LMFDB - Embedded newform 750.2.o.a.469.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			469.4
Character	$\chi$	$=$	750.469
Dual form			750.2.o.a.379.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998027 + 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(0.522536 + 2.17416i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(2.26089 + 3.11184i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(-0.998027 + 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(0.522536 + 2.17416i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(2.26089 + 3.11184i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-0.658021 - 2.13706i) q^{10} +(-0.123491 - 1.96284i) q^{11} +(0.844328 - 0.535827i) q^{12} +(2.53327 + 2.09571i) q^{13} +(-2.45182 - 2.96374i) q^{14} +(1.39852 + 1.74475i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.197784 - 1.56562i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-1.71156 + 3.63726i) q^{19} +(0.790910 + 2.09152i) q^{20} +(3.37067 + 1.85304i) q^{21} +(0.246495 + 1.95121i) q^{22} +(-0.659985 - 1.66693i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-4.45391 + 2.27215i) q^{25} +(-2.65987 - 1.93251i) q^{26} +(0.248690 - 0.968583i) q^{27} +(2.63307 + 2.80394i) q^{28} +(-1.66901 + 1.56730i) q^{29} +(-1.50531 - 1.65349i) q^{30} +(-2.36054 - 0.298205i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(-0.947474 - 1.72345i) q^{33} +(-0.0990875 + 1.57495i) q^{34} +(-5.58424 + 6.54157i) q^{35} +(0.535827 - 0.844328i) q^{36} +(1.26935 + 4.94380i) q^{37} +(1.47980 - 3.73755i) q^{38} +(3.18448 + 0.817637i) q^{39} +(-0.920677 - 2.03773i) q^{40} +(-2.22085 - 0.879297i) q^{41} +(-3.48037 - 1.63774i) q^{42} +(0.229186 + 0.0744670i) q^{43} +(-0.368526 - 1.93188i) q^{44} +(2.00829 + 0.983239i) q^{45} +(0.763350 + 1.62220i) q^{46} +(1.89042 + 0.360618i) q^{47} +(0.770513 - 0.637424i) q^{48} +(-2.40884 + 7.41364i) q^{49} +(4.30245 - 2.54733i) q^{50} +(-0.487649 - 1.50083i) q^{51} +(2.77596 + 1.76168i) q^{52} +(5.69545 - 10.3600i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(4.20299 - 1.29414i) q^{55} +(-2.80394 - 2.63307i) q^{56} +4.01983i q^{57} +(1.56730 - 1.66901i) q^{58} +(3.66056 + 5.76811i) q^{59} +(1.60616 + 1.55571i) q^{60} +(8.69358 - 3.44203i) q^{61} +(2.37460 + 0.149397i) q^{62} +(3.83886 + 0.241520i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-3.23267 + 6.60282i) q^{65} +(1.05382 + 1.66055i) q^{66} +(7.60925 - 8.10303i) q^{67} -1.57806i q^{68} +(-1.30692 - 1.22728i) q^{69} +(5.16247 - 6.87930i) q^{70} +(-2.37507 + 12.4506i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(-2.55495 - 1.62142i) q^{73} +(-1.57727 - 4.85434i) q^{74} +(-3.06259 + 3.95229i) q^{75} +(-1.24220 + 3.82309i) q^{76} +(5.82884 - 4.82203i) q^{77} +(-3.22954 - 0.616068i) q^{78} +(2.15123 + 4.57159i) q^{79} +(1.04681 + 1.97590i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(2.27168 + 0.738113i) q^{82} +(-10.4350 - 4.91036i) q^{83} +(3.57634 + 1.41597i) q^{84} +(3.50725 - 0.388080i) q^{85} +(-0.233410 - 0.0599294i) q^{86} +(-0.842839 + 2.12877i) q^{87} +(0.489103 + 1.90493i) q^{88} +(-1.49820 + 2.36078i) q^{89} +(-2.06607 - 0.855197i) q^{90} +(-0.794065 + 12.6213i) q^{91} +(-0.863703 - 1.57107i) q^{92} +(-2.26285 + 0.735243i) q^{93} +(-1.90934 - 0.241205i) q^{94} +(-8.80231 - 1.82061i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(11.8702 + 12.6405i) q^{97} +(1.93858 - 7.55026i) q^{98} +(-1.59111 - 1.15601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) $ 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{49}{50}\right)$	$1$

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 $

$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$3$	0.904827	−	0.425779i	0.522402	−	0.245824i
$3$	0.904827	−	0.425779i	0.522402	−	0.245824i
$4$	0.992115	−	0.125333i	0.496057	−	0.0626666i
$5$	0.522536	+	2.17416i	0.233685	+	0.972312i
$5$	0.522536	+	2.17416i	0.233685	+	0.972312i
$6$	−0.876307	+	0.481754i	−0.357751	+	0.196675i
$7$	2.26089	+	3.11184i	0.854534	+	1.17617i	0.982845	+	0.184432i	$0.0590444\pi$
$7$	2.26089	+	3.11184i	0.854534	+	1.17617i	−0.128311	+	0.991734i	$0.540956\pi$
$8$	−0.982287	+	0.187381i	−0.347291	+	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	−0.658021	−	2.13706i	−0.208085	−	0.675796i
$11$	−0.123491	−	1.96284i	−0.0372340	−	0.591818i	−0.971767	−	0.235942i	$-0.924183\pi$
$11$	−0.123491	−	1.96284i	−0.0372340	−	0.591818i	0.934533	−	0.355876i	$-0.115817\pi$
$12$	0.844328	−	0.535827i	0.243736	−	0.154680i
$13$	2.53327	+	2.09571i	0.702604	+	0.581245i	0.918619	−	0.395146i	$-0.129306\pi$
$13$	2.53327	+	2.09571i	0.702604	+	0.581245i	−0.216015	+	0.976390i	$0.569306\pi$
$14$	−2.45182	−	2.96374i	−0.655276	−	0.792093i
$15$	1.39852	+	1.74475i	0.361095	+	0.450493i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	0.197784	−	1.56562i	0.0479696	−	0.379719i	−0.949794	−	0.312876i	$-0.898707\pi$
$17$	0.197784	−	1.56562i	0.0479696	−	0.379719i	0.997764	−	0.0668426i	$-0.0212925\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	−1.71156	+	3.63726i	−0.392659	+	0.834444i	0.606564	+	0.795035i	$0.292547\pi$
$19$	−1.71156	+	3.63726i	−0.392659	+	0.834444i	−0.999223	+	0.0394088i	$0.987453\pi$
$20$	0.790910	+	2.09152i	0.176853	+	0.467678i
$21$	3.37067	+	1.85304i	0.735540	+	0.404367i
$22$	0.246495	+	1.95121i	0.0525529	+	0.415999i
$23$	−0.659985	−	1.66693i	−0.137616	−	0.347579i	0.844582	−	0.535426i	$-0.179849\pi$
$23$	−0.659985	−	1.66693i	−0.137616	−	0.347579i	−0.982198	+	0.187847i	$0.939849\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−4.45391	+	2.27215i	−0.890782	+	0.454430i
$26$	−2.65987	−	1.93251i	−0.521643	−	0.378996i
$27$	0.248690	−	0.968583i	0.0478604	−	0.186404i
$28$	2.63307	+	2.80394i	0.497604	+	0.529895i
$29$	−1.66901	+	1.56730i	−0.309927	+	0.291041i	−0.823865	−	0.566787i	$-0.808186\pi$
$29$	−1.66901	+	1.56730i	−0.309927	+	0.291041i	0.513937	+	0.857828i	$0.328186\pi$
$30$	−1.50531	−	1.65349i	−0.274831	−	0.301885i
$31$	−2.36054	−	0.298205i	−0.423965	−	0.0535592i	−0.0895435	−	0.995983i	$-0.528541\pi$
$31$	−2.36054	−	0.298205i	−0.423965	−	0.0535592i	−0.334421	+	0.942424i	$0.608541\pi$
$32$	−0.951057	+	0.309017i	−0.168125	+	0.0546270i
$33$	−0.947474	−	1.72345i	−0.164934	−	0.300014i
$34$	−0.0990875	+	1.57495i	−0.0169934	+	0.270102i
$35$	−5.58424	+	6.54157i	−0.943908	+	1.10573i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	1.26935	+	4.94380i	0.208680	+	0.812756i	0.983550	+	0.180635i	$0.0578154\pi$
$37$	1.26935	+	4.94380i	0.208680	+	0.812756i	−0.774870	+	0.632121i	$0.782185\pi$
$38$	1.47980	−	3.73755i	0.240055	−	0.606310i
$39$	3.18448	+	0.817637i	0.509926	+	0.130927i
$40$	−0.920677	−	2.03773i	−0.145572	−	0.322194i
$41$	−2.22085	−	0.879297i	−0.346839	−	0.137323i	0.188245	−	0.982122i	$-0.439720\pi$
$41$	−2.22085	−	0.879297i	−0.346839	−	0.137323i	−0.535084	+	0.844799i	$0.679720\pi$
$42$	−3.48037	−	1.63774i	−0.537033	−	0.252708i
$43$	0.229186	+	0.0744670i	0.0349505	+	0.0113561i	0.326440	−	0.945218i	$-0.394151\pi$
$43$	0.229186	+	0.0744670i	0.0349505	+	0.0113561i	−0.291490	+	0.956574i	$0.594151\pi$
$44$	−0.368526	−	1.93188i	−0.0555574	−	0.291242i
$45$	2.00829	+	0.983239i	0.299379	+	0.146573i
$46$	0.763350	+	1.62220i	0.112550	+	0.239181i
$47$	1.89042	+	0.360618i	0.275747	+	0.0526015i	0.323400	−	0.946262i	$-0.395174\pi$
$47$	1.89042	+	0.360618i	0.275747	+	0.0526015i	−0.0476530	+	0.998864i	$0.515174\pi$
$48$	0.770513	−	0.637424i	0.111214	−	0.0920042i
$49$	−2.40884	+	7.41364i	−0.344120	+	1.05909i
$50$	4.30245	−	2.54733i	0.608459	−	0.360247i
$51$	−0.487649	−	1.50083i	−0.0682845	−	0.210158i
$52$	2.77596	+	1.76168i	0.384956	+	0.244301i
$53$	5.69545	−	10.3600i	0.782330	−	1.42305i	−0.120346	−	0.992732i	$-0.538400\pi$
$53$	5.69545	−	10.3600i	0.782330	−	1.42305i	0.902676	−	0.430321i	$-0.141600\pi$
$54$	−0.187381	+	0.982287i	−0.0254994	+	0.133672i
$55$	4.20299	−	1.29414i	0.566731	−	0.174502i
$56$	−2.80394	−	2.63307i	−0.374692	−	0.351859i
$57$			4.01983i			0.532440i
$58$	1.56730	−	1.66901i	0.205797	−	0.219152i
$59$	3.66056	+	5.76811i	0.476564	+	0.750944i	0.994529	−	0.104457i	$-0.0333105\pi$
$59$	3.66056	+	5.76811i	0.476564	+	0.750944i	−0.517966	+	0.855401i	$0.673310\pi$
$60$	1.60616	+	1.55571i	0.207355	+	0.200842i
$61$	8.69358	−	3.44203i	1.11310	−	0.440707i	0.261659	−	0.965160i	$-0.415730\pi$
$61$	8.69358	−	3.44203i	1.11310	−	0.440707i	0.851439	+	0.524454i	$0.175730\pi$
$62$	2.37460	+	0.149397i	0.301575	+	0.0189735i
$63$	3.83886	+	0.241520i	0.483651	+	0.0304287i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	−3.23267	+	6.60282i	−0.400963	+	0.818979i
$66$	1.05382	+	1.66055i	0.129716	+	0.204400i
$67$	7.60925	−	8.10303i	0.929618	−	0.989942i	−0.0703536	−	0.997522i	$-0.522413\pi$
$67$	7.60925	−	8.10303i	0.929618	−	0.989942i	0.999971	+	0.00757983i	$0.00241276\pi$
$68$		−	1.57806i		−	0.191368i
$69$	−1.30692	−	1.22728i	−0.157334	−	0.147747i
$70$	5.16247	−	6.87930i	0.617033	−	0.822233i
$71$	−2.37507	+	12.4506i	−0.281869	+	1.47761i	0.506409	+	0.862293i	$0.330972\pi$
$71$	−2.37507	+	12.4506i	−0.281869	+	1.47761i	−0.788279	+	0.615318i	$0.789028\pi$
$72$	−0.481754	+	0.876307i	−0.0567752	+	0.103274i
$73$	−2.55495	−	1.62142i	−0.299035	−	0.189773i	0.377841	−	0.925870i	$-0.376667\pi$
$73$	−2.55495	−	1.62142i	−0.299035	−	0.189773i	−0.676876	+	0.736097i	$0.736667\pi$
$74$	−1.57727	−	4.85434i	−0.183354	−	0.564306i
$75$	−3.06259	+	3.95229i	−0.353637	+	0.456371i
