LMFDB - Embedded newform 324.2.p.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	324.11
Dual form			324.2.p.a.59.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.956045 - 1.04210i) q^{2} +(-0.138112 - 1.72654i) q^{3} +(-0.171958 + 1.99259i) q^{4} +(-0.283509 + 2.42558i) q^{5} +(-1.66719 + 1.79457i) q^{6} +(-1.43973 - 2.86675i) q^{7} +(2.24089 - 1.72581i) q^{8} +(-2.96185 + 0.476909i) q^{9} +O(q^{10})$	\(q+(-0.956045 - 1.04210i) q^{2} +(-0.138112 - 1.72654i) q^{3} +(-0.171958 + 1.99259i) q^{4} +(-0.283509 + 2.42558i) q^{5} +(-1.66719 + 1.79457i) q^{6} +(-1.43973 - 2.86675i) q^{7} +(2.24089 - 1.72581i) q^{8} +(-2.96185 + 0.476909i) q^{9} +(2.79875 - 2.02351i) q^{10} +(-1.56735 + 3.63353i) q^{11} +(3.46403 + 0.0216908i) q^{12} +(-6.41164 + 1.51959i) q^{13} +(-1.61100 + 4.24109i) q^{14} +(4.22700 + 0.154489i) q^{15} +(-3.94086 - 0.685284i) q^{16} +(-0.0431938 + 0.00761624i) q^{17} +(3.32865 + 2.63061i) q^{18} +(-4.50470 - 0.794300i) q^{19} +(-4.78444 - 0.982015i) q^{20} +(-4.75070 + 2.88168i) q^{21} +(5.28497 - 1.84047i) q^{22} +(4.61035 + 2.31541i) q^{23} +(-3.28917 - 3.63062i) q^{24} +(-0.937818 - 0.222267i) q^{25} +(7.71338 + 5.22880i) q^{26} +(1.23247 + 5.04787i) q^{27} +(5.95984 - 2.37585i) q^{28} +(-1.18331 + 0.354259i) q^{29} +(-3.88021 - 4.55267i) q^{30} +(-3.24150 - 4.92846i) q^{31} +(3.05350 + 4.76195i) q^{32} +(6.48988 + 2.20425i) q^{33} +(0.0492321 + 0.0377310i) q^{34} +(7.36169 - 2.67944i) q^{35} +(-0.440973 - 5.98377i) q^{36} +(4.55219 + 1.65686i) q^{37} +(3.47895 + 5.45375i) q^{38} +(3.50914 + 10.8601i) q^{39} +(3.55077 + 5.92473i) q^{40} +(-0.981017 + 0.925542i) q^{41} +(7.54489 + 2.19570i) q^{42} +(1.26027 - 0.938234i) q^{43} +(-6.97062 - 3.74790i) q^{44} +(-0.317068 - 7.31940i) q^{45} +(-1.99481 - 7.01809i) q^{46} +(-5.76986 - 3.79489i) q^{47} +(-0.638888 + 6.89868i) q^{48} +(-1.96529 + 2.63985i) q^{49} +(0.664971 + 1.18980i) q^{50} +(0.0191153 + 0.0735238i) q^{51} +(-1.92539 - 13.0371i) q^{52} +(-8.53190 + 4.92589i) q^{53} +(4.08211 - 6.11035i) q^{54} +(-8.36904 - 4.83187i) q^{55} +(-8.17375 - 3.93935i) q^{56} +(-0.749236 + 7.88723i) q^{57} +(1.50047 + 0.894442i) q^{58} +(-4.33789 - 10.0564i) q^{59} +(-1.03470 + 8.39613i) q^{60} +(-0.185066 + 3.17746i) q^{61} +(-2.03694 + 8.08980i) q^{62} +(5.63146 + 7.80425i) q^{63} +(2.04315 - 7.73470i) q^{64} +(-1.86811 - 15.9827i) q^{65} +(-3.90756 - 8.87049i) q^{66} +(1.14811 + 0.343723i) q^{67} +(-0.00774856 - 0.0873774i) q^{68} +(3.36089 - 8.27972i) q^{69} +(-9.83035 - 5.10998i) q^{70} +(-11.5777 + 9.71483i) q^{71} +(-5.81412 + 6.18029i) q^{72} +(-6.54463 - 5.49160i) q^{73} +(-2.62548 - 6.32789i) q^{74} +(-0.254228 + 1.64987i) q^{75} +(2.35733 - 8.83945i) q^{76} +(12.6730 - 0.738116i) q^{77} +(7.96240 - 14.0396i) q^{78} +(1.32576 + 1.25079i) q^{79} +(2.77948 - 9.36457i) q^{80} +(8.54512 - 2.82507i) q^{81} +(1.90241 + 0.137462i) q^{82} +(5.72637 - 6.06959i) q^{83} +(-4.92511 - 9.96174i) q^{84} +(-0.00622792 - 0.106929i) q^{85} +(-2.18261 - 0.416335i) q^{86} +(0.775070 + 1.99410i) q^{87} +(2.75852 + 10.8473i) q^{88} +(1.91594 - 2.28333i) q^{89} +(-7.32444 + 7.32809i) q^{90} +(13.5873 + 16.1927i) q^{91} +(-5.40645 + 8.78841i) q^{92} +(-8.06147 + 6.27724i) q^{93} +(1.56157 + 9.64087i) q^{94} +(3.20376 - 10.7013i) q^{95} +(7.79994 - 5.92966i) q^{96} +(17.9553 - 2.09867i) q^{97} +(4.62990 - 0.475773i) q^{98} +(2.90939 - 11.5094i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{54}\right)$

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 $

$2$	−0.956045	−	1.04210i	−0.676026	−	0.736878i
$2$	−0.956045	−	1.04210i	−0.676026	−	0.736878i
$3$	−0.138112	−	1.72654i	−0.0797388	−	0.996816i
$3$	−0.138112	−	1.72654i	−0.0797388	−	0.996816i
$4$	−0.171958	+	1.99259i	−0.0859788	+	0.996297i
$5$	−0.283509	+	2.42558i	−0.126789	+	1.08475i	0.768682	+	0.639631i	$0.220913\pi$
$5$	−0.283509	+	2.42558i	−0.126789	+	1.08475i	−0.895471	+	0.445120i	$0.853161\pi$
$6$	−1.66719	+	1.79457i	−0.680626	+	0.732631i
$7$	−1.43973	−	2.86675i	−0.544168	−	1.08353i	−0.982768	−	0.184846i	$-0.940821\pi$
$7$	−1.43973	−	2.86675i	−0.544168	−	1.08353i	0.438599	−	0.898683i	$-0.355475\pi$
$8$	2.24089	−	1.72581i	0.792273	−	0.610166i
$9$	−2.96185	+	0.476909i	−0.987283	+	0.158970i
$10$	2.79875	−	2.02351i	0.885042	−	0.639891i
$11$	−1.56735	+	3.63353i	−0.472574	+	1.09555i	0.500642	+	0.865655i	$0.333097\pi$
$11$	−1.56735	+	3.63353i	−0.472574	+	1.09555i	−0.973216	+	0.229895i	$0.926162\pi$
$12$	3.46403	+	0.0216908i	0.999980	+	0.00626159i
$13$	−6.41164	+	1.51959i	−1.77827	+	0.421457i	−0.982820	−	0.184564i	$-0.940913\pi$
$13$	−6.41164	+	1.51959i	−1.77827	+	0.421457i	−0.795448	+	0.606022i	$0.792764\pi$
$14$	−1.61100	+	4.24109i	−0.430557	+	1.13348i
$15$	4.22700	+	0.154489i	1.09141	+	0.0398888i
$16$	−3.94086	−	0.685284i	−0.985215	−	0.171321i
$17$	−0.0431938	+	0.00761624i	−0.0104760	+	0.00184721i	−0.178884	−	0.983870i	$-0.557249\pi$
$17$	−0.0431938	+	0.00761624i	−0.0104760	+	0.00184721i	0.168408	+	0.985717i	$0.446137\pi$
$18$	3.32865	+	2.63061i	0.784570	+	0.620040i
$19$	−4.50470	−	0.794300i	−1.03345	−	0.182225i	−0.368899	−	0.929469i	$-0.620265\pi$
$19$	−4.50470	−	0.794300i	−1.03345	−	0.182225i	−0.664549	+	0.747244i	$0.731376\pi$
$20$	−4.78444	−	0.982015i	−1.06983	−	0.219585i
$21$	−4.75070	+	2.88168i	−1.03669	+	0.628835i
$22$	5.28497	−	1.84047i	1.12676	−	0.392390i
$23$	4.61035	+	2.31541i	0.961325	+	0.482795i	0.859011	−	0.511957i	$-0.171079\pi$
$23$	4.61035	+	2.31541i	0.961325	+	0.482795i	0.102313	+	0.994752i	$0.467376\pi$
$24$	−3.28917	−	3.63062i	−0.671398	−	0.741097i
$25$	−0.937818	−	0.222267i	−0.187564	−	0.0444534i
$26$	7.71338	+	5.22880i	1.51272	+	1.02545i
$27$	1.23247	+	5.04787i	0.237188	+	0.971464i
$28$	5.95984	−	2.37585i	1.12630	−	0.448993i
$29$	−1.18331	+	0.354259i	−0.219735	+	0.0657843i	−0.394778	−	0.918776i	$-0.629179\pi$
$29$	−1.18331	+	0.354259i	−0.219735	+	0.0657843i	0.175043	+	0.984561i	$0.443993\pi$
$30$	−3.88021	−	4.55267i	−0.708426	−	0.831200i
$31$	−3.24150	−	4.92846i	−0.582190	−	0.885177i	0.417534	−	0.908661i	$-0.362894\pi$
$31$	−3.24150	−	4.92846i	−0.582190	−	0.885177i	−0.999724	+	0.0234844i	$0.992524\pi$
$32$	3.05350	+	4.76195i	0.539788	+	0.841801i
$33$	6.48988	+	2.20425i	1.12974	+	0.383711i
$34$	0.0492321	+	0.0377310i	0.00844324	+	0.00647081i
$35$	7.36169	−	2.67944i	1.24435	−	0.452907i
$36$	−0.440973	−	5.98377i	−0.0734956	−	0.997296i
$37$	4.55219	+	1.65686i	0.748376	+	0.272387i	0.687922	−	0.725784i	$-0.258523\pi$
$37$	4.55219	+	1.65686i	0.748376	+	0.272387i	0.0604539	+	0.998171i	$0.480745\pi$
$38$	3.47895	+	5.45375i	0.564360	+	0.884715i
$39$	3.50914	+	10.8601i	0.561912	+	1.73900i
$40$	3.55077	+	5.92473i	0.561427	+	0.936782i
$41$	−0.981017	+	0.925542i	−0.153209	+	0.144545i	−0.759030	−	0.651056i	$-0.774326\pi$
$41$	−0.981017	+	0.925542i	−0.153209	+	0.144545i	0.605821	+	0.795601i	$0.292845\pi$
$42$	7.54489	+	2.19570i	1.16420	+	0.338804i
$43$	1.26027	−	0.938234i	0.192189	−	0.143079i	−0.496763	−	0.867886i	$-0.665478\pi$
$43$	1.26027	−	0.938234i	0.192189	−	0.143079i	0.688952	+	0.724807i	$0.258071\pi$
$44$	−6.97062	−	3.74790i	−1.05086	−	0.565018i
$45$	−0.317068	−	7.31940i	−0.0472657	−	1.09111i
$46$	−1.99481	−	7.01809i	−0.294119	−	1.03476i
$47$	−5.76986	−	3.79489i	−0.841620	−	0.553542i	0.0539087	−	0.998546i	$-0.482832\pi$
$47$	−5.76986	−	3.79489i	−0.841620	−	0.553542i	−0.895529	+	0.445004i	$0.853202\pi$
$48$	−0.638888	+	6.89868i	−0.0922156	+	0.995739i
$49$	−1.96529	+	2.63985i	−0.280756	+	0.377121i
$50$	0.664971	+	1.18980i	0.0940411	+	0.168263i
$51$	0.0191153	+	0.0735238i	0.00267667	+	0.0102954i
$52$	−1.92539	−	13.0371i	−0.267003	−	1.80792i
$53$	−8.53190	+	4.92589i	−1.17195	+	0.676623i	−0.954138	−	0.299368i	$-0.903224\pi$
$53$	−8.53190	+	4.92589i	−1.17195	+	0.676623i	−0.217808	+	0.975992i	$0.569891\pi$
$54$	4.08211	−	6.11035i	0.555505	−	0.831513i
$55$	−8.36904	−	4.83187i	−1.12848	−	0.651529i
$56$	−8.17375	−	3.93935i	−1.09226	−	0.526418i
$57$	−0.749236	+	7.88723i	−0.0992387	+	1.04469i
$58$	1.50047	+	0.894442i	0.197022	+	0.117446i
$59$	−4.33789	−	10.0564i	−0.564745	−	1.30923i	−0.926269	−	0.376863i	$-0.877003\pi$
$59$	−4.33789	−	10.0564i	−0.564745	−	1.30923i	0.361524	−	0.932363i	$-0.382256\pi$
$60$	−1.03470	+	8.39613i	−0.133579	+	1.08394i
$61$	−0.185066	+	3.17746i	−0.0236953	+	0.406832i	0.965517	+	0.260341i	$0.0838350\pi$
$61$	−0.185066	+	3.17746i	−0.0236953	+	0.406832i	−0.989212	+	0.146491i	$0.953202\pi$
$62$	−2.03694	+	8.08980i	−0.258692	+	1.02741i
$63$	5.63146	+	7.80425i	0.709497	+	0.983243i
$64$	2.04315	−	7.73470i	0.255394	−	0.966837i
$65$	−1.86811	−	15.9827i	−0.231711	−	1.98241i
$66$	−3.90756	−	8.87049i	−0.480987	−	1.09188i
$67$	1.14811	+	0.343723i	0.140264	+	0.0419924i	0.356166	−	0.934423i	$-0.384084\pi$
$67$	1.14811	+	0.343723i	0.140264	+	0.0419924i	−0.215901	+	0.976415i	$0.569269\pi$
$68$	−0.00774856	−	0.0873774i	−0.000939650	−	0.0105961i
$69$	3.36089	−	8.27972i	0.404603	−	0.996761i
$70$	−9.83035	−	5.10998i	−1.17495	−	0.610759i
$71$	−11.5777	+	9.71483i	−1.37402	+	1.15294i	−0.402651	+	0.915353i	$0.631911\pi$
$71$	−11.5777	+	9.71483i	−1.37402	+	1.15294i	−0.971367	+	0.237585i	$0.923644\pi$
$72$	−5.81412	+	6.18029i	−0.685200	+	0.728355i
$73$	−6.54463	−	5.49160i	−0.765991	−	0.642743i	0.173688	−	0.984801i	$-0.444432\pi$
$73$	−6.54463	−	5.49160i	−0.765991	−	0.642743i	−0.939679	+	0.342058i	$0.888876\pi$
$74$	−2.62548	−	6.32789i	−0.305206	−	0.735602i
$75$	−0.254228	+	1.64987i	−0.0293558	+	0.190511i
