LMFDB - Embedded newform 552.2.t.b.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.16
Character	$\chi$	$=$	552.19
Dual form			552.2.t.b.523.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.679570 + 1.24024i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-1.07637 + 1.68565i) q^{4} +(-2.38725 - 1.53419i) q^{5} +(-1.00146 - 0.998540i) q^{6} +(-0.401276 - 2.79093i) q^{7} +(-2.82208 - 0.189432i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.679570 + 1.24024i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-1.07637 + 1.68565i) q^{4} +(-2.38725 - 1.53419i) q^{5} +(-1.00146 - 0.998540i) q^{6} +(-0.401276 - 2.79093i) q^{7} +(-2.82208 - 0.189432i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.280457 - 4.00334i) q^{10} +(4.98944 + 2.27860i) q^{11} +(0.557865 - 1.92062i) q^{12} +(1.75473 + 0.252292i) q^{13} +(3.18872 - 2.39431i) q^{14} +(2.72278 + 0.799480i) q^{15} +(-1.68286 - 3.62877i) q^{16} +(2.60344 - 2.25590i) q^{17} +(1.24221 + 0.675949i) q^{18} +(-2.24237 - 1.94303i) q^{19} +(5.15568 - 2.37272i) q^{20} +(1.17132 + 2.56483i) q^{21} +(0.564671 + 7.73655i) q^{22} +(4.70968 - 0.904939i) q^{23} +(2.76113 - 0.613312i) q^{24} +(1.26814 + 2.77683i) q^{25} +(0.879561 + 2.34773i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(5.13647 + 2.32766i) q^{28} +(3.63711 - 3.15157i) q^{29} +(0.858775 + 3.92019i) q^{30} +(2.66363 - 9.07150i) q^{31} +(3.35691 - 4.55315i) q^{32} +(-5.42929 - 0.780614i) q^{33} +(4.56706 + 1.69584i) q^{34} +(-3.32388 + 7.27828i) q^{35} +(0.00583382 + 1.99999i) q^{36} +(-7.43109 + 4.77567i) q^{37} +(0.885963 - 4.10149i) q^{38} +(-1.75473 + 0.252292i) q^{39} +(6.44637 + 4.78183i) q^{40} +(-5.63816 - 3.62343i) q^{41} +(-2.38500 + 3.19569i) q^{42} +(-0.846556 - 2.88311i) q^{43} +(-9.21141 + 5.95785i) q^{44} -2.83773 q^{45} +(4.32289 + 5.22614i) q^{46} -3.76827i q^{47} +(2.63703 + 3.00767i) q^{48} +(-0.911837 + 0.267740i) q^{49} +(-2.58214 + 3.45984i) q^{50} +(-1.86242 + 2.89799i) q^{51} +(-2.31402 + 2.68631i) q^{52} +(2.03376 + 14.1451i) q^{53} +(-1.38233 - 0.298597i) q^{54} +(-8.41522 - 13.0943i) q^{55} +(0.603739 + 7.95224i) q^{56} +(2.69896 + 1.23257i) q^{57} +(6.38036 + 2.36916i) q^{58} +(1.19282 - 8.29627i) q^{59} +(-4.27836 + 3.72913i) q^{60} +(-11.5177 - 3.38190i) q^{61} +(13.0609 - 2.86119i) q^{62} +(-1.84647 - 2.13094i) q^{63} +(7.92823 + 1.06918i) q^{64} +(-3.80192 - 3.29438i) q^{65} +(-2.72144 - 7.26408i) q^{66} +(6.50409 - 2.97032i) q^{67} +(1.00039 + 6.81668i) q^{68} +(-4.26395 + 2.19515i) q^{69} +(-11.2856 + 0.823707i) q^{70} +(7.23605 - 3.30459i) q^{71} +(-2.47650 + 1.36637i) q^{72} +(0.108926 - 0.125708i) q^{73} +(-10.9729 - 5.97090i) q^{74} +(-1.99909 - 2.30707i) q^{75} +(5.68889 - 1.68845i) q^{76} +(4.35728 - 14.8395i) q^{77} +(-1.50537 - 2.00483i) q^{78} +(0.834900 - 5.80686i) q^{79} +(-1.54983 + 11.2446i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.662378 - 9.45502i) q^{82} +(8.14269 + 12.6703i) q^{83} +(-5.58418 - 0.786266i) q^{84} +(-9.67604 + 1.39120i) q^{85} +(3.00044 - 3.00920i) q^{86} +(-2.60188 + 4.04860i) q^{87} +(-13.6489 - 7.37554i) q^{88} +(3.55645 + 12.1122i) q^{89} +(-1.92843 - 3.51945i) q^{90} -4.99858i q^{91} +(-3.54394 + 8.91294i) q^{92} +9.45447i q^{93} +(4.67355 - 2.56080i) q^{94} +(2.37213 + 8.07872i) q^{95} +(-1.93817 + 5.31446i) q^{96} +(3.45235 - 5.37197i) q^{97} +(-0.951717 - 0.948945i) q^{98} +(5.42929 - 0.780614i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) $ 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9	$ 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9} - 4 q^{12} - 4 q^{16} - 44 q^{17} + 4 q^{18} + 55 q^{20} + 4 q^{24} - 24 q^{25} - 24 q^{27} + 4 q^{32} - 55 q^{34} + 7 q^{36} + 22 q^{38} + 11 q^{40} - 44 q^{42} + 77 q^{44} - 48 q^{46} + 51 q^{48} + 8 q^{49} - 33 q^{50} + 165 q^{52} - 7 q^{54} - 22 q^{56} - 59 q^{58} + 11 q^{60} + 29 q^{62} - 4 q^{64} + 55 q^{66} + 132 q^{70} + 4 q^{72} - 144 q^{73} - 66 q^{74} - 24 q^{75} - 55 q^{76} - 24 q^{81} - 26 q^{82} - 44 q^{84} - 110 q^{86} - 198 q^{88} - 47 q^{92} - 73 q^{94} + 4 q^{96} + 53 q^{98}+O(q^{100}) $ 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9 - 4 * q^12 - 4 * q^16 - 44 * q^17 + 4 * q^18 + 55 * q^20 + 4 * q^24 - 24 * q^25 - 24 * q^27 + 4 * q^32 - 55 * q^34 + 7 * q^36 + 22 * q^38 + 11 * q^40 - 44 * q^42 + 77 * q^44 - 48 * q^46 + 51 * q^48 + 8 * q^49 - 33 * q^50 + 165 * q^52 - 7 * q^54 - 22 * q^56 - 59 * q^58 + 11 * q^60 + 29 * q^62 - 4 * q^64 + 55 * q^66 + 132 * q^70 + 4 * q^72 - 144 * q^73 - 66 * q^74 - 24 * q^75 - 55 * q^76 - 24 * q^81 - 26 * q^82 - 44 * q^84 - 110 * q^86 - 198 * q^88 - 47 * q^92 - 73 * q^94 + 4 * q^96 + 53 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{15}{22}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.679570	+	1.24024i	0.480529	+	0.876979i
$2$	0.679570	+	1.24024i	0.480529	+	0.876979i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$4$	−1.07637	+	1.68565i	−0.538185	+	0.842827i
$5$	−2.38725	−	1.53419i	−1.06761	−	0.686111i	−0.115947	−	0.993255i	$-0.536990\pi$
$5$	−2.38725	−	1.53419i	−1.06761	−	0.686111i	−0.951663	+	0.307144i	$0.900627\pi$
$6$	−1.00146	−	0.998540i	−0.408843	−	0.407652i
$7$	−0.401276	−	2.79093i	−0.151668	−	1.05487i	−0.913424	−	0.407010i	$-0.866572\pi$
$7$	−0.401276	−	2.79093i	−0.151668	−	1.05487i	0.761756	−	0.647864i	$-0.224338\pi$
$8$	−2.82208	−	0.189432i	−0.997755	−	0.0669743i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.280457	−	4.00334i	0.0886882	−	1.26597i
$11$	4.98944	+	2.27860i	1.50437	+	0.687024i	0.985787	−	0.168002i	$-0.0537315\pi$
$11$	4.98944	+	2.27860i	1.50437	+	0.687024i	0.518585	+	0.855026i	$0.326459\pi$
$12$	0.557865	−	1.92062i	0.161042	−	0.554436i
$13$	1.75473	+	0.252292i	0.486675	+	0.0699733i	0.381285	−	0.924458i	$-0.375482\pi$
$13$	1.75473	+	0.252292i	0.486675	+	0.0699733i	0.105390	+	0.994431i	$0.466391\pi$
$14$	3.18872	−	2.39431i	0.852221	−	0.639907i
$15$	2.72278	+	0.799480i	0.703019	+	0.206425i
$16$	−1.68286	−	3.62877i	−0.420715	−	0.907193i
$17$	2.60344	−	2.25590i	0.631427	−	0.547135i	−0.279268	−	0.960213i	$-0.590092\pi$
$17$	2.60344	−	2.25590i	0.631427	−	0.547135i	0.910696	+	0.413078i	$0.135546\pi$
$18$	1.24221	+	0.675949i	0.292792	+	0.159323i
$19$	−2.24237	−	1.94303i	−0.514436	−	0.445761i	0.358547	−	0.933512i	$-0.383272\pi$
$19$	−2.24237	−	1.94303i	−0.514436	−	0.445761i	−0.872983	+	0.487750i	$0.837818\pi$
$20$	5.15568	−	2.37272i	1.15284	−	0.530556i
$21$	1.17132	+	2.56483i	0.255603	+	0.559692i
$22$	0.564671	+	7.73655i	0.120388	+	1.64944i
$23$	4.70968	−	0.904939i	0.982036	−	0.188693i
$23$	4.70968	−	0.904939i	0.982036	−	0.188693i
$24$	2.76113	−	0.613312i	0.563614	−	0.125192i
$25$	1.26814	+	2.77683i	0.253627	+	0.555366i
$26$	0.879561	+	2.34773i	0.172496	+	0.460428i
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$	5.13647	+	2.32766i	0.970701	+	0.439887i
$29$	3.63711	−	3.15157i	0.675394	−	0.585232i	−0.248151	−	0.968721i	$-0.579823\pi$
$29$	3.63711	−	3.15157i	0.675394	−	0.585232i	0.923545	+	0.383489i	$0.125278\pi$
$30$	0.858775	+	3.92019i	0.156790	+	0.715726i
$31$	2.66363	−	9.07150i	0.478402	−	1.62929i	−0.267732	−	0.963493i	$-0.586274\pi$
$31$	2.66363	−	9.07150i	0.478402	−	1.62929i	0.746134	−	0.665795i	$-0.231908\pi$
$32$	3.35691	−	4.55315i	0.593424	−	0.804890i
$33$	−5.42929	−	0.780614i	−0.945117	−	0.135887i
$34$	4.56706	+	1.69584i	0.783245	+	0.290835i
$35$	−3.32388	+	7.27828i	−0.561838	+	1.23025i
$36$	0.00583382	+	1.99999i	0.000972304	+	0.333332i
$37$	−7.43109	+	4.77567i	−1.22166	+	0.785115i	−0.982572	−	0.185882i	$-0.940486\pi$
$37$	−7.43109	+	4.77567i	−1.22166	+	0.785115i	−0.239091	+	0.970997i	$0.576849\pi$
$38$	0.885963	−	4.10149i	0.143722	−	0.665350i
$39$	−1.75473	+	0.252292i	−0.280982	+	0.0403991i
$40$	6.44637	+	4.78183i	1.01926	+	0.756073i
$41$	−5.63816	−	3.62343i	−0.880533	−	0.565884i	0.0204246	−	0.999791i	$-0.493498\pi$
$41$	−5.63816	−	3.62343i	−0.880533	−	0.565884i	−0.900958	+	0.433907i	$0.857135\pi$
$42$	−2.38500	+	3.19569i	−0.368013	+	0.493106i
$43$	−0.846556	−	2.88311i	−0.129099	−	0.439670i	0.869420	−	0.494073i	$-0.164492\pi$
$43$	−0.846556	−	2.88311i	−0.129099	−	0.439670i	−0.998519	+	0.0544034i	$0.982674\pi$
$44$	−9.21141	+	5.95785i	−1.38867	+	0.898180i
$45$	−2.83773			−0.423023
$46$	4.32289	+	5.22614i	0.637376	+	0.770553i
$47$		−	3.76827i		−	0.549659i	−0.961493	−	0.274829i	$-0.911379\pi$
$47$		−	3.76827i		−	0.549659i	0.961493	−	0.274829i	$-0.0886214\pi$
$48$	2.63703	+	3.00767i	0.380623	+	0.434119i
$49$	−0.911837	+	0.267740i	−0.130262	+	0.0382485i
$50$	−2.58214	+	3.45984i	−0.365169	+	0.489295i
$51$	−1.86242	+	2.89799i	−0.260792	+	0.405800i
$52$	−2.31402	+	2.68631i	−0.320896	+	0.372524i
$53$	2.03376	+	14.1451i	0.279358	+	1.94298i	0.329295	+	0.944227i	$0.393189\pi$
$53$	2.03376	+	14.1451i	0.279358	+	1.94298i	−0.0499370	+	0.998752i	$0.515902\pi$
$54$	−1.38233	−	0.298597i	−0.188111	−	0.0406339i
$55$	−8.41522	−	13.0943i	−1.13471	−	1.76564i
$56$	0.603739	+	7.95224i	0.0806780	+	1.06266i
$57$	2.69896	+	1.23257i	0.357485	+	0.163258i
$58$	6.38036	+	2.36916i	0.837783	+	0.311086i
$59$	1.19282	−	8.29627i	0.155292	−	1.08008i	−0.751873	−	0.659308i	$-0.770849\pi$
$59$	1.19282	−	8.29627i	0.155292	−	1.08008i	0.907165	−	0.420774i	$-0.138242\pi$
$60$	−4.27836	+	3.72913i	−0.552334	+	0.481428i
$61$	−11.5177	−	3.38190i	−1.47469	−	0.433008i	−0.557069	−	0.830466i	$-0.688074\pi$
$61$	−11.5177	−	3.38190i	−1.47469	−	0.433008i	−0.917620	+	0.397458i	$0.869892\pi$
$62$	13.0609	−	2.86119i	1.65874	−	0.363371i
$63$	−1.84647	−	2.13094i	−0.232633	−	0.268473i
$64$	7.92823	+	1.06918i	0.991029	+	0.133648i
