LMFDB - Embedded newform 162.2.g.b.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	162.7
Dual form			162.2.g.b.139.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.597159 + 0.802123i) q^{2} +(0.427379 - 1.67850i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(1.23282 - 0.810835i) q^{5} +(1.60157 - 0.659517i) q^{6} +(0.694984 - 0.736640i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.63469 - 1.43471i) q^{9} +O(q^{10})$	\(q+(0.597159 + 0.802123i) q^{2} +(0.427379 - 1.67850i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(1.23282 - 0.810835i) q^{5} +(1.60157 - 0.659517i) q^{6} +(0.694984 - 0.736640i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.63469 - 1.43471i) q^{9} +(1.38658 + 0.504672i) q^{10} +(0.261194 - 0.131176i) q^{11} +(1.48541 + 0.890823i) q^{12} +(1.36323 + 3.16033i) q^{13} +(1.00589 + 0.117572i) q^{14} +(-0.834104 - 2.41581i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(-1.92630 + 1.61636i) q^{17} +(-0.422518 - 2.97010i) q^{18} +(3.04721 + 2.55692i) q^{19} +(0.423196 + 1.41357i) q^{20} +(-0.939425 - 1.48135i) q^{21} +(0.261194 + 0.131176i) q^{22} +(-3.54079 - 3.75302i) q^{23} +(0.172474 + 1.72344i) q^{24} +(-1.11802 + 2.59186i) q^{25} +(-1.72091 + 2.98070i) q^{26} +(-3.53416 + 3.80916i) q^{27} +(0.506370 + 0.877058i) q^{28} +(-9.88356 + 1.15522i) q^{29} +(1.43968 - 2.11168i) q^{30} +(1.32136 - 0.313167i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(-0.108550 - 0.494475i) q^{33} +(-2.44683 - 0.579909i) q^{34} +(0.259493 - 1.47166i) q^{35} +(2.13007 - 2.11253i) q^{36} +(1.03595 + 5.87515i) q^{37} +(-0.231292 + 3.97112i) q^{38} +(5.88722 - 0.937523i) q^{39} +(-0.881145 + 1.18358i) q^{40} +(2.84830 - 3.82593i) q^{41} +(0.627241 - 1.63814i) q^{42} +(0.689149 - 11.8322i) q^{43} +(0.0507544 + 0.287843i) q^{44} +(-4.41140 + 0.367574i) q^{45} +(0.895970 - 5.08130i) q^{46} +(-2.71368 - 0.643154i) q^{47} +(-1.27942 + 1.16751i) q^{48} +(0.347378 + 5.96425i) q^{49} +(-2.74663 + 0.650962i) q^{50} +(1.88979 + 3.92409i) q^{51} +(-3.41855 + 0.399571i) q^{52} +(1.31648 + 2.28021i) q^{53} +(-5.16587 - 0.560162i) q^{54} +(0.215641 - 0.373501i) q^{55} +(-0.401126 + 0.929914i) q^{56} +(5.59409 - 4.02196i) q^{57} +(-6.82868 - 7.23798i) q^{58} +(0.159662 + 0.0801851i) q^{59} +(2.55354 - 0.106201i) q^{60} +(-2.93491 - 9.80328i) q^{61} +(1.04026 + 0.872879i) q^{62} +(-2.88793 + 0.943723i) q^{63} +(0.766044 - 0.642788i) q^{64} +(4.24313 + 2.79075i) q^{65} +(0.331808 - 0.382350i) q^{66} +(8.02516 + 0.938006i) q^{67} +(-0.995986 - 2.30896i) q^{68} +(-7.81268 + 4.33924i) q^{69} +(1.33541 - 0.670668i) q^{70} +(13.2365 + 4.81768i) q^{71} +(2.96650 + 0.447065i) q^{72} +(-1.12990 + 0.411250i) q^{73} +(-4.09397 + 4.33936i) q^{74} +(3.87261 + 2.98430i) q^{75} +(-3.32345 + 2.18587i) q^{76} +(0.0848957 - 0.283571i) q^{77} +(4.26761 + 4.16243i) q^{78} +(5.40569 + 7.26110i) q^{79} -1.47556 q^{80} +(4.88323 + 7.56003i) q^{81} +4.76975 q^{82} +(-7.45078 - 10.0081i) q^{83} +(1.68855 - 0.475103i) q^{84} +(-1.06417 + 3.55459i) q^{85} +(9.90244 - 6.51294i) q^{86} +(-2.28499 + 17.0832i) q^{87} +(-0.200577 + 0.212599i) q^{88} +(10.6875 - 3.88993i) q^{89} +(-2.92915 - 3.31899i) q^{90} +(3.27545 + 1.19217i) q^{91} +(4.61086 - 2.31566i) q^{92} +(0.0390702 - 2.35173i) q^{93} +(-1.10461 - 2.56077i) q^{94} +(5.82989 + 0.681416i) q^{95} +(-1.70051 - 0.329060i) q^{96} +(-8.36554 - 5.50211i) q^{97} +(-4.57662 + 3.84024i) q^{98} +(-0.876365 - 0.0291268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	0.597159	+	0.802123i	0.422255	+	0.567187i
$2$	0.597159	+	0.802123i	0.422255	+	0.567187i
$3$	0.427379	−	1.67850i	0.246747	−	0.969080i
$3$	0.427379	−	1.67850i	0.246747	−	0.969080i
$4$	−0.286803	+	0.957990i	−0.143402	+	0.478995i
$5$	1.23282	−	0.810835i	0.551332	−	0.362617i	−0.243070	−	0.970009i	$-0.578155\pi$
$5$	1.23282	−	0.810835i	0.551332	−	0.362617i	0.794402	+	0.607392i	$0.207784\pi$
$6$	1.60157	−	0.659517i	0.653840	−	0.269247i
$7$	0.694984	−	0.736640i	0.262679	−	0.278424i	−0.582588	−	0.812768i	$-0.697960\pi$
$7$	0.694984	−	0.736640i	0.262679	−	0.278424i	0.845267	+	0.534344i	$0.179441\pi$
$8$	−0.939693	+	0.342020i	−0.332232	+	0.120922i
$9$	−2.63469	−	1.43471i	−0.878231	−	0.478236i
$10$	1.38658	+	0.504672i	0.438474	+	0.159591i
$11$	0.261194	−	0.131176i	0.0787529	−	0.0395512i	−0.408987	−	0.912540i	$-0.634118\pi$
$11$	0.261194	−	0.131176i	0.0787529	−	0.0395512i	0.487740	+	0.872989i	$0.337822\pi$
$12$	1.48541	+	0.890823i	0.428800	+	0.257158i
$13$	1.36323	+	3.16033i	0.378093	+	0.876518i	0.995923	+	0.0902067i	$0.0287528\pi$
$13$	1.36323	+	3.16033i	0.378093	+	0.876518i	−0.617830	+	0.786312i	$0.711988\pi$
$14$	1.00589	+	0.117572i	0.268836	+	0.0314224i
$15$	−0.834104	−	2.41581i	−0.215365	−	0.623759i
$16$	−0.835488	−	0.549509i	−0.208872	−	0.137377i
$17$	−1.92630	+	1.61636i	−0.467197	+	0.392025i	−0.845771	−	0.533546i	$-0.820859\pi$
$17$	−1.92630	+	1.61636i	−0.467197	+	0.392025i	0.378574	+	0.925571i	$0.376415\pi$
$18$	−0.422518	−	2.97010i	−0.0995885	−	0.700059i
$19$	3.04721	+	2.55692i	0.699079	+	0.586597i	0.921511	−	0.388351i	$-0.126955\pi$
$19$	3.04721	+	2.55692i	0.699079	+	0.586597i	−0.222433	+	0.974948i	$0.571400\pi$
$20$	0.423196	+	1.41357i	0.0946296	+	0.316085i
$21$	−0.939425	−	1.48135i	−0.204999	−	0.323258i
$22$	0.261194	+	0.131176i	0.0556867	+	0.0279669i
$23$	−3.54079	−	3.75302i	−0.738306	−	0.782558i	0.244013	−	0.969772i	$-0.421536\pi$
$23$	−3.54079	−	3.75302i	−0.738306	−	0.782558i	−0.982319	+	0.187213i	$0.940054\pi$
$24$	0.172474	+	1.72344i	0.0352062	+	0.351796i
$25$	−1.11802	+	2.59186i	−0.223604	+	0.518372i
$26$	−1.72091	+	2.98070i	−0.337498	+	0.584564i
$27$	−3.53416	+	3.80916i	−0.680150	+	0.733073i
$28$	0.506370	+	0.877058i	0.0956949	+	0.165748i
$29$	−9.88356	+	1.15522i	−1.83533	+	0.214519i	−0.962083	−	0.272756i	$-0.912065\pi$
$29$	−9.88356	+	1.15522i	−1.83533	+	0.214519i	−0.873248	+	0.487276i	$0.837991\pi$
$30$	1.43968	−	2.11168i	0.262849	−	0.385537i
$31$	1.32136	−	0.313167i	0.237322	−	0.0562465i	−0.110233	−	0.993906i	$-0.535160\pi$
$31$	1.32136	−	0.313167i	0.237322	−	0.0562465i	0.347556	+	0.937659i	$0.387012\pi$
$32$	−0.0581448	−	0.998308i	−0.0102787	−	0.176478i
$33$	−0.108550	−	0.494475i	−0.0188962	−	0.0860770i
$34$	−2.44683	−	0.579909i	−0.419628	−	0.0994536i
$35$	0.259493	−	1.47166i	0.0438624	−	0.248756i
$36$	2.13007	−	2.11253i	0.355012	−	0.352088i
$37$	1.03595	+	5.87515i	0.170309	+	0.965869i	0.943420	+	0.331599i	$0.107588\pi$
$37$	1.03595	+	5.87515i	0.170309	+	0.965869i	−0.773112	+	0.634270i	$0.781301\pi$
$38$	−0.231292	+	3.97112i	−0.0375205	+	0.644201i
$39$	5.88722	−	0.937523i	0.942710	−	0.150124i
$40$	−0.881145	+	1.18358i	−0.139321	+	0.187141i
$41$	2.84830	−	3.82593i	0.444829	−	0.597510i	−0.521996	−	0.852948i	$-0.674812\pi$
$41$	2.84830	−	3.82593i	0.444829	−	0.597510i	0.966825	+	0.255438i	$0.0822198\pi$
$42$	0.627241	−	1.63814i	0.0967854	−	0.252770i
$43$	0.689149	−	11.8322i	0.105094	−	1.80440i	−0.374835	−	0.927092i	$-0.622300\pi$
$43$	0.689149	−	11.8322i	0.105094	−	1.80440i	0.479929	−	0.877307i	$-0.340662\pi$
$44$	0.0507544	+	0.287843i	0.00765152	+	0.0433939i
$45$	−4.41140	+	0.367574i	−0.657613	+	0.0547947i
$46$	0.895970	−	5.08130i	0.132104	−	0.749196i
$47$	−2.71368	−	0.643154i	−0.395831	−	0.0938137i	0.0278795	−	0.999611i	$-0.491125\pi$
$47$	−2.71368	−	0.643154i	−0.395831	−	0.0938137i	−0.423711	+	0.905798i	$0.639273\pi$
$48$	−1.27942	+	1.16751i	−0.184668	+	0.168516i
$49$	0.347378	+	5.96425i	0.0496254	+	0.852036i
$50$	−2.74663	+	0.650962i	−0.388431	+	0.0920600i
$51$	1.88979	+	3.92409i	0.264624	+	0.549483i
$52$	−3.41855	+	0.399571i	−0.474067	+	0.0554105i
$53$	1.31648	+	2.28021i	0.180832	+	0.313210i	0.942164	−	0.335152i	$-0.108788\pi$
$53$	1.31648	+	2.28021i	0.180832	+	0.313210i	−0.761332	+	0.648362i	$0.775454\pi$
$54$	−5.16587	−	0.560162i	−0.702986	−	0.0762284i
$55$	0.215641	−	0.373501i	0.0290770	−	0.0503629i
$56$	−0.401126	+	0.929914i	−0.0536027	+	0.124265i
$57$	5.59409	−	4.02196i	0.740955	−	0.532722i
$58$	−6.82868	−	7.23798i	−0.896650	−	0.950394i
$59$	0.159662	+	0.0801851i	0.0207862	+	0.0104392i	0.459162	−	0.888353i	$-0.348150\pi$
$59$	0.159662	+	0.0801851i	0.0207862	+	0.0104392i	−0.438376	+	0.898792i	$0.644446\pi$
$60$	2.55354	−	0.106201i	0.329661	−	0.0137105i
$61$	−2.93491	−	9.80328i	−0.375776	−	1.25518i	−0.911680	−	0.410901i	$-0.865214\pi$
$61$	−2.93491	−	9.80328i	−0.375776	−	1.25518i	0.535903	−	0.844279i	$-0.319971\pi$
$62$	1.04026	+	0.872879i	0.132113	+	0.110856i
$63$	−2.88793	+	0.943723i	−0.363845	+	0.118898i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	4.24313	+	2.79075i	0.526295	+	0.346150i
$66$	0.331808	−	0.382350i	0.0408427	−	0.0470641i
$67$	8.02516	+	0.938006i	0.980429	+	0.114596i	0.591182	−	0.806538i	$-0.298661\pi$
$67$	8.02516	+	0.938006i	0.980429	+	0.114596i	0.389247	+	0.921134i	$0.372735\pi$
$68$	−0.995986	−	2.30896i	−0.120781	−	0.280002i
$69$	−7.81268	+	4.33924i	−0.940537	+	0.522383i
$70$	1.33541	−	0.670668i	0.159612	−	0.0801602i
$71$	13.2365	+	4.81768i	1.57088	+	0.571754i	0.973196	−	0.229977i	$-0.0738651\pi$
$71$	13.2365	+	4.81768i	1.57088	+	0.571754i	0.597685	+	0.801731i	$0.296087\pi$
$72$	2.96650	+	0.447065i	0.349606	+	0.0526872i
$73$	−1.12990	+	0.411250i	−0.132245	+	0.0481332i	−0.407295	−	0.913297i	$-0.633528\pi$
$73$	−1.12990	+	0.411250i	−0.132245	+	0.0481332i	0.275050	+	0.961430i	$0.411306\pi$
$74$	−4.09397	+	4.33936i	−0.475914	+	0.504440i
$75$	3.87261	+	2.98430i	0.447170	+	0.344597i