$76$	−1.24220	+	3.82309i	−0.142490	+	0.438539i
$77$	5.82884	−	4.82203i	0.664258	−	0.549522i
$78$	−3.22954	−	0.616068i	−0.365673	−	0.0697559i
$79$	2.15123	+	4.57159i	0.242032	+	0.514344i	0.988527	−	0.151047i	$-0.0482646\pi$
$79$	2.15123	+	4.57159i	0.242032	+	0.514344i	−0.746495	+	0.665392i	$0.768265\pi$
$80$	1.04681	+	1.97590i	0.117037	+	0.220913i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	2.27168	+	0.738113i	0.250865	+	0.0815110i
$83$	−10.4350	−	4.91036i	−1.14540	−	0.538982i	−0.243057	−	0.970012i	$-0.578150\pi$
$83$	−10.4350	−	4.91036i	−1.14540	−	0.538982i	−0.902338	+	0.431030i	$0.858150\pi$
$84$	3.57634	+	1.41597i	0.390210	+	0.154495i
$85$	3.50725	−	0.388080i	0.380415	−	0.0420932i
$86$	−0.233410	−	0.0599294i	−0.0251692	−	0.00646235i
$87$	−0.842839	+	2.12877i	−0.0903618	+	0.228228i
$88$	0.489103	+	1.90493i	0.0521385	+	0.203066i
$89$	−1.49820	+	2.36078i	−0.158809	+	0.250242i	−0.914410	−	0.404789i	$-0.867345\pi$
$89$	−1.49820	+	2.36078i	−0.158809	+	0.250242i	0.755601	+	0.655032i	$0.227345\pi$
$90$	−2.06607	−	0.855197i	−0.217783	−	0.0901456i
$91$	−0.794065	+	12.6213i	−0.0832406	+	1.32307i
$92$	−0.863703	−	1.57107i	−0.0900472	−	0.163795i
$93$	−2.26285	+	0.735243i	−0.234646	+	0.0762412i
$94$	−1.90934	−	0.241205i	−0.196933	−	0.0248784i
$95$	−8.80231	−	1.82061i	−0.903098	−	0.186790i
$96$	−0.728969	+	0.684547i	−0.0744000	+	0.0698663i
$97$	11.8702	+	12.6405i	1.20524	+	1.28345i	0.948430	+	0.316988i	$0.102671\pi$
$97$	11.8702	+	12.6405i	1.20524	+	1.28345i	0.256810	+	0.966462i	$0.417329\pi$
$98$	1.93858	−	7.55026i	0.195826	−	0.762691i
$99$	−1.59111	−	1.15601i	−0.159912	−	0.116183i
$100$	−4.13402	+	2.81246i	−0.413402	+	0.281246i
$101$	5.81401	−	4.22413i	0.578516	−	0.420316i	−0.259673	−	0.965697i	$-0.583615\pi$
$101$	5.81401	−	4.22413i	0.578516	−	0.420316i	0.838189	+	0.545380i	$0.183615\pi$
$102$	0.580924	+	1.46725i	0.0575201	+	0.145279i
$103$	−2.44688	−	19.3690i	−0.241098	−	1.90849i	−0.392043	−	0.919947i	$-0.628232\pi$
$103$	−2.44688	−	19.3690i	−0.241098	−	1.90849i	0.150945	−	0.988542i	$-0.451768\pi$
$104$	−2.88110	−	1.58390i	−0.282515	−	0.155314i
$105$	−2.26750	+	8.29664i	−0.221286	+	0.809669i
$106$	−5.03370	+	10.6972i	−0.488916	+	1.03900i
$107$	−0.907429	+	1.24897i	−0.0877245	+	0.120742i	−0.850624	−	0.525775i	$-0.823775\pi$
$107$	−0.907429	+	1.24897i	−0.0877245	+	0.120742i	0.762899	+	0.646518i	$0.223775\pi$
$108$	0.125333	−	0.992115i	0.0120602	−	0.0954663i
$109$	−7.69444	+	1.97560i	−0.736993	+	0.189228i	−0.598486	−	0.801134i	$-0.704231\pi$
$109$	−7.69444	+	1.97560i	−0.736993	+	0.189228i	−0.138508	+	0.990361i	$0.544231\pi$
$110$	−4.11343	+	1.55550i	−0.392200	+	0.148311i
$111$	3.25351	+	3.93282i	0.308810	+	0.373287i
$112$	2.96374	+	2.45182i	0.280047	+	0.231675i
$113$	−2.51107	+	1.59358i	−0.236222	+	0.149911i	−0.648669	−	0.761071i	$-0.724674\pi$
$113$	−2.51107	+	1.59358i	−0.236222	+	0.149911i	0.412447	+	0.910981i	$0.364674\pi$
$114$	−0.252408	−	4.01190i	−0.0236401	−	0.375749i
$115$	3.27930	−	2.30594i	0.305797	−	0.215030i
$116$	−1.45941	+	1.76413i	−0.135503	+	0.163795i
$117$	3.22954	−	0.616068i	0.298571	−	0.0569555i
$118$	−4.01552	−	5.52688i	−0.369658	−	0.508791i
$119$	5.31913	−	2.92422i	0.487604	−	0.268063i
$120$	−1.70068	−	1.45179i	−0.155250	−	0.132530i
$121$	7.07578	−	0.893879i	0.643253	−	0.0812617i
$122$	−8.46029	+	3.98111i	−0.765959	+	0.360433i
$123$	−2.38387	+	0.149981i	−0.214947	+	0.0135233i
$124$	−2.37930			−0.213667
$125$	−7.26734	−	8.49622i	−0.650011	−	0.759925i
$126$	−3.84645			−0.342669
$127$	13.9503	−	0.877678i	1.23789	−	0.0778813i	0.569687	−	0.821862i	$-0.307065\pi$
$127$	13.9503	−	0.877678i	1.23789	−	0.0778813i	0.668201	+	0.743981i	$0.267065\pi$
$128$	−0.904827	+	0.425779i	−0.0799762	+	0.0376339i
$129$	0.239080	−	0.0302028i	0.0210498	−	0.00265921i
$130$	2.81169	−	6.79277i	0.246602	−	0.595765i
$131$	−15.9064	+	8.74460i	−1.38975	+	0.764019i	−0.988395	−	0.151905i	$-0.951459\pi$
$131$	−15.9064	+	8.74460i	−1.38975	+	0.764019i	−0.401351	+	0.915924i	$0.631459\pi$
$132$	−1.15601	−	1.59111i	−0.100618	−	0.138488i
$133$	−15.1882	+	2.89731i	−1.31698	+	0.251228i
$134$	−7.08544	+	8.56483i	−0.612089	+	0.739888i
$135$	2.23580	+	0.0345711i	0.192427	+	0.00297541i
$136$	0.0990875	+	1.57495i	0.00849668	+	0.135051i
$137$	8.41727	−	5.34176i	0.719136	−	0.456378i	−0.125241	−	0.992126i	$-0.539971\pi$
$137$	8.41727	−	5.34176i	0.719136	−	0.456378i	0.844378	+	0.535749i	$0.179971\pi$
$138$	1.38140	+	1.14279i	0.117593	+	0.0972810i
$139$	−9.34344	−	11.2943i	−0.792501	−	0.957969i	0.207293	−	0.978279i	$-0.433535\pi$
$139$	−9.34344	−	11.2943i	−0.792501	−	0.957969i	−0.999794	+	0.0203103i	$0.993535\pi$
$140$	−4.72033	+	7.18988i	−0.398940	+	0.607655i
$141$	1.86405	−	0.478607i	0.156981	−	0.0403060i
$142$	1.58861	−	12.5751i	0.133313	−	1.05528i
$143$	3.80069	−	5.23121i	0.317830	−	0.437455i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	−4.27968	−	2.80971i	−0.355408	−	0.233334i
$146$	2.65172	+	1.45780i	0.219458	+	0.120648i
$147$	0.976992	+	7.73369i	0.0805810	+	0.637864i
$148$	1.87897	+	4.74573i	0.154450	+	0.390096i
$149$	2.74520	−	1.99451i	0.224896	−	0.163396i	−0.469632	−	0.882862i	$-0.655613\pi$
$149$	2.74520	−	1.99451i	0.224896	−	0.163396i	0.694528	+	0.719466i	$0.255613\pi$
$150$	2.80838	−	4.13679i	0.229303	−	0.337767i
$151$	−10.9467	−	7.95323i	−0.890829	−	0.647225i	0.0452653	−	0.998975i	$-0.485587\pi$
$151$	−10.9467	−	7.95323i	−0.890829	−	0.647225i	−0.936094	+	0.351750i	$0.885587\pi$
$152$	0.999692	−	3.89354i	0.0810857	−	0.315808i
$153$	−1.08026	−	1.15036i	−0.0873338	−	0.0930010i
$154$	−5.51456	+	5.17851i	−0.444376	+	0.417297i
$155$	−0.585121	−	5.28800i	−0.0469980	−	0.424742i
$156$	3.26185	+	0.412068i	0.261157	+	0.0329918i
$157$	11.6079	−	3.77165i	0.926414	−	0.301010i	0.193319	−	0.981136i	$-0.438075\pi$
$157$	11.6079	−	3.77165i	0.926414	−	0.301010i	0.733096	+	0.680126i	$0.238075\pi$
$158$	−2.43404	−	4.42749i	−0.193641	−	0.352233i
$159$	0.742330	−	11.7990i	0.0588706	−	0.935721i
$160$	−1.16881	−	1.90627i	−0.0924027	−	0.150704i
$161$	3.69508	−	5.82251i	0.291213	−	0.458878i
$162$	0.248690	+	0.968583i	0.0195389	+	0.0760991i
$163$	−1.98503	+	5.01362i	−0.155480	+	0.392697i	−0.986548	−	0.163474i	$-0.947730\pi$
$163$	−1.98503	+	5.01362i	−0.155480	+	0.392697i	0.831068	+	0.556171i	$0.187730\pi$
$164$	−2.31354	−	0.594017i	−0.180657	−	0.0463849i
$165$	3.25196	−	2.96052i	0.253164	−	0.230476i
$166$	10.7228	+	4.24545i	0.832249	+	0.329511i
$167$	8.90375	+	4.18978i	0.688993	+	0.324215i	0.738208	−	0.674573i	$-0.235672\pi$
$167$	8.90375	+	4.18978i	0.688993	+	0.324215i	−0.0492157	+	0.998788i	$0.515672\pi$
$168$	−3.65819	−	1.18862i	−0.282235	−	0.0917038i
$169$	−0.410465	−	2.15173i	−0.0315742	−	0.165518i
$170$	−3.47597	+	0.607537i	−0.266594	+	0.0465959i
$171$	1.71156	+	3.63726i	0.130886	+	0.278148i
$172$	0.236712	+	0.0451552i	0.0180491	+	0.00344305i
$173$	9.62576	−	7.96312i	0.731833	−	0.605425i	−0.195042	−	0.980795i	$-0.562484\pi$
$173$	9.62576	−	7.96312i	0.731833	−	0.605425i	0.926875	+	0.375370i	$0.122484\pi$
$174$	0.707509	−	2.17749i	0.0536361	−	0.165075i
$175$	−17.1404	−	8.72280i	−1.29569	−	0.659382i
$176$	−0.607749	−	1.87046i	−0.0458108	−	0.140991i
$177$	5.76811	+	3.66056i	0.433558	+	0.275144i
$178$	1.34701	−	2.45020i	0.100962	−	0.183650i
$179$	2.31281	−	12.1242i	0.172868	−	0.906204i	−0.785109	−	0.619358i	$-0.787393\pi$
$179$	2.31281	−	12.1242i	0.172868	−	0.906204i	0.957977	−	0.286846i	$-0.0926069\pi$
$180$	2.11569	+	0.723779i	0.157694	+	0.0539473i
$181$	0.446492	+	0.419284i	0.0331875	+	0.0311652i	0.700963	−	0.713197i	$-0.252754\pi$
$181$	0.446492	+	0.419284i	0.0331875	+	0.0311652i	−0.667776	+	0.744362i	$0.732754\pi$
$182$		−	12.6463i		−	0.937403i
$183$	6.40064	−	6.81599i	0.473149	−	0.503852i
$184$	0.960646	+	1.51374i	0.0708198	+	0.111594i
$185$	−10.0853	+	5.34309i	−0.741487	+	0.392832i
$186$	2.21221	−	0.875877i	0.162207	−	0.0642225i
$187$	−3.09748	−	0.194877i	−0.226510	−	0.0142508i
$188$	1.92071	+	0.120841i	0.140083	+	0.00881324i
$189$	3.57634	−	1.41597i	0.260140	−	0.102997i
$190$	8.89926	+	1.26431i	0.645620	+	0.0917229i
$191$	−11.6265	−	18.3205i	−0.841266	−	1.32562i	−0.943673	−	0.330880i	$-0.892655\pi$
$191$	−11.6265	−	18.3205i	−0.841266	−	1.32562i	0.102407	−	0.994743i	$-0.467345\pi$
$192$	0.684547	−	0.728969i	0.0494029	−	0.0526088i
$193$		−	5.00254i		−	0.360090i	−0.983658	−	0.180045i	$-0.942376\pi$
$193$		−	5.00254i		−	0.360090i	0.983658	−	0.180045i	$-0.0576244\pi$
$194$	−12.6405	−	11.8702i	−0.907536	−	0.852233i
$195$	−0.113662	+	7.35081i	−0.00813951	+	0.526402i
$196$	−1.46067	+	7.65709i	−0.104333	+	0.546935i
$197$	−12.4259	+	22.6026i	−0.885307	+	1.61037i	−0.0968307	+	0.995301i	$0.530871\pi$
$197$	−12.4259	+	22.6026i	−0.885307	+	1.61037i	−0.788476	+	0.615066i	$0.789129\pi$
$198$	1.66055	+	1.05382i	0.118010	+	0.0748917i
$199$	−4.02353	−	12.3831i	−0.285220	−	0.877818i	−0.986333	−	0.164767i	$-0.947313\pi$
$199$	−4.02353	−	12.3831i	−0.285220	−	0.877818i	0.701112	−	0.713051i	$-0.252687\pi$
$200$	3.94926	−	3.06648i	0.279255	−	0.216833i
$201$	3.43495	−	10.5717i	0.242283	−	0.745670i
$202$	−5.53730	+	4.58085i	−0.389603	+	0.322308i
$203$	−8.65063	−	1.65020i	−0.607156	−	0.115821i
$204$	−0.671907	−	1.42788i	−0.0470429	−	0.0999713i
$205$	0.751255	−	5.28794i	0.0524699	−	0.369326i
$206$	3.65824	+	19.1772i	0.254882	+	1.33614i
$207$	−1.70508	−	0.554015i	−0.118511	−	0.0385067i
