LMFDB - Embedded newform 946.2.w.b.175.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(175,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 1]))

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

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

chi := DirichletCharacter("946.175");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.w (of order $42$, degree $12$, 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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$22$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			175.11
Character	$\chi$	$=$	946.175
Dual form			946.2.w.b.373.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 + 0.433884i) q^{2} +(-0.0698989 - 0.00523820i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-1.14712 + 3.71888i) q^{5} +(-0.0607040 - 0.0350474i) q^{6} +(-1.82252 - 3.15669i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-2.96163 - 0.446395i) q^{9} +O(q^{10})$	\(q+(0.900969 + 0.433884i) q^{2} +(-0.0698989 - 0.00523820i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-1.14712 + 3.71888i) q^{5} +(-0.0607040 - 0.0350474i) q^{6} +(-1.82252 - 3.15669i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-2.96163 - 0.446395i) q^{9} +(-2.64708 + 2.85288i) q^{10} +(-0.623202 - 3.25755i) q^{11} +(-0.0394859 - 0.0579151i) q^{12} +(-1.32543 - 1.42848i) q^{13} +(-0.272394 - 3.63484i) q^{14} +(0.0996628 - 0.253937i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(0.133633 + 0.433227i) q^{17} +(-2.47466 - 1.68719i) q^{18} +(-5.55288 + 0.836962i) q^{19} +(-3.62276 + 1.42183i) q^{20} +(0.110857 + 0.230196i) q^{21} +(0.851912 - 3.20535i) q^{22} +(2.50168 + 6.37419i) q^{23} +(-0.0104471 - 0.0693120i) q^{24} +(-8.38297 - 5.71542i) q^{25} +(-0.574381 - 1.86210i) q^{26} +(0.409689 + 0.0935088i) q^{27} +(1.33168 - 3.39307i) q^{28} +(-0.207531 - 2.76931i) q^{29} +(0.199972 - 0.185547i) q^{30} +(-0.165651 + 0.112939i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(0.0264974 + 0.230963i) q^{33} +(-0.0675712 + 0.448305i) q^{34} +(13.8300 - 3.15661i) q^{35} +(-1.49754 - 2.59382i) q^{36} +(-7.30483 - 4.21744i) q^{37} +(-5.36612 - 1.65523i) q^{38} +(0.0851637 + 0.106792i) q^{39} +(-3.88090 - 0.290833i) q^{40} +(3.18686 - 6.61759i) q^{41} +0.255498i q^{42} +(3.78975 + 5.35143i) q^{43} +(2.15829 - 2.51829i) q^{44} +(5.05744 - 10.5019i) q^{45} +(-0.511717 + 6.82838i) q^{46} +(-1.09858 - 1.37758i) q^{47} +(0.0206608 - 0.0669808i) q^{48} +(-3.14314 + 5.44408i) q^{49} +(-5.07297 - 8.78665i) q^{50} +(-0.00707146 - 0.0309821i) q^{51} +(0.290434 - 1.92691i) q^{52} +(-4.84350 - 4.49411i) q^{53} +(0.328545 + 0.262006i) q^{54} +(12.8293 + 1.41919i) q^{55} +(2.67200 - 2.47925i) q^{56} +(0.392524 - 0.0294156i) q^{57} +(1.01458 - 2.58511i) q^{58} +(-3.21346 + 14.0791i) q^{59} +(0.260674 - 0.0804074i) q^{60} +(1.75008 + 1.19319i) q^{61} +(-0.198248 + 0.0298811i) q^{62} +(3.98850 + 10.1625i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(6.83277 - 3.29049i) q^{65} +(-0.0763379 + 0.219588i) q^{66} +(-0.930981 + 0.140323i) q^{67} +(-0.255392 + 0.374591i) q^{68} +(-0.141476 - 0.458653i) q^{69} +(13.8300 + 3.15661i) q^{70} +(-7.58417 - 2.97657i) q^{71} +(-0.223823 - 2.98671i) q^{72} +(-5.82531 + 5.40510i) q^{73} +(-4.75154 - 6.96923i) q^{74} +(0.556022 + 0.443413i) q^{75} +(-4.11653 - 3.81958i) q^{76} +(-9.14728 + 7.90419i) q^{77} +(0.0303946 + 0.133167i) q^{78} +(-10.6719 + 6.16145i) q^{79} +(-3.37038 - 1.94589i) q^{80} +(8.55792 + 2.63977i) q^{81} +(5.74253 - 4.57951i) q^{82} +(1.90240 + 0.142565i) q^{83} +(-0.110857 + 0.230196i) q^{84} -1.76441 q^{85} +(1.09254 + 6.46578i) q^{86} +0.194659i q^{87} +(3.03720 - 1.33245i) q^{88} +(3.68408 + 0.276084i) q^{89} +(9.11320 - 7.26753i) q^{90} +(-2.09364 + 6.78741i) q^{91} +(-3.42377 + 5.93014i) q^{92} +(0.0121704 - 0.00702658i) q^{93} +(-0.392079 - 1.71781i) q^{94} +(3.25727 - 21.6106i) q^{95} +(0.0476766 - 0.0513832i) q^{96} +(-8.09747 + 10.1539i) q^{97} +(-5.19397 + 3.54119i) q^{98} +(0.391544 + 9.92586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 44 q^{2} - 44 q^{4} + 44 q^{8} - 20 q^{9}+O(q^{10}) $ 264 * q + 44 * q^2 - 44 * q^4 + 44 * q^8 - 20 * q^9	$ 264 q + 44 q^{2} - 44 q^{4} + 44 q^{8} - 20 q^{9} + 5 q^{11} - 7 q^{13} - 32 q^{15} - 44 q^{16} - q^{17} + 20 q^{18} - 21 q^{19} + 9 q^{22} - q^{23} - 7 q^{24} - 14 q^{25} - 7 q^{26} - 11 q^{29} + 4 q^{30} + 5 q^{31} + 44 q^{32} - 122 q^{33} + 15 q^{34} + 134 q^{36} - 72 q^{37} - 28 q^{38} + 86 q^{39} + 14 q^{40} - 28 q^{41} + 45 q^{43} - 9 q^{44} + 98 q^{45} - 6 q^{46} + 6 q^{47} - 140 q^{49} - 140 q^{50} + 7 q^{51} - 12 q^{53} + 42 q^{54} + 52 q^{55} - 2 q^{57} - 3 q^{58} + 44 q^{59} - 4 q^{60} + 71 q^{61} + 2 q^{62} - 24 q^{63} - 44 q^{64} - 68 q^{65} - 67 q^{66} + 25 q^{67} + 27 q^{68} + 74 q^{69} + 47 q^{71} + 20 q^{72} - 57 q^{73} + 2 q^{74} - 28 q^{75} + 28 q^{76} + 89 q^{77} + 12 q^{78} - 42 q^{79} + 99 q^{81} - 28 q^{82} - 44 q^{83} + 12 q^{85} - 17 q^{86} - 12 q^{88} - 69 q^{89} - 8 q^{92} + 84 q^{93} - 27 q^{94} - 12 q^{95} - 82 q^{97} - 14 q^{98} + 189 q^{99}+O(q^{100}) $ 264 * q + 44 * q^2 - 44 * q^4 + 44 * q^8 - 20 * q^9 + 5 * q^11 - 7 * q^13 - 32 * q^15 - 44 * q^16 - q^17 + 20 * q^18 - 21 * q^19 + 9 * q^22 - q^23 - 7 * q^24 - 14 * q^25 - 7 * q^26 - 11 * q^29 + 4 * q^30 + 5 * q^31 + 44 * q^32 - 122 * q^33 + 15 * q^34 + 134 * q^36 - 72 * q^37 - 28 * q^38 + 86 * q^39 + 14 * q^40 - 28 * q^41 + 45 * q^43 - 9 * q^44 + 98 * q^45 - 6 * q^46 + 6 * q^47 - 140 * q^49 - 140 * q^50 + 7 * q^51 - 12 * q^53 + 42 * q^54 + 52 * q^55 - 2 * q^57 - 3 * q^58 + 44 * q^59 - 4 * q^60 + 71 * q^61 + 2 * q^62 - 24 * q^63 - 44 * q^64 - 68 * q^65 - 67 * q^66 + 25 * q^67 + 27 * q^68 + 74 * q^69 + 47 * q^71 + 20 * q^72 - 57 * q^73 + 2 * q^74 - 28 * q^75 + 28 * q^76 + 89 * q^77 + 12 * q^78 - 42 * q^79 + 99 * q^81 - 28 * q^82 - 44 * q^83 + 12 * q^85 - 17 * q^86 - 12 * q^88 - 69 * q^89 - 8 * q^92 + 84 * q^93 - 27 * q^94 - 12 * q^95 - 82 * q^97 - 14 * q^98 + 189 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

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 $

$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$3$	−0.0698989	−	0.00523820i	−0.0403561	−	0.00302427i	0.0545367	−	0.998512i	$-0.482632\pi$
$3$	−0.0698989	−	0.00523820i	−0.0403561	−	0.00302427i	−0.0948929	+	0.995487i	$0.530251\pi$
$4$	0.623490	+	0.781831i	0.311745	+	0.390916i
$5$	−1.14712	+	3.71888i	−0.513009	+	1.66313i	0.214257	+	0.976777i	$0.431267\pi$
$5$	−1.14712	+	3.71888i	−0.513009	+	1.66313i	−0.727266	+	0.686356i	$0.759209\pi$
$6$	−0.0607040	−	0.0350474i	−0.0247823	−	0.0143081i
$7$	−1.82252	−	3.15669i	−0.688847	−	1.19312i	−0.972211	−	0.234105i	$-0.924784\pi$
$7$	−1.82252	−	3.15669i	−0.688847	−	1.19312i	0.283364	−	0.959012i	$-0.408549\pi$
$8$	0.222521	+	0.974928i	0.0786730	+	0.344689i
$9$	−2.96163	−	0.446395i	−0.987211	−	0.148798i
$10$	−2.64708	+	2.85288i	−0.837081	+	0.902159i
$11$	−0.623202	−	3.25755i	−0.187902	−	0.982188i
$11$	−0.623202	−	3.25755i	−0.187902	−	0.982188i
$12$	−0.0394859	−	0.0579151i	−0.0113986	−	0.0167187i
$13$	−1.32543	−	1.42848i	−0.367609	−	0.396188i	0.521974	−	0.852961i	$-0.325196\pi$
$13$	−1.32543	−	1.42848i	−0.367609	−	0.396188i	−0.889583	+	0.456773i	$0.849005\pi$
$14$	−0.272394	−	3.63484i	−0.0728003	−	0.971453i
$15$	0.0996628	−	0.253937i	0.0257328	−	0.0655662i
$16$	−0.222521	+	0.974928i	−0.0556302	+	0.243732i
$17$	0.133633	+	0.433227i	0.0324107	+	0.105073i	0.970333	−	0.241773i	$-0.0777289\pi$
$17$	0.133633	+	0.433227i	0.0324107	+	0.105073i	−0.937922	+	0.346846i	$0.887253\pi$
$18$	−2.47466	−	1.68719i	−0.583282	−	0.397675i
$19$	−5.55288	+	0.836962i	−1.27392	+	0.192012i	−0.750961	−	0.660347i	$-0.770409\pi$
$19$	−5.55288	+	0.836962i	−1.27392	+	0.192012i	−0.522957	+	0.852359i	$0.675171\pi$
$20$	−3.62276	+	1.42183i	−0.810073	+	0.317930i
$21$	0.110857	+	0.230196i	0.0241909	+	0.0502329i
$22$	0.851912	−	3.20535i	0.181628	−	0.683382i
$23$	2.50168	+	6.37419i	0.521637	+	1.32911i	0.912657	+	0.408727i	$0.134027\pi$
$23$	2.50168	+	6.37419i	0.521637	+	1.32911i	−0.391019	+	0.920382i	$0.627877\pi$
$24$	−0.0104471	−	0.0693120i	−0.00213251	−	0.0141482i
$25$	−8.38297	−	5.71542i	−1.67659	−	1.14308i
$26$	−0.574381	−	1.86210i	−0.112645	−	0.365187i
$27$	0.409689	+	0.0935088i	0.0788447	+	0.0179958i
$28$	1.33168	−	3.39307i	0.251664	−	0.641229i
$29$	−0.207531	−	2.76931i	−0.0385375	−	0.514248i	−0.982753	−	0.184921i	$-0.940797\pi$
$29$	−0.207531	−	2.76931i	−0.0385375	−	0.514248i	0.944216	−	0.329327i	$-0.106822\pi$
$30$	0.199972	−	0.185547i	0.0365097	−	0.0338761i
$31$	−0.165651	+	0.112939i	−0.0297517	+	0.0202844i	−0.578105	−	0.815963i	$-0.696207\pi$
$31$	−0.165651	+	0.112939i	−0.0297517	+	0.0202844i	0.548353	+	0.836247i	$0.315255\pi$
$32$	−0.623490	+	0.781831i	−0.110218	+	0.138210i
$33$	0.0264974	+	0.230963i	0.00461261	+	0.0402056i
$34$	−0.0675712	+	0.448305i	−0.0115884	+	0.0768837i
$35$	13.8300	−	3.15661i	2.33770	−	0.533564i
$36$	−1.49754	−	2.59382i	−0.249591	−	0.432304i
$37$	−7.30483	−	4.21744i	−1.20091	−	0.693343i	−0.240149	−	0.970736i	$-0.577196\pi$
$37$	−7.30483	−	4.21744i	−1.20091	−	0.693343i	−0.960757	+	0.277393i	$0.910530\pi$
$38$	−5.36612	−	1.65523i	−0.870499	−	0.268513i
$39$	0.0851637	+	0.106792i	0.0136371	+	0.0171004i
$40$	−3.88090	−	0.290833i	−0.613624	−	0.0459847i
$41$	3.18686	−	6.61759i	0.497704	−	1.03349i	−0.489198	−	0.872173i	$-0.662710\pi$
$41$	3.18686	−	6.61759i	0.497704	−	1.03349i	0.986902	−	0.161321i	$-0.0515753\pi$
$42$			0.255498i			0.0394242i
$43$	3.78975	+	5.35143i	0.577931	+	0.816086i
$43$	3.78975	+	5.35143i	0.577931	+	0.816086i
$44$	2.15829	−	2.51829i	0.325375	−	0.379646i
$45$	5.05744	−	10.5019i	0.753919	−	1.56553i
$46$	−0.511717	+	6.82838i	−0.0754485	+	1.00679i
$47$	−1.09858	−	1.37758i	−0.160245	−	0.200940i	0.695227	−	0.718790i	$-0.255304\pi$
$47$	−1.09858	−	1.37758i	−0.160245	−	0.200940i	−0.855471	+	0.517850i	$0.826732\pi$
$48$	0.0206608	−	0.0669808i	0.00298213	−	0.00966784i
$49$	−3.14314	+	5.44408i	−0.449020	+	0.777725i
$50$	−5.07297	−	8.78665i	−0.717427	−	1.24262i
