LMFDB - Embedded newform 1110.2.x.c.751.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{13} + 398 x^{12} - 136 x^{11} + 32 x^{10} - 824 x^{9} + 17825 x^{8} - 11480 x^{7} + \cdots + 20736 $ x^16 - 8x^13 + 398x^12 - 136x^11 + 32x^10 - 824x^9 + 17825x^8 - 11480x^7 + 3104x^6 + 11296x^5 + 68320x^4 - 21120x^3 + 4608x^2 + 13824*x + 20736
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.2
Root			$-3.13757 - 3.13757i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.c.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-0.907693 + 1.57217i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-0.907693 + 1.57217i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +0.815387 q^{11} +(0.500000 + 0.866025i) q^{12} +(3.93443 + 2.27154i) q^{13} -1.81539i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(5.34693 - 3.08705i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-1.98914 - 1.14843i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-0.907693 - 1.57217i) q^{21} +(-0.706146 + 0.407693i) q^{22} +4.40231i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -4.54308 q^{26} +1.00000 q^{27} +(0.907693 + 1.57217i) q^{28} +7.75661i q^{29} +(0.500000 - 0.866025i) q^{30} -9.52816i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.407693 + 0.706146i) q^{33} +(-3.08705 + 5.34693i) q^{34} +(-1.57217 + 0.907693i) q^{35} -1.00000 q^{36} +(0.200538 + 6.07946i) q^{37} +2.29686 q^{38} +(-3.93443 + 2.27154i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-4.25141 + 7.36365i) q^{41} +(1.57217 + 0.907693i) q^{42} -11.8338i q^{43} +(0.407693 - 0.706146i) q^{44} -1.00000i q^{45} +(-2.20115 - 3.81251i) q^{46} +4.05346 q^{47} +1.00000 q^{48} +(1.85219 + 3.20808i) q^{49} +(-0.866025 - 0.500000i) q^{50} +6.17410i q^{51} +(3.93443 - 2.27154i) q^{52} +(4.32059 + 7.48348i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.706146 + 0.407693i) q^{55} +(-1.57217 - 0.907693i) q^{56} +(1.98914 - 1.14843i) q^{57} +(-3.87830 - 6.71742i) q^{58} +(-6.20462 + 3.58224i) q^{59} +1.00000i q^{60} +(7.36365 + 4.25141i) q^{61} +(4.76408 + 8.25163i) q^{62} +1.81539 q^{63} -1.00000 q^{64} +(2.27154 + 3.93443i) q^{65} -0.815387i q^{66} +(1.05312 - 1.82405i) q^{67} -6.17410i q^{68} +(-3.81251 - 2.20115i) q^{69} +(0.907693 - 1.57217i) q^{70} +(0.0611155 - 0.105855i) q^{71} +(0.866025 - 0.500000i) q^{72} -12.4879 q^{73} +(-3.21340 - 5.16469i) q^{74} -1.00000 q^{75} +(-1.98914 + 1.14843i) q^{76} +(-0.740121 + 1.28193i) q^{77} +(2.27154 - 3.93443i) q^{78} +(-2.40261 - 1.38715i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -8.50281i q^{82} +(4.34472 + 7.52528i) q^{83} -1.81539 q^{84} +6.17410 q^{85} +(5.91689 + 10.2484i) q^{86} +(-6.71742 - 3.87830i) q^{87} +0.815387i q^{88} +(-6.99306 + 4.03744i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-7.14250 + 4.12373i) q^{91} +(3.81251 + 2.20115i) q^{92} +(8.25163 + 4.76408i) q^{93} +(-3.51040 + 2.02673i) q^{94} +(-1.14843 - 1.98914i) q^{95} +(-0.866025 + 0.500000i) q^{96} -3.49441i q^{97} +(-3.20808 - 1.85219i) q^{98} +(-0.407693 - 0.706146i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$		−	1.00000i		−	0.408248i
$7$	−0.907693	+	1.57217i	−0.343076	+	0.594225i	−0.985002	−	0.172541i	$-0.944802\pi$
$7$	−0.907693	+	1.57217i	−0.343076	+	0.594225i	0.641926	+	0.766766i	$0.278135\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	0.815387			0.245848			0.122924	−	0.992416i	$-0.460773\pi$
$11$	0.815387			0.245848			0.122924	+	0.992416i	$0.460773\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	3.93443	+	2.27154i	1.09121	+	0.630012i	0.933899	−	0.357536i	$-0.116383\pi$
$13$	3.93443	+	2.27154i	1.09121	+	0.630012i	0.157314	+	0.987549i	$0.449716\pi$
$14$		−	1.81539i		−	0.485183i
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	5.34693	−	3.08705i	1.29682	−	0.748720i	0.316967	−	0.948436i	$-0.397335\pi$
$17$	5.34693	−	3.08705i	1.29682	−	0.748720i	0.979854	+	0.199716i	$0.0640021\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−1.98914	−	1.14843i	−0.456340	−	0.263468i	0.254164	−	0.967161i	$-0.418200\pi$
$19$	−1.98914	−	1.14843i	−0.456340	−	0.263468i	−0.710504	+	0.703693i	$0.751533\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	−0.907693	−	1.57217i	−0.198075	−	0.343076i
$22$	−0.706146	+	0.407693i	−0.150551	+	0.0869205i
$23$			4.40231i			0.917944i	0.888451	+	0.458972i	$0.151782\pi$
$23$			4.40231i			0.917944i	−0.888451	+	0.458972i	$0.848218\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−4.54308			−0.890972
$27$	1.00000			0.192450
$28$	0.907693	+	1.57217i	0.171538	+	0.297112i
$29$			7.75661i			1.44037i	0.693784	+	0.720183i	$0.255942\pi$
$29$			7.75661i			1.44037i	−0.693784	+	0.720183i	$0.744058\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$		−	9.52816i		−	1.71131i	−0.517549	−	0.855654i	$-0.673155\pi$
$31$		−	9.52816i		−	1.71131i	0.517549	−	0.855654i	$-0.326845\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.407693	+	0.706146i	−0.0709703	+	0.122924i
$34$	−3.08705	+	5.34693i	−0.529425	+	0.916991i
$35$	−1.57217	+	0.907693i	−0.265745	+	0.153428i
$36$	−1.00000			−0.166667
$37$	0.200538	+	6.07946i	0.0329683	+	0.999456i
$37$	0.200538	+	6.07946i	0.0329683	+	0.999456i
$38$	2.29686			0.372600
$39$	−3.93443	+	2.27154i	−0.630012	+	0.363738i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−4.25141	+	7.36365i	−0.663958	+	1.15001i	0.315609	+	0.948889i	$0.397791\pi$
$41$	−4.25141	+	7.36365i	−0.663958	+	1.15001i	−0.979567	+	0.201120i	$0.935542\pi$
$42$	1.57217	+	0.907693i	0.242591	+	0.140060i
$43$		−	11.8338i		−	1.80464i	−0.431072	−	0.902318i	$-0.641864\pi$
$43$		−	11.8338i		−	1.80464i	0.431072	−	0.902318i	$-0.358136\pi$
$44$	0.407693	−	0.706146i	0.0614621	−	0.106455i
$45$		−	1.00000i		−	0.149071i
$46$	−2.20115	−	3.81251i	−0.324542	−	0.562124i
$47$	4.05346			0.591259			0.295629	−	0.955303i	$-0.404471\pi$
$47$	4.05346			0.591259			0.295629	+	0.955303i	$0.404471\pi$
$48$	1.00000			0.144338
$49$	1.85219	+	3.20808i	0.264598	+	0.458297i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$			6.17410i			0.864547i
$52$	3.93443	−	2.27154i	0.545607	−	0.315006i
$53$	4.32059	+	7.48348i	0.593478	+	1.02793i	0.993760	+	0.111542i	$0.0355790\pi$
$53$	4.32059	+	7.48348i	0.593478	+	1.02793i	−0.400282	+	0.916392i	$0.631088\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	0.706146	+	0.407693i	0.0952167	+	0.0549734i
$56$	−1.57217	−	0.907693i	−0.210090	−	0.121296i
$57$	1.98914	−	1.14843i	0.263468	−	0.152113i
$58$	−3.87830	−	6.71742i	−0.509246	−	0.882040i
$59$	−6.20462	+	3.58224i	−0.807773	+	0.466368i	−0.846182	−	0.532894i	$-0.821104\pi$
$59$	−6.20462	+	3.58224i	−0.807773	+	0.466368i	0.0384089	+	0.999262i	$0.487771\pi$
$60$			1.00000i			0.129099i
$61$	7.36365	+	4.25141i	0.942819	+	0.544337i	0.890843	−	0.454312i	$-0.150115\pi$
$61$	7.36365	+	4.25141i	0.942819	+	0.544337i	0.0519761	+	0.998648i	$0.483448\pi$
$62$	4.76408	+	8.25163i	0.605039	+	1.04796i
$63$	1.81539			0.228717
$64$	−1.00000			−0.125000
$65$	2.27154	+	3.93443i	0.281750	+	0.488005i
$66$		−	0.815387i		−	0.100367i
$67$	1.05312	−	1.82405i	0.128659	−	0.222844i	−0.794498	−	0.607266i	$-0.792266\pi$
$67$	1.05312	−	1.82405i	0.128659	−	0.222844i	0.923157	+	0.384423i	$0.125599\pi$
$68$		−	6.17410i		−	0.748720i
$69$	−3.81251	−	2.20115i	−0.458972	−	0.264988i
$70$	0.907693	−	1.57217i	0.108490	−	0.187910i
$71$	0.0611155	−	0.105855i	0.00725307	−	0.0125627i	−0.862376	−	0.506268i	$-0.831025\pi$
$71$	0.0611155	−	0.105855i	0.00725307	−	0.0125627i	0.869629	+	0.493706i	$0.164358\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−12.4879			−1.46160			−0.730798	−	0.682594i	$-0.760852\pi$
$73$	−12.4879			−1.46160			−0.730798	+	0.682594i	$0.760852\pi$
$74$	−3.21340	−	5.16469i	−0.373550	−	0.600383i
$75$	−1.00000			−0.115470
$76$	−1.98914	+	1.14843i	−0.228170	+	0.131734i
$77$	−0.740121	+	1.28193i	−0.0843446	+	0.146089i
$78$	2.27154	−	3.93443i	0.257201	−	0.445486i
$79$	−2.40261	−	1.38715i	−0.270315	−	0.156067i	0.358716	−	0.933447i	$-0.383215\pi$
$79$	−2.40261	−	1.38715i	−0.270315	−	0.156067i	−0.629031	+	0.777380i	$0.716548\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	8.50281i		−	0.938979i
$83$	4.34472	+	7.52528i	0.476895	+	0.826007i	0.999649	−	0.0264767i	$-0.00842879\pi$
$83$	4.34472	+	7.52528i	0.476895	+	0.826007i	−0.522754	+	0.852483i	$0.675095\pi$
