LMFDB - Embedded newform 552.2.t.b.19.3

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			19.3
Character	$\chi$	$=$	552.19
Dual form			552.2.t.b.523.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34789 - 0.428007i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(1.63362 + 1.15381i) q^{4} +(-0.781202 - 0.502048i) q^{5} +(1.41388 + 0.0309246i) q^{6} +(0.233208 + 1.62200i) q^{7} +(-1.70810 - 2.25441i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-1.34789 - 0.428007i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(1.63362 + 1.15381i) q^{4} +(-0.781202 - 0.502048i) q^{5} +(1.41388 + 0.0309246i) q^{6} +(0.233208 + 1.62200i) q^{7} +(-1.70810 - 2.25441i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.838095 + 1.01107i) q^{10} +(-3.93727 - 1.79809i) q^{11} +(-1.89251 - 0.646831i) q^{12} +(1.76083 + 0.253170i) q^{13} +(0.379887 - 2.28609i) q^{14} +(0.891001 + 0.261622i) q^{15} +(1.33743 + 3.76978i) q^{16} +(1.58730 - 1.37541i) q^{17} +(-1.36532 + 0.368663i) q^{18} +(-1.55505 - 1.34746i) q^{19} +(-0.696918 - 1.72152i) q^{20} +(-0.680732 - 1.49059i) q^{21} +(4.53742 + 4.10881i) q^{22} +(4.31254 + 2.09810i) q^{23} +(2.27405 + 1.68187i) q^{24} +(-1.71885 - 3.76376i) q^{25} +(-2.26505 - 1.09489i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(-1.49051 + 2.91881i) q^{28} +(2.26983 - 1.96682i) q^{29} +(-1.08900 - 0.733992i) q^{30} +(0.269391 - 0.917461i) q^{31} +(-0.189221 - 5.65369i) q^{32} +(4.28437 + 0.615999i) q^{33} +(-2.72820 + 1.17452i) q^{34} +(0.632139 - 1.38419i) q^{35} +(1.99809 + 0.0874469i) q^{36} +(3.95389 - 2.54101i) q^{37} +(1.51931 + 2.48179i) q^{38} +(-1.76083 + 0.253170i) q^{39} +(0.202549 + 2.61870i) q^{40} +(-1.14329 - 0.734745i) q^{41} +(0.279568 + 2.30052i) q^{42} +(-2.72152 - 9.26863i) q^{43} +(-4.35735 - 7.48028i) q^{44} -0.928617 q^{45} +(-4.91483 - 4.67381i) q^{46} -7.78128i q^{47} +(-2.34533 - 3.24028i) q^{48} +(4.13996 - 1.21560i) q^{49} +(0.705910 + 5.80882i) q^{50} +(-1.13551 + 1.76689i) q^{51} +(2.58442 + 2.44525i) q^{52} +(-1.31916 - 9.17495i) q^{53} +(1.20615 - 0.738383i) q^{54} +(2.17308 + 3.38137i) q^{55} +(3.25831 - 3.29629i) q^{56} +(1.87168 + 0.854767i) q^{57} +(-3.90130 + 1.67956i) q^{58} +(0.800927 - 5.57057i) q^{59} +(1.15370 + 1.45544i) q^{60} +(-3.75910 - 1.10377i) q^{61} +(-0.755789 + 1.12134i) q^{62} +(1.07311 + 1.23843i) q^{63} +(-2.16477 + 7.70154i) q^{64} +(-1.24846 - 1.08180i) q^{65} +(-5.51121 - 2.66404i) q^{66} +(0.303170 - 0.138453i) q^{67} +(4.18002 - 0.415442i) q^{68} +(-4.72895 - 0.798132i) q^{69} +(-1.44450 + 1.59518i) q^{70} +(-5.73047 + 2.61702i) q^{71} +(-2.65578 - 0.973064i) q^{72} +(10.1145 - 11.6728i) q^{73} +(-6.41699 + 1.73272i) q^{74} +(2.70960 + 3.12704i) q^{75} +(-0.985645 - 3.99546i) q^{76} +(1.99830 - 6.80559i) q^{77} +(2.48177 + 0.412403i) q^{78} +(-2.11824 + 14.7327i) q^{79} +(0.847808 - 3.61642i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.22655 + 1.47969i) q^{82} +(-0.0674326 - 0.104927i) q^{83} +(0.607809 - 3.22050i) q^{84} +(-1.93053 + 0.277568i) q^{85} +(-0.298729 + 13.6579i) q^{86} +(-1.62377 + 2.52664i) q^{87} +(2.67162 + 11.9476i) q^{88} +(-0.577758 - 1.96766i) q^{89} +(1.25167 + 0.397454i) q^{90} +2.91511i q^{91} +(4.62423 + 8.40336i) q^{92} +0.956193i q^{93} +(-3.33044 + 10.4883i) q^{94} +(0.538318 + 1.83334i) q^{95} +(1.77438 + 5.37136i) q^{96} +(7.20490 - 11.2110i) q^{97} +(-6.10049 - 0.133431i) q^{98} +(-4.28437 + 0.615999i) 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 $

$2$	−1.34789	−	0.428007i	−0.953103	−	0.302646i
$2$	−1.34789	−	0.428007i	−0.953103	−	0.302646i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$4$	1.63362	+	1.15381i	0.816810	+	0.576906i
$5$	−0.781202	−	0.502048i	−0.349364	−	0.224523i	0.354175	−	0.935179i	$-0.384762\pi$
$5$	−0.781202	−	0.502048i	−0.349364	−	0.224523i	−0.703539	+	0.710656i	$0.748398\pi$
$6$	1.41388	+	0.0309246i	0.577212	+	0.0126249i
$7$	0.233208	+	1.62200i	0.0881445	+	0.613058i	0.985234	+	0.171210i	$0.0547678\pi$
$7$	0.233208	+	1.62200i	0.0881445	+	0.613058i	−0.897090	+	0.441848i	$0.854323\pi$
$8$	−1.70810	−	2.25441i	−0.603906	−	0.797056i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.838095	+	1.01107i	0.265029	+	0.319727i
$11$	−3.93727	−	1.79809i	−1.18713	−	0.542145i	−0.278782	−	0.960354i	$-0.589931\pi$
$11$	−3.93727	−	1.79809i	−1.18713	−	0.542145i	−0.908351	+	0.418209i	$0.862658\pi$
$12$	−1.89251	−	0.646831i	−0.546322	−	0.186724i
$13$	1.76083	+	0.253170i	0.488367	+	0.0702166i	0.382100	−	0.924121i	$-0.375201\pi$
$13$	1.76083	+	0.253170i	0.488367	+	0.0702166i	0.106267	+	0.994338i	$0.466110\pi$
$14$	0.379887	−	2.28609i	0.101529	−	0.610984i
$15$	0.891001	+	0.261622i	0.230056	+	0.0675504i
$16$	1.33743	+	3.76978i	0.334358	+	0.942446i
$17$	1.58730	−	1.37541i	0.384978	−	0.333585i	−0.440775	−	0.897618i	$-0.645296\pi$
$17$	1.58730	−	1.37541i	0.384978	−	0.333585i	0.825753	+	0.564033i	$0.190751\pi$
$18$	−1.36532	+	0.368663i	−0.321808	+	0.0868947i
$19$	−1.55505	−	1.34746i	−0.356752	−	0.309128i	0.457983	−	0.888961i	$-0.348572\pi$
$19$	−1.55505	−	1.34746i	−0.356752	−	0.309128i	−0.814735	+	0.579834i	$0.803118\pi$
$20$	−0.696918	−	1.72152i	−0.155836	−	0.384943i
$21$	−0.680732	−	1.49059i	−0.148548	−	0.325274i
$22$	4.53742	+	4.10881i	0.967381	+	0.876002i
$23$	4.31254	+	2.09810i	0.899226	+	0.437484i
$23$	4.31254	+	2.09810i	0.899226	+	0.437484i
$24$	2.27405	+	1.68187i	0.464190	+	0.343310i
$25$	−1.71885	−	3.76376i	−0.343770	−	0.752752i
$26$	−2.26505	−	1.09489i	−0.444213	−	0.214726i
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$	−1.49051	+	2.91881i	−0.281680	+	0.551603i
$29$	2.26983	−	1.96682i	0.421497	−	0.365229i	−0.418135	−	0.908385i	$-0.637316\pi$
$29$	2.26983	−	1.96682i	0.421497	−	0.365229i	0.839632	+	0.543156i	$0.182771\pi$
$30$	−1.08900	−	0.733992i	−0.198823	−	0.134008i
$31$	0.269391	−	0.917461i	0.0483840	−	0.164781i	−0.931757	−	0.363082i	$-0.881724\pi$
$31$	0.269391	−	0.917461i	0.0483840	−	0.164781i	0.980141	+	0.198302i	$0.0635425\pi$
$32$	−0.189221	−	5.65369i	−0.0334499	−	0.999440i
$33$	4.28437	+	0.615999i	0.745813	+	0.107232i
$34$	−2.72820	+	1.17452i	−0.467882	+	0.201429i
$35$	0.632139	−	1.38419i	0.106851	−	0.233971i
$36$	1.99809	+	0.0874469i	0.333015	+	0.0145745i
$37$	3.95389	−	2.54101i	0.650016	−	0.417740i	−0.173656	−	0.984806i	$-0.555558\pi$
$37$	3.95389	−	2.54101i	0.650016	−	0.417740i	0.823672	+	0.567066i	$0.191922\pi$
$38$	1.51931	+	2.48179i	0.246465	+	0.402600i
$39$	−1.76083	+	0.253170i	−0.281959	+	0.0405396i
$40$	0.202549	+	2.61870i	0.0320259	+	0.414053i
$41$	−1.14329	−	0.734745i	−0.178551	−	0.114748i	0.448312	−	0.893877i	$-0.352025\pi$
$41$	−1.14329	−	0.734745i	−0.178551	−	0.114748i	−0.626864	+	0.779129i	$0.715662\pi$
$42$	0.279568	+	2.30052i	0.0431383	+	0.354977i
$43$	−2.72152	−	9.26863i	−0.415027	−	1.41345i	−0.856485	−	0.516171i	$-0.827357\pi$
$43$	−2.72152	−	9.26863i	−0.415027	−	1.41345i	0.441458	−	0.897282i	$-0.354461\pi$
$44$	−4.35735	−	7.48028i	−0.656895	−	1.12769i
$45$	−0.928617			−0.138430
$46$	−4.91483	−	4.67381i	−0.724652	−	0.689115i
$47$		−	7.78128i		−	1.13502i	−0.823368	−	0.567508i	$-0.807907\pi$
$47$		−	7.78128i		−	1.13502i	0.823368	−	0.567508i	$-0.192093\pi$
$48$	−2.34533	−	3.24028i	−0.338519	−	0.467695i
$49$	4.13996	−	1.21560i	0.591422	−	0.173657i
$50$	0.705910	+	5.80882i	0.0998308	+	0.821491i
$51$	−1.13551	+	1.76689i	−0.159003	+	0.247414i
$52$	2.58442	+	2.44525i	0.358395	+	0.339096i
$53$	−1.31916	−	9.17495i	−0.181200	−	1.26028i	−0.853930	−	0.520388i	$-0.825787\pi$
$53$	−1.31916	−	9.17495i	−0.181200	−	1.26028i	0.672730	−	0.739888i	$-0.265122\pi$
$54$	1.20615	−	0.738383i	0.164136	−	0.100481i
$55$	2.17308	+	3.38137i	0.293018	+	0.455944i
$56$	3.25831	−	3.29629i	0.435411	−	0.440485i
$57$	1.87168	+	0.854767i	0.247910	+	0.113217i
$58$	−3.90130	+	1.67956i	−0.512265	+	0.220537i
$59$	0.800927	−	5.57057i	0.104272	−	0.725226i	−0.868873	−	0.495034i	$-0.835155\pi$
$59$	0.800927	−	5.57057i	0.104272	−	0.725226i	0.973145	−	0.230192i	$-0.0739354\pi$
$60$	1.15370	+	1.45544i	0.148941	+	0.187896i
$61$	−3.75910	−	1.10377i	−0.481304	−	0.141323i	0.0320755	−	0.999485i	$-0.489788\pi$
$61$	−3.75910	−	1.10377i	−0.481304	−	0.141323i	−0.513379	+	0.858162i	$0.671606\pi$
$62$	−0.755789	+	1.12134i	−0.0959853	+	0.142410i
$63$	1.07311	+	1.23843i	0.135199	+	0.156028i
$64$	−2.16477	+	7.70154i	−0.270596	+	0.962693i
$65$	−1.24846	−	1.08180i	−0.154853	−	0.134181i
$66$	−5.51121	−	2.66404i	−0.678383	−	0.327920i
$67$	0.303170	−	0.138453i	0.0370381	−	0.0169147i	−0.396810	−	0.917901i	$-0.629883\pi$
$67$	0.303170	−	0.138453i	0.0370381	−	0.0169147i	0.433848	+	0.900986i	$0.357155\pi$
$68$	4.18002	−	0.415442i	0.506901	−	0.0503797i
$69$	−4.72895	−	0.798132i	−0.569299	−	0.0960838i
$70$	−1.44450	+	1.59518i	−0.172650	+	0.190660i
$71$	−5.73047	+	2.61702i	−0.680082	+	0.310583i	−0.725338	−	0.688393i	$-0.758317\pi$
$71$	−5.73047	+	2.61702i	−0.680082	+	0.310583i	0.0452568	+	0.998975i	$0.485589\pi$
$72$	−2.65578	−	0.973064i	−0.312986	−	0.114677i
$73$	10.1145	−	11.6728i	1.18381	−	1.36619i	0.268585	−	0.963256i	$-0.413444\pi$
$73$	10.1145	−	11.6728i	1.18381	−	1.36619i	0.915228	−	0.402937i	$-0.132011\pi$
$74$	−6.41699	+	1.73272i	−0.745960	+	0.201424i
$75$	2.70960	+	3.12704i	0.312877	+	0.361080i
$76$	−0.985645	−	3.99546i	−0.113061	−	0.458311i
$77$	1.99830	−	6.80559i	0.227727	−	0.775568i