$65$	−3.80192	−	3.29438i	−0.471570	−	0.408617i
$66$	−2.72144	−	7.26408i	−0.334986	−	0.894146i
$67$	6.50409	−	2.97032i	0.794601	−	0.362882i	0.0236043	−	0.999721i	$-0.492486\pi$
$67$	6.50409	−	2.97032i	0.794601	−	0.362882i	0.770997	+	0.636839i	$0.219759\pi$
$68$	1.00039	+	6.81668i	0.121316	+	0.826644i
$69$	−4.26395	+	2.19515i	−0.513320	+	0.264265i
$70$	−11.2856	+	0.823707i	−1.34889	+	0.0984519i
$71$	7.23605	−	3.30459i	0.858761	−	0.392183i	0.0631596	−	0.998003i	$-0.479882\pi$
$71$	7.23605	−	3.30459i	0.858761	−	0.392183i	0.795601	+	0.605820i	$0.207155\pi$
$72$	−2.47650	+	1.36637i	−0.291858	+	0.161028i
$73$	0.108926	−	0.125708i	0.0127488	−	0.0147130i	−0.749339	−	0.662186i	$-0.769629\pi$
$73$	0.108926	−	0.125708i	0.0127488	−	0.0147130i	0.762088	+	0.647473i	$0.224174\pi$
$74$	−10.9729	−	5.97090i	−1.27557	−	0.694103i
$75$	−1.99909	−	2.30707i	−0.230835	−	0.266398i
$76$	5.68889	−	1.68845i	0.652561	−	0.193678i
$77$	4.35728	−	14.8395i	0.496558	−	1.69112i
$78$	−1.50537	−	2.00483i	−0.170449	−	0.227002i
$79$	0.834900	−	5.80686i	0.0939336	−	0.653323i	−0.887399	−	0.461003i	$-0.847490\pi$
$79$	0.834900	−	5.80686i	0.0939336	−	0.653323i	0.981332	−	0.192320i	$-0.0616011\pi$
$80$	−1.54983	+	11.2446i	−0.173276	+	1.25719i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	0.662378	−	9.45502i	0.0731474	−	1.04413i
$83$	8.14269	+	12.6703i	0.893777	+	1.39074i	0.920350	+	0.391097i	$0.127904\pi$
$83$	8.14269	+	12.6703i	0.893777	+	1.39074i	−0.0265732	+	0.999647i	$0.508459\pi$
$84$	−5.58418	−	0.786266i	−0.609284	−	0.0857887i
$85$	−9.67604	+	1.39120i	−1.04951	+	0.150897i
$86$	3.00044	−	3.00920i	0.323545	−	0.324491i
$87$	−2.60188	+	4.04860i	−0.278951	+	0.434056i
$88$	−13.6489	−	7.37554i	−1.45498	−	0.786235i
$89$	3.55645	+	12.1122i	0.376983	+	1.28389i	0.901609	+	0.432553i	$0.142387\pi$
$89$	3.55645	+	12.1122i	0.376983	+	1.28389i	−0.524626	+	0.851333i	$0.675795\pi$
$90$	−1.92843	−	3.51945i	−0.203275	−	0.370983i
$91$		−	4.99858i		−	0.523994i
$92$	−3.54394	+	8.91294i	−0.369481	+	0.929238i
$93$			9.45447i			0.980383i
$94$	4.67355	−	2.56080i	0.482039	−	0.264127i
$95$	2.37213	+	8.07872i	0.243375	+	0.828859i
$96$	−1.93817	+	5.31446i	−0.197813	+	0.542405i
$97$	3.45235	−	5.37197i	0.350534	−	0.545441i	−0.620554	−	0.784164i	$-0.713092\pi$
$97$	3.45235	−	5.37197i	0.350534	−	0.545441i	0.971088	+	0.238723i	$0.0767287\pi$
$98$	−0.951717	−	0.948945i	−0.0961380	−	0.0958580i
$99$	5.42929	−	0.780614i	0.545664	−	0.0784546i
$100$	−6.04575	−	0.851256i	−0.604575	−	0.0851256i
$101$	−2.58418	−	4.02107i	−0.257136	−	0.400111i	0.688552	−	0.725187i	$-0.258247\pi$
$101$	−2.58418	−	4.02107i	−0.257136	−	0.400111i	−0.945688	+	0.325076i	$0.894610\pi$
$102$	−4.85984	−	0.340459i	−0.481196	−	0.0337105i
$103$	−5.92461	+	12.9731i	−0.583770	+	1.27828i	0.355365	+	0.934728i	$0.384357\pi$
$103$	−5.92461	+	12.9731i	−0.583770	+	1.27828i	−0.939135	+	0.343549i	$0.888371\pi$
$104$	−4.90420	−	1.04439i	−0.480896	−	0.102411i
$105$	1.13871	−	7.91991i	0.111127	−	0.772904i
$106$	−16.1612	+	12.1349i	−1.56971	+	1.17865i
$107$	5.11678	−	17.4262i	0.494658	−	1.68465i	−0.212143	−	0.977239i	$-0.568044\pi$
$107$	5.11678	−	17.4262i	0.494658	−	1.68465i	0.706801	−	0.707413i	$-0.250138\pi$
$108$	−0.569060	−	1.91733i	−0.0547578	−	0.184496i
$109$	−2.96499	−	3.42179i	−0.283995	−	0.327748i	0.595771	−	0.803154i	$-0.296846\pi$
$109$	−2.96499	−	3.42179i	−0.283995	−	0.327748i	−0.879766	+	0.475407i	$0.842301\pi$
$110$	10.5213	−	19.3354i	1.00317	−	1.84356i
$111$	5.78461	−	6.67580i	0.549051	−	0.633639i
$112$	−9.45237	+	6.15288i	−0.893165	+	0.581393i
$113$	−2.02734	+	0.925857i	−0.190716	+	0.0870973i	−0.508484	−	0.861071i	$-0.669794\pi$
$113$	−2.02734	+	0.925857i	−0.190716	+	0.0870973i	0.317768	+	0.948169i	$0.397067\pi$
$114$	0.305450	+	4.18496i	0.0286080	+	0.391957i
$115$	−12.6315	−	5.06524i	−1.17790	−	0.472336i
$116$	1.39759	+	9.52316i	0.129763	+	0.884204i
$117$	1.61257	−	0.736438i	0.149083	−	0.0680837i
$118$	11.0999	−	4.15851i	1.02183	−	0.382822i
$119$	−7.34075	−	6.36080i	−0.672926	−	0.583093i
$120$	−7.53244	−	2.77198i	−0.687615	−	0.253046i
$121$	12.4990	+	14.4246i	1.13627	+	1.31133i
$122$	−3.63273	−	16.5829i	−0.328892	−	1.50134i
$123$	6.43061	+	1.88820i	0.579829	+	0.170253i
$124$	12.4244	+	14.2542i	1.11574	+	1.28007i
$125$	−0.786420	+	5.46967i	−0.0703396	+	0.489223i
$126$	1.38806	−	3.73818i	0.123658	−	0.333023i
$127$	−10.5867	−	4.83479i	−0.939419	−	0.429018i	−0.113963	−	0.993485i	$-0.536355\pi$
$127$	−10.5867	−	4.83479i	−0.939419	−	0.429018i	−0.825456	+	0.564467i	$0.809082\pi$
$128$	4.06175	+	10.5595i	0.359011	+	0.933333i
$129$	1.62453	+	2.52782i	0.143032	+	0.222562i
$130$	1.50214	−	6.95403i	0.131746	−	0.609909i
$131$	−0.278612	−	1.93779i	−0.0243425	−	0.169306i	0.974024	−	0.226446i	$-0.0727107\pi$
$131$	−0.278612	−	1.93779i	−0.0243425	−	0.169306i	−0.998366	+	0.0571407i	$0.981802\pi$
$132$	7.15976	−	8.31167i	0.623177	−	0.723438i
$133$	−4.52305	+	7.03800i	−0.392198	+	0.610272i
$134$	8.10388	+	6.04806i	0.700068	+	0.522473i
$135$	2.72278	−	0.799480i	0.234340	−	0.0688083i
$136$	−7.77445	+	5.87313i	−0.666654	+	0.503617i
$137$			11.1505i			0.952647i	0.879270	+	0.476324i	$0.158031\pi$
$137$			11.1505i			0.952647i	−0.879270	+	0.476324i	$0.841969\pi$
$138$	−5.62016	−	3.79655i	−0.478420	−	0.323184i
$139$	−3.32636			−0.282139			−0.141069	−	0.990000i	$-0.545054\pi$
$139$	−3.32636			−0.282139			−0.141069	+	0.990000i	$0.545054\pi$
$140$	−8.69094	−	13.4370i	−0.734519	−	1.13564i
$141$	1.06164	+	3.61563i	0.0894066	+	0.304491i
$142$	9.01588	+	6.72870i	0.756595	+	0.564660i
$143$	8.18025	+	5.25713i	0.684067	+	0.439623i
$144$	−3.37757	−	2.14290i	−0.281464	−	0.178575i
$145$	−13.5178	+	1.94357i	−1.12259	+	0.161404i
$146$	0.229930	+	0.0496671i	0.0190291	+	0.00411048i
$147$	0.799470	−	0.513788i	0.0659392	−	0.0423766i
$148$	−0.0515322	−	17.6666i	−0.00423592	−	1.45219i
$149$	1.91607	−	4.19562i	0.156971	−	0.343718i	−0.814764	−	0.579793i	$-0.803134\pi$
$149$	1.91607	−	4.19562i	0.156971	−	0.343718i	0.971735	+	0.236074i	$0.0758609\pi$
$150$	1.50279	−	4.04716i	0.122703	−	0.330449i
$151$	5.14180	+	0.739280i	0.418434	+	0.0601617i	0.348316	−	0.937377i	$-0.386753\pi$
$151$	5.14180	+	0.739280i	0.418434	+	0.0601617i	0.0701176	+	0.997539i	$0.477663\pi$
$152$	5.96008	+	5.90815i	0.483426	+	0.479214i
$153$	0.970526	−	3.30531i	0.0784623	−	0.267218i
$154$	21.3656	−	4.68045i	1.72169	−	0.377161i
$155$	−20.2762	+	17.5694i	−1.62862	+	1.41121i
$156$	1.46346	−	3.22943i	0.117171	−	0.258561i
$157$	−0.141118	+	0.162859i	−0.0112624	+	0.0129976i	−0.761353	−	0.648338i	$-0.775464\pi$
$157$	−0.141118	+	0.162859i	−0.0112624	+	0.0129976i	0.750090	+	0.661335i	$0.230010\pi$
$158$	7.76925	−	2.91069i	0.618088	−	0.231562i
$159$	−5.93651	−	12.9992i	−0.470796	−	1.03090i
$160$	−14.9992	+	5.71934i	−1.18579	+	0.452154i
$161$	−4.41550	−	12.7813i	−0.347991	−	1.00731i
$162$	1.41046	−	0.102946i	0.110816	−	0.00808821i
$163$	7.56694	+	16.5693i	0.592688	+	1.29781i	0.933804	+	0.357785i	$0.116468\pi$
$163$	7.56694	+	16.5693i	0.592688	+	1.29781i	−0.341115	+	0.940021i	$0.610805\pi$
$164$	12.1766	−	5.60384i	0.950832	−	0.437587i
$165$	11.7634	+	10.1931i	0.915783	+	0.793530i
$166$	−10.1806	+	18.7092i	−0.790168	+	1.45212i
$167$	−4.69927	+	4.07194i	−0.363640	+	0.315096i	−0.817447	−	0.576004i	$-0.804611\pi$
$167$	−4.69927	+	4.07194i	−0.363640	+	0.315096i	0.453806	+	0.891100i	$0.350066\pi$
$168$	−2.81969	−	7.46003i	−0.217544	−	0.575554i
$169$	−9.45798	−	2.77711i	−0.727537	−	0.213624i
$170$	−8.30096	−	11.0551i	−0.636655	−	0.847891i
$171$	−2.93688	−	0.422260i	−0.224589	−	0.0322910i
$172$	5.77113	+	1.67629i	0.440044	+	0.127816i
$173$	6.49609	+	2.96667i	0.493889	+	0.225551i	0.646758	−	0.762695i	$-0.276124\pi$
$173$	6.49609	+	2.96667i	0.493889	+	0.225551i	−0.152870	+	0.988246i	$0.548851\pi$
$174$	−6.78938	−	0.475635i	−0.514702	−	0.0360578i
$175$	7.24107	−	4.65356i	0.547374	−	0.351776i
$176$	−0.127996	−	21.9401i	−0.00964808	−	1.65380i
$177$	1.19282	+	8.29627i	0.0896581	+	0.623586i
$178$	−12.6051	+	12.6419i	−0.944790	+	0.947550i
$179$	−19.2820	−	12.3918i	−1.44121	−	0.926207i	−0.999579	−	0.0290086i	$-0.990765\pi$
$179$	−19.2820	−	12.3918i	−1.44121	−	0.926207i	−0.441627	−	0.897199i	$-0.645599\pi$
$180$	3.05444	−	4.78343i	0.227665	−	0.356536i
$181$	−8.74579	+	2.56799i	−0.650069	+	0.190878i	−0.590109	−	0.807323i	$-0.700915\pi$
$181$	−8.74579	+	2.56799i	−0.650069	+	0.190878i	−0.0599598	+	0.998201i	$0.519097\pi$
$182$	6.19942	−	3.39688i	0.459531	−	0.251794i
$183$	12.0039			0.887357
$184$	−13.4625	+	1.66164i	−0.992469	+	0.122498i
$185$	25.0666			1.84294
$186$	−11.7258	+	6.42497i	−0.859775	+	0.471102i
$187$	18.1300	−	5.32345i	1.32580	−	0.389289i
$188$	6.35200	+	4.05605i	0.463267	+	0.295818i
$189$	2.37203	+	1.52441i	0.172540	+	0.110884i
$190$	−8.40749	+	8.43205i	−0.609943	+	0.611725i
$191$	−0.344831	−	2.39835i	−0.0249511	−	0.173539i	0.973535	−	0.228536i	$-0.0733940\pi$
$191$	−0.344831	−	2.39835i	−0.0249511	−	0.173539i	−0.998486	+	0.0549975i	$0.982485\pi$
$192$	−7.90831	+	1.20777i	−0.570733	+	0.0871631i
$193$	12.7820	−	8.21446i	0.920065	−	0.591290i	0.00738874	−	0.999973i	$-0.497648\pi$
$193$	12.7820	−	8.21446i	0.920065	−	0.591290i	0.912677	+	0.408683i	$0.134012\pi$
$194$	9.00862	+	0.631105i	0.646782	+	0.0453107i
$195$	4.57605	+	2.08981i	0.327697	+	0.149654i
$196$	0.530157	−	1.82523i	0.0378684	−	0.130373i
$197$	−5.64662	−	0.811862i	−0.402305	−	0.0578427i	−0.0618074	−	0.998088i	$-0.519686\pi$
$197$	−5.64662	−	0.811862i	−0.402305	−	0.0578427i	−0.340498	+	0.940245i	$0.610596\pi$
$198$	4.65772	+	6.20311i	0.331010	+	0.440836i
$199$	9.82040	+	2.88353i	0.696150	+	0.204408i	0.610616	−	0.791927i	$-0.290922\pi$