$84$	−1.81539			−0.198075
$85$	6.17410			0.669676
$86$	5.91689	+	10.2484i	0.638035	+	1.10511i
$87$	−6.71742	−	3.87830i	−0.720183	−	0.415798i
$88$			0.815387i			0.0869205i
$89$	−6.99306	+	4.03744i	−0.741263	+	0.427968i	−0.822528	−	0.568724i	$-0.807437\pi$
$89$	−6.99306	+	4.03744i	−0.741263	+	0.427968i	0.0812654	+	0.996692i	$0.474104\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−7.14250	+	4.12373i	−0.748738	+	0.432284i
$92$	3.81251	+	2.20115i	0.397482	+	0.229486i
$93$	8.25163	+	4.76408i	0.855654	+	0.494012i
$94$	−3.51040	+	2.02673i	−0.362070	+	0.209041i
$95$	−1.14843	−	1.98914i	−0.117826	−	0.204081i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$		−	3.49441i		−	0.354804i	−0.984138	−	0.177402i	$-0.943231\pi$
$97$		−	3.49441i		−	0.354804i	0.984138	−	0.177402i	$-0.0567693\pi$
$98$	−3.20808	−	1.85219i	−0.324065	−	0.187099i
$99$	−0.407693	−	0.706146i	−0.0409747	−	0.0709703i
$100$	1.00000			0.100000
$101$	−1.17024			−0.116443			−0.0582215	−	0.998304i	$-0.518543\pi$
$101$	−1.17024			−0.116443			−0.0582215	+	0.998304i	$0.518543\pi$
$102$	−3.08705	−	5.34693i	−0.305664	−	0.529425i
$103$			15.9163i			1.56828i	0.620582	+	0.784141i	$0.286896\pi$
$103$			15.9163i			1.56828i	−0.620582	+	0.784141i	$0.713104\pi$
$104$	−2.27154	+	3.93443i	−0.222743	+	0.385802i
$105$		−	1.81539i		−	0.177164i
$106$	−7.48348	−	4.32059i	−0.726859	−	0.419652i
$107$	−4.71963	+	8.17463i	−0.456263	+	0.790272i	−0.998760	−	0.0497866i	$-0.984146\pi$
$107$	−4.71963	+	8.17463i	−0.456263	+	0.790272i	0.542496	+	0.840058i	$0.317479\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−13.5591	+	7.82838i	−1.29873	+	0.749822i	−0.980185	−	0.198085i	$-0.936528\pi$
$109$	−13.5591	+	7.82838i	−1.29873	+	0.749822i	−0.318546	+	0.947908i	$0.603194\pi$
$110$	−0.815387			−0.0777441
$111$	−5.36523	−	2.86606i	−0.509245	−	0.272034i
$112$	1.81539			0.171538
$113$	7.92412	−	4.57499i	0.745438	−	0.430379i	−0.0786051	−	0.996906i	$-0.525047\pi$
$113$	7.92412	−	4.57499i	0.745438	−	0.430379i	0.824043	+	0.566527i	$0.191713\pi$
$114$	−1.14843	+	1.98914i	−0.107560	+	0.186300i
$115$	−2.20115	+	3.81251i	−0.205259	+	0.355518i
$116$	6.71742	+	3.87830i	0.623697	+	0.360091i
$117$		−	4.54308i		−	0.420008i
$118$	3.58224	−	6.20462i	0.329772	−	0.571182i
$119$			11.2084i			1.02747i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	−10.3351			−0.939559
$122$	−8.50281			−0.769808
$123$	−4.25141	−	7.36365i	−0.383336	−	0.663958i
$124$	−8.25163	−	4.76408i	−0.741018	−	0.427827i
$125$			1.00000i			0.0894427i
$126$	−1.57217	+	0.907693i	−0.140060	+	0.0808638i
$127$	9.96077	+	17.2526i	0.883875	+	1.53092i	0.846997	+	0.531597i	$0.178408\pi$
$127$	9.96077	+	17.2526i	0.883875	+	1.53092i	0.0368781	+	0.999320i	$0.488259\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	10.2484	+	5.91689i	0.902318	+	0.520953i
$130$	−3.93443	−	2.27154i	−0.345072	−	0.199227i
$131$	3.17041	−	1.83044i	0.277000	−	0.159926i	−0.355064	−	0.934842i	$-0.615541\pi$
$131$	3.17041	−	1.83044i	0.277000	−	0.159926i	0.632065	+	0.774916i	$0.282208\pi$
$132$	0.407693	+	0.706146i	0.0354852	+	0.0614621i
$133$	3.61105	−	2.08484i	0.313118	−	0.180779i
$134$			2.10624i			0.181951i
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$	3.08705	+	5.34693i	0.264713	+	0.458496i
$137$	2.04304			0.174549			0.0872743	−	0.996184i	$-0.472184\pi$
$137$	2.04304			0.174549			0.0872743	+	0.996184i	$0.472184\pi$
$138$	4.40231			0.374749
$139$	−7.55073	−	13.0782i	−0.640444	−	1.10928i	−0.985334	−	0.170639i	$-0.945417\pi$
$139$	−7.55073	−	13.0782i	−0.640444	−	1.10928i	0.344889	−	0.938643i	$-0.387916\pi$
$140$			1.81539i			0.153428i
$141$	−2.02673	+	3.51040i	−0.170682	+	0.295629i
$142$			0.122231i			0.0102574i
$143$	3.20808	+	1.85219i	0.268273	+	0.154888i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.87830	+	6.71742i	−0.322076	+	0.557851i
$146$	10.8148	−	6.24394i	0.895041	−	0.516752i
$147$	−3.70437			−0.305531
$148$	5.36523	+	2.86606i	0.441019	+	0.235588i
$149$	16.0574			1.31547			0.657735	−	0.753249i	$-0.271515\pi$
$149$	16.0574			1.31547			0.657735	+	0.753249i	$0.271515\pi$
$150$	0.866025	−	0.500000i	0.0707107	−	0.0408248i
$151$	7.71216	−	13.3579i	0.627607	−	1.08705i	−0.360424	−	0.932789i	$-0.617368\pi$
$151$	7.71216	−	13.3579i	0.627607	−	1.08705i	0.988031	−	0.154258i	$-0.0492988\pi$
$152$	1.14843	−	1.98914i	0.0931499	−	0.161340i
$153$	−5.34693	−	3.08705i	−0.432274	−	0.249573i
$154$		−	1.48024i		−	0.119281i
$155$	4.76408	−	8.25163i	0.382660	−	0.662787i
$156$			4.54308i			0.363738i
$157$	−8.16731	−	14.1462i	−0.651822	−	1.12899i	−0.982680	−	0.185309i	$-0.940671\pi$
$157$	−8.16731	−	14.1462i	−0.651822	−	1.12899i	0.330858	−	0.943681i	$-0.392662\pi$
$158$	2.77430			0.220712
$159$	−8.64117			−0.685290
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−6.92118	−	3.99594i	−0.545465	−	0.314925i
$162$		−	1.00000i		−	0.0785674i
$163$	−5.60830	+	3.23795i	−0.439276	+	0.253616i	−0.703290	−	0.710903i	$-0.748287\pi$
$163$	−5.60830	+	3.23795i	−0.439276	+	0.253616i	0.264015	+	0.964519i	$0.414953\pi$
$164$	4.25141	+	7.36365i	0.331979	+	0.575005i
$165$	−0.706146	+	0.407693i	−0.0549734	+	0.0317389i
$166$	−7.52528	−	4.34472i	−0.584075	−	0.337216i
$167$	−2.26769	−	1.30925i	−0.175479	−	0.101313i	0.409688	−	0.912226i	$-0.365638\pi$
$167$	−2.26769	−	1.30925i	−0.175479	−	0.101313i	−0.585167	+	0.810913i	$0.698971\pi$
$168$	1.57217	−	0.907693i	0.121296	−	0.0700301i
$169$	3.81980	+	6.61609i	0.293831	+	0.508930i
$170$	−5.34693	+	3.08705i	−0.410091	+	0.236766i
$171$			2.29686i			0.175645i
$172$	−10.2484	−	5.91689i	−0.781430	−	0.451159i
$173$	0.731339	+	1.26672i	0.0556027	+	0.0963067i	0.892487	−	0.451073i	$-0.148959\pi$
$173$	0.731339	+	1.26672i	0.0556027	+	0.0963067i	−0.836884	+	0.547380i	$0.815625\pi$
$174$	7.75661			0.588027
$175$	−1.81539			−0.137230
$176$	−0.407693	−	0.706146i	−0.0307310	−	0.0532277i
$177$		−	7.16448i		−	0.538515i
$178$	4.03744	−	6.99306i	0.302619	−	0.524152i
$179$			19.2413i			1.43816i	0.694926	+	0.719081i	$0.255437\pi$
$179$			19.2413i			1.43816i	−0.694926	+	0.719081i	$0.744563\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	8.78453	−	15.2153i	0.652949	−	1.13094i	−0.329455	−	0.944171i	$-0.606865\pi$
$181$	8.78453	−	15.2153i	0.652949	−	1.13094i	0.982404	−	0.186770i	$-0.0598018\pi$
$182$	4.12373	−	7.14250i	0.305671	−	0.529438i
$183$	−7.36365	+	4.25141i	−0.544337	+	0.314273i
$184$	−4.40231			−0.324542
$185$	−2.86606	+	5.36523i	−0.210717	+	0.394460i
$186$	−9.52816			−0.698638
$187$	4.35982	−	2.51714i	0.318821	−	0.184072i
$188$	2.02673	−	3.51040i	0.147815	−	0.256022i
$189$	−0.907693	+	1.57217i	−0.0660250	+	0.114359i
$190$	1.98914	+	1.14843i	0.144307	+	0.0833158i
$191$		−	19.8085i		−	1.43329i	−0.697438	−	0.716646i	$-0.745677\pi$
$191$		−	19.8085i		−	1.43329i	0.697438	−	0.716646i	$-0.254323\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$		−	23.5965i		−	1.69851i	−0.527982	−	0.849255i	$-0.677051\pi$
$193$		−	23.5965i		−	1.69851i	0.527982	−	0.849255i	$-0.322949\pi$
$194$	1.74721	+	3.02625i	0.125442	+	0.217272i
$195$	−4.54308			−0.325337
$196$	3.70437			0.264598
$197$	9.61232	+	16.6490i	0.684849	+	1.18619i	0.973484	+	0.228754i	$0.0734652\pi$
$197$	9.61232	+	16.6490i	0.684849	+	1.18619i	−0.288635	+	0.957439i	$0.593201\pi$
$198$	0.706146	+	0.407693i	0.0501836	+	0.0289735i
$199$		−	12.0594i		−	0.854870i	−0.904046	−	0.427435i	$-0.859417\pi$
$199$		−	12.0594i		−	0.854870i	0.904046	−	0.427435i	$-0.140583\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	1.05312	+	1.82405i	0.0742812	+	0.128659i
$202$	1.01345	−	0.585118i	0.0713064	−	0.0411688i
$203$	−12.1947	−	7.04062i	−0.855901	−	0.494155i
$204$	5.34693	+	3.08705i	0.374360	+	0.216137i
$205$	−7.36365	+	4.25141i	−0.514300	+	0.296931i
$206$	−7.95817	−	13.7839i	−0.554472	−	0.960373i
$207$	3.81251	−	2.20115i	0.264988	−	0.152991i
$208$		−	4.54308i		−	0.315006i
$209$	−1.62192	−	0.936414i	−0.112190	−	0.0647731i
$210$	0.907693	+	1.57217i	0.0626368	+	0.108490i
$211$	23.2865			1.60311			0.801555	−	0.597922i	$-0.204007\pi$
$211$	23.2865			1.60311			0.801555	+	0.597922i	$0.204007\pi$
$212$	8.64117			0.593478
$213$	0.0611155	+	0.105855i	0.00418756	+	0.00725307i
$214$		−	9.43925i		−	0.645254i
$215$	5.91689	−	10.2484i	0.403529	−	0.698932i
$216$			1.00000i			0.0680414i
$217$	14.9799	+	8.64865i	1.01690	+	0.587108i
