LMFDB - Embedded newform 75.2.l.a.38.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(2,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("75.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.l (of order $20$, 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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			38.4
Character	$\chi$	$=$	75.38
Dual form			75.2.l.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0809972 - 0.511396i) q^{2} +(-1.50036 + 0.865399i) q^{3} +(1.64715 - 0.535191i) q^{4} +(2.21509 + 0.305570i) q^{5} +(0.564087 + 0.697184i) q^{6} +(0.155466 - 0.155466i) q^{7} +(-0.877235 - 1.72167i) q^{8} +(1.50217 - 2.59682i) q^{9} +O(q^{10})$	\(q+(-0.0809972 - 0.511396i) q^{2} +(-1.50036 + 0.865399i) q^{3} +(1.64715 - 0.535191i) q^{4} +(2.21509 + 0.305570i) q^{5} +(0.564087 + 0.697184i) q^{6} +(0.155466 - 0.155466i) q^{7} +(-0.877235 - 1.72167i) q^{8} +(1.50217 - 2.59682i) q^{9} +(-0.0231486 - 1.15754i) q^{10} +(-2.70163 + 3.71847i) q^{11} +(-2.00816 + 2.22842i) q^{12} +(-2.41331 - 0.382230i) q^{13} +(-0.0920967 - 0.0669122i) q^{14} +(-3.58788 + 1.45847i) q^{15} +(1.99289 - 1.44792i) q^{16} +(-2.76717 + 1.40994i) q^{17} +(-1.44968 - 0.557867i) q^{18} +(-5.97842 - 1.94251i) q^{19} +(3.81212 - 0.682176i) q^{20} +(-0.0987147 + 0.367794i) q^{21} +(2.12043 + 1.08041i) q^{22} +(3.65312 - 0.578598i) q^{23} +(2.80610 + 1.82397i) q^{24} +(4.81325 + 1.35373i) q^{25} +1.26511i q^{26} +(-0.00650455 + 5.19615i) q^{27} +(0.172871 - 0.339279i) q^{28} +(-2.16317 - 6.65756i) q^{29} +(1.03646 + 1.71669i) q^{30} +(-1.02511 + 3.15498i) q^{31} +(-3.63453 - 3.63453i) q^{32} +(0.835454 - 7.91703i) q^{33} +(0.945172 + 1.30092i) q^{34} +(0.391876 - 0.296865i) q^{35} +(1.08450 - 5.08130i) q^{36} +(-0.311136 + 1.96444i) q^{37} +(-0.509155 + 3.21468i) q^{38} +(3.95161 - 1.51499i) q^{39} +(-1.41706 - 4.08171i) q^{40} +(2.06770 + 2.84595i) q^{41} +(0.196084 + 0.0206920i) q^{42} +(1.96137 + 1.96137i) q^{43} +(-2.45989 + 7.57075i) q^{44} +(4.12095 - 5.29318i) q^{45} +(-0.591785 - 1.82133i) q^{46} +(3.93968 - 7.73207i) q^{47} +(-1.73703 + 3.89706i) q^{48} +6.95166i q^{49} +(0.302433 - 2.57113i) q^{50} +(2.93159 - 4.51013i) q^{51} +(-4.17964 + 0.661990i) q^{52} +(5.20184 + 2.65047i) q^{53} +(2.65782 - 0.417547i) q^{54} +(-7.12060 + 7.41121i) q^{55} +(-0.404040 - 0.131281i) q^{56} +(10.6508 - 2.25926i) q^{57} +(-3.22944 + 1.64548i) q^{58} +(-3.39191 + 2.46437i) q^{59} +(-5.12920 + 4.32252i) q^{60} +(3.06553 + 2.22724i) q^{61} +(1.69647 + 0.268695i) q^{62} +(-0.170181 - 0.637252i) q^{63} +(1.33155 - 1.83272i) q^{64} +(-5.22890 - 1.58411i) q^{65} +(-4.11641 + 0.214009i) q^{66} +(-6.01075 - 11.7968i) q^{67} +(-3.80335 + 3.80335i) q^{68} +(-4.98028 + 4.02952i) q^{69} +(-0.183556 - 0.176359i) q^{70} +(0.166802 - 0.0541973i) q^{71} +(-5.78863 - 0.308213i) q^{72} +(-0.552884 - 3.49077i) q^{73} +1.02981 q^{74} +(-8.39314 + 2.13430i) q^{75} -10.8870 q^{76} +(0.158084 + 0.998104i) q^{77} +(-1.09483 - 1.89813i) q^{78} +(10.1802 - 3.30776i) q^{79} +(4.85688 - 2.59831i) q^{80} +(-4.48698 - 7.80173i) q^{81} +(1.28793 - 1.28793i) q^{82} +(6.78245 + 13.3113i) q^{83} +(0.0342424 + 0.658643i) q^{84} +(-6.56036 + 2.27759i) q^{85} +(0.844172 - 1.16190i) q^{86} +(9.00698 + 8.11673i) q^{87} +(8.77193 + 1.38934i) q^{88} +(-10.0645 - 7.31232i) q^{89} +(-3.04070 - 1.67870i) q^{90} +(-0.434610 + 0.315763i) q^{91} +(5.70757 - 2.90815i) q^{92} +(-1.19227 - 5.62074i) q^{93} +(-4.27325 - 1.38846i) q^{94} +(-12.6492 - 6.12966i) q^{95} +(8.59843 + 2.30779i) q^{96} +(15.8386 + 8.07017i) q^{97} +(3.55505 - 0.563065i) q^{98} +(5.59791 + 12.6014i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0809972	−	0.511396i	−0.0572736	−	0.361612i	−0.999635	−	0.0270148i	$-0.991400\pi$
$2$	−0.0809972	−	0.511396i	−0.0572736	−	0.361612i	0.942361	−	0.334597i	$-0.108600\pi$
$3$	−1.50036	+	0.865399i	−0.866234	+	0.499639i
$3$	−1.50036	+	0.865399i	−0.866234	+	0.499639i
$4$	1.64715	−	0.535191i	0.823574	−	0.267595i
$5$	2.21509	+	0.305570i	0.990619	+	0.136655i
$5$	2.21509	+	0.305570i	0.990619	+	0.136655i
$6$	0.564087	+	0.697184i	0.230287	+	0.284624i
$7$	0.155466	−	0.155466i	0.0587605	−	0.0587605i	−0.677116	−	0.735876i	$-0.736770\pi$
$7$	0.155466	−	0.155466i	0.0587605	−	0.0587605i	0.735876	+	0.677116i	$0.236770\pi$
$8$	−0.877235	−	1.72167i	−0.310149	−	0.608702i
$9$	1.50217	−	2.59682i	0.500723	−	0.865608i
$10$	−0.0231486	−	1.15754i	−0.00732022	−	0.366046i
$11$	−2.70163	+	3.71847i	−0.814571	+	1.12116i	0.176031	+	0.984385i	$0.443674\pi$
$11$	−2.70163	+	3.71847i	−0.814571	+	1.12116i	−0.990602	+	0.136776i	$0.956326\pi$
$12$	−2.00816	+	2.22842i	−0.579707	+	0.643289i
$13$	−2.41331	−	0.382230i	−0.669331	−	0.106012i	−0.187485	−	0.982267i	$-0.560034\pi$
$13$	−2.41331	−	0.382230i	−0.669331	−	0.106012i	−0.481846	+	0.876256i	$0.660034\pi$
$14$	−0.0920967	−	0.0669122i	−0.0246139	−	0.0178830i
$15$	−3.58788	+	1.45847i	−0.926386	+	0.376576i
$16$	1.99289	−	1.44792i	0.498223	−	0.361981i
$17$	−2.76717	+	1.40994i	−0.671137	+	0.341961i	−0.756131	−	0.654420i	$-0.772913\pi$
$17$	−2.76717	+	1.40994i	−0.671137	+	0.341961i	0.0849943	+	0.996381i	$0.472913\pi$
$18$	−1.44968	−	0.557867i	−0.341692	−	0.131491i
$19$	−5.97842	−	1.94251i	−1.37154	−	0.445642i	−0.471664	−	0.881779i	$-0.656346\pi$
$19$	−5.97842	−	1.94251i	−1.37154	−	0.445642i	−0.899880	+	0.436137i	$0.856346\pi$
$20$	3.81212	−	0.682176i	0.852416	−	0.152539i
$21$	−0.0987147	+	0.367794i	−0.0215413	+	0.0802593i
$22$	2.12043	+	1.08041i	0.452078	+	0.230345i
$23$	3.65312	−	0.578598i	0.761729	−	0.120646i	0.236528	−	0.971625i	$-0.423990\pi$
$23$	3.65312	−	0.578598i	0.761729	−	0.120646i	0.525200	+	0.850979i	$0.323990\pi$
$24$	2.80610	+	1.82397i	0.572793	+	0.372316i
$25$	4.81325	+	1.35373i	0.962651	+	0.270746i
$26$			1.26511i			0.248109i
$27$	−0.00650455	+	5.19615i	−0.00125180	+	0.999999i
$28$	0.172871	−	0.339279i	0.0326696	−	0.0641176i
$29$	−2.16317	−	6.65756i	−0.401691	−	1.23628i	−0.923627	−	0.383293i	$-0.874790\pi$
$29$	−2.16317	−	6.65756i	−0.401691	−	1.23628i	0.521936	−	0.852985i	$-0.325210\pi$
$30$	1.03646	+	1.71669i	0.189232	+	0.313424i
$31$	−1.02511	+	3.15498i	−0.184116	+	0.566650i	−0.999932	−	0.0116610i	$-0.996288\pi$
$31$	−1.02511	+	3.15498i	−0.184116	+	0.566650i	0.815816	+	0.578311i	$0.196288\pi$
$32$	−3.63453	−	3.63453i	−0.642500	−	0.642500i
$33$	0.835454	−	7.91703i	0.145434	−	1.37818i
$34$	0.945172	+	1.30092i	0.162096	+	0.223105i
$35$	0.391876	−	0.296865i	0.0662391	−	0.0501793i
$36$	1.08450	−	5.08130i	0.180749	−	0.846883i
$37$	−0.311136	+	1.96444i	−0.0511505	+	0.322951i	0.948824	+	0.315805i	$0.102275\pi$
$37$	−0.311136	+	1.96444i	−0.0511505	+	0.322951i	−0.999974	+	0.00714603i	$0.997725\pi$
$38$	−0.509155	+	3.21468i	−0.0825958	+	0.521490i
$39$	3.95161	−	1.51499i	0.632765	−	0.242593i
$40$	−1.41706	−	4.08171i	−0.224057	−	0.645375i
$41$	2.06770	+	2.84595i	0.322921	+	0.444463i	0.939356	−	0.342943i	$-0.111424\pi$
$41$	2.06770	+	2.84595i	0.322921	+	0.444463i	−0.616435	+	0.787406i	$0.711424\pi$
$42$	0.196084	+	0.0206920i	0.0302564	+	0.00319285i
$43$	1.96137	+	1.96137i	0.299106	+	0.299106i	0.840664	−	0.541557i	$-0.182165\pi$
$43$	1.96137	+	1.96137i	0.299106	+	0.299106i	−0.541557	+	0.840664i	$0.682165\pi$
$44$	−2.45989	+	7.57075i	−0.370842	+	1.14133i
$45$	4.12095	−	5.29318i	0.614315	−	0.789061i
$46$	−0.591785	−	1.82133i	−0.0872539	−	0.268540i
$47$	3.93968	−	7.73207i	0.574662	−	1.12784i	−0.402515	−	0.915413i	$-0.631864\pi$
$47$	3.93968	−	7.73207i	0.574662	−	1.12784i	0.977177	−	0.212425i	$-0.0681360\pi$
$48$	−1.73703	+	3.89706i	−0.250719	+	0.562491i
$49$			6.95166i			0.993094i
$50$	0.302433	−	2.57113i	0.0427705	−	0.363612i
$51$	2.93159	−	4.51013i	0.410504	−	0.631544i
$52$	−4.17964	+	0.661990i	−0.579612	+	0.0918015i
$53$	5.20184	+	2.65047i	0.714527	+	0.364070i	0.773161	−	0.634210i	$-0.218674\pi$
$53$	5.20184	+	2.65047i	0.714527	+	0.364070i	−0.0586339	+	0.998280i	$0.518674\pi$
$54$	2.65782	−	0.417547i	0.361683	−	0.0568209i
$55$	−7.12060	+	7.41121i	−0.960141	+	0.999327i
$56$	−0.404040	−	0.131281i	−0.0539921	−	0.0175431i
$57$	10.6508	−	2.25926i	1.41074	−	0.299246i
$58$	−3.22944	+	1.64548i	−0.424046	+	0.216062i
$59$	−3.39191	+	2.46437i	−0.441589	+	0.320833i	−0.786266	−	0.617888i	$-0.787988\pi$
$59$	−3.39191	+	2.46437i	−0.441589	+	0.320833i	0.344677	+	0.938721i	$0.387988\pi$
$60$	−5.12920	+	4.32252i	−0.662177	+	0.558035i
$61$	3.06553	+	2.22724i	0.392502	+	0.285169i	0.766480	−	0.642268i	$-0.222007\pi$
$61$	3.06553	+	2.22724i	0.392502	+	0.285169i	−0.373978	+	0.927437i	$0.622007\pi$
$62$	1.69647	+	0.268695i	0.215452	+	0.0341243i
$63$	−0.170181	−	0.637252i	−0.0214408	−	0.0802862i
$64$	1.33155	−	1.83272i	0.166443	−	0.229090i
$65$	−5.22890	−	1.58411i	−0.648565	−	0.196485i
$66$	−4.11641	+	0.214009i	−0.506695	+	0.0263427i
$67$	−6.01075	−	11.7968i	−0.734329	−	1.44120i	−0.891213	−	0.453586i	$-0.850145\pi$
$67$	−6.01075	−	11.7968i	−0.734329	−	1.44120i	0.156883	−	0.987617i	$-0.449855\pi$
$68$	−3.80335	+	3.80335i	−0.461224	+	0.461224i
$69$	−4.98028	+	4.02952i	−0.599556	+	0.485097i
$70$	−0.183556	−	0.176359i	−0.0219392	−	0.0210789i
$71$	0.166802	−	0.0541973i	0.0197958	−	0.00643204i	−0.299102	−	0.954221i	$-0.596687\pi$
$71$	0.166802	−	0.0541973i	0.0197958	−	0.00643204i	0.318898	+	0.947789i	$0.396687\pi$
$72$	−5.78863	−	0.308213i	−0.682196	−	0.0363233i
$73$	−0.552884	−	3.49077i	−0.0647102	−	0.408564i	−0.998687	−	0.0512301i	$-0.983686\pi$
$73$	−0.552884	−	3.49077i	−0.0647102	−	0.408564i	0.933977	−	0.357334i	$-0.116314\pi$
