LMFDB - Embedded newform 1352.2.i.j.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1352,2,Mod(529,1352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1352.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1352 = 2^{3} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1352.i (of order $3$, degree $2$, not 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:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.3
Root			$-0.623490 + 1.07992i$ of defining polynomial
Character	$\chi$	$=$	1352.529
Dual form			1352.2.i.j.1329.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40097 - 2.42655i) q^{3} +2.80194 q^{5} +(-0.900969 - 1.56052i) q^{7} +(-2.42543 - 4.20096i) q^{9} +O(q^{10})$	\(q+(1.40097 - 2.42655i) q^{3} +2.80194 q^{5} +(-0.900969 - 1.56052i) q^{7} +(-2.42543 - 4.20096i) q^{9} +(3.20291 - 5.54760i) q^{11} +(3.92543 - 6.79904i) q^{15} +(2.81551 + 4.87661i) q^{17} +(0.832437 + 1.44182i) q^{19} -5.04892 q^{21} +(-1.54892 + 2.68280i) q^{23} +2.85086 q^{25} -5.18598 q^{27} +(-3.03803 + 5.26203i) q^{29} -3.58211 q^{31} +(-8.97434 - 15.5440i) q^{33} +(-2.52446 - 4.37249i) q^{35} +(2.57338 - 4.45722i) q^{37} +(-3.54892 + 6.14691i) q^{41} +(1.42058 + 2.46052i) q^{43} +(-6.79590 - 11.7708i) q^{45} +1.51573 q^{47} +(1.87651 - 3.25021i) q^{49} +15.7778 q^{51} -10.7627 q^{53} +(8.97434 - 15.5440i) q^{55} +4.66487 q^{57} +(4.63706 + 8.03163i) q^{59} +(6.41454 + 11.1103i) q^{61} +(-4.37047 + 7.56988i) q^{63} +(1.08546 - 1.88007i) q^{67} +(4.33997 + 7.51705i) q^{69} +(-5.45257 - 9.44414i) q^{71} +1.95108 q^{73} +(3.99396 - 6.91774i) q^{75} -11.5429 q^{77} -11.5646 q^{79} +(0.0108851 - 0.0188536i) q^{81} -0.0392287 q^{83} +(7.88889 + 13.6640i) q^{85} +(8.51238 + 14.7439i) q^{87} +(3.72132 - 6.44552i) q^{89} +(-5.01842 + 8.69215i) q^{93} +(2.33244 + 4.03990i) q^{95} +(0.236094 + 0.408928i) q^{97} -31.0737 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} + 8 q^{5} - q^{7} - q^{9}+O(q^{10}) $ 6 * q + 4 * q^3 + 8 * q^5 - q^7 - q^9	$ 6 q + 4 q^{3} + 8 q^{5} - q^{7} - q^{9} + 6 q^{11} + 10 q^{15} + 2 q^{17} + 6 q^{19} - 12 q^{21} + 9 q^{23} - 10 q^{25} - 2 q^{27} - 3 q^{29} - 10 q^{31} - 22 q^{33} - 6 q^{35} - 12 q^{37} - 3 q^{41} + 17 q^{43} - 13 q^{45} - 16 q^{47} + 16 q^{49} + 10 q^{51} - 30 q^{53} + 22 q^{55} + 30 q^{57} + 17 q^{59} + 28 q^{61} - 12 q^{63} + 17 q^{67} + 2 q^{69} - 7 q^{71} + 30 q^{73} + 5 q^{75} - 32 q^{77} - 26 q^{79} - 3 q^{81} - 26 q^{83} + 5 q^{85} + 4 q^{87} - 19 q^{89} - 2 q^{93} + 15 q^{95} - 5 q^{97} - 74 q^{99}+O(q^{100}) $ 6 * q + 4 * q^3 + 8 * q^5 - q^7 - q^9 + 6 * q^11 + 10 * q^15 + 2 * q^17 + 6 * q^19 - 12 * q^21 + 9 * q^23 - 10 * q^25 - 2 * q^27 - 3 * q^29 - 10 * q^31 - 22 * q^33 - 6 * q^35 - 12 * q^37 - 3 * q^41 + 17 * q^43 - 13 * q^45 - 16 * q^47 + 16 * q^49 + 10 * q^51 - 30 * q^53 + 22 * q^55 + 30 * q^57 + 17 * q^59 + 28 * q^61 - 12 * q^63 + 17 * q^67 + 2 * q^69 - 7 * q^71 + 30 * q^73 + 5 * q^75 - 32 * q^77 - 26 * q^79 - 3 * q^81 - 26 * q^83 + 5 * q^85 + 4 * q^87 - 19 * q^89 - 2 * q^93 + 15 * q^95 - 5 * q^97 - 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	1.40097	−	2.42655i	0.808850	−	1.40097i	−0.104811	−	0.994492i	$-0.533424\pi$
$3$	1.40097	−	2.42655i	0.808850	−	1.40097i	0.913661	−	0.406477i	$-0.133243\pi$
$4$		0			0
$5$	2.80194			1.25306			0.626532	−	0.779395i	$-0.284474\pi$
$5$	2.80194			1.25306			0.626532	+	0.779395i	$0.284474\pi$
$6$		0			0
$7$	−0.900969	−	1.56052i	−0.340534	−	0.589823i	0.643998	−	0.765027i	$-0.277275\pi$
$7$	−0.900969	−	1.56052i	−0.340534	−	0.589823i	−0.984532	+	0.175205i	$0.943941\pi$
$8$		0			0
$9$	−2.42543	−	4.20096i	−0.808476	−	1.40032i
$10$		0			0
$11$	3.20291	−	5.54760i	0.965713	−	1.67266i	0.258025	−	0.966138i	$-0.416928\pi$
$11$	3.20291	−	5.54760i	0.965713	−	1.67266i	0.707688	−	0.706525i	$-0.249738\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	3.92543	−	6.79904i	1.01354	−	1.75550i
$16$		0			0
$17$	2.81551	+	4.87661i	0.682862	+	1.18275i	0.974104	+	0.226102i	$0.0725982\pi$
$17$	2.81551	+	4.87661i	0.682862	+	1.18275i	−0.291242	+	0.956649i	$0.594068\pi$
$18$		0			0
$19$	0.832437	+	1.44182i	0.190974	+	0.330777i	0.945573	−	0.325409i	$-0.105502\pi$
$19$	0.832437	+	1.44182i	0.190974	+	0.330777i	−0.754599	+	0.656186i	$0.772169\pi$
$20$		0			0
$21$	−5.04892			−1.10176
$22$		0			0
$23$	−1.54892	+	2.68280i	−0.322972	+	0.559403i	−0.981100	−	0.193503i	$-0.938015\pi$
$23$	−1.54892	+	2.68280i	−0.322972	+	0.559403i	0.658128	+	0.752906i	$0.271348\pi$
$24$		0			0
$25$	2.85086			0.570171
$26$		0			0
$27$	−5.18598			−0.998042
$28$		0			0
$29$	−3.03803	+	5.26203i	−0.564148	+	0.977134i	0.432980	+	0.901404i	$0.357462\pi$
$29$	−3.03803	+	5.26203i	−0.564148	+	0.977134i	−0.997128	+	0.0757302i	$0.975871\pi$
