LMFDB - Embedded newform 186.2.p.a.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [186,2,Mod(11,186)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(186, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 23]))

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

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

chi := DirichletCharacter("186.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.p (of order $30$, degree $8$, 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:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	186.17
Dual form			186.2.p.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.605161 - 1.62289i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.31329 + 0.758228i) q^{5} +(1.07704 - 1.35646i) q^{6} +(0.0465366 - 0.442766i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.26756 - 1.96422i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(0.605161 - 1.62289i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.31329 + 0.758228i) q^{5} +(1.07704 - 1.35646i) q^{6} +(0.0465366 - 0.442766i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.26756 - 1.96422i) q^{9} +(1.01471 + 1.12695i) q^{10} +(-5.28891 + 2.35477i) q^{11} +(1.44350 - 0.957243i) q^{12} +(0.417276 - 1.96313i) q^{13} +(0.181081 - 0.406715i) q^{14} +(2.02527 - 1.67248i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.46549 + 1.98816i) q^{17} +(-1.54960 - 2.56880i) q^{18} +(3.78335 - 0.804176i) q^{19} +(0.616798 + 1.38535i) q^{20} +(-0.690400 - 0.343469i) q^{21} +(-5.75772 + 0.605161i) q^{22} +(-6.60423 + 4.79825i) q^{23} +(1.66865 - 0.464327i) q^{24} +(-1.35018 - 2.33858i) q^{25} +(1.00349 - 1.73810i) q^{26} +(-4.55996 + 2.49134i) q^{27} +(0.297900 - 0.330852i) q^{28} +(0.598955 - 1.84340i) q^{29} +(2.44297 - 0.964778i) q^{30} +(-5.55810 - 0.327958i) q^{31} +1.00000i q^{32} +(0.620907 + 10.0084i) q^{33} +(3.63256 + 3.27077i) q^{34} +(0.396834 - 0.546195i) q^{35} +(-0.679956 - 2.92193i) q^{36} +(-2.73153 + 1.57705i) q^{37} +(3.84669 + 0.404303i) q^{38} +(-2.93343 - 1.86520i) q^{39} +(0.158513 + 1.50815i) q^{40} +(-0.0381095 + 0.0343139i) q^{41} +(-0.550472 - 0.540003i) q^{42} +(1.25764 + 5.91671i) q^{43} +(-5.66292 - 1.20369i) q^{44} +(-1.48864 - 4.29892i) q^{45} +(-7.76373 + 2.52259i) q^{46} +(2.69949 - 0.877117i) q^{47} +(1.73047 + 0.0740404i) q^{48} +(6.65316 + 1.41417i) q^{49} +(-0.561436 - 2.64135i) q^{50} +(5.92891 - 6.04385i) q^{51} +(1.49148 - 1.34293i) q^{52} +(0.283448 + 2.69683i) q^{53} +(-5.10665 + 0.960300i) q^{54} +(-8.73133 - 0.917700i) q^{55} +(0.385559 - 0.222603i) q^{56} +(0.984443 - 6.62663i) q^{57} +(1.13928 - 1.56809i) q^{58} +(-4.89938 - 4.41142i) q^{59} +(2.62154 - 0.162637i) q^{60} -4.12882i q^{61} +(-5.18472 - 2.02945i) q^{62} +(-0.975216 + 0.912592i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(2.03650 - 2.26176i) q^{65} +(-2.50223 + 9.71038i) q^{66} +(5.67003 - 9.82077i) q^{67} +(2.44404 + 4.23321i) q^{68} +(3.79043 + 13.6217i) q^{69} +(0.546195 - 0.396834i) q^{70} +(9.24128 - 0.971297i) q^{71} +(0.256249 - 2.98904i) q^{72} +(-2.32802 - 5.22881i) q^{73} +(-3.08517 + 0.655774i) q^{74} +(-4.61234 + 0.775981i) q^{75} +(3.53348 + 1.57321i) q^{76} +(0.796487 + 2.45134i) q^{77} +(-2.21348 - 2.68039i) q^{78} +(4.65367 - 10.4523i) q^{79} +(-0.315289 + 1.48332i) q^{80} +(1.28367 + 8.90798i) q^{81} +(-0.0468479 + 0.0208580i) q^{82} +(-4.07770 - 4.52874i) q^{83} +(-0.356660 - 0.683679i) q^{84} +(4.35700 + 5.99689i) q^{85} +(-0.632282 + 6.01576i) q^{86} +(-2.62917 - 2.08759i) q^{87} +(-5.01380 - 2.89472i) q^{88} +(12.7668 + 9.27564i) q^{89} +(-0.0873389 - 4.54853i) q^{90} +(-0.849788 - 0.276113i) q^{91} -8.16327 q^{92} +(-3.89578 + 8.82173i) q^{93} +2.83841 q^{94} +(5.57839 + 1.81253i) q^{95} +(1.62289 + 0.605161i) q^{96} +(-3.13126 - 2.27499i) q^{97} +(5.89052 + 3.40090i) q^{98} +(16.6182 + 5.04899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	0.605161	−	1.62289i	0.349390	−	0.936978i
$3$	0.605161	−	1.62289i	0.349390	−	0.936978i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	1.31329	+	0.758228i	0.587321	+	0.339090i	0.764038	−	0.645172i	$-0.223214\pi$
$5$	1.31329	+	0.758228i	0.587321	+	0.339090i	−0.176716	+	0.984262i	$0.556548\pi$
$6$	1.07704	−	1.35646i	0.439701	−	0.553772i
$7$	0.0465366	−	0.442766i	0.0175892	−	0.167350i	−0.982201	−	0.187833i	$-0.939854\pi$
$7$	0.0465366	−	0.442766i	0.0175892	−	0.167350i	0.999790	+	0.0204829i	$0.00652035\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−2.26756	−	1.96422i	−0.755854	−	0.654740i
$10$	1.01471	+	1.12695i	0.320879	+	0.356372i
$11$	−5.28891	+	2.35477i	−1.59467	+	0.709991i	−0.995860	−	0.0909022i	$-0.971025\pi$
$11$	−5.28891	+	2.35477i	−1.59467	+	0.709991i	−0.598807	+	0.800894i	$0.704358\pi$
$12$	1.44350	−	0.957243i	0.416702	−	0.276332i
$13$	0.417276	−	1.96313i	0.115731	−	0.544473i	−0.881634	−	0.471934i	$-0.843556\pi$
$13$	0.417276	−	1.96313i	0.115731	−	0.544473i	0.997366	−	0.0725399i	$-0.0231105\pi$
$14$	0.181081	−	0.406715i	0.0483960	−	0.108699i
$15$	2.02527	−	1.67248i	0.522924	−	0.431832i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	4.46549	+	1.98816i	1.08304	+	0.482200i	0.869095	−	0.494645i	$-0.164702\pi$
$17$	4.46549	+	1.98816i	1.08304	+	0.482200i	0.213945	+	0.976846i	$0.431369\pi$
$18$	−1.54960	−	2.56880i	−0.365245	−	0.605472i
$19$	3.78335	−	0.804176i	0.867960	−	0.184491i	0.247652	−	0.968849i	$-0.420341\pi$
$19$	3.78335	−	0.804176i	0.867960	−	0.184491i	0.620308	+	0.784358i	$0.287008\pi$
$20$	0.616798	+	1.38535i	0.137920	+	0.309774i
$21$	−0.690400	−	0.343469i	−0.150658	−	0.0749510i
$22$	−5.75772	+	0.605161i	−1.22755	+	0.129021i
$23$	−6.60423	+	4.79825i	−1.37708	+	1.00050i	−0.379930	+	0.925015i	$0.624052\pi$
$23$	−6.60423	+	4.79825i	−1.37708	+	1.00050i	−0.997147	+	0.0754892i	$0.975948\pi$
$24$	1.66865	−	0.464327i	0.340612	−	0.0947804i
$25$	−1.35018	−	2.33858i	−0.270036	−	0.467716i
$26$	1.00349	−	1.73810i	0.196801	−	0.340869i
$27$	−4.55996	+	2.49134i	−0.877564	+	0.479459i
$28$	0.297900	−	0.330852i	0.0562979	−	0.0625251i
$29$	0.598955	−	1.84340i	0.111223	−	0.342310i	−0.879917	−	0.475127i	$-0.842402\pi$
$29$	0.598955	−	1.84340i	0.111223	−	0.342310i	0.991141	+	0.132817i	$0.0424022\pi$
$30$	2.44297	−	0.964778i	0.446024	−	0.176143i
$31$	−5.55810	−	0.327958i	−0.998264	−	0.0589030i
$31$	−5.55810	−	0.327958i	−0.998264	−	0.0589030i
$32$			1.00000i			0.176777i
$33$	0.620907	+	10.0084i	0.108086	+	1.74223i
$34$	3.63256	+	3.27077i	0.622978	+	0.560932i
$35$	0.396834	−	0.546195i	0.0670772	−	0.0923238i
$36$	−0.679956	−	2.92193i	−0.113326	−	0.486988i
$37$	−2.73153	+	1.57705i	−0.449060	+	0.259265i	−0.707433	−	0.706780i	$-0.750147\pi$
$37$	−2.73153	+	1.57705i	−0.449060	+	0.259265i	0.258373	+	0.966045i	$0.416814\pi$
$38$	3.84669	+	0.404303i	0.624015	+	0.0655866i
$39$	−2.93343	−	1.86520i	−0.469724	−	0.298671i
$40$	0.158513	+	1.50815i	0.0250631	+	0.238459i
$41$	−0.0381095	+	0.0343139i	−0.00595170	+	0.00535894i	−0.672101	−	0.740459i	$-0.734608\pi$
$41$	−0.0381095	+	0.0343139i	−0.00595170	+	0.00535894i	0.666149	+	0.745818i	$0.267941\pi$
$42$	−0.550472	−	0.540003i	−0.0849397	−	0.0833243i
$43$	1.25764	+	5.91671i	0.191788	+	0.902290i	0.963788	+	0.266669i	$0.0859229\pi$
$43$	1.25764	+	5.91671i	0.191788	+	0.902290i	−0.772001	+	0.635622i	$0.780744\pi$
$44$	−5.66292	−	1.20369i	−0.853717	−	0.181463i
$45$	−1.48864	−	4.29892i	−0.221913	−	0.640845i
$46$	−7.76373	+	2.52259i	−1.14470	+	0.371936i
$47$	2.69949	−	0.877117i	0.393761	−	0.127941i	−0.105443	−	0.994425i	$-0.533626\pi$
$47$	2.69949	−	0.877117i	0.393761	−	0.127941i	0.499204	+	0.866485i	$0.333626\pi$
$48$	1.73047	+	0.0740404i	0.249771	+	0.0106868i
$49$	6.65316	+	1.41417i	0.950451	+	0.202025i
$50$	−0.561436	−	2.64135i	−0.0793991	−	0.373543i
$51$	5.92891	−	6.04385i	0.830214	−	0.846308i
$52$	1.49148	−	1.34293i	0.206831	−	0.186232i
$53$	0.283448	+	2.69683i	0.0389346	+	0.370438i	0.996589	+	0.0825195i	$0.0262967\pi$
$53$	0.283448	+	2.69683i	0.0389346	+	0.370438i	−0.957655	+	0.287919i	$0.907037\pi$
$54$	−5.10665	+	0.960300i	−0.694926	+	0.130680i
$55$	−8.73133	−	0.917700i	−1.17733	−	0.123743i
$56$	0.385559	−	0.222603i	0.0515225	−	0.0297465i
$57$	0.984443	−	6.62663i	0.130393	−	0.877719i
$58$	1.13928	−	1.56809i	0.149595	−	0.205900i
$59$	−4.89938	−	4.41142i	−0.637844	−	0.574318i	0.285458	−	0.958391i	$-0.407854\pi$
$59$	−4.89938	−	4.41142i	−0.637844	−	0.574318i	−0.923303	+	0.384074i	$0.874521\pi$
$60$	2.62154	−	0.162637i	0.338439	−	0.0209964i
$61$		−	4.12882i		−	0.528641i	−0.964435	−	0.264320i	$-0.914852\pi$
$61$		−	4.12882i		−	0.528641i	0.964435	−	0.264320i	$-0.0851476\pi$
$62$	−5.18472	−	2.02945i	−0.658460	−	0.257741i
$63$	−0.975216	+	0.912592i	−0.122866	+	0.114976i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	2.03650	−	2.26176i	0.252597	−	0.280537i
$66$	−2.50223	+	9.71038i	−0.308004	+	1.19526i
$67$	5.67003	−	9.82077i	0.692704	−	1.19980i	−0.278245	−	0.960510i	$-0.589753\pi$
$67$	5.67003	−	9.82077i	0.692704	−	1.19980i	0.970949	−	0.239288i	$-0.0769140\pi$
$68$	2.44404	+	4.23321i	0.296384	+	0.513352i
$69$	3.79043	+	13.6217i	0.456314	+	1.63986i
$70$	0.546195	−	0.396834i	0.0652828	−	0.0474307i
$71$	9.24128	−	0.971297i	1.09674	−	0.115272i	0.461166	−	0.887314i	$-0.347431\pi$
$71$	9.24128	−	0.971297i	1.09674	−	0.115272i	0.635572	+	0.772042i	$0.280764\pi$
$72$	0.256249	−	2.98904i	0.0301992	−	0.352261i
$73$	−2.32802	−	5.22881i	−0.272474	−	0.611986i	0.724538	−	0.689235i	$-0.242053\pi$