$78$	2.48177	+	0.412403i	0.281005	+	0.0466955i
$79$	−2.11824	+	14.7327i	−0.238320	+	1.65755i	0.422020	+	0.906586i	$0.361321\pi$
$79$	−2.11824	+	14.7327i	−0.238320	+	1.65755i	−0.660340	+	0.750967i	$0.729588\pi$
$80$	0.847808	−	3.61642i	0.0947878	−	0.404328i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	1.22655	+	1.47969i	0.135450	+	0.163404i
$83$	−0.0674326	−	0.104927i	−0.00740169	−	0.0115173i	0.837533	−	0.546387i	$-0.183997\pi$
$83$	−0.0674326	−	0.104927i	−0.00740169	−	0.0115173i	−0.844935	+	0.534870i	$0.820361\pi$
$84$	0.607809	−	3.22050i	0.0663174	−	0.351386i
$85$	−1.93053	+	0.277568i	−0.209395	+	0.0301065i
$86$	−0.298729	+	13.6579i	−0.0322128	+	1.47277i
$87$	−1.62377	+	2.52664i	−0.174086	+	0.270884i
$88$	2.67162	+	11.9476i	0.284796	+	1.27362i
$89$	−0.577758	−	1.96766i	−0.0612422	−	0.208572i	0.923188	−	0.384349i	$-0.125574\pi$
$89$	−0.577758	−	1.96766i	−0.0612422	−	0.208572i	−0.984430	+	0.175778i	$0.943756\pi$
$90$	1.25167	+	0.397454i	0.131938	+	0.0418953i
$91$			2.91511i			0.305587i
$92$	4.62423	+	8.40336i	0.482110	+	0.876111i
$93$			0.956193i			0.0991526i
$94$	−3.33044	+	10.4883i	−0.343509	+	1.08179i
$95$	0.538318	+	1.83334i	0.0552303	+	0.188097i
$96$	1.77438	+	5.37136i	0.181097	+	0.548213i
$97$	7.20490	−	11.2110i	0.731547	−	1.13831i	−0.253719	−	0.967278i	$-0.581654\pi$
$97$	7.20490	−	11.2110i	0.731547	−	1.13831i	0.985266	−	0.171031i	$-0.0547099\pi$
$98$	−6.10049	−	0.133431i	−0.616243	−	0.0134786i
$99$	−4.28437	+	0.615999i	−0.430595	+	0.0619102i
$100$	1.53472	−	8.13178i	0.153472	−	0.813178i
$101$	3.13824	+	4.88320i	0.312267	+	0.485897i	0.961542	−	0.274656i	$-0.0885641\pi$
$101$	3.13824	+	4.88320i	0.312267	+	0.485897i	−0.649275	+	0.760553i	$0.724928\pi$
$102$	2.28678	−	1.89557i	0.226425	−	0.187689i
$103$	−2.76224	+	6.04846i	−0.272171	+	0.595972i	−0.995524	−	0.0945063i	$-0.969873\pi$
$103$	−2.76224	+	6.04846i	−0.272171	+	0.595972i	0.723353	+	0.690479i	$0.242600\pi$
$104$	−2.43694	−	4.40209i	−0.238961	−	0.431660i
$105$	−0.216561	+	1.50622i	−0.0211342	+	0.146992i
$106$	−2.14886	+	12.9314i	−0.208715	+	1.25601i
$107$	0.0330942	−	0.112709i	0.00319934	−	0.0108960i	−0.957878	−	0.287176i	$-0.907284\pi$
$107$	0.0330942	−	0.112709i	0.00319934	−	0.0108960i	0.961077	+	0.276280i	$0.0891017\pi$
$108$	−1.94179	+	0.479022i	−0.186849	+	0.0460939i
$109$	−5.88694	−	6.79389i	−0.563866	−	0.650736i	0.400191	−	0.916432i	$-0.368944\pi$
$109$	−5.88694	−	6.79389i	−0.563866	−	0.650736i	−0.964057	+	0.265696i	$0.914398\pi$
$110$	−1.48182	−	5.48782i	−0.141286	−	0.523243i
$111$	−3.07785	+	3.55202i	−0.292136	+	0.337143i
$112$	−5.80269	+	3.04846i	−0.548302	+	0.288052i
$113$	−0.571944	+	0.261198i	−0.0538040	+	0.0245714i	−0.442135	−	0.896948i	$-0.645779\pi$
$113$	−0.571944	+	0.261198i	−0.0538040	+	0.0245714i	0.388331	+	0.921520i	$0.373052\pi$
$114$	−2.15697	−	1.95322i	−0.202019	−	0.182936i
$115$	−2.31561	−	3.80414i	−0.215932	−	0.354738i
$116$	5.97738	−	0.594078i	0.554986	−	0.0551587i
$117$	1.61818	−	0.738998i	0.149601	−	0.0683204i
$118$	−3.46380	+	7.16572i	−0.318869	+	0.659658i
$119$	2.60108	+	2.25385i	0.238441	+	0.206610i
$120$	−0.932119	−	2.45556i	−0.0850904	−	0.224161i
$121$	5.06552	+	5.84592i	0.460502	+	0.531447i
$122$	4.59444	+	3.09668i	0.415961	+	0.280361i
$123$	1.30398	+	0.382882i	0.117576	+	0.0345233i
$124$	1.49866	−	1.18796i	0.134584	−	0.106682i
$125$	−1.20760	+	8.39902i	−0.108011	+	0.751232i
$126$	−0.916374	−	2.12857i	−0.0816371	−	0.189628i
$127$	5.04435	+	2.30368i	0.447613	+	0.204418i	0.626452	−	0.779460i	$-0.284507\pi$
$127$	5.04435	+	2.30368i	0.447613	+	0.204418i	−0.178838	+	0.983878i	$0.557234\pi$
$128$	6.21418	−	9.45431i	0.549261	−	0.835651i
$129$	5.22255	+	8.12645i	0.459820	+	0.715494i
$130$	1.21977	+	1.99250i	0.106981	+	0.174754i
$131$	2.83854	+	19.7425i	0.248005	+	1.72491i	0.609716	+	0.792620i	$0.291283\pi$
$131$	2.83854	+	19.7425i	0.248005	+	1.72491i	−0.361712	+	0.932290i	$0.617808\pi$
$132$	6.28828	+	5.94967i	0.547325	+	0.517852i
$133$	1.82292	−	2.83652i	0.158067	−	0.245958i
$134$	−0.467899	+	0.0568609i	−0.0404203	+	0.00491204i
$135$	0.891001	−	0.261622i	0.0766852	−	0.0225168i
$136$	−5.81202	−	1.22910i	−0.498376	−	0.105395i
$137$			17.4309i			1.48922i	0.667499	+	0.744611i	$0.267365\pi$
$137$			17.4309i			1.48922i	−0.667499	+	0.744611i	$0.732635\pi$
$138$	6.03251	+	3.09982i	0.513521	+	0.263874i
$139$	−9.40832			−0.798003			−0.399002	−	0.916950i	$-0.630643\pi$
$139$	−9.40832			−0.798003			−0.399002	+	0.916950i	$0.630643\pi$
$140$	2.62977	−	1.53187i	0.222256	−	0.129467i
$141$	2.19224	+	7.46609i	0.184620	+	0.628758i
$142$	8.84415	−	1.07478i	0.742184	−	0.0901932i
$143$	−6.47766	−	4.16294i	−0.541689	−	0.348122i
$144$	3.16322	+	2.44827i	0.263602	+	0.204023i
$145$	−2.76064	+	0.396919i	−0.229258	+	0.0329624i
$146$	−18.6293	+	11.4045i	−1.54177	+	0.943846i
$147$	−3.62978	+	2.33272i	−0.299380	+	0.192400i
$148$	9.39101	+	0.411001i	0.771937	+	0.0337841i
$149$	−5.76815	+	12.6305i	−0.472545	+	1.03473i	0.511901	+	0.859044i	$0.328941\pi$
$149$	−5.76815	+	12.6305i	−0.472545	+	1.03473i	−0.984446	+	0.175685i	$0.943786\pi$
$150$	−2.31385	−	5.37464i	−0.188925	−	0.438837i
$151$	9.28280	+	1.33467i	0.755424	+	0.108614i	0.509258	−	0.860614i	$-0.329920\pi$
$151$	9.28280	+	1.33467i	0.755424	+	0.108614i	0.246166	+	0.969228i	$0.420829\pi$
$152$	−0.381543	+	5.80731i	−0.0309472	+	0.471035i
$153$	0.591724	−	2.01523i	0.0478381	−	0.162922i
$154$	−5.60633	+	8.31790i	−0.451771	+	0.670276i
$155$	−0.671058	+	0.581475i	−0.0539007	+	0.0467052i
$156$	−3.16864	−	1.61809i	−0.253694	−	0.129551i
$157$	7.00413	−	8.08320i	0.558990	−	0.645109i	−0.403964	−	0.914775i	$-0.632368\pi$
$157$	7.00413	−	8.08320i	0.558990	−	0.645109i	0.962954	+	0.269666i	$0.0869132\pi$
$158$	9.16082	−	18.9514i	0.728796	−	1.50769i
$159$	3.85060	+	8.43165i	0.305373	+	0.668673i
$160$	−2.69060	+	4.51167i	−0.212711	+	0.356679i
$161$	−2.39740	+	7.48423i	−0.188942	+	0.589840i
$162$	−0.949263	+	1.04828i	−0.0745811	+	0.0823610i
$163$	1.33191	+	2.91647i	0.104323	+	0.228435i	0.954594	−	0.297910i	$-0.0962894\pi$
$163$	1.33191	+	2.91647i	0.104323	+	0.228435i	−0.850271	+	0.526345i	$0.823562\pi$
$164$	−1.01994	−	2.51943i	−0.0796437	−	0.196735i
$165$	−3.03770	−	2.63218i	−0.236484	−	0.204915i
$166$	0.0459823	+	0.170292i	0.00356892	+	0.0132172i
$167$	1.03699	−	0.898554i	0.0802445	−	0.0695322i	−0.613815	−	0.789450i	$-0.710366\pi$
$167$	1.03699	−	0.898554i	0.0802445	−	0.0695322i	0.694059	+	0.719918i	$0.255820\pi$
$168$	−2.19766	+	4.08074i	−0.169553	+	0.314836i
$169$	−9.43697	−	2.77094i	−0.725921	−	0.213150i
$170$	2.72094	+	0.452147i	0.208687	+	0.0346781i
$171$	−2.03668	−	0.292830i	−0.155749	−	0.0223933i
$172$	6.24834	−	18.2815i	0.476431	−	1.39395i
$173$	15.6615	+	7.15237i	1.19072	+	0.543785i	0.909438	−	0.415840i	$-0.136512\pi$
$173$	15.6615	+	7.15237i	1.19072	+	0.543785i	0.281284	+	0.959624i	$0.409240\pi$
$174$	3.27008	−	2.71064i	0.247904	−	0.205493i
$175$	5.70396	−	3.66571i	0.431179	−	0.277102i
$176$	1.51258	−	17.2475i	0.114015	−	1.30008i
$177$	0.800927	+	5.57057i	0.0602014	+	0.418710i
$178$	−0.0634180	+	2.89948i	−0.00475338	+	0.217325i
$179$	2.84354	+	1.82743i	0.212536	+	0.136589i	0.642578	−	0.766220i	$-0.277865\pi$
$179$	2.84354	+	1.82743i	0.212536	+	0.136589i	−0.430042	+	0.902809i	$0.641501\pi$
$180$	−1.51701	−	1.07145i	−0.113071	−	0.0798611i
$181$	−17.7231	+	5.20397i	−1.31735	+	0.386808i	−0.863535	−	0.504290i	$-0.831754\pi$
$181$	−17.7231	+	5.20397i	−1.31735	+	0.386808i	−0.453812	+	0.891098i	$0.649936\pi$
$182$	1.24769	−	3.92925i	0.0924847	−	0.291256i
$183$	3.91780			0.289612
$184$	−2.63627	−	13.3060i	−0.194348	−	0.980933i
$185$	−4.36450			−0.320884
$186$	0.409257	−	1.28884i	0.0300082	−	0.0945027i
$187$	−8.72276	+	2.56123i	−0.637872	+	0.187296i
$188$	8.97814	−	12.7117i	0.654798	−	0.927094i
$189$	−1.37854	−	0.885937i	−0.100274	−	0.0644424i
$190$	0.0590888	−	2.70155i	0.00428675	−	0.195991i
$191$	−2.71948	−	18.9144i	−0.196774	−	1.36860i	−0.813567	−	0.581471i	$-0.802478\pi$
$191$	−2.71948	−	18.9144i	−0.196774	−	1.36860i	0.616793	−	0.787125i	$-0.288432\pi$
$192$	−0.0926974	−	7.99946i	−0.00668986	−	0.577312i
$193$	10.2126	−	6.56326i	0.735122	−	0.472434i	−0.118746	−	0.992925i	$-0.537887\pi$
$193$	10.2126	−	6.56326i	0.735122	−	0.472434i	0.853867	+	0.520491i	$0.174251\pi$
$194$	−14.5098	+	12.0275i	−1.04174	+	0.863526i
$195$	1.50267	+	0.686246i	0.107608	+	0.0491431i
$196$	8.16569	+	2.79090i	0.583264	+	0.199350i
$197$	−4.93533	−	0.709594i	−0.351628	−	0.0505565i	−0.0357621	−	0.999360i	$-0.511386\pi$
$197$	−4.93533	−	0.709594i	−0.351628	−	0.0505565i	−0.315866	+	0.948804i	$0.602295\pi$
$198$	6.03851	+	1.00344i	0.429138	+	0.0713112i
$199$	−20.0409	−	5.88455i	−1.42066	−	0.417145i	−0.520936	−	0.853596i	$-0.674417\pi$
$199$	−20.0409	−	5.88455i	−1.42066	−	0.417145i	−0.899728	+	0.436451i	$0.856235\pi$
$200$	−5.54909	+	10.3039i	−0.392380	+	0.728595i
$201$	−0.251883	+	0.218258i	−0.0177664	+	0.0153947i
$202$	−2.13997	−	7.92522i	−0.150568	−	0.557616i
$203$	3.71952	+	3.22299i	0.261059	+	0.226209i
$204$	−3.89365	+	1.57626i	−0.272610	+	0.110360i
$205$	0.524260	+	1.14797i	0.0366159	+	0.0801776i
$206$	6.31198	−	6.97041i	0.439776	−	0.485651i
$207$	4.76226	−	0.566498i	0.331000	−	0.0393743i
$208$	1.40060	+	6.97656i	0.0971142	+	0.483737i
$209$	3.69979	+	8.10142i	0.255920	+	0.560387i
$210$	0.936571	−	1.93753i	0.0646295	−	0.133702i
