LMFDB - Embedded newform 1110.2.o.a.487.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			487.17
Character	$\chi$	$=$	1110.487
Dual form			1110.2.o.a.253.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	2.05225	−	0.887844i	0.917794	−	0.397056i
$5$	2.05225	−	0.887844i	0.917794	−	0.397056i
$6$	−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	$0.914051\pi$
$8$	−1.00000			−0.353553
$9$			1.00000i			0.333333i
$10$	−2.05225	+	0.887844i	−0.648979	+	0.280761i
$11$		−	2.12202i		−	0.639813i	−0.947449	−	0.319906i	$-0.896349\pi$
$11$		−	2.12202i		−	0.639813i	0.947449	−	0.319906i	$-0.103651\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−5.07258			−1.40688			−0.703440	−	0.710755i	$-0.748354\pi$
$13$	−5.07258			−1.40688			−0.703440	+	0.710755i	$0.748354\pi$
$14$	1.84414	+	1.84414i	0.492867	+	0.492867i
$15$	2.07896	+	0.823360i	0.536785	+	0.212591i
$16$	1.00000			0.250000
$17$		−	2.93495i		−	0.711831i	−0.934518	−	0.355916i	$-0.884169\pi$
$17$		−	2.93495i		−	0.711831i	0.934518	−	0.355916i	$-0.115831\pi$
$18$		−	1.00000i		−	0.235702i
$19$	2.28458	−	2.28458i	0.524118	−	0.524118i	−0.394694	−	0.918813i	$-0.629149\pi$
$19$	2.28458	−	2.28458i	0.524118	−	0.524118i	0.918813	+	0.394694i	$0.129149\pi$
$20$	2.05225	−	0.887844i	0.458897	−	0.198528i
$21$		−	2.60801i		−	0.569114i
$22$			2.12202i			0.452416i
$23$	−5.76461			−1.20200			−0.601002	−	0.799248i	$-0.705232\pi$
$23$	−5.76461			−1.20200			−0.601002	+	0.799248i	$0.705232\pi$
$24$	−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	−0.997294	−	0.0735173i	$-0.976578\pi$
$29$	−5.76649	−	5.76649i	−1.07081	−	1.07081i	−0.0735173	−	0.997294i	$-0.523422\pi$
$30$	−2.07896	−	0.823360i	−0.379565	−	0.150324i
$31$	1.38171	−	1.38171i	0.248163	−	0.248163i	−0.572054	−	0.820216i	$-0.693853\pi$
$31$	1.38171	−	1.38171i	0.248163	−	0.248163i	0.820216	+	0.572054i	$0.193853\pi$
$32$	−1.00000			−0.176777
$33$	1.50049	−	1.50049i	0.261203	−	0.261203i
$34$			2.93495i			0.503341i
$35$	−5.42195	−	2.14733i	−0.916477	−	0.362965i
$36$			1.00000i			0.166667i
$37$	−2.66745	−	5.46669i	−0.438526	−	0.898719i
$37$	−2.66745	−	5.46669i	−0.438526	−	0.898719i
$38$	−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	$0.181915\pi$
$41$			6.92685i			1.08179i	−0.841089	+	0.540896i	$0.818085\pi$
$42$			2.60801i			0.402425i
$43$	−2.00391			−0.305593			−0.152797	−	0.988258i	$-0.548828\pi$
$43$	−2.00391			−0.305593			−0.152797	+	0.988258i	$0.548828\pi$
$44$		−	2.12202i		−	0.319906i
$45$	0.887844	+	2.05225i	0.132352	+	0.305931i
$46$	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
$50$	−3.42347	+	3.64416i	−0.484151	+	0.515362i
$51$	2.07533	−	2.07533i	0.290604	−	0.290604i
$52$	−5.07258			−0.703440
$53$	−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
$55$	−1.88402	−	4.35492i	−0.254041	−	0.587217i
$56$	1.84414	+	1.84414i	0.246434	+	0.246434i
$57$	3.23088			0.427941
$58$	5.76649	+	5.76649i	0.757178	+	0.757178i
$59$	−8.25437	+	8.25437i	−1.07463	+	1.07463i	−0.0776460	+	0.996981i	$0.524740\pi$
$59$	−8.25437	+	8.25437i	−1.07463	+	1.07463i	−0.996981	+	0.0776460i	$0.975260\pi$
$60$	2.07896	+	0.823360i	0.268393	+	0.106295i
$61$	2.44633	−	2.44633i	0.313221	−	0.313221i	−0.532935	−	0.846156i	$-0.678911\pi$
$61$	2.44633	−	2.44633i	0.313221	−	0.313221i	0.846156	+	0.532935i	$0.178911\pi$
$62$	−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	$-0.423478\pi$
$67$	9.89884	−	9.89884i	1.20934	−	1.20934i	0.971242	−	0.238093i	$-0.0765222\pi$
$68$		−	2.93495i		−	0.355916i
$69$	−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	$0.467881\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−5.92047	−	5.92047i	−0.692939	−	0.692939i	0.269939	−	0.962877i	$-0.412997\pi$
$73$	−5.92047	−	5.92047i	−0.692939	−	0.692939i	−0.962877	+	0.269939i	$0.912997\pi$
$74$	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	$-0.599125\pi$
$79$	5.73733	−	5.73733i	0.645500	−	0.645500i	0.951902	+	0.306402i	$0.0991253\pi$
$80$	2.05225	−	0.887844i	0.229449	−	0.0992640i
$81$	−1.00000			−0.111111
$82$		−	6.92685i		−	0.764943i
$83$	−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
$87$		−	8.15506i		−	0.874314i
$88$			2.12202i			0.226208i
$89$	11.9236	+	11.9236i	1.26390	+	1.26390i	0.949187	+	0.314714i	$0.101908\pi$
$89$	11.9236	+	11.9236i	1.26390	+	1.26390i	0.314714	+	0.949187i	$0.398092\pi$
$90$	−0.887844	−	2.05225i	−0.0935870	−	0.216326i
$91$	9.35455	+	9.35455i	0.980623	+	0.980623i
$92$	−5.76461			−0.601002
$93$	1.95403			0.202624
$94$	−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
$97$		−	7.94678i		−	0.806874i	−0.915008	−	0.403437i	$-0.867816\pi$
$97$		−	7.94678i		−	0.806874i	0.915008	−	0.403437i	$-0.132184\pi$
$98$			0.198289i			0.0200303i
$99$	2.12202			0.213271
$100$	3.42347	−	3.64416i	0.342347	−	0.364416i
$101$		−	15.2228i		−	1.51472i	−0.652997	−	0.757360i	$-0.726489\pi$
$101$		−	15.2228i		−	1.51472i	0.652997	−	0.757360i	$-0.273511\pi$
$102$	−2.07533	+	2.07533i	−0.205488	+	0.205488i
$103$			13.4988i			1.33008i	0.746810	+	0.665038i	$0.231585\pi$
$103$			13.4988i			1.33008i	−0.746810	+	0.665038i	$0.768415\pi$
$104$	5.07258			0.497407
$105$	−2.31550	−	5.35229i	−0.225970	−	0.522330i
$106$	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	$-0.635299\pi$
$109$	5.20603	−	5.20603i	0.498647	−	0.498647i	0.911017	+	0.412369i	$0.135299\pi$
$110$	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
$113$		−	16.6356i		−	1.56494i	−0.622687	−	0.782471i	$-0.713959\pi$
$113$		−	16.6356i		−	1.56494i	0.622687	−	0.782471i	$-0.286041\pi$
