LMFDB - Embedded newform 80.2.q.c.69.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.q (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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.4
Root			$-1.40501 + 0.161069i$ of defining polynomial
Character	$\chi$	$=$	80.69
Dual form			80.2.q.c.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.161069 + 1.40501i) q^{2} +(0.734294 + 0.734294i) q^{3} +(-1.94811 - 0.452606i) q^{4} +(-1.17216 + 1.90421i) q^{5} +(-1.14996 + 0.913419i) q^{6} +1.71452 q^{7} +(0.949697 - 2.66422i) q^{8} -1.92163i q^{9} +O(q^{10})$	\(q+(-0.161069 + 1.40501i) q^{2} +(0.734294 + 0.734294i) q^{3} +(-1.94811 - 0.452606i) q^{4} +(-1.17216 + 1.90421i) q^{5} +(-1.14996 + 0.913419i) q^{6} +1.71452 q^{7} +(0.949697 - 2.66422i) q^{8} -1.92163i q^{9} +(-2.48664 - 1.95361i) q^{10} +(2.82684 + 2.82684i) q^{11} +(-1.09814 - 1.76283i) q^{12} +(-2.59462 - 2.59462i) q^{13} +(-0.276156 + 2.40893i) q^{14} +(-2.25896 + 0.537540i) q^{15} +(3.59030 + 1.76346i) q^{16} -1.89939i q^{17} +(2.69991 + 0.309513i) q^{18} +(2.89623 - 2.89623i) q^{19} +(3.14537 - 3.17910i) q^{20} +(1.25896 + 1.25896i) q^{21} +(-4.42705 + 3.51643i) q^{22} +2.00613 q^{23} +(2.65368 - 1.25896i) q^{24} +(-2.25207 - 4.46410i) q^{25} +(4.06338 - 3.22756i) q^{26} +(3.61392 - 3.61392i) q^{27} +(-3.34009 - 0.776005i) q^{28} +(-6.72307 + 6.72307i) q^{29} +(-0.391402 - 3.26045i) q^{30} -7.11778 q^{31} +(-3.05596 + 4.76037i) q^{32} +4.15146i q^{33} +(2.66867 + 0.305932i) q^{34} +(-2.00970 + 3.26482i) q^{35} +(-0.869740 + 3.74355i) q^{36} +(2.25207 - 2.25207i) q^{37} +(3.60274 + 4.53572i) q^{38} -3.81042i q^{39} +(3.96005 + 4.93133i) q^{40} -1.59630i q^{41} +(-1.97164 + 1.56608i) q^{42} +(-8.06886 + 8.06886i) q^{43} +(-4.22756 - 6.78645i) q^{44} +(3.65919 + 2.25246i) q^{45} +(-0.323124 + 2.81863i) q^{46} -4.43823i q^{47} +(1.34144 + 3.93123i) q^{48} -4.06040 q^{49} +(6.63485 - 2.44515i) q^{50} +(1.39471 - 1.39471i) q^{51} +(3.88027 + 6.22896i) q^{52} +(0.481758 - 0.481758i) q^{53} +(4.49551 + 5.65968i) q^{54} +(-8.69642 + 2.06939i) q^{55} +(1.62828 - 4.56787i) q^{56} +4.25336 q^{57} +(-8.36311 - 10.5289i) q^{58} +(3.08580 + 3.08580i) q^{59} +(4.64401 - 0.0247681i) q^{60} +(3.46410 - 3.46410i) q^{61} +(1.14645 - 10.0006i) q^{62} -3.29468i q^{63} +(-6.19615 - 5.06040i) q^{64} +(7.98203 - 1.89939i) q^{65} +(-5.83285 - 0.668669i) q^{66} +(1.80454 + 1.80454i) q^{67} +(-0.859677 + 3.70023i) q^{68} +(1.47309 + 1.47309i) q^{69} +(-4.26341 - 3.34952i) q^{70} -0.379150i q^{71} +(-5.11964 - 1.82496i) q^{72} +8.37718 q^{73} +(2.80144 + 3.52691i) q^{74} +(1.62428 - 4.93164i) q^{75} +(-6.95303 + 4.33133i) q^{76} +(4.84668 + 4.84668i) q^{77} +(5.35369 + 0.613739i) q^{78} +11.2566 q^{79} +(-7.56641 + 4.76963i) q^{80} -0.457524 q^{81} +(2.24282 + 0.257114i) q^{82} +(-8.24890 - 8.24890i) q^{83} +(-1.88279 - 3.02242i) q^{84} +(3.61685 + 2.22640i) q^{85} +(-10.0372 - 12.6365i) q^{86} -9.87341 q^{87} +(10.2160 - 4.84668i) q^{88} +11.9820i q^{89} +(-3.75411 + 4.77840i) q^{90} +(-4.44854 - 4.44854i) q^{91} +(-3.90816 - 0.907986i) q^{92} +(-5.22654 - 5.22654i) q^{93} +(6.23577 + 0.714859i) q^{94} +(2.12019 + 8.90989i) q^{95} +(-5.73948 + 1.25154i) q^{96} -6.50543i q^{97} +(0.654003 - 5.70491i) q^{98} +(5.43213 - 5.43213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6}+O(q^{10}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36} + 24 q^{40} - 8 q^{44} + 8 q^{45} - 28 q^{46} + 16 q^{49} + 24 q^{50} - 16 q^{51} + 40 q^{54} - 56 q^{56} - 24 q^{59} + 48 q^{60} - 16 q^{64} - 72 q^{66} + 32 q^{69} + 20 q^{70} + 48 q^{75} - 88 q^{76} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 80 q^{84} - 28 q^{86} - 84 q^{90} - 16 q^{91} + 12 q^{94} + 32 q^{95} + 56 q^{96} + 88 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.161069	+	1.40501i	−0.113893	+	0.993493i
$2$	−0.161069	+	1.40501i	−0.113893	+	0.993493i
$3$	0.734294	+	0.734294i	0.423945	+	0.423945i	0.886559	−	0.462615i	$-0.153089\pi$
$3$	0.734294	+	0.734294i	0.423945	+	0.423945i	−0.462615	+	0.886559i	$0.653089\pi$
$4$	−1.94811	−	0.452606i	−0.974057	−	0.226303i
$5$	−1.17216	+	1.90421i	−0.524207	+	0.851591i
$5$	−1.17216	+	1.90421i	−0.524207	+	0.851591i
$6$	−1.14996	+	0.913419i	−0.469470	+	0.372902i
$7$	1.71452			0.648029			0.324015	−	0.946052i	$-0.394967\pi$
$7$	1.71452			0.648029			0.324015	+	0.946052i	$0.394967\pi$
$8$	0.949697	−	2.66422i	0.335768	−	0.941945i
$9$		−	1.92163i		−	0.640542i
$10$	−2.48664	−	1.95361i	−0.786346	−	0.617786i
$11$	2.82684	+	2.82684i	0.852324	+	0.852324i	0.990419	−	0.138095i	$-0.0440980\pi$
$11$	2.82684	+	2.82684i	0.852324	+	0.852324i	−0.138095	+	0.990419i	$0.544098\pi$
$12$	−1.09814	−	1.76283i	−0.317006	−	0.508886i
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	0.248909	−	0.968527i	$-0.419928\pi$
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	−0.968527	+	0.248909i	$0.919928\pi$
$14$	−0.276156	+	2.40893i	−0.0738058	+	0.643813i
$15$	−2.25896	+	0.537540i	−0.583262	+	0.138792i
$16$	3.59030	+	1.76346i	0.897574	+	0.440864i
$17$		−	1.89939i		−	0.460671i	−0.973111	−	0.230335i	$-0.926018\pi$
$17$		−	1.89939i		−	0.460671i	0.973111	−	0.230335i	$-0.0739823\pi$
$18$	2.69991	+	0.309513i	0.636374	+	0.0729530i
$19$	2.89623	−	2.89623i	0.664440	−	0.664440i	−0.291983	−	0.956423i	$-0.594315\pi$
$19$	2.89623	−	2.89623i	0.664440	−	0.664440i	0.956423	+	0.291983i	$0.0943151\pi$
$20$	3.14537	−	3.17910i	0.703326	−	0.710868i
$21$	1.25896	+	1.25896i	0.274729	+	0.274729i
$22$	−4.42705	+	3.51643i	−0.943851	+	0.749704i
$23$	2.00613			0.418306			0.209153	−	0.977883i	$-0.432929\pi$
$23$	2.00613			0.418306			0.209153	+	0.977883i	$0.432929\pi$
$24$	2.65368	−	1.25896i	0.541680	−	0.256985i
$25$	−2.25207	−	4.46410i	−0.450413	−	0.892820i
$26$	4.06338	−	3.22756i	0.796895	−	0.632976i
$27$	3.61392	−	3.61392i	0.695499	−	0.695499i
$28$	−3.34009	−	0.776005i	−0.631218	−	0.146651i
$29$	−6.72307	+	6.72307i	−1.24844	+	1.24844i	−0.292034	+	0.956408i	$0.594332\pi$
$29$	−6.72307	+	6.72307i	−1.24844	+	1.24844i	−0.956408	+	0.292034i	$0.905668\pi$
$30$	−0.391402	−	3.26045i	−0.0714599	−	0.595274i
$31$	−7.11778			−1.27839			−0.639195	−	0.769044i	$-0.720732\pi$
$31$	−7.11778			−1.27839			−0.639195	+	0.769044i	$0.720732\pi$
$32$	−3.05596	+	4.76037i	−0.540223	+	0.841522i
$33$			4.15146i			0.722676i
$34$	2.66867	+	0.305932i	0.457673	+	0.0524670i
$35$	−2.00970	+	3.26482i	−0.339702	+	0.551856i
$36$	−0.869740	+	3.74355i	−0.144957	+	0.623924i
$37$	2.25207	−	2.25207i	0.370237	−	0.370237i	−0.497326	−	0.867564i	$-0.665685\pi$
$37$	2.25207	−	2.25207i	0.370237	−	0.370237i	0.867564	+	0.497326i	$0.165685\pi$
$38$	3.60274	+	4.53572i	0.584442	+	0.735792i
$39$		−	3.81042i		−	0.610156i
$40$	3.96005	+	4.93133i	0.626139	+	0.779712i
$41$		−	1.59630i		−	0.249301i	−0.992201	−	0.124650i	$-0.960219\pi$
$41$		−	1.59630i		−	0.249301i	0.992201	−	0.124650i	$-0.0397809\pi$
$42$	−1.97164	+	1.56608i	−0.304231	+	0.241651i
$43$	−8.06886	+	8.06886i	−1.23049	+	1.23049i	−0.266715	+	0.963776i	$0.585938\pi$
$43$	−8.06886	+	8.06886i	−1.23049	+	1.23049i	−0.963776	+	0.266715i	$0.914062\pi$
$44$	−4.22756	−	6.78645i	−0.637328	−	1.02310i
$45$	3.65919	+	2.25246i	0.545480	+	0.335777i
$46$	−0.323124	+	2.81863i	−0.0476420	+	0.415585i
$47$		−	4.43823i		−	0.647383i	−0.946163	−	0.323691i	$-0.895076\pi$
$47$		−	4.43823i		−	0.647383i	0.946163	−	0.323691i	$-0.104924\pi$
$48$	1.34144	+	3.93123i	0.193620	+	0.567424i
$49$	−4.06040			−0.580058
$50$	6.63485	−	2.44515i	0.938310	−	0.345797i
$51$	1.39471	−	1.39471i	0.195299	−	0.195299i
$52$	3.88027	+	6.22896i	0.538097	+	0.863801i
$53$	0.481758	−	0.481758i	0.0661746	−	0.0661746i	−0.673245	−	0.739420i	$-0.735100\pi$
$53$	0.481758	−	0.481758i	0.0661746	−	0.0661746i	0.739420	+	0.673245i	$0.235100\pi$
$54$	4.49551	+	5.65968i	0.611761	+	0.770186i
$55$	−8.69642	+	2.06939i	−1.17263	+	0.279036i
$56$	1.62828	−	4.56787i	0.217588	−	0.610408i
$57$	4.25336			0.563372
$58$	−8.36311	−	10.5289i	−1.09813	−	1.38251i
$59$	3.08580	+	3.08580i	0.401737	+	0.401737i	0.878845	−	0.477108i	$-0.158315\pi$
$59$	3.08580	+	3.08580i	0.401737	+	0.401737i	−0.477108	+	0.878845i	$0.658315\pi$
$60$	4.64401	−	0.0247681i	0.599540	−	0.00319755i
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	−0.449665	−	0.893197i	$-0.648457\pi$
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	0.893197	+	0.449665i	$0.148457\pi$
$62$	1.14645	−	10.0006i	0.145599	−	1.27007i
$63$		−	3.29468i		−	0.415090i
$64$	−6.19615	−	5.06040i	−0.774519	−	0.632551i
$65$	7.98203	−	1.89939i	0.990049	−	0.235591i
$66$	−5.83285	−	0.668669i	−0.717974	−	0.0823075i
$67$	1.80454	+	1.80454i	0.220460	+	0.220460i	0.808692	−	0.588232i	$-0.200176\pi$
$67$	1.80454	+	1.80454i	0.220460	+	0.220460i	−0.588232	+	0.808692i	$0.700176\pi$
$68$	−0.859677	+	3.70023i	−0.104251	+	0.448719i
$69$	1.47309	+	1.47309i	0.177339	+	0.177339i
$70$	−4.26341	−	3.34952i	−0.509575	−	0.400344i
$71$		−	0.379150i		−	0.0449969i	−0.999747	−	0.0224984i	$-0.992838\pi$
$71$		−	0.379150i		−	0.0449969i	0.999747	−	0.0224984i	$-0.00716208\pi$
