LMFDB - Embedded newform 261.2.x.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	261.2
Dual form			261.2.x.a.131.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20822 - 0.891704i) q^{2} +(0.979461 - 1.42852i) q^{3} +(0.0751402 + 0.243598i) q^{4} +(1.10182 - 2.80739i) q^{5} +(-2.45721 + 0.852566i) q^{6} +(-2.93685 - 0.905898i) q^{7} +(-0.865489 + 2.47342i) q^{8} +(-1.08131 - 2.79835i) q^{9} +O(q^{10})$	\(q+(-1.20822 - 0.891704i) q^{2} +(0.979461 - 1.42852i) q^{3} +(0.0751402 + 0.243598i) q^{4} +(1.10182 - 2.80739i) q^{5} +(-2.45721 + 0.852566i) q^{6} +(-2.93685 - 0.905898i) q^{7} +(-0.865489 + 2.47342i) q^{8} +(-1.08131 - 2.79835i) q^{9} +(-3.83459 + 2.40943i) q^{10} +(4.55594 + 0.862031i) q^{11} +(0.421581 + 0.131256i) q^{12} +(-3.23076 + 0.242112i) q^{13} +(2.74056 + 3.71332i) q^{14} +(-2.93121 - 4.32369i) q^{15} +(3.67252 - 2.50388i) q^{16} +(4.04625 + 4.04625i) q^{17} +(-1.18884 + 4.34522i) q^{18} +(1.37325 + 2.18552i) q^{19} +(0.766666 + 0.0574536i) q^{20} +(-4.17062 + 3.30804i) q^{21} +(-4.73589 - 5.10408i) q^{22} +(0.655426 - 4.34847i) q^{23} +(2.68561 + 3.65899i) q^{24} +(-3.00216 - 2.78559i) q^{25} +(4.11935 + 2.58836i) q^{26} +(-5.05659 - 1.19621i) q^{27} -0.783481i q^{28} +(-4.79072 - 2.45948i) q^{29} +(-0.313922 + 7.83772i) q^{30} +(-0.550880 - 1.26263i) q^{31} +(-1.43263 - 0.0536052i) q^{32} +(5.69380 - 5.66391i) q^{33} +(-1.28069 - 8.49680i) q^{34} +(-5.77908 + 7.24674i) q^{35} +(0.600424 - 0.473674i) q^{36} +(-4.46183 - 1.56126i) q^{37} +(0.289650 - 3.86512i) q^{38} +(-2.81854 + 4.85233i) q^{39} +(5.99025 + 5.15502i) q^{40} +(2.14080 + 0.573625i) q^{41} +(7.98881 - 0.277871i) q^{42} +(3.68514 + 1.60781i) q^{43} +(0.132345 + 1.17459i) q^{44} +(-9.04746 - 0.0476154i) q^{45} +(-4.66944 + 4.66944i) q^{46} +(0.940252 - 4.96935i) q^{47} +(0.0202584 - 7.69870i) q^{48} +(2.02077 + 1.37774i) q^{49} +(1.14333 + 6.04263i) q^{50} +(9.74326 - 1.81698i) q^{51} +(-0.301738 - 0.768816i) q^{52} +(-1.42370 + 1.13536i) q^{53} +(5.04279 + 5.95426i) q^{54} +(7.43988 - 11.8405i) q^{55} +(4.78248 - 6.48003i) q^{56} +(4.46710 + 0.178919i) q^{57} +(3.59510 + 7.24349i) q^{58} +(11.0545 - 6.38235i) q^{59} +(0.832993 - 1.03892i) q^{60} +(8.21787 - 4.34327i) q^{61} +(-0.460311 + 2.01675i) q^{62} +(0.640627 + 9.19790i) q^{63} +(-5.26714 - 4.20040i) q^{64} +(-2.88001 + 9.33676i) q^{65} +(-11.9299 + 1.76605i) q^{66} +(-2.51549 + 3.68954i) q^{67} +(-0.681623 + 1.28969i) q^{68} +(-5.56989 - 5.19544i) q^{69} +(13.4443 - 3.60240i) q^{70} +(12.7371 + 6.13388i) q^{71} +(7.85737 - 0.252600i) q^{72} +(0.111105 - 0.0125185i) q^{73} +(3.99867 + 5.86498i) q^{74} +(-6.91976 + 1.56024i) q^{75} +(-0.429203 + 0.498742i) q^{76} +(-12.5992 - 6.65888i) q^{77} +(7.73226 - 3.34936i) q^{78} +(-5.23741 - 6.08598i) q^{79} +(-2.98291 - 13.0690i) q^{80} +(-6.66153 + 6.05177i) q^{81} +(-2.07504 - 2.60202i) q^{82} +(3.77838 - 4.07213i) q^{83} +(-1.11922 - 0.767390i) q^{84} +(15.8176 - 6.90115i) q^{85} +(-3.01876 - 5.22864i) q^{86} +(-8.20572 + 4.43465i) q^{87} +(-6.07529 + 10.5227i) q^{88} +(0.873041 - 7.74846i) q^{89} +(10.8888 + 8.12519i) q^{90} +(9.70759 + 2.21569i) q^{91} +(1.10853 - 0.167084i) q^{92} +(-2.34325 - 0.449758i) q^{93} +(-5.56722 + 5.16563i) q^{94} +(7.64867 - 1.44721i) q^{95} +(-1.47978 + 1.99403i) q^{96} +(0.607346 + 16.2317i) q^{97} +(-1.21299 - 3.46653i) q^{98} +(-2.51413 - 13.6813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.20822	−	0.891704i	−0.854338	−	0.630530i	0.0760509	−	0.997104i	$-0.475769\pi$
$2$	−1.20822	−	0.891704i	−0.854338	−	0.630530i	−0.930389	+	0.366574i	$0.880531\pi$
$3$	0.979461	−	1.42852i	0.565492	−	0.824754i
$3$	0.979461	−	1.42852i	0.565492	−	0.824754i
$4$	0.0751402	+	0.243598i	0.0375701	+	0.121799i
$5$	1.10182	−	2.80739i	0.492748	−	1.25550i	−0.440980	−	0.897517i	$-0.645369\pi$
$5$	1.10182	−	2.80739i	0.492748	−	1.25550i	0.933728	−	0.357984i	$-0.116536\pi$
$6$	−2.45721	+	0.852566i	−1.00315	+	0.348058i
$7$	−2.93685	−	0.905898i	−1.11003	−	0.342397i	−0.315072	−	0.949068i	$-0.602029\pi$
$7$	−2.93685	−	0.905898i	−1.11003	−	0.342397i	−0.794953	+	0.606670i	$0.792505\pi$
$8$	−0.865489	+	2.47342i	−0.305996	+	0.874488i
$9$	−1.08131	−	2.79835i	−0.360437	−	0.932784i
$10$	−3.83459	+	2.40943i	−1.21260	+	0.761930i
$11$	4.55594	+	0.862031i	1.37367	+	0.259912i	0.819780	−	0.572678i	$-0.194096\pi$
$11$	4.55594	+	0.862031i	1.37367	+	0.259912i	0.553889	+	0.832591i	$0.313143\pi$
$12$	0.421581	+	0.131256i	0.121700	+	0.0378905i
$13$	−3.23076	+	0.242112i	−0.896052	+	0.0671498i	−0.514789	−	0.857317i	$-0.672130\pi$
$13$	−3.23076	+	0.242112i	−0.896052	+	0.0671498i	−0.381263	+	0.924467i	$0.624511\pi$
$14$	2.74056	+	3.71332i	0.732445	+	0.992428i
$15$	−2.93121	−	4.32369i	−0.756834	−	1.11637i
$16$	3.67252	−	2.50388i	0.918129	−	0.625970i
$17$	4.04625	+	4.04625i	0.981359	+	0.981359i	0.999829	−	0.0184707i	$-0.00587974\pi$
$17$	4.04625	+	4.04625i	0.981359	+	0.981359i	−0.0184707	+	0.999829i	$0.505880\pi$
$18$	−1.18884	+	4.34522i	−0.280213	+	1.02418i
$19$	1.37325	+	2.18552i	0.315046	+	0.501393i	0.966283	−	0.257482i	$-0.0828927\pi$
$19$	1.37325	+	2.18552i	0.315046	+	0.501393i	−0.651237	+	0.758874i	$0.725750\pi$
$20$	0.766666	+	0.0574536i	0.171432	+	0.0128470i
$21$	−4.17062	+	3.30804i	−0.910104	+	0.721874i
$22$	−4.73589	−	5.10408i	−1.00970	−	1.08819i
$23$	0.655426	−	4.34847i	0.136666	−	0.906718i	−0.810446	−	0.585814i	$-0.800775\pi$
$23$	0.655426	−	4.34847i	0.136666	−	0.906718i	0.947112	−	0.320904i	$-0.103987\pi$
$24$	2.68561	+	3.65899i	0.548198	+	0.746888i
$25$	−3.00216	−	2.78559i	−0.600431	−	0.557119i
$26$	4.11935	+	2.58836i	0.807871	+	0.507619i
$27$	−5.05659	−	1.19621i	−0.973141	−	0.230210i
$28$		−	0.783481i		−	0.148064i
$29$	−4.79072	−	2.45948i	−0.889614	−	0.456714i
$29$	−4.79072	−	2.45948i	−0.889614	−	0.456714i
$30$	−0.313922	+	7.83772i	−0.0573141	+	1.43097i
$31$	−0.550880	−	1.26263i	−0.0989410	−	0.226775i	0.860051	−	0.510208i	$-0.170432\pi$
$31$	−0.550880	−	1.26263i	−0.0989410	−	0.226775i	−0.958992	+	0.283433i	$0.908527\pi$
$32$	−1.43263	−	0.0536052i	−0.253255	−	0.00947614i
$33$	5.69380	−	5.66391i	0.991163	−	0.985960i
$34$	−1.28069	−	8.49680i	−0.219636	−	1.45719i
$35$	−5.77908	+	7.24674i	−0.976843	+	1.22492i
$36$	0.600424	−	0.473674i	0.100071	−	0.0789457i
$37$	−4.46183	−	1.56126i	−0.733521	−	0.256670i	−0.0624342	−	0.998049i	$-0.519886\pi$
$37$	−4.46183	−	1.56126i	−0.733521	−	0.256670i	−0.671086	+	0.741379i	$0.734172\pi$
$38$	0.289650	−	3.86512i	0.0469875	−	0.627005i
$39$	−2.81854	+	4.85233i	−0.451328	+	0.776995i
$40$	5.99025	+	5.15502i	0.947141	+	0.815081i
$41$	2.14080	+	0.573625i	0.334336	+	0.0895851i	0.422082	−	0.906558i	$-0.361300\pi$
$41$	2.14080	+	0.573625i	0.334336	+	0.0895851i	−0.0877454	+	0.996143i	$0.527966\pi$
$42$	7.98881	−	0.277871i	1.23270	−	0.0428764i
$43$	3.68514	+	1.60781i	0.561979	+	0.245189i	0.661626	−	0.749834i	$-0.269867\pi$
$43$	3.68514	+	1.60781i	0.561979	+	0.245189i	−0.0996470	+	0.995023i	$0.531771\pi$
$44$	0.132345	+	1.17459i	0.0199518	+	0.177077i
$45$	−9.04746	−	0.0476154i	−1.34872	−	0.00709809i
$46$	−4.66944	+	4.66944i	−0.688472	+	0.688472i
$47$	0.940252	−	4.96935i	0.137150	−	0.724855i	−0.844707	−	0.535229i	$-0.820225\pi$
$47$	0.940252	−	4.96935i	0.137150	−	0.724855i	0.981857	−	0.189625i	$-0.0607272\pi$
$48$	0.0202584	−	7.69870i	0.00292405	−	1.11121i
$49$	2.02077	+	1.37774i	0.288681	+	0.196819i
$50$	1.14333	+	6.04263i	0.161691	+	0.854558i
$51$	9.74326	−	1.81698i	1.36433	−	0.254428i
$52$	−0.301738	−	0.768816i	−0.0418435	−	0.106616i
$53$	−1.42370	+	1.13536i	−0.195560	+	0.155954i	−0.716375	−	0.697716i	$-0.754200\pi$
$53$	−1.42370	+	1.13536i	−0.195560	+	0.155954i	0.520814	+	0.853670i	$0.325628\pi$
$54$	5.04279	+	5.95426i	0.686237	+	0.810272i
$55$	7.43988	−	11.8405i	1.00319	−	1.59657i
$56$	4.78248	−	6.48003i	0.639086	−	0.865931i
$57$	4.46710	+	0.178919i	0.591681	+	0.0236984i
$58$	3.59510	+	7.24349i	0.472059	+	0.951116i
$59$	11.0545	−	6.38235i	1.43918	−	0.830911i	0.441387	−	0.897317i	$-0.354487\pi$
$59$	11.0545	−	6.38235i	1.43918	−	0.830911i	0.997793	+	0.0664062i	$0.0211533\pi$
$60$	0.832993	−	1.03892i	0.107539	−	0.134124i
$61$	8.21787	−	4.34327i	1.05219	−	0.556099i	0.150558	−	0.988601i	$-0.451893\pi$
$61$	8.21787	−	4.34327i	1.05219	−	0.556099i	0.901633	+	0.432502i	$0.142369\pi$
$62$	−0.460311	+	2.01675i	−0.0584596	+	0.256128i
$63$	0.640627	+	9.19790i	0.0807114	+	1.15883i
$64$	−5.26714	−	4.20040i	−0.658393	−	0.525051i
$65$	−2.88001	+	9.33676i	−0.357221	+	1.15808i
$66$	−11.9299	+	1.76605i	−1.46847	+	0.217385i
$67$	−2.51549	+	3.68954i	−0.307316	+	0.450749i	−0.948565	−	0.316584i	$-0.897464\pi$
$67$	−2.51549	+	3.68954i	−0.307316	+	0.450749i	0.641249	+	0.767333i	$0.278417\pi$
$68$	−0.681623	+	1.28969i	−0.0826590	+	0.156398i
$69$	−5.56989	−	5.19544i	−0.670535	−	0.625458i
$70$	13.4443	−	3.60240i	1.60690	−	0.430569i
$71$	12.7371	+	6.13388i	1.51162	+	0.727958i	0.991976	−	0.126425i	$-0.0403504\pi$
$71$	12.7371	+	6.13388i	1.51162	+	0.727958i	0.519644	+	0.854383i	$0.326065\pi$
$72$	7.85737	−	0.252600i	0.926000	−	0.0297692i
$73$	0.111105	−	0.0125185i	0.0130039	−	0.00146518i	−0.105460	−	0.994424i	$-0.533632\pi$
$73$	0.111105	−	0.0125185i	0.0130039	−	0.00146518i	0.118464	+	0.992958i	$0.462203\pi$
$74$	3.99867	+	5.86498i	0.464836	+	0.681790i
$75$	−6.91976	+	1.56024i	−0.799025	+	0.180161i
$76$	−0.429203	+	0.498742i	−0.0492329	+	0.0572097i
$77$	−12.5992	−	6.65888i	−1.43581	−	0.758850i
$78$	7.73226	−	3.34936i	0.875505	−	0.379240i