$76$	2.35733	−	8.83945i	0.270405	−	1.01395i
$77$	12.6730	−	0.738116i	1.44422	−	0.0841162i
$78$	7.96240	−	14.0396i	0.901564	−	1.58967i
$79$	1.32576	+	1.25079i	0.149159	+	0.140724i	0.757204	−	0.653178i	$-0.226565\pi$
$79$	1.32576	+	1.25079i	0.149159	+	0.140724i	−0.608045	+	0.793902i	$0.708046\pi$
$80$	2.77948	−	9.36457i	0.310755	−	1.04699i
$81$	8.54512	−	2.82507i	0.949457	−	0.313896i
$82$	1.90241	+	0.137462i	0.210086	+	0.0151801i
$83$	5.72637	−	6.06959i	0.628550	−	0.666225i	−0.332338	−	0.943160i	$-0.607837\pi$
$83$	5.72637	−	6.06959i	0.628550	−	0.666225i	0.960888	+	0.276936i	$0.0893189\pi$
$84$	−4.92511	−	9.96174i	−0.537373	−	1.08691i
$85$	−0.00622792	−	0.106929i	−0.000675512	−	0.0115981i
$86$	−2.18261	−	0.416335i	−0.235357	−	0.0448945i
$87$	0.775070	+	1.99410i	0.0830963	+	0.213790i
$88$	2.75852	+	10.8473i	0.294060	+	1.15632i
$89$	1.91594	−	2.28333i	0.203089	−	0.242032i	−0.654881	−	0.755732i	$-0.727281\pi$
$89$	1.91594	−	2.28333i	0.203089	−	0.242032i	0.857970	+	0.513700i	$0.171726\pi$
$90$	−7.32444	+	7.32809i	−0.772064	+	0.772449i
$91$	13.5873	+	16.1927i	1.42434	+	1.69746i
$92$	−5.40645	+	8.78841i	−0.563661	+	0.916255i
$93$	−8.06147	+	6.27724i	−0.835935	+	0.650919i
$94$	1.56157	+	9.64087i	0.161063	+	0.994380i
$95$	3.20376	−	10.7013i	0.328699	−	1.09793i
$96$	7.79994	−	5.92966i	0.796078	−	0.605193i
$97$	17.9553	−	2.09867i	1.82308	−	0.213087i	0.865431	−	0.501027i	$-0.167044\pi$
$97$	17.9553	−	2.09867i	1.82308	−	0.213087i	0.957649	+	0.287940i	$0.0929703\pi$
$98$	4.62990	−	0.475773i	0.467690	−	0.0480603i
$99$	2.90939	−	11.5094i	0.292405	−	1.15674i
$100$	0.604153	−	1.83047i	0.0604153	−	0.183047i
$101$	−5.65398	−	0.329307i	−0.562592	−	0.0327672i	−0.225507	−	0.974242i	$-0.572404\pi$
$101$	−5.65398	−	0.329307i	−0.562592	−	0.0327672i	−0.337085	+	0.941474i	$0.609441\pi$
$102$	0.0583443	−	0.0902121i	0.00577695	−	0.00893233i
$103$	−11.4395	+	4.93452i	−1.12717	+	0.486212i	−0.876279	−	0.481804i	$-0.839982\pi$
$103$	−11.4395	+	4.93452i	−1.12717	+	0.486212i	−0.250888	+	0.968016i	$0.580723\pi$
$104$	−11.7452	+	14.4705i	−1.15172	+	1.41895i
$105$	−5.64288	−	12.3402i	−0.550688	−	1.20428i
$106$	13.2902	+	4.18174i	1.29085	+	0.406167i
$107$	3.52738	−	6.10960i	0.341005	−	0.590638i	−0.643615	−	0.765350i	$-0.722566\pi$
$107$	3.52738	−	6.10960i	0.341005	−	0.590638i	0.984620	+	0.174712i	$0.0558994\pi$
$108$	−10.2703	+	1.58778i	−0.988260	+	0.152785i
$109$	−6.52977	−	11.3099i	−0.625438	−	1.08329i	−0.988456	−	0.151509i	$-0.951587\pi$
$109$	−6.52977	−	11.3099i	−0.625438	−	1.08329i	0.363018	−	0.931782i	$-0.381746\pi$
$110$	2.96587	+	13.3409i	0.282785	+	1.27200i
$111$	2.23192	−	8.08836i	0.211845	−	0.767713i
$112$	3.70926	+	12.2841i	0.350492	+	1.16074i
$113$	10.4405	+	7.77270i	0.982164	+	0.731194i	0.963244	−	0.268627i	$-0.0865700\pi$
$113$	10.4405	+	7.77270i	0.982164	+	0.731194i	0.0189195	+	0.999821i	$0.493977\pi$
$114$	8.93560	−	6.75976i	0.836896	−	0.633109i
$115$	−6.92327	+	10.5263i	−0.645598	+	0.981584i
$116$	−0.502416	−	2.41877i	−0.0466482	−	0.224577i
$117$	18.2656	−	7.55856i	1.68866	−	0.698789i
$118$	−6.33254	+	14.1348i	−0.582958	+	1.30122i
$119$	0.0840215	+	0.112860i	0.00770223	+	0.0103459i
$120$	9.73885	−	6.94881i	0.889031	−	0.634337i
$121$	−3.19727	−	3.38890i	−0.290661	−	0.308082i
$122$	3.48817	−	2.84494i	0.315804	−	0.257568i
$123$	1.73347	+	1.56593i	0.156302	+	0.141195i
$124$	10.3778	−	5.61150i	0.931955	−	0.503928i
$125$	−3.37121	+	9.26233i	−0.301530	+	0.828448i
$126$	2.74891	−	13.3298i	0.244893	−	1.18751i
$127$	−7.08474	−	19.4652i	−0.628669	−	1.72725i	−0.684699	−	0.728825i	$-0.740067\pi$
$127$	−7.08474	−	19.4652i	−0.628669	−	1.72725i	0.0560302	−	0.998429i	$-0.482156\pi$
$128$	−10.0137	+	5.26554i	−0.885094	+	0.465412i
$129$	−1.79395	−	2.04632i	−0.157949	−	0.180168i
$130$	−14.8697	+	17.2270i	−1.30416	+	1.51091i
$131$	−10.7598	+	7.07682i	−0.940087	+	0.618305i	−0.924340	−	0.381571i	$-0.875383\pi$
$131$	−10.7598	+	7.07682i	−0.940087	+	0.618305i	−0.0157476	+	0.999876i	$0.505013\pi$
$132$	−5.50817	+	12.5527i	−0.479424	+	1.09257i
$133$	4.20851	+	14.0574i	0.364924	+	1.21893i
$134$	−0.739454	−	1.52507i	−0.0638791	−	0.131746i
$135$	−12.5934	+	1.55832i	−1.08387	+	0.134119i
$136$	−0.0836483	+	0.0916115i	−0.00717278	+	0.00785562i
$137$	1.40758	−	5.93904i	0.120258	−	0.507406i	−0.879260	−	0.476342i	$-0.841962\pi$
$137$	1.40758	−	5.93904i	0.120258	−	0.507406i	0.999517	−	0.0310640i	$-0.00988958\pi$
$138$	−11.8415	+	4.41339i	−1.00801	+	0.375693i
$139$	−0.423999	+	0.844251i	−0.0359631	+	0.0716084i	−0.910897	−	0.412635i	$-0.864609\pi$
$139$	−0.423999	+	0.844251i	−0.0359631	+	0.0716084i	0.874934	+	0.484243i	$0.160905\pi$
$140$	4.07313	+	15.1296i	0.344242	+	1.27869i
$141$	−5.75514	+	10.4860i	−0.484670	+	0.883079i
$142$	21.1926	+	2.77733i	1.77845	+	0.233068i
$143$	4.52783	−	25.6786i	0.378636	−	2.14735i
$144$	11.9991	+	0.150275i	0.999922	+	0.0125229i
$145$	−0.523804	−	2.97064i	−0.0434996	−	0.246698i
$146$	0.534148	+	12.0704i	0.0442064	+	0.998953i
$147$	4.82922	+	3.02855i	0.398307	+	0.249791i
$148$	−4.08424	+	8.78577i	−0.335723	+	0.722185i
$149$	4.05523	+	17.1104i	0.332218	+	1.40174i	0.841090	+	0.540895i	$0.181914\pi$
$149$	4.05523	+	17.1104i	0.332218	+	1.40174i	−0.508873	+	0.860842i	$0.669938\pi$
$150$	1.96239	−	1.31242i	0.160229	−	0.107159i
$151$	−15.0417	−	6.48836i	−1.22408	−	0.528015i	−0.316778	−	0.948500i	$-0.602601\pi$
$151$	−15.0417	−	6.48836i	−1.22408	−	0.528015i	−0.907300	+	0.420484i	$0.861860\pi$
$152$	−11.4653	+	5.99432i	−0.929961	+	0.486204i
$153$	0.124301	−	0.0431577i	0.0100492	−	0.00348909i
$154$	−12.8851	−	12.5009i	−1.03831	−	1.00735i
$155$	12.8733	−	6.46523i	1.03401	−	0.519300i
$156$	−22.2431	+	5.12482i	−1.78087	+	0.410314i
$157$	4.75036	+	0.555237i	0.379120	+	0.0443127i	0.303519	−	0.952825i	$-0.401838\pi$
$157$	4.75036	+	0.555237i	0.379120	+	0.0443127i	0.0756008	+	0.997138i	$0.475913\pi$
$158$	0.0359665	−	2.57738i	0.00286134	−	0.205045i
$159$	9.68308	+	14.0503i	0.767918	+	1.11426i
$160$	−12.4162	+	6.05645i	−0.981583	+	0.478804i
$161$		−	16.5503i		−	1.30434i
$162$	−11.1135	−	6.20400i	−0.873161	−	0.487432i
$163$			2.37358i			0.185913i	0.995670	+	0.0929567i	$0.0296318\pi$
$163$			2.37358i			0.185913i	−0.995670	+	0.0929567i	$0.970368\pi$
$164$	−1.67554	−	2.11392i	−0.130837	−	0.165070i
$165$	−7.18653	+	15.1168i	−0.559470	+	1.17684i
$166$	−11.7998	−	0.164662i	−0.915842	−	0.0127803i
$167$	14.8779	+	1.73898i	1.15129	+	0.134566i	0.670251	−	0.742135i	$-0.266187\pi$
$167$	14.8779	+	1.73898i	1.15129	+	0.134566i	0.481036	+	0.876701i	$0.340261\pi$
$168$	−5.67254	+	14.6563i	−0.437646	+	1.13076i
$169$	27.1827	−	13.6517i	2.09098	−	1.05013i
$170$	−0.105477	+	0.108719i	−0.00808972	+	0.00833838i
$171$	13.7211	+	0.204266i	1.04928	+	0.0156206i
$172$	1.65281	+	2.67254i	0.126025	+	0.203779i
$173$	3.66361	+	1.58033i	0.278539	+	0.120150i	0.530767	−	0.847518i	$-0.321904\pi$
$173$	3.66361	+	1.58033i	0.278539	+	0.120150i	−0.252228	+	0.967668i	$0.581163\pi$
$174$	1.33705	−	2.71415i	0.101362	−	0.205759i
$175$	0.713026	+	3.00849i	0.0538997	+	0.227421i
$176$	8.66671	−	13.2451i	0.653277	−	0.998390i
$177$	−16.7635	+	8.87841i	−1.26002	+	0.667343i
$178$	−4.21119	+	0.186357i	−0.315642	+	0.0139680i
$179$	3.08085	+	17.4724i	0.230273	+	1.30595i	0.852343	+	0.522983i	$0.175181\pi$
$179$	3.08085	+	17.4724i	0.230273	+	1.30595i	−0.622069	+	0.782962i	$0.713708\pi$
$180$	14.6391	+	0.626840i	1.09114	+	0.0467219i
$181$	−3.04539	+	17.2712i	−0.226362	+	1.28376i	0.633703	+	0.773576i	$0.281534\pi$
$181$	−3.04539	+	17.2712i	−0.226362	+	1.28376i	−0.860065	+	0.510185i	$0.829577\pi$
$182$	3.88442	−	29.6404i	0.287932	−	2.19709i
$183$	5.51156	−	0.119321i	0.407426	−	0.00882047i
$184$	14.3272	−	2.76803i	1.05622	−	0.204062i
$185$	−5.30944	+	10.5720i	−0.390358	+	0.777266i
$186$	14.2486	+	2.39956i	1.04476	+	0.175944i
$187$	0.0400260	−	0.168883i	0.00292699	−	0.0123500i
$188$	8.55385	−	10.8444i	0.623854	−	0.790911i
$189$	12.6966	−	10.8008i	0.923538	−	0.785640i
$190$	−14.2148	+	6.89227i	−1.03125	+	0.500018i
$191$	0.665145	+	2.22174i	0.0481282	+	0.160759i	0.978676	−	0.205412i	$-0.0658535\pi$
$191$	0.665145	+	2.22174i	0.0481282	+	0.160759i	−0.930547	+	0.366172i	$0.880668\pi$
$192$	−13.6364	−	2.45933i	−0.984123	−	0.177487i
$193$	−9.33270	+	6.13821i	−0.671782	+	0.441838i	−0.839036	−	0.544076i	$-0.816880\pi$
$193$	−9.33270	+	6.13821i	−0.671782	+	0.441838i	0.167254	+	0.985914i	$0.446510\pi$
$194$	−19.3531	−	16.7048i	−1.38947	−	1.19934i
$195$	−27.3368	+	5.43277i	−1.95763	+	0.389048i
$196$	−4.92219	−	4.36997i	−0.351585	−	0.312141i
$197$	−1.65484	−	4.54665i	−0.117903	−	0.323935i	0.866677	−	0.498869i	$-0.166251\pi$
$197$	−1.65484	−	4.54665i	−0.117903	−	0.323935i	−0.984580	+	0.174934i	$0.944029\pi$
$198$	−14.7755	+	7.97165i	−1.05005	+	0.566521i
$199$	−8.01569	+	22.0229i	−0.568217	+	1.56116i	0.239069	+	0.971003i	$0.423158\pi$
$199$	−8.01569	+	22.0229i	−0.568217	+	1.56116i	−0.807286	+	0.590161i	$0.799064\pi$
$200$	−2.48514	+	1.12042i	−0.175726	+	0.0792258i
$201$	0.434882	−	2.02973i	0.0306742	−	0.143166i
$202$	5.06228	+	6.20686i	0.356181	+	0.436713i
$203$	2.71922	+	2.88221i	0.190852	+	0.202291i
$204$	−0.149790	+	0.0254460i	−0.0104874	+	0.00178158i
$205$	−1.96685	−	2.64193i	−0.137370	−	0.184520i
$206$	16.0789	+	7.20352i	1.12027	+	0.501893i
$207$	−14.7594	−	4.65917i	−1.02585	−	0.323834i
$208$	26.3087	−	1.59469i	1.82418	−	0.110572i
$209$	9.94655	−	15.1230i	0.688017	−	1.04608i
$210$	−7.46488	+	17.6782i	−0.515125	+	1.21991i
