LMFDB - Embedded newform 798.2.bf.a.569.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(569,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("798.569");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bf (of order $6$, degree $2$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.11
Character	$\chi$	$=$	798.569
Dual form			798.2.bf.a.683.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.632417 - 1.61247i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.74011 + 1.58200i) q^{5} +(1.71265 + 0.258544i) q^{6} +(1.89471 + 1.84664i) q^{7} +1.00000 q^{8} +(-2.20010 + 2.03950i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.632417 - 1.61247i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.74011 + 1.58200i) q^{5} +(1.71265 + 0.258544i) q^{6} +(1.89471 + 1.84664i) q^{7} +1.00000 q^{8} +(-2.20010 + 2.03950i) q^{9} +(-2.74011 + 1.58200i) q^{10} +(4.68759 - 2.70638i) q^{11} +(-1.08023 + 1.35392i) q^{12} +4.37097i q^{13} +(-2.54659 + 0.717543i) q^{14} +(0.818034 - 5.41883i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.04438 + 1.75767i) q^{17} +(-0.666214 - 2.92509i) q^{18} +(-1.04445 + 4.23192i) q^{19} -3.16401i q^{20} +(1.77940 - 4.22300i) q^{21} +5.41277i q^{22} +(-3.77616 - 2.18017i) q^{23} +(-0.632417 - 1.61247i) q^{24} +(2.50547 + 4.33961i) q^{25} +(-3.78537 - 2.18548i) q^{26} +(4.68001 + 2.25776i) q^{27} +(0.651885 - 2.56419i) q^{28} -4.79774 q^{29} +(4.28382 + 3.41785i) q^{30} +(0.0421785 - 0.0243518i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-7.32847 - 5.84702i) q^{33} -3.51534i q^{34} +(2.27031 + 8.05744i) q^{35} +(2.86631 + 0.885587i) q^{36} +(-3.89567 - 2.24917i) q^{37} +(-3.14272 - 3.02048i) q^{38} +(7.04804 - 2.76428i) q^{39} +(2.74011 + 1.58200i) q^{40} +11.6677 q^{41} +(2.76752 + 3.65251i) q^{42} +9.85672 q^{43} +(-4.68759 - 2.70638i) q^{44} +(-9.25501 + 2.10791i) q^{45} +(3.77616 - 2.18017i) q^{46} +(-4.06140 - 2.34485i) q^{47} +(1.71265 + 0.258544i) q^{48} +(0.179827 + 6.99769i) q^{49} -5.01095 q^{50} +(4.75950 + 3.79737i) q^{51} +(3.78537 - 2.18548i) q^{52} +(1.75859 + 3.04596i) q^{53} +(-4.29529 + 2.92413i) q^{54} +17.1260 q^{55} +(1.89471 + 1.84664i) q^{56} +(7.48435 - 0.992193i) q^{57} +(2.39887 - 4.15496i) q^{58} +(2.50131 + 4.33240i) q^{59} +(-5.10186 + 2.00097i) q^{60} +(0.239218 - 0.414338i) q^{61} +0.0487035i q^{62} +(-7.93477 - 0.198528i) q^{63} +1.00000 q^{64} +(-6.91489 + 11.9769i) q^{65} +(8.72791 - 3.42313i) q^{66} +(-4.74430 + 2.73912i) q^{67} +(3.04438 + 1.75767i) q^{68} +(-1.12734 + 7.46771i) q^{69} +(-8.11310 - 2.06257i) q^{70} +5.15864 q^{71} +(-2.20010 + 2.03950i) q^{72} +(-1.15205 - 1.99540i) q^{73} +(3.89567 - 2.24917i) q^{74} +(5.41297 - 6.78444i) q^{75} +(4.18717 - 1.21144i) q^{76} +(13.8793 + 3.52851i) q^{77} +(-1.13009 + 7.48592i) q^{78} +(2.81253 + 1.62381i) q^{79} +(-2.74011 + 1.58200i) q^{80} +(0.680847 - 8.97421i) q^{81} +(-5.83384 + 10.1045i) q^{82} -4.90503i q^{83} +(-4.54693 + 0.570492i) q^{84} -11.1226 q^{85} +(-4.92836 + 8.53617i) q^{86} +(3.03417 + 7.73619i) q^{87} +(4.68759 - 2.70638i) q^{88} +(5.15324 - 8.92567i) q^{89} +(2.80201 - 9.06903i) q^{90} +(-8.07161 + 8.28170i) q^{91} +4.36033i q^{92} +(-0.0659408 - 0.0526109i) q^{93} +(4.06140 - 2.34485i) q^{94} +(-9.55683 + 9.94360i) q^{95} +(-1.08023 + 1.35392i) q^{96} -18.0918i q^{97} +(-6.15009 - 3.34311i) q^{98} +(-4.79348 + 15.5147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8}+O(q^{10}) $ 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8	$ 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8} + 4 q^{14} + 8 q^{15} - 26 q^{16} + 2 q^{19} + 2 q^{21} + 18 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} - 4 q^{30} - 26 q^{32} + 8 q^{33} + 2 q^{38} + q^{39} + 16 q^{41} + 11 q^{42} - 8 q^{43} + 14 q^{45} + 4 q^{49} - 36 q^{50} - 19 q^{51} - 24 q^{53} - 3 q^{54} + 32 q^{55} - 8 q^{56} - 4 q^{57} + 4 q^{58} + 32 q^{59} - 4 q^{60} - 20 q^{61} - 7 q^{63} + 52 q^{64} - 44 q^{65} + 8 q^{66} + 62 q^{69} - 24 q^{71} - 32 q^{73} + 16 q^{75} - 4 q^{76} - 2 q^{78} - 28 q^{81} - 8 q^{82} - 13 q^{84} + 32 q^{85} + 4 q^{86} + 34 q^{87} - 36 q^{89} - 28 q^{90} + 20 q^{93} + 30 q^{95} - 20 q^{98} - 116 q^{99}+O(q^{100}) $ 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8 + 4 * q^14 + 8 * q^15 - 26 * q^16 + 2 * q^19 + 2 * q^21 + 18 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 - 4 * q^30 - 26 * q^32 + 8 * q^33 + 2 * q^38 + q^39 + 16 * q^41 + 11 * q^42 - 8 * q^43 + 14 * q^45 + 4 * q^49 - 36 * q^50 - 19 * q^51 - 24 * q^53 - 3 * q^54 + 32 * q^55 - 8 * q^56 - 4 * q^57 + 4 * q^58 + 32 * q^59 - 4 * q^60 - 20 * q^61 - 7 * q^63 + 52 * q^64 - 44 * q^65 + 8 * q^66 + 62 * q^69 - 24 * q^71 - 32 * q^73 + 16 * q^75 - 4 * q^76 - 2 * q^78 - 28 * q^81 - 8 * q^82 - 13 * q^84 + 32 * q^85 + 4 * q^86 + 34 * q^87 - 36 * q^89 - 28 * q^90 + 20 * q^93 + 30 * q^95 - 20 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.632417	−	1.61247i	−0.365126	−	0.930958i
$3$	−0.632417	−	1.61247i	−0.365126	−	0.930958i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.74011	+	1.58200i	1.22542	+	0.707494i	0.966067	−	0.258290i	$-0.0831591\pi$
$5$	2.74011	+	1.58200i	1.22542	+	0.707494i	0.259348	+	0.965784i	$0.416492\pi$
$6$	1.71265	+	0.258544i	0.699185	+	0.105550i
$7$	1.89471	+	1.84664i	0.716132	+	0.697965i
$7$	1.89471	+	1.84664i	0.716132	+	0.697965i
$8$	1.00000			0.353553
$9$	−2.20010	+	2.03950i	−0.733365	+	0.679835i
$10$	−2.74011	+	1.58200i	−0.866499	+	0.500274i
$11$	4.68759	−	2.70638i	1.41336	−	0.816006i	0.417659	−	0.908604i	$-0.362851\pi$
$11$	4.68759	−	2.70638i	1.41336	−	0.816006i	0.995704	+	0.0925981i	$0.0295172\pi$
$12$	−1.08023	+	1.35392i	−0.311835	+	0.390844i
$13$			4.37097i			1.21229i	0.795355	+	0.606144i	$0.207284\pi$
$13$			4.37097i			1.21229i	−0.795355	+	0.606144i	$0.792716\pi$
$14$	−2.54659	+	0.717543i	−0.680605	+	0.191771i
$15$	0.818034	−	5.41883i	0.211216	−	1.39913i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.04438	+	1.75767i	−0.738370	+	0.426298i	−0.821476	−	0.570243i	$-0.806849\pi$
$17$	−3.04438	+	1.75767i	−0.738370	+	0.426298i	0.0831064	+	0.996541i	$0.473516\pi$
$18$	−0.666214	−	2.92509i	−0.157028	−	0.689451i
$19$	−1.04445	+	4.23192i	−0.239614	+	0.970868i
$19$	−1.04445	+	4.23192i	−0.239614	+	0.970868i
$20$		−	3.16401i		−	0.707494i
$21$	1.77940	−	4.22300i	0.388297	−	0.921534i
$22$			5.41277i			1.15401i
$23$	−3.77616	−	2.18017i	−0.787384	−	0.454596i	0.0516570	−	0.998665i	$-0.483550\pi$
$23$	−3.77616	−	2.18017i	−0.787384	−	0.454596i	−0.839041	+	0.544069i	$0.816883\pi$
$24$	−0.632417	−	1.61247i	−0.129092	−	0.329143i
$25$	2.50547	+	4.33961i	0.501095	+	0.867922i
$26$	−3.78537	−	2.18548i	−0.742372	−	0.428609i
$27$	4.68001	+	2.25776i	0.900669	+	0.434507i
$28$	0.651885	−	2.56419i	0.123195	−	0.484585i
$29$	−4.79774			−0.890918			−0.445459	−	0.895302i	$-0.646959\pi$
$29$	−4.79774			−0.890918			−0.445459	+	0.895302i	$0.646959\pi$
$30$	4.28382	+	3.41785i	0.782116	+	0.624011i
$31$	0.0421785	−	0.0243518i	0.00757548	−	0.00437371i	−0.496207	−	0.868204i	$-0.665274\pi$
$31$	0.0421785	−	0.0243518i	0.00757548	−	0.00437371i	0.503783	+	0.863830i	$0.331941\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−7.32847	−	5.84702i	−1.27572	−	1.01784i
$34$		−	3.51534i		−	0.602877i
$35$	2.27031	+	8.05744i	0.383753	+	1.36196i
$36$	2.86631	+	0.885587i	0.477718	+	0.147598i
$37$	−3.89567	−	2.24917i	−0.640444	−	0.369761i	0.144341	−	0.989528i	$-0.453894\pi$
$37$	−3.89567	−	2.24917i	−0.640444	−	0.369761i	−0.784786	+	0.619767i	$0.787227\pi$
$38$	−3.14272	−	3.02048i	−0.509817	−	0.489987i
$39$	7.04804	−	2.76428i	1.12859	−	0.442638i
$40$	2.74011	+	1.58200i	0.433250	+	0.250137i
$41$	11.6677			1.82218			0.911092	−	0.412203i	$-0.135241\pi$
$41$	11.6677			1.82218			0.911092	+	0.412203i	$0.135241\pi$
$42$	2.76752	+	3.65251i	0.427038	+	0.563594i
$43$	9.85672			1.50314			0.751568	−	0.659655i	$-0.229298\pi$
$43$	9.85672			1.50314			0.751568	+	0.659655i	$0.229298\pi$
$44$	−4.68759	−	2.70638i	−0.706682	−	0.408003i
$45$	−9.25501	+	2.10791i	−1.37966	+	0.314228i
$46$	3.77616	−	2.18017i	0.556764	−	0.321448i
$47$	−4.06140	−	2.34485i	−0.592416	−	0.342031i	0.173637	−	0.984810i	$-0.444448\pi$
$47$	−4.06140	−	2.34485i	−0.592416	−	0.342031i	−0.766052	+	0.642779i	$0.777782\pi$
$48$	1.71265	+	0.258544i	0.247199	+	0.0373176i
$49$	0.179827	+	6.99769i	0.0256896	+	0.999670i
$50$	−5.01095			−0.708655
$51$	4.75950	+	3.79737i	0.666464	+	0.531739i
$52$	3.78537	−	2.18548i	0.524936	−	0.303072i
$53$	1.75859	+	3.04596i	0.241561	+	0.418395i	0.961159	−	0.275995i	$-0.0890074\pi$
$53$	1.75859	+	3.04596i	0.241561	+	0.418395i	−0.719598	+	0.694391i	$0.755674\pi$
$54$	−4.29529	+	2.92413i	−0.584514	+	0.397923i
$55$	17.1260			2.30928
$56$	1.89471	+	1.84664i	0.253191	+	0.246768i
$57$	7.48435	−	0.992193i	0.991327	−	0.131419i
$58$	2.39887	−	4.15496i	0.314987	−	0.545573i
$59$	2.50131	+	4.33240i	0.325643	+	0.564030i	0.981642	−	0.190731i	$-0.0610859\pi$
$59$	2.50131	+	4.33240i	0.325643	+	0.564030i	−0.655999	+	0.754762i	$0.727753\pi$
$60$	−5.10186	+	2.00097i	−0.658647	+	0.258325i
$61$	0.239218	−	0.414338i	0.0306287	−	0.0530505i	−0.850305	−	0.526291i	$-0.823582\pi$
$61$	0.239218	−	0.414338i	0.0306287	−	0.0530505i	0.880933	+	0.473240i	$0.156916\pi$