$218$	7.82838	−	13.5591i	0.530205	−	0.918341i
$219$	6.24394	−	10.8148i	0.421927	−	0.730798i
$220$	0.706146	−	0.407693i	0.0476083	−	0.0274867i
$221$	28.0495			1.88681
$222$	6.07946	−	0.200538i	0.408026	−	0.0134593i
$223$	17.9980			1.20524			0.602618	−	0.798030i	$-0.294124\pi$
$223$	17.9980			1.20524			0.602618	+	0.798030i	$0.294124\pi$
$224$	−1.57217	+	0.907693i	−0.105045	+	0.0606478i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−4.57499	+	7.92412i	−0.304324	+	0.527104i
$227$	−11.5711	−	6.68056i	−0.767999	−	0.443405i	0.0641611	−	0.997940i	$-0.479563\pi$
$227$	−11.5711	−	6.68056i	−0.767999	−	0.443405i	−0.832160	+	0.554535i	$0.812896\pi$
$228$		−	2.29686i		−	0.152113i
$229$	−7.78559	+	13.4850i	−0.514487	+	0.891117i	0.485372	+	0.874308i	$0.338684\pi$
$229$	−7.78559	+	13.4850i	−0.514487	+	0.891117i	−0.999859	+	0.0168092i	$0.994649\pi$
$230$		−	4.40231i		−	0.290279i
$231$	−0.740121	−	1.28193i	−0.0486964	−	0.0843446i
$232$	−7.75661			−0.509246
$233$	4.84405			0.317344			0.158672	−	0.987331i	$-0.449279\pi$
$233$	4.84405			0.317344			0.158672	+	0.987331i	$0.449279\pi$
$234$	2.27154	+	3.93443i	0.148495	+	0.257201i
$235$	3.51040	+	2.02673i	0.228993	+	0.132209i
$236$			7.16448i			0.466368i
$237$	2.40261	−	1.38715i	0.156067	−	0.0901051i
$238$	−5.60419	−	9.70675i	−0.363266	−	0.629195i
$239$	−5.20735	+	3.00647i	−0.336836	+	0.194472i	−0.658872	−	0.752255i	$-0.728966\pi$
$239$	−5.20735	+	3.00647i	−0.336836	+	0.194472i	0.322036	+	0.946727i	$0.395633\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	25.3799	+	14.6531i	1.63486	+	0.943889i	0.982563	+	0.185929i	$0.0595294\pi$
$241$	25.3799	+	14.6531i	1.63486	+	0.943889i	0.652301	+	0.757960i	$0.273804\pi$
$242$	8.95050	−	5.16757i	0.575360	−	0.332184i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	7.36365	−	4.25141i	0.471409	−	0.272168i
$245$			3.70437i			0.236664i
$246$	7.36365	+	4.25141i	0.469489	+	0.271060i
$247$	−5.21741	−	9.03682i	−0.331976	−	0.574999i
$248$	9.52816			0.605039
$249$	−8.68944			−0.550671
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$		−	24.1959i		−	1.52723i	−0.645671	−	0.763615i	$-0.723422\pi$
$251$		−	24.1959i		−	1.52723i	0.645671	−	0.763615i	$-0.276578\pi$
$252$	0.907693	−	1.57217i	0.0571793	−	0.0990375i
$253$			3.58958i			0.225675i
$254$	−17.2526	−	9.96077i	−1.08252	−	0.624994i
$255$	−3.08705	+	5.34693i	−0.193319	+	0.334838i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.4849	−	7.20816i	0.778787	−	0.449633i	−0.0572133	−	0.998362i	$-0.518222\pi$
$257$	12.4849	−	7.20816i	0.778787	−	0.449633i	0.836000	+	0.548729i	$0.184888\pi$
$258$	−11.8338			−0.736739
$259$	−9.73997	−	5.20300i	−0.605212	−	0.323299i
$260$	4.54308			0.281750
$261$	6.71742	−	3.87830i	0.415798	−	0.240061i
$262$	−1.83044	+	3.17041i	−0.113085	+	0.195869i
$263$	3.08784	−	5.34830i	0.190405	−	0.329790i	−0.754980	−	0.655748i	$-0.772353\pi$
$263$	3.08784	−	5.34830i	0.190405	−	0.329790i	0.945384	+	0.325958i	$0.105687\pi$
$264$	−0.706146	−	0.407693i	−0.0434603	−	0.0250918i
$265$			8.64117i			0.530823i
$266$	−2.08484	+	3.61105i	−0.127830	+	0.221408i
$267$		−	8.07489i		−	0.494175i
$268$	−1.05312	−	1.82405i	−0.0643294	−	0.111422i
$269$	−15.0285			−0.916305			−0.458152	−	0.888874i	$-0.651489\pi$
$269$	−15.0285			−0.916305			−0.458152	+	0.888874i	$0.651489\pi$
$270$	−1.00000			−0.0608581
$271$	−10.8208	−	18.7421i	−0.657314	−	1.13850i	−0.981308	−	0.192442i	$-0.938359\pi$
$271$	−10.8208	−	18.7421i	−0.657314	−	1.13850i	0.323994	−	0.946059i	$-0.394974\pi$
$272$	−5.34693	−	3.08705i	−0.324205	−	0.187180i
$273$		−	8.24745i		−	0.499159i
$274$	−1.76932	+	1.02152i	−0.106889	+	0.0617123i
$275$	0.407693	+	0.706146i	0.0245848	+	0.0425822i
$276$	−3.81251	+	2.20115i	−0.229486	+	0.132494i
$277$	13.1113	+	7.56978i	0.787779	+	0.454824i	0.839180	−	0.543854i	$-0.183035\pi$
$277$	13.1113	+	7.56978i	0.787779	+	0.454824i	−0.0514012	+	0.998678i	$0.516369\pi$
$278$	13.0782	+	7.55073i	0.784381	+	0.452863i
$279$	−8.25163	+	4.76408i	−0.494012	+	0.285218i
$280$	−0.907693	−	1.57217i	−0.0542451	−	0.0939552i
$281$	13.8083	−	7.97221i	0.823733	−	0.475582i	−0.0279694	−	0.999609i	$-0.508904\pi$
$281$	13.8083	−	7.97221i	0.823733	−	0.475582i	0.851702	+	0.524027i	$0.175571\pi$
$282$		−	4.05346i		−	0.241380i
$283$	27.7594	+	16.0269i	1.65012	+	0.952699i	0.977019	+	0.213152i	$0.0683730\pi$
$283$	27.7594	+	16.0269i	1.65012	+	0.952699i	0.673105	+	0.739547i	$0.264960\pi$
$284$	−0.0611155	−	0.105855i	−0.00362654	−	0.00628134i
$285$	2.29686			0.136054
$286$	−3.70437			−0.219044
$287$	−7.71795	−	13.3679i	−0.455576	−	0.789081i
$288$		−	1.00000i		−	0.0589256i
$289$	10.5598	−	18.2901i	0.621163	−	1.07589i
$290$		−	7.75661i		−	0.455484i
$291$	3.02625	+	1.74721i	0.177402	+	0.102423i
$292$	−6.24394	+	10.8148i	−0.365399	+	0.632890i
$293$	4.75948	−	8.24367i	0.278052	−	0.481600i	−0.692849	−	0.721083i	$-0.743645\pi$
$293$	4.75948	−	8.24367i	0.278052	−	0.481600i	0.970901	+	0.239483i	$0.0769779\pi$
$294$	3.20808	−	1.85219i	0.187099	−	0.108022i
$295$	−7.16448			−0.417132
$296$	−6.07946	+	0.200538i	−0.353361	+	0.0116561i
$297$	0.815387			0.0473135
$298$	−13.9061	+	8.02868i	−0.805558	+	0.465089i
$299$	−10.0000	+	17.3205i	−0.578316	+	1.00167i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	18.6047	+	10.7415i	1.07236	+	0.619127i
$302$			15.4243i			0.887570i
$303$	0.585118	−	1.01345i	0.0336142	−	0.0582215i
$304$			2.29686i			0.131734i
$305$	4.25141	+	7.36365i	0.243435	+	0.421641i
$306$	6.17410			0.352950
$307$	7.43723			0.424465			0.212233	−	0.977219i	$-0.431927\pi$
$307$	7.43723			0.424465			0.212233	+	0.977219i	$0.431927\pi$
$308$	0.740121	+	1.28193i	0.0421723	+	0.0730446i
$309$	−13.7839	−	7.95817i	−0.784141	−	0.452724i
$310$			9.52816i			0.541163i
$311$	−2.70324	+	1.56071i	−0.153286	+	0.0885000i	−0.574681	−	0.818377i	$-0.694874\pi$
$311$	−2.70324	+	1.56071i	−0.153286	+	0.0885000i	0.421395	+	0.906877i	$0.361541\pi$
$312$	−2.27154	−	3.93443i	−0.128601	−	0.222743i
$313$	6.22567	−	3.59439i	0.351896	−	0.203167i	−0.313624	−	0.949547i	$-0.601543\pi$
$313$	6.22567	−	3.59439i	0.351896	−	0.203167i	0.665520	+	0.746380i	$0.268210\pi$
$314$	14.1462	+	8.16731i	0.798316	+	0.460908i
$315$	1.57217	+	0.907693i	0.0885818	+	0.0511427i
$316$	−2.40261	+	1.38715i	−0.135158	+	0.0780333i
$317$	−15.0551	−	26.0762i	−0.845578	−	1.46458i	−0.885119	−	0.465365i	$-0.845923\pi$
$317$	−15.0551	−	26.0762i	−0.845578	−	1.46458i	0.0395412	−	0.999218i	$-0.487410\pi$
$318$	7.48348	−	4.32059i	0.419652	−	0.242286i
$319$			6.32463i			0.354112i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−4.71963	−	8.17463i	−0.263424	−	0.456263i
$322$	7.99189			0.445371
$323$	−14.1810			−0.789054
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			4.54308i			0.252005i
$326$	3.23795	−	5.60830i	0.179334	−	0.310615i
$327$		−	15.6568i		−	0.865820i
$328$	−7.36365	−	4.25141i	−0.406590	−	0.234745i
$329$	−3.67930	+	6.37274i	−0.202847	+	0.351341i
$330$	0.407693	−	0.706146i	0.0224428	−	0.0388720i
$331$	−17.0304	+	9.83249i	−0.936074	+	0.540442i	−0.888727	−	0.458436i	$-0.848410\pi$
$331$	−17.0304	+	9.83249i	−0.936074	+	0.540442i	−0.0473464	+	0.998879i	$0.515076\pi$
$332$	8.68944			0.476895
$333$	5.16469	−	3.21340i	0.283023	−	0.176093i
$334$	2.61850			0.143278
$335$	1.82405	−	1.05312i	0.0996587	−	0.0575380i
$336$	−0.907693	+	1.57217i	−0.0495187	+	0.0857690i
$337$	−1.82444	+	3.16003i	−0.0993837	+	0.172138i	−0.911430	−	0.411456i	$-0.865020\pi$
$337$	−1.82444	+	3.16003i	−0.0993837	+	0.172138i	0.812046	+	0.583593i	$0.198354\pi$
$338$	−6.61609	−	3.81980i	−0.359868	−	0.207770i
$339$			9.14998i			0.496959i
$340$	3.08705	−	5.34693i	0.167419	−	0.289978i
$341$		−	7.76913i		−	0.420722i
$342$	−1.14843	−	1.98914i	−0.0620999	−	0.107560i
$343$	−19.4326			−1.04926
$344$	11.8338			0.638035
$345$	−2.20115	−	3.81251i	−0.118506	−	0.205259i
$346$	−1.26672	−	0.731339i	−0.0680991	−	0.0393171i
$347$		−	20.3142i		−	1.09052i	−0.838266	−	0.545261i	$-0.816430\pi$
$347$		−	20.3142i		−	1.09052i	0.838266	−	0.545261i	$-0.183570\pi$
$348$	−6.71742	+	3.87830i	−0.360091	+	0.207899i
$349$	−15.6520	−	27.1101i	−0.837833	−	1.45117i	−0.891703	−	0.452621i	$-0.850489\pi$
$349$	−15.6520	−	27.1101i	−0.837833	−	1.45117i	0.0538706	−	0.998548i	$-0.482844\pi$
$350$	1.57217	−	0.907693i	0.0840361	−	0.0485183i
$351$	3.93443	+	2.27154i	0.210004	+	0.121246i
