LMFDB - Embedded newform 285.2.bi.a.23.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(17,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("285.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.bi (of order $36$, 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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$36$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.32
Character	$\chi$	$=$	285.23
Dual form			285.2.bi.a.62.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01578 + 2.17835i) q^{2} +(0.586022 + 1.62990i) q^{3} +(-2.42782 + 2.89336i) q^{4} +(-2.00549 - 0.988948i) q^{5} +(-2.95522 + 2.93218i) q^{6} +(0.104229 + 0.388987i) q^{7} +(-4.12559 - 1.10545i) q^{8} +(-2.31316 + 1.91032i) q^{9} +O(q^{10})$	\(q+(1.01578 + 2.17835i) q^{2} +(0.586022 + 1.62990i) q^{3} +(-2.42782 + 2.89336i) q^{4} +(-2.00549 - 0.988948i) q^{5} +(-2.95522 + 2.93218i) q^{6} +(0.104229 + 0.388987i) q^{7} +(-4.12559 - 1.10545i) q^{8} +(-2.31316 + 1.91032i) q^{9} +(0.117137 - 5.37321i) q^{10} +(-0.205194 + 0.118469i) q^{11} +(-6.13864 - 2.26153i) q^{12} +(4.48384 - 3.13962i) q^{13} +(-0.741475 + 0.622172i) q^{14} +(0.436627 - 3.84829i) q^{15} +(-0.470898 - 2.67059i) q^{16} +(1.88803 + 4.04888i) q^{17} +(-6.51099 - 3.09840i) q^{18} +(0.558094 + 4.32302i) q^{19} +(7.73034 - 3.40161i) q^{20} +(-0.572930 + 0.397837i) q^{21} +(-0.466498 - 0.326645i) q^{22} +(-0.128117 + 0.0112087i) q^{23} +(-0.615914 - 7.37211i) q^{24} +(3.04397 + 3.96665i) q^{25} +(11.3938 + 6.57821i) q^{26} +(-4.46919 - 2.65073i) q^{27} +(-1.37853 - 0.642818i) q^{28} +(-3.78163 + 1.37640i) q^{29} +(8.82644 - 2.95789i) q^{30} +(4.23074 - 7.32785i) q^{31} +(-1.65824 + 1.16111i) q^{32} +(-0.313340 - 0.265020i) q^{33} +(-6.90206 + 8.22555i) q^{34} +(0.175658 - 0.883185i) q^{35} +(0.0886901 - 11.3307i) q^{36} +(5.80116 - 5.80116i) q^{37} +(-8.85015 + 5.60697i) q^{38} +(7.74490 + 5.46833i) q^{39} +(7.18058 + 6.29695i) q^{40} +(7.51153 - 1.32449i) q^{41} +(-1.44860 - 0.843925i) q^{42} +(-5.29284 - 0.463063i) q^{43} +(0.155400 - 0.881319i) q^{44} +(6.52821 - 1.54352i) q^{45} +(-0.154555 - 0.267697i) q^{46} +(-7.11624 - 3.31836i) q^{47} +(4.07685 - 2.33254i) q^{48} +(5.92173 - 3.41891i) q^{49} +(-5.54874 + 10.6601i) q^{50} +(-5.49286 + 5.45003i) q^{51} +(-1.80190 + 20.5958i) q^{52} +(0.604662 - 0.0529010i) q^{53} +(1.23450 - 12.4280i) q^{54} +(0.528673 - 0.0346616i) q^{55} -1.72002i q^{56} +(-6.71905 + 3.44302i) q^{57} +(-6.83959 - 6.83959i) q^{58} +(-3.38507 - 1.23206i) q^{59} +(10.0744 + 10.6063i) q^{60} +(4.41801 + 3.70715i) q^{61} +(20.2601 + 1.77253i) q^{62} +(-0.984185 - 0.700678i) q^{63} +(-8.91067 - 5.14458i) q^{64} +(-12.0972 + 1.86219i) q^{65} +(0.259022 - 0.951767i) q^{66} +(-0.495644 + 1.06291i) q^{67} +(-16.2986 - 4.36721i) q^{68} +(-0.0933483 - 0.202249i) q^{69} +(2.10232 - 0.514478i) q^{70} +(0.164561 + 0.196117i) q^{71} +(11.6549 - 5.32410i) q^{72} +(-1.25246 + 1.78870i) q^{73} +(18.5296 + 6.74424i) q^{74} +(-4.68141 + 7.28590i) q^{75} +(-13.8630 - 8.88074i) q^{76} +(-0.0674699 - 0.0674699i) q^{77} +(-4.04482 + 22.4257i) q^{78} +(9.95696 - 1.75568i) q^{79} +(-1.69670 + 5.82154i) q^{80} +(1.70139 - 8.83772i) q^{81} +(10.5153 + 15.0174i) q^{82} +(-2.48613 - 9.27835i) q^{83} +(0.239882 - 2.62357i) q^{84} +(0.217721 - 9.98715i) q^{85} +(-4.36765 - 12.0000i) q^{86} +(-4.45952 - 5.35709i) q^{87} +(0.977505 - 0.261922i) q^{88} +(-0.817749 + 4.63769i) q^{89} +(9.99356 + 12.6528i) q^{90} +(1.68862 + 1.41692i) q^{91} +(0.278612 - 0.397900i) q^{92} +(14.4230 + 2.60140i) q^{93} -18.8724i q^{94} +(3.15599 - 9.22170i) q^{95} +(-2.86426 - 2.02233i) q^{96} +(-5.84597 + 2.72602i) q^{97} +(13.4628 + 9.42673i) q^{98} +(0.248333 - 0.666022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	1.01578	+	2.17835i	0.718265	+	1.54032i	0.836881	+	0.547385i	$0.184377\pi$
$2$	1.01578	+	2.17835i	0.718265	+	1.54032i	−0.118616	+	0.992940i	$0.537846\pi$
$3$	0.586022	+	1.62990i	0.338340	+	0.941024i
$3$	0.586022	+	1.62990i	0.338340	+	0.941024i
$4$	−2.42782	+	2.89336i	−1.21391	+	1.44668i
$5$	−2.00549	−	0.988948i	−0.896882	−	0.442271i
$5$	−2.00549	−	0.988948i	−0.896882	−	0.442271i
$6$	−2.95522	+	2.93218i	−1.20646	+	1.19706i
$7$	0.104229	+	0.388987i	0.0393948	+	0.147023i	0.982822	−	0.184557i	$-0.0590850\pi$
$7$	0.104229	+	0.388987i	0.0393948	+	0.147023i	−0.943427	+	0.331580i	$0.892418\pi$
$8$	−4.12559	−	1.10545i	−1.45861	−	0.390835i
$9$	−2.31316	+	1.91032i	−0.771052	+	0.636772i
$10$	0.117137	−	5.37321i	0.0370419	−	1.69916i
$11$	−0.205194	+	0.118469i	−0.0618683	+	0.0357197i	−0.530615	−	0.847613i	$-0.678039\pi$
$11$	−0.205194	+	0.118469i	−0.0618683	+	0.0357197i	0.468747	+	0.883333i	$0.344706\pi$
$12$	−6.13864	−	2.26153i	−1.77207	−	0.652847i
$13$	4.48384	−	3.13962i	1.24359	−	0.870774i	0.248396	−	0.968658i	$-0.420096\pi$
$13$	4.48384	−	3.13962i	1.24359	−	0.870774i	0.995198	+	0.0978845i	$0.0312076\pi$
$14$	−0.741475	+	0.622172i	−0.198168	+	0.166282i
$15$	0.436627	−	3.84829i	0.112737	−	0.993625i
$16$	−0.470898	−	2.67059i	−0.117724	−	0.667648i
$17$	1.88803	+	4.04888i	0.457913	+	0.981998i	0.990740	+	0.135774i	$0.0433521\pi$
$17$	1.88803	+	4.04888i	0.457913	+	0.981998i	−0.532826	+	0.846225i	$0.678870\pi$
$18$	−6.51099	−	3.09840i	−1.53466	−	0.730300i
$19$	0.558094	+	4.32302i	0.128036	+	0.991770i
$19$	0.558094	+	4.32302i	0.128036	+	0.991770i
$20$	7.73034	−	3.40161i	1.72856	−	0.760624i
$21$	−0.572930	+	0.397837i	−0.125024	+	0.0868152i
$22$	−0.466498	−	0.326645i	−0.0994577	−	0.0696410i
$23$	−0.128117	+	0.0112087i	−0.0267141	+	0.00233718i	−0.100505	−	0.994937i	$-0.532046\pi$
$23$	−0.128117	+	0.0112087i	−0.0267141	+	0.00233718i	0.0737908	+	0.997274i	$0.476490\pi$
$24$	−0.615914	−	7.37211i	−0.125723	−	1.50483i
$25$	3.04397	+	3.96665i	0.608793	+	0.793329i
$26$	11.3938	+	6.57821i	2.23451	+	1.29009i
$27$	−4.46919	−	2.65073i	−0.860095	−	0.510133i
$28$	−1.37853	−	0.642818i	−0.260517	−	0.121481i
$29$	−3.78163	+	1.37640i	−0.702231	+	0.255591i	−0.668363	−	0.743835i	$-0.733005\pi$
$29$	−3.78163	+	1.37640i	−0.702231	+	0.255591i	−0.0338681	+	0.999426i	$0.510783\pi$
$30$	8.82644	−	2.95789i	1.61148	−	0.540035i
$31$	4.23074	−	7.32785i	0.759863	−	1.31612i	−0.183057	−	0.983102i	$-0.558599\pi$
$31$	4.23074	−	7.32785i	0.759863	−	1.31612i	0.942920	−	0.333019i	$-0.108067\pi$
$32$	−1.65824	+	1.16111i	−0.293138	+	0.205258i
$33$	−0.313340	−	0.265020i	−0.0545456	−	0.0461341i
$34$	−6.90206	+	8.22555i	−1.18369	+	1.41067i
$35$	0.175658	−	0.883185i	0.0296917	−	0.149286i
$36$	0.0886901	−	11.3307i	0.0147817	−	1.88845i
$37$	5.80116	−	5.80116i	0.953704	−	0.953704i	−0.0452704	−	0.998975i	$-0.514415\pi$
$37$	5.80116	−	5.80116i	0.953704	−	0.953704i	0.998975	+	0.0452704i	$0.0144149\pi$
$38$	−8.85015	+	5.60697i	−1.43568	+	0.909570i
$39$	7.74490	+	5.46833i	1.24018	+	0.875634i
$40$	7.18058	+	6.29695i	1.13535	+	0.995635i
$41$	7.51153	−	1.32449i	1.17310	−	0.206850i	0.447064	−	0.894502i	$-0.352470\pi$
$41$	7.51153	−	1.32449i	1.17310	−	0.206850i	0.726041	+	0.687652i	$0.241358\pi$
$42$	−1.44860	−	0.843925i	−0.223524	−	0.130221i
$43$	−5.29284	−	0.463063i	−0.807150	−	0.0706165i	−0.323892	−	0.946094i	$-0.604991\pi$
$43$	−5.29284	−	0.463063i	−0.807150	−	0.0706165i	−0.483258	+	0.875478i	$0.660547\pi$
$44$	0.155400	−	0.881319i	0.0234275	−	0.132864i
$45$	6.52821	−	1.54352i	0.973168	−	0.230095i
$46$	−0.154555	−	0.267697i	−0.0227879	−	0.0394697i
$47$	−7.11624	−	3.31836i	−1.03801	−	0.484032i	−0.172545	−	0.985002i	$-0.555199\pi$
$47$	−7.11624	−	3.31836i	−1.03801	−	0.484032i	−0.865465	+	0.500970i	$0.832977\pi$
$48$	4.07685	−	2.33254i	0.588442	−	0.336674i
$49$	5.92173	−	3.41891i	0.845962	−	0.488416i
$50$	−5.54874	+	10.6601i	−0.784710	+	1.50756i
$51$	−5.49286	+	5.45003i	−0.769154	+	0.763157i
$52$	−1.80190	+	20.5958i	−0.249878	+	2.85612i
$53$	0.604662	−	0.0529010i	0.0830566	−	0.00726652i	−0.0455517	−	0.998962i	$-0.514505\pi$
$53$	0.604662	−	0.0529010i	0.0830566	−	0.00726652i	0.128608	+	0.991695i	$0.458949\pi$
$54$	1.23450	−	12.4280i	0.167994	−	1.69124i
$55$	0.528673	−	0.0346616i	0.0712863	−	0.00467377i
$56$		−	1.72002i		−	0.229847i
$57$	−6.71905	+	3.44302i	−0.889959	+	0.456040i
$58$	−6.83959	−	6.83959i	−0.898082	−	0.898082i
$59$	−3.38507	−	1.23206i	−0.440698	−	0.160401i	0.112135	−	0.993693i	$-0.464231\pi$
$59$	−3.38507	−	1.23206i	−0.440698	−	0.160401i	−0.552833	+	0.833292i	$0.686453\pi$
$60$	10.0744	+	10.6063i	1.30060	+	1.36926i
$61$	4.41801	+	3.70715i	0.565668	+	0.474652i	0.880205	−	0.474594i	$-0.157405\pi$
$61$	4.41801	+	3.70715i	0.565668	+	0.474652i	−0.314537	+	0.949245i	$0.601849\pi$
$62$	20.2601	+	1.77253i	2.57304	+	0.225112i
$63$	−0.984185	−	0.700678i	−0.123996	−	0.0882771i
$64$	−8.91067	−	5.14458i	−1.11383	−	0.643073i
$65$	−12.0972	+	1.86219i	−1.50047	+	0.230976i
$66$	0.259022	−	0.951767i	0.0318834	−	0.117154i
$67$	−0.495644	+	1.06291i	−0.0605525	+	0.129855i	−0.934255	−	0.356605i	$-0.883934\pi$
$67$	−0.495644	+	1.06291i	−0.0605525	+	0.129855i	0.873703	+	0.486460i	$0.161712\pi$
$68$	−16.2986	−	4.36721i	−1.97650	−	0.529602i
$69$	−0.0933483	−	0.202249i	−0.0112378	−	0.0243479i
$70$	2.10232	−	0.514478i	0.251275	−	0.0614918i
$71$	0.164561	+	0.196117i	0.0195299	+	0.0232748i	0.775721	−	0.631076i	$-0.217386\pi$
$71$	0.164561	+	0.196117i	0.0195299	+	0.0232748i	−0.756191	+	0.654351i	$0.772942\pi$
$72$	11.6549	−	5.32410i	1.37354	−	0.627451i
$73$	−1.25246	+	1.78870i	−0.146590	+	0.209352i	−0.885731	−	0.464198i	$-0.846342\pi$