$30$		0			0
$31$	−3.58211			−0.643365			−0.321683	−	0.946848i	$-0.604248\pi$
$31$	−3.58211			−0.643365			−0.321683	+	0.946848i	$0.604248\pi$
$32$		0			0
$33$	−8.97434	−	15.5440i	−1.56223	−	2.70587i
$34$		0			0
$35$	−2.52446	−	4.37249i	−0.426711	−	0.739086i
$36$		0			0
$37$	2.57338	−	4.45722i	0.423060	−	0.732762i	−0.573177	−	0.819432i	$-0.694289\pi$
$37$	2.57338	−	4.45722i	0.423060	−	0.732762i	0.996237	+	0.0866697i	$0.0276225\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.54892	+	6.14691i	−0.554248	+	0.959985i	0.443714	+	0.896169i	$0.353661\pi$
$41$	−3.54892	+	6.14691i	−0.554248	+	0.959985i	−0.997962	+	0.0638168i	$0.979673\pi$
$42$		0			0
$43$	1.42058	+	2.46052i	0.216637	+	0.375226i	0.953778	−	0.300513i	$-0.0971579\pi$
$43$	1.42058	+	2.46052i	0.216637	+	0.375226i	−0.737141	+	0.675739i	$0.763825\pi$
$44$		0			0
$45$	−6.79590	−	11.7708i	−1.01307	−	1.75469i
$46$		0			0
$47$	1.51573			0.221092			0.110546	−	0.993871i	$-0.464740\pi$
$47$	1.51573			0.221092			0.110546	+	0.993871i	$0.464740\pi$
$48$		0			0
$49$	1.87651	−	3.25021i	0.268073	−	0.464316i
$50$		0			0
$51$	15.7778			2.20933
$52$		0			0
$53$	−10.7627			−1.47837			−0.739186	−	0.673501i	$-0.764790\pi$
$53$	−10.7627			−1.47837			−0.739186	+	0.673501i	$0.764790\pi$
$54$		0			0
$55$	8.97434	−	15.5440i	1.21010	−	2.09596i
$56$		0			0
$57$	4.66487			0.617878
$58$		0			0
$59$	4.63706	+	8.03163i	0.603694	+	1.04563i	0.992256	+	0.124207i	$0.0396385\pi$
$59$	4.63706	+	8.03163i	0.603694	+	1.04563i	−0.388562	+	0.921423i	$0.627028\pi$
$60$		0			0
$61$	6.41454	+	11.1103i	0.821298	+	1.42253i	0.904716	+	0.426015i	$0.140083\pi$
$61$	6.41454	+	11.1103i	0.821298	+	1.42253i	−0.0834180	+	0.996515i	$0.526584\pi$
$62$		0			0
$63$	−4.37047	+	7.56988i	−0.550627	+	0.953715i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.08546	−	1.88007i	0.132610	−	0.229687i	−0.792072	−	0.610428i	$-0.790998\pi$
$67$	1.08546	−	1.88007i	0.132610	−	0.229687i	0.924682	+	0.380741i	$0.124331\pi$
$68$		0			0
$69$	4.33997	+	7.51705i	0.522471	+	0.904946i
$70$		0			0
$71$	−5.45257	−	9.44414i	−0.647102	−	1.12081i	−0.983812	−	0.179204i	$-0.942648\pi$
$71$	−5.45257	−	9.44414i	−0.647102	−	1.12081i	0.336710	−	0.941608i	$-0.390686\pi$
$72$		0			0
$73$	1.95108			0.228357			0.114178	−	0.993460i	$-0.463576\pi$
$73$	1.95108			0.228357			0.114178	+	0.993460i	$0.463576\pi$
$74$		0			0
$75$	3.99396	−	6.91774i	0.461183	−	0.798792i
$76$		0			0
$77$	−11.5429			−1.31543
$78$		0			0
$79$	−11.5646			−1.30112			−0.650562	−	0.759453i	$-0.725467\pi$
$79$	−11.5646			−1.30112			−0.650562	+	0.759453i	$0.725467\pi$
$80$		0			0
$81$	0.0108851	−	0.0188536i	0.00120946	−	0.00209484i
$82$		0			0
$83$	−0.0392287			−0.00430590			−0.00215295	−	0.999998i	$-0.500685\pi$
$83$	−0.0392287			−0.00430590			−0.00215295	+	0.999998i	$0.500685\pi$
$84$		0			0
$85$	7.88889	+	13.6640i	0.855670	+	1.48206i
$86$		0			0
$87$	8.51238	+	14.7439i	0.912623	+	1.58071i
$88$		0			0
$89$	3.72132	−	6.44552i	0.394460	−	0.683224i	−0.598572	−	0.801069i	$-0.704265\pi$
$89$	3.72132	−	6.44552i	0.394460	−	0.683224i	0.993032	+	0.117845i	$0.0375985\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−5.01842	+	8.69215i	−0.520386	+	0.901334i
$94$		0			0
$95$	2.33244	+	4.03990i	0.239303	+	0.414485i
$96$		0			0
$97$	0.236094	+	0.408928i	0.0239718	+	0.0415203i	0.877762	−	0.479096i	$-0.159035\pi$
$97$	0.236094	+	0.408928i	0.0239718	+	0.0415203i	−0.853791	+	0.520616i	$0.825702\pi$
$98$		0			0
$99$	−31.0737			−3.12302
$100$		0			0
$101$	−3.31551	+	5.74263i	−0.329906	+	0.571413i	−0.982493	−	0.186300i	$-0.940350\pi$
$101$	−3.31551	+	5.74263i	−0.329906	+	0.571413i	0.652587	+	0.757714i	$0.273684\pi$
$102$		0			0
$103$	1.21313			0.119533			0.0597665	−	0.998212i	$-0.480964\pi$
$103$	1.21313			0.119533			0.0597665	+	0.998212i	$0.480964\pi$
$104$		0			0
$105$	−14.1468			−1.38058
$106$		0			0
$107$	2.23341	−	3.86837i	0.215912	−	0.373970i	−0.737643	−	0.675191i	$-0.764061\pi$
$107$	2.23341	−	3.86837i	0.215912	−	0.373970i	0.953554	+	0.301222i	$0.0973944\pi$
$108$		0			0
$109$	1.16421			0.111511			0.0557556	−	0.998444i	$-0.482243\pi$
$109$	1.16421			0.111511			0.0557556	+	0.998444i	$0.482243\pi$
$110$		0			0
$111$	−7.21044	−	12.4888i	−0.684385	−	1.18539i
$112$		0			0
$113$	2.57457	+	4.45929i	0.242195	+	0.419495i	0.961339	−	0.275366i	$-0.0887992\pi$
$113$	2.57457	+	4.45929i	0.242195	+	0.419495i	−0.719144	+	0.694861i	$0.755466\pi$
$114$		0			0
$115$	−4.33997	+	7.51705i	−0.404704	+	0.700968i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.07338	−	8.78735i	0.465076	−	0.805535i
$120$		0			0
$121$	−15.0172	−	26.0106i	−1.36520	−	2.36460i
$122$		0			0
$123$	9.94385	+	17.2232i	0.896606	+	1.55297i