$73$	−2.32802	−	5.22881i	−0.272474	−	0.611986i	−0.997012	+	0.0772489i	$0.975386\pi$
$74$	−3.08517	+	0.655774i	−0.358644	+	0.0762321i
$75$	−4.61234	+	0.775981i	−0.532587	+	0.0896025i
$76$	3.53348	+	1.57321i	0.405318	+	0.180459i
$77$	0.796487	+	2.45134i	0.0907681	+	0.279356i
$78$	−2.21348	−	2.68039i	−0.250627	−	0.303494i
$79$	4.65367	−	10.4523i	0.523579	−	1.17598i	−0.437378	−	0.899278i	$-0.644093\pi$
$79$	4.65367	−	10.4523i	0.523579	−	1.17598i	0.960957	−	0.276699i	$-0.0892406\pi$
$80$	−0.315289	+	1.48332i	−0.0352504	+	0.165840i
$81$	1.28367	+	8.90798i	0.142630	+	0.989776i
$82$	−0.0468479	+	0.0208580i	−0.00517348	+	0.00230338i
$83$	−4.07770	−	4.52874i	−0.447586	−	0.497094i	0.476556	−	0.879144i	$-0.341885\pi$
$83$	−4.07770	−	4.52874i	−0.447586	−	0.497094i	−0.924142	+	0.382050i	$0.875218\pi$
$84$	−0.356660	−	0.683679i	−0.0389148	−	0.0745955i
$85$	4.35700	+	5.99689i	0.472583	+	0.650454i
$86$	−0.632282	+	6.01576i	−0.0681807	+	0.648696i
$87$	−2.62917	−	2.08759i	−0.281876	−	0.223813i
$88$	−5.01380	−	2.89472i	−0.534473	−	0.308578i
$89$	12.7668	+	9.27564i	1.35328	+	0.983216i	0.998841	+	0.0481374i	$0.0153285\pi$
$89$	12.7668	+	9.27564i	1.35328	+	0.983216i	0.354440	+	0.935079i	$0.384671\pi$
$90$	−0.0873389	−	4.54853i	−0.00920632	−	0.479457i
$91$	−0.849788	−	0.276113i	−0.0890820	−	0.0289445i
$92$	−8.16327			−0.851080
$93$	−3.89578	+	8.82173i	−0.403974	+	0.914771i
$94$	2.83841			0.292760
$95$	5.57839	+	1.81253i	0.572330	+	0.185961i
$96$	1.62289	+	0.605161i	0.165636	+	0.0617639i
$97$	−3.13126	−	2.27499i	−0.317931	−	0.230991i	0.417361	−	0.908741i	$-0.362955\pi$
$97$	−3.13126	−	2.27499i	−0.317931	−	0.230991i	−0.735292	+	0.677750i	$0.762955\pi$
$98$	5.89052	+	3.40090i	0.595033	+	0.343542i
$99$	16.6182	+	5.04899i	1.67019	+	0.507443i
$100$	0.282264	−	2.68557i	0.0282264	−	0.268557i
$101$	−2.75333	−	3.78963i	−0.273966	−	0.377082i	0.649758	−	0.760142i	$-0.274870\pi$
$101$	−2.75333	−	3.78963i	−0.273966	−	0.377082i	−0.923724	+	0.383059i	$0.874870\pi$
$102$	7.50638	−	3.91591i	0.743243	−	0.387733i
$103$	10.0171	+	11.1251i	0.987010	+	1.09619i	0.995360	+	0.0962204i	$0.0306754\pi$
$103$	10.0171	+	11.1251i	0.987010	+	1.09619i	−0.00835015	+	0.999965i	$0.502658\pi$
$104$	1.83347	−	0.816314i	0.179787	−	0.0800462i
$105$	−0.646268	−	0.974555i	−0.0630693	−	0.0951068i
$106$	−0.563791	+	2.65243i	−0.0547603	+	0.257627i
$107$	4.83006	−	10.8485i	0.466939	−	1.04876i	−0.514587	−	0.857438i	$-0.672055\pi$
$107$	4.83006	−	10.8485i	0.466939	−	1.04876i	0.981527	−	0.191325i	$-0.0612785\pi$
$108$	−5.15346	−	0.664740i	−0.495892	−	0.0639647i
$109$	5.33158	+	16.4089i	0.510673	+	1.57169i	0.791020	+	0.611791i	$0.209551\pi$
$109$	5.33158	+	16.4089i	0.510673	+	1.57169i	−0.280347	+	0.959899i	$0.590449\pi$
$110$	−8.02040	−	3.57091i	−0.764715	−	0.340473i
$111$	0.906368	+	5.38734i	0.0860286	+	0.511344i
$112$	0.435476	−	0.0925634i	0.0411487	−	0.00874642i
$113$	−5.08748	−	11.4267i	−0.478590	−	1.07493i	−0.978008	−	0.208569i	$-0.933119\pi$
$113$	−5.08748	−	11.4267i	−0.478590	−	1.07493i	0.499418	−	0.866361i	$-0.333547\pi$
$114$	2.98400	−	5.99809i	0.279477	−	0.561773i
$115$	−12.3114	+	1.29398i	−1.14805	+	0.120665i
$116$	1.56809	−	1.13928i	0.145593	−	0.105780i
$117$	−4.80221	+	3.63189i	−0.443965	+	0.335768i
$118$	−3.29638	−	5.70950i	−0.303456	−	0.525602i
$119$	1.08810	−	1.88465i	0.0997460	−	0.172765i
$120$	2.54349	+	0.655423i	0.232188	+	0.0598317i
$121$	15.0672	−	16.7338i	1.36974	−	1.52125i
$122$	1.27587	−	3.92674i	0.115512	−	0.355510i
$123$	0.0326255	+	0.0826130i	0.00294174	+	0.00744897i
$124$	−4.30383	−	3.53229i	−0.386495	−	0.317209i
$125$		−	11.6773i		−	1.04445i
$126$	−1.20949	+	0.566568i	−0.107750	+	0.0504739i
$127$	−5.94008	−	5.34847i	−0.527097	−	0.474600i	0.362091	−	0.932143i	$-0.382063\pi$
$127$	−5.94008	−	5.34847i	−0.527097	−	0.474600i	−0.889188	+	0.457543i	$0.848730\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	10.3633	+	1.53955i	0.912434	+	0.135550i
$130$	2.63575	−	1.52175i	0.231171	−	0.133467i
$131$	−16.9294	−	1.77935i	−1.47913	−	0.155463i	−0.669678	−	0.742652i	$-0.733568\pi$
$131$	−16.9294	−	1.77935i	−1.47913	−	0.155463i	−0.809450	+	0.587189i	$0.800234\pi$
$132$	−5.38044	+	8.46189i	−0.468307	+	0.736513i
$133$	−0.179998	−	1.71256i	−0.0156078	−	0.148498i
$134$	8.42730	−	7.58797i	0.728008	−	0.655501i
$135$	−7.87755	−	0.185638i	−0.677992	−	0.0159772i
$136$	1.01629	+	4.78127i	0.0871462	+	0.409990i
$137$	−0.422413	−	0.0897868i	−0.0360892	−	0.00767100i	0.189832	−	0.981817i	$-0.439206\pi$
$137$	−0.422413	−	0.0897868i	−0.0360892	−	0.00767100i	−0.225921	+	0.974146i	$0.572539\pi$
$138$	−0.604412	+	14.1263i	−0.0514510	+	1.20251i
$139$	3.15138	−	1.02395i	0.267297	−	0.0868500i	−0.172302	−	0.985044i	$-0.555121\pi$
$139$	3.15138	−	1.02395i	0.267297	−	0.0868500i	0.439599	+	0.898194i	$0.355121\pi$
$140$	0.642091	−	0.208628i	0.0542666	−	0.0176323i
$141$	0.210157	−	4.91178i	0.0176984	−	0.413646i
$142$	9.08912	+	1.93195i	0.762742	+	0.162126i
$143$	2.41579	+	11.3654i	0.202018	+	0.950422i
$144$	1.16737	−	2.76356i	0.0972809	−	0.230296i
$145$	2.18432	−	1.96677i	0.181398	−	0.163331i
$146$	−0.598284	−	5.69229i	−0.0495143	−	0.471097i
$147$	6.32128	−	9.94156i	0.521370	−	0.819966i
$148$	−3.13682	−	0.329693i	−0.257845	−	0.0271006i
$149$	−5.67147	+	3.27443i	−0.464625	+	0.268251i	−0.713987	−	0.700159i	$-0.753112\pi$
$149$	−5.67147	+	3.27443i	−0.464625	+	0.268251i	0.249362	+	0.968410i	$0.419779\pi$
$150$	−4.62639	−	0.687290i	−0.377743	−	0.0561170i
$151$	−13.3881	+	18.4272i	−1.08951	+	1.49958i	−0.240912	+	0.970547i	$0.577446\pi$
$151$	−13.3881	+	18.4272i	−1.08951	+	1.49958i	−0.848599	+	0.529036i	$0.822554\pi$
$152$	2.87439	+	2.58811i	0.233144	+	0.209924i
$153$	−6.22058	−	13.2795i	−0.502904	−	1.07358i
$154$			2.57749i			0.207700i
$155$	−7.05073	−	4.64501i	−0.566328	−	0.373096i
$156$	−1.27685	−	3.23320i	−0.102230	−	0.258863i
$157$	−5.20192	+	16.0099i	−0.415159	+	1.27773i	0.496950	+	0.867779i	$0.334453\pi$
$157$	−5.20192	+	16.0099i	−0.415159	+	1.27773i	−0.912109	+	0.409948i	$0.865547\pi$
$158$	7.65585	−	8.50268i	0.609066	−	0.676437i
$159$	4.54820	+	1.17201i	0.360696	+	0.0929464i
$160$	−0.758228	+	1.31329i	−0.0599432	+	0.103825i
$161$	1.81717	+	3.14742i	0.143213	+	0.248052i
$162$	−1.53188	+	8.86867i	−0.120355	+	0.696789i
$163$	3.39436	−	2.46615i	0.265867	−	0.193164i	−0.446863	−	0.894603i	$-0.647459\pi$
$163$	3.39436	−	2.46615i	0.265867	−	0.193164i	0.712729	+	0.701439i	$0.247459\pi$
$164$	−0.0510004	+	0.00536036i	−0.00398247	+	0.000418574i
$165$	−6.77318	+	13.6147i	−0.527292	+	1.05990i
$166$	−2.47866	−	5.56717i	−0.192382	−	0.432096i
$167$	6.04365	−	1.28462i	0.467671	−	0.0994066i	0.0319524	−	0.999489i	$-0.489828\pi$
$167$	6.04365	−	1.28462i	0.467671	−	0.0994066i	0.435719	+	0.900083i	$0.356494\pi$
$168$	−0.127935	−	0.760431i	−0.00987040	−	0.0586685i
$169$	8.19634	+	3.64925i	0.630488	+	0.280711i
$170$	2.29061	+	7.04977i	0.175682	+	0.540693i
$171$	−10.1586	−	5.60782i	−0.776845	−	0.428841i
$172$	−2.46031	+	5.52594i	−0.187597	+	0.421349i
$173$	−1.29890	+	6.11083i	−0.0987534	+	0.464598i	0.900786	+	0.434262i	$0.142991\pi$
$173$	−1.29890	+	6.11083i	−0.0987534	+	0.464598i	−0.999540	+	0.0303356i	$0.990342\pi$
$174$	−1.85539	−	2.79787i	−0.140657	−	0.212106i
$175$	−1.09828	+	0.488985i	−0.0830220	+	0.0369638i
$176$	−3.87389	−	4.30239i	−0.292005	−	0.324305i
$177$	−10.1242	+	5.28155i	−0.760979	+	0.396985i
$178$	9.27564	+	12.7668i	0.695239	+	0.956914i
$179$	2.21712	−	21.0945i	0.165715	−	1.57667i	−0.523442	−	0.852061i	$-0.675352\pi$
$179$	2.21712	−	21.0945i	0.165715	−	1.57667i	0.689157	−	0.724612i	$-0.257981\pi$
$180$	1.32251	−	4.35290i	0.0985740	−	0.324446i
$181$	−9.22668	−	5.32703i	−0.685814	−	0.395955i	0.116228	−	0.993223i	$-0.462920\pi$
$181$	−9.22668	−	5.32703i	−0.685814	−	0.395955i	−0.802042	+	0.597268i	$0.796253\pi$
$182$	−0.722873	−	0.525198i	−0.0535829	−	0.0389303i
$183$	−6.70062	−	2.49860i	−0.495324	−	0.184702i
$184$	−7.76373	−	2.52259i	−0.572350	−	0.185968i
$185$	−4.78305			−0.351657
$186$	−6.43117	+	7.18610i	−0.471556	+	0.526910i
$187$	−28.2992			−2.06945
$188$	2.69949	+	0.877117i	0.196880	+	0.0639703i
$189$	0.890876	+	2.13493i	0.0648017	+	0.155294i
$190$	4.74526	+	3.44763i	0.344257	+	0.250118i
$191$	8.14907	+	4.70487i	0.589646	+	0.340432i	0.764958	−	0.644081i	$-0.222760\pi$
$191$	8.14907	+	4.70487i	0.589646	+	0.340432i	−0.175311	+	0.984513i	$0.556093\pi$
$192$	1.35646	+	1.07704i	0.0978939	+	0.0777289i
$193$	−0.877734	+	8.35108i	−0.0631807	+	0.601124i	0.916427	+	0.400203i	$0.131060\pi$
$193$	−0.877734	+	8.35108i	−0.0631807	+	0.601124i	−0.979607	+	0.200921i	$0.935606\pi$
$194$	−2.27499	−	3.13126i	−0.163335	−	0.224811i
$195$	−2.43819	−	4.67375i	−0.174602	−	0.334695i
$196$	4.55129	+	5.05472i	0.325092	+	0.361051i
$197$	4.28977	−	1.90993i	0.305633	−	0.136077i	−0.248189	−	0.968712i	$-0.579835\pi$
$197$	4.28977	−	1.90993i	0.305633	−	0.136077i	0.553822	+	0.832635i	$0.313169\pi$
$198$	14.2447	+	9.93719i	1.01232	+	0.706206i
$199$	−4.11535	+	19.3612i	−0.291729	+	1.37248i	0.551164	+	0.834397i	$0.314184\pi$
$199$	−4.11535	+	19.3612i	−0.291729	+	1.37248i	−0.842893	+	0.538081i	$0.819150\pi$
$200$	1.09834	−	2.46690i	0.0776640	−	0.174436i
$201$	−12.5068	−	15.1450i	−0.882160	−	1.06824i
$202$	−1.44751	−	4.45498i	−0.101846	−	0.313451i
$203$	−0.788320	−	0.350983i	−0.0553292	−	0.0246342i
$204$	8.34908	−	1.40465i	0.584552	−	0.0983452i