$74$	1.02981			0.119713
$75$	−8.39314	+	2.13430i	−0.969156	+	0.246448i
$76$	−10.8870			−1.24882
$77$	0.158084	+	0.998104i	0.0180154	+	0.113744i
$78$	−1.09483	−	1.89813i	−0.123965	−	0.214921i
$79$	10.1802	−	3.30776i	1.14537	−	0.372152i	0.325971	−	0.945380i	$-0.394309\pi$
$79$	10.1802	−	3.30776i	1.14537	−	0.372152i	0.819396	+	0.573227i	$0.194309\pi$
$80$	4.85688	−	2.59831i	0.543016	−	0.290500i
$81$	−4.48698	−	7.80173i	−0.498554	−	0.866859i
$82$	1.28793	−	1.28793i	0.142228	−	0.142228i
$83$	6.78245	+	13.3113i	0.744470	+	1.46111i	0.882319	+	0.470652i	$0.155981\pi$
$83$	6.78245	+	13.3113i	0.744470	+	1.46111i	−0.137849	+	0.990453i	$0.544019\pi$
$84$	0.0342424	+	0.658643i	0.00373616	+	0.0718638i
$85$	−6.56036	+	2.27759i	−0.711571	+	0.247039i
$86$	0.844172	−	1.16190i	0.0910294	−	0.125291i
$87$	9.00698	+	8.11673i	0.965650	+	0.870205i
$88$	8.77193	+	1.38934i	0.935091	+	0.148104i
$89$	−10.0645	−	7.31232i	−1.06684	−	0.775105i	−0.0914984	−	0.995805i	$-0.529166\pi$
$89$	−10.0645	−	7.31232i	−1.06684	−	0.775105i	−0.975342	+	0.220701i	$0.929166\pi$
$90$	−3.04070	−	1.67870i	−0.320518	−	0.176951i
$91$	−0.434610	+	0.315763i	−0.0455595	+	0.0331009i
$92$	5.70757	−	2.90815i	0.595055	−	0.303196i
$93$	−1.19227	−	5.62074i	−0.123633	−	0.582843i
$94$	−4.27325	−	1.38846i	−0.440752	−	0.143209i
$95$	−12.6492	−	6.12966i	−1.29778	−	0.628890i
$96$	8.59843	+	2.30779i	0.877573	+	0.235538i
$97$	15.8386	+	8.07017i	1.60817	+	0.819401i	0.999666	+	0.0258470i	$0.00822828\pi$
$97$	15.8386	+	8.07017i	1.60817	+	0.819401i	0.608500	+	0.793554i	$0.291772\pi$
$98$	3.55505	−	0.563065i	0.359114	−	0.0568781i
$99$	5.59791	+	12.6014i	0.562611	+	1.26649i
$100$	8.65264	−	0.346211i	0.865264	−	0.0346211i
$101$		−	0.615955i		−	0.0612898i	−0.999530	−	0.0306449i	$-0.990244\pi$
$101$		−	0.615955i		−	0.0612898i	0.999530	−	0.0306449i	$-0.00975610\pi$
$102$	−2.54391	−	1.13389i	−0.251885	−	0.112272i
$103$	3.62816	−	7.12067i	0.357494	−	0.701621i	−0.640292	−	0.768131i	$-0.721187\pi$
$103$	3.62816	−	7.12067i	0.357494	−	0.701621i	0.997786	+	0.0665109i	$0.0211867\pi$
$104$	1.45896	+	4.49022i	0.143063	+	0.440303i
$105$	−0.331049	+	0.784534i	−0.0323071	+	0.0765626i
$106$	0.934105	−	2.87488i	0.0907283	−	0.279233i
$107$	0.484124	+	0.484124i	0.0468021	+	0.0468021i	0.730120	−	0.683318i	$-0.239464\pi$
$107$	0.484124	+	0.484124i	0.0468021	+	0.0468021i	−0.683318	+	0.730120i	$0.739464\pi$
$108$	2.77022	+	8.56231i	0.266564	+	0.823908i
$109$	0.119460	+	0.164423i	0.0114422	+	0.0157488i	0.814700	−	0.579883i	$-0.196902\pi$
$109$	0.119460	+	0.164423i	0.0114422	+	0.0157488i	−0.803258	+	0.595632i	$0.796902\pi$
$110$	4.36681	+	3.04116i	0.416359	+	0.289963i
$111$	−1.23321	−	3.21662i	−0.117051	−	0.305308i
$112$	0.0847243	−	0.534928i	0.00800570	−	0.0505460i
$113$	0.803690	−	5.07430i	0.0756048	−	0.477350i	−0.920614	−	0.390473i	$-0.872311\pi$
$113$	0.803690	−	5.07430i	0.0756048	−	0.477350i	0.996219	−	0.0868765i	$-0.0276886\pi$
$114$	−2.01806	−	5.26380i	−0.189009	−	0.493000i
$115$	8.26880	−	0.165360i	0.771069	−	0.0154199i
$116$	−7.12613	−	9.80827i	−0.661644	−	0.910675i
$117$	−4.61778	+	5.69276i	−0.426914	+	0.526296i
$118$	1.53500	+	1.53500i	0.141308	+	0.141308i
$119$	−0.211002	+	0.649397i	−0.0193425	+	0.0595301i
$120$	5.65842	+	4.89772i	0.516540	+	0.447098i
$121$	−3.12904	−	9.63019i	−0.284458	−	0.875472i
$122$	0.890703	−	1.74810i	0.0806404	−	0.158266i
$123$	−5.56519	−	2.48056i	−0.501796	−	0.223665i
$124$			5.74534i			0.515947i
$125$	10.2481	+	4.46943i	0.916621	+	0.399758i
$126$	−0.312104	+	0.138646i	−0.0278044	+	0.0123515i
$127$	−5.58413	+	0.884439i	−0.495511	+	0.0784813i	−0.399189	−	0.916869i	$-0.630708\pi$
$127$	−5.58413	+	0.884439i	−0.495511	+	0.0784813i	−0.0963228	+	0.995350i	$0.530708\pi$
$128$	−10.2046	−	5.19953i	−0.901972	−	0.459578i
$129$	−4.64014	−	1.24540i	−0.408541	−	0.109651i
$130$	−0.386582	+	2.80234i	−0.0339055	+	0.245782i
$131$	5.10340	+	1.65820i	0.445886	+	0.144877i	0.523350	−	0.852118i	$-0.324682\pi$
$131$	5.10340	+	1.65820i	0.445886	+	0.144877i	−0.0774634	+	0.996995i	$0.524682\pi$
$132$	−2.86101	−	13.4876i	−0.249019	−	1.17395i
$133$	−1.23143	+	0.627446i	−0.106779	+	0.0544065i
$134$	−5.54596	+	4.02937i	−0.479098	+	0.348085i
$135$	−1.60220	+	11.5080i	−0.137895	+	0.990447i
$136$	4.85491	+	3.52730i	0.416305	+	0.302463i
$137$	−3.03203	−	0.480226i	−0.259044	−	0.0410285i	0.0255617	−	0.999673i	$-0.491863\pi$
$137$	−3.03203	−	0.480226i	−0.259044	−	0.0410285i	−0.284605	+	0.958645i	$0.591863\pi$
$138$	2.46407	+	2.22052i	0.209755	+	0.189023i
$139$	3.51218	−	4.83410i	0.297899	−	0.410023i	−0.633661	−	0.773611i	$-0.718448\pi$
$139$	3.51218	−	4.83410i	0.297899	−	0.410023i	0.931560	+	0.363588i	$0.118448\pi$
$140$	0.486599	−	0.698708i	0.0411251	−	0.0590516i
$141$	0.780376	+	15.0103i	0.0657195	+	1.26409i
$142$	−0.0412268	−	0.0809121i	−0.00345968	−	0.00679000i
$143$	7.94116	−	7.94116i	0.664073	−	0.664073i
$144$	−0.766337	−	7.35021i	−0.0638615	−	0.612518i
$145$	−2.75727	−	15.4081i	−0.228979	−	1.27957i
$146$	−1.74038	+	0.565485i	−0.144035	+	0.0467999i
$147$	−6.01596	−	10.4300i	−0.496188	−	0.860252i
$148$	0.538861	+	3.40223i	0.0442941	+	0.279662i
$149$	13.8347			1.13338			0.566690	−	0.823931i	$-0.308224\pi$
$149$	13.8347			1.13338			0.566690	+	0.823931i	$0.308224\pi$
$150$	1.77129	+	4.11934i	0.144625	+	0.336343i
$151$	3.13860			0.255415			0.127708	−	0.991812i	$-0.459238\pi$
$151$	3.13860			0.255415			0.127708	+	0.991812i	$0.459238\pi$
$152$	1.90012	+	11.9969i	0.154120	+	0.973077i
$153$	−0.495378	+	9.30382i	−0.0400490	+	0.752169i
$154$	0.497622	−	0.161687i	0.0400995	−	0.0130291i
$155$	−3.23479	+	6.67531i	−0.259824	+	0.536174i
$156$	5.69808	−	4.61028i	0.456212	−	0.369118i
$157$	−11.0791	+	11.0791i	−0.884209	+	0.884209i	−0.993959	−	0.109750i	$-0.964995\pi$
$157$	−11.0791	+	11.0791i	−0.884209	+	0.884209i	0.109750	+	0.993959i	$0.464995\pi$
$158$	−2.51615	−	4.93822i	−0.200174	−	0.392863i
$159$	−10.0983	+	0.525007i	−0.800851	+	0.0416357i
$160$	−6.94021	−	9.16142i	−0.548672	−	0.724274i
$161$	0.477983	−	0.657887i	0.0376703	−	0.0518487i
$162$	−3.62634	+	2.92654i	−0.284912	+	0.229931i
$163$	−9.35728	−	1.48205i	−0.732918	−	0.116083i	−0.221191	−	0.975231i	$-0.570994\pi$
$163$	−9.35728	−	1.48205i	−0.732918	−	0.116083i	−0.511728	+	0.859148i	$0.670994\pi$
$164$	4.92894	+	3.58108i	0.384886	+	0.279636i
$165$	4.26982	−	17.2816i	0.332405	−	1.34537i
$166$	6.25799	−	4.54669i	0.485714	−	0.352892i
$167$	−8.93475	+	4.55248i	−0.691392	+	0.352282i	−0.764124	−	0.645070i	$-0.776828\pi$
$167$	−8.93475	+	4.55248i	−0.691392	+	0.352282i	0.0727319	+	0.997352i	$0.476828\pi$
$168$	0.719816	−	0.152688i	0.0555350	−	0.0117801i
$169$	−6.68578	−	2.17234i	−0.514291	−	0.167103i
$170$	1.69612	+	3.17047i	0.130086	+	0.243164i
$171$	−14.0249	+	12.6069i	−1.07251	+	0.964076i
$172$	4.28038	+	2.18096i	0.326376	+	0.166297i
$173$	−19.7159	+	3.12269i	−1.49897	+	0.237413i	−0.851369	−	0.524567i	$-0.824227\pi$
$173$	−19.7159	+	3.12269i	−1.49897	+	0.237413i	−0.647600	+	0.761980i	$0.724227\pi$
$174$	3.42132	−	5.26357i	0.259370	−	0.399030i
$175$	0.958754	−	0.537836i	0.0724750	−	0.0406566i
$176$			11.3223i			0.853447i
$177$	2.95643	−	6.63279i	0.222219	−	0.498551i
$178$	−2.92429	+	5.73925i	−0.219185	+	0.430175i
$179$	0.463280	+	1.42583i	0.0346272	+	0.106571i	0.966876	−	0.255246i	$-0.0821564\pi$
$179$	0.463280	+	1.42583i	0.0346272	+	0.106571i	−0.932249	+	0.361817i	$0.882156\pi$
$180$	3.95495	−	10.9241i	0.294785	−	0.814238i
$181$	−4.62059	+	14.2207i	−0.343446	+	1.05702i	0.618964	+	0.785419i	$0.287552\pi$
$181$	−4.62059	+	14.2207i	−0.343446	+	1.05702i	−0.962410	+	0.271599i	$0.912448\pi$
$182$	0.196682	+	0.196682i	0.0145790	+	0.0145790i
$183$	−6.52686	−	0.688755i	−0.482480	−	0.0509142i
$184$	−4.20080	−	5.78190i	−0.309687	−	0.426248i
$185$	−1.28947	+	4.25633i	−0.0948036	+	0.312932i
$186$	−2.77785	+	1.06499i	−0.203682	+	0.0780887i
$187$	2.23302	−	14.0988i	0.163295	−	1.03100i
$188$	2.35111	−	14.8443i	0.171472	−	1.08263i
$189$	0.806811	+	0.808833i	0.0586869	+	0.0588340i
$190$	−2.11013	+	6.96522i	−0.153085	+	0.505310i
$191$	1.71008	+	2.35373i	0.123737	+	0.170310i	0.866392	−	0.499365i	$-0.166433\pi$
$191$	1.71008	+	2.35373i	0.123737	+	0.170310i	−0.742654	+	0.669675i	$0.766433\pi$
$192$	−0.411769	+	3.90206i	−0.0297169	+	0.281607i
$193$	3.04363	+	3.04363i	0.219085	+	0.219085i	0.808113	−	0.589028i	$-0.200489\pi$
$193$	3.04363	+	3.04363i	0.219085	+	0.219085i	−0.589028	+	0.808113i	$0.700489\pi$
$194$	2.84417	−	8.75345i	0.204199	−	0.628461i
$195$	9.21612	−	2.14835i	0.659980	−	0.153846i
$196$	3.72046	+	11.4504i	0.265747	+	0.817887i
$197$	−9.35114	+	18.3526i	−0.666241	+	1.30757i	0.272236	+	0.962230i	$0.412237\pi$
$197$	−9.35114	+	18.3526i	−0.666241	+	1.30757i	−0.938477	+	0.345341i	$0.887763\pi$
$198$	5.99089	−	3.88343i	0.425754	−	0.275983i
$199$		−	1.91672i		−	0.135873i	−0.997690	−	0.0679363i	$-0.978359\pi$
$199$		−	1.91672i		−	0.135873i	0.997690	−	0.0679363i	$-0.0216415\pi$
$200$	−1.89167	−	9.47437i	−0.133761	−	0.669939i
$201$	19.2272	+	12.4977i	1.35618	+	0.881519i
$202$	−0.314997	+	0.0498906i	−0.0221631	+	0.00351029i
$203$	−1.37132	−	0.698722i	−0.0962478	−	0.0490407i
$204$	2.41498	−	8.99781i	0.169082	−	0.629973i
$205$	3.71051	+	6.93587i	0.259154	+	0.484422i
$206$	−3.93535	−	1.27867i	−0.274189	−	0.0890894i
$207$	3.98509	−	10.3557i	0.276983	−	0.719768i
$208$	−5.36290	+	2.73254i	−0.371850	+	0.189467i
$209$	23.3746	−	16.9826i	1.61686	−	1.17471i
$210$	0.428021	+	0.105752i	0.0295363	+	0.00729759i