$211$	11.8542	+	8.82513i	0.816077	+	0.607547i	0.922159	−	0.386810i	$-0.126423\pi$
$211$	11.8542	+	8.82513i	0.816077	+	0.607547i	−0.106082	+	0.994357i	$0.533831\pi$
$212$	−8.34818	−	17.8476i	−0.573355	−	1.22578i
$213$	18.3720	+	18.6476i	1.25883	+	1.27771i
$214$	−9.73917	+	2.16516i	−0.665756	+	0.148007i
$215$	1.91846	+	3.32287i	0.130838	+	0.226618i
$216$	11.4735	+	9.18471i	0.780672	+	0.624941i
$217$	−9.46174	+	16.3882i	−0.642305	+	1.11250i
$218$	−5.54332	+	17.6174i	−0.375441	+	1.19320i
$219$	−8.57755	+	12.0580i	−0.579617	+	0.814804i
$220$	11.0671	−	15.8452i	0.746141	−	1.06828i
$221$	0.265370	−	0.114469i	0.0178507	−	0.00770004i
$222$	−10.5627	+	5.40694i	−0.708923	+	0.362890i
$223$	2.97643	+	0.173357i	0.199316	+	0.0116088i	0.157512	−	0.987517i	$-0.449653\pi$
$223$	2.97643	+	0.173357i	0.199316	+	0.0116088i	0.0418037	+	0.999126i	$0.486690\pi$
$224$	9.25506	−	15.6096i	0.618380	−	1.04296i
$225$	2.88368	+	0.211067i	0.192245	+	0.0140712i
$226$	−1.88167	−	18.3112i	−0.125167	−	1.21804i
$227$	7.27305	−	0.850097i	0.482729	−	0.0564229i	0.128752	−	0.991677i	$-0.458903\pi$
$227$	7.27305	−	0.850097i	0.482729	−	0.0564229i	0.353978	+	0.935254i	$0.384829\pi$
$228$	−15.5872	−	2.84919i	−1.03229	−	0.188692i
$229$	2.24530	−	7.49983i	0.148374	−	0.495603i	−0.851199	−	0.524844i	$-0.824124\pi$
$229$	2.24530	−	7.49983i	0.148374	−	0.495603i	0.999572	+	0.0292409i	$0.00930898\pi$
$230$	17.5885	−	2.84887i	1.15975	−	0.187849i
$231$	−3.02467	−	21.7784i	−0.199009	−	1.43291i
$232$	−2.04028	+	2.83602i	−0.133951	+	0.186194i
$233$	−5.32136	−	6.34175i	−0.348614	−	0.415462i	0.563034	−	0.826434i	$-0.309634\pi$
$233$	−5.32136	−	6.34175i	−0.348614	−	0.415462i	−0.911648	+	0.410972i	$0.865189\pi$
$234$	−25.3395	−	11.8083i	−1.65650	−	0.771935i
$235$	10.8406	−	12.9193i	0.707164	−	0.842765i
$236$	20.7842	−	6.91438i	1.35293	−	0.450088i
$237$	1.97642	−	2.46171i	0.128383	−	0.159905i
$238$	0.0372839	−	0.195459i	0.00241676	−	0.0126697i
$239$	1.12133	+	19.2525i	0.0725328	+	1.24534i	0.816587	+	0.577222i	$0.195863\pi$
$239$	1.12133	+	19.2525i	0.0725328	+	1.24534i	−0.744054	+	0.668119i	$0.767100\pi$
$240$	−16.5521	−	3.50551i	−1.06844	−	0.226280i
$241$	16.0114	−	16.9711i	1.03138	−	1.09320i	0.0357962	−	0.999359i	$-0.488603\pi$
$241$	16.0114	−	16.9711i	1.03138	−	1.09320i	0.995587	−	0.0938432i	$-0.0299152\pi$
$242$	−0.474859	+	6.57182i	−0.0305251	+	0.422453i
$243$	−6.05776	−	14.3633i	−0.388605	−	0.921404i
$244$	−6.29957	−	0.915150i	−0.403288	−	0.0585865i
$245$	−5.84597	−	5.51539i	−0.373485	−	0.352365i
$246$	−0.0254118	−	3.30356i	−0.00162020	−	0.210627i
$247$	30.0895	−	1.75251i	1.91455	−	0.111510i
$248$	−15.7694	−	5.44990i	−1.00136	−	0.346069i
$249$	−11.2702	−	9.04849i	−0.714223	−	0.573425i
$250$	12.8753	−	5.34205i	0.814307	−	0.337861i
$251$	−11.5892	−	9.72449i	−0.731504	−	0.613804i	0.199038	−	0.979992i	$-0.436218\pi$
$251$	−11.5892	−	9.72449i	−0.731504	−	0.613804i	−0.930541	+	0.366188i	$0.880663\pi$
$252$	−16.5191	+	9.87920i	−1.04060	+	0.622331i
$253$	−15.6391	+	13.1228i	−0.983223	+	0.825022i
$254$	−13.5114	+	25.9926i	−0.847780	+	1.63092i
$255$	−0.183757	+	0.0255209i	−0.0115073	+	0.00159818i
$256$	15.0608	+	5.40122i	0.941298	+	0.337576i
$257$	−7.28722	−	2.18165i	−0.454564	−	0.136088i	0.0513326	−	0.998682i	$-0.483653\pi$
$257$	−7.28722	−	2.18165i	−0.454564	−	0.136088i	−0.505897	+	0.862594i	$0.668838\pi$
$258$	−0.417373	+	3.82585i	−0.0259845	+	0.238187i
$259$	−1.80414	−	15.4354i	−0.112104	−	0.959111i
$260$	32.1683	−	0.974038i	1.99500	−	0.0604073i
$261$	3.33583	−	1.61359i	0.206483	−	0.0998790i
$262$	17.6616	+	4.44705i	1.09114	+	0.274740i
$263$	−0.544710	+	9.35231i	−0.0335883	+	0.576688i	0.938966	+	0.344011i	$0.111786\pi$
$263$	−0.544710	+	9.35231i	−0.0335883	+	0.576688i	−0.972554	+	0.232677i	$0.925251\pi$
$264$	18.3472	−	6.26082i	1.12919	−	0.385327i
$265$	−9.52926	−	22.0913i	−0.585378	−	1.35706i
$266$	10.6257	−	17.8252i	0.651506	−	1.09293i
$267$	−4.20686	−	2.99258i	−0.257456	−	0.183143i
$268$	−0.882327	+	2.22862i	−0.0538967	+	0.136135i
$269$	1.61221	+	0.930808i	0.0982980	+	0.0567524i	0.548343	−	0.836253i	$-0.315259\pi$
$269$	1.61221	+	0.930808i	0.0982980	+	0.0567524i	−0.450045	+	0.893006i	$0.648592\pi$
$270$	13.6638	+	11.6338i	0.831552	+	0.708011i
$271$	3.03568	−	1.75265i	0.184404	−	0.106466i	−0.404956	−	0.914336i	$-0.632713\pi$
$271$	3.03568	−	1.75265i	0.184404	−	0.106466i	0.589360	+	0.807870i	$0.299380\pi$
$272$	0.175440		0.000414506i	0.0106376		2.51331e-5i
$273$	26.0808	−	25.6954i	1.57848	−	1.55516i
$274$	−7.53480	+	4.21115i	−0.455194	+	0.254405i
$275$	2.27750	−	3.05922i	0.137339	−	0.184478i
$276$	15.9202	+	8.12064i	0.958283	+	0.488805i
$277$	−12.8197	−	8.43165i	−0.770261	−	0.506609i	0.102514	−	0.994732i	$-0.467311\pi$
$277$	−12.8197	−	8.43165i	−0.770261	−	0.506609i	−0.872775	+	0.488123i	$0.837682\pi$
$278$	1.28516	−	0.365291i	0.0770787	−	0.0219087i
$279$	11.9513	+	13.0514i	0.715503	+	0.781370i
$280$	11.8725	−	18.7092i	0.709519	−	1.11809i
$281$	−13.3962	+	9.97313i	−0.799153	+	0.594947i	−0.917368	−	0.398041i	$-0.869690\pi$
$281$	−13.3962	+	9.97313i	−0.799153	+	0.594947i	0.118215	+	0.992988i	$0.462283\pi$
$282$	16.4296	−	4.02762i	0.978371	−	0.239841i
$283$	−19.4859	+	18.3840i	−1.15832	+	1.09281i	−0.163987	+	0.986463i	$0.552435\pi$
$283$	−19.4859	+	18.3840i	−1.15832	+	1.09281i	−0.994329	+	0.106352i	$0.966083\pi$
$284$	−17.3668	−	24.7402i	−1.03053	−	1.46806i
$285$	−18.9187	−	4.05343i	−1.12064	−	0.240104i
$286$	−31.0885	+	19.8314i	−1.83830	+	1.17266i
$287$	4.06570	+	1.47979i	0.239991	+	0.0873494i
$288$	−11.3150	−	12.6479i	−0.666745	−	0.745286i
$289$	−15.9730	+	5.81368i	−0.939586	+	0.341981i
$290$	−2.59494	+	3.38592i	−0.152380	+	0.198828i
$291$	−6.10325	−	30.7105i	−0.357779	−	1.80028i
$292$	12.0679	−	12.0965i	0.706222	−	0.707893i
$293$	2.27945	+	3.46574i	0.133167	+	0.202471i	0.895915	−	0.444225i	$-0.146521\pi$
$293$	2.27945	+	3.46574i	0.133167	+	0.202471i	−0.762748	+	0.646695i	$0.776150\pi$
$294$	−1.46088	−	7.92798i	−0.0852004	−	0.462369i
$295$	25.6223	−	7.67081i	1.49179	−	0.446612i
$296$	13.0604	−	4.14338i	0.759120	−	0.240829i
$297$	−20.2733	−	3.43359i	−1.17638	−	0.199237i
$298$	13.9538	−	20.5843i	0.808321	−	1.19241i
$299$	−33.0784	−	7.83972i	−1.91297	−	0.453383i
$300$	−3.24381	−	0.790282i	−0.187282	−	0.0456270i
$301$	−4.50413	−	2.26206i	−0.259614	−	0.130383i
$302$	7.61901	+	21.8782i	0.438425	+	1.25895i
$303$	0.212320	+	9.80727i	0.0121975	+	0.563413i
$304$	17.2081	+	6.21722i	0.986951	+	0.356582i
$305$	−7.65471	−	1.34973i	−0.438307	−	0.0772854i
$306$	−0.163812	−	0.0882742i	−0.00936453	−	0.00504630i
$307$	0.00915717	−	0.00161466i	0.000522628	−	9.21533e-5i	−0.173387	−	0.984854i	$-0.555471\pi$
$307$	0.00915717	−	0.00161466i	0.000522628	−	9.21533e-5i	0.173909	+	0.984762i	$0.444360\pi$
$308$	−0.708448	+	25.3790i	−0.0403676	+	1.44610i
$309$	10.0995	+	19.0692i	0.574543	+	1.08481i
$310$	−19.0449	−	7.23429i	−1.08168	−	0.410880i
$311$	14.1188	−	3.34622i	0.800605	−	0.189747i	0.190106	−	0.981764i	$-0.439117\pi$
$311$	14.1188	−	3.34622i	0.800605	−	0.189747i	0.610499	+	0.792017i	$0.290969\pi$
$312$	26.6060	+	18.2800i	1.50627	+	1.03490i
$313$	−9.42637	+	21.8528i	−0.532810	+	1.23519i	0.413077	+	0.910696i	$0.364454\pi$
$313$	−9.42637	+	21.8528i	−0.532810	+	1.23519i	−0.945887	+	0.324496i	$0.894805\pi$
$314$	−3.96294	−	5.48119i	−0.223642	−	0.309322i
$315$	−20.5264	+	11.4469i	−1.15653	+	0.644962i
$316$	−2.72028	+	2.42661i	−0.153028	+	0.136508i
$317$	−3.56886	−	7.10619i	−0.200447	−	0.399123i	0.770842	−	0.637027i	$-0.219836\pi$
$317$	−3.56886	−	7.10619i	−0.200447	−	0.399123i	−0.971289	+	0.237904i	$0.923540\pi$
$318$	5.38440	−	23.5235i	0.301942	−	1.31913i
$319$	0.567449	−	4.85483i	0.0317710	−	0.271818i
$320$	18.1818	+	7.14868i	1.01640	+	0.399623i
$321$	−11.0356	−	5.24634i	−0.615948	−	0.292822i
$322$	−17.2471	+	15.8228i	−0.961143	+	0.881770i
$323$	0.200625			0.0111631
$324$	4.15981	+	17.5127i	0.231101	+	0.972930i
$325$	6.35070			0.352274
$326$	2.47352	−	2.26925i	0.136996	−	0.125682i
$327$	−18.6251	+	12.8359i	−1.02997	+	0.709827i
$328$	−0.601039	+	3.76709i	−0.0331868	+	0.208002i
$329$	−2.57194	+	22.0044i	−0.141796	+	1.21314i
$330$	22.6239	−	6.96321i	1.24540	−	0.383312i
$331$	4.17737	+	8.31784i	0.229609	+	0.457190i	0.978705	−	0.205272i	$-0.0658080\pi$
$331$	4.17737	+	8.31784i	0.229609	+	0.457190i	−0.749096	+	0.662462i	$0.769512\pi$
$332$	11.1095	+	12.4540i	0.609715	+	0.683504i
$333$	−14.2731	−	2.73640i	−0.782161	−	0.149954i
$334$	−12.4117	−	17.1668i	−0.679140	−	0.939328i
$335$	−1.15923	+	2.68739i	−0.0633353	+	0.146828i
$336$	20.6966	−	8.10074i	1.12909	−	0.441932i
$337$	12.7585	−	3.02382i	0.694999	−	0.164718i	0.132091	−	0.991238i	$-0.457831\pi$
$337$	12.7585	−	3.02382i	0.694999	−	0.164718i	0.562908	+	0.826520i	$0.309683\pi$
$338$	−40.2144	−	15.2756i	−2.18737	−	0.830883i
$339$	11.9779	−	19.0995i	0.650549	−	1.03734i
$340$	0.214137	+	0.00597759i	0.0116132	+	0.000324180i
$341$	22.9882	−	4.05345i	1.24488	−	0.219506i
$342$	−12.9051	−	14.4940i	−0.697826	−	0.783748i
$343$	−11.7174	−	2.06609i	−0.632678	−	0.111558i
$344$	1.20490	−	4.27746i	0.0649640	−	0.230625i
$345$	19.1302	+	10.4995i	1.02994	+	0.565272i
$346$	−1.85571	−	5.32872i	−0.0997636	−	0.286474i
$347$	−11.7054	−	5.87866i	−0.628378	−	0.315583i	0.105957	−	0.994371i	$-0.466209\pi$
$347$	−11.7054	−	5.87866i	−0.628378	−	0.315583i	−0.734335	+	0.678787i	$0.762506\pi$
$348$	−4.10671	+	1.20150i	−0.220143	+	0.0644072i
$349$	10.5756	+	2.50647i	0.566101	+	0.134168i	0.503694	−	0.863882i	$-0.331974\pi$