$124$		0			0
$125$	−6.02177			−0.538604
$126$		0			0
$127$	5.18114	−	8.97399i	0.459752	−	0.796313i	−0.539196	−	0.842180i	$-0.681272\pi$
$127$	5.18114	−	8.97399i	0.459752	−	0.796313i	0.998948	+	0.0458673i	$0.0146051\pi$
$128$		0			0
$129$	7.96077			0.700907
$130$		0			0
$131$	12.8334			1.12126			0.560630	−	0.828067i	$-0.310559\pi$
$131$	12.8334			1.12126			0.560630	+	0.828067i	$0.310559\pi$
$132$		0			0
$133$	1.50000	−	2.59808i	0.130066	−	0.225282i
$134$		0			0
$135$	−14.5308			−1.25061
$136$		0			0
$137$	−0.396125	−	0.686108i	−0.0338432	−	0.0586181i	0.848608	−	0.529023i	$-0.177441\pi$
$137$	−0.396125	−	0.686108i	−0.0338432	−	0.0586181i	−0.882451	+	0.470405i	$0.844108\pi$
$138$		0			0
$139$	2.94720	+	5.10470i	0.249978	+	0.432975i	0.963519	−	0.267638i	$-0.0862433\pi$
$139$	2.94720	+	5.10470i	0.249978	+	0.432975i	−0.713541	+	0.700613i	$0.752910\pi$
$140$		0			0
$141$	2.12349	−	3.67799i	0.178830	−	0.309743i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−8.51238	+	14.7439i	−0.706914	+	1.22441i
$146$		0			0
$147$	−5.25786	−	9.10689i	−0.433661	−	0.751124i
$148$		0			0
$149$	−2.37047	−	4.10577i	−0.194196	−	0.336358i	0.752440	−	0.658660i	$-0.228877\pi$
$149$	−2.37047	−	4.10577i	−0.194196	−	0.336358i	−0.946637	+	0.322302i	$0.895543\pi$
$150$		0			0
$151$	−5.37196			−0.437164			−0.218582	−	0.975819i	$-0.570143\pi$
$151$	−5.37196			−0.437164			−0.218582	+	0.975819i	$0.570143\pi$
$152$		0			0
$153$	13.6576	−	23.6557i	1.10415	−	1.91245i
$154$		0			0
$155$	−10.0368			−0.806178
$156$		0			0
$157$	−11.2295			−0.896213			−0.448107	−	0.893980i	$-0.647902\pi$
$157$	−11.2295			−0.896213			−0.448107	+	0.893980i	$0.647902\pi$
$158$		0			0
$159$	−15.0782	+	26.1162i	−1.19578	+	2.07115i
$160$		0			0
$161$	5.58211			0.439932
$162$		0			0
$163$	0.519614	+	0.899998i	0.0406993	+	0.0704933i	0.885658	−	0.464339i	$-0.153708\pi$
$163$	0.519614	+	0.899998i	0.0406993	+	0.0704933i	−0.844958	+	0.534832i	$0.820375\pi$
$164$		0			0
$165$	−25.1456	−	43.5534i	−1.95758	−	3.39063i
$166$		0			0
$167$	−1.40581	+	2.43494i	−0.108785	+	0.188421i	−0.915278	−	0.402822i	$-0.868029\pi$
$167$	−1.40581	+	2.43494i	−0.108785	+	0.188421i	0.806493	+	0.591243i	$0.201363\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	4.03803	−	6.99408i	0.308796	−	0.534850i
$172$		0			0
$173$	10.5918	+	18.3455i	0.805279	+	1.39478i	0.916102	+	0.400944i	$0.131318\pi$
$173$	10.5918	+	18.3455i	0.805279	+	1.39478i	−0.110823	+	0.993840i	$0.535349\pi$
$174$		0			0
$175$	−2.56853	−	4.44883i	−0.194163	−	0.336300i
$176$		0			0
$177$	25.9855			1.95319
$178$		0			0
$179$	−9.17845	+	15.8975i	−0.686029	+	1.18824i	0.287083	+	0.957906i	$0.407315\pi$
$179$	−9.17845	+	15.8975i	−0.686029	+	1.18824i	−0.973112	+	0.230332i	$0.926019\pi$
$180$		0			0
$181$	−20.4969			−1.52353			−0.761763	−	0.647856i	$-0.775666\pi$
$181$	−20.4969			−1.52353			−0.761763	+	0.647856i	$0.775666\pi$
$182$		0			0
$183$	35.9463			2.65723
$184$		0			0
$185$	7.21044	−	12.4888i	0.530122	−	0.918198i
$186$		0			0
$187$	36.0713			2.63779
$188$		0			0
$189$	4.67241	+	8.09285i	0.339868	+	0.588668i
$190$		0			0
$191$	1.71648	+	2.97303i	0.124200	+	0.215121i	0.921420	−	0.388568i	$-0.127030\pi$
$191$	1.71648	+	2.97303i	0.124200	+	0.215121i	−0.797220	+	0.603689i	$0.793697\pi$
$192$		0			0
$193$	0.841166	−	1.45694i	0.0605485	−	0.104873i	−0.834162	−	0.551519i	$-0.814048\pi$
$193$	0.841166	−	1.45694i	0.0605485	−	0.104873i	0.894711	+	0.446646i	$0.147382\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.4758	−	23.3408i	0.960114	−	1.66297i	0.237907	−	0.971288i	$-0.423539\pi$
$197$	13.4758	−	23.3408i	0.960114	−	1.66297i	0.722206	−	0.691678i	$-0.243128\pi$
$198$		0			0
$199$	10.0402	+	17.3901i	0.711730	+	1.23275i	0.964207	+	0.265150i	$0.0854214\pi$
$199$	10.0402	+	17.3901i	0.711730	+	1.23275i	−0.252477	+	0.967603i	$0.581245\pi$
$200$		0			0
$201$	−3.04138	−	5.26783i	−0.214523	−	0.371564i
$202$		0			0
$203$	10.9487			0.768447
$204$		0			0
$205$	−9.94385	+	17.2232i	−0.694508	+	1.20292i
$206$		0			0
$207$	15.0271			1.04446
$208$		0			0
$209$	10.6649			0.737705
$210$		0			0
$211$	4.13222	−	7.15721i	0.284474	−	0.492723i	−0.688008	−	0.725703i	$-0.741514\pi$
$211$	4.13222	−	7.15721i	0.284474	−	0.492723i	0.972481	+	0.232980i	$0.0748478\pi$
$212$		0			0
$213$	−30.5555			−2.09363
$214$		0			0
$215$	3.98039	+	6.89423i	0.271460	+	0.470183i
$216$		0			0
$217$	3.22737	+	5.58996i	0.219088	+	0.379471i
$218$		0			0
$219$	2.73341	−	4.73440i	0.184706	−	0.319921i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−11.6540	+	20.1853i	−0.780409	+	1.35171i	0.151295	+	0.988489i	$0.451656\pi$
$223$	−11.6540	+	20.1853i	−0.780409	+	1.35171i	−0.931704	+	0.363219i	$0.881678\pi$
