LMFDB - Embedded newform 342.2.h.g.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(121,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.h (of order $3$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} + \cdots + 19683 $ x^18 + 4x^16 - 6x^15 + x^14 - 21x^13 - 12x^12 + 9x^10 + 135x^9 + 27x^8 - 324x^6 - 1701x^5 + 243x^4 - 4374x^3 + 8748x^2 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$-0.614525 - 1.61937i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.g.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.70968 - 0.277491i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.57955 q^{5} +(-0.614525 - 1.61937i) q^{6} +(2.31561 - 4.01075i) q^{7} -1.00000 q^{8} +(2.84600 + 0.948840i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.70968 - 0.277491i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.57955 q^{5} +(-0.614525 - 1.61937i) q^{6} +(2.31561 - 4.01075i) q^{7} -1.00000 q^{8} +(2.84600 + 0.948840i) q^{9} +(-0.789777 - 1.36793i) q^{10} +(-1.83826 + 3.18396i) q^{11} +(1.09515 - 1.34188i) q^{12} +(2.78676 - 4.82682i) q^{13} +4.63122 q^{14} +(2.70053 + 0.438312i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.65387 - 6.32868i) q^{17} +(0.601280 + 2.93913i) q^{18} +(3.55454 + 2.52294i) q^{19} +(0.789777 - 1.36793i) q^{20} +(-5.07189 + 6.21453i) q^{21} -3.67652 q^{22} +(1.05224 - 1.82254i) q^{23} +(1.70968 + 0.277491i) q^{24} -2.50501 q^{25} +5.57353 q^{26} +(-4.60245 - 2.41195i) q^{27} +(2.31561 + 4.01075i) q^{28} +5.32452 q^{29} +(0.970675 + 2.55788i) q^{30} +(0.587415 + 1.01743i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.02635 - 4.93344i) q^{33} +7.30773 q^{34} +(-3.65763 + 6.33520i) q^{35} +(-2.24472 + 1.99029i) q^{36} +1.16827 q^{37} +(-0.407656 + 4.33979i) q^{38} +(-6.10386 + 7.47900i) q^{39} +1.57955 q^{40} -4.49279 q^{41} +(-7.91789 - 1.28512i) q^{42} +(-4.24734 - 7.35661i) q^{43} +(-1.83826 - 3.18396i) q^{44} +(-4.49541 - 1.49874i) q^{45} +2.10449 q^{46} -5.75562 q^{47} +(0.614525 + 1.61937i) q^{48} +(-7.22408 - 12.5125i) q^{49} +(-1.25250 - 2.16940i) q^{50} +(-8.00309 + 9.80610i) q^{51} +(2.78676 + 4.82682i) q^{52} +(1.69773 + 2.94055i) q^{53} +(-0.212414 - 5.19181i) q^{54} +(2.90363 - 5.02923i) q^{55} +(-2.31561 + 4.01075i) q^{56} +(-5.37703 - 5.29976i) q^{57} +(2.66226 + 4.61117i) q^{58} -1.98482 q^{59} +(-1.72985 + 2.11957i) q^{60} +3.18599 q^{61} +(-0.587415 + 1.01743i) q^{62} +(10.3958 - 9.21745i) q^{63} +1.00000 q^{64} +(-4.40184 + 7.62422i) q^{65} +(6.28566 + 1.02020i) q^{66} +(-6.29213 + 10.8983i) q^{67} +(3.65387 + 6.32868i) q^{68} +(-2.30473 + 2.82396i) q^{69} -7.31525 q^{70} +(4.03312 - 6.98558i) q^{71} +(-2.84600 - 0.948840i) q^{72} +(7.45107 - 12.9056i) q^{73} +(0.584135 + 1.01175i) q^{74} +(4.28276 + 0.695117i) q^{75} +(-3.96220 + 1.81686i) q^{76} +(8.51338 + 14.7456i) q^{77} +(-9.52894 - 1.54660i) q^{78} +(2.99319 + 5.18435i) q^{79} +(0.789777 + 1.36793i) q^{80} +(7.19941 + 5.40079i) q^{81} +(-2.24640 - 3.89087i) q^{82} +(-5.85781 + 10.1460i) q^{83} +(-2.84600 - 7.49965i) q^{84} +(-5.77148 + 9.99650i) q^{85} +(4.24734 - 7.35661i) q^{86} +(-9.10322 - 1.47751i) q^{87} +(1.83826 - 3.18396i) q^{88} +(3.00802 + 5.21004i) q^{89} +(-0.949754 - 4.64251i) q^{90} +(-12.9061 - 22.3540i) q^{91} +(1.05224 + 1.82254i) q^{92} +(-0.721962 - 1.90248i) q^{93} +(-2.87781 - 4.98452i) q^{94} +(-5.61459 - 3.98512i) q^{95} +(-1.09515 + 1.34188i) q^{96} +(5.97017 + 10.3406i) q^{97} +(7.22408 - 12.5125i) q^{98} +(-8.25275 + 7.31733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) $ 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	$ 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} + q^{13} + 10 q^{14} - 3 q^{15} - 9 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 19 q^{21} + 2 q^{22} - 2 q^{23} + 18 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} + 18 q^{29} + 4 q^{31} + 9 q^{32} - 23 q^{33} - 10 q^{34} + 6 q^{35} - 8 q^{36} + 20 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{41} - 23 q^{42} + 7 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} - 38 q^{47} + 6 q^{49} + 9 q^{50} + 4 q^{51} + q^{52} - 10 q^{53} - 18 q^{54} + 6 q^{55} - 5 q^{56} - 33 q^{57} + 9 q^{58} + 10 q^{59} + 3 q^{60} - 36 q^{61} - 4 q^{62} + 12 q^{63} + 18 q^{64} - 45 q^{65} - 7 q^{66} + 22 q^{67} - 5 q^{68} - 26 q^{69} + 12 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} + 10 q^{74} - 6 q^{76} - 2 q^{77} + 23 q^{78} + 2 q^{79} + 4 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} - 7 q^{86} + 3 q^{87} - q^{88} + q^{89} + 60 q^{90} - 25 q^{91} - 2 q^{92} + 25 q^{93} - 19 q^{94} + 21 q^{95} - 6 q^{98} - 19 q^{99}+O(q^{100}) $ 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 + q^13 + 10 * q^14 - 3 * q^15 - 9 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 19 * q^21 + 2 * q^22 - 2 * q^23 + 18 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 + 18 * q^29 + 4 * q^31 + 9 * q^32 - 23 * q^33 - 10 * q^34 + 6 * q^35 - 8 * q^36 + 20 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^41 - 23 * q^42 + 7 * q^43 + q^44 + 30 * q^45 - 4 * q^46 - 38 * q^47 + 6 * q^49 + 9 * q^50 + 4 * q^51 + q^52 - 10 * q^53 - 18 * q^54 + 6 * q^55 - 5 * q^56 - 33 * q^57 + 9 * q^58 + 10 * q^59 + 3 * q^60 - 36 * q^61 - 4 * q^62 + 12 * q^63 + 18 * q^64 - 45 * q^65 - 7 * q^66 + 22 * q^67 - 5 * q^68 - 26 * q^69 + 12 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 + 10 * q^74 - 6 * q^76 - 2 * q^77 + 23 * q^78 + 2 * q^79 + 4 * q^81 - q^82 - 7 * q^83 - 4 * q^84 - 7 * q^86 + 3 * q^87 - q^88 + q^89 + 60 * q^90 - 25 * q^91 - 2 * q^92 + 25 * q^93 - 19 * q^94 + 21 * q^95 - 6 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.70968	−	0.277491i	−0.987083	−	0.160209i
$3$	−1.70968	−	0.277491i	−0.987083	−	0.160209i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.57955			−0.706398			−0.353199	−	0.935548i	$-0.614906\pi$
$5$	−1.57955			−0.706398			−0.353199	+	0.935548i	$0.614906\pi$
$6$	−0.614525	−	1.61937i	−0.250879	−	0.661105i
$7$	2.31561	−	4.01075i	0.875218	−	1.51592i	0.0186867	−	0.999825i	$-0.494051\pi$
$7$	2.31561	−	4.01075i	0.875218	−	1.51592i	0.856531	−	0.516096i	$-0.172615\pi$
$8$	−1.00000			−0.353553
$9$	2.84600	+	0.948840i	0.948666	+	0.316280i
$10$	−0.789777	−	1.36793i	−0.249749	−	0.432579i
$11$	−1.83826	+	3.18396i	−0.554256	+	0.960000i	0.443705	+	0.896173i	$0.353664\pi$
$11$	−1.83826	+	3.18396i	−0.554256	+	0.960000i	−0.997961	+	0.0638268i	$0.979669\pi$
$12$	1.09515	−	1.34188i	0.316143	−	0.387367i
$13$	2.78676	−	4.82682i	0.772909	−	1.33872i	−0.163053	−	0.986617i	$-0.552134\pi$
$13$	2.78676	−	4.82682i	0.772909	−	1.33872i	0.935962	−	0.352101i	$-0.114532\pi$
$14$	4.63122			1.23774
$15$	2.70053	+	0.438312i	0.697273	+	0.113172i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.65387	−	6.32868i	0.886193	−	1.53493i	0.0418529	−	0.999124i	$-0.486674\pi$
$17$	3.65387	−	6.32868i	0.886193	−	1.53493i	0.844340	−	0.535808i	$-0.179993\pi$
$18$	0.601280	+	2.93913i	0.141723	+	0.692759i
$19$	3.55454	+	2.52294i	0.815468	+	0.578802i
$19$	3.55454	+	2.52294i	0.815468	+	0.578802i
$20$	0.789777	−	1.36793i	0.176599	−	0.305879i
$21$	−5.07189	+	6.21453i	−1.10678	+	1.35612i
$22$	−3.67652			−0.783837
$23$	1.05224	−	1.82254i	0.219408	−	0.380025i	−0.735219	−	0.677829i	$-0.762921\pi$
$23$	1.05224	−	1.82254i	0.219408	−	0.380025i	0.954627	+	0.297804i	$0.0962542\pi$
$24$	1.70968	+	0.277491i	0.348987	+	0.0566426i
$25$	−2.50501			−0.501002
$26$	5.57353			1.09306
$27$	−4.60245	−	2.41195i	−0.885741	−	0.464180i
$28$	2.31561	+	4.01075i	0.437609	+	0.757961i
$29$	5.32452			0.988739			0.494369	−	0.869252i	$-0.335399\pi$
$29$	5.32452			0.988739			0.494369	+	0.869252i	$0.335399\pi$
$30$	0.970675	+	2.55788i	0.177220	+	0.467003i
$31$	0.587415	+	1.01743i	0.105503	+	0.182736i	0.913944	−	0.405841i	$-0.133021\pi$
$31$	0.587415	+	1.01743i	0.105503	+	0.182736i	−0.808441	+	0.588578i	$0.799688\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	4.02635	−	4.93344i	0.700898	−	0.858802i
$34$	7.30773			1.25327
$35$	−3.65763	+	6.33520i	−0.618252	+	1.07084i
$36$	−2.24472	+	1.99029i	−0.374120	+	0.331714i
$37$	1.16827			0.192062			0.0960312	−	0.995378i	$-0.469385\pi$
$37$	1.16827			0.192062			0.0960312	+	0.995378i	$0.469385\pi$
$38$	−0.407656	+	4.33979i	−0.0661305	+	0.704008i
$39$	−6.10386	+	7.47900i	−0.977401	+	1.19760i
$40$	1.57955			0.249749
$41$	−4.49279			−0.701656			−0.350828	−	0.936440i	$-0.614100\pi$
$41$	−4.49279			−0.701656			−0.350828	+	0.936440i	$0.614100\pi$
$42$	−7.91789	−	1.28512i	−1.22176	−	0.198298i
$43$	−4.24734	−	7.35661i	−0.647714	−	1.12187i	−0.983668	−	0.179995i	$-0.942392\pi$
$43$	−4.24734	−	7.35661i	−0.647714	−	1.12187i	0.335954	−	0.941878i	$-0.390941\pi$
$44$	−1.83826	−	3.18396i	−0.277128	−	0.480000i
$45$	−4.49541	−	1.49874i	−0.670136	−	0.223419i
$46$	2.10449			0.310289
$47$	−5.75562			−0.839544			−0.419772	−	0.907630i	$-0.637890\pi$
$47$	−5.75562			−0.839544			−0.419772	+	0.907630i	$0.637890\pi$
$48$	0.614525	+	1.61937i	0.0886990	+	0.233736i
$49$	−7.22408	−	12.5125i	−1.03201	−	1.78750i
$50$	−1.25250	−	2.16940i	−0.177131	−	0.306800i
$51$	−8.00309	+	9.80610i	−1.12066	+	1.37313i
$52$	2.78676	+	4.82682i	0.386455	+	0.669359i
$53$	1.69773	+	2.94055i	0.233201	+	0.403916i	0.958748	−	0.284256i	$-0.0917467\pi$
