LMFDB - Embedded newform 1110.2.l.b.43.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.11
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.b.697.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07981 + 0.821222i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.82950 - 1.82950i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07981 + 0.821222i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.82950 - 1.82950i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.821222 + 2.07981i) q^{10} +5.85283i q^{11} +(-0.707107 + 0.707107i) q^{12} +2.62090i q^{13} +(-1.82950 - 1.82950i) q^{14} +(-0.889953 + 2.05134i) q^{15} +1.00000 q^{16} +6.06382 q^{17} -1.00000 q^{18} +(-0.715895 + 0.715895i) q^{19} +(2.07981 - 0.821222i) q^{20} -2.58731i q^{21} +5.85283 q^{22} +5.69636i q^{23} +(0.707107 + 0.707107i) q^{24} +(3.65119 - 3.41597i) q^{25} +2.62090 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.82950 + 1.82950i) q^{28} +(0.103251 + 0.103251i) q^{29} +(2.05134 + 0.889953i) q^{30} +(3.13248 - 3.13248i) q^{31} -1.00000i q^{32} +(4.13858 + 4.13858i) q^{33} -6.06382i q^{34} +(-2.30258 + 5.30744i) q^{35} +1.00000i q^{36} +(-0.709034 + 6.04130i) q^{37} +(0.715895 + 0.715895i) q^{38} +(1.85326 + 1.85326i) q^{39} +(-0.821222 - 2.07981i) q^{40} -7.72641i q^{41} -2.58731 q^{42} -10.7785i q^{43} -5.85283i q^{44} +(0.821222 + 2.07981i) q^{45} +5.69636 q^{46} +(-0.632282 + 0.632282i) q^{47} +(0.707107 - 0.707107i) q^{48} +0.305830i q^{49} +(-3.41597 - 3.65119i) q^{50} +(4.28777 - 4.28777i) q^{51} -2.62090i q^{52} +(6.74389 + 6.74389i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-4.80647 - 12.1728i) q^{55} +(1.82950 + 1.82950i) q^{56} +1.01243i q^{57} +(0.103251 - 0.103251i) q^{58} +(-2.17274 + 2.17274i) q^{59} +(0.889953 - 2.05134i) q^{60} +(-3.93377 + 3.93377i) q^{61} +(-3.13248 - 3.13248i) q^{62} +(-1.82950 - 1.82950i) q^{63} -1.00000 q^{64} +(-2.15235 - 5.45097i) q^{65} +(4.13858 - 4.13858i) q^{66} +(6.21976 + 6.21976i) q^{67} -6.06382 q^{68} +(4.02793 + 4.02793i) q^{69} +(5.30744 + 2.30258i) q^{70} +14.7837 q^{71} +1.00000 q^{72} +(5.43491 - 5.43491i) q^{73} +(6.04130 + 0.709034i) q^{74} +(0.166327 - 4.99723i) q^{75} +(0.715895 - 0.715895i) q^{76} +(10.7078 + 10.7078i) q^{77} +(1.85326 - 1.85326i) q^{78} +(4.38472 - 4.38472i) q^{79} +(-2.07981 + 0.821222i) q^{80} -1.00000 q^{81} -7.72641 q^{82} +(5.79922 + 5.79922i) q^{83} +2.58731i q^{84} +(-12.6116 + 4.97975i) q^{85} -10.7785 q^{86} +0.146019 q^{87} -5.85283 q^{88} +(-2.02306 - 2.02306i) q^{89} +(2.07981 - 0.821222i) q^{90} +(4.79496 + 4.79496i) q^{91} -5.69636i q^{92} -4.43000i q^{93} +(0.632282 + 0.632282i) q^{94} +(0.901015 - 2.07683i) q^{95} +(-0.707107 - 0.707107i) q^{96} -11.9197 q^{97} +0.305830 q^{98} +5.85283 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.07981	+	0.821222i	−0.930118	+	0.367262i
$5$	−2.07981	+	0.821222i	−0.930118	+	0.367262i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	1.82950	−	1.82950i	0.691488	−	0.691488i	−0.271072	−	0.962559i	$-0.587378\pi$
$7$	1.82950	−	1.82950i	0.691488	−	0.691488i	0.962559	+	0.271072i	$0.0873780\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	0.821222	+	2.07981i	0.259693	+	0.657692i
$11$			5.85283i			1.76469i	0.470598	+	0.882347i	$0.344038\pi$
$11$			5.85283i			1.76469i	−0.470598	+	0.882347i	$0.655962\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$			2.62090i			0.726908i	0.931612	+	0.363454i	$0.118403\pi$
$13$			2.62090i			0.726908i	−0.931612	+	0.363454i	$0.881597\pi$
$14$	−1.82950	−	1.82950i	−0.488956	−	0.488956i
$15$	−0.889953	+	2.05134i	−0.229785	+	0.529653i
$16$	1.00000			0.250000
$17$	6.06382			1.47069			0.735346	−	0.677691i	$-0.237019\pi$
$17$	6.06382			1.47069			0.735346	+	0.677691i	$0.237019\pi$
$18$	−1.00000			−0.235702
$19$	−0.715895	+	0.715895i	−0.164238	+	0.164238i	−0.784441	−	0.620203i	$-0.787050\pi$
$19$	−0.715895	+	0.715895i	−0.164238	+	0.164238i	0.620203	+	0.784441i	$0.287050\pi$
$20$	2.07981	−	0.821222i	0.465059	−	0.183631i
$21$		−	2.58731i		−	0.564597i
$22$	5.85283			1.24783
$23$			5.69636i			1.18777i	0.804549	+	0.593886i	$0.202407\pi$
$23$			5.69636i			1.18777i	−0.804549	+	0.593886i	$0.797593\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	3.65119	−	3.41597i	0.730238	−	0.683193i
$26$	2.62090			0.514002
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.82950	+	1.82950i	−0.345744	+	0.345744i
$29$	0.103251	+	0.103251i	0.0191732	+	0.0191732i	0.716628	−	0.697455i	$-0.245684\pi$
$29$	0.103251	+	0.103251i	0.0191732	+	0.0191732i	−0.697455	+	0.716628i	$0.745684\pi$
$30$	2.05134	+	0.889953i	0.374521	+	0.162483i
$31$	3.13248	−	3.13248i	0.562611	−	0.562611i	−0.367438	−	0.930048i	$-0.619765\pi$
$31$	3.13248	−	3.13248i	0.562611	−	0.562611i	0.930048	+	0.367438i	$0.119765\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.13858	+	4.13858i	0.720434	+	0.720434i
$34$		−	6.06382i		−	1.03994i
$35$	−2.30258	+	5.30744i	−0.389208	+	0.897122i
$36$			1.00000i			0.166667i
$37$	−0.709034	+	6.04130i	−0.116565	+	0.993183i
$37$	−0.709034	+	6.04130i	−0.116565	+	0.993183i
$38$	0.715895	+	0.715895i	0.116134	+	0.116134i
$39$	1.85326	+	1.85326i	0.296759	+	0.296759i
$40$	−0.821222	−	2.07981i	−0.129847	−	0.328846i
$41$		−	7.72641i		−	1.20666i	−0.797490	−	0.603332i	$-0.793840\pi$
$41$		−	7.72641i		−	1.20666i	0.797490	−	0.603332i	$-0.206160\pi$
$42$	−2.58731			−0.399231
$43$		−	10.7785i		−	1.64371i	−0.569697	−	0.821855i	$-0.692940\pi$
$43$		−	10.7785i		−	1.64371i	0.569697	−	0.821855i	$-0.307060\pi$
$44$		−	5.85283i		−	0.882347i
$45$	0.821222	+	2.07981i	0.122421	+	0.310039i
$46$	5.69636			0.839882
$47$	−0.632282	+	0.632282i	−0.0922278	+	0.0922278i	−0.751715	−	0.659488i	$-0.770773\pi$
$47$	−0.632282	+	0.632282i	−0.0922278	+	0.0922278i	0.659488	+	0.751715i	$0.270773\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			0.305830i			0.0436900i
$50$	−3.41597	−	3.65119i	−0.483091	−	0.516356i
$51$	4.28777	−	4.28777i	0.600408	−	0.600408i
$52$		−	2.62090i		−	0.363454i
$53$	6.74389	+	6.74389i	0.926344	+	0.926344i	0.997468	−	0.0711231i	$-0.0226583\pi$
$53$	6.74389	+	6.74389i	0.926344	+	0.926344i	−0.0711231	+	0.997468i	$0.522658\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	−4.80647	−	12.1728i	−0.648105	−	1.64137i
$56$	1.82950	+	1.82950i	0.244478	+	0.244478i
$57$			1.01243i			0.134099i
$58$	0.103251	−	0.103251i	0.0135575	−	0.0135575i
$59$	−2.17274	+	2.17274i	−0.282867	+	0.282867i	−0.834251	−	0.551385i	$-0.814100\pi$
$59$	−2.17274	+	2.17274i	−0.282867	+	0.282867i	0.551385	+	0.834251i	$0.314100\pi$
$60$	0.889953	−	2.05134i	0.114892	−	0.264826i
$61$	−3.93377	+	3.93377i	−0.503668	+	0.503668i	−0.912576	−	0.408908i	$-0.865910\pi$
$61$	−3.93377	+	3.93377i	−0.503668	+	0.503668i	0.408908	+	0.912576i	$0.365910\pi$
$62$	−3.13248	−	3.13248i	−0.397826	−	0.397826i
$63$	−1.82950	−	1.82950i	−0.230496	−	0.230496i
$64$	−1.00000			−0.125000
$65$	−2.15235	−	5.45097i	−0.266966	−	0.676110i
$66$	4.13858	−	4.13858i	0.509424	−	0.509424i
$67$	6.21976	+	6.21976i	0.759865	+	0.759865i	0.976298	−	0.216433i	$-0.0694422\pi$
$67$	6.21976	+	6.21976i	0.759865	+	0.759865i	−0.216433	+	0.976298i	$0.569442\pi$
$68$	−6.06382			−0.735346
$69$	4.02793	+	4.02793i	0.484906	+	0.484906i
$70$	5.30744	+	2.30258i	0.634361	+	0.275212i
$71$	14.7837			1.75450			0.877249	−	0.480036i	$-0.159377\pi$
$71$	14.7837			1.75450			0.877249	+	0.480036i	$0.159377\pi$
$72$	1.00000			0.117851
$73$	5.43491	−	5.43491i	0.636108	−	0.636108i	−0.313485	−	0.949593i	$-0.601496\pi$
$73$	5.43491	−	5.43491i	0.636108	−	0.636108i	0.949593	+	0.313485i	$0.101496\pi$
$74$	6.04130	+	0.709034i	0.702287	+	0.0824236i
$75$	0.166327	−	4.99723i	0.0192058	−	0.577031i
$76$	0.715895	−	0.715895i	0.0821188	−	0.0821188i
$77$	10.7078	+	10.7078i	1.22026	+	1.22026i
$78$	1.85326	−	1.85326i	0.209840	−	0.209840i
$79$	4.38472	−	4.38472i	0.493319	−	0.493319i	−0.416031	−	0.909350i	$-0.636579\pi$
$79$	4.38472	−	4.38472i	0.493319	−	0.493319i	0.909350	+	0.416031i	$0.136579\pi$
$80$	−2.07981	+	0.821222i	−0.232529	+	0.0918154i
$81$	−1.00000			−0.111111
$82$	−7.72641			−0.853240
