LMFDB - Embedded newform 288.2.bc.a.277.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			277.33
Character	$\chi$	$=$	288.277
Dual form			288.2.bc.a.157.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.804604 + 1.16302i) q^{2} +(-1.58106 - 0.707273i) q^{3} +(-0.705226 + 1.87154i) q^{4} +(0.422783 - 0.0556605i) q^{5} +(-0.449558 - 2.40788i) q^{6} +(-3.08182 + 0.825772i) q^{7} +(-2.74406 + 0.685655i) q^{8} +(1.99953 + 2.23649i) q^{9} +O(q^{10})$	\(q+(0.804604 + 1.16302i) q^{2} +(-1.58106 - 0.707273i) q^{3} +(-0.705226 + 1.87154i) q^{4} +(0.422783 - 0.0556605i) q^{5} +(-0.449558 - 2.40788i) q^{6} +(-3.08182 + 0.825772i) q^{7} +(-2.74406 + 0.685655i) q^{8} +(1.99953 + 2.23649i) q^{9} +(0.404907 + 0.446920i) q^{10} +(-3.63181 + 2.78679i) q^{11} +(2.43870 - 2.46024i) q^{12} +(-0.682753 + 0.889781i) q^{13} +(-3.44004 - 2.91980i) q^{14} +(-0.707815 - 0.211020i) q^{15} +(-3.00531 - 2.63972i) q^{16} +1.63479i q^{17} +(-0.992249 + 4.12498i) q^{18} +(-0.155186 - 0.374652i) q^{19} +(-0.193987 + 0.830509i) q^{20} +(5.45661 + 0.874091i) q^{21} +(-6.16325 - 1.98161i) q^{22} +(3.65866 + 0.980336i) q^{23} +(4.82348 + 0.856736i) q^{24} +(-4.65398 + 1.24703i) q^{25} +(-1.58418 - 0.0781337i) q^{26} +(-1.57958 - 4.95025i) q^{27} +(0.627919 - 6.35011i) q^{28} +(1.19477 - 9.07514i) q^{29} +(-0.324090 - 0.992990i) q^{30} +(3.54949 + 6.14790i) q^{31} +(0.651955 - 5.61916i) q^{32} +(7.71315 - 1.83741i) q^{33} +(-1.90129 + 1.31535i) q^{34} +(-1.25698 + 0.520659i) q^{35} +(-5.59579 + 2.16497i) q^{36} +(-3.11287 + 7.51513i) q^{37} +(0.310864 - 0.481930i) q^{38} +(1.70880 - 0.923909i) q^{39} +(-1.12198 + 0.442619i) q^{40} +(8.46797 + 2.26899i) q^{41} +(3.37382 + 7.04944i) q^{42} +(-1.41143 + 1.08303i) q^{43} +(-2.65433 - 8.76239i) q^{44} +(0.969852 + 0.834255i) q^{45} +(1.80362 + 5.04387i) q^{46} +(3.74609 + 2.16280i) q^{47} +(2.88459 + 6.29914i) q^{48} +(2.75356 - 1.58977i) q^{49} +(-5.19493 - 4.40930i) q^{50} +(1.15624 - 2.58470i) q^{51} +(-1.18376 - 1.90530i) q^{52} +(6.78118 + 2.80886i) q^{53} +(4.48629 - 5.82007i) q^{54} +(-1.38036 + 1.38036i) q^{55} +(7.89052 - 4.37904i) q^{56} +(-0.0196222 + 0.702107i) q^{57} +(11.5159 - 5.91236i) q^{58} +(7.91541 - 1.04208i) q^{59} +(0.894102 - 1.17589i) q^{60} +(-0.512403 + 3.89209i) q^{61} +(-4.29419 + 9.07475i) q^{62} +(-8.00903 - 5.24131i) q^{63} +(7.05975 - 3.76296i) q^{64} +(-0.239131 + 0.414187i) q^{65} +(8.34296 + 7.49215i) q^{66} +(-10.7158 - 8.22249i) q^{67} +(-3.05957 - 1.15289i) q^{68} +(-5.09122 - 4.13765i) q^{69} +(-1.61691 - 1.04297i) q^{70} +(-0.796166 - 0.796166i) q^{71} +(-7.02029 - 4.76607i) q^{72} +(-2.82724 + 2.82724i) q^{73} +(-11.2449 + 2.42637i) q^{74} +(8.24024 + 1.32000i) q^{75} +(0.810616 - 0.0262220i) q^{76} +(8.89135 - 11.5874i) q^{77} +(2.44943 + 1.24398i) q^{78} +(8.74993 + 5.05177i) q^{79} +(-1.41752 - 0.948751i) q^{80} +(-1.00376 + 8.94385i) q^{81} +(4.17448 + 11.6740i) q^{82} +(-14.3180 - 1.88500i) q^{83} +(-5.48404 + 9.59582i) q^{84} +(0.0909930 + 0.691160i) q^{85} +(-2.39523 - 0.770112i) q^{86} +(-8.30760 + 13.5034i) q^{87} +(8.05514 - 10.1373i) q^{88} +(-0.770168 - 0.770168i) q^{89} +(-0.189908 + 1.79920i) q^{90} +(1.36937 - 3.30595i) q^{91} +(-4.41492 + 6.15597i) q^{92} +(-1.26373 - 12.2307i) q^{93} +(0.498732 + 6.09697i) q^{94} +(-0.0864633 - 0.149759i) q^{95} +(-5.00506 + 8.42314i) q^{96} +(-9.05591 + 15.6853i) q^{97} +(4.06446 + 1.92331i) q^{98} +(-13.4945 - 2.55024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.804604	+	1.16302i	0.568941	+	0.822379i
$2$	0.804604	+	1.16302i	0.568941	+	0.822379i
$3$	−1.58106	−	0.707273i	−0.912828	−	0.408344i
$3$	−1.58106	−	0.707273i	−0.912828	−	0.408344i
$4$	−0.705226	+	1.87154i	−0.352613	+	0.935769i
$5$	0.422783	−	0.0556605i	0.189074	−	0.0248921i	−0.0353942	−	0.999373i	$-0.511269\pi$
$5$	0.422783	−	0.0556605i	0.189074	−	0.0248921i	0.224469	+	0.974481i	$0.427935\pi$
$6$	−0.449558	−	2.40788i	−0.183531	−	0.983014i
$7$	−3.08182	+	0.825772i	−1.16482	+	0.312113i	−0.788889	−	0.614535i	$-0.789344\pi$
$7$	−3.08182	+	0.825772i	−1.16482	+	0.312113i	−0.375931	+	0.926648i	$0.622677\pi$
$8$	−2.74406	+	0.685655i	−0.970172	+	0.242416i
$9$	1.99953	+	2.23649i	0.666510	+	0.745496i
$10$	0.404907	+	0.446920i	0.128043	+	0.141329i
$11$	−3.63181	+	2.78679i	−1.09503	+	0.840248i	−0.988068	−	0.154015i	$-0.950780\pi$
$11$	−3.63181	+	2.78679i	−1.09503	+	0.840248i	−0.106964	+	0.994263i	$0.534113\pi$
$12$	2.43870	−	2.46024i	0.703991	−	0.710209i
$13$	−0.682753	+	0.889781i	−0.189362	+	0.246781i	−0.878380	−	0.477963i	$-0.841375\pi$
$13$	−0.682753	+	0.889781i	−0.189362	+	0.246781i	0.689018	+	0.724744i	$0.258042\pi$
$14$	−3.44004	−	2.91980i	−0.919388	−	0.780350i
$15$	−0.707815	−	0.211020i	−0.182757	−	0.0544852i
$16$	−3.00531	−	2.63972i	−0.751328	−	0.659929i
$17$			1.63479i			0.396494i	0.980152	+	0.198247i	$0.0635248\pi$
$17$			1.63479i			0.396494i	−0.980152	+	0.198247i	$0.936475\pi$
$18$	−0.992249	+	4.12498i	−0.233875	+	0.972267i
$19$	−0.155186	−	0.374652i	−0.0356021	−	0.0859510i	0.905078	−	0.425245i	$-0.139812\pi$
$19$	−0.155186	−	0.374652i	−0.0356021	−	0.0859510i	−0.940680	+	0.339294i	$0.889812\pi$
$20$	−0.193987	+	0.830509i	−0.0433769	+	0.185707i
$21$	5.45661	+	0.874091i	1.19073	+	0.190742i
$22$	−6.16325	−	1.98161i	−1.31401	−	0.422480i
$23$	3.65866	+	0.980336i	0.762884	+	0.204414i	0.619225	−	0.785213i	$-0.287447\pi$
$23$	3.65866	+	0.980336i	0.762884	+	0.204414i	0.143658	+	0.989627i	$0.454113\pi$
$24$	4.82348	+	0.856736i	0.984590	+	0.174880i
$25$	−4.65398	+	1.24703i	−0.930796	+	0.249406i
$26$	−1.58418	−	0.0781337i	−0.310683	−	0.0153233i
$27$	−1.57958	−	4.95025i	−0.303990	−	0.952675i
$28$	0.627919	−	6.35011i	0.118665	−	1.20006i
$29$	1.19477	−	9.07514i	0.221862	−	1.68521i	−0.411542	−	0.911391i	$-0.635010\pi$
$29$	1.19477	−	9.07514i	0.221862	−	1.68521i	0.633405	−	0.773821i	$-0.281657\pi$
$30$	−0.324090	−	0.992990i	−0.0591704	−	0.181294i
$31$	3.54949	+	6.14790i	0.637507	+	1.10420i	0.985978	+	0.166876i	$0.0533678\pi$
$31$	3.54949	+	6.14790i	0.637507	+	1.10420i	−0.348470	+	0.937320i	$0.613299\pi$
$32$	0.651955	−	5.61916i	0.115250	−	0.993336i
$33$	7.71315	−	1.83741i	1.34269	−	0.319852i
$34$	−1.90129	+	1.31535i	−0.326068	+	0.225581i
$35$	−1.25698	+	0.520659i	−0.212469	+	0.0880074i
$36$	−5.59579	+	2.16497i	−0.932632	+	0.360828i
$37$	−3.11287	+	7.51513i	−0.511752	+	1.23548i	0.431111	+	0.902299i	$0.358122\pi$
$37$	−3.11287	+	7.51513i	−0.511752	+	1.23548i	−0.942863	+	0.333180i	$0.891878\pi$
$38$	0.310864	−	0.481930i	0.0504288	−	0.0781794i
$39$	1.70880	−	0.923909i	0.273626	−	0.147944i
$40$	−1.12198	+	0.442619i	−0.177401	+	0.0699843i
$41$	8.46797	+	2.26899i	1.32247	+	0.354356i	0.849904	−	0.526937i	$-0.176660\pi$
$41$	8.46797	+	2.26899i	1.32247	+	0.354356i	0.472570	+	0.881293i	$0.343326\pi$
$42$	3.37382	+	7.04944i	0.520592	+	1.08775i
$43$	−1.41143	+	1.08303i	−0.215241	+	0.165160i	−0.710755	−	0.703440i	$-0.751647\pi$
$43$	−1.41143	+	1.08303i	−0.215241	+	0.165160i	0.495514	+	0.868600i	$0.334980\pi$
$44$	−2.65433	−	8.76239i	−0.400155	−	1.32098i
$45$	0.969852	+	0.834255i	0.144577	+	0.124363i
$46$	1.80362	+	5.04387i	0.265930	+	0.743679i
$47$	3.74609	+	2.16280i	0.546423	+	0.315477i	0.747678	−	0.664061i	$-0.231169\pi$
$47$	3.74609	+	2.16280i	0.546423	+	0.315477i	−0.201255	+	0.979539i	$0.564502\pi$
$48$	2.88459	+	6.29914i	0.416355	+	0.909202i
$49$	2.75356	−	1.58977i	0.393366	−	0.227110i
$50$	−5.19493	−	4.40930i	−0.734674	−	0.623570i
$51$	1.15624	−	2.58470i	0.161906	−	0.361931i
$52$	−1.18376	−	1.90530i	−0.164159	−	0.264217i
$53$	6.78118	+	2.80886i	0.931467	+	0.385826i	0.796235	−	0.604988i	$-0.206822\pi$
$53$	6.78118	+	2.80886i	0.931467	+	0.385826i	0.135232	+	0.990814i	$0.456822\pi$
$54$	4.48629	−	5.82007i	0.610507	−	0.792011i
$55$	−1.38036	+	1.38036i	−0.186127	+	0.186127i
$56$	7.89052	−	4.37904i	1.05442	−	0.585174i
$57$	−0.0196222	+	0.702107i	−0.00259902	+	0.0929964i
$58$	11.5159	−	5.91236i	1.51211	−	0.776330i
$59$	7.91541	−	1.04208i	1.03050	−	0.135668i	0.403734	−	0.914876i	$-0.367712\pi$
$59$	7.91541	−	1.04208i	1.03050	−	0.135668i	0.626765	+	0.779209i	$0.284379\pi$
$60$	0.894102	−	1.17589i	0.115428	−	0.151806i
$61$	−0.512403	+	3.89209i	−0.0656065	+	0.498331i	0.926821	+	0.375502i	$0.122530\pi$
$61$	−0.512403	+	3.89209i	−0.0656065	+	0.498331i	−0.992428	+	0.122828i	$0.960804\pi$
$62$	−4.29419	+	9.07475i	−0.545363	+	1.15249i
$63$	−8.00903	−	5.24131i	−1.00904	−	0.660343i
$64$	7.05975	−	3.76296i	0.882469	−	0.470370i
$65$	−0.239131	+	0.414187i	−0.0296606	+	0.0513736i
$66$	8.34296	+	7.49215i	1.02695	+	0.922220i
$67$	−10.7158	−	8.22249i	−1.30914	−	1.00454i	−0.998541	−	0.0539959i	$-0.982804\pi$
$67$	−10.7158	−	8.22249i	−1.30914	−	1.00454i	−0.310598	−	0.950542i	$-0.600529\pi$
$68$	−3.05957	−	1.15289i	−0.371027	−	0.139809i
$69$	−5.09122	−	4.13765i	−0.612910	−	0.498114i
$70$	−1.61691	−	1.04297i	−0.193257	−	0.124659i
$71$	−0.796166	−	0.796166i	−0.0944876	−	0.0944876i	0.658283	−	0.752771i	$-0.271283\pi$
$71$	−0.796166	−	0.796166i	−0.0944876	−	0.0944876i	−0.752771	+	0.658283i	$0.771283\pi$
$72$	−7.02029	−	4.76607i	−0.827350	−	0.561687i
$73$	−2.82724	+	2.82724i	−0.330904	+	0.330904i	−0.852930	−	0.522026i	$-0.825176\pi$
$73$	−2.82724	+	2.82724i	−0.330904	+	0.330904i	0.522026	+	0.852930i	$0.325176\pi$
$74$	−11.2449	+	2.42637i	−1.30719	+	0.282060i
$75$	8.24024	+	1.32000i	0.951500	+	0.152420i
$76$	0.810616	−	0.0262220i	0.0929841	−	0.00300787i
