LMFDB - Embedded newform 552.2.bb.a.13.29

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			13.29
Character	$\chi$	$=$	552.13
Dual form			552.2.bb.a.85.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.536245 - 1.30860i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(-1.42488 - 1.40346i) q^{4} +(-2.26933 - 1.03637i) q^{5} +(0.810951 + 1.15860i) q^{6} +(-2.49497 - 0.732589i) q^{7} +(-2.60066 + 1.11201i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.536245 - 1.30860i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(-1.42488 - 1.40346i) q^{4} +(-2.26933 - 1.03637i) q^{5} +(0.810951 + 1.15860i) q^{6} +(-2.49497 - 0.732589i) q^{7} +(-2.60066 + 1.11201i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(-2.57311 + 2.41391i) q^{10} +(3.71536 + 3.21937i) q^{11} +(1.95102 - 0.439919i) q^{12} +(1.81486 + 6.18084i) q^{13} +(-2.29658 + 2.87208i) q^{14} +(2.09874 - 1.34878i) q^{15} +(0.0605865 + 3.99954i) q^{16} +(0.253473 + 1.76294i) q^{17} +(-1.41311 + 0.0558281i) q^{18} +(2.93640 + 0.422191i) q^{19} +(1.77903 + 4.66163i) 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} +(9.06148 + 0.939513i) q^{26} +(0.989821 + 0.142315i) q^{27} +(2.52688 + 4.54545i) q^{28} +(-8.21491 + 1.18113i) q^{29} +(-0.639578 - 3.46970i) q^{30} +(-7.54861 + 4.85119i) q^{31} +(5.26630 + 2.06545i) q^{32} +(-4.71698 + 1.38503i) q^{33} +(2.44291 + 0.613673i) q^{34} +(4.90268 + 4.24820i) q^{35} +(-0.684716 + 1.87914i) q^{36} +(-6.44490 + 2.94329i) q^{37} +(2.12711 - 3.61619i) q^{38} +(-6.18084 - 1.81486i) q^{39} +(7.05422 + 0.171730i) q^{40} +(-1.79665 + 3.93411i) q^{41} +(-1.17452 - 3.48477i) q^{42} +(-2.68440 + 4.17701i) q^{43} +(-0.775679 - 9.80160i) q^{44} +2.49478i q^{45} +(-4.76615 - 4.82533i) q^{46} +8.53380 q^{47} +(-3.39738 - 2.11135i) q^{48} +(-0.200594 - 0.128914i) q^{49} +(1.64024 - 0.552833i) q^{50} +(-1.62012 - 0.739884i) q^{51} +(6.08862 - 11.3541i) q^{52} +(-1.11051 + 3.78203i) q^{53} +(0.717020 - 1.21897i) q^{54} +(-5.09492 - 11.1563i) q^{55} +(7.30321 - 0.869209i) q^{56} +(-1.94271 + 2.24201i) q^{57} +(-2.85957 + 11.3834i) q^{58} +(-4.07872 - 13.8908i) q^{59} +(-4.88343 - 1.02365i) q^{60} +(5.74932 + 8.94611i) q^{61} +(2.30039 + 12.4796i) q^{62} +(0.370061 + 2.57383i) q^{63} +(5.52688 - 5.78391i) q^{64} +(2.28712 - 15.9073i) q^{65} +(-0.717000 + 6.91537i) 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} +(2.09187 + 1.90370i) q^{72} +(-1.02497 + 7.12881i) q^{73} +(0.395552 + 10.0121i) q^{74} +(-1.21147 + 0.174184i) q^{75} +(-3.59150 - 4.72270i) q^{76} +(-6.91122 - 10.7541i) q^{77} +(-5.68938 + 7.11506i) q^{78} +(0.901525 - 0.264712i) q^{79} +(4.00751 - 9.13908i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(4.18475 + 4.46074i) q^{82} +(5.74905 - 2.62550i) q^{83} +(-5.19001 - 0.331709i) q^{84} +(1.25185 - 4.26339i) q^{85} +(4.02655 + 5.75271i) q^{86} +(3.44769 - 7.54938i) q^{87} +(-13.2424 - 4.24100i) q^{88} +(-1.07103 - 0.688312i) q^{89} +(3.26468 + 1.33781i) q^{90} -16.7506i q^{91} +(-8.87027 + 3.64943i) q^{92} -8.97304i q^{93} +(4.57620 - 11.1674i) q^{94} +(-6.22613 - 4.00129i) q^{95} +(-4.58474 + 3.31363i) q^{96} +(-3.10826 + 6.80614i) q^{97} +(-0.276264 + 0.193368i) 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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	0.536245	−	1.30860i	0.379182	−	0.925322i
$2$	0.536245	−	1.30860i	0.379182	−	0.925322i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$4$	−1.42488	−	1.40346i	−0.712442	−	0.701731i
$5$	−2.26933	−	1.03637i	−1.01488	−	0.463479i	−0.162668	−	0.986681i	$-0.552010\pi$
$5$	−2.26933	−	1.03637i	−1.01488	−	0.463479i	−0.852208	+	0.523202i	$0.824737\pi$
$6$	0.810951	+	1.15860i	0.331069	+	0.472997i
$7$	−2.49497	−	0.732589i	−0.943009	−	0.276893i	−0.226136	−	0.974096i	$-0.572609\pi$
$7$	−2.49497	−	0.732589i	−0.943009	−	0.276893i	−0.716874	+	0.697203i	$0.754428\pi$
$8$	−2.60066	+	1.11201i	−0.919473	+	0.393154i
$9$	−0.415415	−	0.909632i	−0.138472	−	0.303211i
$10$	−2.57311	+	2.41391i	−0.813690	+	0.763345i
$11$	3.71536	+	3.21937i	1.12022	+	0.970678i	0.999757	−	0.0220398i	$-0.00701604\pi$
$11$	3.71536	+	3.21937i	1.12022	+	0.970678i	0.120465	+	0.992718i	$0.461561\pi$
$12$	1.95102	−	0.439919i	0.563210	−	0.126994i
$13$	1.81486	+	6.18084i	0.503352	+	1.71426i	0.682903	+	0.730509i	$0.260717\pi$
$13$	1.81486	+	6.18084i	0.503352	+	1.71426i	−0.179551	+	0.983749i	$0.557465\pi$
$14$	−2.29658	+	2.87208i	−0.613787	+	0.767595i
$15$	2.09874	−	1.34878i	0.541893	−	0.348254i
$16$	0.0605865	+	3.99954i	0.0151466	+	0.999885i
$17$	0.253473	+	1.76294i	0.0614762	+	0.427576i	0.997196	+	0.0748325i	$0.0238422\pi$
$17$	0.253473	+	1.76294i	0.0614762	+	0.427576i	−0.935720	+	0.352744i	$0.885249\pi$
$18$	−1.41311	+	0.0558281i	−0.333074	+	0.0131588i
$19$	2.93640	+	0.422191i	0.673657	+	0.0968572i	0.470650	−	0.882320i	$-0.344019\pi$
$19$	2.93640	+	0.422191i	0.673657	+	0.0968572i	0.203007	+	0.979177i	$0.434929\pi$
$20$	1.77903	+	4.66163i	0.397803	+	1.04237i
$21$	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
$26$	9.06148	+	0.939513i	1.77710	+	0.184254i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	2.52688	+	4.54545i	0.477535	+	0.859009i
$29$	−8.21491	+	1.18113i	−1.52547	+	0.219329i	−0.853439	−	0.521193i	$-0.825487\pi$
$29$	−8.21491	+	1.18113i	−1.52547	+	0.219329i	−0.672031	+	0.740523i	$0.734578\pi$
$30$	−0.639578	−	3.46970i	−0.116771	−	0.633477i
$31$	−7.54861	+	4.85119i	−1.35577	+	0.871300i	−0.998043	−	0.0625263i	$-0.980084\pi$
$31$	−7.54861	+	4.85119i	−1.35577	+	0.871300i	−0.357726	+	0.933826i	$0.616448\pi$
$32$	5.26630	+	2.06545i	0.930959	+	0.365123i
$33$	−4.71698	+	1.38503i	−0.821121	+	0.241103i
$34$	2.44291	+	0.613673i	0.418956	+	0.105244i
$35$	4.90268	+	4.24820i	0.828704	+	0.718076i
$36$	−0.684716	+	1.87914i	−0.114119	+	0.313190i
$37$	−6.44490	+	2.94329i	−1.05953	+	0.483873i	−0.867460	−	0.497507i	$-0.834249\pi$
$37$	−6.44490	+	2.94329i	−1.05953	+	0.483873i	−0.192075	+	0.981380i	$0.561522\pi$
$38$	2.12711	−	3.61619i	0.345063	−	0.586623i
$39$	−6.18084	−	1.81486i	−0.989727	−	0.290610i
$40$	7.05422	+	0.171730i	1.11537	+	0.0271529i
$41$	−1.79665	+	3.93411i	−0.280589	+	0.614405i	−0.996482	−	0.0838053i	$-0.973293\pi$
$41$	−1.79665	+	3.93411i	−0.280589	+	0.614405i	0.715893	+	0.698210i	$0.246020\pi$
$42$	−1.17452	−	3.48477i	−0.181232	−	0.537711i
$43$	−2.68440	+	4.17701i	−0.409367	+	0.636988i	−0.983316	−	0.181903i	$-0.941774\pi$
$43$	−2.68440	+	4.17701i	−0.409367	+	0.636988i	0.573949	+	0.818891i	$0.305411\pi$
$44$	−0.775679	−	9.80160i	−0.116938	−	1.47765i
$45$			2.49478i			0.371900i
$46$	−4.76615	−	4.82533i	−0.702730	−	0.711457i
$47$	8.53380			1.24478			0.622391	−	0.782706i	$-0.286161\pi$
$47$	8.53380			1.24478			0.622391	+	0.782706i	$0.286161\pi$
$48$	−3.39738	−	2.11135i	−0.490370	−	0.304747i
$49$	−0.200594	−	0.128914i	−0.0286563	−	0.0184163i
$50$	1.64024	−	0.552833i	0.231965	−	0.0781824i
$51$	−1.62012	−	0.739884i	−0.226862	−	0.103604i
$52$	6.08862	−	11.3541i	0.844340	−	1.57453i
$53$	−1.11051	+	3.78203i	−0.152540	+	0.519502i	−0.999934	−	0.0114611i	$-0.996352\pi$
$53$	−1.11051	+	3.78203i	−0.152540	+	0.519502i	0.847395	+	0.530964i	$0.178170\pi$
$54$	0.717020	−	1.21897i	0.0975741	−	0.165880i
$55$	−5.09492	−	11.1563i	−0.686998	−	1.50432i
$56$	7.30321	−	0.869209i	0.975933	−	0.116153i
$57$	−1.94271	+	2.24201i	−0.257318	+	0.296961i
$58$	−2.85957	+	11.3834i	−0.375481	+	1.49472i
$59$	−4.07872	−	13.8908i	−0.531004	−	1.80843i	−0.586468	−	0.809973i	$-0.699482\pi$
$59$	−4.07872	−	13.8908i	−0.531004	−	1.80843i	0.0554637	−	0.998461i	$-0.482336\pi$
$60$	−4.88343	−	1.02365i	−0.630448	−	0.132153i
$61$	5.74932	+	8.94611i	0.736125	+	1.14543i	0.984263	+	0.176708i	$0.0565447\pi$
$61$	5.74932	+	8.94611i	0.736125	+	1.14543i	−0.248139	+	0.968724i	$0.579819\pi$
$62$	2.30039	+	12.4796i	0.292150	+	1.58490i
$63$	0.370061	+	2.57383i	0.0466233	+	0.324272i
$64$	5.52688	−	5.78391i	0.690860	−	0.722989i
$65$	2.28712	−	15.9073i	0.283682	−	1.97305i
$66$	−0.717000	+	6.91537i	−0.0882567	+	0.851224i
$67$	−7.32397	+	6.34625i	−0.894765	+	0.775318i	−0.975173	−	0.221444i	$-0.928923\pi$
$67$	−7.32397	+	6.34625i	−0.894765	+	0.775318i	0.0804081	+	0.996762i	$0.474378\pi$
$68$	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	0.489975	−	0.871737i	$-0.337006\pi$
$71$	−3.72958	−	4.30416i	−0.442620	−	0.510810i	−0.932594	+	0.360926i	$0.882461\pi$
$72$	2.09187	+	1.90370i	0.246529	+	0.224353i
$73$	−1.02497	+	7.12881i	−0.119964	+	0.834365i	0.837629	+	0.546239i	$0.183941\pi$
$73$	−1.02497	+	7.12881i	−0.119964	+	0.834365i	−0.957593	+	0.288125i	$0.906968\pi$
$74$	0.395552	+	10.0121i	0.0459820	+	1.16389i
$75$	−1.21147	+	0.174184i	−0.139889	+	0.0201130i
$76$	−3.59150	−	4.72270i	−0.411974	−	0.541731i
$77$	−6.91122	−	10.7541i	−0.787606	−	1.22554i