$199$	9.82040	+	2.88353i	0.696150	+	0.204408i	0.0855343	+	0.996335i	$0.472740\pi$
$200$	−3.05275	−	8.07665i	−0.215862	−	0.571105i
$201$	−5.40379	+	4.68241i	−0.381154	+	0.330272i
$202$	3.23094	−	5.93759i	0.227328	−	0.417767i
$203$	−10.2553	−	8.88628i	−0.719782	−	0.623695i
$204$	−2.88035	−	6.25871i	−0.201665	−	0.438197i
$205$	7.90066	+	17.3000i	0.551806	+	1.20829i
$206$	−20.1159	+	1.46821i	−1.40154	+	0.102295i
$207$	3.47279	−	3.30753i	0.241375	−	0.229889i
$208$	−2.03745	−	6.79210i	−0.141272	−	0.470947i
$209$	−6.76080	−	14.8041i	−0.467654	−	1.02402i
$210$	10.5964	−	3.96986i	0.731220	−	0.273946i
$211$	−3.67733	+	4.24386i	−0.253158	+	0.292160i	−0.868076	−	0.496431i	$-0.834643\pi$
$211$	−3.67733	+	4.24386i	−0.253158	+	0.292160i	0.614918	+	0.788591i	$0.289189\pi$
$212$	−26.0328	−	11.7971i	−1.78794	−	0.810231i
$213$	−6.01193	+	5.20936i	−0.411930	+	0.356940i
$214$	25.0898	−	5.49628i	1.71510	−	0.375718i
$215$	−2.40230	+	8.18147i	−0.163835	+	0.557972i
$216$	1.99123	−	2.00873i	0.135486	−	0.136677i
$217$	−26.3868	−	3.79385i	−1.79125	−	0.257543i
$218$	2.22890	−	6.00263i	0.150960	−	0.406550i
$219$	−0.0690980	+	0.151304i	−0.00466921	+	0.0102241i
$220$	31.1304	−	0.0908050i	2.09881	−	0.00612207i
$221$	5.13749	−	3.30166i	0.345585	−	0.222094i
$222$	12.2106	+	2.63761i	0.819523	+	0.177025i
$223$	−7.36959	+	1.05959i	−0.493505	+	0.0709552i	−0.384574	−	0.923094i	$-0.625652\pi$
$223$	−7.36959	+	1.05959i	−0.493505	+	0.0709552i	−0.108930	+	0.994049i	$0.534743\pi$
$224$	−14.0546	−	7.54185i	−0.939061	−	0.503911i
$225$	2.56809	+	1.65041i	0.171206	+	0.110027i
$226$	−2.52600	−	1.88520i	−0.168027	−	0.125402i
$227$	2.06605	+	7.03632i	0.137129	+	0.467017i	0.999210	−	0.0397535i	$-0.0126573\pi$
$227$	2.06605	+	7.03632i	0.137129	+	0.467017i	−0.862081	+	0.506771i	$0.830839\pi$
$228$	−4.98276	+	3.22280i	−0.329991	+	0.213435i
$229$	13.1915			0.871717			0.435859	−	0.900015i	$-0.356445\pi$
$229$	13.1915			0.871717			0.435859	+	0.900015i	$0.356445\pi$
$230$	−2.30192	−	19.1082i	−0.151784	−	1.25996i
$231$			15.4660i			1.01759i
$232$	−10.8612	+	8.20500i	−0.713073	+	0.538684i
$233$	−3.61084	+	1.06024i	−0.236554	+	0.0694585i	−0.397861	−	0.917446i	$-0.630247\pi$
$233$	−3.61084	+	1.06024i	−0.236554	+	0.0694585i	0.161307	+	0.986904i	$0.448429\pi$
$234$	2.00921	+	1.49951i	0.131346	+	0.0980261i
$235$	−5.78125	+	8.99580i	−0.377127	+	0.586821i
$236$	12.7007	+	10.9405i	0.826747	+	0.712169i
$237$	0.834900	+	5.80686i	0.0542326	+	0.377196i
$238$	2.90033	−	13.4269i	0.188001	−	0.870335i
$239$	13.4519	+	20.9315i	0.870130	+	1.35395i	0.934478	+	0.356022i	$0.115867\pi$
$239$	13.4519	+	20.9315i	0.870130	+	1.35395i	−0.0643473	+	0.997928i	$0.520497\pi$
$240$	−1.68092	−	11.2258i	−0.108503	−	0.724620i
$241$	−0.370965	−	0.169414i	−0.0238960	−	0.0109129i	0.403431	−	0.915010i	$-0.367817\pi$
$241$	−0.370965	−	0.169414i	−0.0238960	−	0.0109129i	−0.427327	+	0.904097i	$0.640545\pi$
$242$	−9.39598	+	25.3042i	−0.603997	+	1.62662i
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$	18.0980	−	15.7747i	1.15861	−	1.00987i
$245$	2.58755	+	0.759772i	0.165312	+	0.0485400i
$246$	2.02824	+	9.25864i	0.129316	+	0.590309i
$247$	−3.44455	−	3.97523i	−0.219172	−	0.252938i
$248$	−9.23540	+	25.0959i	−0.586449	+	1.59359i
$249$	−11.3825	−	9.86298i	−0.721336	−	0.625041i
$250$	−7.31811	+	2.74168i	−0.462838	+	0.173399i
$251$	16.8296	−	7.68584i	1.06228	−	0.485126i	0.193896	−	0.981022i	$-0.437888\pi$
$251$	16.8296	−	7.68584i	1.06228	−	0.485126i	0.868382	+	0.495896i	$0.165160\pi$
$252$	5.57950	−	0.818830i	0.351476	−	0.0515814i
$253$	25.5606	+	6.21634i	1.60698	+	0.390818i
$254$	−1.19813	−	16.4156i	−0.0751776	−	1.03001i
$255$	8.89214	−	4.06090i	0.556847	−	0.254304i
$256$	−10.3360	+	12.2134i	−0.645999	+	0.763339i
$257$	0.000280682	0	0.000323924i	1.75085e−5	0	2.02059e-5i	−0.755741	−	0.654871i	$-0.772723\pi$
$257$	0.000280682	0	0.000323924i	1.75085e−5	0	2.02059e-5i	0.755758	+	0.654851i	$0.227268\pi$
$258$	−2.03111	+	3.73263i	−0.126451	+	0.232383i
$259$	16.3105	+	18.8233i	1.01348	+	1.16962i
$260$	9.64545	−	2.86275i	0.598185	−	0.177540i
$261$	1.35586	−	4.61764i	0.0839257	−	0.285825i
$262$	2.21398	−	1.66241i	0.136780	−	0.102704i
$263$	−3.80617	+	26.4725i	−0.234699	+	1.63236i	0.442644	+	0.896697i	$0.354040\pi$
$263$	−3.80617	+	26.4725i	−0.234699	+	1.63236i	−0.677343	+	0.735668i	$0.736869\pi$
$264$	15.1740	+	3.23143i	0.933894	+	0.198881i
$265$	16.8462	−	36.8880i	1.03485	−	2.26601i
$266$	−11.8025	−	0.826833i	−0.723659	−	0.0506964i
$267$	−6.82478	−	10.6196i	−0.417670	−	0.649906i
$268$	−1.99387	+	14.1608i	−0.121795	+	0.865009i
$269$	20.8403	−	2.99638i	1.27065	−	0.182692i	0.526196	−	0.850363i	$-0.323618\pi$
$269$	20.8403	−	2.99638i	1.27065	−	0.182692i	0.744457	+	0.667671i	$0.232709\pi$
$270$	2.84186	+	2.83359i	0.172950	+	0.172447i
$271$	5.06976	−	7.88871i	0.307966	−	0.479205i	−0.652428	−	0.757851i	$-0.726249\pi$
$271$	5.06976	−	7.88871i	0.307966	−	0.479205i	0.960394	+	0.278646i	$0.0898857\pi$
$272$	−12.5674	−	5.65095i	−0.762008	−	0.342639i
$273$	1.40826	+	4.79610i	0.0852319	+	0.290273i
$274$	−13.8292	+	7.57751i	−0.835452	+	0.457774i
$275$			16.7444i			1.00972i
$276$	0.889321	−	9.55035i	0.0535308	−	0.574863i
$277$			2.75255i			0.165385i	0.996575	+	0.0826924i	$0.0263519\pi$
$277$			2.75255i			0.165385i	−0.996575	+	0.0826924i	$0.973648\pi$
$278$	−2.26050	−	4.12548i	−0.135576	−	0.247430i
$279$	−2.66363	−	9.07150i	−0.159467	−	0.543096i
$280$	10.7590	−	19.9102i	0.642972	−	1.18986i
$281$	−7.78480	+	12.1134i	−0.464402	+	0.722624i	−0.991912	−	0.126925i	$-0.959489\pi$
$281$	−7.78480	+	12.1134i	−0.464402	+	0.722624i	0.527510	+	0.849549i	$0.323126\pi$
$282$	−3.76277	+	3.77376i	−0.224070	+	0.224724i
$283$	9.41844	−	1.35417i	0.559868	−	0.0804969i	0.143429	−	0.989661i	$-0.454187\pi$
$283$	9.41844	−	1.35417i	0.559868	−	0.0804969i	0.416439	+	0.909164i	$0.363278\pi$
$284$	−2.21826	+	15.7544i	−0.131630	+	0.934854i
$285$	−4.55208	−	7.08317i	−0.269642	−	0.419571i
$286$	−0.961025	+	13.7180i	−0.0568266	+	0.811164i
$287$	−7.85029	+	17.1897i	−0.463388	+	1.01468i
$288$	0.362399	−	5.64523i	0.0213545	−	0.332649i
$289$	−0.730506	+	5.08078i	−0.0429709	+	0.298869i
$290$	−11.5968	−	15.4445i	−0.680986	−	0.906930i
$291$	−1.79905	+	6.12701i	−0.105462	+	0.359172i
$292$	0.0946546	+	0.318920i	0.00553924	+	0.0186634i
$293$	−13.7695	−	15.8908i	−0.804422	−	0.928352i	0.194193	−	0.980963i	$-0.437791\pi$
$293$	−13.7695	−	15.8908i	−0.804422	−	0.928352i	−0.998615	+	0.0526111i	$0.983246\pi$
$294$	1.18051	+	0.642377i	0.0688490	+	0.0374642i
$295$	−15.5756	+	17.9752i	−0.906848	+	1.04656i
$296$	21.8758	−	12.0696i	1.27150	−	0.701532i
$297$	−4.98944	+	2.27860i	−0.289517	+	0.132218i
$298$	6.50566	−	0.474832i	0.376863	−	0.0275063i
$299$	8.49254	−	0.399709i	0.491136	−	0.0231158i
$300$	6.04069	−	0.886511i	0.348759	−	0.0511828i
$301$	−7.70686	+	3.51960i	−0.444216	+	0.202867i
$302$	2.57733	+	6.87944i	0.148309	+	0.395867i
$303$	3.61237	+	3.13014i	0.207525	+	0.179822i
$304$	−3.27721	+	11.4069i	−0.187961	+	0.654231i
$305$	22.3071	+	25.7438i	1.27730	+	1.47408i
$306$	4.75890	−	1.04251i	0.272048	−	0.0595961i
$307$	−19.0525	−	5.59431i	−1.08738	−	0.319284i	−0.311554	−	0.950228i	$-0.600850\pi$
$307$	−19.0525	−	5.59431i	−1.08738	−	0.319284i	−0.775828	+	0.630944i	$0.782668\pi$
$308$	20.3243	+	23.3177i	1.15808	+	1.32865i
$309$	2.02968	−	14.1168i	0.115465	−	0.803074i
$310$	−35.5693	−	13.2076i	−2.02020	−	0.750140i
$311$	12.9452	+	5.91185i	0.734052	+	0.335230i	0.747124	−	0.664684i	$-0.231434\pi$
$311$	12.9452	+	5.91185i	0.734052	+	0.335230i	−0.0130723	+	0.999915i	$0.504161\pi$
$312$	4.99978	−	0.379586i	0.283057	−	0.0214898i
$313$	−2.08919	−	3.25084i	−0.118088	−	0.183748i	0.777178	−	0.629281i	$-0.216651\pi$
$313$	−2.08919	−	3.25084i	−0.118088	−	0.183748i	−0.895266	+	0.445533i	$0.853014\pi$
$314$	−0.297883	−	0.0643456i	−0.0168105	−	0.00363123i
$315$	1.13871	+	7.91991i	0.0641591	+	0.446236i
$316$	8.88969	+	7.65768i	0.500084	+	0.430778i
$317$	−10.7916	+	16.7921i	−0.606119	+	0.943140i	0.393596	+	0.919283i	$0.371231\pi$
$317$	−10.7916	+	16.7921i	−0.606119	+	0.943140i	−0.999715	+	0.0238562i	$0.992406\pi$
$318$	12.0877	−	16.1965i	0.677847	−	0.908255i
$319$	25.3283	−	7.43706i	1.41811	−	0.416395i
$320$	−17.2863	−	14.7158i	−0.966335	−	0.822640i
$321$			18.1619i			1.01370i
$322$	12.8511	−	14.1620i	0.716166	−	0.789219i
$323$	−10.2212			−0.568720
$324$	1.08618	+	1.67935i	0.0603436	+	0.0932970i
$325$	1.52466	+	5.19253i	0.0845732	+	0.288030i
$326$	−15.4076	+	20.6448i	−0.853346	+	1.14341i
$327$	3.80892	+	2.44784i	0.210634	+	0.135366i
$328$	15.2249	+	11.2936i	0.840656	+	0.623587i
$329$	−10.5170	+	1.51212i	−0.579821	+	0.0833656i
$330$	−4.64774	+	21.5164i	−0.255850	+	1.18444i
$331$	6.00733	−	3.86068i	0.330193	−	0.212202i	−0.365031	−	0.930995i	$-0.618942\pi$
$331$	6.00733	−	3.86068i	0.330193	−	0.212202i	0.695224	+	0.718793i	$0.255305\pi$
$332$	−30.1222	+	0.0878643i	−1.65317	+	0.00482218i
$333$	−3.66951	+	8.03510i	−0.201088	+	0.440321i
$334$	−8.24365	−	3.06103i	−0.451072	−	0.167492i
$335$	−20.0839	−	2.88763i	−1.09730	−	0.157768i
$336$	7.33602	−	8.56669i	0.400213	−	0.467351i
$337$	1.93948	−	6.60525i	0.105650	−	0.359811i	−0.889651	−	0.456641i	$-0.849052\pi$
$337$	1.93948	−	6.60525i	0.105650	−	0.359811i	0.995301	+	0.0968304i	$0.0308705\pi$
$338$	−2.98308	−	13.6174i	−0.162258	−	0.740687i
$339$	1.68438	−	1.45952i	0.0914828	−	0.0792703i
$340$	8.06990	−	17.8079i	0.437652	−	0.965769i
$341$	33.9603	−	39.1923i	1.83906	−	2.12238i
$342$	−1.47212	−	3.92938i	−0.0796029	−	0.212477i
$343$	−7.08608	−	15.5164i	−0.382613	−	0.837805i
$344$	1.84289	+	8.29671i	0.0993622	+	0.447329i
