LMFDB - Embedded newform 552.2.t.b.19.18

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			19.18
Character	$\chi$	$=$	552.19
Dual form			552.2.t.b.523.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.945243 + 1.05191i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.213032 + 1.98862i) q^{4} +(-1.87195 - 1.20303i) q^{5} +(-1.20331 - 0.742995i) q^{6} +(0.493720 + 3.43390i) q^{7} +(-2.29322 + 1.65564i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.945243 + 1.05191i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.213032 + 1.98862i) q^{4} +(-1.87195 - 1.20303i) q^{5} +(-1.20331 - 0.742995i) q^{6} +(0.493720 + 3.43390i) q^{7} +(-2.29322 + 1.65564i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.503969 - 3.10629i) q^{10} +(-4.20094 - 1.91850i) q^{11} +(-0.355857 - 1.96809i) q^{12} +(5.08603 + 0.731260i) q^{13} +(-3.14547 + 3.76522i) q^{14} +(2.13506 + 0.626910i) q^{15} +(-3.90923 - 0.847282i) q^{16} +(-4.30843 + 3.73328i) q^{17} +(1.36389 + 0.373887i) q^{18} +(-5.25220 - 4.55106i) q^{19} +(2.79116 - 3.46633i) q^{20} +(-1.44116 - 3.15571i) q^{21} +(-1.95281 - 6.23247i) q^{22} +(-4.79338 - 0.153433i) q^{23} +(1.73388 - 2.23465i) q^{24} +(-0.0201470 - 0.0441158i) q^{25} +(4.03831 + 6.04126i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(-6.93391 + 0.250291i) q^{28} +(-0.511627 + 0.443327i) q^{29} +(1.35870 + 2.83848i) q^{30} +(-0.390868 + 1.33117i) q^{31} +(-2.80391 - 4.91305i) q^{32} +(4.57128 + 0.657250i) q^{33} +(-7.99959 - 1.00323i) q^{34} +(3.20687 - 7.02207i) q^{35} +(0.895916 + 1.78811i) q^{36} +(2.14108 - 1.37599i) q^{37} +(-0.177298 - 9.82670i) q^{38} +(-5.08603 + 0.731260i) q^{39} +(6.28459 - 0.340464i) q^{40} +(2.94204 + 1.89073i) q^{41} +(1.95727 - 4.49888i) q^{42} +(3.48316 + 11.8626i) q^{43} +(4.71012 - 7.94538i) q^{44} -2.22520 q^{45} +(-4.36951 - 5.18724i) q^{46} +10.1857i q^{47} +(3.98959 - 0.288398i) q^{48} +(-4.83147 + 1.41865i) q^{49} +(0.0273621 - 0.0628930i) q^{50} +(3.08212 - 4.79588i) q^{51} +(-2.53769 + 9.95840i) q^{52} +(0.635748 + 4.42172i) q^{53} +(-1.41398 + 0.0255118i) q^{54} +(5.55595 + 8.64522i) q^{55} +(-6.81751 - 7.05727i) q^{56} +(6.32163 + 2.88699i) q^{57} +(-0.949952 - 0.119134i) q^{58} +(-0.470950 + 3.27553i) q^{59} +(-1.70152 + 4.11228i) q^{60} +(2.76359 + 0.811463i) q^{61} +(-1.76974 + 0.847125i) q^{62} +(2.27185 + 2.62186i) q^{63} +(2.51772 - 7.59349i) q^{64} +(-8.64108 - 7.48754i) q^{65} +(3.62960 + 5.42984i) q^{66} +(-3.61803 + 1.65230i) q^{67} +(-6.50624 - 9.36315i) q^{68} +(4.64244 - 1.20323i) q^{69} +(10.4179 - 3.26422i) q^{70} +(7.94323 - 3.62755i) q^{71} +(-1.03407 + 2.63262i) q^{72} +(1.25733 - 1.45103i) q^{73} +(3.47126 + 0.951583i) q^{74} +(0.0317598 + 0.0366527i) q^{75} +(10.1692 - 9.47512i) q^{76} +(4.51387 - 15.3728i) q^{77} +(-5.57675 - 4.65883i) q^{78} +(0.332853 - 2.31504i) q^{79} +(6.29860 + 6.28901i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.792058 + 4.88197i) q^{82} +(2.56208 + 3.98667i) q^{83} +(6.58252 - 2.19366i) q^{84} +(12.5564 - 1.80534i) q^{85} +(-9.18591 + 14.8770i) q^{86} +(0.366003 - 0.569511i) q^{87} +(12.8100 - 2.55569i) q^{88} +(-2.66693 - 9.08273i) q^{89} +(-2.10335 - 2.34071i) q^{90} +17.8259i q^{91} +(1.32626 - 9.49953i) q^{92} -1.38737i q^{93} +(-10.7144 + 9.62791i) q^{94} +(4.35681 + 14.8379i) q^{95} +(4.07450 + 3.92409i) q^{96} +(-6.38085 + 9.92879i) q^{97} +(-6.05920 - 3.74131i) q^{98} +(-4.57128 + 0.657250i) 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 $

$2$	0.945243	+	1.05191i	0.668388	+	0.743813i
$2$	0.945243	+	1.05191i	0.668388	+	0.743813i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$4$	−0.213032	+	1.98862i	−0.106516	+	0.994311i
$5$	−1.87195	−	1.20303i	−0.837164	−	0.538012i	0.0503832	−	0.998730i	$-0.483956\pi$
$5$	−1.87195	−	1.20303i	−0.837164	−	0.538012i	−0.887547	+	0.460718i	$0.847592\pi$
$6$	−1.20331	−	0.742995i	−0.491250	−	0.303327i
$7$	0.493720	+	3.43390i	0.186609	+	1.29789i	0.840710	+	0.541486i	$0.182138\pi$
$7$	0.493720	+	3.43390i	0.186609	+	1.29789i	−0.654101	+	0.756407i	$0.726953\pi$
$8$	−2.29322	+	1.65564i	−0.810776	+	0.585357i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	−0.503969	−	3.10629i	−0.159369	−	0.982294i
$11$	−4.20094	−	1.91850i	−1.26663	−	0.578451i	−0.335124	−	0.942174i	$-0.608778\pi$
$11$	−4.20094	−	1.91850i	−1.26663	−	0.578451i	−0.931507	+	0.363723i	$0.881505\pi$
$12$	−0.355857	−	1.96809i	−0.102727	−	0.568138i
$13$	5.08603	+	0.731260i	1.41061	+	0.202815i	0.805155	−	0.593065i	$-0.202082\pi$
$13$	5.08603	+	0.731260i	1.41061	+	0.202815i	0.605455	+	0.795880i	$0.292991\pi$
$14$	−3.14547	+	3.76522i	−0.840663	+	1.00630i
$15$	2.13506	+	0.626910i	0.551270	+	0.161868i
$16$	−3.90923	−	0.847282i	−0.977309	−	0.211820i
$17$	−4.30843	+	3.73328i	−1.04495	+	0.905453i	−0.995635	−	0.0933306i	$-0.970249\pi$
$17$	−4.30843	+	3.73328i	−1.04495	+	0.905453i	−0.0493130	+	0.998783i	$0.515703\pi$
$18$	1.36389	+	0.373887i	0.321473	+	0.0881260i
$19$	−5.25220	−	4.55106i	−1.20494	−	1.04408i	−0.997835	−	0.0657650i	$-0.979051\pi$
$19$	−5.25220	−	4.55106i	−1.20494	−	1.04408i	−0.207102	−	0.978319i	$-0.566403\pi$
$20$	2.79116	−	3.46633i	0.624123	−	0.775094i
$21$	−1.44116	−	3.15571i	−0.314488	−	0.688632i
$22$	−1.95281	−	6.23247i	−0.416341	−	1.32877i
$23$	−4.79338	−	0.153433i	−0.999488	−	0.0319930i
$23$	−4.79338	−	0.153433i	−0.999488	−	0.0319930i
$24$	1.73388	−	2.23465i	0.353927	−	0.456146i
$25$	−0.0201470	−	0.0441158i	−0.00402940	−	0.00882316i
$26$	4.03831	+	6.04126i	0.791977	+	1.18479i
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$	−6.93391	+	0.250291i	−1.31039	+	0.0473006i
$29$	−0.511627	+	0.443327i	−0.0950067	+	0.0823238i	−0.701069	−	0.713093i	$-0.747294\pi$
$29$	−0.511627	+	0.443327i	−0.0950067	+	0.0823238i	0.606062	+	0.795417i	$0.292748\pi$
$30$	1.35870	+	2.83848i	0.248063	+	0.518232i
$31$	−0.390868	+	1.33117i	−0.0702020	+	0.239086i	−0.987118	−	0.159994i	$-0.948852\pi$
$31$	−0.390868	+	1.33117i	−0.0702020	+	0.239086i	0.916916	+	0.399080i	$0.130671\pi$
$32$	−2.80391	−	4.91305i	−0.495666	−	0.868513i
$33$	4.57128	+	0.657250i	0.795757	+	0.114413i
$34$	−7.99959	−	1.00323i	−1.37192	−	0.172053i
$35$	3.20687	−	7.02207i	0.542060	−	1.18695i
$36$	0.895916	+	1.78811i	0.149319	+	0.298018i
$37$	2.14108	−	1.37599i	0.351992	−	0.226211i	−0.352681	−	0.935744i	$-0.614730\pi$
$37$	2.14108	−	1.37599i	0.351992	−	0.226211i	0.704673	+	0.709532i	$0.251094\pi$
$38$	−0.177298	−	9.82670i	−0.0287615	−	1.59410i
$39$	−5.08603	+	0.731260i	−0.814416	+	0.117095i
$40$	6.28459	−	0.340464i	0.993681	−	0.0538322i
$41$	2.94204	+	1.89073i	0.459470	+	0.295283i	0.749826	−	0.661636i	$-0.230137\pi$
$41$	2.94204	+	1.89073i	0.459470	+	0.295283i	−0.290356	+	0.956919i	$0.593774\pi$
$42$	1.95727	−	4.49888i	0.302014	−	0.694193i
$43$	3.48316	+	11.8626i	0.531177	+	1.80902i	0.585724	+	0.810511i	$0.300810\pi$
$43$	3.48316	+	11.8626i	0.531177	+	1.80902i	−0.0545467	+	0.998511i	$0.517371\pi$
$44$	4.71012	−	7.94538i	0.710077	−	1.19781i
$45$	−2.22520			−0.331713
$46$	−4.36951	−	5.18724i	−0.644249	−	0.764816i
$47$			10.1857i			1.48573i	0.669441	+	0.742865i	$0.266534\pi$
$47$			10.1857i			1.48573i	−0.669441	+	0.742865i	$0.733466\pi$
$48$	3.98959	−	0.288398i	0.575848	−	0.0416266i
$49$	−4.83147	+	1.41865i	−0.690210	+	0.202664i
$50$	0.0273621	−	0.0628930i	0.00386958	−	0.00889441i
$51$	3.08212	−	4.79588i	0.431584	−	0.671557i
$52$	−2.53769	+	9.95840i	−0.351914	+	1.38098i
$53$	0.635748	+	4.42172i	0.0873267	+	0.607371i	0.985747	+	0.168234i	$0.0538064\pi$
$53$	0.635748	+	4.42172i	0.0873267	+	0.607371i	−0.898420	+	0.439136i	$0.855284\pi$
$54$	−1.41398	+	0.0255118i	−0.192419	+	0.00347171i
$55$	5.55595	+	8.64522i	0.749164	+	1.16572i
$56$	−6.81751	−	7.05727i	−0.911028	−	0.943067i
$57$	6.32163	+	2.88699i	0.837320	+	0.382391i
$58$	−0.949952	−	0.119134i	−0.124735	−	0.0156431i
$59$	−0.470950	+	3.27553i	−0.0613124	+	0.426437i	0.935928	+	0.352192i	$0.114564\pi$
$59$	−0.470950	+	3.27553i	−0.0613124	+	0.426437i	−0.997240	+	0.0742449i	$0.976345\pi$
$60$	−1.70152	+	4.11228i	−0.219666	+	0.530893i
$61$	2.76359	+	0.811463i	0.353841	+	0.103897i	0.453822	−	0.891092i	$-0.350060\pi$
$61$	2.76359	+	0.811463i	0.353841	+	0.103897i	−0.0999810	+	0.994989i	$0.531878\pi$
$62$	−1.76974	+	0.847125i	−0.224757	+	0.107585i
$63$	2.27185	+	2.62186i	0.286226	+	0.330323i
$64$	2.51772	−	7.59349i	0.314715	−	0.949186i
$65$	−8.64108	−	7.48754i	−1.07179	−	0.928715i
$66$	3.62960	+	5.42984i	0.446773	+	0.668367i
$67$	−3.61803	+	1.65230i	−0.442013	+	0.201861i	−0.623974	−	0.781445i	$-0.714483\pi$
$67$	−3.61803	+	1.65230i	−0.442013	+	0.201861i	0.181961	+	0.983306i	$0.441756\pi$
$68$	−6.50624	−	9.36315i	−0.788998	−	1.13545i
$69$	4.64244	−	1.20323i	0.558884	−	0.144852i
$70$	10.4179	−	3.26422i	1.24517	−	0.390149i
$71$	7.94323	−	3.62755i	0.942688	−	0.430511i	0.116049	−	0.993244i	$-0.462977\pi$
$71$	7.94323	−	3.62755i	0.942688	−	0.430511i	0.826639	+	0.562732i	$0.190250\pi$
$72$	−1.03407	+	2.63262i	−0.121867	+	0.310257i
$73$	1.25733	−	1.45103i	0.147159	−	0.169831i	−0.677384	−	0.735629i	$-0.736887\pi$
$73$	1.25733	−	1.45103i	0.147159	−	0.169831i	0.824543	+	0.565799i	$0.191432\pi$
$74$	3.47126	+	0.951583i	0.403526	+	0.110619i
$75$	0.0317598	+	0.0366527i	0.00366730	+	0.00423229i
$76$	10.1692	−	9.47512i	1.16649	−	1.08687i
$77$	4.51387	−	15.3728i	0.514403	−	1.75190i
