LMFDB - Embedded newform 483.2.u.a.113.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(113,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("483.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.u (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.11
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06610 + 1.65888i) q^{2} +(-0.893651 - 1.48371i) q^{3} +(-0.784489 - 1.71779i) q^{4} +(-3.45226 - 1.01367i) q^{5} +(3.41401 + 0.0993161i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.217736 - 0.0313058i) q^{8} +(-1.40277 + 2.65183i) q^{9} +O(q^{10})$	\(q+(-1.06610 + 1.65888i) q^{2} +(-0.893651 - 1.48371i) q^{3} +(-0.784489 - 1.71779i) q^{4} +(-3.45226 - 1.01367i) q^{5} +(3.41401 + 0.0993161i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.217736 - 0.0313058i) q^{8} +(-1.40277 + 2.65183i) q^{9} +(5.36201 - 4.64621i) q^{10} +(4.00358 - 2.57295i) q^{11} +(-1.84764 + 2.69906i) q^{12} +(0.0544245 + 0.0628092i) q^{13} +(1.89204 - 0.555552i) q^{14} +(1.58112 + 6.02801i) q^{15} +(2.75740 - 3.18221i) q^{16} +(-2.26201 + 4.95310i) q^{17} +(-2.90358 - 5.15415i) q^{18} +(-1.86231 + 0.850488i) q^{19} +(0.966977 + 6.72547i) q^{20} +(-0.296245 + 1.70653i) q^{21} +9.38448i q^{22} +(-3.58999 - 3.17993i) q^{23} +(0.148132 + 0.351033i) q^{24} +(6.68429 + 4.29573i) q^{25} +(-0.162215 + 0.0233229i) q^{26} +(5.18814 - 0.288509i) q^{27} +(-0.532037 + 1.81195i) q^{28} +(8.37233 + 3.82352i) q^{29} +(-11.6854 - 3.80356i) q^{30} +(-1.07817 + 7.49883i) q^{31} +(2.21530 + 7.54461i) q^{32} +(-7.39531 - 3.64083i) q^{33} +(-5.80508 - 9.03289i) q^{34} +(1.94523 + 3.02683i) q^{35} +(5.65576 + 0.329339i) q^{36} +(2.82055 + 9.60593i) q^{37} +(0.574545 - 3.99605i) q^{38} +(0.0445539 - 0.136879i) q^{39} +(0.719948 + 0.328789i) q^{40} +(0.0896903 - 0.305457i) q^{41} +(-2.51510 - 2.31076i) q^{42} +(2.55865 - 0.367878i) q^{43} +(-7.56055 - 4.85887i) q^{44} +(7.53084 - 7.73286i) q^{45} +(9.10240 - 2.56526i) q^{46} -5.52617i q^{47} +(-7.18562 - 1.24739i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-14.2522 + 6.50876i) q^{50} +(9.37040 - 1.07019i) q^{51} +(0.0651976 - 0.142763i) q^{52} +(-6.37454 + 7.35661i) q^{53} +(-5.05246 + 8.91407i) q^{54} +(-16.4295 + 4.82415i) q^{55} +(0.144053 + 0.166246i) q^{56} +(2.92613 + 2.00308i) q^{57} +(-15.2685 + 9.81245i) q^{58} +(8.06669 - 6.98983i) q^{59} +(9.11449 - 7.44494i) q^{60} +(-2.80244 - 0.402930i) q^{61} +(-11.2902 - 9.78304i) q^{62} +(2.79673 - 1.08550i) q^{63} +(-6.79711 - 1.99581i) q^{64} +(-0.124219 - 0.272002i) q^{65} +(13.9238 - 8.38645i) q^{66} +(4.00537 - 6.23247i) q^{67} +10.2829 q^{68} +(-1.50988 + 8.16825i) q^{69} -7.09495 q^{70} +(1.32333 - 2.05914i) q^{71} +(0.388453 - 0.533486i) q^{72} +(0.121033 + 0.265024i) q^{73} +(-18.9421 - 5.56189i) q^{74} +(0.400184 - 13.7564i) q^{75} +(2.92192 + 2.53186i) q^{76} +(-4.71063 - 0.677286i) q^{77} +(0.179568 + 0.219836i) q^{78} +(0.105511 - 0.0914258i) q^{79} +(-12.7450 + 8.19070i) q^{80} +(-5.06445 - 7.43985i) q^{81} +(0.411098 + 0.474432i) q^{82} +(-0.914788 + 0.268606i) q^{83} +(3.16386 - 0.829865i) q^{84} +(12.8299 - 14.8065i) q^{85} +(-2.11750 + 4.63668i) q^{86} +(-1.80897 - 15.8390i) q^{87} +(-0.952274 + 0.434889i) q^{88} +(0.197763 + 1.37547i) q^{89} +(4.79928 + 20.7367i) q^{90} -0.0831085i q^{91} +(-2.64614 + 8.66148i) q^{92} +(12.0896 - 5.10165i) q^{93} +(9.16725 + 5.89143i) q^{94} +(7.29129 - 1.04833i) q^{95} +(9.21428 - 10.0291i) q^{96} +(2.68473 - 9.14336i) q^{97} +(-1.79372 - 0.819163i) q^{98} +(1.20690 + 14.2261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36} - 44 q^{37} - 308 q^{40} - 44 q^{43} - 184 q^{46} + 98 q^{48} + 48 q^{49} - 28 q^{52} + 28 q^{54} - 44 q^{55} + 66 q^{57} + 4 q^{58} + 220 q^{60} + 84 q^{64} + 176 q^{66} + 44 q^{67} + 102 q^{69} - 8 q^{70} - 60 q^{72} + 4 q^{73} - 8 q^{75} + 176 q^{76} + 18 q^{78} - 16 q^{81} + 20 q^{82} - 154 q^{84} + 84 q^{85} + 28 q^{87} - 418 q^{90} - 188 q^{93} + 12 q^{94} - 412 q^{96} - 132 q^{97}+O(q^{100}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

Coefficient data

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

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

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

$2$	−1.06610	+	1.65888i	−0.753845	+	1.17301i	0.226172	+	0.974087i	$0.427379\pi$
$2$	−1.06610	+	1.65888i	−0.753845	+	1.17301i	−0.980016	+	0.198918i	$0.936257\pi$
$3$	−0.893651	−	1.48371i	−0.515950	−	0.856619i
$3$	−0.893651	−	1.48371i	−0.515950	−	0.856619i
$4$	−0.784489	−	1.71779i	−0.392244	−	0.858895i
$5$	−3.45226	−	1.01367i	−1.54390	−	0.453329i	−0.604627	−	0.796509i	$-0.706678\pi$
$5$	−3.45226	−	1.01367i	−1.54390	−	0.453329i	−0.939270	+	0.343180i	$0.888496\pi$
$6$	3.41401	+	0.0993161i	1.39376	+	0.0405456i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$8$	−0.217736	−	0.0313058i	−0.0769814	−	0.0110683i
$9$	−1.40277	+	2.65183i	−0.467591	+	0.883945i
$10$	5.36201	−	4.64621i	1.69562	−	1.46926i
$11$	4.00358	−	2.57295i	1.20713	−	0.775773i	0.226951	−	0.973906i	$-0.427124\pi$
$11$	4.00358	−	2.57295i	1.20713	−	0.775773i	0.980175	+	0.198133i	$0.0634879\pi$
$12$	−1.84764	+	2.69906i	−0.533367	+	0.779151i
$13$	0.0544245	+	0.0628092i	0.0150946	+	0.0174201i	0.763247	−	0.646107i	$-0.223604\pi$
$13$	0.0544245	+	0.0628092i	0.0150946	+	0.0174201i	−0.748152	+	0.663527i	$0.769059\pi$
$14$	1.89204	−	0.555552i	0.505668	−	0.148478i
$15$	1.58112	+	6.02801i	0.408243	+	1.55643i
$16$	2.75740	−	3.18221i	0.689350	−	0.795552i
$17$	−2.26201	+	4.95310i	−0.548617	+	1.20130i	0.408808	+	0.912621i	$0.365945\pi$
$17$	−2.26201	+	4.95310i	−0.548617	+	1.20130i	−0.957425	+	0.288683i	$0.906783\pi$
$18$	−2.90358	−	5.15415i	−0.684380	−	1.21484i
$19$	−1.86231	+	0.850488i	−0.427243	+	0.195115i	−0.617419	−	0.786635i	$-0.711822\pi$
$19$	−1.86231	+	0.850488i	−0.427243	+	0.195115i	0.190176	+	0.981750i	$0.439094\pi$
$20$	0.966977	+	6.72547i	0.216223	+	1.50386i
$21$	−0.296245	+	1.70653i	−0.0646460	+	0.372395i
$22$			9.38448i			2.00078i
$23$	−3.58999	−	3.17993i	−0.748566	−	0.663061i
$23$	−3.58999	−	3.17993i	−0.748566	−	0.663061i
$24$	0.148132	+	0.351033i	0.0302373	+	0.0716544i
$25$	6.68429	+	4.29573i	1.33686	+	0.859146i
$26$	−0.162215	+	0.0233229i	−0.0318129	+	0.00457401i
$27$	5.18814	−	0.288509i	0.998457	−	0.0555235i
$28$	−0.532037	+	1.81195i	−0.100545	+	0.342426i
$29$	8.37233	+	3.82352i	1.55470	+	0.710009i	0.993086	−	0.117388i	$-0.0374521\pi$
$29$	8.37233	+	3.82352i	1.55470	+	0.710009i	0.561617	+	0.827397i	$0.310179\pi$
$30$	−11.6854	−	3.80356i	−2.13345	−	0.694432i
$31$	−1.07817	+	7.49883i	−0.193645	+	1.34683i	0.628615	+	0.777717i	$0.283622\pi$
$31$	−1.07817	+	7.49883i	−0.193645	+	1.34683i	−0.822260	+	0.569113i	$0.807287\pi$
$32$	2.21530	+	7.54461i	0.391613	+	1.33371i
$33$	−7.39531	−	3.64083i	−1.28736	−	0.633787i
$34$	−5.80508	−	9.03289i	−0.995564	−	1.54913i
$35$	1.94523	+	3.02683i	0.328803	+	0.511628i
$36$	5.65576	+	0.329339i	0.942626	+	0.0548898i
$37$	2.82055	+	9.60593i	0.463696	+	1.57920i	0.776967	+	0.629541i	$0.216757\pi$
$37$	2.82055	+	9.60593i	0.463696	+	1.57920i	−0.313271	+	0.949664i	$0.601425\pi$
$38$	0.574545	−	3.99605i	0.0932036	−	0.648245i
$39$	0.0445539	−	0.136879i	0.00713434	−	0.0219183i
$40$	0.719948	+	0.328789i	0.113834	+	0.0519862i
$41$	0.0896903	−	0.305457i	0.0140073	−	0.0477044i	−0.952193	−	0.305498i	$-0.901177\pi$
$41$	0.0896903	−	0.305457i	0.0140073	−	0.0477044i	0.966200	+	0.257793i	$0.0829954\pi$
$42$	−2.51510	−	2.31076i	−0.388088	−	0.356558i
$43$	2.55865	−	0.367878i	0.390190	−	0.0561008i	0.0555718	−	0.998455i	$-0.482302\pi$
$43$	2.55865	−	0.367878i	0.390190	−	0.0561008i	0.334618	+	0.942354i	$0.391393\pi$
$44$	−7.56055	−	4.85887i	−1.13980	−	0.732503i
$45$	7.53084	−	7.73286i	1.12263	−	1.15275i
$46$	9.10240	−	2.56526i	1.34208	−	0.378226i
$47$		−	5.52617i		−	0.806074i	−0.915184	−	0.403037i	$-0.867955\pi$
$47$		−	5.52617i		−	0.806074i	0.915184	−	0.403037i	$-0.132045\pi$
$48$	−7.18562	−	1.24739i	−1.03715	−	0.180045i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	−14.2522	+	6.50876i	−2.01557	+	0.920478i
$51$	9.37040	−	1.07019i	1.31212	−	0.149857i
$52$	0.0651976	−	0.142763i	0.00904129	−	0.0197977i
$53$	−6.37454	+	7.35661i	−0.875611	+	1.01051i	0.124223	+	0.992254i	$0.460356\pi$
$53$	−6.37454	+	7.35661i	−0.875611	+	1.01051i	−0.999833	+	0.0182542i	$0.994189\pi$
$54$	−5.05246	+	8.91407i	−0.687552	+	1.21305i
$55$	−16.4295	+	4.82415i	−2.21536	+	0.650488i
$56$	0.144053	+	0.166246i	0.0192499	+	0.0222156i
$57$	2.92613	+	2.00308i	0.387575	+	0.265315i
$58$	−15.2685	+	9.81245i	−2.00485	+	1.28844i
$59$	8.06669	−	6.98983i	1.05019	−	0.909998i	0.0541204	−	0.998534i	$-0.482765\pi$
$59$	8.06669	−	6.98983i	1.05019	−	0.909998i	0.996073	+	0.0885367i	$0.0282191\pi$
$60$	9.11449	−	7.44494i	1.17668	−	0.961138i
$61$	−2.80244	−	0.402930i	−0.358816	−	0.0515900i	−0.0394504	−	0.999222i	$-0.512561\pi$
$61$	−2.80244	−	0.402930i	−0.358816	−	0.0515900i	−0.319366	+	0.947632i	$0.603470\pi$
$62$	−11.2902	−	9.78304i	−1.43386	−	1.24245i
$63$	2.79673	−	1.08550i	0.352355	−	0.136760i
$64$	−6.79711	−	1.99581i	−0.849639	−	0.249476i
$65$	−0.124219	−	0.272002i	−0.0154075	−	0.0337377i
$66$	13.9238	−	8.38645i	1.71390	−	1.03230i
$67$	4.00537	−	6.23247i	0.489334	−	0.761418i	−0.505512	−	0.862820i	$-0.668696\pi$
$67$	4.00537	−	6.23247i	0.489334	−	0.761418i	0.994846	+	0.101402i	$0.0323327\pi$
$68$	10.2829			1.24699
$69$	−1.50988	+	8.16825i	−0.181768	+	0.983341i
$70$	−7.09495			−0.848009