$79$	−5.23741	−	6.08598i	−0.589255	−	0.684726i	0.381619	−	0.924320i	$-0.375367\pi$
$79$	−5.23741	−	6.08598i	−0.589255	−	0.684726i	−0.970873	+	0.239593i	$0.922986\pi$
$80$	−2.98291	−	13.0690i	−0.333500	−	1.46116i
$81$	−6.66153	+	6.05177i	−0.740170	+	0.672419i
$82$	−2.07504	−	2.60202i	−0.229150	−	0.287345i
$83$	3.77838	−	4.07213i	0.414731	−	0.446974i	−0.490788	−	0.871279i	$-0.663291\pi$
$83$	3.77838	−	4.07213i	0.414731	−	0.446974i	0.905519	+	0.424305i	$0.139482\pi$
$84$	−1.11922	−	0.767390i	−0.122116	−	0.0837291i
$85$	15.8176	−	6.90115i	1.71566	−	0.748535i
$86$	−3.01876	−	5.22864i	−0.325521	−	0.563819i
$87$	−8.20572	+	4.43465i	−0.879746	+	0.475444i
$88$	−6.07529	+	10.5227i	−0.647628	+	1.12172i
$89$	0.873041	−	7.74846i	0.0925422	−	0.821335i	−0.858614	−	0.512623i	$-0.828674\pi$
$89$	0.873041	−	7.74846i	0.0925422	−	0.821335i	0.951156	−	0.308711i	$-0.0998977\pi$
$90$	10.8888	+	8.12519i	1.14778	+	0.856470i
$91$	9.70759	+	2.21569i	1.01763	+	0.232268i
$92$	1.10853	−	0.167084i	0.115572	−	0.0174197i
$93$	−2.34325	−	0.449758i	−0.242984	−	0.0466377i
$94$	−5.56722	+	5.16563i	−0.574215	+	0.532794i
$95$	7.64867	−	1.44721i	0.784737	−	0.148480i
$96$	−1.47978	+	1.99403i	−0.151029	+	0.203514i
$97$	0.607346	+	16.2317i	0.0616667	+	1.64808i	0.596132	+	0.802886i	$0.296703\pi$
$97$	0.607346	+	16.2317i	0.0616667	+	1.64808i	−0.534466	+	0.845190i	$0.679487\pi$
$98$	−1.21299	−	3.46653i	−0.122531	−	0.350172i
$99$	−2.51413	−	13.6813i	−0.252679	−	1.37502i
$100$	0.452984	−	0.940630i	0.0452984	−	0.0940630i
$101$	−6.92232	+	15.8661i	−0.688796	+	1.57874i	0.121416	+	0.992602i	$0.461256\pi$
$101$	−6.92232	+	15.8661i	−0.688796	+	1.57874i	−0.810213	+	0.586136i	$0.800648\pi$
$102$	−13.3922	−	6.49280i	−1.32602	−	0.642883i
$103$	0.920849	+	12.2879i	0.0907339	+	1.21076i	0.837788	+	0.545996i	$0.183849\pi$
$103$	0.920849	+	12.2879i	0.0907339	+	1.21076i	−0.747054	+	0.664764i	$0.768532\pi$
$104$	2.19734	−	8.20059i	0.215467	−	0.804134i
$105$	4.69169	+	15.3534i	0.457862	+	1.49834i
$106$	2.73255	−	0.102245i	0.265408	−	0.00993088i
$107$	−6.83433	−	14.1916i	−0.660700	−	1.37196i	−0.914454	−	0.404689i	$-0.867380\pi$
$107$	−6.83433	−	14.1916i	−0.660700	−	1.37196i	0.253754	−	0.967269i	$-0.418334\pi$
$108$	−0.0885587	−	1.32166i	−0.00852156	−	0.127177i
$109$	7.81976	−	1.78481i	0.748997	−	0.170954i	0.169049	−	0.985608i	$-0.445930\pi$
$109$	7.81976	−	1.78481i	0.748997	−	0.170954i	0.579947	+	0.814654i	$0.303073\pi$
$110$	−19.5472	+	7.67171i	−1.86375	+	0.731469i
$111$	−6.60048	+	4.84460i	−0.626490	+	0.459829i
$112$	−13.0539	+	4.02659i	−1.23348	+	0.380477i
$113$	−0.623712	+	16.6691i	−0.0586739	+	1.56809i	0.590238	+	0.807229i	$0.299034\pi$
$113$	−0.623712	+	16.6691i	−0.0586739	+	1.56809i	−0.648912	+	0.760864i	$0.724776\pi$
$114$	−5.23768	−	4.19950i	−0.490553	−	0.393319i
$115$	−11.4857	−	6.63125i	−1.07104	−	0.618367i
$116$	0.239150	−	1.35182i	0.0222045	−	0.125513i
$117$	4.17097	+	8.77900i	0.385606	+	0.811619i
$118$	−19.0475	−	2.14613i	−1.75346	−	0.197568i
$119$	−8.21773	−	15.5487i	−0.753318	−	1.42535i
$120$	13.2312	−	3.50801i	1.20784	−	0.320236i
$121$	9.77392	+	3.83598i	0.888539	+	0.348726i
$122$	−13.8019	−	2.08030i	−1.24956	−	0.188341i
$123$	2.91626	−	2.49632i	0.262950	−	0.225085i
$124$	0.266182	−	0.229068i	0.0239038	−	0.0205709i
$125$	2.45792	−	1.18367i	0.219843	−	0.105871i
$126$	7.42779	−	11.6843i	0.661720	−	1.04092i
$127$	0.730103	−	0.255474i	0.0647862	−	0.0226697i	−0.297691	−	0.954662i	$-0.596217\pi$
$127$	0.730103	−	0.255474i	0.0647862	−	0.0226697i	0.362478	+	0.931992i	$0.381931\pi$
$128$	3.36043	+	12.5413i	0.297023	+	1.10850i
$129$	5.90624	−	3.68949i	0.520015	−	0.324842i
$130$	11.8053	−	8.71271i	1.03539	−	0.764155i
$131$	4.28633	−	3.16346i	0.374499	−	0.276393i	−0.390266	−	0.920702i	$-0.627617\pi$
$131$	4.28633	−	3.16346i	0.374499	−	0.276393i	0.764765	+	0.644309i	$0.222855\pi$
$132$	1.80755	+	0.961413i	0.157327	+	0.0836802i
$133$	−2.05318	−	7.66257i	−0.178033	−	0.664429i
$134$	6.32923	−	2.21469i	0.546762	−	0.191320i
$135$	−8.92966	+	12.8778i	−0.768542	+	1.10834i
$136$	−13.5101	+	6.50610i	−1.15848	+	0.557894i
$137$	1.81223	−	1.55955i	0.154829	−	0.133241i	−0.571462	−	0.820629i	$-0.693624\pi$
$137$	1.81223	−	1.55955i	0.154829	−	0.133241i	0.726291	+	0.687388i	$0.241243\pi$
$138$	2.09683	+	11.2439i	0.178494	+	0.957145i
$139$	−7.94558	−	1.19760i	−0.673935	−	0.101579i	−0.196846	−	0.980434i	$-0.563070\pi$
$139$	−7.94558	−	1.19760i	−0.673935	−	0.101579i	−0.477089	+	0.878855i	$0.658308\pi$
$140$	−2.19953	−	0.863254i	−0.185895	−	0.0729583i
$141$	−6.17785	−	6.21045i	−0.520269	−	0.523014i
$142$	−9.91961	−	18.7688i	−0.832435	−	1.57504i
$143$	−14.9279	−	1.68197i	−1.24833	−	0.140653i
$144$	−10.9779	−	7.56952i	−0.914822	−	0.630793i
$145$	−12.1832	+	10.7395i	−1.01176	+	0.891867i
$146$	−0.145402	−	0.0839478i	−0.0120335	−	0.00694757i
$147$	3.94738	−	1.53726i	0.325574	−	0.126791i
$148$	0.0450583	−	1.20421i	0.00370377	−	0.0989853i
$149$	−18.7621	+	5.78736i	−1.53706	+	0.474119i	−0.943695	−	0.330818i	$-0.892675\pi$
$149$	−18.7621	+	5.78736i	−1.53706	+	0.474119i	−0.593361	+	0.804937i	$0.702199\pi$
$150$	9.75184	+	4.28527i	0.796234	+	0.349890i
$151$	22.4222	−	8.80007i	1.82469	−	0.716140i	0.839820	−	0.542864i	$-0.182660\pi$
$151$	22.4222	−	8.80007i	1.82469	−	0.716140i	0.984873	−	0.173275i	$-0.0554350\pi$
$152$	−6.59425	+	1.50509i	−0.534864	+	0.122079i
$153$	6.94756	−	15.6981i	0.561677	−	1.26911i
$154$	9.28483	+	19.2801i	0.748193	+	1.55364i
$155$	−4.15166	+	0.155344i	−0.333470	+	0.0124776i
$156$	−1.39381	−	0.321988i	−0.111594	−	0.0257797i
$157$	3.91661	−	14.6170i	0.312580	−	1.16656i	−0.613642	−	0.789584i	$-0.710296\pi$
$157$	3.91661	−	14.6170i	0.312580	−	1.16656i	0.926222	−	0.376979i	$-0.123037\pi$
$158$	0.901030	+	12.0234i	0.0716821	+	0.956531i
$159$	0.227424	+	3.14582i	0.0180359	+	0.249480i
$160$	−1.72899	+	3.96288i	−0.136688	+	0.313293i
$161$	−5.86416	+	12.1770i	−0.462160	+	0.959686i
$162$	13.4450	−	1.37174i	1.05634	−	0.107774i
$163$	−4.68706	−	13.3948i	−0.367119	−	1.04916i	−0.968243	−	0.250010i	$-0.919566\pi$
$163$	−4.68706	−	13.3948i	−0.367119	−	1.04916i	0.601125	−	0.799155i	$-0.294719\pi$
$164$	0.0211257	+	0.564597i	0.00164964	+	0.0440876i
$165$	−9.62726	−	22.2253i	−0.749481	−	1.73024i
$166$	−8.19624	+	1.55081i	−0.636152	+	0.120366i
$167$	−5.54292	+	5.14308i	−0.428924	+	0.397983i	−0.864875	−	0.501987i	$-0.832602\pi$
$167$	−5.54292	+	5.14308i	−0.428924	+	0.397983i	0.435951	+	0.899970i	$0.356412\pi$
$168$	−4.57257	−	13.1788i	−0.352781	−	1.01677i
$169$	−2.47561	+	0.373138i	−0.190431	+	0.0287029i
$170$	−25.2649	−	5.76654i	−1.93773	−	0.442274i
$171$	4.63094	−	6.20607i	0.354137	−	0.474590i
$172$	−0.114758	+	1.01851i	−0.00875023	+	0.0776604i
$173$	−0.489134	+	0.847204i	−0.0371881	+	0.0644118i	−0.884020	−	0.467448i	$-0.845173\pi$
$173$	−0.489134	+	0.847204i	−0.0371881	+	0.0644118i	0.846832	+	0.531860i	$0.178507\pi$
$174$	13.8687	+	1.95906i	1.05138	+	0.148516i
$175$	6.29342	+	10.9005i	0.475738	+	0.824002i
$176$	18.8902	−	8.24171i	1.42390	−	0.621243i
$177$	1.71022	−	22.0429i	0.128548	−	1.65684i
$178$	−7.96416	+	8.58332i	−0.596939	+	0.643347i
$179$	14.2455	+	17.8633i	1.06476	+	1.33517i	0.939312	+	0.343065i	$0.111465\pi$
$179$	14.2455	+	17.8633i	1.06476	+	1.33517i	0.125448	+	0.992100i	$0.459963\pi$
$180$	−0.668228	−	2.20752i	−0.0498068	−	0.164539i
$181$	3.73324	+	16.3564i	0.277489	+	1.21576i	0.900956	+	0.433910i	$0.142867\pi$
$181$	3.73324	+	16.3564i	0.277489	+	1.21576i	−0.623467	+	0.781850i	$0.714276\pi$
$182$	−9.75313	−	11.3333i	−0.722950	−	0.840083i
$183$	1.84466	−	15.9934i	0.136361	−	1.18227i
$184$	10.1883	+	5.38469i	0.751094	+	0.396965i
$185$	−9.29919	+	10.8059i	−0.683690	+	0.794462i
$186$	2.43011	+	2.63289i	0.178184	+	0.193053i
$187$	14.9465	+	21.9225i	1.09299	+	1.60313i
$188$	1.28118	−	0.144354i	0.0934394	−	0.0105281i
$189$	13.7668	+	8.09384i	1.00139	+	0.588740i
$190$	−10.5317	−	5.07181i	−0.764052	−	0.367948i
$191$	12.3423	−	3.30712i	0.893059	−	0.239295i	0.217026	−	0.976166i	$-0.430364\pi$
$191$	12.3423	−	3.30712i	0.893059	−	0.239295i	0.676033	+	0.736871i	$0.263698\pi$
$192$	−11.1593	+	3.41006i	−0.805353	+	0.246100i
$193$	−6.41252	+	12.1331i	−0.461583	+	0.873358i	0.537955	+	0.842973i	$0.319197\pi$
$193$	−6.41252	+	12.1331i	−0.461583	+	0.873358i	−0.999538	+	0.0303842i	$0.990327\pi$
$194$	13.7400	−	20.1529i	0.986478	−	1.44690i
$195$	10.5168	+	13.2591i	0.753127	+	0.949506i
$196$	−0.183773	+	0.595779i	−0.0131267	+	0.0425556i
$197$	17.4174	+	13.8899i	1.24094	+	0.989617i	0.999817	+	0.0191228i	$0.00608736\pi$
$197$	17.4174	+	13.8899i	1.24094	+	0.989617i	0.241124	+	0.970494i	$0.422484\pi$
$198$	−9.16203	+	18.7718i	−0.651117	+	1.33405i
$199$	−1.53300	+	6.71653i	−0.108672	+	0.476122i	0.891080	+	0.453846i	$0.149948\pi$
$199$	−1.53300	+	6.71653i	−0.108672	+	0.476122i	−0.999752	+	0.0222760i	$0.992909\pi$
$200$	9.48828	−	5.01470i	0.670923	−	0.354593i
$201$	2.80674	+	7.20717i	0.197972	+	0.508355i
$202$	22.5115	−	12.9970i	1.58391	−	0.914469i
$203$	11.8416	+	11.5630i	0.831116	+	0.811565i
$204$	1.17472	+	2.23692i	0.0822472	+	0.156615i
$205$	3.96915	−	5.37801i	0.277218	−	0.375617i
$206$	9.84456	−	15.6675i	0.685903	−	1.09161i
$207$	−12.8773	+	2.86793i	−0.895031	+	0.199335i
$208$	−11.2588	+	8.97860i	−0.780658	+	0.622554i
$209$	4.37248	+	11.1409i	0.302451	+	0.770632i
$210$	8.02212	−	22.7338i	0.553579	−	1.56878i
$211$	0.442516	+	2.33876i	0.0304641	+	0.161007i	0.994495	−	0.104783i	$-0.0334149\pi$