$78$	−5.57675	−	4.65883i	−0.631442	−	0.527508i
$79$	0.332853	−	2.31504i	0.0374488	−	0.260462i	−0.962492	−	0.271309i	$-0.912544\pi$
$79$	0.332853	−	2.31504i	0.0374488	−	0.260462i	0.999941	+	0.0108465i	$0.00345261\pi$
$80$	6.29860	+	6.28901i	0.704205	+	0.703132i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	0.792058	+	4.88197i	0.0874682	+	0.539123i
$83$	2.56208	+	3.98667i	0.281225	+	0.437594i	0.952915	−	0.303238i	$-0.0980677\pi$
$83$	2.56208	+	3.98667i	0.281225	+	0.437594i	−0.671690	+	0.740832i	$0.734431\pi$
$84$	6.58252	−	2.19366i	0.718212	−	0.239348i
$85$	12.5564	−	1.80534i	1.36194	−	0.195817i
$86$	−9.18591	+	14.8770i	−0.990543	+	1.60422i
$87$	0.366003	−	0.569511i	0.0392396	−	0.0610580i
$88$	12.8100	−	2.55569i	1.36555	−	0.272437i
$89$	−2.66693	−	9.08273i	−0.282694	−	0.962768i	−0.971345	−	0.237675i	$-0.923615\pi$
$89$	−2.66693	−	9.08273i	−0.282694	−	0.962768i	0.688651	−	0.725093i	$-0.258203\pi$
$90$	−2.10335	−	2.34071i	−0.221713	−	0.246732i
$91$			17.8259i			1.86867i
$92$	1.32626	−	9.49953i	0.138273	−	0.990394i
$93$		−	1.38737i		−	0.143864i
$94$	−10.7144	+	9.62791i	−1.10511	+	0.993043i
$95$	4.35681	+	14.8379i	0.447000	+	1.52234i
$96$	4.07450	+	3.92409i	0.415852	+	0.400500i
$97$	−6.38085	+	9.92879i	−0.647877	+	1.00812i	0.349584	+	0.936905i	$0.386323\pi$
$97$	−6.38085	+	9.92879i	−0.647877	+	1.00812i	−0.997461	+	0.0712113i	$0.977314\pi$
$98$	−6.05920	−	3.74131i	−0.612072	−	0.377929i
$99$	−4.57128	+	0.657250i	−0.459431	+	0.0660562i
$100$	0.0920216	−	0.0306667i	0.00920216	−	0.00306667i
$101$	2.56378	+	3.98932i	0.255106	+	0.396952i	0.945058	−	0.326903i	$-0.106005\pi$
$101$	2.56378	+	3.98932i	0.255106	+	0.396952i	−0.689952	+	0.723855i	$0.742369\pi$
$102$	7.95819	−	1.29115i	0.787978	−	0.127843i
$103$	−6.20395	+	13.5848i	−0.611294	+	1.33855i	0.310392	+	0.950609i	$0.399540\pi$
$103$	−6.20395	+	13.5848i	−0.611294	+	1.33855i	−0.921686	+	0.387938i	$0.873188\pi$
$104$	−12.8741	+	6.74368i	−1.26241	+	0.661273i
$105$	−1.09863	+	7.64111i	−0.107215	+	0.745696i
$106$	−4.05032	+	4.84835i	−0.393402	+	0.470914i
$107$	0.0538625	−	0.183439i	0.00520708	−	0.0177337i	−0.956848	−	0.290587i	$-0.906149\pi$
$107$	0.0538625	−	0.183439i	0.00520708	−	0.0177337i	0.962056	+	0.272854i	$0.0879675\pi$
$108$	−1.36339	−	1.46327i	−0.131193	−	0.140803i
$109$	−9.78585	−	11.2935i	−0.937314	−	1.08172i	−0.996510	−	0.0834717i	$-0.973399\pi$
$109$	−9.78585	−	11.2935i	−0.937314	−	1.08172i	0.0591961	−	0.998246i	$-0.481146\pi$
$110$	−3.84228	+	14.0162i	−0.366347	+	1.33639i
$111$	−1.66669	+	1.92347i	−0.158196	+	0.182567i
$112$	0.979412	−	13.8422i	0.0925458	−	1.30797i
$113$	12.6359	−	5.77060i	1.18868	−	0.542852i	0.279861	−	0.960041i	$-0.409712\pi$
$113$	12.6359	−	5.77060i	1.18868	−	0.542852i	0.908820	+	0.417188i	$0.136984\pi$
$114$	2.93862	+	9.37870i	0.275227	+	0.878396i
$115$	8.78840	+	6.05381i	0.819522	+	0.564520i
$116$	−0.772617	−	1.11187i	−0.0717357	−	0.103235i
$117$	4.67399	−	2.13454i	0.432110	−	0.197338i
$118$	−3.89072	+	2.60077i	−0.358170	+	0.239420i
$119$	−14.9469	−	12.9515i	−1.37018	−	1.18727i
$120$	−5.93410	+	2.09725i	−0.541707	+	0.191452i
$121$	6.76376	+	7.80580i	0.614888	+	0.709618i
$122$	1.75868	+	3.67408i	0.159223	+	0.332636i
$123$	−3.35555	−	0.985278i	−0.302560	−	0.0888395i
$124$	−2.56394	−	1.06087i	−0.230248	−	0.0952691i
$125$	−1.59875	+	11.1196i	−0.142997	+	0.994564i
$126$	−0.610508	+	4.86808i	−0.0543883	+	0.433683i
$127$	9.29994	+	4.24714i	0.825236	+	0.376873i	0.782836	−	0.622228i	$-0.213772\pi$
$127$	9.29994	+	4.24714i	0.825236	+	0.376873i	0.0423999	+	0.999101i	$0.486500\pi$
$128$	10.3675	−	4.52928i	0.916369	−	0.400336i
$129$	−6.68413	−	10.4007i	−0.588505	−	0.915732i
$130$	−0.291696	−	16.1672i	−0.0255834	−	1.41796i
$131$	−0.553892	−	3.85240i	−0.0483937	−	0.336586i	−0.999607	−	0.0280502i	$-0.991070\pi$
$131$	−0.553892	−	3.85240i	−0.0483937	−	0.336586i	0.951213	−	0.308536i	$-0.0998389\pi$
$132$	−2.28085	+	8.95053i	−0.198523	+	0.779043i
$133$	13.0348	−	20.2825i	1.13026	−	1.75871i
$134$	−5.15799	−	2.24402i	−0.445582	−	0.193854i
$135$	2.13506	−	0.626910i	0.183757	−	0.0539559i
$136$	3.69922	−	15.6944i	0.317206	−	1.34579i
$137$			13.7209i			1.17226i	0.810218	+	0.586128i	$0.199349\pi$
$137$			13.7209i			1.17226i	−0.810218	+	0.586128i	$0.800651\pi$
$138$	5.65392	+	3.74608i	0.481294	+	0.318888i
$139$	−22.2479			−1.88704			−0.943520	−	0.331317i	$-0.892507\pi$
$139$	−22.2479			−1.88704			−0.943520	+	0.331317i	$0.892507\pi$
$140$	13.2811	+	7.87318i	1.12246	+	0.665405i
$141$	−2.86963	−	9.77306i	−0.241666	−	0.823040i
$142$	11.3241	+	4.92665i	0.950301	+	0.413436i
$143$	−19.9632	−	12.8295i	−1.66940	−	1.07286i
$144$	−3.74673	+	1.40071i	−0.312228	+	0.116726i
$145$	1.49108	−	0.214385i	0.123827	−	0.0178037i
$146$	2.71484	−	0.0489824i	0.224682	−	0.00405381i
$147$	4.23608	−	2.72236i	0.349386	−	0.224537i
$148$	2.28021	+	4.55094i	0.187432	+	0.374085i
$149$	−7.48625	+	16.3926i	−0.613298	+	1.34293i	0.306998	+	0.951710i	$0.400676\pi$
$149$	−7.48625	+	16.3926i	−0.613298	+	1.34293i	−0.920295	+	0.391224i	$0.872052\pi$
$150$	−0.00853470	+	0.0680541i	−0.000696856	+	0.00555660i
$151$	16.3817	+	2.35533i	1.33312	+	0.191674i	0.771769	−	0.635903i	$-0.219372\pi$
$151$	16.3817	+	2.35533i	1.33312	+	0.191674i	0.561353	+	0.827577i	$0.310281\pi$
$152$	19.5794	+	1.74083i	1.58810	+	0.141200i
$153$	−1.60612	+	5.46995i	−0.129847	+	0.442219i
$154$	20.4375	−	9.78286i	1.64690	−	0.788325i
$155$	2.33313	−	2.02167i	0.187402	−	0.162385i
$156$	−0.370712	−	10.2700i	−0.0296807	−	0.822255i
$157$	−1.28598	+	1.48410i	−0.102632	+	0.118444i	−0.804742	−	0.593625i	$-0.797696\pi$
$157$	−1.28598	+	1.48410i	−0.102632	+	0.118444i	0.702110	+	0.712069i	$0.252242\pi$
$158$	2.74984	−	1.83814i	0.218766	−	0.146235i
$159$	−1.85574	−	4.06350i	−0.147170	−	0.322257i
$160$	−0.661766	+	12.5702i	−0.0523172	+	0.993762i
$161$	−1.83971	−	16.5357i	−0.144990	−	1.30320i
$162$	1.34952	−	0.422844i	0.106028	−	0.0332217i
$163$	−9.42177	−	20.6308i	−0.737970	−	1.61593i	−0.786865	−	0.617126i	$-0.788297\pi$
$163$	−9.42177	−	20.6308i	−0.737970	−	1.61593i	0.0488943	−	0.998804i	$-0.484430\pi$
$164$	−4.38671	+	5.44782i	−0.342544	+	0.425403i
$165$	−7.76653	−	6.72974i	−0.604624	−	0.523909i
$166$	−1.77184	+	6.46345i	−0.137521	+	0.501661i
$167$	1.70415	−	1.47665i	0.131871	−	0.114267i	−0.586428	−	0.810001i	$-0.699466\pi$
$167$	1.70415	−	1.47665i	0.131871	−	0.114267i	0.718299	+	0.695734i	$0.244921\pi$
$168$	8.52962	+	4.85068i	0.658074	+	0.374238i
$169$	12.8595	+	3.77589i	0.989193	+	0.290453i
$170$	13.7679	+	11.5018i	1.05595	+	0.882145i
$171$	−6.87892	−	0.989039i	−0.526044	−	0.0756337i
$172$	−24.3322	+	4.39958i	−1.85531	+	0.335465i
$173$	5.25707	+	2.40082i	0.399687	+	0.182531i	0.605109	−	0.796142i	$-0.293129\pi$
$173$	5.25707	+	2.40082i	0.399687	+	0.182531i	−0.205422	+	0.978673i	$0.565857\pi$
$174$	0.945036	−	0.153324i	0.0716430	−	0.0116235i
$175$	0.141542	−	0.0909637i	0.0106996	−	0.00687621i
$176$	14.7969	+	11.0593i	1.11536	+	0.833623i
$177$	−0.470950	−	3.27553i	−0.0353988	−	0.246204i
$178$	7.03333	−	11.3908i	0.527170	−	0.853774i
$179$	−10.7688	−	6.92071i	−0.804901	−	0.517278i	0.0723110	−	0.997382i	$-0.476963\pi$
$179$	−10.7688	−	6.92071i	−0.804901	−	0.517278i	−0.877212	+	0.480104i	$0.840599\pi$
$180$	0.474039	−	4.42508i	0.0353328	−	0.329826i
$181$	−13.6959	+	4.02149i	−1.01801	+	0.298915i	−0.747827	−	0.663893i	$-0.768903\pi$
$181$	−13.6959	+	4.02149i	−1.01801	+	0.298915i	−0.270185	+	0.962809i	$0.587085\pi$
$182$	−18.7513	+	16.8498i	−1.38994	+	1.24899i
$183$	−2.88026			−0.212915
$184$	11.2463	−	7.58425i	0.829088	−	0.559118i
$185$	−5.66337			−0.416379
$186$	1.45939	−	1.31140i	0.107008	−	0.0961568i
$187$	25.2618	−	7.41753i	1.84732	−	0.542423i
$188$	−20.2554	−	2.16987i	−1.47728	−	0.158254i
$189$	−2.91849	−	1.87560i	−0.212289	−	0.136430i
$190$	−11.4899	+	18.6084i	−0.833568	+	1.35000i
$191$	−1.64503	−	11.4414i	−0.119030	−	0.827873i	−0.958628	−	0.284663i	$-0.908118\pi$
$191$	−1.64503	−	11.4414i	−0.119030	−	0.827873i	0.839597	−	0.543209i	$-0.182791\pi$
$192$	−0.276397	+	7.99522i	−0.0199473	+	0.577006i
$193$	7.67367	−	4.93157i	0.552363	−	0.354982i	−0.234494	−	0.972118i	$-0.575343\pi$
$193$	7.67367	−	4.93157i	0.552363	−	0.354982i	0.786857	+	0.617135i	$0.211707\pi$
$194$	−16.4757	+	2.67304i	−1.18288	+	0.191913i
$195$	10.4005	+	4.74977i	0.744798	+	0.340138i
$196$	−1.79189	−	9.91018i	−0.127992	−	0.707870i
$197$	−9.82541	−	1.41268i	−0.700032	−	0.100649i	−0.216896	−	0.976195i	$-0.569593\pi$
$197$	−9.82541	−	1.41268i	−0.700032	−	0.100649i	−0.483136	+	0.875545i	$0.660502\pi$
$198$	−5.01234	−	4.18731i	−0.356211	−	0.297579i
$199$	20.1823	+	5.92607i	1.43069	+	0.420088i	0.903106	−	0.429417i	$-0.141281\pi$
$199$	20.1823	+	5.92607i	1.43069	+	0.420088i	0.527581	+	0.849505i	$0.323099\pi$
$200$	0.119241	+	0.0678110i	0.00843163	+	0.00479496i
$201$	3.00597	−	2.60469i	0.212025	−	0.183720i
$202$	−1.77301	+	6.46775i	−0.124749	+	0.455069i
$203$	−1.77494	−	1.53800i	−0.124576	−	0.107946i
$204$	8.88060	+	7.15086i	0.621766	+	0.500660i
$205$	−3.23275	−	7.07874i	−0.225785	−	0.494401i
$206$	−20.1542	+	6.31489i	−1.40421	+	0.439980i
$207$	−4.11540	+	2.46242i	−0.286040	+	0.171150i
$208$	−19.2629	−	7.16796i	−1.33564	−	0.497009i
$209$	13.3330	+	29.1951i	0.922260	+	2.01947i
$210$	−9.07623	+	6.06704i	−0.626319	+	0.418666i
