$	−0.453008	+	0.453008i	−0.0148467	+	0.0148467i
$932$	15.7454	+	15.7454i	0.515757	+	0.515757i
$933$		−	15.6611i		−	0.512721i
$934$		−	34.4641i		−	1.12770i
$935$	−12.7815	+	5.52952i	−0.417999	+	0.180835i
$936$		−	5.07258i		−	0.165802i
$937$	−4.54929	−	4.54929i	−0.148619	−	0.148619i	0.628882	−	0.777501i	$-0.283513\pi$
$937$	−4.54929	−	4.54929i	−0.148619	−	0.148619i	−0.777501	+	0.628882i	$0.783513\pi$
$938$		−	36.5097i		−	1.19208i
$939$	−3.12160	+	3.12160i	−0.101870	+	0.101870i
$940$	−8.47123	+	21.3896i	−0.276301	+	0.697653i
$941$	−59.4050			−1.93655			−0.968273	−	0.249894i	$-0.919604\pi$
$941$	−59.4050			−1.93655			−0.968273	+	0.249894i	$0.919604\pi$
$942$	−5.73047			−0.186709
$943$	39.9306			1.30032
$944$	8.25437	+	8.25437i	0.268657	+	0.268657i
$945$	2.31550	+	5.35229i	0.0753234	+	0.174110i
$946$			4.25233i			0.138255i
$947$	−22.4238			−0.728675			−0.364337	−	0.931267i	$-0.618704\pi$
$947$	−22.4238			−0.728675			−0.364337	+	0.931267i	$0.618704\pi$
$948$		−	8.11381i		−	0.263524i
$949$	−30.0321	+	30.0321i	−0.974882	+	0.974882i
$950$	−0.504183	−	16.1465i	−0.0163579	−	0.523863i
$951$	2.47560			0.0802769
$952$	−5.41247	+	5.41247i	−0.175419	+	0.175419i
$953$	18.1295	+	18.1295i	0.587272	+	0.587272i	0.936892	−	0.349619i	$-0.113689\pi$
$953$	18.1295	+	18.1295i	0.587272	+	0.587272i	−0.349619	+	0.936892i	$0.613689\pi$
$954$	−0.286733	+	0.286733i	−0.00928332	+	0.00928332i
$955$	42.0173	+	16.6407i	1.35965	+	0.538480i
$956$	−10.3297	−	10.3297i	−0.334085	−	0.334085i
$957$		−	17.3052i		−	0.559397i
$958$	15.9403	−	15.9403i	0.515009	−	0.515009i
$959$		−	3.41292i		−	0.110209i
$960$	0.823360	−	2.07896i	0.0265738	−	0.0670982i
$961$		−	27.1817i		−	0.876831i
$962$	−27.7302	−	13.5308i	−0.894058	−	0.436252i
$963$	−2.32171	+	2.32171i	−0.0748162	+	0.0748162i
$964$	6.49380	−	6.49380i	0.209151	−	0.209151i
$965$	−23.5208	+	10.1755i	−0.757160	+	0.327562i
$966$			15.0341i			0.483716i
$967$	−52.0958			−1.67529			−0.837644	−	0.546216i	$-0.816068\pi$
$967$	−52.0958			−1.67529			−0.837644	+	0.546216i	$0.816068\pi$
$968$			6.49703i			0.208823i
$969$		−	9.48250i		−	0.304622i
$970$	16.3088	−	7.05550i	0.523644	−	0.226539i
$971$	7.35800			0.236129			0.118065	−	0.993006i	$-0.462331\pi$
$971$	7.35800			0.236129			0.118065	+	0.993006i	$0.462331\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	10.0386	+	10.0386i	0.321823	+	0.321823i
$974$		−	5.52466i		−	0.177022i
$975$	0.791581	+	25.3505i	0.0253509	+	0.811867i
$976$	2.44633	+	2.44633i	0.0783052	+	0.0783052i
$977$		−	2.33312i		−	0.0746432i	−0.999303	−	0.0373216i	$-0.988117\pi$
$977$		−	2.33312i		−	0.0746432i	0.999303	−	0.0373216i	$-0.0118826\pi$
$978$	−0.142041	+	0.142041i	−0.00454196	+	0.00454196i
$979$	−25.3021	−	25.3021i	−0.808660	−	0.808660i
$980$	0.406940	−	0.176050i	0.0129992	−	0.00562371i
$981$	5.20603	−	5.20603i	0.166216	−	0.166216i
$982$		−	30.9165i		−	0.986585i
$983$	−14.6210	−	14.6210i	−0.466338	−	0.466338i	0.434388	−	0.900726i	$-0.356965\pi$
$983$	−14.6210	−	14.6210i	−0.466338	−	0.466338i	−0.900726	+	0.434388i	$0.856965\pi$
$984$	−4.89802	−	4.89802i	−0.156143	−	0.156143i
$985$	4.21296	−	10.6376i	0.134236	−	0.338942i
$986$	16.9244	+	16.9244i	0.538983	+	0.538983i
$987$	−18.9736	+	18.9736i	−0.603938	+	0.603938i
$988$	−11.5887	+	11.5887i	−0.368686	+	0.368686i
$989$	−11.5517			−0.367324
$990$	4.35492	−	1.88402i	0.138408	−	0.0598781i
$991$	−19.5442	−	19.5442i	−0.620841	−	0.620841i	0.324906	−	0.945746i	$-0.394667\pi$
$991$	−19.5442	−	19.5442i	−0.620841	−	0.620841i	−0.945746	+	0.324906i	$0.894667\pi$