$352$	0.706146	+	0.407693i	0.0376377	+	0.0217301i
$353$	8.68738	−	5.01566i	0.462383	−	0.266957i	−0.250663	−	0.968074i	$-0.580649\pi$
$353$	8.68738	−	5.01566i	0.462383	−	0.266957i	0.713046	+	0.701118i	$0.247315\pi$
$354$	3.58224	+	6.20462i	0.190394	+	0.329772i
$355$	0.105855	−	0.0611155i	0.00561820	−	0.00324367i
$356$			8.07489i			0.427968i
$357$	−9.70675	−	5.60419i	−0.513736	−	0.296605i
$358$	−9.62065	−	16.6635i	−0.508467	−	0.880691i
$359$	−24.9510			−1.31686			−0.658431	−	0.752641i	$-0.728780\pi$
$359$	−24.9510			−1.31686			−0.658431	+	0.752641i	$0.728780\pi$
$360$	1.00000			0.0527046
$361$	−6.86222	−	11.8857i	−0.361169	−	0.625564i
$362$			17.5691i			0.923409i
$363$	5.16757	−	8.95050i	0.271227	−	0.469779i
$364$			8.24745i			0.432284i
$365$	−10.8148	−	6.24394i	−0.566074	−	0.326823i
$366$	4.25141	−	7.36365i	0.222225	−	0.384904i
$367$	−1.87570	+	3.24881i	−0.0979109	+	0.169587i	−0.910820	−	0.412804i	$-0.864549\pi$
$367$	−1.87570	+	3.24881i	−0.0979109	+	0.169587i	0.812909	+	0.582391i	$0.197883\pi$
$368$	3.81251	−	2.20115i	0.198741	−	0.114743i
$369$	8.50281			0.442639
$370$	−0.200538	−	6.07946i	−0.0104255	−	0.316056i
$371$	−15.6871			−0.814432
$372$	8.25163	−	4.76408i	0.427827	−	0.247006i
$373$	−9.27093	+	16.0577i	−0.480031	+	0.831437i	−0.999738	−	0.0229072i	$-0.992708\pi$
$373$	−9.27093	+	16.0577i	−0.480031	+	0.831437i	0.519707	+	0.854345i	$0.326041\pi$
$374$	−2.51714	+	4.35982i	−0.130158	+	0.225441i
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$			4.05346i			0.209041i
$377$	−17.6195	+	30.5178i	−0.907448	+	1.57175i
$378$		−	1.81539i		−	0.0933734i
$379$	−2.86018	−	4.95398i	−0.146918	−	0.254469i	0.783169	−	0.621809i	$-0.213602\pi$
$379$	−2.86018	−	4.95398i	−0.146918	−	0.254469i	−0.930087	+	0.367340i	$0.880269\pi$
$380$	−2.29686			−0.117826
$381$	−19.9215			−1.02061
$382$	9.90424	+	17.1546i	0.506745	+	0.877708i
$383$	9.96097	+	5.75097i	0.508982	+	0.293861i	0.732415	−	0.680858i	$-0.238393\pi$
$383$	9.96097	+	5.75097i	0.508982	+	0.293861i	−0.223433	+	0.974719i	$0.571726\pi$
$384$			1.00000i			0.0510310i
$385$	−1.28193	+	0.740121i	−0.0653331	+	0.0377201i
$386$	11.7982	+	20.4351i	0.600514	+	1.04012i
$387$	−10.2484	+	5.91689i	−0.520953	+	0.300773i
$388$	−3.02625	−	1.74721i	−0.153635	−	0.0887010i
$389$	29.8699	+	17.2454i	1.51447	+	0.874377i	0.999856	+	0.0169525i	$0.00539641\pi$
$389$	29.8699	+	17.2454i	1.51447	+	0.874377i	0.514609	+	0.857425i	$0.327937\pi$
$390$	3.93443	−	2.27154i	0.199227	−	0.115024i
$391$	13.5901	+	23.5388i	0.687283	+	1.19041i
$392$	−3.20808	+	1.85219i	−0.162032	+	0.0935495i
$393$			3.66088i			0.184667i
$394$	−16.6490	−	9.61232i	−0.838765	−	0.484261i
$395$	−1.38715	−	2.40261i	−0.0697951	−	0.120889i
$396$	−0.815387			−0.0409747
$397$	32.5197			1.63212			0.816058	−	0.577970i	$-0.196155\pi$
$397$	32.5197			1.63212			0.816058	+	0.577970i	$0.196155\pi$
$398$	6.02971	+	10.4438i	0.302242	+	0.523499i
$399$			4.16969i			0.208745i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$		−	20.9030i		−	1.04385i	−0.852993	−	0.521923i	$-0.825215\pi$
$401$		−	20.9030i		−	1.04385i	0.852993	−	0.521923i	$-0.174785\pi$
$402$	−1.82405	−	1.05312i	−0.0909756	−	0.0525248i
$403$	21.6436	−	37.4878i	1.07814	−	1.86740i
$404$	−0.585118	+	1.01345i	−0.0291107	+	0.0504213i
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	14.0812			0.698840
$407$	0.163516	+	4.95711i	0.00810521	+	0.245715i
$408$	−6.17410			−0.305664
$409$	0.756522	−	0.436778i	0.0374076	−	0.0215973i	−0.481180	−	0.876622i	$-0.659792\pi$
$409$	0.756522	−	0.436778i	0.0374076	−	0.0215973i	0.518587	+	0.855025i	$0.326458\pi$
$410$	4.25141	−	7.36365i	0.209962	−	0.363665i
$411$	−1.02152	+	1.76932i	−0.0503878	+	0.0872743i
$412$	13.7839	+	7.95817i	0.679086	+	0.392071i
$413$		−	13.0063i		−	0.639998i
$414$	−2.20115	+	3.81251i	−0.108181	+	0.187375i
$415$			8.68944i			0.426548i
$416$	2.27154	+	3.93443i	0.111371	+	0.192901i
$417$	15.1015			0.739521
$418$	1.87283			0.0916030
$419$	4.28092	+	7.41478i	0.209137	+	0.362236i	0.951443	−	0.307825i	$-0.0996013\pi$
$419$	4.28092	+	7.41478i	0.209137	+	0.362236i	−0.742306	+	0.670061i	$0.766268\pi$
$420$	−1.57217	−	0.907693i	−0.0767141	−	0.0442909i
$421$		−	25.7156i		−	1.25330i	−0.779300	−	0.626651i	$-0.784425\pi$
$421$		−	25.7156i		−	1.25330i	0.779300	−	0.626651i	$-0.215575\pi$
$422$	−20.1667	+	11.6433i	−0.981700	+	0.566785i
$423$	−2.02673	−	3.51040i	−0.0985431	−	0.170682i
$424$	−7.48348	+	4.32059i	−0.363430	+	0.209826i
$425$	5.34693	+	3.08705i	0.259364	+	0.149744i
$426$	−0.105855	−	0.0611155i	−0.00512870	−	0.00296105i
$427$	−13.3679	+	7.71795i	−0.646917	+	0.373498i
$428$	4.71963	+	8.17463i	0.228132	+	0.395136i
$429$	−3.20808	+	1.85219i	−0.154888	+	0.0894243i
$430$			11.8338i			0.570676i
$431$	11.1016	+	6.40951i	0.534745	+	0.308735i	0.742947	−	0.669351i	$-0.233428\pi$
$431$	11.1016	+	6.40951i	0.534745	+	0.308735i	−0.208201	+	0.978086i	$0.566761\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−29.6578			−1.42526			−0.712630	−	0.701540i	$-0.752496\pi$
$433$	−29.6578			−1.42526			−0.712630	+	0.701540i	$0.752496\pi$
$434$	−17.2973			−0.830297
$435$	−3.87830	−	6.71742i	−0.185950	−	0.322076i
$436$			15.6568i			0.749822i
$437$	5.05574	−	8.75679i	0.241849	−	0.418894i
$438$			12.4879i			0.596694i
$439$	−1.04777	−	0.604930i	−0.0500073	−	0.0288717i	0.474788	−	0.880100i	$-0.342525\pi$
$439$	−1.04777	−	0.604930i	−0.0500073	−	0.0288717i	−0.524795	+	0.851229i	$0.675858\pi$
$440$	−0.407693	+	0.706146i	−0.0194360	+	0.0336642i
$441$	1.85219	−	3.20808i	0.0881993	−	0.152766i
$442$	−24.2916	+	14.0247i	−1.15543	+	0.667089i
$443$	−14.0407			−0.667092			−0.333546	−	0.942734i	$-0.608245\pi$
$443$	−14.0407			−0.667092			−0.333546	+	0.942734i	$0.608245\pi$
$444$	−5.16469	+	3.21340i	−0.245106	+	0.152501i
$445$	−8.07489			−0.382786
$446$	−15.5867	+	8.99901i	−0.738054	+	0.426115i
$447$	−8.02868	+	13.9061i	−0.379743	+	0.657735i
$448$	0.907693	−	1.57217i	0.0428845	−	0.0742781i
$449$	4.50115	+	2.59874i	0.212422	+	0.122642i	0.602437	−	0.798167i	$-0.294197\pi$
$449$	4.50115	+	2.59874i	0.212422	+	0.122642i	−0.390014	+	0.920809i	$0.627530\pi$
$450$			1.00000i			0.0471405i
$451$	−3.46654	+	6.00422i	−0.163233	+	0.282728i
$452$		−	9.14998i		−	0.430379i
$453$	7.71216	+	13.3579i	0.362349	+	0.627607i
$454$	13.3611			0.627069
$455$	−8.24745			−0.386647
$456$	1.14843	+	1.98914i	0.0537801	+	0.0931499i
$457$	4.18171	+	2.41431i	0.195612	+	0.112937i	0.594607	−	0.804016i	$-0.297308\pi$
$457$	4.18171	+	2.41431i	0.195612	+	0.112937i	−0.398995	+	0.916953i	$0.630641\pi$
$458$		−	15.5712i		−	0.727594i
$459$	5.34693	−	3.08705i	0.249573	−	0.144091i
$460$	2.20115	+	3.81251i	0.102629	+	0.177759i
$461$	25.5524	−	14.7527i	1.19009	−	0.687101i	0.231766	−	0.972772i	$-0.425550\pi$
$461$	25.5524	−	14.7527i	1.19009	−	0.687101i	0.958328	+	0.285671i	$0.0922163\pi$
$462$	1.28193	+	0.740121i	0.0596407	+	0.0344336i
$463$	1.22731	+	0.708590i	0.0570381	+	0.0329310i	0.528248	−	0.849090i	$-0.322849\pi$
$463$	1.22731	+	0.708590i	0.0570381	+	0.0329310i	−0.471210	+	0.882021i	$0.656183\pi$
$464$	6.71742	−	3.87830i	0.311848	−	0.180046i
$465$	4.76408	+	8.25163i	0.220929	+	0.382660i
$466$	−4.19507	+	2.42202i	−0.194333	+	0.112198i
$467$			3.68783i			0.170652i	0.996353	+	0.0853261i	$0.0271932\pi$
$467$			3.68783i			0.170652i	−0.996353	+	0.0853261i	$0.972807\pi$
$468$	−3.93443	−	2.27154i	−0.181869	−	0.105002i
$469$	1.91182	+	3.31136i	0.0882795	+	0.152905i
$470$	−4.05346			−0.186972
$471$	16.3346			0.752660
$472$	−3.58224	−	6.20462i	−0.164886	−	0.285591i
$473$		−	9.64911i		−	0.443667i
$474$	−1.38715	+	2.40261i	−0.0637139	+	0.110356i
$475$		−	2.29686i		−	0.105387i
$476$	9.70675	+	5.60419i	0.444908	+	0.256868i
$477$	4.32059	−	7.48348i	0.197826	−	0.342645i
$478$	3.00647	−	5.20735i	0.137513	−	0.238179i
$479$	−15.7283	+	9.08072i	−0.718643	+	0.414909i	−0.814253	−	0.580510i	$-0.802853\pi$
$479$	−15.7283	+	9.08072i	−0.718643	+	0.414909i	0.0956101	+	0.995419i	$0.469520\pi$
$480$	−1.00000			−0.0456435
$481$	−13.0207	+	24.3747i	−0.593694	+	1.11139i
$482$	−29.3062			−1.33486
$483$	6.92118	−	3.99594i	0.314925	−	0.181822i
$484$	−5.16757	+	8.95050i	−0.234890	+	0.406841i
$485$	1.74721	−	3.02625i	0.0793366	−	0.137415i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$			16.2057i			0.734349i	0.930152	+	0.367175i	$0.119675\pi$