$78$	−5.68938	+	7.11506i	−0.644195	+	0.805622i
$79$	0.901525	−	0.264712i	0.101429	−	0.0297824i	−0.230624	−	0.973043i	$-0.574077\pi$
$79$	0.901525	−	0.264712i	0.101429	−	0.0297824i	0.332053	+	0.943261i	$0.392259\pi$
$80$	4.00751	−	9.13908i	0.448053	−	1.02178i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	4.18475	+	4.46074i	0.462128	+	0.492607i
$83$	5.74905	−	2.62550i	0.631040	−	0.288186i	−0.0741040	−	0.997251i	$-0.523610\pi$
$83$	5.74905	−	2.62550i	0.631040	−	0.288186i	0.705144	+	0.709064i	$0.250882\pi$
$84$	−5.19001	−	0.331709i	−0.566276	−	0.0361924i
$85$	1.25185	−	4.26339i	0.135782	−	0.462430i
$86$	4.02655	+	5.75271i	0.434194	+	0.620331i
$87$	3.44769	−	7.54938i	0.369631	−	0.809379i
$88$	−13.2424	−	4.24100i	−1.41164	−	0.452092i
$89$	−1.07103	−	0.688312i	−0.113529	−	0.0729609i	0.482644	−	0.875817i	$-0.339677\pi$
$89$	−1.07103	−	0.688312i	−0.113529	−	0.0729609i	−0.596173	+	0.802856i	$0.703313\pi$
$90$	3.26468	+	1.33781i	0.344127	+	0.141018i
$91$		−	16.7506i		−	1.75594i
$92$	−8.87027	+	3.64943i	−0.924789	+	0.380480i
$93$		−	8.97304i		−	0.930461i
$94$	4.57620	−	11.1674i	0.471999	−	1.15182i
$95$	−6.22613	−	4.00129i	−0.638787	−	0.410524i
$96$	−4.58474	+	3.31363i	−0.467928	+	0.338196i
$97$	−3.10826	+	6.80614i	−0.315596	+	0.691059i	−0.999249	−	0.0387485i	$-0.987663\pi$
$97$	−3.10826	+	6.80614i	−0.315596	+	0.691059i	0.683653	+	0.729807i	$0.260390\pi$
$98$	−0.276264	+	0.193368i	−0.0279069	+	0.0195332i
$99$	1.38503	−	4.71698i	0.139201	−	0.474075i
$100$	0.156132	−	2.44288i	0.0156132	−	0.244288i
$101$	10.6491	−	4.86327i	1.05962	−	0.483913i	0.192133	−	0.981369i	$-0.438459\pi$
$101$	10.6491	−	4.86327i	1.05962	−	0.483913i	0.867490	+	0.497455i	$0.165732\pi$
$102$	−1.83699	+	1.72333i	−0.181890	+	0.170636i
$103$	2.31960	−	2.67696i	0.228557	−	0.263769i	−0.629875	−	0.776697i	$-0.716894\pi$
$103$	2.31960	−	2.67696i	0.228557	−	0.263769i	0.858432	+	0.512928i	$0.171439\pi$
$104$	−11.5930	−	14.0561i	−1.13679	−	1.37832i
$105$	−6.22440	+	1.82765i	−0.607439	+	0.178360i
$106$	4.35368	+	3.48131i	0.422867	+	0.338134i
$107$	10.0446	+	15.6297i	0.971045	+	1.51098i	0.855584	+	0.517664i	$0.173198\pi$
$107$	10.0446	+	15.6297i	0.971045	+	1.51098i	0.115461	+	0.993312i	$0.463165\pi$
$108$	−1.21065	−	1.59196i	−0.116495	−	0.153186i
$109$	−7.46777	+	1.07370i	−0.715283	+	0.102842i	−0.490342	−	0.871530i	$-0.663128\pi$
$109$	−7.46777	+	1.07370i	−0.715283	+	0.102842i	−0.224941	+	0.974372i	$0.572219\pi$
$110$	−17.3313	+	0.684712i	−1.65248	+	0.0652847i
$111$	1.00833	−	7.01305i	0.0957060	−	0.665650i
$112$	2.77886	−	10.0231i	0.262577	−	0.947095i
$113$	7.98575	+	9.21604i	0.751236	+	0.866972i	0.994687	−	0.102941i	$-0.0328252\pi$
$113$	7.98575	+	9.21604i	0.751236	+	0.866972i	−0.243452	+	0.969913i	$0.578280\pi$
$114$	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
$118$	−20.3648	−	2.11146i	−1.87473	−	0.194376i
$119$	0.659105	−	4.58418i	0.0604201	−	0.420231i
$120$	−3.95827	+	5.84154i	−0.361339	+	0.533257i
$121$	1.87404	+	13.0342i	0.170367	+	1.18493i
$122$	14.7899	−	2.72627i	1.33902	−	0.246825i
$123$	−2.33824	−	3.63838i	−0.210832	−	0.328061i
$124$	17.5644	+	3.68180i	1.57733	+	0.330635i
$125$	2.65405	+	9.03887i	0.237386	+	0.808461i
$126$	3.56657	+	0.895940i	0.317735	+	0.0798167i
$127$	0.500748	−	0.577895i	0.0444342	−	0.0512798i	−0.733097	−	0.680124i	$-0.761926\pi$
$127$	0.500748	−	0.577895i	0.0444342	−	0.0512798i	0.777532	+	0.628844i	$0.216472\pi$
$128$	−4.60509	−	10.3341i	−0.407036	−	0.913412i
$129$	−2.06263	−	4.51652i	−0.181604	−	0.397658i
$130$	−19.5898	−	11.5231i	−1.71814	−	1.01064i
$131$	1.78108	−	6.06579i	0.155614	−	0.529971i	−0.844370	−	0.535761i	$-0.820025\pi$
$131$	1.78108	−	6.06579i	0.155614	−	0.529971i	0.999983	+	0.00578998i	$0.00184302\pi$
$132$	8.66499	+	4.64660i	0.754191	+	0.404435i
$133$	−7.01694	−	3.20453i	−0.608446	−	0.277868i
$134$	4.37729	+	12.9873i	0.378140	+	1.12193i
$135$	−2.09874	−	1.34878i	−0.180631	−	0.116085i
$136$	−2.61960	−	4.30295i	−0.224629	−	0.368975i
$137$	−1.06203			−0.0907357			−0.0453678	−	0.998970i	$-0.514446\pi$
$137$	−1.06203			−0.0907357			−0.0453678	+	0.998970i	$0.514446\pi$
$138$	6.63610	−	1.40076i	0.564903	−	0.119241i
$139$		−	8.91669i		−	0.756304i	−0.925744	−	0.378152i	$-0.876560\pi$
$139$		−	8.91669i		−	0.756304i	0.925744	−	0.378152i	$-0.123440\pi$
$140$	−1.02356	−	12.9339i	−0.0865070	−	1.09312i
$141$	−4.61372	+	7.17909i	−0.388545	+	0.604588i
$142$	−7.63241	+	2.57245i	−0.640498	+	0.215876i
$143$	−13.1556	+	28.8068i	−1.10013	+	2.40894i
$144$	3.61294	−	1.71658i	0.301079	−	0.143048i
$145$	19.8664	+	5.83331i	1.64982	+	0.484430i
$146$	8.77915	+	5.16406i	0.726568	+	0.427381i
$147$	0.216898	−	0.0990542i	0.0178895	−	0.00816985i
$148$	13.3140	+	4.85133i	1.09441	+	0.398777i
$149$	−9.19730	−	7.96951i	−0.753472	−	0.652887i	0.190958	−	0.981598i	$-0.438840\pi$
$149$	−9.19730	−	7.96951i	−0.753472	−	0.652887i	−0.944431	+	0.328711i	$0.893386\pi$
$150$	−0.421709	+	1.67874i	−0.0344324	+	0.137069i
$151$	16.3136	−	4.79011i	1.32758	−	0.389813i	0.460359	−	0.887733i	$-0.347721\pi$
$151$	16.3136	−	4.79011i	1.32758	−	0.389813i	0.867223	+	0.497919i	$0.165902\pi$
$152$	−8.10607	+	2.16733i	−0.657489	+	0.175793i
$153$	1.49833	−	0.962920i	0.121133	−	0.0778474i
$154$	−17.7789	+	3.27723i	−1.43266	+	0.264087i
$155$	22.1579	−	3.18583i	1.77977	−	0.255892i
$156$	6.25990	+	11.2605i	0.501193	+	0.901565i
$157$	−22.2349	−	3.19690i	−1.77454	−	0.255140i	−0.824187	−	0.566317i	$-0.808368\pi$
$157$	−22.2349	−	3.19690i	−1.77454	−	0.255140i	−0.950352	+	0.311177i	$0.899277\pi$
$158$	0.137035	−	1.32169i	0.0109020	−	0.105148i
$159$	−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	$-0.819846\pi$
$163$	−5.53347	+	4.79478i	−0.433415	+	0.375556i	0.410654	+	0.911791i	$0.365301\pi$
$164$	8.08139	−	3.08412i	0.631051	−	0.240829i
$165$	12.1398	+	1.74544i	0.945083	+	0.135882i
$166$	−0.352844	−	8.93113i	−0.0273860	−	0.693190i
$167$	−1.01076	−	7.02997i	−0.0782147	−	0.543995i	−0.990824	−	0.135162i	$-0.956845\pi$
$167$	−1.01076	−	7.02997i	−0.0782147	−	0.543995i	0.912609	−	0.408834i	$-0.134064\pi$
$168$	−3.21719	+	6.61378i	−0.248212	+	0.510264i
$169$	−23.9728	+	15.4064i	−1.84406	+	1.18511i
$170$	−4.90779	−	3.92439i	−0.376411	−	0.300987i
$171$	−0.835787	−	2.84643i	−0.0639142	−	0.217672i
$172$	9.68723	−	2.18430i	0.738645	−	0.166551i
$173$	11.5461	+	10.0048i	0.877837	+	0.760650i	0.972018	−	0.234905i	$-0.0754780\pi$
$173$	11.5461	+	10.0048i	0.877837	+	0.760650i	−0.0941816	+	0.995555i	$0.530023\pi$
$174$	−8.03034	−	8.55997i	−0.608779	−	0.648930i
$175$	−1.32210	−	2.89499i	−0.0999410	−	0.218840i
$176$	−12.6509	+	15.0548i	−0.953599	+	1.13480i
$177$	13.8908	+	4.07872i	1.04410	+	0.306575i
$178$	−1.47506	+	1.03245i	−0.110561	+	0.0773857i
$179$	−18.6525	−	8.51832i	−1.39416	−	0.636689i	−0.430195	−	0.902736i	$-0.641555\pi$
$179$	−18.6525	−	8.51832i	−1.39416	−	0.636689i	−0.963960	+	0.266047i	$0.914282\pi$
$180$	3.50133	−	3.55477i	0.260974	−	0.264957i
$181$	1.26051	−	1.96139i	0.0936927	−	0.145789i	−0.791243	−	0.611502i	$-0.790566\pi$
$181$	1.26051	−	1.96139i	0.0936927	−	0.145789i	0.884936	+	0.465713i	$0.154202\pi$
$182$	−21.9198	−	8.98240i	−1.62481	−	0.665819i
$183$	−10.6343			−0.786107
$184$	0.0190265	+	13.5646i	0.00140266	+	0.999999i
$185$	17.6760			1.29956
$186$	−11.7422	−	4.81175i	−0.860976	−	0.352814i
$187$	−4.73383	+	7.36598i	−0.346172	+	0.538654i
$188$	−12.1597	−	11.9769i	−0.886835	−	0.873502i
$189$	−2.36531	−	1.08020i	−0.172051	−	0.0785732i
$190$	−8.57483	+	6.00186i	−0.622083	+	0.435421i
$191$	−11.1346	−	3.26942i	−0.805673	−	0.236567i	−0.147137	−	0.989116i	$-0.547006\pi$
$191$	−11.1346	−	3.26942i	−0.805673	−	0.236567i	−0.658536	+	0.752549i	$0.728824\pi$
$192$	1.87768	+	7.77652i	0.135510	+	0.561222i
$193$	−4.41382	−	9.66493i	−0.317714	−	0.695697i	0.681638	−	0.731690i	$-0.261268\pi$
$193$	−4.41382	−	9.66493i	−0.317714	−	0.695697i	−0.999352	+	0.0359929i	$0.988541\pi$
$194$	7.23975	+	7.71723i	0.519783	+	0.554065i
$195$	12.1455	+	10.5242i	0.869759	+	0.753651i
$196$	0.104897	+	0.465213i	0.00749265	+	0.0332295i
$197$	−5.00416	−	17.0426i	−0.356531	−	1.21423i	−0.921257	−	0.388955i	$-0.872836\pi$
$197$	−5.00416	−	17.0426i	−0.356531	−	1.21423i	0.564725	−	0.825279i	$-0.308982\pi$
$198$	−5.42994	−	4.34191i	−0.385889	−	0.308566i
$199$	7.18828	−	4.61962i	0.509563	−	0.327476i	−0.260468	−	0.965482i	$-0.583877\pi$
$199$	7.18828	−	4.61962i	0.509563	−	0.327476i	0.770031	+	0.638006i	$0.220241\pi$
$200$	−3.11304	−	1.51430i	−0.220125	−	0.107077i
$201$	−1.37917	−	9.59236i	−0.0972794	−	0.676593i
$202$	−0.653581	−	16.5433i	−0.0459858	−	1.16398i
$203$	21.3612	+	3.07128i	1.49926	+	0.215561i
$204$	1.27008	+	3.32802i	0.0889235	+	0.233008i
$205$	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
$210$	−0.946134	+	9.12533i	−0.0652894	+	0.629708i