$71$	1.32333	−	2.05914i	0.157051	−	0.244375i	−0.753807	−	0.657095i	$-0.771785\pi$
$71$	1.32333	−	2.05914i	0.157051	−	0.244375i	0.910858	+	0.412720i	$0.135421\pi$
$72$	0.388453	−	0.533486i	0.0457796	−	0.0628719i
$73$	0.121033	+	0.265024i	0.0141658	+	0.0310188i	0.916583	−	0.399845i	$-0.130936\pi$
$73$	0.121033	+	0.265024i	0.0141658	+	0.0310188i	−0.902417	+	0.430864i	$0.858209\pi$
$74$	−18.9421	−	5.56189i	−2.20197	−	0.646557i
$75$	0.400184	−	13.7564i	0.0462093	−	1.58845i
$76$	2.92192	+	2.53186i	0.335167	+	0.290424i
$77$	−4.71063	−	0.677286i	−0.536826	−	0.0771839i
$78$	0.179568	+	0.219836i	0.0203320	+	0.0248916i
$79$	0.105511	−	0.0914258i	0.0118709	−	0.0102862i	−0.648905	−	0.760869i	$-0.724773\pi$
$79$	0.105511	−	0.0914258i	0.0118709	−	0.0102862i	0.660776	+	0.750583i	$0.270227\pi$
$80$	−12.7450	+	8.19070i	−1.42493	+	0.915748i
$81$	−5.06445	−	7.43985i	−0.562716	−	0.826650i
$82$	0.411098	+	0.474432i	0.0453982	+	0.0523923i
$83$	−0.914788	+	0.268606i	−0.100411	+	0.0294833i	−0.331552	−	0.943437i	$-0.607572\pi$
$83$	−0.914788	+	0.268606i	−0.100411	+	0.0294833i	0.231141	+	0.972920i	$0.425754\pi$
$84$	3.16386	−	0.829865i	0.345205	−	0.0905457i
$85$	12.8299	−	14.8065i	1.39159	−	1.60599i
$86$	−2.11750	+	4.63668i	−0.228336	+	0.499986i
$87$	−1.80897	−	15.8390i	−0.193942	−	1.69812i
$88$	−0.952274	+	0.434889i	−0.101513	+	0.0463593i
$89$	0.197763	+	1.37547i	0.0209628	+	0.145799i	0.997615	−	0.0690286i	$-0.0219900\pi$
$89$	0.197763	+	1.37547i	0.0209628	+	0.145799i	−0.976652	+	0.214828i	$0.931081\pi$
$90$	4.79928	+	20.7367i	0.505889	+	2.18584i
$91$		−	0.0831085i		−	0.00871213i
$92$	−2.64614	+	8.66148i	−0.275879	+	0.903021i
$93$	12.0896	−	5.10165i	1.25363	−	0.529017i
$94$	9.16725	+	5.89143i	0.945530	+	0.607655i
$95$	7.29129	−	1.04833i	0.748071	−	0.107556i
$96$	9.21428	−	10.0291i	0.940429	−	1.02359i
$97$	2.68473	−	9.14336i	0.272593	−	0.928367i	−0.703442	−	0.710753i	$-0.748354\pi$
$97$	2.68473	−	9.14336i	0.272593	−	0.928367i	0.976035	−	0.217614i	$-0.0698274\pi$
$98$	−1.79372	−	0.819163i	−0.181193	−	0.0827479i
$99$	1.20690	+	14.2261i	0.121298	+	1.42978i
$100$	2.13542	−	14.8522i	0.213542	−	1.48522i
$101$	0.164930	+	0.561700i	0.0164112	+	0.0558913i	0.967292	−	0.253667i	$-0.0816369\pi$
$101$	0.164930	+	0.561700i	0.0164112	+	0.0558913i	−0.950880	+	0.309559i	$0.899819\pi$
$102$	−8.21444	+	16.6853i	−0.813351	+	1.65209i
$103$	7.34315	+	11.4262i	0.723542	+	1.12585i	0.986928	+	0.161163i	$0.0515245\pi$
$103$	7.34315	+	11.4262i	0.723542	+	1.12585i	−0.263385	+	0.964691i	$0.584839\pi$
$104$	−0.00988389	−	0.0153796i	−0.000969196	−	0.00150810i
$105$	2.75258	−	5.59108i	0.268624	−	0.545634i
$106$	−5.40786	−	18.4175i	−0.525257	−	1.78886i
$107$	−2.68262	+	18.6580i	−0.259338	+	1.80374i	0.278226	+	0.960516i	$0.410254\pi$
$107$	−2.68262	+	18.6580i	−0.259338	+	1.80374i	−0.537564	+	0.843223i	$0.680655\pi$
$108$	−4.56563	−	8.68580i	−0.439328	−	0.835792i
$109$	3.54063	+	1.61695i	0.339131	+	0.154876i	0.577699	−	0.816250i	$-0.303951\pi$
$109$	3.54063	+	1.61695i	0.339131	+	0.154876i	−0.238568	+	0.971126i	$0.576678\pi$
$110$	9.51281	−	32.3976i	0.907011	−	3.08899i
$111$	11.7318	−	12.7692i	1.11353	−	1.21200i
$112$	−4.16781	+	0.599240i	−0.393821	+	0.0566229i
$113$	9.41233	+	6.04894i	0.885438	+	0.569036i	0.902438	−	0.430819i	$-0.141775\pi$
$113$	9.41233	+	6.04894i	0.885438	+	0.569036i	−0.0170004	+	0.999855i	$0.505412\pi$
$114$	−6.44241	+	2.71862i	−0.603387	+	0.254622i
$115$	9.17018	+	14.6170i	0.855123	+	1.36304i
$116$		−	17.3814i		−	1.61382i
$117$	−0.242905	+	0.0562175i	−0.0224566	+	0.00519731i
$118$	2.99541	+	20.8335i	0.275749	+	1.91788i
$119$	4.95310	−	2.26201i	0.454050	−	0.207358i
$120$	−0.155556	−	1.36202i	−0.0142002	−	0.124334i
$121$	4.83907	−	10.5961i	0.439915	−	0.963280i
$122$	3.65609	−	4.21935i	0.331007	−	0.382002i
$123$	−0.533361	+	0.139898i	−0.0480915	+	0.0126142i
$124$	13.7272	−	4.03068i	1.23274	−	0.361966i
$125$	−6.94045	−	8.00971i	−0.620773	−	0.716410i
$126$	−1.18087	+	5.79669i	−0.105200	+	0.516410i
$127$	0.450558	−	0.289556i	0.0399805	−	0.0256939i	−0.520498	−	0.853863i	$-0.674254\pi$
$127$	0.450558	−	0.289556i	0.0399805	−	0.0256939i	0.560478	+	0.828169i	$0.310617\pi$
$128$	−1.32790	+	1.15063i	−0.117371	+	0.101703i
$129$	−2.83236	−	3.46753i	−0.249375	−	0.305299i
$130$	0.583649	+	0.0839160i	0.0511894	+	0.00735992i
$131$	14.1365	+	12.2494i	1.23511	+	1.07023i	0.995040	+	0.0994771i	$0.0317170\pi$
$131$	14.1365	+	12.2494i	1.23511	+	1.07023i	0.240074	+	0.970755i	$0.422828\pi$
$132$	−0.452646	+	15.5598i	−0.0393977	+	1.35431i
$133$	1.96439	+	0.576797i	0.170334	+	0.0500147i
$134$	6.06881	+	13.2888i	0.524266	+	1.14798i
$135$	−18.2032	−	4.26308i	−1.56669	−	0.366907i
$136$	0.647582	−	1.00766i	0.0555297	−	0.0864058i
$137$	0.318619			0.0272214			0.0136107	−	0.999907i	$-0.495667\pi$
$137$	0.318619			0.0272214			0.0136107	+	0.999907i	$0.495667\pi$
$138$	−11.9405	−	11.2129i	−1.01644	−	0.954502i
$139$	−18.1577			−1.54012			−0.770058	−	0.637974i	$-0.779773\pi$
$139$	−18.1577			−1.54012			−0.770058	+	0.637974i	$0.779773\pi$
$140$	3.67346	−	5.71601i	0.310464	−	0.483091i
$141$	−8.19922	+	4.93847i	−0.690499	+	0.415894i
$142$	2.00507	+	4.39049i	0.168262	+	0.368442i
$143$	0.379498	+	0.111431i	0.0317352	+	0.00931829i
$144$	4.57068	+	11.7761i	0.380890	+	0.981340i
$145$	−25.0277	−	21.6866i	−2.07843	−	1.80097i
$146$	−0.568676	−	0.0817633i	−0.0470640	−	0.00676678i
$147$	1.34143	−	1.09571i	0.110639	−	0.0903725i
$148$	14.2883	−	12.3809i	1.17449	−	1.01770i
$149$	−17.6148	+	11.3204i	−1.44306	+	0.927400i	−0.443547	+	0.896251i	$0.646280\pi$
$149$	−17.6148	+	11.3204i	−1.44306	+	0.927400i	−0.999515	+	0.0311488i	$0.990083\pi$
$150$	22.3936	+	15.3295i	1.82843	+	1.25165i
$151$	10.5756	+	12.2049i	0.860631	+	0.993221i	0.999996	+	0.00297992i	$0.000948539\pi$
$151$	10.5756	+	12.2049i	0.860631	+	0.993221i	−0.139365	+	0.990241i	$0.544506\pi$
$152$	0.432118	−	0.126881i	0.0350494	−	0.0102914i
$153$	−9.96172	−	12.9466i	−0.805358	−	1.04667i
$154$	6.14553	−	7.09232i	0.495221	−	0.571515i
$155$	11.3235	−	24.7950i	0.909525	−	1.99158i
$156$	−0.270082	+	0.0308461i	−0.0216239	+	0.00246966i
$157$	−8.57109	+	3.91429i	−0.684047	+	0.312394i	−0.726955	−	0.686685i	$-0.759065\pi$
$157$	−8.57109	+	3.91429i	−0.684047	+	0.312394i	0.0429076	+	0.999079i	$0.486338\pi$
$158$	0.0391794	+	0.272499i	0.00311695	+	0.0216788i
$159$	16.6117	+	2.88371i	1.31739	+	0.228693i
$160$		−	28.2915i		−	2.23664i
$161$	0.630726	+	4.75418i	0.0497082	+	0.374682i
$162$	17.7410	−	0.469706i	1.39387	−	0.0369036i
$163$	−11.5722	−	7.43697i	−0.906401	−	0.582508i	0.00228116	−	0.999997i	$-0.499274\pi$
$163$	−11.5722	−	7.43697i	−0.906401	−	0.582508i	−0.908682	+	0.417489i	$0.862910\pi$
$164$	−0.595072	+	0.0855585i	−0.0464674	+	0.00668100i
$165$	21.8399	+	20.0655i	1.70023	+	1.56210i
$166$	0.529668	−	1.80388i	0.0411102	−	0.140008i
$167$	−0.509132	−	0.232513i	−0.0393978	−	0.0179924i	0.395619	−	0.918415i	$-0.370530\pi$
$167$	−0.509132	−	0.232513i	−0.0393978	−	0.0179924i	−0.435016	+	0.900422i	$0.643257\pi$
$168$	0.117927	−	0.362299i	0.00909830	−	0.0279520i
$169$	1.84911	−	12.8608i	0.142239	−	0.989296i
$170$	10.8842	+	37.0683i	0.834783	+	2.84301i
$171$	0.357046	−	6.13158i	0.0273040	−	0.468893i
$172$	−2.63916	−	4.10662i	−0.201234	−	0.313127i
$173$	−3.08721	−	4.80380i	−0.234716	−	0.365226i	0.703836	−	0.710362i	$-0.251469\pi$
$173$	−3.08721	−	4.80380i	−0.234716	−	0.365226i	−0.938552	+	0.345137i	$0.887833\pi$
$174$	28.2035	+	13.8850i	2.13810	+	1.05262i
$175$	−2.23854	−	7.62377i	−0.169218	−	0.576303i
$176$	2.85183	−	19.8349i	0.214964	−	1.49511i
$177$	−17.5797	−	5.72214i	−1.32137	−	0.430102i
$178$	−2.49257	−	1.13832i	−0.186826	−	0.0853207i
$179$	0.276107	−	0.940334i	0.0206372	−	0.0702838i	−0.948531	−	0.316685i	$-0.897430\pi$
$179$	0.276107	−	0.940334i	0.0206372	−	0.0702838i	0.969168	+	0.246402i	$0.0792482\pi$
$180$	−19.1913	−	6.87006i	−1.43043	−	0.512064i
$181$	−4.45851	+	0.641037i	−0.331398	+	0.0476479i	−0.306006	−	0.952030i	$-0.598993\pi$
$181$	−4.45851	+	0.641037i	−0.331398	+	0.0476479i	−0.0253927	+	0.999678i	$0.508084\pi$
$182$	0.137867	+	0.0886017i	0.0102194	+	0.00656760i
$183$	1.90658	+	4.51808i	0.140938	+	0.333986i
$184$	0.682122	+	0.804773i	0.0502867	+	0.0593287i
$185$		−	36.0213i		−	2.64834i
$186$	−4.42564	+	25.4940i	−0.324503	+	1.86931i
$187$	3.68794	+	25.6502i	0.269689	+	1.87573i
$188$	−9.49280	+	4.33522i	−0.692334	+	0.316178i
$189$	−4.10987	−	3.17947i	−0.298949	−	0.231272i
$190$	−6.03417	+	13.2130i	−0.437765	+	0.958572i
$191$	2.79413	−	3.22460i	0.202176	−	0.233324i	−0.645603	−	0.763673i	$-0.723394\pi$
$191$	2.79413	−	3.22460i	0.202176	−	0.233324i	0.847779	+	0.530350i	$0.177939\pi$
$192$	3.11305	+	11.8685i	0.224665	+	0.856534i
$193$	−5.40550	+	1.58720i	−0.389096	+	0.114249i	−0.470429	−	0.882438i	$-0.655901\pi$
$193$	−5.40550	+	1.58720i	−0.389096	+	0.114249i	0.0813323	+	0.996687i	$0.474082\pi$
$194$	12.3055	+	14.2014i	0.883487	+	1.01960i
$195$	−0.292563	+	0.427380i	−0.0209509	+	0.0306053i
$196$	1.58866	−	1.02097i	0.113476	−	0.0729265i
$197$	4.86059	−	4.21173i	0.346303	−	0.300073i	−0.464290	−	0.885683i	$-0.653690\pi$
$197$	4.86059	−	4.21173i	0.346303	−	0.300073i	0.810593	+	0.585610i	$0.199145\pi$
$198$	−24.8861	−	13.1643i	−1.76858	−	0.935547i
$199$	−17.1813	−	2.47030i	−1.21795	−	0.175115i	−0.496782	−	0.867875i	$-0.665485\pi$
$199$	−17.1813	−	2.47030i	−1.21795	−	0.175115i	−0.721168	+	0.692760i	$0.756394\pi$
$200$	−1.32093	−	1.14459i	−0.0934039	−	0.0809349i
$201$	−12.8266	−	0.373134i	−0.904716	−	0.0263189i