$114$	−3.23088			−0.302600
$115$	−11.8304	+	5.11807i	−1.10319	+	0.477262i
$116$	−5.76649	−	5.76649i	−0.535406	−	0.535406i
$117$		−	5.07258i		−	0.468960i
$118$	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
$125$	3.79037	−	10.5182i	0.339021	−	0.940779i
$126$	−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	$0.885314\pi$
$128$	−1.00000			−0.0883883
$129$	−1.41698	−	1.41698i	−0.124758	−	0.124758i
$130$	10.4102	−	4.50366i	0.913035	−	0.394997i
$131$	−2.67417	+	2.67417i	−0.233643	+	0.233643i	−0.814212	−	0.580568i	$-0.802830\pi$
$131$	−2.67417	+	2.67417i	−0.233643	+	0.233643i	0.580568	+	0.814212i	$0.302830\pi$
$132$	1.50049	−	1.50049i	0.130601	−	0.130601i
$133$	−8.42617			−0.730642
$134$	−9.89884	+	9.89884i	−0.855129	+	0.855129i
$135$	−0.823360	+	2.07896i	−0.0708636	+	0.178928i
$136$			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	$-0.425847\pi$
$139$	5.44352			0.461713			0.230857	+	0.972988i	$0.425847\pi$
$140$	−5.42195	−	2.14733i	−0.458238	−	0.181483i
$141$			10.2886i			0.866457i
$142$	−1.69758			−0.142457
$143$			10.7641i			0.900140i
$144$			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
$148$	−2.66745	−	5.46669i	−0.219263	−	0.449359i
$149$		−	16.9497i		−	1.38858i	−0.719698	−	0.694288i	$-0.755720\pi$
$149$		−	16.9497i		−	1.38858i	0.719698	−	0.694288i	$-0.244280\pi$
$150$	−4.99756	+	0.156051i	−0.408049	+	0.0127415i
$151$			1.25999i			0.102536i	0.998685	+	0.0512681i	$0.0163263\pi$
$151$			1.25999i			0.102536i	−0.998685	+	0.0512681i	$0.983674\pi$
$152$	−2.28458	+	2.28458i	−0.185304	+	0.185304i
$153$	2.93495			0.237277
$154$	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
$162$	1.00000			0.0785674
$163$		−	0.200876i		−	0.0157338i	−0.999969	−	0.00786690i	$-0.997496\pi$
$163$		−	0.200876i		−	0.0157338i	0.999969	−	0.00786690i	$-0.00250414\pi$
$164$			6.92685i			0.540896i
$165$	1.74719	−	4.41160i	0.136018	−	0.343442i
$166$	7.41007	−	7.41007i	0.575133	−	0.575133i
$167$		−	7.20812i		−	0.557781i	−0.960323	−	0.278891i	$-0.910033\pi$
$167$		−	7.20812i		−	0.557781i	0.960323	−	0.278891i	$-0.0899667\pi$
$168$			2.60801i			0.201212i
$169$	12.7311			0.979312
$170$	2.60578	+	6.02326i	0.199854	+	0.461963i
$171$	2.28458	+	2.28458i	0.174706	+	0.174706i
$172$	−2.00391			−0.152797
$173$	1.14427	+	1.14427i	0.0869969	+	0.0869969i	0.749266	−	0.662269i	$-0.230406\pi$
$173$	1.14427	+	1.14427i	0.0869969	+	0.0869969i	−0.662269	+	0.749266i	$0.730406\pi$
$174$			8.15506i			0.618233i
$175$	−13.0337	+	0.406983i	−0.985255	+	0.0307650i
$176$		−	2.12202i		−	0.159953i
$177$	−11.6734			−0.877429
$178$	−11.9236	−	11.9236i	−0.893712	−	0.893712i
$179$	9.71351	+	9.71351i	0.726022	+	0.726022i	0.969825	−	0.243803i	$-0.0783950\pi$
$179$	9.71351	+	9.71351i	0.726022	+	0.726022i	−0.243803	+	0.969825i	$0.578395\pi$
$180$	0.887844	+	2.05225i	0.0661760	+	0.152966i
$181$	−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
$183$	3.45964			0.255744
$184$	5.76461			0.424972
$185$	−10.3278	−	8.85074i	−0.759318	−	0.650720i
$186$	−1.95403			−0.143277
$187$	−6.22803			−0.455439
$188$	7.27515	+	7.27515i	0.530595	+	0.530595i
$189$	2.60801			0.189705
$190$	−2.66018	+	6.71688i	−0.192990	+	0.487294i
$191$	−14.2911	−	14.2911i	−1.03407	−	1.03407i	−0.999399	−	0.0346716i	$-0.988961\pi$
$191$	−14.2911	−	14.2911i	−1.03407	−	1.03407i	−0.0346716	−	0.999399i	$-0.511039\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	11.4610			0.824978			0.412489	−	0.910963i	$-0.364660\pi$
$193$	11.4610			0.824978			0.412489	+	0.910963i	$0.364660\pi$
$194$			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	$0.691653\pi$
$198$	−2.12202			−0.150805
$199$	14.1563	+	14.1563i	1.00351	+	1.00351i	0.999994	+	0.00351772i	$0.00111973\pi$
$199$	14.1563	+	14.1563i	1.00351	+	1.00351i	0.00351772	+	0.999994i	$0.498880\pi$
$200$	−3.42347	+	3.64416i	−0.242076	+	0.257681i
$201$	13.9991			0.987418
$202$			15.2228i			1.07107i
$203$			21.2685i			1.49275i
$204$	2.07533	−	2.07533i	0.145302	−	0.145302i
$205$	6.14996	+	14.2156i	0.429532	+	0.992863i
$206$		−	13.4988i		−	0.940505i
$207$		−	5.76461i		−	0.400668i
$208$	−5.07258			−0.351720
$209$	−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
$217$	−5.09614			−0.345949
$218$	−5.20603	+	5.20603i	−0.352597	+	0.352597i
$219$		−	8.37281i		−	0.565782i
$220$	−1.88402	−	4.35492i	−0.127021	−	0.293608i
$221$			14.8878i			1.00146i
$222$	−1.97936	+	5.75171i	−0.132846	+	0.386029i
$223$	−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
$227$			8.71126i			0.578187i	0.957301	+	0.289093i	$0.0933538\pi$
$227$			8.71126i			0.578187i	−0.957301	+	0.289093i	$0.906646\pi$
$228$	3.23088			0.213970
$229$		−	18.0323i		−	1.19160i	−0.803131	−	0.595802i	$-0.796834\pi$
$229$		−	18.0323i		−	1.19160i	0.803131	−	0.595802i	$-0.203166\pi$
$230$	11.8304	−	5.11807i	0.780075	−	0.337476i
$231$	−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	$0.0101966\pi$
$233$	15.7454	+	15.7454i	1.03151	+	1.03151i	0.0320280	+	0.999487i	$0.489803\pi$
$234$			5.07258i			0.331605i
$235$	21.3896	+	8.47123i	1.39531	+	0.552602i
$236$	−8.25437	+	8.25437i	−0.537314	+	0.537314i
$237$	8.11381			0.527048
$238$	5.41247	−	5.41247i	0.350838	−	0.350838i
$239$	−10.3297	+	10.3297i	−0.668170	+	0.668170i	−0.957292	−	0.289122i	$-0.906637\pi$
$239$	−10.3297	+	10.3297i	−0.668170	+	0.668170i	0.289122	+	0.957292i	$0.406637\pi$
$240$	2.07896	+	0.823360i	0.134196	+	0.0531477i
$241$	−6.49380	−	6.49380i	−0.418303	−	0.418303i	0.466316	−	0.884618i	$-0.345581\pi$