$211$	0.978058	+	0.140624i	0.0673323	+	0.00968093i	0.175899	−	0.984408i	$-0.443717\pi$
$211$	0.978058	+	0.140624i	0.0673323	+	0.00968093i	−0.108566	+	0.994089i	$0.534626\pi$
$212$	6.89029	−	3.83041i	0.473227	−	0.263073i
$213$	5.63726	−	0.810515i	0.386258	−	0.0555356i
$214$	25.8394	−	4.76304i	1.76634	−	0.325594i
$215$	10.4207	−	6.69699i	0.710687	−	0.456731i
$216$	−2.73245	+	0.730577i	−0.185919	+	0.0497094i
$217$	22.3875	−	6.57355i	1.51976	−	0.446242i
$218$	−2.59950	+	10.3481i	−0.176060	+	0.700863i
$219$	−5.44300	−	4.71639i	−0.367804	−	0.318704i
$220$	−8.39780	+	23.0470i	−0.566180	+	1.55383i
$221$	−10.4365	+	4.76617i	−0.702032	+	0.320607i
$222$	−8.63660	−	5.08021i	−0.579650	−	0.340961i
$223$	14.3379	+	4.20999i	0.960137	+	0.281922i	0.724001	−	0.689799i	$-0.242301\pi$
$223$	14.3379	+	4.20999i	0.960137	+	0.281922i	0.236135	+	0.971720i	$0.424119\pi$
$224$	−11.6261	−	9.01126i	−0.776803	−	0.602090i
$225$	0.508440	−	1.11333i	0.0338960	−	0.0742219i
$226$	16.3425	−	5.50812i	1.08708	−	0.366395i
$227$	−10.2597	+	15.9644i	−0.680960	+	1.05959i	0.312990	+	0.949756i	$0.398669\pi$
$227$	−10.2597	+	15.9644i	−0.680960	+	1.05959i	−0.993950	+	0.109837i	$0.964967\pi$
$228$	5.91470	−	0.468078i	0.391711	−	0.0309992i
$229$			0.817962i			0.0540525i	0.999635	+	0.0270262i	$0.00860377\pi$
$229$			0.817962i			0.0540525i	−0.999635	+	0.0270262i	$0.991396\pi$
$230$	5.81514	+	15.8898i	0.383439	+	1.04774i
$231$	12.7834			0.841085
$232$	20.0508	−	12.2067i	1.31640	−	0.801412i
$233$	−2.28765	−	1.47019i	−0.149869	−	0.0963151i	0.463557	−	0.886067i	$-0.346573\pi$
$233$	−2.28765	−	1.47019i	−0.149869	−	0.0963151i	−0.613426	+	0.789752i	$0.710209\pi$
$234$	−2.90966	−	8.63290i	−0.190211	−	0.564350i
$235$	−19.3660	−	8.84417i	−1.26330	−	0.576930i
$236$	−13.6836	+	25.5172i	−0.890725	+	1.66103i
$237$	−0.264712	+	0.901525i	−0.0171949	+	0.0585603i
$238$	−5.64543	−	3.32075i	−0.365939	−	0.215252i
$239$	1.95146	+	4.27309i	0.126229	+	0.276403i	0.962187	−	0.272391i	$-0.0878144\pi$
$239$	1.95146	+	4.27309i	0.126229	+	0.276403i	−0.835958	+	0.548794i	$0.815087\pi$
$240$	5.52166	+	8.31229i	0.356422	+	0.536556i
$241$	1.06439	−	1.22837i	0.0685631	−	0.0791260i	−0.720432	−	0.693526i	$-0.756056\pi$
$241$	1.06439	−	1.22837i	0.0685631	−	0.0791260i	0.788995	+	0.614400i	$0.210602\pi$
$242$	18.0615	+	4.53715i	1.16104	+	0.291659i
$243$	−0.281733	−	0.959493i	−0.0180732	−	0.0615515i
$244$	4.36342	−	20.8161i	0.279340	−	1.33262i
$245$	0.321612	+	0.500438i	0.0205470	+	0.0319718i
$246$	−6.01506	+	1.10877i	−0.383506	+	0.0706927i
$247$	2.71966	+	18.9157i	0.173048	+	1.20357i
$248$	14.2368	−	21.0104i	0.904038	−	1.33416i
$249$	−0.899457	+	6.25586i	−0.0570008	+	0.396449i
$250$	13.2515	+	1.37394i	0.838099	+	0.0868959i
$251$	−3.66156	+	3.17276i	−0.231116	+	0.200263i	−0.762718	−	0.646731i	$-0.776136\pi$
$251$	−3.66156	+	3.17276i	−0.231116	+	0.200263i	0.531602	+	0.846994i	$0.321590\pi$
$252$	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
$256$	−15.9927	+	0.484636i	−0.999541	+	0.0302898i
$257$	−0.351940	+	2.44779i	−0.0219534	+	0.152689i	−0.997850	−	0.0655463i	$-0.979121\pi$
$257$	−0.351940	+	2.44779i	−0.0219534	+	0.152689i	0.975896	+	0.218235i	$0.0700301\pi$
$258$	−7.01641	+	0.277199i	−0.436822	+	0.0172577i
$259$	18.2360	−	2.62195i	1.13313	−	0.162920i
$260$	−25.5841	+	19.4561i	−1.58666	+	1.20662i
$261$	4.48698	+	6.98188i	0.277737	+	0.432168i
$262$	−6.98262	−	5.58347i	−0.431388	−	0.344948i
$263$	5.90435	−	1.73367i	0.364078	−	0.106903i	−0.0945768	−	0.995518i	$-0.530150\pi$
$263$	5.90435	−	1.73367i	0.364078	−	0.106903i	0.458654	+	0.888615i	$0.348332\pi$
$264$	10.7271	−	8.84732i	0.660208	−	0.544515i
$265$	6.43969	−	7.43180i	0.395587	−	0.456532i
$266$	−7.95625	+	7.46398i	−0.487829	+	0.457646i
$267$	1.15809	−	0.528882i	0.0708739	−	0.0323670i
$268$	19.3425	+	1.23624i	1.18153	+	0.0755154i
$269$	1.89761	−	6.46268i	0.115700	−	0.394037i	−0.881198	−	0.472748i	$-0.843262\pi$
$269$	1.89761	−	6.46268i	0.115700	−	0.394037i	0.996897	+	0.0787109i	$0.0250804\pi$
$270$	−2.89046	+	2.02315i	−0.175908	+	0.123125i
$271$	5.51868	−	12.0842i	0.335236	−	0.734064i	−0.664679	−	0.747129i	$-0.731432\pi$
$271$	5.51868	−	12.0842i	0.335236	−	0.734064i	0.999915	+	0.0130652i	$0.00415891\pi$
$272$	−7.03560	+	1.12059i	−0.426596	+	0.0679455i
$273$	14.0915	+	9.05604i	0.852854	+	0.548096i
$274$	−0.569510	+	1.38978i	−0.0344053	+	0.0839597i
$275$			6.01700i			0.362839i
$276$	1.72553	−	9.43518i	0.103865	−	0.567931i
$277$			17.0554i			1.02476i	0.858758	+	0.512381i	$0.171237\pi$
$277$			17.0554i			1.02476i	−0.858758	+	0.512381i	$0.828763\pi$
$278$	−11.6684	−	4.78153i	−0.699824	−	0.286777i
$279$	7.54861	+	4.85119i	0.451923	+	0.290433i
$280$	−17.4742	−	5.59630i	−1.04429	−	0.334443i
$281$	5.94061	−	13.0081i	0.354387	−	0.775999i	−0.645538	−	0.763728i	$-0.723367\pi$
$281$	5.94061	−	13.0081i	0.354387	−	0.775999i	0.999925	−	0.0122709i	$-0.00390603\pi$
$282$	6.92049	+	9.88727i	0.412109	+	0.588778i
$283$	−1.43324	+	4.88117i	−0.0851974	+	0.290156i	−0.991060	−	0.133416i	$-0.957405\pi$
$283$	−1.43324	+	4.88117i	−0.0851974	+	0.290156i	0.905863	+	0.423571i	$0.139224\pi$
$284$	−0.726516	+	11.3673i	−0.0431108	+	0.674523i
$285$	6.73220	−	3.07449i	0.398781	−	0.182117i
$286$	30.6420	+	32.6629i	1.81190	+	1.93140i
$287$	7.36467	−	8.49928i	0.434722	−	0.501696i
$288$	−0.308902	−	5.64841i	−0.0182022	−	0.332836i
$289$	13.2677	−	3.89574i	0.780451	−	0.229161i
$290$	18.2868	−	22.8692i	1.07384	−	1.34293i
$291$	−4.04524	−	6.29451i	−0.237136	−	0.368991i
$292$	11.4655	−	8.71923i	0.670967	−	0.510254i
$293$	1.93509	−	0.278224i	0.113049	−	0.0162540i	−0.0855581	−	0.996333i	$-0.527267\pi$
$293$	1.93509	−	0.278224i	0.113049	−	0.0162540i	0.198607	+	0.980079i	$0.436358\pi$
$294$	−0.0133120	−	0.336951i	−0.000776373	−	0.0196514i
$295$	−5.14007	+	35.7500i	−0.299267	+	2.08145i
$296$	13.4880	−	14.8213i	0.783976	−	0.861469i
$297$	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
$302$	2.47973	−	23.9167i	0.142693	−	1.37625i
$303$	−1.66608	+	11.5879i	−0.0957139	+	0.665705i
$304$	−1.51066	+	11.7698i	−0.0866425	+	0.675047i
$305$	−3.77564	−	26.2601i	−0.216192	−	1.50365i
$306$	−0.456607	−	2.47708i	−0.0261025	−	0.141605i
$307$	5.82245	+	9.05991i	0.332305	+	0.517077i	0.966693	−	0.255938i	$-0.0823843\pi$
$307$	5.82245	+	9.05991i	0.332305	+	0.517077i	−0.634388	+	0.773015i	$0.718748\pi$
$308$	−5.24525	+	25.0229i	−0.298876	+	1.42581i
$309$	0.997931	+	3.39864i	0.0567703	+	0.193342i
$310$	7.71308	−	30.7043i	0.438074	−	1.74389i
$311$	−9.14397	+	10.5527i	−0.518507	+	0.598389i	−0.953256	−	0.302163i	$-0.902291\pi$
$311$	−9.14397	+	10.5527i	−0.518507	+	0.598389i	0.434750	+	0.900551i	$0.356837\pi$
$312$	18.0924	−	2.15331i	1.02428	−	0.121907i
$313$	−9.66041	−	21.1534i	−0.546039	−	1.19566i	−0.958607	−	0.284732i	$-0.908096\pi$
$313$	−9.66041	−	21.1534i	−0.546039	−	1.19566i	0.412569	−	0.910927i	$-0.364632\pi$
$314$	−16.1068	+	27.3824i	−0.908961	+	1.54528i
$315$	1.82765	−	6.22440i	0.102976	−	0.350705i
$316$	−1.65608	−	0.888073i	−0.0931618	−	0.0499580i
$317$	−9.37272	−	4.28038i	−0.526424	−	0.240410i	0.134431	−	0.990923i	$-0.457079\pi$
$317$	−9.37272	−	4.28038i	−0.526424	−	0.240410i	−0.660856	+	0.750513i	$0.729806\pi$
$318$	−5.28244	+	1.78041i	−0.296224	+	0.0998405i
$319$	−34.3238	−	22.0586i	−1.92176	−	1.23504i
$320$	−18.5366	+	7.39773i	−1.03623	+	0.413546i
$321$	−18.5790			−1.03698
$322$	8.35640	+	15.5307i	0.465684	+	0.865491i
$323$			5.28372i			0.293994i
$324$	1.99377	−	0.157783i	0.110765	−	0.00876571i
$325$	−4.26258	+	6.63270i	−0.236445	+	0.367916i
$326$	3.30717	+	9.81229i	0.183167	+	0.543453i
$327$	3.13413	−	6.86278i	0.173318	−	0.379513i
$328$	0.297711	−	12.2292i	0.0164383	−	0.675243i
$329$	−21.2915	−	6.25176i	−1.17384	−	0.344671i
$330$	8.79399	−	14.9502i	0.484093	−	0.822982i
$331$	8.60315	−	3.92893i	0.472872	−	0.215953i	−0.164701	−	0.986344i	$-0.552666\pi$
$331$	8.60315	−	3.92893i	0.472872	−	0.215953i	0.637573	+	0.770390i	$0.279939\pi$
$332$	−11.8765	−	4.32754i	−0.651808	−	0.237504i
$333$	5.35462	+	4.63980i	0.293431	+	0.254260i
$334$	−9.74145	−	2.44710i	−0.533028	−	0.133900i
$335$	23.1976	−	6.81143i	1.26742	−	0.372148i
$336$	6.92962	+	7.75663i	0.378042	+	0.423159i
$337$	−11.7394	+	7.54444i	−0.639484	+	0.410972i	−0.819810	−	0.572635i	$-0.805921\pi$
$337$	−11.7394	+	7.54444i	−0.639484	+	0.410972i	0.180326	+	0.983607i	$0.442285\pi$
$338$	7.30557	+	39.6325i	0.397370	+	2.15572i
$339$	−12.0704	+	1.73547i	−0.655577	+	0.0942577i
$340$	−7.76725	+	4.31792i	−0.421238	+	0.234172i
$341$	−43.6636	−	6.27787i	−2.36451	−	0.339966i
$342$	−4.17303	−	0.432669i	−0.225652	−	0.0233961i
$343$	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	$-0.619711\pi$
$347$	9.33432	−	8.08823i	0.501092	−	0.434199i	0.868373	+	0.495911i	$0.165166\pi$
$348$	−15.5078	+	5.91829i	−0.831307	+	0.317254i
