LMFDB - Embedded newform 230.2.l.a.103.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			103.2
Character	$\chi$	$=$	230.103
Dual form			230.2.l.a.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.212565 + 0.977147i) q^{2} +(-0.409159 + 0.306293i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.0488687 - 2.23553i) q^{5} +(-0.212320 - 0.464916i) q^{6} +(-0.318744 + 4.45663i) q^{7} +(0.599278 - 0.800541i) q^{8} +(-0.771602 + 2.62783i) q^{9} +O(q^{10})$	\(q+(-0.212565 + 0.977147i) q^{2} +(-0.409159 + 0.306293i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.0488687 - 2.23553i) q^{5} +(-0.212320 - 0.464916i) q^{6} +(-0.318744 + 4.45663i) q^{7} +(0.599278 - 0.800541i) q^{8} +(-0.771602 + 2.62783i) q^{9} +(2.19483 + 0.427445i) q^{10} +(-3.31624 + 5.16017i) q^{11} +(0.499423 - 0.108643i) q^{12} +(5.72063 - 0.409147i) q^{13} +(-4.28703 - 1.25878i) q^{14} +(0.704723 + 0.899722i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.199099 - 0.533806i) q^{17} +(-2.40376 - 1.31255i) q^{18} +(-1.30909 + 2.86651i) q^{19} +(-0.884222 + 2.05381i) q^{20} +(-1.23462 - 1.92110i) q^{21} +(-4.33733 - 4.33733i) q^{22} +(0.973320 - 4.69602i) q^{23} +0.511103i q^{24} +(-4.99522 + 0.218495i) q^{25} +(-0.816210 + 5.67686i) q^{26} +(-1.02502 - 2.74817i) q^{27} +(2.14129 - 3.92148i) q^{28} +(1.09164 - 0.498537i) q^{29} +(-1.02896 + 0.497368i) q^{30} +(-0.682538 - 4.74716i) q^{31} +(-0.877679 + 0.479249i) q^{32} +(-0.223653 - 3.12707i) q^{33} +(0.479285 + 0.308018i) q^{34} +(9.97852 + 0.494774i) q^{35} +(1.79352 - 2.06983i) q^{36} +(1.77395 + 3.24874i) q^{37} +(-2.52274 - 1.88850i) q^{38} +(-2.21533 + 1.91959i) q^{39} +(-1.81892 - 1.30058i) q^{40} +(3.17909 - 0.933464i) q^{41} +(2.13963 - 0.798042i) q^{42} +(3.83212 + 5.11911i) q^{43} +(5.16017 - 3.31624i) q^{44} +(5.91232 + 1.59652i) q^{45} +(4.38181 + 1.94929i) q^{46} +(2.83845 - 2.83845i) q^{47} +(-0.499423 - 0.108643i) q^{48} +(-12.8312 - 1.84484i) q^{49} +(0.848309 - 4.92751i) q^{50} +(0.0820375 + 0.279394i) q^{51} +(-5.37363 - 2.00426i) q^{52} +(-3.02013 - 0.216004i) q^{53} +(2.90325 - 0.417425i) q^{54} +(11.6978 + 7.16140i) q^{55} +(3.37670 + 2.92593i) q^{56} +(-0.342365 - 1.57383i) q^{57} +(0.255098 + 1.17267i) q^{58} +(-0.100712 - 0.0872672i) q^{59} +(-0.267281 - 1.11117i) q^{60} +(8.41993 - 1.21060i) q^{61} +(4.78375 + 0.342141i) q^{62} +(-11.4653 - 4.27635i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(-1.19422 - 12.7687i) q^{65} +(3.10315 + 0.446166i) q^{66} +(3.29980 + 0.717828i) q^{67} +(-0.402858 + 0.402858i) q^{68} +(1.04012 + 2.21954i) q^{69} +(-2.60455 + 9.64531i) q^{70} +(-4.82259 + 3.09929i) q^{71} +(1.64129 + 2.19250i) q^{72} +(-0.0305242 + 0.0113849i) q^{73} +(-3.55158 + 1.04284i) q^{74} +(1.97692 - 1.61940i) q^{75} +(2.38159 - 2.06366i) q^{76} +(-21.9399 - 16.4240i) q^{77} +(-1.40482 - 2.57274i) q^{78} +(-2.54719 + 2.93961i) q^{79} +(1.65750 - 1.50090i) q^{80} +(-5.65087 - 3.63159i) q^{81} +(0.236368 + 3.30486i) q^{82} +(15.8196 - 8.63813i) q^{83} +(0.324992 + 2.26037i) q^{84} +(-1.20307 - 0.419007i) q^{85} +(-5.81670 + 2.65640i) q^{86} +(-0.293958 + 0.538344i) q^{87} +(2.14358 + 5.74716i) q^{88} +(0.587398 - 4.08544i) q^{89} +(-2.81679 + 5.43784i) q^{90} +25.6251i q^{91} +(-2.83616 + 3.86732i) q^{92} +(1.73329 + 1.73329i) q^{93} +(2.17022 + 3.37693i) q^{94} +(6.47216 + 2.78644i) q^{95} +(0.212320 - 0.464916i) q^{96} +(8.59298 + 4.69212i) q^{97} +(4.53015 - 12.1458i) q^{98} +(-11.0013 - 12.6961i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 240 * q - 8 * q^3 - 8 * q^6	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.212565	+	0.977147i	−0.150306	+	0.690947i
$2$	−0.212565	+	0.977147i	−0.150306	+	0.690947i
$3$	−0.409159	+	0.306293i	−0.236228	+	0.176838i	−0.710833	−	0.703361i	$-0.751682\pi$
$3$	−0.409159	+	0.306293i	−0.236228	+	0.176838i	0.474605	+	0.880199i	$0.342591\pi$
$4$	−0.909632	−	0.415415i	−0.454816	−	0.207708i
$5$	−0.0488687	−	2.23553i	−0.0218547	−	0.999761i
$5$	−0.0488687	−	2.23553i	−0.0218547	−	0.999761i
$6$	−0.212320	−	0.464916i	−0.0866793	−	0.189801i
$7$	−0.318744	+	4.45663i	−0.120474	+	1.68445i	0.474151	+	0.880444i	$0.342755\pi$
$7$	−0.318744	+	4.45663i	−0.120474	+	1.68445i	−0.594625	+	0.804003i	$0.702699\pi$
$8$	0.599278	−	0.800541i	0.211877	−	0.283034i
$9$	−0.771602	+	2.62783i	−0.257201	+	0.875945i
$10$	2.19483	+	0.427445i	0.694067	+	0.135170i
$11$	−3.31624	+	5.16017i	−0.999884	+	1.55585i	−0.179722	+	0.983717i	$0.557520\pi$
$11$	−3.31624	+	5.16017i	−0.999884	+	1.55585i	−0.820161	+	0.572132i	$0.806116\pi$
$12$	0.499423	−	0.108643i	0.144171	−	0.0313625i
$13$	5.72063	−	0.409147i	1.58662	−	0.113477i	0.750065	−	0.661365i	$-0.230022\pi$
$13$	5.72063	−	0.409147i	1.58662	−	0.113477i	0.836552	+	0.547888i	$0.184568\pi$
$14$	−4.28703	−	1.25878i	−1.14576	−	0.336424i
$15$	0.704723	+	0.899722i	0.181959	+	0.232307i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	0.199099	−	0.533806i	0.0482886	−	0.129467i	−0.910567	−	0.413363i	$-0.864354\pi$
$17$	0.199099	−	0.533806i	0.0482886	−	0.129467i	0.958855	+	0.283896i	$0.0916269\pi$
$18$	−2.40376	−	1.31255i	−0.566573	−	0.309372i
$19$	−1.30909	+	2.86651i	−0.300326	+	0.657623i	−0.998287	−	0.0585133i	$-0.981364\pi$
$19$	−1.30909	+	2.86651i	−0.300326	+	0.657623i	0.697960	+	0.716137i	$0.254091\pi$
$20$	−0.884222	+	2.05381i	−0.197718	+	0.459247i
$21$	−1.23462	−	1.92110i	−0.269415	−	0.419218i
$22$	−4.33733	−	4.33733i	−0.924721	−	0.924721i
$23$	0.973320	−	4.69602i	0.202951	−	0.979189i
$23$	0.973320	−	4.69602i	0.202951	−	0.979189i
$24$			0.511103i			0.104329i
$25$	−4.99522	+	0.218495i	−0.999045	+	0.0436990i
$26$	−0.816210	+	5.67686i	−0.160072	+	1.11332i
$27$	−1.02502	−	2.74817i	−0.197264	−	0.528886i
$28$	2.14129	−	3.92148i	0.404666	−	0.741090i
$29$	1.09164	−	0.498537i	0.202713	−	0.0925760i	−0.311472	−	0.950255i	$-0.600822\pi$
$29$	1.09164	−	0.498537i	0.202713	−	0.0925760i	0.514185	+	0.857679i	$0.328095\pi$
$30$	−1.02896	+	0.497368i	−0.187861	+	0.0908066i
$31$	−0.682538	−	4.74716i	−0.122587	−	0.852615i	−0.954607	−	0.297868i	$-0.903724\pi$
$31$	−0.682538	−	4.74716i	−0.122587	−	0.852615i	0.832019	−	0.554746i	$-0.187185\pi$
$32$	−0.877679	+	0.479249i	−0.155153	+	0.0847201i
$33$	−0.223653	−	3.12707i	−0.0389329	−	0.544353i
$34$	0.479285	+	0.308018i	0.0821967	+	0.0528246i
$35$	9.97852	+	0.494774i	1.68668	+	0.0836321i
$36$	1.79352	−	2.06983i	0.298919	−	0.344971i
$37$	1.77395	+	3.24874i	0.291635	+	0.534090i	0.981884	−	0.189482i	$-0.0606809\pi$
$37$	1.77395	+	3.24874i	0.291635	+	0.534090i	−0.690249	+	0.723572i	$0.742499\pi$
$38$	−2.52274	−	1.88850i	−0.409242	−	0.306355i
$39$	−2.21533	+	1.91959i	−0.354737	+	0.307381i
$40$	−1.81892	−	1.30058i	−0.287597	−	0.205640i
$41$	3.17909	−	0.933464i	0.496490	−	0.145783i	−0.0238950	−	0.999714i	$-0.507607\pi$
$41$	3.17909	−	0.933464i	0.496490	−	0.145783i	0.520385	+	0.853932i	$0.325789\pi$
$42$	2.13963	−	0.798042i	0.330153	−	0.123141i
$43$	3.83212	+	5.11911i	0.584393	+	0.780657i	0.991131	−	0.132887i	$-0.0424249\pi$
$43$	3.83212	+	5.11911i	0.584393	+	0.780657i	−0.406739	+	0.913545i	$0.633334\pi$
$44$	5.16017	−	3.31624i	0.777925	−	0.499942i
$45$	5.91232	+	1.59652i	0.881356	+	0.237996i
$46$	4.38181	+	1.94929i	0.646063	+	0.287407i
$47$	2.83845	−	2.83845i	0.414030	−	0.414030i	−0.469110	−	0.883140i	$-0.655425\pi$
$47$	2.83845	−	2.83845i	0.414030	−	0.414030i	0.883140	+	0.469110i	$0.155425\pi$
$48$	−0.499423	−	0.108643i	−0.0720855	−	0.0156812i
$49$	−12.8312	−	1.84484i	−1.83303	−	0.263549i
$50$	0.848309	−	4.92751i	0.119969	−	0.696855i
$51$	0.0820375	+	0.279394i	0.0114876	+	0.0391230i
$52$	−5.37363	−	2.00426i	−0.745189	−	0.277941i
$53$	−3.02013	−	0.216004i	−0.414847	−	0.0296704i	−0.137644	−	0.990482i	$-0.543953\pi$
$53$	−3.02013	−	0.216004i	−0.414847	−	0.0296704i	−0.277203	+	0.960811i	$0.589407\pi$
$54$	2.90325	−	0.417425i	0.395083	−	0.0568043i
$55$	11.6978	+	7.16140i	1.57733	+	0.965642i
$56$	3.37670	+	2.92593i	0.451230	+	0.390993i
$57$	−0.342365	−	1.57383i	−0.0453474	−	0.208458i
$58$	0.255098	+	1.17267i	0.0334961	+	0.153979i
$59$	−0.100712	−	0.0872672i	−0.0131115	−	0.0113612i	0.648280	−	0.761402i	$-0.275488\pi$
$59$	−0.100712	−	0.0872672i	−0.0131115	−	0.0113612i	−0.661392	+	0.750041i	$0.730034\pi$
$60$	−0.267281	−	1.11117i	−0.0345058	−	0.143451i
$61$	8.41993	−	1.21060i	1.07806	−	0.155002i	0.419669	−	0.907677i	$-0.362146\pi$
$61$	8.41993	−	1.21060i	1.07806	−	0.155002i	0.658392	+	0.752675i	$0.271237\pi$
$62$	4.78375	+	0.342141i	0.607537	+	0.0434519i
$63$	−11.4653	−	4.27635i	−1.44450	−	0.538769i
$64$	−0.281733	−	0.959493i	−0.0352166	−	0.119937i
$65$	−1.19422	−	12.7687i	−0.148125	−	1.58376i
$66$	3.10315	+	0.446166i	0.381971	+	0.0549192i
$67$	3.29980	+	0.717828i	0.403135	+	0.0876967i	0.409561	−	0.912283i	$-0.365682\pi$
$67$	3.29980	+	0.717828i	0.403135	+	0.0876967i	−0.00642607	+	0.999979i	$0.502045\pi$
$68$	−0.402858	+	0.402858i	−0.0488537	+	0.0488537i
$69$	1.04012	+	2.21954i	0.125215	+	0.267202i
$70$	−2.60455	+	9.64531i	−0.311304	+	1.15283i
$71$	−4.82259	+	3.09929i	−0.572336	+	0.367818i	−0.794567	−	0.607176i	$-0.792302\pi$
$71$	−4.82259	+	3.09929i	−0.572336	+	0.367818i	0.222231	+	0.974994i	$0.428666\pi$
$72$	1.64129	+	2.19250i	0.193427	+	0.258389i
$73$	−0.0305242	+	0.0113849i	−0.00357258	+	0.00133250i	−0.351250	−	0.936282i	$-0.614243\pi$
$73$	−0.0305242	+	0.0113849i	−0.00357258	+	0.00133250i	0.347677	+	0.937614i	$0.386970\pi$
$74$	−3.55158	+	1.04284i	−0.412862	+	0.121227i