$76$	−3.32345	+	2.18587i	−0.381226	+	0.250736i
$77$	0.0848957	−	0.283571i	0.00967476	−	0.0323159i
$78$	4.26761	+	4.16243i	0.483212	+	0.471302i
$79$	5.40569	+	7.26110i	0.608187	+	0.816937i	0.994423	−	0.105463i	$-0.0336323\pi$
$79$	5.40569	+	7.26110i	0.608187	+	0.816937i	−0.386236	+	0.922400i	$0.626225\pi$
$80$	−1.47556			−0.164973
$81$	4.88323	+	7.56003i	0.542581	+	0.840003i
$82$	4.76975			0.526731
$83$	−7.45078	−	10.0081i	−0.817830	−	1.09854i	−0.993471	−	0.114082i	$-0.963607\pi$
$83$	−7.45078	−	10.0081i	−0.817830	−	1.09854i	0.175642	−	0.984454i	$-0.443800\pi$
$84$	1.68855	−	0.475103i	0.184236	−	0.0518380i
$85$	−1.06417	+	3.55459i	−0.115426	+	0.385549i
$86$	9.90244	−	6.51294i	1.06781	−	0.702308i
$87$	−2.28499	+	17.0832i	−0.244977	+	1.83151i
$88$	−0.200577	+	0.212599i	−0.0213816	+	0.0226631i
$89$	10.6875	−	3.88993i	1.13287	−	0.412332i	0.293537	−	0.955948i	$-0.405167\pi$
$89$	10.6875	−	3.88993i	1.13287	−	0.412332i	0.839334	+	0.543616i	$0.182945\pi$
$90$	−2.92915	−	3.31899i	−0.308759	−	0.349852i
$91$	3.27545	+	1.19217i	0.343361	+	0.124973i
$92$	4.61086	−	2.31566i	0.480716	−	0.241424i
$93$	0.0390702	−	2.35173i	0.00405139	−	0.243863i
$94$	−1.10461	−	2.56077i	−0.113932	−	0.264124i
$95$	5.82989	+	0.681416i	0.598134	+	0.0699118i
$96$	−1.70051	−	0.329060i	−0.173557	−	0.0335846i
$97$	−8.36554	−	5.50211i	−0.849392	−	0.558654i	0.0485231	−	0.998822i	$-0.484549\pi$
$97$	−8.36554	−	5.50211i	−0.849392	−	0.558654i	−0.897915	+	0.440168i	$0.854919\pi$
$98$	−4.57662	+	3.84024i	−0.462309	+	0.387923i
$99$	−0.876365	−	0.0291268i	−0.0880780	−	0.00292735i
$100$	−2.16232	−	1.81440i	−0.216232	−	0.181440i
$101$	1.75773	+	5.87122i	0.174901	+	0.584209i	0.999820	+	0.0189587i	$0.00603510\pi$
$101$	1.75773	+	5.87122i	0.174901	+	0.584209i	−0.824920	+	0.565250i	$0.808780\pi$
$102$	−2.01910	+	3.85915i	−0.199921	+	0.382113i
$103$	3.43637	+	1.72581i	0.338595	+	0.170049i	0.609969	−	0.792425i	$-0.291182\pi$
$103$	3.43637	+	1.72581i	0.338595	+	0.170049i	−0.271374	+	0.962474i	$0.587478\pi$
$104$	−2.36192	−	2.50349i	−0.231605	−	0.245487i
$105$	−2.35927	−	1.06451i	−0.230241	−	0.103886i
$106$	−1.04286	+	2.41762i	−0.101292	+	0.234820i
$107$	5.61980	−	9.73378i	0.543286	−	0.941000i	−0.455426	−	0.890274i	$-0.650513\pi$
$107$	5.61980	−	9.73378i	0.543286	−	0.941000i	0.998713	−	0.0507261i	$-0.0161535\pi$
$108$	−2.63552	−	4.47817i	−0.253604	−	0.430912i
$109$	−4.65880	−	8.06927i	−0.446232	−	0.772896i	0.551905	−	0.833907i	$-0.313901\pi$
$109$	−4.65880	−	8.06927i	−0.446232	−	0.772896i	−0.998137	+	0.0610106i	$0.980568\pi$
$110$	0.428366	−	0.0500688i	0.0408431	−	0.00477387i
$111$	10.3042	+	0.772083i	0.978028	+	0.0732829i
$112$	−0.985441	+	0.233554i	−0.0931154	+	0.0220688i
$113$	−0.369387	−	6.34212i	−0.0347490	−	0.596617i	−0.970071	−	0.242820i	$-0.921928\pi$
$113$	−0.369387	−	6.34212i	−0.0347490	−	0.596617i	0.935322	−	0.353797i	$-0.115110\pi$
$114$	6.56666	+	2.08540i	0.615024	+	0.195315i
$115$	−7.40822	−	1.75578i	−0.690820	−	0.163727i
$116$	1.72795	−	9.79967i	0.160436	−	0.909877i
$117$	0.942446	−	10.2824i	0.0871292	−	0.950604i
$118$	0.0310250	+	0.175952i	0.00285608	+	0.0161977i
$119$	−0.148074	+	2.54234i	−0.0135739	+	0.233056i
$120$	1.61006	+	1.98484i	0.146977	+	0.181190i
$121$	−6.51773	+	8.75483i	−0.592521	+	0.795894i
$122$	6.11083	−	8.20827i	0.553248	−	0.743142i
$123$	−5.20450	−	6.41598i	−0.469274	−	0.578509i
$124$	−0.0789583	+	1.35566i	−0.00709067	+	0.121742i
$125$	2.00441	+	11.3675i	0.179279	+	1.01674i
$126$	−2.48154	−	1.75293i	−0.221073	−	0.156163i
$127$	1.81665	−	10.3027i	0.161202	−	0.914220i	−0.791693	−	0.610919i	$-0.790800\pi$
$127$	1.81665	−	10.3027i	0.161202	−	0.914220i	0.952895	−	0.303301i	$-0.0980888\pi$
$128$	0.973045	+	0.230616i	0.0860058	+	0.0203838i
$129$	−19.5658	−	6.21358i	−1.72268	−	0.547076i
$130$	0.295296	+	5.07003i	0.0258991	+	0.444671i
$131$	−12.9203	+	3.06218i	−1.12886	+	0.267544i	−0.752281	−	0.658843i	$-0.771046\pi$
$131$	−12.9203	+	3.06218i	−1.12886	+	0.267544i	−0.376575	+	0.926386i	$0.622898\pi$
$132$	0.504834	+	0.0378268i	0.0439402	+	0.00329240i
$133$	4.00129	−	0.467684i	0.346956	−	0.0405533i
$134$	4.03989	+	6.99730i	0.348994	+	0.604475i
$135$	−1.26837	+	7.56161i	−0.109164	+	0.650800i
$136$	1.25731	−	2.17772i	0.107813	−	0.186738i
$137$	7.16269	−	16.6050i	0.611950	−	1.41866i	−0.277096	−	0.960842i	$-0.589372\pi$
$137$	7.16269	−	16.6050i	0.611950	−	1.41866i	0.889046	−	0.457817i	$-0.151369\pi$
$138$	−8.14602	−	3.67552i	−0.693435	−	0.312881i
$139$	−14.1586	−	15.0072i	−1.20092	−	1.27290i	−0.952603	−	0.304218i	$-0.901605\pi$
$139$	−14.1586	−	15.0072i	−1.20092	−	1.27290i	−0.248314	−	0.968680i	$-0.579876\pi$
$140$	1.33541	+	0.670668i	0.112863	+	0.0566818i
$141$	−2.23930	+	4.28003i	−0.188583	+	0.360444i
$142$	4.03990	+	13.4942i	0.339021	+	1.13241i
$143$	0.770629	+	0.646635i	0.0644433	+	0.0540743i
$144$	1.41287	+	2.64647i	0.117739	+	0.220539i
$145$	−11.2479	+	9.43812i	−0.934088	+	0.783793i
$146$	−1.00460	−	0.660737i	−0.0831415	−	0.0546830i
$147$	10.1594	+	1.96592i	0.837936	+	0.162147i
$148$	−5.92545	−	0.692586i	−0.487069	−	0.0569302i
$149$	5.84986	+	13.5615i	0.479239	+	1.11100i	0.970742	+	0.240125i	$0.0771885\pi$
$149$	5.84986	+	13.5615i	0.479239	+	1.11100i	−0.491503	+	0.870876i	$0.663552\pi$
$150$	−0.0812129	+	4.88841i	−0.00663100	+	0.399137i
$151$	0.0952090	−	0.0478158i	0.00774800	−	0.00389119i	−0.444921	−	0.895570i	$-0.646768\pi$
$151$	0.0952090	−	0.0478158i	0.00774800	−	0.00389119i	0.452669	+	0.891679i	$0.350472\pi$
$152$	−3.73796	−	1.36051i	−0.303189	−	0.110352i
$153$	7.39423	−	1.49493i	0.597788	−	0.120858i
$154$	0.278155	−	0.101240i	0.0224144	−	0.00815817i
$155$	1.37506	−	1.45748i	0.110448	−	0.117068i
$156$	−0.790337	+	5.90878i	−0.0632776	+	0.473081i
$157$	−19.3773	+	12.7447i	−1.54648	+	1.01714i	−0.565110	+	0.825016i	$0.691166\pi$
$157$	−19.3773	+	12.7447i	−1.54648	+	1.01714i	−0.981371	+	0.192121i	$0.938464\pi$
$158$	−2.59624	+	8.67205i	−0.206546	+	0.689912i
$159$	4.38995	−	1.23519i	0.348146	−	0.0979569i
$160$	−0.881145	−	1.18358i	−0.0696607	−	0.0935705i
$161$	−5.22542			−0.411821
$162$	−3.14801	+	8.43149i	−0.247331	+	0.662440i
$163$	12.3733			0.969151			0.484575	−	0.874750i	$-0.338974\pi$
$163$	12.3733			0.969151			0.484575	+	0.874750i	$0.338974\pi$
$164$	2.84830	+	3.82593i	0.222415	+	0.298755i
$165$	−0.534760	−	0.521579i	−0.0416310	−	0.0406049i
$166$	3.57846	−	11.9529i	0.277742	−	0.927724i
$167$	−7.87067	+	5.17662i	−0.609051	+	0.400579i	−0.816233	−	0.577723i	$-0.803941\pi$
$167$	−7.87067	+	5.17662i	−0.609051	+	0.400579i	0.207182	+	0.978302i	$0.433571\pi$
$168$	1.38942	+	1.07071i	0.107196	+	0.0826073i
$169$	0.791849	−	0.839311i	0.0609115	−	0.0645624i
$170$	−3.48670	+	1.26905i	−0.267418	+	0.0973321i
$171$	−4.36005	−	11.1085i	−0.333421	−	0.849492i
$172$	11.1375	+	4.05372i	0.849227	+	0.309093i
$173$	8.30471	−	4.17078i	0.631395	−	0.317099i	−0.104163	−	0.994560i	$-0.533216\pi$
$173$	8.30471	−	4.17078i	0.631395	−	0.317099i	0.735558	+	0.677462i	$0.236920\pi$
$174$	−15.0674	+	8.36855i	−1.14225	+	0.634418i
$175$	1.13226	+	2.62488i	0.0855910	+	0.198422i
$176$	−0.290307	−	0.0339320i	−0.0218827	−	0.00255772i
$177$	0.202826	−	0.233722i	0.0152454	−	0.0175676i
$178$	9.50233	+	6.24978i	0.712229	+	0.468441i
$179$	−7.25336	+	6.08629i	−0.542141	+	0.454911i	−0.872269	−	0.489025i	$-0.837353\pi$
$179$	−7.25336	+	6.08629i	−0.542141	+	0.454911i	0.330128	+	0.943936i	$0.392908\pi$
$180$	0.913073	−	4.33150i	0.0680564	−	0.322851i
$181$	−15.8413	−	13.2924i	−1.17747	−	0.988017i	−0.999992	−	0.00389225i	$-0.998761\pi$
$181$	−15.8413	−	13.2924i	−1.17747	−	0.988017i	−0.177480	−	0.984124i	$-0.556794\pi$
$182$	0.999700	+	3.33923i	0.0741027	+	0.247520i
$183$	−17.7091	+	0.736516i	−1.30909	+	0.0544448i
$184$	4.61086	+	2.31566i	0.339917	+	0.170713i
$185$	6.04092	+	6.40300i	0.444137	+	0.470758i
$186$	1.90971	−	1.37302i	0.140027	−	0.100674i
$187$	−0.291110	+	0.674869i	−0.0212881	+	0.0493513i
$188$	1.39443	−	2.41522i	0.101699	−	0.176148i
$189$	0.349792	+	5.25071i	0.0254436	+	0.381933i
$190$	2.93479	+	5.08320i	0.212912	+	0.368774i
$191$	−24.7404	+	2.89174i	−1.79015	+	0.209239i	−0.945399	−	0.325914i	$-0.894328\pi$
$191$	−24.7404	+	2.89174i	−1.79015	+	0.209239i	−0.844755	+	0.535153i	$0.820254\pi$
$192$	−0.751525	−	1.56052i	−0.0542366	−	0.112621i
$193$	18.9072	−	4.48109i	1.36097	−	0.322556i	0.515643	−	0.856804i	$-0.327553\pi$
$193$	18.9072	−	4.48109i	1.36097	−	0.322556i	0.845328	+	0.534248i	$0.179405\pi$
$194$	−0.582191	−	9.99583i	−0.0417989	−	0.717659i
$195$	6.49768	−	5.92936i	0.465309	−	0.424610i
$196$	−5.81332	−	1.37778i	−0.415237	−	0.0984130i
$197$	0.819992	−	4.65040i	0.0584220	−	0.331328i	−0.941563	−	0.336837i	$-0.890643\pi$
$197$	0.819992	−	4.65040i	0.0584220	−	0.331328i	0.999985	+	0.00550983i	$0.00175384\pi$
$198$	−0.499966	−	0.720346i	−0.0355310	−	0.0511928i
$199$	2.01799	+	11.4446i	0.143051	+	0.811285i	0.968911	+	0.247409i	$0.0795792\pi$
$199$	2.01799	+	11.4446i	0.143051	+	0.811285i	−0.825860	+	0.563876i	$0.809310\pi$
$200$	0.164126	−	2.81794i	0.0116055	−	0.199258i
$201$	5.00422	−	13.0693i	0.352971	−	0.921838i
$202$	−3.65980	+	4.91597i	−0.257503	+	0.345886i
$203$	−6.01793	+	8.08349i	−0.422376	+	0.567350i
$204$	−4.30124	+	0.684959i	−0.301147	+	0.0479568i
$205$	0.409227	−	7.02616i	0.0285817	−	0.490729i
$206$	0.667745	+	3.78697i	0.0465240	+	0.263851i
$207$	3.94442	+	14.9681i	0.274156	+	1.04035i
$208$	0.597665	−	3.38953i	0.0414406	−	0.235022i
$209$	1.13132	+	0.268128i	0.0782550	+	0.0185468i