$77$	8.89135	−	11.5874i	1.01326	−	1.32051i
$78$	2.44943	+	1.24398i	0.277343	+	0.140853i
$79$	8.74993	+	5.05177i	0.984444	+	0.568369i	0.903609	−	0.428358i	$-0.140908\pi$
$79$	8.74993	+	5.05177i	0.984444	+	0.568369i	0.0808352	+	0.996727i	$0.474241\pi$
$80$	−1.41752	−	0.948751i	−0.158484	−	0.106074i
$81$	−1.00376	+	8.94385i	−0.111529	+	0.993761i
$82$	4.17448	+	11.6740i	0.460995	+	1.28918i
$83$	−14.3180	−	1.88500i	−1.57160	−	0.206906i	−0.706212	−	0.708001i	$-0.749597\pi$
$83$	−14.3180	−	1.88500i	−1.57160	−	0.206906i	−0.865392	+	0.501095i	$0.832931\pi$
$84$	−5.48404	+	9.59582i	−0.598358	+	1.04699i
$85$	0.0909930	+	0.691160i	0.00986958	+	0.0749669i
$86$	−2.39523	−	0.770112i	−0.258284	−	0.0830433i
$87$	−8.30760	+	13.5034i	−0.890668	+	1.44771i
$88$	8.05514	−	10.1373i	0.858681	−	1.08064i
$89$	−0.770168	−	0.770168i	−0.0816376	−	0.0816376i	0.665109	−	0.746746i	$-0.268385\pi$
$89$	−0.770168	−	0.770168i	−0.0816376	−	0.0816376i	−0.746746	+	0.665109i	$0.768385\pi$
$90$	−0.189908	+	1.79920i	−0.0200181	+	0.189652i
$91$	1.36937	−	3.30595i	0.143549	−	0.346558i
$92$	−4.41492	+	6.15597i	−0.460287	+	0.641804i
$93$	−1.26373	−	12.2307i	−0.131043	−	1.26826i
$94$	0.498732	+	6.09697i	0.0514403	+	0.628854i
$95$	−0.0864633	−	0.149759i	−0.00887095	−	0.0153649i
$96$	−5.00506	+	8.42314i	−0.510827	+	0.859684i
$97$	−9.05591	+	15.6853i	−0.919489	+	1.59260i	−0.119295	+	0.992859i	$0.538064\pi$
$97$	−9.05591	+	15.6853i	−0.919489	+	1.59260i	−0.800193	+	0.599742i	$0.795270\pi$
$98$	4.06446	+	1.92331i	0.410572	+	0.194284i
$99$	−13.4945	−	2.55024i	−1.35625	−	0.256309i
$100$	0.948244	−	9.58954i	0.0948244	−	0.958954i
$101$	−0.655132	−	0.853785i	−0.0651881	−	0.0849548i	0.759621	−	0.650366i	$-0.225384\pi$
$101$	−0.655132	−	0.853785i	−0.0651881	−	0.0849548i	−0.824809	+	0.565411i	$0.808718\pi$
$102$	3.93637	−	0.734932i	0.389759	−	0.0727691i
$103$	1.42471	−	5.31708i	0.140381	−	0.523907i	−0.859537	−	0.511073i	$-0.829248\pi$
$103$	1.42471	−	5.31708i	0.140381	−	0.523907i	0.999918	−	0.0128339i	$-0.00408528\pi$
$104$	1.26343	−	2.90975i	0.123890	−	0.285324i
$105$	2.35562	+	0.0658337i	0.229885	+	0.00642471i
$106$	2.18941	+	10.1467i	0.212654	+	0.985531i
$107$	2.11074	+	0.874299i	0.204053	+	0.0845217i	0.482369	−	0.875968i	$-0.339776\pi$
$107$	2.11074	+	0.874299i	0.204053	+	0.0845217i	−0.278316	+	0.960490i	$0.589776\pi$
$108$	10.3785	+	0.534800i	0.998675	+	0.0514611i
$109$	−3.48045	−	8.40255i	−0.333367	−	0.804819i	−0.998320	−	0.0579340i	$-0.981549\pi$
$109$	−3.48045	−	8.40255i	−0.333367	−	0.804819i	0.664954	−	0.746885i	$-0.268451\pi$
$110$	−2.71602	−	0.494741i	−0.258962	−	0.0471717i
$111$	10.2369	−	9.68025i	0.971643	−	0.918809i
$112$	11.4416	+	5.65344i	1.08113	+	0.534200i
$113$	−15.5031	+	8.95073i	−1.45841	+	0.842014i	−0.998933	−	0.0461749i	$-0.985297\pi$
$113$	−15.5031	+	8.95073i	−1.45841	+	0.842014i	−0.459478	+	0.888189i	$0.651964\pi$
$114$	−0.832352	+	0.542097i	−0.0779569	+	0.0507721i
$115$	1.60139	+	0.210827i	0.149330	+	0.0196597i
$116$	16.1419	+	8.63608i	1.49874	+	0.801840i
$117$	−3.35517	+	0.252175i	−0.310186	+	0.0233136i
$118$	7.58073	+	8.36731i	0.697863	+	0.770273i
$119$	−1.34996	−	5.03812i	−0.123751	−	0.461844i
$120$	2.08698	+	0.0937362i	0.190514	+	0.00855691i
$121$	2.57686	−	9.61698i	0.234260	−	0.874271i
$122$	−4.93885	+	2.53565i	−0.447143	+	0.229567i
$123$	−11.7836	−	9.57658i	−1.06249	−	0.863491i
$124$	−14.0092	+	2.30735i	−1.25807	+	0.207206i
$125$	−3.86807	+	1.60221i	−0.345971	+	0.143306i
$126$	−0.348356	−	13.5318i	−0.0310340	−	1.20551i
$127$	8.29468			0.736034			0.368017	−	0.929819i	$-0.380037\pi$
$127$	8.29468			0.736034			0.368017	+	0.929819i	$0.380037\pi$
$128$	10.0567	+	5.18294i	0.888895	+	0.458111i
$129$	2.99756	−	0.714072i	0.263921	−	0.0628706i
$130$	−0.674113	+	0.0551425i	−0.0591236	+	0.00483632i
$131$	8.35287	+	6.40938i	0.729794	+	0.559990i	0.905446	−	0.424462i	$-0.139537\pi$
$131$	8.35287	+	6.40938i	0.729794	+	0.559990i	−0.175652	+	0.984452i	$0.556203\pi$
$132$	−2.00073	+	15.7312i	−0.174141	+	1.36923i
$133$	0.787633	+	1.02646i	0.0682964	+	0.0890056i
$134$	0.940976	−	19.0785i	0.0812879	−	1.64813i
$135$	−0.943353	−	2.00496i	−0.0811909	−	0.172560i
$136$	−1.12090	−	4.48596i	−0.0961163	−	0.384667i
$137$	−4.31805	−	16.1152i	−0.368916	−	1.37681i	−0.862034	−	0.506850i	$-0.830810\pi$
$137$	−4.31805	−	16.1152i	−0.368916	−	1.37681i	0.493119	−	0.869962i	$-0.335857\pi$
$138$	0.715750	−	9.25035i	0.0609287	−	0.787442i
$139$	0.394428	+	2.99598i	0.0334550	+	0.254116i	0.999997	−	0.00239208i	$-0.000761424\pi$
$139$	0.394428	+	2.99598i	0.0334550	+	0.254116i	−0.966542	+	0.256508i	$0.917428\pi$
$140$	−0.0879765	−	2.71967i	−0.00743538	−	0.229854i
$141$	−4.39311	−	6.06904i	−0.369967	−	0.511105i
$142$	0.285358	−	1.56656i	0.0239467	−	0.131462i
$143$		−	5.13421i		−	0.429344i
$144$	−0.105519	−	11.9995i	−0.00879324	−	0.999961i
$145$		−	3.90332i		−	0.324153i
$146$	−5.56295	−	1.01333i	−0.460393	−	0.0838636i
$147$	−5.47796	+	0.566009i	−0.451815	+	0.0466837i
$148$	−11.8696	−	11.1257i	−0.975673	−	0.914528i
$149$	−0.639002	−	4.85370i	−0.0523491	−	0.397631i	−0.997481	−	0.0709406i	$-0.977400\pi$
$149$	−0.639002	−	4.85370i	−0.0523491	−	0.397631i	0.945131	−	0.326690i	$-0.105933\pi$
$150$	5.09494	+	10.6456i	0.416000	+	0.869212i
$151$	−1.78792	−	6.67262i	−0.145499	−	0.543010i	−0.999733	−	0.0231206i	$-0.992640\pi$
$151$	−1.78792	−	6.67262i	−0.145499	−	0.543010i	0.854234	−	0.519889i	$-0.174027\pi$
$152$	0.682722	+	0.921664i	0.0553760	+	0.0747568i
$153$	−3.65618	+	3.26880i	−0.295585	+	0.264267i
$154$	20.6304	+	1.01752i	1.66245	+	0.0819940i
$155$	1.84286	+	2.40166i	0.148022	+	0.192906i
$156$	0.524044	+	3.84964i	0.0419571	+	0.308218i
$157$	−10.3514	−	7.94293i	−0.826134	−	0.633915i	0.106672	−	0.994294i	$-0.465981\pi$
$157$	−10.3514	−	7.94293i	−0.826134	−	0.633915i	−0.932806	+	0.360379i	$0.882647\pi$
$158$	1.16492	+	14.2410i	0.0926757	+	1.13295i
$159$	−8.73486	−	9.23713i	−0.692719	−	0.732552i
$160$	−0.0371294	−	2.41198i	−0.00293534	−	0.190683i
$161$	−12.0849			−0.952423
$162$	−11.2095	+	6.02887i	−0.880701	+	0.473672i
$163$	−11.8634	+	4.91400i	−0.929216	+	0.384894i	−0.795381	−	0.606110i	$-0.792729\pi$
$163$	−11.8634	+	4.91400i	−0.929216	+	0.384894i	−0.133835	+	0.991004i	$0.542729\pi$
$164$	−10.2183	+	14.2480i	−0.797917	+	1.11258i
$165$	3.15872	−	1.20614i	0.245906	−	0.0938981i
$166$	−9.32802	−	18.1688i	−0.723995	−	1.41017i
$167$	−3.36812	+	12.5700i	−0.260633	+	0.972695i	0.704237	+	0.709965i	$0.251289\pi$
$167$	−3.36812	+	12.5700i	−0.260633	+	0.972695i	−0.964870	+	0.262729i	$0.915377\pi$
$168$	−15.5726	+	1.34279i	−1.20145	+	0.103599i
$169$	3.03909	+	11.3420i	0.233776	+	0.872464i
$170$	−0.730619	+	0.661937i	−0.0560360	+	0.0507682i
$171$	0.527605	−	1.09620i	0.0403470	−	0.0838284i
$172$	−1.03155	−	3.40533i	−0.0786552	−	0.259654i
$173$	22.3103	+	2.93720i	1.69622	+	0.223311i	0.915711	−	0.401837i	$-0.131628\pi$
$173$	22.3103	+	2.93720i	1.69622	+	0.223311i	0.780506	+	0.625148i	$0.214961\pi$
$174$	−22.3890	+	1.20295i	−1.69730	+	0.0911956i
$175$	13.3130	−	7.68626i	1.00637	−	0.581026i
$176$	18.2710	+	1.21179i	1.37723	+	0.0913418i
$177$	−13.2518	−	3.95075i	−0.996067	−	0.296957i
$178$	0.276040	−	1.51540i	0.0206901	−	0.113584i
$179$	4.47071	+	10.7932i	0.334156	+	0.806725i	0.998253	+	0.0590785i	$0.0188162\pi$
$179$	4.47071	+	10.7932i	0.334156	+	0.806725i	−0.664097	+	0.747646i	$0.731184\pi$
$180$	−2.24531	+	1.22678i	−0.167355	+	0.0914386i
$181$	20.8398	+	8.63212i	1.54901	+	0.641620i	0.983136	−	0.182873i	$-0.0585398\pi$
$181$	20.8398	+	8.63212i	1.54901	+	0.641620i	0.565872	+	0.824493i	$0.308540\pi$
$182$	4.94668	−	1.06738i	0.366672	−	0.0791192i
$183$	3.56291	−	5.79123i	0.263378	−	0.428100i
$184$	−10.7118	−	0.181522i	−0.789682	−	0.0133820i
$185$	−0.897773	+	3.35053i	−0.0660056	+	0.246336i
$186$	13.2077	−	11.3106i	0.968437	−	0.829333i
$187$	−4.55580	−	5.93723i	−0.333153	−	0.434174i
$188$	−6.68961	+	5.48568i	−0.487890	+	0.400084i
$189$	8.95576	+	13.9514i	0.651436	+	1.01482i
$190$	0.104604	−	0.221055i	0.00758875	−	0.0160370i
$191$	−1.56698	+	2.71408i	−0.113383	+	0.196384i	−0.917132	−	0.398584i	$-0.869502\pi$
$191$	−1.56698	+	2.71408i	−0.113383	+	0.196384i	0.803750	+	0.594968i	$0.202835\pi$
$192$	−13.8234	+	0.956309i	−0.997616	+	0.0690157i
$193$	−6.46227	−	11.1930i	−0.465164	−	0.805688i	0.534045	−	0.845456i	$-0.320671\pi$
$193$	−6.46227	−	11.1930i	−0.465164	−	0.805688i	−0.999209	+	0.0397683i	$0.987338\pi$
$194$	−25.5287	+	2.08825i	−1.83286	+	0.149928i
$195$	0.671025	−	0.485726i	0.0480531	−	0.0347835i
$196$	1.03343	+	6.27455i	0.0738165	+	0.448182i
$197$	−1.17469	+	2.83595i	−0.0836930	+	0.202053i	−0.960186	−	0.279362i	$-0.909877\pi$
$197$	−1.17469	+	2.83595i	−0.0836930	+	0.202053i	0.876493	+	0.481415i	$0.159877\pi$
$198$	−7.89177	−	17.7463i	−0.560844	−	1.26118i
$199$	16.3291	+	16.3291i	1.15754	+	1.15754i	0.985003	+	0.172535i	$0.0551957\pi$
$199$	16.3291	+	16.3291i	1.15754	+	1.15754i	0.172535	+	0.985003i	$0.444804\pi$
$200$	11.9158	−	6.61295i	0.842573	−	0.467607i
$201$	11.1268	+	20.5793i	0.784821	+	1.45155i
$202$	0.465846	−	1.44889i	0.0327768	−	0.101944i
$203$	3.81194	+	28.9546i	0.267546	+	2.03221i
$204$	4.02196	+	3.98675i	0.281593	+	0.279128i
$205$	3.70641	+	0.487958i	0.258867	+	0.0340805i
$206$	7.33019	−	2.62118i	0.510718	−	0.182626i
$207$	5.12310	+	10.1428i	0.356080	+	0.704971i
$208$	4.40066	−	0.871796i	0.305131	−	0.0604482i
$209$	1.60768	+	0.928195i	0.111206	+	0.0642046i
