LMFDB - Embedded newform 270.2.p.a.259.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(49,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

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

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

chi := DirichletCharacter("270.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.p (of order $18$, degree $6$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			259.12
Character	$\chi$	$=$	270.259
Dual form			270.2.p.a.49.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(-1.30051 - 1.14397i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.97504 + 1.04843i) q^{5} +(-1.71229 + 0.260916i) q^{6} +(-2.45578 - 0.433021i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.382651 + 2.97550i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(-1.30051 - 1.14397i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.97504 + 1.04843i) q^{5} +(-1.71229 + 0.260916i) q^{6} +(-2.45578 - 0.433021i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.382651 + 2.97550i) q^{9} +(-0.466386 + 2.18689i) q^{10} +(0.239158 - 0.0870462i) q^{11} +(-0.900763 + 1.47940i) q^{12} +(-3.26437 - 3.89032i) q^{13} +(-1.91026 + 1.60290i) q^{14} +(3.76794 + 0.895897i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-5.39990 + 3.11764i) q^{17} +(2.52533 + 1.61948i) q^{18} +(-0.718067 + 1.24373i) q^{19} +(1.37547 + 1.76298i) q^{20} +(2.69840 + 3.37250i) q^{21} +(0.0870462 - 0.239158i) q^{22} +(6.29938 - 1.11075i) q^{23} +(0.554288 + 1.64096i) q^{24} +(2.80158 - 4.14140i) q^{25} -5.07845 q^{26} +(2.90625 - 4.30740i) q^{27} +2.49367i q^{28} +(-1.44548 - 1.21291i) q^{29} +(3.10828 - 2.31054i) q^{30} +(-1.61192 - 9.14166i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.410605 - 0.160385i) q^{33} +(-1.08274 + 6.14054i) q^{34} +(5.30426 - 1.71949i) q^{35} +(2.86385 - 0.893527i) q^{36} +(-5.20496 + 3.00509i) q^{37} +(0.491186 + 1.34952i) q^{38} +(-0.205082 + 8.79375i) q^{39} +(2.23465 + 0.0795510i) q^{40} +(-1.57268 + 1.31963i) q^{41} +(4.31798 + 0.100701i) q^{42} +(-3.22860 - 8.87051i) q^{43} +(-0.127253 - 0.220409i) q^{44} +(-3.87536 - 5.47554i) q^{45} +(3.19828 - 5.53958i) q^{46} +(4.52860 + 0.798515i) q^{47} +(1.61334 + 0.630183i) q^{48} +(-0.734489 - 0.267332i) q^{49} +(-1.37168 - 4.80817i) q^{50} +(10.5891 + 2.12283i) q^{51} +(-3.26437 + 3.89032i) q^{52} +1.27500i q^{53} +(-1.43156 - 4.99506i) q^{54} +(-0.381084 + 0.422661i) q^{55} +(1.91026 + 1.60290i) q^{56} +(2.35664 - 0.796031i) q^{57} +(-1.85828 + 0.327665i) q^{58} +(-6.31108 - 2.29705i) q^{59} +(0.227990 - 3.86627i) q^{60} +(2.18744 - 12.4056i) q^{61} +(-8.03904 - 4.64134i) q^{62} +(0.348745 - 7.47287i) q^{63} +(0.500000 + 0.866025i) q^{64} +(10.5260 + 4.26108i) q^{65} +(-0.386794 + 0.211448i) q^{66} +(6.65166 + 7.92715i) q^{67} +(4.00796 + 4.77650i) q^{68} +(-9.46307 - 5.76178i) q^{69} +(2.09231 - 5.16857i) q^{70} +(2.38639 + 4.13335i) q^{71} +(1.15636 - 2.76818i) q^{72} +(9.84831 + 5.68592i) q^{73} +(-1.04366 + 5.91886i) q^{74} +(-8.38112 + 2.18100i) q^{75} +(1.34952 + 0.491186i) q^{76} +(-0.625012 + 0.110206i) q^{77} +(6.60458 + 5.80962i) q^{78} +(2.78956 + 2.34072i) q^{79} +(1.49735 - 1.66071i) q^{80} +(-8.70716 + 2.27715i) q^{81} +2.05299i q^{82} +(-6.05105 + 7.21136i) q^{83} +(2.85269 - 3.24304i) q^{84} +(7.39640 - 11.8189i) q^{85} +(-8.87051 - 3.22860i) q^{86} +(0.492335 + 3.23099i) q^{87} +(-0.250640 - 0.0441945i) q^{88} +(-7.33307 + 12.7012i) q^{89} +(-6.68554 - 0.550914i) q^{90} +(6.33199 + 10.9673i) q^{91} +(-2.18775 - 6.01080i) q^{92} +(-8.36150 + 13.7328i) q^{93} +(3.52263 - 2.95583i) q^{94} +(0.114246 - 3.20926i) q^{95} +(1.51978 - 0.830817i) q^{96} +(-0.692131 - 1.90161i) q^{97} +(-0.676909 + 0.390813i) q^{98} +(0.350520 + 0.678304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9	$ 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} - 12 q^{11} + 6 q^{14} + 18 q^{15} + 12 q^{20} - 72 q^{21} - 18 q^{25} - 72 q^{26} + 6 q^{29} + 36 q^{30} + 36 q^{31} + 18 q^{35} - 30 q^{36} - 48 q^{39} - 12 q^{41} - 12 q^{44} - 66 q^{45} + 18 q^{49} - 12 q^{50} + 48 q^{51} - 36 q^{54} - 6 q^{56} - 84 q^{59} + 18 q^{60} - 18 q^{61} + 54 q^{64} - 6 q^{65} - 60 q^{69} - 48 q^{74} + 12 q^{75} - 72 q^{79} - 12 q^{81} - 36 q^{86} - 132 q^{89} + 30 q^{90} - 36 q^{94} - 18 q^{95} - 36 q^{99}+O(q^{100}) $ 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9 - 12 * q^11 + 6 * q^14 + 18 * q^15 + 12 * q^20 - 72 * q^21 - 18 * q^25 - 72 * q^26 + 6 * q^29 + 36 * q^30 + 36 * q^31 + 18 * q^35 - 30 * q^36 - 48 * q^39 - 12 * q^41 - 12 * q^44 - 66 * q^45 + 18 * q^49 - 12 * q^50 + 48 * q^51 - 36 * q^54 - 6 * q^56 - 84 * q^59 + 18 * q^60 - 18 * q^61 + 54 * q^64 - 6 * q^65 - 60 * q^69 - 48 * q^74 + 12 * q^75 - 72 * q^79 - 12 * q^81 - 36 * q^86 - 132 * q^89 + 30 * q^90 - 36 * q^94 - 18 * q^95 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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 $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	−1.30051	−	1.14397i	−0.750850	−	0.660473i
$3$	−1.30051	−	1.14397i	−0.750850	−	0.660473i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	−1.97504	+	1.04843i	−0.883265	+	0.468874i
$5$	−1.97504	+	1.04843i	−0.883265	+	0.468874i
$6$	−1.71229	+	0.260916i	−0.699038	+	0.106519i
$7$	−2.45578	−	0.433021i	−0.928198	−	0.163666i	−0.310942	−	0.950429i	$-0.600645\pi$
$7$	−2.45578	−	0.433021i	−0.928198	−	0.163666i	−0.617256	+	0.786762i	$0.711756\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	0.382651	+	2.97550i	0.127550	+	0.991832i
$10$	−0.466386	+	2.18689i	−0.147484	+	0.691555i
$11$	0.239158	−	0.0870462i	0.0721087	−	0.0262454i	−0.305714	−	0.952123i	$-0.598895\pi$
$11$	0.239158	−	0.0870462i	0.0721087	−	0.0262454i	0.377823	+	0.925878i	$0.376673\pi$
$12$	−0.900763	+	1.47940i	−0.260028	+	0.427066i
$13$	−3.26437	−	3.89032i	−0.905373	−	1.07898i	−0.996537	−	0.0831454i	$-0.973503\pi$
$13$	−3.26437	−	3.89032i	−0.905373	−	1.07898i	0.0911647	−	0.995836i	$-0.470941\pi$
$14$	−1.91026	+	1.60290i	−0.510538	+	0.428393i
$15$	3.76794	+	0.895897i	0.972878	+	0.231320i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−5.39990	+	3.11764i	−1.30967	+	0.756138i	−0.982041	−	0.188669i	$-0.939583\pi$
$17$	−5.39990	+	3.11764i	−1.30967	+	0.756138i	−0.327628	+	0.944807i	$0.606249\pi$
$18$	2.52533	+	1.61948i	0.595225	+	0.381716i
$19$	−0.718067	+	1.24373i	−0.164736	+	0.285331i	−0.936561	−	0.350504i	$-0.886010\pi$
$19$	−0.718067	+	1.24373i	−0.164736	+	0.285331i	0.771826	+	0.635834i	$0.219344\pi$
$20$	1.37547	+	1.76298i	0.307564	+	0.394214i
$21$	2.69840	+	3.37250i	0.588840	+	0.735939i
$22$	0.0870462	−	0.239158i	0.0185583	−	0.0509886i
$23$	6.29938	−	1.11075i	1.31351	−	0.231607i	0.527360	−	0.849642i	$-0.323182\pi$
$23$	6.29938	−	1.11075i	1.31351	−	0.231607i	0.786151	+	0.618034i	$0.212071\pi$
$24$	0.554288	+	1.64096i	0.113144	+	0.334961i
$25$	2.80158	−	4.14140i	0.560315	−	0.828279i
$26$	−5.07845			−0.995967
$27$	2.90625	−	4.30740i	0.559308	−	0.828960i
$28$			2.49367i			0.471259i
$29$	−1.44548	−	1.21291i	−0.268420	−	0.225231i	0.498636	−	0.866812i	$-0.333835\pi$
$29$	−1.44548	−	1.21291i	−0.268420	−	0.225231i	−0.767056	+	0.641581i	$0.778279\pi$
$30$	3.10828	−	2.31054i	0.567492	−	0.421845i
$31$	−1.61192	−	9.14166i	−0.289510	−	1.64189i	−0.688717	−	0.725030i	$-0.741826\pi$
$31$	−1.61192	−	9.14166i	−0.289510	−	1.64189i	0.399207	−	0.916861i	$-0.369285\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−0.410605	−	0.160385i	−0.0714772	−	0.0279195i
$34$	−1.08274	+	6.14054i	−0.185689	+	1.05309i
$35$	5.30426	−	1.71949i	0.896584	−	0.290647i
$36$	2.86385	−	0.893527i	0.477308	−	0.148921i
$37$	−5.20496	+	3.00509i	−0.855690	+	0.494033i	−0.862567	−	0.505943i	$-0.831144\pi$
$37$	−5.20496	+	3.00509i	−0.855690	+	0.494033i	0.00687650	+	0.999976i	$0.497811\pi$
$38$	0.491186	+	1.34952i	0.0796810	+	0.218922i
$39$	−0.205082	+	8.79375i	−0.0328395	+	1.40813i
$40$	2.23465	+	0.0795510i	0.353330	+	0.0125781i
$41$	−1.57268	+	1.31963i	−0.245611	+	0.206092i	−0.757280	−	0.653091i	$-0.773472\pi$
$41$	−1.57268	+	1.31963i	−0.245611	+	0.206092i	0.511669	+	0.859183i	$0.329028\pi$
$42$	4.31798	+	0.100701i	0.666279	+	0.0155385i
$43$	−3.22860	−	8.87051i	−0.492357	−	1.35274i	−0.898517	−	0.438939i	$-0.855355\pi$
$43$	−3.22860	−	8.87051i	−0.492357	−	1.35274i	0.406160	−	0.913802i	$-0.366868\pi$
$44$	−0.127253	−	0.220409i	−0.0191841	−	0.0332279i
$45$	−3.87536	−	5.47554i	−0.577705	−	0.816246i
$46$	3.19828	−	5.53958i	0.471560	−	0.816767i
$47$	4.52860	+	0.798515i	0.660564	+	0.116475i	0.493873	−	0.869534i	$-0.335581\pi$
$47$	4.52860	+	0.798515i	0.660564	+	0.116475i	0.166691	+	0.986009i	$0.446692\pi$
$48$	1.61334	+	0.630183i	0.232866	+	0.0909590i
$49$	−0.734489	−	0.267332i	−0.104927	−	0.0381903i
$50$	−1.37168	−	4.80817i	−0.193984	−	0.679978i
$51$	10.5891	+	2.12283i	1.48277	+	0.297256i
$52$	−3.26437	+	3.89032i	−0.452686	+	0.539491i
$53$			1.27500i			0.175135i	0.996159	+	0.0875675i	$0.0279094\pi$
$53$			1.27500i			0.175135i	−0.996159	+	0.0875675i	$0.972091\pi$
$54$	−1.43156	−	4.99506i	−0.194811	−	0.679742i
$55$	−0.381084	+	0.422661i	−0.0513853	+	0.0569915i
$56$	1.91026	+	1.60290i	0.255269	+	0.214196i
$57$	2.35664	−	0.796031i	0.312145	−	0.105437i
$58$	−1.85828	+	0.327665i	−0.244004	+	0.0430245i
$59$	−6.31108	−	2.29705i	−0.821633	−	0.299050i	−0.103213	−	0.994659i	$-0.532912\pi$
$59$	−6.31108	−	2.29705i	−0.821633	−	0.299050i	−0.718420	+	0.695609i	$0.755134\pi$
$60$	0.227990	−	3.86627i	0.0294334	−	0.499133i
$61$	2.18744	−	12.4056i	0.280073	−	1.58837i	−0.442299	−	0.896867i	$-0.645837\pi$
$61$	2.18744	−	12.4056i	0.280073	−	1.58837i	0.722372	−	0.691504i	$-0.243052\pi$