$349$	28.6029	+	4.11248i	1.53108	+	0.220136i	0.855753	−	0.517384i	$-0.173094\pi$
$349$	28.6029	+	4.11248i	1.53108	+	0.220136i	0.675325	+	0.737520i	$0.264003\pi$
$350$	−4.49735	+	0.177678i	−0.240394	+	0.00949729i
$351$	0.916761	+	6.37621i	0.0489331	+	0.340337i
$352$	12.9167	+	24.6281i	0.688464	+	1.31268i
$353$	−9.74320	+	6.26157i	−0.518578	+	0.333270i	−0.773609	−	0.633663i	$-0.781551\pi$
$353$	−9.74320	+	6.26157i	−0.518578	+	0.333270i	0.255031	+	0.966933i	$0.417914\pi$
$354$	12.7863	−	15.9904i	0.679585	−	0.849880i
$355$	4.00295	+	13.6328i	0.212455	+	0.723554i
$356$	0.560079	+	2.48392i	0.0296841	+	0.131647i
$357$	3.50012	+	3.03287i	0.185246	+	0.160516i
$358$	−21.1494	+	19.8408i	−1.11778	+	1.04862i
$359$	5.26744	+	11.5341i	0.278005	+	0.608745i	0.996200	−	0.0870963i	$-0.0277588\pi$
$359$	5.26744	+	11.5341i	0.278005	+	0.608745i	−0.718195	+	0.695842i	$0.755031\pi$
$360$	−2.77422	−	6.48808i	−0.146214	−	0.341952i
$361$	−9.78615	−	2.87347i	−0.515061	−	0.151235i
$362$	−1.89074	−	2.70129i	−0.0993749	−	0.141976i
$363$	−11.9783	−	5.47028i	−0.628695	−	0.287115i
$364$	−23.5088	+	23.8676i	−1.23219	+	1.25100i
$365$	9.71408	−	15.1154i	0.508458	−	0.791176i
$366$	−5.70257	+	13.9160i	−0.298078	+	0.727402i
$367$	27.1188			1.41559			0.707795	−	0.706418i	$-0.249690\pi$
$367$	27.1188			1.41559			0.707795	+	0.706418i	$0.249690\pi$
$368$	17.7609	+	7.24907i	0.925853	+	0.377884i
$369$	4.32495			0.225148
$370$	9.47863	−	23.1308i	0.492771	−	1.20251i
$371$	5.54135	−	8.62251i	0.287693	−	0.447659i
$372$	−12.5933	+	12.7855i	−0.652934	+	0.662900i
$373$	−4.61647	−	2.10827i	−0.239032	−	0.109162i	0.292298	−	0.956327i	$-0.405580\pi$
$373$	−4.61647	−	2.10827i	−0.239032	−	0.109162i	−0.531330	+	0.847165i	$0.678307\pi$
$374$	7.10066	+	10.1447i	0.367166	+	0.524568i
$375$	−9.03887	−	2.65405i	−0.466765	−	0.137055i
$376$	−22.1935	+	9.48965i	−1.14454	+	0.489391i
$377$	−22.2093	−	48.6315i	−1.14383	−	2.50465i
$378$	−2.68194	+	2.51601i	−0.137944	+	0.129409i
$379$	13.4409	+	11.6466i	0.690412	+	0.598245i	0.927759	−	0.373180i	$-0.121732\pi$
$379$	13.4409	+	11.6466i	0.690412	+	0.598245i	−0.237347	+	0.971425i	$0.576278\pi$
$380$	3.25585	+	14.4395i	0.167021	+	0.740731i
$381$	0.215431	+	0.733690i	0.0110369	+	0.0375881i
$382$	−10.2493	+	12.8176i	−0.524398	+	0.655805i
$383$	−18.6265	+	11.9705i	−0.951769	+	0.611665i	−0.921708	−	0.387884i	$-0.873206\pi$
$383$	−18.6265	+	11.9705i	−0.951769	+	0.611665i	−0.0300603	+	0.999548i	$0.509570\pi$
$384$	11.1833	+	1.71298i	0.570694	+	0.0874151i
$385$	4.53867	+	31.5671i	0.231312	+	1.60881i
$386$	−15.0144	+	0.593179i	−0.764215	+	0.0301920i
$387$	4.91468	+	0.706624i	0.249827	+	0.0359197i
$388$	13.9811	−	5.33563i	0.709781	−	0.270876i
$389$	2.34444	−	2.03147i	0.118868	−	0.103000i	−0.593399	−	0.804909i	$-0.702214\pi$
$389$	2.34444	−	2.03147i	0.118868	−	0.103000i	0.712266	+	0.701909i	$0.247669\pi$
$390$	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
$394$	−24.9854	−	2.59054i	−1.25875	−	0.130510i
$395$	−2.32020	−	0.333594i	−0.116742	−	0.0167850i
$396$	−8.59362	+	4.77731i	−0.431845	+	0.240069i
$397$	9.15193	−	1.31585i	0.459322	−	0.0660406i	0.0912301	−	0.995830i	$-0.470920\pi$
$397$	9.15193	−	1.31585i	0.459322	−	0.0660406i	0.368092	+	0.929789i	$0.380011\pi$
$398$	−2.19058	−	11.8838i	−0.109804	−	0.595683i
$399$	6.48946	−	4.17053i	0.324880	−	0.208787i
$400$	−3.65096	+	3.26170i	−0.182548	+	0.163085i
$401$	15.7838	−	4.63454i	0.788205	−	0.231438i	0.137232	−	0.990539i	$-0.456179\pi$
$401$	15.7838	−	4.63454i	0.788205	−	0.231438i	0.650973	+	0.759101i	$0.274361\pi$
$402$	−13.2922	−	3.33906i	−0.662953	−	0.166537i
$403$	−43.6841	−	37.8525i	−2.17606	−	1.88557i
$404$	−21.9991	−	8.01598i	−1.09450	−	0.398810i
$405$	2.26933	−	1.03637i	0.112764	−	0.0514976i
$406$	15.4739	−	26.3064i	0.767958	−	1.30556i
$407$	−33.4206	−	9.81318i	−1.65660	−	0.486421i
$408$	5.03614	+	0.122601i	0.249326	+	0.00606967i
$409$	−9.56672	+	20.9482i	−0.473044	+	1.03582i	0.511274	+	0.859418i	$0.329174\pi$
$409$	−9.56672	+	20.9482i	−0.473044	+	1.03582i	−0.984318	+	0.176404i	$0.943554\pi$
$410$	−4.87360	−	14.4599i	−0.240690	−	0.714121i
$411$	0.574179	−	0.893440i	0.0283222	−	0.0440701i
$412$	−7.06217	+	0.558886i	−0.347928	+	0.0275343i
$413$			37.6452i			1.85240i
$414$	−2.40935	+	6.33996i	−0.118413	+	0.311592i
$415$	−15.7675			−0.773996
$416$	−3.20862	+	36.2987i	−0.157315	+	1.77969i
$417$	7.50120	+	4.82073i	0.367335	+	0.236072i
$418$	19.5448	−	6.58746i	0.955969	−	0.322203i
$419$	−15.9425	−	7.28070i	−0.778842	−	0.355685i	−0.0139993	−	0.999902i	$-0.504456\pi$
$419$	−15.9425	−	7.28070i	−0.778842	−	0.355685i	−0.764843	+	0.644217i	$0.777184\pi$
$420$	11.4341	+	6.13152i	0.557926	+	0.299188i
$421$	−11.0122	+	37.5040i	−0.536701	+	1.82784i	0.0238500	+	0.999716i	$0.492408\pi$
$421$	−11.0122	+	37.5040i	−0.536701	+	1.82784i	−0.560551	+	0.828120i	$0.689411\pi$
$422$	0.708499	−	1.20448i	0.0344892	−	0.0586332i
$423$	−3.54507	−	7.76261i	−0.172367	−	0.377431i
$424$	−1.31760	−	11.0707i	−0.0639885	−	0.537640i
$425$	−1.42754	+	1.64747i	−0.0692458	+	0.0799139i
$426$	1.96231	−	7.81157i	0.0950740	−	0.378472i
$427$	−7.79054	−	26.5321i	−0.377011	−	1.28398i
$428$	7.62329	−	36.3676i	0.368486	−	1.75790i
$429$	−17.1213	−	26.6413i	−0.826625	−	1.28625i
$430$	−3.17565	−	17.2278i	−0.153143	−	0.830799i
$431$	3.11827	+	21.6881i	0.150202	+	1.04468i	0.915880	+	0.401453i	$0.131495\pi$
$431$	3.11827	+	21.6881i	0.150202	+	1.04468i	−0.765678	+	0.643225i	$0.777596\pi$
$432$	−0.509224	+	3.96745i	−0.0245001	+	0.190884i
$433$	1.91696	−	13.3328i	0.0921233	−	0.640731i	−0.890481	−	0.455020i	$-0.849632\pi$
$433$	1.91696	−	13.3328i	0.0921233	−	0.640731i	0.982604	−	0.185711i	$-0.0594589\pi$
$434$	3.40298	−	32.8213i	0.163348	−	1.57547i
$435$	−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	0.958712	−	0.284378i	$-0.0917872\pi$
$439$	11.3308	+	13.0764i	0.540790	+	0.624104i	−0.417923	+	0.908483i	$0.637242\pi$
$440$	25.6561	+	23.3482i	1.22310	+	1.11308i
$441$	−0.0339345	+	0.236019i	−0.00161593	+	0.0112390i
$442$	0.640531	+	16.2130i	0.0304670	+	0.771174i
$443$	−3.13276	+	0.450424i	−0.148842	+	0.0214003i	−0.216333	−	0.976320i	$-0.569410\pi$
$443$	−3.13276	+	0.450424i	−0.148842	+	0.0214003i	0.0674910	+	0.997720i	$0.478501\pi$
$444$	−11.2793	+	8.57764i	−0.535292	+	0.407077i
$445$	1.71719	+	2.67199i	0.0814025	+	0.126665i
$446$	13.1978	−	16.5050i	0.624935	−	0.781536i
$447$	11.6768	−	3.42862i	0.552294	−	0.162168i
$448$	−18.0266	+	10.3817i	−0.851677	+	0.490491i
$449$	0.393845	−	0.454521i	0.0185867	−	0.0214502i	−0.746380	−	0.665520i	$-0.768210\pi$
$449$	0.393845	−	0.454521i	0.0185867	−	0.0214502i	0.764967	+	0.644070i	$0.222755\pi$
$450$	−1.18426	−	1.26236i	−0.0558264	−	0.0595083i
$451$	−19.3406	+	8.83254i	−0.910711	+	0.415908i
$452$	1.55561	−	24.3395i	0.0731698	−	1.14483i
$453$	−4.79011	+	16.3136i	−0.225059	+	0.766480i
$454$	15.3893	+	21.9867i	0.722258	+	1.03189i
$455$	−17.3598	+	38.0126i	−0.813838	+	1.78206i
$456$	2.55920	−	7.99100i	0.119845	−	0.374213i
$457$	25.5683	+	16.4318i	1.19604	+	0.768646i	0.978266	−	0.207354i	$-0.0664853\pi$
$457$	25.5683	+	16.4318i	1.19604	+	0.768646i	0.217770	+	0.976000i	$0.430122\pi$
$458$	1.07039	+	0.438628i	0.0500159	+	0.0204957i
$459$			1.78107i			0.0831333i
$460$	23.9117	+	0.911097i	1.11489	+	0.0424801i
$461$			22.3125i			1.03920i	0.854410	+	0.519599i	$0.173919\pi$
$461$			22.3125i			1.03920i	−0.854410	+	0.519599i	$0.826081\pi$
$462$	6.85502	−	16.7284i	0.318924	−	0.778274i
$463$	24.5615	+	15.7847i	1.14147	+	0.733577i	0.967923	−	0.251248i	$-0.0808411\pi$
$463$	24.5615	+	15.7847i	1.14147	+	0.733577i	0.173546	+	0.984826i	$0.444477\pi$
$464$	−5.22167	−	32.7843i	−0.242410	−	1.52197i
$465$	−9.29939	+	20.3628i	−0.431249	+	0.944303i
$466$	−3.15063	+	2.20525i	−0.145950	+	0.102156i
$467$	−0.287045	+	0.977585i	−0.0132828	+	0.0452372i	−0.965868	−	0.259036i	$-0.916595\pi$
$467$	−0.287045	+	0.977585i	−0.0132828	+	0.0452372i	0.952585	+	0.304273i	$0.0984135\pi$
$468$	−12.8573	−	0.821751i	−0.594330	−	0.0379855i
$469$	22.9223	−	10.4682i	1.05845	−	0.483379i
$470$	−21.9584	+	20.5998i	−1.01287	+	0.950198i
$471$	14.7105	−	16.9768i	0.677824	−	0.782251i
$472$	26.0541	+	31.5898i	1.19924	+	1.45404i
$473$	−23.4209	+	6.87698i	−1.07689	+	0.316204i
$474$	1.03779	+	0.829840i	0.0476672	+	0.0381158i
$475$	1.96302	+	3.05452i	0.0900696	+	0.140151i
$476$	−7.37287	+	5.60689i	−0.337935	+	0.256991i
$477$	3.90158	−	0.560963i	0.178641	−	0.0256847i
$478$	6.63824	−	0.262259i	0.303626	−	0.0119954i
$479$	−0.341375	+	2.37431i	−0.0155978	+	0.108485i	−0.996133	−	0.0878584i	$-0.971998\pi$
$479$	−0.341375	+	2.37431i	−0.0155978	+	0.108485i	0.980535	+	0.196344i	$0.0629068\pi$
$480$	13.8385	−	2.76824i	0.631636	−	0.126352i
$481$	−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