$73$	−1.25246	+	1.78870i	−0.146590	+	0.209352i	0.739142	+	0.673550i	$0.235231\pi$
$74$	18.5296	+	6.74424i	2.15403	+	0.784002i
$75$	−4.68141	+	7.28590i	−0.540563	+	0.841304i
$76$	−13.8630	−	8.88074i	−1.59020	−	1.01869i
$77$	−0.0674699	−	0.0674699i	−0.00768890	−	0.00768890i
$78$	−4.04482	+	22.4257i	−0.457985	+	2.53921i
$79$	9.95696	−	1.75568i	1.12025	−	0.197530i	0.417297	−	0.908770i	$-0.362977\pi$
$79$	9.95696	−	1.75568i	1.12025	−	0.197530i	0.702949	+	0.711241i	$0.251866\pi$
$80$	−1.69670	+	5.82154i	−0.189697	+	0.650868i
$81$	1.70139	−	8.83772i	0.189043	−	0.981969i
$82$	10.5153	+	15.0174i	1.16122	+	1.65839i
$83$	−2.48613	−	9.27835i	−0.272888	−	1.01843i	−0.957244	−	0.289283i	$-0.906583\pi$
$83$	−2.48613	−	9.27835i	−0.272888	−	1.01843i	0.684356	−	0.729148i	$-0.260083\pi$
$84$	0.239882	−	2.62357i	0.0261733	−	0.286255i
$85$	0.217721	−	9.98715i	0.0236152	−	1.08326i
$86$	−4.36765	−	12.0000i	−0.470976	−	1.29399i
$87$	−4.45952	−	5.35709i	−0.478110	−	0.574340i
$88$	0.977505	−	0.261922i	0.104202	−	0.0279210i
$89$	−0.817749	+	4.63769i	−0.0866813	+	0.491594i	0.910300	+	0.413949i	$0.135851\pi$
$89$	−0.817749	+	4.63769i	−0.0866813	+	0.491594i	−0.996981	+	0.0776444i	$0.975260\pi$
$90$	9.99356	+	12.6528i	1.05341	+	1.33373i
$91$	1.68862	+	1.41692i	0.177015	+	0.148533i
$92$	0.278612	−	0.397900i	0.0290474	−	0.0414839i
$93$	14.4230	+	2.60140i	1.49559	+	0.269753i
$94$		−	18.8724i		−	1.94654i
$95$	3.15599	−	9.22170i	0.323798	−	0.946126i
$96$	−2.86426	−	2.02233i	−0.292333	−	0.206403i
$97$	−5.84597	+	2.72602i	−0.593568	+	0.276785i	−0.696100	−	0.717944i	$-0.745083\pi$
$97$	−5.84597	+	2.72602i	−0.593568	+	0.276785i	0.102533	+	0.994730i	$0.467305\pi$
$98$	13.4628	+	9.42673i	1.35994	+	0.952243i
$99$	0.248333	−	0.666022i	0.0249584	−	0.0669377i
$100$	−18.8671	−	0.823003i	−1.88671	−	0.0823003i
$101$	7.21041	+	1.27139i	0.717462	+	0.126508i	0.520449	−	0.853893i	$-0.325765\pi$
$101$	7.21041	+	1.27139i	0.717462	+	0.126508i	0.197013	+	0.980401i	$0.436876\pi$
$102$	−17.4516	−	6.42932i	−1.72797	−	0.636598i
$103$	−4.22599	+	15.7716i	−0.416399	+	1.55402i	0.365618	+	0.930765i	$0.380858\pi$
$103$	−4.22599	+	15.7716i	−0.416399	+	1.55402i	−0.782017	+	0.623257i	$0.785809\pi$
$104$	−21.9692	+	7.99612i	−2.15425	+	0.784084i
$105$	1.54244	−	0.231260i	0.150527	−	0.0225687i
$106$	0.729440	+	1.26343i	0.0708495	+	0.122715i
$107$	14.0412	−	3.76233i	1.35742	−	0.363719i	0.494549	−	0.869150i	$-0.335333\pi$
$107$	14.0412	−	3.76233i	1.35742	−	0.363719i	0.862867	+	0.505431i	$0.168667\pi$
$108$	18.5199	−	6.49547i	1.78208	−	0.625027i
$109$	−2.50481	−	2.98511i	−0.239917	−	0.285922i	0.632628	−	0.774456i	$-0.281976\pi$
$109$	−2.50481	−	2.98511i	−0.239917	−	0.285922i	−0.872545	+	0.488534i	$0.837532\pi$
$110$	0.612521	+	1.11643i	0.0584016	+	0.106447i
$111$	12.8549	+	6.05571i	1.22013	+	0.574782i
$112$	0.989745	−	0.461526i	0.0935221	−	0.0436101i
$113$	10.5042	−	10.5042i	0.988151	−	0.988151i	−0.0117801	−	0.999931i	$-0.503750\pi$
$113$	10.5042	−	10.5042i	0.988151	−	0.988151i	0.999931	+	0.0117801i	$0.00374980\pi$
$114$	−14.3252	−	11.1391i	−1.34168	−	1.04327i
$115$	0.268021	+	0.104222i	0.0249931	+	0.00971871i
$116$	5.19868	−	14.2833i	0.482686	−	1.32617i
$117$	−4.37416	+	15.8280i	−0.404392	+	1.46330i
$118$	−0.754622	−	8.62536i	−0.0694685	−	0.794029i
$119$	−1.37818	+	1.15643i	−0.126337	+	0.106009i
$120$	−6.05543	+	15.3938i	−0.552782	+	1.40525i
$121$	−5.47193	+	9.47766i	−0.497448	+	0.861606i
$122$	−3.58773	+	13.3896i	−0.324818	+	1.21224i
$123$	6.56071	+	11.4669i	0.591559	+	1.03393i
$124$	10.9307	+	30.0317i	0.981601	+	2.69693i
$125$	−2.18183	−	10.9654i	−0.195149	−	0.980774i
$126$	0.526604	−	2.85563i	0.0469136	−	0.254400i
$127$	−10.8707	−	15.5250i	−0.964619	−	1.37762i	−0.925651	−	0.378378i	$-0.876482\pi$
$127$	−10.8707	−	15.5250i	−0.964619	−	1.37762i	−0.0389678	−	0.999240i	$-0.512407\pi$
$128$	1.80253	−	20.6030i	0.159323	−	1.82107i
$129$	−2.34697	−	8.89817i	−0.206639	−	0.783440i
$130$	−16.3446	−	24.4604i	−1.43352	−	2.14532i
$131$	−6.88439	+	18.9147i	−0.601492	+	1.65259i	0.146760	+	0.989172i	$0.453115\pi$
$131$	−6.88439	+	18.9147i	−0.601492	+	1.65259i	−0.748252	+	0.663414i	$0.769107\pi$
$132$	1.52753	−	0.263185i	0.132955	−	0.0229073i
$133$	−1.62343	+	0.667674i	−0.140769	+	0.0578947i
$134$	−2.81886			−0.243512
$135$	6.34147	+	9.73580i	0.545787	+	0.837924i
$136$	−3.31338	−	18.7911i	−0.284120	−	1.61133i
$137$	−1.93762	−	22.1470i	−0.165542	−	1.89215i	−0.394775	−	0.918778i	$-0.629177\pi$
$137$	−1.93762	−	22.1470i	−0.165542	−	1.89215i	0.229233	−	0.973372i	$-0.426378\pi$
$138$	0.345747	−	0.408785i	0.0294319	−	0.0347981i
$139$	−6.12416	−	1.07985i	−0.519444	−	0.0915920i	−0.0922215	−	0.995739i	$-0.529397\pi$
$139$	−6.12416	−	1.07985i	−0.519444	−	0.0915920i	−0.427223	+	0.904147i	$0.640508\pi$
$140$	2.12891	+	2.65245i	0.179925	+	0.224173i
$141$	1.23832	−	13.5434i	0.104285	−	1.14056i
$142$	−0.260052	+	0.557684i	−0.0218231	+	0.0467998i
$143$	−0.548110	+	1.17543i	−0.0458353	+	0.0982940i
$144$	6.19094	+	5.27794i	0.515911	+	0.439828i
$145$	8.94521	+	0.979479i	0.742859	+	0.0813413i
$146$	−5.16864	−	0.911371i	−0.427760	−	0.0754256i
$147$	9.04275	+	7.64828i	0.745834	+	0.630819i
$148$	2.70068	+	30.8690i	0.221995	+	2.53741i
$149$	−2.25086	−	12.7653i	−0.184398	−	1.04577i	−0.926727	−	0.375736i	$-0.877390\pi$
$149$	−2.25086	−	12.7653i	−0.184398	−	1.04577i	0.742329	−	0.670035i	$-0.233721\pi$
$150$	−20.6265	−	2.79686i	−1.68415	−	0.228363i
$151$	−15.7480			−1.28155			−0.640777	−	0.767727i	$-0.721388\pi$
$151$	−15.7480			−1.28155			−0.640777	+	0.767727i	$0.721388\pi$
$152$	2.47641	−	18.4519i	0.200863	−	1.49665i
$153$	−12.1019	−	5.75898i	−0.978384	−	0.465586i
$154$	0.0784383	−	0.215507i	0.00632074	−	0.0173661i
$155$	−15.7316	+	10.5119i	−1.26359	+	0.844339i
$156$	−34.6250	+	9.13267i	−2.77222	+	0.731198i
$157$	1.42462	−	16.2834i	0.113697	−	1.29956i	−0.698261	−	0.715843i	$-0.746042\pi$
$157$	1.42462	−	16.2834i	0.113697	−	1.29956i	0.811958	−	0.583716i	$-0.198402\pi$
$158$	13.9386	+	19.9063i	1.10889	+	1.58366i
$159$	0.440568	+	0.954537i	0.0349393	+	0.0756997i
$160$	4.47386	−	0.688684i	0.353690	−	0.0544452i
$161$	−0.0177135	−	0.0486674i	−0.00139602	−	0.00383553i
$162$	20.9799	−	5.27097i	1.64833	−	0.414126i
$163$	2.55536	−	9.53675i	0.200151	−	0.746976i	−0.790721	−	0.612176i	$-0.790294\pi$
$163$	2.55536	−	9.53675i	0.200151	−	0.746976i	0.990873	−	0.134799i	$-0.0430390\pi$
$164$	−14.4044	+	24.9492i	−1.12480	+	1.94820i
$165$	0.366309	+	0.841373i	0.0285171	+	0.0655008i
$166$	17.6861	−	14.8404i	1.37271	−	1.15184i
$167$	0.284094	+	3.24721i	0.0219839	+	0.251277i	0.999232	+	0.0391785i	$0.0124741\pi$
$167$	0.284094	+	3.24721i	0.0219839	+	0.251277i	−0.977248	+	0.212098i	$0.931970\pi$
$168$	2.80346	−	1.00797i	0.216292	−	0.0777664i
$169$	5.80137	−	15.9391i	0.446259	−	1.22609i
$170$	21.9766	−	9.67047i	1.68553	−	0.741692i
$171$	−9.54930	−	8.93369i	−0.730253	−	0.683177i
$172$	14.1898	−	14.1898i	1.08197	−	1.08197i
$173$	−4.22850	+	1.97178i	−0.321487	+	0.149912i	−0.576661	−	0.816983i	$-0.695645\pi$
$173$	−4.22850	+	1.97178i	−0.321487	+	0.149912i	0.255175	+	0.966895i	$0.417867\pi$
$174$	7.13971	−	15.1560i	0.541260	−	1.14897i
$175$	−1.22570	+	1.59750i	−0.0926546	+	0.120760i
$176$	0.413007	+	0.492203i	0.0311316	+	0.0371012i
$177$	0.0244186	−	6.23934i	0.00183542	−	0.468978i
$178$	−10.9332	+	2.92953i	−0.819474	+	0.219578i
$179$	−1.22958	−	2.12969i	−0.0919028	−	0.159180i	0.816409	−	0.577474i	$-0.195962\pi$
$179$	−1.22958	−	2.12969i	−0.0919028	−	0.159180i	−0.908312	+	0.418294i	$0.862628\pi$
$180$	−11.3833	+	22.6358i	−0.848463	+	1.68718i
$181$	7.12475	−	2.59320i	0.529579	−	0.192751i	−0.0633715	−	0.997990i	$-0.520185\pi$
$181$	7.12475	−	2.59320i	0.529579	−	0.192751i	0.592950	+	0.805239i	$0.297963\pi$
$182$	−1.37128	+	5.11767i	−0.101646	+	0.379347i
$183$	−3.45324	+	9.37338i	−0.255271	+	0.692900i
$184$	0.540946	+	0.0953834i	0.0398791	+	0.00703176i
$185$	−17.3712	+	5.89711i	−1.27716	+	0.433564i
$186$	8.98382	+	34.0607i	0.658726	+	2.49745i
$187$	−0.867077	−	0.607134i	−0.0634070	−	0.0443980i
$188$	26.8781	−	12.5335i	1.96029	−	0.914097i
$189$	0.565282	−	2.01474i	0.0411182	−	0.146551i
$190$	23.2939	−	2.49237i	1.68991	−	0.180815i
$191$			5.40434i			0.391044i	0.980699	+	0.195522i	$0.0626401\pi$
$191$			5.40434i			0.391044i	−0.980699	+	0.195522i	$0.937360\pi$
$192$	3.16331	−	17.5384i	0.228292	−	1.26572i
$193$	−13.0289	+	18.6072i	−0.937839	+	1.33937i	0.00281176	+	0.999996i	$0.499105\pi$
$193$	−13.0289	+	18.6072i	−0.937839	+	1.33937i	−0.940651	+	0.339377i	$0.889784\pi$
$194$	−11.8764	−	9.96551i	−0.852678	−	0.715482i
$195$	−10.1244	−	18.6260i	−0.725024	−	1.33383i
$196$	−4.48473	+	25.4342i	−0.320338	+	1.81673i
$197$	−21.3634	+	5.72431i	−1.52208	+	0.407840i	−0.920426	−	0.390917i	$-0.872158\pi$
$197$	−21.3634	+	5.72431i	−1.52208	+	0.407840i	−0.601654	+	0.798757i	$0.705491\pi$
$198$	1.70308	−	0.135577i	0.121033	−	0.00963500i
$199$	5.67856	+	15.6017i	0.402542	+	1.10598i	0.961025	+	0.276460i	$0.0891613\pi$
$199$	5.67856	+	15.6017i	0.402542	+	1.10598i	−0.558483	+	0.829516i	$0.688616\pi$
$200$	−8.17322	−	19.7297i	−0.577934	−	1.39510i
$201$	−2.02290	−	0.184961i	−0.142684	−	0.0130461i
$202$	4.55466	+	16.9982i	0.320465	+	1.19599i
$203$	−0.929557	−	1.32754i	−0.0652421	−	0.0931754i
$204$	−2.43324	−	29.1245i	−0.170361	−	2.03912i
$205$	−16.3741	−	4.77227i	−1.14362	−	0.333310i
$206$	−38.6487	+	6.81481i	−2.69278	+	0.474810i
$207$	0.274941	−	0.270671i	0.0191097	−	0.0188129i
$208$	−10.4961	−	10.4961i	−0.727772	−	0.727772i