$72$	−5.11964	−	1.82496i	−0.603355	−	0.215074i
$73$	8.37718			0.980475			0.490237	−	0.871589i	$-0.336910\pi$
$73$	8.37718			0.980475			0.490237	+	0.871589i	$0.336910\pi$
$74$	2.80144	+	3.52691i	0.325661	+	0.409995i
$75$	1.62428	−	4.93164i	0.187556	−	0.569456i
$76$	−6.95303	+	4.33133i	−0.797567	+	0.496838i
$77$	4.84668	+	4.84668i	0.552331	+	0.552331i
$78$	5.35369	+	0.613739i	0.606186	+	0.0694923i
$79$	11.2566			1.26646			0.633231	−	0.773963i	$-0.281728\pi$
$79$	11.2566			1.26646			0.633231	+	0.773963i	$0.281728\pi$
$80$	−7.56641	+	4.76963i	−0.845951	+	0.533261i
$81$	−0.457524			−0.0508360
$82$	2.24282	+	0.257114i	0.247678	+	0.0283935i
$83$	−8.24890	−	8.24890i	−0.905435	−	0.905435i	0.0904649	−	0.995900i	$-0.471165\pi$
$83$	−8.24890	−	8.24890i	−0.905435	−	0.905435i	−0.995900	+	0.0904649i	$0.971165\pi$
$84$	−1.88279	−	3.02242i	−0.205429	−	0.329773i
$85$	3.61685	+	2.22640i	0.392303	+	0.241487i
$86$	−10.0372	−	12.6365i	−1.08234	−	1.36263i
$87$	−9.87341			−1.05854
$88$	10.2160	−	4.84668i	1.08903	−	0.516658i
$89$			11.9820i			1.27009i	0.772474	+	0.635046i	$0.219019\pi$
$89$			11.9820i			1.27009i	−0.772474	+	0.635046i	$0.780981\pi$
$90$	−3.75411	+	4.77840i	−0.395718	+	0.503688i
$91$	−4.44854	−	4.44854i	−0.466334	−	0.466334i
$92$	−3.90816	−	0.907986i	−0.407454	−	0.0946640i
$93$	−5.22654	−	5.22654i	−0.541967	−	0.541967i
$94$	6.23577	+	0.714859i	0.643170	+	0.0737321i
$95$	2.12019	+	8.90989i	0.217526	+	0.914136i
$96$	−5.73948	+	1.25154i	−0.585783	+	0.127734i
$97$		−	6.50543i		−	0.660526i	−0.943889	−	0.330263i	$-0.892863\pi$
$97$		−	6.50543i		−	0.660526i	0.943889	−	0.330263i	$-0.107137\pi$
$98$	0.654003	−	5.70491i	0.0660643	−	0.576283i
$99$	5.43213	−	5.43213i	0.545949	−	0.545949i
$100$	2.36680	+	9.71588i	0.236680	+	0.971588i
$101$	−6.72307	−	6.72307i	−0.668970	−	0.668970i	0.288508	−	0.957478i	$-0.406841\pi$
$101$	−6.72307	−	6.72307i	−0.668970	−	0.668970i	−0.957478	+	0.288508i	$0.906841\pi$
$102$	1.73494	+	2.18423i	0.171785	+	0.216271i
$103$	15.1733			1.49506			0.747532	−	0.664225i	$-0.231238\pi$
$103$	15.1733			1.49506			0.747532	+	0.664225i	$0.231238\pi$
$104$	−9.37674	+	4.44854i	−0.919465	+	0.436215i
$105$	−3.87305	+	0.921626i	−0.377971	+	0.0899415i
$106$	0.599280	+	0.754472i	0.0582072	+	0.0732808i
$107$	−1.69781	+	1.69781i	−0.164134	+	0.164134i	−0.784395	−	0.620262i	$-0.787026\pi$
$107$	−1.69781	+	1.69781i	−0.164134	+	0.164134i	0.620262	+	0.784395i	$0.287026\pi$
$108$	−8.67601	+	5.40464i	−0.834849	+	0.520062i
$109$	3.11120	−	3.11120i	0.297999	−	0.297999i	−0.542231	−	0.840230i	$-0.682420\pi$
$109$	3.11120	−	3.11120i	0.297999	−	0.297999i	0.840230	+	0.542231i	$0.182420\pi$
$110$	−1.50680	−	12.5519i	−0.143667	−	1.19678i
$111$	3.30735			0.313920
$112$	6.15565	+	3.02349i	0.581654	+	0.285693i
$113$			15.8259i			1.48877i	0.667748	+	0.744387i	$0.267258\pi$
$113$			15.8259i			1.48877i	−0.667748	+	0.744387i	$0.732742\pi$
$114$	−0.685083	+	5.97602i	−0.0641639	+	0.559706i
$115$	−2.35151	+	3.82010i	−0.219279	+	0.356226i
$116$	16.1402	−	10.0544i	1.49858	−	0.933527i
$117$	−4.98589	+	4.98589i	−0.460946	+	0.460946i
$118$	−4.83261	+	3.83856i	−0.444878	+	0.353368i
$119$		−	3.25656i		−	0.298528i
$120$	−0.713205	+	6.52888i	−0.0651064	+	0.596003i
$121$			4.98203i			0.452912i
$122$	4.30914	+	5.42506i	0.390132	+	0.491162i
$123$	1.17216	−	1.17216i	0.105690	−	0.105690i
$124$	13.8662	+	3.22155i	1.24523	+	0.289304i
$125$	11.1404	+	0.944243i	0.996427	+	0.0844556i
$126$	4.62906	+	0.530669i	0.412389	+	0.0472757i
$127$			18.3239i			1.62598i	0.582276	+	0.812991i	$0.302162\pi$
$127$			18.3239i			1.62598i	−0.582276	+	0.812991i	$0.697838\pi$
$128$	8.10793	−	7.89059i	0.716647	−	0.697436i
$129$	−11.8498			−1.04332
$130$	1.38302	+	11.5208i	0.121298	+	1.01044i
$131$	−10.2036	+	10.2036i	−0.891491	+	0.891491i	−0.994663	−	0.103172i	$-0.967101\pi$
$131$	−10.2036	+	10.2036i	−0.891491	+	0.891491i	0.103172	+	0.994663i	$0.467101\pi$
$132$	1.87898	−	8.08751i	0.163544	−	0.703928i
$133$	4.96565	−	4.96565i	0.430577	−	0.430577i
$134$	−2.82606	+	2.24475i	−0.244134	+	0.193917i
$135$	2.64557	+	11.1178i	0.227695	+	0.956866i
$136$	−5.06040	−	1.80385i	−0.433926	−	0.154679i
$137$	−14.9845			−1.28021			−0.640107	−	0.768286i	$-0.721110\pi$
$137$	−14.9845			−1.28021			−0.640107	+	0.768286i	$0.721110\pi$
$138$	−2.30697	+	1.83244i	−0.196382	+	0.155987i
$139$	−8.29094	−	8.29094i	−0.703228	−	0.703228i	0.261874	−	0.965102i	$-0.415660\pi$
$139$	−8.29094	−	8.29094i	−0.703228	−	0.703228i	−0.965102	+	0.261874i	$0.915660\pi$
$140$	5.39281	−	5.45064i	0.455776	−	0.460663i
$141$	3.25896	−	3.25896i	0.274454	−	0.274454i
$142$	0.532711	+	0.0610692i	0.0447041	+	0.00512481i
$143$		−	14.6691i		−	1.22670i
$144$	3.38870	−	6.89920i	0.282392	−	0.574934i
$145$	−4.92163	−	20.6827i	−0.408719	−	1.71760i
$146$	−1.34930	+	11.7700i	−0.111669	+	0.974095i
$147$	−2.98153	−	2.98153i	−0.245912	−	0.245912i
$148$	−5.40658	+	3.36798i	−0.444418	+	0.276846i
$149$	−7.30735	−	7.30735i	−0.598642	−	0.598642i	0.341309	−	0.939951i	$-0.389130\pi$
$149$	−7.30735	−	7.30735i	−0.598642	−	0.598642i	−0.939951	+	0.341309i	$0.889130\pi$
$150$	6.66739	+	3.07647i	0.544390	+	0.251193i
$151$			4.56873i			0.371798i	0.982569	+	0.185899i	$0.0595197\pi$
$151$			4.56873i			0.371798i	−0.982569	+	0.185899i	$0.940480\pi$
$152$	−4.96565	−	10.4667i	−0.402768	−	0.848964i
$153$	−3.64992			−0.295079
$154$	−7.59030	+	6.02900i	−0.611643	+	0.485831i
$155$	8.34320	−	13.5538i	0.670142	−	1.08867i
$156$	−1.72462	+	7.42314i	−0.138080	+	0.594327i
$157$	−1.52966	−	1.52966i	−0.122080	−	0.122080i	0.643427	−	0.765507i	$-0.277512\pi$
$157$	−1.52966	−	1.52966i	−0.122080	−	0.122080i	−0.765507	+	0.643427i	$0.777512\pi$
$158$	−1.81308	+	15.8156i	−0.144241	+	1.25822i
$159$	0.707504			0.0561087
$160$	−5.48268	−	11.3991i	−0.433444	−	0.901181i
$161$	3.43955			0.271075
$162$	0.0736928	−	0.642827i	0.00578985	−	0.0505053i
$163$	10.1361	+	10.1361i	0.793918	+	0.793918i	0.982129	−	0.188211i	$-0.0602689\pi$
$163$	10.1361	+	10.1361i	0.793918	+	0.793918i	−0.188211	+	0.982129i	$0.560269\pi$
$164$	−0.722497	+	3.10978i	−0.0564175	+	0.242833i
$165$	−7.90527	−	4.86619i	−0.615424	−	0.378832i
$166$	12.9184	−	10.2612i	1.00267	−	0.796421i
$167$	2.57967			0.199621			0.0998105	−	0.995006i	$-0.468176\pi$
$167$	2.57967			0.199621			0.0998105	+	0.995006i	$0.468176\pi$
$168$	4.54979	−	2.15853i	0.351024	−	0.166534i
$169$			0.464102i			0.0357001i
$170$	−3.71068	+	4.72312i	−0.284596	+	0.362246i
$171$	−5.56547	−	5.56547i	−0.425602	−	0.425602i
$172$	19.3711	−	12.0670i	1.47703	−	0.920104i
$173$	−14.1773	−	14.1773i	−1.07788	−	1.07788i	−0.996700	−	0.0811779i	$-0.974132\pi$
$173$	−14.1773	−	14.1773i	−1.07788	−	1.07788i	−0.0811779	−	0.996700i	$-0.525868\pi$
$174$	1.59030	−	13.8723i	0.120560	−	1.05165i
$175$	−3.86122	−	7.65381i	−0.291881	−	0.578574i
$176$	5.16418	+	15.1342i	0.389264	+	1.14078i
$177$			4.53177i			0.340629i
$178$	−16.8349	−	1.92993i	−1.26183	−	0.144654i
$179$	−9.88067	+	9.88067i	−0.738516	+	0.738516i	−0.972291	−	0.233775i	$-0.924892\pi$
$179$	−9.88067	+	9.88067i	−0.738516	+	0.738516i	0.233775	+	0.972291i	$0.424892\pi$
$180$	−6.10904	−	6.04422i	−0.455341	−	0.450510i
$181$	6.20514	+	6.20514i	0.461224	+	0.461224i	0.899057	−	0.437832i	$-0.144254\pi$
$181$	6.20514	+	6.20514i	0.461224	+	0.461224i	−0.437832	+	0.899057i	$0.644254\pi$
$182$	6.96677	−	5.53373i	0.516411	−	0.410187i
$183$	5.08733			0.376067
$184$	1.90521	−	5.34477i	0.140454	−	0.394021i
$185$	1.64863	+	6.92820i	0.121209	+	0.509372i
$186$	8.18518	−	6.50152i	0.600166	−	0.476714i
$187$	5.36928	−	5.36928i	0.392641	−	0.392641i
$188$	−2.00877	+	8.64618i	−0.146505	+	0.630587i
$189$	6.19615	−	6.19615i	0.450704	−	0.450704i
$190$	−12.8600	+	1.54378i	−0.932962	+	0.111998i
$191$	18.9282			1.36960			0.684798	−	0.728733i	$-0.259890\pi$
$191$	18.9282			1.36960			0.684798	+	0.728733i	$0.259890\pi$
$192$	−0.833972	−	8.26562i	−0.0601868	−	0.596520i
$193$			4.42987i			0.318869i	0.987209	+	0.159434i	$0.0509670\pi$
$193$			4.42987i			0.318869i	−0.987209	+	0.159434i	$0.949033\pi$
$194$	9.14020	+	1.04782i	0.656228	+	0.0752291i
$195$	7.25587	+	4.46644i	0.519603	+	0.319849i
$196$	7.91013	+	1.83776i	0.565009	+	0.131269i
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	−0.897179	−	0.441667i	$-0.854387\pi$
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	0.441667	+	0.897179i	$0.354387\pi$
$198$	6.75725	+	8.50714i	0.480217	+	0.604576i
$199$			5.85641i			0.415150i	0.978219	+	0.207575i	$0.0665570\pi$
$199$			5.85641i			0.415150i	−0.978219	+	0.207575i	$0.933443\pi$
$200$	−14.0321	+	1.76046i	−0.992222	+	0.124483i
$201$			2.65013i			0.186926i
$202$	10.5289	−	8.36311i	0.740808	−	0.588426i
$203$	−11.5269	+	11.5269i	−0.809027	+	0.809027i
$204$	−3.34831	+	2.08580i	−0.234429	+	0.146035i
$205$	3.03970	+	1.87113i	0.212302	+	0.130685i
$206$	−2.44393	+	21.3186i	−0.170277	+	1.48534i
$207$		−	3.85503i		−	0.267943i
$208$	−4.73995	−	13.8910i	−0.328656	−	0.963164i
$209$	16.3743			1.13264
$210$	−0.671068	−	5.59013i	−0.0463081	−	0.385755i