$205$	−0.0760666	+	0.0161685i	−0.00531272	+	0.00112925i
$206$	6.08895	+	13.6760i	0.424237	+	0.952853i
$207$	24.4003	+	2.09183i	1.69594	+	0.145392i
$208$	1.99599	−	0.209787i	0.138397	−	0.0145461i
$209$	−18.1162	+	13.1622i	−1.25312	+	0.910446i
$210$	−0.313483	−	1.12656i	−0.0216324	−	0.0777403i
$211$	−2.58650	−	4.47996i	−0.178062	−	0.308413i	0.763155	−	0.646216i	$-0.223650\pi$
$211$	−2.58650	−	4.47996i	−0.178062	−	0.308413i	−0.941217	+	0.337803i	$0.890316\pi$
$212$	−1.35584	+	2.34839i	−0.0931197	+	0.161288i
$213$	4.01614	−	15.5854i	0.275182	−	1.06789i
$214$	7.94603	−	8.82496i	0.543179	−	0.603262i
$215$	−2.83458	+	8.72394i	−0.193317	+	0.594967i
$216$	−4.69581	−	2.22471i	−0.319510	−	0.151372i
$217$	−0.403864	+	2.44568i	−0.0274161	+	0.166023i
$218$			17.2534i			1.16855i
$219$	−9.89462	+	0.613851i	−0.668616	+	0.0414802i
$220$	−6.52438	−	5.87458i	−0.439874	−	0.396064i
$221$	5.76636	−	7.93671i	0.387887	−	0.533881i
$222$	−0.802774	+	5.40375i	−0.0538787	+	0.362676i
$223$	1.74777	−	1.00908i	0.117039	−	0.0675727i	−0.440338	−	0.897832i	$-0.645141\pi$
$223$	1.74777	−	1.00908i	0.117039	−	0.0675727i	0.557377	+	0.830260i	$0.311808\pi$
$224$	0.442766	+	0.0465366i	0.0295836	+	0.00310936i
$225$	−1.53187	+	7.95493i	−0.102125	+	0.530328i
$226$	−1.30745	−	12.4395i	−0.0869701	−	0.827465i
$227$	−21.2323	+	19.1177i	−1.40924	+	1.26888i	−0.491971	+	0.870611i	$0.663723\pi$
$227$	−21.2323	+	19.1177i	−1.40924	+	1.26888i	−0.917267	+	0.398272i	$0.869610\pi$
$228$	4.69147	−	4.78242i	0.310700	−	0.316723i
$229$	−4.60625	−	21.6707i	−0.304389	−	1.43204i	−0.818595	−	0.574372i	$-0.805246\pi$
$229$	−4.60625	−	21.6707i	−0.304389	−	1.43204i	0.514205	−	0.857667i	$-0.328087\pi$
$230$	−12.1087	−	2.57379i	−0.798426	−	0.169711i
$231$	4.46026	+	0.190838i	0.293463	+	0.0125562i
$232$	1.84340	−	0.598955i	0.121025	−	0.0393233i
$233$	−8.14229	+	2.64559i	−0.533419	+	0.173318i	−0.563327	−	0.826234i	$-0.690479\pi$
$233$	−8.14229	+	2.64559i	−0.533419	+	0.173318i	0.0299075	+	0.999553i	$0.490479\pi$
$234$	−5.68949	+	1.97017i	−0.371934	+	0.128794i
$235$	4.21027	+	0.894920i	0.274648	+	0.0583781i
$236$	−1.37071	−	6.44869i	−0.0892258	−	0.419774i
$237$	−14.1468	−	13.8777i	−0.918931	−	0.901456i
$238$	1.61723	−	1.45616i	0.104830	−	0.0943890i
$239$	2.47825	+	23.5790i	0.160305	+	1.52520i	0.718522	+	0.695504i	$0.244819\pi$
$239$	2.47825	+	23.5790i	0.160305	+	1.52520i	−0.558217	+	0.829695i	$0.688515\pi$
$240$	2.21647	+	1.40933i	0.143072	+	0.0909716i
$241$	13.2675	+	1.39447i	0.854635	+	0.0898258i	0.521705	−	0.853126i	$-0.325296\pi$
$241$	13.2675	+	1.39447i	0.854635	+	0.0898258i	0.332930	+	0.942952i	$0.391963\pi$
$242$	19.5008	−	11.2588i	1.25356	−	0.723741i
$243$	15.2335	+	3.30750i	0.977231	+	0.212176i
$244$	2.42686	−	3.34028i	0.155364	−	0.213840i
$245$	7.66526	+	6.90183i	0.489715	+	0.440942i
$246$	0.00549984	+	0.0886515i	0.000350657	+	0.00565221i
$247$		−	7.76276i		−	0.493933i
$248$	−3.00164	−	4.68936i	−0.190605	−	0.297775i
$249$	−9.81733	+	3.87705i	−0.622148	+	0.245698i
$250$	3.60847	−	11.1057i	0.228220	−	0.702388i
$251$	12.2127	−	13.5636i	0.770859	−	0.856126i	−0.222046	−	0.975036i	$-0.571273\pi$
$251$	12.2127	−	13.5636i	0.770859	−	0.856126i	0.992905	+	0.118910i	$0.0379401\pi$
$252$	−1.32537	+	0.165085i	−0.0834907	+	0.0103994i
$253$	23.6304	−	40.9290i	1.48563	−	2.57318i
$254$	−3.99658	−	6.92228i	−0.250768	−	0.434343i
$255$	12.3690	−	3.44186i	0.774577	−	0.215537i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.50364	−	0.158039i	0.0937943	−	0.00985818i	−0.0575150	−	0.998345i	$-0.518318\pi$
$257$	1.50364	−	0.158039i	0.0937943	−	0.00985818i	0.151309	+	0.988486i	$0.451651\pi$
$258$	9.38030	+	4.66663i	0.583992	+	0.290531i
$259$	0.571148	+	1.28282i	0.0354894	+	0.0797105i
$260$	2.97700	−	0.632780i	0.184625	−	0.0392434i
$261$	−4.97900	+	3.00353i	−0.308193	+	0.185914i
$262$	−15.5510	−	6.92373i	−0.960741	−	0.427750i
$263$	−4.83712	−	14.8871i	−0.298269	−	0.917979i	−0.982104	−	0.188341i	$-0.939689\pi$
$263$	−4.83712	−	14.8871i	−0.298269	−	0.917979i	0.683834	−	0.729637i	$-0.260311\pi$
$264$	−7.73197	+	6.38509i	−0.475870	+	0.392975i
$265$	−1.67256	+	3.75664i	−0.102745	+	0.230769i
$266$	0.358024	−	1.68437i	0.0219518	−	0.103275i
$267$	22.7794	−	15.1059i	1.39407	−	0.924468i
$268$	10.3597	−	4.61241i	0.632816	−	0.281748i
$269$	8.96818	+	9.96017i	0.546800	+	0.607282i	0.951682	−	0.307087i	$-0.0993541\pi$
$269$	8.96818	+	9.96017i	0.546800	+	0.607282i	−0.404882	+	0.914369i	$0.632687\pi$
$270$	−7.43463	−	2.61085i	−0.452457	−	0.158891i
$271$	18.9726	+	26.1135i	1.15250	+	1.58628i	0.735738	+	0.677266i	$0.236835\pi$
$271$	18.9726	+	26.1135i	1.15250	+	1.58628i	0.416763	+	0.909015i	$0.363165\pi$
$272$	−0.510944	+	4.86131i	−0.0309805	+	0.294760i
$273$	−0.962360	+	1.21202i	−0.0582447	+	0.0733549i
$274$	−0.373993	−	0.215925i	−0.0225938	−	0.0130445i
$275$	12.6478	+	9.18917i	0.762692	+	0.554128i
$276$	−4.94009	+	13.2481i	−0.297358	+	0.797443i
$277$	−27.9823	−	9.09198i	−1.68129	−	0.546284i	−0.696129	−	0.717916i	$-0.745096\pi$
$277$	−27.9823	−	9.09198i	−1.68129	−	0.546284i	−0.985161	+	0.171632i	$0.945096\pi$
$278$	3.31356			0.198734
$279$	11.9591	+	11.6610i	0.715975	+	0.698126i
$280$	0.675134			0.0403470
$281$	−2.52970	−	0.821948i	−0.150909	−	0.0490333i	0.232588	−	0.972575i	$-0.425280\pi$
$281$	−2.52970	−	0.821948i	−0.150909	−	0.0490333i	−0.383497	+	0.923542i	$0.625280\pi$
$282$	1.71769	−	4.60644i	0.102287	−	0.274309i
$283$	13.2056	+	9.59441i	0.784990	+	0.570328i	0.906472	−	0.422265i	$-0.138765\pi$
$283$	13.2056	+	9.59441i	0.784990	+	0.570328i	−0.121483	+	0.992594i	$0.538765\pi$
$284$	8.04726	+	4.64609i	0.477517	+	0.275695i
$285$	6.31736	−	7.95625i	0.374208	−	0.471288i
$286$	−1.21455	+	11.5557i	−0.0718177	+	0.683300i
$287$	0.0134196	+	0.0184705i	0.000792132	+	0.00109028i
$288$	1.96422	−	2.26756i	0.115743	−	0.133617i
$289$	4.61257	+	5.12278i	0.271328	+	0.301340i
$290$	2.68517	−	1.19552i	0.157679	−	0.0702031i
$291$	−5.58699	+	3.70496i	−0.327515	+	0.217189i
$292$	1.19001	−	5.59857i	0.0696402	−	0.327631i
$293$	−0.444331	+	0.997984i	−0.0259581	+	0.0583029i	−0.926059	−	0.377378i	$-0.876826\pi$
$293$	−0.444331	+	0.997984i	−0.0259581	+	0.0583029i	0.900101	+	0.435681i	$0.143492\pi$
$294$	9.08400	−	7.50160i	0.529790	−	0.437502i
$295$	−3.08944	−	9.50832i	−0.179874	−	0.553596i
$296$	−2.88141	−	1.28289i	−0.167479	−	0.0745663i
$297$	18.2507	−	23.9142i	1.05901	−	1.38764i
$298$	−6.40574	+	1.36158i	−0.371075	+	0.0788744i
$299$	6.66379	+	14.9671i	0.385377	+	0.865571i
$300$	−4.18757	−	2.08328i	−0.241770	−	0.120278i
$301$	2.67825	−	0.281495i	0.154372	−	0.0162251i
$302$	−18.4272	+	13.3881i	−1.06037	+	0.770401i
$303$	−7.81636	+	2.17502i	−0.449038	+	0.124952i
$304$	1.93394	+	3.34968i	0.110919	+	0.192117i
$305$	3.13058	−	5.42233i	0.179257	−	0.310482i
$306$	−1.81253	−	14.5518i	−0.103616	−	0.831872i
$307$	−9.38507	+	10.4232i	−0.535634	+	0.594882i	−0.948841	−	0.315755i	$-0.897742\pi$
$307$	−9.38507	+	10.4232i	−0.535634	+	0.594882i	0.413206	+	0.910637i	$0.364409\pi$
$308$	−0.796487	+	2.45134i	−0.0453841	+	0.139678i
$309$	24.1167	−	9.52416i	1.37195	−	0.541810i
$310$	−5.27025	−	6.59646i	−0.299330	−	0.374654i
$311$			8.81000i			0.499569i	0.968301	+	0.249785i	$0.0803598\pi$
$311$			8.81000i			0.499569i	−0.968301	+	0.249785i	$0.919640\pi$
$312$	−0.215246	−	3.46953i	−0.0121859	−	0.196423i
$313$	8.09230	+	7.28634i	0.457404	+	0.411849i	0.865358	−	0.501154i	$-0.167091\pi$
$313$	8.09230	+	7.28634i	0.457404	+	0.411849i	−0.407954	+	0.913002i	$0.633758\pi$
$314$	−9.89464	+	13.6188i	−0.558387	+	0.768554i
$315$	−1.97269	+	0.459061i	−0.111149	+	0.0258652i
$316$	9.90861	−	5.72074i	0.557403	−	0.321817i
$317$	−24.4835	−	2.57332i	−1.37513	−	0.144532i	−0.612041	−	0.790826i	$-0.709651\pi$
$317$	−24.4835	−	2.57332i	−1.37513	−	0.144532i	−0.763089	+	0.646294i	$0.776318\pi$
$318$	3.96342	+	2.52012i	0.222258	+	0.141321i
$319$	1.17296	+	11.1600i	0.0656731	+	0.624838i
$320$	−1.12695	+	1.01471i	−0.0629982	+	0.0567239i
$321$	−14.6830	−	14.4037i	−0.819524	−	0.803939i
$322$	0.755620	+	3.55491i	0.0421091	+	0.198108i
$323$	18.4933	+	3.93088i	1.02900	+	0.218720i
$324$	−4.19747	+	7.96123i	−0.233193	+	0.442291i
$325$	−5.15433	+	1.67474i	−0.285911	+	0.0928980i
$326$	3.99031	−	1.29653i	0.221003	−	0.0718082i
$327$	29.8564	+	1.27745i	1.65106	+	0.0706429i
$328$	−0.0501607	−	0.0106620i	−0.00276966	−	0.000588710i
$329$	−0.262733	−	1.23606i	−0.0144849	−	0.0681462i
$330$	−10.6488	+	10.8553i	−0.586199	+	0.597563i
$331$	13.7730	−	12.4013i	0.757033	−	0.681635i	−0.197313	−	0.980341i	$-0.563221\pi$
$331$	13.7730	−	12.4013i	0.757033	−	0.681635i	0.954345	+	0.298705i	$0.0965548\pi$
$332$	−0.636999	−	6.06064i	−0.0349599	−	0.332621i
$333$	9.29158	+	1.78927i	0.509175	+	0.0980514i
$334$	6.14482	+	0.645846i	0.336229	+	0.0353391i
$335$	14.8928	−	8.59835i	0.813679	−	0.469778i
$336$	0.113313	−	0.762747i	0.00618172	−	0.0416113i
$337$	−4.86237	+	6.69248i	−0.264870	+	0.364563i	−0.920650	−	0.390390i	$-0.872340\pi$
$337$	−4.86237	+	6.69248i	−0.264870	+	0.364563i	0.655779	+	0.754953i	$0.272340\pi$
$338$	6.66751	+	6.00345i	0.362664	+	0.326545i
$339$	−21.6230	+	1.34147i	−1.17440	+	0.0728585i
$340$			7.41257i			0.402003i
$341$	30.1685	−	11.3535i	1.63372	−	0.614828i
$342$	−7.92846	−	8.47252i	−0.428722	−	0.458142i
$343$	1.89880	−	5.84389i	0.102525	−	0.315540i
$344$	−4.04750	+	4.49521i	−0.218227	+	0.242365i
$345$	−5.35040	+	20.7632i	−0.288056	+	1.11785i
