LMFDB - Embedded newform 171.2.x.a.110.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			110.15
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30761 - 1.09721i) q^{2} +(0.387860 + 1.68807i) q^{3} +(0.158664 - 0.899827i) q^{4} +(1.05557 - 2.90015i) q^{5} +(2.35933 + 1.78176i) q^{6} +(-0.421554 - 0.730152i) q^{7} +(0.927128 + 1.60583i) q^{8} +(-2.69913 + 1.30947i) q^{9} +O(q^{10})$	\(q+(1.30761 - 1.09721i) q^{2} +(0.387860 + 1.68807i) q^{3} +(0.158664 - 0.899827i) q^{4} +(1.05557 - 2.90015i) q^{5} +(2.35933 + 1.78176i) q^{6} +(-0.421554 - 0.730152i) q^{7} +(0.927128 + 1.60583i) q^{8} +(-2.69913 + 1.30947i) q^{9} +(-1.80181 - 4.95044i) q^{10} +5.25332i q^{11} +(1.58051 - 0.0811718i) q^{12} +(-2.06528 - 5.67432i) q^{13} +(-1.35236 - 0.492218i) q^{14} +(5.30506 + 0.657017i) q^{15} +(4.69147 + 1.70755i) q^{16} +(0.911301 - 2.50378i) q^{17} +(-2.09264 + 4.67378i) q^{18} +(-3.91070 + 1.92521i) q^{19} +(-2.44215 - 1.40998i) q^{20} +(1.06904 - 0.994807i) q^{21} +(5.76401 + 6.86928i) q^{22} +(-5.64507 - 0.995378i) q^{23} +(-2.35115 + 2.18789i) q^{24} +(-3.46643 - 2.90868i) q^{25} +(-8.92651 - 5.15373i) q^{26} +(-3.25735 - 4.04842i) q^{27} +(-0.723896 + 0.263476i) q^{28} +(-0.889964 + 5.04724i) q^{29} +(7.65781 - 4.96165i) q^{30} +4.15289i q^{31} +(4.52328 - 1.64634i) q^{32} +(-8.86796 + 2.03755i) q^{33} +(-1.55555 - 4.27385i) q^{34} +(-2.56253 + 0.451843i) q^{35} +(0.750038 + 2.63651i) q^{36} -4.72641i q^{37} +(-3.00129 + 6.80828i) q^{38} +(8.77759 - 5.68718i) q^{39} +(5.63581 - 0.993745i) q^{40} +(-2.20913 + 1.85368i) q^{41} +(0.306371 - 2.47378i) q^{42} +(-0.757486 - 4.29592i) q^{43} +(4.72708 + 0.833512i) q^{44} +(0.948531 + 9.21012i) q^{45} +(-8.47367 + 4.89227i) q^{46} +(5.55641 + 0.979745i) q^{47} +(-1.06283 + 8.58179i) q^{48} +(3.14459 - 5.44658i) q^{49} -7.72417 q^{50} +(4.58000 + 0.567221i) q^{51} +(-5.43359 + 0.958089i) q^{52} +(9.57018 + 8.03034i) q^{53} +(-8.70130 - 1.71974i) q^{54} +(15.2354 + 5.54525i) q^{55} +(0.781668 - 1.35389i) q^{56} +(-4.76669 - 5.85480i) q^{57} +(4.37417 + 7.57628i) q^{58} +(-0.518580 - 2.94101i) q^{59} +(1.43292 - 4.66939i) q^{60} +(6.29738 - 2.29206i) q^{61} +(4.55661 + 5.43035i) q^{62} +(2.09394 + 1.41877i) q^{63} +(-0.884270 + 1.53160i) q^{64} -18.6365 q^{65} +(-9.36017 + 12.3943i) q^{66} +(-1.11799 + 1.33237i) q^{67} +(-2.10838 - 1.21727i) q^{68} +(-0.509232 - 9.91531i) q^{69} +(-2.85501 + 3.40247i) q^{70} +(5.22326 - 4.38284i) q^{71} +(-4.60522 - 3.12031i) q^{72} +(-0.376772 - 2.13678i) q^{73} +(-5.18587 - 6.18028i) q^{74} +(3.56556 - 6.97973i) q^{75} +(1.11187 + 3.82441i) q^{76} +(3.83573 - 2.21456i) q^{77} +(5.23759 - 17.0675i) q^{78} +(1.27977 - 3.51615i) q^{79} +(9.90433 - 11.8035i) q^{80} +(5.57060 - 7.06883i) q^{81} +(-0.854794 + 4.84778i) q^{82} +(7.69241 - 4.44121i) q^{83} +(-0.725535 - 1.11979i) q^{84} +(-6.29940 - 5.28582i) q^{85} +(-5.70403 - 4.78625i) q^{86} +(-8.86525 + 0.455303i) q^{87} +(-8.43596 + 4.87050i) q^{88} +(-1.29317 + 7.33393i) q^{89} +(11.3458 + 11.0025i) q^{90} +(-3.27249 + 3.90000i) q^{91} +(-1.79133 + 4.92165i) q^{92} +(-7.01036 + 1.61074i) q^{93} +(8.34058 - 4.81544i) q^{94} +(1.45540 + 13.3738i) q^{95} +(4.53352 + 6.99704i) q^{96} +(1.81856 + 2.16727i) q^{97} +(-1.86417 - 10.5723i) q^{98} +(-6.87905 - 14.1794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	1.30761	−	1.09721i	0.924617	−	0.775846i	−0.0502260	−	0.998738i	$-0.515994\pi$
$2$	1.30761	−	1.09721i	0.924617	−	0.775846i	0.974843	+	0.222892i	$0.0715497\pi$
$3$	0.387860	+	1.68807i	0.223931	+	0.974605i
$3$	0.387860	+	1.68807i	0.223931	+	0.974605i
$4$	0.158664	−	0.899827i	0.0793318	−	0.449913i
$5$	1.05557	−	2.90015i	0.472065	−	1.29699i	−0.444025	−	0.896014i	$-0.646450\pi$
$5$	1.05557	−	2.90015i	0.472065	−	1.29699i	0.916090	−	0.400973i	$-0.131328\pi$
$6$	2.35933	+	1.78176i	0.963194	+	0.727401i
$7$	−0.421554	−	0.730152i	−0.159332	−	0.275972i	0.775296	−	0.631598i	$-0.217601\pi$
$7$	−0.421554	−	0.730152i	−0.159332	−	0.275972i	−0.934628	+	0.355627i	$0.884267\pi$
$8$	0.927128	+	1.60583i	0.327789	+	0.567748i
$9$	−2.69913	+	1.30947i	−0.899710	+	0.436488i
$10$	−1.80181	−	4.95044i	−0.569783	−	1.56547i
$11$			5.25332i			1.58394i	0.610562	+	0.791969i	$0.290944\pi$
$11$			5.25332i			1.58394i	−0.610562	+	0.791969i	$0.709056\pi$
$12$	1.58051	−	0.0811718i	0.456253	−	0.0234323i
$13$	−2.06528	−	5.67432i	−0.572807	−	1.57377i	−0.800048	−	0.599936i	$-0.795193\pi$
$13$	−2.06528	−	5.67432i	−0.572807	−	1.57377i	0.227241	−	0.973838i	$-0.427029\pi$
$14$	−1.35236	−	0.492218i	−0.361433	−	0.131551i
$15$	5.30506	+	0.657017i	1.36976	+	0.169641i
$16$	4.69147	+	1.70755i	1.17287	+	0.426888i
$17$	0.911301	−	2.50378i	0.221023	−	0.607256i	−0.778776	−	0.627302i	$-0.784159\pi$
$17$	0.911301	−	2.50378i	0.221023	−	0.607256i	0.999799	+	0.0200463i	$0.00638136\pi$
$18$	−2.09264	+	4.67378i	−0.493239	+	1.10162i
$19$	−3.91070	+	1.92521i	−0.897176	+	0.441674i
$19$	−3.91070	+	1.92521i	−0.897176	+	0.441674i
$20$	−2.44215	−	1.40998i	−0.546082	−	0.315281i
$21$	1.06904	−	0.994807i	0.233284	−	0.217085i
$22$	5.76401	+	6.86928i	1.22889	+	1.46454i
$23$	−5.64507	−	0.995378i	−1.17708	−	0.207551i	−0.449311	−	0.893375i	$-0.648331\pi$
$23$	−5.64507	−	0.995378i	−1.17708	−	0.207551i	−0.727767	+	0.685825i	$0.759442\pi$
$24$	−2.35115	+	2.18789i	−0.479927	+	0.446601i
$25$	−3.46643	−	2.90868i	−0.693287	−	0.581737i
$26$	−8.92651	−	5.15373i	−1.75063	−	1.01073i
$27$	−3.25735	−	4.04842i	−0.626877	−	0.779118i
$28$	−0.723896	+	0.263476i	−0.136803	+	0.0497924i
$29$	−0.889964	+	5.04724i	−0.165262	+	0.937249i	0.783531	+	0.621352i	$0.213416\pi$
$29$	−0.889964	+	5.04724i	−0.165262	+	0.937249i	−0.948794	+	0.315896i	$0.897695\pi$
$30$	7.65781	−	4.96165i	1.39812	−	0.905870i
$31$			4.15289i			0.745882i	0.927855	+	0.372941i	$0.121651\pi$
$31$			4.15289i			0.745882i	−0.927855	+	0.372941i	$0.878349\pi$
$32$	4.52328	−	1.64634i	0.799610	−	0.291034i
$33$	−8.86796	+	2.03755i	−1.54371	+	0.354693i
$34$	−1.55555	−	4.27385i	−0.266775	−	0.732959i
$35$	−2.56253	+	0.451843i	−0.433147	+	0.0763755i
$36$	0.750038	+	2.63651i	0.125006	+	0.439419i
$37$		−	4.72641i		−	0.777017i	−0.921445	−	0.388508i	$-0.872990\pi$
$37$		−	4.72641i		−	0.777017i	0.921445	−	0.388508i	$-0.127010\pi$
$38$	−3.00129	+	6.80828i	−0.486873	+	1.10445i
$39$	8.77759	−	5.68718i	1.40554	−	0.910677i
$40$	5.63581	−	0.993745i	0.891099	−	0.157125i
$41$	−2.20913	+	1.85368i	−0.345009	+	0.289497i	−0.798782	−	0.601620i	$-0.794522\pi$
$41$	−2.20913	+	1.85368i	−0.345009	+	0.289497i	0.453773	+	0.891117i	$0.350078\pi$
$42$	0.306371	−	2.47378i	0.0472741	−	0.381712i
$43$	−0.757486	−	4.29592i	−0.115516	−	0.655121i	−0.986494	−	0.163800i	$-0.947625\pi$
$43$	−0.757486	−	4.29592i	−0.115516	−	0.655121i	0.870978	−	0.491322i	$-0.163486\pi$
$44$	4.72708	+	0.833512i	0.712634	+	0.125657i
$45$	0.948531	+	9.21012i	0.141399	+	1.37296i
$46$	−8.47367	+	4.89227i	−1.24937	+	0.721326i
$47$	5.55641	+	0.979745i	0.810485	+	0.142910i	0.563508	−	0.826111i	$-0.309451\pi$
$47$	5.55641	+	0.979745i	0.810485	+	0.142910i	0.246978	+	0.969021i	$0.420563\pi$
$48$	−1.06283	+	8.58179i	−0.153407	+	1.23868i
$49$	3.14459	−	5.44658i	0.449226	−	0.778083i
$50$	−7.72417			−1.09236
$51$	4.58000	+	0.567221i	0.641328	+	0.0794268i
$52$	−5.43359	+	0.958089i	−0.753504	+	0.132863i
$53$	9.57018	+	8.03034i	1.31457	+	1.10305i	0.987427	+	0.158075i	$0.0505289\pi$
$53$	9.57018	+	8.03034i	1.31457	+	1.10305i	0.327139	+	0.944976i	$0.393916\pi$
$54$	−8.70130	−	1.71974i	−1.18410	−	0.234027i
$55$	15.2354	+	5.54525i	2.05435	+	0.747721i
$56$	0.781668	−	1.35389i	0.104455	−	0.180921i
$57$	−4.76669	−	5.85480i	−0.631363	−	0.775487i
$58$	4.37417	+	7.57628i	0.574356	+	0.994814i
$59$	−0.518580	−	2.94101i	−0.0675133	−	0.382887i	−0.999777	−	0.0211081i	$-0.993281\pi$
$59$	−0.518580	−	2.94101i	−0.0675133	−	0.382887i	0.932264	−	0.361779i	$-0.117831\pi$
$60$	1.43292	−	4.66939i	0.184989	−	0.602815i
$61$	6.29738	−	2.29206i	0.806297	−	0.293468i	0.0942040	−	0.995553i	$-0.469969\pi$
$61$	6.29738	−	2.29206i	0.806297	−	0.293468i	0.712094	+	0.702085i	$0.247747\pi$
$62$	4.55661	+	5.43035i	0.578689	+	0.689655i
$63$	2.09394	+	1.41877i	0.263811	+	0.178748i
$64$	−0.884270	+	1.53160i	−0.110534	+	0.191450i
$65$	−18.6365			−2.31157
$66$	−9.36017	+	12.3943i	−1.15216	+	1.52564i
$67$	−1.11799	+	1.33237i	−0.136584	+	0.162774i	−0.830001	−	0.557762i	$-0.811660\pi$
$67$	−1.11799	+	1.33237i	−0.136584	+	0.162774i	0.693417	+	0.720537i	$0.256105\pi$
$68$	−2.10838	−	1.21727i	−0.255678	−	0.147616i
$69$	−0.509232	−	9.91531i	−0.0613044	−	1.19366i
$70$	−2.85501	+	3.40247i	−0.341239	+	0.406673i
$71$	5.22326	−	4.38284i	0.619887	−	0.520147i	−0.277881	−	0.960615i	$-0.589632\pi$
$71$	5.22326	−	4.38284i	0.619887	−	0.520147i	0.897768	+	0.440469i	$0.145188\pi$
$72$	−4.60522	−	3.12031i	−0.542730	−	0.367732i
$73$	−0.376772	−	2.13678i	−0.0440978	−	0.250091i	0.954788	−	0.297288i	$-0.0960822\pi$
$73$	−0.376772	−	2.13678i	−0.0440978	−	0.250091i	−0.998886	+	0.0471971i	$0.984971\pi$
$74$	−5.18587	−	6.18028i	−0.602845	−	0.718443i
$75$	3.56556	−	6.97973i	0.411715	−	0.805949i
$76$	1.11187	+	3.82441i	0.127540	+	0.438690i
$77$	3.83573	−	2.21456i	0.437122	−	0.252372i
$78$	5.23759	−	17.0675i	0.593040	−	1.93251i