$224$		0			0
$225$	−6.91454	−	11.9763i	−0.460969	−	0.798423i
$226$		0			0
$227$	7.11260	+	12.3194i	0.472080	+	0.817667i	0.999490	−	0.0319444i	$-0.0101700\pi$
$227$	7.11260	+	12.3194i	0.472080	+	0.817667i	−0.527409	+	0.849611i	$0.676837\pi$
$228$		0			0
$229$	26.8713			1.77571			0.887853	−	0.460128i	$-0.152196\pi$
$229$	26.8713			1.77571			0.887853	+	0.460128i	$0.152196\pi$
$230$		0			0
$231$	−16.1712	+	28.0094i	−1.06399	+	1.84288i
$232$		0			0
$233$	−2.05861			−0.134864			−0.0674319	−	0.997724i	$-0.521481\pi$
$233$	−2.05861			−0.134864			−0.0674319	+	0.997724i	$0.521481\pi$
$234$		0			0
$235$	4.24698			0.277042
$236$		0			0
$237$	−16.2017	+	28.0622i	−1.05241	+	1.82283i
$238$		0			0
$239$	9.03923			0.584699			0.292350	−	0.956312i	$-0.405563\pi$
$239$	9.03923			0.584699			0.292350	+	0.956312i	$0.405563\pi$
$240$		0			0
$241$	−4.14191	−	7.17399i	−0.266804	−	0.462118i	0.701231	−	0.712934i	$-0.252634\pi$
$241$	−4.14191	−	7.17399i	−0.266804	−	0.462118i	−0.968035	+	0.250817i	$0.919301\pi$
$242$		0			0
$243$	−7.80947	−	13.5264i	−0.500978	−	0.867719i
$244$		0			0
$245$	5.25786	−	9.10689i	0.335913	−	0.581818i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.0549581	+	0.0951903i	−0.00348283	+	0.00603244i
$250$		0			0
$251$	−2.64310	−	4.57799i	−0.166831	−	0.288960i	0.770473	−	0.637473i	$-0.220020\pi$
$251$	−2.64310	−	4.57799i	−0.166831	−	0.288960i	−0.937304	+	0.348513i	$0.886687\pi$
$252$		0			0
$253$	9.92208	+	17.1855i	0.623796	+	1.08045i
$254$		0			0
$255$	44.2083			2.76843
$256$		0			0
$257$	−9.73005	+	16.8529i	−0.606944	+	1.05126i	0.384797	+	0.923001i	$0.374271\pi$
$257$	−9.73005	+	16.8529i	−0.606944	+	1.05126i	−0.991741	+	0.128257i	$0.959062\pi$
$258$		0			0
$259$	−9.27413			−0.576266
$260$		0			0
$261$	29.4741			1.82440
$262$		0			0
$263$	9.69836	−	16.7980i	0.598026	−	1.03581i	−0.395086	−	0.918644i	$-0.629285\pi$
$263$	9.69836	−	16.7980i	0.598026	−	1.03581i	0.993112	−	0.117168i	$-0.0373815\pi$
$264$		0			0
$265$	−30.1564			−1.85250
$266$		0			0
$267$	−10.4269	−	18.0600i	−0.638117	−	1.10525i
$268$		0			0
$269$	1.80678	+	3.12944i	0.110161	+	0.190805i	0.915835	−	0.401554i	$-0.131530\pi$
$269$	1.80678	+	3.12944i	0.110161	+	0.190805i	−0.805674	+	0.592359i	$0.798197\pi$
$270$		0			0
$271$	−1.57404	+	2.72632i	−0.0956161	+	0.165612i	−0.909866	−	0.414903i	$-0.863815\pi$
$271$	−1.57404	+	2.72632i	−0.0956161	+	0.165612i	0.814249	+	0.580515i	$0.197149\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.13102	−	15.8154i	0.550621	−	0.953704i
$276$		0			0
$277$	−4.85354	−	8.40658i	−0.291621	−	0.505103i	0.682572	−	0.730818i	$-0.260861\pi$
$277$	−4.85354	−	8.40658i	−0.291621	−	0.505103i	−0.974193	+	0.225716i	$0.927528\pi$
$278$		0			0
$279$	8.68814	+	15.0483i	0.520145	+	0.900918i
$280$		0			0
$281$	12.3569			0.737151			0.368575	−	0.929598i	$-0.379846\pi$
$281$	12.3569			0.737151			0.368575	+	0.929598i	$0.379846\pi$
$282$		0			0
$283$	7.25667	−	12.5689i	0.431364	−	0.747145i	−0.565627	−	0.824661i	$-0.691366\pi$
$283$	7.25667	−	12.5689i	0.431364	−	0.747145i	0.996991	+	0.0775166i	$0.0246991\pi$
$284$		0			0
$285$	13.0707			0.774241
$286$		0			0
$287$	12.7899			0.754961
$288$		0			0
$289$	−7.35421	+	12.7379i	−0.432600	+	0.749286i
$290$		0			0
$291$	1.32304			0.0775582
$292$		0			0
$293$	−7.04072	−	12.1949i	−0.411323	−	0.712433i	0.583711	−	0.811961i	$-0.301600\pi$
$293$	−7.04072	−	12.1949i	−0.411323	−	0.712433i	−0.995035	+	0.0995283i	$0.968267\pi$
$294$		0			0
$295$	12.9928	+	22.5041i	0.756468	+	1.31024i
$296$		0			0
$297$	−16.6102	+	28.7697i	−0.963822	+	1.66939i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	2.55980	−	4.43371i	0.147545	−	0.255555i
$302$		0			0
$303$	9.28986	+	16.0905i	0.533688	+	0.924375i
$304$		0			0
$305$	17.9731	+	31.1304i	1.02914	+	1.78252i
$306$		0			0
$307$	−19.9952			−1.14119			−0.570594	−	0.821233i	$-0.693287\pi$
$307$	−19.9952			−1.14119			−0.570594	+	0.821233i	$0.693287\pi$
$308$		0			0
$309$	1.69955	−	2.94371i	0.0966843	−	0.167462i
$310$		0			0
$311$	21.6256			1.22628			0.613139	−	0.789975i	$-0.289907\pi$
$311$	21.6256			1.22628			0.613139	+	0.789975i	$0.289907\pi$
$312$		0			0
$313$	1.42088			0.0803128			0.0401564	−	0.999193i	$-0.487214\pi$
$313$	1.42088			0.0803128			0.0401564	+	0.999193i	$0.487214\pi$
$314$		0			0
$315$	−12.2458	+	21.2103i	−0.689972	+	1.19507i
$316$		0			0
$317$	9.65817			0.542457			0.271228	−	0.962515i	$-0.412570\pi$
$317$	9.65817			0.542457			0.271228	+	0.962515i	$0.412570\pi$
$318$		0			0
$319$	19.4611	+	33.7076i	1.08961	+	1.88726i
$320$		0			0
$321$	−6.25786	−	10.8389i	−0.349280	−	0.604971i
$322$		0			0
$323$	−4.68747	+	8.11894i	−0.260818	+	0.451750i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.63102	−	2.82501i	0.0901958	−	0.156224i