$346$	−3.12368	+	5.41037i	−0.167930	+	0.290863i
$347$	−6.56431	−	11.3697i	−0.352391	−	0.610359i	0.634277	−	0.773106i	$-0.281298\pi$
$347$	−6.56431	−	11.3697i	−0.352391	−	0.610359i	−0.986668	+	0.162747i	$0.947964\pi$
$348$	−0.899987	−	3.23428i	−0.0482444	−	0.173376i
$349$	−16.3305	+	11.8648i	−0.874152	+	0.635109i	−0.931698	−	0.363234i	$-0.881673\pi$
$349$	−16.3305	+	11.8648i	−0.874152	+	0.635109i	0.0575457	+	0.998343i	$0.481673\pi$
$350$	−1.19563	+	0.125666i	−0.0639090	+	0.00671711i
$351$	2.98806	+	9.99135i	0.159491	+	0.533299i
$352$	−2.35477	−	5.28891i	−0.125510	−	0.281900i
$353$	−33.7575	+	7.17537i	−1.79673	+	0.381907i	−0.980609	−	0.195976i	$-0.937213\pi$
$353$	−33.7575	+	7.17537i	−1.79673	+	0.381907i	−0.816120	+	0.577882i	$0.803879\pi$
$354$	−11.2607	+	1.89451i	−0.598502	+	0.100692i
$355$	12.8729	+	5.73140i	0.683225	+	0.304191i
$356$	4.87649	+	15.0083i	0.258454	+	0.795439i
$357$	−2.40010	−	2.90638i	−0.127027	−	0.153822i
$358$	8.62715	−	19.3769i	0.455959	−	1.02410i
$359$	−5.73074	+	26.9610i	−0.302457	+	1.42295i	0.520022	+	0.854153i	$0.325924\pi$
$359$	−5.73074	+	26.9610i	−0.302457	+	1.42295i	−0.822479	+	0.568796i	$0.807410\pi$
$360$	2.60290	−	3.73118i	0.137185	−	0.196650i
$361$	−3.69031	+	1.64303i	−0.194227	+	0.0864754i
$362$	−7.12895	−	7.91750i	−0.374689	−	0.416135i
$363$	−18.0391	−	34.5790i	−0.946807	−	1.81493i
$364$	−0.525198	−	0.722873i	−0.0275278	−	0.0378888i
$365$	0.907271	−	8.63211i	0.0474887	−	0.451825i
$366$	−5.60056	−	4.44691i	−0.292746	−	0.232444i
$367$	−31.6580	−	18.2778i	−1.65254	−	0.954092i	−0.976025	−	0.217659i	$-0.930158\pi$
$367$	−31.6580	−	18.2778i	−1.65254	−	0.954092i	−0.676511	−	0.736433i	$-0.736509\pi$
$368$	−6.60423	−	4.79825i	−0.344269	−	0.250126i
$369$	0.153816	−	0.00295350i	0.00800733	−	0.000153753i
$370$	−4.54895	−	1.47804i	−0.236489	−	0.0768398i
$371$	1.20726			0.0626777
$372$	−8.33704	+	4.84704i	−0.432255	+	0.251308i
$373$	15.7886			0.817502			0.408751	−	0.912646i	$-0.365964\pi$
$373$	15.7886			0.817502			0.408751	+	0.912646i	$0.365964\pi$
$374$	−26.9142	−	8.74495i	−1.39170	−	0.452190i
$375$	−18.9509	−	7.06662i	−0.978622	−	0.364919i
$376$	2.29632	+	1.66838i	0.118424	+	0.0860399i
$377$	−3.36889	−	1.94503i	−0.173507	−	0.100174i
$378$	0.187543	+	2.30574i	0.00964616	+	0.118594i
$379$	−2.85044	+	27.1201i	−0.146417	+	1.39307i	0.636662	+	0.771143i	$0.280315\pi$
$379$	−2.85044	+	27.1201i	−0.146417	+	1.39307i	−0.783079	+	0.621922i	$0.786352\pi$
$380$	3.44763	+	4.74526i	0.176860	+	0.243427i
$381$	−12.2747	+	6.40343i	−0.628852	+	0.328058i
$382$	6.29634	+	6.99280i	0.322149	+	0.357783i
$383$	−3.77097	+	1.67894i	−0.192687	+	0.0857900i	−0.500812	−	0.865556i	$-0.666965\pi$
$383$	−3.77097	+	1.67894i	−0.192687	+	0.0857900i	0.308125	+	0.951346i	$0.400299\pi$
$384$	0.957243	+	1.44350i	0.0488491	+	0.0736632i
$385$	−0.812653	+	3.82323i	−0.0414166	+	0.194850i
$386$	−3.41540	+	7.67112i	−0.173839	+	0.390449i
$387$	8.76997	−	15.8868i	0.445802	−	0.807571i
$388$	−1.19604	−	3.68102i	−0.0607195	−	0.186875i
$389$	−14.1418	−	6.29632i	−0.717016	−	0.319236i	0.0156002	−	0.999878i	$-0.495034\pi$
$389$	−14.1418	−	6.29632i	−0.717016	−	0.319236i	−0.732616	+	0.680642i	$0.761701\pi$
$390$	−0.874588	−	5.19845i	−0.0442865	−	0.263234i
$391$	−39.0308	+	8.29625i	−1.97387	+	0.419560i
$392$	2.76654	+	6.21375i	0.139731	+	0.313842i
$393$	−13.1327	+	26.3978i	−0.662457	+	1.33159i
$394$	4.67001	−	0.490838i	0.235272	−	0.0247281i
$395$	14.0369	−	10.1984i	0.706271	−	0.513136i
$396$	10.4767	+	13.8527i	0.526474	+	0.696123i
$397$	−5.35373	−	9.27293i	−0.268696	−	0.465395i	0.699829	−	0.714310i	$-0.253259\pi$
$397$	−5.35373	−	9.27293i	−0.268696	−	0.465395i	−0.968525	+	0.248915i	$0.919926\pi$
$398$	−9.89686	+	17.1419i	−0.496085	+	0.859244i
$399$	−2.88824	−	0.744259i	−0.144593	−	0.0372596i
$400$	1.80689	−	2.00676i	0.0903447	−	0.100338i
$401$	6.30852	−	19.4156i	0.315033	−	0.969571i	−0.660708	−	0.750643i	$-0.729744\pi$
$401$	6.30852	−	19.4156i	0.315033	−	0.969571i	0.975741	−	0.218928i	$-0.0702560\pi$
$402$	−7.21460	−	18.2685i	−0.359832	−	0.911152i
$403$	−2.96308	+	10.7744i	−0.147602	+	0.536711i
$404$		−	4.68424i		−	0.233050i
$405$	−5.06845	+	12.6721i	−0.251853	+	0.629681i
$406$	−0.641277	−	0.577409i	−0.0318261	−	0.0286563i
$407$	10.7332	−	14.7730i	0.532026	−	0.732271i
$408$	8.37451	+	1.24411i	0.414600	+	0.0615924i
$409$	20.1660	−	11.6429i	0.997146	−	0.575702i	0.0897434	−	0.995965i	$-0.471395\pi$
$409$	20.1660	−	11.6429i	0.997146	−	0.575702i	0.907403	+	0.420262i	$0.138062\pi$
$410$	−0.0773399	−	0.00812876i	−0.00381955	−	0.000401451i
$411$	−0.401342	+	0.631196i	−0.0197968	+	0.0311346i
$412$	1.56482	+	14.8882i	0.0770930	+	0.733491i
$413$	−2.18123	+	1.96399i	−0.107331	+	0.0966415i
$414$	22.5597	+	9.52956i	1.10875	+	0.468352i
$415$	−1.92138	−	9.03938i	−0.0943168	−	0.443726i
$416$	1.96313	+	0.417276i	0.0962502	+	0.0204586i
$417$	0.245337	−	5.73401i	0.0120142	−	0.280796i
$418$	−21.2968	+	6.91976i	−1.04166	+	0.338456i
$419$	26.4966	−	8.60926i	1.29444	−	0.420590i	0.420798	−	0.907154i	$-0.361750\pi$
$419$	26.4966	−	8.60926i	1.29444	−	0.420590i	0.873645	+	0.486565i	$0.161750\pi$
$420$	0.0499872	−	1.16830i	0.00243913	−	0.0570071i
$421$	3.78824	+	0.805216i	0.184628	+	0.0392438i	0.299297	−	0.954160i	$-0.403248\pi$
$421$	3.78824	+	0.805216i	0.184628	+	0.0392438i	−0.114670	+	0.993404i	$0.536581\pi$
$422$	−1.07553	−	5.05996i	−0.0523559	−	0.246315i
$423$	−7.84411	−	3.31348i	−0.381394	−	0.161107i
$424$	−2.01518	+	1.81447i	−0.0978656	+	0.0881186i
$425$	−1.37973	−	13.1273i	−0.0669269	−	0.636767i
$426$	8.63573	−	13.5815i	0.418403	−	0.658027i
$427$	−1.82810	−	0.192141i	−0.0884680	−	0.00929836i
$428$	10.2842	−	5.93757i	0.497105	−	0.287004i
$429$	19.9068	+	2.95732i	0.961107	+	0.142781i
$430$	−5.39169	+	7.42102i	−0.260010	+	0.357873i
$431$	7.13571	+	6.42502i	0.343715	+	0.309482i	0.822850	−	0.568259i	$-0.192383\pi$
$431$	7.13571	+	6.42502i	0.343715	+	0.309482i	−0.479135	+	0.877741i	$0.659049\pi$
$432$	−3.77851	−	3.56691i	−0.181794	−	0.171613i
$433$		−	6.69986i		−	0.321975i	−0.986956	−	0.160987i	$-0.948532\pi$
$433$		−	6.69986i		−	0.321975i	0.986956	−	0.160987i	$-0.0514679\pi$
$434$	−1.13985	+	2.20118i	−0.0547147	+	0.105660i
$435$	−1.86999	−	4.73512i	−0.0896592	−	0.227032i
$436$	−5.33158	+	16.4089i	−0.255336	+	0.785845i
$437$	−21.1275	+	23.4644i	−1.01066	+	1.12246i
$438$	−9.60003	−	2.47380i	−0.458707	−	0.118203i
$439$	−2.48466	+	4.30355i	−0.118586	+	0.205397i	−0.919208	−	0.393773i	$-0.871170\pi$
$439$	−2.48466	+	4.30355i	−0.118586	+	0.205397i	0.800621	+	0.599171i	$0.204503\pi$
$440$	−4.38971	−	7.60320i	−0.209271	−	0.362469i
$441$	−12.3087	−	16.2750i	−0.586128	−	0.775000i
$442$	7.93671	−	5.76636i	0.377511	−	0.274278i
$443$	7.46121	−	0.784204i	0.354493	−	0.0372587i	0.0743913	−	0.997229i	$-0.476299\pi$
$443$	7.46121	−	0.784204i	0.354493	−	0.0372587i	0.280101	+	0.959970i	$0.409632\pi$
$444$	−2.43333	+	4.89120i	−0.115481	+	0.232126i
$445$	9.73349	+	21.8618i	0.461412	+	1.03635i
$446$	1.97405	−	0.419597i	0.0934739	−	0.0198685i
$447$	1.88189	+	11.1857i	0.0890104	+	0.529067i
$448$	0.406715	+	0.181081i	0.0192155	+	0.00855529i
$449$	9.33448	+	28.7286i	0.440521	+	1.35579i	0.887321	+	0.461152i	$0.152564\pi$
$449$	9.33448	+	28.7286i	0.440521	+	1.35579i	−0.446800	+	0.894634i	$0.647436\pi$
$450$	−3.91510	+	7.09221i	−0.184560	+	0.334330i
$451$	0.120756	−	0.271223i	0.00568618	−	0.0127714i
$452$	2.60057	−	12.2347i	0.122320	−	0.575472i
$453$	21.8034	+	32.8789i	1.02441	+	1.54479i
$454$	−26.1008	+	11.6208i	−1.22497	+	0.545393i
$455$	−0.906661	−	1.00695i	−0.0425049	−	0.0472065i
$456$	5.93970	−	3.09860i	0.278152	−	0.145105i
$457$	16.3963	+	22.5675i	0.766985	+	1.05566i	0.996601	+	0.0823829i	$0.0262531\pi$
$457$	16.3963	+	22.5675i	0.766985	+	1.05566i	−0.229616	+	0.973281i	$0.573747\pi$
$458$	2.31581	−	22.0335i	0.108211	−	1.02956i
$459$	−25.3156	+	2.05911i	−1.18163	+	0.0961108i
$460$	−10.7207	−	6.18962i	−0.499857	−	0.288593i
$461$	−1.15666	−	0.840360i	−0.0538708	−	0.0391395i	0.560524	−	0.828138i	$-0.310600\pi$
$461$	−1.15666	−	0.840360i	−0.0538708	−	0.0391395i	−0.614395	+	0.788999i	$0.710600\pi$
$462$	4.18298	+	1.55979i	0.194610	+	0.0725681i
$463$	5.56056	+	1.80673i	0.258421	+	0.0839660i	0.435362	−	0.900255i	$-0.356620\pi$
$463$	5.56056	+	1.80673i	0.258421	+	0.0839660i	−0.176941	+	0.984221i	$0.556620\pi$
$464$	1.93826			0.0899815
$465$	−11.8052	+	8.63159i	−0.547452	+	0.400281i
$466$	−8.56131			−0.396595
$467$	−9.20360	−	2.99043i	−0.425892	−	0.138381i	0.0882255	−	0.996101i	$-0.471880\pi$
$467$	−9.20360	−	2.99043i	−0.425892	−	0.138381i	−0.514117	+	0.857720i	$0.671880\pi$
$468$	−6.01984	+	0.115590i	−0.278267	+	0.00534317i
$469$	−4.08444	−	2.96752i	−0.188602	−	0.137027i
$470$	3.72766	+	2.15216i	0.171944	+	0.0992719i
$471$	22.8343	+	18.1307i	1.05215	+	0.835419i
$472$	0.689131	−	6.55664i	0.0317198	−	0.301794i
$473$	−20.5841	−	28.3315i	−0.946456	−	1.30268i
$474$	−9.16592	−	17.5701i	−0.421005	−	0.807021i
$475$	−6.98884	−	7.76189i	−0.320670	−	0.356140i
$476$	1.98806	−	0.885141i	0.0911225	−	0.0405704i
$477$	4.65444	−	6.67199i	0.213112	−	0.305489i
$478$	−4.92935	+	23.1908i	−0.225463	+	1.06072i
$479$	4.07232	−	9.14657i	0.186069	−	0.417917i	−0.796292	−	0.604912i	$-0.793208\pi$
$479$	4.07232	−	9.14657i	0.186069	−	0.417917i	0.982361	+	0.186995i	$0.0598748\pi$
$480$	1.67248	+	2.02527i	0.0763379	+	0.0924407i
$481$	1.95615	+	6.02040i	0.0891926	+	0.274507i
$482$	12.1872	+	5.42610i	0.555113	+	0.247152i