$75$	1.97692	−	1.61940i	0.228275	−	0.186992i
$76$	2.38159	−	2.06366i	0.273187	−	0.236718i
$77$	−21.9399	−	16.4240i	−2.50029	−	1.87169i
$78$	−1.40482	−	2.57274i	−0.159065	−	0.291306i
$79$	−2.54719	+	2.93961i	−0.286581	+	0.330732i	−0.880726	−	0.473626i	$-0.842945\pi$
$79$	−2.54719	+	2.93961i	−0.286581	+	0.330732i	0.594145	+	0.804358i	$0.297490\pi$
$80$	1.65750	−	1.50090i	0.185314	−	0.167805i
$81$	−5.65087	−	3.63159i	−0.627874	−	0.403510i
$82$	0.236368	+	3.30486i	0.0261025	+	0.364960i
$83$	15.8196	−	8.63813i	1.73642	−	0.948158i	0.798006	−	0.602650i	$-0.205889\pi$
$83$	15.8196	−	8.63813i	1.73642	−	0.948158i	0.938416	−	0.345508i	$-0.112293\pi$
$84$	0.324992	+	2.26037i	0.0354596	+	0.246627i
$85$	−1.20307	−	0.419007i	−0.130491	−	0.0454476i
$86$	−5.81670	+	2.65640i	−0.627231	+	0.286447i
$87$	−0.293958	+	0.538344i	−0.0315156	+	0.0577165i
$88$	2.14358	+	5.74716i	0.228506	+	0.612649i
$89$	0.587398	−	4.08544i	0.0622640	−	0.433056i	−0.934716	−	0.355396i	$-0.884346\pi$
$89$	0.587398	−	4.08544i	0.0622640	−	0.433056i	0.996980	−	0.0776600i	$-0.0247449\pi$
$90$	−2.81679	+	5.43784i	−0.296916	+	0.573198i
$91$			25.6251i			2.68624i
$92$	−2.83616	+	3.86732i	−0.295690	+	0.403196i
$93$	1.73329	+	1.73329i	0.179734	+	0.179734i
$94$	2.17022	+	3.37693i	0.223841	+	0.348304i
$95$	6.47216	+	2.78644i	0.664030	+	0.285883i
$96$	0.212320	−	0.464916i	0.0216698	−	0.0474503i
$97$	8.59298	+	4.69212i	0.872485	+	0.476413i	0.852100	−	0.523380i	$-0.175329\pi$
$97$	8.59298	+	4.69212i	0.872485	+	0.476413i	0.0203850	+	0.999792i	$0.493511\pi$
$98$	4.53015	−	12.1458i	0.457614	−	1.22691i
$99$	−11.0013	−	12.6961i	−1.10567	−	1.27601i
$100$	4.63458	+	1.87634i	0.463458	+	0.187634i
$101$	−5.32716	−	1.56420i	−0.530072	−	0.155643i	0.00573494	−	0.999984i	$-0.498175\pi$
$101$	−5.32716	−	1.56420i	−0.530072	−	0.155643i	−0.535807	+	0.844340i	$0.679993\pi$
$102$	−0.290448	+	0.0207732i	−0.0287586	+	0.00205685i
$103$	0.540618	−	0.117604i	0.0532687	−	0.0115879i	−0.185852	−	0.982578i	$-0.559504\pi$
$103$	0.540618	−	0.117604i	0.0532687	−	0.0115879i	0.239121	+	0.970990i	$0.423141\pi$
$104$	3.10070	−	4.82479i	0.304049	−	0.473110i
$105$	−4.23435	+	2.85391i	−0.413230	+	0.278513i
$106$	0.853043	−	2.90520i	0.0828548	−	0.282178i
$107$	4.28754	−	5.72748i	0.414492	−	0.553697i	−0.543901	−	0.839150i	$-0.683053\pi$
$107$	4.28754	−	5.72748i	0.414492	−	0.553697i	0.958393	+	0.285453i	$0.0921441\pi$
$108$	−0.209245	+	2.92563i	−0.0201347	+	0.281519i
$109$	7.45567	+	16.3256i	0.714124	+	1.56371i	0.821960	+	0.569545i	$0.192880\pi$
$109$	7.45567	+	16.3256i	0.714124	+	1.56371i	−0.107837	+	0.994169i	$0.534392\pi$
$110$	−9.48428	+	9.90820i	−0.904291	+	0.944710i
$111$	−1.72089	−	0.785906i	−0.163340	−	0.0745949i
$112$	−3.57683	+	2.67758i	−0.337978	+	0.253007i
$113$	0.111723	−	0.513582i	0.0105100	−	0.0483137i	−0.971593	−	0.236657i	$-0.923948\pi$
$113$	0.111723	−	0.513582i	0.0105100	−	0.0483137i	0.982103	+	0.188343i	$0.0603118\pi$
$114$	1.61063			0.150850
$115$	−10.5457	−	1.94640i	−0.983390	−	0.181503i
$116$	−1.20009			−0.111426
$117$	−3.33887	+	15.3486i	−0.308679	+	1.41897i
$118$	0.106681	−	0.0798601i	0.00982075	−	0.00735172i
$119$	2.31551	+	1.05746i	0.212263	+	0.0969370i
$120$	1.14259	−	0.0249770i	0.104304	−	0.00228007i
$121$	−11.0603	−	24.2188i	−1.00549	−	2.20171i
$122$	−0.606848	+	8.48484i	−0.0549414	+	0.768181i
$123$	−1.01484	+	1.35567i	−0.0915050	+	0.122236i
$124$	−1.35118	+	4.60170i	−0.121340	+	0.413245i
$125$	0.732564	+	11.1563i	0.0655225	+	0.997851i
$126$	6.61575	−	10.2943i	0.589378	−	0.917090i
$127$	−8.54197	+	1.85819i	−0.757977	+	0.164888i	−0.574915	−	0.818213i	$-0.694965\pi$
$127$	−8.54197	+	1.85819i	−0.757977	+	0.164888i	−0.183063	+	0.983101i	$0.558601\pi$
$128$	0.997452	−	0.0713392i	0.0881631	−	0.00630555i
$129$	−3.13589	−	0.920782i	−0.276100	−	0.0810703i
$130$	12.7307	+	1.54724i	1.11656	+	0.135702i
$131$	−7.93958	−	9.16277i	−0.693685	−	0.800555i	0.294200	−	0.955744i	$-0.404947\pi$
$131$	−7.93958	−	9.16277i	−0.693685	−	0.800555i	−0.987885	+	0.155189i	$0.950401\pi$
$132$	−1.09559	+	2.93739i	−0.0953590	+	0.255667i
$133$	−12.3577	−	6.74782i	−1.07155	−	0.585110i
$134$	−1.40285	+	3.07181i	−0.121188	+	0.265364i
$135$	−6.09354	+	2.42576i	−0.524449	+	0.208776i
$136$	−0.308018	−	0.479285i	−0.0264123	−	0.0410983i
$137$	−5.33407	−	5.33407i	−0.455720	−	0.455720i	0.441527	−	0.897248i	$-0.354437\pi$
$137$	−5.33407	−	5.33407i	−0.455720	−	0.455720i	−0.897248	+	0.441527i	$0.854437\pi$
$138$	−2.38991	+	0.544548i	−0.203443	+	0.0463550i
$139$			7.25972i			0.615761i	0.951425	+	0.307881i	$0.0996198\pi$
$139$			7.25972i			0.615761i	−0.951425	+	0.307881i	$0.900380\pi$
$140$	−8.87124	−	4.59529i	−0.749757	−	0.388373i
$141$	−0.291981	+	2.03077i	−0.0245892	+	0.171022i
$142$	−2.00335	−	5.37118i	−0.168117	−	0.450739i
$143$	−16.8597	+	30.8762i	−1.40988	+	2.58200i
$144$	−2.49128	+	1.13773i	−0.207606	+	0.0948106i
$145$	−1.16784	−	2.41604i	−0.0969842	−	0.200642i
$146$	−0.00463636	−	0.0322466i	−0.000383708	−	0.00266875i
$147$	5.81506	−	3.17526i	0.479618	−	0.261891i
$148$	−0.264063	−	3.69208i	−0.0217058	−	0.303487i
$149$	15.8637	+	10.1950i	1.29960	+	0.835205i	0.993169	−	0.116687i	$-0.0372274\pi$
$149$	15.8637	+	10.1950i	1.29960	+	0.835205i	0.306435	+	0.951892i	$0.400864\pi$
$150$	1.16217	+	2.27597i	0.0948906	+	0.185832i
$151$	9.11134	−	10.5150i	0.741470	−	0.855702i	−0.252242	−	0.967664i	$-0.581168\pi$
$151$	9.11134	−	10.5150i	0.741470	−	0.855702i	0.993712	+	0.111962i	$0.0357135\pi$
$152$	1.51025	+	2.76582i	0.122498	+	0.224338i
$153$	1.24913	+	0.935085i	0.100986	+	0.0755971i
$154$	20.7123	−	17.9473i	1.66905	−	1.44624i
$155$	−10.5791	+	1.75782i	−0.849732	+	0.141192i
$156$	2.81256	−	0.825843i	0.225185	−	0.0661204i
$157$	8.43919	−	3.14766i	0.673521	−	0.251210i	0.0106491	−	0.999943i	$-0.496610\pi$
$157$	8.43919	−	3.14766i	0.673521	−	0.251210i	0.662872	+	0.748733i	$0.269337\pi$
$158$	−2.33099	−	3.11384i	−0.185443	−	0.247723i
$159$	1.30188	−	0.836665i	0.103245	−	0.0663518i
$160$	1.11427	+	1.93866i	0.0880907	+	0.153265i
$161$	20.6182	+	5.83455i	1.62494	+	0.459827i
$162$	4.74978	−	4.74978i	0.373178	−	0.373178i
$163$	8.08877	+	1.75960i	0.633562	+	0.137823i	0.517866	−	0.855462i	$-0.326727\pi$
$163$	8.08877	+	1.75960i	0.633562	+	0.137823i	0.115696	+	0.993285i	$0.463090\pi$
$164$	−3.27957	−	0.471531i	−0.256092	−	0.0368204i
$165$	−6.97975	+	0.652799i	−0.543373	+	0.0508203i
$166$	5.07803	+	17.2942i	0.394132	+	1.34229i
$167$	15.8275	+	5.90336i	1.22477	+	0.456816i	0.876875	−	0.480718i	$-0.159624\pi$
$167$	15.8275	+	5.90336i	1.22477	+	0.456816i	0.347895	+	0.937534i	$0.386897\pi$
$168$	−2.27780	−	0.162911i	−0.175736	−	0.0125689i
$169$	19.6905	−	2.83107i	1.51465	−	0.217774i
$170$	0.665162	−	1.08651i	0.0510156	−	0.0833315i
$171$	−6.52262	−	5.65188i	−0.498797	−	0.432210i
$172$	−1.35926	−	6.24843i	−0.103643	−	0.476438i
$173$	4.51369	+	20.7491i	0.343170	+	1.57753i	0.748360	+	0.663293i	$0.230842\pi$
$173$	4.51369	+	20.7491i	0.343170	+	1.57753i	−0.405190	+	0.914232i	$0.632795\pi$
$174$	−0.463556	−	0.401673i	−0.0351421	−	0.0304508i
$175$	0.618447	−	22.3315i	0.0467502	−	1.68810i
$176$	−6.07147	+	0.872946i	−0.457654	+	0.0658008i
$177$	0.0679364	+	0.00485891i	0.00510641	+	0.000365218i
$178$	3.86722	+	1.44240i	0.289860	+	0.108112i
$179$	1.66028	+	5.65441i	0.124095	+	0.422630i	0.997982	−	0.0634999i	$-0.0202263\pi$
$179$	1.66028	+	5.65441i	0.124095	+	0.422630i	−0.873886	+	0.486130i	$0.838408\pi$
$180$	−4.71481	−	3.90831i	−0.351422	−	0.291309i
$181$	−15.8098	−	2.27311i	−1.17513	−	0.168959i	−0.473038	−	0.881042i	$-0.656843\pi$
$181$	−15.8098	−	2.27311i	−1.17513	−	0.168959i	−0.702095	+	0.712083i	$0.747752\pi$
$182$	−25.0395	−	5.44701i	−1.85605	−	0.403759i
$183$	−3.07429	+	3.07429i	−0.227258	+	0.227258i
$184$	−3.17607	−	3.59341i	−0.234143	−	0.264909i
$185$	7.17598	−	4.12448i	0.527589	−	0.303238i
$186$	−2.06211	+	1.32524i	−0.151201	+	0.0971713i
$187$	2.09427	+	2.79761i	0.153148	+	0.204582i
$188$	−3.76107	+	1.40281i	−0.274304	+	0.102310i
$189$	12.5743	−	3.69215i	0.914646	−	0.268564i
$190$	−4.09852	+	5.73195i	−0.297338	+	0.415840i
$191$	5.46478	−	4.73526i	0.395418	−	0.342631i	−0.434346	−	0.900746i	$-0.643021\pi$
$191$	5.46478	−	4.73526i	0.395418	−	0.342631i	0.829764	+	0.558115i	$0.188475\pi$
$192$	0.409159	+	0.306293i	0.0295285	+	0.0221048i
$193$	−2.11937	−	3.88134i	−0.152556	−	0.279385i	0.790213	−	0.612832i	$-0.209970\pi$
$193$	−2.11937	−	3.88134i	−0.152556	−	0.279385i	−0.942769	+	0.333447i	$0.891788\pi$
$194$	−6.41146	+	7.39922i	−0.460316	+	0.531233i
$195$	4.39958	+	4.85864i	0.315060	+	0.347934i
$196$	10.9053	+	7.00839i	0.778948	+	0.500600i
$197$	−1.58746	−	22.1956i	−0.113102	−	1.58137i	−0.664605	−	0.747195i	$-0.731400\pi$
$197$	−1.58746	−	22.1956i	−0.113102	−	1.58137i	0.551503	−	0.834173i	$-0.314055\pi$
$198$	14.7445	−	8.05108i	1.04784	−	0.572166i
$199$	−1.73103	−	12.0396i	−0.122710	−	0.853464i	−0.954465	−	0.298322i	$-0.903573\pi$
$199$	−1.73103	−	12.0396i	−0.122710	−	0.853464i	0.831756	−	0.555142i	$-0.187336\pi$
$200$	−2.81861	+	4.12982i	−0.199306	+	0.292023i
$201$	−1.57001	+	0.717000i	−0.110740	+	0.0505733i
$202$	2.66082	−	4.87293i	0.187215	−	0.342858i
$203$	1.87384	+	5.02396i	0.131518	+	0.352613i
$204$	0.0414406	−	0.288226i	0.00290142	−	0.0201798i
$205$	−2.24215	−	7.06134i	−0.156598	−	0.493185i
$206$			0.553262i			0.0385476i
$207$	11.5894	+	6.18118i	0.805516	+	0.429622i
$208$	4.05543	+	4.05543i	0.281193	+	0.281193i
$209$	−10.4504	−	16.2612i	−0.722871	−	1.12481i