$202$	−1.10763	−	0.325228i	−0.0779322	−	0.0228830i
$203$	−3.82352	−	8.37233i	−0.268358	−	0.587623i
$204$	−9.18934	−	15.2568i	−0.643382	−	1.06819i
$205$	−0.619268	+	0.963600i	−0.0432516	+	0.0673008i
$206$	−26.7832			−1.86607
$207$	13.4686	−	5.05935i	0.936132	−	0.351649i
$208$	0.349942			0.0242641
$209$	−5.26765	+	8.19663i	−0.364371	+	0.566972i
$210$	6.34041	+	10.5268i	0.437530	+	0.726421i
$211$	6.65171	+	14.5652i	0.457923	+	1.00271i	0.987956	+	0.154734i	$0.0494520\pi$
$211$	6.65171	+	14.5652i	0.457923	+	1.00271i	−0.530034	+	0.847977i	$0.677821\pi$
$212$	17.6379	+	5.17895i	1.21137	+	0.355692i
$213$	−4.23776	−	0.123280i	−0.290367	−	0.00844698i
$214$	−28.0915	−	24.3414i	−1.92029	−	1.66394i
$215$	−9.20601	−	1.32362i	−0.627845	−	0.0902705i
$216$	−1.13868	−	0.0995997i	−0.0774772	−	0.00677690i
$217$	5.72551	−	4.96119i	0.388673	−	0.336787i
$218$	−6.45699	+	4.14966i	−0.437323	+	0.281050i
$219$	0.285058	−	0.416416i	0.0192624	−	0.0281388i
$220$	21.1757	+	24.4380i	1.42766	+	1.64761i
$221$	−0.434209	+	0.127495i	−0.0292080	+	0.00857626i
$222$	8.67538	+	33.0749i	0.582254	+	2.21984i
$223$	−11.5816	+	13.3659i	−0.775564	+	0.895048i	−0.996781	−	0.0801763i	$-0.974452\pi$
$223$	−11.5816	+	13.3659i	−0.775564	+	0.895048i	0.221217	+	0.975225i	$0.428997\pi$
$224$	3.26646	−	7.15254i	0.218249	−	0.477899i
$225$	−20.7681	+	11.6997i	−1.38454	+	0.779978i
$226$	−20.0689	+	9.16517i	−1.33497	+	0.609658i
$227$	2.27541	+	15.8258i	0.151024	+	1.05040i	0.914507	+	0.404570i	$0.132579\pi$
$227$	2.27541	+	15.8258i	0.151024	+	1.05040i	−0.763483	+	0.645828i	$0.776512\pi$
$228$	1.14536	−	6.59787i	0.0758532	−	0.436955i
$229$			21.5619i			1.42485i	0.701748	+	0.712426i	$0.252403\pi$
$229$			21.5619i			1.42485i	−0.701748	+	0.712426i	$0.747597\pi$
$230$	−34.0242	−	0.370946i	−2.24349	−	0.0244595i
$231$	3.20477	+	7.59445i	0.210858	+	0.499678i
$232$	−1.70326	−	1.09462i	−0.111825	−	0.0718654i
$233$	11.6461	−	1.67445i	0.762959	−	0.109697i	0.250158	−	0.968205i	$-0.419517\pi$
$233$	11.6461	−	1.67445i	0.762959	−	0.109697i	0.512800	+	0.858508i	$0.328608\pi$
$234$	0.165702	−	0.462883i	0.0108323	−	0.0302596i
$235$	−5.60174	+	19.0778i	−0.365417	+	1.24450i
$236$	−18.3353	−	8.37344i	−1.19353	−	0.545065i
$237$	−0.229939	−	0.0748446i	−0.0149361	−	0.00486168i
$238$	−1.52809	+	10.6281i	−0.0990516	+	0.688919i
$239$	7.56314	+	25.7577i	0.489219	+	1.66613i	0.720669	+	0.693279i	$0.243835\pi$
$239$	7.56314	+	25.7577i	0.489219	+	1.66613i	−0.231450	+	0.972847i	$0.574347\pi$
$240$	23.5422	+	11.5902i	1.51964	+	0.748143i
$241$	−0.402228	−	0.625878i	−0.0259098	−	0.0403164i	0.828057	−	0.560644i	$-0.189446\pi$
$241$	−0.402228	−	0.625878i	−0.0259098	−	0.0403164i	−0.853967	+	0.520327i	$0.825810\pi$
$242$	12.4187	+	19.3239i	0.798304	+	1.24219i
$243$	−6.51271	+	14.1628i	−0.417790	+	0.908543i
$244$	1.50633	+	5.13010i	0.0964332	+	0.328421i
$245$	0.512049	−	3.56138i	0.0327136	−	0.227528i
$246$	0.336541	−	1.03393i	0.0214570	−	0.0659207i
$247$	−0.154774	−	0.0706828i	−0.00984801	−	0.00449744i
$248$	0.469513	−	1.59901i	0.0298141	−	0.101538i
$249$	1.21603	+	1.11724i	0.0770630	+	0.0708020i
$250$	20.6864	−	2.97425i	1.30832	−	0.188108i
$251$	7.36204	+	4.73130i	0.464688	+	0.298637i	0.751956	−	0.659214i	$-0.229111\pi$
$251$	7.36204	+	4.73130i	0.464688	+	0.298637i	−0.287268	+	0.957850i	$0.592747\pi$
$252$	−4.05866	−	3.95263i	−0.255672	−	0.248992i
$253$	−22.5546	−	3.49424i	−1.41800	−	0.219681i
$254$			1.05612i			0.0662666i
$255$	−33.4339	−	5.80396i	−2.09371	−	0.363458i
$256$	−2.50943	−	17.4534i	−0.156839	−	1.09084i
$257$	−6.09906	+	2.78535i	−0.380449	+	0.173745i	−0.596455	−	0.802647i	$-0.703424\pi$
$257$	−6.09906	+	2.78535i	−0.380449	+	0.173745i	0.216005	+	0.976392i	$0.430697\pi$
$258$	8.77178	−	1.00182i	0.546107	−	0.0623708i
$259$	4.15891	−	9.10675i	0.258422	−	0.565866i
$260$	−0.369794	+	0.426765i	−0.0229337	+	0.0264669i
$261$	−21.8838	+	16.8385i	−1.35457	+	1.04228i
$262$	−35.3911	+	10.3918i	−2.18647	+	0.642006i
$263$	−15.4202	−	17.7959i	−0.950853	−	1.09734i	−0.995154	−	0.0983247i	$-0.968652\pi$
$263$	−15.4202	−	17.7959i	−0.950853	−	1.09734i	0.0443014	−	0.999018i	$-0.485894\pi$
$264$	1.49625	+	1.02426i	0.0920877	+	0.0630386i
$265$	29.4638	−	18.9352i	1.80995	−	1.16318i
$266$	−3.05107	+	2.64377i	−0.187073	+	0.162100i
$267$	1.86406	−	1.52261i	0.114079	−	0.0931823i
$268$	−13.8483	−	1.99108i	−0.845917	−	0.121624i
$269$	10.2853	+	8.91228i	0.627107	+	0.543392i	0.909393	−	0.415939i	$-0.136547\pi$
$269$	10.2853	+	8.91228i	0.627107	+	0.543392i	−0.282285	+	0.959331i	$0.591092\pi$
$270$	26.4784	−	25.6521i	1.61142	−	1.56114i
$271$	15.4172	+	4.52689i	0.936526	+	0.274989i	0.714166	−	0.699976i	$-0.246806\pi$
$271$	15.4172	+	4.52689i	0.936526	+	0.274989i	0.222359	+	0.974965i	$0.428624\pi$
$272$	9.52455	+	20.8559i	0.577511	+	1.26457i
$273$	−0.123309	+	0.0742700i	−0.00746298	+	0.00449502i
$274$	−0.339678	+	0.528550i	−0.0205207	+	0.0319309i
$275$	37.8138			2.28026
$276$	15.2158	−	3.81424i	0.915885	−	0.229590i
$277$	−1.18710			−0.0713257			−0.0356629	−	0.999364i	$-0.511354\pi$
$277$	−1.18710			−0.0713257			−0.0356629	+	0.999364i	$0.511354\pi$
$278$	19.3579	−	30.1214i	1.16101	−	1.80656i
$279$	−18.3732	−	13.3783i	−1.09998	−	0.800937i
$280$	−0.328789	−	0.719948i	−0.0196489	−	0.0430251i
$281$	−6.37183	−	1.87094i	−0.380111	−	0.111611i	0.0860947	−	0.996287i	$-0.472561\pi$
$281$	−6.37183	−	1.87094i	−0.380111	−	0.111611i	−0.466206	+	0.884676i	$0.654379\pi$
$282$	0.548837	−	18.8664i	0.0326828	−	1.12348i
$283$	19.9984	+	17.3287i	1.18878	+	1.03009i	0.998833	+	0.0482925i	$0.0153780\pi$
$283$	19.9984	+	17.3287i	1.18878	+	1.03009i	0.189950	+	0.981794i	$0.439167\pi$
$284$	−4.57532	−	0.657831i	−0.271495	−	0.0390351i
$285$	−8.07129	−	9.88130i	−0.478102	−	0.585318i
$286$	−0.589431	+	0.510745i	−0.0348538	+	0.0302010i
$287$	−0.267815	+	0.172114i	−0.0158086	+	0.0101596i
$288$	−23.1146	−	4.70878i	−1.36204	−	0.277468i
$289$	−8.28392	−	9.56016i	−0.487290	−	0.562362i
$290$	62.6574	−	18.3979i	3.67937	−	1.08036i
$291$	−15.9653	+	4.18762i	−0.935901	+	0.245482i
$292$	0.360308	−	0.415817i	0.0210854	−	0.0243339i
$293$	0.639253	−	1.39977i	0.0373456	−	0.0817754i	−0.890040	−	0.455883i	$-0.849324\pi$
$293$	0.639253	−	1.39977i	0.0373456	−	0.0817754i	0.927385	+	0.374107i	$0.122051\pi$
$294$	0.387559	+	3.39340i	0.0226029	+	0.197907i
$295$	−34.9337	+	15.9537i	−2.03392	+	0.928860i
$296$	−0.313416	−	2.17986i	−0.0182170	−	0.126702i
$297$	20.0288	−	14.5039i	1.16219	−	0.841600i
$298$		−	41.2895i		−	2.39183i
$299$	0.00434517	−	0.398550i	0.000251288	−	0.0230488i
$300$	−23.9446	+	10.1043i	−1.38244	+	0.583373i
$301$	−2.17460	−	1.39753i	−0.125342	−	0.0805525i
$302$	−31.5211	+	4.53205i	−1.81384	+	0.260790i
$303$	0.686009	−	0.746672i	0.0394102	−	0.0428952i
$304$	−2.42870	+	8.27139i	−0.139295	+	0.474397i
$305$	9.26632	+	4.23178i	0.530588	+	0.242311i
$306$	32.0969	−	2.72302i	1.83486	−	0.155665i
$307$	4.73151	−	32.9084i	0.270042	−	1.87818i	−0.177799	−	0.984067i	$-0.556898\pi$
$307$	4.73151	−	32.9084i	0.270042	−	1.87818i	0.447841	−	0.894113i	$-0.352193\pi$
$308$	2.53200	+	8.62320i	0.144274	+	0.491352i
$309$	10.3909	−	21.1061i	0.591116	−	1.20068i
$310$	29.0600	+	45.2182i	1.65049	+	2.56822i
$311$	0.429736	+	0.668683i	0.0243681	+	0.0379175i	0.853224	−	0.521545i	$-0.174644\pi$
$311$	0.429736	+	0.668683i	0.0243681	+	0.0379175i	−0.828856	+	0.559462i	$0.811008\pi$
$312$	−0.0139861	+	0.0284088i	−0.000791809	+	0.00160833i
$313$	0.910502	+	3.10089i	0.0514646	+	0.175272i	0.981215	−	0.192919i	$-0.0617954\pi$
$313$	0.910502	+	3.10089i	0.0514646	+	0.175272i	−0.929750	+	0.368191i	$0.879977\pi$
$314$	2.64429	−	18.3914i	0.149226	−	1.03789i
$315$	−10.7554	+	0.912456i	−0.605997	+	0.0514111i
$316$	−0.239822	−	0.109523i	−0.0134911	−	0.00616116i
$317$	−3.86023	+	13.1467i	−0.216812	+	0.738394i	0.777212	+	0.629238i	$0.216633\pi$
$317$	−3.86023	+	13.1467i	−0.216812	+	0.738394i	−0.994025	+	0.109156i	$0.965185\pi$
$318$	−22.4934	+	24.4825i	−1.26137	+	1.37291i
$319$	43.3571	−	6.23380i	2.42753	−	0.349026i
$320$	21.4423	+	13.7801i	1.19866	+	0.770332i
$321$	30.0804	−	12.6935i	1.67892	−	0.708484i
$322$	−8.55902	−	4.02211i	−0.476976	−	0.224144i
$323$		−	11.1480i		−	0.620292i
$324$	−8.80710	+	14.5361i	−0.489283	+	0.807563i
$325$	0.0939774	+	0.653627i	0.00521293	+	0.0362567i
$326$	24.6741	−	11.2683i	1.36657	−	0.624092i
$327$	−0.765007	−	6.69826i	−0.0423050	−	0.370414i
$328$	−0.0290914	+	0.0637013i	−0.00160630	+	0.00351732i
$329$	−3.61887	+	4.17640i	−0.199515	+	0.230252i
$330$	−56.5698	+	14.8380i	−3.11406	+	0.816804i
$331$	22.1829	−	6.51349i	1.21928	−	0.358014i	0.392088	−	0.919928i	$-0.371753\pi$
$331$	22.1829	−	6.51349i	1.21928	−	0.358014i	0.827196	+	0.561914i	$0.189935\pi$
$332$	1.17905	+	1.36070i	0.0647087	+	0.0746779i
$333$	−29.4299	−	5.99531i	−1.61275	−	0.328541i
$334$	0.928495	−	0.596707i	0.0508050	−	0.0326504i
$335$	−20.1453	+	17.4560i	−1.10065	+	0.953722i
$336$	4.61366	+	5.64829i	0.251696	+	0.308140i
$337$	−25.4381	−	3.65745i	−1.38570	−	0.199234i	−0.591214	−	0.806515i	$-0.701351\pi$
$337$	−25.4381	−	3.65745i	−1.38570	−	0.199234i	−0.794487	+	0.607281i	$0.792260\pi$
$338$	19.3633	+	16.7784i	1.05322	+	0.912622i
$339$	0.563511	−	19.3708i	0.0306057	−	1.05208i
$340$	−35.4993	−	10.4235i	−1.92522	−	0.565295i
$341$	14.9776	+	32.7963i	0.811080	+	1.77602i
$342$	9.79090	+	7.12916i	0.529431	+	0.385501i
$343$	0.540641	−	0.841254i	0.0291919	−	0.0454234i
$344$	−0.568627			−0.0306583
$345$	13.4924	−	26.6684i	0.726408	−	1.43578i