$345$	13.5469	+	1.30135i	0.729341	+	0.0700621i
$346$	0.735184	+	10.0727i	0.0395237	+	0.541514i
$347$	1.02175	+	2.23732i	0.0548505	+	0.120106i	0.935073	−	0.354456i	$-0.115334\pi$
$347$	1.02175	+	2.23732i	0.0548505	+	0.120106i	−0.880222	+	0.474562i	$0.842607\pi$
$348$	−4.02396	−	8.74366i	−0.215707	−	0.468710i
$349$	−19.8550	−	17.2045i	−1.06281	−	0.920933i	−0.0657749	−	0.997834i	$-0.520952\pi$
$349$	−19.8550	−	17.2045i	−1.06281	−	0.920933i	−0.997039	+	0.0769013i	$0.975497\pi$
$350$	10.6923	+	5.81822i	0.571529	+	0.310997i
$351$	−1.33978	+	1.16092i	−0.0715119	+	0.0619654i
$352$	27.1239	−	15.0686i	1.44571	−	0.803158i
$353$	−10.7773	−	3.16451i	−0.573620	−	0.168430i	−0.0179587	−	0.999839i	$-0.505717\pi$
$353$	−10.7773	−	3.16451i	−0.573620	−	0.168430i	−0.555661	+	0.831409i	$0.687535\pi$
$354$	−9.47873	+	7.11728i	−0.503789	+	0.378279i
$355$	−22.3441	−	3.21260i	−1.18590	−	0.170507i
$356$	−24.2450	−	7.04221i	−1.28498	−	0.373236i
$357$	8.83544	+	4.03501i	0.467621	+	0.213555i
$358$	2.26527	−	32.3354i	0.119723	−	1.70898i
$359$	0.769252	−	0.494368i	0.0405996	−	0.0260918i	−0.520184	−	0.854054i	$-0.674136\pi$
$359$	0.769252	−	0.494368i	0.0405996	−	0.0260918i	0.560783	+	0.827963i	$0.310500\pi$
$360$	8.00828	+	0.537556i	0.422074	+	0.0283317i
$361$	−1.45110	−	10.0926i	−0.0763737	−	0.531191i
$362$	−9.12829	−	9.10171i	−0.479772	−	0.478375i
$363$	−16.0566	−	10.3189i	−0.842752	−	0.541604i
$364$	8.42588	+	5.38032i	0.441636	+	0.282005i
$365$	−0.452893	+	0.132981i	−0.0237055	+	0.00696057i
$366$	8.15752	+	14.8877i	0.426400	+	0.778193i
$367$	7.38465			0.385476			0.192738	−	0.981250i	$-0.438263\pi$
$367$	7.38465			0.385476			0.192738	+	0.981250i	$0.438263\pi$
$368$	−11.2095	−	15.5675i	−0.584338	−	0.811511i
$369$	−6.70210			−0.348897
$370$	17.0345	+	31.0885i	0.885583	+	1.61622i
$371$	38.6619	−	11.3522i	2.00723	−	0.589375i
$372$	−15.9370	−	10.1765i	−0.826293	−	0.527627i
$373$	−4.14480	−	2.66370i	−0.214609	−	0.137921i	0.428920	−	0.903342i	$-0.358894\pi$
$373$	−4.14480	−	2.66370i	−0.214609	−	0.137921i	−0.643529	+	0.765421i	$0.722531\pi$
$374$	18.9229	+	18.8678i	0.978481	+	0.975631i
$375$	−0.786420	−	5.46967i	−0.0406106	−	0.282453i
$376$	−0.713831	+	10.6344i	−0.0368130	+	0.548425i
$377$	7.17727	−	4.61255i	0.369648	−	0.237558i
$378$	−0.278668	+	3.97781i	−0.0143332	+	0.204597i
$379$	26.4203	+	12.0657i	1.35712	+	0.619776i	0.955217	−	0.295906i	$-0.0956216\pi$
$379$	26.4203	+	12.0657i	1.35712	+	0.619776i	0.401903	+	0.915682i	$0.368349\pi$
$380$	−16.1712	−	4.69710i	−0.829565	−	0.240956i
$381$	11.5200	+	1.65633i	0.590187	+	0.0848561i
$382$	2.74019	−	2.05752i	0.140200	−	0.105272i
$383$	32.6333	+	9.58201i	1.66748	+	0.489618i	0.973176	−	0.230060i	$-0.0738922\pi$
$383$	32.6333	+	9.58201i	1.66748	+	0.489618i	0.694308	+	0.719678i	$0.255710\pi$
$384$	−6.87216	−	8.98740i	−0.350694	−	0.458636i
$385$	−33.1686	+	28.7408i	−1.69043	+	1.46476i
$386$	18.8741	+	10.2703i	0.960667	+	0.522746i
$387$	−2.27089	−	1.96774i	−0.115436	−	0.100026i
$388$	5.33927	+	11.6017i	0.271060	+	0.588987i
$389$	−1.67270	−	3.66270i	−0.0848091	−	0.185706i	0.862476	−	0.506098i	$-0.168913\pi$
$389$	−1.67270	−	3.66270i	−0.0848091	−	0.185706i	−0.947285	+	0.320392i	$0.896185\pi$
$390$	0.517886	+	7.09555i	0.0262242	+	0.359297i
$391$	10.2199	−	12.9805i	0.516844	−	0.656452i
$392$	2.62399	−	0.582850i	0.132532	−	0.0294384i
$393$	0.813265	+	1.78080i	0.0410238	+	0.0898296i
$394$	−2.83037	−	7.55486i	−0.142592	−	0.380608i
$395$	−10.9019	+	12.5815i	−0.548536	+	0.633045i
$396$	−4.52807	+	9.99213i	−0.227544	+	0.502123i
$397$	12.9721	−	11.2404i	0.651052	−	0.564140i	−0.265472	−	0.964118i	$-0.585528\pi$
$397$	12.9721	−	11.2404i	0.651052	−	0.564140i	0.916524	+	0.399979i	$0.130982\pi$
$398$	3.09739	+	14.1392i	0.155258	+	0.708733i
$399$	2.35700	−	8.02721i	0.117998	−	0.401863i
$400$	7.94239	−	9.27478i	0.397119	−	0.463739i
$401$	11.3142	+	1.62674i	0.565005	+	0.0812355i	0.418898	−	0.908033i	$-0.362416\pi$
$401$	11.3142	+	1.62674i	0.565005	+	0.0812355i	0.146107	+	0.989269i	$0.453326\pi$
$402$	−9.47955	−	3.51995i	−0.472797	−	0.175559i
$403$	6.96263	−	15.2460i	0.346833	−	0.759459i
$404$	9.55966	−	0.0278848i	0.475611	−	0.00138732i
$405$	−2.38725	+	1.53419i	−0.118623	+	0.0762346i
$406$	4.05188	−	18.7579i	0.201091	−	0.930937i
$407$	−47.9588	+	6.89543i	−2.37723	+	0.341794i
$408$	5.80488	−	7.82555i	0.287384	−	0.387422i
$409$	20.1636	+	12.9584i	0.997026	+	0.640750i	0.934004	−	0.357262i	$-0.116290\pi$
$409$	20.1636	+	12.9584i	0.997026	+	0.640750i	0.0630219	+	0.998012i	$0.479926\pi$
$410$	−16.0871	+	21.5553i	−0.794484	+	1.06454i
$411$	−3.14145	−	10.6988i	−0.154956	−	0.527732i
$412$	−15.4911	−	23.9507i	−0.763191	−	1.17997i
$413$	−23.6330			−1.16290
$414$	6.46212	+	2.05938i	0.317596	+	0.101213i
$415$		−	42.7395i		−	2.09800i
$416$	7.03921	−	7.14263i	0.345126	−	0.350196i
$417$	3.19162	−	0.937145i	0.156294	−	0.0458922i
$418$	13.7661	−	18.4454i	0.673323	−	0.902194i
$419$	9.00805	−	14.0168i	0.440072	−	0.684766i	−0.548392	−	0.836221i	$-0.684760\pi$
$419$	9.00805	−	14.0168i	0.440072	−	0.684766i	0.988464	+	0.151456i	$0.0483961\pi$
$420$	12.1245	+	10.4442i	0.591617	+	0.509626i
$421$	5.27816	+	36.7104i	0.257242	+	1.78916i	0.552267	+	0.833668i	$0.313763\pi$
$421$	5.27816	+	36.7104i	0.257242	+	1.78916i	−0.295025	+	0.955490i	$0.595328\pi$
$422$	−7.76239	−	1.67675i	−0.377867	−	0.0816230i
$423$	−2.03728	−	3.17007i	−0.0990560	−	0.154134i
$424$	−3.05989	−	40.3038i	−0.148601	−	1.95733i
$425$	9.56575	+	4.36853i	0.464007	+	0.211905i
$426$	−10.5464	−	3.91608i	−0.510973	−	0.189735i
$427$	−4.81689	+	33.5022i	−0.233106	+	1.62128i
$428$	23.8669	+	27.3821i	1.15365	+	1.32356i
$429$	−9.33000	−	2.73954i	−0.450457	−	0.132266i
$430$	−11.7795	+	2.58047i	−0.568057	+	0.124441i
$431$	6.25596	+	7.21977i	0.301339	+	0.347764i	0.886144	−	0.463410i	$-0.153374\pi$
$431$	6.25596	+	7.21977i	0.301339	+	0.347764i	−0.584805	+	0.811174i	$0.698829\pi$
$432$	3.84448	+	1.10452i	0.184968	+	0.0531413i
$433$	17.0592	+	14.7819i	0.819812	+	0.710371i	0.960075	−	0.279743i	$-0.0902493\pi$
$433$	17.0592	+	14.7819i	0.819812	+	0.710371i	−0.140263	+	0.990114i	$0.544795\pi$
$434$	−13.2264	−	35.3040i	−0.634888	−	1.69465i
$435$	12.4227	−	5.67324i	0.595621	−	0.272011i
$436$	8.95937	−	1.31485i	0.429076	−	0.0629698i
$437$	−12.3192	−	7.12183i	−0.589306	−	0.340683i
$438$	−0.234609	+	0.0171235i	−0.0112101	+	0.000818194i
$439$	−8.23903	+	3.76264i	−0.393228	+	0.179581i	−0.602209	−	0.798339i	$-0.705713\pi$
$439$	−8.23903	+	3.76264i	−0.393228	+	0.179581i	0.208981	+	0.977920i	$0.432985\pi$
$440$	21.2679	+	38.5473i	1.01391	+	1.83767i
$441$	−0.622335	+	0.718213i	−0.0296350	+	0.0342006i
$442$	7.58612	+	4.12799i	0.360835	+	0.196348i
$443$	−18.7834	−	21.6772i	−0.892427	−	1.02992i	−0.999364	−	0.0356502i	$-0.988650\pi$
$443$	−18.7834	−	21.6772i	−0.892427	−	1.02992i	0.106937	−	0.994266i	$-0.465896\pi$
$444$	5.02671	+	16.9365i	0.238557	+	0.803770i
$445$	10.0922	−	34.3710i	0.478418	−	1.62934i
$446$	−6.32229	−	8.41997i	−0.299369	−	0.398697i
$447$	−0.656418	+	4.56548i	−0.0310475	+	0.215940i
$448$	−0.197389	−	22.5562i	−0.00932574	−	1.06568i
$449$	7.71927	−	16.9028i	0.364295	−	0.797694i	−0.635380	−	0.772199i	$-0.719157\pi$
$449$	7.71927	−	16.9028i	0.364295	−	0.797694i	0.999675	−	0.0254946i	$-0.00811607\pi$
$450$	−0.301702	+	4.30661i	−0.0142224	+	0.203015i
$451$	−19.8749	−	30.9260i	−0.935873	−	1.45625i
$452$	0.621496	−	4.41396i	0.0292327	−	0.207615i
$453$	−5.14180	+	0.739280i	−0.241583	+	0.0347344i
$454$	−7.32267	+	7.34406i	−0.343670	+	0.344674i
$455$	−7.66878	+	11.9328i	−0.359518	+	0.559421i
$456$	−7.38317	−	3.98968i	−0.345749	−	0.186834i
$457$	−0.523053	−	1.78136i	−0.0244674	−	0.0833283i	0.946354	−	0.323131i	$-0.104735\pi$
$457$	−0.523053	−	1.78136i	−0.0244674	−	0.0833283i	−0.970822	+	0.239803i	$0.922917\pi$
$458$	8.96453	+	16.3605i	0.418885	+	0.764478i
$459$			3.44485i			0.160792i
$460$	22.1344	−	15.8403i	1.03202	−	0.738558i
$461$			6.24955i			0.291070i	0.989353	+	0.145535i	$0.0464904\pi$
$461$			6.24955i			0.291070i	−0.989353	+	0.145535i	$0.953510\pi$
$462$	−19.1815	+	10.5102i	−0.892405	+	0.488981i
$463$	0.422530	+	1.43900i	0.0196366	+	0.0668762i	0.968728	−	0.248123i	$-0.0798138\pi$
$463$	0.422530	+	1.43900i	0.0196366	+	0.0668762i	−0.949092	+	0.315000i	$0.897996\pi$
$464$	−17.5571	−	7.89459i	−0.815067	−	0.366497i
$465$	14.5050	−	22.5702i	0.672651	−	1.04667i
$466$	−3.76877	−	3.75779i	−0.174585	−	0.174076i
$467$	−23.1351	+	3.32633i	−1.07057	+	0.153924i	−0.654992	−	0.755635i	$-0.727328\pi$
$467$	−23.1351	+	3.32633i	−1.07057	+	0.153924i	−0.415574	+	0.909560i	$0.636419\pi$
$468$	−0.494346	+	3.51092i	−0.0228511	+	0.162292i
$469$	−10.8999	−	16.9606i	−0.503310	−	0.783166i
$470$	−15.0857	−	1.05684i	−0.695850	−	0.0487482i
$471$	0.0895191	−	0.196019i	0.00412482	−	0.00903210i
$472$	−4.93782	+	23.1868i	−0.227282	+	1.06726i
$473$	2.34561	−	16.3140i	0.107851	−	0.750121i
$474$	−6.63450	+	4.98164i	−0.304733	+	0.228814i
$475$	2.55182	−	8.69071i	0.117086	−	0.398757i
$476$	18.6235	−	5.52740i	0.853605	−	0.253348i
$477$	9.35833	+	10.8001i	0.428488	+	0.494502i
$478$	−16.8186	+	30.9080i	−0.769263	+	1.41370i
$479$	−13.5262	+	15.6101i	−0.618028	+	0.713243i	−0.975331	−	0.220746i	$-0.929151\pi$
$479$	−13.5262	+	15.6101i	−0.618028	+	0.713243i	0.357303	+	0.933989i	$0.383696\pi$
$480$	12.7803	−	9.71342i	0.583337	−	0.443355i
$481$	−14.2444	+	6.50521i	−0.649490	+	0.296612i
$482$	−0.0419834	−	0.575213i	−0.00191229	−	0.0262002i
$483$	7.83755	+	11.0196i	0.356621	+	0.501407i
$484$	−37.7685	+	5.54278i	−1.71675	+	0.251944i
$485$	−16.4833	+	7.52765i	−0.748466	+	0.341813i
$486$	−1.32432	+	0.496149i	−0.0600726	+	0.0225058i