$211$	7.60373	−	7.60373i	0.523462	−	0.523462i	−0.395153	−	0.918615i	$-0.629308\pi$
$211$	7.60373	−	7.60373i	0.523462	−	0.523462i	0.918615	+	0.395153i	$0.129308\pi$
$212$	−1.15657	+	0.720473i	−0.0794334	+	0.0494823i
$213$	0.278408	−	0.278408i	0.0190762	−	0.0190762i
$214$	−2.11198	−	2.65891i	−0.144372	−	0.181759i
$215$	−5.90682	−	24.8229i	−0.402842	−	1.69291i
$216$	−6.19615	−	13.0604i	−0.421595	−	0.888648i
$217$	−12.2036			−0.828435
$218$	3.87016	+	4.87239i	0.262120	+	0.330000i
$219$	6.15131	+	6.15131i	0.415667	+	0.415667i
$220$	17.8782	−	0.0953508i	1.20535	−	0.00642855i
$221$	−4.92820	+	4.92820i	−0.331507	+	0.331507i
$222$	−0.532711	+	4.64687i	−0.0357532	+	0.311877i
$223$			9.22430i			0.617705i	0.951110	+	0.308853i	$0.0999450\pi$
$223$			9.22430i			0.617705i	−0.951110	+	0.308853i	$0.900055\pi$
$224$	−5.23952	+	8.16177i	−0.350080	+	0.545331i
$225$	−8.57833	+	4.32763i	−0.571889	+	0.288508i
$226$	−22.2356	−	2.54905i	−1.47909	−	0.169560i
$227$	9.21725	+	9.21725i	0.611770	+	0.611770i	0.943407	−	0.331637i	$-0.107601\pi$
$227$	9.21725	+	9.21725i	0.611770	+	0.611770i	−0.331637	+	0.943407i	$0.607601\pi$
$228$	−8.28603	−	1.92510i	−0.548756	−	0.127493i
$229$	1.63811	+	1.63811i	0.108250	+	0.108250i	0.759157	−	0.650907i	$-0.225611\pi$
$229$	1.63811	+	1.63811i	0.108250	+	0.108250i	−0.650907	+	0.759157i	$0.725611\pi$
$230$	−4.98852	−	3.91919i	−0.328934	−	0.258424i
$231$			7.11778i			0.468315i
$232$	11.5269	+	24.2966i	0.756776	+	1.59515i
$233$	12.3798			0.811026			0.405513	−	0.914089i	$-0.367093\pi$
$233$	12.3798			0.811026			0.405513	+	0.914089i	$0.367093\pi$
$234$	−6.20216	−	7.80830i	−0.405448	−	0.510445i
$235$	8.45134	+	5.20233i	0.551305	+	0.339363i
$236$	−4.61484	−	7.40815i	−0.300401	−	0.482229i
$237$	8.26562	+	8.26562i	0.536910	+	0.536910i
$238$	4.57550	+	0.524529i	0.296586	+	0.0340002i
$239$	−7.77449			−0.502890			−0.251445	−	0.967872i	$-0.580906\pi$
$239$	−7.77449			−0.502890			−0.251445	+	0.967872i	$0.580906\pi$
$240$	−9.05828	−	2.05366i	−0.584709	−	0.132563i
$241$	−3.47068			−0.223566			−0.111783	−	0.993733i	$-0.535656\pi$
$241$	−3.47068			−0.223566			−0.111783	+	0.993733i	$0.535656\pi$
$242$	−6.99981	−	0.802448i	−0.449965	−	0.0515833i
$243$	−11.1777	−	11.1777i	−0.717051	−	0.717051i
$244$	−8.31634	+	5.18059i	−0.532399	+	0.331653i
$245$	4.75946	−	7.73188i	0.304071	−	0.493972i
$246$	1.45809	+	1.83569i	0.0929647	+	0.117039i
$247$	−15.0292			−0.956286
$248$	−6.75973	+	18.9633i	−0.429243	+	1.20417i
$249$		−	12.1142i		−	0.767708i
$250$	−3.12104	+	15.5003i	−0.197392	+	0.980325i
$251$	8.94765	+	8.94765i	0.564771	+	0.564771i	0.930659	−	0.365888i	$-0.119235\pi$
$251$	8.94765	+	8.94765i	0.564771	+	0.564771i	−0.365888	+	0.930659i	$0.619235\pi$
$252$	−1.49119	+	6.41840i	−0.0939362	+	0.404321i
$253$	5.67100	+	5.67100i	0.356533	+	0.356533i
$254$	−25.7453	−	2.95140i	−1.61540	−	0.185187i
$255$	1.02100	+	4.29066i	0.0639375	+	0.268692i
$256$	9.78044	+	12.6627i	0.611277	+	0.791416i
$257$			3.62228i			0.225952i	0.993598	+	0.112976i	$0.0360383\pi$
$257$			3.62228i			0.225952i	−0.993598	+	0.112976i	$0.963962\pi$
$258$	1.90863	−	16.6491i	0.118826	−	1.03653i
$259$	3.86122	−	3.86122i	0.239925	−	0.239925i
$260$	−16.4096	+	0.0875179i	−1.01768	+	0.00542763i
$261$	12.9192	+	12.9192i	0.799680	+	0.799680i
$262$	−12.6927	−	15.9796i	−0.784156	−	0.987224i
$263$	13.7416			0.847345			0.423673	−	0.905815i	$-0.360741\pi$
$263$	13.7416			0.847345			0.423673	+	0.905815i	$0.360741\pi$
$264$	11.0604	+	3.94263i	0.680721	+	0.242652i
$265$	0.352672	+	1.48207i	0.0216644	+	0.0910429i
$266$	6.17699	+	7.77661i	0.378736	+	0.476815i
$267$	−8.79833	+	8.79833i	−0.538449	+	0.538449i
$268$	−2.69871	−	4.33221i	−0.164850	−	0.264632i
$269$	−4.22240	+	4.22240i	−0.257444	+	0.257444i	−0.824014	−	0.566570i	$-0.808270\pi$
$269$	−4.22240	+	4.22240i	−0.257444	+	0.257444i	0.566570	+	0.824014i	$0.308270\pi$
$270$	−16.0467	+	1.92633i	−0.976572	+	0.117233i
$271$	−5.40015			−0.328036			−0.164018	−	0.986457i	$-0.552445\pi$
$271$	−5.40015			−0.328036			−0.164018	+	0.986457i	$0.552445\pi$
$272$	3.34950	−	6.81938i	0.203093	−	0.413486i
$273$		−	6.53307i		−	0.395399i
$274$	2.41353	−	21.0534i	0.145807	−	1.27188i
$275$	6.25307	−	18.9855i	0.377074	−	1.14487i
$276$	−2.20301	−	3.53647i	−0.132606	−	0.212870i
$277$	5.08733	−	5.08733i	0.305668	−	0.305668i	−0.537558	−	0.843227i	$-0.680653\pi$
$277$	5.08733	−	5.08733i	0.305668	−	0.305668i	0.843227	+	0.537558i	$0.180653\pi$
$278$	12.9843	−	10.3135i	0.778745	−	0.618560i
$279$			13.6777i			0.818863i
$280$	6.78960	+	8.45489i	0.405756	+	0.505276i
$281$		−	21.2780i		−	1.26934i	−0.772784	−	0.634669i	$-0.781136\pi$
$281$		−	21.2780i		−	1.26934i	0.772784	−	0.634669i	$-0.218864\pi$
$282$	4.05397	+	5.10380i	0.241410	+	0.303927i
$283$	−4.08521	+	4.08521i	−0.242840	+	0.242840i	−0.818024	−	0.575184i	$-0.804931\pi$
$283$	−4.08521	+	4.08521i	−0.242840	+	0.242840i	0.575184	+	0.818024i	$0.304931\pi$
$284$	−0.171606	+	0.738628i	−0.0101829	+	0.0438295i
$285$	−4.98564	+	8.09931i	−0.295324	+	0.479762i
$286$	20.6103	+	2.36274i	1.21871	+	0.139712i
$287$		−	2.73690i		−	0.161554i
$288$	9.14765	+	5.87241i	0.539030	+	0.346035i
$289$	13.3923			0.787783
$290$	29.8521	−	3.58361i	1.75298	−	0.210437i
$291$	4.77689	−	4.77689i	0.280026	−	0.280026i
$292$	−16.3197	−	3.79156i	−0.955038	−	0.221884i
$293$	7.40400	−	7.40400i	0.432547	−	0.432547i	−0.456947	−	0.889494i	$-0.651057\pi$
$293$	7.40400	−	7.40400i	0.432547	−	0.432547i	0.889494	+	0.456947i	$0.151057\pi$
$294$	4.66931	−	3.70885i	0.272320	−	0.216305i
$295$	−9.49310	+	2.25896i	−0.552709	+	0.131522i
$296$	−3.86122	−	8.13878i	−0.224429	−	0.473057i
$297$	20.4319			1.18558
$298$	11.4439	−	9.08993i	0.662927	−	0.526566i
$299$	−5.20514	−	5.20514i	−0.301021	−	0.301021i
$300$	−5.39638	+	8.87223i	−0.311560	+	0.512238i
$301$	−13.8343	+	13.8343i	−0.797394	+	0.797394i
$302$	−6.41911	−	0.735878i	−0.369378	−	0.0423450i
$303$		−	9.87341i		−	0.567212i
$304$	15.5057	−	5.29094i	0.889312	−	0.303456i
$305$	2.53590	+	10.6569i	0.145205	+	0.610212i
$306$	0.587888	−	5.12818i	0.0336073	−	0.293159i
$307$	−16.6634	−	16.6634i	−0.951030	−	0.951030i	0.0478262	−	0.998856i	$-0.484771\pi$
$307$	−16.6634	−	16.6634i	−0.951030	−	0.951030i	−0.998856	+	0.0478262i	$0.984771\pi$
$308$	−7.24825	−	11.6355i	−0.413008	−	0.662996i
$309$	11.1416	+	11.1416i	0.633825	+	0.633825i
$310$	17.6994	+	13.9054i	1.00526	+	0.789772i
$311$		−	21.9072i		−	1.24224i	−0.783714	−	0.621122i	$-0.786677\pi$
$311$		−	21.9072i		−	1.24224i	0.783714	−	0.621122i	$-0.213323\pi$
$312$	−10.1518	−	3.61875i	−0.574733	−	0.204871i
$313$	12.4820			0.705525			0.352763	−	0.935713i	$-0.385242\pi$
$313$	12.4820			0.705525			0.352763	+	0.935713i	$0.385242\pi$
$314$	2.39556	−	1.90280i	0.135189	−	0.107381i
$315$	6.27377	+	3.86190i	0.353487	+	0.217593i
$316$	−21.9291	−	5.09479i	−1.23361	−	0.286604i
$317$	−4.24325	−	4.24325i	−0.238324	−	0.238324i	0.577832	−	0.816156i	$-0.303899\pi$
$317$	−4.24325	−	4.24325i	−0.238324	−	0.238324i	−0.816156	+	0.577832i	$0.803899\pi$
$318$	−0.113957	+	0.994051i	−0.00639037	+	0.0557436i
$319$	−38.0100			−2.12815
$320$	16.8990	−	5.86718i	0.944683	−	0.327985i
$321$	−2.49338			−0.139167
$322$	−0.554004	+	4.83261i	−0.0308734	+	0.269311i
$323$	−5.50108	−	5.50108i	−0.306088	−	0.306088i
$324$	0.891310	+	0.207078i	0.0495172	+	0.0115044i
$325$	−5.73939	+	17.4259i	−0.318364	+	0.966615i
$326$	−15.8739	+	12.6087i	−0.879173	+	0.698330i
$327$	4.56907			0.252670
$328$	−4.25290	−	1.51600i	−0.234827	−	0.0837073i
$329$		−	7.60946i		−	0.419523i
$330$	8.11034	−	10.3232i	0.446460	−	0.568273i
$331$	1.10377	+	1.10377i	0.0606688	+	0.0606688i	0.736790	−	0.676121i	$-0.236341\pi$
$331$	1.10377	+	1.10377i	0.0606688	+	0.0606688i	−0.676121	+	0.736790i	$0.736341\pi$
$332$	12.3363	+	19.8033i	0.677042	+	1.08685i
$333$	−4.32763	−	4.32763i	−0.237152	−	0.237152i
$334$	−0.415504	+	3.62447i	−0.0227354	+	0.198322i
$335$	−5.55146	+	1.32102i	−0.303309	+	0.0721749i
$336$	2.29992	+	6.74018i	0.125471	+	0.367707i
$337$		−	7.47635i		−	0.407263i	−0.979048	−	0.203631i	$-0.934726\pi$
$337$		−	7.47635i		−	0.407263i	0.979048	−	0.203631i	$-0.0652744\pi$
$338$	−0.652068	−	0.0747522i	−0.0354678	−	0.00406598i
$339$	−11.6208	+	11.6208i	−0.631158	+	0.631158i
$340$	−6.03836	−	5.97429i	−0.327476	−	0.324001i
$341$	−20.1208	−	20.1208i	−1.08960	−	1.08960i
$342$	8.71597	−	6.92312i	0.471305	−	0.374360i
$343$	−18.9633			−1.02392
$344$	13.8343	+	29.1602i	0.745894	+	1.57221i
$345$	−4.53177	+	1.07837i	−0.243982	+	0.0580577i
$346$	22.2027	−	17.6357i	1.19363	−	0.948102i
$347$	8.56074	−	8.56074i	0.459565	−	0.459565i	−0.438948	−	0.898512i	$-0.644649\pi$
$347$	8.56074	−	8.56074i	0.459565	−	0.459565i	0.898512	+	0.438948i	$0.144649\pi$
$348$	19.2345	+	4.46877i	1.03108	+	0.239551i
$349$	7.91567	−	7.91567i	0.423716	−	0.423716i	−0.462765	−	0.886481i	$-0.653143\pi$
$349$	7.91567	−	7.91567i	0.423716	−	0.423716i	0.886481	+	0.462765i	$0.153143\pi$
$350$	11.3756	−	4.19227i	0.608052	−	0.224086i
$351$	−18.7535			−1.00099
$352$	−22.0955	+	4.81809i	−1.17769	+	0.256805i