$53$	1.69773	+	2.94055i	0.233201	+	0.403916i	−0.725547	+	0.688172i	$0.758413\pi$
$54$	−0.212414	−	5.19181i	−0.0289059	−	0.706516i
$55$	2.90363	−	5.02923i	0.391525	−	0.678142i
$56$	−2.31561	+	4.01075i	−0.309436	+	0.535959i
$57$	−5.37703	−	5.29976i	−0.712206	−	0.701971i
$58$	2.66226	+	4.61117i	0.349572	+	0.605476i
$59$	−1.98482			−0.258402			−0.129201	−	0.991618i	$-0.541241\pi$
$59$	−1.98482			−0.258402			−0.129201	+	0.991618i	$0.541241\pi$
$60$	−1.72985	+	2.11957i	−0.223323	+	0.273635i
$61$	3.18599			0.407925			0.203962	−	0.978979i	$-0.434618\pi$
$61$	3.18599			0.407925			0.203962	+	0.978979i	$0.434618\pi$
$62$	−0.587415	+	1.01743i	−0.0746018	+	0.129214i
$63$	10.3958	−	9.21745i	1.30974	−	1.16129i
$64$	1.00000			0.125000
$65$	−4.40184	+	7.62422i	−0.545981	+	0.945668i
$66$	6.28566	+	1.02020i	0.773712	+	0.125578i
$67$	−6.29213	+	10.8983i	−0.768706	+	1.33144i	0.169559	+	0.985520i	$0.445766\pi$
$67$	−6.29213	+	10.8983i	−0.768706	+	1.33144i	−0.938265	+	0.345918i	$0.887568\pi$
$68$	3.65387	+	6.32868i	0.443097	+	0.767466i
$69$	−2.30473	+	2.82396i	−0.277457	+	0.339965i
$70$	−7.31525			−0.874340
$71$	4.03312	−	6.98558i	0.478644	−	0.829035i	−0.521056	−	0.853522i	$-0.674462\pi$
$71$	4.03312	−	6.98558i	0.478644	−	0.829035i	0.999700	+	0.0244869i	$0.00779519\pi$
$72$	−2.84600	−	0.948840i	−0.335404	−	0.111822i
$73$	7.45107	−	12.9056i	0.872082	−	1.51049i	0.0122430	−	0.999925i	$-0.496103\pi$
$73$	7.45107	−	12.9056i	0.872082	−	1.51049i	0.859839	−	0.510565i	$-0.170564\pi$
$74$	0.584135	+	1.01175i	0.0679043	+	0.117614i
$75$	4.28276	+	0.695117i	0.494531	+	0.0802652i
$76$	−3.96220	+	1.81686i	−0.454496	+	0.208408i
$77$	8.51338	+	14.7456i	0.970189	+	1.68042i
$78$	−9.52894	−	1.54660i	−1.07894	−	0.175118i
$79$	2.99319	+	5.18435i	0.336760	+	0.583285i	0.983821	−	0.179153i	$-0.0573357\pi$
$79$	2.99319	+	5.18435i	0.336760	+	0.583285i	−0.647062	+	0.762438i	$0.724002\pi$
$80$	0.789777	+	1.36793i	0.0882997	+	0.152940i
$81$	7.19941	+	5.40079i	0.799934	+	0.600088i
$82$	−2.24640	−	3.89087i	−0.248073	−	0.429675i
$83$	−5.85781	+	10.1460i	−0.642978	+	1.11367i	0.341787	+	0.939778i	$0.388968\pi$
$83$	−5.85781	+	10.1460i	−0.642978	+	1.11367i	−0.984765	+	0.173893i	$0.944365\pi$
$84$	−2.84600	−	7.49965i	−0.310524	−	0.818279i
$85$	−5.77148	+	9.99650i	−0.626005	+	1.08427i
$86$	4.24734	−	7.35661i	0.458003	−	0.793284i
$87$	−9.10322	−	1.47751i	−0.975967	−	0.158405i
$88$	1.83826	−	3.18396i	0.195959	−	0.339411i
$89$	3.00802	+	5.21004i	0.318849	+	0.552263i	0.980248	−	0.197771i	$-0.0633703\pi$
$89$	3.00802	+	5.21004i	0.318849	+	0.552263i	−0.661399	+	0.750034i	$0.730037\pi$
$90$	−0.949754	−	4.64251i	−0.100113	−	0.489363i
$91$	−12.9061	−	22.3540i	−1.35293	−	2.34334i
$92$	1.05224	+	1.82254i	0.109704	+	0.190013i
$93$	−0.721962	−	1.90248i	−0.0748640	−	0.197278i
$94$	−2.87781	−	4.98452i	−0.296824	−	0.514114i
$95$	−5.61459	−	3.98512i	−0.576045	−	0.408864i
$96$	−1.09515	+	1.34188i	−0.111774	+	0.136955i
$97$	5.97017	+	10.3406i	0.606179	+	1.04993i	0.991864	+	0.127303i	$0.0406320\pi$
$97$	5.97017	+	10.3406i	0.606179	+	1.04993i	−0.385684	+	0.922631i	$0.626035\pi$
$98$	7.22408	−	12.5125i	0.729742	−	1.26395i
$99$	−8.25275	+	7.31733i	−0.829432	+	0.735419i
$100$	1.25250	−	2.16940i	0.125250	−	0.216940i
$101$	10.8932			1.08392			0.541959	−	0.840405i	$-0.317683\pi$
$101$	10.8932			1.08392			0.541959	+	0.840405i	$0.317683\pi$
$102$	−12.4939	−	2.02783i	−1.23708	−	0.200785i
$103$	6.09893	+	10.5637i	0.600945	+	1.04087i	0.992678	+	0.120789i	$0.0385423\pi$
$103$	6.09893	+	10.5637i	0.600945	+	1.04087i	−0.391733	+	0.920079i	$0.628124\pi$
$104$	−2.78676	+	4.82682i	−0.273265	+	0.473308i
$105$	8.01132	−	9.81619i	0.781825	−	0.957962i
$106$	−1.69773	+	2.94055i	−0.164898	+	0.285612i
$107$	−6.89925			−0.666976			−0.333488	−	0.942754i	$-0.608226\pi$
$107$	−6.89925			−0.666976			−0.333488	+	0.942754i	$0.608226\pi$
$108$	4.39003	−	2.77986i	0.422431	−	0.267492i
$109$	−2.02428	+	3.50615i	−0.193890	+	0.335828i	−0.946536	−	0.322598i	$-0.895444\pi$
$109$	−2.02428	+	3.50615i	−0.193890	+	0.335828i	0.752646	+	0.658426i	$0.228777\pi$
$110$	5.80726			0.553701
$111$	−1.99737	−	0.324184i	−0.189582	−	0.0307702i
$112$	−4.63122			−0.437609
$113$	−0.671292	−	1.16271i	−0.0631498	−	0.109379i	0.832722	−	0.553691i	$-0.186781\pi$
$113$	−0.671292	−	1.16271i	−0.0631498	−	0.109379i	−0.895872	+	0.444313i	$0.853448\pi$
$114$	1.90121	−	7.30653i	0.178065	−	0.684319i
$115$	−1.66207	+	2.87880i	−0.154989	+	0.268449i
$116$	−2.66226	+	4.61117i	−0.247185	+	0.428136i
$117$	12.5110	−	11.0929i	1.15664	−	1.02554i
$118$	−0.992410	−	1.71891i	−0.0913588	−	0.158238i
$119$	−16.9218	−	29.3095i	−1.55122	−	2.68680i
$120$	−2.70053	−	0.438312i	−0.246523	−	0.0400122i
$121$	−1.25840	−	2.17961i	−0.114400	−	0.198146i
$122$	1.59300	+	2.75915i	0.144223	+	0.249802i
$123$	7.68123	+	1.24671i	0.692593	+	0.112412i
$124$	−1.17483			−0.105503
$125$	11.8546			1.06030
$126$	13.1804	+	4.39428i	1.17421	+	0.391474i
$127$	−3.95754	−	6.85466i	−0.351175	−	0.608253i	0.635281	−	0.772281i	$-0.280884\pi$
$127$	−3.95754	−	6.85466i	−0.351175	−	0.608253i	−0.986456	+	0.164029i	$0.947551\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.22020	+	13.7560i	0.459613	+	1.21115i
$130$	−8.80369			−0.772134
$131$	−1.39300			−0.121707			−0.0608537	−	0.998147i	$-0.519382\pi$
$131$	−1.39300			−0.121707			−0.0608537	+	0.998147i	$0.519382\pi$
$132$	2.25931	+	5.95364i	0.196648	+	0.518198i
$133$	18.3498	−	8.41426i	1.59113	−	0.729609i
$134$	−12.5843			−1.08711
$135$	7.26981	+	3.80980i	0.625686	+	0.327896i
$136$	−3.65387	+	6.32868i	−0.313317	+	0.542680i
$137$	2.40884			0.205801			0.102901	−	0.994692i	$-0.467188\pi$
$137$	2.40884			0.205801			0.102901	+	0.994692i	$0.467188\pi$
$138$	−3.59799	−	0.583975i	−0.306281	−	0.0497113i
$139$	4.23509	−	7.33539i	0.359216	−	0.622180i	−0.628614	−	0.777717i	$-0.716378\pi$
$139$	4.23509	−	7.33539i	0.359216	−	0.622180i	0.987830	+	0.155538i	$0.0497110\pi$
$140$	−3.65763	−	6.33520i	−0.309126	−	0.535422i
$141$	9.84026	+	1.59713i	0.828699	+	0.134503i
$142$	8.06625			0.676905
$143$	10.2456	+	17.7459i	0.856779	+	1.48399i
$144$	−0.601280	−	2.93913i	−0.0501066	−	0.244927i
$145$	−8.41037			−0.698443
$146$	14.9021			1.23331
$147$	8.87876	+	23.3969i	0.732307	+	1.92975i
$148$	−0.584135	+	1.01175i	−0.0480156	+	0.0831655i
$149$	−9.62256			−0.788310			−0.394155	−	0.919044i	$-0.628963\pi$
$149$	−9.62256			−0.788310			−0.394155	+	0.919044i	$0.628963\pi$
$150$	1.53939	+	4.05654i	0.125691	+	0.331215i
$151$	−11.4046	+	19.7534i	−0.928094	+	1.60751i	−0.141587	+	0.989926i	$0.545220\pi$
$151$	−11.4046	+	19.7534i	−0.928094	+	1.60751i	−0.786507	+	0.617581i	$0.788113\pi$
$152$	−3.55454	−	2.52294i	−0.288312	−	0.204637i
$153$	16.4038	−	14.5445i	1.32617	−	1.17585i
$154$	−8.51338	+	14.7456i	−0.686027	+	1.18823i
$155$	−0.927853	−	1.60709i	−0.0745270	−	0.129085i
$156$	−3.42507	−	9.02560i	−0.274225	−	0.722626i
$157$	−4.37348			−0.349041			−0.174521	−	0.984654i	$-0.555838\pi$
$157$	−4.37348			−0.349041			−0.174521	+	0.984654i	$0.555838\pi$
$158$	−2.99319	+	5.18435i	−0.238125	+	0.412445i
$159$	−2.08659	−	5.49850i	−0.165478	−	0.436060i
$160$	−0.789777	+	1.36793i	−0.0624373	+	0.108145i
$161$	−4.87316	−	8.44056i	−0.384059	−	0.665210i
$162$	−1.07752	+	8.93526i	−0.0846579	+	0.702021i
$163$	6.36953			0.498900			0.249450	−	0.968388i	$-0.419750\pi$
$163$	6.36953			0.498900			0.249450	+	0.968388i	$0.419750\pi$
$164$	2.24640	−	3.89087i	0.175414	−	0.303826i
$165$	−6.35984	+	7.79264i	−0.495113	+	0.606656i
$166$	−11.7156			−0.909308
$167$	3.08570	−	5.34459i	0.238779	−	0.413577i	−0.721585	−	0.692325i	$-0.756586\pi$
$167$	3.08570	−	5.34459i	0.238779	−	0.413577i	0.960364	+	0.278749i	$0.0899197\pi$
$168$	5.07189	−	6.21453i	0.391305	−	0.479462i
$169$	−9.03210	−	15.6441i	−0.694777	−	1.20339i
$170$	−11.5430			−0.885305
$171$	7.72236	+	10.5530i	0.590544	+	0.807006i
$172$	8.49469			0.647714
$173$	3.75669	+	6.50678i	0.285616	+	0.494701i	0.972758	−	0.231821i	$-0.0744685\pi$
$173$	3.75669	+	6.50678i	0.285616	+	0.494701i	−0.687142	+	0.726523i	$0.741135\pi$
$174$	−3.27205	−	8.62237i	−0.248054	−	0.653660i
$175$	−5.80062	+	10.0470i	−0.438486	+	0.759479i
$176$	3.67652			0.277128
$177$	3.39340	+	0.550769i	0.255064	+	0.0413984i
$178$	−3.00802	+	5.21004i	−0.225460	+	0.390509i
$179$	21.7463			1.62540			0.812698	−	0.582685i	$-0.197998\pi$
$179$	21.7463			1.62540			0.812698	+	0.582685i	$0.197998\pi$
$180$	3.54565	−	3.14376i	0.264277	−	0.234322i
$181$	2.33180	+	4.03880i	0.173322	+	0.300202i	0.939579	−	0.342332i	$-0.111217\pi$
$181$	2.33180	+	4.03880i	0.173322	+	0.300202i	−0.766258	+	0.642534i	$0.777883\pi$
$182$	12.9061	−	22.3540i	0.956664	−	1.65699i
$183$	−5.44702	−	0.884083i	−0.402655	−	0.0653533i
$184$	−1.05224	+	1.82254i	−0.0775723	+	0.134359i
$185$	−1.84535			−0.135673
$186$	1.28662	−	1.57648i	0.0943394	−	0.115593i
$187$	13.4335	+	23.2675i	0.982356	+	1.70149i
$188$	2.87781	−	4.98452i	0.209886	−	0.363533i
$189$	−20.3312	+	12.8741i	−1.47888	+	0.936456i
$190$	0.643914	−	6.85494i	0.0467145	−	0.497310i
$191$	2.83934	−	4.91788i	0.205447	−	0.355845i	−0.744828	−	0.667257i	$-0.767468\pi$
$191$	2.83934	−	4.91788i	0.205447	−	0.355845i	0.950275	+	0.311411i	$0.100802\pi$
$192$	−1.70968	−	0.277491i	−0.123385	−	0.0200262i