$79$	1.27977	−	3.51615i	0.143986	−	0.395598i	−0.846646	−	0.532156i	$-0.821382\pi$
$79$	1.27977	−	3.51615i	0.143986	−	0.395598i	0.990632	+	0.136558i	$0.0436041\pi$
$80$	9.90433	−	11.8035i	1.10734	−	1.31967i
$81$	5.57060	−	7.06883i	0.618956	−	0.785426i
$82$	−0.854794	+	4.84778i	−0.0943962	+	0.535347i
$83$	7.69241	−	4.44121i	0.844351	−	0.487486i	−0.0143896	−	0.999896i	$-0.504581\pi$
$83$	7.69241	−	4.44121i	0.844351	−	0.487486i	0.858741	+	0.512410i	$0.171247\pi$
$84$	−0.725535	−	1.11979i	−0.0791624	−	0.122179i
$85$	−6.29940	−	5.28582i	−0.683266	−	0.573328i
$86$	−5.70403	−	4.78625i	−0.615081	−	0.516114i
$87$	−8.86525	+	0.455303i	−0.950455	+	0.0488136i
$88$	−8.43596	+	4.87050i	−0.899276	+	0.519197i
$89$	−1.29317	+	7.33393i	−0.137076	+	0.777395i	0.836316	+	0.548248i	$0.184705\pi$
$89$	−1.29317	+	7.33393i	−0.137076	+	0.777395i	−0.973392	+	0.229147i	$0.926406\pi$
$90$	11.3458	+	11.0025i	1.19595	+	1.15976i
$91$	−3.27249	+	3.90000i	−0.343050	+	0.408831i
$92$	−1.79133	+	4.92165i	−0.186760	+	0.513118i
$93$	−7.01036	+	1.61074i	−0.726940	+	0.167026i
$94$	8.34058	−	4.81544i	0.860265	−	0.496674i
$95$	1.45540	+	13.3738i	0.149321	+	1.37212i
$96$	4.53352	+	6.99704i	0.462701	+	0.714132i
$97$	1.81856	+	2.16727i	0.184647	+	0.220053i	0.850425	−	0.526096i	$-0.176345\pi$
$97$	1.81856	+	2.16727i	0.184647	+	0.220053i	−0.665778	+	0.746150i	$0.731900\pi$
$98$	−1.86417	−	10.5723i	−0.188310	−	1.06796i
$99$	−6.87905	−	14.1794i	−0.691370	−	1.42508i
$100$	−3.16731	+	2.65769i	−0.316731	+	0.265769i
$101$	0.671009	−	0.799678i	0.0667679	−	0.0795709i	−0.731627	−	0.681706i	$-0.761239\pi$
$101$	0.671009	−	0.799678i	0.0667679	−	0.0795709i	0.798395	+	0.602135i	$0.205683\pi$
$102$	6.61120	−	4.28353i	0.654606	−	0.424133i
$103$	−3.33129	−	1.92332i	−0.328242	−	0.189511i	0.326818	−	0.945087i	$-0.394023\pi$
$103$	−3.33129	−	1.92332i	−0.328242	−	0.189511i	−0.655060	+	0.755577i	$0.727357\pi$
$104$	7.19723	−	8.57733i	0.705747	−	0.841076i
$105$	−1.75664	−	4.15047i	−0.171431	−	0.405044i
$106$	21.3250			2.07127
$107$	−6.95920	+	12.0537i	−0.672771	+	1.16527i	0.304344	+	0.952562i	$0.401563\pi$
$107$	−6.95920	+	12.0537i	−0.672771	+	1.16527i	−0.977115	+	0.212712i	$0.931770\pi$
$108$	−4.15970	+	2.28871i	−0.400267	+	0.220231i
$109$	−1.45183	−	1.73023i	−0.139060	−	0.165726i	0.692019	−	0.721879i	$-0.256721\pi$
$109$	−1.45183	−	1.73023i	−0.139060	−	0.165726i	−0.831080	+	0.556153i	$0.812277\pi$
$110$	26.0063	−	9.46551i	2.47960	−	0.902501i
$111$	7.97849	−	1.83318i	0.757284	−	0.173998i
$112$	−0.730930	−	4.14531i	−0.0690664	−	0.391695i
$113$	6.79531	+	11.7698i	0.639249	+	1.10721i	0.985598	+	0.169106i	$0.0540880\pi$
$113$	6.79531	+	11.7698i	0.639249	+	1.10721i	−0.346349	+	0.938106i	$0.612579\pi$
$114$	−12.6569	−	2.42571i	−1.18543	−	0.227188i
$115$	−8.84551	+	15.3209i	−0.824848	+	1.42868i
$116$	4.40043	+	1.60163i	0.408570	+	0.148707i
$117$	13.0048	+	12.6113i	1.20229	+	1.16592i
$118$	−3.90501	−	3.27669i	−0.359485	−	0.301644i
$119$	−2.21230	+	0.390089i	−0.202801	+	0.0357594i
$120$	3.86341	+	9.12818i	0.352679	+	0.833285i
$121$	−16.5974			−1.50886
$122$	5.71962	−	9.90668i	0.517830	−	0.896908i
$123$	−3.98597	−	3.01019i	−0.359403	−	0.271420i
$124$	3.73688	+	0.658914i	0.335582	+	0.0591722i
$125$	1.26929	−	0.732825i	0.113529	−	0.0655459i
$126$	4.29473	−	0.442306i	0.382605	−	0.0394037i
$127$	4.48127	+	0.790169i	0.397649	+	0.0701162i	0.368897	−	0.929470i	$-0.379736\pi$
$127$	4.48127	+	0.790169i	0.397649	+	0.0701162i	0.0287519	+	0.999587i	$0.490847\pi$
$128$	2.19595	+	12.4538i	0.194096	+	1.10077i
$129$	6.95799	−	2.94490i	0.612617	−	0.259284i
$130$	−24.3691	+	20.4481i	−2.13731	+	1.79342i
$131$	−0.0561722	+	0.00990467i	−0.00490779	+	0.000865375i	−0.176102	−	0.984372i	$-0.556349\pi$
$131$	−0.0561722	+	0.00990467i	−0.00490779	+	0.000865375i	0.171194	+	0.985237i	$0.445238\pi$
$132$	0.426422	+	8.30291i	0.0371153	+	0.722675i
$133$	3.05427	+	2.04382i	0.264839	+	0.177222i
$134$			2.96888i			0.256472i
$135$	−15.1794	+	5.17342i	−1.30643	+	0.445257i
$136$	4.86554	−	0.857927i	0.417217	−	0.0735666i
$137$	−1.14762	−	3.15307i	−0.0980481	−	0.269385i	0.880965	−	0.473181i	$-0.156894\pi$
$137$	−1.14762	−	3.15307i	−0.0980481	−	0.269385i	−0.979013	+	0.203796i	$0.934672\pi$
$138$	−11.5451	−	12.4066i	−0.982782	−	1.05612i
$139$	−0.560012	+	0.203828i	−0.0474996	+	0.0172884i	−0.365661	−	0.930748i	$-0.619157\pi$
$139$	−0.560012	+	0.203828i	−0.0474996	+	0.0172884i	0.318161	+	0.948037i	$0.396935\pi$
$140$			2.37752i			0.200938i
$141$	0.501234	+	9.75958i	0.0422115	+	0.821905i
$142$	2.02107	−	11.4620i	0.169604	−	0.961874i
$143$	29.8091	−	10.8496i	2.49276	−	0.907290i
$144$	−14.8989	+	1.53440i	−1.24157	+	0.127867i
$145$	13.6983	+	7.90874i	1.13759	+	0.656785i
$146$	−2.83717	−	2.38067i	−0.234806	−	0.197025i
$147$	10.4138	+	3.19576i	0.858919	+	0.263581i
$148$	−4.25295	−	0.749909i	−0.349590	−	0.0616422i
$149$	−6.09518	−	7.26395i	−0.499336	−	0.595086i	0.456230	−	0.889862i	$-0.349199\pi$
$149$	−6.09518	−	7.26395i	−0.499336	−	0.595086i	−0.955566	+	0.294776i	$0.904755\pi$
$150$	−2.99590	−	13.0389i	−0.244614	−	1.06462i
$151$	−8.17957	−	4.72248i	−0.665644	−	0.384310i	0.128780	−	0.991673i	$-0.458894\pi$
$151$	−8.17957	−	4.72248i	−0.665644	−	0.384310i	−0.794424	+	0.607363i	$0.792227\pi$
$152$	−6.71729	−	4.49501i	−0.544844	−	0.364593i
$153$	0.818893	+	7.95134i	0.0662035	+	0.642828i
$154$	2.58578	−	7.10437i	0.208368	−	0.572487i
$155$	12.0440	+	4.38367i	0.967399	+	0.352105i
$156$	−3.72479	−	8.80066i	−0.298222	−	0.704616i
$157$	−17.1957	−	6.25873i	−1.37237	−	0.499501i	−0.452512	−	0.891758i	$-0.649472\pi$
$157$	−17.1957	−	6.25873i	−1.37237	−	0.499501i	−0.919855	+	0.392257i	$0.871694\pi$
$158$	−2.18452	−	6.00192i	−0.173791	−	0.477487i
$159$	−9.84385	+	19.2697i	−0.780668	+	1.52819i
$160$		−	14.8560i		−	1.17447i
$161$	1.65292	+	4.54136i	0.130268	+	0.357910i
$162$	−0.471856	−	15.3554i	−0.0370725	−	1.20643i
$163$	−9.42971	−	16.3327i	−0.738592	−	1.27928i	−0.953129	−	0.302563i	$-0.902158\pi$
$163$	−9.42971	−	16.3327i	−0.738592	−	1.27928i	0.214538	−	0.976716i	$-0.431175\pi$
$164$	1.31748	+	2.28195i	0.102878	+	0.178190i
$165$	−3.45152	+	27.8692i	−0.268701	+	2.16961i
$166$	5.18569	−	14.2476i	0.402487	−	1.10582i
$167$	2.55052	−	14.4647i	0.197365	−	1.11932i	−0.711644	−	0.702540i	$-0.752049\pi$
$167$	2.55052	−	14.4647i	0.197365	−	1.11932i	0.909010	−	0.416775i	$-0.136840\pi$
$168$	2.58863	+	0.794388i	0.199717	+	0.0612884i
$169$	−17.9740	+	15.0819i	−1.38261	+	1.16015i
$170$	−14.0368			−1.07657
$171$	8.03448	−	10.3173i	0.614412	−	0.788985i
$172$	−3.98577			−0.303912
$173$	−12.5938	+	10.5674i	−0.957485	+	0.803426i	−0.980542	−	0.196308i	$-0.937105\pi$
$173$	−12.5938	+	10.5674i	−0.957485	+	0.803426i	0.0230568	+	0.999734i	$0.492660\pi$
$174$	−11.0927	+	10.3224i	−0.840935	+	0.782540i
$175$	−0.662494	+	3.75719i	−0.0500798	+	0.284017i
$176$	−8.97034	+	24.6458i	−0.676164	+	1.85775i
$177$	4.76348	−	2.01610i	0.358045	−	0.151539i
$178$	6.35592	+	11.0088i	0.476396	+	0.825142i
$179$	−0.582498	−	1.00892i	−0.0435380	−	0.0754100i	0.843435	−	0.537231i	$-0.180530\pi$
$179$	−0.582498	−	1.00892i	−0.0435380	−	0.0754100i	−0.886973	+	0.461821i	$0.847196\pi$
$180$	8.43801	+	0.607798i	0.628932	+	0.0453026i
$181$	4.35224	+	11.9577i	0.323500	+	0.888808i	0.989716	+	0.143049i	$0.0456908\pi$
$181$	4.35224	+	11.9577i	0.323500	+	0.888808i	−0.666216	+	0.745759i	$0.732087\pi$
$182$			8.69028i			0.644167i
$183$	6.31165	+	9.74140i	0.466571	+	0.720105i
$184$	−3.63529	−	9.98788i	−0.267997	−	0.736316i
$185$	−13.7073	−	4.98905i	−1.00778	−	0.366802i
$186$	−7.39946	+	9.79806i	−0.542555	+	0.718429i
$187$	13.1532	+	4.78736i	0.961855	+	0.350087i
$188$	1.76320	−	4.84435i	0.128595	−	0.353311i
$189$	−1.58282	+	4.08498i	−0.115133	+	0.297139i
$190$	16.5770	+	15.8908i	1.20262	+	1.15284i
$191$	−2.43204	−	1.40414i	−0.175976	−	0.101600i	0.409425	−	0.912344i	$-0.365729\pi$
$191$	−2.43204	−	1.40414i	−0.175976	−	0.101600i	−0.585401	+	0.810744i	$0.699063\pi$
$192$	−2.92842	−	0.898660i	−0.211340	−	0.0648552i
$193$	−3.88688	−	4.63220i	−0.279784	−	0.333433i	0.607791	−	0.794097i	$-0.292056\pi$
$193$	−3.88688	−	4.63220i	−0.279784	−	0.333433i	−0.887575	+	0.460664i	$0.847611\pi$
$194$	4.75592	+	0.838597i	0.341455	+	0.0602077i
$195$	−7.22833	−	31.4595i	−0.517631	−	2.25286i
$196$	−4.40205	−	3.69376i	−0.314432	−	0.263840i
$197$	−2.17478	−	1.25561i	−0.154946	−	0.0894584i	0.420522	−	0.907282i	$-0.361847\pi$
$197$	−2.17478	−	1.25561i	−0.154946	−	0.0894584i	−0.575468	+	0.817824i	$0.695180\pi$
$198$	−24.5529	−	10.9933i	−1.74490	−	0.781260i
$199$	−16.1606	+	5.88197i	−1.14559	+	0.416962i	−0.843930	−	0.536453i	$-0.819764\pi$
$199$	−16.1606	+	5.88197i	−1.14559	+	0.416962i	−0.301663	+	0.953415i	$0.597542\pi$
$200$	1.45703	−	8.26323i	0.103028	−	0.584299i
$201$	−2.68274	−	1.37047i	−0.189226	−	0.0966652i
$202$		−	1.78190i		−	0.125374i
$203$	4.06042	−	1.47787i	0.284986	−	0.103726i
$204$	1.23708	−	4.03121i	0.0866129	−	0.282241i
$205$	3.04407	+	8.36351i	0.212607	+	0.584133i
$206$	−6.46631	+	1.14018i	−0.450529	+	0.0794404i
$207$	16.5402	−	4.70537i	1.14962	−	0.327046i
$208$		−	30.1475i		−	2.09035i
$209$	−10.1138	−	20.5442i	−0.699584	−	1.42107i
$210$	−6.85094	−	3.49977i	−0.472760	−	0.241507i
$211$	15.2539	−	2.68967i	1.05012	−	0.185165i	0.378152	−	0.925744i	$-0.376560\pi$