$210$	−1.88861	−	4.74422i	−0.130327	−	0.327383i
$211$	−4.47719	+	9.80367i	−0.308222	+	0.674913i	−0.998832	−	0.0483148i	$-0.984615\pi$
$211$	−4.47719	+	9.80367i	−0.308222	+	0.674913i	0.690610	+	0.723228i	$0.257342\pi$
$212$	2.65748	+	1.45109i	0.182516	+	0.0996614i
$213$	1.02392	−	2.74523i	0.0701576	−	0.188100i
$214$	4.68521	+	5.40702i	0.320274	+	0.369616i
$215$	11.2567	−	8.81700i	0.767699	−	0.601314i
$216$	−2.81430	−	0.826352i	−0.191489	−	0.0562261i
$217$	21.3739	−	1.52869i	1.45095	−	0.103774i
$218$	−17.5374	+	3.81502i	−1.18778	+	0.258386i
$219$	0.00900212	−	0.0140076i	0.000608307	−	0.000946544i
$220$	−7.66574	−	11.3737i	−0.516824	−	0.766813i
$221$	0.920567	−	3.13516i	0.0619240	−	0.210894i
$222$	1.13375	−	1.51451i	0.0760922	−	0.101647i
$223$	0.677693	−	9.47539i	0.0453817	−	0.634519i	−0.922961	−	0.384894i	$-0.874238\pi$
$223$	0.677693	−	9.47539i	0.0453817	−	0.634519i	0.968343	−	0.249625i	$-0.0803074\pi$
$224$	−1.85608	−	4.06425i	−0.124014	−	0.271554i
$225$	3.28015	−	13.2952i	0.218677	−	0.886347i
$226$	0.478097	+	0.218339i	0.0318025	+	0.0145237i
$227$	−17.8296	+	13.3471i	−1.18339	+	0.885878i	−0.995354	−	0.0962832i	$-0.969305\pi$
$227$	−17.8296	+	13.3471i	−1.18339	+	0.885878i	−0.188041	+	0.982161i	$0.560214\pi$
$228$	−0.342365	+	1.57383i	−0.0226737	+	0.104229i
$229$	−13.1134			−0.866560			−0.433280	−	0.901259i	$-0.642644\pi$
$229$	−13.1134			−0.866560			−0.433280	+	0.901259i	$0.642644\pi$
$230$	4.14357	−	9.89095i	0.273219	−	0.652190i
$231$	14.0075			0.921625
$232$	0.255098	−	1.17267i	0.0167480	−	0.0769894i
$233$	−2.98909	+	2.23761i	−0.195822	+	0.146590i	−0.692690	−	0.721236i	$-0.743574\pi$
$233$	−2.98909	+	2.23761i	−0.195822	+	0.146590i	0.496868	+	0.867826i	$0.334483\pi$
$234$	−14.2881	−	6.52514i	−0.934040	−	0.426562i
$235$	−6.48415	−	6.20673i	−0.422979	−	0.404882i
$236$	0.0553585	+	0.121218i	0.00360353	+	0.00789063i
$237$	0.141824	−	1.98296i	0.00921244	−	0.128807i
$238$	−1.52549	+	2.03782i	−0.0988828	+	0.132092i
$239$	5.21092	−	17.7468i	0.337067	−	1.14794i	−0.600351	−	0.799736i	$-0.704973\pi$
$239$	5.21092	−	17.7468i	0.337067	−	1.14794i	0.937418	−	0.348207i	$-0.113209\pi$
$240$	−0.218469	+	1.12179i	−0.0141021	+	0.0724110i
$241$	−3.22611	+	5.01993i	−0.207812	+	0.323362i	−0.929477	−	0.368881i	$-0.879741\pi$
$241$	−3.22611	+	5.01993i	−0.207812	+	0.323362i	0.721665	+	0.692243i	$0.243377\pi$
$242$	26.0163	−	5.65951i	1.67239	−	0.363807i
$243$	12.2013	−	0.872657i	0.782716	−	0.0559810i
$244$	−8.16194	−	2.39656i	−0.522515	−	0.153424i
$245$	−3.49717	+	28.7747i	−0.223426	+	1.83835i
$246$	−1.10897	−	1.27981i	−0.0707051	−	0.0815980i
$247$	−6.31601	+	16.9339i	−0.401878	+	1.07748i
$248$	−4.20933	−	2.29847i	−0.267292	−	0.145953i
$249$	−3.82692	+	8.37979i	−0.242521	+	0.531047i
$250$	−11.0571	−	1.65562i	−0.699311	−	0.104711i
$251$	−7.00900	−	10.9062i	−0.442404	−	0.688395i	0.546415	−	0.837515i	$-0.315992\pi$
$251$	−7.00900	−	10.9062i	−0.442404	−	0.688395i	−0.988819	+	0.149120i	$0.952356\pi$
$252$	8.65277	+	8.65277i	0.545074	+	0.545074i
$253$	21.0045	+	20.5956i	1.32054	+	1.29484i
$254$		−	8.74174i		−	0.548506i
$255$	0.620586	−	0.197051i	0.0388626	−	0.0123398i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	0.798035	+	2.13961i	0.0497800	+	0.133465i	0.959460	−	0.281844i	$-0.0909460\pi$
$257$	0.798035	+	2.13961i	0.0497800	+	0.133465i	−0.909680	+	0.415309i	$0.863673\pi$
$258$	1.56632	−	2.86850i	0.0975149	−	0.178585i
$259$	−15.0439	+	6.87030i	−0.934780	+	0.426900i
$260$	−4.21799	+	12.1109i	−0.261589	+	0.751085i
$261$	0.467758	+	3.25333i	0.0289535	+	0.201376i
$262$	10.6411	−	5.81045i	0.657406	−	0.358971i
$263$	0.482341	+	6.74401i	0.0297424	+	0.415854i	0.990411	+	0.138155i	$0.0441171\pi$
$263$	0.482341	+	6.74401i	0.0297424	+	0.415854i	−0.960668	+	0.277699i	$0.910428\pi$
$264$	−2.63738	−	1.69494i	−0.162320	−	0.104316i
$265$	−0.335295	+	6.76216i	−0.0205970	+	0.415396i
$266$	9.22044	−	10.6410i	0.565341	−	0.652439i
$267$	1.01100	+	1.85151i	0.0618723	+	0.113311i
$268$	−2.70341	−	2.02375i	−0.165137	−	0.123620i
$269$	−6.48388	+	5.61832i	−0.395329	+	0.342555i	−0.829730	−	0.558165i	$-0.811506\pi$
$269$	−6.48388	+	5.61832i	−0.395329	+	0.342555i	0.434401	+	0.900720i	$0.356960\pi$
$270$	−1.07504	−	6.46992i	−0.0654252	−	0.393747i
$271$	−14.0335	+	4.12060i	−0.852473	+	0.250309i	−0.678644	−	0.734467i	$-0.737432\pi$
$271$	−14.0335	+	4.12060i	−0.852473	+	0.250309i	−0.173829	+	0.984776i	$0.555614\pi$
$272$	0.533806	−	0.199099i	0.0323667	−	0.0120722i
$273$	−7.84879	−	10.4848i	−0.475030	−	0.634566i
$274$	6.34601	−	4.07833i	0.383376	−	0.246381i
$275$	15.4379	−	26.5008i	0.930940	−	1.59806i
$276$	−0.0240911	−	2.45105i	−0.00145011	−	0.147536i
$277$	11.9944	−	11.9944i	0.720674	−	0.720674i	−0.248068	−	0.968743i	$-0.579796\pi$
$277$	11.9944	−	11.9944i	0.720674	−	0.720674i	0.968743	+	0.248068i	$0.0797957\pi$
$278$	−7.09381	−	1.54316i	−0.425459	−	0.0925529i
$279$	13.0014	+	1.86932i	0.778373	+	0.111913i
$280$	6.37599	−	7.69171i	0.381038	−	0.459667i
$281$	0.724282	+	2.46668i	0.0432071	+	0.147150i	0.978271	−	0.207328i	$-0.0664768\pi$
$281$	0.724282	+	2.46668i	0.0432071	+	0.147150i	−0.935064	+	0.354478i	$0.884659\pi$
$282$	−1.92230	−	0.716980i	−0.114471	−	0.0426955i
$283$	0.189955	+	0.0135859i	0.0112917	+	0.000807596i	0.0769839	−	0.997032i	$-0.475471\pi$
$283$	0.189955	+	0.0135859i	0.0112917	+	0.000807596i	−0.0656922	+	0.997840i	$0.520926\pi$
$284$	5.67427	−	0.815837i	0.336706	−	0.0484110i
$285$	−3.50161	+	0.842279i	−0.207418	+	0.0498923i
$286$	−26.5868	−	23.0376i	−1.57211	−	1.36224i
$287$	3.14678	+	14.4655i	0.185749	+	0.853874i
$288$	−0.582168	−	2.67618i	−0.0343046	−	0.157696i
$289$	12.6024	+	10.9201i	0.741320	+	0.642357i
$290$	2.60907	−	0.627588i	0.153210	−	0.0368532i
$291$	−4.95306	+	0.712143i	−0.290354	+	0.0417465i
$292$	0.0324952	+	0.00232410i	0.00190164	+	0.000136008i
$293$	−17.2279	−	6.42569i	−1.00647	−	0.375393i	−0.208453	−	0.978032i	$-0.566843\pi$
$293$	−17.2279	−	6.42569i	−1.00647	−	0.375393i	−0.798014	+	0.602640i	$0.794116\pi$
$294$	1.86662	+	6.35712i	0.108863	+	0.370755i
$295$	−0.190167	+	0.229409i	−0.0110720	+	0.0133567i
$296$	3.66384	+	0.526780i	0.212956	+	0.0306185i
$297$	17.5802	+	3.82435i	1.02011	+	0.221911i
$298$	−13.3341	+	13.3341i	−0.772421	+	0.772421i
$299$	3.64663	−	27.2624i	0.210890	−	1.57663i
$300$	−2.47099	+	0.651817i	−0.142663	+	0.0376327i
$301$	−24.0354	+	15.4466i	−1.38538	+	0.890329i
$302$	8.33799	+	11.1382i	0.479797	+	0.640934i
$303$	2.65876	−	0.991666i	0.152742	−	0.0569697i
$304$	−3.02364	+	0.887821i	−0.173418	+	0.0509200i
$305$	−3.11781	−	18.7639i	−0.178526	−	1.07442i
$306$	−1.17924	+	1.02181i	−0.0674124	+	0.0584132i
$307$	−23.7765	−	17.7989i	−1.35700	−	1.01584i	−0.996545	−	0.0830581i	$-0.973531\pi$
$307$	−23.7765	−	17.7989i	−1.35700	−	1.01584i	−0.360453	−	0.932777i	$-0.617378\pi$
$308$	13.1345	+	24.0540i	0.748406	+	1.37060i
$309$	−0.185178	+	0.213706i	−0.0105344	+	0.0121573i
$310$	0.531092	−	10.7110i	0.0301640	−	0.608342i
$311$	13.0141	+	8.36367i	0.737963	+	0.474260i	0.854843	−	0.518886i	$-0.173653\pi$
$311$	13.0141	+	8.36367i	0.737963	+	0.474260i	−0.116880	+	0.993146i	$0.537289\pi$
$312$	0.209117	+	2.92383i	0.0118389	+	0.165529i
$313$	−8.49304	+	4.63755i	−0.480055	+	0.262130i	−0.701006	−	0.713155i	$-0.747266\pi$
$313$	−8.49304	+	4.63755i	−0.480055	+	0.262130i	0.220951	+	0.975285i	$0.429084\pi$
$314$	1.28184	+	8.91541i	0.0723386	+	0.503126i
$315$	−8.99962	+	25.8401i	−0.507071	+	1.45593i
$316$	3.53816	−	1.61582i	0.199037	−	0.0908972i
$317$	−11.2019	+	20.5147i	−0.629160	+	1.15222i	0.347551	+	0.937661i	$0.387013\pi$
$317$	−11.2019	+	20.5147i	−0.629160	+	1.15222i	−0.976711	+	0.214559i	$0.931169\pi$
$318$	0.540811	+	1.44997i	0.0303272	+	0.0813103i
$319$	−1.04762	+	7.28634i	−0.0586553	+	0.407957i
$320$	−2.13121	+	0.676712i	−0.119138	+	0.0378293i
$321$			3.65670i			0.204097i
$322$	−10.0839	+	18.9068i	−0.561955	+	1.05363i
$323$	1.26952	+	1.26952i	0.0706381	+	0.0706381i
$324$	3.63159	+	5.65087i	0.201755	+	0.313937i
$325$	−28.4864	+	3.29371i	−1.58014	+	0.182702i
$326$	−3.43878	+	7.52989i	−0.190457	+	0.417042i
$327$	−8.05099	−	4.39617i	−0.445221	−	0.243109i
$328$	1.15788	−	3.10439i	0.0639332	−	0.171411i
$329$	11.7452	+	13.5546i	0.647531	+	0.747291i
$330$	0.845771	−	6.95900i	0.0465582	−	0.383080i
$331$	19.3784	+	5.69002i	1.06514	+	0.312752i	0.766917	−	0.641746i	$-0.221790\pi$
$331$	19.3784	+	5.69002i	1.06514	+	0.312752i	0.298218	+	0.954498i	$0.403608\pi$
$332$	−17.9784	+	1.28584i	−0.986692	+	0.0705696i
$333$	−9.90593	+	2.15490i	−0.542842	+	0.118088i
$334$	−9.13283	+	14.2110i	−0.499726	+	0.777589i
$335$	1.44347	−	7.41190i	0.0788653	−	0.404955i
$336$	0.643369	−	2.19111i	0.0350987	−	0.119535i
$337$	9.53990	−	12.7438i	0.519671	−	0.694199i	−0.461544	−	0.887117i	$-0.652704\pi$
$337$	9.53990	−	12.7438i	0.519671	−	0.694199i	0.981215	+	0.192918i	$0.0617951\pi$
$338$	−1.41915	+	19.8423i	−0.0771915	+	1.07928i
$339$	0.111594	+	0.244357i	0.00606096	+	0.0132716i
$340$	0.920290	+	0.880915i	0.0499097	+	0.0477743i
$341$	26.7596	+	12.2207i	1.44911	+	0.661788i
$342$	6.90920	−	5.17217i	0.373607	−	0.279679i
$343$	5.66344	−	26.0344i	0.305797	−	1.40573i
$344$	6.39456			0.344772
$345$	4.91104	−	2.43368i	0.264401	−	0.131025i
$346$	−21.2344			−1.14157
$347$	−0.165106	+	0.758978i	−0.00886333	+	0.0407441i	−0.981366	−	0.192147i	$-0.938455\pi$
$347$	−0.165106	+	0.758978i	−0.00886333	+	0.0407441i	0.972503	+	0.232891i	$0.0748186\pi$
$348$	0.491030	−	0.367580i	0.0263220	−	0.0197044i