$51$	−0.00707146	−	0.0309821i	−0.000990202	−	0.00433836i
$52$	0.290434	−	1.92691i	0.0402760	−	0.267214i
$53$	−4.84350	−	4.49411i	−0.665306	−	0.617313i	0.273455	−	0.961885i	$-0.411834\pi$
$53$	−4.84350	−	4.49411i	−0.665306	−	0.617313i	−0.938760	+	0.344572i	$0.888024\pi$
$54$	0.328545	+	0.262006i	0.0447093	+	0.0356545i
$55$	12.8293	+	1.41919i	1.72990	+	0.191364i
$56$	2.67200	−	2.47925i	0.357061	−	0.331304i
$57$	0.392524	−	0.0294156i	0.0519911	−	0.00389619i
$58$	1.01458	−	2.58511i	0.133221	−	0.339441i
$59$	−3.21346	+	14.0791i	−0.418357	+	1.83294i	0.123333	+	0.992365i	$0.460642\pi$
$59$	−3.21346	+	14.0791i	−0.418357	+	1.83294i	−0.541691	+	0.840578i	$0.682216\pi$
$60$	0.260674	−	0.0804074i	0.0336529	−	0.0103805i
$61$	1.75008	+	1.19319i	0.224075	+	0.152772i	0.670155	−	0.742221i	$-0.266228\pi$
$61$	1.75008	+	1.19319i	0.224075	+	0.152772i	−0.446079	+	0.894993i	$0.647180\pi$
$62$	−0.198248	+	0.0298811i	−0.0251776	+	0.00379491i
$63$	3.98850	+	10.1625i	0.502504	+	1.28036i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	6.83277	−	3.29049i	0.847501	−	0.408135i
$66$	−0.0763379	+	0.219588i	−0.00939655	+	0.0270294i
$67$	−0.930981	+	0.140323i	−0.113737	+	0.0171432i	−0.205664	−	0.978623i	$-0.565935\pi$
$67$	−0.930981	+	0.140323i	−0.113737	+	0.0171432i	0.0919269	+	0.995766i	$0.470697\pi$
$68$	−0.255392	+	0.374591i	−0.0309708	+	0.0454258i
$69$	−0.141476	−	0.458653i	−0.0170317	−	0.0552153i
$70$	13.8300	+	3.15661i	1.65300	+	0.377287i
$71$	−7.58417	−	2.97657i	−0.900076	−	0.353254i	−0.130230	−	0.991484i	$-0.541572\pi$
$71$	−7.58417	−	2.97657i	−0.900076	−	0.353254i	−0.769846	+	0.638230i	$0.779667\pi$
$72$	−0.223823	−	2.98671i	−0.0263778	−	0.351987i
$73$	−5.82531	+	5.40510i	−0.681801	+	0.632619i	−0.943049	−	0.332653i	$-0.892056\pi$
$73$	−5.82531	+	5.40510i	−0.681801	+	0.632619i	0.261249	+	0.965272i	$0.415866\pi$
$74$	−4.75154	−	6.96923i	−0.552355	−	0.810157i
$75$	0.556022	+	0.443413i	0.0642039	+	0.0512009i
$76$	−4.11653	−	3.81958i	−0.472198	−	0.438136i
$77$	−9.14728	+	7.90419i	−1.04243	+	0.900767i
$78$	0.0303946	+	0.133167i	0.00344151	+	0.0150782i
$79$	−10.6719	+	6.16145i	−1.20069	+	0.693217i	−0.960708	−	0.277561i	$-0.910474\pi$
$79$	−10.6719	+	6.16145i	−1.20069	+	0.693217i	−0.239979	+	0.970778i	$0.577140\pi$
$80$	−3.37038	−	1.94589i	−0.376820	−	0.217557i
$81$	8.55792	+	2.63977i	0.950880	+	0.293308i
$82$	5.74253	−	4.57951i	0.634156	−	0.505723i
$83$	1.90240	+	0.142565i	0.208816	+	0.0156486i	0.178727	−	0.983899i	$-0.442802\pi$
$83$	1.90240	+	0.142565i	0.208816	+	0.0156486i	0.0300886	+	0.999547i	$0.490421\pi$
$84$	−0.110857	+	0.230196i	−0.0120954	+	0.0251164i
$85$	−1.76441			−0.191377
$86$	1.09254	+	6.46578i	0.117812	+	0.697223i
$87$			0.194659i			0.0208696i
$88$	3.03720	−	1.33245i	0.323767	−	0.142040i
$89$	3.68408	+	0.276084i	0.390512	+	0.0292648i	0.268539	−	0.963269i	$-0.413459\pi$
$89$	3.68408	+	0.276084i	0.390512	+	0.0292648i	0.121972	+	0.992533i	$0.461078\pi$
$90$	9.11320	−	7.26753i	0.960615	−	0.766065i
$91$	−2.09364	+	6.78741i	−0.219473	+	0.711514i
$92$	−3.42377	+	5.93014i	−0.356952	+	0.618259i
$93$	0.0121704	−	0.00702658i	0.00126201	−	0.000728622i
$94$	−0.392079	−	1.71781i	−0.0404399	−	0.177179i
$95$	3.25727	−	21.6106i	0.334189	−	2.21720i
$96$	0.0476766	−	0.0513832i	0.00486598	−	0.00524427i
$97$	−8.09747	+	10.1539i	−0.822174	+	1.03097i	0.176734	+	0.984259i	$0.443447\pi$
$97$	−8.09747	+	10.1539i	−0.822174	+	1.03097i	−0.998908	+	0.0467149i	$0.985125\pi$
$98$	−5.19397	+	3.54119i	−0.524670	+	0.357714i
$99$	0.391544	+	9.92586i	0.0393517	+	0.997586i
$100$	−0.758208	−	10.1176i	−0.0758208	−	1.01176i
$101$	−15.1382	−	5.94132i	−1.50631	−	0.591183i	−0.538447	−	0.842659i	$-0.680989\pi$
$101$	−15.1382	−	5.94132i	−1.50631	−	0.591183i	−0.967864	+	0.251476i	$0.919084\pi$
$102$	0.00707146	−	0.0309821i	0.000700179	−	0.00306768i
$103$	18.4855	−	5.70204i	1.82144	−	0.561838i	0.821471	−	0.570251i	$-0.193154\pi$
$103$	18.4855	−	5.70204i	1.82144	−	0.561838i	0.999965	+	0.00841243i	$0.00267779\pi$
$104$	1.09773	−	1.61007i	0.107641	−	0.157880i
$105$	−0.983237	+	0.148199i	−0.0959541	+	0.0144628i
$106$	−2.41392	−	6.15057i	−0.234461	−	0.597396i
$107$	4.42768	+	9.19418i	0.428040	+	0.888835i	0.997754	+	0.0669911i	$0.0213399\pi$
$107$	4.42768	+	9.19418i	0.428040	+	0.888835i	−0.569713	+	0.821843i	$0.692946\pi$
$108$	0.182329	+	0.378610i	0.0175446	+	0.0364317i
$109$	2.80663	−	1.10152i	0.268826	−	0.105507i	−0.227099	−	0.973872i	$-0.572924\pi$
$109$	2.80663	−	1.10152i	0.268826	−	0.105507i	0.495925	+	0.868365i	$0.334829\pi$
$110$	10.9430	+	6.84508i	1.04338	+	0.652653i
$111$	0.488507	+	0.333059i	0.0463671	+	0.0316125i
$112$	3.48310	−	1.07439i	0.329122	−	0.101521i
$113$	−6.88098	−	1.57054i	−0.647308	−	0.147744i	−0.113753	−	0.993509i	$-0.536287\pi$
$113$	−6.88098	−	1.57054i	−0.647308	−	0.147744i	−0.533555	+	0.845765i	$0.679144\pi$
$114$	0.366415	+	0.143807i	0.0343179	+	0.0134688i
$115$	−26.5746	+	1.99149i	−2.47809	+	0.185707i
$116$	2.03574	−	1.88889i	0.189014	−	0.175379i
$117$	3.28778	+	4.82229i	0.303956	+	0.445821i
$118$	−9.00392	+	11.2906i	−0.828878	+	1.03938i
$119$	1.12402	−	1.21140i	0.103038	−	0.111049i
$120$	0.269747	+	0.0406578i	0.0246244	+	0.00371153i
$121$	−10.2232	+	4.06022i	−0.929385	+	0.369111i
$122$	1.05907	+	1.83436i	0.0958834	+	0.166075i
$123$	−0.257422	+	0.445869i	−0.0232110	+	0.0402026i
$124$	−0.191581	−	0.0590948i	−0.0172044	−	0.00530687i
$125$	15.6577	−	12.4866i	1.40046	−	1.11683i
$126$	−0.815843	+	10.8867i	−0.0726811	+	0.969862i
$127$	2.18761	−	4.54261i	0.194119	−	0.403092i	−0.781077	−	0.624434i	$-0.785330\pi$
$127$	2.18761	−	4.54261i	0.194119	−	0.403092i	0.975196	+	0.221343i	$0.0710439\pi$
$128$	−1.00000			−0.0883883
$129$	−0.236867	−	0.393911i	−0.0208550	−	0.0346819i
$130$	7.58380			0.665143
$131$	11.3641	+	5.47266i	0.992885	+	0.478148i	0.858518	−	0.512783i	$-0.171386\pi$
$131$	11.3641	+	5.47266i	0.992885	+	0.478148i	0.134367	+	0.990932i	$0.457100\pi$
$132$	−0.164054	+	0.164720i	−0.0142790	+	0.0143370i
$133$	12.7622	+	16.0034i	1.10663	+	1.38767i
$134$	−0.899669	−	0.277511i	−0.0777195	−	0.0239733i
$135$	−0.817711	+	1.41632i	−0.0703774	+	0.121897i
$136$	−0.392629	+	0.226685i	−0.0336677	+	0.0194380i
$137$	−9.31670	+	2.12648i	−0.795979	+	0.181677i	−0.601125	−	0.799155i	$-0.705281\pi$
$137$	−9.31670	+	2.12648i	−0.795979	+	0.181677i	−0.194854	+	0.980832i	$0.562423\pi$
$138$	0.0715368	−	0.474616i	0.00608962	−	0.0404020i
$139$	−0.977359	+	1.05334i	−0.0828985	+	0.0893433i	−0.773139	−	0.634237i	$-0.781314\pi$
$139$	−0.977359	+	1.05334i	−0.0828985	+	0.0893433i	0.690240	+	0.723580i	$0.257505\pi$
$140$	11.0908	+	8.84462i	0.937344	+	0.747507i
$141$	0.0695736	+	0.102046i	0.00585915	+	0.00859380i
$142$	−5.54162	−	5.97245i	−0.465042	−	0.501197i
$143$	−3.82732	+	5.20789i	−0.320057	+	0.435506i
$144$	1.09423	−	2.78805i	0.0911857	−	0.232337i
$145$	10.5368	+	2.40495i	0.875033	+	0.199720i
$146$	−7.59360	+	2.34232i	−0.628451	+	0.193852i
$147$	0.248219	−	0.364071i	0.0204728	−	0.0300280i
$148$	−1.25715	−	8.34068i	−0.103337	−	0.685599i
$149$	6.91040	+	17.6074i	0.566122	+	1.44246i	0.871582	+	0.490251i	$0.163095\pi$
$149$	6.91040	+	17.6074i	0.566122	+	1.44246i	−0.305459	+	0.952205i	$0.598810\pi$
$150$	0.308569	+	0.640750i	0.0251946	+	0.0523170i
$151$	−15.8194	+	7.61821i	−1.28736	+	0.619961i	−0.947272	−	0.320431i	$-0.896172\pi$
$151$	−15.8194	+	7.61821i	−1.28736	+	0.619961i	−0.340091	+	0.940393i	$0.610458\pi$
$152$	−2.05161	−	5.22742i	−0.166407	−	0.423999i
$153$	−0.202381	−	1.34271i	−0.0163616	−	0.108552i
$154$	−11.6709	+	3.15258i	−0.940469	+	0.254042i
$155$	−0.229984	−	0.745589i	−0.0184727	−	0.0598872i
$156$	−0.0303946	+	0.133167i	−0.00243351	+	0.0106619i
$157$	7.81387	+	3.06672i	0.623614	+	0.244751i	0.656043	−	0.754723i	$-0.272229\pi$
$157$	7.81387	+	3.06672i	0.623614	+	0.244751i	−0.0324287	+	0.999474i	$0.510324\pi$
$158$	−12.2884	+	0.920891i	−0.977615	+	0.0732621i
$159$	0.315014	+	0.339504i	0.0249822	+	0.0269244i
$160$	−2.19232	−	3.21554i	−0.173318	−	0.254211i
$161$	15.5620	−	19.5141i	1.22646	−	1.53793i
$162$	6.56507	+	6.09149i	0.515801	+	0.478593i
$163$	−1.87712	+	12.4539i	−0.147028	+	0.975464i	0.786663	+	0.617383i	$0.211807\pi$
$163$	−1.87712	+	12.4539i	−0.147028	+	0.975464i	−0.933690	+	0.358081i	$0.883431\pi$
$164$	7.16081	−	1.63441i	0.559166	−	0.127626i
$165$	−0.889321	−	0.166403i	−0.0692335	−	0.0129544i
$166$	1.65215	+	0.953869i	0.128232	+	0.0740346i
$167$	3.87650	−	12.5673i	0.299972	−	0.972486i	−0.672624	−	0.739985i	$-0.734833\pi$
$167$	3.87650	−	12.5673i	0.299972	−	0.972486i	0.972596	−	0.232501i	$-0.0746910\pi$
$168$	−0.199757	+	0.159301i	−0.0154116	+	0.0122903i
$169$	0.687717	−	9.17694i	0.0529013	−	0.705919i
$170$	−1.58968	−	0.765550i	−0.121923	−	0.0587150i
$171$	16.8192			1.28620
$172$	−1.82105	+	6.29951i	−0.138854	+	0.480333i
$173$		−	7.70607i		−	0.585881i	−0.956131	−	0.292941i	$-0.905366\pi$
$173$		−	7.70607i		−	0.585881i	0.956131	−	0.292941i	$-0.0946338\pi$
$174$	−0.0844593	+	0.175381i	−0.00640284	+	0.0132956i
$175$	−2.76369	+	36.8789i	−0.208916	+	2.78778i
$176$	3.31455	+	0.117296i	0.249844	+	0.00884151i
$177$	0.298367	−	0.967281i	0.0224266	−	0.0727053i
$178$	3.19945	+	1.84721i	0.239809	+	0.138454i
$179$	13.2478	−	7.64862i	0.990186	−	0.571684i	0.0848564	−	0.996393i	$-0.472957\pi$
$179$	13.2478	−	7.64862i	0.990186	−	0.571684i	0.905330	+	0.424709i	$0.139624\pi$
$180$	11.3640	−	2.59375i	0.847020	−	0.193327i
$181$	18.0771	+	2.72468i	1.34366	+	0.202524i	0.781188	−	0.624295i	$-0.214614\pi$
$181$	18.0771	+	2.72468i	1.34366	+	0.202524i	0.562468	+	0.826819i	$0.309852\pi$
$182$	−4.83125	+	5.20685i	−0.358116	+	0.385957i
$183$	−0.116079	−	0.0925697i	−0.00858079	−	0.00684295i
$184$	−5.65770	+	3.85735i	−0.417091	+	0.284368i
$185$	24.0637	−	22.3278i	1.76920	−	1.64158i
$186$	0.0140139	−	0.00105019i	0.00102755	−	7.70039e-5i
$187$	1.32798	−	0.705303i	0.0971114	−	0.0515769i
$188$	0.392079	−	1.71781i	0.0285953	−	0.125284i
$189$	−0.451487	−	1.46368i	−0.0328408	−	0.106467i
$190$	12.3112	−	18.0572i	0.893147	−	1.31001i
$191$	−3.25062	−	21.5664i	−0.235206	−	1.56049i	−0.725059	−	0.688687i	$-0.758188\pi$