$487$			16.2057i			0.734349i	−0.930152	+	0.367175i	$0.880325\pi$
$488$	−4.25141	+	7.36365i	−0.192452	+	0.333337i
$489$		−	6.47590i		−	0.292850i
$490$	−1.85219	−	3.20808i	−0.0836732	−	0.144926i
$491$	8.42841			0.380369			0.190184	−	0.981748i	$-0.439091\pi$
$491$	8.42841			0.380369			0.190184	+	0.981748i	$0.439091\pi$
$492$	−8.50281			−0.383336
$493$	23.9450	+	41.4740i	1.07843	+	1.86790i
$494$	9.03682	+	5.21741i	0.406586	+	0.234742i
$495$		−	0.815387i		−	0.0366489i
$496$	−8.25163	+	4.76408i	−0.370509	+	0.213913i
$497$	0.110948	+	0.192168i	0.00497671	+	0.00861991i
$498$	7.52528	−	4.34472i	0.337216	−	0.194692i
$499$	5.57011	+	3.21590i	0.249352	+	0.143964i	0.619468	−	0.785022i	$-0.287349\pi$
$499$	5.57011	+	3.21590i	0.249352	+	0.143964i	−0.370115	+	0.928986i	$0.620682\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	2.26769	−	1.30925i	0.101313	−	0.0584930i
$502$	12.0979	+	20.9543i	0.539958	+	0.935234i
$503$	−19.2019	+	11.0862i	−0.856171	+	0.494311i	−0.862728	−	0.505668i	$-0.831246\pi$
$503$	−19.2019	+	11.0862i	−0.856171	+	0.494311i	0.00655715	+	0.999979i	$0.497913\pi$
$504$			1.81539i			0.0808638i
$505$	−1.01345	−	0.585118i	−0.0450982	−	0.0260374i
$506$	−1.79479	−	3.10867i	−0.0797882	−	0.138197i
$507$	−7.63961			−0.339287
$508$	19.9215			0.883875
$509$	−18.0052	−	31.1858i	−0.798064	−	1.38229i	−0.920875	−	0.389858i	$-0.872524\pi$
$509$	−18.0052	−	31.1858i	−0.798064	−	1.38229i	0.122811	−	0.992430i	$-0.460809\pi$
$510$		−	6.17410i		−	0.273394i
$511$	11.3352	−	19.6331i	0.501439	−	0.868517i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.98914	−	1.14843i	−0.0878226	−	0.0507044i
$514$	−7.20816	+	12.4849i	−0.317938	+	0.550685i
$515$	−7.95817	+	13.7839i	−0.350679	+	0.607393i
$516$	10.2484	−	5.91689i	0.451159	−	0.260477i
$517$	3.30514			0.145360
$518$	11.0366	−	0.364055i	0.484919	−	0.0159957i
$519$	−1.46268			−0.0642045
$520$	−3.93443	+	2.27154i	−0.172536	+	0.0996137i
$521$	−19.4867	+	33.7520i	−0.853728	+	1.47870i	0.0240914	+	0.999710i	$0.492331\pi$
$521$	−19.4867	+	33.7520i	−0.853728	+	1.47870i	−0.877820	+	0.478991i	$0.841003\pi$
$522$	−3.87830	+	6.71742i	−0.169749	+	0.294013i
$523$	3.11397	+	1.79785i	0.136164	+	0.0786145i	0.566535	−	0.824038i	$-0.308284\pi$
$523$	3.11397	+	1.79785i	0.136164	+	0.0786145i	−0.430370	+	0.902652i	$0.641617\pi$
$524$		−	3.66088i		−	0.159926i
$525$	0.907693	−	1.57217i	0.0396150	−	0.0686152i
$526$			6.17569i			0.269273i
$527$	−29.4139	−	50.9464i	−1.28129	−	2.21926i
$528$	0.815387			0.0354852
$529$	3.61970			0.157378
$530$	−4.32059	−	7.48348i	−0.187674	−	0.325061i
$531$	6.20462	+	3.58224i	0.269258	+	0.155456i
$532$		−	4.16969i		−	0.180779i
$533$	−33.4537	+	19.3145i	−1.44904	+	0.836604i
$534$	4.03744	+	6.99306i	0.174717	+	0.302619i
$535$	−8.17463	+	4.71963i	−0.353420	+	0.204047i
$536$	1.82405	+	1.05312i	0.0787872	+	0.0454878i
$537$	−16.6635	−	9.62065i	−0.719081	−	0.415162i
$538$	13.0151	−	7.51426i	0.561120	−	0.323963i
$539$	1.51025	+	2.61583i	0.0650510	+	0.112672i
$540$	0.866025	−	0.500000i	0.0372678	−	0.0215166i
$541$		−	13.8632i		−	0.596024i	−0.954562	−	0.298012i	$-0.903677\pi$
$541$		−	13.8632i		−	0.596024i	0.954562	−	0.298012i	$-0.0963235\pi$
$542$	18.7421	+	10.8208i	0.805042	+	0.464791i
$543$	8.78453	+	15.2153i	0.376980	+	0.652949i
$544$	6.17410			0.264713
$545$	−15.6568			−0.670662
$546$	4.12373	+	7.14250i	0.176479	+	0.305671i
$547$		−	18.8508i		−	0.806003i	−0.915199	−	0.403001i	$-0.867967\pi$
$547$		−	18.8508i		−	0.806003i	0.915199	−	0.403001i	$-0.132033\pi$
$548$	1.02152	−	1.76932i	0.0436372	−	0.0755818i
$549$		−	8.50281i		−	0.362891i
$550$	−0.706146	−	0.407693i	−0.0301102	−	0.0173841i
$551$	8.90791	−	15.4290i	0.379490	−	0.657296i
$552$	2.20115	−	3.81251i	0.0936873	−	0.162271i
$553$	4.36168	−	2.51821i	0.185477	−	0.107085i
$554$	−15.1396			−0.643219
$555$	−3.21340	−	5.16469i	−0.136401	−	0.219229i
$556$	−15.1015			−0.640444
$557$	−16.9855	+	9.80661i	−0.719701	+	0.415519i	−0.814643	−	0.579963i	$-0.803067\pi$
$557$	−16.9855	+	9.80661i	−0.719701	+	0.415519i	0.0949417	+	0.995483i	$0.469734\pi$
$558$	4.76408	−	8.25163i	0.201680	−	0.349319i
$559$	26.8809	−	46.5592i	1.13694	−	1.96924i
$560$	1.57217	+	0.907693i	0.0664364	+	0.0383570i
$561$			5.03428i			0.212548i
$562$	−7.97221	+	13.8083i	−0.336287	+	0.582467i
$563$			18.9201i			0.797386i	0.917084	+	0.398693i	$0.130536\pi$
$563$			18.9201i			0.797386i	−0.917084	+	0.398693i	$0.869464\pi$
$564$	2.02673	+	3.51040i	0.0853408	+	0.147815i
$565$	9.14998			0.384943
$566$	−32.0538			−1.34732
$567$	−0.907693	−	1.57217i	−0.0381195	−	0.0660250i
$568$	0.105855	+	0.0611155i	0.00444158	+	0.00256435i
$569$		−	6.48187i		−	0.271734i	−0.990727	−	0.135867i	$-0.956618\pi$
$569$		−	6.48187i		−	0.271734i	0.990727	−	0.135867i	$-0.0433820\pi$
$570$	−1.98914	+	1.14843i	−0.0833158	+	0.0481024i
$571$	12.2944	+	21.2945i	0.514504	+	0.891148i	0.999858	+	0.0168300i	$0.00535741\pi$
$571$	12.2944	+	21.2945i	0.514504	+	0.891148i	−0.485354	+	0.874318i	$0.661309\pi$
$572$	3.20808	−	1.85219i	0.134137	−	0.0774438i
$573$	17.1546	+	9.90424i	0.716646	+	0.413756i
$574$	13.3679	+	7.71795i	0.557964	+	0.322141i
$575$	−3.81251	+	2.20115i	−0.158993	+	0.0917944i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−9.49001	+	5.47906i	−0.395074	+	0.228096i	−0.684356	−	0.729148i	$-0.739917\pi$
$577$	−9.49001	+	5.47906i	−0.395074	+	0.228096i	0.289282	+	0.957244i	$0.406583\pi$
$578$			21.1196i			0.878458i
$579$	20.4351	+	11.7982i	0.849255	+	0.490318i
$580$	3.87830	+	6.71742i	0.161038	+	0.278926i
$581$	−15.7747			−0.654445
$582$	−3.49441			−0.144848
$583$	3.52295	+	6.10193i	0.145906	+	0.252716i
$584$		−	12.4879i		−	0.516752i
$585$	2.27154	−	3.93443i	0.0939167	−	0.162668i
$586$			9.51897i			0.393225i
$587$	35.5260	+	20.5110i	1.46632	+	0.846578i	0.999290	−	0.0376660i	$-0.0119923\pi$
$587$	35.5260	+	20.5110i	1.46632	+	0.846578i	0.467025	+	0.884244i	$0.345326\pi$
$588$	−1.85219	+	3.20808i	−0.0763828	+	0.132299i
$589$	−10.9424	+	18.9528i	−0.450874	+	0.780937i
$590$	6.20462	−	3.58224i	0.255440	−	0.147479i
$591$	−19.2246			−0.790796
$592$	5.16469	−	3.21340i	0.212268	−	0.132070i
$593$	−16.9383			−0.695574			−0.347787	−	0.937574i	$-0.613067\pi$
$593$	−16.9383			−0.695574			−0.347787	+	0.937574i	$0.613067\pi$
$594$	−0.706146	+	0.407693i	−0.0289735	+	0.0167279i
$595$	−5.60419	+	9.70675i	−0.229750	+	0.397938i
$596$	8.02868	−	13.9061i	0.328867	−	0.569615i
$597$	10.4438	+	6.02971i	0.427435	+	0.246780i
$598$		−	20.0000i		−	0.817863i
$599$	11.4310	−	19.7992i	0.467060	−	0.808971i	−0.532232	−	0.846599i	$-0.678647\pi$
$599$	11.4310	−	19.7992i	0.467060	−	0.808971i	0.999292	+	0.0376271i	$0.0119799\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	3.41363	+	5.91259i	0.139245	+	0.241179i	0.927211	−	0.374539i	$-0.122199\pi$
$601$	3.41363	+	5.91259i	0.139245	+	0.241179i	−0.787966	+	0.615719i	$0.788866\pi$
$602$	−21.4829			−0.875578
$603$	−2.10624			−0.0857726
$604$	−7.71216	−	13.3579i	−0.313803	−	0.543524i
$605$	−8.95050	−	5.16757i	−0.363889	−	0.210092i
$606$			1.17024i			0.0475376i
$607$	−5.82475	+	3.36292i	−0.236419	+	0.136497i	−0.613530	−	0.789672i	$-0.710251\pi$
$607$	−5.82475	+	3.36292i	−0.236419	+	0.136497i	0.377111	+	0.926168i	$0.376918\pi$
$608$	−1.14843	−	1.98914i	−0.0465750	−	0.0806702i
$609$	12.1947	−	7.04062i	0.494155	−	0.285300i
$610$	−7.36365	−	4.25141i	−0.298146	−	0.172134i
$611$	15.9481	+	9.20761i	0.645189	+	0.372500i
$612$	−5.34693	+	3.08705i	−0.216137	+	0.124787i
$613$	−23.3059	−	40.3670i	−0.941316	−	1.63041i	−0.762964	−	0.646441i	$-0.776256\pi$
$613$	−23.3059	−	40.3670i	−0.941316	−	1.63041i	−0.178353	−	0.983967i	$-0.557077\pi$
$614$	−6.44083	+	3.71862i	−0.259931	+	0.150071i
$615$		−	8.50281i		−	0.342866i
$616$	−1.28193	−	0.740121i	−0.0516503	−	0.0298203i
$617$	1.25390	+	2.17181i	0.0504799	+	0.0874338i	0.890161	−	0.455646i	$-0.150592\pi$
$617$	1.25390	+	2.17181i	0.0504799	+	0.0874338i	−0.839681	+	0.543079i	$0.817258\pi$
$618$	15.9163			0.640249
$619$	−6.60602			−0.265518			−0.132759	−	0.991148i	$-0.542384\pi$
$619$	−6.60602			−0.265518			−0.132759	+	0.991148i	$0.542384\pi$
$620$	−4.76408	−	8.25163i	−0.191330	−	0.331393i
$621$			4.40231i			0.176658i
$622$	1.56071	−	2.70324i	0.0625789	−	0.108390i
$623$		−	14.6590i		−	0.587302i
$624$	3.93443	+	2.27154i	0.157503	+	0.0909344i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.59439	+	6.22567i	−0.143661	+	0.248828i