$62$	−8.03904	−	4.64134i	−1.02096	−	0.589451i
$63$	0.348745	−	7.47287i	0.0439377	−	0.941493i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	10.5260	+	4.26108i	1.30559	+	0.528521i
$66$	−0.386794	+	0.211448i	−0.0476111	+	0.0260275i
$67$	6.65166	+	7.92715i	0.812630	+	0.968455i	0.999904	−	0.0138528i	$-0.00440963\pi$
$67$	6.65166	+	7.92715i	0.812630	+	0.968455i	−0.187274	+	0.982308i	$0.559965\pi$
$68$	4.00796	+	4.77650i	0.486036	+	0.579235i
$69$	−9.46307	−	5.76178i	−1.13922	−	0.693637i
$70$	2.09231	−	5.16857i	0.250079	−	0.617762i
$71$	2.38639	+	4.13335i	0.283213	+	0.490539i	0.972174	−	0.234259i	$-0.0752664\pi$
$71$	2.38639	+	4.13335i	0.283213	+	0.490539i	−0.688962	+	0.724798i	$0.741933\pi$
$72$	1.15636	−	2.76818i	0.136279	−	0.326233i
$73$	9.84831	+	5.68592i	1.15266	+	0.665487i	0.949533	−	0.313666i	$-0.101557\pi$
$73$	9.84831	+	5.68592i	1.15266	+	0.665487i	0.203124	+	0.979153i	$0.434891\pi$
$74$	−1.04366	+	5.91886i	−0.121322	+	0.688054i
$75$	−8.38112	+	2.18100i	−0.967769	+	0.251840i
$76$	1.34952	+	0.491186i	0.154801	+	0.0563430i
$77$	−0.625012	+	0.110206i	−0.0712267	+	0.0125592i
$78$	6.60458	+	5.80962i	0.747821	+	0.657810i
$79$	2.78956	+	2.34072i	0.313850	+	0.263351i	0.786081	−	0.618123i	$-0.212107\pi$
$79$	2.78956	+	2.34072i	0.313850	+	0.263351i	−0.472231	+	0.881475i	$0.656551\pi$
$80$	1.49735	−	1.66071i	0.167408	−	0.185673i
$81$	−8.70716	+	2.27715i	−0.967462	+	0.253017i
$82$			2.05299i			0.226714i
$83$	−6.05105	+	7.21136i	−0.664189	+	0.791549i	−0.987980	−	0.154579i	$-0.950598\pi$
$83$	−6.05105	+	7.21136i	−0.664189	+	0.791549i	0.323792	+	0.946128i	$0.395042\pi$
$84$	2.85269	−	3.24304i	0.311254	−	0.353844i
$85$	7.39640	−	11.8189i	0.802252	−	1.28194i
$86$	−8.87051	−	3.22860i	−0.956532	−	0.348149i
$87$	0.492335	+	3.23099i	0.0527839	+	0.346399i
$88$	−0.250640	−	0.0441945i	−0.0267183	−	0.00471115i
$89$	−7.33307	+	12.7012i	−0.777304	+	1.34633i	0.156187	+	0.987727i	$0.450080\pi$
$89$	−7.33307	+	12.7012i	−0.777304	+	1.34633i	−0.933491	+	0.358602i	$0.883254\pi$
$90$	−6.68554	−	0.550914i	−0.704718	−	0.0580715i
$91$	6.33199	+	10.9673i	0.663773	+	1.14969i
$92$	−2.18775	−	6.01080i	−0.228089	−	0.626669i
$93$	−8.36150	+	13.7328i	−0.867047	+	1.42403i
$94$	3.52263	−	2.95583i	0.363331	−	0.304871i
$95$	0.114246	−	3.20926i	0.0117214	−	0.329263i
$96$	1.51978	−	0.830817i	0.155112	−	0.0847950i
$97$	−0.692131	−	1.90161i	−0.0702752	−	0.193080i	0.899583	−	0.436750i	$-0.143871\pi$
$97$	−0.692131	−	1.90161i	−0.0702752	−	0.193080i	−0.969858	+	0.243671i	$0.921648\pi$
$98$	−0.676909	+	0.390813i	−0.0683781	+	0.0394781i
$99$	0.350520	+	0.678304i	0.0352285	+	0.0681721i
$100$	−4.56497	−	2.03987i	−0.456497	−	0.203987i
$101$	0.932240	−	5.28700i	0.0927614	−	0.526076i	−0.902649	−	0.430377i	$-0.858380\pi$
$101$	0.932240	−	5.28700i	0.0927614	−	0.526076i	0.995410	−	0.0956984i	$-0.0305084\pi$
$102$	8.43274	−	6.74721i	0.834965	−	0.668073i
$103$	0.121009	−	0.332469i	0.0119234	−	0.0327592i	−0.933588	−	0.358348i	$-0.883340\pi$
$103$	0.121009	−	0.332469i	0.0119234	−	0.0327592i	0.945512	+	0.325589i	$0.105562\pi$
$104$	0.881864	+	5.00130i	0.0864739	+	0.490418i
$105$	−8.86530	−	3.83172i	−0.865164	−	0.373938i
$106$	0.976708	+	0.819556i	0.0948663	+	0.0796023i
$107$		−	11.5113i		−	1.11284i	−0.830901	−	0.556420i	$-0.812175\pi$
$107$		−	11.5113i		−	1.11284i	0.830901	−	0.556420i	$-0.187825\pi$
$108$	−4.74663	−	2.11412i	−0.456745	−	0.203431i
$109$	−5.00724			−0.479607			−0.239803	−	0.970821i	$-0.577083\pi$
$109$	−5.00724			−0.479607			−0.239803	+	0.970821i	$0.577083\pi$
$110$	0.0788208	+	0.563608i	0.00751527	+	0.0537379i
$111$	10.2068	+	2.04619i	0.968790	+	0.194216i
$112$	2.45578	−	0.433021i	0.232050	−	0.0409166i
$113$	1.11510	−	3.06371i	0.104900	−	0.288209i	−0.876128	−	0.482079i	$-0.839882\pi$
$113$	1.11510	−	3.06371i	0.104900	−	0.288209i	0.981027	+	0.193870i	$0.0621040\pi$
$114$	0.905026	−	2.31697i	0.0847635	−	0.217004i
$115$	−11.2770	+	8.79826i	−1.05158	+	0.820442i
$116$	−0.943473	+	1.63414i	−0.0875993	+	0.151726i
$117$	10.3265	−	11.2017i	0.954688	−	1.03560i
$118$	−5.81632	+	3.35806i	−0.535436	+	0.309134i
$119$	14.6110	−	5.31797i	1.33939	−	0.487497i
$120$	−2.81518	−	2.65984i	−0.256990	−	0.242809i
$121$	−8.37687	+	7.02903i	−0.761534	+	0.639003i
$122$	−8.09717	−	9.64983i	−0.733083	−	0.873654i
$123$	3.55491	+	0.0829053i	0.320535	+	0.00747532i
$124$	−8.72287	+	3.17487i	−0.783337	+	0.285111i
$125$	−1.19125	+	11.1167i	−0.106549	+	0.994307i
$126$	−5.50038	−	5.07062i	−0.490013	−	0.451727i
$127$	5.98618	+	3.45612i	0.531188	+	0.306681i	0.741500	−	0.670953i	$-0.234115\pi$
$127$	5.98618	+	3.45612i	0.531188	+	0.306681i	−0.210312	+	0.977634i	$0.567448\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	−5.94880	+	15.2296i	−0.523763	+	1.34089i
$130$	10.0302	−	5.32442i	0.879703	−	0.466983i
$131$	0.586596	+	3.32675i	0.0512511	+	0.290660i	0.999651	−	0.0264172i	$-0.00840983\pi$
$131$	0.586596	+	3.32675i	0.0512511	+	0.290660i	−0.948400	+	0.317077i	$0.897299\pi$
$132$	−0.0866479	+	0.432218i	−0.00754173	+	0.0376197i
$133$	2.30197	−	2.74339i	0.199607	−	0.237882i
$134$	10.3482			0.893944
$135$	−1.22393	+	11.5543i	−0.105339	+	0.994436i
$136$	6.23527			0.534670
$137$	−12.9209	+	15.3985i	−1.10390	+	1.31558i	−0.159350	+	0.987222i	$0.550940\pi$
$137$	−12.9209	+	15.3985i	−1.10390	+	1.31558i	−0.944553	+	0.328358i	$0.893505\pi$
$138$	−10.4965	+	3.54553i	−0.893523	+	0.301816i
$139$	−0.364881	−	2.06935i	−0.0309488	−	0.175520i	0.965415	−	0.260717i	$-0.0839590\pi$
$139$	−0.364881	−	2.06935i	−0.0309488	−	0.175520i	−0.996364	+	0.0851975i	$0.972848\pi$
$140$	−2.61444	−	4.92509i	−0.220961	−	0.416246i
$141$	−4.97601	−	6.21907i	−0.419056	−	0.523741i
$142$	4.70027	+	0.828785i	0.394438	+	0.0695501i
$143$	−1.11934	−	0.646249i	−0.0936036	−	0.0540421i
$144$	−1.37725	−	2.66518i	−0.114771	−	0.222098i
$145$	4.12654	+	0.880045i	0.342691	+	0.0730837i
$146$	10.6860	−	3.88940i	0.884383	−	0.321889i
$147$	0.649389	+	1.18790i	0.0535607	+	0.0979767i
$148$	3.86326	+	4.60406i	0.317558	+	0.378451i
$149$	13.3991	−	11.2432i	1.09770	−	0.921080i	0.100432	−	0.994944i	$-0.467978\pi$
$149$	13.3991	−	11.2432i	1.09770	−	0.921080i	0.997268	+	0.0738640i	$0.0235331\pi$
$150$	−3.71654	+	7.82223i	−0.303454	+	0.638683i
$151$	−14.4728	+	5.26767i	−1.17778	+	0.428677i	−0.855417	−	0.517939i	$-0.826699\pi$
$151$	−14.4728	+	5.26767i	−1.17778	+	0.428677i	−0.322363	+	0.946616i	$0.604477\pi$
$152$	1.24373	−	0.718067i	0.100880	−	0.0582429i
$153$	−11.3428	−	14.8744i	−0.917010	−	1.20253i
$154$	−0.317327	+	0.549626i	−0.0255709	+	0.0442901i
$155$	12.7680	+	16.3652i	1.02555	+	1.31448i
$156$	8.69577	−	1.32505i	0.696218	−	0.106089i
$157$	−4.72782	+	12.9896i	−0.377321	+	1.03668i	0.595141	+	0.803621i	$0.297096\pi$
$157$	−4.72782	+	12.9896i	−0.377321	+	1.03668i	−0.972462	+	0.233060i	$0.925126\pi$
$158$	3.58619	−	0.632341i	0.285302	−	0.0503064i
$159$	1.45857	−	1.65815i	0.115672	−	0.131500i
$160$	−0.309701	−	2.21452i	−0.0244840	−	0.175073i
$161$	−15.9509			−1.25711
$162$	−3.85245	+	8.13379i	−0.302677	+	0.639051i
$163$		−	17.9745i		−	1.40787i	−0.710263	−	0.703936i	$-0.751424\pi$
$163$		−	17.9745i		−	1.40787i	0.710263	−	0.703936i	$-0.248576\pi$
$164$	1.57268	+	1.31963i	0.122806	+	0.103046i
$165$	0.979116	−	0.113724i	0.0762241	−	0.00885343i
$166$	1.63468	+	9.27074i	0.126876	+	0.719549i
$167$	7.87747	−	21.6432i	0.609577	−	1.67480i	−0.121573	−	0.992583i	$-0.538794\pi$
$167$	7.87747	−	21.6432i	0.609577	−	1.67480i	0.731150	−	0.682217i	$-0.238984\pi$
$168$	−0.650638	−	4.26987i	−0.0501979	−	0.329428i
$169$	−2.22108	+	12.5964i	−0.170852	+	0.968953i
$170$	−4.29949	−	13.2630i	−0.329756	−	1.01723i
$171$	−3.97548	−	1.66069i	−0.304012	−	0.126996i
$172$	−8.17511	+	4.71990i	−0.623346	+	0.359889i
$173$	−3.42659	−	9.41449i	−0.260519	−	0.715771i	−0.999133	−	0.0416414i	$-0.986741\pi$
$173$	−3.42659	−	9.41449i	−0.260519	−	0.715771i	0.738613	−	0.674129i	$-0.235481\pi$
$174$	2.79155	+	1.69969i	0.211627	+	0.128853i
$175$	−8.67337	+	8.95723i	−0.655645	+	0.677103i
$176$	−0.194963	+	0.163593i	−0.0146959	+	0.0123313i
$177$	5.57986	+	10.2070i	0.419408	+	0.767208i
$178$	5.01611	+	13.7817i	0.375974	+	1.03298i
$179$	−3.71155	−	6.42859i	−0.277414	−	0.480495i	0.693327	−	0.720623i	$-0.256144\pi$
$179$	−3.71155	−	6.42859i	−0.277414	−	0.480495i	−0.970741	+	0.240127i	$0.922811\pi$
$180$	−4.71941	+	4.76730i	−0.351764	+	0.355334i
$181$	1.98039	−	3.43014i	0.147201	−	0.254960i	−0.782991	−	0.622033i	$-0.786307\pi$
$181$	1.98039	−	3.43014i	0.147201	−	0.254960i	0.930192	+	0.367073i	$0.119640\pi$
$182$	12.4716	+	2.19908i	0.924455	+	0.163006i
$183$	−17.0364	+	13.6312i	−1.25937	+	1.00765i
$184$	−6.01080	−	2.18775i	−0.443122	−	0.161283i
$185$	7.12938	−	11.3922i	0.524162	−	0.837573i
$186$	5.14528	+	15.2326i	0.377270	+	1.11691i
$187$	−1.02005	+	1.21565i	−0.0745934	+	0.0888970i
$188$		−	4.59846i		−	0.335377i
$189$	−9.00230	+	9.31958i	−0.654821	+	0.677900i
$190$	−2.38500	−	2.15039i	−0.173026	−	0.156006i
$191$	−13.2485	−	11.1168i	−0.958630	−	0.804386i	0.0220998	−	0.999756i	$-0.492965\pi$
$191$	−13.2485	−	11.1168i	−0.958630	−	0.804386i	−0.980730	+	0.195370i	$0.937409\pi$
$192$	0.340455	−	1.69826i	0.0245702	−	0.122561i
$193$	5.45111	−	0.961177i	0.392379	−	0.0691871i	0.0260222	−	0.999661i	$-0.491716\pi$
$193$	5.45111	−	0.961177i	0.392379	−	0.0691871i	0.366357	+	0.930474i	$0.380605\pi$
$194$	−1.90161	−	0.692131i	−0.136528	−	0.0496921i
$195$	−8.81461	−	17.5830i	−0.631228	−	1.25915i
$196$	−0.135728	+	0.769752i	−0.00969486	+	0.0549823i
$197$	−7.08302	−	4.08938i	−0.504644	−	0.291357i	0.225985	−	0.974131i	$-0.427440\pi$
