LMFDB - Embedded newform 552.2.bb.a.85.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (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:	$4.40774219157$
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			85.4
Character	$\chi$	$=$	552.85
Dual form			552.2.bb.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37160 - 0.344553i) q^{2} +(0.540641 + 0.841254i) q^{3} +(1.76257 + 0.945176i) q^{4} +(2.26933 - 1.03637i) q^{5} +(-0.451686 - 1.34014i) q^{6} +(-2.49497 + 0.732589i) q^{7} +(-2.09187 - 1.90370i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.37160 - 0.344553i) q^{2} +(0.540641 + 0.841254i) q^{3} +(1.76257 + 0.945176i) q^{4} +(2.26933 - 1.03637i) q^{5} +(-0.451686 - 1.34014i) q^{6} +(-2.49497 + 0.732589i) q^{7} +(-2.09187 - 1.90370i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-3.46970 + 0.639578i) q^{10} +(-3.71536 + 3.21937i) q^{11} +(0.157783 + 1.99377i) q^{12} +(-1.81486 + 6.18084i) q^{13} +(3.67451 - 0.145170i) q^{14} +(2.09874 + 1.34878i) q^{15} +(2.21328 + 3.33187i) q^{16} +(0.253473 - 1.76294i) q^{17} +(0.883199 - 1.10452i) q^{18} +(-2.93640 + 0.422191i) q^{19} +(4.97940 + 0.318249i) q^{20} +(-1.96517 - 1.70283i) q^{21} +(6.20522 - 3.13555i) q^{22} +(1.87931 + 4.41228i) q^{23} +(0.470543 - 2.78901i) q^{24} +(0.801505 - 0.924986i) q^{25} +(4.61889 - 7.85233i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(-5.08997 - 1.06695i) q^{28} +(8.21491 + 1.18113i) q^{29} +(-2.41391 - 2.57311i) q^{30} +(-7.54861 - 4.85119i) q^{31} +(-1.88773 - 5.33259i) q^{32} +(-4.71698 - 1.38503i) q^{33} +(-0.955090 + 2.33071i) q^{34} +(-4.90268 + 4.24820i) q^{35} +(-1.59196 + 1.21065i) q^{36} +(6.44490 + 2.94329i) q^{37} +(4.17303 + 0.432669i) q^{38} +(-6.18084 + 1.81486i) q^{39} +(-6.72009 - 2.15218i) q^{40} +(-1.79665 - 3.93411i) q^{41} +(2.10872 + 3.01271i) q^{42} +(2.68440 + 4.17701i) q^{43} +(-9.59144 + 2.16270i) q^{44} +2.49478i q^{45} +(-1.05740 - 6.69940i) q^{46} +8.53380 q^{47} +(-1.60636 + 3.66328i) q^{48} +(-0.200594 + 0.128914i) q^{49} +(-1.41805 + 0.992549i) q^{50} +(1.62012 - 0.739884i) q^{51} +(-9.04080 + 9.17879i) q^{52} +(1.11051 + 3.78203i) q^{53} +(1.40667 + 0.145847i) q^{54} +(-5.09492 + 11.1563i) q^{55} +(6.61378 + 3.21719i) q^{56} +(-1.94271 - 2.24201i) q^{57} +(-10.8606 - 4.45050i) q^{58} +(4.07872 - 13.8908i) q^{59} +(2.42434 + 4.36100i) q^{60} +(-5.74932 + 8.94611i) q^{61} +(8.68217 + 9.25479i) q^{62} +(0.370061 - 2.57383i) q^{63} +(0.751854 + 7.96459i) q^{64} +(2.28712 + 15.9073i) q^{65} +(5.99259 + 3.52496i) q^{66} +(7.32397 + 6.34625i) q^{67} +(2.11305 - 2.86773i) q^{68} +(-2.69581 + 3.96644i) q^{69} +(8.18824 - 4.13759i) q^{70} +(-3.72958 + 4.30416i) q^{71} +(2.60066 - 1.11201i) q^{72} +(-1.02497 - 7.12881i) q^{73} +(-7.82570 - 6.25762i) q^{74} +(1.21147 + 0.174184i) q^{75} +(-5.57465 - 2.03128i) q^{76} +(6.91122 - 10.7541i) q^{77} +(9.10295 - 0.359633i) q^{78} +(0.901525 + 0.264712i) q^{79} +(8.47573 + 5.26735i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(1.10877 + 6.01506i) q^{82} +(-5.74905 - 2.62550i) q^{83} +(-1.85427 - 4.85879i) q^{84} +(-1.25185 - 4.26339i) q^{85} +(-2.24272 - 6.65410i) q^{86} +(3.44769 + 7.54938i) q^{87} +(13.9008 + 0.338405i) q^{88} +(-1.07103 + 0.688312i) q^{89} +(0.859584 - 3.42184i) q^{90} -16.7506i q^{91} +(-0.857962 + 9.55321i) q^{92} -8.97304i q^{93} +(-11.7049 - 2.94034i) q^{94} +(-6.22613 + 4.00129i) q^{95} +(3.46547 - 4.47107i) q^{96} +(-3.10826 - 6.80614i) q^{97} +(0.319552 - 0.107703i) q^{98} +(-1.38503 - 4.71698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.37160	−	0.344553i	−0.969867	−	0.243636i
$2$	−1.37160	−	0.344553i	−0.969867	−	0.243636i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$4$	1.76257	+	0.945176i	0.881283	+	0.472588i
$5$	2.26933	−	1.03637i	1.01488	−	0.463479i	0.162668	−	0.986681i	$-0.447990\pi$
$5$	2.26933	−	1.03637i	1.01488	−	0.463479i	0.852208	+	0.523202i	$0.175263\pi$
$6$	−0.451686	−	1.34014i	−0.184400	−	0.547111i
$7$	−2.49497	+	0.732589i	−0.943009	+	0.276893i	−0.716874	−	0.697203i	$-0.754428\pi$
$7$	−2.49497	+	0.732589i	−0.943009	+	0.276893i	−0.226136	+	0.974096i	$0.572609\pi$
$8$	−2.09187	−	1.90370i	−0.739588	−	0.673060i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	−3.46970	+	0.639578i	−1.09721	+	0.202252i
$11$	−3.71536	+	3.21937i	−1.12022	+	0.970678i	−0.999757	−	0.0220398i	$-0.992984\pi$
$11$	−3.71536	+	3.21937i	−1.12022	+	0.970678i	−0.120465	+	0.992718i	$0.538439\pi$
$12$	0.157783	+	1.99377i	0.0455480	+	0.575551i
$13$	−1.81486	+	6.18084i	−0.503352	+	1.71426i	0.179551	+	0.983749i	$0.442535\pi$
$13$	−1.81486	+	6.18084i	−0.503352	+	1.71426i	−0.682903	+	0.730509i	$0.739283\pi$
$14$	3.67451	−	0.145170i	0.982054	−	0.0387983i
$15$	2.09874	+	1.34878i	0.541893	+	0.348254i
$16$	2.21328	+	3.33187i	0.553321	+	0.832968i
$17$	0.253473	−	1.76294i	0.0614762	−	0.427576i	−0.935720	−	0.352744i	$-0.885249\pi$
$17$	0.253473	−	1.76294i	0.0614762	−	0.427576i	0.997196	−	0.0748325i	$-0.0238422\pi$
$18$	0.883199	−	1.10452i	0.208172	−	0.260337i
$19$	−2.93640	+	0.422191i	−0.673657	+	0.0968572i	−0.470650	−	0.882320i	$-0.655981\pi$
$19$	−2.93640	+	0.422191i	−0.673657	+	0.0968572i	−0.203007	+	0.979177i	$0.565071\pi$
$20$	4.97940	+	0.318249i	1.11343	+	0.0711626i
$21$	−1.96517	−	1.70283i	−0.428836	−	0.371589i
$22$	6.20522	−	3.13555i	1.32296	−	0.668502i
$23$	1.87931	+	4.41228i	0.391864	+	0.920023i
$23$	1.87931	+	4.41228i	0.391864	+	0.920023i
$24$	0.470543	−	2.78901i	0.0960492	−	0.569305i
$25$	0.801505	−	0.924986i	0.160301	−	0.184997i
$26$	4.61889	−	7.85233i	0.905838	−	1.53997i
$27$	−0.989821	+	0.142315i	−0.190491	+	0.0273885i
$28$	−5.08997	−	1.06695i	−0.961915	−	0.201634i
$29$	8.21491	+	1.18113i	1.52547	+	0.219329i	0.853439	−	0.521193i	$-0.174513\pi$
$29$	8.21491	+	1.18113i	1.52547	+	0.219329i	0.672031	+	0.740523i	$0.265422\pi$
$30$	−2.41391	−	2.57311i	−0.440717	−	0.469784i
$31$	−7.54861	−	4.85119i	−1.35577	−	0.871300i	−0.357726	−	0.933826i	$-0.616448\pi$
$31$	−7.54861	−	4.85119i	−1.35577	−	0.871300i	−0.998043	+	0.0625263i	$0.980084\pi$
$32$	−1.88773	−	5.33259i	−0.333707	−	0.942677i
$33$	−4.71698	−	1.38503i	−0.821121	−	0.241103i
$34$	−0.955090	+	2.33071i	−0.163797	+	0.399714i
$35$	−4.90268	+	4.24820i	−0.828704	+	0.718076i
$36$	−1.59196	+	1.21065i	−0.265327	+	0.201774i
$37$	6.44490	+	2.94329i	1.05953	+	0.483873i	0.867460	−	0.497507i	$-0.165751\pi$
$37$	6.44490	+	2.94329i	1.05953	+	0.483873i	0.192075	+	0.981380i	$0.438478\pi$
$38$	4.17303	+	0.432669i	0.676955	+	0.0701882i
$39$	−6.18084	+	1.81486i	−0.989727	+	0.290610i
$40$	−6.72009	−	2.15218i	−1.06254	−	0.340289i
$41$	−1.79665	−	3.93411i	−0.280589	−	0.614405i	0.715893	−	0.698210i	$-0.246020\pi$
$41$	−1.79665	−	3.93411i	−0.280589	−	0.614405i	−0.996482	+	0.0838053i	$0.973293\pi$
$42$	2.10872	+	3.01271i	0.325382	+	0.464871i
$43$	2.68440	+	4.17701i	0.409367	+	0.636988i	0.983316	−	0.181903i	$-0.0582257\pi$
$43$	2.68440	+	4.17701i	0.409367	+	0.636988i	−0.573949	+	0.818891i	$0.694589\pi$
$44$	−9.59144	+	2.16270i	−1.44596	+	0.326039i
$45$			2.49478i			0.371900i
$46$	−1.05740	−	6.69940i	−0.155906	−	0.987772i
$47$	8.53380			1.24478			0.622391	−	0.782706i	$-0.286161\pi$
$47$	8.53380			1.24478			0.622391	+	0.782706i	$0.286161\pi$
$48$	−1.60636	+	3.66328i	−0.231858	+	0.528749i
$49$	−0.200594	+	0.128914i	−0.0286563	+	0.0184163i
$50$	−1.41805	+	0.992549i	−0.200543	+	0.140368i
$51$	1.62012	−	0.739884i	0.226862	−	0.103604i
$52$	−9.04080	+	9.17879i	−1.25373	+	1.27287i
$53$	1.11051	+	3.78203i	0.152540	+	0.519502i	0.999934	−	0.0114611i	$-0.00364827\pi$
$53$	1.11051	+	3.78203i	0.152540	+	0.519502i	−0.847395	+	0.530964i	$0.821830\pi$
$54$	1.40667	+	0.145847i	0.191424	+	0.0198472i
$55$	−5.09492	+	11.1563i	−0.686998	+	1.50432i
$56$	6.61378	+	3.21719i	0.883804	+	0.429915i
$57$	−1.94271	−	2.24201i	−0.257318	−	0.296961i
$58$	−10.8606	−	4.45050i	−1.42607	−	0.584379i
$59$	4.07872	−	13.8908i	0.531004	−	1.80843i	−0.0554637	−	0.998461i	$-0.517664\pi$
$59$	4.07872	−	13.8908i	0.531004	−	1.80843i	0.586468	−	0.809973i	$-0.300518\pi$
$60$	2.42434	+	4.36100i	0.312981	+	0.563002i
$61$	−5.74932	+	8.94611i	−0.736125	+	1.14543i	0.248139	+	0.968724i	$0.420181\pi$
$61$	−5.74932	+	8.94611i	−0.736125	+	1.14543i	−0.984263	+	0.176708i	$0.943455\pi$
$62$	8.68217	+	9.25479i	1.10264	+	1.17536i
$63$	0.370061	−	2.57383i	0.0466233	−	0.324272i
$64$	0.751854	+	7.96459i	0.0939817	+	0.995574i
$65$	2.28712	+	15.9073i	0.283682	+	1.97305i
$66$	5.99259	+	3.52496i	0.737637	+	0.433892i
$67$	7.32397	+	6.34625i	0.894765	+	0.775318i	0.975173	−	0.221444i	$-0.0710769\pi$
$67$	7.32397	+	6.34625i	0.894765	+	0.775318i	−0.0804081	+	0.996762i	$0.525622\pi$
$68$	2.11305	−	2.86773i	0.256245	−	0.347763i
$69$	−2.69581	+	3.96644i	−0.324537	+	0.477503i
$70$	8.18824	−	4.13759i	0.978682	−	0.494537i
$71$	−3.72958	+	4.30416i	−0.442620	+	0.510810i	−0.932594	−	0.360926i	$-0.882461\pi$
$71$	−3.72958	+	4.30416i	−0.442620	+	0.510810i	0.489975	+	0.871737i	$0.337006\pi$
$72$	2.60066	−	1.11201i	0.306491	−	0.131051i
$73$	−1.02497	−	7.12881i	−0.119964	−	0.834365i	−0.957593	−	0.288125i	$-0.906968\pi$
$73$	−1.02497	−	7.12881i	−0.119964	−	0.834365i	0.837629	−	0.546239i	$-0.183941\pi$
$74$	−7.82570	−	6.25762i	−0.909719	−	0.727433i
$75$	1.21147	+	0.174184i	0.139889	+	0.0201130i
$76$	−5.57465	−	2.03128i	−0.639456	−	0.233004i