$349$	33.3546	+	15.2326i	1.78543	+	0.815380i	0.972457	+	0.233084i	$0.0748817\pi$
$349$	33.3546	+	15.2326i	1.78543	+	0.815380i	0.812977	+	0.582296i	$0.197846\pi$
$350$	21.6897	+	5.35121i	1.15936	+	0.286034i
$351$	−6.98814	−	15.3019i	−0.372999	−	0.816755i
$352$	0.437588	−	6.11828i	0.0233235	−	0.326105i
$353$	−9.73569	+	13.0054i	−0.518179	+	0.692206i	−0.980947	−	0.194273i	$-0.937765\pi$
$353$	−9.73569	+	13.0054i	−0.518179	+	0.692206i	0.462769	+	0.886479i	$0.346856\pi$
$354$	−0.0191888	+	0.0653510i	−0.00101987	+	0.00347337i
$355$	7.16424	+	10.6296i	0.380238	+	0.564161i
$356$	−2.23147	+	3.47223i	−0.118268	+	0.184028i
$357$	−1.27130	+	0.276555i	−0.0672846	+	0.0146369i
$358$	−5.87810	+	0.420410i	−0.310667	+	0.0222194i
$359$	−7.02282	−	2.06209i	−0.370650	−	0.108833i	0.0911021	−	0.995842i	$-0.470961\pi$
$359$	−7.02282	−	2.06209i	−0.370650	−	0.108833i	−0.461753	+	0.887009i	$0.652779\pi$
$360$	4.82120	−	3.77629i	0.254100	−	0.199028i
$361$	5.93918	+	6.85418i	0.312588	+	0.360746i
$362$	5.58177	−	14.9653i	0.293371	−	0.786559i
$363$	11.9435	+	6.52163i	0.626870	+	0.342297i
$364$	10.6451	−	23.3094i	0.557953	−	1.22175i
$365$	0.0269430	+	0.0676814i	0.00141026	+	0.00354261i
$366$	−2.35055	−	3.65752i	−0.122865	−	0.191182i
$367$	11.8404	+	11.8404i	0.618063	+	0.618063i	0.945034	−	0.326971i	$-0.106028\pi$
$367$	11.8404	+	11.8404i	0.618063	+	0.618063i	−0.326971	+	0.945034i	$0.606028\pi$
$368$	4.18641	−	2.33966i	0.218232	−	0.121963i
$369$			9.07437i			0.472393i
$370$	2.50486	+	7.88871i	0.130221	+	0.410114i
$371$	1.92530	−	13.3907i	0.0999566	−	0.695213i
$372$	−0.856620	−	2.29669i	−0.0444137	−	0.119078i
$373$	7.32581	−	13.4162i	0.379316	−	0.694665i	−0.616370	−	0.787457i	$-0.711397\pi$
$373$	7.32581	−	13.4162i	0.379316	−	0.694665i	0.995686	+	0.0927916i	$0.0295790\pi$
$374$	−3.17885	+	1.45173i	−0.164374	+	0.0750672i
$375$	−3.71683	−	4.34033i	−0.191937	−	0.224134i
$376$	−0.571276	−	3.97331i	−0.0294613	−	0.204908i
$377$	6.04091	−	3.29859i	0.311123	−	0.169886i
$378$	0.934911	+	13.0718i	0.0480866	+	0.672339i
$379$	−24.8776	−	15.9878i	−1.27787	−	0.821240i	−0.287250	−	0.957856i	$-0.592741\pi$
$379$	−24.8776	−	15.9878i	−1.27787	−	0.821240i	−0.990624	+	0.136616i	$0.956377\pi$
$380$	−4.72976	−	5.22327i	−0.242631	−	0.267948i
$381$	2.92588	−	3.37664i	0.149897	−	0.172991i
$382$	3.46542	+	6.34645i	0.177306	+	0.324713i
$383$	3.00745	+	2.25135i	0.153673	+	0.115038i	0.673348	−	0.739326i	$-0.264856\pi$
$383$	3.00745	+	2.25135i	0.153673	+	0.115038i	−0.519674	+	0.854365i	$0.673947\pi$
$384$	−0.386266	+	0.334702i	−0.0197116	+	0.0170802i
$385$	−35.6443	+	49.8501i	−1.81660	+	2.54059i
$386$	4.24314	−	1.24590i	0.215970	−	0.0634146i
$387$	−16.4090	+	6.12026i	−0.834118	+	0.311110i
$388$	−5.86727	−	7.83776i	−0.297866	−	0.397902i
$389$	−19.2939	+	12.3994i	−0.978240	+	0.628676i	−0.928988	−	0.370110i	$-0.879320\pi$
$389$	−19.2939	+	12.3994i	−0.978240	+	0.628676i	−0.0492516	+	0.998786i	$0.515684\pi$
$390$	−5.68280	+	3.26626i	−0.287760	+	0.165393i
$391$	−2.31298	−	1.45454i	−0.116972	−	0.0735592i
$392$	−9.16631	+	9.16631i	−0.462969	+	0.462969i
$393$	6.05505	+	1.31719i	0.305437	+	0.0664437i
$394$	22.0258	+	3.16683i	1.10964	+	0.159542i
$395$	6.69608	+	5.55067i	0.336916	+	0.279285i
$396$	4.73293	+	16.1189i	0.237839	+	0.810004i
$397$	−4.40169	−	1.64175i	−0.220914	−	0.0823968i	0.236570	−	0.971614i	$-0.423977\pi$
$397$	−4.40169	−	1.64175i	−0.220914	−	0.0823968i	−0.457484	+	0.889218i	$0.651249\pi$
$398$	12.1324	+	0.867727i	0.608143	+	0.0434952i
$399$	7.12309	−	1.02415i	0.356600	−	0.0512714i
$400$	−3.43630	−	3.63205i	−0.171815	−	0.181603i
$401$	−7.06627	−	6.12296i	−0.352873	−	0.305766i	0.460328	−	0.887749i	$-0.347732\pi$
$401$	−7.06627	−	6.12296i	−0.352873	−	0.305766i	−0.813201	+	0.581983i	$0.802277\pi$
$402$	−0.366884	−	1.68654i	−0.0182985	−	0.0841170i
$403$	−5.84683	−	26.8775i	−0.291252	−	1.33886i
$404$	4.19597	+	3.63583i	0.208757	+	0.180889i
$405$	−7.84240	+	12.8102i	−0.389692	+	0.636543i
$406$	−5.30746	+	0.763097i	−0.263405	+	0.0378719i
$407$	−22.6469	−	1.61974i	−1.12256	−	0.0802874i
$408$	0.272830	+	0.101760i	0.0135071	+	0.00503788i
$409$	−8.34712	−	28.4277i	−0.412739	−	1.40566i	−0.859560	−	0.511036i	$-0.829262\pi$
$409$	−8.34712	−	28.4277i	−0.412739	−	1.40566i	0.446821	−	0.894623i	$-0.352556\pi$
$410$	7.37657	−	0.689913i	0.364303	−	0.0340724i
$411$	3.81627	+	0.548697i	0.188243	+	0.0270652i
$412$	−0.540618	−	0.117604i	−0.0266343	−	0.00579395i
$413$	0.421018	−	0.421018i	0.0207170	−	0.0207170i
$414$	−8.50342	+	10.0106i	−0.417920	+	0.491994i
$415$	−20.0839	−	34.9430i	−0.985880	−	1.71528i
$416$	−4.82479	+	3.10070i	−0.236555	+	0.152025i
$417$	−2.22360	−	2.97038i	−0.108890	−	0.145460i
$418$	18.1110	−	6.75504i	0.885836	−	0.330400i
$419$	−12.3291	+	3.62016i	−0.602317	+	0.176856i	−0.568654	−	0.822577i	$-0.692536\pi$
$419$	−12.3291	+	3.62016i	−0.602317	+	0.176856i	−0.0336635	+	0.999433i	$0.510717\pi$
$420$	5.03726	−	0.836993i	0.245793	−	0.0408411i
$421$	23.3092	−	20.1975i	1.13602	−	0.984368i	0.136041	−	0.990703i	$-0.456562\pi$
$421$	23.3092	−	20.1975i	1.13602	−	0.984368i	0.999980	+	0.00633557i	$0.00201669\pi$
$422$	−8.62793	−	6.45879i	−0.420001	−	0.314409i
$423$	5.26881	+	9.64911i	0.256178	+	0.469156i
$424$	−1.98282	+	2.28829i	−0.0962941	+	0.111129i
$425$	−0.877911	+	2.70998i	−0.0425849	+	0.131453i
$426$	2.46484	+	1.58406i	0.119422	+	0.0767478i
$427$	2.71140	+	37.9103i	0.131214	+	1.83461i
$428$	−6.27936	+	3.42879i	−0.303525	+	0.165737i
$429$	−2.55887	−	17.7973i	−0.123543	−	0.859262i
$430$	6.22272	+	12.8736i	0.300086	+	0.620821i
$431$	−25.6027	+	11.6923i	−1.23324	+	0.563200i	−0.922021	−	0.387139i	$-0.873463\pi$
$431$	−25.6027	+	11.6923i	−1.23324	+	0.563200i	−0.311215	+	0.950339i	$0.600736\pi$
$432$	1.40569	−	2.57433i	0.0676312	−	0.123857i
$433$	−7.28628	−	19.5353i	−0.350156	−	0.938805i	−0.985964	−	0.166958i	$-0.946606\pi$
$433$	−7.28628	−	19.5353i	−0.350156	−	0.938805i	0.635808	−	0.771847i	$-0.280667\pi$
$434$	−3.04959	+	21.2104i	−0.146385	+	1.01813i
$435$	1.21785	+	0.630845i	0.0583915	+	0.0302467i
$436$		−	17.9475i		−	0.859531i
$437$	12.1871	+	8.93757i	0.582986	+	0.427542i
$438$	0.0117739	+	0.0117739i	0.000562580	+	0.000562580i
$439$	−19.2423	−	29.9417i	−0.918387	−	1.42904i	−0.903232	−	0.429152i	$-0.858812\pi$
$439$	−19.2423	−	29.9417i	−0.918387	−	1.42904i	−0.0151544	−	0.999885i	$-0.504824\pi$
$440$	12.7432	−	5.07290i	0.607509	−	0.241841i
$441$	14.7485	−	32.2947i	0.702310	−	1.53784i
$442$	2.86783	+	1.56596i	0.136409	+	0.0744849i
$443$	0.891949	−	2.39141i	0.0423778	−	0.113619i	−0.914037	−	0.405631i	$-0.867052\pi$
$443$	0.891949	−	2.39141i	0.0423778	−	0.113619i	0.956415	+	0.292012i	$0.0943246\pi$
$444$	1.23890	+	1.42977i	0.0587957	+	0.0678539i
$445$	−9.16185	−	1.11350i	−0.434313	−	0.0527848i
$446$	9.11479	+	2.67634i	0.431598	+	0.126729i
$447$	−9.61342	+	0.687566i	−0.454699	+	0.0325207i
$448$	4.36590	−	0.949744i	0.206270	−	0.0448712i
$449$	11.3354	−	17.6382i	0.534951	−	0.832400i	−0.463609	−	0.886040i	$-0.653446\pi$
$449$	11.3354	−	17.6382i	0.534951	−	0.832400i	0.998560	+	0.0536395i	$0.0170822\pi$
$450$	12.2941	+	6.03129i	0.579551	+	0.284318i
$451$	−5.72578	+	19.5002i	−0.269616	+	0.918229i
$452$	−0.314977	+	0.420759i	−0.0148152	+	0.0197909i
$453$	−0.507306	+	7.09307i	−0.0238353	+	0.333261i
$454$	−9.25211	−	20.2593i	−0.434223	−	0.950816i
$455$	57.2858	−	1.25227i	2.68560	−	0.0587071i
$456$	−1.46508	−	0.669082i	−0.0686089	−	0.0313326i
$457$	28.8674	−	21.6099i	1.35036	−	1.01087i	0.353202	−	0.935547i	$-0.385093\pi$
$457$	28.8674	−	21.6099i	1.35036	−	1.01087i	0.997159	−	0.0753205i	$-0.0239980\pi$
$458$	2.78746	−	12.8138i	0.130250	−	0.598747i
$459$	−1.67107			−0.0779989
$460$	8.78413	+	6.15135i	0.409562	+	0.286808i
$461$	23.7689			1.10703			0.553513	−	0.832841i	$-0.313287\pi$
$461$	23.7689			1.10703			0.553513	+	0.832841i	$0.313287\pi$
$462$	−2.97750	+	13.6874i	−0.138526	+	0.636794i
$463$	−6.24391	+	4.67413i	−0.290179	+	0.217225i	−0.734443	−	0.678671i	$-0.762556\pi$
$463$	−6.24391	+	4.67413i	−0.290179	+	0.217225i	0.444264	+	0.895896i	$0.353465\pi$
$464$	1.09164	+	0.498537i	0.0506783	+	0.0231440i
$465$	3.79012	−	3.95953i	0.175763	−	0.183619i
$466$	−1.55109	−	3.39642i	−0.0718530	−	0.157336i
$467$	0.960504	−	13.4296i	0.0444468	−	0.621448i	−0.925596	−	0.378513i	$-0.876435\pi$
$467$	0.960504	−	13.4296i	0.0444468	−	0.621448i	0.970043	−	0.242934i	$-0.0781100\pi$
$468$	9.41317	−	12.5745i	0.435124	−	0.581257i
$469$	−4.25089	+	14.4772i	−0.196288	+	0.668494i
$470$	7.44319	−	5.01663i	0.343329	−	0.231400i
$471$	−2.48887	+	3.87276i	−0.114681	+	0.178447i
$472$	−0.130215	+	0.0283266i	−0.00599364	+	0.00130384i
$473$	−39.1237	+	2.79818i	−1.79891	+	0.128661i
$474$	1.90749	+	0.560090i	0.0876140	+	0.0257258i
$475$	5.91289	−	14.6049i	0.271302	−	0.670119i
$476$	−1.66698	−	1.92380i	−0.0764058	−	0.0881770i
$477$	2.89796	−	7.76973i	0.132689	−	0.355752i
$478$	16.2335	+	8.86418i	0.742505	+	0.405438i
$479$	−12.9734	+	28.4079i	−0.592771	+	1.29799i	0.340981	+	0.940070i	$0.389241\pi$
$479$	−12.9734	+	28.4079i	−0.592771	+	1.29799i	−0.933753	+	0.357918i	$0.883487\pi$
$480$	−1.04971	−	0.451929i	−0.0479125	−	0.0206276i
$481$	11.4773	+	17.8590i	0.523320	+	0.814302i
$482$	−4.21945	−	4.21945i	−0.192191	−	0.192191i
$483$	−10.2232	+	3.92794i	−0.465172	+	0.178728i
$484$			26.6248i			1.21022i
$485$	10.0695	−	19.4392i	0.457231	−	0.882688i
$486$	−1.74087	+	12.1080i	−0.0789673	+	0.549230i
$487$	−9.92239	−	26.6029i	−0.449626	−	1.20549i	−0.942149	−	0.335195i	$-0.891198\pi$