$211$	6.28941	−	7.25836i	0.432981	−	0.499686i	−0.496767	−	0.867884i	$-0.665480\pi$
$211$	6.28941	−	7.25836i	0.432981	−	0.499686i	0.929748	+	0.368198i	$0.120025\pi$
$212$	8.43116	−	16.5104i	0.579055	−	1.13394i
$213$	4.76105	−	4.12547i	0.326221	−	0.282673i
$214$	−0.0928474	+	0.137754i	−0.00634692	+	0.00941669i
$215$	−2.52724	+	8.60701i	−0.172357	+	0.586993i
$216$	2.82234	+	0.185429i	0.192036	+	0.0126168i
$217$	1.55095	+	0.222992i	0.105285	+	0.0151377i
$218$	5.02712	+	11.6771i	0.340480	+	0.790871i
$219$	−6.41620	+	14.0495i	−0.433566	+	0.949378i
$220$	−0.351488	+	8.03121i	−0.0236973	+	0.541464i
$221$	3.14319	−	2.02000i	0.211434	−	0.135880i
$222$	5.66889	−	3.47040i	0.380471	−	0.232918i
$223$	2.43565	−	0.350194i	0.163103	−	0.0234507i	−0.0602793	−	0.998182i	$-0.519199\pi$
$223$	2.43565	−	0.350194i	0.163103	−	0.0234507i	0.223383	+	0.974731i	$0.428290\pi$
$224$	9.12615	−	1.62540i	0.609767	−	0.108602i
$225$	−3.48083	−	2.23699i	−0.232055	−	0.149133i
$226$	0.882713	−	0.107271i	0.0587172	−	0.00713554i
$227$	−6.34212	−	21.5993i	−0.420941	−	1.43359i	−0.848302	−	0.529513i	$-0.822375\pi$
$227$	−6.34212	−	21.5993i	−0.420941	−	1.43359i	0.427360	−	0.904081i	$-0.359444\pi$
$228$	2.07137	+	3.55593i	0.137180	+	0.235497i
$229$	3.87362			0.255976			0.127988	−	0.991776i	$-0.459148\pi$
$229$	3.87362			0.255976			0.127988	+	0.991776i	$0.459148\pi$
$230$	1.49300	+	6.11867i	0.0984454	+	0.403453i
$231$			7.09290i			0.466678i
$232$	−8.31113	−	1.75761i	−0.545653	−	0.115393i
$233$	−20.0134	+	5.87646i	−1.31112	+	0.384979i	−0.861280	−	0.508130i	$-0.830337\pi$
$233$	−20.0134	+	5.87646i	−1.31112	+	0.384979i	−0.449839	+	0.893109i	$0.648519\pi$
$234$	−2.49743	+	0.303497i	−0.163262	+	0.0198402i
$235$	−3.90658	+	6.07876i	−0.254837	+	0.396534i
$236$	7.73580	−	8.17608i	0.503558	−	0.532217i
$237$	−2.11824	−	14.7327i	−0.137594	−	0.956989i
$238$	−2.54131	−	4.15123i	−0.164729	−	0.269084i
$239$	−13.4708	−	20.9609i	−0.871351	−	1.35585i	−0.933798	−	0.357800i	$-0.883527\pi$
$239$	−13.4708	−	20.9609i	−0.871351	−	1.35585i	0.0624478	−	0.998048i	$-0.480109\pi$
$240$	0.205397	+	3.70878i	0.0132584	+	0.239401i
$241$	−8.57429	−	3.91575i	−0.552318	−	0.252235i	0.119649	−	0.992816i	$-0.461823\pi$
$241$	−8.57429	−	3.91575i	−0.552318	−	0.252235i	−0.671967	+	0.740581i	$0.734550\pi$
$242$	−4.32568	−	10.0477i	−0.278065	−	0.645893i
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$	−4.86740	−	6.14044i	−0.311603	−	0.393102i
$245$	−3.84443	−	1.12883i	−0.245612	−	0.0721181i
$246$	−1.59374	−	1.07419i	−0.101613	−	0.0684881i
$247$	−2.39704	−	2.76633i	−0.152520	−	0.176018i
$248$	−2.52848	+	0.959799i	−0.160559	+	0.0609473i
$249$	0.0942625	+	0.0816789i	0.00597364	+	0.00517619i
$250$	5.22255	−	10.8041i	0.330303	−	0.683312i
$251$	11.8998	−	5.43445i	0.751108	−	0.343020i	−0.00280288	−	0.999996i	$-0.500892\pi$
$251$	11.8998	−	5.43445i	0.751108	−	0.343020i	0.753911	+	0.656976i	$0.228165\pi$
$252$	0.324132	+	3.26129i	0.0204184	+	0.205442i
$253$	−13.2071	−	16.0151i	−0.830320	−	1.00686i
$254$	−5.81324	−	5.26412i	−0.364755	−	0.330300i
$255$	1.77413	−	0.810216i	0.111100	−	0.0507377i
$256$	−12.4225	+	10.0837i	−0.776409	+	0.630229i
$257$	−5.97406	+	6.89443i	−0.372652	+	0.430063i	−0.910839	−	0.412763i	$-0.864564\pi$
$257$	−5.97406	+	6.89443i	−0.372652	+	0.430063i	0.538187	+	0.842825i	$0.319109\pi$
$258$	−3.56126	−	13.1889i	−0.221714	−	0.821102i
$259$	5.04360	+	5.82063i	0.313394	+	0.361676i
$260$	−0.791321	−	3.20774i	−0.0490757	−	0.198936i
$261$	0.846160	−	2.88176i	0.0523760	−	0.178376i
$262$	4.62387	−	27.8256i	0.285664	−	1.71907i
$263$	−0.696390	+	4.84350i	−0.0429413	+	0.298663i	0.957021	+	0.290017i	$0.0936611\pi$
$263$	−0.696390	+	4.84350i	−0.0429413	+	0.298663i	−0.999963	+	0.00864566i	$0.997248\pi$
$264$	−5.92943	−	10.7109i	−0.364931	−	0.659212i
$265$	−3.57574	+	7.82977i	−0.219656	+	0.480979i
$266$	−3.67115	+	3.04310i	−0.225093	+	0.186584i
$267$	1.10871	+	1.72519i	0.0678519	+	0.105580i
$268$	0.655014	+	0.123622i	0.0400113	+	0.00755139i
$269$	−11.6294	+	1.67206i	−0.709057	+	0.101947i	−0.487402	−	0.873178i	$-0.662055\pi$
$269$	−11.6294	+	1.67206i	−0.709057	+	0.101947i	−0.221656	+	0.975125i	$0.571146\pi$
$270$	−1.31295	−	0.0287171i	−0.0799035	−	0.00174766i
$271$	17.1135	−	26.6291i	1.03957	−	1.61760i	0.288386	−	0.957514i	$-0.406882\pi$
$271$	17.1135	−	26.6291i	1.03957	−	1.61760i	0.751186	−	0.660091i	$-0.229482\pi$
$272$	7.30790	+	4.14428i	0.443107	+	0.251284i
$273$	−0.821282	−	2.79703i	−0.0497062	−	0.169284i
$274$	7.46054	−	23.4949i	0.450707	−	1.41938i
$275$			17.9096i			1.07999i
$276$	−6.80442	−	6.76017i	−0.409578	−	0.406914i
$277$			7.39171i			0.444125i	0.975032	+	0.222062i	$0.0712788\pi$
$277$			7.39171i			0.444125i	−0.975032	+	0.222062i	$0.928721\pi$
$278$	12.6814	+	4.02682i	0.760579	+	0.241513i
$279$	−0.269391	−	0.917461i	−0.0161280	−	0.0549269i
$280$	−4.20030	+	0.939238i	−0.251016	+	0.0561302i
$281$	2.60452	−	4.05271i	0.155372	−	0.241764i	−0.754837	−	0.655912i	$-0.772284\pi$
$281$	2.60452	−	4.05271i	0.155372	−	0.241764i	0.910209	+	0.414148i	$0.135920\pi$
$282$	0.240633	−	11.0018i	0.0143295	−	0.655146i
$283$	−12.2273	+	1.75802i	−0.726838	+	0.104504i	−0.495795	−	0.868440i	$-0.665123\pi$
$283$	−12.2273	+	1.75802i	−0.726838	+	0.104504i	−0.231044	+	0.972943i	$0.574214\pi$
$284$	−12.3810	−	2.33667i	−0.734675	−	0.138656i
$285$	−1.03302	−	1.60742i	−0.0611911	−	0.0952152i
$286$	6.94941	+	8.38367i	0.410927	+	0.495737i
$287$	0.925133	−	2.02576i	0.0546088	−	0.119577i
$288$	−3.21580	−	4.65388i	−0.189493	−	0.274233i
$289$	−1.79156	+	12.4606i	−0.105386	+	0.732976i
$290$	3.89092	+	0.646566i	0.228483	+	0.0379677i
$291$	−3.75454	+	12.7868i	−0.220095	+	0.749574i
$292$	29.9914	−	7.39862i	1.75512	−	0.432971i
$293$	18.9359	+	21.8532i	1.10625	+	1.27668i	0.957699	+	0.287773i	$0.0929147\pi$
$293$	18.9359	+	21.8532i	1.10625	+	1.27668i	0.148549	+	0.988905i	$0.452540\pi$
$294$	5.89097	−	1.59068i	0.343569	−	0.0927704i
$295$	−3.42238	+	3.94964i	−0.199259	+	0.229957i
$296$	−12.4822	−	4.57340i	−0.725510	−	0.265823i
$297$	3.93727	−	1.79809i	0.228464	−	0.104336i
$298$	13.1808	−	14.5557i	0.763542	−	0.843190i
$299$	7.06248	+	4.78621i	0.408434	+	0.276794i
$300$	0.818434	+	8.23477i	0.0472523	+	0.475435i
$301$	14.3990	−	6.57582i	0.829946	−	0.379024i
$302$	−11.9410	−	5.77209i	−0.687125	−	0.332146i
$303$	−4.38688	−	3.80125i	−0.252020	−	0.218376i
$304$	2.99985	−	7.66432i	0.172053	−	0.439579i
$305$	2.38247	+	2.74952i	0.136420	+	0.157437i
$306$	−1.66011	+	2.46305i	−0.0949022	+	0.140803i
$307$	−20.1071	−	5.90399i	−1.14757	−	0.336958i	−0.347982	−	0.937501i	$-0.613133\pi$
$307$	−20.1071	−	5.90399i	−1.14757	−	0.336958i	−0.799592	+	0.600543i	$0.794951\pi$
$308$	11.1168	−	8.81208i	0.633440	−	0.502115i
$309$	0.946301	−	6.58166i	0.0538332	−	0.374418i
$310$	1.15339	−	0.496548i	0.0655081	−	0.0282020i
$311$	26.9571	+	12.3109i	1.52860	+	0.698087i	0.989550	−	0.144189i	$-0.0460574\pi$
$311$	26.9571	+	12.3109i	1.52860	+	0.698087i	0.539046	+	0.842276i	$0.318785\pi$
$312$	3.57843	+	3.53721i	0.202589	+	0.200255i
$313$	6.62078	+	10.3021i	0.374229	+	0.582311i	0.976377	−	0.216073i	$-0.0693249\pi$
$313$	6.62078	+	10.3021i	0.374229	+	0.582311i	−0.602149	+	0.798384i	$0.705689\pi$
$314$	−12.9005	+	7.89745i	−0.728015	+	0.445679i
$315$	−0.216561	−	1.50622i	−0.0122018	−	0.0848656i
$316$	−20.4591	+	21.6235i	−1.15092	+	1.21642i
$317$	4.88263	−	7.59751i	0.274236	−	0.426719i	−0.676630	−	0.736323i	$-0.736560\pi$
$317$	4.88263	−	7.59751i	0.274236	−	0.426719i	0.950865	+	0.309604i	$0.100197\pi$
$318$	−1.58139	−	13.0130i	−0.0886802	−	0.729734i
$319$	−12.4735	+	3.66254i	−0.698380	+	0.205063i
$320$	5.55767	−	4.92965i	0.310683	−	0.275576i
$321$			0.117467i			0.00655636i
$322$	6.43473	−	9.06182i	0.358594	−	0.504995i
$323$	−4.32163			−0.240462
$324$	1.72818	−	1.00668i	0.0960097	−	0.0559268i
$325$	−2.07374	−	7.06251i	−0.115030	−	0.391758i
$326$	−0.546997	−	4.50114i	−0.0302953	−	0.249295i
$327$	7.56253	+	4.86014i	0.418209	+	0.268767i
$328$	0.296430	+	3.83246i	0.0163676	+	0.211612i
$329$	12.6212	−	1.81466i	0.695831	−	0.100045i
$330$	2.96789	+	4.84804i	0.163377	+	0.266876i
$331$	26.0789	−	16.7599i	1.43342	−	0.921206i	0.433627	−	0.901093i	$-0.357234\pi$
$331$	26.0789	−	16.7599i	1.43342	−	0.921206i	0.999798	−	0.0201134i	$-0.00640271\pi$
$332$	0.0109070	−	0.249216i	0.000598600	−	0.0136775i
$333$	1.95245	−	4.27527i	0.106994	−	0.234283i
$334$	−1.78233	+	0.767316i	−0.0975249	+	0.0419857i
$335$	−0.306347	−	0.0440461i	−0.0167375	−	0.00240649i
$336$	4.70879	−	4.55978i	0.256885	−	0.248757i
$337$	1.25903	−	4.28785i	0.0685835	−	0.233574i	−0.918067	−	0.396425i	$-0.870251\pi$
$337$	1.25903	−	4.28785i	0.0685835	−	0.233574i	0.986651	+	0.162851i	$0.0520689\pi$
$338$	11.5340	+	7.77402i	0.627368	+	0.422851i
$339$	0.475188	−	0.411753i	0.0258087	−	0.0223633i
$340$	−3.47401	−	1.77403i	−0.188405	−	0.0962100i
$341$	−2.71035	+	3.12791i	−0.146773	+	0.169386i
$342$	2.61989	+	1.26641i	0.141667	+	0.0684799i
$343$	7.70230	+	16.8657i	0.415885	+	0.910661i
$344$	−16.2467	+	21.9672i	−0.875963	+	1.18439i
$345$	3.29357	+	2.99766i	0.177320	+	0.161389i
$346$	−18.0487	−	16.3438i	−0.970307	−	0.878651i
$347$	8.02830	+	17.5795i	0.430982	+	0.943718i	0.993166	+	0.116706i	$0.0372337\pi$
$347$	8.02830	+	17.5795i	0.430982	+	0.943718i	−0.562185	+	0.827012i	$0.690039\pi$
$348$	−5.56789	+	2.25404i	−0.298470	+	0.120829i