$241$	−6.49380	−	6.49380i	−0.418303	−	0.418303i	−0.884618	+	0.466316i	$0.845581\pi$
$242$	−6.49703			−0.417645
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	2.44633	−	2.44633i	0.156610	−	0.156610i
$245$	−0.176050	−	0.406940i	−0.0112474	−	0.0259984i
$246$	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	−0.790447	−	0.612530i	$-0.790152\pi$
$251$	−2.81874	+	2.81874i	−0.177917	+	0.177917i	0.612530	+	0.790447i	$0.290152\pi$
$252$	1.84414	−	1.84414i	0.116170	−	0.116170i
$253$			12.2326i			0.769057i
$254$	6.57279	+	6.57279i	0.412413	+	0.412413i
$255$	2.41652	−	6.10166i	0.151329	−	0.382101i
$256$	1.00000			0.0625000
$257$		−	11.1961i		−	0.698394i	−0.937049	−	0.349197i	$-0.886454\pi$
$257$		−	11.1961i		−	0.698394i	0.937049	−	0.349197i	$-0.113546\pi$
$258$	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	0.623541	−	0.781790i	$-0.285693\pi$
$263$	−2.56637	−	2.56637i	−0.158249	−	0.158249i	−0.781790	+	0.623541i	$0.785693\pi$
$264$	−1.50049	+	1.50049i	−0.0923490	+	0.0923490i
$265$	−0.333874	+	0.843022i	−0.0205097	+	0.0517864i
$266$	8.42617			0.516642
$267$			16.8625i			1.03197i
$268$	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	$0.343322\pi$
$272$		−	2.93495i		−	0.177958i
$273$			13.2293i			0.800675i
$274$	−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
$277$	14.4437			0.867838			0.433919	−	0.900952i	$-0.357130\pi$
$277$	14.4437			0.867838			0.433919	+	0.900952i	$0.357130\pi$
$278$	−5.44352			−0.326481
$279$	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	0.942137	−	0.335229i	$-0.108814\pi$
$281$	10.1736	+	10.1736i	0.606908	+	0.606908i	−0.335229	+	0.942137i	$0.608814\pi$
$282$		−	10.2886i		−	0.612678i
$283$			11.7533i			0.698659i	0.937000	+	0.349330i	$0.113591\pi$
$283$			11.7533i			0.698659i	−0.937000	+	0.349330i	$0.886409\pi$
$284$	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
$288$		−	1.00000i		−	0.0589256i
$289$	8.38604			0.493296
$290$	16.9540	+	6.71455i	0.995576	+	0.394292i
$291$	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
$298$			16.9497i			0.981871i
$299$	29.2414			1.69107
$300$	4.99756	−	0.156051i	0.288535	−	0.00900961i
$301$	3.69549	+	3.69549i	0.213005	+	0.213005i
$302$		−	1.25999i		−	0.0725041i
$303$	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	−0.0694214	−	0.997587i	$-0.522115\pi$
$307$	16.2628	−	16.2628i	0.928166	−	0.928166i	0.997587	+	0.0694214i	$0.0221153\pi$
$308$	−3.91330	+	3.91330i	−0.222981	+	0.222981i
$309$	−9.54509	+	9.54509i	−0.543001	+	0.543001i
$310$	−1.60887	+	4.06236i	−0.0913779	+	0.230727i
$311$	11.0741	−	11.0741i	0.627952	−	0.627952i	−0.319600	−	0.947552i	$-0.603549\pi$
$311$	11.0741	−	11.0741i	0.627952	−	0.627952i	0.947552	+	0.319600i	$0.103549\pi$
$312$	3.58685	+	3.58685i	0.203066	+	0.203066i
$313$	4.41462			0.249529			0.124764	−	0.992186i	$-0.460182\pi$
$313$	4.41462			0.249529			0.124764	+	0.992186i	$0.460182\pi$
$314$	−4.05205	−	4.05205i	−0.228671	−	0.228671i
$315$	2.14733	−	5.42195i	0.120988	−	0.305492i
$316$	5.73733	−	5.73733i	0.322750	−	0.322750i
$317$	1.75051	−	1.75051i	0.0983187	−	0.0983187i	−0.656237	−	0.754555i	$-0.727853\pi$
$317$	1.75051	−	1.75051i	0.0983187	−	0.0983187i	0.754555	+	0.656237i	$0.227853\pi$
$318$	0.405502			0.0227394
$319$	−12.2366	+	12.2366i	−0.685119	+	0.685119i
$320$	2.05225	−	0.887844i	0.114724	−	0.0496320i
$321$			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
$325$	−17.3658	+	18.4853i	−0.963281	+	1.02538i
$326$			0.200876i			0.0111255i
$327$	7.36244			0.407144
$328$		−	6.92685i		−	0.382471i
$329$		−	26.8328i		−	1.47934i
$330$	−1.74719	+	4.41160i	−0.0961794	+	0.242850i
$331$	−17.0019	−	17.0019i	−0.934511	−	0.934511i	0.0634724	−	0.997984i	$-0.479783\pi$
$331$	−17.0019	−	17.0019i	−0.934511	−	0.934511i	−0.997984	+	0.0634724i	$0.979783\pi$
$332$	−7.41007	+	7.41007i	−0.406680	+	0.406680i
$333$	5.46669	−	2.66745i	0.299573	−	0.146175i
$334$			7.20812i			0.394411i
$335$	11.5263	−	29.1035i	0.629748	−	1.59009i
$336$		−	2.60801i		−	0.142279i
$337$	−16.7264	+	16.7264i	−0.911145	+	0.911145i	−0.996362	−	0.0852173i	$-0.972842\pi$
$337$	−16.7264	+	16.7264i	−0.911145	+	0.911145i	0.0852173	+	0.996362i	$0.472842\pi$
$338$	−12.7311			−0.692478
$339$	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
$347$	−27.1062			−1.45514			−0.727568	−	0.686036i	$-0.759349\pi$
$347$	−27.1062			−1.45514			−0.727568	+	0.686036i	$0.759349\pi$
$348$		−	8.15506i		−	0.437157i
$349$			1.86734i			0.0999566i	0.998750	+	0.0499783i	$0.0159152\pi$
$349$			1.86734i			0.0999566i	−0.998750	+	0.0499783i	$0.984085\pi$
$350$	13.0337	−	0.406983i	0.696680	−	0.0217541i
$351$	3.58685	−	3.58685i	0.191452	−	0.191452i
$352$			2.12202i			0.113104i
$353$		−	15.2302i		−	0.810619i	−0.914179	−	0.405310i	$-0.867164\pi$
$353$		−	15.2302i		−	0.810619i	0.914179	−	0.405310i	$-0.132836\pi$
$354$	11.6734			0.620436
$355$	3.48385	−	1.50718i	0.184904	−	0.0799929i
$356$	11.9236	+	11.9236i	0.631950	+	0.631950i
$357$	−7.65439			−0.405113
$358$	−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
$362$	1.59280			0.0837159
$363$	4.59410	+	4.59410i	0.241128	+	0.241128i
$364$	9.35455	+	9.35455i	0.490312	+	0.490312i
$365$	−17.4067	−	6.89384i	−0.911111	−	0.360840i
$366$	−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	$-0.592028\pi$
$368$	−5.76461			−0.300501
$369$	−6.92685			−0.360598
$370$	10.3278	+	8.85074i	0.536919	+	0.460128i
$371$	1.05755			0.0549054
$372$	1.95403			0.101312
$373$	2.47846	+	2.47846i	0.128330	+	0.128330i	0.768354	−	0.640025i	$-0.221076\pi$