$211$	0.442516	+	2.33876i	0.0304641	+	0.161007i	−0.964031	+	0.265790i	$0.914367\pi$
$212$	−0.383550	−	0.261500i	−0.0263423	−	0.0179599i
$213$	21.2379	−	12.1873i	1.45520	−	0.835059i
$214$	−4.39739	+	23.2408i	−0.300600	+	1.58871i
$215$	8.57411	−	8.57411i	0.584749	−	0.584749i
$216$	7.33515	−	11.4718i	0.499094	−	0.780556i
$217$	0.474038	+	4.20720i	0.0321798	+	0.285603i
$218$	−11.0395	−	4.81648i	−0.747688	−	0.326213i
$219$	0.0909403	−	0.170977i	0.00614517	−	0.0115535i
$220$	3.44336	+	0.922645i	0.232151	+	0.0622047i
$221$	−14.0521	−	12.0928i	−0.945246	−	0.813450i
$222$	12.2948	+	0.0323525i	0.825170	+	0.00217136i
$223$	−0.809031	+	10.7958i	−0.0541767	+	0.722938i	0.902296	+	0.431117i	$0.141880\pi$
$223$	−0.809031	+	10.7958i	−0.0541767	+	0.722938i	−0.956473	+	0.291821i	$0.905739\pi$
$224$	4.15885	+	1.45525i	0.277875	+	0.0972327i
$225$	−4.54880	+	11.4132i	−0.303254	+	0.760878i
$226$	15.6175	−	19.5837i	1.03886	−	1.30269i
$227$	−3.27544	−	21.7311i	−0.217398	−	1.44234i	−0.785233	−	0.619201i	$-0.787457\pi$
$227$	−3.27544	−	21.7311i	−0.217398	−	1.44234i	0.567834	−	0.823143i	$-0.307781\pi$
$228$	0.292074	+	1.10162i	0.0193431	+	0.0729567i
$229$	0.477741	+	0.0178758i	0.0315700	+	0.00118127i	0.0531715	−	0.998585i	$-0.483067\pi$
$229$	0.477741	+	0.0178758i	0.0315700	+	0.00118127i	−0.0216015	+	0.999767i	$0.506877\pi$
$230$	7.96405	+	18.2538i	0.525134	+	1.20362i
$231$	−21.8528	+	11.4761i	−1.43781	+	0.755069i
$232$	10.2296	−	9.72083i	0.671609	−	0.638203i
$233$		−	9.60932i		−	0.629528i	−0.949170	−	0.314764i	$-0.898075\pi$
$233$		−	9.60932i		−	0.629528i	0.949170	−	0.314764i	$-0.101925\pi$
$234$	2.78884	−	14.3262i	0.182312	−	0.936534i
$235$	−12.9149	−	8.11497i	−0.842475	−	0.529362i
$236$	2.38537	+	2.21330i	0.155274	+	0.144074i
$237$	−13.8238	+	1.52074i	−0.897950	+	0.0987825i
$238$	−3.93605	+	26.1140i	−0.255136	+	1.69272i
$239$	13.7702	+	14.8407i	0.890720	+	0.959968i	0.999418	−	0.0341068i	$-0.0108586\pi$
$239$	13.7702	+	14.8407i	0.890720	+	0.959968i	−0.108698	+	0.994075i	$0.534668\pi$
$240$	−21.5909	−	8.53944i	−1.39369	−	0.551218i
$241$	−16.0196	−	1.20051i	−1.03192	−	0.0773314i	−0.452008	−	0.892014i	$-0.649292\pi$
$241$	−16.0196	−	1.20051i	−1.03192	−	0.0773314i	−0.579907	+	0.814682i	$0.696911\pi$
$242$	−8.38845	−	13.3501i	−0.539230	−	0.858180i
$243$	2.12034	+	15.4436i	0.136020	+	0.990706i
$244$	1.67551	+	1.67551i	0.107263	+	0.107263i
$245$	6.09435	−	4.15506i	0.389354	−	0.265457i
$246$	−5.74945	+	0.415651i	−0.366572	+	0.0265009i
$247$	−4.96579	−	6.72841i	−0.315966	−	0.428118i
$248$	3.59980	−	0.269768i	0.228588	−	0.0171303i
$249$	−2.11632	−	9.38597i	−0.134116	−	0.594812i
$250$	−4.02519	−	0.761607i	−0.254575	−	0.0481682i
$251$	−3.38219	+	2.12517i	−0.213482	+	0.134140i	−0.634529	−	0.772899i	$-0.718806\pi$
$251$	−3.38219	+	2.12517i	−0.213482	+	0.134140i	0.421047	+	0.907039i	$0.361663\pi$
$252$	−2.19246	+	0.847187i	−0.138112	+	0.0533678i
$253$	6.73460	−	19.2464i	0.423401	−	1.21001i
$254$	−1.10993	−	0.342368i	−0.0696432	−	0.0214821i
$255$	5.63433	−	29.3551i	0.352836	−	1.83829i
$256$	2.20045	−	5.60665i	0.137528	−	0.350416i
$257$	−1.57032	−	5.09084i	−0.0979536	−	0.317558i	0.893312	−	0.449437i	$-0.148375\pi$
$257$	−1.57032	−	5.09084i	−0.0979536	−	0.317558i	−0.991266	+	0.131879i	$0.957899\pi$
$258$	−10.4260	−	0.808912i	−0.649092	−	0.0503607i
$259$	11.6894	+	8.62716i	0.726343	+	0.536066i
$260$	−2.49082			−0.154474
$261$	−1.70223	+	16.0656i	−0.105365	+	0.994434i
$262$	−7.99969			−0.494222
$263$	14.8301	+	10.9451i	0.914463	+	0.674904i	0.945850	−	0.324603i	$-0.105231\pi$
$263$	14.8301	+	10.9451i	0.914463	+	0.674904i	−0.0313875	+	0.999507i	$0.509993\pi$
$264$	9.08134	+	18.9852i	0.558918	+	1.16846i
$265$	1.61874	+	5.24784i	0.0994386	+	0.322372i
$266$	−4.35206	+	11.0889i	−0.266842	+	0.679903i
$267$	−10.2137	−	8.83647i	−0.625067	−	0.540783i
$268$	−1.08778	−	0.335536i	−0.0664468	−	0.0204961i
$269$	−5.37070	+	15.3486i	−0.327457	+	0.935819i	0.656013	+	0.754749i	$0.272242\pi$
$269$	−5.37070	+	15.3486i	−0.327457	+	0.935819i	−0.983470	+	0.181069i	$0.942044\pi$
$270$	22.2721	−	7.59655i	1.35544	−	0.462311i
$271$	−2.25137	+	1.41463i	−0.136761	+	0.0859328i	−0.598675	−	0.800992i	$-0.704306\pi$
$271$	−2.25137	+	1.41463i	−0.136761	+	0.0859328i	0.461914	+	0.886925i	$0.347163\pi$
$272$	24.9912	+	4.72859i	1.51532	+	0.286713i
$273$	12.6734	−	11.6973i	0.767027	−	0.707950i
$274$	−3.58021	+	0.268300i	−0.216289	+	0.0162086i
$275$	−11.2764	−	15.2790i	−0.679992	−	0.921356i
$276$	0.847079	−	1.74720i	0.0509882	−	0.105169i
$277$	−13.6525	+	9.30815i	−0.820302	+	0.559272i	−0.899163	−	0.437613i	$-0.855824\pi$
$277$	−13.6525	+	9.30815i	−0.820302	+	0.559272i	0.0788614	+	0.996886i	$0.474872\pi$
$278$	8.53207	+	8.53207i	0.511720	+	0.511720i
$279$	−2.93761	+	2.90685i	−0.175870	+	0.174029i
$280$	−12.9225	−	20.5661i	−0.772269	−	1.22906i
$281$	−27.5371	−	2.06362i	−1.64273	−	0.123105i	−0.778987	−	0.627040i	$-0.784266\pi$
$281$	−27.5371	−	2.06362i	−1.64273	−	0.123105i	−0.863742	+	0.503935i	$0.831885\pi$
$282$	1.92630	+	13.0124i	0.114709	+	0.774877i
$283$	−17.5074	−	18.8685i	−1.04071	−	1.12162i	−0.992433	−	0.122784i	$-0.960818\pi$
$283$	−17.5074	−	18.8685i	−1.04071	−	1.12162i	−0.0482756	−	0.998834i	$-0.515373\pi$
$284$	−0.537133	+	3.56365i	−0.0318730	+	0.211464i
$285$	5.42422	−	12.3437i	0.321303	−	0.731179i
$286$	16.5363	+	15.3434i	0.977811	+	0.907276i
$287$	−5.76755	−	3.62399i	−0.340448	−	0.213918i
$288$	1.39911	+	4.06696i	0.0824434	+	0.239648i
$289$			15.7442i			0.926130i
$290$	24.2964	−	2.11182i	1.42673	−	0.124011i
$291$	23.7821	+	15.0307i	1.39413	+	0.881115i
$292$	0.0113980	+	0.0261244i	0.000667015	+	0.00152881i
$293$	10.9092	+	0.408195i	0.637325	+	0.0238470i	0.354101	−	0.935207i	$-0.384787\pi$
$293$	10.9092	+	0.408195i	0.637325	+	0.0238470i	0.283223	+	0.959054i	$0.408596\pi$
$294$	−6.14007	−	1.66256i	−0.358096	−	0.0969622i
$295$	−5.73761	−	38.0666i	−0.334057	−	2.21632i
$296$	7.72333	−	9.68475i	0.448909	−	0.562915i
$297$	−22.0064	−	9.80879i	−1.27694	−	0.569164i
$298$	27.8293	+	9.73791i	1.61211	+	0.564102i
$299$	−1.06471	+	14.2075i	−0.0615736	+	0.821643i
$300$	−0.900024	−	1.56840i	−0.0519629	−	0.0905519i
$301$	−9.36620	−	8.06027i	−0.539859	−	0.464586i
$302$	−34.9380	−	9.36160i	−2.01045	−	0.538699i
$303$	15.8848	+	25.4289i	0.912561	+	1.46085i
$304$	10.5156	+	4.58790i	0.603109	+	0.263134i
$305$	−3.13864	−	27.8562i	−0.179718	−	1.59504i
$306$	−22.3922	+	12.7715i	−1.28008	+	0.730097i
$307$	3.95869	−	3.95869i	0.225934	−	0.225934i	−0.585058	−	0.810992i	$-0.698928\pi$
$307$	3.95869	−	3.95869i	0.225934	−	0.225934i	0.810992	+	0.585058i	$0.198928\pi$
$308$	0.675385	−	3.56950i	0.0384837	−	0.203391i
$309$	18.4553	+	10.7200i	1.04989	+	0.609842i
$310$	5.15463	+	3.51437i	0.292763	+	0.199603i
$311$	1.45695	+	7.70018i	0.0826162	+	0.436637i	0.999313	+	0.0370542i	$0.0117974\pi$
$311$	1.45695	+	7.70018i	0.0826162	+	0.436637i	−0.916697	+	0.399583i	$0.869155\pi$
$312$	−9.56245	−	11.1711i	−0.541367	−	0.632439i
$313$	−7.25936	−	18.4966i	−0.410323	−	1.04549i	−0.975399	−	0.220448i	$-0.929248\pi$
$313$	−7.25936	−	18.4966i	−0.410323	−	1.04549i	0.565075	−	0.825039i	$-0.308847\pi$
$314$	−17.7662	+	14.1680i	−1.00260	+	0.799548i
$315$	26.5279	+	8.33592i	1.49468	+	0.469676i
$316$	1.08900	−	1.73313i	0.0612608	−	0.0974960i
$317$	1.68009	−	2.27644i	0.0943631	−	0.127858i	−0.754872	−	0.655872i	$-0.772301\pi$
$317$	1.68009	−	2.27644i	0.0943631	−	0.127858i	0.849236	+	0.528014i	$0.177063\pi$
$318$	2.53036	−	4.00363i	0.141896	−	0.224512i
$319$	−19.7061	−	15.3350i	−1.10333	−	0.858595i
$320$	−17.5956	+	10.1588i	−0.983623	+	0.567895i
$321$	−26.9669	−	4.13721i	−1.50515	−	0.230917i
$322$	17.9435	−	9.48341i	0.999952	−	0.528490i
$323$	−3.28663	+	14.3997i	−0.182873	+	0.801219i
$324$	−1.97475	−	1.16801i	−0.109708	−	0.0648893i
$325$	10.3737	+	8.27273i	0.575428	+	0.458888i
$326$	−6.28126	+	20.3633i	−0.347887	+	1.12782i
$327$	5.10952	−	12.9188i	0.282557	−	0.714411i
$328$	−3.27165	+	4.79863i	−0.180647	+	0.264960i
$329$	−7.26311	+	13.7425i	−0.400428	+	0.757647i
$330$	−8.18657	+	35.4376i	−0.450656	+	1.95078i
$331$	5.75278	−	1.54145i	0.316202	−	0.0847259i	−0.0972278	−	0.995262i	$-0.530998\pi$
$331$	5.75278	−	1.54145i	0.316202	−	0.0847259i	0.413429	+	0.910536i	$0.364331\pi$
$332$	1.27587	+	0.614428i	0.0700226	+	0.0337211i
$333$	0.455668	+	14.1740i	0.0249704	+	0.776729i
$334$	11.2831	−	1.27131i	0.617386	−	0.0695627i
$335$	7.58636	+	11.1271i	0.414487	+	0.607941i
$336$	−7.03374	+	22.5916i	−0.383722	+	1.23247i
$337$	−19.4619	+	22.6151i	−1.06016	+	1.23192i	−0.0883623	+	0.996088i	$0.528163\pi$
$337$	−19.4619	+	22.6151i	−1.06016	+	1.23192i	−0.971793	+	0.235835i	$0.924218\pi$
$338$	3.32380	+	1.75668i	0.180791	+	0.0955507i
$339$	23.2011	+	17.2177i	1.26011	+	0.935136i
$340$	2.86965	+	3.33459i	0.155628	+	0.180843i
$341$	−1.42135	−	6.22735i	−0.0769706	−	0.337230i
$342$	−11.1292	+	3.36885i	−0.601796	+	0.182166i
$343$	8.72700	+	10.9433i	0.471214	+	0.590883i
$344$	−7.16625	+	7.72338i	−0.386378	+	0.416417i
$345$	−20.7226	+	9.91239i	−1.11567	+	0.533665i
$346$	1.34644	−	0.587444i	0.0723848	−	0.0315812i
$347$	0.588210	+	1.01881i	0.0315767	+	0.0546925i	0.881382	−	0.472404i	$-0.156614\pi$
$347$	0.588210	+	1.01881i	0.0315767	+	0.0546925i	−0.849805	+	0.527097i	$0.823280\pi$
$348$	−1.69685	−	1.66568i	−0.0909608	−	0.0892899i
$349$	−12.2144	+	21.1559i	−0.653821	+	1.13245i	0.328367	+	0.944550i	$0.393502\pi$