$191$	−3.25062	−	21.5664i	−0.235206	−	1.56049i	0.489853	−	0.871805i	$-0.337050\pi$
$192$	0.0652495	−	0.0256085i	0.00470898	−	0.00184814i
$193$	−5.27264	−	10.9488i	−0.379533	−	0.788108i	−0.999993	−	0.00386996i	$-0.998768\pi$
$193$	−5.27264	−	10.9488i	−0.379533	−	0.788108i	0.620459	−	0.784239i	$-0.286946\pi$
$194$	−11.7012	+	5.63500i	−0.840096	+	0.404569i
$195$	−0.494839	+	0.194210i	−0.0354362	+	0.0139077i
$196$	−6.21607	+	0.936921i	−0.444005	+	0.0669229i
$197$	3.76720	−	5.52547i	0.268402	−	0.393674i	−0.668249	−	0.743938i	$-0.732956\pi$
$197$	3.76720	−	5.52547i	0.268402	−	0.393674i	0.936651	+	0.350264i	$0.113908\pi$
$198$	−3.95390	+	9.11277i	−0.280991	+	0.647617i
$199$	−15.3010	−	3.49236i	−1.08466	−	0.247567i	−0.357416	−	0.933945i	$-0.616342\pi$
$199$	−15.3010	−	3.49236i	−1.08466	−	0.247567i	−0.727244	+	0.686379i	$0.759199\pi$
$200$	3.70673	−	9.44460i	0.262105	−	0.667834i
$201$	0.0658096	−	0.00493175i	0.00464185	−	0.000347859i
$202$	−11.0612	−	11.9212i	−0.778266	−	0.838771i
$203$	−8.36363	+	5.70223i	−0.587012	+	0.400218i
$204$	0.0198138	−	0.0248457i	0.00138724	−	0.00173955i
$205$	20.9543	+	19.4427i	1.46351	+	1.35794i
$206$	19.1289	+	2.88322i	1.33278	+	0.200884i
$207$	−4.56367	−	19.9947i	−0.317197	−	1.38973i
$208$	1.68760	−	0.974336i	0.117014	−	0.0675580i
$209$	6.18701	+	17.5672i	0.427964	+	1.21515i
$210$	−0.950167	−	0.293088i	−0.0655678	−	0.0202250i
$211$	−11.8824	−	14.9001i	−0.818021	−	1.02577i	−0.999105	−	0.0422980i	$-0.986532\pi$
$211$	−11.8824	−	14.9001i	−0.818021	−	1.02577i	0.181084	−	0.983468i	$-0.442039\pi$
$212$	0.493765	−	6.58883i	0.0339119	−	0.452523i
$213$	0.514533	+	0.247786i	0.0352553	+	0.0169780i
$214$			10.2048i			0.697583i
$215$	−24.2486	+	7.95486i	−1.65374	+	0.542517i
$216$			0.420225i			0.0285927i
$217$	0.658414	+	0.317075i	0.0446961	+	0.0215245i
$218$	3.00662	+	0.225315i	0.203634	+	0.0152602i
$219$	0.435496	−	0.347296i	0.0294281	−	0.0234681i
$220$	6.88938	+	10.9152i	0.464482	+	0.735904i
$221$	0.441734	−	0.765105i	0.0297142	−	0.0514666i
$222$	0.295621	+	0.512031i	0.0198408	+	0.0343653i
$223$	−1.62133	+	0.370059i	−0.108573	+	0.0247810i	−0.276462	−	0.961025i	$-0.589162\pi$
$223$	−1.62133	+	0.370059i	−0.108573	+	0.0247810i	0.167889	+	0.985806i	$0.446305\pi$
$224$	3.60432	+	0.543264i	0.240824	+	0.0362984i
$225$	22.2760	+	20.6691i	1.48506	+	1.37794i
$226$	−5.51812	−	4.40055i	−0.367060	−	0.292720i
$227$	13.3611	−	9.10945i	0.886808	−	0.604616i	−0.0319269	−	0.999490i	$-0.510164\pi$
$227$	13.3611	−	9.10945i	0.886808	−	0.604616i	0.918735	+	0.394875i	$0.129212\pi$
$228$	0.267733	+	0.288547i	0.0177310	+	0.0191095i
$229$	−0.439568	−	5.86563i	−0.0290475	−	0.387612i	−0.992713	−	0.120501i	$-0.961550\pi$
$229$	−0.439568	−	5.86563i	−0.0290475	−	0.387612i	0.963666	−	0.267111i	$-0.0860690\pi$
$230$	−24.8069	−	9.73600i	−1.63572	−	0.641973i
$231$	0.680789	−	0.504579i	0.0447926	−	0.0331989i
$232$	2.65370	−	0.818557i	0.174224	−	0.0537409i
$233$	−9.98838	−	6.80996i	−0.654360	−	0.446135i	0.190092	−	0.981766i	$-0.439121\pi$
$233$	−9.98838	−	6.80996i	−0.654360	−	0.446135i	−0.844452	+	0.535631i	$0.820074\pi$
$234$	0.869876	+	5.77125i	0.0568656	+	0.377279i
$235$	6.38325	−	2.50524i	0.416397	−	0.163424i
$236$	−13.0110	+	6.26579i	−0.846947	+	0.407868i
$237$	0.778231	−	0.374776i	0.0505516	−	0.0243443i
$238$	1.53831	−	0.603743i	0.0997139	−	0.0391348i
$239$	0.223673	+	1.48397i	0.0144682	+	0.0959903i	0.994899	−	0.100871i	$-0.0321631\pi$
$239$	0.223673	+	1.48397i	0.0144682	+	0.0959903i	−0.980431	+	0.196862i	$0.936925\pi$
$240$	0.225393	+	0.153670i	0.0145490	+	0.00991937i
$241$	9.43267	−	2.90959i	0.607612	−	0.187423i	0.0243444	−	0.999704i	$-0.492250\pi$
$241$	9.43267	−	2.90959i	0.607612	−	0.187423i	0.583267	+	0.812280i	$0.301774\pi$
$242$	−10.9725	−	0.777566i	−0.705338	−	0.0499838i
$243$	−1.75789	−	0.689921i	−0.112769	−	0.0442585i
$244$	0.158288	+	2.11221i	0.0101334	+	0.135220i
$245$	−16.6403	−	17.9340i	−1.06311	−	1.14576i
$246$	−0.425385	+	0.290022i	−0.0271215	+	0.0184911i
$247$	8.55555	+	6.82283i	0.544377	+	0.434126i
$248$	−0.146968	−	0.136366i	−0.00933247	−	0.00865926i
$249$	−0.132229	−	0.0199303i	−0.00837968	−	0.00126303i
$250$	19.5248	−	4.45640i	1.23486	−	0.281848i
$251$	14.9770	+	25.9410i	0.945342	+	1.63738i	0.755065	+	0.655650i	$0.227605\pi$
$251$	14.9770	+	25.9410i	0.945342	+	1.63738i	0.190277	+	0.981730i	$0.439061\pi$
$252$	−5.45860	+	9.45457i	−0.343859	+	0.595582i
$253$	19.2052	−	12.1218i	1.20742	−	0.762088i
$254$	3.94193	−	3.14358i	0.247339	−	0.197246i
$255$	0.123330	+	0.00924234i	0.00772325	+	0.000578778i
$256$	−0.900969	−	0.433884i	−0.0563106	−	0.0271177i
$257$			2.12644i			0.132644i	0.997798	+	0.0663219i	$0.0211264\pi$
$257$			2.12644i			0.132644i	−0.997798	+	0.0663219i	$0.978874\pi$
$258$	−0.0424986	−	0.457674i	−0.00264585	−	0.0284935i
$259$			30.7455i			1.91043i
$260$	6.83277	+	3.29049i	0.423750	+	0.204067i
$261$	−0.621573	+	8.29432i	−0.0384744	+	0.513406i
$262$	7.86420	+	9.86139i	0.485852	+	0.609239i
$263$	−15.9800	−	4.92918i	−0.985369	−	0.303946i	−0.240128	−	0.970741i	$-0.577189\pi$
$263$	−15.9800	−	4.92918i	−0.985369	−	0.303946i	−0.745241	+	0.666795i	$0.767666\pi$
$264$	−0.219276	+	0.0772273i	−0.0134955	+	0.00475301i
$265$	22.2691	−	12.8571i	1.36798	−	0.789805i
$266$	4.55479	+	19.9559i	0.279272	+	1.22357i
$267$	−0.256067	−	0.0385959i	−0.0156710	−	0.00236203i
$268$	−0.690166	−	0.640381i	−0.0421586	−	0.0391175i
$269$	−2.40433	+	3.01493i	−0.146594	+	0.183824i	−0.849707	−	0.527255i	$-0.823221\pi$
$269$	−2.40433	+	3.01493i	−0.146594	+	0.183824i	0.703113	+	0.711078i	$0.251793\pi$
$270$	−1.35125	+	0.921266i	−0.0822344	+	0.0560665i
$271$	14.8027	+	15.9535i	0.899200	+	0.969107i	0.999666	−	0.0258337i	$-0.00822403\pi$
$271$	14.8027	+	15.9535i	0.899200	+	0.969107i	−0.100467	+	0.994940i	$0.532034\pi$
$272$	−0.452101	+	0.0338803i	−0.0274127	+	0.00205430i
$273$	0.181897	−	0.463466i	0.0110089	−	0.0280502i
$274$	−9.31670	−	2.12648i	−0.562842	−	0.128465i
$275$	−13.3940	+	30.8698i	−0.807686	+	1.86152i
$276$	0.270381	−	0.396575i	0.0162750	−	0.0238710i
$277$	−22.6934	+	3.42048i	−1.36352	+	0.205517i	−0.789713	−	0.613476i	$-0.789771\pi$
$277$	−22.6934	+	3.42048i	−1.36352	+	0.205517i	−0.573803	+	0.818993i	$0.694533\pi$
$278$	−1.33760	+	0.524969i	−0.0802238	+	0.0314855i
$279$	0.541012	−	0.260538i	0.0323895	−	0.0155980i
$280$	6.15493	+	12.7808i	0.367828	+	0.763802i
$281$	−17.6467	+	6.92581i	−1.05271	+	0.413159i	−0.827685	−	0.561194i	$-0.810342\pi$
$281$	−17.6467	+	6.92581i	−1.05271	+	0.413159i	−0.225027	+	0.974352i	$0.572247\pi$
$282$	0.0184077	+	0.122127i	0.00109616	+	0.00727255i
$283$	−1.02994	+	1.51064i	−0.0612234	+	0.0897983i	−0.855630	−	0.517589i	$-0.826830\pi$
$283$	−1.02994	+	1.51064i	−0.0612234	+	0.0897983i	0.794406	+	0.607387i	$0.207782\pi$
$284$	−2.40148	−	7.78541i	−0.142502	−	0.461979i
$285$	−0.340880	+	1.49349i	−0.0201920	+	0.0884669i
$286$	−5.70792	+	3.03154i	−0.337516	+	0.179259i
$287$	−26.6978	+	2.00072i	−1.57592	+	0.118099i
$288$	2.19555	−	2.03718i	0.129374	−	0.120042i
$289$	13.8762	−	9.46065i	0.816249	−	0.556509i
$290$	8.44985	+	6.73853i	0.496192	+	0.395700i
$291$	0.619193	−	0.667331i	0.0362977	−	0.0391196i
$292$	−7.85789	−	1.18439i	−0.459849	−	0.0693110i
$293$	−27.9651	+	6.38286i	−1.63374	+	0.372891i	−0.938335	−	0.345727i	$-0.887632\pi$
$293$	−27.9651	+	6.38286i	−1.63374	+	0.372891i	−0.695406	+	0.718618i	$0.744775\pi$
$294$	0.381602	−	0.220318i	0.0222555	−	0.0128492i
$295$	−48.6722	−	28.1009i	−2.83381	−	1.63610i
$296$	2.48623	−	8.06015i	0.144509	−	0.468487i
$297$	0.0492906	−	1.39286i	0.00286013	−	0.0808217i
$298$	−1.41351	+	18.8620i	−0.0818827	+	1.09265i
$299$	5.78957	−	12.0222i	0.334819	−	0.695259i
$300$			0.711179i			0.0410599i
$301$	9.98595	−	21.7161i	0.575580	−	1.25170i
$302$	−17.5582			−1.01036
$303$	1.02702	+	0.494589i	0.0590010	+	0.0284134i
$304$	0.419654	−	5.59990i	0.0240688	−	0.321176i
$305$	−6.44488	+	5.13962i	−0.369033	+	0.294294i
$306$	0.400242	−	1.29755i	0.0228803	−	0.0741762i
$307$	19.2977	+	11.1415i	1.10138	+	0.635879i	0.936582	−	0.350449i	$-0.113971\pi$
$307$	19.2977	+	11.1415i	1.10138	+	0.635879i	0.164793	+	0.986328i	$0.447304\pi$
$308$	−11.8830	−	2.22345i	−0.677096	−	0.126693i
$309$	−1.32199	+	0.301735i	−0.0752053	+	0.0171651i
$310$	0.116291	−	0.771539i	0.00660487	−	0.0438205i
$311$	11.7319	+	10.8857i	0.665258	+	0.617269i	0.938747	−	0.344606i	$-0.111988\pi$
$311$	11.7319	+	10.8857i	0.665258	+	0.617269i	−0.273490	+	0.961875i	$0.588178\pi$
$312$	−0.0851637	+	0.106792i	−0.00482144	+	0.00604590i
$313$	−9.92009	−	14.5501i	−0.560716	−	0.822420i	0.436285	−	0.899809i	$-0.356294\pi$
$313$	−9.92009	−	14.5501i	−0.560716	−	0.822420i	−0.997001	+	0.0773888i	$0.975342\pi$
$314$	5.70945	+	6.15333i	0.322203	+	0.347252i
$315$	−42.3685	+	3.17508i	−2.38720	+	0.178896i
$316$	−11.4711	−	4.50206i	−0.645297	−	0.253261i
$317$	−6.33229	+	27.7436i	−0.355657	+	1.55823i	0.408227	+	0.912880i	$0.366147\pi$
$317$	−6.33229	+	27.7436i	−0.355657	+	1.55823i	−0.763884	+	0.645354i	$0.776710\pi$
$318$	0.136512	+	0.442562i	0.00765524	+	0.0248177i
$319$	−8.89182	+	2.40188i	−0.497847	+	0.134480i
$320$	−0.580040	−	3.84831i	−0.0324252	−	0.215127i
$321$	−0.261329	−	0.665856i	−0.0145860	−	0.0371644i
$322$	22.4877	−	10.8295i	1.25319	−	0.603505i
$323$	−1.10464	−	2.29381i	−0.0614639	−	0.127631i
$324$	3.27192	+	8.33672i	0.181773	+	0.463151i
$325$	2.94673	+	19.5503i	0.163455	+	1.08446i
$326$	−7.09477	+	10.4061i	−0.392943	+	0.576341i
$327$	−0.201950	+	0.0622934i	−0.0111679	+	0.00344483i
$328$	7.16081	+	1.63441i	0.395390	+	0.0902451i
$329$	−2.34640	+	5.97854i	−0.129361	+	0.329608i
$330$	−0.729051	−	0.535785i	−0.0401329	−	0.0294940i
$331$	−9.85335	−	10.6194i	−0.541589	−	0.583694i	0.401656	−	0.915790i	$-0.368435\pi$
$331$	−9.85335	−	10.6194i	−0.541589	−	0.583694i	−0.943246	+	0.332096i	$0.892244\pi$
$332$	1.07467	+	1.57625i	0.0589800	+	0.0865078i
$333$	19.7516	+	15.7514i	1.08238	+	0.863169i
$334$	8.94534	−	9.64079i	0.489467	−	0.527520i
$335$	0.546105	−	3.62317i	0.0298369	−	0.197955i