$349$	10.5756	+	2.50647i	0.566101	+	0.134168i	0.0624074	+	0.998051i	$0.480122\pi$
$350$	2.45347	−	3.61930i	0.131144	−	0.193460i
$351$	−15.5728	−	30.4923i	−0.831215	−	1.62756i
$352$	−22.0886	+	3.63134i	−1.17732	+	0.193551i
$353$	−11.4119	+	3.41651i	−0.607396	+	0.181842i	−0.575708	−	0.817655i	$-0.695274\pi$
$353$	−11.4119	+	3.41651i	−0.607396	+	0.181842i	−0.0316882	+	0.999498i	$0.510088\pi$
$354$	25.2789	+	8.98117i	1.34356	+	0.477344i
$355$	−20.2817	−	30.8368i	−1.07644	−	1.63665i
$356$	4.22029	+	4.21033i	0.223675	+	0.223147i
$357$	0.183253	−	0.160653i	0.00969879	−	0.00850268i
$358$	15.2626	−	19.9149i	0.806652	−	1.05254i
$359$	0.456242	−	0.166059i	0.0240795	−	0.00876424i	−0.329952	−	0.943998i	$-0.607033\pi$
$359$	0.456242	−	0.166059i	0.0240795	−	0.00876424i	0.354032	+	0.935233i	$0.384810\pi$
$360$	−13.3424	−	15.8548i	−0.703207	−	0.835619i
$361$	1.80724	+	0.657782i	0.0951179	+	0.0346201i
$362$	20.9099	−	13.3385i	1.09900	−	0.701054i
$363$	−5.40948	+	5.98824i	−0.283924	+	0.314301i
$364$	−34.6020	+	24.2896i	−1.81364	+	1.27312i
$365$	15.1758	−	14.3176i	0.794335	−	0.749417i
$366$	−5.39364	−	5.62954i	−0.281930	−	0.294261i
$367$	−11.5321	+	8.58531i	−0.601969	+	0.448150i	−0.854509	−	0.519437i	$-0.826142\pi$
$367$	−11.5321	+	8.58531i	−0.601969	+	0.448150i	0.252539	+	0.967587i	$0.418734\pi$
$368$	−16.5820	−	12.2841i	−0.864399	−	0.640352i
$369$	2.46423	−	3.20917i	0.128283	−	0.167063i
$370$	16.0931	−	4.57428i	0.836642	−	0.237806i
$371$	26.4050	+	17.3668i	1.37088	+	0.901640i
$372$	−11.1218	−	17.1426i	−0.576636	−	0.888805i
$373$	8.29281	−	11.1392i	0.429385	−	0.576765i	−0.533797	−	0.845612i	$-0.679235\pi$
$373$	8.29281	−	11.1392i	0.429385	−	0.576765i	0.963183	+	0.268848i	$0.0866429\pi$
$374$	−0.214260	+	0.119749i	−0.0110791	+	0.00619205i
$375$	16.4573	+	4.54128i	0.849854	+	0.234511i
$376$	−19.4789	+	1.45375i	−1.00455	+	0.0749714i
$377$	7.04862	−	4.06952i	0.363023	−	0.209591i
$378$	−23.3940	−	2.90510i	−1.20326	−	0.149422i
$379$	28.3794	+	16.3849i	1.45775	+	0.841634i	0.998901	−	0.0468784i	$-0.0149273\pi$
$379$	28.3794	+	16.3849i	1.45775	+	0.841634i	0.458852	+	0.888513i	$0.348261\pi$
$380$	20.7724	+	8.22396i	1.06560	+	0.421880i
$381$	−32.6288	+	14.9204i	−1.67163	+	0.764397i
$382$	1.67937	−	2.81723i	0.0859242	−	0.144142i
$383$	−3.62436	−	8.40221i	−0.185196	−	0.429333i	0.800172	−	0.599770i	$-0.204741\pi$
$383$	−3.62436	−	8.40221i	−0.185196	−	0.429333i	−0.985369	+	0.170437i	$0.945482\pi$
$384$	10.4741	+	16.5618i	0.534506	+	0.845164i
$385$	−1.80255	+	30.9485i	−0.0918662	+	1.57728i
$386$	15.3191	+	3.85723i	0.779723	+	0.196328i
$387$	−3.28527	+	3.37994i	−0.167000	+	0.171812i
$388$	1.09425	+	36.1384i	0.0555521	+	1.83465i
$389$	−0.350109	−	2.99537i	−0.0177512	−	0.151871i	0.981456	−	0.191689i	$-0.0613964\pi$
$389$	−0.350109	−	2.99537i	−0.0177512	−	0.151871i	−0.999207	+	0.0398175i	$0.987322\pi$
$390$	31.7967	+	23.2937i	1.61009	+	1.17952i
$391$	−0.216773	−	0.0648977i	−0.0109627	−	0.00328202i
$392$	0.151876	+	9.30732i	0.00767087	+	0.470091i
$393$	13.7044	+	17.5998i	0.691298	+	0.887791i
$394$	−3.15597	+	6.07132i	−0.158996	+	0.305869i
$395$	−3.40974	+	2.86111i	−0.171563	+	0.143958i
$396$	22.4334	+	7.77638i	1.12732	+	0.390778i
$397$	3.50581	+	2.94172i	0.175952	+	0.147641i	0.726510	−	0.687155i	$-0.241141\pi$
$397$	3.50581	+	2.94172i	0.175952	+	0.147641i	−0.550559	+	0.834796i	$0.685585\pi$
$398$	30.6135	−	12.7017i	1.53452	−	0.636680i
$399$	23.6894	−	9.20764i	1.18595	−	0.460959i
$400$	3.54349	+	1.51859i	0.177175	+	0.0759297i
$401$	1.47771	−	0.0860670i	0.0737935	−	0.00429798i	−0.0212083	−	0.999775i	$-0.506751\pi$
$401$	1.47771	−	0.0860670i	0.0737935	−	0.00429798i	0.0950019	+	0.995477i	$0.469714\pi$
$402$	−2.53096	+	1.48732i	−0.126233	+	0.0741809i
$403$	28.2725	+	26.6737i	1.40835	+	1.32871i
$404$	1.62842	−	11.2095i	0.0810169	−	0.557691i
$405$	4.42980	+	21.5278i	0.220118	+	1.06972i
$406$	0.403860	−	5.58923i	0.0200432	−	0.277389i
$407$	−13.1551	+	13.9436i	−0.652076	+	0.691160i
$408$	0.169723	+	0.131769i	0.00840256	+	0.00652355i
$409$	−1.33743	−	22.9628i	−0.0661318	−	1.13544i	−0.854232	−	0.519892i	$-0.825972\pi$
$409$	−1.33743	−	22.9628i	−0.0661318	−	1.13544i	0.788100	−	0.615547i	$-0.211065\pi$
$410$	−0.872773	+	4.57546i	−0.0431032	+	0.225966i
$411$	−10.4484	−	1.60998i	−0.515380	−	0.0794146i
$412$	−7.86538	−	23.6428i	−0.387499	−	1.16480i
$413$	−22.5836	+	26.9141i	−1.11127	+	1.32436i
$414$	9.25532	+	19.8352i	0.454874	+	0.974847i
$415$	13.0988	+	15.6105i	0.642994	+	0.766291i
$416$	−26.8141	−	25.8918i	−1.31467	−	1.26945i
$417$	1.51619	+	0.615448i	0.0742481	+	0.0301386i
$418$	−25.2691	+	4.09293i	−1.23595	+	0.200192i
$419$	3.81061	−	12.7283i	0.186160	−	0.621819i	−0.813054	−	0.582188i	$-0.802197\pi$
$419$	3.81061	−	12.7283i	0.186160	−	0.621819i	0.999214	−	0.0396309i	$-0.0126182\pi$
$420$	25.5593	−	9.12198i	1.24716	−	0.445107i
$421$	3.78364	−	0.442244i	0.184403	−	0.0215536i	−0.0233900	−	0.999726i	$-0.507446\pi$
$421$	3.78364	−	0.442244i	0.184403	−	0.0215536i	0.207793	+	0.978173i	$0.433372\pi$
$422$	−2.13645	−	20.7905i	−0.104001	−	1.01207i
$423$	18.8993	+	8.48821i	0.918914	+	0.412711i
$424$	−10.6179	+	25.7628i	−0.515649	+	1.25115i
$425$	0.0422008	+	0.00245792i	0.00204704	+	0.000119226i
$426$	1.86821	−	36.9734i	0.0905151	−	1.79137i
$427$	9.37542	−	4.04416i	0.453709	−	0.195711i
$428$	11.5674	+	8.07923i	0.559131	+	0.390524i
$429$	−44.9603	−	4.27094i	−2.17071	−	0.206203i
$430$	1.62864	−	5.17605i	0.0785401	−	0.249611i
$431$	−13.7184	+	23.7610i	−0.660793	+	1.14453i	0.319615	+	0.947547i	$0.396446\pi$
$431$	−13.7184	+	23.7610i	−0.660793	+	1.14453i	−0.980408	+	0.196979i	$0.936887\pi$
$432$	−1.39775	−	20.7376i	−0.0672495	−	0.997736i
$433$	4.47373	+	7.74873i	0.214994	+	0.372380i	0.953271	−	0.302118i	$-0.0976935\pi$
$433$	4.47373	+	7.74873i	0.214994	+	0.372380i	−0.738277	+	0.674498i	$0.764360\pi$
$434$	26.1241	−	5.80776i	1.25399	−	0.278781i
$435$	−5.05658	+	1.31465i	−0.242444	+	0.0630325i
$436$	23.6589	−	11.0664i	1.13305	−	0.529982i
$437$	−18.9291	−	14.0922i	−0.905502	−	0.674122i
$438$	20.7662	−	2.58929i	0.992247	−	0.123721i
$439$	18.3003	−	27.8243i	0.873427	−	1.32798i	−0.0703927	−	0.997519i	$-0.522425\pi$
$439$	18.3003	−	27.8243i	0.873427	−	1.32798i	0.943819	−	0.330462i	$-0.107204\pi$
$440$	−27.0930	+	3.61571i	−1.29161	+	0.172372i
$441$	4.56194	−	8.75610i	0.217235	−	0.416957i
$442$	−0.372994	−	0.167105i	−0.0177415	−	0.00794836i
$443$	3.19745	+	4.29493i	0.151916	+	0.204058i	0.871566	−	0.490279i	$-0.163105\pi$
$443$	3.19745	+	4.29493i	0.151916	+	0.204058i	−0.719650	+	0.694337i	$0.755698\pi$
$444$	15.7330	+	5.83817i	0.746656	+	0.277067i
$445$	4.99520	+	5.29460i	0.236795	+	0.250988i
$446$	−2.66494	−	3.26748i	−0.126189	−	0.154720i
$447$	28.9816	−	9.36465i	1.37078	−	0.442933i
$448$	−25.1150	+	5.27870i	−1.18657	+	0.249395i
$449$	−5.73466	+	15.7558i	−0.270635	+	0.743565i	0.727700	+	0.685895i	$0.240589\pi$
$449$	−5.73466	+	15.7558i	−0.270635	+	0.743565i	−0.998336	+	0.0576694i	$0.981633\pi$
$450$	−2.53697	−	3.20688i	−0.119594	−	0.151174i
$451$	−1.82538	−	5.01520i	−0.0859539	−	0.236157i
$452$	−17.2832	+	19.4672i	−0.812931	+	0.915660i
$453$	−9.12495	+	26.8662i	−0.428728	+	1.26228i
$454$	−7.83925	−	6.76653i	−0.367914	−	0.317569i
$455$	−43.1289	+	28.3663i	−2.02191	+	1.32983i
$456$	11.9329	+	18.9674i	0.558809	+	0.888231i
$457$	−6.43068	−	21.4800i	−0.300814	−	1.00479i	−0.966093	−	0.258195i	$-0.916872\pi$
$457$	−6.43068	−	21.4800i	−0.300814	−	1.00479i	0.665278	−	0.746595i	$-0.268313\pi$
$458$	−9.96221	+	4.83034i	−0.465503	+	0.225707i
$459$	−0.0916807	−	0.208650i	−0.00427929	−	0.00973896i
$460$	−19.7842	−	15.6053i	−0.922442	−	0.727603i
$461$	4.15296	−	17.5227i	0.193423	−	0.816115i	−0.786637	−	0.617415i	$-0.788180\pi$
$461$	4.15296	−	17.5227i	0.193423	−	0.816115i	0.980060	−	0.198700i	$-0.0636720\pi$
$462$	−19.8036	+	23.9731i	−0.921347	+	1.11533i
$463$	4.62177	−	9.20270i	0.214792	−	0.427686i	−0.760274	−	0.649603i	$-0.774935\pi$
$463$	4.62177	−	9.20270i	0.214792	−	0.427686i	0.975066	+	0.221917i	$0.0712314\pi$
$464$	4.90603	−	0.585185i	0.227756	−	0.0271665i
$465$	−12.9404	−	21.3334i	−0.600097	−	0.989311i
$466$	−1.52130	+	11.6084i	−0.0704728	+	0.537748i
$467$	−1.49638	+	8.48642i	−0.0692444	+	0.392705i	0.930413	+	0.366514i	$0.119449\pi$
$467$	−1.49638	+	8.48642i	−0.0692444	+	0.392705i	−0.999657	+	0.0261906i	$0.991662\pi$
$468$	11.9202	+	37.6957i	0.551012	+	1.74248i
$469$	−0.667613	−	3.78622i	−0.0308275	−	0.174832i
$470$	−23.8274	+	1.05443i	−1.09908	+	0.0486371i
$471$	0.302557	−	8.27834i	0.0139411	−	0.381446i
$472$	−27.0761	−	15.0488i	−1.24628	−	0.692676i
$473$	1.43382	+	6.04976i	0.0659270	+	0.278168i
$474$	−4.45491	+	0.293869i	−0.204621	+	0.0134978i
$475$	4.04804	+	1.74615i	0.185737	+	0.0801191i
$476$	−0.239333	+	0.148013i	−0.0109698	+	0.00678418i
$477$	22.9210	−	18.6587i	1.04948	−	0.854323i
$478$	18.9911	−	19.5748i	0.868630	−	0.895330i
$479$	−31.5489	+	15.8444i	−1.44151	+	0.723951i	−0.986072	−	0.166318i	$-0.946812\pi$
$479$	−31.5489	+	15.8444i	−1.44151	+	0.723951i	−0.455434	+	0.890270i	$0.650516\pi$
$480$	12.1715	+	20.6005i	0.555550	+	0.940279i
$481$	−31.7048	−	3.70576i	−1.44561	−	0.168968i
$482$	−32.9932	−	0.460408i	−1.50280	−	0.0209710i
$483$	−28.5746	+	2.28579i	−1.30019	+	0.104007i
$484$	7.30250	−	5.78811i	0.331932	−	0.263096i
$485$			44.1468i			2.00460i
$486$	−9.17652	+	20.0447i	−0.416256	+	0.909248i
$487$		−	36.5213i		−	1.65494i	−0.561513	−	0.827468i	$-0.689780\pi$