$197$	−7.08302	−	4.08938i	−0.504644	−	0.291357i	−0.730629	+	0.682774i	$0.760773\pi$
$198$	0.744921	+	0.167492i	0.0529392	+	0.0119031i
$199$	6.70053	+	11.6057i	0.474988	+	0.822704i	0.999590	−	0.0286442i	$-0.00911898\pi$
$199$	6.70053	+	11.6057i	0.474988	+	0.822704i	−0.524601	+	0.851348i	$0.675786\pi$
$200$	−4.49693	+	2.18577i	−0.317981	+	0.154557i
$201$	0.417888	−	17.9187i	0.0294755	−	1.26388i
$202$	−3.45084	−	4.11255i	−0.242800	−	0.289358i
$203$	3.02458	+	3.60456i	0.212284	+	0.252990i
$204$	0.251798	−	10.7969i	0.0176294	−	0.755932i
$205$	1.72256	−	4.25518i	0.120309	−	0.297195i
$206$	−0.176903	−	0.306406i	−0.0123254	−	0.0213483i
$207$	5.71550	+	18.3187i	0.397254	+	1.27324i
$208$	4.39807	+	2.53923i	0.304951	+	0.176064i
$209$	−0.0634692	+	0.359952i	−0.00439026	+	0.0248984i
$210$	−8.63377	+	4.32823i	−0.595787	+	0.298676i
$211$	−7.83539	−	2.85185i	−0.539411	−	0.196329i	0.0579247	−	0.998321i	$-0.481552\pi$
$211$	−7.83539	−	2.85185i	−0.539411	−	0.196329i	−0.597335	+	0.801991i	$0.703774\pi$
$212$	1.25563	−	0.221402i	0.0862372	−	0.0152059i
$213$	1.62492	−	8.10543i	0.111338	−	0.555375i
$214$	−8.81817	−	7.39933i	−0.602798	−	0.505807i
$215$	15.6768	+	14.1347i	1.06915	+	0.963976i
$216$	−4.67059	+	2.27720i	−0.317793	+	0.154944i
$217$			23.1479i			1.57138i
$218$	−3.21859	+	3.83577i	−0.217991	+	0.259791i
$219$	−6.30328	−	18.6608i	−0.425936	−	1.26098i
$220$	0.482414	+	0.301900i	0.0325243	+	0.0203541i
$221$	29.7559	+	10.8303i	2.00160	+	0.728522i
$222$	8.12830	−	6.50362i	0.545536	−	0.436495i
$223$	−6.58229	−	1.16064i	−0.440783	−	0.0777219i	−0.0511476	−	0.998691i	$-0.516288\pi$
$223$	−6.58229	−	1.16064i	−0.440783	−	0.0777219i	−0.389635	+	0.920969i	$0.627399\pi$
$224$	1.24683	−	2.15958i	0.0833076	−	0.144293i
$225$	13.3947	+	6.75137i	0.892982	+	0.450091i
$226$	−1.63016	−	2.82353i	−0.108437	−	0.187818i
$227$	−5.59754	−	15.3791i	−0.371522	−	1.02075i	−0.974773	−	0.223197i	$-0.928351\pi$
$227$	−5.59754	−	15.3791i	−0.371522	−	1.02075i	0.603251	−	0.797551i	$-0.293872\pi$
$228$	−1.19316	−	2.18261i	−0.0790192	−	0.144547i
$229$	21.1001	−	17.7051i	1.39433	−	1.16999i	0.430786	−	0.902454i	$-0.358237\pi$
$229$	21.1001	−	17.7051i	1.39433	−	1.16999i	0.963549	−	0.267531i	$-0.0862079\pi$
$230$	−0.508852	+	14.2941i	−0.0335527	+	0.942524i
$231$	0.938907	+	0.571672i	0.0617755	+	0.0376133i
$232$	0.645373	+	1.77315i	0.0423708	+	0.116413i
$233$	11.2917	−	6.51927i	0.739744	−	0.427092i	−0.0822320	−	0.996613i	$-0.526205\pi$
$233$	11.2917	−	6.51927i	0.739744	−	0.427092i	0.821976	+	0.569522i	$0.192872\pi$
$234$	−1.94327	−	15.1109i	−0.127036	−	0.987832i
$235$	−9.78136	+	3.17084i	−0.638066	+	0.206843i
$236$	−1.16624	+	6.61408i	−0.0759158	+	0.430540i
$237$	−0.950129	−	6.23530i	−0.0617175	−	0.405026i
$238$	5.31797	−	14.6110i	0.344713	−	0.947090i
$239$	−1.36027	−	7.71447i	−0.0879885	−	0.499008i	−0.996672	−	0.0815212i	$-0.974022\pi$
$239$	−1.36027	−	7.71447i	−0.0879885	−	0.499008i	0.908683	−	0.417487i	$-0.137089\pi$
$240$	−3.84712	+	0.446843i	−0.248331	+	0.0288436i
$241$	−12.6084	−	10.5797i	−0.812180	−	0.681500i	0.138947	−	0.990300i	$-0.455628\pi$
$241$	−12.6084	−	10.5797i	−0.812180	−	0.681500i	−0.951127	+	0.308800i	$0.900073\pi$
$242$			10.9352i			0.702943i
$243$	13.9287	+	6.99930i	0.893529	+	0.449005i
$244$	−12.5970			−0.806438
$245$	1.73093	−	0.242071i	0.110585	−	0.0154653i
$246$	2.34856	−	2.66993i	0.149739	−	0.170228i
$247$	7.18254	−	1.26647i	0.457014	−	0.0805839i
$248$	−3.17487	+	8.72287i	−0.201604	+	0.553903i
$249$	16.1190	−	2.45620i	1.02150	−	0.155656i
$250$	7.75016	+	8.05823i	0.490163	+	0.509647i
$251$	−9.89267	+	17.1346i	−0.624420	+	1.08153i	0.364233	+	0.931308i	$0.381331\pi$
$251$	−9.89267	+	17.1346i	−0.624420	+	1.08153i	−0.988653	+	0.150219i	$0.952002\pi$
$252$	−7.41990	+	0.954203i	−0.467410	+	0.0601092i
$253$	1.40986	−	0.813982i	0.0886370	−	0.0511746i
$254$	6.49539	−	2.36413i	0.407557	−	0.148339i
$255$	−23.1396	+	6.90931i	−1.44906	+	0.432678i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−10.4092	−	12.4052i	−0.649311	−	0.773818i	0.336499	−	0.941684i	$-0.390757\pi$
$257$	−10.4092	−	12.4052i	−0.649311	−	0.773818i	−0.985810	+	0.167866i	$0.946313\pi$
$258$	7.84275	+	14.3465i	0.488268	+	0.893171i
$259$	14.0835	−	5.12598i	0.875107	−	0.318513i
$260$	2.36852	−	11.1060i	0.146889	−	0.688766i
$261$	3.05588	−	4.76515i	0.189154	−	0.294956i
$262$	2.92550	+	1.68904i	0.180738	+	0.104349i
$263$	0.834935	+	0.147222i	0.0514843	+	0.00907807i	0.199331	−	0.979932i	$-0.436123\pi$
$263$	0.834935	+	0.147222i	0.0514843	+	0.00907807i	−0.147847	+	0.989010i	$0.547234\pi$
$264$	0.275402	+	0.344200i	0.0169498	+	0.0211841i
$265$	−1.33675	−	2.51818i	−0.0821162	−	0.154691i
$266$	−0.621875	−	3.52683i	−0.0381296	−	0.216244i
$267$	24.0666	−	8.12926i	1.47285	−	0.497503i
$268$	6.65166	−	7.92715i	0.406315	−	0.484227i
$269$	−1.30043			−0.0792888			−0.0396444	−	0.999214i	$-0.512623\pi$
$269$	−1.30043			−0.0792888			−0.0396444	+	0.999214i	$0.512623\pi$
$270$	8.06438	+	8.36455i	0.490783	+	0.509050i
$271$	19.2898			1.17177			0.585885	−	0.810394i	$-0.300747\pi$
$271$	19.2898			1.17177			0.585885	+	0.810394i	$0.300747\pi$
$272$	4.00796	−	4.77650i	0.243018	−	0.289618i
$273$	4.31151	−	21.5067i	0.260945	−	1.30165i
$274$	3.49055	+	19.7959i	0.210872	+	1.19591i
$275$	0.309525	−	1.23431i	0.0186651	−	0.0744319i
$276$	−4.03100	+	10.3198i	−0.242638	+	0.621181i
$277$	6.21068	+	1.09511i	0.373163	+	0.0657988i	0.357085	−	0.934072i	$-0.383771\pi$
$277$	6.21068	+	1.09511i	0.373163	+	0.0657988i	0.0160786	+	0.999871i	$0.494882\pi$
$278$	−1.81975	−	1.05063i	−0.109141	−	0.0630129i
$279$	26.5842	−	8.29433i	1.59155	−	0.496569i
$280$	−5.45337	−	1.16301i	−0.325901	−	0.0695032i
$281$	27.1134	−	9.86846i	1.61745	−	0.588703i	0.634555	−	0.772878i	$-0.281183\pi$
$281$	27.1134	−	9.86846i	1.61745	−	0.588703i	0.982894	+	0.184175i	$0.0589612\pi$
$282$	−7.96260	−	0.185699i	−0.474166	−	0.0110582i
$283$	−12.2507	−	14.5998i	−0.728227	−	0.867867i	0.267175	−	0.963648i	$-0.413910\pi$
$283$	−12.2507	−	14.5998i	−0.728227	−	0.867867i	−0.995402	+	0.0957807i	$0.969465\pi$
$284$	3.65616	−	3.06789i	0.216953	−	0.182046i
$285$	−3.81988	+	4.04298i	−0.226270	+	0.239485i
$286$	−1.21455	+	0.442060i	−0.0718179	+	0.0261396i
$287$	4.43358	−	2.55973i	0.261706	−	0.151096i
$288$	−2.92693	−	0.658106i	−0.172471	−	0.0387792i
$289$	10.9393	−	18.9474i	0.643489	−	1.11456i
$290$	3.32664	−	2.59543i	0.195347	−	0.152409i
$291$	−1.27527	+	3.26485i	−0.0747578	+	0.191389i
$292$	3.88940	−	10.6860i	0.227610	−	0.625353i
$293$	0.488280	−	0.0860969i	0.0285256	−	0.00502984i	−0.159367	−	0.987219i	$-0.550945\pi$
$293$	0.488280	−	0.0860969i	0.0285256	−	0.00502984i	0.187893	+	0.982190i	$0.439834\pi$
$294$	1.32741	+	0.266109i	0.0774159	+	0.0155198i
$295$	14.8729	−	2.07999i	0.865936	−	0.121101i
$296$	6.01017			0.349334
$297$	0.320108	−	1.28313i	0.0185745	−	0.0744545i
$298$		−	17.4913i		−	1.01325i
$299$	−24.8847	−	20.8807i	−1.43912	−	1.20756i
$300$	3.60323	+	7.87507i	0.208033	+	0.454667i
$301$	4.08763	+	23.1821i	0.235607	+	1.33619i
$302$	−5.26767	+	14.4728i	−0.303120	+	0.832816i
$303$	−7.26057	+	5.80933i	−0.417109	+	0.333737i
$304$	0.249382	−	1.41432i	0.0143030	−	0.0811165i
$305$	8.68614	+	26.7949i	0.497367	+	1.53427i
$306$	−18.6855	−	0.872016i	−1.06818	−	0.0498499i
$307$	−14.6436	+	8.45449i	−0.835755	+	0.482523i	−0.855819	−	0.517275i	$-0.826946\pi$
$307$	−14.6436	+	8.45449i	−0.835755	+	0.482523i	0.0200640	+	0.999799i	$0.493613\pi$
$308$	0.217064	+	0.596379i	0.0123684	+	0.0339819i
$309$	−0.537710	+	0.293949i	−0.0305892	+	0.0167222i
$310$	20.7436	+	0.738447i	1.17816	+	0.0419410i
$311$	−2.25290	+	1.89041i	−0.127750	+	0.107195i	−0.704424	−	0.709779i	$-0.748795\pi$
$311$	−2.25290	+	1.89041i	−0.127750	+	0.107195i	0.576674	+	0.816974i	$0.304350\pi$
$312$	4.57448	−	7.51307i	0.258979	−	0.425344i
$313$	8.77835	+	24.1183i	0.496181	+	1.36325i	0.894938	+	0.446191i	$0.147220\pi$
$313$	8.77835	+	24.1183i	0.496181	+	1.36325i	−0.398757	+	0.917057i	$0.630558\pi$
$314$	6.91161	+	11.9713i	0.390045	+	0.675577i
$315$	7.14602	+	15.1249i	0.402632	+	0.852189i
$316$	1.82075	−	3.15364i	0.102425	−	0.177406i
$317$	−16.5595	−	2.91989i	−0.930076	−	0.163998i	−0.311970	−	0.950092i	$-0.600989\pi$
$317$	−16.5595	−	2.91989i	−0.930076	−	0.163998i	−0.618106	+	0.786094i	$0.712100\pi$
$318$	−0.332669	−	2.18317i	−0.0186552	−	0.122426i
$319$	−0.451277	−	0.164252i	−0.0252667	−	0.00919632i
$320$	−1.89549	−	1.18622i	−0.105961	−	0.0663117i
$321$	−13.1686	+	14.9706i	−0.735001	+	0.835576i
$322$	−10.2530	+	12.2191i	−0.571379	+	0.680943i
$323$		−	8.95468i		−	0.498252i
$324$	3.75454	+	8.17945i	0.208585	+	0.454414i
$325$	−25.2567	+	2.62001i	−1.40099	+	0.145332i
$326$	−13.7693	−	11.5538i	−0.762610	−	0.639905i
$327$	6.51197	+	5.72815i	0.360113	+	0.316768i
$328$	2.02180	−	0.356497i	0.111635	−	0.0196843i
$329$	−10.7755	−	3.92196i	−0.594072	−	0.216224i
$330$	0.542246	−	0.823147i	0.0298496	−	0.0453127i
$331$	2.87968	−	16.3315i	0.158281	−	0.897658i	−0.797443	−	0.603395i	$-0.793814\pi$
$331$	2.87968	−	16.3315i	0.158281	−	0.897658i	0.955724	−	0.294264i	$-0.0950745\pi$
$332$	8.15255	+	4.70688i	0.447429	+	0.258324i
$333$	−10.9333	−	14.3374i	−0.599141	−	0.785687i
$334$	−11.5161	−	19.9465i	−0.630133	−	1.09142i
$335$	−21.4484	−	8.68261i	−1.17185	−	0.474382i
$336$	−3.68913	−	2.24620i	−0.201259	−	0.122540i
$337$	5.19822	+	6.19499i	0.283165	+	0.337463i	0.888813	−	0.458270i	$-0.151531\pi$
$337$	5.19822	+	6.19499i	0.283165	+	0.337463i	−0.605648	+	0.795732i	$0.707086\pi$
$338$	8.22171	+	9.79825i	0.447202	+	0.532954i
$339$	−4.95499	+	2.70874i	−0.269118	+	0.147118i
$340$	−12.9237	−	5.23170i	−0.700887	−	0.283729i
$341$	−1.18125	−	2.04599i	−0.0639683	−	0.110796i