$210$	−0.554987	−	2.52811i	−0.0382978	−	0.174456i
$211$	−1.07665	−	18.4853i	−0.0741195	−	1.27258i	−0.806315	−	0.591487i	$-0.798541\pi$
$211$	−1.07665	−	18.4853i	−0.0741195	−	1.27258i	0.732195	−	0.681095i	$-0.238496\pi$
$212$	−2.56198	+	0.607201i	−0.175958	+	0.0417027i
$213$	13.7435	−	20.1584i	0.941686	−	1.38123i
$214$	11.1636	−	1.30484i	0.763128	−	0.0891968i
$215$	−8.74440	−	15.1458i	−0.596363	−	1.03293i
$216$	2.01822	−	4.78819i	0.137322	−	0.325795i
$217$	0.687630	−	1.19101i	0.0466793	−	0.0808510i
$218$	3.69051	−	8.55557i	0.249953	−	0.579456i
$219$	0.207386	+	2.07229i	0.0140138	+	0.140032i
$220$	0.295964	+	0.313703i	0.0199539	+	0.0211499i
$221$	−7.73424	−	3.88428i	−0.520261	−	0.261285i
$222$	5.53391	+	8.72626i	0.371412	+	0.585668i
$223$	−0.596094	−	1.99109i	−0.0399174	−	0.133333i	0.935708	−	0.352775i	$-0.114762\pi$
$223$	−0.596094	−	1.99109i	−0.0399174	−	0.133333i	−0.975626	+	0.219441i	$0.929577\pi$
$224$	−0.775804	−	0.650976i	−0.0518356	−	0.0434952i
$225$	6.66420	−	5.22473i	0.444280	−	0.348315i
$226$	4.86658	−	4.08355i	0.323720	−	0.271634i
$227$	−7.78356	−	5.11933i	−0.516613	−	0.339782i	0.264281	−	0.964446i	$-0.414866\pi$
$227$	−7.78356	−	5.11933i	−0.516613	−	0.339782i	−0.780894	+	0.624664i	$0.785236\pi$
$228$	2.24859	+	6.51259i	0.148917	+	0.431307i
$229$	24.3104	+	2.84147i	1.60647	+	0.187770i	0.871524	−	0.490352i	$-0.163132\pi$
$229$	24.3104	+	2.84147i	1.60647	+	0.187770i	0.734949	+	0.678122i	$0.237206\pi$
$230$	−3.01553	−	6.99079i	−0.198838	−	0.460959i
$231$	−0.439690	−	0.263689i	−0.0289295	−	0.0173495i
$232$	8.89240	−	4.46593i	0.583815	−	0.293203i
$233$	12.4662	+	4.53733i	0.816689	+	0.297250i	0.716384	−	0.697706i	$-0.245796\pi$
$233$	12.4662	+	4.53733i	0.816689	+	0.297250i	0.100305	+	0.994957i	$0.468018\pi$
$234$	8.81050	−	5.38424i	0.575961	−	0.351979i
$235$	−3.86696	+	1.40746i	−0.252253	+	0.0918125i
$236$	−0.122608	+	0.129957i	−0.00798110	+	0.00845948i
$237$	14.4980	−	5.97018i	0.941746	−	0.387805i
$238$	−2.12769	+	1.39940i	−0.137918	+	0.0907099i
$239$	−6.15279	+	20.5518i	−0.397991	+	1.32938i	0.490881	+	0.871227i	$0.336675\pi$
$239$	−6.15279	+	20.5518i	−0.397991	+	1.32938i	−0.888872	+	0.458156i	$0.848510\pi$
$240$	−0.630625	+	2.47673i	−0.0407067	+	0.159872i
$241$	11.8121	+	15.8665i	0.760887	+	1.02205i	0.998712	+	0.0507402i	$0.0161581\pi$
$241$	11.8121	+	15.8665i	0.760887	+	1.02205i	−0.237825	+	0.971308i	$0.576435\pi$
$242$	−10.9146			−0.701615
$243$	14.7765	−	4.96548i	0.947911	−	0.318536i
$244$	10.2332			0.655112
$245$	5.26428	+	7.07115i	0.336322	+	0.451759i
$246$	2.03849	−	8.00601i	0.129969	−	0.510444i
$247$	−3.92664	+	13.1159i	−0.249846	+	0.834543i
$248$	−1.13456	+	0.746211i	−0.0720445	+	0.0473844i
$249$	−19.9829	+	8.22884i	−1.26637	+	0.521481i
$250$	−7.92122	+	8.39601i	−0.500982	+	0.531010i
$251$	−0.508965	+	0.185248i	−0.0321256	+	0.0116928i	−0.358033	−	0.933709i	$-0.616552\pi$
$251$	−0.508965	+	0.185248i	−0.0321256	+	0.0116928i	0.325907	+	0.945402i	$0.394330\pi$
$252$	−0.0758077	−	3.03727i	−0.00477544	−	0.191330i
$253$	−1.41714	−	0.515797i	−0.0890948	−	0.0324279i
$254$	9.34889	−	4.69519i	0.586602	−	0.294602i
$255$	5.51156	+	3.30537i	0.345147	+	0.206990i
$256$	0.396080	+	0.918216i	0.0247550	+	0.0573885i
$257$	7.83901	+	0.916248i	0.488984	+	0.0571540i	0.357013	−	0.934100i	$-0.383795\pi$
$257$	7.83901	+	0.916248i	0.488984	+	0.0571540i	0.131971	+	0.991254i	$0.457869\pi$
$258$	−6.69984	−	19.4047i	−0.417114	−	1.20808i
$259$	5.04784	+	3.32002i	0.313658	+	0.206296i
$260$	−3.89045	+	3.26447i	−0.241275	+	0.202454i
$261$	27.6976	+	11.1364i	1.71444	+	0.689323i
$262$	−10.1717	−	8.53510i	−0.628412	−	0.527300i
$263$	2.50201	+	8.35730i	0.154281	+	0.515333i	0.999828	−	0.0185680i	$-0.00591070\pi$
$263$	2.50201	+	8.35730i	0.154281	+	0.515333i	−0.845547	+	0.533901i	$0.820726\pi$
$264$	0.271124	+	0.427528i	0.0166865	+	0.0263125i
$265$	3.47184	+	1.74363i	0.213274	+	0.107110i
$266$	2.76454	+	2.93025i	0.169505	+	0.179665i
$267$	−1.96162	−	19.6014i	−0.120049	−	1.19958i
$268$	−3.20024	+	7.41899i	−0.195486	+	0.453187i
$269$	−10.4195	+	18.0470i	−0.635286	+	1.10035i	0.351169	+	0.936312i	$0.385784\pi$
$269$	−10.4195	+	18.0470i	−0.635286	+	1.10035i	−0.986455	+	0.164035i	$0.947549\pi$
$270$	−6.82276	+	3.49809i	−0.415220	+	0.212887i
$271$	−5.05259	−	8.75134i	−0.306923	−	0.531606i	0.670765	−	0.741670i	$-0.265966\pi$
$271$	−5.05259	−	8.75134i	−0.306923	−	0.531606i	−0.977688	+	0.210064i	$0.932633\pi$
$272$	2.49761	−	0.291928i	0.151440	−	0.0177008i
$273$	3.40091	−	4.98833i	0.205832	−	0.301907i
$274$	17.5965	−	4.17045i	1.06304	−	0.251946i
$275$	0.0479713	+	0.823635i	0.00289278	+	0.0496671i
$276$	−1.91624	−	8.72898i	−0.115344	−	0.525423i
$277$	13.6284	+	3.23000i	0.818853	+	0.194072i	0.618634	−	0.785680i	$-0.287687\pi$
$277$	13.6284	+	3.23000i	0.818853	+	0.194072i	0.200219	+	0.979751i	$0.435835\pi$
$278$	3.58272	−	20.3186i	0.214878	−	1.21863i
$279$	−3.93067	−	1.07066i	−0.235323	−	0.0640987i
$280$	0.259493	+	1.47166i	0.0155077	+	0.0879484i
$281$	−1.20751	+	20.7322i	−0.0720343	+	1.23678i	0.747700	+	0.664037i	$0.231158\pi$
$281$	−1.20751	+	20.7322i	−0.0720343	+	1.23678i	−0.819734	+	0.572744i	$0.805879\pi$
$282$	−4.77033	+	0.759662i	−0.284069	+	0.0452372i
$283$	14.4041	−	19.3480i	0.856233	−	1.15012i	−0.131086	−	0.991371i	$-0.541846\pi$
$283$	14.4041	−	19.3480i	0.856233	−	1.15012i	0.987319	−	0.158750i	$-0.0507463\pi$
$284$	−8.41156	+	11.2987i	−0.499134	+	0.670453i
$285$	3.63533	−	9.49422i	0.215338	−	0.562389i
$286$	−0.0584928	+	1.00428i	−0.00345875	+	0.0593845i
$287$	−0.838810	−	4.75713i	−0.0495134	−	0.280804i
$288$	−1.27909	+	2.71366i	−0.0753709	+	0.159904i
$289$	−1.85400	+	10.5145i	−0.109059	+	0.618502i
$290$	−14.2873	−	3.38616i	−0.838980	−	0.198842i
$291$	−12.8105	+	11.6900i	−0.750966	+	0.685283i
$292$	−0.0699142	−	1.20038i	−0.00409142	−	0.0702469i
$293$	−0.633850	+	0.150225i	−0.0370299	+	0.00877625i	−0.249089	−	0.968481i	$-0.580131\pi$
$293$	−0.633850	+	0.150225i	−0.0370299	+	0.00877625i	0.212059	+	0.977257i	$0.431983\pi$
$294$	4.48988	+	9.32308i	0.261855	+	0.543733i
$295$	0.261850	−	0.0306059i	0.0152455	−	0.00178195i
$296$	−2.98289	−	5.16652i	−0.173377	−	0.300298i
$297$	−0.423429	+	1.45853i	−0.0245699	+	0.0846323i
$298$	−7.38470	+	12.7907i	−0.427784	+	0.740944i
$299$	7.03386	−	16.3063i	0.406779	−	0.943019i
$300$	−3.96960	+	2.85401i	−0.229185	+	0.164776i
$301$	−8.23715	−	8.73087i	−0.474782	−	0.503239i
$302$	0.0952090	+	0.0478158i	0.00547866	+	0.00275149i
$303$	10.6060	−	0.441103i	0.609301	−	0.0253407i
$304$	−1.14086	−	3.81074i	−0.0654329	−	0.218561i
$305$	−11.5670	−	9.70590i	−0.662327	−	0.555758i
$306$	5.61465	+	5.03837i	0.320968	+	0.288024i
$307$	−22.7388	+	19.0801i	−1.29777	+	1.08896i	−0.307245	+	0.951631i	$0.599407\pi$
$307$	−22.7388	+	19.0801i	−1.29777	+	1.08896i	−0.990526	+	0.137328i	$0.956149\pi$
$308$	0.247310	+	0.162658i	0.0140918	+	0.00926832i
$309$	4.36539	−	5.03035i	0.248339	−	0.286167i
$310$	1.99021	+	0.232622i	0.113036	+	0.0132120i
$311$	7.73217	+	17.9252i	0.438451	+	1.01644i	0.983968	+	0.178344i	$0.0570740\pi$
$311$	7.73217	+	17.9252i	0.438451	+	1.01644i	−0.545517	+	0.838100i	$0.683667\pi$
$312$	−5.21153	+	2.89453i	−0.295045	+	0.163871i
$313$	6.93327	−	3.48202i	0.391891	−	0.196815i	−0.241932	−	0.970293i	$-0.577781\pi$
$313$	6.93327	−	3.48202i	0.391891	−	0.196815i	0.633823	+	0.773478i	$0.281485\pi$
$314$	−21.7942	−	7.93242i	−1.22992	−	0.447653i
$315$	−2.79509	+	3.50507i	−0.157485	+	0.197489i
$316$	−8.50642	+	3.09609i	−0.478524	+	0.174168i
$317$	6.35622	−	6.73720i	0.357001	−	0.378399i	−0.523835	−	0.851819i	$-0.675499\pi$
$317$	6.35622	−	6.73720i	0.357001	−	0.378399i	0.880837	+	0.473420i	$0.156981\pi$
$318$	3.61227	+	2.78368i	0.202566	+	0.156101i
$319$	−2.42999	+	1.59823i	−0.136053	+	0.0894835i
$320$	0.423196	−	1.41357i	0.0236574	−	0.0790212i
$321$	−13.9363	−	13.5928i	−0.777849	−	0.758677i
$322$	−3.12040	−	4.19143i	−0.173893	−	0.233579i
$323$	−10.0028			−0.556568
$324$	−8.64296	+	2.50984i	−0.480164	+	0.139436i
$325$	−9.71526			−0.538906
$326$	7.38881	+	9.92490i	0.409229	+	0.549689i
$327$	−15.5353	+	4.37113i	−0.859105	+	0.241724i
$328$	−1.36798	+	4.56937i	−0.0755341	+	0.252301i
$329$	−2.35974	+	1.55202i	−0.130097	+	0.0855659i
$330$	0.0990344	−	0.740409i	0.00545166	−	0.0407582i
$331$	−14.0917	+	14.9364i	−0.774552	+	0.820978i	−0.987752	−	0.156031i	$-0.950130\pi$
$331$	−14.0917	+	14.9364i	−0.774552	+	0.820978i	0.213200	+	0.977009i	$0.431611\pi$
$332$	11.7246	−	4.26741i	0.643471	−	0.234204i
$333$	5.69972	−	16.9655i	0.312343	−	0.929704i
$334$	−8.85233	−	3.22198i	−0.484378	−	0.176299i
$335$	10.6541	−	5.35069i	0.582096	−	0.292340i
$336$	−0.0291378	+	1.75387i	−0.00158959	+	0.0956817i
$337$	−2.49237	−	5.77797i	−0.135768	−	0.314746i	0.836745	−	0.547592i	$-0.184455\pi$
$337$	−2.49237	−	5.77797i	−0.135768	−	0.314746i	−0.972514	+	0.232846i	$0.925196\pi$
$338$	1.14609	+	0.133959i	0.0623391	+	0.00728640i
$339$	−10.8031	−	2.09048i	−0.586744	−	0.113539i
$340$	−3.10005	−	2.03894i	−0.168124	−	0.110577i
$341$	0.304050	−	0.255128i	0.0164652	−	0.0138160i
$342$	6.30678	−	10.1309i	0.341032	−	0.547814i
$343$	10.0656	+	8.44600i	0.543489	+	0.456041i
$344$	3.39927	+	11.3544i	0.183277	+	0.612187i
$345$	−6.11319	+	11.6843i	−0.329123	+	0.629061i
$346$	8.30471	+	4.17078i	0.446464	+	0.224223i
$347$	−7.40994	−	7.85408i	−0.397786	−	0.421629i	0.497260	−	0.867601i	$-0.334339\pi$
$347$	−7.40994	−	7.85408i	−0.397786	−	0.421629i	−0.895047	+	0.445972i	$0.852858\pi$