$487$		−	36.5213i		−	1.65494i	0.561513	−	0.827468i	$-0.310220\pi$
$488$	5.06899	+	7.43972i	0.229462	+	0.336780i
$489$	4.09808	−	0.327820i	0.185322	−	0.0148245i
$490$	−0.158595	+	11.3651i	−0.00716461	+	0.513421i
$491$	−8.96130	−	1.04743i	−0.404418	−	0.0472697i	−0.0885473	−	0.996072i	$-0.528222\pi$
$491$	−8.96130	−	1.04743i	−0.404418	−	0.0472697i	−0.315870	+	0.948802i	$0.602297\pi$
$492$	−3.41835	+	3.18483i	−0.154111	+	0.143583i
$493$	0.0484135	−	0.0243142i	0.00218044	−	0.00109506i
$494$	−30.5932	−	29.6809i	−1.37645	−	1.33541i
$495$	27.0922	+	10.3200i	1.21770	+	0.463849i
$496$	9.39690	+	21.6437i	0.421933	+	0.971831i
$497$	44.5187	+	19.2035i	1.99694	+	0.861395i
$498$	1.34539	+	20.3955i	0.0602886	+	0.913945i
$499$	0.409918	+	1.72958i	0.0183505	+	0.0774266i	0.981450	−	0.191720i	$-0.0614065\pi$
$499$	0.409918	+	1.72958i	0.0183505	+	0.0774266i	−0.963099	+	0.269147i	$0.913258\pi$
$500$	−17.8764	−	8.31019i	−0.799455	−	0.371643i
$501$	0.947595	−	25.9274i	0.0423354	−	1.15835i
$502$	0.945866	+	21.3742i	0.0422161	+	0.953976i
$503$	5.68735	+	32.2546i	0.253587	+	1.43816i	0.799675	+	0.600433i	$0.205005\pi$
$503$	5.68735	+	32.2546i	0.253587	+	1.43816i	−0.546088	+	0.837728i	$0.683884\pi$
$504$	26.0881	+	7.76963i	1.16206	+	0.346087i
$505$	2.40171	−	13.6208i	0.106875	−	0.606117i
$506$	28.6270	+	3.75161i	1.27262	+	0.166780i
$507$	−27.3244	−	45.0465i	−1.21352	−	2.00059i
$508$	40.0045	−	10.7698i	1.77491	−	0.477834i
$509$	−4.11496	+	8.19355i	−0.182392	+	0.363173i	−0.966185	−	0.257850i	$-0.916986\pi$
$509$	−4.11496	+	8.19355i	−0.182392	+	0.363173i	0.783793	+	0.621022i	$0.213282\pi$
$510$	0.202275	+	0.167095i	0.00895689	+	0.00739907i
$511$	−6.32049	+	26.6683i	−0.279602	+	1.17973i
$512$	−8.77015	−	20.8587i	−0.387589	−	0.921832i
$513$	−1.54236	−	23.7181i	−0.0680971	−	1.04718i
$514$	4.69340	+	9.67979i	0.207017	+	0.426957i
$515$	−8.72584	−	29.1464i	−0.384507	−	1.28434i
$516$	4.38596	−	3.22274i	0.193081	−	0.141873i
$517$	22.8322	−	15.0170i	1.00416	−	0.660447i
$518$	−14.3605	+	16.6371i	−0.630963	+	0.730991i
$519$	2.22250	−	6.54361i	0.0975571	−	0.287233i
$520$	−31.7694	−	32.5915i	−1.39318	−	1.42923i
$521$	−8.51499	−	23.3947i	−0.373049	−	1.02494i	−0.974176	−	0.225789i	$-0.927504\pi$
$521$	−8.51499	−	23.3947i	−0.373049	−	1.02494i	0.601128	−	0.799153i	$-0.294718\pi$
$522$	−4.87074	−	1.93362i	−0.213186	−	0.0846321i
$523$	−1.18937	+	3.26776i	−0.0520074	+	0.142889i	−0.962976	−	0.269586i	$-0.913113\pi$
$523$	−1.18937	+	3.26776i	−0.0520074	+	0.142889i	0.910969	+	0.412475i	$0.135335\pi$
$524$	−12.2510	−	22.6568i	−0.535188	−	0.989767i
$525$	5.09579	−	1.64657i	0.222399	−	0.0718623i
$526$	10.2668	−	8.37358i	0.447655	−	0.365105i
$527$	0.177549	+	0.188191i	0.00773415	+	0.00819772i
$528$	−24.0652	−	13.1341i	−1.04730	−	0.571587i
$529$	2.15959	+	2.90083i	0.0938951	+	0.126123i
$530$	−13.9110	+	31.0507i	−0.604256	+	1.34876i
$531$	17.6441	+	27.7166i	0.765690	+	1.20280i
$532$	−28.7344	+	5.96858i	−1.24579	+	0.258771i
$533$	4.88349	−	7.42498i	0.211527	−	0.321612i
$534$	0.903365	+	7.24503i	0.0390924	+	0.313523i
$535$	13.8193	+	10.2881i	0.597459	+	0.444792i
$536$	3.16600	−	1.21118i	0.136750	−	0.0523152i
$537$	29.7412	−	7.73233i	1.28343	−	0.333675i
$538$	−0.571344	−	2.56998i	−0.0246324	−	0.110800i
$539$	−6.51165	−	11.2785i	−0.280477	−	0.485800i
$540$	−0.939570	−	25.3615i	−0.0404326	−	1.09139i
$541$	−18.6219	+	32.2541i	−0.800619	+	1.38671i	0.118590	+	0.992943i	$0.462162\pi$
$541$	−18.6219	+	32.2541i	−0.800619	+	1.38671i	−0.919209	+	0.393769i	$0.871171\pi$
$542$	−4.72869	−	1.48788i	−0.203114	−	0.0639099i
$543$	30.2400	+	2.87261i	1.29772	+	0.123275i
$544$	−0.168161	−	0.182430i	−0.00720982	−	0.00782164i
$545$	29.2842	−	12.6320i	1.25440	−	0.541095i
$546$	−51.7117	−	2.61291i	−2.21305	−	0.111822i
$547$	−3.02145	−	0.175979i	−0.129188	−	0.00752434i	−0.00657096	−	0.999978i	$-0.502092\pi$
$547$	−3.02145	−	0.175979i	−0.129188	−	0.00752434i	−0.122617	+	0.992454i	$0.539129\pi$
$548$	11.5921	+	3.82600i	0.495188	+	0.163438i
$549$	−0.967223	−	9.49943i	−0.0412801	−	0.405426i
$550$	−5.36541	+	0.551355i	−0.228782	+	0.0235099i
$551$	5.61184	−	0.655930i	0.239072	−	0.0279436i
$552$	−6.75786	−	24.3542i	−0.287634	−	1.03658i
$553$	1.67695	−	5.60141i	0.0713112	−	0.238196i
$554$	3.46956	+	21.4205i	0.147407	+	0.910069i
$555$	18.9862	+	7.70682i	0.805918	+	0.327136i
$556$	−1.60934	−	0.990033i	−0.0682512	−	0.0419868i
$557$	−19.3406	−	23.0492i	−0.819487	−	0.976627i	0.180489	−	0.983577i	$-0.442232\pi$
$557$	−19.3406	−	23.0492i	−0.819487	−	0.976627i	−0.999976	+	0.00695029i	$0.997788\pi$
$558$	2.17503	−	24.9322i	0.0920762	−	1.05546i
$559$	−6.65465	+	7.93070i	−0.281462	+	0.335433i
$560$	−30.8476	+	5.51444i	−1.30355	+	0.233028i
$561$	−0.297111	−	0.0457817i	−0.0125440	−	0.00193290i
$562$	23.2004	+	4.42551i	0.978651	+	0.186679i
$563$	0.278730	+	4.78561i	0.0117471	+	0.201690i	0.999075	+	0.0429974i	$0.0136907\pi$
$563$	0.278730	+	4.78561i	0.0117471	+	0.201690i	−0.987328	+	0.158692i	$0.949272\pi$
$564$	−19.9047	−	13.2708i	−0.838137	−	0.558801i
$565$	−21.8133	+	23.1207i	−0.917691	+	0.972695i
$566$	37.7874	+	2.73039i	1.58832	+	0.114767i
$567$	−20.4014	−	20.4293i	−0.856780	−	0.857952i
$568$	−9.17833	+	41.7507i	−0.385114	+	1.75182i
$569$	18.5756	+	17.5252i	0.778731	+	0.734695i	0.969006	−	0.247036i	$-0.0794567\pi$
$569$	18.5756	+	17.5252i	0.778731	+	0.734695i	−0.190276	+	0.981731i	$0.560938\pi$
$570$	13.8630	+	23.5904i	0.580656	+	0.988095i
$571$	−24.6821	+	1.43757i	−1.03291	+	0.0601603i	−0.566216	−	0.824257i	$-0.691593\pi$
$571$	−24.6821	+	1.43757i	−1.03291	+	0.0601603i	−0.466697	+	0.884417i	$0.654556\pi$
$572$	50.3884	+	13.4377i	2.10684	+	0.561861i
$573$	3.74405	−	1.45524i	0.156410	−	0.0607937i
$574$	−2.34489	−	5.65163i	−0.0978739	−	0.235894i
$575$	−3.80903	−	3.19616i	−0.158848	−	0.133289i
$576$	−2.36277	+	23.8834i	−0.0984487	+	0.995142i
$577$	3.60364	−	3.02381i	0.150021	−	0.125883i	−0.564688	−	0.825305i	$-0.691003\pi$
$577$	3.60364	−	3.02381i	0.150021	−	0.125883i	0.714709	+	0.699422i	$0.246559\pi$
$578$	21.3293	+	11.0873i	0.887183	+	0.461172i
$579$	11.8868	+	15.2655i	0.493998	+	0.634411i
$580$	6.00936	−	0.532905i	0.249525	−	0.0221277i
$581$	−25.6444	−	7.67744i	−1.06391	−	0.318514i
$582$	−26.1686	+	35.7209i	−1.08472	+	1.48068i
$583$	−4.52589	−	38.7215i	−0.187443	−	1.60368i
$584$	−24.1432	−	1.01126i	−0.999055	−	0.0418461i
$585$	13.1554	+	46.4475i	0.543908	+	1.92037i
$586$	1.43240	−	5.68883i	0.0591719	−	0.235003i
$587$	−0.219084	+	3.76152i	−0.00904255	+	0.155255i	0.990764	+	0.135596i	$0.0432949\pi$
$587$	−0.219084	+	3.76152i	−0.00904255	+	0.155255i	−0.999807	+	0.0196585i	$0.993742\pi$
$588$	−6.86510	+	9.10189i	−0.283112	+	0.375356i
$589$	10.6873	+	24.7759i	0.440362	+	1.02087i
$590$	−32.4898	−	19.3674i	−1.33758	−	0.797344i
$591$	−7.62140	+	3.48509i	−0.313502	+	0.143358i
$592$	−16.8041	−	9.64901i	−0.690646	−	0.396572i
$593$	−14.9986	−	8.65945i	−0.615919	−	0.355601i	0.159360	−	0.987221i	$-0.449057\pi$
$593$	−14.9986	−	8.65945i	−0.615919	−	0.355601i	−0.775278	+	0.631620i	$0.782390\pi$
$594$	15.8040	+	24.4095i	0.648447	+	1.00153i
$595$	−0.297572	+	0.171803i	−0.0121993	+	0.00704326i
$596$	−34.7914	+	5.13817i	−1.42511	+	0.210468i
$597$	39.1304	+	10.7977i	1.60150	+	0.441922i
$598$	23.4546	+	41.9662i	0.959130	+	1.71612i
$599$	−19.0239	+	25.5535i	−0.777295	+	1.04409i	0.220345	+	0.975422i	$0.429282\pi$
$599$	−19.0239	+	25.5535i	−0.777295	+	1.04409i	−0.997640	+	0.0686662i	$0.978126\pi$
$600$	2.27767	+	4.13593i	0.0929856	+	0.168849i
$601$	−10.5162	−	6.91663i	−0.428966	−	0.282135i	0.316610	−	0.948556i	$-0.397455\pi$
$601$	−10.5162	−	6.91663i	−0.428966	−	0.282135i	−0.745576	+	0.666421i	$0.767826\pi$
$602$	1.94885	+	6.85640i	0.0794292	+	0.279446i
$603$	−3.56447	−	0.470509i	−0.145156	−	0.0191606i
$604$	15.5152	−	28.8563i	0.631305	−	1.17415i
$605$	9.12650	−	6.79443i	0.371045	−	0.276233i
$606$	10.0172	−	9.59745i	0.406921	−	0.389870i
$607$	20.4626	−	19.3055i	0.830552	−	0.783585i	−0.148130	−	0.988968i	$-0.547325\pi$
$607$	20.4626	−	19.3055i	0.830552	−	0.783585i	0.978682	+	0.205383i	$0.0658439\pi$
$608$	−9.97270	−	23.8765i	−0.404446	−	0.968321i
$609$	4.60068	−	5.09290i	0.186429	−	0.206375i
$610$	5.91168	+	9.26740i	0.239357	+	0.375226i
$611$	42.7609	+	15.5637i	1.72992	+	0.629640i
$612$	0.0646212	+	0.255103i	0.00261216	+	0.0103119i
$613$	15.3157	−	5.57444i	0.618594	−	0.225150i	−0.0136655	−	0.999907i	$-0.504350\pi$
$613$	15.3157	−	5.57444i	0.618594	−	0.225150i	0.632259	+	0.774757i	$0.282128\pi$
$614$	−0.0104373	−	0.00799904i	−0.000421215	−	0.000322815i
$615$	−4.28974	+	3.76071i	−0.172979	+	0.151646i
$616$	27.1248	−	23.5252i	1.09289	−	0.947857i
$617$	3.27680	+	4.98213i	0.131919	+	0.200573i	0.895407	−	0.445249i	$-0.146885\pi$
$617$	3.27680	+	4.98213i	0.131919	+	0.200573i	−0.763488	+	0.645822i	$0.776515\pi$
$618$	10.2164	−	28.7558i	0.410965	−	1.15673i
$619$	−45.5653	+	13.6414i	−1.83143	+	0.548293i	−0.999973	−	0.00730285i	$-0.997675\pi$
$619$	−45.5653	+	13.6414i	−1.83143	+	0.548293i	−0.831453	+	0.555596i	$0.812490\pi$
$620$	10.6689	+	26.7631i	0.428474	+	1.07483i
$621$	−6.00577	+	26.1261i	−0.241003	+	1.04841i
$622$	−16.9853	−	11.5141i	−0.681050	−	0.461675i
$623$	−9.30417	−	2.20513i	−0.372764	−	0.0883466i
$624$	−6.38682	−	45.2027i	−0.255678	−	1.80956i
$625$	−25.8171	−	12.9658i	−1.03268	−	0.518634i
$626$	31.7849	−	11.0690i	1.27038	−	0.442406i
$627$	−27.4841	−	15.0844i	−1.09761	−	0.602413i
$628$	−1.92322	+	9.37005i	−0.0767449	+	0.373906i