$62$			0.0487035i			0.00618536i
$63$	−7.93477	−	0.198528i	−0.999687	−	0.0250122i
$64$	1.00000			0.125000
$65$	−6.91489	+	11.9769i	−0.857686	+	1.48556i
$66$	8.72791	−	3.42313i	1.07433	−	0.421358i
$67$	−4.74430	+	2.73912i	−0.579608	+	0.334637i	−0.760978	−	0.648778i	$-0.775280\pi$
$67$	−4.74430	+	2.73912i	−0.579608	+	0.334637i	0.181370	+	0.983415i	$0.441947\pi$
$68$	3.04438	+	1.75767i	0.369185	+	0.213149i
$69$	−1.12734	+	7.46771i	−0.135715	+	0.899006i
$70$	−8.11310	−	2.06257i	−0.969701	−	0.246524i
$71$	5.15864			0.612217			0.306109	−	0.951997i	$-0.400973\pi$
$71$	5.15864			0.612217			0.306109	+	0.951997i	$0.400973\pi$
$72$	−2.20010	+	2.03950i	−0.259284	+	0.240358i
$73$	−1.15205	−	1.99540i	−0.134837	−	0.233544i	0.790698	−	0.612206i	$-0.209718\pi$
$73$	−1.15205	−	1.99540i	−0.134837	−	0.233544i	−0.925535	+	0.378662i	$0.876384\pi$
$74$	3.89567	−	2.24917i	0.452862	−	0.261460i
$75$	5.41297	−	6.78444i	0.625036	−	0.783400i
$76$	4.18717	−	1.21144i	0.480302	−	0.138961i
$77$	13.8793	+	3.52851i	1.58170	+	0.402110i
$78$	−1.13009	+	7.48592i	−0.127957	+	0.847613i
$79$	2.81253	+	1.62381i	0.316434	+	0.182693i	0.649802	−	0.760103i	$-0.274852\pi$
$79$	2.81253	+	1.62381i	0.316434	+	0.182693i	−0.333368	+	0.942797i	$0.608185\pi$
$80$	−2.74011	+	1.58200i	−0.306354	+	0.176873i
$81$	0.680847	−	8.97421i	0.0756496	−	0.997134i
$82$	−5.83384	+	10.1045i	−0.644239	+	1.11586i
$83$		−	4.90503i		−	0.538396i	−0.963085	−	0.269198i	$-0.913241\pi$
$83$		−	4.90503i		−	0.538396i	0.963085	−	0.269198i	$-0.0867587\pi$
$84$	−4.54693	+	0.570492i	−0.496110	+	0.0622458i
$85$	−11.1226			−1.20641
$86$	−4.92836	+	8.53617i	−0.531439	+	0.920479i
$87$	3.03417	+	7.73619i	0.325298	+	0.829407i
$88$	4.68759	−	2.70638i	0.499699	−	0.288502i
$89$	5.15324	−	8.92567i	0.546242	−	0.946119i	−0.452285	−	0.891873i	$-0.649391\pi$
$89$	5.15324	−	8.92567i	0.546242	−	0.946119i	0.998528	−	0.0542461i	$-0.0172755\pi$
$90$	2.80201	−	9.06903i	0.295357	−	0.955960i
$91$	−8.07161	+	8.28170i	−0.846135	+	0.868158i
$92$			4.36033i			0.454596i
$93$	−0.0659408	−	0.0526109i	−0.00683775	−	0.00545550i
$94$	4.06140	−	2.34485i	0.418901	−	0.241853i
$95$	−9.55683	+	9.94360i	−0.980510	+	1.02019i
$96$	−1.08023	+	1.35392i	−0.110250	+	0.138184i
$97$		−	18.0918i		−	1.83694i	−0.395487	−	0.918472i	$-0.629424\pi$
$97$		−	18.0918i		−	1.83694i	0.395487	−	0.918472i	$-0.370576\pi$
$98$	−6.15009	−	3.34311i	−0.621253	−	0.337705i
$99$	−4.79348	+	15.5147i	−0.481763	+	1.55928i
$100$	2.50547	−	4.33961i	0.250547	−	0.433961i
$101$	15.1119	−	8.72483i	1.50369	−	0.868153i	0.503694	−	0.863882i	$-0.331974\pi$
$101$	15.1119	−	8.72483i	1.50369	−	0.868153i	0.999991	−	0.00427125i	$-0.00135959\pi$
$102$	−5.66837	+	2.22317i	−0.561253	+	0.220126i
$103$	13.7075	+	7.91404i	1.35064	+	0.779794i	0.988339	−	0.152267i	$-0.0486573\pi$
$103$	13.7075	+	7.91404i	1.35064	+	0.779794i	0.362303	+	0.932060i	$0.381991\pi$
$104$			4.37097i			0.428609i
$105$	11.5566	−	8.75647i	1.12781	−	0.854544i
$106$	−3.51718			−0.341618
$107$	−2.89411	+	5.01275i	−0.279784	+	0.484600i	−0.971331	−	0.237731i	$-0.923596\pi$
$107$	−2.89411	+	5.01275i	−0.279784	+	0.484600i	0.691547	+	0.722332i	$0.256930\pi$
$108$	−0.384725	−	5.18189i	−0.0370202	−	0.498628i
$109$	−7.16383	+	4.13604i	−0.686170	+	0.396161i	−0.802176	−	0.597088i	$-0.796324\pi$
$109$	−7.16383	+	4.13604i	−0.686170	+	0.396161i	0.116005	+	0.993249i	$0.462991\pi$
$110$	−8.56302	+	14.8316i	−0.816452	+	1.41414i
$111$	−1.16302	+	7.70405i	−0.110389	+	0.731236i
$112$	−2.54659	+	0.717543i	−0.240630	+	0.0678015i
$113$	−20.0632			−1.88739			−0.943694	−	0.330819i	$-0.892675\pi$
$113$	−20.0632			−1.88739			−0.943694	+	0.330819i	$0.892675\pi$
$114$	−2.88291	+	6.97774i	−0.270010	+	0.653525i
$115$	−6.89807	−	11.9478i	−0.643248	−	1.11414i
$116$	2.39887	+	4.15496i	0.222729	+	0.385779i
$117$	−8.91460	−	9.61655i	−0.824155	−	0.889050i
$118$	−5.00262			−0.460529
$119$	−9.01399	−	2.29160i	−0.826311	−	0.210071i
$120$	0.818034	−	5.41883i	0.0746760	−	0.494669i
$121$	9.14903	−	15.8466i	0.831730	−	1.44060i
$122$	0.239218	+	0.414338i	0.0216578	+	0.0375124i
$123$	−7.37884	−	18.8137i	−0.665328	−	1.69638i
$124$	−0.0421785	−	0.0243518i	−0.00378774	−	0.00218685i
$125$			0.0346441i			0.00309866i
$126$	4.13932	−	6.77245i	0.368760	−	0.603338i
$127$		−	13.2873i		−	1.17905i	−0.807749	−	0.589527i	$-0.799314\pi$
$127$		−	13.2873i		−	1.17905i	0.807749	−	0.589527i	$-0.200686\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−6.23357	−	15.8936i	−0.548835	−	1.39936i
$130$	−6.91489	−	11.9769i	−0.606476	−	1.05045i
$131$	−13.1060	−	7.56675i	−1.14508	−	0.661110i	−0.197394	−	0.980324i	$-0.563248\pi$
$131$	−13.1060	−	7.56675i	−1.14508	−	0.661110i	−0.947683	+	0.319214i	$0.896581\pi$
$132$	−1.39944	+	9.27015i	−0.121805	+	0.806863i
$133$	−9.79377	+	6.08951i	−0.849227	+	0.528028i
$134$		−	5.47824i		−	0.473248i
$135$	9.25196	+	13.5903i	0.796282	+	1.16967i
$136$	−3.04438	+	1.75767i	−0.261053	+	0.150719i
$137$	−15.1346	+	8.73798i	−1.29304	+	0.746536i	−0.979192	−	0.202938i	$-0.934951\pi$
$137$	−15.1346	+	8.73798i	−1.29304	+	0.746536i	−0.313846	+	0.949474i	$0.601618\pi$
$138$	−5.90355	−	4.71015i	−0.502544	−	0.400955i
$139$	3.81174			0.323308			0.161654	−	0.986848i	$-0.448317\pi$
$139$	3.81174			0.323308			0.161654	+	0.986848i	$0.448317\pi$
$140$	5.84279	−	5.99487i	0.493806	−	0.506659i
$141$	−1.21249	+	8.03179i	−0.102110	+	0.676399i
$142$	−2.57932	+	4.46751i	−0.216452	+	0.374905i
$143$	11.8295	+	20.4893i	0.989234	+	1.71340i
$144$	−0.666214	−	2.92509i	−0.0555178	−	0.243758i
$145$	−13.1463	−	7.59004i	−1.09174	−	0.630319i
$146$	2.30409			0.190688
$147$	11.1698	−	4.71543i	0.921271	−	0.388922i
$148$			4.49833i			0.369761i
$149$	−5.63489	−	3.25330i	−0.461628	−	0.266521i	0.251100	−	0.967961i	$-0.419208\pi$
$149$	−5.63489	−	3.25330i	−0.461628	−	0.266521i	−0.712729	+	0.701440i	$0.752541\pi$
$150$	3.16901	+	8.07999i	0.258749	+	0.659728i
$151$	7.84451	−	4.52903i	0.638377	−	0.368567i	−0.145612	−	0.989342i	$-0.546515\pi$
$151$	7.84451	−	4.52903i	0.638377	−	0.368567i	0.783989	+	0.620775i	$0.213182\pi$
$152$	−1.04445	+	4.23192i	−0.0847163	+	0.343254i
$153$	3.11314	−	10.0761i	0.251683	−	0.814602i
$154$	−9.99545	+	10.2556i	−0.805456	+	0.826421i
$155$	0.154098			0.0123775
$156$	−5.91795	−	4.72164i	−0.473815	−	0.378034i
$157$	−0.862063	−	1.49314i	−0.0688001	−	0.119165i	0.829573	−	0.558398i	$-0.188584\pi$
$157$	−0.862063	−	1.49314i	−0.0688001	−	0.119165i	−0.898373	+	0.439233i	$0.855250\pi$
$158$	−2.81253	+	1.62381i	−0.223753	+	0.129184i
$159$	3.79935	−	4.76199i	0.301308	−	0.377650i
$160$		−	3.16401i		−	0.250137i
$161$	−3.12873	−	11.1040i	−0.246578	−	0.875117i
$162$	7.43147	+	5.07674i	0.583871	+	0.398866i
$163$	3.97494	−	6.88481i	0.311342	−	0.539260i	−0.667311	−	0.744779i	$-0.732555\pi$
$163$	3.97494	−	6.88481i	0.311342	−	0.539260i	0.978653	+	0.205519i	$0.0658883\pi$
$164$	−5.83384	−	10.1045i	−0.455546	−	0.789029i
$165$	−10.8308	−	27.6152i	−0.843177	−	2.14984i
$166$	4.24788	+	2.45251i	0.329699	+	0.190352i
$167$	8.20239			0.634720			0.317360	−	0.948305i	$-0.397204\pi$
$167$	8.20239			0.634720			0.317360	+	0.948305i	$0.397204\pi$
$168$	1.77940	−	4.22300i	0.137284	−	0.325812i
$169$	−6.10535			−0.469642
$170$	5.56129	−	9.63244i	0.426531	−	0.738774i
$171$	−6.33311	−	11.4408i	−0.484305	−	0.874899i
$172$	−4.92836	−	8.53617i	−0.375784	−	0.650877i
$173$	−0.910514	+	1.57706i	−0.0692251	+	0.119901i	−0.898560	−	0.438850i	$-0.855386\pi$
$173$	−0.910514	+	1.57706i	−0.0692251	+	0.119901i	0.829335	+	0.558751i	$0.188719\pi$
$174$	−8.21683	−	1.24042i	−0.622916	−	0.0940364i
$175$	−3.26657	+	12.8490i	−0.246929	+	0.971293i
$176$			5.41277i			0.408003i
$177$	5.40398	−	6.77317i	0.406188	−	0.509102i
$178$	5.15324	+	8.92567i	0.386252	+	0.669007i
$179$	7.56878	+	13.1095i	0.565717	+	0.979851i	0.996983	+	0.0776261i	$0.0247341\pi$
$179$	7.56878	+	13.1095i	0.565717	+	0.979851i	−0.431265	+	0.902225i	$0.641933\pi$
$180$	6.45301	+	6.96112i	0.480979	+	0.518851i
$181$			1.55088i			0.115276i	0.998338	+	0.0576378i	$0.0183569\pi$
$181$			1.55088i			0.115276i	−0.998338	+	0.0576378i	$0.981643\pi$
$182$	−3.13636	−	11.1311i	−0.232482	−	0.825090i
$183$	−0.819392	−	0.123697i	−0.0605712	−	0.00914392i
$184$	−3.77616	−	2.18017i	−0.278382	−	0.160724i
$185$	−7.11638	−	12.3259i	−0.523207	−	0.906221i
$186$	0.0785328	−	0.0308010i	0.00575831	−	0.00225844i
$187$	−9.51387	+	16.4785i	−0.695723	+	1.20503i
$188$			4.68970i			0.342031i
$189$	4.69797	+	12.9201i	0.341727	+	0.939799i
$190$	−3.83299	−	13.2483i	−0.278075	−	0.961129i
$191$	−5.90541	−	3.40949i	−0.427301	−	0.246702i	0.270895	−	0.962609i	$-0.412680\pi$
$191$	−5.90541	−	3.40949i	−0.427301	−	0.246702i	−0.698196	+	0.715907i	$0.746014\pi$
$192$	−0.632417	−	1.61247i	−0.0456408	−	0.116370i
$193$	20.0230	−	11.5603i	1.44128	−	0.832126i	0.443349	−	0.896349i	$-0.353790\pi$
$193$	20.0230	−	11.5603i	1.44128	−	0.832126i	0.997936	+	0.0642228i	$0.0204568\pi$
$194$	15.6680	+	9.04590i	1.12489	+	0.649457i
$195$	23.6855	+	3.57560i	1.69615	+	0.256054i
$196$	5.97026	−	3.65458i	0.426447	−	0.261041i
$197$			2.20107i			0.156820i	0.996921	+	0.0784100i	$0.0249843\pi$
$197$			2.20107i			0.156820i	−0.996921	+	0.0784100i	$0.975016\pi$
$198$	−11.0394	−	11.9086i	−0.784533	−	0.846308i