$211$	15.2539	−	2.68967i	1.05012	−	0.185165i	0.671969	+	0.740579i	$0.265449\pi$
$212$	8.74435	−	7.33738i	0.600565	−	0.503933i
$213$	9.42441	+	7.11728i	0.645750	+	0.487668i
$214$	4.12556	+	23.3972i	0.282017	+	1.59940i
$215$	−13.2584	−	2.33781i	−0.904215	−	0.159438i
$216$	3.48110	−	8.98416i	0.236859	−	0.611294i
$217$	3.03225	−	1.75067i	0.205842	−	0.118843i
$218$	−3.79685	−	0.669487i	−0.257155	−	0.0453434i
$219$	3.46089	−	1.46479i	0.233865	−	0.0989811i
$220$	7.40707	−	12.8294i	0.499385	−	0.864960i
$221$	−16.0894			−1.08229
$222$	8.42133	−	11.1512i	0.565202	−	0.748418i
$223$	1.28090	−	0.225857i	0.0857752	−	0.0151245i	−0.130596	−	0.991436i	$-0.541689\pi$
$223$	1.28090	−	0.225857i	0.0857752	−	0.0151245i	0.216371	+	0.976311i	$0.430578\pi$
$224$	−3.10888	−	2.60866i	−0.207721	−	0.174298i
$225$	13.1652	+	3.31174i	0.877678	+	0.220783i
$226$	21.7996	+	7.93440i	1.45009	+	0.527788i
$227$	−11.2122	+	19.4200i	−0.744177	+	1.28895i	0.206402	+	0.978467i	$0.433825\pi$
$227$	−11.2122	+	19.4200i	−0.744177	+	1.28895i	−0.950578	+	0.310484i	$0.899509\pi$
$228$	−6.02461	+	3.36025i	−0.398989	+	0.222538i
$229$	12.6808	+	21.9638i	0.837970	+	1.45141i	0.891589	+	0.452845i	$0.149591\pi$
$229$	12.6808	+	21.9638i	0.837970	+	1.45141i	−0.0536196	+	0.998561i	$0.517076\pi$
$230$	5.24380	+	29.7391i	0.345766	+	1.96094i
$231$	5.22604	+	5.61602i	0.343848	+	0.369507i
$232$	−8.93013	+	3.25030i	−0.586292	+	0.213393i
$233$	−0.0698519	−	0.0832462i	−0.00457615	−	0.00545364i	0.763752	−	0.645510i	$-0.223355\pi$
$233$	−0.0698519	−	0.0832462i	−0.00457615	−	0.00545364i	−0.768328	+	0.640057i	$0.778911\pi$
$234$	30.8424	+	2.22161i	2.01623	+	0.145231i
$235$	8.70658	−	15.0802i	0.567955	−	0.983726i
$236$	−2.72868			−0.177622
$237$	6.43186	+	0.796569i	0.417794	+	0.0517427i
$238$	−2.46481	+	2.93745i	−0.159770	+	0.190406i
$239$	6.50725	+	3.75696i	0.420919	+	0.243018i	0.695470	−	0.718555i	$-0.255196\pi$
$239$	6.50725	+	3.75696i	0.420919	+	0.243018i	−0.274552	+	0.961572i	$0.588529\pi$
$240$	23.7666	+	12.1410i	1.53413	+	0.783701i
$241$	0.596283	−	0.710622i	0.0384100	−	0.0457752i	−0.746497	−	0.665388i	$-0.768266\pi$
$241$	0.596283	−	0.710622i	0.0384100	−	0.0457752i	0.784907	+	0.619613i	$0.212710\pi$
$242$	−21.7029	+	18.2109i	−1.39511	+	1.17064i
$243$	14.0933	+	6.66182i	0.904083	+	0.427356i
$244$	−1.06329	−	6.03022i	−0.0680702	−	0.386045i
$245$	−12.4766	−	14.8690i	−0.797100	−	0.949947i
$246$	−8.51490	+	0.437310i	−0.542890	+	0.0278818i
$247$	19.0010	+	18.2144i	1.20900	+	1.15896i
$248$	−6.66885	+	3.85026i	−0.423473	+	0.244492i
$249$	10.4806	+	11.2627i	0.664183	+	0.713746i
$250$	0.855668	−	2.35093i	0.0541172	−	0.148686i
$251$	−4.49211	+	5.35349i	−0.283539	+	0.337909i	−0.888950	−	0.458004i	$-0.848564\pi$
$251$	−4.49211	+	5.35349i	−0.283539	+	0.337909i	0.605411	+	0.795913i	$0.293009\pi$
$252$	1.60887	−	1.65907i	0.101350	−	0.104512i
$253$	5.22904	−	29.6554i	0.328747	−	1.86442i
$254$	6.72672	−	3.88367i	0.422072	−	0.243683i
$255$	6.47953	−	12.6840i	0.405764	−	0.794300i
$256$	13.8264	+	11.6017i	0.864149	+	0.725107i
$257$	12.9368	+	10.8553i	0.806974	+	0.677132i	0.949884	−	0.312604i	$-0.101201\pi$
$257$	12.9368	+	10.8553i	0.806974	+	0.677132i	−0.142909	+	0.989736i	$0.545646\pi$
$258$	5.86714	−	11.4852i	0.365272	−	0.715035i
$259$	−3.45100	+	1.99243i	−0.214435	+	0.123804i
$260$	−2.95693	+	16.7696i	−0.183381	+	1.04000i
$261$	−4.20705	−	14.7885i	−0.260410	−	0.915387i
$262$	−0.0625836	+	0.0745842i	−0.00386643	+	0.00460783i
$263$	6.61100	−	18.1636i	0.407652	−	1.12001i	−0.550770	−	0.834657i	$-0.685666\pi$
$263$	6.61100	−	18.1636i	0.407652	−	1.12001i	0.958421	−	0.285356i	$-0.0921120\pi$
$264$	−11.4937	−	12.3514i	−0.707388	−	0.760175i
$265$	33.3912	−	19.2784i	2.05120	−	1.18426i
$266$	6.23629	−	0.678661i	0.382371	−	0.0416114i
$267$	−12.8817	+	0.661581i	−0.788348	+	0.0404881i
$268$	1.02151	+	1.21739i	0.0623989	+	0.0743641i
$269$	−0.767052	−	4.35017i	−0.0467680	−	0.265235i	0.952454	−	0.304684i	$-0.0985508\pi$
$269$	−0.767052	−	4.35017i	−0.0467680	−	0.265235i	−0.999222	+	0.0394492i	$0.987440\pi$
$270$	−14.1723	+	23.4198i	−0.862500	+	1.42528i
$271$	−9.87758	+	8.28828i	−0.600020	+	0.503477i	−0.891452	−	0.453115i	$-0.850313\pi$
$271$	−9.87758	+	8.28828i	−0.600020	+	0.503477i	0.291432	+	0.956592i	$0.405868\pi$
$272$	8.55068	−	10.1903i	0.518461	−	0.617878i
$273$	−7.85273	−	4.01152i	−0.475269	−	0.242789i
$274$	−4.96022	−	2.86379i	−0.299658	−	0.173008i
$275$	15.2803	−	18.2103i	0.921434	−	1.09812i
$276$	−9.00286	−	1.11498i	−0.541908	−	0.0671139i
$277$	−15.1580			−0.910756			−0.455378	−	0.890298i	$-0.650496\pi$
$277$	−15.1580			−0.910756			−0.455378	+	0.890298i	$0.650496\pi$
$278$	−0.508633	+	0.880978i	−0.0305058	+	0.0528376i
$279$	−5.43807	−	11.2092i	−0.325569	−	0.671077i
$280$	−3.10138	−	3.69608i	−0.185343	−	0.220883i
$281$	−12.0009	+	4.36795i	−0.715911	+	0.260570i	−0.674189	−	0.738559i	$-0.735507\pi$
$281$	−12.0009	+	4.36795i	−0.715911	+	0.260570i	−0.0417220	+	0.999129i	$0.513284\pi$
$282$	11.3637	+	12.2117i	0.676701	+	0.727198i
$283$	−1.01381	−	5.74958i	−0.0602645	−	0.341777i	0.939735	−	0.341902i	$-0.111071\pi$
$283$	−1.01381	−	5.74958i	−0.0602645	−	0.341777i	−1.00000		0.000125315i	$0.999960\pi$
$284$	−3.11505	−	5.39542i	−0.184844	−	0.320160i
$285$	−22.0114	+	7.64397i	−1.30384	+	0.452790i
$286$	27.0742	−	46.8939i	1.60093	−	2.77289i
$287$	2.28474	+	0.831577i	0.134864	+	0.0490864i
$288$	−10.0531	+	10.3668i	−0.592384	+	0.610867i
$289$	7.58431	+	6.36399i	0.446136	+	0.374353i
$290$	26.5896	−	4.68846i	1.56139	−	0.275316i
$291$	−2.95315	+	3.91045i	−0.173117	+	0.229234i
$292$	−1.98251			−0.116018
$293$	−1.26404	+	2.18938i	−0.0738459	+	0.127905i	−0.900584	−	0.434682i	$-0.856861\pi$
$293$	−1.26404	+	2.18938i	−0.0738459	+	0.127905i	0.826738	+	0.562587i	$0.190194\pi$
$294$	17.1236	−	7.24740i	0.998670	−	0.422677i
$295$	−9.07678	−	1.60048i	−0.528471	−	0.0931836i
$296$	7.58982	−	4.38198i	0.441149	−	0.254698i
$297$	21.2677	−	17.1119i	1.23407	−	0.992933i
$298$	−15.9402	−	2.81068i	−0.923390	−	0.162819i
$299$	6.01058	+	34.0877i	0.347601	+	1.97134i
$300$	−5.71482	−	4.31581i	−0.329945	−	0.249174i
$301$	−2.81735	+	2.36404i	−0.162390	+	0.136261i
$302$	−15.8772	+	2.79958i	−0.913631	+	0.161098i
$303$	1.61017	+	0.822545i	0.0925016	+	0.0472540i
$304$	−21.6343	+	2.35434i	−1.24081	+	0.135031i
$305$		−	20.6828i		−	1.18429i
$306$	9.79510	+	9.49873i	0.559948	+	0.543006i
$307$	−19.7596	+	3.48415i	−1.12774	+	0.198851i	−0.706237	−	0.707975i	$-0.749609\pi$
$307$	−19.7596	+	3.48415i	−1.12774	+	0.198851i	−0.421504	+	0.906827i	$0.638498\pi$
$308$	−1.38413	−	3.80286i	−0.0788680	−	0.216688i
$309$	1.95462	−	6.36942i	0.111194	−	0.362343i
$310$	20.5587	−	7.48274i	1.16765	−	0.424991i
$311$		−	22.2149i		−	1.25969i	−0.776720	−	0.629846i	$-0.783118\pi$
$311$		−	22.2149i		−	1.25969i	0.776720	−	0.629846i	$-0.216882\pi$
$312$	17.2706	+	8.82260i	0.977755	+	0.499481i
$313$	4.53572	−	25.7234i	0.256374	−	1.45397i	−0.536146	−	0.844125i	$-0.680120\pi$
$313$	4.53572	−	25.7234i	0.256374	−	1.45397i	0.792520	−	0.609845i	$-0.208768\pi$
$314$	−29.3524	+	10.6834i	−1.65645	+	0.602899i
$315$	6.32493	−	4.57513i	0.356369	−	0.257779i
$316$	−2.96087	−	1.70946i	−0.166562	−	0.0961646i
$317$	9.65795	+	8.10398i	0.542444	+	0.455165i	0.872373	−	0.488841i	$-0.162580\pi$
$317$	9.65795	+	8.10398i	0.542444	+	0.455165i	−0.329929	+	0.944006i	$0.607025\pi$
$318$	8.27111	+	35.9980i	0.463821	+	2.01867i
$319$	−26.5148	−	4.67527i	−1.48454	−	0.261765i
$320$	3.50847	+	4.18123i	0.196129	+	0.233738i
$321$	−23.0466	−	7.07244i	−1.28634	−	0.394745i
$322$	7.14421	+	4.12471i	0.398131	+	0.229861i
$323$	1.25649	+	11.5460i	0.0699127	+	0.642435i
$324$	−5.47687	−	6.13414i	−0.304271	−	0.340786i
$325$	−9.34564	+	25.6769i	−0.518403	+	1.42430i
$326$	−30.2508	−	11.0104i	−1.67544	−	0.609809i
$327$	2.35763	−	3.12187i	0.130377	−	0.172640i
$328$	−5.02486	−	1.82890i	−0.277451	−	0.100984i
$329$	−1.62696	−	4.47004i	−0.0896973	−	0.246441i
$330$	26.0652	+	40.2290i	1.43484	+	2.21453i
$331$			1.46474i			0.0805094i	0.999189	+	0.0402547i	$0.0128169\pi$
$331$			1.46474i			0.0805094i	−0.999189	+	0.0402547i	$0.987183\pi$
$332$	−2.77582	−	7.62649i	−0.152343	−	0.418558i
$333$	6.18907	+	12.7572i	0.339159	+	0.699090i
$334$	−12.5358	−	21.7126i	−0.685929	−	1.18806i
$335$	2.68395	+	4.64874i	0.146640	+	0.253988i
$336$	6.71405	−	2.84166i	0.366282	−	0.155025i
$337$	3.75439	−	10.3151i	0.204515	−	0.561899i	−0.794453	−	0.607326i	$-0.792242\pi$
$337$	3.75439	−	10.3151i	0.204515	−	0.561899i	0.998968	+	0.0454263i	$0.0144646\pi$
$338$	−6.95478	+	39.4425i	−0.378290	+	2.14539i
$339$	−17.2326	+	16.0360i	−0.935946	+	0.870954i
$340$	−5.75581	+	4.82970i	−0.312153	+	0.261927i
$341$	−21.8165			−1.18143
$342$	−0.814353	−	22.3065i	−0.0440352	−	1.20620i
$343$	−11.2042			−0.604970
$344$	6.19624	−	5.19926i	0.334079	−	0.280325i
$345$	−29.2934	−	8.98945i	−1.57711	−	0.483975i
$346$	−4.87298	+	27.6360i	−0.261973	+	1.48572i
$347$	−8.48361	+	23.3085i	−0.455424	+	1.25127i	0.473433	+	0.880830i	$0.343015\pi$
$347$	−8.48361	+	23.3085i	−0.455424	+	1.25127i	−0.928857	+	0.370438i	$0.879208\pi$
$348$	−0.996900	+	8.04943i	−0.0534394	+	0.431495i
$349$	−8.37756	−	14.5104i	−0.448440	−	0.776721i	0.549844	−	0.835267i	$-0.314687\pi$