$83$	5.79922	+	5.79922i	0.636547	+	0.636547i	0.949702	−	0.313155i	$-0.101386\pi$
$83$	5.79922	+	5.79922i	0.636547	+	0.636547i	−0.313155	+	0.949702i	$0.601386\pi$
$84$			2.58731i			0.282299i
$85$	−12.6116	+	4.97975i	−1.36792	+	0.540129i
$86$	−10.7785			−1.16228
$87$	0.146019			0.0156548
$88$	−5.85283			−0.623914
$89$	−2.02306	−	2.02306i	−0.214444	−	0.214444i	0.591708	−	0.806152i	$-0.298454\pi$
$89$	−2.02306	−	2.02306i	−0.214444	−	0.214444i	−0.806152	+	0.591708i	$0.798454\pi$
$90$	2.07981	−	0.821222i	0.219231	−	0.0865644i
$91$	4.79496	+	4.79496i	0.502648	+	0.502648i
$92$		−	5.69636i		−	0.593886i
$93$		−	4.43000i		−	0.459370i
$94$	0.632282	+	0.632282i	0.0652149	+	0.0652149i
$95$	0.901015	−	2.07683i	0.0924421	−	0.213079i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−11.9197			−1.21026			−0.605129	−	0.796127i	$-0.706879\pi$
$97$	−11.9197			−1.21026			−0.605129	+	0.796127i	$0.706879\pi$
$98$	0.305830			0.0308935
$99$	5.85283			0.588232
$100$	−3.65119	+	3.41597i	−0.365119	+	0.341597i
$101$			13.3071i			1.32411i	0.749456	+	0.662054i	$0.230315\pi$
$101$			13.3071i			1.32411i	−0.749456	+	0.662054i	$0.769685\pi$
$102$	−4.28777	−	4.28777i	−0.424552	−	0.424552i
$103$	−3.67851			−0.362454			−0.181227	−	0.983441i	$-0.558007\pi$
$103$	−3.67851			−0.362454			−0.181227	+	0.983441i	$0.558007\pi$
$104$	−2.62090			−0.257001
$105$	2.12476	+	5.38110i	0.207355	+	0.525142i
$106$	6.74389	−	6.74389i	0.655024	−	0.655024i
$107$	4.08936	−	4.08936i	0.395333	−	0.395333i	−0.481250	−	0.876583i	$-0.659817\pi$
$107$	4.08936	−	4.08936i	0.395333	−	0.395333i	0.876583	+	0.481250i	$0.159817\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	2.01498	−	2.01498i	0.193000	−	0.193000i	−0.603991	−	0.796991i	$-0.706424\pi$
$109$	2.01498	−	2.01498i	0.193000	−	0.193000i	0.796991	+	0.603991i	$0.206424\pi$
$110$	−12.1728	+	4.80647i	−1.16063	+	0.458279i
$111$	3.77048	+	4.77321i	0.357878	+	0.453053i
$112$	1.82950	−	1.82950i	0.172872	−	0.172872i
$113$	3.21356			0.302306			0.151153	−	0.988510i	$-0.451701\pi$
$113$	3.21356			0.302306			0.151153	+	0.988510i	$0.451701\pi$
$114$	1.01243			0.0948227
$115$	−4.67797	−	11.8473i	−0.436223	−	1.10477i
$116$	−0.103251	−	0.103251i	−0.00958659	−	0.00958659i
$117$	2.62090			0.242303
$118$	2.17274	+	2.17274i	0.200017	+	0.200017i
$119$	11.0938	−	11.0938i	1.01697	−	1.01697i
$120$	−2.05134	−	0.889953i	−0.187261	−	0.0812413i
$121$	−23.2556			−2.11415
$122$	3.93377	+	3.93377i	0.356147	+	0.356147i
$123$	−5.46340	−	5.46340i	−0.492618	−	0.492618i
$124$	−3.13248	+	3.13248i	−0.281305	+	0.281305i
$125$	−4.78850	+	10.1030i	−0.428296	+	0.903638i
$126$	−1.82950	+	1.82950i	−0.162985	+	0.162985i
$127$	−7.24373	+	7.24373i	−0.642777	+	0.642777i	−0.951237	−	0.308460i	$-0.900186\pi$
$127$	−7.24373	+	7.24373i	−0.642777	+	0.642777i	0.308460	+	0.951237i	$0.400186\pi$
$128$			1.00000i			0.0883883i
$129$	−7.62157	−	7.62157i	−0.671041	−	0.671041i
$130$	−5.45097	+	2.15235i	−0.478082	+	0.188773i
$131$	−4.64106	+	4.64106i	−0.405491	+	0.405491i	−0.880163	−	0.474672i	$-0.842567\pi$
$131$	−4.64106	+	4.64106i	−0.405491	+	0.405491i	0.474672	+	0.880163i	$0.342567\pi$
$132$	−4.13858	−	4.13858i	−0.360217	−	0.360217i
$133$			2.61947i			0.227137i
$134$	6.21976	−	6.21976i	0.537305	−	0.537305i
$135$	2.05134	+	0.889953i	0.176551	+	0.0765950i
$136$			6.06382i			0.519968i
$137$	−12.5072	+	12.5072i	−1.06856	+	1.06856i	−0.0710923	+	0.997470i	$0.522648\pi$
$137$	−12.5072	+	12.5072i	−1.06856	+	1.06856i	−0.997470	+	0.0710923i	$0.977352\pi$
$138$	4.02793	−	4.02793i	0.342880	−	0.342880i
$139$	−14.0516			−1.19184			−0.595919	−	0.803045i	$-0.703212\pi$
$139$	−14.0516			−1.19184			−0.595919	+	0.803045i	$0.703212\pi$
$140$	2.30258	−	5.30744i	0.194604	−	0.448561i
$141$			0.894182i			0.0753037i
$142$		−	14.7837i		−	1.24062i
$143$	−15.3397			−1.28277
$144$		−	1.00000i		−	0.0833333i
$145$	−0.299533	−	0.129950i	−0.0248749	−	0.0107917i
$146$	−5.43491	−	5.43491i	−0.449797	−	0.449797i
$147$	0.216254	+	0.216254i	0.0178364	+	0.0178364i
$148$	0.709034	−	6.04130i	0.0582823	−	0.496592i
$149$		−	18.5571i		−	1.52026i	−0.649773	−	0.760128i	$-0.725136\pi$
$149$		−	18.5571i		−	1.52026i	0.649773	−	0.760128i	$-0.274864\pi$
$150$	−4.99723	−	0.166327i	−0.408022	−	0.0135806i
$151$		−	9.48777i		−	0.772104i	−0.922477	−	0.386052i	$-0.873839\pi$
$151$		−	9.48777i		−	0.772104i	0.922477	−	0.386052i	$-0.126161\pi$
$152$	−0.715895	−	0.715895i	−0.0580668	−	0.0580668i
$153$		−	6.06382i		−	0.490231i
$154$	10.7078	−	10.7078i	0.862857	−	0.862857i
$155$	−3.94249	+	9.08742i	−0.316669	+	0.729919i
$156$	−1.85326	−	1.85326i	−0.148380	−	0.148380i
$157$	7.61926	−	7.61926i	0.608083	−	0.608083i	−0.334362	−	0.942445i	$-0.608521\pi$
$157$	7.61926	−	7.61926i	0.608083	−	0.608083i	0.942445	+	0.334362i	$0.108521\pi$
$158$	−4.38472	−	4.38472i	−0.348829	−	0.348829i
$159$	9.53730			0.756357
$160$	0.821222	+	2.07981i	0.0649233	+	0.164423i
$161$	10.4215	+	10.4215i	0.821330	+	0.821330i
$162$			1.00000i			0.0785674i
$163$	3.03125			0.237426			0.118713	−	0.992929i	$-0.462123\pi$
$163$	3.03125			0.237426			0.118713	+	0.992929i	$0.462123\pi$
$164$			7.72641i			0.603332i
$165$	−12.0061	−	5.20875i	−0.934676	−	0.405500i
$166$	5.79922	−	5.79922i	0.450107	−	0.450107i
$167$	−9.24944			−0.715743			−0.357872	−	0.933771i	$-0.616497\pi$
$167$	−9.24944			−0.715743			−0.357872	+	0.933771i	$0.616497\pi$
$168$	2.58731			0.199615
$169$	6.13086			0.471604
$170$	4.97975	+	12.6116i	0.381929	+	0.967264i
$171$	0.715895	+	0.715895i	0.0547459	+	0.0547459i
$172$			10.7785i			0.821855i
$173$	−0.562678	+	0.562678i	−0.0427796	+	0.0427796i	−0.728173	−	0.685393i	$-0.759630\pi$
$173$	−0.562678	+	0.562678i	−0.0427796	+	0.0427796i	0.685393	+	0.728173i	$0.259630\pi$
$174$		−	0.146019i		−	0.0110696i
$175$	0.430341	−	12.9294i	0.0325307	−	0.977370i
$176$			5.85283i			0.441174i
$177$			3.07272i			0.230960i
$178$	−2.02306	+	2.02306i	−0.151635	+	0.151635i
$179$	−1.52571	−	1.52571i	−0.114037	−	0.114037i	0.647786	−	0.761823i	$-0.275695\pi$
$179$	−1.52571	−	1.52571i	−0.114037	−	0.114037i	−0.761823	+	0.647786i	$0.775695\pi$
$180$	−0.821222	−	2.07981i	−0.0612103	−	0.155020i
$181$	8.91916			0.662956			0.331478	−	0.943463i	$-0.392453\pi$
$181$	8.91916			0.662956			0.331478	+	0.943463i	$0.392453\pi$
$182$	4.79496	−	4.79496i	0.355426	−	0.355426i
$183$			5.56319i			0.411243i
$184$	−5.69636			−0.419941
$185$	−3.48659	−	13.1470i	−0.256339	−	0.966587i
$186$	−4.43000			−0.324823
$187$			35.4905i			2.59532i
$188$	0.632282	−	0.632282i	0.0461139	−	0.0461139i
$189$	−2.58731			−0.188199
$190$	−2.07683	−	0.901015i	−0.150669	−	0.0653665i
$191$	1.72650	+	1.72650i	0.124925	+	0.124925i	0.766805	−	0.641880i	$-0.221845\pi$
$191$	1.72650	+	1.72650i	0.124925	+	0.124925i	−0.641880	+	0.766805i	$0.721845\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$		−	15.4244i		−	1.11027i	−0.831759	−	0.555137i	$-0.812666\pi$
$193$		−	15.4244i		−	1.11027i	0.831759	−	0.555137i	$-0.187334\pi$
$194$			11.9197i			0.855782i
$195$	−5.37636	−	2.33248i	−0.385009	−	0.167033i
$196$		−	0.305830i		−	0.0218450i
$197$	−16.3457	+	16.3457i	−1.16458	+	1.16458i	−0.181125	+	0.983460i	$0.557974\pi$
$197$	−16.3457	+	16.3457i	−1.16458	+	1.16458i	−0.983460	+	0.181125i	$0.942026\pi$
$198$		−	5.85283i		−	0.415943i
$199$	18.8595	+	18.8595i	1.33691	+	1.33691i	0.899032	+	0.437882i	$0.144271\pi$
$199$	18.8595	+	18.8595i	1.33691	+	1.33691i	0.437882	+	0.899032i	$0.355729\pi$
$200$	3.41597	+	3.65119i	0.241545	+	0.258178i
$201$	8.79607			0.620427
$202$	13.3071			0.936286
$203$	0.377795			0.0265160
$204$	−4.28777	+	4.28777i	−0.300204	+	0.300204i
$205$	6.34510	+	16.0694i	0.443161	+	1.12234i
$206$			3.67851i			0.256294i
$207$	5.69636			0.395924
$208$			2.62090i			0.181727i
$209$	−4.19001	−	4.19001i	−0.289829	−	0.289829i
$210$	5.38110	−	2.12476i	0.371331	−	0.146622i
$211$	13.0270			0.896819			0.448409	−	0.893828i	$-0.351991\pi$
$211$	13.0270			0.896819			0.448409	+	0.893828i	$0.351991\pi$
$212$	−6.74389	−	6.74389i	−0.463172	−	0.463172i
$213$	10.4536	−	10.4536i	0.716270	−	0.716270i
$214$	−4.08936	−	4.08936i	−0.279543	−	0.279543i