$210$	1.81877	+	2.79260i	0.125507	+	0.192707i
$211$	−8.46821	+	11.0360i	−0.582976	+	0.759749i	−0.987983	−	0.154565i	$-0.950602\pi$
$211$	−8.46821	+	11.0360i	−0.582976	+	0.759749i	0.405007	+	0.914314i	$0.367269\pi$
$212$	−10.0392	+	10.7104i	−0.689492	+	0.735591i
$213$	0.695684	+	1.82190i	0.0476675	+	0.124834i
$214$	0.681486	+	3.15830i	0.0465854	+	0.215897i
$215$	−0.536448	+	0.536448i	−0.0365854	+	0.0365854i
$216$	7.72862	+	12.5007i	0.525866	+	0.850567i
$217$	−16.0157	−	16.0157i	−1.08721	−	1.08721i
$218$	6.97195	−	10.8086i	0.472200	−	0.732048i
$219$	6.46969	−	2.47042i	0.437181	−	0.166936i
$220$	−1.60993	−	3.55685i	−0.108541	−	0.239803i
$221$	−1.45460	−	1.11616i	−0.0978472	−	0.0750808i
$222$	19.4950	+	4.11693i	1.30842	+	0.276310i
$223$	10.4184	−	18.0451i	0.697665	−	1.20839i	−0.271609	−	0.962408i	$-0.587556\pi$
$223$	10.4184	−	18.0451i	0.697665	−	1.20839i	0.969274	−	0.245984i	$-0.0791110\pi$
$224$	2.63094	+	17.8556i	0.175787	+	1.19303i
$225$	−12.0947	−	7.91510i	−0.806316	−	0.527673i
$226$	−22.8837	−	10.8286i	−1.52220	−	0.720310i
$227$	−0.649852	+	4.93612i	−0.0431322	+	0.327622i	0.956252	+	0.292543i	$0.0945015\pi$
$227$	−0.649852	+	4.93612i	−0.0431322	+	0.327622i	−0.999385	+	0.0350786i	$0.988832\pi$
$228$	−1.30018	−	0.531868i	−0.0861067	−	0.0352238i
$229$	−19.8575	+	2.61429i	−1.31222	+	0.172757i	−0.753966	−	0.656914i	$-0.771862\pi$
$229$	−19.8575	+	2.61429i	−1.31222	+	0.172757i	−0.558253	+	0.829671i	$0.688528\pi$
$230$	1.04329	+	2.03208i	0.0687923	+	0.133991i
$231$	−22.2533	+	12.0319i	−1.46416	+	0.791639i
$232$	2.94391	+	25.7219i	0.193277	+	1.68873i
$233$	12.5249	−	12.5249i	0.820532	−	0.820532i	−0.165652	−	0.986184i	$-0.552973\pi$
$233$	12.5249	−	12.5249i	0.820532	−	0.820532i	0.986184	+	0.165652i	$0.0529728\pi$
$234$	−2.99287	−	3.69923i	−0.195650	−	0.241826i
$235$	1.70417	+	0.705889i	0.111168	+	0.0460471i
$236$	−3.63186	+	15.5489i	−0.236414	+	1.01215i
$237$	−10.2612	−	14.1758i	−0.666538	−	0.920815i
$238$	4.77325	−	5.62372i	0.309404	−	0.364532i
$239$	1.06216	−	0.613239i	0.0687055	−	0.0396671i	−0.465254	−	0.885177i	$-0.654037\pi$
$239$	1.06216	−	0.613239i	0.0687055	−	0.0396671i	0.533959	+	0.845510i	$0.320704\pi$
$240$	1.57017	+	2.50261i	0.101354	+	0.161543i
$241$	−1.95561	−	1.12907i	−0.125972	−	0.0727298i	0.435690	−	0.900097i	$-0.356504\pi$
$241$	−1.95561	−	1.12907i	−0.125972	−	0.0727298i	−0.561662	+	0.827367i	$0.689838\pi$
$242$	13.2581	−	4.74092i	0.852262	−	0.304758i
$243$	7.91275	−	13.4309i	0.507603	−	0.861591i
$244$	−6.92283	−	3.70378i	−0.443189	−	0.237110i
$245$	1.07567	−	0.825393i	0.0687222	−	0.0527324i
$246$	1.65660	−	21.4099i	0.105621	−	1.36505i
$247$	0.439312	+	0.117713i	0.0279527	+	0.00748992i
$248$	−13.9554	−	14.4365i	−0.886166	−	0.916718i
$249$	21.3045	+	13.1070i	1.35012	+	0.830624i
$250$	−4.97566	−	3.20950i	−0.314689	−	0.202987i
$251$	−6.80853	+	16.4372i	−0.429750	+	1.03751i	0.549616	+	0.835417i	$0.314774\pi$
$251$	−6.80853	+	16.4372i	−0.429750	+	1.03751i	−0.979367	+	0.202092i	$0.935226\pi$
$252$	15.4575	−	11.2929i	0.973730	−	0.711386i
$253$	−16.0196	+	6.63552i	−1.00714	+	0.417171i
$254$	6.67393	+	9.64687i	0.418760	+	0.605298i
$255$	0.344973	−	1.15713i	0.0216031	−	0.0724621i
$256$	2.06380	+	15.8663i	0.128987	+	0.991646i
$257$	−3.83270	−	6.63843i	−0.239077	−	0.414094i	0.721373	−	0.692547i	$-0.243512\pi$
$257$	−3.83270	−	6.63843i	−0.239077	−	0.414094i	−0.960450	+	0.278453i	$0.910178\pi$
$258$	3.24233	+	2.91168i	0.201859	+	0.181273i
$259$	3.38753	−	25.7308i	0.210491	−	1.59884i
$260$	−0.606526	−	0.739639i	−0.0376151	−	0.0458704i
$261$	22.6854	−	15.4739i	1.40419	−	0.957813i
$262$	−0.733485	+	14.8716i	−0.0453148	+	0.918768i
$263$	25.8546	−	6.92772i	1.59426	−	0.427182i	0.650960	−	0.759112i	$-0.274367\pi$
$263$	25.8546	−	6.92772i	1.59426	−	0.427182i	0.943304	+	0.331930i	$0.107700\pi$
$264$	−19.9055	+	10.3305i	−1.22510	+	0.635799i
$265$	3.02331	+	0.810094i	0.185721	+	0.0497637i
$266$	−0.560064	+	1.74193i	−0.0343397	+	0.106804i
$267$	0.672966	+	1.76240i	0.0411848	+	0.107857i
$268$	22.9457	−	14.2562i	1.40163	−	0.870839i
$269$	4.46311	+	10.7749i	0.272120	+	0.656957i	0.999574	−	0.0292006i	$-0.00929617\pi$
$269$	4.46311	+	10.7749i	0.272120	+	0.656957i	−0.727453	+	0.686157i	$0.759296\pi$
$270$	1.57278	−	2.71034i	0.0957165	−	0.164946i
$271$		−	16.7504i		−	1.01752i	−0.860909	−	0.508759i	$-0.830105\pi$
$271$		−	16.7504i		−	1.01752i	0.860909	−	0.508759i	$-0.169895\pi$
$272$	4.31537	−	4.91304i	0.261658	−	0.297897i
$273$	−4.50327	+	4.25840i	−0.272550	+	0.257730i
$274$	15.2679	−	17.9883i	0.922370	−	1.08671i
$275$	13.4272	−	17.4986i	0.809689	−	1.05521i
$276$	11.3342	−	6.61043i	0.682240	−	0.397901i
$277$	−22.8394	+	17.5253i	−1.37229	+	1.05299i	−0.380542	+	0.924764i	$0.624262\pi$
$277$	−22.8394	+	17.5253i	−1.37229	+	1.05299i	−0.991745	+	0.128229i	$0.959071\pi$
$278$	−3.16702	+	2.86930i	−0.189945	+	0.172089i
$279$	−6.65239	+	20.2313i	−0.398268	+	1.21122i
$280$	3.09224	−	2.29058i	0.184797	−	0.136888i
$281$	−15.5584	+	4.16886i	−0.928136	+	0.248693i	−0.691060	−	0.722798i	$-0.742856\pi$
$281$	−15.5584	+	4.16886i	−0.928136	+	0.248693i	−0.237076	+	0.971491i	$0.576189\pi$
$282$	3.52369	−	9.99244i	0.209833	−	0.595041i
$283$	29.7616	−	3.91819i	1.76915	−	0.232912i	0.825623	−	0.564222i	$-0.190824\pi$
$283$	29.7616	−	3.91819i	1.76915	−	0.232912i	0.943522	+	0.331310i	$0.107490\pi$
$284$	2.05153	−	0.928579i	0.121736	−	0.0551010i
$285$	0.0307837	+	0.297932i	0.00182347	+	0.0176479i
$286$	5.97118	−	4.13100i	0.353083	−	0.244271i
$287$	−27.9705			−1.65104
$288$	13.8708	−	9.77759i	0.817344	−	0.576150i
$289$	14.3275			0.842793
$290$	4.53964	−	3.14063i	0.266577	−	0.184424i
$291$	25.4118	−	18.3945i	1.48966	−	1.07830i
$292$	−3.29745	−	7.28514i	−0.192969	−	0.426331i
$293$	15.2006	−	2.00120i	0.888030	−	0.116911i	0.327310	−	0.944917i	$-0.393858\pi$
$293$	15.2006	−	2.00120i	0.888030	−	0.116911i	0.560720	+	0.828005i	$0.310524\pi$
$294$	−5.06587	−	5.91556i	−0.295447	−	0.345003i
$295$	3.28850	−	0.881151i	0.191464	−	0.0513026i
$296$	3.38912	−	22.7563i	0.196988	−	1.32268i
$297$	19.5320	+	13.5764i	1.13336	+	0.787783i
$298$	5.13081	−	4.64848i	0.297220	−	0.269279i
$299$	−3.37025	+	2.58608i	−0.194906	+	0.149557i
$300$	−8.28166	+	14.4910i	−0.478142	+	0.836639i
$301$	3.45545	−	4.50323i	0.199169	−	0.259562i
$302$	6.32181	−	7.44820i	0.363779	−	0.428596i
$303$	0.431947	+	1.81325i	0.0248147	+	0.104168i
$304$	−0.522592	+	1.53559i	−0.0299727	+	0.0880723i
$305$			1.67403i			0.0958547i
$306$	−6.74346	−	1.62211i	−0.385498	−	0.0927301i
$307$	8.23007	+	19.8691i	0.469715	+	1.13399i	0.964288	+	0.264856i	$0.0853244\pi$
$307$	8.23007	+	19.8691i	0.469715	+	1.13399i	−0.494573	+	0.869136i	$0.664676\pi$
$308$	15.4159	+	24.8123i	0.878403	+	1.41381i
$309$	−6.01318	+	7.39899i	−0.342078	+	0.420914i
$310$	−1.31041	+	4.07567i	−0.0744261	+	0.231482i
$311$	−16.0474	−	4.29987i	−0.909962	−	0.243824i	−0.226672	−	0.973971i	$-0.572785\pi$
$311$	−16.0474	−	4.29987i	−0.909962	−	0.243824i	−0.683289	+	0.730148i	$0.739451\pi$
$312$	−4.05556	+	3.70691i	−0.229601	+	0.209862i
$313$	9.54233	−	2.55686i	0.539365	−	0.144522i	0.0211554	−	0.999776i	$-0.493266\pi$
$313$	9.54233	−	2.55686i	0.539365	−	0.144522i	0.518209	+	0.855254i	$0.326599\pi$
$314$	0.908983	−	18.4298i	0.0512969	−	1.04005i
$315$	−3.67782	−	1.77015i	−0.207222	−	0.0997367i
$316$	−15.6253	+	12.8132i	−0.878990	+	0.720798i
$317$	0.852361	−	6.47433i	0.0478734	−	0.363634i	−0.950694	−	0.310130i	$-0.899627\pi$
$317$	0.852361	−	6.47433i	0.0478734	−	0.363634i	0.998568	−	0.0535046i	$-0.0170392\pi$
$318$	3.71486	−	17.5910i	0.208319	−	0.986456i
$319$	20.9513	+	36.2888i	1.17305	+	2.03178i
$320$	2.77530	−	1.98387i	0.155144	−	0.110901i
$321$	−2.71886	−	2.87520i	−0.151752	−	0.160478i
$322$	−9.72354	−	14.0550i	−0.541872	−	0.783252i
$323$	0.612476	−	0.253696i	0.0340791	−	0.0141160i
$324$	−16.0309	−	8.18601i	−0.890605	−	0.454778i
$325$	2.06794	−	4.99244i	0.114708	−	0.276931i
$326$	−15.2604	−	9.84359i	−0.845198	−	0.545186i
$327$	−0.440079	+	15.7466i	−0.0243364	+	0.870789i
$328$	−24.7924	−	0.420132i	−1.36893	−	0.0231979i
$329$	−13.3308	−	3.57197i	−0.734949	−	0.196929i
$330$	3.94428	+	2.70318i	0.217126	+	0.148805i
$331$	14.4637	−	11.0984i	0.794998	−	0.610024i	−0.129339	−	0.991600i	$-0.541286\pi$
$331$	14.4637	−	11.0984i	0.794998	−	0.610024i	0.924337	+	0.381577i	$0.124619\pi$
$332$	13.6253	−	25.4673i	0.747784	−	1.39770i
$333$	−23.0318	+	8.06483i	−1.26213	+	0.441950i
$334$	−17.3291	+	6.19667i	−0.948208	+	0.339067i
$335$	−4.98811	−	2.87989i	−0.272530	−	0.157345i
$336$	−14.0915	−	17.0308i	−0.768752	−	0.929107i
$337$	8.45873	−	4.88365i	0.460777	−	0.266029i	−0.251594	−	0.967833i	$-0.580955\pi$
$337$	8.45873	−	4.88365i	0.460777	−	0.266029i	0.712371	+	0.701803i	$0.247621\pi$
$338$	−10.7457	+	12.6604i	−0.584491	+	0.688633i
$339$	30.8421	−	3.18675i	1.67511	−	0.173080i
$340$	−1.35770	−	0.317128i	−0.0736318	−	0.0171987i
$341$	−30.0240	−	12.4363i	−1.62589	−	0.673465i
$342$	1.69941	−	0.268390i	0.0918938	−	0.0145129i
$343$	8.61915	−	8.61915i	0.465391	−	0.465391i
$344$	3.13047	−	3.93966i	0.168784	−	0.212412i
$345$	−2.38279	−	1.46595i	−0.128285	−	0.0789240i
$346$	14.5349	+	28.3105i	0.781401	+	1.52198i
$347$	8.26633	−	1.08828i	0.443760	−	0.0584221i	0.0946644	−	0.995509i	$-0.469822\pi$
$347$	8.26633	−	1.08828i	0.443760	−	0.0584221i	0.349096	+	0.937087i	$0.386489\pi$
$348$	−19.4133	−	25.0709i	−1.04066	−	1.34394i
$349$	0.546847	−	4.15371i	0.0292720	−	0.222343i	−0.970556	−	0.240875i	$-0.922566\pi$