$349$	−8.37756	−	14.5104i	−0.448440	−	0.776721i	−0.998285	+	0.0585456i	$0.981354\pi$
$350$	3.25615	+	5.63982i	0.174049	+	0.301461i
$351$	−16.2447	+	26.8444i	−0.867077	+	1.43285i
$352$	8.64875	+	23.7622i	0.460980	+	1.26653i
$353$		−	25.2115i		−	1.34187i	−0.741516	−	0.670936i	$-0.765893\pi$
$353$		−	25.2115i		−	1.34187i	0.741516	−	0.670936i	$-0.234107\pi$
$354$	4.01668	−	7.86281i	0.213484	−	0.417904i
$355$	−7.19738	−	19.7746i	−0.381997	−	1.04953i
$356$	6.39408	+	2.32726i	0.338886	+	0.123344i
$357$	−1.51656	−	3.58321i	−0.0802648	−	0.189644i
$358$	−1.86867	−	0.680142i	−0.0987625	−	0.0359466i
$359$	4.28165	−	11.7637i	0.225977	−	0.620866i	−0.773947	−	0.633251i	$-0.781720\pi$
$359$	4.28165	−	11.7637i	0.225977	−	0.620866i	0.999923	+	0.0123848i	$0.00394232\pi$
$360$	−13.9105	+	10.0621i	−0.733148	+	0.530321i
$361$	11.5871	−	15.0579i	0.609848	−	0.792518i
$362$	18.8111	+	10.8606i	0.988692	+	0.570821i
$363$	−6.43747	−	28.0175i	−0.337880	−	1.47054i
$364$	2.99010	+	3.56346i	0.156724	+	0.186776i
$365$	−6.59469	−	1.16282i	−0.345182	−	0.0608649i
$366$	18.9415	+	5.81270i	0.990090	+	0.303834i
$367$	21.1256	+	17.7265i	1.10275	+	0.925316i	0.997607	−	0.0691408i	$-0.0220258\pi$
$367$	21.1256	+	17.7265i	1.10275	+	0.925316i	0.105142	+	0.994457i	$0.466470\pi$
$368$	−24.7840	−	14.3090i	−1.29195	−	0.745910i
$369$	3.53540	−	7.89612i	0.184046	−	0.411055i
$370$	−23.3978	+	8.51610i	−1.21639	+	0.442731i
$371$	1.82902	−	10.3729i	0.0949582	−	0.538535i
$372$	0.337098	+	6.56367i	0.0174777	+	0.340311i
$373$			38.2882i			1.98249i	0.132051	+	0.991243i	$0.457844\pi$
$373$			38.2882i			1.98249i	−0.132051	+	0.991243i	$0.542156\pi$
$374$	22.4519	−	8.17183i	1.16096	−	0.422555i
$375$	1.72936	+	1.85841i	0.0893040	+	0.0959680i
$376$	3.57819	+	9.83101i	0.184531	+	0.506996i
$377$	30.4777	−	5.37404i	1.56968	−	0.276777i
$378$	2.41239	+	7.07823i	0.124080	+	0.364065i
$379$			36.6769i			1.88397i	0.335661	+	0.941983i	$0.391040\pi$
$379$			36.6769i			1.88397i	−0.335661	+	0.941983i	$0.608960\pi$
$380$	12.2650	+	0.812332i	0.629183	+	0.0416717i
$381$	0.404248	+	7.87115i	0.0207103	+	0.403251i
$382$	−4.72078	+	0.832402i	−0.241536	+	0.0425894i
$383$	21.7757	−	18.2720i	1.11269	−	0.933656i	0.114476	−	0.993426i	$-0.463481\pi$
$383$	21.7757	−	18.2720i	1.11269	−	0.933656i	0.998212	+	0.0597700i	$0.0190367\pi$
$384$	−20.1712	+	8.53725i	−1.02936	+	0.435665i
$385$	−2.37368	−	13.4618i	−0.120974	−	0.686077i
$386$	−10.1650	−	1.79237i	−0.517386	−	0.0912291i
$387$	7.66991	+	10.6033i	0.389883	+	0.538998i
$388$	2.23871	−	1.29252i	0.113653	−	0.0656178i
$389$	−3.26304	−	0.575363i	−0.165443	−	0.0291720i	0.0903131	−	0.995913i	$-0.471213\pi$
$389$	−3.26304	−	0.575363i	−0.165443	−	0.0291720i	−0.255756	+	0.966741i	$0.582324\pi$
$390$	−43.9696	−	33.2057i	−2.22649	−	1.68144i
$391$	−7.63657	+	13.2269i	−0.386198	+	0.668914i
$392$	11.6617			0.589006
$393$	−0.0385067	−	0.0909807i	−0.00194240	−	0.00458937i
$394$	−4.22142	+	0.744350i	−0.212672	+	0.0374998i
$395$	−8.84648	−	7.42308i	−0.445115	−	0.373496i
$396$	−13.8505	+	3.94019i	−0.696012	+	0.198002i
$397$	29.4627	+	10.7236i	1.47869	+	0.538200i	0.950445	−	0.310892i	$-0.100628\pi$
$397$	29.4627	+	10.7236i	1.47869	+	0.538200i	0.528246	+	0.849091i	$0.322850\pi$
$398$	−14.6779	+	25.4229i	−0.735737	+	1.27433i
$399$	−2.26548	+	5.94852i	−0.113416	+	0.297798i
$400$	−11.2959	−	19.5651i	−0.564796	−	0.978255i
$401$	−6.37617	−	36.1611i	−0.318411	−	1.80580i	−0.552423	−	0.833564i	$-0.686297\pi$
$401$	−6.37617	−	36.1611i	−0.318411	−	1.80580i	0.234012	−	0.972234i	$-0.424815\pi$
$402$	−5.01166	+	1.15151i	−0.249959	+	0.0574321i
$403$	23.5649	−	8.57691i	1.17385	−	0.427246i
$404$	−0.613106	−	0.730672i	−0.0305032	−	0.0363523i
$405$	−14.6205	−	23.6172i	−0.726500	−	1.17355i
$406$	3.68789	−	6.38761i	0.183027	−	0.317012i
$407$	24.8294			1.23075
$408$	3.33539	+	7.88060i	0.165126	+	0.390148i
$409$	24.7951	−	29.5496i	1.22604	−	1.46113i	0.382592	−	0.923917i	$-0.375031\pi$
$409$	24.7951	−	29.5496i	1.22604	−	1.46113i	0.843445	−	0.537216i	$-0.180524\pi$
$410$	13.1570	+	7.59619i	0.649778	+	0.375149i
$411$	4.87747	−	3.16021i	0.240588	−	0.155882i
$412$	−2.25921	+	2.69242i	−0.111303	+	0.132646i
$413$	−1.92878	+	1.61844i	−0.0949089	+	0.0796380i
$414$	16.4653	−	24.3009i	0.809224	−	1.19432i
$415$	−4.76033	−	26.9972i	−0.233675	−	1.32524i
$416$	−18.6837	−	22.2664i	−0.916044	−	1.09170i
$417$	−0.561281	−	0.866280i	−0.0274860	−	0.0424219i
$418$	−35.7661	−	15.7667i	−1.74938	−	0.771176i
$419$	−20.5941	+	11.8900i	−1.00609	+	0.580866i	−0.910044	−	0.414511i	$-0.863953\pi$
$419$	−20.5941	+	11.8900i	−1.00609	+	0.580866i	−0.0960454	+	0.995377i	$0.530619\pi$
$420$	−4.01342	+	0.922146i	−0.195835	+	0.0449961i
$421$	4.84630	−	13.3151i	0.236194	−	0.648939i	−0.763800	−	0.645454i	$-0.776668\pi$
$421$	4.84630	−	13.3151i	0.236194	−	0.648939i	0.999994	−	0.00348518i	$-0.00110937\pi$
$422$	16.9949	−	20.2538i	0.827301	−	0.985939i
$423$	−16.2804	+	4.63147i	−0.791580	+	0.225190i
$424$	−4.02259	+	22.8133i	−0.195354	+	1.10791i
$425$	−10.4417	+	6.02850i	−0.506495	+	0.292425i
$426$	20.1326	−	1.03397i	0.975426	−	0.0500961i
$427$	−4.32824	−	3.63182i	−0.209458	−	0.175756i
$428$	9.74206	+	8.17456i	0.470900	+	0.395132i
$429$	29.8766	+	46.1115i	1.44246	+	2.22629i
$430$	−19.9018	+	11.4903i	−0.959752	+	0.554113i
$431$	−2.00314	+	11.3604i	−0.0964878	+	0.547209i	0.897794	+	0.440417i	$0.145169\pi$
$431$	−2.00314	+	11.3604i	−0.0964878	+	0.547209i	−0.994281	+	0.106793i	$0.965942\pi$
$432$	−8.36884	−	24.5551i	−0.402646	−	1.18141i
$433$	−7.68929	+	9.16374i	−0.369524	+	0.440381i	−0.918479	−	0.395471i	$-0.870581\pi$
$433$	−7.68929	+	9.16374i	−0.369524	+	0.440381i	0.548955	+	0.835852i	$0.315026\pi$
$434$	2.04413	−	5.61620i	0.0981213	−	0.269586i
$435$	−8.03744	+	26.1912i	−0.385366	+	1.25577i
$436$	−1.78726	+	1.03187i	−0.0855940	+	0.0494177i
$437$	23.9925	−	6.97534i	1.14772	−	0.333676i
$438$	2.91830	−	5.71269i	0.139442	−	0.272963i
$439$	−18.0905	−	21.5595i	−0.863415	−	1.02898i	−0.999268	−	0.0382485i	$-0.987822\pi$
$439$	−18.0905	−	21.5595i	−0.863415	−	1.02898i	0.135854	−	0.990729i	$-0.456622\pi$
$440$	5.22046	+	29.6067i	0.248876	+	1.41145i
$441$	−1.35553	+	18.8188i	−0.0645492	+	0.896131i
$442$	−21.0385	+	17.6534i	−1.00070	+	0.839688i
$443$	17.7886	−	21.1997i	0.845163	−	1.00723i	−0.154652	−	0.987969i	$-0.549426\pi$
$443$	17.7886	−	21.1997i	0.845163	−	1.00723i	0.999815	−	0.0192567i	$-0.00612999\pi$
$444$	−0.383651	−	7.47011i	−0.0182073	−	0.354516i
$445$	19.9045	+	11.4919i	0.943563	+	0.544766i
$446$	1.42710	−	1.70075i	0.0675750	−	0.0805327i
$447$	9.89794	−	13.1064i	0.468157	−	0.619914i
$448$	1.49107			0.0704464
$449$	−15.5597	+	26.9501i	−0.734306	+	1.27185i	0.220722	+	0.975337i	$0.429159\pi$
$449$	−15.5597	+	26.9501i	−0.734306	+	1.27185i	−0.955027	+	0.296518i	$0.904175\pi$
$450$	20.8485	−	10.1145i	0.982810	−	0.476804i
$451$	−9.73800	−	11.6053i	−0.458545	−	0.546472i
$452$	11.6690	−	4.24716i	0.548862	−	0.199769i
$453$	4.79933	−	15.6393i	0.225492	−	0.734799i
$454$	6.64679	+	37.6958i	0.311949	+	1.76915i
$455$	7.85626	+	13.6074i	0.368307	+	0.637927i
$456$	4.98250	−	13.0827i	0.233327	−	0.612651i
$457$	−2.38710	+	4.13458i	−0.111664	+	0.193407i	−0.916441	−	0.400169i	$-0.868951\pi$
$457$	−2.38710	+	4.13458i	−0.111664	+	0.193407i	0.804777	+	0.593577i	$0.202285\pi$
$458$	40.6804	+	14.8064i	1.90087	+	0.691860i
$459$	−13.1048	+	4.46635i	−0.611678	+	0.208471i
$460$	12.3827	+	10.3903i	0.577345	+	0.484450i
$461$	1.86616	−	0.329055i	0.0869158	−	0.0153256i	−0.130021	−	0.991511i	$-0.541505\pi$
$461$	1.86616	−	0.329055i	0.0869158	−	0.0153256i	0.216937	+	0.976186i	$0.430393\pi$
$462$	12.9956	+	1.60947i	0.604609	+	0.0748791i
$463$	30.6339			1.42368			0.711839	−	0.702343i	$-0.247863\pi$
$463$	30.6339			1.42368			0.711839	+	0.702343i	$0.247863\pi$
$464$	−12.7937	+	22.1593i	−0.593931	+	1.02872i
$465$	−2.72852	+	22.0314i	−0.126532	+	1.02168i
$466$	−0.182677	−	0.0322110i	−0.00846237	−	0.00149214i
$467$	−34.1973	+	19.7438i	−1.58246	+	0.913636i	−0.587965	+	0.808886i	$0.700071\pi$
$467$	−34.1973	+	19.7438i	−1.58246	+	0.913636i	−0.994499	+	0.104749i	$0.966596\pi$
$468$	13.4114	−	9.70111i	0.619942	−	0.448434i
$469$	1.44412	+	0.254638i	0.0666834	+	0.0117581i
$470$	−5.16144	−	29.2720i	−0.238079	−	1.35022i
$471$	3.89562	−	31.4550i	0.179501	−	1.44937i
$472$	4.24198	−	3.55945i	0.195253	−	0.163837i
$473$	22.5679	−	3.97932i	1.03767	−	0.182969i
$474$	9.28435	−	6.01552i	0.426444	−	0.276302i
$475$	19.1560	+	4.70136i	0.878938	+	0.215713i
$476$			2.05258i			0.0940799i
$477$	−36.3466	−	9.14310i	−1.66420	−	0.418634i
$478$	12.6311	−	2.22720i	0.577733	−	0.101870i
$479$	2.01165	+	5.52697i	0.0919147	+	0.252534i	0.977128	−	0.212652i	$-0.0682100\pi$
$479$	2.01165	+	5.52697i	0.0919147	+	0.252534i	−0.885213	+	0.465185i	$0.845988\pi$
$480$	25.0779	−	5.76205i	1.14465	−	0.263000i
$481$	−26.8192	+	9.76138i	−1.22285	+	0.445081i
$482$		−	1.58346i		−	0.0721247i
$483$	−7.02502	+	4.55165i	−0.319649	+	0.207107i
$484$	−2.63341	+	14.9348i	−0.119700	+	0.678855i
$485$	8.20504	−	2.98639i	0.372572	−	0.135605i
$486$	25.7379	−	6.75226i	1.16749	−	0.306289i
$487$	−13.3900	−	7.73070i	−0.606757	−	0.350312i	0.164938	−	0.986304i	$-0.447258\pi$
$487$	−13.3900	−	7.73070i	−0.606757	−	0.350312i	−0.771695	+	0.635992i	$0.780591\pi$