$353$		−	9.67314i		−	0.514849i	−0.966298	−	0.257425i	$-0.917126\pi$
$353$		−	9.67314i		−	0.514849i	0.966298	−	0.257425i	$-0.0828739\pi$
$354$	−6.36719	−	0.729926i	−0.338412	−	0.0387951i
$355$	0.721984	+	0.444426i	0.0383189	+	0.0235877i
$356$	5.42314	−	23.3424i	0.287426	−	1.23714i
$357$	2.39127	−	2.39127i	0.126559	−	0.126559i
$358$	−12.2910	−	15.4739i	−0.649599	−	0.817822i
$359$		−	17.0867i		−	0.901799i	−0.892575	−	0.450900i	$-0.851103\pi$
$359$		−	17.0867i		−	0.901799i	0.892575	−	0.450900i	$-0.148897\pi$
$360$	9.47617	−	7.60973i	0.499438	−	0.401068i
$361$			2.22373i			0.117038i
$362$	−9.71774	+	7.71884i	−0.510753	+	0.405693i
$363$	−3.65827	+	3.65827i	−0.192010	+	0.192010i
$364$	6.65283	+	10.6797i	0.348703	+	0.559768i
$365$	−9.81943	+	15.9519i	−0.513972	+	0.834963i
$366$	−0.819410	+	7.14776i	−0.0428312	+	0.373620i
$367$		−	13.4500i		−	0.702086i	−0.936359	−	0.351043i	$-0.885827\pi$
$367$		−	13.4500i		−	0.702086i	0.936359	−	0.351043i	$-0.114173\pi$
$368$	7.20259	+	3.53772i	0.375461	+	0.184416i
$369$	−3.06750			−0.159688
$370$	−9.99975	+	1.20042i	−0.519862	+	0.0624070i
$371$	0.825987	−	0.825987i	0.0428831	−	0.0428831i
$372$	7.81633	+	12.5475i	0.405258	+	0.650555i
$373$	−12.0271	+	12.0271i	−0.622740	+	0.622740i	−0.946231	−	0.323491i	$-0.895143\pi$
$373$	−12.0271	+	12.0271i	−0.622740	+	0.622740i	0.323491	+	0.946231i	$0.395143\pi$
$374$	6.67908	+	8.40872i	0.345367	+	0.434804i
$375$	7.48697	+	8.87367i	0.386625	+	0.458234i
$376$	−11.8244	−	4.21497i	−0.609798	−	0.217371i
$377$	34.8876			1.79680
$378$	7.70766	+	9.70367i	0.396439	+	0.499103i
$379$	19.1552	+	19.1552i	0.983936	+	0.983936i	0.999873	−	0.0159369i	$-0.00507308\pi$
$379$	19.1552	+	19.1552i	0.983936	+	0.983936i	−0.0159369	+	0.999873i	$0.505073\pi$
$380$	−0.0976914	−	18.3171i	−0.00501146	−	0.939647i
$381$	−13.4551	+	13.4551i	−0.689327	+	0.689327i
$382$	−3.04874	+	26.5943i	−0.155987	+	1.36068i
$383$			17.7503i			0.907000i	0.891256	+	0.453500i	$0.149825\pi$
$383$			17.7503i			0.907000i	−0.891256	+	0.453500i	$0.850175\pi$
$384$	11.7476	+	0.159590i	0.599493	+	0.00814406i
$385$	−14.9102	+	3.54802i	−0.759896	+	0.180824i
$386$	−6.22401	−	0.713512i	−0.316794	−	0.0363168i
$387$	15.5053	+	15.5053i	0.788181	+	0.788181i
$388$	−2.94440	+	12.6733i	−0.149479	+	0.643390i
$389$	−1.18654	−	1.18654i	−0.0601602	−	0.0601602i	0.676387	−	0.736547i	$-0.263545\pi$
$389$	−1.18654	−	1.18654i	−0.0601602	−	0.0601602i	−0.736547	+	0.676387i	$0.763545\pi$
$390$	−7.44409	+	9.47517i	−0.376946	+	0.479794i
$391$		−	3.81042i		−	0.192701i
$392$	−3.85615	+	10.8178i	−0.194765	+	0.546382i
$393$	−14.9848			−0.755886
$394$	−7.95303	−	10.0126i	−0.400668	−	0.504427i
$395$	−13.1945	+	21.4349i	−0.663889	+	1.07851i
$396$	−13.0410	+	8.12379i	−0.655336	+	0.408236i
$397$	−4.74478	−	4.74478i	−0.238134	−	0.238134i	0.577943	−	0.816077i	$-0.303855\pi$
$397$	−4.74478	−	4.74478i	−0.238134	−	0.238134i	−0.816077	+	0.577943i	$0.803855\pi$
$398$	−8.22832	−	0.943283i	−0.412448	−	0.0472825i
$399$	7.29250			0.365081
$400$	−0.213328	−	19.9989i	−0.0106664	−	0.999943i
$401$	0.632677			0.0315944			0.0157972	−	0.999875i	$-0.494971\pi$
$401$	0.632677			0.0315944			0.0157972	+	0.999875i	$0.494971\pi$
$402$	−3.72346	−	0.426853i	−0.185709	−	0.0212895i
$403$	18.4679	+	18.4679i	0.919953	+	0.919953i
$404$	10.0544	+	16.1402i	0.500225	+	0.803005i
$405$	0.536293	−	0.871224i	0.0266486	−	0.0432915i
$406$	−14.3388	−	18.0520i	−0.711621	−	0.895905i
$407$	12.7324			0.631124
$408$	−2.39127	−	5.04038i	−0.118385	−	0.249536i
$409$		−	26.3809i		−	1.30445i	−0.758024	−	0.652226i	$-0.773835\pi$
$409$		−	26.3809i		−	1.30445i	0.758024	−	0.652226i	$-0.226165\pi$
$410$	−3.11856	+	3.96944i	−0.154015	+	0.196037i
$411$	−11.0030	−	11.0030i	−0.542739	−	0.542739i
$412$	−29.5592	−	6.86751i	−1.45628	−	0.338338i
$413$	5.29069	+	5.29069i	0.260338	+	0.260338i
$414$	5.41636	+	0.620923i	0.266199	+	0.0305167i
$415$	25.3767	−	6.03862i	1.24570	−	0.296424i
$416$	20.2804	−	4.42229i	0.994328	−	0.216821i
$417$		−	12.1760i		−	0.596260i
$418$	−2.63739	+	23.0061i	−0.128999	+	1.12527i
$419$	−1.37589	+	1.37589i	−0.0672167	+	0.0672167i	−0.739916	−	0.672699i	$-0.765135\pi$
$419$	−1.37589	+	1.37589i	−0.0672167	+	0.0672167i	0.672699	+	0.739916i	$0.265135\pi$
$420$	7.96228	−	0.0424656i	0.388519	−	0.00207211i
$421$	6.65671	+	6.65671i	0.324428	+	0.324428i	0.850463	−	0.526035i	$-0.176322\pi$
$421$	6.65671	+	6.65671i	0.324428	+	0.324428i	−0.526035	+	0.850463i	$0.676322\pi$
$422$	9.45861	+	11.9081i	0.460438	+	0.579675i
$423$	−8.52862			−0.414676
$424$	−0.825987	−	1.74104i	−0.0401135	−	0.0845522i
$425$	−8.47908	+	4.27756i	−0.411296	+	0.207492i
$426$	0.346323	+	0.436009i	0.0167794	+	0.0211247i
$427$	5.93929	−	5.93929i	0.287422	−	0.287422i
$428$	4.07597	−	2.53909i	0.197019	−	0.122731i
$429$	10.7715	−	10.7715i	0.520051	−	0.520051i
$430$	35.8278	−	4.30096i	1.72777	−	0.207411i
$431$	4.08798			0.196911			0.0984556	−	0.995141i	$-0.468610\pi$
$431$	4.08798			0.196911			0.0984556	+	0.995141i	$0.468610\pi$
$432$	19.3480	−	6.60204i	0.930882	−	0.317641i
$433$			29.2913i			1.40765i	0.710373	+	0.703826i	$0.248526\pi$
$433$			29.2913i			1.40765i	−0.710373	+	0.703826i	$0.751474\pi$
$434$	1.96562	−	17.1462i	0.0943526	−	0.823044i
$435$	11.5732	−	18.8011i	0.554895	−	0.901443i
$436$	−7.46912	+	4.65283i	−0.357706	+	0.222830i
$437$	5.81020	−	5.81020i	0.277940	−	0.277940i
$438$	−9.63344	+	7.65188i	−0.460304	+	0.365621i
$439$			26.9790i			1.28764i	0.765178	+	0.643819i	$0.222651\pi$
$439$			26.9790i			1.28764i	−0.765178	+	0.643819i	$0.777349\pi$
$440$	−2.74565	+	25.1345i	−0.130894	+	1.19824i
$441$			7.80258i			0.371551i
$442$	−6.13040	−	7.71796i	−0.291594	−	0.367106i
$443$	14.5286	−	14.5286i	0.690276	−	0.690276i	−0.272017	−	0.962293i	$-0.587691\pi$
$443$	14.5286	−	14.5286i	0.690276	−	0.690276i	0.962293	+	0.272017i	$0.0876906\pi$
$444$	−6.44310	−	1.49693i	−0.305776	−	0.0710411i
$445$	−22.8164	−	14.0449i	−1.08160	−	0.665792i
$446$	−12.9603	−	1.48575i	−0.613686	−	0.0703521i
$447$		−	10.7315i		−	0.507582i
$448$	−10.6235	−	8.67619i	−0.501911	−	0.409911i
$449$	23.1572			1.09286			0.546428	−	0.837506i	$-0.315987\pi$
$449$	23.1572			1.09286			0.546428	+	0.837506i	$0.315987\pi$
$450$	−4.69867	−	12.7497i	−0.221497	−	0.601027i
$451$	4.51249	−	4.51249i	0.212485	−	0.212485i
$452$	7.16290	−	30.8306i	0.336914	−	1.45015i
$453$	−3.35479	+	3.35479i	−0.157622	+	0.157622i
$454$	−14.4349	+	11.4657i	−0.677466	+	0.538113i
$455$	13.6854	−	3.25656i	0.641581	−	0.152670i
$456$	4.03940	−	11.3319i	0.189162	−	0.530665i
$457$	−37.7026			−1.76365			−0.881827	−	0.471572i	$-0.843687\pi$
$457$	−37.7026			−1.76365			−0.881827	+	0.471572i	$0.843687\pi$
$458$	−2.56542	+	2.03772i	−0.119874	+	0.0952165i
$459$	−6.86425	−	6.86425i	−0.320396	−	0.320396i
$460$	6.31001	−	6.37768i	0.294206	−	0.297361i
$461$	11.3737	−	11.3737i	0.529727	−	0.529727i	−0.390764	−	0.920491i	$-0.627789\pi$
$461$	11.3737	−	11.3737i	0.529727	−	0.529727i	0.920491	+	0.390764i	$0.127789\pi$
$462$	−10.0006	−	1.14645i	−0.465268	−	0.0533377i
$463$		−	7.94895i		−	0.369419i	−0.982793	−	0.184710i	$-0.940866\pi$
$463$		−	7.94895i		−	0.369419i	0.982793	−	0.184710i	$-0.0591344\pi$
$464$	−35.9936	+	12.2820i	−1.67096	+	0.570175i
$465$	16.0788	−	3.82609i	0.745637	−	0.177431i
$466$	−1.99399	+	17.3937i	−0.0923699	+	0.805749i
$467$	5.34999	+	5.34999i	0.247568	+	0.247568i	0.819972	−	0.572404i	$-0.193989\pi$
$467$	5.34999	+	5.34999i	0.247568	+	0.247568i	−0.572404	+	0.819972i	$0.693989\pi$
$468$	11.9697	−	7.45643i	0.553301	−	0.344674i
$469$	3.09394	+	3.09394i	0.142865	+	0.142865i
$470$	−8.67058	+	11.0363i	−0.399944	+	0.509067i
$471$		−	2.24643i		−	0.103510i
$472$	11.1518	−	5.29069i	0.513305	−	0.243524i
$473$	−45.6187			−2.09755
$474$	−12.9446	+	10.2820i	−0.594566	+	0.472266i
$475$	−19.4515	−	6.40656i	−0.892498	−	0.293953i
$476$	−1.47394	+	6.34414i	−0.0675578	+	0.290783i
$477$	−0.925759	−	0.925759i	−0.0423876	−	0.0423876i
$478$	1.25222	−	10.9232i	0.0572754	−	0.499617i
$479$	−9.58973			−0.438166			−0.219083	−	0.975706i	$-0.570307\pi$
$479$	−9.58973			−0.438166			−0.219083	+	0.975706i	$0.570307\pi$
$480$	4.34442	−	12.3962i	0.198295	−	0.565807i
$481$	−11.6865			−0.532859
$482$	0.559017	−	4.87634i	0.0254625	−	0.222111i
$483$	2.52564	+	2.52564i	0.114921	+	0.114921i
$484$	2.25490	−	9.70556i	0.102495	−	0.441162i
$485$	12.3877	+	7.62543i	0.562498	+	0.346253i
$486$	17.5052	−	13.9044i	0.794052	−	0.630718i
$487$	36.6487			1.66071			0.830357	−	0.557232i	$-0.188137\pi$
$487$	36.6487			1.66071			0.830357	+	0.557232i	$0.188137\pi$
$488$	−5.93929	−	12.5190i	−0.268859	−	0.566708i
$489$			14.8857i			0.673154i
$490$	10.0968	+	7.93246i	0.456126	+	0.358352i
$491$	23.4273	+	23.4273i	1.05726	+	1.05726i	0.998258	+	0.0590019i	$0.0187918\pi$
$491$	23.4273	+	23.4273i	1.05726	+	1.05726i	0.0590019	+	0.998258i	$0.481208\pi$
$492$	−2.81402	+	1.75297i	−0.126866	+	0.0790298i
$493$	12.7697	+	12.7697i	0.575120	+	0.575120i
$494$	2.42073	−	21.1162i	0.108914	−	0.950064i
$495$	3.97659	+	16.7113i	0.178735	+	0.751116i
$496$	−25.5549	−	12.5519i	−1.14745	−	0.563597i