$346$	11.2602			0.605352
$347$	−7.12350	+	11.0844i	−0.382409	+	0.595041i	−0.978090	−	0.208181i	$-0.933246\pi$
$347$	−7.12350	+	11.0844i	−0.382409	+	0.595041i	0.595681	+	0.803221i	$0.296882\pi$
$348$	−25.7889	+	15.5329i	−1.38243	+	0.832653i
$349$	−0.0119686	−	0.0262077i	−0.000640667	−	0.00140286i	0.909311	−	0.416116i	$-0.136609\pi$
$349$	−0.0119686	−	0.0262077i	−0.000640667	−	0.00140286i	−0.909952	+	0.414713i	$0.863882\pi$
$350$	15.0334	+	4.41421i	0.803570	+	0.235950i
$351$	0.300483	+	0.310161i	0.0160386	+	0.0165552i
$352$	28.2810	+	24.5056i	1.50738	+	1.30615i
$353$	13.4936	+	1.94009i	0.718193	+	0.103261i	0.491716	−	0.870756i	$-0.336370\pi$
$353$	13.4936	+	1.94009i	0.718193	+	0.103261i	0.226478	+	0.974016i	$0.427279\pi$
$354$	28.2340	−	23.0622i	1.50062	−	1.22574i
$355$	−6.65578	+	5.76727i	−0.353252	+	0.306095i
$356$	2.20763	−	1.41875i	0.117004	−	0.0751939i
$357$	−7.78250	−	5.32751i	−0.411894	−	0.281962i
$358$	1.26554	+	1.46052i	0.0668861	+	0.0771906i
$359$	8.82520	−	2.59131i	0.465776	−	0.136764i	−0.0404196	−	0.999183i	$-0.512869\pi$
$359$	8.82520	−	2.59131i	0.465776	−	0.136764i	0.506196	+	0.862419i	$0.331051\pi$
$360$	−1.88182	+	1.44797i	−0.0991806	+	0.0763145i
$361$	−9.69749	+	11.1915i	−0.510394	+	0.589026i
$362$	3.68980	−	8.07954i	0.193932	−	0.424651i
$363$	−20.0459	+	2.28944i	−1.05214	+	0.120164i
$364$	−0.142763	+	0.0651976i	−0.00748281	+	0.00341729i
$365$	−0.149187	−	1.03762i	−0.00780882	−	0.0543115i
$366$	−9.52755	−	1.65394i	−0.498013	−	0.0864527i
$367$		−	14.7893i		−	0.771996i	−0.922500	−	0.385998i	$-0.873857\pi$
$367$		−	14.7893i		−	0.771996i	0.922500	−	0.385998i	$-0.126143\pi$
$368$	−20.0182	+	2.65578i	−1.04352	+	0.138442i
$369$	0.684206	+	0.666331i	0.0356184	+	0.0346878i
$370$	59.7550	+	38.4022i	3.10651	+	1.99643i
$371$	9.63511	−	1.38532i	0.500230	−	0.0719222i
$372$	−18.2477	−	16.7652i	−0.946100	−	0.869234i
$373$	−1.91476	+	6.52107i	−0.0991425	+	0.337648i	−0.994095	−	0.108513i	$-0.965391\pi$
$373$	−1.91476	+	6.52107i	−0.0991425	+	0.337648i	0.894953	+	0.446161i	$0.147209\pi$
$374$	−46.4823	−	21.2278i	−2.40354	−	1.09766i
$375$	−5.68172	+	17.4555i	−0.293403	+	0.901398i
$376$	−0.173001	+	1.20325i	−0.00892184	+	0.0620528i
$377$	0.215508	+	0.733952i	0.0110992	+	0.0378005i
$378$	9.65587	−	3.42815i	0.496644	−	0.176325i
$379$	−11.5679	−	18.0001i	−0.594206	−	0.924602i	−0.999944	−	0.0106126i	$-0.996622\pi$
$379$	−11.5679	−	18.0001i	−0.594206	−	0.924602i	0.405738	−	0.913989i	$-0.367015\pi$
$380$	−7.52075	−	11.7025i	−0.385806	−	0.600326i
$381$	−0.832258	−	0.409734i	−0.0426379	−	0.0209913i
$382$	2.37040	+	8.07286i	0.121280	+	0.413043i
$383$	−1.32783	+	9.23525i	−0.0678489	+	0.471899i	0.927363	+	0.374162i	$0.122070\pi$
$383$	−1.32783	+	9.23525i	−0.0678489	+	0.471899i	−0.995212	+	0.0977374i	$0.968839\pi$
$384$	2.89388	+	0.941952i	0.147678	+	0.0480688i
$385$	15.5758	+	7.11321i	0.793814	+	0.362523i
$386$	3.12982	−	10.6592i	0.159304	−	0.542538i
$387$	−2.61365	+	7.30115i	−0.132859	+	0.371138i
$388$	−17.8125	+	2.56105i	−0.904293	+	0.130018i
$389$	−18.8563	−	12.1182i	−0.956050	−	0.614416i	−0.0331478	−	0.999450i	$-0.510553\pi$
$389$	−18.8563	−	12.1182i	−0.956050	−	0.614416i	−0.922902	+	0.385034i	$0.874190\pi$
$390$	−0.397072	−	0.940956i	−0.0201065	−	0.0476471i
$391$	23.8711	−	10.5886i	1.20721	−	0.535488i
$392$		−	0.219975i		−	0.0111104i
$393$	5.54135	−	31.9211i	0.279524	−	1.61021i
$394$	1.80489	+	12.5533i	0.0909288	+	0.632424i
$395$	−0.456927	+	0.208672i	−0.0229905	+	0.0104994i
$396$	23.4907	−	13.2334i	1.18045	−	0.665005i
$397$	−0.985720	+	2.15843i	−0.0494719	+	0.108328i	−0.932754	−	0.360514i	$-0.882601\pi$
$397$	−0.985720	+	2.15843i	−0.0494719	+	0.108328i	0.883282	+	0.468842i	$0.155329\pi$
$398$	22.4149	−	25.8681i	1.12356	−	1.29665i
$399$	−0.899682	−	3.43004i	−0.0450405	−	0.171717i
$400$	32.1011	−	9.42575i	1.60506	−	0.471287i
$401$	−23.3147	−	26.9066i	−1.16428	−	1.34365i	−0.928273	−	0.371899i	$-0.878707\pi$
$401$	−23.3147	−	26.9066i	−1.16428	−	1.34365i	−0.236007	−	0.971751i	$-0.575839\pi$
$402$	14.2934	−	20.8799i	0.712888	−	1.04140i
$403$	−0.529674	+	0.340401i	−0.0263849	+	0.0169566i
$404$	0.835498	−	0.723963i	0.0415676	−	0.0360185i
$405$	9.94220	+	30.8180i	0.494032	+	1.53136i
$406$	17.9649	+	2.58297i	0.891585	+	0.128191i
$407$	36.0079	+	31.2010i	1.78484	+	1.54658i
$408$	−2.07378	−	0.0603278i	−0.102667	−	0.00298667i
$409$	24.9638	+	7.33004i	1.23438	+	0.362447i	0.832902	−	0.553421i	$-0.186678\pi$
$409$	24.9638	+	7.33004i	1.23438	+	0.362447i	0.401480	+	0.915868i	$0.368496\pi$
$410$	−0.938297	−	2.05458i	−0.0463392	−	0.101469i
$411$	−0.284734	−	0.472737i	−0.0140449	−	0.0233184i
$412$	13.8671	−	21.5777i	0.683185	−	1.06306i
$413$	−10.6738			−0.525221
$414$	−5.96598	+	27.7365i	−0.293212	+	1.36318i
$415$	3.43036			0.168390
$416$	−0.353304	+	0.549752i	−0.0173222	+	0.0269538i
$417$	16.2267	+	26.9407i	0.794623	+	1.31929i
$418$	−7.98139	−	17.4768i	−0.390382	−	0.854818i
$419$	−4.65367	−	1.36644i	−0.227347	−	0.0667550i	0.166075	−	0.986113i	$-0.446891\pi$
$419$	−4.65367	−	1.36644i	−0.227347	−	0.0667550i	−0.393422	+	0.919358i	$0.628709\pi$
$420$	−11.7637	−	0.342214i	−0.574009	−	0.0166983i
$421$	6.48324	+	5.61776i	0.315974	+	0.273793i	0.798379	−	0.602155i	$-0.205691\pi$
$421$	6.48324	+	5.61776i	0.315974	+	0.273793i	−0.482405	+	0.875948i	$0.660237\pi$
$422$	−31.2533	−	4.49355i	−1.52139	−	0.218742i
$423$	14.6545	+	7.75197i	0.712525	+	0.376914i
$424$	1.61827	−	1.40224i	0.0785903	−	0.0680989i
$425$	−36.3971	+	23.3910i	−1.76552	+	1.13463i
$426$	4.72237	−	6.89851i	0.228800	−	0.334234i
$427$	1.85408	+	2.13972i	0.0897253	+	0.103549i
$428$	34.1550	−	10.0288i	1.65095	−	0.484762i
$429$	−0.173808	−	0.662644i	−0.00839154	−	0.0319927i
$430$	12.0102	−	13.8606i	0.579185	−	0.668415i
$431$	2.42794	−	5.31644i	0.116950	−	0.256084i	−0.842100	−	0.539321i	$-0.818681\pi$
$431$	2.42794	−	5.31644i	0.116950	−	0.256084i	0.959050	+	0.283237i	$0.0914083\pi$
$432$	13.3877	−	17.3053i	0.644114	−	0.832600i
$433$	9.41937	−	4.30168i	0.452666	−	0.206726i	−0.176017	−	0.984387i	$-0.556321\pi$
$433$	9.41937	−	4.30168i	0.452666	−	0.206726i	0.628683	+	0.777661i	$0.283594\pi$
$434$	2.12606	+	14.7870i	0.102054	+	0.709801i
$435$	−9.81055	+	56.5140i	−0.470380	+	2.70964i
$436$		−	7.35055i		−	0.352027i
$437$	9.39017	+	2.86876i	0.449193	+	0.137231i
$438$	0.386886	+	0.916817i	0.0184861	+	0.0438072i
$439$	10.6398	+	6.83776i	0.507808	+	0.326349i	0.769333	−	0.638848i	$-0.220589\pi$
$439$	10.6398	+	6.83776i	0.507808	+	0.326349i	−0.261524	+	0.965197i	$0.584225\pi$
$440$	3.72833	−	0.536053i	0.177741	−	0.0255553i
$441$	−2.82448	−	1.01110i	−0.134499	−	0.0481477i
$442$	0.251410	−	0.856223i	0.0119583	−	0.0407264i
$443$	−8.38602	−	3.82977i	−0.398432	−	0.181958i	0.206114	−	0.978528i	$-0.433918\pi$
$443$	−8.38602	−	3.82977i	−0.398432	−	0.181958i	−0.604546	+	0.796570i	$0.706645\pi$
$444$	−31.1383	−	10.1354i	−1.47776	−	0.481007i
$445$	0.711550	−	4.94894i	0.0337307	−	0.234602i
$446$	−9.82531	−	33.4619i	−0.465242	−	1.58447i
$447$	32.5376	+	16.0188i	1.53898	+	0.757662i
$448$	3.82994	+	5.95950i	0.180947	+	0.281560i
$449$	−7.16503	−	11.1490i	−0.338139	−	0.526154i	0.629991	−	0.776602i	$-0.283058\pi$
$449$	−7.16503	−	11.1490i	−0.338139	−	0.526154i	−0.968130	+	0.250448i	$0.919422\pi$
$450$	2.73246	−	46.9248i	0.128810	−	2.21206i
$451$	−0.426843	−	1.45369i	−0.0200992	−	0.0684517i
$452$	3.00694	−	20.9137i	0.141435	−	0.983700i
$453$	8.65760	−	26.5980i	0.406769	−	1.24968i
$454$	−28.6790	−	13.0973i	−1.34597	−	0.614685i
$455$	−0.0842449	+	0.286912i	−0.00394946	+	0.0134506i
$456$	−0.574417	−	0.527748i	−0.0268995	−	0.0247141i
$457$	1.11579	−	0.160427i	0.0521946	−	0.00750445i	−0.116168	−	0.993230i	$-0.537061\pi$
$457$	1.11579	−	0.160427i	0.0521946	−	0.00750445i	0.168363	+	0.985725i	$0.446152\pi$
$458$	−35.7686	−	22.9871i	−1.67136	−	1.07412i
$459$	−10.3066	+	26.3500i	−0.481070	+	1.22991i
$460$	17.9151	−	27.2193i	0.835295	−	1.26911i
$461$		−	20.5233i		−	0.955867i	−0.878396	−	0.477933i	$-0.841386\pi$
$461$		−	20.5233i		−	0.955867i	0.878396	−	0.477933i	$-0.158614\pi$
$462$	−16.0149	−	2.78010i	−0.745080	−	0.129342i
$463$	0.397593	+	2.76532i	0.0184777	+	0.128515i	0.996972	−	0.0777570i	$-0.0247758\pi$
$463$	0.397593	+	2.76532i	0.0184777	+	0.128515i	−0.978495	+	0.206272i	$0.933867\pi$
$464$	35.2531	−	16.0995i	1.63658	−	0.747403i
$465$	−46.9078	+	5.35733i	−2.17530	+	0.248440i
$466$	−9.63812	+	21.1045i	−0.446477	+	0.977649i
$467$	−9.75104	+	11.2533i	−0.451224	+	0.520740i	−0.935094	−	0.354399i	$-0.884685\pi$
$467$	−9.75104	+	11.2533i	−0.451224	+	0.520740i	0.483870	+	0.875140i	$0.339231\pi$
$468$	0.287126	+	0.373158i	0.0132724	+	0.0172492i
$469$	−7.10846	+	2.08723i	−0.328238	+	0.0963794i
$470$	−25.6757	−	29.6314i	−1.18433	−	1.36679i
$471$	13.4672	+	9.21898i	0.620537	+	0.424788i
$472$	−1.97523	+	1.26941i	−0.0909175	+	0.0584291i
$473$	9.29722	−	8.05609i	0.427487	−	0.370419i
$474$	0.369296	−	0.301650i	0.0169623	−	0.0138552i
$475$	−16.1017	−	2.31507i	−0.738795	−	0.106223i
$476$	−7.77131	−	6.73388i	−0.356197	−	0.308647i
$477$	−10.5665	−	27.2239i	−0.483806	−	1.24650i
$478$	−50.7919	−	14.9139i	−2.32317	−	0.682144i
$479$	10.8083	+	23.6669i	0.493845	+	1.08137i	0.978421	+	0.206620i	$0.0662465\pi$
$479$	10.8083	+	23.6669i	0.493845	+	1.08137i	−0.484577	+	0.874749i	$0.661026\pi$
$480$	−41.9763	+	25.2828i	−1.91595	+	1.15399i
$481$	−0.449833	+	0.699954i	−0.0205106	+	0.0319152i
$482$	1.46707			0.0668232
$483$	6.49016	−	5.18439i	0.295312	−	0.235898i
