LMFDB - Embedded newform 288.2.bc.a.229.27

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			229.27
Character	$\chi$	$=$	288.229
Dual form			288.2.bc.a.205.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.218918 - 1.39717i) q^{2} +(-1.55142 - 0.770122i) q^{3} +(-1.90415 - 0.611729i) q^{4} +(-0.538426 + 0.413148i) q^{5} +(-1.41562 + 1.99900i) q^{6} +(-0.988129 + 3.68775i) q^{7} +(-1.27154 + 2.52650i) q^{8} +(1.81383 + 2.38957i) q^{9} +O(q^{10})$	\(q+(0.218918 - 1.39717i) q^{2} +(-1.55142 - 0.770122i) q^{3} +(-1.90415 - 0.611729i) q^{4} +(-0.538426 + 0.413148i) q^{5} +(-1.41562 + 1.99900i) q^{6} +(-0.988129 + 3.68775i) q^{7} +(-1.27154 + 2.52650i) q^{8} +(1.81383 + 2.38957i) q^{9} +(0.459366 + 0.842716i) q^{10} +(-1.69590 + 0.223269i) q^{11} +(2.48304 + 2.41548i) q^{12} +(0.0564933 - 0.429109i) q^{13} +(4.93608 + 2.18790i) q^{14} +(1.15350 - 0.226315i) q^{15} +(3.25158 + 2.32965i) q^{16} -4.07155i q^{17} +(3.73570 - 2.01110i) q^{18} +(-3.36176 + 1.39249i) q^{19} +(1.27798 - 0.457326i) q^{20} +(4.37302 - 4.96028i) q^{21} +(-0.0593176 + 2.41833i) q^{22} +(0.711506 + 2.65538i) q^{23} +(3.91841 - 2.94043i) q^{24} +(-1.17488 + 4.38473i) q^{25} +(-0.587170 - 0.172870i) q^{26} +(-0.973753 - 5.10410i) q^{27} +(4.13745 - 6.41756i) q^{28} +(-2.92689 + 3.81440i) q^{29} +(-0.0636780 - 1.66118i) q^{30} +(-4.37057 + 7.57005i) q^{31} +(3.96673 - 4.03299i) q^{32} +(2.80299 + 0.959661i) q^{33} +(-5.68863 - 0.891334i) q^{34} +(-0.991554 - 2.39382i) q^{35} +(-1.99203 - 5.65967i) q^{36} +(0.647468 + 0.268190i) q^{37} +(1.20959 + 5.00178i) q^{38} +(-0.418111 + 0.622223i) q^{39} +(-0.359189 - 1.88567i) q^{40} +(0.0278379 + 0.103892i) q^{41} +(-5.97301 - 7.19573i) q^{42} +(-12.5144 + 1.64756i) q^{43} +(3.36582 + 0.612291i) q^{44} +(-1.96386 - 0.537225i) q^{45} +(3.86577 - 0.412784i) q^{46} +(2.24350 - 1.29529i) q^{47} +(-3.25046 - 6.11838i) q^{48} +(-6.56092 - 3.78795i) q^{49} +(5.86900 + 2.60140i) q^{50} +(-3.13559 + 6.31669i) q^{51} +(-0.370070 + 0.782530i) q^{52} +(1.09742 - 2.64940i) q^{53} +(-7.34445 + 0.243118i) q^{54} +(0.820870 - 0.820870i) q^{55} +(-8.06064 - 7.18563i) q^{56} +(6.28789 + 0.428628i) q^{57} +(4.68860 + 4.92439i) q^{58} +(8.88549 - 6.81808i) q^{59} +(-2.33488 - 0.274692i) q^{60} +(4.13476 - 5.38853i) q^{61} +(9.61983 + 7.76364i) q^{62} +(-10.6044 + 4.32773i) q^{63} +(-4.76637 - 6.42508i) q^{64} +(0.146868 + 0.254383i) q^{65} +(1.95443 - 3.70616i) q^{66} +(6.60416 + 0.869454i) q^{67} +(-2.49068 + 7.75284i) q^{68} +(0.941117 - 4.66756i) q^{69} +(-3.56164 + 0.861316i) q^{70} +(-6.52056 - 6.52056i) q^{71} +(-8.34359 + 1.54419i) q^{72} +(-5.76621 + 5.76621i) q^{73} +(0.516448 - 0.845909i) q^{74} +(5.19952 - 5.89777i) q^{75} +(7.25312 - 0.595017i) q^{76} +(0.852405 - 6.47466i) q^{77} +(0.777817 + 0.720387i) q^{78} +(-7.01068 + 4.04762i) q^{79} +(-2.71322 + 0.0890414i) q^{80} +(-2.42007 + 8.66852i) q^{81} +(0.151249 - 0.0161503i) q^{82} +(-9.20605 - 7.06405i) q^{83} +(-11.3612 + 6.77001i) q^{84} +(1.68215 + 2.19223i) q^{85} +(-0.437720 + 17.8454i) q^{86} +(7.47840 - 3.66368i) q^{87} +(1.59231 - 4.56857i) q^{88} +(10.8421 + 10.8421i) q^{89} +(-1.18052 + 2.62623i) q^{90} +(1.52662 + 0.632348i) q^{91} +(0.269557 - 5.49149i) q^{92} +(12.6105 - 8.37848i) q^{93} +(-1.31859 - 3.41810i) q^{94} +(1.23475 - 2.13866i) q^{95} +(-9.25998 + 3.20201i) q^{96} +(-4.40178 - 7.62411i) q^{97} +(-6.72870 + 8.33745i) q^{98} +(-3.60957 - 3.64749i) 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.218918	−	1.39717i	0.154798	−	0.987946i
$2$	0.218918	−	1.39717i	0.154798	−	0.987946i
$3$	−1.55142	−	0.770122i	−0.895714	−	0.444630i
$3$	−1.55142	−	0.770122i	−0.895714	−	0.444630i
$4$	−1.90415	−	0.611729i	−0.952075	−	0.305865i
$5$	−0.538426	+	0.413148i	−0.240791	+	0.184766i	−0.722106	−	0.691782i	$-0.756826\pi$
$5$	−0.538426	+	0.413148i	−0.240791	+	0.184766i	0.481315	+	0.876548i	$0.340159\pi$
$6$	−1.41562	+	1.99900i	−0.577925	+	0.816090i
$7$	−0.988129	+	3.68775i	−0.373478	+	1.39384i	0.482078	+	0.876128i	$0.339882\pi$
$7$	−0.988129	+	3.68775i	−0.373478	+	1.39384i	−0.855556	+	0.517710i	$0.826785\pi$
$8$	−1.27154	+	2.52650i	−0.449557	+	0.893252i
$9$	1.81383	+	2.38957i	0.604609	+	0.796523i
$10$	0.459366	+	0.842716i	0.145264	+	0.266490i
$11$	−1.69590	+	0.223269i	−0.511332	+	0.0673181i	−0.381777	−	0.924254i	$-0.624688\pi$
$11$	−1.69590	+	0.223269i	−0.511332	+	0.0673181i	−0.129554	+	0.991572i	$0.541355\pi$
$12$	2.48304	+	2.41548i	0.716791	+	0.697288i
$13$	0.0564933	−	0.429109i	0.0156684	−	0.119013i	−0.981823	−	0.189798i	$-0.939217\pi$
$13$	0.0564933	−	0.429109i	0.0156684	−	0.119013i	0.997492	+	0.0707842i	$0.0225502\pi$
$14$	4.93608	+	2.18790i	1.31922	+	0.584740i
$15$	1.15350	−	0.226315i	0.297832	−	0.0584342i
$16$	3.25158	+	2.32965i	0.812894	+	0.582412i
$17$		−	4.07155i		−	0.987496i	−0.869605	−	0.493748i	$-0.835627\pi$
$17$		−	4.07155i		−	0.987496i	0.869605	−	0.493748i	$-0.164373\pi$
$18$	3.73570	−	2.01110i	0.880514	−	0.474020i
$19$	−3.36176	+	1.39249i	−0.771240	+	0.319458i	−0.733375	−	0.679825i	$-0.762056\pi$
$19$	−3.36176	+	1.39249i	−0.771240	+	0.319458i	−0.0378656	+	0.999283i	$0.512056\pi$
$20$	1.27798	−	0.457326i	0.285765	−	0.102261i
$21$	4.37302	−	4.96028i	0.954272	−	1.08242i
$22$	−0.0593176	+	2.41833i	−0.0126466	+	0.515589i
$23$	0.711506	+	2.65538i	0.148359	+	0.553685i	0.999583	+	0.0288813i	$0.00919448\pi$
$23$	0.711506	+	2.65538i	0.148359	+	0.553685i	−0.851223	+	0.524803i	$0.824139\pi$
$24$	3.91841	−	2.94043i	0.799841	−	0.600212i
$25$	−1.17488	+	4.38473i	−0.234977	+	0.876946i
$26$	−0.587170	−	0.172870i	−0.115153	−	0.0339026i
$27$	−0.973753	−	5.10410i	−0.187399	−	0.982284i
$28$	4.13745	−	6.41756i	0.781905	−	1.21281i
$29$	−2.92689	+	3.81440i	−0.543510	+	0.708316i	−0.981672	−	0.190580i	$-0.938963\pi$
$29$	−2.92689	+	3.81440i	−0.543510	+	0.708316i	0.438162	+	0.898896i	$0.355630\pi$
$30$	−0.0636780	−	1.66118i	−0.0116260	−	0.303288i
$31$	−4.37057	+	7.57005i	−0.784978	+	1.35962i	0.144034	+	0.989573i	$0.453992\pi$
$31$	−4.37057	+	7.57005i	−0.784978	+	1.35962i	−0.929012	+	0.370049i	$0.879341\pi$
$32$	3.96673	−	4.03299i	0.701226	−	0.712939i
$33$	2.80299	+	0.959661i	0.487939	+	0.167056i
$34$	−5.68863	−	0.891334i	−0.975592	−	0.152863i
$35$	−0.991554	−	2.39382i	−0.167603	−	0.404630i
$36$	−1.99203	−	5.65967i	−0.332005	−	0.943278i
$37$	0.647468	+	0.268190i	0.106443	+	0.0440902i	0.435269	−	0.900300i	$-0.356653\pi$
$37$	0.647468	+	0.268190i	0.106443	+	0.0440902i	−0.328826	+	0.944390i	$0.606653\pi$
$38$	1.20959	+	5.00178i	0.196221	+	0.811395i
$39$	−0.418111	+	0.622223i	−0.0669514	+	0.0996354i
$40$	−0.359189	−	1.88567i	−0.0567928	−	0.298150i
$41$	0.0278379	+	0.103892i	0.00434755	+	0.0162253i	0.968066	−	0.250697i	$-0.0806599\pi$
$41$	0.0278379	+	0.103892i	0.00434755	+	0.0162253i	−0.963718	+	0.266923i	$0.913993\pi$
$42$	−5.97301	−	7.19573i	−0.921655	−	1.11033i
$43$	−12.5144	+	1.64756i	−1.90843	+	0.251250i	−0.989649	−	0.143510i	$-0.954161\pi$
$43$	−12.5144	+	1.64756i	−1.90843	+	0.251250i	−0.918784	+	0.394760i	$0.870828\pi$
$44$	3.36582	+	0.612291i	0.507416	+	0.0923063i
$45$	−1.96386	−	0.537225i	−0.292754	−	0.0800848i
$46$	3.86577	−	0.412784i	0.569976	−	0.0608617i
$47$	2.24350	−	1.29529i	0.327248	−	0.188937i	−0.327371	−	0.944896i	$-0.606163\pi$
$47$	2.24350	−	1.29529i	0.327248	−	0.188937i	0.654619	+	0.755959i	$0.272829\pi$
$48$	−3.25046	−	6.11838i	−0.469163	−	0.883112i
$49$	−6.56092	−	3.78795i	−0.937274	−	0.541135i
$50$	5.86900	+	2.60140i	0.830001	+	0.367894i
$51$	−3.13559	+	6.31669i	−0.439070	+	0.884514i
$52$	−0.370070	+	0.782530i	−0.0513195	+	0.108517i
$53$	1.09742	−	2.64940i	0.150742	−	0.363923i	−0.830412	−	0.557149i	$-0.811895\pi$
$53$	1.09742	−	2.64940i	0.150742	−	0.363923i	0.981154	+	0.193226i	$0.0618951\pi$
$54$	−7.34445	+	0.243118i	−0.999453	+	0.0330842i
$55$	0.820870	−	0.820870i	0.110686	−	0.110686i
$56$	−8.06064	−	7.18563i	−1.07715	−	0.960220i
$57$	6.28789	+	0.428628i	0.832852	+	0.0567732i
$58$	4.68860	+	4.92439i	0.615644	+	0.646605i
$59$	8.88549	−	6.81808i	1.15679	−	0.887638i	0.161725	−	0.986836i	$-0.448294\pi$
$59$	8.88549	−	6.81808i	1.15679	−	0.887638i	0.995068	+	0.0991979i	$0.0316277\pi$
$60$	−2.33488	−	0.274692i	−0.301432	−	0.0354626i
$61$	4.13476	−	5.38853i	0.529402	−	0.689931i	−0.449728	−	0.893166i	$-0.648479\pi$
$61$	4.13476	−	5.38853i	0.529402	−	0.689931i	0.979130	+	0.203235i	$0.0651456\pi$
$62$	9.61983	+	7.76364i	1.22172	+	0.985983i
$63$	−10.6044	+	4.32773i	−1.33603	+	0.545243i
$64$	−4.76637	−	6.42508i	−0.595797	−	0.803135i
$65$	0.146868	+	0.254383i	0.0182168	+	0.0315524i
$66$	1.95443	−	3.70616i	0.240574	−	0.456197i
$67$	6.60416	+	0.869454i	0.806826	+	0.106221i	0.522646	−	0.852550i	$-0.324945\pi$
$67$	6.60416	+	0.869454i	0.806826	+	0.106221i	0.284181	+	0.958771i	$0.408278\pi$
$68$	−2.49068	+	7.75284i	−0.302040	+	0.940170i
$69$	0.941117	−	4.66756i	0.113297	−	0.561908i
$70$	−3.56164	+	0.861316i	−0.425697	+	0.102947i
$71$	−6.52056	−	6.52056i	−0.773848	−	0.773848i	0.204929	−	0.978777i	$-0.434304\pi$
$71$	−6.52056	−	6.52056i	−0.773848	−	0.773848i	−0.978777	+	0.204929i	$0.934304\pi$
$72$	−8.34359	+	1.54419i	−0.983301	+	0.181985i
$73$	−5.76621	+	5.76621i	−0.674884	+	0.674884i	−0.958838	−	0.283954i	$-0.908354\pi$
$73$	−5.76621	+	5.76621i	−0.674884	+	0.674884i	0.283954	+	0.958838i	$0.408354\pi$
$74$	0.516448	−	0.845909i	0.0600359	−	0.0983350i
$75$	5.19952	−	5.89777i	0.600389	−	0.681015i
$76$	7.25312	−	0.595017i	0.831990	−	0.0682531i