$348$	−15.7102	−	7.08852i	−0.842156	−	0.379985i
$349$	−3.58166	+	8.30322i	−0.191722	+	0.444461i	−0.986779	−	0.162074i	$-0.948182\pi$
$349$	−3.58166	+	8.30322i	−0.191722	+	0.444461i	0.795057	+	0.606535i	$0.207441\pi$
$350$	−1.42934	+	2.47568i	−0.0764012	+	0.132331i
$351$	−16.8561	−	5.97635i	−0.899712	−	0.318994i
$352$	−0.146142	−	0.253125i	−0.00778937	−	0.0134916i
$353$	10.3434	−	1.20897i	0.550523	−	0.0643469i	0.163716	−	0.986508i	$-0.447652\pi$
$353$	10.3434	−	1.20897i	0.550523	−	0.0643469i	0.386807	+	0.922161i	$0.373578\pi$
$354$	0.308593	+	0.0231227i	0.0164016	+	0.00122896i
$355$	20.2245	−	4.79329i	1.07340	−	0.254402i
$356$	0.661304	+	11.3541i	0.0350490	+	0.601769i
$357$	4.20402	+	1.33508i	0.222500	+	0.0706601i
$358$	−9.21336	−	2.18361i	−0.486941	−	0.115407i
$359$	−2.29332	+	13.0061i	−0.121037	+	0.686435i	0.862546	+	0.505979i	$0.168869\pi$
$359$	−2.29332	+	13.0061i	−0.121037	+	0.686435i	−0.983583	+	0.180456i	$0.942243\pi$
$360$	4.01965	−	1.85420i	0.211854	−	0.0977247i
$361$	−0.551625	−	3.12842i	−0.0290329	−	0.164654i
$362$	1.20239	−	20.6443i	0.0631965	−	1.08504i
$363$	11.9094	+	14.6816i	0.625082	+	0.770585i
$364$	−2.08149	+	2.79593i	−0.109100	+	0.146547i
$365$	−1.05950	+	1.42316i	−0.0554569	+	0.0744915i
$366$	−11.1659	−	13.7650i	−0.583651	−	0.719510i
$367$	−0.773313	+	13.2773i	−0.0403666	+	0.693068i	0.916050	+	0.401063i	$0.131359\pi$
$367$	−0.773313	+	13.2773i	−0.0403666	+	0.693068i	−0.956417	+	0.292005i	$0.905678\pi$
$368$	0.895970	+	5.08130i	0.0467057	+	0.264881i
$369$	−12.9935	+	5.99368i	−0.676414	+	0.312018i
$370$	−1.52861	+	8.66916i	−0.0794685	+	0.450688i
$371$	2.59462	+	0.614937i	0.134706	+	0.0319259i
$372$	2.24173	+	0.711913i	0.116228	+	0.0369110i
$373$	−1.04263	−	17.9013i	−0.0539855	−	0.926896i	−0.911207	−	0.411948i	$-0.864848\pi$
$373$	−1.04263	−	17.9013i	−0.0539855	−	0.926896i	0.857222	−	0.514948i	$-0.172189\pi$
$374$	−0.715167	+	0.169498i	−0.0369804	+	0.00876451i
$375$	19.9370	+	1.49387i	1.02954	+	0.0771429i
$376$	2.77000	−	0.323766i	0.142852	−	0.0166970i
$377$	−17.1245	−	29.6605i	−0.881956	−	1.52759i
$378$	−4.00284	+	3.41608i	−0.205884	+	0.175704i
$379$	8.70708	−	15.0811i	0.447253	−	0.774665i	−0.550953	−	0.834536i	$-0.685736\pi$
$379$	8.70708	−	15.0811i	0.447253	−	0.774665i	0.998206	+	0.0598715i	$0.0190691\pi$
$380$	−2.32482	+	5.38954i	−0.119261	+	0.276478i
$381$	−16.5167	−	7.45241i	−0.846176	−	0.381799i
$382$	−17.0935	−	18.1180i	−0.874579	−	0.927000i
$383$	−6.49080	−	3.25980i	−0.331664	−	0.166568i	0.275172	−	0.961395i	$-0.411265\pi$
$383$	−6.49080	−	3.25980i	−0.331664	−	0.166568i	−0.606836	+	0.794827i	$0.707562\pi$
$384$	0.802947	−	1.53469i	0.0409752	−	0.0783169i
$385$	−0.125269	−	0.418427i	−0.00638430	−	0.0213250i
$386$	14.8850	+	12.4900i	0.757626	+	0.635724i
$387$	−18.7915	+	30.1856i	−0.955225	+	1.53442i
$388$	7.67022	−	6.43608i	0.389397	−	0.326743i
$389$	24.6039	+	16.1822i	1.24747	+	0.820473i	0.989338	−	0.145638i	$-0.0465234\pi$
$389$	24.6039	+	16.1822i	1.24747	+	0.820473i	0.258130	+	0.966110i	$0.416894\pi$
$390$	8.63622	+	1.67117i	0.437312	+	0.0846231i
$391$	12.8869	+	1.50626i	0.651717	+	0.0761748i
$392$	−2.36632	−	5.48575i	−0.119517	−	0.277072i
$393$	−0.382032	+	22.9954i	−0.0192709	+	1.15997i
$394$	4.21986	−	2.11929i	0.212594	−	0.106769i
$395$	12.5518	+	4.56847i	0.631548	+	0.229865i
$396$	0.279248	−	0.831195i	0.0140327	−	0.0417691i
$397$	−15.0174	+	5.46590i	−0.753704	+	0.274326i	−0.690164	−	0.723653i	$-0.742461\pi$
$397$	−15.0174	+	5.46590i	−0.753704	+	0.274326i	−0.0635405	+	0.997979i	$0.520239\pi$
$398$	−7.97491	+	8.45291i	−0.399746	+	0.423706i
$399$	0.925062	−	6.91603i	0.0463110	−	0.346234i
$400$	2.35834	−	1.55111i	0.117917	−	0.0775553i
$401$	9.90488	−	33.0846i	0.494626	−	1.65217i	−0.237796	−	0.971315i	$-0.576425\pi$
$401$	9.90488	−	33.0846i	0.494626	−	1.65217i	0.732422	−	0.680851i	$-0.238390\pi$
$402$	13.4715	−	3.79045i	0.671898	−	0.189050i
$403$	2.79103	+	3.74900i	0.139031	+	0.186751i
$404$	−6.12869			−0.304914
$405$	12.1501	+	5.36063i	0.603741	+	0.266372i
$406$	−10.0776			−0.500144
$407$	1.04126	+	1.39866i	0.0516136	+	0.0693291i
$408$	−3.11794	−	3.04109i	−0.154361	−	0.150556i
$409$	−7.51744	+	25.1100i	−0.371713	+	1.24161i	0.543764	+	0.839238i	$0.316999\pi$
$409$	−7.51744	+	25.1100i	−0.371713	+	1.24161i	−0.915477	+	0.402370i	$0.868186\pi$
$410$	5.88022	−	3.86748i	0.290404	−	0.191001i
$411$	−24.8102	−	19.1192i	−1.22380	−	0.943079i
$412$	−2.63887	+	2.79704i	−0.130008	+	0.137800i
$413$	0.170030	−	0.0618858i	0.00836663	−	0.00304520i
$414$	−9.65078	+	12.1022i	−0.474310	+	0.594791i
$415$	−17.3004	−	6.29683i	−0.849243	−	0.309099i
$416$	3.07572	−	1.54468i	0.150800	−	0.0757344i
$417$	−31.2407	+	17.3514i	−1.52986	+	0.849700i
$418$	0.460506	+	1.06757i	0.0225241	+	0.0522167i
$419$	24.6224	+	2.87794i	1.20288	+	0.140597i	0.693830	−	0.720139i	$-0.255922\pi$
$419$	24.6224	+	2.87794i	1.20288	+	0.140597i	0.509052	+	0.860736i	$0.329996\pi$
$420$	1.69644	−	1.95485i	0.0827778	−	0.0953869i
$421$	−5.86400	−	3.85682i	−0.285794	−	0.187970i	0.398515	−	0.917162i	$-0.369526\pi$
$421$	−5.86400	−	3.85682i	−0.285794	−	0.187970i	−0.684309	+	0.729192i	$0.739896\pi$
$422$	14.1846	−	11.9023i	0.690494	−	0.579394i
$423$	6.22698	+	5.58785i	0.302766	+	0.271691i
$424$	−2.01696	−	1.69243i	−0.0979522	−	0.0821917i
$425$	−2.03574	−	6.79983i	−0.0987477	−	0.329840i
$426$	24.3765	−	1.01381i	1.18105	−	0.0491195i
$427$	−9.26120	−	4.65115i	−0.448181	−	0.225085i
$428$	7.71308	+	8.17539i	0.372826	+	0.395172i
$429$	1.41472	−	1.01714i	0.0683035	−	0.0491080i
$430$	6.92696	−	16.0585i	0.334048	−	0.774410i
$431$	3.67191	−	6.35994i	0.176870	−	0.306347i	−0.763937	−	0.645291i	$-0.776736\pi$
$431$	3.67191	−	6.35994i	0.176870	−	0.306347i	0.940807	+	0.338943i	$0.110070\pi$
$432$	5.04592	−	1.24045i	0.242772	−	0.0596813i
$433$	5.89605	+	10.2123i	0.283346	+	0.490770i	0.972207	−	0.234124i	$-0.0752221\pi$
$433$	5.89605	+	10.2123i	0.283346	+	0.490770i	−0.688860	+	0.724894i	$0.741889\pi$
$434$	1.36596	−	0.159658i	0.0655682	−	0.00766382i
$435$	11.0347	+	22.9132i	0.529074	+	1.09860i
$436$	9.06644	−	2.14879i	0.434204	−	0.102908i
$437$	−1.19339	−	20.4897i	−0.0570877	−	0.980157i
$438$	−1.53839	+	1.40384i	−0.0735072	+	0.0670778i
$439$	−11.0238	−	2.61268i	−0.526136	−	0.124696i	−0.0410400	−	0.999158i	$-0.513067\pi$
$439$	−11.0238	−	2.61268i	−0.526136	−	0.124696i	−0.485096	+	0.874461i	$0.661215\pi$
$440$	−0.0748914	+	0.424730i	−0.00357031	+	0.0202482i
$441$	7.64172	−	16.2124i	0.363891	−	0.772017i
$442$	−1.50290	−	8.52334i	−0.0714855	−	0.405414i
$443$	0.214947	−	3.69050i	0.0102124	−	0.175341i	−0.989345	−	0.145591i	$-0.953492\pi$
$443$	0.214947	−	3.69050i	0.0102124	−	0.175341i	0.999557	−	0.0297502i	$-0.00947118\pi$
$444$	−3.69491	+	9.64984i	−0.175353	+	0.457961i
$445$	10.0216	−	13.4614i	0.475070	−	0.638130i
$446$	1.24114	−	1.66714i	0.0587696	−	0.0789413i
$447$	25.2630	−	4.02306i	1.19490	−	0.190284i
$448$	0.0588856	−	1.01103i	0.00278208	−	0.0477665i
$449$	−2.13648	−	12.1166i	−0.100827	−	0.571817i	−0.992805	−	0.119739i	$-0.961794\pi$
$449$	−2.13648	−	12.1166i	−0.100827	−	0.571817i	0.891979	−	0.452078i	$-0.149317\pi$
$450$	8.17046	+	2.22552i	0.385159	+	0.104912i
$451$	0.242086	−	1.37294i	0.0113994	−	0.0646491i
$452$	6.18163	+	1.46507i	0.290759	+	0.0689112i
$453$	−0.0395682	−	0.180243i	−0.00185908	−	0.00846857i
$454$	−0.541688	−	9.30042i	−0.0254227	−	0.436491i
$455$	5.00468	−	1.18613i	0.234623	−	0.0556067i
$456$	−3.88113	+	5.69270i	−0.181751	+	0.266585i
$457$	3.08603	−	0.360705i	0.144358	−	0.0168731i	−0.0436068	−	0.999049i	$-0.513885\pi$
$457$	3.08603	−	0.360705i	0.144358	−	0.0168731i	0.187965	+	0.982176i	$0.439811\pi$
$458$	12.2379	+	21.1967i	0.571841	+	0.990457i
$459$	0.650896	−	13.0501i	0.0303812	−	0.609125i
$460$	3.80672	−	6.59343i	0.177489	−	0.307420i
$461$	−4.34834	+	10.0806i	−0.202522	+	0.469499i	−0.988962	−	0.148167i	$-0.952663\pi$
$461$	−4.34834	+	10.0806i	−0.202522	+	0.469499i	0.786440	+	0.617667i	$0.211922\pi$
$462$	−0.0510536	−	0.510150i	−0.00237523	−	0.0237343i
$463$	−15.2156	−	16.1276i	−0.707128	−	0.749512i	0.269838	−	0.962906i	$-0.413030\pi$
$463$	−15.2156	−	16.1276i	−0.707128	−	0.749512i	−0.976966	+	0.213394i	$0.931548\pi$
$464$	8.89240	+	4.46593i	0.412819	+	0.207326i
$465$	−1.85870	−	2.93093i	−0.0861951	−	0.135919i
$466$	3.80481	+	12.7089i	0.176254	+	0.588730i
$467$	−11.3543	−	9.52736i	−0.525413	−	0.440873i	0.341101	−	0.940027i	$-0.389200\pi$
$467$	−11.3543	−	9.52736i	−0.525413	−	0.440873i	−0.866514	+	0.499153i	$0.833645\pi$
$468$	9.58009	+	3.85187i	0.442840	+	0.178053i
$469$	6.26833	−	5.25975i	0.289445	−	0.242873i
$470$	−3.43814	−	2.26130i	−0.158590	−	0.104306i
$471$	13.1104	+	37.9716i	0.604096	+	1.74964i
$472$	−0.177458	−	0.0207419i	−0.00816816	−	0.000954721i
$473$	−1.37211	−	3.18091i	−0.0630896	−	0.146258i
$474$	13.4464	+	8.06404i	0.617615	+	0.370393i
$475$	−10.0340	+	5.03927i	−0.460392	+	0.231217i
$476$	−2.39306	−	0.871004i	−0.109686	−	0.0399224i
$477$	−0.197088	−	7.89640i	−0.00902402	−	0.361552i
$478$	−20.1592	+	7.33736i	−0.922062	+	0.335603i
$479$	0.0945719	−	0.100240i	0.00432110	−	0.00458010i	−0.725209	−	0.688528i	$-0.758257\pi$
$479$	0.0945719	−	0.100240i	0.00432110	−	0.00458010i	0.729531	+	0.683948i	$0.239739\pi$
$480$	−2.36322	+	0.973160i	−0.107866	+	0.0444185i
$481$	−17.1552	+	11.2831i	−0.782210	+	0.514467i
$482$	−5.67313	+	18.9496i	−0.258404	+	0.863130i
$483$	−2.23323	+	8.77084i	−0.101616	+	0.399087i