$215$	8.85156	+	22.4172i	0.603671	+	1.52884i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$		−	11.4618i		−	0.778076i
$218$	−2.01498	−	2.01498i	−0.136472	−	0.136472i
$219$		−	7.68613i		−	0.519380i
$220$	4.80647	+	12.1728i	0.324052	+	0.820687i
$221$			15.8927i			1.06906i
$222$	4.77321	−	3.77048i	0.320357	−	0.253058i
$223$	0.107034	+	0.107034i	0.00716756	+	0.00716756i	0.710681	−	0.703514i	$-0.248387\pi$
$223$	0.107034	+	0.107034i	0.00716756	+	0.00716756i	−0.703514	+	0.710681i	$0.748387\pi$
$224$	−1.82950	−	1.82950i	−0.122239	−	0.122239i
$225$	−3.41597	−	3.65119i	−0.227731	−	0.243413i
$226$		−	3.21356i		−	0.213763i
$227$	−21.9455			−1.45657			−0.728287	−	0.685272i	$-0.759683\pi$
$227$	−21.9455			−1.45657			−0.728287	+	0.685272i	$0.759683\pi$
$228$		−	1.01243i		−	0.0670497i
$229$			2.18787i			0.144578i	0.997384	+	0.0722891i	$0.0230304\pi$
$229$			2.18787i			0.144578i	−0.997384	+	0.0722891i	$0.976970\pi$
$230$	−11.8473	+	4.67797i	−0.781189	+	0.308456i
$231$	15.1431			0.996342
$232$	−0.103251	+	0.103251i	−0.00677874	+	0.00677874i
$233$	6.86597	−	6.86597i	0.449805	−	0.449805i	−0.445485	−	0.895290i	$-0.646969\pi$
$233$	6.86597	−	6.86597i	0.449805	−	0.449805i	0.895290	+	0.445485i	$0.146969\pi$
$234$		−	2.62090i		−	0.171334i
$235$	0.795780	−	1.83427i	0.0519110	−	0.119654i
$236$	2.17274	−	2.17274i	0.141433	−	0.141433i
$237$		−	6.20093i		−	0.402793i
$238$	−11.0938	−	11.0938i	−0.719103	−	0.719103i
$239$	−16.2612	+	16.2612i	−1.05185	+	1.05185i	−0.0532724	+	0.998580i	$0.516965\pi$
$239$	−16.2612	+	16.2612i	−1.05185	+	1.05185i	−0.998580	+	0.0532724i	$0.983035\pi$
$240$	−0.889953	+	2.05134i	−0.0574462	+	0.132413i
$241$	−3.13810	−	3.13810i	−0.202143	−	0.202143i	0.598775	−	0.800917i	$-0.295654\pi$
$241$	−3.13810	−	3.13810i	−0.202143	−	0.202143i	−0.800917	+	0.598775i	$0.795654\pi$
$242$			23.2556i			1.49493i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	3.93377	−	3.93377i	0.251834	−	0.251834i
$245$	−0.251154	−	0.636067i	−0.0160457	−	0.0406368i
$246$	−5.46340	+	5.46340i	−0.348334	+	0.348334i
$247$	−1.87629	−	1.87629i	−0.119386	−	0.119386i
$248$	3.13248	+	3.13248i	0.198913	+	0.198913i
$249$	8.20134			0.519738
$250$	10.1030	+	4.78850i	0.638969	+	0.302851i
$251$	6.31198	−	6.31198i	0.398409	−	0.398409i	−0.479263	−	0.877671i	$-0.659096\pi$
$251$	6.31198	−	6.31198i	0.398409	−	0.398409i	0.877671	+	0.479263i	$0.159096\pi$
$252$	1.82950	+	1.82950i	0.115248	+	0.115248i
$253$	−33.3398			−2.09606
$254$	7.24373	+	7.24373i	0.454512	+	0.454512i
$255$	−5.39652	+	12.4389i	−0.337943	+	0.778957i
$256$	1.00000			0.0625000
$257$	4.49126			0.280157			0.140079	−	0.990140i	$-0.455264\pi$
$257$	4.49126			0.280157			0.140079	+	0.990140i	$0.455264\pi$
$258$	−7.62157	+	7.62157i	−0.474498	+	0.474498i
$259$	9.75540	+	12.3498i	0.606171	+	0.767377i
$260$	2.15235	+	5.45097i	0.133483	+	0.338055i
$261$	0.103251	−	0.103251i	0.00639106	−	0.00639106i
$262$	4.64106	+	4.64106i	0.286726	+	0.286726i
$263$	−1.08580	+	1.08580i	−0.0669534	+	0.0669534i	−0.739791	−	0.672837i	$-0.765075\pi$
$263$	−1.08580	+	1.08580i	−0.0669534	+	0.0669534i	0.672837	+	0.739791i	$0.265075\pi$
$264$	−4.13858	+	4.13858i	−0.254712	+	0.254712i
$265$	−19.5642	−	8.48775i	−1.20182	−	0.521398i
$266$	2.61947			0.160610
$267$	−2.86104			−0.175093
$268$	−6.21976	−	6.21976i	−0.379932	−	0.379932i
$269$		−	26.9109i		−	1.64079i	−0.571799	−	0.820393i	$-0.693754\pi$
$269$		−	26.9109i		−	1.64079i	0.571799	−	0.820393i	$-0.306246\pi$
$270$	0.889953	−	2.05134i	0.0541608	−	0.124840i
$271$	32.0228			1.94525			0.972623	−	0.232390i	$-0.0746545\pi$
$271$	32.0228			1.94525			0.972623	+	0.232390i	$0.0746545\pi$
$272$	6.06382			0.367673
$273$	6.78109			0.410410
$274$	12.5072	+	12.5072i	0.755587	+	0.755587i
$275$	19.9931	+	21.3698i	1.20563	+	1.28865i
$276$	−4.02793	−	4.02793i	−0.242453	−	0.242453i
$277$			13.1694i			0.791273i	0.918407	+	0.395636i	$0.129476\pi$
$277$			13.1694i			0.791273i	−0.918407	+	0.395636i	$0.870524\pi$
$278$			14.0516i			0.842756i
$279$	−3.13248	−	3.13248i	−0.187537	−	0.187537i
$280$	−5.30744	−	2.30258i	−0.317180	−	0.137606i
$281$	−0.967442	−	0.967442i	−0.0577128	−	0.0577128i	0.677661	−	0.735374i	$-0.262994\pi$
$281$	−0.967442	−	0.967442i	−0.0577128	−	0.0577128i	−0.735374	+	0.677661i	$0.762994\pi$
$282$	0.894182			0.0532477
$283$	−30.4158			−1.80803			−0.904014	−	0.427502i	$-0.859394\pi$
$283$	−30.4158			−1.80803			−0.904014	+	0.427502i	$0.859394\pi$
$284$	−14.7837			−0.877249
$285$	−0.831429	−	2.10566i	−0.0492496	−	0.124728i
$286$			15.3397i			0.907056i
$287$	−14.1355	−	14.1355i	−0.834393	−	0.834393i
$288$	−1.00000			−0.0589256
$289$	19.7699			1.16294
$290$	−0.129950	+	0.299533i	−0.00763091	+	0.0175892i
$291$	−8.42848	+	8.42848i	−0.494086	+	0.494086i
$292$	−5.43491	+	5.43491i	−0.318054	+	0.318054i
$293$	−22.5564	−	22.5564i	−1.31776	−	1.31776i	−0.915544	−	0.402218i	$-0.868240\pi$
$293$	−22.5564	−	22.5564i	−1.31776	−	1.31776i	−0.402218	−	0.915544i	$-0.631760\pi$
$294$	0.216254	−	0.216254i	0.0126122	−	0.0126122i
$295$	2.73458	−	6.30318i	0.159213	−	0.366985i
$296$	−6.04130	−	0.709034i	−0.351143	−	0.0412118i
$297$	4.13858	−	4.13858i	0.240145	−	0.240145i
$298$	−18.5571			−1.07498
$299$	−14.9296			−0.863401
$300$	−0.166327	+	4.99723i	−0.00960292	+	0.288515i
$301$	−19.7193	−	19.7193i	−1.13660	−	1.13660i
$302$	−9.48777			−0.545960
$303$	9.40956	+	9.40956i	0.540565	+	0.540565i
$304$	−0.715895	+	0.715895i	−0.0410594	+	0.0410594i
$305$	4.95098	−	11.4120i	0.283492	−	0.653448i
$306$	−6.06382			−0.346646
$307$	7.64356	+	7.64356i	0.436241	+	0.436241i	0.890745	−	0.454504i	$-0.150183\pi$
$307$	7.64356	+	7.64356i	0.436241	+	0.436241i	−0.454504	+	0.890745i	$0.650183\pi$
$308$	−10.7078	−	10.7078i	−0.610132	−	0.610132i
$309$	−2.60110	+	2.60110i	−0.147971	+	0.147971i
$310$	9.08742	+	3.94249i	0.516131	+	0.223919i
$311$	0.319209	−	0.319209i	0.0181007	−	0.0181007i	−0.697999	−	0.716099i	$-0.745926\pi$
$311$	0.319209	−	0.319209i	0.0181007	−	0.0181007i	0.716099	+	0.697999i	$0.245926\pi$
$312$	−1.85326	+	1.85326i	−0.104920	+	0.104920i
$313$		−	8.27338i		−	0.467639i	−0.972280	−	0.233820i	$-0.924878\pi$
$313$		−	8.27338i		−	0.467639i	0.972280	−	0.233820i	$-0.0751225\pi$
$314$	−7.61926	−	7.61926i	−0.429979	−	0.429979i
$315$	5.30744	+	2.30258i	0.299041	+	0.129736i
$316$	−4.38472	+	4.38472i	−0.246660	+	0.246660i
$317$	2.74457	+	2.74457i	0.154151	+	0.154151i	0.779969	−	0.625818i	$-0.215235\pi$
$317$	2.74457	+	2.74457i	0.154151	+	0.154151i	−0.625818	+	0.779969i	$0.715235\pi$
$318$		−	9.53730i		−	0.534825i
$319$	−0.604309	+	0.604309i	−0.0338348	+	0.0338348i
$320$	2.07981	−	0.821222i	0.116265	−	0.0459077i
$321$		−	5.78323i		−	0.322788i
$322$	10.4215	−	10.4215i	0.580768	−	0.580768i
$323$	−4.34106	+	4.34106i	−0.241543	+	0.241543i
$324$	1.00000			0.0555556
$325$	8.95292	+	9.56942i	0.496619	+	0.530816i
$326$		−	3.03125i		−	0.167885i
$327$		−	2.84962i		−	0.157584i
$328$	7.72641			0.426620
$329$			2.31352i			0.127549i
$330$	−5.20875	+	12.0061i	−0.286732	+	0.660916i
$331$	−18.2992	−	18.2992i	−1.00582	−	1.00582i	−0.999983	−	0.00583452i	$-0.998143\pi$
$331$	−18.2992	−	18.2992i	−1.00582	−	1.00582i	−0.00583452	−	0.999983i	$-0.501857\pi$
$332$	−5.79922	−	5.79922i	−0.318274	−	0.318274i
$333$	6.04130	+	0.709034i	0.331061	+	0.0388548i
$334$			9.24944i			0.506107i
$335$	−18.0437	−	7.82809i	−0.985833	−	0.427694i
$336$		−	2.58731i		−	0.141149i
$337$	−20.4697	−	20.4697i	−1.11506	−	1.11506i	−0.992456	−	0.122602i	$-0.960876\pi$
$337$	−20.4697	−	20.4697i	−1.11506	−	1.11506i	−0.122602	−	0.992456i	$-0.539124\pi$
$338$		−	6.13086i		−	0.333475i
$339$	2.27233	−	2.27233i	0.123416	−	0.123416i
$340$	12.6116	−	4.97975i	0.683959	−	0.270065i
$341$	18.3339	+	18.3339i	0.992836	+	0.992836i
$342$	0.715895	−	0.715895i	0.0387112	−	0.0387112i
$343$	13.3660	+	13.3660i	0.721699	+	0.721699i
$344$	10.7785			0.581139
$345$	−11.6851	−	5.06949i	−0.629107	−	0.272932i
$346$	0.562678	+	0.562678i	0.0302498	+	0.0302498i
$347$			8.65774i			0.464772i	0.972624	+	0.232386i	$0.0746532\pi$
$347$			8.65774i			0.464772i	−0.972624	+	0.232386i	$0.925347\pi$
$348$	−0.146019			−0.00782742
$349$		−	3.35610i		−	0.179648i	−0.995958	−	0.0898239i	$-0.971370\pi$