$193$	9.87222			0.710618			0.355309	−	0.934749i	$-0.384376\pi$
$193$	9.87222			0.710618			0.355309	+	0.934749i	$0.384376\pi$
$194$	−5.97017	+	10.3406i	−0.428634	+	0.742415i
$195$	9.64138	−	11.8135i	0.690434	−	0.845981i
$196$	14.4482			1.03201
$197$	−25.0810			−1.78695			−0.893474	−	0.449114i	$-0.851740\pi$
$197$	−25.0810			−1.78695			−0.893474	+	0.449114i	$0.851740\pi$
$198$	−10.4634	−	3.48843i	−0.743599	−	0.247912i
$199$	4.46649	+	7.73619i	0.316621	+	0.548404i	0.979781	−	0.200074i	$-0.0641183\pi$
$199$	4.46649	+	7.73619i	0.316621	+	0.548404i	−0.663160	+	0.748478i	$0.730785\pi$
$200$	2.50501			0.177131
$201$	13.7817	−	16.8866i	0.972086	−	1.19109i
$202$	5.44662	+	9.43383i	0.383223	+	0.663762i
$203$	12.3295	−	21.3553i	0.865361	−	1.49885i
$204$	−4.49079	−	11.8339i	−0.314418	−	0.828541i
$205$	7.09661			0.495648
$206$	−6.09893	+	10.5637i	−0.424932	+	0.736004i
$207$	4.72398	−	4.18853i	0.328339	−	0.291123i
$208$	−5.57353			−0.386455
$209$	−14.5671	+	6.67971i	−1.00763	+	0.462045i
$210$	12.5067	+	2.02992i	0.863046	+	0.140077i
$211$	6.32457			0.435401			0.217701	−	0.976016i	$-0.430144\pi$
$211$	6.32457			0.435401			0.217701	+	0.976016i	$0.430144\pi$
$212$	−3.39546			−0.233201
$213$	−8.83378	+	10.8239i	−0.605280	+	0.741644i
$214$	−3.44963	−	5.97493i	−0.235812	−	0.408438i
$215$	6.70891	+	11.6202i	0.457544	+	0.792489i
$216$	4.60245	+	2.41195i	0.313157	+	0.164112i
$217$	5.44089			0.369352
$218$	−4.04855			−0.274202
$219$	−16.3201	+	19.9969i	−1.10281	+	1.35126i
$220$	2.90363	+	5.02923i	0.195763	+	0.339071i
$221$	−20.3649	−	35.2731i	−1.36989	−	2.37272i
$222$	−0.717931	−	1.89186i	−0.0481844	−	0.126973i
$223$	−0.878811	−	1.52215i	−0.0588496	−	0.101930i	0.835100	−	0.550099i	$-0.185410\pi$
$223$	−0.878811	−	1.52215i	−0.0588496	−	0.101930i	−0.893949	+	0.448168i	$0.852077\pi$
$224$	−2.31561	−	4.01075i	−0.154718	−	0.267980i
$225$	−7.12925	−	2.37685i	−0.475283	−	0.158457i
$226$	0.671292	−	1.16271i	0.0446537	−	0.0773424i
$227$	−6.41556	+	11.1121i	−0.425816	+	0.737535i	−0.996496	−	0.0836376i	$-0.973346\pi$
$227$	−6.41556	+	11.1121i	−0.425816	+	0.737535i	0.570680	+	0.821172i	$0.306680\pi$
$228$	7.27825	−	2.00677i	0.482014	−	0.132901i
$229$	−0.207385	−	0.359201i	−0.0137044	−	0.0237367i	0.859092	−	0.511821i	$-0.171029\pi$
$229$	−0.207385	−	0.359201i	−0.0137044	−	0.0237367i	−0.872796	+	0.488085i	$0.837696\pi$
$230$	−3.32415			−0.219188
$231$	−10.4634	−	27.5726i	−0.688439	−	1.81414i
$232$	−5.32452			−0.349572
$233$	−6.42184	+	11.1229i	−0.420709	+	0.728689i	−0.996009	−	0.0892537i	$-0.971552\pi$
$233$	−6.42184	+	11.1229i	−0.420709	+	0.728689i	0.575300	+	0.817942i	$0.304885\pi$
$234$	15.8622	+	5.28838i	1.03695	+	0.345712i
$235$	9.09132			0.593052
$236$	0.992410	−	1.71891i	0.0646004	−	0.111891i
$237$	−3.67877	−	9.69415i	−0.238962	−	0.629703i
$238$	16.9218	−	29.3095i	1.09688	−	1.89985i
$239$	6.27082	+	10.8614i	0.405626	+	0.702564i	0.994394	−	0.105738i	$-0.0337204\pi$
$239$	6.27082	+	10.8614i	0.405626	+	0.702564i	−0.588768	+	0.808302i	$0.700387\pi$
$240$	−0.970675	−	2.55788i	−0.0626568	−	0.165111i
$241$	−4.04956			−0.260855			−0.130427	−	0.991458i	$-0.541635\pi$
$241$	−4.04956			−0.260855			−0.130427	+	0.991458i	$0.541635\pi$
$242$	1.25840	−	2.17961i	0.0808928	−	0.140110i
$243$	−10.8100	−	11.2314i	−0.693462	−	0.720494i
$244$	−1.59300	+	2.75915i	−0.101981	+	0.176637i
$245$	11.4108	+	19.7641i	0.729011	+	1.26268i
$246$	2.76093	+	7.27549i	0.176031	+	0.463868i
$247$	22.0834	−	10.1263i	1.40513	−	0.644321i
$248$	−0.587415	−	1.01743i	−0.0373009	−	0.0646070i
$249$	12.8304	−	15.7209i	0.813093	−	0.996274i
$250$	5.92728	+	10.2664i	0.374874	+	0.649301i
$251$	−9.59620	−	16.6211i	−0.605707	−	1.04912i	−0.991939	−	0.126714i	$-0.959557\pi$
$251$	−9.59620	−	16.6211i	−0.605707	−	1.04912i	0.386232	−	0.922402i	$-0.373776\pi$
$252$	2.78466	+	13.6117i	0.175417	+	0.857458i
$253$	3.86859	+	6.70059i	0.243216	+	0.421263i
$254$	3.95754	−	6.85466i	0.248318	−	0.430100i
$255$	12.6413	−	15.4893i	0.791629	−	0.969975i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.784594	−	1.35896i	0.0489416	−	0.0847694i	−0.840517	−	0.541785i	$-0.817749\pi$
$257$	0.784594	−	1.35896i	0.0489416	−	0.0847694i	0.889458	+	0.457016i	$0.151082\pi$
$258$	−9.30298	+	11.3988i	−0.579178	+	0.709661i
$259$	2.70526	−	4.68564i	0.168096	−	0.291152i
$260$	−4.40184	−	7.62422i	−0.272991	−	0.472834i
$261$	15.1536	+	5.05212i	0.937983	+	0.312718i
$262$	−0.696502	−	1.20638i	−0.0430301	−	0.0745302i
$263$	−13.9124	−	24.0970i	−0.857876	−	1.48588i	−0.873951	−	0.486014i	$-0.838450\pi$
$263$	−13.9124	−	24.0970i	−0.857876	−	1.48588i	0.0160751	−	0.999871i	$-0.494883\pi$
$264$	−4.02635	+	4.93344i	−0.247805	+	0.303633i
$265$	−2.68165	−	4.64476i	−0.164733	−	0.285325i
$266$	16.4619	+	11.6843i	1.00934	+	0.716408i
$267$	−3.69700	−	9.74219i	−0.226253	−	0.596212i
$268$	−6.29213	−	10.8983i	−0.384353	−	0.665719i
$269$	0.0554458	−	0.0960349i	0.00338059	−	0.00585535i	−0.864330	−	0.502925i	$-0.832257\pi$
$269$	0.0554458	−	0.0960349i	0.00338059	−	0.00585535i	0.867711	+	0.497069i	$0.165591\pi$
$270$	0.335520	+	8.20074i	0.0204191	+	0.499081i
$271$	−4.79718	+	8.30896i	−0.291408	+	0.504733i	−0.974143	−	0.225933i	$-0.927457\pi$
$271$	−4.79718	+	8.30896i	−0.291408	+	0.504733i	0.682735	+	0.730666i	$0.260790\pi$
$272$	−7.30773			−0.443097
$273$	15.8622	+	41.7995i	0.960027	+	2.52982i
$274$	1.20442	+	2.08612i	0.0727617	+	0.126027i
$275$	4.60486	−	7.97585i	0.277683	−	0.480962i
$276$	−1.29326	−	3.40794i	−0.0778450	−	0.205134i
$277$	−7.63856	+	13.2304i	−0.458956	+	0.794936i	−0.998906	−	0.0467615i	$-0.985110\pi$
$277$	−7.63856	+	13.2304i	−0.458956	+	0.794936i	0.539950	+	0.841697i	$0.318443\pi$
$278$	8.47018			0.508007
$279$	0.706401	+	3.45297i	0.0422911	+	0.206724i
$280$	3.65763	−	6.33520i	0.218585	−	0.378600i
$281$	4.45297			0.265642			0.132821	−	0.991140i	$-0.457597\pi$
$281$	4.45297			0.265642			0.132821	+	0.991140i	$0.457597\pi$
$282$	3.53697	+	9.32048i	0.210624	+	0.555027i
$283$	5.78180			0.343692			0.171846	−	0.985124i	$-0.445027\pi$
$283$	5.78180			0.343692			0.171846	+	0.985124i	$0.445027\pi$
$284$	4.03312	+	6.98558i	0.239322	+	0.414518i
$285$	8.49332	+	8.37126i	0.503101	+	0.495871i
$286$	−10.2456	+	17.7459i	−0.605834	+	1.04934i
$287$	−10.4035	+	18.0195i	−0.614102	+	1.06366i
$288$	2.24472	−	1.99029i	0.132271	−	0.117279i
$289$	−18.2015	−	31.5259i	−1.07068	−	1.85447i
$290$	−4.20518	−	7.28359i	−0.246937	−	0.427707i
$291$	−7.33764	−	19.3358i	−0.430140	−	1.13349i
$292$	7.45107	+	12.9056i	0.436041	+	0.755245i
$293$	−9.50767	−	16.4678i	−0.555444	−	0.962057i	−0.997869	−	0.0652515i	$-0.979215\pi$
$293$	−9.50767	−	16.4678i	−0.555444	−	0.962057i	0.442425	−	0.896806i	$-0.354118\pi$
$294$	−15.8229	+	19.3877i	−0.922813	+	1.13071i
$295$	3.13513			0.182534
$296$	−1.16827			−0.0679043
$297$	16.1400	−	10.2202i	0.936540	−	0.593037i
$298$	−4.81128	−	8.33338i	−0.278710	−	0.482740i
$299$	−5.86470	−	10.1580i	−0.339164	−	0.587450i
$300$	−2.74337	+	3.36142i	−0.158388	+	0.194072i
$301$	−39.3407			−2.26756
$302$	−22.8092			−1.31252
$303$	−18.6239	−	3.02277i	−1.06992	−	0.173654i
$304$	0.407656	−	4.33979i	0.0233807	−	0.248904i
$305$	−5.03245			−0.288157
$306$	20.7978	+	6.93387i	1.18893	+	0.396383i
$307$	−12.2704	+	21.2529i	−0.700306	+	1.21297i	0.268053	+	0.963404i	$0.413620\pi$
$307$	−12.2704	+	21.2529i	−0.700306	+	1.21297i	−0.968359	+	0.249561i	$0.919714\pi$
$308$	−17.0268			−0.970189
$309$	−7.49589	−	19.7528i	−0.426426	−	1.12370i
$310$	0.927853	−	1.60709i	0.0526985	−	0.0912765i
$311$	1.73597	+	3.00679i	0.0984379	+	0.170500i	0.911038	−	0.412322i	$-0.135282\pi$
$311$	1.73597	+	3.00679i	0.0984379	+	0.170500i	−0.812600	+	0.582821i	$0.801949\pi$
$312$	6.10386	−	7.47900i	0.345563	−	0.423415i
$313$	4.12085			0.232924			0.116462	−	0.993195i	$-0.462845\pi$
$313$	4.12085			0.232924			0.116462	+	0.993195i	$0.462845\pi$
$314$	−2.18674	−	3.78754i	−0.123405	−	0.213743i
$315$	−16.4207	+	14.5595i	−0.925201	+	0.820332i
$316$	−5.98637			−0.336760
$317$	−21.6390			−1.21537			−0.607683	−	0.794180i	$-0.707901\pi$
$317$	−21.6390			−1.21537			−0.607683	+	0.794180i	$0.707901\pi$
$318$	3.71855	−	4.55629i	0.208526	−	0.255504i
$319$	−9.78785	+	16.9531i	−0.548014	+	0.949189i
$320$	−1.57955			−0.0882997
$321$	11.7955	+	1.91448i	0.658361	+	0.106856i
$322$	4.87316	−	8.44056i	0.271571	−	0.470374i
$323$	28.9547	−	13.2771i	1.61108	−	0.738758i
$324$	−8.27693	+	3.53447i	−0.459829	+	0.196360i
$325$	−6.98087	+	12.0912i	−0.387229	+	0.670700i
$326$	3.18476	+	5.51617i	0.176388	+	0.305512i
$327$	4.43378	−	5.43267i	0.245189	−	0.300427i
$328$	4.49279			0.248073
$329$	−13.3278	+	23.0844i	−0.734783	+	1.27268i
$330$	−9.92854	−	1.61146i	−0.546548	−	0.0887080i
$331$	−8.48039	+	14.6885i	−0.466125	+	0.807352i	−0.999252	−	0.0386837i	$-0.987684\pi$
$331$	−8.48039	+	14.6885i	−0.466125	+	0.807352i	0.533127	+	0.846035i	$0.321017\pi$
$332$	−5.85781	−	10.1460i	−0.321489	−	0.556835i
$333$	3.32489	+	1.10850i	0.182203	+	0.0607455i
$334$	6.17140			0.337684
$335$	9.93876	−	17.2144i	0.543012	−	0.940525i
$336$	7.91789	+	1.28512i	0.431956	+	0.0701090i
$337$	−23.2326			−1.26556			−0.632779	−	0.774332i	$-0.718086\pi$
$337$	−23.2326			−1.26556			−0.632779	+	0.774332i	$0.718086\pi$
$338$	9.03210	−	15.6441i	0.491282	−	0.850925i