$373$	2.47846	+	2.47846i	0.128330	+	0.128330i	−0.640025	+	0.768354i	$0.721076\pi$
$374$	6.22803			0.322044
$375$	10.1177	−	4.75731i	0.522476	−	0.245667i
$376$	−7.27515	−	7.27515i	−0.375187	−	0.375187i
$377$	29.2510	+	29.2510i	1.50650	+	1.50650i
$378$	−2.60801			−0.134142
$379$			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
$383$	12.7864			0.653357			0.326678	−	0.945136i	$-0.394071\pi$
$383$	12.7864			0.653357			0.326678	+	0.945136i	$0.394071\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−4.55668	+	11.5055i	−0.232230	+	0.586374i
$386$	−11.4610			−0.583347
$387$		−	2.00391i		−	0.101864i
$388$		−	7.94678i		−	0.403437i
$389$	−15.4731	+	15.4731i	−0.784518	+	0.784518i	−0.980590	−	0.196071i	$-0.937182\pi$
$389$	−15.4731	+	15.4731i	−0.784518	+	0.784518i	0.196071	+	0.980590i	$0.437182\pi$
$390$	10.5457	+	4.17656i	0.534002	+	0.211488i
$391$			16.9189i			0.855623i
$392$			0.198289i			0.0100151i
$393$	−3.78185			−0.190769
$394$	−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	−0.348359	−	0.937361i	$-0.613261\pi$
$397$	11.7358	−	11.7358i	0.589002	−	0.589002i	0.937361	+	0.348359i	$0.113261\pi$
$398$	−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	−0.935532	−	0.353241i	$-0.885079\pi$
$401$	−11.6604	+	11.6604i	−0.582291	+	0.582291i	0.353241	+	0.935532i	$0.385079\pi$
$402$	−13.9991			−0.698210
$403$	−7.00884	+	7.00884i	−0.349135	+	0.349135i
$404$		−	15.2228i		−	0.757360i
$405$	−2.05225	+	0.887844i	−0.101977	+	0.0441173i
$406$		−	21.2685i		−	1.05554i
$407$	−11.6004	+	5.66038i	−0.575012	+	0.280575i
$408$	−2.07533	+	2.07533i	−0.102744	+	0.102744i
$409$	−22.9972	−	22.9972i	−1.13714	−	1.13714i	−0.988961	−	0.148176i	$-0.952660\pi$
$409$	−22.9972	−	22.9972i	−1.13714	−	1.13714i	−0.148176	−	0.988961i	$-0.547340\pi$
$410$	−6.14996	−	14.2156i	−0.303725	−	0.702060i
$411$			1.30863i			0.0645499i
$412$			13.4988i			0.665038i
$413$	30.4444			1.49807
$414$			5.76461i			0.283315i
$415$	−8.62833	+	21.7863i	−0.423548	+	1.06945i
$416$	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	$-0.201353\pi$
$420$	−2.31550	−	5.35229i	−0.112985	−	0.261165i
$421$	−9.91998	+	9.91998i	−0.483470	+	0.483470i	−0.906238	−	0.422768i	$-0.861059\pi$
$421$	−9.91998	+	9.91998i	−0.483470	+	0.483470i	0.422768	+	0.906238i	$0.361059\pi$
$422$	−8.13385			−0.395949
$423$	−7.27515	+	7.27515i	−0.353730	+	0.353730i
$424$	0.286733	−	0.286733i	0.0139250	−	0.0139250i
$425$	−10.6954	−	10.0477i	−0.518805	−	0.487386i
$426$	−1.20037	−	1.20037i	−0.0581580	−	0.0581580i
$427$	−9.02276			−0.436642
$428$	2.32171	+	2.32171i	0.112224	+	0.112224i
$429$	−7.61138	+	7.61138i	−0.367481	+	0.367481i
$430$	4.11252	−	1.77916i	0.198324	−	0.0857986i
$431$	18.4635	−	18.4635i	0.889356	−	0.889356i	−0.105105	−	0.994461i	$-0.533518\pi$
$431$	18.4635	−	18.4635i	0.889356	−	0.889356i	0.994461	+	0.105105i	$0.0335180\pi$
$432$	−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
$438$			8.37281i			0.400068i
$439$	−6.00049	−	6.00049i	−0.286388	−	0.286388i	0.549262	−	0.835650i	$-0.314909\pi$
$439$	−6.00049	−	6.00049i	−0.286388	−	0.286388i	−0.835650	+	0.549262i	$0.814909\pi$
$440$	1.88402	+	4.35492i	0.0898172	+	0.207612i
$441$	0.198289			0.00944235
$442$		−	14.8878i		−	0.708140i
$443$	19.3252	+	19.3252i	0.918168	+	0.918168i	0.996896	−	0.0787279i	$-0.0250858\pi$
$443$	19.3252	+	19.3252i	0.918168	+	0.918168i	−0.0787279	+	0.996896i	$0.525086\pi$
$444$	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	0.120538	−	0.992709i	$-0.461538\pi$
$449$	23.5893	−	23.5893i	1.11325	−	1.11325i	0.992709	−	0.120538i	$-0.0384620\pi$
$450$	−3.64416	−	3.42347i	−0.171787	−	0.161384i
$451$	14.6989			0.692145
$452$		−	16.6356i		−	0.782471i
$453$	−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
$457$		−	10.5479i		−	0.493409i	−0.969091	−	0.246704i	$-0.920652\pi$
$457$		−	10.5479i		−	0.493409i	0.969091	−	0.246704i	$-0.0793476\pi$
$458$			18.0323i			0.842592i
$459$	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	−0.953541	−	0.301265i	$-0.902591\pi$
$461$	−26.9418	−	26.9418i	−1.25481	−	1.25481i	−0.301265	−	0.953541i	$-0.597409\pi$
$462$	5.53425			0.257476
$463$	−16.5851			−0.770773			−0.385387	−	0.922755i	$-0.625932\pi$
$463$	−16.5851			−0.770773			−0.385387	+	0.922755i	$0.625932\pi$
$464$	−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
$467$			34.4641i			1.59481i	0.603447	+	0.797403i	$0.293793\pi$
$467$			34.4641i			1.59481i	−0.603447	+	0.797403i	$0.706207\pi$
$468$		−	5.07258i		−	0.234480i
$469$	−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
$473$			4.25233i			0.195523i
$474$	−8.11381			−0.372680
$475$	−0.504183	−	16.1465i	−0.0231335	−	0.740854i
$476$	−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	$-0.922212\pi$
$479$	−15.9403	+	15.9403i	−0.728333	+	0.728333i	0.241954	+	0.970288i	$0.422212\pi$
$480$	−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
$483$			15.0341i			0.684077i
$484$	6.49703			0.295320
$485$	−7.05550	−	16.3088i	−0.320374	−	0.740544i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$			5.52466i			0.250346i	0.992135	+	0.125173i	$0.0399486\pi$
$487$			5.52466i			0.250346i	−0.992135	+	0.125173i	$0.960051\pi$
$488$	−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
$495$	4.35492	−	1.88402i	0.195739	−	0.0846805i
$496$	1.38171	−	1.38171i	0.0620407	−	0.0620407i
$497$	−3.13057	−	3.13057i	−0.140425	−	0.140425i
$498$	10.4794			0.469594
$499$	−15.3419	−	15.3419i	−0.686798	−	0.686798i	0.274725	−	0.961523i	$-0.411413\pi$