$77$	0.852405	−	6.47466i	0.0971405	−	0.737855i
$78$	0.777817	+	0.720387i	0.0880705	+	0.0815677i
$79$	−7.01068	+	4.04762i	−0.788763	+	0.455393i	−0.839527	−	0.543318i	$-0.817168\pi$
$79$	−7.01068	+	4.04762i	−0.788763	+	0.455393i	0.0507638	+	0.998711i	$0.483834\pi$
$80$	−2.71322	+	0.0890414i	−0.303347	+	0.00995513i
$81$	−2.42007	+	8.66852i	−0.268897	+	0.963169i
$82$	0.151249	−	0.0161503i	0.0167027	−	0.00178350i
$83$	−9.20605	−	7.06405i	−1.01050	−	0.775380i	−0.0359002	−	0.999355i	$-0.511430\pi$
$83$	−9.20605	−	7.06405i	−1.01050	−	0.775380i	−0.974595	+	0.223975i	$0.928097\pi$
$84$	−11.3612	+	6.77001i	−1.23961	+	0.738669i
$85$	1.68215	+	2.19223i	0.182455	+	0.237780i
$86$	−0.437720	+	17.8454i	−0.0472005	+	1.92432i
$87$	7.47840	−	3.66368i	0.801768	−	0.392788i
$88$	1.59231	−	4.56857i	0.169741	−	0.487011i
$89$	10.8421	+	10.8421i	1.14926	+	1.14926i	0.986698	+	0.162566i	$0.0519771\pi$
$89$	10.8421	+	10.8421i	1.14926	+	1.14926i	0.162566	+	0.986698i	$0.448023\pi$
$90$	−1.18052	+	2.62623i	−0.124437	+	0.276829i
$91$	1.52662	+	0.632348i	0.160034	+	0.0662881i
$92$	0.269557	−	5.49149i	0.0281032	−	0.572527i
$93$	12.6105	−	8.37848i	1.30764	−	0.868808i
$94$	−1.31859	−	3.41810i	−0.136002	−	0.352551i
$95$	1.23475	−	2.13866i	0.126683	−	0.219421i
$96$	−9.25998	+	3.20201i	−0.945092	+	0.326804i
$97$	−4.40178	−	7.62411i	−0.446933	−	0.774111i	0.551252	−	0.834339i	$-0.314150\pi$
$97$	−4.40178	−	7.62411i	−0.446933	−	0.774111i	−0.998185	+	0.0602284i	$0.980817\pi$
$98$	−6.72870	+	8.33745i	−0.679701	+	0.842210i
$99$	−3.60957	−	3.64749i	−0.362776	−	0.366586i
$100$	4.91942	−	7.63047i	0.491942	−	0.763047i
$101$	2.38080	+	18.0840i	0.236899	+	1.79942i	0.534960	+	0.844878i	$0.320327\pi$
$101$	2.38080	+	18.0840i	0.236899	+	1.79942i	−0.298061	+	0.954547i	$0.596340\pi$
$102$	8.13904	+	5.76377i	0.805885	+	0.570699i
$103$	19.0272	−	5.09833i	1.87481	−	0.502354i	0.874975	−	0.484168i	$-0.160878\pi$
$103$	19.0272	−	5.09833i	1.87481	−	0.502354i	0.999835	−	0.0181859i	$-0.00578908\pi$
$104$	1.01231	+	0.688359i	0.0992651	+	0.0674992i
$105$	−0.305215	+	4.47745i	−0.0297859	+	0.436954i
$106$	−3.46141	−	2.11328i	−0.336202	−	0.205260i
$107$	0.291447	−	0.703615i	0.0281752	−	0.0680210i	−0.909166	−	0.416435i	$-0.863280\pi$
$107$	0.291447	−	0.703615i	0.0281752	−	0.0680210i	0.937341	+	0.348414i	$0.113280\pi$
$108$	−1.26815	+	10.3146i	−0.122028	+	0.992527i
$109$	4.41974	−	1.83071i	0.423334	−	0.175351i	−0.160838	−	0.986981i	$-0.551420\pi$
$109$	4.41974	−	1.83071i	0.423334	−	0.175351i	0.584172	+	0.811630i	$0.301420\pi$
$110$	−0.967189	−	1.32660i	−0.0922179	−	0.126486i
$111$	−0.797958	−	0.914705i	−0.0757388	−	0.0868200i
$112$	−11.8041	+	9.68900i	−1.11539	+	0.915525i
$113$	−16.4809	−	9.51525i	−1.55039	−	0.895120i	−0.998109	−	0.0614634i	$-0.980423\pi$
$113$	−16.4809	−	9.51525i	−1.55039	−	0.895120i	−0.552284	−	0.833656i	$-0.686243\pi$
$114$	1.97540	−	8.69140i	0.185013	−	0.814024i
$115$	−1.48016	−	1.13577i	−0.138026	−	0.105911i
$116$	7.90662	−	5.47272i	0.734111	−	0.508130i
$117$	1.12785	−	0.643335i	0.104270	−	0.0594763i
$118$	−7.58080	−	13.9071i	−0.697869	−	1.28025i
$119$	15.0149	+	4.02322i	1.37641	+	0.368808i
$120$	−0.894937	+	3.20208i	−0.0816962	+	0.292309i
$121$	−7.79897	+	2.08973i	−0.708998	+	0.189975i
$122$	−6.62350	−	6.95660i	−0.599664	−	0.629821i
$123$	0.0368214	−	0.182620i	0.00332008	−	0.0164663i
$124$	12.9530	−	11.7409i	1.16322	−	1.05436i
$125$	−2.47754	−	5.98130i	−0.221598	−	0.534984i
$126$	3.72507	+	15.7636i	0.331855	+	1.40433i
$127$	18.4532			1.63745			0.818727	−	0.574182i	$-0.194680\pi$
$127$	18.4532			1.63745			0.818727	+	0.574182i	$0.194680\pi$
$128$	−10.0204	+	5.25286i	−0.885683	+	0.464291i
$129$	20.6840	+	7.08158i	1.82112	+	0.623498i
$130$	0.387568	−	0.149511i	0.0339920	−	0.0131129i
$131$	−8.69448	−	1.14465i	−0.759640	−	0.100008i	−0.259252	−	0.965810i	$-0.583476\pi$
$131$	−8.69448	−	1.14465i	−0.759640	−	0.100008i	−0.500388	+	0.865801i	$0.666809\pi$
$132$	−4.75027	−	3.54201i	−0.413458	−	0.308293i
$133$	−1.81329	−	13.7733i	−0.157232	−	1.19429i
$134$	2.66054	−	9.03677i	0.229836	−	0.780658i
$135$	2.63304	+	2.34587i	0.226616	+	0.201900i
$136$	10.2868	+	5.17713i	0.882082	+	0.443936i
$137$	0.759712	+	0.203564i	0.0649065	+	0.0173917i	0.291126	−	0.956685i	$-0.405970\pi$
$137$	0.759712	+	0.203564i	0.0649065	+	0.0173917i	−0.226220	+	0.974076i	$0.572637\pi$
$138$	−6.31533	−	2.33671i	−0.537597	−	0.198914i
$139$	6.76681	+	8.81868i	0.573954	+	0.747991i	0.986646	−	0.162880i	$-0.0520782\pi$
$139$	6.76681	+	8.81868i	0.573954	+	0.747991i	−0.412692	+	0.910870i	$0.635412\pi$
$140$	0.423697	+	5.16476i	0.0358089	+	0.436502i
$141$	−4.47814	+	0.281768i	−0.377128	+	0.0237291i
$142$	−10.5378	+	7.68284i	−0.884310	+	0.644730i
$143$			0.740337i			0.0619101i
$144$	0.330939	+	11.9954i	0.0275782	+	0.999620i
$145$		−	3.26301i		−	0.270978i
$146$	6.79403	+	9.31869i	0.562278	+	0.771220i
$147$	7.26158	+	10.9294i	0.598925	+	0.901443i
$148$	−1.06882	−	0.906749i	−0.0878562	−	0.0745343i
$149$	−0.777563	−	1.01334i	−0.0637005	−	0.0830161i	0.760417	−	0.649436i	$-0.224995\pi$
$149$	−0.777563	−	1.01334i	−0.0637005	−	0.0830161i	−0.824117	+	0.566420i	$0.808328\pi$
$150$	−7.10190	−	8.55572i	−0.579867	−	0.698572i
$151$	−1.42460	−	0.381719i	−0.115932	−	0.0310639i	0.200387	−	0.979717i	$-0.435780\pi$
$151$	−1.42460	−	0.381719i	−0.115932	−	0.0310639i	−0.316319	+	0.948653i	$0.602447\pi$
$152$	0.756497	−	10.2641i	0.0613600	−	0.832526i
$153$	9.72924	−	7.38508i	0.786563	−	0.597048i
$154$	−8.85957	−	2.60837i	−0.713924	−	0.210188i
$155$	−0.774328	−	5.88160i	−0.0621955	−	0.472422i
$156$	1.17678	−	0.929035i	0.0942177	−	0.0743823i
$157$	13.7456	+	1.80964i	1.09701	+	0.144425i	0.657239	−	0.753683i	$-0.271724\pi$
$157$	13.7456	+	1.80964i	1.09701	+	0.144425i	0.439776	+	0.898107i	$0.355058\pi$
$158$	4.12044	+	10.6812i	0.327804	+	0.849749i
$159$	−3.74292	+	3.26520i	−0.296833	+	0.258947i
$160$	−0.469566	+	3.81032i	−0.0371225	+	0.301232i
$161$	−10.4954			−0.827156
$162$	11.5816	+	5.27894i	0.909934	+	0.414753i
$163$	3.79891	+	9.17139i	0.297554	+	0.718359i	0.999978	+	0.00660019i	$0.00210092\pi$
$163$	3.79891	+	9.17139i	0.297554	+	0.718359i	−0.702424	+	0.711758i	$0.747899\pi$
$164$	0.0105465	−	0.214856i	0.000823542	−	0.0167774i
$165$	−1.90569	+	0.641347i	−0.148357	+	0.0499288i
$166$	−11.8850	+	11.3159i	−0.922457	+	0.878287i
$167$	19.4583	−	5.21382i	1.50573	−	0.403458i	0.590712	−	0.806882i	$-0.298847\pi$
$167$	19.4583	−	5.21382i	1.50573	−	0.403458i	0.915013	+	0.403424i	$0.132180\pi$
$168$	6.97166	+	17.3556i	0.537875	+	1.33901i
$169$	12.3761	+	3.31616i	0.952007	+	0.255090i
$170$	3.43116	−	1.87033i	0.263158	−	0.143448i
$171$	−9.42508	−	5.50742i	−0.720754	−	0.421163i
$172$	24.8372	+	4.51825i	1.89382	+	0.344513i
$173$	2.04733	+	1.57097i	0.155656	+	0.119439i	0.683653	−	0.729807i	$-0.260390\pi$
$173$	2.04733	+	1.57097i	0.155656	+	0.119439i	−0.527997	+	0.849246i	$0.677057\pi$
$174$	−3.48162	−	11.2506i	−0.263941	−	0.852907i
$175$	−15.0088	−	8.66536i	−1.13456	−	0.655040i
$176$	−6.03447	−	3.22486i	−0.454865	−	0.243083i
$177$	−19.0359	+	3.73481i	−1.43083	+	0.280726i
$178$	17.5218	−	12.7747i	1.31331	−	0.957507i
$179$	−15.8305	+	6.55719i	−1.18322	+	0.490108i	−0.885543	−	0.464558i	$-0.846213\pi$
$179$	−15.8305	+	6.55719i	−1.18322	+	0.490108i	−0.297682	+	0.954665i	$0.596213\pi$
$180$	3.41084	+	2.22431i	0.254229	+	0.165790i
$181$	−4.48676	+	10.8320i	−0.333498	+	0.805135i	0.664811	+	0.747011i	$0.268512\pi$
$181$	−4.48676	+	10.8320i	−0.333498	+	0.805135i	−0.998309	+	0.0581241i	$0.981488\pi$
$182$	1.21770	−	1.99452i	0.0902620	−	0.147843i
$183$	−10.5646	+	5.17562i	−0.780957	+	0.382593i
$184$	−7.61351	−	1.57880i	−0.561276	−	0.116391i
$185$	−0.459416	+	0.123100i	−0.0337769	+	0.00905049i
$186$	−8.94548	−	19.4531i	−0.655915	−	1.42637i
$187$	0.909050	+	6.90492i	0.0664763	+	0.504938i
$188$	−5.06432	+	1.09400i	−0.369354	+	0.0797884i
$189$	19.7848	+	1.45255i	1.43913	+	0.105658i
$190$	−2.71775	−	2.19335i	−0.197166	−	0.159122i
$191$	9.91579	+	17.1747i	0.717481	+	1.24271i	0.961995	+	0.273068i	$0.0880385\pi$
$191$	9.91579	+	17.1747i	0.717481	+	1.24271i	−0.244513	+	0.969646i	$0.578628\pi$
$192$	2.44657	+	13.6387i	0.176566	+	0.984289i
$193$	−0.789870	+	1.36810i	−0.0568561	+	0.0984777i	−0.893053	−	0.449952i	$-0.851441\pi$
$193$	−0.789870	+	1.36810i	−0.0568561	+	0.0984777i	0.836196	+	0.548430i	$0.184774\pi$
$194$	−11.6158	+	4.48097i	−0.833964	+	0.321715i
$195$	−0.0319487	−	0.507763i	−0.00228790	−	0.0363616i
$196$	10.1758	+	11.2263i	0.726841	+	0.801880i
$197$	−14.3888	−	5.96006i	−1.02516	−	0.424636i	−0.194199	−	0.980962i	$-0.562211\pi$
$197$	−14.3888	−	5.96006i	−1.02516	−	0.424636i	−0.830964	+	0.556326i	$0.812211\pi$
$198$	−5.88635	+	4.24468i	−0.418324	+	0.301656i
$199$	5.82783	+	5.82783i	0.413124	+	0.413124i	0.882825	−	0.469701i	$-0.155638\pi$
$199$	5.82783	+	5.82783i	0.413124	+	0.413124i	−0.469701	+	0.882825i	$0.655638\pi$
$200$	−9.58409	−	8.54370i	−0.677698	−	0.604131i
$201$	−9.57626	−	6.43490i	−0.675457	−	0.453883i
$202$	25.7876	+	0.632527i	1.81441	+	0.0445044i
$203$	−11.1744	−	14.5628i	−0.784289	−	1.02211i
$204$	9.83473	−	10.1098i	0.688569	−	0.707828i
$205$	−0.0579116	−	0.0444371i	−0.00404472	−	0.00310362i
$206$	−2.95782	−	27.7003i	−0.206081	−	1.92997i
$207$	−5.05466	+	6.51659i	−0.351323	+	0.452934i
$208$	1.18337	−	1.26367i	0.0820516	−	0.0876198i
$209$	5.39029	−	3.11209i	0.372854	−	0.215268i
$210$	6.18892	+	1.40663i	0.427076	+	0.0970666i