$483$	6.20761	−	1.04437i	0.282456	−	0.0475204i
$484$	22.0255	−	4.68166i	1.00116	−	0.212803i
$485$	−2.38729	−	5.36194i	−0.108401	−	0.243473i
$486$	13.4659	+	7.85304i	0.610824	+	0.356221i
$487$	30.1876	−	3.17284i	1.36793	−	0.143775i	0.608080	−	0.793875i	$-0.291940\pi$
$487$	30.1876	−	3.17284i	1.36793	−	0.143775i	0.759848	+	0.650100i	$0.225273\pi$
$488$	3.34028	−	2.42686i	0.151207	−	0.109859i
$489$	−1.94816	−	7.00110i	−0.0880988	−	0.316601i
$490$	5.15731	+	8.93272i	0.232984	+	0.403539i
$491$	4.73158	−	8.19534i	0.213533	−	0.369851i	−0.739284	−	0.673393i	$-0.764836\pi$
$491$	4.73158	−	8.19534i	0.213533	−	0.369851i	0.952818	+	0.303543i	$0.0981694\pi$
$492$	−0.0221642	+	0.0860121i	−0.000999238	+	0.00387773i
$493$	6.33960	−	7.04084i	0.285521	−	0.317103i
$494$	2.39883	−	7.38283i	0.107928	−	0.332169i
$495$	17.9963	+	19.2312i	0.808872	+	0.864378i
$496$	−1.40564	−	5.38741i	−0.0631151	−	0.241902i
$497$		−	4.13693i		−	0.185567i
$498$	−10.5349	+	0.653574i	−0.472081	+	0.0292874i
$499$	−21.3394	−	19.2141i	−0.955282	−	0.860140i	0.0349753	−	0.999388i	$-0.488865\pi$
$499$	−21.3394	−	19.2141i	−0.955282	−	0.860140i	−0.990258	+	0.139248i	$0.955531\pi$
$500$	6.86372	−	9.44710i	0.306955	−	0.422487i
$501$	1.57258	−	10.5856i	0.0702577	−	0.472929i
$502$	15.8064	−	9.12580i	0.705472	−	0.407304i
$503$	−15.5895	−	1.63852i	−0.695102	−	0.0730581i	−0.249613	−	0.968346i	$-0.580303\pi$
$503$	−15.5895	−	1.63852i	−0.695102	−	0.0730581i	−0.445489	+	0.895288i	$0.646970\pi$
$504$	−1.31152	−	0.252558i	−0.0584197	−	0.0112498i
$505$	−0.742512	−	7.06453i	−0.0330414	−	0.314367i
$506$	35.1216	−	31.6236i	1.56134	−	1.40584i
$507$	10.8824	−	11.0934i	0.483306	−	0.492675i
$508$	−1.66187	−	7.81850i	−0.0737337	−	0.346890i
$509$	28.2421	+	6.00304i	1.25181	+	0.266080i	0.785678	−	0.618636i	$-0.212314\pi$
$509$	28.2421	+	6.00304i	1.25181	+	0.266080i	0.466130	+	0.884716i	$0.345648\pi$
$510$	12.8272	+	0.548830i	0.567998	+	0.0243026i
$511$	−2.42348	+	0.787436i	−0.107208	+	0.0348341i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−15.2485	+	13.0926i	−0.673236	+	0.578054i
$514$	1.47888	+	0.314346i	0.0652306	+	0.0138652i
$515$	4.71996	+	22.2057i	0.207986	+	0.978498i
$516$	7.47913	+	7.33690i	0.329250	+	0.322989i
$517$	−12.2119	+	10.9957i	−0.537081	+	0.483590i
$518$	0.146781	+	1.39653i	0.00644919	+	0.0613599i
$519$	9.13118	+	5.80601i	0.400815	+	0.254855i
$520$	3.02683	+	0.318133i	0.132735	+	0.0139510i
$521$	11.1483	−	6.43646i	0.488415	−	0.281987i	−0.235502	−	0.971874i	$-0.575673\pi$
$521$	11.1483	−	6.43646i	0.488415	−	0.281987i	0.723917	+	0.689887i	$0.242340\pi$
$522$	−5.66346	+	1.31793i	−0.247883	+	0.0576843i
$523$	18.9299	−	26.0547i	0.827745	−	1.13929i	−0.160594	−	0.987021i	$-0.551341\pi$
$523$	18.9299	−	26.0547i	0.827745	−	1.13929i	0.988339	−	0.152272i	$-0.0486591\pi$
$524$	−12.6503	−	11.3904i	−0.552630	−	0.497591i
$525$	0.128935	+	2.07830i	0.00562720	+	0.0907045i
$526$		−	15.6532i		−	0.682513i
$527$	−24.1676	−	12.5149i	−1.05276	−	0.545158i
$528$	−9.32664	+	3.68327i	−0.405890	+	0.160294i
$529$	13.4852	−	41.5032i	0.586313	−	1.80449i
$530$	−2.75157	+	3.05593i	−0.119520	+	0.132741i
$531$	2.44464	+	19.6266i	0.106088	+	0.851723i
$532$	0.860999	−	1.49129i	0.0373290	−	0.0646558i
$533$	0.0514605	+	0.0891321i	0.00222900	+	0.00386074i
$534$	26.3324	−	7.32739i	1.13952	−	0.317087i
$535$	14.5689	−	10.5849i	0.629868	−	0.457626i
$536$	11.2779	−	1.18536i	0.487132	−	0.0511997i
$537$	−32.8923	−	16.3637i	−1.41941	−	0.706145i
$538$	5.45138	+	12.2440i	0.235026	+	0.527877i
$539$	−38.5180	+	8.18726i	−1.65909	+	0.352650i
$540$	−6.26396	−	4.78049i	−0.269558	−	0.205720i
$541$	−13.0901	−	5.82810i	−0.562788	−	0.250569i	0.105566	−	0.994412i	$-0.466334\pi$
$541$	−13.0901	−	5.82810i	−0.562788	−	0.250569i	−0.668355	+	0.743843i	$0.733001\pi$
$542$	9.97446	+	30.6982i	0.428440	+	1.31860i
$543$	−14.2288	+	11.7502i	−0.610617	+	0.504250i
$544$	−1.98816	+	4.46549i	−0.0852418	+	0.191456i
$545$	−5.43980	+	25.5922i	−0.233015	+	1.09625i
$546$	−1.28979	+	0.855316i	−0.0551981	+	0.0366042i
$547$	31.1143	−	13.8530i	1.33035	−	0.592310i	0.386379	−	0.922340i	$-0.373726\pi$
$547$	31.1143	−	13.8530i	1.33035	−	0.592310i	0.943970	+	0.330030i	$0.107059\pi$
$548$	−0.288964	−	0.320927i	−0.0123439	−	0.0137093i
$549$	−8.10991	+	9.36234i	−0.346122	+	0.399575i
$550$	9.18917	+	12.6478i	0.391828	+	0.539304i
$551$	0.783644	−	7.45588i	0.0333844	−	0.317631i
$552$	−8.79220	+	11.0731i	−0.374221	+	0.471304i
$553$	−4.41137	−	2.54690i	−0.187590	−	0.108305i
$554$	−23.8031	−	17.2940i	−1.01130	−	0.734751i
$555$	−2.89451	+	7.76238i	−0.122865	+	0.329495i
$556$	3.15138	+	1.02395i	0.133648	+	0.0434250i
$557$	−39.4877			−1.67315			−0.836574	−	0.547854i	$-0.815445\pi$
$557$	−39.4877			−1.67315			−0.836574	+	0.547854i	$0.815445\pi$
$558$	7.77038	+	14.7858i	0.328946	+	0.625935i
$559$	12.1400			0.513469
$560$	0.642091	+	0.208628i	0.0271333	+	0.00881614i
$561$	−17.1256	+	45.9266i	−0.723043	+	1.93902i
$562$	−2.15189	−	1.56344i	−0.0907719	−	0.0659496i
$563$	−29.9644	−	17.2999i	−1.26285	−	0.729106i	−0.289224	−	0.957262i	$-0.593397\pi$
$563$	−29.9644	−	17.2999i	−1.26285	−	0.729106i	−0.973625	+	0.228156i	$0.926730\pi$
$564$	3.05709	−	3.85018i	0.128727	−	0.162122i
$565$	1.98269	−	18.8640i	0.0834122	−	0.793614i
$566$	9.59441	+	13.2056i	0.403283	+	0.555071i
$567$	4.00389	−	0.153819i	0.168148	−	0.00645978i
$568$	6.21768	+	6.90544i	0.260888	+	0.289746i
$569$	17.2623	−	7.68568i	0.723675	−	0.322201i	−0.0116348	−	0.999932i	$-0.503704\pi$
$569$	17.2623	−	7.68568i	0.723675	−	0.322201i	0.735309	+	0.677732i	$0.237037\pi$
$570$	8.46678	−	5.61468i	0.354634	−	0.235173i
$571$	−0.562858	+	2.64804i	−0.0235549	+	0.110817i	−0.988354	−	0.152169i	$-0.951374\pi$
$571$	−0.562858	+	2.64804i	−0.0235549	+	0.110817i	0.964800	+	0.262986i	$0.0847074\pi$
$572$	−4.72600	+	10.6148i	−0.197604	+	0.443825i
$573$	12.5670	−	10.3779i	0.524994	−	0.433542i
$574$	0.00705508	+	0.0217133i	0.000294474	+	0.000906296i
$575$	20.1380	+	8.96601i	0.839812	+	0.373908i
$576$	2.56880	−	1.54960i	0.107033	−	0.0645667i
$577$	−11.3752	+	2.41787i	−0.473554	+	0.100657i	−0.438505	−	0.898729i	$-0.644492\pi$
$577$	−11.3752	+	2.41787i	−0.473554	+	0.100657i	−0.0350489	+	0.999386i	$0.511159\pi$
$578$	2.80379	+	6.29741i	0.116622	+	0.261938i
$579$	13.0217	+	6.47821i	0.541165	+	0.269225i
$580$	2.92319	−	0.307239i	0.121379	−	0.0127574i
$581$	−2.19494	+	1.59472i	−0.0910614	+	0.0661600i
$582$	−6.45844	+	1.79716i	−0.267711	+	0.0744945i
$583$	−7.84956	−	13.5958i	−0.325096	−	0.563082i
$584$	2.86182	−	4.95682i	0.118423	−	0.205115i
$585$	−9.06050	+	1.12855i	−0.374606	+	0.0466598i
$586$	−0.730978	+	0.811834i	−0.0301964	+	0.0335365i
$587$	−6.04469	+	18.6037i	−0.249491	+	0.767855i	0.745374	+	0.666646i	$0.232271\pi$
$587$	−6.04469	+	18.6037i	−0.249491	+	0.767855i	−0.994865	+	0.101208i	$0.967729\pi$
$588$	10.9575	−	4.32734i	0.451881	−	0.178456i
$589$	−21.2920	+	3.22891i	−0.877321	+	0.133045i
$590$		−	9.99763i		−	0.411596i
$591$	−0.503610	−	8.11765i	−0.0207157	−	0.333915i
$592$	−2.34395	−	2.11050i	−0.0963358	−	0.0867411i
$593$	19.6516	−	27.0480i	0.806993	−	1.11073i	−0.184788	−	0.982778i	$-0.559160\pi$
$593$	19.6516	−	27.0480i	0.806993	−	1.11073i	0.991780	−	0.127952i	$-0.0408402\pi$
$594$	24.7473	−	17.1039i	1.01539	−	0.701783i
$595$	2.85798	−	1.65006i	0.117166	−	0.0676457i
$596$	−6.51298	−	0.684541i	−0.266782	−	0.0280399i
$597$	28.9307	+	18.3954i	1.18405	+	0.752873i
$598$	1.71255	+	16.2938i	0.0700313	+	0.666303i
$599$	−2.19117	+	1.97294i	−0.0895287	+	0.0806120i	−0.712680	−	0.701489i	$-0.752519\pi$
$599$	−2.19117	+	1.97294i	−0.0895287	+	0.0806120i	0.623151	+	0.782101i	$0.285852\pi$
$600$	−3.33885	−	3.27535i	−0.136308	−	0.133716i
$601$	4.59804	+	21.6321i	0.187558	+	0.882390i	0.966774	+	0.255635i	$0.0822844\pi$
$601$	4.59804	+	21.6321i	0.187558	+	0.882390i	−0.779216	+	0.626756i	$0.784382\pi$
$602$	2.63415	+	0.559906i	0.107360	+	0.0228201i
$603$	−32.1473	+	11.1320i	−1.30914	+	0.453331i
$604$	−21.6625	+	7.03856i	−0.881433	+	0.286395i
$605$	32.4756	−	10.5520i	1.32032	−	0.428998i
$606$	−8.10592	−	0.346823i	−0.329281	−	0.0140887i
$607$	4.58018	+	0.973547i	0.185904	+	0.0395151i	0.299923	−	0.953964i	$-0.403039\pi$
$607$	4.58018	+	0.973547i	0.185904	+	0.0395151i	−0.114019	+	0.993479i	$0.536372\pi$
$608$	0.804176	+	3.78335i	0.0326137	+	0.153435i
$609$	−1.04667	+	1.06696i	−0.0424131	+	0.0432353i
$610$	4.65295	−	4.18954i	0.188393	−	0.169629i
$611$	−0.595462	−	5.66544i	−0.0240898	−	0.229199i
$612$	2.77294	−	14.3997i	0.112089	−	0.582073i
$613$	−8.74491	−	0.919127i	−0.353204	−	0.0371232i	−0.0737346	−	0.997278i	$-0.523492\pi$
$613$	−8.74491	−	0.919127i	−0.353204	−	0.0371232i	−0.279469	+	0.960155i	$0.590158\pi$
$614$	−12.1467	+	7.01288i	−0.490200	+	0.283017i
$615$	−0.0197928	+	0.133232i	−0.000798124	+	0.00537245i
$616$	−1.51501	+	2.08523i	−0.0610414	+	0.0840163i
$617$	14.0825	+	12.6799i	0.566939	+	0.510474i	0.902008	−	0.431719i	$-0.142093\pi$
$617$	14.0825	+	12.6799i	0.566939	+	0.510474i	−0.335069	+	0.942194i	$0.608760\pi$
$618$	25.8795	−	1.60553i	1.04103	−	0.0645841i
$619$		−	7.72738i		−	0.310590i	−0.987868	−	0.155295i	$-0.950367\pi$
$619$		−	7.72738i		−	0.310590i	0.987868	−	0.155295i	$-0.0496328\pi$
$620$	−2.97389	−	7.90220i	−0.119434	−	0.317360i
$621$	18.1609	−	38.3332i	0.728773	−	1.53826i
$622$	−2.72244	+	8.37881i	−0.109160	+	0.335959i
$623$	4.70107	−	5.22106i	0.188344	−	0.209178i