$209$	−0.626660	−	0.820941i	−0.0433470	−	0.0567857i
$210$	2.07055	+	3.12507i	0.142882	+	0.215650i
$211$	−4.88408	−	1.77766i	−0.336234	−	0.122379i	0.168385	−	0.985721i	$-0.446145\pi$
$211$	−4.88408	−	1.77766i	−0.336234	−	0.122379i	−0.504619	+	0.863342i	$0.668367\pi$
$212$	−1.31495	+	1.87794i	−0.0903108	+	0.128977i
$213$	−0.223214	+	0.383148i	−0.0152944	+	0.0262528i
$214$	22.4585	+	26.7650i	1.53523	+	1.82962i
$215$	10.1568	+	6.16301i	0.692686	+	0.420314i
$216$	15.5078	+	15.8763i	1.05517	+	1.08024i
$217$	3.29140	+	0.881929i	0.223435	+	0.0598692i
$218$	3.95828	−	8.48856i	0.268089	−	0.574918i
$219$	−3.64938	−	0.993171i	−0.246602	−	0.0671123i
$220$	−1.18323	+	1.61379i	−0.0797735	+	0.108802i
$221$	21.1776	+	12.2269i	1.42456	+	0.822468i
$222$	−0.133666	+	34.1538i	−0.00897107	+	2.29225i
$223$	5.38210	+	0.470873i	0.360412	+	0.0315320i	0.265924	−	0.963994i	$-0.414323\pi$
$223$	5.38210	+	0.470873i	0.360412	+	0.0315320i	0.0944882	+	0.995526i	$0.469879\pi$
$224$	−0.624494	−	0.524012i	−0.0417257	−	0.0350120i
$225$	−14.6187	−	3.36054i	−0.974581	−	0.224036i
$226$	33.5517	+	12.2118i	2.23183	+	0.812319i
$227$	7.13413	+	7.13413i	0.473509	+	0.473509i	0.903048	−	0.429539i	$-0.141324\pi$
$227$	7.13413	+	7.13413i	0.473509	+	0.473509i	−0.429539	+	0.903048i	$0.641324\pi$
$228$	6.35070	−	27.7996i	0.420586	−	1.84108i
$229$		−	5.42675i		−	0.358610i	−0.983794	−	0.179305i	$-0.942615\pi$
$229$		−	5.42675i		−	0.358610i	0.983794	−	0.179305i	$-0.0573848\pi$
$230$	0.0452197	+	0.689709i	0.00298170	+	0.0454781i
$231$	0.0704304	−	0.149508i	0.00463398	−	0.00983691i
$232$	17.1230	−	1.49807i	1.12418	−	0.0983529i
$233$	−0.542352	+	6.19911i	−0.0355307	+	0.406117i	0.957515	+	0.288385i	$0.0931182\pi$
$233$	−0.542352	+	6.19911i	−0.0355307	+	0.406117i	−0.993045	+	0.117733i	$0.962437\pi$
$234$	−38.9221	+	6.54931i	−2.54441	+	0.428142i
$235$	10.9898	+	13.6925i	0.716899	+	0.893201i
$236$	11.7831	−	6.80299i	0.767016	−	0.442837i
$237$	8.69659	+	15.2000i	0.564904	+	0.987346i
$238$	−3.91903	−	1.82747i	−0.254033	−	0.118457i
$239$	10.5879	+	18.3389i	0.684877	+	1.18624i	0.973475	+	0.228792i	$0.0734774\pi$
$239$	10.5879	+	18.3389i	0.684877	+	1.18624i	−0.288598	+	0.957450i	$0.593189\pi$
$240$	−10.4828	+	0.646099i	−0.676664	+	0.0417055i
$241$	−1.93117	+	10.9522i	−0.124397	+	0.705492i	0.857267	+	0.514873i	$0.172161\pi$
$241$	−1.93117	+	10.9522i	−0.124397	+	0.705492i	−0.981664	+	0.190620i	$0.938950\pi$
$242$	−26.2039	−	2.29255i	−1.68445	−	0.147370i
$243$	15.4017	−	2.40600i	0.988017	−	0.154345i
$244$	−21.4522	+	3.78260i	−1.37334	+	0.242156i
$245$	−15.2571	+	1.00031i	−0.974739	+	0.0639073i
$246$	−18.3146	+	25.9393i	−1.16770	+	1.65383i
$247$	16.0751	+	17.6316i	1.02283	+	1.12187i
$248$	−25.5548	+	25.5548i	−1.62273	+	1.62273i
$249$	13.6659	−	9.48945i	0.866039	−	0.601370i
$250$	21.6702	−	15.8912i	1.37054	−	1.00505i
$251$	1.50668	−	1.79559i	0.0951008	−	0.113337i	−0.716395	−	0.697695i	$-0.754209\pi$
$251$	1.50668	−	1.79559i	0.0951008	−	0.113337i	0.811496	+	0.584358i	$0.198654\pi$
$252$	4.41673	−	1.14648i	0.278228	−	0.0722217i
$253$	0.0249608	−	0.0174778i	0.00156927	−	0.00109882i
$254$	22.7766	−	39.4501i	1.42913	−	2.47532i
$255$	16.4057	−	5.49782i	1.02736	−	0.344287i
$256$	27.3743	−	9.96343i	1.71089	−	0.622714i
$257$	−2.63630	−	1.22933i	−0.164448	−	0.0766833i	0.338651	−	0.940912i	$-0.390029\pi$
$257$	−2.63630	−	1.22933i	−0.164448	−	0.0766833i	−0.503099	+	0.864229i	$0.667807\pi$
$258$	16.9993	−	14.1511i	1.05833	−	0.881009i
$259$	2.86122	+	1.65193i	0.177788	+	0.102646i
$260$	23.9818	−	39.5226i	1.48729	−	2.45109i
$261$	6.11815	−	10.4079i	0.378704	−	0.644236i
$262$	−48.1959	+	4.21659i	−2.97755	+	0.260502i
$263$	0.601794	+	0.421381i	0.0371082	+	0.0259835i	0.591983	−	0.805950i	$-0.298345\pi$
$263$	0.601794	+	0.421381i	0.0371082	+	0.0259835i	−0.554875	+	0.831934i	$0.687234\pi$
$264$	0.999746	+	1.43975i	0.0615301	+	0.0886102i
$265$	−1.26496	−	0.491886i	−0.0777057	−	0.0302163i
$266$	−3.10348	−	2.85819i	−0.190286	−	0.175247i
$267$	−8.03819	+	1.38494i	−0.491929	+	0.0847567i
$268$	−1.87205	−	4.01463i	−0.114354	−	0.245232i
$269$	1.50771	+	8.55063i	0.0919265	+	0.521341i	0.995646	+	0.0932160i	$0.0297147\pi$
$269$	1.50771	+	8.55063i	0.0919265	+	0.521341i	−0.903719	+	0.428125i	$0.859174\pi$
$270$	−14.7664	+	23.7034i	−0.898656	+	1.44254i
$271$	−2.27893	+	1.91225i	−0.138435	+	0.116161i	−0.709376	−	0.704830i	$-0.751023\pi$
$271$	−2.27893	+	1.91225i	−0.138435	+	0.116161i	0.570941	+	0.820991i	$0.306579\pi$
$272$	9.92385	−	6.94876i	0.601722	−	0.421330i
$273$	−1.31987	+	3.58262i	−0.0798821	+	0.216830i
$274$	46.2758	−	26.7173i	2.79562	−	1.61405i
$275$	−1.09453	−	0.453317i	−0.0660024	−	0.0273360i
$276$	0.811811	+	0.220933i	0.0488653	+	0.0132986i
$277$	−28.0584	−	7.51823i	−1.68587	−	0.451727i	−0.716549	−	0.697537i	$-0.754279\pi$
$277$	−28.0584	−	7.51823i	−1.68587	−	0.451727i	−0.969318	+	0.245810i	$0.920946\pi$
$278$	−3.86850	−	14.4374i	−0.232017	−	0.865900i
$279$	4.21215	+	25.0325i	0.252175	+	1.49866i
$280$	−1.70101	+	3.44948i	−0.101655	+	0.206146i
$281$	20.2958	−	24.1876i	1.21075	−	1.44291i	0.347833	−	0.937556i	$-0.386918\pi$
$281$	20.2958	−	24.1876i	1.21075	−	1.44291i	0.862912	−	0.505354i	$-0.168638\pi$
$282$	30.7601	−	11.0596i	1.83174	−	0.658591i
$283$	−5.28445	−	11.3325i	−0.314128	−	0.673650i	0.684329	−	0.729173i	$-0.260095\pi$
$283$	−5.28445	−	11.3325i	−0.314128	−	0.673650i	−0.998457	+	0.0555231i	$0.982317\pi$
$284$	−0.966961			−0.0573786
$285$	16.8799	−	0.260160i	0.999881	−	0.0154105i
$286$	−3.11725			−0.184327
$287$	1.29813	+	2.78384i	0.0766259	+	0.164325i
$288$	1.61768	−	5.85360i	0.0953226	−	0.344926i
$289$	−1.90143	+	2.26603i	−0.111849	+	0.133296i
$290$	6.95272	+	20.4807i	0.408278	+	1.20267i
$291$	−7.86901	−	7.93084i	−0.461289	−	0.464914i
$292$	−2.13461	−	7.96646i	−0.124918	−	0.466202i
$293$	−13.9892	−	3.74839i	−0.817256	−	0.218983i	−0.174110	−	0.984726i	$-0.555705\pi$
$293$	−13.9892	−	3.74839i	−0.817256	−	0.218983i	−0.643147	+	0.765743i	$0.722371\pi$
$294$	−7.47516	+	27.4672i	−0.435960	+	1.60192i
$295$	5.57027	+	5.81855i	0.324314	+	0.338769i
$296$	−30.3460	+	17.5203i	−1.76383	+	1.01835i
$297$	1.23108	+	0.0144546i	0.0714344	+	0.000838743i
$298$	25.5208	−	17.8699i	1.47838	−	1.03517i
$299$	−0.539263	+	0.452496i	−0.0311864	+	0.0261685i
$300$	−9.71513	−	31.2338i	−0.560903	−	1.80329i
$301$	−0.371540	−	2.10711i	−0.0214152	−	0.121452i
$302$	−15.9965	−	34.3046i	−0.920496	−	1.97401i
$303$	2.15322	+	12.4973i	0.123699	+	0.717952i
$304$	11.2822	−	3.52614i	0.647080	−	0.202238i
$305$	−5.19408	−	11.8038i	−0.297412	−	0.675885i
$306$	0.252138	−	32.2121i	0.0144138	−	1.84144i
$307$	−22.3218	−	15.6299i	−1.27397	−	0.892045i	−0.276356	−	0.961055i	$-0.589127\pi$
$307$	−22.3218	−	15.6299i	−1.27397	−	0.892045i	−0.997616	+	0.0690108i	$0.978016\pi$
$308$	0.359019	−	0.0314101i	0.0204570	−	0.00178976i
$309$	−28.1827	+	2.35456i	−1.60326	+	0.133946i
$310$	−38.8785	−	23.5910i	−2.20815	−	1.33988i
$311$	7.56022	+	4.36490i	0.428701	+	0.247511i	0.698793	−	0.715324i	$-0.253721\pi$
$311$	7.56022	+	4.36490i	0.428701	+	0.247511i	−0.270092	+	0.962834i	$0.587054\pi$
$312$	−25.9073	−	31.1217i	−1.46671	−	1.76192i
$313$	0.985206	+	0.459409i	0.0556871	+	0.0259673i	0.450262	−	0.892896i	$-0.351330\pi$
$313$	0.985206	+	0.459409i	0.0556871	+	0.0259673i	−0.394575	+	0.918864i	$0.629108\pi$
$314$	36.9181	−	13.4371i	2.08341	−	0.758299i
$315$	1.28084	+	2.37851i	0.0721670	+	0.134014i
$316$	−19.0939	+	33.0715i	−1.07411	+	1.86042i
$317$	13.8538	−	9.70053i	0.778107	−	0.544836i	−0.115702	−	0.993284i	$-0.536912\pi$
$317$	13.8538	−	9.70053i	0.778107	−	0.544836i	0.893809	+	0.448448i	$0.148023\pi$
$318$	−1.63179	+	1.92931i	−0.0915065	+	0.108190i
$319$	0.612907	−	0.730434i	0.0343162	−	0.0408965i
$320$	12.7825	+	19.1296i	0.714565	+	1.06938i
$321$	14.3607	+	20.6810i	0.801536	+	1.15430i
$322$	0.0880215	−	0.0880215i	0.00490525	−	0.00490525i
$323$	−16.4497	+	10.4216i	−0.915287	+	0.579875i
$324$	21.4400	+	26.3791i	1.19111	+	1.46550i
$325$	26.1024	+	8.22892i	1.44790	+	0.456458i
$326$	23.3700	−	4.12077i	1.29435	−	0.228228i
$327$	3.39757	−	5.83193i	0.187886	−	0.322506i
$328$	−32.4536	−	2.83932i	−1.79195	−	0.156775i
$329$	0.549081	−	3.11399i	0.0302718	−	0.171680i
$330$	−1.46071	+	1.65260i	−0.0804096	+	0.0909726i
$331$	−0.252223	−	0.436863i	−0.0138634	−	0.0240122i	0.859010	−	0.511958i	$-0.171080\pi$
$331$	−0.252223	−	0.436863i	−0.0138634	−	0.0240122i	−0.872874	+	0.487946i	$0.837746\pi$
$332$	32.8814	+	15.3329i	1.80460	+	0.841500i
$333$	−2.33694	+	24.5010i	−0.128064	+	1.34265i
$334$	−6.78498	+	3.91731i	−0.371257	+	0.214346i
$335$	2.04517	−	1.64149i	0.111740	−	0.0896842i
$336$	1.33225	+	1.34272i	0.0726804	+	0.0732515i
$337$	−1.07021	+	12.2325i	−0.0582980	+	0.666349i	0.909679	+	0.415312i	$0.136327\pi$
$337$	−1.07021	+	12.2325i	−0.0582980	+	0.666349i	−0.967977	+	0.251038i	$0.919228\pi$
$338$	40.6139	−	3.55325i	2.20910	−	0.193271i
$339$	23.2765	+	10.9651i	1.26420	+	0.595543i
$340$	28.3678	+	24.8769i	1.53846	+	1.34914i
$341$			2.00484i			0.108568i
$342$	9.76071	−	29.8764i	0.527799	−	1.61553i
$343$	3.94043	+	3.94043i	0.212763	+	0.212763i
$344$	21.3242	+	7.76136i	1.14972	+	0.418464i
$345$	−0.0128046	+	0.497924i	−0.000689377	+	0.0268073i
$346$	−8.59045	−	7.20824i	−0.461825	−	0.387518i
$347$	−12.6758	−	1.10899i	−0.680475	−	0.0595339i	−0.258323	−	0.966059i	$-0.583170\pi$
$347$	−12.6758	−	1.10899i	−0.680475	−	0.0595339i	−0.422152	+	0.906525i	$0.638725\pi$