$339$	0.825051	+	2.17414i	0.0448106	+	0.118083i
$340$	−5.77148	−	9.99650i	−0.313002	−	0.542136i
$341$	−4.31928			−0.233902
$342$	−5.27796	+	11.9642i	−0.285399	+	0.646952i
$343$	−34.4940			−1.86250
$344$	4.24734	+	7.35661i	0.229001	+	0.396642i
$345$	3.64045	−	4.46060i	0.195995	−	0.240151i
$346$	−3.75669	+	6.50678i	−0.201961	+	0.349807i
$347$	16.4030			0.880559			0.440280	−	0.897861i	$-0.354879\pi$
$347$	16.4030			0.880559			0.440280	+	0.897861i	$0.354879\pi$
$348$	5.83117	−	7.14486i	0.312583	−	0.383005i
$349$	1.92719	−	3.33798i	0.103160	−	0.178678i	−0.809825	−	0.586671i	$-0.800438\pi$
$349$	1.92719	−	3.33798i	0.103160	−	0.178678i	0.912985	+	0.407993i	$0.133771\pi$
$350$	−11.6012			−0.620112
$351$	−24.4680	+	15.4936i	−1.30600	+	0.826989i
$352$	1.83826	+	3.18396i	0.0979796	+	0.169706i
$353$	−4.42315	+	7.66112i	−0.235421	+	0.407760i	−0.959395	−	0.282067i	$-0.908980\pi$
$353$	−4.42315	+	7.66112i	−0.235421	+	0.407760i	0.723974	+	0.689827i	$0.242313\pi$
$354$	1.21972	+	3.21416i	0.0648275	+	0.170831i
$355$	−6.37054	+	11.0341i	−0.338113	+	0.585629i
$356$	−6.01603			−0.318849
$357$	20.7978	+	54.8055i	1.10074	+	2.90061i
$358$	10.8732	+	18.8329i	0.574664	+	0.995348i
$359$	−11.0150	+	19.0785i	−0.581349	+	1.00693i	0.413971	+	0.910290i	$0.364142\pi$
$359$	−11.0150	+	19.0785i	−0.581349	+	1.00693i	−0.995320	+	0.0966358i	$0.969192\pi$
$360$	4.49541	+	1.49874i	0.236929	+	0.0789907i
$361$	6.26957	+	17.9358i	0.329977	+	0.943989i
$362$	−2.33180	+	4.03880i	−0.122557	+	0.212275i
$363$	1.54663	+	4.07562i	0.0811771	+	0.213914i
$364$	25.8122			1.35293
$365$	−11.7694	+	20.3851i	−0.616037	+	1.06701i
$366$	−1.95787	−	5.15930i	−0.102340	−	0.269681i
$367$	12.3653			0.645463			0.322731	−	0.946491i	$-0.395399\pi$
$367$	12.3653			0.645463			0.322731	+	0.946491i	$0.395399\pi$
$368$	−2.10449			−0.109704
$369$	−12.7865	−	4.26294i	−0.665637	−	0.221920i
$370$	−0.922673	−	1.59812i	−0.0479675	−	0.0830821i
$371$	15.7251			0.816406
$372$	2.00858	+	0.326004i	0.104140	+	0.0169025i
$373$	3.36121	+	5.82178i	0.174037	+	0.301440i	0.939827	−	0.341649i	$-0.110986\pi$
$373$	3.36121	+	5.82178i	0.174037	+	0.301440i	−0.765791	+	0.643090i	$0.777652\pi$
$374$	−13.4335	+	23.2675i	−0.694630	+	1.20314i
$375$	−20.2675	−	3.28953i	−1.04661	−	0.169871i
$376$	5.75562			0.296824
$377$	14.8382	−	25.7005i	0.764205	−	1.32364i
$378$	−21.3149	−	11.1703i	−1.09632	−	0.574536i
$379$	26.1451			1.34298			0.671491	−	0.741013i	$-0.265654\pi$
$379$	26.1451			1.34298			0.671491	+	0.741013i	$0.265654\pi$
$380$	6.25851	−	2.86982i	0.321055	−	0.147219i
$381$	4.86402	+	12.8174i	0.249191	+	0.656658i
$382$	5.67868			0.290546
$383$	13.7394			0.702052			0.351026	−	0.936366i	$-0.385833\pi$
$383$	13.7394			0.702052			0.351026	+	0.936366i	$0.385833\pi$
$384$	−0.614525	−	1.61937i	−0.0313598	−	0.0826381i
$385$	−13.4473	−	23.2915i	−0.685340	−	1.18704i
$386$	4.93611	+	8.54959i	0.251241	+	0.435163i
$387$	−5.10768	−	24.9670i	−0.259638	−	1.26914i
$388$	−11.9403			−0.606179
$389$	30.4005			1.54137			0.770683	−	0.637219i	$-0.219915\pi$
$389$	30.4005			1.54137			0.770683	+	0.637219i	$0.219915\pi$
$390$	15.0515	+	2.44294i	0.762161	+	0.123703i
$391$	−7.68951	−	13.3186i	−0.388875	−	0.673552i
$392$	7.22408	+	12.5125i	0.364871	+	0.631975i
$393$	2.38159	+	0.386546i	0.120135	+	0.0194987i
$394$	−12.5405	−	21.7208i	−0.631782	−	1.09428i
$395$	−4.72790	−	8.18896i	−0.237886	−	0.412031i
$396$	−2.21062	−	10.8058i	−0.111088	−	0.543010i
$397$	9.16006	−	15.8657i	0.459730	−	0.796277i	−0.539216	−	0.842168i	$-0.681279\pi$
$397$	9.16006	−	15.8657i	0.459730	−	0.796277i	0.998946	+	0.0458910i	$0.0146127\pi$
$398$	−4.46649	+	7.73619i	−0.223885	+	0.387780i
$399$	−33.7071	+	9.29377i	−1.68747	+	0.465270i
$400$	1.25250	+	2.16940i	0.0626252	+	0.108470i
$401$	34.6046			1.72807			0.864035	−	0.503431i	$-0.167929\pi$
$401$	34.6046			1.72807			0.864035	+	0.503431i	$0.167929\pi$
$402$	21.5150	+	3.49202i	1.07307	+	0.174166i
$403$	6.54794			0.326176
$404$	−5.44662	+	9.43383i	−0.270980	+	0.469350i
$405$	−11.3719	−	8.53084i	−0.565072	−	0.423901i
$406$	24.6590			1.22381
$407$	−2.14758	+	3.71972i	−0.106452	+	0.184380i
$408$	8.00309	−	9.80610i	0.396212	−	0.485474i
$409$	2.50569	−	4.33998i	0.123898	−	0.214598i	−0.797403	−	0.603447i	$-0.793794\pi$
$409$	2.50569	−	4.33998i	0.123898	−	0.214598i	0.921302	+	0.388848i	$0.127127\pi$
$410$	3.54830	+	6.14584i	0.175238	+	0.303521i
$411$	−4.11834	−	0.668431i	−0.203143	−	0.0329713i
$412$	−12.1979			−0.600945
$413$	−4.59607	+	7.96062i	−0.226158	+	0.391717i
$414$	5.98936	+	1.99682i	0.294361	+	0.0981383i
$415$	9.25272	−	16.0262i	0.454198	−	0.786695i
$416$	−2.78676	−	4.82682i	−0.136632	−	0.236654i
$417$	−9.27614	+	11.3660i	−0.454255	+	0.556593i
$418$	−13.0684	−	9.27563i	−0.639194	−	0.453686i
$419$	−14.5553	−	25.2106i	−0.711074	−	1.23162i	−0.964454	−	0.264250i	$-0.914876\pi$
$419$	−14.5553	−	25.2106i	−0.711074	−	1.23162i	0.253380	−	0.967367i	$-0.418458\pi$
$420$	4.49541	+	11.8461i	0.219353	+	0.578031i
$421$	1.71985	+	2.97887i	0.0838204	+	0.145181i	0.904888	−	0.425650i	$-0.139954\pi$
$421$	1.71985	+	2.97887i	0.0838204	+	0.145181i	−0.821068	+	0.570831i	$0.806621\pi$
$422$	3.16229	+	5.47724i	0.153938	+	0.266628i
$423$	−16.3805	−	5.46116i	−0.796447	−	0.265531i
$424$	−1.69773	−	2.94055i	−0.0824490	−	0.142806i
$425$	−9.15297	+	15.8534i	−0.443984	+	0.769004i
$426$	−13.7907	−	2.23831i	−0.668161	−	0.108446i
$427$	7.37751	−	12.7782i	0.357023	−	0.618382i
$428$	3.44963	−	5.97493i	0.166744	−	0.288809i
$429$	−12.5923	−	33.1828i	−0.607964	−	1.60208i
$430$	−6.70891	+	11.6202i	−0.323532	+	0.560374i
$431$	−4.96062	−	8.59205i	−0.238945	−	0.413865i	0.721467	−	0.692449i	$-0.243468\pi$
$431$	−4.96062	−	8.59205i	−0.238945	−	0.413865i	−0.960412	+	0.278584i	$0.910135\pi$
$432$	0.212414	+	5.19181i	0.0102198	+	0.249791i
$433$	0.263521	+	0.456432i	0.0126640	+	0.0219347i	0.872288	−	0.488993i	$-0.162635\pi$
$433$	0.263521	+	0.456432i	0.0126640	+	0.0219347i	−0.859624	+	0.510927i	$0.829302\pi$
$434$	2.72044	+	4.71195i	0.130586	+	0.226181i
$435$	14.3790	+	2.33380i	0.689421	+	0.111897i
$436$	−2.02428	−	3.50615i	−0.0969452	−	0.167914i
$437$	8.33839	−	3.82355i	0.398879	−	0.182905i
$438$	−25.4779	−	4.13521i	−1.21738	−	0.197588i
$439$	8.17519	+	14.1598i	0.390180	+	0.675812i	0.992473	−	0.122463i	$-0.0390793\pi$
$439$	8.17519	+	14.1598i	0.390180	+	0.675812i	−0.602293	+	0.798275i	$0.705746\pi$
$440$	−2.90363	+	5.02923i	−0.138425	+	0.239759i
$441$	−8.68738	−	42.4650i	−0.413685	−	2.02214i
$442$	20.3649	−	35.2731i	0.968661	−	1.67777i
$443$	5.78636			0.274918			0.137459	−	0.990507i	$-0.456106\pi$
$443$	5.78636			0.274918			0.137459	+	0.990507i	$0.456106\pi$
$444$	1.27943	−	1.56768i	0.0607193	−	0.0743987i
$445$	−4.75133	−	8.22954i	−0.225234	−	0.390117i
$446$	0.878811	−	1.52215i	0.0416129	−	0.0720757i
$447$	16.4515	+	2.67017i	0.778128	+	0.126295i
$448$	2.31561	−	4.01075i	0.109402	−	0.189490i
$449$	−10.4180			−0.491658			−0.245829	−	0.969313i	$-0.579060\pi$
$449$	−10.4180			−0.491658			−0.245829	+	0.969313i	$0.579060\pi$
$450$	−1.50621	−	7.36254i	−0.0710035	−	0.347073i
$451$	8.25892	−	14.3049i	0.388897	−	0.673590i
$452$	1.34258			0.0631498
$453$	24.9796	−	30.6072i	1.17364	−	1.43805i
$454$	−12.8311			−0.602194
$455$	20.3859	+	35.3094i	0.955705	+	1.65533i
$456$	5.37703	+	5.29976i	0.251803	+	0.248184i
$457$	−10.3149	+	17.8659i	−0.482510	+	0.835733i	−0.999798	−	0.0200789i	$-0.993608\pi$
$457$	−10.3149	+	17.8659i	−0.482510	+	0.835733i	0.517288	+	0.855811i	$0.326942\pi$
$458$	0.207385	−	0.359201i	0.00969047	−	0.0167844i
$459$	−32.0812	+	20.3145i	−1.49742	+	0.948199i
$460$	−1.66207	−	2.87880i	−0.0774946	−	0.134225i
$461$	7.65320	+	13.2557i	0.356445	+	0.617381i	0.987364	−	0.158468i	$-0.0506554\pi$
$461$	7.65320	+	13.2557i	0.356445	+	0.617381i	−0.630919	+	0.775849i	$0.717322\pi$
$462$	18.6469	−	22.8478i	0.867532	−	1.06298i
$463$	4.73547	+	8.20208i	0.220076	+	0.381183i	0.954831	−	0.297150i	$-0.0960361\pi$
$463$	4.73547	+	8.20208i	0.220076	+	0.381183i	−0.734755	+	0.678333i	$0.762703\pi$
$464$	−2.66226	−	4.61117i	−0.123592	−	0.214068i
$465$	1.14038	+	3.00508i	0.0528838	+	0.139357i
$466$	−12.8437			−0.594972
$467$	−15.0904			−0.698299			−0.349149	−	0.937067i	$-0.613529\pi$
$467$	−15.0904			−0.698299			−0.349149	+	0.937067i	$0.613529\pi$
$468$	3.35125	+	16.3813i	0.154912	+	0.757226i
$469$	29.1402	+	50.4723i	1.34557	+	2.33060i
$470$	4.54566	+	7.87331i	0.209676	+	0.363169i
$471$	7.47723	+	1.21360i	0.344533	+	0.0559197i
$472$	1.98482			0.0913588
$473$	31.2309			1.43600
$474$	6.55599	−	8.03299i	0.301127	−	0.368967i
$475$	−8.90417	−	6.31998i	−0.408551	−	0.289981i
$476$	33.8437			1.55122
$477$	2.04162	+	9.97968i	0.0934793	+	0.456938i
$478$	−6.27082	+	10.8614i	−0.286821	+	0.496788i
$479$	27.7856			1.26956			0.634779	−	0.772694i	$-0.281091\pi$
$479$	27.7856			1.26956			0.634779	+	0.772694i	$0.281091\pi$
$480$	1.72985	−	2.11957i	0.0789566	−	0.0967447i
$481$	3.25569	−	5.63903i	0.148447	−	0.257117i
$482$	−2.02478	−	3.50702i	−0.0922261	−	0.159740i
$483$	5.98936	+	15.7829i	0.272525	+	0.718147i
$484$	2.51679			0.114400
$485$	−9.43021	−	16.3336i	−0.428204	−	0.741671i
$486$	4.32166	−	14.9774i	0.196035	−	0.679390i
$487$	26.0008			1.17821			0.589105	−	0.808057i	$-0.299480\pi$