$211$	−1.14986	+	1.32701i	−0.0791598	+	0.0913553i	−0.793948	−	0.607986i	$-0.791978\pi$
$211$	−1.14986	+	1.32701i	−0.0791598	+	0.0913553i	0.714788	+	0.699341i	$0.246523\pi$
$212$	−8.92857	+	0.322292i	−0.613217	+	0.0221351i
$213$	−6.59947	+	5.71848i	−0.452189	+	0.391824i
$214$	0.243874	−	0.116736i	0.0166709	−	0.00797988i
$215$	7.75072	−	26.3965i	0.528594	−	1.80023i
$216$	0.250491	−	2.81731i	0.0170438	−	0.191694i
$217$	−4.76410	−	0.684974i	−0.323408	−	0.0464991i
$218$	2.62972	−	20.9689i	0.178107	−	1.42019i
$219$	−0.797594	+	1.74649i	−0.0538964	+	0.118017i
$220$	−18.3757	+	9.20696i	−1.23889	+	0.620733i
$221$	−24.6428	+	15.8370i	−1.65765	+	1.06531i
$222$	−3.59874	+	0.0649303i	−0.241532	+	0.00435783i
$223$	−18.8648	+	2.71235i	−1.26328	+	0.181633i	−0.741213	−	0.671270i	$-0.765749\pi$
$223$	−18.8648	+	2.71235i	−1.26328	+	0.181633i	−0.522070	+	0.852903i	$0.674840\pi$
$224$	15.4866	−	12.0540i	1.03474	−	0.805394i
$225$	−0.0407995	−	0.0262203i	−0.00271997	−	0.00174802i
$226$	18.0141	+	7.83717i	1.19828	+	0.521321i
$227$	2.69376	+	9.17411i	0.178791	+	0.608907i	0.999305	+	0.0372800i	$0.0118694\pi$
$227$	2.69376	+	9.17411i	0.178791	+	0.608907i	−0.820514	+	0.571627i	$0.806312\pi$
$228$	−7.08785	+	11.9563i	−0.469404	+	0.791826i
$229$	6.48318			0.428420			0.214210	−	0.976788i	$-0.431282\pi$
$229$	6.48318			0.428420			0.214210	+	0.976788i	$0.431282\pi$
$230$	1.93911	+	14.9669i	0.127861	+	0.986890i
$231$			16.0218i			1.05416i
$232$	0.439283	−	1.86372i	0.0288403	−	0.122359i
$233$	10.3794	−	3.04768i	0.679979	−	0.199660i	0.0765372	−	0.997067i	$-0.475614\pi$
$233$	10.3794	−	3.04768i	0.679979	−	0.199660i	0.603442	+	0.797407i	$0.293795\pi$
$234$	6.66339	+	2.89896i	0.435600	+	0.189511i
$235$	12.2537	−	19.0671i	0.799341	−	1.24380i
$236$	−6.41346	−	1.63433i	−0.417481	−	0.106386i
$237$	0.332853	+	2.31504i	0.0216211	+	0.150378i
$238$	−0.504560	−	27.9651i	−0.0327058	−	1.81271i
$239$	7.22127	+	11.2365i	0.467105	+	0.726830i	0.992260	−	0.124177i	$-0.0396290\pi$
$239$	7.22127	+	11.2365i	0.467105	+	0.726830i	−0.525155	+	0.851007i	$0.675993\pi$
$240$	−7.81528	−	4.25974i	−0.504474	−	0.274965i
$241$	−2.00335	−	0.914902i	−0.129047	−	0.0589340i	0.349845	−	0.936808i	$-0.386234\pi$
$241$	−2.00335	−	0.914902i	−0.129047	−	0.0589340i	−0.478892	+	0.877874i	$0.658962\pi$
$242$	−1.81761	+	14.4933i	−0.116840	+	0.931662i
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$	−2.20243	+	5.32287i	−0.140996	+	0.340762i
$245$	10.7510	+	3.15677i	0.686854	+	0.201679i
$246$	−2.13538	−	4.46106i	−0.136147	−	0.284427i
$247$	−23.3848	−	26.9875i	−1.48794	−	1.71717i
$248$	−1.30760	−	3.69981i	−0.0830326	−	0.234938i
$249$	−3.58147	−	3.10336i	−0.226967	−	0.196668i
$250$	−13.2080	+	8.82894i	−0.835347	+	0.558391i
$251$	21.2383	−	9.69922i	1.34055	−	0.612209i	0.389439	−	0.921052i	$-0.372669\pi$
$251$	21.2383	−	9.69922i	1.34055	−	0.612209i	0.951113	+	0.308843i	$0.0999418\pi$
$252$	−5.69786	+	3.95931i	−0.358931	+	0.249413i
$253$	19.8423	+	9.84068i	1.24748	+	0.618678i
$254$	4.32309	+	13.7973i	0.271255	+	0.865718i
$255$	−11.5392	+	5.26977i	−0.722612	+	0.330006i
$256$	14.5642	+	6.62444i	0.910264	+	0.414028i
$257$	−4.14628	+	4.78506i	−0.258638	+	0.298484i	−0.870186	−	0.492723i	$-0.836002\pi$
$257$	−4.14628	+	4.78506i	−0.258638	+	0.298484i	0.611548	+	0.791207i	$0.290547\pi$
$258$	4.62250	−	16.8623i	0.287784	−	1.04980i
$259$	5.78211	+	6.67291i	0.359283	+	0.414635i
$260$	16.7307	−	15.5888i	1.03759	−	0.966773i
$261$	−0.190727	+	0.649557i	−0.0118057	+	0.0402065i
$262$	3.52882	−	4.22410i	0.218011	−	0.260966i
$263$	4.46060	−	31.0242i	0.275053	−	1.91303i	−0.117076	−	0.993123i	$-0.537352\pi$
$263$	4.46060	−	31.0242i	0.275053	−	1.91303i	0.392129	−	0.919910i	$-0.371739\pi$
$264$	−11.5711	+	6.06117i	−0.712153	+	0.373039i
$265$	4.12939	−	9.04209i	0.253666	−	0.555451i
$266$	33.6564	−	5.46047i	2.06361	−	0.334803i
$267$	5.11780	+	7.96346i	0.313204	+	0.487356i
$268$	−2.51504	−	7.54689i	−0.153631	−	0.461000i
$269$	20.5428	−	2.95361i	1.25252	−	0.180085i	0.516049	−	0.856559i	$-0.327402\pi$
$269$	20.5428	−	2.95361i	1.25252	−	0.180085i	0.736466	+	0.676474i	$0.236493\pi$
$270$	2.67760	+	1.65331i	0.162954	+	0.100617i
$271$	−17.4562	+	27.1623i	−1.06039	+	1.64999i	−0.365607	+	0.930769i	$0.619139\pi$
$271$	−17.4562	+	27.1623i	−1.06039	+	1.64999i	−0.694779	+	0.719223i	$0.744498\pi$
$272$	20.0058	−	10.9438i	1.21303	−	0.663565i
$273$	−5.02215	−	17.1039i	−0.303954	−	1.03517i
$274$	−14.4332	+	12.9696i	−0.871940	+	0.783522i
$275$			0.223980i			0.0135065i
$276$	1.40378	+	9.48838i	0.0844979	+	0.571133i
$277$		−	20.6513i		−	1.24082i	−0.784279	−	0.620408i	$-0.786967\pi$
$277$		−	20.6513i		−	1.24082i	0.784279	−	0.620408i	$-0.213033\pi$
$278$	−21.0296	−	23.4028i	−1.26127	−	1.40360i
$279$	0.390868	+	1.33117i	0.0234007	+	0.0796953i
$280$	4.27195	+	21.4126i	0.255298	+	1.27965i
$281$	11.0901	−	17.2566i	0.661581	−	1.02944i	−0.334620	−	0.942353i	$-0.608608\pi$
$281$	11.0901	−	17.2566i	0.661581	−	1.02944i	0.996201	−	0.0870864i	$-0.0277556\pi$
$282$	7.56789	−	12.2565i	0.450661	−	0.729864i
$283$	−1.46290	+	0.210333i	−0.0869604	+	0.0125030i	−0.185658	−	0.982614i	$-0.559442\pi$
$283$	−1.46290	+	0.210333i	−0.0869604	+	0.0125030i	0.0986973	+	0.995118i	$0.468532\pi$
$284$	5.52166	+	16.5689i	0.327651	+	0.983182i
$285$	−8.36066	−	13.0094i	−0.495243	−	0.770613i
$286$	−5.37450	−	33.1265i	−0.317801	−	1.95881i
$287$	−5.04005	+	11.0362i	−0.297505	+	0.651445i
$288$	−5.01500	−	2.61721i	−0.295512	−	0.154221i
$289$	2.20587	−	15.3422i	0.129757	−	0.902481i
$290$	1.63494	+	1.36584i	0.0960073	+	0.0802047i
$291$	3.32511	−	11.3243i	0.194922	−	0.663842i
$292$	2.61771	+	2.80947i	0.153190	+	0.164412i
$293$	−20.9179	−	24.1406i	−1.22204	−	1.41031i	−0.882894	−	0.469572i	$-0.844408\pi$
$293$	−20.9179	−	24.1406i	−1.22204	−	1.41031i	−0.339144	−	0.940735i	$-0.610137\pi$
$294$	6.86781	+	1.88268i	0.400539	+	0.109800i
$295$	4.82216	−	5.56507i	0.280757	−	0.324011i
$296$	−2.63183	+	6.70031i	−0.152972	+	0.389448i
$297$	4.20094	−	1.91850i	0.243763	−	0.111323i
$298$	−24.3199	+	7.62012i	−1.40881	+	0.441422i
$299$	−24.2670	−	4.28557i	−1.40340	−	0.247841i
$300$	−0.0796542	+	0.0553499i	−0.00459884	+	0.00319563i
$301$	−39.0151	+	17.8176i	−2.24879	+	1.02699i
$302$	13.0071	+	19.4584i	0.748472	+	1.11971i
$303$	−3.58385	−	3.10543i	−0.205887	−	0.178402i
$304$	16.6761	+	22.2412i	0.956437	+	1.27562i
$305$	−4.19710	−	4.84371i	−0.240325	−	0.277350i
$306$	−7.27207	+	3.48093i	−0.415717	+	0.198992i
$307$	−25.1509	−	7.38496i	−1.43544	−	0.421482i	−0.530738	−	0.847536i	$-0.678085\pi$
$307$	−25.1509	−	7.38496i	−1.43544	−	0.421482i	−0.904698	+	0.426054i	$0.859904\pi$
$308$	29.6091	+	12.2513i	1.68714	+	0.698082i
$309$	2.12538	−	14.7823i	0.120909	−	0.840938i
$310$	4.33200	+	0.543278i	0.246041	+	0.0308561i
$311$	−4.21989	−	1.92716i	−0.239288	−	0.109279i	0.292162	−	0.956369i	$-0.405625\pi$
$311$	−4.21989	−	1.92716i	−0.239288	−	0.109279i	−0.531450	+	0.847090i	$0.678353\pi$
$312$	10.4527	−	10.0976i	0.591766	−	0.571662i
$313$	−8.76270	−	13.6350i	−0.495297	−	0.770698i	0.500157	−	0.865935i	$-0.333276\pi$
$313$	−8.76270	−	13.6350i	−0.495297	−	0.770698i	−0.995455	+	0.0952369i	$0.969639\pi$
$314$	−2.77670	+	0.0500985i	−0.156698	+	0.00282722i
$315$	−1.09863	−	7.64111i	−0.0619005	−	0.430528i
$316$	4.53283	+	1.15510i	0.254992	+	0.0649792i
$317$	−0.0252409	+	0.0392756i	−0.00141767	+	0.00220594i	−0.841962	−	0.539537i	$-0.818599\pi$
$317$	−0.0252409	+	0.0392756i	−0.00141767	+	0.00220594i	0.840544	+	0.541743i	$0.182236\pi$
$318$	2.52032	−	5.79307i	0.141332	−	0.324859i
$319$	2.99984	−	0.880832i	0.167959	−	0.0493171i
$320$	−13.8483	+	11.1858i	−0.774142	+	0.625304i
$321$			0.191183i			0.0106708i
$322$	15.6551	−	17.5655i	0.872427	−	0.978887i
$323$	39.6191			2.20447
$324$	1.72042	+	1.01988i	0.0955787	+	0.0566602i
$325$	−0.0702080	−	0.239107i	−0.00389444	−	0.0132633i
$326$	12.7959	−	29.4120i	0.708700	−	1.62898i
$327$	12.5712	+	8.07901i	0.695188	+	0.446770i
$328$	−9.87712	+	0.535088i	−0.545373	+	0.0295453i
$329$	−34.9765	+	5.02886i	−1.92832	+	0.277250i
$330$	−0.262174	−	14.5309i	−0.0144322	−	0.799901i
$331$	0.943025	−	0.606045i	0.0518333	−	0.0333113i	−0.514468	−	0.857510i	$-0.672010\pi$
$331$	0.943025	−	0.606045i	0.0518333	−	0.0333113i	0.566301	+	0.824199i	$0.308374\pi$
$332$	−8.47379	+	4.24572i	−0.465060	+	0.233014i
$333$	1.05728	−	2.31511i	0.0579384	−	0.126867i
$334$	3.16414	+	0.396817i	0.173134	+	0.0217128i
$335$	8.76056	+	1.25958i	0.478641	+	0.0688181i
$336$	2.96007	+	13.5575i	0.161485	+	0.739621i
$337$	−1.22305	+	4.16531i	−0.0666236	+	0.226899i	−0.986074	−	0.166307i	$-0.946816\pi$
$337$	−1.22305	+	4.16531i	−0.0666236	+	0.226899i	0.919451	+	0.393206i	$0.128634\pi$
$338$	8.18345	+	17.0962i	0.445121	+	0.929910i
$339$	−10.4982	+	9.09678i	−0.570187	+	0.494069i
$340$	0.915218	+	25.3546i	0.0496347	+	1.37505i
$341$	4.19588	−	4.84230i	0.227220	−	0.262225i
$342$	−5.46187	−	8.17089i	−0.295344	−	0.441831i
$343$	2.83125	+	6.19958i	0.152873	+	0.334746i
$344$	−27.6278	−	21.4366i	−1.48959	−	1.15578i
$345$	−10.1380	−	3.33261i	−0.545810	−	0.179422i
$346$	2.44375	+	7.79932i	0.131377	+	0.419294i
$347$	3.14435	+	6.88516i	0.168797	+	0.369615i	0.975059	−	0.221944i	$-0.0712402\pi$
$347$	3.14435	+	6.88516i	0.168797	+	0.369615i	−0.806262	+	0.591558i	$0.798513\pi$
$348$	1.05457	+	0.849165i	0.0565310	+	0.0455200i