$486$	−1.40667	−	0.145847i	−0.0638080	−	0.00661575i
$487$	0.0974437	−	0.677736i	0.00441560	−	0.0307111i	−0.987495	−	0.157653i	$-0.949607\pi$
$487$	0.0974437	−	0.677736i	0.00441560	−	0.0307111i	0.991910	+	0.126942i	$0.0405163\pi$
$488$	−24.9002	−	16.8725i	−1.12718	−	0.763783i
$489$	−1.04201	−	7.24731i	−0.0471211	−	0.327735i
$490$	0.827337	−	0.152505i	0.0373753	−	0.00688948i
$491$	−20.6265	−	32.0954i	−0.930859	−	1.44845i	−0.893459	−	0.449145i	$-0.851729\pi$
$491$	−20.6265	−	32.0954i	−0.930859	−	1.44845i	−0.0374007	−	0.999300i	$-0.511908\pi$
$492$	−1.77460	+	8.46590i	−0.0800052	+	0.381672i
$493$	−4.16451	−	14.1830i	−0.187560	−	0.638771i
$494$	26.2115	+	6.58446i	1.17931	+	0.296249i
$495$	−8.03163	+	9.26900i	−0.360995	+	0.416611i
$496$	−19.8599	−	29.8970i	−0.891736	−	1.34242i
$497$	6.15200	+	13.4710i	0.275955	+	0.604257i
$498$	7.70411	+	4.53170i	0.345229	+	0.203070i
$499$	−10.2975	+	35.0701i	−0.460980	+	1.56995i	0.321270	+	0.946988i	$0.395890\pi$
$499$	−10.2975	+	35.0701i	−0.460980	+	1.56995i	−0.782250	+	0.622965i	$0.785928\pi$
$500$	8.90400	−	16.6042i	0.398199	−	0.742562i
$501$	6.46044	+	2.95039i	0.288631	+	0.131813i
$502$	2.18839	+	6.49291i	0.0976728	+	0.289793i
$503$	11.4471	+	7.35660i	0.510401	+	0.328015i	0.770365	−	0.637604i	$-0.220074\pi$
$503$	11.4471	+	7.35660i	0.510401	+	0.328015i	−0.259964	+	0.965618i	$0.583711\pi$
$504$	−3.82452	−	6.28215i	−0.170358	−	0.279829i
$505$	−29.2064			−1.29967
$506$	−2.17337	−	33.2718i	−0.0966180	−	1.47911i
$507$		−	28.4966i		−	1.26558i
$508$	−1.52456	+	0.120651i	−0.0676415	+	0.00535301i
$509$	−5.41814	+	8.43080i	−0.240155	+	0.373689i	−0.940319	−	0.340293i	$-0.889474\pi$
$509$	−5.41814	+	8.43080i	−0.240155	+	0.373689i	0.700164	+	0.713982i	$0.253110\pi$
$510$	5.95476	−	2.00701i	0.263681	−	0.0888721i
$511$	7.77975	−	17.0353i	0.344156	−	0.753597i
$512$	−7.94178	+	21.1879i	−0.350980	+	0.936383i
$513$	2.84643	+	0.835787i	0.125673	+	0.0369009i
$514$	3.01446	+	1.77316i	0.132962	+	0.0782109i
$515$	−8.03826	+	3.67095i	−0.354208	+	0.161761i
$516$	−3.39977	+	9.33034i	−0.149666	+	0.410745i
$517$	31.7061	+	27.4735i	1.39443	+	1.20828i
$518$	6.34789	−	25.2697i	0.278910	−	1.11029i
$519$	−14.6589	+	4.30423i	−0.643453	+	0.188935i
$520$	11.7410	+	43.9127i	0.514876	+	1.92570i
$521$	22.1454	−	14.2320i	0.970207	−	0.623514i	0.0434020	−	0.999058i	$-0.486180\pi$
$521$	22.1454	−	14.2320i	0.970207	−	0.623514i	0.926805	+	0.375544i	$0.122544\pi$
$522$	11.5426	−	2.12768i	0.505207	−	0.0931262i
$523$	18.6887	−	2.68703i	0.817200	−	0.117496i	0.278977	−	0.960298i	$-0.410005\pi$
$523$	18.6887	−	2.68703i	0.817200	−	0.117496i	0.538224	+	0.842802i	$0.319096\pi$
$524$	−11.0509	+	6.14338i	−0.482763	+	0.268375i
$525$	3.15020	+	0.452930i	0.137486	+	0.0197675i
$526$	0.897484	−	8.65612i	0.0391322	−	0.377425i
$527$	−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
$532$	5.50089	+	14.4141i	0.238494	+	0.624930i
$533$	−27.5768	−	3.96494i	−1.19448	−	0.171741i
$534$	−0.0710771	−	1.79909i	−0.00307580	−	0.0778542i
$535$	−6.59637	−	45.8788i	−0.285186	−	1.98351i
$536$	11.9901	−	24.6488i	0.517892	−	1.06466i
$537$	17.2504	−	11.0861i	0.744409	−	0.478403i
$538$	−7.43950	−	5.94880i	−0.320740	−	0.256471i
$539$	−0.330256	−	1.12475i	−0.0142251	−	0.0484463i
$540$	1.09750	+	4.86736i	0.0472290	+	0.209458i
$541$	−25.2084	−	21.8432i	−1.08379	−	0.939113i	−0.0854332	−	0.996344i	$-0.527227\pi$
$541$	−25.2084	−	21.8432i	−1.08379	−	0.939113i	−0.998361	+	0.0572309i	$0.981773\pi$
$542$	−12.8541	−	13.7019i	−0.552130	−	0.588545i
$543$	0.968542	+	2.12081i	0.0415641	+	0.0910127i
$544$	−2.30640	+	9.80772i	−0.0988862	+	0.420502i
$545$	18.0596	+	5.30278i	0.773589	+	0.227146i
$546$	19.4072	−	13.5839i	0.830553	−	0.581337i
$547$	−4.52157	−	2.06493i	−0.193328	−	0.0882900i	0.316399	−	0.948626i	$-0.397526\pi$
$547$	−4.52157	−	2.06493i	−0.193328	−	0.0882900i	−0.509727	+	0.860336i	$0.670254\pi$
$548$	1.51327	+	1.49052i	0.0646439	+	0.0636720i
$549$	5.74932	−	8.94611i	0.245375	−	0.381811i
$550$	7.87386	+	3.22658i	0.335743	+	0.137582i
$551$	−24.6209			−1.04889
$552$	−11.4216	−	7.31760i	−0.486135	−	0.311458i
$553$	−2.44320			−0.103895
$554$	22.3188	+	9.14589i	0.948235	+	0.388572i
$555$	−9.55634	+	14.8700i	−0.405644	+	0.631195i
$556$	−12.5142	+	12.7052i	−0.530722	+	0.538822i
$557$	−0.148531	−	0.0678319i	−0.00629347	−	0.00287413i	0.412266	−	0.911064i	$-0.364738\pi$
$557$	−0.148531	−	0.0678319i	−0.00629347	−	0.00287413i	−0.418559	+	0.908189i	$0.637465\pi$
$558$	10.3962	−	7.27670i	0.440106	−	0.308047i
$559$	−30.6893	−	9.01118i	−1.29802	−	0.381132i
$560$	−16.6938	+	19.8659i	−0.705442	+	0.839486i
$561$	−3.63736	−	7.96470i	−0.153569	−	0.336270i
$562$	−13.8368	−	14.7494i	−0.583672	−	0.622167i
$563$	20.9140	+	18.1221i	0.881420	+	0.763755i	0.972699	−	0.232071i	$-0.0745501\pi$
$563$	20.9140	+	18.1221i	0.881420	+	0.763755i	−0.0912791	+	0.995825i	$0.529096\pi$
$564$	16.6496	−	3.75418i	0.701074	−	0.158080i
$565$	−8.57109	−	29.1904i	−0.360588	−	1.22805i
$566$	5.61895	+	4.49305i	0.236182	+	0.188857i
$567$	2.18751	−	1.40583i	0.0918668	−	0.0590392i
$568$	14.4856	+	7.04635i	0.607804	+	0.295658i
$569$	−3.43240	−	23.8728i	−0.143894	−	1.00080i	−0.925964	−	0.377612i	$-0.876745\pi$
$569$	−3.43240	−	23.8728i	−0.143894	−	1.00080i	0.782070	−	0.623190i	$-0.214164\pi$
$570$	−0.413185	−	10.4585i	−0.0173064	−	0.438056i
$571$	−5.55222	−	0.798289i	−0.232353	−	0.0334074i	0.0251545	−	0.999684i	$-0.491992\pi$
$571$	−5.55222	−	0.798289i	−0.232353	−	0.0334074i	−0.257508	+	0.966276i	$0.582901\pi$
$572$	59.1744	−	22.5829i	2.47421	−	0.944237i
$573$	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	0.521967	−	0.852965i	$-0.325198\pi$
$577$	−9.52665	−	10.9943i	−0.396600	−	0.457701i	−0.918567	+	0.395265i	$0.870653\pi$
$578$	2.01674	−	19.4512i	0.0838853	−	0.809062i
$579$	10.5169	+	1.51211i	0.437069	+	0.0628411i
$580$	−20.1205	−	36.1936i	−0.835459	−	1.50286i
$581$	−16.2671	+	2.33886i	−0.674873	+	0.0970321i
$582$	−10.4063	+	1.91821i	−0.431353	+	0.0795124i
$583$	−16.3017	+	10.4765i	−0.675148	+	0.433891i
$584$	−5.26170	−	19.6794i	−0.217731	−	0.814340i
$585$	−15.4199	+	4.52768i	−0.637533	+	0.187196i
$586$	0.673596	−	2.68146i	0.0278260	−	0.110770i
$587$	10.4445	+	9.05017i	0.431089	+	0.373541i	0.843206	−	0.537590i	$-0.180665\pi$
$587$	10.4445	+	9.05017i	0.431089	+	0.373541i	−0.412117	+	0.911131i	$0.635211\pi$
$588$	−0.448074	−	0.163268i	−0.0184783	−	0.00673306i
$589$	−24.2139	+	11.0581i	−0.997715	+	0.455641i
$590$	44.0262	+	25.8971i	1.81253	+	1.06616i
$591$	17.0426	+	5.00416i	0.701038	+	0.205843i
$592$	−12.1623	−	25.5983i	−0.499866	−	1.05208i
$593$	10.6045	−	23.2206i	0.435474	−	0.953555i	−0.556933	−	0.830557i	$-0.688022\pi$
$593$	10.6045	−	23.2206i	0.435474	−	0.953555i	0.992407	−	0.122998i	$-0.0392508\pi$
$594$	6.58830	−	2.22054i	0.270321	−	0.0911100i
$595$	−6.24663	+	9.71995i	−0.256087	+	0.398479i
$596$	1.92018	+	24.2637i	0.0786536	+	0.993879i
$597$			8.54472i			0.349712i
$598$	21.1748	−	38.2161i	0.865900	−	1.56277i
$599$	24.3980			0.996877			0.498438	−	0.866925i	$-0.333907\pi$
$599$	24.3980			0.996877			0.498438	+	0.866925i	$0.333907\pi$
$600$	2.95694	−	1.80016i	0.120717	−	0.0734913i
$601$	13.7405	+	8.83047i	0.560486	+	0.360202i	0.790004	−	0.613102i	$-0.210079\pi$
$601$	13.7405	+	8.83047i	0.560486	+	0.360202i	−0.229518	+	0.973304i	$0.573715\pi$
$602$	−5.83174	−	17.3026i	−0.237684	−	0.705203i
$603$	8.81524	+	4.02579i	0.358984	+	0.163943i
$604$	−29.9677	−	16.0702i	−1.21937	−	0.653887i
$605$	9.25544	−	31.5211i	0.376287	−	1.28152i
$606$	14.2705	+	8.39416i	0.579698	+	0.340990i
$607$	−7.33012	−	16.0507i	−0.297520	−	0.651479i	0.700548	−	0.713605i	$-0.252939\pi$
$607$	−7.33012	−	16.0507i	−0.297520	−	0.651479i	−0.998068	+	0.0621266i	$0.980212\pi$
$608$	14.5920	+	8.28837i	0.591782	+	0.336138i
$609$	−14.1325	+	16.3097i	−0.572676	+	0.660904i
$610$	−36.3887	−	9.14104i	−1.47334	−	0.370110i
$611$	15.4876	+	52.7461i	0.626563	+	2.13388i
$612$	−3.48637	−	0.730805i	−0.140928	−	0.0295410i
$613$	−8.07873	−	12.5707i	−0.326297	−	0.507728i	0.638887	−	0.769301i	$-0.279395\pi$
$613$	−8.07873	−	12.5707i	−0.326297	−	0.507728i	−0.965184	+	0.261573i	$0.915759\pi$
$614$	14.9781	−	2.76095i	0.604467	−	0.111423i
$615$	1.53555	+	10.6800i	0.0619193	+	0.430658i
$616$	29.9323	+	20.2824i	1.20601	+	0.817199i
$617$	−0.423933	+	2.94852i	−0.0170669	+	0.118703i	−0.996574	−	0.0827074i	$-0.973643\pi$
$617$	−0.423933	+	2.94852i	−0.0170669	+	0.118703i	0.979507	+	0.201410i	$0.0645524\pi$
$618$	4.98261	+	0.516607i	0.200430	+	0.0207810i
$619$	24.6741	−	21.3803i	0.991737	−	0.859345i	0.00167853	−	0.999999i	$-0.499466\pi$
$619$	24.6741	−	21.3803i	0.991737	−	0.859345i	0.990059	+	0.140653i	$0.0449203\pi$
$620$	−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
$624$	6.88413	−	24.8305i	0.275586	−	0.994016i