$499$	−15.3419	−	15.3419i	−0.686798	−	0.686798i	−0.961523	+	0.274725i	$0.911413\pi$
$500$	3.79037	−	10.5182i	0.169511	−	0.470389i
$501$	5.09691	−	5.09691i	0.227713	−	0.227713i
$502$	2.81874	−	2.81874i	0.125806	−	0.125806i
$503$	6.97745			0.311109			0.155555	−	0.987827i	$-0.450284\pi$
$503$	6.97745			0.311109			0.155555	+	0.987827i	$0.450284\pi$
$504$	−1.84414	+	1.84414i	−0.0821446	+	0.0821446i
$505$	−13.5154	−	31.2409i	−0.601429	−	1.39020i
$506$		−	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	$-0.384821\pi$
$509$	15.9733			0.708002			0.354001	+	0.935245i	$0.384821\pi$
$510$	−2.41652	+	6.10166i	−0.107006	+	0.270186i
$511$			21.8364i			0.965984i
$512$	−1.00000			−0.0441942
$513$			3.23088i			0.142647i
$514$			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
$518$	5.16220	−	15.0005i	0.226814	−	0.659084i
$519$			1.61824i			0.0710327i
$520$	10.4102	−	4.50366i	0.456518	−	0.197498i
$521$			38.5368i			1.68833i	0.536084	+	0.844165i	$0.319903\pi$
$521$			38.5368i			1.68833i	−0.536084	+	0.844165i	$0.680097\pi$
$522$	−5.76649	+	5.76649i	−0.252393	+	0.252393i
$523$	−14.7060			−0.643047			−0.321523	−	0.946902i	$-0.604195\pi$
$523$	−14.7060			−0.643047			−0.321523	+	0.946902i	$0.604195\pi$
$524$	−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
$532$	−8.42617			−0.365321
$533$		−	35.1370i		−	1.52195i
$534$		−	16.8625i		−	0.729713i
$535$	6.82606	+	2.70342i	0.295116	+	0.116879i
$536$	−9.89884	+	9.89884i	−0.427565	+	0.427565i
$537$			13.7370i			0.592794i
$538$		−	32.1166i		−	1.38465i
$539$	−0.420774			−0.0181240
$540$	−0.823360	+	2.07896i	−0.0354318	+	0.0894642i
$541$	−24.9509	−	24.9509i	−1.07272	−	1.07272i	−0.997139	−	0.0755841i	$-0.975918\pi$
$541$	−24.9509	−	24.9509i	−1.07272	−	1.07272i	−0.0755841	−	0.997139i	$-0.524082\pi$
$542$	−15.5594			−0.668333
$543$	−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
$547$	36.4914			1.56026			0.780131	−	0.625617i	$-0.215153\pi$
$547$	36.4914			1.56026			0.780131	+	0.625617i	$0.215153\pi$
$548$	0.925340	+	0.925340i	0.0395286	+	0.0395286i
$549$	2.44633	+	2.44633i	0.104407	+	0.104407i
$550$	7.73297	+	7.26466i	0.329735	+	0.309766i
$551$	−26.3480			−1.12246
$552$	4.07619	+	4.07619i	0.173494	+	0.173494i
$553$	−21.1609			−0.899852
$554$	−14.4437			−0.613654
$555$	−1.04447	−	13.5613i	−0.0443351	−	0.575645i
$556$	5.44352			0.230857
$557$	−32.6303			−1.38259			−0.691296	−	0.722572i	$-0.742960\pi$
$557$	−32.6303			−1.38259			−0.691296	+	0.722572i	$0.742960\pi$
$558$	−1.38171	−	1.38171i	−0.0584925	−	0.0584925i
$559$	10.1650			0.429933
$560$	−5.42195	−	2.14733i	−0.229119	−	0.0907413i
$561$	−4.40388	−	4.40388i	−0.185932	−	0.185932i
$562$	−10.1736	−	10.1736i	−0.429149	−	0.429149i
$563$	20.4470			0.861738			0.430869	−	0.902415i	$-0.358207\pi$
$563$	20.4470			0.861738			0.430869	+	0.902415i	$0.358207\pi$
$564$			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
$568$	−1.69758			−0.0712287
$569$	−11.2342	−	11.2342i	−0.470964	−	0.470964i	0.431263	−	0.902226i	$-0.358068\pi$
$569$	−11.2342	−	11.2342i	−0.470964	−	0.470964i	−0.902226	+	0.431263i	$0.858068\pi$
$570$	−6.63058	+	2.86852i	−0.277725	+	0.120149i
$571$	26.4113			1.10528			0.552639	−	0.833421i	$-0.313621\pi$
$571$	26.4113			1.10528			0.552639	+	0.833421i	$0.313621\pi$
$572$			10.7641i			0.450070i
$573$		−	20.2107i		−	0.844315i
$574$	−12.7741	+	12.7741i	−0.533180	+	0.533180i
$575$	−19.7349	+	21.0071i	−0.823004	+	0.876058i
$576$			1.00000i			0.0416667i
$577$		−	7.95386i		−	0.331123i	−0.986199	−	0.165562i	$-0.947056\pi$
$577$		−	7.95386i		−	0.331123i	0.986199	−	0.165562i	$-0.0529437\pi$
$578$	−8.38604			−0.348813
$579$	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
$587$	−12.8759			−0.531445			−0.265723	−	0.964050i	$-0.585611\pi$
$587$	−12.8759			−0.531445			−0.265723	+	0.964050i	$0.585611\pi$
$588$	0.140212	−	0.140212i	0.00578224	−	0.00578224i
$589$		−	6.31326i		−	0.260133i
$590$	9.61144	−	24.2686i	0.395697	−	0.999123i
$591$			5.11678i			0.210476i
$592$	−2.66745	−	5.46669i	−0.109631	−	0.224680i
$593$	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
$597$			20.0200i			0.819364i
$598$	−29.2414			−1.19577
$599$		−	28.1341i		−	1.14953i	−0.818320	−	0.574763i	$-0.805094\pi$
$599$		−	28.1341i		−	1.14953i	0.818320	−	0.574763i	$-0.194906\pi$
$600$	−4.99756	+	0.156051i	−0.204025	+	0.00637076i
$601$	−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
$605$	13.3335	−	5.76835i	0.542086	−	0.234517i
$606$	−10.7641	+	10.7641i	−0.437262	+	0.437262i
$607$	5.21022			0.211476			0.105738	−	0.994394i	$-0.466279\pi$
$607$	5.21022			0.211476			0.105738	+	0.994394i	$0.466279\pi$
$608$	−2.28458	+	2.28458i	−0.0926519	+	0.0926519i
$609$	−15.0391	+	15.0391i	−0.609414	+	0.609414i
$610$	−2.84853	+	7.19245i	−0.115333	+	0.291214i
$611$	−36.9038	−	36.9038i	−1.49297	−	1.49297i
$612$	2.93495			0.118639
$613$	−15.0091	−	15.0091i	−0.606211	−	0.606211i	0.335743	−	0.941954i	$-0.391013\pi$
$613$	−15.0091	−	15.0091i	−0.606211	−	0.606211i	−0.941954	+	0.335743i	$0.891013\pi$
$614$	−16.2628	+	16.2628i	−0.656312	+	0.656312i
$615$	−5.70329	+	14.4007i	−0.229979	+	0.580690i
$616$	3.91330	−	3.91330i	0.157671	−	0.157671i
$617$	6.06777	−	6.06777i	0.244279	−	0.244279i	−0.574339	−	0.818618i	$-0.694741\pi$
$617$	6.06777	−	6.06777i	0.244279	−	0.244279i	0.818618	+	0.574339i	$0.194741\pi$
$618$	9.54509	−	9.54509i	0.383960	−	0.383960i
$619$	20.1898			0.811495			0.405747	−	0.913985i	$-0.367011\pi$