$349$	0.546847	−	4.15371i	0.0292720	−	0.222343i	0.999828	+	0.0185314i	$0.00589908\pi$
$350$	19.6509	+	9.29887i	1.05039	+	0.497045i
$351$	5.48310	+	1.97432i	0.292666	+	0.105381i
$352$	13.2916	+	22.2246i	0.708446	+	1.18457i
$353$	−5.75216	+	9.96303i	−0.306156	+	0.530279i	−0.977518	−	0.210851i	$-0.932376\pi$
$353$	−5.75216	+	9.96303i	−0.306156	+	0.530279i	0.671362	+	0.741130i	$0.265710\pi$
$354$	−6.06766	−	18.5909i	−0.322492	−	0.988095i
$355$	−0.380921	−	0.292291i	−0.0202172	−	0.0155132i
$356$	1.98454	−	0.898256i	0.105180	−	0.0476075i
$357$	−1.42895	+	8.92039i	−0.0756282	+	0.472117i
$358$	−8.95560	+	13.8838i	−0.473318	+	0.733782i
$359$	18.5666	+	18.5666i	0.979910	+	0.979910i	0.999802	−	0.0198925i	$-0.00633239\pi$
$359$	18.5666	+	18.5666i	0.979910	+	0.979910i	−0.0198925	+	0.999802i	$0.506332\pi$
$360$	−3.23335	−	1.62426i	−0.170412	−	0.0856062i
$361$	13.3187	−	13.3187i	0.700987	−	0.700987i
$362$	6.72844	+	31.1825i	0.353639	+	1.63891i
$363$	−10.8760	+	13.3825i	−0.570843	+	0.702400i
$364$	5.22150	+	4.89427i	0.273681	+	0.256529i
$365$	−1.03795	+	1.35268i	−0.0543286	+	0.0708024i
$366$	9.60204	−	0.515914i	0.501907	−	0.0269673i
$367$	−13.8597	−	8.00187i	−0.723468	−	0.417694i	0.0925598	−	0.995707i	$-0.470495\pi$
$367$	−13.8597	−	8.00187i	−0.723468	−	0.417694i	−0.816028	+	0.578013i	$0.803828\pi$
$368$	−8.40761	−	12.6040i	−0.438277	−	0.657031i
$369$	11.8574	+	23.4754i	0.617272	+	1.22208i
$370$	−4.61909	+	1.65172i	−0.240135	+	0.0858691i
$371$	−23.2179	−	3.05669i	−1.20541	−	0.158696i
$372$	23.7814	+	6.26028i	1.23301	+	0.324580i
$373$	3.83333	+	29.1170i	0.198482	+	1.50762i	0.743237	+	0.669028i	$0.233289\pi$
$373$	3.83333	+	29.1170i	0.198482	+	1.50762i	−0.544755	+	0.838595i	$0.683377\pi$
$374$	3.23950	−	10.0756i	0.167511	−	0.520997i
$375$	7.24887	+	0.202588i	0.374330	+	0.0104616i
$376$	−11.7624	−	3.36635i	−0.606601	−	0.173606i
$377$	7.25916	+	7.25916i	0.373866	+	0.373866i
$378$	−9.01992	+	21.6411i	−0.463935	+	1.11310i
$379$	−2.08645	+	5.03714i	−0.107174	+	0.258741i	−0.968364	−	0.249543i	$-0.919720\pi$
$379$	−2.08645	+	5.03714i	−0.107174	+	0.258741i	0.861190	+	0.508283i	$0.169720\pi$
$380$	0.341256	−	0.0562055i	0.0175060	−	0.00288328i
$381$	−13.1144	−	5.86660i	−0.671872	−	0.300555i
$382$	−4.41733	+	0.361338i	−0.226010	+	0.0184876i
$383$	−1.29839	−	2.24887i	−0.0663445	−	0.114912i	0.830945	−	0.556354i	$-0.187800\pi$
$383$	−1.29839	−	2.24887i	−0.0663445	−	0.114912i	−0.897290	+	0.441442i	$0.854467\pi$
$384$	−12.2345	−	15.3074i	−0.624341	−	0.781152i
$385$	3.11415	−	5.39387i	0.158712	−	0.274897i
$386$	7.81808	−	16.5216i	0.397930	−	0.840930i
$387$	−5.24438	−	0.991100i	−0.266587	−	0.0503804i
$388$	−22.9692	−	28.0102i	−1.16608	−	1.42200i
$389$	−15.5286	−	20.2373i	−0.787334	−	1.02607i	−0.998814	−	0.0486909i	$-0.984495\pi$
$389$	−15.5286	−	20.2373i	−0.787334	−	1.02607i	0.211480	−	0.977382i	$-0.432172\pi$
$390$	1.10482	+	0.389598i	0.0559446	+	0.0197281i
$391$	−1.60264	+	5.98113i	−0.0810489	+	0.302479i
$392$	−6.46591	+	6.25042i	−0.326578	+	0.315694i
$393$	−8.67325	−	16.0414i	−0.437507	−	0.809182i
$394$	−4.24342	+	0.915628i	−0.213780	+	0.0461287i
$395$	3.98051	+	1.64878i	0.200281	+	0.0829592i
$396$	14.2896	−	23.4570i	0.718078	−	1.17876i
$397$	−2.56031	−	6.18113i	−0.128498	−	0.310222i	0.846516	−	0.532363i	$-0.178696\pi$
$397$	−2.56031	−	6.18113i	−0.128498	−	0.310222i	−0.975015	+	0.222140i	$0.928696\pi$
$398$	−5.85260	+	32.1295i	−0.293364	+	1.61051i
$399$	−0.519309	−	2.17998i	−0.0259980	−	0.109135i
$400$	17.2785	+	8.53747i	0.863924	+	0.426874i
$401$	−0.997516	+	0.575916i	−0.0498135	+	0.0287599i	−0.524700	−	0.851287i	$-0.675822\pi$
$401$	−0.997516	+	0.575916i	−0.0498135	+	0.0287599i	0.474886	+	0.880047i	$0.342489\pi$
$402$	−14.9814	+	29.4988i	−0.747206	+	1.47127i
$403$	−7.89371	−	1.03923i	−0.393214	−	0.0517676i
$404$	2.05991	−	0.623994i	0.102484	−	0.0310448i
$405$	0.0734471	+	3.83718i	0.00364962	+	0.190671i
$406$	−30.6076	+	27.7303i	−1.51903	+	1.37623i
$407$	−9.63771	−	35.9684i	−0.477723	−	1.78289i
$408$	−1.40058	+	7.88537i	−0.0693390	+	0.390384i
$409$	−1.12025	+	4.18082i	−0.0553927	+	0.206728i	−0.988076	−	0.153969i	$-0.950795\pi$
$409$	−1.12025	+	4.18082i	−0.0553927	+	0.206728i	0.932683	+	0.360697i	$0.117461\pi$
$410$	2.41469	+	4.70324i	0.119253	+	0.232276i
$411$	−4.57071	+	28.5332i	−0.225457	+	1.40744i
$412$	8.94638	+	6.41614i	0.440756	+	0.316100i
$413$	−23.5334	+	9.74785i	−1.15800	+	0.479660i
$414$	−7.67417	+	14.1192i	−0.377165	+	0.693919i
$415$	−6.15833			−0.302300
$416$	4.55470	+	4.41660i	0.223313	+	0.216542i
$417$	1.49536	−	5.01581i	0.0732280	−	0.245625i
$418$	0.214037	+	2.61659i	0.0104689	+	0.127982i
$419$	−8.95241	−	6.86943i	−0.437354	−	0.335593i	0.366502	−	0.930417i	$-0.380555\pi$
$419$	−8.95241	−	6.86943i	−0.437354	−	0.335593i	−0.803856	+	0.594824i	$0.797222\pi$
$420$	−1.78445	+	4.36220i	−0.0870724	+	0.212853i
$421$	4.34036	+	5.65647i	0.211536	+	0.275679i	0.887055	−	0.461663i	$-0.152747\pi$
$421$	4.34036	+	5.65647i	0.211536	+	0.275679i	−0.675519	+	0.737342i	$0.736080\pi$
$422$	−19.6486	−	0.969095i	−0.956479	−	0.0471748i
$423$	2.65333	+	12.7027i	0.129009	+	0.617625i
$424$	−20.5339	−	3.05813i	−0.997214	−	0.148516i
$425$	−2.03863	−	7.60826i	−0.0988880	−	0.369055i
$426$	−1.55915	+	2.27500i	−0.0755412	+	0.110224i
$427$	−1.63484	−	12.4179i	−0.0791155	−	0.600942i
$428$	−3.12484	+	3.33376i	−0.151045	+	0.161143i
$429$	−3.63128	+	8.11751i	−0.175320	+	0.391917i
$430$	−1.05553	−	0.192271i	−0.0509020	−	0.00927214i
$431$		−	32.4200i		−	1.56162i	−0.624771	−	0.780808i	$-0.714808\pi$
$431$		−	32.4200i		−	1.56162i	0.624771	−	0.780808i	$-0.285192\pi$
$432$	−8.32011	+	19.0467i	−0.400302	+	0.916383i
$433$		−	23.3172i		−	1.12055i	−0.828306	−	0.560276i	$-0.810695\pi$
$433$		−	23.3172i		−	1.12055i	0.828306	−	0.560276i	$-0.189305\pi$
$434$	5.74026	−	31.5128i	0.275542	−	1.51266i
$435$	−2.76071	+	6.17140i	−0.132366	+	0.295896i
$436$	18.1802	−	0.588098i	0.870674	−	0.0281648i
$437$	−0.200488	−	1.52286i	−0.00959065	−	0.0728482i
$438$	8.07868	+	5.53666i	0.386014	+	0.264552i
$439$	1.51685	+	5.66095i	0.0723952	+	0.270182i	0.992630	−	0.121184i	$-0.0386691\pi$
$439$	1.51685	+	5.66095i	0.0723952	+	0.270182i	−0.920235	+	0.391367i	$0.872002\pi$
$440$	2.84133	−	4.73423i	0.135455	−	0.225695i
$441$	9.06133	+	2.97952i	0.431492	+	0.141882i
$442$	0.127732	−	2.58979i	0.00607559	−	0.123184i
$443$	23.4235	+	30.5261i	1.11288	+	1.45034i	0.878216	+	0.478264i	$0.158734\pi$
$443$	23.4235	+	30.5261i	1.11288	+	1.45034i	0.234669	+	0.972075i	$0.424599\pi$
$444$	10.8976	+	25.9855i	0.517179	+	1.23322i
$445$	−0.368482	−	0.282746i	−0.0174677	−	0.0134035i
$446$	29.3695	−	2.40243i	1.39069	−	0.113758i
$447$	−2.42259	+	8.12597i	−0.114585	+	0.384345i
$448$	−18.6496	+	17.4265i	−0.881110	+	0.823326i
$449$	−16.0967			−0.759652			−0.379826	−	0.925058i	$-0.624016\pi$
$449$	−16.0967			−0.759652			−0.379826	+	0.925058i	$0.624016\pi$
$450$	−0.526066	−	20.4349i	−0.0247990	−	0.963312i
$451$	−37.0772	+	15.3579i	−1.74590	+	0.723175i
$452$	−5.81843	−	35.3270i	−0.273676	−	1.66164i
$453$	−1.89254	+	11.8144i	−0.0889193	+	0.555088i
$454$	−6.26367	+	3.21583i	−0.293969	+	0.150926i
$455$	0.394936	−	1.47392i	0.0185149	−	0.0690984i
$456$	−0.427559	−	1.94008i	−0.0200223	−	0.0908526i
$457$	−2.35708	−	8.79673i	−0.110259	−	0.411494i	0.888629	−	0.458626i	$-0.151658\pi$
$457$	−2.35708	−	8.79673i	−0.110259	−	0.411494i	−0.998889	+	0.0471327i	$0.984992\pi$
$458$	−19.0179	−	20.9912i	−0.888646	−	0.980852i
$459$	8.09259	−	2.58227i	0.377730	−	0.120530i
$460$	−1.52391	+	2.84838i	−0.0710527	+	0.132806i
$461$	10.4820	+	1.37998i	0.488194	+	0.0642719i	0.370605	−	0.928790i	$-0.379150\pi$
$461$	10.4820	+	1.37998i	0.488194	+	0.0642719i	0.117589	+	0.993062i	$0.462484\pi$
$462$	−31.8984	−	16.2001i	−1.48405	−	0.753697i
$463$	−32.3830	+	18.6963i	−1.50496	+	0.868891i	−0.504981	+	0.863131i	$0.668500\pi$
$463$	−32.3830	+	18.6963i	−1.50496	+	0.868891i	−0.999983	+	0.00576076i	$0.998166\pi$
$464$	−27.5464	+	24.1198i	−1.27881	+	1.11973i
$465$	−1.21505	−	5.10059i	−0.0563466	−	0.236534i
$466$	24.6442	+	4.48911i	1.14162	+	0.207954i
$467$	−11.4688	−	27.6880i	−0.530710	−	1.28125i	−0.931053	−	0.364883i	$-0.881109\pi$
$467$	−11.4688	−	27.6880i	−0.530710	−	1.28125i	0.400343	−	0.916365i	$-0.368891\pi$
$468$	1.89420	−	6.45717i	0.0875594	−	0.298483i
$469$	39.8140	+	16.4915i	1.83844	+	0.761507i
$470$	0.550216	+	2.54994i	0.0253796	+	0.117620i
$471$	10.7485	+	19.8796i	0.495263	+	0.916002i
$472$	−21.0059	+	8.28678i	−0.966874	+	0.381430i
$473$	2.10788	−	7.86672i	0.0969205	−	0.361712i
$474$	8.23047	−	23.3399i	0.378038	−	1.07204i
$475$	1.18943	+	1.55010i	0.0545750	+	0.0711235i
$476$	10.3811	+	1.02651i	0.475816	+	0.0470501i
$477$	7.27720	+	20.7824i	0.333200	+	0.951562i
$478$	1.56783	+	0.741899i	0.0717107	+	0.0339337i
$479$	7.85459	−	13.6046i	0.358886	−	0.621608i	−0.628889	−	0.777495i	$-0.716490\pi$
$479$	7.85459	−	13.6046i	0.358886	−	0.621608i	0.987775	+	0.155887i	$0.0498235\pi$
$480$	−1.64722	+	3.83975i	−0.0751850	+	0.175260i
$481$	−4.56150	−	7.90075i	−0.207987	−	0.360243i
$482$	−0.260358	−	3.18286i	−0.0118590	−	0.144975i
$483$	19.1070	+	8.54731i	0.869398	+	0.388916i
$484$	16.1813	+	11.6048i	0.735512	+	0.527493i
$485$	−2.95564	+	7.13554i	−0.134209	+	0.324008i
$486$	21.9870	−	1.60385i	0.997350	−	0.0727523i
$487$	−17.3325	−	17.3325i	−0.785412	−	0.785412i	0.195326	−	0.980738i	$-0.437423\pi$