$627$	1.62192	−	0.936414i	0.0647731	−	0.0373968i
$628$	−16.3346			−0.651822
$629$	19.8399	+	31.8874i	0.791067	+	1.27143i
$630$	−1.81539			−0.0723267
$631$	−29.5099	+	17.0376i	−1.17477	+	0.678254i	−0.954799	−	0.297252i	$-0.903930\pi$
$631$	−29.5099	+	17.0376i	−1.17477	+	0.678254i	−0.219972	+	0.975506i	$0.570597\pi$
$632$	1.38715	−	2.40261i	0.0551779	−	0.0955709i
$633$	−11.6433	+	20.1667i	−0.462778	+	0.801555i
$634$	26.0762	+	15.0551i	1.03562	+	0.597914i
$635$			19.9215i			0.790562i
$636$	−4.32059	+	7.48348i	−0.171322	+	0.296739i
$637$			16.8293i			0.666800i
$638$	−3.16232	−	5.47729i	−0.125197	−	0.216848i
$639$	−0.122231			−0.00483538
$640$	1.00000			0.0395285
$641$	−5.22823	−	9.05556i	−0.206503	−	0.357673i	0.744108	−	0.668060i	$-0.232875\pi$
$641$	−5.22823	−	9.05556i	−0.206503	−	0.357673i	−0.950610	+	0.310387i	$0.899542\pi$
$642$	8.17463	+	4.71963i	0.322627	+	0.186269i
$643$			43.7564i			1.72558i	0.505561	+	0.862791i	$0.331286\pi$
$643$			43.7564i			1.72558i	−0.505561	+	0.862791i	$0.668714\pi$
$644$	−6.92118	+	3.99594i	−0.272733	+	0.157462i
$645$	5.91689	+	10.2484i	0.232977	+	0.403529i
$646$	12.2811	−	7.09052i	0.483195	−	0.278973i
$647$	0.586928	+	0.338863i	0.0230745	+	0.0133221i	0.511493	−	0.859288i	$-0.329093\pi$
$647$	0.586928	+	0.338863i	0.0230745	+	0.0133221i	−0.488418	+	0.872610i	$0.662426\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−5.05917	+	2.92091i	−0.198590	+	0.114656i
$650$	−2.27154	−	3.93443i	−0.0890972	−	0.154321i
$651$	−14.9799	+	8.64865i	−0.587108	+	0.338967i
$652$			6.47590i			0.253616i
$653$	−26.8352	−	15.4933i	−1.05014	−	0.606301i	−0.127454	−	0.991844i	$-0.540681\pi$
$653$	−26.8352	−	15.4933i	−1.05014	−	0.606301i	−0.922690	+	0.385544i	$0.874014\pi$
$654$	7.82838	+	13.5591i	0.306114	+	0.530205i
$655$	3.66088			0.143042
$656$	8.50281			0.331979
$657$	6.24394	+	10.8148i	0.243599	+	0.421927i
$658$		−	7.35861i		−	0.286868i
$659$	14.4721	−	25.0664i	0.563752	−	0.976448i	−0.433412	−	0.901196i	$-0.642691\pi$
$659$	14.4721	−	25.0664i	0.563752	−	0.976448i	0.997165	−	0.0752519i	$-0.0239761\pi$
$660$			0.815387i			0.0317389i
$661$	12.6351	+	7.29489i	0.491449	+	0.283738i	0.725175	−	0.688564i	$-0.241759\pi$
$661$	12.6351	+	7.29489i	0.491449	+	0.283738i	−0.233726	+	0.972302i	$0.575092\pi$
$662$	9.83249	−	17.0304i	0.382151	−	0.661904i
$663$	−14.0247	+	24.2916i	−0.544676	+	0.943406i
$664$	−7.52528	+	4.34472i	−0.292037	+	0.168608i
$665$	4.16969			0.161694
$666$	−2.86606	+	5.36523i	−0.111057	+	0.207899i
$667$	−34.1470			−1.32218
$668$	−2.26769	+	1.30925i	−0.0877395	+	0.0506564i
$669$	−8.99901	+	15.5867i	−0.347922	+	0.602618i
$670$	−1.05312	+	1.82405i	−0.0406855	+	0.0704694i
$671$	6.00422	+	3.46654i	0.231791	+	0.133824i
$672$		−	1.81539i		−	0.0700301i
$673$	−14.1396	+	24.4905i	−0.545041	+	0.944039i	0.453563	+	0.891224i	$0.350153\pi$
$673$	−14.1396	+	24.4905i	−0.545041	+	0.944039i	−0.998604	+	0.0528146i	$0.983181\pi$
$674$		−	3.64888i		−	0.140550i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	7.63961			0.293831
$677$	40.3908			1.55234			0.776172	−	0.630522i	$-0.217159\pi$
$677$	40.3908			1.55234			0.776172	+	0.630522i	$0.217159\pi$
$678$	−4.57499	−	7.92412i	−0.175701	−	0.304324i
$679$	5.49382	+	3.17186i	0.210833	+	0.121725i
$680$			6.17410i			0.236766i
$681$	11.5711	−	6.68056i	0.443405	−	0.256000i
$682$	3.88457	+	6.72827i	0.148748	+	0.257639i
$683$	−5.60471	+	3.23588i	−0.214458	+	0.123818i	−0.603382	−	0.797453i	$-0.706180\pi$
$683$	−5.60471	+	3.23588i	−0.214458	+	0.123818i	0.388923	+	0.921270i	$0.372847\pi$
$684$	1.98914	+	1.14843i	0.0760566	+	0.0439113i
$685$	1.76932	+	1.02152i	0.0676024	+	0.0390303i
$686$	16.8291	−	9.71629i	0.642538	−	0.370970i
$687$	−7.78559	−	13.4850i	−0.297039	−	0.514487i
$688$	−10.2484	+	5.91689i	−0.390715	+	0.225579i
$689$			39.2576i			1.49559i
$690$	3.81251	+	2.20115i	0.145140	+	0.0837965i
$691$	−9.50376	−	16.4610i	−0.361540	−	0.626206i	0.626674	−	0.779281i	$-0.284416\pi$
$691$	−9.50376	−	16.4610i	−0.361540	−	0.626206i	−0.988215	+	0.153075i	$0.951082\pi$
$692$	1.46268			0.0556027
$693$	1.48024			0.0562298
$694$	10.1571	+	17.5926i	0.385558	+	0.667806i
$695$		−	15.1015i		−	0.572831i
$696$	3.87830	−	6.71742i	0.147007	−	0.254623i
$697$			52.4972i			1.98847i
$698$	27.1101	+	15.6520i	1.02613	+	0.592437i
$699$	−2.42202	+	4.19507i	−0.0916094	+	0.158672i
$700$	−0.907693	+	1.57217i	−0.0343076	+	0.0594225i
$701$	7.74062	−	4.46905i	0.292359	−	0.168794i	−0.346646	−	0.937996i	$-0.612680\pi$
$701$	7.74062	−	4.46905i	0.292359	−	0.168794i	0.639005	+	0.769202i	$0.279346\pi$
$702$	−4.54308			−0.171468
$703$	6.58293	−	12.3232i	0.248280	−	0.464778i
$704$	−0.815387			−0.0307310
$705$	−3.51040	+	2.02673i	−0.132209	+	0.0763312i
$706$	−5.01566	+	8.68738i	−0.188767	+	0.326954i
$707$	1.06222	−	1.83981i	0.0399488	−	0.0691933i
$708$	−6.20462	−	3.58224i	−0.233184	−	0.134629i
$709$		−	3.50557i		−	0.131655i	−0.997831	−	0.0658273i	$-0.979031\pi$
$709$		−	3.50557i		−	0.131655i	0.997831	−	0.0658273i	$-0.0209686\pi$
$710$	−0.0611155	+	0.105855i	−0.00229362	+	0.00397267i
$711$			2.77430i			0.104044i
$712$	−4.03744	−	6.99306i	−0.151310	−	0.262076i
$713$	41.9459			1.57088
$714$	11.2084			0.419463
$715$	1.85219	+	3.20808i	0.0692678	+	0.119975i
$716$	16.6635	+	9.62065i	0.622743	+	0.359541i
$717$		−	6.01293i		−	0.224557i
$718$	21.6082	−	12.4755i	0.806410	−	0.465581i
$719$	11.1350	+	19.2864i	0.415267	+	0.719263i	0.995456	−	0.0952182i	$-0.0303549\pi$
$719$	11.1350	+	19.2864i	0.415267	+	0.719263i	−0.580190	+	0.814481i	$0.697022\pi$
$720$	−0.866025	+	0.500000i	−0.0322749	+	0.0186339i
$721$	−25.0232	−	14.4472i	−0.931913	−	0.538040i
$722$	11.8857	+	6.86222i	0.442340	+	0.255385i
$723$	−25.3799	+	14.6531i	−0.943889	+	0.544955i
$724$	−8.78453	−	15.2153i	−0.326475	−	0.565470i
$725$	−6.71742	+	3.87830i	−0.249479	+	0.144037i
$726$			10.3351i			0.383573i
$727$	−5.32467	−	3.07420i	−0.197481	−	0.114016i	0.397999	−	0.917386i	$-0.369705\pi$
$727$	−5.32467	−	3.07420i	−0.197481	−	0.114016i	−0.595480	+	0.803370i	$0.703038\pi$
$728$	−4.12373	−	7.14250i	−0.152835	−	0.264719i
$729$	1.00000			0.0370370
$730$	12.4879			0.462197
$731$	−36.5315	−	63.2744i	−1.35117	−	2.34029i
$732$			8.50281i			0.314273i
$733$	11.8690	−	20.5577i	0.438391	−	0.759316i	−0.559175	−	0.829050i	$-0.688882\pi$
$733$	11.8690	−	20.5577i	0.438391	−	0.759316i	0.997566	+	0.0697343i	$0.0222152\pi$
$734$		−	3.75140i		−	0.138467i
$735$	−3.20808	−	1.85219i	−0.118332	−	0.0683189i
$736$	−2.20115	+	3.81251i	−0.0811356	+	0.140531i
$737$	0.858699	−	1.48731i	0.0316306	−	0.0547858i
$738$	−7.36365	+	4.25141i	−0.271060	+	0.156496i
$739$	49.8019			1.83199			0.915996	−	0.401187i	$-0.131402\pi$
$739$	49.8019			1.83199			0.915996	+	0.401187i	$0.131402\pi$
$740$	3.21340	+	5.16469i	0.118127	+	0.189858i
$741$	10.4348			0.383333
$742$	13.5854	−	7.84354i	0.498736	−	0.287945i
$743$	−18.9361	+	32.7983i	−0.694698	+	1.20325i	0.275585	+	0.961277i	$0.411129\pi$
$743$	−18.9361	+	32.7983i	−0.694698	+	1.20325i	−0.970282	+	0.241975i	$0.922205\pi$
$744$	−4.76408	+	8.25163i	−0.174660	+	0.302519i
$745$	13.9061	+	8.02868i	0.509479	+	0.294148i
$746$		−	18.5419i		−	0.678866i
$747$	4.34472	−	7.52528i	0.158965	−	0.275336i
$748$		−	5.03428i		−	0.184072i
$749$	−8.56795	−	14.8401i	−0.313066	−	0.542246i
$750$	1.00000			0.0365148
$751$	−50.4498			−1.84094			−0.920470	−	0.390814i	$-0.872194\pi$
$751$	−50.4498			−1.84094			−0.920470	+	0.390814i	$0.872194\pi$
$752$	−2.02673	−	3.51040i	−0.0739073	−	0.128011i
$753$	20.9543	+	12.0979i	0.763615	+	0.440874i
$754$		−	35.2389i		−	1.28333i
$755$	13.3579	−	7.71216i	0.486142	−	0.280674i
$756$	0.907693	+	1.57217i	0.0330125	+	0.0571793i
$757$	11.2379	−	6.48821i	0.408449	−	0.235818i	−0.281674	−	0.959510i	$-0.590890\pi$
$757$	11.2379	−	6.48821i	0.408449	−	0.235818i	0.690123	+	0.723692i	$0.257556\pi$
$758$	4.95398	+	2.86018i	0.179937	+	0.103887i
$759$	−3.10867	−	1.79479i	−0.112838	−	0.0651468i
$760$	1.98914	−	1.14843i	0.0721536	−	0.0416579i
$761$	−16.8896	−	29.2537i	−0.612248	−	1.06044i	−0.990861	−	0.134890i	$-0.956932\pi$
$761$	−16.8896	−	29.2537i	−0.612248	−	1.06044i	0.378613	−	0.925555i	$-0.376401\pi$
$762$	17.2526	−	9.96077i	0.624994	−	0.360841i
$763$		−	28.4231i		−	1.02898i
$764$	−17.1546	−	9.90424i	−0.620633	−	0.358323i