$487$	26.0008			1.17821			0.589105	+	0.808057i	$0.299480\pi$
$488$	−3.18599			−0.144223
$489$	−10.8898	−	1.76748i	−0.492455	−	0.0799284i
$490$	−11.4108	+	19.7641i	−0.515488	+	0.892852i
$491$	−32.9529			−1.48714			−0.743572	−	0.668656i	$-0.766870\pi$
$491$	−32.9529			−1.48714			−0.743572	+	0.668656i	$0.766870\pi$
$492$	−4.92029	+	6.02878i	−0.221824	+	0.271799i
$493$	19.4551	−	33.6972i	0.876213	−	1.51765i
$494$	19.8113	+	14.0617i	0.891355	+	0.632664i
$495$	13.0357	−	11.5581i	0.585909	−	0.519498i
$496$	0.587415	−	1.01743i	0.0263757	−	0.0456841i
$497$	−18.6783	−	32.3517i	−0.837835	−	1.45117i
$498$	20.0299	+	3.25097i	0.897563	+	0.145680i
$499$	4.08509			0.182874			0.0914368	−	0.995811i	$-0.470854\pi$
$499$	4.08509			0.182874			0.0914368	+	0.995811i	$0.470854\pi$
$500$	−5.92728	+	10.2664i	−0.265076	+	0.459125i
$501$	−6.75863	+	8.28127i	−0.301953	+	0.369980i
$502$	9.59620	−	16.6211i	0.428300	−	0.741837i
$503$	4.15278	+	7.19283i	0.185163	+	0.320712i	0.943632	−	0.330998i	$-0.107385\pi$
$503$	4.15278	+	7.19283i	0.185163	+	0.320712i	−0.758468	+	0.651710i	$0.774052\pi$
$504$	−10.3958	+	9.21745i	−0.463065	+	0.410578i
$505$	−17.2065			−0.765678
$506$	−3.86859	+	6.70059i	−0.171980	+	0.297878i
$507$	11.1009	+	29.2526i	0.493008	+	1.29915i
$508$	7.91508			0.351175
$509$	7.38166	−	12.7854i	0.327186	−	0.566704i	−0.654766	−	0.755832i	$-0.727233\pi$
$509$	7.38166	−	12.7854i	0.327186	−	0.566704i	0.981952	+	0.189128i	$0.0605661\pi$
$510$	19.7347	+	3.20306i	0.873869	+	0.141834i
$511$	−34.5075	−	59.7688i	−1.52652	−	2.64402i
$512$	−1.00000			−0.0441942
$513$	−10.2744	−	20.1851i	−0.453626	−	0.891192i
$514$	1.56919			0.0692139
$515$	−9.63358	−	16.6859i	−0.424506	−	0.735267i
$516$	−14.5232	−	2.35720i	−0.639347	−	0.103770i
$517$	10.5803	−	18.3257i	0.465322	−	0.805962i
$518$	5.41051			0.237724
$519$	−4.61716	−	12.1669i	−0.202671	−	0.534070i
$520$	4.40184	−	7.62422i	0.193034	−	0.334344i
$521$	31.7044			1.38899			0.694497	−	0.719495i	$-0.255627\pi$
$521$	31.7044			1.38899			0.694497	+	0.719495i	$0.255627\pi$
$522$	3.20153	+	15.6494i	0.140127	+	0.684957i
$523$	14.4395	+	25.0100i	0.631396	+	1.09361i	0.987267	+	0.159075i	$0.0508511\pi$
$523$	14.4395	+	25.0100i	0.631396	+	1.09361i	−0.355870	+	0.934535i	$0.615816\pi$
$524$	0.696502	−	1.20638i	0.0304268	−	0.0527008i
$525$	12.7051	−	15.5675i	0.554497	−	0.679420i
$526$	13.9124	−	24.0970i	0.606610	−	1.05068i
$527$	8.58534			0.373983
$528$	−6.28566	−	1.02020i	−0.273548	−	0.0443985i
$529$	9.28557	+	16.0831i	0.403720	+	0.699264i
$530$	2.68165	−	4.64476i	0.116484	−	0.201756i
$531$	−5.64880	−	1.88328i	−0.245137	−	0.0817273i
$532$	−1.88794	+	20.0985i	−0.0818527	+	0.871382i
$533$	−12.5203	+	21.6859i	−0.542316	+	0.939320i
$534$	6.58848	−	8.07279i	0.285111	−	0.349344i
$535$	10.8977			0.471151
$536$	6.29213	−	10.8983i	0.271779	−	0.470734i
$537$	−37.1792	−	6.03440i	−1.60440	−	0.260404i
$538$	0.110892			0.00478087
$539$	53.1189			2.28799
$540$	−6.93429	+	4.39094i	−0.298404	+	0.188956i
$541$	−14.3701	−	24.8898i	−0.617820	−	1.07010i	−0.989883	−	0.141888i	$-0.954683\pi$
$541$	−14.3701	−	24.8898i	−0.617820	−	1.07010i	0.372063	−	0.928208i	$-0.378651\pi$
$542$	−9.59436			−0.412113
$543$	−2.86590	−	7.55211i	−0.122988	−	0.324092i
$544$	−3.65387	−	6.32868i	−0.156658	−	0.271340i
$545$	3.19745	−	5.53815i	0.136964	−	0.237228i
$546$	−28.2683	+	34.6369i	−1.20977	+	1.48232i
$547$	6.24240			0.266906			0.133453	−	0.991055i	$-0.457393\pi$
$547$	6.24240			0.266906			0.133453	+	0.991055i	$0.457393\pi$
$548$	−1.20442	+	2.08612i	−0.0514503	+	0.0891145i
$549$	9.06733	+	3.02300i	0.386984	+	0.129018i
$550$	9.20972			0.392704
$551$	18.9262	+	13.4334i	0.806285	+	0.572284i
$552$	2.30473	−	2.82396i	0.0980960	−	0.120196i
$553$	27.7242			1.17895
$554$	−15.2771			−0.649062
$555$	3.15495	+	0.512066i	0.133920	+	0.0217360i
$556$	4.23509	+	7.33539i	0.179608	+	0.311090i
$557$	6.56478	+	11.3705i	0.278159	+	0.481785i	0.970927	−	0.239375i	$-0.0769426\pi$
$557$	6.56478	+	11.3705i	0.278159	+	0.481785i	−0.692769	+	0.721160i	$0.743609\pi$
$558$	−2.63716	+	2.33825i	−0.111640	+	0.0989859i
$559$	−47.3454			−2.00250
$560$	7.31525			0.309126
$561$	−16.5105	−	43.5077i	−0.697072	−	1.83689i
$562$	2.22648	+	3.85638i	0.0939185	+	0.162672i
$563$	−6.22302	−	10.7786i	−0.262269	−	0.454264i	0.704575	−	0.709629i	$-0.251137\pi$
$563$	−6.22302	−	10.7786i	−0.262269	−	0.454264i	−0.966845	+	0.255366i	$0.917804\pi$
$564$	−6.30329	+	7.72335i	−0.265416	+	0.325212i
$565$	1.06034	+	1.83657i	0.0446089	+	0.0772649i
$566$	2.89090	+	5.00718i	0.121514	+	0.210468i
$567$	38.3322	−	16.3689i	1.60980	−	0.687430i
$568$	−4.03312	+	6.98558i	−0.169226	+	0.293108i
$569$	−17.5284	+	30.3601i	−0.734830	+	1.27276i	0.219968	+	0.975507i	$0.429405\pi$
$569$	−17.5284	+	30.3601i	−0.734830	+	1.27276i	−0.954798	+	0.297255i	$0.903929\pi$
$570$	−3.00307	+	11.5411i	−0.125785	+	0.483402i
$571$	−3.38933	−	5.87049i	−0.141839	−	0.245672i	0.786350	−	0.617781i	$-0.211968\pi$
$571$	−3.38933	−	5.87049i	−0.141839	−	0.245672i	−0.928189	+	0.372109i	$0.878635\pi$
$572$	−20.4912			−0.856779
$573$	−6.21902	+	7.62010i	−0.259803	+	0.318334i
$574$	−20.8071			−0.868471
$575$	−2.63588	+	4.56547i	−0.109924	+	0.190393i
$576$	2.84600	+	0.948840i	0.118583	+	0.0395350i
$577$	−40.8352			−1.69999			−0.849997	−	0.526788i	$-0.823396\pi$
$577$	−40.8352			−1.69999			−0.849997	+	0.526788i	$0.823396\pi$
$578$	18.2015	−	31.5259i	0.757082	−	1.31131i
$579$	−16.8783	−	2.73945i	−0.701439	−	0.113848i
$580$	4.20518	−	7.28359i	0.174611	−	0.302435i
$581$	27.1288	+	46.9884i	1.12549	+	1.94941i
$582$	13.0765	−	16.0225i	0.542039	−	0.664154i
$583$	−12.4835			−0.517012
$584$	−7.45107	+	12.9056i	−0.308328	+	0.534039i
$585$	−19.7618	+	17.5219i	−0.817050	+	0.724440i
$586$	9.50767	−	16.4678i	0.392758	−	0.680277i
$587$	−6.10104	−	10.5673i	−0.251817	−	0.436159i	0.712209	−	0.701967i	$-0.247695\pi$
$587$	−6.10104	−	10.5673i	−0.251817	−	0.436159i	−0.964026	+	0.265808i	$0.914361\pi$
$588$	−24.7017	−	4.00923i	−1.01868	−	0.165338i
$589$	−0.478926	+	5.09852i	−0.0197338	+	0.210081i
$590$	1.56757	+	2.71510i	0.0645357	+	0.111779i
$591$	42.8805	+	6.95975i	1.76387	+	0.286286i
$592$	−0.584135	−	1.01175i	−0.0240078	−	0.0415827i
$593$	5.17093	+	8.95632i	0.212345	+	0.367792i	0.952448	−	0.304702i	$-0.0985567\pi$
$593$	5.17093	+	8.95632i	0.212345	+	0.367792i	−0.740103	+	0.672493i	$0.765223\pi$
$594$	16.9210	+	8.86757i	0.694276	+	0.363841i
$595$	26.7290	+	46.2959i	1.09578	+	1.89795i
$596$	4.81128	−	8.33338i	0.197078	−	0.341348i
$597$	−5.48954	−	14.4658i	−0.224672	−	0.592046i
$598$	5.86470	−	10.1580i	0.239826	−	0.415390i
$599$	−6.57091	+	11.3811i	−0.268480	+	0.465021i	−0.968470	−	0.249132i	$-0.919855\pi$
$599$	−6.57091	+	11.3811i	−0.268480	+	0.465021i	0.699989	+	0.714153i	$0.253188\pi$
$600$	−4.28276	−	0.695117i	−0.174843	−	0.0283780i
$601$	−4.17421	+	7.22994i	−0.170269	+	0.294915i	−0.938514	−	0.345241i	$-0.887797\pi$
$601$	−4.17421	+	7.22994i	−0.170269	+	0.294915i	0.768245	+	0.640156i	$0.221130\pi$
$602$	−19.6704	−	34.0701i	−0.801704	−	1.38859i
$603$	−28.2481	+	25.0463i	−1.15035	+	1.01996i
$604$	−11.4046	−	19.7534i	−0.464047	−	0.803753i
$605$	1.98770	+	3.44281i	0.0808117	+	0.139970i
$606$	−6.69417	−	17.6402i	−0.271932	−	0.716584i
$607$	2.44638	+	4.23725i	0.0992953	+	0.171985i	0.911393	−	0.411537i	$-0.135008\pi$
$607$	2.44638	+	4.23725i	0.0992953	+	0.171985i	−0.812098	+	0.583521i	$0.801674\pi$
$608$	3.96220	−	1.81686i	0.160688	−	0.0736833i
$609$	−27.0054	+	33.0894i	−1.09431	+	1.34085i
$610$	−2.51622	−	4.35823i	−0.101879	−	0.176459i
$611$	−16.0396	+	27.7813i	−0.648891	+	1.12391i
$612$	4.39399	+	21.4784i	0.177617	+	0.868211i
$613$	−5.76017	+	9.97691i	−0.232651	+	0.402964i	−0.958587	−	0.284798i	$-0.908073\pi$
$613$	−5.76017	+	9.97691i	−0.232651	+	0.402964i	0.725936	+	0.687762i	$0.241407\pi$
$614$	−24.5407			−0.990382
$615$	−12.1329	−	1.96924i	−0.489246	−	0.0794075i
$616$	−8.51338	−	14.7456i	−0.343014	−	0.594117i
$617$	10.4427	−	18.0872i	0.420406	−	0.728165i	−0.575573	−	0.817750i	$-0.695221\pi$
$617$	10.4427	−	18.0872i	0.420406	−	0.728165i	0.995979	+	0.0895856i	$0.0285543\pi$
$618$	13.3585	−	16.3680i	0.537358	−	0.658419i
$619$	22.7753	−	39.4479i	0.915415	−	1.58555i	0.109124	−	0.994028i	$-0.465196\pi$
$619$	22.7753	−	39.4479i	0.915415	−	1.58555i	0.806292	−	0.591518i	$-0.201471\pi$
$620$	1.85571			0.0745270
$621$	−9.23876	+	5.85018i	−0.370738	+	0.234759i
$622$	−1.73597	+	3.00679i	−0.0696061	+	0.120561i
$623$	27.8616			1.11625
$624$	9.52894	+	1.54660i	0.381463	+	0.0619136i
$625$	−6.19988			−0.247995
$626$	2.06042	+	3.56876i	0.0823511	+	0.142636i
$627$	26.7586	−	7.37792i	1.06864	−	0.294646i
$628$	2.18674	−	3.78754i	0.0872603	−	0.151139i
$629$	4.26870	−	7.39361i	0.170204	−	0.294803i
$630$	−20.8192	−	6.94100i	−0.829457	−	0.276536i
$631$	19.0978	+	33.0784i	0.760272	+	1.31683i	0.942710	+	0.333612i	$0.108268\pi$
$631$	19.0978	+	33.0784i	0.760272	+	1.31683i	−0.182439	+	0.983217i	$0.558399\pi$
$632$	−2.99319	−	5.18435i	−0.119063	−	0.206222i
$633$	−10.8130	−	1.75501i	−0.429777	−	0.0697554i
$634$	−10.8195	−	18.7399i	−0.429697	−	0.744257i
$635$	6.25115	+	10.8273i	0.248069	+	0.429669i
$636$	5.80514	+	0.942208i	0.230189	+	0.0373610i
$637$	−80.5272			−3.19060
$638$	−19.5757			−0.775010