$619$	20.1898			0.811495			0.405747	+	0.913985i	$0.367011\pi$
$620$	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
$623$		−	43.9776i		−	1.76193i
$624$	−3.58685	−	3.58685i	−0.143589	−	0.143589i
$625$	−1.55975	−	24.9513i	−0.0623900	−	0.998052i
$626$	−4.41462			−0.176444
$627$		−	6.85600i		−	0.273802i
$628$	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	−0.674746	−	0.738050i	$-0.735747\pi$
$631$	1.59016	−	1.59016i	0.0633034	−	0.0633034i	0.738050	+	0.674746i	$0.235747\pi$
$632$	−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
$635$	−19.3246	−	7.65340i	−0.766874	−	0.303716i
$636$	−0.405502			−0.0160792
$637$			1.00584i			0.0398528i
$638$	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	$0.679218\pi$
$642$		−	3.28340i		−	0.129585i
$643$		−	18.0452i		−	0.711635i	−0.934556	−	0.355817i	$-0.884203\pi$
$643$		−	18.0452i		−	0.711635i	0.934556	−	0.355817i	$-0.115797\pi$
$644$	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
$647$	−2.13093			−0.0837754			−0.0418877	−	0.999122i	$-0.513337\pi$
$647$	−2.13093			−0.0837754			−0.0418877	+	0.999122i	$0.513337\pi$
$648$	1.00000			0.0392837
$649$	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
$652$		−	0.200876i		−	0.00786690i
$653$		−	12.1928i		−	0.477142i	−0.971125	−	0.238571i	$-0.923321\pi$
$653$		−	12.1928i		−	0.477142i	0.971125	−	0.238571i	$-0.0766790\pi$
$654$	−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
$658$			26.8328i			1.04605i
$659$	19.4303			0.756898			0.378449	−	0.925622i	$-0.376457\pi$
$659$	19.4303			0.756898			0.378449	+	0.925622i	$0.376457\pi$
$660$	1.74719	−	4.41160i	0.0680091	−	0.171721i
$661$	25.0660	−	25.0660i	0.974956	−	0.974956i	−0.0247380	−	0.999694i	$-0.507875\pi$
$661$	25.0660	−	25.0660i	0.974956	−	0.974956i	0.999694	+	0.0247380i	$0.00787514\pi$
$662$	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
$668$		−	7.20812i		−	0.278891i
$669$	−26.1830			−1.01229
$670$	−11.5263	+	29.1035i	−0.445299	+	1.12437i
$671$	−5.19117	−	5.19117i	−0.200403	−	0.200403i
$672$			2.60801i			0.100606i
$673$	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	−0.625077	−	0.780563i	$-0.714932\pi$
$677$	4.04562	−	4.04562i	0.155486	−	0.155486i	0.780563	+	0.625077i	$0.214932\pi$
$678$	−11.7631	+	11.7631i	−0.451760	+	0.451760i
$679$	−14.6550	+	14.6550i	−0.562407	+	0.562407i
$680$	2.60578	+	6.02326i	0.0999272	+	0.230982i
$681$	−6.15979	+	6.15979i	−0.236044	+	0.236044i
$682$	2.93202	+	2.93202i	0.112273	+	0.112273i
$683$	49.4497			1.89214			0.946070	−	0.323961i	$-0.105015\pi$
$683$	49.4497			1.89214			0.946070	+	0.323961i	$0.105015\pi$
$684$	2.28458	+	2.28458i	0.0873531	+	0.0873531i
$685$	2.72059	+	1.07747i	0.103948	+	0.0411681i
$686$	13.2747	−	13.2747i	0.506829	−	0.506829i
$687$	12.7507	−	12.7507i	0.486471	−	0.486471i
$688$	−2.00391			−0.0763983
$689$	1.45448	−	1.45448i	0.0554111	−	0.0554111i
$690$	11.9844	+	4.74635i	0.456238	+	0.180690i
$691$			9.04475i			0.344078i	0.985090	+	0.172039i	$0.0550356\pi$
$691$			9.04475i			0.344078i	−0.985090	+	0.172039i	$0.944964\pi$
$692$	1.14427	+	1.14427i	0.0434985	+	0.0434985i
$693$	−3.91330	−	3.91330i	−0.148654	−	0.148654i
$694$	27.1062			1.02894
$695$	11.1715	−	4.83299i	0.423758	−	0.183326i
$696$			8.15506i			0.309117i
$697$	20.3300			0.770054
$698$		−	1.86734i		−	0.0706800i
$699$			22.2673i			0.842228i
$700$	−13.0337	+	0.406983i	−0.492627	+	0.0153825i
$701$	−6.79801	−	6.79801i	−0.256757	−	0.256757i	0.566977	−	0.823734i	$-0.308113\pi$
$701$	−6.79801	−	6.79801i	−0.256757	−	0.256757i	−0.823734	+	0.566977i	$0.808113\pi$
$702$	−3.58685	+	3.58685i	−0.135377	+	0.135377i
$703$	−18.5831	−	6.39509i	−0.700875	−	0.241195i
$704$		−	2.12202i		−	0.0799766i
$705$	9.13468	+	21.1148i	0.344032	+	0.795230i
$706$			15.2302i			0.573194i
$707$	−28.0729	+	28.0729i	−1.05579	+	1.05579i
$708$	−11.6734			−0.438715
$709$	−12.7014	+	12.7014i	−0.477012	+	0.477012i	−0.904175	−	0.427163i	$-0.859513\pi$
$709$	−12.7014	+	12.7014i	−0.477012	+	0.477012i	0.427163	+	0.904175i	$0.359513\pi$
$710$	−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
$717$	−14.6083			−0.545558
$718$		−	18.9718i		−	0.708022i
$719$		−	25.0596i		−	0.934567i	−0.884108	−	0.467283i	$-0.845233\pi$
$719$		−	25.0596i		−	0.934567i	0.884108	−	0.467283i	$-0.154767\pi$
$720$	0.887844	+	2.05225i	0.0330880	+	0.0764829i
$721$	24.8937	−	24.8937i	0.927089	−	0.927089i
$722$		−	8.56139i		−	0.318622i
$723$		−	9.18363i		−	0.341543i
$724$	−1.59280			−0.0591961
$725$	−40.7554	+	1.27261i	−1.51362	+	0.0472634i
$726$	−4.59410	−	4.59410i	−0.170503	−	0.170503i
$727$	28.9528			1.07380			0.536899	−	0.843646i	$-0.319596\pi$
$727$	28.9528			1.07380			0.536899	+	0.843646i	$0.319596\pi$
$728$	−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
$732$	3.45964			0.127872
$733$	−12.6845	−	12.6845i	−0.468513	−	0.468513i	0.432920	−	0.901433i	$-0.357483\pi$
$733$	−12.6845	−	12.6845i	−0.468513	−	0.468513i	−0.901433	+	0.432920i	$0.857483\pi$
$734$	23.8239	+	23.8239i	0.879358	+	0.879358i
$735$	0.163264	−	0.412236i	0.00602207	−	0.0152055i
$736$	5.76461			0.212486
$737$	−21.0055	−	21.0055i	−0.773748	−	0.773748i
$738$	6.92685			0.254981
$739$	5.09966			0.187594			0.0937970	−	0.995591i	$-0.470100\pi$
$739$	5.09966			0.187594			0.0937970	+	0.995591i	$0.470100\pi$
$740$	−10.3278	−	8.85074i	−0.379659	−	0.325360i
$741$	−16.3889			−0.602062
$742$	−1.05755			−0.0388240
$743$	5.46112	+	5.46112i	0.200349	+	0.200349i	0.800150	−	0.599801i	$-0.204753\pi$
$743$	5.46112	+	5.46112i	0.200349	+	0.200349i	−0.599801	+	0.800150i	$0.704753\pi$