$487$	−9.92239	−	26.6029i	−0.449626	−	1.20549i	0.492523	−	0.870300i	$-0.336075\pi$
$488$	4.07674	−	7.46599i	0.184545	−	0.337969i
$489$	−3.84855	+	1.75757i	−0.174038	+	0.0794803i
$490$	−27.3737	−	9.53375i	−1.23662	−	0.430691i
$491$	−1.50194	−	10.4462i	−0.0677815	−	0.471431i	−0.995236	−	0.0974948i	$-0.968917\pi$
$491$	−1.50194	−	10.4462i	−0.0677815	−	0.471431i	0.927455	−	0.373936i	$-0.121992\pi$
$492$	1.48629	−	0.811578i	0.0670073	−	0.0365888i
$493$	−0.0487765	−	0.681984i	−0.00219678	−	0.0307150i
$494$	−15.2043	−	9.77122i	−0.684074	−	0.439628i
$495$	−27.8450	+	25.2141i	−1.25154	+	1.13329i
$496$	3.14070	−	3.62456i	0.141021	−	0.162747i
$497$	−12.2752	−	22.4804i	−0.550618	−	1.00838i
$498$	−7.37481	−	5.52072i	−0.330473	−	0.247389i
$499$	16.8076	−	14.5639i	0.752411	−	0.651968i	−0.191753	−	0.981443i	$-0.561417\pi$
$499$	16.8076	−	14.5639i	0.752411	−	0.651968i	0.944164	+	0.329475i	$0.106872\pi$
$500$	3.96814	−	10.4525i	0.177460	−	0.467448i
$501$	−8.28413	+	2.43244i	−0.370108	+	0.108673i
$502$	12.1469	−	4.53054i	0.542141	−	0.202208i
$503$	−12.1327	−	16.2074i	−0.540969	−	0.722650i	0.443876	−	0.896088i	$-0.353603\pi$
$503$	−12.1327	−	16.2074i	−0.540969	−	0.722650i	−0.984845	+	0.173438i	$0.944512\pi$
$504$	−10.2943	+	6.61575i	−0.458545	+	0.294689i
$505$	−3.23648	+	11.9855i	−0.144022	+	0.533347i
$506$	−24.5898	+	16.1466i	−1.09315	+	0.717803i
$507$	−7.18942	+	7.18942i	−0.319293	+	0.319293i
$508$	8.54197	+	1.85819i	0.378989	+	0.0824439i
$509$	0.499367	+	0.0717981i	0.0221340	+	0.00318240i	0.153373	−	0.988168i	$-0.450986\pi$
$509$	0.499367	+	0.0717981i	0.0221340	+	0.00318240i	−0.131239	+	0.991351i	$0.541896\pi$
$510$	0.0606330	+	0.648290i	0.00268488	+	0.0287068i
$511$	−0.0410089	−	0.139664i	−0.00181413	−	0.00617836i
$512$	−0.936950	−	0.349464i	−0.0414077	−	0.0154443i
$513$	9.21952	+	0.659393i	0.407052	+	0.0291129i
$514$	−2.26035	+	0.324990i	−0.0996998	+	0.0143347i
$515$	−0.289328	−	1.20282i	−0.0127493	−	0.0530027i
$516$	2.47000	+	2.14027i	0.108736	+	0.0942201i
$517$	5.23389	+	24.0598i	0.230186	+	1.05815i
$518$	−3.51549	−	16.1605i	−0.154462	−	0.710050i
$519$	−8.20212	−	7.10718i	−0.360033	−	0.311971i
$520$	−10.9375	−	6.69595i	−0.479642	−	0.293637i
$521$	4.98844	−	0.717230i	0.218548	−	0.0314224i	−0.0321711	−	0.999482i	$-0.510242\pi$
$521$	4.98844	−	0.717230i	0.218548	−	0.0314224i	0.250719	+	0.968060i	$0.419333\pi$
$522$	−3.27841	−	0.234477i	−0.143492	−	0.0102628i
$523$	0.138286	+	0.0515781i	0.00604683	+	0.00225535i	0.352486	−	0.935817i	$-0.385336\pi$
$523$	0.138286	+	0.0515781i	0.00604683	+	0.00225535i	−0.346439	+	0.938073i	$0.612609\pi$
$524$	3.41575	+	11.6330i	0.149218	+	0.508189i
$525$	6.58693	+	9.32657i	0.287477	+	0.407045i
$526$	−6.69242	−	0.962224i	−0.291803	−	0.0419550i
$527$	−2.66995	−	0.580813i	−0.116305	−	0.0253006i
$528$	2.21682	−	2.21682i	0.0964748	−	0.0964748i
$529$	−21.1053	−	9.14147i	−0.917622	−	0.397455i
$530$	−6.53635	−	1.76503i	−0.283921	−	0.0766681i
$531$	0.307033	−	0.197318i	0.0133241	−	0.00856287i
$532$	8.43783	+	11.2716i	0.365826	+	0.488687i
$533$	17.8044	−	6.64071i	0.771196	−	0.287641i
$534$	−2.02410	+	0.594330i	−0.0875915	+	0.0257192i
$535$	−13.0135	−	9.30504i	−0.562623	−	0.402292i
$536$	2.55215	−	2.21145i	0.110236	−	0.0955201i
$537$	−2.41123	−	1.80502i	−0.104052	−	0.0778924i
$538$	−4.11167	−	7.52997i	−0.177267	−	0.324640i
$539$	52.0710	−	60.0931i	2.24286	−	2.58839i
$540$	6.55058	+	0.324803i	0.281892	+	0.0139773i
$541$	15.4943	+	9.95756i	0.666151	+	0.428109i	0.829536	−	0.558453i	$-0.188605\pi$
$541$	15.4943	+	9.95756i	0.666151	+	0.428109i	−0.163385	+	0.986562i	$0.552241\pi$
$542$	−1.04340	−	14.5887i	−0.0448179	−	0.626637i
$543$	7.16496	−	3.91237i	0.307478	−	0.167896i
$544$	0.0810806	+	0.563928i	0.00347630	+	0.0241782i
$545$	36.1322	−	17.4652i	1.54773	−	0.748128i
$546$	11.9135	−	5.44073i	0.509852	−	0.232842i
$547$	8.81319	−	16.1401i	0.376825	−	0.690103i	−0.618594	−	0.785710i	$-0.712298\pi$
$547$	8.81319	−	16.1401i	0.376825	−	0.690103i	0.995419	+	0.0956076i	$0.0304794\pi$
$548$	2.63619	+	7.06789i	0.112612	+	0.301925i
$549$	−3.31557	+	23.0603i	−0.141505	+	0.984188i
$550$	22.6136	+	20.7182i	0.964247	+	0.883428i
$551$			3.78184i			0.161112i
$552$	2.40015	+	0.497467i	0.102157	+	0.0211736i
$553$	−12.2889	−	12.2889i	−0.522575	−	0.522575i
$554$	9.17071	+	14.2699i	0.389626	+	0.606270i
$555$	−1.67282	+	3.88552i	−0.0710073	+	0.164931i
$556$	3.01580	−	6.60367i	0.127898	−	0.280058i
$557$	−23.6489	−	12.9133i	−1.00204	−	0.547153i	−0.107527	−	0.994202i	$-0.534293\pi$
$557$	−23.6489	−	12.9133i	−1.00204	−	0.547153i	−0.894510	+	0.447049i	$0.852475\pi$
$558$	−4.59024	+	12.3069i	−0.194320	+	0.520993i
$559$	24.0166	+	27.7166i	1.01579	+	1.17229i
$560$	6.16061	+	7.86527i	0.260333	+	0.332368i
$561$	−1.71378	−	0.503211i	−0.0723557	−	0.0212456i
$562$	−2.56426	+	0.183400i	−0.108167	+	0.00773626i
$563$	31.6719	−	6.88979i	1.33481	−	0.290370i	0.512146	−	0.858898i	$-0.328851\pi$
$563$	31.6719	−	6.88979i	1.33481	−	0.290370i	0.822664	+	0.568528i	$0.192487\pi$
$564$	1.10921	−	1.72596i	0.0467061	−	0.0726761i
$565$	−1.15359	−	0.224662i	−0.0485319	−	0.00945162i
$566$	−0.0536533	+	0.182726i	−0.00225521	+	0.00768056i
$567$	17.9858	−	24.0263i	0.755334	−	1.00901i
$568$	−0.408961	+	5.71802i	−0.0171596	+	0.239923i
$569$	13.2561	+	29.0268i	0.555724	+	1.21687i	0.954057	+	0.299625i	$0.0968617\pi$
$569$	13.2561	+	29.0268i	0.555724	+	1.21687i	−0.398333	+	0.917241i	$0.630411\pi$
$570$	−0.0787096	−	3.60063i	−0.00329678	−	0.150814i
$571$	−19.0532	−	8.70130i	−0.797351	−	0.364138i	−0.0252848	−	0.999680i	$-0.508049\pi$
$571$	−19.0532	−	8.70130i	−0.797351	−	0.364138i	−0.772066	+	0.635542i	$0.780777\pi$
$572$	28.1626	−	21.0822i	1.17754	−	0.881493i
$573$	−0.785590	+	3.61130i	−0.0328185	+	0.150864i
$574$	−14.8039			−0.617901
$575$	−3.83589	+	23.6704i	−0.159968	+	0.987122i
$576$	2.73877			0.114116
$577$	−1.15438	+	5.30658i	−0.0480573	+	0.220916i	−0.994912	−	0.100745i	$-0.967877\pi$
$577$	−1.15438	+	5.30658i	−0.0480573	+	0.220916i	0.946855	+	0.321661i	$0.104241\pi$
$578$	−13.3494	+	9.99320i	−0.555260	+	0.415662i
$579$	2.05599	+	0.938937i	0.0854439	+	0.0390209i
$580$	0.0586470	+	2.68285i	0.00243519	+	0.111399i
$581$	33.4545	+	73.2552i	1.38793	+	3.03914i
$582$	0.356981	−	4.99124i	0.0147973	−	0.206894i
$583$	11.1301	−	14.8681i	0.460962	−	0.615772i
$584$	−0.00917834	+	0.0312586i	−0.000379803	+	0.00129349i
$585$	34.4754	+	6.71410i	1.42538	+	0.277594i
$586$	9.94090	−	15.4683i	0.410655	−	0.638992i
$587$	17.2149	−	3.74487i	0.710535	−	0.154567i	0.157249	−	0.987559i	$-0.449737\pi$
$587$	17.2149	−	3.74487i	0.710535	−	0.154567i	0.553286	+	0.832992i	$0.313374\pi$
$588$	−6.60862	+	0.472658i	−0.272535	+	0.0194921i
$589$	14.5013	+	4.25797i	0.597516	+	0.175446i
$590$	−0.183743	−	0.234585i	−0.00756459	−	0.00965773i
$591$	7.44786	+	8.59529i	0.306364	+	0.353563i
$592$	−1.29355	+	3.46813i	−0.0531644	+	0.142539i
$593$	−10.2303	−	5.58618i	−0.420109	−	0.229397i	0.255267	−	0.966871i	$-0.417837\pi$
$593$	−10.2303	−	5.58618i	−0.420109	−	0.229397i	−0.675376	+	0.737474i	$0.736019\pi$
$594$	−7.47390	+	16.3656i	−0.306658	+	0.671487i
$595$	2.25083	−	5.22808i	0.0922750	−	0.214330i
$596$	−10.1950	−	15.8637i	−0.417602	−	0.649802i
$597$	4.39591	+	4.39591i	0.179913	+	0.179913i
$598$	25.8643	+	9.35835i	1.05767	+	0.382691i
$599$		−	5.17327i		−	0.211374i	−0.994399	−	0.105687i	$-0.966296\pi$
$599$		−	5.17327i		−	0.211374i	0.994399	−	0.105687i	$-0.0337042\pi$
$600$	−0.111674	−	2.55308i	−0.00455906	−	0.104229i
$601$	2.47490	−	17.2133i	0.100953	−	0.702147i	−0.874993	−	0.484136i	$-0.839134\pi$
$601$	2.47490	−	17.2133i	0.100953	−	0.702147i	0.975946	−	0.218011i	$-0.0699569\pi$
$602$	−9.98453	−	26.7696i	−0.406939	−	1.09105i
$603$	−4.43247	+	8.11745i	−0.180504	+	0.330568i
$604$	−12.6561	+	5.77983i	−0.514968	+	0.235178i
$605$	−53.6014	+	25.9093i	−2.17921	+	1.05336i
$606$	0.403844	+	2.80879i	0.0164050	+	0.114099i
$607$	−39.8916	+	21.7825i	−1.61915	+	0.884123i	−0.624477	+	0.781043i	$0.714688\pi$
$607$	−39.8916	+	21.7825i	−1.61915	+	0.884123i	−0.994673	+	0.103080i	$0.967130\pi$
$608$	−0.224810	−	3.14326i	−0.00911727	−	0.127476i
$609$	−2.30550	−	1.48166i	−0.0934236	−	0.0600397i
$610$	18.9978	+	0.941985i	0.769198	+	0.0381399i
$611$	15.0763	−	17.3990i	0.609924	−	0.703889i
$612$	−0.747798	−	1.36949i	−0.0302279	−	0.0553583i
$613$	4.56193	+	3.41502i	0.184255	+	0.137931i	0.687423	−	0.726257i	$-0.258742\pi$
$613$	4.56193	+	3.41502i	0.184255	+	0.137931i	−0.503169	+	0.864188i	$0.667833\pi$
$614$	22.4462	−	19.4497i	0.905854	−	0.784927i
$615$	3.08023	+	2.20246i	0.124207	+	0.0888117i
$616$	−26.2962	+	7.72126i	−1.05950	+	0.311099i
$617$	−37.2549	+	13.8954i	−1.49983	+	0.559407i	−0.959416	−	0.281994i	$-0.909004\pi$
$617$	−37.2549	+	13.8954i	−1.49983	+	0.559407i	−0.540411	+	0.841401i	$0.681731\pi$
$618$	−0.169460	−	0.226372i	−0.00681669	−	0.00910603i
$619$	−11.4717	+	7.37244i	−0.461088	+	0.296324i	−0.750487	−	0.660885i	$-0.770181\pi$
$619$	−11.4717	+	7.37244i	−0.461088	+	0.296324i	0.289399	+	0.957209i	$0.406545\pi$
$620$	10.3533	+	2.79573i	0.415798	+	0.112279i
$621$	−13.9032	+	2.13865i	−0.557915	+	0.0858210i
$622$	−10.9389	+	10.9389i	−0.438609	+	0.438609i
$623$	18.0201	+	3.92002i	0.721958	+	0.157052i
$624$	−2.90146	−	0.417168i	−0.116152	−	0.0167001i
$625$	24.9045	−	2.18287i	0.996181	−	0.0873146i
$626$	−2.72624	−	9.28473i	−0.108963	−	0.371092i
$627$	9.25658	+	3.45252i	0.369672	+	0.137881i