$488$	9.51915	+	7.98751i	0.430912	+	0.361578i
$489$	23.9133	−	22.2528i	1.08140	−	1.00631i
$490$	−32.6289	−	5.75336i	−1.47402	−	0.259910i
$491$	−13.9315	−	16.6030i	−0.628721	−	0.749281i	0.353822	−	0.935313i	$-0.384882\pi$
$491$	−13.9315	−	16.6030i	−0.628721	−	0.749281i	−0.982544	+	0.186032i	$0.940437\pi$
$492$	−3.34108	+	3.10908i	−0.150628	+	0.140168i
$493$	11.8261	+	6.82783i	0.532623	+	0.307510i
$494$	44.8309	+	2.96922i	2.01704	+	0.133592i
$495$	−48.3837	+	4.98294i	−2.17469	+	0.223967i
$496$	−7.09129	+	19.4832i	−0.318408	+	0.874820i
$497$	−5.40202	−	1.96617i	−0.242314	−	0.0881950i
$498$	26.0621	+	3.22772i	1.16787	+	0.144638i
$499$	−4.11397	−	1.49736i	−0.184167	−	0.0670311i	0.248291	−	0.968686i	$-0.420131\pi$
$499$	−4.11397	−	1.49736i	−0.184167	−	0.0670311i	−0.432457	+	0.901654i	$0.642353\pi$
$500$	−0.458025	−	1.25841i	−0.0204835	−	0.0562780i
$501$	25.4067	−	1.30484i	1.13509	−	0.0582959i
$502$			11.9290i			0.532419i
$503$	−7.08844	−	19.4753i	−0.316058	−	0.868362i	−0.991401	−	0.130858i	$-0.958227\pi$
$503$	−7.08844	−	19.4753i	−0.316058	−	0.868362i	0.675343	−	0.737503i	$-0.263995\pi$
$504$	−0.336953	+	4.67789i	−0.0150091	+	0.208370i
$505$	−1.61089	−	2.79014i	−0.0716837	−	0.124160i
$506$	−25.7007	−	44.5149i	−1.14254	−	1.97893i
$507$	−32.4307	−	24.4915i	−1.44030	−	1.08771i
$508$	1.42203	−	3.90700i	0.0630924	−	0.173345i
$509$	−4.92642	+	27.9391i	−0.218360	+	1.23838i	0.656621	+	0.754221i	$0.271985\pi$
$509$	−4.92642	+	27.9391i	−0.218360	+	1.23838i	−0.874980	+	0.484158i	$0.839126\pi$
$510$	−5.44431	−	23.6950i	−0.241078	−	1.04923i
$511$	−1.40134	+	1.17587i	−0.0619918	+	0.0520173i
$512$	5.51707			0.243822
$513$	20.5326	+	9.56105i	0.906535	+	0.422131i
$514$	28.8267			1.27149
$515$	−9.09433	+	7.63105i	−0.400744	+	0.336264i
$516$	−1.54592	−	6.72824i	−0.0680553	−	0.296194i
$517$	−5.14692	+	29.1896i	−0.226361	+	1.28376i
$518$	−2.32642	+	6.39179i	−0.102217	+	0.280839i
$519$	−22.7231	−	17.1604i	−0.997433	−	0.753258i
$520$	−17.2784	−	29.9270i	−0.757707	−	1.31239i
$521$	8.19213	+	14.1892i	0.358904	+	0.621639i	0.987778	−	0.155868i	$-0.0498174\pi$
$521$	8.19213	+	14.1892i	0.358904	+	0.621639i	−0.628874	+	0.777507i	$0.716484\pi$
$522$	−21.7273	−	14.7215i	−0.950979	−	0.644344i
$523$	−5.96067	−	16.3768i	−0.260642	−	0.716108i	−0.999125	−	0.0418354i	$-0.986679\pi$
$523$	−5.96067	−	16.3768i	−0.260642	−	0.716108i	0.738482	−	0.674273i	$-0.235543\pi$
$524$			0.0521167i			0.00227673i
$525$	−6.59934	+	0.338930i	−0.288019	+	0.0147921i
$526$	−11.2847	−	31.0045i	−0.492036	−	1.35186i
$527$	10.3979	+	3.78454i	0.452941	+	0.164857i
$528$	−45.0829	−	5.58340i	−1.96198	−	0.242986i
$529$	9.26309	+	3.37149i	0.402743	+	0.146587i
$530$	22.5100	−	61.8458i	0.977773	−	2.68641i
$531$	5.25087	+	7.25911i	0.227868	+	0.315019i
$532$	2.32369	−	2.42403i	0.100745	−	0.105095i
$533$	15.0809	+	8.70696i	0.653226	+	0.377140i
$534$	−16.1183	+	14.9991i	−0.697508	+	0.649073i
$535$	27.6116	+	32.9062i	1.19375	+	1.42266i
$536$	−3.17608	−	0.560028i	−0.137186	−	0.0241895i
$537$	1.47719	−	1.37461i	0.0637454	−	0.0593190i
$538$	−5.77606	−	4.84669i	−0.249024	−	0.208956i
$539$	28.6127	+	16.5195i	1.23243	+	0.711546i
$540$	2.24676	+	14.4796i	0.0966852	+	0.623105i
$541$	37.3634	−	13.5992i	1.60638	−	0.584673i	0.625658	−	0.780098i	$-0.284831\pi$
$541$	37.3634	−	13.5992i	1.60638	−	0.584673i	0.980719	+	0.195424i	$0.0626084\pi$
$542$	−3.82199	+	21.6756i	−0.164169	+	0.931047i
$543$	−18.4973	+	11.9848i	−0.793795	+	0.514316i
$544$		−	12.8256i		−	0.549893i
$545$	−6.55043	+	2.38416i	−0.280589	+	0.102126i
$546$	−14.6698	+	3.37061i	−0.627808	+	0.144249i
$547$	14.0818	+	38.6893i	0.602093	+	1.65424i	0.747026	+	0.664794i	$0.231481\pi$
$547$	14.0818	+	38.6893i	0.602093	+	1.65424i	−0.144934	+	0.989441i	$0.546297\pi$
$548$	−3.01930	+	0.532384i	−0.128978	+	0.0227423i
$549$	−13.9961	+	14.4328i	−0.597338	+	0.615976i
$550$		−	40.5776i		−	1.73023i
$551$	−6.23663	−	21.4516i	−0.265689	−	0.913869i
$552$	15.4502	−	10.0105i	0.657605	−	0.426075i
$553$	−3.10682	+	0.547816i	−0.132115	+	0.0232955i
$554$	−19.8207	+	16.6315i	−0.842101	+	0.706607i
$555$	3.10533	−	25.0739i	0.131814	−	1.06433i
$556$	0.0945560	+	0.536254i	0.00401007	+	0.0227422i
$557$	−12.0628	−	2.12699i	−0.511115	−	0.0901234i	−0.0878581	−	0.996133i	$-0.528002\pi$
$557$	−12.0628	−	2.12699i	−0.511115	−	0.0901234i	−0.423257	+	0.906010i	$0.639113\pi$
$558$	−19.4097	−	8.69050i	−0.821679	−	0.367898i
$559$	−22.8120	+	13.1705i	−0.964845	+	0.557054i
$560$	−12.7936	−	2.25585i	−0.540627	−	0.0953272i
$561$	−2.97979	+	24.0602i	−0.125807	+	1.01582i
$562$	−10.8998	+	18.8790i	−0.459781	+	0.796364i
$563$	−9.31383			−0.392531			−0.196266	−	0.980551i	$-0.562881\pi$
$563$	−9.31383			−0.392531			−0.196266	+	0.980551i	$0.562881\pi$
$564$	8.86146	+	1.09747i	0.373135	+	0.0462117i
$565$	41.3072	−	7.28357i	1.73781	−	0.306422i
$566$	−7.63417	−	6.40583i	−0.320888	−	0.269257i
$567$	−7.50963	−	1.08749i	−0.315375	−	0.0456705i
$568$	11.8807	+	4.32423i	0.498504	+	0.181441i
$569$	5.75004	−	9.95937i	0.241054	−	0.417518i	−0.719961	−	0.694015i	$-0.755840\pi$
$569$	5.75004	−	9.95937i	0.241054	−	0.417518i	0.961015	+	0.276497i	$0.0891735\pi$
$570$	−20.3952	+	34.1465i	−0.854259	+	1.43024i
$571$	1.97798	+	3.42596i	0.0827759	+	0.143372i	0.904441	−	0.426598i	$-0.140288\pi$
$571$	1.97798	+	3.42596i	0.0827759	+	0.143372i	−0.821665	+	0.569970i	$0.806955\pi$
$572$	−5.03315	−	28.5444i	−0.210447	−	1.19350i
$573$	1.42699	−	4.65005i	0.0596132	−	0.194259i
$574$	3.89996	−	1.41947i	0.162781	−	0.0592474i
$575$	16.6730	+	19.8701i	0.695313	+	0.828642i
$576$	0.381182	−	5.29191i	0.0158826	−	0.220496i
$577$	−7.74244	+	13.4103i	−0.322322	+	0.558278i	−0.980967	−	0.194176i	$-0.937797\pi$
$577$	−7.74244	+	13.4103i	−0.322322	+	0.558278i	0.658645	+	0.752454i	$0.271130\pi$
$578$	16.8999			0.702945
$579$	6.31190	−	8.35795i	0.262313	−	0.347345i
$580$	9.28992	−	11.0713i	0.385743	−	0.459711i
$581$	−6.48552	−	3.74442i	−0.269065	−	0.155345i
$582$	0.429023	+	8.35356i	0.0177836	+	0.346266i
$583$	−42.1860	+	50.2753i	−1.74716	+	2.08219i
$584$	3.08199	−	2.58610i	0.127534	−	0.107014i
$585$	50.3022	−	24.4038i	2.07974	−	1.00897i
$586$	0.749348	+	4.24976i	0.0309553	+	0.175556i
$587$	25.1223	+	29.9396i	1.03691	+	1.23574i	0.971290	+	0.237897i	$0.0764580\pi$
$587$	25.1223	+	29.9396i	1.03691	+	1.23574i	0.0656198	+	0.997845i	$0.479098\pi$
$588$	4.52792	−	8.86360i	0.186728	−	0.365529i
$589$	−7.99521	−	16.2407i	−0.329437	−	0.669187i
$590$	−13.6249	+	7.86635i	−0.560929	+	0.323853i
$591$	1.27604	−	4.15816i	0.0524893	−	0.171044i
$592$	8.07060	−	22.1738i	0.331699	−	0.911337i
$593$	15.7935	−	18.8220i	0.648562	−	0.772927i	−0.337134	−	0.941457i	$-0.609458\pi$
$593$	15.7935	−	18.8220i	0.648562	−	0.772927i	0.985697	+	0.168530i	$0.0539020\pi$
$594$	9.03434	−	45.7108i	0.370683	−	1.87553i
$595$	−1.20392	+	6.82778i	−0.0493560	+	0.279912i
$596$	−7.50338	+	4.33208i	−0.307350	+	0.177449i
$597$	−16.1972	−	24.9987i	−0.662907	−	1.02313i
$598$	45.2609	+	37.9784i	1.85086	+	1.55305i
$599$	−9.83133	−	8.24946i	−0.401697	−	0.337064i	0.419452	−	0.907777i	$-0.362222\pi$
$599$	−9.83133	−	8.24946i	−0.401697	−	0.337064i	−0.821149	+	0.570714i	$0.806667\pi$
$600$	14.5140	−	0.745412i	0.592532	−	0.0304313i
$601$	35.6324	−	20.5724i	1.45348	−	0.839165i	0.454799	−	0.890594i	$-0.349711\pi$
$601$	35.6324	−	20.5724i	1.45348	−	0.839165i	0.998677	+	0.0514293i	$0.0163777\pi$
$602$	−1.09014	+	6.18247i	−0.0444306	+	0.251979i
$603$	1.27291	−	5.06020i	0.0518368	−	0.206067i
$604$	−5.54721	+	6.61091i	−0.225713	+	0.268994i
$605$	−17.5197	+	48.1350i	−0.712278	+	1.95697i
$606$	3.00797	−	0.691128i	0.122190	−	0.0280752i
$607$	4.17295	−	2.40925i	0.169375	−	0.0977886i	−0.412916	−	0.910769i	$-0.635490\pi$
$607$	4.17295	−	2.40925i	0.169375	−	0.0977886i	0.582291	+	0.812980i	$0.302156\pi$
$608$	−14.5196	+	15.1466i	−0.588848	+	0.614276i
$609$	4.06962	+	6.28105i	0.164909	+	0.254521i
$610$	−22.6934	−	27.0450i	−0.918830	−	1.09502i
$611$	−5.91618	−	33.5523i	−0.239343	−	1.35738i
$612$	7.28476	+	0.524728i	0.294469	+	0.0212109i
$613$	−12.9157	+	10.8376i	−0.521661	+	0.437725i	−0.865210	−	0.501409i	$-0.832815\pi$
$613$	−12.9157	+	10.8376i	−0.521661	+	0.437725i	0.343549	+	0.939135i	$0.388371\pi$
$614$	−22.0149	+	26.2364i	−0.888451	+	1.05881i
$615$	−12.9375	+	8.38246i	−0.521690	+	0.338013i
$616$	7.11242	+	4.10636i	0.286568	+	0.165450i
$617$	−28.5518	+	34.0267i	−1.14945	+	1.36986i	−0.231663	+	0.972796i	$0.574417\pi$
$617$	−28.5518	+	34.0267i	−1.14945	+	1.36986i	−0.917789	+	0.397067i	$0.870028\pi$
$618$	−4.43273	−	10.4733i	−0.178310	−	0.421299i
$619$	−3.18483			−0.128009			−0.0640046	−	0.997950i	$-0.520387\pi$
$619$	−3.18483			−0.128009			−0.0640046	+	0.997950i	$0.520387\pi$
$620$	5.85549	−	10.1420i	0.235162	−	0.407313i
$621$	14.3582	+	26.0959i	0.576176	+	1.04719i
$622$	−24.3745	−	29.0484i	−0.977327	−	1.16473i
$623$	5.90002	−	2.14743i	0.236379	−	0.0860351i
$624$	50.8909	−	11.6930i	2.03727	−	0.468094i
$625$	−4.71436	−	26.7365i	−0.188575	−	1.06946i
$626$	−22.2930	−	38.6127i	−0.891009	−	1.54327i
$627$	30.7572	−	25.0410i	1.22832	−	1.00004i
$628$	−8.36010	+	14.4801i	−0.333605	+	0.577820i
$629$	−11.8339	−	4.30718i	−0.471848	−	0.171739i
$630$	3.25063	−	12.9223i	0.129508	−	0.514835i