$744$	−1.95403			−0.0716384
$745$	−15.0487	−	34.7851i	−0.551342	−	1.27443i
$746$	−2.47846	−	2.47846i	−0.0907429	−	0.0907429i
$747$	−7.41007	−	7.41007i	−0.271120	−	0.271120i
$748$	−6.22803			−0.227719
$749$		−	8.56313i		−	0.312890i
$750$	−10.1177	+	4.75731i	−0.369446	+	0.173712i
$751$			50.1472i			1.82990i	0.403569	+	0.914949i	$0.367770\pi$
$751$			50.1472i			1.82990i	−0.403569	+	0.914949i	$0.632230\pi$
$752$	7.27515	+	7.27515i	0.265297	+	0.265297i
$753$	−3.98630			−0.145269
$754$	−29.2510	−	29.2510i	−1.06526	−	1.06526i
$755$	1.11867	+	2.58581i	0.0407126	+	0.0941072i
$756$	2.60801			0.0948524
$757$		−	38.6619i		−	1.40519i	−0.711589	−	0.702596i	$-0.752024\pi$
$757$		−	38.6619i		−	1.40519i	0.711589	−	0.702596i	$-0.247976\pi$
$758$		−	31.6861i		−	1.15089i
$759$	−8.64976	+	8.64976i	−0.313966	+	0.313966i
$760$	−2.66018	+	6.71688i	−0.0964949	+	0.243647i
$761$		−	2.58952i		−	0.0938702i	−0.998898	−	0.0469351i	$-0.985055\pi$
$761$		−	2.58952i		−	0.0938702i	0.998898	−	0.0469351i	$-0.0149454\pi$
$762$			9.29533i			0.336734i
$763$	−19.2013			−0.695134
$764$	−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	$-0.257882\pi$
$769$	−0.970999	−	0.970999i	−0.0350151	−	0.0350151i	−0.724398	+	0.689382i	$0.757882\pi$
$770$	4.55668	−	11.5055i	0.164211	−	0.414629i
$771$	7.91684	−	7.91684i	0.285118	−	0.285118i
$772$	11.4610			0.412489
$773$	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
$775$	−0.304929	−	9.76541i	−0.0109534	−	0.350784i
$776$			7.94678i			0.285273i
$777$	−14.2572	+	6.95673i	−0.511473	+	0.249571i
$778$	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
$782$		−	16.9189i		−	0.605017i
$783$	8.15506			0.291438
$784$		−	0.198289i		−	0.00708176i
$785$	11.9134	+	4.71824i	0.425208	+	0.168401i
$786$	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
$790$	−6.68059	+	16.8683i	−0.237685	+	0.600147i
$791$	−30.6783	+	30.6783i	−1.09080	+	1.09080i
$792$	−2.12202			−0.0754027
$793$	−12.4092	+	12.4092i	−0.440664	+	0.440664i
$794$	−11.7358	+	11.7358i	−0.416487	+	0.416487i
$795$	−0.832191	+	0.360022i	−0.0295148	+	0.0127687i
$796$	14.1563	+	14.1563i	0.501756	+	0.501756i
$797$	46.2735			1.63909			0.819546	−	0.573014i	$-0.194226\pi$
$797$	46.2735			1.63909			0.819546	+	0.573014i	$0.194226\pi$
$798$	5.95820	+	5.95820i	0.210918	+	0.210918i
$799$	21.3522	−	21.3522i	0.755388	−	0.755388i
$800$	−3.42347	+	3.64416i	−0.121038	+	0.128840i
$801$	−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
$808$			15.2228i			0.535535i
$809$	5.77592	+	5.77592i	0.203070	+	0.203070i	0.801314	−	0.598244i	$-0.204135\pi$
$809$	5.77592	+	5.77592i	0.203070	+	0.203070i	−0.598244	+	0.801314i	$0.704135\pi$
$810$	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	$0.828609\pi$
$812$			21.2685i			0.746377i
$813$	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
$820$	6.14996	+	14.2156i	0.214766	+	0.496432i
$821$	11.8926			0.415053			0.207527	−	0.978229i	$-0.433459\pi$
$821$	11.8926			0.415053			0.207527	+	0.978229i	$0.433459\pi$
$822$		−	1.30863i		−	0.0456437i
$823$	−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
$827$			1.44766i			0.0503400i	0.999683	+	0.0251700i	$0.00801271\pi$
$827$			1.44766i			0.0503400i	−0.999683	+	0.0251700i	$0.991987\pi$
$828$		−	5.76461i		−	0.200334i
$829$	17.0831	+	17.0831i	0.593320	+	0.593320i	0.938527	−	0.345207i	$-0.112191\pi$
$829$	17.0831	+	17.0831i	0.593320	+	0.593320i	−0.345207	+	0.938527i	$0.612191\pi$
$830$	8.62833	−	21.7863i	0.299494	−	0.756213i
$831$	10.2132	+	10.2132i	0.354293	+	0.354293i
$832$	−5.07258			−0.175860
$833$	−0.581970			−0.0201641
$834$	−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
$837$			1.95403i			0.0675413i
$838$			24.2039i			0.836109i
$839$	24.1753			0.834624			0.417312	−	0.908763i	$-0.362972\pi$
$839$	24.1753			0.834624			0.417312	+	0.908763i	$0.362972\pi$
$840$	2.31550	+	5.35229i	0.0798925	+	0.184671i
$841$			37.5049i			1.29327i
$842$	9.91998	−	9.91998i	0.341865	−	0.341865i
$843$			14.3877i			0.495538i
$844$	8.13385			0.279979
$845$	26.1273	−	11.3032i	0.898807	−	0.388841i
$846$	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
$853$			51.8584i			1.77560i	0.460232	+	0.887799i	$0.347766\pi$
$853$			51.8584i			1.77560i	−0.460232	+	0.887799i	$0.652234\pi$
$854$	9.02276			0.308753
$855$	6.71688	+	2.66018i	0.229712	+	0.0909762i
$856$	−2.32171	−	2.32171i	−0.0793545	−	0.0793545i
$857$			50.1319i			1.71247i	0.516585	+	0.856236i	$0.327203\pi$
$857$			50.1319i			1.71247i	−0.516585	+	0.856236i	$0.672797\pi$
$858$	7.61138	−	7.61138i	0.259848	−	0.259848i
$859$	−22.7307	+	22.7307i	−0.775560	+	0.775560i	−0.979072	−	0.203512i	$-0.934764\pi$
$859$	−22.7307	+	22.7307i	−0.775560	+	0.775560i	0.203512	+	0.979072i	$0.434764\pi$
$860$	−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
$865$	3.36425	+	1.33239i	0.114388	+	0.0453027i
$866$	−20.6095	+	20.6095i	−0.700338	+	0.700338i
$867$	5.92983	+	5.92983i	0.201387	+	0.201387i
$868$	−5.09614			−0.172974
$869$	−12.1747	−	12.1747i	−0.412999	−	0.412999i
$870$	7.24042	+	16.7362i	0.245473	+	0.567411i
$871$	−50.2126	+	50.2126i	−1.70139	+	1.70139i
$872$	−5.20603	+	5.20603i	−0.176298	+	0.176298i
$873$	7.94678			0.268958
$874$	13.1697	−	13.1697i	0.445472	−	0.445472i
$875$	−26.3871	+	12.4071i	−0.892046	+	0.419437i
$876$		−	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
$880$	−1.88402	−	4.35492i	−0.0635104	−	0.146804i
$881$			44.7156i			1.50651i	0.657731	+	0.753253i	$0.271516\pi$