$208$	2.97487	+	1.39987i	0.206270	+	0.0970633i
$209$	7.35070	+	2.91035i	0.508459	+	0.201313i
$210$	1.74208	−	8.42265i	0.120215	−	0.581218i
$211$	−16.2347	−	4.16835i	−1.11764	−	0.286961i	−0.355695	−	0.934602i	$-0.615756\pi$
$211$	−16.2347	−	4.16835i	−1.11764	−	0.286961i	−0.761946	+	0.647641i	$0.775756\pi$
$212$	4.35209	−	10.9921i	0.298903	−	0.754942i
$213$	3.15217	+	12.2769i	0.215983	+	0.841198i
$214$	0.827215	−	1.30348i	0.0565473	−	0.0891042i
$215$	−0.0421450	+	0.537198i	−0.00287427	+	0.0366366i
$216$	−0.0627905	+	0.998027i	−0.00427235	+	0.0679071i
$217$	−4.40893	−	8.01982i	−0.299298	−	0.544421i
$218$	7.55520	−	2.45483i	0.511703	−	0.166262i
$219$	−3.00216	−	0.379261i	−0.202867	−	0.0256281i
$220$	4.00765	−	1.81071i	0.270195	−	0.122078i
$221$	3.78212	−	3.55165i	0.254413	−	0.238910i
$222$	−3.49404	−	3.72077i	−0.234504	−	0.249722i
$223$	6.13032	−	23.8760i	0.410516	−	1.59886i	−0.341614	−	0.939840i	$-0.610973\pi$
$223$	6.13032	−	23.8760i	0.410516	−	1.59886i	0.752130	−	0.659015i	$-0.229027\pi$
$224$	−3.11184	−	2.26089i	−0.207919	−	0.151062i
$225$	−1.08831	+	4.88012i	−0.0725539	+	0.325341i
$226$	2.40606	−	1.74810i	0.160049	−	0.116282i
$227$	−9.28468	−	23.4504i	−0.616246	−	1.55646i	−0.816889	−	0.576795i	$-0.804303\pi$
$227$	−9.28468	−	23.4504i	−0.616246	−	1.55646i	0.200644	−	0.979664i	$-0.435697\pi$
$228$	0.503819	+	3.98814i	0.0333662	+	0.264121i
$229$	−21.1741	−	11.6406i	−1.39922	−	0.769230i	−0.409513	−	0.912304i	$-0.634301\pi$
$229$	−21.1741	−	11.6406i	−1.39922	−	0.769230i	−0.989712	+	0.143074i	$0.954301\pi$
$230$	−3.12804	+	2.50730i	−0.206257	+	0.165327i
$231$	3.22097	−	6.84491i	0.211924	−	0.450362i
$232$	1.34576	−	1.85228i	0.0883536	−	0.121608i
$233$	−0.343968	+	2.72278i	−0.0225341	+	0.178376i	−0.999365	−	0.0356380i	$-0.988654\pi$
$233$	−0.343968	+	2.72278i	−0.0225341	+	0.178376i	0.976831	+	0.214014i	$0.0686537\pi$
$234$	−3.18448	+	0.817637i	−0.208176	+	0.0534506i
$235$	0.203775	+	4.29851i	0.0132928	+	0.280404i
$236$	4.35463	+	5.26384i	0.283462	+	0.342647i
$237$	3.89298	+	3.22055i	0.252876	+	0.209197i
$238$	−5.12502	+	3.25244i	−0.332206	+	0.210824i
$239$	0.188527	+	2.99656i	0.0121948	+	0.193831i	0.999407	+	0.0344218i	$0.0109590\pi$
$239$	0.188527	+	2.99656i	0.0121948	+	0.193831i	−0.987213	+	0.159409i	$0.949041\pi$
$240$	1.78848	+	1.34214i	0.115446	+	0.0866347i
$241$	−15.4863	+	18.7197i	−0.997558	+	1.20584i	−0.0190109	+	0.999819i	$0.506052\pi$
$241$	−15.4863	+	18.7197i	−0.997558	+	1.20584i	−0.978547	+	0.206022i	$0.933948\pi$
$242$	−7.00569	+	1.33641i	−0.450343	+	0.0859075i
$243$	−0.587785	−	0.809017i	−0.0377064	−	0.0518985i
$244$	8.19362	−	4.50448i	0.524543	−	0.288370i
$245$	−17.3771	−	1.36330i	−1.11018	−	0.0870977i
$246$	2.36975	−	0.299369i	0.151090	−	0.0190871i
$247$	−11.9585	+	5.62723i	−0.760900	+	0.358052i
$248$	2.37460	−	0.149397i	0.150787	−	0.00948674i
$249$	−11.5326			−0.730851
$250$	7.78648	+	8.02314i	0.492460	+	0.507428i
$251$	7.11427			0.449049			0.224524	−	0.974468i	$-0.427917\pi$
$251$	7.11427			0.449049			0.224524	+	0.974468i	$0.427917\pi$
$252$	3.83886	−	0.241520i	0.241825	−	0.0152144i
$253$	−3.19041	+	1.50129i	−0.200580	+	0.0943856i
$254$	−13.8677	+	1.75189i	−0.870134	+	0.109923i
$255$	3.00822	−	1.84446i	0.188382	−	0.115505i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	−5.31293	−	7.31262i	−0.331412	−	0.456149i	0.610497	−	0.792019i	$-0.290970\pi$
$257$	−5.31293	−	7.31262i	−0.331412	−	0.456149i	−0.941908	+	0.335870i	$0.890970\pi$
$258$	−0.236712	+	0.0451552i	−0.0147370	+	0.00281124i
$259$	−12.5145	+	15.1274i	−0.777611	+	0.939971i
$260$	−2.37962	+	6.95591i	−0.147578	+	0.431387i
$261$	0.143762	+	2.28503i	0.00889864	+	0.141440i
$262$	15.3259	−	9.72612i	0.946838	−	0.600881i
$263$	14.2997	+	11.8297i	0.881756	+	0.729452i	0.963644	−	0.267190i	$-0.0860951\pi$
$263$	14.2997	+	11.8297i	0.881756	+	0.729452i	−0.0818884	+	0.996642i	$0.526095\pi$
$264$	1.25363	+	1.51538i	0.0771558	+	0.0932653i
$265$	25.5003	+	6.96933i	1.56647	+	0.428123i
$266$	14.9763	−	3.84526i	0.918257	−	0.235768i
$267$	−0.350438	+	2.77400i	−0.0214464	+	0.169766i
$268$	6.53367	−	8.99282i	0.399107	−	0.549324i
$269$	10.1228	−	21.5120i	0.617197	−	1.31161i	−0.314805	−	0.949157i	$-0.601939\pi$
$269$	10.1228	−	21.5120i	0.617197	−	1.31161i	0.932002	−	0.362454i	$-0.118061\pi$
$270$	−2.23356	+	0.105884i	−0.135930	+	0.00644391i
$271$	10.4593	+	5.75005i	0.635357	+	0.349291i	0.766661	−	0.642052i	$-0.221917\pi$
$271$	10.4593	+	5.75005i	0.635357	+	0.349291i	−0.131304	+	0.991342i	$0.541917\pi$
$272$	−0.197784	−	1.56562i	−0.0119924	−	0.0949297i
$273$	4.65540	+	11.7582i	0.281757	+	0.711638i
$274$	−8.06525	+	5.85975i	−0.487240	+	0.354000i
$275$	5.00988	+	8.46171i	0.302107	+	0.510261i
$276$	−1.45043	−	1.05380i	−0.0873056	−	0.0634313i
$277$	−2.94957	+	11.4878i	−0.177222	+	0.690235i	0.816401	+	0.577485i	$0.195966\pi$
$277$	−2.94957	+	11.4878i	−0.177222	+	0.690235i	−0.993623	+	0.112750i	$0.964034\pi$
$278$	10.0342	+	10.6853i	0.601810	+	0.640863i
$279$	−1.73443	+	1.62874i	−0.103838	+	0.0975101i
$280$	4.25956	−	7.47208i	0.254557	−	0.446542i
$281$	21.7704	+	2.75024i	1.29871	+	0.164066i	0.744114	−	0.668053i	$-0.232872\pi$
$281$	21.7704	+	2.75024i	1.29871	+	0.164066i	0.554598	+	0.832118i	$0.312872\pi$
$282$	−1.83032	+	0.594707i	−0.108994	+	0.0354143i
$283$	−14.0715	−	25.5960i	−0.836464	−	1.52152i	−0.853152	−	0.521662i	$-0.825312\pi$
$283$	−14.0715	−	25.5960i	−0.836464	−	1.52152i	0.0166880	−	0.999861i	$-0.494688\pi$
$284$	−0.795875	+	12.6501i	−0.0472265	+	0.750644i
$285$	−8.73975	+	2.10051i	−0.517698	+	0.124423i
$286$	−3.46472	+	5.45953i	−0.204873	+	0.322829i
$287$	−2.28486	−	8.89892i	−0.134871	−	0.525287i
$288$	−0.368125	+	0.929776i	−0.0216919	+	0.0547876i
$289$	14.0539	+	3.60842i	0.826698	+	0.212260i
$290$	4.44766	+	2.53545i	0.261175	+	0.148886i
$291$	16.1226	+	6.38338i	0.945122	+	0.374200i
$292$	−2.73802	−	1.28842i	−0.160231	−	0.0753989i
$293$	27.0649	+	8.79392i	1.58115	+	0.513746i	0.962352	−	0.271806i	$-0.0876209\pi$
$293$	27.0649	+	8.79392i	1.58115	+	0.513746i	0.618796	+	0.785552i	$0.287621\pi$
$294$	−1.46067	−	7.65709i	−0.0851878	−	0.446570i
$295$	−10.6280	+	10.9727i	−0.618786	+	0.638853i
$296$	−2.17325	−	4.61838i	−0.126317	−	0.268438i
$297$	−1.93188	−	0.368526i	−0.112099	−	0.0213841i
$298$	−2.61455	+	2.16294i	−0.151457	+	0.125296i
$299$	1.82148	−	5.60593i	0.105339	−	0.324199i
$300$	−2.54308	+	4.30497i	−0.146825	+	0.248547i
$301$	0.286434	+	0.881552i	0.0165098	+	0.0508118i
$302$	11.4245	+	7.25019i	0.657404	+	0.417202i
$303$	3.46213	−	6.29759i	0.198894	−	0.361787i
$304$	−0.753242	+	3.94863i	−0.0432014	+	0.226470i
$305$	12.0262	+	17.1026i	0.688619	+	0.979293i
$306$	1.15036	+	1.08026i	0.0657617	+	0.0617543i
$307$		−	22.1639i		−	1.26496i	−0.774576	−	0.632480i	$-0.782037\pi$
$307$		−	22.1639i		−	1.26496i	0.774576	−	0.632480i	$-0.217963\pi$
$308$	5.17851	−	5.51456i	0.295073	−	0.314221i
$309$	−10.4609	−	16.4838i	−0.595102	−	0.937731i
$310$	0.916002	+	5.24082i	0.0520254	+	0.297659i
$311$	−24.6502	+	9.75970i	−1.39778	+	0.553422i	−0.941681	−	0.336506i	$-0.890755\pi$
$311$	−24.6502	+	9.75970i	−1.39778	+	0.553422i	−0.456102	+	0.889927i	$0.650755\pi$
$312$	−3.28129	−	0.206441i	−0.185766	−	0.0116874i
$313$	0.202526	+	0.0127419i	0.0114474	+	0.000720212i	0.0685132	−	0.997650i	$-0.478174\pi$
$313$	0.202526	+	0.0127419i	0.0114474	+	0.000720212i	−0.0570658	+	0.998370i	$0.518174\pi$
$314$	−11.3482	+	4.49307i	−0.640417	+	0.253559i
$315$	1.48084	+	8.47248i	0.0834358	+	0.477370i
$316$	2.70724	+	4.26592i	0.152294	+	0.239977i
$317$	−3.59641	+	3.82978i	−0.201994	+	0.215102i	−0.821988	−	0.569505i	$-0.807135\pi$
$317$	−3.59641	+	3.82978i	−0.201994	+	0.215102i	0.619994	+	0.784607i	$0.287135\pi$
$318$			11.8223i			0.662963i
$319$	3.28247	+	3.08244i	0.183783	+	0.172584i
$320$	1.28620	+	1.82912i	0.0719009	+	0.102251i
$321$	−0.289281	+	1.51647i	−0.0161461	+	0.0846409i
$322$	−3.32219	+	6.04303i	−0.185138	+	0.336765i
$323$	5.35604	+	3.39905i	0.298018	+	0.189128i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−16.0447	−	3.57811i	−0.890002	−	0.198478i
$326$	1.66631	−	5.12837i	0.0922883	−	0.284034i
$327$	−6.12097	+	5.06370i	−0.338490	+	0.280023i
$328$	2.34628	+	0.447576i	0.129551	+	0.0247133i
$329$	3.15185	+	6.69801i	0.173767	+	0.369273i
$330$	−3.05965	+	3.15887i	−0.168428	+	0.173890i
$331$	0.569801	+	2.98700i	0.0313191	+	0.164181i	0.994511	−	0.104636i	$-0.0333676\pi$
$331$	0.569801	+	2.98700i	0.0313191	+	0.164181i	−0.963192	+	0.268816i	$0.913368\pi$
$332$	−10.9682	−	3.56378i	−0.601958	−	0.195588i
$333$	4.61838	+	2.17325i	0.253086	+	0.119093i
$334$	−9.14926	−	3.62245i	−0.500625	−	0.198211i
$335$	21.5934	+	12.3096i	1.17977	+	0.672544i
$336$	3.72560	+	0.956573i	0.203248	+	0.0521853i
$337$	−7.60879	+	19.2176i	−0.414477	+	1.04685i	0.561208	+	0.827675i	$0.310337\pi$
$337$	−7.60879	+	19.2176i	−0.414477	+	1.04685i	−0.975686	+	0.219175i	$0.929663\pi$
$338$	0.544763	+	2.12171i	0.0296312	+	0.115406i
$339$	−1.59358	+	2.51107i	−0.0865511	+	0.136383i
$340$	3.43096	−	0.824595i	0.186070	−	0.0447200i
$341$	−0.293822	+	4.67017i	−0.0159114	+	0.252904i
$342$	−1.93657	−	3.52261i	−0.104718	−	0.190481i
$343$	−2.90884	+	0.945140i	−0.157063	+	0.0510328i
$344$	−0.239080	−	0.0302028i	−0.0128903	−	0.00162843i
$345$	1.98538	−	3.48274i	0.106889	−	0.187504i
$346$	−9.10676	+	8.55181i	−0.489582	+	0.459748i
$347$	13.6309	+	14.5154i	0.731745	+	0.779229i	0.981986	−	0.188954i	$-0.0605098\pi$