$77$	6.91122	−	10.7541i	0.787606	−	1.22554i
$78$	9.10295	−	0.359633i	1.03071	−	0.0407204i
$79$	0.901525	+	0.264712i	0.101429	+	0.0297824i	0.332053	−	0.943261i	$-0.392259\pi$
$79$	0.901525	+	0.264712i	0.101429	+	0.0297824i	−0.230624	+	0.973043i	$0.574077\pi$
$80$	8.47573	+	5.26735i	0.947615	+	0.588907i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	1.10877	+	6.01506i	0.122443	+	0.664252i
$83$	−5.74905	−	2.62550i	−0.631040	−	0.288186i	0.0741040	−	0.997251i	$-0.476390\pi$
$83$	−5.74905	−	2.62550i	−0.631040	−	0.288186i	−0.705144	+	0.709064i	$0.749118\pi$
$84$	−1.85427	−	4.85879i	−0.202318	−	0.530138i
$85$	−1.25185	−	4.26339i	−0.135782	−	0.462430i
$86$	−2.24272	−	6.65410i	−0.241839	−	0.717530i
$87$	3.44769	+	7.54938i	0.369631	+	0.809379i
$88$	13.9008	+	0.338405i	1.48183	+	0.0360741i
$89$	−1.07103	+	0.688312i	−0.113529	+	0.0729609i	−0.596173	−	0.802856i	$-0.703313\pi$
$89$	−1.07103	+	0.688312i	−0.113529	+	0.0729609i	0.482644	+	0.875817i	$0.339677\pi$
$90$	0.859584	−	3.42184i	0.0906081	−	0.360693i
$91$		−	16.7506i		−	1.75594i
$92$	−0.857962	+	9.55321i	−0.0894487	+	0.995991i
$93$		−	8.97304i		−	0.930461i
$94$	−11.7049	−	2.94034i	−1.20727	−	0.303273i
$95$	−6.22613	+	4.00129i	−0.638787	+	0.410524i
$96$	3.46547	−	4.47107i	0.353693	−	0.456327i
$97$	−3.10826	−	6.80614i	−0.315596	−	0.691059i	0.683653	−	0.729807i	$-0.260390\pi$
$97$	−3.10826	−	6.80614i	−0.315596	−	0.691059i	−0.999249	+	0.0387485i	$0.987663\pi$
$98$	0.319552	−	0.107703i	0.0322796	−	0.0108796i
$99$	−1.38503	−	4.71698i	−0.139201	−	0.474075i
$100$	2.28698	−	0.872787i	0.228698	−	0.0872787i
$101$	−10.6491	−	4.86327i	−1.05962	−	0.483913i	−0.192133	−	0.981369i	$-0.561541\pi$
$101$	−10.6491	−	4.86327i	−1.05962	−	0.483913i	−0.867490	+	0.497455i	$0.834268\pi$
$102$	−2.47708	+	0.456607i	−0.245268	+	0.0452108i
$103$	2.31960	+	2.67696i	0.228557	+	0.263769i	0.858432	−	0.512928i	$-0.171439\pi$
$103$	2.31960	+	2.67696i	0.228557	+	0.263769i	−0.629875	+	0.776697i	$0.716894\pi$
$104$	15.5629	−	9.47459i	1.52607	−	0.929060i
$105$	−6.22440	−	1.82765i	−0.607439	−	0.178360i
$106$	−0.220058	−	5.57006i	−0.0213739	−	0.541012i
$107$	−10.0446	+	15.6297i	−0.971045	+	1.51098i	−0.115461	+	0.993312i	$0.536835\pi$
$107$	−10.0446	+	15.6297i	−0.971045	+	1.51098i	−0.855584	+	0.517664i	$0.826802\pi$
$108$	−1.87914	−	0.684716i	−0.180820	−	0.0658869i
$109$	7.46777	+	1.07370i	0.715283	+	0.102842i	0.490342	−	0.871530i	$-0.336872\pi$
$109$	7.46777	+	1.07370i	0.715283	+	0.102842i	0.224941	+	0.974372i	$0.427781\pi$
$110$	10.8321	−	13.5465i	1.03280	−	1.29161i
$111$	1.00833	+	7.01305i	0.0957060	+	0.665650i
$112$	−7.96297	−	6.69149i	−0.752430	−	0.632286i
$113$	7.98575	−	9.21604i	0.751236	−	0.866972i	−0.243452	−	0.969913i	$-0.578280\pi$
$113$	7.98575	−	9.21604i	0.751236	−	0.866972i	0.994687	+	0.102941i	$0.0328252\pi$
$114$	1.89213	+	3.74450i	0.177214	+	0.350704i
$115$	8.83754	+	8.06526i	0.824105	+	0.752089i
$116$	13.3630	+	9.84635i	1.24072	+	0.914210i
$117$	−4.86837	−	4.21847i	−0.450081	−	0.389998i
$118$	−10.3805	+	17.6473i	−0.955602	+	1.62457i
$119$	0.659105	+	4.58418i	0.0604201	+	0.420231i
$120$	−1.82263	−	6.81685i	−0.166382	−	0.622291i
$121$	1.87404	−	13.0342i	0.170367	−	1.18493i
$122$	10.9682	−	10.2895i	0.993011	−	0.931571i
$123$	2.33824	−	3.63838i	0.210832	−	0.328061i
$124$	−8.71969	−	15.6853i	−0.783051	−	1.40858i
$125$	−2.65405	+	9.03887i	−0.237386	+	0.808461i
$126$	−1.39440	+	3.40276i	−0.124223	+	0.303142i
$127$	0.500748	+	0.577895i	0.0444342	+	0.0512798i	0.777532	−	0.628844i	$-0.216472\pi$
$127$	0.500748	+	0.577895i	0.0444342	+	0.0512798i	−0.733097	+	0.680124i	$0.761926\pi$
$128$	1.71298	−	11.1833i	0.151407	−	0.988471i
$129$	−2.06263	+	4.51652i	−0.181604	+	0.397658i
$130$	2.34388	−	22.6064i	0.205572	−	1.98271i
$131$	−1.78108	−	6.06579i	−0.155614	−	0.529971i	0.844370	−	0.535761i	$-0.179975\pi$
$131$	−1.78108	−	6.06579i	−0.155614	−	0.529971i	−0.999983	+	0.00578998i	$0.998157\pi$
$132$	−7.00490	−	6.89959i	−0.609698	−	0.600532i
$133$	7.01694	−	3.20453i	0.608446	−	0.277868i
$134$	−7.85893	−	11.2280i	−0.678908	−	0.969952i
$135$	−2.09874	+	1.34878i	−0.180631	+	0.116085i
$136$	−3.88635	+	3.20531i	−0.333251	+	0.274853i
$137$	−1.06203			−0.0907357			−0.0453678	−	0.998970i	$-0.514446\pi$
$137$	−1.06203			−0.0907357			−0.0453678	+	0.998970i	$0.514446\pi$
$138$	5.06421	−	4.51151i	0.431095	−	0.384045i
$139$		−	8.91669i		−	0.756304i	−0.925744	−	0.378152i	$-0.876560\pi$
$139$		−	8.91669i		−	0.756304i	0.925744	−	0.378152i	$-0.123440\pi$
$140$	−12.6566	+	2.85383i	−1.06968	+	0.241193i
$141$	4.61372	+	7.17909i	0.388545	+	0.604588i
$142$	6.59850	−	4.61855i	0.553734	−	0.387580i
$143$	−13.1556	−	28.8068i	−1.10013	−	2.40894i
$144$	−3.95021	+	0.629164i	−0.329184	+	0.0524303i
$145$	19.8664	−	5.83331i	1.64982	−	0.484430i
$146$	−1.05041	+	10.1310i	−0.0869323	+	0.838450i
$147$	−0.216898	−	0.0990542i	−0.0178895	−	0.00816985i
$148$	8.57764	+	11.2793i	0.705078	+	0.927153i
$149$	9.19730	−	7.96951i	0.753472	−	0.652887i	−0.190958	−	0.981598i	$-0.561160\pi$
$149$	9.19730	−	7.96951i	0.753472	−	0.652887i	0.944431	+	0.328711i	$0.106614\pi$
$150$	−1.60164	−	0.656327i	−0.130773	−	0.0535889i
$151$	16.3136	+	4.79011i	1.32758	+	0.389813i	0.867223	−	0.497919i	$-0.165902\pi$
$151$	16.3136	+	4.79011i	1.32758	+	0.389813i	0.460359	+	0.887733i	$0.347721\pi$
$152$	6.94630	+	4.70686i	0.563419	+	0.381777i
$153$	1.49833	+	0.962920i	0.121133	+	0.0778474i
$154$	−13.1848	+	12.3690i	−1.06246	+	0.996721i
$155$	−22.1579	−	3.18583i	−1.77977	−	0.255892i
$156$	−12.6095	−	2.64318i	−1.00957	−	0.211623i
$157$	22.2349	−	3.19690i	1.77454	−	0.255140i	0.824187	−	0.566317i	$-0.191632\pi$
$157$	22.2349	−	3.19690i	1.77454	−	0.255140i	0.950352	+	0.311177i	$0.100723\pi$
$158$	−1.14532	−	0.673701i	−0.0911171	−	0.0535968i
$159$	−2.58127	+	2.97894i	−0.204708	+	0.236245i
$160$	−9.81042	−	10.1450i	−0.775582	−	0.802034i
$161$	−7.92121	−	9.63172i	−0.624279	−	0.759086i
$162$	0.637811	+	1.26222i	0.0501111	+	0.0991693i
$163$	5.53347	+	4.79478i	0.433415	+	0.375556i	0.844069	−	0.536235i	$-0.180154\pi$
$163$	5.53347	+	4.79478i	0.433415	+	0.375556i	−0.410654	+	0.911791i	$0.634699\pi$
$164$	0.551715	−	8.63228i	0.0430817	−	0.674068i
$165$	−12.1398	+	1.74544i	−0.945083	+	0.135882i
$166$	6.98076	+	5.58198i	0.541812	+	0.433246i
$167$	−1.01076	+	7.02997i	−0.0782147	+	0.543995i	0.912609	+	0.408834i	$0.134064\pi$
$167$	−1.01076	+	7.02997i	−0.0782147	+	0.543995i	−0.990824	+	0.135162i	$0.956845\pi$
$168$	0.869209	+	7.30321i	0.0670609	+	0.563455i
$169$	−23.9728	−	15.4064i	−1.84406	−	1.18511i
$170$	0.248066	+	6.27899i	0.0190258	+	0.481577i
$171$	0.835787	−	2.84643i	0.0639142	−	0.217672i
$172$	0.783426	+	9.89949i	0.0597357	+	0.754829i
$173$	−11.5461	+	10.0048i	−0.877837	+	0.760650i	−0.972018	−	0.234905i	$-0.924522\pi$
$173$	−11.5461	+	10.0048i	−0.877837	+	0.760650i	0.0941816	+	0.995555i	$0.469977\pi$
$174$	−2.12768	−	11.5426i	−0.161299	−	0.875045i
$175$	−1.32210	+	2.89499i	−0.0999410	+	0.218840i
$176$	−18.9497	−	5.25370i	−1.42839	−	0.396013i
$177$	13.8908	−	4.07872i	1.04410	−	0.306575i
$178$	1.70619	−	0.575060i	0.127884	−	0.0431026i
$179$	18.6525	−	8.51832i	1.39416	−	0.636689i	0.430195	−	0.902736i	$-0.358445\pi$
$179$	18.6525	−	8.51832i	1.39416	−	0.636689i	0.963960	+	0.266047i	$0.0857175\pi$
$180$	−2.35801	+	4.39722i	−0.175756	+	0.327749i
$181$	−1.26051	−	1.96139i	−0.0936927	−	0.145789i	0.791243	−	0.611502i	$-0.209434\pi$
$181$	−1.26051	−	1.96139i	−0.0936927	−	0.145789i	−0.884936	+	0.465713i	$0.845798\pi$
$182$	−5.77145	+	22.9750i	−0.427808	+	1.70302i
$183$	−10.6343			−0.786107
$184$	4.46837	−	12.8076i	0.329412	−	0.944186i
$185$	17.6760			1.29956
$186$	−3.09169	+	12.3074i	−0.226693	+	0.902424i
$187$	4.73383	+	7.36598i	0.346172	+	0.538654i
$188$	15.0414	+	8.06594i	1.09701	+	0.588269i
$189$	2.36531	−	1.08020i	0.172051	−	0.0785732i
$190$	9.91840	−	3.34293i	0.719557	−	0.242522i
$191$	−11.1346	+	3.26942i	−0.805673	+	0.236567i	−0.658536	−	0.752549i	$-0.728824\pi$
$191$	−11.1346	+	3.26942i	−0.805673	+	0.236567i	−0.147137	+	0.989116i	$0.547006\pi$
$192$	−6.29376	+	4.93848i	−0.454213	+	0.356404i
$193$	−4.41382	+	9.66493i	−0.317714	+	0.695697i	−0.999352	−	0.0359929i	$-0.988541\pi$
$193$	−4.41382	+	9.66493i	−0.317714	+	0.695697i	0.681638	+	0.731690i	$0.261268\pi$
$194$	1.91821	+	10.4063i	0.137720	+	0.747125i
$195$	−12.1455	+	10.5242i	−0.869759	+	0.753651i
$196$	−0.475406	+	0.0376227i	−0.0339576	+	0.00268734i
$197$	5.00416	−	17.0426i	0.356531	−	1.21423i	−0.564725	−	0.825279i	$-0.691018\pi$
$197$	5.00416	−	17.0426i	0.356531	−	1.21423i	0.921257	−	0.388955i	$-0.127164\pi$
$198$	0.274458	+	6.94702i	0.0195049	+	0.493704i
$199$	7.18828	+	4.61962i	0.509563	+	0.327476i	0.770031	−	0.638006i	$-0.220241\pi$
$199$	7.18828	+	4.61962i	0.509563	+	0.327476i	−0.260468	+	0.965482i	$0.583877\pi$
$200$	−3.43754	+	0.409127i	−0.243071	+	0.0289297i
$201$	−1.37917	+	9.59236i	−0.0972794	+	0.676593i
$202$	12.9306	+	10.3396i	0.909794	+	0.727493i
$203$	−21.3612	+	3.07128i	−1.49926	+	0.215561i
$204$	3.55489	+	0.227204i	0.248892	+	0.0159074i
$205$	−8.15438	−	7.06581i	−0.569527	−	0.493498i
$206$	−2.25920	−	4.47094i	−0.157406	−	0.311505i
$207$	−4.79424	−	0.123441i	−0.333223	−	0.00857978i
$208$	−24.6106	+	7.63308i	−1.70644	+	0.529259i
$209$	9.55059	−	11.0220i	0.660628	−	0.762405i
$210$	7.90766	+	4.65143i	0.545680	+	0.320979i