$765$	−3.08705	−	5.34693i	−0.111613	−	0.193319i
$766$	−11.5019			−0.415582
$767$	−32.5488			−1.17527
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	11.6998i		−	0.421905i	−0.977496	−	0.210953i	$-0.932343\pi$
$769$		−	11.6998i		−	0.421905i	0.977496	−	0.210953i	$-0.0676566\pi$
$770$	0.740121	−	1.28193i	0.0266721	−	0.0461975i
$771$			14.4163i			0.519191i
$772$	−20.4351	−	11.7982i	−0.735477	−	0.424628i
$773$	15.9789	−	27.6763i	0.574722	−	0.995448i	−0.421350	−	0.906898i	$-0.638444\pi$
$773$	15.9789	−	27.6763i	0.574722	−	0.995448i	0.996072	−	0.0885495i	$-0.0282231\pi$
$774$	5.91689	−	10.2484i	0.212678	−	0.368370i
$775$	8.25163	−	4.76408i	0.296407	−	0.171131i
$776$	3.49441			0.125442
$777$	9.37592	−	5.83356i	0.336359	−	0.209278i
$778$	−34.4908			−1.23656
$779$	16.9133	−	9.76488i	0.605981	−	0.349863i
$780$	−2.27154	+	3.93443i	−0.0813342	+	0.140875i
$781$	0.0498327	−	0.0863128i	0.00178316	−	0.00308852i
$782$	−23.5388	−	13.5901i	−0.841747	−	0.485983i
$783$			7.75661i			0.277198i
$784$	1.85219	−	3.20808i	0.0661495	−	0.114574i
$785$		−	16.3346i		−	0.583008i
$786$	−1.83044	−	3.17041i	−0.0652896	−	0.113085i
$787$	−0.415438			−0.0148087			−0.00740437	−	0.999973i	$-0.502357\pi$
$787$	−0.415438			−0.0148087			−0.00740437	+	0.999973i	$0.502357\pi$
$788$	19.2246			0.684849
$789$	3.08784	+	5.34830i	0.109930	+	0.190405i
$790$	2.40261	+	1.38715i	0.0854812	+	0.0493526i
$791$			16.6108i			0.590610i
$792$	0.706146	−	0.407693i	0.0250918	−	0.0144868i
$793$	19.3145	+	33.4537i	0.685878	+	1.18798i
$794$	−28.1629	+	16.2598i	−0.999463	+	0.577040i
$795$	−7.48348	−	4.32059i	−0.265412	−	0.153235i
$796$	−10.4438	−	6.02971i	−0.370169	−	0.213717i
$797$	−2.62094	+	1.51320i	−0.0928386	+	0.0536004i	−0.545701	−	0.837980i	$-0.683736\pi$
$797$	−2.62094	+	1.51320i	−0.0928386	+	0.0536004i	0.452862	+	0.891581i	$0.350403\pi$
$798$	−2.08484	−	3.61105i	−0.0738027	−	0.127830i
$799$	21.6736	−	12.5133i	0.766757	−	0.442687i
$800$			1.00000i			0.0353553i
$801$	6.99306	+	4.03744i	0.247088	+	0.142656i
$802$	10.4515	+	18.1025i	0.369055	+	0.639222i
$803$	−10.1825			−0.359331
$804$	2.10624			0.0742812
$805$	−3.99594	−	6.92118i	−0.140839	−	0.243939i
$806$			43.2872i			1.52473i
$807$	7.51426	−	13.0151i	0.264514	−	0.458152i
$808$		−	1.17024i		−	0.0411688i
$809$	−22.0140	−	12.7098i	−0.773972	−	0.446853i	0.0603176	−	0.998179i	$-0.480789\pi$
$809$	−22.0140	−	12.7098i	−0.773972	−	0.446853i	−0.834290	+	0.551326i	$0.814122\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	17.2789	−	29.9280i	0.606745	−	1.05091i	−0.385028	−	0.922905i	$-0.625808\pi$
$811$	17.2789	−	29.9280i	0.606745	−	1.05091i	0.991773	−	0.128009i	$-0.0408586\pi$
$812$	−12.1947	+	7.04062i	−0.427950	+	0.247077i
$813$	21.6415			0.759001
$814$	−2.62016	−	4.21122i	−0.0918367	−	0.147603i
$815$	−6.47590			−0.226841
$816$	5.34693	−	3.08705i	0.187180	−	0.108068i
$817$	−13.5903	+	23.5390i	−0.475463	+	0.823527i
$818$	−0.436778	+	0.756522i	−0.0152716	+	0.0264512i
$819$	7.14250	+	4.12373i	0.249579	+	0.144095i
$820$			8.50281i			0.296931i
$821$	14.7695	−	25.5815i	0.515458	−	0.892799i	−0.484381	−	0.874857i	$-0.660955\pi$
$821$	14.7695	−	25.5815i	0.515458	−	0.892799i	0.999839	−	0.0179423i	$-0.00571153\pi$
$822$		−	2.04304i		−	0.0712592i
$823$	−11.6479	−	20.1748i	−0.406020	−	0.703248i	0.588419	−	0.808556i	$-0.299750\pi$
$823$	−11.6479	−	20.1748i	−0.406020	−	0.703248i	−0.994440	+	0.105308i	$0.966417\pi$
$824$	−15.9163			−0.554472
$825$	−0.815387			−0.0283881
$826$	6.50315	+	11.2638i	0.226274	+	0.391917i
$827$	−34.3653	−	19.8408i	−1.19500	−	0.689933i	−0.235563	−	0.971859i	$-0.575693\pi$
$827$	−34.3653	−	19.8408i	−1.19500	−	0.689933i	−0.959436	+	0.281926i	$0.909027\pi$
$828$		−	4.40231i		−	0.152991i
$829$	39.2751	−	22.6755i	1.36408	−	0.787553i	0.373917	−	0.927462i	$-0.378014\pi$
$829$	39.2751	−	22.6755i	1.36408	−	0.787553i	0.990164	+	0.139909i	$0.0446811\pi$
$830$	−4.34472	−	7.52528i	−0.150808	−	0.261206i
$831$	−13.1113	+	7.56978i	−0.454824	+	0.262593i
$832$	−3.93443	−	2.27154i	−0.136402	−	0.0787515i
$833$	19.8070	+	11.4356i	0.686272	+	0.396219i
$834$	−13.0782	+	7.55073i	−0.452863	+	0.261460i
$835$	−1.30925	−	2.26769i	−0.0453085	−	0.0784766i
$836$	−1.62192	+	0.936414i	−0.0560952	+	0.0323866i
$837$		−	9.52816i		−	0.329341i
$838$	−7.41478	−	4.28092i	−0.256139	−	0.147882i
$839$	9.27538	+	16.0654i	0.320222	+	0.554640i	0.980534	−	0.196351i	$-0.0629092\pi$
$839$	9.27538	+	16.0654i	0.320222	+	0.554640i	−0.660312	+	0.750991i	$0.729576\pi$
$840$	1.81539			0.0626368
$841$	−31.1649			−1.07465
$842$	12.8578	+	22.2704i	0.443109	+	0.767488i
$843$			15.9444i			0.549155i
$844$	11.6433	−	20.1667i	0.400777	−	0.694167i
$845$			7.63961i			0.262810i
$846$	3.51040	+	2.02673i	0.120690	+	0.0696805i
$847$	9.38114	−	16.2486i	0.322340	−	0.558309i
$848$	4.32059	−	7.48348i	0.148370	−	0.256984i
$849$	−27.7594	+	16.0269i	−0.952699	+	0.550041i
$850$	−6.17410			−0.211770
$851$	−26.7636	+	0.882832i	−0.917445	+	0.0302631i
$852$	0.122231			0.00418756
$853$	21.0047	−	12.1270i	0.719186	−	0.415222i	−0.0952672	−	0.995452i	$-0.530371\pi$
$853$	21.0047	−	12.1270i	0.719186	−	0.415222i	0.814453	+	0.580230i	$0.197037\pi$
$854$	7.71795	−	13.3679i	0.264103	−	0.457439i
$855$	−1.14843	+	1.98914i	−0.0392755	+	0.0680271i
$856$	−8.17463	−	4.71963i	−0.279403	−	0.161313i
$857$		−	25.1273i		−	0.858333i	−0.903225	−	0.429167i	$-0.858807\pi$
$857$		−	25.1273i		−	0.858333i	0.903225	−	0.429167i	$-0.141193\pi$
$858$	1.85219	−	3.20808i	0.0632326	−	0.109522i
$859$			0.721475i			0.0246164i	0.999924	+	0.0123082i	$0.00391792\pi$
$859$			0.721475i			0.0246164i	−0.999924	+	0.0123082i	$0.996082\pi$
$860$	−5.91689	−	10.2484i	−0.201764	−	0.349466i
$861$	15.4359			0.526054
$862$	−12.8190			−0.436618
$863$	1.46324	+	2.53440i	0.0498092	+	0.0862721i	0.889855	−	0.456243i	$-0.150805\pi$
$863$	1.46324	+	2.53440i	0.0498092	+	0.0862721i	−0.840046	+	0.542515i	$0.817472\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$			1.46268i			0.0497326i
$866$	25.6844	−	14.8289i	0.872790	−	0.503906i
$867$	10.5598	+	18.2901i	0.358629	+	0.621163i
$868$	14.9799	−	8.64865i	0.508451	−	0.293554i
$869$	−1.95906	−	1.13106i	−0.0664566	−	0.0383687i
$870$	6.71742	+	3.87830i	0.227742	+	0.131487i
$871$	8.28683	−	4.78440i	0.280789	−	0.162113i
$872$	−7.82838	−	13.5591i	−0.265102	−	0.459171i
$873$	−3.02625	+	1.74721i	−0.102423	+	0.0591340i
$874$			10.1115i			0.342026i
$875$	−1.57217	−	0.907693i	−0.0531491	−	0.0306856i
$876$	−6.24394	−	10.8148i	−0.210963	−	0.365399i
$877$	9.84941			0.332591			0.166295	−	0.986076i	$-0.446819\pi$
$877$	9.84941			0.332591			0.166295	+	0.986076i	$0.446819\pi$
$878$	1.20986			0.0408308
$879$	4.75948	+	8.24367i	0.160533	+	0.278052i
$880$		−	0.815387i		−	0.0274867i
$881$	−10.1673	+	17.6102i	−0.342544	+	0.593303i	−0.984904	−	0.173099i	$-0.944622\pi$
$881$	−10.1673	+	17.6102i	−0.342544	+	0.593303i	0.642361	+	0.766403i	$0.277955\pi$
$882$			3.70437i			0.124733i
$883$	7.91015	+	4.56693i	0.266198	+	0.153689i	0.627158	−	0.778892i	$-0.284218\pi$
$883$	7.91015	+	4.56693i	0.266198	+	0.153689i	−0.360961	+	0.932581i	$0.617551\pi$
$884$	14.0247	−	24.2916i	0.471703	−	0.817013i
$885$	3.58224	−	6.20462i	0.120416	−	0.208566i
$886$	12.1596	−	7.02033i	0.408509	−	0.235853i
$887$	−38.9341			−1.30728			−0.653639	−	0.756806i	$-0.726759\pi$
$887$	−38.9341			−1.30728			−0.653639	+	0.756806i	$0.726759\pi$
$888$	2.86606	−	5.36523i	0.0961786	−	0.180045i
$889$	−36.1653			−1.21295
$890$	6.99306	−	4.03744i	0.234408	−	0.135335i
$891$	−0.407693	+	0.706146i	−0.0136582	+	0.0236568i
$892$	8.99901	−	15.5867i	0.301309	−	0.521883i
$893$	−8.06290	−	4.65512i	−0.269815	−	0.155778i
$894$		−	16.0574i		−	0.537038i
$895$	−9.62065	+	16.6635i	−0.321583	+	0.556998i
$896$			1.81539i			0.0606478i
$897$	−10.0000	−	17.3205i	−0.333891	−	0.578316i
$898$	−5.19748			−0.173442
$899$	73.9062			2.46491
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	46.2038	+	26.6757i	1.53927	+	0.888698i
$902$		−	6.93308i		−	0.230846i
$903$	−18.6047	+	10.7415i	−0.619127	+	0.357453i
$904$	4.57499	+	7.92412i	0.152162	+	0.263552i
$905$	15.2153	−	8.78453i	0.505772	−	0.292008i
$906$	−13.3579	−	7.71216i	−0.443785	−	0.256219i
$907$	13.6884	+	7.90297i	0.454514	+	0.262414i	0.709735	−	0.704469i	$-0.248815\pi$
$907$	13.6884	+	7.90297i	0.454514	+	0.262414i	−0.255221	+	0.966883i	$0.582148\pi$