$347$	13.6309	+	14.5154i	0.731745	+	0.779229i	−0.250241	+	0.968184i	$0.580510\pi$
$348$	−0.569387	+	2.21762i	−0.0305224	+	0.118877i
$349$	19.1728	+	13.9298i	1.02629	+	0.745646i	0.967564	−	0.252627i	$-0.0812947\pi$
$349$	19.1728	+	13.9298i	1.02629	+	0.745646i	0.0587307	+	0.998274i	$0.481295\pi$
$350$	17.6542	+	7.62933i	0.943659	+	0.407805i
$351$	2.65987	−	1.93251i	0.141973	−	0.103150i
$352$	0.723997	+	1.82861i	0.0385892	+	0.0974651i
$353$	2.87347	+	22.7459i	0.152939	+	1.21064i	0.862523	+	0.506018i	$0.168883\pi$
$353$	2.87347	+	22.7459i	0.152939	+	1.21064i	−0.709583	+	0.704621i	$0.751117\pi$
$354$	−5.98658	−	3.29115i	−0.318183	−	0.174923i
$355$	−28.3106	+	1.34209i	−1.50257	+	0.0712308i
$356$	−1.19050	+	2.52994i	−0.0630964	+	0.134087i
$357$	3.56782	−	4.91069i	0.188829	−	0.259901i
$358$	−1.54696	+	12.2455i	−0.0817596	+	0.647194i
$359$	13.3179	−	3.41944i	0.702889	−	0.180471i	0.119703	−	0.992810i	$-0.461806\pi$
$359$	13.3179	−	3.41944i	0.702889	−	0.180471i	0.583186	+	0.812338i	$0.301806\pi$
$360$	−2.15696	−	0.589506i	−0.113682	−	0.0310697i
$361$	1.81088	+	2.18897i	0.0953093	+	0.115209i
$362$	−0.471938	−	0.390421i	−0.0248045	−	0.0205201i
$363$	6.02176	−	3.82153i	0.316061	−	0.200578i
$364$	0.794065	+	12.6213i	0.0416203	+	0.661536i
$365$	2.19017	−	6.40212i	0.114639	−	0.335102i
$366$	−5.96003	+	7.20444i	−0.311536	+	0.376582i
$367$	−7.35166	+	1.40240i	−0.383754	+	0.0732049i	−0.375648	−	0.926762i	$-0.622580\pi$
$367$	−7.35166	+	1.40240i	−0.383754	+	0.0732049i	−0.00810514	+	0.999967i	$0.502580\pi$
$368$	−1.05380	−	1.45043i	−0.0549331	−	0.0756089i
$369$	−2.09313	+	1.15071i	−0.108964	+	0.0599036i
$370$	9.72992	−	5.96581i	0.505835	−	0.310147i
$371$	45.1154	−	5.69940i	2.34227	−	0.295898i
$372$	−2.15285	+	1.01306i	−0.111620	+	0.0525245i
$373$	−27.7387	+	1.74517i	−1.43626	+	0.0903616i	−0.761732	−	0.647892i	$-0.775651\pi$
$373$	−27.7387	+	1.74517i	−1.43626	+	0.0903616i	−0.674523	+	0.738253i	$0.735651\pi$
$374$	3.10361			0.160484
$375$	−10.1932	−	4.59333i	−0.526375	−	0.237198i
$376$	−1.92451			−0.0992491
$377$	−7.51266	+	0.472657i	−0.386922	+	0.0243431i
$378$	−3.48037	+	1.63774i	−0.179011	+	0.0842361i
$379$	16.2103	−	2.04783i	0.832666	−	0.105190i	0.302569	−	0.953127i	$-0.402156\pi$
$379$	16.2103	−	2.04783i	0.832666	−	0.105190i	0.530097	+	0.847937i	$0.322156\pi$
$380$	−8.96109	−	0.703029i	−0.459694	−	0.0360646i
$381$	12.2489	−	6.73389i	0.627530	−	0.344988i
$382$	12.7539	+	17.5543i	0.652548	+	0.898155i
$383$	−30.5779	+	5.83305i	−1.56246	+	0.298055i	−0.894819	−	0.446430i	$-0.852695\pi$
$383$	−30.5779	+	5.83305i	−1.56246	+	0.298055i	−0.667639	+	0.744485i	$0.732695\pi$
$384$	−0.637424	+	0.770513i	−0.0325284	+	0.0393201i
$385$	13.5296	+	10.1531i	0.689534	+	0.517451i
$386$	0.314112	+	4.99266i	0.0159879	+	0.254120i
$387$	0.203466	−	0.129124i	0.0103428	−	0.00656373i
$388$	13.3609	+	11.0531i	0.678297	+	0.561136i
$389$	3.28528	+	3.97122i	0.166570	+	0.201349i	0.847193	−	0.531285i	$-0.178291\pi$
$389$	3.28528	+	3.97122i	0.166570	+	0.201349i	−0.680623	+	0.732634i	$0.738291\pi$
$390$	−0.348124	−	7.34344i	−0.0176279	−	0.371850i
$391$	−2.74032	+	0.703594i	−0.138584	+	0.0355823i
$392$	0.976992	−	7.73369i	0.0493456	−	0.390610i
$393$	−10.6692	+	14.6850i	−0.538192	+	0.740758i
$394$	10.9821	−	23.3382i	0.553271	−	1.17576i
$395$	−8.81526	+	7.06593i	−0.443544	+	0.355525i
$396$	−1.72345	−	0.947474i	−0.0866065	−	0.0476123i
$397$	−2.59844	−	20.5688i	−0.130412	−	1.03232i	−0.912479	−	0.409124i	$-0.865834\pi$
$397$	−2.59844	−	20.5688i	−0.130412	−	1.03232i	0.782067	−	0.623195i	$-0.214166\pi$
$398$	4.79313	+	12.1061i	0.240258	+	0.606822i
$399$	−12.5091	+	9.08838i	−0.626238	+	0.454988i
$400$	−3.74892	+	3.30841i	−0.187446	+	0.165420i
$401$	−8.38956	−	6.09537i	−0.418954	−	0.304388i	0.358263	−	0.933621i	$-0.383369\pi$
$401$	−8.38956	−	6.09537i	−0.418954	−	0.304388i	−0.777217	+	0.629233i	$0.783369\pi$
$402$	−2.76437	+	10.7665i	−0.137874	+	0.536985i
$403$	−5.35493	−	5.70242i	−0.266748	−	0.284058i
$404$	5.23874	−	4.91951i	0.260637	−	0.244755i
$405$	2.03773	−	0.920677i	0.101256	−	0.0457488i
$406$	8.73718	+	1.10376i	0.433619	+	0.0547788i
$407$	9.54713	−	3.10205i	0.473233	−	0.153763i
$408$	0.760238	+	1.38287i	0.0376374	+	0.0684622i
$409$	0.00174376	−	0.0277162i	8.62232e−5	−	0.00137048i	−0.997983	−	0.0634757i	$-0.979781\pi$
$409$	0.00174376	−	0.0277162i	8.62232e−5	−	0.00137048i	0.998070	+	0.0621053i	$0.0197815\pi$
$410$	−0.417740	+	5.32468i	−0.0206307	+	0.262967i
$411$	5.34176	−	8.41727i	0.263490	−	0.415193i
$412$	−4.85517	−	18.9096i	−0.239197	−	0.931611i
$413$	−9.67336	+	24.4321i	−0.475995	+	1.20223i
$414$	1.73651	+	0.445859i	0.0853446	+	0.0219128i
$415$	5.22320	−	25.2533i	0.256397	−	1.23963i
$416$	−3.05690	−	1.21031i	−0.149877	−	0.0593404i
$417$	−13.2631	−	6.24113i	−0.649495	−	0.305629i
$418$	−7.51894	−	2.44305i	−0.367763	−	0.119494i
$419$	−1.94928	−	10.2185i	−0.0952287	−	0.499206i	−0.997660	−	0.0683722i	$-0.978219\pi$
$419$	−1.94928	−	10.2185i	−0.0952287	−	0.499206i	0.902431	−	0.430834i	$-0.141781\pi$
$420$	−1.20978	+	8.51541i	−0.0590312	+	0.415510i
$421$	−6.18350	−	13.1406i	−0.301365	−	0.640434i	0.695587	−	0.718441i	$-0.255144\pi$
$421$	−6.18350	−	13.1406i	−0.301365	−	0.640434i	−0.996953	+	0.0780075i	$0.975144\pi$
$422$	16.4644	+	3.14074i	0.801472	+	0.152889i
$423$	1.48286	−	1.22673i	0.0720992	−	0.0596457i
$424$	−3.65330	+	11.2437i	−0.177420	+	0.546042i
$425$	2.67641	+	7.42253i	0.129825	+	0.360046i
$426$	−3.91682	−	12.0547i	−0.189770	−	0.584053i
$427$	30.3662	+	19.2710i	1.46952	+	0.932589i
$428$	−0.743737	+	1.35285i	−0.0359499	+	0.0653926i
$429$	1.21163	−	6.35159i	0.0584981	−	0.306658i
$430$	0.00833096	−	0.538784i	0.000401754	−	0.0259825i
$431$	−17.6982	−	16.6197i	−0.852494	−	0.800545i	0.129079	−	0.991634i	$-0.458798\pi$
$431$	−17.6982	−	16.6197i	−0.852494	−	0.800545i	−0.981573	+	0.191089i	$0.938798\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	12.1819	−	12.9724i	0.585423	−	0.623413i	−0.366253	−	0.930515i	$-0.619360\pi$
$433$	12.1819	−	12.9724i	0.585423	−	0.623413i	0.951676	+	0.307103i	$0.0993595\pi$
$434$	4.90380	+	7.72715i	0.235390	+	0.370915i
$435$	−5.06869	−	0.720105i	−0.243025	−	0.0345264i
$436$	−7.38616	+	2.92439i	−0.353733	+	0.140053i
$437$	7.19266	+	0.452524i	0.344072	+	0.0216471i
$438$	3.02005	+	0.190005i	0.144304	+	0.00907881i
$439$	9.56838	−	3.78839i	0.456674	−	0.180810i	−0.128514	−	0.991708i	$-0.541021\pi$
$439$	9.56838	−	3.78839i	0.456674	−	0.180810i	0.585188	+	0.810898i	$0.301021\pi$
$440$	−3.88604	+	2.05878i	−0.185260	+	0.0981485i
$441$	4.17685	+	6.58167i	0.198898	+	0.313413i
$442$	−3.55165	+	3.78212i	−0.168935	+	0.179897i
$443$			11.2961i			0.536694i	0.963322	+	0.268347i	$0.0864773\pi$
$443$			11.2961i			0.536694i	−0.963322	+	0.268347i	$0.913523\pi$
$444$	3.72077	+	3.49404i	0.176580	+	0.165820i
$445$	−5.91557	−	2.02372i	−0.280425	−	0.0959337i
$446$	−4.61903	+	24.2138i	−0.218718	+	1.14656i
$447$	1.63471	−	2.97353i	0.0773193	−	0.140643i
$448$	3.24766	+	2.06103i	0.153438	+	0.0973745i
$449$	−5.27168	−	16.2246i	−0.248786	−	0.765685i	−0.994991	−	0.0999682i	$-0.968126\pi$
$449$	−5.27168	−	16.2246i	−0.248786	−	0.765685i	0.746205	−	0.665717i	$-0.231874\pi$
$450$	0.779736	−	4.93883i	0.0367571	−	0.232819i
$451$	−1.45166	+	4.46775i	−0.0683560	+	0.210378i
$452$	−2.29154	+	1.89573i	−0.107785	+	0.0891677i
$453$	−13.2912	−	2.53543i	−0.624474	−	0.119125i
$454$	10.7388	+	22.8212i	0.503998	+	1.07105i
$455$	−27.8556	+	4.86866i	−1.30589	+	0.228246i
$456$	−0.753242	−	3.94863i	−0.0352738	−	0.184912i
$457$	27.6264	+	8.97637i	1.29231	+	0.419897i	0.872900	−	0.487900i	$-0.162237\pi$
$457$	27.6264	+	8.97637i	1.29231	+	0.419897i	0.419411	+	0.907797i	$0.362237\pi$
$458$	21.8632	+	10.2881i	1.02160	+	0.480730i
$459$	−1.46725	−	0.580924i	−0.0684852	−	0.0271152i
$460$	2.96443	−	2.69876i	0.138217	−	0.125831i
$461$	−6.04515	−	1.55213i	−0.281551	−	0.0722900i	0.105274	−	0.994443i	$-0.466428\pi$
$461$	−6.04515	−	1.55213i	−0.281551	−	0.0722900i	−0.386825	+	0.922153i	$0.626428\pi$
$462$	−2.78482	+	7.03365i	−0.129561	+	0.327235i
$463$	−1.77629	−	6.91819i	−0.0825511	−	0.321515i	0.913874	−	0.405998i	$-0.133076\pi$
$463$	−1.77629	−	6.91819i	−0.0825511	−	0.321515i	−0.996425	+	0.0844830i	$0.973076\pi$
$464$	−1.22680	+	1.93313i	−0.0569528	+	0.0897433i
$465$	−2.78095	−	4.53559i	−0.128964	−	0.210333i
$466$	0.172324	−	2.73901i	0.00798275	−	0.126882i
$467$	6.77801	+	12.3292i	0.313649	+	0.570525i	0.985401	−	0.170251i	$-0.0544579\pi$
$467$	6.77801	+	12.3292i	0.313649	+	0.570525i	−0.671752	+	0.740776i	$0.734458\pi$
$468$	3.12686	−	1.01598i	0.144539	−	0.0469636i
$469$	42.4190	+	5.35876i	1.95873	+	0.247445i
$470$	−0.473279	−	4.27724i	−0.0218307	−	0.197294i
$471$	8.89729	−	8.35511i	0.409965	−	0.384983i
$472$	−4.67655	−	4.98002i	−0.215256	−	0.229224i
$473$	0.117864	−	0.459051i	0.00541940	−	0.0211072i
$474$	−4.08752	−	2.96975i	−0.187746	−	0.136405i
$475$	−0.641242	−	20.0889i	−0.0294222	−	0.921744i
$476$	4.91069	−	3.56782i	0.225081	−	0.163531i
$477$	−4.35209	−	10.9921i	−0.199268	−	0.503294i
$478$	−0.376311	−	2.97880i	−0.0172120	−	0.136247i
$479$	22.7887	+	12.5282i	1.04124	+	0.572428i	0.908137	−	0.418674i	$-0.137505\pi$
$479$	22.7887	+	12.5282i	1.04124	+	0.572428i	0.133106	+	0.991102i	$0.457505\pi$
$480$	−1.86922	−	1.22719i	−0.0853181	−	0.0560134i
$481$	−7.14514	+	15.1842i	−0.325790	+	0.692340i
$482$	14.2803	−	19.6551i	0.650450	−	0.895267i