$484$	−6.51773	−	8.75483i	−0.296260	−	0.397947i
$485$	−14.7745			−0.670874
$486$	12.8068	+	8.88737i	0.580929	+	0.403139i
$487$	16.2267			0.735304			0.367652	−	0.929964i	$-0.380162\pi$
$487$	16.2267			0.735304			0.367652	+	0.929964i	$0.380162\pi$
$488$	6.11083	+	8.20827i	0.276624	+	0.371571i
$489$	5.28808	−	20.7685i	0.239135	−	0.939184i
$490$	−2.52833	+	8.44520i	−0.114218	+	0.381515i
$491$	13.8751	−	9.12579i	0.626174	−	0.411841i	−0.196380	−	0.980528i	$-0.562919\pi$
$491$	13.8751	−	9.12579i	0.626174	−	0.411841i	0.822554	+	0.568687i	$0.192548\pi$
$492$	7.63911	−	3.14573i	0.344398	−	0.141821i
$493$	17.1715	−	18.2007i	0.773365	−	0.819719i
$494$	−12.8654	+	4.68261i	−0.578841	+	0.210681i
$495$	−1.10401	+	0.674680i	−0.0496217	+	0.0303246i
$496$	−1.27606	−	0.464449i	−0.0572970	−	0.0208544i
$497$	12.7480	−	6.40231i	0.571828	−	0.287183i
$498$	−18.5335	−	11.1148i	−0.830507	−	0.498068i
$499$	−4.81631	−	11.1655i	−0.215608	−	0.499835i	0.775747	−	0.631044i	$-0.217373\pi$
$499$	−4.81631	−	11.1655i	−0.215608	−	0.499835i	−0.991355	+	0.131209i	$0.958114\pi$
$500$	−11.4649	−	1.34005i	−0.512724	−	0.0599289i
$501$	5.32518	+	15.4233i	0.237911	+	0.689061i
$502$	−0.452525	−	0.297630i	−0.0201972	−	0.0132839i
$503$	23.2557	−	19.5138i	1.03692	−	0.870079i	0.0452612	−	0.998975i	$-0.485588\pi$
$503$	23.2557	−	19.5138i	1.03692	−	0.870079i	0.991658	+	0.128897i	$0.0411435\pi$
$504$	2.39100	−	1.87454i	0.106504	−	0.0834987i
$505$	6.92755	+	5.81291i	0.308272	+	0.258671i
$506$	−0.432525	−	1.44473i	−0.0192281	−	0.0642262i
$507$	−1.07036	−	1.68782i	−0.0475364	−	0.0749587i
$508$	9.34889	+	4.69519i	0.414790	+	0.208315i
$509$	−1.02916	−	1.09085i	−0.0456167	−	0.0483509i	0.704163	−	0.710038i	$-0.251322\pi$
$509$	−1.02916	−	1.09085i	−0.0456167	−	0.0483509i	−0.749780	+	0.661687i	$0.769841\pi$
$510$	0.639961	+	6.39478i	0.0283379	+	0.283165i
$511$	−0.482319	+	1.11814i	−0.0213365	+	0.0494637i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−20.5090	+	2.57076i	−0.905496	+	0.113502i
$514$	3.94619	+	6.83499i	0.174059	+	0.301479i
$515$	5.63575	−	0.658725i	0.248341	−	0.0290269i
$516$	11.5641	−	16.9618i	0.509081	−	0.746701i
$517$	−0.793163	+	0.187983i	−0.0348833	+	0.00826749i
$518$	0.351299	+	6.03157i	0.0154352	+	0.265012i
$519$	−3.45138	−	15.7219i	−0.151499	−	0.690116i
$520$	−4.94173	−	1.17121i	−0.216709	−	0.0513610i
$521$	−7.06081	+	40.0438i	−0.309340	+	1.75435i	0.293000	+	0.956113i	$0.405347\pi$
$521$	−7.06081	+	40.0438i	−0.309340	+	1.75435i	−0.602339	+	0.798240i	$0.705765\pi$
$522$	7.60711	+	28.8670i	0.332954	+	1.26348i
$523$	0.0742445	+	0.421062i	0.00324649	+	0.0184117i	0.986388	−	0.164435i	$-0.0525800\pi$
$523$	0.0742445	+	0.421062i	0.00324649	+	0.0184117i	−0.983141	+	0.182846i	$0.941469\pi$
$524$	0.772062	−	13.2558i	0.0337277	−	0.579082i
$525$	4.88975	−	0.778679i	0.213406	−	0.0339843i
$526$	−5.20948	+	6.99755i	−0.227144	+	0.305108i
$527$	−2.03914	+	2.73904i	−0.0888264	+	0.119315i
$528$	−0.181026	+	0.472777i	−0.00787813	+	0.0205750i
$529$	−0.210621	+	3.61622i	−0.00915742	+	0.157227i
$530$	0.674639	+	3.82607i	0.0293045	+	0.166194i
$531$	−0.305618	−	0.440331i	−0.0132627	−	0.0191087i
$532$	−0.699547	+	3.96733i	−0.0303292	+	0.172005i
$533$	15.9741	+	3.78593i	0.691915	+	0.163987i
$534$	14.5513	−	13.2786i	0.629697	−	0.574621i
$535$	−0.964317	−	16.5567i	−0.0416910	−	0.715808i
$536$	−7.86200	+	1.86333i	−0.339587	+	0.0804835i
$537$	7.11588	+	14.7759i	0.307073	+	0.637626i
$538$	−20.6980	+	2.41925i	−0.892355	+	0.104301i
$539$	0.873102	+	1.51226i	0.0376072	+	0.0651375i
$540$	−6.88017	−	3.38378i	−0.296076	−	0.145615i
$541$	14.2644	−	24.7067i	0.613275	−	1.06222i	−0.377410	−	0.926046i	$-0.623185\pi$
$541$	14.2644	−	24.7067i	0.613275	−	1.06222i	0.990685	−	0.136177i	$-0.0434814\pi$
$542$	4.00246	−	9.27874i	0.171920	−	0.398556i
$543$	−29.0815	+	20.9086i	−1.24801	+	0.897274i
$544$	1.72563	+	1.82906i	0.0739858	+	0.0784204i
$545$	−12.2863	−	6.17041i	−0.526287	−	0.264311i
$546$	6.03213	−	0.250875i	0.258151	−	0.0107365i
$547$	−4.21852	−	14.0909i	−0.180371	−	0.602481i	−0.999580	−	0.0289859i	$-0.990772\pi$
$547$	−4.21852	−	14.0909i	−0.180371	−	0.602481i	0.819209	−	0.573495i	$-0.194413\pi$
$548$	13.8531	+	11.6241i	0.591776	+	0.496559i
$549$	−6.33225	+	30.0394i	−0.270254	+	1.28205i
$550$	−0.632010	+	0.530320i	−0.0269490	+	0.0226129i
$551$	−33.0711	−	21.7512i	−1.40888	−	0.926633i
$552$	5.85741	−	6.74965i	0.249308	−	0.287284i
$553$	9.10568	+	1.06430i	0.387213	+	0.0452587i
$554$	5.54748	+	12.8605i	0.235690	+	0.546390i
$555$	13.3292	−	7.40314i	0.565791	−	0.314246i
$556$	18.4375	−	9.25966i	0.781924	−	0.392697i
$557$	−33.4429	−	12.1722i	−1.41702	−	0.515753i	−0.483838	−	0.875157i	$-0.660758\pi$
$557$	−33.4429	−	12.1722i	−1.41702	−	0.515753i	−0.933182	+	0.359404i	$0.882980\pi$
$558$	−1.48843	−	3.79224i	−0.0630104	−	0.160538i
$559$	38.3333	−	13.9522i	1.62132	−	0.590114i
$560$	−1.02549	+	1.08696i	−0.0433350	+	0.0459324i
$561$	1.00835	+	0.777052i	0.0425726	+	0.0328071i
$562$	−17.3509	+	11.4118i	−0.731902	+	0.481380i
$563$	2.19211	−	7.32215i	0.0923864	−	0.308592i	−0.899289	−	0.437355i	$-0.855915\pi$
$563$	2.19211	−	7.32215i	0.0923864	−	0.308592i	0.991675	+	0.128763i	$0.0411006\pi$
$564$	−3.45799	−	3.37276i	−0.145608	−	0.142019i
$565$	−5.59780	−	7.51916i	−0.235501	−	0.316333i
$566$	24.1210			1.01388
$567$	8.96279	+	1.65692i	0.376402	+	0.0695841i
$568$	−14.0860			−0.591034
$569$	3.14062	+	4.21859i	0.131662	+	0.176852i	0.863065	−	0.505093i	$-0.168542\pi$
$569$	3.14062	+	4.21859i	0.131662	+	0.176852i	−0.731403	+	0.681945i	$0.761134\pi$
$570$	9.78640	−	2.75357i	0.409907	−	0.115335i
$571$	−10.8128	+	36.1171i	−0.452500	+	1.51145i	0.362495	+	0.931986i	$0.381925\pi$
$571$	−10.8128	+	36.1171i	−0.452500	+	1.51145i	−0.814994	+	0.579469i	$0.803260\pi$
$572$	−0.840488	+	0.552798i	−0.0351426	+	0.0231136i
$573$	−5.71976	+	42.7626i	−0.238947	+	1.78643i
$574$	3.31490	−	3.51359i	0.138361	−	0.146654i
$575$	13.6860	−	4.98129i	0.570744	−	0.207734i
$576$	−2.94051	+	0.594499i	−0.122521	+	0.0247708i
$577$	−18.5516	−	6.75224i	−0.772314	−	0.281099i	−0.0743500	−	0.997232i	$-0.523688\pi$
$577$	−18.5516	−	6.75224i	−0.772314	−	0.281099i	−0.697964	+	0.716133i	$0.745910\pi$
$578$	−9.54108	+	4.79171i	−0.396856	+	0.199309i
$579$	0.559053	−	33.6508i	0.0232334	−	1.39848i
$580$	−5.81568	−	13.4823i	−0.241483	−	0.559821i
$581$	−12.5506	−	1.46695i	−0.520685	−	0.0608594i
$582$	−17.0268	−	3.29480i	−0.705782	−	0.136574i
$583$	0.642965	+	0.422885i	0.0266289	+	0.0175141i
$584$	0.921103	−	0.772897i	0.0381155	−	0.0319827i
$585$	−7.17543	−	13.4404i	−0.296668	−	0.555693i
$586$	−0.499008	−	0.418717i	−0.0206138	−	0.0172971i
$587$	1.45939	+	4.87471i	0.0602356	+	0.201201i	0.982811	−	0.184617i	$-0.0591045\pi$
$587$	1.45939	+	4.87471i	0.0602356	+	0.201201i	−0.922575	+	0.385818i	$0.873919\pi$
$588$	−4.79709	+	9.16879i	−0.197829	+	0.378115i
$589$	4.82719	+	2.42431i	0.198901	+	0.0998918i
$590$	0.180916	+	0.191760i	0.00744819	+	0.00789462i
$591$	−7.45524	−	3.36384i	−0.306667	−	0.138370i
$592$	2.36293	−	5.47788i	0.0971157	−	0.225140i
$593$	−5.37983	+	9.31815i	−0.220923	+	0.382650i	−0.955089	−	0.296320i	$-0.904240\pi$
$593$	−5.37983	+	9.31815i	−0.220923	+	0.382650i	0.734165	+	0.678971i	$0.237574\pi$
$594$	−1.42277	+	0.531330i	−0.0583771	+	0.0218007i
$595$	1.87887	+	3.25430i	0.0770261	+	0.133413i
$596$	−14.6695	+	1.71462i	−0.600887	+	0.0702337i
$597$	20.0721	+	1.50399i	0.821497	+	0.0615542i
$598$	17.2800	−	4.09544i	0.706632	−	0.167475i
$599$	1.42782	+	24.5147i	0.0583390	+	1.00164i	0.892765	+	0.450522i	$0.148762\pi$
$599$	1.42782	+	24.5147i	0.0583390	+	1.00164i	−0.834426	+	0.551120i	$0.814201\pi$
$600$	−4.65975	−	1.47981i	−0.190233	−	0.0604131i
$601$	24.8634	+	5.89272i	1.01420	+	0.240369i	0.703922	−	0.710277i	$-0.251431\pi$
$601$	24.8634	+	5.89272i	1.01420	+	0.240369i	0.310276	+	0.950647i	$0.399579\pi$
$602$	2.08435	−	11.8209i	0.0849517	−	0.481785i
$603$	−19.7981	−	13.9851i	−0.806240	−	0.569518i
$604$	0.0185007	+	0.104923i	0.000752785	+	0.00426925i
$605$	−0.936431	+	16.0779i	−0.0380713	+	0.653659i
$606$	6.68731	+	8.24394i	0.271653	+	0.334887i
$607$	−20.3020	+	27.2703i	−0.824033	+	1.10687i	0.168597	+	0.985685i	$0.446076\pi$
$607$	−20.3020	+	27.2703i	−0.824033	+	1.10687i	−0.992630	+	0.121183i	$0.961331\pi$
$608$	2.37541	−	3.19073i	0.0963356	−	0.129401i
$609$	10.9962	+	13.5558i	0.445587	+	0.549308i
$610$	0.877970	−	15.0742i	0.0355480	−	0.610335i
$611$	−1.66680	−	9.45291i	−0.0674316	−	0.382424i
$612$	−0.688557	+	7.51234i	−0.0278332	+	0.303668i
$613$	−1.14418	+	6.48896i	−0.0462129	+	0.262086i	−0.999157	−	0.0410607i	$-0.986926\pi$
$613$	−1.14418	+	6.48896i	−0.0462129	+	0.262086i	0.952944	+	0.303147i	$0.0980374\pi$
$614$	−28.8832	−	6.84545i	−1.16563	−	0.276260i
$615$	−11.6185	−	3.68972i	−0.468503	−	0.148784i
$616$	0.0172113	+	0.295506i	0.000693461	+	0.0119063i
$617$	34.6803	−	8.21937i	1.39618	−	0.330900i	0.537432	−	0.843307i	$-0.319394\pi$
$617$	34.6803	−	8.21937i	1.39618	−	0.330900i	0.858743	+	0.512407i	$0.171246\pi$
$618$	6.64180	+	0.497665i	0.267172	+	0.0200190i
$619$	3.37117	−	0.394034i	0.135499	−	0.0158376i	−0.0480731	−	0.998844i	$-0.515308\pi$
$619$	3.37117	−	0.394034i	0.135499	−	0.0158376i	0.183572	+	0.983006i	$0.441234\pi$
$620$	1.00188	+	1.73530i	0.0402364	+	0.0696915i
$621$	26.8096	−	0.223654i	1.07583	−	0.00897493i
$622$	−9.76087	+	16.9063i	−0.391375	+	0.677882i
$623$	4.56216	−	10.5763i	0.182779	−	0.423729i
$624$	−5.43388	−	2.45179i	−0.217529	−	0.0981502i