$199$	3.23984	+	5.61156i	0.229666	+	0.397793i	0.957709	−	0.287738i	$-0.0929033\pi$
$199$	3.23984	+	5.61156i	0.229666	+	0.397793i	−0.728043	+	0.685531i	$0.759570\pi$
$200$	2.50547	+	4.33961i	0.177164	+	0.306857i
$201$	7.41712	+	5.91775i	0.523163	+	0.417406i
$202$			17.4497i			1.22775i
$203$	−9.09031	−	8.85971i	−0.638015	−	0.621829i
$204$	0.908870	−	6.02054i	0.0636336	−	0.421522i
$205$	31.9707	+	18.4583i	2.23293	+	1.28918i
$206$	−13.7075	+	7.91404i	−0.955048	+	0.551397i
$207$	12.7544	−	2.90492i	0.886490	−	0.201906i
$208$	−3.78537	−	2.18548i	−0.262468	−	0.151536i
$209$	6.55722	+	22.6642i	0.453572	+	1.56772i
$210$	1.80504	+	14.3865i	0.124560	+	0.992764i
$211$		−	23.2601i		−	1.60129i	−0.599140	−	0.800644i	$-0.704491\pi$
$211$		−	23.2601i		−	1.60129i	0.599140	−	0.800644i	$-0.295509\pi$
$212$	1.75859	−	3.04596i	0.120780	−	0.209198i
$213$	−3.26241	−	8.31813i	−0.223537	−	0.569949i
$214$	−2.89411	−	5.01275i	−0.197837	−	0.342664i
$215$	27.0085	+	15.5934i	1.84197	+	1.06346i
$216$	4.68001	+	2.25776i	0.318434	+	0.153621i
$217$	0.124885	+	0.0317491i	0.00847774	+	0.00215527i
$218$		−	8.27208i		−	0.560256i
$219$	−2.48894	+	3.11956i	−0.168187	+	0.210800i
$220$	−8.56302	−	14.8316i	−0.577319	−	0.999946i
$221$	−7.68273	−	13.3069i	−0.516796	−	0.895117i
$222$	−6.09040	−	4.85923i	−0.408761	−	0.326130i
$223$			20.3040i			1.35966i	0.733370	+	0.679830i	$0.237946\pi$
$223$			20.3040i			1.35966i	−0.733370	+	0.679830i	$0.762054\pi$
$224$	0.651885	−	2.56419i	0.0435559	−	0.171327i
$225$	−14.3629	−	4.43763i	−0.957529	−	0.295842i
$226$	10.0316	−	17.3753i	0.667293	−	1.15578i
$227$	0.910098	+	1.57634i	0.0604053	+	0.104625i	0.894647	−	0.446774i	$-0.147427\pi$
$227$	0.910098	+	1.57634i	0.0604053	+	0.104625i	−0.834241	+	0.551400i	$0.814094\pi$
$228$	−4.60144	−	5.98554i	−0.304738	−	0.396402i
$229$	−1.30087	+	2.25318i	−0.0859640	+	0.148894i	−0.905802	−	0.423702i	$-0.860730\pi$
$229$	−1.30087	+	2.25318i	−0.0859640	+	0.148894i	0.819838	+	0.572596i	$0.194064\pi$
$230$	13.7961			0.909690
$231$	−3.08794	−	24.6115i	−0.203172	−	1.61932i
$232$	−4.79774			−0.314987
$233$	−1.66391	−	0.960657i	−0.109006	−	0.0629347i	0.444506	−	0.895776i	$-0.353379\pi$
$233$	−1.66391	−	0.960657i	−0.109006	−	0.0629347i	−0.553512	+	0.832841i	$0.686713\pi$
$234$	12.7855	−	2.91200i	0.835813	−	0.190363i
$235$	−7.41912	−	12.8503i	−0.483970	−	0.838261i
$236$	2.50131	−	4.33240i	0.162822	−	0.282015i
$237$	0.839654	−	5.56204i	0.0545414	−	0.361293i
$238$	6.49158	−	6.66055i	0.420787	−	0.431739i
$239$		−	21.1285i		−	1.36669i	−0.730096	−	0.683344i	$-0.760525\pi$
$239$		−	21.1285i		−	1.36669i	0.730096	−	0.683344i	$-0.239475\pi$
$240$	4.28382	+	3.41785i	0.276520	+	0.220621i
$241$	−22.9630	+	13.2577i	−1.47918	+	0.854003i	−0.999722	−	0.0235634i	$-0.992499\pi$
$241$	−22.9630	+	13.2577i	−1.47918	+	0.854003i	−0.479455	+	0.877567i	$0.659166\pi$
$242$	9.14903	+	15.8466i	0.588122	+	1.01866i
$243$	−14.9012	+	4.57760i	−0.955912	+	0.293653i
$244$	−0.478436			−0.0306287
$245$	−10.5776	+	19.4589i	−0.675780	+	1.24319i
$246$	19.9826	+	3.01660i	1.27404	+	0.192332i
$247$	−18.4976	−	4.56527i	−1.17697	−	0.290481i
$248$	0.0421785	−	0.0243518i	0.00267834	−	0.00154634i
$249$	−7.90919	+	3.10202i	−0.501224	+	0.196583i
$250$	−0.0300027	−	0.0173220i	−0.00189754	−	0.00109554i
$251$		−	15.9433i		−	1.00633i	−0.864190	−	0.503165i	$-0.832169\pi$
$251$		−	15.9433i		−	1.00633i	0.864190	−	0.503165i	$-0.167831\pi$
$252$	3.79546	+	6.97098i	0.239091	+	0.439130i
$253$	−23.6015			−1.48381
$254$	11.5071	+	6.64363i	0.722020	+	0.416858i
$255$	7.03411	+	17.9348i	0.440493	+	1.12312i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.96898	+	5.14243i	−0.185200	+	0.320776i	−0.943644	−	0.330963i	$-0.892627\pi$
$257$	−2.96898	+	5.14243i	−0.185200	+	0.320776i	0.758444	+	0.651738i	$0.225960\pi$
$258$	16.8811	+	2.54839i	1.05097	+	0.158656i
$259$	−3.22775	−	11.4554i	−0.200562	−	0.711805i
$260$	13.8298			0.857686
$261$	10.5555	−	9.78501i	0.653368	−	0.605677i
$262$	13.1060	−	7.56675i	0.809691	−	0.467475i
$263$	−6.51788	+	3.76310i	−0.401910	+	0.232043i	−0.687308	−	0.726366i	$-0.741208\pi$
$263$	−6.51788	+	3.76310i	−0.401910	+	0.232043i	0.285398	+	0.958409i	$0.407874\pi$
$264$	−7.32847	−	5.84702i	−0.451036	−	0.359860i
$265$			11.1284i			0.683611i
$266$	−0.376787	−	11.5264i	−0.0231023	−	0.706729i
$267$	−17.6513	−	2.66467i	−1.08024	−	0.163075i
$268$	4.74430	+	2.73912i	0.289804	+	0.167318i
$269$	−11.7210	−	20.3013i	−0.714641	−	1.23779i	−0.963098	−	0.269152i	$-0.913257\pi$
$269$	−11.7210	−	20.3013i	−0.714641	−	1.23779i	0.248457	−	0.968643i	$-0.420077\pi$
$270$	−16.3955	+	1.21727i	−0.997801	+	0.0740809i
$271$	10.7091	−	18.5487i	0.650530	−	1.12675i	−0.332464	−	0.943116i	$-0.607880\pi$
$271$	10.7091	−	18.5487i	0.650530	−	1.12675i	0.982994	−	0.183636i	$-0.0587867\pi$
$272$		−	3.51534i		−	0.213149i
$273$	18.4586	+	7.77771i	1.11716	+	0.470728i
$274$		−	17.4760i		−	1.05576i
$275$	23.4893	+	13.5616i	1.41646	+	0.817793i
$276$	7.03089	−	2.75755i	0.423210	−	0.165985i
$277$	8.07583	+	13.9878i	0.485230	+	0.840443i	0.999856	−	0.0169720i	$-0.00540261\pi$
$277$	8.07583	+	13.9878i	0.485230	+	0.840443i	−0.514626	+	0.857415i	$0.672069\pi$
$278$	−1.90587	+	3.30106i	−0.114306	+	0.197985i
$279$	−0.0431312	+	0.139599i	−0.00258220	+	0.00835760i
$280$	2.27031	+	8.05744i	0.135677	+	0.481524i
$281$	−27.8861			−1.66355			−0.831773	−	0.555116i	$-0.812674\pi$
$281$	−27.8861			−1.66355			−0.831773	+	0.555116i	$0.812674\pi$
$282$	−6.34949	−	5.06594i	−0.378106	−	0.301672i
$283$	−8.11491	−	14.0554i	−0.482382	−	0.835509i	0.517414	−	0.855735i	$-0.326895\pi$
$283$	−8.11491	−	14.0554i	−0.482382	−	0.835509i	−0.999795	+	0.0202259i	$0.993561\pi$
$284$	−2.57932	−	4.46751i	−0.153054	−	0.265098i
$285$	22.0776	+	9.12156i	1.30777	+	0.540315i
$286$	−23.6590			−1.39899
$287$	22.1068	+	21.5460i	1.30492	+	1.27182i
$288$	2.86631	+	0.885587i	0.168899	+	0.0521837i
$289$	−2.32118	+	4.02040i	−0.136540	+	0.236494i
$290$	13.1463	−	7.59004i	0.771980	−	0.445703i
$291$	−29.1724	+	11.4416i	−1.71012	+	0.670716i
$292$	−1.15205	+	1.99540i	−0.0674184	+	0.116772i
$293$	−12.6869			−0.741178			−0.370589	−	0.928797i	$-0.620844\pi$
$293$	−12.6869			−0.741178			−0.370589	+	0.928797i	$0.620844\pi$
$294$	−1.50123	+	12.0311i	−0.0875534	+	0.701665i
$295$			15.8283i			0.921562i
$296$	−3.89567	−	2.24917i	−0.226431	−	0.130730i
$297$	28.0484	−	2.08243i	1.62753	−	0.120835i
$298$	5.63489	−	3.25330i	0.326420	−	0.188459i
$299$	9.52944	−	16.5055i	0.551101	−	0.954536i
$300$	−8.58198	−	1.29555i	−0.495481	−	0.0747986i
$301$	18.6756	+	18.2018i	1.07644	+	1.04914i
$302$			9.05806i			0.521233i
$303$	−23.6255	−	18.8496i	−1.35725	−	1.08288i
$304$	−3.14272	−	3.02048i	−0.180247	−	0.173236i
$305$	1.31097	−	0.756888i	0.0750658	−	0.0433393i
$306$	7.16956	+	7.73410i	0.409856	+	0.442129i
$307$		−	0.419187i		−	0.0239242i	−0.999928	−	0.0119621i	$-0.996192\pi$
$307$		−	0.419187i		−	0.0239242i	0.999928	−	0.0119621i	$-0.00380775\pi$
$308$	−3.88390	−	13.7841i	−0.221305	−	0.785423i
$309$	4.09225	−	27.1079i	0.232800	−	1.54211i
$310$	−0.0770492	+	0.133453i	−0.00437610	+	0.00757963i
$311$	−4.32711	+	2.49826i	−0.245368	+	0.141663i	−0.617641	−	0.786460i	$-0.711912\pi$
$311$	−4.32711	+	2.49826i	−0.245368	+	0.141663i	0.372273	+	0.928123i	$0.378578\pi$
$312$	7.04804	−	2.76428i	0.399017	−	0.156496i
$313$	−11.6571	+	20.1907i	−0.658900	+	1.14125i	0.322001	+	0.946739i	$0.395645\pi$
$313$	−11.6571	+	20.1907i	−0.658900	+	1.14125i	−0.980901	+	0.194509i	$0.937689\pi$
$314$	1.72413			0.0972980
$315$	−21.4281	−	13.0968i	−1.20734	−	0.737923i
$316$		−	3.24763i		−	0.182693i
$317$	5.57956	−	9.66409i	0.313380	−	0.542789i	−0.665712	−	0.746209i	$-0.731872\pi$
$317$	5.57956	−	9.66409i	0.313380	−	0.542789i	0.979092	+	0.203419i	$0.0652055\pi$
$318$	2.22432	+	5.67133i	0.124734	+	0.318032i
$319$	−22.4899	+	12.9845i	−1.25919	+	0.726994i
$320$	2.74011	+	1.58200i	0.153177	+	0.0884367i
$321$	9.91317	+	1.49651i	0.553299	+	0.0835269i
$322$	11.1807	+	2.84244i	0.623076	+	0.158403i
$323$	−4.25861	−	14.7194i	−0.236956	−	0.819007i
$324$	−8.11232	+	3.89747i	−0.450684	+	0.216526i
$325$	−18.9683	+	10.9513i	−1.05217	+	0.607471i
$326$	3.97494	+	6.88481i	0.220152	+	0.381314i
$327$	11.1998	+	8.93573i	0.619348	+	0.494147i
$328$	11.6677			0.644239
$329$	−3.36506	−	11.9427i	−0.185522	−	0.658425i
$330$	29.3308	+	4.42783i	1.61461	+	0.243744i
$331$	−2.08921	−	1.20621i	−0.114833	−	0.0662991i	0.441483	−	0.897270i	$-0.354452\pi$
$331$	−2.08921	−	1.20621i	−0.114833	−	0.0662991i	−0.556317	+	0.830970i	$0.687786\pi$
$332$	−4.24788	+	2.45251i	−0.233133	+	0.134599i
$333$	13.1580	−	2.99685i	0.721056	−	0.164227i
$334$	−4.10120	+	7.10348i	−0.224408	+	0.388685i
$335$	−17.3332			−0.947014
$336$	2.76752	+	3.65251i	0.150981	+	0.199261i
$337$			12.4305i			0.677131i	0.940943	+	0.338565i	$0.109942\pi$
$337$			12.4305i			0.677131i	−0.940943	+	0.338565i	$0.890058\pi$
$338$	3.05267	−	5.28739i	0.166044	−	0.287596i
$339$	12.6883	+	32.3513i	0.689135	+	1.75708i
$340$	5.56129	+	9.63244i	0.301603	+	0.522392i
$341$	0.131810	−	0.228302i	0.00713794	−	0.0123633i
$342$	13.0746	+	0.235757i	0.706992	+	0.0127483i
$343$	−12.5815	+	13.5906i	−0.679338	+	0.733826i
$344$	9.85672			0.531439
$345$	−14.9030	+	18.6789i	−0.802349	+	1.00564i