$211$	2.07426	+	1.50704i	0.142798	+	0.103749i	0.656891	−	0.753986i	$-0.271871\pi$
$211$	2.07426	+	1.50704i	0.142798	+	0.103749i	−0.514093	+	0.857735i	$0.671871\pi$
$212$	9.98670	+	1.58174i	0.685889	+	0.108634i
$213$	−0.203361	+	0.225666i	−0.0139341	+	0.0154624i
$214$	0.208367	−	0.286792i	0.0142436	−	0.0196047i
$215$	3.74528	+	4.94395i	0.255426	+	0.337175i
$216$	8.95176	−	4.54704i	0.609090	−	0.309387i
$217$	0.331120	+	0.649860i	0.0224779	+	0.0441154i
$218$	0.0744092	−	0.0744092i	0.00503963	−	0.00503963i
$219$	3.85044	+	4.75895i	0.260188	+	0.321580i
$220$	−7.76227	+	16.0182i	−0.523332	+	1.07995i
$221$	7.21695	−	2.34493i	0.485465	−	0.157737i
$222$	−1.54508	+	0.891194i	−0.103699	+	0.0598130i
$223$	−0.0407959	−	0.257575i	−0.00273189	−	0.0172485i	0.986285	−	0.165053i	$-0.0527794\pi$
$223$	−0.0407959	−	0.257575i	−0.00273189	−	0.0172485i	−0.989017	+	0.147804i	$0.952779\pi$
$224$	−1.13009			−0.0755072
$225$	10.7457	−	10.4656i	0.716381	−	0.697709i
$226$	−2.66007			−0.176945
$227$	−2.58619	−	16.3286i	−0.171651	−	1.08376i	−0.911593	−	0.411093i	$-0.865147\pi$
$227$	−2.58619	−	16.3286i	−0.171651	−	1.08376i	0.739942	−	0.672671i	$-0.234853\pi$
$228$	16.3344	−	9.42156i	1.08177	−	0.623958i
$229$	−10.7830	+	3.50360i	−0.712559	+	0.231524i	−0.642794	−	0.766039i	$-0.722225\pi$
$229$	−10.7830	+	3.50360i	−0.712559	+	0.231524i	−0.0697647	+	0.997563i	$0.522225\pi$
$230$	−0.754314	−	4.21524i	−0.0497380	−	0.277944i
$231$	−1.10094	−	1.36071i	−0.0724366	−	0.0895281i
$232$	−9.56451	+	9.56451i	−0.627941	+	0.627941i
$233$	−9.21620	−	18.0878i	−0.603773	−	1.18497i	−0.967359	−	0.253411i	$-0.918448\pi$
$233$	−9.21620	−	18.0878i	−0.603773	−	1.18497i	0.363586	−	0.931561i	$-0.381552\pi$
$234$	3.28528	+	1.90041i	0.214765	+	0.124234i
$235$	11.0895	−	15.9234i	0.723396	−	1.03873i
$236$	−4.26807	+	5.87449i	−0.277828	+	0.382397i
$237$	−12.4115	+	13.7728i	−0.806214	+	0.894641i
$238$	0.349190	+	0.0553062i	0.0226346	+	0.00358497i
$239$	6.93955	+	5.04188i	0.448882	+	0.326132i	0.789154	−	0.614195i	$-0.210519\pi$
$239$	6.93955	+	5.04188i	0.448882	+	0.326132i	−0.340272	+	0.940327i	$0.610519\pi$
$240$	−5.03850	+	8.10155i	−0.325234	+	0.522953i
$241$	2.67852	−	1.94606i	0.172539	−	0.125357i	−0.498164	−	0.867083i	$-0.665992\pi$
$241$	2.67852	−	1.94606i	0.172539	−	0.125357i	0.670703	+	0.741726i	$0.265992\pi$
$242$	−4.67140	+	2.38020i	−0.300289	+	0.153005i
$243$	13.4837	+	7.82238i	0.864980	+	0.501806i
$244$	6.24139	+	2.02795i	0.399564	+	0.129826i
$245$	−2.12422	+	15.3986i	−0.135712	+	0.983778i
$246$	−0.817786	+	3.04693i	−0.0521401	+	0.194265i
$247$	13.6853	+	6.97300i	0.870774	+	0.443681i
$248$	6.33109	−	1.00275i	0.402025	−	0.0636745i
$249$	−21.6957	−	14.1022i	−1.37491	−	0.893693i
$250$	1.45558	−	5.60286i	0.0920588	−	0.354356i
$251$		−	30.6042i		−	1.93172i	−0.259059	−	0.965861i	$-0.583412\pi$
$251$		−	30.6042i		−	1.93172i	0.259059	−	0.965861i	$-0.416588\pi$
$252$	−0.621365	−	0.958569i	−0.0391423	−	0.0603842i
$253$	−7.71787	+	15.1472i	−0.485218	+	0.952295i
$254$	0.904597	+	2.78406i	0.0567595	+	0.174688i
$255$	7.87190	−	9.09454i	0.492957	−	0.569522i
$256$	−0.432398	+	1.33079i	−0.0270249	+	0.0831741i
$257$	0.569354	+	0.569354i	0.0355153	+	0.0355153i	0.724641	−	0.689126i	$-0.242005\pi$
$257$	0.569354	+	0.569354i	0.0355153	+	0.0355153i	−0.689126	+	0.724641i	$0.742005\pi$
$258$	−0.261053	+	2.47382i	−0.0162524	+	0.154013i
$259$	0.257031	+	0.353773i	0.0159712	+	0.0219824i
$260$	−9.46056	+	0.189193i	−0.586719	+	0.0117333i
$261$	−20.5379	−	4.38339i	−1.27127	−	0.271325i
$262$	0.434634	−	2.74417i	0.0268518	−	0.169535i
$263$	−2.64927	+	16.7268i	−0.163361	+	1.03142i	0.760681	+	0.649126i	$0.224865\pi$
$263$	−2.64927	+	16.7268i	−0.163361	+	1.03142i	−0.924041	+	0.382293i	$0.875135\pi$
$264$	−14.3634	+	5.50672i	−0.884006	+	0.338915i
$265$	10.7126	+	7.46055i	0.658072	+	0.458298i
$266$	0.420616	+	0.578928i	0.0257896	+	0.0354963i
$267$	21.4285	+	2.26127i	1.31141	+	0.138388i
$268$	−16.2141	−	16.2141i	−0.990434	−	0.990434i
$269$	−0.0824539	+	0.253767i	−0.00502730	+	0.0154724i	−0.953539	−	0.301271i	$-0.902589\pi$
$269$	−0.0824539	+	0.253767i	−0.00502730	+	0.0154724i	0.948511	+	0.316743i	$0.102589\pi$
$270$	6.01489	−	0.112754i	0.366055	−	0.00686200i
$271$	−8.11476	−	24.9747i	−0.492936	−	1.51710i	−0.820148	−	0.572151i	$-0.806109\pi$
$271$	−8.11476	−	24.9747i	−0.492936	−	1.51710i	0.327212	−	0.944951i	$-0.393891\pi$
$272$	−3.47318	+	6.81651i	−0.210593	+	0.413312i
$273$	0.378811	−	0.849869i	0.0229267	−	0.0514364i
$274$			1.58946i			0.0960231i
$275$	−18.0374	+	14.2407i	−1.08770	+	0.858744i
$276$	−6.04671	+	9.30261i	−0.363969	+	0.559951i
$277$	0.366690	−	0.0580780i	0.0220323	−	0.00348957i	−0.145409	−	0.989372i	$-0.546450\pi$
$277$	0.366690	−	0.0580780i	0.0220323	−	0.00348957i	0.167441	+	0.985882i	$0.446450\pi$
$278$	−2.75661	−	1.40457i	−0.165331	−	0.0842402i
$279$	6.65302	+	7.40134i	0.398306	+	0.443107i
$280$	−0.854870	−	0.414261i	−0.0510883	−	0.0247568i
$281$	18.8210	+	6.11532i	1.12277	+	0.364809i	0.810823	−	0.585291i	$-0.199020\pi$
$281$	18.8210	+	6.11532i	1.12277	+	0.364809i	0.311944	+	0.950100i	$0.399020\pi$
$282$	7.61300	−	1.61487i	0.453347	−	0.0961642i
$283$	27.7809	−	14.1551i	1.65140	−	0.841432i	0.655099	−	0.755543i	$-0.272627\pi$
$283$	27.7809	−	14.1551i	1.65140	−	0.841432i	0.996305	−	0.0858898i	$-0.0273733\pi$
$284$	0.245742	−	0.178542i	0.0145821	−	0.0105945i
$285$	24.2829	−	1.74989i	1.43840	−	0.103654i
$286$	−4.70429	−	3.41787i	−0.278170	−	0.202103i
$287$	0.763904	+	0.120991i	0.0450918	+	0.00714185i
$288$	−14.8979	+	3.97856i	−0.877868	+	0.234439i
$289$	−4.32307	+	5.95019i	−0.254298	+	0.350011i
$290$	−7.65631	+	2.65807i	−0.449594	+	0.156087i
$291$	−30.7475	+	1.59854i	−1.80245	+	0.0937084i
$292$	−2.77891	−	5.45392i	−0.162623	−	0.319166i
$293$	−18.6110	+	18.6110i	−1.08727	+	1.08727i	−0.0914563	+	0.995809i	$0.529152\pi$
$293$	−18.6110	+	18.6110i	−1.08727	+	1.08727i	−0.995809	+	0.0914563i	$0.970848\pi$
$294$	−4.84659	+	3.92134i	−0.282659	+	0.228697i
$295$	−8.26642	+	4.42233i	−0.481290	+	0.257478i
$296$	3.65505	−	1.18760i	0.212446	−	0.0690277i
$297$	−19.3041	−	14.0622i	−1.12014	−	0.815973i
$298$	−1.12057	−	7.07500i	−0.0649128	−	0.409844i
$299$	−9.03726			−0.522638
$300$	−12.6825	+	8.00744i	−0.732223	+	0.462310i
$301$	0.609852			0.0351513
$302$	−0.254217	−	1.60507i	−0.0146286	−	0.0923612i
$303$	0.533047	+	0.924154i	0.0306227	+	0.0530913i
$304$	−14.7270	+	4.78508i	−0.844649	+	0.274443i
$305$	6.10986	+	5.87028i	0.349849	+	0.336131i
$306$	4.79806	−	0.500248i	0.274287	−	0.0285973i
$307$	−8.85260	+	8.85260i	−0.505245	+	0.505245i	−0.913063	−	0.407818i	$-0.866290\pi$
$307$	−8.85260	+	8.85260i	−0.505245	+	0.505245i	0.407818	+	0.913063i	$0.366290\pi$
$308$	0.794564	+	1.55942i	0.0452745	+	0.0888561i
$309$	0.718669	+	13.8234i	0.0408837	+	0.786385i
$310$	3.67574	+	1.11358i	0.208768	+	0.0632469i
$311$	9.83580	−	13.5378i	0.557737	−	0.767659i	−0.433300	−	0.901250i	$-0.642651\pi$
$311$	9.83580	−	13.5378i	0.557737	−	0.767659i	0.991037	+	0.133591i	$0.0426508\pi$
$312$	−6.07481	−	5.47437i	−0.343918	−	0.309925i
$313$	−7.15603	−	1.13340i	−0.404483	−	0.0640638i	−0.0491215	−	0.998793i	$-0.515642\pi$
$313$	−7.15603	−	1.13340i	−0.404483	−	0.0640638i	−0.355361	+	0.934729i	$0.615642\pi$
$314$	6.56319	+	4.76844i	0.370382	+	0.269098i
$315$	−0.182242	−	1.46357i	−0.0102682	−	0.0824630i
$316$	14.9981	−	10.8967i	0.843708	−	0.612990i
$317$	9.74457	−	4.96511i	0.547310	−	0.278868i	−0.158393	−	0.987376i	$-0.550631\pi$
$317$	9.74457	−	4.96511i	0.547310	−	0.278868i	0.705703	+	0.708508i	$0.250631\pi$
$318$	1.08642	+	5.12173i	0.0609236	+	0.287212i
$319$	30.6000	+	9.94254i	1.71327	+	0.556675i
$320$	3.50952	−	3.65275i	0.196188	−	0.204195i
$321$	−1.14532	−	0.307401i	−0.0639257	−	0.0171574i
$322$	−0.375156	−	0.191151i	−0.0209066	−	0.0106525i
$323$	19.2821	−	3.05399i	1.07289	−	0.169928i
$324$	−11.5661	−	10.4492i	−0.642563	−	0.580511i
$325$	−11.0984	−	5.10674i	−0.615630	−	0.283271i
$326$			4.90532i			0.271680i
$327$	−0.321525	−	0.143313i	−0.0177804	−	0.00792521i
$328$	3.08593	−	6.05647i	0.170392	−	0.334413i
$329$	−0.589585	−	1.81456i	−0.0325049	−	0.100040i
$330$	−9.18361	−	0.783802i	−0.505541	−	0.0431469i
$331$	−1.89990	+	5.84731i	−0.104428	+	0.321397i	−0.989596	−	0.143875i	$-0.954044\pi$
$331$	−1.89990	+	5.84731i	−0.104428	+	0.321397i	0.885168	+	0.465272i	$0.154044\pi$
$332$	18.2958	+	18.2958i	1.00411	+	1.00411i
$333$	4.63392	+	3.75888i	0.253937	+	0.205985i
$334$	3.05181	+	4.20046i	0.166988	+	0.229839i
$335$	−9.70961	−	27.9676i	−0.530493	−	1.52803i
$336$	0.335810	+	0.875906i	0.0183199	+	0.0477846i
$337$	4.70943	−	29.7342i	0.256539	−	1.61972i	−0.437107	−	0.899409i	$-0.643997\pi$
$337$	4.70943	−	29.7342i	0.256539	−	1.61972i	0.693647	−	0.720316i	$-0.256003\pi$
$338$	−0.569398	+	3.59504i	−0.0309712	+	0.195544i
$339$	3.18547	+	8.30879i	0.173011	+	0.451272i
$340$	−9.58695	+	7.26257i	−0.519925	+	0.393868i
$341$	−8.96220	−	12.3354i	−0.485331	−	0.668000i
$342$	7.58312	+	6.15117i	0.410048	+	0.332617i
$343$	2.16900	+	2.16900i	0.117115	+	0.117115i
$344$	1.65625	−	5.09742i	0.0892991	−	0.274834i
$345$	−12.2631	+	7.40391i	−0.660222	+	0.398613i
$346$	3.19386	+	9.82969i	0.171703	+	0.528447i
$347$	5.06822	−	9.94693i	0.272076	−	0.533979i	−0.714026	−	0.700119i	$-0.753130\pi$
$347$	5.06822	−	9.94693i	0.272076	−	0.533979i	0.986102	+	0.166140i	$0.0531303\pi$
$348$	19.1798	+	8.54900i	1.02815	+	0.458275i
$349$		−	28.1680i		−	1.50780i	−0.656991	−	0.753898i	$-0.728171\pi$