$348$	26.3269	+	0.103034i	1.41127	+	0.00552321i
$349$	−1.39265	−	0.804048i	−0.0745469	−	0.0430397i	0.462263	−	0.886743i	$-0.347038\pi$
$349$	−1.39265	−	0.804048i	−0.0745469	−	0.0430397i	−0.536810	+	0.843703i	$0.680371\pi$
$350$	−4.72496	−	1.04730i	−0.252560	−	0.0559806i
$351$	−28.3614	+	2.14609i	−1.51382	+	0.114550i
$352$	0.202705	−	0.434703i	0.0108042	−	0.0231697i
$353$	17.7782	+	4.76364i	0.946236	+	0.253543i	0.698764	−	0.715352i	$-0.253734\pi$
$353$	17.7782	+	4.76364i	0.946236	+	0.253543i	0.247472	+	0.968895i	$0.420400\pi$
$354$	13.6163	−	6.28461i	0.723696	−	0.334023i
$355$	−0.136077	−	0.556052i	−0.00722221	−	0.0295122i
$356$	−11.4331	−	13.6255i	−0.605956	−	0.722150i
$357$	−2.69250	−	1.56860i	−0.142502	−	0.0830191i
$358$	3.39022	−	4.84174i	0.179179	−	0.255894i
$359$	19.2018	+	6.98887i	1.01343	+	0.368858i	0.794749	−	0.606938i	$-0.207602\pi$
$359$	19.2018	+	6.98887i	1.01343	+	0.368858i	0.218681	+	0.975796i	$0.429825\pi$
$360$	−28.6390	−	0.848648i	−1.50941	−	0.0447277i
$361$	−18.3771	+	4.82531i	−0.967214	+	0.253963i
$362$	12.8861	+	12.8861i	0.677277	+	0.677277i
$363$	−18.6543	−	3.36459i	−0.979098	−	0.176595i
$364$	−8.19930	+	1.44576i	−0.429760	+	0.0757783i
$365$	4.28073	−	2.34860i	0.224064	−	0.122931i
$366$	−23.9262	+	1.99895i	−1.25064	+	0.104487i
$367$	19.3010	+	27.5647i	1.00750	+	1.43886i	0.895451	+	0.445161i	$0.146853\pi$
$367$	19.3010	+	27.5647i	1.00750	+	1.43886i	0.112052	+	0.993702i	$0.464258\pi$
$368$	0.0902638	+	0.336869i	0.00470532	+	0.0175605i
$369$	−14.8452	+	17.4131i	−0.772809	+	0.906492i
$370$	−30.4913	−	31.8503i	−1.58517	−	1.65582i
$371$	0.0836009	+	0.229692i	0.00434034	+	0.0119250i
$372$	−42.5431	+	35.4151i	−2.20576	+	1.83619i
$373$	−17.5898	+	4.71317i	−0.910764	+	0.244039i	−0.683633	−	0.729826i	$-0.739601\pi$
$373$	−17.5898	+	4.71317i	−0.910764	+	0.244039i	−0.227131	+	0.973864i	$0.572935\pi$
$374$	0.441789	−	2.50551i	0.0228444	−	0.129557i
$375$	16.5939	−	9.98212i	0.856905	−	0.515475i
$376$	25.6904	+	21.5568i	1.32488	+	1.11171i
$377$	−12.6349	+	18.0445i	−0.650729	+	0.929337i
$378$	4.96300	−	0.815151i	0.255269	−	0.0419268i
$379$			17.6842i			0.908378i	0.890905	+	0.454189i	$0.150071\pi$
$379$			17.6842i			0.908378i	−0.890905	+	0.454189i	$0.849929\pi$
$380$	19.0195	+	31.5200i	0.975680	+	1.61694i
$381$	18.9337	−	26.8161i	0.970003	−	1.37383i
$382$	−11.7725	+	5.48962i	−0.602335	+	0.280873i
$383$	−6.56835	−	4.59921i	−0.335627	−	0.235009i	0.393598	−	0.919283i	$-0.371230\pi$
$383$	−6.56835	−	4.59921i	−0.335627	−	0.235009i	−0.729225	+	0.684274i	$0.760119\pi$
$384$	34.6373	−	9.13589i	1.76758	−	0.466214i
$385$	0.0685858	+	0.202034i	0.00349546	+	0.0102966i
$386$	−53.7673	−	9.48063i	−2.73669	−	0.482552i
$387$	13.1278	−	9.03985i	0.667321	−	0.459522i
$388$	6.30558	−	23.5327i	0.320117	−	1.19469i
$389$	7.82553	−	2.84826i	0.396770	−	0.144413i	−0.135926	−	0.990719i	$-0.543401\pi$
$389$	7.82553	−	2.84826i	0.396770	−	0.144413i	0.532696	+	0.846306i	$0.321179\pi$
$390$	30.2897	−	40.9744i	1.53378	−	2.07482i
$391$	−0.287270	−	0.497567i	−0.0145279	−	0.0251630i
$392$	−28.2100	+	7.55886i	−1.42482	+	0.381780i
$393$	−34.8635	−	0.136444i	−1.75863	−	0.00688268i
$394$	−34.1701	−	40.7223i	−1.72146	−	2.05156i
$395$	−21.7048	−	6.32592i	−1.09209	−	0.318291i
$396$	1.32413	+	2.33549i	0.0665402	+	0.117363i
$397$	20.1561	−	9.39894i	1.01161	−	0.471719i	0.155123	−	0.987895i	$-0.450423\pi$
$397$	20.1561	−	9.39894i	1.01161	−	0.471719i	0.856483	+	0.516176i	$0.172645\pi$
$398$	−28.2178	+	28.2178i	−1.41443	+	1.41443i
$399$	−2.03961	−	2.25476i	−0.102108	−	0.112879i
$400$	9.15990	−	9.99708i	0.457995	−	0.499854i
$401$	−5.23924	+	14.3947i	−0.261635	+	0.718837i	0.737422	+	0.675432i	$0.236043\pi$
$401$	−5.23924	+	14.3947i	−0.261635	+	0.718837i	−0.999058	+	0.0434049i	$0.986179\pi$
$402$	−1.65191	−	4.59446i	−0.0823899	−	0.229151i
$403$	−4.03671	−	46.1398i	−0.201083	−	2.29839i
$404$	−21.1841	+	17.7756i	−1.05395	+	0.884369i
$405$	−12.1522	+	16.0414i	−0.603845	+	0.797102i
$406$	1.94763	−	3.37339i	0.0966592	−	0.167419i
$407$	−0.503106	+	1.87762i	−0.0249380	+	0.0930700i
$408$	28.6860	−	16.4125i	1.42017	−	0.812540i
$409$	7.96049	+	21.8713i	0.393621	+	1.08146i	0.965336	+	0.261012i	$0.0840562\pi$
$409$	7.96049	+	21.8713i	0.393621	+	1.08146i	−0.571715	+	0.820453i	$0.693722\pi$
$410$	−6.23686	−	40.5162i	−0.308017	−	2.00095i
$411$	34.9620	−	16.1368i	1.72455	−	0.795968i
$412$	−35.3730	−	50.5178i	−1.74270	−	2.48883i
$413$	0.126435	−	1.44516i	0.00622148	−	0.0711119i
$414$	0.868895	+	0.323976i	0.0427039	+	0.0159226i
$415$	−4.18990	+	21.0663i	−0.205674	+	1.03410i
$416$	−3.78984	+	10.4125i	−0.185812	+	0.510514i
$417$	−1.82883	−	10.6146i	−0.0895584	−	0.519799i
$418$	1.15175	−	2.19898i	0.0563337	−	0.107556i
$419$	−30.3193			−1.48119			−0.740597	−	0.671949i	$-0.765457\pi$
$419$	−30.3193			−1.48119			−0.740597	+	0.671949i	$0.765457\pi$
$420$	−3.07565	+	5.02430i	−0.150076	+	0.245161i
$421$	−0.300564	−	1.70458i	−0.0146486	−	0.0830763i	0.976607	−	0.215032i	$-0.0689855\pi$
$421$	−0.300564	−	1.70458i	−0.0146486	−	0.0830763i	−0.991256	+	0.131955i	$0.957874\pi$
$422$	−1.08879	−	12.4449i	−0.0530015	−	0.605810i
$423$	22.8001	−	5.91838i	1.10858	−	0.287762i
$424$	−2.55306	−	0.450174i	−0.123988	−	0.0218624i
$425$	−10.3134	+	19.8138i	−0.500273	+	0.961110i
$426$	−1.06137	−	0.0970445i	−0.0514233	−	0.00470182i
$427$	−0.981549	+	2.10494i	−0.0475005	+	0.101865i
$428$	−23.2037	+	49.7605i	−1.12159	+	2.40527i
$429$	−2.23703	−	0.204540i	−0.108005	−	0.00987528i
$430$	−3.10812	+	28.3853i	−0.149887	+	1.36886i
$431$	−29.1548	−	5.14078i	−1.40434	−	0.247623i	−0.580414	−	0.814322i	$-0.697109\pi$
$431$	−29.1548	−	5.14078i	−1.40434	−	0.247623i	−0.823925	+	0.566699i	$0.808220\pi$
$432$	−4.97449	+	13.1836i	−0.239335	+	0.634296i
$433$	−0.962209	−	10.9981i	−0.0462408	−	0.528535i	−0.983624	−	0.180234i	$-0.942314\pi$
$433$	−0.962209	−	10.9981i	−0.0462408	−	0.528535i	0.937383	−	0.348301i	$-0.113241\pi$
$434$	1.42219	+	8.06567i	0.0682675	+	0.387164i
$435$	3.64563	+	15.1538i	0.174795	+	0.726569i
$436$	14.7182			0.704874
$437$	−0.119957	−	0.547595i	−0.00573831	−	0.0261950i
$438$	−1.54349	−	8.95846i	−0.0737509	−	0.428052i
$439$	−9.37632	+	25.7612i	−0.447507	+	1.22952i	0.486946	+	0.873432i	$0.338111\pi$
$439$	−9.37632	+	25.7612i	−0.447507	+	1.22952i	−0.934454	+	0.356085i	$0.884111\pi$
$440$	−2.21940	−	0.441421i	−0.105806	−	0.0210439i
$441$	−7.16669	+	19.2209i	−0.341271	+	0.915279i
$442$	−5.12263	+	58.5519i	−0.243659	+	2.78503i
$443$	−8.50943	−	12.1527i	−0.404295	−	0.577394i	0.564445	−	0.825471i	$-0.309090\pi$
$443$	−8.50943	−	12.1527i	−0.404295	−	0.577394i	−0.968740	+	0.248077i	$0.920201\pi$
$444$	−48.7307	+	22.4917i	−2.31266	+	1.06741i
$445$	6.22642	−	8.49212i	0.295160	−	0.402565i
$446$	4.44131	+	12.2024i	0.210302	+	0.577800i
$447$	19.4871	−	11.1494i	0.921707	−	0.527349i
$448$	1.07243	−	4.00235i	0.0506674	−	0.189093i
$449$	18.6178	−	32.2470i	0.878628	−	1.52183i	0.0257816	−	0.999668i	$-0.491793\pi$
$449$	18.6178	−	32.2470i	0.878628	−	1.52183i	0.852847	−	0.522161i	$-0.174874\pi$
$450$	−7.52898	−	35.2582i	−0.354920	−	1.66209i
$451$	−1.38441	+	1.16166i	−0.0651893	+	0.0547003i
$452$	4.89014	+	55.8946i	0.230013	+	2.62906i
$453$	−9.22867	−	25.6677i	−0.433601	−	1.20597i
$454$	−8.29391	+	22.7873i	−0.389252	+	1.06946i
$455$	−1.98524	−	4.51156i	−0.0930696	−	0.211505i
$456$	31.5261	−	6.77694i	1.47634	−	0.317359i
$457$	6.71248	−	6.71248i	0.313996	−	0.313996i	−0.532459	−	0.846456i	$-0.678732\pi$
$457$	6.71248	−	6.71248i	0.313996	−	0.313996i	0.846456	+	0.532459i	$0.178732\pi$
$458$	11.8213	−	5.51238i	0.552375	−	0.257577i
$459$	2.29456	−	23.0999i	0.107101	−	1.07821i
$460$	−0.952256	+	0.522450i	−0.0443992	+	0.0243594i
$461$	12.9416	+	15.4233i	0.602752	+	0.718332i	0.978003	−	0.208591i	$-0.0668878\pi$
$461$	12.9416	+	15.4233i	0.602752	+	0.718332i	−0.375250	+	0.926923i	$0.622443\pi$
$462$	0.397222	+	0.00155459i	0.0184805	+	7.23261e-5i
$463$	−10.4891	+	2.81056i	−0.487472	+	0.130618i	−0.494180	−	0.869360i	$-0.664531\pi$
$463$	−10.4891	+	2.81056i	−0.487472	+	0.130618i	0.00670790	+	0.999978i	$0.497865\pi$
$464$	5.45657	+	9.45106i	0.253315	+	0.438754i
$465$	−26.3525	−	19.4807i	−1.22207	−	0.903394i
$466$	−14.0547	+	5.11551i	−0.651073	+	0.236971i
$467$	0.688460	−	2.56937i	0.0318581	−	0.118896i	−0.948166	−	0.317776i	$-0.897064\pi$
$467$	0.688460	−	2.56937i	0.0318581	−	0.118896i	0.980024	+	0.198880i	$0.0637305\pi$
$468$	−35.1764	−	51.0835i	−1.62603	−	2.36133i
$469$	−0.465119	−	0.0820130i	−0.0214772	−	0.00378701i
$470$	−18.6638	+	37.8483i	−0.860896	+	1.74581i
$471$	27.3753	−	7.22047i	1.26139	−	0.332702i
$472$	12.6034	+	8.82500i	0.580119	+	0.406204i
$473$	1.14092	−	0.532018i	0.0524594	−	0.0244622i
$474$	−24.2771	+	34.3841i	−1.11508	+	1.57931i
$475$	−15.4491	+	15.3729i	−0.708853	+	0.705357i
$476$		−	6.79515i		−	0.311455i
$477$	−1.29762	+	1.27746i	−0.0594139	+	0.0584910i
$478$	−29.1934	+	41.6925i	−1.33527	+	1.90697i
$479$	23.0045	+	19.3031i	1.05110	+	0.881980i	0.993209	−	0.116342i	$-0.0371170\pi$
$479$	23.0045	+	19.3031i	1.05110	+	0.881980i	0.0578941	+	0.998323i	$0.481561\pi$
$480$	3.74427	+	6.88837i	0.170902	+	0.314409i
$481$	7.79804	−	44.2249i	0.355560	−	2.01648i
$482$	−25.8193	+	6.91826i	−1.17604	+	0.315118i
$483$	0.0689425	−	0.0573914i	0.00313699	−	0.00261140i
$484$	−14.1374	−	38.8423i	−0.642611	−	1.76556i
$485$	14.4199	+	0.314356i	0.654774	+	0.0142742i
$486$	20.8858	+	31.1062i	0.947400	+	1.41101i
$487$	−2.61033	−	9.74187i	−0.118285	−	0.441446i	0.881227	−	0.472694i	$-0.156718\pi$