$629$	−0.209246	−	0.0368957i	−0.00834317	−	0.00147113i
$630$	31.5530	+	10.4468i	1.25710	+	0.416211i
$631$	17.2343	−	3.03887i	0.686087	−	0.120976i	0.180271	−	0.983617i	$-0.442303\pi$
$631$	17.2343	−	3.03887i	0.686087	−	0.120976i	0.505816	+	0.862641i	$0.331191\pi$
$632$	5.12949	+	0.514867i	0.204040	+	0.0204803i
$633$	13.5997	−	21.6856i	0.540539	−	0.861924i
$634$	−3.99339	+	10.5130i	−0.158598	+	0.417523i
$635$	49.2228	−	11.6660i	1.95335	−	0.462952i
$636$	−29.6616	+	16.8784i	−1.17616	+	0.669272i
$637$	8.58927	−	19.9122i	0.340319	−	0.788949i
$638$	−5.60174	+	4.05010i	−0.221775	+	0.160345i
$639$	29.6583	−	34.2954i	1.17326	−	1.35670i
$640$	−9.93299	−	25.7818i	−0.392636	−	1.01912i
$641$	18.1965	+	36.2322i	0.718719	+	1.43109i	0.894688	+	0.446692i	$0.147398\pi$
$641$	18.1965	+	36.2322i	0.718719	+	1.43109i	−0.175969	+	0.984396i	$0.556306\pi$
$642$	5.08331	+	16.5160i	0.200622	+	0.651834i
$643$	−2.92109	+	24.9915i	−0.115196	+	0.985568i	0.804774	+	0.593581i	$0.202286\pi$
$643$	−2.92109	+	24.9915i	−0.115196	+	0.985568i	−0.919971	+	0.391987i	$0.871788\pi$
$644$	32.9780	+	2.84595i	1.29951	+	0.112146i
$645$	5.47210	−	3.77122i	0.215464	−	0.148492i
$646$	−0.191806	−	0.209072i	−0.00754651	−	0.00822581i
$647$	−26.8998			−1.05754			−0.528769	−	0.848765i	$-0.677346\pi$
$647$	−26.8998			−1.05754			−0.528769	+	0.848765i	$0.677346\pi$
$648$	14.2731	−	21.0779i	0.560701	−	0.828019i
$649$	43.3390			1.70120
$650$	−6.07156	−	6.61809i	−0.238146	−	0.259583i
$651$	29.6016	+	14.0726i	1.16018	+	0.551550i
$652$	−4.72959	−	0.408156i	−0.185225	−	0.0159846i
$653$	4.49346	−	38.4440i	0.175843	−	1.50443i	−0.560689	−	0.828027i	$-0.689464\pi$
$653$	4.49346	−	38.4440i	0.175843	−	1.50443i	0.736531	−	0.676403i	$-0.236462\pi$
$654$	31.1827	+	7.13757i	1.21934	+	0.279101i
$655$	−14.1149	−	28.1050i	−0.551514	−	1.09815i
$656$	4.50031	−	2.97516i	0.175708	−	0.116160i
$657$	22.0032	+	13.1441i	0.858427	+	0.512800i
$658$	25.3897	−	18.3569i	0.989793	−	0.715627i
$659$	7.92625	−	18.3751i	0.308763	−	0.715793i	−0.691214	−	0.722651i	$-0.742924\pi$
$659$	7.92625	−	18.3751i	0.308763	−	0.715793i	0.999976	+	0.00685758i	$0.00218285\pi$
$660$	−28.8858	−	16.9193i	−1.12438	−	0.658582i
$661$	−1.11888	+	0.265179i	−0.0435193	+	0.0103143i	−0.252318	−	0.967644i	$-0.581193\pi$
$661$	−1.11888	+	0.265179i	−0.0435193	+	0.0103143i	0.208799	+	0.977959i	$0.433045\pi$
$662$	4.67429	−	12.3055i	0.181671	−	0.478266i
$663$	−0.234286	−	0.442361i	−0.00909891	−	0.0171799i
$664$	2.35717	−	23.4839i	0.0914760	−	0.911352i
$665$	−35.2905	+	6.22266i	−1.36851	+	0.241305i
$666$	10.7941	+	17.4902i	0.418263	+	0.677730i
$667$	−6.27572	−	1.10658i	−0.242997	−	0.0428469i
$668$	−6.02344	+	29.3466i	−0.233054	+	1.13545i
$669$	−0.111772	−	5.16285i	−0.00432134	−	0.199607i
$670$	3.90881	−	1.36123i	0.151010	−	0.0525889i
$671$	−11.2553	−	5.65264i	−0.434507	−	0.218218i
$672$	−28.2287	−	13.8233i	−1.08895	−	0.533247i
$673$	46.4101	+	10.9994i	1.78898	+	0.423996i	0.985267	−	0.171023i	$-0.0547074\pi$
$673$	46.4101	+	10.9994i	1.78898	+	0.423996i	0.803712	+	0.595019i	$0.202856\pi$
$674$	−15.3488	−	10.4048i	−0.591214	−	0.400776i
$675$	−0.0338538	−	5.00792i	−0.00130303	−	0.192755i
$676$	22.5280	+	56.5117i	0.866461	+	2.17353i
$677$	42.6657	−	12.7733i	1.63978	−	0.490917i	0.671542	−	0.740966i	$-0.265632\pi$
$677$	42.6657	−	12.7733i	1.63978	−	0.490917i	0.968233	+	0.250050i	$0.0804470\pi$
$678$	−31.3550	+	5.77776i	−1.20418	+	0.221894i
$679$	−31.8672	−	48.4516i	−1.22295	−	1.85940i
$680$	−0.198496	−	0.228868i	−0.00761196	−	0.00877669i
$681$	−2.47222	−	12.4398i	−0.0947355	−	0.476693i
$682$	−26.2019	−	20.0808i	−1.00332	−	0.768935i
$683$	−2.17028	+	0.789918i	−0.0830435	+	0.0302254i	−0.383208	−	0.923662i	$-0.625181\pi$
$683$	−2.17028	+	0.789918i	−0.0830435	+	0.0302254i	0.300164	+	0.953888i	$0.402958\pi$
$684$	−2.76646	+	27.3054i	−0.105778	+	1.04405i
$685$	14.0065	+	5.09796i	0.535162	+	0.194783i
$686$	9.04925	+	14.1860i	0.345502	+	0.541623i
$687$	−13.2588	−	2.84078i	−0.505856	−	0.108383i
$688$	−5.60950	+	2.83381i	−0.213860	+	0.108038i
$689$	47.2181	−	44.5480i	1.79887	−	1.69714i
$690$	−7.34785	−	29.9736i	−0.279728	−	1.14108i
$691$	37.0974	−	27.6180i	1.41125	−	1.05064i	0.421655	−	0.906756i	$-0.361449\pi$
$691$	37.0974	−	27.6180i	1.41125	−	1.05064i	0.989595	−	0.143880i	$-0.0459580\pi$
$692$	−3.77893	+	7.02834i	−0.143654	+	0.267177i
$693$	−37.1834	+	8.23004i	−1.41248	+	0.312634i
$694$	5.06469	+	17.8185i	0.192253	+	0.676380i
$695$	−1.92759	−	1.26779i	−0.0731176	−	0.0480902i
$696$	5.17828	+	3.13092i	0.196282	+	0.118677i
$697$	0.0353247	−	0.0474493i	0.00133802	−	0.00179727i
$698$	−7.49878	−	13.4172i	−0.283833	−	0.507849i
$699$	−10.2143	+	10.0634i	−0.386341	+	0.380632i
$700$	−6.11731	+	0.903437i	−0.231213	+	0.0341467i
$701$	−20.8180	+	12.0193i	−0.786286	+	0.453962i	−0.838653	−	0.544666i	$-0.816657\pi$
$701$	−20.8180	+	12.0193i	−0.786286	+	0.453962i	0.0523675	+	0.998628i	$0.483323\pi$
$702$	−16.8878	+	45.3805i	−0.637390	+	1.71278i
$703$	−19.1902	−	11.0795i	−0.723773	−	0.417870i
$704$	24.9019	+	19.5468i	0.938525	+	0.736699i
$705$	−23.8029	−	16.9324i	−0.896469	−	0.637711i
$706$	14.4707	+	8.62608i	0.544611	+	0.324647i
$707$	7.19619	+	16.6826i	0.270640	+	0.627415i
$708$	−14.8085	−	34.9296i	−0.556536	−	1.31274i
$709$	−0.221573	+	3.80426i	−0.00832134	+	0.142872i	0.991588	+	0.129432i	$0.0413153\pi$
$709$	−0.221573	+	3.80426i	−0.00832134	+	0.142872i	−0.999910	+	0.0134401i	$0.995722\pi$
$710$	−12.7449	+	50.6169i	−0.478309	+	1.89962i
$711$	−4.52320	−	3.07238i	−0.169633	−	0.115223i
$712$	0.352813	−	8.42323i	0.0132222	−	0.315674i
$713$	−3.53306	−	30.2273i	−0.132314	−	1.13202i
$714$	−0.342616	−	0.0373769i	−0.0128221	−	0.00139880i
$715$	61.0017	+	18.2627i	2.28133	+	0.682986i
$716$	−35.3451	+	3.13437i	−1.32091	+	0.117137i
$717$	33.0853	−	4.59501i	1.23559	−	0.171604i
$718$	−0.609238	−	0.316692i	−0.0227366	−	0.0118188i
$719$	−15.4778	+	12.9875i	−0.577226	+	0.484350i	−0.884035	−	0.467421i	$-0.845183\pi$
$719$	−15.4778	+	12.9875i	−0.577226	+	0.484350i	0.306809	+	0.951771i	$0.400739\pi$
$720$	−3.76635	+	29.0620i	−0.140363	+	1.08308i
$721$	30.6158	+	25.6897i	1.14019	+	0.956736i
$722$	−1.04233	−	2.51220i	−0.0387914	−	0.0934944i
$723$	−31.5125	−	25.3003i	−1.17196	−	0.940928i
$724$	−33.8909	−	9.03814i	−1.25954	−	0.335900i
$725$	1.18847	−	0.0692204i	0.0441386	−	0.00257078i
$726$	11.4121	−	0.0877847i	0.423542	−	0.00325800i
$727$	12.1138	+	11.4288i	0.449275	+	0.423869i	0.877333	−	0.479882i	$-0.159321\pi$
$727$	12.1138	+	11.4288i	0.449275	+	0.423869i	−0.428058	+	0.903751i	$0.640802\pi$
$728$	58.3933	+	12.8370i	2.16420	+	0.475770i
$729$	−23.9621	+	12.4427i	−0.887483	+	0.460840i
$730$	−29.4291	−	2.12645i	−1.08922	−	0.0787035i
$731$	−0.0472900	+	0.0501244i	−0.00174908	+	0.00185392i
$732$	−0.709997	+	11.0028i	−0.0262422	+	0.406676i
$733$	0.309515	+	5.31417i	0.0114322	+	0.196283i	0.999188	+	0.0402785i	$0.0128245\pi$
$733$	0.309515	+	5.31417i	0.0114322	+	0.196283i	−0.987756	+	0.156005i	$0.950138\pi$
$734$	19.9720	+	3.80967i	0.737178	+	0.140618i
$735$	−8.71512	+	10.8550i	−0.321462	+	0.400393i
$736$	3.05188	+	29.0243i	0.112494	+	1.06985i
$737$	−3.04842	+	3.63297i	−0.112290	+	0.133822i
$738$	−5.70020	+	0.500134i	−0.209827	+	0.0184102i
$739$	−11.2624	−	13.4220i	−0.414293	−	0.493735i	0.518030	−	0.855363i	$-0.326666\pi$
$739$	−11.2624	−	13.4220i	−0.414293	−	0.493735i	−0.932323	+	0.361627i	$0.882221\pi$
$740$	−20.1526	−	12.3975i	−0.740825	−	0.455741i
$741$	−7.18149	−	51.7086i	−0.263819	−	1.89956i
$742$	−7.14630	−	44.1201i	−0.262349	−	1.61970i
$743$	0.845153	−	2.82301i	0.0310057	−	0.103566i	−0.941086	−	0.338167i	$-0.890193\pi$
$743$	0.845153	−	2.82301i	0.0310057	−	0.103566i	0.972092	+	0.234601i	$0.0753783\pi$
$744$	−7.23152	+	27.9791i	−0.265120	+	1.02577i
$745$	−42.6522	+	4.98533i	−1.56266	+	0.182648i
$746$	−19.5365	+	2.00759i	−0.715281	+	0.0735029i
$747$	−14.0660	+	20.7082i	−0.514648	+	0.757673i
$748$	0.329633	+	0.108796i	0.0120526	+	0.00397799i
$749$	−22.5932	−	1.31590i	−0.825537	−	0.0480820i
$750$	−11.0015	−	21.4919i	−0.401717	−	0.784774i
$751$	−28.2803	+	12.1989i	−1.03196	+	0.445145i	−0.843610	−	0.536957i	$-0.819574\pi$
$751$	−28.2803	+	12.1989i	−1.03196	+	0.445145i	−0.188352	+	0.982102i	$0.560314\pi$
$752$	20.1376	+	18.9091i	0.734344	+	0.689545i
$753$	−15.1891	+	21.3522i	−0.553521	+	0.778118i
$754$	−10.9797	−	3.45475i	−0.399856	−	0.125814i
$755$	20.0025	−	34.6453i	0.727965	−	1.26087i
$756$	19.3383	+	27.1563i	0.703326	+	0.987667i
$757$	−21.1776	−	36.6808i	−0.769715	−	1.33318i	−0.937718	−	0.347398i	$-0.887065\pi$
$757$	−21.1776	−	36.6808i	−0.769715	−	1.33318i	0.168003	−	0.985786i	$-0.446268\pi$
$758$	−10.0573	−	45.2389i	−0.365297	−	1.64315i
$759$	24.8169	+	25.1891i	0.900796	+	0.914306i
$760$	−11.2892	−	29.5095i	−0.409501	−	1.07042i
$761$	−11.8395	−	8.81419i	−0.429182	−	0.319514i	0.360801	−	0.932643i	$-0.382503\pi$
$761$	−11.8395	−	8.81419i	−0.429182	−	0.319514i	−0.789983	+	0.613129i	$0.789911\pi$
$762$	46.7432	+	19.7380i	1.69333	+	0.715033i
$763$	−23.0215	+	35.0024i	−0.833433	+	1.26717i
$764$	−4.54140	+	0.943319i	−0.164302	+	0.0341281i
$765$	0.0694417	+	0.313738i	0.00251067	+	0.0113432i
$766$	−5.29092	+	11.8098i	−0.191169	+	0.426707i
$767$	43.0945	+	57.8859i	1.55605	+	2.09014i
$768$	7.24532	−	26.7489i	0.261443	−	0.965219i
$769$	−8.25389	−	8.74861i	−0.297643	−	0.315483i	0.561242	−	0.827652i	$-0.310324\pi$
$769$	−8.25389	−	8.74861i	−0.297643	−	0.315483i	−0.858885	+	0.512169i	$0.828842\pi$