$349$		−	28.1680i		−	1.50780i	0.656991	−	0.753898i	$-0.271829\pi$
$350$	−0.352704	−	0.446740i	−0.0188528	−	0.0238792i
$351$	2.00182	−	12.5374i	0.106849	−	0.669198i
$352$	23.3340	−	3.69575i	1.24371	−	0.196984i
$353$	1.26099	+	0.642505i	0.0671155	+	0.0341971i	0.487226	−	0.873276i	$-0.338009\pi$
$353$	1.26099	+	0.642505i	0.0671155	+	0.0341971i	−0.420111	+	0.907473i	$0.638009\pi$
$354$	−3.63145	−	0.974667i	−0.193009	−	0.0518030i
$355$	0.386043	−	0.0690822i	0.0204890	−	0.00366650i
$356$	−20.4913	−	6.65802i	−1.08604	−	0.352874i
$357$	−0.245409	−	1.15693i	−0.0129884	−	0.0612313i
$358$	0.691639	−	0.352408i	0.0365543	−	0.0186253i
$359$	−23.3881	+	16.9925i	−1.23438	+	0.896828i	−0.997210	−	0.0746410i	$-0.976219\pi$
$359$	−23.3881	+	16.9925i	−1.23438	+	0.896828i	−0.237167	+	0.971469i	$0.576219\pi$
$360$	−12.7281	−	2.45155i	−0.670832	−	0.129208i
$361$	16.5969	+	12.0583i	0.873519	+	0.634649i
$362$	7.64668	+	1.21111i	0.401900	+	0.0636548i
$363$	13.0287	+	11.7409i	0.683827	+	0.616237i
$364$	−0.546873	+	0.752707i	−0.0286640	+	0.0394526i
$365$	−0.158011	−	7.90132i	−0.00827070	−	0.413574i
$366$	0.176431	+	3.39360i	0.00922220	+	0.177386i
$367$	−1.75220	−	3.43889i	−0.0914642	−	0.179509i	0.840742	−	0.541436i	$-0.182119\pi$
$367$	−1.75220	−	3.43889i	−0.0914642	−	0.179509i	−0.932206	+	0.361927i	$0.882119\pi$
$368$	6.44252	−	6.44252i	0.335840	−	0.335840i
$369$	10.4965	−	1.09437i	0.546424	−	0.0569705i
$370$	2.28111	+	0.314678i	0.118589	+	0.0163593i
$371$	1.22076	−	0.396650i	0.0633789	−	0.0205930i
$372$	−4.97202	−	8.62009i	−0.257787	−	0.446931i
$373$	3.91421	+	24.7134i	0.202670	+	1.27961i	0.853783	+	0.520629i	$0.174303\pi$
$373$	3.91421	+	24.7134i	0.202670	+	1.27961i	−0.651113	+	0.758981i	$0.725697\pi$
$374$	−7.39092			−0.382175
$375$	−19.2437	+	2.16297i	−0.993742	+	0.111695i
$376$	−16.7681			−0.864748
$377$	2.67568	+	16.8936i	0.137804	+	0.870063i
$378$	0.348285	−	0.478113i	0.0179138	−	0.0245915i
$379$	0.795559	−	0.258493i	0.0408651	−	0.0132779i	−0.288513	−	0.957476i	$-0.593161\pi$
$379$	0.795559	−	0.258493i	0.0408651	−	0.0132779i	0.329378	+	0.944198i	$0.393161\pi$
$380$	−24.1156	−	3.32673i	−1.23710	−	0.170658i
$381$	7.61282	−	6.15948i	0.390017	−	0.315560i
$382$	1.06517	−	1.06517i	0.0544991	−	0.0544991i
$383$	1.39684	+	2.74145i	0.0713752	+	0.140082i	0.923937	−	0.382545i	$-0.124952\pi$
$383$	1.39684	+	2.74145i	0.0713752	+	0.140082i	−0.852562	+	0.522627i	$0.824952\pi$
$384$	19.8103	−	1.02993i	1.01094	−	0.0525582i
$385$	0.0451796	+	2.25920i	0.00230257	+	0.115139i
$386$	1.30997	−	1.80302i	0.0666759	−	0.0917715i
$387$	8.03965	−	2.14703i	0.408678	−	0.109140i
$388$	30.4076	+	4.81609i	1.54371	+	0.244500i
$389$	21.7362	+	15.7923i	1.10207	+	0.800701i	0.981397	−	0.191991i	$-0.0614944\pi$
$389$	21.7362	+	15.7923i	1.10207	+	0.800701i	0.120674	+	0.992692i	$0.461494\pi$
$390$	−1.84514	−	4.53908i	−0.0934320	−	0.229845i
$391$	−9.29301	+	6.75177i	−0.469968	+	0.341452i
$392$	11.9685	−	6.09824i	0.604499	−	0.308007i
$393$	−9.09195	+	1.92859i	−0.458628	+	0.0972844i
$394$	10.1429	+	3.29562i	0.510991	+	0.166031i
$395$	23.5609	−	4.21621i	1.18548	−	0.212141i
$396$	15.9647	+	17.7604i	0.802258	+	0.892495i
$397$	−17.0668	−	8.69598i	−0.856559	−	0.436439i	−0.0301746	−	0.999545i	$-0.509606\pi$
$397$	−17.0668	−	8.69598i	−0.856559	−	0.436439i	−0.826385	+	0.563106i	$0.809606\pi$
$398$	−0.980202	+	0.155249i	−0.0491331	+	0.00778192i
$399$	1.30460	−	2.00708i	0.0653117	−	0.100479i
$400$	11.5524	−	4.27137i	0.577620	−	0.213569i
$401$			3.09816i			0.154715i	0.997003	+	0.0773573i	$0.0246482\pi$
$401$			3.09816i			0.154715i	−0.997003	+	0.0773573i	$0.975352\pi$
$402$	4.83392	−	10.8450i	0.241094	−	0.540899i
$403$	3.67984	−	7.22210i	0.183306	−	0.359758i
$404$	−0.329653	−	1.01457i	−0.0164009	−	0.0504767i
$405$	−7.55510	−	18.6526i	−0.375416	−	0.926856i
$406$	−0.246251	+	0.757882i	−0.0122212	+	0.0376130i
$407$	−6.46412	−	6.46412i	−0.320415	−	0.320415i
$408$	−10.3366	−	1.09079i	−0.511740	−	0.0540019i
$409$	6.76439	+	9.31039i	0.334478	+	0.460369i	0.942818	−	0.333307i	$-0.108165\pi$
$409$	6.76439	+	9.31039i	0.334478	+	0.460369i	−0.608341	+	0.793676i	$0.708165\pi$
$410$	3.24643	−	2.45933i	0.160330	−	0.121458i
$411$	4.96473	−	1.90340i	0.244892	−	0.0938880i
$412$	2.16520	−	13.6706i	0.106672	−	0.673500i
$413$	−0.144201	+	0.910449i	−0.00709566	+	0.0448003i
$414$	−5.61863	−	1.19918i	−0.276140	−	0.0589364i
$415$	10.9562	+	31.5583i	0.537818	+	1.54913i
$416$	7.38201	+	10.1605i	0.361933	+	0.498158i
$417$	−1.08611	+	10.2923i	−0.0531870	+	0.504018i
$418$	−10.5781	−	10.5781i	−0.517393	−	0.517393i
$419$	−0.937784	+	2.88620i	−0.0458137	+	0.141000i	−0.971347	−	0.237667i	$-0.923617\pi$
$419$	−0.937784	+	2.88620i	−0.0458137	+	0.141000i	0.925533	+	0.378667i	$0.123617\pi$
$420$	−0.125412	+	1.46942i	−0.00611946	+	0.0717002i
$421$	−4.88657	−	15.0393i	−0.238157	−	0.732972i	−0.996687	−	0.0813338i	$-0.974082\pi$
$421$	−4.88657	−	15.0393i	−0.238157	−	0.732972i	0.758530	−	0.651638i	$-0.225918\pi$
$422$	0.602683	−	1.18283i	0.0293381	−	0.0575794i
$423$	−14.1607	−	21.8455i	−0.688519	−	1.06217i
$424$		−	11.2809i		−	0.547850i
$425$	−15.2278	+	3.04041i	−0.738655	+	0.147481i
$426$	0.131876	+	0.0857198i	0.00638943	+	0.00415314i
$427$	0.822845	−	0.130326i	0.0398202	−	0.00630691i
$428$	1.05652	+	0.538326i	0.0510690	+	0.0260209i
$429$	−5.04233	+	18.7869i	−0.243446	+	0.907039i
$430$	2.22496	−	2.31577i	0.107297	−	0.111676i
$431$	−14.3573	−	4.66498i	−0.691568	−	0.224704i	−0.0579151	−	0.998322i	$-0.518445\pi$
$431$	−14.3573	−	4.66498i	−0.691568	−	0.224704i	−0.633653	+	0.773617i	$0.718445\pi$
$432$	7.51065	+	10.3648i	0.361357	+	0.498676i
$433$	−6.02441	+	3.06959i	−0.289515	+	0.147515i	−0.592716	−	0.805411i	$-0.701944\pi$
$433$	−6.02441	+	3.06959i	−0.289515	+	0.147515i	0.303201	+	0.952926i	$0.401944\pi$
$434$	0.305516	−	0.221970i	0.0146652	−	0.0106549i
$435$	17.4711	+	20.7316i	0.837673	+	0.994003i
$436$	0.284766	+	0.206895i	0.0136378	+	0.00990845i
$437$	−22.9638	−	3.63711i	−1.09851	−	0.173987i
$438$	2.12184	−	2.35456i	0.101385	−	0.112505i
$439$	−16.2327	+	22.3425i	−0.774747	+	1.06635i	0.221096	+	0.975252i	$0.429037\pi$
$439$	−16.2327	+	22.3425i	−0.774747	+	1.06635i	−0.995842	+	0.0910951i	$0.970963\pi$
$440$	19.0061	+	5.75795i	0.906080	+	0.274500i
$441$	18.0522	+	10.4426i	0.859630	+	0.497265i
$442$	−1.78374	−	3.50079i	−0.0848438	−	0.166515i
$443$	8.42939	−	8.42939i	0.400492	−	0.400492i	−0.477914	−	0.878407i	$-0.658607\pi$
$443$	8.42939	−	8.42939i	0.400492	−	0.400492i	0.878407	+	0.477914i	$0.158607\pi$
$444$	−3.75278	−	4.63825i	−0.178099	−	0.220122i
$445$	−20.0595	−	19.2729i	−0.950909	−	0.913622i
$446$	−0.128418	+	0.0417257i	−0.00608079	+	0.00197577i
$447$	−20.7570	+	11.9725i	−0.981773	+	0.566281i
$448$	−0.0779147	−	0.491934i	−0.00368112	−	0.0232417i
$449$	−37.7012			−1.77923			−0.889614	−	0.456712i	$-0.849027\pi$
$449$	−37.7012			−1.77923			−0.889614	+	0.456712i	$0.849027\pi$
$450$	−6.22246	−	4.64763i	−0.293329	−	0.219091i
$451$	−16.1687			−0.761356
$452$	−1.39192	−	8.78824i	−0.0654705	−	0.413364i
$453$	−4.70903	+	2.71614i	−0.221250	+	0.127615i
$454$	−8.14088	+	2.64513i	−0.382071	+	0.124142i
$455$	−1.05919	+	0.566639i	−0.0496555	+	0.0265644i
$456$	−13.2330	−	16.3553i	−0.619691	−	0.765908i
$457$	−19.9252	+	19.9252i	−0.932062	+	0.932062i	−0.997835	−	0.0657729i	$-0.979049\pi$
$457$	−19.9252	+	19.9252i	−0.932062	+	0.932062i	0.0657729	+	0.997835i	$0.479049\pi$
$458$	2.66512	+	5.23058i	0.124533	+	0.244409i
$459$	−7.30827	−	14.3878i	−0.341121	−	0.671564i
$460$	13.5314	−	4.69776i	0.630906	−	0.219034i
$461$	7.12006	−	9.79992i	0.331614	−	0.456428i	−0.610355	−	0.792128i	$-0.708973\pi$
$461$	7.12006	−	9.79992i	0.331614	−	0.456428i	0.941969	+	0.335701i	$0.108973\pi$
$462$	−0.606688	+	0.673231i	−0.0282257	+	0.0313215i
$463$	−27.2062	−	4.30904i	−1.26438	−	0.200258i	−0.511999	−	0.858986i	$-0.671095\pi$
$463$	−27.2062	−	4.30904i	−1.26438	−	0.200258i	−0.752381	+	0.658728i	$0.771095\pi$
$464$	−13.9506	−	10.1357i	−0.647640	−	0.470538i
$465$	−0.923463	−	12.8148i	−0.0428246	−	0.594270i
$466$	−8.50355	+	6.17819i	−0.393919	+	0.286199i
$467$	3.88027	−	1.97710i	0.179557	−	0.0914891i	−0.361901	−	0.932216i	$-0.617872\pi$
$467$	3.88027	−	1.97710i	0.179557	−	0.0914891i	0.541459	+	0.840727i	$0.317872\pi$
$468$	−4.55945	+	11.8482i	−0.210761	+	0.547683i
$469$	−2.76845	−	0.899525i	−0.127835	−	0.0415362i
$470$	−9.04137	−	4.38135i	−0.417047	−	0.202097i
$471$	7.03481	−	26.2105i	0.324147	−	1.20772i
$472$	7.21832	+	3.67792i	0.332250	+	0.169290i
$473$	−12.5922	+	1.99441i	−0.578990	+	0.0917029i
$474$	8.04866	+	5.23164i	0.369687	+	0.240297i
$475$	−26.1460	−	17.4430i	−1.19966	−	0.800338i
$476$			1.18258i			0.0542034i
$477$	14.6968	−	9.52680i	0.672921	−	0.436202i
$478$	2.01631	−	3.95723i	0.0922239	−	0.181000i
$479$	5.68805	+	17.5060i	0.259894	+	0.799871i	0.992826	+	0.119569i	$0.0381513\pi$
$479$	5.68805	+	17.5060i	0.259894	+	0.799871i	−0.732932	+	0.680302i	$0.761849\pi$
$480$	18.3411	+	7.73938i	0.837153	+	0.353253i
$481$	1.50173	−	4.62186i	0.0684732	−	0.210739i
$482$	−1.21216	−	1.21216i	−0.0552124	−	0.0552124i
$483$	−0.147812	+	1.40071i	−0.00672567	+	0.0637347i
$484$	−10.3080	−	14.1877i	−0.468544	−	0.644896i
$485$	32.6179	+	22.7160i	1.48110	+	1.03148i
$486$	2.90819	−	7.52910i	0.131918	−	0.341527i
$487$	−5.46472	+	34.5029i	−0.247630	+	1.56348i	0.479852	+	0.877349i	$0.340690\pi$
$487$	−5.46472	+	34.5029i	−0.247630	+	1.56348i	−0.727482	+	0.686127i	$0.759310\pi$
$488$	1.14538	−	7.23165i	0.0518490	−	0.327361i