$625$	2.00296	+	2.12301i	0.0801184	+	0.0849205i
$626$	6.93327	+	3.48202i	0.277109	+	0.139169i
$627$	0.933553	−	1.78432i	0.0372825	−	0.0712590i
$628$	−6.65179	−	22.2185i	−0.265435	−	0.886615i
$629$	−11.4919	−	9.64286i	−0.458213	−	0.384486i
$630$	−4.48061	−	0.148917i	−0.178512	−	0.00593300i
$631$	30.5244	−	25.6130i	1.21516	−	1.01964i	0.216092	−	0.976373i	$-0.430669\pi$
$631$	30.5244	−	25.6130i	1.21516	−	1.01964i	0.999064	−	0.0432637i	$-0.0137756\pi$
$632$	−7.56313	−	4.97435i	−0.300845	−	0.197869i
$633$	−31.4877	−	6.09309i	−1.25152	−	0.242179i
$634$	9.19974	+	1.07530i	0.365368	+	0.0427054i
$635$	−6.11423	−	14.1744i	−0.242636	−	0.562493i
$636$	−0.0757533	+	4.55978i	−0.00300381	+	0.180807i
$637$	−18.3755	+	9.22850i	−0.728062	+	0.365647i
$638$	−2.73306	−	0.994753i	−0.108203	−	0.0393827i
$639$	−27.9621	−	31.6836i	−1.10616	−	1.25338i
$640$	1.38658	−	0.504672i	0.0548092	−	0.0199489i
$641$	−2.73470	+	2.89862i	−0.108014	+	0.114488i	−0.779125	−	0.626869i	$-0.784336\pi$
$641$	−2.73470	+	2.89862i	−0.108014	+	0.114488i	0.671110	+	0.741357i	$0.265818\pi$
$642$	2.58092	−	19.2957i	0.101861	−	0.761541i
$643$	−2.33370	+	1.53490i	−0.0920322	+	0.0605305i	−0.594691	−	0.803954i	$-0.702726\pi$
$643$	−2.33370	+	1.53490i	−0.0920322	+	0.0605305i	0.502659	+	0.864485i	$0.332355\pi$
$644$	1.49867	−	5.00589i	0.0590557	−	0.197260i
$645$	−29.1592	+	8.20447i	−1.14814	+	0.323051i
$646$	−5.97323	−	8.02344i	−0.235014	−	0.315678i
$647$	33.0307			1.29857			0.649286	−	0.760544i	$-0.275068\pi$
$647$	33.0307			1.29857			0.649286	+	0.760544i	$0.275068\pi$
$648$	−7.17442	−	5.43394i	−0.281838	−	0.213465i
$649$	0.0522210			0.00204986
$650$	−5.80155	−	7.79283i	−0.227556	−	0.305660i
$651$	−1.70523	−	1.66320i	−0.0668331	−	0.0651858i
$652$	−3.54870	+	11.8535i	−0.138978	+	0.464218i
$653$	−32.8991	+	21.6381i	−1.28744	+	0.846763i	−0.994018	−	0.109220i	$-0.965165\pi$
$653$	−32.8991	+	21.6381i	−1.28744	+	0.846763i	−0.293423	+	0.955983i	$0.594794\pi$
$654$	−12.7832	−	9.85097i	−0.499864	−	0.385204i
$655$	−13.4455	+	14.2514i	−0.525358	+	0.556847i
$656$	−4.48210	+	1.63135i	−0.174997	+	0.0636936i
$657$	3.56696	+	0.537558i	0.139161	+	0.0209721i
$658$	−2.65405	−	0.965996i	−0.103466	−	0.0376585i
$659$	−7.78382	+	3.90918i	−0.303215	+	0.152280i	−0.593901	−	0.804538i	$-0.702413\pi$
$659$	−7.78382	+	3.90918i	−0.303215	+	0.152280i	0.290686	+	0.956818i	$0.406116\pi$
$660$	0.653038	−	0.362704i	0.0254195	−	0.0141182i
$661$	−9.21346	−	21.3592i	−0.358362	−	0.830777i	−0.998066	−	0.0621557i	$-0.980202\pi$
$661$	−9.21346	−	21.3592i	−0.358362	−	0.830777i	0.639704	−	0.768621i	$-0.279057\pi$
$662$	−20.3958	−	2.38393i	−0.792706	−	0.0926541i
$663$	−9.82520	+	11.3218i	−0.381579	+	0.439703i
$664$	10.4244	+	6.85626i	0.404546	+	0.266074i
$665$	4.55364	−	3.82096i	0.176583	−	0.148170i
$666$	17.0121	−	5.55923i	0.659204	−	0.215416i
$667$	39.3312	+	33.0028i	1.52291	+	1.27787i
$668$	−2.70182	−	9.02469i	−0.104536	−	0.349176i
$669$	−3.59680	+	0.149590i	−0.139060	+	0.00578348i
$670$	10.6541	+	5.35069i	0.411604	+	0.206715i
$671$	−2.05254	−	2.17556i	−0.0792373	−	0.0839867i
$672$	−1.42422	+	1.02397i	−0.0549406	+	0.0395005i
$673$	0.0541399	−	0.125510i	0.00208694	−	0.00483807i	−0.917169	−	0.398497i	$-0.869532\pi$
$673$	0.0541399	−	0.125510i	0.00208694	−	0.00483807i	0.919256	+	0.393659i	$0.128791\pi$
$674$	3.14630	−	5.44955i	0.121191	−	0.209909i
$675$	−5.92154	−	13.4188i	−0.227920	−	0.516489i
$676$	0.576946	+	0.999300i	0.0221902	+	0.0384346i
$677$	−36.1462	+	4.22489i	−1.38921	+	0.162376i	−0.777589	−	0.628773i	$-0.783557\pi$
$677$	−36.1462	+	4.22489i	−1.38921	+	0.162376i	−0.611624	+	0.791149i	$0.709483\pi$
$678$	−4.77434	−	9.91376i	−0.183357	−	0.380736i
$679$	−9.86699	+	2.33852i	−0.378660	+	0.0897442i
$680$	−0.215745	−	3.70419i	−0.00827343	−	0.142049i
$681$	−11.9193	+	10.8768i	−0.456748	+	0.416799i
$682$	0.386210	+	0.0915334i	0.0147887	+	0.00350500i
$683$	−8.32718	+	47.2258i	−0.318631	+	1.80704i	0.232468	+	0.972604i	$0.425320\pi$
$683$	−8.32718	+	47.2258i	−0.318631	+	1.80704i	−0.551099	+	0.834440i	$0.685791\pi$
$684$	11.8923	−	0.990914i	0.454715	−	0.0378885i
$685$	−4.63363	−	26.2786i	−0.177042	−	1.00406i
$686$	−0.764002	+	13.1174i	−0.0291698	+	0.500825i
$687$	15.1591	−	39.5904i	0.578357	−	1.51047i
$688$	−7.07770	+	9.50700i	−0.269835	+	0.362451i
$689$	−5.41154	+	7.26896i	−0.206163	+	0.276925i
$690$	−13.0228	+	2.07384i	−0.495769	+	0.0789497i
$691$	−2.10628	+	36.1634i	−0.0801267	+	1.37572i	0.683446	+	0.730001i	$0.260480\pi$
$691$	−2.10628	+	36.1634i	−0.0801267	+	1.37572i	−0.763573	+	0.645722i	$0.776557\pi$
$692$	1.61375	+	9.15202i	0.0613455	+	0.347907i
$693$	−0.630516	+	0.625323i	−0.0239513	+	0.0237541i
$694$	1.87503	−	10.6338i	0.0711751	−	0.403654i
$695$	−29.6233	−	7.02086i	−1.12368	−	0.266316i
$696$	−3.69562	−	16.8345i	−0.140082	−	0.638110i
$697$	0.697393	+	11.9738i	0.0264156	+	0.453539i
$698$	−8.79902	+	2.08541i	−0.333048	+	0.0789338i
$699$	12.9437	−	18.9853i	0.489575	−	0.718091i
$700$	−2.83934	+	0.331872i	−0.107317	+	0.0125436i
$701$	11.2890	+	19.5531i	0.426379	+	0.738510i	0.996548	−	0.0830175i	$-0.0264557\pi$
$701$	11.2890	+	19.5531i	0.426379	+	0.738510i	−0.570169	+	0.821527i	$0.693122\pi$
$702$	−5.27199	−	17.0895i	−0.198979	−	0.645002i
$703$	−11.8655	+	20.5517i	−0.447516	+	0.775121i
$704$	0.115767	−	0.268379i	0.00436315	−	0.0101149i
$705$	0.709755	+	7.09220i	0.0267309	+	0.267108i
$706$	7.14638	+	7.57472i	0.268958	+	0.285078i
$707$	5.54657	+	2.78559i	0.208600	+	0.104763i
$708$	0.165732	+	0.261338i	0.00622859	+	0.00982168i
$709$	2.33458	+	7.79803i	0.0876768	+	0.292861i	0.990571	−	0.137003i	$-0.0437468\pi$
$709$	2.33458	+	7.79803i	0.0876768	+	0.292861i	−0.902894	+	0.429864i	$0.858562\pi$
$710$	15.9220	+	13.3602i	0.597543	+	0.501398i
$711$	−3.82478	−	26.8864i	−0.143441	−	1.00832i
$712$	−8.71252	+	7.31067i	−0.326516	+	0.273979i
$713$	−5.85396	−	3.85021i	−0.219233	−	0.144192i
$714$	1.43956	+	4.16940i	0.0538743	+	0.156036i
$715$	1.47436	+	0.172328i	0.0551379	+	0.00644469i
$716$	−3.75032	−	8.69421i	−0.140156	−	0.324918i
$717$	31.8664	+	19.1108i	1.19007	+	0.713707i
$718$	−11.8020	+	5.92717i	−0.440445	+	0.221200i
$719$	35.9377	+	13.0803i	1.34025	+	0.487811i	0.909891	−	0.414847i	$-0.136165\pi$
$719$	35.9377	+	13.0803i	1.34025	+	0.487811i	0.430359	+	0.902658i	$0.358387\pi$
$720$	3.88766	+	2.11700i	0.144885	+	0.0788960i
$721$	3.65952	−	1.33196i	0.136288	−	0.0496047i
$722$	2.17997	−	2.31063i	0.0811301	−	0.0859929i
$723$	31.6800	−	13.0456i	1.17819	−	0.485172i
$724$	17.2773	−	11.3635i	0.642106	−	0.422320i
$725$	8.05584	−	26.9084i	0.299186	−	0.999352i
$726$	−4.66466	+	18.3201i	−0.173122	+	0.679921i
$727$	−7.07018	−	9.49690i	−0.262219	−	0.352221i	0.651442	−	0.758698i	$-0.274164\pi$
$727$	−7.07018	−	9.49690i	−0.262219	−	0.352221i	−0.913661	+	0.406478i	$0.866757\pi$
$728$	−3.48566			−0.129187
$729$	−2.01938	−	26.9244i	−0.0747920	−	0.997199i
$730$	−1.77424			−0.0656675
$731$	17.7977	+	23.9064i	0.658270	+	0.884210i
$732$	4.37344	−	17.1763i	0.161647	−	0.634856i
$733$	−14.6597	+	48.9667i	−0.541467	+	1.80863i	0.0454318	+	0.998967i	$0.485534\pi$
$733$	−14.6597	+	48.9667i	−0.541467	+	1.80863i	−0.586899	+	0.809660i	$0.699652\pi$
$734$	−11.1118	+	7.30835i	−0.410144	+	0.269756i
$735$	14.1187	−	5.81401i	0.520778	−	0.214453i
$736$	−3.54079	+	3.75302i	−0.130515	+	0.138338i
$737$	2.21916	−	0.807710i	0.0817440	−	0.0297524i
$738$	−12.5668	−	6.84320i	−0.462592	−	0.251902i
$739$	39.7127	+	14.4542i	1.46086	+	0.531708i	0.945601	−	0.325329i	$-0.105475\pi$
$739$	39.7127	+	14.4542i	1.46086	+	0.531708i	0.515255	+	0.857037i	$0.327697\pi$
$740$	−7.86656	+	3.95073i	−0.289180	+	0.145232i
$741$	20.3368	+	12.1963i	0.747090	+	0.448042i
$742$	1.05615	+	2.44842i	0.0387723	+	0.0898843i
$743$	−19.8229	−	2.31697i	−0.727232	−	0.0850012i	−0.255582	−	0.966787i	$-0.582267\pi$
$743$	−19.8229	−	2.31697i	−0.727232	−	0.0850012i	−0.471650	+	0.881786i	$0.656341\pi$
$744$	0.767625	+	2.22327i	0.0281425	+	0.0815089i
$745$	18.2079	+	11.9756i	0.667087	+	0.438750i
$746$	13.7365	−	11.5263i	0.502927	−	0.422006i
$747$	5.27179	+	37.0581i	0.192885	+	1.35588i
$748$	−0.563026	−	0.472435i	−0.0205863	−	0.0172739i
$749$	−3.26462	−	10.9046i	−0.119287	−	0.398445i
$750$	10.7073	+	16.8840i	0.390975	+	0.616517i
$751$	12.7486	+	6.40258i	0.465203	+	0.233634i	0.665931	−	0.746013i	$-0.268035\pi$
$751$	12.7486	+	6.40258i	0.465203	+	0.233634i	−0.200728	+	0.979647i	$0.564331\pi$
$752$	1.91383	+	2.02854i	0.0697902	+	0.0739733i
$753$	0.0934172	+	0.933467i	0.00340431	+	0.0340174i
$754$	13.5653	−	31.4480i	0.494020	−	1.14527i
$755$	0.0786044	−	0.136147i	0.00286071	−	0.00495489i
$756$	−5.13045	−	1.17082i	−0.186593	−	0.0425824i
$757$	12.8586	+	22.2718i	0.467354	+	0.809481i	0.999304	−	0.0372945i	$-0.0118740\pi$
$757$	12.8586	+	22.2718i	0.467354	+	0.809481i	−0.531950	+	0.846776i	$0.678541\pi$
$758$	17.2964	−	2.02166i	0.628234	−	0.0734300i
$759$	−1.47142	+	2.15822i	−0.0534091	+	0.0783385i
$760$	−5.71136	+	1.35362i	−0.207173	+	0.0491009i
$761$	−1.46071	−	25.0794i	−0.0529506	−	0.909127i	−0.915290	−	0.402796i	$-0.868038\pi$
$761$	−1.46071	−	25.0794i	−0.0529506	−	0.909127i	0.862339	−	0.506331i	$-0.168999\pi$
$762$	−3.88534	−	17.6987i	−0.140751	−	0.641156i
$763$	−9.18194	−	2.17616i	−0.332409	−	0.0787823i
$764$	4.32538	−	24.5304i	0.156487	−	0.887480i
$765$	7.90357	−	7.83848i	0.285754	−	0.283401i
$766$	−1.26127	−	7.15304i	−0.0455717	−	0.258450i
$767$	−0.0357553	+	0.613895i	−0.00129105	+	0.0221665i
$768$	1.71050	−	0.272392i	0.0617223	−	0.00982909i