$484$	−21.9980			−0.999911
$485$	−18.5368	+	28.8438i	−0.841712	+	1.30973i
$486$	−16.5512	−	25.9027i	−0.750777	−	1.17497i
$487$	−9.78620	−	21.4288i	−0.443455	−	0.971031i	−0.990951	−	0.134223i	$-0.957146\pi$
$487$	−9.78620	−	21.4288i	−0.443455	−	0.971031i	0.547496	−	0.836808i	$-0.315581\pi$
$488$	0.597580	+	0.175465i	0.0270512	+	0.00794294i
$489$	−0.692817	+	23.8157i	−0.0313303	+	1.07699i
$490$	5.36201	+	4.64621i	0.242231	+	0.209894i
$491$	23.7281	+	3.41158i	1.07083	+	0.153963i	0.655114	−	0.755530i	$-0.272621\pi$
$491$	23.7281	+	3.41158i	1.07083	+	0.153963i	0.415719	+	0.909493i	$0.363530\pi$
$492$	0.658731	+	0.806454i	0.0296979	+	0.0363577i
$493$	−37.8765	+	32.8202i	−1.70587	+	1.47815i
$494$	0.282258	−	0.181396i	0.0126994	−	0.00816140i
$495$	10.2541	−	50.3356i	0.460887	−	2.26242i
$496$	20.8899	+	24.1082i	0.937984	+	1.08249i
$497$	−2.34856	+	0.689599i	−0.105347	+	0.0309328i
$498$	−3.14977	+	0.826170i	−0.141145	+	0.0370216i
$499$	16.9859	−	19.6028i	0.760394	−	0.877542i	−0.235138	−	0.971962i	$-0.575554\pi$
$499$	16.9859	−	19.6028i	0.760394	−	0.877542i	0.995532	+	0.0944203i	$0.0300997\pi$
$500$	−8.31430	+	18.2058i	−0.371827	+	0.814187i
$501$	0.110006	+	0.963188i	0.00491469	+	0.0430321i
$502$	−15.6973	+	7.16872i	−0.700605	+	0.319956i
$503$	1.70443	+	11.8545i	0.0759966	+	0.528568i	0.991885	+	0.127136i	$0.0405784\pi$
$503$	1.70443	+	11.8545i	0.0759966	+	0.528568i	−0.915889	+	0.401432i	$0.868512\pi$
$504$	−0.642932	+	0.148799i	−0.0286385	+	0.00662804i
$505$		−	2.10632i		−	0.0937300i
$506$	29.8420	−	33.6902i	1.32664	−	1.49771i
$507$	−20.7342	+	8.74957i	−0.920837	+	0.388582i
$508$	−0.850854	−	0.546811i	−0.0377505	−	0.0242608i
$509$	9.63162	−	1.38482i	0.426914	−	0.0613810i	0.0744909	−	0.997222i	$-0.476267\pi$
$509$	9.63162	−	1.38482i	0.426914	−	0.0613810i	0.352423	+	0.935841i	$0.385358\pi$
$510$	45.2718	−	49.2752i	2.00467	−	2.18194i
$511$	0.0820838	−	0.279552i	0.00363117	−	0.0123666i
$512$	28.4319	+	12.9844i	1.25652	+	0.573835i
$513$	−9.41654	+	4.94974i	−0.415750	+	0.218536i
$514$	1.88164	−	13.0871i	0.0829954	−	0.577246i
$515$	−13.7680	−	46.8897i	−0.606693	−	2.06620i
$516$	−3.73453	+	7.58564i	−0.164404	+	0.333939i
$517$	−14.2185	−	22.1245i	−0.625331	−	0.973034i
$518$	10.6732	+	16.6078i	0.468953	+	0.729705i
$519$	−4.36854	+	8.87344i	−0.191757	+	0.389501i
$520$	0.0185318	+	0.0631135i	0.000812674	+	0.00276771i
$521$	−2.35485	+	16.3783i	−0.103168	+	0.717547i	0.870928	+	0.491411i	$0.163519\pi$
$521$	−2.35485	+	16.3783i	−0.103168	+	0.717547i	−0.974096	+	0.226136i	$0.927391\pi$
$522$	−4.60277	−	54.2541i	−0.201458	−	2.37464i
$523$	19.9959	+	9.13181i	0.874358	+	0.399306i	0.801471	−	0.598034i	$-0.204051\pi$
$523$	19.9959	+	9.13181i	0.874358	+	0.399306i	0.0728877	+	0.997340i	$0.476779\pi$
$524$	9.95190	−	33.8931i	0.434751	−	1.48063i
$525$	−9.31097	+	10.1343i	−0.406364	+	0.442299i
$526$	45.9608	−	6.60816i	2.00398	−	0.288129i
$527$	−34.7037	−	22.3027i	−1.51171	−	0.971520i
$528$	−31.9777	+	13.4942i	−1.39165	+	0.587259i
$529$	2.77611	+	22.8318i	0.120701	+	0.992689i
$530$			69.0637i			2.99993i
$531$	7.22011	+	31.1967i	0.313326	+	1.35382i
$532$	−0.550226	−	3.82690i	−0.0238553	−	0.165917i
$533$	0.0240669	−	0.0109910i	0.00104245	−	0.000476072i
$534$	0.538558	+	4.71551i	0.0233057	+	0.204060i
$535$	28.1742	−	61.6930i	1.21808	−	2.66722i
$536$	−1.06723	+	1.23164i	−0.0460972	+	0.0531990i
$537$	−1.64192	+	0.430669i	−0.0708542	+	0.0185847i
$538$	−25.7496	+	7.56075i	−1.11014	+	0.325967i
$539$	3.11653	+	3.59667i	0.134238	+	0.154919i
$540$	6.95717	+	34.6137i	0.299389	+	1.48954i
$541$	19.6740	−	12.6437i	0.845851	−	0.543596i	−0.0444269	−	0.999013i	$-0.514146\pi$
$541$	19.6740	−	12.6437i	0.845851	−	0.543596i	0.890278	+	0.455417i	$0.150510\pi$
$542$	−23.9458	+	20.7491i	−1.02856	+	0.891251i
$543$	4.93547	+	6.04226i	0.211801	+	0.259298i
$544$	−42.3802	−	6.09336i	−1.81704	−	0.261251i
$545$	−10.5841	−	9.17119i	−0.453374	−	0.392851i
$546$	0.00825401	−	0.283733i	0.000353239	−	0.0121427i
$547$	6.29633	+	1.84877i	0.269212	+	0.0790476i	0.413552	−	0.910480i	$-0.364288\pi$
$547$	6.29633	+	1.84877i	0.269212	+	0.0790476i	−0.144341	+	0.989528i	$0.546106\pi$
$548$	−0.249953	−	0.547320i	−0.0106775	−	0.0233804i
$549$	4.99970	−	6.86639i	0.213382	−	0.293050i
$550$	−40.3132	+	62.7285i	−1.71896	+	2.67475i
$551$	−18.8437			−0.802770
$552$	0.584469	−	1.73126i	0.0248766	−	0.0736872i
$553$	−0.139611			−0.00593686
$554$	1.26556	−	1.96925i	0.0537685	−	0.0836654i
$555$	−53.4450	+	32.1905i	−2.26861	+	1.36641i
$556$	14.2445	+	31.1911i	0.604102	+	1.32280i
$557$	−5.11104	−	1.50074i	−0.216562	−	0.0635882i	0.171652	−	0.985158i	$-0.445090\pi$
$557$	−5.11104	−	1.50074i	−0.216562	−	0.0635882i	−0.388214	+	0.921569i	$0.626908\pi$
$558$	41.7806	−	16.2164i	1.76871	−	0.686495i
$559$	0.162359	+	0.140685i	0.00686705	+	0.00595034i
$560$	14.9958	+	2.15607i	0.633687	+	0.0911105i
$561$	34.7616	−	28.3942i	1.46764	−	1.19880i
$562$	9.89665	−	8.57549i	0.417465	−	0.361735i
$563$	31.3583	−	20.1528i	1.32160	−	0.849339i	0.326211	−	0.945297i	$-0.394228\pi$
$563$	31.3583	−	20.1528i	1.32160	−	0.849339i	0.995385	+	0.0959583i	$0.0305916\pi$
$564$	14.9154	+	10.2104i	0.628054	+	0.429934i
$565$	−26.3622	−	30.4236i	−1.10906	−	1.27993i
$566$	−50.0666	+	14.7009i	−2.10445	+	0.617924i
$567$	−1.04461	+	8.93917i	−0.0438695	+	0.375410i
$568$	−0.352600	+	0.406922i	−0.0147948	+	0.0170741i
$569$	6.35010	−	13.9048i	0.266210	−	0.582919i	−0.728569	−	0.684973i	$-0.759814\pi$
$569$	6.35010	−	13.9048i	0.266210	−	0.582919i	0.994779	+	0.102054i	$0.0325413\pi$
$570$	24.9967	−	2.85487i	1.04700	−	0.119577i
$571$	−23.4413	+	10.7053i	−0.980990	+	0.448003i	−0.840342	−	0.542057i	$-0.817646\pi$
$571$	−23.4413	+	10.7053i	−0.980990	+	0.448003i	−0.140648	+	0.990060i	$0.544919\pi$
$572$	−0.106297	−	0.739314i	−0.00444451	−	0.0309123i
$573$	−7.28133	−	1.26400i	−0.304182	−	0.0528045i
$574$		−	0.627764i		−	0.0262024i
$575$	−10.3364	−	36.6772i	−0.431059	−	1.52954i
$576$	14.8274	−	15.2251i	0.617807	−	0.634381i
$577$	25.4496	+	16.3555i	1.05948	+	0.680888i	0.949730	−	0.313071i	$-0.101358\pi$
$577$	25.4496	+	16.3555i	1.05948	+	0.680888i	0.109752	+	0.993959i	$0.464994\pi$
$578$	24.6906	−	3.54998i	1.02699	−	0.147660i
$579$	7.18557	+	6.60178i	0.298622	+	0.274360i
$580$	−17.6191	+	60.0052i	−0.731594	+	2.49158i
$581$	0.867250	+	0.396060i	0.0359796	+	0.0164313i
$582$	10.0738	−	30.9489i	0.417572	−	1.28287i
$583$	−6.59284	+	45.8542i	−0.273047	+	1.89909i
$584$	−0.0180564	−	0.0614945i	−0.000747179	−	0.00254466i
$585$	0.895556	+	0.0521489i	0.0370267	+	0.00215609i
$586$	1.64054	+	2.55273i	0.0677702	+	0.105453i
$587$	8.37417	+	13.0305i	0.345639	+	0.537825i	0.969935	−	0.243363i	$-0.0782506\pi$
$587$	8.37417	+	13.0305i	0.345639	+	0.537825i	−0.624296	+	0.781188i	$0.714614\pi$
$588$	−2.93453	−	1.44472i	−0.121018	−	0.0595791i
$589$	−4.36978	−	14.8821i	−0.180054	−	0.613207i
$590$	10.7775	−	74.9590i	0.443702	−	3.08601i
$591$	−10.5926	−	3.44788i	−0.435723	−	0.141827i
$592$	38.3454	+	17.5118i	1.57599	+	0.719730i
$593$	9.40547	−	32.0321i	0.386236	−	1.31540i	−0.505493	−	0.862831i	$-0.668689\pi$
$593$	9.40547	−	32.0321i	0.386236	−	1.31540i	0.891729	−	0.452569i	$-0.149493\pi$
$594$	2.70750	+	48.6880i	0.111090	+	1.99769i
$595$	−19.3923	+	2.78820i	−0.795008	+	0.114305i
$596$	33.2646	+	21.3779i	1.36257	+	0.875672i
$597$	11.6889	+	27.6996i	0.478395	+	1.13367i
$598$	0.656515	+	0.432102i	0.0268469	+	0.0176700i
$599$			7.22688i			0.295282i	0.989041	+	0.147641i	$0.0471681\pi$
$599$			7.22688i			0.295282i	−0.989041	+	0.147641i	$0.952832\pi$
$600$	−0.517789	+	2.98274i	−0.0211387	+	0.121770i
$601$	3.71987	+	25.8723i	0.151737	+	1.05535i	0.913308	+	0.407271i	$0.133519\pi$
$601$	3.71987	+	25.8723i	0.151737	+	1.05535i	−0.761571	+	0.648082i	$0.775571\pi$
$602$	4.63668	−	2.11750i	0.188977	−	0.0863029i
$603$	10.9089	+	19.3643i	0.444243	+	0.788576i
$604$	12.6690	−	27.7413i	0.515495	−	1.12878i
$605$	−27.4467	+	31.6752i	−1.11587	+	1.28778i
$606$	0.507287	+	1.93403i	0.0206071	+	0.0785647i
$607$	−28.1721	+	8.27207i	−1.14347	+	0.335753i	−0.797989	−	0.602672i	$-0.794103\pi$
$607$	−28.1721	+	8.27207i	−1.14347	+	0.335753i	−0.345482	+	0.938426i	$0.612284\pi$
$608$	−10.5422	−	12.1663i	−0.427541	−	0.493409i
$609$	−9.00520	+	13.1549i	−0.364909	+	0.533065i
$610$	−16.8988	+	10.8602i	−0.684213	+	0.439717i
$611$	0.347094	−	0.300759i	0.0140419	−	0.0121674i
$612$	−14.4246	+	27.2686i	−0.583080	+	1.10227i
$613$	29.1853	+	4.19621i	1.17878	+	0.169483i	0.703726	−	0.710472i	$-0.251518\pi$
$613$	29.1853	+	4.19621i	1.17878	+	0.169483i	0.475057	+	0.879955i	$0.342427\pi$
$614$	49.5468	+	42.9325i	1.99955	+	1.73262i
$615$	1.98311	+	0.0576901i	0.0799667	+	0.00232629i
$616$	1.00447	+	0.294940i	0.0404713	+	0.0118835i
$617$	−10.6170	−	23.2479i	−0.427423	−	0.935926i	−0.993738	−	0.111737i	$-0.964359\pi$
$617$	−10.6170	−	23.2479i	−0.427423	−	0.935926i	0.566315	−	0.824189i	$-0.308369\pi$
$618$	23.9348	+	39.7384i	0.962799	+	1.59851i
$619$	−0.322308	+	0.501521i	−0.0129547	+	0.0201578i	−0.847670	−	0.530523i	$-0.821996\pi$
$619$	−0.322308	+	0.501521i	−0.0129547	+	0.0201578i	0.834716	+	0.550681i	$0.185632\pi$
$620$	−51.4757			−2.06732
$621$	−19.5428	−	15.4622i	−0.784226	−	0.620475i
$622$	−1.56741			−0.0628472
$623$	0.751282	−	1.16902i	0.0300995	−	0.0468357i
$624$	−0.312726	−	0.519211i	−0.0125191	−	0.0207851i
$625$	−0.662656	−	1.45101i	−0.0265063	−	0.0580406i
$626$	−6.11468	−	1.79543i	−0.244392	−	0.0717599i
$627$	16.8688	+	0.490727i	0.673676	+	0.0195977i