$349$	−5.99409	−	5.19391i	−0.320856	−	0.278023i	0.479508	−	0.877537i	$-0.340815\pi$
$349$	−5.99409	−	5.19391i	−0.320856	−	0.278023i	−0.800364	+	0.599514i	$0.795361\pi$
$350$	−9.25727	+	2.49965i	−0.494822	+	0.133612i
$351$	−1.34443	+	1.16496i	−0.0717605	+	0.0621809i
$352$	−9.42084	+	22.6004i	−0.502133	+	1.20460i
$353$	−28.8624	−	8.47475i	−1.53619	−	0.451066i	−0.599251	−	0.800562i	$-0.704535\pi$
$353$	−28.8624	−	8.47475i	−1.53619	−	0.451066i	−0.936938	+	0.349496i	$0.886353\pi$
$354$	1.30468	−	7.85132i	0.0693429	−	0.417293i
$355$	5.79052	+	0.832552i	0.307329	+	0.0441872i
$356$	1.32648	−	3.88104i	0.0703032	−	0.205695i
$357$	−3.13070	−	1.42974i	−0.165694	−	0.0756701i
$358$	−3.05063	−	3.68023i	−0.161231	−	0.194506i
$359$	−9.90220	+	6.36375i	−0.522618	+	0.335866i	−0.775207	−	0.631708i	$-0.782354\pi$
$359$	−9.90220	+	6.36375i	−0.522618	+	0.335866i	0.252589	+	0.967574i	$0.418718\pi$
$360$	1.58617	+	2.09349i	0.0835987	+	0.110336i
$361$	−2.10145	−	14.6159i	−0.110603	−	0.769258i
$362$	26.1161	+	0.571217i	1.37263	+	0.0300225i
$363$	−6.50732	−	4.18200i	−0.341546	−	0.219498i
$364$	−3.36349	+	4.76219i	−0.176295	+	0.249606i
$365$	−13.7618	+	4.04082i	−0.720323	+	0.211506i
$366$	−5.28077	−	1.67684i	−0.276030	−	0.0876500i
$367$	6.99972			0.365382			0.182691	−	0.983170i	$-0.441519\pi$
$367$	6.99972			0.365382			0.182691	+	0.983170i	$0.441519\pi$
$368$	−2.14166	+	19.0634i	−0.111642	+	0.993749i
$369$	−1.35903			−0.0707481
$370$	5.88287	+	1.86803i	0.305836	+	0.0971145i
$371$	14.5741	−	4.27935i	0.756651	−	0.222173i
$372$	−1.10327	+	1.56206i	−0.0572018	+	0.0809889i
$373$	23.5499	+	15.1346i	1.21937	+	0.783640i	0.982202	−	0.187829i	$-0.0601451\pi$
$373$	23.5499	+	15.1346i	1.21937	+	0.783640i	0.237166	+	0.971469i	$0.423781\pi$
$374$	12.8536	+	0.281135i	0.664642	+	0.0145372i
$375$	−1.20760	−	8.39902i	−0.0623601	−	0.433724i
$376$	−17.5422	+	13.2912i	−0.904672	+	0.685443i
$377$	4.49473	−	2.88859i	0.231490	−	0.148770i
$378$	1.47894	+	1.78417i	0.0760685	+	0.0917679i
$379$	−15.3579	−	7.01371i	−0.788881	−	0.360270i	−0.0201132	−	0.999798i	$-0.506403\pi$
$379$	−15.3579	−	7.01371i	−0.788881	−	0.360270i	−0.768768	+	0.639528i	$0.779130\pi$
$380$	−1.23593	+	3.61611i	−0.0634017	+	0.185502i
$381$	−5.48904	−	0.789204i	−0.281212	−	0.0404322i
$382$	−4.42992	+	26.6585i	−0.226654	+	1.36397i
$383$	4.53433	+	1.33140i	0.231693	+	0.0680313i	0.395518	−	0.918458i	$-0.370565\pi$
$383$	4.53433	+	1.33140i	0.231693	+	0.0680313i	−0.163825	+	0.986489i	$0.552383\pi$
$384$	−3.29888	+	10.8221i	−0.168345	+	0.552262i
$385$	−4.97781	+	4.31330i	−0.253693	+	0.219826i
$386$	−16.5746	+	4.47549i	−0.843627	+	0.227796i
$387$	−7.30048	−	6.32591i	−0.371104	−	0.321564i
$388$	24.7055	−	10.0015i	1.25423	−	0.507749i
$389$	11.8242	+	25.8915i	0.599513	+	1.31275i	0.929520	+	0.368772i	$0.120222\pi$
$389$	11.8242	+	25.8915i	0.599513	+	1.31275i	−0.330007	+	0.943978i	$0.607051\pi$
$390$	−1.73172	−	1.56814i	−0.0876889	−	0.0794057i
$391$	9.73105	−	2.60117i	0.492120	−	0.131547i
$392$	−9.81194	−	7.25680i	−0.495578	−	0.366524i
$393$	−8.28566	−	18.1431i	−0.417956	−	0.915197i
$394$	6.34858	+	3.06881i	0.319837	+	0.154604i
$395$	9.05127	−	10.4457i	0.455419	−	0.525581i
$396$	−7.70978	−	3.93705i	−0.387431	−	0.197844i
$397$	8.94099	−	7.74741i	0.448735	−	0.388831i	−0.400968	−	0.916092i	$-0.631326\pi$
$397$	8.94099	−	7.74741i	0.448735	−	0.388831i	0.849704	+	0.527261i	$0.176781\pi$
$398$	24.4944	+	16.5094i	1.22779	+	0.827541i
$399$	−0.949940	+	3.23520i	−0.0475565	+	0.161963i
$400$	11.8897	−	11.5135i	0.594485	−	0.575673i
$401$	2.29297	+	0.329679i	0.114505	+	0.0164634i	0.199329	−	0.979933i	$-0.436124\pi$
$401$	2.29297	+	0.329679i	0.114505	+	0.0164634i	−0.0848239	+	0.996396i	$0.527033\pi$
$402$	0.432926	−	0.186380i	0.0215924	−	0.00929579i
$403$	0.706625	−	1.54729i	0.0351995	−	0.0770762i
$404$	−0.507601	+	11.5983i	−0.0252541	+	0.577035i
$405$	−0.781202	+	0.502048i	−0.0388182	+	0.0249470i
$406$	−3.63405	−	5.93621i	−0.180355	−	0.294609i
$407$	−20.1365	+	2.89520i	−0.998131	+	0.143510i
$408$	5.92287	−	0.458118i	0.293226	−	0.0226802i
$409$	−8.84886	−	5.68682i	−0.437548	−	0.281195i	0.303265	−	0.952906i	$-0.401923\pi$
$409$	−8.84886	−	5.68682i	−0.437548	−	0.281195i	−0.740813	+	0.671711i	$0.765560\pi$
$410$	−0.215307	−	1.77172i	−0.0106332	−	0.0874992i
$411$	−4.91085	−	16.7248i	−0.242234	−	0.824974i
$412$	−11.4912	+	6.69378i	−0.566133	+	0.329779i
$413$	9.22224			0.453797
$414$	−6.66147	−	1.27470i	−0.327393	−	0.0626481i
$415$			0.115824i			0.00568556i
$416$	1.09815	−	10.0031i	0.0538415	−	0.490443i
$417$	9.02722	−	2.65063i	0.442065	−	0.129802i
$418$	−1.51946	−	12.5034i	−0.0743191	−	0.611560i
$419$	14.8971	−	23.1804i	0.727772	−	1.13244i	−0.258291	−	0.966067i	$-0.583159\pi$
$419$	14.8971	−	23.1804i	0.727772	−	1.13244i	0.986064	−	0.166369i	$-0.0532042\pi$
$420$	−2.09167	+	2.21071i	−0.102063	+	0.107872i
$421$	4.09291	+	28.4668i	0.199476	+	1.38739i	0.805809	+	0.592175i	$0.201731\pi$
$421$	4.09291	+	28.4668i	0.199476	+	1.38739i	−0.606333	+	0.795211i	$0.707360\pi$
$422$	−11.5841	+	7.09157i	−0.563903	+	0.345212i
$423$	−4.20688	−	6.54603i	−0.204545	−	0.318279i
$424$	−18.4309	+	18.6457i	−0.895082	+	0.905514i
$425$	−7.90504	−	3.61011i	−0.383451	−	0.175116i
$426$	−8.18310	+	3.52292i	−0.396472	+	0.170686i
$427$	0.913663	−	6.35467i	0.0442153	−	0.307524i
$428$	0.184108	−	0.145939i	0.00889920	−	0.00705421i
$429$	7.38810	+	2.16934i	0.356701	+	0.104737i
$430$	7.09031	−	10.5196i	0.341925	−	0.507301i
$431$	−20.2197	−	23.3348i	−0.973949	−	1.12400i	−0.992262	−	0.124165i	$-0.960375\pi$
$431$	−20.2197	−	23.3348i	−0.973949	−	1.12400i	0.0183121	−	0.999832i	$-0.494171\pi$
$432$	−3.72485	−	1.45792i	−0.179212	−	0.0701442i
$433$	−8.30635	−	7.19750i	−0.399178	−	0.345890i	0.432022	−	0.901863i	$-0.357800\pi$
$433$	−8.30635	−	7.19750i	−0.399178	−	0.345890i	−0.831200	+	0.555973i	$0.812346\pi$
$434$	−1.99506	−	0.964384i	−0.0957661	−	0.0462919i
$435$	2.53698	−	1.15860i	0.121639	−	0.0555507i
$436$	−1.77815	−	17.8911i	−0.0851579	−	0.856826i
$437$	−3.87910	−	9.07360i	−0.185562	−	0.434049i
$438$	14.6616	−	16.1910i	0.700559	−	0.773638i
$439$	−16.0240	+	7.31793i	−0.764785	+	0.349266i	−0.759318	−	0.650720i	$-0.774467\pi$
$439$	−16.0240	+	7.31793i	−0.764785	+	0.349266i	−0.00546667	+	0.999985i	$0.501740\pi$
$440$	3.91118	−	10.6748i	0.186458	−	0.508899i
$441$	2.82555	−	3.26086i	0.134550	−	0.155279i
$442$	−5.10125	+	1.37744i	−0.242642	+	0.0655182i
$443$	−1.14890	−	1.32590i	−0.0545860	−	0.0629956i	0.727800	−	0.685790i	$-0.240543\pi$
$443$	−1.14890	−	1.32590i	−0.0545860	−	0.0629956i	−0.782386	+	0.622794i	$0.785997\pi$
$444$	−9.12640	+	2.25140i	−0.433120	+	0.106847i
$445$	−0.536516	+	1.82721i	−0.0254333	+	0.0866178i
$446$	−3.43288	−	0.570452i	−0.162552	−	0.0270117i
$447$	1.97608	−	13.7439i	0.0934654	−	0.650066i
$448$	−12.9967	−	1.71519i	−0.614038	−	0.0810349i
$449$	−7.66364	+	16.7810i	−0.361669	+	0.791946i	0.638089	+	0.769963i	$0.279725\pi$
$449$	−7.66364	+	16.7810i	−0.361669	+	0.791946i	−0.999758	+	0.0219829i	$0.993002\pi$
$450$	3.73433	+	4.50504i	0.176038	+	0.212370i
$451$	3.18029	+	4.94863i	0.149754	+	0.233022i
$452$	−1.23571	−	0.233218i	−0.0581230	−	0.0109696i
$453$	−9.28280	+	1.33467i	−0.436144	+	0.0627081i
$454$	−0.696147	+	31.8280i	−0.0326718	+	1.49376i
$455$	1.46353	−	2.27729i	0.0686112	−	0.106761i
$456$	−1.27002	−	5.67957i	−0.0594742	−	0.265970i
$457$	3.04902	+	10.3840i	0.142627	+	0.485743i	0.999559	−	0.0296862i	$-0.00945080\pi$
$457$	3.04902	+	10.3840i	0.142627	+	0.485743i	−0.856932	+	0.515429i	$0.827633\pi$
$458$	−5.22121	−	1.65793i	−0.243971	−	0.0774702i
$459$			2.10030i			0.0980338i
$460$	0.606431	−	8.88631i	0.0282750	−	0.414326i
$461$			21.1598i			0.985512i	0.870168	+	0.492756i	$0.164010\pi$
$461$			21.1598i			0.985512i	−0.870168	+	0.492756i	$0.835990\pi$
$462$	3.03581	−	9.56045i	0.141239	−	0.444793i
$463$	−9.60865	−	32.7241i	−0.446552	−	1.52082i	−0.808431	−	0.588591i	$-0.799683\pi$
$463$	−9.60865	−	32.7241i	−0.446552	−	1.52082i	0.361879	−	0.932225i	$-0.382135\pi$
$464$	10.4502	+	5.92628i	0.485140	+	0.275121i
$465$	0.480055	−	0.746980i	0.0222620	−	0.0346404i
$466$	29.4910	+	0.645033i	1.36614	+	0.0298806i
$467$	21.5307	−	3.09565i	0.996324	−	0.143250i	0.375185	−	0.926950i	$-0.377579\pi$
$467$	21.5307	−	3.09565i	0.996324	−	0.143250i	0.621139	+	0.783700i	$0.286670\pi$
$468$	3.49616	+	0.659834i	0.161610	+	0.0305009i
$469$	0.295273	+	0.459453i	0.0136344	+	0.0212156i
$470$	7.86739	−	6.52146i	0.362896	−	0.300812i
$471$	−4.44311	+	9.72906i	−0.204728	+	0.448291i
$472$	−13.9264	+	7.70949i	−0.641016	+	0.354858i
$473$	−5.95051	+	41.3867i	−0.273605	+	1.90296i
$474$	−3.45052	+	20.7646i	−0.158488	+	0.953751i
$475$	−2.39860	+	8.16889i	−0.110055	+	0.374815i
$476$	1.64866	+	6.68310i	0.0755662	+	0.306319i
$477$	−6.07010	−	7.00527i	−0.277931	−	0.320749i
$478$	9.18570	+	34.0186i	0.420144	+	1.55597i
$479$	10.1418	−	11.7043i	0.463391	−	0.534781i	−0.475171	−	0.879894i	$-0.657614\pi$
$479$	10.1418	−	11.7043i	0.463391	−	0.534781i	0.938561	+	0.345112i	$0.112159\pi$
$480$	1.31053	−	5.08695i	0.0598173	−	0.232186i
$481$	7.60545	−	3.47329i	0.346779	−	0.158369i
$482$	9.88124	+	8.94785i	0.450078	+	0.407563i
$483$	0.191738	−	7.85649i	0.00872440	−	0.357483i
$484$	1.53004	+	15.3947i	0.0695473	+	0.699758i
$485$	−11.2570	+	5.14089i	−0.511153	+	0.233436i
$486$	0.615475	−	1.27326i	0.0279185	−	0.0577562i