$349$	16.6719	+	14.4463i	0.892424	+	0.773290i	0.974746	−	0.223316i	$-0.0716881\pi$
$349$	16.6719	+	14.4463i	0.892424	+	0.773290i	−0.0823218	+	0.996606i	$0.526234\pi$
$350$	0.229477	+	0.0629070i	0.0122661	+	0.00336252i
$351$	−3.88329	+	3.36489i	−0.207275	+	0.179604i
$352$	2.35335	+	26.0188i	0.125434	+	1.38680i
$353$	9.16590	+	2.69135i	0.487852	+	0.143246i	0.516402	−	0.856346i	$-0.327271\pi$
$353$	9.16590	+	2.69135i	0.487852	+	0.143246i	−0.0285506	+	0.999592i	$0.509089\pi$
$354$	3.00040	−	3.59157i	0.159470	−	0.190890i
$355$	−19.2334	−	2.76535i	−1.02080	−	0.146770i
$356$	18.6303	−	3.36860i	0.987402	−	0.178536i
$357$	17.9903	+	8.21589i	0.952147	+	0.434831i
$358$	−2.89919	−	17.8696i	−0.153227	−	0.944438i
$359$	8.45810	−	5.43569i	0.446402	−	0.286885i	−0.298064	−	0.954546i	$-0.596341\pi$
$359$	8.45810	−	5.43569i	0.446402	−	0.286885i	0.744465	+	0.667661i	$0.232704\pi$
$360$	5.10287	−	3.68412i	0.268945	−	0.194170i
$361$	4.16950	+	28.9995i	0.219448	+	1.52629i
$362$	−17.1762	−	10.6056i	−0.902764	−	0.557419i
$363$	−8.68893	−	5.58404i	−0.456051	−	0.293086i
$364$	−35.4491	−	3.79750i	−1.85804	−	0.199043i
$365$	−4.09930	+	1.20366i	−0.214567	+	0.0630026i
$366$	−2.72255	−	3.02978i	−0.142310	−	0.158369i
$367$	5.38574			0.281133			0.140567	−	0.990071i	$-0.455108\pi$
$367$	5.38574			0.281133			0.140567	+	0.990071i	$0.455108\pi$
$368$	18.6084	+	4.66115i	0.970032	+	0.242979i
$369$	3.49721			0.182057
$370$	−5.35326	−	5.95736i	−0.278303	−	0.309709i
$371$	−14.8699	+	4.36619i	−0.772006	+	0.226681i
$372$	2.75896	+	0.295555i	0.143045	+	0.0153238i
$373$	5.36672	+	3.44898i	0.277878	+	0.178581i	0.672155	−	0.740410i	$-0.265369\pi$
$373$	5.36672	+	3.44898i	0.277878	+	0.178581i	−0.394277	+	0.918992i	$0.629005\pi$
$374$	31.6811	+	19.5618i	1.63819	+	1.01151i
$375$	−1.59875	−	11.1196i	−0.0825592	−	0.574212i
$376$	−16.8638	−	23.3579i	−0.869682	−	1.20459i
$377$	−2.92633	+	1.88064i	−0.150714	+	0.0968579i
$378$	−0.785717	−	4.84288i	−0.0404129	−	0.249091i
$379$	16.4992	+	7.53492i	0.847506	+	0.387043i	0.791338	−	0.611379i	$-0.209385\pi$
$379$	16.4992	+	7.53492i	0.847506	+	0.387043i	0.0561673	+	0.998421i	$0.482112\pi$
$380$	−30.4352	+	5.50309i	−1.56129	+	0.282303i
$381$	−10.1198	−	1.45500i	−0.518452	−	0.0745422i
$382$	10.4804	−	12.5454i	0.536224	−	0.641876i
$383$	−20.9684	−	6.15689i	−1.07144	−	0.314602i	−0.301989	−	0.953312i	$-0.597650\pi$
$383$	−20.9684	−	6.15689i	−1.07144	−	0.314602i	−0.769448	+	0.638709i	$0.779469\pi$
$384$	−8.67152	+	7.26668i	−0.442517	+	0.370826i
$385$	−26.9437	+	23.3469i	−1.37318	+	1.18987i
$386$	12.4411	+	3.41049i	0.633233	+	0.173589i
$387$	9.34360	+	8.09628i	0.474962	+	0.411557i
$388$	−18.3853	−	14.8042i	−0.933372	−	0.751572i
$389$	7.55106	+	16.5345i	0.382854	+	0.838333i	0.998725	+	0.0504861i	$0.0160771\pi$
$389$	7.55106	+	16.5345i	0.382854	+	0.838333i	−0.615871	+	0.787847i	$0.711196\pi$
$390$	4.83470	+	15.4301i	0.244815	+	0.781335i
$391$	21.2247	−	17.2339i	1.07338	−	0.871558i
$392$	8.73085	−	11.2524i	0.440975	−	0.568334i
$393$	1.61680	+	3.54030i	0.0815569	+	0.178585i
$394$	−7.80139	−	11.6708i	−0.393028	−	0.587966i
$395$	−3.40815	+	3.93322i	−0.171483	+	0.197902i
$396$	−0.333193	−	9.23056i	−0.0167436	−	0.463853i
$397$	−19.9972	+	17.3276i	−1.00363	+	0.869649i	−0.991478	−	0.130277i	$-0.958413\pi$
$397$	−19.9972	+	17.3276i	−1.00363	+	0.869649i	−0.0121509	+	0.999926i	$0.503868\pi$
$398$	12.8435	+	26.8316i	0.643787	+	1.34495i
$399$	−6.79253	+	23.1332i	−0.340052	+	1.15811i
$400$	0.0413809	+	0.189529i	0.00206904	+	0.00947645i
$401$	−28.7913	−	4.13957i	−1.43777	−	0.206720i	−0.621058	−	0.783765i	$-0.713297\pi$
$401$	−28.7913	−	4.13957i	−1.43777	−	0.206720i	−0.816713	+	0.577044i	$0.804206\pi$
$402$	5.58127	+	0.699950i	0.278368	+	0.0349103i
$403$	−2.96140	+	6.48456i	−0.147518	+	0.323019i
$404$	−8.47942	+	4.24854i	−0.421867	+	0.211373i
$405$	−1.87195	+	1.20303i	−0.0930182	+	0.0597792i
$406$	−0.0599165	−	3.32086i	−0.00297361	−	0.164811i
$407$	−11.6344	+	1.67278i	−0.576696	+	0.0829164i
$408$	0.872257	+	16.1009i	0.0431832	+	0.797113i
$409$	−13.7881	−	8.86107i	−0.681777	−	0.438152i	0.153377	−	0.988168i	$-0.450985\pi$
$409$	−13.7881	−	8.86107i	−0.681777	−	0.438152i	−0.835154	+	0.550016i	$0.814622\pi$
$410$	4.39047	−	10.0917i	0.216830	−	0.498393i
$411$	−3.86563	−	13.1651i	−0.190677	−	0.649388i
$412$	−25.6933	−	15.2313i	−1.26582	−	0.750393i
$413$	−11.4804			−0.564911
$414$	−6.48029	−	2.00145i	−0.318489	−	0.0983658i
$415$		−	10.5451i		−	0.517640i
$416$	−10.6680	−	27.0383i	−0.523044	−	1.32566i
$417$	21.3467	−	6.26795i	1.04535	−	0.306943i
$418$	−18.1078	+	41.6215i	−0.885679	+	2.03578i
$419$	−6.21998	+	9.67847i	−0.303866	+	0.472824i	−0.959285	−	0.282441i	$-0.908856\pi$
$419$	−6.21998	+	9.67847i	−0.303866	+	0.472824i	0.655419	+	0.755266i	$0.272492\pi$
$420$	−14.9612	−	3.81255i	−0.730033	−	0.186034i
$421$	1.61415	+	11.2266i	0.0786687	+	0.547152i	0.990598	+	0.136805i	$0.0436834\pi$
$421$	1.61415	+	11.2266i	0.0786687	+	0.547152i	−0.911929	+	0.410347i	$0.865407\pi$
$422$	−2.48280	+	0.0447958i	−0.120861	+	0.00218063i
$423$	5.50678	+	8.56871i	0.267749	+	0.416625i
$424$	−8.77869	−	9.08742i	−0.426331	−	0.441324i
$425$	0.251498	+	0.114855i	0.0121995	+	0.00557131i
$426$	−12.2534	−	1.53671i	−0.593681	−	0.0744538i
$427$	−1.42204	+	9.89053i	−0.0688175	+	0.478636i
$428$	0.353316	+	0.146190i	0.0170782	+	0.00706638i
$429$	22.7690	+	6.68558i	1.09930	+	0.322783i
$430$	35.0931	−	16.7981i	1.69234	−	0.810074i
$431$	3.13075	+	3.61308i	0.150803	+	0.174036i	0.826125	−	0.563487i	$-0.190541\pi$
$431$	3.13075	+	3.61308i	0.150803	+	0.174036i	−0.675322	+	0.737523i	$0.735995\pi$
$432$	3.20034	−	2.39955i	0.153976	−	0.115448i
$433$	13.5666	+	11.7555i	0.651969	+	0.564934i	0.916793	−	0.399362i	$-0.130768\pi$
$433$	13.5666	+	11.7555i	0.651969	+	0.564934i	−0.264824	+	0.964297i	$0.585314\pi$
$434$	−3.78270	−	5.65888i	−0.181575	−	0.271635i
$435$	−1.37028	+	0.625786i	−0.0656999	+	0.0300041i
$436$	24.5431	−	17.0545i	1.17540	−	0.816761i
$437$	24.4775	+	22.6208i	1.17092	+	1.08210i
$438$	−2.59107	+	0.811856i	−0.123806	+	0.0387920i
$439$	−12.8809	+	5.88249i	−0.614770	+	0.280756i	−0.698363	−	0.715744i	$-0.746088\pi$
$439$	−12.8809	+	5.88249i	−0.614770	+	0.280756i	0.0835931	+	0.996500i	$0.473360\pi$
$440$	−27.0544	−	10.6267i	−1.28977	−	0.506610i
$441$	−3.29751	+	3.80553i	−0.157024	+	0.181216i
$442$	−39.9525	−	10.9522i	−1.90035	−	0.520945i
$443$	26.3145	+	30.3685i	1.25024	+	1.44285i	0.850289	+	0.526316i	$0.176427\pi$
$443$	26.3145	+	30.3685i	1.25024	+	1.44285i	0.399950	+	0.916537i	$0.369027\pi$
$444$	−3.46999	−	3.72418i	−0.164678	−	0.176742i
$445$	−5.93445	+	20.2109i	−0.281320	+	0.958087i
$446$	−20.6850	−	17.2803i	−0.979463	−	0.818245i
$447$	2.56468	−	17.8377i	0.121305	−	0.843695i
$448$	27.3183	+	4.89653i	1.29067	+	0.231339i
$449$	0.838009	−	1.83498i	0.0395481	−	0.0865982i	−0.888827	−	0.458243i	$-0.848479\pi$
$449$	0.838009	−	1.83498i	0.0395481	−	0.0865982i	0.928375	+	0.371645i	$0.121206\pi$
$450$	−0.0109841	−	0.0677020i	−0.000517794	−	0.00319150i
$451$	−8.73195	−	13.5872i	−0.411171	−	0.639795i
$452$	8.78370	+	26.3573i	0.413150	+	1.23974i
$453$	−16.3817	+	2.35533i	−0.769678	+	0.110663i
$454$	−7.10409	+	11.5054i	−0.333411	+	0.539973i
$455$	21.4452	−	33.3694i	1.00537	−	1.56438i
$456$	−19.2767	+	3.84583i	−0.902715	+	0.180098i
$457$	−0.851694	−	2.90060i	−0.0398406	−	0.135685i	0.937171	−	0.348870i	$-0.113434\pi$
$457$	−0.851694	−	2.90060i	−0.0398406	−	0.135685i	−0.977012	+	0.213185i	$0.931616\pi$
$458$	6.12818	+	6.81972i	0.286351	+	0.318665i
$459$		−	5.70087i		−	0.266094i
$460$	−13.9109	+	16.1871i	−0.648601	+	0.754730i
$461$			35.9108i			1.67253i	0.548323	+	0.836267i	$0.315266\pi$
$461$			35.9108i			1.67253i	−0.548323	+	0.836267i	$0.684734\pi$
$462$	−16.8535	+	15.1445i	−0.784097	+	0.704586i
$463$	−3.88798	−	13.2412i	−0.180690	−	0.615373i	−0.999166	−	0.0408323i	$-0.986999\pi$
$463$	−3.88798	−	13.2412i	−0.180690	−	0.615373i	0.818476	−	0.574540i	$-0.194819\pi$
$464$	2.37569	−	1.29958i	0.110289	−	0.0603314i
$465$	−1.66905	+	2.59710i	−0.0774005	+	0.120438i
$466$	13.0170	+	8.03744i	0.602999	+	0.372327i
$467$	16.6352	−	2.39179i	0.769787	−	0.110679i	0.253779	−	0.967262i	$-0.418327\pi$
$467$	16.6352	−	2.39179i	0.769787	−	0.110679i	0.516008	+	0.856584i	$0.327417\pi$
$468$	3.24908	+	9.74952i	0.150189	+	0.450672i
$469$	−7.46013	−	11.6082i	−0.344477	−	0.536016i
$470$	31.6396	−	5.13325i	1.45942	−	0.236779i
$471$	0.815768	−	1.78628i	0.0375886	−	0.0823075i
$472$	−4.34310	−	8.29123i	−0.199907	−	0.381635i
$473$	8.12582	−	56.5163i	0.373626	−	2.59862i
$474$	−2.12059	+	2.53841i	−0.0974019	+	0.116593i
$475$	−0.0949574	+	0.323395i	−0.00435694	+	0.0148384i
$476$	28.9399	−	26.9646i	1.32646	−	1.23592i
$477$	2.92539	+	3.37608i	0.133944	+	0.154580i
$478$	−4.99396	+	18.2174i	−0.228418	+	0.833243i
$479$	15.8408	−	18.2813i	0.723785	−	0.835293i	−0.267972	−	0.963427i	$-0.586353\pi$
$479$	15.8408	−	18.2813i	0.723785	−	0.835293i	0.991757	+	0.128134i	$0.0408988\pi$
$480$	−2.90648	−	12.2475i	−0.132662	−	0.559018i
$481$	11.8958	−	5.43264i	0.542402	−	0.247707i
$482$	−0.931262	−	2.97215i	−0.0424178	−	0.135378i
$483$	6.42385	+	15.3476i	0.292295	+	0.698341i
$484$	−16.9637	+	11.7877i	−0.771077	+	0.535804i
$485$	23.8893	−	10.9099i	1.08476	−	0.495392i
$486$	−1.17573	+	0.785919i	−0.0533320	+	0.0356500i
$487$	−3.55769	−	3.08275i	−0.161214	−	0.139693i	0.570518	−	0.821285i	$-0.306742\pi$