$489$	15.3219	−	5.87418i	0.692878	−	0.265639i
$490$	8.04682	−	0.160921i	0.363518	−	0.00726967i
$491$	16.5130	+	22.7282i	0.745223	+	1.02571i	0.998301	+	0.0582652i	$0.0185569\pi$
$491$	16.5130	+	22.7282i	0.745223	+	1.02571i	−0.253079	+	0.967446i	$0.581443\pi$
$492$	−10.4943	−	1.10742i	−0.473118	−	0.0499263i
$493$	15.3726	+	15.3726i	0.692349	+	0.692349i
$494$	2.45749	−	7.56339i	0.110568	−	0.340293i
$495$	8.54926	+	29.6238i	0.384261	+	1.33149i
$496$	2.52522	+	7.77182i	0.113386	+	0.348965i
$497$	0.0175062	−	0.0343578i	0.000785260	−	0.00154116i
$498$	−5.45453	+	12.2373i	−0.244424	+	0.548368i
$499$		−	2.32959i		−	0.104287i	−0.998640	−	0.0521434i	$-0.983395\pi$
$499$		−	2.32959i		−	0.104287i	0.998640	−	0.0521434i	$-0.0166053\pi$
$500$	19.2722	+	1.87710i	0.861878	+	0.0839466i
$501$	9.46564	−	14.5625i	0.422893	−	0.650604i
$502$	−15.6509	+	2.47886i	−0.698533	+	0.110637i
$503$	16.6021	+	8.45919i	0.740251	+	0.377177i	0.783093	−	0.621905i	$-0.213641\pi$
$503$	16.6021	+	8.45919i	0.740251	+	0.377177i	−0.0428417	+	0.999082i	$0.513641\pi$
$504$	−0.947849	+	0.852016i	−0.0422205	+	0.0379518i
$505$	0.188217	−	1.36440i	0.00837557	−	0.0607148i
$506$	8.37133	+	2.72001i	0.372151	+	0.120919i
$507$	11.9110	−	2.52657i	0.528988	−	0.112209i
$508$	−8.72454	+	4.44538i	−0.387089	+	0.197232i
$509$	20.1453	−	14.6364i	0.892924	−	0.648747i	−0.0437146	−	0.999044i	$-0.513919\pi$
$509$	20.1453	−	14.6364i	0.892924	−	0.648747i	0.936639	+	0.350297i	$0.113919\pi$
$510$	−5.28851	−	3.28902i	−0.234179	−	0.145640i
$511$	−0.628649	−	0.456741i	−0.0278098	−	0.0202050i
$512$	−21.9083	−	3.46993i	−0.968219	−	0.153351i
$513$	10.1324	−	31.0521i	0.447358	−	1.37098i
$514$	0.245049	−	0.337281i	0.0108087	−	0.0148768i
$515$	10.2126	−	14.6643i	0.450020	−	0.646185i
$516$	−8.30952	+	0.432007i	−0.365806	+	0.0190180i
$517$	18.1079	+	35.5387i	0.796384	+	1.56299i
$518$	0.160099	−	0.160099i	0.00703436	−	0.00703436i
$519$	26.8786	−	21.7473i	1.17984	−	0.954599i
$520$	1.85965	+	10.3921i	0.0815512	+	0.455722i
$521$	−35.9678	+	11.6866i	−1.57578	+	0.512001i	−0.960964	−	0.276672i	$-0.910768\pi$
$521$	−35.9678	+	11.6866i	−1.57578	+	0.512001i	−0.614813	+	0.788673i	$0.710768\pi$
$522$	−0.578134	+	10.8581i	−0.0253042	+	0.475245i
$523$	−1.50336	−	9.49182i	−0.0657372	−	0.415048i	−0.998509	−	0.0545817i	$-0.982617\pi$
$523$	−1.50336	−	9.49182i	−0.0657372	−	0.415048i	0.932772	−	0.360467i	$-0.117383\pi$
$524$	9.29351			0.405989
$525$	−0.973034	+	1.63665i	−0.0424667	+	0.0714294i
$526$	8.76860			0.382329
$527$	−1.61167	−	10.1757i	−0.0702056	−	0.443260i
$528$	−9.79827	−	16.9875i	−0.426415	−	0.739285i
$529$	−8.86377	+	2.88001i	−0.385381	+	0.125218i
$530$	2.94760	−	6.08268i	0.128036	−	0.264215i
$531$	1.30431	+	12.5101i	0.0566021	+	0.542891i
$532$	−1.69255	+	1.69255i	−0.0733812	+	0.0733812i
$533$	−3.90220	−	7.65849i	−0.169023	−	0.331726i
$534$	−0.579246	−	11.1416i	−0.0250664	−	0.482145i
$535$	0.924445	+	1.22031i	0.0399673	+	0.0527588i
$536$	−15.0373	+	20.6970i	−0.649511	+	0.893976i
$537$	−1.92900	−	1.73834i	−0.0832425	−	0.0750148i
$538$	0.136454	+	0.0216122i	0.00588295	+	0.000931767i
$539$	−25.8495	−	18.7808i	−1.11342	−	0.808946i
$540$	3.51989	+	19.8128i	0.151472	+	0.852606i
$541$	13.5693	−	9.85869i	0.583391	−	0.423858i	−0.256554	−	0.966530i	$-0.582587\pi$
$541$	13.5693	−	9.85869i	0.583391	−	0.423858i	0.839945	+	0.542672i	$0.182587\pi$
$542$	−12.1147	+	6.17273i	−0.520369	+	0.265141i
$543$	−5.37405	−	25.3349i	−0.230622	−	1.08722i
$544$	15.1818	+	4.93288i	0.650916	+	0.211495i
$545$	0.214372	+	0.400715i	0.00918270	+	0.0171647i
$546$	−0.465302	−	0.124885i	−0.0199131	−	0.00534460i
$547$	2.01355	+	1.02595i	0.0860931	+	0.0438666i	0.496507	−	0.868033i	$-0.334616\pi$
$547$	2.01355	+	1.02595i	0.0860931	+	0.0438666i	−0.410414	+	0.911899i	$0.634616\pi$
$548$	−5.25121	+	0.831710i	−0.224321	+	0.0355289i
$549$	10.3887	−	4.61496i	0.443379	−	0.196962i
$550$	8.74359	+	8.07081i	0.372828	+	0.344140i
$551$			44.0037i			1.87462i
$552$	11.3064	+	5.03958i	0.481231	+	0.214499i
$553$	1.06843	−	2.09692i	0.0454345	−	0.0891702i
$554$	−0.0594017	−	0.182820i	−0.00252374	−	0.00776726i
$555$	−1.74876	−	7.50194i	−0.0742306	−	0.318440i
$556$	3.19791	−	9.84216i	0.135622	−	0.417401i
$557$	−3.31621	−	3.31621i	−0.140512	−	0.140512i	0.633352	−	0.773864i	$-0.281679\pi$
$557$	−3.31621	−	3.31621i	−0.140512	−	0.140512i	−0.773864	+	0.633352i	$0.781679\pi$
$558$	3.24614	−	4.00182i	0.137420	−	0.169410i
$559$	−3.98370	−	5.48309i	−0.168492	−	0.231910i
$560$	0.351130	−	1.15903i	0.0148380	−	0.0489778i
$561$	8.85072	+	23.0857i	0.373678	+	0.974679i
$562$	1.60290	−	10.1203i	0.0676143	−	0.426900i
$563$	−1.15712	+	7.30580i	−0.0487670	+	0.307903i	−1.00000		0.000571082i	$-0.999818\pi$
$563$	−1.15712	+	7.30580i	−0.0487670	+	0.307903i	0.951233	+	0.308474i	$0.0998182\pi$
$564$	9.31876	+	24.3065i	0.392391	+	1.02349i
$565$	3.33080	−	10.9944i	0.140128	−	0.462540i
$566$	−9.48903	−	13.0605i	−0.398854	−	0.548975i
$567$	−1.91047	−	0.515329i	−0.0802323	−	0.0216418i
$568$	−0.239635	−	0.239635i	−0.0100548	−	0.0100548i
$569$	10.3197	−	31.7608i	0.432625	−	1.33148i	−0.462876	−	0.886423i	$-0.653183\pi$
$569$	10.3197	−	31.7608i	0.432625	−	1.33148i	0.895501	−	0.445059i	$-0.146817\pi$
$570$	−2.86173	−	12.2765i	−0.119865	−	0.514204i
$571$	3.58833	+	11.0437i	0.150167	+	0.462166i	0.997639	−	0.0686736i	$-0.0218767\pi$
$571$	3.58833	+	11.0437i	0.150167	+	0.462166i	−0.847472	+	0.530839i	$0.821877\pi$
$572$	8.83023	−	17.3303i	0.369210	−	0.724616i
$573$	−4.60266	−	2.05154i	−0.192279	−	0.0857042i
$574$		−	0.400457i		−	0.0167148i
$575$	18.3667	+	2.16041i	0.765943	+	0.0900954i
$576$	−2.75904	−	6.21084i	−0.114960	−	0.258785i
$577$	26.4919	−	4.19590i	1.10287	−	0.174678i	0.421652	−	0.906758i	$-0.361450\pi$
$577$	26.4919	−	4.19590i	1.10287	−	0.174678i	0.681219	+	0.732080i	$0.261450\pi$
$578$	3.39306	+	1.72885i	0.141133	+	0.0719107i
$579$	−7.20049	−	1.93259i	−0.299242	−	0.0803155i
$580$	−12.7879	−	23.9037i	−0.530989	−	0.992549i
$581$	3.12389	+	1.01501i	0.129601	+	0.0421098i
$582$	3.30795	+	15.5947i	0.137119	+	0.646420i
$583$	−23.9091	+	12.1823i	−0.990213	+	0.504539i
$584$	−5.52495	+	4.01411i	−0.228624	+	0.166105i
$585$	−11.9683	+	11.1989i	−0.494830	+	0.463018i
$586$	11.0250	+	8.01015i	0.455439	+	0.330896i
$587$	−26.6044	−	4.21372i	−1.09808	−	0.173919i	−0.419002	−	0.907985i	$-0.637620\pi$
$587$	−26.6044	−	4.21372i	−1.09808	−	0.173919i	−0.679077	+	0.734067i	$0.737620\pi$
$588$	−15.4912	−	13.9601i	−0.638847	−	0.575703i
$589$	12.2571	−	16.8705i	0.505046	−	0.695136i
$590$	2.93112	+	3.86922i	0.120672	+	0.159293i
$591$	−1.85228	−	35.6281i	−0.0761926	−	1.46554i
$592$	2.22429	+	4.36541i	0.0914178	+	0.179417i
$593$	13.4502	−	13.4502i	0.552334	−	0.552334i	−0.374780	−	0.927114i	$-0.622282\pi$
$593$	13.4502	−	13.4502i	0.552334	−	0.552334i	0.927114	+	0.374780i	$0.122282\pi$
$594$	−5.62779	+	11.0111i	−0.230911	+	0.451789i
$595$	−0.665825	+	1.37400i	−0.0272962	+	0.0563284i
$596$	22.7878	−	7.40419i	0.933423	−	0.303287i
$597$	1.65873	+	2.87577i	0.0678872	+	0.117697i
$598$	0.731993	+	4.62162i	0.0299334	+	0.188992i
$599$	25.9797			1.06150			0.530750	−	0.847528i	$-0.321910\pi$
$599$	25.9797			1.06150			0.530750	+	0.847528i	$0.321910\pi$
$600$	11.0373	+	12.5779i	0.450596	+	0.513492i
$601$	19.7493			0.805592			0.402796	−	0.915290i	$-0.368038\pi$
$601$	19.7493			0.805592			0.402796	+	0.915290i	$0.368038\pi$
$602$	−0.0493963	−	0.311876i	−0.00201324	−	0.0127111i
$603$	−39.6632	−	2.11185i	−1.61521	−	0.0860014i
$604$	5.16973	−	1.67975i	0.210353	−	0.0683480i
$605$	−3.98840	−	22.2879i	−0.162152	−	0.906132i
$606$	0.429434	−	0.347452i	0.0174445	−	0.0141143i
$607$	11.2538	−	11.2538i	0.456778	−	0.456778i	−0.440819	−	0.897596i	$-0.645312\pi$
$607$	11.2538	−	11.2538i	0.456778	−	0.456778i	0.897596	+	0.440819i	$0.145312\pi$
$608$	14.6687	+	28.7888i	0.594892	+	1.16754i
$609$	2.66215	−	0.138403i	0.107876	−	0.00560839i
$610$	2.50716	−	3.60003i	0.101512	−	0.145761i
$611$	−12.4631	+	17.1540i	−0.504203	+	0.693976i
$612$	4.16336	+	15.5899i	0.168294	+	0.630184i
$613$	10.3466	+	1.63875i	0.417897	+	0.0661884i	0.361842	−	0.932239i	$-0.382148\pi$
$613$	10.3466	+	1.63875i	0.417897	+	0.0661884i	0.0560547	+	0.998428i	$0.482148\pi$
$614$	5.24422	+	3.81015i	0.211640	+	0.153765i
$615$	−11.5694	−	7.19523i	−0.466524	−	0.290140i
$616$	1.57973	−	1.14774i	0.0636490	−	0.0462437i
$617$	25.6535	−	13.0711i	1.03277	−	0.526223i	0.146412	−	0.989224i	$-0.453227\pi$
$617$	25.6535	−	13.0711i	1.03277	−	0.526223i	0.886358	+	0.463001i	$0.153227\pi$
$618$	7.01102	−	1.48718i	0.282024	−	0.0598232i
$619$	−13.6261	−	4.42739i	−0.547679	−	0.177952i	0.0220908	−	0.999756i	$-0.492968\pi$
$619$	−13.6261	−	4.42739i	−0.547679	−	0.177952i	−0.569770	+	0.821804i	$0.692968\pi$
$620$	−1.75561	+	12.7265i	−0.0705069	+	0.511107i
$621$	2.98272	+	18.9859i	0.119692	+	0.761879i
$622$	−7.71985	−	3.93346i	−0.309538	−	0.157717i
$623$	−2.70151	+	0.427876i	−0.108234	+	0.0171425i
$624$	5.68156	−	8.74084i	0.227444	−	0.349914i
$625$	21.3348	+	13.0317i	0.853393	+	0.521269i
$626$			3.75137i			0.149935i
$627$	−20.3736	+	45.7085i	−0.813642	+	1.82542i
$628$	−12.3195	+	24.1784i	−0.491601	+	0.964822i
$629$	−1.90878	−	5.87461i	−0.0761079	−	0.234236i
$630$	−0.733705	+	0.211743i	−0.0292315	+	0.00843604i
$631$	−6.27729	+	19.3195i	−0.249895	+	0.769098i	0.744898	+	0.667179i	$0.232498\pi$
$631$	−6.27729	+	19.3195i	−0.249895	+	0.769098i	−0.994793	+	0.101919i	$0.967502\pi$
$632$	−14.6253	−	14.6253i	−0.581765	−	0.581765i
$633$	−4.41632	−	0.466037i	−0.175533	−	0.0185233i