$487$	13.4497	+	11.6542i	0.609462	+	0.528102i	0.903997	−	0.427539i	$-0.140619\pi$
$487$	13.4497	+	11.6542i	0.609462	+	0.528102i	−0.294535	+	0.955641i	$0.595165\pi$
$488$	31.8632	+	11.7258i	1.44238	+	0.530802i
$489$	−11.9285	−	13.7663i	−0.539427	−	0.622532i
$490$	0.816122	+	3.72548i	0.0368686	+	0.168300i
$491$	−19.1360	−	5.61885i	−0.863597	−	0.253575i	−0.180207	−	0.983629i	$-0.557677\pi$
$491$	−19.1360	−	5.61885i	−0.863597	−	0.253575i	−0.683390	+	0.730054i	$0.739495\pi$
$492$	−10.1046	+	8.80739i	−0.455549	+	0.397068i
$493$	2.35938	−	16.4099i	0.106261	−	0.739064i
$494$	2.58940	−	6.97350i	0.116503	−	0.313753i
$495$	−14.1587	−	6.46604i	−0.636385	−	0.290627i
$496$	−37.4009	+	5.60033i	−1.67935	+	0.251462i
$497$	−12.1265	−	18.8693i	−0.543950	−	0.846403i
$498$	4.49722	−	20.8195i	0.201525	−	0.932946i
$499$	−3.54751	−	24.6735i	−0.158808	−	1.10454i	−0.900834	−	0.434164i	$-0.857044\pi$
$499$	−3.54751	−	24.6735i	−0.158808	−	1.10454i	0.742026	−	0.670372i	$-0.233865\pi$
$500$	−8.37350	−	7.21302i	−0.374474	−	0.322576i
$501$	3.36172	−	5.23093i	0.150190	−	0.233701i
$502$	20.9692	+	15.6497i	0.935900	+	0.698478i
$503$	−40.6492	+	11.9357i	−1.81246	+	0.532186i	−0.998792	−	0.0491460i	$-0.984350\pi$
$503$	−40.6492	+	11.9357i	−1.81246	+	0.532186i	−0.813667	+	0.581332i	$0.802532\pi$
$504$	4.80720	+	6.36345i	0.214130	+	0.283450i
$505$			13.5639i			0.603586i
$506$	9.66052	+	35.9257i	0.429463	+	1.59709i
$507$	9.85726			0.437776
$508$	19.5450	−	12.6415i	0.867169	−	0.560877i
$509$	−7.83006	−	26.6667i	−0.347061	−	1.18198i	−0.929412	−	0.369044i	$-0.879685\pi$
$509$	−7.83006	−	26.6667i	−0.347061	−	1.18198i	0.582351	−	0.812938i	$-0.302133\pi$
$510$	11.0793	+	8.26868i	0.490600	+	0.366143i
$511$	−0.394551	−	0.253562i	−0.0174539	−	0.0112169i
$512$	−22.1715	−	4.51917i	−0.979853	−	0.199721i
$513$	2.93688	−	0.422260i	0.129667	−	0.0186432i
$514$	0.000592486	0	0.000127983i	2.61334e−5	0	5.64507e-6i
$515$	34.0467	−	21.8805i	1.50028	−	0.964170i
$516$	−6.00962	+	0.0175296i	−0.264559	+	0.000771698i
$517$	8.58638	−	18.8016i	0.377629	−	0.826892i
$518$	−12.2612	+	33.0206i	−0.538727	+	1.45084i
$519$	−7.06876	−	1.01633i	−0.310284	−	0.0446121i
$520$	10.1052	+	10.0172i	0.443144	+	0.439283i
$521$	−8.24278	+	28.0723i	−0.361123	+	1.22987i	0.555971	+	0.831201i	$0.312346\pi$
$521$	−8.24278	+	28.0723i	−0.361123	+	1.22987i	−0.917094	+	0.398670i	$0.869472\pi$
$522$	6.64837	−	1.45642i	0.290991	−	0.0637459i
$523$	−22.8143	+	19.7687i	−0.997600	+	0.864425i	−0.990770	−	0.135551i	$-0.956719\pi$
$523$	−22.8143	+	19.7687i	−0.997600	+	0.864425i	−0.00682973	+	0.999977i	$0.502174\pi$
$524$	3.56633	+	1.61613i	0.155796	+	0.0706011i
$525$	−5.63670	+	6.50510i	−0.246006	+	0.283906i
$526$	−35.4187	+	13.2694i	−1.54433	+	0.578572i
$527$	−13.5297	−	29.6260i	−0.589365	−	1.29053i
$528$	6.30405	+	21.0153i	0.274349	+	0.914574i
$529$	21.3622	−	8.52395i	0.928790	−	0.370606i
$530$	57.1980	−	4.17474i	2.48452	−	0.181339i
$531$	−3.48184	−	7.62416i	−0.151099	−	0.330860i
$532$	−6.99517	−	15.1998i	−0.303279	−	0.658994i
$533$	−8.97930	−	7.78061i	−0.388937	−	0.337016i
$534$	8.53284	−	15.6811i	0.369252	−	0.678586i
$535$	−38.9501	+	33.7505i	−1.68396	+	1.45916i
$536$	−18.9177	+	7.15038i	−0.817120	+	0.308849i
$537$	21.9921	+	6.45748i	0.949031	+	0.278661i
$538$	17.8786	+	23.8106i	0.770802	+	1.02655i
$539$	−5.15963	−	0.741842i	−0.222241	−	0.0319534i
$540$	−1.58307	+	5.45020i	−0.0681245	+	0.234539i
$541$	16.8009	+	7.67273i	0.722328	+	0.329876i	0.742432	−	0.669922i	$-0.233672\pi$
$541$	16.8009	+	7.67273i	0.722328	+	0.329876i	−0.0201035	+	0.999798i	$0.506400\pi$
$542$	13.2291	+	0.926774i	0.568239	+	0.0398084i
$543$	7.66803	−	4.92795i	0.329067	−	0.211478i
$544$	−1.53189	−	19.4267i	−0.0656793	−	0.832913i
$545$	1.82850	+	12.7175i	0.0783245	+	0.544759i
$546$	−4.99128	+	5.00586i	−0.213607	+	0.214231i
$547$	−18.9301	−	12.1656i	−0.809392	−	0.520164i	0.0692764	−	0.997598i	$-0.477931\pi$
$547$	−18.9301	−	12.1656i	−0.809392	−	0.520164i	−0.878668	+	0.477433i	$0.841567\pi$
$548$	−18.7958	−	12.0020i	−0.802917	−	0.512700i
$549$	−11.5177	+	3.38190i	−0.491563	+	0.144336i
$550$	−20.7670	+	11.3790i	−0.885507	+	0.485201i
$551$	−14.2793			−0.608321
$552$	12.4490	−	5.38716i	0.529866	−	0.229293i
$553$	−16.5416			−0.703420
$554$	−3.41381	+	1.87055i	−0.145039	+	0.0794721i
$555$	−24.0513	+	7.06209i	−1.02092	+	0.299769i
$556$	3.58040	−	5.60710i	0.151843	−	0.237794i
$557$	−6.96591	−	4.47672i	−0.295155	−	0.189685i	0.384679	−	0.923050i	$-0.374312\pi$
$557$	−6.96591	−	4.47672i	−0.295155	−	0.189685i	−0.679835	+	0.733366i	$0.737948\pi$
$558$	9.44067	−	9.46825i	0.399655	−	0.400823i
$559$	−0.758094	−	5.27266i	−0.0320640	−	0.223010i
$560$	32.0049	−	0.186713i	1.35245	−	0.00789006i
$561$	−15.8958	+	10.2156i	−0.671122	+	0.431304i
$562$	−20.3138	−	1.42309i	−0.856884	−	0.0600296i
$563$	17.4967	+	7.99046i	0.737397	+	0.336758i	0.748459	−	0.663181i	$-0.230794\pi$
$563$	17.4967	+	7.99046i	0.737397	+	0.336758i	−0.0110623	+	0.999939i	$0.503521\pi$
$564$	−7.23742	−	2.10219i	−0.304750	−	0.0885181i
$565$	6.26021	+	0.900083i	0.263369	+	0.0378668i
$566$	8.07998	+	10.7608i	0.339627	+	0.452312i
$567$	−2.70542	−	0.794383i	−0.113617	−	0.0333609i
$568$	−21.0467	+	7.95508i	−0.883099	+	0.333788i
$569$	−24.9530	+	21.6219i	−1.04608	+	0.906435i	−0.995732	−	0.0922962i	$-0.970579\pi$
$569$	−24.9530	+	21.6219i	−1.04608	+	0.906435i	−0.0503506	+	0.998732i	$0.516034\pi$
$570$	5.69134	−	10.4592i	0.238384	−	0.438086i
$571$	7.84726	+	6.79969i	0.328398	+	0.284558i	0.803416	−	0.595417i	$-0.203013\pi$
$571$	7.84726	+	6.79969i	0.328398	+	0.284558i	−0.475019	+	0.879976i	$0.657559\pi$
$572$	−17.6667	+	8.13046i	−0.738681	+	0.339952i
$573$	1.00656	+	2.20405i	0.0420496	+	0.0920757i
$574$	−26.6541	+	1.94542i	−1.11252	+	0.0812002i
$575$	8.48537	+	11.9304i	0.353864	+	0.497532i
$576$	7.24770	−	3.38687i	0.301987	−	0.141120i
$577$	16.7169	+	36.6048i	0.695932	+	1.52388i	0.844835	+	0.535027i	$0.179699\pi$
$577$	16.7169	+	36.6048i	0.695932	+	1.52388i	−0.148903	+	0.988852i	$0.547574\pi$
$578$	−6.79780	+	2.54675i	−0.282751	+	0.105931i
$579$	−9.94991	+	11.4828i	−0.413504	+	0.477209i
$580$	11.2740	−	24.8783i	0.468126	−	1.03302i
$581$	32.0944	−	27.8100i	1.33150	−	1.15375i
$582$	−8.82152	+	1.93248i	−0.365664	+	0.0801040i
$583$	−22.0837	+	75.2102i	−0.914614	+	3.11489i
$584$	−0.331211	+	0.334122i	−0.0137056	+	0.0138261i
$585$	−4.97945	−	0.715937i	−0.205875	−	0.0296003i
$586$	10.3510	−	27.8763i	0.427598	−	1.15156i
$587$	−4.73940	+	10.3778i	−0.195616	+	0.428339i	−0.981868	−	0.189567i	$-0.939292\pi$
$587$	−4.73940	+	10.3778i	−0.195616	+	0.428339i	0.786252	+	0.617906i	$0.212019\pi$
$588$	0.00554407	+	1.90066i	0.000228634	+	0.0783818i
$589$	−23.5990	+	15.1662i	−0.972381	+	0.624911i
$590$	−32.8783	−	7.10202i	−1.35358	−	0.292386i
$591$	5.64662	−	0.811862i	0.232271	−	0.0333955i
$592$	29.8353	+	18.9289i	1.22622	+	0.777975i
$593$	−22.3999	−	14.3955i	−0.919852	−	0.591153i	−0.00723734	−	0.999974i	$-0.502304\pi$
$593$	−22.3999	−	14.3955i	−0.919852	−	0.591153i	−0.912615	+	0.408821i	$0.865940\pi$
$594$	−6.21667	−	4.63961i	−0.255073	−	0.190366i
$595$	7.76551	+	26.4469i	0.318355	+	1.08422i
$596$	5.00995	+	7.74587i	0.205216	+	0.317283i
$597$	−10.2350			−0.418890
$598$	6.26701	+	10.2611i	0.256277	+	0.419608i
$599$			8.19839i			0.334977i	0.985874	+	0.167489i	$0.0535657\pi$
$599$			8.19839i			0.334977i	−0.985874	+	0.167489i	$0.946434\pi$
$600$	5.20455	+	6.88943i	0.212475	+	0.281260i
$601$	−0.494957	+	0.145332i	−0.0201897	+	0.00592823i	−0.291812	−	0.956476i	$-0.594258\pi$
$601$	−0.494957	+	0.145332i	−0.0201897	+	0.00592823i	0.271622	+	0.962404i	$0.412440\pi$
$602$	−9.60249	−	7.16650i	−0.391368	−	0.292085i
$603$	3.86571	−	6.01517i	0.157424	−	0.244956i
$604$	−6.78065	+	7.87156i	−0.275901	+	0.320289i
$605$	−7.70810	−	53.6110i	−0.313379	−	2.17960i
$606$	−1.42725	+	6.60734i	−0.0579780	+	0.268405i
$607$	19.2974	+	30.0273i	0.783255	+	1.21877i	0.971591	+	0.236665i	$0.0760543\pi$
$607$	19.2974	+	30.0273i	0.783255	+	1.21877i	−0.188336	+	0.982105i	$0.560309\pi$
$608$	−16.3743	+	3.68728i	−0.664067	+	0.149539i
$609$	12.3435	+	5.63707i	0.500182	+	0.228426i
$610$	−16.7691	+	45.1608i	−0.678961	+	1.82851i
$611$	0.950706	−	6.61231i	0.0384615	−	0.267505i
$612$	4.52696	+	5.19370i	0.182991	+	0.209943i
$613$	10.7231	+	3.14860i	0.433103	+	0.127171i	0.491015	−	0.871151i	$-0.336626\pi$
$613$	10.7231	+	3.14860i	0.433103	+	0.127171i	−0.0579117	+	0.998322i	$0.518444\pi$
$614$	−6.00923	−	27.4313i	−0.242513	−	1.10704i
$615$	−12.4546	−	14.3734i	−0.502218	−	0.579591i
$616$	−15.1077	+	41.0529i	−0.608705	+	1.65407i
$617$	−28.2517	−	24.4802i	−1.13737	−	0.985537i	−0.137383	−	0.990518i	$-0.543869\pi$
$617$	−28.2517	−	24.4802i	−1.13737	−	0.985537i	−0.999988	+	0.00498057i	$0.998415\pi$
$618$	18.8874	−	7.07604i	0.759763	−	0.284640i
$619$	21.5813	−	9.85584i	0.867425	−	0.396140i	0.0685575	−	0.997647i	$-0.478160\pi$
$619$	21.5813	−	9.85584i	0.867425	−	0.396140i	0.798867	+	0.601508i	$0.205433\pi$
$620$	−7.79128	−	53.0897i	−0.312905	−	2.13214i
$621$	−2.40028	+	4.15195i	−0.0963198	+	0.166612i
$622$	1.46505	+	20.0726i	0.0587430	+	0.804836i
$623$	32.3771	−	14.7861i	1.29716	−	0.592394i
$624$	3.86848	+	5.94295i	0.154863	+	0.237908i
$625$	20.2644	−	23.3863i	0.810574	−	0.935453i
$626$	2.61206	−	4.80026i	0.104399	−	0.191857i
$627$	10.6577	+	12.2997i	0.425629	+	0.491202i
$628$	−0.122629	−	0.413172i	−0.00489341	−	0.0164874i
$629$	−8.57299	+	29.1969i	−0.341828	+	1.16416i
$630$	−9.04872	+	6.79440i	−0.360510	+	0.270695i
$631$	−0.0753389	+	0.523994i	−0.00299919	+	0.0208599i	−0.991266	−	0.131877i	$-0.957900\pi$