$211$	−2.45664	+	18.6601i	−0.169122	+	1.28461i	0.670691	+	0.741737i	$0.265998\pi$
$211$	−2.45664	+	18.6601i	−0.169122	+	1.28461i	−0.839813	+	0.542875i	$0.817336\pi$
$212$	−3.71036	+	4.37354i	−0.254829	+	0.300376i
$213$	5.09452	+	15.1378i	0.349071	+	1.03722i
$214$	−0.919264	−	0.561234i	−0.0628396	−	0.0383651i
$215$	6.05741	−	6.05741i	0.413112	−	0.413112i
$216$	14.1337	+	4.02988i	0.961673	+	0.274198i
$217$	−23.5978	−	23.5978i	−1.60192	−	1.60192i
$218$	−1.59026	−	6.57588i	−0.107706	−	0.445375i
$219$	13.3865	−	4.50515i	0.904577	−	0.304430i
$220$	−2.06521	+	1.06091i	−0.139236	+	0.0715265i
$221$	−1.74714	−	0.230015i	−0.117525	−	0.0154725i
$222$	−1.45268	+	0.914635i	−0.0974977	+	0.0613863i
$223$	−4.33559	−	7.50946i	−0.290332	−	0.502870i	0.683556	−	0.729898i	$-0.260433\pi$
$223$	−4.33559	−	7.50946i	−0.290332	−	0.502870i	−0.973888	+	0.227028i	$0.927099\pi$
$224$	10.9530	+	18.6134i	0.731829	+	1.24366i
$225$	−12.6086	+	5.14567i	−0.840576	+	0.343045i
$226$	−16.9024	+	20.9435i	−1.12433	+	1.39314i
$227$	8.77048	−	11.4299i	0.582117	−	0.758630i	−0.405741	−	0.913988i	$-0.632987\pi$
$227$	8.77048	−	11.4299i	0.582117	−	0.758630i	0.987858	+	0.155358i	$0.0496532\pi$
$228$	−11.7109	−	4.66266i	−0.775572	−	0.308792i
$229$	−10.6261	+	8.15372i	−0.702195	+	0.538813i	−0.897001	−	0.442029i	$-0.854259\pi$
$229$	−10.6261	+	8.15372i	−0.702195	+	0.538813i	0.194806	+	0.980842i	$0.437592\pi$
$230$	−1.91089	+	1.81939i	−0.126000	+	0.119967i
$231$	−6.30871	+	9.38847i	−0.415083	+	0.617716i
$232$	−5.91541	−	12.2449i	−0.388366	−	0.803920i
$233$	−10.1761	+	10.1761i	−0.666658	+	0.666658i	−0.956941	−	0.290283i	$-0.906251\pi$
$233$	−10.1761	+	10.1761i	−0.666658	+	0.666658i	0.290283	+	0.956941i	$0.406251\pi$
$234$	−0.651938	−	1.71664i	−0.0426185	−	0.112220i
$235$	−0.672813	+	1.62431i	−0.0438895	+	0.105959i
$236$	−21.0901	+	7.54713i	−1.37285	+	0.491276i
$237$	13.9937	−	0.880492i	0.908988	−	0.0571941i
$238$	8.90812	−	20.0975i	0.577428	−	1.30273i
$239$	−0.369172	−	0.213142i	−0.0238797	−	0.0137870i	0.488013	−	0.872837i	$-0.337722\pi$
$239$	−0.369172	−	0.213142i	−0.0238797	−	0.0137870i	−0.511892	+	0.859050i	$0.671055\pi$
$240$	4.27793	+	1.95137i	0.276139	+	0.125960i
$241$	1.41141	−	0.814879i	0.0909170	−	0.0524910i	−0.453852	−	0.891077i	$-0.649951\pi$
$241$	1.41141	−	0.814879i	0.0909170	−	0.0524910i	0.544769	+	0.838586i	$0.316617\pi$
$242$	1.21237	+	11.3539i	0.0779339	+	0.729859i
$243$	10.4304	−	11.5848i	0.669109	−	0.743165i
$244$	−11.1695	+	7.73122i	−0.715056	+	0.494940i
$245$	5.09755	−	0.671105i	0.325671	−	0.0428753i
$246$	−0.247089	−	0.0914243i	−0.0157538	−	0.00582900i
$247$	0.407612	+	1.52123i	0.0259357	+	0.0967934i
$248$	−13.5684	−	20.6679i	−0.861592	−	1.31241i
$249$	8.84230	+	18.0491i	0.560358	+	1.14382i
$250$	−8.89925	+	2.15212i	−0.562838	+	0.136112i
$251$	7.49186	+	3.10323i	0.472882	+	0.195874i	0.606380	−	0.795175i	$-0.292621\pi$
$251$	7.49186	+	3.10323i	0.472882	+	0.195874i	−0.133498	+	0.991049i	$0.542621\pi$
$252$	22.8398	−	1.75362i	1.43877	−	0.110468i
$253$	−1.79950	−	4.34439i	−0.113134	−	0.273129i
$254$	4.03973	−	25.7822i	0.253475	−	1.61772i
$255$	−0.921452	−	4.69653i	−0.0577036	−	0.294108i
$256$	5.14548	+	15.1500i	0.321593	+	0.946878i
$257$	2.59118	−	4.48805i	0.161633	−	0.279957i	−0.773821	−	0.633404i	$-0.781657\pi$
$257$	2.59118	−	4.48805i	0.161633	−	0.279957i	0.935455	+	0.353447i	$0.114991\pi$
$258$	14.4222	−	27.3487i	0.897889	−	1.70266i
$259$	−1.62880	+	2.12269i	−0.101209	+	0.131898i
$260$	−0.124046	−	0.574228i	−0.00769298	−	0.0356121i
$261$	−14.4236	−	0.0753515i	−0.892801	−	0.00466414i
$262$	−3.50264	+	11.8970i	−0.216394	+	0.735002i
$263$	1.87736	−	7.00639i	0.115763	−	0.432032i	−0.883580	−	0.468280i	$-0.844874\pi$
$263$	1.87736	−	7.00639i	0.115763	−	0.432032i	0.999343	+	0.0362476i	$0.0115405\pi$
$264$	−5.98870	+	5.86151i	−0.368579	+	0.360751i
$265$	0.503718	+	1.87990i	0.0309432	+	0.115481i
$266$	−19.6405	−	0.481750i	−1.20424	−	0.0295380i
$267$	−8.47097	−	25.1705i	−0.518415	−	1.54041i
$268$	−12.0434	−	5.69553i	−0.735670	−	0.347910i
$269$	−21.2979	+	8.82188i	−1.29856	+	0.537880i	−0.921524	−	0.388321i	$-0.873055\pi$
$269$	−21.2979	+	8.82188i	−1.29856	+	0.537880i	−0.377032	+	0.926200i	$0.623055\pi$
$270$	3.85399	−	3.16525i	0.234547	−	0.192631i
$271$		−	31.2767i		−	1.89992i	−0.312366	−	0.949962i	$-0.601121\pi$
$271$		−	31.2767i		−	1.89992i	0.312366	−	0.949962i	$-0.398879\pi$
$272$	9.48527	−	13.2389i	0.575129	−	0.802729i
$273$	−1.88145	−	2.15673i	−0.113871	−	0.130531i
$274$	0.450727	−	1.01688i	0.0272294	−	0.0614320i
$275$	1.01351	−	7.69836i	0.0611168	−	0.464228i
$276$	−4.64731	+	8.31203i	−0.279735	+	0.500325i
$277$	15.1860	−	1.99927i	0.912437	−	0.120125i	0.340333	−	0.940305i	$-0.389460\pi$
$277$	15.1860	−	1.99927i	0.912437	−	0.120125i	0.572105	+	0.820180i	$0.306127\pi$
$278$	13.8025	−	7.52380i	0.827822	−	0.451248i
$279$	−26.0166	+	3.28698i	−1.55757	+	0.196786i
$280$	7.30879	+	0.538682i	0.436783	+	0.0321924i
$281$	0.840916	−	3.13834i	0.0501648	−	0.187218i	−0.936297	−	0.351210i	$-0.885770\pi$
$281$	0.840916	−	3.13834i	0.0501648	−	0.187218i	0.986462	+	0.163992i	$0.0524371\pi$
$282$	−0.586669	+	6.31840i	−0.0349356	+	0.376255i
$283$	−11.1762	+	8.57580i	−0.664356	+	0.509778i	−0.885009	−	0.465574i	$-0.845848\pi$
$283$	−11.1762	+	8.57580i	−0.664356	+	0.509778i	0.220653	+	0.975352i	$0.429181\pi$
$284$	8.42730	+	16.4049i	0.500069	+	0.973454i
$285$	−3.56265	+	2.36705i	−0.211033	+	0.140212i
$286$	1.03437	+	0.162073i	0.0611639	+	0.00958357i
$287$	−0.410637			−0.0242391
$288$	16.8321	+	2.16364i	0.991839	+	0.127494i
$289$	0.422494			0.0248526
$290$	−4.55897	−	0.714330i	−0.267712	−	0.0419469i
$291$	0.957533	+	15.2181i	0.0561316	+	0.892102i
$292$	14.5071	−	7.45237i	0.848963	−	0.436117i
$293$	−12.3856	+	9.50380i	−0.723574	+	0.555218i	−0.903565	−	0.428450i	$-0.859060\pi$
$293$	−12.3856	+	9.50380i	−0.723574	+	0.555218i	0.179991	+	0.983668i	$0.442393\pi$
$294$	16.8599	−	7.75299i	0.983289	−	0.452164i
$295$	−1.96730	+	7.34205i	−0.114540	+	0.427471i
$296$	−1.50086	+	1.29481i	−0.0872359	+	0.0752594i
$297$	2.79097	+	8.43860i	0.161948	+	0.489658i
$298$	−1.58603	+	0.864548i	−0.0918761	+	0.0500819i
$299$	1.17964	−	0.155303i	0.0682205	−	0.00898140i
$300$	−13.5085	+	8.04954i	−0.779913	+	0.464740i
$301$	6.29011	−	47.7781i	0.362556	−	2.75388i
$302$	−0.845195	+	1.90683i	−0.0486355	+	0.109726i
$303$	10.2332	−	29.8894i	0.587884	−	1.71710i
$304$	−14.1750	−	3.30394i	−0.812993	−	0.189494i
$305$			4.60959i			0.263945i
$306$	−8.18828	−	15.2101i	−0.468093	−	0.869503i
$307$	19.8252	−	8.21186i	1.13148	−	0.468675i	0.263198	−	0.964742i	$-0.415223\pi$
$307$	19.8252	−	8.21186i	1.13148	−	0.468675i	0.868285	+	0.496066i	$0.165223\pi$
$308$	−5.58384	+	11.8073i	−0.318169	+	0.672782i
$309$	−33.4456	−	6.74362i	−1.90266	−	0.383631i
$310$	−8.38710	−	0.205722i	−0.476355	−	0.0116842i
$311$	4.67320	+	17.4406i	0.264993	+	0.988967i	0.962255	+	0.272150i	$0.0877348\pi$
$311$	4.67320	+	17.4406i	0.264993	+	0.988967i	−0.697262	+	0.716816i	$0.745599\pi$
$312$	−1.04040	−	1.84754i	−0.0589010	−	0.104596i
$313$	1.18849	−	4.43550i	0.0671774	−	0.250709i	−0.924169	−	0.381985i	$-0.875241\pi$
$313$	1.18849	−	4.43550i	0.0671774	−	0.250709i	0.991346	+	0.131276i	$0.0419073\pi$
$314$	5.53751	−	18.8087i	0.312500	−	1.06144i
$315$	3.92170	−	6.71136i	0.220963	−	0.378142i
$316$	15.8254	−	3.41864i	0.890250	−	0.192313i
$317$	−16.3873	+	21.3564i	−0.920404	+	1.19949i	0.0591373	+	0.998250i	$0.481165\pi$
$317$	−16.3873	+	21.3564i	−0.920404	+	1.19949i	−0.979541	+	0.201244i	$0.935502\pi$
$318$	3.74263	+	5.94429i	0.209876	+	0.333339i
$319$	4.11206	−	7.12230i	0.230231	−	0.398772i
$320$	5.22085	+	1.49021i	0.291854	+	0.0833052i
$321$	−0.994026	+	0.867155i	−0.0554811	+	0.0483999i
$322$	−2.29764	+	14.6639i	−0.128042	+	0.817185i
$323$	5.66957	+	13.6876i	0.315464	+	0.761596i
$324$	9.91097	−	15.0257i	0.550609	−	0.834763i
$325$	1.81515	+	0.751862i	0.100687	+	0.0417058i
$326$	13.6456	−	3.29994i	0.755760	−	0.182767i
$327$	−8.26675	−	0.563521i	−0.457152	−	0.0311628i
$328$	−0.297881	−	0.0617710i	−0.0164477	−	0.00341073i
$329$	2.55982	+	9.55338i	0.141127	+	0.526695i
$330$	0.478880	+	2.80296i	0.0263615	+	0.154298i
$331$	6.48717	−	0.854052i	0.356567	−	0.0469429i	0.0498850	−	0.998755i	$-0.484115\pi$
$331$	6.48717	−	0.854052i	0.356567	−	0.0469429i	0.306682	+	0.951812i	$0.400781\pi$
$332$	13.2084	+	19.0826i	0.724906	+	1.04729i
$333$	0.533536	+	2.03362i	0.0292376	+	0.111442i
$334$	−3.02483	−	28.3278i	−0.165511	−	1.55003i
$335$	−3.91506	+	2.26036i	−0.213903	+	0.123497i
$336$	25.7749	−	5.94112i	1.40614	−	0.324115i
$337$	−2.79799	−	1.61542i	−0.152416	−	0.0879976i	0.421852	−	0.906665i	$-0.361380\pi$
$337$	−2.79799	−	1.61542i	−0.152416	−	0.0879976i	−0.574269	+	0.818667i	$0.694713\pi$
$338$	7.34258	−	16.5655i	0.399384	−	0.901044i
$339$	18.2409	+	27.4545i	0.990712	+	1.49112i
$340$	−1.86203	−	5.20335i	−0.100983	−	0.282191i
$341$	5.72187	−	13.8138i	0.309857	−	0.748061i
$342$	−9.75811	+	11.9627i	−0.527658	+	0.646871i
$343$	1.55470	−	1.55470i	0.0839460	−	0.0839460i
$344$	11.7501	−	33.7126i	0.633520	−	1.81766i
$345$	1.42167	+	2.90195i	0.0765404	+	0.156236i
$346$	2.64311	−	2.51655i	0.142095	−	0.135291i
$347$	5.14100	−	3.94483i	0.275984	−	0.211770i	−0.461490	−	0.887145i	$-0.652685\pi$
$347$	5.14100	−	3.94483i	0.275984	−	0.211770i	0.737474	+	0.675376i	$0.236018\pi$
$348$	−16.4812	+	2.40145i	−0.883483	+	0.128731i