$625$	4.21560	−	29.3201i	0.168624	−	1.17281i
$626$	−32.8617	+	1.29827i	−1.31342	+	0.0518895i
$627$	−14.4357	+	2.07554i	−0.576507	+	0.0828891i
$628$	27.1954	+	35.7611i	1.08522	+	1.42702i
$629$	−6.82245	−	10.6159i	−0.272029	−	0.423285i
$630$	−7.16520	−	5.72947i	−0.285468	−	0.228267i
$631$	−16.7757	+	4.92578i	−0.667829	+	0.196092i	−0.598036	−	0.801469i	$-0.704052\pi$
$631$	−16.7757	+	4.92578i	−0.667829	+	0.196092i	−0.0697928	+	0.997562i	$0.522234\pi$
$632$	−2.05020	+	1.69093i	−0.0815526	+	0.0672615i
$633$	−0.647078	+	0.746768i	−0.0257191	+	0.0296814i
$634$	−10.6274	+	9.96984i	−0.422067	+	0.395953i
$635$	−1.73528	+	0.792474i	−0.0688624	+	0.0314484i
$636$	−0.502826	+	7.86735i	−0.0199384	+	0.311961i
$637$	0.432747	−	1.47380i	0.0171461	−	0.0583941i
$638$	−47.2718	+	33.0874i	−1.87151	+	1.30994i
$639$	−2.36588	+	5.18056i	−0.0935929	+	0.204940i
$640$	−0.259452	+	28.2240i	−0.0102557	+	1.11565i
$641$	−22.8736	−	14.7000i	−0.903454	−	0.580614i	0.00435895	−	0.999990i	$-0.498612\pi$
$641$	−22.8736	−	14.7000i	−0.903454	−	0.580614i	−0.907813	+	0.419376i	$0.862249\pi$
$642$	−9.96289	+	24.3125i	−0.393204	+	0.959540i
$643$			27.6854i			1.09181i	0.837848	+	0.545904i	$0.183814\pi$
$643$			27.6854i			1.09181i	−0.837848	+	0.545904i	$0.816186\pi$
$644$	24.8046	−	2.60696i	0.977437	−	0.102729i
$645$			12.3871i			0.487743i
$646$	6.91429	+	2.83337i	0.272039	+	0.111477i
$647$	6.18926	+	3.97759i	0.243325	+	0.156375i	0.656620	−	0.754222i	$-0.271986\pi$
$647$	6.18926	+	3.97759i	0.243325	+	0.156375i	−0.413295	+	0.910597i	$0.635622\pi$
$648$	0.862671	−	2.69366i	0.0338889	−	0.105817i
$649$	29.5659	−	64.7403i	1.16056	−	2.54128i
$650$	6.39379	+	9.13477i	0.250785	+	0.358295i
$651$	−6.57355	+	22.3875i	−0.257638	+	0.877434i
$652$	14.6138	+	0.934015i	0.572322	+	0.0365789i
$653$	−16.9152	+	7.72490i	−0.661942	+	0.302299i	−0.717912	−	0.696134i	$-0.754902\pi$
$653$	−16.9152	+	7.72490i	−0.661942	+	0.302299i	0.0559703	+	0.998432i	$0.482175\pi$
$654$	−7.30000	−	7.78146i	−0.285452	−	0.304279i
$655$	−10.3283	+	11.9195i	−0.403559	+	0.465731i
$656$	−15.8435	−	6.94741i	−0.618584	−	0.271251i
$657$	6.91038	−	2.02907i	0.269600	−	0.0791616i
$658$	−19.5986	+	24.5097i	−0.764031	+	0.955488i
$659$	10.9244	+	16.9986i	0.425553	+	0.662173i	0.986139	−	0.165923i	$-0.0530605\pi$
$659$	10.9244	+	16.9986i	0.425553	+	0.662173i	−0.560586	+	0.828096i	$0.689424\pi$
$660$	−14.8482	−	19.5248i	−0.577964	−	0.760002i
$661$	47.6931	−	6.85723i	1.85505	−	0.266715i	0.877831	−	0.478970i	$-0.158990\pi$
$661$	47.6931	−	6.85723i	1.85505	−	0.266715i	0.977214	+	0.212255i	$0.0680808\pi$
$662$	−0.528014	−	13.3650i	−0.0205218	−	0.519445i
$663$	1.63282	−	11.3565i	0.0634134	−	0.441050i
$664$	−12.0317	+	13.2210i	−0.466922	+	0.513075i
$665$	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
$670$	3.52613	−	34.0090i	0.136226	−	1.31388i
$671$	−7.44012	+	51.7472i	−0.287223	+	1.99768i
$672$	13.8663	−	4.90867i	0.534905	−	0.189356i
$673$	−1.76993	−	12.3102i	−0.0682259	−	0.474522i	−0.995078	−	0.0990950i	$-0.968405\pi$
$673$	−1.76993	−	12.3102i	−0.0682259	−	0.474522i	0.926852	−	0.375427i	$-0.122504\pi$
$674$	3.57750	+	19.4078i	0.137800	+	0.747562i
$675$	0.661708	+	1.02964i	0.0254691	+	0.0396308i
$676$	55.7808	+	11.6926i	2.14542	+	0.449717i
$677$	8.59802	+	29.2822i	0.330449	+	1.12540i	0.942394	+	0.334505i	$0.108569\pi$
$677$	8.59802	+	29.2822i	0.330449	+	1.12540i	−0.611945	+	0.790900i	$0.709613\pi$
$678$	−4.20167	+	16.7261i	−0.161364	+	0.642360i
$679$	12.7411	−	14.7040i	0.488959	−	0.564289i
$680$	1.48530	+	12.4797i	0.0569587	+	0.478575i
$681$	−7.88329	−	17.2620i	−0.302088	−	0.661481i
$682$	−31.6296	+	53.7718i	−1.21116	+	2.05903i
$683$	−2.83608	+	9.65880i	−0.108520	+	0.369584i	−0.995790	−	0.0916662i	$-0.970781\pi$
$683$	−2.83608	+	9.65880i	−0.108520	+	0.369584i	0.887270	+	0.461250i	$0.152599\pi$
$684$	−2.80396	+	5.22883i	−0.107212	+	0.199929i
$685$	2.41011	+	1.10066i	0.0920855	+	0.0420540i
$686$	25.2243	−	8.50169i	0.963069	−	0.324596i
$687$	−0.688114	−	0.442224i	−0.0262532	−	0.0168719i
$688$	−16.8688	−	10.4833i	−0.643115	−	0.399672i
$689$	−25.3916			−0.967342
$690$	−16.5112	−	3.69866i	−0.628572	−	0.140805i
$691$		−	38.4909i		−	1.46426i	−0.681164	−	0.732131i	$-0.738526\pi$
$691$		−	38.4909i		−	1.46426i	0.681164	−	0.732131i	$-0.261474\pi$
$692$	−2.41056	−	30.4602i	−0.0916358	−	1.15792i
$693$	−6.91122	+	10.7541i	−0.262535	+	0.408513i
$694$	−5.57881	−	16.5522i	−0.211769	−	0.628312i
$695$	−9.24098	+	20.2349i	−0.350530	+	0.767555i
$696$	−0.571294	+	23.4672i	−0.0216549	+	0.889524i
$697$	−7.39101	−	2.17020i	−0.279955	−	0.0822021i
$698$	20.7198	−	35.2246i	0.784254	−	1.33327i
$699$	2.47360	−	1.12965i	0.0935601	−	0.0427274i
$700$	−2.17917	+	5.98053i	−0.0823649	+	0.226043i
$701$	19.0953	+	16.5461i	0.721218	+	0.624939i	0.936114	−	0.351698i	$-0.114396\pi$
$701$	19.0953	+	16.5461i	0.721218	+	0.624939i	−0.214895	+	0.976637i	$0.568941\pi$
$702$	8.83554	+	2.21953i	0.333476	+	0.0837709i
$703$	−20.1674	+	5.92170i	−0.760630	+	0.223341i
$704$	39.1549	−	3.69620i	1.47571	−	0.139306i
$705$	17.9102	−	11.5102i	0.674539	−	0.433500i
$706$	2.96918	+	16.1077i	0.111746	+	0.606222i
$707$	−30.1319	+	4.33231i	−1.13323	+	0.162933i
$708$	−14.0685	−	25.3070i	−0.528727	−	0.951094i
$709$	41.2840	+	5.93574i	1.55045	+	0.222921i	0.863713	−	0.503984i	$-0.168133\pi$
$709$	41.2840	+	5.93574i	1.55045	+	0.222921i	0.686738	+	0.726905i	$0.259042\pi$
$710$	19.9865	+	2.07224i	0.750080	+	0.0777698i
$711$	−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
$716$	14.6225	+	38.3157i	0.546470	+	1.43193i
$717$	−4.64979	−	0.668539i	−0.173650	−	0.0249670i
$718$	17.9182	−	0.707898i	0.668700	−	0.0264185i
$719$	−1.27591	−	8.87417i	−0.0475835	−	0.330951i	−0.999683	−	0.0251633i	$-0.991989\pi$
$719$	−1.27591	−	8.87417i	−0.0475835	−	0.330951i	0.952100	−	0.305787i	$-0.0989197\pi$
$720$	−9.97798	+	0.151150i	−0.371857	+	0.00563303i
$721$	−7.74843	+	4.97961i	−0.288567	+	0.185451i
$722$	−9.00801	+	11.2653i	−0.335243	+	0.419251i
$723$	0.457917	+	1.55952i	0.0170301	+	0.0579993i
$724$	−4.54881	+	1.02567i	−0.169055	+	0.0381189i
$725$	−7.67682	−	6.65200i	−0.285110	−	0.247049i
$726$	−13.5817	+	12.7414i	−0.504064	+	0.472876i
$727$	−3.40334	−	7.45227i	−0.126223	−	0.276389i	0.835962	−	0.548788i	$-0.184910\pi$
$727$	−3.40334	−	7.45227i	−0.126223	−	0.276389i	−0.962185	+	0.272398i	$0.912183\pi$
$728$	18.6268	+	43.5625i	0.690353	+	1.61453i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	−14.5709	−	20.8174i	−0.539295	−	0.770488i
$731$	−8.04425	−	3.67368i	−0.297527	−	0.135876i
$732$	15.1526	+	14.9248i	0.560056	+	0.551636i
$733$	−4.83784	+	7.52783i	−0.178690	+	0.278047i	−0.919032	−	0.394184i	$-0.871027\pi$
$733$	−4.83784	+	7.52783i	−0.178690	+	0.278047i	0.740342	+	0.672231i	$0.234664\pi$
$734$	14.5423	−	35.4877i	0.536766	−	1.30988i
$735$	−0.594871			−0.0219422
$736$	19.0104	−	19.3547i	0.700731	−	0.713425i
$737$	−47.6421			−1.75492
$738$	2.31923	−	5.65964i	0.0853720	−	0.208334i
$739$	10.7346	−	16.7033i	0.394878	−	0.614442i	−0.585710	−	0.810520i	$-0.699184\pi$
$739$	10.7346	−	16.7033i	0.394878	−	0.614442i	0.980588	+	0.196079i	$0.0628207\pi$
$740$	−25.1862	−	24.8075i	−0.925862	−	0.911943i
$741$	−17.3832	−	7.93866i	−0.638589	−	0.291634i
$742$	−8.31193	−	11.8752i	−0.305140	−	0.435953i
$743$	9.71237	+	2.85181i	0.356312	+	0.104623i	0.454990	−	0.890497i	$-0.349643\pi$
$743$	9.71237	+	2.85181i	0.356312	+	0.104623i	−0.0986773	+	0.995119i	$0.531461\pi$
$744$	9.97810	+	23.3358i	0.365815	+	0.855534i
$745$	12.6124	+	27.6173i	0.462082	+	1.01182i
$746$	−5.23445	+	4.91058i	−0.191647	+	0.179789i
$747$	−4.77648	−	4.13884i	−0.174762	−	0.151432i
$748$	17.0830	−	3.85192i	0.624618	−	0.140840i
$749$	−13.6108	−	46.3540i	−0.497327	−	1.69374i
$750$	−8.32014	+	10.4051i	−0.303809	+	0.379939i
$751$	−15.2735	+	9.81569i	−0.557338	+	0.358180i	−0.788786	−	0.614668i	$-0.789290\pi$
$751$	−15.2735	+	9.81569i	−0.557338	+	0.358180i	0.231448	+	0.972847i	$0.425654\pi$
$752$	0.517033	+	34.1313i	0.0188542	+	1.24464i
$753$	−0.689507	−	4.79563i	−0.0251270	−	0.174762i
$754$	−75.5489	+	2.98473i	−2.75133	+	0.108697i
$755$	−41.9853	−	6.03658i	−1.52800	−	0.219694i
$756$	1.85427	+	4.85879i	0.0674393	+	0.176713i
$757$	13.4627	−	11.6655i	0.489312	−	0.423991i	−0.374941	−	0.927049i	$-0.622337\pi$
$757$	13.4627	−	11.6655i	0.489312	−	0.423991i	0.864253	+	0.503058i	$0.167792\pi$
$758$	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	−0.998114	−	0.0613901i	$-0.980447\pi$
$761$	−25.2920	−	29.1885i	−0.916833	−	1.05808i	0.0812812	−	0.996691i	$-0.474099\pi$
$762$	1.07563	+	0.111524i	0.0389660	+	0.00404008i
$763$	19.4184	+	2.79195i	0.702995	+	0.101075i
$764$	11.2770	+	20.2856i	0.407989	+	0.733906i
$765$	−4.39815	+	0.632359i	−0.159016	+	0.0228630i
$766$	5.67630	+	30.7938i	0.205093	+	1.11262i