$483$	0.864301	−	6.84165i	0.0393271	−	0.311306i
$484$	6.90795	−	1.77366i	0.313998	−	0.0806210i
$485$	−21.2798	+	32.4129i	−0.966267	+	1.47179i
$486$	0.637424	+	0.770513i	0.0289141	+	0.0349512i
$487$	−0.904679	−	0.748415i	−0.0409949	−	0.0339139i	0.616701	−	0.787198i	$-0.288469\pi$
$487$	−0.904679	−	0.748415i	−0.0409949	−	0.0339139i	−0.657696	+	0.753284i	$0.728469\pi$
$488$	−7.89462	+	5.01008i	−0.357372	+	0.226795i
$489$	0.338584	+	5.38165i	0.0153113	+	0.243366i
$490$	17.4284	+	0.269487i	0.787336	+	0.0121742i
$491$	7.75621	−	9.37565i	0.350033	−	0.423117i	−0.565884	−	0.824485i	$-0.691465\pi$
$491$	7.75621	−	9.37565i	0.350033	−	0.423117i	0.915917	+	0.401368i	$0.131465\pi$
$492$	−2.34628	+	0.447576i	−0.105778	+	0.0201783i
$493$	2.12370	+	2.92302i	0.0956466	+	0.131646i
$494$	11.5815	−	6.36701i	0.521078	−	0.286465i
$495$	1.68193	−	4.06337i	0.0755971	−	0.182635i
$496$	−2.36054	+	0.298205i	−0.105991	+	0.0133898i
$497$	−44.1140	+	20.7585i	−1.97878	+	0.931144i
$498$	11.5099	−	0.724141i	0.515770	−	0.0324495i
$499$	−32.0840			−1.43628			−0.718139	−	0.695900i	$-0.755006\pi$
$499$	−32.0840			−1.43628			−0.718139	+	0.695900i	$0.755006\pi$
$500$	−8.27489	−	7.51839i	−0.370064	−	0.336232i
$501$	9.84027			0.439631
$502$	−7.10023	+	0.446709i	−0.316899	+	0.0199376i
$503$	21.2745	−	10.0110i	0.948584	−	0.446370i	0.111695	−	0.993742i	$-0.464372\pi$
$503$	21.2745	−	10.0110i	0.948584	−	0.446370i	0.836889	+	0.547373i	$0.184372\pi$
$504$	−3.81612	+	0.482088i	−0.169983	+	0.0214739i
$505$	12.2219	+	10.4333i	0.543869	+	0.464276i
$506$	3.08985	−	1.69866i	0.137361	−	0.0755146i
$507$	−1.28756	−	1.77218i	−0.0571827	−	0.0787052i
$508$	13.7303	−	2.61919i	0.609183	−	0.116208i
$509$	−18.7498	+	22.6646i	−0.831069	+	1.00459i	0.168752	+	0.985659i	$0.446026\pi$
$509$	−18.7498	+	22.6646i	−0.831069	+	1.00459i	−0.999821	+	0.0189315i	$0.993974\pi$
$510$	−2.88647	+	2.02971i	−0.127815	+	0.0898771i
$511$	−0.730846	−	11.6165i	−0.0323307	−	0.513882i
$512$	−0.844328	+	0.535827i	−0.0373144	+	0.0236804i
$513$	3.09734	+	2.56234i	0.136751	+	0.113130i
$514$	5.76161	+	6.96459i	0.254134	+	0.307195i
$515$	40.8328	−	15.4409i	1.79931	−	0.680408i
$516$	0.233410	−	0.0599294i	0.0102753	−	0.00263824i
$517$	0.474383	−	3.75513i	0.0208633	−	0.165150i
$518$	11.5399	−	15.8833i	0.507035	−	0.697874i
$519$	5.31912	−	11.3037i	0.233483	−	0.496177i
$520$	1.93816	−	7.09161i	0.0849941	−	0.310987i
$521$	2.18996	+	1.20394i	0.0959438	+	0.0527455i	0.529003	−	0.848620i	$-0.322566\pi$
$521$	2.18996	+	1.20394i	0.0959438	+	0.0527455i	−0.433059	+	0.901365i	$0.642566\pi$
$522$	−0.286956	−	2.27149i	−0.0125597	−	0.0994206i
$523$	−9.91685	−	25.0471i	−0.433634	−	1.09523i	−0.968216	−	0.250117i	$-0.919531\pi$
$523$	−9.91685	−	25.0471i	−0.433634	−	1.09523i	0.534582	−	0.845117i	$-0.320469\pi$
$524$	−14.6850	+	10.6692i	−0.641515	+	0.466088i
$525$	−19.2230	−	0.594615i	−0.838962	−	0.0259511i
$526$	−15.0142	−	10.9085i	−0.654652	−	0.475633i
$527$	−0.933752	+	3.63672i	−0.0406749	+	0.158418i
$528$	−1.34631	−	1.43368i	−0.0585907	−	0.0623927i
$529$	14.4232	−	13.5443i	0.627096	−	0.588882i
$530$	−25.8876	−	5.35440i	−1.12448	−	0.232580i
$531$	6.77773	+	0.856227i	0.294129	+	0.0371571i
$532$	−14.7053	+	4.77805i	−0.637556	+	0.207155i
$533$	−3.78328	−	6.88175i	−0.163872	−	0.298082i
$534$	0.175565	−	2.79053i	0.00759746	−	0.120758i
$535$	−3.18962	−	1.32026i	−0.137899	−	0.0570799i
$536$	−5.95611	+	9.38533i	−0.257265	+	0.405385i
$537$	−3.06953	−	11.9550i	−0.132460	−	0.515898i
$538$	−8.75206	+	22.1052i	−0.377328	+	0.953022i
$539$	14.8492	+	3.81263i	0.639602	+	0.164222i
$540$	2.22250	−	0.245922i	0.0956413	−	0.0105828i
$541$	18.5057	+	7.32692i	0.795622	+	0.315009i	0.730539	−	0.682871i	$-0.239269\pi$
$541$	18.5057	+	7.32692i	0.795622	+	0.315009i	0.0650828	+	0.997880i	$0.479269\pi$
$542$	−10.7997	−	5.08196i	−0.463887	−	0.218289i
$543$	0.582521	+	0.189273i	0.0249984	+	0.00812246i
$544$	0.295700	+	1.55011i	0.0126780	+	0.0664605i
$545$	−8.31587	−	15.6966i	−0.356213	−	0.672368i
$546$	−5.38451	−	11.4427i	−0.230436	−	0.489701i
$547$	−1.62103	−	0.309228i	−0.0693103	−	0.0132216i	0.152610	−	0.988287i	$-0.451232\pi$
$547$	−1.62103	−	0.309228i	−0.0693103	−	0.0132216i	−0.221920	+	0.975065i	$0.571232\pi$
$548$	7.68140	−	6.35461i	0.328133	−	0.271455i
$549$	2.88936	−	8.89255i	0.123315	−	0.379525i
$550$	−5.53131	−	8.13044i	−0.235856	−	0.346683i
$551$	−2.84407	−	8.75315i	−0.121161	−	0.372897i
$552$	1.51374	+	0.960646i	0.0644289	+	0.0408878i
$553$	−9.36239	+	17.0301i	−0.398129	+	0.724195i
$554$	2.22242	−	11.6503i	0.0944216	−	0.494976i
$555$	−6.85049	+	9.12869i	−0.290787	+	0.387491i
$556$	−10.6853	−	10.0342i	−0.453158	−	0.425544i
$557$			6.40063i			0.271203i	0.990763	+	0.135602i	$0.0432968\pi$
$557$			6.40063i			0.271203i	−0.990763	+	0.135602i	$0.956703\pi$
$558$	1.62874	−	1.73443i	0.0689501	−	0.0734244i
$559$	0.424530	+	0.668952i	0.0179557	+	0.0282937i
$560$	−3.78198	+	7.72479i	−0.159818	+	0.326432i
$561$	−2.88566	+	1.14251i	−0.121833	+	0.0482370i
$562$	−21.9001	−	1.37784i	−0.923801	−	0.0581206i
$563$	−20.8962	−	1.31468i	−0.880669	−	0.0554070i	−0.383986	−	0.923339i	$-0.625449\pi$
$563$	−20.8962	−	1.31468i	−0.880669	−	0.0554070i	−0.496683	+	0.867932i	$0.665449\pi$
$564$	1.78937	−	0.708460i	0.0753459	−	0.0298316i
$565$	−4.77681	−	4.62676i	−0.200962	−	0.194649i
$566$	15.6509	+	24.6619i	0.657857	+	1.03662i
$567$	2.63307	−	2.80394i	0.110579	−	0.117754i
$568$		−	12.6751i		−	0.531835i
$569$	25.5990	+	24.0391i	1.07317	+	1.00777i	0.999945	+	0.0104537i	$0.00332757\pi$
$569$	25.5990	+	24.0391i	1.07317	+	1.00777i	0.0732201	+	0.997316i	$0.476672\pi$
$570$	8.59061	−	2.64514i	0.359821	−	0.110793i
$571$	−1.29741	+	6.80124i	−0.0542947	+	0.284623i	−0.999071	−	0.0430929i	$-0.986279\pi$
$571$	−1.29741	+	6.80124i	−0.0542947	+	0.284623i	0.944776	+	0.327716i	$0.106279\pi$
$572$	3.11508	−	5.66631i	0.130248	−	0.236920i
$573$	−18.3205	−	11.6265i	−0.765348	−	0.485705i
$574$	2.83911	+	8.73790i	0.118502	+	0.364713i
$575$	6.72703	+	5.92478i	0.280537	+	0.247080i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	32.9534	−	27.2614i	1.37187	−	1.13491i	0.395578	−	0.918432i	$-0.370544\pi$
$577$	32.9534	−	27.2614i	1.37187	−	1.13491i	0.976288	−	0.216474i	$-0.0694558\pi$
$578$	−14.2527	−	2.71885i	−0.592834	−	0.113089i
$579$	−2.12998	−	4.52643i	−0.0885188	−	0.188112i
$580$	−4.59808	−	2.25117i	−0.190925	−	0.0934748i
$581$	−8.31218	−	43.5740i	−0.344847	−	1.80775i
$582$	−16.4916	−	5.35844i	−0.683598	−	0.222114i
$583$	−21.0383	−	9.89987i	−0.871317	−	0.410011i
$584$	2.81352	+	1.11395i	0.116424	+	0.0460957i
$585$	3.02698	+	6.69961i	0.125150	+	0.276995i
$586$	−27.5637	−	7.07714i	−1.13864	−	0.292354i
$587$	7.99647	−	20.1968i	0.330049	−	0.833610i	−0.666094	−	0.745868i	$-0.732035\pi$
$587$	7.99647	−	20.1968i	0.330049	−	0.833610i	0.996143	−	0.0877418i	$-0.0279650\pi$
$588$	1.93858	+	7.55026i	0.0799456	+	0.311367i
$589$	5.12485	−	8.07547i	0.211166	−	0.332744i
$590$	9.91806	−	11.6184i	0.408320	−	0.478320i
$591$	−1.61956	+	25.7421i	−0.0666196	+	1.05889i
$592$	2.45895	+	4.47281i	0.101062	+	0.183831i
$593$	32.4720	−	10.5508i	1.33347	−	0.433269i	0.446367	−	0.894850i	$-0.352718\pi$
$593$	32.4720	−	10.5508i	1.33347	−	0.433269i	0.887098	+	0.461581i	$0.152718\pi$
$594$	1.95121	+	0.246495i	0.0800591	+	0.0101138i
$595$	9.13714	+	10.0366i	0.374586	+	0.411461i
$596$	2.47358	−	2.32284i	0.101322	−	0.0951474i
$597$	−8.91308	−	9.49147i	−0.364788	−	0.388460i
$598$	−1.46588	+	5.70924i	−0.0599444	+	0.233468i
$599$	−29.1941	−	21.2108i	−1.19284	−	0.866648i	−0.199278	−	0.979943i	$-0.563860\pi$
$599$	−29.1941	−	21.2108i	−1.19284	−	0.866648i	−0.993561	+	0.113295i	$0.963860\pi$
$600$	2.26775	−	4.45615i	0.0925807	−	0.181922i
$601$	−4.88473	+	3.54897i	−0.199252	+	0.144765i	−0.682938	−	0.730477i	$-0.739298\pi$
$601$	−4.88473	+	3.54897i	−0.199252	+	0.144765i	0.483685	+	0.875242i	$0.339298\pi$
$602$	−0.341221	−	0.861827i	−0.0139071	−	0.0351254i
$603$	−1.39317	−	11.0281i	−0.0567343	−	0.449099i
$604$	−11.8572	−	6.51854i	−0.482461	−	0.265235i
$605$	5.64078	+	14.9168i	0.229331	+	0.606453i
$606$	−3.05987	+	6.50255i	−0.124299	+	0.264148i
$607$	1.56204	−	2.14997i	0.0634013	−	0.0872644i	−0.776139	−	0.630562i	$-0.782824\pi$
$607$	1.56204	−	2.14997i	0.0634013	−	0.0872644i	0.839540	+	0.543298i	$0.182824\pi$
$608$	0.503819	−	3.98814i	0.0204326	−	0.161740i
$609$	−8.52995	+	2.19012i	−0.345651	+	0.0887481i
$610$	−13.0764	−	16.3137i	−0.529447	−	0.660524i
$611$	4.03321	+	4.87532i	0.163166	+	0.197234i
$612$	−1.21592	−	1.00590i	−0.0491506	−	0.0406609i
$613$	−24.1889	+	15.3508i	−0.976982	+	0.620012i	−0.925534	−	0.378664i	$-0.876384\pi$
$613$	−24.1889	+	15.3508i	−0.976982	+	0.620012i	−0.0514477	+	0.998676i	$0.516384\pi$
$614$	1.39168	+	22.1202i	0.0561638	+	0.892697i
$615$	−1.57174	−	5.10454i	−0.0633787	−	0.205835i
$616$	−4.82203	+	5.82884i	−0.194285	+	0.234851i
$617$	−33.7019	+	6.42899i	−1.35679	+	0.258821i	−0.813910	−	0.580990i	$-0.802665\pi$
$617$	−33.7019	+	6.42899i	−1.35679	+	0.258821i	−0.542878	+	0.839812i	$0.682665\pi$
$618$	11.4753	+	15.7944i	0.461605	+	0.635345i
$619$	4.57094	−	2.51289i	0.183722	−	0.101002i	−0.387239	−	0.921980i	$-0.626571\pi$
$619$	4.57094	−	2.51289i	0.183722	−	0.101002i	0.570960	+	0.820978i	$0.306571\pi$
$620$	−1.24327	−	5.17296i	−0.0499309	−	0.207751i
$621$	−1.77869	+	0.224701i	−0.0713765	+	0.00901695i
$622$	23.9887	−	11.2882i	0.961860	−	0.452617i