$497$		−	0.650063i		−	0.0291593i
$498$	17.0206	+	1.95122i	0.762713	+	0.0874363i
$499$	−9.50152	+	9.50152i	−0.425346	+	0.425346i	−0.887040	−	0.461693i	$-0.847242\pi$
$499$	−9.50152	+	9.50152i	−0.425346	+	0.425346i	0.461693	+	0.887040i	$0.347242\pi$
$500$	−21.2754	−	6.88170i	−0.951464	−	0.307759i
$501$	1.89424	+	1.89424i	0.0846283	+	0.0846283i
$502$	−14.0127	+	11.1304i	−0.625419	+	0.496772i
$503$	−20.6875			−0.922411			−0.461206	−	0.887293i	$-0.652583\pi$
$503$	−20.6875			−0.922411			−0.461206	+	0.887293i	$0.652583\pi$
$504$	−8.77775	−	3.12894i	−0.390992	−	0.139374i
$505$	20.6827	−	4.92163i	0.920368	−	0.219009i
$506$	−8.88124	+	7.05440i	−0.394819	+	0.313606i
$507$	−0.340787	+	0.340787i	−0.0151349	+	0.0151349i
$508$	8.29351	−	35.6970i	0.367965	−	1.58380i
$509$	11.6381	−	11.6381i	0.515850	−	0.515850i	−0.400463	−	0.916313i	$-0.631151\pi$
$509$	11.6381	−	11.6381i	0.515850	−	0.515850i	0.916313	+	0.400463i	$0.131151\pi$
$510$	−6.19288	+	0.743426i	−0.274225	+	0.0329195i
$511$	14.3629			0.635377
$512$	−19.3665	+	11.7021i	−0.855887	+	0.517163i
$513$		−	20.9335i		−	0.924235i
$514$	−5.08935	−	0.583436i	−0.224482	−	0.0257343i
$515$	−17.7855	+	28.8931i	−0.783724	+	1.27318i
$516$	23.0848	+	5.36331i	1.01625	+	0.236106i
$517$	12.5462	−	12.5462i	0.551780	−	0.551780i
$518$	4.80314	+	6.04698i	0.211038	+	0.265689i
$519$		−	20.8205i		−	0.913921i
$520$	2.52010	−	23.0697i	0.110514	−	1.01168i
$521$			5.18654i			0.227227i	0.993525	+	0.113613i	$0.0362425\pi$
$521$			5.18654i			0.227227i	−0.993525	+	0.113613i	$0.963758\pi$
$522$	−20.2325	+	16.0708i	−0.885554	+	0.703398i
$523$	26.9589	−	26.9589i	1.17883	−	1.17883i	0.198788	−	0.980043i	$-0.436300\pi$
$523$	26.9589	−	26.9589i	1.17883	−	1.17883i	0.980043	−	0.198788i	$-0.0637004\pi$
$524$	24.4959	−	15.2595i	1.07011	−	0.666616i
$525$	2.78488	−	8.45542i	0.121542	−	0.369025i
$526$	−2.21334	+	19.3071i	−0.0965064	+	0.841832i
$527$			13.5195i			0.588917i
$528$	−7.32092	+	14.9050i	−0.318602	+	0.648655i
$529$	−18.9755			−0.825020
$530$	−2.13913	+	0.256793i	−0.0929179	+	0.0111544i
$531$	5.92976	−	5.92976i	0.257330	−	0.257330i
$532$	−11.9211	+	7.42617i	−0.516847	+	0.321965i
$533$	−4.14180	+	4.14180i	−0.179401	+	0.179401i
$534$	−10.9446	−	13.7789i	−0.473620	−	0.596271i
$535$	−1.24288	−	5.22311i	−0.0537345	−	0.225815i
$536$	6.52148	−	3.09394i	0.281685	−	0.133638i
$537$	−14.5106			−0.626179
$538$	−5.25243	−	6.61262i	−0.226448	−	0.285090i
$539$	−11.4781	−	11.4781i	−0.494397	−	0.494397i
$540$	−0.121899	−	22.8561i	−0.00524572	−	0.983570i
$541$	27.4945	−	27.4945i	1.18208	−	1.18208i	0.202878	−	0.979204i	$-0.434971\pi$
$541$	27.4945	−	27.4945i	1.18208	−	1.18208i	0.979204	−	0.202878i	$-0.0650294\pi$
$542$	0.869794	−	7.58727i	0.0373609	−	0.325901i
$543$			9.11278i			0.391067i
$544$	9.04181	+	5.80447i	0.387664	+	0.248865i
$545$	2.27756	+	9.57123i	0.0975598	+	0.409986i
$546$	9.17903	+	1.05227i	0.392826	+	0.0450331i
$547$	−22.5197	−	22.5197i	−0.962873	−	0.962873i	0.0364619	−	0.999335i	$-0.488391\pi$
$547$	−22.5197	−	22.5197i	−0.962873	−	0.962873i	−0.999335	+	0.0364619i	$0.988391\pi$
$548$	29.1915	+	6.78208i	1.24700	+	0.289716i
$549$	−6.65671	−	6.65671i	−0.284101	−	0.284101i
$550$	25.6677	+	11.8436i	1.09447	+	0.505013i
$551$			38.9431i			1.65903i
$552$	5.32361	−	2.52564i	0.226588	−	0.107499i
$553$	19.2996			0.820704
$554$	6.32835	+	7.96717i	0.268866	+	0.338493i
$555$	−3.87676	+	6.29791i	−0.164559	+	0.267331i
$556$	12.3992	+	19.9042i	0.525842	+	0.844127i
$557$	−13.7333	−	13.7333i	−0.581897	−	0.581897i	0.353527	−	0.935424i	$-0.384982\pi$
$557$	−13.7333	−	13.7333i	−0.581897	−	0.581897i	−0.935424	+	0.353527i	$0.884982\pi$
$558$	−19.2173	−	2.20305i	−0.813535	−	0.0932625i
$559$	41.8713			1.77097
$560$	−12.9728	+	8.17765i	−0.548201	+	0.345569i
$561$	7.88525			0.332916
$562$	29.8958	+	3.42721i	1.26108	+	0.144568i
$563$	0.229223	+	0.229223i	0.00966061	+	0.00966061i	0.711921	−	0.702260i	$-0.247826\pi$
$563$	0.229223	+	0.229223i	0.00966061	+	0.00966061i	−0.702260	+	0.711921i	$0.747826\pi$
$564$	−7.82386	+	4.87381i	−0.329444	+	0.205224i
$565$	−30.1359	−	18.5505i	−1.26783	−	0.780427i
$566$	−5.08177	−	6.39776i	−0.213603	−	0.268918i
$567$	−0.784437			−0.0329433
$568$	−1.01014	−	0.360078i	−0.0423846	−	0.0151085i
$569$			23.0376i			0.965787i	0.875679	+	0.482894i	$0.160414\pi$
$569$			23.0376i			0.965787i	−0.875679	+	0.482894i	$0.839586\pi$
$570$	−10.5766	−	8.30942i	−0.443005	−	0.348043i
$571$	−11.8610	−	11.8610i	−0.496367	−	0.496367i	0.413938	−	0.910305i	$-0.364153\pi$
$571$	−11.8610	−	11.8610i	−0.496367	−	0.496367i	−0.910305	+	0.413938i	$0.864153\pi$
$572$	−6.63934	+	28.5772i	−0.277605	+	1.19487i
$573$	13.8989	+	13.8989i	0.580633	+	0.580633i
$574$	3.84538	+	0.440829i	0.160503	+	0.0183998i
$575$	−4.51793	−	8.95556i	−0.188411	−	0.373473i
$576$	−9.72421	+	11.9067i	−0.405175	+	0.496112i
$577$			39.7168i			1.65343i	0.562621	+	0.826715i	$0.309793\pi$
$577$			39.7168i			1.65343i	−0.562621	+	0.826715i	$0.690207\pi$
$578$	−2.15708	+	18.8163i	−0.0897226	+	0.782657i
$579$	−3.25282	+	3.25282i	−0.135183	+	0.135183i
$580$	0.226773	+	42.5198i	0.00941622	+	1.76554i
$581$	−14.1429	−	14.1429i	−0.586748	−	0.586748i
$582$	5.94218	+	7.48100i	0.246311	+	0.310097i
$583$	2.72371			0.112804
$584$	7.95578	−	22.3187i	0.329213	−	0.923553i
$585$	−3.64992	−	15.3385i	−0.150906	−	0.634168i
$586$	9.21016	+	11.5953i	0.380468	+	0.478996i
$587$	−8.63887	+	8.63887i	−0.356564	+	0.356564i	−0.862545	−	0.505980i	$-0.831131\pi$
$587$	−8.63887	+	8.63887i	−0.356564	+	0.356564i	0.505980	+	0.862545i	$0.331131\pi$
$588$	4.45890	+	7.15782i	0.183882	+	0.295183i
$589$	−20.6147	+	20.6147i	−0.849414	+	0.849414i
$590$	−1.64483	−	13.7018i	−0.0677167	−	0.564092i
$591$	−9.38927			−0.386223
$592$	12.0570	−	4.11416i	0.495540	−	0.169091i
$593$		−	45.8229i		−	1.88172i	−0.338795	−	0.940860i	$-0.610019\pi$
$593$		−	45.8229i		−	1.88172i	0.338795	−	0.940860i	$-0.389981\pi$
$594$	−3.29094	+	28.7071i	−0.135029	+	1.17787i
$595$	6.20118	+	3.81722i	0.254224	+	0.156491i
$596$	10.9282	+	17.5429i	0.447637	+	0.718586i
$597$	−4.30032	+	4.30032i	−0.176000	+	0.176000i
$598$	8.15166	−	6.47489i	0.333346	−	0.264778i
$599$			17.0609i			0.697090i	0.937292	+	0.348545i	$0.113324\pi$
$599$			17.0609i			0.697090i	−0.937292	+	0.348545i	$0.886676\pi$
$600$	−11.5964	−	9.01101i	−0.473421	−	0.367873i
$601$			38.0363i			1.55153i	0.631020	+	0.775766i	$0.282636\pi$
$601$			38.0363i			1.55153i	−0.631020	+	0.775766i	$0.717364\pi$
$602$	−17.2090	−	21.6656i	−0.701388	−	0.883023i
$603$	3.46766	−	3.46766i	0.141214	−	0.141214i
$604$	2.06783	−	8.90040i	0.0841390	−	0.362152i
$605$	−9.48685	−	5.83975i	−0.385695	−	0.237420i
$606$	13.8723	+	1.59030i	0.563522	+	0.0646013i
$607$			8.67169i			0.351973i	0.984393	+	0.175987i	$0.0563115\pi$
$607$			8.67169i			0.351973i	−0.984393	+	0.175987i	$0.943688\pi$
$608$	4.93635	+	22.6379i	0.200196	+	0.918087i
$609$	−16.9282			−0.685965
$610$	−15.3815	+	1.84648i	−0.622779	+	0.0747617i
$611$	−11.5155	+	11.5155i	−0.465868	+	0.465868i
$612$	7.11047	+	1.65198i	0.287424	+	0.0667773i
$613$	−13.9739	+	13.9739i	−0.564401	+	0.564401i	−0.930554	−	0.366153i	$-0.880675\pi$
$613$	−13.9739	+	13.9739i	−0.564401	+	0.564401i	0.366153	+	0.930554i	$0.380675\pi$
$614$	26.0962	−	20.7283i	1.05316	−	0.836526i
$615$	0.858077	+	3.60599i	0.0346010	+	0.145408i
$616$	17.5155	−	8.30976i	0.705720	−	0.334810i
$617$	37.3904			1.50528			0.752641	−	0.658431i	$-0.228780\pi$
$617$	37.3904			1.50528			0.752641	+	0.658431i	$0.228780\pi$
$618$	−17.4487	+	13.8595i	−0.701888	+	0.557512i
$619$	−23.2754	−	23.2754i	−0.935516	−	0.935516i	0.0625269	−	0.998043i	$-0.480084\pi$
$619$	−23.2754	−	23.2754i	−0.935516	−	0.935516i	−0.998043	+	0.0625269i	$0.980084\pi$
$620$	−22.3880	+	22.6281i	−0.899125	+	0.908767i
$621$	7.24998	−	7.24998i	0.290932	−	0.290932i
$622$	30.7799	+	3.52856i	1.23416	+	0.141482i
$623$			20.5435i			0.823058i
$624$	6.71952	−	13.6806i	0.268996	−	0.547660i
$625$	−14.8564	+	20.1069i	−0.594256	+	0.804276i
$626$	−2.01046	+	17.5374i	−0.0803541	+	0.700934i
$627$	12.0236	+	12.0236i	0.480175	+	0.480175i
$628$	2.28761	+	3.67228i	0.0912857	+	0.146540i
$629$	−4.27756	−	4.27756i	−0.170557	−	0.170557i
$630$	−6.43652	+	8.19269i	−0.256437	+	0.326404i
$631$		−	19.1834i		−	0.763680i	−0.924228	−	0.381840i	$-0.875290\pi$
$631$		−	19.1834i		−	0.763680i	0.924228	−	0.381840i	$-0.124710\pi$
$632$	10.6903	−	29.9900i	0.425238	−	1.19294i
$633$	11.1667			0.443838
$634$	6.64526	−	5.27835i	0.263917	−	0.209630i
$635$	−34.8926	−	21.4786i	−1.38467	−	0.852352i
$636$	−1.37830	−	0.320221i	−0.0546531	−	0.0126976i
$637$	10.5352	+	10.5352i	0.417420	+	0.417420i
$638$	6.12222	−	53.4045i	0.242381	−	2.11431i
$639$	−0.728585			−0.0288224
$640$	5.52156	+	24.6883i	0.218259	+	0.975891i
$641$	−16.1765			−0.638933			−0.319466	−	0.947598i	$-0.603504\pi$
$641$	−16.1765			−0.638933			−0.319466	+	0.947598i	$0.603504\pi$
$642$	0.401605	−	3.50323i	0.0158501	−	0.138261i
$643$	−15.0289	−	15.0289i	−0.592681	−	0.592681i	0.345674	−	0.938355i	$-0.387650\pi$