$767$	78.4548	−	50.4199i	2.83284	−	1.82056i
$768$	8.23858	−	13.7159i	0.297284	−	0.494930i
$769$	37.0275	−	10.8723i	1.33525	−	0.392064i	0.465275	−	0.885166i	$-0.345955\pi$
$769$	37.0275	−	10.8723i	1.33525	−	0.392064i	0.869971	+	0.493102i	$0.164137\pi$
$770$	43.7427	+	10.9884i	1.57638	+	0.395994i
$771$	−1.86894	−	1.61945i	−0.0673083	−	0.0583230i
$772$	−7.27518	+	19.9660i	−0.261839	+	0.718593i
$773$	−8.89825	+	4.06369i	−0.320048	+	0.146161i	−0.568960	−	0.822365i	$-0.692654\pi$
$773$	−8.89825	+	4.06369i	−0.320048	+	0.146161i	0.248912	+	0.968526i	$0.419927\pi$
$774$	3.56016	−	6.05244i	0.127967	−	0.217551i
$775$	−10.5375	−	3.09410i	−0.378519	−	0.111143i
$776$	0.515050	−	21.1569i	0.0184892	−	0.759487i
$777$	−7.65342	+	16.7587i	−0.274565	+	0.601214i
$778$	−1.40119	−	4.15731i	−0.0502352	−	0.149047i
$779$	−6.93663	+	10.7936i	−0.248530	+	0.386721i
$780$	−2.53570	−	32.0415i	−0.0907926	−	1.14727i
$781$		−	27.9984i		−	1.00186i
$782$	7.29870	−	9.62553i	0.261001	−	0.344208i
$783$	−8.29938			−0.296596
$784$	0.503443	−	0.810094i	0.0179801	−	0.0289319i
$785$	47.1453	+	30.2984i	1.68269	+	1.08140i
$786$	8.47221	−	2.85550i	0.302194	−	0.101852i
$787$	−12.0450	−	5.50076i	−0.429357	−	0.196081i	0.189002	−	0.981977i	$-0.439475\pi$
$787$	−12.0450	−	5.50076i	−0.429357	−	0.196081i	−0.618359	+	0.785896i	$0.712202\pi$
$788$	−16.7883	+	31.3069i	−0.598058	+	1.11526i
$789$	−1.73367	+	5.90435i	−0.0617204	+	0.210200i
$790$	−1.68074	+	2.85733i	−0.0597979	+	0.101659i
$791$	−13.1726	−	28.8440i	−0.468364	−	1.02557i
$792$	1.64333	+	13.8074i	0.0583930	+	0.490626i
$793$	−44.8603	+	51.7716i	−1.59304	+	1.83846i
$794$	3.18575	−	12.6819i	0.113058	−	0.450063i
$795$	2.77047	+	9.43535i	0.0982584	+	0.334637i
$796$	−16.7259	−	3.50605i	−0.592835	−	0.124269i
$797$	8.56676	+	13.3301i	0.303450	+	0.472178i	0.959171	−	0.282825i	$-0.0912717\pi$
$797$	8.56676	+	13.3301i	0.303450	+	0.472178i	−0.655721	+	0.755003i	$0.727635\pi$
$798$	−1.97762	−	10.7286i	−0.0700071	−	0.379787i
$799$	2.16309	+	15.0446i	0.0765245	+	0.532239i
$800$	2.31046	+	6.52672i	0.0816870	+	0.230755i
$801$	−0.181187	+	1.26018i	−0.00640192	+	0.0445263i
$802$	2.39920	−	23.1400i	0.0847187	−	0.817101i
$803$	−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
$808$	−22.2866	+	24.4896i	−0.784041	+	0.861540i
$809$	−7.36931	+	51.2547i	−0.259091	+	1.80202i	0.280244	+	0.959929i	$0.409585\pi$
$809$	−7.36931	+	51.2547i	−0.259091	+	1.80202i	−0.539336	+	0.842091i	$0.681325\pi$
$810$	−0.139279	−	3.52540i	−0.00489376	−	0.123870i
$811$	−22.8971	+	3.29210i	−0.804025	+	0.115601i	−0.532061	−	0.846706i	$-0.678582\pi$
$811$	−22.8971	+	3.29210i	−0.804025	+	0.115601i	−0.271964	+	0.962307i	$0.587673\pi$
$812$	−26.1268	−	34.3559i	−0.916871	−	1.20565i
$813$	7.18227	+	11.1758i	0.251893	+	0.391953i
$814$	−30.7632	+	38.4721i	−1.07825	+	1.34845i
$815$	17.5265	−	5.14623i	0.613925	−	0.180265i
$816$	2.86104	−	6.52456i	0.100156	−	0.228405i
$817$	−9.64597	+	11.1320i	−0.337470	+	0.389461i
$818$	22.2828	+	23.7524i	0.779099	+	0.830483i
$819$	−15.2368	+	6.95843i	−0.532418	+	0.243147i
$820$	−21.5357	−	1.37641i	−0.752058	−	0.0480663i
$821$	−8.71484	+	29.6800i	−0.304150	+	1.03584i	0.655629	+	0.755083i	$0.272403\pi$
$821$	−8.71484	+	29.6800i	−0.304150	+	1.03584i	−0.959779	+	0.280756i	$0.909415\pi$
$822$	−0.861258	−	1.23047i	−0.0300398	−	0.0429177i
$823$	−15.2355	+	33.3610i	−0.531075	+	1.16289i	0.433999	+	0.900914i	$0.357102\pi$
$823$	−15.2355	+	33.3610i	−0.531075	+	1.16289i	−0.965074	+	0.261979i	$0.915625\pi$
$824$	−3.05569	+	9.54127i	−0.106450	+	0.332386i
$825$	−5.06182	−	3.25304i	−0.176230	−	0.113256i
$826$	49.2627	+	20.1870i	1.71407	+	0.702397i
$827$		−	18.3082i		−	0.636638i	−0.947984	−	0.318319i	$-0.896882\pi$
$827$		−	18.3082i		−	0.636638i	0.947984	−	0.318319i	$-0.103118\pi$
$828$	7.00448	+	6.55265i	0.243423	+	0.227720i
$829$		−	13.7874i		−	0.478858i	−0.970914	−	0.239429i	$-0.923040\pi$
$829$		−	13.7874i		−	0.478858i	0.970914	−	0.239429i	$-0.0769602\pi$
$830$	−8.45523	+	20.6334i	−0.293485	+	0.716195i
$831$	−14.3480	−	9.22087i	−0.497725	−	0.319869i
$832$	45.7800	+	23.6638i	1.58713	+	0.820394i
$833$	0.176423	−	0.386312i	0.00611268	−	0.0133849i
$834$	10.3309	−	7.23100i	0.357730	−	0.250389i
$835$	−4.99190	+	17.0009i	−0.172752	+	0.588339i
$836$	1.86044	−	29.1089i	0.0643446	−	1.00675i
$837$	−8.16217	+	3.72754i	−0.282126	+	0.128843i
$838$	−18.0766	+	16.9582i	−0.624447	+	0.585810i
$839$	−9.68051	+	11.1719i	−0.334208	+	0.385697i	−0.897835	−	0.440333i	$-0.854860\pi$
$839$	−9.68051	+	11.1719i	−0.334208	+	0.385697i	0.563626	+	0.826030i	$0.309406\pi$
$840$	14.1552	−	11.6747i	0.488401	−	0.402815i
$841$	38.2643	−	11.2354i	1.31946	−	0.387428i
$842$	43.1727	+	34.5219i	1.48783	+	1.18970i
$843$	7.73139	+	12.0303i	0.266283	+	0.414345i
$844$	−1.19626	−	1.57304i	−0.0411770	−	0.0541463i
$845$	70.3691	−	10.1175i	2.42077	−	0.348054i
$846$	−12.0592	+	0.476426i	−0.414604	+	0.0163799i
$847$	4.87305	−	33.8928i	0.167440	−	1.16457i
$848$	−15.1937	−	4.21237i	−0.521753	−	0.144653i
$849$	−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	$-0.962881\pi$
$853$	−29.7725	+	25.7980i	−1.01939	+	0.883308i	−0.0261830	+	0.999657i	$0.508335\pi$
$854$	−38.8977	−	4.03299i	−1.33105	−	0.138006i
$855$	−1.05327	+	7.32568i	−0.0360212	+	0.250533i
$856$	−43.5028	−	29.4778i	−1.48690	−	1.00753i
$857$	3.77630	+	26.2648i	0.128996	+	0.897187i	0.946830	+	0.321733i	$0.104265\pi$
$857$	3.77630	+	26.2648i	0.128996	+	0.897187i	−0.817834	+	0.575454i	$0.804825\pi$
$858$	−44.0441	+	8.11876i	−1.50364	+	0.277170i
$859$	−18.7610	−	29.1927i	−0.640118	−	0.996044i	−0.998058	−	0.0622987i	$-0.980157\pi$
$859$	−18.7610	−	29.1927i	−0.640118	−	0.996044i	0.357939	−	0.933745i	$-0.383480\pi$
$860$	−24.2473	−	5.08266i	−0.826826	−	0.173317i
$861$	3.16841	+	10.7906i	0.107979	+	0.367743i
$862$	30.0532	+	7.54953i	1.02362	+	0.257138i
$863$	9.94341	−	11.4753i	0.338477	−	0.390624i	−0.560837	−	0.827926i	$-0.689521\pi$
$863$	9.94341	−	11.4753i	0.338477	−	0.390624i	0.899315	+	0.437302i	$0.144066\pi$
$864$	4.91875	+	2.79390i	0.167339	+	0.0950503i
$865$	−15.8334	−	34.6703i	−0.538351	−	1.17882i
$866$	−16.4193	−	9.65816i	−0.557951	−	0.328198i
$867$	−3.89574	+	13.2677i	−0.132306	+	0.450593i
$868$	−41.1253	−	22.0534i	−1.39588	−	0.748542i
$869$	4.20169	+	1.91885i	0.142533	+	0.0650925i
$870$	9.35223	+	27.7478i	0.317070	+	0.940739i
$871$	−52.5172	−	33.7507i	−1.77948	−	1.14360i
$872$	18.2272	−	11.0966i	0.617250	−	0.375777i
$873$	7.48230			0.253237
$874$	−11.9581	−	16.1813i	−0.404489	−	0.547342i
$875$		−	24.4960i		−	0.828116i
$876$	1.13637	+	14.3593i	0.0383944	+	0.485157i
$877$	−21.9385	+	34.1369i	−0.740810	+	1.15272i	0.242388	+	0.970179i	$0.422069\pi$
$877$	−21.9385	+	34.1369i	−0.740810	+	1.15272i	−0.983198	+	0.182543i	$0.941567\pi$
$878$	23.1879	−	7.81535i	0.782555	−	0.263755i
$879$	−0.812131	+	1.77832i	−0.0273925	+	0.0599812i
$880$	44.3114	−	21.0533i	1.49374	−	0.709705i
$881$	46.5654	+	13.6728i	1.56883	+	0.460649i	0.946660	−	0.322235i	$-0.104434\pi$
$881$	46.5654	+	13.6728i	1.56883	+	0.460649i	0.622167	+	0.782884i	$0.286252\pi$
$882$	0.290658	+	0.170971i	0.00978698	+	0.00575689i
$883$	3.01396	−	1.37643i	0.101428	−	0.0463205i	−0.364055	−	0.931377i	$-0.618608\pi$
$883$	3.01396	−	1.37643i	0.101428	−	0.0463205i	0.465483	+	0.885057i	$0.345881\pi$
$884$	21.5599	+	7.85594i	0.725137	+	0.264224i
$885$	−27.2959	−	23.6520i	−0.917541	−	0.795054i
$886$	−1.09050	+	4.34108i	−0.0366361	+	0.145842i
$887$	33.2161	−	9.75314i	1.11529	−	0.327478i	0.328379	−	0.944546i	$-0.393498\pi$
$887$	33.2161	−	9.75314i	1.11529	−	0.327478i	0.786910	+	0.617068i	$0.211680\pi$
$888$	5.17626	+	19.3598i	0.173704	+	0.649674i
$889$	−1.67271	+	1.07499i	−0.0561009	+	0.0360539i
$890$	4.41741	−	0.814273i	0.148072	−	0.0272945i
$891$	−4.86608	+	0.699637i	−0.163020	+	0.0234387i
$892$	−14.5213	−	26.1214i	−0.486208	−	0.874611i
$893$	25.0587	+	3.60289i	0.838556	+	0.120566i
$894$	1.77492	−	17.1189i	0.0593623	−	0.572541i
$895$	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
$900$	−2.28698	+	0.872787i	−0.0762327	+	0.0290929i
$901$	−6.94899	−	0.999114i	−0.231504	−	0.0332853i
$902$	1.18702	+	30.0455i	0.0395233	+	1.00041i
$903$	1.83743	+	12.7796i	0.0611460	+	0.425280i
$904$	−31.0165	−	15.0876i	−1.03159	−	0.501806i
$905$	−4.89323	+	3.14469i	−0.162656	+	0.104533i
$906$	18.7794	+	15.0164i	0.623903	+	0.498888i
$907$	−3.94953	−	13.4509i	−0.131142	−	0.446628i	0.867573	−	0.497310i	$-0.165679\pi$
$907$	−3.94953	−	13.4509i	−0.131142	−	0.446628i	−0.998715	+	0.0506817i	$0.983861\pi$
$908$	37.0243	−	8.34831i	1.22869	−	0.277048i
$909$	−8.84757	−	7.66647i	−0.293455	−	0.254281i
$910$	40.4343	+	43.1011i	1.34038	+	1.42879i
$911$	−20.2729	−	44.3915i	−0.671672	−	1.47076i	−0.871232	−	0.490872i	$-0.836678\pi$
$911$	−20.2729	−	44.3915i	−0.671672	−	1.47076i	0.199559	−	0.979886i	$-0.436049\pi$