$908$	−11.5711	+	6.68056i	−0.384000	+	0.221702i
$909$	0.585118	+	1.01345i	0.0194072	+	0.0336142i
$910$	7.14250	−	4.12373i	0.236772	−	0.136700i
$911$			52.6474i			1.74429i	0.489251	+	0.872143i	$0.337270\pi$
$911$			52.6474i			1.74429i	−0.489251	+	0.872143i	$0.662730\pi$
$912$	−1.98914	−	1.14843i	−0.0658669	−	0.0380283i
$913$	3.54263	+	6.13601i	0.117244	+	0.203072i
$914$	−4.82862			−0.159717
$915$	−8.50281			−0.281094
$916$	7.78559	+	13.4850i	0.257243	+	0.445558i
$917$			6.64591i			0.219467i
$918$	−3.08705	+	5.34693i	−0.101888	+	0.176475i
$919$		−	8.16970i		−	0.269493i	−0.990880	−	0.134747i	$-0.956978\pi$
$919$		−	8.16970i		−	0.269493i	0.990880	−	0.134747i	$-0.0430221\pi$
$920$	−3.81251	−	2.20115i	−0.125695	−	0.0725699i
$921$	−3.71862	+	6.44083i	−0.122533	+	0.212233i
$922$	−14.7527	+	25.5524i	−0.485854	+	0.841523i
$923$	0.480909	−	0.277653i	0.0158293	−	0.00913905i
$924$	−1.48024			−0.0486964
$925$	−5.16469	+	3.21340i	−0.169814	+	0.105656i
$926$	−1.41718			−0.0465714
$927$	13.7839	−	7.95817i	0.452724	−	0.261380i
$928$	−3.87830	+	6.71742i	−0.127312	+	0.220510i
$929$	14.6365	−	25.3512i	0.480209	−	0.831747i	−0.519533	−	0.854450i	$-0.673894\pi$
$929$	14.6365	−	25.3512i	0.480209	−	0.831747i	0.999742	+	0.0227038i	$0.00722745\pi$
$930$	−8.25163	−	4.76408i	−0.270581	−	0.156220i
$931$		−	8.50842i		−	0.278852i
$932$	2.42202	−	4.19507i	0.0793361	−	0.137414i
$933$		−	3.12143i		−	0.102191i
$934$	−1.84391	−	3.19375i	−0.0603347	−	0.104503i
$935$	5.03428			0.164639
$936$	4.54308			0.148495
$937$	6.63531	+	11.4927i	0.216766	+	0.375450i	0.953817	−	0.300387i	$-0.0971158\pi$
$937$	6.63531	+	11.4927i	0.216766	+	0.375450i	−0.737051	+	0.675837i	$0.763782\pi$
$938$	−3.31136	−	1.91182i	−0.108120	−	0.0624230i
$939$			7.18878i			0.234597i
$940$	3.51040	−	2.02673i	0.114497	−	0.0661047i
$941$	−27.2763	−	47.2440i	−0.889182	−	1.54011i	−0.840844	−	0.541278i	$-0.817941\pi$
$941$	−27.2763	−	47.2440i	−0.889182	−	1.54011i	−0.0483386	−	0.998831i	$-0.515393\pi$
$942$	−14.1462	+	8.16731i	−0.460908	+	0.266105i
$943$	−32.4170	−	18.7160i	−1.05564	−	0.609477i
$944$	6.20462	+	3.58224i	0.201943	+	0.116592i
$945$	−1.57217	+	0.907693i	−0.0511427	+	0.0295273i
$946$	4.82456	+	8.35638i	0.156860	+	0.271689i
$947$	−35.3514	+	20.4102i	−1.14877	+	0.663241i	−0.948587	−	0.316518i	$-0.897486\pi$
$947$	−35.3514	+	20.4102i	−1.14877	+	0.663241i	−0.200181	+	0.979759i	$0.564153\pi$
$948$		−	2.77430i		−	0.0901051i
$949$	−49.1327	−	28.3668i	−1.59491	−	0.920824i
$950$	1.14843	+	1.98914i	0.0372600	+	0.0645362i
$951$	30.1102			0.976389
$952$	−11.2084			−0.363266
$953$	−14.3565	−	24.8662i	−0.465053	−	0.805495i	0.534151	−	0.845389i	$-0.320631\pi$
$953$	−14.3565	−	24.8662i	−0.465053	−	0.805495i	−0.999204	+	0.0398940i	$0.987298\pi$
$954$			8.64117i			0.279768i
$955$	9.90424	−	17.1546i	0.320494	−	0.555111i
$956$			6.01293i			0.194472i
$957$	−5.47729	−	3.16232i	−0.177056	−	0.102223i
$958$	9.08072	−	15.7283i	0.293385	−	0.508157i
$959$	−1.85445	+	3.21201i	−0.0598834	+	0.103721i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	−59.7858			−1.92857
$962$	−0.911063	−	27.6195i	−0.0293738	−	0.890488i
$963$	9.43925			0.304176
$964$	25.3799	−	14.6531i	0.817432	−	0.471945i
$965$	11.7982	−	20.4351i	0.379799	−	0.657830i
$966$	−3.99594	+	6.92118i	−0.128567	+	0.222685i
$967$	9.55325	+	5.51557i	0.307212	+	0.177369i	0.645678	−	0.763610i	$-0.276575\pi$
$967$	9.55325	+	5.51557i	0.307212	+	0.177369i	−0.338466	+	0.940978i	$0.609908\pi$
$968$		−	10.3351i		−	0.332184i
$969$	7.09052	−	12.2811i	0.227780	−	0.394527i
$970$			3.49441i			0.112199i
$971$	−4.04709	−	7.00976i	−0.129877	−	0.224954i	0.793752	−	0.608242i	$-0.208125\pi$
$971$	−4.04709	−	7.00976i	−0.129877	−	0.224954i	−0.923629	+	0.383288i	$0.874792\pi$
$972$	−1.00000			−0.0320750
$973$	27.4150			0.878884
$974$	−8.10284	−	14.0345i	−0.259632	−	0.449695i
$975$	−3.93443	−	2.27154i	−0.126002	−	0.0727476i
$976$		−	8.50281i		−	0.272168i
$977$	−4.51581	+	2.60720i	−0.144474	+	0.0834118i	−0.570494	−	0.821302i	$-0.693248\pi$
$977$	−4.51581	+	2.60720i	−0.144474	+	0.0834118i	0.426021	+	0.904713i	$0.359915\pi$
$978$	3.23795	+	5.60830i	0.103538	+	0.179334i
$979$	−5.70205	+	3.29208i	−0.182238	+	0.105215i
$980$	3.20808	+	1.85219i	0.102478	+	0.0591659i
$981$	13.5591	+	7.82838i	0.432910	+	0.249941i
$982$	−7.29922	+	4.21421i	−0.232927	+	0.134481i
$983$	−7.77077	−	13.4594i	−0.247849	−	0.429287i	0.715080	−	0.699043i	$-0.246390\pi$
$983$	−7.77077	−	13.4594i	−0.247849	−	0.429287i	−0.962929	+	0.269756i	$0.913057\pi$
$984$	7.36365	−	4.25141i	0.234745	−	0.135530i
$985$			19.2246i			0.612548i
$986$	−41.4740	−	23.9450i	−1.32080	−	0.762566i
$987$	−3.67930	−	6.37274i	−0.117114	−	0.202847i
$988$	−10.4348			−0.331976
$989$	52.0959			1.65655
$990$	0.407693	+	0.706146i	0.0129573	+	0.0224428i
$991$			35.9892i			1.14323i	0.820521	+	0.571617i	$0.193684\pi$
$991$			35.9892i			1.14323i	−0.820521	+	0.571617i	$0.806316\pi$
$992$	4.76408	−	8.25163i	0.151260	−	0.261989i
$993$		−	19.6650i		−	0.624049i
$994$	−0.192168	−	0.110948i	−0.00609520	−	0.00351906i
$995$	6.02971	−	10.4438i	0.191155	−	0.331090i
$996$	−4.34472	+	7.52528i	−0.137668	+	0.238448i
$997$	3.20185	−	1.84859i	0.101404	−	0.0585454i	−0.448441	−	0.893813i	$-0.648020\pi$
$997$	3.20185	−	1.84859i	0.101404	−	0.0585454i	0.549844	+	0.835267i	$0.314687\pi$
$998$	−6.43181			−0.203595
$999$	0.200538	+	6.07946i	0.00634476	+	0.192345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.c.751.2	✓	16
37.27	even	6	inner	1110.2.x.c.841.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.c.751.2	✓	16	1.1	even	1	trivial
1110.2.x.c.841.2	yes	16	37.27	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-0.907693 + 1.57217i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-0.907693 + 1.57217i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +0.815387 q^{11} +(0.500000 + 0.866025i) q^{12} +(3.93443 + 2.27154i) q^{13} -1.81539i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(5.34693 - 3.08705i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-1.98914 - 1.14843i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-0.907693 - 1.57217i) q^{21} +(-0.706146 + 0.407693i) q^{22} +4.40231i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -4.54308 q^{26} +1.00000 q^{27} +(0.907693 + 1.57217i) q^{28} +7.75661i q^{29} +(0.500000 - 0.866025i) q^{30} -9.52816i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.407693 + 0.706146i) q^{33} +(-3.08705 + 5.34693i) q^{34} +(-1.57217 + 0.907693i) q^{35} -1.00000 q^{36} +(0.200538 + 6.07946i) q^{37} +2.29686 q^{38} +(-3.93443 + 2.27154i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-4.25141 + 7.36365i) q^{41} +(1.57217 + 0.907693i) q^{42} -11.8338i q^{43} +(0.407693 - 0.706146i) q^{44} -1.00000i q^{45} +(-2.20115 - 3.81251i) q^{46} +4.05346 q^{47} +1.00000 q^{48} +(1.85219 + 3.20808i) q^{49} +(-0.866025 - 0.500000i) q^{50} +6.17410i q^{51} +(3.93443 - 2.27154i) q^{52} +(4.32059 + 7.48348i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.706146 + 0.407693i) q^{55} +(-1.57217 - 0.907693i) q^{56} +(1.98914 - 1.14843i) q^{57} +(-3.87830 - 6.71742i) q^{58} +(-6.20462 + 3.58224i) q^{59} +1.00000i q^{60} +(7.36365 + 4.25141i) q^{61} +(4.76408 + 8.25163i) q^{62} +1.81539 q^{63} -1.00000 q^{64} +(2.27154 + 3.93443i) q^{65} -0.815387i q^{66} +(1.05312 - 1.82405i) q^{67} -6.17410i q^{68} +(-3.81251 - 2.20115i) q^{69} +(0.907693 - 1.57217i) q^{70} +(0.0611155 - 0.105855i) q^{71} +(0.866025 - 0.500000i) q^{72} -12.4879 q^{73} +(-3.21340 - 5.16469i) q^{74} -1.00000 q^{75} +(-1.98914 + 1.14843i) q^{76} +(-0.740121 + 1.28193i) q^{77} +(2.27154 - 3.93443i) q^{78} +(-2.40261 - 1.38715i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -8.50281i q^{82} +(4.34472 + 7.52528i) q^{83} -1.81539 q^{84} +6.17410 q^{85} +(5.91689 + 10.2484i) q^{86} +(-6.71742 - 3.87830i) q^{87} +0.815387i q^{88} +(-6.99306 + 4.03744i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-7.14250 + 4.12373i) q^{91} +(3.81251 + 2.20115i) q^{92} +(8.25163 + 4.76408i) q^{93} +(-3.51040 + 2.02673i) q^{94} +(-1.14843 - 1.98914i) q^{95} +(-0.866025 + 0.500000i) q^{96} -3.49441i q^{97} +(-3.20808 - 1.85219i) q^{98} +(-0.407693 - 0.706146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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