$211$	−0.978058	+	0.140624i	−0.0673323	+	0.00968093i	−0.175899	−	0.984408i	$-0.556283\pi$
$211$	−0.978058	+	0.140624i	−0.0673323	+	0.00968093i	0.108566	+	0.994089i	$0.465374\pi$
$212$	−1.61735	+	7.71571i	−0.111080	+	0.529917i
$213$	−5.63726	−	0.810515i	−0.386258	−	0.0555356i
$214$	19.1624	−	17.9767i	1.30991	−	1.22886i
$215$	10.4207	+	6.69699i	0.710687	+	0.456731i
$216$	2.34150	+	1.58662i	0.159319	+	0.107956i
$217$	22.3875	+	6.57355i	1.51976	+	0.446242i
$218$	−9.87284	−	4.04573i	−0.668673	−	0.274012i
$219$	5.44300	−	4.71639i	0.367804	−	0.318704i
$220$	−19.5248	+	14.8482i	−1.31636	+	1.00106i
$221$	10.4365	+	4.76617i	0.702032	+	0.320607i
$222$	1.03335	−	9.96652i	0.0693539	−	0.668909i
$223$	14.3379	−	4.20999i	0.960137	−	0.281922i	0.236135	−	0.971720i	$-0.424119\pi$
$223$	14.3379	−	4.20999i	0.960137	−	0.281922i	0.724001	+	0.689799i	$0.242301\pi$
$224$	8.61642	+	11.9217i	0.575709	+	0.796552i
$225$	0.508440	+	1.11333i	0.0338960	+	0.0742219i
$226$	−14.1287	+	9.88920i	−0.939824	+	0.657820i
$227$	10.2597	+	15.9644i	0.680960	+	1.05959i	0.993950	+	0.109837i	$0.0350330\pi$
$227$	10.2597	+	15.9644i	0.680960	+	1.05959i	−0.312990	+	0.949756i	$0.601331\pi$
$228$	−1.30506	−	5.78789i	−0.0864300	−	0.383312i
$229$			0.817962i			0.0540525i	0.999635	+	0.0270262i	$0.00860377\pi$
$229$			0.817962i			0.0540525i	−0.999635	+	0.0270262i	$0.991396\pi$
$230$	−9.34265	−	14.1073i	−0.616036	−	0.930208i
$231$	12.7834			0.841085
$232$	−14.9360	−	18.1095i	−0.980598	−	1.18895i
$233$	−2.28765	+	1.47019i	−0.149869	+	0.0963151i	−0.613426	−	0.789752i	$-0.710209\pi$
$233$	−2.28765	+	1.47019i	−0.149869	+	0.0963151i	0.463557	+	0.886067i	$0.346573\pi$
$234$	5.22397	+	7.46346i	0.341502	+	0.487902i
$235$	19.3660	−	8.84417i	1.26330	−	0.576930i
$236$	20.3183	−	20.6284i	1.32261	−	1.34280i
$237$	0.264712	+	0.901525i	0.0171949	+	0.0585603i
$238$	0.675463	−	6.51475i	0.0437837	−	0.422288i
$239$	1.95146	−	4.27309i	0.126229	−	0.276403i	−0.835958	−	0.548794i	$-0.815087\pi$
$239$	1.95146	−	4.27309i	0.126229	−	0.276403i	0.962187	+	0.272391i	$0.0878144\pi$
$240$	0.151150	+	9.97798i	0.00975669	+	0.644076i
$241$	1.06439	+	1.22837i	0.0685631	+	0.0791260i	0.788995	−	0.614400i	$-0.210602\pi$
$241$	1.06439	+	1.22837i	0.0685631	+	0.0791260i	−0.720432	+	0.693526i	$0.756056\pi$
$242$	−7.06140	+	17.2320i	−0.453924	+	1.10771i
$243$	0.281733	−	0.959493i	0.0180732	−	0.0615515i
$244$	−18.5892	+	10.3340i	−1.19005	+	0.661567i
$245$	−0.321612	+	0.500438i	−0.0205470	+	0.0319718i
$246$	−4.46074	+	4.18475i	−0.284407	+	0.266810i
$247$	2.71966	−	18.9157i	0.173048	−	1.20357i
$248$	6.55550	+	24.5184i	0.416274	+	1.55692i
$249$	−0.899457	−	6.25586i	−0.0570008	−	0.396449i
$250$	6.75466	−	11.4832i	0.427202	−	0.726264i
$251$	3.66156	+	3.17276i	0.231116	+	0.200263i	0.762718	−	0.646731i	$-0.223864\pi$
$251$	3.66156	+	3.17276i	0.231116	+	0.200263i	−0.531602	+	0.846994i	$0.678410\pi$
$252$	3.08498	−	4.18678i	0.194336	−	0.263742i
$253$	−21.1871	−	10.3430i	−1.33202	−	0.650256i
$254$	−0.487711	−	0.965174i	−0.0306017	−	0.0605604i
$255$	2.90980	−	3.35808i	0.182219	−	0.210291i
$256$	−6.20275	+	14.7488i	−0.387672	+	0.921797i
$257$	−0.351940	−	2.44779i	−0.0219534	−	0.152689i	0.975896	−	0.218235i	$-0.0700301\pi$
$257$	−0.351940	−	2.44779i	−0.0219534	−	0.152689i	−0.997850	+	0.0655463i	$0.979121\pi$
$258$	4.38528	−	5.48417i	0.273015	−	0.341430i
$259$	−18.2360	−	2.62195i	−1.13313	−	0.162920i
$260$	−11.0040	+	30.1993i	−0.682437	+	1.87288i
$261$	−4.48698	+	6.98188i	−0.277737	+	0.432168i
$262$	0.352939	+	8.93351i	0.0218046	+	0.551914i
$263$	5.90435	+	1.73367i	0.364078	+	0.106903i	0.458654	−	0.888615i	$-0.348332\pi$
$263$	5.90435	+	1.73367i	0.364078	+	0.106903i	−0.0945768	+	0.995518i	$0.530150\pi$
$264$	7.23064	+	11.8770i	0.445015	+	0.730980i
$265$	6.43969	+	7.43180i	0.395587	+	0.456532i
$266$	−10.7286	+	1.97762i	−0.657810	+	0.121256i
$267$	−1.15809	−	0.528882i	−0.0708739	−	0.0323670i
$268$	6.91065	+	18.1081i	0.422135	+	1.10613i
$269$	−1.89761	−	6.46268i	−0.115700	−	0.394037i	0.881198	−	0.472748i	$-0.156738\pi$
$269$	−1.89761	−	6.46268i	−0.115700	−	0.394037i	−0.996897	+	0.0787109i	$0.974920\pi$
$270$	3.34336	−	1.12686i	0.203470	−	0.0685784i
$271$	5.51868	+	12.0842i	0.335236	+	0.734064i	0.999915	−	0.0130652i	$-0.00415891\pi$
$271$	5.51868	+	12.0842i	0.335236	+	0.734064i	−0.664679	+	0.747129i	$0.731432\pi$
$272$	6.43491	−	3.05735i	0.390174	−	0.185379i
$273$	14.0915	−	9.05604i	0.852854	−	0.548096i
$274$	1.45668	+	0.365927i	0.0880015	+	0.0221064i
$275$			6.01700i			0.362839i
$276$	−8.50052	+	4.44309i	−0.511671	+	0.267443i
$277$			17.0554i			1.02476i	0.858758	+	0.512381i	$0.171237\pi$
$277$			17.0554i			1.02476i	−0.858758	+	0.512381i	$0.828763\pi$
$278$	−3.07227	+	12.2301i	−0.184262	+	0.733514i
$279$	7.54861	−	4.85119i	0.451923	−	0.290433i
$280$	18.3431	+	0.446550i	1.09621	+	0.0266864i
$281$	5.94061	+	13.0081i	0.354387	+	0.775999i	0.999925	+	0.0122709i	$0.00390603\pi$
$281$	5.94061	+	13.0081i	0.354387	+	0.775999i	−0.645538	+	0.763728i	$0.723367\pi$
$282$	−3.85460	−	11.4365i	−0.229538	−	0.681033i
$283$	1.43324	+	4.88117i	0.0851974	+	0.290156i	0.991060	−	0.133416i	$-0.0425945\pi$
$283$	1.43324	+	4.88117i	0.0851974	+	0.290156i	−0.905863	+	0.423571i	$0.860776\pi$
$284$	−10.6418	+	4.06127i	−0.631476	+	0.240992i
$285$	−6.73220	−	3.07449i	−0.398781	−	0.182117i
$286$	8.11876	+	44.0441i	0.480073	+	2.60438i
$287$	7.36467	+	8.49928i	0.434722	+	0.501696i
$288$	5.63488	+	0.498095i	0.332039	+	0.0293505i
$289$	13.2677	+	3.89574i	0.780451	+	0.229161i
$290$	−29.2587	+	1.15593i	−1.71813	+	0.0678785i
$291$	4.04524	−	6.29451i	0.237136	−	0.368991i
$292$	4.93141	−	13.5338i	0.288589	−	0.792005i
$293$	−1.93509	−	0.278224i	−0.113049	−	0.0162540i	0.0855581	−	0.996333i	$-0.472733\pi$
$293$	−1.93509	−	0.278224i	−0.113049	−	0.0162540i	−0.198607	+	0.980079i	$0.563642\pi$
$294$	0.263368	+	0.210596i	0.0153599	+	0.0122822i
$295$	−5.14007	−	35.7500i	−0.299267	−	2.08145i
$296$	−7.87877	−	18.4261i	−0.457944	−	1.07100i
$297$	3.21937	−	3.71536i	0.186807	−	0.215587i
$298$	−15.3609	+	7.76201i	−0.889834	+	0.449641i
$299$	−30.6823	+	3.60809i	−1.77440	+	0.208661i
$300$	1.97067	+	1.45207i	0.113777	+	0.0838352i
$301$	−9.75752	−	8.45494i	−0.562414	−	0.487335i
$302$	−20.7253	−	12.1910i	−1.19261	−	0.701513i
$303$	−1.66608	−	11.5879i	−0.0957139	−	0.665705i
$304$	−7.90578	−	8.84929i	−0.453427	−	0.507542i
$305$	−3.77564	+	26.2601i	−0.216192	+	1.50365i
$306$	−1.72333	−	1.83699i	−0.0985165	−	0.105014i
$307$	−5.82245	+	9.05991i	−0.332305	+	0.517077i	−0.966693	−	0.255938i	$-0.917616\pi$
$307$	−5.82245	+	9.05991i	−0.332305	+	0.517077i	0.634388	+	0.773015i	$0.281252\pi$
$308$	22.3460	−	12.4224i	1.27328	−	0.707834i
$309$	−0.997931	+	3.39864i	−0.0567703	+	0.193342i
$310$	29.2941	+	12.0043i	1.66379	+	0.681796i
$311$	−9.14397	−	10.5527i	−0.518507	−	0.598389i	0.434750	−	0.900551i	$-0.356837\pi$
$311$	−9.14397	−	10.5527i	−0.518507	−	0.598389i	−0.953256	+	0.302163i	$0.902291\pi$
$312$	16.3845	+	7.97002i	0.927589	+	0.451214i
$313$	−9.66041	+	21.1534i	−0.546039	+	1.19566i	0.412569	+	0.910927i	$0.364632\pi$
$313$	−9.66041	+	21.1534i	−0.546039	+	1.19566i	−0.958607	+	0.284732i	$0.908096\pi$
$314$	−31.5989	−	3.27624i	−1.78323	−	0.184889i
$315$	−1.82765	−	6.22440i	−0.102976	−	0.350705i
$316$	1.33880	+	1.31867i	0.0753133	+	0.0741811i
$317$	9.37272	−	4.28038i	0.526424	−	0.240410i	−0.134431	−	0.990923i	$-0.542921\pi$
$317$	9.37272	−	4.28038i	0.526424	−	0.240410i	0.660856	+	0.750513i	$0.270194\pi$
$318$	4.56686	−	3.19653i	0.256097	−	0.179252i
$319$	−34.3238	+	22.0586i	−1.92176	+	1.23504i
$320$	9.96047	+	17.2951i	0.556807	+	0.966826i
$321$	−18.5790			−1.03698
$322$	7.54609	+	15.9401i	0.420527	+	0.888309i
$323$			5.28372i			0.293994i
$324$	−0.439919	−	1.95102i	−0.0244400	−	0.108390i
$325$	4.26258	+	6.63270i	0.236445	+	0.367916i
$326$	−5.93765	−	8.48309i	−0.328856	−	0.469835i
$327$	3.13413	+	6.86278i	0.173318	+	0.379513i
$328$	−3.73101	+	11.6499i	−0.206010	+	0.643260i
$329$	−21.2915	+	6.25176i	−1.17384	+	0.344671i
$330$	17.2523	+	1.78876i	0.949710	+	0.0984679i
$331$	−8.60315	−	3.92893i	−0.472872	−	0.215953i	0.164701	−	0.986344i	$-0.447334\pi$
$331$	−8.60315	−	3.92893i	−0.472872	−	0.215953i	−0.637573	+	0.770390i	$0.720061\pi$
$332$	−7.65152	−	10.0615i	−0.419932	−	0.552196i
$333$	−5.35462	+	4.63980i	−0.293431	+	0.254260i
$334$	3.80855	−	9.29404i	0.208394	−	0.508547i
$335$	23.1976	+	6.81143i	1.26742	+	0.372148i
$336$	1.32414	−	10.3166i	0.0722375	−	0.562815i
$337$	−11.7394	−	7.54444i	−0.639484	−	0.410972i	0.180326	−	0.983607i	$-0.442285\pi$
$337$	−11.7394	−	7.54444i	−0.639484	−	0.410972i	−0.819810	+	0.572635i	$0.805921\pi$
$338$	27.5728	+	29.3913i	1.49976	+	1.59868i
$339$	12.0704	+	1.73547i	0.655577	+	0.0942577i
$340$	1.82320	−	8.69773i	0.0988768	−	0.471701i
$341$	43.6636	−	6.27787i	2.36451	−	0.339966i
$342$	−2.12711	+	3.61619i	−0.115021	+	0.195541i
$343$	12.3259	−	14.2248i	0.665534	−	0.768068i
$344$	2.33635	−	13.8481i	0.125968	−	0.746637i
$345$	−2.00699	+	11.7950i	−0.108053	+	0.635022i
$346$	19.2838	−	9.74430i	1.03671	−	0.523857i
$347$	−9.33432	−	8.08823i	−0.501092	−	0.434199i	0.367281	−	0.930110i	$-0.380289\pi$
$347$	−9.33432	−	8.08823i	−0.501092	−	0.434199i	−0.868373	+	0.495911i	$0.834834\pi$
$348$	−1.05872	+	16.5650i	−0.0567532	+	0.887975i