$336$	−0.249092	+	0.0568537i	−0.0135891	+	0.00310162i
$337$	28.3702	−	16.3796i	1.54542	−	0.892251i	0.546942	−	0.837170i	$-0.315792\pi$
$337$	28.3702	−	16.3796i	1.54542	−	0.892251i	0.998482	−	0.0550808i	$-0.0175416\pi$
$338$	4.60134	−	7.96975i	0.250280	−	0.433497i
$339$	0.472746	+	0.145823i	0.0256760	+	0.00792001i
$340$	−1.10009	−	1.37947i	−0.0596609	−	0.0748124i
$341$	0.471137	+	0.469231i	0.0255135	+	0.0254103i
$342$	15.1536	+	7.29758i	0.819412	+	0.394608i
$343$	−2.60154			−0.140470
$344$	−4.37396	+	4.88554i	−0.235828	+	0.263410i
$345$	1.86796			0.100568
$346$	3.34354	−	6.94292i	0.179750	−	0.373254i
$347$	1.94774	−	25.9908i	0.104560	−	1.39526i	−0.660269	−	0.751029i	$-0.729558\pi$
$347$	1.94774	−	25.9908i	0.104560	−	1.39526i	0.764830	−	0.644233i	$-0.222823\pi$
$348$	−0.152190	+	0.121368i	−0.00815826	+	0.00650599i
$349$	−21.3239	−	6.57756i	−1.14144	−	0.352089i	−0.334313	−	0.942462i	$-0.608504\pi$
$349$	−21.3239	−	6.57756i	−1.14144	−	0.352089i	−0.807130	+	0.590374i	$0.798980\pi$
$350$	−18.4912	+	32.0276i	−0.988394	+	1.71195i
$351$	−0.409440	−	0.709171i	−0.0218543	−	0.0378528i
$352$	2.93541	+	1.54381i	0.156458	+	0.0822853i
$353$	−17.2562	−	2.60095i	−0.918454	−	0.138435i	−0.327233	−	0.944944i	$-0.606116\pi$
$353$	−17.2562	−	2.60095i	−0.918454	−	0.138435i	−0.591222	+	0.806509i	$0.701354\pi$
$354$	0.688506	−	0.742034i	0.0365937	−	0.0394386i
$355$	19.7695	−	24.7901i	1.04925	−	1.31572i
$356$	2.08114	+	3.05247i	0.110300	+	0.161780i
$357$	−0.0849131	+	0.0787878i	−0.00449408	+	0.00416989i
$358$	15.2545	−	1.14316i	0.806223	−	0.0604181i
$359$	16.2655	+	6.38373i	0.858459	+	0.336920i	0.753414	−	0.657547i	$-0.228406\pi$
$359$	16.2655	+	6.38373i	0.858459	+	0.336920i	0.105046	+	0.994467i	$0.466501\pi$
$360$	11.3640	+	2.59375i	0.598934	+	0.136703i
$361$	11.9781	−	3.69475i	0.630425	−	0.194460i
$362$	15.1047	+	10.2982i	0.793884	+	0.541261i
$363$	0.735861	−	0.230253i	0.0386227	−	0.0120852i
$364$	−6.61198	+	2.59501i	−0.346562	+	0.136015i
$365$	−13.4186	−	27.8639i	−0.702359	−	1.45846i
$366$	−0.0644189	−	0.133767i	−0.00336723	−	0.00699212i
$367$	−7.48039	−	19.0597i	−0.390473	−	0.994910i	−0.982043	−	0.188656i	$-0.939587\pi$
$367$	−7.48039	−	19.0597i	−0.390473	−	0.994910i	0.591570	−	0.806254i	$-0.298508\pi$
$368$	−6.77105	+	1.02057i	−0.352965	+	0.0532010i
$369$	−12.3924	+	18.1763i	−0.645121	+	0.946219i
$370$	31.3683	−	9.67584i	1.63076	−	0.503023i
$371$	−5.35916	+	23.4800i	−0.278234	+	1.21902i
$372$	0.0130817	+	0.00513419i	0.000678255	+	0.000266196i
$373$	−0.977910	−	13.0493i	−0.0506343	−	0.675667i	−0.963552	−	0.267523i	$-0.913795\pi$
$373$	−0.977910	−	13.0493i	−0.0506343	−	0.675667i	0.912917	−	0.408145i	$-0.133824\pi$
$374$	1.50249	−	0.0592684i	0.0776917	−	0.00306469i
$375$	−1.15986	+	0.790779i	−0.0598949	+	0.0408356i
$376$	1.09858	−	1.37758i	0.0566550	−	0.0710431i
$377$	−3.68083	+	3.96699i	−0.189572	+	0.204310i
$378$	0.228293	−	1.51463i	0.0117421	−	0.0779040i
$379$	2.76197	+	12.1010i	0.141873	+	0.621585i	0.994999	+	0.0998813i	$0.0318463\pi$
$379$	2.76197	+	12.1010i	0.141873	+	0.621585i	−0.853127	+	0.521704i	$0.825297\pi$
$380$	18.9267	−	10.9273i	0.970920	−	0.560561i
$381$	−0.176706	+	0.306064i	−0.00905294	+	0.0156802i
$382$	6.42862	−	20.8411i	0.328917	−	1.06632i
$383$	21.0074	−	16.7528i	1.07343	−	0.856030i	0.0833460	−	0.996521i	$-0.473439\pi$
$383$	21.0074	−	16.7528i	1.07343	−	0.856030i	0.990082	+	0.140490i	$0.0448679\pi$
$384$	0.0698989	+	0.00523820i	0.00356701	+	0.000267311i
$385$	−18.9017	−	43.0847i	−0.963319	−	2.19580i
$386$		−	12.1522i		−	0.618531i
$387$	−8.83499	−	17.5407i	−0.449108	−	0.891644i
$388$	−12.9873			−0.659332
$389$	3.03097	−	6.29388i	0.153676	−	0.319112i	−0.809890	−	0.586582i	$-0.800473\pi$
$389$	3.03097	−	6.29388i	0.153676	−	0.319112i	0.963566	+	0.267470i	$0.0861875\pi$
$390$	−0.530099	−	0.0397254i	−0.0268426	−	0.00201158i
$391$	−2.42716	+	1.93560i	−0.122747	+	0.0978874i
$392$	−6.00700	−	1.85291i	−0.303399	−	0.0935862i
$393$	−0.765671	−	0.442060i	−0.0386230	−	0.0222990i
$394$	5.79154	−	3.34375i	0.291774	−	0.168456i
$395$	−10.6717	−	46.7556i	−0.536949	−	2.35253i
$396$	−7.51623	+	6.49479i	−0.377705	+	0.326376i
$397$	10.7297	+	9.95568i	0.538507	+	0.499661i	0.901883	−	0.431981i	$-0.142185\pi$
$397$	10.7297	+	9.95568i	0.538507	+	0.499661i	−0.363376	+	0.931643i	$0.618376\pi$
$398$	−12.2705	−	9.78536i	−0.615062	−	0.490496i
$399$	−0.808238	−	1.18547i	−0.0404625	−	0.0593476i
$400$	7.43751	−	6.90100i	0.371875	−	0.345050i
$401$	−0.228556	−	3.04987i	−0.0114135	−	0.152303i	−0.999999	−	0.00163970i	$-0.999478\pi$
$401$	−0.228556	−	3.04987i	−0.0114135	−	0.152303i	0.988585	−	0.150663i	$-0.0481410\pi$
$402$	0.0614322	+	0.0241104i	0.00306396	+	0.00120252i
$403$	0.380889	+	0.0869355i	0.0189734	+	0.00433057i
$404$	−4.79342	−	15.5399i	−0.238482	−	0.773139i
$405$	−19.6340	+	28.7977i	−0.975620	+	1.43097i
$406$	−10.0095	+	1.50869i	−0.496762	+	0.0748748i
$407$	−9.18614	+	26.4241i	−0.455340	+	1.30980i
$408$	0.0286318	−	0.0137883i	0.00141748	−	0.000682624i
$409$	17.6264	−	8.48841i	0.871568	−	0.419725i	0.0560301	−	0.998429i	$-0.482156\pi$
$409$	17.6264	−	8.48841i	0.871568	−	0.419725i	0.815537	+	0.578704i	$0.196441\pi$
$410$	10.4433	+	26.6090i	0.515756	+	1.31413i
$411$	0.662366	−	0.0998356i	0.0326721	−	0.00492453i
$412$	15.9836	+	10.8974i	0.787455	+	0.536877i
$413$	50.3000	−	15.5155i	2.47510	−	0.763468i
$414$	4.56367	−	19.9947i	0.224292	−	0.982688i
$415$	−2.71247	+	6.91126i	−0.133150	+	0.339261i
$416$	1.94322	−	0.145624i	0.0952744	−	0.00713983i
$417$	0.0738339	−	0.0685079i	0.00361566	−	0.00335484i
$418$	−2.04781	+	18.5119i	−0.100162	+	0.905448i
$419$	15.9901	+	12.7516i	0.781166	+	0.622959i	0.930694	−	0.365799i	$-0.119204\pi$
$419$	15.9901	+	12.7516i	0.781166	+	0.622959i	−0.149528	+	0.988757i	$0.547776\pi$
$420$	−0.728905	−	0.676325i	−0.0355669	−	0.0330013i
$421$	−5.47568	+	36.3288i	−0.266869	+	1.77056i	0.307098	+	0.951678i	$0.400642\pi$
$421$	−5.47568	+	36.3288i	−0.266869	+	1.77056i	−0.573966	+	0.818879i	$0.694596\pi$
$422$	−4.24079	−	18.5801i	−0.206439	−	0.904466i
$423$	2.63865	+	4.57028i	0.128296	+	0.222215i
$424$	3.30365	−	5.72209i	0.160440	−	0.277889i
$425$	1.35583	−	4.39550i	0.0657675	−	0.213213i
$426$	0.356068	+	0.446495i	0.0172516	+	0.0216328i
$427$	0.576966	−	7.69908i	0.0279214	−	0.372585i
$428$	−4.42768	+	9.19418i	−0.214020	+	0.444417i
$429$	0.294806	−	0.343978i	0.0142333	−	0.0166074i
$430$	−25.2987	−	3.35400i	−1.22001	−	0.161744i
$431$		−	23.2143i		−	1.11820i	−0.829102	−	0.559098i	$-0.811148\pi$
$431$		−	23.2143i		−	1.11820i	0.829102	−	0.559098i	$-0.188852\pi$
$432$	−0.182329	+	0.378610i	−0.00877230	+	0.0182159i
$433$	−10.9819	−	0.822976i	−0.527754	−	0.0395497i	−0.191811	−	0.981432i	$-0.561436\pi$
$433$	−10.9819	−	0.822976i	−0.527754	−	0.0395497i	−0.335943	+	0.941882i	$0.609055\pi$
$434$	0.455637	+	0.571350i	0.0218713	+	0.0274257i
$435$	−0.723912	−	0.223297i	−0.0347089	−	0.0107063i
$436$	2.61111	+	1.50752i	0.125049	+	0.0721973i
$437$	−19.2265	−	33.3013i	−0.919728	−	1.59302i
$438$	0.543054	−	0.123949i	0.0259481	−	0.00592249i
$439$	0.945963	−	6.27606i	0.0451484	−	0.299540i	−0.954849	−	0.297093i	$-0.903983\pi$
$439$	0.945963	−	6.27606i	0.0451484	−	0.299540i	0.999997	−	0.00244712i	$-0.000778944\pi$
$440$	1.47118	+	12.8235i	0.0701357	+	0.611334i
$441$	11.7390	−	14.7203i	0.559002	−	0.700966i
$442$	0.729955	−	0.497675i	0.0347204	−	0.0236720i
$443$	13.2687	−	12.3116i	0.630416	−	0.584941i	−0.298874	−	0.954293i	$-0.596611\pi$
$443$	13.2687	−	12.3116i	0.630416	−	0.584941i	0.929289	+	0.369352i	$0.120420\pi$
$444$	0.0441836	+	0.589589i	0.00209686	+	0.0279807i
$445$	−5.25281	+	13.3840i	−0.249007	+	0.634460i
$446$	−1.62133	−	0.370059i	−0.0767724	−	0.0175228i
$447$	−0.390798	−	1.26694i	−0.0184841	−	0.0599241i
$448$	3.01167	+	2.05332i	0.142288	+	0.0970103i
$449$	2.06745	+	13.7166i	0.0975688	+	0.647326i	0.983144	+	0.182831i	$0.0585262\pi$
$449$	2.06745	+	13.7166i	0.0975688	+	0.647326i	−0.885576	+	0.464495i	$0.846236\pi$
$450$	11.1020	+	28.2874i	0.523352	+	1.33348i
$451$	−23.5432	−	6.25726i	−1.10860	−	0.294643i
$452$	−3.06232	−	6.35898i	−0.144040	−	0.299101i
$453$	1.14566	−	0.449639i	0.0538279	−	0.0211259i
$454$	15.9904	−	2.41016i	0.750466	−	0.113115i
$455$	−22.8399	−	15.5720i	−1.07075	−	0.730026i
$456$	0.116023	+	0.376137i	0.00543327	+	0.0176142i
$457$	5.00479	−	21.9274i	0.234114	−	1.02572i	−0.712074	−	0.702105i	$-0.752244\pi$
$457$	5.00479	−	21.9274i	0.234114	−	1.02572i	0.946188	−	0.323617i	$-0.104899\pi$
$458$	2.14896	−	5.47547i	0.100414	−	0.255852i
$459$	0.0142374	+	0.189984i	0.000664543	+	0.00886771i
$460$	−18.1260	−	19.5352i	−0.845128	−	0.910831i
$461$	−12.0143	−	17.6217i	−0.559560	−	0.820724i	0.437349	−	0.899292i	$-0.355918\pi$
$461$	−12.0143	−	17.6217i	−0.559560	−	0.820724i	−0.996909	+	0.0785679i	$0.974965\pi$
$462$	0.832298	−	0.159227i	0.0387220	−	0.00740791i
$463$	−11.0576	+	11.9173i	−0.513892	+	0.553843i	−0.935679	−	0.352851i	$-0.885212\pi$
$463$	−11.0576	+	11.9173i	−0.513892	+	0.553843i	0.421788	+	0.906695i	$0.361403\pi$
$464$	2.74606	+	0.413901i	0.127482	+	0.0192149i
$465$	0.0121701	+	0.0533205i	0.000564373	+	0.00247268i
$466$	−6.04449	−	10.4694i	−0.280005	−	0.484984i
$467$	−14.0220	−	8.09562i	−0.648862	−	0.374620i	0.139158	−	0.990270i	$-0.455560\pi$
$467$	−14.0220	−	8.09562i	−0.648862	−	0.374620i	−0.788020	+	0.615650i	$0.788894\pi$
$468$	−1.72032	+	5.57714i	−0.0795219	+	0.257804i
$469$	2.13969	+	2.68308i	0.0988015	+	0.123893i
$470$	6.83809	+	0.512444i	0.315418	+	0.0236373i
$471$	−0.530116	−	0.255291i	−0.0244265	−	0.0117632i
$472$	−14.4412			−0.664709
$473$	15.0708	−	15.6803i	0.692955	−	0.720981i
$474$	0.863772			0.0396743
$475$	51.3332	+	24.7208i	2.35533	+	1.13427i
$476$	1.64793	+	0.123495i	0.0755325	+	0.00566038i
$477$	12.3385	+	15.4720i	0.564942	+	0.708415i
$478$	−0.442350	+	1.43406i	−0.0202326	+	0.0655925i
$479$	−11.7197	−	6.76640i	−0.535489	−	0.309165i	0.207760	−	0.978180i	$-0.433383\pi$
$479$	−11.7197	−	6.76640i	−0.535489	−	0.309165i	−0.743249	+	0.669015i	$0.766716\pi$
$480$	0.136397	+	0.236246i	0.00622564	+	0.0107831i