$639$	18.1065	−	16.0541i	0.716280	−	0.635092i
$640$	−0.789777	−	1.36793i	−0.0312187	−	0.0540723i
$641$	17.7856	+	30.8056i	0.702491	+	1.21675i	0.967590	+	0.252528i	$0.0812620\pi$
$641$	17.7856	+	30.8056i	0.702491	+	1.21675i	−0.265099	+	0.964221i	$0.585405\pi$
$642$	4.23976	+	11.1724i	0.167330	+	0.440941i
$643$	8.68472			0.342492			0.171246	−	0.985228i	$-0.445221\pi$
$643$	8.68472			0.342492			0.171246	+	0.985228i	$0.445221\pi$
$644$	9.74632			0.384059
$645$	−8.24558	−	21.7284i	−0.324669	−	0.855555i
$646$	25.9757	+	18.4370i	1.02200	+	0.725392i
$647$	8.66501			0.340657			0.170328	−	0.985387i	$-0.445517\pi$
$647$	8.66501			0.340657			0.170328	+	0.985387i	$0.445517\pi$
$648$	−7.19941	−	5.40079i	−0.282819	−	0.212163i
$649$	3.64862	−	6.31959i	0.143221	−	0.248066i
$650$	−13.9617			−0.547624
$651$	−9.30217	−	1.50980i	−0.364581	−	0.0591736i
$652$	−3.18476	+	5.51617i	−0.124725	+	0.216030i
$653$	22.1970	+	38.4463i	0.868635	+	1.50452i	0.863392	+	0.504533i	$0.168335\pi$
$653$	22.1970	+	38.4463i	0.868635	+	1.50452i	0.00524262	+	0.999986i	$0.498331\pi$
$654$	6.92172	+	1.12344i	0.270661	+	0.0439298i
$655$	2.20033			0.0859738
$656$	2.24640	+	3.89087i	0.0877070	+	0.151913i
$657$	33.4511	−	29.6595i	1.30505	−	1.15713i
$658$	−26.6555			−1.03914
$659$	−9.04193			−0.352224			−0.176112	−	0.984370i	$-0.556352\pi$
$659$	−9.04193			−0.352224			−0.176112	+	0.984370i	$0.556352\pi$
$660$	−3.56871	−	9.40410i	−0.138912	−	0.366054i
$661$	−3.69025	+	6.39170i	−0.143534	+	0.248608i	−0.928825	−	0.370519i	$-0.879180\pi$
$661$	−3.69025	+	6.39170i	−0.143534	+	0.248608i	0.785291	+	0.619127i	$0.212513\pi$
$662$	−16.9608			−0.659200
$663$	25.0295	+	65.9567i	0.972066	+	2.56155i
$664$	5.85781	−	10.1460i	0.227327	−	0.393742i
$665$	−28.9845	+	13.2908i	−1.12397	+	0.515394i
$666$	0.702457	+	3.43369i	0.0272197	+	0.133053i
$667$	5.60269	−	9.70414i	0.216937	−	0.375746i
$668$	3.08570	+	5.34459i	0.119389	+	0.206788i
$669$	1.08010	+	2.84624i	0.0417592	+	0.110042i
$670$	19.8775			0.767936
$671$	−5.85668	+	10.1441i	−0.226095	+	0.391607i
$672$	2.84600	+	7.49965i	0.109787	+	0.289305i
$673$	10.3428	−	17.9142i	0.398685	−	0.690544i	−0.594879	−	0.803816i	$-0.702800\pi$
$673$	10.3428	−	17.9142i	0.398685	−	0.690544i	0.993564	+	0.113272i	$0.0361332\pi$
$674$	−11.6163	−	20.1200i	−0.447442	−	0.774993i
$675$	11.5292	+	6.04195i	0.443758	+	0.232555i
$676$	18.0642			0.694777
$677$	13.9362	−	24.1381i	0.535610	−	0.927704i	−0.463524	−	0.886085i	$-0.653415\pi$
$677$	13.9362	−	24.1381i	0.535610	−	0.927704i	0.999134	−	0.0416191i	$-0.0132516\pi$
$678$	−1.47033	+	1.80159i	−0.0564679	+	0.0691895i
$679$	55.2983			2.12216
$680$	5.77148	−	9.99650i	0.221326	−	0.383348i
$681$	14.0520	−	17.2178i	0.538476	−	0.659788i
$682$	−2.15964	−	3.74061i	−0.0826970	−	0.143235i
$683$	−22.0360			−0.843183			−0.421591	−	0.906786i	$-0.638528\pi$
$683$	−22.0360			−0.843183			−0.421591	+	0.906786i	$0.638528\pi$
$684$	−13.0003	+	1.41128i	−0.497080	+	0.0539616i
$685$	−3.80489			−0.145378
$686$	−17.2470	−	29.8727i	−0.658494	−	1.14055i
$687$	0.254887	+	0.671666i	0.00972453	+	0.0256257i
$688$	−4.24734	+	7.35661i	−0.161928	+	0.280468i
$689$	18.9247			0.720973
$690$	5.68322	+	0.922420i	0.216357	+	0.0351159i
$691$	11.6097	−	20.1087i	0.441656	−	0.764970i	−0.556157	−	0.831077i	$-0.687725\pi$
$691$	11.6097	−	20.1087i	0.441656	−	0.764970i	0.997813	+	0.0661073i	$0.0210580\pi$
$692$	−7.51338			−0.285616
$693$	10.2378	+	50.0438i	0.388903	+	1.90101i
$694$	8.20150	+	14.2054i	0.311325	+	0.539230i
$695$	−6.68955	+	11.5866i	−0.253749	+	0.439506i
$696$	9.10322	+	1.47751i	0.345057	+	0.0560047i
$697$	−16.4161	+	28.4335i	−0.621803	+	1.07699i
$698$	3.85437			0.145890
$699$	14.0658	−	17.2347i	0.532017	−	0.651875i
$700$	−5.80062	−	10.0470i	−0.219243	−	0.379740i
$701$	−0.439487	+	0.761215i	−0.0165992	+	0.0287507i	−0.874206	−	0.485556i	$-0.838617\pi$
$701$	−0.439487	+	0.761215i	−0.0165992	+	0.0287507i	0.857606	+	0.514306i	$0.171951\pi$
$702$	−25.6519	−	13.4431i	−0.968167	−	0.507376i
$703$	4.15267	+	2.94747i	0.156621	+	0.111166i
$704$	−1.83826	+	3.18396i	−0.0692820	+	0.120000i
$705$	−15.5432	−	2.52276i	−0.585392	−	0.0950125i
$706$	−8.84630			−0.332935
$707$	25.2245	−	43.6901i	0.948664	−	1.64313i
$708$	−2.17368	+	2.66339i	−0.0816920	+	0.100096i
$709$	−11.1131			−0.417363			−0.208682	−	0.977984i	$-0.566917\pi$
$709$	−11.1131			−0.417363			−0.208682	+	0.977984i	$0.566917\pi$
$710$	−12.7411			−0.478164
$711$	3.59948	+	17.5947i	0.134991	+	0.659853i
$712$	−3.00802	−	5.21004i	−0.112730	−	0.195254i
$713$	2.47241			0.0925925
$714$	−37.0640	+	45.4142i	−1.38709	+	1.69958i
$715$	−16.1835	−	28.0306i	−0.605227	−	1.04828i
$716$	−10.8732	+	18.8329i	−0.406349	+	0.703817i
$717$	−7.70715	−	20.3096i	−0.287829	−	0.758474i
$718$	−22.0300			−0.822152
$719$	−2.95842	+	5.12414i	−0.110331	+	0.191098i	−0.915904	−	0.401398i	$-0.868524\pi$
$719$	−2.95842	+	5.12414i	−0.110331	+	0.191098i	0.805573	+	0.592497i	$0.201858\pi$
$720$	0.949754	+	4.64251i	0.0353952	+	0.173016i
$721$	56.4909			2.10383
$722$	−12.3981	+	14.3975i	−0.461408	+	0.535820i
$723$	6.92344	+	1.12371i	0.257485	+	0.0417914i
$724$	−4.66361			−0.173322
$725$	−13.3380			−0.495360
$726$	−2.75627	+	3.37723i	−0.102295	+	0.125341i
$727$	−20.0288	−	34.6909i	−0.742828	−	1.28662i	−0.951203	−	0.308566i	$-0.900151\pi$
$727$	−20.0288	−	34.6909i	−0.742828	−	1.28662i	0.208375	−	0.978049i	$-0.433183\pi$
$728$	12.9061	+	22.3540i	0.478332	+	0.828495i
$729$	15.3650	+	22.2017i	0.569074	+	0.822286i
$730$	−23.5387			−0.871208
$731$	−62.0769			−2.29600
$732$	3.48915	−	4.27522i	0.128963	−	0.158017i
$733$	17.5793	+	30.4482i	0.649306	+	1.12463i	0.983289	+	0.182052i	$0.0582738\pi$
$733$	17.5793	+	30.4482i	0.649306	+	1.12463i	−0.333983	+	0.942579i	$0.608393\pi$
$734$	6.18264	+	10.7087i	0.228205	+	0.395264i
$735$	−14.0245	−	36.9567i	−0.517300	−	1.36317i
$736$	−1.05224	−	1.82254i	−0.0387862	−	0.0671796i
$737$	−23.1331	−	40.0678i	−0.852120	−	1.47592i
$738$	−2.70142	−	13.2049i	−0.0994408	−	0.486078i
$739$	6.34630	−	10.9921i	0.233453	−	0.404352i	−0.725369	−	0.688360i	$-0.758331\pi$
$739$	6.34630	−	10.9921i	0.233453	−	0.404352i	0.958822	+	0.284008i	$0.0916643\pi$
$740$	0.922673	−	1.59812i	0.0339181	−	0.0587479i
$741$	−40.5655	+	11.1848i	−1.49021	+	0.410883i
$742$	7.86255	+	13.6183i	0.288643	+	0.499945i
$743$	−5.78991			−0.212411			−0.106206	−	0.994344i	$-0.533870\pi$
$743$	−5.78991			−0.212411			−0.106206	+	0.994344i	$0.533870\pi$
$744$	0.721962	+	1.90248i	0.0264684	+	0.0697484i
$745$	15.1993			0.556861
$746$	−3.36121	+	5.82178i	−0.123062	+	0.213150i
$747$	−26.2983	+	23.3174i	−0.962203	+	0.853140i
$748$	−26.8670			−0.982356
$749$	−15.9760	+	27.6712i	−0.583749	+	1.01108i
$750$	−7.28493	−	19.1969i	−0.266008	−	0.700973i
$751$	1.63799	−	2.83708i	0.0597712	−	0.103527i	−0.834591	−	0.550869i	$-0.814296\pi$
$751$	1.63799	−	2.83708i	0.0597712	−	0.103527i	0.894363	+	0.447343i	$0.147630\pi$
$752$	2.87781	+	4.98452i	0.104943	+	0.181767i
$753$	11.7942	+	31.0796i	0.429805	+	1.13260i
$754$	29.6764			1.08075
$755$	18.0142	−	31.2015i	0.655604	−	1.13554i
$756$	−0.983736	−	24.0444i	−0.0357781	−	0.874486i
$757$	−25.2937	+	43.8099i	−0.919314	+	1.59230i	−0.118854	+	0.992912i	$0.537922\pi$
$757$	−25.2937	+	43.8099i	−0.919314	+	1.59230i	−0.800460	+	0.599386i	$0.795411\pi$
$758$	13.0725	+	22.6423i	0.474816	+	0.822405i
$759$	−4.75469	−	12.5294i	−0.172584	−	0.454787i
$760$	5.61459	+	3.98512i	0.203663	+	0.144555i
$761$	−17.8934	−	30.9923i	−0.648636	−	1.12347i	−0.983449	−	0.181186i	$-0.942006\pi$
$761$	−17.8934	−	30.9923i	−0.648636	−	1.12347i	0.334813	−	0.942285i	$-0.391327\pi$
$762$	−8.66823	+	10.6211i	−0.314017	+	0.384761i
$763$	9.37486	+	16.2377i	0.339393	+	0.587845i
$764$	2.83934	+	4.91788i	0.102724	+	0.177923i
$765$	−25.9107	+	22.9738i	−0.936803	+	0.830619i
$766$	6.86972	+	11.8987i	0.248213	+	0.429917i
$767$	−5.53123	+	9.58037i	−0.199721	+	0.345927i
$768$	1.09515	−	1.34188i	0.0395179	−	0.0484209i
$769$	18.6819	−	32.3580i	0.673687	−	1.16686i	−0.303163	−	0.952939i	$-0.598043\pi$
$769$	18.6819	−	32.3580i	0.673687	−	1.16686i	0.976851	−	0.213922i	$-0.0686239\pi$
$770$	13.4473	−	23.2915i	0.484608	−	0.839366i
$771$	−1.71850	+	2.10566i	−0.0618903	+	0.0758335i
$772$	−4.93611	+	8.54959i	−0.177654	+	0.307706i
$773$	−9.33015	−	16.1603i	−0.335582	−	0.581245i	0.648014	−	0.761628i	$-0.275600\pi$
$773$	−9.33015	−	16.1603i	−0.335582	−	0.581245i	−0.983596	+	0.180383i	$0.942266\pi$
$774$	19.0682	−	16.9069i	0.685391	−	0.607705i
$775$	−1.47148	−	2.54868i	−0.0528571	−	0.0915512i
$776$	−5.97017	−	10.3406i	−0.214317	−	0.371208i
$777$	−5.92534	+	7.26025i	−0.212570	+	0.260460i
$778$	15.2002	+	26.3276i	0.544955	+	0.943889i
$779$	−15.9698	−	11.3350i	−0.572178	−	0.406120i
$780$	5.41008	+	14.2564i	0.193712	+	0.510462i
$781$	14.8279	+	25.6826i	0.530583	+	0.918996i
$782$	7.68951	−	13.3186i	0.274976	−	0.476273i
$783$	−24.5058	−	12.8425i	−0.875767	−	0.458952i
$784$	−7.22408	+	12.5125i	−0.258003	+	0.446874i
$785$	6.90814			0.246562
$786$	0.856036	+	2.25579i	0.0305338	+	0.0804614i
$787$	15.7775	+	27.3274i	0.562406	+	0.974116i	0.997286	+	0.0736276i	$0.0234576\pi$
$787$	15.7775	+	27.3274i	0.562406	+	0.974116i	−0.434880	+	0.900489i	$0.643209\pi$
$788$	12.5405	−	21.7208i	0.446737	−	0.773771i