$628$	13.4478	+	11.6526i	0.536628	+	0.464990i
$629$	−53.9593	−	7.75817i	−2.15150	−	0.309339i
$630$	9.95262	−	18.8146i	0.396522	−	0.749593i
$631$	−20.8981	+	18.1083i	−0.831941	+	0.720881i	−0.962711	−	0.270531i	$-0.912801\pi$
$631$	−20.8981	+	18.1083i	−0.831941	+	0.720881i	0.130770	+	0.991413i	$0.458255\pi$
$632$	−0.0258357	+	0.0166036i	−0.00102769	+	0.000660456i
$633$	15.6662	−	22.8854i	0.622676	−	0.909613i
$634$	−17.6935	−	20.4194i	−0.702698	−	0.810956i
$635$	−1.84896	+	0.542903i	−0.0733736	+	0.0215444i
$636$	−8.07807	−	30.7976i	−0.320316	−	1.22121i
$637$	−0.0544245	+	0.0628092i	−0.00215638	+	0.00248859i
$638$	−35.8817	+	78.5700i	−1.42057	+	3.11062i
$639$	3.60417	+	6.39777i	0.142579	+	0.253092i
$640$	5.75063	−	2.62622i	0.227313	−	0.103811i
$641$	6.54007	+	45.4872i	0.258317	+	1.79663i	0.544818	+	0.838555i	$0.316599\pi$
$641$	6.54007	+	45.4872i	0.258317	+	1.79663i	−0.286501	+	0.958080i	$0.592492\pi$
$642$	−11.0115	+	63.4323i	−0.434590	+	2.50347i
$643$			2.83828i			0.111931i	0.998433	+	0.0559654i	$0.0178236\pi$
$643$			2.83828i			0.111931i	−0.998433	+	0.0559654i	$0.982176\pi$
$644$	7.67188	−	4.81305i	0.302314	−	0.189661i
$645$	6.26309	+	14.8419i	0.246609	+	0.584399i
$646$	18.4932	+	11.8849i	0.727606	+	0.467604i
$647$	−13.6791	+	1.96676i	−0.537782	+	0.0773214i	−0.405854	−	0.913938i	$-0.633026\pi$
$647$	−13.6791	+	1.96676i	−0.537782	+	0.0773214i	−0.131928	+	0.991259i	$0.542117\pi$
$648$	0.869804	+	1.77847i	0.0341691	+	0.0698650i
$649$	14.3112	−	48.7395i	0.561764	−	1.91319i
$650$	−1.18448	−	0.540933i	−0.0464591	−	0.0212171i
$651$	−12.4776	−	4.06142i	−0.489034	−	0.159179i
$652$	−3.69694	+	25.7128i	−0.144783	+	1.00699i
$653$	14.1803	+	48.2937i	0.554919	+	1.88988i	0.443939	+	0.896057i	$0.353581\pi$
$653$	14.1803	+	48.2937i	0.554919	+	1.88988i	0.110979	+	0.993823i	$0.464601\pi$
$654$	11.9272	+	5.87194i	0.466389	+	0.229611i
$655$	−36.3860	−	56.6178i	−1.42172	−	2.21224i
$656$	−0.724716	−	1.12768i	−0.0282954	−	0.0440285i
$657$	−0.872582	−	0.0508111i	−0.0340427	−	0.00198233i
$658$	−3.07008	−	10.4557i	−0.119684	−	0.407606i
$659$	−1.00239	+	6.97175i	−0.0390475	+	0.271581i	−0.999987	−	0.00517878i	$-0.998352\pi$
$659$	−1.00239	+	6.97175i	−0.0390475	+	0.271581i	0.960939	+	0.276760i	$0.0892606\pi$
$660$	17.3352	−	53.2576i	0.674772	−	2.07305i
$661$	−17.9090	−	8.17878i	−0.696580	−	0.318118i	0.0354676	−	0.999371i	$-0.488708\pi$
$661$	−17.9090	−	8.17878i	−0.696580	−	0.318118i	−0.732048	+	0.681253i	$0.761435\pi$
$662$	−12.8441	+	43.7428i	−0.499198	+	1.70011i
$663$	0.577197	+	0.530303i	0.0224165	+	0.0205952i
$664$	0.207591	−	0.0298471i	0.00805611	−	0.00115829i
$665$	−6.19690	−	3.98251i	−0.240305	−	0.154435i
$666$	41.3207	−	42.4291i	1.60114	−	1.64410i
$667$	−17.8981	−	40.3498i	−0.693018	−	1.56235i
$668$			1.05699i			0.0408960i
$669$	30.1811	+	5.23928i	1.16687	+	0.202562i
$670$	−7.48055	−	52.0283i	−0.288999	−	2.01003i
$671$	−12.2565	+	5.59737i	−0.473158	+	0.216084i
$672$	−13.5314	+	1.54541i	−0.521983	+	0.0596156i
$673$	−6.08347	+	13.3209i	−0.234501	+	0.513485i	−0.989898	−	0.141782i	$-0.954717\pi$
$673$	−6.08347	+	13.3209i	−0.234501	+	0.513485i	0.755397	+	0.655267i	$0.227444\pi$
$674$	33.1868	−	38.2996i	1.27831	−	1.47524i
$675$	35.9183	+	20.3584i	1.38250	+	0.783594i
$676$	−23.5428	+	6.91280i	−0.905494	+	0.265877i
$677$	3.98997	+	4.60467i	0.153347	+	0.176972i	0.827225	−	0.561871i	$-0.189918\pi$
$677$	3.98997	+	4.60467i	0.153347	+	0.176972i	−0.673878	+	0.738843i	$0.735373\pi$
$678$	31.5331	+	21.5859i	1.21102	+	0.829003i
$679$	−8.01661	+	5.15196i	−0.307649	+	0.197714i
$680$	−3.25706	+	2.82225i	−0.124902	+	0.108229i
$681$	21.4475	−	17.5188i	0.821870	−	0.671323i
$682$	−70.3726	−	10.1181i	−2.69471	−	0.387440i
$683$	35.4835	+	30.7466i	1.35774	+	1.17649i	0.966640	+	0.256139i	$0.0824504\pi$
$683$	35.4835	+	30.7466i	1.35774	+	1.17649i	0.391099	+	0.920349i	$0.372095\pi$
$684$	−10.8129	+	4.19682i	−0.413440	+	0.160470i
$685$	−1.09995	−	0.322976i	−0.0420271	−	0.0123403i
$686$	0.819163	+	1.79372i	0.0312758	+	0.0684844i
$687$	31.9916	−	19.2688i	1.22055	−	0.735152i
$688$	5.88454	−	9.15653i	0.224346	−	0.349089i
$689$	−0.808994			−0.0308202
$690$	29.8554	+	50.8134i	1.13657	+	1.93443i
$691$	−0.927625			−0.0352885			−0.0176443	−	0.999844i	$-0.505617\pi$
$691$	−0.927625			−0.0352885			−0.0176443	+	0.999844i	$0.505617\pi$
$692$	−5.83003	+	9.07171i	−0.221625	+	0.344855i
$693$	8.40400	−	11.5417i	0.319242	−	0.438434i
$694$	−10.7933	−	23.6340i	−0.409708	−	0.897136i
$695$	62.6851	+	18.4060i	2.37778	+	0.698179i
$696$	−0.101973	+	3.50535i	−0.00386529	+	0.132870i
$697$	1.31008	+	1.13519i	0.0496228	+	0.0429984i
$698$	0.0562351	+	0.00808539i	0.00212853	+	0.000306036i
$699$	−12.8919	−	15.7830i	−0.487617	−	0.596967i
$700$	−11.3399	+	9.82611i	−0.428609	+	0.371392i
$701$	−7.30874	+	4.69704i	−0.276047	+	0.177405i	−0.671338	−	0.741151i	$-0.734280\pi$
$701$	−7.30874	+	4.69704i	−0.276047	+	0.177405i	0.395291	+	0.918556i	$0.370644\pi$
$702$	−0.834863	+	0.167803i	−0.0315099	+	0.00633331i
$703$	−13.4225	−	15.4904i	−0.506238	−	0.584230i
$704$	−32.3479	+	9.49821i	−1.21916	+	0.357977i
$705$	33.3118	−	8.73753i	1.25460	−	0.329074i
$706$	−17.6039	+	20.3160i	−0.662532	+	0.764602i
$707$	0.243190	−	0.532511i	0.00914609	−	0.0200271i
$708$	3.96161	+	34.6871i	0.148887	+	1.30362i
$709$	31.8610	−	14.5504i	1.19657	−	0.546453i	0.285366	−	0.958419i	$-0.407885\pi$
$709$	31.8610	−	14.5504i	1.19657	−	0.546453i	0.911200	+	0.411965i	$0.135157\pi$
$710$	−2.47149	−	17.1896i	−0.0927535	−	0.645115i
$711$	0.0944379	+	0.408047i	0.00354170	+	0.0153030i
$712$		−	0.305681i		−	0.0114559i
$713$	27.7164	−	23.4923i	1.03799	−	0.879792i
$714$	17.1346	−	7.23059i	0.641246	−	0.270598i
$715$	−1.19717	−	0.769374i	−0.0447716	−	0.0287730i
$716$	−1.83190	+	0.263387i	−0.0684613	+	0.00984325i
$717$	31.4581	−	34.2399i	1.17482	−	1.27871i
$718$	−5.10985	+	17.4025i	−0.190698	+	0.649457i
$719$	−31.0077	−	14.1608i	−1.15639	−	0.528107i	−0.257502	−	0.966278i	$-0.582899\pi$
$719$	−31.0077	−	14.1608i	−1.15639	−	0.528107i	−0.898892	+	0.438171i	$0.855627\pi$
$720$	−3.84205	−	45.2873i	−0.143185	−	1.68776i
$721$	1.93296	−	13.4441i	0.0719874	−	0.500683i
$722$	−8.22688	−	28.0182i	−0.306173	−	1.04273i
$723$	−0.569169	+	1.15611i	−0.0211676	+	0.0429960i
$724$	4.59882	+	7.15590i	0.170914	+	0.265947i
$725$	39.5383	+	61.5228i	1.46841	+	2.28490i
$726$	17.5730	−	35.6945i	0.652195	−	1.32475i
$727$	−11.7974	−	40.1781i	−0.437540	−	1.49012i	−0.823343	−	0.567544i	$-0.807894\pi$
$727$	−11.7974	−	40.1781i	−0.437540	−	1.49012i	0.385803	−	0.922581i	$-0.373924\pi$
$728$	−0.00260177	+	0.0180957i	−9.64281e−5	+	0.000670672i
$729$	26.8335	−	2.99364i	0.993834	−	0.110876i
$730$	1.88034	+	0.858721i	0.0695944	+	0.0317827i
$731$	−3.96554	+	13.5054i	−0.146671	+	0.499514i
$732$	6.26543	−	6.81948i	0.231577	−	0.252055i
$733$	22.8047	−	3.27882i	0.842311	−	0.121106i	0.292366	−	0.956307i	$-0.405558\pi$
$733$	22.8047	−	3.27882i	0.842311	−	0.121106i	0.549945	+	0.835201i	$0.314648\pi$
$734$	24.5337	+	15.7668i	0.905555	+	0.581965i
$735$	−5.74164	+	2.42290i	−0.211784	+	0.0893701i
$736$	16.0384	−	34.1296i	0.591183	−	1.25803i
$737$		−	35.2578i		−	1.29874i
$738$	−1.83479	+	0.424642i	−0.0675397	+	0.0156313i
$739$	2.48629	+	17.2925i	0.0914596	+	0.636115i	0.983059	+	0.183290i	$0.0586748\pi$
$739$	2.48629	+	17.2925i	0.0914596	+	0.636115i	−0.891599	+	0.452825i	$0.850416\pi$
$740$	−61.8770	+	28.2583i	−2.27464	+	1.03880i
$741$	0.0334412	+	0.292805i	0.00122849	+	0.0107564i
$742$	−7.97389	+	17.4604i	−0.292731	+	0.640991i
$743$	−7.45462	+	8.60309i	−0.273483	+	0.315617i	−0.875832	−	0.482617i	$-0.839686\pi$
$743$	−7.45462	+	8.60309i	−0.273483	+	0.315617i	0.602348	+	0.798233i	$0.294232\pi$
$744$	−2.79205	+	0.732342i	−0.102362	+	0.0268490i
$745$	72.2861	−	21.2251i	2.64836	−	0.777628i
$746$	−8.77635	−	10.1285i	−0.321325	−	0.370829i
$747$	0.570942	−	2.80266i	0.0208897	−	0.102544i
$748$	41.1685	−	26.4574i	1.50527	−	0.967378i
$749$	14.2458	−	12.3440i	0.520530	−	0.451042i
$750$	−22.8993	−	28.0345i	−0.836164	−	1.02368i
$751$	−24.1744	−	3.47575i	−0.882136	−	0.126832i	−0.313663	−	0.949534i	$-0.601556\pi$
$751$	−24.1744	−	3.47575i	−0.882136	−	0.126832i	−0.568472	+	0.822702i	$0.692465\pi$
$752$	−17.5854	−	15.2378i	−0.641274	−	0.555667i
$753$	0.440761	−	15.1512i	0.0160622	−	0.552142i
$754$	−1.44729	−	0.424963i	−0.0527072	−	0.0154762i
$755$	−24.1379	−	52.8547i	−0.878470	−	1.92358i
$756$	−2.23752	+	9.55414i	−0.0813777	+	0.347481i
$757$	−0.623190	+	0.969702i	−0.0226502	+	0.0352444i	−0.852394	−	0.522900i	$-0.824850\pi$
$757$	−0.623190	+	0.969702i	−0.0226502	+	0.0352444i	0.829744	+	0.558144i	$0.188486\pi$
$758$	42.1925			1.53250
$759$	14.9715	+	36.5871i	0.543433	+	1.32803i
$760$	−1.62040			−0.0587780
$761$	17.9461	−	27.9247i	0.650545	−	1.01227i	−0.346691	−	0.937979i	$-0.612695\pi$
$761$	17.9461	−	27.9247i	0.650545	−	1.01227i	0.997237	−	0.0742892i	$-0.0236688\pi$
$762$	1.56697	−	0.943799i	0.0567652	−	0.0341902i
$763$	−1.61695	−	3.54063i	−0.0585376	−	0.128180i
$764$	−7.73114	−	2.27007i	−0.279703	−	0.0821282i
$765$	21.2669	+	54.7928i	0.768905	+	1.98104i
$766$	−13.9046	−	12.0484i	−0.502393	−	0.435326i
$767$	0.878050	+	0.126245i	0.0317046	+	0.00455843i
$768$	−23.6532	+	19.3205i	−0.853513	+	0.697170i
$769$	−19.7547	+	17.1175i	−0.712373	+	0.617275i	−0.933755	−	0.357913i	$-0.883489\pi$
$769$	−19.7547	+	17.1175i	−0.712373	+	0.617275i	0.221382	+	0.975187i	$0.428943\pi$
$770$	−28.4052	+	18.2549i	−1.02365	+	0.657863i