$628$	−8.98414	−	0.642558i	−0.358506	−	0.0256409i
$629$	2.08739	−	0.300121i	0.0832296	−	0.0119666i
$630$	−23.3366	−	14.2867i	−0.929752	−	0.569194i
$631$	−8.75742	−	7.58835i	−0.348627	−	0.302087i	0.462890	−	0.886416i	$-0.346813\pi$
$631$	−8.75742	−	7.58835i	−0.348627	−	0.302087i	−0.811517	+	0.584328i	$0.801358\pi$
$632$	0.826807	+	3.80077i	0.0328886	+	0.151187i
$633$	−1.17091	−	5.38260i	−0.0465396	−	0.213939i
$634$	−17.6647	−	15.3066i	−0.701556	−	0.607902i
$635$	4.57148	+	19.0051i	0.181414	+	0.754192i
$636$	−1.53179	+	0.220238i	−0.0607395	+	0.00873301i
$637$	−74.1572	−	5.30383i	−2.93822	−	0.210145i
$638$	−6.89713	−	2.57250i	−0.273060	−	0.101846i
$639$	−4.42330	−	15.0644i	−0.174983	−	0.595938i
$640$	−0.208225	−	2.22635i	−0.00823083	−	0.0880043i
$641$	−25.5357	−	3.67148i	−1.00860	−	0.145015i	−0.381842	−	0.924228i	$-0.624710\pi$
$641$	−25.5357	−	3.67148i	−1.00860	−	0.145015i	−0.626759	+	0.779213i	$0.715619\pi$
$642$	−3.57313	−	0.777286i	−0.141020	−	0.0306770i
$643$	18.6997	−	18.6997i	0.737443	−	0.737443i	−0.234639	−	0.972082i	$-0.575391\pi$
$643$	18.6997	−	18.6997i	0.737443	−	0.737443i	0.972082	+	0.234639i	$0.0753909\pi$
$644$	−16.3312	−	13.8724i	−0.643540	−	0.546649i
$645$	−1.90519	+	7.05540i	−0.0750168	+	0.277806i
$646$	−1.51037	+	0.970653i	−0.0594245	+	0.0381898i
$647$	−8.95400	−	11.9611i	−0.352018	−	0.470241i	0.589226	−	0.807968i	$-0.299433\pi$
$647$	−8.95400	−	11.9611i	−0.352018	−	0.470241i	−0.941244	+	0.337727i	$0.890342\pi$
$648$	−6.29368	+	2.34742i	−0.247239	+	0.0922154i
$649$	0.784297	−	0.230290i	0.0307864	−	0.00903969i
$650$	2.83678	−	28.5355i	0.111268	−	1.11926i
$651$	−8.27709	+	7.17214i	−0.324405	+	0.281098i
$652$	−6.62684	−	4.96079i	−0.259527	−	0.194280i
$653$	−3.83207	−	7.01792i	−0.149961	−	0.274632i	0.791890	−	0.610663i	$-0.209097\pi$
$653$	−3.83207	−	7.01792i	−0.149961	−	0.274632i	−0.941851	+	0.336031i	$0.890915\pi$
$654$	6.00707	−	6.93252i	0.234895	−	0.271083i
$655$	−20.0957	+	18.1970i	−0.785203	+	0.711015i
$656$	2.78732	+	1.79130i	0.108827	+	0.0699387i
$657$	−0.00636519	−	0.0889970i	−0.000248330	−	0.00347210i
$658$	−15.7415	+	8.59550i	−0.613667	+	0.335087i
$659$	6.28235	+	43.6947i	0.244726	+	1.70211i	0.627790	+	0.778383i	$0.283960\pi$
$659$	6.28235	+	43.6947i	0.244726	+	1.70211i	−0.383064	+	0.923722i	$0.625131\pi$
$660$	6.62018	+	2.30568i	0.257690	+	0.0897487i
$661$	43.5621	−	19.8942i	1.69437	−	0.773793i	0.695921	−	0.718118i	$-0.254996\pi$
$661$	43.5621	−	19.8942i	1.69437	−	0.773793i	0.998449	−	0.0556751i	$-0.0177311\pi$
$662$	−9.67917	+	17.7261i	−0.376192	+	0.688944i
$663$	0.583620	+	1.56474i	0.0226659	+	0.0607697i
$664$	2.56513	−	17.8408i	0.0995462	−	0.692359i
$665$	−14.4811	+	27.9558i	−0.561552	+	1.08408i
$666$		−	10.1376i		−	0.392824i
$667$	−1.27862	−	5.61162i	−0.0495085	−	0.217283i
$668$	−11.9449	−	11.9449i	−0.462161	−	0.462161i
$669$	2.62496	+	4.08452i	0.101487	+	0.157917i
$670$	6.93568	+	2.98600i	0.267949	+	0.115359i
$671$	−21.6756	+	47.4629i	−0.836776	+	1.83228i
$672$	2.00428	+	1.09442i	0.0773168	+	0.0422182i
$673$	−4.65315	+	12.4756i	−0.179366	+	0.480898i	−0.995254	−	0.0973116i	$-0.968976\pi$
$673$	−4.65315	+	12.4756i	−0.179366	+	0.480898i	0.815888	+	0.578210i	$0.196248\pi$
$674$	10.4247	+	12.0308i	0.401545	+	0.463408i
$675$	5.72065	+	13.5038i	0.220188	+	0.519761i
$676$	−19.0872	−	5.60450i	−0.734122	−	0.215558i
$677$	−12.2615	+	0.876958i	−0.471247	+	0.0337042i	−0.304943	−	0.952370i	$-0.598638\pi$
$677$	−12.2615	+	0.876958i	−0.471247	+	0.0337042i	−0.166303	+	0.986075i	$0.553183\pi$
$678$	−0.262494	+	0.0571020i	−0.0100810	+	0.00219299i
$679$	−23.6500	+	36.8001i	−0.907604	+	1.41226i
$680$	−1.05641	+	0.712006i	−0.0405113	+	0.0273042i
$681$	3.20704	−	10.9222i	0.122894	−	0.418539i
$682$	−17.6296	+	23.5504i	−0.675072	+	0.901790i
$683$	1.07557	−	15.0385i	0.0411556	−	0.575431i	−0.934477	−	0.356022i	$-0.884133\pi$
$683$	1.07557	−	15.0385i	0.0411556	−	0.575431i	0.975633	−	0.219408i	$-0.0704127\pi$
$684$	3.58531	+	7.85073i	0.137088	+	0.300180i
$685$	−11.6638	+	12.1852i	−0.445652	+	0.465571i
$686$	24.2356	+	11.0680i	0.925320	+	0.422579i
$687$	5.36549	−	4.01655i	0.204706	−	0.153241i
$688$	−1.35926	+	6.24843i	−0.0518214	+	0.238219i
$689$	−17.3654			−0.661570
$690$	1.33415	+	5.31612i	0.0507901	+	0.202381i
$691$	8.21404			0.312477			0.156238	−	0.987719i	$-0.450063\pi$
$691$	8.21404			0.312477			0.156238	+	0.987719i	$0.450063\pi$
$692$	4.51369	−	20.7491i	0.171585	−	0.788763i
$693$	60.0885	−	44.9817i	2.28257	−	1.70871i
$694$	−0.706537	−	0.322665i	−0.0268198	−	0.0122482i
$695$	16.2293	−	0.354773i	0.615614	−	0.0134573i
$696$	0.254804	+	0.557943i	0.00965832	+	0.0211488i
$697$	0.134665	−	1.88287i	0.00510081	−	0.0713186i
$698$	−21.9745	+	29.3545i	−0.831747	+	1.11108i
$699$	0.537652	−	1.83108i	0.0203359	−	0.0692576i
$700$	−9.83940	+	20.0565i	−0.371894	+	0.758066i
$701$	−17.8187	+	27.7264i	−0.673002	+	1.04721i	0.321940	+	0.946760i	$0.395665\pi$
$701$	−17.8187	+	27.7264i	−0.673002	+	1.04721i	−0.994942	+	0.100451i	$0.967971\pi$
$702$	16.4376	−	3.57579i	0.620399	−	0.134959i
$703$	−11.6348	+	0.832139i	−0.438816	+	0.0313847i
$704$	5.88544	+	1.72812i	0.221816	+	0.0651310i
$705$	4.55413	+	0.553492i	0.171518	+	0.0208457i
$706$	−10.6387	−	12.2777i	−0.400392	−	0.462077i
$707$	8.66904	−	23.2426i	0.326033	−	0.874128i
$708$	−0.0597787	−	0.0326416i	−0.00224662	−	0.00122675i
$709$	−1.15260	+	2.52384i	−0.0432867	+	0.0947848i	−0.930040	−	0.367458i	$-0.880228\pi$
$709$	−1.15260	+	2.52384i	−0.0432867	+	0.0947848i	0.886753	+	0.462243i	$0.152955\pi$
$710$	−11.9096	+	4.74103i	−0.446957	+	0.177928i
$711$	−5.75940	−	8.96179i	−0.215994	−	0.336094i
$712$	−2.91855	−	2.91855i	−0.109377	−	0.109377i
$713$	−22.9571	−	1.41529i	−0.859750	−	0.0530029i
$714$		−	1.30104i		−	0.0486901i
$715$	69.8488	+	36.1816i	2.61220	+	1.35311i
$716$	0.838678	−	5.83314i	0.0313429	−	0.217995i
$717$	3.30361	+	8.85733i	0.123376	+	0.330783i
$718$	3.50777	−	6.42400i	0.130909	−	0.239742i
$719$	9.61586	−	4.39142i	0.358611	−	0.163772i	−0.227959	−	0.973671i	$-0.573205\pi$
$719$	9.61586	−	4.39142i	0.358611	−	0.163772i	0.586570	+	0.809899i	$0.300478\pi$
$720$	2.66517	+	5.51373i	0.0993252	+	0.205485i
$721$	0.351799	+	2.44682i	0.0131017	+	0.0911243i
$722$	−7.96000	+	4.34649i	−0.296241	+	0.161760i
$723$	−0.217574	−	3.04209i	−0.00809167	−	0.113136i
$724$	13.4368	+	8.63532i	0.499375	+	0.320929i
$725$	−5.34408	+	2.72882i	−0.198474	+	0.101346i
$726$	−8.91136	+	10.2843i	−0.330732	+	0.381685i
$727$	5.62997	+	10.3105i	0.208804	+	0.382396i	0.961002	−	0.276541i	$-0.0891882\pi$
$727$	5.62997	+	10.3105i	0.208804	+	0.382396i	−0.752198	+	0.658937i	$0.771006\pi$
$728$	20.5140	+	15.3566i	0.760298	+	0.569152i
$729$	10.5046	−	9.10225i	0.389058	−	0.337120i
$730$	−0.0718618	+	0.0119406i	−0.00265973	+	0.000441941i
$731$	3.49558	−	1.02640i	0.129289	−	0.0379626i
$732$	4.07358	−	1.51937i	0.150564	−	0.0561575i
$733$	−25.7919	−	34.4540i	−0.952646	−	1.27259i	−0.962119	−	0.272631i	$-0.912106\pi$
$733$	−25.7919	−	34.4540i	−0.952646	−	1.27259i	0.00947268	−	0.999955i	$-0.496985\pi$
$734$	−14.0866	+	9.05294i	−0.519947	+	0.334150i
$735$	−7.38258	−	12.8446i	−0.272311	−	0.473780i
$736$	1.39630	+	4.58806i	0.0514684	+	0.169118i
$737$	−14.6470	+	14.6470i	−0.539531	+	0.539531i
$738$	−8.86699	−	1.92890i	−0.326399	−	0.0710037i
$739$	−6.04689	−	0.869412i	−0.222439	−	0.0319818i	0.0301943	−	0.999544i	$-0.490387\pi$
$739$	−6.04689	−	0.869412i	−0.222439	−	0.0319818i	−0.252633	+	0.967562i	$0.581296\pi$
$740$	−8.24087	+	0.770749i	−0.302941	+	0.0283333i
$741$	−2.60247	−	8.86320i	−0.0956041	−	0.325598i
$742$	12.6755	+	4.72771i	0.465331	+	0.173560i
$743$	−13.2628	−	0.948574i	−0.486565	−	0.0347998i	−0.174098	−	0.984728i	$-0.555701\pi$
$743$	−13.2628	−	0.948574i	−0.486565	−	0.0347998i	−0.312467	+	0.949929i	$0.601155\pi$
$744$	2.42629	−	0.348848i	0.0889521	−	0.0127894i
$745$	22.0160	−	35.9620i	0.806603	−	1.31755i
$746$	11.5524	+	10.0102i	0.422963	+	0.366500i
$747$	10.4932	+	48.2363i	0.383925	+	1.76488i
$748$	−0.742842	−	3.41479i	−0.0271610	−	0.124857i
$749$	24.1586	+	20.9336i	0.882737	+	0.764896i
$750$	5.03121	−	2.70929i	0.183714	−	0.0989293i
$751$	−11.4305	+	1.64346i	−0.417106	+	0.0599709i	−0.347673	−	0.937616i	$-0.613028\pi$
$751$	−11.4305	+	1.64346i	−0.417106	+	0.0599709i	−0.0694332	+	0.997587i	$0.522119\pi$
$752$	4.00394	+	0.286367i	0.146009	+	0.0104427i
$753$	6.20830	+	2.31558i	0.226243	+	0.0843843i
$754$	1.93912	+	6.60403i	0.0706185	+	0.240504i
$755$	−23.9520	−	19.8548i	−0.871702	−	0.722592i
$756$	−12.9718	−	1.86506i	−0.471778	−	0.0678315i
$757$	50.6366	+	11.0153i	1.84042	+	0.400358i	0.991709	−	0.128503i	$-0.0410173\pi$
$757$	50.6366	+	11.0153i	1.84042	+	0.400358i	0.848708	+	0.528861i	$0.177381\pi$
$758$	20.9106	−	20.9106i	0.759506	−	0.759506i
$759$	−14.9025	−	1.99336i	−0.540926	−	0.0723545i
$760$	6.10928	−	3.51138i	0.221607	−	0.127371i
$761$	−0.00809119	+	0.00519989i	−0.000293305	+	0.000188496i	−0.540787	−	0.841159i	$-0.681874\pi$
$761$	−0.00809119	+	0.00519989i	−0.000293305	+	0.000188496i	0.540494	+	0.841348i	$0.318237\pi$
$762$	2.67753	+	3.57677i	0.0969968	+	0.129573i
$763$	−75.1338	+	28.0234i	−2.72003	+	1.01452i
$764$	−6.93804	+	2.03719i	−0.251009	+	0.0737030i
$765$	2.02937	−	2.83816i	0.0733720	−	0.102614i
$766$	−2.83918	+	2.46016i	−0.102584	+	0.0888892i
$767$	−0.611839	−	0.458017i	−0.0220922	−	0.0165380i
$768$	−0.244946	−	0.448585i	−0.00883872	−	0.0161869i
$769$	−21.9636	+	25.3473i	−0.792027	+	0.914048i	−0.997916	−	0.0645275i	$-0.979446\pi$