$487$	−17.3325	−	17.3325i	−0.785412	−	0.785412i	−0.980738	+	0.195326i	$0.937423\pi$
$488$	−1.26256	−	11.0315i	−0.0571535	−	0.499371i
$489$	22.2324	+	0.621341i	1.00538	+	0.0280980i
$490$	1.82544	+	0.586914i	0.0824649	+	0.0265141i
$491$	−4.99064	−	37.9077i	−0.225225	−	1.71075i	−0.613906	−	0.789379i	$-0.710403\pi$
$491$	−4.99064	−	37.9077i	−0.225225	−	1.71075i	0.388682	−	0.921372i	$-0.372931\pi$
$492$	26.2330	−	15.2998i	1.18268	−	0.689770i
$493$	14.8359	+	1.95319i	0.668176	+	0.0879670i
$494$	0.216569	+	0.605641i	0.00974391	+	0.0272491i
$495$	−5.84721	−	0.327086i	−0.262813	−	0.0147014i
$496$	5.56138	−	27.8460i	0.249713	−	1.25032i
$497$	3.11110	+	1.79619i	0.139552	+	0.0805703i
$498$	1.89792	+	35.3235i	0.0850477	+	1.58288i
$499$	10.0282	−	13.0690i	0.448924	−	0.585049i	−0.512993	−	0.858393i	$-0.671463\pi$
$499$	10.0282	−	13.0690i	0.448924	−	0.585049i	0.961916	+	0.273344i	$0.0881298\pi$
$500$	−0.270728	−	8.36917i	−0.0121073	−	0.374280i
$501$	14.2156	−	17.4918i	0.635107	−	0.781475i
$502$	−24.5950	+	5.30701i	−1.09773	+	0.236864i
$503$	−4.50424	+	4.50424i	−0.200834	+	0.200834i	−0.800357	−	0.599523i	$-0.795357\pi$
$503$	−4.50424	+	4.50424i	−0.200834	+	0.200834i	0.599523	+	0.800357i	$0.295357\pi$
$504$	25.5710	+	8.89104i	1.13902	+	0.396038i
$505$	−0.324501	−	0.324501i	−0.0144401	−	0.0144401i
$506$	−20.6066	−	13.2921i	−0.916076	−	0.590905i
$507$	3.21692	−	20.0820i	0.142868	−	0.891871i
$508$	−5.84963	+	15.5238i	−0.259535	+	0.688758i
$509$	16.8562	+	12.9342i	0.747136	+	0.573298i	0.910618	−	0.413249i	$-0.135606\pi$
$509$	16.8562	+	12.9342i	0.747136	+	0.573298i	−0.163482	+	0.986546i	$0.552273\pi$
$510$	1.62333	−	0.529817i	0.0718821	−	0.0234607i
$511$	6.37841	−	11.0477i	0.282164	−	0.488723i
$512$	−16.7923	+	15.1664i	−0.742122	+	0.670264i
$513$	−1.60949	+	1.36000i	−0.0710607	+	0.0600455i
$514$	4.63681	−	9.79880i	0.204521	−	0.432207i
$515$	0.306391	−	2.32727i	0.0135012	−	0.102552i
$516$	−0.777545	+	6.11364i	−0.0342295	+	0.269138i
$517$	−19.6323	+	2.58465i	−0.863430	+	0.113673i
$518$	32.6510	−	16.7634i	1.43460	−	0.736539i
$519$	−33.1966	−	20.4233i	−1.45717	−	0.896485i
$520$	0.372201	−	1.30052i	0.0163221	−	0.0570314i
$521$	7.90659	−	7.90659i	0.346394	−	0.346394i	−0.512371	−	0.858764i	$-0.671233\pi$
$521$	7.90659	−	7.90659i	0.346394	−	0.346394i	0.858764	+	0.512371i	$0.171233\pi$
$522$	36.2493	+	13.9332i	1.58659	+	0.609839i
$523$	−36.2499	−	15.0152i	−1.58510	−	0.656568i	−0.595886	−	0.803069i	$-0.703199\pi$
$523$	−36.2499	−	15.0152i	−1.58510	−	0.656568i	−0.989211	+	0.146501i	$0.953199\pi$
$524$	−17.8861	+	11.1127i	−0.781357	+	0.485459i
$525$	−26.4850	+	2.73655i	−1.15590	+	0.119433i
$526$	28.8598	+	24.4953i	1.25835	+	1.06805i
$527$	−10.0505	+	5.80266i	−0.437807	+	0.252768i
$528$	−28.0306	−	14.8385i	−1.21988	−	0.645764i
$529$	−7.49383	−	4.32657i	−0.325819	−	0.188112i
$530$	1.49041	+	4.16798i	0.0647394	+	0.181045i
$531$	18.1577	+	15.6190i	0.787978	+	0.677809i
$532$	−2.47652	+	0.750196i	−0.107371	+	0.0325251i
$533$	−7.80043	+	5.98548i	−0.337874	+	0.259260i
$534$	−1.50824	+	2.20071i	−0.0652678	+	0.0952339i
$535$	0.941052	+	0.252154i	0.0406852	+	0.0109016i
$536$	35.0425	+	15.2157i	1.51361	+	0.657219i
$537$	0.565290	−	20.2268i	0.0243941	−	0.872852i
$538$	−8.94037	+	13.8602i	−0.385447	+	0.597555i
$539$	−5.57007	+	13.4473i	−0.239920	+	0.579218i
$540$	4.41764	−	0.351570i	0.190105	−	0.0151292i
$541$	22.5706	−	9.34903i	0.970384	−	0.401946i	0.159529	−	0.987193i	$-0.449002\pi$
$541$	22.5706	−	9.34903i	0.970384	−	0.401946i	0.810855	+	0.585247i	$0.199002\pi$
$542$	19.4811	−	13.4775i	0.836784	−	0.578907i
$543$	−26.8438	−	28.3873i	−1.15198	−	1.21822i
$544$	9.18612	+	1.06581i	0.393852	+	0.0456961i
$545$	−1.93917	−	3.35874i	−0.0830648	−	0.143872i
$546$	−8.57595	−	1.81106i	−0.367017	−	0.0775063i
$547$	−1.89660	+	14.4061i	−0.0810926	+	0.615959i	0.901850	+	0.432048i	$0.142209\pi$
$547$	−1.89660	+	14.4061i	−0.0810926	+	0.615959i	−0.982943	+	0.183911i	$0.941124\pi$
$548$	33.2054	+	3.28345i	1.41846	+	0.140262i
$549$	−9.72917	+	6.63636i	−0.415231	+	0.283233i
$550$	31.1548	+	1.53659i	1.32844	+	0.0655206i
$551$	−3.58543	+	0.960713i	−0.152744	+	0.0409277i
$552$	16.8076	+	7.86314i	0.715379	+	0.334677i
$553$	−31.1374	−	8.34323i	−1.32410	−	0.354790i
$554$	−38.7589	−	12.4617i	−1.64671	−	0.529449i
$555$	3.78918	−	4.66244i	0.160842	−	0.197910i
$556$	−5.88525	−	1.37466i	−0.249590	−	0.0582984i
$557$	10.2697	+	24.7933i	0.435142	+	1.05053i	0.977605	+	0.210446i	$0.0674916\pi$
$557$	10.2697	+	24.7933i	0.435142	+	1.05053i	−0.542464	+	0.840079i	$0.682508\pi$
$558$	−28.8819	+	8.54133i	−1.22267	+	0.361583i
$559$		−	1.99531i		−	0.0843925i
$560$	5.15201	+	1.75333i	0.217712	+	0.0740918i
$561$	3.00377	+	12.6093i	0.126819	+	0.532367i
$562$	−17.3668	−	14.7404i	−0.732574	−	0.621787i
$563$	2.42281	−	3.15747i	0.102109	−	0.133071i	−0.739504	−	0.673152i	$-0.764940\pi$
$563$	2.42281	−	3.15747i	0.102109	−	0.133071i	0.841613	+	0.540081i	$0.181606\pi$
$564$	14.4566	−	3.94183i	0.608732	−	0.165981i
$565$	−6.05626	+	4.64713i	−0.254789	+	0.195506i
$566$	28.5032	+	31.4607i	1.19808	+	1.32239i
$567$	−4.29218	−	28.3923i	−0.180255	−	1.19236i
$568$	2.73063	+	1.63883i	0.114575	+	0.0687640i
$569$	18.7500	−	5.02405i	0.786042	−	0.210619i	0.156595	−	0.987663i	$-0.449948\pi$
$569$	18.7500	−	5.02405i	0.786042	−	0.210619i	0.629447	+	0.777044i	$0.283282\pi$
$570$	−0.321731	+	0.275519i	−0.0134758	+	0.0115402i
$571$	−23.3358	+	3.07222i	−0.976575	+	0.128569i	−0.601886	−	0.798582i	$-0.705584\pi$
$571$	−23.3358	+	3.07222i	−0.976575	+	0.128569i	−0.374689	+	0.927151i	$0.622250\pi$
$572$	9.60886	+	3.62078i	0.401767	+	0.151392i
$573$	4.39709	−	3.18286i	0.183691	−	0.132966i
$574$	−22.5051	−	32.5302i	−0.939346	−	1.35778i
$575$	−18.2499			−0.761072
$576$	22.5320	+	8.26491i	0.938834	+	0.344371i
$577$	34.6404			1.44210			0.721050	−	0.692884i	$-0.243660\pi$
$577$	34.6404			1.44210			0.721050	+	0.692884i	$0.243660\pi$
$578$	11.5279	+	16.6631i	0.479499	+	0.693095i
$579$	2.30077	+	22.2674i	0.0956169	+	0.925402i
$580$	7.30521	+	2.75272i	0.303332	+	0.114301i
$581$	45.6821	−	6.01416i	1.89521	−	0.249510i
$582$	41.8395	+	14.7541i	1.73430	+	0.611578i
$583$	−32.4557	+	8.69647i	−1.34418	+	0.360171i
$584$	5.81962	−	9.69665i	0.240818	−	0.401250i
$585$	−1.40447	+	0.293366i	−0.0580679	+	0.0121292i
$586$	14.5579	+	16.0684i	0.601382	+	0.663782i
$587$	−12.2976	+	9.43632i	−0.507578	+	0.389478i	−0.830562	−	0.556926i	$-0.811981\pi$
$587$	−12.2976	+	9.43632i	−0.507578	+	0.389478i	0.322984	+	0.946404i	$0.395314\pi$
$588$	2.80389	−	10.6514i	0.115631	−	0.439256i
$589$	1.75249	−	2.28389i	0.0722101	−	0.0941061i
$590$	3.67074	+	3.11561i	0.151122	+	0.128268i
$591$	3.86304	−	3.65299i	0.158904	−	0.150264i
$592$	29.1929	−	14.3682i	1.19982	−	0.590530i
$593$			16.7958i			0.689720i	0.938654	+	0.344860i	$0.112074\pi$
$593$			16.7958i			0.689720i	−0.938654	+	0.344860i	$0.887926\pi$
$594$	−0.0740921	+	33.6397i	−0.00304004	+	1.38025i
$595$	−0.851166	−	2.05490i	−0.0348944	−	0.0842425i
$596$	9.53453	+	2.22704i	0.390550	+	0.0912232i
$597$	−14.2682	−	37.3665i	−0.583959	−	1.52931i
$598$	−5.71938	−	1.83889i	−0.233883	−	0.0751979i
$599$	−16.4323	−	4.40303i	−0.671406	−	0.179903i	−0.0930180	−	0.995664i	$-0.529651\pi$
$599$	−16.4323	−	4.40303i	−0.671406	−	0.179903i	−0.578388	+	0.815762i	$0.696318\pi$
$600$	−23.5168	+	2.02780i	−0.960069	+	0.0827846i
$601$	37.3326	−	10.0032i	1.52283	−	0.408040i	0.602156	−	0.798378i	$-0.294308\pi$
$601$	37.3326	−	10.0032i	1.52283	−	0.408040i	0.920672	+	0.390338i	$0.127642\pi$
$602$	8.01761	+	0.395439i	0.326773	+	0.0161169i
$603$	−3.03698	−	40.4068i	−0.123675	−	1.64549i
$604$	13.7490	+	1.35954i	0.559437	+	0.0553189i
$605$	0.554168	−	4.20933i	0.0225302	−	0.171134i
$606$	−1.76129	+	1.96131i	−0.0715476	+	0.0796727i
$607$	18.9333	+	32.7934i	0.768478	+	1.33104i	0.938388	+	0.345583i	$0.112319\pi$
$607$	18.9333	+	32.7934i	0.768478	+	1.33104i	−0.169910	+	0.985460i	$0.554348\pi$
$608$	−2.20640	+	0.627758i	−0.0894814	+	0.0254589i
$609$	14.4519	−	48.4752i	0.585619	−	1.96431i
$610$	−1.94693	+	1.34693i	−0.0788288	+	0.0545356i
$611$	−4.48208	+	1.85654i	−0.181325	+	0.0751074i
$612$	−3.53926	−	9.14793i	−0.143066	−	0.369783i
$613$	−4.47908	+	10.8135i	−0.180908	+	0.436752i	−0.988154	−	0.153464i	$-0.950957\pi$
$613$	−4.47908	+	10.8135i	−0.180908	+	0.436752i	0.807246	+	0.590215i	$0.200957\pi$
$614$	−16.4862	+	25.5585i	−0.665331	+	1.03146i
$615$	−5.51495	−	3.39294i	−0.222384	−	0.136816i
$616$	−16.4534	+	37.8930i	−0.662928	+	1.52675i
$617$	−32.2429	−	8.63947i	−1.29805	−	0.347812i	−0.457339	−	0.889292i	$-0.651197\pi$
$617$	−32.2429	−	8.63947i	−1.29805	−	0.347812i	−0.840713	+	0.541480i	$0.817864\pi$
$618$	−13.4434	−	1.04019i	−0.540772	−	0.0418425i
$619$	5.32184	−	4.08359i	0.213903	−	0.164133i	−0.496253	−	0.868178i	$-0.665291\pi$
$619$	5.32184	−	4.08359i	0.213903	−	0.164133i	0.710156	+	0.704045i	$0.248625\pi$
$620$	−5.79444	+	1.75527i	−0.232710	+	0.0704933i
$621$	−0.926245	−	19.6598i	−0.0371689	−	0.788920i
$622$	−7.91092	−	22.1231i	−0.317199	−	0.887054i
$623$	3.00950	+	1.73754i	0.120573	+	0.0696130i
$624$	−7.57432	−	1.73410i	−0.303215	−	0.0694195i
$625$	19.3171	−	11.1527i	0.772682	−	0.446108i
$626$	10.6515	+	9.04066i	0.425718	+	0.361337i
$627$	−1.88536	−	2.60460i	−0.0752940	−	0.104018i
$628$	22.1656	−	13.7715i	0.884504	−	0.549544i
$629$	−12.2856	−	5.08887i	−0.489860	−	0.202907i
$630$	−0.900467	−	5.70164i	−0.0358755	−	0.227159i
$631$	−26.2568	+	26.2568i	−1.04527	+	1.04527i	−0.0463429	+	0.998926i	$0.514757\pi$