$481$	3.65754	+	16.0247i	0.166769	+	0.730664i
$482$	9.76097	+	1.47123i	0.444600	+	0.0670127i
$483$	−1.18998	+	1.28250i	−0.0541462	+	0.0583557i
$484$	−9.54849	−	5.46134i	−0.434022	−	0.248243i
$485$	−28.4724	−	41.7613i	−1.29286	−	1.89628i
$486$	−1.28446	−	1.38432i	−0.0582643	−	0.0627939i
$487$	−1.12737	−	15.0437i	−0.0510859	−	0.681695i	−0.962687	−	0.270618i	$-0.912772\pi$
$487$	−1.12737	−	15.0437i	−0.0510859	−	0.681695i	0.911601	−	0.411076i	$-0.134847\pi$
$488$	−0.773841	+	1.97171i	−0.0350301	+	0.0892553i
$489$	0.196445	−	0.860680i	0.00888354	−	0.0389213i
$490$	−7.21113	−	23.3779i	−0.325766	−	1.05611i
$491$	−4.72539	−	3.22171i	−0.213254	−	0.145394i	0.451983	−	0.892027i	$-0.350717\pi$
$491$	−4.72539	−	3.22171i	−0.213254	−	0.145394i	−0.665236	+	0.746633i	$0.731669\pi$
$492$	−0.509094	+	0.0767336i	−0.0229517	+	0.00345942i
$493$	1.17201	−	0.459979i	0.0527845	−	0.0207164i
$494$	4.74797	+	9.85927i	0.213621	+	0.443590i
$495$	−37.3622	−	9.93007i	−1.67931	−	0.446323i
$496$	−0.0732464	−	0.186629i	−0.00328886	−	0.00837987i
$497$	4.42618	+	29.3658i	0.198541	+	1.31723i
$498$	−0.110487	−	0.0753286i	−0.00495103	−	0.00337556i
$499$	10.3326	+	33.4976i	0.462552	+	1.49956i	0.823687	+	0.567044i	$0.191913\pi$
$499$	10.3326	+	33.4976i	0.462552	+	1.49956i	−0.361135	+	0.932513i	$0.617611\pi$
$500$	19.5248	+	4.45640i	0.873174	+	0.199296i
$501$	−0.336793	+	0.858134i	−0.0150468	+	0.0383386i
$502$	2.23847	+	29.8703i	0.0999078	+	1.33318i
$503$	−26.6661	+	24.7426i	−1.18898	+	1.10322i	−0.196543	+	0.980495i	$0.562972\pi$
$503$	−26.6661	+	24.7426i	−1.18898	+	1.10322i	−0.992441	+	0.122721i	$0.960838\pi$
$504$	−9.02021	+	6.14988i	−0.401792	+	0.273937i
$505$	39.4605	−	49.4818i	1.75597	−	2.20191i
$506$	22.5627	−	2.58852i	1.00303	−	0.115074i
$507$	−0.0961413	+	0.637856i	−0.00426978	+	0.0283282i
$508$	4.91551	−	1.12193i	0.218090	−	0.0497777i
$509$	−2.57144	−	4.45387i	−0.113977	−	0.197414i	0.803393	−	0.595449i	$-0.203026\pi$
$509$	−2.57144	−	4.45387i	−0.113977	−	0.197414i	−0.917370	+	0.398034i	$0.869692\pi$
$510$	0.107107	+	0.0618381i	0.00474277	+	0.00273824i
$511$	27.6790	+	8.53783i	1.22444	+	0.377691i
$512$	−0.623490	−	0.781831i	−0.0275546	−	0.0345524i
$513$	−2.35322	−	0.176349i	−0.103897	−	0.00778601i
$514$	−0.922628	+	1.91586i	−0.0406954	+	0.0845048i
$515$			75.2864i			3.31752i
$516$	0.160287	−	0.430789i	0.00705626	−	0.0189644i
$517$	−3.80289	+	4.43719i	−0.167251	+	0.195147i
$518$	−13.3400	+	27.7007i	−0.586124	+	1.21710i
$519$	−0.0403659	+	0.538645i	−0.00177187	+	0.0236439i
$520$	4.72842	+	5.92925i	0.207355	+	0.260015i
$521$	13.3272	−	43.2057i	0.583874	−	1.89287i	0.160119	−	0.987098i	$-0.448812\pi$
$521$	13.3272	−	43.2057i	0.583874	−	1.89287i	0.423756	−	0.905777i	$-0.360712\pi$
$522$	−4.15879	+	7.20323i	−0.182025	+	0.315277i
$523$	−1.59586	−	2.76412i	−0.0697822	−	0.120866i	0.829023	−	0.559214i	$-0.188897\pi$
$523$	−1.59586	−	2.76412i	−0.0697822	−	0.120866i	−0.898805	+	0.438348i	$0.855564\pi$
$524$	2.80670	+	12.2970i	0.122611	+	0.537195i
$525$	0.386358	−	2.56332i	0.0168620	−	0.111872i
$526$	−12.2588	−	11.3745i	−0.534509	−	0.495952i
$527$	−0.0710645	−	0.0566720i	−0.00309562	−	0.00246867i
$528$	−0.231069	−	0.0255611i	−0.0100560	−	0.00111240i
$529$	−17.5116	+	16.2484i	−0.761375	+	0.706453i
$530$	25.6423	−	1.92162i	1.11383	−	0.0834700i
$531$	15.8019	−	40.2627i	0.685746	−	1.74725i
$532$	−4.55479	+	19.9559i	−0.197475	+	0.865196i
$533$	−13.6770	+	4.21881i	−0.592419	+	0.182737i
$534$	−0.213962	−	0.145877i	−0.00925905	−	0.00631272i
$535$	−39.2711	+	5.91917i	−1.69784	+	0.255908i
$536$	−0.343967	−	0.876415i	−0.0148571	−	0.0378554i
$537$	−0.966071	+	0.465235i	−0.0416890	+	0.0200764i
$538$	−3.47435	+	1.67316i	−0.149790	+	0.0721351i
$539$	19.6932	+	6.84617i	0.848244	+	0.294885i
$540$	−1.61716	+	0.243747i	−0.0695913	+	0.0104892i
$541$	−10.1840	+	14.9372i	−0.437845	+	0.642201i	−0.980214	−	0.197940i	$-0.936575\pi$
$541$	−10.1840	+	14.9372i	−0.437845	+	0.642201i	0.542369	+	0.840140i	$0.317527\pi$
$542$	6.41480	+	20.7963i	0.275539	+	0.893276i
$543$	−1.24929	−	0.285143i	−0.0536123	−	0.0122367i
$544$	−0.422029	−	0.165634i	−0.0180944	−	0.00710151i
$545$	0.876876	+	11.7011i	0.0375612	+	0.501220i
$546$	0.364974	−	0.338646i	0.0156194	−	0.0144927i
$547$	2.72982	+	4.00391i	0.116719	+	0.171195i	0.880152	−	0.474691i	$-0.157440\pi$
$547$	2.72982	+	4.00391i	0.116719	+	0.171195i	−0.763434	+	0.645886i	$0.776488\pi$
$548$	−7.47141	−	5.95825i	−0.319163	−	0.254524i
$549$	−4.65048	−	4.31501i	−0.198477	−	0.184160i
$550$	−25.4614	+	22.0013i	−1.08568	+	0.938139i
$551$	3.47020	+	15.2039i	0.147836	+	0.647710i
$552$	0.415672	−	0.239988i	0.0176922	−	0.0102146i
$553$	38.8996	+	22.4587i	1.65418	+	0.955040i
$554$	−21.9302	−	6.76456i	−0.931724	−	0.287399i
$555$	−1.79898	+	1.43464i	−0.0763626	+	0.0608971i
$556$	−1.43291	−	0.107382i	−0.0607689	−	0.00455400i
$557$	−3.95594	+	8.21459i	−0.167619	+	0.348063i	−0.967810	−	0.251681i	$-0.919017\pi$
$557$	−3.95594	+	8.21459i	−0.167619	+	0.348063i	0.800192	+	0.599744i	$0.204731\pi$
$558$	0.600478			0.0254203
$559$	2.62134	−	12.5065i	0.110871	−	0.528970i
$560$			14.1857i			0.599454i
$561$	−0.0965187	+	0.0423437i	−0.00407502	+	0.00178775i
$562$	−18.9041	−	1.41667i	−0.797421	−	0.0597584i
$563$	9.32818	−	7.43898i	0.393136	−	0.313516i	−0.406894	−	0.913475i	$-0.633388\pi$
$563$	9.32818	−	7.43898i	0.393136	−	0.313516i	0.800030	+	0.599960i	$0.204817\pi$
$564$	−0.0364041	+	0.118019i	−0.00153289	+	0.00496951i
$565$	13.7340	−	23.7879i	0.577792	−	1.00077i
$566$	−1.58338	+	0.914167i	−0.0665546	+	0.0384253i
$567$	−7.26402	−	31.8258i	−0.305060	−	1.33656i
$568$	1.21430	−	8.05637i	0.0509510	−	0.338038i
$569$	−9.95193	+	10.7256i	−0.417207	+	0.449642i	−0.906329	−	0.422574i	$-0.861127\pi$
$569$	−9.95193	+	10.7256i	−0.417207	+	0.449642i	0.489122	+	0.872215i	$0.337317\pi$
$570$	−0.955125	+	1.19769i	−0.0400058	+	0.0501657i
$571$	−13.8040	+	9.41141i	−0.577679	+	0.393855i	−0.816617	−	0.577180i	$-0.804153\pi$
$571$	−13.8040	+	9.41141i	−0.577679	+	0.393855i	0.238938	+	0.971035i	$0.423201\pi$
$572$	−6.45799	+	0.254747i	−0.270022	+	0.0106515i
$573$	0.114245	+	1.52450i	0.00477266	+	0.0636868i
$574$	−24.9220	−	9.78115i	−1.04022	−	0.408257i
$575$	15.4596	−	67.7328i	0.644709	−	2.82465i
$576$	2.86202	−	0.882817i	0.119251	−	0.0367841i
$577$	−3.97330	+	5.82776i	−0.165411	+	0.242613i	−0.899991	−	0.435909i	$-0.856427\pi$
$577$	−3.97330	+	5.82776i	−0.165411	+	0.242613i	0.734580	+	0.678522i	$0.237379\pi$
$578$	16.6069	−	2.50308i	0.690755	−	0.104115i
$579$	0.311200	+	0.792925i	0.0129330	+	0.0329528i
$580$	4.68931	+	9.73746i	0.194713	+	0.404326i
$581$	−3.01713	−	6.26513i	−0.125172	−	0.259921i
$582$	0.847417	−	0.332587i	0.0351266	−	0.0137862i
$583$	−11.6213	+	18.5787i	−0.481305	+	0.769450i
$584$	−6.56583	−	4.47651i	−0.271696	−	0.185239i
$585$	−21.7050	+	6.69511i	−0.897392	+	0.276809i
$586$	−27.9651	−	6.38286i	−1.15523	−	0.263674i
$587$	−10.9358	−	4.29200i	−0.451370	−	0.177150i	0.128756	−	0.991676i	$-0.458902\pi$
$587$	−10.9358	−	4.29200i	−0.451370	−	0.177150i	−0.580126	+	0.814527i	$0.696997\pi$
$588$	0.439404	−	0.0329288i	0.0181207	−	0.00135796i
$589$	0.825313	−	0.765778i	0.0340064	−	0.0315533i
$590$	−31.6596	−	46.4362i	−1.30341	−	1.91175i
$591$	−0.292267	+	0.366491i	−0.0120222	+	0.0150754i
$592$	5.73718	−	6.18321i	0.235797	−	0.254128i
$593$	−12.1221	−	1.82711i	−0.497794	−	0.0750304i	−0.104653	−	0.994509i	$-0.533373\pi$
$593$	−12.1221	−	1.82711i	−0.497794	−	0.0750304i	−0.393141	+	0.919478i	$0.628611\pi$
$594$	0.648747	−	1.23353i	0.0266184	−	0.0506125i
$595$	3.21567	+	5.56971i	0.131830	+	0.228336i
$596$	−9.45747	+	16.3808i	−0.387393	+	0.670984i
$597$	1.05123	+	0.324261i	0.0430240	+	0.0132711i
$598$	10.4324	−	8.31959i	0.426614	−	0.340213i
$599$	−2.60919	+	34.8173i	−0.106609	+	1.42259i	0.645603	+	0.763673i	$0.276606\pi$
$599$	−2.60919	+	34.8173i	−0.106609	+	1.42259i	−0.752212	+	0.658921i	$0.771013\pi$
$600$	−0.308569	+	0.640750i	−0.0125973	+	0.0261585i
$601$	−43.1116			−1.75856			−0.879280	−	0.476306i	$-0.841975\pi$
$601$	−43.1116			−1.75856			−0.879280	+	0.476306i	$0.841975\pi$
$602$	18.4193	−	15.2328i	0.750715	−	0.620844i
$603$	2.81986			0.114834
$604$	−15.8194	−	7.61821i	−0.643681	−	0.309981i
$605$	−3.37216	−	42.6766i	−0.137098	−	1.73505i
$606$	0.710723	+	0.891218i	0.0288711	+	0.0362033i
$607$	1.14090	+	0.351920i	0.0463075	+	0.0142840i	0.317822	−	0.948150i	$-0.397048\pi$
$607$	1.14090	+	0.351920i	0.0463075	+	0.0142840i	−0.271515	+	0.962434i	$0.587525\pi$
$608$	2.80780	−	4.86325i	0.113871	−	0.197231i
$609$	0.614478	−	0.354769i	0.0248999	−	0.0143760i
$610$	−8.03663	+	1.83431i	−0.325394	+	0.0742690i
$611$	−0.511742	+	3.39519i	−0.0207029	+	0.137354i
$612$	0.923593	−	0.995396i	0.0373340	−	0.0402365i
$613$	−35.4916	−	28.3036i	−1.43349	−	1.14317i	−0.965803	−	0.259277i	$-0.916516\pi$
$613$	−35.4916	−	28.3036i	−1.43349	−	1.14317i	−0.467688	−	0.883894i	$-0.654913\pi$
$614$	12.5525	+	18.4111i	0.506576	+	0.743011i
$615$	−1.36284	−	1.46879i	−0.0549549	−	0.0592273i
$616$	−9.74148	−	7.15909i	−0.392495	−	0.288448i
$617$	9.34887	−	23.8205i	0.376371	−	0.958979i	−0.609696	−	0.792635i	$-0.708709\pi$
$617$	9.34887	−	23.8205i	0.376371	−	0.958979i	0.986068	−	0.166344i	$-0.0531962\pi$
$618$	−1.32199	−	0.301735i	−0.0531781	−	0.0121376i
$619$	2.59663	−	0.800956i	0.104368	−	0.0321931i	−0.242132	−	0.970243i	$-0.577847\pi$
$619$	2.59663	−	0.800956i	0.104368	−	0.0321931i	0.346499	+	0.938050i	$0.387370\pi$
$620$	0.439532	−	0.644676i	0.0176520	−	0.0258908i
$621$	0.428870	+	2.84536i	0.0172099	+	0.114181i
$622$	5.84701	+	14.8979i	0.234444	+	0.597353i
$623$	−5.84279	−	12.1327i	−0.234086	−	0.486086i
$624$	−0.123065	+	0.0592650i	−0.00492655	+	0.00237250i
$625$	9.94111	+	25.3295i	0.397644	+	1.01318i
$626$	−2.62464	−	17.4133i	−0.104902	−	0.695977i
$627$	−0.340445	−	1.26033i	−0.0135960	−	0.0503329i
$628$	2.47421	+	8.02119i	0.0987317	+	0.320080i
$629$	0.850946	−	3.72824i	0.0339294	−	0.148655i
$630$	−39.5503	−	15.5224i	−1.57572	−	0.618426i
$631$	−22.8973	+	1.71592i	−0.911529	+	0.0683096i	−0.522233	−	0.852803i	$-0.674901\pi$