$487$	−3.55769	−	3.08275i	−0.161214	−	0.139693i	−0.731732	+	0.681592i	$0.761288\pi$
$488$	−7.68101	+	2.71465i	−0.347703	+	0.122886i
$489$	14.8525	+	17.1407i	0.671653	+	0.775129i
$490$	6.84163	+	14.2930i	0.309074	+	0.645691i
$491$	−11.6999	−	3.43539i	−0.528008	−	0.155037i	0.00685429	−	0.999977i	$-0.497818\pi$
$491$	−11.6999	−	3.43539i	−0.528008	−	0.155037i	−0.534862	+	0.844939i	$0.679636\pi$
$492$	2.67419	−	6.46302i	0.120562	−	0.291376i
$493$	0.549246	−	3.82009i	0.0247368	−	0.172048i
$494$	6.28413	−	50.1085i	0.282736	−	2.25449i
$495$	9.34792	+	4.26905i	0.420158	+	0.191880i
$496$	2.65587	−	4.87270i	0.119252	−	0.218791i
$497$	16.3784	+	25.4853i	0.734671	+	1.14317i
$498$	−0.120899	−	6.70082i	−0.00541763	−	0.300271i
$499$	1.43891	+	10.0078i	0.0644143	+	0.448011i	0.996348	+	0.0853830i	$0.0272114\pi$
$499$	1.43891	+	10.0078i	0.0644143	+	0.448011i	−0.931934	+	0.362628i	$0.881880\pi$
$500$	−21.7720	−	5.54814i	−0.973674	−	0.248120i
$501$	−1.21910	+	1.89695i	−0.0544653	+	0.0847496i
$502$	30.2781	+	13.1727i	1.35138	+	0.587927i
$503$	7.53702	−	2.21307i	0.336059	−	0.0986759i	−0.109349	−	0.994003i	$-0.534877\pi$
$503$	7.53702	−	2.21307i	0.336059	−	0.0986759i	0.445408	+	0.895328i	$0.353058\pi$
$504$	−9.55070	−	2.25113i	−0.425422	−	0.100273i
$505$		−	10.5521i		−	0.469564i
$506$	8.40429	+	30.1742i	0.373616	+	1.34141i
$507$	−13.4024			−0.595221
$508$	−10.4271	+	17.5893i	−0.462630	+	0.780398i
$509$	6.84291	+	23.3048i	0.303307	+	1.03297i	0.960276	+	0.279051i	$0.0900198\pi$
$509$	6.84291	+	23.3048i	0.303307	+	1.03297i	−0.656970	+	0.753917i	$0.728162\pi$
$510$	−16.4507	−	7.15699i	−0.728448	−	0.316917i
$511$	5.60347	+	3.60113i	0.247883	+	0.159305i
$512$	6.79841	+	21.5820i	0.300450	+	0.953798i
$513$	6.87892	−	0.989039i	0.303712	−	0.0436672i
$514$	−8.95270	+	0.161529i	−0.394887	+	0.00712473i
$515$	27.9564	−	17.9665i	1.23191	−	0.791699i
$516$	22.1070	−	11.0765i	0.973208	−	0.487617i
$517$	19.5412	−	42.7893i	0.859422	−	1.88187i
$518$	−1.55381	+	12.3898i	−0.0682705	+	0.544376i
$519$	−5.72051	−	0.822485i	−0.251102	−	0.0361031i
$520$	32.2126	+	2.86406i	1.41261	+	0.125597i
$521$	1.01195	−	3.44638i	0.0443342	−	0.150989i	−0.934351	−	0.356353i	$-0.884020\pi$
$521$	1.01195	−	3.44638i	0.0443342	−	0.150989i	0.978685	+	0.205365i	$0.0658381\pi$
$522$	−0.863559	+	0.413361i	−0.0377969	+	0.0180923i
$523$	−15.3242	+	13.2785i	−0.670079	+	0.580627i	−0.922032	−	0.387113i	$-0.873472\pi$
$523$	−15.3242	+	13.2785i	−0.670079	+	0.580627i	0.251953	+	0.967739i	$0.418927\pi$
$524$	7.77897	−	0.280795i	0.339826	−	0.0122666i
$525$	−0.110181	+	0.127156i	−0.00480871	+	0.00554955i
$526$	36.8510	−	24.6332i	1.60678	−	1.07406i
$527$	−3.28562	−	7.19449i	−0.143124	−	0.313397i
$528$	−17.3133	−	6.44251i	−0.753465	−	0.280374i
$529$	22.9529	+	1.47093i	0.997953	+	0.0639533i
$530$	13.4147	−	4.20323i	0.582699	−	0.182577i
$531$	1.37470	+	3.01016i	0.0596567	+	0.130630i
$532$	37.5574	+	30.2420i	1.62832	+	1.31116i
$533$	13.5807	+	11.7677i	0.588244	+	0.509717i
$534$	−3.53928	+	12.9109i	−0.153160	+	0.558708i
$535$	−0.321511	+	0.278591i	−0.0139001	+	0.0120445i
$536$	5.56133	−	9.77924i	0.240213	−	0.422399i
$537$	12.2824	+	3.60644i	0.530025	+	0.155629i
$538$	22.5248	+	18.8173i	0.971115	+	0.811271i
$539$	23.0184	+	3.30954i	0.991472	+	0.142552i
$540$	0.791851	+	4.37938i	0.0340758	+	0.188459i
$541$	20.0032	+	9.13516i	0.860005	+	0.392751i	0.796071	−	0.605203i	$-0.206908\pi$
$541$	20.0032	+	9.13516i	0.860005	+	0.392751i	0.0639340	+	0.997954i	$0.479635\pi$
$542$	−45.0726	+	7.31266i	−1.93604	+	0.314106i
$543$	12.0082	−	7.71719i	0.515320	−	0.331176i
$544$	30.4222	+	10.6998i	1.30434	+	0.458749i
$545$	4.73225	+	32.9135i	0.202707	+	1.40986i
$546$	13.2446	−	21.4502i	0.566816	−	0.917982i
$547$	−23.0198	−	14.7939i	−0.984256	−	0.632543i	−0.0536477	−	0.998560i	$-0.517085\pi$
$547$	−23.0198	−	14.7939i	−0.984256	−	0.632543i	−0.930608	+	0.366017i	$0.880721\pi$
$548$	−27.2857	−	2.92300i	−1.16559	−	0.124864i
$549$	2.76359	−	0.811463i	0.117947	−	0.0346324i
$550$	−0.235607	+	0.211715i	−0.0100463	+	0.00902757i
$551$	4.70477			0.200430
$552$	−8.65401	+	10.4455i	−0.368339	+	0.444589i
$553$	8.11396			0.345041
$554$	21.7233	−	19.5205i	0.922936	−	0.829347i
$555$	5.43397	−	1.59556i	0.230659	−	0.0677276i
$556$	4.73951	−	44.2426i	0.201000	−	1.87630i
$557$	8.17144	+	5.25147i	0.346235	+	0.222512i	0.702187	−	0.711992i	$-0.252207\pi$
$557$	8.17144	+	5.25147i	0.346235	+	0.222512i	−0.355952	+	0.934504i	$0.615843\pi$
$558$	−1.03081	+	1.66944i	−0.0436377	+	0.0706731i
$559$	9.04083	+	62.8803i	0.382386	+	2.65955i
$560$	−18.4861	+	24.7338i	−0.781180	+	1.04519i
$561$	−22.1487	+	14.2341i	−0.935120	+	0.600965i
$562$	28.6352	−	4.64582i	1.20790	−	0.195972i
$563$	18.8624	+	8.61418i	0.794956	+	0.363044i	0.771135	−	0.636672i	$-0.219689\pi$
$563$	18.8624	+	8.61418i	0.794956	+	0.363044i	0.0238215	+	0.999716i	$0.492417\pi$
$564$	20.0462	−	3.62463i	0.844099	−	0.152624i
$565$	−30.5960	−	4.39904i	−1.28718	−	0.185069i
$566$	−1.60405	−	1.34002i	−0.0674231	−	0.0563254i
$567$	3.32869	+	0.977390i	0.139792	+	0.0410465i
$568$	−12.2097	+	21.4699i	−0.512306	+	0.900857i
$569$	−23.9457	+	20.7491i	−1.00386	+	0.869847i	−0.991504	−	0.130077i	$-0.958478\pi$
$569$	−23.9457	+	20.7491i	−1.00386	+	0.869847i	−0.0123529	+	0.999924i	$0.503932\pi$
$570$	5.78192	−	21.0918i	0.242178	−	0.883436i
$571$	−17.6739	−	15.3145i	−0.739630	−	0.640893i	0.201286	−	0.979532i	$-0.435488\pi$
$571$	−17.6739	−	15.3145i	−0.739630	−	0.640893i	−0.940916	+	0.338640i	$0.890033\pi$
$572$	29.7659	−	36.9661i	1.24458	−	1.54563i
$573$	4.80182	+	10.5145i	0.200599	+	0.439250i
$574$	−16.3731	+	5.13018i	−0.683402	+	0.214129i
$575$	0.0898033	+	0.214555i	0.00374506	+	0.00894755i
$576$	−1.98731	−	7.74923i	−0.0828047	−	0.322885i
$577$	−8.21477	−	17.9878i	−0.341985	−	0.748843i	0.658006	−	0.753013i	$-0.271400\pi$
$577$	−8.21477	−	17.9878i	−0.341985	−	0.748843i	−0.999991	+	0.00416944i	$0.998673\pi$
$578$	18.2237	−	12.1817i	0.758005	−	0.506692i
$579$	−5.97345	+	6.89373i	−0.248248	+	0.286494i
$580$	0.108682	+	3.01086i	0.00451278	+	0.125019i
$581$	−12.4249	+	10.7662i	−0.515471	+	0.446658i
$582$	15.0552	−	7.20649i	0.624058	−	0.298719i
$583$	5.81236	−	19.7951i	0.240723	−	0.819829i
$584$	−0.480941	+	5.40922i	−0.0199015	+	0.223835i
$585$	−11.3174	−	1.62720i	−0.467917	−	0.0672763i
$586$	5.62121	−	44.8225i	0.232210	−	1.85160i
$587$	−7.16684	+	15.6932i	−0.295807	+	0.647727i	−0.997929	−	0.0643297i	$-0.979509\pi$
$587$	−7.16684	+	15.6932i	−0.295807	+	0.647727i	0.702121	+	0.712057i	$0.252236\pi$
$588$	4.51133	+	9.00391i	0.186044	+	0.371315i
$589$	8.11117	−	5.21273i	0.334215	−	0.214787i
$590$	10.4121	−	0.187860i	0.428658	−	0.00773406i
$591$	9.82541	−	1.41268i	0.404164	−	0.0581099i
$592$	−9.53585	+	3.56497i	−0.391921	+	0.146519i
$593$	−10.9917	−	7.06391i	−0.451373	−	0.290080i	0.295136	−	0.955455i	$-0.404635\pi$
$593$	−10.9917	−	7.06391i	−0.451373	−	0.290080i	−0.746509	+	0.665375i	$0.768272\pi$
$594$	5.98900	+	2.60556i	0.245732	+	0.106907i
$595$	12.3987	+	42.2263i	0.508299	+	1.73111i
$596$	−31.0039	−	18.3795i	−1.26997	−	0.752853i
$597$	−21.0344			−0.860880
$598$	−18.4302	−	29.5777i	−0.753667	−	1.20952i
$599$		−	12.3566i		−	0.504877i	−0.967613	−	0.252438i	$-0.918768\pi$
$599$		−	12.3566i		−	0.504877i	0.967613	−	0.252438i	$-0.0812325\pi$
$600$	−0.133516	−	0.0314700i	−0.00545076	−	0.00128476i
$601$	−34.0628	+	10.0017i	−1.38945	+	0.407980i	−0.889048	−	0.457813i	$-0.848633\pi$
$601$	−34.0628	+	10.0017i	−1.38945	+	0.407980i	−0.500403	+	0.865793i	$0.666815\pi$
$602$	−55.6213	−	24.1985i	−2.26695	−	0.986256i
$603$	−2.15038	+	3.34606i	−0.0875703	+	0.136262i
$604$	−8.17369	+	32.0752i	−0.332583	+	1.30512i
$605$	−3.27083	−	22.7491i	−0.132978	−	0.924884i
$606$	−0.120980	−	6.70527i	−0.00491447	−	0.272383i
$607$	8.47592	+	13.1888i	0.344027	+	0.535316i	0.969551	−	0.244888i	$-0.0787513\pi$
$607$	8.47592	+	13.1888i	0.344027	+	0.535316i	−0.625524	+	0.780205i	$0.715115\pi$
$608$	−7.63288	+	38.5651i	−0.309554	+	1.56402i
$609$	2.13635	+	0.975637i	0.0865692	+	0.0395348i
$610$	1.12787	−	8.99346i	0.0456663	−	0.364134i
$611$	−7.44836	+	51.8045i	−0.301328	+	2.09578i
$612$	−10.5355	−	4.35924i	−0.425872	−	0.176212i
$613$	−24.5965	−	7.22220i	−0.993445	−	0.291702i	−0.255681	−	0.966761i	$-0.582300\pi$
$613$	−24.5965	−	7.22220i	−0.993445	−	0.291702i	−0.737763	+	0.675059i	$0.764118\pi$
$614$	−16.0054	−	33.4371i	−0.645924	−	1.34941i
$615$	5.09611	+	5.88123i	0.205495	+	0.237154i
$616$	15.1006	+	42.7266i	0.608419	+	1.72150i
$617$	7.79189	+	6.75171i	0.313690	+	0.271814i	0.797448	−	0.603388i	$-0.206183\pi$
$617$	7.79189	+	6.75171i	0.313690	+	0.271814i	−0.483758	+	0.875202i	$0.660728\pi$
$618$	17.5587	−	11.7372i	0.706315	−	0.472139i
$619$	33.1946	−	15.1595i	1.33420	−	0.609310i	0.384692	−	0.923045i	$-0.374308\pi$
$619$	33.1946	−	15.1595i	1.33420	−	0.609310i	0.949510	+	0.313735i	$0.101580\pi$
$620$	3.52331	+	5.07040i	0.141499	+	0.203632i
$621$	3.25495	−	3.52211i	0.130617	−	0.141338i
$622$	−1.96162	−	6.26057i	−0.0786538	−	0.251026i
$623$	29.8725	−	13.6423i	1.19682	−	0.546568i
$624$	20.5020	+	1.45063i	0.820739	+	0.0580716i
$625$	16.2112	−	18.7087i	0.648447	−	0.748348i
$626$	6.05996	−	22.1060i	0.242205	−	0.883533i
$627$	−21.0181	−	24.2562i	−0.839381	−	0.968698i
$628$	−2.67735	−	2.87348i	−0.106838	−	0.114664i