$342$	−3.82755	+	1.97792i	−0.206970	+	0.106954i
$343$	16.8050	+	9.70239i	0.907387	+	0.523880i
$344$	−1.63920	+	9.29639i	−0.0883800	+	0.501228i
$345$	24.7308	+	1.45835i	1.33146	+	0.0785151i
$346$	−9.41449	−	3.42659i	−0.506126	−	0.184215i
$347$	−14.0119	+	2.47067i	−0.752198	+	0.132633i	−0.536585	−	0.843846i	$-0.680286\pi$
$347$	−14.0119	+	2.47067i	−0.752198	+	0.132633i	−0.215613	+	0.976479i	$0.569175\pi$
$348$	3.09641	−	1.04591i	0.165985	−	0.0560667i
$349$	14.1804	+	11.8988i	0.759062	+	0.636928i	0.937882	−	0.346953i	$-0.112784\pi$
$349$	14.1804	+	11.8988i	0.759062	+	0.636928i	−0.178821	+	0.983882i	$0.557228\pi$
$350$	1.28650	+	12.4018i	0.0687663	+	0.662903i
$351$	−26.2442	+	2.75471i	−1.40081	+	0.147036i
$352$			0.254506i			0.0135652i
$353$	−14.9197	+	17.7806i	−0.794097	+	0.946368i	−0.999478	−	0.0323144i	$-0.989712\pi$
$353$	−14.9197	+	17.7806i	−0.794097	+	0.946368i	0.205381	+	0.978682i	$0.434157\pi$
$354$	11.4057	+	2.28653i	0.606207	+	0.121528i
$355$	−9.04677	−	5.66157i	−0.480153	−	0.300485i
$356$	13.7817	+	5.01611i	0.730426	+	0.265853i
$357$	−25.0853	−	9.79852i	−1.32766	−	0.518592i
$358$	−7.31032	−	1.28901i	−0.386363	−	0.0681262i
$359$	14.9035	−	25.8136i	0.786575	−	1.36239i	−0.141479	−	0.989941i	$-0.545186\pi$
$359$	14.9035	−	25.8136i	0.786575	−	1.36239i	0.928054	−	0.372447i	$-0.121481\pi$
$360$	0.618388	+	6.67964i	0.0325919	+	0.352048i
$361$	8.46876	+	14.6683i	0.445724	+	0.772017i
$362$	−1.35467	−	3.72192i	−0.0711997	−	0.195620i
$363$	18.9352	+	0.441595i	0.993841	+	0.0231777i
$364$	9.70117	−	8.14025i	0.508479	−	0.426665i
$365$	−25.4121	−	0.904642i	−1.33013	−	0.0473511i
$366$	−0.508701	+	21.8126i	−0.0265902	+	1.14016i
$367$	−8.70455	−	23.9156i	−0.454374	−	1.24838i	−0.929617	−	0.368527i	$-0.879862\pi$
$367$	−8.70455	−	23.9156i	−0.454374	−	1.24838i	0.475243	−	0.879854i	$-0.342360\pi$
$368$	−5.53958	+	3.19828i	−0.288771	+	0.166722i
$369$	−4.52835	−	4.17454i	−0.235737	−	0.217318i
$370$	−4.14427	−	12.7842i	−0.215450	−	0.664619i
$371$	0.552102	−	3.13113i	0.0286637	−	0.162560i
$372$	14.9761	+	5.84979i	0.776477	+	0.303297i
$373$	−1.68968	+	4.64235i	−0.0874881	+	0.240372i	−0.975719	−	0.219025i	$-0.929712\pi$
$373$	−1.68968	+	4.64235i	−0.0874881	+	0.240372i	0.888231	+	0.459397i	$0.151934\pi$
$374$	0.275565	+	1.56281i	0.0142491	+	0.0808108i
$375$	14.2664	−	13.0946i	0.736716	−	0.676203i
$376$	−3.52263	−	2.95583i	−0.181666	−	0.152436i
$377$			9.58277i			0.493538i
$378$	1.35264	+	12.8867i	0.0695724	+	0.662819i
$379$	10.9541			0.562675			0.281337	−	0.959609i	$-0.409222\pi$
$379$	10.9541			0.562675			0.281337	+	0.959609i	$0.409222\pi$
$380$	−3.18034	+	0.444772i	−0.163148	+	0.0228163i
$381$	−3.83137	−	11.3428i	−0.196287	−	0.581107i
$382$	−17.0320	+	3.00320i	−0.871432	+	0.153657i
$383$	−4.72071	+	12.9700i	−0.241217	+	0.662738i	0.758719	+	0.651418i	$0.225826\pi$
$383$	−4.72071	+	12.9700i	−0.241217	+	0.662738i	−0.999936	+	0.0113200i	$0.996397\pi$
$384$	−1.08210	−	1.35242i	−0.0552208	−	0.0690156i
$385$	1.11888	−	0.872945i	0.0570234	−	0.0444894i
$386$	2.76760	−	4.79362i	0.140867	−	0.243989i
$387$	25.1588	−	13.0010i	1.27889	−	0.660878i
$388$	−1.75254	+	1.01183i	−0.0889716	+	0.0513678i
$389$	−23.7382	+	8.64001i	−1.20358	+	0.438066i	−0.864471	−	0.502683i	$-0.832346\pi$
$389$	−23.7382	+	8.64001i	−1.20358	+	0.438066i	−0.339105	+	0.940749i	$0.610124\pi$
$390$	−19.1353	−	4.54977i	−0.968954	−	0.230387i
$391$	−30.5531	+	25.6371i	−1.54514	+	1.29652i
$392$	0.502420	+	0.598761i	0.0253760	+	0.0302420i
$393$	3.04284	−	4.99752i	0.153491	−	0.252092i
$394$	−7.68553	+	2.79730i	−0.387191	+	0.140926i
$395$	−7.96358	−	1.69835i	−0.400691	−	0.0854531i
$396$	0.607132	−	0.462981i	0.0305095	−	0.0232657i
$397$	−26.7140	−	15.4233i	−1.34074	−	0.774076i	−0.353823	−	0.935313i	$-0.615118\pi$
$397$	−26.7140	−	15.4233i	−1.34074	−	0.774076i	−0.986916	+	0.161237i	$0.948452\pi$
$398$	13.1975	+	2.32707i	0.661530	+	0.116646i
$399$	−6.13210	+	0.934404i	−0.306989	+	0.0467787i
$400$	−1.21618	+	4.84984i	−0.0608090	+	0.242492i
$401$	6.11554	+	34.6830i	0.305396	+	1.73198i	0.621637	+	0.783306i	$0.286468\pi$
$401$	6.11554	+	34.6830i	0.305396	+	1.73198i	−0.316241	+	0.948679i	$0.602421\pi$
$402$	−13.4579	−	11.8380i	−0.671218	−	0.590426i
$403$	−30.3021	+	36.1126i	−1.50946	+	1.79890i
$404$	−5.36856			−0.267096
$405$	14.8096	−	13.6263i	0.735893	−	0.677098i
$406$	4.70541			0.233526
$407$	−0.983224	+	1.17176i	−0.0487366	+	0.0580820i
$408$	−8.10903	−	7.13298i	−0.401457	−	0.353135i
$409$	−1.45114	−	8.22980i	−0.0717540	−	0.406937i	−0.999436	−	0.0335671i	$-0.989313\pi$
$409$	−1.45114	−	8.22980i	−0.0717540	−	0.406937i	0.927682	−	0.373370i	$-0.121798\pi$
$410$	−2.15242	−	4.05473i	−0.106300	−	0.200249i
$411$	34.4191	−	5.24475i	1.69777	−	0.258705i
$412$	−0.348432	−	0.0614379i	−0.0171660	−	0.00302683i
$413$	14.5040	+	8.37387i	0.713694	+	0.412051i
$414$	17.7068	+	7.39674i	0.870243	+	0.363530i
$415$	4.39044	−	20.5868i	0.215518	−	1.01057i
$416$	4.77219	−	1.73693i	0.233976	−	0.0851602i
$417$	−1.89274	+	3.10862i	−0.0926881	+	0.152230i
$418$	0.234942	+	0.279993i	0.0114914	+	0.0136949i
$419$	−5.73306	+	4.81061i	−0.280078	+	0.235014i	−0.771995	−	0.635629i	$-0.780741\pi$
$419$	−5.73306	+	4.81061i	−0.280078	+	0.235014i	0.491917	+	0.870642i	$0.336296\pi$
$420$	−2.23407	+	9.39599i	−0.109011	+	0.458477i
$421$	24.7209	−	8.99766i	1.20482	−	0.438519i	0.339917	−	0.940455i	$-0.389601\pi$
$421$	24.7209	−	8.99766i	1.20482	−	0.438519i	0.864905	+	0.501936i	$0.167379\pi$
$422$	−7.22114	+	4.16913i	−0.351520	+	0.202950i
$423$	−0.643105	+	13.7804i	−0.0312688	+	0.670025i
$424$	0.637501	−	1.10418i	0.0309598	−	0.0536239i
$425$	−2.21687	+	31.0974i	−0.107534	+	1.50845i
$426$	−5.16464	−	6.45483i	−0.250228	−	0.312738i
$427$	−10.7437	+	29.5182i	−0.519926	+	1.42849i
$428$	−11.3364	+	1.99892i	−0.547967	+	0.0966213i
$429$	0.716416	+	2.12094i	0.0345889	+	0.102400i
$430$	20.9046	−	2.92352i	1.00811	−	0.140984i
$431$	−21.1933			−1.02084			−0.510422	−	0.859924i	$-0.670511\pi$
$431$	−21.1933			−1.02084			−0.510422	+	0.859924i	$0.670511\pi$
$432$	−1.25776	+	5.04163i	−0.0605140	+	0.242566i
$433$		−	24.7069i		−	1.18734i	−0.804710	−	0.593669i	$-0.797679\pi$
$433$		−	24.7069i		−	1.18734i	0.804710	−	0.593669i	$-0.202321\pi$
$434$	17.7323	+	14.8792i	0.851180	+	0.714224i
$435$	−4.35986	−	5.86516i	−0.209039	−	0.281213i
$436$	0.869499	+	4.93117i	0.0416414	+	0.236160i
$437$	−3.14190	+	8.63231i	−0.150298	+	0.412939i
$438$	−18.3467	−	7.16634i	−0.876638	−	0.342421i
$439$	5.24586	−	29.7507i	0.250371	−	1.41993i	−0.557309	−	0.830305i	$-0.688166\pi$
$439$	5.24586	−	29.7507i	0.250371	−	1.41993i	0.807681	−	0.589620i	$-0.200723\pi$
$440$	0.541359	−	0.175493i	0.0258083	−	0.00836629i
$441$	0.514393	−	2.28776i	0.0244949	−	0.108941i
$442$	27.4232	−	15.8328i	1.30439	−	0.753088i
$443$	1.49999	+	4.12119i	0.0712667	+	0.195804i	0.970212	−	0.242257i	$-0.0778877\pi$
$443$	1.49999	+	4.12119i	0.0712667	+	0.195804i	−0.898945	+	0.438061i	$0.855666\pi$
$444$	0.242708	−	10.4071i	0.0115184	−	0.493899i
$445$	1.16671	−	32.7737i	0.0553071	−	1.55362i
$446$	−5.12012	+	4.29629i	−0.242445	+	0.203435i
$447$	−30.2876	−	0.706349i	−1.43256	−	0.0334092i
$448$	−0.852884	−	2.34328i	−0.0402950	−	0.110710i
$449$	3.36031	+	5.82022i	0.158583	+	0.274673i	0.934358	−	0.356336i	$-0.115974\pi$
$449$	3.36031	+	5.82022i	0.158583	+	0.274673i	−0.775775	+	0.631010i	$0.782641\pi$
$450$	13.7818	−	5.92127i	0.649681	−	0.279131i
$451$	−0.261249	+	0.452496i	−0.0123017	+	0.0213072i
$452$	−3.21080	−	0.566150i	−0.151023	−	0.0266294i
$453$	24.8481	+	9.70584i	1.16747	+	0.456020i
$454$	−15.3791	−	5.59754i	−0.721778	−	0.262706i
$455$	−24.0044	−	15.0223i	−1.12535	−	0.704254i
$456$	−2.43893	−	0.488939i	−0.114213	−	0.0228967i
$457$	−1.26407	+	1.50647i	−0.0591309	+	0.0704695i	−0.794799	−	0.606873i	$-0.792424\pi$
$457$	−1.26407	+	1.50647i	−0.0591309	+	0.0704695i	0.735668	+	0.677342i	$0.236868\pi$
$458$		−	27.5442i		−	1.28706i
$459$	−2.26454	+	32.3202i	−0.105700	+	1.50858i
$460$	10.6228	+	9.57786i	0.495291	+	0.446570i
$461$	−18.4473	−	15.4791i	−0.859175	−	0.720933i	0.102615	−	0.994721i	$-0.467279\pi$
$461$	−18.4473	−	15.4791i	−0.859175	−	0.720933i	−0.961790	+	0.273788i	$0.911723\pi$
$462$	1.04144	−	0.351781i	0.0484524	−	0.0163663i
$463$	−20.2665	+	3.57353i	−0.941864	+	0.166076i	−0.623439	−	0.781872i	$-0.714265\pi$
$463$	−20.2665	+	3.57353i	−0.941864	+	0.166076i	−0.318425	+	0.947948i	$0.603154\pi$
$464$	1.77315	+	0.645373i	0.0823164	+	0.0299607i
$465$	2.11636	−	35.8893i	0.0981440	−	1.66433i
$466$	2.26412	−	12.8405i	0.104883	−	0.594823i
$467$	2.13259	+	1.23125i	0.0986843	+	0.0569754i	0.548530	−	0.836131i	$-0.315188\pi$
$467$	2.13259	+	1.23125i	0.0986843	+	0.0569754i	−0.449846	+	0.893106i	$0.648521\pi$
$468$	−12.8248	−	8.22448i	−0.592824	−	0.380177i
$469$	−12.9024	−	22.3476i	−0.595778	−	1.03192i
$470$	−3.85834	+	9.53113i	−0.177972	+	0.439638i
$471$	21.0083	−	11.4846i	0.968011	−	0.529181i
$472$	4.31703	+	5.14484i	0.198708	+	0.236811i
$473$	−1.54429	−	1.84041i	−0.0710065	−	0.0846223i
$474$	−5.38725	−	3.28013i	−0.247445	−	0.150662i
$475$	3.13905	+	6.45820i	0.144030	+	0.296322i
$476$	−7.77435	−	13.4656i	−0.356337	−	0.617193i
$477$	−3.79376	+	0.487880i	−0.173705	+	0.0223385i
$478$	−6.78399	−	3.91674i	−0.310293	−	0.179148i
$479$	−4.91490	+	27.8738i	−0.224567	+	1.27359i	0.638943	+	0.769254i	$0.279372\pi$
$479$	−4.91490	+	27.8738i	−0.224567	+	1.27359i	−0.863510	+	0.504331i	$0.831739\pi$
$480$	−2.13058	+	3.23429i	−0.0972472	+	0.147624i
$481$	28.6817	+	10.4393i	1.30777	+	0.475990i
$482$	−16.2091	+	2.85810i	−0.738303	+	0.130183i
$483$	20.7443	+	18.2474i	0.943897	+	0.830285i