$328$		0			0
$329$	−1.36563	−	2.36533i	−0.0752893	−	0.130405i
$330$		0			0
$331$	−15.9678	−	27.6570i	−0.877668	−	1.52017i	−0.853893	−	0.520448i	$-0.825765\pi$
$331$	−15.9678	−	27.6570i	−0.877668	−	1.52017i	−0.0237750	−	0.999717i	$-0.507569\pi$
$332$		0			0
$333$	−24.9661			−1.36814
$334$		0			0
$335$	3.04138	−	5.26783i	0.166169	−	0.287812i
$336$		0			0
$337$	−6.75302			−0.367860			−0.183930	−	0.982939i	$-0.558882\pi$
$337$	−6.75302			−0.367860			−0.183930	+	0.982939i	$0.558882\pi$
$338$		0			0
$339$	14.4276			0.783599
$340$		0			0
$341$	−11.4731	+	19.8721i	−0.621306	+	1.07613i
$342$		0			0
$343$	−19.3763			−1.04622
$344$		0			0
$345$	12.1603	+	21.0623i	0.654690	+	1.13396i
$346$		0			0
$347$	−18.0003	−	31.1774i	−0.966306	−	1.67369i	−0.706063	−	0.708149i	$-0.749531\pi$
$347$	−18.0003	−	31.1774i	−0.966306	−	1.67369i	−0.260243	−	0.965543i	$-0.583803\pi$
$348$		0			0
$349$	−12.8029	+	22.1753i	−0.685323	+	1.18701i	0.288012	+	0.957627i	$0.407006\pi$
$349$	−12.8029	+	22.1753i	−0.685323	+	1.18701i	−0.973335	+	0.229388i	$0.926328\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.12080	+	10.6015i	−0.325777	+	0.564263i	−0.981669	−	0.190592i	$-0.938959\pi$
$353$	−6.12080	+	10.6015i	−0.325777	+	0.564263i	0.655892	+	0.754855i	$0.272293\pi$
$354$		0			0
$355$	−15.2778	−	26.4619i	−0.810860	−	1.40445i
$356$		0			0
$357$	−14.2153	−	24.6216i	−0.752353	−	1.30311i
$358$		0			0
$359$	21.0737			1.11223			0.556113	−	0.831107i	$-0.312292\pi$
$359$	21.0737			1.11223			0.556113	+	0.831107i	$0.312292\pi$
$360$		0			0
$361$	8.11410	−	14.0540i	0.427058	−	0.739686i
$362$		0			0
$363$	−84.1546			−4.41697
$364$		0			0
$365$	5.46681			0.286146
$366$		0			0
$367$	−3.83728	+	6.64637i	−0.200304	+	0.346938i	−0.948627	−	0.316398i	$-0.897526\pi$
$367$	−3.83728	+	6.64637i	−0.200304	+	0.346938i	0.748322	+	0.663336i	$0.230860\pi$
$368$		0			0
$369$	34.4306			1.79238
$370$		0			0
$371$	9.69687	+	16.7955i	0.503436	+	0.871977i
$372$		0			0
$373$	12.0341	+	20.8438i	0.623105	+	1.07925i	0.988904	+	0.148555i	$0.0474622\pi$
$373$	12.0341	+	20.8438i	0.623105	+	1.07925i	−0.365800	+	0.930694i	$0.619204\pi$
$374$		0			0
$375$	−8.43631	+	14.6121i	−0.435649	+	0.754567i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−13.5051	+	23.3916i	−0.693712	+	1.20155i	0.276900	+	0.960899i	$0.410693\pi$
$379$	−13.5051	+	23.3916i	−0.693712	+	1.20155i	−0.970613	+	0.240647i	$0.922641\pi$
$380$		0			0
$381$	−14.5172	−	25.1446i	−0.743740	−	1.28820i
$382$		0			0
$383$	−0.0120816	−	0.0209259i	−0.000617340	−	0.00106926i	0.865717	−	0.500535i	$-0.166863\pi$
$383$	−0.0120816	−	0.0209259i	−0.000617340	−	0.00106926i	−0.866334	+	0.499465i	$0.833530\pi$
$384$		0			0
$385$	−32.3424			−1.64832
$386$		0			0
$387$	6.89104	−	11.9356i	0.350291	−	0.606723i
$388$		0			0
$389$	23.0422			1.16829			0.584143	−	0.811651i	$-0.301431\pi$
$389$	23.0422			1.16829			0.584143	+	0.811651i	$0.301431\pi$
$390$		0			0
$391$	−17.4440			−0.882180
$392$		0			0
$393$	17.9792	−	31.1409i	0.906930	−	1.57085i
$394$		0			0
$395$	−32.4034			−1.63039
$396$		0			0
$397$	16.5625	+	28.6871i	0.831248	+	1.43976i	0.897049	+	0.441930i	$0.145706\pi$
$397$	16.5625	+	28.6871i	0.831248	+	1.43976i	−0.0658018	+	0.997833i	$0.520961\pi$
$398$		0			0
$399$	−4.20291	−	7.27965i	−0.210409	−	0.364438i
$400$		0			0
$401$	13.1908	−	22.8472i	0.658718	−	1.14093i	−0.322229	−	0.946662i	$-0.604432\pi$
$401$	13.1908	−	22.8472i	0.658718	−	1.14093i	0.980948	−	0.194272i	$-0.0622345\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.0304995	−	0.0528266i	0.00151553	−	0.00262498i
$406$		0			0
$407$	−16.4846	−	28.5521i	−0.817110	−	1.41528i
$408$		0			0
$409$	2.84601	+	4.92944i	0.140726	+	0.243745i	0.927770	−	0.373152i	$-0.121723\pi$
$409$	2.84601	+	4.92944i	0.140726	+	0.243745i	−0.787044	+	0.616897i	$0.788390\pi$
$410$		0			0
$411$	−2.21983			−0.109496
$412$		0			0
$413$	8.35570	−	14.4725i	0.411157	−	0.712145i
$414$		0			0
$415$	−0.109916			−0.00539558
$416$		0			0
$417$	16.5157			0.808779
$418$		0			0
$419$	13.1489	−	22.7746i	0.642366	−	1.11261i	−0.342537	−	0.939504i	$-0.611286\pi$
$419$	13.1489	−	22.7746i	0.642366	−	1.11261i	0.984903	−	0.173107i	$-0.0553805\pi$
$420$		0			0
$421$	31.2083			1.52100			0.760501	−	0.649337i	$-0.224954\pi$
$421$	31.2083			1.52100			0.760501	+	0.649337i	$0.224954\pi$
$422$		0			0
$423$	−3.67629	−	6.36752i	−0.178747	−	0.309600i
$424$		0			0
$425$	8.02661	+	13.9025i	0.389348	+	0.674371i
$426$		0			0
$427$	11.5586	−	20.0201i	0.559360	−	0.968840i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−16.2071	+	28.0715i	−0.780668	+	1.35216i	0.150885	+	0.988551i	$0.451788\pi$