$487$	15.3070	+	13.2636i	0.693627	+	0.601031i	0.928649	−	0.370959i	$-0.120971\pi$
$487$	15.3070	+	13.2636i	0.693627	+	0.601031i	−0.235022	+	0.971990i	$0.575516\pi$
$488$	3.93257	+	10.3599i	0.178019	+	0.468972i
$489$	−2.09962	−	2.42309i	−0.0949480	−	0.109576i
$490$	4.69873	+	3.16698i	0.212267	+	0.143069i
$491$	41.0975	+	12.0673i	1.85470	+	0.544590i	0.999661	+	0.0260321i	$0.00828722\pi$
$491$	41.0975	+	12.0673i	1.85470	+	0.544590i	0.855042	+	0.518558i	$0.173531\pi$
$492$	1.68843	+	2.13003i	0.0761202	+	0.0960291i
$493$	0.897735	−	6.24388i	0.0404320	−	0.281210i
$494$	2.04694	+	4.75467i	0.0920963	+	0.213923i
$495$	3.65622	+	1.66974i	0.164335	+	0.0750492i
$496$	3.81892	−	0.211497i	0.171475	−	0.00949650i
$497$	−5.58119	−	8.68451i	−0.250351	−	0.389553i
$498$	−0.0920965	−	0.150439i	−0.00412694	−	0.00674135i
$499$	3.03951	+	21.1402i	0.136067	+	0.946366i	0.937426	+	0.348183i	$0.113201\pi$
$499$	3.03951	+	21.1402i	0.136067	+	0.946366i	−0.801359	+	0.598183i	$0.795890\pi$
$500$	−11.6637	+	12.3275i	−0.521615	+	0.551302i
$501$	−0.741830	+	1.15431i	−0.0331425	+	0.0515707i
$502$	−18.3656	+	2.23186i	−0.819697	+	0.0996128i
$503$	−20.4249	+	5.99728i	−0.910700	+	0.267406i	−0.703336	−	0.710858i	$-0.748307\pi$
$503$	−20.4249	+	5.99728i	−0.910700	+	0.267406i	−0.207365	+	0.978264i	$0.566489\pi$
$504$	0.958959	−	4.53459i	0.0427154	−	0.201987i
$505$		−	5.39032i		−	0.239866i
$506$	10.9471	+	27.2394i	0.486657	+	1.21094i
$507$	9.83537			0.436804
$508$	5.58254	+	9.58356i	0.247685	+	0.425202i
$509$	2.53901	+	8.64707i	0.112540	+	0.383275i	0.996430	−	0.0844186i	$-0.0269033\pi$
$509$	2.53901	+	8.64707i	0.112540	+	0.383275i	−0.883891	+	0.467693i	$0.845085\pi$
$510$	−2.73811	+	0.332746i	−0.121245	+	0.0147342i
$511$	21.2920	+	13.6835i	0.941902	+	0.605324i
$512$	21.0601	−	8.27475i	0.930734	−	0.365696i
$513$	2.03668	−	0.292830i	0.0899215	−	0.0129288i
$514$	11.0032	−	6.73601i	0.485332	−	0.297113i
$515$	5.19448	−	3.33829i	0.228896	−	0.147103i
$516$	−0.844731	+	19.3014i	−0.0371872	+	0.849696i
$517$	−13.9915	+	30.6370i	−0.615344	+	1.34742i
$518$	−4.30696	−	10.0043i	−0.189237	−	0.439562i
$519$	−17.0422	−	2.45029i	−0.748068	−	0.107556i
$520$	−0.306320	+	4.66238i	−0.0134330	+	0.204459i
$521$	8.48741	−	28.9055i	0.371840	−	1.26637i	−0.534984	−	0.844862i	$-0.679682\pi$
$521$	8.48741	−	28.9055i	0.371840	−	1.26637i	0.906824	−	0.421509i	$-0.138499\pi$
$522$	−2.37394	+	3.52213i	−0.103905	+	0.154160i
$523$	−16.7427	+	14.5076i	−0.732108	+	0.634375i	−0.938972	−	0.343995i	$-0.888220\pi$
$523$	−16.7427	+	14.5076i	−0.732108	+	0.634375i	0.206864	+	0.978370i	$0.433674\pi$
$524$	−18.1420	+	35.5269i	−0.792539	+	1.55200i
$525$	−4.44016	+	5.12422i	−0.193785	+	0.223639i
$526$	3.01171	−	6.23045i	0.131317	−	0.271661i
$527$	−0.834277	−	1.82681i	−0.0363417	−	0.0795772i
$528$	3.40787	+	16.9750i	0.148309	+	0.738742i
$529$	14.1959	+	18.0963i	0.617215	+	0.786795i
$530$	8.17089	−	9.02324i	0.354921	−	0.391944i
$531$	−2.33789	−	5.11927i	−0.101456	−	0.222158i
$532$	6.25078	−	2.53049i	0.271006	−	0.109711i
$533$	−1.82712	−	1.58321i	−0.0791414	−	0.0685764i
$534$	−0.756029	−	2.79990i	−0.0327166	−	0.121163i
$535$	−0.0824384	+	0.0714333i	−0.00356412	+	0.00308833i
$536$	−0.829976	−	0.446979i	−0.0358495	−	0.0193065i
$537$	−3.24320	−	0.952290i	−0.139955	−	0.0410944i
$538$	16.3908	+	2.72371i	0.706659	+	0.117428i
$539$	−18.4859	−	2.65787i	−0.796244	−	0.114483i
$540$	1.75742	+	0.600658i	0.0756273	+	0.0258482i
$541$	−6.46432	−	2.95216i	−0.277923	−	0.126923i	0.271578	−	0.962417i	$-0.412455\pi$
$541$	−6.46432	−	2.95216i	−0.277923	−	0.126923i	−0.549500	+	0.835493i	$0.685182\pi$
$542$	−34.4646	+	28.5685i	−1.48038	+	1.22712i
$543$	15.5390	−	9.98634i	0.666844	−	0.428555i
$544$	−8.07648	−	8.71387i	−0.346276	−	0.373604i
$545$	1.18803	+	8.26292i	0.0508896	+	0.353945i
$546$	−0.0901485	+	4.12160i	−0.00385800	+	0.176388i
$547$	28.5793	+	18.3668i	1.22196	+	0.785307i	0.982620	−	0.185629i	$-0.0594322\pi$
$547$	28.5793	+	18.3668i	1.22196	+	0.785307i	0.239341	+	0.970936i	$0.423069\pi$
$548$	−20.1120	+	28.4755i	−0.859141	+	1.21641i
$549$	−3.75910	+	1.10377i	−0.160435	+	0.0471078i
$550$	7.66543	−	24.1402i	0.326855	−	1.02934i
$551$	−6.17990			−0.263272
$552$	6.27822	+	12.0243i	0.267219	+	0.511789i
$553$	−24.3903			−1.03718
$554$	3.16370	−	9.96322i	0.134413	−	0.423297i
$555$	4.18771	−	1.22962i	0.177758	−	0.0521945i
$556$	−15.3696	−	10.8554i	−0.651817	−	0.460373i
$557$	−0.790381	−	0.507947i	−0.0334895	−	0.0215224i	0.523789	−	0.851848i	$-0.324518\pi$
$557$	−0.790381	−	0.507947i	−0.0334895	−	0.0215224i	−0.557278	+	0.830326i	$0.688154\pi$
$558$	−0.0295699	+	1.35194i	−0.00125179	+	0.0572321i
$559$	−2.44560	−	17.0095i	−0.103438	−	0.719426i
$560$	6.06354	+	0.531765i	0.256232	+	0.0224712i
$561$	7.64785	−	4.91497i	0.322892	−	0.207510i
$562$	−5.24519	+	4.34786i	−0.221255	+	0.183403i
$563$	−12.7478	−	5.82175i	−0.537258	−	0.245357i	0.128259	−	0.991741i	$-0.459061\pi$
$563$	−12.7478	−	5.82175i	−0.537258	−	0.245357i	−0.665516	+	0.746383i	$0.731789\pi$
$564$	−5.03318	+	14.7262i	−0.211935	+	0.620084i
$565$	0.577938	+	0.0830949i	0.0243140	+	0.00349583i
$566$	17.2335	+	2.86375i	0.724379	+	0.120372i
$567$	1.57230	+	0.461669i	0.0660304	+	0.0193883i
$568$	15.6881	+	8.44871i	0.658257	+	0.354500i
$569$	9.28108	−	8.04210i	0.389083	−	0.337142i	−0.438251	−	0.898853i	$-0.644402\pi$
$569$	9.28108	−	8.04210i	0.389083	−	0.337142i	0.827334	+	0.561710i	$0.189856\pi$
$570$	0.704419	+	2.60877i	0.0295049	+	0.109269i
$571$	14.8880	+	12.9006i	0.623045	+	0.539872i	0.908161	−	0.418622i	$-0.137487\pi$
$571$	14.8880	+	12.9006i	0.623045	+	0.539872i	−0.285116	+	0.958493i	$0.592032\pi$
$572$	−5.77879	−	14.2747i	−0.241623	−	0.596854i
$573$	7.93811	+	17.3820i	0.331619	+	0.726145i
$574$	−2.11402	+	2.33454i	−0.0882373	+	0.0974417i
$575$	0.484140	−	19.8377i	0.0201900	−	0.827288i
$576$	2.34265	+	7.64931i	0.0976105	+	0.318721i
$577$	−3.80339	−	8.32825i	−0.158337	−	0.346710i	0.813792	−	0.581156i	$-0.197399\pi$
$577$	−3.80339	−	8.32825i	−0.158337	−	0.346710i	−0.972129	+	0.234447i	$0.924672\pi$
$578$	7.74804	−	16.0287i	0.322276	−	0.666706i
$579$	−7.94987	+	9.17464i	−0.330385	+	0.381285i
$580$	−4.96780	−	2.53684i	−0.206277	−	0.105337i
$581$	0.154466	−	0.133846i	0.00640833	−	0.00555285i
$582$	10.5335	−	15.6282i	0.436629	−	0.647810i
$583$	−11.3035	+	38.4962i	−0.468144	+	1.59435i
$584$	−43.5918	−	2.86400i	−1.80384	−	0.118513i
$585$	−1.63514	−	0.235097i	−0.0676047	−	0.00972008i
$586$	−16.1702	−	37.5604i	−0.667986	−	1.55161i
$587$	15.1808	−	33.2414i	0.626580	−	1.37202i	−0.284055	−	0.958808i	$-0.591680\pi$
$587$	15.1808	−	33.2414i	0.626580	−	1.37202i	0.910635	−	0.413211i	$-0.135593\pi$
$588$	−8.62121	−	0.377310i	−0.355533	−	0.0155600i
$589$	−1.65515	+	1.06370i	−0.0681994	+	0.0438291i
$590$	6.30346	−	3.85888i	0.259510	−	0.158868i
$591$	4.93533	−	0.709594i	0.203013	−	0.0291888i
$592$	14.8671	+	11.5069i	0.611036	+	0.472930i
$593$	−32.9899	−	21.2013i	−1.35473	−	0.870633i	−0.356753	−	0.934199i	$-0.616116\pi$
$593$	−32.9899	−	21.2013i	−1.35473	−	0.870633i	−0.997978	+	0.0635659i	$0.979753\pi$
$594$	−6.07661	+	0.738454i	−0.249326	+	0.0302991i
$595$	−0.900429	−	3.06658i	−0.0369140	−	0.125718i
$596$	−23.9962	+	13.9781i	−0.982922	+	0.572564i
$597$	20.8870			0.854848
$598$	−7.47092	−	9.47408i	−0.305509	−	0.387424i
$599$			11.0679i			0.452220i	0.974102	+	0.226110i	$0.0726009\pi$
$599$			11.0679i			0.452220i	−0.974102	+	0.226110i	$0.927399\pi$
$600$	2.42138	−	11.4499i	0.0988523	−	0.467439i
$601$	38.0058	−	11.1595i	1.55029	−	0.455206i	0.609101	−	0.793092i	$-0.291530\pi$
$601$	38.0058	−	11.1595i	1.55029	−	0.455206i	0.941187	+	0.337887i	$0.109712\pi$
$602$	−22.2228	+	2.70060i	−0.905735	+	0.110068i
$603$	0.180189	−	0.280380i	0.00733788	−	0.0114180i
$604$	13.6246	+	12.8910i	0.554378	+	0.524526i
$605$	−1.02226	−	7.10998i	−0.0415608	−	0.289062i
$606$	4.28608	+	7.00129i	0.174110	+	0.284408i
$607$	−10.4737	−	16.2974i	−0.425114	−	0.661491i	0.560951	−	0.827849i	$-0.310436\pi$
$607$	−10.4737	−	16.2974i	−0.425114	−	0.661491i	−0.986065	+	0.166358i	$0.946799\pi$
$608$	−7.32385	+	9.04672i	−0.297021	+	0.366893i
$609$	−4.47688	−	2.04452i	−0.181412	−	0.0828482i
$610$	−2.03450	−	4.72576i	−0.0823745	−	0.191341i
$611$	1.96998	−	13.7015i	0.0796970	−	0.554305i
$612$	3.29185	−	2.60938i	0.133065	−	0.105478i
$613$	−12.3852	−	3.63661i	−0.500232	−	0.146881i	0.0218760	−	0.999761i	$-0.493036\pi$
$613$	−12.3852	−	3.63661i	−0.500232	−	0.146881i	−0.522108	+	0.852879i	$0.674854\pi$
$614$	24.5753	+	16.5639i	0.991777	+	0.668465i
$615$	−0.826444	−	0.953767i	−0.0333254	−	0.0384596i
$616$	−18.7559	+	7.11965i	−0.755697	+	0.286859i
$617$	−1.33341	−	1.15541i	−0.0536810	−	0.0465149i	0.627607	−	0.778530i	$-0.284034\pi$
$617$	−1.33341	−	1.15541i	−0.0536810	−	0.0465149i	−0.681288	+	0.732015i	$0.738580\pi$
$618$	−4.09251	+	8.46634i	−0.164625	+	0.340566i
$619$	−9.51373	+	4.34477i	−0.382389	+	0.174631i	−0.597330	−	0.801996i	$-0.703772\pi$
$619$	−9.51373	+	4.34477i	−0.382389	+	0.174631i	0.214940	+	0.976627i	$0.431044\pi$
$620$	−1.76717	+	0.175635i	−0.0709712	+	0.00705365i
$621$	−4.40975	+	1.88523i	−0.176957	+	0.0756518i
$622$	−31.0661	−	28.1316i	−1.24564	−	1.12797i
$623$	3.05681	−	1.39600i	0.122469	−	0.0559295i
$624$	−3.30939	−	6.29936i	−0.132482	−	0.252176i
$625$	−8.38790	+	9.68015i	−0.335516	+	0.387206i
$626$	−4.51471	−	16.7199i	−0.180444	−	0.668261i
$627$	−5.83236	−	6.73090i	−0.232922	−	0.268806i