$771$	9.58308	+	6.56009i	0.345126	+	0.236256i
$772$	6.96703	+	8.04038i	0.250749	+	0.289379i
$773$	6.82712	−	2.00462i	0.245554	−	0.0721013i	−0.156639	−	0.987656i	$-0.550066\pi$
$773$	6.82712	−	2.00462i	0.245554	−	0.0721013i	0.402194	+	0.915555i	$0.368248\pi$
$774$	−9.32533	−	12.1195i	−0.335192	−	0.435625i
$775$	−39.4197	+	45.4928i	−1.41600	+	1.63415i
$776$	−0.870803	+	1.90679i	−0.0312600	+	0.0684499i
$777$	−17.2284	+	1.96765i	−0.618064	+	0.0705890i
$778$	40.2052	−	18.3611i	1.44143	−	0.658277i
$779$	0.0927566	+	0.645136i	0.00332335	+	0.0231144i
$780$	0.963662	+	0.167287i	0.0345046	+	0.00598984i
$781$		−	11.6488i		−	0.416827i
$782$	−7.88371	+	50.8878i	−0.281921	+	1.81974i
$783$	44.5399	+	17.4214i	1.59173	+	0.622591i
$784$	3.54224	+	2.27646i	0.126508	+	0.0813020i
$785$	33.5574	−	4.82483i	1.19772	−	0.172206i
$786$	47.0457	+	43.2234i	1.67806	+	1.54173i
$787$	3.64987	−	12.4303i	0.130104	−	0.443093i	−0.868513	−	0.495666i	$-0.834924\pi$
$787$	3.64987	−	12.4303i	0.130104	−	0.443093i	0.998617	+	0.0525731i	$0.0167423\pi$
$788$	−11.0480	−	5.04543i	−0.393567	−	0.179736i
$789$	−12.6236	+	38.7825i	−0.449412	+	1.38069i
$790$	0.140968	−	0.980451i	0.00501540	−	0.0348829i
$791$	−3.15215	−	10.7353i	−0.112078	−	0.381702i
$792$	0.182572	−	3.13532i	0.00648742	−	0.111409i
$793$	−0.127214	−	0.197948i	−0.00451749	−	0.00702935i
$794$	−2.52970	−	3.93628i	−0.0897755	−	0.139693i
$795$	−54.4247	−	26.7941i	−1.93024	−	0.950290i
$796$	9.23508	+	31.4518i	0.327329	+	1.11478i
$797$	−2.96149	+	20.5976i	−0.104901	+	0.729604i	0.867694	+	0.497099i	$0.165601\pi$
$797$	−2.96149	+	20.5976i	−0.104901	+	0.729604i	−0.972595	+	0.232505i	$0.925308\pi$
$798$	6.64917	+	2.16429i	0.235378	+	0.0766149i
$799$	27.3717	+	12.5002i	0.968340	+	0.442226i
$800$	−17.6019	+	59.9466i	−0.622322	+	2.11943i
$801$	−3.92493	−	1.40504i	−0.138681	−	0.0496446i
$802$	69.4905	−	9.99123i	2.45380	−	0.352803i
$803$	1.16646	+	0.749637i	0.0411634	+	0.0264541i
$804$	9.42133	+	22.3261i	0.332265	+	0.787380i
$805$	2.64176	−	17.0520i	0.0931097	−	0.601004i
$806$		−	1.24157i		−	0.0437323i
$807$	4.03173	−	23.2249i	0.141923	−	0.817555i
$808$	−0.0183268	−	0.127466i	−0.000644735	−	0.00448423i
$809$	−40.4803	+	18.4867i	−1.42321	+	0.649959i	−0.970368	−	0.241631i	$-0.922318\pi$
$809$	−40.4803	+	18.4867i	−1.42321	+	0.649959i	−0.452843	+	0.891590i	$0.649590\pi$
$810$	−61.7227	−	16.3621i	−2.16871	−	0.574904i
$811$	−8.54142	+	18.7031i	−0.299930	+	0.656755i	−0.998257	−	0.0590245i	$-0.981201\pi$
$811$	−8.54142	+	18.7031i	−0.299930	+	0.656755i	0.698327	+	0.715779i	$0.253928\pi$
$812$	−11.3824	+	13.1360i	−0.399444	+	0.460983i
$813$	−7.06099	−	26.9200i	−0.247640	−	0.944126i
$814$	−90.1466	+	26.4694i	−3.15964	+	0.927753i
$815$	32.4114	+	37.4047i	1.13532	+	1.31023i
$816$	22.4324	−	32.7695i	0.785289	−	1.14716i
$817$	−4.45211	+	2.86120i	−0.155760	+	0.100101i
$818$	−38.7735	+	33.5974i	−1.35568	+	1.17471i
$819$	0.220390	+	0.116582i	0.00770104	+	0.00407372i
$820$	2.14107	+	0.307840i	0.0747695	+	0.0107502i
$821$	−9.72401	−	8.42590i	−0.339370	−	0.294066i	0.468456	−	0.883487i	$-0.344811\pi$
$821$	−9.72401	−	8.42590i	−0.339370	−	0.294066i	−0.807826	+	0.589421i	$0.799356\pi$
$822$	1.08777	+	0.0316440i	0.0379403	+	0.00110371i
$823$	−9.33000	−	2.73954i	−0.325223	−	0.0954942i	0.115045	−	0.993360i	$-0.463299\pi$
$823$	−9.33000	−	2.73954i	−0.325223	−	0.0954942i	−0.440269	+	0.897866i	$0.645117\pi$
$824$	−1.24117	−	2.71777i	−0.0432381	−	0.0946782i
$825$	−33.7923	−	56.1046i	−1.17650	−	1.95331i
$826$	11.3793	−	17.7065i	0.395935	−	0.616087i
$827$	−14.9167			−0.518704			−0.259352	−	0.965783i	$-0.583509\pi$
$827$	−14.9167			−0.518704			−0.259352	+	0.965783i	$0.583509\pi$
$828$	−19.2569	−	19.1672i	−0.669222	−	0.666107i
$829$	−39.3208			−1.36567			−0.682833	−	0.730574i	$-0.739252\pi$
$829$	−39.3208			−1.36567			−0.682833	+	0.730574i	$0.739252\pi$
$830$	−3.65710	+	5.69056i	−0.126940	+	0.197522i
$831$	1.06085	+	1.76130i	0.0368005	+	0.0610990i
$832$	−0.244574	−	0.535542i	−0.00847907	−	0.0185666i
$833$	−5.22460	−	1.53408i	−0.181022	−	0.0531528i
$834$	−61.9906	−	1.80335i	−2.14656	−	0.0624450i
$835$	1.52196	+	1.31879i	0.0526697	+	0.0456385i
$836$	18.2125	+	2.61856i	0.629892	+	0.0905649i
$837$	−3.43021	+	39.2160i	−0.118565	+	1.35550i
$838$	7.22803	−	6.26312i	0.249688	−	0.216356i
$839$	−5.21538	+	3.35172i	−0.180055	+	0.115714i	−0.627564	−	0.778565i	$-0.715948\pi$
$839$	−5.21538	+	3.35172i	−0.180055	+	0.115714i	0.447509	+	0.894280i	$0.352311\pi$
$840$	−0.774369	+	1.13121i	−0.0267183	+	0.0390305i
$841$	36.4857	+	42.1068i	1.25813	+	1.45196i
$842$	−16.2309	+	4.76584i	−0.559355	+	0.164242i
$843$	2.91827	+	11.1259i	0.100511	+	0.383196i
$844$	19.8018	−	22.8525i	0.681606	−	0.786615i
$845$	−19.4203	+	42.5246i	−0.668079	+	1.46289i
$846$	−28.4827	+	16.0457i	−0.979255	+	0.551662i
$847$	−10.5961	+	4.83907i	−0.364085	+	0.166272i
$848$	5.83312	+	40.5702i	0.200310	+	1.39319i
$849$	7.83915	−	45.1577i	0.269039	−	1.54981i
$850$		−	85.3155i		−	2.92630i
$851$	20.4204	−	43.4544i	0.700002	−	1.48960i
$852$	3.11271	+	7.37630i	0.106640	+	0.252708i
$853$	6.17100	+	3.96586i	0.211291	+	0.135788i	0.642006	−	0.766699i	$-0.278102\pi$
$853$	6.17100	+	3.96586i	0.211291	+	0.135788i	−0.430715	+	0.902488i	$0.641739\pi$
$854$	−5.52618	+	0.794544i	−0.189102	+	0.0271887i
$855$	−7.44804	+	20.8059i	−0.254718	+	0.711546i
$856$	1.16821	−	3.97855i	0.0399285	−	0.135984i
$857$	−11.0111	−	5.02858i	−0.376130	−	0.171773i	0.218374	−	0.975865i	$-0.429925\pi$
$857$	−11.0111	−	5.02858i	−0.376130	−	0.171773i	−0.594505	+	0.804092i	$0.702652\pi$
$858$	1.28454	+	0.418115i	0.0438536	+	0.0142742i
$859$	−3.51753	+	24.4650i	−0.120017	+	0.834733i	0.837517	+	0.546411i	$0.184006\pi$
$859$	−3.51753	+	24.4650i	−0.120017	+	0.834733i	−0.957533	+	0.288322i	$0.906903\pi$
$860$	4.94830	+	16.8524i	0.168736	+	0.574661i
$861$	0.494701	+	0.243549i	0.0168594	+	0.00830013i
$862$	6.23091	+	9.69549i	0.212226	+	0.330230i
$863$	−16.6162	−	25.8553i	−0.565622	−	0.880125i	0.434164	−	0.900834i	$-0.357044\pi$
$863$	−16.6162	−	25.8553i	−0.565622	−	0.880125i	−0.999786	+	0.0207092i	$0.993408\pi$
$864$	13.6699	+	38.5033i	0.465061	+	1.30991i
$865$	5.78837	+	19.7134i	0.196810	+	0.670275i
$866$	−2.90599	+	20.2116i	−0.0987496	+	0.686819i
$867$	−6.78154	+	20.8344i	−0.230313	+	0.707572i
$868$	−13.0139	−	5.94324i	−0.441720	−	0.201727i
$869$	0.187188	−	0.637505i	0.00634993	−	0.0216259i
$870$	−83.2909	−	76.5239i	−2.82383	−	2.59440i
$871$	0.609447	−	0.0876252i	0.0206503	−	0.00296907i
$872$	−0.720305	−	0.462912i	−0.0243926	−	0.0156762i
$873$	20.4806	+	19.9455i	0.693163	+	0.675054i
$874$	−14.7698	+	12.5188i	−0.499595	+	0.423454i
$875$			10.5984i			0.358290i
$876$	−0.938941	−	0.162996i	−0.0317239	−	0.00550711i
$877$	−3.63234	−	25.2635i	−0.122656	−	0.853088i	−0.954528	−	0.298121i	$-0.903640\pi$
$877$	−3.63234	−	25.2635i	−0.122656	−	0.853088i	0.831873	−	0.554967i	$-0.187269\pi$
$878$	−22.6861	+	10.3604i	−0.765617	+	0.349646i
$879$	−2.64812	+	0.302441i	−0.0893188	+	0.0102011i
$880$	−29.9514	+	65.5843i	−1.00966	+	2.21085i
$881$	30.2033	−	34.8565i	1.01758	−	1.17434i	0.0329872	−	0.999456i	$-0.489498\pi$
$881$	30.2033	−	34.8565i	1.01758	−	1.17434i	0.984588	−	0.174889i	$-0.0559566\pi$
$882$	4.68846	−	3.60754i	0.157869	−	0.121472i
$883$	41.1043	−	12.0693i	1.38327	−	0.406165i	0.496364	−	0.868114i	$-0.334668\pi$
$883$	41.1043	−	12.0693i	1.38327	−	0.406165i	0.886906	+	0.461949i	$0.152850\pi$
$884$	0.559642	+	0.645861i	0.0188228	+	0.0217227i
$885$	54.8892	+	37.5744i	1.84508	+	1.26305i
$886$	15.2934	−	9.82850i	0.513793	−	0.330195i
$887$	15.0427	−	13.0345i	0.505083	−	0.437657i	−0.364675	−	0.931135i	$-0.618820\pi$
$887$	15.0427	−	13.0345i	0.505083	−	0.437657i	0.869758	+	0.493478i	$0.164275\pi$
$888$	−2.95419	+	2.41305i	−0.0991360	+	0.0809767i
$889$	−0.530128	−	0.0762208i	−0.0177799	−	0.00255636i
$890$	7.45112	+	6.45643i	0.249762	+	0.216420i
$891$	−39.4183	−	16.7555i	−1.32056	−	0.561331i
$892$	32.0455	+	9.40941i	1.07296	+	0.315050i
$893$	4.69994	+	10.2914i	0.157278	+	0.344390i
$894$	−61.2615	+	36.8984i	−2.04889	+	1.23407i
$895$	−1.90638	+	2.96639i	−0.0637234	+	0.0991556i
$896$	1.75707			0.0586994
$897$	−0.595215	+	0.349718i	−0.0198737	+	0.0116768i
$898$	26.1335			0.872085
$899$	−37.6987	+	58.6603i	−1.25732	+	1.95643i
$900$	36.3899	+	26.4970i	1.21300	+	0.883233i
$901$	−22.0188	−	48.2145i	−0.733553	−	1.60626i
$902$	2.86656	+	0.841697i	0.0954459	+	0.0280254i
$903$	−0.130192	+	4.47538i	−0.00433252	+	0.148931i
$904$	−1.86004	−	1.61173i	−0.0618640	−	0.0536055i
$905$	16.0417	+	2.30645i	0.533245	+	0.0766691i
$906$	34.8931	+	42.7180i	1.15925	+	1.41921i
$907$	29.6455	−	25.6880i	0.984362	−	0.852955i	−0.00476913	−	0.999989i	$-0.501518\pi$
$907$	29.6455	−	25.6880i	0.984362	−	0.852955i	0.989131	+	0.147034i	$0.0469726\pi$
$908$	25.4005	−	16.3239i	0.842944	−	0.541727i
$909$	−1.72090	−	0.350572i	−0.0570785	−	0.0116277i
$910$	−0.386139	−	0.445628i	−0.0128004	−	0.0147724i
$911$	−33.9139	+	9.95802i	−1.12362	+	0.329924i	−0.790196	−	0.612854i	$-0.790021\pi$
$911$	−33.9139	+	9.95802i	−1.12362	+	0.329924i	−0.333421	+	0.942778i	$0.608203\pi$
$912$	14.4427	−	3.78826i	0.478247	−	0.125442i
$913$	−2.97132	+	3.42909i	−0.0983364	+	0.113486i
$914$	−0.923415	+	2.02200i	−0.0305438	+	0.0668817i
$915$	−2.00213	−	17.5302i	−0.0661883	−	0.579532i
$916$	37.0388	−	16.9151i	1.22380	−	0.558890i
$917$	−2.66204	−	18.5149i	−0.0879083	−	0.611416i
$918$	−32.7236	−	45.1890i	−1.08004	−	1.49146i