$349$	−12.2144	+	21.1559i	−0.653821	+	1.13245i	−0.982188	+	0.187901i	$0.939831\pi$
$350$	2.11623	−	18.7821i	0.113117	−	1.00394i
$351$	16.6262	+	2.64040i	0.887443	+	0.140934i
$352$	−6.48076	−	1.47919i	−0.345426	−	0.0788412i
$353$	−0.700912	+	0.105646i	−0.0373058	+	0.00562295i	−0.167669	−	0.985843i	$-0.553624\pi$
$353$	−0.700912	+	0.105646i	−0.0373058	+	0.00562295i	0.130363	+	0.991466i	$0.458386\pi$
$354$	−21.7220	+	25.1075i	−1.15451	+	1.33445i
$355$	31.2542	−	28.9996i	1.65880	−	1.53914i
$356$	1.95311	−	0.369549i	0.103515	−	0.0195860i
$357$	−30.2605	−	3.49020i	−1.60156	−	0.184721i
$358$	−1.28287	−	34.2855i	−0.0678020	−	1.81205i
$359$	0.991361	+	2.83315i	0.0523220	+	0.149528i	0.967079	−	0.254477i	$-0.0819035\pi$
$359$	0.991361	+	2.83315i	0.0523220	+	0.149528i	−0.914757	+	0.404005i	$0.867618\pi$
$360$	7.94825	−	22.3370i	0.418909	−	1.17726i
$361$	5.35312	−	11.1159i	0.281743	−	0.585046i
$362$	10.0745	−	23.0910i	0.529504	−	1.21364i
$363$	15.0529	−	10.2050i	0.790074	−	0.535624i
$364$	0.189690	+	2.53124i	0.00994247	+	0.132673i
$365$	0.0872733	−	0.325708i	0.00456809	−	0.0170483i
$366$	−16.4902	+	17.6786i	−0.861954	+	0.924077i
$367$	−16.9292	+	0.633448i	−0.883700	+	0.0330657i	−0.475387	−	0.879777i	$-0.657692\pi$
$367$	−16.9292	+	0.633448i	−0.883700	+	0.0330657i	−0.408312	+	0.912842i	$0.633883\pi$
$368$	−8.48097	−	17.6109i	−0.442101	−	0.918033i
$369$	−0.709664	−	6.61097i	−0.0369436	−	0.344153i
$370$	20.8711	−	4.76369i	1.08504	−	0.247652i
$371$	5.20972	−	2.04466i	0.270475	−	0.106154i
$372$	−0.0665122	−	0.604608i	−0.00344850	−	0.0313475i
$373$	3.69524	−	1.13983i	0.191332	−	0.0590182i	−0.197608	−	0.980281i	$-0.563317\pi$
$373$	3.69524	−	1.13983i	0.191332	−	0.0590182i	0.388940	+	0.921263i	$0.372841\pi$
$374$	1.48977	−	39.8149i	0.0770341	−	2.05878i
$375$	0.716545	−	4.67054i	0.0370022	−	0.241186i
$376$	11.4775	+	6.62656i	0.591909	+	0.341739i
$377$	16.0731	+	6.78609i	0.827808	+	0.349502i
$378$	−9.41597	−	22.0550i	−0.484305	−	1.13439i
$379$	18.0908	+	2.03834i	0.929260	+	0.104702i	0.563602	−	0.826047i	$-0.309415\pi$
$379$	18.0908	+	2.03834i	0.929260	+	0.104702i	0.365658	+	0.930749i	$0.380844\pi$
$380$	0.927260	+	1.75446i	0.0475674	+	0.0900019i
$381$	0.350159	−	1.29319i	0.0179392	−	0.0662521i
$382$	−17.8612	−	7.00999i	−0.913857	−	0.358663i
$383$	13.4588	+	2.02859i	0.687712	+	0.103656i	0.483597	−	0.875291i	$-0.339330\pi$
$383$	13.4588	+	2.02859i	0.687712	+	0.103656i	0.204115	+	0.978947i	$0.434568\pi$
$384$	21.2068	+	7.48329i	1.08221	+	0.381880i
$385$	−32.5761	+	28.0340i	−1.66023	+	1.42874i
$386$	18.5668	−	8.94131i	0.945026	−	0.455101i
$387$	0.514435	−	12.0509i	0.0261502	−	0.612580i
$388$	−3.90837	+	1.36760i	−0.198418	+	0.0694293i
$389$	2.31433	+	8.63719i	0.117341	+	0.437923i	0.999451	−	0.0331199i	$-0.0105443\pi$
$389$	2.31433	+	8.63719i	0.117341	+	0.437923i	−0.882110	+	0.471043i	$0.843878\pi$
$390$	−0.883400	−	25.3978i	−0.0447327	−	1.28607i
$391$	20.2470	−	14.9429i	1.02393	−	0.755697i
$392$	−5.15667	+	3.80580i	−0.260451	+	0.192222i
$393$	−0.320750	−	9.22158i	−0.0161797	−	0.465167i
$394$	−8.65831	−	32.3133i	−0.436199	−	1.62792i
$395$	−22.8564	+	7.99779i	−1.15003	+	0.402413i
$396$	3.14382	−	1.64045i	0.157983	−	0.0824357i
$397$	17.6324	−	8.49130i	0.884943	−	0.426166i	0.0645158	−	0.997917i	$-0.479450\pi$
$397$	17.6324	−	8.49130i	0.884943	−	0.426166i	0.820428	+	0.571750i	$0.193735\pi$
$398$	7.84136	−	6.74803i	0.393052	−	0.338248i
$399$	−12.9571	−	4.57219i	−0.648667	−	0.228896i
$400$	−18.0003	−	2.71310i	−0.900013	−	0.135655i
$401$	9.54161	+	3.74481i	0.476485	+	0.187007i	0.591416	−	0.806367i	$-0.298569\pi$
$401$	9.54161	+	3.74481i	0.476485	+	0.187007i	−0.114930	+	0.993374i	$0.536664\pi$
$402$	3.03551	−	11.2106i	0.151398	−	0.559135i
$403$	2.08546	+	3.94588i	0.103884	+	0.196559i
$404$	−4.38511	−	0.494083i	−0.218167	−	0.0245815i
$405$	9.64987	+	25.3695i	0.479506	+	1.26062i
$406$	−3.99640	−	24.5298i	−0.198338	−	1.21739i
$407$	−18.9820	−	10.9593i	−0.940903	−	0.543231i
$408$	−3.93852	+	25.6718i	−0.194986	+	1.27094i
$409$	0.689629	−	18.4307i	0.0341000	−	0.911341i	−0.872313	−	0.488948i	$-0.837381\pi$
$409$	0.689629	−	18.4307i	0.0341000	−	0.911341i	0.906413	−	0.422393i	$-0.138810\pi$
$410$	−9.59120	+	2.95849i	−0.473675	+	0.146110i
$411$	−0.452830	−	4.11631i	−0.0223365	−	0.203042i
$412$	−2.92411	+	1.14763i	−0.144061	+	0.0565397i
$413$	−38.2473	+	8.72970i	−1.88203	+	0.429560i
$414$	18.1159	+	8.01762i	0.890346	+	0.394044i
$415$	−7.26895	−	15.0941i	−0.356819	−	0.740941i
$416$	4.64146	−	0.173671i	0.227566	−	0.00851492i
$417$	−9.49318	+	10.1774i	−0.464883	+	0.498388i
$418$	4.65148	−	17.3596i	0.227511	−	0.849084i
$419$	−1.69271	−	22.5876i	−0.0826941	−	1.10348i	−0.872010	−	0.489489i	$-0.837183\pi$
$419$	−1.69271	−	22.5876i	−0.0826941	−	1.10348i	0.789316	−	0.613988i	$-0.210436\pi$
$420$	−3.38753	+	2.29655i	−0.165295	+	0.112060i
$421$	4.16824	−	9.55371i	0.203148	−	0.465620i	−0.784928	−	0.619587i	$-0.787300\pi$
$421$	4.16824	−	9.55371i	0.203148	−	0.465620i	0.988076	+	0.153967i	$0.0492050\pi$
$422$	1.55082	−	3.22032i	0.0754929	−	0.156763i
$423$	−14.9227	+	2.74226i	−0.725566	+	0.133333i
$424$	−1.57604	−	4.50406i	−0.0765392	−	0.218736i
$425$	−0.876264	−	23.4187i	−0.0425051	−	1.13597i
$426$	−36.5274	−	4.21302i	−1.76976	−	0.204121i
$427$	−28.0692	+	5.31098i	−1.35837	+	0.257017i
$428$	2.94353	−	2.73119i	0.142281	−	0.132017i
$429$	−17.0240	+	19.6773i	−0.821926	+	0.950028i
$430$	−18.0049	+	2.71381i	−0.868276	+	0.130872i
$431$	12.7306	+	2.90567i	0.613210	+	0.139961i	0.517835	−	0.855480i	$-0.326738\pi$
$431$	12.7306	+	2.90567i	0.613210	+	0.139961i	0.0953743	+	0.995441i	$0.469595\pi$
$432$	−21.5656	+	8.26800i	−1.03757	+	0.397794i
$433$	−1.13811	+	10.1010i	−0.0546940	+	0.485423i	0.936269	+	0.351285i	$0.114255\pi$
$433$	−1.13811	+	10.1010i	−0.0546940	+	0.485423i	−0.990963	+	0.134138i	$0.957173\pi$
$434$	3.17884	−	5.50591i	0.152589	−	0.264292i
$435$	3.40856	+	27.9228i	0.163428	+	1.33880i
$436$	1.02235	+	1.77077i	0.0489619	+	0.0848045i
$437$	10.4037	−	4.53910i	0.497678	−	0.217134i
$438$	−0.262336	+	0.125485i	−0.0125349	+	0.00599591i
$439$	−14.7282	+	15.8732i	−0.702939	+	0.757588i	−0.979068	−	0.203532i	$-0.934758\pi$
$439$	−14.7282	+	15.8732i	−0.702939	+	0.757588i	0.276129	+	0.961121i	$0.410948\pi$
$440$	22.8474	+	28.6498i	1.08921	+	1.36582i
$441$	1.67031	−	7.14457i	0.0795386	−	0.340218i
$442$	6.19477	+	27.1410i	0.294655	+	1.29097i
$443$	13.9909	+	16.2578i	0.664729	+	0.772429i	0.984560	−	0.175045i	$-0.0560072\pi$
$443$	13.9909	+	16.2578i	0.664729	+	0.772429i	−0.319831	+	0.947474i	$0.603626\pi$
$444$	−1.67610	−	1.24384i	−0.0795441	−	0.0590301i
$445$	−20.7910	−	10.9884i	−0.985587	−	0.520898i
$446$	10.6041	−	12.3222i	0.502120	−	0.583474i
$447$	−10.1095	+	32.4705i	−0.478162	+	1.53580i
$448$	11.6637	+	17.1075i	0.551056	+	0.808251i
$449$	27.0806	−	3.05125i	1.27801	−	0.143997i	0.553260	−	0.833008i	$-0.313383\pi$
$449$	27.0806	−	3.05125i	1.27801	−	0.143997i	0.724751	+	0.689011i	$0.241955\pi$
$450$	15.6731	−	9.73340i	0.738838	−	0.458837i
$451$	9.25887	+	4.45884i	0.435983	+	0.209958i
$452$	−4.10742	+	1.10058i	−0.193197	+	0.0517669i
$453$	9.39066	−	40.6498i	0.441212	−	1.90989i
$454$	−15.4203	+	29.1766i	−0.723710	+	1.36933i
$455$	16.9163	−	24.8117i	0.793049	−	1.16319i
$456$	−4.30876	+	10.8942i	−0.201776	+	0.510166i
$457$	2.61981	−	8.49321i	0.122549	−	0.397296i	−0.873422	−	0.486964i	$-0.838104\pi$
$457$	2.61981	−	8.49321i	0.122549	−	0.397296i	0.995972	+	0.0896681i	$0.0285806\pi$
$458$	−0.561275	−	0.447602i	−0.0262267	−	0.0209151i
$459$	−15.6201	−	25.3003i	−0.729082	−	1.18092i
$460$	0.752328	−	3.29616i	0.0350775	−	0.153684i
$461$	−8.17383	+	4.32000i	−0.380693	+	0.201202i	−0.646657	−	0.762781i	$-0.723834\pi$
$461$	−8.17383	+	4.32000i	−0.380693	+	0.201202i	0.265964	+	0.963983i	$0.414310\pi$
$462$	36.6361	+	5.62064i	1.70447	+	0.261496i
$463$	24.2022	−	13.9732i	1.12477	−	0.649389i	0.182159	−	0.983269i	$-0.441692\pi$
$463$	24.2022	−	13.9732i	1.12477	−	0.649389i	0.942615	+	0.333881i	$0.108358\pi$
$464$	−23.7522	+	2.96291i	−1.10267	+	0.137549i
$465$	−3.84448	+	6.08287i	−0.178284	+	0.282086i
$466$	−8.56867	+	11.6101i	−0.396936	+	0.537829i
$467$	−14.1602	+	22.5358i	−0.655255	+	1.04283i	0.339506	+	0.940604i	$0.389740\pi$
$467$	−14.1602	+	22.5358i	−0.655255	+	1.04283i	−0.994761	+	0.102228i	$0.967403\pi$
$468$	−1.82514	+	1.67570i	−0.0843673	+	0.0774591i
$469$	10.7300	−	8.55686i	0.495463	−	0.395119i
$470$	8.36784	+	21.3209i	0.385980	+	0.983461i
$471$	−17.0444	−	19.9117i	−0.785366	−	0.917484i
$472$	6.21866	+	32.8664i	0.286237	+	1.51280i
$473$	15.4033	+	10.5018i	0.708246	+	0.482874i
$474$	18.0581	+	10.4893i	0.829438	+	0.481791i
$475$	1.96525	−	10.3866i	0.0901718	−	0.476570i
$476$	3.17016	−	3.17016i	0.145304	−	0.145304i
$477$	4.71661	+	2.75633i	0.215959	+	0.126204i
$478$	−3.40383	−	30.2098i	−0.155687	−	1.38176i
$479$	−4.14154	−	1.80694i	−0.189232	−	0.0825610i	0.303140	−	0.952946i	$-0.401965\pi$
$479$	−4.14154	−	1.80694i	−0.189232	−	0.0825610i	−0.492372	+	0.870385i	$0.663870\pi$
$480$	3.96756	+	6.35137i	0.181093	+	0.289899i
$481$	14.7931	+	3.96380i	0.674508	+	0.180734i
$482$	18.2847	+	15.7353i	0.832845	+	0.716721i
$483$	11.6514	+	20.3040i	0.530156	+	0.923863i
$484$	−0.200025	+	2.66915i	−0.00909205	+	0.121325i
$485$	46.2378	+	16.1793i	2.09955	+	0.734664i
$486$	11.2093	−	20.5499i	0.508463	−	0.932163i
$487$	−8.38844	+	10.5188i	−0.380117	+	0.476651i	−0.934680	−	0.355490i	$-0.884314\pi$