$349$	−28.6029	+	4.11248i	−1.53108	+	0.220136i	−0.855753	−	0.517384i	$-0.826906\pi$
$349$	−28.6029	+	4.11248i	−1.53108	+	0.220136i	−0.675325	+	0.737520i	$0.735997\pi$
$350$	2.81086	−	3.51523i	0.150247	−	0.187897i
$351$	0.916761	−	6.37621i	0.0489331	−	0.340337i
$352$	24.1812	+	13.7351i	1.28886	+	0.732085i
$353$	−9.74320	−	6.26157i	−0.518578	−	0.333270i	0.255031	−	0.966933i	$-0.417914\pi$
$353$	−9.74320	−	6.26157i	−0.518578	−	0.333270i	−0.773609	+	0.633663i	$0.781551\pi$
$354$	−20.4580	+	0.808239i	−1.08733	+	0.0429574i
$355$	−4.00295	+	13.6328i	−0.212455	+	0.723554i
$356$	−2.53834	+	0.200880i	−0.134532	+	0.0106466i
$357$	−3.50012	+	3.03287i	−0.185246	+	0.160516i
$358$	−28.5188	+	5.25694i	−1.50727	+	0.277838i
$359$	5.26744	−	11.5341i	0.278005	−	0.608745i	−0.718195	−	0.695842i	$-0.755031\pi$
$359$	5.26744	−	11.5341i	0.278005	−	0.608745i	0.996200	+	0.0870963i	$0.0277588\pi$
$360$	4.74931	−	5.21876i	0.250311	−	0.275053i
$361$	−9.78615	+	2.87347i	−0.515061	+	0.151235i
$362$	1.05311	+	3.12455i	0.0553502	+	0.164223i
$363$	11.9783	−	5.47028i	0.628695	−	0.287115i
$364$	15.8322	−	29.5240i	0.829834	−	1.54748i
$365$	−9.71408	−	15.1154i	−0.508458	−	0.791176i
$366$	14.5859	+	3.66406i	0.762419	+	0.191524i
$367$	27.1188			1.41559			0.707795	−	0.706418i	$-0.249690\pi$
$367$	27.1188			1.41559			0.707795	+	0.706418i	$0.249690\pi$
$368$	−10.5417	+	16.0273i	−0.549523	+	0.835478i
$369$	4.32495			0.225148
$370$	−24.2443	−	6.09030i	−1.26040	−	0.316619i
$371$	−5.54135	−	8.62251i	−0.287693	−	0.447659i
$372$	8.48111	−	15.8156i	0.439725	−	0.820000i
$373$	4.61647	−	2.10827i	0.239032	−	0.109162i	−0.292298	−	0.956327i	$-0.594420\pi$
$373$	4.61647	−	2.10827i	0.239032	−	0.109162i	0.531330	+	0.847165i	$0.321693\pi$
$374$	−3.95495	−	11.7342i	−0.204505	−	0.606762i
$375$	−9.03887	+	2.65405i	−0.466765	+	0.137055i
$376$	−17.8516	−	16.2458i	−0.920626	−	0.837812i
$377$	−22.2093	+	48.6315i	−1.14383	+	2.50465i
$378$	−3.61645	+	0.666630i	−0.186010	+	0.0342877i
$379$	−13.4409	+	11.6466i	−0.690412	+	0.598245i	−0.927759	−	0.373180i	$-0.878268\pi$
$379$	−13.4409	+	11.6466i	−0.690412	+	0.598245i	0.237347	+	0.971425i	$0.423722\pi$
$380$	−14.7559	+	1.16775i	−0.756961	+	0.0599044i
$381$	−0.215431	+	0.733690i	−0.0110369	+	0.0375881i
$382$	16.3987	−	0.647869i	0.839032	−	0.0331478i
$383$	−18.6265	−	11.9705i	−0.951769	−	0.611665i	−0.0300603	−	0.999548i	$-0.509570\pi$
$383$	−18.6265	−	11.9705i	−0.951769	−	0.611665i	−0.921708	+	0.387884i	$0.873206\pi$
$384$	10.3341	−	4.60509i	0.527359	−	0.235002i
$385$	4.53867	−	31.5671i	0.231312	−	1.60881i
$386$	9.38407	−	11.7356i	0.477637	−	0.597327i
$387$	−4.91468	+	0.706624i	−0.249827	+	0.0359197i
$388$	0.954486	−	14.9341i	0.0484567	−	0.758165i
$389$	−2.34444	−	2.03147i	−0.118868	−	0.103000i	0.593399	−	0.804909i	$-0.297786\pi$
$389$	−2.34444	−	2.03147i	−0.118868	−	0.103000i	−0.712266	+	0.701909i	$0.752331\pi$
$390$	20.2849	−	10.2502i	1.02717	−	0.519037i
$391$	8.25494	−	2.19473i	0.417470	−	0.110992i
$392$	0.665030	+	0.112199i	0.0335891	+	0.00566692i
$393$	4.13995	−	4.77775i	0.208833	−	0.241006i
$394$	−12.7358	+	21.6514i	−0.641619	+	1.09078i
$395$	2.32020	−	0.333594i	0.116742	−	0.0167850i
$396$	2.01717	−	9.62310i	0.101367	−	0.483579i
$397$	−9.15193	−	1.31585i	−0.459322	−	0.0660406i	−0.0912301	−	0.995830i	$-0.529080\pi$
$397$	−9.15193	−	1.31585i	−0.459322	−	0.0660406i	−0.368092	+	0.929789i	$0.619989\pi$
$398$	−8.26773	−	8.81301i	−0.414424	−	0.441756i
$399$	6.48946	+	4.17053i	0.324880	+	0.208787i
$400$	4.85590	+	0.623256i	0.242795	+	0.0311628i
$401$	15.7838	+	4.63454i	0.788205	+	0.231438i	0.650973	−	0.759101i	$-0.274361\pi$
$401$	15.7838	+	4.63454i	0.788205	+	0.231438i	0.137232	+	0.990539i	$0.456179\pi$
$402$	5.19675	−	12.6817i	0.259190	−	0.632504i
$403$	43.6841	−	37.8525i	2.17606	−	1.88557i
$404$	−14.1731	−	18.6371i	−0.705136	−	0.927230i
$405$	−2.26933	−	1.03637i	−0.112764	−	0.0514976i
$406$	30.3572	+	3.14750i	1.50660	+	0.156208i
$407$	−33.4206	+	9.81318i	−1.65660	+	0.486421i
$408$	−4.79760	−	1.53648i	−0.237516	−	0.0760670i
$409$	−9.56672	−	20.9482i	−0.473044	−	1.03582i	−0.984318	−	0.176404i	$-0.943554\pi$
$409$	−9.56672	−	20.9482i	−0.473044	−	1.03582i	0.511274	−	0.859418i	$-0.329174\pi$
$410$	8.75000	+	12.5011i	0.432132	+	0.617384i
$411$	−0.574179	−	0.893440i	−0.0283222	−	0.0440701i
$412$	1.55825	+	6.91075i	0.0767694	+	0.340468i
$413$			37.6452i			1.85240i
$414$	6.53325	+	1.82118i	0.321092	+	0.0895062i
$415$	−15.7675			−0.773996
$416$	36.3859	−	1.98988i	1.78396	−	0.0975620i
$417$	7.50120	−	4.82073i	0.367335	−	0.236072i
$418$	−16.8972	+	11.8270i	−0.826470	+	0.578479i
$419$	15.9425	−	7.28070i	0.778842	−	0.355685i	0.0139993	−	0.999902i	$-0.495544\pi$
$419$	15.9425	−	7.28070i	0.778842	−	0.355685i	0.764843	+	0.644217i	$0.222816\pi$
$420$	−9.24347	−	9.10451i	−0.451035	−	0.444254i
$421$	11.0122	+	37.5040i	0.536701	+	1.82784i	0.560551	+	0.828120i	$0.310589\pi$
$421$	11.0122	+	37.5040i	0.536701	+	1.82784i	−0.0238500	+	0.999716i	$0.507592\pi$
$422$	1.38996	+	0.144114i	0.0676620	+	0.00701534i
$423$	−3.54507	+	7.76261i	−0.172367	+	0.377431i
$424$	4.87682	−	10.0256i	0.236840	−	0.486886i
$425$	−1.42754	−	1.64747i	−0.0692458	−	0.0799139i
$426$	7.45279	+	3.05403i	0.361089	+	0.147968i
$427$	7.79054	−	26.5321i	0.377011	−	1.28398i
$428$	−32.4770	+	18.0544i	−1.56984	+	0.872694i
$429$	17.1213	−	26.6413i	0.826625	−	1.28625i
$430$	−11.9856	−	12.7761i	−0.577996	−	0.616117i
$431$	3.11827	−	21.6881i	0.150202	−	1.04468i	−0.765678	−	0.643225i	$-0.777596\pi$
$431$	3.11827	−	21.6881i	0.150202	−	1.04468i	0.915880	−	0.401453i	$-0.131495\pi$
$432$	−2.66493	−	2.98298i	−0.128217	−	0.143518i
$433$	1.91696	+	13.3328i	0.0921233	+	0.640731i	0.982604	+	0.185711i	$0.0594589\pi$
$433$	1.91696	+	13.3328i	0.0921233	+	0.640731i	−0.890481	+	0.455020i	$0.849632\pi$
$434$	−28.4417	−	16.7299i	−1.36524	−	0.803063i
$435$	15.6479	+	13.5590i	0.750259	+	0.650104i
$436$	12.1476	+	8.95084i	0.581765	+	0.428667i
$437$	−7.38124	−	12.1628i	−0.353093	−	0.581825i
$438$	−9.09066	+	4.59359i	−0.434368	+	0.219490i
$439$	11.3308	−	13.0764i	0.540790	−	0.624104i	−0.417923	−	0.908483i	$-0.637242\pi$
$439$	11.3308	−	13.0764i	0.540790	−	0.624104i	0.958712	+	0.284378i	$0.0917872\pi$
$440$	31.8962	−	13.6384i	1.52059	−	0.650184i
$441$	−0.0339345	−	0.236019i	−0.00161593	−	0.0112390i
$442$	−12.6724	−	10.1332i	−0.602766	−	0.481986i
$443$	3.13276	+	0.450424i	0.148842	+	0.0214003i	0.216333	−	0.976320i	$-0.430590\pi$
$443$	3.13276	+	0.450424i	0.148842	+	0.0214003i	−0.0674910	+	0.997720i	$0.521499\pi$
$444$	−4.85133	+	13.3140i	−0.230234	+	0.631856i
$445$	−1.71719	+	2.67199i	−0.0814025	+	0.126665i
$446$	−21.1164	+	0.834251i	−0.999891	+	0.0395029i
$447$	11.6768	+	3.42862i	0.552294	+	0.162168i
$448$	−7.71062	−	19.3206i	−0.364293	−	0.912813i
$449$	0.393845	+	0.454521i	0.0185867	+	0.0214502i	0.764967	−	0.644070i	$-0.222755\pi$
$449$	0.393845	+	0.454521i	0.0185867	+	0.0214502i	−0.746380	+	0.665520i	$0.768210\pi$
$450$	−0.313775	−	1.70222i	−0.0147915	−	0.0802436i
$451$	19.3406	+	8.83254i	0.910711	+	0.415908i
$452$	22.7862	−	8.69595i	1.07177	−	0.409023i
$453$	4.79011	+	16.3136i	0.225059	+	0.766480i
$454$	−8.57161	−	25.4317i	−0.402285	−	1.19357i
$455$	−17.3598	−	38.0126i	−0.813838	−	1.78206i
$456$	−0.204208	+	8.38832i	−0.00956292	+	0.392819i
$457$	25.5683	−	16.4318i	1.19604	−	0.768646i	0.217770	−	0.976000i	$-0.430122\pi$
$457$	25.5683	−	16.4318i	1.19604	−	0.768646i	0.978266	+	0.207354i	$0.0664853\pi$
$458$	0.281831	−	1.12192i	0.0131691	−	0.0524237i
$459$			1.78107i			0.0831333i
$460$	7.95366	+	22.5686i	0.370841	+	1.05227i
$461$			22.3125i			1.03920i	0.854410	+	0.519599i	$0.173919\pi$
$461$			22.3125i			1.03920i	−0.854410	+	0.519599i	$0.826081\pi$
$462$	−17.5337	−	4.40455i	−0.815740	−	0.204918i
$463$	24.5615	−	15.7847i	1.14147	−	0.733577i	0.173546	−	0.984826i	$-0.444477\pi$
$463$	24.5615	−	15.7847i	1.14147	−	0.733577i	0.967923	+	0.251248i	$0.0808411\pi$
$464$	14.2466	+	29.9852i	0.661380	+	1.39203i
$465$	−9.29939	−	20.3628i	−0.431249	−	0.944303i
$466$	3.64430	−	1.22829i	0.168819	−	0.0568993i
$467$	0.287045	+	0.977585i	0.0132828	+	0.0452372i	0.965868	−	0.259036i	$-0.0834047\pi$
$467$	0.287045	+	0.977585i	0.0132828	+	0.0452372i	−0.952585	+	0.304273i	$0.901587\pi$
$468$	−4.59364	−	12.0368i	−0.212341	−	0.556402i
$469$	−22.9223	−	10.4682i	−1.05845	−	0.483379i
$470$	−29.6097	+	5.45803i	−1.36579	+	0.251760i
$471$	14.7105	+	16.9768i	0.677824	+	0.782251i
$472$	−34.9761	+	21.2932i	−1.60991	+	0.980099i
$473$	−23.4209	−	6.87698i	−1.07689	−	0.316204i
$474$	−0.0524553	−	1.32774i	−0.00240935	−	0.0609850i
$475$	−1.96302	+	3.05452i	−0.0900696	+	0.140151i
$476$	−3.17114	+	8.70289i	−0.145349	+	0.398896i
$477$	−3.90158	−	0.560963i	−0.178641	−	0.0256847i
$478$	−4.14892	+	5.18859i	−0.189767	+	0.237321i
$479$	−0.341375	−	2.37431i	−0.0155978	−	0.108485i	0.980535	−	0.196344i	$-0.0629068\pi$
$479$	−0.341375	−	2.37431i	−0.0155978	−	0.108485i	−0.996133	+	0.0878584i	$0.971998\pi$
$480$	3.23062	−	13.7379i	0.147457	−	0.627045i
$481$	−29.8886	+	34.4933i	−1.36280	+	1.57276i
$482$	−1.03667	−	2.05156i	−0.0472192	−	0.0934461i
$483$	3.82019	−	11.8711i	0.173825	−	0.540152i
$484$	15.6227	−	21.2024i	0.710124	−	0.963744i
$485$	−14.1073	−	12.2241i	−0.640582	−	0.555067i
$486$	−0.717020	+	1.21897i	−0.0325247	+	0.0552935i