$349$	−6.35414	+	8.28087i	−0.340129	+	0.443265i	−0.931831	−	0.362892i	$-0.881789\pi$
$349$	−6.35414	+	8.28087i	−0.340129	+	0.443265i	0.591702	+	0.806157i	$0.298456\pi$
$350$	−15.3927	+	19.0729i	−0.822772	+	1.01949i
$351$	−2.24522	+	0.129499i	−0.119841	+	0.00691214i
$352$	−5.82672	+	7.72518i	−0.310565	+	0.411753i
$353$	−14.5795	−	25.2525i	−0.775990	−	1.34405i	−0.934236	−	0.356655i	$-0.883917\pi$
$353$	−14.5795	−	25.2525i	−0.775990	−	1.34405i	0.158246	−	0.987400i	$-0.449416\pi$
$354$	1.05086	+	27.4139i	0.0558526	+	1.45703i
$355$	6.20479	+	0.816876i	0.329316	+	0.0433553i
$356$	−14.0126	−	27.2775i	−0.742666	−	1.44570i
$357$	−20.1960	−	17.8050i	−1.06889	−	0.942339i
$358$	5.69592	+	23.5533i	0.301039	+	1.24483i
$359$	−1.32004	−	1.32004i	−0.0696690	−	0.0696690i	0.671414	−	0.741083i	$-0.265687\pi$
$359$	−1.32004	−	1.32004i	−0.0696690	−	0.0696690i	−0.741083	+	0.671414i	$0.765687\pi$
$360$	3.85442	−	4.27857i	0.203146	−	0.225501i
$361$	−4.07263	+	4.07263i	−0.214349	+	0.214349i
$362$	14.1519	+	8.64006i	0.743806	+	0.454112i
$363$	13.7088	+	2.76410i	0.719528	+	0.145078i
$364$	−2.52010	−	2.13797i	−0.132089	−	0.112060i
$365$	0.722374	−	5.48698i	0.0378108	−	0.287202i
$366$	4.91843	+	15.8935i	0.257090	+	0.830768i
$367$	−0.503962	+	0.290963i	−0.0263066	+	0.0151881i	−0.513096	−	0.858331i	$-0.671501\pi$
$367$	−0.503962	+	0.290963i	−0.0263066	+	0.0151881i	0.486789	+	0.873520i	$0.338168\pi$
$368$	−3.87258	+	10.2917i	−0.201872	+	0.536493i
$369$	−0.197765	+	0.254963i	−0.0102952	+	0.0132729i
$370$	0.0714171	+	0.668829i	0.00371280	+	0.0347708i
$371$	8.68594	+	6.66495i	0.450951	+	0.346027i
$372$	−29.1376	+	8.23970i	−1.51071	+	0.427208i
$373$	11.9807	+	15.6135i	0.620336	+	0.808437i	0.992822	−	0.119600i	$-0.0381613\pi$
$373$	11.9807	+	15.6135i	0.620336	+	0.808437i	−0.372486	+	0.928038i	$0.621495\pi$
$374$	9.84633	+	0.241515i	0.509142	+	0.0124884i
$375$	−0.762623	+	11.1875i	−0.0393817	+	0.577722i
$376$	0.419836	+	7.31520i	0.0216514	+	0.377253i
$377$	1.47144	+	1.47144i	0.0757832	+	0.0757832i
$378$	6.36071	−	27.3247i	0.327159	−	1.40543i
$379$	−19.5075	−	8.08027i	−1.00203	−	0.415056i	−0.179491	−	0.983760i	$-0.557445\pi$
$379$	−19.5075	−	8.08027i	−1.00203	−	0.415056i	−0.822542	+	0.568704i	$0.807445\pi$
$380$	−3.65943	+	3.31699i	−0.187725	+	0.170158i
$381$	−28.6287	−	14.2112i	−1.46669	−	0.728061i
$382$	26.1666	−	10.0942i	1.33880	−	0.516463i
$383$	−9.55995	+	16.5583i	−0.488491	+	0.846090i	−0.999912	−	0.0132394i	$-0.995786\pi$
$383$	−9.55995	+	16.5583i	−0.488491	+	0.846090i	0.511422	+	0.859330i	$0.329119\pi$
$384$	19.5911	−	0.432510i	0.999756	−	0.0220714i
$385$	2.21604	+	3.83829i	0.112940	+	0.195617i
$386$	1.73854	+	1.40308i	0.0884894	+	0.0714149i
$387$	−26.6360	−	26.9157i	−1.35398	−	1.36820i
$388$	3.71776	+	17.2101i	0.188741	+	0.873712i
$389$	4.51564	+	34.2997i	0.228952	+	1.73906i	0.590793	+	0.806823i	$0.298815\pi$
$389$	4.51564	+	34.2997i	0.228952	+	1.73906i	−0.361842	+	0.932240i	$0.617852\pi$
$390$	−0.716423	−	0.0665205i	−0.0362775	−	0.00336840i
$391$	10.8115	−	2.89693i	0.546761	−	0.146504i
$392$	17.9127	−	11.7596i	0.904728	−	0.593950i
$393$	12.6073	+	8.47164i	0.635954	+	0.427338i
$394$	−11.4772	+	18.7989i	−0.578211	+	0.947073i
$395$	2.10246	−	5.07579i	0.105786	−	0.255391i
$396$	4.64190	+	9.15344i	0.233264	+	0.459978i
$397$	−0.793701	+	0.328762i	−0.0398347	+	0.0165001i	−0.402512	−	0.915415i	$-0.631863\pi$
$397$	−0.793701	+	0.328762i	−0.0398347	+	0.0165001i	0.362677	+	0.931915i	$0.381863\pi$
$398$	9.41827	−	6.86664i	0.472095	−	0.344194i
$399$	−7.79392	+	22.7646i	−0.390184	+	1.13966i
$400$	−14.0351	+	11.5202i	−0.701755	+	0.576011i
$401$	31.9482	+	18.4453i	1.59542	+	0.921114i	0.992355	+	0.123418i	$0.0393857\pi$
$401$	31.9482	+	18.4453i	1.59542	+	0.921114i	0.603061	+	0.797695i	$0.293948\pi$
$402$	−11.0870	+	11.9709i	−0.552971	+	0.597055i
$403$	3.00147	+	2.30311i	0.149514	+	0.114726i
$404$	6.52910	−	35.8910i	0.324835	−	1.78565i
$405$	−2.27836	−	5.66720i	−0.113212	−	0.281606i
$406$	−22.7929	+	12.4245i	−1.13119	+	0.616615i
$407$	−1.15792	−	0.310263i	−0.0573958	−	0.0153792i
$408$	−11.9721	−	15.9540i	−0.592706	−	0.789840i
$409$	−16.5936	+	4.44624i	−0.820501	+	0.219853i	−0.644566	−	0.764549i	$-0.722962\pi$
$409$	−16.5936	+	4.44624i	−0.820501	+	0.219853i	−0.175936	+	0.984402i	$0.556295\pi$
$410$	−0.0747640	+	0.0711841i	−0.00369233	+	0.00351553i
$411$	−1.02186	−	0.900884i	−0.0504049	−	0.0444373i
$412$	−39.3495	−	1.93152i	−1.93861	−	0.0951593i
$413$	16.3633	+	39.5046i	0.805188	+	1.94389i
$414$	7.99820	+	8.48880i	0.393090	+	0.417202i
$415$	7.87527			0.386582
$416$	−1.50650	−	1.93000i	−0.0738622	−	0.0946260i
$417$	−3.70673	−	18.8928i	−0.181519	−	0.925183i
$418$	−3.16807	−	8.21243i	−0.154956	−	0.401683i
$419$	27.1614	+	3.57587i	1.32692	+	0.174693i	0.760454	−	0.649391i	$-0.224976\pi$
$419$	27.1614	+	3.57587i	1.32692	+	0.174693i	0.566468	+	0.824084i	$0.308310\pi$
$420$	3.32016	−	8.33902i	0.162007	−	0.406903i
$421$	1.83644	+	13.9491i	0.0895025	+	0.679839i	0.976104	+	0.217305i	$0.0697265\pi$
$421$	1.83644	+	13.9491i	0.0895025	+	0.679839i	−0.886601	+	0.462534i	$0.846940\pi$
$422$	25.5334	+	7.51736i	1.24295	+	0.365939i
$423$	7.16449	+	3.01157i	0.348349	+	0.146428i
$424$	5.29829	+	6.14144i	0.257308	+	0.298255i
$425$	17.8526	+	4.78360i	0.865980	+	0.232039i
$426$	22.2653	−	3.80397i	1.07876	−	0.184303i
$427$	15.7859	+	20.5725i	0.763932	+	0.995575i
$428$	−0.985380	+	1.16150i	−0.0476301	+	0.0561433i
$429$	0.570150	−	1.14858i	0.0275271	−	0.0554538i
$430$	−7.13713	−	9.78928i	−0.344183	−	0.472081i
$431$			19.2416i			0.926835i	0.886140	+	0.463417i	$0.153377\pi$
$431$			19.2416i			0.926835i	−0.886140	+	0.463417i	$0.846623\pi$
$432$	8.72452	−	18.8649i	0.419759	−	0.907636i
$433$			1.38001i			0.0663190i	0.999450	+	0.0331595i	$0.0105569\pi$
$433$			1.38001i			0.0663190i	−0.999450	+	0.0331595i	$0.989443\pi$
$434$	−38.1360	+	27.8040i	−1.83059	+	1.33464i
$435$	−2.51291	+	5.06231i	−0.120485	+	0.242719i
$436$	−9.53574	+	0.782275i	−0.456679	+	0.0374642i
$437$	−6.08949	−	7.93598i	−0.291300	−	0.379629i
$438$	−3.36390	−	19.6895i	−0.160733	−	0.940798i
$439$	15.1004	+	4.04615i	0.720704	+	0.193112i	0.600486	−	0.799635i	$-0.294974\pi$
$439$	15.1004	+	4.04615i	0.720704	+	0.193112i	0.120218	+	0.992748i	$0.461641\pi$
$440$	1.03016	+	3.11769i	0.0491108	+	0.148630i
$441$	−2.84880	−	22.5484i	−0.135657	−	1.07374i
$442$	−0.703849	+	2.39069i	−0.0334787	+	0.113713i
$443$	2.92165	+	22.1921i	0.138812	+	1.05438i	0.909069	+	0.416646i	$0.136794\pi$
$443$	2.92165	+	22.1921i	0.138812	+	1.05438i	−0.770257	+	0.637733i	$0.779872\pi$
$444$	0.959880	+	2.22987i	0.0455539	+	0.105825i
$445$	−10.3171	−	1.35827i	−0.489077	−	0.0643882i
$446$	−11.4411	+	4.41358i	−0.541752	+	0.208989i
$447$	0.425934	+	2.17094i	0.0201460	+	0.102682i
$448$	28.4039	−	11.2284i	1.34196	−	0.530491i
$449$	12.1807			0.574842			0.287421	−	0.957804i	$-0.407202\pi$
$449$	12.1807			0.574842			0.287421	+	0.957804i	$0.407202\pi$
$450$	4.42910	+	18.7429i	0.208790	+	0.883547i
$451$	−0.0704061	−	0.169975i	−0.00331529	−	0.00800382i
$452$	25.5614	+	28.2003i	1.20231	+	1.32643i
$453$	1.91618	+	1.68932i	0.0900300	+	0.0793712i
$454$	−14.0495	−	14.7560i	−0.659375	−	0.692535i
$455$	−1.08323	+	0.290250i	−0.0507825	+	0.0136071i
$456$	−9.07823	+	15.3413i	−0.425127	+	0.718423i
$457$	11.4939	+	3.07978i	0.537661	+	0.144066i	0.517424	−	0.855729i	$-0.326891\pi$
$457$	11.4939	+	3.07978i	0.537661	+	0.144066i	0.0202374	+	0.999795i	$0.493558\pi$
$458$	9.06586	+	16.6315i	0.423620	+	0.777138i
$459$	−20.7816	+	3.96468i	−0.970001	+	0.185055i
$460$	2.12366	+	3.06812i	0.0990163	+	0.143052i
$461$	−5.26542	−	4.04030i	−0.245235	−	0.188175i	0.478829	−	0.877908i	$-0.341061\pi$
$461$	−5.26542	−	4.04030i	−0.245235	−	0.188175i	−0.724064	+	0.689733i	$0.757728\pi$
$462$	11.7362	+	10.8696i	0.546016	+	0.505701i
$463$	−36.4988	−	21.0726i	−1.69624	−	0.979325i	−0.949267	−	0.314473i	$-0.898172\pi$
$463$	−36.4988	−	21.0726i	−1.69624	−	0.979325i	−0.746974	−	0.664853i	$-0.768494\pi$
$464$	−18.4032	+	5.58418i	−0.854348	+	0.259239i
$465$	−3.32824	+	9.72118i	−0.154343	+	0.450809i
$466$	11.9900	+	16.4454i	0.555425	+	0.761820i
$467$	−33.9040	+	14.0435i	−1.56889	+	0.649855i	−0.986605	−	0.163130i	$-0.947841\pi$
$467$	−33.9040	+	14.0435i	−1.56889	+	0.649855i	−0.582284	+	0.812985i	$0.697841\pi$
$468$	−2.54115	+	0.535064i	−0.117465	+	0.0247334i
$469$	−9.73209	+	23.4953i	−0.449386	+	1.08491i
$470$	2.12215	+	1.29562i	0.0978873	+	0.0597626i
$471$	−19.9315	−	13.3933i	−0.918397	−	0.617129i
$472$	5.92760	+	31.1186i	0.272840	+	1.43235i
$473$	20.8553	−	5.58817i	0.958929	−	0.256944i
$474$	1.83327	−	19.7443i	0.0842050	−	0.906884i
$475$	−2.15600	−	16.3764i	−0.0989239	−	0.751401i
$476$	−26.1294	−	16.8458i	−1.19764	−	0.772127i
$477$	8.32145	−	2.18320i	0.381013	−	0.0999617i
$478$	−0.378613	+	0.469134i	−0.0173173	+	0.0214577i
$479$	−11.5174	−	19.9487i	−0.526242	−	0.911478i	−0.999533	−	0.0305719i	$-0.990267\pi$
$479$	−11.5174	−	19.9487i	−0.526242	−	0.911478i	0.473290	−	0.880907i	$-0.343066\pi$
$480$	3.66290	−	5.54979i	0.167188	−	0.253312i
$481$	0.151660	−	0.262683i	0.00691512	−	0.0119773i
$482$	−0.829539	−	2.15037i	−0.0377845	−	0.0979466i
$483$	16.2829	+	8.08276i	0.740895	+	0.367778i
$484$	16.1288	+	0.791701i	0.733126	+	0.0359864i
$485$	5.51992	+	2.28642i	0.250647	+	0.103821i
$486$	−13.9025	−	17.1091i	−0.630630	−	0.776084i
$487$	−5.14893	−	5.14893i	−0.233320	−	0.233320i	0.580757	−	0.814077i	$-0.302757\pi$