$912$	−9.08469	−	7.63411i	−0.300824	−	0.252791i
$913$	29.8122	+	8.75366i	0.986641	+	0.289704i
$914$	35.2135	−	24.6473i	1.16476	−	0.815262i
$915$	24.1327	+	11.0210i	0.797802	+	0.364344i
$916$	1.14798	−	1.16550i	0.0379303	−	0.0385092i
$917$	−8.88747	+	13.8292i	−0.293490	+	0.456679i
$918$	2.33071	+	0.955090i	0.0769251	+	0.0315227i
$919$	36.1028			1.19092			0.595461	−	0.803384i	$-0.296970\pi$
$919$	36.1028			1.19092			0.595461	+	0.803384i	$0.296970\pi$
$920$	14.0148	−	30.8024i	0.462055	−	1.01553i
$921$	−10.7695			−0.354868
$922$	29.1982	+	11.9650i	0.961593	+	0.394045i
$923$	19.8347	−	30.8634i	0.652867	−	1.01588i
$924$	−18.2148	−	17.9410i	−0.599224	−	0.590215i
$925$	−7.88812	−	3.60238i	−0.259360	−	0.118446i
$926$	33.8269	−	23.6768i	1.11162	−	0.778067i
$927$	−3.39864	−	0.997931i	−0.111626	−	0.0327764i
$928$	−45.7017	−	10.7473i	−1.50023	−	0.352798i
$929$	21.2409	+	46.5110i	0.696890	+	1.52598i	0.843702	+	0.536812i	$0.180371\pi$
$929$	21.2409	+	46.5110i	0.696890	+	1.52598i	−0.146812	+	0.989164i	$0.546901\pi$
$930$	21.6601	+	23.0887i	0.710263	+	0.757107i
$931$	−0.534598	−	0.463232i	−0.0175207	−	0.0151818i
$932$	1.19629	+	5.30548i	0.0391858	+	0.173787i
$933$	−3.93389	−	13.3976i	−0.128790	−	0.438618i
$934$	1.12534	+	0.899852i	0.0368224	+	0.0294441i
$935$	18.3765	−	11.8099i	0.600976	−	0.386224i
$936$	−7.97002	+	16.3845i	−0.260508	+	0.535544i
$937$	5.06836	+	35.2512i	0.165576	+	1.15161i	0.887895	+	0.460047i	$0.152167\pi$
$937$	5.06836	+	35.2512i	0.165576	+	1.15161i	−0.722319	+	0.691560i	$0.756924\pi$
$938$	−1.40684	−	35.6097i	−0.0459350	−	1.16270i
$939$	23.0181	+	3.30951i	0.751169	+	0.108002i
$940$	15.1819	+	39.7814i	0.495178	+	1.29753i
$941$	9.87223	−	8.55434i	0.321825	−	0.278863i	−0.478932	−	0.877852i	$-0.658976\pi$
$941$	9.87223	−	8.55434i	0.321825	−	0.278863i	0.800758	+	0.598989i	$0.204431\pi$
$942$	−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
$946$	−3.56006	+	34.3363i	−0.115748	+	1.11637i
$947$	0.192295	+	0.0276479i	0.00624875	+	0.000898435i	0.145439	−	0.989367i	$-0.453541\pi$
$947$	0.192295	+	0.0276479i	0.00624875	+	0.000898435i	−0.139190	+	0.990266i	$0.544450\pi$
$948$	1.64244	−	0.913055i	0.0533440	−	0.0296547i
$949$	−45.9223	+	6.60263i	−1.49070	+	0.214330i
$950$	5.04981	−	0.930845i	0.163838	−	0.0302006i
$951$	8.66816	−	5.57069i	0.281084	−	0.180642i
$952$	3.38353	+	12.6548i	0.109661	+	0.410145i
$953$	25.2340	−	7.40936i	0.817408	−	0.240013i	0.153809	−	0.988101i	$-0.450846\pi$
$953$	25.2340	−	7.40936i	0.817408	−	0.240013i	0.663600	+	0.748088i	$0.269028\pi$
$954$	1.35812	−	5.40643i	0.0439709	−	0.175040i
$955$	21.8798	+	18.9590i	0.708015	+	0.613498i
$956$	3.21653	−	8.82745i	0.104030	−	0.285500i
$957$	37.1137	−	16.9492i	1.19971	−	0.547891i
$958$	2.92397	+	1.71994i	0.0944693	+	0.0555686i
$959$	2.64974	+	0.778034i	0.0855646	+	0.0251240i
$960$	3.79827	−	19.5935i	0.122589	−	0.632377i
$961$	20.5695	−	45.0409i	0.663532	−	1.45293i
$962$	−61.1656	+	20.6155i	−1.97206	+	0.664669i
$963$	10.0446	−	15.6297i	0.323682	−	0.503659i
$964$	−3.24059	+	0.256454i	−0.104372	+	0.00825983i
$965$			26.5073i			0.853300i
$966$	−17.5831	−	1.36667i	−0.565725	−	0.0439720i
$967$	−13.1658			−0.423383			−0.211691	−	0.977337i	$-0.567897\pi$
$967$	−13.1658			−0.423383			−0.211691	+	0.977337i	$0.567897\pi$
$968$	−19.3679	−	31.8136i	−0.622507	−	1.02253i
$969$	−4.44495	−	2.85660i	−0.142792	−	0.0917671i
$970$	−8.43149	−	25.0160i	−0.270719	−	0.803216i
$971$	−8.58742	−	3.92174i	−0.275583	−	0.125855i	0.272829	−	0.962062i	$-0.412041\pi$
$971$	−8.58742	−	3.92174i	−0.275583	−	0.125855i	−0.548413	+	0.836208i	$0.684768\pi$
$972$	−0.945176	+	1.76257i	−0.0303165	+	0.0565344i
$973$	−6.53227	+	22.2469i	−0.209415	+	0.713201i
$974$	−0.834633	−	0.490947i	−0.0267434	−	0.0157310i
$975$	−3.27526	−	7.17182i	−0.104892	−	0.229682i
$976$	−35.4320	+	23.5366i	−1.13415	+	0.753390i
$977$	−25.9722	+	29.9735i	−0.830923	+	0.958936i	−0.999643	−	0.0267277i	$-0.991491\pi$
$977$	−25.9722	+	29.9735i	−0.830923	+	0.958936i	0.168720	+	0.985664i	$0.446037\pi$
$978$	−10.0426	−	2.52276i	−0.321127	−	0.0806689i
$979$	−1.76334	−	6.00538i	−0.0563566	−	0.191933i
$980$	0.244086	−	1.16444i	0.00779705	−	0.0371965i
$981$	4.07890	+	6.34689i	0.130229	+	0.202641i
$982$	−53.0610	+	9.78087i	−1.69324	+	0.312120i
$983$	−0.165213	−	1.14908i	−0.00526947	−	0.0366500i	0.987017	−	0.160615i	$-0.0513479\pi$
$983$	−0.165213	−	1.14908i	−0.00526947	−	0.0366500i	−0.992287	+	0.123965i	$0.960439\pi$
$984$	10.1269	+	6.86204i	0.322833	+	0.218754i
$985$	−6.30633	+	43.8615i	−0.200936	+	1.39754i
$986$	−20.7931	−	2.15588i	−0.662189	−	0.0686571i
$987$	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	0.366864	−	0.930274i	$-0.380431\pi$
$991$	−19.0817	−	22.0215i	−0.606151	−	0.699536i	−0.973016	+	0.230738i	$0.925886\pi$
$992$	−49.7731	+	9.95659i	−1.58030	+	0.316122i
$993$	−1.34599	+	9.36157i	−0.0427137	+	0.297081i
$994$	20.9272	−	0.826775i	0.663770	−	0.0262237i
$995$	−21.1002	+	3.03375i	−0.668922	+	0.0961765i
$996$	10.0615	−	7.65152i	0.318810	−	0.242448i
$997$	12.7963	+	19.9115i	0.405264	+	0.630603i	0.982563	−	0.185930i	$-0.0595297\pi$
$997$	12.7963	+	19.9115i	0.405264	+	0.630603i	−0.577299	+	0.816533i	$0.695893\pi$
$998$	40.3708	+	32.2815i	1.27792	+	1.02185i
$999$	−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.13.29	yes	480
8.5	even	2	inner	552.2.bb.a.13.4	✓	480
23.16	even	11	inner	552.2.bb.a.85.4	yes	480
184.85	even	22	inner	552.2.bb.a.85.29	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.4	✓	480	8.5	even	2	inner
552.2.bb.a.13.29	yes	480	1.1	even	1	trivial
552.2.bb.a.85.4	yes	480	23.16	even	11	inner
552.2.bb.a.85.29	yes	480	184.85	even	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.536245 - 1.30860i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(-1.42488 - 1.40346i) q^{4} +(-2.26933 - 1.03637i) q^{5} +(0.810951 + 1.15860i) q^{6} +(-2.49497 - 0.732589i) q^{7} +(-2.60066 + 1.11201i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.536245 - 1.30860i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(-1.42488 - 1.40346i) q^{4} +(-2.26933 - 1.03637i) q^{5} +(0.810951 + 1.15860i) q^{6} +(-2.49497 - 0.732589i) q^{7} +(-2.60066 + 1.11201i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(-2.57311 + 2.41391i) q^{10} +(3.71536 + 3.21937i) q^{11} +(1.95102 - 0.439919i) q^{12} +(1.81486 + 6.18084i) q^{13} +(-2.29658 + 2.87208i) q^{14} +(2.09874 - 1.34878i) q^{15} +(0.0605865 + 3.99954i) q^{16} +(0.253473 + 1.76294i) q^{17} +(-1.41311 + 0.0558281i) q^{18} +(2.93640 + 0.422191i) q^{19} +(1.77903 + 4.66163i) 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} +(9.06148 + 0.939513i) q^{26} +(0.989821 + 0.142315i) q^{27} +(2.52688 + 4.54545i) q^{28} +(-8.21491 + 1.18113i) q^{29} +(-0.639578 - 3.46970i) q^{30} +(-7.54861 + 4.85119i) q^{31} +(5.26630 + 2.06545i) q^{32} +(-4.71698 + 1.38503i) q^{33} +(2.44291 + 0.613673i) q^{34} +(4.90268 + 4.24820i) q^{35} +(-0.684716 + 1.87914i) q^{36} +(-6.44490 + 2.94329i) q^{37} +(2.12711 - 3.61619i) q^{38} +(-6.18084 - 1.81486i) q^{39} +(7.05422 + 0.171730i) q^{40} +(-1.79665 + 3.93411i) q^{41} +(-1.17452 - 3.48477i) q^{42} +(-2.68440 + 4.17701i) q^{43} +(-0.775679 - 9.80160i) q^{44} +2.49478i q^{45} +(-4.76615 - 4.82533i) q^{46} +8.53380 q^{47} +(-3.39738 - 2.11135i) q^{48} +(-0.200594 - 0.128914i) q^{49} +(1.64024 - 0.552833i) q^{50} +(-1.62012 - 0.739884i) q^{51} +(6.08862 - 11.3541i) q^{52} +(-1.11051 + 3.78203i) q^{53} +(0.717020 - 1.21897i) q^{54} +(-5.09492 - 11.1563i) q^{55} +(7.30321 - 0.869209i) q^{56} +(-1.94271 + 2.24201i) q^{57} +(-2.85957 + 11.3834i) q^{58} +(-4.07872 - 13.8908i) q^{59} +(-4.88343 - 1.02365i) q^{60} +(5.74932 + 8.94611i) q^{61} +(2.30039 + 12.4796i) q^{62} +(0.370061 + 2.57383i) q^{63} +(5.52688 - 5.78391i) q^{64} +(2.28712 - 15.9073i) q^{65} +(-0.717000 + 6.91537i) 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} +(2.09187 + 1.90370i) q^{72} +(-1.02497 + 7.12881i) q^{73} +(0.395552 + 10.0121i) q^{74} +(-1.21147 + 0.174184i) q^{75} +(-3.59150 - 4.72270i) q^{76} +(-6.91122 - 10.7541i) q^{77} +(-5.68938 + 7.11506i) q^{78} +(0.901525 - 0.264712i) q^{79} +(4.00751 - 9.13908i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(4.18475 + 4.46074i) q^{82} +(5.74905 - 2.62550i) q^{83} +(-5.19001 - 0.331709i) q^{84} +(1.25185 - 4.26339i) q^{85} +(4.02655 + 5.75271i) q^{86} +(3.44769 - 7.54938i) q^{87} +(-13.2424 - 4.24100i) q^{88} +(-1.07103 - 0.688312i) q^{89} +(3.26468 + 1.33781i) q^{90} -16.7506i q^{91} +(-8.87027 + 3.64943i) q^{92} -8.97304i q^{93} +(4.57620 - 11.1674i) q^{94} +(-6.22613 - 4.00129i) q^{95} +(-4.58474 + 3.31363i) q^{96} +(-3.10826 + 6.80614i) q^{97} +(-0.276264 + 0.193368i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more