$631$	−22.8973	+	1.71592i	−0.911529	+	0.0683096i	−0.389296	+	0.921113i	$0.627282\pi$
$632$	−8.38169	−	9.03332i	−0.333406	−	0.359326i
$633$	0.752519	+	1.10374i	0.0299100	+	0.0438699i
$634$	−17.7427	+	22.2486i	−0.704652	+	0.883605i
$635$	14.3840	+	13.3464i	0.570810	+	0.529635i
$636$	−0.0690272	+	0.457965i	−0.00273711	+	0.0181595i
$637$	11.9428	−	2.72586i	0.473190	−	0.108002i
$638$	−9.05339	−	1.69400i	−0.358427	−	0.0670660i
$639$	21.1328	+	12.2010i	0.836002	+	0.482666i
$640$	1.14712	−	3.71888i	0.0453440	−	0.147002i
$641$	28.9597	−	23.0946i	1.14384	−	0.912182i	0.146807	−	0.989165i	$-0.453100\pi$
$641$	28.9597	−	23.0946i	1.14384	−	0.912182i	0.997032	+	0.0769832i	$0.0245288\pi$
$642$	0.0534546	−	0.713302i	0.00210968	−	0.0281518i
$643$	29.6319	+	14.2700i	1.16857	+	0.562753i	0.914560	−	0.404449i	$-0.132537\pi$
$643$	29.6319	+	14.2700i	1.16857	+	0.562753i	0.254008	+	0.967202i	$0.418251\pi$
$644$	24.9595			0.983542
$645$	1.73662	−	0.429017i	0.0683794	−	0.0168925i
$646$		−	2.54594i		−	0.100169i
$647$	3.10714	−	6.45204i	0.122154	−	0.253656i	−0.830920	−	0.556391i	$-0.812186\pi$
$647$	3.10714	−	6.45204i	0.122154	−	0.253656i	0.953075	+	0.302735i	$0.0978998\pi$
$648$	−0.669268	+	8.93076i	−0.0262913	+	0.350833i
$649$	47.8660	+	1.69389i	1.87890	+	0.0664910i
$650$	−5.82764	+	18.8927i	−0.228579	+	0.741034i
$651$	−0.0443615	−	0.0256121i	−0.00173866	−	0.00100382i
$652$	−10.9072	+	6.29728i	−0.427159	+	0.246621i
$653$	−4.69324	+	1.07120i	−0.183661	+	0.0419194i	−0.313362	−	0.949634i	$-0.601455\pi$
$653$	−4.69324	+	1.07120i	−0.183661	+	0.0419194i	0.129701	+	0.991553i	$0.458598\pi$
$654$	−0.208979	−	0.0314985i	−0.00817172	−	0.00123169i
$655$	−33.3882	+	35.9839i	−1.30458	+	1.40601i
$656$	5.74253	+	4.57951i	0.224208	+	0.178800i
$657$	19.6652	−	13.4075i	0.767214	−	0.523078i
$658$	−4.70803	+	4.36841i	−0.183538	+	0.170298i
$659$	20.3944	−	1.52835i	0.794452	−	0.0595360i	0.328681	−	0.944441i	$-0.393396\pi$
$659$	20.3944	−	1.52835i	0.794452	−	0.0595360i	0.465771	+	0.884905i	$0.345777\pi$
$660$	−0.424384	−	0.799049i	−0.0165191	−	0.0311029i
$661$	5.52604	−	24.2112i	0.214938	−	0.941705i	−0.746219	−	0.665701i	$-0.768133\pi$
$661$	5.52604	−	24.2112i	0.214938	−	0.941705i	0.961157	−	0.276004i	$-0.0890102\pi$
$662$	−4.26998	−	13.8429i	−0.165958	−	0.538021i
$663$	−0.0348845	+	0.0511661i	−0.00135480	+	0.00198713i
$664$	0.284333	+	1.88643i	0.0110343	+	0.0732077i
$665$	−74.1544	+	29.1035i	−2.87558	+	1.12858i
$666$	10.9613	+	22.7614i	0.424742	+	0.881985i
$667$	17.1329	−	8.25078i	0.663389	−	0.319471i
$668$	12.2425	−	4.80481i	0.473675	−	0.185904i
$669$	0.115268	−	0.0173738i	0.00445651	−	0.000671711i
$670$	2.06406	−	3.02742i	0.0797416	−	0.116959i
$671$	2.79621	−	6.44458i	0.107946	−	0.248790i
$672$	−0.249092	−	0.0568537i	−0.00960895	−	0.00219318i
$673$	−9.15171	+	23.3182i	−0.352772	+	0.898849i	0.638809	+	0.769365i	$0.279427\pi$
$673$	−9.15171	+	23.3182i	−0.352772	+	0.898849i	−0.991582	+	0.129484i	$0.958668\pi$
$674$	32.6675	−	2.44809i	1.25831	−	0.0942969i
$675$	−2.89997	−	3.12542i	−0.111620	−	0.120298i
$676$	7.60361	−	5.18405i	0.292446	−	0.199387i
$677$	16.6790	−	20.9148i	0.641027	−	0.803823i	−0.350104	−	0.936711i	$-0.613854\pi$
$677$	16.6790	−	20.9148i	0.641027	−	0.803823i	0.991131	+	0.132888i	$0.0424251\pi$
$678$	0.362659	+	0.336499i	0.0139278	+	0.0129232i
$679$	46.8106	+	7.05556i	1.79642	+	0.270767i
$680$	−0.392619	−	1.72017i	−0.0150562	−	0.0659657i
$681$	−0.981644	+	0.566752i	−0.0376167	+	0.0217180i
$682$	0.220888	+	0.627182i	0.00845824	+	0.0240160i
$683$	−17.2424	−	5.31857i	−0.659762	−	0.203509i	−0.0532464	−	0.998581i	$-0.516957\pi$
$683$	−17.2424	−	5.31857i	−0.659762	−	0.203509i	−0.606515	+	0.795072i	$0.707433\pi$
$684$	10.4866	+	13.1498i	0.400965	+	0.502795i
$685$	2.77929	−	37.0870i	0.106191	−	1.41702i
$686$	−2.34391	−	1.12877i	−0.0894908	−	0.0430965i
$687$			0.412303i			0.0157304i
$688$	−6.06056	+	2.50392i	−0.231057	+	0.0954612i
$689$			12.8755i			0.490516i
$690$	1.68298	+	0.810479i	0.0640699	+	0.0308544i
$691$	−15.2599	−	1.14357i	−0.580515	−	0.0435036i	−0.218763	−	0.975778i	$-0.570202\pi$
$691$	−15.2599	−	1.14357i	−0.580515	−	0.0435036i	−0.361752	+	0.932274i	$0.617821\pi$
$692$	6.02484	−	4.80465i	0.229030	−	0.182646i
$693$	30.6193	−	19.3260i	1.16313	−	0.734135i
$694$	13.0319	−	22.5718i	0.494683	−	0.856816i
$695$	−2.79610	−	4.84299i	−0.106062	−	0.183705i
$696$	−0.189778	+	0.0433156i	−0.00719352	+	0.00164188i
$697$	3.29279	+	0.496308i	0.124723	+	0.0187990i
$698$	−16.3583	−	15.1783i	−0.619170	−	0.574506i
$699$	0.662505	+	0.528330i	0.0250582	+	0.0199833i
$700$	−30.5562	+	20.8329i	−1.15492	+	0.787409i
$701$	7.00421	+	7.54874i	0.264545	+	0.285112i	0.851330	−	0.524631i	$-0.175797\pi$
$701$	7.00421	+	7.54874i	0.264545	+	0.285112i	−0.586784	+	0.809743i	$0.699606\pi$
$702$	−0.0611950	−	0.816591i	−0.00230966	−	0.0308202i
$703$	44.0927	+	17.3051i	1.66299	+	0.652674i
$704$	1.97488	+	2.66455i	0.0744312	+	0.100424i
$705$	−0.459305	+	0.141677i	−0.0172984	+	0.00533586i
$706$	−14.4188	−	9.83056i	−0.542658	−	0.369978i
$707$	8.83478	+	58.6149i	0.332266	+	2.20444i
$708$	0.942279	−	0.369817i	0.0354130	−	0.0138986i
$709$	−8.73958	+	4.20876i	−0.328222	+	0.158063i	−0.590736	−	0.806865i	$-0.701163\pi$
$709$	−8.73958	+	4.20876i	−0.328222	+	0.158063i	0.262514	+	0.964928i	$0.415448\pi$
$710$	28.5677	−	13.7575i	1.07213	−	0.516309i
$711$	34.3568	−	13.4841i	1.28848	−	0.505692i
$712$	0.550624	+	3.65315i	0.0206355	+	0.136908i
$713$	−1.13430	−	0.773351i	−0.0424798	−	0.0289622i
$714$	−0.110689	+	0.0341430i	−0.00414242	+	0.00127777i
$715$	−14.9771	−	20.2074i	−0.560112	−	0.755715i
$716$	14.2398	+	5.58871i	0.532166	+	0.208860i
$717$	−0.00786115	−	0.104900i	−0.000293580	−	0.00391755i
$718$	11.8849	+	12.8089i	0.443540	+	0.478023i
$719$	17.7431	−	12.0971i	0.661708	−	0.451145i	−0.185331	−	0.982676i	$-0.559336\pi$
$719$	17.7431	−	12.0971i	0.661708	−	0.451145i	0.847038	+	0.531532i	$0.178383\pi$
$720$	9.11320	+	7.26753i	0.339629	+	0.270845i
$721$	−51.6898	−	47.9611i	−1.92503	−	1.78617i
$722$	12.3950	+	1.86824i	0.461293	+	0.0695287i
$723$	−0.674574	+	0.153967i	−0.0250877	+	0.00572610i
$724$	9.14062	+	15.8320i	0.339708	+	0.588392i
$725$	−14.0880	+	24.4012i	−0.523216	+	0.906237i
$726$	0.762891	+	0.111827i	0.0283136	+	0.00415029i
$727$	7.11391	−	5.67315i	0.263840	−	0.210406i	−0.482630	−	0.875824i	$-0.660318\pi$
$727$	7.11391	−	5.67315i	0.263840	−	0.210406i	0.746470	+	0.665419i	$0.231747\pi$
$728$	−7.08312	−	0.530806i	−0.262518	−	0.0196730i
$729$	−24.0874	−	11.5999i	−0.892127	−	0.429626i
$730$		−	30.9266i		−	1.14465i
$731$	−1.81195	+	2.35695i	−0.0670174	+	0.0871749i
$732$		−	0.148470i		−	0.00548762i
$733$	2.26453	+	1.09054i	0.0836424	+	0.0402800i	0.475237	−	0.879858i	$-0.342362\pi$
$733$	2.26453	+	1.09054i	0.0836424	+	0.0402800i	−0.391595	+	0.920138i	$0.628077\pi$
$734$	1.53011	−	20.4178i	0.0564772	−	0.753636i
$735$	1.06920	+	1.34073i	0.0394379	+	0.0494536i
$736$	−6.54331	−	2.01835i	−0.241190	−	0.0743972i
$737$	1.03730	+	2.94527i	0.0382093	+	0.108490i
$738$	−19.0515	+	10.9994i	−0.701297	+	0.404894i
$739$	6.36313	+	27.8787i	0.234072	+	1.02553i	0.946225	+	0.323510i	$0.104863\pi$
$739$	6.36313	+	27.8787i	0.234072	+	1.02553i	−0.712153	+	0.702024i	$0.752280\pi$
$740$	32.4601	+	4.89257i	1.19326	+	0.179854i
$741$	−0.562284	−	0.521724i	−0.0206560	−	0.0191660i
$742$	−15.0160	+	18.8295i	−0.551256	+	0.691253i
$743$	−25.4994	+	17.3852i	−0.935481	+	0.637800i	−0.932103	−	0.362194i	$-0.882028\pi$
$743$	−25.4994	+	17.3852i	−0.935481	+	0.637800i	−0.00337817	+	0.999994i	$0.501075\pi$
$744$	0.00955857	+	0.0103017i	0.000350434	+	0.000377678i
$745$	−73.4069	+	5.50109i	−2.68942	+	0.201544i
$746$	4.78081	−	12.1813i	0.175038	−	0.445990i
$747$	−5.57058	−	1.27145i	−0.203817	−	0.0465199i
$748$	1.37941	+	0.598506i	0.0504362	+	0.0218835i
$749$	20.9537	−	30.7334i	0.765630	−	1.12297i
$750$	−1.38810	+	0.209223i	−0.0506864	+	0.00763974i
$751$	−17.2774	+	6.78087i	−0.630460	+	0.247437i	−0.658986	−	0.752156i	$-0.729014\pi$
$751$	−17.2774	+	6.78087i	−0.630460	+	0.247437i	0.0285251	+	0.999593i	$0.490919\pi$
$752$	1.58750	−	0.764498i	0.0578900	−	0.0278784i
$753$	−0.910994	−	1.89170i	−0.0331985	−	0.0689373i
$754$	−5.03752	+	1.97708i	−0.183456	+	0.0720011i
$755$	−10.1844	−	67.5694i	−0.370650	−	2.45910i
$756$	0.862857	−	1.26558i	0.0313818	−	0.0460286i
$757$	2.89794	+	9.39488i	0.105327	+	0.341463i	0.992861	−	0.119281i	$-0.0380589\pi$
$757$	2.89794	+	9.39488i	0.105327	+	0.341463i	−0.887533	+	0.460744i	$0.847583\pi$
$758$	−2.76197	+	12.1010i	−0.100319	+	0.439527i
$759$	−1.40592	+	0.746697i	−0.0510315	+	0.0271034i
$760$	21.7936	−	1.63320i	0.790536	−	0.0592425i
$761$	−28.5164	+	26.4593i	−1.03372	+	0.959150i	−0.999189	−	0.0402535i	$-0.987183\pi$
$761$	−28.5164	+	26.4593i	−1.03372	+	0.959150i	−0.0345286	+	0.999404i	$0.510993\pi$
$762$	−0.292003	+	0.199084i	−0.0105782	+	0.00721207i
$763$	−8.59229	−	6.85212i	−0.311062	−	0.248064i
$764$	14.8346	−	15.9879i	0.536696	−	0.578421i
$765$	5.22554	+	0.787624i	0.188930	+	0.0284766i
$766$	26.1958	−	5.97902i	0.946493	−	0.216031i
$767$	24.3709	−	14.0706i	0.879983	−	0.508058i
$768$	0.0607040	+	0.0350474i	0.00219047	+	0.00126467i
$769$	−14.4833	+	46.9537i	−0.522281	+	1.69319i	0.182022	+	0.983294i	$0.441736\pi$
$769$	−14.4833	+	46.9537i	−0.522281	+	1.69319i	−0.704303	+	0.709899i	$0.748741\pi$
$770$	1.66392	−	47.0191i	0.0599635	−	1.69445i
$771$	0.0111387	−	0.148636i	0.000401151	−	0.00535299i
$772$	5.27264	−	10.9488i	0.189767	−	0.394054i
$773$		−	35.7190i		−	1.28472i	−0.766402	−	0.642362i	$-0.777955\pi$
$773$		−	35.7190i		−	1.28472i	0.766402	−	0.642362i	$-0.222045\pi$
$774$	−0.349428	−	19.6370i	−0.0125599	−	0.705837i
$775$	2.03414			0.0730683
$776$	−11.7012	−	5.63500i	−0.420048	−	0.202285i
$777$	0.161051	−	2.14907i	0.00577766	−	0.0770976i
$778$	5.46162	−	4.35550i	0.195809	−	0.156152i
$779$	−12.1576	+	39.4139i	−0.435591	+	1.41215i
$780$	−0.460367	−	0.265793i	−0.0164838	−	0.00951691i
$781$	−4.96985	+	26.5608i	−0.177835	+	0.950421i
$782$	−3.02662	+	0.690807i	−0.108232	+	0.0247032i
$783$	0.173932	−	1.15396i	0.00621581	−	0.0412392i