$487$	−2.61033	−	9.74187i	−0.118285	−	0.441446i	−0.999512	+	0.0312480i	$0.990052\pi$
$488$	−14.1288	−	20.1780i	−0.639581	−	0.913416i
$489$	17.0415	−	1.42375i	0.770641	−	0.0643843i
$490$	−17.6769	−	32.2192i	−0.798560	−	1.45551i
$491$	−14.1811	+	2.50052i	−0.639986	+	0.112847i	−0.484219	−	0.874947i	$-0.660896\pi$
$491$	−14.1811	+	2.50052i	−0.639986	+	0.112847i	−0.155767	+	0.987794i	$0.549785\pi$
$492$	−49.1060	−	8.85701i	−2.21387	−	0.399305i
$493$	−12.7127	−	12.7127i	−0.572551	−	0.572551i
$494$	−22.0789	+	52.9269i	−0.993378	+	2.38129i
$495$	−1.15669	+	1.09011i	−0.0519893	+	0.0489968i
$496$	−21.5620	−	7.84791i	−0.968160	−	0.352382i
$497$	−0.0591348	+	0.0844532i	−0.00265256	+	0.00378825i
$498$	34.5528	+	20.1298i	1.54835	+	0.902038i
$499$	−7.59794	−	9.05488i	−0.340131	−	0.405352i	0.568681	−	0.822558i	$-0.307454\pi$
$499$	−7.59794	−	9.05488i	−0.340131	−	0.405352i	−0.908812	+	0.417206i	$0.863009\pi$
$500$	37.0239	+	20.3091i	1.65576	+	0.908251i
$501$	−5.12615	+	2.36598i	−0.229019	+	0.105704i
$502$	5.44188	+	1.45815i	0.242883	+	0.0650803i
$503$	7.24505	−	15.5371i	0.323041	−	0.692763i	−0.675984	−	0.736916i	$-0.736281\pi$
$503$	7.24505	−	15.5371i	0.323041	−	0.692763i	0.999025	+	0.0441531i	$0.0140589\pi$
$504$	3.28578	+	3.97867i	0.146360	+	0.177224i
$505$	−13.2030	−	9.68047i	−0.587528	−	0.430775i
$506$	0.0634274	+	0.0366198i	0.00281969	+	0.00162795i
$507$	29.3789	+	0.114979i	1.30476	+	0.00510639i
$508$	71.3114	+	6.23894i	3.16393	+	0.276808i
$509$	5.47696	+	4.59572i	0.242762	+	0.203702i	0.756048	−	0.654516i	$-0.227128\pi$
$509$	5.47696	+	4.59572i	0.242762	+	0.203702i	−0.513286	+	0.858218i	$0.671572\pi$
$510$	28.6407	+	30.1526i	1.26823	+	1.33518i
$511$	−0.826324	−	0.300757i	−0.0365544	−	0.0133047i
$512$	20.2617	+	20.2617i	0.895449	+	0.895449i
$513$	8.96494	−	20.7998i	0.395812	−	0.918332i
$514$		−	6.99151i		−	0.308382i
$515$	24.0724	−	27.4505i	1.06076	−	1.20961i
$516$	31.4436	+	14.8125i	1.38423	+	0.652083i
$517$	1.85333	−	0.162145i	0.0815093	−	0.00713114i
$518$	−0.692099	+	7.91073i	−0.0304091	+	0.347578i
$519$	−5.69180	−	5.73653i	−0.249842	−	0.251806i
$520$	51.9666	+	5.69022i	2.27889	+	0.249533i
$521$	−7.50434	+	4.33263i	−0.328771	+	0.189816i	−0.655295	−	0.755373i	$-0.727456\pi$
$521$	−7.50434	+	4.33263i	−0.328771	+	0.189816i	0.326524	+	0.945189i	$0.394122\pi$
$522$	28.8868	+	2.75527i	1.26434	+	0.120595i
$523$	18.7005	+	8.72019i	0.817716	+	0.381307i	0.786028	−	0.618190i	$-0.212134\pi$
$523$	18.7005	+	8.72019i	0.817716	+	0.381307i	0.0316880	+	0.999498i	$0.489912\pi$
$524$	−38.0130	−	65.8405i	−1.66061	−	2.87625i
$525$	−3.32206	−	1.06161i	−0.144987	−	0.0463323i
$526$	−0.306623	+	1.73895i	−0.0133694	+	0.0758217i
$527$	37.6574	+	3.29459i	1.64038	+	0.143515i
$528$	−0.560210	+	0.961602i	−0.0243800	+	0.0418484i
$529$	−22.6343	+	3.99104i	−0.984100	+	0.173523i
$530$	−0.213420	−	3.25517i	−0.00927037	−	0.141395i
$531$	10.1838	−	3.61659i	0.441940	−	0.156947i
$532$	2.00957	−	6.31816i	0.0871258	−	0.273927i
$533$	29.5222	−	29.5222i	1.27875	−	1.27875i
$534$	−11.1819	−	16.1032i	−0.483889	−	0.696853i
$535$	−31.8803	−	6.34072i	−1.37830	−	0.274133i
$536$	3.21981	−	3.83722i	0.139075	−	0.165743i
$537$	2.75062	−	3.25213i	0.118698	−	0.140340i
$538$	−17.0948	+	11.9699i	−0.737007	+	0.516058i
$539$	−0.810068	+	1.40308i	−0.0348921	+	0.0604349i
$540$	−43.5651	−	5.28859i	−1.87474	−	0.227585i
$541$	38.8268	−	14.1318i	1.66929	−	0.607573i	0.677511	−	0.735512i	$-0.263058\pi$
$541$	38.8268	−	14.1318i	1.66929	−	0.607573i	0.991782	+	0.127939i	$0.0408362\pi$
$542$	−6.48043	−	3.02188i	−0.278358	−	0.129801i
$543$	8.40192	+	10.0930i	0.360561	+	0.433131i
$544$	−7.83201	−	4.52181i	−0.335794	−	0.193871i
$545$	2.07124	+	8.46373i	0.0887222	+	0.362546i
$546$	−9.14490	+	0.764023i	−0.391365	+	0.0326972i
$547$	−1.34458	+	0.117636i	−0.0574903	+	0.00502975i	−0.115865	−	0.993265i	$-0.536964\pi$
$547$	−1.34458	+	0.117636i	−0.0574903	+	0.00502975i	0.0583743	+	0.998295i	$0.481408\pi$
$548$	68.7835	+	48.1627i	2.93829	+	2.05741i
$549$	−17.3014	−	0.135425i	−0.738404	−	0.00577981i
$550$	−0.124317	−	2.84473i	−0.00530090	−	0.121300i
$551$	−8.06072	−	15.5799i	−0.343398	−	0.663727i
$552$	0.161541	+	0.937586i	0.00687564	+	0.0399063i
$553$	1.72074	+	3.69014i	0.0731732	+	0.156921i
$554$	−12.1239	−	68.7579i	−0.515094	−	2.92124i
$555$	−19.7916	−	24.8575i	−0.840107	−	1.05514i
$556$	17.9927	−	15.0977i	0.763062	−	0.640285i
$557$	27.2886	−	19.1077i	1.15625	−	0.809618i	0.171778	−	0.985136i	$-0.445049\pi$
$557$	27.2886	−	19.1077i	1.15625	−	0.809618i	0.984476	+	0.175518i	$0.0561600\pi$
$558$	−50.2509	+	34.6031i	−2.12729	+	1.46486i
$559$	−25.1861	+	14.5412i	−1.06526	+	0.615027i
$560$	−2.44135	−	0.0532217i	−0.103166	−	0.00224903i
$561$	0.481442	−	1.76904i	0.0203265	−	0.0746891i
$562$	73.3050	+	19.6420i	3.09219	+	0.828549i
$563$	5.22944	+	19.5165i	0.220395	+	0.822524i	0.984197	+	0.177074i	$0.0566633\pi$
$563$	5.22944	+	19.5165i	0.220395	+	0.822524i	−0.763803	+	0.645450i	$0.776670\pi$
$564$	36.1795	+	36.4638i	1.52343	+	1.53540i
$565$	−31.4541	+	10.6779i	−1.32328	+	0.449224i
$566$	19.3184	−	23.0228i	0.812013	−	0.967719i
$567$	3.61509	−	0.259327i	0.151820	−	0.0108907i
$568$	−0.462116	−	0.991010i	−0.0193899	−	0.0415819i
$569$	−11.9701			−0.501813			−0.250906	−	0.968011i	$-0.580729\pi$
$569$	−11.9701			−0.501813			−0.250906	+	0.968011i	$0.580729\pi$
$570$	17.7130	+	36.5061i	0.741917	+	1.52907i
$571$	−22.5534			−0.943832			−0.471916	−	0.881643i	$-0.656437\pi$
$571$	−22.5534			−0.943832			−0.471916	+	0.881643i	$0.656437\pi$
$572$	−2.07022	−	4.43960i	−0.0865601	−	0.185629i
$573$	−8.80854	+	3.16706i	−0.367982	+	0.132306i
$574$	−4.74556	+	5.65554i	−0.198076	+	0.236058i
$575$	−0.434443	−	0.474074i	−0.0181175	−	0.0197702i
$576$	30.4396	−	5.12198i	1.26831	−	0.213416i
$577$	6.12161	+	22.8462i	0.254846	+	0.951099i	0.968176	+	0.250270i	$0.0805195\pi$
$577$	6.12161	+	22.8462i	0.254846	+	0.951099i	−0.713330	+	0.700828i	$0.752814\pi$
$578$	−6.86764	−	1.84018i	−0.285656	−	0.0765413i
$579$	−37.9630	−	10.3316i	−1.57769	−	0.429366i
$580$	−24.5513	+	23.5037i	−1.01944	+	0.975938i
$581$	3.35003	−	1.93414i	0.138983	−	0.0802417i
$582$	9.28295	−	25.1974i	0.384791	−	1.04447i
$583$	−0.117806	+	0.0824884i	−0.00487901	+	0.00341632i
$584$	7.14445	−	5.99491i	0.295640	−	0.248071i
$585$	24.4254	−	27.4170i	1.00987	−	1.13355i
$586$	−6.04464	−	34.2808i	−0.249702	−	1.41613i
$587$	−3.90686	−	8.37828i	−0.161253	−	0.345809i	0.809035	−	0.587760i	$-0.199990\pi$
$587$	−3.90686	−	8.37828i	−0.161253	−	0.345809i	−0.970288	+	0.241952i	$0.922212\pi$
$588$	−44.0834	+	7.59532i	−1.81797	+	0.313226i
$589$	34.0396	+	14.1999i	1.40258	+	0.585099i
$590$	−7.01665	+	18.0443i	−0.288871	+	0.742874i
$591$	−21.8495	−	31.4657i	−0.898768	−	1.29433i
$592$	−18.2243	−	12.7608i	−0.749013	−	0.524465i
$593$	−9.11455	+	0.797419i	−0.374290	+	0.0327461i	−0.272749	−	0.962085i	$-0.587933\pi$
$593$	−9.11455	+	0.797419i	−0.374290	+	0.0327461i	−0.101541	+	0.994831i	$0.532377\pi$
$594$	1.21902	+	2.69640i	0.0500169	+	0.110635i
$595$	3.90756	−	0.956257i	0.160194	−	0.0392027i
$596$	42.3992	+	24.4792i	1.73674	+	1.00271i
$597$	−22.1015	+	18.3984i	−0.904554	+	0.752998i
$598$	−1.53347	−	0.715067i	−0.0627081	−	0.0292413i
$599$	−5.38397	+	1.95960i	−0.219983	+	0.0800673i	−0.449661	−	0.893200i	$-0.648455\pi$
$599$	−5.38397	+	1.95960i	−0.219983	+	0.0800673i	0.229678	+	0.973267i	$0.426233\pi$
$600$	27.3677	−	24.8836i	1.11728	−	1.01587i
$601$	8.00573	−	13.8663i	0.326561	−	0.565620i	−0.655266	−	0.755398i	$-0.727444\pi$
$601$	8.00573	−	13.8663i	0.326561	−	0.565620i	0.981827	+	0.189778i	$0.0607769\pi$
$602$	4.21261	−	2.94970i	0.171693	−	0.120221i
$603$	−0.883995	−	3.40552i	−0.0359991	−	0.138683i
$604$	38.2332	−	45.5646i	1.55569	−	1.85400i
$605$	20.3468	−	13.5959i	0.827215	−	0.552751i
$606$	−25.0363	+	17.3850i	−1.01703	+	0.706217i
$607$	18.8213	−	18.8213i	0.763933	−	0.763933i	−0.213098	−	0.977031i	$-0.568355\pi$
$607$	18.8213	−	18.8213i	0.763933	−	0.763933i	0.977031	+	0.213098i	$0.0683554\pi$
$608$	−5.94497	−	6.52060i	−0.241100	−	0.264445i
$609$	1.61903	−	2.29306i	0.0656062	−	0.0929193i
$610$	20.4368	−	23.3046i	0.827461	−	0.943576i
$611$	−42.3265	+	7.46330i	−1.71235	+	0.301933i
$612$	46.0441	−	21.0335i	1.86122	−	0.850230i
$613$	28.4442	+	2.48854i	1.14885	+	0.100511i	0.645632	−	0.763649i	$-0.276594\pi$
$613$	28.4442	+	2.48854i	1.14885	+	0.100511i	0.503217	+	0.864160i	$0.332150\pi$
$614$	11.3733	−	64.5012i	0.458989	−	2.60305i
$615$	−1.81727	−	29.4849i	−0.0732795	−	1.18895i
$616$	0.203768	+	0.352937i	0.00821006	+	0.0142202i
$617$	9.43652	+	4.40032i	0.379900	+	0.177150i	0.603182	−	0.797604i	$-0.293899\pi$
$617$	9.43652	+	4.40032i	0.379900	+	0.177150i	−0.223282	+	0.974754i	$0.571677\pi$
$618$	−33.7565	−	58.9999i	−1.35788	−	2.37333i
$619$	18.4684	−	10.6627i	0.742306	−	0.428571i	−0.0806011	−	0.996746i	$-0.525684\pi$
$619$	18.4684	−	10.6627i	0.742306	−	0.428571i	0.822907	+	0.568176i	$0.192351\pi$
$620$	7.77850	−	71.0381i	0.312392	−	2.85296i
$621$	0.602288	+	0.289508i	0.0241690	+	0.0116176i
$622$	−1.82874	+	20.9026i	−0.0733257	+	0.838117i
$623$	−1.88923	+	0.165286i	−0.0756905	+	0.00662206i
$624$	10.9566	−	23.2585i	0.438617	−	0.931085i
$625$	−6.46855	+	24.1487i	−0.258742	+	0.965946i
$626$			2.61278i			0.104428i
$627$	0.970816	−	1.50248i	0.0387707	−	0.0600034i
$628$	43.6551	+	43.6551i	1.74203	+	1.74203i
$629$	34.4409	+	12.5355i	1.37325	+	0.499822i
$630$	−3.88017	+	5.20615i	−0.154590	+	0.207418i