$487$	−5.14893	−	5.14893i	−0.233320	−	0.233320i	−0.814077	+	0.580757i	$0.802757\pi$
$488$	8.35659	+	17.2982i	0.378285	+	0.783053i
$489$	1.16936	−	17.1543i	0.0528804	−	0.775745i
$490$	0.178298	−	7.26905i	0.00805468	−	0.328382i
$491$	−15.3283	−	19.9762i	−0.691755	−	0.901513i	0.306984	−	0.951715i	$-0.400680\pi$
$491$	−15.3283	−	19.9762i	−0.691755	−	0.901513i	−0.998739	+	0.0502017i	$0.984014\pi$
$492$	−0.181827	+	0.325210i	−0.00819741	+	0.0146616i
$493$	15.5305	+	11.9170i	0.699459	+	0.536714i
$494$	2.21464	−	0.236478i	0.0996414	−	0.0106396i
$495$	3.45044	+	0.472610i	0.155086	+	0.0212422i
$496$	−31.8468	+	14.4327i	−1.42996	+	0.648047i
$497$	30.4893	−	17.6030i	1.36763	−	0.789604i
$498$	27.1533	−	8.40290i	1.21677	−	0.376543i
$499$	3.85781	−	29.3030i	0.172699	−	1.31178i	−0.657135	−	0.753773i	$-0.728232\pi$
$499$	3.85781	−	29.3030i	0.172699	−	1.31178i	0.829834	−	0.558010i	$-0.188435\pi$
$500$	1.05867	+	12.9049i	0.0473449	+	0.577124i
$501$	−34.2033	−	6.89638i	−1.52809	−	0.308107i
$502$	5.97583	−	9.78803i	0.266714	−	0.436861i
$503$	6.40742	−	6.40742i	0.285693	−	0.285693i	−0.549682	−	0.835374i	$-0.685251\pi$
$503$	6.40742	−	6.40742i	0.285693	−	0.285693i	0.835374	+	0.549682i	$0.185251\pi$
$504$	2.54994	−	32.2949i	0.113583	−	1.43853i
$505$	−8.75326	−	8.75326i	−0.389515	−	0.389515i
$506$	−6.46377	+	1.56314i	−0.287350	+	0.0694902i
$507$	−16.6467	−	14.6759i	−0.739306	−	0.651778i
$508$	−35.1376	−	11.2883i	−1.55898	−	0.500839i
$509$	11.7812	+	1.55102i	0.522192	+	0.0687479i	0.387015	−	0.922074i	$-0.373506\pi$
$509$	11.7812	+	1.55102i	0.522192	+	0.0687479i	0.135177	+	0.990821i	$0.456840\pi$
$510$	−6.76356	+	0.259268i	−0.299495	+	0.0114806i
$511$	−15.5666	−	26.9621i	−0.688625	−	1.19273i
$512$	22.2936	−	3.87248i	0.985247	−	0.171141i
$513$	10.3809	+	15.8028i	0.458328	+	0.697711i
$514$	−5.70330	−	4.60282i	−0.251562	−	0.203022i
$515$	−8.13838	+	10.6061i	−0.358620	+	0.467363i
$516$	−35.0534	−	26.1374i	−1.54314	−	1.15063i
$517$	−3.51554	+	2.69757i	−0.154613	+	0.118639i
$518$	2.60918	+	2.74040i	0.114641	+	0.120406i
$519$	−1.96644	−	4.01394i	−0.0863171	−	0.176192i
$520$	−0.829448	+	0.0476038i	−0.0363737	+	0.00208757i
$521$	22.1523	−	22.1523i	0.970509	−	0.970509i	−0.0290689	−	0.999577i	$-0.509254\pi$
$521$	22.1523	−	22.1523i	0.970509	−	0.970509i	0.999577	+	0.0290689i	$0.00925421\pi$
$522$	−3.26287	+	20.1357i	−0.142812	+	0.881317i
$523$	−0.436978	+	1.05496i	−0.0191077	+	0.0461301i	−0.933145	−	0.359499i	$-0.882948\pi$
$523$	−0.436978	+	1.05496i	−0.0191077	+	0.0461301i	0.914038	+	0.405629i	$0.132948\pi$
$524$	15.8554	+	7.49825i	0.692645	+	0.327562i
$525$	16.6117	+	25.0023i	0.724993	+	1.09119i
$526$	−9.37811	−	4.15680i	−0.408905	−	0.181245i
$527$	30.8218	+	17.7950i	1.34262	+	0.775162i
$528$	6.87848	+	9.65040i	0.299347	+	0.419980i
$529$	13.3738	−	7.72136i	0.581469	−	0.335711i
$530$	2.73681	−	0.292235i	0.118879	−	0.0126939i
$531$	32.4090	+	8.86568i	1.40643	+	0.384738i
$532$	−4.97274	+	27.3356i	−0.215596	+	1.18515i
$533$	0.0461538	−	0.00607627i	0.00199914	−	0.000263192i
$534$	−37.0218	+	6.32510i	−1.60209	+	0.273714i
$535$	0.133775	+	0.499255i	0.00578360	+	0.0215847i
$536$	−10.5941	+	15.5798i	−0.457596	+	0.672947i
$537$	29.6096	+	2.01840i	1.27775	+	0.0871005i
$538$	7.66315	+	31.6880i	0.330382	+	1.36617i
$539$	11.9724	+	4.95911i	0.515686	+	0.213604i
$540$	−3.57867	−	6.07760i	−0.154001	−	0.261538i
$541$	4.81834	+	11.6325i	0.207157	+	0.500120i	0.992973	−	0.118339i	$-0.0377570\pi$
$541$	4.81834	+	11.6325i	0.207157	+	0.500120i	−0.785817	+	0.618460i	$0.787757\pi$
$542$	−43.6988	−	6.84702i	−1.87702	−	0.294105i
$543$	15.3028	−	13.3496i	0.656706	−	0.572888i
$544$	−16.4205	−	16.1507i	−0.704024	−	0.692458i
$545$	−1.62334	+	2.81171i	−0.0695363	+	0.120440i
$546$	−3.42519	+	2.15656i	−0.146585	+	0.0922923i
$547$	−8.75020	+	11.4035i	−0.374131	+	0.487578i	−0.942034	−	0.335518i	$-0.891089\pi$
$547$	−8.75020	+	11.4035i	−0.374131	+	0.487578i	0.567902	+	0.823096i	$0.307755\pi$
$548$	−1.32208	−	0.852354i	−0.0564764	−	0.0364108i
$549$	20.3760	+	0.106448i	0.869627	+	0.00454308i
$550$	−10.5340	−	3.10135i	−0.449172	−	0.132242i
$551$	4.52800	−	16.8987i	0.192899	−	0.719911i
$552$	10.5959	+	8.31272i	0.450992	+	0.353813i
$553$	−7.99914	−	29.8532i	−0.340158	−	1.26949i
$554$	0.531163	−	21.6550i	0.0225669	−	0.920034i
$555$	0.807550	+	0.162826i	0.0342786	+	0.00691156i
$556$	−7.49038	−	20.9316i	−0.317663	−	0.887696i
$557$	−12.4153	+	5.14261i	−0.526055	+	0.217899i	−0.629874	−	0.776697i	$-0.716894\pi$
$557$	−12.4153	+	5.14261i	−0.526055	+	0.217899i	0.103819	+	0.994596i	$0.466894\pi$
$558$	−1.10304	+	37.0691i	−0.0466955	+	1.56926i
$559$			5.46313i			0.231066i
$560$	2.35265	−	10.0937i	0.0994177	−	0.426535i
$561$	3.90731	−	11.4125i	0.164967	−	0.481837i
$562$	−4.20069	−	1.86194i	−0.177196	−	0.0785411i
$563$	1.42503	−	10.8242i	0.0600580	−	0.456185i	−0.934822	−	0.355118i	$-0.884441\pi$
$563$	1.42503	−	10.8242i	0.0600580	−	0.456185i	0.994880	−	0.101068i	$-0.0322259\pi$
$564$	8.69943	+	2.20288i	0.366312	+	0.0927581i
$565$	12.8050	−	1.68580i	0.538708	−	0.0709223i
$566$	9.53516	+	17.4924i	0.400793	+	0.735261i
$567$	−29.5760	−	17.4902i	−1.24207	−	0.734521i
$568$	24.7653	−	8.18302i	1.03913	−	0.343352i
$569$	3.35500	−	12.5210i	0.140649	−	0.524908i	−0.859262	−	0.511536i	$-0.829077\pi$
$569$	3.35500	−	12.5210i	0.140649	−	0.524908i	0.999911	−	0.0133722i	$-0.00425663\pi$
$570$	2.52723	+	5.49580i	0.105854	+	0.230194i
$571$	−12.5511	+	9.63078i	−0.525246	+	0.403036i	−0.837063	−	0.547107i	$-0.815729\pi$
$571$	−12.5511	+	9.63078i	−0.525246	+	0.403036i	0.311817	+	0.950142i	$0.399063\pi$
$572$	0.452886	−	1.40971i	0.0189361	−	0.0589431i
$573$	−2.15701	−	34.2815i	−0.0901106	−	1.43213i
$574$	−0.0898956	+	0.573728i	−0.00375217	+	0.0239469i
$575$	−12.4791			−0.520413
$576$	6.70780	−	23.0436i	0.279492	−	0.960148i
$577$	31.2512			1.30100			0.650502	−	0.759504i	$-0.274558\pi$
$577$	31.2512			1.30100			0.650502	+	0.759504i	$0.274558\pi$
$578$	0.0924914	−	0.590295i	0.00384714	−	0.0245530i
$579$	2.27902	−	1.51420i	0.0947129	−	0.0629279i
$580$	−1.99608	+	6.21326i	−0.0828826	+	0.257992i
$581$	35.1472	−	26.9694i	1.45815	−	1.11888i
$582$	21.4719	+	1.99368i	0.890038	+	0.0826407i
$583$	−1.26958	+	4.73813i	−0.0525805	+	0.196233i
$584$	−7.23635	−	21.9003i	−0.299442	−	0.906240i
$585$	−0.341473	+	0.812359i	−0.0141182	+	0.0335869i
$586$	10.5670	+	19.3853i	0.436517	+	0.800799i
$587$	28.2174	−	3.71489i	1.16466	−	0.153330i	0.476689	−	0.879072i	$-0.341837\pi$
$587$	28.2174	−	3.71489i	1.16466	−	0.153330i	0.687967	+	0.725742i	$0.258503\pi$
$588$	−7.14130	−	25.2534i	−0.294502	−	1.04143i
$589$	4.15162	−	31.5346i	0.171064	−	1.29936i
$590$	9.82740	+	4.35595i	0.404588	+	0.179332i
$591$	17.7332	+	20.3277i	0.729447	+	0.836171i
$592$	1.48050	+	2.38041i	0.0608483	+	0.0978343i
$593$		−	28.8525i		−	1.18483i	−0.805634	−	0.592414i	$-0.798175\pi$
$593$		−	28.8525i		−	1.18483i	0.805634	−	0.592414i	$-0.201825\pi$
$594$	12.4011	−	2.05209i	0.508825	−	0.0841982i
$595$	−9.74656	+	4.03716i	−0.399570	+	0.165507i
$596$	0.860708	+	2.40521i	0.0352560	+	0.0985213i
$597$	−4.55330	−	13.5296i	−0.186354	−	0.553729i
$598$	0.0412606	−	1.68216i	0.00168727	−	0.0687885i
$599$	−0.716783	−	2.67507i	−0.0292870	−	0.109300i	0.949735	−	0.313055i	$-0.101352\pi$
$599$	−0.716783	−	2.67507i	−0.0292870	−	0.109300i	−0.979022	+	0.203754i	$0.934686\pi$
$600$	8.28930	+	20.6358i	0.338409	+	0.842453i
$601$	−0.897163	+	3.34826i	−0.0365960	+	0.136578i	−0.981807	−	0.189882i	$-0.939189\pi$
$601$	−0.897163	+	3.34826i	−0.0365960	+	0.136578i	0.945211	+	0.326461i	$0.105856\pi$
$602$	−65.3770	−	19.2478i	−2.66457	−	0.784482i
$603$	9.90117	+	17.3581i	0.403207	+	0.706877i
$604$	2.47914	+	1.59832i	0.100875	+	0.0650346i
$605$	3.33580	−	4.34730i	0.135619	−	0.176743i
$606$	−39.5203	−	20.8409i	−1.60540	−	0.846602i
$607$	−15.2631	+	26.4365i	−0.619512	+	1.07303i	0.370063	+	0.929007i	$0.379336\pi$
$607$	−15.2631	+	26.4365i	−0.619512	+	1.07303i	−0.989575	+	0.144019i	$0.953997\pi$
$608$	−7.71932	+	19.0816i	−0.313060	+	0.773860i
$609$	6.12112	+	31.1986i	0.248040	+	1.26423i
$610$	6.44037	+	1.00912i	0.260763	+	0.0408581i
$611$	−0.429076	−	1.03588i	−0.0173586	−	0.0419073i
$612$	−23.0436	+	8.11064i	−0.931483	+	0.327853i
$613$	33.4385	+	13.8507i	1.35057	+	0.559424i	0.936451	−	0.350799i	$-0.114090\pi$
$613$	33.4385	+	13.8507i	1.35057	+	0.559424i	0.414118	+	0.910223i	$0.364090\pi$
$614$	−7.13325	−	29.4968i	−0.287875	−	1.19039i
$615$	0.0556234	+	0.113540i	0.00224295	+	0.00457837i
$616$	15.2743	+	10.3864i	0.615420	+	0.418479i
$617$	−2.14514	−	8.00579i	−0.0863603	−	0.322301i	0.909208	−	0.416342i	$-0.136688\pi$
$617$	−2.14514	−	8.00579i	−0.0863603	−	0.322301i	−0.995568	+	0.0940412i	$0.970021\pi$
$618$	−16.7438	+	45.2528i	−0.673534	+	1.82034i
$619$	29.3542	−	3.86455i	1.17984	−	0.155329i	0.485016	−	0.874505i	$-0.338814\pi$
$619$	29.3542	−	3.86455i	1.17984	−	0.155329i	0.694828	+	0.719176i	$0.255481\pi$
$620$	−2.12351	+	11.6731i	−0.0852823	+	0.468804i
$621$	12.8605	−	6.21728i	0.516073	−	0.249491i
$622$	25.3905	−	2.71118i	1.01807	−	0.108708i
$623$	−50.6965	+	29.2696i	−2.03111	+	1.17266i
$624$	−2.80908	+	1.04915i	−0.112453	+	0.0419997i
$625$	−15.8511	−	9.15162i	−0.634043	−	0.366065i
$626$	−5.93695	−	2.63153i	−0.237288	−	0.105177i
$627$	−10.7593	+	0.676982i	−0.429685	+	0.0270361i
$628$	−25.0666	−	11.8544i	−1.00027	−	0.473041i
$629$	1.09195	−	2.63620i	0.0435388	−	0.105112i
$630$	−8.51836	−	6.94850i	−0.339380	−	0.276835i