$346$	−0.910514	−	1.57706i	−0.0489495	−	0.0847831i
$347$	−2.60696	+	1.50513i	−0.139949	+	0.0807995i	−0.568340	−	0.822794i	$-0.692414\pi$
$347$	−2.60696	+	1.50513i	−0.139949	+	0.0807995i	0.428391	+	0.903594i	$0.359081\pi$
$348$	5.18265	−	6.49577i	0.277819	−	0.348210i
$349$	30.6024			1.63811			0.819054	−	0.573716i	$-0.194499\pi$
$349$	30.6024			1.63811			0.819054	+	0.573716i	$0.194499\pi$
$350$	−9.49428	−	9.25343i	−0.507491	−	0.494617i
$351$	−9.86861	+	20.4562i	−0.526747	+	1.09187i
$352$	−4.68759	−	2.70638i	−0.249850	−	0.144251i
$353$	−10.8604	+	6.27026i	−0.578041	+	0.333732i	−0.760355	−	0.649508i	$-0.774975\pi$
$353$	−10.8604	+	6.27026i	−0.578041	+	0.333732i	0.182313	+	0.983241i	$0.441642\pi$
$354$	3.16375	+	8.06656i	0.168151	+	0.428733i
$355$	14.1352	+	8.16098i	0.750221	+	0.433140i
$356$	−10.3065			−0.546242
$357$	2.00548	+	15.9840i	0.106141	+	0.845964i
$358$	−15.1376			−0.800045
$359$	0.641694	+	0.370482i	0.0338673	+	0.0195533i	0.516838	−	0.856083i	$-0.327109\pi$
$359$	0.641694	+	0.370482i	0.0338673	+	0.0195533i	−0.482971	+	0.875636i	$0.660442\pi$
$360$	−9.25501	+	2.10791i	−0.487782	+	0.111096i
$361$	−16.8182	−	8.84007i	−0.885170	−	0.465267i
$362$	−1.34310	−	0.775438i	−0.0705916	−	0.0407561i
$363$	−31.3381	−	4.73085i	−1.64482	−	0.248305i
$364$	11.2080	+	2.84937i	0.587457	+	0.149348i
$365$		−	7.29016i		−	0.381585i
$366$	0.516820	−	0.647766i	0.0270146	−	0.0338593i
$367$	7.09660	+	12.2917i	0.370440	+	0.641620i	0.989633	−	0.143618i	$-0.0458737\pi$
$367$	7.09660	+	12.2917i	0.370440	+	0.641620i	−0.619193	+	0.785238i	$0.712540\pi$
$368$	3.77616	−	2.18017i	0.196846	−	0.113649i
$369$	−25.6700	+	23.7963i	−1.33633	+	1.23878i
$370$	14.2328			0.739926
$371$	−2.29280	+	9.01869i	−0.119036	+	0.468227i
$372$	−0.0125920	+	0.0834119i	−0.000652864	+	0.00432471i
$373$	−21.8335	−	12.6056i	−1.13050	−	0.652693i	−0.186437	−	0.982467i	$-0.559694\pi$
$373$	−21.8335	−	12.6056i	−1.13050	−	0.652693i	−0.944060	+	0.329774i	$0.893027\pi$
$374$	−9.51387	−	16.4785i	−0.491951	−	0.852083i
$375$	0.0558624	−	0.0219095i	0.00288472	−	0.00113140i
$376$	−4.06140	−	2.34485i	−0.209451	−	0.120926i
$377$		−	20.9708i		−	1.08005i
$378$	−13.5381	−	2.39149i	−0.696326	−	0.123005i
$379$		−	11.5132i		−	0.591391i	−0.955282	−	0.295696i	$-0.904449\pi$
$379$		−	11.5132i		−	0.591391i	0.955282	−	0.295696i	$-0.0955514\pi$
$380$	13.3898	+	3.30466i	0.686883	+	0.169525i
$381$	−21.4253	+	8.40310i	−1.09765	+	0.430504i
$382$	5.90541	−	3.40949i	0.302147	−	0.174445i
$383$	12.2078	−	21.1446i	0.623791	−	1.08044i	−0.364983	−	0.931014i	$-0.618925\pi$
$383$	12.2078	−	21.1446i	0.623791	−	1.08044i	0.988773	−	0.149423i	$-0.0477415\pi$
$384$	1.71265	+	0.258544i	0.0873981	+	0.0131937i
$385$	32.4488	+	31.6257i	1.65375	+	1.61179i
$386$			23.1205i			1.17680i
$387$	−21.6857	+	20.1028i	−1.10235	+	1.02188i
$388$	−15.6680	+	9.04590i	−0.795420	+	0.459236i
$389$	23.3828	−	13.5001i	1.18556	−	0.684481i	0.228263	−	0.973600i	$-0.426695\pi$
$389$	23.3828	−	13.5001i	1.18556	−	0.684481i	0.957293	+	0.289118i	$0.0933621\pi$
$390$	−14.9393	+	18.7244i	−0.756482	+	0.948149i
$391$	15.3281			0.775174
$392$	0.179827	+	6.99769i	0.00908264	+	0.353437i
$393$	−3.91267	+	25.9183i	−0.197368	+	1.30741i
$394$	−1.90619	−	1.10054i	−0.0960322	−	0.0554442i
$395$	5.13776	+	8.89887i	0.258509	+	0.447751i
$396$	15.8328	−	3.60606i	0.795630	−	0.181211i
$397$	−8.64453	+	14.9728i	−0.433857	+	0.751462i	−0.997202	−	0.0747600i	$-0.976181\pi$
$397$	−8.64453	+	14.9728i	−0.433857	+	0.751462i	0.563345	+	0.826222i	$0.309514\pi$
$398$	−6.47967			−0.324797
$399$	16.0129	+	11.9410i	0.801647	+	0.597798i
$400$	−5.01095			−0.250547
$401$	0.482762	−	0.836168i	0.0241080	−	0.0417562i	−0.853720	−	0.520733i	$-0.825659\pi$
$401$	0.482762	−	0.836168i	0.0241080	−	0.0417562i	0.877828	+	0.478977i	$0.158992\pi$
$402$	−8.83348	+	3.46454i	−0.440574	+	0.172795i
$403$	0.106441	+	0.184361i	0.00530219	+	0.00918367i
$404$	−15.1119	−	8.72483i	−0.751843	−	0.434077i
$405$	16.0628	−	23.5132i	0.798169	−	1.16838i
$406$	12.2179	−	3.44258i	0.606363	−	0.170853i
$407$	−24.3484			−1.20691
$408$	4.75950	+	3.79737i	0.235631	+	0.187998i
$409$	15.0977	−	8.71669i	0.746536	−	0.431013i	−0.0779052	−	0.996961i	$-0.524823\pi$
$409$	15.0977	−	8.71669i	0.746536	−	0.431013i	0.824441	+	0.565948i	$0.191490\pi$
$410$	−31.9707	+	18.4583i	−1.57892	+	0.911591i
$411$	23.6611	+	18.8780i	1.16712	+	0.931184i
$412$		−	15.8281i		−	0.779794i
$413$	−3.26114	+	12.8277i	−0.160470	+	0.631208i
$414$	−3.86146	+	12.4981i	−0.189780	+	0.614247i
$415$	7.75977	−	13.4403i	0.380912	−	0.659759i
$416$	3.78537	−	2.18548i	0.185593	−	0.107152i
$417$	−2.41061	−	6.14630i	−0.118048	−	0.300986i
$418$	−22.9064	−	5.65338i	−1.12039	−	0.276516i
$419$		−	15.3308i		−	0.748958i	−0.927235	−	0.374479i	$-0.877822\pi$
$419$		−	15.3308i		−	0.748958i	0.927235	−	0.374479i	$-0.122178\pi$
$420$	−13.3616	−	5.63004i	−0.651980	−	0.274718i
$421$			32.6724i			1.59236i	0.605062	+	0.796179i	$0.293148\pi$
$421$			32.6724i			1.59236i	−0.605062	+	0.796179i	$0.706852\pi$
$422$	20.1438	+	11.6300i	0.980585	+	0.566141i
$423$	13.7178	−	3.12434i	0.666982	−	0.151911i
$424$	1.75859	+	3.04596i	0.0854046	+	0.147925i
$425$	−15.2552	−	8.80761i	−0.739987	−	0.427232i
$426$	8.83492	+	1.33373i	0.428053	+	0.0646195i
$427$	1.21838	−	0.343299i	0.0589616	−	0.0166134i
$428$	5.78822			0.279784
$429$	25.5572	−	32.0325i	1.23391	−	1.54654i
$430$	−27.0085	+	15.5934i	−1.30247	+	0.751980i
$431$	0.992332	+	1.71877i	0.0477989	+	0.0827902i	0.888935	−	0.458033i	$-0.151446\pi$
$431$	0.992332	+	1.71877i	0.0477989	+	0.0827902i	−0.841136	+	0.540824i	$0.818113\pi$
$432$	−4.29529	+	2.92413i	−0.206657	+	0.140687i
$433$		−	22.6783i		−	1.08985i	−0.838485	−	0.544924i	$-0.816558\pi$
$433$		−	22.6783i		−	1.08985i	0.838485	−	0.544924i	$-0.183442\pi$
$434$	−0.0899380	+	0.0922789i	−0.00431716	+	0.00442953i
$435$	−3.92471	+	25.9981i	−0.188176	+	1.24651i
$436$	7.16383	+	4.13604i	0.343085	+	0.198080i
$437$	13.1703	−	13.7033i	0.630021	−	0.655518i
$438$	−1.45715	−	3.71527i	−0.0696252	−	0.177522i
$439$	−2.42953	−	1.40269i	−0.115955	−	0.0669468i	0.440901	−	0.897556i	$-0.354659\pi$
$439$	−2.42953	−	1.40269i	−0.115955	−	0.0669468i	−0.556856	+	0.830609i	$0.687992\pi$
$440$	17.1260			0.816452
$441$	−14.6675	−	15.0288i	−0.698450	−	0.715659i
$442$	15.3655			0.730860
$443$	−21.3943	−	12.3520i	−1.01647	−	0.586861i	−0.103393	−	0.994641i	$-0.532970\pi$
$443$	−21.3943	−	12.3520i	−1.01647	−	0.586861i	−0.913080	+	0.407779i	$0.866303\pi$
$444$	7.25341	−	2.84482i	0.344232	−	0.135009i
$445$	28.2409	−	16.3049i	1.33875	−	0.772926i
$446$	−17.5838	−	10.1520i	−0.832618	−	0.480712i
$447$	−1.68224	+	11.1435i	−0.0795673	+	0.527070i
$448$	1.89471	+	1.84664i	0.0895165	+	0.0872456i
$449$	−12.4692			−0.588460			−0.294230	−	0.955735i	$-0.595063\pi$
$449$	−12.4692			−0.588460			−0.294230	+	0.955735i	$0.595063\pi$
$450$	11.0246	−	10.2199i	0.519703	−	0.481768i
$451$	54.6933	−	31.5772i	2.57541	−	1.48691i
$452$	10.0316	+	17.3753i	0.471847	+	0.817263i
$453$	−12.2639	−	9.78477i	−0.576209	−	0.459729i
$454$	−1.82020			−0.0854260
$455$	−35.2188	+	9.92346i	−1.65108	+	0.465219i
$456$	7.48435	−	0.992193i	0.350487	−	0.0464637i
$457$	−7.62887	+	13.2136i	−0.356863	+	0.618105i	−0.987435	−	0.158026i	$-0.949487\pi$
$457$	−7.62887	+	13.2136i	−0.356863	+	0.618105i	0.630572	+	0.776131i	$0.282820\pi$
$458$	−1.30087	−	2.25318i	−0.0607857	−	0.105284i
$459$	−18.2161	+	1.35244i	−0.850256	+	0.0631266i
$460$	−6.89807	+	11.9478i	−0.321624	+	0.557069i
$461$			33.9540i			1.58139i	0.612208	+	0.790697i	$0.290282\pi$
$461$			33.9540i			1.58139i	−0.612208	+	0.790697i	$0.709718\pi$
$462$	22.8581	+	9.63149i	1.06346	+	0.448098i
$463$	37.0043			1.71974			0.859869	−	0.510515i	$-0.170545\pi$
$463$	37.0043			1.71974			0.859869	+	0.510515i	$0.170545\pi$
$464$	2.39887	−	4.15496i	0.111365	−	0.192889i
$465$	−0.0974545	−	0.248478i	−0.00451935	−	0.0115229i
$466$	1.66391	−	0.960657i	0.0770790	−	0.0445016i
$467$	18.3407	+	10.5890i	0.848708	+	0.490002i	0.860215	−	0.509932i	$-0.170330\pi$
$467$	18.3407	+	10.5890i	0.848708	+	0.490002i	−0.0115070	+	0.999934i	$0.503663\pi$
$468$	−3.87087	+	12.5285i	−0.178931	+	0.579132i
$469$	−14.0472	−	3.57119i	−0.648641	−	0.164902i
$470$	14.8382			0.684437
$471$	−1.86245	+	2.33433i	−0.0858171	+	0.107560i
$472$	2.50131	+	4.33240i	0.115132	+	0.199415i
$473$	46.2043	−	26.6761i	2.12448	−	1.22657i
$474$	4.39704	+	3.50818i	0.201963	+	0.161136i
$475$	−20.9817	+	6.07044i	−0.962707	+	0.278531i
$476$	2.52241	+	8.95215i	0.115615	+	0.410321i
$477$	−10.0813	−	3.11477i	−0.461592	−	0.142615i
$478$	18.2978	+	10.5642i	0.836923	+	0.483197i
$479$	−3.65838	+	2.11217i	−0.167156	+	0.0965074i	−0.581244	−	0.813729i	$-0.697434\pi$
$479$	−3.65838	+	2.11217i	−0.167156	+	0.0965074i	0.414088	+	0.910237i	$0.364100\pi$
$480$	−5.10186	+	2.00097i	−0.232867	+	0.0913316i
$481$	9.83103	−	17.0278i	0.448256	−	0.776403i
$482$		−	26.5154i		−	1.20774i
$483$	−15.9261	+	12.0673i	−0.724665	+	0.549082i
$484$	−18.2981			−0.831730
$485$	28.6213	−	49.5735i	1.29963	−	2.25102i
$486$	3.48627	−	15.1936i	0.158141	−	0.689196i
$487$	1.53299	−	0.885072i	0.0694664	−	0.0401064i	−0.464865	−	0.885382i	$-0.653897\pi$
$487$	1.53299	−	0.885072i	0.0694664	−	0.0401064i	0.534331	+	0.845275i	$0.320564\pi$