$623$	−10.7336	+	0.675303i	−0.430034	+	0.0270554i
$624$	3.28778			0.131616
$625$	14.6747	−	20.2399i	0.586987	−	0.809597i
$626$	−0.202926			−0.00811057
$627$	7.89028	−	0.496414i	0.315107	−	0.0198249i
$628$	11.0437	−	5.19677i	0.440691	−	0.207374i
$629$	7.99118	−	1.00952i	0.318629	−	0.0402522i
$630$	−2.00991	−	8.36278i	−0.0800766	−	0.333181i
$631$	−40.0151	+	21.9985i	−1.59298	+	0.875746i	−0.595605	+	0.803278i	$0.703087\pi$
$631$	−40.0151	+	21.9985i	−1.59298	+	0.875746i	−0.997371	+	0.0724678i	$0.976913\pi$
$632$	−2.96975	−	4.08752i	−0.118130	−	0.162593i
$633$	−16.4644	+	3.14074i	−0.654399	+	0.124833i
$634$	3.34883	−	4.04805i	0.132999	−	0.160768i
$635$	9.19774	+	29.8715i	0.365001	+	1.18541i
$636$	−0.742330	−	11.7990i	−0.0294353	−	0.467861i
$637$	−21.6391	+	13.7326i	−0.857371	+	0.544104i
$638$	−3.46954	−	2.87025i	−0.137360	−	0.113634i
$639$	8.07940	+	9.76632i	0.319616	+	0.386350i
$640$	−1.39852	−	1.74475i	−0.0552812	−	0.0689673i
$641$	23.6950	−	6.08384i	0.935895	−	0.240297i	0.250207	−	0.968192i	$-0.419501\pi$
$641$	23.6950	−	6.08384i	0.935895	−	0.240297i	0.685688	+	0.727895i	$0.259501\pi$
$642$	0.193491	−	1.53164i	0.00763647	−	0.0604489i
$643$	−18.3225	+	25.2187i	−0.722569	+	0.994530i	0.276866	+	0.960909i	$0.410704\pi$
$643$	−18.3225	+	25.2187i	−0.722569	+	0.994530i	−0.999435	+	0.0336218i	$0.989296\pi$
$644$	2.93619	−	6.23971i	0.115702	−	0.245879i
$645$	0.190594	+	0.504016i	0.00750462	+	0.0198456i
$646$	−5.55890	−	3.05603i	−0.218712	−	0.120238i
$647$	3.57735	+	28.3177i	0.140640	+	1.11328i	0.891565	+	0.452894i	$0.149608\pi$
$647$	3.57735	+	28.3177i	0.140640	+	1.11328i	−0.750924	+	0.660388i	$0.770392\pi$
$648$	0.368125	+	0.929776i	0.0144613	+	0.0365251i
$649$	10.8698	−	7.89739i	0.426678	−	0.310000i
$650$	16.2378	+	2.56360i	0.636897	+	0.100553i
$651$	−7.40399	−	5.37932i	−0.290185	−	0.210832i
$652$	−1.34101	+	5.22288i	−0.0525179	+	0.204544i
$653$	23.9951	+	25.5522i	0.939002	+	0.999936i	0.999998	+	0.00179757i	$0.000572184\pi$
$653$	23.9951	+	25.5522i	0.939002	+	0.999936i	−0.0609964	+	0.998138i	$0.519428\pi$
$654$	5.79094	−	5.43805i	0.226444	−	0.212645i
$655$	−27.3238	−	30.0136i	−1.06763	−	1.17273i
$656$	−2.36975	−	0.299369i	−0.0925232	−	0.0116884i
$657$	−2.87792	+	0.935092i	−0.112278	+	0.0364814i
$658$	−3.56620	−	6.48689i	−0.139025	−	0.252885i
$659$	−0.844566	+	13.4240i	−0.0328996	+	0.522924i	0.946719	+	0.322060i	$0.104375\pi$
$659$	−0.844566	+	13.4240i	−0.0328996	+	0.522924i	−0.979619	+	0.200865i	$0.935625\pi$
$660$	2.85526	−	3.34475i	0.111141	−	0.130194i
$661$	−1.19824	+	1.88812i	−0.0466061	+	0.0734394i	−0.866832	−	0.498600i	$-0.833848\pi$
$661$	−1.19824	+	1.88812i	−0.0466061	+	0.0734394i	0.820226	+	0.572040i	$0.193848\pi$
$662$	−0.756233	−	2.94533i	−0.0293918	−	0.114474i
$663$	1.90995	−	4.82398i	0.0741763	−	0.187348i
$664$	11.1703	+	2.86805i	0.433493	+	0.111302i
$665$	−14.2356	−	31.5076i	−0.552032	−	1.22181i
$666$	−4.74573	−	1.87897i	−0.183893	−	0.0728085i
$667$	3.71411	+	1.74773i	0.143811	+	0.0676722i
$668$	9.35866	+	3.04081i	0.362097	+	0.117653i
$669$	−4.61903	−	24.2138i	−0.178582	−	0.936160i
$670$	−22.3237	−	10.9294i	−0.862439	−	0.422241i
$671$	−7.82972	−	16.6390i	−0.302263	−	0.642342i
$672$	−3.77832	−	0.720752i	−0.145752	−	0.0278036i
$673$	23.5033	−	19.4436i	0.905985	−	0.749496i	−0.0626362	−	0.998036i	$-0.519951\pi$
$673$	23.5033	−	19.4436i	0.905985	−	0.749496i	0.968622	+	0.248540i	$0.0799508\pi$
$674$	6.38709	−	19.6574i	0.246022	−	0.757177i
$675$	1.09312	+	4.87905i	0.0420743	+	0.187795i
$676$	−0.676912	−	2.08332i	−0.0260351	−	0.0801277i
$677$	−33.1625	−	21.0456i	−1.27454	−	0.808848i	−0.285771	−	0.958298i	$-0.592250\pi$
$677$	−33.1625	−	21.0456i	−1.27454	−	0.808848i	−0.988769	+	0.149450i	$0.952250\pi$
$678$	1.43276	−	2.60618i	0.0550248	−	0.100090i
$679$	−12.4980	+	65.5170i	−0.479631	+	2.51431i
$680$	−3.37241	+	1.03840i	−0.129326	+	0.0398208i
$681$	−18.3857	−	17.2653i	−0.704543	−	0.661610i
$682$		−	4.67941i		−	0.179184i
$683$	17.0133	−	18.1174i	0.650997	−	0.693242i	−0.315789	−	0.948830i	$-0.602269\pi$
$683$	17.0133	−	18.1174i	0.650997	−	0.693242i	0.966786	+	0.255588i	$0.0822690\pi$
$684$	2.15394	+	3.39406i	0.0823578	+	0.129775i
$685$	16.0122	+	15.5092i	0.611793	+	0.592576i
$686$	2.84376	−	1.12592i	0.108575	−	0.0429879i
$687$	−24.1152	−	1.51720i	−0.920053	−	0.0578848i
$688$	0.240505	+	0.0151313i	0.00916916	+	0.000576875i
$689$	36.1396	−	14.3087i	1.37681	−	0.545118i
$690$	−1.76278	+	3.60053i	−0.0671079	+	0.137070i
$691$	−17.6027	−	27.7374i	−0.669638	−	1.05518i	−0.994014	−	0.109253i	$-0.965154\pi$
$691$	−17.6027	−	27.7374i	−0.669638	−	1.05518i	0.324376	−	0.945928i	$-0.394846\pi$
$692$	8.55181	−	9.10676i	0.325091	−	0.346187i
$693$		−	7.56488i		−	0.287366i
$694$	−14.5154	−	13.6309i	−0.550998	−	0.517422i
$695$	19.6733	−	26.2158i	0.746249	−	0.994421i
$696$	0.429018	−	2.24899i	0.0162619	−	0.0852479i
$697$	−1.81589	+	3.30310i	−0.0687819	+	0.125114i
$698$	−20.0096	−	12.6985i	−0.757374	−	0.480644i
$699$	0.848074	+	2.61010i	0.0320771	+	0.0987232i
$700$	−18.0985	−	6.50576i	−0.684057	−	0.245895i
$701$	9.04435	−	27.8357i	0.341600	−	1.05134i	−0.621778	−	0.783193i	$-0.713589\pi$
$701$	9.04435	−	27.8357i	0.341600	−	1.05134i	0.963379	−	0.268145i	$-0.0864105\pi$
$702$	−2.53327	+	2.09571i	−0.0956123	+	0.0790974i
$703$	−20.1544	−	3.84467i	−0.760139	−	0.145004i
$704$	−0.837388	−	1.77954i	−0.0315602	−	0.0670689i
$705$	2.01460	+	3.80265i	0.0758742	+	0.143216i
$706$	−4.29602	−	22.5205i	−0.161683	−	0.847572i
$707$	26.2896	+	8.54201i	0.988723	+	0.321255i
$708$	6.18142	+	2.90875i	0.232312	+	0.109318i
$709$	−6.33013	−	2.50628i	−0.237733	−	0.0941251i	0.246237	−	0.969210i	$-0.420806\pi$
$709$	−6.33013	−	2.50628i	−0.237733	−	0.0941251i	−0.483970	+	0.875084i	$0.660806\pi$
$710$	28.1704	−	3.11708i	1.05722	−	0.116982i
$711$	4.89372	+	1.25649i	0.183529	+	0.0471222i
$712$	1.02929	−	2.59970i	0.0385744	−	0.0974279i
$713$	1.06083	+	4.13166i	0.0397284	+	0.154732i
$714$	−3.25244	+	5.12502i	−0.121719	+	0.191799i
$715$	13.3595	+	5.52981i	0.499616	+	0.206803i
$716$	0.775011	−	12.3184i	0.0289635	−	0.460362i
$717$	1.44646	+	2.63109i	0.0540189	+	0.0982600i
$718$	−13.0769	+	4.24893i	−0.488024	+	0.158569i
$719$	−42.8281	−	5.41045i	−1.59722	−	0.201776i	−0.724245	−	0.689543i	$-0.757812\pi$
$719$	−42.8281	−	5.41045i	−1.59722	−	0.201776i	−0.872974	+	0.487767i	$0.837812\pi$
$720$	2.18972	+	0.452906i	0.0816061	+	0.0168788i
$721$	54.7413	−	51.4055i	2.03867	−	1.91444i
$722$	−1.94475	−	2.07095i	−0.0723761	−	0.0770727i
$723$	−6.04194	+	23.5318i	−0.224702	+	0.875157i
$724$	0.495522	+	0.360018i	0.0184159	+	0.0133800i
$725$	3.87247	−	10.7729i	0.143820	−	0.400094i
$726$	−5.76993	+	4.19210i	−0.214142	+	0.155583i
$727$	16.3760	+	41.3610i	0.607352	+	1.53400i	0.829222	+	0.558920i	$0.188784\pi$
$727$	16.3760	+	41.3610i	0.607352	+	1.53400i	−0.221870	+	0.975076i	$0.571216\pi$
$728$	−1.58500	−	12.5465i	−0.0587439	−	0.465006i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	−1.78386	+	6.52701i	−0.0660235	+	0.241575i
$731$	0.161916	−	0.344090i	0.00598870	−	0.0127266i
$732$	5.49590	−	7.56445i	0.203134	−	0.279590i
$733$	−5.18764	+	41.0644i	−0.191610	+	1.51675i	0.543851	+	0.839182i	$0.316966\pi$
$733$	−5.18764	+	41.0644i	−0.191610	+	1.51675i	−0.735461	+	0.677567i	$0.763034\pi$
$734$	7.24910	−	1.86125i	0.267569	−	0.0687000i
$735$	−16.3037	+	6.16527i	−0.601373	+	0.227409i
$736$	1.14279	+	1.38140i	0.0421239	+	0.0509191i
$737$	−16.8446	−	13.9351i	−0.620479	−	0.513305i
$738$	2.01675	−	1.27987i	0.0742376	−	0.0471126i
$739$	2.86054	+	45.4670i	0.105227	+	1.67253i	0.597331	+	0.801994i	$0.296228\pi$
$739$	2.86054	+	45.4670i	0.105227	+	1.67253i	−0.492105	+	0.870536i	$0.663772\pi$
$740$	−9.33613	+	6.56498i	−0.343203	+	0.241333i
$741$	−8.42440	+	10.1833i	−0.309478	+	0.374095i
$742$	−44.6685	+	8.52097i	−1.63983	+	0.312815i
$743$	26.7306	+	36.7915i	0.980649	+	1.34975i	0.936479	+	0.350724i	$0.114064\pi$
$743$	26.7306	+	36.7915i	0.980649	+	1.34975i	0.0441703	+	0.999024i	$0.485936\pi$
$744$	2.08499	−	1.14623i	0.0764396	−	0.0420230i
$745$	5.77083	+	4.92630i	0.211427	+	0.180486i
$746$	27.5744	−	3.48346i	1.00957	−	0.127538i
$747$	−10.4350	+	4.91036i	−0.381798	+	0.179661i
$748$	−3.09748	+	0.194877i	−0.113255	+	0.00712541i
$749$	−5.93819			−0.216977
$750$	10.4615	+	3.94423i	0.382000	+	0.144023i
$751$	−19.9278			−0.727177			−0.363589	−	0.931560i	$-0.618449\pi$
$751$	−19.9278			−0.727177			−0.363589	+	0.931560i	$0.618449\pi$
$752$	1.92071	−	0.120841i	0.0700413	−	0.00440662i
$753$	6.43719	−	3.02911i	0.234584	−	0.110387i
$754$	7.46816	−	0.943448i	0.271974	−	0.0343584i
$755$	11.5715	−	27.9557i	0.421131	−	1.01741i
$756$	3.37067	−	1.85304i	0.122590	−	0.0673944i
$757$	11.1308	+	15.3202i	0.404554	+	0.556821i	0.961880	−	0.273473i	$-0.0881724\pi$
$757$	11.1308	+	15.3202i	0.404554	+	0.556821i	−0.557325	+	0.830294i	$0.688172\pi$
$758$	−16.0497	+	3.06164i	−0.582951	+	0.111204i
$759$	−2.24755	+	2.71682i	−0.0815809	+	0.0986144i
$760$	8.98755	+	0.138970i	0.326013	+	0.00504098i
$761$	2.67667	+	42.5445i	0.0970292	+	1.54224i	0.682103	+	0.731256i	$0.261065\pi$
$761$	2.67667	+	42.5445i	0.0970292	+	1.54224i	−0.585074	+	0.810980i	$0.698935\pi$
$762$	−11.8019	+	7.48972i	−0.427538	+	0.271324i
$763$	−23.5440	−	19.4773i	−0.852349	−	0.705125i
$764$	−13.8310	−	16.7188i	−0.500388	−	0.604865i
$765$	1.93659	−	2.94976i	0.0700174	−	0.106649i
$766$	30.1513	−	7.74154i	1.08941	−	0.279713i
$767$	−2.81508	+	22.2837i	−0.101647	+	0.804617i