$628$	20.7686	−	5.12342i	0.828757	−	0.204447i
$629$	2.78110	−	9.47157i	0.110890	−	0.377656i
$630$	−0.352769	+	2.12290i	−0.0140547	+	0.0845785i
$631$	1.59463	−	11.0909i	0.0634813	−	0.441522i	−0.933149	−	0.359491i	$-0.882950\pi$
$631$	1.59463	−	11.0909i	0.0634813	−	0.441522i	0.996630	−	0.0820308i	$-0.0261406\pi$
$632$	36.8317	−	20.3895i	1.46509	−	0.811051i
$633$	−3.98972	+	8.73628i	−0.158577	+	0.347236i
$634$	−9.83304	+	8.15083i	−0.390520	+	0.323711i
$635$	−2.78410	−	4.33214i	−0.110484	−	0.171916i
$636$	−3.43811	+	18.2170i	−0.136330	+	0.722351i
$637$	7.59752	−	1.09236i	0.301025	−	0.0432808i
$638$	18.3805	+	0.402021i	0.727690	+	0.0159162i
$639$	−3.40591	+	5.29970i	−0.134736	+	0.209653i
$640$	−9.60105	+	4.26591i	−0.379515	+	0.168625i
$641$	−11.7063	−	39.8681i	−0.462372	−	1.57470i	−0.779556	−	0.626332i	$-0.784555\pi$
$641$	−11.7063	−	39.8681i	−0.462372	−	1.57470i	0.317184	−	0.948364i	$-0.397263\pi$
$642$	0.0502766	−	0.158332i	0.00198426	−	0.00624888i
$643$		−	21.4867i		−	0.847355i	−0.905813	−	0.423677i	$-0.860739\pi$
$643$		−	21.4867i		−	0.847355i	0.905813	−	0.423677i	$-0.139261\pi$
$644$	−12.5518	+	9.46024i	−0.494612	+	0.372785i
$645$		−	8.97037i		−	0.353208i
$646$	5.82509	+	1.84969i	0.229185	+	0.0727750i
$647$	−4.35406	−	14.8286i	−0.171176	−	0.582971i	−0.999734	−	0.0230678i	$-0.992657\pi$
$647$	−4.35406	−	14.8286i	−0.171176	−	0.582971i	0.828558	−	0.559903i	$-0.189162\pi$
$648$	−2.76026	+	0.617228i	−0.108433	+	0.0242470i
$649$	−13.1699	+	20.4927i	−0.516963	+	0.804409i
$650$	−0.227625	+	10.4071i	−0.00892820	+	0.408199i
$651$	−1.55095	+	0.222992i	−0.0607863	+	0.00873975i
$652$	−1.18923	+	6.30117i	−0.0465737	+	0.246773i
$653$	13.2811	+	20.6658i	0.519730	+	0.808716i	0.997566	−	0.0697333i	$-0.0222148\pi$
$653$	13.2811	+	20.6658i	0.519730	+	0.808716i	−0.477835	+	0.878449i	$0.658578\pi$
$654$	−8.11330	−	9.78776i	−0.317255	−	0.382732i
$655$	7.69421	−	16.8480i	0.300638	−	0.658304i
$656$	1.24076	−	5.29261i	0.0484436	−	0.206642i
$657$	2.19809	−	15.2881i	0.0857557	−	0.596444i
$658$	−17.7887	−	2.95601i	−0.693477	−	0.115237i
$659$	9.91865	−	33.7798i	0.386376	−	1.31587i	−0.505200	−	0.863002i	$-0.668581\pi$
$659$	9.91865	−	33.7798i	0.386376	−	1.31587i	0.891575	−	0.452872i	$-0.149601\pi$
$660$	−1.92540	−	7.80491i	−0.0749462	−	0.303806i
$661$	−23.0637	−	26.6169i	−0.897073	−	1.03528i	−0.999179	−	0.0405044i	$-0.987104\pi$
$661$	−23.0637	−	26.6169i	−0.897073	−	1.03528i	0.102106	−	0.994774i	$-0.467442\pi$
$662$	−42.3248	+	11.4286i	−1.64500	+	0.444183i
$663$	−2.44677	+	2.82372i	−0.0950245	+	0.109664i
$664$	−0.121367	+	0.331248i	−0.00470997	+	0.0128549i
$665$	−2.84814	+	1.30070i	−0.110446	+	0.0504391i
$666$	−4.46154	+	4.92694i	−0.172881	+	0.190915i
$667$	13.9153	−	3.71965i	0.538803	−	0.144025i
$668$	2.73081	−	0.271408i	0.105658	−	0.0105011i
$669$	−2.23833	+	1.02221i	−0.0865388	+	0.0395210i
$670$	0.394071	+	0.190488i	0.0152243	+	0.00735919i
$671$	12.8159	+	11.1051i	0.494753	+	0.428706i
$672$	−8.29855	+	4.13070i	−0.320123	+	0.159345i
$673$	14.4472	+	16.6729i	0.556898	+	0.642694i	0.962476	−	0.271366i	$-0.0874754\pi$
$673$	14.4472	+	16.6729i	0.556898	+	0.642694i	−0.405578	+	0.914060i	$0.632930\pi$
$674$	−3.53226	+	5.24068i	−0.136058	+	0.201864i
$675$	3.97007	+	1.16572i	0.152808	+	0.0448685i
$676$	−12.2193	−	15.4152i	−0.469972	−	0.592891i
$677$	2.82168	−	19.6252i	0.108446	−	0.754259i	−0.860938	−	0.508710i	$-0.830123\pi$
$677$	2.82168	−	19.6252i	0.108446	−	0.754259i	0.969384	−	0.245549i	$-0.0789682\pi$
$678$	−0.816735	+	0.351614i	−0.0313665	+	0.0135037i
$679$	19.8646	+	9.07184i	0.762332	+	0.348145i
$680$	3.92329	+	3.87809i	0.150451	+	0.148718i
$681$	12.1704	+	18.9376i	0.466372	+	0.725690i
$682$	4.99201	−	3.05603i	0.191154	−	0.117021i
$683$	−1.23090	−	8.56106i	−0.0470989	−	0.327580i	−0.999725	−	0.0234371i	$-0.992539\pi$
$683$	−1.23090	−	8.56106i	−0.0470989	−	0.327580i	0.952626	−	0.304143i	$-0.0983700\pi$
$684$	−2.98929	−	2.82832i	−0.114298	−	0.108143i
$685$	8.75114	−	13.6170i	0.334364	−	0.520281i
$686$	−3.16324	−	26.0297i	−0.120773	−	0.993820i
$687$	−3.71671	+	1.09132i	−0.141801	+	0.0416366i
$688$	31.3009	−	22.6557i	1.19334	−	0.863740i
$689$		−	16.4895i		−	0.628201i
$690$	−3.15635	−	5.45019i	−0.120160	−	0.207485i
$691$	36.7981			1.39986			0.699932	−	0.714209i	$-0.253214\pi$
$691$	36.7981			1.39986			0.699932	+	0.714209i	$0.253214\pi$
$692$	17.3325	+	29.7547i	0.658882	+	1.13110i
$693$	−1.99830	−	6.80559i	−0.0759092	−	0.258523i
$694$	−3.29712	−	27.1314i	−0.125157	−	1.02990i
$695$	7.34980	+	4.72343i	0.278794	+	0.179170i
$696$	8.46965	−	0.655104i	0.321041	−	0.0248317i
$697$	−2.82532	+	0.406219i	−0.107017	+	0.0153867i
$698$	5.85635	+	9.56633i	0.221666	+	0.362091i
$699$	17.5471	−	11.2768i	0.663692	−	0.426529i
$700$	13.5477	+	0.592918i	0.512053	+	0.0224102i
$701$	−13.6191	+	29.8217i	−0.514387	+	1.12635i	0.457134	+	0.889398i	$0.348876\pi$
$701$	−13.6191	+	29.8217i	−0.514387	+	1.12635i	−0.971521	+	0.236953i	$0.923851\pi$
$702$	2.31076	−	0.994810i	0.0872140	−	0.0375467i
$703$	−9.57239	−	1.37630i	−0.361030	−	0.0519082i
$704$	22.3714	−	26.4306i	0.843153	−	0.996142i
$705$	2.03575	−	6.93313i	0.0766708	−	0.261117i
$706$	35.2761	+	23.7763i	1.32763	+	0.894834i
$707$	−7.18869	+	6.22904i	−0.270359	+	0.234267i
$708$	−5.11898	+	10.0243i	−0.192383	+	0.376737i
$709$	−14.9847	+	17.2933i	−0.562763	+	0.649463i	−0.963809	−	0.266595i	$-0.914101\pi$
$709$	−14.9847	+	17.2933i	−0.562763	+	0.649463i	0.401046	+	0.916058i	$0.368647\pi$
$710$	−7.44866	−	3.60057i	−0.279543	−	0.135127i
$711$	6.18310	+	13.5391i	0.231884	+	0.507756i
$712$	−3.44906	+	4.66348i	−0.129259	+	0.174771i
$713$	3.08668	−	3.39137i	0.115597	−	0.127008i
$714$	3.60791	+	3.26710i	0.135023	+	0.122268i
$715$	2.97037	+	6.50419i	0.111085	+	0.243243i
$716$	2.53675	+	6.26624i	0.0948028	+	0.234180i
$717$	18.8305	+	16.3167i	0.703236	+	0.609358i
$718$	16.0708	−	4.33944i	0.599757	−	0.161947i
$719$	27.1328	−	23.5107i	1.01188	−	0.876802i	0.0194783	−	0.999810i	$-0.493799\pi$
$719$	27.1328	−	23.5107i	1.01188	−	0.876802i	0.992406	+	0.123008i	$0.0392540\pi$
$720$	−1.24196	−	3.50068i	−0.0462852	−	0.130463i
$721$	−10.4548	−	3.06980i	−0.389356	−	0.114325i
$722$	−3.42318	+	20.6001i	−0.127397	+	0.766655i
$723$	9.33016	+	1.34147i	0.346992	+	0.0498900i
$724$	−34.9572	−	11.9478i	−1.29917	−	0.444037i
$725$	−11.3041	−	5.16243i	−0.419825	−	0.191728i
$726$	6.98123	+	8.42205i	0.259098	+	0.312572i
$727$	0.175381	−	0.112710i	0.00650451	−	0.00418019i	−0.537385	−	0.843337i	$-0.680588\pi$
$727$	0.175381	−	0.112710i	0.00650451	−	0.00418019i	0.543889	+	0.839157i	$0.316951\pi$
$728$	6.57187	−	4.97931i	0.243570	−	0.184546i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	20.2788	+	0.443543i	0.750554	+	0.0164163i
$731$	−17.0680	−	10.9689i	−0.631283	−	0.405701i
$732$	6.40020	+	4.52041i	0.236558	+	0.167079i
$733$	−26.8134	+	7.87313i	−0.990377	+	0.290801i	−0.736501	−	0.676436i	$-0.763523\pi$
$733$	−26.8134	+	7.87313i	−0.990377	+	0.290801i	−0.253875	+	0.967237i	$0.581705\pi$
$734$	−9.43485	−	2.99592i	−0.348247	−	0.110582i
$735$	4.00673			0.147791
$736$	11.0460	−	24.7787i	0.407161	−	0.913357i
$737$	−1.44261			−0.0531394
$738$	1.83182	+	0.581672i	0.0674302	+	0.0214117i
$739$	−41.4404	+	12.1680i	−1.52441	+	0.447607i	−0.933334	−	0.359010i	$-0.883114\pi$
$739$	−41.4404	+	12.1680i	−1.52441	+	0.447607i	−0.591075	+	0.806617i	$0.701296\pi$
$740$	−7.12994	−	5.03582i	−0.262102	−	0.185120i
$741$	3.07931	+	1.97895i	0.113121	+	0.0726987i
$742$	−21.4759	−	0.469725i	−0.788406	−	0.0172442i
$743$	−3.69516	−	25.7004i	−0.135562	−	0.942857i	−0.938127	−	0.346292i	$-0.887441\pi$
$743$	−3.69516	−	25.7004i	−0.135562	−	0.942857i	0.802564	−	0.596565i	$-0.203468\pi$
$744$	2.15566	−	1.63328i	0.0790302	−	0.0598788i
$745$	10.8472	−	6.97107i	0.397411	−	0.255400i
$746$	−25.2650	−	30.4793i	−0.925017	−	1.11593i
$747$	−0.113456	−	0.0518135i	−0.00415113	−	0.00189576i
$748$	−17.2049	−	5.88035i	−0.629072	−	0.215007i
$749$	0.190531	+	0.0273942i	0.00696186	+	0.00100096i
$750$	−1.96713	+	11.8378i	−0.0718294	+	0.432256i
$751$	−33.8560	−	9.94101i	−1.23542	−	0.362753i	−0.402128	−	0.915583i	$-0.631729\pi$
$751$	−33.8560	−	9.94101i	−1.23542	−	0.362753i	−0.833294	+	0.552831i	$0.813548\pi$
$752$	29.3338	−	10.4069i	1.06969	−	0.379502i
$753$	−9.88670	+	8.56688i	−0.360292	+	0.312194i
$754$	−7.29474	+	1.96973i	−0.265659	+	0.0717333i
$755$	−6.58168	−	5.70306i	−0.239532	−	0.207556i
$756$	−1.22981	−	3.03787i	−0.0447279	−	0.110486i
$757$	15.5067	+	33.9549i	0.563599	+	1.23411i	0.950136	+	0.311836i	$0.100944\pi$
$757$	15.5067	+	33.9549i	0.563599	+	1.23411i	−0.386537	+	0.922274i	$0.626329\pi$
$758$	17.6988	+	16.0270i	0.642851	+	0.582126i
$759$	17.1841	+	11.6456i	0.623742	+	0.422707i
$760$	3.21361	−	4.34513i	0.116570	−	0.157614i
$761$	8.99145	+	19.6885i	0.325940	+	0.713709i	0.999681	−	0.0252586i	$-0.00804092\pi$
$761$	8.99145	+	19.6885i	0.325940	+	0.713709i	−0.673741	+	0.738968i	$0.735314\pi$
$762$	7.06084	+	3.41310i	0.255787	+	0.123644i
$763$	9.64680	−	11.1330i	0.349237	−	0.403042i
$764$	17.3810	−	34.0367i	0.628824	−	1.23140i
$765$	−1.47400	+	1.27723i	−0.0532925	+	0.0461782i
$766$	−5.54193	−	3.73530i	−0.200238	−	0.134962i
$767$	2.82060	−	9.60607i	0.101846	−	0.346855i
$768$	9.07845	−	13.1750i	0.327590	−	0.475413i
$769$	−26.8764	−	3.86424i	−0.969186	−	0.139348i	−0.360500	−	0.932759i	$-0.617394\pi$