$631$	−26.2568	+	26.2568i	−1.04527	+	1.04527i	−0.998926	+	0.0463429i	$0.985243\pi$
$632$	−27.4741	−	7.86295i	−1.09286	−	0.312771i
$633$	21.1942	−	11.4593i	0.842395	−	0.455465i
$634$	8.21558	−	4.21795i	0.326282	−	0.167516i
$635$	3.50685	−	0.461686i	0.139165	−	0.0183214i
$636$	23.4477	−	9.83335i	0.929762	−	0.389918i
$637$	−0.465456	+	3.53549i	−0.0184420	+	0.140081i
$638$	−25.3470	+	53.5648i	−1.00350	+	2.12065i
$639$	0.188658	−	3.37258i	0.00746319	−	0.133417i
$640$	4.54029	+	1.63150i	0.179471	+	0.0644907i
$641$	−14.6121	+	25.3089i	−0.577144	+	0.999643i	0.418661	+	0.908143i	$0.362500\pi$
$641$	−14.6121	+	25.3089i	−0.577144	+	0.999643i	−0.995805	+	0.0915002i	$0.970834\pi$
$642$	1.15631	−	5.47547i	0.0456358	−	0.216100i
$643$	18.0571	+	13.8557i	0.712101	+	0.546414i	0.900062	−	0.435762i	$-0.143521\pi$
$643$	18.0571	+	13.8557i	0.712101	+	0.546414i	−0.187961	+	0.982177i	$0.560188\pi$
$644$	8.52258	−	22.6173i	0.335837	−	0.891248i
$645$	1.22757	−	0.468744i	0.0483357	−	0.0184568i
$646$	0.787853	+	0.508196i	0.0309977	+	0.0199947i
$647$	−17.5307	−	17.5307i	−0.689203	−	0.689203i	0.272853	−	0.962056i	$-0.412033\pi$
$647$	−17.5307	−	17.5307i	−0.689203	−	0.689203i	−0.962056	+	0.272853i	$0.912033\pi$
$648$	−3.37802	−	25.2307i	−0.132701	−	0.991156i
$649$	−25.8432	+	25.8432i	−1.01443	+	1.01443i
$650$	7.47017	−	1.61189i	0.293004	−	0.0632234i
$651$	13.9944	+	36.6493i	0.548482	+	1.43640i
$652$	−0.830326	−	25.6684i	−0.0325181	−	1.00525i
$653$	−0.390285	+	0.508630i	−0.0152730	+	0.0199042i	−0.800927	−	0.598761i	$-0.795660\pi$
$653$	−0.390285	+	0.508630i	−0.0152730	+	0.0199042i	0.785654	+	0.618666i	$0.212326\pi$
$654$	−18.6677	+	12.1580i	−0.729965	+	0.475414i
$655$	3.88821	+	2.24486i	0.151925	+	0.0877138i
$656$	−19.4594	−	29.1720i	−0.759762	−	1.13898i
$657$	−11.9763	−	0.669937i	−0.467238	−	0.0261368i
$658$	−6.57171	−	18.3779i	−0.256192	−	0.716447i
$659$	11.8330	+	1.55784i	0.460949	+	0.0606850i	0.357425	−	0.933942i	$-0.383655\pi$
$659$	11.8330	+	1.55784i	0.460949	+	0.0606850i	0.103524	+	0.994627i	$0.466988\pi$
$660$	0.0297317	+	6.76227i	0.00115730	+	0.263221i
$661$	−3.54669	−	26.9398i	−0.137950	−	1.04784i	−0.910683	−	0.413106i	$-0.864444\pi$
$661$	−3.54669	−	26.9398i	−0.137950	−	1.04784i	0.772733	−	0.634732i	$-0.218889\pi$
$662$	24.5452	+	7.89177i	0.953977	+	0.306722i
$663$	1.51039	+	2.79352i	0.0586588	+	0.108491i
$664$	40.5819	−	4.64465i	1.57488	−	0.180247i
$665$	0.390131	+	0.390131i	0.0151286	+	0.0151286i
$666$	−27.9110	−	20.2974i	−1.08153	−	0.786508i
$667$	13.2679	−	32.0316i	0.513736	−	1.24027i
$668$	−21.1499	−	15.1682i	−0.818315	−	0.586877i
$669$	−29.2349	+	21.1619i	−1.13029	+	0.818166i
$670$	−0.664089	−	8.11844i	−0.0256560	−	0.313643i
$671$	−8.98546	−	15.5633i	−0.346880	−	0.600814i
$672$	8.46912	−	30.0917i	0.326703	−	1.16081i
$673$	8.51778	−	14.7532i	0.328336	−	0.568695i	−0.653846	−	0.756628i	$-0.726845\pi$
$673$	8.51778	−	14.7532i	0.328336	−	0.568695i	0.982182	+	0.187933i	$0.0601787\pi$
$674$	12.4857	+	5.90826i	0.480931	+	0.227578i
$675$	13.5244	+	21.0686i	0.520556	+	0.810930i
$676$	−23.3703	−	2.31093i	−0.898858	−	0.0888819i
$677$	5.09678	+	6.64225i	0.195885	+	0.255282i	0.880961	−	0.473190i	$-0.156897\pi$
$677$	5.09678	+	6.64225i	0.195885	+	0.255282i	−0.685076	+	0.728472i	$0.740231\pi$
$678$	28.5219	+	33.3058i	1.09538	+	1.27910i
$679$	14.9562	−	55.8175i	0.573968	−	2.14208i
$680$	−0.723588	−	1.83420i	−0.0277483	−	0.0703383i
$681$	4.51864	−	7.34470i	0.173155	−	0.281450i
$682$	−9.69370	−	44.9248i	−0.371191	−	1.72026i
$683$	30.1210	+	12.4765i	1.15255	+	0.477401i	0.875387	−	0.483422i	$-0.160606\pi$
$683$	30.1210	+	12.4765i	1.15255	+	0.477401i	0.277161	+	0.960823i	$0.410606\pi$
$684$	1.67950	+	1.76050i	0.0642172	+	0.0673145i
$685$	−2.72258	−	6.57288i	−0.104024	−	0.251137i
$686$	16.9592	+	3.08924i	0.647507	+	0.117948i
$687$	33.2450	+	9.91130i	1.26837	+	0.378140i
$688$	7.10068	+	0.470937i	0.270711	+	0.0179543i
$689$	−7.12914	+	4.11601i	−0.271599	+	0.156808i
$690$	−0.212271	−	3.95073i	−0.00808104	−	0.150402i
$691$	2.67329	+	0.351945i	0.101697	+	0.0133886i	0.181203	−	0.983446i	$-0.442001\pi$
$691$	2.67329	+	0.351945i	0.101697	+	0.0133886i	−0.0795060	+	0.996834i	$0.525334\pi$
$692$	−21.2309	+	39.6831i	−0.807076	+	1.50853i
$693$	43.6937	−	3.28403i	1.65979	−	0.124750i
$694$	7.91681	+	8.73826i	0.300518	+	0.331700i
$695$	0.333515	+	1.24470i	0.0126510	+	0.0472140i
$696$	13.5379	−	42.7502i	0.513154	−	1.62044i
$697$	−3.70931	+	13.8433i	−0.140500	+	0.524353i
$698$	5.27084	−	2.70610i	0.199504	−	0.102427i
$699$	−28.6612	+	10.9441i	−1.08406	+	0.413945i
$700$	4.99646	+	30.3363i	0.188848	+	1.14661i
$701$	32.5898	−	13.4991i	1.23090	−	0.509856i	0.330041	−	0.943967i	$-0.392937\pi$
$701$	32.5898	−	13.4991i	1.23090	−	0.509856i	0.900859	+	0.434111i	$0.142937\pi$
$702$	2.11555	+	7.96549i	0.0798464	+	0.300638i
$703$	3.29863			0.124410
$704$	−15.1531	+	33.3404i	−0.571105	+	1.25656i
$705$	−2.19514	−	2.32137i	−0.0826738	−	0.0874277i
$706$	−16.2154	+	1.32642i	−0.610275	+	0.0499205i
$707$	2.72403	+	2.09022i	0.102448	+	0.0786110i
$708$	16.7395	−	22.0151i	0.629110	−	0.827378i
$709$	−6.84568	−	8.92147i	−0.257095	−	0.335053i	0.646917	−	0.762561i	$-0.276058\pi$
$709$	−6.84568	−	8.92147i	−0.257095	−	0.335053i	−0.904012	+	0.427508i	$0.859392\pi$
$710$	0.0334495	−	0.678197i	0.00125534	−	0.0254523i
$711$	6.19752	+	29.6703i	0.232425	+	1.11272i
$712$	2.64146	+	1.58532i	0.0989928	+	0.0594123i
$713$	6.95939	+	25.9728i	0.260631	+	0.972688i
$714$	−11.5243	+	5.51548i	−0.431287	+	0.206412i
$715$	−0.285772	−	2.17066i	−0.0106873	−	0.0811780i
$716$	−23.3528	+	0.755423i	−0.872736	+	0.0282315i
$717$	−2.11307	+	0.218333i	−0.0789141	+	0.00815378i
$718$	−6.65457	+	36.5321i	−0.248346	+	1.36337i
$719$			39.5700i			1.47571i	0.674957	+	0.737857i	$0.264162\pi$
$719$			39.5700i			1.47571i	−0.674957	+	0.737857i	$0.735838\pi$
$720$	−0.712512	−	5.06733i	−0.0265537	−	0.188848i
$721$			17.5628i			0.654072i
$722$	26.2063	+	4.77364i	0.975296	+	0.177657i
$723$	2.29338	+	3.16828i	0.0852917	+	0.117830i
$724$	−30.8521	+	32.9148i	−1.14661	+	1.22327i
$725$	5.75656	+	43.7254i	0.213793	+	1.62392i
$726$	−24.3150	−	1.88139i	−0.902414	−	0.0698248i
$727$	−2.51716	−	9.39415i	−0.0933562	−	0.348410i	0.903409	−	0.428780i	$-0.141056\pi$
$727$	−2.51716	−	9.39415i	−0.0933562	−	0.348410i	−0.996765	+	0.0803701i	$0.974390\pi$
$728$	−1.49089	+	10.0106i	−0.0552562	+	0.371019i
$729$	−22.0099	+	15.6386i	−0.815180	+	0.579208i
$730$	−2.40832	−	0.118782i	−0.0891361	−	0.00439631i
$731$	−1.77052	−	2.30739i	−0.0654851	−	0.0853419i
$732$	8.32585	+	10.7522i	0.307732	+	0.397415i
$733$	23.5943	+	18.1046i	0.871477	+	0.668708i	0.944460	−	0.328625i	$-0.106585\pi$
$733$	23.5943	+	18.1046i	0.871477	+	0.668708i	−0.0729834	+	0.997333i	$0.523252\pi$
$734$	−1.84519	−	22.5574i	−0.0681074	−	0.832608i
$735$	−2.28449	+	0.544205i	−0.0842646	+	0.0200733i
$736$	7.89395	−	19.9195i	0.290975	−	0.734241i
$737$	61.8320			2.27761
$738$	−17.7618	+	32.6788i	−0.653823	+	1.20292i
$739$	−8.44783	+	3.49921i	−0.310759	+	0.128720i	−0.532612	−	0.846360i	$-0.678789\pi$
$739$	−8.44783	+	3.49921i	−0.310759	+	0.128720i	0.221853	+	0.975080i	$0.428789\pi$
$740$	−5.63752	−	4.04310i	−0.207239	−	0.148627i
$741$	−0.611325	−	0.496826i	−0.0224576	−	0.0182513i
$742$	−15.1262	−	29.4623i	−0.555300	−	1.08159i
$743$	−1.09655	+	4.09237i	−0.0402284	+	0.150134i	−0.983119	−	0.182969i	$-0.941429\pi$
$743$	−1.09655	+	4.09237i	−0.0402284	+	0.150134i	0.942890	+	0.333103i	$0.108096\pi$
$744$	11.8538	+	32.6953i	0.434581	+	1.19867i
$745$	−0.540319	−	2.01650i	−0.0197958	−	0.0738788i
$746$	−30.7794	+	27.8859i	−1.12691	+	1.02098i
$747$	−24.4135	−	35.7911i	−0.893242	−	1.30953i
$748$	14.3246	−	4.33926i	0.523760	−	0.158659i
$749$	−7.22691	−	0.951441i	−0.264066	−	0.0347649i
$750$	5.59685	+	8.59358i	0.204368	+	0.313793i
$751$	5.31558	−	3.06895i	0.193968	−	0.111988i	−0.399871	−	0.916572i	$-0.630945\pi$
$751$	5.31558	−	3.06895i	0.193968	−	0.111988i	0.593839	+	0.804584i	$0.297612\pi$
$752$	−5.54897	−	16.3885i	−0.202350	−	0.597627i
$753$	22.3903	−	21.1728i	0.815949	−	0.771581i
$754$	−2.60180	+	14.2833i	−0.0947518	+	0.520167i
$755$	−1.12731	−	2.72156i	−0.0410268	−	0.0990475i
$756$	−32.4264	+	6.92215i	−1.17934	+	0.251756i
$757$	−1.56737	−	0.649228i	−0.0569672	−	0.0235966i	0.354018	−	0.935239i	$-0.384815\pi$
$757$	−1.56737	−	0.649228i	−0.0569672	−	0.0235966i	−0.410985	+	0.911642i	$0.634815\pi$
$758$	−7.53706	+	1.62632i	−0.273758	+	0.0590706i
$759$	30.0211	+	0.839015i	1.08970	+	0.0304543i
$760$	0.339944	+	0.351664i	0.0123311	+	0.0127562i
$761$	−5.25411	+	19.6086i	−0.190461	+	0.710812i	0.802934	+	0.596068i	$0.203271\pi$
$761$	−5.25411	+	19.6086i	−0.190461	+	0.710812i	−0.993395	+	0.114743i	$0.963395\pi$
$762$	−3.72894	−	19.9726i	−0.135085	−	0.723531i
$763$	17.6647	+	23.0211i	0.639506	+	0.833421i
$764$	−3.97444	−	4.84670i	−0.143790	−	0.175348i
$765$	−1.36383	+	1.58550i	−0.0493093	+	0.0573239i
$766$	1.57079	−	3.31950i	0.0567551	−	0.119938i
$767$	−4.47705	+	7.75447i	−0.161657	+	0.279998i
$768$	7.95883	−	26.5454i	0.287190	−	0.957874i
$769$	21.7196	+	37.6194i	0.783228	+	1.35659i	0.930052	+	0.367428i	$0.119762\pi$
$769$	21.7196	+	37.6194i	0.783228	+	1.35659i	−0.146824	+	0.989163i	$0.546905\pi$
$770$	8.77883	−	0.718109i	0.316367	−	0.0258789i
$771$	1.36456	+	13.2065i	0.0491435	+	0.475622i
$772$	25.5054	−	4.20080i	0.917961	−	0.151190i