$488$	0.239218	−	0.414338i	0.0108289	−	0.0187562i
$489$	−13.6153	−	2.05539i	−0.615707	−	0.0929481i
$490$	−11.5631	−	18.8900i	−0.522369	−	0.853362i
$491$		−	1.22724i		−	0.0553846i	−0.999616	−	0.0276923i	$-0.991184\pi$
$491$		−	1.22724i		−	0.0553846i	0.999616	−	0.0276923i	$-0.00881586\pi$
$492$	−12.6037	+	15.7971i	−0.568221	+	0.712189i
$493$	14.6061	−	8.43285i	0.657827	−	0.379797i
$494$	13.2024	−	13.7367i	0.594005	−	0.618045i
$495$	−37.6789	+	34.9286i	−1.69354	+	1.56993i
$496$			0.0487035i			0.00218685i
$497$	9.77410	+	9.52615i	0.438428	+	0.427306i
$498$	1.26816	−	8.40057i	0.0568277	−	0.376439i
$499$	1.82984	−	3.16938i	0.0819150	−	0.141881i	−0.822157	−	0.569260i	$-0.807230\pi$
$499$	1.82984	−	3.16938i	0.0819150	−	0.141881i	0.904072	+	0.427379i	$0.140563\pi$
$500$	0.0300027	−	0.0173220i	0.00134176	−	0.000774666i
$501$	−5.18734	−	13.2261i	−0.231753	−	0.590898i
$502$	13.8073	+	7.97164i	0.616249	+	0.355792i
$503$			34.8443i			1.55363i	0.629729	+	0.776815i	$0.283166\pi$
$503$			34.8443i			1.55363i	−0.629729	+	0.776815i	$0.716834\pi$
$504$	−7.93477	−	0.198528i	−0.353443	−	0.00884314i
$505$	55.2109			2.45685
$506$	11.8007	−	20.4395i	0.524607	−	0.908645i
$507$	3.86113	+	9.84467i	0.171479	+	0.437217i
$508$	−11.5071	+	6.64363i	−0.510545	+	0.294763i
$509$	17.2532	−	29.8834i	0.764734	−	1.32456i	−0.175654	−	0.984452i	$-0.556204\pi$
$509$	17.2532	−	29.8834i	0.764734	−	1.32456i	0.940387	−	0.340106i	$-0.110463\pi$
$510$	−19.0490	−	2.87567i	−0.843506	−	0.127337i
$511$	1.50200	−	5.90811i	0.0664447	−	0.261360i
$512$	1.00000			0.0441942
$513$	−14.4427	+	17.4473i	−0.637662	+	0.770317i
$514$	−2.96898	−	5.14243i	−0.130956	−	0.226823i
$515$	25.0401	+	43.3707i	1.10340	+	1.91114i
$516$	−10.6475	+	13.3452i	−0.468731	+	0.587492i
$517$	−25.3842			−1.11640
$518$	11.5346	+	2.93240i	0.506799	+	0.128842i
$519$	3.11878	+	0.470815i	0.136899	+	0.0206665i
$520$	−6.91489	+	11.9769i	−0.303238	+	0.525223i
$521$	17.8687	+	30.9496i	0.782844	+	1.35593i	0.930279	+	0.366854i	$0.119565\pi$
$521$	17.8687	+	30.9496i	0.782844	+	1.35593i	−0.147435	+	0.989072i	$0.547102\pi$
$522$	3.19632	+	14.0338i	0.139899	+	0.614244i
$523$	−11.6140	−	6.70536i	−0.507846	−	0.293205i	0.224102	−	0.974566i	$-0.428055\pi$
$523$	−11.6140	−	6.70536i	−0.507846	−	0.293205i	−0.731948	+	0.681361i	$0.761389\pi$
$524$			15.1335i			0.661110i
$525$	22.7844	−	2.85871i	0.994394	−	0.124764i
$526$		−	7.52620i		−	0.328158i
$527$	−0.0856048	+	0.148272i	−0.00372901	+	0.00645883i
$528$	8.72791	−	3.42313i	0.379833	−	0.148973i
$529$	−1.99375	−	3.45327i	−0.0866847	−	0.150142i
$530$	−9.63746	−	5.56419i	−0.418624	−	0.241693i
$531$	−14.3391	−	4.43026i	−0.622263	−	0.192257i
$532$	10.1706	+	5.43690i	0.440949	+	0.235719i
$533$			50.9990i			2.20901i
$534$	11.1333	−	13.9542i	0.481787	−	0.603856i
$535$	−15.8604	+	9.15699i	−0.685704	+	0.395891i
$536$	−4.74430	+	2.73912i	−0.204922	+	0.118312i
$537$	16.3520	−	20.4951i	0.705642	−	0.884429i
$538$	23.4420			1.01066
$539$	19.7814	+	32.3157i	0.852045	+	1.39193i
$540$	7.14358	−	14.8076i	0.307411	−	0.637217i
$541$	3.03710	−	5.26041i	0.130575	−	0.226162i	−0.793323	−	0.608800i	$-0.791651\pi$
$541$	3.03710	−	5.26041i	0.130575	−	0.226162i	0.923898	+	0.382638i	$0.124984\pi$
$542$	10.7091	+	18.5487i	0.459994	+	0.796734i
$543$	2.50073	−	0.980801i	0.107317	−	0.0420902i
$544$	3.04438	+	1.75767i	0.130527	+	0.0753596i
$545$	−26.1729			−1.12112
$546$	−15.9650	+	12.0968i	−0.683238	+	0.517693i
$547$		−	9.10634i		−	0.389359i	−0.980867	−	0.194680i	$-0.937633\pi$
$547$		−	9.10634i		−	0.389359i	0.980867	−	0.194680i	$-0.0623667\pi$
$548$	15.1346	+	8.73798i	0.646519	+	0.373268i
$549$	0.318741	+	1.39947i	0.0136035	+	0.0597279i
$550$	−23.4893	+	13.5616i	−1.00159	+	0.578267i
$551$	5.01101	−	20.3036i	0.213476	−	0.864964i
$552$	−1.12734	+	7.46771i	−0.0479826	+	0.317847i
$553$	2.33031	+	8.27039i	0.0990950	+	0.351693i
$554$	−16.1517			−0.686219
$555$	−15.3746	+	19.2701i	−0.652617	+	0.817969i
$556$	−1.90587	−	3.30106i	−0.0808269	−	0.139996i
$557$	−38.6690	+	22.3256i	−1.63846	+	0.945965i	−0.657095	+	0.753808i	$0.728215\pi$
$557$	−38.6690	+	22.3256i	−1.63846	+	0.945965i	−0.981364	+	0.192157i	$0.938452\pi$
$558$	−0.0993311	−	0.107152i	−0.00420502	−	0.00453613i
$559$			43.0834i			1.82223i
$560$	−8.11310	−	2.06257i	−0.342841	−	0.0871595i
$561$	32.5878	+	4.91950i	1.37586	+	0.207702i
$562$	13.9431	−	24.1501i	0.588152	−	1.01871i
$563$	−12.9271	−	22.3904i	−0.544813	−	0.943645i	−0.998619	−	0.0525437i	$-0.983267\pi$
$563$	−12.9271	−	22.3904i	−0.544813	−	0.943645i	0.453805	−	0.891101i	$-0.350066\pi$
$564$	7.56198	−	2.96585i	0.318417	−	0.124885i
$565$	−54.9755	−	31.7401i	−2.31283	−	1.33532i
$566$	16.2298			0.682191
$567$	17.8622	−	15.7462i	0.750140	−	0.661279i
$568$	5.15864			0.216452
$569$	8.98565	−	15.5636i	0.376698	−	0.652460i	−0.613882	−	0.789398i	$-0.710393\pi$
$569$	8.98565	−	15.5636i	0.376698	−	0.652460i	0.990580	+	0.136938i	$0.0437261\pi$
$570$	−18.9383	+	14.5590i	−0.793239	+	0.609809i
$571$	−1.81215	−	3.13874i	−0.0758361	−	0.131352i	0.825613	−	0.564236i	$-0.190829\pi$
$571$	−1.81215	−	3.13874i	−0.0758361	−	0.131352i	−0.901450	+	0.432884i	$0.857496\pi$
$572$	11.8295	−	20.4893i	0.494617	−	0.856702i
$573$	−1.76300	+	11.6785i	−0.0736506	+	0.487876i
$574$	−29.7128	+	8.37206i	−1.24019	+	0.349443i
$575$		−	21.8494i		−	0.911183i
$576$	−2.20010	+	2.03950i	−0.0916707	+	0.0849793i
$577$	−2.43441	−	4.21653i	−0.101346	−	0.175536i	0.810893	−	0.585194i	$-0.198982\pi$
$577$	−2.43441	−	4.21653i	−0.101346	−	0.175536i	−0.912239	+	0.409657i	$0.865648\pi$
$578$	−2.32118	−	4.02040i	−0.0965482	−	0.167226i
$579$	−31.3034	−	24.9755i	−1.30093	−	1.03794i
$580$			15.1801i			0.630319i
$581$	9.05783	−	9.29358i	0.375782	−	0.385563i
$582$	4.67752	−	30.9848i	0.193889	−	1.28436i
$583$	16.4871	+	9.51883i	0.682826	+	0.394230i
$584$	−1.15205	−	1.99540i	−0.0476720	−	0.0825703i
$585$	−9.21359	−	40.4534i	−0.380935	−	1.67254i
$586$	6.34346	−	10.9872i	0.262046	−	0.453877i
$587$		−	5.66695i		−	0.233900i	−0.993138	−	0.116950i	$-0.962688\pi$
$587$		−	5.66695i		−	0.233900i	0.993138	−	0.116950i	$-0.0373117\pi$
$588$	−9.66859	−	7.31563i	−0.398726	−	0.301691i
$589$	0.0590012	+	0.203930i	0.00243110	+	0.00840280i
$590$	−13.7077	−	7.91417i	−0.564339	−	0.325821i
$591$	3.54916	−	1.39200i	0.145993	−	0.0572591i
$592$	3.89567	−	2.24917i	0.160111	−	0.0924402i
$593$	1.43314	+	0.827424i	0.0588520	+	0.0339782i	0.529137	−	0.848536i	$-0.322516\pi$
$593$	1.43314	+	0.827424i	0.0588520	+	0.0339782i	−0.470285	+	0.882514i	$0.655849\pi$
$594$	−12.2208	+	25.3318i	−0.501423	+	1.03938i
$595$	−21.0740	−	20.5394i	−0.863951	−	0.842034i
$596$			6.50661i			0.266521i
$597$	6.99953	−	8.77298i	0.286472	−	0.359054i
$598$	9.52944	+	16.5055i	0.389688	+	0.674959i
$599$	−6.93598	−	12.0135i	−0.283396	−	0.490857i	0.688823	−	0.724930i	$-0.258128\pi$
$599$	−6.93598	−	12.0135i	−0.283396	−	0.490857i	−0.972219	+	0.234073i	$0.924795\pi$
$600$	5.41297	−	6.78444i	0.220984	−	0.276974i
$601$		−	28.0765i		−	1.14526i	−0.819813	−	0.572631i	$-0.805923\pi$
$601$		−	28.0765i		−	1.14526i	0.819813	−	0.572631i	$-0.194077\pi$
$602$	−25.1011	+	7.07263i	−1.02304	+	0.288259i
$603$	4.85146	−	15.7023i	0.197567	−	0.639449i
$604$	−7.84451	−	4.52903i	−0.319189	−	0.184284i
$605$	50.1387	−	28.9476i	2.03843	−	1.17689i
$606$	28.1370	−	11.0355i	1.14299	−	0.448285i
$607$	0.699538	+	0.403879i	0.0283934	+	0.0163929i	0.514130	−	0.857713i	$-0.328115\pi$
$607$	0.699538	+	0.403879i	0.0283934	+	0.0163929i	−0.485736	+	0.874105i	$0.661448\pi$
$608$	4.18717	−	1.21144i	0.169812	−	0.0491302i
$609$	−8.53711	+	20.2608i	−0.345941	+	0.821011i
$610$			1.51378i			0.0612910i
$611$	10.2493	−	17.7522i	0.414640	−	0.718178i
$612$	−10.2827	+	2.34197i	−0.415654	+	0.0946686i
$613$	19.8763	+	34.4267i	0.802796	+	1.39048i	0.917769	+	0.397114i	$0.129988\pi$
$613$	19.8763	+	34.4267i	0.802796	+	1.39048i	−0.114974	+	0.993369i	$0.536678\pi$
$614$	0.363026	+	0.209593i	0.0146506	+	0.00845850i
$615$	9.54455	−	63.2251i	0.384874	−	2.54948i
$616$	13.8793	+	3.52851i	0.559215	+	0.142168i
$617$			1.53345i			0.0617346i	0.999523	+	0.0308673i	$0.00982692\pi$
$617$			1.53345i			0.0617346i	−0.999523	+	0.0308673i	$0.990173\pi$
$618$	21.4300	+	17.0979i	0.862041	+	0.687780i
$619$	3.16582	+	5.48336i	0.127245	+	0.220395i	0.922608	−	0.385738i	$-0.126053\pi$
$619$	3.16582	+	5.48336i	0.127245	+	0.220395i	−0.795363	+	0.606133i	$0.792720\pi$
$620$	−0.0770492	−	0.133453i	−0.00309437	−	0.00535961i
$621$	−12.7502	−	18.7289i	−0.511647	−	0.751564i
$622$		−	4.99652i		−	0.200342i
$623$	26.2464	−	7.39534i	1.05154	−	0.296288i
$624$	−1.13009	+	7.48592i	−0.0452396	+	0.299677i
$625$	12.4726	−	21.6031i	0.498903	−	0.864125i
$626$	−11.6571	−	20.1907i	−0.465913	−	0.806984i
$627$	32.3984	−	24.9065i	1.29387	−	0.994671i
$628$	−0.862063	+	1.49314i	−0.0344000	+	0.0595826i
$629$	15.8132			0.630513
$630$	22.0562	−	12.0089i	0.878741	−	0.478444i
$631$	−37.5625			−1.49534			−0.747670	−	0.664070i	$-0.768828\pi$
$631$	−37.5625			−1.49534			−0.747670	+	0.664070i	$0.768828\pi$
$632$	2.81253	+	1.62381i	0.111876	+	0.0645919i
$633$	−37.5061	+	14.7101i	−1.49073	+	0.584673i
$634$	5.57956	+	9.66409i	0.221593	+	0.383810i
$635$	21.0205	−	36.4086i	0.834173	−	1.44483i
$636$	−6.02368	−	0.909344i	−0.238854	−	0.0360578i