$631$	−1.96846	−	1.65173i	−0.0783631	−	0.0657544i	0.602765	−	0.797919i	$-0.294066\pi$
$631$	−1.96846	−	1.65173i	−0.0783631	−	0.0657544i	−0.681128	+	0.732165i	$0.738510\pi$
$632$	−43.0191	−	3.76368i	−1.71121	−	0.149711i
$633$	0.0352319	−	9.00231i	0.00140034	−	0.357810i
$634$	35.2035	+	20.3248i	1.39811	+	0.807200i
$635$	6.44768	+	41.8857i	0.255868	+	1.66218i
$636$	−3.83144	−	1.04272i	−0.151926	−	0.0413465i
$637$	15.8180	−	33.9219i	0.626733	−	1.34403i
$638$	2.21372	+	0.593164i	0.0876420	+	0.0234836i
$639$	−0.755301	−	0.139284i	−0.0298793	−	0.00551000i
$640$	−23.9903	+	39.5366i	−0.948300	+	1.56282i
$641$	29.0352	+	34.6028i	1.14682	+	1.36673i	0.919587	+	0.392886i	$0.128523\pi$
$641$	29.0352	+	34.6028i	1.14682	+	1.36673i	0.227233	+	0.973840i	$0.427032\pi$
$642$	−30.4631	+	52.2899i	−1.20228	+	2.06372i
$643$	14.3023	−	20.4259i	0.564029	−	0.805517i	−0.431284	−	0.902216i	$-0.641939\pi$
$643$	14.3023	−	20.4259i	0.564029	−	0.805517i	0.995314	+	0.0966987i	$0.0308283\pi$
$644$	0.183817	+	0.0669040i	0.00724341	+	0.00263639i
$645$	−4.09300	+	20.1662i	−0.161162	+	0.794043i
$646$	−39.4113	−	25.2471i	−1.55062	−	0.993335i
$647$	−33.0810	−	33.0810i	−1.30055	−	1.30055i	−0.928022	−	0.372526i	$-0.878492\pi$
$647$	−33.0810	−	33.0810i	−1.30055	−	1.30055i	−0.372526	−	0.928022i	$-0.621508\pi$
$648$	−16.7888	+	34.5800i	−0.659528	+	1.35843i
$649$	0.840556	−	0.148213i	0.0329947	−	0.00581786i
$650$	8.58888	+	65.2189i	0.336884	+	2.55810i
$651$	0.491377	+	5.88149i	0.0192586	+	0.230514i
$652$	21.3893	+	30.5470i	0.837669	+	1.19631i
$653$	−11.1904	−	41.7633i	−0.437915	−	1.63432i	−0.733992	−	0.679158i	$-0.762345\pi$
$653$	−11.1904	−	41.7633i	−0.437915	−	1.63432i	0.296077	−	0.955164i	$-0.404322\pi$
$654$	16.1552	+	1.47712i	0.631716	+	0.0577601i
$655$	32.5122	−	31.1249i	1.27036	−	1.21615i
$656$	−7.07433	−	19.4366i	−0.276206	−	0.758870i
$657$	−0.519843	−	6.53014i	−0.0202810	−	0.254765i
$658$	7.34110	−	1.96704i	0.286186	−	0.0766833i
$659$	7.95480	−	45.1139i	0.309875	−	1.75739i	−0.289745	−	0.957104i	$-0.593570\pi$
$659$	7.95480	−	45.1139i	0.309875	−	1.75739i	0.599620	−	0.800285i	$-0.295318\pi$
$660$	−3.32372	−	0.982834i	−0.129376	−	0.0382568i
$661$	−19.1357	−	16.0567i	−0.744291	−	0.624535i	0.189695	−	0.981843i	$-0.439250\pi$
$661$	−19.1357	−	16.0567i	−0.744291	−	0.624535i	−0.933986	+	0.357308i	$0.883694\pi$
$662$	0.695437	−	0.993186i	0.0270289	−	0.0386013i
$663$	−7.51808	+	41.6826i	−0.291978	+	1.61882i
$664$			41.0269i			1.59215i
$665$	3.91606	+	0.266474i	0.151858	+	0.0103334i
$666$	−55.7456	+	19.7970i	−2.16010	+	0.767118i
$667$	0.469062	−	0.218727i	0.0181621	−	0.00846915i
$668$	−10.0851	−	7.06164i	−0.390203	−	0.273223i
$669$	2.38655	+	9.04824i	0.0922695	+	0.349825i
$670$	5.65318	+	2.78770i	0.218402	+	0.107698i
$671$	−1.34573	−	0.237288i	−0.0519513	−	0.00916041i
$672$	0.488121	−	1.32495i	0.0188297	−	0.0511109i
$673$	−0.502266	+	1.87448i	−0.0193609	+	0.0722560i	−0.974930	−	0.222510i	$-0.928575\pi$
$673$	−0.502266	+	1.87448i	−0.0193609	+	0.0722560i	0.955569	+	0.294766i	$0.0952417\pi$
$674$	−27.7339	+	10.0943i	−1.06827	+	0.388818i
$675$	−3.08954	−	25.7964i	−0.118917	−	0.992904i
$676$	32.0329	+	55.4827i	1.23204	+	2.13395i
$677$	−29.0891	+	7.79439i	−1.11798	+	0.299563i	−0.770067	−	0.637963i	$-0.779777\pi$
$677$	−29.0891	+	7.79439i	−1.11798	+	0.299563i	−0.347916	+	0.937526i	$0.613111\pi$
$678$	−0.242030	+	61.8424i	−0.00929509	+	2.37504i
$679$	−1.66970	−	1.98987i	−0.0640773	−	0.0763644i
$680$	−11.9385	+	40.9621i	−0.457820	+	1.57083i
$681$	−7.44717	+	15.8087i	−0.285376	+	0.605790i
$682$	−4.36724	+	2.03648i	−0.167230	+	0.0779807i
$683$	−10.6780	+	10.6780i	−0.408581	+	0.408581i	−0.881243	−	0.472663i	$-0.843293\pi$
$683$	−10.6780	+	10.6780i	−0.408581	+	0.408581i	0.472663	+	0.881243i	$0.343293\pi$
$684$	49.0323	−	5.94018i	1.87480	−	0.227128i
$685$	−18.0164	+	46.3318i	−0.688371	+	1.77025i
$686$	−4.58102	+	12.5863i	−0.174904	+	0.480545i
$687$	8.84506	−	3.18019i	0.337460	−	0.121332i
$688$	1.25573	+	14.3531i	0.0478743	+	0.547206i
$689$	2.54512	−	2.13561i	0.0969613	−	0.0813602i
$690$	−1.09766	+	0.477889i	−0.0417871	+	0.0181929i
$691$	−18.6920	+	32.3755i	−0.711076	+	1.23162i	0.253377	+	0.967368i	$0.418459\pi$
$691$	−18.6920	+	32.3755i	−0.711076	+	1.23162i	−0.964453	+	0.264253i	$0.914875\pi$
$692$	4.56095	−	17.0217i	0.173381	−	0.647067i
$693$	0.284957	+	0.0271796i	0.0108246	+	0.00103247i
$694$	−10.4601	−	28.7389i	−0.397060	−	1.09091i
$695$	11.2140	+	8.22210i	0.425371	+	0.311882i
$696$	12.4761	+	27.0309i	0.472907	+	1.02460i
$697$	19.5447	+	27.9127i	0.740307	+	1.05727i
$698$	0.336868	−	3.85042i	0.0127506	−	0.145740i
$699$	−10.4218	+	2.74884i	−0.394188	+	0.103971i
$700$	−1.64636	−	7.42484i	−0.0622265	−	0.280633i
$701$	8.99483	−	24.7131i	0.339730	−	0.933400i	−0.645741	−	0.763556i	$-0.723451\pi$
$701$	8.99483	−	24.7131i	0.339730	−	0.933400i	0.985471	−	0.169844i	$-0.0543263\pi$
$702$	−33.4839	−	59.6011i	−1.26377	−	2.24950i
$703$	28.3161	+	21.8409i	1.06796	+	0.823747i
$704$	2.43789			0.0918813
$705$	−15.8771	+	25.9365i	−0.597968	+	0.976824i
$706$	7.68183	+	43.5658i	0.289110	+	1.63962i
$707$	0.256978	+	2.93727i	0.00966464	+	0.110467i
$708$	17.9934	+	15.2186i	0.676232	+	0.571951i
$709$	7.29092	+	1.28559i	0.273816	+	0.0482812i	0.308870	−	0.951104i	$-0.400049\pi$
$709$	7.29092	+	1.28559i	0.273816	+	0.0482812i	−0.0350539	+	0.999385i	$0.511160\pi$
$710$	1.07305	−	0.861250i	0.0402709	−	0.0323221i
$711$	−19.6781	+	23.0821i	−0.737987	+	0.865647i
$712$	8.50041	−	18.2292i	0.318566	−	0.683168i
$713$	−0.459891	+	0.986240i	−0.0172231	+	0.0369350i
$714$	0.681963	−	7.45856i	0.0255218	−	0.279130i
$715$	2.26166	−	1.81525i	0.0845814	−	0.0678865i
$716$	9.14714	+	1.61289i	0.341845	+	0.0602764i
$717$	−23.6858	+	28.0043i	−0.884561	+	1.04584i
$718$	4.28058	+	48.9273i	0.159750	+	1.82595i
$719$	1.41680	+	8.03507i	0.0528377	+	0.299658i	0.999762	−	0.0217979i	$-0.00693903\pi$
$719$	1.41680	+	8.03507i	0.0528377	+	0.299658i	−0.946925	+	0.321456i	$0.895828\pi$
$720$	−7.19625	−	16.7074i	−0.268188	−	0.622646i
$721$	−6.57541			−0.244881
$722$	−29.1783	−	35.1302i	−1.08590	−	1.30741i
$723$	−18.9827	+	3.27061i	−0.705974	+	0.121635i
$724$	−9.79454	+	26.9103i	−0.364011	+	1.00011i
$725$	−16.9709	−	10.8107i	−0.630282	−	0.401498i
$726$	−11.6195	−	44.0533i	−0.431238	−	1.63497i
$727$	1.43083	−	16.3545i	0.0530667	−	0.606555i	−0.922375	−	0.386296i	$-0.873754\pi$
$727$	1.43083	−	16.3545i	0.0530667	−	0.606555i	0.975441	−	0.220259i	$-0.0706902\pi$
$728$	−5.40020	−	7.71229i	−0.200145	−	0.285836i
$729$	12.9473	+	23.6932i	0.479528	+	0.877526i
$730$	9.46435	+	6.93926i	0.350291	+	0.256833i
$731$	−8.11812	−	22.3044i	−0.300260	−	0.824956i
$732$	−18.7367	−	32.7483i	−0.692530	−	1.21041i
$733$	−2.57560	+	9.61228i	−0.0951321	+	0.355038i	−0.997039	−	0.0768918i	$-0.975500\pi$
$733$	−2.57560	+	9.61228i	−0.0951321	+	0.355038i	0.901907	+	0.431930i	$0.142167\pi$
$734$	−40.4399	+	70.0439i	−1.49266	+	2.58537i
$735$	−10.5714	−	24.2813i	−0.389932	−	0.895631i
$736$	0.199433	−	0.167344i	0.00735121	−	0.00616840i
$737$	−0.0242187	−	0.276821i	−0.000892108	−	0.0101968i
$738$	−53.0113	−	14.6500i	−1.95137	−	0.539274i
$739$	6.01879	−	16.5365i	0.221405	−	0.608305i	−0.778406	−	0.627761i	$-0.783971\pi$
$739$	6.01879	−	16.5365i	0.221405	−	0.608305i	0.999811	+	0.0194566i	$0.00619362\pi$
$740$	25.1116	−	64.5782i	0.923121	−	2.37394i
$741$	−19.3174	+	36.5332i	−0.709641	+	1.34208i
$742$	−0.415428	+	0.415428i	−0.0152508	+	0.0152508i
$743$	−19.0712	+	8.89303i	−0.699653	+	0.326254i	−0.739693	−	0.672945i	$-0.765029\pi$
$743$	−19.0712	+	8.89303i	−0.699653	+	0.326254i	0.0400400	+	0.999198i	$0.487251\pi$
$744$	−56.6275	−	26.6761i	−2.07607	−	0.977995i
$745$	−8.11010	+	27.8266i	−0.297131	+	1.01949i
$746$	−28.1343	−	33.5291i	−1.03007	−	1.22759i
$747$	23.4754	+	16.7130i	0.858919	+	0.611496i
$748$	3.86176	−	1.03476i	0.141200	−	0.0378344i
$749$	2.92700	+	5.06971i	0.106950	+	0.185243i
$750$	38.6003	+	26.0076i	1.40948	+	0.949664i
$751$	−2.56529	+	0.933688i	−0.0936086	+	0.0340708i	−0.388400	−	0.921491i	$-0.626972\pi$
$751$	−2.56529	+	0.933688i	−0.0936086	+	0.0340708i	0.294791	+	0.955562i	$0.404750\pi$
$752$	−5.51096	+	20.5672i	−0.200964	+	0.750008i
$753$	3.80958	+	1.40348i	0.138829	+	0.0511458i
$754$	−52.1414	−	9.19393i	−1.89888	−	0.334823i
$755$	31.5824	+	15.5739i	1.14940	+	0.566794i
$756$	4.45696	+	6.52697i	0.162098	+	0.237384i
$757$	9.48014	+	6.63807i	0.344562	+	0.241265i	0.733028	−	0.680198i	$-0.238106\pi$
$757$	9.48014	+	6.63807i	0.344562	+	0.241265i	−0.388467	+	0.921463i	$0.626995\pi$
$758$	−38.5224	+	17.9633i	−1.39920	+	0.652456i
$759$	0.0431146	+	0.0304413i	0.00156496	+	0.00110495i
$760$	−23.2144	+	34.5561i	−0.842075	+	1.25348i
$761$		−	2.09174i		−	0.0758254i	−0.999281	−	0.0379127i	$-0.987929\pi$
$761$		−	2.09174i		−	0.0758254i	0.999281	−	0.0379127i	$-0.0120709\pi$
$762$	77.6474	+	14.0049i	2.81287	+	0.507343i
$763$	0.900097	−	1.28547i	0.0325857	−	0.0465372i
$764$	−15.6367	−	13.1207i	−0.565715	−	0.474692i
$765$	18.5750	+	23.5177i	0.671580	+	0.850286i
$766$	3.34668	−	18.9799i	0.120920	−	0.685773i
$767$	−19.0463	+	5.10345i	−0.687723	+	0.184275i
$768$	32.2813	+	38.7786i	1.16485	+	1.39930i
$769$	−10.0204	−	27.5308i	−0.361344	−	0.992784i	−0.978555	−	0.205987i	$-0.933960\pi$
$769$	−10.0204	−	27.5308i	−0.361344	−	0.992784i	0.617211	−	0.786798i	$-0.288263\pi$
$770$	−0.370433	+	0.354626i	−0.0133495	+	0.0127798i
$771$	0.458752	−	5.01732i	0.0165216	−	0.180695i