$773$	1.52810	−	3.68915i	0.0549618	−	0.132690i	−0.894013	−	0.448040i	$-0.852122\pi$
$773$	1.52810	−	3.68915i	0.0549618	−	0.132690i	0.948975	+	0.315351i	$0.102122\pi$
$774$	−3.06698	−	6.89676i	−0.110240	−	0.247899i
$775$	−24.1859	−	24.1859i	−0.868783	−	0.868783i
$776$	14.0953	−	49.2507i	0.505991	−	1.76800i
$777$	−23.5546	+	38.2862i	−0.845017	+	1.37351i
$778$	11.0420	−	34.3431i	0.395875	−	1.23126i
$779$	−0.464030	−	3.52465i	−0.0166256	−	0.126284i
$780$	0.435830	+	1.59840i	0.0156052	+	0.0572317i
$781$	5.11027	+	0.672780i	0.182860	+	0.0240740i
$782$	−8.24566	+	2.94854i	−0.294864	+	0.105440i
$783$	−46.8114	+	8.42052i	−1.67290	+	0.300925i
$784$	−12.4719	−	2.49087i	−0.445423	−	0.0889596i
$785$	−4.81852	−	2.78197i	−0.171980	−	0.0992929i
$786$	11.6779	−	22.9941i	0.416538	−	0.820173i
$787$	−23.9647	+	31.2315i	−0.854251	+	1.11328i	0.138171	+	0.990408i	$0.455878\pi$
$787$	−23.9647	+	31.2315i	−0.854251	+	1.11328i	−0.992422	+	0.122873i	$0.960789\pi$
$788$	−4.47916	−	4.19845i	−0.159563	−	0.149564i
$789$	−45.7776	−	7.33309i	−1.62973	−	0.261065i
$790$	1.28517	+	5.95602i	0.0457242	+	0.211906i
$791$	40.3866	−	40.3866i	1.43598	−	1.43598i
$792$	38.7784	−	2.25458i	1.37793	−	0.0801130i
$793$	−3.11326	−	3.11326i	−0.110555	−	0.110555i
$794$	5.12874	−	7.95105i	0.182012	−	0.282172i
$795$	−4.20710	−	3.41912i	−0.149210	−	0.121264i
$796$	−42.0762	+	19.0448i	−1.49135	+	0.675025i
$797$	26.2852	+	20.1693i	0.931068	+	0.714434i	0.958471	−	0.285191i	$-0.0920569\pi$
$797$	26.2852	+	20.1693i	0.931068	+	0.714434i	−0.0274025	+	0.999624i	$0.508724\pi$
$798$	2.11751	−	2.35798i	0.0749592	−	0.0834717i
$799$	−3.53572	+	6.12405i	−0.125085	+	0.216653i
$800$	3.97308	+	26.9645i	0.140469	+	0.953338i
$801$	0.182497	−	3.26244i	0.00644822	−	0.115273i
$802$	−1.47241	−	0.696746i	−0.0519925	−	0.0246029i
$803$	2.38909	−	18.1469i	0.0843092	−	0.640392i
$804$	−46.3618	+	6.31113i	−1.63505	+	0.222577i
$805$	−5.10929	+	0.672651i	−0.180079	+	0.0237078i
$806$	−5.14267	−	10.0167i	−0.181143	−	0.352823i
$807$	0.564329	−	20.1924i	0.0198653	−	0.710807i
$808$	2.38313	+	1.89364i	0.0838381	+	0.0666182i
$809$	37.9142	−	37.9142i	1.33299	−	1.33299i	0.430315	−	0.902679i	$-0.358403\pi$
$809$	37.9142	−	37.9142i	1.33299	−	1.33299i	0.902679	−	0.430315i	$-0.141597\pi$
$810$	−4.40362	+	3.17283i	−0.154727	+	0.111482i
$811$	−15.3551	−	6.36028i	−0.539190	−	0.223340i	0.0964329	−	0.995339i	$-0.469257\pi$
$811$	−15.3551	−	6.36028i	−0.539190	−	0.223340i	−0.635623	+	0.772000i	$0.719257\pi$
$812$	−56.8779	−	13.2853i	−1.99602	−	0.466224i
$813$	−11.8471	+	26.4835i	−0.415497	+	0.928818i
$814$	34.0774	−	40.1492i	1.19441	−	1.40723i
$815$	−4.74215	+	2.73788i	−0.166110	+	0.0959038i
$816$	−10.2977	+	4.71569i	−0.360493	+	0.165082i
$817$	0.624793	+	0.360725i	0.0218588	+	0.0126202i
$818$	−5.76373	+	2.06104i	−0.201524	+	0.0720624i
$819$	10.1318	−	3.54777i	0.354034	−	0.123969i
$820$	−3.52709	+	6.59257i	−0.123171	+	0.230222i
$821$	−8.98376	+	6.89348i	−0.313535	+	0.240584i	−0.753526	−	0.657418i	$-0.771648\pi$
$821$	−8.98376	+	6.89348i	−0.313535	+	0.240584i	0.439990	+	0.898002i	$0.354982\pi$
$822$	−36.8622	+	17.6421i	−1.28572	+	0.615337i
$823$	−6.05107	−	1.62138i	−0.210927	−	0.0565177i	0.151808	−	0.988410i	$-0.451490\pi$
$823$	−6.05107	−	1.62138i	−0.210927	−	0.0565177i	−0.362735	+	0.931892i	$0.618157\pi$
$824$	−0.263803	+	15.5673i	−0.00919002	+	0.542311i
$825$	−33.6055	+	18.1698i	−1.16999	+	0.632591i
$826$	−30.2720	−	19.5266i	−1.05330	−	0.679418i
$827$	−9.32345	+	22.5088i	−0.324208	+	0.782708i	0.674792	+	0.738008i	$0.264233\pi$
$827$	−9.32345	+	22.5088i	−0.324208	+	0.782708i	−0.999000	+	0.0447001i	$0.985767\pi$
$828$	−22.5955	+	2.43513i	−0.785248	+	0.0846266i
$829$	−10.5016	+	4.34989i	−0.364735	+	0.151078i	−0.557521	−	0.830163i	$-0.688247\pi$
$829$	−10.5016	+	4.34989i	−0.364735	+	0.151078i	0.192787	+	0.981241i	$0.438247\pi$
$830$	−4.95501	−	7.16225i	−0.171991	−	0.248605i
$831$	48.5057	−	11.5549i	1.68264	−	0.400836i
$832$	−1.47186	+	8.85081i	−0.0510275	+	0.306847i
$833$	2.59893	+	4.50149i	0.0900477	+	0.155967i
$834$	7.03665	−	2.29660i	0.243659	−	0.0795249i
$835$	−0.724332	+	5.50185i	−0.0250666	+	0.190399i
$836$	−2.87093	+	2.35425i	−0.0992932	+	0.0814234i
$837$	24.8269	−	27.2819i	0.858143	−	0.943002i
$838$	0.786132	−	15.9390i	0.0271565	−	0.550603i
$839$	45.4816	−	12.1868i	1.57020	−	0.420734i	0.634326	−	0.773066i	$-0.281278\pi$
$839$	45.4816	−	12.1868i	1.57020	−	0.420734i	0.935875	+	0.352332i	$0.114611\pi$
$840$	−6.50910	+	1.43449i	−0.224585	+	0.0494945i
$841$	−52.9189	−	14.1796i	−1.82479	−	0.488951i
$842$	−3.08631	+	9.59914i	−0.106361	+	0.330808i
$843$	27.5473	+	4.41279i	0.948781	+	0.151985i
$844$	−14.6823	−	23.6314i	−0.505384	−	0.813428i
$845$	1.91618	+	4.62607i	0.0659186	+	0.159142i
$846$	−12.6386	+	13.3065i	−0.434523	+	0.457486i
$847$			31.7657i			1.09148i
$848$	−12.9650	−	26.3419i	−0.445219	−	0.904584i
$849$	−49.8263	−	14.8547i	−1.71003	−	0.509811i
$850$	7.20827	−	8.49260i	0.247242	−	0.291294i
$851$	−18.7563	+	24.4437i	−0.642957	+	0.837918i
$852$	−3.90037	+	0.0171488i	−0.133624	+	0.000587507i
$853$	8.11354	−	6.22574i	0.277802	−	0.213165i	−0.460457	−	0.887682i	$-0.652315\pi$
$853$	8.11354	−	6.22574i	0.277802	−	0.213165i	0.738260	+	0.674517i	$0.235648\pi$
$854$	13.1268	−	11.8928i	0.449190	−	0.406963i
$855$	0.162048	−	0.492822i	0.00554192	−	0.0168541i
$856$	−6.39148	−	0.951888i	−0.218456	−	0.0325349i
$857$	−22.3177	+	5.98001i	−0.762358	+	0.204273i	−0.618993	−	0.785397i	$-0.712459\pi$
$857$	−22.3177	+	5.98001i	−0.762358	+	0.204273i	−0.143365	+	0.989670i	$0.545792\pi$
$858$	−12.3626	+	2.30813i	−0.422051	+	0.0787981i
$859$	25.3145	−	3.33272i	0.863720	−	0.113711i	0.314367	−	0.949301i	$-0.398208\pi$
$859$	25.3145	−	3.33272i	0.863720	−	0.113711i	0.549353	+	0.835590i	$0.314874\pi$
$860$	−0.625666	−	1.38230i	−0.0213350	−	0.0471360i
$861$	44.2231	+	19.7827i	1.50712	+	0.674194i
$862$	37.7051	−	26.0852i	1.28424	−	0.888467i
$863$	−10.0405			−0.341783			−0.170892	−	0.985290i	$-0.554665\pi$
$863$	−10.0405			−0.341783			−0.170892	+	0.985290i	$0.554665\pi$
$864$	−28.8460	+	5.64857i	−0.981362	+	0.192168i
$865$	9.59589			0.326270
$866$	27.1183	−	18.7611i	0.921518	−	0.637528i
$867$	−22.6527	−	10.1334i	−0.769325	−	0.344149i
$868$	41.2686	−	18.6793i	1.40075	−	0.634016i
$869$	−45.8563	+	6.03710i	−1.55557	+	0.204795i
$870$	−9.39874	+	1.75477i	−0.318647	+	0.0594923i
$871$	14.6324	−	3.92075i	0.495801	−	0.132850i
$872$	15.3118	+	20.6707i	0.518524	+	0.700000i
$873$	−53.1876	+	11.1098i	−1.80013	+	0.376010i
$874$	1.60980	−	1.45847i	0.0544523	−	0.0493335i
$875$	10.5977	−	8.13187i	0.358266	−	0.274907i
$876$	0.0608965	+	13.8505i	0.00205750	+	0.467964i
$877$	6.16440	−	8.03360i	0.208157	−	0.271275i	−0.677594	−	0.735436i	$-0.736977\pi$
$877$	6.16440	−	8.03360i	0.208157	−	0.271275i	0.885751	+	0.464161i	$0.153644\pi$
$878$	−5.36333	+	6.31894i	−0.181004	+	0.213254i
$879$	−25.4486	−	7.58697i	−0.858359	−	0.255902i
$880$	7.79214	−	0.504652i	0.262673	−	0.0170118i
$881$		−	14.6056i		−	0.492075i	−0.969260	−	0.246037i	$-0.920871\pi$
$881$		−	14.6056i		−	0.492075i	0.969260	−	0.246037i	$-0.0791286\pi$
$882$	3.82555	+	12.9358i	0.128813	+	0.435572i
$883$	5.11351	+	12.3451i	0.172083	+	0.415446i	0.986266	−	0.165162i	$-0.0528148\pi$
$883$	5.11351	+	12.3451i	0.172083	+	0.415446i	−0.814183	+	0.580608i	$0.802815\pi$
$884$	3.11475	−	1.93520i	0.104760	−	0.0650879i
$885$	−5.82255	−	0.932711i	−0.195723	−	0.0313527i
$886$	−16.6558	+	51.8034i	−0.559563	+	1.74037i
$887$	43.4339	+	11.6381i	1.45837	+	0.390769i	0.898926	−	0.438101i	$-0.144349\pi$
$887$	43.4339	+	11.6381i	1.45837	+	0.390769i	0.559442	+	0.828869i	$0.311015\pi$
$888$	−21.4533	+	33.5822i	−0.719927	+	1.12694i
$889$	−25.5627	+	6.84952i	−0.857347	+	0.229725i
$890$	0.0323572	−	0.656050i	0.00108462	−	0.0219908i
$891$	−21.2791	−	35.2796i	−0.712878	−	1.18191i
$892$	26.4249	+	32.2243i	0.884770	+	1.07895i
$893$	0.228959	−	1.73911i	0.00766181	−	0.0581973i
$894$	−11.3999	+	3.72067i	−0.381269	+	0.124438i
$895$	2.49090	+	4.31436i	0.0832616	+	0.144213i
$896$	−35.2729	−	7.66836i	−1.17838	−	0.256182i
$897$	7.15765	−	1.70508i	0.238987	−	0.0569309i
$898$	−12.9515	−	18.7208i	−0.432197	−	0.624721i
$899$	60.0339	−	24.8668i	2.00224	−	0.829356i
$900$	23.3429	−	17.0538i	0.778098	−	0.568462i
$901$	−4.59188	+	11.0858i	−0.152978	+	0.369321i
$902$	−47.6940	−	30.7645i	−1.58804	−	1.02435i
$903$	−8.64830	+	4.67595i	−0.287797	+	0.155606i
$904$	36.4044	−	35.1912i	1.21079	−	1.17044i
$905$	9.29118	+	2.48956i	0.308849	+	0.0827559i
$906$	−15.2631	+	7.30484i	−0.507083	+	0.242687i
$907$	−33.3829	+	25.6156i	−1.10846	+	0.850553i	−0.989812	−	0.142383i	$-0.954524\pi$
$907$	−33.3829	+	25.6156i	−1.10846	+	0.850553i	−0.118651	+	0.992936i	$0.537857\pi$
$908$	−8.77984	−	4.69731i	−0.291369	−	0.155886i
$909$	0.599523	−	3.17236i	0.0198849	−	0.105221i
$910$	2.03196	−	0.726604i	0.0673589	−	0.0240867i
$911$	−11.3293	−	6.54098i	−0.375357	−	0.216712i	0.300439	−	0.953801i	$-0.402867\pi$
$911$	−11.3293	−	6.54098i	−0.375357	−	0.216712i	−0.675796	+	0.737089i	$0.736200\pi$
$912$	1.91234	−	2.05825i	0.0633237	−	0.0681556i
$913$	57.2533	−	33.0552i	1.89481	−	1.09397i
$914$	8.33425	−	9.81920i	0.275672	−	0.324790i
$915$	1.18400	−	2.64675i	0.0391417	−	0.0874988i
$916$	9.11128	−	39.0077i	0.301045	−	1.28885i
$917$	−31.0348	−	12.8550i	−1.02486	−	0.424510i
$918$	9.51456	+	7.33413i	0.314027	+	0.242062i
$919$	−10.1089	+	10.1089i	−0.333461	+	0.333461i	−0.853899	−	0.520438i	$-0.825769\pi$