$431$	−16.2071	+	28.0715i	−0.780668	+	1.35216i	−0.931553	+	0.363605i	$0.881546\pi$
$432$		0			0
$433$	16.4988	+	28.5768i	0.792882	+	1.37331i	0.924175	+	0.381968i	$0.124754\pi$
$433$	16.4988	+	28.5768i	0.792882	+	1.37331i	−0.131294	+	0.991344i	$0.541913\pi$
$434$		0			0
$435$	23.8512	+	41.3114i	1.14358	+	1.98073i
$436$		0			0
$437$	−5.15751			−0.246717
$438$		0			0
$439$	2.32693	−	4.03036i	0.111058	−	0.192359i	−0.805139	−	0.593086i	$-0.797909\pi$
$439$	2.32693	−	4.03036i	0.111058	−	0.192359i	0.916197	+	0.400728i	$0.131243\pi$
$440$		0			0
$441$	−18.2054			−0.866922
$442$		0			0
$443$	−29.4819			−1.40073			−0.700363	−	0.713787i	$-0.746979\pi$
$443$	−29.4819			−1.40073			−0.700363	+	0.713787i	$0.746979\pi$
$444$		0			0
$445$	10.4269	−	18.0600i	0.494283	−	0.856124i
$446$		0			0
$447$	−13.2838			−0.628303
$448$		0			0
$449$	−10.6652	−	18.4726i	−0.503320	−	0.871777i	−0.999993	−	0.00383842i	$-0.998778\pi$
$449$	−10.6652	−	18.4726i	−0.503320	−	0.871777i	0.496672	−	0.867938i	$-0.334555\pi$
$450$		0			0
$451$	22.7337	+	39.3759i	1.07049	+	1.85414i
$452$		0			0
$453$	−7.52595	+	13.0353i	−0.353600	+	0.612453i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.29374	+	9.16903i	−0.247631	+	0.428909i	−0.962868	−	0.269973i	$-0.912985\pi$
$457$	−5.29374	+	9.16903i	−0.247631	+	0.428909i	0.715237	+	0.698882i	$0.246319\pi$
$458$		0			0
$459$	−14.6012	−	25.2900i	−0.681525	−	1.18044i
$460$		0			0
$461$	3.34213	+	5.78873i	0.155658	+	0.269608i	0.933299	−	0.359101i	$-0.116917\pi$
$461$	3.34213	+	5.78873i	0.155658	+	0.269608i	−0.777640	+	0.628710i	$0.783583\pi$
$462$		0			0
$463$	−2.69633			−0.125309			−0.0626546	−	0.998035i	$-0.519957\pi$
$463$	−2.69633			−0.125309			−0.0626546	+	0.998035i	$0.519957\pi$
$464$		0			0
$465$	−14.0613	+	24.3549i	−0.652077	+	1.12943i
$466$		0			0
$467$	−2.30127			−0.106490			−0.0532451	−	0.998581i	$-0.516956\pi$
$467$	−2.30127			−0.106490			−0.0532451	+	0.998581i	$0.516956\pi$
$468$		0			0
$469$	−3.91185			−0.180633
$470$		0			0
$471$	−15.7322	+	27.2490i	−0.724902	+	1.25557i
$472$		0			0
$473$	18.2000			0.836836
$474$		0			0
$475$	2.37316	+	4.11043i	0.108888	+	0.188599i
$476$		0			0
$477$	26.1042	+	45.2138i	1.19523	+	2.07020i
$478$		0			0
$479$	3.24847	−	5.62652i	0.148426	−	0.257082i	−0.782220	−	0.623003i	$-0.785913\pi$
$479$	3.24847	−	5.62652i	0.148426	−	0.257082i	0.930646	+	0.365921i	$0.119246\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	7.82036	−	13.5453i	0.355839	−	0.616330i
$484$		0			0
$485$	0.661522	+	1.14579i	0.0300382	+	0.0520276i
$486$		0			0
$487$	−7.44385	−	12.8931i	−0.337313	−	0.584243i	0.646614	−	0.762818i	$-0.276185\pi$
$487$	−7.44385	−	12.8931i	−0.337313	−	0.584243i	−0.983926	+	0.178575i	$0.942851\pi$
$488$		0			0
$489$	2.91185			0.131679
$490$		0			0
$491$	20.8138	−	36.0505i	0.939313	−	1.62694i	0.172556	−	0.985000i	$-0.444797\pi$
$491$	20.8138	−	36.0505i	0.939313	−	1.62694i	0.766757	−	0.641938i	$-0.221869\pi$
$492$		0			0
$493$	−34.2145			−1.54094
$494$		0			0
$495$	−87.0665			−3.91335
$496$		0			0
$497$	−9.82520	+	17.0177i	−0.440720	+	0.763350i
$498$		0			0
$499$	5.79523			0.259430			0.129715	−	0.991551i	$-0.458594\pi$
$499$	5.79523			0.259430			0.129715	+	0.991551i	$0.458594\pi$
$500$		0			0
$501$	3.93900	+	6.82255i	0.175982	+	0.304809i
$502$		0			0
$503$	−14.6707	−	25.4104i	−0.654133	−	1.13299i	−0.982110	−	0.188306i	$-0.939700\pi$
$503$	−14.6707	−	25.4104i	−0.654133	−	1.13299i	0.327977	−	0.944686i	$-0.393633\pi$
$504$		0			0
$505$	−9.28986	+	16.0905i	−0.413393	+	0.716018i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.7087	+	27.2083i	−0.696276	+	1.20599i	0.273472	+	0.961880i	$0.411828\pi$
$509$	−15.7087	+	27.2083i	−0.696276	+	1.20599i	−0.969749	+	0.244106i	$0.921505\pi$
$510$		0			0
$511$	−1.75786	−	3.04471i	−0.0777634	−	0.134690i
$512$		0			0
$513$	−4.31700	−	7.47727i	−0.190600	−	0.330129i
$514$		0			0
$515$	3.39911			0.149783
$516$		0			0
$517$	4.85474	−	8.40866i	0.213511	−	0.369812i
$518$		0			0
$519$	59.3551			2.60540
$520$		0			0
$521$	37.2150			1.63042			0.815210	−	0.579165i	$-0.196621\pi$
$521$	37.2150			1.63042			0.815210	+	0.579165i	$0.196621\pi$
$522$		0			0
$523$	−11.2962	+	19.5656i	−0.493948	+	0.855543i	−0.999976	−	0.00697420i	$-0.997780\pi$
$523$	−11.2962	+	19.5656i	−0.493948	+	0.855543i	0.506028	+	0.862517i	$0.331113\pi$
$524$		0			0
$525$	−14.3937			−0.628194
$526$		0			0
$527$	−10.0855	−	17.4685i	−0.439329	−	0.760941i
$528$		0			0
$529$	6.70171	+	11.6077i	0.291379	+	0.504683i
$530$		0			0
$531$	22.4937	−	38.9603i	0.976144	−	1.69073i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	6.25786	−	10.8389i	0.270551	−	0.468608i
$536$		0			0
$537$	25.7174	+	44.5439i	1.10979	+	1.92221i
$538$		0			0