$349$		−	3.35610i		−	0.179648i	0.995958	−	0.0898239i	$-0.0286304\pi$
$350$	−12.9294	−	0.430341i	−0.691105	−	0.0230027i
$351$	1.85326	−	1.85326i	0.0989197	−	0.0989197i
$352$	5.85283			0.311957
$353$	−0.899775			−0.0478902			−0.0239451	−	0.999713i	$-0.507623\pi$
$353$	−0.899775			−0.0478902			−0.0239451	+	0.999713i	$0.507623\pi$
$354$	3.07272			0.163313
$355$	−30.7471	+	12.1407i	−1.63189	+	0.644360i
$356$	2.02306	+	2.02306i	0.107222	+	0.107222i
$357$		−	15.6890i		−	0.830349i
$358$	−1.52571	+	1.52571i	−0.0806364	+	0.0806364i
$359$		−	2.41605i		−	0.127514i	−0.997965	−	0.0637572i	$-0.979692\pi$
$359$		−	2.41605i		−	0.127514i	0.997965	−	0.0637572i	$-0.0203083\pi$
$360$	−2.07981	+	0.821222i	−0.109615	+	0.0432822i
$361$			17.9750i			0.946052i
$362$		−	8.91916i		−	0.468781i
$363$	−16.4442	+	16.4442i	−0.863097	+	0.863097i
$364$	−4.79496	−	4.79496i	−0.251324	−	0.251324i
$365$	−6.84029	+	15.7668i	−0.358037	+	0.825274i
$366$	5.56319			0.290793
$367$	10.8446	−	10.8446i	0.566086	−	0.566086i	−0.364944	−	0.931030i	$-0.618912\pi$
$367$	10.8446	−	10.8446i	0.566086	−	0.566086i	0.931030	+	0.364944i	$0.118912\pi$
$368$			5.69636i			0.296943i
$369$	−7.72641			−0.402221
$370$	−13.1470	+	3.48659i	−0.683480	+	0.181259i
$371$	24.6759			1.28111
$372$			4.43000i			0.229685i
$373$	15.8141	−	15.8141i	0.818823	−	0.818823i	−0.167115	−	0.985937i	$-0.553445\pi$
$373$	15.8141	−	15.8141i	0.818823	−	0.818823i	0.985937	+	0.167115i	$0.0534451\pi$
$374$	35.4905			1.83517
$375$	3.75791	+	10.5299i	0.194058	+	0.543760i
$376$	−0.632282	−	0.632282i	−0.0326074	−	0.0326074i
$377$	−0.270610	+	0.270610i	−0.0139371	+	0.0139371i
$378$			2.58731i			0.133077i
$379$		−	27.2166i		−	1.39802i	−0.715111	−	0.699010i	$-0.753624\pi$
$379$		−	27.2166i		−	1.39802i	0.715111	−	0.699010i	$-0.246376\pi$
$380$	−0.901015	+	2.07683i	−0.0462211	+	0.106539i
$381$			10.2442i			0.524825i
$382$	1.72650	−	1.72650i	0.0883356	−	0.0883356i
$383$			24.8308i			1.26880i	0.773007	+	0.634398i	$0.218752\pi$
$383$			24.8308i			1.26880i	−0.773007	+	0.634398i	$0.781248\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−31.0636	−	13.4766i	−1.58315	−	0.686833i
$386$	−15.4244			−0.785083
$387$	−10.7785			−0.547903
$388$	11.9197			0.605129
$389$	−6.54126	+	6.54126i	−0.331655	+	0.331655i	−0.853215	−	0.521560i	$-0.825350\pi$
$389$	−6.54126	+	6.54126i	−0.331655	+	0.331655i	0.521560	+	0.853215i	$0.325350\pi$
$390$	−2.33248	+	5.37636i	−0.118110	+	0.272243i
$391$			34.5417i			1.74685i
$392$	−0.305830			−0.0154467
$393$			6.56345i			0.331082i
$394$	16.3457	+	16.3457i	0.823486	+	0.823486i
$395$	−5.51854	+	12.7202i	−0.277668	+	0.640022i
$396$	−5.85283			−0.294116
$397$	−15.5615	−	15.5615i	−0.781009	−	0.781009i	0.198992	−	0.980001i	$-0.436233\pi$
$397$	−15.5615	−	15.5615i	−0.781009	−	0.781009i	−0.980001	+	0.198992i	$0.936233\pi$
$398$	18.8595	−	18.8595i	0.945341	−	0.945341i
$399$	1.85224	+	1.85224i	0.0927281	+	0.0927281i
$400$	3.65119	−	3.41597i	0.182559	−	0.170798i
$401$	−5.50296	+	5.50296i	−0.274805	+	0.274805i	−0.831031	−	0.556226i	$-0.812249\pi$
$401$	−5.50296	+	5.50296i	−0.274805	+	0.274805i	0.556226	+	0.831031i	$0.312249\pi$
$402$		−	8.79607i		−	0.438708i
$403$	8.20994	+	8.20994i	0.408966	+	0.408966i
$404$		−	13.3071i		−	0.662054i
$405$	2.07981	−	0.821222i	0.103346	−	0.0408069i
$406$		−	0.377795i		−	0.0187497i
$407$	−35.3587	−	4.14986i	−1.75267	−	0.205701i
$408$	4.28777	+	4.28777i	0.212276	+	0.212276i
$409$	−12.6514	−	12.6514i	−0.625573	−	0.625573i	0.321378	−	0.946951i	$-0.395854\pi$
$409$	−12.6514	−	12.6514i	−0.625573	−	0.625573i	−0.946951	+	0.321378i	$0.895854\pi$
$410$	16.0694	−	6.34510i	0.793613	−	0.313362i
$411$			17.6878i			0.872477i
$412$	3.67851			0.181227
$413$			7.95007i			0.391197i
$414$		−	5.69636i		−	0.279961i
$415$	−16.8237	−	7.29881i	−0.825843	−	0.358284i
$416$	2.62090			0.128500
$417$	−9.93595	+	9.93595i	−0.486565	+	0.486565i
$418$	−4.19001	+	4.19001i	−0.204940	+	0.204940i
$419$		−	27.1721i		−	1.32745i	−0.747979	−	0.663723i	$-0.768975\pi$
$419$		−	27.1721i		−	1.32745i	0.747979	−	0.663723i	$-0.231025\pi$
$420$	−2.12476	−	5.38110i	−0.103677	−	0.262571i
$421$	21.6723	−	21.6723i	1.05624	−	1.05624i	0.0579219	−	0.998321i	$-0.481553\pi$
$421$	21.6723	−	21.6723i	1.05624	−	1.05624i	0.998321	−	0.0579219i	$-0.0184474\pi$
$422$		−	13.0270i		−	0.634147i
$423$	0.632282	+	0.632282i	0.0307426	+	0.0307426i
$424$	−6.74389	+	6.74389i	−0.327512	+	0.327512i
$425$	22.1402	−	20.7138i	1.07396	−	1.00477i
$426$	−10.4536	−	10.4536i	−0.506480	−	0.506480i
$427$			14.3937i			0.696560i
$428$	−4.08936	+	4.08936i	−0.197667	+	0.197667i
$429$	−10.8468	+	10.8468i	−0.523689	+	0.523689i
$430$	22.4172	−	8.85156i	1.08106	−	0.426860i
$431$	−18.8713	+	18.8713i	−0.908997	+	0.908997i	−0.996191	−	0.0871945i	$-0.972210\pi$
$431$	−18.8713	+	18.8713i	−0.908997	+	0.908997i	0.0871945	+	0.996191i	$0.472210\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	3.46396	+	3.46396i	0.166467	+	0.166467i	0.785425	−	0.618957i	$-0.212445\pi$
$433$	3.46396	+	3.46396i	0.166467	+	0.166467i	−0.618957	+	0.785425i	$0.712445\pi$
$434$	−11.4618			−0.550183
$435$	−0.303690	+	0.119914i	−0.0145608	+	0.00574942i
$436$	−2.01498	+	2.01498i	−0.0965002	+	0.0965002i
$437$	−4.07799	−	4.07799i	−0.195077	−	0.195077i
$438$	−7.68613			−0.367257
$439$	18.5669	+	18.5669i	0.886148	+	0.886148i	0.994151	−	0.108003i	$-0.0344456\pi$
$439$	18.5669	+	18.5669i	0.886148	+	0.886148i	−0.108003	+	0.994151i	$0.534446\pi$
$440$	12.1728	−	4.80647i	0.580313	−	0.229140i
$441$	0.305830			0.0145633
$442$	15.8927			0.755939
$443$	19.7588	−	19.7588i	0.938768	−	0.938768i	−0.0594628	−	0.998231i	$-0.518939\pi$
$443$	19.7588	−	19.7588i	0.938768	−	0.938768i	0.998231	+	0.0594628i	$0.0189388\pi$
$444$	−3.77048	−	4.77321i	−0.178939	−	0.226526i
$445$	5.86895	+	2.54619i	0.278215	+	0.120701i
$446$	0.107034	−	0.107034i	0.00506823	−	0.00506823i
$447$	−13.1218	−	13.1218i	−0.620642	−	0.620642i
$448$	−1.82950	+	1.82950i	−0.0864359	+	0.0864359i
$449$	−13.2346	+	13.2346i	−0.624580	+	0.624580i	−0.946699	−	0.322119i	$-0.895605\pi$
$449$	−13.2346	+	13.2346i	−0.624580	+	0.624580i	0.322119	+	0.946699i	$0.395605\pi$
$450$	−3.65119	+	3.41597i	−0.172119	+	0.161030i
$451$	45.2214			2.12939
$452$	−3.21356			−0.151153
$453$	−6.70886	−	6.70886i	−0.315210	−	0.315210i
$454$			21.9455i			1.02995i
$455$	−13.9103	−	6.03486i	−0.652125	−	0.282918i
$456$	−1.01243			−0.0474113
$457$	37.9505			1.77525			0.887625	−	0.460567i	$-0.152354\pi$
$457$	37.9505			1.77525			0.887625	+	0.460567i	$0.152354\pi$
$458$	2.18787			0.102232
$459$	−4.28777	−	4.28777i	−0.200136	−	0.200136i
$460$	4.67797	+	11.8473i	0.218112	+	0.552384i
$461$	−26.8463	−	26.8463i	−1.25036	−	1.25036i	−0.955560	−	0.294795i	$-0.904749\pi$
$461$	−26.8463	−	26.8463i	−1.25036	−	1.25036i	−0.294795	−	0.955560i	$-0.595251\pi$
$462$		−	15.1431i		−	0.704520i
$463$			20.8264i			0.967887i	0.875099	+	0.483943i	$0.160796\pi$
$463$			20.8264i			0.967887i	−0.875099	+	0.483943i	$0.839204\pi$
$464$	0.103251	+	0.103251i	0.00479329	+	0.00479329i
$465$	3.63801	+	9.21354i	0.168709	+	0.427268i
$466$	−6.86597	−	6.86597i	−0.318060	−	0.318060i
$467$	38.4944			1.78131			0.890655	−	0.454681i	$-0.150247\pi$
$467$	38.4944			1.78131			0.890655	+	0.454681i	$0.150247\pi$
$468$	−2.62090			−0.121151
$469$	22.7582			1.05087
$470$	−1.83427	−	0.795780i	−0.0846085	−	0.0367066i
$471$		−	10.7753i		−	0.496498i
$472$	−2.17274	−	2.17274i	−0.100008	−	0.100008i
$473$	63.0849			2.90065
$474$	−6.20093			−0.284818
$475$	−0.168395	+	5.05934i	−0.00772648	+	0.232139i
$476$	−11.0938	+	11.0938i	−0.508483	+	0.508483i
$477$	6.74389	−	6.74389i	0.308781	−	0.308781i
$478$	16.2612	+	16.2612i	0.743772	+	0.743772i
$479$	16.4225	−	16.4225i	0.750363	−	0.750363i	−0.224184	−	0.974547i	$-0.571972\pi$
$479$	16.4225	−	16.4225i	0.750363	−	0.750363i	0.974547	+	0.224184i	$0.0719717\pi$
$480$	2.05134	+	0.889953i	0.0936303	+	0.0406206i
$481$	−15.8337	−	1.85831i	−0.721953	−	0.0847317i
$482$	−3.13810	+	3.13810i	−0.142936	+	0.142936i
$483$	14.7382			0.670613
$484$	23.2556			1.05707