$487$	0.0974437	+	0.677736i	0.00441560	+	0.0307111i	0.991910	−	0.126942i	$-0.0405163\pi$
$487$	0.0974437	+	0.677736i	0.00441560	+	0.0307111i	−0.987495	+	0.157653i	$0.949607\pi$
$488$	29.0575	−	7.76914i	1.31537	−	0.351693i
$489$	−1.04201	+	7.24731i	−0.0471211	+	0.327735i
$490$	0.613550	−	0.575588i	0.0277173	−	0.0260024i
$491$	20.6265	−	32.0954i	0.930859	−	1.44845i	0.0374007	−	0.999300i	$-0.488092\pi$
$491$	20.6265	−	32.0954i	0.930859	−	1.44845i	0.893459	−	0.449145i	$-0.148271\pi$
$492$	7.56022	−	4.20283i	0.340841	−	0.189478i
$493$	4.16451	−	14.1830i	0.187560	−	0.638771i
$494$	−10.2477	+	25.0076i	−0.461067	+	1.12515i
$495$	−8.03163	−	9.26900i	−0.360995	−	0.416611i
$496$	−0.543645	−	35.8881i	−0.0244104	−	1.61142i
$497$	6.15200	−	13.4710i	0.275955	−	0.604257i
$498$	−0.921779	+	8.89044i	−0.0413059	+	0.398390i
$499$	10.2975	+	35.0701i	0.460980	+	1.56995i	0.782250	+	0.622965i	$0.214072\pi$
$499$	10.2975	+	35.0701i	0.460980	+	1.56995i	−0.321270	+	0.946988i	$0.604110\pi$
$500$	−13.2213	+	13.4231i	−0.591273	+	0.600298i
$501$	−6.46044	+	2.95039i	−0.288631	+	0.131813i
$502$	−3.92901	−	5.61336i	−0.175360	−	0.250537i
$503$	11.4471	−	7.35660i	0.510401	−	0.328015i	−0.259964	−	0.965618i	$-0.583711\pi$
$503$	11.4471	−	7.35660i	0.510401	−	0.328015i	0.770365	+	0.637604i	$0.220074\pi$
$504$	−5.67392	+	4.67964i	−0.252737	+	0.208448i
$505$	−29.2064			−1.29967
$506$	25.4965	+	21.4865i	1.13346	+	0.955190i
$507$		−	28.4966i		−	1.26558i
$508$	0.336390	+	1.49187i	0.0149249	+	0.0661912i
$509$	5.41814	+	8.43080i	0.240155	+	0.373689i	0.940319	−	0.340293i	$-0.110526\pi$
$509$	5.41814	+	8.43080i	0.240155	+	0.373689i	−0.700164	+	0.713982i	$0.746890\pi$
$510$	−5.14811	+	3.60337i	−0.227962	+	0.159560i
$511$	7.77975	+	17.0353i	0.344156	+	0.753597i
$512$	13.5894	−	18.0922i	0.600573	−	0.799570i
$513$	2.84643	−	0.835787i	0.125673	−	0.0369009i
$514$	−0.360674	+	3.47865i	−0.0159086	+	0.153437i
$515$	8.03826	+	3.67095i	0.354208	+	0.161761i
$516$	−7.90443	+	6.01113i	−0.347973	+	0.264625i
$517$	−31.7061	+	27.4735i	−1.39443	+	1.20828i
$518$	24.1091	+	9.87953i	1.05929	+	0.434082i
$519$	−14.6589	−	4.30423i	−0.643453	−	0.188935i
$520$	25.4983	−	37.6299i	1.11817	−	1.65018i
$521$	22.1454	+	14.2320i	0.970207	+	0.623514i	0.926805	−	0.375544i	$-0.122544\pi$
$521$	22.1454	+	14.2320i	0.970207	+	0.623514i	0.0434020	+	0.999058i	$0.486180\pi$
$522$	8.55997	−	8.03034i	0.374660	−	0.351479i
$523$	−18.6887	−	2.68703i	−0.817200	−	0.117496i	−0.278977	−	0.960298i	$-0.589995\pi$
$523$	−18.6887	−	2.68703i	−0.817200	−	0.117496i	−0.538224	+	0.842802i	$0.680904\pi$
$524$	2.59398	−	12.3748i	0.113318	−	0.540596i
$525$	−3.15020	+	0.452930i	−0.137486	+	0.0197675i
$526$	−7.50105	−	4.41226i	−0.327061	−	0.192384i
$527$	−10.4657	+	12.0781i	−0.455895	+	0.526131i
$528$	−5.82527	−	18.7819i	−0.253513	−	0.817375i
$529$	−15.9364	+	16.5841i	−0.692885	+	0.721048i
$530$	−6.27203	−	12.4123i	−0.272439	−	0.539154i
$531$	10.9412	+	9.48060i	0.474807	+	0.411423i
$532$	15.3967	+	0.984048i	0.667530	+	0.0426639i
$533$	27.5768	−	3.96494i	1.19448	−	0.171741i
$534$	1.40621	+	1.12444i	0.0608525	+	0.0486591i
$535$	−6.59637	+	45.8788i	−0.285186	+	1.98351i
$536$	−3.23944	−	27.2182i	−0.139922	−	1.17565i
$537$	17.2504	+	11.0861i	0.744409	+	0.478403i
$538$	0.376031	+	9.51804i	0.0162119	+	0.410352i
$539$	0.330256	−	1.12475i	0.0142251	−	0.0484463i
$540$	−4.97401	+	0.393633i	−0.214047	+	0.0169393i
$541$	25.2084	−	21.8432i	1.08379	−	0.939113i	0.0854332	−	0.996344i	$-0.472773\pi$
$541$	25.2084	−	21.8432i	1.08379	−	0.939113i	0.998361	+	0.0572309i	$0.0182271\pi$
$542$	−3.40576	−	18.4762i	−0.146290	−	0.793620i
$543$	0.968542	−	2.12081i	0.0415641	−	0.0910127i
$544$	−9.87953	+	1.97630i	−0.423581	+	0.0847330i
$545$	18.0596	−	5.30278i	0.773589	−	0.227146i
$546$	−22.4481	+	7.56600i	−0.960691	+	0.323795i
$547$	4.52157	−	2.06493i	0.193328	−	0.0882900i	−0.316399	−	0.948626i	$-0.602474\pi$
$547$	4.52157	−	2.06493i	0.193328	−	0.0882900i	0.509727	+	0.860336i	$0.329746\pi$
$548$	−1.87191	−	1.00381i	−0.0799638	−	0.0428806i
$549$	−5.74932	−	8.94611i	−0.245375	−	0.381811i
$550$	2.07317	−	8.25291i	0.0884004	−	0.351905i
$551$	−24.6209			−1.04889
$552$	13.1902	−	3.16526i	0.561412	−	0.134723i
$553$	−2.44320			−0.103895
$554$	5.87650	−	23.3932i	0.249669	−	0.993883i
$555$	9.55634	+	14.8700i	0.405644	+	0.631195i
$556$	8.42784	−	15.7163i	0.357420	−	0.666518i
$557$	0.148531	−	0.0678319i	0.00629347	−	0.00287413i	−0.412266	−	0.911064i	$-0.635262\pi$
$557$	0.148531	−	0.0678319i	0.00629347	−	0.00287413i	0.418559	+	0.908189i	$0.362535\pi$
$558$	−12.0252	+	4.05300i	−0.509065	+	0.171577i
$559$	−30.6893	+	9.01118i	−1.29802	+	0.381132i
$560$	−25.0055	−	6.93264i	−1.05667	−	0.292958i
$561$	−3.63736	+	7.96470i	−0.153569	+	0.336270i
$562$	−3.66615	−	19.8888i	−0.154647	−	0.838957i
$563$	−20.9140	+	18.1221i	−0.881420	+	0.763755i	−0.972699	−	0.232071i	$-0.925450\pi$
$563$	−20.9140	+	18.1221i	−0.881420	+	0.763755i	0.0912791	+	0.995825i	$0.470904\pi$
$564$	1.34649	+	17.0144i	0.0566973	+	0.716435i
$565$	8.57109	−	29.1904i	0.360588	−	1.22805i
$566$	−0.284011	−	7.18884i	−0.0119379	−	0.302169i
$567$	2.18751	+	1.40583i	0.0918668	+	0.0590392i
$568$	15.9956	−	1.90376i	0.671162	−	0.0798800i
$569$	−3.43240	+	23.8728i	−0.143894	+	1.00080i	0.782070	+	0.623190i	$0.214164\pi$
$569$	−3.43240	+	23.8728i	−0.143894	+	1.00080i	−0.925964	+	0.377612i	$0.876745\pi$
$570$	8.17455	+	6.53657i	0.342394	+	0.273787i
$571$	5.55222	−	0.798289i	0.232353	−	0.0334074i	−0.0251545	−	0.999684i	$-0.508008\pi$
$571$	5.55222	−	0.798289i	0.232353	−	0.0334074i	0.257508	+	0.966276i	$0.417099\pi$
$572$	4.03983	−	63.2082i	0.168914	−	2.64287i
$573$	−8.77024	−	7.59946i	−0.366382	−	0.317472i
$574$	−7.17292	−	14.1951i	−0.299392	−	0.592493i
$575$	5.58758	+	1.79812i	0.233018	+	0.0749869i
$576$	−7.55718	−	2.62470i	−0.314882	−	0.109363i
$577$	−9.52665	+	10.9943i	−0.396600	+	0.457701i	−0.918567	−	0.395265i	$-0.870653\pi$
$577$	−9.52665	+	10.9943i	−0.396600	+	0.457701i	0.521967	+	0.852965i	$0.325198\pi$
$578$	−16.8556	−	9.91480i	−0.701102	−	0.412401i
$579$	−10.5169	+	1.51211i	−0.437069	+	0.0628411i
$580$	40.5294	+	8.49568i	1.68289	+	0.352764i
$581$	16.2671	+	2.33886i	0.674873	+	0.0970321i
$582$	−7.71723	+	7.23975i	−0.319890	+	0.300097i
$583$	−16.3017	−	10.4765i	−0.675148	−	0.433891i
$584$	−11.4270	+	16.8638i	−0.472853	+	0.697829i
$585$	−15.4199	−	4.52768i	−0.637533	−	0.187196i
$586$	2.55830	+	1.04835i	0.105682	+	0.0433070i
$587$	−10.4445	+	9.05017i	−0.431089	+	0.373541i	−0.843206	−	0.537590i	$-0.819335\pi$
$587$	−10.4445	+	9.05017i	−0.431089	+	0.373541i	0.412117	+	0.911131i	$0.364789\pi$
$588$	−0.288674	−	0.379597i	−0.0119047	−	0.0156543i
$589$	24.2139	+	11.0581i	0.997715	+	0.455641i
$590$	−5.26764	+	50.8057i	−0.216865	+	2.09164i
$591$	17.0426	−	5.00416i	0.701038	−	0.205843i
$592$	4.45773	+	27.9879i	0.183212	+	1.15030i
$593$	10.6045	+	23.2206i	0.435474	+	0.953555i	0.992407	+	0.122998i	$0.0392508\pi$
$593$	10.6045	+	23.2206i	0.435474	+	0.953555i	−0.556933	+	0.830557i	$0.688022\pi$
$594$	−5.69583	+	3.98673i	−0.233703	+	0.163578i
$595$	6.24663	+	9.71995i	0.256087	+	0.398479i
$596$	23.7434	−	5.35372i	0.972570	−	0.219297i
$597$			8.54472i			0.349712i
$598$	43.3270	+	5.62282i	1.77177	+	0.229934i
$599$	24.3980			0.996877			0.498438	−	0.866925i	$-0.333907\pi$
$599$	24.3980			0.996877			0.498438	+	0.866925i	$0.333907\pi$
$600$	−2.20266	−	2.67065i	−0.0899230	−	0.109029i
$601$	13.7405	−	8.83047i	0.560486	−	0.360202i	−0.229518	−	0.973304i	$-0.573715\pi$
$601$	13.7405	−	8.83047i	0.560486	−	0.360202i	0.790004	+	0.613102i	$0.210079\pi$
$602$	10.4702	+	14.9588i	0.426735	+	0.609674i
$603$	−8.81524	+	4.02579i	−0.358984	+	0.163943i
$604$	24.2263	+	23.8621i	0.985755	+	0.970936i
$605$	−9.25544	−	31.5211i	−0.376287	−	1.28152i
$606$	−1.70743	+	16.4679i	−0.0693596	+	0.668964i
$607$	−7.33012	+	16.0507i	−0.297520	+	0.651479i	−0.998068	−	0.0621266i	$-0.980212\pi$
$607$	−7.33012	+	16.0507i	−0.297520	+	0.651479i	0.700548	+	0.713605i	$0.252939\pi$
$608$	7.79451	+	14.8616i	0.316109	+	0.602719i
$609$	−14.1325	−	16.3097i	−0.572676	−	0.660904i
$610$	14.2267	−	34.7174i	0.576020	−	1.40567i
$611$	−15.4876	+	52.7461i	−0.626563	+	2.13388i
$612$	1.73078	+	3.11340i	0.0699627	+	0.125852i
$613$	8.07873	−	12.5707i	0.326297	−	0.507728i	−0.638887	−	0.769301i	$-0.720605\pi$
$613$	8.07873	−	12.5707i	0.326297	−	0.507728i	0.965184	+	0.261573i	$0.0842412\pi$
$614$	11.1077	−	10.4204i	0.448270	−	0.420534i
$615$	1.53555	−	10.6800i	0.0619193	−	0.430658i
$616$	−34.9299	+	9.33924i	−1.40737	+	0.376289i
$617$	−0.423933	−	2.94852i	−0.0170669	−	0.118703i	0.979507	−	0.201410i	$-0.0645524\pi$
$617$	−0.423933	−	2.94852i	−0.0170669	−	0.118703i	−0.996574	+	0.0827074i	$0.973643\pi$
$618$	2.53977	−	4.31773i	0.102165	−	0.173685i
$619$	−24.6741	−	21.3803i	−0.991737	−	0.859345i	−0.00167853	−	0.999999i	$-0.500534\pi$
$619$	−24.6741	−	21.3803i	−0.991737	−	0.859345i	−0.990059	+	0.140653i	$0.955080\pi$
$620$	−36.0437	−	26.5584i	−1.44755	−	1.06661i
$621$	−2.48812	−	4.09991i	−0.0998447	−	0.164524i
$622$	8.90589	+	17.6246i	0.357094	+	0.706684i
$623$	2.16795	−	2.50194i	0.0868569	−	0.100238i
$624$	−19.7268	−	16.5770i	−0.789706	−	0.663611i
$625$	4.21560	+	29.3201i	0.168624	+	1.17281i
$626$	20.5387	−	25.6854i	0.820890	−	1.02659i
$627$	14.4357	+	2.07554i	0.576507	+	0.0828891i