$770$	33.9749	−	27.7097i	1.22437	−	0.998589i
$771$	−2.76025	+	12.8830i	−0.0994079	+	0.463968i
$772$	−10.6261	−	19.6518i	−0.382443	−	0.707283i
$773$	4.37064	−	12.0082i	0.157201	−	0.431906i	−0.835941	−	0.548819i	$-0.815078\pi$
$773$	4.37064	−	12.0082i	0.157201	−	0.431906i	0.993142	+	0.116913i	$0.0372998\pi$
$774$	6.66311	+	0.192215i	0.239501	+	0.00690903i
$775$	1.94450	+	5.34247i	0.0698485	+	0.191907i
$776$	36.6138	−	35.6903i	1.31436	−	1.28121i
$777$	−26.4007	+	5.24673i	−0.947118	+	0.188225i
$778$	−2.78676	+	3.22856i	−0.0999104	+	0.115749i
$779$	5.15434	−	3.39007i	0.184674	−	0.121462i
$780$	−6.12453	−	55.4053i	−0.219293	−	1.98383i
$781$	−17.1528	−	57.2943i	−0.613776	−	2.05015i
$782$	0.139615	+	0.287945i	0.00499262	+	0.0102969i
$783$	−3.24665	−	5.53658i	−0.116026	−	0.197861i
$784$	9.55399	−	9.05648i	0.341214	−	0.323446i
$785$	−2.69354	+	11.3649i	−0.0961365	+	0.405632i
$786$	5.23872	−	31.1076i	0.186859	−	1.10957i
$787$	0.689558	−	1.37302i	0.0245801	−	0.0489430i	−0.881007	−	0.473102i	$-0.843134\pi$
$787$	0.689558	−	1.37302i	0.0245801	−	0.0489430i	0.905588	+	0.424159i	$0.139430\pi$
$788$	9.34419	−	2.51560i	0.332873	−	0.0896146i
$789$	16.2223	−	0.351201i	0.577530	−	0.0125031i
$790$	6.24144	+	0.817951i	0.222060	+	0.0291014i
$791$	7.25074	−	41.1210i	0.257807	−	1.46210i
$792$	−13.3435	−	30.8124i	−0.474141	−	1.09487i
$793$	−3.64185	−	20.6540i	−0.129326	−	0.733444i
$794$	−0.286131	−	6.46583i	−0.0101544	−	0.229464i
$795$	−36.8253	+	19.5037i	−1.30606	+	0.691724i
$796$	−42.5044	−	19.7590i	−1.50653	−	0.700340i
$797$	6.77953	+	28.6051i	0.240143	+	1.01324i	0.950824	+	0.309730i	$0.100239\pi$
$797$	6.77953	+	28.6051i	0.240143	+	1.01324i	−0.710681	+	0.703514i	$0.751613\pi$
$798$	−32.2434	−	15.8839i	−1.14140	−	0.562283i
$799$	0.278125	+	0.119971i	0.00983935	+	0.00424428i
$800$	−1.80521	−	5.14453i	−0.0638237	−	0.181887i
$801$	−4.58579	+	7.67661i	−0.162031	+	0.271240i
$802$	−1.50245	−	1.45765i	−0.0530534	−	0.0514713i
$803$	30.2116	−	15.1728i	1.06614	−	0.535438i
$804$	3.96965	+	1.21557i	0.139999	+	0.0428699i
$805$	40.1440	+	4.69216i	1.41489	+	0.165377i
$806$	0.767006	−	54.9642i	0.0270166	−	1.93603i
$807$	1.38441	−	2.91209i	0.0487335	−	0.102510i
$808$	−13.2382	+	9.01975i	−0.465720	+	0.317314i
$809$		−	24.4449i		−	0.859437i	−0.902963	−	0.429718i	$-0.858613\pi$
$809$		−	24.4449i		−	0.859437i	0.902963	−	0.429718i	$-0.141387\pi$
$810$	18.1991	−	25.1978i	0.639450	−	0.885361i
$811$			1.62195i			0.0569544i	0.999594	+	0.0284772i	$0.00906579\pi$
$811$			1.62195i			0.0569544i	−0.999594	+	0.0284772i	$0.990934\pi$
$812$	−6.21066	+	4.92269i	−0.217952	+	0.172753i
$813$	−3.44527	−	4.99915i	−0.120831	−	0.175328i
$814$	27.1076	+	0.378277i	0.950121	+	0.0132586i
$815$	−5.75731	−	0.672933i	−0.201670	−	0.0235718i
$816$	−0.0249460	−	0.302846i	−0.000873284	−	0.0106017i
$817$	−6.42237	+	3.22543i	−0.224690	+	0.112844i
$818$	−22.6510	+	23.3472i	−0.791973	+	0.816317i
$819$	−47.9661	−	41.4806i	−1.67607	−	1.44945i
$820$	5.60251	−	3.46482i	0.195648	−	0.120997i
$821$	−20.2122	−	8.71871i	−0.705412	−	0.304285i	0.0129878	−	0.999916i	$-0.495866\pi$
$821$	−20.2122	−	8.71871i	−0.705412	−	0.304285i	−0.718400	+	0.695631i	$0.755125\pi$
$822$	8.31134	+	12.4275i	0.289891	+	0.433459i
$823$	7.19336	+	30.3512i	0.250745	+	1.05797i	0.942066	+	0.335427i	$0.108881\pi$
$823$	7.19336	+	30.3512i	0.250745	+	1.05797i	−0.691321	+	0.722547i	$0.742971\pi$
$824$	−17.1186	+	30.8001i	−0.596354	+	1.07297i
$825$	−5.59639	−	3.50967i	−0.194841	−	0.122191i
$826$	49.6382	−	2.19663i	1.72713	−	0.0764304i
$827$	−4.06791	−	23.0703i	−0.141455	−	0.802232i	−0.970145	−	0.242524i	$-0.922025\pi$
$827$	−4.06791	−	23.0703i	−0.141455	−	0.802232i	0.828690	−	0.559708i	$-0.189087\pi$
$828$	11.8218	−	28.6083i	0.410837	−	0.994208i
$829$	5.21908	−	29.5988i	0.181266	−	1.02801i	−0.749394	−	0.662125i	$-0.769655\pi$
$829$	5.21908	−	29.5988i	0.181266	−	1.02801i	0.930660	−	0.365886i	$-0.119234\pi$
$830$	3.74475	−	28.5746i	0.129982	−	0.991840i
$831$	−12.7870	+	23.2982i	−0.443576	+	0.808205i
$832$	−1.34642	+	52.6968i	−0.0466789	+	1.82693i
$833$	0.0647828	−	0.128993i	0.00224459	−	0.00446935i
$834$	−0.808184	−	2.16842i	−0.0279851	−	0.0750863i
$835$	−8.43604	+	35.5945i	−0.291941	+	1.23180i
$836$	28.4236	+	22.4200i	0.983051	+	0.775410i
$837$	20.8832	−	22.4368i	0.721828	−	0.775530i
$838$	−16.9073	+	8.19780i	−0.584054	+	0.283188i
$839$	−13.0775	−	43.6818i	−0.451485	−	1.50806i	−0.816656	−	0.577124i	$-0.804175\pi$
$839$	−13.0775	−	43.6818i	−0.451485	−	1.50806i	0.365171	−	0.930940i	$-0.381010\pi$
$840$	−33.9418	−	17.9144i	−1.17110	−	0.618105i
$841$	−22.9544	+	15.0974i	−0.791532	+	0.520599i
$842$	−4.07819	−	3.52014i	−0.140544	−	0.121312i
$843$	19.0691	+	21.7517i	0.656776	+	0.749168i
$844$	−19.6233	+	22.1031i	−0.675463	+	0.760819i
$845$	25.4067	+	69.8042i	0.874015	+	2.40134i
$846$	−9.22295	−	27.8101i	−0.317092	−	0.956131i
$847$	−5.11192	+	14.0449i	−0.175648	+	0.482588i
$848$	36.9987	−	13.5655i	1.27054	−	0.465841i
$849$	34.4318	+	31.1040i	1.18170	+	1.06749i
$850$	−0.0377844	−	0.0463274i	−0.00129600	−	0.00158902i
$851$	17.1509	+	18.1789i	0.587925	+	0.623165i
$852$	−40.3162	+	33.4014i	−1.38121	+	1.14431i
$853$	−20.6049	−	27.6772i	−0.705498	−	0.947648i	0.294470	−	0.955661i	$-0.404857\pi$
$853$	−20.6049	−	27.6772i	−0.705498	−	0.947648i	−0.999968	+	0.00801267i	$0.997449\pi$
$854$	−13.1778	−	5.90376i	−0.450934	−	0.202022i
$855$	−4.38551	+	33.2235i	−0.149981	+	1.13622i
$856$	−2.63956	−	19.7785i	−0.0902182	−	0.676016i
$857$	−1.85316	+	2.81759i	−0.0633028	+	0.0962472i	−0.865752	−	0.500473i	$-0.833159\pi$
$857$	−1.85316	+	2.81759i	−0.0633028	+	0.0962472i	0.802449	+	0.596720i	$0.203530\pi$
$858$	38.5333	+	50.9365i	1.31551	+	1.73894i
$859$	20.1595	+	15.0082i	0.687833	+	0.512073i	0.883401	−	0.468617i	$-0.155248\pi$
$859$	20.1595	+	15.0082i	0.687833	+	0.512073i	−0.195568	+	0.980690i	$0.562655\pi$
$860$	−6.95103	+	3.25132i	−0.237028	+	0.110869i
$861$	1.99340	−	7.22395i	0.0679347	−	0.246192i
$862$	37.8768	−	8.42056i	1.29009	−	0.286805i
$863$	−6.07199	−	10.5170i	−0.206693	−	0.358003i	0.743978	−	0.668204i	$-0.232937\pi$
$863$	−6.07199	−	10.5170i	−0.206693	−	0.358003i	−0.950671	+	0.310202i	$0.899603\pi$
$864$	−20.2744	+	21.2826i	−0.689748	+	0.724050i
$865$	−4.87187	+	8.43833i	−0.165649	+	0.286912i
$866$	3.79789	−	12.0702i	0.129058	−	0.410163i
$867$	12.2436	+	26.7750i	0.415814	+	0.909325i
$868$	−31.0280	−	21.6715i	−1.05316	−	0.735578i
$869$	−6.62269	+	2.85675i	−0.224659	+	0.0969086i
$870$	6.20431	+	4.01261i	0.210346	+	0.136040i
$871$	−7.88361	−	0.459168i	−0.267126	−	0.0155583i
$872$	−34.1512	−	14.0750i	−1.15651	−	0.476641i
$873$	−52.1799	+	14.7790i	−1.76602	+	0.500192i
$874$	3.41155	+	33.1989i	0.115397	+	1.12297i
$875$	31.4064	−	3.67088i	1.06173	−	0.124098i
$876$	−22.5517	−	19.1650i	−0.761952	−	0.647527i
$877$	−8.22976	+	27.4893i	−0.277899	+	0.928248i	0.699103	+	0.715021i	$0.253583\pi$
$877$	−8.22976	+	27.4893i	−0.277899	+	0.928248i	−0.977003	+	0.213227i	$0.931603\pi$
$878$	−46.4917	+	7.53044i	−1.56902	+	0.254140i
$879$	5.66890	−	4.41421i	0.191207	−	0.148888i
$880$	29.6700	+	24.7769i	1.00018	+	0.835228i
$881$	22.6735	+	27.0212i	0.763889	+	0.910368i	0.998087	−	0.0618211i	$-0.0196908\pi$
$881$	22.6735	+	27.0212i	0.763889	+	0.910368i	−0.234198	+	0.972189i	$0.575246\pi$
$882$	−13.4862	+	3.61721i	−0.454103	+	0.121798i
$883$	−19.0825	+	22.7417i	−0.642178	+	0.765318i	−0.984712	−	0.174188i	$-0.944270\pi$
$883$	−19.0825	+	22.7417i	−0.642178	+	0.765318i	0.342535	+	0.939505i	$0.388715\pi$
$884$	0.182458	+	0.548458i	0.00613674	+	0.0184466i
$885$	−16.7827	−	43.1783i	−0.564143	−	1.45142i
$886$	1.41885	−	7.43822i	0.0476671	−	0.249892i
$887$	−0.905852	−	15.5529i	−0.0304155	−	0.522215i	−0.978765	−	0.204987i	$-0.934285\pi$
$887$	−0.905852	−	15.5529i	−0.0304155	−	0.522215i	0.948349	−	0.317228i	$-0.102752\pi$
$888$	−8.95749	−	21.9770i	−0.300594	−	0.737499i
$889$	−45.6016	+	48.3348i	−1.52943	+	1.62110i
$890$	0.741888	−	10.2674i	0.0248681	−	0.344164i
$891$	−3.12823	+	35.4768i	−0.104800	+	1.18852i
$892$	−0.857249	+	5.90100i	−0.0287028	+	0.197580i
$893$	22.9772	+	21.6779i	0.768902	+	0.725422i
$894$	−37.4666	−	21.2488i	−1.25307	−	0.710666i
$895$	−43.2540	+	2.51926i	−1.44582	+	0.0842095i
$896$	29.5120	+	21.1258i	0.985928	+	0.705762i
$897$	−8.96704	+	58.1937i	−0.299401	+	1.94303i
$898$	21.9018	−	9.08719i	0.730873	−	0.303243i
$899$	5.58164	+	4.68356i	0.186158	+	0.156205i
$900$	−0.916442	+	5.70970i	−0.0305481	+	0.190323i
$901$	0.331008	−	0.277749i	0.0110275	−	0.00925316i
$902$	−3.48121	+	6.69699i	−0.115912	+	0.222985i
$903$	−3.28345	+	8.08896i	−0.109266	+	0.269184i
$904$	36.8103	−	0.600665i	1.22429	−	0.0199778i
$905$	−41.0293	−	12.2834i	−1.36386	−	0.408313i
$906$	36.7212	−	16.1761i	1.21998	−	0.537415i
$907$	−2.71183	−	23.2012i	−0.0900448	−	0.770382i	−0.960528	−	0.278184i	$-0.910268\pi$
$907$	−2.71183	−	23.2012i	−0.0900448	−	0.770382i	0.870483	−	0.492198i	$-0.163807\pi$
$908$	0.443242	+	14.6384i	0.0147095	+	0.485793i
$909$	16.9033	−	1.72108i	0.560646	−	0.0570845i
$910$	70.7937	+	17.8253i	2.34679	+	0.590902i
$911$	0.752067	−	12.9125i	0.0249171	−	0.427810i	−0.962664	−	0.270699i	$-0.912745\pi$
$911$	0.752067	−	12.9125i	0.0249171	−	0.427810i	0.987581	−	0.157111i	$-0.0502179\pi$
$912$	8.35762	−	30.5690i	0.276749	−	1.01224i
$913$	13.0788	+	30.3201i	0.432845	+	1.00345i
$914$	−16.2363	+	27.2372i	−0.537050	+	0.900928i
$915$	−1.27316	+	13.4025i	−0.0420892	+	0.443074i
$916$	14.5580	+	5.76363i	0.481011	+	0.190436i