$772$	−22.2055	−	82.8720i	−0.799193	−	2.98263i
$773$	10.4005	+	14.8534i	0.374080	+	0.534241i	0.961415	−	0.275103i	$-0.0887118\pi$
$773$	10.4005	+	14.8534i	0.374080	+	0.534241i	−0.587335	+	0.809344i	$0.699823\pi$
$774$	33.0269	+	19.4143i	1.18713	+	0.697833i
$775$	41.9452	−	5.52389i	1.50672	−	0.198424i
$776$	27.1315	−	4.78402i	0.973964	−	0.171736i
$777$	−1.01574	+	5.63157i	−0.0364394	+	0.202032i
$778$	14.1535	+	14.1535i	0.507429	+	0.507429i
$779$	9.91793	+	31.7334i	0.355347	+	1.13697i
$780$	78.4718	+	15.9269i	2.80974	+	0.570275i
$781$	−0.0570007	−	0.0207466i	−0.00203964	−	0.000742370i
$782$	0.792070	−	1.13119i	0.0283244	−	0.0404514i
$783$	20.5493	+	3.87269i	0.734372	+	0.138399i
$784$	−11.9191	−	14.2046i	−0.425681	−	0.507306i
$785$	−18.9605	+	31.2474i	−0.676730	+	1.11527i
$786$	−35.1165	−	76.0835i	−1.25256	−	2.71381i
$787$	17.0240	+	4.56156i	0.606839	+	0.162602i	0.549138	−	0.835732i	$-0.314956\pi$
$787$	17.0240	+	4.56156i	0.606839	+	0.162602i	0.0577011	+	0.998334i	$0.481623\pi$
$788$	35.3040	−	75.7096i	1.25765	−	2.69704i
$789$	−0.334145	+	1.22780i	−0.0118959	+	0.0437110i
$790$	−8.26731	−	53.7065i	−0.294138	−	1.91079i
$791$	5.18083	+	2.99115i	0.184209	+	0.106353i
$792$	−1.76077	+	2.47321i	−0.0625662	+	0.0878817i
$793$	31.4487	+	2.75140i	1.11678	+	0.0977052i
$794$	40.9483	+	34.3597i	1.45320	+	1.21938i
$795$	0.0604329	−	2.35001i	0.00214334	−	0.0833464i
$796$	−58.9278	−	21.4480i	−2.08864	−	0.760203i
$797$	3.12824	+	3.12824i	0.110808	+	0.110808i	0.760337	−	0.649529i	$-0.225034\pi$
$797$	3.12824	+	3.12824i	0.110808	+	0.110808i	−0.649529	+	0.760337i	$0.725034\pi$
$798$	2.83986	−	6.73332i	0.100530	−	0.238357i
$799$		−	35.0780i		−	1.24097i
$800$	−9.65334	−	3.04327i	−0.341297	−	0.107596i
$801$	−6.96787	−	12.2899i	−0.246197	−	0.434241i
$802$	−36.6786	+	3.20896i	−1.29517	+	0.113312i
$803$	0.0450923	−	0.515408i	0.00159127	−	0.0181883i
$804$	5.44638	−	5.40392i	0.192079	−	0.190582i
$805$	−0.0126053	+	0.115120i	−0.000444279	+	0.00405743i
$806$	96.4082	−	55.6613i	3.39583	−	1.96059i
$807$	−13.0531	+	7.46827i	−0.459492	+	0.262896i
$808$	−28.3417	−	13.2159i	−0.997057	−	0.464935i
$809$	−5.28369	−	9.15163i	−0.185765	−	0.321754i	0.758069	−	0.652174i	$-0.226143\pi$
$809$	−5.28369	−	9.15163i	−0.185765	−	0.321754i	−0.943834	+	0.330420i	$0.892810\pi$
$810$	−47.2876	−	10.1771i	−1.66152	−	0.357588i
$811$	5.61148	−	31.8243i	0.197046	−	1.11750i	−0.712430	−	0.701743i	$-0.752405\pi$
$811$	5.61148	−	31.8243i	0.197046	−	1.11750i	0.909475	−	0.415758i	$-0.136484\pi$
$812$	6.09786	+	0.533493i	0.213993	+	0.0187219i
$813$	−4.45228	−	2.59381i	−0.156148	−	0.0909688i
$814$	−4.60115	+	0.811307i	−0.161270	+	0.0284363i
$815$	−14.5561	+	16.5987i	−0.509878	+	0.581427i
$816$	17.1414	+	12.1028i	0.600068	+	0.423682i
$817$	−0.952067	−	23.1395i	−0.0333086	−	0.809548i
$818$	−39.5571	+	39.5571i	−1.38308	+	1.38308i
$819$	−6.61279	−	0.0517612i	−0.231070	−	0.00180868i
$820$	53.5613	−	35.7901i	1.87044	−	1.24984i
$821$	0.477423	−	0.568971i	0.0166622	−	0.0198572i	−0.757649	−	0.652662i	$-0.773652\pi$
$821$	0.477423	−	0.568971i	0.0166622	−	0.0198572i	0.774311	+	0.632805i	$0.218097\pi$
$822$	70.6652	+	59.7680i	2.46473	+	2.08465i
$823$	−30.4019	+	21.2876i	−1.05974	+	0.742040i	−0.967289	−	0.253676i	$-0.918360\pi$
$823$	−30.4019	+	21.2876i	−1.05974	+	0.742040i	−0.0924544	+	0.995717i	$0.529471\pi$
$824$	34.8693	−	60.3955i	1.21473	−	2.10398i
$825$	0.0974449	−	2.04962i	0.00339259	−	0.0713587i
$826$	3.27650	−	1.19255i	0.114004	−	0.0414941i
$827$	10.5316	+	4.91096i	0.366219	+	0.170771i	0.597012	−	0.802232i	$-0.296354\pi$
$827$	10.5316	+	4.91096i	0.366219	+	0.170771i	−0.230793	+	0.973003i	$0.574132\pi$
$828$	0.115640	+	1.45264i	0.00401877	+	0.0504828i
$829$	−14.2071	−	8.20248i	−0.493433	−	0.284884i	0.232564	−	0.972581i	$-0.425288\pi$
$829$	−14.2071	−	8.20248i	−0.493433	−	0.284884i	−0.725998	+	0.687697i	$0.758622\pi$
$830$	−50.1457	+	12.2716i	−1.74058	+	0.425954i
$831$	−4.18887	−	50.1383i	−0.145310	−	1.73928i
$832$	−56.1061	+	4.90865i	−1.94513	+	0.170177i
$833$	25.0232	+	17.5214i	0.867001	+	0.607081i
$834$	21.2646	−	14.7659i	0.736332	−	0.511302i
$835$	2.64157	−	6.79319i	0.0914154	−	0.235088i
$836$	3.89669	+	0.179941i	0.134770	+	0.00622338i
$837$	−38.3321	+	21.5350i	−1.32495	+	0.744358i
$838$	−30.7978	−	66.0460i	−1.06389	−	2.28152i
$839$	−3.55582	−	20.1660i	−0.122760	−	0.696209i	−0.982613	−	0.185666i	$-0.940556\pi$
$839$	−3.55582	−	20.1660i	−0.122760	−	0.696209i	0.859852	−	0.510543i	$-0.170555\pi$
$840$	−6.61913	−	0.751006i	−0.228382	−	0.0259122i
$841$	−9.80903	+	8.23075i	−0.338242	+	0.283819i
$842$	3.40787	−	2.38622i	0.117443	−	0.0822345i
$843$	51.3172	+	18.9057i	1.76746	+	0.651146i
$844$	17.0011	−	9.81556i	0.585200	−	0.337866i
$845$	−27.3975	+	26.2285i	−0.942503	+	0.902287i
$846$	36.0522	+	43.6547i	1.23950	+	1.50088i
$847$	−4.25702	−	1.14066i	−0.146273	−	0.0391937i
$848$	−0.426011	−	1.58989i	−0.0146293	−	0.0545972i
$849$	15.3741	−	15.2543i	0.527639	−	0.523525i
$850$	−53.6375	−	2.33972i	−1.83975	−	0.0802518i
$851$	−0.678201	+	0.808248i	−0.0232484	+	0.0277064i
$852$	−0.566660	−	1.57605i	−0.0194135	−	0.0539946i
$853$	−15.0846	−	32.3490i	−0.516486	−	1.10761i	−0.975665	−	0.219265i	$-0.929634\pi$
$853$	−15.0846	−	32.3490i	−0.516486	−	1.10761i	0.459179	−	0.888344i	$-0.348144\pi$
$854$	−5.58233			−0.191023
$855$	10.3160	+	27.3602i	0.352801	+	0.935698i
$856$	−62.0873			−2.12210
$857$	−0.843680	−	1.80928i	−0.0288196	−	0.0618038i	0.891371	−	0.453274i	$-0.149744\pi$
$857$	−0.843680	−	1.80928i	−0.0288196	−	0.0618038i	−0.920191	+	0.391471i	$0.871966\pi$
$858$	−1.82677	−	5.08080i	−0.0623651	−	0.173456i
$859$	6.61120	−	7.87892i	0.225571	−	0.268825i	−0.641374	−	0.767228i	$-0.721635\pi$
$859$	6.61120	−	7.87892i	0.225571	−	0.268825i	0.866946	+	0.498403i	$0.166080\pi$
$860$	−42.4906	+	14.4245i	−1.44892	+	0.491873i
$861$	−3.77665	+	3.74721i	−0.128708	+	0.127704i
$862$	−18.4165	−	68.7313i	−0.627268	−	2.34100i
$863$	20.6032	+	5.52060i	0.701340	+	0.187924i	0.591831	−	0.806062i	$-0.298405\pi$
$863$	20.6032	+	5.52060i	0.701340	+	0.187924i	0.109509	+	0.993986i	$0.465072\pi$
$864$	10.4888	−	0.793680i	0.356835	−	0.0270016i
$865$	10.4302	+	0.227380i	0.354637	+	0.00773114i
$866$	22.9803	−	13.2677i	0.780903	−	0.450854i
$867$	−4.80769	−	1.77119i	−0.163278	−	0.0601529i
$868$	−10.5427	+	7.38205i	−0.357841	+	0.250563i
$869$	−1.83511	+	1.53984i	−0.0622520	+	0.0522356i
$870$	−29.3071	+	23.3344i	−0.993604	+	0.791110i
$871$	1.11475	+	6.32206i	0.0377719	+	0.214215i
$872$	7.03391	+	15.0843i	0.238198	+	0.510818i
$873$	8.31508	−	17.4733i	0.281423	−	0.591383i
$874$	1.07100	−	0.817544i	0.0362272	−	0.0276538i
$875$	4.03798	−	1.99161i	0.136509	−	0.0673288i
$876$	11.7336	−	8.14772i	0.396442	−	0.275286i
$877$	14.1517	+	9.90916i	0.477871	+	0.334609i	0.787569	−	0.616226i	$-0.211339\pi$
$877$	14.1517	+	9.90916i	0.477871	+	0.334609i	−0.309699	+	0.950835i	$0.600228\pi$
$878$	−65.6412	+	5.74286i	−2.21528	+	0.193812i
$879$	−2.08846	−	24.9976i	−0.0704420	−	0.843148i
$880$	−0.341518	−	1.39555i	−0.0115126	−	0.0470439i
$881$	22.1656	+	12.7973i	0.746777	+	0.431152i	0.824528	−	0.565821i	$-0.191441\pi$
$881$	22.1656	+	12.7973i	0.746777	+	0.431152i	−0.0777515	+	0.996973i	$0.524774\pi$
$882$	−49.1495	+	3.91263i	−1.65495	+	0.131745i
$883$	−40.0673	−	18.6837i	−1.34837	−	0.628756i	−0.391746	−	0.920074i	$-0.628129\pi$
$883$	−40.0673	−	18.6837i	−1.34837	−	0.628756i	−0.956627	+	0.291317i	$0.905906\pi$
$884$	−86.7920	+	31.5897i	−2.91913	+	1.06248i
$885$	−6.21936	+	12.4888i	−0.209061	+	0.419806i
$886$	17.8292	−	30.8810i	0.598982	−	1.03747i
$887$	−6.07655	+	4.25484i	−0.204030	+	0.142864i	−0.671126	−	0.741343i	$-0.734189\pi$
$887$	−6.07655	+	4.25484i	−0.204030	+	0.142864i	0.467096	+	0.884207i	$0.345300\pi$
$888$	−46.3398	−	39.1938i	−1.55506	−	1.31526i
$889$	4.90597	−	5.84671i	0.164541	−	0.196092i
$890$	24.8235	+	4.93718i	0.832084	+	0.165495i
$891$	0.697879	+	2.01501i	0.0233798	+	0.0675053i
$892$	−14.4292	+	14.4292i	−0.483124	+	0.483124i
$893$	10.3738	−	32.6156i	0.347146	−	1.09144i
$894$	44.0819	+	31.1243i	1.47432	+	1.04095i
$895$	0.359750	+	5.48705i	0.0120251	+	0.183412i
$896$	8.20219	−	1.44627i	0.274016	−	0.0483164i
$897$	−1.05354	−	0.613773i	−0.0351768	−	0.0204933i
$898$	89.1567	+	7.80020i	2.97520	+	0.260296i
$899$	−5.91302	+	33.5344i	−0.197210	+	1.11844i
$900$	45.2148	−	34.1384i	1.50716	−	1.13795i
$901$	1.35581	+	2.34833i	0.0451685	+	0.0782341i
$902$	−3.93675	−	1.83574i	−0.131080	−	0.0611234i
$903$	3.21665	−	1.84039i	0.107043	−	0.0612442i
$904$	−54.9477	+	31.7241i	−1.82753	+	1.05513i
$905$	−16.8531	−	1.84538i	−0.560218	−	0.0613425i
$906$	46.5388	−	46.1760i	1.54615	−	1.53409i
$907$	0.881150	−	10.0716i	0.0292581	−	0.334422i	−0.967432	−	0.253130i	$-0.918540\pi$
$907$	0.881150	−	10.0716i	0.0292581	−	0.334422i	0.996690	−	0.0812917i	$-0.0259045\pi$
$908$	−37.9619	+	3.32124i	−1.25981	+	0.110219i
$909$	−19.1076	+	10.8332i	−0.633758	+	0.359316i
$910$	7.81119	−	8.90731i	0.258938	−	0.295274i
$911$		−	26.7159i		−	0.885137i	−0.896735	−	0.442569i	$-0.854067\pi$
$911$		−	26.7159i		−	0.885137i	0.896735	−	0.442569i	$-0.145933\pi$
$912$	12.3589	+	16.3225i	0.409244	+	0.540493i
$913$	1.60933	+	1.60933i	0.0532611	+	0.0532611i
$914$	21.4405	+	7.80371i	0.709189	+	0.258124i
$915$	16.1952	−	15.3831i	0.535397	−	0.508551i
$916$	15.7015	+	13.1751i	0.518793	+	0.435319i
$917$	−8.07513	−	0.706482i	−0.266664	−	0.0233301i
$918$	52.6503	−	18.4660i	1.73772	−	0.609470i