$484$	8.37687	+	7.02903i	0.380767	+	0.319501i
$485$	3.36070	+	3.03011i	0.152602	+	0.137590i
$486$	14.3150	−	6.17097i	0.649341	−	0.279921i
$487$		−	27.1547i		−	1.23050i	−0.788333	−	0.615249i	$-0.789056\pi$
$487$		−	27.1547i		−	1.23050i	0.788333	−	0.615249i	$-0.210944\pi$
$488$	−8.09717	+	9.64983i	−0.366542	+	0.436827i
$489$	−20.5624	+	23.3760i	−0.929862	+	1.05710i
$490$	0.927181	−	1.48157i	0.0418858	−	0.0669303i
$491$	14.7453	+	5.36684i	0.665444	+	0.242202i	0.652585	−	0.757715i	$-0.273684\pi$
$491$	14.7453	+	5.36684i	0.665444	+	0.242202i	0.0128592	+	0.999917i	$0.495907\pi$
$492$	−0.535658	−	3.51530i	−0.0241493	−	0.158482i
$493$	11.5869	+	2.04308i	0.521847	+	0.0920156i
$494$	3.64667	−	6.31622i	0.164071	−	0.284180i
$495$	−1.40345	−	0.972182i	−0.0630803	−	0.0436964i
$496$	4.64134	+	8.03904i	0.208402	+	0.360964i
$497$	−4.07063	−	11.1840i	−0.182593	−	0.501670i
$498$	8.47956	−	13.9267i	0.379978	−	0.624071i
$499$	−8.84931	+	7.42545i	−0.396149	+	0.332409i	−0.819003	−	0.573789i	$-0.805473\pi$
$499$	−8.84931	+	7.42545i	−0.396149	+	0.332409i	0.422854	+	0.906198i	$0.361028\pi$
$500$	11.1547	−	0.757241i	0.498852	−	0.0338648i
$501$	−35.0039	+	19.1355i	−1.56386	+	0.854913i
$502$	6.76698	+	18.5921i	0.302025	+	0.829808i
$503$	19.2608	−	11.1202i	0.858795	−	0.495826i	−0.00481350	−	0.999988i	$-0.501532\pi$
$503$	19.2608	−	11.1202i	0.858795	−	0.495826i	0.863609	+	0.504163i	$0.168199\pi$
$504$	−4.03846	+	6.29732i	−0.179887	+	0.280505i
$505$	3.70185	+	11.4194i	0.164730	+	0.508158i
$506$	0.282693	−	1.60323i	0.0125672	−	0.0712723i
$507$	17.2985	−	13.8409i	0.768252	−	0.614694i
$508$	2.36413	−	6.49539i	0.104891	−	0.288186i
$509$	4.05931	+	23.0215i	0.179926	+	1.02041i	0.932303	+	0.361678i	$0.117796\pi$
$509$	4.05931	+	23.0215i	0.179926	+	1.02041i	−0.752377	+	0.658732i	$0.771093\pi$
$510$	−9.58101	+	22.1672i	−0.424254	+	0.981579i
$511$	−21.7232	−	18.2279i	−0.960977	−	0.806355i
$512$		−	1.00000i		−	0.0441942i
$513$	3.27036	+	6.70758i	0.144390	+	0.296147i
$514$	−16.1939			−0.714282
$515$	0.109574	+	0.783511i	0.00482842	+	0.0345256i
$516$	16.0312	+	3.21383i	0.705736	+	0.141481i
$517$	1.15256	−	0.203227i	0.0506894	−	0.00893791i
$518$	5.12598	−	14.0835i	0.225223	−	0.618794i
$519$	−6.31361	+	16.1636i	−0.277137	+	0.709502i
$520$	−6.98525	−	8.95320i	−0.306323	−	0.392624i
$521$	−1.35871	+	2.35335i	−0.0595261	+	0.103102i	−0.894253	−	0.447562i	$-0.852292\pi$
$521$	−1.35871	+	2.35335i	−0.0595261	+	0.103102i	0.834727	+	0.550664i	$0.185626\pi$
$522$	−1.68604	−	5.40392i	−0.0737958	−	0.236523i
$523$	4.02427	−	2.32341i	0.175969	−	0.101596i	−0.409428	−	0.912342i	$-0.634272\pi$
$523$	4.02427	−	2.32341i	0.175969	−	0.101596i	0.585397	+	0.810747i	$0.300939\pi$
$524$	3.17435	−	1.15537i	0.138672	−	0.0504725i
$525$	21.5266	−	1.72686i	0.939499	−	0.0753663i
$526$	0.649464	−	0.544965i	0.0283180	−	0.0237616i
$527$	37.2046	+	44.3387i	1.62066	+	1.93142i
$528$	0.440698	+	0.0102777i	0.0191789	+	0.000447278i
$529$	16.8355	−	6.12761i	0.731977	−	0.266418i
$530$	−2.78829	−	0.594643i	−0.121116	−	0.0258296i
$531$	4.41991	−	19.6576i	0.191808	−	0.853066i
$532$	−3.10144	−	1.79062i	−0.134465	−	0.0776332i
$533$	10.2676	+	1.81045i	0.444739	+	0.0784195i
$534$	9.24234	−	23.6615i	0.399955	−	1.02393i
$535$	12.0688	+	22.7353i	0.521781	+	0.982933i
$536$	−1.79694	−	10.1909i	−0.0776159	−	0.440182i
$537$	−2.52723	+	12.6064i	−0.109058	+	0.544004i
$538$	−0.835902	+	0.996190i	−0.0360383	+	0.0429488i
$539$	−0.198929			−0.00856847
$540$	11.5913	−	0.801045i	0.498810	−	0.0344715i
$541$	−7.77485			−0.334267			−0.167134	−	0.985934i	$-0.553451\pi$
$541$	−7.77485			−0.334267			−0.167134	+	0.985934i	$0.553451\pi$
$542$	12.3992	−	14.7768i	0.532592	−	0.634719i
$543$	−6.49950	+	2.19541i	−0.278920	+	0.0942141i
$544$	−1.08274	−	6.14054i	−0.0464223	−	0.263274i
$545$	9.88951	−	5.24976i	0.423620	−	0.224875i
$546$	−13.7037	−	17.1271i	−0.586465	−	0.732971i
$547$	17.9485	+	3.16480i	0.767421	+	0.135317i	0.543635	−	0.839321i	$-0.317047\pi$
$547$	17.9485	+	3.16480i	0.767421	+	0.135317i	0.223785	+	0.974638i	$0.428159\pi$
$548$	17.4082	+	10.0506i	0.743642	+	0.429342i
$549$	37.7498	+	1.76171i	1.61112	+	0.0751880i
$550$	−0.746580	−	1.03051i	−0.0318343	−	0.0439411i
$551$	2.54648	−	0.926842i	0.108484	−	0.0394848i
$552$	5.31437	+	9.72138i	0.226195	+	0.413770i
$553$	−5.83697	−	6.95623i	−0.248213	−	0.295809i
$554$	4.83105	−	4.05373i	0.205252	−	0.172227i
$555$	−22.3042	+	6.65987i	−0.946761	+	0.282696i
$556$	−1.97455	+	0.718676i	−0.0837394	+	0.0304787i
$557$	2.16179	−	1.24811i	0.0915980	−	0.0528841i	−0.453501	−	0.891256i	$-0.649825\pi$
$557$	2.16179	−	1.24811i	0.0915980	−	0.0528841i	0.545099	+	0.838371i	$0.316492\pi$
$558$	10.7342	−	25.6962i	0.454413	−	1.08781i
$559$	−23.9698	+	41.5169i	−1.01381	+	1.75598i
$560$	−4.39628	+	3.42996i	−0.185777	+	0.144942i
$561$	2.71725	−	0.414052i	0.114722	−	0.0174813i
$562$	9.86846	−	27.1134i	0.416276	−	1.14371i
$563$	−22.8982	+	4.03757i	−0.965044	+	0.170163i	−0.633898	−	0.773416i	$-0.718546\pi$
$563$	−22.8982	+	4.03757i	−0.965044	+	0.170163i	−0.331146	+	0.943580i	$0.607435\pi$
$564$	−5.26052	+	5.98034i	−0.221508	+	0.251818i
$565$	1.00973	+	7.22005i	0.0424795	+	0.303750i
$566$	−19.0587			−0.801096
$567$	22.3689	−	1.82181i	0.939407	−	0.0765088i
$568$		−	4.77278i		−	0.200262i
$569$	−12.8615	−	10.7921i	−0.539184	−	0.452429i	0.332075	−	0.943253i	$-0.392251\pi$
$569$	−12.8615	−	10.7921i	−0.539184	−	0.452429i	−0.871259	+	0.490824i	$0.836696\pi$
$570$	0.641727	+	5.52498i	0.0268790	+	0.231416i
$571$	1.84745	+	10.4774i	0.0773135	+	0.438467i	0.998752	+	0.0499427i	$0.0159039\pi$
$571$	1.84745	+	10.4774i	0.0773135	+	0.438467i	−0.921439	+	0.388524i	$0.872985\pi$
$572$	−0.442060	+	1.21455i	−0.0184835	+	0.0507829i
$573$	4.51248	+	29.6135i	0.188511	+	1.23712i
$574$	0.888985	−	5.04168i	0.0371055	−	0.210436i
$575$	13.0481	−	29.2001i	0.544145	−	1.21773i
$576$	−2.38553	+	1.81913i	−0.0993971	+	0.0757972i
$577$	28.9675	−	16.7244i	1.20593	−	0.696245i	0.244063	−	0.969759i	$-0.421519\pi$
$577$	28.9675	−	16.7244i	1.20593	−	0.696245i	0.961868	+	0.273514i	$0.0881862\pi$
$578$	−7.48293	−	20.5592i	−0.311249	−	0.855149i
$579$	−8.18878	−	4.98590i	−0.340314	−	0.207207i
$580$	0.150108	−	4.21667i	0.00623291	−	0.175088i
$581$	17.9827	−	15.0893i	0.746049	−	0.626009i
$582$	1.68129	+	3.07552i	0.0696916	+	0.127484i
$583$	0.110984	+	0.304926i	0.00459649	+	0.0126288i
$584$	−5.68592	−	9.84831i	−0.235285	−	0.407526i
$585$	−8.65103	+	32.9506i	−0.357676	+	1.36234i
$586$	0.247906	−	0.429386i	0.0102409	−	0.0177378i
$587$	28.2700	+	4.98477i	1.16683	+	0.205743i	0.723311	−	0.690522i	$-0.242619\pi$
$587$	28.2700	+	4.98477i	1.16683	+	0.205743i	0.443518	+	0.896266i	$0.353730\pi$
$588$	1.05709	−	0.845801i	0.0435937	−	0.0348802i
$589$	12.5272	+	4.55953i	0.516175	+	0.187872i
$590$	7.96678	−	12.7303i	0.327987	−	0.524099i
$591$	4.53339	+	13.4211i	0.186479	+	0.552069i
$592$	3.86326	−	4.60406i	0.158779	−	0.189226i
$593$			31.7193i			1.30255i	0.758840	+	0.651277i	$0.225766\pi$
$593$			31.7193i			1.30255i	−0.758840	+	0.651277i	$0.774234\pi$
$594$	−0.777170	−	1.06999i	−0.0318877	−	0.0439024i
$595$	−23.2818	+	25.8218i	−0.954460	+	1.05859i
$596$	−13.3991	−	11.2432i	−0.548850	−	0.460540i
$597$	4.56246	−	22.7585i	0.186729	−	0.931444i
$598$	−31.9911	+	5.64090i	−1.30821	+	0.230673i
$599$	−38.4399	−	13.9910i	−1.57061	−	0.571656i	−0.597475	−	0.801887i	$-0.703829\pi$
$599$	−38.4399	−	13.9910i	−1.57061	−	0.571656i	−0.973136	+	0.230231i	$0.926052\pi$
$600$	8.34877	+	2.30176i	0.340837	+	0.0939690i
$601$	−5.18241	+	29.3909i	−0.211395	+	1.19888i	0.675659	+	0.737214i	$0.263859\pi$
$601$	−5.18241	+	29.3909i	−0.211395	+	1.19888i	−0.887054	+	0.461666i	$0.847252\pi$
$602$	20.3860	+	11.7699i	0.830871	+	0.479704i
$603$	−21.0419	+	22.8253i	−0.856894	+	0.929519i
$604$	7.70082	+	13.3382i	0.313342	+	0.542724i
$605$	9.17520	−	22.6652i	0.373025	−	0.921472i
$606$	−0.216797	+	9.29609i	−0.00880680	+	0.377628i
$607$	−10.4908	−	12.5024i	−0.425808	−	0.507458i	0.509900	−	0.860234i	$-0.329682\pi$
$607$	−10.4908	−	12.5024i	−0.425808	−	0.507458i	−0.935708	+	0.352776i	$0.885238\pi$
$608$	−0.923129	−	1.10014i	−0.0374378	−	0.0446166i
$609$	0.190018	−	8.14780i	0.00769991	−	0.330166i
$610$	26.1094	+	10.5695i	1.05714	+	0.427945i
$611$	−11.6765	−	20.2244i	−0.472382	−	0.818190i
$612$	−12.6788	+	13.7534i	−0.512510	+	0.555948i
$613$	17.3906	+	10.0405i	0.702401	+	0.405532i	0.808241	−	0.588852i	$-0.200420\pi$
$613$	17.3906	+	10.0405i	0.702401	+	0.405532i	−0.105840	+	0.994383i	$0.533753\pi$
$614$	−2.93621	+	16.6521i	−0.118496	+	0.672024i
$615$	−7.10801	+	3.56334i	−0.286623	+	0.143688i
$616$	0.596379	+	0.217064i	0.0240288	+	0.00874577i
$617$	33.4323	−	5.89501i	1.34593	−	0.237324i	0.546187	−	0.837663i	$-0.316079\pi$
$617$	33.4323	−	5.89501i	1.34593	−	0.237324i	0.799746	+	0.600339i	$0.204968\pi$
$618$	−0.120455	+	0.600856i	−0.00484542	+	0.0241700i
$619$	5.15762	+	4.32776i	0.207302	+	0.173947i	0.740528	−	0.672026i	$-0.234576\pi$
$619$	5.15762	+	4.32776i	0.207302	+	0.173947i	−0.533225	+	0.845973i	$0.679020\pi$
$620$	13.8994	−	15.4158i	0.558213	−	0.619115i
$621$	13.5231	−	30.3621i	0.542663	−	1.21839i
$622$			2.94095i			0.117921i
$623$	23.5083	−	28.0161i	0.941841	−	1.12244i
$624$	−2.81493	−	8.33357i	−0.112687	−	0.333610i
$625$	−9.30234	−	23.2049i	−0.372094	−	0.928195i
$626$	24.1183	+	8.77835i	0.963961	+	0.350853i
$627$	0.494318	−	0.395514i	0.0197411	−	0.0157953i
$628$	13.6132	+	2.40038i	0.543226	+	0.0957854i
$629$	18.7375	−	32.4543i	0.747114	−	1.29404i
$630$	16.1797	+	4.24790i	0.644614	+	0.169241i
$631$	−11.0312	−	19.1065i	−0.439144	−	0.760619i	0.558480	−	0.829518i	$-0.311385\pi$