$629$	−4.08776	+	13.9216i	−0.162990	+	0.555091i
$630$	6.99929	−	8.37836i	0.278859	−	0.333802i
$631$	5.87556	−	40.8654i	0.233902	−	1.62683i	−0.447058	−	0.894505i	$-0.647528\pi$
$631$	5.87556	−	40.8654i	0.233902	−	1.62683i	0.680960	−	0.732321i	$-0.261563\pi$
$632$	3.06957	+	5.85998i	0.122101	+	0.233098i
$633$	0.729423	−	1.59721i	0.0289920	−	0.0634835i
$634$	−0.0651732	+	0.0105738i	−0.00258836	+	0.000419939i
$635$	−12.2996	−	19.1386i	−0.488095	−	0.759491i
$636$	8.47610	−	2.82471i	0.336099	−	0.112007i
$637$	−25.6104	+	3.68221i	−1.01472	+	0.145895i
$638$	3.76213	+	2.32296i	0.148944	+	0.0919669i
$639$	4.72107	−	7.34613i	0.186763	−	0.290608i
$640$	−24.8564	−	3.99386i	−0.982536	−	0.157871i
$641$	10.6280	+	36.1957i	0.419782	+	1.42964i	0.849934	+	0.526889i	$0.176641\pi$
$641$	10.6280	+	36.1957i	0.419782	+	1.42964i	−0.430153	+	0.902756i	$0.641540\pi$
$642$	−0.201107	+	0.180714i	−0.00793708	+	0.00713223i
$643$		−	19.4798i		−	0.768208i	−0.923290	−	0.384104i	$-0.874510\pi$
$643$		−	19.4798i		−	0.768208i	0.923290	−	0.384104i	$-0.125490\pi$
$644$	33.2752	−	0.135848i	1.31123	−	0.00535318i
$645$			27.5109i			1.08324i
$646$	37.4497	+	41.6758i	1.47344	+	1.63971i
$647$	5.15080	+	17.5420i	0.202499	+	0.689648i	0.996639	+	0.0819136i	$0.0261032\pi$
$647$	5.15080	+	17.5420i	0.202499	+	0.689648i	−0.794141	+	0.607734i	$0.792079\pi$
$648$	0.553385	+	2.77376i	0.0217390	+	0.108964i
$649$	8.26255	−	12.8568i	0.324333	−	0.504673i
$650$	0.185155	−	0.299866i	0.00726238	−	0.0117617i
$651$	4.76410	−	0.684974i	0.186720	−	0.0268463i
$652$	43.0340	−	14.3413i	1.68534	−	0.561649i
$653$	−4.55241	−	7.08368i	−0.178149	−	0.277206i	0.740682	−	0.671855i	$-0.234502\pi$
$653$	−4.55241	−	7.08368i	−0.178149	−	0.277206i	−0.918832	+	0.394649i	$0.870866\pi$
$654$	3.38442	+	20.8604i	0.132341	+	0.815706i
$655$	−3.59770	+	7.87787i	−0.140574	+	0.307814i
$656$	−9.89914	−	9.88406i	−0.386497	−	0.385908i
$657$	0.273243	−	1.90045i	0.0106602	−	0.0741436i
$658$	−38.3512	−	32.0387i	−1.49509	−	1.24900i
$659$	9.38936	−	31.9772i	0.365758	−	1.24566i	−0.546992	−	0.837138i	$-0.684227\pi$
$659$	9.38936	−	31.9772i	0.365758	−	1.24566i	0.912750	−	0.408519i	$-0.133954\pi$
$660$	15.0374	−	14.0110i	0.585331	−	0.545379i
$661$	6.94576	+	8.01583i	0.270159	+	0.311780i	0.874576	−	0.484888i	$-0.161140\pi$
$661$	6.94576	+	8.01583i	0.270159	+	0.311780i	−0.604418	+	0.796668i	$0.706594\pi$
$662$	1.52889	+	0.419118i	0.0594221	+	0.0162895i
$663$	19.1828	−	22.1381i	0.744998	−	0.859774i
$664$	−12.4759	−	4.90044i	−0.484159	−	0.190174i
$665$	−48.8010	+	22.2867i	−1.89242	+	0.864240i
$666$	3.43468	−	1.07618i	0.133091	−	0.0417013i
$667$	2.52044	−	2.04653i	0.0975918	−	0.0792421i
$668$	2.57347	+	3.70348i	0.0995704	+	0.143292i
$669$	17.3365	−	7.91732i	0.670269	−	0.306101i
$670$	6.95589	+	10.4059i	0.268730	+	0.402016i
$671$	−10.0529	−	8.71087i	−0.388087	−	0.336279i
$672$	−11.4633	+	15.9288i	−0.442205	+	0.614468i
$673$	10.3718	+	11.9697i	0.399804	+	0.461399i	0.919579	−	0.392904i	$-0.128530\pi$
$673$	10.3718	+	11.9697i	0.399804	+	0.461399i	−0.519775	+	0.854303i	$0.673984\pi$
$674$	−5.53761	+	2.65070i	−0.213301	+	0.102101i
$675$	0.0465340	+	0.0136636i	0.00179109	+	0.000525912i
$676$	−10.2483	+	24.7683i	−0.394166	+	0.952627i
$677$	−1.80172	+	12.5313i	−0.0692458	+	0.481615i	0.925459	+	0.378847i	$0.123679\pi$
$677$	−1.80172	+	12.5313i	−0.0692458	+	0.481615i	−0.994705	+	0.102769i	$0.967230\pi$
$678$	−19.4924	−	2.44455i	−0.748601	−	0.0938824i
$679$	−37.2448	−	17.0092i	−1.42933	−	0.652751i
$680$	−25.8057	+	24.9290i	−0.989603	+	0.955983i
$681$	−5.16929	−	8.04357i	−0.198088	−	0.308230i
$682$	9.05979	−	0.163461i	0.346917	−	0.00625925i
$683$	0.891673	+	6.20172i	0.0341189	+	0.237302i	0.999744	−	0.0226376i	$-0.00720638\pi$
$683$	0.891673	+	6.20172i	0.0341189	+	0.237302i	−0.965625	+	0.259940i	$0.916297\pi$
$684$	3.43226	−	13.4689i	0.131236	−	0.514995i
$685$	16.5067	−	25.6849i	0.630689	−	0.981371i
$686$	−3.84518	+	8.83834i	−0.146810	+	0.337449i
$687$	−6.22056	+	1.82652i	−0.237329	+	0.0696862i
$688$	−3.56557	−	49.3247i	−0.135936	−	1.88049i
$689$			22.9539i			0.874474i
$690$	−6.07723	−	13.8144i	−0.231356	−	0.525903i
$691$	38.2471			1.45499			0.727494	−	0.686114i	$-0.240685\pi$
$691$	38.2471			1.45499			0.727494	+	0.686114i	$0.240685\pi$
$692$	−5.89425	+	9.94286i	−0.224066	+	0.377971i
$693$	−4.51387	−	15.3728i	−0.171468	−	0.583965i
$694$	−4.27040	+	9.81572i	−0.162102	+	0.372599i
$695$	41.6470	+	26.7649i	1.57976	+	1.01525i
$696$	0.103581	+	1.91198i	0.00392621	+	0.0724735i
$697$	−19.7342	+	2.83735i	−0.747487	+	0.107472i
$698$	0.562790	+	31.1925i	0.0213019	+	1.18065i
$699$	−9.10036	+	5.84845i	−0.344207	+	0.221209i
$700$	0.150739	+	0.300852i	0.00569741	+	0.0113711i
$701$	−17.0218	+	37.2725i	−0.642903	+	1.40776i	0.254728	+	0.967013i	$0.418014\pi$
$701$	−17.0218	+	37.2725i	−0.642903	+	1.40776i	−0.897631	+	0.440748i	$0.854713\pi$
$702$	−7.21021	−	0.904236i	−0.272132	−	0.0341282i
$703$	−17.5076	−	2.51721i	−0.660312	−	0.0949386i
$704$	−25.1449	+	27.0695i	−0.947685	+	1.02022i
$705$	−6.38549	+	21.7470i	−0.240491	+	0.819039i
$706$	5.83294	+	12.1857i	0.219526	+	0.458614i
$707$	−12.4331	+	10.7734i	−0.467597	+	0.405175i
$708$	6.61411	−	0.238748i	0.248574	−	0.00897269i
$709$	4.83820	−	5.58358i	0.181703	−	0.209696i	−0.657590	−	0.753376i	$-0.728424\pi$
$709$	4.83820	−	5.58358i	0.181703	−	0.209696i	0.839293	+	0.543680i	$0.182970\pi$
$710$	−15.2714	−	22.8458i	−0.573124	−	0.857387i
$711$	−0.971592	−	2.12749i	−0.0364375	−	0.0797871i
$712$	21.1536	+	16.4132i	0.792764	+	0.615112i
$713$	2.07782	−	6.32085i	0.0778151	−	0.236718i
$714$	8.36280	+	26.6902i	0.312970	+	0.998855i
$715$	21.9358	+	48.0327i	0.820352	+	1.79632i
$716$	16.0568	−	19.9408i	0.600070	−	0.745223i
$717$	−10.0944	−	8.74689i	−0.376984	−	0.326659i
$718$	13.7128	+	3.75912i	0.511758	+	0.140289i
$719$	−31.9928	+	27.7219i	−1.19313	+	1.03385i	−0.194535	+	0.980896i	$0.562320\pi$
$719$	−31.9928	+	27.7219i	−1.19313	+	1.03385i	−0.998597	+	0.0529584i	$0.983135\pi$
$720$	8.69882	+	1.88537i	0.324186	+	0.0702635i
$721$	−49.7118	−	14.5967i	−1.85136	−	0.543609i
$722$	−26.5637	+	31.7975i	−0.988599	+	1.18338i
$723$	2.17996	+	0.313431i	0.0810737	+	0.0116566i
$724$	−5.07955	−	28.0928i	−0.188780	−	1.04406i
$725$	0.0298655	+	0.0136391i	0.00110918	+	0.000506543i
$726$	−2.33924	−	14.4183i	−0.0868174	−	0.535112i
$727$	35.3765	−	22.7351i	1.31204	−	0.843197i	0.317572	−	0.948234i	$-0.397133\pi$
$727$	35.3765	−	22.7351i	1.31204	−	0.843197i	0.994468	+	0.105037i	$0.0334962\pi$
$728$	−29.5133	−	40.8788i	−1.09384	−	1.51507i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−5.14098	−	3.17434i	−0.190276	−	0.117488i
$731$	−59.2932	−	38.1054i	−2.19304	−	1.40938i
$732$	0.613589	−	5.72775i	0.0226789	−	0.211704i
$733$	12.5368	−	3.68115i	0.463059	−	0.135966i	−0.0418778	−	0.999123i	$-0.513334\pi$
$733$	12.5368	−	3.68115i	0.463059	−	0.135966i	0.504937	+	0.863156i	$0.331516\pi$
$734$	5.09083	+	5.66532i	0.187906	+	0.209111i
$735$	−11.2048			−0.413297
$736$	12.6864	+	23.9803i	0.467626	+	0.883926i
$737$	18.3691			0.676634
$738$	3.30571	+	3.67875i	0.121685	+	0.135417i
$739$	8.38592	−	2.46233i	0.308481	−	0.0905782i	−0.123828	−	0.992304i	$-0.539517\pi$
$739$	8.38592	−	2.46233i	0.308481	−	0.0905782i	0.432309	+	0.901725i	$0.357699\pi$
$740$	1.20648	−	11.2623i	0.0443511	−	0.414011i
$741$	30.0408	+	19.3061i	1.10358	+	0.709226i
$742$	−18.6485	−	11.5147i	−0.684608	−	0.422717i
$743$	−4.46509	−	31.0554i	−0.163808	−	1.13931i	−0.891372	−	0.453272i	$-0.850257\pi$
$743$	−4.46509	−	31.0554i	−0.163808	−	1.13931i	0.727564	−	0.686040i	$-0.240652\pi$
$744$	2.29699	+	3.18155i	0.0842117	+	0.116641i
$745$	33.7348	−	21.6800i	1.23595	−	0.794294i
$746$	1.44483	+	8.90543i	0.0528990	+	0.326051i
$747$	4.31072	+	1.96864i	0.157721	+	0.0720287i
$748$	9.36908	+	51.8163i	0.342567	+	1.89459i
$749$	0.656503	+	0.0943910i	0.0239881	+	0.00344897i
$750$	10.1856	−	12.1924i	0.371925	−	0.445204i
$751$	−4.11260	−	1.20757i	−0.150071	−	0.0440648i	0.205834	−	0.978587i	$-0.434009\pi$
$751$	−4.11260	−	1.20757i	−0.150071	−	0.0440648i	−0.355905	+	0.934522i	$0.615827\pi$
$752$	8.63011	−	39.8181i	0.314708	−	1.45202i
$753$	−17.6454	+	15.2899i	−0.643036	+	0.557194i
$754$	−4.74436	−	1.30058i	−0.172779	−	0.0473643i
$755$	−27.8322	−	24.1168i	−1.01292	−	0.877698i
$756$	4.35159	−	5.40421i	0.158266	−	0.196549i
$757$	18.0827	+	39.5957i	0.657229	+	1.43913i	0.885082	+	0.465435i	$0.154102\pi$
$757$	18.0827	+	39.5957i	0.657229	+	1.43913i	−0.227854	+	0.973695i	$0.573171\pi$
$758$	7.66966	+	24.4780i	0.278575	+	0.889080i
$759$	−21.8110	−	3.85183i	−0.791689	−	0.139813i
$760$	−34.5574	−	26.8134i	−1.25353	−	0.972623i
$761$	−16.2112	−	35.4975i	−0.587655	−	1.28678i	−0.936849	−	0.349734i	$-0.886272\pi$
$761$	−16.2112	−	35.4975i	−0.587655	−	1.28678i	0.349194	−	0.937050i	$-0.386455\pi$
$762$	−8.03511	−	12.0204i	−0.291081	−	0.435455i
$763$	33.9492	−	39.1794i	1.22904	−	1.41839i
$764$	23.1031	−	0.833946i	0.835842	−	0.0301711i
$765$	9.58711	−	8.30728i	0.346623	−	0.300350i
$766$	−13.3438	−	27.8767i	−0.482130	−	1.00722i
$767$	−4.79052	+	16.3150i	−0.172976	+	0.589102i
$768$	−15.8406	−	2.25289i	−0.571598	−	0.0812942i
$769$	−16.0503	−	2.30769i	−0.578789	−	0.0832173i	−0.153298	−	0.988180i	$-0.548989\pi$
$769$	−16.0503	−	2.30769i	−0.578789	−	0.0832173i	−0.425491	+	0.904963i	$0.639899\pi$