$631$	−0.0753389	+	0.523994i	−0.00299919	+	0.0208599i	0.988267	+	0.152737i	$0.0488087\pi$
$632$	−3.45616	+	16.2292i	−0.137479	+	0.645565i
$633$	2.33274	−	5.10798i	0.0927179	−	0.203024i
$634$	−28.1599	−	1.97276i	−1.11837	−	0.0783482i
$635$	17.8556	+	27.7839i	0.708579	+	1.10257i
$636$	28.3020	+	3.98498i	1.12225	+	0.158015i
$637$	−1.66758	+	0.239762i	−0.0660719	+	0.00949970i
$638$	26.4361	+	26.3591i	1.04661	+	1.04357i
$639$	4.30075	−	6.69210i	0.170135	−	0.264736i
$640$	6.50383	−	31.4395i	0.257086	−	1.24276i
$641$	−12.9716	−	44.1773i	−0.512348	−	1.74490i	−0.655498	−	0.755197i	$-0.727541\pi$
$641$	−12.9716	−	44.1773i	−0.512348	−	1.74490i	0.143149	−	0.989701i	$-0.454277\pi$
$642$	−22.5250	+	12.3422i	−0.888990	+	0.487110i
$643$			18.7475i			0.739328i	0.929165	+	0.369664i	$0.120527\pi$
$643$			18.7475i			0.739328i	−0.929165	+	0.369664i	$0.879473\pi$
$644$	26.2975	+	6.31436i	1.03627	+	0.248821i
$645$		−	8.52687i		−	0.335745i
$646$	−6.94599	−	12.6766i	−0.273286	−	0.498756i
$647$	0.437655	+	1.49052i	0.0172060	+	0.0585982i	0.967649	−	0.252302i	$-0.0811877\pi$
$647$	0.437655	+	1.49052i	0.0172060	+	0.0585982i	−0.950443	+	0.310900i	$0.899369\pi$
$648$	−1.34465	+	2.48836i	−0.0528227	+	0.0977519i
$649$	24.8554	−	38.6758i	0.975660	−	1.51816i
$650$	−5.40385	+	5.41963i	−0.211956	+	0.212575i
$651$	26.3868	−	3.79385i	1.03418	−	0.148693i
$652$	−36.0749	−	5.07943i	−1.41280	−	0.198926i
$653$	26.0895	+	40.5961i	1.02096	+	1.58865i	0.787531	+	0.616275i	$0.211359\pi$
$653$	26.0895	+	40.5961i	1.02096	+	1.58865i	0.233431	+	0.972373i	$0.425005\pi$
$654$	−0.447476	+	6.38744i	−0.0174977	+	0.249769i
$655$	−2.30782	+	5.05343i	−0.0901741	+	0.197454i
$656$	−3.66036	+	26.5573i	−0.142913	+	1.03689i
$657$	0.0236719	−	0.164642i	0.000923530	−	0.00642329i
$658$	−9.02241	−	12.0160i	−0.351730	−	0.468431i
$659$	−5.09254	+	17.3436i	−0.198377	+	0.675610i	0.798873	+	0.601500i	$0.205430\pi$
$659$	−5.09254	+	17.3436i	−0.198377	+	0.675610i	−0.997250	+	0.0741104i	$0.976388\pi$
$660$	−29.8438	+	8.85757i	−1.16167	+	0.344781i
$661$	−17.4327	−	20.1184i	−0.678053	−	0.782515i	0.307561	−	0.951529i	$-0.400487\pi$
$661$	−17.4327	−	20.1184i	−0.678053	−	0.782515i	−0.985614	+	0.169013i	$0.945942\pi$
$662$	8.87056	+	4.82691i	0.344764	+	0.187603i
$663$	−3.99920	+	4.61532i	−0.155316	+	0.179244i
$664$	−20.5791	−	37.2990i	−0.798626	−	1.44748i
$665$	21.5953	−	9.86224i	0.837429	−	0.382441i
$666$	−12.4591	+	0.909359i	−0.482780	+	0.0352369i
$667$	14.2776	−	18.1343i	0.552832	−	0.702161i
$668$	−1.80573	−	12.3043i	−0.0698659	−	0.476066i
$669$	6.77255	−	3.09292i	0.261842	−	0.119579i
$670$	−10.0671	−	26.8711i	−0.388925	−	1.03812i
$671$	−49.7608	−	43.1180i	−1.92100	−	1.66455i
$672$	15.6101	+	3.27673i	0.602171	+	0.126402i
$673$	−11.3901	−	13.1449i	−0.439056	−	0.506697i	0.492492	−	0.870317i	$-0.336086\pi$
$673$	−11.3901	−	13.1449i	−0.439056	−	0.506697i	−0.931547	+	0.363620i	$0.881541\pi$
$674$	9.51008	−	2.08332i	0.366315	−	0.0802466i
$675$	−2.92904	−	0.860044i	−0.112739	−	0.0331031i
$676$	14.8615	−	12.9537i	0.571597	−	0.498218i
$677$	2.61114	−	18.1609i	0.100354	−	0.697979i	−0.876080	−	0.482165i	$-0.839851\pi$
$677$	2.61114	−	18.1609i	0.100354	−	0.697979i	0.976435	−	0.215814i	$-0.0692404\pi$
$678$	2.95480	+	1.09718i	0.113479	+	0.0421369i
$679$	−16.3782	−	7.47965i	−0.628536	−	0.287043i
$680$	27.5700	−	2.09313i	1.05726	−	0.0802680i
$681$	−3.96472	−	6.16923i	−0.151929	−	0.236405i
$682$	71.6861	+	15.4849i	2.74500	+	0.592947i
$683$	5.89907	+	41.0289i	0.225721	+	1.56993i	0.715835	+	0.698269i	$0.246046\pi$
$683$	5.89907	+	41.0289i	0.225721	+	1.56993i	−0.490114	+	0.871658i	$0.663045\pi$
$684$	3.87296	−	4.49606i	0.148086	−	0.171911i
$685$	17.1069	−	26.6189i	0.653622	−	1.01706i
$686$	14.4285	−	19.3329i	0.550881	−	0.738132i
$687$	−12.6571	+	3.71647i	−0.482900	+	0.141792i
$688$	−9.03750	+	7.92382i	−0.344552	+	0.302093i
$689$			25.3340i			0.965147i
$690$	7.59209	+	17.6857i	0.289026	+	0.673283i
$691$	−15.3318			−0.583248			−0.291624	−	0.956533i	$-0.594196\pi$
$691$	−15.3318			−0.583248			−0.291624	+	0.956533i	$0.594196\pi$
$692$	−11.9930	+	7.75693i	−0.455904	+	0.294874i
$693$	−4.35728	−	14.8395i	−0.165519	−	0.563707i
$694$	−2.08046	+	2.78763i	−0.0789730	+	0.105817i
$695$	7.94086	+	5.10328i	0.301214	+	0.193578i
$696$	8.10964	−	10.9326i	0.307395	−	0.414399i
$697$	−22.8527	+	3.28572i	−0.865608	+	0.124456i
$698$	7.84472	−	36.3165i	0.296927	−	1.37460i
$699$	3.16587	−	2.03458i	0.119744	−	0.0769550i
$700$	0.0502145	+	17.2149i	0.00189793	+	0.650662i
$701$	14.4901	−	31.7288i	0.547282	−	1.19838i	−0.410758	−	0.911744i	$-0.634736\pi$
$701$	14.4901	−	31.7288i	0.547282	−	1.19838i	0.958040	−	0.286635i	$-0.0925368\pi$
$702$	−2.35029	−	0.872709i	−0.0887059	−	0.0329383i
$703$	25.9425	+	3.72997i	0.978441	+	0.140679i
$704$	37.1212	+	23.3999i	1.39906	+	0.881916i
$705$	3.01266	−	10.2602i	0.113463	−	0.386420i
$706$	−3.39922	−	15.5170i	−0.127931	−	0.583988i
$707$	−10.1856	+	8.82584i	−0.383067	+	0.331930i
$708$	−15.2686	−	6.91916i	−0.573828	−	0.260038i
$709$	−28.5743	+	32.9766i	−1.07313	+	1.23846i	−0.103309	+	0.994649i	$0.532943\pi$
$709$	−28.5743	+	32.9766i	−1.07313	+	1.23846i	−0.969823	+	0.243811i	$0.921602\pi$
$710$	−11.2000	−	29.8952i	−0.420329	−	1.12195i
$711$	−2.43706	−	5.33642i	−0.0913970	−	0.200131i
$712$	−7.74214	−	34.8551i	−0.290149	−	1.30625i
$713$	4.33570	−	45.1343i	0.162373	−	1.69029i
$714$	0.999936	+	13.7001i	0.0374217	+	0.512714i
$715$	−11.4629	−	25.1001i	−0.428686	−	0.938692i
$716$	41.6429	−	19.1647i	1.55627	−	0.716217i
$717$	−18.8041	−	16.2938i	−0.702252	−	0.608505i
$718$	1.13589	+	0.618096i	0.0423912	+	0.0230671i
$719$	10.7705	−	9.33266i	0.401671	−	0.348050i	−0.430479	−	0.902601i	$-0.641655\pi$
$719$	10.7705	−	9.33266i	0.401671	−	0.348050i	0.832150	+	0.554551i	$0.187110\pi$
$720$	4.77549	+	10.2975i	0.177972	+	0.383764i
$721$	38.5845	+	11.3294i	1.43696	+	0.421930i
$722$	11.5311	−	8.65835i	0.429143	−	0.322230i
$723$	0.403668	+	0.0580387i	0.0150126	+	0.00215848i
$724$	5.08495	−	17.5065i	0.188981	−	0.650623i
$725$	13.3637	+	6.10301i	0.496316	+	0.226660i
$726$	1.88635	−	26.9264i	0.0700089	−	0.999333i
$727$	16.7246	−	10.7482i	0.620280	−	0.398630i	−0.192420	−	0.981313i	$-0.561633\pi$
$727$	16.7246	−	10.7482i	0.620280	−	0.398630i	0.812700	+	0.582683i	$0.197997\pi$
$728$	−0.946890	+	14.1064i	−0.0350941	+	0.522817i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−0.472701	−	0.471324i	−0.0174954	−	0.0174445i
$731$	−8.70795	−	5.59626i	−0.322075	−	0.206985i
$732$	−12.9207	+	20.2345i	−0.477562	+	0.747888i
$733$	38.7386	−	11.3747i	1.43084	−	0.420133i	0.527684	−	0.849441i	$-0.323060\pi$
$733$	38.7386	−	11.3747i	1.43084	−	0.420133i	0.903159	+	0.429307i	$0.141242\pi$
$734$	5.01839	+	9.15871i	0.185232	+	0.338054i
$735$	−2.69678			−0.0994724
$736$	11.6897	−	24.4817i	0.430887	−	0.902406i
$737$	39.2199			1.44468
$738$	−4.55454	−	8.31218i	−0.167655	−	0.305976i
$739$	21.9401	−	6.44220i	0.807080	−	0.236980i	0.147936	−	0.988997i	$-0.452737\pi$
$739$	21.9401	−	6.44220i	0.807080	−	0.236980i	0.659144	+	0.752017i	$0.270919\pi$
$740$	−26.9810	+	42.2537i	−0.991840	+	1.55328i
$741$	4.42498	+	2.84376i	0.162556	+	0.104468i
$742$	40.3529	+	40.2353i	1.48140	+	1.47709i
$743$	3.12912	+	21.7635i	0.114796	+	0.798426i	0.963144	+	0.268987i	$0.0866887\pi$
$743$	3.12912	+	21.7635i	0.114796	+	0.798426i	−0.848348	+	0.529440i	$0.822402\pi$
$744$	1.79098	−	26.6812i	0.0656604	−	0.978181i
$745$	−11.0110	+	7.07635i	−0.403413	+	0.259257i
$746$	0.486935	−	6.95069i	0.0178280	−	0.254483i
$747$	13.7001	+	6.25664i	0.501262	+	0.228919i
$748$	−10.5411	+	36.2909i	−0.385420	+	1.32693i
$749$	−50.6885	−	7.28791i	−1.85212	−	0.266294i
$750$	6.24926	−	4.69237i	0.228191	−	0.171341i
$751$	−9.34547	−	2.74408i	−0.341021	−	0.100133i	0.106738	−	0.994287i	$-0.465959\pi$
$751$	−9.34547	−	2.74408i	−0.341021	−	0.100133i	−0.447759	+	0.894154i	$0.647778\pi$
$752$	−13.6742	+	6.34147i	−0.498647	+	0.231250i
$753$	−13.9826	+	12.1160i	−0.509553	+	0.441530i
$754$	10.5981	+	5.76696i	0.385960	+	0.210020i
$755$	−11.1406	−	9.65335i	−0.405447	−	0.351322i
$756$	−5.12280	+	2.35759i	−0.186315	+	0.0857447i
$757$	12.4336	+	27.2257i	0.451906	+	0.989537i	0.989258	+	0.146179i	$0.0466974\pi$
$757$	12.4336	+	27.2257i	0.451906	+	0.989537i	−0.537352	+	0.843358i	$0.680575\pi$
$758$	2.99007	+	40.9669i	0.108604	+	1.48799i
$759$	−26.2766	+	1.23673i	−0.953780	+	0.0448906i
$760$	−5.16395	−	23.2481i	−0.187316	−	0.843298i
$761$	20.0763	+	43.9611i	0.727767	+	1.59359i	0.802689	+	0.596398i	$0.203402\pi$
$761$	20.0763	+	43.9611i	0.727767	+	1.59359i	−0.0749225	+	0.997189i	$0.523871\pi$
$762$	5.77441	+	15.4131i	0.209185	+	0.558358i
$763$	−8.36020	+	9.64818i	−0.302659	+	0.349288i
$764$	4.41396	+	2.00025i	0.159692	+	0.0723665i
$765$	−7.38786	+	6.40161i	−0.267109	+	0.231451i
$766$	10.2927	+	46.9847i	0.371890	+	1.69762i
$767$	4.18617	−	14.2568i	0.151154	−	0.514783i
$768$	6.47638	−	14.6307i	0.233696	−	0.527939i
$769$	−2.21157	−	0.317976i	−0.0797513	−	0.0114665i	0.102324	−	0.994751i	$-0.467372\pi$
$769$	−2.21157	−	0.317976i	−0.0797513	−	0.0114665i	−0.182075	+	0.983285i	$0.558281\pi$
$770$	−58.1857	−	21.6055i	−2.09687	−	0.778609i
$771$	−0.000178052	0	0.000389881i	−6.41240e−6	0	1.40412e-5i
$772$	0.0886387	+	30.3878i	0.00319018	+	1.09368i
$773$	−1.30154	+	0.836449i	−0.0468131	+	0.0300850i	−0.563838	−	0.825885i	$-0.690676\pi$
$773$	−1.30154	+	0.836449i	−0.0468131	+	0.0300850i	0.517025	+	0.855970i	$0.327039\pi$
$774$	0.897231	−	4.15366i	0.0322503	−	0.149300i
$775$	28.5678	−	4.10744i	1.02619	−	0.147543i
$776$	−10.7604	+	14.5061i	−0.386277	+	0.520739i
$777$	−20.9529	−	13.4656i	−0.751683	−	0.483077i