$769$	−21.9636	+	25.3473i	−0.792027	+	0.914048i	0.205889	+	0.978575i	$0.433991\pi$
$770$	−41.1341	−	45.4261i	−1.48237	−	1.63704i
$771$	−0.981872	−	0.631011i	−0.0353613	−	0.0227253i
$772$	0.315481	+	4.41101i	0.0113544	+	0.158756i
$773$	24.3141	−	13.2765i	0.874518	−	0.477523i	0.0217202	−	0.999764i	$-0.493086\pi$
$773$	24.3141	−	13.2765i	0.874518	−	0.477523i	0.852798	+	0.522241i	$0.174904\pi$
$774$	−2.49240	−	17.3350i	−0.0895873	−	0.623094i
$775$	4.44666	+	23.5640i	0.159729	+	0.846443i
$776$	8.90582	−	4.06715i	0.319700	−	0.146002i
$777$	4.05101	−	7.41888i	0.145329	−	0.266151i
$778$	−8.01486	−	21.4887i	−0.287347	−	0.770406i
$779$	−1.48593	+	10.3349i	−0.0532390	+	0.370286i
$780$	−1.98365	−	6.24722i	−0.0710259	−	0.223686i
$781$		−	35.1634i		−	1.25824i
$782$	1.91296	−	1.95093i	0.0684072	−	0.0697653i
$783$	−2.48902	−	2.48902i	−0.0889503	−	0.0889503i
$784$	−7.00839	−	10.9053i	−0.250300	−	0.389474i
$785$	−7.44910	−	18.7123i	−0.265870	−	0.667870i
$786$	−2.57419	+	5.63668i	−0.0918181	+	0.201054i
$787$	10.7893	+	5.89140i	0.384597	+	0.210006i	0.659903	−	0.751351i	$-0.270597\pi$
$787$	10.7893	+	5.89140i	0.384597	+	0.210006i	−0.275306	+	0.961357i	$0.588779\pi$
$788$	−7.77637	+	20.8492i	−0.277022	+	0.742724i
$789$	−2.26300	−	2.61164i	−0.0805648	−	0.0929768i
$790$	−6.84717	+	5.36317i	−0.243611	+	0.190813i
$791$	2.25323	+	0.661609i	0.0801157	+	0.0235241i
$792$	−16.7566	+	1.19845i	−0.595419	+	0.0425852i
$793$	47.6720	−	10.3704i	1.69288	−	0.368264i
$794$	2.53987	−	3.95212i	0.0901367	−	0.140255i
$795$	−1.93401	−	2.86950i	−0.0685924	−	0.101771i
$796$	−3.42683	+	11.6707i	−0.121461	+	0.413657i
$797$	−20.1537	+	26.9221i	−0.713879	+	0.953631i	−0.999990	−	0.00456585i	$-0.998547\pi$
$797$	−20.1537	+	26.9221i	−0.713879	+	0.953631i	0.286111	+	0.958197i	$0.407638\pi$
$798$	−0.513381	+	7.17800i	−0.0181735	+	0.254098i
$799$	−0.950046	−	2.08031i	−0.0336102	−	0.0735961i
$800$	4.27949	−	2.58572i	0.151303	−	0.0914192i
$801$	10.2826	+	4.69592i	0.363319	+	0.165922i
$802$	7.48508	−	5.60326i	0.264307	−	0.197858i
$803$	0.0424773	−	0.195265i	0.00149899	−	0.00689075i
$804$	1.72598			0.0608708
$805$	12.0358	−	46.3778i	0.424205	−	1.63460i
$806$	27.5061			0.968860
$807$	0.932091	−	4.28475i	0.0328112	−	0.150831i
$808$	−4.44465	+	3.32723i	−0.156362	+	0.117051i
$809$	11.6443	+	5.31776i	0.409391	+	0.186962i	0.609456	−	0.792820i	$-0.291388\pi$
$809$	11.6443	+	5.31776i	0.409391	+	0.186962i	−0.200065	+	0.979783i	$0.564115\pi$
$810$	−10.8504	−	10.3862i	−0.381244	−	0.364933i
$811$	19.3589	+	42.3902i	0.679784	+	1.48852i	0.862871	+	0.505424i	$0.168664\pi$
$811$	19.3589	+	42.3902i	0.679784	+	1.48852i	−0.183087	+	0.983097i	$0.558609\pi$
$812$	0.382523	−	5.34837i	0.0134239	−	0.187691i
$813$	4.47982	−	5.98434i	0.157114	−	0.209880i
$814$	6.39666	−	21.7850i	0.224203	−	0.763565i
$815$	3.53837	−	18.1687i	0.123944	−	0.636422i
$816$	−0.157429	+	0.244964i	−0.00551111	+	0.00857546i
$817$	−19.6906	+	4.28343i	−0.688887	+	0.149858i
$818$	29.5523	−	2.11363i	1.03327	−	0.0739012i
$819$	−67.3385	−	19.7724i	−2.35300	−	0.690903i
$820$	−0.893856	+	7.35464i	−0.0312148	+	0.256835i
$821$	−32.2170	−	37.1805i	−1.12438	−	1.29761i	−0.949763	−	0.312971i	$-0.898676\pi$
$821$	−32.2170	−	37.1805i	−1.12438	−	1.29761i	−0.174620	−	0.984636i	$-0.555870\pi$
$822$	−1.34736	+	3.61242i	−0.0469947	+	0.125998i
$823$	39.8992	+	21.7866i	1.39080	+	0.759433i	0.987794	−	0.155766i	$-0.0497846\pi$
$823$	39.8992	+	21.7866i	1.39080	+	0.759433i	0.403003	+	0.915199i	$0.367966\pi$
$824$	0.229833	−	0.503265i	0.00800662	−	0.0175321i
$825$	1.80045	+	15.5716i	0.0626835	+	0.542132i
$826$	0.321903	+	0.500891i	0.0112004	+	0.0174282i
$827$	27.5997	+	27.5997i	0.959735	+	0.959735i	0.999220	−	0.0394850i	$-0.0125717\pi$
$827$	27.5997	+	27.5997i	0.959735	+	0.959735i	−0.0394850	+	0.999220i	$0.512572\pi$
$828$	−7.97429	−	10.4370i	−0.277126	−	0.362711i
$829$		−	37.9421i		−	1.31778i	−0.752238	−	0.658891i	$-0.771026\pi$
$829$		−	37.9421i		−	1.31778i	0.752238	−	0.658891i	$-0.228974\pi$
$830$	38.4136	−	12.1973i	1.33336	−	0.423373i
$831$	−1.23382	+	8.58143i	−0.0428008	+	0.297686i
$832$	−2.00426	−	5.37363i	−0.0694852	−	0.186297i
$833$	−3.53947	+	6.48205i	−0.122635	+	0.224590i
$834$	3.37516	−	1.54138i	0.116872	−	0.0533738i
$835$	12.4237	−	35.6714i	0.429939	−	1.23446i
$836$	2.75090	+	19.1330i	0.0951420	+	0.661727i
$837$	−12.3464	+	6.74165i	−0.426754	+	0.233025i
$838$	−0.916682	−	12.8169i	−0.0316663	−	0.442752i
$839$	1.77235	+	1.13902i	0.0611885	+	0.0393234i	0.570877	−	0.821035i	$-0.306603\pi$
$839$	1.77235	+	1.13902i	0.0611885	+	0.0393234i	−0.509689	+	0.860359i	$0.670240\pi$
$840$	−0.252881	+	5.10005i	−0.00872521	+	0.175969i
$841$	−18.0478	+	20.8283i	−0.622338	+	0.718217i
$842$	14.7812	+	27.0698i	0.509395	+	0.932887i
$843$	−1.05187	−	0.787422i	−0.0362284	−	0.0271203i
$844$	8.14519	−	7.05784i	0.280369	−	0.242941i
$845$	−7.29119	−	43.8804i	−0.250825	−	1.50953i
$846$	−10.5486	+	3.09734i	−0.362667	+	0.106489i
$847$	111.459	−	41.5722i	3.82979	−	1.42844i
$848$	−1.81452	−	2.42392i	−0.0623109	−	0.0832376i
$849$	−0.0818832	+	0.0526231i	−0.00281022	+	0.00180602i
$850$	−2.46144	−	1.43390i	−0.0844265	−	0.0491822i
$851$	16.9828	−	5.16844i	0.582163	−	0.177172i
$852$	−2.07180	+	2.07180i	−0.0709786	+	0.0709786i
$853$	10.3795	+	2.25793i	0.355389	+	0.0773101i	0.386715	−	0.922199i	$-0.373610\pi$
$853$	10.3795	+	2.25793i	0.355389	+	0.0773101i	−0.0313266	+	0.999509i	$0.509973\pi$
$854$	−37.6203	−	5.40899i	−1.28734	−	0.185092i
$855$	−12.3162	+	14.8577i	−0.421206	+	0.508124i
$856$	−2.01566	−	6.86470i	−0.0688938	−	0.234631i
$857$	−27.2177	−	10.1517i	−0.929738	−	0.346775i	−0.161452	−	0.986881i	$-0.551618\pi$
$857$	−27.2177	−	10.1517i	−0.929738	−	0.346775i	−0.768287	+	0.640106i	$0.778890\pi$
$858$	17.9345	+	1.28270i	0.612274	+	0.0437907i
$859$	−26.9309	+	3.87208i	−0.918870	+	0.132114i	−0.585491	−	0.810679i	$-0.699098\pi$
$859$	−26.9309	+	3.87208i	−0.918870	+	0.132114i	−0.333379	+	0.942793i	$0.608189\pi$
$860$	−13.9021	+	3.34403i	−0.474059	+	0.114030i
$861$	−5.71823	−	4.95487i	−0.194877	−	0.168862i
$862$	−5.98290	−	27.5029i	−0.203778	−	0.936754i
$863$	2.95056	+	13.5635i	0.100438	+	0.461707i	0.999705	+	0.0243057i	$0.00773750\pi$
$863$	2.95056	+	13.5635i	0.100438	+	0.461707i	−0.899266	+	0.437402i	$0.855899\pi$
$864$	2.21669	+	1.92078i	0.0754135	+	0.0653461i
$865$	46.1648	−	11.1045i	1.56965	−	0.377564i
$866$	20.6376	−	2.96724i	0.701295	−	0.100831i
$867$	−8.50114	−	0.608014i	−0.288714	−	0.0206492i
$868$	−20.0774	−	7.48848i	−0.681471	−	0.254176i
$869$	−6.72181	−	22.8924i	−0.228022	−	0.776571i
$870$	−0.875301	+	1.05592i	−0.0296755	+	0.0357992i
$871$	19.1706	+	2.75632i	0.649572	+	0.0933944i
$872$	17.5374	+	3.81502i	0.593890	+	0.129193i
$873$	−18.9605	+	18.9605i	−0.641715	+	0.641715i
$874$	−11.3239	+	10.0087i	−0.383035	+	0.338550i
$875$	−49.9530	−	0.291249i	−1.68872	−	0.00984600i
$876$	−0.0140076	+	0.00900212i	−0.000473272	+	0.000304154i
$877$	1.40920	+	1.88247i	0.0475852	+	0.0635664i	0.823703	−	0.567022i	$-0.191905\pi$
$877$	1.40920	+	1.88247i	0.0475852	+	0.0635664i	−0.776117	+	0.630588i	$0.782814\pi$
$878$	33.3476	−	12.4380i	1.12543	−	0.419763i
$879$	9.01712	−	2.64766i	0.304140	−	0.0893035i
$880$	2.24820	+	13.5303i	0.0757870	+	0.456107i
$881$	33.8845	−	29.3611i	1.14160	−	0.989200i	0.141598	−	0.989924i	$-0.454776\pi$
$881$	33.8845	−	29.3611i	1.14160	−	0.989200i	1.00000		0.000724076i	$0.000230480\pi$
$882$	28.4217	+	21.2762i	0.957007	+	0.716407i
$883$	−4.31708	−	7.90614i	−0.145281	−	0.266063i	0.794898	−	0.606743i	$-0.207524\pi$
$883$	−4.31708	−	7.90614i	−0.145281	−	0.266063i	−0.940179	+	0.340680i	$0.889343\pi$
$884$	−2.13977	+	2.46943i	−0.0719683	+	0.0830558i
$885$	0.00754229	−	0.152112i	0.000253531	−	0.00511318i
$886$	2.14716	+	1.37990i	0.0721352	+	0.0463585i
$887$	−0.881969	−	12.3315i	−0.0296136	−	0.414052i	−0.990538	−	0.137240i	$-0.956177\pi$
$887$	−0.881969	−	12.3315i	−0.0296136	−	0.414052i	0.960924	−	0.276812i	$-0.0892779\pi$
$888$	−1.66044	+	0.906671i	−0.0557208	+	0.0304259i
$889$	−5.55856	−	38.6607i	−0.186428	−	1.29664i
$890$	3.03554	−	8.71578i	0.101752	−	0.292154i
$891$	37.4793	−	17.1162i	1.25560	−	0.573414i
$892$	−4.55267	+	8.33759i	−0.152435	+	0.279163i
$893$	4.42065	+	11.8522i	0.147932	+	0.396620i
$894$	1.37163	−	9.53988i	0.0458741	−	0.319061i
$895$	12.5595	−	3.98794i	0.419817	−	0.133302i
$896$			4.46801i			0.149266i
$897$	6.85824	+	12.2716i	0.228990	+	0.409737i
$898$	14.8256	+	14.8256i	0.494738	+	0.494738i
$899$	−3.11172	−	4.84194i	−0.103782	−	0.161488i
$900$	−8.50676	+	10.7311i	−0.283559	+	0.357704i
$901$	−0.716610	+	1.56916i	−0.0238737	+	0.0522762i
$902$	−17.8375	−	9.73999i	−0.593923	−	0.324306i
$903$	5.10313	−	13.6820i	0.169822	−	0.455309i
$904$	−0.344191	−	0.397217i	−0.0114476	−	0.0132112i
$905$	−4.30900	+	35.4544i	−0.143236	+	1.17855i
$906$	−6.82313	−	2.00345i	−0.226683	−	0.0665602i
$907$	−23.0704	+	1.65002i	−0.766038	+	0.0547882i	−0.448889	−	0.893587i	$-0.648180\pi$
$907$	−23.0704	+	1.65002i	−0.766038	+	0.0547882i	−0.317149	+	0.948376i	$0.602726\pi$
$908$	21.7630	−	4.73425i	0.722230	−	0.157112i
$909$	8.22089	−	12.7920i	0.272670	−	0.424283i
$910$	−10.9533	+	56.2428i	−0.363099	+	1.86443i
$911$	−15.7322	+	53.5790i	−0.521232	+	1.77515i	0.103849	+	0.994593i	$0.466884\pi$
$911$	−15.7322	+	53.5790i	−0.521232	+	1.77515i	−0.625081	+	0.780560i	$0.714934\pi$
$912$	0.965217	−	1.28938i	0.0319615	−	0.0426956i
$913$	−7.88721	+	110.278i	−0.261029	+	3.64966i