$992$	1.38171	−	1.38171i	0.0438694	−	0.0438694i
$993$	24.0444			0.763025
$994$	−3.13057	+	3.13057i	−0.0992956	+	0.0992956i
$995$	41.6208	+	16.4837i	1.31947	+	0.522567i
$996$	−10.4794			−0.332053
$997$	−23.0867			−0.731162			−0.365581	−	0.930780i	$-0.619130\pi$
$997$	−23.0867			−0.731162			−0.365581	+	0.930780i	$0.619130\pi$
$998$	−15.3419	−	15.3419i	−0.485640	−	0.485640i
$999$	−5.75171	+	1.97936i	−0.181976	+	0.0626243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.697.2	yes	36
5.3	odd	4		1110.2.o.a.253.17	yes	36
37.6	odd	4		1110.2.o.a.487.17	yes	36
185.43	even	4	inner	1110.2.l.a.43.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.2	✓	36	185.43	even	4	inner
1110.2.l.a.697.2	yes	36	1.1	even	1	trivial
1110.2.o.a.253.17	yes	36	5.3	odd	4
1110.2.o.a.487.17	yes	36	37.6	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.887844 - 2.05225i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.84414 - 1.84414i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.887844 - 2.05225i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.84414 - 1.84414i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-2.05225 + 0.887844i) q^{10} +2.12202i q^{11} +(0.707107 + 0.707107i) q^{12} +5.07258i q^{13} +(-1.84414 + 1.84414i) q^{14} +(-0.823360 + 2.07896i) q^{15} +1.00000 q^{16} -2.93495 q^{17} +1.00000 q^{18} +(-2.28458 - 2.28458i) q^{19} +(0.887844 + 2.05225i) q^{20} +2.60801i q^{21} +2.12202 q^{22} +5.76461i q^{23} +(0.707107 - 0.707107i) q^{24} +(-3.42347 + 3.64416i) q^{25} +5.07258 q^{26} +(0.707107 - 0.707107i) q^{27} +(1.84414 + 1.84414i) q^{28} +(5.76649 - 5.76649i) q^{29} +(2.07896 + 0.823360i) q^{30} +(1.38171 + 1.38171i) q^{31} -1.00000i q^{32} +(1.50049 - 1.50049i) q^{33} +2.93495i q^{34} +(-2.14733 + 5.42195i) q^{35} -1.00000i q^{36} +(-5.46669 - 2.66745i) q^{37} +(-2.28458 + 2.28458i) q^{38} +(3.58685 - 3.58685i) q^{39} +(2.05225 - 0.887844i) q^{40} -6.92685i q^{41} +2.60801 q^{42} +2.00391i q^{43} -2.12202i q^{44} +(2.05225 - 0.887844i) q^{45} +5.76461 q^{46} +(7.27515 + 7.27515i) q^{47} +(-0.707107 - 0.707107i) q^{48} -0.198289i q^{49} +(3.64416 + 3.42347i) q^{50} +(2.07533 + 2.07533i) q^{51} -5.07258i q^{52} +(-0.286733 + 0.286733i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(4.35492 - 1.88402i) q^{55} +(1.84414 - 1.84414i) q^{56} +3.23088i q^{57} +(-5.76649 - 5.76649i) q^{58} +(8.25437 + 8.25437i) q^{59} +(0.823360 - 2.07896i) q^{60} +(2.44633 + 2.44633i) q^{61} +(1.38171 - 1.38171i) q^{62} +(1.84414 - 1.84414i) q^{63} -1.00000 q^{64} +(10.4102 - 4.50366i) q^{65} +(-1.50049 - 1.50049i) q^{66} +(-9.89884 + 9.89884i) q^{67} +2.93495 q^{68} +(4.07619 - 4.07619i) q^{69} +(5.42195 + 2.14733i) q^{70} +1.69758 q^{71} -1.00000 q^{72} +(5.92047 + 5.92047i) q^{73} +(-2.66745 + 5.46669i) q^{74} +(4.99756 - 0.156051i) q^{75} +(2.28458 + 2.28458i) q^{76} +(3.91330 - 3.91330i) q^{77} +(-3.58685 - 3.58685i) q^{78} +(-5.73733 - 5.73733i) q^{79} +(-0.887844 - 2.05225i) q^{80} -1.00000 q^{81} -6.92685 q^{82} +(-7.41007 + 7.41007i) q^{83} -2.60801i q^{84} +(2.60578 + 6.02326i) q^{85} +2.00391 q^{86} -8.15506 q^{87} -2.12202 q^{88} +(-11.9236 + 11.9236i) q^{89} +(-0.887844 - 2.05225i) q^{90} +(9.35455 - 9.35455i) q^{91} -5.76461i q^{92} -1.95403i q^{93} +(7.27515 - 7.27515i) q^{94} +(-2.66018 + 6.71688i) q^{95} +(-0.707107 + 0.707107i) q^{96} -7.94678 q^{97} -0.198289 q^{98} -2.12202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more