$631$	−11.0312	−	19.1065i	−0.439144	−	0.760619i	−0.997624	+	0.0688989i	$0.978051\pi$
$632$	−1.24547	−	3.42190i	−0.0495421	−	0.136116i
$633$	6.92757	+	12.6723i	0.275346	+	0.503680i
$634$	−12.8810	+	10.8085i	−0.511571	+	0.429259i
$635$	−15.4465	−	0.549876i	−0.612975	−	0.0218212i
$636$	−1.88624	−	1.14847i	−0.0747943	−	0.0455400i
$637$	1.35763	+	3.73007i	0.0537914	+	0.147791i
$638$	−0.415899	+	0.240120i	−0.0164656	+	0.00950643i
$639$	−11.3856	+	8.68233i	−0.450408	+	0.343468i
$640$	−2.12709	+	0.689543i	−0.0840808	+	0.0272566i
$641$	6.89027	−	39.0767i	0.272149	−	1.54343i	−0.475725	−	0.879594i	$-0.657814\pi$
$641$	6.89027	−	39.0767i	0.272149	−	1.54343i	0.747874	−	0.663841i	$-0.231075\pi$
$642$	3.00349	+	19.7106i	0.118538	+	0.777917i
$643$	−6.45923	+	17.7466i	−0.254727	+	0.699857i	0.744744	+	0.667350i	$0.232571\pi$
$643$	−6.45923	+	17.7466i	−0.254727	+	0.699857i	−0.999472	+	0.0325070i	$0.989651\pi$
$644$	2.76984	+	15.7086i	0.109147	+	0.619004i
$645$	−4.21811	−	36.3161i	−0.166088	−	1.42994i
$646$	−6.85968	−	5.75596i	−0.269891	−	0.226465i
$647$		−	23.2385i		−	0.913599i	−0.889570	−	0.456800i	$-0.848996\pi$
$647$		−	23.2385i		−	0.913599i	0.889570	−	0.456800i	$-0.151004\pi$
$648$	8.67919	+	2.38151i	0.340951	+	0.0935545i
$649$	−1.70929			−0.0670956
$650$	−14.2277	+	21.0319i	−0.558055	+	0.824939i
$651$	26.4806	−	30.1041i	1.03786	−	1.17987i
$652$	−17.7014	+	3.12124i	−0.693242	+	0.122237i
$653$	−7.59676	+	20.8719i	−0.297284	+	0.816781i	0.697667	+	0.716422i	$0.254221\pi$
$653$	−7.59676	+	20.8719i	−0.297284	+	0.816781i	−0.994951	+	0.100359i	$0.968001\pi$
$654$	8.57383	−	1.30647i	0.335263	−	0.0510871i
$655$	−4.64643	−	5.95546i	−0.181551	−	0.232699i
$656$	1.02649	−	1.77794i	0.0400778	−	0.0694168i
$657$	−13.1500	+	31.4793i	−0.513030	+	1.22813i
$658$	−9.93074	+	5.73352i	−0.387141	+	0.223516i
$659$	7.41081	−	2.69731i	0.288684	−	0.105072i	−0.193619	−	0.981077i	$-0.562023\pi$
$659$	7.41081	−	2.69731i	0.288684	−	0.105072i	0.482303	+	0.876004i	$0.339800\pi$
$660$	−0.282018	−	0.944493i	−0.0109775	−	0.0367643i
$661$	−25.4524	+	21.3571i	−0.989983	+	0.830694i	−0.985565	−	0.169296i	$-0.945851\pi$
$661$	−25.4524	+	21.3571i	−0.989983	+	0.830694i	−0.00441775	+	0.999990i	$0.501406\pi$
$662$	−10.6596	−	12.7036i	−0.414297	−	0.493740i
$663$	−26.3083	−	48.1248i	−1.02173	−	1.86901i
$664$	8.84604	−	3.21969i	0.343293	−	0.124948i
$665$	−1.67024	+	7.83177i	−0.0647691	+	0.303703i
$666$	−18.0109	−	0.840535i	−0.697909	−	0.0325701i
$667$	−10.4529	−	6.03498i	−0.404737	−	0.233675i
$668$	−22.6823	−	3.99950i	−0.877604	−	0.154745i
$669$	7.23260	+	9.03939i	0.279629	+	0.349483i
$670$	−20.4380	+	10.8493i	−0.789590	+	0.419147i
$671$	−0.556717	−	3.15730i	−0.0214918	−	0.121886i
$672$	−4.09202	+	1.38221i	−0.157853	+	0.0533199i
$673$	30.0475	−	35.8092i	1.15825	−	1.38034i	0.246728	−	0.969085i	$-0.420645\pi$
$673$	30.0475	−	35.8092i	1.15825	−	1.38034i	0.911518	−	0.411259i	$-0.134911\pi$
$674$	8.08699			0.311499
$675$	−9.69660	−	24.1034i	−0.373222	−	0.927742i
$676$	12.7907			0.491950
$677$	−5.53851	+	6.60054i	−0.212862	+	0.253679i	−0.861902	−	0.507075i	$-0.830727\pi$
$677$	−5.53851	+	6.60054i	−0.212862	+	0.253679i	0.649040	+	0.760755i	$0.275171\pi$
$678$	−1.10999	+	5.53689i	−0.0426291	+	0.212643i
$679$	0.876285	+	4.96966i	0.0336287	+	0.190718i
$680$	−12.3149	+	6.53727i	−0.472256	+	0.250693i
$681$	−10.3136	+	26.4041i	−0.395220	+	1.01181i
$682$	−2.32661	−	0.410244i	−0.0890905	−	0.0157091i
$683$	−34.9727	−	20.1915i	−1.33819	−	0.772606i	−0.351653	−	0.936130i	$-0.614380\pi$
$683$	−34.9727	−	20.1915i	−1.33819	−	0.772606i	−0.986539	+	0.163525i	$0.947714\pi$
$684$	−0.945127	+	4.20346i	−0.0361378	+	0.160723i
$685$	9.37495	−	43.9593i	0.358198	−	1.67960i
$686$	18.2345	−	6.63683i	0.696198	−	0.253395i
$687$	−47.6951	−	1.11231i	−1.81968	−	0.0424374i
$688$	6.06779	+	7.23131i	0.231332	+	0.275691i
$689$	4.96017	−	4.16208i	0.188967	−	0.158562i
$690$	17.0138	−	18.0075i	0.647705	−	0.685533i
$691$	24.7869	−	9.02168i	0.942936	−	0.343201i	0.175612	−	0.984460i	$-0.443810\pi$
$691$	24.7869	−	9.02168i	0.942936	−	0.343201i	0.767325	+	0.641259i	$0.221587\pi$
$692$	−8.67644	+	5.00935i	−0.329829	+	0.190427i
$693$	−0.567080	−	1.81755i	−0.0215416	−	0.0690430i
$694$	−7.11402	+	12.3219i	−0.270045	+	0.467731i
$695$	2.89023	+	3.70449i	0.109633	+	0.140519i
$696$	1.18912	−	3.04429i	0.0450735	−	0.115393i
$697$	4.37817	−	12.0289i	0.165835	−	0.455628i
$698$	18.2300	−	3.21445i	0.690017	−	0.121669i
$699$	−22.1428	−	4.43904i	−0.837519	−	0.167900i
$700$	10.3273	+	6.98620i	0.390334	+	0.264053i
$701$	13.4895			0.509490			0.254745	−	0.967008i	$-0.418008\pi$
$701$	13.4895			0.509490			0.254745	+	0.967008i	$0.418008\pi$
$702$	−14.7592	+	21.8750i	−0.557052	+	0.825617i
$703$		−	8.63140i		−	0.325540i
$704$	0.194963	+	0.163593i	0.00734795	+	0.00616566i
$705$	16.3481	+	7.06591i	0.615705	+	0.266118i
$706$	4.03054	+	22.8583i	0.151691	+	0.860285i
$707$	−4.57876	+	12.5800i	−0.172202	+	0.473121i
$708$	9.08304	−	7.26753i	0.341361	−	0.273130i
$709$	−4.55918	+	25.8564i	−0.171223	+	0.971057i	0.771190	+	0.636605i	$0.219662\pi$
$709$	−4.55918	+	25.8564i	−0.171223	+	0.971057i	−0.942413	+	0.334451i	$0.891449\pi$
$710$	−10.1522	+	3.29104i	−0.381004	+	0.123510i
$711$	−5.89737	+	9.19599i	−0.221169	+	0.344877i
$712$	12.7012	−	7.33307i	0.475999	−	0.274818i
$713$	−20.3082	−	55.7964i	−0.760548	−	2.08959i
$714$	−23.6306	+	12.9181i	−0.884355	+	0.483449i
$715$	2.88828	+	0.102819i	0.108016	+	0.00384523i
$716$	−5.68642	+	4.77148i	−0.212512	+	0.178318i
$717$	−7.05611	+	11.5889i	−0.263515	+	0.432794i
$718$	−10.1946	−	28.0094i	−0.380458	−	1.04530i
$719$	5.04858	+	8.74441i	0.188280	+	0.326111i	0.944677	−	0.328002i	$-0.106375\pi$
$719$	5.04858	+	8.74441i	0.188280	+	0.326111i	−0.756397	+	0.654113i	$0.773042\pi$
$720$	5.51439	+	3.81988i	0.205509	+	0.142358i
$721$	−0.441138	+	0.764073i	−0.0164288	+	0.0284556i
$722$	16.6802	+	2.94117i	0.620773	+	0.109459i
$723$	4.29445	+	28.1827i	0.159712	+	1.04813i
$724$	−3.72192	−	1.35467i	−0.138324	−	0.0503458i
$725$	−9.07276	+	2.58828i	−0.336954	+	0.0961262i
$726$	12.5096	−	14.2214i	0.464275	−	0.527804i
$727$	18.1889	−	21.6767i	0.674589	−	0.803944i	−0.314812	−	0.949154i	$-0.601941\pi$
$727$	18.1889	−	21.6767i	0.674589	−	0.803944i	0.989401	+	0.145210i	$0.0463858\pi$
$728$		−	12.6640i		−	0.469358i
$729$	−10.1075	−	25.0368i	−0.374350	−	0.927287i
$730$	−17.0276	+	18.8853i	−0.630220	+	0.698977i
$731$	45.0892	+	37.8343i	1.66768	+	1.39935i
$732$	16.3825	+	14.4106i	0.605513	+	0.532630i
$733$	10.6785	−	1.88291i	0.394421	−	0.0695470i	0.0270795	−	0.999633i	$-0.491379\pi$
$733$	10.6785	−	1.88291i	0.394421	−	0.0695470i	0.367341	+	0.930086i	$0.380268\pi$
$734$	−23.9156	−	8.70455i	−0.882739	−	0.321291i
$735$	−2.52801	−	1.66532i	−0.0932470	−	0.0614262i
$736$	−1.11075	+	6.29938i	−0.0409428	+	0.232198i
$737$	2.28082	+	1.31683i	0.0840152	+	0.0485062i
$738$	−6.10865	+	0.785576i	−0.224863	+	0.0289175i
$739$	3.01972	+	5.23030i	0.111082	+	0.192400i	0.916207	−	0.400706i	$-0.131235\pi$
$739$	3.01972	+	5.23030i	0.111082	+	0.192400i	−0.805125	+	0.593106i	$0.797902\pi$
$740$	−12.4572	−	5.04283i	−0.457934	−	0.185378i
$741$	−10.7898	−	6.56957i	−0.396372	−	0.241339i
$742$	−2.04370	−	2.43559i	−0.0750265	−	0.0894131i
$743$	0.120174	+	0.143217i	0.00440874	+	0.00525413i	0.768244	−	0.640157i	$-0.221131\pi$
$743$	0.120174	+	0.143217i	0.00440874	+	0.00525413i	−0.763836	+	0.645411i	$0.776686\pi$
$744$	14.1077	−	7.71222i	0.517213	−	0.282744i
$745$	−14.6761	+	36.2539i	−0.537691	+	1.32824i
$746$	2.47014	+	4.27841i	0.0904383	+	0.156644i
$747$	−23.7728	−	15.2454i	−0.869801	−	0.557801i
$748$	1.37431	+	0.793458i	0.0502497	+	0.0290117i
$749$	−4.98463	+	28.2693i	−0.182135	+	1.03294i
$750$	−0.860766	−	19.3458i	−0.0314307	−	0.706408i
$751$	−35.6113	−	12.9615i	−1.29947	−	0.472970i	−0.402649	−	0.915354i	$-0.631910\pi$
$751$	−35.6113	−	12.9615i	−1.29947	−	0.472970i	−0.896826	+	0.442384i	$0.854133\pi$
$752$	−4.52860	+	0.798515i	−0.165141	+	0.0291188i
$753$	32.4670	−	10.9668i	1.18316	−	0.399651i
$754$	7.34083	+	6.15968i	0.267337	+	0.224322i
$755$	23.0616	−	25.5776i	0.839297	−	0.930865i
$756$	10.7412	+	7.24721i	0.390655	+	0.263579i
$757$			32.5666i			1.18365i	0.806065	+	0.591827i	$0.201593\pi$
$757$			32.5666i			1.18365i	−0.806065	+	0.591827i	$0.798407\pi$
$758$	7.04117	−	8.39134i	0.255747	−	0.304787i
$759$	−2.76471	−	0.554248i	−0.100352	−	0.0201179i
$760$	−1.70357	+	2.72218i	−0.0617949	+	0.0987437i
$761$	25.6898	+	9.35031i	0.931254	+	0.338949i	0.762706	−	0.646745i	$-0.223870\pi$
$761$	25.6898	+	9.35031i	0.931254	+	0.338949i	0.168547	+	0.985694i	$0.446092\pi$
$762$	−11.1518	−	4.35598i	−0.403988	−	0.157800i
$763$	12.2967	+	2.16824i	0.445170	+	0.0784956i
$764$	−8.64736	+	14.9777i	−0.312851	+	0.541873i
$765$	37.9973	+	17.4855i	1.37380	+	0.632188i
$766$	6.90121	+	11.9533i	0.249351	+	0.431889i
$767$	11.6654	+	32.0505i	0.421215	+	1.15728i
$768$	−1.73158	−	0.0403828i	−0.0624830	−	0.00145719i
$769$	−24.5537	+	20.6030i	−0.885430	+	0.742964i	−0.967288	−	0.253680i	$-0.918359\pi$
$769$	−24.5537	+	20.6030i	−0.885430	+	0.742964i	0.0818581	+	0.996644i	$0.473915\pi$
$770$	0.0504873	−	1.41823i	0.00181944	−	0.0511095i
$771$	−0.653955	+	28.0410i	−0.0235516	+	1.00987i
$772$	−1.89315	−	5.20139i	−0.0681360	−	0.187202i
$773$	−0.236858	+	0.136750i	−0.00851917	+	0.00491855i	−0.504254	−	0.863556i	$-0.668232\pi$
$773$	−0.236858	+	0.136750i	−0.00851917	+	0.00491855i	0.495734	+	0.868474i	$0.334899\pi$
$774$	6.21239	−	27.6296i	0.223300	−	0.993126i
$775$	−42.3752	−	18.9355i	−1.52216	−	0.680182i
$776$	−0.351404	+	1.99291i	−0.0126147	+	0.0715413i
$777$	−24.1797	−	9.44478i	−0.867443	−	0.338829i