$637$	−30.5867	+	0.786018i	−1.21189	+	0.0311432i
$638$		−	25.9690i		−	1.02812i
$639$	−11.3495	+	10.5211i	−0.448979	+	0.416207i
$640$	−2.74011	+	1.58200i	−0.108312	+	0.0625342i
$641$	5.09574	+	8.82608i	0.201270	+	0.348609i	0.948938	−	0.315463i	$-0.102160\pi$
$641$	5.09574	+	8.82608i	0.201270	+	0.348609i	−0.747668	+	0.664073i	$0.768827\pi$
$642$	−6.25260	+	7.83680i	−0.246770	+	0.309294i
$643$	−3.63365			−0.143297			−0.0716485	−	0.997430i	$-0.522826\pi$
$643$	−3.63365			−0.143297			−0.0716485	+	0.997430i	$0.522826\pi$
$644$	−8.05197	+	8.26155i	−0.317292	+	0.325551i
$645$	8.06314	−	53.4119i	0.317486	−	2.10309i
$646$	14.8766	+	3.67161i	0.585314	+	0.144458i
$647$	−30.1963	+	17.4339i	−1.18714	+	0.685395i	−0.957655	−	0.287917i	$-0.907037\pi$
$647$	−30.1963	+	17.4339i	−1.18714	+	0.685395i	−0.229484	+	0.973312i	$0.573704\pi$
$648$	0.680847	−	8.97421i	0.0267462	−	0.352540i
$649$	23.4503	+	13.5390i	0.920504	+	0.531453i
$650$		−	21.9027i		−	0.859094i
$651$	−0.0277850	−	0.221451i	−0.00108898	−	0.00867936i
$652$	−7.94989			−0.311342
$653$	−30.9321	−	17.8587i	−1.21047	−	0.698864i	−0.247607	−	0.968861i	$-0.579644\pi$
$653$	−30.9321	−	17.8587i	−1.21047	−	0.698864i	−0.962861	+	0.269996i	$0.912978\pi$
$654$	−13.3384	+	5.23141i	−0.521575	+	0.204564i
$655$	−23.9413	−	41.4675i	−0.935463	−	1.62027i
$656$	−5.83384	+	10.1045i	−0.227773	+	0.394514i
$657$	6.60424	+	2.04047i	0.257656	+	0.0796064i
$658$	12.0253	+	3.05715i	0.468793	+	0.119180i
$659$	37.1929			1.44883			0.724414	−	0.689365i	$-0.242110\pi$
$659$	37.1929			1.44883			0.724414	+	0.689365i	$0.242110\pi$
$660$	−18.5000	+	23.1873i	−0.720113	+	0.902566i
$661$	−4.36207	+	2.51845i	−0.169665	+	0.0979562i	−0.582428	−	0.812882i	$-0.697897\pi$
$661$	−4.36207	+	2.51845i	−0.169665	+	0.0979562i	0.412763	+	0.910839i	$0.364564\pi$
$662$	2.08921	−	1.20621i	0.0811995	−	0.0468806i
$663$	−16.5982	+	20.8036i	−0.644620	+	0.807946i
$664$		−	4.90503i		−	0.190352i
$665$	−36.4696	+	1.19216i	−1.41423	+	0.0462299i
$666$	−3.98367	+	12.8936i	−0.154364	+	0.499618i
$667$	18.1170	+	10.4599i	0.701494	+	0.405008i
$668$	−4.10120	−	7.10348i	−0.158680	−	0.274842i
$669$	32.7396	−	12.8406i	1.26579	−	0.496448i
$670$	8.66660	−	15.0110i	0.334820	−	0.579925i
$671$		−	2.58966i		−	0.0999729i
$672$	−4.54693	+	0.570492i	−0.175401	+	0.0220072i
$673$			10.1160i			0.389944i	0.980809	+	0.194972i	$0.0624616\pi$
$673$			10.1160i			0.389944i	−0.980809	+	0.194972i	$0.937538\pi$
$674$	−10.7651	−	6.21523i	−0.414656	−	0.239402i
$675$	1.92784	+	25.9662i	0.0742025	+	0.999439i
$676$	3.05267	+	5.28739i	0.117411	+	0.203361i
$677$	19.1874	−	33.2335i	0.737431	−	1.27727i	−0.216218	−	0.976345i	$-0.569372\pi$
$677$	19.1874	−	33.2335i	0.737431	−	1.27727i	0.953649	−	0.300922i	$-0.0972945\pi$
$678$	−34.3612	−	5.18722i	−1.31963	−	0.199214i
$679$	33.4091	−	34.2786i	1.28212	−	1.31549i
$680$	−11.1226			−0.426531
$681$	1.96623	−	2.46440i	0.0753460	−	0.0944362i
$682$	0.131810	+	0.228302i	0.00504728	+	0.00874215i
$683$	−0.0340951	−	0.0590545i	−0.00130461	−	0.00225966i	0.865372	−	0.501129i	$-0.167082\pi$
$683$	−0.0340951	−	0.0590545i	−0.00130461	−	0.00225966i	−0.866677	+	0.498870i	$0.833749\pi$
$684$	−6.74146	+	11.2050i	−0.257766	+	0.428435i
$685$	−55.2941			−2.11268
$686$	−5.47909	−	17.6912i	−0.209193	−	0.675454i
$687$	4.45587	+	0.672664i	0.170002	+	0.0256637i
$688$	−4.92836	+	8.53617i	−0.187892	+	0.325439i
$689$	−13.3138	+	7.68673i	−0.507216	+	0.292841i
$690$	−8.72491	−	22.2458i	−0.332152	−	0.846883i
$691$	20.5238	−	35.5482i	0.780761	−	1.35232i	−0.150737	−	0.988574i	$-0.548165\pi$
$691$	20.5238	−	35.5482i	0.780761	−	1.35232i	0.931499	−	0.363745i	$-0.118502\pi$
$692$	1.82103			0.0692251
$693$	−37.7323	+	20.5439i	−1.43333	+	0.780399i
$694$		−	3.01026i		−	0.114268i
$695$	10.4446	+	6.03019i	0.396186	+	0.228738i
$696$	3.03417	+	7.73619i	0.115010	+	0.293240i
$697$	−35.5208	+	20.5079i	−1.34545	+	0.776794i
$698$	−15.3012	+	26.5024i	−0.579159	+	1.00313i
$699$	−0.496743	+	3.29053i	−0.0187886	+	0.124459i
$700$	12.7608	−	3.59557i	0.482315	−	0.135900i
$701$		−	21.9875i		−	0.830457i	−0.909717	−	0.415228i	$-0.863702\pi$
$701$		−	21.9875i		−	0.830457i	0.909717	−	0.415228i	$-0.136298\pi$
$702$	−12.7813	−	18.7746i	−0.482398	−	0.708600i
$703$	13.5871	−	14.1370i	0.512448	−	0.533187i
$704$	4.68759	−	2.70638i	0.176670	−	0.102001i
$705$	−16.0287	+	20.0898i	−0.603675	+	0.756627i
$706$		−	12.5405i		−	0.471969i
$707$	44.7442	+	11.3752i	1.68278	+	0.427808i
$708$	−8.56772	−	1.29340i	−0.321995	−	0.0486088i
$709$	0.658384	−	1.14035i	0.0247261	−	0.0428269i	−0.853398	−	0.521261i	$-0.825462\pi$
$709$	0.658384	−	1.14035i	0.0247261	−	0.0428269i	0.878124	+	0.478434i	$0.158795\pi$
$710$	−14.1352	+	8.16098i	−0.530486	+	0.306276i
$711$	−9.49961	+	2.16362i	−0.356263	+	0.0811420i
$712$	5.15324	−	8.92567i	0.193126	−	0.334504i
$713$	−0.212364			−0.00795308
$714$	−14.8453	−	6.25521i	−0.555571	−	0.234095i
$715$			74.8574i			2.79951i
$716$	7.56878	−	13.1095i	0.282859	−	0.489926i
$717$	−34.0690	+	13.3620i	−1.27233	+	0.499014i
$718$	−0.641694	+	0.370482i	−0.0239478	+	0.0138263i
$719$	40.5454	+	23.4089i	1.51209	+	0.873004i	0.999900	+	0.0141304i	$0.00449798\pi$
$719$	40.5454	+	23.4089i	1.51209	+	0.873004i	0.512187	+	0.858874i	$0.328835\pi$
$720$	2.80201	−	9.06903i	0.104425	−	0.337983i
$721$	11.3573	+	40.3077i	0.422969	+	1.50114i
$722$	16.0648	−	10.1450i	0.597872	−	0.377557i
$723$	35.8998	+	28.6427i	1.33513	+	1.06523i
$724$	1.34310	−	0.775438i	0.0499158	−	0.0288189i
$725$	−12.0206	−	20.8203i	−0.446434	−	0.773247i
$726$	19.7661	−	24.7742i	0.733588	−	0.919455i
$727$	1.00884			0.0374159			0.0187079	−	0.999825i	$-0.494045\pi$
$727$	1.00884			0.0374159			0.0187079	+	0.999825i	$0.494045\pi$
$728$	−8.07161	+	8.28170i	−0.299154	+	0.306940i
$729$	16.8050	+	21.1327i	0.622408	+	0.782693i
$730$	6.31347	+	3.64508i	0.233672	+	0.134911i
$731$	−30.0076	+	17.3249i	−1.10987	+	0.640784i
$732$	0.302571	+	0.771462i	0.0111834	+	0.0285141i
$733$	−11.9495	+	20.6972i	−0.441366	+	0.764469i	−0.997791	−	0.0664289i	$-0.978839\pi$
$733$	−11.9495	+	20.6972i	−0.441366	+	0.764469i	0.556425	+	0.830898i	$0.312173\pi$
$734$	−14.1932			−0.523881
$735$	38.0664	+	4.74990i	1.40410	+	0.175203i
$736$			4.36033i			0.160724i
$737$	−14.8262	+	25.6798i	−0.546131	+	0.945927i
$738$	−7.77317	−	34.1290i	−0.286134	−	1.25631i
$739$	−11.4593	−	19.8480i	−0.421536	−	0.730121i	0.574554	−	0.818467i	$-0.305175\pi$
$739$	−11.4593	−	19.8480i	−0.421536	−	0.730121i	−0.996090	+	0.0883452i	$0.971842\pi$
$740$	−7.11638	+	12.3259i	−0.261603	+	0.453110i
$741$	4.33684	+	32.7139i	0.159318	+	1.20177i
$742$	−6.66402	−	6.49497i	−0.244644	−	0.238438i
$743$	−21.0700			−0.772984			−0.386492	−	0.922293i	$-0.626313\pi$
$743$	−21.0700			−0.772984			−0.386492	+	0.922293i	$0.626313\pi$
$744$	−0.0659408	−	0.0526109i	−0.00241751	−	0.00192881i
$745$	−10.2935	−	17.8288i	−0.377124	−	0.653198i
$746$	21.8335	−	12.6056i	0.799382	−	0.461523i
$747$	10.0038	+	10.7915i	0.366021	+	0.394841i
$748$	19.0277			0.695723
$749$	−14.7402	+	4.15330i	−0.538596	+	0.151758i
$750$	−0.00895701	+	0.0593331i	−0.000327064	+	0.00216654i
$751$	−30.2398	−	17.4590i	−1.10347	−	0.637087i	−0.166338	−	0.986069i	$-0.553194\pi$
$751$	−30.2398	−	17.4590i	−1.10347	−	0.637087i	−0.937130	+	0.348982i	$0.886528\pi$
$752$	4.06140	−	2.34485i	0.148104	−	0.0855078i
$753$	−25.7080	+	10.0828i	−0.936852	+	0.367438i
$754$	18.1612	+	10.4854i	0.661392	+	0.381855i
$755$	28.6598			1.04304
$756$	8.84015	−	10.5286i	0.321513	−	0.382922i
$757$	−15.7250			−0.571534			−0.285767	−	0.958299i	$-0.592248\pi$
$757$	−15.7250			−0.571534			−0.285767	+	0.958299i	$0.592248\pi$
$758$	9.97068	+	5.75658i	0.362152	+	0.209088i
$759$	14.9260	+	38.0566i	0.541779	+	1.38137i
$760$	−9.55683	+	9.94360i	−0.346663	+	0.360692i
$761$	30.0916	+	17.3734i	1.09082	+	0.629785i	0.933795	−	0.357810i	$-0.116476\pi$
$761$	30.0916	+	17.3734i	1.09082	+	0.629785i	0.157025	+	0.987595i	$0.449810\pi$
$762$	3.43534	−	22.7564i	0.124449	−	0.824376i
$763$	−21.2111	−	5.39245i	−0.767895	−	0.195220i
$764$			6.81898i			0.246702i
$765$	24.4707	−	22.6845i	0.884742	−	0.820161i
$766$	12.2078	+	21.1446i	0.441087	+	0.763984i
$767$	−18.9368	+	10.9332i	−0.683767	+	0.394773i
$768$	−1.08023	+	1.35392i	−0.0389794	+	0.0488555i
$769$	−42.8834			−1.54641			−0.773207	−	0.634154i	$-0.781348\pi$
$769$	−42.8834			−1.54641			−0.773207	+	0.634154i	$0.781348\pi$
$770$	−43.6131	+	12.2887i	−1.57171	+	0.442853i
$771$	10.1696	+	1.53522i	0.366250	+	0.0552897i
$772$	−20.0230	−	11.5603i	−0.720642	−	0.416063i
$773$	13.8722	+	24.0274i	0.498948	+	0.864204i	0.999999	−	0.00121377i	$-0.000386357\pi$
$773$	13.8722	+	24.0274i	0.498948	+	0.864204i	−0.501051	+	0.865418i	$0.667053\pi$
$774$	−6.56669	−	28.8318i	−0.236035	−	1.03634i
$775$	0.211354	+	0.122025i	0.00759207	+	0.00438328i
$776$		−	18.0918i		−	0.649457i
$777$	−16.4302	+	12.4492i	−0.589430	+	0.446614i
$778$			27.0002i			0.968003i
$779$	−12.1863	+	49.3766i	−0.436621	+	1.76910i
$780$	−8.74619	−	22.3000i	−0.313164	−	0.798470i
$781$	24.1816	−	13.9613i	0.865286	−	0.499573i
$782$	−7.66404	+	13.2745i	−0.274065	+	0.474695i
$783$	−22.4535	−	10.8322i	−0.802422	−	0.387110i
$784$	−6.15009	−	3.34311i	−0.219646	−	0.119397i
$785$		−	5.45515i		−	0.194703i