$631$	−12.1757	+	12.1757i	−0.484706	+	0.484706i	−0.906631	−	0.421925i	$-0.861354\pi$
$631$	−12.1757	+	12.1757i	−0.484706	+	0.484706i	0.421925	+	0.906631i	$0.361354\pi$
$632$	−1.31194	−	22.8592i	−0.0521861	−	0.909289i
$633$	18.1818	−	27.0577i	0.722662	−	1.07545i
$634$	26.2509	+	27.5711i	1.04256	+	1.09499i
$635$	−9.93566	+	7.62390i	−0.394285	+	0.302545i
$636$	9.12450	−	3.92777i	0.361810	−	0.155746i
$637$	−1.99609	+	2.60136i	−0.0790880	+	0.103069i
$638$	−9.05084	−	7.30444i	−0.358326	−	0.289185i
$639$	3.75416	−	27.4085i	0.148512	−	1.08426i
$640$	3.22501	−	6.96817i	0.127480	−	0.275441i
$641$	−18.4787	−	32.0060i	−0.729863	−	1.26416i	−0.956941	−	0.290283i	$-0.906250\pi$
$641$	−18.4787	−	32.0060i	−0.729863	−	1.26416i	0.227077	−	0.973877i	$-0.427083\pi$
$642$	0.993950	+	1.57866i	0.0392281	+	0.0623046i
$643$	14.9035	+	1.96208i	0.587737	+	0.0773771i	0.418529	−	0.908203i	$-0.362546\pi$
$643$	14.9035	+	1.96208i	0.587737	+	0.0773771i	0.169208	+	0.985580i	$0.445879\pi$
$644$	19.9849	+	6.42036i	0.787514	+	0.252998i
$645$	−14.0625	+	4.73266i	−0.553712	+	0.186348i
$646$	20.3650	−	4.92489i	0.801249	−	0.193767i
$647$	−19.1772	−	19.1772i	−0.753933	−	0.753933i	0.221278	−	0.975211i	$-0.428977\pi$
$647$	−19.1772	−	19.1772i	−0.753933	−	0.753933i	−0.975211	+	0.221278i	$0.928977\pi$
$648$	−18.8238	−	17.1367i	−0.739468	−	0.673192i
$649$	−13.5466	+	13.5466i	−0.531750	+	0.531750i
$650$	1.44785	−	2.37148i	0.0567892	−	0.0930170i
$651$	18.4370	+	54.7833i	0.722602	+	2.14713i
$652$	−1.62330	−	19.7876i	−0.0635732	−	0.774942i
$653$	−4.24734	+	32.2617i	−0.166211	+	1.26250i	0.681412	+	0.731900i	$0.261366\pi$
$653$	−4.24734	+	32.2617i	−0.166211	+	1.26250i	−0.847623	+	0.530599i	$0.821967\pi$
$654$	−2.59707	+	11.4267i	−0.101554	+	0.446818i
$655$	5.15424	−	2.97580i	0.201393	−	0.116274i
$656$	−0.151516	+	0.402666i	−0.00591569	+	0.0157215i
$657$	−24.2377	−	3.31985i	−0.945601	−	0.129520i
$658$	13.9081	−	1.48509i	0.542192	−	0.0578949i
$659$	−13.6493	−	10.4735i	−0.531701	−	0.407988i	0.307715	−	0.951479i	$-0.400436\pi$
$659$	−13.6493	−	10.4735i	−0.531701	−	0.407988i	−0.839415	+	0.543490i	$0.817102\pi$
$660$	4.02104	−	0.0554571i	0.156519	−	0.00215867i
$661$	3.89590	+	5.07723i	0.151533	+	0.197481i	0.862951	−	0.505287i	$-0.168614\pi$
$661$	3.89590	+	5.07723i	0.151533	+	0.197481i	−0.711418	+	0.702769i	$0.751947\pi$
$662$	0.226903	−	9.25062i	0.00881883	−	0.359536i
$663$	2.53341	+	1.70236i	0.0983895	+	0.0661142i
$664$	29.5532	−	14.2768i	1.14688	−	0.554049i
$665$	6.66673	+	6.66673i	0.258525	+	0.258525i
$666$	2.95811	−	0.300243i	0.114624	−	0.0116342i
$667$	−12.2112	−	5.05803i	−0.472818	−	0.195848i
$668$	−40.2409	−	1.97528i	−1.55697	−	0.0764257i
$669$	0.943134	+	14.9893i	0.0364637	+	0.579519i
$670$	2.30103	+	5.96483i	0.0888964	+	0.230441i
$671$	−5.80904	+	10.0615i	−0.224255	+	0.388422i
$672$	−2.65815	−	37.3125i	−0.102540	−	1.43936i
$673$	5.70778	+	9.88617i	0.220019	+	0.381084i	0.954813	−	0.297206i	$-0.0960548\pi$
$673$	5.70778	+	9.88617i	0.220019	+	0.381084i	−0.734795	+	0.678290i	$0.762721\pi$
$674$	−2.86954	+	3.55562i	−0.110531	+	0.136957i
$675$	23.5241	+	1.72708i	0.905444	+	0.0664755i
$676$	−21.5373	−	13.8853i	−0.828359	−	0.534050i
$677$	−2.50482	−	19.0260i	−0.0962680	−	0.731228i	−0.969703	−	0.244287i	$-0.921446\pi$
$677$	−2.50482	−	19.0260i	−0.0962680	−	0.731228i	0.873435	−	0.486941i	$-0.161887\pi$
$678$	42.3518	−	19.4754i	1.62651	−	0.747947i
$679$	32.4653	−	8.69906i	1.24590	−	0.333839i
$680$	−7.67758	+	1.46246i	−0.294422	+	0.0560826i
$681$	−22.4091	+	10.9783i	−0.858720	+	0.420689i
$682$	−18.0476	−	11.0185i	−0.691078	−	0.421920i
$683$	−11.8377	+	28.5787i	−0.452956	+	1.09353i	0.518237	+	0.855237i	$0.326589\pi$
$683$	−11.8377	+	28.5787i	−0.452956	+	1.09353i	−0.971193	+	0.238296i	$0.923411\pi$
$684$	14.5777	+	16.2526i	0.557393	+	0.621432i
$685$	−0.493150	+	0.204270i	−0.0188423	+	0.00780474i
$686$	−1.83182	−	2.51253i	−0.0699394	−	0.0959288i
$687$	22.7650	−	4.46645i	0.868538	−	0.170406i
$688$	−44.5298	−	23.7971i	−1.69768	−	0.907255i
$689$	−1.07489	−	0.620585i	−0.0409499	−	0.0236424i
$690$	4.36574	−	1.35103i	0.166201	−	0.0514327i
$691$	−18.3020	−	14.0437i	−0.696243	−	0.534246i	0.198903	−	0.980019i	$-0.436262\pi$
$691$	−18.3020	−	14.0437i	−0.696243	−	0.534246i	−0.895146	+	0.445773i	$0.852929\pi$
$692$	−2.93742	−	4.24378i	−0.111664	−	0.161324i
$693$	17.0177	−	9.70702i	0.646451	−	0.368739i
$694$	−4.38613	−	8.04643i	−0.166495	−	0.305438i
$695$	−7.28685	−	1.95251i	−0.276406	−	0.0740628i
$696$	−0.252791	+	23.5527i	−0.00958203	+	0.892761i
$697$	0.423003	−	0.113343i	0.0160224	−	0.00429318i
$698$	10.1787	+	10.6906i	0.385270	+	0.404646i
$699$	23.6243	−	7.95060i	0.893551	−	0.300719i
$700$	23.2782	+	25.6815i	0.879835	+	0.970669i
$701$	−10.8587	−	26.2153i	−0.410129	−	0.990139i	−0.985103	−	0.171967i	$-0.944988\pi$
$701$	−10.8587	−	26.2153i	−0.410129	−	0.990139i	0.574974	−	0.818172i	$-0.305012\pi$
$702$	−0.310588	+	3.16530i	−0.0117224	+	0.119467i
$703$	−2.55008			−0.0961782
$704$	9.51779	+	9.83208i	0.358715	+	0.370561i
$705$	2.29474	−	2.00185i	0.0864247	−	0.0753940i
$706$	−38.4737	+	14.8418i	−1.44798	+	0.558579i
$707$	−69.0418	−	9.08952i	−2.59658	−	0.341847i
$708$	38.5319	+	4.53317i	1.44812	+	0.170367i
$709$	−0.376109	−	2.85683i	−0.0141251	−	0.107291i	0.982930	−	0.183980i	$-0.0588983\pi$
$709$	−0.376109	−	2.85683i	−0.0141251	−	0.107291i	−0.997055	+	0.0766897i	$0.975565\pi$
$710$	2.49965	−	8.49030i	0.0938102	−	0.318635i
$711$	−22.3882	−	9.41082i	−0.839624	−	0.352934i
$712$	−41.1788	+	13.6064i	−1.54324	+	0.509922i
$713$	−23.2110	−	6.21938i	−0.869260	−	0.232918i
$714$	−29.2978	+	24.3194i	−1.09644	+	0.910130i
$715$	−0.305869	−	0.398616i	−0.0114389	−	0.0149074i
$716$	34.1548	−	2.80193i	1.27643	−	0.104713i
$717$	0.408597	+	0.614980i	0.0152593	+	0.0229668i
$718$	−2.13330	+	1.55534i	−0.0796139	+	0.0580446i
$719$		−	12.6691i		−	0.472476i	−0.971695	−	0.236238i	$-0.924085\pi$
$719$		−	12.6691i		−	0.472476i	0.971695	−	0.236238i	$-0.0759146\pi$
$720$	−5.13408	−	6.32192i	−0.191336	−	0.235604i
$721$			75.2055i			2.80080i
$722$	4.79857	+	6.58171i	0.178584	+	0.244946i
$723$	−2.81725	+	0.177263i	−0.104775	+	0.00659249i
$724$	15.1697	−	17.8811i	0.563777	−	0.664544i
$725$	−13.2863	−	17.3151i	−0.493443	−	0.643067i
$726$	6.86302	−	18.5484i	0.254711	−	0.688397i
$727$	−36.0763	−	9.66660i	−1.33799	−	0.358514i	−0.482304	−	0.876004i	$-0.660200\pi$
$727$	−36.0763	−	9.66660i	−1.33799	−	0.358514i	−0.855690	+	0.517489i	$0.826867\pi$
$728$	−3.53879	+	3.05296i	−0.131156	+	0.113150i
$729$	−25.1036	+	9.94026i	−0.929763	+	0.368158i
$730$	−7.50808	−	2.21047i	−0.277887	−	0.0818133i
$731$	6.70811	+	50.9531i	0.248108	+	1.88457i
$732$	23.2826	−	3.39249i	0.860551	−	0.125390i
$733$	−8.27572	−	1.08952i	−0.305671	−	0.0402423i	−0.0238694	−	0.999715i	$-0.507599\pi$
$733$	−8.27572	−	1.08952i	−0.305671	−	0.0402423i	−0.281801	+	0.959473i	$0.590932\pi$
$734$	0.296197	+	0.767816i	0.0109328	+	0.0283406i
$735$	−8.42529	−	2.88457i	−0.310771	−	0.106399i
$736$	13.5315	+	7.66368i	0.498777	+	0.282487i
$737$	−11.3941			−0.419706
$738$	0.312932	+	0.332126i	0.0115192	+	0.0122257i
$739$	−19.5007	−	47.0789i	−0.717345	−	1.73182i	−0.680775	−	0.732493i	$-0.738357\pi$
$739$	−19.5007	−	47.0789i	−0.717345	−	1.73182i	−0.0365705	−	0.999331i	$-0.511643\pi$
$740$	0.950100	+	0.0466369i	0.0349264	+	0.00171441i
$741$	0.539152	−	2.67398i	0.0198062	−	0.0982310i
$742$	11.2136	−	10.6766i	0.411663	−	0.391951i
$743$	−27.9739	+	7.49559i	−1.02626	+	0.274987i	−0.732410	−	0.680864i	$-0.761605\pi$
$743$	−27.9739	+	7.49559i	−1.02626	+	0.274987i	−0.293854	+	0.955850i	$0.594938\pi$
$744$	5.13350	+	42.5139i	0.188203	+	1.55863i
$745$	0.837320	+	0.224359i	0.0306770	+	0.00821989i
$746$	24.4375	−	13.3209i	0.894719	−	0.487714i
$747$	0.181861	−	34.8114i	0.00665394	−	1.27368i
$748$	2.49297	−	13.7041i	0.0911521	−	0.501071i
$749$	2.30677	+	1.77005i	0.0842875	+	0.0646760i
$750$	15.4639	+	3.51466i	0.564662	+	0.128337i
$751$	24.8841	+	14.3668i	0.908033	+	0.524253i	0.879798	−	0.475348i	$-0.157678\pi$
$751$	24.8841	+	14.3668i	0.908033	+	0.524253i	0.0282354	+	0.999601i	$0.491011\pi$
$752$	10.3125	+	1.01485i	0.376057	+	0.0370077i
$753$	−9.23318	−	10.5841i	−0.336476	−	0.385705i
$754$	2.37798	−	1.73373i	0.0866008	−	0.0631386i
$755$	0.924746	−	0.383042i	0.0336549	−	0.0139403i
$756$	−36.7847	−	14.8688i	−1.33785	−	0.540774i
$757$	−4.53759	+	10.9547i	−0.164922	+	0.398156i	−0.984637	−	0.174616i	$-0.944132\pi$
$757$	−4.53759	+	10.9547i	−0.164922	+	0.398156i	0.819715	+	0.572771i	$0.194132\pi$
$758$	−15.5600	+	25.4863i	−0.565165	+	0.925705i
$759$	−0.553914	+	8.12582i	−0.0201058	+	0.294948i
$760$	3.83327	+	5.83898i	0.139047	+	0.211802i
$761$	−18.4295	+	4.93818i	−0.668070	+	0.179009i	−0.576885	−	0.816825i	$-0.695732\pi$
$761$	−18.4295	+	4.93818i	−0.668070	+	0.179009i	−0.0911846	+	0.995834i	$0.529065\pi$
$762$	−26.1227	+	36.8880i	−0.946327	+	1.33631i
$763$	2.38395	+	18.1079i	0.0863046	+	0.655549i
$764$	−8.37492	−	38.7689i	−0.302994	−	1.40261i
$765$	−2.18734	+	7.99594i	−0.0790834	+	0.289094i
$766$	21.0419	+	16.9818i	0.760274	+	0.613576i
$767$	−2.42373	−	4.19802i	−0.0875158	−	0.151582i
$768$	3.68456	−	27.4668i	0.132955	−	0.991122i
$769$	9.94103	−	17.2184i	0.358483	−	0.620910i	−0.629225	−	0.777223i	$-0.716628\pi$
$769$	9.94103	−	17.2184i	0.358483	−	0.620910i	0.987708	+	0.156313i	$0.0499609\pi$
$770$	5.84786	−	2.25590i	0.210742	−	0.0812971i
$771$	−7.47635	+	4.96734i	−0.269254	+	0.178894i