$487$	−8.38844	+	10.5188i	−0.380117	+	0.476651i	0.554563	+	0.832142i	$0.312885\pi$
$488$	3.63028	+	24.0853i	0.164335	+	1.09029i
$489$	−23.7255	−	6.42420i	−1.07291	−	0.290512i
$490$	−11.0684	−	0.414150i	−0.500019	−	0.0187094i
$491$	12.8470	+	29.4457i	0.579778	+	1.32886i	0.921249	+	0.388973i	$0.127170\pi$
$491$	12.8470	+	29.4457i	0.579778	+	1.32886i	−0.341472	+	0.939892i	$0.610925\pi$
$492$	0.827227	+	0.522822i	0.0372943	+	0.0235707i
$493$	−9.43277	−	29.3361i	−0.424830	−	1.32123i
$494$			12.5574i			0.564984i
$495$	−41.1787	−	8.01613i	−1.85084	−	0.360298i
$496$	−5.18459	−	3.25770i	−0.232795	−	0.146275i
$497$	−31.8504	−	29.5528i	−1.42869	−	1.32563i
$498$	−5.81254	+	13.2274i	−0.260466	+	0.592735i
$499$	0.680500	−	4.51482i	0.0304634	−	0.202111i	−0.968422	−	0.249318i	$-0.919794\pi$
$499$	0.680500	−	4.51482i	0.0304634	−	0.202111i	0.998885	+	0.0472063i	$0.0150318\pi$
$500$	0.473029	+	0.509805i	0.0211545	+	0.0227992i
$501$	1.91789	+	12.9556i	0.0856849	+	0.578813i
$502$	5.98144	+	0.448247i	0.266965	+	0.0200062i
$503$	−13.5976	−	21.6404i	−0.606286	−	0.964899i	−0.998977	−	0.0452282i	$-0.985598\pi$
$503$	−13.5976	−	21.6404i	−0.606286	−	0.964899i	0.392691	−	0.919671i	$-0.371544\pi$
$504$	−23.3048	−	6.37613i	−1.03808	−	0.284015i
$505$	36.9152	+	36.9152i	1.64270	+	1.64270i
$506$	−25.2989	+	17.2485i	−1.12467	+	0.766790i
$507$	−1.89173	+	3.90192i	−0.0840146	+	0.173290i
$508$	0.117093	+	0.158656i	0.00519517	+	0.00703920i
$509$	−20.1258	+	1.50822i	−0.892061	+	0.0668507i	−0.512869	−	0.858467i	$-0.671417\pi$
$509$	−20.1258	+	1.50822i	−0.892061	+	0.0668507i	−0.379192	+	0.925318i	$0.623798\pi$
$510$	−32.9836	+	30.4431i	−1.46054	+	1.34805i
$511$	−0.337640	−	0.0638849i	−0.0149363	−	0.00282610i
$512$	14.3291	−	9.00359i	0.633264	−	0.397906i
$513$	−4.32964	−	12.6940i	−0.191158	−	0.560452i
$514$	−2.64224	+	7.55109i	−0.116544	+	0.333064i
$515$	35.5114	+	10.9538i	1.56482	+	0.482683i
$516$	1.34255	+	1.16152i	0.0591025	+	0.0511331i
$517$	8.56747	−	21.8296i	0.376797	−	0.960063i
$518$	−6.43043	−	20.8470i	−0.282537	−	0.915963i
$519$	0.731157	+	1.52854i	0.0320942	+	0.0670954i
$520$	−20.6011	−	15.2043i	−0.903420	−	0.666754i
$521$	−22.2500			−0.974790			−0.487395	−	0.873182i	$-0.662053\pi$
$521$	−22.2500			−0.974790			−0.487395	+	0.873182i	$0.662053\pi$
$522$	16.3824	−	17.8928i	0.717038	−	0.783147i
$523$	−8.32311			−0.363944			−0.181972	−	0.983304i	$-0.558248\pi$
$523$	−8.32311			−0.363944			−0.181972	+	0.983304i	$0.558248\pi$
$524$	1.09269	+	0.806441i	0.0477343	+	0.0352295i
$525$	21.7357	+	1.68639i	0.948624	+	0.0736003i
$526$	−8.15817	−	26.4481i	−0.355713	−	1.15319i
$527$	2.87992	−	7.33791i	0.125451	−	0.319645i
$528$	6.72882	−	35.0574i	0.292834	−	1.52568i
$529$	3.49860	+	1.07917i	0.152113	+	0.0469207i
$530$	2.72373	−	7.78397i	0.118311	−	0.338114i
$531$	−29.8134	−	24.0332i	−1.29379	−	1.04295i
$532$	1.71231	−	1.07592i	0.0742382	−	0.0466470i
$533$	−7.05528	−	1.33493i	−0.305598	−	0.0578223i
$534$	4.46082	+	19.7839i	0.193038	+	0.856135i
$535$	−47.3716	+	3.55001i	−2.04805	+	0.153480i
$536$	−6.94868	−	9.41512i	−0.300137	−	0.406671i
$537$	39.4709	−	2.85351i	1.70330	−	0.123138i
$538$	20.1753	−	13.7553i	0.869821	−	0.593034i
$539$	8.01885	+	8.01885i	0.345396	+	0.345396i
$540$	−3.80799	−	1.20761i	−0.163870	−	0.0519673i
$541$	−7.67562	−	12.2157i	−0.330001	−	0.525193i	0.639975	−	0.768396i	$-0.278945\pi$
$541$	−7.67562	−	12.2157i	−0.330001	−	0.525193i	−0.969975	+	0.243203i	$0.921802\pi$
$542$	3.98158	+	0.298378i	0.171024	+	0.0128164i
$543$	27.0219	+	10.6875i	1.15962	+	0.458643i
$544$	−5.57987	−	6.01366i	−0.239235	−	0.257834i
$545$	3.60530	−	23.9196i	0.154434	−	1.02460i
$546$	−25.7427	+	2.83192i	−1.10168	+	0.121195i
$547$	24.7423	+	22.9575i	1.05790	+	0.981591i	0.999860	−	0.0167229i	$-0.00532330\pi$
$547$	24.7423	+	22.9575i	1.05790	+	0.981591i	0.0580435	+	0.998314i	$0.481514\pi$
$548$	0.516074	+	0.324271i	0.0220456	+	0.0138522i
$549$	−21.0401	−	18.3001i	−0.897969	−	0.781028i
$550$			28.5155i			1.21590i
$551$	−1.20363	−	13.8477i	−0.0512763	−	0.589931i
$552$	17.6712	−	9.28010i	0.752136	−	0.394987i
$553$	9.86821	+	22.6182i	0.419639	+	0.961823i
$554$	24.7953	+	0.927776i	1.05345	+	0.0394174i
$555$	6.32813	+	23.8680i	0.268614	+	1.01314i
$556$	−0.305298	−	2.02552i	−0.0129475	−	0.0859011i
$557$	16.2793	−	20.4135i	0.689774	−	0.864949i	−0.306439	−	0.951890i	$-0.599138\pi$
$557$	16.2793	−	20.4135i	0.689774	−	0.864949i	0.996213	+	0.0869408i	$0.0277091\pi$
$558$	6.14133	−	0.892627i	0.259983	−	0.0377879i
$559$	−12.2951	−	4.30224i	−0.520027	−	0.181965i
$560$	−3.07881	+	41.0839i	−0.130104	+	1.73611i
$561$	45.9561	+	0.120929i	1.94027	+	0.00510563i
$562$	31.4307	+	27.0483i	1.32582	+	1.14096i
$563$	−5.97613	−	1.60130i	−0.251864	−	0.0674867i	0.130678	−	0.991425i	$-0.458285\pi$
$563$	−5.97613	−	1.60130i	−0.251864	−	0.0674867i	−0.382542	+	0.923938i	$0.624951\pi$
$564$	1.04865	−	1.97157i	0.0441562	−	0.0830181i
$565$	46.1093	+	20.1173i	1.93983	+	0.846340i
$566$	4.32762	+	38.4087i	0.181904	+	1.61444i
$567$	25.0462	−	11.7385i	1.05184	−	0.492970i
$568$	−26.1955	+	26.1955i	−1.09914	+	1.09914i
$569$	3.61352	−	19.0979i	0.151487	−	0.800626i	−0.821579	−	0.570095i	$-0.806906\pi$
$569$	3.61352	−	19.0979i	0.151487	−	0.800626i	0.973065	−	0.230530i	$-0.0740461\pi$
$570$	−17.5606	+	10.0771i	−0.735532	+	0.422083i
$571$	11.6201	+	7.92246i	0.486286	+	0.331544i	0.781520	−	0.623881i	$-0.214445\pi$
$571$	11.6201	+	7.92246i	0.486286	+	0.331544i	−0.295233	+	0.955425i	$0.595397\pi$
$572$	−0.711958	−	3.76279i	−0.0297685	−	0.157330i
$573$	7.36457	−	20.8704i	0.307659	−	0.871873i
$574$	3.73692	+	9.52152i	0.155976	+	0.397421i
$575$	−14.0807	+	11.2290i	−0.587208	+	0.468283i
$576$	−6.05879	+	19.2813i	−0.252450	+	0.803385i
$577$	3.25424	−	5.17910i	0.135476	−	0.215609i	−0.772095	−	0.635507i	$-0.780791\pi$
$577$	3.25424	−	5.17910i	0.135476	−	0.215609i	0.907571	+	0.419898i	$0.137934\pi$
$578$	14.0392	−	19.0224i	0.583953	−	0.791228i
$579$	11.0515	+	21.0442i	0.459283	+	0.874569i
$580$	−3.53157	−	2.16084i	−0.146641	−	0.0897240i
$581$	−14.7855	+	8.53640i	−0.613405	+	0.354150i
$582$	−15.3309	−	39.3669i	−0.635488	−	1.63181i
$583$	−7.46502	+	3.94538i	−0.309169	+	0.163401i
$584$	−0.0651966	+	0.285645i	−0.00269785	+	0.0118201i
$585$	29.2417	−	2.03666i	1.20900	−	0.0842057i
$586$	−12.8167	−	10.2210i	−0.529455	−	0.422226i
$587$	6.97670	−	22.6179i	0.287959	−	0.933541i	−0.689834	−	0.723968i	$-0.742316\pi$
$587$	6.97670	−	22.6179i	0.287959	−	0.933541i	0.977793	−	0.209573i	$-0.0672075\pi$
$588$	0.671080	+	0.846065i	0.0276749	+	0.0348912i
$589$	2.00301	−	2.93787i	0.0825325	−	0.121053i
$590$	−27.0118	+	51.1089i	−1.11206	+	2.10412i
$591$	36.9017	−	11.2764i	1.51793	−	0.463849i
$592$	−20.2954	+	5.43813i	−0.834134	+	0.223506i
$593$	10.2065	+	4.91518i	0.419130	+	0.201842i	0.631548	−	0.775336i	$-0.282420\pi$
$593$	10.2065	+	4.91518i	0.419130	+	0.201842i	−0.212418	+	0.977179i	$0.568134\pi$
$594$	17.8419	+	31.4743i	0.732063	+	1.29141i
$595$	−52.7057	+	5.93850i	−2.16072	+	0.243455i
$596$	−2.81958	−	4.13557i	−0.115495	−	0.169399i
$597$	8.09314	+	8.76850i	0.331230	+	0.358871i
$598$	13.9553	−	16.2164i	0.570676	−	0.663137i
$599$	−30.7649	−	16.2597i	−1.25702	−	0.664355i	−0.299880	−	0.953977i	$-0.596946\pi$
$599$	−30.7649	−	16.2597i	−1.25702	−	0.664355i	−0.957141	+	0.289622i	$0.906470\pi$
$600$	2.12983	−	18.4659i	0.0869498	−	0.753866i
$601$	14.9229	+	17.3408i	0.608719	+	0.707344i	0.974760	−	0.223255i	$-0.0716681\pi$
$601$	14.9229	+	17.3408i	0.608719	+	0.707344i	−0.366041	+	0.930599i	$0.619287\pi$
$602$	4.12902	+	18.0904i	0.168286	+	0.737311i
$603$	13.0447	+	3.04967i	0.531219	+	0.124192i
$604$	3.82849	+	4.80078i	0.155779	+	0.195341i
$605$	21.5382	−	23.2126i	0.875651	−	0.943727i
$606$	3.48271	−	44.8882i	0.141475	−	1.82346i
$607$	−29.7766	+	12.9914i	−1.20860	+	0.527305i	−0.904966	−	0.425485i	$-0.860104\pi$
$607$	−29.7766	+	12.9914i	−1.20860	+	0.527305i	−0.303631	+	0.952790i	$0.598199\pi$
$608$	−1.85021	−	3.20465i	−0.0750357	−	0.129966i
$609$	28.1163	−	5.59035i	1.13933	−	0.226532i
$610$	−21.0474	+	36.4551i	−0.852183	+	1.47602i
$611$	−1.83459	+	16.2824i	−0.0742195	+	0.658717i
$612$	4.34606	+	0.512861i	0.175679	+	0.0207312i
$613$	6.89657	+	1.57410i	0.278550	+	0.0635772i	0.359514	−	0.933140i	$-0.382943\pi$
$613$	6.89657	+	1.57410i	0.278550	+	0.0635772i	−0.0809636	+	0.996717i	$0.525800\pi$
$614$	−8.31293	+	1.25297i	−0.335482	+	0.0505658i
$615$	−3.79494	−	10.9376i	−0.153027	−	0.441045i
$616$	27.3747	−	25.4000i	1.10296	−	1.02340i
$617$	27.1623	−	5.13938i	1.09351	−	0.206904i	0.392287	−	0.919843i	$-0.371684\pi$
$617$	27.1623	−	5.13938i	1.09351	−	0.206904i	0.701226	+	0.712939i	$0.252636\pi$
$618$	−12.7389	−	29.4089i	−0.512435	−	1.18300i
$619$	0.802117	+	21.4370i	0.0322398	+	0.861627i	0.917786	+	0.397076i	$0.129975\pi$
$619$	0.802117	+	21.4370i	0.0322398	+	0.861627i	−0.885546	+	0.464552i	$0.846216\pi$
$620$	−0.349798	−	0.999666i	−0.0140482	−	0.0401476i
$621$	−8.51589	+	21.2044i	−0.341731	+	0.850902i
$622$	5.10597	−	10.6027i	0.204731	−	0.425128i
$623$	−9.58331	+	21.9652i	−0.383947	+	0.880016i
$624$	1.79850	+	24.8776i	0.0719975	+	0.995899i
$625$	−2.14510	−	28.6244i	−0.0858040	−	1.14497i
$626$	−7.72258	+	28.8210i	−0.308656	+	1.15192i
$627$	20.1976	+	4.66592i	0.806615	+	0.186339i
$628$	3.85497	−	0.144243i	0.153830	−	0.00575592i
$629$	−11.7364	−	24.3709i	−0.467962	−	0.971732i
$630$	−24.6183	−	33.7266i	−0.980815	−	1.34370i
$631$	−25.6836	+	5.86211i	−1.02245	+	0.233367i	−0.700698	−	0.713458i	$-0.747128\pi$