$768$	0.587785	−	0.809017i	0.0212099	−	0.0291929i
$769$	5.07249	−	10.7796i	0.182919	−	0.388722i	−0.792246	−	0.610201i	$-0.791089\pi$
$769$	5.07249	−	10.7796i	0.182919	−	0.388722i	0.975165	+	0.221479i	$0.0710886\pi$
$770$	−14.1405	−	9.28355i	−0.509587	−	0.334556i
$771$	−7.92085	−	4.35452i	−0.285262	−	0.156824i
$772$	−0.626984	−	4.96309i	−0.0225656	−	0.178625i
$773$	−8.38427	−	21.1762i	−0.301561	−	0.761657i	−0.998987	−	0.0449996i	$-0.985671\pi$
$773$	−8.38427	−	21.1762i	−0.301561	−	0.761657i	0.697426	−	0.716657i	$-0.254329\pi$
$774$	−0.194957	+	0.141645i	−0.00700759	+	0.00509131i
$775$	11.1912	−	4.03531i	0.401999	−	0.144953i
$776$	−14.0286	−	10.1924i	−0.503596	−	0.365884i
$777$	−4.88250	+	19.0161i	−0.175159	+	0.682198i
$778$	−3.52815	−	3.75710i	−0.126490	−	0.134699i
$779$	6.99935	−	6.57283i	0.250778	−	0.235496i
$780$	0.808535	+	7.30709i	0.0289502	+	0.261636i
$781$	24.7317	+	3.12435i	0.884972	+	0.111798i
$782$	2.69073	−	0.874271i	0.0962203	−	0.0312639i
$783$	1.10300	+	2.00635i	0.0394179	+	0.0717009i
$784$	−0.489462	+	7.77978i	−0.0174808	+	0.277849i
$785$	14.2657	+	23.2667i	0.509165	+	0.830423i
$786$	9.72612	−	15.3259i	0.346919	−	0.546657i
$787$	−4.11382	−	16.0223i	−0.146642	−	0.571133i	−0.998851	−	0.0479308i	$-0.984737\pi$
$787$	−4.11382	−	16.0223i	−0.146642	−	0.571133i	0.852209	−	0.523202i	$-0.175263\pi$
$788$	−9.49503	+	23.9817i	−0.338247	+	0.854313i
$789$	17.9756	+	4.61534i	0.639948	+	0.164311i
$790$	8.35419	−	7.60550i	0.297229	−	0.270592i
$791$	−10.6362	−	4.21117i	−0.378180	−	0.149732i
$792$	1.77954	+	0.837388i	0.0632332	+	0.0297553i
$793$	29.2367	+	9.49958i	1.03823	+	0.337340i
$794$	3.88484	+	20.3650i	0.137868	+	0.722729i
$795$	26.0408	−	4.55146i	0.923570	−	0.161424i
$796$	−5.54382	−	11.7812i	−0.196495	−	0.417574i
$797$	−22.4036	−	4.27372i	−0.793577	−	0.151383i	−0.225375	−	0.974272i	$-0.572361\pi$
$797$	−22.4036	−	4.27372i	−0.793577	−	0.151383i	−0.568202	+	0.822889i	$0.692361\pi$
$798$	11.9137	−	9.85590i	0.421742	−	0.348895i
$799$	0.938486	−	2.88836i	0.0332012	−	0.102183i
$800$	3.53379	−	3.53728i	0.124938	−	0.125062i
$801$	0.864027	+	2.65920i	0.0305289	+	0.0939582i
$802$	8.75573	+	5.55656i	0.309176	+	0.196209i
$803$	−2.86707	+	5.21519i	−0.101177	+	0.184040i
$804$	2.08288	−	10.9189i	0.0734576	−	0.385078i
$805$	14.5899	+	4.99120i	0.514225	+	0.175917i
$806$	5.70242	+	5.35493i	0.200859	+	0.188619i
$807$		−	23.7747i		−	0.836910i
$808$	−4.91951	+	5.23874i	−0.173068	+	0.184298i
$809$	−0.632455	−	0.996589i	−0.0222359	−	0.0350382i	0.833028	−	0.553231i	$-0.186605\pi$
$809$	−0.632455	−	0.996589i	−0.0222359	−	0.0350382i	−0.855264	+	0.518192i	$0.826605\pi$
$810$	−1.97590	+	1.04681i	−0.0694261	+	0.0367812i
$811$	−2.79832	+	1.10793i	−0.0982623	+	0.0389048i	−0.416741	−	0.909025i	$-0.636828\pi$
$811$	−2.79832	+	1.10793i	−0.0982623	+	0.0389048i	0.318479	+	0.947930i	$0.396828\pi$
$812$	−8.78925	−	0.552973i	−0.308442	−	0.0194055i
$813$	11.9121	+	0.749446i	0.417776	+	0.0262842i
$814$	−9.33351	+	3.69540i	−0.327139	+	0.129524i
$815$	−11.9376	−	1.69597i	−0.418158	−	0.0594074i
$816$	−0.845569	−	1.33240i	−0.0296008	−	0.0466435i
$817$	−0.663122	+	0.706153i	−0.0231997	+	0.0247052i
$818$			0.0277710i			0.000970991i
$819$	9.21872	+	8.65696i	0.322128	+	0.302499i
$820$	0.0825760	−	5.34040i	0.00288368	−	0.186495i
$821$	4.69765	−	24.6259i	0.163949	−	0.859451i	−0.801329	−	0.598224i	$-0.795873\pi$
$821$	4.69765	−	24.6259i	0.163949	−	0.859451i	0.965278	−	0.261226i	$-0.0841269\pi$
$822$	−4.80270	+	8.73607i	−0.167513	+	0.304706i
$823$	18.3691	+	11.6574i	0.640306	+	0.406351i	0.815966	−	0.578100i	$-0.196206\pi$
$823$	18.3691	+	11.6574i	0.640306	+	0.406351i	−0.175659	+	0.984451i	$0.556206\pi$
$824$	6.03294	+	18.5675i	0.210167	+	0.646828i
$825$	8.13590	+	5.52328i	0.283256	+	0.192296i
$826$	8.12016	−	24.9913i	0.282537	−	0.869558i
$827$	−16.9900	+	14.0553i	−0.590799	+	0.488751i	−0.884118	−	0.467263i	$-0.845240\pi$
$827$	−16.9900	+	14.0553i	−0.590799	+	0.488751i	0.293319	+	0.956015i	$0.405240\pi$
$828$	−1.76107	−	0.335943i	−0.0612016	−	0.0116748i
$829$	−0.800181	−	1.70047i	−0.0277914	−	0.0590598i	0.890449	−	0.455082i	$-0.150390\pi$
$829$	−0.800181	−	1.70047i	−0.0277914	−	0.0590598i	−0.918241	+	0.396023i	$0.870390\pi$
$830$	−3.62723	+	25.5314i	−0.125903	+	0.886208i
$831$	2.22242	+	11.6503i	0.0770950	+	0.404146i
$832$	3.12686	+	1.01598i	0.108404	+	0.0352227i
$833$	11.1305	+	5.23762i	0.385649	+	0.181473i
$834$	13.6288	+	5.39602i	0.471926	+	0.186849i
$835$	−4.45672	+	21.5475i	−0.154231	+	0.745680i
$836$	7.65750	+	1.96611i	0.264840	+	0.0679994i
$837$	−0.875877	+	2.21221i	−0.0302748	+	0.0764653i
$838$	2.58706	+	10.0759i	0.0893685	+	0.348067i
$839$	14.8144	−	23.3438i	0.511451	−	0.805917i	−0.486241	−	0.873825i	$-0.661632\pi$
$839$	14.8144	−	23.3438i	0.511451	−	0.805917i	0.997692	+	0.0679074i	$0.0216323\pi$
$840$	0.672705	−	8.57457i	0.0232105	−	0.295851i
$841$	−1.49178	+	23.7111i	−0.0514405	+	0.817624i
$842$	6.99640	+	12.7264i	0.241112	+	0.438581i
$843$	20.8694	−	6.78089i	0.718781	−	0.233546i
$844$	−16.6291	−	2.10074i	−0.572396	−	0.0723105i
$845$	4.46372	−	2.01677i	0.153557	−	0.0693791i
$846$	−1.40291	+	1.31742i	−0.0482330	+	0.0452938i
$847$	18.7791	+	19.9978i	0.645259	+	0.687131i
$848$	2.94009	−	11.4509i	0.100963	−	0.393226i
$849$	−23.6305	−	17.1686i	−0.810997	−	0.589224i
$850$	−3.13720	−	7.23983i	−0.107605	−	0.248324i
$851$	7.40323	−	5.37876i	0.253779	−	0.184381i
$852$	4.66601	+	11.7850i	0.159855	+	0.403747i
$853$	−3.01390	−	23.8575i	−0.103194	−	0.816865i	−0.955740	−	0.294213i	$-0.904943\pi$
$853$	−3.01390	−	23.8575i	−0.103194	−	0.816865i	0.852546	−	0.522652i	$-0.175057\pi$
$854$	−31.5163	−	17.3263i	−1.07847	−	0.592892i
$855$	−7.01361	+	5.62180i	−0.239860	+	0.192262i
$856$	0.657323	−	1.39688i	0.0224668	−	0.0477444i
$857$	−22.6391	+	31.1600i	−0.773337	+	1.06441i	0.222649	+	0.974899i	$0.428529\pi$
$857$	−22.6391	+	31.1600i	−0.773337	+	1.06441i	−0.995986	+	0.0895080i	$0.971471\pi$
$858$	−0.810421	+	6.41514i	−0.0276673	+	0.219009i
$859$	−36.0721	+	9.26174i	−1.23076	+	0.316006i	−0.807428	−	0.589966i	$-0.799141\pi$
$859$	−36.0721	+	9.26174i	−1.23076	+	0.316006i	−0.423336	+	0.905973i	$0.639141\pi$
$860$	0.0255160	+	0.538244i	0.000870089	+	0.0183540i
$861$	−5.85638	−	7.07914i	−0.199585	−	0.241257i
$862$	18.7069	+	15.4757i	0.637159	+	0.527103i
$863$	−4.29952	+	2.72856i	−0.146357	+	0.0928812i	−0.606989	−	0.794710i	$-0.707623\pi$
$863$	−4.29952	+	2.72856i	−0.146357	+	0.0928812i	0.460632	+	0.887591i	$0.347623\pi$
$864$	0.0627905	+	0.998027i	0.00213618	+	0.0339536i
$865$	22.3429	+	16.7669i	0.759681	+	0.570091i
$866$	−11.3433	+	13.7117i	−0.385461	+	0.465942i
$867$	14.2527	−	2.71885i	0.484047	−	0.0923370i
$868$	−5.37932	−	7.40399i	−0.182586	−	0.251308i
$869$	8.70763	−	4.78706i	0.295386	−	0.162390i
$870$	5.10390	+	0.400419i	0.173038	+	0.0135755i
$871$	36.2579	−	4.58044i	1.22855	−	0.155202i
$872$	7.18796	−	3.38240i	0.243415	−	0.114542i
$873$	17.3061	−	1.08880i	0.585721	−	0.0368505i
$874$	−7.20688			−0.243776
$875$	10.0083	−	41.8238i	0.338341	−	1.41390i
$876$	−3.02602			−0.102240
$877$	50.4692	−	3.17525i	1.70422	−	0.107221i	0.819423	−	0.573189i	$-0.194294\pi$
$877$	50.4692	−	3.17525i	1.70422	−	0.107221i	0.884801	+	0.465969i	$0.154294\pi$
$878$	−9.31162	+	4.38172i	−0.314252	+	0.147876i
$879$	28.2333	−	3.56670i	0.952286	−	0.120302i
$880$	3.74910	−	2.29872i	0.126382	−	0.0774900i
$881$	−30.7459	+	16.9027i	−1.03585	+	0.569466i	−0.906532	−	0.422137i	$-0.861280\pi$
$881$	−30.7459	+	16.9027i	−1.03585	+	0.569466i	−0.129322	+	0.991603i	$0.541280\pi$
$882$	−4.58188	−	6.30642i	−0.154280	−	0.212348i
$883$	−56.6228	+	10.8014i	−1.90551	+	0.363495i	−0.998357	−	0.0573049i	$-0.981749\pi$
$883$	−56.6228	+	10.8014i	−1.90551	+	0.363495i	−0.907153	+	0.420800i	$0.861749\pi$
$884$	3.30716	−	3.99767i	0.111232	−	0.134456i
$885$	−4.94457	+	14.4536i	−0.166210	+	0.485851i
$886$	−0.709288	−	11.2738i	−0.0238290	−	0.378751i
$887$	−31.0239	+	19.6884i	−1.04168	+	0.661070i	−0.942571	−	0.334006i	$-0.891599\pi$
$887$	−31.0239	+	19.6884i	−1.04168	+	0.661070i	−0.0991090	+	0.995077i	$0.531599\pi$
$888$	−3.93282	−	3.25351i	−0.131977	−	0.109181i
$889$	34.2712	+	41.4268i	1.14942	+	1.38941i
$890$	6.03097	+	1.64829i	0.202159	+	0.0552507i
$891$	−1.90493	+	0.489103i	−0.0638176	+	0.0163856i
$892$	3.08952	−	24.4561i	0.103445	−	0.818850i
$893$	−4.54724	+	6.25873i	−0.152167	+	0.209441i
$894$	−1.44478	+	3.07031i	−0.0483206	+	0.102687i
$895$	27.5684	−	1.30691i	0.921510	−	0.0436851i
$896$	−3.37067	−	1.85304i	−0.112606	−	0.0619057i
$897$	−0.738767	−	5.84794i	−0.0246667	−	0.195257i
$898$	6.28003	+	15.8615i	0.209567	+	0.529307i
$899$	4.40713	−	3.20197i	0.146986	−	0.106792i
$900$	−0.468086	+	4.97804i	−0.0156029	+	0.165935i
$901$	−15.0933	−	10.9659i	−0.502832	−	0.365329i
$902$	1.16826	−	4.55009i	0.0388989	−	0.151501i
$903$	0.634519	+	0.675694i	0.0211155	+	0.0224857i
$904$	2.16799	−	2.03588i	0.0721062	−	0.0677123i
$905$	−0.678281	+	1.18984i	−0.0225468	+	0.0395515i
$906$	13.4242	+	1.69586i	0.445988	+	0.0563413i
$907$	−11.4589	+	3.72322i	−0.380486	+	0.123627i	−0.493014	−	0.870021i	$-0.664105\pi$
$907$	−11.4589	+	3.72322i	−0.380486	+	0.123627i	0.112529	+	0.993648i	$0.464105\pi$
$908$	−12.1506	−	22.1018i	−0.403231	−	0.733475i
$909$	0.451245	−	7.17233i	0.0149668	−	0.237891i
$910$	27.4949	−	6.60812i	0.911448	−	0.219057i
$911$	−1.48528	+	2.34043i	−0.0492096	+	0.0775420i	−0.868042	−	0.496491i	$-0.834622\pi$