$772$	2.34094	−	2.12187i	0.0842521	−	0.0763679i
$773$	4.55137	+	1.88524i	0.163701	+	0.0678073i	0.463029	−	0.886343i	$-0.346762\pi$
$773$	4.55137	+	1.88524i	0.163701	+	0.0678073i	−0.299328	+	0.954150i	$0.596762\pi$
$774$	−43.4368	+	31.3225i	−1.56130	+	1.12587i
$775$	−28.0577	−	28.0577i	−1.00786	−	1.00786i
$776$	24.8593	−	1.42673i	0.892398	−	0.0512166i
$777$	4.16169	−	2.03882i	0.149300	−	0.0731423i
$778$	48.9109	+	1.19971i	1.75354	+	0.0430115i
$779$	−0.238253	−	0.310497i	−0.00853630	−	0.0111247i
$780$	−0.249778	+	0.986400i	−0.00894349	+	0.0353188i
$781$	12.5140	+	9.60234i	0.447787	+	0.343599i
$782$	−1.68067	−	15.7397i	−0.0601006	−	0.562849i
$783$	22.3191	+	11.2249i	0.797621	+	0.401144i
$784$	−12.5087	−	27.6014i	−0.446741	−	0.985765i
$785$	−8.14861	+	4.70460i	−0.290836	+	0.167914i
$786$	14.5962	−	15.7599i	0.520631	−	0.562137i
$787$	−3.42552	+	26.0194i	−0.122107	+	0.927492i	0.815247	+	0.579113i	$0.196601\pi$
$787$	−3.42552	+	26.0194i	−0.122107	+	0.927492i	−0.937354	+	0.348379i	$0.886732\pi$
$788$	23.7526	+	20.1509i	0.846151	+	0.717847i
$789$	−8.30834	+	9.42408i	−0.295785	+	0.335506i
$790$	−6.63146	−	4.04867i	−0.235937	−	0.144045i
$791$	51.3751	−	51.3751i	1.82669	−	1.82669i
$792$	13.8051	−	4.48166i	0.490542	−	0.159249i
$793$	−2.07868	−	2.07868i	−0.0738161	−	0.0738161i
$794$	0.285580	+	1.18090i	0.0101348	+	0.0419087i
$795$	0.666273	−	3.30445i	0.0236303	−	0.117197i
$796$	−7.53202	−	14.6621i	−0.266965	−	0.519685i
$797$	−22.0543	−	2.90351i	−0.781204	−	0.102847i	−0.270632	−	0.962683i	$-0.587233\pi$
$797$	−22.0543	−	2.90351i	−0.781204	−	0.102847i	−0.510572	+	0.859835i	$0.670566\pi$
$798$	30.0998	+	15.8730i	1.06552	+	0.561898i
$799$	−5.27382	−	9.13452i	−0.186574	−	0.323156i
$800$	13.0231	+	22.1314i	0.460437	+	0.782462i
$801$	−6.24228	+	45.5738i	−0.220560	+	1.61027i
$802$	32.7652	−	40.5989i	1.15698	−	1.43360i
$803$	8.49148	−	11.0663i	0.299658	−	0.390521i
$804$	14.2982	+	18.1111i	0.504259	+	0.638729i
$805$	5.65101	−	4.33617i	0.199172	−	0.152830i
$806$	3.87490	−	3.68936i	0.136488	−	0.129952i
$807$	39.8360	+	2.71551i	1.40229	+	0.0955904i
$808$	−48.7164	−	16.9794i	−1.71384	−	0.597334i
$809$	−14.6260	+	14.6260i	−0.514222	+	0.514222i	−0.915817	−	0.401595i	$-0.868456\pi$
$809$	−14.6260	+	14.6260i	−0.514222	+	0.514222i	0.401595	+	0.915817i	$0.368456\pi$
$810$	−8.41680	+	1.94259i	−0.295736	+	0.0682558i
$811$	−12.3089	+	29.7164i	−0.432225	+	1.04348i	0.546344	+	0.837561i	$0.316019\pi$
$811$	−12.3089	+	29.7164i	−0.432225	+	1.04348i	−0.978569	+	0.205922i	$0.933981\pi$
$812$	12.3693	+	34.5654i	0.434076	+	1.21301i
$813$	−24.0869	+	48.5234i	−0.844763	+	1.70179i
$814$	−0.686977	+	1.54988i	−0.0240785	+	0.0543233i
$815$	−5.83458	−	3.36859i	−0.204376	−	0.117997i
$816$	−24.9113	+	13.2344i	−0.872069	+	0.463296i
$817$	39.7763	−	22.9649i	1.39160	−	0.803439i
$818$	2.57951	+	24.1574i	0.0901905	+	0.844644i
$819$	1.25799	+	4.79494i	0.0439577	+	0.167549i
$820$	0.0830889	+	0.120041i	0.00290159	+	0.00419202i
$821$	41.9332	−	5.52060i	1.46348	−	0.192670i	0.643667	−	0.765306i	$-0.277412\pi$
$821$	41.9332	−	5.52060i	1.46348	−	0.192670i	0.819810	+	0.572635i	$0.194079\pi$
$822$	−1.48239	+	1.23050i	−0.0517043	+	0.0429185i
$823$	4.74962	+	17.7258i	0.165561	+	0.617883i	0.997968	+	0.0637179i	$0.0202958\pi$
$823$	4.74962	+	17.7258i	0.165561	+	0.617883i	−0.832407	+	0.554165i	$0.813038\pi$
$824$	−11.3130	+	54.5550i	−0.394106	+	1.90051i
$825$	−7.50105	+	11.1629i	−0.261153	+	0.388642i
$826$	58.7768	−	14.2141i	2.04510	−	0.494571i
$827$	10.6673	+	4.41856i	0.370940	+	0.153648i	0.560363	−	0.828247i	$-0.310662\pi$
$827$	10.6673	+	4.41856i	0.370940	+	0.153648i	−0.189423	+	0.981896i	$0.560662\pi$
$828$	13.6112	−	9.31648i	0.473022	−	0.323770i
$829$	4.84576	+	11.6987i	0.168300	+	0.406312i	0.985416	−	0.170161i	$-0.0544286\pi$
$829$	4.84576	+	11.6987i	0.168300	+	0.406312i	−0.817116	+	0.576473i	$0.804429\pi$
$830$	1.72404	−	11.0031i	0.0598422	−	0.381922i
$831$	−25.0996	−	8.59334i	−0.870694	−	0.298100i
$832$	−3.02633	+	1.68232i	−0.104919	+	0.0583240i
$833$	−15.4228	+	26.7131i	−0.534369	+	0.925554i
$834$	−27.2078	+	1.04296i	−0.942130	+	0.0361147i
$835$	−8.32274	+	10.8464i	−0.288020	+	0.375355i
$836$	−12.1677	+	2.62848i	−0.420828	+	0.0909079i
$837$	42.8941	+	14.9365i	1.48264	+	0.516280i
$838$	10.9422	−	37.1662i	0.377992	−	1.28389i
$839$	−10.5135	+	39.2367i	−0.362965	+	1.35460i	0.507194	+	0.861832i	$0.330683\pi$
$839$	−10.5135	+	39.2367i	−0.362965	+	1.35460i	−0.870159	+	0.492771i	$0.835984\pi$
$840$	−10.9242	−	6.46438i	−0.376920	−	0.223042i
$841$	1.52281	+	5.68320i	0.0525106	+	0.195972i
$842$	19.8913	+	0.487901i	0.685499	+	0.0168142i
$843$	−3.72152	+	4.22129i	−0.128176	+	0.145389i
$844$	16.0927	−	34.0288i	0.553935	−	1.17132i
$845$	−8.03367	+	3.32766i	−0.276367	+	0.114475i
$846$	5.77611	−	9.35070i	0.198587	−	0.321484i
$847$		−	30.8256i		−	1.05918i
$848$	9.74051	−	6.05813i	0.334490	−	0.208037i
$849$	23.9434	−	4.69766i	0.821736	−	0.161223i
$850$	10.5917	−	23.8959i	0.363294	−	0.819623i
$851$	−0.251468	+	1.91009i	−0.00862022	+	0.0654771i
$852$	−0.440522	−	31.9410i	−0.0150920	−	1.09428i
$853$	−35.7963	+	4.71267i	−1.22564	+	0.161359i	−0.715426	−	0.698689i	$-0.753767\pi$
$853$	−35.7963	+	4.71267i	−1.22564	+	0.161359i	−0.510215	+	0.860047i	$0.670434\pi$
$854$	32.1991	−	17.5518i	1.10183	−	0.600610i
$855$	7.35009	−	0.928621i	0.251368	−	0.0317582i
$856$	1.40709	+	1.63101i	0.0480935	+	0.0557469i
$857$	−6.54068	+	24.4101i	−0.223425	+	0.833835i	0.759604	+	0.650386i	$0.225393\pi$
$857$	−6.54068	+	24.4101i	−0.223425	+	0.833835i	−0.983029	+	0.183449i	$0.941274\pi$
$858$	−1.47994	−	1.04804i	−0.0505242	−	0.0357794i
$859$	−21.4845	+	16.4857i	−0.733043	+	0.562483i	−0.906423	−	0.422372i	$-0.861198\pi$
$859$	−21.4845	+	16.4857i	−0.733043	+	0.562483i	0.173380	+	0.984855i	$0.444531\pi$
$860$	−15.2397	+	7.82872i	−0.519669	+	0.266957i
$861$	0.637071	+	0.316240i	0.0217113	+	0.0107774i
$862$	26.8837	+	4.21232i	0.915663	+	0.143472i
$863$	50.8578			1.73122			0.865609	−	0.500720i	$-0.166931\pi$
$863$	50.8578			1.73122			0.865609	+	0.500720i	$0.166931\pi$
$864$	−24.4474	−	16.3195i	−0.831717	−	0.555199i
$865$	−1.75138			−0.0595488
$866$	1.92810	+	0.302108i	0.0655196	+	0.0102661i
$867$	−0.655467	−	0.325372i	−0.0222608	−	0.0110502i
$868$	30.4983	+	59.3691i	1.03518	+	2.01512i
$869$	10.9857	−	8.42960i	0.372663	−	0.285955i
$870$	6.52277	+	4.61919i	0.221143	+	0.156605i
$871$	0.746181	−	2.78479i	0.0252834	−	0.0943589i
$872$	−0.994574	+	13.4943i	−0.0336805	+	0.456974i
$873$	10.2343	−	24.3472i	0.346377	−	0.824026i
$874$	−12.4210	+	6.77071i	−0.420146	+	0.229023i
$875$	24.5057	−	3.22623i	0.828443	−	0.109067i
$876$	−28.2459	+	0.389559i	−0.954339	+	0.0131620i
$877$	−2.87740	+	21.8560i	−0.0971629	+	0.738025i	0.871632	+	0.490161i	$0.163062\pi$
$877$	−2.87740	+	21.8560i	−0.0971629	+	0.738025i	−0.968795	+	0.247864i	$0.920271\pi$
$878$	8.95889	−	20.2120i	0.302348	−	0.682123i
$879$	26.5344	−	5.20600i	0.894982	−	0.175594i
$880$	4.58146	−	0.756783i	0.154441	−	0.0255111i
$881$		−	32.4733i		−	1.09405i	−0.837115	−	0.547027i	$-0.815759\pi$
$881$		−	32.4733i		−	1.09405i	0.837115	−	0.547027i	$-0.184241\pi$
$882$	−32.1276	−	0.956000i	−1.08179	−	0.0321902i
$883$	50.1310	−	20.7649i	1.68704	−	0.698796i	0.687420	−	0.726260i	$-0.258743\pi$
$883$	50.1310	−	20.7649i	1.68704	−	0.698796i	0.999623	+	0.0274646i	$0.00874336\pi$
$884$	3.18611	+	1.50676i	0.107160	+	0.0506778i
$885$	8.70638	−	9.87557i	0.292662	−	0.331964i
$886$	31.6457	+	0.776217i	1.06316	+	0.0260775i
$887$	2.06176	+	7.69458i	0.0692270	+	0.258359i	0.991862	−	0.127315i	$-0.0406358\pi$
$887$	2.06176	+	7.69458i	0.0692270	+	0.258359i	−0.922635	+	0.385673i	$0.873969\pi$
$888$	3.32563	−	0.852954i	0.111601	−	0.0286233i
$889$	−18.2341	+	68.0507i	−0.611553	+	2.28235i
$890$	−4.15632	+	14.1173i	−0.139320	+	0.473215i
$891$	2.16878	−	15.2412i	0.0726568	−	0.510600i
$892$	3.66185	+	16.9513i	0.122608	+	0.567573i
$893$	−5.73844	+	7.47848i	−0.192030	+	0.250258i
$894$	3.12641	−	0.119845i	0.104563	−	0.00400821i
$895$	5.81443	−	10.0709i	0.194355	−	0.336633i
$896$	−9.46981	−	42.1431i	−0.316364	−	1.40790i
$897$	−1.94973	−	0.667528i	−0.0650995	−	0.0222881i
$898$	2.66657	−	17.0185i	0.0889845	−	0.567913i
$899$	−16.0830	−	38.8278i	−0.536398	−	1.29498i
$900$	27.1565	−	2.08505i	0.905217	−	0.0695016i
$901$	−10.7872	−	4.46819i	−0.359373	−	0.148857i
$902$	−0.252897	+	0.0611584i	−0.00842055	+	0.00203635i
$903$	−46.5536	+	69.2799i	−1.54921	+	2.30549i
$904$	44.9964	−	29.5399i	1.49656	−	0.982483i
$905$	−2.05943	−	7.68592i	−0.0684579	−	0.255488i
$906$	2.77975	−	2.30740i	0.0923509	−	0.0766583i
$907$	3.48912	−	0.459352i	0.115854	−	0.0152525i	−0.0723760	−	0.997377i	$-0.523058\pi$
$907$	3.48912	−	0.459352i	0.115854	−	0.0152525i	0.188230	+	0.982125i	$0.439725\pi$
$908$	−23.6923	+	16.3991i	−0.786257	+	0.544223i
$909$	−38.8946	+	38.4903i	−1.29005	+	1.27664i
$910$	0.168390	+	1.57699i	0.00558207	+	0.0522767i
$911$	−5.25069	+	3.03149i	−0.173963	+	0.100438i	−0.584453	−	0.811427i	$-0.698691\pi$
$911$	−5.25069	+	3.03149i	−0.173963	+	0.100438i	0.410490	+	0.911865i	$0.365358\pi$
$912$	19.4470	+	16.0423i	0.643955	+	0.531213i
$913$	17.1897	+	9.92446i	0.568895	+	0.328452i
$914$	6.81918	−	15.3847i	0.225558	−	0.508879i
$915$	3.54995	−	7.15143i	0.117358	−	0.236419i
$916$	25.2216	−	9.02559i	0.833346	−	0.298214i
$917$	12.8124	−	30.9320i	0.423104	−	1.02146i
$918$	0.989866	+	29.9033i	0.0326705	+	0.986955i