$631$	−25.6836	+	5.86211i	−1.02245	+	0.233367i	−0.321749	+	0.946825i	$0.604271\pi$
$632$	19.5861	−	7.68699i	0.779095	−	0.305772i
$633$	3.77438	+	1.65858i	0.150018	+	0.0659226i
$634$	−4.05982	+	1.25229i	−0.161236	+	0.0497347i
$635$	0.0872261	−	2.33117i	0.00346146	−	0.0925095i
$636$	−0.749228	+	0.291778i	−0.0297088	+	0.0115697i
$637$	−6.86218	−	3.96188i	−0.271889	−	0.156975i
$638$	10.1350	+	36.1000i	0.401247	+	1.42921i
$639$	3.39195	−	42.2756i	0.134183	−	1.67240i
$640$	38.9108	+	4.38420i	1.53809	+	0.173301i
$641$	−13.7463	−	26.0092i	−0.542945	−	1.02730i	−0.991071	−	0.133332i	$-0.957432\pi$
$641$	−13.7463	−	26.0092i	−0.542945	−	1.02730i	0.448126	−	0.893970i	$-0.352091\pi$
$642$	28.8927	+	29.0452i	1.14031	+	1.14632i
$643$	−9.43768	−	3.70402i	−0.372186	−	0.146072i	0.171873	−	0.985119i	$-0.445018\pi$
$643$	−9.43768	−	3.70402i	−0.372186	−	0.146072i	−0.544059	+	0.839047i	$0.683113\pi$
$644$	−3.40694	−	0.513514i	−0.134252	−	0.0202353i
$645$	−3.85024	−	20.6462i	−0.151603	−	0.812945i
$646$	16.8112	−	14.4672i	0.661428	−	0.569205i
$647$	−0.271360	+	0.130680i	−0.0106683	+	0.00513756i	−0.439210	−	0.898384i	$-0.644742\pi$
$647$	−0.271360	+	0.130680i	−0.0106683	+	0.00513756i	0.428542	+	0.903522i	$0.359027\pi$
$648$	−9.20312	−	21.7145i	−0.361533	−	0.853028i
$649$	55.8657	−	19.5483i	2.19292	−	0.767336i
$650$	−5.15681	−	19.2455i	−0.202267	−	0.754870i
$651$	6.47435	+	3.44362i	0.253750	+	0.134966i
$652$	2.91078	−	2.14825i	0.113995	−	0.0841320i
$653$	−17.0872	+	12.6109i	−0.668674	+	0.493504i	−0.874463	−	0.485093i	$-0.838786\pi$
$653$	−17.0872	+	12.6109i	−0.668674	+	0.493504i	0.205789	+	0.978596i	$0.434024\pi$
$654$	−17.6932	+	11.0525i	−0.691857	+	0.432187i
$655$	−4.15829	−	15.5189i	−0.162478	−	0.606375i
$656$	9.29840	−	3.25365i	0.363042	−	0.127034i
$657$	−0.155171	−	0.297375i	−0.00605378	−	0.0116017i
$658$	21.0296	−	10.1273i	0.819820	−	0.394805i
$659$	2.18347	−	1.87903i	0.0850561	−	0.0731967i	−0.608732	−	0.793376i	$-0.708321\pi$
$659$	2.18347	−	1.87903i	0.0850561	−	0.0731967i	0.693788	+	0.720179i	$0.255941\pi$
$660$	4.69065	−	4.01520i	0.182583	−	0.156291i
$661$	−18.5654	−	2.79829i	−0.722112	−	0.108841i	−0.222304	−	0.974977i	$-0.571358\pi$
$661$	−18.5654	−	2.79829i	−0.722112	−	0.108841i	−0.499808	+	0.866136i	$0.666596\pi$
$662$	−8.32513	−	3.26737i	−0.323565	−	0.126990i
$663$	−31.0382	+	8.22919i	−1.20543	+	0.319595i
$664$	6.80195	+	12.8699i	0.263967	+	0.499450i
$665$	−23.7740	−	2.67869i	−0.921917	−	0.103875i
$666$	12.0885	−	17.5316i	0.468418	−	0.679334i
$667$	−13.8349	+	19.2203i	−0.535690	+	0.744212i
$668$	−1.66934	−	0.963794i	−0.0645887	−	0.0372903i
$669$	14.6295	+	11.7298i	0.565609	+	0.453498i
$670$	0.756160	−	20.2088i	0.0292130	−	0.780734i
$671$	41.1842	−	12.7036i	1.58990	−	0.490419i
$672$	6.15228	−	4.51563i	0.237329	−	0.174194i
$673$	−46.1531	+	18.1138i	−1.77907	+	0.698234i	−0.781874	+	0.623437i	$0.785736\pi$
$673$	−46.1531	+	18.1138i	−1.77907	+	0.698234i	−0.997199	+	0.0747977i	$0.976169\pi$
$674$	43.6801	−	9.96971i	1.68250	−	0.384019i
$675$	11.8485	+	17.6768i	0.456050	+	0.680380i
$676$	−0.276913	−	0.575016i	−0.0106505	−	0.0221160i
$677$	−16.6952	+	0.624690i	−0.641649	+	0.0240088i	−0.356236	−	0.934396i	$-0.615940\pi$
$677$	−16.6952	+	0.624690i	−0.641649	+	0.0240088i	−0.285413	+	0.958405i	$0.592131\pi$
$678$	−12.6789	−	41.4912i	−0.486929	−	1.59346i
$679$	12.9206	−	48.2202i	0.495846	−	1.85052i
$680$	3.37952	+	45.0965i	0.129599	+	1.72937i
$681$	−34.2514	−	16.6058i	−1.31252	−	0.636334i
$682$	−3.83566	+	8.79142i	−0.146875	+	0.336641i
$683$	0.724536	−	1.50452i	0.0277236	−	0.0575687i	−0.886647	−	0.462447i	$-0.846972\pi$
$683$	0.724536	−	1.50452i	0.0277236	−	0.0575687i	0.914371	+	0.404878i	$0.132686\pi$
$684$	1.85976	+	0.661764i	0.0711096	+	0.0253032i
$685$	−2.38151	−	6.80595i	−0.0909926	−	0.260042i
$686$	−0.785907	−	21.0038i	−0.0300061	−	0.801929i
$687$	0.493465	−	0.664952i	0.0188269	−	0.0253695i
$688$	17.5595	−	3.32244i	0.669451	−	0.126667i
$689$	4.32475	−	4.01278i	0.164760	−	0.152875i
$690$	33.8763	+	6.50213i	1.28965	+	0.247532i
$691$	−38.2041	+	5.75834i	−1.45335	+	0.219058i	−0.827756	−	0.561089i	$-0.810383\pi$
$691$	−38.2041	+	5.75834i	−1.45335	+	0.219058i	−0.625597	+	0.780146i	$0.715145\pi$
$692$	−0.243131	−	0.0554931i	−0.00924246	−	0.00210953i
$693$	−5.01021	+	42.4573i	−0.190322	+	1.61282i
$694$	0.197792	−	1.75545i	0.00750807	−	0.0666360i
$695$	−12.1167	+	20.9868i	−0.459613	+	0.796074i
$696$	−3.86681	−	24.1344i	−0.146571	−	0.914811i
$697$	6.34116	+	10.9832i	0.240189	+	0.416019i
$698$	33.6225	−	14.6693i	1.27263	−	0.555243i
$699$	−13.7271	−	9.41196i	−0.519205	−	0.355993i
$700$	−2.18246	+	2.35213i	−0.0824892	+	0.0889023i
$701$	2.22477	+	2.78978i	0.0840285	+	0.105368i	0.822069	−	0.569388i	$-0.192820\pi$
$701$	2.22477	+	2.78978i	0.0840285	+	0.105368i	−0.738040	+	0.674757i	$0.764249\pi$
$702$	−17.7336	−	18.0159i	−0.669313	−	0.679965i
$703$	−2.71505	−	11.8954i	−0.102400	−	0.448645i
$704$	−20.3759	−	23.6773i	−0.767946	−	0.892370i
$705$	−24.2420	+	10.5008i	−0.913007	+	0.395484i
$706$	0.941059	+	0.497364i	0.0354172	+	0.0187185i
$707$	34.7029	−	40.3255i	1.30514	−	1.51660i
$708$	5.49811	−	1.23970i	0.206632	−	0.0465906i
$709$	1.15832	+	1.69894i	0.0435016	+	0.0638051i	0.847373	−	0.530997i	$-0.178183\pi$
$709$	1.15832	+	1.69894i	0.0435016	+	0.0638051i	−0.803872	+	0.594803i	$0.797230\pi$
$710$	−63.6209	+	7.16836i	−2.38765	+	0.269024i
$711$	−11.3674	+	21.2369i	−0.426312	+	0.796448i
$712$	18.4096	+	8.86560i	0.689929	+	0.332253i
$713$	−5.85157	+	1.56792i	−0.219143	+	0.0587192i
$714$	33.4490	+	31.2004i	1.25180	+	1.16764i
$715$	−21.1697	+	40.0551i	−0.791703	+	1.49798i
$716$	−3.28106	+	4.81243i	−0.122619	+	0.179849i
$717$	34.6876	−	5.13500i	1.29543	−	0.191770i
$718$	1.32855	−	4.30706i	0.0495811	−	0.160738i
$719$	−30.9936	−	24.7165i	−1.15587	−	0.921772i	−0.158023	−	0.987435i	$-0.550512\pi$
$719$	−30.9936	−	24.7165i	−1.15587	−	0.921772i	−0.997842	+	0.0656638i	$0.979084\pi$
$720$	−33.3462	+	22.4789i	−1.24274	+	0.837738i
$721$	8.42717	−	36.9218i	0.313844	−	1.37504i
$722$	−16.3798	+	8.65697i	−0.609593	+	0.322179i
$723$	−17.4056	+	21.7084i	−0.647320	+	0.807346i
$724$	−3.70387	+	2.13843i	−0.137653	+	0.0794742i
$725$	7.53137	+	20.7287i	0.279708	+	0.769845i
$726$	−27.2871	−	1.09292i	−1.01272	−	0.0405621i
$727$	8.49832	−	11.5148i	0.315185	−	0.427061i	−0.618154	−	0.786057i	$-0.712119\pi$
$727$	8.49832	−	11.5148i	0.315185	−	0.427061i	0.933339	+	0.358996i	$0.116881\pi$
$728$	−13.8822	+	22.0933i	−0.514507	+	0.818833i
$729$	24.1382	+	12.0975i	0.894007	+	0.448054i
$730$	−0.395880	+	0.315704i	−0.0146522	+	0.0116847i
$731$	8.40540	+	21.4166i	0.310885	+	0.792122i
$732$	4.03458	−	0.752393i	0.149122	−	0.0278092i
$733$	−3.31735	−	17.5326i	−0.122529	−	0.647582i	−0.988948	−	0.148264i	$-0.952632\pi$
$733$	−3.31735	−	17.5326i	−0.122529	−	0.647582i	0.866419	−	0.499318i	$-0.166416\pi$
$734$	21.0190	+	14.3305i	0.775827	+	0.528950i
$735$	0.0336178	−	12.7756i	0.00124001	−	0.471235i
$736$	−1.17208	+	6.19460i	−0.0432035	+	0.228336i
$737$	−14.6409	+	14.6409i	−0.539305	+	0.539305i
$738$	−5.03760	+	8.62029i	−0.185437	+	0.317317i
$739$	1.15029	+	10.2091i	0.0423139	+	0.375546i	0.996967	+	0.0778258i	$0.0247978\pi$
$739$	1.15029	+	10.2091i	0.0423139	+	0.375546i	−0.954653	+	0.297721i	$0.903774\pi$
$740$	−3.33103	−	1.45331i	−0.122451	−	0.0534249i
$741$	−14.4754	+	0.503492i	−0.531768	+	0.0184962i
$742$	−8.11770	−	2.17513i	−0.298010	−	0.0798516i
$743$	7.99364	+	6.87908i	0.293258	+	0.252369i	0.786595	−	0.617469i	$-0.211842\pi$
$743$	7.99364	+	6.87908i	0.293258	+	0.252369i	−0.493337	+	0.869838i	$0.664223\pi$
$744$	3.14050	−	5.40660i	0.115136	−	0.198216i
$745$	−4.42513	+	59.0492i	−0.162124	+	2.16340i
$746$	−5.48104	−	1.91790i	−0.200675	−	0.0702193i
$747$	−15.4809	−	6.17000i	−0.566415	−	0.225749i
$748$	−4.21720	+	5.28820i	−0.154196	+	0.193356i
$749$	7.21523	+	47.8699i	0.263639	+	1.74913i
$750$	−5.03048	+	5.00408i	−0.183687	+	0.182723i
$751$	−33.4970	−	1.25337i	−1.22232	−	0.0457361i	−0.581578	−	0.813491i	$-0.697564\pi$
$751$	−33.4970	−	1.25337i	−1.22232	−	0.0457361i	−0.640744	+	0.767755i	$0.721374\pi$
$752$	−8.98957	−	20.6043i	−0.327816	−	0.751362i
$753$	−0.276886	+	6.91303i	−0.0100903	+	0.251925i
$754$	−13.3686	−	22.5315i	−0.486857	−	0.820551i
$755$		−	72.6439i		−	2.64378i
$756$	−0.937206	+	3.96174i	−0.0340859	+	0.144087i
$757$	35.0152	+	22.0015i	1.27265	+	0.799659i	0.987316	−	0.158770i	$-0.0507527\pi$
$757$	35.0152	+	22.0015i	1.27265	+	0.799659i	0.285334	+	0.958428i	$0.407896\pi$
$758$	−20.0400	−	18.5944i	−0.727884	−	0.675378i
$759$	−20.8975	−	28.4716i	−0.758530	−	1.03345i
$760$	−3.04028	+	20.1710i	−0.110283	+	0.731677i
$761$	−12.7450	−	13.7358i	−0.462004	−	0.497922i	0.458478	−	0.888706i	$-0.348395\pi$
$761$	−12.7450	−	13.7358i	−0.462004	−	0.497922i	−0.920483	+	0.390783i	$0.872204\pi$
$762$	−1.57621	+	1.25022i	−0.0571001	+	0.0452905i
$763$	−24.5823	−	1.84219i	−0.889939	−	0.0666917i
$764$	1.73301	+	2.75807i	0.0626982	+	0.0997836i
$765$	−36.4156	−	36.8009i	−1.31661	−	1.33054i
$766$	−14.4522	−	14.4522i	−0.522180	−	0.522180i
$767$	−34.1694	+	23.2963i	−1.23378	+	0.841180i
$768$	−5.85393	−	8.63487i	−0.211236	−	0.311584i
$769$	28.7284	+	38.9256i	1.03597	+	1.40369i	0.911419	+	0.411480i	$0.134988\pi$
$769$	28.7284	+	38.9256i	1.03597	+	1.40369i	0.124554	+	0.992213i	$0.460250\pi$
$770$	64.3570	−	4.82289i	2.31927	−	0.173805i
$771$	−8.81040	−	2.74306i	−0.317299	−	0.0987889i