$634$	−3.32842	−	4.58117i	−0.132188	−	0.181942i
$635$	−12.6396	+	0.252768i	−0.501588	+	0.0100308i
$636$	−16.3525	+	6.26930i	−0.648418	+	0.248594i
$637$	2.65714	−	16.7765i	0.105280	−	0.664709i
$638$	2.60606	−	16.4540i	0.103175	−	0.651421i
$639$	0.109824	−	0.514569i	0.00434457	−	0.0203560i
$640$	−21.0154	−	14.6357i	−0.830706	−	0.578525i
$641$	12.7247	+	17.5141i	0.502596	+	0.691764i	0.982649	−	0.185476i	$-0.0593826\pi$
$641$	12.7247	+	17.5141i	0.502596	+	0.691764i	−0.480053	+	0.877240i	$0.659383\pi$
$642$	−0.0644355	+	0.610612i	−0.00254307	+	0.0240989i
$643$	11.9096	+	11.9096i	0.469671	+	0.469671i	0.901808	−	0.432137i	$-0.142240\pi$
$643$	11.9096	+	11.9096i	0.469671	+	0.469671i	−0.432137	+	0.901808i	$0.642240\pi$
$644$	0.435213	−	1.33945i	0.0171498	−	0.0527817i
$645$	−9.89777	−	4.17655i	−0.389724	−	0.164452i
$646$	−3.12359	−	9.61343i	−0.122896	−	0.378235i
$647$	−5.58012	+	10.9516i	−0.219377	+	0.430552i	−0.974298	−	0.225264i	$-0.927675\pi$
$647$	−5.58012	+	10.9516i	−0.219377	+	0.430552i	0.754921	+	0.655816i	$0.227675\pi$
$648$	−9.49586	+	14.5691i	−0.373033	+	0.572326i
$649$		−	19.2705i		−	0.756433i
$650$	−1.71263	+	6.08932i	−0.0671748	+	0.238843i
$651$	−1.05919	−	0.688474i	−0.0415129	−	0.0269834i
$652$	−16.2060	+	2.56678i	−0.634676	+	0.100523i
$653$	−3.44991	−	1.75782i	−0.135005	−	0.0687887i	0.385183	−	0.922840i	$-0.374138\pi$
$653$	−3.44991	−	1.75782i	−0.135005	−	0.0687887i	−0.520189	+	0.854051i	$0.674138\pi$
$654$	−0.0472470	+	0.176034i	−0.00184750	+	0.00688349i
$655$	10.7978	+	5.23250i	0.421905	+	0.204451i
$656$	8.24143	+	2.67780i	0.321774	+	0.104551i
$657$	−9.89544	−	3.80798i	−0.386058	−	0.148564i
$658$	−0.880202	+	0.448485i	−0.0343138	+	0.0174838i
$659$	−22.9326	+	16.6615i	−0.893326	+	0.649039i	−0.936743	−	0.350018i	$-0.886176\pi$
$659$	−22.9326	+	16.6615i	−0.893326	+	0.649039i	0.0434170	+	0.999057i	$0.486176\pi$
$660$	−2.21596	−	30.7506i	−0.0862562	−	1.19697i
$661$	−14.5824	−	10.5948i	−0.567191	−	0.412088i	0.266893	−	0.963726i	$-0.414003\pi$
$661$	−14.5824	−	10.5948i	−0.567191	−	0.412088i	−0.834084	+	0.551638i	$0.814003\pi$
$662$	3.14418	+	0.497988i	0.122202	+	0.0193549i
$663$	−8.79873	+	9.76378i	−0.341714	+	0.379194i
$664$	16.9679	−	23.3543i	0.658481	−	0.906321i
$665$	−2.91946	+	1.01356i	−0.113212	+	0.0393042i
$666$	1.54694	−	2.67422i	0.0599428	−	0.103624i
$667$	−11.7544	−	23.0693i	−0.455131	−	0.893245i
$668$	−12.2804	+	12.2804i	−0.475143	+	0.475143i
$669$	0.284114	+	0.351151i	0.0109845	+	0.0135763i
$670$	−13.5161	+	7.23075i	−0.522171	+	0.279348i
$671$	−16.5639	+	5.38192i	−0.639440	+	0.207767i
$672$	1.69554	−	0.977978i	0.0654069	−	0.0377263i
$673$	−6.19277	−	39.0996i	−0.238714	−	1.50718i	−0.757816	−	0.652468i	$-0.773734\pi$
$673$	−6.19277	−	39.0996i	−0.238714	−	1.50718i	0.519102	−	0.854712i	$-0.326266\pi$
$674$	−15.5874			−0.600404
$675$	−7.06550	+	25.0016i	−0.271951	+	0.962311i
$676$	−12.1751			−0.468273
$677$	−3.06139	−	19.3289i	−0.117659	−	0.742869i	−0.974015	−	0.226483i	$-0.927277\pi$
$677$	−3.06139	−	19.3289i	−0.117659	−	0.742869i	0.856356	−	0.516386i	$-0.172723\pi$
$678$	3.99107	−	2.30202i	0.153276	−	0.0884087i
$679$	3.71699	−	1.20772i	0.142645	−	0.0463482i
$680$	9.67623	+	9.29680i	0.371066	+	0.356516i
$681$	18.0109	+	22.2606i	0.690181	+	0.853030i
$682$	−5.58237	+	5.58237i	−0.213760	+	0.213760i
$683$	5.24668	+	10.2972i	0.200759	+	0.394011i	0.969334	−	0.245749i	$-0.0790338\pi$
$683$	5.24668	+	10.2972i	0.200759	+	0.394011i	−0.768575	+	0.639760i	$0.779034\pi$
$684$	−16.3540	+	28.2715i	−0.625312	+	1.08099i
$685$	−6.56948	−	1.99024i	−0.251007	−	0.0760433i
$686$	0.933536	−	1.28490i	0.0356426	−	0.0490578i
$687$	13.1463	−	14.5882i	0.501564	−	0.556576i
$688$	6.74872	+	1.06889i	0.257293	+	0.0407511i
$689$	−11.5405	−	8.38469i	−0.439659	−	0.319431i
$690$	4.77961	+	5.67159i	0.181957	+	0.215914i
$691$	−3.42761	+	2.49030i	−0.130392	+	0.0947356i	−0.651070	−	0.759018i	$-0.725679\pi$
$691$	−3.42761	+	2.49030i	−0.130392	+	0.0947356i	0.520677	+	0.853754i	$0.325679\pi$
$692$	−30.8037	+	15.6953i	−1.17098	+	0.596645i
$693$	2.82937	+	1.08880i	0.107479	+	0.0413602i
$694$	−5.49733	−	1.78619i	−0.208676	−	0.0678029i
$695$	9.25695	−	9.63475i	0.351136	−	0.365467i
$696$	6.07310	−	22.6273i	0.230200	−	0.857687i
$697$	−9.73431	−	4.95988i	−0.368713	−	0.187869i
$698$	−14.4050	+	2.28152i	−0.545237	+	0.0863570i
$699$	29.4808	+	19.1626i	1.11507	+	0.724794i
$700$	1.29136	−	1.39901i	0.0488090	−	0.0528777i
$701$		−	25.9124i		−	0.978699i	−0.872088	−	0.489349i	$-0.837234\pi$
$701$		−	25.9124i		−	0.978699i	0.872088	−	0.489349i	$-0.162766\pi$
$702$	−6.57373	−	0.00822900i	−0.248109	−	0.000310584i
$703$	5.67604	−	11.1398i	0.214076	−	0.420147i
$704$	3.21756	+	9.90263i	0.121266	+	0.373219i
$705$	−2.85810	+	33.4876i	−0.107642	+	1.26122i
$706$	0.226438	−	0.696904i	0.00852210	−	0.0262283i
$707$	−0.0957597	−	0.0957597i	−0.00360142	−	0.00360142i
$708$	1.31986	−	12.5074i	0.0496035	−	0.470058i
$709$	22.8098	+	31.3950i	0.856641	+	1.17907i	0.982360	+	0.186999i	$0.0598762\pi$
$709$	22.8098	+	31.3950i	0.856641	+	1.17907i	−0.125719	+	0.992066i	$0.540124\pi$
$710$	−0.0665967	−	0.191825i	−0.00249933	−	0.00719908i
$711$	6.70276	−	31.4051i	0.251373	−	1.17778i
$712$	−3.76043	+	23.7424i	−0.140928	+	0.889786i
$713$	−1.91940	+	12.1186i	−0.0718822	+	0.453847i
$714$	−0.571772	+	0.219209i	−0.0213980	+	0.00820370i
$715$	20.0170	−	15.1638i	0.748593	−	0.567094i
$716$	1.52618	+	2.10061i	0.0570361	+	0.0785034i
$717$	−14.7751	−	1.55916i	−0.551785	−	0.0582277i
$718$	10.5842	+	10.5842i	0.395001	+	0.395001i
$719$	−10.3859	+	31.9646i	−0.387329	+	1.19208i	0.547447	+	0.836840i	$0.315600\pi$
$719$	−10.3859	+	31.9646i	−0.387329	+	1.19208i	−0.934776	+	0.355237i	$0.884400\pi$
$720$	0.548501	−	16.5156i	0.0204414	−	0.615499i
$721$	−0.542965	−	1.67107i	−0.0202211	−	0.0622340i
$722$	4.82228	−	9.46426i	0.179467	−	0.352223i
$723$	−2.33463	+	5.23779i	−0.0868259	+	0.194795i
$724$			25.8965i			0.962437i
$725$	−1.39934	−	34.9729i	−0.0519702	−	1.29886i
$726$	4.94896	−	7.61378i	0.183673	−	0.282574i
$727$	4.52625	−	0.716888i	0.167869	−	0.0265879i	−0.0719338	−	0.997409i	$-0.522917\pi$
$727$	4.52625	−	0.716888i	0.167869	−	0.0265879i	0.239803	+	0.970821i	$0.422917\pi$
$728$	0.924894	+	0.471257i	0.0342788	+	0.0174659i
$729$	−26.9999	−	0.0675972i	−0.999997	−	0.00250360i
$730$	−4.02791	+	0.720791i	−0.149079	+	0.0266777i
$731$	−8.19287	−	2.66202i	−0.303024	−	0.0984585i
$732$	−11.1193	+	2.35864i	−0.410982	+	0.0871777i
$733$	25.5351	−	13.0108i	0.943161	−	0.480564i	0.0863897	−	0.996261i	$-0.472467\pi$
$733$	25.5351	−	13.0108i	0.943161	−	0.480564i	0.856771	+	0.515697i	$0.172467\pi$
$734$	−1.61671	+	1.17461i	−0.0596739	+	0.0433556i
$735$	−10.1388	−	24.9417i	−0.373975	−	0.919989i
$736$	−15.3803	−	11.1745i	−0.566926	−	0.411896i
$737$	60.1046	+	9.51964i	2.21398	+	0.350660i
$738$	−1.40984	−	5.27921i	−0.0518969	−	0.194330i
$739$	−22.4645	+	30.9198i	−0.826372	+	1.13740i	0.162216	+	0.986755i	$0.448136\pi$
$739$	−22.4645	+	30.9198i	−0.826372	+	1.13740i	−0.988588	+	0.150648i	$0.951864\pi$
$740$	0.154004	+	7.70092i	0.00566129	+	0.283091i
$741$	−26.5673	+	1.38122i	−0.975974	+	0.0507403i
$742$	−0.301724	−	0.592166i	−0.0110766	−	0.0217391i
$743$	23.5600	−	23.5600i	0.864333	−	0.864333i	−0.127505	−	0.991838i	$-0.540697\pi$
$743$	23.5600	−	23.5600i	0.864333	−	0.864333i	0.991838	+	0.127505i	$0.0406969\pi$
$744$	−8.63115	+	6.98340i	−0.316433	+	0.256024i
$745$	30.6451	+	4.22747i	1.12275	+	0.154882i
$746$	12.3213	−	4.00343i	0.451114	−	0.146576i
$747$	44.7555	+	2.38299i	1.63752	+	0.0871890i
$748$	−3.86741	−	24.4178i	−0.141406	−	0.892805i
$749$	0.150529			0.00550022
$750$	2.66482	+	9.66598i	0.0973056	+	0.352952i
$751$	30.4621			1.11158			0.555790	−	0.831323i	$-0.312416\pi$
$751$	30.4621			1.11158			0.555790	+	0.831323i	$0.312416\pi$
$752$	−3.34406	−	21.1135i	−0.121945	−	0.769932i
$753$	26.4849	+	45.9174i	0.965163	+	1.67332i
$754$	8.42258	−	2.73666i	0.306732	−	0.0996633i
$755$	6.95228	+	0.959062i	0.253019	+	0.0349039i
$756$	1.76182	+	0.900470i	0.0640767	+	0.0327498i
$757$	32.8785	−	32.8785i	1.19499	−	1.19499i	0.219339	−	0.975649i	$-0.429610\pi$
$757$	32.8785	−	32.8785i	1.19499	−	1.19499i	0.975649	−	0.219339i	$-0.0703901\pi$
$758$	−0.196630	−	0.385908i	−0.00714193	−	0.0140168i
$759$	−1.52876	−	29.4053i	−0.0554905	−	1.06734i
$760$	0.543045	+	27.1548i	0.0196983	+	0.985010i
$761$	4.75745	−	6.54807i	0.172457	−	0.237367i	−0.714035	−	0.700110i	$-0.753134\pi$
$761$	4.75745	−	6.54807i	0.172457	−	0.237367i	0.886493	+	0.462742i	$0.153134\pi$
$762$	−3.76655	−	3.39426i	−0.136448	−	0.122961i
$763$	0.0441340	+	0.00699014i	0.00159776	+	0.000253060i
$764$	4.07645	+	2.96172i	0.147481	+	0.107151i
$765$	−3.94028	+	20.4574i	−0.142461	+	0.739640i
$766$	1.28883	−	0.936389i	0.0465673	−	0.0338331i
$767$	9.12767	−	4.65078i	0.329581	−	0.167930i
$768$	−0.502907	−	2.37086i	−0.0181471	−	0.0855509i
$769$	−33.4604	−	10.8720i	−1.20661	−	0.392053i	−0.364424	−	0.931233i	$-0.618734\pi$
$769$	−33.4604	−	10.8720i	−1.20661	−	0.392053i	−0.842190	+	0.539180i	$0.818734\pi$
$770$	1.15168	−	0.206093i	0.0415038	−	0.00742708i
$771$	−1.34696	−	0.361518i	−0.0485094	−	0.0130198i
$772$	6.64222	+	3.38438i	0.239059	+	0.121807i
$773$	16.4924	−	2.61215i	0.593192	−	0.0939524i	0.147382	−	0.989080i	$-0.452915\pi$
$773$	16.4924	−	2.61215i	0.593192	−	0.0939524i	0.445811	+	0.895127i	$0.352915\pi$
$774$	−1.74917	−	3.93754i	−0.0628726	−	0.141532i
$775$	−9.20513	+	13.7980i	−0.330658	+	0.495638i