$539$	−12.0206	−	20.8202i	−0.517763	−	0.896791i
$540$		0			0
$541$	−24.6340			−1.05910			−0.529549	−	0.848279i	$-0.677639\pi$
$541$	−24.6340			−1.05910			−0.529549	+	0.848279i	$0.677639\pi$
$542$		0			0
$543$	−28.7156	+	49.7368i	−1.23230	+	2.13441i
$544$		0			0
$545$	3.26205			0.139731
$546$		0			0
$547$	21.0248			0.898954			0.449477	−	0.893292i	$-0.351610\pi$
$547$	21.0248			0.898954			0.449477	+	0.893292i	$0.351610\pi$
$548$		0			0
$549$	31.1160	−	53.8945i	1.32800	−	2.30016i
$550$		0			0
$551$	−10.1159			−0.430951
$552$		0			0
$553$	10.4194	+	18.0469i	0.443077	+	0.767433i
$554$		0			0
$555$	−20.2032	−	34.9930i	−0.857578	−	1.48537i
$556$		0			0
$557$	−7.43147	+	12.8717i	−0.314881	+	0.545391i	−0.979412	−	0.201870i	$-0.935298\pi$
$557$	−7.43147	+	12.8717i	−0.314881	+	0.545391i	0.664531	+	0.747261i	$0.268631\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	50.5347	−	87.5287i	2.13358	−	3.69547i
$562$		0			0
$563$	14.4553	+	25.0372i	0.609217	+	1.05519i	0.991370	+	0.131095i	$0.0418494\pi$
$563$	14.4553	+	25.0372i	0.609217	+	1.05519i	−0.382153	+	0.924099i	$0.624817\pi$
$564$		0			0
$565$	7.21379	+	12.4947i	0.303486	+	0.525654i
$566$		0			0
$567$	−0.0392287			−0.00164745
$568$		0			0
$569$	−15.1658	+	26.2680i	−0.635785	+	1.10121i	0.350563	+	0.936539i	$0.385990\pi$
$569$	−15.1658	+	26.2680i	−0.635785	+	1.10121i	−0.986348	+	0.164673i	$0.947343\pi$
$570$		0			0
$571$	31.9017			1.33504			0.667522	−	0.744590i	$-0.267355\pi$
$571$	31.9017			1.33504			0.667522	+	0.744590i	$0.267355\pi$
$572$		0			0
$573$	9.61894			0.401837
$574$		0			0
$575$	−4.41574	+	7.64828i	−0.184149	+	0.318955i
$576$		0			0
$577$	−43.8364			−1.82493			−0.912466	−	0.409152i	$-0.865825\pi$
$577$	−43.8364			−1.82493			−0.912466	+	0.409152i	$0.865825\pi$
$578$		0			0
$579$	−2.35690	−	4.08226i	−0.0979492	−	0.169653i
$580$		0			0
$581$	0.0353438	+	0.0612173i	0.00146631	+	0.00253972i
$582$		0			0
$583$	−34.4720	+	59.7072i	−1.42768	+	2.47282i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.05615	−	1.82931i	0.0435922	−	0.0755038i	−0.843406	−	0.537277i	$-0.819453\pi$
$587$	1.05615	−	1.82931i	0.0435922	−	0.0755038i	0.886998	+	0.461773i	$0.152786\pi$
$588$		0			0
$589$	−2.98188	−	5.16476i	−0.122866	−	0.212810i
$590$		0			0
$591$	−37.7585	−	65.3996i	−1.55318	−	2.69018i
$592$		0			0
$593$	−1.98062			−0.0813344			−0.0406672	−	0.999173i	$-0.512948\pi$
$593$	−1.98062			−0.0813344			−0.0406672	+	0.999173i	$0.512948\pi$
$594$		0			0
$595$	14.2153	−	24.6216i	0.582770	−	1.00939i
$596$		0			0
$597$	56.2640			2.30273
$598$		0			0
$599$	−14.6045			−0.596722			−0.298361	−	0.954453i	$-0.596440\pi$
$599$	−14.6045			−0.596722			−0.298361	+	0.954453i	$0.596440\pi$
$600$		0			0
$601$	−7.89911	+	13.6817i	−0.322211	+	0.558086i	−0.980944	−	0.194291i	$-0.937760\pi$
$601$	−7.89911	+	13.6817i	−0.322211	+	0.558086i	0.658733	+	0.752377i	$0.271093\pi$
$602$		0			0
$603$	−10.5308			−0.428847
$604$		0			0
$605$	−42.0773	−	72.8801i	−1.71069	−	2.96300i
$606$		0			0
$607$	−12.9998	−	22.5163i	−0.527644	−	0.913906i	−0.999481	−	0.0322204i	$-0.989742\pi$
$607$	−12.9998	−	22.5163i	−0.527644	−	0.913906i	0.471837	−	0.881686i	$-0.343591\pi$
$608$		0			0
$609$	15.3388	−	26.5675i	0.621558	−	1.07657i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−6.22790	+	10.7870i	−0.251542	+	0.435684i	−0.963951	−	0.266081i	$-0.914271\pi$
$613$	−6.22790	+	10.7870i	−0.251542	+	0.435684i	0.712408	+	0.701765i	$0.247604\pi$
$614$		0			0
$615$	27.8620	+	48.2585i	1.12351	+	1.94597i
$616$		0			0
$617$	−19.0362	−	32.9716i	−0.766367	−	1.32739i	−0.939521	−	0.342492i	$-0.888729\pi$
$617$	−19.0362	−	32.9716i	−0.766367	−	1.32739i	0.173153	−	0.984895i	$-0.444604\pi$
$618$		0			0
$619$	−25.8678			−1.03972			−0.519858	−	0.854253i	$-0.674015\pi$
$619$	−25.8678			−1.03972			−0.519858	+	0.854253i	$0.674015\pi$
$620$		0			0
$621$	8.03266	−	13.9130i	0.322339	−	0.558308i
$622$		0			0
$623$	−13.4112			−0.537308
$624$		0			0
$625$	−31.1269			−1.24508
$626$		0			0
$627$	14.9412	−	25.8788i	0.596692	−	1.03350i
$628$		0			0
$629$	28.9815			1.15557
$630$		0			0
$631$	−3.54072	−	6.13271i	−0.140954	−	0.244139i	0.786902	−	0.617078i	$-0.211684\pi$
$631$	−3.54072	−	6.13271i	−0.140954	−	0.244139i	−0.927856	+	0.372938i	$0.878350\pi$
$632$		0			0
$633$	−11.5782	−	20.0541i	−0.460193	−	0.797078i
$634$		0			0
$635$	14.5172	−	25.1446i	0.576098	−	0.997832i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−26.4496	+	45.8121i	−1.04633	+	1.81230i
$640$		0			0
$641$	2.39815	+	4.15372i	0.0947212	+	0.164062i	0.909492	−	0.415721i	$-0.136471\pi$
$641$	2.39815	+	4.15372i	0.0947212	+	0.164062i	−0.814771	+	0.579783i	$0.803137\pi$
$642$		0			0
$643$	−10.1697	−	17.6145i	−0.401055	−	0.694647i	0.592799	−	0.805351i	$-0.298023\pi$