$778$	3.40589	−	4.56360i	0.122107	−	0.163613i
$779$	5.60245	+	19.0802i	0.200728	+	0.683618i
$780$	−8.44821	+	5.46422i	−0.302494	+	0.195651i
$781$	43.6337			1.56134
$782$	23.0440	+	3.85396i	0.824053	+	0.137817i
$783$			4.81259i			0.171988i
$784$	2.50606	+	2.85828i	0.0895021	+	0.102081i
$785$	0.586740	−	0.172282i	0.0209417	−	0.00614903i
$786$	−1.65594	+	2.21882i	−0.0590656	+	0.0791427i
$787$	20.5672	−	32.0031i	0.733140	−	1.14079i	−0.251781	−	0.967784i	$-0.581016\pi$
$787$	20.5672	−	32.0031i	0.733140	−	1.14079i	0.984921	−	0.173004i	$-0.0553475\pi$
$788$	7.44637	−	8.64439i	0.265266	−	0.307944i
$789$	−3.80617	−	26.4725i	−0.135503	−	0.942446i
$790$	−23.0127	−	4.97096i	−0.818754	−	0.176859i
$791$	3.39753	+	5.28666i	0.120802	+	0.187972i
$792$	−15.4697	+	1.17447i	−0.549693	+	0.0417330i
$793$	−19.3572	−	8.84016i	−0.687396	−	0.313923i
$794$	22.7562	+	8.44985i	0.807588	+	0.299874i
$795$	−5.77125	+	40.1399i	−0.204685	+	1.42362i
$796$	−15.4310	+	13.4501i	−0.546938	+	0.476725i
$797$	1.09526	+	0.321596i	0.0387960	+	0.0113915i	0.301073	−	0.953601i	$-0.402655\pi$
$797$	1.09526	+	0.321596i	0.0387960	+	0.0113915i	−0.262277	+	0.964993i	$0.584473\pi$
$798$	11.5574	−	2.53181i	0.409127	−	0.0896252i
$799$	−8.50083	−	9.81048i	−0.300738	−	0.347070i
$800$	16.9003	+	3.54757i	0.597517	+	0.125426i
$801$	9.54020	+	8.26663i	0.337086	+	0.292087i
$802$	5.67127	+	15.1378i	0.200259	+	0.534534i
$803$	0.829918	−	0.379011i	0.0292872	−	0.0133750i
$804$	−2.07645	−	14.1489i	−0.0732308	−	0.498994i
$805$	−9.06801	+	37.2863i	−0.319605	+	1.31417i
$806$	23.6403	−	1.72544i	0.832693	−	0.0607762i
$807$	−19.1519	+	8.74638i	−0.674179	+	0.307887i
$808$	6.53104	+	11.8373i	0.229761	+	0.416434i
$809$	−26.9760	+	31.1320i	−0.948427	+	1.09454i	0.0469885	+	0.998895i	$0.485038\pi$
$809$	−26.9760	+	31.1320i	−0.948427	+	1.09454i	−0.995415	+	0.0956474i	$0.969508\pi$
$810$	−3.52506	−	1.91816i	−0.123858	−	0.0673973i
$811$	10.0456	+	11.5933i	0.352749	+	0.407094i	0.904197	−	0.427115i	$-0.140470\pi$
$811$	10.0456	+	11.5933i	0.352749	+	0.407094i	−0.551448	+	0.834209i	$0.685925\pi$
$812$	26.0177	−	7.72199i	0.913042	−	0.270989i
$813$	−2.64190	+	8.99748i	−0.0926554	+	0.315555i
$814$	−41.1433	−	54.7943i	−1.44207	−	1.92054i
$815$	7.35629	−	51.1641i	0.257680	−	1.79220i
$816$	13.6503	+	1.88141i	0.477858	+	0.0658625i
$817$	−3.70366	+	8.10988i	−0.129575	+	0.283729i
$818$	−2.36884	+	33.8137i	−0.0828246	+	1.18227i
$819$	−2.70244	−	4.20507i	−0.0944308	−	0.146937i
$820$	−37.6659	−	5.30345i	−1.31535	−	0.185204i
$821$	39.5027	−	5.67962i	1.37865	−	0.198220i	0.587195	−	0.809445i	$-0.300232\pi$
$821$	39.5027	−	5.67962i	1.37865	−	0.198220i	0.791457	+	0.611225i	$0.209323\pi$
$822$	11.1342	−	11.1667i	0.388349	−	0.389483i
$823$	17.4580	−	27.1652i	0.608549	−	0.946920i	−0.391098	−	0.920349i	$-0.627905\pi$
$823$	17.4580	−	27.1652i	0.608549	−	0.946920i	0.999647	−	0.0265711i	$-0.00845884\pi$
$824$	19.1772	−	35.4888i	0.668071	−	1.23631i
$825$	−4.71744	−	16.0661i	−0.164240	−	0.559351i
$826$	−16.0603	−	29.3105i	−0.558808	−	1.01984i
$827$		−	29.3001i		−	1.01886i	−0.860511	−	0.509431i	$-0.829856\pi$
$827$		−	29.3001i		−	1.01886i	0.860511	−	0.509431i	$-0.170144\pi$
$828$	1.83735	+	9.41404i	0.0638522	+	0.327161i
$829$			1.69458i			0.0588552i	0.999567	+	0.0294276i	$0.00936844\pi$
$829$			1.69458i			0.0588552i	−0.999567	+	0.0294276i	$0.990632\pi$
$830$	53.0071	−	29.0445i	1.83990	−	1.00815i
$831$	−0.775483	−	2.64105i	−0.0269012	−	0.0916171i
$832$	13.6422	+	3.87636i	0.472957	+	0.134389i
$833$	−1.76992	+	2.75405i	−0.0613242	+	0.0954223i
$834$	3.33121	+	3.32151i	0.115350	+	0.115014i
$835$	17.4655	−	2.51115i	0.604417	−	0.0869020i
$836$	32.2317	+	4.53830i	1.11476	+	0.156960i
$837$	5.11147	+	7.95361i	0.176678	+	0.274917i
$838$	23.5057	+	1.64671i	0.811992	+	0.0568847i
$839$	16.0412	−	35.1254i	0.553804	−	1.21266i	−0.401178	−	0.916000i	$-0.631399\pi$
$839$	16.0412	−	35.1254i	0.553804	−	1.21266i	0.954983	−	0.296662i	$-0.0958735\pi$
$840$	−4.71381	+	22.1349i	−0.162642	+	0.763726i
$841$	−0.830980	+	5.77959i	−0.0286545	+	0.199296i
$842$	−41.9427	+	31.4935i	−1.44544	+	1.08534i
$843$	4.05672	−	13.8159i	0.139721	−	0.475846i
$844$	−3.19552	−	10.7667i	−0.109994	−	0.370604i
$845$	18.3179	+	21.1400i	0.630155	+	0.727238i
$846$	2.54716	−	4.68100i	0.0875732	−	0.160936i
$847$	35.2426	−	40.6721i	1.21095	−	1.39751i
$848$	47.9068	−	31.1843i	1.64513	−	1.07087i
$849$	−8.65541	+	3.95280i	−0.297053	+	0.135660i
$850$	1.08259	+	14.8325i	0.0371324	+	0.508751i
$851$	−30.6764	+	29.2166i	−1.05157	+	1.00153i
$852$	−2.31013	−	15.7412i	−0.0791438	−	0.539286i
$853$	−20.7883	+	9.49370i	−0.711778	+	0.325058i	−0.738190	−	0.674593i	$-0.764319\pi$
$853$	−20.7883	+	9.49370i	−0.711778	+	0.325058i	0.0264117	+	0.999651i	$0.491592\pi$
$854$	−44.8240	+	16.7930i	−1.53385	+	0.574645i
$855$	6.36324	+	5.51378i	0.217618	+	0.188567i
$856$	−17.7410	+	48.2087i	−0.606376	+	1.64774i
$857$	9.35752	+	10.7992i	0.319647	+	0.368892i	0.892720	−	0.450612i	$-0.148794\pi$
$857$	9.35752	+	10.7992i	0.319647	+	0.368892i	−0.573073	+	0.819504i	$0.694249\pi$
$858$	−2.94272	−	13.4331i	−0.100463	−	0.458599i
$859$	−55.1658	−	16.1981i	−1.88223	−	0.552673i	−0.995991	−	0.0894485i	$-0.971490\pi$
$859$	−55.1658	−	16.1981i	−1.88223	−	0.552673i	−0.886241	−	0.463225i	$-0.846692\pi$
$860$	−11.2054	−	12.8557i	−0.382100	−	0.438376i
$861$	2.68939	−	18.7051i	0.0916541	−	0.637468i
$862$	−4.70285	+	12.6652i	−0.160180	+	0.431379i
$863$	11.8582	+	5.41547i	0.403658	+	0.184345i	0.606890	−	0.794786i	$-0.292417\pi$
$863$	11.8582	+	5.41547i	0.403658	+	0.184345i	−0.203231	+	0.979131i	$0.565144\pi$
$864$	1.24273	+	5.51866i	0.0422784	+	0.187749i
$865$	−10.9563	−	17.0484i	−0.372527	−	0.579663i
$866$	−6.74009	+	31.2027i	−0.229038	+	1.06031i
$867$	−0.730506	−	5.08078i	−0.0248093	−	0.172552i
$868$	34.7971	−	40.3954i	1.18109	−	1.37111i
$869$	17.3972	−	27.0706i	0.590159	−	0.918306i
$870$	15.4782	+	11.5517i	0.524761	+	0.391638i
$871$	12.1623	−	3.57118i	0.412105	−	0.121005i
$872$	7.71924	+	10.2182i	0.261407	+	0.346032i
$873$		−	6.38567i		−	0.216122i
$874$	0.460997	−	20.1185i	0.0155935	−	0.680517i
$875$	15.5811			0.526736
$876$	−0.180670	−	0.279334i	−0.00610429	−	0.00943782i
$877$	10.0393	+	34.1906i	0.339002	+	1.15453i	0.935914	+	0.352228i	$0.114576\pi$
$877$	10.0393	+	34.1906i	0.339002	+	1.15453i	−0.596913	+	0.802306i	$0.703606\pi$
$878$	−10.2656	−	7.66137i	−0.346446	−	0.258559i
$879$	17.6887	+	11.3678i	0.596625	+	0.383427i
$880$	−33.3547	+	52.5728i	−1.12439	+	1.77223i
$881$	−11.6521	+	1.67532i	−0.392569	+	0.0564430i	−0.335773	−	0.941943i	$-0.608998\pi$
$881$	−11.6521	+	1.67532i	−0.392569	+	0.0564430i	−0.0567961	+	0.998386i	$0.518089\pi$
$882$	−1.31367	−	0.283766i	−0.0442337	−	0.00955491i
$883$	28.9479	−	18.6037i	0.974176	−	0.626065i	0.0462897	−	0.998928i	$-0.485260\pi$
$883$	28.9479	−	18.6037i	0.974176	−	0.626065i	0.927886	+	0.372863i	$0.121624\pi$
$884$	0.0356268	+	12.2138i	0.00119826	+	0.410796i
$885$	9.88050	−	21.6353i	0.332129	−	0.727262i
$886$	14.1202	−	38.0271i	0.474378	−	1.27754i
$887$	55.1619	+	7.93108i	1.85215	+	0.266300i	0.976323	−	0.216317i	$-0.0694044\pi$
$887$	55.1619	+	7.93108i	1.85215	+	0.266300i	0.875832	+	0.482617i	$0.160314\pi$
$888$	−17.5892	+	17.7438i	−0.590256	+	0.595444i
$889$	−9.24539	+	31.4869i	−0.310080	+	1.05604i
$890$	49.4865	−	10.8407i	1.65879	−	0.363383i
$891$	4.14537	−	3.59199i	0.138875	−	0.120336i
$892$	6.14631	−	13.5631i	0.205794	−	0.454126i
$893$	−7.32186	+	8.44987i	−0.245017	+	0.282764i
$894$	−6.10836	+	2.28845i	−0.204294	+	0.0765373i
$895$	27.0196	+	59.1646i	0.903165	+	1.97766i
$896$	27.8409	−	15.5733i	0.930098	−	0.520268i
$897$	−8.03592	+	2.77614i	−0.268311	+	0.0926927i
$898$	26.2093	−	1.91295i	0.874615	−	0.0638359i
$899$	−18.9016	−	41.3887i	−0.630402	−	1.38039i
$900$	−5.54624	+	2.55246i	−0.184875	+	0.0850820i
$901$	37.2046	+	32.2380i	1.23947	+	1.07400i
$902$	24.8491	−	45.6660i	0.827385	−	1.52051i
$903$	6.40309	−	5.54831i	0.213081	−	0.184636i
$904$	5.89670	−	2.22879i	0.196121	−	0.0741286i
$905$	24.8182	+	7.28727i	0.824984	+	0.242237i
$906$	−4.41110	−	5.87466i	−0.146549	−	0.195172i
$907$	−44.7356	−	6.43201i	−1.48542	−	0.213571i	−0.648635	−	0.761100i	$-0.724660\pi$
$907$	−44.7356	−	6.43201i	−1.48542	−	0.213571i	−0.836787	+	0.547529i	$0.815569\pi$
$908$	−14.0846	−	4.09104i	−0.467415	−	0.135766i
$909$	−4.34791	−	1.98562i	−0.144211	−	0.0658589i
$910$	−20.0110	−	1.40188i	−0.663359	−	0.0464720i
$911$	−1.83360	+	1.17838i	−0.0607498	+	0.0390415i	−0.570663	−	0.821184i	$-0.693314\pi$
$911$	−1.83360	+	1.17838i	−0.0607498	+	0.0390415i	0.509913	+	0.860226i	$0.329677\pi$
$912$	−0.0692375	−	11.8681i	−0.00229268	−	0.392993i
$913$	11.7570	+	81.7715i	0.389099	+	2.70624i
$914$	1.85385	−	1.85926i	0.0613199	−	0.0614990i
$915$	−28.6564	−	18.4163i	−0.947351	−	0.608825i
$916$	−14.1989	+	22.2363i	−0.469145	+	0.734707i
$917$	−5.29644	+	1.55518i	−0.174904	+	0.0513564i
$918$	−4.27242	+	2.34101i	−0.141011	+	0.0772650i
$919$	−15.3334			−0.505803			−0.252902	−	0.967492i	$-0.581385\pi$
$919$	−15.3334			−0.505803			−0.252902	+	0.967492i	$0.581385\pi$
$920$	34.6876	+	16.6873i	1.14362	+	0.550164i
$921$	19.8568			0.654304
$922$	−7.75091	+	4.24700i	−0.255263	+	0.139868i
$923$	13.5311	−	3.97308i	0.445380	−	0.130775i
$924$	−26.0704	−	16.6471i	−0.857652	−	0.547651i
$925$	−22.6848	−	14.5787i	−0.745873	−	0.479343i
$926$	−1.49757	+	1.50194i	−0.0492130	+	0.0493568i
$927$	2.02968	+	14.1168i	0.0666635	+	0.463655i
$928$	−2.14011	−	27.1398i	−0.0702526	−	0.890909i
$929$	39.5213	−	25.3988i	1.29665	−	0.833308i	0.303810	−	0.952733i	$-0.401741\pi$