$485$	24.7906	−	9.78869i	1.12568	−	0.444482i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−29.4782			−1.33578			−0.667892	−	0.744259i	$-0.732803\pi$
$487$	−29.4782			−1.33578			−0.667892	+	0.744259i	$0.732803\pi$
$488$	−3.93377	−	3.93377i	−0.178073	−	0.178073i
$489$	2.14342	−	2.14342i	0.0969286	−	0.0969286i
$490$	−0.636067	+	0.251154i	−0.0287346	+	0.0113460i
$491$	−0.748995			−0.0338017			−0.0169008	−	0.999857i	$-0.505380\pi$
$491$	−0.748995			−0.0338017			−0.0169008	+	0.999857i	$0.505380\pi$
$492$	5.46340	+	5.46340i	0.246309	+	0.246309i
$493$	0.626094	+	0.626094i	0.0281979	+	0.0281979i
$494$	−1.87629	+	1.87629i	−0.0844184	+	0.0844184i
$495$	−12.1728	+	4.80647i	−0.547125	+	0.216035i
$496$	3.13248	−	3.13248i	0.140653	−	0.140653i
$497$	27.0468	−	27.0468i	1.21321	−	1.21321i
$498$		−	8.20134i		−	0.367511i
$499$	2.21532	+	2.21532i	0.0991712	+	0.0991712i	0.754952	−	0.655780i	$-0.227660\pi$
$499$	2.21532	+	2.21532i	0.0991712	+	0.0991712i	−0.655780	+	0.754952i	$0.727660\pi$
$500$	4.78850	−	10.1030i	0.214148	−	0.451819i
$501$	−6.54034	+	6.54034i	−0.292201	+	0.292201i
$502$	−6.31198	−	6.31198i	−0.281717	−	0.281717i
$503$		−	20.3022i		−	0.905229i	−0.891706	−	0.452615i	$-0.850491\pi$
$503$		−	20.3022i		−	0.905229i	0.891706	−	0.452615i	$-0.149509\pi$
$504$	1.82950	−	1.82950i	0.0814926	−	0.0814926i
$505$	−10.9281	−	27.6762i	−0.486294	−	1.23158i
$506$			33.3398i			1.48214i
$507$	4.33517	−	4.33517i	0.192532	−	0.192532i
$508$	7.24373	−	7.24373i	0.321389	−	0.321389i
$509$	−17.7017			−0.784616			−0.392308	−	0.919834i	$-0.628323\pi$
$509$	−17.7017			−0.784616			−0.392308	+	0.919834i	$0.628323\pi$
$510$	12.4389	+	5.39652i	0.550806	+	0.238962i
$511$		−	19.8864i		−	0.879722i
$512$		−	1.00000i		−	0.0441942i
$513$	1.01243			0.0446998
$514$		−	4.49126i		−	0.198101i
$515$	7.65058	−	3.02087i	0.337125	−	0.133115i
$516$	7.62157	+	7.62157i	0.335521	+	0.335521i
$517$	−3.70064	−	3.70064i	−0.162754	−	0.162754i
$518$	12.3498	−	9.75540i	0.542617	−	0.428628i
$519$			0.795747i			0.0349294i
$520$	5.45097	−	2.15235i	0.239041	−	0.0943866i
$521$		−	39.0272i		−	1.70981i	−0.518783	−	0.854906i	$-0.673615\pi$
$521$		−	39.0272i		−	1.70981i	0.518783	−	0.854906i	$-0.326385\pi$
$522$	−0.103251	−	0.103251i	−0.00451916	−	0.00451916i
$523$		−	33.9331i		−	1.48379i	−0.670516	−	0.741895i	$-0.733927\pi$
$523$		−	33.9331i		−	1.48379i	0.670516	−	0.741895i	$-0.266073\pi$
$524$	4.64106	−	4.64106i	0.202746	−	0.202746i
$525$	−8.83816	−	9.44675i	−0.385729	−	0.412290i
$526$	1.08580	+	1.08580i	0.0473432	+	0.0473432i
$527$	18.9948	−	18.9948i	0.827427	−	0.827427i
$528$	4.13858	+	4.13858i	0.180108	+	0.180108i
$529$	−9.44847			−0.410803
$530$	−8.48775	+	19.5642i	−0.368684	+	0.849815i
$531$	2.17274	+	2.17274i	0.0942888	+	0.0942888i
$532$		−	2.61947i		−	0.113568i
$533$	20.2502			0.877133
$534$			2.86104i			0.123809i
$535$	−5.14680	+	11.8634i	−0.222516	+	0.512897i
$536$	−6.21976	+	6.21976i	−0.268653	+	0.268653i
$537$	−2.15768			−0.0931109
$538$	−26.9109			−1.16021
$539$	−1.78997			−0.0770995
$540$	−2.05134	−	0.889953i	−0.0882755	−	0.0382975i
$541$	−3.31128	−	3.31128i	−0.142363	−	0.142363i	0.632333	−	0.774696i	$-0.282097\pi$
$541$	−3.31128	−	3.31128i	−0.142363	−	0.142363i	−0.774696	+	0.632333i	$0.782097\pi$
$542$		−	32.0228i		−	1.37550i
$543$	6.30680	−	6.30680i	0.270651	−	0.270651i
$544$		−	6.06382i		−	0.259984i
$545$	−2.53603	+	5.84552i	−0.108631	+	0.250395i
$546$		−	6.78109i		−	0.290204i
$547$			42.6743i			1.82462i	0.409498	+	0.912311i	$0.365704\pi$
$547$			42.6743i			1.82462i	−0.409498	+	0.912311i	$0.634296\pi$
$548$	12.5072	−	12.5072i	0.534281	−	0.534281i
$549$	3.93377	+	3.93377i	0.167889	+	0.167889i
$550$	21.3698	−	19.9931i	0.911211	−	0.852507i
$551$	−0.147833			−0.00629791
$552$	−4.02793	+	4.02793i	−0.171440	+	0.171440i
$553$		−	16.0437i		−	0.682248i
$554$	13.1694			0.559514
$555$	−11.7617	−	6.83094i	−0.499258	−	0.289957i
$556$	14.0516			0.595919
$557$			42.5144i			1.80140i	0.434447	+	0.900698i	$0.356944\pi$
$557$			42.5144i			1.80140i	−0.434447	+	0.900698i	$0.643056\pi$
$558$	−3.13248	+	3.13248i	−0.132609	+	0.132609i
$559$	28.2495			1.19483
$560$	−2.30258	+	5.30744i	−0.0973020	+	0.224280i
$561$	25.0956	+	25.0956i	1.05954	+	1.05954i
$562$	−0.967442	+	0.967442i	−0.0408091	+	0.0408091i
$563$		−	14.8057i		−	0.623984i	−0.950085	−	0.311992i	$-0.899004\pi$
$563$		−	14.8057i		−	0.623984i	0.950085	−	0.311992i	$-0.100996\pi$
$564$		−	0.894182i		−	0.0376518i
$565$	−6.68358	+	2.63905i	−0.281180	+	0.111026i
$566$			30.4158i			1.27847i
$567$	−1.82950	+	1.82950i	−0.0768319	+	0.0768319i
$568$			14.7837i			0.620308i
$569$	−20.9393	−	20.9393i	−0.877822	−	0.877822i	0.115487	−	0.993309i	$-0.463157\pi$
$569$	−20.9393	−	20.9393i	−0.877822	−	0.877822i	−0.993309	+	0.115487i	$0.963157\pi$
$570$	−2.10566	+	0.831429i	−0.0881962	+	0.0348247i
$571$	11.4454			0.478977			0.239488	−	0.970899i	$-0.423020\pi$
$571$	11.4454			0.478977			0.239488	+	0.970899i	$0.423020\pi$
$572$	15.3397			0.641386
$573$	2.44164			0.102001
$574$	−14.1355	+	14.1355i	−0.590005	+	0.590005i
$575$	19.4586	+	20.7985i	0.811478	+	0.867356i
$576$			1.00000i			0.0416667i
$577$	−31.3440			−1.30487			−0.652433	−	0.757846i	$-0.726252\pi$
$577$	−31.3440			−1.30487			−0.652433	+	0.757846i	$0.726252\pi$
$578$		−	19.7699i		−	0.822321i
$579$	−10.9067	−	10.9067i	−0.453268	−	0.453268i
$580$	0.299533	+	0.129950i	0.0124374	+	0.00539587i
$581$	21.2194			0.880329
$582$	8.42848	+	8.42848i	0.349372	+	0.349372i
$583$	−39.4708	+	39.4708i	−1.63472	+	1.63472i
$584$	5.43491	+	5.43491i	0.224898	+	0.224898i
$585$	−5.45097	+	2.15235i	−0.225370	+	0.0889885i
$586$	−22.5564	+	22.5564i	−0.931798	+	0.931798i
$587$		−	25.8658i		−	1.06760i	−0.845612	−	0.533798i	$-0.820764\pi$
$587$		−	25.8658i		−	1.06760i	0.845612	−	0.533798i	$-0.179236\pi$
$588$	−0.216254	−	0.216254i	−0.00891818	−	0.00891818i
$589$			4.48506i			0.184804i
$590$	−6.30318	−	2.73458i	−0.259498	−	0.112581i
$591$			23.1163i			0.950880i
$592$	−0.709034	+	6.04130i	−0.0291411	+	0.248296i
$593$	−27.5010	−	27.5010i	−1.12933	−	1.12933i	−0.990286	−	0.139043i	$-0.955597\pi$
$593$	−27.5010	−	27.5010i	−1.12933	−	1.12933i	−0.139043	−	0.990286i	$-0.544403\pi$
$594$	−4.13858	−	4.13858i	−0.169808	−	0.169808i
$595$	−13.9625	+	32.1834i	−0.572405	+	1.31939i
$596$			18.5571i			0.760128i
$597$	26.6714			1.09159
$598$			14.9296i			0.610517i
$599$		−	42.3519i		−	1.73045i	−0.501384	−	0.865225i	$-0.667176\pi$
$599$		−	42.3519i		−	1.73045i	0.501384	−	0.865225i	$-0.332824\pi$
$600$	4.99723	+	0.166327i	0.204011	+	0.00679029i
$601$	28.8266			1.17586			0.587930	−	0.808912i	$-0.299943\pi$
$601$	28.8266			1.17586			0.587930	+	0.808912i	$0.299943\pi$
$602$	−19.7193	+	19.7193i	−0.803701	+	0.803701i
$603$	6.21976	−	6.21976i	0.253288	−	0.253288i
$604$			9.48777i			0.386052i
$605$	48.3672	−	19.0980i	1.96641	−	0.776446i
$606$	9.40956	−	9.40956i	0.382237	−	0.382237i
$607$			4.76298i			0.193324i	0.995317	+	0.0966618i	$0.0308165\pi$
$607$			4.76298i			0.193324i	−0.995317	+	0.0966618i	$0.969183\pi$
$608$	0.715895	+	0.715895i	0.0290334	+	0.0290334i
$609$	0.267142	−	0.267142i	0.0108251	−	0.0108251i
$610$	−11.4120	−	4.95098i	−0.462058	−	0.200459i
$611$	−1.65715	−	1.65715i	−0.0670411	−	0.0670411i
$612$			6.06382i			0.245115i
$613$	−16.5517	+	16.5517i	−0.668515	+	0.668515i	−0.957372	−	0.288857i	$-0.906725\pi$
$613$	−16.5517	+	16.5517i	−0.668515	+	0.668515i	0.288857	+	0.957372i	$0.406725\pi$
$614$	7.64356	−	7.64356i	0.308469	−	0.308469i
$615$	15.8495	+	6.87615i	0.639113	+	0.277273i
$616$	−10.7078	+	10.7078i	−0.431429	+	0.431429i
$617$	−8.89134	−	8.89134i	−0.357952	−	0.357952i	0.505106	−	0.863058i	$-0.331454\pi$
$617$	−8.89134	−	8.89134i	−0.357952	−	0.357952i	−0.863058	+	0.505106i	$0.831454\pi$
$618$	2.60110	+	2.60110i	0.104631	+	0.104631i
$619$	17.1276			0.688418			0.344209	−	0.938893i	$-0.388147\pi$
$619$	17.1276			0.688418			0.344209	+	0.938893i	$0.388147\pi$
$620$	3.94249	−	9.08742i	0.158334	−	0.364960i
$621$	4.02793	−	4.02793i	0.161635	−	0.161635i
$622$	−0.319209	−	0.319209i	−0.0127991	−	0.0127991i
$623$	−7.40239			−0.296570
$624$	1.85326	+	1.85326i	0.0741898	+	0.0741898i
$625$	1.66235	−	24.9447i	0.0664942	−	0.997787i