$643$	−15.0289	−	15.0289i	−0.592681	−	0.592681i	−0.938355	+	0.345674i	$0.887650\pi$
$644$	−6.70064	−	1.55676i	−0.264042	−	0.0613451i
$645$	13.8899	−	22.5646i	0.546916	−	0.888481i
$646$	8.61512	−	6.84302i	0.338958	−	0.269235i
$647$	−49.3812			−1.94138			−0.970688	−	0.240345i	$-0.922739\pi$
$647$	−49.3812			−1.94138			−0.970688	+	0.240345i	$0.922739\pi$
$648$	−0.434509	+	1.21895i	−0.0170691	+	0.0478847i
$649$			17.4461i			0.684821i
$650$	−23.5591	−	10.8707i	−0.924066	−	0.426383i
$651$	−8.96103	−	8.96103i	−0.351210	−	0.351210i
$652$	−15.1586	−	24.3338i	−0.593655	−	0.952987i
$653$	19.8685	+	19.8685i	0.777514	+	0.777514i	0.979408	−	0.201893i	$-0.0647094\pi$
$653$	19.8685	+	19.8685i	0.777514	+	0.777514i	−0.201893	+	0.979408i	$0.564709\pi$
$654$	−0.735933	+	6.41960i	−0.0287773	+	0.251026i
$655$	−7.46954	−	31.3901i	−0.291859	−	1.22651i
$656$	2.81501	−	5.73120i	0.109908	−	0.223766i
$657$		−	16.0978i		−	0.628035i
$658$	10.6914	+	1.22564i	0.416793	+	0.0477806i
$659$	4.94765	−	4.94765i	0.192733	−	0.192733i	−0.604143	−	0.796876i	$-0.706484\pi$
$659$	4.94765	−	4.94765i	0.192733	−	0.192733i	0.796876	+	0.604143i	$0.206484\pi$
$660$	13.1979	+	13.0579i	0.513727	+	0.508277i
$661$	12.1602	+	12.1602i	0.472977	+	0.472977i	0.902877	−	0.429899i	$-0.141451\pi$
$661$	12.1602	+	12.1602i	0.472977	+	0.472977i	−0.429899	+	0.902877i	$0.641451\pi$
$662$	−1.72860	+	1.37303i	−0.0671838	+	0.0533643i
$663$	−7.23750			−0.281081
$664$	−29.8109	+	14.1429i	−1.15689	+	0.548853i
$665$	3.63511	+	15.2762i	0.140964	+	0.592387i
$666$	6.77741	−	5.38332i	0.262619	−	0.208599i
$667$	−13.4873	+	13.4873i	−0.522231	+	0.522231i
$668$	−5.02550	−	1.16758i	−0.194442	−	0.0451749i
$669$	−6.77335	+	6.77335i	−0.261873	+	0.261873i
$670$	−0.961880	−	8.01264i	−0.0371607	−	0.309555i
$671$	19.5849			0.756067
$672$	−9.84048	+	2.14579i	−0.379605	+	0.0827756i
$673$		−	32.9882i		−	1.27160i	−0.771853	−	0.635801i	$-0.780670\pi$
$673$		−	32.9882i		−	1.27160i	0.771853	−	0.635801i	$-0.219330\pi$
$674$	10.5044	+	1.20420i	0.404613	+	0.0463842i
$675$	−24.2717	−	7.99412i	−0.934217	−	0.307694i
$676$	0.210055	−	0.904123i	0.00807905	−	0.0347740i
$677$	−18.4610	+	18.4610i	−0.709513	+	0.709513i	−0.966433	−	0.256920i	$-0.917292\pi$
$677$	−18.4610	+	18.4610i	−0.709513	+	0.709513i	0.256920	+	0.966433i	$0.417292\pi$
$678$	−14.4557	−	18.1992i	−0.555167	−	0.698935i
$679$		−	11.1537i		−	0.428040i
$680$	9.36653	−	7.52169i	0.359190	−	0.288444i
$681$			13.5363i			0.518713i
$682$	31.5108	−	25.0291i	1.20661	−	0.958415i
$683$	12.2374	−	12.2374i	0.468251	−	0.468251i	−0.433097	−	0.901347i	$-0.642579\pi$
$683$	12.2374	−	12.2374i	0.468251	−	0.468251i	0.901347	+	0.433097i	$0.142579\pi$
$684$	8.32320	+	13.3611i	0.318245	+	0.510875i
$685$	17.5643	−	28.5337i	0.671097	−	1.09022i
$686$	3.05440	−	26.6437i	0.116617	−	1.01726i
$687$			2.40571i			0.0917837i
$688$	−43.1987	+	14.7405i	−1.64693	+	0.561977i
$689$	−2.49996			−0.0952409
$690$	−0.785202	−	6.54088i	−0.0298921	−	0.249007i
$691$	−9.46014	+	9.46014i	−0.359881	+	0.359881i	−0.863769	−	0.503888i	$-0.831902\pi$
$691$	−9.46014	+	9.46014i	−0.359881	+	0.359881i	0.503888	+	0.863769i	$0.331902\pi$
$692$	21.2022	+	34.0356i	0.805987	+	1.29384i
$693$	9.31352	−	9.31352i	0.353791	−	0.353791i
$694$	10.6491	+	13.4068i	0.404233	+	0.508915i
$695$	25.5061	−	6.06939i	0.967500	−	0.230225i
$696$	−9.37674	+	26.3049i	−0.355425	+	0.997086i
$697$	−3.03201			−0.114845
$698$	9.84664	+	12.3966i	0.372701	+	0.469217i
$699$	9.09039	+	9.09039i	0.343830	+	0.343830i
$700$	4.05794	+	16.6581i	0.153376	+	0.629617i
$701$	−5.14714	+	5.14714i	−0.194405	+	0.194405i	−0.797596	−	0.603192i	$-0.793895\pi$
$701$	−5.14714	+	5.14714i	−0.194405	+	0.194405i	0.603192	+	0.797596i	$0.293895\pi$
$702$	3.02060	−	26.3489i	0.114005	−	0.994474i
$703$		−	13.0450i		−	0.492001i
$704$	−3.21058	−	31.8205i	−0.121003	−	1.19928i
$705$	2.38573	+	10.0258i	0.0898517	+	0.377594i
$706$	13.5909	+	1.55804i	0.511499	+	0.0586375i
$707$	−11.5269	−	11.5269i	−0.433512	−	0.433512i
$708$	2.05111	−	8.82840i	0.0770853	−	0.331792i
$709$	−18.0125	−	18.0125i	−0.676472	−	0.676472i	0.282728	−	0.959200i	$-0.408761\pi$
$709$	−18.0125	−	18.0125i	−0.676472	−	0.676472i	−0.959200	+	0.282728i	$0.908761\pi$
$710$	−0.740713	+	0.942812i	−0.0277985	+	0.0353831i
$711$		−	21.6309i		−	0.811222i
$712$	31.9228	+	11.3793i	1.19636	+	0.426457i
$713$	−14.2792			−0.534759
$714$	2.97460	+	3.74492i	0.111322	+	0.140150i
$715$	27.9332	+	17.1946i	1.04464	+	0.643043i
$716$	23.7207	−	14.7766i	0.886485	−	0.552228i
$717$	−5.70875	−	5.70875i	−0.213197	−	0.213197i
$718$	24.0069	+	2.75212i	0.895931	+	0.102708i
$719$	34.5017			1.28669			0.643347	−	0.765574i	$-0.277545\pi$
$719$	34.5017			1.28669			0.643347	+	0.765574i	$0.277545\pi$
$720$	9.16545	+	14.5398i	0.341576	+	0.541867i
$721$	26.0149			0.968846
$722$	−3.12437	−	0.358173i	−0.116277	−	0.0133298i
$723$	−2.54850	−	2.54850i	−0.0947796	−	0.0947796i
$724$	−9.27983	−	14.8968i	−0.344882	−	0.553635i
$725$	45.1532	+	14.8717i	1.67695	+	0.552320i
$726$	−4.55068	−	5.72915i	−0.168892	−	0.212629i
$727$	12.8421			0.476288			0.238144	−	0.971230i	$-0.423461\pi$
$727$	12.8421			0.476288			0.238144	+	0.971230i	$0.423461\pi$
$728$	−16.0767	+	7.62713i	−0.595841	+	0.282680i
$729$		−	15.0429i		−	0.557143i
$730$	−20.8311	−	16.3658i	−0.770992	−	0.605724i
$731$	15.3259	+	15.3259i	0.566851	+	0.566851i
$732$	−9.91071	−	2.30256i	−0.366310	−	0.0851050i
$733$	24.1490	+	24.1490i	0.891965	+	0.891965i	0.994708	−	0.102743i	$-0.0327618\pi$
$733$	24.1490	+	24.1490i	0.891965	+	0.891965i	−0.102743	+	0.994708i	$0.532762\pi$
$734$	18.8974	+	2.16638i	0.697517	+	0.0799624i
$735$	9.17231	−	2.18263i	0.338326	−	0.0805075i
$736$	−6.13065	+	9.54990i	−0.225979	+	0.352014i
$737$			10.2023i			0.375807i
$738$	0.494077	−	4.30987i	0.0181872	−	0.158648i
$739$	35.9398	−	35.9398i	1.32207	−	1.32207i	0.409966	−	0.912101i	$-0.365540\pi$
$739$	35.9398	−	35.9398i	1.32207	−	1.32207i	0.912101	−	0.409966i	$-0.134460\pi$
$740$	−0.0759634	−	14.2431i	−0.00279247	−	0.523587i
$741$	−11.0359	−	11.0359i	−0.405412	−	0.405412i
$742$	1.02748	+	1.29356i	0.0377200	+	0.0474881i
$743$	−45.9502			−1.68575			−0.842875	−	0.538109i	$-0.819139\pi$
$743$	−45.9502			−1.68575			−0.842875	+	0.538109i	$0.819139\pi$
$744$	−18.8883	+	8.96103i	−0.692478	+	0.328527i
$745$	22.4802	−	5.34935i	0.823610	−	0.195985i
$746$	−14.9610	−	18.8354i	−0.547762	−	0.689613i
$747$	−15.8513	+	15.8513i	−0.579969	+	0.579969i
$748$	−12.8901	+	8.02980i	−0.471310	+	0.293598i
$749$	−2.91094	+	2.91094i	−0.106363	+	0.106363i
$750$	−13.6735	+	9.09001i	−0.499287	+	0.331920i
$751$	−24.4820			−0.893361			−0.446680	−	0.894694i	$-0.647394\pi$
$751$	−24.4820			−0.893361			−0.446680	+	0.894694i	$0.647394\pi$
$752$	7.82663	−	15.9346i	0.285408	−	0.581074i
$753$			13.1404i			0.478863i
$754$	−5.61929	+	49.0175i	−0.204643	+	1.78511i
$755$	−8.69983	−	5.35529i	−0.316619	−	0.194899i
$756$	−14.8752	+	9.26639i	−0.541007	+	0.337015i
$757$	17.0328	−	17.0328i	0.619067	−	0.619067i	−0.326225	−	0.945292i	$-0.605777\pi$
$757$	17.0328	−	17.0328i	0.619067	−	0.619067i	0.945292	+	0.326225i	$0.105777\pi$
$758$	−29.9986	+	23.8280i	−1.08960	+	0.865471i
$759$			8.32835i			0.302300i
$760$	25.7515	+	2.81305i	0.934104	+	0.102040i
$761$		−	8.53590i		−	0.309426i	−0.987959	−	0.154713i	$-0.950555\pi$
$761$		−	8.53590i		−	0.309426i	0.987959	−	0.154713i	$-0.0494453\pi$
$762$	−16.7374	−	21.0718i	−0.606332	−	0.763350i
$763$	5.33423	−	5.33423i	0.193112	−	0.193112i
$764$	−36.8743	−	8.56702i	−1.33407	−	0.309944i
$765$	4.27831	−	6.95024i	0.154683	−	0.251286i
$766$	−24.9394	−	2.85902i	−0.901099	−	0.103301i
$767$		−	16.0130i		−	0.578195i
$768$	−2.11640	+	16.4798i	−0.0763689	+	0.594664i
$769$	−1.87438			−0.0675917			−0.0337959	−	0.999429i	$-0.510760\pi$
$769$	−1.87438			−0.0675917			−0.0337959	+	0.999429i	$0.510760\pi$
$770$	−2.58344	−	21.5205i	−0.0931007	−	0.775546i
$771$	−2.65982	+	2.65982i	−0.0957911	+	0.0957911i
$772$	2.00498	−	8.62988i	0.0721610	−	0.310596i
$773$	21.5374	−	21.5374i	0.774645	−	0.774645i	−0.204270	−	0.978915i	$-0.565482\pi$
$773$	21.5374	−	21.5374i	0.774645	−	0.774645i	0.978915	+	0.204270i	$0.0654820\pi$
$774$	−24.2826	+	19.2878i	−0.872820	+	0.693284i
$775$	16.0297	+	31.7745i	0.575804	+	1.14137i
$776$	−17.3319	−	6.17818i	−0.622179	−	0.221784i
$777$	5.67054			0.203429
$778$	1.85822	−	1.47599i	0.0666205	−	0.0529169i
$779$	−4.62326	−	4.62326i	−0.165645	−	0.165645i
$780$	−12.1137	−	11.9852i	−0.433741	−	0.429139i
$781$	1.07180	−	1.07180i	0.0383519	−	0.0383519i
$782$	5.35369	+	0.613739i	0.191448	+	0.0219473i
$783$			48.5932i			1.73658i
$784$	−14.5781	−	7.16035i	−0.520645	−	0.255727i
$785$	4.70580	−	1.11979i	0.167957	−	0.0399669i
$786$	2.41359	−	21.0539i	0.0860898	−	0.750967i
$787$	−7.03687	−	7.03687i	−0.250837	−	0.250837i	0.570477	−	0.821314i	$-0.306759\pi$
$787$	−7.03687	−	7.03687i	−0.250837	−	0.250837i	−0.821314	+	0.570477i	$0.806759\pi$
$788$	15.3488	−	9.56139i	0.546778	−	0.340610i
$789$	10.0904	+	10.0904i	0.359227	+	0.359227i
$790$	−27.9911	−	21.9909i	−0.995877	−	0.782403i