$911$	−1.48528	+	2.34043i	−0.0492096	+	0.0775420i	0.818832	+	0.574033i	$0.194622\pi$
$912$	0.999692	+	3.89354i	0.0331031	+	0.128928i
$913$	−8.34960	+	21.0887i	−0.276331	+	0.697934i
$914$	−28.1356	−	7.22398i	−0.930641	−	0.238948i
$915$	18.1636	+	10.3544i	0.600470	+	0.342306i
$916$	−22.4661	−	8.89496i	−0.742301	−	0.293898i
$917$	−63.1743	−	29.7276i	−2.08620	−	0.981691i
$918$	1.50083	+	0.487649i	0.0495347	+	0.0160948i
$919$	1.77993	+	9.33074i	0.0587146	+	0.307793i	0.999514	−	0.0311709i	$-0.00992363\pi$
$919$	1.77993	+	9.33074i	0.0587146	+	0.307793i	−0.940799	+	0.338964i	$0.889924\pi$
$920$	−2.78913	+	2.87958i	−0.0919548	+	0.0949369i
$921$	−9.43693	−	20.0545i	−0.310957	−	0.660818i
$922$	6.13068	+	1.16949i	0.201903	+	0.0385151i
$923$	−32.1095	+	26.5633i	−1.05690	+	0.874340i
$924$	2.33768	−	7.19463i	0.0769039	−	0.236686i
$925$	−16.8866	−	19.1351i	−0.555230	−	0.629158i
$926$	2.20718	+	6.79300i	0.0725324	+	0.223232i
$927$	−16.4838	−	10.4609i	−0.541399	−	0.343582i
$928$	1.10300	−	2.00635i	0.0362077	−	0.0658615i
$929$	−5.78087	+	30.3044i	−0.189664	+	0.994255i	0.752371	+	0.658740i	$0.228910\pi$
$929$	−5.78087	+	30.3044i	−0.189664	+	0.994255i	−0.942035	+	0.335515i	$0.891090\pi$
$930$	3.06026	+	4.35202i	0.100350	+	0.142708i
$931$	−22.8424	−	21.4505i	−0.748630	−	0.703010i
$932$			2.74443i			0.0898966i
$933$	−18.1487	+	19.3264i	−0.594161	+	0.632717i
$934$	−7.53879	−	11.8792i	−0.246677	−	0.388700i
$935$	−1.19485	−	6.83624i	−0.0390759	−	0.223569i
$936$	−3.05690	+	1.21031i	−0.0999178	+	0.0395602i
$937$	9.51128	+	0.598399i	0.310720	+	0.0195488i	0.217385	−	0.976086i	$-0.430247\pi$
$937$	9.51128	+	0.598399i	0.310720	+	0.0195488i	0.0933349	+	0.995635i	$0.470247\pi$
$938$	−42.6717	−	2.68468i	−1.39328	−	0.0876579i
$939$	0.188676	−	0.0747022i	0.00615722	−	0.00243781i
$940$	0.740915	+	4.23908i	0.0241660	+	0.138263i
$941$	−15.8555	−	24.9843i	−0.516876	−	0.814466i	0.481191	−	0.876616i	$-0.340204\pi$
$941$	−15.8555	−	24.9843i	−0.516876	−	0.814466i	−0.998067	+	0.0621501i	$0.980204\pi$
$942$	−8.35511	+	8.89729i	−0.272224	+	0.289889i
$943$			4.28233i			0.139452i
$944$	4.98002	+	4.67655i	0.162086	+	0.152209i
$945$	4.94731	+	7.03562i	0.160936	+	0.228869i
$946$	−0.0888076	+	0.465546i	−0.00288738	+	0.0151362i
$947$	−10.0316	+	18.2473i	−0.325982	+	0.592959i	−0.987620	−	0.156864i	$-0.949861\pi$
$947$	−10.0316	+	18.2473i	−0.325982	+	0.592959i	0.661638	+	0.749823i	$0.269861\pi$
$948$	4.26592	+	2.70724i	0.138551	+	0.0879270i
$949$	−3.07437	−	9.46194i	−0.0997983	−	0.307148i
$950$	1.90137	+	20.0090i	0.0616886	+	0.649179i
$951$	−1.62348	+	4.99657i	−0.0526450	+	0.162025i
$952$	−4.67697	+	3.86913i	−0.151581	+	0.125399i
$953$	−13.2989	−	2.53690i	−0.430794	−	0.0821784i	−0.0325764	−	0.999469i	$-0.510371\pi$
$953$	−13.2989	−	2.53690i	−0.430794	−	0.0821784i	−0.398218	+	0.917291i	$0.630371\pi$
$954$	5.03370	+	10.6972i	0.162972	+	0.346333i
$955$	33.7563	−	34.8510i	1.09233	−	1.12775i
$956$	0.562609	+	2.94930i	0.0181961	+	0.0953871i
$957$	4.28251	+	1.39147i	0.138434	+	0.0449799i
$958$	−23.5304	−	11.0726i	−0.760232	−	0.357738i
$959$	35.6532	+	14.1161i	1.15130	+	0.455833i
$960$	1.94259	+	1.10740i	0.0626969	+	0.0357412i
$961$	−24.5429	−	6.30154i	−0.791706	−	0.203275i
$962$	6.17762	−	15.6029i	0.199174	−	0.503057i
$963$	0.383930	+	1.49531i	0.0123720	+	0.0481857i
$964$	−13.0180	+	20.5130i	−0.419280	+	0.660680i
$965$	10.8763	−	2.61401i	0.350120	−	0.0841478i
$966$	−0.433005	+	6.88242i	−0.0139317	+	0.221438i
$967$	−2.22321	−	4.04400i	−0.0714935	−	0.130046i	0.838144	−	0.545449i	$-0.183641\pi$
$967$	−2.22321	−	4.04400i	−0.0714935	−	0.130046i	−0.909638	+	0.415403i	$0.863641\pi$
$968$	−6.78295	+	2.20392i	−0.218012	+	0.0708365i
$969$	6.29354	+	0.795059i	0.202178	+	0.0255410i
$970$	19.2026	−	33.6851i	0.616559	−	1.08156i
$971$	−13.0908	+	12.2930i	−0.420102	+	0.394502i	−0.865564	−	0.500799i	$-0.833040\pi$
$971$	−13.0908	+	12.2930i	−0.420102	+	0.394502i	0.445461	+	0.895301i	$0.353040\pi$
$972$	−0.684547	−	0.728969i	−0.0219569	−	0.0233817i
$973$	14.0216	−	54.6104i	0.449511	−	1.75073i
$974$	0.949887	+	0.690133i	0.0304363	+	0.0221133i
$975$	−16.0412	+	3.59394i	−0.513730	+	0.115098i
$976$	7.56445	−	5.49590i	0.242132	−	0.175919i
$977$	−9.71087	−	24.5269i	−0.310678	−	0.784684i	−0.998282	−	0.0585973i	$-0.981337\pi$
$977$	−9.71087	−	24.5269i	−0.310678	−	0.784684i	0.687603	−	0.726086i	$-0.258663\pi$
$978$	−0.675833	−	5.34977i	−0.0216107	−	0.171067i
$979$	4.81884	+	2.64918i	0.154011	+	0.0846682i
$980$	−17.4110	+	0.825384i	−0.556172	+	0.0263659i
$981$	−3.38240	+	7.18796i	−0.107992	+	0.229494i
$982$	−7.15221	+	9.84417i	−0.228236	+	0.314140i
$983$	−0.862341	+	6.82614i	−0.0275044	+	0.217720i	−0.999876	−	0.0157165i	$-0.994997\pi$
$983$	−0.862341	+	6.82614i	−0.0275044	+	0.217720i	0.972372	+	0.233436i	$0.0749971\pi$
$984$	2.31354	−	0.594017i	0.0737531	−	0.0189366i
$985$	−55.6345	−	15.2051i	−1.77266	−	0.484476i
$986$	−2.30305	−	2.78391i	−0.0733440	−	0.0886576i
$987$	5.70375	+	4.71855i	0.181552	+	0.150193i
$988$	−11.1589	+	7.08166i	−0.355012	+	0.225297i
$989$	−0.0271278	−	0.431184i	−0.000862614	−	0.0137109i
$990$	−1.42347	+	4.16097i	−0.0452408	+	0.132244i
$991$	12.9500	−	15.6538i	0.411369	−	0.497260i	−0.523612	−	0.851957i	$-0.675416\pi$
$991$	12.9500	−	15.6538i	0.411369	−	0.497260i	0.934981	+	0.354697i	$0.115416\pi$
$992$	2.33715	−	0.445836i	0.0742047	−	0.0141553i
$993$	1.78738	+	2.46011i	0.0567207	+	0.0780693i
$994$	42.7235	−	23.4874i	1.35511	−	0.744976i
$995$	24.8205	−	15.2184i	0.786861	−	0.482456i
$996$	−11.4417	+	1.44542i	−0.362544	+	0.0458000i
$997$	−37.5386	+	17.6643i	−1.18886	+	0.559435i	−0.915438	−	0.402460i	$-0.868155\pi$
$997$	−37.5386	+	17.6643i	−1.18886	+	0.559435i	−0.273421	+	0.961894i	$0.588155\pi$
$998$	32.0207	−	2.01457i	1.01360	−	0.0637702i
$999$	5.10416			0.161488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.469.4	yes	240
125.4	even	50	inner	750.2.o.a.379.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.379.4	✓	240	125.4	even	50	inner
750.2.o.a.469.4	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(0.522536 + 2.17416i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(2.26089 + 3.11184i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(0.522536 + 2.17416i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(2.26089 + 3.11184i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-0.658021 - 2.13706i) q^{10} +(-0.123491 - 1.96284i) q^{11} +(0.844328 - 0.535827i) q^{12} +(2.53327 + 2.09571i) q^{13} +(-2.45182 - 2.96374i) q^{14} +(1.39852 + 1.74475i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.197784 - 1.56562i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-1.71156 + 3.63726i) q^{19} +(0.790910 + 2.09152i) q^{20} +(3.37067 + 1.85304i) q^{21} +(0.246495 + 1.95121i) q^{22} +(-0.659985 - 1.66693i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-4.45391 + 2.27215i) q^{25} +(-2.65987 - 1.93251i) q^{26} +(0.248690 - 0.968583i) q^{27} +(2.63307 + 2.80394i) q^{28} +(-1.66901 + 1.56730i) q^{29} +(-1.50531 - 1.65349i) q^{30} +(-2.36054 - 0.298205i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(-0.947474 - 1.72345i) q^{33} +(-0.0990875 + 1.57495i) q^{34} +(-5.58424 + 6.54157i) q^{35} +(0.535827 - 0.844328i) q^{36} +(1.26935 + 4.94380i) q^{37} +(1.47980 - 3.73755i) q^{38} +(3.18448 + 0.817637i) q^{39} +(-0.920677 - 2.03773i) q^{40} +(-2.22085 - 0.879297i) q^{41} +(-3.48037 - 1.63774i) q^{42} +(0.229186 + 0.0744670i) q^{43} +(-0.368526 - 1.93188i) q^{44} +(2.00829 + 0.983239i) q^{45} +(0.763350 + 1.62220i) q^{46} +(1.89042 + 0.360618i) q^{47} +(0.770513 - 0.637424i) q^{48} +(-2.40884 + 7.41364i) q^{49} +(4.30245 - 2.54733i) q^{50} +(-0.487649 - 1.50083i) q^{51} +(2.77596 + 1.76168i) q^{52} +(5.69545 - 10.3600i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(4.20299 - 1.29414i) q^{55} +(-2.80394 - 2.63307i) q^{56} +4.01983i q^{57} +(1.56730 - 1.66901i) q^{58} +(3.66056 + 5.76811i) q^{59} +(1.60616 + 1.55571i) q^{60} +(8.69358 - 3.44203i) q^{61} +(2.37460 + 0.149397i) q^{62} +(3.83886 + 0.241520i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-3.23267 + 6.60282i) q^{65} +(1.05382 + 1.66055i) q^{66} +(7.60925 - 8.10303i) q^{67} -1.57806i q^{68} +(-1.30692 - 1.22728i) q^{69} +(5.16247 - 6.87930i) q^{70} +(-2.37507 + 12.4506i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(-2.55495 - 1.62142i) q^{73} +(-1.57727 - 4.85434i) q^{74} +(-3.06259 + 3.95229i) q^{75} +(-1.24220 + 3.82309i) q^{76} +(5.82884 - 4.82203i) q^{77} +(-3.22954 - 0.616068i) q^{78} +(2.15123 + 4.57159i) q^{79} +(1.04681 + 1.97590i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(2.27168 + 0.738113i) q^{82} +(-10.4350 - 4.91036i) q^{83} +(3.57634 + 1.41597i) q^{84} +(3.50725 - 0.388080i) q^{85} +(-0.233410 - 0.0599294i) q^{86} +(-0.842839 + 2.12877i) q^{87} +(0.489103 + 1.90493i) q^{88} +(-1.49820 + 2.36078i) q^{89} +(-2.06607 - 0.855197i) q^{90} +(-0.794065 + 12.6213i) q^{91} +(-0.863703 - 1.57107i) q^{92} +(-2.26285 + 0.735243i) q^{93} +(-1.90934 - 0.241205i) q^{94} +(-8.80231 - 1.82061i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(11.8702 + 12.6405i) q^{97} +(1.93858 - 7.55026i) q^{98} +(-1.59111 - 1.15601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) \) 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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