$772$	−3.43743	−	0.650398i	−0.123716	−	0.0234083i
$773$	8.35767	−	5.25147i	0.300604	−	0.188882i	−0.373281	−	0.927718i	$-0.621767\pi$
$773$	8.35767	−	5.25147i	0.300604	−	0.188882i	0.673885	+	0.738836i	$0.264624\pi$
$774$	−11.3674	+	14.1013i	−0.408591	+	0.506862i
$775$	−1.86335	+	5.32514i	−0.0669335	+	0.191285i
$776$	−40.6735	−	12.5461i	−1.46009	−	0.450379i
$777$	23.7733	−	8.24850i	0.852864	−	0.295913i
$778$	4.90561	−	12.4993i	0.175875	−	0.448121i
$779$	1.68619	+	5.46648i	0.0604139	+	0.195857i
$780$	−2.43966	+	3.55818i	−0.0873540	+	0.127403i
$781$	52.7421	+	38.9254i	1.88726	+	1.39286i
$782$	−37.7874			−1.35128
$783$	21.2826	+	18.1673i	0.760579	+	0.649245i
$784$	10.8710			0.388249
$785$	−36.7202	−	27.1007i	−1.31060	−	0.967266i
$786$	−7.83538	+	11.4277i	−0.279479	+	0.407612i
$787$	7.88984	+	25.5782i	0.281242	+	0.911765i	0.980437	+	0.196834i	$0.0630659\pi$
$787$	7.88984	+	25.5782i	0.281242	+	0.911765i	−0.699195	+	0.714931i	$0.746458\pi$
$788$	−2.07482	+	5.28655i	−0.0739123	+	0.188326i
$789$	30.1608	−	10.4647i	1.07375	−	0.372553i
$790$	34.7471	+	10.7181i	1.23625	+	0.381332i
$791$	16.9322	−	48.3895i	0.602041	−	1.72053i
$792$	36.0155	+	5.62247i	1.27975	+	0.199786i
$793$	−25.4984	+	16.0217i	−0.905475	+	0.568948i
$794$	−28.8755	−	5.46353i	−1.02475	−	0.193893i
$795$	9.08211	+	2.82765i	0.322109	+	0.100287i
$796$	−1.75133	+	0.131244i	−0.0620741	+	0.00465181i
$797$	−22.0285	−	29.8476i	−0.780291	−	1.05726i	−0.996718	−	0.0809580i	$-0.974202\pi$
$797$	−22.0285	−	29.8476i	−0.780291	−	1.05726i	0.216426	−	0.976299i	$-0.430560\pi$
$798$	11.5779	+	17.0781i	0.409855	+	0.604559i
$799$	23.9117	−	16.3027i	0.845936	−	0.576749i
$800$	4.15165	+	4.15165i	0.146783	+	0.146783i
$801$	−22.6269	+	5.93541i	−0.799483	+	0.209718i
$802$	−8.18907	−	13.0328i	−0.289166	−	0.460205i
$803$	0.516980	+	0.0387423i	0.0182438	+	0.00136719i
$804$	−1.54476	+	1.22527i	−0.0544794	+	0.0432118i
$805$	27.7244	+	29.8798i	0.977158	+	1.05313i
$806$	0.998874	−	6.62710i	0.0351838	−	0.233430i
$807$	16.6653	+	22.7054i	0.586645	+	0.799270i
$808$	−33.2525	−	30.8538i	−1.16982	−	1.08543i
$809$	−38.4908	−	24.1854i	−1.35326	−	0.850312i	−0.356788	−	0.934185i	$-0.616128\pi$
$809$	−38.4908	−	24.1854i	−1.35326	−	0.850312i	−0.996476	+	0.0838730i	$0.973271\pi$
$810$	10.9629	−	39.2566i	0.385198	−	1.37934i
$811$			1.56852i			0.0550782i	0.999621	+	0.0275391i	$0.00876708\pi$
$811$			1.56852i			0.0550782i	−0.999621	+	0.0275391i	$0.991233\pi$
$812$	−1.92696	+	3.75344i	−0.0676229	+	0.131720i
$813$	−0.184310	+	4.60170i	−0.00646405	+	0.161389i
$814$	13.1619	+	30.1675i	0.461326	+	1.05737i
$815$	−42.7688	−	1.60029i	−1.49812	−	0.0560559i
$816$	31.2328	−	31.0689i	1.09337	−	1.08763i
$817$	1.54673	+	10.2619i	0.0541133	+	0.359018i
$818$	−17.2680	+	21.6534i	−0.603761	+	0.757092i
$819$	−4.29663	−	29.5611i	−0.150137	−	1.03295i
$820$	1.60832	+	0.562775i	0.0561649	+	0.0196530i
$821$	−0.274378	+	3.66131i	−0.00957584	+	0.127781i	−0.999943	−	0.0106862i	$-0.996598\pi$
$821$	−0.274378	+	3.66131i	−0.00957584	+	0.127781i	0.990367	+	0.138467i	$0.0442175\pi$
$822$	−3.12341	+	5.37718i	−0.108941	+	0.187551i
$823$	−22.7490	−	19.5771i	−0.792981	−	0.682415i	0.159438	−	0.987208i	$-0.449032\pi$
$823$	−22.7490	−	19.5771i	−0.792981	−	0.682415i	−0.952419	+	0.304793i	$0.901413\pi$
$824$	−31.1901	−	8.35736i	−1.08656	−	0.291143i
$825$	−32.8710	+	1.14334i	−1.14442	+	0.0398059i
$826$	53.9953	+	23.5579i	1.87874	+	0.819685i
$827$	−2.06721	−	18.3470i	−0.0718841	−	0.637989i	−0.977062	−	0.212956i	$-0.931691\pi$
$827$	−2.06721	−	18.3470i	−0.0718841	−	0.637989i	0.905178	−	0.425033i	$-0.139738\pi$
$828$	−1.66622	−	2.92138i	−0.0579052	−	0.101525i
$829$	3.55491	−	3.55491i	0.123467	−	0.123467i	−0.642673	−	0.766140i	$-0.722175\pi$
$829$	3.55491	−	3.55491i	0.123467	−	0.123467i	0.766140	+	0.642673i	$0.222175\pi$
$830$	−4.67703	+	24.7187i	−0.162342	+	0.857999i
$831$	−0.0753105	+	28.6198i	−0.00261249	+	0.992811i
$832$	18.0338	+	12.2953i	0.625211	+	0.426262i
$833$	2.60186	+	13.7512i	0.0901492	+	0.476450i
$834$	20.5450	−	3.83136i	0.711416	−	0.132669i
$835$	8.33131	+	21.2278i	0.288317	+	0.734620i
$836$	−2.38535	+	1.90226i	−0.0824992	+	0.0657909i
$837$	1.27521	+	7.04357i	0.0440776	+	0.243462i
$838$	−18.0963	+	28.8001i	−0.625127	+	0.994883i
$839$	−5.68891	+	7.70820i	−0.196403	+	0.266117i	−0.891721	−	0.452586i	$-0.850502\pi$
$839$	−5.68891	+	7.70820i	−0.196403	+	0.266117i	0.695318	+	0.718702i	$0.255264\pi$
$840$	−42.0361	−	1.68366i	−1.45038	−	0.0580918i
$841$	16.9019	+	23.5653i	0.582825	+	0.812597i
$842$	−13.5552	+	7.82612i	−0.467144	+	0.269706i
$843$	−29.9195	+	37.3160i	−1.03048	+	1.28523i
$844$	−0.536466	+	0.283531i	−0.0184659	+	0.00975953i
$845$	−1.68013	+	7.36111i	−0.0577981	+	0.253230i
$846$	20.4751	+	9.99339i	0.703950	+	0.343580i
$847$	−25.2295	−	20.1199i	−0.866897	−	0.691328i
$848$	−2.38575	+	7.73441i	−0.0819270	+	0.265601i
$849$	−44.1018	+	6.52864i	−1.51357	+	0.224062i
$850$	−19.8238	+	29.0762i	−0.679951	+	0.997304i
$851$	−9.71350	+	18.3788i	−0.332974	+	0.630018i
$852$	4.56462	+	4.25776i	0.156381	+	0.145868i
$853$	−26.6569	+	7.14269i	−0.912714	+	0.244561i	−0.684468	−	0.729043i	$-0.739966\pi$
$853$	−26.6569	+	7.14269i	−0.912714	+	0.244561i	−0.228246	+	0.973604i	$0.573299\pi$
$854$	38.6495	+	18.6126i	1.32256	+	0.636911i
$855$	−12.3204	−	19.8388i	−0.421348	−	0.678472i
$856$	41.0170	−	4.62150i	1.40193	−	0.157960i
$857$	10.8074	+	15.8515i	0.369173	+	0.541478i	0.965209	−	0.261480i	$-0.0842106\pi$
$857$	10.8074	+	15.8515i	0.369173	+	0.541478i	−0.596035	+	0.802958i	$0.703258\pi$
$858$	38.1150	−	8.59404i	1.30122	−	0.293396i
$859$	10.3170	−	11.9886i	0.352012	−	0.409045i	−0.553852	−	0.832615i	$-0.686842\pi$
$859$	10.3170	−	11.9886i	0.352012	−	0.409045i	0.905863	+	0.423571i	$0.139223\pi$
$860$	2.73290	+	1.44438i	0.0931911	+	0.0492529i
$861$	−10.8260	+	4.68948i	−0.368950	+	0.159817i
$862$	−12.7903	−	14.8626i	−0.435639	−	0.506221i
$863$	0.546926	+	2.39624i	0.0186176	+	0.0815689i	0.983383	−	0.181542i	$-0.0581087\pi$
$863$	0.546926	+	2.39624i	0.0186176	+	0.0815689i	−0.964766	+	0.263111i	$0.915252\pi$
$864$	7.18009	+	1.98478i	0.244272	+	0.0675236i
$865$	1.83949	+	2.30665i	0.0625447	+	0.0784285i
$866$	10.3822	−	11.1893i	0.352801	−	0.380229i
$867$	22.4908	+	15.4208i	0.763829	+	0.523719i
$868$	−0.989248	+	0.431605i	−0.0335773	+	0.0146496i
$869$	−18.6150	−	32.2422i	−0.631472	−	1.09374i
$870$	20.7806	−	36.7762i	0.704529	−	1.24683i
$871$	7.23365	−	12.5291i	0.245103	−	0.424531i
$872$	−2.35332	+	20.8863i	−0.0796935	+	0.707299i
$873$	44.7652	−	19.2511i	1.51507	−	0.651549i
$874$	−16.6175	−	3.79283i	−0.562095	−	0.128294i
$875$	−8.29084	+	1.24964i	−0.280281	+	0.0422456i
$876$	0.0484829	+	0.00930568i	0.00163809	+	0.000314410i
$877$	−37.1202	+	34.4425i	−1.25346	+	1.16304i	−0.273927	+	0.961751i	$0.588323\pi$
$877$	−37.1202	+	34.4425i	−1.25346	+	1.16304i	−0.979532	+	0.201289i	$0.935487\pi$
$878$	31.9491	−	6.04510i	1.07823	−	0.204012i
$879$	11.2683	−	15.1842i	0.380070	−	0.512151i
$880$	−2.32410	−	62.1130i	−0.0783455	−	2.09383i
$881$	−1.95517	−	5.58755i	−0.0658712	−	0.188249i	0.906243	−	0.422757i	$-0.138938\pi$
$881$	−1.95517	−	5.58755i	−0.0658712	−	0.188249i	−0.972114	+	0.234508i	$0.924652\pi$
$882$	−8.38894	+	7.14277i	−0.282470	+	0.240510i
$883$	6.35820	−	13.2029i	0.213970	−	0.444314i	−0.766165	−	0.642644i	$-0.777837\pi$
$883$	6.35820	−	13.2029i	0.213970	−	0.444314i	0.980135	+	0.198330i	$0.0635517\pi$
$884$	1.88991	−	4.33172i	0.0635646	−	0.145692i
$885$	−59.9984	−	29.0885i	−2.01683	−	0.977798i
$886$	−2.40696	−	32.1187i	−0.0808634	−	1.07905i
$887$	6.45282	−	24.0823i	0.216665	−	0.808603i	−0.768909	−	0.639358i	$-0.779200\pi$
$887$	6.45282	−	24.0823i	0.216665	−	0.808603i	0.985574	−	0.169245i	$-0.0541330\pi$
$888$	−6.27011	−	20.5187i	−0.210411	−	0.688563i
$889$	−2.37564	+	0.0888901i	−0.0796763	+	0.00298128i
$890$	15.3216	+	31.8157i	0.513583	+	1.06647i
$891$	−35.5664	+	21.8291i	−1.19152	+	0.731302i
$892$	−2.69062	+	0.614117i	−0.0900887	+	0.0205622i
$893$	12.1518	−	4.76924i	0.406645	−	0.159596i
$894$	41.1685	−	30.2167i	1.37688	−	1.01060i
$895$	65.8451	−	20.3105i	2.20096	−	0.678906i
$896$	1.49206	−	39.8761i	0.0498462	−	1.33217i
$897$	19.2528	+	15.4367i	0.642834	+	0.515416i
$898$	−35.4400	−	20.4613i	−1.18265	−	0.682802i
$899$	−0.466301	+	7.40379i	−0.0155520	+	0.246930i
$900$	−3.12203	−	0.250493i	−0.104068	−	0.00834978i
$901$	−10.3546	−	1.16668i	−0.344962	−	0.0388678i
$902$	−7.21075	−	13.6434i	−0.240092	−	0.454276i
$903$	−20.6881	+	5.48504i	−0.688455	+	0.182531i
$904$	−40.6898	−	15.9696i	−1.35332	−	0.531141i
$905$	50.0320	+	7.54112i	1.66312	+	0.250675i
$906$	−47.5936	+	40.7401i	−1.58119	+	1.35350i
$907$	−28.0212	+	24.1142i	−0.930430	+	0.800699i	−0.980190	−	0.198062i	$-0.936535\pi$
$907$	−28.0212	+	24.1142i	−0.930430	+	0.800699i	0.0497600	+	0.998761i	$0.484154\pi$
$908$	5.04754	−	2.43077i	0.167509	−	0.0806679i
$909$	51.8841	+	2.21486i	1.72089	+	0.0734623i
$910$	−42.5632	+	14.8935i	−1.41096	+	0.493715i
$911$	10.8747	+	40.5849i	0.360295	+	1.34464i	0.873689	+	0.486486i	$0.161721\pi$
$911$	10.8747	+	40.5849i	0.360295	+	1.34464i	−0.513394	+	0.858153i	$0.671612\pi$
$912$	16.8535	−	10.5280i	0.558074	−	0.348616i
$913$	20.7244	−	15.2953i	0.685878	−	0.506201i
$914$	−10.7387	+	7.92554i	−0.355205	+	0.262154i
$915$	−42.8672	−	22.8005i	−1.41715	−	0.753762i
$916$	0.0315430	+	0.117720i	0.00104221	+	0.00388959i
$917$	−15.4541	+	5.40762i	−0.510339	+	0.178575i
$918$	−3.68803	+	44.4968i	−0.121723	+	1.46861i