$791$			27.1339i			0.964770i
$792$	−9.31352	−	19.6313i	−0.330941	−	0.697566i
$793$	−17.9761			−0.638348
$794$	7.43071	−	5.90224i	0.263706	−	0.209463i
$795$	−0.829311	+	1.34724i	−0.0294126	+	0.0477817i
$796$	2.65065	−	11.4089i	0.0939497	−	0.404379i
$797$	−8.07933	−	8.07933i	−0.286185	−	0.286185i	0.549385	−	0.835569i	$-0.314862\pi$
$797$	−8.07933	−	8.07933i	−0.286185	−	0.286185i	−0.835569	+	0.549385i	$0.814862\pi$
$798$	−1.17459	+	10.2460i	−0.0415801	+	0.362706i
$799$	−8.42995			−0.298230
$800$	28.1330	+	2.92146i	0.994651	+	0.103289i
$801$	23.0250			0.813548
$802$	−0.101904	+	0.888918i	−0.00359837	+	0.0313888i
$803$	23.6809	+	23.6809i	0.835682	+	0.835682i
$804$	1.19947	−	5.16276i	0.0423019	−	0.182076i
$805$	−4.03172	+	6.54965i	−0.142099	+	0.230845i
$806$	−28.9222	+	22.9730i	−1.01874	+	0.809191i
$807$	−6.20097			−0.218284
$808$	−24.2966	+	11.5269i	−0.854752	+	0.405514i
$809$		−	5.40185i		−	0.189919i	−0.995481	−	0.0949595i	$-0.969728\pi$
$809$		−	5.40185i		−	0.189919i	0.995481	−	0.0949595i	$-0.0302722\pi$
$810$	1.13770	+	0.893825i	0.0399747	+	0.0314058i
$811$	−10.3478	−	10.3478i	−0.363360	−	0.363360i	0.501688	−	0.865049i	$-0.332712\pi$
$811$	−10.3478	−	10.3478i	−0.363360	−	0.363360i	−0.865049	+	0.501688i	$0.832712\pi$
$812$	27.6728	−	17.2385i	0.971124	−	0.604953i
$813$	−3.96530	−	3.96530i	−0.139069	−	0.139069i
$814$	−2.05080	+	17.8892i	−0.0718804	+	0.627017i
$815$	−31.1824	+	7.42011i	−1.09227	+	0.259915i
$816$	7.46694	−	2.54791i	0.261395	−	0.0891948i
$817$			46.7385i			1.63517i
$818$	37.0655	+	4.24913i	1.29596	+	0.148568i
$819$	−8.54843	+	8.54843i	−0.298706	+	0.298706i
$820$	−5.07480	−	5.02096i	−0.177220	−	0.175340i
$821$	10.7321	+	10.7321i	0.374551	+	0.374551i	0.869132	−	0.494581i	$-0.164678\pi$
$821$	10.7321	+	10.7321i	0.374551	+	0.374551i	−0.494581	+	0.869132i	$0.664678\pi$
$822$	17.2316	−	13.6871i	0.601022	−	0.477394i
$823$	−3.51588			−0.122556			−0.0612780	−	0.998121i	$-0.519518\pi$
$823$	−3.51588			−0.122556			−0.0612780	+	0.998121i	$0.519518\pi$
$824$	14.4100	−	40.4249i	0.501996	−	1.40827i
$825$	18.5325	−	9.34935i	0.645220	−	0.325503i
$826$	−8.28564	+	6.58131i	−0.288294	+	0.228993i
$827$	−27.7375	+	27.7375i	−0.964529	+	0.964529i	−0.999392	−	0.0348631i	$-0.988900\pi$
$827$	−27.7375	+	27.7375i	−0.964529	+	0.964529i	0.0348631	+	0.999392i	$0.488900\pi$
$828$	−1.74481	+	7.51003i	−0.0606363	+	0.260992i
$829$	−19.5849	+	19.5849i	−0.680212	+	0.680212i	−0.960048	−	0.279836i	$-0.909720\pi$
$829$	−19.5849	+	19.5849i	−0.680212	+	0.680212i	0.279836	+	0.960048i	$0.409720\pi$
$830$	4.39693	+	36.6272i	0.152620	+	1.27135i
$831$	7.47119			0.259173
$832$	2.94683	+	29.2065i	0.102163	+	1.01255i
$833$			7.71231i			0.267216i
$834$	17.1074	+	1.96117i	0.592380	+	0.0679096i
$835$	−3.02380	+	4.91225i	−0.104643	+	0.169995i
$836$	−31.8991	−	7.41113i	−1.10325	−	0.256319i
$837$	−25.7231	+	25.7231i	−0.889119	+	0.889119i
$838$	−1.71153	−	2.15476i	−0.0591238	−	0.0744348i
$839$		−	40.0520i		−	1.38275i	−0.722496	−	0.691375i	$-0.757005\pi$
$839$		−	40.0520i		−	1.38275i	0.722496	−	0.691375i	$-0.242995\pi$
$840$	−1.22281	+	11.1939i	−0.0421909	+	0.386227i
$841$		−	61.3992i		−	2.11722i
$842$	−10.4249	+	8.28056i	−0.359267	+	0.285367i
$843$	15.6243	−	15.6243i	0.538129	−	0.538129i
$844$	−18.2544	+	11.3714i	−0.628343	+	0.391421i
$845$	−0.883749	−	0.544003i	−0.0304019	−	0.0187143i
$846$	1.37369	−	11.9828i	0.0472285	−	0.411977i
$847$			8.54182i			0.293500i
$848$	2.57922	−	0.880095i	0.0885706	−	0.0302226i
$849$	−5.99948			−0.205902
$850$	−4.64430	−	12.6022i	−0.159298	−	0.432252i
$851$	4.51793	−	4.51793i	0.154873	−	0.154873i
$852$	−0.668379	+	0.416361i	−0.0228983	+	0.0142643i
$853$	−13.7328	+	13.7328i	−0.470202	+	0.470202i	−0.901980	−	0.431778i	$-0.857886\pi$
$853$	−13.7328	+	13.7328i	−0.470202	+	0.470202i	0.431778	+	0.901980i	$0.357886\pi$
$854$	7.38814	+	9.30140i	0.252817	+	0.318287i
$855$	17.1215	−	4.07420i	0.585542	−	0.139335i
$856$	2.91094	+	6.13575i	0.0994938	+	0.209716i
$857$	−39.9485			−1.36462			−0.682308	−	0.731065i	$-0.739024\pi$
$857$	−39.9485			−1.36462			−0.682308	+	0.731065i	$0.739024\pi$
$858$	13.3991	+	16.8690i	0.457437	+	0.575897i
$859$	33.6366	+	33.6366i	1.14766	+	1.14766i	0.987011	+	0.160654i	$0.0513602\pi$
$859$	33.6366	+	33.6366i	1.14766	+	1.14766i	0.160654	+	0.987011i	$0.448640\pi$
$860$	0.272167	+	51.0312i	0.00928082	+	1.74015i
$861$	2.00969	−	2.00969i	0.0684900	−	0.0684900i
$862$	−0.658445	+	5.74366i	−0.0224267	+	0.195630i
$863$		−	16.5303i		−	0.562697i	−0.959606	−	0.281349i	$-0.909218\pi$
$863$		−	16.5303i		−	0.562697i	0.959606	−	0.281349i	$-0.0907817\pi$
$864$	6.15959	+	28.2476i	0.209554	+	0.961002i
$865$	43.6146	−	10.3785i	1.48294	−	0.352879i
$866$	−41.1546	−	4.71791i	−1.39849	−	0.160321i
$867$	9.83388	+	9.83388i	0.333976	+	0.333976i
$868$	23.7740	+	5.52343i	0.806943	+	0.187477i
$869$	31.8205	+	31.8205i	1.07944	+	1.07944i
$870$	24.5517	+	19.2888i	0.832379	+	0.653952i
$871$		−	9.36421i		−	0.317294i
$872$	−5.33423	−	11.2436i	−0.180640	−	0.380757i
$873$	−12.5010			−0.423095
$874$	7.22756	+	9.09924i	0.244476	+	0.307786i
$875$	19.1005	+	1.61893i	0.645714	+	0.0547297i
$876$	−9.19933	−	14.7676i	−0.310817	−	0.498950i
$877$	9.66381	+	9.66381i	0.326324	+	0.326324i	0.851187	−	0.524863i	$-0.175883\pi$
$877$	9.66381	+	9.66381i	0.326324	+	0.326324i	−0.524863	+	0.851187i	$0.675883\pi$
$878$	−37.9058	−	4.34547i	−1.27926	−	0.146652i
$879$	10.8734			0.366752
$880$	−34.8720	−	7.90605i	−1.17554	−	0.266513i
$881$	−43.4299			−1.46319			−0.731596	−	0.681739i	$-0.761224\pi$
$881$	−43.4299			−1.46319			−0.731596	+	0.681739i	$0.761224\pi$
$882$	−10.9627	−	1.25675i	−0.369134	−	0.0423170i
$883$	22.3879	+	22.3879i	0.753413	+	0.753413i	0.975115	−	0.221701i	$-0.0711610\pi$
$883$	22.3879	+	22.3879i	0.753413	+	0.753413i	−0.221701	+	0.975115i	$0.571161\pi$
$884$	11.8312	−	7.37017i	0.397928	−	0.247885i
$885$	−8.62946	−	5.31198i	−0.290076	−	0.178560i
$886$	18.0728	+	22.7530i	0.607167	+	0.764402i
$887$	31.6913			1.06409			0.532045	−	0.846716i	$-0.321424\pi$
$887$	31.6913			1.06409			0.532045	+	0.846716i	$0.321424\pi$
$888$	3.14098	−	8.81152i	0.105404	−	0.295695i
$889$			31.4168i			1.05368i
$890$	23.4082	−	29.7950i	0.784646	−	0.998732i
$891$	−1.29335	−	1.29335i	−0.0433288	−	0.0433288i
$892$	4.17498	−	17.9700i	0.139789	−	0.601680i
$893$	−12.8541	−	12.8541i	−0.430147	−	0.430147i
$894$	15.0779	+	1.72850i	0.504279	+	0.0578098i
$895$	−7.23315	−	30.3967i	−0.241778	−	1.01605i
$896$	13.9012	−	13.5286i	0.464408	−	0.451959i
$897$		−	7.64420i		−	0.255232i
$898$	−3.72989	+	32.5361i	−0.124468	+	1.08574i
$899$	47.8533	−	47.8533i	1.59600	−	1.59600i
$900$	18.6703	−	4.54810i	0.622343	−	0.151603i
$901$	−0.915049	−	0.915049i	−0.0304847	−	0.0304847i
$902$	5.61328	+	7.06692i	0.186902	+	0.235303i
$903$	−20.3168			−0.676102
$904$	42.1637	+	15.0298i	1.40234	+	0.499884i
$905$	−19.0893	+	4.54248i	−0.634551	+	0.150997i
$906$	−4.17316	−	5.25386i	−0.138644	−	0.174548i
$907$	24.9184	−	24.9184i	0.827401	−	0.827401i	−0.159755	−	0.987157i	$-0.551071\pi$
$907$	24.9184	−	24.9184i	0.827401	−	0.827401i	0.987157	+	0.159755i	$0.0510705\pi$
$908$	−13.7845	−	22.1280i	−0.457454	−	0.734345i
$909$	−12.9192	+	12.9192i	−0.428503	+	0.428503i
$910$	2.37121	+	19.7527i	0.0786050	+	0.654794i
$911$	−47.0459			−1.55870			−0.779350	−	0.626589i	$-0.784451\pi$
$911$	−47.0459			−1.55870			−0.779350	+	0.626589i	$0.784451\pi$
$912$	15.2708	+	7.50062i	0.505668	+	0.248370i
$913$		−	46.6366i		−	1.54345i
$914$	6.07271	−	52.9726i	0.200867	−	1.75218i
$915$	−5.96319	+	9.68738i	−0.197137	+	0.320255i
$916$	−2.44981	−	3.93266i	−0.0809441	−	0.129939i
$917$	−17.4943	+	17.4943i	−0.577712	+	0.577712i
$918$	10.7500	−	8.53874i	0.354802	−	0.281820i
$919$		−	12.5442i		−	0.413796i	−0.978362	−	0.206898i	$-0.933663\pi$
$919$		−	12.5442i		−	0.413796i	0.978362	−	0.206898i	$-0.0663369\pi$
$920$	7.94436	+	9.89287i	0.261918	+	0.326158i
$921$		−	24.4716i		−	0.806368i
$922$	14.1482	+	17.8121i	0.465948	+	0.586612i
$923$	−0.983751	+	0.983751i	−0.0323806	+	0.0323806i
$924$	3.22155	−	13.8662i	0.105981	−	0.456166i
$925$	−15.1252	−	4.98165i	−0.497315	−	0.163796i
$926$	11.1684	+	1.28033i	0.367015	+	0.0420741i
$927$		−	29.1573i		−	0.957652i
$928$	−11.4588	−	52.5497i	−0.376155	−	1.72503i
$929$	−26.7421			−0.877380			−0.438690	−	0.898639i	$-0.644557\pi$
$929$	−26.7421			−0.877380			−0.438690	+	0.898639i	$0.644557\pi$
$930$	2.78591	+	23.2072i	0.0913537	+	0.760993i
$931$	−11.7599	+	11.7599i	−0.385414	+	0.385414i
$932$	−24.1172	−	5.60316i	−0.789986	−	0.183538i
$933$	16.0863	−	16.0863i	0.526642	−	0.526642i
$934$	−8.37851	+	6.65508i	−0.274153	+	0.217761i
$935$	3.93058	+	16.5179i	0.128544	+	0.540194i
$936$	8.54843	+	18.0186i	0.279414	+	0.588956i
$937$	−3.06580			−0.100155			−0.0500777	−	0.998745i	$-0.515947\pi$
$937$	−3.06580			−0.100155			−0.0500777	+	0.998745i	$0.515947\pi$
$938$	−4.84535	+	3.84868i	−0.158206	+	0.125664i
$939$	9.16546	+	9.16546i	0.299104	+	0.299104i
$940$	−14.1096	−	13.9599i	−0.460203	−	0.455321i