$778$	−8.64001	+	23.7382i	−0.309759	+	0.851056i
$779$	−0.511977	−	2.90357i	−0.0183435	−	0.104031i
$780$	−15.7853	+	11.7340i	−0.565203	+	0.420143i
$781$	0.930517	+	0.780796i	0.0332965	+	0.0279391i
$782$			39.8843i			1.42626i
$783$	−9.42541	+	2.70128i	−0.336837	+	0.0965359i
$784$	0.781627			0.0279152
$785$	−4.28106	−	30.6117i	−0.152798	−	1.09258i
$786$	−1.87242	−	5.54330i	−0.0667871	−	0.197723i
$787$	35.2371	−	6.21325i	1.25607	−	0.221478i	0.494278	−	0.869304i	$-0.335433\pi$
$787$	35.2371	−	6.21325i	1.25607	−	0.221478i	0.761789	+	0.647826i	$0.224321\pi$
$788$	−2.79730	+	7.68553i	−0.0996498	+	0.273786i
$789$	−0.917423	−	1.14661i	−0.0326611	−	0.0408203i
$790$	−6.41990	+	5.00878i	−0.228410	+	0.178204i
$791$	−4.06508	+	7.04093i	−0.144538	+	0.250347i
$792$	0.0355932	−	0.762688i	0.00126475	−	0.0271010i
$793$	−55.4023	+	31.9865i	−1.96739	+	1.13588i
$794$	−28.9864	+	10.5502i	−1.02869	+	0.374412i
$795$	−1.14227	+	4.80413i	−0.0405122	+	0.170385i
$796$	10.2658	−	8.61404i	0.363862	−	0.305317i
$797$	−4.15592	−	4.95283i	−0.147210	−	0.175438i	0.687401	−	0.726279i	$-0.258752\pi$
$797$	−4.15592	−	4.95283i	−0.147210	−	0.175438i	−0.834611	+	0.550840i	$0.814307\pi$
$798$	−3.22584	+	5.29809i	−0.114194	+	0.187550i
$799$	−26.9435	+	9.80663i	−0.953192	+	0.346934i
$800$	2.93344	+	4.04906i	0.103713	+	0.143156i
$801$	−40.5985	−	16.9594i	−1.43448	−	0.599230i
$802$	30.4997	+	17.6090i	1.07698	+	0.621796i
$803$	2.85024	+	0.502574i	0.100583	+	0.0177354i
$804$	−17.7190	+	2.70000i	−0.624901	+	0.0952218i
$805$	31.5036	−	16.7234i	1.11036	−	0.589423i
$806$	8.18607	+	46.4255i	0.288342	+	1.63527i
$807$	1.69123	+	1.48766i	0.0595340	+	0.0523681i
$808$	−3.45084	+	4.11255i	−0.121400	+	0.144679i
$809$	7.50354			0.263811			0.131905	−	0.991262i	$-0.457891\pi$
$809$	7.50354			0.263811			0.131905	+	0.991262i	$0.457891\pi$
$810$	−0.918984	−	20.1036i	−0.0322898	−	0.706369i
$811$	38.4579			1.35044			0.675220	−	0.737617i	$-0.264049\pi$
$811$	38.4579			1.35044			0.675220	+	0.737617i	$0.264049\pi$
$812$	3.02458	−	3.60456i	0.106142	−	0.126495i
$813$	−25.0865	−	22.0670i	−0.879823	−	0.773923i
$814$	0.265617	+	1.50639i	0.00930986	+	0.0527988i
$815$	18.8451	+	35.5004i	0.660114	+	1.24352i
$816$	−10.6766	+	1.62688i	−0.373755	+	0.0569524i
$817$	13.3509	+	2.35412i	0.467087	+	0.0823601i
$818$	−7.23716	−	4.17838i	−0.253041	−	0.146094i
$819$	−30.2103	+	23.0375i	−1.05563	+	0.804994i
$820$	−4.48965	−	0.957483i	−0.156785	−	0.0334368i
$821$	−10.7302	+	3.90548i	−0.374487	+	0.136302i	−0.522405	−	0.852697i	$-0.674965\pi$
$821$	−10.7302	+	3.90548i	−0.374487	+	0.136302i	0.147918	+	0.989000i	$0.452743\pi$
$822$	18.1065	−	29.7379i	0.631536	−	1.03723i
$823$	3.02443	+	3.60438i	0.105425	+	0.125641i	0.816177	−	0.577802i	$-0.196090\pi$
$823$	3.02443	+	3.60438i	0.105425	+	0.125641i	−0.710752	+	0.703443i	$0.751645\pi$
$824$	−0.271032	+	0.227423i	−0.00944183	+	0.00792264i
$825$	−1.81456	+	1.25115i	−0.0631749	+	0.0435594i
$826$	15.7377	−	5.72807i	0.547586	−	0.199305i
$827$	12.5908	−	7.26931i	0.437826	−	0.252779i	−0.264849	−	0.964290i	$-0.585322\pi$
$827$	12.5908	−	7.26931i	0.437826	−	0.252779i	0.702675	+	0.711511i	$0.251989\pi$
$828$	17.0480	−	8.80968i	0.592458	−	0.306158i
$829$	2.00837	−	3.47859i	0.0697534	−	0.120816i	−0.829039	−	0.559190i	$-0.811112\pi$
$829$	2.00837	−	3.47859i	0.0697534	−	0.120816i	0.898793	+	0.438374i	$0.144445\pi$
$830$	−12.9483	−	16.5962i	−0.449443	−	0.576064i
$831$	−6.82427	−	8.52905i	−0.236731	−	0.295869i
$832$	1.73693	−	4.77219i	0.0602173	−	0.165446i
$833$	4.79961	−	0.846302i	0.166297	−	0.0293226i
$834$	1.16471	+	3.44811i	0.0403305	+	0.119398i
$835$	7.13309	+	51.0052i	0.246851	+	1.76511i
$836$	0.365505			0.0126412
$837$	−44.0615	−	19.6247i	−1.52299	−	0.678330i
$838$			7.48398i			0.258530i
$839$	39.6507	+	33.2709i	1.36889	+	1.14864i	0.973122	+	0.230289i	$0.0739670\pi$
$839$	39.6507	+	33.2709i	1.36889	+	1.14864i	0.395771	+	0.918349i	$0.370477\pi$
$840$	5.76171	+	7.75102i	0.198798	+	0.267436i
$841$	−4.41751	−	25.0530i	−0.152328	−	0.863895i
$842$	8.99766	−	24.7209i	0.310080	−	0.851937i
$843$	−46.5505	−	18.1829i	−1.60328	−	0.626254i
$844$	−1.44792	+	8.21158i	−0.0498395	+	0.282654i
$845$	−8.81974	−	27.2070i	−0.303408	−	0.935950i
$846$	10.1430	+	9.35051i	0.348724	+	0.321477i
$847$	23.6155	−	13.6344i	0.811438	−	0.468484i
$848$	−0.436076	−	1.19811i	−0.0149749	−	0.0411433i
$849$	−0.769643	+	33.0016i	−0.0264141	+	1.13261i
$850$	22.3970	+	21.6873i	0.768212	+	0.743867i
$851$	−29.4501	+	24.7116i	−1.00954	+	0.847102i
$852$	−8.26446	−	0.192738i	−0.283136	−	0.00660311i
$853$	9.61768	+	26.4243i	0.329303	+	0.904752i	0.988289	+	0.152597i	$0.0487636\pi$
$853$	9.61768	+	26.4243i	0.329303	+	0.904752i	−0.658986	+	0.752156i	$0.729014\pi$
$854$	15.7063	+	27.2041i	0.537459	+	0.930906i
$855$	9.59285	−	0.888087i	0.328069	−	0.0303719i
$856$	−5.75565	+	9.96908i	−0.196724	+	0.340736i
$857$	−19.2812	−	3.39979i	−0.658633	−	0.116135i	−0.165665	−	0.986182i	$-0.552977\pi$
$857$	−19.2812	−	3.39979i	−0.658633	−	0.116135i	−0.492968	+	0.870047i	$0.664088\pi$
$858$	2.08524	+	0.814510i	0.0711889	+	0.0278069i
$859$	48.9371	+	17.8117i	1.66971	+	0.607726i	0.991844	−	0.127457i	$-0.0406816\pi$
$859$	48.9371	+	17.8117i	1.66971	+	0.607726i	0.677869	+	0.735183i	$0.262904\pi$
$860$	11.1977	−	17.8931i	0.381838	−	0.610148i
$861$	−8.69418	−	1.74295i	−0.296297	−	0.0593994i
$862$	−13.6228	+	16.2350i	−0.463994	+	0.552966i
$863$			35.8160i			1.21919i	0.792713	+	0.609595i	$0.208668\pi$
$863$			35.8160i			1.21919i	−0.792713	+	0.609595i	$0.791332\pi$
$864$	3.05364	+	4.20420i	0.103887	+	0.143030i
$865$	16.6381	+	15.0015i	0.565713	+	0.510065i
$866$	−18.9266	−	15.8813i	−0.643151	−	0.539668i
$867$	−35.9020	+	12.1271i	−1.21930	+	0.411856i
$868$	22.7963	−	4.01960i	0.773755	−	0.136434i
$869$	0.870894	+	0.316980i	0.0295431	+	0.0107528i
$870$	−7.29544	−	0.430206i	−0.247338	−	0.0145853i
$871$	9.12567	−	51.7542i	0.309211	−	1.75363i
$872$	4.33640	+	2.50362i	0.146849	+	0.0847833i
$873$	5.39340	−	2.78709i	0.182539	−	0.0943286i
$874$	4.59315	+	7.95558i	0.155366	+	0.269101i
$875$	7.73921	−	26.7843i	0.261633	−	0.905476i
$876$	−17.2827	+	9.44793i	−0.583930	+	0.319216i
$877$	−30.2046	−	35.9964i	−1.01994	−	1.21551i	−0.976290	−	0.216465i	$-0.930547\pi$
$877$	−30.2046	−	35.9964i	−1.01994	−	1.21551i	−0.0436450	−	0.999047i	$-0.513897\pi$
$878$	−19.4184	−	23.1420i	−0.655340	−	0.781004i
$879$	−0.733506	−	0.446609i	−0.0247405	−	0.0150638i
$880$	0.213543	−	0.527509i	0.00719854	−	0.0177823i
$881$	3.97962	+	6.89290i	0.134077	+	0.232228i	0.925244	−	0.379372i	$-0.123860\pi$
$881$	3.97962	+	6.89290i	0.134077	+	0.232228i	−0.791168	+	0.611599i	$0.790526\pi$
$882$	−1.42188	−	1.86459i	−0.0478773	−	0.0627842i
$883$	48.2981	+	27.8849i	1.62536	+	0.938402i	0.985453	+	0.169950i	$0.0543606\pi$
$883$	48.2981	+	27.8849i	1.62536	+	0.938402i	0.639907	+	0.768452i	$0.278973\pi$
$884$	5.49867	−	31.1845i	0.184940	−	1.04885i
$885$	−21.7219	−	14.3092i	−0.730172	−	0.480999i
$886$	4.12119	+	1.49999i	0.138454	+	0.0503931i
$887$	5.36849	−	0.946609i	0.180256	−	0.0317840i	−0.0827914	−	0.996567i	$-0.526384\pi$
$887$	5.36849	−	0.946609i	0.180256	−	0.0317840i	0.263047	+	0.964783i	$0.415272\pi$
$888$	−7.81628	−	6.87547i	−0.262297	−	0.230726i
$889$	−13.2042	−	11.0796i	−0.442854	−	0.371599i
$890$	−24.3562	−	21.9603i	−0.816421	−	0.736110i
$891$	−1.88417	+	1.30252i	−0.0631219	+	0.0436362i
$892$			6.68384i			0.223791i
$893$	−4.24497	+	5.05896i	−0.142053	+	0.169292i
$894$	−20.0096	+	22.7477i	−0.669222	+	0.760795i
$895$	14.0704	+	8.80542i	0.470322	+	0.294333i
$896$	−2.34328	−	0.852884i	−0.0782835	−	0.0284929i
$897$	8.47577	+	55.6230i	0.282998	+	1.85720i
$898$	6.61851	+	1.16702i	0.220863	+	0.0389440i
$899$	−8.75796	+	15.1692i	−0.292094	+	0.505922i
$900$	4.32283	−	14.3636i	0.144094	−	0.478787i
$901$	−3.97499	−	6.88489i	−0.132426	−	0.229369i
$902$	0.178705	+	0.490987i	0.00595021	+	0.0163481i
$903$	21.2037	−	34.8247i	0.705615	−	1.15889i
$904$	−2.49756	+	2.09570i	−0.0830675	+	0.0697019i
$905$	−0.315084	+	8.85097i	−0.0104737	+	0.294216i
$906$	23.4072	−	12.7959i	0.777651	−	0.425117i
$907$	−12.9264	−	35.5150i	−0.429214	−	1.17926i	−0.946291	−	0.323317i	$-0.895202\pi$
$907$	−12.9264	−	35.5150i	−0.429214	−	1.17926i	0.517076	−	0.855939i	$-0.327020\pi$
$908$	−14.1735	+	8.18306i	−0.470363	+	0.271564i
$909$	16.0882	+	0.750804i	0.533611	+	0.0249026i
$910$	−26.9375	+	8.73235i	−0.892968	+	0.289475i
$911$	3.73492	−	21.1818i	0.123743	−	0.701784i	−0.858303	−	0.513144i	$-0.828481\pi$
$911$	3.73492	−	21.1818i	0.123743	−	0.701784i	0.982046	−	0.188640i	$-0.0604081\pi$
$912$	−1.94226	+	1.55404i	−0.0643147	+	0.0514595i
$913$	−0.819432	+	2.25137i	−0.0271192	+	0.0745095i
$914$	0.341488	+	1.93667i	0.0112954	+	0.0640595i
$915$	19.3563	−	44.7838i	0.639898	−	1.48051i
$916$	−21.1001	−	17.7051i	−0.697167	−	0.584993i
$917$		−	8.42378i		−	0.278178i
$918$	23.3031	+	22.5098i	0.769116	+	0.742933i
$919$	−23.4067			−0.772116			−0.386058	−	0.922474i	$-0.626164\pi$
$919$	−23.4067			−0.772116			−0.386058	+	0.922474i	$0.626164\pi$
$920$	14.1653	−	1.98102i	0.467016	−	0.0653123i
$921$	28.7159	+	5.75675i	0.946220	+	0.189691i
$922$	−23.7153	+	4.18166i	−0.781023	+	0.137715i
$923$	8.29001	−	22.7766i	0.272869	−	0.749701i
$924$	0.399948	−	1.02391i	0.0131573	−	0.0336843i
$925$	−2.13684	+	29.9748i	−0.0702589	+	0.985565i
$926$	−10.2896	+	17.8221i	−0.338136	+	0.585669i
$927$	1.03557	+	0.232842i	0.0340124	+	0.00764754i
$928$	1.63414	−	0.943473i	0.0536434	−	0.0309710i
$929$	25.5770	−	9.30926i	0.839153	−	0.305427i	0.113543	−	0.993533i	$-0.463780\pi$
$929$	25.5770	−	9.30926i	0.839153	−	0.305427i	0.725610	+	0.688106i	$0.241558\pi$