$776$		−	34.3483i		−	1.23303i
$777$	−0.691795	−	0.308353i	−0.0248180	−	0.0110621i
$778$	6.31554	−	12.3950i	0.226423	−	0.444381i
$779$	−6.83333	−	21.0308i	−0.244829	−	0.753507i
$780$	14.0305	−	8.47103i	0.502374	−	0.303311i
$781$	−0.249106	+	0.766669i	−0.00891371	+	0.0274336i
$782$	4.20554	+	4.20554i	0.150390	+	0.150390i
$783$	34.6077	−	11.1969i	1.23678	−	0.400143i
$784$	10.0655	+	13.8539i	0.359481	+	0.494783i
$785$	−27.9267	+	21.1558i	−0.996746	+	0.755082i
$786$	1.72269	+	4.49338i	0.0614465	+	0.160273i
$787$	−2.65455	+	16.7602i	−0.0946247	+	0.597437i	0.894120	+	0.447827i	$0.147802\pi$
$787$	−2.65455	+	16.7602i	−0.0946247	+	0.597437i	−0.988745	+	0.149610i	$0.952198\pi$
$788$	−5.58054	+	35.2341i	−0.198799	+	1.25516i
$789$	−10.5005	−	27.3889i	−0.373828	−	0.975071i
$790$	−4.06452	−	11.7075i	−0.144609	−	0.416533i
$791$	−0.663932	−	0.913825i	−0.0236067	−	0.0324919i
$792$	16.7848	−	20.6921i	0.596421	−	0.735263i
$793$	−6.54676	−	6.54676i	−0.232482	−	0.232482i
$794$	−3.06473	+	9.43226i	−0.108763	+	0.334738i
$795$	−22.5292	−	1.92282i	−0.799028	−	0.0681953i
$796$	−1.02581	−	3.15712i	−0.0363589	−	0.111901i
$797$	−11.7282	+	23.0179i	−0.415435	+	0.815337i	0.584557	+	0.811353i	$0.301268\pi$
$797$	−11.7282	+	23.0179i	−0.415435	+	0.815337i	−0.999992	+	0.00398464i	$0.998732\pi$
$798$	−1.13208	−	0.504600i	−0.0400752	−	0.0178627i
$799$			26.9507i			0.953446i
$800$	−12.5737	−	22.4141i	−0.444549	−	0.792458i
$801$	−34.1074	+	15.1515i	−1.20513	+	0.535353i
$802$	1.58439	−	0.250942i	0.0559466	−	0.00886107i
$803$	14.4740	+	7.37488i	0.510777	+	0.260254i
$804$	38.3587	+	10.2953i	1.35281	+	0.363088i
$805$	1.25981	−	1.31122i	0.0444023	−	0.0462145i
$806$	−3.99141	−	1.29689i	−0.140591	−	0.0456809i
$807$	−0.0958992	−	0.452098i	−0.00337581	−	0.0159146i
$808$	−1.06047	+	0.540337i	−0.0373072	+	0.0190090i
$809$	6.30289	−	4.57932i	0.221598	−	0.161000i	−0.471448	−	0.881894i	$-0.656268\pi$
$809$	6.30289	−	4.57932i	0.221598	−	0.161000i	0.693046	+	0.720894i	$0.256268\pi$
$810$	−8.92694	+	5.37446i	−0.313661	+	0.188839i
$811$	−13.5989	−	9.88021i	−0.477524	−	0.346941i	0.322843	−	0.946453i	$-0.395362\pi$
$811$	−13.5989	−	9.88021i	−0.477524	−	0.346941i	−0.800366	+	0.599511i	$0.795362\pi$
$812$	−2.63272	−	0.416981i	−0.0923902	−	0.0146332i
$813$	33.7881	+	30.4485i	1.18500	+	1.06788i
$814$	−2.78215	+	3.82930i	−0.0975143	+	0.134217i
$815$	−20.2743	−	6.14218i	−0.710179	−	0.215151i
$816$	−0.687971	−	13.2329i	−0.0240838	−	0.463245i
$817$	−7.91593	−	15.5359i	−0.276943	−	0.543532i
$818$	4.21340	−	4.21340i	0.147318	−	0.147318i
$819$	0.167123	+	1.60293i	0.00583974	+	0.0560110i
$820$	9.82378	+	9.43857i	0.343061	+	0.329609i
$821$	−7.71891	+	2.50803i	−0.269392	+	0.0875307i	−0.440598	−	0.897705i	$-0.645234\pi$
$821$	−7.71891	+	2.50803i	−0.269392	+	0.0875307i	0.171206	+	0.985235i	$0.445234\pi$
$822$	−1.37552	−	2.38477i	−0.0479768	−	0.0831784i
$823$	7.07469	+	44.6679i	0.246608	+	1.55702i	0.731126	+	0.682242i	$0.238995\pi$
$823$	7.07469	+	44.6679i	0.246608	+	1.55702i	−0.484518	+	0.874781i	$0.661005\pi$
$824$	−15.4422			−0.537954
$825$	14.7388	−	36.9757i	0.513139	−	1.28733i
$826$	0.477280			0.0166067
$827$	3.16199	+	19.9640i	0.109953	+	0.694216i	0.979663	+	0.200652i	$0.0643061\pi$
$827$	3.16199	+	19.9640i	0.109953	+	0.694216i	−0.869710	+	0.493564i	$0.835694\pi$
$828$	1.02177	−	19.1901i	0.0355089	−	0.666902i
$829$	36.2738	−	11.7861i	1.25984	−	0.409347i	0.398403	−	0.917210i	$-0.369564\pi$
$829$	36.2738	−	11.7861i	1.25984	−	0.409347i	0.861438	+	0.507863i	$0.169564\pi$
$830$	15.2513	−	8.15908i	0.529382	−	0.283206i
$831$	−0.499907	+	0.404471i	−0.0173416	+	0.0140310i
$832$	−3.91395	+	3.91395i	−0.135692	+	0.135692i
$833$	−9.80144	−	19.2364i	−0.339600	−	0.666502i
$834$	5.35143	−	0.278217i	0.185305	−	0.00963388i
$835$	−21.1824	+	7.35397i	−0.733047	+	0.254494i
$836$	29.4125	−	40.4828i	1.01725	−	1.40013i
$837$	−16.3871	−	5.34716i	−0.566419	−	0.184825i
$838$	1.55195	+	0.245805i	0.0536112	+	0.00849118i
$839$	−7.25367	−	5.27010i	−0.250425	−	0.181944i	0.455490	−	0.890241i	$-0.349464\pi$
$839$	−7.25367	−	5.27010i	−0.250425	−	0.181944i	−0.705915	+	0.708297i	$0.749464\pi$
$840$	1.64112	−	0.118263i	0.0566239	−	0.00408045i
$841$	−16.1823	+	11.7571i	−0.558009	+	0.405417i
$842$	−7.29525	+	3.71712i	−0.251411	+	0.128100i
$843$	−33.5305	+	7.11251i	−1.15485	+	0.244968i
$844$	4.22316	+	1.37219i	0.145367	+	0.0472326i
$845$	−14.1458	−	6.85491i	−0.486631	−	0.235816i
$846$	−10.0247	+	9.01117i	−0.344657	+	0.309811i
$847$	−1.98362	−	1.01071i	−0.0681580	−	0.0347283i
$848$	14.2044	−	2.24975i	0.487780	−	0.0772568i
$849$	−29.4316	+	45.2793i	−1.01009	+	1.55398i
$850$	2.78826	+	7.54115i	0.0956364	+	0.258659i
$851$			7.35635i			0.252172i
$852$	−0.214192	+	0.480542i	−0.00733808	+	0.0164631i
$853$	18.2134	−	35.7458i	0.623615	−	1.22391i	−0.335805	−	0.941931i	$-0.609008\pi$
$853$	18.2134	−	35.7458i	0.623615	−	1.22391i	0.959420	−	0.281981i	$-0.0909916\pi$
$854$	−0.133296	−	0.410243i	−0.00456130	−	0.0140382i
$855$	−34.9188	+	23.6399i	−1.19420	+	0.808467i
$856$	0.408812	−	1.25819i	0.0139729	−	0.0430041i
$857$	30.4535	+	30.4535i	1.04027	+	1.04027i	0.999154	+	0.0411191i	$0.0130923\pi$
$857$	30.4535	+	30.4535i	1.04027	+	1.04027i	0.0411191	+	0.999154i	$0.486908\pi$
$858$	10.0160	+	1.05694i	0.341939	+	0.0360835i
$859$	−24.3660	−	33.5369i	−0.831356	−	1.14426i	−0.987669	−	0.156555i	$-0.949961\pi$
$859$	−24.3660	−	33.5369i	−0.831356	−	1.14426i	0.156313	−	0.987707i	$-0.450039\pi$
$860$	8.81499	+	6.13898i	0.300589	+	0.209338i
$861$	−1.25084	+	0.479553i	−0.0426284	+	0.0163431i
$862$	−1.22275	+	7.72013i	−0.0416470	+	0.262949i
$863$	1.10445	−	6.97325i	0.0375960	−	0.237372i	−0.961733	−	0.273987i	$-0.911657\pi$
$863$	1.10445	−	6.97325i	0.0375960	−	0.237372i	0.999329	+	0.0366149i	$0.0116575\pi$
$864$	18.9092	−	18.8619i	0.643304	−	0.641695i
$865$	−44.6266	+	0.892448i	−1.51735	+	0.0303441i
$866$	2.05774	+	2.83223i	0.0699248	+	0.0962432i
$867$	1.33687	−	12.6686i	0.0454025	−	0.430249i
$868$	0.893203	+	0.893203i	0.0303173	+	0.0303173i
$869$	−15.2034	+	46.7913i	−0.515740	+	1.58728i
$870$	9.18693	−	10.6138i	0.311466	−	0.359842i
$871$	9.99670	+	30.7667i	0.338725	+	1.04249i
$872$	0.178287	−	0.349908i	0.00603756	−	0.0118494i
$873$	44.7490	−	29.0073i	1.51452	−	0.981748i
$874$			12.0382i			0.407198i
$875$	2.28807	−	0.898390i	0.0773510	−	0.0303711i
$876$	8.88919	+	5.77798i	0.300338	+	0.195220i
$877$	−37.8279	+	5.99135i	−1.27736	+	0.202314i	−0.758006	−	0.652247i	$-0.773826\pi$
$877$	−37.8279	+	5.99135i	−1.27736	+	0.202314i	−0.519351	+	0.854561i	$0.673826\pi$
$878$	12.7406	+	6.49168i	0.429976	+	0.219084i
$879$	11.8173	−	44.0291i	0.398586	−	1.48507i
$880$	−3.45975	+	25.0798i	−0.116628	+	0.845441i
$881$	−31.3727	−	10.1936i	−1.05697	−	0.343431i	−0.271571	−	0.962418i	$-0.587543\pi$
$881$	−31.3727	−	10.1936i	−1.05697	−	0.343431i	−0.785401	+	0.618987i	$0.787543\pi$
$882$	3.87810	−	10.0777i	0.130583	−	0.339332i
$883$	−31.0006	+	15.7956i	−1.04325	+	0.531564i	−0.889685	−	0.456574i	$-0.849076\pi$
$883$	−31.0006	+	15.7956i	−1.04325	+	0.531564i	−0.153568	+	0.988138i	$0.549076\pi$
$884$	10.6324	−	7.72489i	0.357606	−	0.259816i
$885$	8.57554	−	13.7888i	0.288264	−	0.463507i
$886$	−4.99351	−	3.62800i	−0.167760	−	0.121885i
$887$	43.8719	+	6.94863i	1.47308	+	0.233312i	0.840764	−	0.541402i	$-0.182106\pi$
$887$	43.8719	+	6.94863i	1.47308	+	0.233312i	0.632311	+	0.774714i	$0.282106\pi$
$888$	−4.45615	+	4.94490i	−0.149539	+	0.165940i
$889$	−0.730640	+	1.00564i	−0.0245049	+	0.0337281i
$890$	−8.23132	+	11.8194i	−0.275914	+	0.396186i
$891$	41.1326	+	4.39264i	1.37799	+	0.147159i
$892$	−0.205049	−	0.402431i	−0.00686554	−	0.0134744i
$893$	−38.5727	+	38.5727i	−1.29079	+	1.29079i
$894$	7.80396	+	9.64531i	0.261003	+	0.322587i
$895$	0.590516	+	3.29991i	0.0197388	+	0.110304i
$896$	−2.39482	+	0.778124i	−0.0800053	+	0.0259953i
$897$	13.5592	−	7.82084i	0.452727	−	0.261130i
$898$	3.05369	+	19.2802i	0.101903	+	0.643390i
$899$	23.2219			0.774495
$900$	12.0987	−	22.9895i	0.403289	−	0.766315i
$901$	−18.1314			−0.604043
$902$	1.30962	+	8.26863i	0.0436056	+	0.275315i
$903$	−0.914998	+	0.527765i	−0.0304492	+	0.0175629i
$904$	−9.44129	+	3.06766i	−0.314013	+	0.102029i
$905$	−14.5805	+	30.0883i	−0.484671	+	1.00017i
$906$	1.77044	+	2.18818i	0.0588190	+	0.0726974i
$907$	31.7406	−	31.7406i	1.05393	−	1.05393i	0.0554679	−	0.998460i	$-0.482335\pi$
$907$	31.7406	−	31.7406i	1.05393	−	1.05393i	0.998460	−	0.0554679i	$-0.0176650\pi$
$908$	−12.9987	−	25.5114i	−0.431378	−	0.846627i
$909$	−1.59953	−	0.925267i	−0.0530529	−	0.0306892i
$910$	0.375568	+	0.495768i	0.0124500	+	0.0164346i
$911$	−10.0074	+	13.7741i	−0.331561	+	0.456355i	−0.941953	−	0.335745i	$-0.891012\pi$
$911$	−10.0074	+	13.7741i	−0.331561	+	0.456355i	0.610392	+	0.792100i	$0.291012\pi$
$912$	17.9548	−	19.9240i	0.594541	−	0.659751i
$913$	−67.8213	−	10.7418i	−2.24456	−	0.355503i
$914$	11.8036	+	8.57578i	0.390427	+	0.283662i
$915$	−14.2471	−	3.52007i	−0.470996	−	0.116370i
$916$	−15.8860	+	11.5419i	−0.524890	+	0.381355i
$917$	1.05120	−	0.535611i	0.0347136	−	0.0176874i
$918$	−6.76591	+	4.90279i	−0.223308	+	0.161816i
$919$	−40.8894	−	13.2858i	−1.34882	−	0.438257i	−0.456523	−	0.889712i	$-0.650905\pi$
$919$	−40.8894	−	13.2858i	−1.34882	−	0.438257i	−0.892294	+	0.451454i	$0.850905\pi$
$920$	−7.53837	−	14.0911i	−0.248533	−	0.464569i
$921$	5.62106	−	20.9431i	0.185220	−	0.690100i
$922$	−5.58834	−	2.84740i	−0.184042	−	0.0937742i
$923$	−0.423261	+	0.0670379i	−0.0139318	+	0.00220658i