$631$	11.1833	+	9.38394i	0.445202	+	0.373569i	0.837652	−	0.546205i	$-0.183928\pi$
$631$	11.1833	+	9.38394i	0.445202	+	0.373569i	−0.392450	+	0.919773i	$0.628372\pi$
$632$	6.83286	−	1.20482i	0.271797	−	0.0479251i
$633$	10.4567	+	24.7063i	0.415617	+	0.981989i
$634$	21.5206			0.854691
$635$	7.02190	−	12.1623i	0.278656	−	0.482646i
$636$	15.7776	+	11.9152i	0.625621	+	0.472467i
$637$	−37.4001	−	6.59465i	−1.48185	−	0.261290i
$638$	−39.8007	+	22.9789i	−1.57572	+	0.909744i
$639$	−8.35908	+	18.6695i	−0.330680	+	0.738555i
$640$	38.4360	+	6.77731i	1.51932	+	0.267897i
$641$	3.62461	+	20.5562i	0.143164	+	0.811921i	0.968823	+	0.247753i	$0.0796921\pi$
$641$	3.62461	+	20.5562i	0.143164	+	0.811921i	−0.825660	+	0.564169i	$0.809197\pi$
$642$	−37.8959	+	16.0390i	−1.49563	+	0.633010i
$643$	−31.1611	+	26.1473i	−1.22887	+	1.03115i	−0.230564	+	0.973057i	$0.574057\pi$
$643$	−31.1611	+	26.1473i	−1.22887	+	1.03115i	−0.998311	+	0.0580911i	$0.981499\pi$
$644$	4.34870	−	0.766793i	0.171363	−	0.0302159i
$645$	−1.19602	−	23.2878i	−0.0470932	−	0.916956i
$646$	14.3114	+	13.7190i	0.563073	+	0.539765i
$647$		−	12.2419i		−	0.481278i	−0.970615	−	0.240639i	$-0.922643\pi$
$647$		−	12.2419i		−	0.481278i	0.970615	−	0.240639i	$-0.0773570\pi$
$648$	16.5160	+	2.39174i	0.648811	+	0.0939564i
$649$	15.4501	−	2.72427i	0.606469	−	0.106937i
$650$	15.9526	+	43.8294i	0.625713	+	1.71913i
$651$	4.13133	+	4.43961i	0.161919	+	0.174002i
$652$	−16.1928	+	5.89369i	−0.634158	+	0.230815i
$653$			4.78927i			0.187419i	0.995600	+	0.0937093i	$0.0298724\pi$
$653$			4.78927i			0.187419i	−0.995600	+	0.0937093i	$0.970128\pi$
$654$	−0.342507	−	6.66900i	−0.0133931	−	0.260778i
$655$	−0.0305686	+	0.173363i	−0.00119441	+	0.00677385i
$656$	−13.5293	+	4.92428i	−0.528232	+	0.192261i
$657$	3.81499	+	5.27407i	0.148837	+	0.205761i
$658$	−7.03200	−	4.05993i	−0.274136	−	0.158272i
$659$	−9.86935	−	8.28137i	−0.384455	−	0.322596i	0.429993	−	0.902832i	$-0.358516\pi$
$659$	−9.86935	−	8.28137i	−0.384455	−	0.322596i	−0.814449	+	0.580236i	$0.802960\pi$
$660$	24.5298	+	7.52760i	0.954822	+	0.293012i
$661$	−6.98262	−	1.23122i	−0.271593	−	0.0478891i	0.0361931	−	0.999345i	$-0.488477\pi$
$661$	−6.98262	−	1.23122i	−0.271593	−	0.0478891i	−0.307786	+	0.951456i	$0.599588\pi$
$662$	1.60713	+	1.91530i	0.0624629	+	0.0744404i
$663$	−6.24041	−	27.1599i	−0.242358	−	1.05480i
$664$	14.2637	+	8.23515i	0.553539	+	0.319586i
$665$	9.15139	−	6.70044i	0.354876	−	0.259832i
$666$	22.0902	+	9.89066i	0.855978	+	0.383255i
$667$	10.0478	−	27.6062i	0.389053	−	1.06891i
$668$	−12.6111	−	4.59006i	−0.487937	−	0.177595i
$669$	0.878070	+	2.07464i	0.0339481	+	0.0802101i
$670$	8.61020	+	3.13386i	0.332641	+	0.121071i
$671$	12.0409	+	33.0822i	0.464835	+	1.27712i
$672$	3.19778	−	6.25979i	0.123357	−	0.241477i
$673$		−	0.277587i		−	0.0107002i	−0.999986	−	0.00535010i	$-0.998297\pi$
$673$		−	0.277587i		−	0.0107002i	0.999986	−	0.00535010i	$-0.00170300\pi$
$674$	−6.40859	−	17.6074i	−0.246850	−	0.678214i
$675$	−0.484189	+	23.5082i	−0.0186364	+	0.904830i
$676$	10.7193	+	18.5664i	0.412282	+	0.714093i
$677$	−17.6385	−	30.5507i	−0.677901	−	1.17416i	−0.975612	−	0.219503i	$-0.929557\pi$
$677$	−17.6385	−	30.5507i	−0.677901	−	1.17416i	0.297711	−	0.954656i	$-0.403777\pi$
$678$	−4.93860	+	39.8765i	−0.189666	+	1.53145i
$679$	0.815820	−	2.24145i	0.0313083	−	0.0860188i
$680$	2.64780	−	15.0164i	0.101538	−	0.575853i
$681$	−37.1310	−	11.3946i	−1.42286	−	0.436642i
$682$	−28.5274	+	23.9373i	−1.09237	+	0.916608i
$683$	6.21218			0.237703			0.118851	−	0.992912i	$-0.462079\pi$
$683$	6.21218			0.237703			0.118851	+	0.992912i	$0.462079\pi$
$684$	−8.00902	−	8.86662i	−0.306233	−	0.339024i
$685$	−10.3558			−0.395674
$686$	−14.6507	+	12.2934i	−0.559365	+	0.469363i
$687$	−32.1579	+	29.9249i	−1.22690	+	1.14170i
$688$	3.78179	−	21.4476i	0.144179	−	0.817682i
$689$	25.8016	−	70.8892i	0.982962	−	2.70067i
$690$	−48.1676	+	20.3865i	−1.83371	+	0.776099i
$691$	15.9848	+	27.6865i	0.608092	+	1.05325i	0.991555	+	0.129689i	$0.0413980\pi$
$691$	15.9848	+	27.6865i	0.608092	+	1.05325i	−0.383463	+	0.923556i	$0.625269\pi$
$692$	7.51067	+	13.0089i	0.285513	+	0.494523i
$693$	−7.45324	+	11.0001i	−0.283125	+	0.417860i
$694$	14.4812	+	39.7867i	0.549698	+	1.51028i
$695$			1.83927i			0.0697676i
$696$	−8.95036	−	13.8140i	−0.339263	−	0.523618i
$697$	2.62803	+	7.22045i	0.0995437	+	0.273494i
$698$	−26.8755	−	9.78187i	−1.01725	−	0.370249i
$699$	0.113432	−	0.150202i	0.00429040	−	0.00568117i
$700$	3.27571	+	1.19226i	0.123810	+	0.0450632i
$701$	−8.28759	+	22.7700i	−0.313018	+	0.860010i	0.679026	+	0.734115i	$0.262403\pi$
$701$	−8.28759	+	22.7700i	−0.313018	+	0.860010i	−0.992044	+	0.125895i	$0.959820\pi$
$702$	8.21232	+	52.9257i	0.309954	+	1.99755i
$703$	9.09934	+	18.4836i	0.343188	+	0.697120i
$704$	−8.04600	−	4.64536i	−0.303245	−	0.175079i
$705$	28.8334	+	8.84826i	1.08593	+	0.333245i
$706$	−27.6623	−	32.9667i	−1.04109	−	1.24072i
$707$	−0.866753	−	0.152832i	−0.0325976	−	0.00574783i
$708$	−1.05835	−	4.60619i	−0.0397751	−	0.173111i
$709$	−14.0713	−	11.8072i	−0.528460	−	0.443430i	0.339109	−	0.940747i	$-0.389874\pi$
$709$	−14.0713	−	11.8072i	−0.528460	−	0.443430i	−0.867569	+	0.497317i	$0.834319\pi$
$710$	−31.1083	−	17.9604i	−1.16747	−	0.674041i
$711$	1.15000	+	11.1664i	0.0431284	+	0.418771i
$712$	−12.9760	+	4.72288i	−0.486296	+	0.176997i
$713$	4.13370	−	23.4434i	0.154808	−	0.877961i
$714$	−5.91460	−	3.02144i	−0.221348	−	0.113075i
$715$		−	97.9033i		−	3.66138i
$716$	−1.00027	+	0.364069i	−0.0373819	+	0.0136059i
$717$	−3.81810	+	12.4418i	−0.142589	+	0.464649i
$718$	−7.30860	−	20.0802i	−0.272754	−	0.749387i
$719$	5.31190	−	0.936632i	0.198101	−	0.0349305i	−0.0737174	−	0.997279i	$-0.523486\pi$
$719$	5.31190	−	0.936632i	0.198101	−	0.0349305i	0.271818	+	0.962349i	$0.412375\pi$
$720$	−11.2768	+	44.8286i	−0.420260	+	1.67066i
$721$			3.24313i			0.120781i
$722$	−1.37028	−	32.4033i	−0.0509964	−	1.20592i
$723$	1.43085	+	0.730943i	0.0532139	+	0.0271840i
$724$	11.4504	−	2.01901i	0.425550	−	0.0750360i
$725$	17.7658	−	14.9073i	0.659806	−	0.553643i
$726$	−39.1588	−	29.5726i	−1.45332	−	1.09754i
$727$	−4.37217	−	24.7958i	−0.162155	−	0.919625i	−0.951950	−	0.306254i	$-0.900924\pi$
$727$	−4.37217	−	24.7958i	−0.162155	−	0.919625i	0.789795	−	0.613371i	$-0.210187\pi$
$728$	−9.29677	−	1.63927i	−0.344561	−	0.0607554i
$729$	−5.77938	+	26.3742i	−0.214051	+	0.976822i
$730$	−9.89912	+	5.71526i	−0.366383	+	0.211531i
$731$	−11.4463	−	2.01830i	−0.423358	−	0.0746494i
$732$	9.76700	−	4.13378i	0.360999	−	0.152789i
$733$	13.6945	−	23.7196i	0.505818	−	0.876103i	−0.494159	−	0.869371i	$-0.664524\pi$
$733$	13.6945	−	23.7196i	0.505818	−	0.876103i	0.999977	−	0.00673135i	$-0.00214267\pi$
$734$	47.0737			1.73752
$735$	20.2607	−	26.8284i	0.747327	−	0.989580i
$736$	−27.1729	+	4.79132i	−1.00161	+	0.176610i
$737$	−6.99935	−	5.87315i	−0.257824	−	0.216340i
$738$	−4.04080	−	14.2041i	−0.148744	−	0.522860i
$739$	−5.11867	−	1.86304i	−0.188293	−	0.0685331i	0.246153	−	0.969231i	$-0.420834\pi$
$739$	−5.11867	−	1.86304i	−0.188293	−	0.0685331i	−0.434446	+	0.900698i	$0.643056\pi$
$740$	−6.66413	+	11.5426i	−0.244978	+	0.424315i
$741$	−23.3775	+	39.1396i	−0.858793	+	1.43783i
$742$	−8.98963	−	15.5705i	−0.330020	−	0.571611i
$743$	2.19250	+	12.4343i	0.0804351	+	0.456170i	0.998249	+	0.0591584i	$0.0188417\pi$
$743$	2.19250	+	12.4343i	0.0804351	+	0.456170i	−0.917813	+	0.397012i	$0.870047\pi$
$744$	−9.08608	−	9.76410i	−0.333112	−	0.357969i
$745$	−27.5004	+	10.0093i	−1.00754	+	0.366714i
$746$	42.0102	+	50.0658i	1.53810	+	1.83304i
$747$	−14.9472	+	22.0604i	−0.546889	+	0.807146i
$748$	6.39473	−	11.0760i	0.233814	−	0.404978i
$749$	11.7347			0.428777
$750$	4.30040	+	0.532593i	0.157028	+	0.0194475i
$751$	−29.9152	+	35.6515i	−1.09162	+	1.30094i	−0.141197	+	0.989982i	$0.545095\pi$
$751$	−29.9152	+	35.6515i	−1.09162	+	1.30094i	−0.950423	+	0.310960i	$0.899350\pi$
$752$	24.3947	+	14.0843i	0.889584	+	0.513602i
$753$	−10.7793	−	5.50657i	−0.392821	−	0.200671i
$754$	33.9564	−	40.4676i	1.23662	−	1.47374i
$755$	−22.3300	+	18.7371i	−0.812672	+	0.681913i
$756$	3.42464	+	2.07240i	0.124553	+	0.0753724i
$757$	−5.64213	−	31.9981i	−0.205067	−	1.16299i	−0.897335	−	0.441351i	$-0.854499\pi$
$757$	−5.64213	−	31.9981i	−0.205067	−	1.16299i	0.692268	−	0.721641i	$-0.256612\pi$
$758$	40.2423	+	47.9589i	1.46167	+	1.74195i
$759$	52.0884	−	2.67516i	1.89069	−	0.0971022i
$760$	−20.1268	+	14.7364i	−0.730074	+	0.534544i
$761$	20.0966	−	11.6028i	0.728501	−	0.420600i	−0.0893728	−	0.995998i	$-0.528486\pi$
$761$	20.0966	−	11.6028i	0.728501	−	0.420600i	0.817873	+	0.575398i	$0.195153\pi$
$762$	9.16492	+	9.84883i	0.332010	+	0.356785i
$763$	−0.651303	+	1.78944i	−0.0235788	+	0.0647821i
$764$	−1.64936	+	1.96563i	−0.0596716	+	0.0711139i
$765$	23.9245	+	6.01828i	0.864992	+	0.217591i
$766$	8.42582	−	47.7852i	0.304437	−	1.72655i
$767$	−15.6172	+	9.01662i	−0.563906	+	0.325571i
$768$	−14.2218	+	27.8397i	−0.513183	+	1.00458i
$769$	−20.5945	−	17.2808i	−0.742657	−	0.623163i	0.190893	−	0.981611i	$-0.438862\pi$
$769$	−20.5945	−	17.2808i	−0.742657	−	0.623163i	−0.933550	+	0.358448i	$0.883306\pi$
$770$	−17.8743	−	14.9983i	−0.644145	−	0.540502i
$771$	−13.3067	+	26.0485i	−0.479230	+	0.938112i
$772$	−4.78489	+	2.76256i	−0.172212	+	0.0994265i