$769$	−16.8641	+	22.6525i	−0.608136	+	0.816869i	−0.994418	−	0.105512i	$-0.966352\pi$
$769$	−16.8641	+	22.6525i	−0.608136	+	0.816869i	0.386282	+	0.922381i	$0.373759\pi$
$770$	0.260825	−	0.350349i	0.00939948	−	0.0126257i
$771$	4.88815	−	12.7662i	0.176042	−	0.459762i
$772$	−1.12981	+	19.3981i	−0.0406628	+	0.698153i
$773$	2.38629	+	13.5333i	0.0858288	+	0.486759i	0.997175	+	0.0751178i	$0.0239333\pi$
$773$	2.38629	+	13.5333i	0.0858288	+	0.486759i	−0.911346	+	0.411641i	$0.864956\pi$
$774$	−35.4341	+	2.95250i	−1.27365	+	0.106125i
$775$	−0.665616	+	3.77489i	−0.0239096	+	0.135598i
$776$	9.74287	+	2.30910i	0.349749	+	0.0828920i
$777$	7.72997	−	7.05387i	0.277311	−	0.253056i
$778$	1.71228	+	29.3987i	0.0613883	+	1.05400i
$779$	18.4619	−	4.37556i	0.661468	−	0.156771i
$780$	3.81671	+	7.92527i	0.136660	+	0.283770i
$781$	4.08925	−	0.477965i	0.146325	−	0.0171029i
$782$	6.48730	+	11.2363i	0.231985	+	0.401810i
$783$	30.5297	−	41.7308i	1.09104	−	1.49134i
$784$	2.98718	−	5.17395i	0.106685	−	0.184784i
$785$	−13.5549	+	31.4237i	−0.483793	+	1.12156i
$786$	−18.6733	+	13.4255i	−0.666055	+	0.478871i
$787$	−20.0808	−	21.2844i	−0.715802	−	0.758706i	0.262715	−	0.964874i	$-0.415382\pi$
$787$	−20.0808	−	21.2844i	−0.715802	−	0.758706i	−0.978517	+	0.206168i	$0.933901\pi$
$788$	4.21986	+	2.11929i	0.150326	+	0.0754967i
$789$	15.0970	−	0.627880i	0.537467	−	0.0223531i
$790$	3.83092	+	12.7962i	0.136298	+	0.455267i
$791$	−4.92858	−	4.13557i	−0.175240	−	0.147044i
$792$	0.833476	−	0.272364i	0.0296163	−	0.00967805i
$793$	26.9806	−	22.6394i	0.958111	−	0.803950i
$794$	−13.3521	−	8.78183i	−0.473849	−	0.311656i
$795$	4.41046	−	5.08229i	0.156423	−	0.180250i
$796$	−11.5426	−	1.34913i	−0.409115	−	0.0478187i
$797$	−3.97697	−	9.21966i	−0.140872	−	0.326577i	0.833145	−	0.553055i	$-0.186538\pi$
$797$	−3.97697	−	9.21966i	−0.140872	−	0.326577i	−0.974016	+	0.226478i	$0.927279\pi$
$798$	6.09991	−	3.38795i	0.215935	−	0.119932i
$799$	6.26694	−	3.14738i	0.221709	−	0.111346i
$800$	2.65248	+	0.965424i	0.0937794	+	0.0341329i
$801$	−33.7392	−	5.08465i	−1.19212	−	0.179657i
$802$	32.4527	−	11.8118i	1.14594	−	0.417090i
$803$	−0.241176	+	0.255632i	−0.00851093	+	0.00902106i
$804$	11.0850	+	8.54231i	0.390939	+	0.301264i
$805$	−6.44197	+	4.23695i	−0.227050	+	0.149333i
$806$	−1.34047	+	4.47750i	−0.0472162	+	0.157713i
$807$	25.8388	+	25.2019i	0.909569	+	0.887150i
$808$	−3.65980	−	4.91597i	−0.128751	−	0.172943i
$809$	37.5147			1.31895			0.659473	−	0.751728i	$-0.270779\pi$
$809$	37.5147			1.31895			0.659473	+	0.751728i	$0.270779\pi$
$810$	2.95563	+	12.9470i	0.103850	+	0.454911i
$811$	−33.8326			−1.18802			−0.594012	−	0.804456i	$-0.702457\pi$
$811$	−33.8326			−1.18802			−0.594012	+	0.804456i	$0.702457\pi$
$812$	−6.01793	−	8.08349i	−0.211188	−	0.283675i
$813$	−16.8485	+	4.74061i	−0.590901	+	0.166260i
$814$	−0.500098	+	1.67044i	−0.0175284	+	0.0585491i
$815$	15.2540	−	10.0327i	0.534324	−	0.351430i
$816$	0.577424	−	4.31699i	0.0202139	−	0.151125i
$817$	32.3540	−	34.2932i	1.13192	−	1.19977i
$818$	−24.6304	+	8.96473i	−0.861182	+	0.313445i
$819$	−6.91941	−	7.84031i	−0.241784	−	0.273963i
$820$	6.61362	+	2.40716i	0.230958	+	0.0840618i
$821$	−49.8792	+	25.0503i	−1.74080	+	0.874261i	−0.768725	+	0.639579i	$0.779109\pi$
$821$	−49.8792	+	25.0503i	−1.74080	+	0.874261i	−0.972072	+	0.234682i	$0.924595\pi$
$822$	0.520298	−	31.3180i	0.0181475	−	1.09234i
$823$	−6.48460	−	15.0330i	−0.226039	−	0.524017i	0.767022	−	0.641621i	$-0.221738\pi$
$823$	−6.48460	−	15.0330i	−0.226039	−	0.524017i	−0.993061	+	0.117604i	$0.962479\pi$
$824$	−3.81939	−	0.446423i	−0.133055	−	0.0155519i
$825$	1.40297	+	0.271485i	0.0488451	+	0.00945189i
$826$	0.151175	+	0.0994293i	0.00526005	+	0.00345959i
$827$	−16.8499	+	14.1387i	−0.585927	+	0.491651i	−0.886888	−	0.461985i	$-0.847137\pi$
$827$	−16.8499	+	14.1387i	−0.585927	+	0.491651i	0.300960	+	0.953637i	$0.402693\pi$
$828$	−15.4705	−	0.514176i	−0.537637	−	0.0178689i
$829$	−17.8569	−	14.9837i	−0.620195	−	0.520405i	0.277670	−	0.960677i	$-0.410438\pi$
$829$	−17.8569	−	14.9837i	−0.620195	−	0.520405i	−0.897865	+	0.440271i	$0.854882\pi$
$830$	−5.28025	−	17.6373i	−0.183280	−	0.612198i
$831$	11.2460	−	21.4948i	0.390121	−	0.745647i
$832$	3.07572	+	1.54468i	0.106631	+	0.0535523i
$833$	−10.3095	−	10.9275i	−0.357204	−	0.378614i
$834$	−32.5736	−	14.6973i	−1.12793	−	0.508927i
$835$	−5.50570	+	12.7636i	−0.190533	+	0.441704i
$836$	−0.581330	+	1.00689i	−0.0201057	+	0.0348241i
$837$	−3.47698	+	6.14004i	−0.120182	+	0.212231i
$838$	12.3950	+	21.4688i	0.428178	+	0.741626i
$839$	33.9198	−	3.96466i	1.17104	−	0.136875i	0.491745	−	0.870739i	$-0.336359\pi$
$839$	33.9198	−	3.96466i	1.17104	−	0.136875i	0.679296	+	0.733864i	$0.262285\pi$
$840$	2.58107	+	0.193398i	0.0890555	+	0.00667286i
$841$	68.1319	−	16.1476i	2.34938	−	0.556813i
$842$	−0.408099	−	7.00678i	−0.0140640	−	0.241470i
$843$	34.2829	+	10.8873i	1.18076	+	0.374979i
$844$	18.0175	+	4.27023i	0.620189	+	0.146987i
$845$	0.295661	−	1.67678i	0.0101710	−	0.0576828i
$846$	−0.763651	+	8.33164i	−0.0262549	+	0.286448i
$847$	1.91944	+	10.8857i	0.0659528	+	0.374037i
$848$	0.153093	−	2.62850i	0.00525722	−	0.0902631i
$849$	−26.3196	−	32.4461i	−0.903286	−	1.11355i
$850$	4.23864	−	5.69349i	0.145384	−	0.195285i
$851$	18.3815	−	24.6906i	0.630109	−	0.846383i
$852$	15.3699	+	18.9476i	0.526563	+	0.649133i
$853$	2.03057	−	34.8635i	0.0695253	−	1.19370i	−0.765479	−	0.643461i	$-0.777498\pi$
$853$	2.03057	−	34.8635i	0.0695253	−	1.19370i	0.835005	−	0.550243i	$-0.185465\pi$
$854$	−1.79961	−	10.2061i	−0.0615814	−	0.349245i
$855$	−14.3823	−	10.1595i	−0.491866	−	0.347448i
$856$	−1.95174	+	11.0688i	−0.0667089	+	0.378325i
$857$	16.9001	+	4.00540i	0.577297	+	0.136822i	0.508884	−	0.860835i	$-0.330058\pi$
$857$	16.9001	+	4.00540i	0.577297	+	0.136822i	0.0684129	+	0.997657i	$0.478206\pi$
$858$	1.66069	+	0.527389i	0.0566949	+	0.0180048i
$859$	−2.56080	−	43.9673i	−0.0873734	−	1.50014i	−0.702482	−	0.711702i	$-0.747925\pi$
$859$	−2.56080	−	43.9673i	−0.0873734	−	1.50014i	0.615109	−	0.788442i	$-0.289112\pi$
$860$	17.0174	−	4.03320i	0.580288	−	0.137531i
$861$	−8.34331	−	0.625158i	−0.284339	−	0.0213053i
$862$	7.29417	−	0.852566i	0.248440	−	0.0290385i
$863$	0.797525	+	1.38135i	0.0271481	+	0.0470218i	0.879280	−	0.476305i	$-0.158024\pi$
$863$	0.797525	+	1.38135i	0.0271481	+	0.0470218i	−0.852132	+	0.523327i	$0.824691\pi$
$864$	4.00821	+	3.30670i	0.136362	+	0.112496i
$865$	6.85636	−	11.8756i	0.233123	−	0.403781i
$866$	−4.67062	+	10.8277i	−0.158714	+	0.367940i
$867$	16.8562	+	7.60561i	0.572468	+	0.258300i
$868$	0.943760	+	1.00033i	0.0320333	+	0.0339533i
$869$	2.36442	+	1.18745i	0.0802073	+	0.0402816i
$870$	−11.7898	+	22.5340i	−0.399710	+	0.763975i
$871$	7.97576	+	26.6409i	0.270248	+	0.902692i
$872$	7.13769	+	5.98923i	0.241713	+	0.202821i
$873$	14.1467	+	26.4985i	0.478795	+	0.896838i
$874$	15.7227	−	13.1929i	0.531827	−	0.446256i
$875$	9.76682	+	6.42374i	0.330179	+	0.217162i
$876$	−2.04471	−	0.395667i	−0.0690844	−	0.0133683i
$877$	−46.7884	−	5.46879i	−1.57993	−	0.184668i	−0.719596	−	0.694393i	$-0.755673\pi$
$877$	−46.7884	−	5.46879i	−1.57993	−	0.184668i	−0.860337	+	0.509725i	$0.829747\pi$
$878$	−4.48725	−	10.4026i	−0.151437	−	0.351071i
$879$	−0.0187418	+	1.12812i	−0.000632146	+	0.0380505i
$880$	−0.385408	+	0.193559i	−0.0129921	+	0.00652488i
$881$	−28.9882	−	10.5508i	−0.976638	−	0.355467i	−0.196106	−	0.980583i	$-0.562830\pi$
$881$	−28.9882	−	10.5508i	−0.976638	−	0.355467i	−0.780532	+	0.625116i	$0.785052\pi$
$882$	17.5676	−	3.55175i	0.591533	−	0.119594i
$883$	38.2989	−	13.9397i	1.28886	−	0.469107i	0.395507	−	0.918463i	$-0.370569\pi$
$883$	38.2989	−	13.9397i	1.28886	−	0.469107i	0.893353	+	0.449356i	$0.148347\pi$
$884$	5.93931	−	6.29530i	0.199760	−	0.211734i
$885$	0.0605375	−	0.452595i	0.00203494	−	0.0152138i
$886$	3.08859	−	2.03140i	0.103763	−	0.0682461i
$887$	0.776268	−	2.59292i	0.0260645	−	0.0870616i	−0.943968	−	0.330038i	$-0.892938\pi$
$887$	0.776268	−	2.59292i	0.0260645	−	0.0870616i	0.970032	+	0.242976i	$0.0781237\pi$
$888$	−9.94681	+	2.79871i	−0.333793	+	0.0939186i
$889$	−6.32687	−	8.49846i	−0.212196	−	0.285029i
$890$	16.7822			0.562539
$891$	2.26717	+	1.33407i	0.0759529	+	0.0446930i
$892$	2.07841			0.0695902
$893$	−6.62467	−	8.89848i	−0.221686	−	0.297776i
$894$	18.3130	+	17.8616i	0.612479	+	0.597383i
$895$	−4.00707	+	13.3846i	−0.133942	+	0.447396i
$896$	0.846132	−	0.556509i	0.0282673	−	0.0185917i
$897$	−24.3640	−	18.7753i	−0.813489	−	0.626888i
$898$	8.44317	−	8.94924i	0.281752	−	0.298640i
$899$	−12.6979	+	4.62167i	−0.423499	+	0.154141i
$900$	3.09392	+	7.88270i	0.103131	+	0.262757i
$901$	−6.22157	−	2.26447i	−0.207271	−	0.0754403i
$902$	1.24583	−	0.625679i	0.0414816	−	0.0208328i
$903$	−18.1751	+	10.0946i	−0.604830	+	0.335928i
$904$	2.51624	+	5.83331i	0.0836890	+	0.194013i
$905$	−30.3073	−	3.54242i	−1.00745	−	0.117754i
$906$	0.120949	−	0.139372i	0.00401826	−	0.00463034i
$907$	−21.2759	−	13.9934i	−0.706456	−	0.464643i	0.144755	−	0.989468i	$-0.453761\pi$
$907$	−21.2759	−	13.9934i	−0.706456	−	0.464643i	−0.851211	+	0.524824i	$0.824131\pi$
$908$	7.13661	−	5.98833i	0.236837	−	0.198730i
$909$	3.79241	−	17.9907i	0.125786	−	0.596714i
$910$	3.94001	+	3.30606i	0.130610	+	0.109595i
$911$	4.39134	+	14.6681i	0.145492	+	0.485976i	0.999407	−	0.0344360i	$-0.0109635\pi$
$911$	4.39134	+	14.6681i	0.145492	+	0.485976i	−0.853915	+	0.520412i	$0.825778\pi$
$912$	−6.88389	+	0.286299i	−0.227949	+	0.00948032i