$919$	0.154400	+	0.0891431i	0.00509320	+	0.00294056i	0.502544	−	0.864551i	$-0.332397\pi$
$919$	0.154400	+	0.0891431i	0.00509320	+	0.00294056i	−0.497451	+	0.867492i	$0.665731\pi$
$920$	−0.990532	−	0.726258i	−0.0326569	−	0.0239440i
$921$	12.3941	−	45.5418i	0.408400	−	1.50065i
$922$	−20.4513	+	43.8580i	−0.673529	+	1.44439i
$923$	1.35360	+	0.362696i	0.0445543	+	0.0119383i
$924$	0.261588	+	0.566758i	0.00860562	+	0.0186450i
$925$	40.6697	+	5.35261i	1.33721	+	0.175993i
$926$	−16.7770	−	19.9941i	−0.551328	−	0.657047i
$927$	−20.3534	−	44.5551i	−0.668492	−	1.46338i
$928$	4.67270	−	6.67330i	0.153389	−	0.219062i
$929$	−19.2416	−	7.00336i	−0.631295	−	0.229773i	0.00649974	−	0.999979i	$-0.497931\pi$
$929$	−19.2416	−	7.00336i	−0.631295	−	0.229773i	−0.637795	+	0.770206i	$0.720153\pi$
$930$	15.6673	−	77.1929i	0.513752	−	2.53126i
$931$	18.0849	+	23.6917i	0.592709	+	0.776464i
$932$	−16.6195	−	16.6195i	−0.544391	−	0.544391i
$933$	−2.68389	+	14.8803i	−0.0878668	+	0.487160i
$934$	6.29630	−	1.11021i	0.206021	−	0.0363271i
$935$	1.13849	+	2.07509i	0.0372326	+	0.0678628i
$936$	35.5430	−	60.4643i	1.16176	−	1.97634i
$937$	19.9074	+	28.4307i	0.650346	+	0.928790i	0.999967	−	0.00810070i	$-0.00257856\pi$
$937$	19.9074	+	28.4307i	0.650346	+	0.928790i	−0.349621	+	0.936891i	$0.613690\pi$
$938$	−0.293806	−	1.09650i	−0.00959310	−	0.0358019i
$939$	−0.171439	+	1.87501i	−0.00559471	+	0.0611887i
$940$	−66.2987	−	1.44532i	−2.16242	−	0.0471412i
$941$	10.6583	+	29.2834i	0.347450	+	0.954611i	0.983170	+	0.182692i	$0.0584810\pi$
$941$	10.6583	+	29.2834i	0.347450	+	0.954611i	−0.635720	+	0.771920i	$0.719297\pi$
$942$	43.5359	+	52.2984i	1.41848	+	1.70397i
$943$	−0.947506	+	0.253883i	−0.0308550	+	0.00826758i
$944$	−1.69632	+	9.62032i	−0.0552106	+	0.313115i
$945$	−3.12614	+	3.48150i	−0.101693	+	0.113253i
$946$	2.31784	+	1.94490i	0.0753595	+	0.0632341i
$947$	−13.7417	+	19.6252i	−0.446546	+	0.637733i	−0.977815	−	0.209470i	$-0.932826\pi$
$947$	−13.7417	+	19.6252i	−0.446546	+	0.637733i	0.531270	+	0.847203i	$0.321715\pi$
$948$	−65.0928	−	11.7405i	−2.11411	−	0.381312i
$949$			11.9525i			0.387995i
$950$	−49.1804	−	18.0380i	−1.59562	−	0.585230i
$951$	23.9295	+	16.8956i	0.775968	+	0.547877i
$952$	6.96415	−	3.24744i	0.225709	−	0.105250i
$953$	48.8322	+	34.1927i	1.58183	+	1.10761i	0.940213	+	0.340586i	$0.110625\pi$
$953$	48.8322	+	34.1927i	1.58183	+	1.10761i	0.641618	+	0.767024i	$0.278263\pi$
$954$	−4.10086	−	1.52904i	−0.132770	−	0.0495046i
$955$	5.34461	−	10.8383i	0.172947	−	0.350720i
$956$	−78.7665	−	13.8887i	−2.54749	−	0.449191i
$957$	1.54971	+	0.570927i	0.0500951	+	0.0184555i
$958$	−18.6813	+	69.7195i	−0.603565	+	2.25254i
$959$	8.41295	−	3.06206i	0.271668	−	0.0988792i
$960$	−23.6885	+	32.0446i	−0.764543	+	1.03424i
$961$	−20.2983	−	35.1576i	−0.654783	−	1.13412i
$962$	104.258	−	27.9359i	3.36142	−	0.900691i
$963$	−25.2923	+	35.5260i	−0.815033	+	1.14481i
$964$	−27.0001	−	32.1774i	−0.869614	−	1.03637i
$965$	44.5308	−	24.4316i	1.43350	−	0.786480i
$966$	0.195049	+	0.0918838i	0.00627560	+	0.00295631i
$967$	−20.1567	+	9.39923i	−0.648196	+	0.302259i	−0.718770	−	0.695248i	$-0.755295\pi$
$967$	−20.1567	+	9.39923i	−0.648196	+	0.302259i	0.0705739	+	0.997507i	$0.477517\pi$
$968$	33.0520	−	33.0520i	1.06233	−	1.06233i
$969$	−26.6261	−	20.7041i	−0.855355	−	0.665112i
$970$	13.9627	+	31.7309i	0.448315	+	1.01882i
$971$	−12.7554	+	35.0453i	−0.409342	+	1.12466i	0.548196	+	0.836350i	$0.315315\pi$
$971$	−12.7554	+	35.0453i	−0.409342	+	1.12466i	−0.957538	+	0.288307i	$0.906908\pi$
$972$	−30.4310	+	50.4039i	−0.976074	+	1.61670i
$973$	−0.218264	−	2.49477i	−0.00699722	−	0.0799786i
$974$	18.5697	−	15.5818i	0.595010	−	0.499273i
$975$	1.88427	+	47.3667i	0.0603448	+	1.51695i
$976$	7.81985	−	13.5444i	0.250307	−	0.433545i
$977$	0.424284	−	1.58345i	0.0135740	−	0.0506590i	−0.958807	−	0.284060i	$-0.908319\pi$
$977$	0.424284	−	1.58345i	0.0135740	−	0.0506590i	0.972381	+	0.233401i	$0.0749853\pi$
$978$	20.4118	+	35.6760i	0.652698	+	1.14079i
$979$	−0.381624	−	1.04850i	−0.0121967	−	0.0335103i
$980$	34.1472	−	46.5728i	1.09079	−	1.48771i
$981$	11.4965	+	2.12006i	0.367055	+	0.0676883i
$982$	−19.8519	−	28.3515i	−0.633500	−	0.904732i
$983$	2.03537	−	23.2644i	0.0649182	−	0.742018i	−0.892071	−	0.451895i	$-0.850748\pi$
$983$	2.03537	−	23.2644i	0.0649182	−	0.742018i	0.956989	−	0.290123i	$-0.0936963\pi$
$984$	−14.3907	−	54.5601i	−0.458759	−	1.73931i
$985$	48.5051	+	9.64726i	1.54550	+	0.307387i
$986$	14.7794	−	40.6060i	0.470671	−	1.29316i
$987$	5.39727	−	0.929920i	0.171797	−	0.0295997i
$988$	−90.0417	+	3.70473i	−2.86461	+	0.117863i
$989$	0.683290			0.0217274
$990$	−3.54958	−	1.41236i	−0.112813	−	0.0448877i
$991$	8.82541	+	50.0514i	0.280348	+	1.58993i	0.721443	+	0.692474i	$0.243479\pi$
$991$	8.82541	+	50.0514i	0.280348	+	1.58993i	−0.441095	+	0.897461i	$0.645410\pi$
$992$	1.49288	+	17.0637i	0.0473990	+	0.541773i
$993$	0.564235	−	0.667110i	0.0179055	−	0.0211701i
$994$	−0.244037	−	0.0430302i	−0.00774037	−	0.00136484i
$995$	4.04099	−	36.9048i	0.128108	−	1.16996i
$996$	−5.72181	+	62.5789i	−0.181303	+	1.98289i
$997$	−11.8366	+	25.3836i	−0.374868	+	0.803906i	0.624864	+	0.780734i	$0.285154\pi$
$997$	−11.8366	+	25.3836i	−0.374868	+	0.803906i	−0.999731	+	0.0231724i	$0.992623\pi$
$998$	12.0068	−	25.7487i	0.380070	−	0.815062i
$999$	−41.3038	+	10.5492i	−1.30679	+	0.333760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.bi.a.23.32	yes	432
3.2	odd	2	inner	285.2.bi.a.23.5	✓	432
5.2	odd	4	inner	285.2.bi.a.137.5	yes	432
15.2	even	4	inner	285.2.bi.a.137.32	yes	432
19.5	even	9	inner	285.2.bi.a.233.32	yes	432
57.5	odd	18	inner	285.2.bi.a.233.5	yes	432
95.62	odd	36	inner	285.2.bi.a.62.5	yes	432
285.62	even	36	inner	285.2.bi.a.62.32	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.bi.a.23.5	✓	432	3.2	odd	2	inner
285.2.bi.a.23.32	yes	432	1.1	even	1	trivial
285.2.bi.a.62.5	yes	432	95.62	odd	36	inner
285.2.bi.a.62.32	yes	432	285.62	even	36	inner
285.2.bi.a.137.5	yes	432	5.2	odd	4	inner
285.2.bi.a.137.32	yes	432	15.2	even	4	inner
285.2.bi.a.233.5	yes	432	57.5	odd	18	inner
285.2.bi.a.233.32	yes	432	19.5	even	9	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01578 + 2.17835i) q^{2} +(0.586022 + 1.62990i) q^{3} +(-2.42782 + 2.89336i) q^{4} +(-2.00549 - 0.988948i) q^{5} +(-2.95522 + 2.93218i) q^{6} +(0.104229 + 0.388987i) q^{7} +(-4.12559 - 1.10545i) q^{8} +(-2.31316 + 1.91032i) q^{9} +O(q^{10})\)	\(q+(1.01578 + 2.17835i) q^{2} +(0.586022 + 1.62990i) q^{3} +(-2.42782 + 2.89336i) q^{4} +(-2.00549 - 0.988948i) q^{5} +(-2.95522 + 2.93218i) q^{6} +(0.104229 + 0.388987i) q^{7} +(-4.12559 - 1.10545i) q^{8} +(-2.31316 + 1.91032i) q^{9} +(0.117137 - 5.37321i) q^{10} +(-0.205194 + 0.118469i) q^{11} +(-6.13864 - 2.26153i) q^{12} +(4.48384 - 3.13962i) q^{13} +(-0.741475 + 0.622172i) q^{14} +(0.436627 - 3.84829i) q^{15} +(-0.470898 - 2.67059i) q^{16} +(1.88803 + 4.04888i) q^{17} +(-6.51099 - 3.09840i) q^{18} +(0.558094 + 4.32302i) q^{19} +(7.73034 - 3.40161i) q^{20} +(-0.572930 + 0.397837i) q^{21} +(-0.466498 - 0.326645i) q^{22} +(-0.128117 + 0.0112087i) q^{23} +(-0.615914 - 7.37211i) q^{24} +(3.04397 + 3.96665i) q^{25} +(11.3938 + 6.57821i) q^{26} +(-4.46919 - 2.65073i) q^{27} +(-1.37853 - 0.642818i) q^{28} +(-3.78163 + 1.37640i) q^{29} +(8.82644 - 2.95789i) q^{30} +(4.23074 - 7.32785i) q^{31} +(-1.65824 + 1.16111i) q^{32} +(-0.313340 - 0.265020i) q^{33} +(-6.90206 + 8.22555i) q^{34} +(0.175658 - 0.883185i) q^{35} +(0.0886901 - 11.3307i) q^{36} +(5.80116 - 5.80116i) q^{37} +(-8.85015 + 5.60697i) q^{38} +(7.74490 + 5.46833i) q^{39} +(7.18058 + 6.29695i) q^{40} +(7.51153 - 1.32449i) q^{41} +(-1.44860 - 0.843925i) q^{42} +(-5.29284 - 0.463063i) q^{43} +(0.155400 - 0.881319i) q^{44} +(6.52821 - 1.54352i) q^{45} +(-0.154555 - 0.267697i) q^{46} +(-7.11624 - 3.31836i) q^{47} +(4.07685 - 2.33254i) q^{48} +(5.92173 - 3.41891i) q^{49} +(-5.54874 + 10.6601i) q^{50} +(-5.49286 + 5.45003i) q^{51} +(-1.80190 + 20.5958i) q^{52} +(0.604662 - 0.0529010i) q^{53} +(1.23450 - 12.4280i) q^{54} +(0.528673 - 0.0346616i) q^{55} -1.72002i q^{56} +(-6.71905 + 3.44302i) q^{57} +(-6.83959 - 6.83959i) q^{58} +(-3.38507 - 1.23206i) q^{59} +(10.0744 + 10.6063i) q^{60} +(4.41801 + 3.70715i) q^{61} +(20.2601 + 1.77253i) q^{62} +(-0.984185 - 0.700678i) q^{63} +(-8.91067 - 5.14458i) q^{64} +(-12.0972 + 1.86219i) q^{65} +(0.259022 - 0.951767i) q^{66} +(-0.495644 + 1.06291i) q^{67} +(-16.2986 - 4.36721i) q^{68} +(-0.0933483 - 0.202249i) q^{69} +(2.10232 - 0.514478i) q^{70} +(0.164561 + 0.196117i) q^{71} +(11.6549 - 5.32410i) q^{72} +(-1.25246 + 1.78870i) q^{73} +(18.5296 + 6.74424i) q^{74} +(-4.68141 + 7.28590i) q^{75} +(-13.8630 - 8.88074i) q^{76} +(-0.0674699 - 0.0674699i) q^{77} +(-4.04482 + 22.4257i) q^{78} +(9.95696 - 1.75568i) q^{79} +(-1.69670 + 5.82154i) q^{80} +(1.70139 - 8.83772i) q^{81} +(10.5153 + 15.0174i) q^{82} +(-2.48613 - 9.27835i) q^{83} +(0.239882 - 2.62357i) q^{84} +(0.217721 - 9.98715i) q^{85} +(-4.36765 - 12.0000i) q^{86} +(-4.45952 - 5.35709i) q^{87} +(0.977505 - 0.261922i) q^{88} +(-0.817749 + 4.63769i) q^{89} +(9.99356 + 12.6528i) q^{90} +(1.68862 + 1.41692i) q^{91} +(0.278612 - 0.397900i) q^{92} +(14.4230 + 2.60140i) q^{93} -18.8724i q^{94} +(3.15599 - 9.22170i) q^{95} +(-2.86426 - 2.02233i) q^{96} +(-5.84597 + 2.72602i) q^{97} +(13.4628 + 9.42673i) q^{98} +(0.248333 - 0.666022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

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