$930$	−26.1325	−	24.6905i	−0.856917	−	0.809632i
$931$	0.859900	−	0.721542i	0.0281821	−	0.0236476i
$932$	−8.38101	−	9.98810i	−0.274529	−	0.327171i
$933$	5.09249	+	0.118764i	0.166721	+	0.00388815i
$934$	2.31399	−	0.842224i	0.0757161	−	0.0275584i
$935$	0.740115	−	3.47041i	0.0242043	−	0.113494i
$936$	−14.5439	+	4.53774i	−0.475383	+	0.148321i
$937$	−49.4760	−	28.5650i	−1.61631	−	0.933177i	−0.987864	−	0.155323i	$-0.950358\pi$
$937$	−49.4760	−	28.5650i	−1.61631	−	0.933177i	−0.628446	−	0.777853i	$-0.716309\pi$
$938$	−25.4128	−	4.48096i	−0.829758	−	0.146309i
$939$	16.1744	−	41.4083i	0.527831	−	1.35131i
$940$	4.82118	+	9.08215i	0.157250	+	0.296227i
$941$	−5.63931	−	31.9821i	−0.183836	−	1.04259i	−0.927441	−	0.373968i	$-0.877997\pi$
$941$	−5.63931	−	31.9821i	−0.183836	−	1.04259i	0.743605	−	0.668619i	$-0.233114\pi$
$942$	4.70618	−	23.4754i	0.153336	−	0.764871i
$943$	−8.44111	+	10.0597i	−0.274880	+	0.327590i
$944$	6.71611			0.218591
$945$	8.00897	−	27.8449i	0.260532	−	0.905794i
$946$	−2.40249			−0.0781116
$947$	−3.18711	+	3.79825i	−0.103567	+	0.123427i	−0.815338	−	0.578985i	$-0.803449\pi$
$947$	−3.18711	+	3.79825i	−0.103567	+	0.123427i	0.711771	+	0.702412i	$0.247893\pi$
$948$	−5.97559	+	2.01844i	−0.194078	+	0.0655560i
$949$	−10.0284	−	56.8740i	−0.325537	−	1.84621i
$950$	6.96501	+	1.74660i	0.225975	+	0.0566670i
$951$	18.1956	+	22.7410i	0.590031	+	0.737428i
$952$	−15.3125	−	2.70000i	−0.496280	−	0.0875076i
$953$	9.99580	+	5.77108i	0.323796	+	0.186943i	0.653083	−	0.757286i	$-0.273475\pi$
$953$	9.99580	+	5.77108i	0.323796	+	0.186943i	−0.329288	+	0.944230i	$0.606809\pi$
$954$	−2.06485	+	3.21980i	−0.0668519	+	0.104245i
$955$	37.8216	+	8.06601i	1.22388	+	0.261010i
$956$	−7.36107	+	2.67921i	−0.238074	+	0.0866518i
$957$	0.398991	+	0.729860i	0.0128976	+	0.0235930i
$958$	18.1933	+	21.6819i	0.587799	+	0.700512i
$959$	38.3987	−	32.2203i	1.23996	−	1.04045i
$960$	1.10810	+	3.71108i	0.0357638	+	0.119775i
$961$	−51.8412	+	18.8687i	−1.67230	+	0.608667i
$962$	26.4332	−	15.2612i	0.852239	−	0.492040i
$963$	34.2519	−	4.40481i	1.10375	−	0.141943i
$964$	−8.22956	+	14.2540i	−0.265056	+	0.459091i
$965$	−9.75843	+	7.61349i	−0.314135	+	0.245087i
$966$	27.3125	−	4.16185i	0.878764	−	0.133905i
$967$	3.22470	−	8.85979i	0.103699	−	0.284912i	−0.876982	−	0.480523i	$-0.840447\pi$
$967$	3.22470	−	8.85979i	0.103699	−	0.284912i	0.980682	+	0.195611i	$0.0626691\pi$
$968$	10.7691	−	1.89888i	0.346132	−	0.0610324i
$969$	−10.2439	+	11.6456i	−0.329082	+	0.374112i
$970$	4.48142	−	0.626728i	0.143890	−	0.0201230i
$971$	−7.33232			−0.235305			−0.117653	−	0.993055i	$-0.537537\pi$
$971$	−7.33232			−0.235305			−0.117653	+	0.993055i	$0.537537\pi$
$972$	4.47426	−	14.9325i	0.143512	−	0.478962i
$973$			5.23986i			0.167982i
$974$	−20.8017	−	17.4547i	−0.666530	−	0.559285i
$975$	35.8439	+	25.4857i	1.14792	+	0.816195i
$976$	2.18744	+	12.4056i	0.0700182	+	0.397093i
$977$	−8.27704	+	22.7410i	−0.264806	+	0.727549i	0.734021	+	0.679127i	$0.237641\pi$
$977$	−8.27704	+	22.7410i	−0.264806	+	0.727549i	−0.998827	+	0.0484217i	$0.984581\pi$
$978$	4.68984	+	30.7775i	0.149965	+	0.984156i
$979$	−0.648163	+	3.67591i	−0.0207154	+	0.117483i
$980$	−0.538965	−	1.66259i	−0.0172166	−	0.0531096i
$981$	−1.91603	−	14.8990i	−0.0611740	−	0.475690i
$982$	13.5893	−	7.84579i	0.433652	−	0.250369i
$983$	20.5024	+	56.3299i	0.653925	+	1.79664i	0.602716	+	0.797956i	$0.294085\pi$
$983$	20.5024	+	56.3299i	0.653925	+	1.79664i	0.0512086	+	0.998688i	$0.483693\pi$
$984$	−3.03719	−	1.84925i	−0.0968220	−	0.0589520i
$985$	18.2767	+	0.650629i	0.582344	+	0.0207308i
$986$	9.01299	−	7.56280i	0.287032	−	0.240848i
$987$	9.52701	+	17.4274i	0.303248	+	0.554720i
$988$	−2.49447	−	6.85350i	−0.0793596	−	0.218039i
$989$	−30.1911	−	52.2926i	−0.960022	−	1.66281i
$990$	−1.64685	+	0.450196i	−0.0523404	+	0.0143082i
$991$	24.5353	−	42.4965i	0.779391	−	1.34994i	−0.152903	−	0.988241i	$-0.548862\pi$
$991$	24.5353	−	42.4965i	0.779391	−	1.34994i	0.932293	−	0.361703i	$-0.117805\pi$
$992$	9.14166	+	1.61192i	0.290248	+	0.0511786i
$993$	−22.4278	+	17.9450i	−0.711725	+	0.569466i
$994$	−11.1840	−	4.07063i	−0.354734	−	0.129113i
$995$	−25.4016	−	15.8966i	−0.805285	−	0.503956i
$996$	−5.21793	−	15.4476i	−0.165336	−	0.489477i
$997$	21.3364	−	25.4278i	0.675732	−	0.805306i	−0.313820	−	0.949483i	$-0.601609\pi$
$997$	21.3364	−	25.4278i	0.675732	−	0.805306i	0.989552	+	0.144176i	$0.0460533\pi$
$998$			11.5519i			0.365671i
$999$	−2.18279	+	31.1534i	−0.0690603	+	0.985649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.p.a.259.12	yes	108
3.2	odd	2		810.2.p.a.289.8		108
5.4	even	2	inner	270.2.p.a.259.7	yes	108
15.14	odd	2		810.2.p.a.289.15		108
27.5	odd	18		810.2.p.a.199.15		108
27.22	even	9	inner	270.2.p.a.49.7	✓	108
135.49	even	18	inner	270.2.p.a.49.12	yes	108
135.59	odd	18		810.2.p.a.199.8		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.p.a.49.7	✓	108	27.22	even	9	inner
270.2.p.a.49.12	yes	108	135.49	even	18	inner
270.2.p.a.259.7	yes	108	5.4	even	2	inner
270.2.p.a.259.12	yes	108	1.1	even	1	trivial
810.2.p.a.199.8		108	135.59	odd	18
810.2.p.a.199.15		108	27.5	odd	18
810.2.p.a.289.8		108	3.2	odd	2
810.2.p.a.289.15		108	15.14	odd	2

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(-1.30051 - 1.14397i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.97504 + 1.04843i) q^{5} +(-1.71229 + 0.260916i) q^{6} +(-2.45578 - 0.433021i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.382651 + 2.97550i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(-1.30051 - 1.14397i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.97504 + 1.04843i) q^{5} +(-1.71229 + 0.260916i) q^{6} +(-2.45578 - 0.433021i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.382651 + 2.97550i) q^{9} +(-0.466386 + 2.18689i) q^{10} +(0.239158 - 0.0870462i) q^{11} +(-0.900763 + 1.47940i) q^{12} +(-3.26437 - 3.89032i) q^{13} +(-1.91026 + 1.60290i) q^{14} +(3.76794 + 0.895897i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-5.39990 + 3.11764i) q^{17} +(2.52533 + 1.61948i) q^{18} +(-0.718067 + 1.24373i) q^{19} +(1.37547 + 1.76298i) q^{20} +(2.69840 + 3.37250i) q^{21} +(0.0870462 - 0.239158i) q^{22} +(6.29938 - 1.11075i) q^{23} +(0.554288 + 1.64096i) q^{24} +(2.80158 - 4.14140i) q^{25} -5.07845 q^{26} +(2.90625 - 4.30740i) q^{27} +2.49367i q^{28} +(-1.44548 - 1.21291i) q^{29} +(3.10828 - 2.31054i) q^{30} +(-1.61192 - 9.14166i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.410605 - 0.160385i) q^{33} +(-1.08274 + 6.14054i) q^{34} +(5.30426 - 1.71949i) q^{35} +(2.86385 - 0.893527i) q^{36} +(-5.20496 + 3.00509i) q^{37} +(0.491186 + 1.34952i) q^{38} +(-0.205082 + 8.79375i) q^{39} +(2.23465 + 0.0795510i) q^{40} +(-1.57268 + 1.31963i) q^{41} +(4.31798 + 0.100701i) q^{42} +(-3.22860 - 8.87051i) q^{43} +(-0.127253 - 0.220409i) q^{44} +(-3.87536 - 5.47554i) q^{45} +(3.19828 - 5.53958i) q^{46} +(4.52860 + 0.798515i) q^{47} +(1.61334 + 0.630183i) q^{48} +(-0.734489 - 0.267332i) q^{49} +(-1.37168 - 4.80817i) q^{50} +(10.5891 + 2.12283i) q^{51} +(-3.26437 + 3.89032i) q^{52} +1.27500i q^{53} +(-1.43156 - 4.99506i) q^{54} +(-0.381084 + 0.422661i) q^{55} +(1.91026 + 1.60290i) q^{56} +(2.35664 - 0.796031i) q^{57} +(-1.85828 + 0.327665i) q^{58} +(-6.31108 - 2.29705i) q^{59} +(0.227990 - 3.86627i) q^{60} +(2.18744 - 12.4056i) q^{61} +(-8.03904 - 4.64134i) q^{62} +(0.348745 - 7.47287i) q^{63} +(0.500000 + 0.866025i) q^{64} +(10.5260 + 4.26108i) q^{65} +(-0.386794 + 0.211448i) q^{66} +(6.65166 + 7.92715i) q^{67} +(4.00796 + 4.77650i) q^{68} +(-9.46307 - 5.76178i) q^{69} +(2.09231 - 5.16857i) q^{70} +(2.38639 + 4.13335i) q^{71} +(1.15636 - 2.76818i) q^{72} +(9.84831 + 5.68592i) q^{73} +(-1.04366 + 5.91886i) q^{74} +(-8.38112 + 2.18100i) q^{75} +(1.34952 + 0.491186i) q^{76} +(-0.625012 + 0.110206i) q^{77} +(6.60458 + 5.80962i) q^{78} +(2.78956 + 2.34072i) q^{79} +(1.49735 - 1.66071i) q^{80} +(-8.70716 + 2.27715i) q^{81} +2.05299i q^{82} +(-6.05105 + 7.21136i) q^{83} +(2.85269 - 3.24304i) q^{84} +(7.39640 - 11.8189i) q^{85} +(-8.87051 - 3.22860i) q^{86} +(0.492335 + 3.23099i) q^{87} +(-0.250640 - 0.0441945i) q^{88} +(-7.33307 + 12.7012i) q^{89} +(-6.68554 - 0.550914i) q^{90} +(6.33199 + 10.9673i) q^{91} +(-2.18775 - 6.01080i) q^{92} +(-8.36150 + 13.7328i) q^{93} +(3.52263 - 2.95583i) q^{94} +(0.114246 - 3.20926i) q^{95} +(1.51978 - 0.830817i) q^{96} +(-0.692131 - 1.90161i) q^{97} +(-0.676909 + 0.390813i) q^{98} +(0.350520 + 0.678304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9	\( 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} - 12 q^{11} + 6 q^{14} + 18 q^{15} + 12 q^{20} - 72 q^{21} - 18 q^{25} - 72 q^{26} + 6 q^{29} + 36 q^{30} + 36 q^{31} + 18 q^{35} - 30 q^{36} - 48 q^{39} - 12 q^{41} - 12 q^{44} - 66 q^{45} + 18 q^{49} - 12 q^{50} + 48 q^{51} - 36 q^{54} - 6 q^{56} - 84 q^{59} + 18 q^{60} - 18 q^{61} + 54 q^{64} - 6 q^{65} - 60 q^{69} - 48 q^{74} + 12 q^{75} - 72 q^{79} - 12 q^{81} - 36 q^{86} - 132 q^{89} + 30 q^{90} - 36 q^{94} - 18 q^{95} - 36 q^{99}+O(q^{100}) \) 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9 - 12 * q^11 + 6 * q^14 + 18 * q^15 + 12 * q^20 - 72 * q^21 - 18 * q^25 - 72 * q^26 + 6 * q^29 + 36 * q^30 + 36 * q^31 + 18 * q^35 - 30 * q^36 - 48 * q^39 - 12 * q^41 - 12 * q^44 - 66 * q^45 + 18 * q^49 - 12 * q^50 + 48 * q^51 - 36 * q^54 - 6 * q^56 - 84 * q^59 + 18 * q^60 - 18 * q^61 + 54 * q^64 - 6 * q^65 - 60 * q^69 - 48 * q^74 + 12 * q^75 - 72 * q^79 - 12 * q^81 - 36 * q^86 - 132 * q^89 + 30 * q^90 - 36 * q^94 - 18 * q^95 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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