$784$	−4.60817	−	4.27576i	−0.164577	−	0.152706i
$785$	−20.3682	+	25.5409i	−0.726972	+	0.911595i
$786$	−0.498043	−	0.730494i	−0.0177646	−	0.0260559i
$787$	9.22688	+	9.94421i	0.328903	+	0.354473i	0.875755	−	0.482757i	$-0.160364\pi$
$787$	9.22688	+	9.94421i	0.328903	+	0.354473i	−0.546852	+	0.837229i	$0.684174\pi$
$788$	6.66880	−	0.499757i	0.237566	−	0.0178031i
$789$	1.09116	+	0.428250i	0.0388465	+	0.0152461i
$790$	10.6717	−	46.7556i	0.379680	−	1.66349i
$791$	7.58300	+	24.5835i	0.269620	+	0.874088i
$792$	−9.58987	+	2.59044i	−0.340761	+	0.0920472i
$793$	−0.615179	−	4.08145i	−0.0218456	−	0.144936i
$794$	5.34749	+	13.6252i	0.189775	+	0.483540i
$795$	−1.62394	+	0.782046i	−0.0575950	+	0.0277363i
$796$	−6.80959	−	14.1403i	−0.241359	−	0.501188i
$797$	−9.49249	−	24.1865i	−0.336241	−	0.856728i	−0.994577	−	0.104004i	$-0.966835\pi$
$797$	−9.49249	−	24.1865i	−0.336241	−	0.856728i	0.658336	−	0.752724i	$-0.271261\pi$
$798$	−0.213842	−	1.41875i	−0.00756994	−	0.0502232i
$799$	0.449997	−	0.660025i	0.0159198	−	0.0233500i
$800$	9.69519	−	2.99057i	0.342777	−	0.105733i
$801$	−10.7877	−	2.46221i	−0.381163	−	0.0869980i
$802$	1.11737	−	2.84700i	0.0394556	−	0.100531i
$803$	21.2377	+	15.6078i	0.749462	+	0.550786i
$804$	0.0448874	+	0.0483771i	0.00158306	+	0.00170613i
$805$	54.7191	+	80.2582i	1.92860	+	2.82873i
$806$	0.305450	+	0.243588i	0.0107590	+	0.00858002i
$807$	0.183853	−	0.198146i	0.00647192	−	0.00697507i
$808$	2.42378	−	16.0808i	0.0852684	−	0.565719i
$809$	−5.90463	+	1.34769i	−0.207596	+	0.0473824i	−0.325054	−	0.945695i	$-0.605382\pi$
$809$	−5.90463	+	1.34769i	−0.207596	+	0.0473824i	0.117458	+	0.993078i	$0.462525\pi$
$810$	−30.1845	+	17.4270i	−1.06057	+	0.612323i
$811$	−21.8487	+	37.8431i	−0.767213	+	1.32885i	0.171856	+	0.985122i	$0.445024\pi$
$811$	−21.8487	+	37.8431i	−0.767213	+	1.32885i	−0.939069	+	0.343730i	$0.888310\pi$
$812$	−9.67282	−	2.98367i	−0.339449	−	0.104706i
$813$	−0.951124	−	1.19267i	−0.0333574	−	0.0418288i
$814$	−19.7414	+	19.8216i	−0.691937	+	0.694747i
$815$	−44.1612	−	21.2669i	−1.54690	−	0.744948i
$816$	0.0317789			0.00111248
$817$	−25.5229	−	26.5440i	−0.892935	−	0.928656i
$818$	19.5638			0.684032
$819$	9.23046	−	19.1672i	0.322538	−	0.669758i
$820$	−2.13616	+	28.5051i	−0.0745979	+	0.995440i
$821$	−11.1135	+	8.86272i	−0.387864	+	0.309311i	−0.797936	−	0.602742i	$-0.794075\pi$
$821$	−11.1135	+	8.86272i	−0.387864	+	0.309311i	0.410072	+	0.912053i	$0.365503\pi$
$822$	0.640088	+	0.197441i	0.0223256	+	0.00688654i
$823$	−16.5266	+	28.6250i	−0.576082	+	0.997804i	0.419841	+	0.907598i	$0.362086\pi$
$823$	−16.5266	+	28.6250i	−0.576082	+	0.997804i	−0.995923	+	0.0902059i	$0.971247\pi$
$824$	9.67250	+	16.7533i	0.336957	+	0.583627i
$825$	1.09792	−	2.08760i	0.0382248	−	0.0726811i
$826$	52.0507	+	7.84537i	1.81107	+	0.272975i
$827$	34.3974	−	37.0716i	1.19612	−	1.28911i	0.248893	−	0.968531i	$-0.419933\pi$
$827$	34.3974	−	37.0716i	1.19612	−	1.28911i	0.947223	−	0.320575i	$-0.103876\pi$
$828$	12.7871	−	16.0345i	0.444383	−	0.557239i
$829$	24.4807	+	35.9067i	0.850251	+	1.24709i	0.967216	+	0.253954i	$0.0817311\pi$
$829$	24.4807	+	35.9067i	0.850251	+	1.24709i	−0.116965	+	0.993136i	$0.537317\pi$
$830$	−5.44254	+	5.04994i	−0.188913	+	0.175286i
$831$	1.60416	−	0.120215i	0.0556478	−	0.00417023i
$832$	1.81397	+	0.711930i	0.0628880	+	0.0246817i
$833$	−2.77855	−	0.634186i	−0.0962710	−	0.0219732i
$834$	0.0962465	−	0.0296881i	0.00333274	−	0.00102802i
$835$	42.2894	+	28.8324i	1.46349	+	0.997787i
$836$	−9.87703	+	15.7902i	−0.341604	+	0.546114i
$837$	−0.0784260	+	0.0307799i	−0.00271080	+	0.00106391i
$838$	8.87381	+	18.4267i	0.306541	+	0.636539i
$839$	5.68872	+	11.8127i	0.196396	+	0.407821i	0.975789	−	0.218715i	$-0.0701865\pi$
$839$	5.68872	+	11.8127i	0.196396	+	0.407821i	−0.779393	+	0.626536i	$0.784472\pi$
$840$	−0.363274	−	0.925608i	−0.0125342	−	0.0319365i
$841$	21.0501	−	3.17279i	0.725865	−	0.109407i
$842$	−20.6959	+	30.3553i	−0.713228	+	1.04611i
$843$	1.26976	−	0.391669i	0.0437329	−	0.0134898i
$844$	4.24079	−	18.5801i	0.145974	−	0.639554i
$845$	33.3390	+	13.0846i	1.14690	+	0.450124i
$846$	0.394373	+	5.26255i	0.0135588	+	0.180930i
$847$	31.4489	+	24.8718i	1.08060	+	0.854605i
$848$	5.45921	−	3.72203i	0.187470	−	0.127815i
$849$	0.0799045	−	0.100197i	0.00274232	−	0.00343876i
$850$	3.12870	−	3.37193i	0.107313	−	0.115656i
$851$	8.60840	−	57.1130i	0.295092	−	1.95781i
$852$	0.127079	+	0.556771i	0.00435366	+	0.0190746i
$853$	22.9391	−	13.2439i	0.785419	−	0.453462i	−0.0529286	−	0.998598i	$-0.516856\pi$
$853$	22.9391	−	13.2439i	0.785419	−	0.453462i	0.838347	+	0.545137i	$0.183522\pi$
$854$	3.86033	−	6.68630i	0.132098	−	0.228800i
$855$	−19.2937	+	62.5486i	−0.659830	+	2.13912i
$856$	−7.97841	+	6.36257i	−0.272696	+	0.217468i
$857$	−35.7878	−	2.68192i	−1.22249	−	0.0916127i	−0.552198	−	0.833713i	$-0.686211\pi$
$857$	−35.7878	−	2.68192i	−1.22249	−	0.0916127i	−0.670289	+	0.742100i	$0.733830\pi$
$858$	0.414857	−	0.182002i	0.0141630	−	0.00621344i
$859$			17.0078i			0.580298i	0.956982	+	0.290149i	$0.0937048\pi$
$859$			17.0078i			0.580298i	−0.956982	+	0.290149i	$0.906295\pi$
$860$	−21.3381	−	13.9986i	−0.727624	−	0.477347i
$861$	1.87663			0.0639553
$862$	10.0723	−	20.9154i	0.343065	−	0.712381i
$863$	−28.6380	−	2.14612i	−0.974849	−	0.0730548i	−0.422230	−	0.906489i	$-0.638752\pi$
$863$	−28.6380	−	2.14612i	−0.974849	−	0.0730548i	−0.552619	+	0.833434i	$0.686372\pi$
$864$	−0.328545	+	0.262006i	−0.0111773	+	0.00891362i
$865$	28.6579	+	8.83980i	0.974399	+	0.300562i
$866$	−9.53723	−	5.50632i	−0.324088	−	0.187112i
$867$	−1.01949	+	0.588603i	−0.0346237	+	0.0199900i
$868$	0.162615	+	0.712462i	0.00551951	+	0.0241825i
$869$	26.7220	+	30.9245i	0.906481	+	1.04904i
$870$	−0.555337	−	0.515278i	−0.0188277	−	0.0174695i
$871$	1.43440	+	1.14390i	0.0486028	+	0.0387595i
$872$	1.69844	+	2.49115i	0.0575163	+	0.0843610i
$873$	28.5144	−	26.4575i	0.965066	−	0.895451i
$874$	−2.87360	−	38.3455i	−0.0972008	−	1.29705i
$875$	−67.9526	−	26.6694i	−2.29722	−	0.901591i
$876$	0.543054	+	0.123949i	0.0183481	+	0.00418783i
$877$	−9.72619	−	31.5315i	−0.328430	−	1.06474i	−0.957751	−	0.287599i	$-0.907143\pi$
$877$	−9.72619	−	31.5315i	−0.328430	−	1.06474i	0.629321	−	0.777146i	$-0.283333\pi$
$878$	3.57536	−	5.24409i	0.120663	−	0.176980i
$879$	1.98817	−	0.299668i	0.0670592	−	0.0101075i
$880$	−4.23840	+	12.1919i	−0.142877	+	0.410987i
$881$	−18.6306	+	8.97202i	−0.627681	+	0.302275i	−0.720550	−	0.693403i	$-0.756110\pi$
$881$	−18.6306	+	8.97202i	−0.627681	+	0.302275i	0.0928691	+	0.995678i	$0.470396\pi$
$882$	16.9634	−	8.16914i	0.571187	−	0.275069i
$883$	4.22908	+	10.7755i	0.142320	+	0.362625i	0.984205	−	0.177031i	$-0.0566494\pi$
$883$	4.22908	+	10.7755i	0.142320	+	0.362625i	−0.841885	+	0.539656i	$0.818554\pi$
$884$	0.873600	−	0.131674i	0.0293823	−	0.00442868i
$885$	3.25494	+	2.21918i	0.109414	+	0.0745969i
$886$	17.2965	−	5.33526i	0.581087	−	0.179242i
$887$	1.48087	−	6.48811i	0.0497227	−	0.217849i	−0.943963	−	0.330052i	$-0.892934\pi$
$887$	1.48087	−	6.48811i	0.0497227	−	0.217849i	0.993685	+	0.112203i	$0.0357907\pi$
$888$	−0.216005	+	0.550372i	−0.00724866	+	0.0184693i
$889$	−18.3266	+	1.37339i	−0.614654	+	0.0460619i
$890$	−10.5397	+	9.77941i	−0.353292	+	0.327807i
$891$	3.26586	−	29.5230i	0.109411	−	0.989056i
$892$	−1.30021	−	1.03688i	−0.0435342	−	0.0347174i
$893$	7.25327	+	6.73005i	0.242721	+	0.225212i
$894$	0.197606	−	1.31103i	0.00660894	−	0.0438475i
$895$	13.2474	+	58.0408i	0.442813	+	1.94009i
$896$	1.82252	+	3.15669i	0.0608860	+	0.105458i
$897$	−0.467659	+	0.810009i	−0.0156147	+	0.0270454i
$898$	−4.08871	+	13.2553i	−0.136442	+	0.442334i
$899$	0.347140	+	0.435300i	0.0115778	+	0.0145181i
$900$	−2.27090	+	30.3030i	−0.0756966	+	1.01010i
$901$	1.29972	−	2.69890i	0.0432999	−	0.0899132i
$902$	−18.4967	−	15.8526i	−0.615874	−	0.527834i
$903$	−0.811760	+	1.46563i	−0.0270137	+	0.0487730i
$904$		−	7.05794i		−	0.234744i
$905$	−30.8693	+	64.1008i	−1.02613	+	2.13078i
$906$	1.22730	+	0.0919732i	0.0407742	+	0.00305561i
$907$	6.66360	+	8.35589i	0.221261	+	0.277453i	0.880056	−	0.474870i	$-0.157505\pi$
$907$	6.66360	+	8.35589i	0.221261	+	0.277453i	−0.658795	+	0.752323i	$0.728933\pi$
$908$	15.4526	+	4.76649i	0.512812	+	0.158181i
$909$	42.1817	+	24.3536i	1.39908	+	0.807759i
$910$	−13.8216	−	23.9397i	−0.458182	−	0.793594i
$911$	−39.8431	+	9.09392i	−1.32006	+	0.301295i	−0.823801	−	0.566880i	$-0.808150\pi$
$911$	−39.8431	+	9.09392i	−1.32006	+	0.301295i	−0.496259	+	0.868175i	$0.665293\pi$
$912$	−0.0586667	+	0.389228i	−0.00194265	+	0.0128886i
$913$	−0.721167	−	6.28602i	−0.0238671	−	0.208037i
$914$	14.0231	−	17.5844i	0.463844	−	0.581642i
$915$	0.477412	−	0.325494i	0.0157828	−	0.0107605i
$916$	4.31187	−	4.00083i	0.142468	−	0.132191i
$917$	−3.43575	−	45.8470i	−0.113459	−	1.51400i
$918$	−0.0696037	+	0.177347i	−0.00229726	+	0.00585333i
$919$	−51.2174	−	11.6900i	−1.68951	−	0.385619i	−0.733668	−	0.679508i	$-0.762193\pi$
$919$	−51.2174	−	11.6900i	−1.68951	−	0.385619i	−0.955840	+	0.293889i	$0.905050\pi$
$920$	−7.85495	−	25.4651i	−0.258970	−	0.839561i
$921$	−1.29052	−	0.879864i	−0.0425242	−	0.0289925i
$922$	−3.17871	−	21.0894i	−0.104685	−	0.694542i
$923$	5.80036	+	14.7791i	0.190921	+	0.486459i
$924$	0.818961	+	0.217662i	0.0269418	+	0.00716055i
$925$	37.1317	+	77.1048i	1.22088	+	2.53519i
$926$	−15.1333	+	5.93938i	−0.497311	+	0.195180i
$927$	−57.2928	+	8.63550i	−1.88174	+	0.283627i
$928$	2.29453	+	1.56438i	0.0753215	+	0.0513533i
$929$	3.24387	+	10.5164i	0.106428	+	0.345031i	0.993085	−	0.117397i	$-0.0374549\pi$
$929$	3.24387	+	10.5164i	0.106428	+	0.345031i	−0.886657	+	0.462427i	$0.846979\pi$
$930$	−0.0121701	+	0.0533205i	−0.000399072	+	0.00174845i
$931$	12.8970	−	32.8610i	0.422682	−	1.07698i
$932$	−0.903410	−	12.0552i	−0.0295922	−	0.394880i
$933$	−0.763029	−	0.822349i	−0.0249804	−	0.0269225i
$934$	−9.12085	−	13.3778i	−0.298443	−	0.437736i
$935$	1.09958	+	5.74766i	0.0359603	+	0.187969i
$936$	−3.96979	+	4.27841i	−0.129757	+	0.139844i
$937$	29.3099	+	4.41775i	0.957512	+	0.144322i	0.609165	−	0.793044i	$-0.291505\pi$