$919$	−2.85134	+	1.37313i	−0.0940571	+	0.0452955i	−0.480321	−	0.877093i	$-0.659480\pi$
$919$	−2.85134	+	1.37313i	−0.0940571	+	0.0452955i	0.386264	+	0.922388i	$0.373765\pi$
$920$	26.3426	−	22.6696i	0.868490	−	0.747396i
$921$	−1.77766	−	9.53242i	−0.0585760	−	0.314104i
$922$	13.7279	+	2.06915i	0.452105	+	0.0681439i
$923$	−42.6357	−	16.7333i	−1.40337	−	0.550783i
$924$	−4.43757	−	4.46098i	−0.145985	−	0.146756i
$925$	9.04607	+	17.1160i	0.297433	+	0.562771i
$926$	−41.7015	−	4.69863i	−1.37040	−	0.154407i
$927$	33.3900	−	15.8639i	1.09667	−	0.521038i
$928$	6.73147	+	3.78032i	0.220971	+	0.124095i
$929$	18.1758	+	10.4938i	0.596329	+	0.344291i	0.767596	−	0.640934i	$-0.221453\pi$
$929$	18.1758	+	10.4938i	0.596329	+	0.344291i	−0.171267	+	0.985225i	$0.554786\pi$
$930$	10.0691	−	3.92128i	0.330178	−	0.128584i
$931$	−0.236044	+	6.30840i	−0.00773602	+	0.206750i
$932$	2.34082	−	0.722046i	0.0766760	−	0.0236514i
$933$	12.4269	+	5.46075i	0.406837	+	0.178777i
$934$	37.2038	−	14.6014i	1.21735	−	0.477773i
$935$	78.0131	−	17.8060i	2.55130	−	0.582318i
$936$	−25.3241	+	2.71845i	−0.827745	+	0.0888555i
$937$	−6.88417	−	14.2951i	−0.224896	−	0.467002i	0.757737	−	0.652560i	$-0.226305\pi$
$937$	−6.88417	−	14.2951i	−0.224896	−	0.467002i	−0.982633	+	0.185558i	$0.940591\pi$
$938$	−20.5943	+	0.770584i	−0.672428	+	0.0251605i
$939$	−33.5329	−	7.74655i	−1.09430	−	0.252799i
$940$	1.00637	−	3.75581i	0.0328241	−	0.122501i
$941$	0.634948	+	8.47279i	0.0206987	+	0.276205i	0.997944	+	0.0640926i	$0.0204153\pi$
$941$	0.634948	+	8.47279i	0.0206987	+	0.276205i	−0.977245	+	0.212113i	$0.931966\pi$
$942$	2.83799	+	39.2563i	0.0924667	+	1.27904i
$943$	3.89752	−	8.93321i	0.126921	−	0.290905i
$944$	24.6174	−	51.1185i	0.801228	−	1.66377i
$945$	37.8910	−	29.7308i	1.23260	−	0.967143i
$946$	−9.24605	−	26.4237i	−0.300615	−	0.859108i
$947$	−0.997906	−	26.6696i	−0.0324276	−	0.866645i	−0.916677	−	0.399630i	$-0.869139\pi$
$947$	−0.997906	−	26.6696i	−0.0324276	−	0.866645i	0.884249	−	0.467016i	$-0.154671\pi$
$948$	−1.40917	−	3.25318i	−0.0457677	−	0.105658i
$949$	−0.355923	+	0.0673443i	−0.0115538	+	0.00218609i
$950$	−11.6362	+	10.7968i	−0.377529	+	0.350295i
$951$	−1.60635	−	4.62971i	−0.0520893	−	0.150129i
$952$	45.5709	−	6.86871i	1.47696	−	0.222616i
$953$	33.0551	+	7.54461i	1.07076	+	0.244394i	0.721346	−	0.692575i	$-0.243524\pi$
$953$	33.0551	+	7.54461i	1.07076	+	0.244394i	0.349414	+	0.936969i	$0.386381\pi$
$954$	−3.24085	−	7.53606i	−0.104926	−	0.243989i
$955$	4.31464	−	38.2935i	0.139619	−	1.23915i
$956$	−2.58049	+	4.46953i	−0.0834589	+	0.144555i
$957$	−41.2076	+	13.1304i	−1.33205	+	0.424446i
$958$	3.39263	+	5.87620i	0.109611	+	0.189851i
$959$	−6.73502	+	2.93846i	−0.217485	+	0.0948879i
$960$	−2.72217	+	35.0857i	−0.0878578	+	1.13239i
$961$	19.7946	−	21.3335i	0.638535	−	0.688177i
$962$	−14.3387	−	17.9802i	−0.462300	−	0.579705i
$963$	−32.3231	+	34.4704i	−1.04160	+	1.11079i
$964$	−0.911277	−	3.99256i	−0.0293503	−	0.128592i
$965$	26.9968	+	31.3708i	0.869058	+	1.00986i
$966$	4.02776	−	34.9212i	0.129591	−	1.12357i
$967$	−26.9859	−	14.2625i	−0.867808	−	0.458650i	−0.0267797	−	0.999641i	$-0.508525\pi$
$967$	−26.9859	−	14.2625i	−0.867808	−	0.458650i	−0.841028	+	0.540992i	$0.818049\pi$
$968$	−17.9472	+	20.8551i	−0.576846	+	0.670307i
$969$	17.3510	+	18.7989i	0.557395	+	0.603908i
$970$	−41.4381	−	60.7785i	−1.33050	−	1.95148i
$971$	−22.9847	+	2.58975i	−0.737613	+	0.0831091i	−0.472774	−	0.881184i	$-0.656747\pi$
$971$	−22.9847	+	2.58975i	−0.737613	+	0.0831091i	−0.264839	+	0.964293i	$0.585319\pi$
$972$	−3.60271	+	1.67694i	−0.115557	+	0.0537880i
$973$	22.2501	+	10.7151i	0.713305	+	0.343509i
$974$	19.5147	−	5.22895i	0.625291	−	0.167546i
$975$	21.9783	−	6.71613i	0.703870	−	0.215088i
$976$	19.3052	−	36.5273i	0.617946	−	1.16921i
$977$	−15.4426	+	22.6502i	−0.494053	+	0.724643i	−0.989585	−	0.143947i	$-0.954021\pi$
$977$	−15.4426	+	22.6502i	−0.494053	+	0.724643i	0.495532	+	0.868589i	$0.334973\pi$
$978$	22.9371	+	28.9180i	0.733447	+	0.924695i
$979$	10.6569	−	34.5490i	0.340597	−	1.10419i
$980$	1.47010	+	1.17236i	0.0469605	+	0.0374498i
$981$	−13.4501	−	19.9525i	−0.429429	−	0.637034i
$982$	10.7349	−	47.0325i	0.342563	−	1.50087i
$983$	22.5732	−	11.9303i	0.719973	−	0.380517i	−0.0667942	−	0.997767i	$-0.521277\pi$
$983$	22.5732	−	11.9303i	0.719973	−	0.380517i	0.786767	+	0.617250i	$0.211753\pi$
$984$	3.65046	+	9.37368i	0.116372	+	0.298822i
$985$	58.1853	−	33.5933i	1.85394	−	1.07037i
$986$	−14.7623	+	43.8556i	−0.470127	+	1.39665i
$987$	12.5174	+	23.8357i	0.398433	+	0.758698i
$988$	1.26590	−	1.71523i	0.0402736	−	0.0545688i
$989$	9.40686	−	14.9709i	0.299121	−	0.476048i
$990$	42.6047	+	46.4044i	1.35407	+	1.47483i
$991$	−32.2352	+	25.7067i	−1.02399	+	0.816601i	−0.983194	−	0.182566i	$-0.941560\pi$
$991$	−32.2352	+	25.7067i	−1.02399	+	0.816601i	−0.0407921	+	0.999168i	$0.512988\pi$
$992$	0.721523	+	1.83841i	0.0229084	+	0.0583696i
$993$	3.43264	−	9.72773i	0.108931	−	0.308700i
$994$	12.1298	+	64.1074i	0.384733	+	2.03336i
$995$	17.1668	+	11.7041i	0.544224	+	0.371046i
$996$	2.12739	−	1.22079i	0.0674088	−	0.0386824i
$997$	0.277283	−	1.46547i	0.00878163	−	0.0464120i	−0.977902	−	0.209066i	$-0.932958\pi$
$997$	0.277283	−	1.46547i	0.00878163	−	0.0464120i	0.986683	+	0.162654i	$0.0520053\pi$
$998$	−4.84808	+	4.84808i	−0.153463	+	0.153463i
$999$	20.6941	+	13.2319i	0.654731	+	0.418640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.2.8	✓	672
3.2	odd	2		783.2.be.a.89.21		672
9.4	even	3		783.2.be.a.611.21		672
9.5	odd	6	inner	261.2.x.a.176.8	yes	672
29.15	odd	28	inner	261.2.x.a.218.8	yes	672
87.44	even	28		783.2.be.a.305.21		672
261.131	even	84	inner	261.2.x.a.131.8	yes	672
261.247	odd	84		783.2.be.a.44.21		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.2.8	✓	672	1.1	even	1	trivial
261.2.x.a.131.8	yes	672	261.131	even	84	inner
261.2.x.a.176.8	yes	672	9.5	odd	6	inner
261.2.x.a.218.8	yes	672	29.15	odd	28	inner
783.2.be.a.44.21		672	261.247	odd	84
783.2.be.a.89.21		672	3.2	odd	2
783.2.be.a.305.21		672	87.44	even	28
783.2.be.a.611.21		672	9.4	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20822 - 0.891704i) q^{2} +(0.979461 - 1.42852i) q^{3} +(0.0751402 + 0.243598i) q^{4} +(1.10182 - 2.80739i) q^{5} +(-2.45721 + 0.852566i) q^{6} +(-2.93685 - 0.905898i) q^{7} +(-0.865489 + 2.47342i) q^{8} +(-1.08131 - 2.79835i) q^{9} +O(q^{10})\)	\(q+(-1.20822 - 0.891704i) q^{2} +(0.979461 - 1.42852i) q^{3} +(0.0751402 + 0.243598i) q^{4} +(1.10182 - 2.80739i) q^{5} +(-2.45721 + 0.852566i) q^{6} +(-2.93685 - 0.905898i) q^{7} +(-0.865489 + 2.47342i) q^{8} +(-1.08131 - 2.79835i) q^{9} +(-3.83459 + 2.40943i) q^{10} +(4.55594 + 0.862031i) q^{11} +(0.421581 + 0.131256i) q^{12} +(-3.23076 + 0.242112i) q^{13} +(2.74056 + 3.71332i) q^{14} +(-2.93121 - 4.32369i) q^{15} +(3.67252 - 2.50388i) q^{16} +(4.04625 + 4.04625i) q^{17} +(-1.18884 + 4.34522i) q^{18} +(1.37325 + 2.18552i) q^{19} +(0.766666 + 0.0574536i) q^{20} +(-4.17062 + 3.30804i) q^{21} +(-4.73589 - 5.10408i) q^{22} +(0.655426 - 4.34847i) q^{23} +(2.68561 + 3.65899i) q^{24} +(-3.00216 - 2.78559i) q^{25} +(4.11935 + 2.58836i) q^{26} +(-5.05659 - 1.19621i) q^{27} -0.783481i q^{28} +(-4.79072 - 2.45948i) q^{29} +(-0.313922 + 7.83772i) q^{30} +(-0.550880 - 1.26263i) q^{31} +(-1.43263 - 0.0536052i) q^{32} +(5.69380 - 5.66391i) q^{33} +(-1.28069 - 8.49680i) q^{34} +(-5.77908 + 7.24674i) q^{35} +(0.600424 - 0.473674i) q^{36} +(-4.46183 - 1.56126i) q^{37} +(0.289650 - 3.86512i) q^{38} +(-2.81854 + 4.85233i) q^{39} +(5.99025 + 5.15502i) q^{40} +(2.14080 + 0.573625i) q^{41} +(7.98881 - 0.277871i) q^{42} +(3.68514 + 1.60781i) q^{43} +(0.132345 + 1.17459i) q^{44} +(-9.04746 - 0.0476154i) q^{45} +(-4.66944 + 4.66944i) q^{46} +(0.940252 - 4.96935i) q^{47} +(0.0202584 - 7.69870i) q^{48} +(2.02077 + 1.37774i) q^{49} +(1.14333 + 6.04263i) q^{50} +(9.74326 - 1.81698i) q^{51} +(-0.301738 - 0.768816i) q^{52} +(-1.42370 + 1.13536i) q^{53} +(5.04279 + 5.95426i) q^{54} +(7.43988 - 11.8405i) q^{55} +(4.78248 - 6.48003i) q^{56} +(4.46710 + 0.178919i) q^{57} +(3.59510 + 7.24349i) q^{58} +(11.0545 - 6.38235i) q^{59} +(0.832993 - 1.03892i) q^{60} +(8.21787 - 4.34327i) q^{61} +(-0.460311 + 2.01675i) q^{62} +(0.640627 + 9.19790i) q^{63} +(-5.26714 - 4.20040i) q^{64} +(-2.88001 + 9.33676i) q^{65} +(-11.9299 + 1.76605i) q^{66} +(-2.51549 + 3.68954i) q^{67} +(-0.681623 + 1.28969i) q^{68} +(-5.56989 - 5.19544i) q^{69} +(13.4443 - 3.60240i) q^{70} +(12.7371 + 6.13388i) q^{71} +(7.85737 - 0.252600i) q^{72} +(0.111105 - 0.0125185i) q^{73} +(3.99867 + 5.86498i) q^{74} +(-6.91976 + 1.56024i) q^{75} +(-0.429203 + 0.498742i) q^{76} +(-12.5992 - 6.65888i) q^{77} +(7.73226 - 3.34936i) q^{78} +(-5.23741 - 6.08598i) q^{79} +(-2.98291 - 13.0690i) q^{80} +(-6.66153 + 6.05177i) q^{81} +(-2.07504 - 2.60202i) q^{82} +(3.77838 - 4.07213i) q^{83} +(-1.11922 - 0.767390i) q^{84} +(15.8176 - 6.90115i) q^{85} +(-3.01876 - 5.22864i) q^{86} +(-8.20572 + 4.43465i) q^{87} +(-6.07529 + 10.5227i) q^{88} +(0.873041 - 7.74846i) q^{89} +(10.8888 + 8.12519i) q^{90} +(9.70759 + 2.21569i) q^{91} +(1.10853 - 0.167084i) q^{92} +(-2.34325 - 0.449758i) q^{93} +(-5.56722 + 5.16563i) q^{94} +(7.64867 - 1.44721i) q^{95} +(-1.47978 + 1.99403i) q^{96} +(0.607346 + 16.2317i) q^{97} +(-1.21299 - 3.46653i) q^{98} +(-2.51413 - 13.6813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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