$789$	17.0990	+	45.0587i	0.608742	+	1.60413i
$790$	4.72790	−	8.18896i	0.168211	−	0.291350i
$791$	−6.21780			−0.221079
$792$	8.25275	−	7.31733i	0.293249	−	0.260010i
$793$	8.87861	−	15.3782i	0.315289	−	0.546096i
$794$	18.3201			0.650157
$795$	3.29589	+	8.68518i	0.116893	+	0.308032i
$796$	−8.93298			−0.316621
$797$	−16.9685	−	29.3903i	−0.601055	−	1.04106i	−0.992662	−	0.120926i	$-0.961414\pi$
$797$	−16.9685	−	29.3903i	−0.601055	−	1.04106i	0.391606	−	0.920133i	$-0.371920\pi$
$798$	−24.9022	−	24.5444i	−0.881529	−	0.868861i
$799$	−21.0303	+	36.4255i	−0.743998	+	1.28864i
$800$	−1.25250	+	2.16940i	−0.0442827	+	0.0766999i
$801$	3.61732	+	17.6819i	0.127812	+	0.624759i
$802$	17.3023	+	29.9685i	0.610965	+	1.05822i
$803$	27.3940	+	47.4478i	0.966714	+	1.67440i
$804$	7.73334	+	20.3786i	0.272734	+	0.718697i
$805$	7.69742	+	13.3323i	0.271298	+	0.469903i
$806$	3.27397	+	5.67069i	0.115321	+	0.199741i
$807$	−0.121443	+	0.148803i	−0.00427500	+	0.00523812i
$808$	−10.8932			−0.383223
$809$	41.0728			1.44404			0.722021	−	0.691871i	$-0.243213\pi$
$809$	41.0728			1.44404			0.722021	+	0.691871i	$0.243213\pi$
$810$	1.70200	−	14.1137i	0.0598022	−	0.495906i
$811$	−21.7934	−	37.7472i	−0.765269	−	1.32549i	−0.940104	−	0.340887i	$-0.889273\pi$
$811$	−21.7934	−	37.7472i	−0.765269	−	1.32549i	0.174835	−	0.984598i	$-0.444061\pi$
$812$	12.3295	+	21.3553i	0.432681	+	0.749425i
$813$	10.5073	−	12.8745i	0.368507	−	0.451527i
$814$	−4.29517			−0.150546
$815$	−10.0610			−0.352422
$816$	12.4939	+	2.02783i	0.437373	+	0.0709882i
$817$	3.46291	−	36.8652i	0.121152	−	1.28975i
$818$	5.01138			0.175219
$819$	−15.5204	−	75.8653i	−0.542325	−	2.65095i
$820$	−3.54830	+	6.14584i	−0.123912	+	0.214622i
$821$	−22.2616			−0.776935			−0.388467	−	0.921462i	$-0.626995\pi$
$821$	−22.2616			−0.776935			−0.388467	+	0.921462i	$0.626995\pi$
$822$	−1.48029	−	3.90080i	−0.0516311	−	0.136056i
$823$	0.707725	−	1.22581i	0.0246697	−	0.0427292i	−0.853427	−	0.521212i	$-0.825480\pi$
$823$	0.707725	−	1.22581i	0.0246697	−	0.0427292i	0.878097	+	0.478483i	$0.158813\pi$
$824$	−6.09893	−	10.5637i	−0.212466	−	0.368002i
$825$	−10.0860	+	12.3583i	−0.351151	+	0.430262i
$826$	−9.19213			−0.319835
$827$	−27.8318	−	48.2061i	−0.967807	−	1.67629i	−0.701876	−	0.712300i	$-0.747654\pi$
$827$	−27.8318	−	48.2061i	−0.967807	−	1.67629i	−0.265932	−	0.963992i	$-0.585680\pi$
$828$	1.26538	+	6.18535i	0.0439751	+	0.214956i
$829$	−35.2830			−1.22543			−0.612714	−	0.790305i	$-0.709922\pi$
$829$	−35.2830			−1.22543			−0.612714	+	0.790305i	$0.709922\pi$
$830$	18.5054			0.642333
$831$	16.7308	−	20.5000i	0.580384	−	0.711138i
$832$	2.78676	−	4.82682i	0.0966136	−	0.167340i
$833$	−105.583			−3.65825
$834$	−14.4813	−	2.35040i	−0.501446	−	0.0813875i
$835$	−4.87403	+	8.44206i	−0.168673	+	0.292150i
$836$	1.49875	−	15.9553i	0.0518355	−	0.551827i
$837$	−0.249551	−	6.09949i	−0.00862573	−	0.210829i
$838$	14.5553	−	25.2106i	0.502805	−	0.870885i
$839$	−15.4460	−	26.7532i	−0.533255	−	0.923624i	−0.999246	−	0.0388347i	$-0.987635\pi$
$839$	−15.4460	−	26.7532i	−0.533255	−	0.923624i	0.465991	−	0.884789i	$-0.345698\pi$
$840$	−8.01132	+	9.81619i	−0.276417	+	0.338691i
$841$	−0.649476			−0.0223957
$842$	−1.71985	+	2.97887i	−0.0592700	+	0.102659i
$843$	−7.61314	−	1.23566i	−0.262210	−	0.0425583i
$844$	−3.16229	+	5.47724i	−0.108850	+	0.188534i
$845$	14.2667	+	24.7106i	0.490789	+	0.850072i
$846$	−3.46074	−	16.9165i	−0.118983	−	0.581601i
$847$	−11.6558			−0.400498
$848$	1.69773	−	2.94055i	0.0583003	−	0.100979i
$849$	−9.88501	−	1.60439i	−0.339253	−	0.0550627i
$850$	−18.3059			−0.627889
$851$	1.22930	−	2.12922i	0.0421400	−	0.0729886i
$852$	−4.95691	−	13.0622i	−0.169821	−	0.447505i
$853$	17.4963	+	30.3045i	0.599062	+	1.03761i	0.992960	+	0.118452i	$0.0377931\pi$
$853$	17.4963	+	30.3045i	0.599062	+	1.03761i	−0.393898	+	0.919154i	$0.628874\pi$
$854$	14.7550			0.504906
$855$	−12.1979	−	16.6690i	−0.417159	−	0.570067i
$856$	6.89925			0.235812
$857$	−6.27992	−	10.8771i	−0.214518	−	0.371556i	0.738605	−	0.674138i	$-0.235485\pi$
$857$	−6.27992	−	10.8771i	−0.214518	−	0.371556i	−0.953123	+	0.302582i	$0.902151\pi$
$858$	22.4410	−	27.4967i	0.766122	−	0.938721i
$859$	−5.41813	+	9.38447i	−0.184864	+	0.320194i	−0.943531	−	0.331285i	$-0.892518\pi$
$859$	−5.41813	+	9.38447i	−0.184864	+	0.320194i	0.758667	+	0.651479i	$0.225851\pi$
$860$	−13.4178			−0.457544
$861$	22.7869	−	27.9206i	0.776577	−	0.951531i
$862$	4.96062	−	8.59205i	0.168959	−	0.292646i
$863$	53.4590			1.81977			0.909883	−	0.414866i	$-0.136171\pi$
$863$	53.4590			1.81977			0.909883	+	0.414866i	$0.136171\pi$
$864$	−4.39003	+	2.77986i	−0.149352	+	0.0945728i
$865$	−5.93390	−	10.2778i	−0.201759	−	0.349456i
$866$	−0.263521	+	0.456432i	−0.00895482	+	0.0155102i
$867$	22.3705	+	58.9499i	0.759744	+	2.00204i
$868$	−2.72044	+	4.71195i	−0.0923379	+	0.159934i
$869$	−22.0090			−0.746604
$870$	5.16838	+	13.6195i	0.175225	+	0.461744i
$871$	35.0694	+	60.7419i	1.18828	+	2.05816i
$872$	2.02428	−	3.50615i	0.0685506	−	0.118733i
$873$	7.17949	+	35.0942i	0.242989	+	1.18776i
$874$	7.48049	+	5.30948i	0.253031	+	0.179596i
$875$	27.4505	−	47.5457i	0.927997	−	1.60734i
$876$	−9.15774	−	24.1321i	−0.309411	−	0.815348i
$877$	2.18593			0.0738137			0.0369068	−	0.999319i	$-0.488250\pi$
$877$	2.18593			0.0738137			0.0369068	+	0.999319i	$0.488250\pi$
$878$	−8.17519	+	14.1598i	−0.275899	+	0.477871i
$879$	11.6854	+	30.7929i	0.394139	+	1.03862i
$880$	−5.80726			−0.195763
$881$	29.8678			1.00627			0.503135	−	0.864208i	$-0.332180\pi$
$881$	29.8678			1.00627			0.503135	+	0.864208i	$0.332180\pi$
$882$	32.4320	−	28.7560i	1.09204	−	0.968264i
$883$	3.18840	+	5.52247i	0.107298	+	0.185846i	0.914675	−	0.404191i	$-0.132447\pi$
$883$	3.18840	+	5.52247i	0.107298	+	0.185846i	−0.807377	+	0.590036i	$0.799113\pi$
$884$	40.7299			1.36989
$885$	−5.36007	−	0.869970i	−0.180177	−	0.0292437i
$886$	2.89318	+	5.01113i	0.0971982	+	0.168352i
$887$	12.5079	−	21.6644i	0.419976	−	0.727419i	−0.575961	−	0.817477i	$-0.695372\pi$
$887$	12.5079	−	21.6644i	0.419976	−	0.727419i	0.995937	+	0.0900580i	$0.0287053\pi$
$888$	1.99737	+	0.324184i	0.0670272	+	0.0108789i
$889$	−36.6564			−1.22942
$890$	4.75133	−	8.22954i	0.159265	−	0.275855i
$891$	−30.4303	+	12.9946i	−1.01945	+	0.435334i
$892$	1.75762			0.0588496
$893$	−20.4586	−	14.5211i	−0.684621	−	0.485929i
$894$	5.91330	+	15.5825i	0.197770	+	0.521156i
$895$	−34.3495			−1.14818
$896$	4.63122			0.154718
$897$	7.20801	+	18.9942i	0.240669	+	0.634199i
$898$	−5.20902	−	9.02229i	−0.173827	−	0.301078i
$899$	3.12770	+	5.41734i	0.104315	+	0.180678i
$900$	5.62304	−	4.98569i	0.187435	−	0.166190i
$901$	24.8131			0.826644
$902$	16.5178			0.549984
$903$	67.2600	+	10.9167i	2.23827	+	0.363285i
$904$	0.671292	+	1.16271i	0.0223268	+	0.0386712i
$905$	−3.68321	−	6.37951i	−0.122434	−	0.212062i
$906$	38.9964	+	6.32935i	1.29557	+	0.210279i
$907$	6.06572	+	10.5061i	0.201409	+	0.348851i	0.948983	−	0.315328i	$-0.102115\pi$
$907$	6.06572	+	10.5061i	0.201409	+	0.348851i	−0.747574	+	0.664179i	$0.768781\pi$
$908$	−6.41556	−	11.1121i	−0.212908	−	0.368767i
$909$	31.0021	+	10.3359i	1.02828	+	0.342822i
$910$	−20.3859	+	35.3094i	−0.675785	+	1.17049i
$911$	−5.82232	+	10.0846i	−0.192902	+	0.334116i	−0.946211	−	0.323551i	$-0.895123\pi$
$911$	−5.82232	+	10.0846i	−0.192902	+	0.334116i	0.753309	+	0.657667i	$0.228457\pi$
$912$	−1.90121	+	7.30653i	−0.0629555	+	0.241943i
$913$	−21.5363	−	37.3020i	−0.712749	−	1.23452i
$914$	−20.6298			−0.682373
$915$	8.60386	+	1.39646i	0.284435	+	0.0461655i
$916$	0.414770			0.0137044
$917$	−3.22565	+	5.58699i	−0.106520	+	0.184499i
$918$	−33.6335	−	17.6259i	−1.11007	−	0.581741i
$919$	−49.1168			−1.62021			−0.810107	−	0.586282i	$-0.800591\pi$
$919$	−49.1168			−1.62021			−0.810107	+	0.586282i	$0.800591\pi$
$920$	1.66207	−	2.87880i	0.0547969	−	0.0949111i
$921$	26.8758	−	32.9307i	0.885589	−	1.08510i
$922$	−7.65320	+	13.2557i	−0.252045	+	0.436554i
$923$	−22.4787	−	38.9343i	−0.739896	−	1.28154i
$924$	29.1103	+	4.72477i	0.957657	+	0.155433i
$925$	−2.92653			−0.0962237
$926$	−4.73547	+	8.20208i	−0.155617	+	0.269537i
$927$	7.33432	+	35.8510i	0.240891	+	1.17750i
$928$	2.66226	−	4.61117i	0.0873930	−	0.151369i
$929$	−19.3012	−	33.4307i	−0.633253	−	1.09683i	−0.986882	−	0.161441i	$-0.948386\pi$
$929$	−19.3012	−	33.4307i	−0.633253	−	1.09683i	0.353630	−	0.935386i	$-0.384947\pi$
$930$	−2.03228	+	2.49013i	−0.0666412	+	0.0816547i
$931$	5.88988	−	62.7020i	0.193033	−	2.05498i
$932$	−6.42184	−	11.1229i	−0.210354	−	0.364344i
$933$	−2.13360	−	5.62236i	−0.0698508	−	0.184068i
$934$	−7.54518	−	13.0686i	−0.246886	−	0.427619i
$935$	−21.2190	−	36.7523i	−0.693934	−	1.20193i
$936$	−12.5110	+	11.0929i	−0.408935	+	0.362583i
$937$	14.3272	+	24.8154i	0.468049	+	0.810685i	0.999333	−	0.0365089i	$-0.0116237\pi$
$937$	14.3272	+	24.8154i	0.468049	+	0.810685i	−0.531284	+	0.847194i	$0.678290\pi$
$938$	−29.1402	+	50.4723i	−0.951462	+	1.64798i
$939$	−7.04532	−	1.14350i	−0.229915	−	0.0373166i
$940$	−4.54566	+	7.87331i	−0.148263	+	0.256799i
$941$	−30.1051	+	52.1435i	−0.981398	+	1.69983i	−0.324434	+	0.945908i	$0.605174\pi$
$941$	−30.1051	+	52.1435i	−0.981398	+	1.69983i	−0.656963	+	0.753922i	$0.728159\pi$
$942$	2.68761	+	7.08227i	0.0875671	+	0.230753i
$943$	−4.72751	+	8.18828i	−0.153949	+	0.266647i