$628$	42.2122	+	15.3812i	1.68445	+	0.613775i
$629$	6.82245	−	10.6159i	0.272029	−	0.423285i
$630$	0.362167	+	9.16710i	0.0144291	+	0.365226i
$631$	−16.7757	−	4.92578i	−0.667829	−	0.196092i	−0.0697928	−	0.997562i	$-0.522234\pi$
$631$	−16.7757	−	4.92578i	−0.667829	−	0.196092i	−0.598036	+	0.801469i	$0.704052\pi$
$632$	−1.38194	−	2.26998i	−0.0549708	−	0.0902948i
$633$	−0.647078	−	0.746768i	−0.0257191	−	0.0296814i
$634$	−14.3304	+	2.64156i	−0.569134	+	0.104910i
$635$	1.73528	+	0.792474i	0.0688624	+	0.0314484i
$636$	−7.36528	+	2.81083i	−0.292052	+	0.111457i
$637$	−0.432747	−	1.47380i	−0.0171461	−	0.0583941i
$638$	54.6788	−	18.4291i	2.16475	−	0.729617i
$639$	−2.36588	−	5.18056i	−0.0935929	−	0.204940i
$640$	−7.70269	−	27.1539i	−0.304475	−	1.07335i
$641$	−22.8736	+	14.7000i	−0.903454	+	0.580614i	−0.907813	−	0.419376i	$-0.862249\pi$
$641$	−22.8736	+	14.7000i	−0.903454	+	0.580614i	0.00435895	+	0.999990i	$0.498612\pi$
$642$	25.4829	+	6.40145i	1.00573	+	0.252645i
$643$			27.6854i			1.09181i	0.837848	+	0.545904i	$0.183814\pi$
$643$			27.6854i			1.09181i	−0.837848	+	0.545904i	$0.816186\pi$
$644$	−4.85799	−	24.4635i	−0.191432	−	0.963997i
$645$			12.3871i			0.487743i
$646$	1.82052	−	7.24715i	0.0716274	−	0.285135i
$647$	6.18926	−	3.97759i	0.243325	−	0.156375i	−0.413295	−	0.910597i	$-0.635622\pi$
$647$	6.18926	−	3.97759i	0.243325	−	0.156375i	0.656620	+	0.754222i	$0.271986\pi$
$648$	−0.0688358	+	2.82759i	−0.00270412	+	0.111078i
$649$	29.5659	+	64.7403i	1.16056	+	2.54128i
$650$	−3.56123	−	10.5661i	−0.139683	−	0.414436i
$651$	6.57355	+	22.3875i	0.257638	+	0.877434i
$652$	5.22120	+	13.6812i	0.204478	+	0.535798i
$653$	16.9152	+	7.72490i	0.661942	+	0.302299i	0.717912	−	0.696134i	$-0.245098\pi$
$653$	16.9152	+	7.72490i	0.661942	+	0.302299i	−0.0559703	+	0.998432i	$0.517825\pi$
$654$	−1.93417	−	10.4929i	−0.0756322	−	0.410303i
$655$	−10.3283	−	11.9195i	−0.403559	−	0.465731i
$656$	9.13146	−	14.6935i	0.356524	−	0.573685i
$657$	6.91038	+	2.02907i	0.269600	+	0.0791616i
$658$	31.3575	−	1.23885i	1.22244	−	0.0482954i
$659$	−10.9244	+	16.9986i	−0.425553	+	0.662173i	−0.986139	−	0.165923i	$-0.946940\pi$
$659$	−10.9244	+	16.9986i	−0.425553	+	0.662173i	0.560586	+	0.828096i	$0.310576\pi$
$660$	−23.0470	−	8.39780i	−0.897102	−	0.326884i
$661$	−47.6931	−	6.85723i	−1.85505	−	0.266715i	−0.877831	−	0.478970i	$-0.841010\pi$
$661$	−47.6931	−	6.85723i	−1.85505	−	0.266715i	−0.977214	+	0.212255i	$0.931919\pi$
$662$	10.4464	+	8.35315i	0.406009	+	0.324655i
$663$	1.63282	+	11.3565i	0.0634134	+	0.441050i
$664$	7.02810	+	16.4367i	0.272743	+	0.637866i
$665$	12.6027	−	14.5443i	0.488711	−	0.564003i
$666$	8.94304	−	4.51900i	0.346536	−	0.175108i
$667$	10.2269	+	38.4661i	0.395989	+	1.48941i
$668$	−8.42609	+	11.4354i	−0.326015	+	0.442451i
$669$	11.2933	+	9.78572i	0.436625	+	0.378338i
$670$	−29.4709	−	17.3353i	−1.13856	−	0.669722i
$671$	−7.44012	−	51.7472i	−0.287223	−	1.99768i
$672$	−5.37078	+	13.6940i	−0.207182	+	0.528256i
$673$	−1.76993	+	12.3102i	−0.0682259	+	0.474522i	0.926852	+	0.375427i	$0.122504\pi$
$673$	−1.76993	+	12.3102i	−0.0682259	+	0.474522i	−0.995078	+	0.0990950i	$0.968405\pi$
$674$	13.5023	+	14.3928i	0.520087	+	0.554389i
$675$	−0.661708	+	1.02964i	−0.0254691	+	0.0396308i
$676$	−27.6920	−	49.8134i	−1.06508	−	1.91590i
$677$	−8.59802	+	29.2822i	−0.330449	+	1.12540i	0.611945	+	0.790900i	$0.290387\pi$
$677$	−8.59802	+	29.2822i	−0.330449	+	1.12540i	−0.942394	+	0.334505i	$0.891431\pi$
$678$	−15.9579	−	6.53927i	−0.612858	−	0.251139i
$679$	12.7411	+	14.7040i	0.488959	+	0.564289i
$680$	−5.49752	+	11.3016i	−0.210820	+	0.433397i
$681$	−7.88329	+	17.2620i	−0.302088	+	0.661481i
$682$	−62.0520	−	6.43368i	−2.37609	−	0.246358i
$683$	2.83608	+	9.65880i	0.108520	+	0.369584i	0.995790	−	0.0916662i	$-0.0292193\pi$
$683$	2.83608	+	9.65880i	0.108520	+	0.369584i	−0.887270	+	0.461250i	$0.847401\pi$
$684$	4.16351	−	4.22706i	0.159196	−	0.161626i
$685$	−2.41011	+	1.10066i	−0.0920855	+	0.0420540i
$686$	−21.8073	+	15.2638i	−0.832608	+	0.582775i
$687$	−0.688114	+	0.442224i	−0.0262532	+	0.0168719i
$688$	−7.97592	+	18.1890i	−0.304079	+	0.693449i
$689$	−25.3916			−0.967342
$690$	6.81680	−	15.4865i	0.259511	−	0.589562i
$691$		−	38.4909i		−	1.46426i	−0.681164	−	0.732131i	$-0.738526\pi$
$691$		−	38.4909i		−	1.46426i	0.681164	−	0.732131i	$-0.261474\pi$
$692$	−29.8071	+	6.72097i	−1.13310	+	0.255493i
$693$	6.91122	+	10.7541i	0.262535	+	0.408513i
$694$	10.0161	+	14.3100i	0.380207	+	0.543199i
$695$	−9.24098	−	20.2349i	−0.350530	−	0.767555i
$696$	7.15964	−	22.3557i	0.271385	−	0.847391i
$697$	−7.39101	+	2.17020i	−0.279955	+	0.0822021i
$698$	40.6487	+	4.21454i	1.53858	+	0.159523i
$699$	−2.47360	−	1.12965i	−0.0935601	−	0.0427274i
$700$	−5.06655	+	3.85299i	−0.191498	+	0.145629i
$701$	−19.0953	+	16.5461i	−0.721218	+	0.624939i	−0.936114	−	0.351698i	$-0.885604\pi$
$701$	−19.0953	+	16.5461i	−0.721218	+	0.624939i	0.214895	+	0.976637i	$0.431059\pi$
$702$	−3.45437	+	8.42974i	−0.130377	+	0.318160i
$703$	−20.1674	−	5.92170i	−0.760630	−	0.223341i
$704$	−28.4344	−	27.1708i	−1.07166	−	1.02404i
$705$	17.9102	+	11.5102i	0.674539	+	0.433500i
$706$	11.2063	+	11.9454i	0.421755	+	0.449572i
$707$	30.1319	+	4.33231i	1.13323	+	0.162933i
$708$	28.3386	+	5.94028i	1.06503	+	0.223249i
$709$	−41.2840	+	5.93574i	−1.55045	+	0.222921i	−0.863713	−	0.503984i	$-0.831867\pi$
$709$	−41.2840	+	5.93574i	−1.55045	+	0.222921i	−0.686738	+	0.726905i	$0.740958\pi$
$710$	10.1877	−	17.3195i	0.382336	−	0.649990i
$711$	−0.615297	+	0.710091i	−0.0230754	+	0.0266305i
$712$	3.55080	+	0.599067i	0.133072	+	0.0224510i
$713$	7.21861	−	42.4234i	0.270339	−	1.58877i
$714$	5.84574	−	2.95390i	0.218771	−	0.110547i
$715$	−59.7089	−	51.7380i	−2.23299	−	1.93489i
$716$	40.9276	+	2.61581i	1.52954	+	0.0977574i
$717$	4.64979	−	0.668539i	0.173650	−	0.0249670i
$718$	−11.1989	+	14.0052i	−0.417940	+	0.522670i
$719$	−1.27591	+	8.87417i	−0.0475835	+	0.330951i	0.952100	+	0.305787i	$0.0989197\pi$
$719$	−1.27591	+	8.87417i	−0.0475835	+	0.330951i	−0.999683	+	0.0251633i	$0.991989\pi$
$720$	−8.31229	+	5.52166i	−0.309781	+	0.205780i
$721$	−7.74843	−	4.97961i	−0.288567	−	0.185451i
$722$	14.4127	−	0.569408i	0.536387	−	0.0211912i
$723$	−0.457917	+	1.55952i	−0.0170301	+	0.0579993i
$724$	−0.367871	−	4.64848i	−0.0136718	−	0.172759i
$725$	7.67682	−	6.65200i	0.285110	−	0.247049i
$726$	−18.3142	+	3.37590i	−0.679702	+	0.125291i
$727$	−3.40334	+	7.45227i	−0.126223	+	0.276389i	−0.962185	−	0.272398i	$-0.912183\pi$
$727$	−3.40334	+	7.45227i	−0.126223	+	0.276389i	0.835962	+	0.548788i	$0.184910\pi$
$728$	−31.8880	+	35.0400i	−1.18185	+	1.29867i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	8.11577	+	24.0793i	0.300378	+	0.891214i
$731$	8.04425	−	3.67368i	0.297527	−	0.135876i
$732$	−18.7436	−	10.0513i	−0.692783	−	0.371505i
$733$	4.83784	+	7.52783i	0.178690	+	0.278047i	0.919032	−	0.394184i	$-0.128973\pi$
$733$	4.83784	+	7.52783i	0.178690	+	0.278047i	−0.740342	+	0.672231i	$0.765336\pi$
$734$	−37.1961	−	9.34386i	−1.37293	−	0.344888i
$735$	−0.594871			−0.0219422
$736$	19.9812	−	18.3508i	0.736517	−	0.676419i
$737$	−47.6421			−1.75492
$738$	−5.93209	−	1.49017i	−0.218363	−	0.0548540i
$739$	−10.7346	−	16.7033i	−0.394878	−	0.614442i	0.585710	−	0.810520i	$-0.300816\pi$
$739$	−10.7346	−	16.7033i	−0.394878	−	0.614442i	−0.980588	+	0.196079i	$0.937179\pi$
$740$	31.1550	+	16.7069i	1.14528	+	0.614157i
$741$	17.3832	−	7.93866i	0.638589	−	0.291634i
$742$	4.62960	+	13.7359i	0.169958	+	0.504261i
$743$	9.71237	−	2.85181i	0.356312	−	0.104623i	−0.0986773	−	0.995119i	$-0.531461\pi$
$743$	9.71237	−	2.85181i	0.356312	−	0.104623i	0.454990	+	0.890497i	$0.349643\pi$
$744$	−17.0820	+	18.7705i	−0.626256	+	0.688158i
$745$	12.6124	−	27.6173i	0.462082	−	1.01182i
$746$	−7.05836	+	1.30109i	−0.258425	+	0.0476361i
$747$	4.77648	−	4.13884i	0.174762	−	0.151432i
$748$	1.38154	+	17.4573i	0.0505141	+	0.638303i
$749$	13.6108	−	46.3540i	0.497327	−	1.69374i
$750$	13.3122	−	0.525927i	0.486091	−	0.0192041i
$751$	−15.2735	−	9.81569i	−0.557338	−	0.358180i	0.231448	−	0.972847i	$-0.425654\pi$
$751$	−15.2735	−	9.81569i	−0.557338	−	0.358180i	−0.788786	+	0.614668i	$0.789290\pi$
$752$	18.8877	+	28.4335i	0.688764	+	1.03686i
$753$	−0.689507	+	4.79563i	−0.0251270	+	0.174762i
$754$	47.2183	−	59.0506i	1.71959	−	2.15050i
$755$	41.9853	−	6.03658i	1.52800	−	0.219694i
$756$	5.19001	+	0.331709i	0.188759	+	0.0120641i
$757$	−13.4627	−	11.6655i	−0.489312	−	0.423991i	0.374941	−	0.927049i	$-0.377663\pi$
$757$	−13.4627	−	11.6655i	−0.489312	−	0.423991i	−0.864253	+	0.503058i	$0.832208\pi$
$758$	22.4484	−	11.3434i	0.815361	−	0.412009i
$759$	−2.75355	−	23.4155i	−0.0999476	−	0.849930i
$760$	20.6415	+	3.48249i	0.748746	+	0.126323i
$761$	−25.2920	+	29.1885i	−0.916833	+	1.05808i	0.0812812	+	0.996691i	$0.474099\pi$
$761$	−25.2920	+	29.1885i	−0.916833	+	1.05808i	−0.998114	+	0.0613901i	$0.980447\pi$
$762$	0.548279	−	0.932101i	0.0198621	−	0.0337664i
$763$	−19.4184	+	2.79195i	−0.702995	+	0.101075i
$764$	−22.7157	−	4.76161i	−0.821825	−	0.172269i
$765$	4.39815	+	0.632359i	0.159016	+	0.0228630i
$766$	21.4236	+	22.8365i	0.774066	+	0.825118i
$767$	78.4548	+	50.4199i	2.83284	+	1.82056i
$768$	−15.7609	+	2.75570i	−0.568723	+	0.0994376i
$769$	37.0275	+	10.8723i	1.33525	+	0.392064i	0.869971	−	0.493102i	$-0.164137\pi$
$769$	37.0275	+	10.8723i	1.33525	+	0.392064i	0.465275	+	0.885166i	$0.345955\pi$