$624$	0.867433	−	3.36623i	0.0347251	−	0.134757i
$625$	2.10313	−	3.64273i	0.0841252	−	0.145709i
$626$	5.44464	+	9.43038i	0.217611	+	0.376914i
$627$	10.3976	+	37.3658i	0.415240	+	1.49225i
$628$	−13.6188	+	9.89464i	−0.543450	+	0.394839i
$629$	−15.3330	+	1.61157i	−0.611368	+	0.0642574i
$630$	−2.01800	−	0.173003i	−0.0803991	−	0.00689259i
$631$	−1.62998	−	3.66100i	−0.0648886	−	0.145742i	0.878190	−	0.478312i	$-0.158751\pi$
$631$	−1.62998	−	3.66100i	−0.0648886	−	0.145742i	−0.943079	+	0.332569i	$0.892084\pi$
$632$	11.1915	−	2.37882i	0.445172	−	0.0946243i
$633$	−8.83574	+	1.48653i	−0.351189	+	0.0590841i
$634$	−22.4900	−	10.0132i	−0.893192	−	0.397675i
$635$	−3.74568	−	11.5280i	−0.148643	−	0.457476i
$636$	2.99068	+	3.62154i	0.118588	+	0.143603i
$637$	5.55240	−	12.4709i	0.219994	−	0.494115i
$638$	−2.33307	+	10.9762i	−0.0923670	+	0.434552i
$639$	−22.8630	−	15.9494i	−0.904447	−	0.630950i
$640$	−1.38535	+	0.616798i	−0.0547608	+	0.0243811i
$641$	4.15635	+	4.61610i	0.164166	+	0.182325i	0.819615	−	0.572914i	$-0.194187\pi$
$641$	4.15635	+	4.61610i	0.164166	+	0.182325i	−0.655449	+	0.755239i	$0.727521\pi$
$642$	−9.51334	−	18.2361i	−0.375461	−	0.719720i
$643$	−20.7930	−	28.6191i	−0.819996	−	1.12863i	−0.989704	−	0.143133i	$-0.954282\pi$
$643$	−20.7930	−	28.6191i	−0.819996	−	1.12863i	0.169708	−	0.985494i	$-0.445718\pi$
$644$	−0.379891	+	3.61442i	−0.0149698	+	0.142428i
$645$	12.4426	+	9.87960i	0.489928	+	0.389009i
$646$	16.3735	+	9.45325i	0.644207	+	0.371933i
$647$	−8.66503	−	6.29551i	−0.340657	−	0.247502i	0.404282	−	0.914634i	$-0.367522\pi$
$647$	−8.66503	−	6.29551i	−0.340657	−	0.247502i	−0.744939	+	0.667132i	$0.767522\pi$
$648$	−6.45219	+	6.27449i	−0.253466	+	0.246485i
$649$	36.3003	+	11.7947i	1.42491	+	0.462981i
$650$	−5.41958			−0.212573
$651$	3.72467	+	2.13545i	0.145981	+	0.0836951i
$652$	4.19566			0.164315
$653$	35.6623	+	11.5874i	1.39557	+	0.453450i	0.907757	−	0.419496i	$-0.137793\pi$
$653$	35.6623	+	11.5874i	1.39557	+	0.453450i	0.487818	+	0.872946i	$0.337793\pi$
$654$	28.0004	+	10.4411i	1.09490	+	0.408277i
$655$	−20.8840	−	15.1731i	−0.816007	−	0.592864i
$656$	−0.0444110	−	0.0256407i	−0.00173396	−	0.00100110i
$657$	−4.99162	+	16.4294i	−0.194742	+	0.640971i
$658$	0.132090	−	1.25675i	0.00514941	−	0.0489933i
$659$	−25.5163	−	35.1202i	−0.993975	−	1.36809i	−0.928950	−	0.370205i	$-0.879287\pi$
$659$	−25.5163	−	35.1202i	−0.993975	−	1.36809i	−0.0650248	−	0.997884i	$-0.520713\pi$
$660$	−13.4821	+	7.03331i	−0.524791	+	0.273771i
$661$	2.38791	+	2.65204i	0.0928788	+	0.103152i	0.787792	−	0.615941i	$-0.211224\pi$
$661$	2.38791	+	2.65204i	0.0928788	+	0.103152i	−0.694914	+	0.719093i	$0.744557\pi$
$662$	16.9311	−	7.53821i	0.658046	−	0.292981i
$663$	−9.39086	−	14.1612i	−0.364711	−	0.549974i
$664$	1.26702	−	5.96086i	0.0491699	−	0.231326i
$665$	1.06213	−	2.38557i	0.0411875	−	0.0925086i
$666$	8.28390	+	4.57295i	0.320995	+	0.177198i
$667$	4.88944	+	15.0481i	0.189320	+	0.582666i
$668$	5.64449	+	2.51309i	0.218392	+	0.0972343i
$669$	−0.579940	−	3.44710i	−0.0224218	−	0.133272i
$670$	16.8209	−	3.57539i	0.649848	−	0.138129i
$671$	9.72243	+	21.8369i	0.375330	+	0.843006i
$672$	0.343469	−	0.690400i	0.0132496	−	0.0266328i
$673$	−31.4236	+	3.30275i	−1.21129	+	0.127312i	−0.688555	−	0.725184i	$-0.741755\pi$
$673$	−31.4236	+	3.30275i	−1.21129	+	0.127312i	−0.522734	+	0.852496i	$0.675088\pi$
$674$	−6.69248	+	4.86237i	−0.257785	+	0.187292i
$675$	11.9830	+	7.30007i	0.461224	+	0.280980i
$676$	4.48601	+	7.76999i	0.172539	+	0.298846i
$677$	−0.517745	+	0.896760i	−0.0198985	+	0.0344653i	−0.875803	−	0.482668i	$-0.839668\pi$
$677$	−0.517745	+	0.896760i	−0.0198985	+	0.0344653i	0.855905	+	0.517134i	$0.173001\pi$
$678$	−20.9792	−	5.40606i	−0.805702	−	0.207619i
$679$	−1.15301	+	1.28055i	−0.0442484	+	0.0491429i
$680$	−2.29061	+	7.04977i	−0.0878409	+	0.270346i
$681$	18.1770	+	46.0270i	0.696543	+	1.76376i
$682$	32.2004	−	1.47525i	1.23302	−	0.0564903i
$683$			3.29130i			0.125938i	0.998015	+	0.0629691i	$0.0200570\pi$
$683$			3.29130i			0.125938i	−0.998015	+	0.0629691i	$0.979943\pi$
$684$	−4.92226	−	10.5079i	−0.188207	−	0.401779i
$685$	−0.486672	−	0.438202i	−0.0185948	−	0.0167428i
$686$	3.61172	−	4.97111i	0.137896	−	0.189798i
$687$	−37.9567	−	5.63880i	−1.44814	−	0.215134i
$688$	−5.23850	+	3.02445i	−0.199716	+	0.115306i
$689$	5.41250	+	0.568877i	0.206200	+	0.0216725i
$690$	−11.5047	+	18.0936i	−0.437977	+	0.688812i
$691$	−2.53028	−	24.0740i	−0.0962565	−	0.915820i	−0.930960	−	0.365121i	$-0.881028\pi$
$691$	−2.53028	−	24.0740i	−0.0962565	−	0.915820i	0.834704	−	0.550699i	$-0.185639\pi$
$692$	−4.64269	+	4.18029i	−0.176488	+	0.158911i
$693$	3.00888	−	7.12303i	0.114298	−	0.270582i
$694$	−2.72959	−	12.8417i	−0.103614	−	0.487465i
$695$	4.91506	+	1.04473i	0.186439	+	0.0396288i
$696$	0.143510	−	3.35410i	0.00543972	−	0.127137i
$697$	−0.238399	+	0.0774606i	−0.00903001	+	0.00293403i
$698$	−19.1977	+	6.23770i	−0.726642	+	0.236100i
$699$	−0.633883	+	14.8151i	−0.0239757	+	0.560357i
$700$	−1.17594	−	0.249954i	−0.0444465	−	0.00944739i
$701$	−7.98943	−	37.5873i	−0.301757	−	1.41965i	−0.823870	−	0.566778i	$-0.808190\pi$
$701$	−7.98943	−	37.5873i	−0.301757	−	1.41965i	0.522114	−	0.852876i	$-0.325144\pi$
$702$	−0.245686	+	10.4257i	−0.00927283	+	0.393493i
$703$	−9.06611	+	8.16316i	−0.341935	+	0.307879i
$704$	−0.605161	−	5.75772i	−0.0228078	−	0.217002i
$705$	4.00025	−	6.29124i	0.150658	−	0.236942i
$706$	−34.3226	−	3.60745i	−1.29175	−	0.135768i
$707$	−1.80605	+	1.04272i	−0.0679235	+	0.0392157i
$708$	−11.2950	−	1.67798i	−0.424494	−	0.0630622i
$709$	−16.5675	+	22.8032i	−0.622206	+	0.856393i	−0.997511	−	0.0705082i	$-0.977538\pi$
$709$	−16.5675	+	22.8032i	−0.622206	+	0.856393i	0.375305	+	0.926901i	$0.377538\pi$
$710$	10.4718	+	9.42885i	0.392999	+	0.353858i
$711$	−31.0831	+	14.5604i	−1.16571	+	0.546059i
$712$			15.7807i			0.591405i
$713$	38.2806	−	24.5032i	1.43362	−	0.917653i
$714$	−1.38451	−	3.50581i	−0.0518140	−	0.131202i
$715$	−5.44493	+	16.7578i	−0.203629	+	0.626705i
$716$	14.1927	−	15.7626i	0.530406	−	0.589075i
$717$	39.7659	+	10.2471i	1.48509	+	0.382686i
$718$	−13.7817	+	23.8706i	−0.514328	+	0.890841i
$719$	−10.0625	−	17.4288i	−0.375268	−	0.649984i	0.615099	−	0.788450i	$-0.289116\pi$
$719$	−10.0625	−	17.4288i	−0.375268	−	0.649984i	−0.990367	+	0.138466i	$0.955783\pi$
$720$	3.62850	−	2.74422i	0.135226	−	0.102271i
$721$	5.39197	−	3.91749i	0.200807	−	0.145895i
$722$	−4.01742	+	0.422248i	−0.149513	+	0.0157144i
$723$	10.2920	−	20.6879i	0.382765	−	0.769390i
$724$	−4.33339	−	9.73296i	−0.161049	−	0.361723i
$725$	−5.11963	+	1.08821i	−0.190138	+	0.0404151i
$726$	−6.47069	−	38.4610i	−0.240150	−	1.42742i
$727$	40.3783	+	17.9776i	1.49755	+	0.666751i	0.981788	−	0.189981i	$-0.0608428\pi$
$727$	40.3783	+	17.9776i	1.49755	+	0.666751i	0.515761	+	0.856733i	$0.327509\pi$
$728$	−0.276113	−	0.849788i	−0.0102334	−	0.0314952i
$729$	14.5864	−	22.7208i	0.540239	−	0.841512i
$730$	3.53033	−	7.92926i	0.130664	−	0.293475i
$731$	−6.14743	+	28.9214i	−0.227371	+	1.06970i
$732$	−3.95228	−	5.95993i	−0.146081	−	0.220286i
$733$	−25.6166	+	11.4052i	−0.946170	+	0.421262i	−0.821035	−	0.570878i	$-0.806603\pi$
$733$	−25.6166	+	11.4052i	−0.946170	+	0.421262i	−0.125135	+	0.992140i	$0.539936\pi$
$734$	−24.4604	−	27.1661i	−0.902851	−	1.00272i
$735$	15.8396	−	8.26318i	0.584254	−	0.304792i
$736$	−4.79825	−	6.60423i	−0.176866	−	0.243435i
$737$	−6.86255	+	65.2928i	−0.252785	+	2.40509i
$738$	0.147200	+	0.0447227i	0.00541851	+	0.00164627i
$739$	35.9604	+	20.7617i	1.32282	+	0.763733i	0.984178	−	0.177181i	$-0.0566978\pi$
$739$	35.9604	+	20.7617i	1.32282	+	0.763733i	0.338646	+	0.940914i	$0.390031\pi$
$740$	−3.86957	−	2.81141i	−0.142248	−	0.103349i
$741$	−12.5981	−	4.69772i	−0.462804	−	0.172575i
$742$	1.14817	+	0.373063i	0.0421506	+	0.0136956i
$743$	−0.914304			−0.0335425			−0.0167713	−	0.999859i	$-0.505339\pi$
$743$	−0.914304			−0.0335425			−0.0167713	+	0.999859i	$0.505339\pi$
$744$	−9.42681	+	2.03353i	−0.345604	+	0.0745528i
$745$	−9.93105			−0.363845
$746$	15.0158	+	4.87894i	0.549769	+	0.178631i
$747$	0.350980	+	18.2787i	0.0128417	+	0.668783i
$748$	−22.8946	−	16.6339i	−0.837108	−	0.608195i
$749$	−4.57857	−	2.64344i	−0.167297	−	0.0965892i
$750$	−15.8397	−	12.5769i	−0.578384	−	0.459244i
$751$	1.35910	−	12.9310i	0.0495942	−	0.471857i	−0.941335	−	0.337473i	$-0.890428\pi$
$751$	1.35910	−	12.9310i	0.0495942	−	0.471857i	0.990929	−	0.134384i	$-0.0429056\pi$
$752$	1.66838	+	2.29632i	0.0608394	+	0.0837383i
$753$	−14.6216	−	28.0281i	−0.532841	−	1.02140i
$754$	−2.60296	−	2.89088i	−0.0947941	−	0.105280i
$755$	−31.5545	+	14.0490i	−1.14839	+	0.511295i
$756$	−0.534149	+	2.25084i	−0.0194268	+	0.0818624i
$757$	2.08803	−	9.82343i	0.0758909	−	0.357039i	−0.923774	−	0.382939i	$-0.874912\pi$
$757$	2.08803	−	9.82343i	0.0758909	−	0.357039i	0.999665	+	0.0259004i	$0.00824528\pi$
$758$	−11.0915	+	24.9119i	−0.402861	+	0.904841i
$759$	−52.1232	−	63.1181i	−1.89195	−	2.29104i
$760$	1.81253	+	5.57839i	0.0657473	+	0.202349i
$761$	−7.26212	−	3.23330i	−0.263252	−	0.117207i	0.270867	−	0.962617i	$-0.412690\pi$
$761$	−7.26212	−	3.23330i	−0.263252	−	0.117207i	−0.534118	+	0.845410i	$0.679356\pi$
$762$	−13.6527	+	2.29693i	−0.494585	+	0.0832091i
$763$	7.51343	−	1.59703i	0.272005	−	0.0578163i
$764$	3.82729	+	8.59622i	0.138466	+	0.311000i
$765$	1.89946	−	22.1564i	0.0686753	−	0.801068i
$766$	−4.10523	+	0.431477i	−0.148328	+	0.0155899i
$767$	−10.7046	+	7.77732i	−0.386519	+	0.280823i