$626$	−8.27338			−0.330671
$627$	−5.92558			−0.236645
$628$	−7.61926	+	7.61926i	−0.304041	+	0.304041i
$629$	−4.29946	+	36.6334i	−0.171431	+	1.46067i
$630$	2.30258	−	5.30744i	0.0917372	−	0.211454i
$631$	5.10169	−	5.10169i	0.203095	−	0.203095i	−0.598230	−	0.801325i	$-0.704129\pi$
$631$	5.10169	−	5.10169i	0.203095	−	0.203095i	0.801325	+	0.598230i	$0.204129\pi$
$632$	4.38472	+	4.38472i	0.174415	+	0.174415i
$633$	9.21151	−	9.21151i	0.366125	−	0.366125i
$634$	2.74457	−	2.74457i	0.109001	−	0.109001i
$635$	9.11684	−	21.0143i	0.361791	−	0.833926i
$636$	−9.53730			−0.378179
$637$	−0.801551			−0.0317586
$638$	0.604309	+	0.604309i	0.0239248	+	0.0239248i
$639$		−	14.7837i		−	0.584832i
$640$	−0.821222	−	2.07981i	−0.0324617	−	0.0822116i
$641$	21.4055			0.845468			0.422734	−	0.906254i	$-0.361070\pi$
$641$	21.4055			0.845468			0.422734	+	0.906254i	$0.361070\pi$
$642$	−5.78323			−0.228246
$643$	−2.10178			−0.0828859			−0.0414430	−	0.999141i	$-0.513195\pi$
$643$	−2.10178			−0.0828859			−0.0414430	+	0.999141i	$0.513195\pi$
$644$	−10.4215	−	10.4215i	−0.410665	−	0.410665i
$645$	22.1104	+	9.59238i	0.870595	+	0.377700i
$646$	4.34106	+	4.34106i	0.170797	+	0.170797i
$647$		−	12.8550i		−	0.505384i	−0.967547	−	0.252692i	$-0.918684\pi$
$647$		−	12.8550i		−	0.505384i	0.967547	−	0.252692i	$-0.0813159\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−12.7167	−	12.7167i	−0.499173	−	0.499173i
$650$	9.56942	−	8.95292i	0.375343	−	0.351162i
$651$	−8.10470	−	8.10470i	−0.317648	−	0.317648i
$652$	−3.03125			−0.118713
$653$	32.0200			1.25304			0.626519	−	0.779406i	$-0.284479\pi$
$653$	32.0200			1.25304			0.626519	+	0.779406i	$0.284479\pi$
$654$	−2.84962			−0.111429
$655$	5.84117	−	13.4639i	0.228233	−	0.526076i
$656$		−	7.72641i		−	0.301666i
$657$	−5.43491	−	5.43491i	−0.212036	−	0.212036i
$658$	2.31352			0.0901906
$659$	−22.1502			−0.862849			−0.431424	−	0.902149i	$-0.641989\pi$
$659$	−22.1502			−0.862849			−0.431424	+	0.902149i	$0.641989\pi$
$660$	12.0061	+	5.20875i	0.467338	+	0.202750i
$661$	25.2922	−	25.2922i	0.983754	−	0.983754i	−0.0161163	−	0.999870i	$-0.505130\pi$
$661$	25.2922	−	25.2922i	0.983754	−	0.983754i	0.999870	+	0.0161163i	$0.00513020\pi$
$662$	−18.2992	+	18.2992i	−0.711220	+	0.711220i
$663$	11.2378	+	11.2378i	0.436441	+	0.436441i
$664$	−5.79922	+	5.79922i	−0.225053	+	0.225053i
$665$	−2.15116	−	5.44798i	−0.0834186	−	0.211264i
$666$	0.709034	−	6.04130i	0.0274745	−	0.234096i
$667$	−0.588153	+	0.588153i	−0.0227734	+	0.0227734i
$668$	9.24944			0.357872
$669$	0.151370			0.00585229
$670$	−7.82809	+	18.0437i	−0.302426	+	0.697089i
$671$	−23.0237	−	23.0237i	−0.888820	−	0.888820i
$672$	−2.58731			−0.0998076
$673$	−31.9558	−	31.9558i	−1.23181	−	1.23181i	−0.963269	−	0.268538i	$-0.913459\pi$
$673$	−31.9558	−	31.9558i	−1.23181	−	1.23181i	−0.268538	−	0.963269i	$-0.586541\pi$
$674$	−20.4697	+	20.4697i	−0.788465	+	0.788465i
$675$	−4.99723	−	0.166327i	−0.192344	−	0.00640195i
$676$	−6.13086			−0.235802
$677$	−6.71777	−	6.71777i	−0.258185	−	0.258185i	0.566131	−	0.824316i	$-0.308440\pi$
$677$	−6.71777	−	6.71777i	−0.258185	−	0.258185i	−0.824316	+	0.566131i	$0.808440\pi$
$678$	−2.27233	−	2.27233i	−0.0872683	−	0.0872683i
$679$	−21.8071	+	21.8071i	−0.836879	+	0.836879i
$680$	−4.97975	−	12.6116i	−0.190965	−	0.483632i
$681$	−15.5178	+	15.5178i	−0.594644	+	0.594644i
$682$	18.3339	−	18.3339i	0.702041	−	0.702041i
$683$			23.3063i			0.891789i	0.895086	+	0.445894i	$0.147114\pi$
$683$			23.3063i			0.891789i	−0.895086	+	0.445894i	$0.852886\pi$
$684$	−0.715895	−	0.715895i	−0.0273729	−	0.0273729i
$685$	15.7414	−	36.2837i	0.601447	−	1.38633i
$686$	13.3660	−	13.3660i	0.510318	−	0.510318i
$687$	1.54705	+	1.54705i	0.0590238	+	0.0590238i
$688$		−	10.7785i		−	0.410927i
$689$	−17.6751	+	17.6751i	−0.673367	+	0.673367i
$690$	−5.06949	+	11.6851i	−0.192992	+	0.444846i
$691$			4.64816i			0.176824i	0.996084	+	0.0884121i	$0.0281792\pi$
$691$			4.64816i			0.176824i	−0.996084	+	0.0884121i	$0.971821\pi$
$692$	0.562678	−	0.562678i	0.0213898	−	0.0213898i
$693$	10.7078	−	10.7078i	0.406755	−	0.406755i
$694$	8.65774			0.328643
$695$	29.2245	−	11.5394i	1.10855	−	0.437716i
$696$			0.146019i			0.00553482i
$697$		−	46.8516i		−	1.77463i
$698$	−3.35610			−0.127030
$699$		−	9.70995i		−	0.367264i
$700$	−0.430341	+	12.9294i	−0.0162653	+	0.488685i
$701$	−9.07074	−	9.07074i	−0.342597	−	0.342597i	0.514746	−	0.857343i	$-0.327886\pi$
$701$	−9.07074	−	9.07074i	−0.342597	−	0.342597i	−0.857343	+	0.514746i	$0.827886\pi$
$702$	−1.85326	−	1.85326i	−0.0699468	−	0.0699468i
$703$	−3.81734	−	4.83253i	−0.143974	−	0.182262i
$704$		−	5.85283i		−	0.220587i
$705$	−0.734322	−	1.85972i	−0.0276562	−	0.0700413i
$706$			0.899775i			0.0338635i
$707$	24.3454	+	24.3454i	0.915605	+	0.915605i
$708$		−	3.07272i		−	0.115480i
$709$	−13.2820	+	13.2820i	−0.498816	+	0.498816i	−0.911069	−	0.412254i	$-0.864742\pi$
$709$	−13.2820	+	13.2820i	−0.498816	+	0.498816i	0.412254	+	0.911069i	$0.364742\pi$
$710$	12.1407	+	30.7471i	0.455631	+	1.15392i
$711$	−4.38472	−	4.38472i	−0.164440	−	0.164440i
$712$	2.02306	−	2.02306i	0.0758173	−	0.0758173i
$713$	17.8437	+	17.8437i	0.668253	+	0.668253i
$714$	−15.6890			−0.587146
$715$	31.9036	−	12.5973i	1.19313	−	0.471113i
$716$	1.52571	+	1.52571i	0.0570186	+	0.0570186i
$717$			22.9969i			0.858834i
$718$	−2.41605			−0.0901663
$719$			15.2786i			0.569795i	0.958558	+	0.284897i	$0.0919595\pi$
$719$			15.2786i			0.569795i	−0.958558	+	0.284897i	$0.908040\pi$
$720$	0.821222	+	2.07981i	0.0306051	+	0.0775098i
$721$	−6.72984	+	6.72984i	−0.250632	+	0.250632i
$722$	17.9750			0.668960
$723$	−4.43794			−0.165049
$724$	−8.91916			−0.331478
$725$	0.729689	+	0.0242869i	0.0271000	+	0.000901993i
$726$	16.4442	+	16.4442i	0.610302	+	0.610302i
$727$			4.24493i			0.157436i	0.996897	+	0.0787178i	$0.0250826\pi$
$727$			4.24493i			0.157436i	−0.996897	+	0.0787178i	$0.974917\pi$
$728$	−4.79496	+	4.79496i	−0.177713	+	0.177713i
$729$			1.00000i			0.0370370i
$730$	15.7668	+	6.84029i	0.583557	+	0.253171i
$731$		−	65.3590i		−	2.41739i
$732$		−	5.56319i		−	0.205622i
$733$	−1.62240	+	1.62240i	−0.0599248	+	0.0599248i	−0.736434	−	0.676509i	$-0.763492\pi$
$733$	−1.62240	+	1.62240i	−0.0599248	+	0.0599248i	0.676509	+	0.736434i	$0.263492\pi$
$734$	−10.8446	−	10.8446i	−0.400283	−	0.400283i
$735$	−0.627360	−	0.272174i	−0.0231405	−	0.0100393i
$736$	5.69636			0.209970
$737$	−36.4032	+	36.4032i	−1.34093	+	1.34093i
$738$			7.72641i			0.284413i
$739$	−1.68171			−0.0618626			−0.0309313	−	0.999522i	$-0.509847\pi$
$739$	−1.68171			−0.0618626			−0.0309313	+	0.999522i	$0.509847\pi$
$740$	3.48659	+	13.1470i	0.128170	+	0.483293i
$741$	−2.65348			−0.0974780
$742$		−	24.6759i		−	0.905882i
$743$	−5.50045	+	5.50045i	−0.201792	+	0.201792i	−0.800767	−	0.598975i	$-0.795575\pi$
$743$	−5.50045	+	5.50045i	−0.201792	+	0.201792i	0.598975	+	0.800767i	$0.295575\pi$
$744$	4.43000			0.162412
$745$	15.2395	+	38.5951i	0.558332	+	1.41402i
$746$	−15.8141	−	15.8141i	−0.578995	−	0.578995i
$747$	5.79922	−	5.79922i	0.212182	−	0.212182i
$748$		−	35.4905i		−	1.29766i
$749$		−	14.9630i		−	0.546736i
$750$	10.5299	−	3.75791i	0.384496	−	0.137219i
$751$		−	23.1417i		−	0.844454i	−0.906490	−	0.422227i	$-0.861248\pi$
$751$		−	23.1417i		−	0.844454i	0.906490	−	0.422227i	$-0.138752\pi$
$752$	−0.632282	+	0.632282i	−0.0230569	+	0.0230569i
$753$		−	8.92648i		−	0.325299i
$754$	0.270610	+	0.270610i	0.00985504	+	0.00985504i
$755$	7.79156	+	19.7327i	0.283564	+	0.718147i
$756$	2.58731			0.0940995
$757$	−48.5193			−1.76346			−0.881732	−	0.471751i	$-0.843622\pi$
$757$	−48.5193			−1.76346			−0.881732	+	0.471751i	$0.843622\pi$
$758$	−27.2166			−0.988550
$759$	−23.5748	+	23.5748i	−0.855711	+	0.855711i
$760$	2.07683	+	0.901015i	0.0753346	+	0.0326832i
$761$		−	21.1818i		−	0.767839i	−0.923367	−	0.383919i	$-0.874574\pi$
$761$		−	21.1818i		−	0.767839i	0.923367	−	0.383919i	$-0.125426\pi$
$762$	10.2442			0.371107
$763$		−	7.37284i		−	0.266915i
$764$	−1.72650	−	1.72650i	−0.0624627	−	0.0624627i
$765$	4.97975	+	12.6116i	0.180043	+	0.455972i
$766$	24.8308			0.897174