$944$	0.992410	+	1.71891i	0.0323002	+	0.0559456i
$945$	32.1142	−	20.3354i	1.04467	−	0.661510i
$946$	15.6154	+	27.0467i	0.507702	+	0.879365i
$947$	11.3315	+	19.6267i	0.368223	+	0.637781i	0.989288	−	0.145979i	$-0.0466330\pi$
$947$	11.3315	+	19.6267i	0.368223	+	0.637781i	−0.621065	+	0.783759i	$0.713300\pi$
$948$	10.2348	+	1.66116i	0.332410	+	0.0539520i
$949$	−41.5287	−	71.9299i	−1.34808	−	2.33494i
$950$	1.02118	−	10.8712i	0.0331315	−	0.352709i
$951$	36.9957	+	6.00462i	1.19967	+	0.194713i
$952$	16.9218	+	29.3095i	0.548440	+	0.949926i
$953$	0.368894	−	0.638943i	0.0119496	−	0.0206974i	−0.859989	−	0.510313i	$-0.829530\pi$
$953$	0.368894	−	0.638943i	0.0119496	−	0.0206974i	0.871938	+	0.489616i	$0.162863\pi$
$954$	−7.62185	+	6.75793i	−0.246766	+	0.218796i
$955$	−4.48489	+	7.76806i	−0.145128	+	0.251368i
$956$	−12.5416			−0.405626
$957$	21.4384	−	26.2682i	0.693005	−	0.849131i
$958$	13.8928	+	24.0631i	0.448857	+	0.777443i
$959$	5.57793	−	9.66126i	0.180121	−	0.311978i
$960$	2.70053	+	0.438312i	0.0871592	+	0.0141464i
$961$	14.8099	−	25.6515i	0.477738	−	0.827467i
$962$	6.51139			0.209935
$963$	−19.6353	−	6.54629i	−0.632738	−	0.210951i
$964$	2.02478	−	3.50702i	0.0652137	−	0.112953i
$965$	−15.5937			−0.501979
$966$	−10.6737	+	13.0784i	−0.343421	+	0.420790i
$967$	43.0984			1.38595			0.692975	−	0.720962i	$-0.256300\pi$
$967$	43.0984			1.38595			0.692975	+	0.720962i	$0.256300\pi$
$968$	1.25840	+	2.17961i	0.0404464	+	0.0700552i
$969$	−53.1875	+	14.6649i	−1.70863	+	0.471105i
$970$	9.43021	−	16.3336i	0.302786	−	0.524441i
$971$	−15.9702	+	27.6611i	−0.512507	+	0.887687i	0.487388	+	0.873185i	$0.337950\pi$
$971$	−15.9702	+	27.6611i	−0.512507	+	0.887687i	−0.999895	+	0.0145021i	$0.995384\pi$
$972$	15.1317	−	3.74604i	0.485348	−	0.120154i
$973$	−19.6136	−	33.9718i	−0.628783	−	1.08908i
$974$	13.0004	+	22.5174i	0.416560	+	0.721503i
$975$	15.2902	−	18.7350i	0.489680	−	0.599999i
$976$	−1.59300	−	2.75915i	−0.0509906	−	0.0883183i
$977$	−2.30771	−	3.99708i	−0.0738303	−	0.127878i	0.826747	−	0.562574i	$-0.190189\pi$
$977$	−2.30771	−	3.99708i	−0.0738303	−	0.127878i	−0.900577	+	0.434697i	$0.856856\pi$
$978$	−3.91423	−	10.3146i	−0.125163	−	0.329825i
$979$	−22.1181			−0.706896
$980$	−22.8216			−0.729011
$981$	−9.08786	+	8.05778i	−0.290153	+	0.257265i
$982$	−16.4765	−	28.5381i	−0.525785	−	0.910686i
$983$	−12.7271	−	22.0440i	−0.405932	−	0.703094i	0.588498	−	0.808499i	$-0.299720\pi$
$983$	−12.7271	−	22.0440i	−0.405932	−	0.703094i	−0.994429	+	0.105405i	$0.966386\pi$
$984$	−7.68123	−	1.24671i	−0.244869	−	0.0397436i
$985$	39.6168			1.26230
$986$	38.9102			1.23915
$987$	29.1919	−	35.7685i	0.929188	−	1.13852i
$988$	−2.27208	+	24.1880i	−0.0722845	+	0.769522i
$989$	−17.8769			−0.568454
$990$	16.5274	+	5.51016i	0.525277	+	0.175124i
$991$	2.51258	−	4.35191i	0.0798147	−	0.138243i	−0.823355	−	0.567526i	$-0.807900\pi$
$991$	2.51258	−	4.35191i	0.0798147	−	0.138243i	0.903170	+	0.429283i	$0.141234\pi$
$992$	1.17483			0.0373009
$993$	18.5747	−	22.7593i	0.589449	−	0.722246i
$994$	18.6783	−	32.3517i	0.592439	−	1.02613i
$995$	−7.05506	−	12.2197i	−0.223661	−	0.387392i
$996$	7.19954	+	18.9719i	0.228126	+	0.601148i
$997$	−51.3469			−1.62617			−0.813086	−	0.582143i	$-0.802214\pi$
$997$	−51.3469			−1.62617			−0.813086	+	0.582143i	$0.802214\pi$
$998$	2.04254	+	3.53779i	0.0646556	+	0.111987i
$999$	−5.37690	−	2.81781i	−0.170118	−	0.0891515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.h.g.277.1	yes	18
3.2	odd	2		1026.2.h.g.505.7		18
9.4	even	3		342.2.f.g.49.7	yes	18
9.5	odd	6		1026.2.f.g.847.3		18
19.7	even	3		342.2.f.g.7.7	✓	18
57.26	odd	6		1026.2.f.g.235.3		18
171.121	even	3	inner	342.2.h.g.121.1	yes	18
171.140	odd	6		1026.2.h.g.577.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.7	✓	18	19.7	even	3
342.2.f.g.49.7	yes	18	9.4	even	3
342.2.h.g.121.1	yes	18	171.121	even	3	inner
342.2.h.g.277.1	yes	18	1.1	even	1	trivial
1026.2.f.g.235.3		18	57.26	odd	6
1026.2.f.g.847.3		18	9.5	odd	6
1026.2.h.g.505.7		18	3.2	odd	2
1026.2.h.g.577.7		18	171.140	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.70968 - 0.277491i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.57955 q^{5} +(-0.614525 - 1.61937i) q^{6} +(2.31561 - 4.01075i) q^{7} -1.00000 q^{8} +(2.84600 + 0.948840i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.70968 - 0.277491i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.57955 q^{5} +(-0.614525 - 1.61937i) q^{6} +(2.31561 - 4.01075i) q^{7} -1.00000 q^{8} +(2.84600 + 0.948840i) q^{9} +(-0.789777 - 1.36793i) q^{10} +(-1.83826 + 3.18396i) q^{11} +(1.09515 - 1.34188i) q^{12} +(2.78676 - 4.82682i) q^{13} +4.63122 q^{14} +(2.70053 + 0.438312i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.65387 - 6.32868i) q^{17} +(0.601280 + 2.93913i) q^{18} +(3.55454 + 2.52294i) q^{19} +(0.789777 - 1.36793i) q^{20} +(-5.07189 + 6.21453i) q^{21} -3.67652 q^{22} +(1.05224 - 1.82254i) q^{23} +(1.70968 + 0.277491i) q^{24} -2.50501 q^{25} +5.57353 q^{26} +(-4.60245 - 2.41195i) q^{27} +(2.31561 + 4.01075i) q^{28} +5.32452 q^{29} +(0.970675 + 2.55788i) q^{30} +(0.587415 + 1.01743i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.02635 - 4.93344i) q^{33} +7.30773 q^{34} +(-3.65763 + 6.33520i) q^{35} +(-2.24472 + 1.99029i) q^{36} +1.16827 q^{37} +(-0.407656 + 4.33979i) q^{38} +(-6.10386 + 7.47900i) q^{39} +1.57955 q^{40} -4.49279 q^{41} +(-7.91789 - 1.28512i) q^{42} +(-4.24734 - 7.35661i) q^{43} +(-1.83826 - 3.18396i) q^{44} +(-4.49541 - 1.49874i) q^{45} +2.10449 q^{46} -5.75562 q^{47} +(0.614525 + 1.61937i) q^{48} +(-7.22408 - 12.5125i) q^{49} +(-1.25250 - 2.16940i) q^{50} +(-8.00309 + 9.80610i) q^{51} +(2.78676 + 4.82682i) q^{52} +(1.69773 + 2.94055i) q^{53} +(-0.212414 - 5.19181i) q^{54} +(2.90363 - 5.02923i) q^{55} +(-2.31561 + 4.01075i) q^{56} +(-5.37703 - 5.29976i) q^{57} +(2.66226 + 4.61117i) q^{58} -1.98482 q^{59} +(-1.72985 + 2.11957i) q^{60} +3.18599 q^{61} +(-0.587415 + 1.01743i) q^{62} +(10.3958 - 9.21745i) q^{63} +1.00000 q^{64} +(-4.40184 + 7.62422i) q^{65} +(6.28566 + 1.02020i) q^{66} +(-6.29213 + 10.8983i) q^{67} +(3.65387 + 6.32868i) q^{68} +(-2.30473 + 2.82396i) q^{69} -7.31525 q^{70} +(4.03312 - 6.98558i) q^{71} +(-2.84600 - 0.948840i) q^{72} +(7.45107 - 12.9056i) q^{73} +(0.584135 + 1.01175i) q^{74} +(4.28276 + 0.695117i) q^{75} +(-3.96220 + 1.81686i) q^{76} +(8.51338 + 14.7456i) q^{77} +(-9.52894 - 1.54660i) q^{78} +(2.99319 + 5.18435i) q^{79} +(0.789777 + 1.36793i) q^{80} +(7.19941 + 5.40079i) q^{81} +(-2.24640 - 3.89087i) q^{82} +(-5.85781 + 10.1460i) q^{83} +(-2.84600 - 7.49965i) q^{84} +(-5.77148 + 9.99650i) q^{85} +(4.24734 - 7.35661i) q^{86} +(-9.10322 - 1.47751i) q^{87} +(1.83826 - 3.18396i) q^{88} +(3.00802 + 5.21004i) q^{89} +(-0.949754 - 4.64251i) q^{90} +(-12.9061 - 22.3540i) q^{91} +(1.05224 + 1.82254i) q^{92} +(-0.721962 - 1.90248i) q^{93} +(-2.87781 - 4.98452i) q^{94} +(-5.61459 - 3.98512i) q^{95} +(-1.09515 + 1.34188i) q^{96} +(5.97017 + 10.3406i) q^{97} +(7.22408 - 12.5125i) q^{98} +(-8.25275 + 7.31733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) \) 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	\( 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} + q^{13} + 10 q^{14} - 3 q^{15} - 9 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 19 q^{21} + 2 q^{22} - 2 q^{23} + 18 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} + 18 q^{29} + 4 q^{31} + 9 q^{32} - 23 q^{33} - 10 q^{34} + 6 q^{35} - 8 q^{36} + 20 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{41} - 23 q^{42} + 7 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} - 38 q^{47} + 6 q^{49} + 9 q^{50} + 4 q^{51} + q^{52} - 10 q^{53} - 18 q^{54} + 6 q^{55} - 5 q^{56} - 33 q^{57} + 9 q^{58} + 10 q^{59} + 3 q^{60} - 36 q^{61} - 4 q^{62} + 12 q^{63} + 18 q^{64} - 45 q^{65} - 7 q^{66} + 22 q^{67} - 5 q^{68} - 26 q^{69} + 12 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} + 10 q^{74} - 6 q^{76} - 2 q^{77} + 23 q^{78} + 2 q^{79} + 4 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} - 7 q^{86} + 3 q^{87} - q^{88} + q^{89} + 60 q^{90} - 25 q^{91} - 2 q^{92} + 25 q^{93} - 19 q^{94} + 21 q^{95} - 6 q^{98} - 19 q^{99}+O(q^{100}) \) 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 + q^13 + 10 * q^14 - 3 * q^15 - 9 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 19 * q^21 + 2 * q^22 - 2 * q^23 + 18 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 + 18 * q^29 + 4 * q^31 + 9 * q^32 - 23 * q^33 - 10 * q^34 + 6 * q^35 - 8 * q^36 + 20 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^41 - 23 * q^42 + 7 * q^43 + q^44 + 30 * q^45 - 4 * q^46 - 38 * q^47 + 6 * q^49 + 9 * q^50 + 4 * q^51 + q^52 - 10 * q^53 - 18 * q^54 + 6 * q^55 - 5 * q^56 - 33 * q^57 + 9 * q^58 + 10 * q^59 + 3 * q^60 - 36 * q^61 - 4 * q^62 + 12 * q^63 + 18 * q^64 - 45 * q^65 - 7 * q^66 + 22 * q^67 - 5 * q^68 - 26 * q^69 + 12 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 + 10 * q^74 - 6 * q^76 - 2 * q^77 + 23 * q^78 + 2 * q^79 + 4 * q^81 - q^82 - 7 * q^83 - 4 * q^84 - 7 * q^86 + 3 * q^87 - q^88 + q^89 + 60 * q^90 - 25 * q^91 - 2 * q^92 + 25 * q^93 - 19 * q^94 + 21 * q^95 - 6 * q^98 - 19 * q^99

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