$770$	−17.1018	+	41.7336i	−0.616305	+	1.50398i
$771$	1.86894	−	1.61945i	0.0673083	−	0.0583230i
$772$	−16.9147	+	12.8632i	−0.608774	+	0.462958i
$773$	8.89825	+	4.06369i	0.320048	+	0.146161i	0.568960	−	0.822365i	$-0.307346\pi$
$773$	8.89825	+	4.06369i	0.320048	+	0.146161i	−0.248912	+	0.968526i	$0.580073\pi$
$774$	6.98444	+	0.724161i	0.251051	+	0.0260294i
$775$	−10.5375	+	3.09410i	−0.378519	+	0.111143i
$776$	−6.45477	+	20.1548i	−0.231713	+	0.723514i
$777$	−7.65342	−	16.7587i	−0.274565	−	0.601214i
$778$	2.51568	+	3.59414i	0.0901916	+	0.128856i
$779$	6.93663	+	10.7936i	0.248530	+	0.386721i
$780$	−31.3545	+	7.06987i	−1.12267	+	0.253142i
$781$		−	27.9984i		−	1.00186i
$782$	−12.0787	+	0.166026i	−0.431932	+	0.00593709i
$783$	−8.29938			−0.296596
$784$	−0.873496	−	0.383030i	−0.0311963	−	0.0136797i
$785$	47.1453	−	30.2984i	1.68269	−	1.08140i
$786$	−7.32454	+	5.12673i	−0.261258	+	0.182864i
$787$	12.0450	−	5.50076i	0.429357	−	0.196081i	−0.189002	−	0.981977i	$-0.560525\pi$
$787$	12.0450	−	5.50076i	0.429357	−	0.196081i	0.618359	+	0.785896i	$0.287798\pi$
$788$	24.9284	−	25.3089i	0.888038	−	0.901592i
$789$	1.73367	+	5.90435i	0.0617204	+	0.210200i
$790$	−3.29732	−	0.341873i	−0.117314	−	0.0121633i
$791$	−13.1726	+	28.8440i	−0.468364	+	1.02557i
$792$	−6.08241	+	12.5040i	−0.216129	+	0.444311i
$793$	−44.8603	−	51.7716i	−1.59304	−	1.83846i
$794$	12.0994	+	4.95814i	0.429392	+	0.175958i
$795$	−2.77047	+	9.43535i	−0.0982584	+	0.334637i
$796$	8.30346	+	14.9366i	0.294308	+	0.529413i
$797$	−8.56676	+	13.3301i	−0.303450	+	0.472178i	−0.959171	−	0.282825i	$-0.908728\pi$
$797$	−8.56676	+	13.3301i	−0.303450	+	0.472178i	0.655721	+	0.755003i	$0.272365\pi$
$798$	−7.46398	−	7.95625i	−0.264222	−	0.281648i
$799$	2.16309	−	15.0446i	0.0765245	−	0.532239i
$800$	−6.44560	−	2.52797i	−0.227886	−	0.0893772i
$801$	−0.181187	−	1.26018i	−0.00640192	−	0.0445263i
$802$	−20.0522	−	11.7951i	−0.708068	−	0.416499i
$803$	26.7584	+	23.1863i	0.944285	+	0.818228i
$804$	−11.4974	+	15.6036i	−0.405480	+	0.550297i
$805$	−27.9579	−	13.6483i	−0.985386	−	0.481039i
$806$	−72.9593	+	36.8670i	−2.56988	+	1.29858i
$807$	4.41083	−	5.09037i	0.155268	−	0.179189i
$808$	13.0183	+	30.4460i	0.457982	+	1.07109i
$809$	−7.36931	−	51.2547i	−0.259091	−	1.80202i	−0.539336	−	0.842091i	$-0.681325\pi$
$809$	−7.36931	−	51.2547i	−0.259091	−	1.80202i	0.280244	−	0.959929i	$-0.409585\pi$
$810$	2.75553	+	2.20339i	0.0968195	+	0.0774192i
$811$	22.8971	+	3.29210i	0.804025	+	0.115601i	0.532061	−	0.846706i	$-0.321418\pi$
$811$	22.8971	+	3.29210i	0.804025	+	0.115601i	0.271964	+	0.962307i	$0.412327\pi$
$812$	−40.5535	−	14.7768i	−1.42315	−	0.518563i
$813$	−7.18227	+	11.1758i	−0.251893	+	0.391953i
$814$	49.2209	−	1.94458i	1.72519	−	0.0681575i
$815$	17.5265	+	5.14623i	0.613925	+	0.180265i
$816$	6.05098	+	3.76046i	0.211827	+	0.131642i
$817$	−9.64597	−	11.1320i	−0.337470	−	0.389461i
$818$	5.90395	+	32.0288i	0.206427	+	1.11986i
$819$	15.2368	+	6.95843i	0.532418	+	0.243147i
$820$	−7.69421	−	20.1613i	−0.268693	−	0.704063i
$821$	8.71484	+	29.6800i	0.304150	+	1.03584i	0.959779	+	0.280756i	$0.0905853\pi$
$821$	8.71484	+	29.6800i	0.304150	+	1.03584i	−0.655629	+	0.755083i	$0.727597\pi$
$822$	0.479706	+	1.42328i	0.0167317	+	0.0496424i
$823$	−15.2355	−	33.3610i	−0.531075	−	1.16289i	−0.965074	−	0.261979i	$-0.915625\pi$
$823$	−15.2355	−	33.3610i	−0.531075	−	1.16289i	0.433999	−	0.900914i	$-0.357102\pi$
$824$	0.243825	−	10.0157i	0.00849404	−	0.348912i
$825$	−5.06182	+	3.25304i	−0.176230	+	0.113256i
$826$	12.9708	−	51.6342i	0.451311	−	1.79658i
$827$		−	18.3082i		−	0.636638i	−0.947984	−	0.318319i	$-0.896882\pi$
$827$		−	18.3082i		−	0.636638i	0.947984	−	0.318319i	$-0.103118\pi$
$828$	−8.33350	−	4.74898i	−0.289609	−	0.165038i
$829$		−	13.7874i		−	0.478858i	−0.970914	−	0.239429i	$-0.923040\pi$
$829$		−	13.7874i		−	0.478858i	0.970914	−	0.239429i	$-0.0769602\pi$
$830$	21.6267	+	5.43273i	0.750673	+	0.188573i
$831$	−14.3480	+	9.22087i	−0.497725	+	0.319869i
$832$	−50.5924	−	9.80753i	−1.75398	−	0.340015i
$833$	0.176423	+	0.386312i	0.00611268	+	0.0133849i
$834$	−11.9496	+	4.02754i	−0.413782	+	0.139462i
$835$	4.99190	+	17.0009i	0.172752	+	0.588339i
$836$	27.2513	−	10.4000i	0.942504	−	0.359690i
$837$	8.16217	+	3.72754i	0.282126	+	0.128843i
$838$	−24.3753	+	4.49316i	−0.842031	+	0.155214i
$839$	−9.68051	−	11.1719i	−0.334208	−	0.385697i	0.563626	−	0.826030i	$-0.309406\pi$
$839$	−9.68051	−	11.1719i	−0.334208	−	0.385697i	−0.897835	+	0.440333i	$0.854860\pi$
$840$	9.54135	+	15.6726i	0.329208	+	0.540756i
$841$	38.2643	+	11.2354i	1.31946	+	0.387428i
$842$	−2.18217	−	55.2348i	−0.0752027	−	1.90352i
$843$	−7.73139	+	12.0303i	−0.266283	+	0.414345i
$844$	−1.85681	−	0.676579i	−0.0639140	−	0.0232888i
$845$	−70.3691	−	10.1175i	−2.42077	−	0.348054i
$846$	7.53704	−	9.42573i	0.259129	−	0.324063i
$847$	4.87305	+	33.8928i	0.167440	+	1.16457i
$848$	−10.1434	+	12.0708i	−0.348326	+	0.414512i
$849$	−3.33143	+	3.84468i	−0.114335	+	0.131949i
$850$	1.39037	+	2.75153i	0.0476893	+	0.0943765i
$851$	−0.874604	+	33.9680i	−0.0299810	+	1.16441i
$852$	−9.16996	−	6.75679i	−0.314158	−	0.231484i
$853$	29.7725	+	25.7980i	1.01939	+	0.883308i	0.993208	−	0.116350i	$-0.0371193\pi$
$853$	29.7725	+	25.7980i	1.01939	+	0.883308i	0.0261830	+	0.999657i	$0.491665\pi$
$854$	−19.8272	+	33.7072i	−0.678474	+	1.15344i
$855$	−1.05327	−	7.32568i	−0.0360212	−	0.250533i
$856$	50.7661	−	13.5734i	1.73515	−	0.463929i
$857$	3.77630	−	26.2648i	0.128996	−	0.897187i	−0.817834	−	0.575454i	$-0.804825\pi$
$857$	3.77630	−	26.2648i	0.128996	−	0.897187i	0.946830	−	0.321733i	$-0.104265\pi$
$858$	−32.6629	+	30.6420i	−1.11509	+	1.04610i
$859$	18.7610	−	29.1927i	0.640118	−	0.996044i	−0.357939	−	0.933745i	$-0.616520\pi$
$859$	18.7610	−	29.1927i	0.640118	−	0.996044i	0.998058	−	0.0622987i	$-0.0198431\pi$
$860$	12.0374	+	21.6533i	0.410471	+	0.738372i
$861$	−3.16841	+	10.7906i	−0.107979	+	0.367743i
$862$	−11.7497	+	28.6729i	−0.400197	+	0.976604i
$863$	9.94341	+	11.4753i	0.338477	+	0.390624i	0.899315	−	0.437302i	$-0.144066\pi$
$863$	9.94341	+	11.4753i	0.338477	+	0.390624i	−0.560837	+	0.827926i	$0.689521\pi$
$864$	2.62742	+	5.00966i	0.0893868	+	0.170432i
$865$	−15.8334	+	34.6703i	−0.538351	+	1.17882i
$866$	1.96454	−	18.9477i	0.0667577	−	0.643869i
$867$	3.89574	+	13.2677i	0.132306	+	0.450593i
$868$	33.2462	+	32.7464i	1.12845	+	1.11149i
$869$	−4.20169	+	1.91885i	−0.142533	+	0.0650925i
$870$	−16.7909	−	23.9890i	−0.569263	−	0.813304i
$871$	−52.5172	+	33.7507i	−1.77948	+	1.14360i
$872$	−13.5776	−	16.4625i	−0.459796	−	0.557489i
$873$	7.48230			0.253237
$874$	5.93339	+	19.2257i	0.200700	+	0.650319i
$875$		−	24.4960i		−	0.828116i
$876$	14.0515	−	3.16835i	0.474755	−	0.107049i
$877$	21.9385	+	34.1369i	0.740810	+	1.15272i	0.983198	+	0.182543i	$0.0584328\pi$
$877$	21.9385	+	34.1369i	0.740810	+	1.15272i	−0.242388	+	0.970179i	$0.577931\pi$
$878$	−20.0468	+	14.0316i	−0.676548	+	0.473543i
$879$	−0.812131	−	1.77832i	−0.0273925	−	0.0599812i
$880$	−48.4479	+	7.71647i	−1.63318	+	0.260122i
$881$	46.5654	−	13.6728i	1.56883	−	0.460649i	0.622167	−	0.782884i	$-0.286252\pi$
$881$	46.5654	−	13.6728i	1.56883	−	0.460649i	0.946660	+	0.322235i	$0.104434\pi$
$882$	−0.0347766	+	0.335416i	−0.00117099	+	0.0112940i
$883$	−3.01396	−	1.37643i	−0.101428	−	0.0463205i	0.364055	−	0.931377i	$-0.381392\pi$
$883$	−3.01396	−	1.37643i	−0.101428	−	0.0463205i	−0.465483	+	0.885057i	$0.654119\pi$
$884$	13.8901	+	18.2650i	0.467174	+	0.614318i
$885$	27.2959	−	23.6520i	0.917541	−	0.795054i
$886$	−4.14170	−	1.69720i	−0.139143	−	0.0570186i
$887$	33.2161	+	9.75314i	1.11529	+	0.327478i	0.786910	−	0.617068i	$-0.211680\pi$
$887$	33.2161	+	9.75314i	1.11529	+	0.327478i	0.328379	+	0.944546i	$0.393498\pi$
$888$	11.2415	−	16.5900i	0.377239	−	0.556723i
$889$	−1.67271	−	1.07499i	−0.0561009	−	0.0360539i
$890$	3.27593	−	3.07324i	0.109810	−	0.103015i
$891$	4.86608	+	0.699637i	0.163020	+	0.0234387i
$892$	29.2507	+	6.13146i	0.979385	+	0.205296i
$893$	−25.0587	+	3.60289i	−0.838556	+	0.120566i
$894$	−14.8346	−	8.72597i	−0.496142	−	0.291840i
$895$	33.5007	−	38.6618i	1.11980	−	1.29232i
$896$	3.91891	+	29.1568i	0.130922	+	0.974061i
$897$	−19.6234	−	23.8609i	−0.655207	−	0.796692i
$898$	−0.383591	−	0.759121i	−0.0128006	−	0.0253322i
$899$	−56.2812	−	48.7680i	−1.87708	−	1.62650i
$900$	−0.156132	+	2.44288i	−0.00520440	+	0.0814294i
$901$	6.94899	−	0.999114i	0.231504	−	0.0332853i
$902$	−23.4842	−	18.7785i	−0.781939	−	0.625257i
$903$	1.83743	−	12.7796i	0.0611460	−	0.425280i
$904$	−34.2497	+	4.07631i	−1.13913	+	0.135576i
$905$	−4.89323	−	3.14469i	−0.162656	−	0.104533i
$906$	−0.949208	−	24.0262i	−0.0315353	−	0.798216i
$907$	3.94953	−	13.4509i	0.131142	−	0.446628i	−0.867573	−	0.497310i	$-0.834321\pi$
$907$	3.94953	−	13.4509i	0.131142	−	0.446628i	0.998715	+	0.0506817i	$0.0161394\pi$
$908$	2.99423	+	37.8355i	0.0993670	+	1.25562i
$909$	8.84757	−	7.66647i	0.293455	−	0.254281i
$910$	10.7133	+	58.1194i	0.355142	+	1.92664i
$911$	−20.2729	+	44.3915i	−0.671672	+	1.47076i	0.199559	+	0.979886i	$0.436049\pi$
$911$	−20.2729	+	44.3915i	−0.671672	+	1.47076i	−0.871232	+	0.490872i	$0.836678\pi$
$912$	3.17031	−	11.4351i	0.104979	−	0.378652i
$913$	29.8122	−	8.75366i	0.986641	−	0.289704i
$914$	−40.7311	+	13.7282i	−1.34727	+	0.454087i
$915$	−24.1327	+	11.0210i	−0.797802	+	0.364344i