$913$	−3.25893	−	1.63670i	−0.107855	−	0.0541667i
$914$	2.13218	+	2.25998i	0.0705262	+	0.0747534i
$915$	−21.2348	+	15.2671i	−0.702002	+	0.504716i
$916$	−9.69439	+	22.4741i	−0.320312	+	0.742566i
$917$	−6.72371	+	11.6458i	−0.222036	+	0.384578i
$918$	10.8565	−	7.27087i	0.358317	−	0.239974i
$919$	−27.4733	−	47.5851i	−0.906260	−	1.56969i	−0.819218	−	0.573483i	$-0.805592\pi$
$919$	−27.4733	−	47.5851i	−0.906260	−	1.56969i	−0.0870420	−	0.996205i	$-0.527741\pi$
$920$	7.56196	−	0.883867i	0.249311	−	0.0291402i
$921$	22.3078	+	46.3214i	0.735066	+	1.52634i
$922$	−10.6825	+	2.53180i	−0.351810	+	0.0833805i
$923$	2.81894	+	48.3993i	0.0927865	+	1.59308i
$924$	0.378716	−	0.345592i	0.0124589	−	0.0113691i
$925$	−16.3858	−	3.88350i	−0.538761	−	0.127689i
$926$	3.85019	−	21.8355i	0.126525	−	0.717559i
$927$	−6.57775	−	9.47716i	−0.216042	−	0.311271i
$928$	1.72795	+	9.79967i	0.0567226	+	0.321690i
$929$	0.0571022	−	0.980406i	0.00187346	−	0.0321661i	−0.997242	−	0.0742203i	$-0.976353\pi$
$929$	0.0571022	−	0.980406i	0.00187346	−	0.0321661i	0.999115	+	0.0420542i	$0.0133902\pi$
$930$	1.24103	−	3.24114i	0.0406949	−	0.106281i
$931$	−14.1915	+	19.0626i	−0.465109	+	0.624750i
$932$	−7.92207	+	10.6412i	−0.259496	+	0.348563i
$933$	33.3919	−	5.31756i	1.09320	−	0.174089i
$934$	0.861819	−	14.7969i	0.0281996	−	0.484168i
$935$	0.188323	+	1.06803i	0.00615881	+	0.0349283i
$936$	2.63116	+	9.98459i	0.0860022	+	0.326356i
$937$	−2.79599	+	15.8568i	−0.0913410	+	0.518021i	0.904466	+	0.426545i	$0.140269\pi$
$937$	−2.79599	+	15.8568i	−0.0913410	+	0.518021i	−0.995807	+	0.0914755i	$0.970842\pi$
$938$	7.96216	+	1.88707i	0.259974	+	0.0616149i
$939$	−2.88142	−	13.1256i	−0.0940315	−	0.428338i
$940$	−0.239274	−	4.10817i	−0.00780425	−	0.133994i
$941$	7.68558	−	1.82152i	0.250543	−	0.0593797i	−0.103425	−	0.994637i	$-0.532980\pi$
$941$	7.68558	−	1.82152i	0.250543	−	0.0593797i	0.353968	+	0.935257i	$0.384832\pi$
$942$	−22.6289	+	33.1912i	−0.737290	+	1.08143i
$943$	−24.4440	+	2.85709i	−0.796006	+	0.0930398i
$944$	−0.0893330	−	0.154729i	−0.00290754	−	0.00503601i
$945$	4.68869	+	6.18953i	0.152523	+	0.201346i
$946$	1.73211	−	3.00011i	0.0563158	−	0.0975418i
$947$	−9.40975	+	21.8143i	−0.305776	+	0.708868i	−0.999940	−	0.0109485i	$-0.996515\pi$
$947$	−9.40975	+	21.8143i	−0.305776	+	0.708868i	0.694164	+	0.719817i	$0.255774\pi$
$948$	1.56130	+	15.6012i	0.0507086	+	0.506703i
$949$	−2.84000	−	3.01023i	−0.0921904	−	0.0977162i
$950$	−10.0340	−	5.03927i	−0.325546	−	0.163495i
$951$	−8.59185	−	13.5482i	−0.278610	−	0.439332i
$952$	−0.730386	−	2.43966i	−0.0236720	−	0.0790698i
$953$	−6.59171	−	5.53110i	−0.213526	−	0.179170i	0.529751	−	0.848153i	$-0.322285\pi$
$953$	−6.59171	−	5.53110i	−0.213526	−	0.179170i	−0.743277	+	0.668983i	$0.766730\pi$
$954$	6.21620	−	4.87349i	0.201257	−	0.157785i
$955$	−28.1557	+	23.6254i	−0.911096	+	0.764500i
$956$	−17.9237	−	11.7886i	−0.579695	−	0.381271i
$957$	1.64409	+	4.76177i	0.0531459	+	0.153926i
$958$	0.136880	+	0.0159989i	0.00442238	+	0.000516902i
$959$	−7.25394	−	16.8165i	−0.234242	−	0.543034i
$960$	−2.19181	−	1.31447i	−0.0707405	−	0.0424242i
$961$	−26.0547	+	13.0852i	−0.840474	+	0.422102i
$962$	−19.2948	−	7.02275i	−0.622091	−	0.226423i
$963$	−28.7716	+	17.5828i	−0.927151	+	0.566596i
$964$	−18.5877	+	6.76535i	−0.598668	+	0.217897i
$965$	19.6757	−	20.8550i	0.633382	−	0.671346i
$966$	−8.36889	+	3.44625i	−0.269265	+	0.110881i
$967$	5.71212	−	3.75692i	0.183689	−	0.120814i	−0.454334	−	0.890831i	$-0.650123\pi$
$967$	5.71212	−	3.75692i	0.183689	−	0.120814i	0.638023	+	0.770017i	$0.279752\pi$
$968$	3.13033	−	10.4560i	0.100613	−	0.336070i
$969$	−4.27497	+	16.7896i	−0.137332	+	0.539359i
$970$	−8.82270	−	11.8509i	−0.283280	−	0.380511i
$971$	11.1814			0.358830			0.179415	−	0.983774i	$-0.442580\pi$
$971$	11.1814			0.358830			0.179415	+	0.983774i	$0.442580\pi$
$972$	0.518939	+	15.5798i	0.0166450	+	0.499723i
$973$	−20.8949			−0.669861
$974$	9.68994	+	13.0158i	0.310486	+	0.417054i
$975$	−4.15210	+	16.3070i	−0.132974	+	0.522243i
$976$	−2.93491	+	9.80328i	−0.0939441	+	0.313795i
$977$	22.1906	−	14.5950i	0.709939	−	0.466934i	−0.142477	−	0.989798i	$-0.545507\pi$
$977$	22.1906	−	14.5950i	0.709939	−	0.466934i	0.852416	+	0.522864i	$0.175136\pi$
$978$	19.8167	−	8.16040i	0.633669	−	0.260941i
$979$	2.28124	−	2.41797i	0.0729087	−	0.0772787i
$980$	−8.28390	+	3.01509i	−0.264620	+	0.0963137i
$981$	0.697460	+	27.9441i	0.0222682	+	0.892186i
$982$	15.6056	+	5.67999i	0.497996	+	0.181256i
$983$	−49.4675	+	24.8435i	−1.57777	+	0.792385i	−0.999721	−	0.0236172i	$-0.992482\pi$
$983$	−49.4675	+	24.8435i	−1.57777	+	0.792385i	−0.578048	+	0.816003i	$0.696185\pi$
$984$	7.08502	+	4.24900i	0.225862	+	0.135453i
$985$	−2.75981	−	6.39797i	−0.0879350	−	0.203856i
$986$	24.8533	+	2.90494i	0.791491	+	0.0925120i
$987$	1.59656	+	4.62411i	0.0508192	+	0.147187i
$988$	−11.4387	−	7.52335i	−0.363914	−	0.239350i
$989$	−46.8467	+	39.3091i	−1.48964	+	1.24996i
$990$	−1.20045	−	0.482664i	−0.0381527	−	0.0153401i
$991$	−23.5575	−	19.7671i	−0.748328	−	0.627922i	0.186732	−	0.982411i	$-0.440210\pi$
$991$	−23.5575	−	19.7671i	−0.748328	−	0.627922i	−0.935060	+	0.354489i	$0.884655\pi$
$992$	−0.389467	−	1.30091i	−0.0123656	−	0.0413040i
$993$	19.0481	+	30.0364i	0.604474	+	0.953177i
$994$	12.7480	+	6.40231i	0.404343	+	0.203069i
$995$	11.7675	+	12.4728i	0.373054	+	0.395414i
$996$	−2.15197	−	21.5035i	−0.0681879	−	0.681364i
$997$	15.6677	−	36.3219i	0.496202	−	1.15033i	−0.467657	−	0.883910i	$-0.654902\pi$
$997$	15.6677	−	36.3219i	0.496202	−	1.15033i	0.963858	−	0.266415i	$-0.0858391\pi$
$998$	6.07998	−	10.5308i	0.192458	−	0.333348i
$999$	−26.0406	−	16.8177i	−0.823888	−	0.532087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.7.3	✓	90
3.2	odd	2		486.2.g.b.343.2		90
81.23	odd	54		486.2.g.b.469.2		90
81.58	even	27	inner	162.2.g.b.139.3	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.7.3	✓	90	1.1	even	1	trivial
162.2.g.b.139.3	yes	90	81.58	even	27	inner
486.2.g.b.343.2		90	3.2	odd	2
486.2.g.b.469.2		90	81.23	odd	54

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.597159 + 0.802123i) q^{2} +(0.427379 - 1.67850i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(1.23282 - 0.810835i) q^{5} +(1.60157 - 0.659517i) q^{6} +(0.694984 - 0.736640i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.63469 - 1.43471i) q^{9} +O(q^{10})\)	\(q+(0.597159 + 0.802123i) q^{2} +(0.427379 - 1.67850i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(1.23282 - 0.810835i) q^{5} +(1.60157 - 0.659517i) q^{6} +(0.694984 - 0.736640i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.63469 - 1.43471i) q^{9} +(1.38658 + 0.504672i) q^{10} +(0.261194 - 0.131176i) q^{11} +(1.48541 + 0.890823i) q^{12} +(1.36323 + 3.16033i) q^{13} +(1.00589 + 0.117572i) q^{14} +(-0.834104 - 2.41581i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(-1.92630 + 1.61636i) q^{17} +(-0.422518 - 2.97010i) q^{18} +(3.04721 + 2.55692i) q^{19} +(0.423196 + 1.41357i) q^{20} +(-0.939425 - 1.48135i) q^{21} +(0.261194 + 0.131176i) q^{22} +(-3.54079 - 3.75302i) q^{23} +(0.172474 + 1.72344i) q^{24} +(-1.11802 + 2.59186i) q^{25} +(-1.72091 + 2.98070i) q^{26} +(-3.53416 + 3.80916i) q^{27} +(0.506370 + 0.877058i) q^{28} +(-9.88356 + 1.15522i) q^{29} +(1.43968 - 2.11168i) q^{30} +(1.32136 - 0.313167i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(-0.108550 - 0.494475i) q^{33} +(-2.44683 - 0.579909i) q^{34} +(0.259493 - 1.47166i) q^{35} +(2.13007 - 2.11253i) q^{36} +(1.03595 + 5.87515i) q^{37} +(-0.231292 + 3.97112i) q^{38} +(5.88722 - 0.937523i) q^{39} +(-0.881145 + 1.18358i) q^{40} +(2.84830 - 3.82593i) q^{41} +(0.627241 - 1.63814i) q^{42} +(0.689149 - 11.8322i) q^{43} +(0.0507544 + 0.287843i) q^{44} +(-4.41140 + 0.367574i) q^{45} +(0.895970 - 5.08130i) q^{46} +(-2.71368 - 0.643154i) q^{47} +(-1.27942 + 1.16751i) q^{48} +(0.347378 + 5.96425i) q^{49} +(-2.74663 + 0.650962i) q^{50} +(1.88979 + 3.92409i) q^{51} +(-3.41855 + 0.399571i) q^{52} +(1.31648 + 2.28021i) q^{53} +(-5.16587 - 0.560162i) q^{54} +(0.215641 - 0.373501i) q^{55} +(-0.401126 + 0.929914i) q^{56} +(5.59409 - 4.02196i) q^{57} +(-6.82868 - 7.23798i) q^{58} +(0.159662 + 0.0801851i) q^{59} +(2.55354 - 0.106201i) q^{60} +(-2.93491 - 9.80328i) q^{61} +(1.04026 + 0.872879i) q^{62} +(-2.88793 + 0.943723i) q^{63} +(0.766044 - 0.642788i) q^{64} +(4.24313 + 2.79075i) q^{65} +(0.331808 - 0.382350i) q^{66} +(8.02516 + 0.938006i) q^{67} +(-0.995986 - 2.30896i) q^{68} +(-7.81268 + 4.33924i) q^{69} +(1.33541 - 0.670668i) q^{70} +(13.2365 + 4.81768i) q^{71} +(2.96650 + 0.447065i) q^{72} +(-1.12990 + 0.411250i) q^{73} +(-4.09397 + 4.33936i) q^{74} +(3.87261 + 2.98430i) q^{75} +(-3.32345 + 2.18587i) q^{76} +(0.0848957 - 0.283571i) q^{77} +(4.26761 + 4.16243i) q^{78} +(5.40569 + 7.26110i) q^{79} -1.47556 q^{80} +(4.88323 + 7.56003i) q^{81} +4.76975 q^{82} +(-7.45078 - 10.0081i) q^{83} +(1.68855 - 0.475103i) q^{84} +(-1.06417 + 3.55459i) q^{85} +(9.90244 - 6.51294i) q^{86} +(-2.28499 + 17.0832i) q^{87} +(-0.200577 + 0.212599i) q^{88} +(10.6875 - 3.88993i) q^{89} +(-2.92915 - 3.31899i) q^{90} +(3.27545 + 1.19217i) q^{91} +(4.61086 - 2.31566i) q^{92} +(0.0390702 - 2.35173i) q^{93} +(-1.10461 - 2.56077i) q^{94} +(5.82989 + 0.681416i) q^{95} +(-1.70051 - 0.329060i) q^{96} +(-8.36554 - 5.50211i) q^{97} +(-4.57662 + 3.84024i) q^{98} +(-0.876365 - 0.0291268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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