$924$	−2.54165	−	1.65208i	−0.0836142	−	0.0543493i
$925$	−4.15690	+	9.03414i	−0.136678	+	0.297041i
$926$			14.2622i			0.468684i
$927$	−13.0410	−	20.1181i	−0.428323	−	0.660766i
$928$	−16.3350	+	32.0592i	−0.536222	+	1.05239i
$929$	6.35196	+	19.5493i	0.208401	+	0.641393i	0.999557	+	0.0297776i	$0.00947991\pi$
$929$	6.35196	+	19.5493i	0.208401	+	0.641393i	−0.791155	+	0.611615i	$0.790520\pi$
$930$	−6.47862	+	1.51021i	−0.212442	+	0.0495219i
$931$	13.5036	−	41.5600i	0.442564	−	1.36207i
$932$	−24.8609	−	24.8609i	−0.814345	−	0.814345i
$933$	−3.04163	+	28.8235i	−0.0995786	+	0.943639i
$934$	−1.32537	−	1.82421i	−0.0433674	−	0.0596901i
$935$	9.25452	−	30.5477i	0.302655	−	0.999016i
$936$	13.8519	+	2.95640i	0.452764	+	0.0966330i
$937$	1.47274	−	9.29850i	0.0481123	−	0.303769i	−0.951884	−	0.306458i	$-0.900856\pi$
$937$	1.47274	−	9.29850i	0.0481123	−	0.303769i	0.999996	+	0.00268933i	$0.000856040\pi$
$938$	−0.235777	+	1.48863i	−0.00769838	+	0.0486056i
$939$	11.7175	−	4.49231i	0.382386	−	0.146601i
$940$	9.74392	−	32.1631i	0.317812	−	1.04905i
$941$	−29.1869	−	40.1723i	−0.951466	−	1.30958i	−0.950873	−	0.309581i	$-0.899811\pi$
$941$	−29.1869	−	40.1723i	−0.951466	−	1.30958i	−0.000593457	−	1.00000i	$-0.500189\pi$
$942$	−13.9738	−	1.47460i	−0.455290	−	0.0480449i
$943$	9.20024	+	9.20024i	0.299601	+	0.299601i
$944$	−3.19150	+	9.82244i	−0.103875	+	0.319693i
$945$	1.54000	+	2.03818i	0.0500963	+	0.0663019i
$946$	2.03986	+	6.27806i	0.0663217	+	0.204117i
$947$	9.19754	−	18.0512i	0.298880	−	0.586585i	−0.691911	−	0.721982i	$-0.743231\pi$
$947$	9.19754	−	18.0512i	0.298880	−	0.586585i	0.990791	+	0.135397i	$0.0432311\pi$
$948$	−13.0725	+	29.3284i	−0.424575	+	0.952542i
$949$			8.63563i			0.280325i
$950$	−6.80251	+	14.7838i	−0.220702	+	0.479650i
$951$	−10.3236	+	15.8824i	−0.334765	+	0.515022i
$952$	1.30315	−	0.206398i	0.0422352	−	0.00668939i
$953$	−25.5176	−	13.0019i	−0.826597	−	0.421172i	−0.0111034	−	0.999938i	$-0.503534\pi$
$953$	−25.5176	−	13.0019i	−0.826597	−	0.421172i	−0.815494	+	0.578766i	$0.803534\pi$
$954$	−6.06237	−	6.74425i	−0.196276	−	0.218353i
$955$	3.06876	+	5.73627i	0.0993027	+	0.185621i
$956$	14.1288	+	4.59073i	0.456959	+	0.148475i
$957$	−54.5153	+	11.5638i	−1.76223	+	0.373805i
$958$	8.49180	−	4.32679i	0.274357	−	0.139792i
$959$	−0.546035	+	0.396718i	−0.0176324	+	0.0128107i
$960$	−2.10446	+	8.51759i	−0.0679211	+	0.274904i
$961$	16.1765	+	11.7529i	0.521823	+	0.379127i
$962$	−2.48524	−	0.393623i	−0.0801273	−	0.0126909i
$963$	1.98442	−	0.529950i	0.0639471	−	0.0170774i
$964$	3.37041	−	4.63897i	0.108554	−	0.149411i
$965$	5.81187	+	7.67195i	0.187091	+	0.246969i
$966$	0.728292	−	0.0378634i	0.0234324	−	0.00121824i
$967$	−1.68069	−	3.29854i	−0.0540473	−	0.106074i	0.862403	−	0.506222i	$-0.168959\pi$
$967$	−1.68069	−	3.29854i	−0.0540473	−	0.106074i	−0.916450	+	0.400149i	$0.868959\pi$
$968$	−13.8351	+	13.8351i	−0.444677	+	0.444677i
$969$	−26.2872	+	21.2688i	−0.844467	+	0.683253i
$970$	8.97489	−	18.5206i	0.288166	−	0.594661i
$971$	19.3167	−	6.27638i	0.619902	−	0.201418i	0.0178054	−	0.999841i	$-0.494332\pi$
$971$	19.3167	−	6.27638i	0.619902	−	0.201418i	0.602097	+	0.798423i	$0.294332\pi$
$972$	26.3961	+	5.66825i	0.846656	+	0.181809i
$973$	−0.205513	−	1.29756i	−0.00658845	−	0.0415978i
$974$	18.0873			0.579554
$975$	21.0710	−	1.94261i	0.674812	−	0.0622132i
$976$	9.33416			0.298779
$977$	6.15143	+	38.8386i	0.196802	+	1.24256i	0.866217	+	0.499669i	$0.166545\pi$
$977$	6.15143	+	38.8386i	0.196802	+	1.24256i	−0.669415	+	0.742889i	$0.733455\pi$
$978$	−4.24506	−	7.35974i	−0.135742	−	0.235339i
$979$	54.3813	−	17.6695i	1.73803	−	0.564721i
$980$	4.74226	+	26.5006i	0.151486	+	0.846530i
$981$	0.606426	−	0.0632263i	0.0193617	−	0.00201866i
$982$	10.2856	−	10.2856i	0.328227	−	0.328227i
$983$	−19.5609	−	38.3903i	−0.623894	−	1.22446i	−0.959300	−	0.282388i	$-0.908874\pi$
$983$	−19.5609	−	38.3903i	−0.623894	−	1.22446i	0.335406	−	0.942074i	$-0.391126\pi$
$984$	0.611262	+	11.7575i	0.0194863	+	0.374814i
$985$	−26.3216	+	37.7953i	−0.838677	+	1.20426i
$986$	6.61636	−	9.10664i	0.210708	−	0.290015i
$987$	2.45491	+	2.21226i	0.0781405	+	0.0704171i
$988$	26.2736	+	4.16132i	0.835873	+	0.132389i
$989$	8.29998	+	6.03029i	0.263924	+	0.191752i
$990$	14.4570	−	6.77150i	0.459475	−	0.215213i
$991$	−5.31678	+	3.86287i	−0.168893	+	0.122708i	−0.669021	−	0.743244i	$-0.733286\pi$
$991$	−5.31678	+	3.86287i	−0.168893	+	0.122708i	0.500128	+	0.865952i	$0.333286\pi$
$992$	15.1927	−	7.74105i	0.482367	−	0.245778i
$993$	−2.20971	−	10.4172i	−0.0701231	−	0.330581i
$994$	−0.0189884	−	0.00616971i	−0.000602275	−	0.000195691i
$995$	0.585693	−	4.24571i	0.0185677	−	0.134598i
$996$	−43.2834	−	11.6171i	−1.37149	−	0.368103i
$997$	12.7643	+	6.50376i	0.404251	+	0.205976i	0.644280	−	0.764790i	$-0.277157\pi$
$997$	12.7643	+	6.50376i	0.404251	+	0.205976i	−0.240029	+	0.970766i	$0.577157\pi$
$998$	−1.19134	+	0.188690i	−0.0377113	+	0.00597289i
$999$	−10.2055	−	1.62949i	−0.322887	−	0.0515547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.l.a.38.4	yes	64
3.2	odd	2	inner	75.2.l.a.38.5	yes	64
5.2	odd	4		375.2.l.a.332.5		64
5.3	odd	4		375.2.l.b.332.4		64
5.4	even	2		375.2.l.c.293.5		64
15.2	even	4		375.2.l.a.332.4		64
15.8	even	4		375.2.l.b.332.5		64
15.14	odd	2		375.2.l.c.293.4		64
25.2	odd	20	inner	75.2.l.a.2.5	yes	64
25.11	even	5		375.2.l.a.218.4		64
25.14	even	10		375.2.l.b.218.5		64
25.23	odd	20		375.2.l.c.32.4		64
75.2	even	20	inner	75.2.l.a.2.4	✓	64
75.11	odd	10		375.2.l.a.218.5		64
75.14	odd	10		375.2.l.b.218.4		64
75.23	even	20		375.2.l.c.32.5		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.2.4	✓	64	75.2	even	20	inner
75.2.l.a.2.5	yes	64	25.2	odd	20	inner
75.2.l.a.38.4	yes	64	1.1	even	1	trivial
75.2.l.a.38.5	yes	64	3.2	odd	2	inner
375.2.l.a.218.4		64	25.11	even	5
375.2.l.a.218.5		64	75.11	odd	10
375.2.l.a.332.4		64	15.2	even	4
375.2.l.a.332.5		64	5.2	odd	4
375.2.l.b.218.4		64	75.14	odd	10
375.2.l.b.218.5		64	25.14	even	10
375.2.l.b.332.4		64	5.3	odd	4
375.2.l.b.332.5		64	15.8	even	4
375.2.l.c.32.4		64	25.23	odd	20
375.2.l.c.32.5		64	75.23	even	20
375.2.l.c.293.4		64	15.14	odd	2
375.2.l.c.293.5		64	5.4	even	2

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0809972 - 0.511396i) q^{2} +(-1.50036 + 0.865399i) q^{3} +(1.64715 - 0.535191i) q^{4} +(2.21509 + 0.305570i) q^{5} +(0.564087 + 0.697184i) q^{6} +(0.155466 - 0.155466i) q^{7} +(-0.877235 - 1.72167i) q^{8} +(1.50217 - 2.59682i) q^{9} +O(q^{10})\)	\(q+(-0.0809972 - 0.511396i) q^{2} +(-1.50036 + 0.865399i) q^{3} +(1.64715 - 0.535191i) q^{4} +(2.21509 + 0.305570i) q^{5} +(0.564087 + 0.697184i) q^{6} +(0.155466 - 0.155466i) q^{7} +(-0.877235 - 1.72167i) q^{8} +(1.50217 - 2.59682i) q^{9} +(-0.0231486 - 1.15754i) q^{10} +(-2.70163 + 3.71847i) q^{11} +(-2.00816 + 2.22842i) q^{12} +(-2.41331 - 0.382230i) q^{13} +(-0.0920967 - 0.0669122i) q^{14} +(-3.58788 + 1.45847i) q^{15} +(1.99289 - 1.44792i) q^{16} +(-2.76717 + 1.40994i) q^{17} +(-1.44968 - 0.557867i) q^{18} +(-5.97842 - 1.94251i) q^{19} +(3.81212 - 0.682176i) q^{20} +(-0.0987147 + 0.367794i) q^{21} +(2.12043 + 1.08041i) q^{22} +(3.65312 - 0.578598i) q^{23} +(2.80610 + 1.82397i) q^{24} +(4.81325 + 1.35373i) q^{25} +1.26511i q^{26} +(-0.00650455 + 5.19615i) q^{27} +(0.172871 - 0.339279i) q^{28} +(-2.16317 - 6.65756i) q^{29} +(1.03646 + 1.71669i) q^{30} +(-1.02511 + 3.15498i) q^{31} +(-3.63453 - 3.63453i) q^{32} +(0.835454 - 7.91703i) q^{33} +(0.945172 + 1.30092i) q^{34} +(0.391876 - 0.296865i) q^{35} +(1.08450 - 5.08130i) q^{36} +(-0.311136 + 1.96444i) q^{37} +(-0.509155 + 3.21468i) q^{38} +(3.95161 - 1.51499i) q^{39} +(-1.41706 - 4.08171i) q^{40} +(2.06770 + 2.84595i) q^{41} +(0.196084 + 0.0206920i) q^{42} +(1.96137 + 1.96137i) q^{43} +(-2.45989 + 7.57075i) q^{44} +(4.12095 - 5.29318i) q^{45} +(-0.591785 - 1.82133i) q^{46} +(3.93968 - 7.73207i) q^{47} +(-1.73703 + 3.89706i) q^{48} +6.95166i q^{49} +(0.302433 - 2.57113i) q^{50} +(2.93159 - 4.51013i) q^{51} +(-4.17964 + 0.661990i) q^{52} +(5.20184 + 2.65047i) q^{53} +(2.65782 - 0.417547i) q^{54} +(-7.12060 + 7.41121i) q^{55} +(-0.404040 - 0.131281i) q^{56} +(10.6508 - 2.25926i) q^{57} +(-3.22944 + 1.64548i) q^{58} +(-3.39191 + 2.46437i) q^{59} +(-5.12920 + 4.32252i) q^{60} +(3.06553 + 2.22724i) q^{61} +(1.69647 + 0.268695i) q^{62} +(-0.170181 - 0.637252i) q^{63} +(1.33155 - 1.83272i) q^{64} +(-5.22890 - 1.58411i) q^{65} +(-4.11641 + 0.214009i) q^{66} +(-6.01075 - 11.7968i) q^{67} +(-3.80335 + 3.80335i) q^{68} +(-4.98028 + 4.02952i) q^{69} +(-0.183556 - 0.176359i) q^{70} +(0.166802 - 0.0541973i) q^{71} +(-5.78863 - 0.308213i) q^{72} +(-0.552884 - 3.49077i) q^{73} +1.02981 q^{74} +(-8.39314 + 2.13430i) q^{75} -10.8870 q^{76} +(0.158084 + 0.998104i) q^{77} +(-1.09483 - 1.89813i) q^{78} +(10.1802 - 3.30776i) q^{79} +(4.85688 - 2.59831i) q^{80} +(-4.48698 - 7.80173i) q^{81} +(1.28793 - 1.28793i) q^{82} +(6.78245 + 13.3113i) q^{83} +(0.0342424 + 0.658643i) q^{84} +(-6.56036 + 2.27759i) q^{85} +(0.844172 - 1.16190i) q^{86} +(9.00698 + 8.11673i) q^{87} +(8.77193 + 1.38934i) q^{88} +(-10.0645 - 7.31232i) q^{89} +(-3.04070 - 1.67870i) q^{90} +(-0.434610 + 0.315763i) q^{91} +(5.70757 - 2.90815i) q^{92} +(-1.19227 - 5.62074i) q^{93} +(-4.27325 - 1.38846i) q^{94} +(-12.6492 - 6.12966i) q^{95} +(8.59843 + 2.30779i) q^{96} +(15.8386 + 8.07017i) q^{97} +(3.55505 - 0.563065i) q^{98} +(5.59791 + 12.6014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Introduction

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