$929$	39.5213	−	25.3988i	1.29665	−	0.833308i	0.992843	+	0.119424i	$0.0381049\pi$
$930$	37.8495	+	2.65157i	1.24113	+	0.0869483i
$931$	2.56490	+	1.17135i	0.0840614	+	0.0383895i
$932$	2.09940	−	7.22784i	0.0687682	−	0.236756i
$933$	−14.0863	−	2.02531i	−0.461166	−	0.0663057i
$934$	−19.8474	−	26.4325i	−0.649426	−	0.864899i
$935$	−51.4480	−	15.1065i	−1.68253	−	0.494035i
$936$	−4.69031	+	1.77281i	−0.153308	+	0.0579461i
$937$	−37.8690	+	32.8137i	−1.23713	+	1.07198i	−0.242321	+	0.970196i	$0.577909\pi$
$937$	−37.8690	+	32.8137i	−1.23713	+	1.07198i	−0.994807	+	0.101781i	$0.967546\pi$
$938$	13.6279	−	25.0443i	0.444965	−	0.817726i
$939$	2.92043	+	2.53057i	0.0953046	+	0.0825819i
$940$	−8.94104	−	19.4280i	−0.291625	−	0.633671i
$941$	14.4062	+	31.5452i	0.469628	+	1.02834i	0.985186	+	0.171488i	$0.0548574\pi$
$941$	14.4062	+	31.5452i	0.469628	+	1.02834i	−0.515558	+	0.856855i	$0.672415\pi$
$942$	0.303945	−	0.0221842i	0.00990306	−	0.000722799i
$943$	−29.8329	−	11.9630i	−0.971494	−	0.389568i
$944$	−32.1126	+	9.63296i	−1.04518	+	0.313526i
$945$	−3.32388	−	7.27828i	−0.108126	−	0.236763i
$946$	21.8273	−	8.17743i	0.709666	−	0.265871i
$947$	28.3568	−	32.7254i	0.921471	−	1.06343i	−0.0763257	−	0.997083i	$-0.524319\pi$
$947$	28.3568	−	32.7254i	0.921471	−	1.06343i	0.997796	−	0.0663508i	$-0.0211357\pi$
$948$	−10.6870	−	4.84297i	−0.347098	−	0.157292i
$949$	0.222851	−	0.193102i	0.00723406	−	0.00626835i
$950$	12.5127	−	2.74108i	0.405965	−	0.0889325i
$951$	5.62362	−	19.1523i	0.182358	−	0.621055i
$952$	19.5112	+	19.3412i	0.632362	+	0.626853i
$953$	3.00519	+	0.432081i	0.0973476	+	0.0139965i	0.190816	−	0.981626i	$-0.438886\pi$
$953$	3.00519	+	0.432081i	0.0973476	+	0.0139965i	−0.0934689	+	0.995622i	$0.529796\pi$
$954$	−7.03501	+	18.9459i	−0.227767	+	0.613398i
$955$	−2.85634	+	6.25450i	−0.0924289	+	0.202391i
$956$	−49.7625	+	0.145154i	−1.60944	+	0.00469460i
$957$	−22.2071	+	14.2716i	−0.717853	+	0.461336i
$958$	−28.5522	−	6.16755i	−0.922479	−	0.199264i
$959$	31.1202	−	4.47441i	1.00492	−	0.144486i
$960$	20.7320	+	9.24961i	0.669123	+	0.298530i
$961$	−49.1183	−	31.5664i	−1.58446	−	1.01827i
$962$	−17.7481	−	13.2457i	−0.572221	−	0.427059i
$963$	−5.11678	−	17.4262i	−0.164886	−	0.561550i
$964$	0.684869	−	0.442967i	0.0220582	−	0.0142670i
$965$	−43.1163			−1.38796
$966$	−8.34068	+	17.2090i	−0.268357	+	0.553689i
$967$			23.3754i			0.751703i	0.926680	+	0.375851i	$0.122650\pi$
$967$			23.3754i			0.751703i	−0.926680	+	0.375851i	$0.877350\pi$
$968$	−32.5407	−	43.0751i	−1.04590	−	1.38449i
$969$	9.80713	−	2.87963i	0.315050	−	0.0925071i
$970$	−20.5376	−	15.3276i	−0.659422	−	0.492138i
$971$	−4.35360	+	6.77434i	−0.139714	+	0.217399i	−0.904058	−	0.427409i	$-0.859426\pi$
$971$	−4.35360	+	6.77434i	−0.139714	+	0.217399i	0.764345	+	0.644808i	$0.223063\pi$
$972$	−1.51531	−	1.30531i	−0.0486037	−	0.0418677i
$973$	1.33479	+	9.28366i	0.0427914	+	0.297621i
$974$	−5.31397	+	24.6006i	−0.170270	+	0.788254i
$975$	−2.92581	−	4.55265i	−0.0937009	−	0.145801i
$976$	7.11050	+	47.4863i	0.227602	+	1.52000i
$977$	9.45032	+	4.31582i	0.302342	+	0.138075i	0.560809	−	0.827945i	$-0.310490\pi$
$977$	9.45032	+	4.31582i	0.302342	+	0.138075i	−0.258467	+	0.966020i	$0.583217\pi$
$978$	8.96714	−	24.1493i	0.286737	−	0.772210i
$979$	−9.85407	+	68.5366i	−0.314937	+	2.19044i
$980$	−4.06587	+	3.54391i	−0.129879	+	0.113206i
$981$	−4.34427	−	1.27559i	−0.138702	−	0.0407265i
$982$	−6.03558	−	27.5516i	−0.192603	−	0.879207i
$983$	17.6553	+	20.3753i	0.563116	+	0.649870i	0.963888	−	0.266307i	$-0.0858036\pi$
$983$	17.6553	+	20.3753i	0.563116	+	0.649870i	−0.400772	+	0.916178i	$0.631258\pi$
$984$	−17.7900	−	6.54680i	−0.567124	−	0.208705i
$985$	12.2343	+	10.6011i	0.389818	+	0.337780i
$986$	21.9555	−	8.22547i	0.699205	−	0.261952i
$987$	9.66497	−	4.41384i	0.307639	−	0.140494i
$988$	10.4085	−	1.52751i	0.331137	−	0.0485967i
$989$	−6.59605	−	12.8124i	−0.209742	−	0.407411i
$990$	−1.60238	−	21.9542i	−0.0509271	−	0.697751i
$991$	−41.4388	+	18.9245i	−1.31635	+	0.601156i	−0.944919	−	0.327305i	$-0.893860\pi$
$991$	−41.4388	+	18.9245i	−1.31635	+	0.601156i	−0.371430	+	0.928461i	$0.621132\pi$
$992$	−32.3623	−	42.5801i	−1.02750	−	1.35192i
$993$	−4.67632	+	5.39676i	−0.148398	+	0.171261i
$994$	15.1615	−	27.8628i	0.480894	−	0.883754i
$995$	−19.0198	−	21.9501i	−0.602970	−	0.695864i
$996$	28.8773	−	8.57072i	0.915013	−	0.271574i
$997$	−5.39607	+	18.3773i	−0.170895	+	0.582016i	0.828851	+	0.559470i	$0.188995\pi$
$997$	−5.39607	+	18.3773i	−0.170895	+	0.582016i	−0.999746	+	0.0225457i	$0.992823\pi$
$998$	28.1901	−	21.1671i	0.892343	−	0.670032i
$999$	1.25712	−	8.74344i	0.0397734	−	0.276630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.b.19.16	yes	240
8.3	odd	2	inner	552.2.t.b.19.14	✓	240
23.17	odd	22	inner	552.2.t.b.523.14	yes	240
184.155	even	22	inner	552.2.t.b.523.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.b.19.14	✓	240	8.3	odd	2	inner
552.2.t.b.19.16	yes	240	1.1	even	1	trivial
552.2.t.b.523.14	yes	240	23.17	odd	22	inner
552.2.t.b.523.16	yes	240	184.155	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.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.679570 + 1.24024i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-1.07637 + 1.68565i) q^{4} +(-2.38725 - 1.53419i) q^{5} +(-1.00146 - 0.998540i) q^{6} +(-0.401276 - 2.79093i) q^{7} +(-2.82208 - 0.189432i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.679570 + 1.24024i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-1.07637 + 1.68565i) q^{4} +(-2.38725 - 1.53419i) q^{5} +(-1.00146 - 0.998540i) q^{6} +(-0.401276 - 2.79093i) q^{7} +(-2.82208 - 0.189432i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.280457 - 4.00334i) q^{10} +(4.98944 + 2.27860i) q^{11} +(0.557865 - 1.92062i) q^{12} +(1.75473 + 0.252292i) q^{13} +(3.18872 - 2.39431i) q^{14} +(2.72278 + 0.799480i) q^{15} +(-1.68286 - 3.62877i) q^{16} +(2.60344 - 2.25590i) q^{17} +(1.24221 + 0.675949i) q^{18} +(-2.24237 - 1.94303i) q^{19} +(5.15568 - 2.37272i) q^{20} +(1.17132 + 2.56483i) q^{21} +(0.564671 + 7.73655i) q^{22} +(4.70968 - 0.904939i) q^{23} +(2.76113 - 0.613312i) q^{24} +(1.26814 + 2.77683i) q^{25} +(0.879561 + 2.34773i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(5.13647 + 2.32766i) q^{28} +(3.63711 - 3.15157i) q^{29} +(0.858775 + 3.92019i) q^{30} +(2.66363 - 9.07150i) q^{31} +(3.35691 - 4.55315i) q^{32} +(-5.42929 - 0.780614i) q^{33} +(4.56706 + 1.69584i) q^{34} +(-3.32388 + 7.27828i) q^{35} +(0.00583382 + 1.99999i) q^{36} +(-7.43109 + 4.77567i) q^{37} +(0.885963 - 4.10149i) q^{38} +(-1.75473 + 0.252292i) q^{39} +(6.44637 + 4.78183i) q^{40} +(-5.63816 - 3.62343i) q^{41} +(-2.38500 + 3.19569i) q^{42} +(-0.846556 - 2.88311i) q^{43} +(-9.21141 + 5.95785i) q^{44} -2.83773 q^{45} +(4.32289 + 5.22614i) q^{46} -3.76827i q^{47} +(2.63703 + 3.00767i) q^{48} +(-0.911837 + 0.267740i) q^{49} +(-2.58214 + 3.45984i) q^{50} +(-1.86242 + 2.89799i) q^{51} +(-2.31402 + 2.68631i) q^{52} +(2.03376 + 14.1451i) q^{53} +(-1.38233 - 0.298597i) q^{54} +(-8.41522 - 13.0943i) q^{55} +(0.603739 + 7.95224i) q^{56} +(2.69896 + 1.23257i) q^{57} +(6.38036 + 2.36916i) q^{58} +(1.19282 - 8.29627i) q^{59} +(-4.27836 + 3.72913i) q^{60} +(-11.5177 - 3.38190i) q^{61} +(13.0609 - 2.86119i) q^{62} +(-1.84647 - 2.13094i) q^{63} +(7.92823 + 1.06918i) q^{64} +(-3.80192 - 3.29438i) q^{65} +(-2.72144 - 7.26408i) q^{66} +(6.50409 - 2.97032i) q^{67} +(1.00039 + 6.81668i) q^{68} +(-4.26395 + 2.19515i) q^{69} +(-11.2856 + 0.823707i) q^{70} +(7.23605 - 3.30459i) q^{71} +(-2.47650 + 1.36637i) q^{72} +(0.108926 - 0.125708i) q^{73} +(-10.9729 - 5.97090i) q^{74} +(-1.99909 - 2.30707i) q^{75} +(5.68889 - 1.68845i) q^{76} +(4.35728 - 14.8395i) q^{77} +(-1.50537 - 2.00483i) q^{78} +(0.834900 - 5.80686i) q^{79} +(-1.54983 + 11.2446i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.662378 - 9.45502i) q^{82} +(8.14269 + 12.6703i) q^{83} +(-5.58418 - 0.786266i) q^{84} +(-9.67604 + 1.39120i) q^{85} +(3.00044 - 3.00920i) q^{86} +(-2.60188 + 4.04860i) q^{87} +(-13.6489 - 7.37554i) q^{88} +(3.55645 + 12.1122i) q^{89} +(-1.92843 - 3.51945i) q^{90} -4.99858i q^{91} +(-3.54394 + 8.91294i) q^{92} +9.45447i q^{93} +(4.67355 - 2.56080i) q^{94} +(2.37213 + 8.07872i) q^{95} +(-1.93817 + 5.31446i) q^{96} +(3.45235 - 5.37197i) q^{97} +(-0.951717 - 0.948945i) q^{98} +(5.42929 - 0.780614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9	\( 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9} - 4 q^{12} - 4 q^{16} - 44 q^{17} + 4 q^{18} + 55 q^{20} + 4 q^{24} - 24 q^{25} - 24 q^{27} + 4 q^{32} - 55 q^{34} + 7 q^{36} + 22 q^{38} + 11 q^{40} - 44 q^{42} + 77 q^{44} - 48 q^{46} + 51 q^{48} + 8 q^{49} - 33 q^{50} + 165 q^{52} - 7 q^{54} - 22 q^{56} - 59 q^{58} + 11 q^{60} + 29 q^{62} - 4 q^{64} + 55 q^{66} + 132 q^{70} + 4 q^{72} - 144 q^{73} - 66 q^{74} - 24 q^{75} - 55 q^{76} - 24 q^{81} - 26 q^{82} - 44 q^{84} - 110 q^{86} - 198 q^{88} - 47 q^{92} - 73 q^{94} + 4 q^{96} + 53 q^{98}+O(q^{100}) \) 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9 - 4 * q^12 - 4 * q^16 - 44 * q^17 + 4 * q^18 + 55 * q^20 + 4 * q^24 - 24 * q^25 - 24 * q^27 + 4 * q^32 - 55 * q^34 + 7 * q^36 + 22 * q^38 + 11 * q^40 - 44 * q^42 + 77 * q^44 - 48 * q^46 + 51 * q^48 + 8 * q^49 - 33 * q^50 + 165 * q^52 - 7 * q^54 - 22 * q^56 - 59 * q^58 + 11 * q^60 + 29 * q^62 - 4 * q^64 + 55 * q^66 + 132 * q^70 + 4 * q^72 - 144 * q^73 - 66 * q^74 - 24 * q^75 - 55 * q^76 - 24 * q^81 - 26 * q^82 - 44 * q^84 - 110 * q^86 - 198 * q^88 - 47 * q^92 - 73 * q^94 + 4 * q^96 + 53 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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