$768$	0.464327	+	1.66865i	0.0167550	+	0.0602123i
$769$	−3.53908	−	6.12986i	−0.127622	−	0.221049i	0.795133	−	0.606436i	$-0.207401\pi$
$769$	−3.53908	−	6.12986i	−0.127622	−	0.221049i	−0.922755	+	0.385387i	$0.874068\pi$
$770$	−1.95432	+	3.38499i	−0.0704289	+	0.121986i
$771$	0.653462	−	2.53588i	0.0235339	−	0.0913275i
$772$	−5.61874	+	6.24025i	−0.202223	+	0.224591i
$773$	−0.733266	+	2.25676i	−0.0263738	+	0.0811701i	−0.963377	−	0.268150i	$-0.913588\pi$
$773$	−0.733266	+	2.25676i	−0.0263738	+	0.0811701i	0.937003	+	0.349321i	$0.113588\pi$
$774$	13.2500	−	12.3992i	0.476262	−	0.445679i
$775$	6.73747	+	13.4409i	0.242017	+	0.482810i
$776$		−	3.87045i		−	0.138941i
$777$	2.42751	−	0.150600i	0.0870866	−	0.00540275i
$778$	−11.5039	−	10.3582i	−0.412436	−	0.371359i
$779$	−0.116587	+	0.160468i	−0.00417717	+	0.00574938i
$780$	0.774626	−	5.21428i	0.0277361	−	0.186701i
$781$	−46.5891	+	26.8982i	−1.66709	+	0.962494i
$782$	−39.6842	−	4.17098i	−1.41910	−	0.149154i
$783$	1.86131	+	9.89801i	0.0665179	+	0.353726i
$784$	0.710981	+	6.76453i	0.0253922	+	0.241590i
$785$	−18.9708	+	17.0814i	−0.677096	+	0.609660i
$786$	−20.6473	+	21.0476i	−0.736465	+	0.750742i
$787$	6.46072	+	30.3953i	0.230300	+	1.08348i	0.929578	+	0.368626i	$0.120172\pi$
$787$	6.46072	+	30.3953i	0.230300	+	1.08348i	−0.699278	+	0.714850i	$0.746495\pi$
$788$	4.59312	+	0.976298i	0.163623	+	0.0347792i
$789$	−27.0874	−	1.15897i	−0.964337	−	0.0412605i
$790$	16.5013	−	5.36160i	0.587090	−	0.190757i
$791$	−5.29610	+	1.72081i	−0.188308	+	0.0611848i
$792$	5.68323	+	16.4122i	0.201945	+	0.583180i
$793$	−8.10539	−	1.72285i	−0.287831	−	0.0611803i
$794$	−2.22621	−	10.4735i	−0.0790051	−	0.371690i
$795$	5.08445	+	4.98776i	0.180327	+	0.176898i
$796$	−14.7096	+	13.2446i	−0.521368	+	0.469442i
$797$	0.857016	+	8.15396i	0.0303571	+	0.288828i	0.999159	+	0.0409936i	$0.0130523\pi$
$797$	0.857016	+	8.15396i	0.0303571	+	0.288828i	−0.968802	+	0.247835i	$0.920281\pi$
$798$	−2.51689	−	1.60035i	−0.0890968	−	0.0566517i
$799$	13.7984	+	1.45027i	0.488152	+	0.0513068i
$800$	2.33858	−	1.35018i	0.0826813	−	0.0477361i
$801$	−10.7302	−	46.1100i	−0.379131	−	1.62922i
$802$	11.9995	−	16.5159i	0.423718	−	0.583198i
$803$	24.6253	+	22.1727i	0.869009	+	0.782459i
$804$	−1.21620	−	19.6039i	−0.0428921	−	0.691375i
$805$			5.51131i			0.194248i
$806$	−6.14753	+	9.33142i	−0.216538	+	0.328685i
$807$	21.5915	−	8.52689i	0.760056	−	0.300161i
$808$	1.44751	−	4.45498i	0.0509232	−	0.156725i
$809$	24.5966	−	27.3173i	0.864772	−	0.960426i	−0.134765	−	0.990878i	$-0.543028\pi$
$809$	24.5966	−	27.3173i	0.864772	−	0.960426i	0.999536	+	0.0304513i	$0.00969446\pi$
$810$	−8.73627	+	10.4856i	−0.306961	+	0.368427i
$811$	−5.94022	+	10.2888i	−0.208589	+	0.361288i	−0.951270	−	0.308358i	$-0.900221\pi$
$811$	−5.94022	+	10.2888i	−0.208589	+	0.361288i	0.742681	+	0.669645i	$0.233554\pi$
$812$	−0.431462	−	0.747314i	−0.0151413	−	0.0262256i
$813$	53.8608	−	14.9876i	1.88898	−	0.525637i
$814$	14.7730	−	10.7332i	0.517793	−	0.376199i
$815$	6.32768	−	0.665066i	0.221649	−	0.0232962i
$816$	7.58018	+	3.77108i	0.265359	+	0.132014i
$817$	9.51616	+	21.3736i	0.332928	+	0.747769i
$818$	22.7769	−	4.84137i	0.796375	−	0.169275i
$819$	1.38460	+	2.29527i	0.0483818	+	0.0802034i
$820$	−0.0710427	−	0.0316303i	−0.00248092	−	0.00110458i
$821$	8.24535	+	25.3766i	0.287765	+	0.885649i	0.985556	+	0.169348i	$0.0541662\pi$
$821$	8.24535	+	25.3766i	0.287765	+	0.885649i	−0.697792	+	0.716301i	$0.745834\pi$
$822$	−0.576750	+	0.476282i	−0.0201164	+	0.0166122i
$823$	−1.59308	+	3.57811i	−0.0555313	+	0.124725i	−0.939180	−	0.343425i	$-0.888413\pi$
$823$	−1.59308	+	3.57811i	−0.0555313	+	0.124725i	0.883649	+	0.468150i	$0.155079\pi$
$824$	−3.11249	+	14.6431i	−0.108429	+	0.510117i
$825$	22.5670	−	14.9651i	0.785682	−	0.521018i
$826$	−2.68138	+	1.19383i	−0.0932970	+	0.0415385i
$827$	−6.97434	−	7.74579i	−0.242522	−	0.269347i	0.609579	−	0.792725i	$-0.291338\pi$
$827$	−6.97434	−	7.74579i	−0.242522	−	0.269347i	−0.852101	+	0.523378i	$0.824672\pi$
$828$	18.5107	+	16.0345i	0.643292	+	0.557236i
$829$	−20.4338	−	28.1247i	−0.709694	−	0.976811i	−0.999804	−	0.0198170i	$-0.993692\pi$
$829$	−20.4338	−	28.1247i	−0.709694	−	0.976811i	0.290109	−	0.956994i	$-0.406308\pi$
$830$	0.965982	−	9.19070i	0.0335297	−	0.319014i
$831$	−31.6891	+	39.9101i	−1.09928	+	1.38447i
$832$	1.73810	+	1.00349i	0.0602578	+	0.0347898i
$833$	26.8980	+	19.5425i	0.931960	+	0.677109i
$834$	2.00524	−	5.37755i	0.0694356	−	0.186209i
$835$	8.91109	+	2.89539i	0.308381	+	0.100199i
$836$	−22.3928			−0.774471
$837$	26.1617	−	12.3516i	0.904282	−	0.426935i
$838$	27.8602			0.962413
$839$	23.5469	+	7.65086i	0.812930	+	0.264137i	0.685838	−	0.727754i	$-0.259436\pi$
$839$	23.5469	+	7.65086i	0.812930	+	0.264137i	0.127092	+	0.991891i	$0.459436\pi$
$840$	0.408565	−	1.09567i	0.0140968	−	0.0378042i
$841$	20.4221	+	14.8375i	0.704212	+	0.511640i
$842$	3.35401	+	1.93644i	0.115587	+	0.0667340i
$843$	−2.86481	+	3.60801i	−0.0986691	+	0.124267i
$844$	0.540726	−	5.14467i	0.0186126	−	0.177087i
$845$	7.99721	+	11.0072i	0.275112	+	0.378660i
$846$	−6.43627	−	5.57527i	−0.221284	−	0.191682i
$847$	−6.70799	−	7.44997i	−0.230489	−	0.255984i
$848$	−2.47725	+	1.10294i	−0.0850691	+	0.0378752i
$849$	23.5622	−	15.6251i	0.808652	−	0.536251i
$850$	2.74435	−	12.9111i	0.0941304	−	0.442849i
$851$	10.4726	−	23.5217i	0.358995	−	0.806315i
$852$	12.4100	−	10.2482i	0.425159	−	0.351098i
$853$	4.53923	+	13.9703i	0.155420	+	0.478335i	0.998203	−	0.0599189i	$-0.0190842\pi$
$853$	4.53923	+	13.9703i	0.155420	+	0.478335i	−0.842783	+	0.538254i	$0.819084\pi$
$854$	−1.67925	−	0.747651i	−0.0574628	−	0.0255841i
$855$	−9.08913	−	15.0672i	−0.310842	−	0.515287i
$856$	11.6156	−	2.46898i	0.397015	−	0.0843881i
$857$	−11.7054	−	26.2907i	−0.399848	−	0.898073i	−0.995494	−	0.0948259i	$-0.969771\pi$
$857$	−11.7054	−	26.2907i	−0.399848	−	0.898073i	0.595646	−	0.803247i	$-0.296896\pi$
$858$	18.0186	+	8.96410i	0.615144	+	0.306029i
$859$	18.4609	−	1.94032i	0.629878	−	0.0662028i	0.215790	−	0.976440i	$-0.430767\pi$
$859$	18.4609	−	1.94032i	0.629878	−	0.0662028i	0.414088	+	0.910237i	$0.364101\pi$
$860$	−7.42102	+	5.39169i	−0.253055	+	0.183855i
$861$	0.0380966	−	0.0106009i	0.00129833	−	0.000361279i
$862$	4.80102	+	8.31562i	0.163523	+	0.283231i
$863$	−10.6573	+	18.4590i	−0.362780	+	0.628353i	−0.988417	−	0.151761i	$-0.951506\pi$
$863$	−10.6573	+	18.4590i	−0.362780	+	0.628353i	0.625637	+	0.780114i	$0.284839\pi$
$864$	−2.49134	−	4.55996i	−0.0847571	−	0.155133i
$865$	−6.33923	+	7.04043i	−0.215540	+	0.239382i
$866$	2.07037	−	6.37195i	0.0703541	−	0.216528i
$867$	11.1051	−	4.38560i	0.377148	−	0.148943i
$868$	−1.76427	+	1.74121i	−0.0598831	+	0.0591005i
$869$			66.2397i			2.24703i
$870$	−0.315234	−	5.08123i	−0.0106874	−	0.172270i
$871$	−16.9135	−	15.2289i	−0.573091	−	0.516013i
$872$	−10.1413	+	13.9583i	−0.343427	+	0.472686i
$873$	2.63174	+	11.3092i	0.0890708	+	0.382758i
$874$	−27.3443	+	15.7873i	−0.924936	+	0.534012i
$875$	−5.17030	−	0.543420i	−0.174788	−	0.0183710i
$876$	−8.36573	−	5.31929i	−0.282652	−	0.179722i
$877$	−0.458228	−	4.35975i	−0.0154733	−	0.147218i	0.984057	−	0.177851i	$-0.0569145\pi$
$877$	−0.458228	−	4.35975i	−0.0154733	−	0.147218i	−0.999531	+	0.0306326i	$0.990248\pi$
$878$	−3.69292	+	3.32512i	−0.124630	+	0.112217i
$879$	1.35073	+	1.32504i	0.0455590	+	0.0446926i
$880$	−1.82534	−	8.58757i	−0.0615324	−	0.289487i
$881$	5.04761	+	1.07290i	0.170058	+	0.0361470i	0.292154	−	0.956371i	$-0.405628\pi$
$881$	5.04761	+	1.07290i	0.170058	+	0.0361470i	−0.122095	+	0.992518i	$0.538961\pi$
$882$	−6.67702	−	19.2820i	−0.224827	−	0.649260i
$883$	3.13892	−	1.01990i	0.105633	−	0.0343223i	−0.255724	−	0.966750i	$-0.582314\pi$
$883$	3.13892	−	1.01990i	0.105633	−	0.0343223i	0.361357	+	0.932428i	$0.382314\pi$
$884$	9.33016	−	3.03155i	0.313807	−	0.101962i
$885$	−17.3006	−	0.740229i	−0.581553	−	0.0248825i
$886$	7.33836	+	1.55982i	0.246537	+	0.0524031i
$887$	−6.31757	−	29.7218i	−0.212123	−	0.997961i	−0.947365	−	0.320156i	$-0.896265\pi$
$887$	−6.31757	−	29.7218i	−0.212123	−	0.997961i	0.735242	−	0.677805i	$-0.237069\pi$
$888$	−3.82570	+	3.89987i	−0.128382	+	0.130871i
$889$	−2.64455	+	2.38117i	−0.0886955	+	0.0798618i
$890$	2.50144	+	23.7996i	0.0838484	+	0.797764i
$891$	−27.7655	−	44.0908i	−0.930180	−	1.47710i
$892$	2.00709	+	0.210954i	0.0672025	+	0.00706327i
$893$	9.50776	−	5.48931i	0.318165	−	0.183693i
$894$	−1.66680	+	11.2198i	−0.0557461	+	0.375247i
$895$	18.9061	−	26.0220i	0.631962	−	0.869821i
$896$	0.330852	+	0.297900i	0.0110530	+	0.00995216i
$897$	28.3227	−	1.75711i	0.945668	−	0.0586682i
$898$			30.2070i			1.00802i
$899$	−3.93361	+	10.0493i	−0.131193	+	0.335164i
$900$	−5.91510	+	5.53526i	−0.197170	+	0.184509i
$901$	−4.09601	+	12.6062i	−0.136458	+	0.419974i
$902$	0.198658	−	0.220632i	0.00661460	−	0.00734625i
$903$	1.16393	−	4.51686i	0.0387333	−	0.150312i
$904$	6.25402	−	10.8323i	0.208006	−	0.360276i
$905$	−8.07820	−	13.9919i	−0.268529	−	0.465105i
$906$	10.5761	+	38.0073i	0.351367	+	1.26271i
$907$	−8.63900	+	6.27660i	−0.286853	+	0.208411i	−0.721901	−	0.691996i	$-0.756731\pi$
$907$	−8.63900	+	6.27660i	−0.286853	+	0.208411i	0.435048	+	0.900407i	$0.356731\pi$
$908$	−28.4144	+	2.98647i	−0.942965	+	0.0991096i
$909$	−1.20033	+	14.0014i	−0.0398125	+	0.464396i
$910$	−0.551122	−	1.23784i	−0.0182695	−	0.0410340i
$911$	42.2028	−	8.97048i	1.39824	−	0.297205i	0.553709	−	0.832710i	$-0.313212\pi$