$770$	−50.0272	−	6.27394i	−1.80286	−	0.226097i
$771$	2.63022	−	5.75938i	0.0947250	−	0.207419i
$772$	8.17229	+	16.3106i	0.294127	+	0.587032i
$773$	−7.29142	+	4.68591i	−0.262254	+	0.168541i	−0.665160	−	0.746701i	$-0.731637\pi$
$773$	−7.29142	+	4.68591i	−0.262254	+	0.168541i	0.402906	+	0.915242i	$0.368000\pi$
$774$	0.315411	+	17.4816i	0.0113372	+	0.628362i
$775$	0.0666006	−	0.00957572i	0.00239236	−	0.000343970i
$776$	−1.80581	−	33.3333i	−0.0648249	−	1.19660i
$777$	−7.42787	−	4.77361i	−0.266474	−	0.171252i
$778$	−10.2553	+	23.5722i	−0.367669	+	0.845103i
$779$	−6.84734	−	23.3199i	−0.245332	−	0.835523i
$780$	−11.6611	+	19.6709i	−0.417536	+	0.704331i
$781$	−40.3285			−1.44307
$782$	38.1911	+	6.03627i	1.36571	+	0.215857i
$783$		−	0.676979i		−	0.0241933i
$784$	20.0893	−	1.45221i	0.717476	−	0.0518646i
$785$	4.19271	−	1.23109i	0.149644	−	0.0439395i
$786$	−2.19581	+	5.04718i	−0.0783220	+	0.180027i
$787$	1.60207	−	2.49288i	0.0571078	−	0.0888614i	−0.811526	−	0.584317i	$-0.801362\pi$
$787$	1.60207	−	2.49288i	0.0571078	−	0.0888614i	0.868633	+	0.495456i	$0.164999\pi$
$788$	4.90242	−	19.2381i	0.174641	−	0.685329i
$789$	4.46060	+	31.0242i	0.158802	+	1.10449i
$790$	−7.35893	+	0.132773i	−0.261819	+	0.00472386i
$791$	26.0543	+	40.5412i	0.926383	+	1.44148i
$792$	9.39477	−	9.07561i	0.333829	−	0.322488i
$793$	13.4623	+	6.14803i	0.478060	+	0.218323i
$794$	−37.1293	−	4.65640i	−1.31767	−	0.165250i
$795$	−1.41466	+	9.83921i	−0.0501730	+	0.348961i
$796$	−16.0842	+	38.8726i	−0.570089	+	1.37780i
$797$	9.07664	+	2.66514i	0.321511	+	0.0944042i	0.438506	−	0.898728i	$-0.355508\pi$
$797$	9.07664	+	2.66514i	0.321511	+	0.0944042i	−0.116995	+	0.993133i	$0.537326\pi$
$798$	−30.7547	+	14.7214i	−1.08870	+	0.521131i
$799$	−38.0259	−	43.8842i	−1.34526	−	1.55251i
$800$	−0.160253	+	0.222680i	−0.00566579	+	0.00787293i
$801$	−7.15406	−	6.19903i	−0.252776	−	0.219032i
$802$	−22.8603	−	34.1988i	−0.807227	−	1.20760i
$803$	−8.06577	+	3.68351i	−0.284635	+	0.129988i
$804$	4.53937	+	6.53262i	0.160091	+	0.230388i
$805$	−16.4492	+	33.1674i	−0.579757	+	1.16900i
$806$	−9.62042	+	3.01436i	−0.338865	+	0.106176i
$807$	−18.8785	+	8.62154i	−0.664556	+	0.303492i
$808$	−12.4842	−	4.90369i	−0.439192	−	0.172511i
$809$	14.3634	−	16.5763i	0.504991	−	0.582791i	−0.444818	−	0.895621i	$-0.646732\pi$
$809$	14.3634	−	16.5763i	0.504991	−	0.582791i	0.949809	+	0.312830i	$0.101277\pi$
$810$	−3.03493	−	0.831972i	−0.106637	−	0.0292325i
$811$	−17.2958	−	19.9604i	−0.607336	−	0.700904i	0.365914	−	0.930648i	$-0.380756\pi$
$811$	−17.2958	−	19.9604i	−0.607336	−	0.700904i	−0.973251	+	0.229745i	$0.926211\pi$
$812$	3.43661	−	3.20205i	0.120601	−	0.112370i
$813$	9.09655	−	30.9800i	0.319030	−	1.08652i
$814$	−12.7569	−	10.6572i	−0.447131	−	0.373534i
$815$	−7.18239	+	49.9546i	−0.251588	+	1.74983i
$816$	−16.1122	+	16.1368i	−0.564040	+	0.564901i
$817$	35.6929	−	78.1566i	1.24874	−	2.73435i
$818$	−3.71204	−	22.8797i	−0.129788	−	0.799970i
$819$	9.63743	+	14.9961i	0.336759	+	0.524008i
$820$	14.7656	−	4.92072i	0.515638	−	0.171839i
$821$	−15.9878	+	2.29871i	−0.557980	+	0.0802254i	−0.415535	−	0.909577i	$-0.636406\pi$
$821$	−15.9878	+	2.29871i	−0.557980	+	0.0802254i	−0.142445	+	0.989803i	$0.545496\pi$
$822$	10.1946	−	16.5105i	0.355577	−	0.575871i
$823$	−1.89460	+	2.94805i	−0.0660415	+	0.102763i	−0.872704	−	0.488250i	$-0.837635\pi$
$823$	−1.89460	+	2.94805i	−0.0660415	+	0.102763i	0.806662	+	0.591013i	$0.201272\pi$
$824$	−8.26444	−	41.4244i	−0.287905	−	1.44309i
$825$	−0.0631024	−	0.214907i	−0.00219694	−	0.00748210i
$826$	−10.8517	−	12.0763i	−0.377580	−	0.420189i
$827$		−	11.0482i		−	0.384185i	−0.981377	−	0.192092i	$-0.938473\pi$
$827$		−	11.0482i		−	0.384185i	0.981377	−	0.192092i	$-0.0615273\pi$
$828$	−4.02011	−	8.70854i	−0.139708	−	0.302643i
$829$		−	8.14814i		−	0.282997i	−0.989938	−	0.141498i	$-0.954808\pi$
$829$		−	8.14814i		−	0.282997i	0.989938	−	0.141498i	$-0.0451920\pi$
$830$	11.0925	−	9.96771i	0.385028	−	0.345984i
$831$	5.81815	+	19.8148i	0.201829	+	0.687367i
$832$	18.3580	−	36.7796i	0.636449	−	1.27510i
$833$	15.5198	−	24.1494i	0.537731	−	0.836725i
$834$	26.7711	+	16.5301i	0.927008	+	0.572389i
$835$	−4.96655	+	0.714083i	−0.171875	+	0.0247118i
$836$	−60.8983	+	20.2947i	−2.10621	+	0.701907i
$837$	−0.750070	−	1.16713i	−0.0259262	−	0.0403420i
$838$	−16.0603	+	2.60565i	−0.554793	+	0.0900105i
$839$	4.10642	−	8.99179i	0.141769	−	0.310431i	−0.825407	−	0.564538i	$-0.809054\pi$
$839$	4.10642	−	8.99179i	0.141769	−	0.310431i	0.967176	+	0.254107i	$0.0817815\pi$
$840$	−10.1315	−	19.3417i	−0.349571	−	0.667351i
$841$	−4.06191	+	28.2512i	−0.140066	+	0.974179i
$842$	−10.2837	+	12.3098i	−0.354398	+	0.424225i
$843$	−5.77915	+	19.6820i	−0.199045	+	0.677884i
$844$	−2.39397	−	2.56934i	−0.0824038	−	0.0884403i
$845$	−19.5299	−	22.5387i	−0.671849	−	0.775355i
$846$	−3.80828	+	13.8922i	−0.130931	+	0.477622i
$847$	−23.4649	+	27.0800i	−0.806265	+	0.930479i
$848$	1.26116	−	17.8242i	0.0433083	−	0.612086i
$849$	1.34438	−	0.613960i	0.0461392	−	0.0210710i
$850$	0.116909	+	0.373120i	0.00400996	+	0.0127979i
$851$	−10.4741	+	6.26713i	−0.359049	+	0.214834i
$852$	−9.96599	−	14.3421i	−0.341429	−	0.491352i
$853$	−0.944548	+	0.431361i	−0.0323407	+	0.0147695i	−0.431520	−	0.902104i	$-0.642022\pi$
$853$	−0.944548	+	0.431361i	−0.0323407	+	0.0147695i	0.399179	+	0.916873i	$0.369295\pi$
$854$	−11.7481	+	7.85309i	−0.402013	+	0.268727i
$855$	11.6872	+	10.1270i	0.399693	+	0.346336i
$856$	0.180190	+	0.509842i	0.00615876	+	0.0174260i
$857$	−4.37886	−	5.05348i	−0.149579	−	0.172624i	0.676015	−	0.736888i	$-0.263705\pi$
$857$	−4.37886	−	5.05348i	−0.149579	−	0.172624i	−0.825594	+	0.564264i	$0.809160\pi$
$858$	14.4896	+	30.2705i	0.494667	+	1.03342i
$859$	18.6468	+	5.47520i	0.636222	+	0.186812i	0.583909	−	0.811819i	$-0.301523\pi$
$859$	18.6468	+	5.47520i	0.636222	+	0.186812i	0.0523128	+	0.998631i	$0.483341\pi$
$860$	50.8415	+	21.0366i	1.73368	+	0.717341i
$861$	1.72664	−	12.0091i	0.0588439	−	0.409268i
$862$	−0.841317	+	6.70851i	−0.0286554	+	0.228493i
$863$	−5.03031	−	2.29727i	−0.171234	−	0.0781998i	0.327954	−	0.944694i	$-0.393641\pi$
$863$	−5.03031	−	2.29727i	−0.171234	−	0.0781998i	−0.499188	+	0.866494i	$0.666368\pi$
$864$	5.54921	+	1.09831i	0.188788	+	0.0373653i
$865$	−6.95272	−	10.8186i	−0.236400	−	0.367845i
$866$	0.457966	+	25.3827i	0.0155623	+	0.862538i
$867$	2.20587	+	15.3422i	0.0749153	+	0.521048i
$868$	2.37706	−	9.32808i	0.0806828	−	0.316616i
$869$	−5.83971	+	9.08677i	−0.198099	+	0.308247i
$870$	−1.95352	−	0.849893i	−0.0662305	−	0.0288141i
$871$	−19.6097	+	5.75792i	−0.664448	+	0.195100i
$872$	41.1390	+	9.69657i	1.39314	+	0.328367i
$873$			11.8024i			0.399450i
$874$	−0.657886	+	47.1303i	−0.0222533	+	1.59421i
$875$	−38.9728			−1.31752
$876$	−3.30319	−	1.95817i	−0.111604	−	0.0661604i
$877$	11.9193	+	40.5933i	0.402485	+	1.37074i	0.872730	+	0.488203i	$0.162347\pi$
$877$	11.9193	+	40.5933i	0.402485	+	1.37074i	−0.470245	+	0.882536i	$0.655834\pi$
$878$	−18.3634	−	7.98913i	−0.619734	−	0.269620i
$879$	26.8718	+	17.2694i	0.906363	+	0.582484i
$880$	−14.3946	−	38.5036i	−0.485240	−	1.29796i
$881$	−13.0249	+	1.87269i	−0.438819	+	0.0630926i	−0.358184	−	0.933651i	$-0.616604\pi$
$881$	−13.0249	+	1.87269i	−0.438819	+	0.0630926i	−0.0806349	+	0.996744i	$0.525695\pi$
$882$	−7.12003	+	0.128463i	−0.239744	+	0.00432557i
$883$	19.7581	−	12.6978i	0.664914	−	0.427314i	−0.164175	−	0.986431i	$-0.552496\pi$
$883$	19.7581	−	12.6978i	0.664914	−	0.427314i	0.829089	+	0.559117i	$0.188860\pi$
$884$	−26.2440	−	52.3790i	−0.882682	−	1.76170i
$885$	−3.05897	+	6.69821i	−0.102826	+	0.225158i
$886$	−7.07141	+	56.3861i	−0.237569	+	1.89433i
$887$	13.1587	+	1.89193i	0.441825	+	0.0635248i	0.359638	−	0.933092i	$-0.382900\pi$
$887$	13.1587	+	1.89193i	0.441825	+	0.0635248i	0.0821873	+	0.996617i	$0.473809\pi$
$888$	0.637527	−	7.17037i	0.0213940	−	0.240622i
$889$	−9.99269	+	34.0320i	−0.335144	+	1.14140i
$890$	−26.8695	+	12.8617i	−0.900669	+	0.431124i
$891$	−3.49027	+	3.02433i	−0.116928	+	0.101319i
$892$	−1.37503	−	38.0928i	−0.0460393	−	1.27544i
$893$	46.3555	−	53.4971i	1.55123	−	1.79021i
$894$	21.1879	−	14.1632i	0.708630	−	0.473687i
$895$	11.8329	+	25.9105i	0.395531	+	0.866093i
$896$	20.6718	+	33.3649i	0.690595	+	1.11464i
$897$	24.4914	−	2.72484i	0.817745	−	0.0909797i
$898$	2.72236	−	0.852994i	0.0908463	−	0.0284648i
$899$	−0.390167	−	0.854347i	−0.0130128	−	0.0284941i
$900$	0.0608338	−	0.0755491i	0.00202779	−	0.00251830i
$901$	−19.2466	−	16.6773i	−0.641197	−	0.555601i
$902$	6.03869	−	22.0284i	0.201066	−	0.733466i
$903$	32.4149	−	28.0877i	1.07870	−	0.934700i
$904$	−19.4228	+	34.1537i	−0.645991	+	1.13593i
$905$	30.4762	+	8.94861i	1.01306	+	0.297462i
$906$	−17.9623	−	15.0057i	−0.596756	−	0.498531i
$907$	−45.9079	−	6.60056i	−1.52435	−	0.219168i	−0.671372	−	0.741120i	$-0.734295\pi$
$907$	−45.9079	−	6.60056i	−1.52435	−	0.219168i	−0.852975	+	0.521952i	$0.825204\pi$
$908$	−18.8177	+	3.40249i	−0.624487	+	0.112916i
$909$	4.31358	+	1.96995i	0.143072	+	0.0653390i
$910$	55.3725	−	8.98373i	1.83558	−	0.297808i
$911$	−10.4493	+	6.71533i	−0.346200	+	0.222489i	−0.702172	−	0.712008i	$-0.747786\pi$
$911$	−10.4493	+	6.71533i	−0.346200	+	0.222489i	0.355972	+	0.934497i	$0.384150\pi$
$912$	−22.2666	−	16.6421i	−0.737322	−	0.551076i
$913$	−3.11469	−	21.6631i	−0.103081	−	0.716945i
$914$	2.24612	−	3.63768i	0.0742950	−	0.120324i