$767$	−5.69454	−	5.69454i	−0.205618	−	0.205618i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−7.00591	−	7.00591i	−0.252640	−	0.252640i	0.569412	−	0.822052i	$-0.307171\pi$
$769$	−7.00591	−	7.00591i	−0.252640	−	0.252640i	−0.822052	+	0.569412i	$0.807171\pi$
$770$	−13.4766	+	31.0636i	−0.485664	+	1.11945i
$771$	3.17580	−	3.17580i	0.114374	−	0.114374i
$772$			15.4244i			0.555137i
$773$	5.53424	+	5.53424i	0.199053	+	0.199053i	0.799594	−	0.600541i	$-0.205048\pi$
$773$	5.53424	+	5.53424i	0.199053	+	0.199053i	−0.600541	+	0.799594i	$0.705048\pi$
$774$			10.7785i			0.387426i
$775$	0.736831	−	22.1377i	0.0264677	−	0.795211i
$776$		−	11.9197i		−	0.427891i
$777$	15.6307	+	1.83449i	0.560748	+	0.0658120i
$778$	6.54126	+	6.54126i	0.234516	+	0.234516i
$779$	5.53130	+	5.53130i	0.198180	+	0.198180i
$780$	5.37636	+	2.33248i	0.192505	+	0.0835163i
$781$			86.5262i			3.09615i
$782$	34.5417			1.23521
$783$		−	0.146019i		−	0.00521828i
$784$			0.305830i			0.0109225i
$785$	−9.58947	+	22.1037i	−0.342263	+	0.788914i
$786$	6.56345			0.234111
$787$	9.05047	−	9.05047i	0.322614	−	0.322614i	−0.527155	−	0.849769i	$-0.676741\pi$
$787$	9.05047	−	9.05047i	0.322614	−	0.322614i	0.849769	+	0.527155i	$0.176741\pi$
$788$	16.3457	−	16.3457i	0.582292	−	0.582292i
$789$			1.53556i			0.0546672i
$790$	12.7202	+	5.51854i	0.452564	+	0.196341i
$791$	5.87922	−	5.87922i	0.209041	−	0.209041i
$792$			5.85283i			0.207971i
$793$	−10.3100	−	10.3100i	−0.366120	−	0.366120i
$794$	−15.5615	+	15.5615i	−0.552257	+	0.552257i
$795$	−19.8357	+	7.83224i	−0.703501	+	0.277781i
$796$	−18.8595	−	18.8595i	−0.668457	−	0.668457i
$797$		−	15.0407i		−	0.532768i	−0.963867	−	0.266384i	$-0.914171\pi$
$797$		−	15.0407i		−	0.532768i	0.963867	−	0.266384i	$-0.0858289\pi$
$798$	1.85224	−	1.85224i	0.0655687	−	0.0655687i
$799$	−3.83404	+	3.83404i	−0.135639	+	0.135639i
$800$	−3.41597	−	3.65119i	−0.120773	−	0.129089i
$801$	−2.02306	+	2.02306i	−0.0714813	+	0.0714813i
$802$	5.50296	+	5.50296i	0.194316	+	0.194316i
$803$	31.8096	+	31.8096i	1.12254	+	1.12254i
$804$	−8.79607			−0.310213
$805$	−30.2331	−	13.1163i	−1.06558	−	0.462290i
$806$	8.20994	−	8.20994i	0.289183	−	0.289183i
$807$	−19.0289	−	19.0289i	−0.669848	−	0.669848i
$808$	−13.3071			−0.468143
$809$	−37.9128	−	37.9128i	−1.33294	−	1.33294i	−0.902725	−	0.430217i	$-0.858437\pi$
$809$	−37.9128	−	37.9128i	−1.33294	−	1.33294i	−0.430217	−	0.902725i	$-0.641563\pi$
$810$	−0.821222	−	2.07981i	−0.0288548	−	0.0730769i
$811$	32.4818			1.14059			0.570295	−	0.821440i	$-0.306829\pi$
$811$	32.4818			1.14059			0.570295	+	0.821440i	$0.306829\pi$
$812$	−0.377795			−0.0132580
$813$	22.6435	−	22.6435i	0.794143	−	0.794143i
$814$	−4.14986	+	35.3587i	−0.145452	+	1.23932i
$815$	−6.30441	+	2.48933i	−0.220834	+	0.0871974i
$816$	4.28777	−	4.28777i	0.150102	−	0.150102i
$817$	7.71629	+	7.71629i	0.269959	+	0.269959i
$818$	−12.6514	+	12.6514i	−0.442347	+	0.442347i
$819$	4.79496	−	4.79496i	0.167549	−	0.167549i
$820$	−6.34510	−	16.0694i	−0.221581	−	0.561169i
$821$	−31.7012			−1.10638			−0.553190	−	0.833055i	$-0.686590\pi$
$821$	−31.7012			−1.10638			−0.553190	+	0.833055i	$0.686590\pi$
$822$	17.6878			0.616935
$823$	26.3023	+	26.3023i	0.916839	+	0.916839i	0.996798	−	0.0799590i	$-0.0254789\pi$
$823$	26.3023	+	26.3023i	0.916839	+	0.916839i	−0.0799590	+	0.996798i	$0.525479\pi$
$824$		−	3.67851i		−	0.128147i
$825$	29.2480	+	0.973487i	1.01828	+	0.0338925i
$826$	7.95007			0.276618
$827$	31.1749			1.08406			0.542029	−	0.840360i	$-0.317656\pi$
$827$	31.1749			1.08406			0.542029	+	0.840360i	$0.317656\pi$
$828$	−5.69636			−0.197962
$829$	−14.1132	−	14.1132i	−0.490172	−	0.490172i	0.418188	−	0.908360i	$-0.362665\pi$
$829$	−14.1132	−	14.1132i	−0.490172	−	0.490172i	−0.908360	+	0.418188i	$0.862665\pi$
$830$	−7.29881	+	16.8237i	−0.253345	+	0.583959i
$831$	9.31218	+	9.31218i	0.323036	+	0.323036i
$832$		−	2.62090i		−	0.0908635i
$833$			1.85450i			0.0642546i
$834$	9.93595	+	9.93595i	0.344054	+	0.344054i
$835$	19.2370	−	7.59585i	0.665725	−	0.262865i
$836$	4.19001	+	4.19001i	0.144915	+	0.144915i
$837$	−4.43000			−0.153123
$838$	−27.1721			−0.938646
$839$	38.6415			1.33405			0.667026	−	0.745035i	$-0.267567\pi$
$839$	38.6415			1.33405			0.667026	+	0.745035i	$0.267567\pi$
$840$	−5.38110	+	2.12476i	−0.185666	+	0.0733110i
$841$		−	28.9787i		−	0.999265i
$842$	−21.6723	−	21.6723i	−0.746877	−	0.746877i
$843$	−1.36817			−0.0471223
$844$	−13.0270			−0.448409
$845$	−12.7510	+	5.03480i	−0.438648	+	0.173202i
$846$	0.632282	−	0.632282i	0.0217383	−	0.0217383i
$847$	−42.5463	+	42.5463i	−1.46191	+	1.46191i
$848$	6.74389	+	6.74389i	0.231586	+	0.231586i
$849$	−21.5072	+	21.5072i	−0.738125	+	0.738125i
$850$	−20.7138	−	22.1402i	−0.710478	−	0.759401i
$851$	−34.4134	−	4.03891i	−1.17968	−	0.138452i
$852$	−10.4536	+	10.4536i	−0.358135	+	0.358135i
$853$	−38.5567			−1.32016			−0.660078	−	0.751197i	$-0.729477\pi$
$853$	−38.5567			−1.32016			−0.660078	+	0.751197i	$0.729477\pi$
$854$	14.3937			0.492542
$855$	−2.07683	−	0.901015i	−0.0710262	−	0.0308140i
$856$	4.08936	+	4.08936i	0.139771	+	0.139771i
$857$	−33.2708			−1.13651			−0.568254	−	0.822853i	$-0.692381\pi$
$857$	−33.2708			−1.13651			−0.568254	+	0.822853i	$0.692381\pi$
$858$	10.8468	+	10.8468i	0.370304	+	0.370304i
$859$	8.16819	−	8.16819i	0.278695	−	0.278695i	−0.553893	−	0.832588i	$-0.686858\pi$
$859$	8.16819	−	8.16819i	0.278695	−	0.278695i	0.832588	+	0.553893i	$0.186858\pi$
$860$	−8.85156	−	22.4172i	−0.301836	−	0.764421i
$861$	−19.9906			−0.681279
$862$	18.8713	+	18.8713i	0.642758	+	0.642758i
$863$	19.4833	+	19.4833i	0.663219	+	0.663219i	0.956137	−	0.292919i	$-0.0946265\pi$
$863$	19.4833	+	19.4833i	0.663219	+	0.663219i	−0.292919	+	0.956137i	$0.594626\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	0.708178	−	1.63234i	0.0240788	−	0.0555014i
$866$	3.46396	−	3.46396i	0.117710	−	0.117710i
$867$	13.9795	−	13.9795i	0.474767	−	0.474767i
$868$			11.4618i			0.389038i
$869$	25.6630	+	25.6630i	0.870558	+	0.870558i
$870$	0.119914	+	0.303690i	0.00406545	+	0.0102961i
$871$	−16.3014	+	16.3014i	−0.552352	+	0.552352i
$872$	2.01498	+	2.01498i	0.0682360	+	0.0682360i
$873$			11.9197i			0.403420i
$874$	−4.07799	+	4.07799i	−0.137940	+	0.137940i
$875$	9.72287	+	27.2440i	0.328693	+	0.921016i
$876$			7.68613i			0.259690i
$877$	−14.5889	+	14.5889i	−0.492633	+	0.492633i	−0.909135	−	0.416502i	$-0.863256\pi$
$877$	−14.5889	+	14.5889i	−0.492633	+	0.492633i	0.416502	+	0.909135i	$0.363256\pi$
$878$	18.5669	−	18.5669i	0.626601	−	0.626601i
$879$	−31.8996			−1.07595
$880$	−4.80647	−	12.1728i	−0.162026	−	0.410343i
$881$		−	9.70985i		−	0.327133i	−0.986532	−	0.163567i	$-0.947700\pi$
$881$		−	9.70985i		−	0.327133i	0.986532	−	0.163567i	$-0.0522999\pi$
$882$		−	0.305830i		−	0.0102978i
$883$	30.2572			1.01824			0.509118	−	0.860696i	$-0.329972\pi$
$883$	30.2572			1.01824			0.509118	+	0.860696i	$0.329972\pi$
$884$		−	15.8927i		−	0.534529i
$885$	−2.52338	−	6.39066i	−0.0848226	−	0.214820i
$886$	−19.7588	−	19.7588i	−0.663809	−	0.663809i
$887$	31.8848	+	31.8848i	1.07059	+	1.07059i	0.997312	+	0.0732734i	$0.0233446\pi$
$887$	31.8848	+	31.8848i	1.07059	+	1.07059i	0.0732734	+	0.997312i	$0.476655\pi$
$888$	−4.77321	+	3.77048i	−0.160178	+	0.126529i
$889$			26.5049i			0.888945i
$890$	2.54619	−	5.86895i	0.0853485	−	0.196728i
$891$		−	5.85283i		−	0.196077i
$892$	−0.107034	−	0.107034i	−0.00358378	−	0.00358378i
$893$		−	0.905295i		−	0.0302946i
$894$	−13.1218	+	13.1218i	−0.438860	+	0.438860i
$895$	4.42614	+	1.92024i	0.147949	+	0.0641865i
$896$	1.82950	+	1.82950i	0.0611194	+	0.0611194i
$897$	−10.5568	+	10.5568i	−0.352482	+	0.352482i
$898$	13.2346	+	13.2346i	0.441645	+	0.441645i
$899$	0.646862			0.0215741
$900$	3.41597	+	3.65119i	0.113866	+	0.121706i
$901$	40.8937	+	40.8937i	1.36237	+	1.36237i
$902$		−	45.2214i		−	1.50571i
$903$	−27.8874			−0.928034
$904$			3.21356i			0.106881i
$905$	−18.5501	+	7.32461i	−0.616627	+	0.243478i
$906$	−6.70886	+	6.70886i	−0.222887	+	0.222887i
$907$	31.0505			1.03102			0.515508	−	0.856885i	$-0.327603\pi$
$907$	31.0505			1.03102			0.515508	+	0.856885i	$0.327603\pi$
$908$	21.9455			0.728287
$909$	13.3071			0.441370
$910$	−6.03486	+	13.9103i	−0.200054	+	0.461122i