$911$	42.2028	−	8.97048i	1.39824	−	0.297205i	0.844532	+	0.535505i	$0.179879\pi$
$912$	6.60651	−	1.11148i	0.218763	−	0.0368048i
$913$	32.2308	+	14.3501i	1.06668	+	0.474918i
$914$	8.62003	+	26.5297i	0.285125	+	0.877525i
$915$	−6.90536	−	8.36198i	−0.228284	−	0.276439i
$916$	9.01118	−	20.2394i	0.297738	−	0.668730i
$917$	−1.57567	+	7.41296i	−0.0520333	+	0.244797i
$918$	−24.7129	−	5.86463i	−0.815647	−	0.193562i
$919$	37.2111	−	16.5675i	1.22748	−	0.546510i	0.312466	−	0.949929i	$-0.398845\pi$
$919$	37.2111	−	16.5675i	1.22748	−	0.546510i	0.915015	+	0.403419i	$0.132178\pi$
$920$	−8.28333	−	9.19957i	−0.273093	−	0.303301i
$921$	11.2362	+	21.5387i	0.370246	+	0.709723i
$922$	−0.840360	−	1.15666i	−0.0276758	−	0.0380924i
$923$	1.94938	−	18.5471i	0.0641646	−	0.610485i
$924$	3.49625	+	2.77606i	0.115018	+	0.0913258i
$925$	7.37611	+	4.25860i	0.242525	+	0.140022i
$926$	4.73009	+	3.43661i	0.155440	+	0.112934i
$927$	−0.862198	−	44.9025i	−0.0283183	−	1.47479i
$928$	1.84340	+	0.598955i	0.0605124	+	0.0196617i
$929$	24.0138			0.787867			0.393934	−	0.919139i	$-0.371114\pi$
$929$	24.0138			0.787867			0.393934	+	0.919139i	$0.371114\pi$
$930$	−13.8947	+	4.56113i	−0.455625	+	0.149565i
$931$	26.3085			0.862226
$932$	−8.14229	−	2.64559i	−0.266710	−	0.0866592i
$933$	14.2977	+	5.33146i	0.468085	+	0.174544i
$934$	−7.82905	−	5.68814i	−0.256174	−	0.186122i
$935$	−37.1651	−	21.4573i	−1.21543	−	0.701728i
$936$	−5.76093	−	1.75030i	−0.188302	−	0.0572104i
$937$	5.74496	−	54.6596i	0.187680	−	1.78565i	−0.344265	−	0.938872i	$-0.611872\pi$
$937$	5.74496	−	54.6596i	0.187680	−	1.78565i	0.531945	−	0.846779i	$-0.321461\pi$
$938$	−2.96752	−	4.08444i	−0.0968930	−	0.133362i
$939$	16.7221	−	8.72353i	0.545705	−	0.284682i
$940$	2.88016	+	3.19874i	0.0939403	+	0.104331i
$941$	8.38482	−	3.73316i	0.273337	−	0.121698i	−0.265491	−	0.964113i	$-0.585534\pi$
$941$	8.38482	−	3.73316i	0.273337	−	0.121698i	0.538828	+	0.842416i	$0.318867\pi$
$942$	16.1140	+	24.2995i	0.525023	+	0.791721i
$943$	0.0870368	−	0.409476i	0.00283431	−	0.0133344i
$944$	2.68152	−	6.02279i	0.0872760	−	0.196025i
$945$	−0.448789	+	3.47928i	−0.0145991	+	0.113181i
$946$	−10.8217	−	33.3057i	−0.351843	−	1.08286i
$947$	26.1412	+	11.6388i	0.849473	+	0.378210i	0.784839	−	0.619699i	$-0.212745\pi$
$947$	26.1412	+	11.6388i	0.849473	+	0.378210i	0.0646339	+	0.997909i	$0.479412\pi$
$948$	−3.28785	−	19.5426i	−0.106784	−	0.634714i
$949$	−11.2362	+	2.38834i	−0.364744	+	0.0775287i
$950$	−4.24822	−	9.54166i	−0.137831	−	0.309572i
$951$	−18.9927	+	38.1768i	−0.615879	+	1.23797i
$952$	2.16428	−	0.227475i	0.0701447	−	0.00737251i
$953$	−30.8526	+	22.4157i	−0.999414	+	0.726116i	−0.961962	−	0.273182i	$-0.911924\pi$
$953$	−30.8526	+	22.4157i	−0.999414	+	0.726116i	−0.0374512	+	0.999298i	$0.511924\pi$
$954$	6.48839	−	4.90714i	0.210069	−	0.158874i
$955$	7.13473	+	12.3577i	0.230874	+	0.399886i
$956$	−11.8544	+	20.5325i	−0.383400	+	0.664068i
$957$	18.8212	+	4.84998i	0.608404	+	0.156778i
$958$	6.69945	−	7.44049i	0.216449	−	0.240391i
$959$	−0.0594122	+	0.182852i	−0.00191852	+	0.00590460i
$960$	0.964778	+	2.44297i	0.0311381	+	0.0788467i
$961$	30.7849	+	3.64565i	0.993061	+	0.117602i
$962$			6.33022i			0.204095i
$963$	−32.2613	+	15.1123i	−1.03961	+	0.486988i
$964$	9.91399	+	8.92659i	0.319308	+	0.287506i
$965$	−7.48474	+	10.3019i	−0.240942	+	0.331629i
$966$	6.22651	+	0.925003i	0.200335	+	0.0297615i
$967$	−14.2132	+	8.20597i	−0.457065	+	0.263886i	−0.710809	−	0.703385i	$-0.751671\pi$
$967$	−14.2132	+	8.20597i	−0.457065	+	0.263886i	0.253745	+	0.967271i	$0.418338\pi$
$968$	22.3942	+	2.35372i	0.719776	+	0.0756516i
$969$	17.5708	−	27.6339i	0.564457	−	0.887729i
$970$	−0.613516	−	5.83722i	−0.0196988	−	0.187422i
$971$	14.0545	−	12.6547i	0.451030	−	0.406110i	−0.412062	−	0.911156i	$-0.635191\pi$
$971$	14.0545	−	12.6547i	0.451030	−	0.406110i	0.863092	+	0.505046i	$0.168525\pi$
$972$	10.3801	+	11.6299i	0.332941	+	0.373028i
$973$	−0.306714	−	1.44298i	−0.00983281	−	0.0462597i
$974$	29.6905	+	6.31092i	0.951346	+	0.202215i
$975$	−0.401268	+	9.37841i	−0.0128509	+	0.300349i
$976$	3.92674	−	1.27587i	0.125692	−	0.0408397i
$977$	15.4533	−	5.02108i	0.494394	−	0.160638i	−0.0511990	−	0.998688i	$-0.516304\pi$
$977$	15.4533	−	5.02108i	0.494394	−	0.160638i	0.545593	+	0.838050i	$0.316304\pi$
$978$	0.310648	−	7.26045i	0.00993344	−	0.232164i
$979$	−89.3647	−	18.9950i	−2.85611	−	0.607084i
$980$	2.14453	+	10.0892i	0.0685045	+	0.322288i
$981$	20.1411	−	47.6806i	0.643055	−	1.52233i
$982$	7.03250	−	6.33210i	0.224416	−	0.202065i
$983$	1.30725	+	12.4377i	0.0416949	+	0.396701i	0.995389	+	0.0959218i	$0.0305799\pi$
$983$	1.30725	+	12.4377i	0.0416949	+	0.396701i	−0.953694	+	0.300779i	$0.902753\pi$
$984$	−0.0476586	+	0.0749533i	−0.00151930	+	0.00238942i
$985$	7.08187	+	0.744334i	0.225647	+	0.0237165i
$986$	8.20506	−	4.73719i	0.261302	−	0.150863i
$987$	−2.16499	−	0.321628i	−0.0689124	−	0.0102375i
$988$	4.56284	−	6.28021i	0.145163	−	0.199800i
$989$	−36.6956	−	33.0409i	−1.16685	−	1.05064i
$990$	11.1727	+	23.8511i	0.355091	+	0.758038i
$991$		−	47.4390i		−	1.50695i	−0.657477	−	0.753474i	$-0.728377\pi$
$991$		−	47.4390i		−	1.50695i	0.657477	−	0.753474i	$-0.271623\pi$
$992$	0.327958	−	5.55810i	0.0104127	−	0.176470i
$993$	−11.7910	−	29.8569i	−0.374178	−	0.947479i
$994$	1.27838	−	3.93445i	0.0405478	−	0.124793i
$995$	−20.0848	+	22.3065i	−0.636732	+	0.707163i
$996$	−10.2213	−	2.63388i	−0.323873	−	0.0834577i
$997$	−23.2503	+	40.2707i	−0.736344	+	1.27538i	0.217787	+	0.975996i	$0.430116\pi$
$997$	−23.2503	+	40.2707i	−0.736344	+	1.27538i	−0.954131	+	0.299389i	$0.903217\pi$
$998$	−14.3575	−	24.8679i	−0.454478	−	0.787180i
$999$	8.52669	−	13.9964i	0.269773	−	0.442828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.p.a.17.9	yes	80
3.2	odd	2	inner	186.2.p.a.17.1	yes	80
31.11	odd	30	inner	186.2.p.a.11.1	✓	80
93.11	even	30	inner	186.2.p.a.11.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.p.a.11.1	✓	80	31.11	odd	30	inner
186.2.p.a.11.9	yes	80	93.11	even	30	inner
186.2.p.a.17.1	yes	80	3.2	odd	2	inner
186.2.p.a.17.9	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.605161 - 1.62289i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.31329 + 0.758228i) q^{5} +(1.07704 - 1.35646i) q^{6} +(0.0465366 - 0.442766i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.26756 - 1.96422i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.605161 - 1.62289i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.31329 + 0.758228i) q^{5} +(1.07704 - 1.35646i) q^{6} +(0.0465366 - 0.442766i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.26756 - 1.96422i) q^{9} +(1.01471 + 1.12695i) q^{10} +(-5.28891 + 2.35477i) q^{11} +(1.44350 - 0.957243i) q^{12} +(0.417276 - 1.96313i) q^{13} +(0.181081 - 0.406715i) q^{14} +(2.02527 - 1.67248i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.46549 + 1.98816i) q^{17} +(-1.54960 - 2.56880i) q^{18} +(3.78335 - 0.804176i) q^{19} +(0.616798 + 1.38535i) q^{20} +(-0.690400 - 0.343469i) q^{21} +(-5.75772 + 0.605161i) q^{22} +(-6.60423 + 4.79825i) q^{23} +(1.66865 - 0.464327i) q^{24} +(-1.35018 - 2.33858i) q^{25} +(1.00349 - 1.73810i) q^{26} +(-4.55996 + 2.49134i) q^{27} +(0.297900 - 0.330852i) q^{28} +(0.598955 - 1.84340i) q^{29} +(2.44297 - 0.964778i) q^{30} +(-5.55810 - 0.327958i) q^{31} +1.00000i q^{32} +(0.620907 + 10.0084i) q^{33} +(3.63256 + 3.27077i) q^{34} +(0.396834 - 0.546195i) q^{35} +(-0.679956 - 2.92193i) q^{36} +(-2.73153 + 1.57705i) q^{37} +(3.84669 + 0.404303i) q^{38} +(-2.93343 - 1.86520i) q^{39} +(0.158513 + 1.50815i) q^{40} +(-0.0381095 + 0.0343139i) q^{41} +(-0.550472 - 0.540003i) q^{42} +(1.25764 + 5.91671i) q^{43} +(-5.66292 - 1.20369i) q^{44} +(-1.48864 - 4.29892i) q^{45} +(-7.76373 + 2.52259i) q^{46} +(2.69949 - 0.877117i) q^{47} +(1.73047 + 0.0740404i) q^{48} +(6.65316 + 1.41417i) q^{49} +(-0.561436 - 2.64135i) q^{50} +(5.92891 - 6.04385i) q^{51} +(1.49148 - 1.34293i) q^{52} +(0.283448 + 2.69683i) q^{53} +(-5.10665 + 0.960300i) q^{54} +(-8.73133 - 0.917700i) q^{55} +(0.385559 - 0.222603i) q^{56} +(0.984443 - 6.62663i) q^{57} +(1.13928 - 1.56809i) q^{58} +(-4.89938 - 4.41142i) q^{59} +(2.62154 - 0.162637i) q^{60} -4.12882i q^{61} +(-5.18472 - 2.02945i) q^{62} +(-0.975216 + 0.912592i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(2.03650 - 2.26176i) q^{65} +(-2.50223 + 9.71038i) q^{66} +(5.67003 - 9.82077i) q^{67} +(2.44404 + 4.23321i) q^{68} +(3.79043 + 13.6217i) q^{69} +(0.546195 - 0.396834i) q^{70} +(9.24128 - 0.971297i) q^{71} +(0.256249 - 2.98904i) q^{72} +(-2.32802 - 5.22881i) q^{73} +(-3.08517 + 0.655774i) q^{74} +(-4.61234 + 0.775981i) q^{75} +(3.53348 + 1.57321i) q^{76} +(0.796487 + 2.45134i) q^{77} +(-2.21348 - 2.68039i) q^{78} +(4.65367 - 10.4523i) q^{79} +(-0.315289 + 1.48332i) q^{80} +(1.28367 + 8.90798i) q^{81} +(-0.0468479 + 0.0208580i) q^{82} +(-4.07770 - 4.52874i) q^{83} +(-0.356660 - 0.683679i) q^{84} +(4.35700 + 5.99689i) q^{85} +(-0.632282 + 6.01576i) q^{86} +(-2.62917 - 2.08759i) q^{87} +(-5.01380 - 2.89472i) q^{88} +(12.7668 + 9.27564i) q^{89} +(-0.0873389 - 4.54853i) q^{90} +(-0.849788 - 0.276113i) q^{91} -8.16327 q^{92} +(-3.89578 + 8.82173i) q^{93} +2.83841 q^{94} +(5.57839 + 1.81253i) q^{95} +(1.62289 + 0.605161i) q^{96} +(-3.13126 - 2.27499i) q^{97} +(5.89052 + 3.40090i) q^{98} +(16.6182 + 5.04899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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