$915$	5.39172	+	3.46505i	0.178245	+	0.114551i
$916$	−1.38113	+	12.8926i	−0.0456337	+	0.425983i
$917$	12.9553	−	3.80402i	0.427822	−	0.125620i
$918$	5.99681	−	5.38871i	0.197924	−	0.177854i
$919$	18.9134			0.623895			0.311948	−	0.950099i	$-0.399019\pi$
$919$	18.9134			0.623895			0.311948	+	0.950099i	$0.399019\pi$
$920$	−30.1767	+	0.667709i	−0.994895	+	0.0220137i
$921$	26.2127			0.863737
$922$	−37.7750	+	33.9444i	−1.24405	+	1.11790i
$923$	43.0522	−	12.6413i	1.41708	−	0.416092i
$924$	−31.8613	−	3.41316i	−1.04816	−	0.112285i
$925$	−0.103839	−	0.0667335i	−0.00341422	−	0.00219418i
$926$	10.2535	−	16.6060i	0.336951	−	0.545707i
$927$	2.12538	+	14.7823i	0.0698066	+	0.485516i
$928$	3.61264	+	1.27060i	0.118591	+	0.0417095i
$929$	5.18955	−	3.33512i	0.170263	−	0.109422i	−0.452734	−	0.891646i	$-0.649551\pi$
$929$	5.18955	−	3.33512i	0.170263	−	0.109422i	0.622997	+	0.782224i	$0.285915\pi$
$930$	−4.30958	+	0.699193i	−0.141317	+	0.0229274i
$931$	31.8322	+	14.5373i	1.04326	+	0.476440i
$932$	3.84952	+	21.2900i	0.126095	+	0.697378i
$933$	4.59189	+	0.660215i	0.150332	+	0.0216145i
$934$	18.2403	+	15.2380i	0.596840	+	0.498601i
$935$	−56.2124	−	16.5055i	−1.83834	−	0.539786i
$936$	−7.18445	+	12.6334i	−0.234831	+	0.412936i
$937$	−6.78970	+	5.88331i	−0.221810	+	0.192199i	−0.758676	−	0.651468i	$-0.774153\pi$
$937$	−6.78970	+	5.88331i	−0.221810	+	0.192199i	0.536866	+	0.843667i	$0.319608\pi$
$938$	5.15914	−	18.8199i	0.168452	−	0.614493i
$939$	12.2492	+	10.6140i	0.399737	+	0.346374i
$940$	35.3068	+	28.4298i	1.15158	+	0.927278i
$941$	−21.9200	−	47.9981i	−0.714572	−	1.56469i	−0.821358	−	0.570413i	$-0.806783\pi$
$941$	−21.9200	−	47.9981i	−0.714572	−	1.56469i	0.106786	−	0.994282i	$-0.465944\pi$
$942$	2.65011	−	0.830355i	0.0863452	−	0.0270544i
$943$	−13.8122	−	9.51441i	−0.449787	−	0.309832i
$944$	4.61635	−	12.4058i	0.150249	−	0.403774i
$945$	3.20687	+	7.02207i	0.104320	+	0.228428i
$946$	67.1310	−	44.8740i	2.18262	−	1.45898i
$947$	−18.8670	+	21.7737i	−0.613094	+	0.707549i	−0.974380	−	0.224906i	$-0.927792\pi$
$947$	−18.8670	+	21.7737i	−0.613094	+	0.707549i	0.361286	+	0.932455i	$0.382338\pi$
$948$	−4.67465	+	0.168739i	−0.151826	+	0.00548040i
$949$	7.45588	−	6.46056i	0.242028	−	0.209719i
$950$	−0.429940	+	0.205800i	−0.0139491	+	0.00667704i
$951$	0.0131532	−	0.0447958i	0.000426523	−	0.00145260i
$952$	55.7195	+	4.95409i	1.80588	+	0.160563i
$953$	16.2221	+	2.33238i	0.525484	+	0.0755532i	0.399952	−	0.916536i	$-0.369027\pi$
$953$	16.2221	+	2.33238i	0.525484	+	0.0755532i	0.125533	+	0.992089i	$0.459936\pi$
$954$	−0.786131	+	6.26846i	−0.0254519	+	0.202949i
$955$	−10.6850	+	23.3969i	−0.345758	+	0.757105i
$956$	−23.8835	+	11.9666i	−0.772449	+	0.387029i
$957$	−2.63016	+	1.69030i	−0.0850211	+	0.0546398i
$958$	34.2037	−	0.617119i	1.10507	−	0.0199382i
$959$	−47.1163	+	6.77430i	−1.52146	+	0.218753i
$960$	10.1359	−	14.6342i	0.327135	−	0.472316i
$961$	24.4596	+	15.7192i	0.789020	+	0.507072i
$962$	16.9591	+	7.37817i	0.546783	+	0.237882i
$963$	−0.0538625	−	0.183439i	−0.00173569	−	0.00591123i
$964$	2.24617	−	3.78901i	0.0723444	−	0.122036i
$965$	−20.2976			−0.653403
$966$	−10.0722	+	21.2645i	−0.324069	+	0.684175i
$967$		−	54.2527i		−	1.74465i	−0.488927	−	0.872325i	$-0.662611\pi$
$967$		−	54.2527i		−	1.74465i	0.488927	−	0.872325i	$-0.337389\pi$
$968$	−28.4344	−	6.70206i	−0.913916	−	0.215412i
$969$	−38.0143	+	11.1620i	−1.22119	+	0.358575i
$970$	34.0574	+	14.8169i	1.09352	+	0.475743i
$971$	−22.2605	+	34.6380i	−0.714372	+	1.11158i	0.274322	+	0.961638i	$0.411547\pi$
$971$	−22.2605	+	34.6380i	−0.714372	+	1.11158i	−0.988694	+	0.149947i	$0.952090\pi$
$972$	−1.93806	−	0.493874i	−0.0621634	−	0.0158410i
$973$	−10.9842	−	76.3970i	−0.352138	−	2.44917i
$974$	−0.120096	−	6.65632i	−0.00384814	−	0.213282i
$975$	0.134728	+	0.209641i	0.00431476	+	0.00671389i
$976$	−10.1160	−	5.51374i	−0.323805	−	0.176491i
$977$	−38.4782	−	17.5724i	−1.23103	−	0.562192i	−0.309647	−	0.950852i	$-0.600211\pi$
$977$	−38.4782	−	17.5724i	−1.23103	−	0.562192i	−0.921381	+	0.388660i	$0.872938\pi$
$978$	−3.99127	+	31.8256i	−0.127627	+	1.01767i
$979$	−6.22165	+	43.2725i	−0.198845	+	1.38300i
$980$	−8.56792	+	20.7071i	−0.273692	+	0.661464i
$981$	−14.3381	−	4.21004i	−0.457780	−	0.134416i
$982$	−7.44549	−	15.5545i	−0.237595	−	0.496364i
$983$	7.40981	+	8.55137i	0.236336	+	0.272746i	0.861512	−	0.507738i	$-0.169518\pi$
$983$	7.40981	+	8.55137i	0.236336	+	0.272746i	−0.625176	+	0.780484i	$0.714973\pi$
$984$	9.32628	−	3.29612i	0.297311	−	0.105076i
$985$	16.6932	+	14.4648i	0.531891	+	0.460886i
$986$	4.53756	−	3.03315i	0.144505	−	0.0965953i
$987$	32.1429	−	14.6792i	1.02312	−	0.467244i
$988$	58.6497	−	40.7543i	1.86590	−	1.29657i
$989$	−14.8760	−	57.3961i	−0.473029	−	1.82509i
$990$	4.34539	+	13.8685i	0.138106	+	0.440769i
$991$	−15.8240	+	7.22658i	−0.502666	+	0.229560i	−0.650576	−	0.759441i	$-0.725473\pi$
$991$	−15.8240	+	7.22658i	−0.502666	+	0.229560i	0.147910	+	0.989001i	$0.452745\pi$
$992$	7.63609	−	1.81214i	0.242446	−	0.0575355i
$993$	−0.734083	+	0.847177i	−0.0232954	+	0.0268843i
$994$	−11.3267	+	41.3184i	−0.359260	+	1.31054i
$995$	−30.6512	−	35.3733i	−0.971707	−	1.12141i
$996$	6.93439	−	6.46108i	0.219724	−	0.204727i
$997$	−2.50867	+	8.54374i	−0.0794503	+	0.270583i	−0.989632	−	0.143626i	$-0.954124\pi$
$997$	−2.50867	+	8.54374i	−0.0794503	+	0.270583i	0.910182	+	0.414209i	$0.135942\pi$
$998$	−9.16721	+	10.9734i	−0.290183	+	0.347357i
$999$	−0.362207	+	2.51921i	−0.0114597	+	0.0797041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.b.19.18	yes	240
8.3	odd	2	inner	552.2.t.b.19.13	✓	240
23.17	odd	22	inner	552.2.t.b.523.13	yes	240
184.155	even	22	inner	552.2.t.b.523.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.b.19.13	✓	240	8.3	odd	2	inner
552.2.t.b.19.18	yes	240	1.1	even	1	trivial
552.2.t.b.523.13	yes	240	23.17	odd	22	inner
552.2.t.b.523.18	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)

\(f(q)\)	\(=\)	\(q+(0.945243 + 1.05191i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.213032 + 1.98862i) q^{4} +(-1.87195 - 1.20303i) q^{5} +(-1.20331 - 0.742995i) q^{6} +(0.493720 + 3.43390i) q^{7} +(-2.29322 + 1.65564i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.945243 + 1.05191i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.213032 + 1.98862i) q^{4} +(-1.87195 - 1.20303i) q^{5} +(-1.20331 - 0.742995i) q^{6} +(0.493720 + 3.43390i) q^{7} +(-2.29322 + 1.65564i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.503969 - 3.10629i) q^{10} +(-4.20094 - 1.91850i) q^{11} +(-0.355857 - 1.96809i) q^{12} +(5.08603 + 0.731260i) q^{13} +(-3.14547 + 3.76522i) q^{14} +(2.13506 + 0.626910i) q^{15} +(-3.90923 - 0.847282i) q^{16} +(-4.30843 + 3.73328i) q^{17} +(1.36389 + 0.373887i) q^{18} +(-5.25220 - 4.55106i) q^{19} +(2.79116 - 3.46633i) q^{20} +(-1.44116 - 3.15571i) q^{21} +(-1.95281 - 6.23247i) q^{22} +(-4.79338 - 0.153433i) q^{23} +(1.73388 - 2.23465i) q^{24} +(-0.0201470 - 0.0441158i) q^{25} +(4.03831 + 6.04126i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(-6.93391 + 0.250291i) q^{28} +(-0.511627 + 0.443327i) q^{29} +(1.35870 + 2.83848i) q^{30} +(-0.390868 + 1.33117i) q^{31} +(-2.80391 - 4.91305i) q^{32} +(4.57128 + 0.657250i) q^{33} +(-7.99959 - 1.00323i) q^{34} +(3.20687 - 7.02207i) q^{35} +(0.895916 + 1.78811i) q^{36} +(2.14108 - 1.37599i) q^{37} +(-0.177298 - 9.82670i) q^{38} +(-5.08603 + 0.731260i) q^{39} +(6.28459 - 0.340464i) q^{40} +(2.94204 + 1.89073i) q^{41} +(1.95727 - 4.49888i) q^{42} +(3.48316 + 11.8626i) q^{43} +(4.71012 - 7.94538i) q^{44} -2.22520 q^{45} +(-4.36951 - 5.18724i) q^{46} +10.1857i q^{47} +(3.98959 - 0.288398i) q^{48} +(-4.83147 + 1.41865i) q^{49} +(0.0273621 - 0.0628930i) q^{50} +(3.08212 - 4.79588i) q^{51} +(-2.53769 + 9.95840i) q^{52} +(0.635748 + 4.42172i) q^{53} +(-1.41398 + 0.0255118i) q^{54} +(5.55595 + 8.64522i) q^{55} +(-6.81751 - 7.05727i) q^{56} +(6.32163 + 2.88699i) q^{57} +(-0.949952 - 0.119134i) q^{58} +(-0.470950 + 3.27553i) q^{59} +(-1.70152 + 4.11228i) q^{60} +(2.76359 + 0.811463i) q^{61} +(-1.76974 + 0.847125i) q^{62} +(2.27185 + 2.62186i) q^{63} +(2.51772 - 7.59349i) q^{64} +(-8.64108 - 7.48754i) q^{65} +(3.62960 + 5.42984i) q^{66} +(-3.61803 + 1.65230i) q^{67} +(-6.50624 - 9.36315i) q^{68} +(4.64244 - 1.20323i) q^{69} +(10.4179 - 3.26422i) q^{70} +(7.94323 - 3.62755i) q^{71} +(-1.03407 + 2.63262i) q^{72} +(1.25733 - 1.45103i) q^{73} +(3.47126 + 0.951583i) q^{74} +(0.0317598 + 0.0366527i) q^{75} +(10.1692 - 9.47512i) q^{76} +(4.51387 - 15.3728i) q^{77} +(-5.57675 - 4.65883i) q^{78} +(0.332853 - 2.31504i) q^{79} +(6.29860 + 6.28901i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.792058 + 4.88197i) q^{82} +(2.56208 + 3.98667i) q^{83} +(6.58252 - 2.19366i) q^{84} +(12.5564 - 1.80534i) q^{85} +(-9.18591 + 14.8770i) q^{86} +(0.366003 - 0.569511i) q^{87} +(12.8100 - 2.55569i) q^{88} +(-2.66693 - 9.08273i) q^{89} +(-2.10335 - 2.34071i) q^{90} +17.8259i q^{91} +(1.32626 - 9.49953i) q^{92} -1.38737i q^{93} +(-10.7144 + 9.62791i) q^{94} +(4.35681 + 14.8379i) q^{95} +(4.07450 + 3.92409i) q^{96} +(-6.38085 + 9.92879i) q^{97} +(-6.05920 - 3.74131i) q^{98} +(-4.57128 + 0.657250i) 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

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Database

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