$919$		−	24.3059i		−	0.801777i	−0.916127	−	0.400889i	$-0.868701\pi$
$919$		−	24.3059i		−	0.801777i	0.916127	−	0.400889i	$-0.131299\pi$
$920$	−1.53908	−	3.46974i	−0.0507421	−	0.114394i
$921$	−53.0547	+	22.3884i	−1.74821	+	0.737724i
$922$	34.0457	+	21.8799i	1.12124	+	0.720575i
$923$	0.201355	−	0.0289504i	0.00662767	−	0.000952915i
$924$	10.5316	−	11.4629i	0.346464	−	0.377101i
$925$	−22.4111	+	76.3251i	−0.736871	+	2.50955i
$926$	−5.01120	−	2.28854i	−0.164678	−	0.0752061i
$927$	−40.6011	+	3.44449i	−1.33351	+	0.113132i
$928$	−10.2997	+	71.6362i	−0.338105	+	2.35157i
$929$	−11.9782	−	40.7941i	−0.392993	−	1.33841i	−0.884095	−	0.467308i	$-0.845224\pi$
$929$	−11.9782	−	40.7941i	−0.392993	−	1.33841i	0.491102	−	0.871102i	$-0.336594\pi$
$930$	41.1211	−	83.5258i	1.34841	−	2.73892i
$931$	−1.10687	−	1.72232i	−0.0362761	−	0.0564466i
$932$	−12.0126	−	18.6919i	−0.393484	−	0.612274i
$933$	0.608095	−	1.23517i	0.0199081	−	0.0404377i
$934$	−8.27231	−	28.1729i	−0.270678	−	0.921846i
$935$	13.2692	−	92.2895i	0.433950	−	3.01819i
$936$	0.0546491	−	0.00463628i	0.00178626	−	0.000151542i
$937$	36.2181	+	16.5402i	1.18319	+	0.540346i	0.907154	−	0.420800i	$-0.138251\pi$
$937$	36.2181	+	16.5402i	1.18319	+	0.540346i	0.276040	+	0.961146i	$0.410978\pi$
$938$	4.11584	−	14.0173i	0.134387	−	0.457680i
$939$	3.78713	−	4.12203i	0.123588	−	0.134517i
$940$	37.1661	−	5.34368i	1.21222	−	0.174292i
$941$	−16.1701	−	10.3919i	−0.527131	−	0.338766i	0.249856	−	0.968283i	$-0.419617\pi$
$941$	−16.1701	−	10.3919i	−0.527131	−	0.338766i	−0.776987	+	0.629517i	$0.783253\pi$
$942$	−29.6506	+	12.5122i	−0.966067	+	0.407669i
$943$	−1.29332	+	0.811381i	−0.0421163	+	0.0264222i
$944$		−	44.9436i		−	1.46279i
$945$	10.9654	+	15.1424i	0.356704	+	0.492583i
$946$	3.45234	+	24.0115i	0.112245	+	0.780683i
$947$	12.4926	−	5.70516i	0.405953	−	0.185393i	−0.201964	−	0.979393i	$-0.564732\pi$
$947$	12.4926	−	5.70516i	0.405953	−	0.185393i	0.607917	+	0.794000i	$0.292005\pi$
$948$	0.0518172	+	0.453702i	0.00168295	+	0.0147356i
$949$	−0.0100588	+	0.0220258i	−0.000326524	+	0.000714987i
$950$	21.0064	−	24.2426i	0.681537	−	0.786535i
$951$	22.9556	−	6.02115i	0.744387	−	0.195249i
$952$	−1.14928	+	0.337460i	−0.0372485	+	0.0109372i
$953$	1.60890	+	1.85676i	0.0521172	+	0.0601465i	0.781210	−	0.624269i	$-0.214603\pi$
$953$	1.60890	+	1.85676i	0.0521172	+	0.0601465i	−0.729092	+	0.684415i	$0.760058\pi$
$954$	56.4261	+	11.4948i	1.82686	+	0.372158i
$955$	−12.9147	+	8.29980i	−0.417911	+	0.268575i
$956$	38.3131	−	33.1985i	1.23913	−	1.07372i
$957$	−47.9952	−	58.7583i	−1.55147	−	1.89939i
$958$	−50.7833	−	7.30154i	−1.64073	−	0.235902i
$959$	−0.240796	−	0.208651i	−0.00777571	−	0.00673769i
$960$	1.28374	−	44.1287i	0.0414324	−	1.42425i
$961$	−25.3257	−	7.43630i	−0.816959	−	0.239881i
$962$	−0.681574	−	1.49244i	−0.0219748	−	0.0481182i
$963$	−45.7149	−	33.2868i	−1.47314	−	1.07265i
$964$	−0.759585	+	1.18194i	−0.0244646	+	0.0380676i
$965$	20.2701			0.652517
$966$	1.68114	+	16.2935i	0.0540898	+	0.524233i
$967$	9.17279			0.294977			0.147489	−	0.989064i	$-0.452881\pi$
$967$	9.17279			0.294977			0.147489	+	0.989064i	$0.452881\pi$
$968$	−1.38536	+	2.15566i	−0.0445271	+	0.0692855i
$969$	−16.5404	+	9.96244i	−0.531354	+	0.320040i
$970$	−28.0864	−	61.5006i	−0.901799	−	1.97466i
$971$	−42.3531	−	12.4360i	−1.35917	−	0.399090i	−0.480702	−	0.876884i	$-0.659618\pi$
$971$	−42.3531	−	12.4360i	−1.35917	−	0.399090i	−0.878472	+	0.477794i	$0.841436\pi$
$972$	29.4379	+	0.0769207i	0.944220	+	0.00246723i
$973$	13.7227	+	11.8908i	0.439929	+	0.381200i
$974$	45.9808	+	6.61104i	1.47332	+	0.211831i
$975$	0.885808	−	0.723550i	0.0283686	−	0.0231721i
$976$	−9.00966	+	7.80691i	−0.288392	+	0.249893i
$977$	−16.0856	+	10.3376i	−0.514624	+	0.330729i	−0.772042	−	0.635571i	$-0.780765\pi$
$977$	−16.0856	+	10.3376i	−0.514624	+	0.330729i	0.257418	+	0.966300i	$0.417128\pi$
$978$	−38.7688	−	26.5392i	−1.23969	−	0.848630i
$979$	4.33077	+	4.99797i	0.138412	+	0.159736i
$980$	−6.51940	+	1.91427i	−0.208255	+	0.0611491i
$981$	−9.25460	+	7.12095i	−0.295477	+	0.227355i
$982$	−30.9558	+	35.7249i	−0.987841	+	1.14003i
$983$	18.8900	−	41.3633i	0.602497	−	1.31929i	−0.325091	−	0.945683i	$-0.605395\pi$
$983$	18.8900	−	41.3633i	0.602497	−	1.31929i	0.927589	−	0.373603i	$-0.121878\pi$
$984$	0.120512	−	0.0137636i	0.00384177	−	0.000438768i
$985$	−21.0494	+	9.61292i	−0.670688	+	0.306293i
$986$	−14.0647	−	97.8222i	−0.447911	−	3.11529i
$987$	9.43056	+	1.63710i	0.300178	+	0.0521095i
$988$			0.321319i			0.0102225i
$989$	−10.3553	−	6.81563i	−0.329281	−	0.216724i
$990$	72.5689	+	70.6730i	2.30639	+	2.24613i
$991$	−37.8486	−	24.3238i	−1.20230	−	0.772672i	−0.222948	−	0.974830i	$-0.571568\pi$
$991$	−37.8486	−	24.3238i	−1.20230	−	0.772672i	−0.979353	+	0.202158i	$0.935204\pi$
$992$	−58.9642	+	8.47777i	−1.87211	+	0.269169i
$993$	−29.4879	−	27.0922i	−0.935771	−	0.859744i
$994$	1.35983	−	4.63116i	0.0431312	−	0.146891i
$995$	56.8102	+	25.9444i	1.80101	+	0.822491i
$996$	0.965215	−	2.96535i	0.0305840	−	0.0939607i
$997$	1.30617	−	9.08462i	0.0413668	−	0.287713i	−0.958628	−	0.284660i	$-0.908119\pi$
$997$	1.30617	−	9.08462i	0.0413668	−	0.287713i	0.999995	−	0.00305256i	$-0.000971660\pi$
$998$	14.4100	+	49.0761i	0.456142	+	1.55348i
$999$	17.4048	+	49.0231i	0.550664	+	1.55102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.11	✓	480
3.2	odd	2	inner	483.2.u.a.113.38	yes	480
23.11	odd	22	inner	483.2.u.a.218.38	yes	480
69.11	even	22	inner	483.2.u.a.218.11	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.11	✓	480	1.1	even	1	trivial
483.2.u.a.113.38	yes	480	3.2	odd	2	inner
483.2.u.a.218.11	yes	480	69.11	even	22	inner
483.2.u.a.218.38	yes	480	23.11	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06610 + 1.65888i) q^{2} +(-0.893651 - 1.48371i) q^{3} +(-0.784489 - 1.71779i) q^{4} +(-3.45226 - 1.01367i) q^{5} +(3.41401 + 0.0993161i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.217736 - 0.0313058i) q^{8} +(-1.40277 + 2.65183i) q^{9} +O(q^{10})\)	\(q+(-1.06610 + 1.65888i) q^{2} +(-0.893651 - 1.48371i) q^{3} +(-0.784489 - 1.71779i) q^{4} +(-3.45226 - 1.01367i) q^{5} +(3.41401 + 0.0993161i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.217736 - 0.0313058i) q^{8} +(-1.40277 + 2.65183i) q^{9} +(5.36201 - 4.64621i) q^{10} +(4.00358 - 2.57295i) q^{11} +(-1.84764 + 2.69906i) q^{12} +(0.0544245 + 0.0628092i) q^{13} +(1.89204 - 0.555552i) q^{14} +(1.58112 + 6.02801i) q^{15} +(2.75740 - 3.18221i) q^{16} +(-2.26201 + 4.95310i) q^{17} +(-2.90358 - 5.15415i) q^{18} +(-1.86231 + 0.850488i) q^{19} +(0.966977 + 6.72547i) q^{20} +(-0.296245 + 1.70653i) q^{21} +9.38448i q^{22} +(-3.58999 - 3.17993i) q^{23} +(0.148132 + 0.351033i) q^{24} +(6.68429 + 4.29573i) q^{25} +(-0.162215 + 0.0233229i) q^{26} +(5.18814 - 0.288509i) q^{27} +(-0.532037 + 1.81195i) q^{28} +(8.37233 + 3.82352i) q^{29} +(-11.6854 - 3.80356i) q^{30} +(-1.07817 + 7.49883i) q^{31} +(2.21530 + 7.54461i) q^{32} +(-7.39531 - 3.64083i) q^{33} +(-5.80508 - 9.03289i) q^{34} +(1.94523 + 3.02683i) q^{35} +(5.65576 + 0.329339i) q^{36} +(2.82055 + 9.60593i) q^{37} +(0.574545 - 3.99605i) q^{38} +(0.0445539 - 0.136879i) q^{39} +(0.719948 + 0.328789i) q^{40} +(0.0896903 - 0.305457i) q^{41} +(-2.51510 - 2.31076i) q^{42} +(2.55865 - 0.367878i) q^{43} +(-7.56055 - 4.85887i) q^{44} +(7.53084 - 7.73286i) q^{45} +(9.10240 - 2.56526i) q^{46} -5.52617i q^{47} +(-7.18562 - 1.24739i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-14.2522 + 6.50876i) q^{50} +(9.37040 - 1.07019i) q^{51} +(0.0651976 - 0.142763i) q^{52} +(-6.37454 + 7.35661i) q^{53} +(-5.05246 + 8.91407i) q^{54} +(-16.4295 + 4.82415i) q^{55} +(0.144053 + 0.166246i) q^{56} +(2.92613 + 2.00308i) q^{57} +(-15.2685 + 9.81245i) q^{58} +(8.06669 - 6.98983i) q^{59} +(9.11449 - 7.44494i) q^{60} +(-2.80244 - 0.402930i) q^{61} +(-11.2902 - 9.78304i) q^{62} +(2.79673 - 1.08550i) q^{63} +(-6.79711 - 1.99581i) q^{64} +(-0.124219 - 0.272002i) q^{65} +(13.9238 - 8.38645i) q^{66} +(4.00537 - 6.23247i) q^{67} +10.2829 q^{68} +(-1.50988 + 8.16825i) q^{69} -7.09495 q^{70} +(1.32333 - 2.05914i) q^{71} +(0.388453 - 0.533486i) q^{72} +(0.121033 + 0.265024i) q^{73} +(-18.9421 - 5.56189i) q^{74} +(0.400184 - 13.7564i) q^{75} +(2.92192 + 2.53186i) q^{76} +(-4.71063 - 0.677286i) q^{77} +(0.179568 + 0.219836i) q^{78} +(0.105511 - 0.0914258i) q^{79} +(-12.7450 + 8.19070i) q^{80} +(-5.06445 - 7.43985i) q^{81} +(0.411098 + 0.474432i) q^{82} +(-0.914788 + 0.268606i) q^{83} +(3.16386 - 0.829865i) q^{84} +(12.8299 - 14.8065i) q^{85} +(-2.11750 + 4.63668i) q^{86} +(-1.80897 - 15.8390i) q^{87} +(-0.952274 + 0.434889i) q^{88} +(0.197763 + 1.37547i) q^{89} +(4.79928 + 20.7367i) q^{90} -0.0831085i q^{91} +(-2.64614 + 8.66148i) q^{92} +(12.0896 - 5.10165i) q^{93} +(9.16725 + 5.89143i) q^{94} +(7.29129 - 1.04833i) q^{95} +(9.21428 - 10.0291i) q^{96} +(2.68473 - 9.14336i) q^{97} +(-1.79372 - 0.819163i) q^{98} +(1.20690 + 14.2261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36} - 44 q^{37} - 308 q^{40} - 44 q^{43} - 184 q^{46} + 98 q^{48} + 48 q^{49} - 28 q^{52} + 28 q^{54} - 44 q^{55} + 66 q^{57} + 4 q^{58} + 220 q^{60} + 84 q^{64} + 176 q^{66} + 44 q^{67} + 102 q^{69} - 8 q^{70} - 60 q^{72} + 4 q^{73} - 8 q^{75} + 176 q^{76} + 18 q^{78} - 16 q^{81} + 20 q^{82} - 154 q^{84} + 84 q^{85} + 28 q^{87} - 418 q^{90} - 188 q^{93} + 12 q^{94} - 412 q^{96} - 132 q^{97}+O(q^{100}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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