$917$	35.7787	+	20.6568i	1.18152	+	0.682149i
$918$	−0.129784	+	0.295020i	−0.00428351	+	0.00973710i
$919$	47.1233	−	27.2066i	1.55445	−	0.897464i	0.556683	−	0.830725i	$-0.312074\pi$
$919$	47.1233	−	27.2066i	1.55445	−	0.897464i	0.997770	−	0.0667391i	$-0.0212595\pi$
$920$	2.65217	+	35.5366i	0.0874394	+	1.17161i
$921$	−0.00405247	−	0.0155872i	−0.000133534	−	0.000513615i
$922$	−22.2309	+	12.4247i	−0.732136	+	0.409186i
$923$	59.4694	−	79.8813i	1.95746	−	2.62932i
$924$	43.9156	−	2.28197i	1.44472	−	0.0750714i
$925$	−3.90086	−	2.56564i	−0.128260	−	0.0843577i
$926$	−14.0088	+	3.98183i	−0.460357	+	0.130851i
$927$	31.5288	−	20.0709i	1.03554	−	0.659215i
$928$	−5.30020	−	4.55312i	−0.173988	−	0.149464i
$929$	−47.2762	+	35.1959i	−1.55108	+	1.15474i	−0.623084	+	0.782155i	$0.714121\pi$
$929$	−47.2762	+	35.1959i	−1.55108	+	1.15474i	−0.927999	+	0.372584i	$0.878472\pi$
$930$	−9.85994	+	33.8809i	−0.323320	+	1.11100i
$931$	10.9499	−	10.3307i	0.358868	−	0.338574i
$932$	13.5516	−	9.51279i	0.443897	−	0.311602i
$933$	−7.72735	−	23.9145i	−0.252982	−	0.782926i
$934$	10.2743	−	6.55401i	0.336186	−	0.214454i
$935$	0.398291	+	0.144966i	0.0130255	+	0.00474090i
$936$	27.8865	−	48.4609i	0.911500	−	1.58399i
$937$	−13.1332	+	4.78010i	−0.429044	+	0.156159i	−0.547510	−	0.836799i	$-0.684424\pi$
$937$	−13.1332	+	4.78010i	−0.429044	+	0.156159i	0.118467	+	0.992958i	$0.462202\pi$
$938$	−3.30737	+	4.31552i	−0.107989	+	0.140907i
$939$	39.0315	+	13.2568i	1.27374	+	0.432621i
$940$	23.8789	+	23.8225i	0.778843	+	0.777005i
$941$	−29.7533	−	45.2378i	−0.969931	−	1.47471i	−0.877838	−	0.478959i	$-0.841014\pi$
$941$	−29.7533	−	45.2378i	−0.969931	−	1.47471i	−0.0920938	−	0.995750i	$-0.529356\pi$
$942$	−8.91615	+	7.59917i	−0.290504	+	0.247594i
$943$	−6.66584	+	1.99562i	−0.217070	+	0.0649864i
$944$	10.2036	+	42.6034i	0.332097	+	1.38662i
$945$	22.5985	+	33.8586i	0.735129	+	1.10142i
$946$	4.93368	−	7.27802i	0.160408	−	0.236629i
$947$	−23.6467	−	5.60436i	−0.768413	−	0.182117i	−0.172329	−	0.985039i	$-0.555129\pi$
$947$	−23.6467	−	5.60436i	−0.768413	−	0.182117i	−0.596084	+	0.802922i	$0.703277\pi$
$948$	4.56533	+	4.36152i	0.148275	+	0.141656i
$949$	50.3068	+	25.2650i	1.63303	+	0.820137i
$950$	−2.05043	−	5.88788i	−0.0665249	−	0.191028i
$951$	−11.7762	+	7.14321i	−0.381869	+	0.231635i
$952$	0.383058	+	0.107902i	0.0124150	+	0.00349713i
$953$	−5.35751	−	0.944673i	−0.173547	−	0.0306010i	0.0861994	−	0.996278i	$-0.472528\pi$
$953$	−5.35751	−	0.944673i	−0.173547	−	0.0306010i	−0.259746	+	0.965677i	$0.583639\pi$
$954$	−41.3578	−	6.04750i	−1.33901	−	0.195795i
$955$	−5.57757	+	0.983476i	−0.180486	+	0.0318245i
$956$	−38.5552	−	1.07626i	−1.24697	−	0.0348087i
$957$	−8.46041	−	0.309212i	−0.273486	−	0.00999539i
$958$	46.6737	+	17.7292i	1.50796	+	0.572804i
$959$	−19.0523	+	4.51547i	−0.615230	+	0.145812i
$960$	9.83133	−	32.3789i	0.317305	−	1.04502i
$961$	−1.50390	+	3.48644i	−0.0485130	+	0.112466i
$962$	26.4494	+	36.5825i	0.852763	+	1.17947i
$963$	−7.53385	+	19.7780i	−0.242775	+	0.637336i
$964$	31.0632	+	34.8225i	1.00048	+	1.12156i
$965$	−12.2428	−	24.3774i	−0.394109	−	0.784736i
$966$	29.7007	+	27.5924i	0.955603	+	0.887771i
$967$	−6.56209	+	56.1422i	−0.211022	+	1.80541i	0.308788	+	0.951131i	$0.400077\pi$
$967$	−6.56209	+	56.1422i	−0.211022	+	1.80541i	−0.519810	+	0.854282i	$0.673997\pi$
$968$	−13.0133	−	2.07628i	−0.418264	−	0.0667340i
$969$	−0.0277086	−	0.346386i	−0.000890128	−	0.0111275i
$970$	46.0056	−	42.2063i	1.47715	−	1.35516i
$971$	−24.4690			−0.785249			−0.392624	−	0.919699i	$-0.628433\pi$
$971$	−24.4690			−0.785249			−0.392624	+	0.919699i	$0.628433\pi$
$972$	29.6618	−	9.60078i	0.951404	−	0.307945i
$973$	3.03070			0.0971598
$974$	−38.0589	+	34.9160i	−1.21949	+	1.11878i
$975$	−0.877106	−	10.9647i	−0.0280899	−	0.351152i
$976$	2.90678	−	12.3951i	0.0930438	−	0.396758i
$977$	−3.55947	+	30.4532i	−0.113878	+	0.974286i	0.808633	+	0.588314i	$0.200208\pi$
$977$	−3.55947	+	30.4532i	−0.113878	+	0.974286i	−0.922511	+	0.385972i	$0.873866\pi$
$978$	−4.25957	−	3.95721i	−0.136206	−	0.126538i
$979$	5.29358	+	10.5404i	0.169184	+	0.336872i
$980$	11.9952	−	10.7002i	0.383172	−	0.341806i
$981$	24.7340	+	30.3841i	0.789695	+	0.970089i
$982$	7.47587	+	10.3400i	0.238565	+	0.329962i
$983$	14.2475	−	33.0294i	0.454425	−	1.05348i	−0.524897	−	0.851166i	$-0.675896\pi$
$983$	14.2475	−	33.0294i	0.454425	−	1.05348i	0.979322	−	0.202310i	$-0.0648447\pi$
$984$	6.58702	+	0.517437i	0.209986	+	0.0164953i
$985$	11.4974	−	2.72493i	0.366338	−	0.0868236i
$986$	−0.0716234	−	0.0272064i	−0.00228095	−	0.000866429i
$987$	38.3465	+	1.40149i	1.22058	+	0.0446099i
$988$	−1.68207	+	60.2575i	−0.0535139	+	1.91705i
$989$	7.98267	−	1.40756i	0.253834	−	0.0447578i
$990$	−15.1468	−	38.0992i	−0.481398	−	1.21087i
$991$	−9.10143	−	1.60483i	−0.289116	−	0.0509790i	0.0272090	−	0.999630i	$-0.491338\pi$
$991$	−9.10143	−	1.60483i	−0.289116	−	0.0509790i	−0.316325	+	0.948651i	$0.602449\pi$
$992$	13.5711	−	30.4849i	0.430883	−	0.967896i
$993$	13.7841	−	8.36117i	0.437425	−	0.265334i
$994$	−22.5499	−	64.7525i	−0.715238	−	2.05383i
$995$	−51.1457	−	25.6864i	−1.62143	−	0.814312i
$996$	19.9680	−	20.9011i	0.632710	−	0.662276i
$997$	−40.8978	−	9.69295i	−1.29525	−	0.306979i	−0.475504	−	0.879713i	$-0.657734\pi$
$997$	−40.8978	−	9.69295i	−1.29525	−	0.306979i	−0.819741	+	0.572734i	$0.805883\pi$
$998$	1.41050	−	2.08073i	0.0446486	−	0.0658644i
$999$	−2.75321	+	25.0209i	−0.0871077	+	0.791627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.11.15	yes	936
3.2	odd	2		972.2.p.a.359.38		936
4.3	odd	2	inner	324.2.p.a.11.12	✓	936
12.11	even	2		972.2.p.a.359.41		936
81.22	even	27		972.2.p.a.287.41		936
81.59	odd	54	inner	324.2.p.a.59.12	yes	936
324.59	even	54	inner	324.2.p.a.59.15	yes	936
324.103	odd	54		972.2.p.a.287.38		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.11.12	✓	936	4.3	odd	2	inner
324.2.p.a.11.15	yes	936	1.1	even	1	trivial
324.2.p.a.59.12	yes	936	81.59	odd	54	inner
324.2.p.a.59.15	yes	936	324.59	even	54	inner
972.2.p.a.287.38		936	324.103	odd	54
972.2.p.a.287.41		936	81.22	even	27
972.2.p.a.359.38		936	3.2	odd	2
972.2.p.a.359.41		936	12.11	even	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.956045 - 1.04210i) q^{2} +(-0.138112 - 1.72654i) q^{3} +(-0.171958 + 1.99259i) q^{4} +(-0.283509 + 2.42558i) q^{5} +(-1.66719 + 1.79457i) q^{6} +(-1.43973 - 2.86675i) q^{7} +(2.24089 - 1.72581i) q^{8} +(-2.96185 + 0.476909i) q^{9} +O(q^{10})\)	\(q+(-0.956045 - 1.04210i) q^{2} +(-0.138112 - 1.72654i) q^{3} +(-0.171958 + 1.99259i) q^{4} +(-0.283509 + 2.42558i) q^{5} +(-1.66719 + 1.79457i) q^{6} +(-1.43973 - 2.86675i) q^{7} +(2.24089 - 1.72581i) q^{8} +(-2.96185 + 0.476909i) q^{9} +(2.79875 - 2.02351i) q^{10} +(-1.56735 + 3.63353i) q^{11} +(3.46403 + 0.0216908i) q^{12} +(-6.41164 + 1.51959i) q^{13} +(-1.61100 + 4.24109i) q^{14} +(4.22700 + 0.154489i) q^{15} +(-3.94086 - 0.685284i) q^{16} +(-0.0431938 + 0.00761624i) q^{17} +(3.32865 + 2.63061i) q^{18} +(-4.50470 - 0.794300i) q^{19} +(-4.78444 - 0.982015i) q^{20} +(-4.75070 + 2.88168i) q^{21} +(5.28497 - 1.84047i) q^{22} +(4.61035 + 2.31541i) q^{23} +(-3.28917 - 3.63062i) q^{24} +(-0.937818 - 0.222267i) q^{25} +(7.71338 + 5.22880i) q^{26} +(1.23247 + 5.04787i) q^{27} +(5.95984 - 2.37585i) q^{28} +(-1.18331 + 0.354259i) q^{29} +(-3.88021 - 4.55267i) q^{30} +(-3.24150 - 4.92846i) q^{31} +(3.05350 + 4.76195i) q^{32} +(6.48988 + 2.20425i) q^{33} +(0.0492321 + 0.0377310i) q^{34} +(7.36169 - 2.67944i) q^{35} +(-0.440973 - 5.98377i) q^{36} +(4.55219 + 1.65686i) q^{37} +(3.47895 + 5.45375i) q^{38} +(3.50914 + 10.8601i) q^{39} +(3.55077 + 5.92473i) q^{40} +(-0.981017 + 0.925542i) q^{41} +(7.54489 + 2.19570i) q^{42} +(1.26027 - 0.938234i) q^{43} +(-6.97062 - 3.74790i) q^{44} +(-0.317068 - 7.31940i) q^{45} +(-1.99481 - 7.01809i) q^{46} +(-5.76986 - 3.79489i) q^{47} +(-0.638888 + 6.89868i) q^{48} +(-1.96529 + 2.63985i) q^{49} +(0.664971 + 1.18980i) q^{50} +(0.0191153 + 0.0735238i) q^{51} +(-1.92539 - 13.0371i) q^{52} +(-8.53190 + 4.92589i) q^{53} +(4.08211 - 6.11035i) q^{54} +(-8.36904 - 4.83187i) q^{55} +(-8.17375 - 3.93935i) q^{56} +(-0.749236 + 7.88723i) q^{57} +(1.50047 + 0.894442i) q^{58} +(-4.33789 - 10.0564i) q^{59} +(-1.03470 + 8.39613i) q^{60} +(-0.185066 + 3.17746i) q^{61} +(-2.03694 + 8.08980i) q^{62} +(5.63146 + 7.80425i) q^{63} +(2.04315 - 7.73470i) q^{64} +(-1.86811 - 15.9827i) q^{65} +(-3.90756 - 8.87049i) q^{66} +(1.14811 + 0.343723i) q^{67} +(-0.00774856 - 0.0873774i) q^{68} +(3.36089 - 8.27972i) q^{69} +(-9.83035 - 5.10998i) q^{70} +(-11.5777 + 9.71483i) q^{71} +(-5.81412 + 6.18029i) q^{72} +(-6.54463 - 5.49160i) q^{73} +(-2.62548 - 6.32789i) q^{74} +(-0.254228 + 1.64987i) q^{75} +(2.35733 - 8.83945i) q^{76} +(12.6730 - 0.738116i) q^{77} +(7.96240 - 14.0396i) q^{78} +(1.32576 + 1.25079i) q^{79} +(2.77948 - 9.36457i) q^{80} +(8.54512 - 2.82507i) q^{81} +(1.90241 + 0.137462i) q^{82} +(5.72637 - 6.06959i) q^{83} +(-4.92511 - 9.96174i) q^{84} +(-0.00622792 - 0.106929i) q^{85} +(-2.18261 - 0.416335i) q^{86} +(0.775070 + 1.99410i) q^{87} +(2.75852 + 10.8473i) q^{88} +(1.91594 - 2.28333i) q^{89} +(-7.32444 + 7.32809i) q^{90} +(13.5873 + 16.1927i) q^{91} +(-5.40645 + 8.78841i) q^{92} +(-8.06147 + 6.27724i) q^{93} +(1.56157 + 9.64087i) q^{94} +(3.20376 - 10.7013i) q^{95} +(7.79994 - 5.92966i) q^{96} +(17.9553 - 2.09867i) q^{97} +(4.62990 - 0.475773i) q^{98} +(2.90939 - 11.5094i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more