$919$	7.49145	−	7.49145i	0.247120	−	0.247120i	−0.572668	−	0.819788i	$-0.694091\pi$
$919$	7.49145	−	7.49145i	0.247120	−	0.247120i	0.819788	+	0.572668i	$0.194091\pi$
$920$	4.75159	−	2.29545i	0.156655	−	0.0756786i
$921$	−37.0814	−	2.52773i	−1.22187	−	0.0832916i
$922$	−6.79767	+	6.47218i	−0.223869	+	0.213150i
$923$	−3.16640	+	2.42966i	−0.104223	+	0.0799733i
$924$	17.7559	−	14.0178i	0.584127	−	0.461153i
$925$	−1.93664	+	2.52388i	−0.0636764	+	0.0829847i
$926$	−37.4321	+	46.3817i	−1.23010	+	1.52420i
$927$	46.6949	+	36.2194i	1.53366	+	1.18960i
$928$	3.77324	+	26.9348i	0.123863	+	0.884179i
$929$	−6.56883	−	11.3775i	−0.215516	−	0.373285i	0.737916	−	0.674893i	$-0.235810\pi$
$929$	−6.56883	−	11.3775i	−0.215516	−	0.373285i	−0.953432	+	0.301608i	$0.902477\pi$
$930$	12.8535	+	6.77825i	0.421483	+	0.222267i
$931$	27.3309	+	3.59818i	0.895734	+	0.117926i
$932$	25.6018	−	13.1518i	0.838616	−	0.430801i
$933$	6.18129	−	30.6567i	0.202366	−	1.00366i
$934$	12.1989	+	50.4439i	0.399161	+	1.65057i
$935$	−3.34221	−	3.34221i	−0.109302	−	0.109302i
$936$	0.191271	+	3.66755i	0.00625190	+	0.119877i
$937$	15.6043	−	15.6043i	0.509769	−	0.509769i	−0.404687	−	0.914455i	$-0.632619\pi$
$937$	15.6043	−	15.6043i	0.509769	−	0.509769i	0.914455	+	0.404687i	$0.132619\pi$
$938$	30.6964	+	18.7409i	1.00227	+	0.611912i
$939$	−5.25972	+	5.96606i	−0.171645	+	0.194695i
$940$	2.27478	−	2.68136i	0.0741950	−	0.0874562i
$941$	6.01751	−	45.7075i	0.196165	−	1.49002i	−0.556075	−	0.831132i	$-0.687693\pi$
$941$	6.01751	−	45.7075i	0.196165	−	1.49002i	0.752240	−	0.658889i	$-0.228974\pi$
$942$	−23.0760	+	24.9157i	−0.751856	+	0.811796i
$943$	−0.256067	+	0.147840i	−0.00833868	+	0.00481434i
$944$	44.7756	−	1.46943i	1.45732	−	0.0478258i
$945$	−11.2528	+	7.39198i	−0.366053	+	0.240461i
$946$	−3.24200	−	30.3617i	−0.105407	−	0.987144i
$947$	−13.3109	−	10.2138i	−0.432545	−	0.331904i	0.369433	−	0.929258i	$-0.379552\pi$
$947$	−13.3109	−	10.2138i	−0.432545	−	0.331904i	−0.801978	+	0.597354i	$0.796219\pi$
$948$	−27.1847	−	6.88376i	−0.882918	−	0.223574i
$949$	2.14858	+	2.80009i	0.0697459	+	0.0908946i
$950$	−23.3526	−	0.572801i	−0.757657	−	0.0185841i
$951$	41.8707	−	20.5125i	1.35775	−	0.665165i
$952$	−29.2566	+	32.8193i	−0.948213	+	1.06368i
$953$	37.8565	+	37.8565i	1.22629	+	1.22629i	0.965355	+	0.260938i	$0.0840319\pi$
$953$	37.8565	+	37.8565i	1.22629	+	1.22629i	0.260938	+	0.965355i	$0.415968\pi$
$954$	−1.22858	−	12.1044i	−0.0397767	−	0.391894i
$955$	−12.4346	−	5.15058i	−0.402374	−	0.166669i
$956$	0.572574	+	0.631687i	0.0185184	+	0.0204302i
$957$	−11.8646	+	7.88292i	−0.383528	+	0.254818i
$958$	−30.3930	+	11.7246i	−0.981953	+	0.378804i
$959$	−1.50139	+	2.60048i	−0.0484823	+	0.0839738i
$960$	−6.95210	−	6.33263i	−0.224378	−	0.204385i
$961$	−22.7038	−	39.3241i	−0.732381	−	1.26852i
$962$	−0.333811	−	0.269401i	−0.0107625	−	0.00868583i
$963$	2.20997	−	0.579803i	0.0712153	−	0.0186839i
$964$	−3.18602	+	0.688250i	−0.102615	+	0.0221670i
$965$	−0.139940	−	1.06295i	−0.00450483	−	0.0342176i
$966$	14.8576	−	20.9804i	0.478034	−	0.675033i
$967$	−4.97253	+	1.33239i	−0.159906	+	0.0428466i	−0.337884	−	0.941188i	$-0.609711\pi$
$967$	−4.97253	+	1.33239i	−0.159906	+	0.0428466i	0.177978	+	0.984034i	$0.443044\pi$
$968$	4.63701	−	22.3613i	0.149039	−	0.718718i
$969$	1.74518	−	25.6015i	0.0560632	−	0.822437i
$970$	4.40292	−	7.21171i	0.141369	−	0.231554i
$971$	−4.70368	+	11.3557i	−0.150948	+	0.364421i	−0.981207	−	0.192956i	$-0.938192\pi$
$971$	−4.70368	+	11.3557i	−0.150948	+	0.364421i	0.830259	+	0.557378i	$0.188192\pi$
$972$	−26.9477	+	15.6786i	−0.864349	+	0.502892i
$973$	−39.2076	+	16.2403i	−1.25694	+	0.520641i
$974$	−8.32111	+	6.06673i	−0.266626	+	0.194390i
$975$	−2.23705	−	2.56434i	−0.0716428	−	0.0821248i
$976$	25.9979	−	7.88867i	0.832172	−	0.252510i
$977$	−17.6714	−	10.2026i	−0.565357	−	0.326409i	0.189936	−	0.981796i	$-0.439172\pi$
$977$	−17.6714	−	10.2026i	−0.565357	−	0.326409i	−0.755293	+	0.655388i	$0.772505\pi$
$978$	−23.7115	−	5.38918i	−0.758209	−	0.172327i
$979$	−20.8078	−	15.9664i	−0.665021	−	0.510289i
$980$	−10.1170	−	1.84043i	−0.323177	−	0.0587905i
$981$	12.3912	+	7.24066i	0.395622	+	0.231177i
$982$	−31.2657	+	17.0430i	−0.997729	+	0.543864i
$983$	−28.7959	−	7.71584i	−0.918447	−	0.246097i	−0.231526	−	0.972829i	$-0.574372\pi$
$983$	−28.7959	−	7.71584i	−0.918447	−	0.246097i	−0.686922	+	0.726732i	$0.741038\pi$
$984$	0.414568	+	0.325237i	0.0132159	+	0.0103682i
$985$	10.2097	−	2.73568i	0.325308	−	0.0871661i
$986$	20.0499	−	19.0899i	0.638519	−	0.607945i
$987$	3.38590	−	16.7927i	0.107774	−	0.534517i
$988$	0.154425	−	3.14599i	0.00491292	−	0.100087i
$989$	−13.2790	−	32.0583i	−0.422247	−	1.01939i
$990$	1.41568	−	4.71738i	0.0449932	−	0.149928i
$991$	2.54204			0.0807506			0.0403753	−	0.999185i	$-0.487145\pi$
$991$	2.54204			0.0807506			0.0403753	+	0.999185i	$0.487145\pi$
$992$	13.1931	+	47.6549i	0.418880	+	1.51304i
$993$	−10.7221	−	3.67091i	−0.340254	−	0.116493i
$994$	−17.9197	−	46.4523i	−0.568379	−	1.47338i
$995$	−5.54562	−	0.730094i	−0.175808	−	0.0231455i
$996$	−5.79590	−	39.7773i	−0.183650	−	1.26039i
$997$	−2.84908	−	21.6409i	−0.0902314	−	0.685375i	−0.975453	−	0.220206i	$-0.929327\pi$
$997$	−2.84908	−	21.6409i	−0.0902314	−	0.685375i	0.885222	−	0.465169i	$-0.154006\pi$
$998$	−40.0966	−	11.8050i	−1.26924	−	0.373679i
$999$	0.738394	−	3.56589i	0.0233618	−	0.112820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.229.27	yes	368
3.2	odd	2		864.2.bk.a.37.20		368
9.2	odd	6		864.2.bk.a.613.41		368
9.7	even	3	inner	288.2.bc.a.133.6	yes	368
32.13	even	8	inner	288.2.bc.a.13.6	✓	368
96.77	odd	8		864.2.bk.a.685.41		368
288.173	odd	24		864.2.bk.a.397.20		368
288.205	even	24	inner	288.2.bc.a.205.27	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.6	✓	368	32.13	even	8	inner
288.2.bc.a.133.6	yes	368	9.7	even	3	inner
288.2.bc.a.205.27	yes	368	288.205	even	24	inner
288.2.bc.a.229.27	yes	368	1.1	even	1	trivial
864.2.bk.a.37.20		368	3.2	odd	2
864.2.bk.a.397.20		368	288.173	odd	24
864.2.bk.a.613.41		368	9.2	odd	6
864.2.bk.a.685.41		368	96.77	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)

\(f(q)\)	\(=\)	\(q+(0.218918 - 1.39717i) q^{2} +(-1.55142 - 0.770122i) q^{3} +(-1.90415 - 0.611729i) q^{4} +(-0.538426 + 0.413148i) q^{5} +(-1.41562 + 1.99900i) q^{6} +(-0.988129 + 3.68775i) q^{7} +(-1.27154 + 2.52650i) q^{8} +(1.81383 + 2.38957i) q^{9} +O(q^{10})\)	\(q+(0.218918 - 1.39717i) q^{2} +(-1.55142 - 0.770122i) q^{3} +(-1.90415 - 0.611729i) q^{4} +(-0.538426 + 0.413148i) q^{5} +(-1.41562 + 1.99900i) q^{6} +(-0.988129 + 3.68775i) q^{7} +(-1.27154 + 2.52650i) q^{8} +(1.81383 + 2.38957i) q^{9} +(0.459366 + 0.842716i) q^{10} +(-1.69590 + 0.223269i) q^{11} +(2.48304 + 2.41548i) q^{12} +(0.0564933 - 0.429109i) q^{13} +(4.93608 + 2.18790i) q^{14} +(1.15350 - 0.226315i) q^{15} +(3.25158 + 2.32965i) q^{16} -4.07155i q^{17} +(3.73570 - 2.01110i) q^{18} +(-3.36176 + 1.39249i) q^{19} +(1.27798 - 0.457326i) q^{20} +(4.37302 - 4.96028i) q^{21} +(-0.0593176 + 2.41833i) q^{22} +(0.711506 + 2.65538i) q^{23} +(3.91841 - 2.94043i) q^{24} +(-1.17488 + 4.38473i) q^{25} +(-0.587170 - 0.172870i) q^{26} +(-0.973753 - 5.10410i) q^{27} +(4.13745 - 6.41756i) q^{28} +(-2.92689 + 3.81440i) q^{29} +(-0.0636780 - 1.66118i) q^{30} +(-4.37057 + 7.57005i) q^{31} +(3.96673 - 4.03299i) q^{32} +(2.80299 + 0.959661i) q^{33} +(-5.68863 - 0.891334i) q^{34} +(-0.991554 - 2.39382i) q^{35} +(-1.99203 - 5.65967i) q^{36} +(0.647468 + 0.268190i) q^{37} +(1.20959 + 5.00178i) q^{38} +(-0.418111 + 0.622223i) q^{39} +(-0.359189 - 1.88567i) q^{40} +(0.0278379 + 0.103892i) q^{41} +(-5.97301 - 7.19573i) q^{42} +(-12.5144 + 1.64756i) q^{43} +(3.36582 + 0.612291i) q^{44} +(-1.96386 - 0.537225i) q^{45} +(3.86577 - 0.412784i) q^{46} +(2.24350 - 1.29529i) q^{47} +(-3.25046 - 6.11838i) q^{48} +(-6.56092 - 3.78795i) q^{49} +(5.86900 + 2.60140i) q^{50} +(-3.13559 + 6.31669i) q^{51} +(-0.370070 + 0.782530i) q^{52} +(1.09742 - 2.64940i) q^{53} +(-7.34445 + 0.243118i) q^{54} +(0.820870 - 0.820870i) q^{55} +(-8.06064 - 7.18563i) q^{56} +(6.28789 + 0.428628i) q^{57} +(4.68860 + 4.92439i) q^{58} +(8.88549 - 6.81808i) q^{59} +(-2.33488 - 0.274692i) q^{60} +(4.13476 - 5.38853i) q^{61} +(9.61983 + 7.76364i) q^{62} +(-10.6044 + 4.32773i) q^{63} +(-4.76637 - 6.42508i) q^{64} +(0.146868 + 0.254383i) q^{65} +(1.95443 - 3.70616i) q^{66} +(6.60416 + 0.869454i) q^{67} +(-2.49068 + 7.75284i) q^{68} +(0.941117 - 4.66756i) q^{69} +(-3.56164 + 0.861316i) q^{70} +(-6.52056 - 6.52056i) q^{71} +(-8.34359 + 1.54419i) q^{72} +(-5.76621 + 5.76621i) q^{73} +(0.516448 - 0.845909i) q^{74} +(5.19952 - 5.89777i) q^{75} +(7.25312 - 0.595017i) q^{76} +(0.852405 - 6.47466i) q^{77} +(0.777817 + 0.720387i) q^{78} +(-7.01068 + 4.04762i) q^{79} +(-2.71322 + 0.0890414i) q^{80} +(-2.42007 + 8.66852i) q^{81} +(0.151249 - 0.0161503i) q^{82} +(-9.20605 - 7.06405i) q^{83} +(-11.3612 + 6.77001i) q^{84} +(1.68215 + 2.19223i) q^{85} +(-0.437720 + 17.8454i) q^{86} +(7.47840 - 3.66368i) q^{87} +(1.59231 - 4.56857i) q^{88} +(10.8421 + 10.8421i) q^{89} +(-1.18052 + 2.62623i) q^{90} +(1.52662 + 0.632348i) q^{91} +(0.269557 - 5.49149i) q^{92} +(12.6105 - 8.37848i) q^{93} +(-1.31859 - 3.41810i) q^{94} +(1.23475 - 2.13866i) q^{95} +(-9.25998 + 3.20201i) q^{96} +(-4.40178 - 7.62411i) q^{97} +(-6.72870 + 8.33745i) q^{98} +(-3.60957 - 3.64749i) 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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