$769$	−26.8764	−	3.86424i	−0.969186	−	0.139348i	−0.608686	+	0.793411i	$0.708303\pi$
$770$	8.55566	−	3.68332i	0.308325	−	0.132738i
$771$	3.78968	−	8.29825i	0.136482	−	0.298854i
$772$	24.2563	+	1.06159i	0.873005	+	0.0382073i
$773$	40.3684	−	25.9432i	1.45195	−	0.933112i	0.452812	−	0.891606i	$-0.350421\pi$
$773$	40.3684	−	25.9432i	1.45195	−	0.933112i	0.999138	−	0.0415060i	$-0.0132156\pi$
$774$	7.13273	+	11.6513i	0.256381	+	0.418797i
$775$	−3.91614	+	0.563056i	−0.140672	+	0.0202256i
$776$	−37.5811	+	2.90679i	−1.34908	+	0.104348i
$777$	−6.47916	−	4.16390i	−0.232439	−	0.149379i
$778$	−4.85607	−	39.9598i	−0.174098	−	1.43263i
$779$	0.787826	+	2.68309i	0.0282268	+	0.0961317i
$780$	1.66299	+	2.85487i	0.0595447	+	0.102221i
$781$	27.2681			0.975728
$782$	−14.2297	−	0.658864i	−0.508854	−	0.0235609i
$783$			3.00342i			0.107333i
$784$	10.1195	+	13.9810i	0.361409	+	0.499320i
$785$	−9.52979	+	2.79820i	−0.340133	+	0.0998720i
$786$	3.40282	+	28.0012i	0.121374	+	0.998770i
$787$	9.15357	−	14.2432i	0.326290	−	0.507716i	−0.638892	−	0.769296i	$-0.720607\pi$
$787$	9.15357	−	14.2432i	0.326290	−	0.507716i	0.965182	+	0.261580i	$0.0842434\pi$
$788$	−7.24372	−	6.85366i	−0.258047	−	0.244151i
$789$	−0.696390	−	4.84350i	−0.0247922	−	0.172433i
$790$	−16.6710	+	10.2057i	−0.593126	+	0.363102i
$791$	−0.557045	−	0.866779i	−0.0198062	−	0.0308191i
$792$	8.70686	+	8.60655i	0.309385	+	0.305820i
$793$	−6.33971	−	2.89525i	−0.225130	−	0.102813i
$794$	−15.3674	+	6.61586i	−0.545369	+	0.234788i
$795$	1.22499	−	8.52001i	0.0434460	−	0.302174i
$796$	−25.9496	−	32.7366i	−0.919760	−	1.16032i
$797$	−5.20043	−	1.52698i	−0.184209	−	0.0540886i	0.188327	−	0.982106i	$-0.439693\pi$
$797$	−5.20043	−	1.52698i	−0.184209	−	0.0540886i	−0.372536	+	0.928018i	$0.621512\pi$
$798$	2.66510	−	3.95412i	0.0943436	−	0.139974i
$799$	−10.7024	−	12.3513i	−0.378625	−	0.436956i
$800$	−20.9539	+	10.4300i	−0.740831	+	0.368757i
$801$	−1.54984	−	1.34294i	−0.0547609	−	0.0474506i
$802$	−2.94956	−	1.42578i	−0.104153	−	0.0503459i
$803$	−60.8123	+	27.7720i	−2.14602	+	0.980054i
$804$	−0.663309	+	0.0659247i	−0.0233931	+	0.00232498i
$805$	5.63030	−	4.64308i	0.198442	−	0.163647i
$806$	−1.61471	+	1.78314i	−0.0568756	+	0.0628085i
$807$	10.6873	−	4.88071i	0.376209	−	0.171809i
$808$	5.64832	−	15.4159i	0.198707	−	0.542330i
$809$	−5.84085	+	6.74070i	−0.205353	+	0.236990i	−0.849079	−	0.528266i	$-0.822842\pi$
$809$	−5.84085	+	6.74070i	−0.205353	+	0.236990i	0.643726	+	0.765256i	$0.277388\pi$
$810$	1.26786	−	0.342346i	0.0445479	−	0.0120288i
$811$	30.2479	+	34.9079i	1.06215	+	1.22578i	0.973252	+	0.229741i	$0.0737879\pi$
$811$	30.2479	+	34.9079i	1.06215	+	1.22578i	0.0888944	+	0.996041i	$0.471667\pi$
$812$	2.35757	+	9.55677i	0.0827345	+	0.335377i
$813$	−8.91800	+	30.3719i	−0.312768	+	1.06519i
$814$	28.3810	+	4.71616i	0.994754	+	0.165301i
$815$	0.423719	−	2.94703i	0.0148422	−	0.103230i
$816$	−8.17946	−	1.91753i	−0.286338	−	0.0671271i
$817$	−8.25698	+	18.0803i	−0.288875	+	0.632549i
$818$	9.49331	+	11.4526i	0.331926	+	0.400430i
$819$	1.57603	+	2.45235i	0.0550709	+	0.0856919i
$820$	−0.468099	+	2.48024i	−0.0163467	+	0.0866139i
$821$	−8.80989	+	1.26667i	−0.307467	+	0.0442071i	−0.294321	−	0.955706i	$-0.595094\pi$
$821$	−8.80989	+	1.26667i	−0.307467	+	0.0442071i	−0.0131458	+	0.999914i	$0.504185\pi$
$822$	−0.539042	+	24.6451i	−0.0188013	+	0.859597i
$823$	−5.23087	+	8.13939i	−0.182337	+	0.283721i	−0.920375	−	0.391038i	$-0.872116\pi$
$823$	−5.23087	+	8.13939i	−0.182337	+	0.283721i	0.738038	+	0.674759i	$0.235753\pi$
$824$	18.3539	−	4.10416i	0.639389	−	0.142975i
$825$	−5.04572	−	17.1841i	−0.175669	−	0.598275i
$826$	−12.4306	−	3.94718i	−0.432515	−	0.137340i
$827$			26.8476i			0.933581i	0.884368	+	0.466791i	$0.154590\pi$
$827$			26.8476i			0.933581i	−0.884368	+	0.466791i	$0.845410\pi$
$828$	8.43335	+	4.56931i	0.293079	+	0.158794i
$829$		−	54.0267i		−	1.87643i	−0.346058	−	0.938213i	$-0.612480\pi$
$829$		−	54.0267i		−	1.87643i	0.346058	−	0.938213i	$-0.387520\pi$
$830$	0.0495733	−	0.156118i	0.00172072	−	0.00541893i
$831$	−2.08248	−	7.09229i	−0.0722406	−	0.246029i
$832$	−5.76159	+	13.0131i	−0.199747	+	0.451147i
$833$	4.89942	−	7.62365i	0.169755	−	0.264144i
$834$	−13.3022	−	0.290948i	−0.460617	−	0.0100747i
$835$	−1.26121	+	0.181335i	−0.0436461	+	0.00627536i
$836$	−3.30346	+	17.5035i	−0.114253	+	0.605372i
$837$	0.516957	+	0.804401i	0.0178687	+	0.0278042i
$838$	−30.0011	+	24.8686i	−1.03637	+	0.859070i
$839$	−15.0359	+	32.9240i	−0.519096	+	1.13666i	0.450685	+	0.892683i	$0.351180\pi$
$839$	−15.0359	+	32.9240i	−0.519096	+	1.13666i	−0.969781	+	0.243978i	$0.921547\pi$
$840$	3.76554	−	2.08455i	0.129924	−	0.0719239i
$841$	−2.84338	+	19.7761i	−0.0980475	+	0.681935i
$842$	6.66718	−	40.1219i	0.229766	−	1.38269i
$843$	−1.35724	+	4.62232i	−0.0467457	+	0.159201i
$844$	18.6493	−	4.60061i	0.641935	−	0.158360i
$845$	5.98103	+	6.90248i	0.205754	+	0.237453i
$846$	2.86867	+	10.6239i	0.0986269	+	0.365258i
$847$	−8.30076	+	9.57959i	−0.285218	+	0.329159i
$848$	32.8233	−	17.2438i	1.12716	−	0.592155i
$849$	11.2367	−	5.13164i	0.385644	−	0.176117i
$850$	9.10998	+	8.24944i	0.312470	+	0.282954i
$851$	22.3826	−	2.66254i	0.767266	−	0.0912707i
$852$	12.5378	−	1.24610i	0.429537	−	0.0426906i
$853$	24.7100	−	11.2847i	0.846054	−	0.386380i	0.0552673	−	0.998472i	$-0.482399\pi$
$853$	24.7100	−	11.2847i	0.846054	−	0.386380i	0.790787	+	0.612092i	$0.209672\pi$
$854$	−3.95136	+	8.17435i	−0.135213	+	0.279720i
$855$	1.44404	+	1.25127i	0.0493852	+	0.0427925i
$856$	−0.310620	+	0.117910i	−0.0106168	+	0.00403007i
$857$	−14.2206	−	16.4115i	−0.485767	−	0.560605i	0.458963	−	0.888456i	$-0.348221\pi$
$857$	−14.2206	−	16.4115i	−0.485767	−	0.560605i	−0.944730	+	0.327851i	$0.893676\pi$
$858$	−9.02987	−	6.08620i	−0.308275	−	0.207779i
$859$	−10.2413	−	3.00710i	−0.349427	−	0.102601i	0.102309	−	0.994753i	$-0.467377\pi$
$859$	−10.2413	−	3.00710i	−0.349427	−	0.102601i	−0.451736	+	0.892152i	$0.649195\pi$
$860$	−14.0594	+	11.1446i	−0.479423	+	0.380028i
$861$	−0.316936	+	2.20434i	−0.0108012	+	0.0751237i
$862$	17.2665	+	40.1069i	0.588100	+	1.36605i
$863$	47.8604	+	21.8571i	1.62919	+	0.744025i	0.999462	−	0.0327924i	$-0.0104400\pi$
$863$	47.8604	+	21.8571i	1.62919	+	0.744025i	0.629726	+	0.776818i	$0.283167\pi$
$864$	4.39669	+	3.55937i	0.149578	+	0.121092i
$865$	−8.64397	−	13.4503i	−0.293904	−	0.457323i
$866$	8.11548	+	13.2566i	0.275775	+	0.450478i
$867$	−1.79156	−	12.4606i	−0.0608446	−	0.423184i
$868$	2.27636	+	2.15378i	0.0772649	+	0.0731042i
$869$	34.8308	−	54.1977i	1.18155	−	1.83853i
$870$	−3.91547	+	0.475823i	−0.132747	+	0.0161319i
$871$	0.568884	−	0.167039i	0.0192759	−	0.00565991i
$872$	−5.26074	+	24.8762i	−0.178151	+	0.842416i
$873$		−	13.3266i		−	0.451037i
$874$	1.34504	+	13.8905i	0.0454967	+	0.469853i
$875$	−13.9048			−0.470069
$876$	−26.6921	+	15.5485i	−0.901844	+	0.525335i
$877$	9.56927	+	32.5899i	0.323131	+	1.10048i	0.947607	+	0.319439i	$0.103495\pi$
$877$	9.56927	+	32.5899i	0.323131	+	1.10048i	−0.624476	+	0.781044i	$0.714687\pi$
$878$	24.7308	−	3.00538i	0.834623	−	0.101427i
$879$	−24.3256	−	15.6331i	−0.820483	−	0.527292i
$880$	−9.84071	+	12.7144i	−0.331730	+	0.428602i
$881$	48.2337	−	6.93496i	1.62504	−	0.233645i	0.731240	−	0.682120i	$-0.238942\pi$
$881$	48.2337	−	6.93496i	1.62504	−	0.233645i	0.893795	+	0.448475i	$0.148033\pi$
$882$	−5.20420	+	3.18593i	−0.175235	+	0.107276i
$883$	−3.95951	+	2.54462i	−0.133248	+	0.0856333i	−0.605567	−	0.795795i	$-0.707054\pi$
$883$	−3.95951	+	2.54462i	−0.133248	+	0.0856333i	0.472319	+	0.881428i	$0.343417\pi$
$884$	7.46549	+	0.326729i	0.251091	+	0.0109891i
$885$	2.17101	−	4.75384i	0.0729776	−	0.159799i
$886$	0.981099	+	2.27891i	0.0329607	+	0.0765615i
$887$	34.5003	+	4.96040i	1.15841	+	0.166554i	0.694610	−	0.719387i	$-0.255577\pi$
$887$	34.5003	+	4.96040i	1.15841	+	0.166554i	0.463798	+	0.885941i	$0.346486\pi$
$888$	13.2650	+	0.871517i	0.445145	+	0.0292462i
$889$	−2.56018	+	8.71916i	−0.0858656	+	0.292431i
$890$	1.50522	−	2.23324i	0.0504551	−	0.0748584i
$891$	−3.27121	+	2.83452i	−0.109590	+	0.0949598i
$892$	4.38299	+	2.23820i	0.146753	+	0.0749405i
$893$	−10.4849	+	12.1003i	−0.350865	+	0.404920i
$894$	−8.54604	+	17.6796i	−0.285822	+	0.591293i
$895$	−1.30392	−	2.85519i	−0.0435852	−	0.0954384i
$896$	16.7841	+	7.87458i	0.560717	+	0.263071i
$897$	−8.12483	−	2.60260i	−0.271280	−	0.0868984i
$898$	17.5121	−	19.3389i	0.584388	−	0.645348i
$899$	−1.19301	−	2.61232i	−0.0397891	−	0.0871259i
$900$	−3.10528	−	7.67063i	−0.103509	−	0.255688i
$901$	−14.7132	−	12.7491i	−0.490168	−	0.424733i
$902$	−2.16864	−	8.03140i	−0.0722078	−	0.267416i
$903$	−11.9631	+	10.3661i	−0.398109	+	0.344963i
$904$	1.56579	+	0.843245i	0.0520773	+	0.0280459i
$905$	16.4580	+	4.83249i	0.547081	+	0.160637i
$906$	13.0835	+	2.17412i	0.434669	+	0.0722302i
$907$	−7.24699	−	1.04196i	−0.240633	−	0.0345977i	0.0209433	−	0.999781i	$-0.493333\pi$
$907$	−7.24699	−	1.04196i	−0.240633	−	0.0345977i	−0.261576	+	0.965183i	$0.584242\pi$
$908$	14.5609	−	42.6027i	0.483221	−	1.41382i
$909$	5.28012	+	2.41135i	0.175131	+	0.0799794i
$910$	−2.94737	+	2.44314i	−0.0977043	+	0.0809893i
$911$	31.6039	−	20.3106i	1.04709	−	0.672921i	0.100356	−	0.994952i	$-0.468002\pi$
$911$	31.6039	−	20.3106i	1.04709	−	0.672921i	0.946729	+	0.322031i	$0.104365\pi$
$912$	−0.719042	+	8.19902i	−0.0238099	+	0.271497i
$913$	0.0768318	+	0.534377i	0.00254276	+	0.0176853i