$937$	29.3099	+	4.41775i	0.957512	+	0.144322i	0.348348	+	0.937365i	$0.386743\pi$
$938$	0.763645	+	3.34575i	0.0249339	+	0.109243i
$939$	0.617187	+	1.06900i	0.0201411	+	0.0348855i
$940$	5.93857	+	3.42863i	0.193695	+	0.111830i
$941$	−13.0636	+	42.3511i	−0.425860	+	1.38061i	0.447828	+	0.894120i	$0.352198\pi$
$941$	−13.0636	+	42.3511i	−0.425860	+	1.38061i	−0.873688	+	0.486486i	$0.838279\pi$
$942$	−0.366852	−	0.460018i	−0.0119527	−	0.0149882i
$943$	50.1543	+	3.75854i	1.63325	+	0.122395i
$944$	−13.0110	−	6.26579i	−0.423474	−	0.203934i
$945$	5.96117			0.193917
$946$	20.3817	−	7.58850i	0.662667	−	0.246724i
$947$	19.2276			0.624812			0.312406	−	0.949949i	$-0.398865\pi$
$947$	19.2276			0.624812			0.312406	+	0.949949i	$0.398865\pi$
$948$	0.778231	+	0.374776i	0.0252758	+	0.0121722i
$949$	15.4421	+	1.15723i	0.501272	+	0.0375652i
$950$	35.5237	+	44.5453i	1.15254	+	1.44524i
$951$	0.587946	−	1.90608i	0.0190655	−	0.0618087i
$952$	1.43115	+	0.826273i	0.0463837	+	0.0267797i
$953$	22.1598	+	38.3819i	0.717826	+	1.24331i	0.961859	+	0.273545i	$0.0881961\pi$
$953$	22.1598	+	38.3819i	0.717826	+	1.24331i	−0.244033	+	0.969767i	$0.578471\pi$
$954$	4.40357	+	19.2933i	0.142571	+	0.624643i
$955$	83.9318	+	12.6507i	2.71597	+	0.409366i
$956$	−1.02076	+	1.10012i	−0.0330137	+	0.0355803i
$957$	0.634110	−	0.121312i	0.0204979	−	0.00392145i
$958$	−7.62330	−	11.1813i	−0.246297	−	0.361252i
$959$	23.6925	+	25.5344i	0.765070	+	0.824549i
$960$	0.0203859	+	0.272031i	0.000657952	+	0.00877976i
$961$	−11.3109	+	28.8197i	−0.364867	+	0.929667i
$962$	−3.65754	+	16.0247i	−0.117924	+	0.516658i
$963$	−9.00894	−	29.2063i	−0.290309	−	0.941159i
$964$	8.15599	+	5.56066i	0.262687	+	0.179097i
$965$	46.7654	−	7.04876i	1.50543	−	0.226908i
$966$	−1.62859	+	0.639176i	−0.0523991	+	0.0205651i
$967$	−16.1899	−	33.6188i	−0.520634	−	1.08111i	−0.981113	−	0.193436i	$-0.938037\pi$
$967$	−16.1899	−	33.6188i	−0.520634	−	1.08111i	0.460479	−	0.887670i	$-0.347678\pi$
$968$	−6.23331	−	9.06344i	−0.200346	−	0.291310i
$969$	0.0651978	+	0.166121i	0.00209445	+	0.00533658i
$970$	−7.53317	−	49.9793i	−0.241876	−	1.60474i
$971$	−16.6932	−	11.3812i	−0.535711	−	0.365241i	0.265042	−	0.964237i	$-0.414614\pi$
$971$	−16.6932	−	11.3812i	−0.535711	−	0.365241i	−0.800752	+	0.598996i	$0.795567\pi$
$972$	−0.556625	−	1.80453i	−0.0178537	−	0.0578804i
$973$	5.10633	+	1.16549i	0.163702	+	0.0373638i
$974$	5.51149	−	14.0430i	0.176599	−	0.449968i
$975$	−0.103565	−	1.38198i	−0.00331674	−	0.0442588i
$976$	−1.55270	+	1.44070i	−0.0497008	+	0.0461156i
$977$	−10.4867	+	7.14969i	−0.335498	+	0.228739i	−0.719337	−	0.694661i	$-0.755554\pi$
$977$	−10.4867	+	7.14969i	−0.335498	+	0.228739i	0.383839	+	0.923400i	$0.374602\pi$
$978$	0.550426	−	0.690212i	0.0176007	−	0.0220706i
$979$	−1.39657	−	12.1731i	−0.0446346	−	0.389055i
$980$	3.64629	−	24.1916i	0.116476	−	0.772771i
$981$	−8.80392	+	2.00944i	−0.281088	+	0.0641564i
$982$	−2.85958	−	4.95293i	−0.0912528	−	0.158054i
$983$	33.5969	+	19.3972i	1.07157	+	0.618674i	0.928611	−	0.371054i	$-0.121004\pi$
$983$	33.5969	+	19.3972i	1.07157	+	0.618674i	0.142963	+	0.989728i	$0.454337\pi$
$984$	−0.491972	−	0.151753i	−0.0156835	−	0.00483771i
$985$	16.2271	+	20.3482i	0.517039	+	0.648346i
$986$	1.25552	+	0.0940881i	0.0399839	+	0.00299638i
$987$	0.195328	−	0.405602i	0.00621735	−	0.0129105i
$988$			10.9430i			0.348142i
$989$	−24.6303	+	37.5441i	−0.783197	+	1.19383i
$990$	−29.3537	−	25.1575i	−0.932922	−	0.799559i
$991$	3.60260	−	7.48087i	0.114440	−	0.237638i	−0.835880	−	0.548913i	$-0.815042\pi$
$991$	3.60260	−	7.48087i	0.114440	−	0.237638i	0.950320	+	0.311275i	$0.100756\pi$
$992$	0.0149825	−	0.199927i	0.000475694	−	0.00634769i
$993$	0.633112	+	0.793897i	0.0200912	+	0.0251936i
$994$	−8.75348	+	28.3781i	−0.277643	+	0.900098i
$995$	30.5398	−	52.8964i	0.968176	−	1.67693i
$996$	−0.0668613	−	0.115807i	−0.00211858	−	0.00366949i
$997$	3.62620	+	15.8874i	0.114843	+	0.503159i	0.999330	+	0.0365952i	$0.0116512\pi$
$997$	3.62620	+	15.8874i	0.114843	+	0.503159i	−0.884487	+	0.466564i	$0.845492\pi$
$998$	−5.22467	+	34.6634i	−0.165384	+	1.09725i
$999$	−2.59834	−	2.41091i	−0.0822078	−	0.0762777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.w.b.175.11	yes	264
11.10	odd	2		946.2.w.a.175.11	✓	264
43.29	odd	42		946.2.w.a.373.11	yes	264
473.373	even	42	inner	946.2.w.b.373.11	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.w.a.175.11	✓	264	11.10	odd	2
946.2.w.a.373.11	yes	264	43.29	odd	42
946.2.w.b.175.11	yes	264	1.1	even	1	trivial
946.2.w.b.373.11	yes	264	473.373	even	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.w (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 + 0.433884i) q^{2} +(-0.0698989 - 0.00523820i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-1.14712 + 3.71888i) q^{5} +(-0.0607040 - 0.0350474i) q^{6} +(-1.82252 - 3.15669i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-2.96163 - 0.446395i) q^{9} +O(q^{10})\)	\(q+(0.900969 + 0.433884i) q^{2} +(-0.0698989 - 0.00523820i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-1.14712 + 3.71888i) q^{5} +(-0.0607040 - 0.0350474i) q^{6} +(-1.82252 - 3.15669i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-2.96163 - 0.446395i) q^{9} +(-2.64708 + 2.85288i) q^{10} +(-0.623202 - 3.25755i) q^{11} +(-0.0394859 - 0.0579151i) q^{12} +(-1.32543 - 1.42848i) q^{13} +(-0.272394 - 3.63484i) q^{14} +(0.0996628 - 0.253937i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(0.133633 + 0.433227i) q^{17} +(-2.47466 - 1.68719i) q^{18} +(-5.55288 + 0.836962i) q^{19} +(-3.62276 + 1.42183i) q^{20} +(0.110857 + 0.230196i) q^{21} +(0.851912 - 3.20535i) q^{22} +(2.50168 + 6.37419i) q^{23} +(-0.0104471 - 0.0693120i) q^{24} +(-8.38297 - 5.71542i) q^{25} +(-0.574381 - 1.86210i) q^{26} +(0.409689 + 0.0935088i) q^{27} +(1.33168 - 3.39307i) q^{28} +(-0.207531 - 2.76931i) q^{29} +(0.199972 - 0.185547i) q^{30} +(-0.165651 + 0.112939i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(0.0264974 + 0.230963i) q^{33} +(-0.0675712 + 0.448305i) q^{34} +(13.8300 - 3.15661i) q^{35} +(-1.49754 - 2.59382i) q^{36} +(-7.30483 - 4.21744i) q^{37} +(-5.36612 - 1.65523i) q^{38} +(0.0851637 + 0.106792i) q^{39} +(-3.88090 - 0.290833i) q^{40} +(3.18686 - 6.61759i) q^{41} +0.255498i q^{42} +(3.78975 + 5.35143i) q^{43} +(2.15829 - 2.51829i) q^{44} +(5.05744 - 10.5019i) q^{45} +(-0.511717 + 6.82838i) q^{46} +(-1.09858 - 1.37758i) q^{47} +(0.0206608 - 0.0669808i) q^{48} +(-3.14314 + 5.44408i) q^{49} +(-5.07297 - 8.78665i) q^{50} +(-0.00707146 - 0.0309821i) q^{51} +(0.290434 - 1.92691i) q^{52} +(-4.84350 - 4.49411i) q^{53} +(0.328545 + 0.262006i) q^{54} +(12.8293 + 1.41919i) q^{55} +(2.67200 - 2.47925i) q^{56} +(0.392524 - 0.0294156i) q^{57} +(1.01458 - 2.58511i) q^{58} +(-3.21346 + 14.0791i) q^{59} +(0.260674 - 0.0804074i) q^{60} +(1.75008 + 1.19319i) q^{61} +(-0.198248 + 0.0298811i) q^{62} +(3.98850 + 10.1625i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(6.83277 - 3.29049i) q^{65} +(-0.0763379 + 0.219588i) q^{66} +(-0.930981 + 0.140323i) q^{67} +(-0.255392 + 0.374591i) q^{68} +(-0.141476 - 0.458653i) q^{69} +(13.8300 + 3.15661i) q^{70} +(-7.58417 - 2.97657i) q^{71} +(-0.223823 - 2.98671i) q^{72} +(-5.82531 + 5.40510i) q^{73} +(-4.75154 - 6.96923i) q^{74} +(0.556022 + 0.443413i) q^{75} +(-4.11653 - 3.81958i) q^{76} +(-9.14728 + 7.90419i) q^{77} +(0.0303946 + 0.133167i) q^{78} +(-10.6719 + 6.16145i) q^{79} +(-3.37038 - 1.94589i) q^{80} +(8.55792 + 2.63977i) q^{81} +(5.74253 - 4.57951i) q^{82} +(1.90240 + 0.142565i) q^{83} +(-0.110857 + 0.230196i) q^{84} -1.76441 q^{85} +(1.09254 + 6.46578i) q^{86} +0.194659i q^{87} +(3.03720 - 1.33245i) q^{88} +(3.68408 + 0.276084i) q^{89} +(9.11320 - 7.26753i) q^{90} +(-2.09364 + 6.78741i) q^{91} +(-3.42377 + 5.93014i) q^{92} +(0.0121704 - 0.00702658i) q^{93} +(-0.392079 - 1.71781i) q^{94} +(3.25727 - 21.6106i) q^{95} +(0.0476766 - 0.0513832i) q^{96} +(-8.09747 + 10.1539i) q^{97} +(-5.19397 + 3.54119i) q^{98} +(0.391544 + 9.92586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 44 q^{2} - 44 q^{4} + 44 q^{8} - 20 q^{9}+O(q^{10}) \) 264 * q + 44 * q^2 - 44 * q^4 + 44 * q^8 - 20 * q^9	\( 264 q + 44 q^{2} - 44 q^{4} + 44 q^{8} - 20 q^{9} + 5 q^{11} - 7 q^{13} - 32 q^{15} - 44 q^{16} - q^{17} + 20 q^{18} - 21 q^{19} + 9 q^{22} - q^{23} - 7 q^{24} - 14 q^{25} - 7 q^{26} - 11 q^{29} + 4 q^{30} + 5 q^{31} + 44 q^{32} - 122 q^{33} + 15 q^{34} + 134 q^{36} - 72 q^{37} - 28 q^{38} + 86 q^{39} + 14 q^{40} - 28 q^{41} + 45 q^{43} - 9 q^{44} + 98 q^{45} - 6 q^{46} + 6 q^{47} - 140 q^{49} - 140 q^{50} + 7 q^{51} - 12 q^{53} + 42 q^{54} + 52 q^{55} - 2 q^{57} - 3 q^{58} + 44 q^{59} - 4 q^{60} + 71 q^{61} + 2 q^{62} - 24 q^{63} - 44 q^{64} - 68 q^{65} - 67 q^{66} + 25 q^{67} + 27 q^{68} + 74 q^{69} + 47 q^{71} + 20 q^{72} - 57 q^{73} + 2 q^{74} - 28 q^{75} + 28 q^{76} + 89 q^{77} + 12 q^{78} - 42 q^{79} + 99 q^{81} - 28 q^{82} - 44 q^{83} + 12 q^{85} - 17 q^{86} - 12 q^{88} - 69 q^{89} - 8 q^{92} + 84 q^{93} - 27 q^{94} - 12 q^{95} - 82 q^{97} - 14 q^{98} + 189 q^{99}+O(q^{100}) \) 264 * q + 44 * q^2 - 44 * q^4 + 44 * q^8 - 20 * q^9 + 5 * q^11 - 7 * q^13 - 32 * q^15 - 44 * q^16 - q^17 + 20 * q^18 - 21 * q^19 + 9 * q^22 - q^23 - 7 * q^24 - 14 * q^25 - 7 * q^26 - 11 * q^29 + 4 * q^30 + 5 * q^31 + 44 * q^32 - 122 * q^33 + 15 * q^34 + 134 * q^36 - 72 * q^37 - 28 * q^38 + 86 * q^39 + 14 * q^40 - 28 * q^41 + 45 * q^43 - 9 * q^44 + 98 * q^45 - 6 * q^46 + 6 * q^47 - 140 * q^49 - 140 * q^50 + 7 * q^51 - 12 * q^53 + 42 * q^54 + 52 * q^55 - 2 * q^57 - 3 * q^58 + 44 * q^59 - 4 * q^60 + 71 * q^61 + 2 * q^62 - 24 * q^63 - 44 * q^64 - 68 * q^65 - 67 * q^66 + 25 * q^67 + 27 * q^68 + 74 * q^69 + 47 * q^71 + 20 * q^72 - 57 * q^73 + 2 * q^74 - 28 * q^75 + 28 * q^76 + 89 * q^77 + 12 * q^78 - 42 * q^79 + 99 * q^81 - 28 * q^82 - 44 * q^83 + 12 * q^85 - 17 * q^86 - 12 * q^88 - 69 * q^89 - 8 * q^92 + 84 * q^93 - 27 * q^94 - 12 * q^95 - 82 * q^97 - 14 * q^98 + 189 * q^99

Introduction

L-functions

Modular forms

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