$919$	−10.1089	+	10.1089i	−0.333461	+	0.333461i	0.520438	+	0.853899i	$0.325769\pi$
$920$	−4.53886	+	0.519478i	−0.149642	+	0.0171267i
$921$	1.04064	−	37.2353i	0.0342901	−	1.22694i
$922$	6.82889	+	13.3011i	0.224897	+	0.438047i
$923$	1.25200	−	0.164829i	0.0412101	−	0.00542541i
$924$	−6.82451	−	50.1331i	−0.224510	−	1.64926i
$925$	5.11563	−	38.8571i	0.168201	−	1.27761i
$926$	−47.7996	−	22.6189i	−1.57079	−	0.743303i
$927$	14.7403	−	7.44532i	0.484136	−	0.244536i
$928$	−50.2157	−	12.6302i	−1.64841	−	0.414605i
$929$	−27.6427	+	47.8786i	−0.906928	+	1.57085i	−0.0886197	+	0.996066i	$0.528246\pi$
$929$	−27.6427	+	47.8786i	−0.906928	+	1.57085i	−0.818308	+	0.574780i	$0.805088\pi$
$930$	4.95445	−	5.51708i	0.162463	−	0.180912i
$931$	−1.02292	−	0.784917i	−0.0335250	−	0.0257246i
$932$	14.6079	+	32.2737i	0.478498	+	1.05716i
$933$	22.3307	+	18.1482i	0.731075	+	0.594147i
$934$	22.9739	−	35.6162i	0.751729	−	1.16540i
$935$	−2.25659	−	2.25659i	−0.0737983	−	0.0737983i
$936$	9.03389	−	2.99247i	0.295282	−	0.0978121i
$937$	16.0529	−	16.0529i	0.524424	−	0.524424i	−0.394480	−	0.918904i	$-0.629075\pi$
$937$	16.0529	−	16.0529i	0.524424	−	0.524424i	0.918904	+	0.394480i	$0.129075\pi$
$938$	12.8546	+	59.5736i	0.419716	+	1.94515i
$939$	−16.8954	−	2.70647i	−0.551362	−	0.0883224i
$940$	−2.52292	+	2.69160i	−0.0822886	+	0.0877903i
$941$	−9.18139	+	11.9654i	−0.299305	+	0.390062i	−0.918660	−	0.395049i	$-0.870727\pi$
$941$	−9.18139	+	11.9654i	−0.299305	+	0.390062i	0.619355	+	0.785111i	$0.287394\pi$
$942$	−14.4721	+	28.4958i	−0.471525	+	0.928444i
$943$	28.7571	+	16.6029i	0.936459	+	0.540665i
$944$	−26.5391	−	17.7627i	−0.863774	−	0.578125i
$945$	4.56289	+	5.39994i	0.148431	+	0.175660i
$946$	10.8451	−	3.87808i	0.352606	−	0.126087i
$947$	−19.8872	−	2.61820i	−0.646246	−	0.0850799i	−0.199724	−	0.979852i	$-0.564004\pi$
$947$	−19.8872	−	2.61820i	−0.646246	−	0.0850799i	−0.446523	+	0.894772i	$0.647338\pi$
$948$	33.7670	−	9.20715i	1.09670	−	0.299034i
$949$	−0.585319	−	4.44594i	−0.0190003	−	0.144321i
$950$	−0.845774	+	2.63055i	−0.0274405	+	0.0853464i
$951$	−5.92675	+	9.63348i	−0.192188	+	0.312387i
$952$	7.15879	+	12.8993i	0.232018	+	0.418069i
$953$	0.762021	+	0.762021i	0.0246843	+	0.0246843i	0.719341	−	0.694657i	$-0.244444\pi$
$953$	0.762021	+	0.762021i	0.0246843	+	0.0246843i	−0.694657	+	0.719341i	$0.744444\pi$
$954$	−18.3151	+	25.1851i	−0.592973	+	0.815399i
$955$	−0.511425	+	1.23469i	−0.0165493	+	0.0399536i
$956$	0.398636	+	2.42035i	0.0128928	+	0.0782796i
$957$	−7.45934	−	72.1932i	−0.241126	−	2.33367i
$958$	22.1422	−	1.81123i	0.715382	−	0.0585183i
$959$	26.6149	+	46.0984i	0.859441	+	1.48859i
$960$	−5.79106	+	1.17373i	−0.186906	+	0.0378819i
$961$	−9.69778	+	16.7970i	−0.312832	+	0.541840i
$962$	5.51852	−	11.6621i	0.177924	−	0.376001i
$963$	2.26514	+	6.46884i	0.0729931	+	0.208455i
$964$	3.49224	−	2.86374i	0.112478	−	0.0922350i
$965$	−3.35515	−	4.37251i	−0.108006	−	0.140756i
$966$	5.43286	+	29.0990i	0.174800	+	0.936245i
$967$	2.70693	−	10.1024i	0.0870490	−	0.324871i	−0.908645	−	0.417569i	$-0.862882\pi$
$967$	2.70693	−	10.1024i	0.0870490	−	0.324871i	0.995694	+	0.0926975i	$0.0295489\pi$
$968$	−0.477140	+	28.1564i	−0.0153358	+	0.904982i
$969$	−1.14780	−	0.0320781i	−0.0368725	−	0.00103050i
$970$	−10.6769	+	2.30382i	−0.342814	+	0.0739712i
$971$	26.7021	+	11.0604i	0.856912	+	0.354944i	0.767499	−	0.641050i	$-0.221501\pi$
$971$	26.7021	+	11.0604i	0.856912	+	0.354944i	0.0894127	+	0.995995i	$0.471501\pi$
$972$	19.5561	+	24.2808i	0.627263	+	0.778808i
$973$	−3.68956	−	8.90737i	−0.118282	−	0.285557i
$974$	6.21225	−	34.1039i	0.199053	−	1.09276i
$975$	−6.80056	+	6.43078i	−0.217792	+	0.205950i
$976$	11.8139	−	10.3443i	0.378155	−	0.331114i
$977$	20.8266	−	12.0242i	0.666301	−	0.384689i	−0.128372	−	0.991726i	$-0.540975\pi$
$977$	20.8266	−	12.0242i	0.666301	−	0.384689i	0.794674	+	0.607037i	$0.207642\pi$
$978$	17.1656	+	26.3566i	0.548897	+	0.842792i
$979$	4.94339	+	0.650810i	0.157992	+	0.0208000i
$980$	0.786162	+	2.59525i	0.0251130	+	0.0829023i
$981$	11.8329	−	24.5851i	0.377797	−	0.784943i
$982$	40.0719	−	36.3049i	1.27875	−	1.15854i
$983$	5.20037	+	19.4080i	0.165866	+	0.619020i	0.997928	+	0.0643378i	$0.0204935\pi$
$983$	5.20037	+	19.4080i	0.165866	+	0.619020i	−0.832062	+	0.554682i	$0.812840\pi$
$984$	38.9012	+	18.1992i	1.24012	+	0.580170i
$985$	−0.338788	+	1.26437i	−0.0107947	+	0.0402863i
$986$	9.66544	+	18.8260i	0.307810	+	0.599542i
$987$	18.5504	+	15.0760i	0.590467	+	0.479874i
$988$	−0.530119	+	0.739175i	−0.0168653	+	0.0235163i
$989$	−6.22568	+	2.57876i	−0.197965	+	0.0819999i
$990$	−4.32428	−	7.06359i	−0.137435	−	0.224496i
$991$	−27.8962			−0.886153			−0.443076	−	0.896484i	$-0.646113\pi$
$991$	−27.8962			−0.886153			−0.443076	+	0.896484i	$0.646113\pi$
$992$	36.8601	−	15.9370i	1.17031	−	0.506000i
$993$	−30.7177	+	7.31750i	−0.974796	+	0.232214i
$994$	0.414194	+	5.06349i	0.0131374	+	0.160604i
$995$	7.81255	+	5.99478i	0.247675	+	0.190047i
$996$	−39.5548	+	30.6287i	−1.25334	+	0.970507i
$997$	33.6241	+	43.8198i	1.06489	+	1.38779i	0.917048	+	0.398777i	$0.130565\pi$
$997$	33.6241	+	43.8198i	1.06489	+	1.38779i	0.147839	+	0.989011i	$0.452768\pi$
$998$	23.2682	+	1.14762i	0.736542	+	0.0363272i
$999$	42.1187	+	3.53872i	1.33258	+	0.111960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.277.33	yes	368
3.2	odd	2		864.2.bk.a.181.14		368
9.4	even	3	inner	288.2.bc.a.85.2	yes	368
9.5	odd	6		864.2.bk.a.469.45		368
32.29	even	8	inner	288.2.bc.a.61.2	✓	368
96.29	odd	8		864.2.bk.a.829.45		368
288.157	even	24	inner	288.2.bc.a.157.33	yes	368
288.221	odd	24		864.2.bk.a.253.14		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.61.2	✓	368	32.29	even	8	inner
288.2.bc.a.85.2	yes	368	9.4	even	3	inner
288.2.bc.a.157.33	yes	368	288.157	even	24	inner
288.2.bc.a.277.33	yes	368	1.1	even	1	trivial
864.2.bk.a.181.14		368	3.2	odd	2
864.2.bk.a.253.14		368	288.221	odd	24
864.2.bk.a.469.45		368	9.5	odd	6
864.2.bk.a.829.45		368	96.29	odd	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bc (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.804604 + 1.16302i) q^{2} +(-1.58106 - 0.707273i) q^{3} +(-0.705226 + 1.87154i) q^{4} +(0.422783 - 0.0556605i) q^{5} +(-0.449558 - 2.40788i) q^{6} +(-3.08182 + 0.825772i) q^{7} +(-2.74406 + 0.685655i) q^{8} +(1.99953 + 2.23649i) q^{9} +O(q^{10})\)	\(q+(0.804604 + 1.16302i) q^{2} +(-1.58106 - 0.707273i) q^{3} +(-0.705226 + 1.87154i) q^{4} +(0.422783 - 0.0556605i) q^{5} +(-0.449558 - 2.40788i) q^{6} +(-3.08182 + 0.825772i) q^{7} +(-2.74406 + 0.685655i) q^{8} +(1.99953 + 2.23649i) q^{9} +(0.404907 + 0.446920i) q^{10} +(-3.63181 + 2.78679i) q^{11} +(2.43870 - 2.46024i) q^{12} +(-0.682753 + 0.889781i) q^{13} +(-3.44004 - 2.91980i) q^{14} +(-0.707815 - 0.211020i) q^{15} +(-3.00531 - 2.63972i) q^{16} +1.63479i q^{17} +(-0.992249 + 4.12498i) q^{18} +(-0.155186 - 0.374652i) q^{19} +(-0.193987 + 0.830509i) q^{20} +(5.45661 + 0.874091i) q^{21} +(-6.16325 - 1.98161i) q^{22} +(3.65866 + 0.980336i) q^{23} +(4.82348 + 0.856736i) q^{24} +(-4.65398 + 1.24703i) q^{25} +(-1.58418 - 0.0781337i) q^{26} +(-1.57958 - 4.95025i) q^{27} +(0.627919 - 6.35011i) q^{28} +(1.19477 - 9.07514i) q^{29} +(-0.324090 - 0.992990i) q^{30} +(3.54949 + 6.14790i) q^{31} +(0.651955 - 5.61916i) q^{32} +(7.71315 - 1.83741i) q^{33} +(-1.90129 + 1.31535i) q^{34} +(-1.25698 + 0.520659i) q^{35} +(-5.59579 + 2.16497i) q^{36} +(-3.11287 + 7.51513i) q^{37} +(0.310864 - 0.481930i) q^{38} +(1.70880 - 0.923909i) q^{39} +(-1.12198 + 0.442619i) q^{40} +(8.46797 + 2.26899i) q^{41} +(3.37382 + 7.04944i) q^{42} +(-1.41143 + 1.08303i) q^{43} +(-2.65433 - 8.76239i) q^{44} +(0.969852 + 0.834255i) q^{45} +(1.80362 + 5.04387i) q^{46} +(3.74609 + 2.16280i) q^{47} +(2.88459 + 6.29914i) q^{48} +(2.75356 - 1.58977i) q^{49} +(-5.19493 - 4.40930i) q^{50} +(1.15624 - 2.58470i) q^{51} +(-1.18376 - 1.90530i) q^{52} +(6.78118 + 2.80886i) q^{53} +(4.48629 - 5.82007i) q^{54} +(-1.38036 + 1.38036i) q^{55} +(7.89052 - 4.37904i) q^{56} +(-0.0196222 + 0.702107i) q^{57} +(11.5159 - 5.91236i) q^{58} +(7.91541 - 1.04208i) q^{59} +(0.894102 - 1.17589i) q^{60} +(-0.512403 + 3.89209i) q^{61} +(-4.29419 + 9.07475i) q^{62} +(-8.00903 - 5.24131i) q^{63} +(7.05975 - 3.76296i) q^{64} +(-0.239131 + 0.414187i) q^{65} +(8.34296 + 7.49215i) q^{66} +(-10.7158 - 8.22249i) q^{67} +(-3.05957 - 1.15289i) q^{68} +(-5.09122 - 4.13765i) q^{69} +(-1.61691 - 1.04297i) q^{70} +(-0.796166 - 0.796166i) q^{71} +(-7.02029 - 4.76607i) q^{72} +(-2.82724 + 2.82724i) q^{73} +(-11.2449 + 2.42637i) q^{74} +(8.24024 + 1.32000i) q^{75} +(0.810616 - 0.0262220i) q^{76} +(8.89135 - 11.5874i) q^{77} +(2.44943 + 1.24398i) q^{78} +(8.74993 + 5.05177i) q^{79} +(-1.41752 - 0.948751i) q^{80} +(-1.00376 + 8.94385i) q^{81} +(4.17448 + 11.6740i) q^{82} +(-14.3180 - 1.88500i) q^{83} +(-5.48404 + 9.59582i) q^{84} +(0.0909930 + 0.691160i) q^{85} +(-2.39523 - 0.770112i) q^{86} +(-8.30760 + 13.5034i) q^{87} +(8.05514 - 10.1373i) q^{88} +(-0.770168 - 0.770168i) q^{89} +(-0.189908 + 1.79920i) q^{90} +(1.36937 - 3.30595i) q^{91} +(-4.41492 + 6.15597i) q^{92} +(-1.26373 - 12.2307i) q^{93} +(0.498732 + 6.09697i) q^{94} +(-0.0864633 - 0.149759i) q^{95} +(-5.00506 + 8.42314i) q^{96} +(-9.05591 + 15.6853i) q^{97} +(4.06446 + 1.92331i) q^{98} +(-13.4945 - 2.55024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

L-functions

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