$914$	0.334677	−	15.3015i	0.0110701	−	0.506128i
$915$	−3.06059	−	1.96692i	−0.101180	−	0.0650245i
$916$	6.32802	+	4.46943i	0.209084	+	0.147674i
$917$	−31.3603	+	9.20823i	−1.03561	+	0.304082i
$918$	0.898944	−	2.83098i	0.0296696	−	0.0934363i
$919$	−28.9377			−0.954567			−0.477284	−	0.878749i	$-0.658379\pi$
$919$	−28.9377			−0.954567			−0.477284	+	0.878749i	$0.658379\pi$
$920$	−4.62080	+	11.7182i	−0.152343	+	0.386338i
$921$	20.9560			0.690523
$922$	9.05655	−	28.5212i	0.298262	−	0.939294i
$923$	−10.7529	+	3.15735i	−0.353938	+	0.103925i
$924$	−8.18388	+	11.5871i	−0.269230	+	0.381188i
$925$	−16.3599	−	10.5139i	−0.537910	−	0.345694i
$926$	−1.05470	+	48.2210i	−0.0346596	+	1.58464i
$927$	0.946301	+	6.58166i	0.0310806	+	0.216170i
$928$	−11.5493	−	12.4608i	−0.379124	−	0.409044i
$929$	4.77264	−	3.06719i	0.156585	−	0.100631i	−0.460002	−	0.887918i	$-0.652151\pi$
$929$	4.77264	−	3.06719i	0.156585	−	0.100631i	0.616587	+	0.787287i	$0.288515\pi$
$930$	−0.966774	+	0.801381i	−0.0317018	+	0.0262783i
$931$	−8.07579	−	3.68809i	−0.264673	−	0.120872i
$932$	−39.4746	−	13.4918i	−1.29303	−	0.441938i
$933$	−29.3335	−	4.21752i	−0.960336	−	0.138076i
$934$	−30.3461	−	5.04270i	−0.992953	−	0.165002i
$935$	8.10010	+	2.37840i	0.264902	+	0.0777822i
$936$	−4.43003	−	2.38576i	−0.144800	−	0.0779811i
$937$	1.22065	−	1.05770i	0.0398769	−	0.0345535i	−0.634694	−	0.772763i	$-0.718874\pi$
$937$	1.22065	−	1.05770i	0.0398769	−	0.0345535i	0.674571	+	0.738210i	$0.264329\pi$
$938$	−0.201346	−	0.745671i	−0.00657419	−	0.0243470i
$939$	−9.25504	−	8.01954i	−0.302027	−	0.261708i
$940$	−13.3956	+	5.42292i	−0.436917	+	0.176876i
$941$	12.6097	+	27.6113i	0.411063	+	0.900103i	0.996028	+	0.0890443i	$0.0283813\pi$
$941$	12.6097	+	27.6113i	0.411063	+	0.900103i	−0.584964	+	0.811059i	$0.698891\pi$
$942$	10.1529	−	11.2120i	0.330801	−	0.365308i
$943$	−3.38889	−	5.56735i	−0.110358	−	0.181298i
$944$	22.0710	−	4.43094i	0.718351	−	0.144215i
$945$	0.632139	+	1.38419i	0.0205635	+	0.0450277i
$946$	25.7344	−	53.2379i	0.836698	−	1.73091i
$947$	−31.2054	+	36.0129i	−1.01404	+	1.17026i	−0.0287114	+	0.999588i	$0.509140\pi$
$947$	−31.2054	+	36.0129i	−1.01404	+	1.17026i	−0.985327	+	0.170675i	$0.945405\pi$
$948$	13.5383	−	26.5116i	0.439704	−	0.861057i
$949$	20.7651	−	17.9931i	0.674065	−	0.584080i
$950$	6.72940	−	9.98416i	0.218330	−	0.323929i
$951$	−2.54438	+	8.66536i	−0.0825071	+	0.280993i
$952$	0.638196	−	9.71373i	0.0206840	−	0.314824i
$953$	−13.8306	−	1.98854i	−0.448018	−	0.0644152i	−0.0853864	−	0.996348i	$-0.527212\pi$
$953$	−13.8306	−	1.98854i	−0.448018	−	0.0644152i	−0.362631	+	0.931933i	$0.618122\pi$
$954$	5.18353	+	12.0404i	0.167823	+	0.389822i
$955$	−7.37146	+	16.1413i	−0.238535	+	0.522319i
$956$	2.17885	−	49.7849i	0.0704691	−	1.61016i
$957$	10.9364	−	7.02837i	0.353522	−	0.227195i
$958$	−18.6795	+	11.4353i	−0.603509	+	0.369458i
$959$	−28.2729	+	4.06503i	−0.912979	+	0.131267i
$960$	−3.94370	+	6.29574i	−0.127282	+	0.203194i
$961$	25.3097	+	16.2656i	0.816442	+	0.524695i
$962$	−11.7379	+	1.42644i	−0.378445	+	0.0459902i
$963$	−0.0330942	−	0.112709i	−0.00106645	−	0.00363198i
$964$	−9.48910	−	16.2900i	−0.305623	−	0.524664i
$965$	−11.2732			−0.362897
$966$	−3.62107	+	10.5076i	−0.116506	+	0.338077i
$967$			53.3923i			1.71698i	0.512829	+	0.858491i	$0.328597\pi$
$967$			53.3923i			1.71698i	−0.512829	+	0.858491i	$0.671403\pi$
$968$	4.52670	−	21.4052i	0.145494	−	0.687990i
$969$	4.14658	−	1.21754i	0.133207	−	0.0391132i
$970$	17.3735	−	2.11130i	0.557830	−	0.0677896i
$971$	−0.503556	+	0.783549i	−0.0161599	+	0.0251453i	−0.849240	−	0.528008i	$-0.822939\pi$
$971$	−0.503556	+	0.783549i	−0.0161599	+	0.0251453i	0.833080	+	0.553153i	$0.186576\pi$
$972$	−1.37456	+	1.45279i	−0.0440889	+	0.0465982i
$973$	−2.19410	−	15.2603i	−0.0703395	−	0.489222i
$974$	−14.9553	−	24.4294i	−0.479198	−	0.782769i
$975$	3.97948	+	6.19219i	0.127445	+	0.198309i
$976$	−0.866564	−	15.6472i	−0.0277380	−	0.500855i
$977$	52.9766	+	24.1936i	1.69487	+	0.774022i	0.998407	+	0.0564302i	$0.0179718\pi$
$977$	52.9766	+	24.1936i	1.69487	+	0.774022i	0.696464	+	0.717591i	$0.254755\pi$
$978$	1.79296	+	4.16471i	0.0573325	+	0.133173i
$979$	−1.26325	+	8.78609i	−0.0403736	+	0.280805i
$980$	−4.97789	−	6.27983i	−0.159013	−	0.200602i
$981$	−8.62546	−	2.53266i	−0.275390	−	0.0808617i
$982$	−50.2300	−	33.8554i	−1.60291	−	1.08037i
$983$	−12.3640	−	14.2688i	−0.394350	−	0.455104i	0.523504	−	0.852023i	$-0.324625\pi$
$983$	−12.3640	−	14.2688i	−0.394350	−	0.455104i	−0.917853	+	0.396920i	$0.870079\pi$
$984$	−1.36415	−	3.59371i	−0.0434876	−	0.114563i
$985$	3.49924	+	3.03211i	0.111495	+	0.0966111i
$986$	−3.88247	+	8.03184i	−0.123643	+	0.255786i
$987$	−11.5987	+	5.29697i	−0.369192	+	0.168604i
$988$	−0.724026	−	7.28488i	−0.0230343	−	0.231763i
$989$	7.70989	−	45.6813i	0.245160	−	1.45258i
$990$	−4.21352	−	3.81551i	−0.133915	−	0.121265i
$991$	37.2415	−	17.0076i	1.18301	−	0.540264i	0.275915	−	0.961182i	$-0.411019\pi$
$991$	37.2415	−	17.0076i	1.18301	−	0.540264i	0.907099	+	0.420917i	$0.138292\pi$
$992$	−5.23801	−	1.34945i	−0.166307	−	0.0428450i
$993$	−20.3007	+	23.4282i	−0.644223	+	0.743473i
$994$	3.80581	+	14.0946i	0.120713	+	0.447052i
$995$	12.7017	+	14.6585i	0.402671	+	0.464707i
$996$	0.0597470	+	0.242194i	0.00189316	+	0.00767420i
$997$	−6.32137	+	21.5286i	−0.200200	+	0.681818i	0.796788	+	0.604259i	$0.206531\pi$
$997$	−6.32137	+	21.5286i	−0.200200	+	0.681818i	−0.996988	+	0.0775590i	$0.975287\pi$
$998$	4.95123	−	29.7957i	0.156729	−	0.943165i
$999$	−0.668880	+	4.65216i	−0.0211624	+	0.147188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.b.19.3	✓	240
8.3	odd	2	inner	552.2.t.b.19.15	yes	240
23.17	odd	22	inner	552.2.t.b.523.15	yes	240
184.155	even	22	inner	552.2.t.b.523.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.b.19.3	✓	240	1.1	even	1	trivial
552.2.t.b.19.15	yes	240	8.3	odd	2	inner
552.2.t.b.523.3	yes	240	184.155	even	22	inner
552.2.t.b.523.15	yes	240	23.17	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34789 - 0.428007i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(1.63362 + 1.15381i) q^{4} +(-0.781202 - 0.502048i) q^{5} +(1.41388 + 0.0309246i) q^{6} +(0.233208 + 1.62200i) q^{7} +(-1.70810 - 2.25441i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-1.34789 - 0.428007i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(1.63362 + 1.15381i) q^{4} +(-0.781202 - 0.502048i) q^{5} +(1.41388 + 0.0309246i) q^{6} +(0.233208 + 1.62200i) q^{7} +(-1.70810 - 2.25441i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.838095 + 1.01107i) q^{10} +(-3.93727 - 1.79809i) q^{11} +(-1.89251 - 0.646831i) q^{12} +(1.76083 + 0.253170i) q^{13} +(0.379887 - 2.28609i) q^{14} +(0.891001 + 0.261622i) q^{15} +(1.33743 + 3.76978i) q^{16} +(1.58730 - 1.37541i) q^{17} +(-1.36532 + 0.368663i) q^{18} +(-1.55505 - 1.34746i) q^{19} +(-0.696918 - 1.72152i) q^{20} +(-0.680732 - 1.49059i) q^{21} +(4.53742 + 4.10881i) q^{22} +(4.31254 + 2.09810i) q^{23} +(2.27405 + 1.68187i) q^{24} +(-1.71885 - 3.76376i) q^{25} +(-2.26505 - 1.09489i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(-1.49051 + 2.91881i) q^{28} +(2.26983 - 1.96682i) q^{29} +(-1.08900 - 0.733992i) q^{30} +(0.269391 - 0.917461i) q^{31} +(-0.189221 - 5.65369i) q^{32} +(4.28437 + 0.615999i) q^{33} +(-2.72820 + 1.17452i) q^{34} +(0.632139 - 1.38419i) q^{35} +(1.99809 + 0.0874469i) q^{36} +(3.95389 - 2.54101i) q^{37} +(1.51931 + 2.48179i) q^{38} +(-1.76083 + 0.253170i) q^{39} +(0.202549 + 2.61870i) q^{40} +(-1.14329 - 0.734745i) q^{41} +(0.279568 + 2.30052i) q^{42} +(-2.72152 - 9.26863i) q^{43} +(-4.35735 - 7.48028i) q^{44} -0.928617 q^{45} +(-4.91483 - 4.67381i) q^{46} -7.78128i q^{47} +(-2.34533 - 3.24028i) q^{48} +(4.13996 - 1.21560i) q^{49} +(0.705910 + 5.80882i) q^{50} +(-1.13551 + 1.76689i) q^{51} +(2.58442 + 2.44525i) q^{52} +(-1.31916 - 9.17495i) q^{53} +(1.20615 - 0.738383i) q^{54} +(2.17308 + 3.38137i) q^{55} +(3.25831 - 3.29629i) q^{56} +(1.87168 + 0.854767i) q^{57} +(-3.90130 + 1.67956i) q^{58} +(0.800927 - 5.57057i) q^{59} +(1.15370 + 1.45544i) q^{60} +(-3.75910 - 1.10377i) q^{61} +(-0.755789 + 1.12134i) q^{62} +(1.07311 + 1.23843i) q^{63} +(-2.16477 + 7.70154i) q^{64} +(-1.24846 - 1.08180i) q^{65} +(-5.51121 - 2.66404i) q^{66} +(0.303170 - 0.138453i) q^{67} +(4.18002 - 0.415442i) q^{68} +(-4.72895 - 0.798132i) q^{69} +(-1.44450 + 1.59518i) q^{70} +(-5.73047 + 2.61702i) q^{71} +(-2.65578 - 0.973064i) q^{72} +(10.1145 - 11.6728i) q^{73} +(-6.41699 + 1.73272i) q^{74} +(2.70960 + 3.12704i) q^{75} +(-0.985645 - 3.99546i) q^{76} +(1.99830 - 6.80559i) q^{77} +(2.48177 + 0.412403i) q^{78} +(-2.11824 + 14.7327i) q^{79} +(0.847808 - 3.61642i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.22655 + 1.47969i) q^{82} +(-0.0674326 - 0.104927i) q^{83} +(0.607809 - 3.22050i) q^{84} +(-1.93053 + 0.277568i) q^{85} +(-0.298729 + 13.6579i) q^{86} +(-1.62377 + 2.52664i) q^{87} +(2.67162 + 11.9476i) q^{88} +(-0.577758 - 1.96766i) q^{89} +(1.25167 + 0.397454i) q^{90} +2.91511i q^{91} +(4.62423 + 8.40336i) q^{92} +0.956193i q^{93} +(-3.33044 + 10.4883i) q^{94} +(0.538318 + 1.83334i) q^{95} +(1.77438 + 5.37136i) q^{96} +(7.20490 - 11.2110i) q^{97} +(-6.10049 - 0.133431i) q^{98} +(-4.28437 + 0.615999i) 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

Properties

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