$881$			44.7156i			1.50651i	−0.657731	+	0.753253i	$0.728484\pi$
$882$	−0.198289			−0.00667675
$883$		−	19.8417i		−	0.667727i	−0.942621	−	0.333863i	$-0.891648\pi$
$883$		−	19.8417i		−	0.667727i	0.942621	−	0.333863i	$-0.108352\pi$
$884$			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	−0.294320	−	0.955707i	$-0.595093\pi$
$887$	19.6978	−	19.6978i	0.661387	−	0.661387i	0.955707	+	0.294320i	$0.0950930\pi$
$888$	−1.97936	+	5.75171i	−0.0664231	+	0.193015i
$889$			24.2423i			0.813060i
$890$	−35.0565	−	13.8839i	−1.17510	−	0.465391i
$891$			2.12202i			0.0710903i
$892$	−18.5142	+	18.5142i	−0.619901	+	0.619901i
$893$	33.2413			1.11238
$894$	−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
$902$	−14.6989			−0.489420
$903$			5.22621i			0.173917i
$904$			16.6356i			0.553291i
$905$	−3.26883	+	1.41416i	−0.108660	+	0.0470083i
$906$	0.890945	−	0.890945i	0.0295997	−	0.0295997i
$907$		−	53.6798i		−	1.78241i	−0.453603	−	0.891204i	$-0.649862\pi$
$907$		−	53.6798i		−	1.78241i	0.453603	−	0.891204i	$-0.350138\pi$
$908$			8.71126i			0.289093i
$909$	15.2228			0.504907
$910$	−27.5033	−	10.8925i	−0.911724	−	0.361083i
$911$	6.84880	+	6.84880i	0.226911	+	0.226911i	0.811401	−	0.584490i	$-0.198705\pi$
$911$	6.84880	+	6.84880i	0.226911	+	0.226911i	−0.584490	+	0.811401i	$0.698705\pi$
$912$	3.23088			0.106985
$913$	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
$917$	9.86309			0.325708
$918$	−2.07533	−	2.07533i	−0.0684960	−	0.0684960i
$919$	−18.9548	−	18.9548i	−0.625261	−	0.625261i	0.321611	−	0.946872i	$-0.395776\pi$
$919$	−18.9548	−	18.9548i	−0.625261	−	0.625261i	−0.946872	+	0.321611i	$0.895776\pi$
$920$	11.8304	−	5.11807i	0.390037	−	0.168738i
$921$	22.9990			0.757844
$922$	26.9418	+	26.9418i	0.887281	+	0.887281i
$923$	−8.61108			−0.283437
$924$	−5.53425			−0.182063
$925$	−29.0534	−	8.99444i	−0.955270	−	0.295735i
$926$	16.5851			0.545019
$927$	−13.4988			−0.443359
$928$	5.76649	+	5.76649i	0.189294	+	0.189294i
$929$	−43.3213			−1.42133			−0.710663	−	0.703532i	$-0.751605\pi$
$929$	−43.3213			−1.42133			−0.710663	+	0.703532i	$0.751605\pi$
$930$	−4.01017	+	1.73488i	−0.131499	+	0.0568889i
$931$	−0.453008	−	0.453008i	−0.0148467	−	0.0148467i
$932$	15.7454	+	15.7454i	0.515757	+	0.515757i
$933$	15.6611			0.512721
$934$		−	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	$0.783513\pi$
$938$	36.5097			1.19208
$939$	3.12160	+	3.12160i	0.101870	+	0.101870i
$940$	21.3896	+	8.47123i	0.697653	+	0.276301i
$941$	−59.4050			−1.93655			−0.968273	−	0.249894i	$-0.919604\pi$
$941$	−59.4050			−1.93655			−0.968273	+	0.249894i	$0.919604\pi$
$942$		−	5.73047i		−	0.186709i
$943$		−	39.9306i		−	1.30032i
$944$	−8.25437	+	8.25437i	−0.268657	+	0.268657i
$945$	5.35229	−	2.31550i	0.174110	−	0.0753234i
$946$		−	4.25233i		−	0.138255i
$947$		−	22.4238i		−	0.728675i	−0.931267	−	0.364337i	$-0.881296\pi$
$947$		−	22.4238i		−	0.728675i	0.931267	−	0.364337i	$-0.118704\pi$
$948$	8.11381			0.263524
$949$	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	0.349619	−	0.936892i	$-0.386311\pi$
$953$	−18.1295	−	18.1295i	−0.587272	−	0.587272i	−0.936892	+	0.349619i	$0.886311\pi$
$954$	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
$957$	−17.3052			−0.559397
$958$	15.9403	−	15.9403i	0.515009	−	0.515009i
$959$		−	3.41292i		−	0.110209i
$960$	2.07896	+	0.823360i	0.0670982	+	0.0265738i
$961$			27.1817i			0.876831i
$962$	−13.5308	−	27.7302i	−0.436252	−	0.894058i
$963$	−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
$967$		−	52.0958i		−	1.67529i	−0.546216	−	0.837644i	$-0.683932\pi$
$967$		−	52.0958i		−	1.67529i	0.546216	−	0.837644i	$-0.316068\pi$
$968$	−6.49703			−0.208823
$969$		−	9.48250i		−	0.304622i
$970$	7.05550	+	16.3088i	0.226539	+	0.523644i
$971$	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
$975$	−25.3505	+	0.791581i	−0.811867	+	0.0253509i
$976$	2.44633	−	2.44633i	0.0783052	−	0.0783052i
$977$	−2.33312			−0.0746432			−0.0373216	−	0.999303i	$-0.511883\pi$
$977$	−2.33312			−0.0746432			−0.0373216	+	0.999303i	$0.511883\pi$
$978$	−0.142041	+	0.142041i	−0.00454196	+	0.00454196i
$979$	25.3021	−	25.3021i	0.808660	−	0.808660i
$980$	−0.176050	−	0.406940i	−0.00562371	−	0.0129992i
$981$	5.20603	+	5.20603i	0.166216	+	0.166216i
$982$	−30.9165			−0.986585
$983$	14.6210	+	14.6210i	0.466338	+	0.466338i	0.900726	−	0.434388i	$-0.143035\pi$
$983$	14.6210	+	14.6210i	0.466338	+	0.466338i	−0.434388	+	0.900726i	$0.643035\pi$
$984$	4.89802	−	4.89802i	0.156143	−	0.156143i
$985$	10.6376	+	4.21296i	0.338942	+	0.134236i
$986$	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	−0.945746	−	0.324906i	$-0.894667\pi$
$991$	−19.5442	+	19.5442i	−0.620841	+	0.620841i	0.324906	+	0.945746i	$0.394667\pi$
$992$	−1.38171	+	1.38171i	−0.0438694	+	0.0438694i
$993$		−	24.0444i		−	0.763025i
$994$	3.13057	+	3.13057i	0.0992956	+	0.0992956i
$995$	41.6208	+	16.4837i	1.31947	+	0.522567i
$996$	−10.4794			−0.332053
$997$		−	23.0867i		−	0.731162i	−0.930780	−	0.365581i	$-0.880870\pi$
$997$		−	23.0867i		−	0.731162i	0.930780	−	0.365581i	$-0.119130\pi$
$998$	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.o.a.487.17	yes	36
5.3	odd	4		1110.2.l.a.43.2	✓	36
37.31	odd	4		1110.2.l.a.697.2	yes	36
185.68	even	4	inner	1110.2.o.a.253.17	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.2	✓	36	5.3	odd	4
1110.2.l.a.697.2	yes	36	37.31	odd	4
1110.2.o.a.253.17	yes	36	185.68	even	4	inner
1110.2.o.a.487.17	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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