$941$	−14.6023	+	14.6023i	−0.476020	+	0.476020i	−0.903856	−	0.427836i	$-0.859276\pi$
$941$	−14.6023	+	14.6023i	−0.476020	+	0.476020i	0.427836	+	0.903856i	$0.359276\pi$
$942$	3.15626	+	0.361830i	0.102837	+	0.0117890i
$943$		−	3.20239i		−	0.104284i
$944$	5.63726	+	16.5206i	0.183477	+	0.537701i
$945$	4.53590	+	19.0617i	0.147553	+	0.620077i
$946$	7.34774	−	64.0949i	0.238896	−	2.08390i
$947$	29.4872	+	29.4872i	0.958204	+	0.958204i	0.999161	−	0.0409570i	$-0.0130407\pi$
$947$	29.4872	+	29.4872i	0.958204	+	0.958204i	−0.0409570	+	0.999161i	$0.513041\pi$
$948$	−12.3613	−	19.8434i	−0.401476	−	0.644485i
$949$	−21.7356	−	21.7356i	−0.705567	−	0.705567i
$950$	12.1343	−	26.2978i	0.393689	−	0.853212i
$951$		−	6.23158i		−	0.202073i
$952$	−8.67619	−	3.09274i	−0.281197	−	0.100236i
$953$	33.6807			1.09103			0.545513	−	0.838103i	$-0.316335\pi$
$953$	33.6807			1.09103			0.545513	+	0.838103i	$0.316335\pi$
$954$	1.44981	−	1.15159i	0.0469394	−	0.0372842i
$955$	−22.1870	+	36.0434i	−0.717953	+	1.16634i
$956$	15.1456	+	3.51878i	0.489843	+	0.113805i
$957$	−27.9105	−	27.9105i	−0.902219	−	0.902219i
$958$	1.54460	−	13.4737i	0.0499039	−	0.435315i
$959$	−25.6913			−0.829616
$960$	16.7171	+	8.10059i	0.539541	+	0.261446i
$961$	19.6628			0.634283
$962$	1.88233	−	16.4197i	0.0606887	−	0.529391i
$963$	3.26256	+	3.26256i	0.105134	+	0.105134i
$964$	6.76128	+	1.57085i	0.217766	+	0.0505937i
$965$	−8.43541	−	5.19253i	−0.271546	−	0.167153i
$966$	−3.95536	+	3.14176i	−0.127262	+	0.101084i
$967$	8.70089			0.279802			0.139901	−	0.990166i	$-0.455322\pi$
$967$	8.70089			0.279802			0.139901	+	0.990166i	$0.455322\pi$
$968$	13.2732	+	4.73142i	0.426618	+	0.152074i
$969$		−	8.07881i		−	0.259529i
$970$	−12.7091	+	16.1767i	−0.408064	+	0.519402i
$971$	−5.87523	−	5.87523i	−0.188545	−	0.188545i	0.606522	−	0.795067i	$-0.292564\pi$
$971$	−5.87523	−	5.87523i	−0.188545	−	0.188545i	−0.795067	+	0.606522i	$0.792564\pi$
$972$	16.7164	+	26.8346i	0.536177	+	0.860719i
$973$	−14.2150	−	14.2150i	−0.455713	−	0.455713i
$974$	−5.90296	+	51.4919i	−0.189143	+	1.64991i
$975$	−17.0101	+	8.58132i	−0.544760	+	0.274822i
$976$	18.5459	−	6.32835i	0.593641	−	0.202566i
$977$		−	41.8541i		−	1.33903i	−0.742798	−	0.669516i	$-0.766502\pi$
$977$		−	41.8541i		−	1.33903i	0.742798	−	0.669516i	$-0.233498\pi$
$978$	−20.9146	−	2.39762i	−0.668774	−	0.0766673i
$979$	−33.8713	+	33.8713i	−1.08253	+	1.08253i
$980$	−12.7715	+	12.9084i	−0.407969	+	0.412344i
$981$	−5.97856	−	5.97856i	−0.190881	−	0.190881i
$982$	−36.6890	+	29.1422i	−1.17079	+	0.929966i
$983$	57.4539			1.83250			0.916248	−	0.400612i	$-0.131203\pi$
$983$	57.4539			1.83250			0.916248	+	0.400612i	$0.131203\pi$
$984$	−2.00969	−	4.23607i	−0.0640665	−	0.135041i
$985$	−4.68030	−	19.6685i	−0.149127	−	0.626692i
$986$	−19.9984	+	15.8848i	−0.636880	+	0.505876i
$987$	5.58758	−	5.58758i	0.177854	−	0.177854i
$988$	29.2786	+	6.80232i	0.931477	+	0.216411i
$989$	−16.1872	+	16.1872i	−0.514722	+	0.514722i
$990$	−24.1200	+	2.89550i	−0.766585	+	0.0920249i
$991$	12.8205			0.407258			0.203629	−	0.979048i	$-0.434726\pi$
$991$	12.8205			0.407258			0.203629	+	0.979048i	$0.434726\pi$
$992$	21.7516	−	33.8832i	0.690616	−	1.07579i
$993$			1.62099i			0.0514404i
$994$	0.913345	+	0.104705i	0.0289696	+	0.00332103i
$995$	−11.1519	−	6.86467i	−0.353538	−	0.217625i
$996$	−5.48298	+	23.5999i	−0.173735	+	0.747792i
$997$	15.0860	−	15.0860i	0.477777	−	0.477777i	−0.426643	−	0.904420i	$-0.640304\pi$
$997$	15.0860	−	15.0860i	0.477777	−	0.477777i	0.904420	+	0.426643i	$0.140304\pi$
$998$	−11.8193	−	14.8801i	−0.374135	−	0.471022i
$999$		−	16.2776i		−	0.514999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.q.c.69.4	yes	16
3.2	odd	2		720.2.bm.f.469.5		16
4.3	odd	2		320.2.q.c.49.3		16
5.2	odd	4		400.2.l.i.101.1		16
5.3	odd	4		400.2.l.i.101.8		16
5.4	even	2	inner	80.2.q.c.69.5	yes	16
8.3	odd	2		640.2.q.f.609.6		16
8.5	even	2		640.2.q.e.609.3		16
15.14	odd	2		720.2.bm.f.469.4		16
16.3	odd	4		320.2.q.c.209.6		16
16.5	even	4		640.2.q.e.289.6		16
16.11	odd	4		640.2.q.f.289.3		16
16.13	even	4	inner	80.2.q.c.29.5	yes	16
20.3	even	4		1600.2.l.h.1201.6		16
20.7	even	4		1600.2.l.h.1201.3		16
20.19	odd	2		320.2.q.c.49.6		16
40.19	odd	2		640.2.q.f.609.3		16
40.29	even	2		640.2.q.e.609.6		16
48.29	odd	4		720.2.bm.f.109.4		16
80.3	even	4		1600.2.l.h.401.6		16
80.13	odd	4		400.2.l.i.301.8		16
80.19	odd	4		320.2.q.c.209.3		16
80.29	even	4	inner	80.2.q.c.29.4	✓	16
80.59	odd	4		640.2.q.f.289.6		16
80.67	even	4		1600.2.l.h.401.3		16
80.69	even	4		640.2.q.e.289.3		16
80.77	odd	4		400.2.l.i.301.1		16
240.29	odd	4		720.2.bm.f.109.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.4	✓	16	80.29	even	4	inner
80.2.q.c.29.5	yes	16	16.13	even	4	inner
80.2.q.c.69.4	yes	16	1.1	even	1	trivial
80.2.q.c.69.5	yes	16	5.4	even	2	inner
320.2.q.c.49.3		16	4.3	odd	2
320.2.q.c.49.6		16	20.19	odd	2
320.2.q.c.209.3		16	80.19	odd	4
320.2.q.c.209.6		16	16.3	odd	4
400.2.l.i.101.1		16	5.2	odd	4
400.2.l.i.101.8		16	5.3	odd	4
400.2.l.i.301.1		16	80.77	odd	4
400.2.l.i.301.8		16	80.13	odd	4
640.2.q.e.289.3		16	80.69	even	4
640.2.q.e.289.6		16	16.5	even	4
640.2.q.e.609.3		16	8.5	even	2
640.2.q.e.609.6		16	40.29	even	2
640.2.q.f.289.3		16	16.11	odd	4
640.2.q.f.289.6		16	80.59	odd	4
640.2.q.f.609.3		16	40.19	odd	2
640.2.q.f.609.6		16	8.3	odd	2
720.2.bm.f.109.4		16	48.29	odd	4
720.2.bm.f.109.5		16	240.29	odd	4
720.2.bm.f.469.4		16	15.14	odd	2
720.2.bm.f.469.5		16	3.2	odd	2
1600.2.l.h.401.3		16	80.67	even	4
1600.2.l.h.401.6		16	80.3	even	4
1600.2.l.h.1201.3		16	20.7	even	4
1600.2.l.h.1201.6		16	20.3	even	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.161069 + 1.40501i) q^{2} +(0.734294 + 0.734294i) q^{3} +(-1.94811 - 0.452606i) q^{4} +(-1.17216 + 1.90421i) q^{5} +(-1.14996 + 0.913419i) q^{6} +1.71452 q^{7} +(0.949697 - 2.66422i) q^{8} -1.92163i q^{9} +O(q^{10})\)	\(q+(-0.161069 + 1.40501i) q^{2} +(0.734294 + 0.734294i) q^{3} +(-1.94811 - 0.452606i) q^{4} +(-1.17216 + 1.90421i) q^{5} +(-1.14996 + 0.913419i) q^{6} +1.71452 q^{7} +(0.949697 - 2.66422i) q^{8} -1.92163i q^{9} +(-2.48664 - 1.95361i) q^{10} +(2.82684 + 2.82684i) q^{11} +(-1.09814 - 1.76283i) q^{12} +(-2.59462 - 2.59462i) q^{13} +(-0.276156 + 2.40893i) q^{14} +(-2.25896 + 0.537540i) q^{15} +(3.59030 + 1.76346i) q^{16} -1.89939i q^{17} +(2.69991 + 0.309513i) q^{18} +(2.89623 - 2.89623i) q^{19} +(3.14537 - 3.17910i) q^{20} +(1.25896 + 1.25896i) q^{21} +(-4.42705 + 3.51643i) q^{22} +2.00613 q^{23} +(2.65368 - 1.25896i) q^{24} +(-2.25207 - 4.46410i) q^{25} +(4.06338 - 3.22756i) q^{26} +(3.61392 - 3.61392i) q^{27} +(-3.34009 - 0.776005i) q^{28} +(-6.72307 + 6.72307i) q^{29} +(-0.391402 - 3.26045i) q^{30} -7.11778 q^{31} +(-3.05596 + 4.76037i) q^{32} +4.15146i q^{33} +(2.66867 + 0.305932i) q^{34} +(-2.00970 + 3.26482i) q^{35} +(-0.869740 + 3.74355i) q^{36} +(2.25207 - 2.25207i) q^{37} +(3.60274 + 4.53572i) q^{38} -3.81042i q^{39} +(3.96005 + 4.93133i) q^{40} -1.59630i q^{41} +(-1.97164 + 1.56608i) q^{42} +(-8.06886 + 8.06886i) q^{43} +(-4.22756 - 6.78645i) q^{44} +(3.65919 + 2.25246i) q^{45} +(-0.323124 + 2.81863i) q^{46} -4.43823i q^{47} +(1.34144 + 3.93123i) q^{48} -4.06040 q^{49} +(6.63485 - 2.44515i) q^{50} +(1.39471 - 1.39471i) q^{51} +(3.88027 + 6.22896i) q^{52} +(0.481758 - 0.481758i) q^{53} +(4.49551 + 5.65968i) q^{54} +(-8.69642 + 2.06939i) q^{55} +(1.62828 - 4.56787i) q^{56} +4.25336 q^{57} +(-8.36311 - 10.5289i) q^{58} +(3.08580 + 3.08580i) q^{59} +(4.64401 - 0.0247681i) q^{60} +(3.46410 - 3.46410i) q^{61} +(1.14645 - 10.0006i) q^{62} -3.29468i q^{63} +(-6.19615 - 5.06040i) q^{64} +(7.98203 - 1.89939i) q^{65} +(-5.83285 - 0.668669i) q^{66} +(1.80454 + 1.80454i) q^{67} +(-0.859677 + 3.70023i) q^{68} +(1.47309 + 1.47309i) q^{69} +(-4.26341 - 3.34952i) q^{70} -0.379150i q^{71} +(-5.11964 - 1.82496i) q^{72} +8.37718 q^{73} +(2.80144 + 3.52691i) q^{74} +(1.62428 - 4.93164i) q^{75} +(-6.95303 + 4.33133i) q^{76} +(4.84668 + 4.84668i) q^{77} +(5.35369 + 0.613739i) q^{78} +11.2566 q^{79} +(-7.56641 + 4.76963i) q^{80} -0.457524 q^{81} +(2.24282 + 0.257114i) q^{82} +(-8.24890 - 8.24890i) q^{83} +(-1.88279 - 3.02242i) q^{84} +(3.61685 + 2.22640i) q^{85} +(-10.0372 - 12.6365i) q^{86} -9.87341 q^{87} +(10.2160 - 4.84668i) q^{88} +11.9820i q^{89} +(-3.75411 + 4.77840i) q^{90} +(-4.44854 - 4.44854i) q^{91} +(-3.90816 - 0.907986i) q^{92} +(-5.22654 - 5.22654i) q^{93} +(6.23577 + 0.714859i) q^{94} +(2.12019 + 8.90989i) q^{95} +(-5.73948 + 1.25154i) q^{96} -6.50543i q^{97} +(0.654003 - 5.70491i) q^{98} +(5.43213 - 5.43213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36} + 24 q^{40} - 8 q^{44} + 8 q^{45} - 28 q^{46} + 16 q^{49} + 24 q^{50} - 16 q^{51} + 40 q^{54} - 56 q^{56} - 24 q^{59} + 48 q^{60} - 16 q^{64} - 72 q^{66} + 32 q^{69} + 20 q^{70} + 48 q^{75} - 88 q^{76} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 80 q^{84} - 28 q^{86} - 84 q^{90} - 16 q^{91} + 12 q^{94} + 32 q^{95} + 56 q^{96} + 88 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

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