$914$	14.9798	+	32.8012i	0.495488	+	1.08497i
$915$	7.02292	+	6.72245i	0.232171	+	0.222237i
$916$	11.9284	+	5.44752i	0.394126	+	0.179991i
$917$	43.3657	−	32.4632i	1.43206	−	1.07203i
$918$	0.355212	−	1.63288i	0.0117237	−	0.0538931i
$919$	−26.2863			−0.867107			−0.433553	−	0.901128i	$-0.642740\pi$
$919$	−26.2863			−0.867107			−0.433553	+	0.901128i	$0.642740\pi$
$920$	−7.87797	+	7.27582i	−0.259729	+	0.239877i
$921$	15.1801			0.500200
$922$	−5.05243	+	23.2257i	−0.166393	+	0.764897i
$923$	−26.3202	+	19.7030i	−0.866339	+	0.648533i
$924$	−12.7417	−	5.81892i	−0.419170	−	0.191428i
$925$	−9.57110	−	15.8406i	−0.314696	−	0.520835i
$926$	−3.24007	−	7.09477i	−0.106475	−	0.233149i
$927$	−0.108097	+	1.51140i	−0.00355038	+	0.0496408i
$928$	−0.719190	+	0.960725i	−0.0236086	+	0.0315373i
$929$	6.29175	−	21.4277i	0.206425	−	0.703021i	−0.789574	−	0.613656i	$-0.789698\pi$
$929$	6.29175	−	21.4277i	0.206425	−	0.703021i	0.995999	−	0.0893646i	$-0.0284836\pi$
$930$	3.06339	+	4.54516i	0.100453	+	0.149042i
$931$	22.0855	−	34.3657i	0.723822	−	1.12629i
$932$	3.64851	−	0.793685i	0.119511	−	0.0259980i
$933$	−7.88658	+	0.564059i	−0.258195	+	0.0184665i
$934$	12.9185	+	3.79322i	0.422707	+	0.124118i
$935$	6.15181	−	4.81852i	0.201186	−	0.157582i
$936$	10.2862	+	11.8710i	0.336216	+	0.388014i
$937$	12.2403	−	32.8175i	0.399873	−	1.07210i	−0.568519	−	0.822670i	$-0.692483\pi$
$937$	12.2403	−	32.8175i	0.399873	−	1.07210i	0.968392	−	0.249432i	$-0.0802438\pi$
$938$	−13.2427	−	7.23109i	−0.432391	−	0.236103i
$939$	2.05456	−	4.49885i	0.0670480	−	0.146815i
$940$	3.31982	+	8.33945i	0.108281	+	0.272003i
$941$	13.5260	+	21.0469i	0.440935	+	0.686108i	0.988596	−	0.150592i	$-0.0481181\pi$
$941$	13.5260	+	21.0469i	0.440935	+	0.686108i	−0.547661	+	0.836700i	$0.684482\pi$
$942$	−3.25520	−	3.25520i	−0.106060	−	0.106060i
$943$	−1.28930	−	15.8376i	−0.0419854	−	0.515744i
$944$		−	0.133261i		−	0.00433726i
$945$	−8.86841	−	27.9298i	−0.288489	−	0.908558i
$946$	5.58211	−	38.8244i	0.181490	−	1.26229i
$947$	3.68148	+	9.87043i	0.119632	+	0.320746i	0.982939	−	0.183934i	$-0.0588833\pi$
$947$	3.68148	+	9.87043i	0.119632	+	0.320746i	−0.863307	+	0.504680i	$0.831611\pi$
$948$	−0.952757	+	1.74484i	−0.0309441	+	0.0566699i
$949$	−0.169959	+	0.0776178i	−0.00551711	+	0.00251958i
$950$	13.0143	+	8.88226i	0.422238	+	0.288179i
$951$	−1.70015	−	11.8248i	−0.0551313	−	0.383446i
$952$	2.23417	−	1.21995i	0.0724100	−	0.0395388i
$953$	−2.19129	−	30.6382i	−0.0709828	−	0.992469i	−0.900744	−	0.434351i	$-0.856978\pi$
$953$	−2.19129	−	30.6382i	−0.0709828	−	0.992469i	0.829761	−	0.558119i	$-0.188477\pi$
$954$	6.97617	+	4.48331i	0.225862	+	0.145152i
$955$	−10.8529	−	11.9853i	−0.351191	−	0.387835i
$956$	−12.1123	+	13.9783i	−0.391740	+	0.452092i
$957$	−1.80311	−	3.30215i	−0.0582863	−	0.106743i
$958$	−25.0010	−	18.7155i	−0.807744	−	0.604670i
$959$	25.4722	−	22.0718i	0.822539	−	0.712734i
$960$	0.664733	−	0.929658i	0.0214542	−	0.0300046i
$961$	7.67463	−	2.25348i	0.247569	−	0.0726928i
$962$	−19.8906	+	7.41880i	−0.641298	+	0.239192i
$963$	11.7426	+	15.6863i	0.378400	+	0.505483i
$964$	5.01993	−	3.22611i	0.161681	−	0.103906i
$965$	−8.57329	+	4.92760i	−0.275984	+	0.158625i
$966$	−1.66508	−	10.8245i	−0.0535730	−	0.348273i
$967$	3.74754	−	3.74754i	0.120513	−	0.120513i	−0.644278	−	0.764791i	$-0.722842\pi$
$967$	3.74754	−	3.74754i	0.120513	−	0.120513i	0.764791	+	0.644278i	$0.222842\pi$
$968$	−26.0163	−	5.65951i	−0.836197	−	0.181903i
$969$	−0.908282	−	0.130591i	−0.0291782	−	0.00419519i
$970$	16.8545	+	13.9714i	0.541166	+	0.448596i
$971$	−2.89934	−	9.87425i	−0.0930443	−	0.316880i	0.899799	−	0.436305i	$-0.143713\pi$
$971$	−2.89934	−	9.87425i	−0.0930443	−	0.316880i	−0.992843	+	0.119425i	$0.961895\pi$
$972$	−11.4612	−	4.27482i	−0.367619	−	0.137115i
$973$	−32.3539	−	2.31399i	−1.03722	−	0.0741832i
$974$	28.1041	−	4.04077i	0.900515	−	0.129474i
$975$	10.6466	−	10.0728i	0.340965	−	0.322589i
$976$	6.42879	+	5.57058i	0.205781	+	0.178310i
$977$	−10.3440	−	47.5507i	−0.330934	−	1.52128i	−0.778853	−	0.627206i	$-0.784198\pi$
$977$	−10.3440	−	47.5507i	−0.330934	−	1.52128i	0.447919	−	0.894074i	$-0.352165\pi$
$978$	−0.899340	−	4.13420i	−0.0287577	−	0.132197i
$979$	19.1336	+	16.5794i	0.611513	+	0.529879i
$980$	15.1346	−	24.7216i	0.483456	−	0.789703i
$981$	−48.6539	+	6.99537i	−1.55340	+	0.223345i
$982$	10.5267	+	0.752887i	0.335922	+	0.0240256i
$983$	27.1196	+	10.1151i	0.864980	+	0.322621i	0.742497	−	0.669850i	$-0.233641\pi$
$983$	27.1196	+	10.1151i	0.864980	+	0.322621i	0.122483	+	0.992471i	$0.460914\pi$
$984$	0.477097	+	1.62484i	0.0152093	+	0.0517981i
$985$	−49.5413	+	4.63348i	−1.57852	+	0.147635i
$986$	0.676767	+	0.0973044i	0.0215526	+	0.00309880i
$987$	−8.95733	−	1.94855i	−0.285115	−	0.0620229i
$988$	12.7798	−	12.7798i	0.406580	−	0.406580i
$989$	27.7693	−	13.0132i	0.883014	−	0.413795i
$990$	−18.7190	−	32.5683i	−0.594929	−	1.03509i
$991$	−17.1429	+	11.0171i	−0.544562	+	0.349968i	−0.783821	−	0.620987i	$-0.786732\pi$
$991$	−17.1429	+	11.0171i	−0.544562	+	0.349968i	0.239259	+	0.970956i	$0.423095\pi$
$992$	2.87412	+	3.83937i	0.0912534	+	0.121900i
$993$	−9.67168	+	3.60735i	−0.306922	+	0.114476i
$994$	24.5759	−	7.21613i	0.779500	−	0.228882i
$995$	−26.8303	+	4.45814i	−0.850579	+	0.141333i
$996$	6.96218	−	6.03276i	0.220605	−	0.191155i
$997$	−1.00840	−	0.754880i	−0.0319364	−	0.0239073i	0.583190	−	0.812336i	$-0.301804\pi$
$997$	−1.00840	−	0.754880i	−0.0319364	−	0.0239073i	−0.615127	+	0.788428i	$0.710895\pi$
$998$	10.6583	+	19.5193i	0.337383	+	0.617871i
$999$	7.10978	−	8.20513i	0.224944	−	0.259599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.103.2	yes	240
5.2	odd	4	inner	230.2.l.a.57.5	✓	240
23.21	odd	22	inner	230.2.l.a.113.5	yes	240
115.67	even	44	inner	230.2.l.a.67.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.5	✓	240	5.2	odd	4	inner
230.2.l.a.67.2	yes	240	115.67	even	44	inner
230.2.l.a.103.2	yes	240	1.1	even	1	trivial
230.2.l.a.113.5	yes	240	23.21	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.212565 + 0.977147i) q^{2} +(-0.409159 + 0.306293i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.0488687 - 2.23553i) q^{5} +(-0.212320 - 0.464916i) q^{6} +(-0.318744 + 4.45663i) q^{7} +(0.599278 - 0.800541i) q^{8} +(-0.771602 + 2.62783i) q^{9} +O(q^{10})\)	\(q+(-0.212565 + 0.977147i) q^{2} +(-0.409159 + 0.306293i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.0488687 - 2.23553i) q^{5} +(-0.212320 - 0.464916i) q^{6} +(-0.318744 + 4.45663i) q^{7} +(0.599278 - 0.800541i) q^{8} +(-0.771602 + 2.62783i) q^{9} +(2.19483 + 0.427445i) q^{10} +(-3.31624 + 5.16017i) q^{11} +(0.499423 - 0.108643i) q^{12} +(5.72063 - 0.409147i) q^{13} +(-4.28703 - 1.25878i) q^{14} +(0.704723 + 0.899722i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.199099 - 0.533806i) q^{17} +(-2.40376 - 1.31255i) q^{18} +(-1.30909 + 2.86651i) q^{19} +(-0.884222 + 2.05381i) q^{20} +(-1.23462 - 1.92110i) q^{21} +(-4.33733 - 4.33733i) q^{22} +(0.973320 - 4.69602i) q^{23} +0.511103i q^{24} +(-4.99522 + 0.218495i) q^{25} +(-0.816210 + 5.67686i) q^{26} +(-1.02502 - 2.74817i) q^{27} +(2.14129 - 3.92148i) q^{28} +(1.09164 - 0.498537i) q^{29} +(-1.02896 + 0.497368i) q^{30} +(-0.682538 - 4.74716i) q^{31} +(-0.877679 + 0.479249i) q^{32} +(-0.223653 - 3.12707i) q^{33} +(0.479285 + 0.308018i) q^{34} +(9.97852 + 0.494774i) q^{35} +(1.79352 - 2.06983i) q^{36} +(1.77395 + 3.24874i) q^{37} +(-2.52274 - 1.88850i) q^{38} +(-2.21533 + 1.91959i) q^{39} +(-1.81892 - 1.30058i) q^{40} +(3.17909 - 0.933464i) q^{41} +(2.13963 - 0.798042i) q^{42} +(3.83212 + 5.11911i) q^{43} +(5.16017 - 3.31624i) q^{44} +(5.91232 + 1.59652i) q^{45} +(4.38181 + 1.94929i) q^{46} +(2.83845 - 2.83845i) q^{47} +(-0.499423 - 0.108643i) q^{48} +(-12.8312 - 1.84484i) q^{49} +(0.848309 - 4.92751i) q^{50} +(0.0820375 + 0.279394i) q^{51} +(-5.37363 - 2.00426i) q^{52} +(-3.02013 - 0.216004i) q^{53} +(2.90325 - 0.417425i) q^{54} +(11.6978 + 7.16140i) q^{55} +(3.37670 + 2.92593i) q^{56} +(-0.342365 - 1.57383i) q^{57} +(0.255098 + 1.17267i) q^{58} +(-0.100712 - 0.0872672i) q^{59} +(-0.267281 - 1.11117i) q^{60} +(8.41993 - 1.21060i) q^{61} +(4.78375 + 0.342141i) q^{62} +(-11.4653 - 4.27635i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(-1.19422 - 12.7687i) q^{65} +(3.10315 + 0.446166i) q^{66} +(3.29980 + 0.717828i) q^{67} +(-0.402858 + 0.402858i) q^{68} +(1.04012 + 2.21954i) q^{69} +(-2.60455 + 9.64531i) q^{70} +(-4.82259 + 3.09929i) q^{71} +(1.64129 + 2.19250i) q^{72} +(-0.0305242 + 0.0113849i) q^{73} +(-3.55158 + 1.04284i) q^{74} +(1.97692 - 1.61940i) q^{75} +(2.38159 - 2.06366i) q^{76} +(-21.9399 - 16.4240i) q^{77} +(-1.40482 - 2.57274i) q^{78} +(-2.54719 + 2.93961i) q^{79} +(1.65750 - 1.50090i) q^{80} +(-5.65087 - 3.63159i) q^{81} +(0.236368 + 3.30486i) q^{82} +(15.8196 - 8.63813i) q^{83} +(0.324992 + 2.26037i) q^{84} +(-1.20307 - 0.419007i) q^{85} +(-5.81670 + 2.65640i) q^{86} +(-0.293958 + 0.538344i) q^{87} +(2.14358 + 5.74716i) q^{88} +(0.587398 - 4.08544i) q^{89} +(-2.81679 + 5.43784i) q^{90} +25.6251i q^{91} +(-2.83616 + 3.86732i) q^{92} +(1.73329 + 1.73329i) q^{93} +(2.17022 + 3.37693i) q^{94} +(6.47216 + 2.78644i) q^{95} +(0.212320 - 0.464916i) q^{96} +(8.59298 + 4.69212i) q^{97} +(4.53015 - 12.1458i) q^{98} +(-11.0013 - 12.6961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 240 * q - 8 * q^3 - 8 * q^6	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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