$773$	−2.24914	+	12.7555i	−0.0808959	+	0.458784i	0.917271	+	0.398263i	$0.130387\pi$
$773$	−2.24914	+	12.7555i	−0.0808959	+	0.458784i	−0.998167	+	0.0605201i	$0.980724\pi$
$774$	21.6633	+	5.44947i	0.778672	+	0.195877i
$775$	12.0795	−	14.3957i	0.433907	−	0.517110i
$776$	−1.79424	+	4.92964i	−0.0644096	+	0.176964i
$777$	−4.70186	−	5.05272i	−0.168678	−	0.181265i
$778$	−4.89807	+	2.82790i	−0.175604	+	0.101385i
$779$	5.07052	−	11.5022i	0.181670	−	0.412111i
$780$	−29.4550	+	1.51275i	−1.05466	+	0.0541653i
$781$	23.0245	+	27.4395i	0.823880	+	0.981862i
$782$	4.52711	+	25.6745i	0.161889	+	0.918119i
$783$	23.3323	−	12.8377i	0.833827	−	0.458781i
$784$	24.0530	−	20.1829i	0.859037	−	0.720818i
$785$	−36.3025	+	43.2637i	−1.29569	+	1.54415i
$786$	−0.150177	−	0.0767169i	−0.00535662	−	0.00273640i
$787$	16.3494	+	9.43930i	0.582791	+	0.336475i	0.762242	−	0.647292i	$-0.224099\pi$
$787$	16.3494	+	9.43930i	0.582791	+	0.336475i	−0.179451	+	0.983767i	$0.557432\pi$
$788$	−1.47489	+	1.75770i	−0.0525407	+	0.0626155i
$789$	33.2254	+	4.11488i	1.18286	+	0.146494i
$790$	−19.7124			−0.701336
$791$	5.72917	−	9.92322i	0.203706	−	0.352829i
$792$	16.3920	−	24.1927i	0.582464	−	0.859651i
$793$	−26.0118	−	30.9996i	−0.923706	−	1.10083i
$794$	50.2916	−	18.3047i	1.78478	−	0.649608i
$795$	45.4943	+	48.8892i	1.61352	+	1.73392i
$796$	2.72865	+	15.4750i	0.0967146	+	0.548496i
$797$	−16.0748	−	27.8423i	−0.569397	−	0.986225i	−0.996626	−	0.0820812i	$-0.973843\pi$
$797$	−16.0748	−	27.8423i	−0.569397	−	0.986225i	0.427228	−	0.904144i	$-0.359490\pi$
$798$	3.56443	+	10.2640i	0.126179	+	0.363343i
$799$	7.51663	−	13.0192i	0.265919	−	0.460585i
$800$	−20.4683	−	7.44986i	−0.723664	−	0.263392i
$801$	−6.11309	−	21.4886i	−0.215996	−	0.759262i
$802$	−48.0139	−	40.2884i	−1.69543	−	1.42263i
$803$	11.2252	−	1.97930i	0.396129	−	0.0698481i
$804$	−1.65884	+	2.19656i	−0.0585026	+	0.0774667i
$805$	14.9154			0.525699
$806$	21.4029	−	37.0709i	0.753884	−	1.30577i
$807$	7.04586	−	2.98209i	0.248026	−	0.104975i
$808$	1.90626	+	0.336125i	0.0670620	+	0.0118248i
$809$	11.0378	−	6.37270i	0.388070	−	0.224052i	−0.293254	−	0.956035i	$-0.594738\pi$
$809$	11.0378	−	6.37270i	0.388070	−	0.224052i	0.681323	+	0.731982i	$0.261405\pi$
$810$	−45.0310	−	14.8402i	−1.58223	−	0.521432i
$811$	2.01967	+	0.356122i	0.0709201	+	0.0125051i	0.208996	−	0.977917i	$-0.432981\pi$
$811$	2.01967	+	0.356122i	0.0709201	+	0.0125051i	−0.138076	+	0.990422i	$0.544092\pi$
$812$	−0.685587	−	3.88816i	−0.0240594	−	0.136448i
$813$	−17.8223	−	13.4593i	−0.625054	−	0.472039i
$814$	32.4670	−	27.2431i	1.13797	−	0.954869i
$815$	−57.3211	+	10.1073i	−2.00787	+	0.354042i
$816$	20.5184	+	10.4817i	0.718286	+	0.366933i
$817$	11.2329	+	15.3417i	0.392988	+	0.536739i
$818$		−	65.8447i		−	2.30220i
$819$	3.72596	−	14.8118i	0.130196	−	0.517567i
$820$	8.00870	−	1.41215i	0.279676	−	0.0493144i
$821$	−5.16544	−	14.1919i	−0.180275	−	0.495301i	0.816334	−	0.577579i	$-0.196003\pi$
$821$	−5.16544	−	14.1919i	−0.180275	−	0.495301i	−0.996609	+	0.0822781i	$0.973780\pi$
$822$	2.91039	−	9.48393i	0.101511	−	0.330790i
$823$	−10.3595	+	3.77054i	−0.361108	+	0.131433i	−0.516202	−	0.856467i	$-0.672654\pi$
$823$	−10.3595	+	3.77054i	−0.361108	+	0.131433i	0.155093	+	0.987900i	$0.450432\pi$
$824$		−	7.13266i		−	0.248478i
$825$	36.6668	+	18.7310i	1.27657	+	0.652131i
$826$	−0.746314	+	4.23255i	−0.0259676	+	0.147269i
$827$	36.6643	−	13.3447i	1.27494	−	0.464042i	0.386187	−	0.922420i	$-0.373792\pi$
$827$	36.6643	−	13.3447i	1.27494	−	0.464042i	0.888757	+	0.458379i	$0.151570\pi$
$828$	−1.60969	−	15.6299i	−0.0559405	−	0.543175i
$829$	−37.5280	−	21.6668i	−1.30340	−	0.752519i	−0.322416	−	0.946598i	$-0.604495\pi$
$829$	−37.5280	−	21.6668i	−1.30340	−	0.752519i	−0.980986	+	0.194079i	$0.937828\pi$
$830$	−35.8462	−	30.0786i	−1.24424	−	1.04404i
$831$	−5.87918	−	25.5877i	−0.203947	−	0.887628i
$832$	10.5171	+	1.85444i	0.364614	+	0.0642913i
$833$	−10.7714	−	12.8368i	−0.373206	−	0.444770i
$834$	−1.68443	−	0.516910i	−0.0583269	−	0.0178991i
$835$	−39.2577	−	22.6654i	−1.35857	−	0.784370i
$836$	−20.0909	+	5.84102i	−0.694857	+	0.202016i
$837$	16.8127	−	13.5274i	0.581130	−	0.467576i
$838$	−13.8831	+	38.1436i	−0.479585	+	1.31765i
$839$	18.0414	+	6.56652i	0.622857	+	0.226702i	0.634120	−	0.773235i	$-0.281363\pi$
$839$	18.0414	+	6.56652i	0.622857	+	0.226702i	−0.0112622	+	0.999937i	$0.503585\pi$
$840$	5.03632	−	6.66889i	0.173770	−	0.230099i
$841$	2.56851	+	0.934860i	0.0885692	+	0.0322366i
$842$	−8.27244	−	22.7283i	−0.285087	−	0.783270i
$843$	−12.0280	−	18.5641i	−0.414268	−	0.639381i
$844$		−	14.1526i		−	0.487153i
$845$	24.7672	+	68.0473i	0.852017	+	2.34090i
$846$	−16.2067	+	23.9192i	−0.557196	+	0.822359i
$847$	6.99670	+	12.1186i	0.240410	+	0.416402i
$848$	31.1860	+	54.0157i	1.07093	+	1.85491i
$849$	9.31245	−	3.94140i	0.319603	−	0.135269i
$850$	−7.03905	+	19.3396i	−0.241437	+	0.663344i
$851$	−4.70456	+	26.6809i	−0.161270	+	0.914609i
$852$	7.89963	−	7.35108i	0.270637	−	0.251844i
$853$	40.1026	−	33.6500i	1.37309	−	1.15216i	0.401393	−	0.915906i	$-0.368526\pi$
$853$	40.1026	−	33.6500i	1.37309	−	1.15216i	0.971692	−	0.236250i	$-0.0759183\pi$
$854$	−9.64451			−0.330028
$855$	−21.4409	−	34.1919i	−0.733262	−	1.16934i
$856$	−25.8083			−0.882109
$857$	7.46438	−	6.26336i	0.254978	−	0.213952i	−0.506334	−	0.862337i	$-0.669000\pi$
$857$	7.46438	−	6.26336i	0.254978	−	0.213952i	0.761312	+	0.648385i	$0.224555\pi$
$858$	89.6609	+	27.5148i	3.06097	+	0.939338i
$859$	0.491295	−	2.78627i	0.0167628	−	0.0950663i	−0.975279	−	0.220979i	$-0.929075\pi$
$859$	0.491295	−	2.78627i	0.0167628	−	0.0950663i	0.992041	+	0.125913i	$0.0401859\pi$
$860$	−4.20725	+	11.5593i	−0.143466	+	0.394170i
$861$	−0.517598	+	4.17932i	−0.0176397	+	0.142431i
$862$	9.84541	+	17.0527i	0.335336	+	0.580819i
$863$	−17.1036	−	29.6244i	−0.582214	−	1.00842i	−0.995216	−	0.0976947i	$-0.968853\pi$
$863$	−17.1036	−	29.6244i	−0.582214	−	1.00842i	0.413002	−	0.910730i	$-0.364480\pi$
$864$	−21.3989	−	12.9494i	−0.728007	−	0.440548i
$865$	17.3535	+	47.6784i	0.590038	+	1.62112i
$866$			20.4193i			0.693877i
$867$	−7.80119	+	15.2712i	−0.264942	+	0.518636i
$868$	−1.09419	−	3.00626i	−0.0371392	−	0.102039i
$869$	18.4715	+	6.72307i	0.626602	+	0.228064i
$870$	18.2275	+	43.0665i	0.617969	+	1.46009i
$871$	9.86924	+	3.59211i	0.334406	+	0.121714i
$872$	1.43242	−	3.93554i	0.0485078	−	0.133274i
$873$	−7.74650	−	3.46841i	−0.262179	−	0.117388i
$874$	23.7193	−	35.4458i	0.802317	−	1.19897i
$875$	−1.07015	−	0.617850i	−0.0361776	−	0.0208871i
$876$	−0.768936	−	3.34661i	−0.0259799	−	0.113071i
$877$	17.3662	+	20.6963i	0.586416	+	0.698863i	0.974913	−	0.222587i	$-0.0714500\pi$
$877$	17.3662	+	20.6963i	0.586416	+	0.698863i	−0.388497	+	0.921450i	$0.627006\pi$
$878$	−47.3106	−	8.34214i	−1.59666	−	0.281534i
$879$	−4.18608	−	1.28461i	−0.141193	−	0.0433287i
$880$	62.0077	+	52.0307i	2.09028	+	1.75395i
$881$	0.110323	+	0.0636951i	0.00371688	+	0.00214594i	0.501857	−	0.864950i	$-0.332650\pi$
$881$	0.110323	+	0.0636951i	0.00371688	+	0.00214594i	−0.498140	+	0.867096i	$0.665984\pi$
$882$	18.8757	+	26.0948i	0.635576	+	0.878659i
$883$	43.6696	−	15.8944i	1.46960	−	0.534890i	0.521607	−	0.853186i	$-0.325333\pi$
$883$	43.6696	−	15.8944i	1.46960	−	0.534890i	0.947991	+	0.318296i	$0.103111\pi$
$884$	−2.55280	+	14.4776i	−0.0858598	+	0.486935i
$885$	−0.818801	−	15.9430i	−0.0275237	−	0.535917i
$886$		−	47.2387i		−	1.58701i
$887$	−43.0517	+	15.6695i	−1.44553	+	0.526131i	−0.941340	−	0.337460i	$-0.890432\pi$
$887$	−43.0517	+	15.6695i	−1.44553	+	0.526131i	−0.504193	+	0.863591i	$0.668210\pi$
$888$	10.3409	+	11.1125i	0.347017	+	0.372912i
$889$	−1.31215	−	3.60511i	−0.0440082	−	0.120911i
$890$	38.6362	−	6.81261i	1.29509	−	0.228359i
$891$	37.1349	+	29.2642i	1.24407	+	0.980387i
$892$		−	1.18842i		−	0.0397913i
$893$	−23.6156	+	6.86578i	−0.790268	+	0.229755i
$894$	−1.43794	−	27.9982i	−0.0480918	−	0.936400i
$895$	−3.54088	+	0.624353i	−0.118359	+	0.0208698i
$896$	8.16749	−	6.85334i	0.272857	−	0.228954i
$897$	−55.2110	+	23.3675i	−1.84344	+	0.780218i
$898$	9.22408	+	52.3124i	0.307812	+	1.74569i
$899$	−20.9607	−	3.69593i	−0.699077	−	0.123266i
$900$	5.06882	−	11.3209i	0.168961	−	0.377364i
$901$	28.8275	−	16.6436i	0.960384	−	0.554478i
$902$	−25.4669	−	4.49051i	−0.847956	−	0.149518i
$903$	−5.08339	−	3.83896i	−0.169165	−	0.127753i
$904$	−12.6002	+	21.8243i	−0.419078	+	0.725864i
$905$	39.2732			1.30549
$906$	−10.8840	−	25.7159i	−0.361597	−	0.854355i
$907$	−20.5161	+	3.61754i	−0.681226	+	0.120119i	−0.503544	−	0.863969i	$-0.667971\pi$
$907$	−20.5161	+	3.61754i	−0.681226	+	0.120119i	−0.177682	+	0.984088i	$0.556860\pi$
$908$	15.6957	+	13.1702i	0.520880	+	0.437070i
$909$	−0.763991	+	3.03710i	−0.0253400	+	0.100734i
$910$	25.2031	+	9.17320i	0.835476	+	0.304088i
$911$	12.5512	−	21.7393i	0.415840	−	0.720255i	−0.579677	−	0.814847i	$-0.696821\pi$
$911$	12.5512	−	21.7393i	0.415840	−	0.720255i	0.995516	+	0.0945912i	$0.0301544\pi$
$912$	−12.3654	−	35.6070i	−0.409458	−	1.17906i
$913$	23.3311	+	40.4107i	0.772148	+	1.33740i
$914$	1.41512	+	8.02556i	0.0468081	+	0.265462i
$915$	34.9139	−	8.02203i	1.15422	−	0.265200i
$916$	21.7756	−	7.92565i	0.719485	−	0.261871i
$917$	0.0309115	+	0.0368389i	0.00102079	+	0.00121653i
$918$	−12.2353	+	20.2189i	−0.403827	+	0.667324i