$786$	−20.4896	−	16.3476i	−0.730840	−	0.583101i
$787$	27.8567	−	16.0830i	0.992982	−	0.573299i	0.0868180	−	0.996224i	$-0.472330\pi$
$787$	27.8567	−	16.0830i	0.992982	−	0.573299i	0.906164	+	0.422926i	$0.138997\pi$
$788$	1.90619	−	1.10054i	0.0679050	−	0.0392050i
$789$	10.1899	+	8.13002i	0.362770	+	0.289436i
$790$	−10.2755			−0.365587
$791$	−38.0139	−	37.0496i	−1.35162	−	1.31733i
$792$	−4.79348	+	15.5147i	−0.170329	+	0.551290i
$793$	1.81106	+	1.04561i	0.0643125	+	0.0371309i
$794$	−8.64453	−	14.9728i	−0.306783	−	0.531364i
$795$	17.9441	−	7.03778i	0.636413	−	0.249604i
$796$	3.23984	−	5.61156i	0.114833	−	0.198897i
$797$	−3.88551			−0.137632			−0.0688159	−	0.997629i	$-0.521922\pi$
$797$	−3.88551			−0.137632			−0.0688159	+	0.997629i	$0.521922\pi$
$798$	−18.3477	+	7.89706i	−0.649500	+	0.279553i
$799$	16.4859			0.583229
$800$	2.50547	−	4.33961i	0.0885819	−	0.153428i
$801$	6.86632	+	30.1474i	0.242610	+	1.06521i
$802$	0.482762	+	0.836168i	0.0170469	+	0.0295261i
$803$	−10.8006	−	6.23575i	−0.381146	−	0.220055i
$804$	1.41636	−	9.38229i	0.0499513	−	0.330888i
$805$	8.99350	−	35.3758i	0.316979	−	1.24683i
$806$	−0.212882			−0.00749843
$807$	−25.3227	+	31.7386i	−0.891400	+	1.11725i
$808$	15.1119	−	8.72483i	0.531633	−	0.306938i
$809$	−4.55556	+	2.63016i	−0.160165	+	0.0924714i	−0.577940	−	0.816079i	$-0.696143\pi$
$809$	−4.55556	+	2.63016i	−0.160165	+	0.0924714i	0.417775	+	0.908550i	$0.362810\pi$
$810$	12.3316	+	25.6674i	0.433290	+	0.901862i
$811$		−	38.6325i		−	1.35657i	−0.734799	−	0.678285i	$-0.762723\pi$
$811$		−	38.6325i		−	1.35657i	0.734799	−	0.678285i	$-0.237277\pi$
$812$	−3.12758	+	12.3023i	−0.109756	+	0.431726i
$813$	−36.6817	−	5.53753i	−1.28648	−	0.194210i
$814$	12.1742	−	21.0864i	0.426706	−	0.739077i
$815$	21.7836	−	12.5768i	0.763046	−	0.440545i
$816$	−5.66837	+	2.22317i	−0.198433	+	0.0778264i
$817$	−10.2949	+	41.7128i	−0.360172	+	1.45935i
$818$			17.4334i			0.609544i
$819$	0.867759	−	34.6826i	0.0303220	−	1.21191i
$820$		−	36.9166i		−	1.28918i
$821$	18.3486	+	10.5936i	0.640370	+	0.369718i	0.784757	−	0.619803i	$-0.212788\pi$
$821$	18.3486	+	10.5936i	0.640370	+	0.369718i	−0.144387	+	0.989521i	$0.546121\pi$
$822$	−28.1794	+	11.0521i	−0.982869	+	0.385486i
$823$	11.4608	+	19.8507i	0.399498	+	0.691950i	0.993664	−	0.112392i	$-0.0358512\pi$
$823$	11.4608	+	19.8507i	0.399498	+	0.691950i	−0.594166	+	0.804342i	$0.702518\pi$
$824$	13.7075	+	7.91404i	0.477524	+	0.275699i
$825$	7.01251	−	46.4523i	0.244144	−	1.61726i
$826$	−9.47851	−	9.23806i	−0.329799	−	0.321433i
$827$	−35.6142			−1.23843			−0.619214	−	0.785222i	$-0.712549\pi$
$827$	−35.6142			−1.23843			−0.619214	+	0.785222i	$0.712549\pi$
$828$	−8.89292	−	9.59315i	−0.309050	−	0.333385i
$829$	22.4730	−	12.9748i	0.780518	−	0.450632i	−0.0560959	−	0.998425i	$-0.517865\pi$
$829$	22.4730	−	12.9748i	0.780518	−	0.450632i	0.836614	+	0.547793i	$0.184532\pi$
$830$	7.75977	+	13.4403i	0.269346	+	0.466520i
$831$	17.4475	−	21.8681i	0.605247	−	0.758596i
$832$			4.37097i			0.151536i
$833$	−12.8471	−	20.9875i	−0.445126	−	0.727175i
$834$	6.52816	+	0.985501i	0.226052	+	0.0341251i
$835$	22.4755	+	12.9762i	0.777796	+	0.449061i
$836$	16.3492	−	17.0108i	0.565448	−	0.588332i
$837$	0.252376	−	0.0187375i	0.00872340	−	0.000647662i
$838$	13.2769	+	7.66540i	0.458641	+	0.264797i
$839$	−27.6592			−0.954903			−0.477451	−	0.878658i	$-0.658439\pi$
$839$	−27.6592			−0.954903			−0.477451	+	0.878658i	$0.658439\pi$
$840$	11.5566	−	8.75647i	0.398739	−	0.302127i
$841$	−5.98170			−0.206266
$842$	−28.2952	−	16.3362i	−0.975116	−	0.562983i
$843$	17.6357	+	44.9654i	0.607404	+	1.54869i
$844$	−20.1438	+	11.6300i	−0.693378	+	0.400322i
$845$	−16.7293	−	9.65869i	−0.575507	−	0.332269i
$846$	−4.15314	+	13.4421i	−0.142788	+	0.462150i
$847$	46.5977	−	13.1296i	1.60112	−	0.451140i
$848$	−3.51718			−0.120780
$849$	−17.5319	+	21.9739i	−0.601694	+	0.754143i
$850$	15.2552	−	8.80761i	0.523250	−	0.302098i
$851$	9.80711	+	16.9864i	0.336184	+	0.582287i
$852$	−5.57250	+	6.98440i	−0.190911	+	0.239281i
$853$	35.7437			1.22384			0.611921	−	0.790919i	$-0.290397\pi$
$853$	35.7437			1.22384			0.611921	+	0.790919i	$0.290397\pi$
$854$	−0.311886	+	1.22680i	−0.0106725	+	0.0419802i
$855$	0.745937	−	41.3681i	0.0255105	−	1.41476i
$856$	−2.89411	+	5.01275i	−0.0989186	+	0.171332i
$857$	6.12247	+	10.6044i	0.209140	+	0.362241i	0.951444	−	0.307823i	$-0.0996003\pi$
$857$	6.12247	+	10.6044i	0.209140	+	0.362241i	−0.742304	+	0.670063i	$0.766267\pi$
$858$	14.9624	+	38.1494i	0.510807	+	1.30240i
$859$	9.83602	−	17.0365i	0.335601	−	0.581277i	−0.647999	−	0.761641i	$-0.724394\pi$
$859$	9.83602	−	17.0365i	0.335601	−	0.581277i	0.983600	+	0.180363i	$0.0577274\pi$
$860$		−	31.1868i		−	1.06346i
$861$	20.7615	−	49.2726i	0.707549	−	1.67920i
$862$	−1.98466			−0.0675979
$863$	11.9473	−	20.6933i	0.406689	−	0.704407i	−0.587827	−	0.808987i	$-0.700016\pi$
$863$	11.9473	−	20.6933i	0.406689	−	0.704407i	0.994516	+	0.104580i	$0.0333498\pi$
$864$	−0.384725	−	5.18189i	−0.0130886	−	0.176291i
$865$	−4.98982	+	2.88087i	−0.169659	+	0.0979527i
$866$	19.6400	+	11.3391i	0.667393	+	0.385320i
$867$	7.95071	+	1.20025i	0.270020	+	0.0407627i
$868$	−0.0349469	−	0.124028i	−0.00118617	−	0.00420979i
$869$	17.5787			0.596315
$870$	−20.5527	−	16.3980i	−0.696801	−	0.555943i
$871$	−11.9726	−	20.7372i	−0.405676	−	0.702652i
$872$	−7.16383	+	4.13604i	−0.242598	+	0.140064i
$873$	36.8983	+	39.8037i	1.24882	+	1.34715i
$874$	5.28226	+	18.2575i	0.178675	+	0.617568i
$875$	−0.0639752	+	0.0656404i	−0.00216276	+	0.00221905i
$876$	3.94609	+	0.595708i	0.133326	+	0.0201271i
$877$	−27.2416	−	15.7279i	−0.919884	−	0.531095i	−0.0362857	−	0.999341i	$-0.511553\pi$
$877$	−27.2416	−	15.7279i	−0.919884	−	0.531095i	−0.883598	+	0.468246i	$0.844886\pi$
$878$	2.42953	−	1.40269i	0.0819927	−	0.0473385i
$879$	8.02343	+	20.4572i	0.270624	+	0.690006i
$880$	−8.56302	+	14.8316i	−0.288659	+	0.499973i
$881$		−	33.8095i		−	1.13907i	−0.821967	−	0.569535i	$-0.807123\pi$
$881$		−	33.8095i		−	1.13907i	0.821967	−	0.569535i	$-0.192877\pi$
$882$	20.3491	−	5.18797i	0.685189	−	0.174688i
$883$	−24.7638			−0.833368			−0.416684	−	0.909051i	$-0.636808\pi$
$883$	−24.7638			−0.833368			−0.416684	+	0.909051i	$0.636808\pi$
$884$	−7.68273	+	13.3069i	−0.258398	+	0.447559i
$885$	25.5227	−	10.0101i	0.857935	−	0.336487i
$886$	21.3943	−	12.3520i	0.718755	−	0.414973i
$887$	−2.48300	+	4.30068i	−0.0833710	+	0.144403i	−0.904696	−	0.426058i	$-0.859902\pi$
$887$	−2.48300	+	4.30068i	−0.0833710	+	0.144403i	0.821325	+	0.570461i	$0.193235\pi$
$888$	−1.16302	+	7.70405i	−0.0390282	+	0.258531i
$889$	24.5368	−	25.1755i	0.822938	−	0.844358i
$890$			32.6098i			1.09308i
$891$	−21.0961	−	43.9101i	−0.706747	−	1.47104i
$892$	17.5838	−	10.1520i	0.588750	−	0.339915i
$893$	14.1651	−	14.7384i	0.474018	−	0.493202i
$894$	−8.80945	−	7.02862i	−0.294632	−	0.235072i
$895$			47.8954i			1.60097i
$896$	−2.54659	+	0.717543i	−0.0850757	+	0.0239714i
$897$	−32.6411	−	4.92755i	−1.08985	−	0.164526i
$898$	6.23462	−	10.7987i	0.208052	−	0.360357i
$899$	−0.202361	+	0.116833i	−0.00674913	+	0.00389661i
$900$	3.33837	+	14.6575i	0.111279	+	0.488583i
$901$	−10.7076	−	6.18204i	−0.356722	−	0.205954i
$902$			63.1544i			2.10281i
$903$	17.5391	−	41.6249i	0.583664	−	1.38519i
$904$	−20.0632			−0.667293
$905$	−2.45349	+	4.24957i	−0.0815568	+	0.141261i
$906$	14.6058	−	5.72847i	0.485246	−	0.190316i
$907$	−18.7984	+	10.8533i	−0.624191	+	0.360377i	−0.778499	−	0.627646i	$-0.784019\pi$
$907$	−18.7984	+	10.8533i	−0.624191	+	0.360377i	0.154308	+	0.988023i	$0.450685\pi$
$908$	0.910098	−	1.57634i	0.0302027	−	0.0523125i
$909$	−15.4532	+	50.0161i	−0.512550	+	1.65893i
$910$	9.01543	−	35.4621i	0.298859	−	1.17556i
$911$	40.1704			1.33091			0.665453	−	0.746440i	$-0.268239\pi$
$911$	40.1704			1.33091			0.665453	+	0.746440i	$0.268239\pi$
$912$	−2.88291	+	6.97774i	−0.0954628	+	0.231056i
$913$	−13.2749	−	22.9928i	−0.439335	−	0.760950i
$914$	−7.62887	−	13.2136i	−0.252340	−	0.437066i
$915$	−2.04954	−	1.63522i	−0.0677556	−	0.0540588i
$916$	2.60174			0.0859640
$917$	−10.8589	−	38.5389i	−0.358594	−	1.27267i
$918$	7.93682	−	16.4519i	0.261954	−	0.542992i
$919$	−13.2581	+	22.9638i	−0.437345	+	0.757504i	−0.997484	−	0.0708947i	$-0.977415\pi$
$919$	−13.2581	+	22.9638i	−0.437345	+	0.757504i	0.560139	+	0.828399i	$0.310748\pi$
$920$	−6.89807	−	11.9478i	−0.227422	−	0.393907i
$921$	−0.675924	+	0.265101i	−0.0222725	+	0.00873538i
$922$	−29.4050	−	16.9770i	−0.968402	−	0.559107i
$923$			22.5482i			0.742184i
$924$	−19.7702	+	14.9800i	−0.650391	+	0.492805i
$925$		−	22.5409i		−	0.741141i
$926$	−18.5022	+	32.0467i	−0.608019	+	1.05312i
$927$	−46.2986	+	10.5449i	−1.52065	+	0.346340i
$928$	2.39887	+	4.15496i	0.0787467	+	0.136393i
$929$	−21.3155	−	12.3065i	−0.699340	−	0.403764i	0.107762	−	0.994177i	$-0.465632\pi$
$929$	−21.3155	−	12.3065i	−0.699340	−	0.403764i	−0.807102	+	0.590413i	$0.798965\pi$
$930$	0.263916	+	0.0398412i	0.00865414	+	0.00130644i
$931$	−29.8015	−	6.54774i	−0.976703	−	0.214594i
$932$			1.92131i			0.0629347i
$933$	6.76490	+	5.39738i	0.221473	+	0.176702i
$934$	−18.3407	+	10.5890i	−0.600127	+	0.346483i
$935$	−52.1381	+	30.1020i	−1.70510	+	0.984440i
$936$	−8.91460	−	9.61655i	−0.291383	−	0.314327i
$937$	−22.9964			−0.751259			−0.375630	−	0.926770i	$-0.622574\pi$