$911$	29.5411	+	29.5411i	0.978741	+	0.978741i	0.999779	−	0.0210382i	$-0.00669715\pi$
$911$	29.5411	+	29.5411i	0.978741	+	0.978741i	−0.0210382	+	0.999779i	$0.506697\pi$
$912$			1.01243i			0.0335249i
$913$	−33.9419	+	33.9419i	−1.12331	+	1.12331i
$914$		−	37.9505i		−	1.25529i
$915$	−4.56862	−	11.5704i	−0.151034	−	0.382504i
$916$		−	2.18787i		−	0.0722891i
$917$			16.9817i			0.560785i
$918$	−4.28777	+	4.28777i	−0.141517	+	0.141517i
$919$	−18.3529	−	18.3529i	−0.605407	−	0.605407i	0.336335	−	0.941742i	$-0.390812\pi$
$919$	−18.3529	−	18.3529i	−0.605407	−	0.605407i	−0.941742	+	0.336335i	$0.890812\pi$
$920$	11.8473	−	4.67797i	0.390594	−	0.154228i
$921$	10.8096			0.356189
$922$	−26.8463	+	26.8463i	−0.884135	+	0.884135i
$923$			38.7466i			1.27536i
$924$	−15.1431			−0.498171
$925$	18.0480	+	24.4800i	0.593416	+	0.804896i
$926$	20.8264			0.684399
$927$			3.67851i			0.120818i
$928$	0.103251	−	0.103251i	0.00338937	−	0.00338937i
$929$	45.6309			1.49710			0.748551	−	0.663077i	$-0.230750\pi$
$929$	45.6309			1.49710			0.748551	+	0.663077i	$0.230750\pi$
$930$	9.21354	−	3.63801i	0.302124	−	0.119295i
$931$	−0.218942	−	0.218942i	−0.00717554	−	0.00717554i
$932$	−6.86597	+	6.86597i	−0.224902	+	0.224902i
$933$		−	0.451430i		−	0.0147791i
$934$		−	38.4944i		−	1.25958i
$935$	−29.1456	−	73.8134i	−0.953163	−	2.41396i
$936$			2.62090i			0.0856670i
$937$	−25.4346	+	25.4346i	−0.830913	+	0.830913i	−0.987642	−	0.156729i	$-0.949905\pi$
$937$	−25.4346	+	25.4346i	−0.830913	+	0.830913i	0.156729	+	0.987642i	$0.449905\pi$
$938$		−	22.7582i		−	0.743080i
$939$	−5.85016	−	5.85016i	−0.190913	−	0.190913i
$940$	−0.795780	+	1.83427i	−0.0259555	+	0.0598272i
$941$	−52.7814			−1.72062			−0.860312	−	0.509767i	$-0.829732\pi$
$941$	−52.7814			−1.72062			−0.860312	+	0.509767i	$0.829732\pi$
$942$	−10.7753			−0.351077
$943$	44.0124			1.43324
$944$	−2.17274	+	2.17274i	−0.0707166	+	0.0707166i
$945$	5.38110	−	2.12476i	0.175047	−	0.0691183i
$946$		−	63.0849i		−	2.05107i
$947$	22.3652			0.726772			0.363386	−	0.931639i	$-0.381621\pi$
$947$	22.3652			0.726772			0.363386	+	0.931639i	$0.381621\pi$
$948$			6.20093i			0.201397i
$949$	14.2444	+	14.2444i	0.462392	+	0.462392i
$950$	5.05934	+	0.168395i	0.164147	+	0.00546345i
$951$	3.88142			0.125864
$952$	11.0938	+	11.0938i	0.359552	+	0.359552i
$953$	39.2467	−	39.2467i	1.27132	−	1.27132i	0.325931	−	0.945394i	$-0.394322\pi$
$953$	39.2467	−	39.2467i	1.27132	−	1.27132i	0.945394	−	0.325931i	$-0.105678\pi$
$954$	−6.74389	−	6.74389i	−0.218341	−	0.218341i
$955$	−5.00863	−	2.17295i	−0.162076	−	0.0703150i
$956$	16.2612	−	16.2612i	0.525926	−	0.525926i
$957$			0.854622i			0.0276260i
$958$	−16.4225	−	16.4225i	−0.530587	−	0.530587i
$959$			45.7639i			1.47779i
$960$	0.889953	−	2.05134i	0.0287231	−	0.0662066i
$961$			11.3751i			0.366939i
$962$	−1.85831	+	15.8337i	−0.0599144	+	0.510498i
$963$	−4.08936	−	4.08936i	−0.131778	−	0.131778i
$964$	3.13810	+	3.13810i	0.101071	+	0.101071i
$965$	12.6669	+	32.0798i	0.407761	+	1.03269i
$966$		−	14.7382i		−	0.474195i
$967$	−4.40358			−0.141609			−0.0708047	−	0.997490i	$-0.522557\pi$
$967$	−4.40358			−0.141609			−0.0708047	+	0.997490i	$0.522557\pi$
$968$		−	23.2556i		−	0.747464i
$969$			6.13919i			0.197219i
$970$	−9.78869	−	24.7906i	−0.314296	−	0.795978i
$971$	−46.3548			−1.48759			−0.743797	−	0.668405i	$-0.766977\pi$
$971$	−46.3548			−1.48759			−0.743797	+	0.668405i	$0.766977\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−25.7074	+	25.7074i	−0.824141	+	0.824141i
$974$			29.4782i			0.944541i
$975$	13.0973	+	0.435928i	0.419448	+	0.0139609i
$976$	−3.93377	+	3.93377i	−0.125917	+	0.125917i
$977$			39.0822i			1.25035i	0.780484	+	0.625176i	$0.214973\pi$
$977$			39.0822i			1.25035i	−0.780484	+	0.625176i	$0.785027\pi$
$978$	−2.14342	−	2.14342i	−0.0685389	−	0.0685389i
$979$	11.8406	−	11.8406i	0.378428	−	0.378428i
$980$	0.251154	+	0.636067i	0.00802283	+	0.0203184i
$981$	−2.01498	−	2.01498i	−0.0643335	−	0.0643335i
$982$			0.748995i			0.0239014i
$983$	−34.5124	+	34.5124i	−1.10077	+	1.10077i	−0.106457	+	0.994317i	$0.533951\pi$
$983$	−34.5124	+	34.5124i	−1.10077	+	1.10077i	−0.994317	+	0.106457i	$0.966049\pi$
$984$	5.46340	−	5.46340i	0.174167	−	0.174167i
$985$	20.5725	−	47.4194i	0.655494	−	1.51091i
$986$	0.626094	−	0.626094i	0.0199389	−	0.0199389i
$987$	1.63591	+	1.63591i	0.0520716	+	0.0520716i
$988$	1.87629	+	1.87629i	0.0596928	+	0.0596928i
$989$	61.3983			1.95235
$990$	4.80647	+	12.1728i	0.152760	+	0.386876i
$991$	−25.5433	+	25.5433i	−0.811411	+	0.811411i	−0.984845	−	0.173434i	$-0.944514\pi$
$991$	−25.5433	+	25.5433i	−0.811411	+	0.811411i	0.173434	+	0.984845i	$0.444514\pi$
$992$	−3.13248	−	3.13248i	−0.0994564	−	0.0994564i
$993$	−25.8790			−0.821247
$994$	−27.0468	−	27.0468i	−0.857871	−	0.857871i
$995$	−54.7120	−	23.7363i	−1.73449	−	0.752490i
$996$	−8.20134			−0.259869
$997$	42.3605			1.34157			0.670785	−	0.741651i	$-0.265957\pi$
$997$	42.3605			1.34157			0.670785	+	0.741651i	$0.265957\pi$
$998$	2.21532	−	2.21532i	0.0701246	−	0.0701246i
$999$	4.77321	−	3.77048i	0.151018	−	0.119293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.43.11	✓	40
5.2	odd	4		1110.2.o.b.487.10	yes	40
37.31	odd	4		1110.2.o.b.253.10	yes	40
185.142	even	4	inner	1110.2.l.b.697.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.11	✓	40	1.1	even	1	trivial
1110.2.l.b.697.11	yes	40	185.142	even	4	inner
1110.2.o.b.253.10	yes	40	37.31	odd	4
1110.2.o.b.487.10	yes	40	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07981 + 0.821222i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.82950 - 1.82950i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07981 + 0.821222i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.82950 - 1.82950i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.821222 + 2.07981i) q^{10} +5.85283i q^{11} +(-0.707107 + 0.707107i) q^{12} +2.62090i q^{13} +(-1.82950 - 1.82950i) q^{14} +(-0.889953 + 2.05134i) q^{15} +1.00000 q^{16} +6.06382 q^{17} -1.00000 q^{18} +(-0.715895 + 0.715895i) q^{19} +(2.07981 - 0.821222i) q^{20} -2.58731i q^{21} +5.85283 q^{22} +5.69636i q^{23} +(0.707107 + 0.707107i) q^{24} +(3.65119 - 3.41597i) q^{25} +2.62090 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.82950 + 1.82950i) q^{28} +(0.103251 + 0.103251i) q^{29} +(2.05134 + 0.889953i) q^{30} +(3.13248 - 3.13248i) q^{31} -1.00000i q^{32} +(4.13858 + 4.13858i) q^{33} -6.06382i q^{34} +(-2.30258 + 5.30744i) q^{35} +1.00000i q^{36} +(-0.709034 + 6.04130i) q^{37} +(0.715895 + 0.715895i) q^{38} +(1.85326 + 1.85326i) q^{39} +(-0.821222 - 2.07981i) q^{40} -7.72641i q^{41} -2.58731 q^{42} -10.7785i q^{43} -5.85283i q^{44} +(0.821222 + 2.07981i) q^{45} +5.69636 q^{46} +(-0.632282 + 0.632282i) q^{47} +(0.707107 - 0.707107i) q^{48} +0.305830i q^{49} +(-3.41597 - 3.65119i) q^{50} +(4.28777 - 4.28777i) q^{51} -2.62090i q^{52} +(6.74389 + 6.74389i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-4.80647 - 12.1728i) q^{55} +(1.82950 + 1.82950i) q^{56} +1.01243i q^{57} +(0.103251 - 0.103251i) q^{58} +(-2.17274 + 2.17274i) q^{59} +(0.889953 - 2.05134i) q^{60} +(-3.93377 + 3.93377i) q^{61} +(-3.13248 - 3.13248i) q^{62} +(-1.82950 - 1.82950i) q^{63} -1.00000 q^{64} +(-2.15235 - 5.45097i) q^{65} +(4.13858 - 4.13858i) q^{66} +(6.21976 + 6.21976i) q^{67} -6.06382 q^{68} +(4.02793 + 4.02793i) q^{69} +(5.30744 + 2.30258i) q^{70} +14.7837 q^{71} +1.00000 q^{72} +(5.43491 - 5.43491i) q^{73} +(6.04130 + 0.709034i) q^{74} +(0.166327 - 4.99723i) q^{75} +(0.715895 - 0.715895i) q^{76} +(10.7078 + 10.7078i) q^{77} +(1.85326 - 1.85326i) q^{78} +(4.38472 - 4.38472i) q^{79} +(-2.07981 + 0.821222i) q^{80} -1.00000 q^{81} -7.72641 q^{82} +(5.79922 + 5.79922i) q^{83} +2.58731i q^{84} +(-12.6116 + 4.97975i) q^{85} -10.7785 q^{86} +0.146019 q^{87} -5.85283 q^{88} +(-2.02306 - 2.02306i) q^{89} +(2.07981 - 0.821222i) q^{90} +(4.79496 + 4.79496i) q^{91} -5.69636i q^{92} -4.43000i q^{93} +(0.632282 + 0.632282i) q^{94} +(0.901015 - 2.07683i) q^{95} +(-0.707107 - 0.707107i) q^{96} -11.9197 q^{97} +0.305830 q^{98} +5.85283 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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