$916$	−0.773119	+	1.44171i	−0.0255446	+	0.0476355i
$917$	8.88747	+	13.8292i	0.293490	+	0.456679i
$918$	0.613673	−	2.44291i	0.0202542	−	0.0806282i
$919$	36.1028			1.19092			0.595461	−	0.803384i	$-0.296970\pi$
$919$	36.1028			1.19092			0.595461	+	0.803384i	$0.296970\pi$
$920$	−3.13316	−	33.6955i	−0.103297	−	1.11091i
$921$	−10.7695			−0.354868
$922$	7.68784	−	30.6038i	0.253186	−	1.00788i
$923$	−19.8347	−	30.8634i	−0.652867	−	1.01588i
$924$	22.5316	+	12.0825i	0.741234	+	0.397487i
$925$	7.88812	−	3.60238i	0.259360	−	0.118446i
$926$	−39.1272	+	13.1876i	−1.28580	+	0.433370i
$927$	−3.39864	+	0.997931i	−0.111626	+	0.0327764i
$928$	−9.20909	−	46.0363i	−0.302303	−	1.51122i
$929$	21.2409	−	46.5110i	0.696890	−	1.52598i	−0.146812	−	0.989164i	$-0.546901\pi$
$929$	21.2409	−	46.5110i	0.696890	−	1.52598i	0.843702	−	0.536812i	$-0.180371\pi$
$930$	5.73897	+	31.1338i	0.188188	+	1.02092i
$931$	0.534598	−	0.463232i	0.0175207	−	0.0151818i
$932$	−5.42173	+	0.429065i	−0.177595	+	0.0140545i
$933$	3.93389	−	13.3976i	0.128790	−	0.438618i
$934$	−0.0568808	−	1.43976i	−0.00186120	−	0.0471103i
$935$	18.3765	+	11.8099i	0.600976	+	0.386224i
$936$	2.15331	+	18.0924i	0.0703832	+	0.591369i
$937$	5.06836	−	35.2512i	0.165576	−	1.15161i	−0.722319	−	0.691560i	$-0.756924\pi$
$937$	5.06836	−	35.2512i	0.165576	−	1.15161i	0.887895	−	0.460047i	$-0.152167\pi$
$938$	27.8333	+	22.2562i	0.908789	+	0.726690i
$939$	−23.0181	+	3.30951i	−0.751169	+	0.108002i
$940$	42.4932	+	2.71587i	1.38598	+	0.0885819i
$941$	−9.87223	−	8.55434i	−0.321825	−	0.278863i	0.478932	−	0.877852i	$-0.341024\pi$
$941$	−9.87223	−	8.55434i	−0.321825	−	0.278863i	−0.800758	+	0.598989i	$0.795569\pi$
$942$	−14.3275	−	28.3539i	−0.466815	−	0.923821i
$943$	13.9819	−	15.3207i	0.455314	−	0.498912i
$944$	55.3099	−	17.1546i	1.80018	−	0.558335i
$945$	4.24820	−	4.90268i	0.138194	−	0.159484i
$946$	29.7545	+	17.5022i	0.967403	+	0.569045i
$947$	−0.192295	+	0.0276479i	−0.00624875	+	0.000898435i	−0.145439	−	0.989367i	$-0.546459\pi$
$947$	−0.192295	+	0.0276479i	−0.00624875	+	0.000898435i	0.139190	+	0.990266i	$0.455550\pi$
$948$	−0.385528	+	1.83920i	−0.0125214	+	0.0597344i
$949$	45.9223	+	6.60263i	1.49070	+	0.214330i
$950$	3.74492	−	3.51321i	0.121501	−	0.113984i
$951$	8.66816	+	5.57069i	0.281084	+	0.180642i
$952$	7.34813	−	10.8442i	0.238154	−	0.351464i
$953$	25.2340	+	7.40936i	0.817408	+	0.240013i	0.663600	−	0.748088i	$-0.269028\pi$
$953$	25.2340	+	7.40936i	0.817408	+	0.240013i	0.153809	+	0.988101i	$0.450846\pi$
$954$	5.15812	+	2.11372i	0.167000	+	0.0684341i
$955$	−21.8798	+	18.9590i	−0.708015	+	0.613498i
$956$	7.47840	−	5.68714i	0.241869	−	0.183935i
$957$	−37.1137	−	16.9492i	−1.19971	−	0.547891i
$958$	−0.349847	+	3.37423i	−0.0113030	+	0.109016i
$959$	2.64974	−	0.778034i	0.0855646	−	0.0251240i
$960$	−9.16454	+	17.7297i	−0.295784	+	0.572224i
$961$	20.5695	+	45.0409i	0.663532	+	1.45293i
$962$	52.8799	−	37.0127i	1.70492	−	1.19334i
$963$	−10.0446	−	15.6297i	−0.323682	−	0.503659i
$964$	0.715028	+	3.17111i	0.0230295	+	0.102135i
$965$			26.5073i			0.853300i
$966$	−9.32997	+	14.9661i	−0.300187	+	0.481525i
$967$	−13.1658			−0.423383			−0.211691	−	0.977337i	$-0.567897\pi$
$967$	−13.1658			−0.423383			−0.211691	+	0.977337i	$0.567897\pi$
$968$	−28.7335	+	23.6983i	−0.923528	+	0.761692i
$969$	−4.44495	+	2.85660i	−0.142792	+	0.0917671i
$970$	15.1378	+	21.6273i	0.486045	+	0.694410i
$971$	8.58742	−	3.92174i	0.275583	−	0.125855i	−0.272829	−	0.962062i	$-0.587959\pi$
$971$	8.58742	−	3.92174i	0.275583	−	0.125855i	0.548413	+	0.836208i	$0.315232\pi$
$972$	1.40346	−	1.42488i	0.0450161	−	0.0457032i
$973$	6.53227	+	22.2469i	0.209415	+	0.713201i
$974$	0.0998620	−	0.963156i	0.00319979	−	0.0308615i
$975$	−3.27526	+	7.17182i	−0.104892	+	0.229682i
$976$	−42.5322	+	0.644292i	−1.36142	+	0.0206233i
$977$	−25.9722	−	29.9735i	−0.830923	−	0.958936i	0.168720	−	0.985664i	$-0.446037\pi$
$977$	−25.9722	−	29.9735i	−0.830923	−	0.958936i	−0.999643	+	0.0267277i	$0.991491\pi$
$978$	3.92629	−	9.58137i	0.125549	−	0.306378i
$979$	1.76334	−	6.00538i	0.0563566	−	0.191933i
$980$	−1.03986	+	0.578075i	−0.0332172	+	0.0184659i
$981$	−4.07890	+	6.34689i	−0.130229	+	0.202641i
$982$	−39.3498	+	36.9151i	−1.25570	+	1.17801i
$983$	−0.165213	+	1.14908i	−0.00526947	+	0.0366500i	−0.992287	−	0.123965i	$-0.960439\pi$
$983$	−0.165213	+	1.14908i	−0.00526947	+	0.0366500i	0.987017	+	0.160615i	$0.0513479\pi$
$984$	−11.8177	+	3.15971i	−0.376734	+	0.100728i
$985$	−6.30633	−	43.8615i	−0.200936	−	1.39754i
$986$	−10.5988	+	18.0185i	−0.337536	+	0.573827i
$987$	−16.7704	−	14.5316i	−0.533808	−	0.462547i
$988$	22.6722	−	30.7696i	0.721299	−	0.978910i
$989$	−13.3853	+	19.6942i	−0.425627	+	0.626240i
$990$	7.82252	+	15.4807i	0.248616	+	0.492008i
$991$	−19.0817	+	22.0215i	−0.606151	+	0.699536i	−0.973016	−	0.230738i	$-0.925886\pi$
$991$	−19.0817	+	22.0215i	−0.606151	+	0.699536i	0.366864	+	0.930274i	$0.380431\pi$
$992$	−11.6197	+	49.4113i	−0.368925	+	1.56881i
$993$	−1.34599	−	9.36157i	−0.0427137	−	0.297081i
$994$	−13.0795	+	16.3571i	−0.414858	+	0.518817i
$995$	21.1002	+	3.03375i	0.668922	+	0.0961765i
$996$	4.32754	−	11.8765i	0.137123	−	0.376322i
$997$	−12.7963	+	19.9115i	−0.405264	+	0.630603i	−0.982563	−	0.185930i	$-0.940470\pi$
$997$	−12.7963	+	19.9115i	−0.405264	+	0.630603i	0.577299	+	0.816533i	$0.304107\pi$
$998$	−2.04055	−	51.6501i	−0.0645926	−	1.63496i
$999$	−6.79817	−	1.99612i	−0.215085	−	0.0631546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.85.4	yes	480
8.5	even	2	inner	552.2.bb.a.85.29	yes	480
23.13	even	11	inner	552.2.bb.a.13.29	yes	480
184.13	even	22	inner	552.2.bb.a.13.4	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.4	✓	480	184.13	even	22	inner
552.2.bb.a.13.29	yes	480	23.13	even	11	inner
552.2.bb.a.85.4	yes	480	1.1	even	1	trivial
552.2.bb.a.85.29	yes	480	8.5	even	2	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37160 - 0.344553i) q^{2} +(0.540641 + 0.841254i) q^{3} +(1.76257 + 0.945176i) q^{4} +(2.26933 - 1.03637i) q^{5} +(-0.451686 - 1.34014i) q^{6} +(-2.49497 + 0.732589i) q^{7} +(-2.09187 - 1.90370i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.37160 - 0.344553i) q^{2} +(0.540641 + 0.841254i) q^{3} +(1.76257 + 0.945176i) q^{4} +(2.26933 - 1.03637i) q^{5} +(-0.451686 - 1.34014i) q^{6} +(-2.49497 + 0.732589i) q^{7} +(-2.09187 - 1.90370i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-3.46970 + 0.639578i) q^{10} +(-3.71536 + 3.21937i) q^{11} +(0.157783 + 1.99377i) q^{12} +(-1.81486 + 6.18084i) q^{13} +(3.67451 - 0.145170i) q^{14} +(2.09874 + 1.34878i) q^{15} +(2.21328 + 3.33187i) q^{16} +(0.253473 - 1.76294i) q^{17} +(0.883199 - 1.10452i) q^{18} +(-2.93640 + 0.422191i) q^{19} +(4.97940 + 0.318249i) q^{20} +(-1.96517 - 1.70283i) q^{21} +(6.20522 - 3.13555i) q^{22} +(1.87931 + 4.41228i) q^{23} +(0.470543 - 2.78901i) q^{24} +(0.801505 - 0.924986i) q^{25} +(4.61889 - 7.85233i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(-5.08997 - 1.06695i) q^{28} +(8.21491 + 1.18113i) q^{29} +(-2.41391 - 2.57311i) q^{30} +(-7.54861 - 4.85119i) q^{31} +(-1.88773 - 5.33259i) q^{32} +(-4.71698 - 1.38503i) q^{33} +(-0.955090 + 2.33071i) q^{34} +(-4.90268 + 4.24820i) q^{35} +(-1.59196 + 1.21065i) q^{36} +(6.44490 + 2.94329i) q^{37} +(4.17303 + 0.432669i) q^{38} +(-6.18084 + 1.81486i) q^{39} +(-6.72009 - 2.15218i) q^{40} +(-1.79665 - 3.93411i) q^{41} +(2.10872 + 3.01271i) q^{42} +(2.68440 + 4.17701i) q^{43} +(-9.59144 + 2.16270i) q^{44} +2.49478i q^{45} +(-1.05740 - 6.69940i) q^{46} +8.53380 q^{47} +(-1.60636 + 3.66328i) q^{48} +(-0.200594 + 0.128914i) q^{49} +(-1.41805 + 0.992549i) q^{50} +(1.62012 - 0.739884i) q^{51} +(-9.04080 + 9.17879i) q^{52} +(1.11051 + 3.78203i) q^{53} +(1.40667 + 0.145847i) q^{54} +(-5.09492 + 11.1563i) q^{55} +(6.61378 + 3.21719i) q^{56} +(-1.94271 - 2.24201i) q^{57} +(-10.8606 - 4.45050i) q^{58} +(4.07872 - 13.8908i) q^{59} +(2.42434 + 4.36100i) q^{60} +(-5.74932 + 8.94611i) q^{61} +(8.68217 + 9.25479i) q^{62} +(0.370061 - 2.57383i) q^{63} +(0.751854 + 7.96459i) q^{64} +(2.28712 + 15.9073i) q^{65} +(5.99259 + 3.52496i) q^{66} +(7.32397 + 6.34625i) q^{67} +(2.11305 - 2.86773i) q^{68} +(-2.69581 + 3.96644i) q^{69} +(8.18824 - 4.13759i) q^{70} +(-3.72958 + 4.30416i) q^{71} +(2.60066 - 1.11201i) q^{72} +(-1.02497 - 7.12881i) q^{73} +(-7.82570 - 6.25762i) q^{74} +(1.21147 + 0.174184i) q^{75} +(-5.57465 - 2.03128i) q^{76} +(6.91122 - 10.7541i) q^{77} +(9.10295 - 0.359633i) q^{78} +(0.901525 + 0.264712i) q^{79} +(8.47573 + 5.26735i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(1.10877 + 6.01506i) q^{82} +(-5.74905 - 2.62550i) q^{83} +(-1.85427 - 4.85879i) q^{84} +(-1.25185 - 4.26339i) q^{85} +(-2.24272 - 6.65410i) q^{86} +(3.44769 + 7.54938i) q^{87} +(13.9008 + 0.338405i) q^{88} +(-1.07103 + 0.688312i) q^{89} +(0.859584 - 3.42184i) q^{90} -16.7506i q^{91} +(-0.857962 + 9.55321i) q^{92} -8.97304i q^{93} +(-11.7049 - 2.94034i) q^{94} +(-6.22613 + 4.00129i) q^{95} +(3.46547 - 4.47107i) q^{96} +(-3.10826 - 6.80614i) q^{97} +(0.319552 - 0.107703i) q^{98} +(-1.38503 - 4.71698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

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Representations

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Database

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