$937$	−22.9964			−0.751259			−0.375630	+	0.926770i	$0.622574\pi$
$938$	10.1164	−	10.3797i	0.330311	−	0.338908i
$939$	39.9291	+	6.02775i	1.30304	+	0.196708i
$940$	−7.41912	+	12.8503i	−0.241985	+	0.419130i
$941$	−8.90731	−	15.4279i	−0.290370	−	0.502936i	0.683527	−	0.729925i	$-0.260445\pi$
$941$	−8.90731	−	15.4279i	−0.290370	−	0.502936i	−0.973897	+	0.226989i	$0.927112\pi$
$942$	−1.09037	−	2.78009i	−0.0355261	−	0.0905804i
$943$	−44.0590	−	25.4375i	−1.43476	−	0.828358i
$944$	−5.00262			−0.162822
$945$	−7.56670	+	42.8347i	−0.246145	+	1.39341i
$946$			53.3522i			1.73463i
$947$	−38.2039	−	22.0570i	−1.24146	−	0.716757i	−0.272068	−	0.962278i	$-0.587708\pi$
$947$	−38.2039	−	22.0570i	−1.24146	−	0.716757i	−0.969391	+	0.245521i	$0.921041\pi$
$948$	−5.23669	+	2.05386i	−0.170080	+	0.0667062i
$949$	8.72183	−	5.03555i	0.283123	−	0.163461i
$950$	5.23370	−	21.2059i	0.169804	−	0.688011i
$951$	−19.1116	−	2.88512i	−0.619737	−	0.0935565i
$952$	−9.01399	−	2.29160i	−0.292145	−	0.0742712i
$953$	8.97247			0.290647			0.145323	−	0.989384i	$-0.453578\pi$
$953$	8.97247			0.290647			0.145323	+	0.989384i	$0.453578\pi$
$954$	7.73813	−	7.17330i	0.250531	−	0.232244i
$955$	−10.7877	−	18.6848i	−0.349081	−	0.604625i
$956$	−18.2978	+	10.5642i	−0.591794	+	0.341672i
$957$	35.1601	+	28.0525i	1.13656	+	0.906808i
$958$		−	4.22434i		−	0.136482i
$959$	−44.8116	−	11.3923i	−1.44704	−	0.367877i
$960$	0.818034	−	5.41883i	0.0264019	−	0.174892i
$961$	−15.4988	+	26.8447i	−0.499962	+	0.865959i
$962$	9.83103	+	17.0278i	0.316965	+	0.549000i
$963$	−3.85619	−	16.9311i	−0.124264	−	0.545596i
$964$	22.9630	+	13.2577i	0.739589	+	0.427002i
$965$	73.1536			2.35490
$966$	−2.48754	−	19.8261i	−0.0800351	−	0.637895i
$967$	41.2508			1.32654			0.663268	−	0.748382i	$-0.269169\pi$
$967$	41.2508			1.32654			0.663268	+	0.748382i	$0.269169\pi$
$968$	9.14903	−	15.8466i	0.294061	−	0.509329i
$969$	−21.0412	+	16.1757i	−0.675942	+	0.519637i
$970$	28.6213	+	49.5735i	0.918974	+	1.59171i
$971$	−20.6990	+	35.8517i	−0.664262	+	1.15054i	0.315223	+	0.949018i	$0.397921\pi$
$971$	−20.6990	+	35.8517i	−0.664262	+	1.15054i	−0.979485	+	0.201518i	$0.935413\pi$
$972$	11.4149	+	10.6160i	0.366134	+	0.340509i
$973$	7.22213	+	7.03892i	0.231531	+	0.225657i
$974$			1.77014i			0.0567191i
$975$	29.6546	+	23.6599i	0.949706	+	0.757723i
$976$	0.239218	+	0.414338i	0.00765719	+	0.0132626i
$977$	−15.7682	−	27.3114i	−0.504470	−	0.873768i	−0.999987	−	0.00516976i	$-0.998354\pi$
$977$	−15.7682	−	27.3114i	−0.504470	−	0.873768i	0.495516	−	0.868599i	$-0.334979\pi$
$978$	8.58770	−	10.7635i	0.274604	−	0.344180i
$979$		−	55.7866i		−	1.78295i
$980$	22.1407	−	0.568974i	0.707260	−	0.0181752i
$981$	7.32565	−	23.7103i	0.233890	−	0.757013i
$982$	1.06282	+	0.613620i	0.0339160	+	0.0195814i
$983$	14.3768	+	24.9014i	0.458550	+	0.794231i	0.998885	−	0.0472189i	$-0.0150358\pi$
$983$	14.3768	+	24.9014i	0.458550	+	0.794231i	−0.540335	+	0.841450i	$0.681702\pi$
$984$	−7.37884	−	18.8137i	−0.235229	−	0.599760i
$985$	−3.48211	+	6.03119i	−0.110949	+	0.192170i
$986$			16.8657i			0.537113i
$987$	−17.1292	+	12.9788i	−0.545227	+	0.413121i
$988$	5.29514	+	18.3020i	0.168461	+	0.582264i
$989$	−37.2206	−	21.4893i	−1.18354	−	0.683320i
$990$	−11.4096	−	50.0952i	−0.362621	−	1.59213i
$991$	39.6728	−	22.9051i	1.26025	−	0.727604i	0.287125	−	0.957893i	$-0.407301\pi$
$991$	39.6728	−	22.9051i	1.26025	−	0.727604i	0.973122	+	0.230289i	$0.0739672\pi$
$992$	−0.0421785	−	0.0243518i	−0.00133917	−	0.000773169i
$993$	−0.623714	+	4.13161i	−0.0197930	+	0.131113i
$994$	−13.1369	+	3.70154i	−0.416679	+	0.117406i
$995$			20.5017i			0.649949i
$996$	6.64103	+	5.29855i	0.210429	+	0.167891i
$997$	16.9573	+	29.3709i	0.537043	+	0.930185i	0.999061	+	0.0433149i	$0.0137919\pi$
$997$	16.9573	+	29.3709i	0.537043	+	0.930185i	−0.462019	+	0.886870i	$0.652875\pi$
$998$	1.82984	+	3.16938i	0.0579226	+	0.100325i
$999$	−13.1537	−	19.3216i	−0.416165	−	0.611309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bf.a.569.11	yes	52
3.2	odd	2		798.2.bf.b.569.19	yes	52
7.4	even	3	inner	798.2.bf.a.683.8	yes	52
19.18	odd	2		798.2.bf.b.569.16	yes	52
21.11	odd	6		798.2.bf.b.683.16	yes	52
57.56	even	2	inner	798.2.bf.a.569.8	✓	52
133.18	odd	6		798.2.bf.b.683.19	yes	52
399.284	even	6	inner	798.2.bf.a.683.11	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bf.a.569.8	✓	52	57.56	even	2	inner
798.2.bf.a.569.11	yes	52	1.1	even	1	trivial
798.2.bf.a.683.8	yes	52	7.4	even	3	inner
798.2.bf.a.683.11	yes	52	399.284	even	6	inner
798.2.bf.b.569.16	yes	52	19.18	odd	2
798.2.bf.b.569.19	yes	52	3.2	odd	2
798.2.bf.b.683.16	yes	52	21.11	odd	6
798.2.bf.b.683.19	yes	52	133.18	odd	6

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.632417 - 1.61247i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.74011 + 1.58200i) q^{5} +(1.71265 + 0.258544i) q^{6} +(1.89471 + 1.84664i) q^{7} +1.00000 q^{8} +(-2.20010 + 2.03950i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.632417 - 1.61247i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.74011 + 1.58200i) q^{5} +(1.71265 + 0.258544i) q^{6} +(1.89471 + 1.84664i) q^{7} +1.00000 q^{8} +(-2.20010 + 2.03950i) q^{9} +(-2.74011 + 1.58200i) q^{10} +(4.68759 - 2.70638i) q^{11} +(-1.08023 + 1.35392i) q^{12} +4.37097i q^{13} +(-2.54659 + 0.717543i) q^{14} +(0.818034 - 5.41883i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.04438 + 1.75767i) q^{17} +(-0.666214 - 2.92509i) q^{18} +(-1.04445 + 4.23192i) q^{19} -3.16401i q^{20} +(1.77940 - 4.22300i) q^{21} +5.41277i q^{22} +(-3.77616 - 2.18017i) q^{23} +(-0.632417 - 1.61247i) q^{24} +(2.50547 + 4.33961i) q^{25} +(-3.78537 - 2.18548i) q^{26} +(4.68001 + 2.25776i) q^{27} +(0.651885 - 2.56419i) q^{28} -4.79774 q^{29} +(4.28382 + 3.41785i) q^{30} +(0.0421785 - 0.0243518i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-7.32847 - 5.84702i) q^{33} -3.51534i q^{34} +(2.27031 + 8.05744i) q^{35} +(2.86631 + 0.885587i) q^{36} +(-3.89567 - 2.24917i) q^{37} +(-3.14272 - 3.02048i) q^{38} +(7.04804 - 2.76428i) q^{39} +(2.74011 + 1.58200i) q^{40} +11.6677 q^{41} +(2.76752 + 3.65251i) q^{42} +9.85672 q^{43} +(-4.68759 - 2.70638i) q^{44} +(-9.25501 + 2.10791i) q^{45} +(3.77616 - 2.18017i) q^{46} +(-4.06140 - 2.34485i) q^{47} +(1.71265 + 0.258544i) q^{48} +(0.179827 + 6.99769i) q^{49} -5.01095 q^{50} +(4.75950 + 3.79737i) q^{51} +(3.78537 - 2.18548i) q^{52} +(1.75859 + 3.04596i) q^{53} +(-4.29529 + 2.92413i) q^{54} +17.1260 q^{55} +(1.89471 + 1.84664i) q^{56} +(7.48435 - 0.992193i) q^{57} +(2.39887 - 4.15496i) q^{58} +(2.50131 + 4.33240i) q^{59} +(-5.10186 + 2.00097i) q^{60} +(0.239218 - 0.414338i) q^{61} +0.0487035i q^{62} +(-7.93477 - 0.198528i) q^{63} +1.00000 q^{64} +(-6.91489 + 11.9769i) q^{65} +(8.72791 - 3.42313i) q^{66} +(-4.74430 + 2.73912i) q^{67} +(3.04438 + 1.75767i) q^{68} +(-1.12734 + 7.46771i) q^{69} +(-8.11310 - 2.06257i) q^{70} +5.15864 q^{71} +(-2.20010 + 2.03950i) q^{72} +(-1.15205 - 1.99540i) q^{73} +(3.89567 - 2.24917i) q^{74} +(5.41297 - 6.78444i) q^{75} +(4.18717 - 1.21144i) q^{76} +(13.8793 + 3.52851i) q^{77} +(-1.13009 + 7.48592i) q^{78} +(2.81253 + 1.62381i) q^{79} +(-2.74011 + 1.58200i) q^{80} +(0.680847 - 8.97421i) q^{81} +(-5.83384 + 10.1045i) q^{82} -4.90503i q^{83} +(-4.54693 + 0.570492i) q^{84} -11.1226 q^{85} +(-4.92836 + 8.53617i) q^{86} +(3.03417 + 7.73619i) q^{87} +(4.68759 - 2.70638i) q^{88} +(5.15324 - 8.92567i) q^{89} +(2.80201 - 9.06903i) q^{90} +(-8.07161 + 8.28170i) q^{91} +4.36033i q^{92} +(-0.0659408 - 0.0526109i) q^{93} +(4.06140 - 2.34485i) q^{94} +(-9.55683 + 9.94360i) q^{95} +(-1.08023 + 1.35392i) q^{96} -18.0918i q^{97} +(-6.15009 - 3.34311i) q^{98} +(-4.79348 + 15.5147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8}+O(q^{10}) \) 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8	\( 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8} + 4 q^{14} + 8 q^{15} - 26 q^{16} + 2 q^{19} + 2 q^{21} + 18 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} - 4 q^{30} - 26 q^{32} + 8 q^{33} + 2 q^{38} + q^{39} + 16 q^{41} + 11 q^{42} - 8 q^{43} + 14 q^{45} + 4 q^{49} - 36 q^{50} - 19 q^{51} - 24 q^{53} - 3 q^{54} + 32 q^{55} - 8 q^{56} - 4 q^{57} + 4 q^{58} + 32 q^{59} - 4 q^{60} - 20 q^{61} - 7 q^{63} + 52 q^{64} - 44 q^{65} + 8 q^{66} + 62 q^{69} - 24 q^{71} - 32 q^{73} + 16 q^{75} - 4 q^{76} - 2 q^{78} - 28 q^{81} - 8 q^{82} - 13 q^{84} + 32 q^{85} + 4 q^{86} + 34 q^{87} - 36 q^{89} - 28 q^{90} + 20 q^{93} + 30 q^{95} - 20 q^{98} - 116 q^{99}+O(q^{100}) \) 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8 + 4 * q^14 + 8 * q^15 - 26 * q^16 + 2 * q^19 + 2 * q^21 + 18 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 - 4 * q^30 - 26 * q^32 + 8 * q^33 + 2 * q^38 + q^39 + 16 * q^41 + 11 * q^42 - 8 * q^43 + 14 * q^45 + 4 * q^49 - 36 * q^50 - 19 * q^51 - 24 * q^53 - 3 * q^54 + 32 * q^55 - 8 * q^56 - 4 * q^57 + 4 * q^58 + 32 * q^59 - 4 * q^60 - 20 * q^61 - 7 * q^63 + 52 * q^64 - 44 * q^65 + 8 * q^66 + 62 * q^69 - 24 * q^71 - 32 * q^73 + 16 * q^75 - 4 * q^76 - 2 * q^78 - 28 * q^81 - 8 * q^82 - 13 * q^84 + 32 * q^85 + 4 * q^86 + 34 * q^87 - 36 * q^89 - 28 * q^90 + 20 * q^93 + 30 * q^95 - 20 * q^98 - 116 * q^99

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