$919$	−13.0600	+	22.6205i	−0.430808	+	0.746182i	−0.996943	−	0.0781310i	$-0.975105\pi$
$919$	−13.0600	+	22.6205i	−0.430808	+	0.746182i	0.566135	+	0.824313i	$0.308438\pi$
$920$	−32.8037			−1.08150
$921$	−13.5454	−	32.0042i	−0.446337	−	1.05457i
$922$	2.07916	−	2.47785i	0.0684735	−	0.0816036i
$923$	−35.6571	−	20.5867i	−1.17367	−	0.677618i
$924$	5.88263	−	3.81147i	0.193524	−	0.125388i
$925$	−13.7476	+	16.3838i	−0.452019	+	0.538695i
$926$	40.0571	−	33.6119i	1.31636	−	1.10455i
$927$	11.5101	+	0.829084i	0.378042	+	0.0272307i
$928$	4.28391	+	24.2952i	0.140626	+	0.797530i
$929$	14.8713	+	17.7229i	0.487912	+	0.581471i	0.952685	−	0.303959i	$-0.0983085\pi$
$929$	14.8713	+	17.7229i	0.487912	+	0.581471i	−0.464773	+	0.885430i	$0.653864\pi$
$930$	20.6052	+	31.8021i	0.675672	+	1.04283i
$931$	−1.81169	+	27.3539i	−0.0593758	+	0.896489i
$932$	−0.0859901	+	0.0496464i	−0.00281670	+	0.00162622i
$933$	37.5002	−	8.61627i	1.22770	−	0.282084i
$934$	−23.0535	+	63.3389i	−0.754332	+	2.07251i
$935$	27.7682	−	33.0928i	0.908116	−	1.08225i
$936$	−8.19455	+	32.5758i	−0.267847	+	1.06477i
$937$	2.47293	−	14.0247i	0.0807870	−	0.458166i	−0.917399	−	0.397968i	$-0.869716\pi$
$937$	2.47293	−	14.0247i	0.0807870	−	0.458166i	0.998186	−	0.0601983i	$-0.0191733\pi$
$938$	2.16773	−	1.25154i	0.0707790	−	0.0408643i
$939$	45.1819	−	2.32046i	1.47446	−	0.0757254i
$940$	−12.1882	−	10.2271i	−0.397535	−	0.333571i
$941$	28.7136	+	24.0936i	0.936037	+	0.785429i	0.976891	−	0.213737i	$-0.0685634\pi$
$941$	28.7136	+	24.0936i	0.936037	+	0.785429i	−0.0408540	+	0.999165i	$0.513008\pi$
$942$	−29.4189	−	45.4051i	−0.958518	−	1.47938i
$943$	14.3158	−	8.26525i	0.466188	−	0.269153i
$944$	2.58904	−	14.6832i	0.0842660	−	0.477896i
$945$	10.1763	+	8.90239i	0.331035	+	0.289595i
$946$	25.1437	−	29.9651i	0.817493	−	0.974250i
$947$	0.164128	−	0.450937i	0.00533344	−	0.0146535i	−0.936997	−	0.349336i	$-0.886407\pi$
$947$	0.164128	−	0.450937i	0.00533344	−	0.0146535i	0.942331	+	0.334683i	$0.108629\pi$
$948$	1.73728	−	5.66117i	0.0564241	−	0.183866i
$949$	−11.3466	+	6.55098i	−0.368327	+	0.212654i
$950$	30.2069	−	14.8707i	0.980041	−	0.482468i
$951$	−9.93412	+	19.4465i	−0.322136	+	0.630594i
$952$	−2.67750	−	3.19093i	−0.0867784	−	0.103418i
$953$	−4.83195	−	27.4033i	−0.156522	−	0.887681i	−0.957381	−	0.288828i	$-0.906734\pi$
$953$	−4.83195	−	27.4033i	−0.156522	−	0.887681i	0.800859	−	0.598853i	$-0.204377\pi$
$954$	−57.5590	+	27.9244i	−1.86354	+	0.904085i
$955$	−6.63940	+	5.57111i	−0.214846	+	0.180277i
$956$	4.41308	−	5.25930i	0.142729	−	0.170098i
$957$	−2.39185	−	46.5720i	−0.0773177	−	1.50546i
$958$	8.69470	+	5.01989i	0.280913	+	0.162185i
$959$	−1.81844	+	2.16713i	−0.0587203	+	0.0699802i
$960$	−5.69740	+	7.54425i	−0.183883	+	0.243490i
$961$	13.7535			0.443660
$962$	−24.3586	+	42.1903i	−0.785353	+	1.36027i
$963$	2.99989	−	41.6473i	0.0966703	−	1.34207i
$964$	−0.544828	−	0.649301i	−0.0175477	−	0.0209126i
$965$	−17.5370	+	6.38293i	−0.564535	+	0.205474i
$966$	−4.19183	+	13.6597i	−0.134870	+	0.439494i
$967$	−8.76050	−	49.6832i	−0.281719	−	1.59771i	−0.716776	−	0.697303i	$-0.754383\pi$
$967$	−8.76050	−	49.6832i	−0.281719	−	1.59771i	0.435058	−	0.900402i	$-0.356728\pi$
$968$	−15.3879	−	26.6527i	−0.494587	−	0.856650i
$969$	−19.0030	+	6.59925i	−0.610465	+	0.211998i
$970$	7.45226	−	12.9077i	0.239278	−	0.414441i
$971$	12.0151	+	4.37313i	0.385582	+	0.140341i	0.527536	−	0.849533i	$-0.323116\pi$
$971$	12.0151	+	4.37313i	0.385582	+	0.140341i	−0.141953	+	0.989873i	$0.545338\pi$
$972$	8.23057	−	11.6245i	0.263996	−	0.372856i
$973$	0.384900	+	0.322970i	0.0123393	+	0.0103539i
$974$	−25.9910	+	4.58292i	−0.832806	+	0.146846i
$975$	−46.9691	−	5.81700i	−1.50422	−	0.186293i
$976$	33.4578			1.07096
$977$	−15.9051	+	27.5485i	−0.508851	+	0.881355i	0.491097	+	0.871105i	$0.336596\pi$
$977$	−15.9051	+	27.5485i	−0.508851	+	0.881355i	−0.999947	+	0.0102500i	$0.996737\pi$
$978$	6.85319	−	55.3358i	0.219141	−	1.76945i
$979$	−38.5275	−	6.79344i	−1.23134	−	0.217119i
$980$	−15.3591	+	8.86759i	−0.490629	+	0.283265i
$981$	6.18435	+	2.76898i	0.197451	+	0.0884067i
$982$	−36.4339	−	6.42428i	−1.16265	−	0.205007i
$983$	−2.19294	−	12.4368i	−0.0699439	−	0.396672i	−0.999601	−	0.0282457i	$-0.991008\pi$
$983$	−2.19294	−	12.4368i	−0.0699439	−	0.396672i	0.929657	−	0.368426i	$-0.120103\pi$
$984$	1.13836	−	9.19164i	0.0362896	−	0.293019i
$985$	−5.93708	+	4.98180i	−0.189171	+	0.158733i
$986$	22.9555	−	4.04768i	0.731053	−	0.128904i
$987$	6.91468	−	4.48016i	0.220097	−	0.142605i
$988$	19.4046	−	14.2076i	0.617343	−	0.452005i
$989$			25.0047i			0.795105i
$990$	−57.7995	+	59.6029i	−1.83699	+	1.89431i
$991$	38.6497	−	6.81498i	1.22775	−	0.216485i	0.478090	−	0.878311i	$-0.341329\pi$
$991$	38.6497	−	6.81498i	1.22775	−	0.216485i	0.749657	+	0.661826i	$0.230218\pi$
$992$	6.83707	+	18.7847i	0.217077	+	0.596415i
$993$	−2.47258	+	0.568114i	−0.0784649	+	0.0180285i
$994$	−9.22103	+	3.35618i	−0.292473	+	0.106452i
$995$			53.0769i			1.68265i
$996$	11.7974	−	7.64377i	0.373815	−	0.242202i
$997$	−2.26979	+	12.8726i	−0.0718850	+	0.407680i	0.927538	+	0.373728i	$0.121921\pi$
$997$	−2.26979	+	12.8726i	−0.0718850	+	0.407680i	−0.999423	+	0.0339524i	$0.989191\pi$
$998$	−7.02238	+	2.55594i	−0.222289	+	0.0809067i
$999$	−19.1345	+	15.3955i	−0.605388	+	0.487094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.15	yes	108
3.2	odd	2		513.2.bo.a.224.4		108
9.4	even	3		513.2.cd.a.395.15		108
9.5	odd	6		171.2.bd.a.167.4	yes	108
19.14	odd	18		171.2.bd.a.128.4	yes	108
57.14	even	18		513.2.cd.a.413.15		108
171.14	even	18	inner	171.2.x.a.14.15	✓	108
171.166	odd	18		513.2.bo.a.71.4		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.15	✓	108	171.14	even	18	inner
171.2.x.a.110.15	yes	108	1.1	even	1	trivial
171.2.bd.a.128.4	yes	108	19.14	odd	18
171.2.bd.a.167.4	yes	108	9.5	odd	6
513.2.bo.a.71.4		108	171.166	odd	18
513.2.bo.a.224.4		108	3.2	odd	2
513.2.cd.a.395.15		108	9.4	even	3
513.2.cd.a.413.15		108	57.14	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30761 - 1.09721i) q^{2} +(0.387860 + 1.68807i) q^{3} +(0.158664 - 0.899827i) q^{4} +(1.05557 - 2.90015i) q^{5} +(2.35933 + 1.78176i) q^{6} +(-0.421554 - 0.730152i) q^{7} +(0.927128 + 1.60583i) q^{8} +(-2.69913 + 1.30947i) q^{9} +O(q^{10})\)	\(q+(1.30761 - 1.09721i) q^{2} +(0.387860 + 1.68807i) q^{3} +(0.158664 - 0.899827i) q^{4} +(1.05557 - 2.90015i) q^{5} +(2.35933 + 1.78176i) q^{6} +(-0.421554 - 0.730152i) q^{7} +(0.927128 + 1.60583i) q^{8} +(-2.69913 + 1.30947i) q^{9} +(-1.80181 - 4.95044i) q^{10} +5.25332i q^{11} +(1.58051 - 0.0811718i) q^{12} +(-2.06528 - 5.67432i) q^{13} +(-1.35236 - 0.492218i) q^{14} +(5.30506 + 0.657017i) q^{15} +(4.69147 + 1.70755i) q^{16} +(0.911301 - 2.50378i) q^{17} +(-2.09264 + 4.67378i) q^{18} +(-3.91070 + 1.92521i) q^{19} +(-2.44215 - 1.40998i) q^{20} +(1.06904 - 0.994807i) q^{21} +(5.76401 + 6.86928i) q^{22} +(-5.64507 - 0.995378i) q^{23} +(-2.35115 + 2.18789i) q^{24} +(-3.46643 - 2.90868i) q^{25} +(-8.92651 - 5.15373i) q^{26} +(-3.25735 - 4.04842i) q^{27} +(-0.723896 + 0.263476i) q^{28} +(-0.889964 + 5.04724i) q^{29} +(7.65781 - 4.96165i) q^{30} +4.15289i q^{31} +(4.52328 - 1.64634i) q^{32} +(-8.86796 + 2.03755i) q^{33} +(-1.55555 - 4.27385i) q^{34} +(-2.56253 + 0.451843i) q^{35} +(0.750038 + 2.63651i) q^{36} -4.72641i q^{37} +(-3.00129 + 6.80828i) q^{38} +(8.77759 - 5.68718i) q^{39} +(5.63581 - 0.993745i) q^{40} +(-2.20913 + 1.85368i) q^{41} +(0.306371 - 2.47378i) q^{42} +(-0.757486 - 4.29592i) q^{43} +(4.72708 + 0.833512i) q^{44} +(0.948531 + 9.21012i) q^{45} +(-8.47367 + 4.89227i) q^{46} +(5.55641 + 0.979745i) q^{47} +(-1.06283 + 8.58179i) q^{48} +(3.14459 - 5.44658i) q^{49} -7.72417 q^{50} +(4.58000 + 0.567221i) q^{51} +(-5.43359 + 0.958089i) q^{52} +(9.57018 + 8.03034i) q^{53} +(-8.70130 - 1.71974i) q^{54} +(15.2354 + 5.54525i) q^{55} +(0.781668 - 1.35389i) q^{56} +(-4.76669 - 5.85480i) q^{57} +(4.37417 + 7.57628i) q^{58} +(-0.518580 - 2.94101i) q^{59} +(1.43292 - 4.66939i) q^{60} +(6.29738 - 2.29206i) q^{61} +(4.55661 + 5.43035i) q^{62} +(2.09394 + 1.41877i) q^{63} +(-0.884270 + 1.53160i) q^{64} -18.6365 q^{65} +(-9.36017 + 12.3943i) q^{66} +(-1.11799 + 1.33237i) q^{67} +(-2.10838 - 1.21727i) q^{68} +(-0.509232 - 9.91531i) q^{69} +(-2.85501 + 3.40247i) q^{70} +(5.22326 - 4.38284i) q^{71} +(-4.60522 - 3.12031i) q^{72} +(-0.376772 - 2.13678i) q^{73} +(-5.18587 - 6.18028i) q^{74} +(3.56556 - 6.97973i) q^{75} +(1.11187 + 3.82441i) q^{76} +(3.83573 - 2.21456i) q^{77} +(5.23759 - 17.0675i) q^{78} +(1.27977 - 3.51615i) q^{79} +(9.90433 - 11.8035i) q^{80} +(5.57060 - 7.06883i) q^{81} +(-0.854794 + 4.84778i) q^{82} +(7.69241 - 4.44121i) q^{83} +(-0.725535 - 1.11979i) q^{84} +(-6.29940 - 5.28582i) q^{85} +(-5.70403 - 4.78625i) q^{86} +(-8.86525 + 0.455303i) q^{87} +(-8.43596 + 4.87050i) q^{88} +(-1.29317 + 7.33393i) q^{89} +(11.3458 + 11.0025i) q^{90} +(-3.27249 + 3.90000i) q^{91} +(-1.79133 + 4.92165i) q^{92} +(-7.01036 + 1.61074i) q^{93} +(8.34058 - 4.81544i) q^{94} +(1.45540 + 13.3738i) q^{95} +(4.53352 + 6.99704i) q^{96} +(1.81856 + 2.16727i) q^{97} +(-1.86417 - 10.5723i) q^{98} +(-6.87905 - 14.1794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

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