$643$	−10.1697	−	17.6145i	−0.401055	−	0.694647i	−0.993853	+	0.110704i	$0.964690\pi$
$644$		0			0
$645$	22.3056			0.878282
$646$		0			0
$647$	3.01208	−	5.21708i	0.118417	−	0.205105i	−0.800723	−	0.599034i	$-0.795551\pi$
$647$	3.01208	−	5.21708i	0.118417	−	0.205105i	0.919141	+	0.393930i	$0.128885\pi$
$648$		0			0
$649$	59.4083			2.33198
$650$		0			0
$651$	18.0858			0.708837
$652$		0			0
$653$	9.59568	−	16.6202i	0.375508	−	0.650399i	−0.614895	−	0.788609i	$-0.710802\pi$
$653$	9.59568	−	16.6202i	0.375508	−	0.650399i	0.990403	+	0.138210i	$0.0441349\pi$
$654$		0			0
$655$	35.9584			1.40501
$656$		0			0
$657$	−4.73221	−	8.19643i	−0.184621	−	0.319773i
$658$		0			0
$659$	−18.8376	−	32.6276i	−0.733808	−	1.27099i	−0.955244	−	0.295818i	$-0.904408\pi$
$659$	−18.8376	−	32.6276i	−0.733808	−	1.27099i	0.221437	−	0.975175i	$-0.428925\pi$
$660$		0			0
$661$	1.84063	−	3.18807i	0.0715924	−	0.124002i	−0.828007	−	0.560718i	$-0.810525\pi$
$661$	1.84063	−	3.18807i	0.0715924	−	0.124002i	0.899599	+	0.436716i	$0.143859\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.20291	−	7.27965i	0.162982	−	0.282293i
$666$		0			0
$667$	−9.41132	−	16.3009i	−0.364408	−	0.631173i
$668$		0			0
$669$	32.6538	+	56.5580i	1.26247	+	2.18666i
$670$		0			0
$671$	82.1807			3.17255
$672$		0			0
$673$	−2.31431	+	4.00851i	−0.0892103	+	0.154517i	−0.907178	−	0.420748i	$-0.861768\pi$
$673$	−2.31431	+	4.00851i	−0.0892103	+	0.154517i	0.817967	+	0.575265i	$0.195101\pi$
$674$		0			0
$675$	−14.7845			−0.569055
$676$		0			0
$677$	−1.57109			−0.0603818			−0.0301909	−	0.999544i	$-0.509612\pi$
$677$	−1.57109			−0.0603818			−0.0301909	+	0.999544i	$0.509612\pi$
$678$		0			0
$679$	0.425428	−	0.736862i	0.0163264	−	0.0282782i
$680$		0			0
$681$	39.8582			1.52737
$682$		0			0
$683$	−22.0716	−	38.2292i	−0.844548	−	1.46280i	−0.886013	−	0.463660i	$-0.846536\pi$
$683$	−22.0716	−	38.2292i	−0.844548	−	1.46280i	0.0414650	−	0.999140i	$-0.486798\pi$
$684$		0			0
$685$	−1.10992	−	1.92243i	−0.0424077	−	0.0734523i
$686$		0			0
$687$	37.6459	−	65.2045i	1.43628	−	2.48771i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	15.6223	−	27.0586i	0.594300	−	1.02936i	−0.399345	−	0.916801i	$-0.630762\pi$
$691$	15.6223	−	27.0586i	0.594300	−	1.02936i	0.993645	−	0.112557i	$-0.0359042\pi$
$692$		0			0
$693$	27.9964	+	48.4912i	1.06350	+	1.84203i
$694$		0			0
$695$	8.25786	+	14.3030i	0.313239	+	0.542545i
$696$		0			0
$697$	−39.9681			−1.51390
$698$		0			0
$699$	−2.88404	+	4.99531i	−0.109085	+	0.188940i
$700$		0			0
$701$	6.88876			0.260185			0.130092	−	0.991502i	$-0.458473\pi$
$701$	6.88876			0.260185			0.130092	+	0.991502i	$0.458473\pi$
$702$		0			0
$703$	8.56870			0.323174
$704$		0			0
$705$	5.94989	−	10.3055i	0.224086	−	0.388128i
$706$		0			0
$707$	11.9487			0.449377
$708$		0			0
$709$	−11.7133	−	20.2880i	−0.439901	−	0.761930i	0.557781	−	0.829988i	$-0.311653\pi$
$709$	−11.7133	−	20.2880i	−0.439901	−	0.761930i	−0.997681	+	0.0680580i	$0.978320\pi$
$710$		0			0
$711$	28.0492	+	48.5827i	1.05193	+	1.82199i
$712$		0			0
$713$	5.54838	−	9.61008i	0.207789	−	0.359900i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	12.6637	−	21.9341i	0.472934	−	0.819145i
$718$		0			0
$719$	−8.08330	−	14.0007i	−0.301456	−	0.522138i	0.675010	−	0.737809i	$-0.264139\pi$
$719$	−8.08330	−	14.0007i	−0.301456	−	0.522138i	−0.976466	+	0.215671i	$0.930806\pi$
$720$		0			0
$721$	−1.09299	−	1.89311i	−0.0407051	−	0.0705033i
$722$		0			0
$723$	−23.2107			−0.863217
$724$		0			0
$725$	−8.66099	+	15.0013i	−0.321661	+	0.557133i
$726$		0			0
$727$	−45.2054			−1.67657			−0.838287	−	0.545229i	$-0.816443\pi$
$727$	−45.2054			−1.67657			−0.838287	+	0.545229i	$0.816443\pi$
$728$		0			0
$729$	−43.6980			−1.61844
$730$		0			0
$731$	−7.99934	+	13.8553i	−0.295866	+	0.512455i
$732$		0			0
$733$	−51.4631			−1.90083			−0.950416	−	0.310980i	$-0.899343\pi$
$733$	−51.4631			−1.90083			−0.950416	+	0.310980i	$0.899343\pi$
$734$		0			0
$735$	−14.7322	−	25.5169i	−0.543406	−	0.941206i
$736$		0			0
$737$	−6.95324	−	12.0434i	−0.256126	−	0.443623i
$738$		0			0
$739$	6.10752	−	10.5785i	0.224669	−	0.389138i	−0.731551	−	0.681787i	$-0.761203\pi$
$739$	6.10752	−	10.5785i	0.224669	−	0.389138i	0.956220	+	0.292649i	$0.0945366\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.7591	−	44.6161i	0.945010	−	1.63681i	0.189280	−	0.981923i	$-0.439385\pi$
$743$	25.7591	−	44.6161i	0.945010	−	1.63681i	0.755730	−	0.654883i	$-0.227282\pi$
$744$		0			0
$745$	−6.64191	−	11.5041i	−0.243341	−	0.421478i
$746$		0			0
$747$	0.0951463	+	0.164798i	0.00348122	+	0.00602965i
$748$		0			0
$749$	−8.04892			−0.294101
$750$		0			0
$751$	−10.6625	+	18.4680i	−0.389079	+	0.673905i	−0.992326	−	0.123649i	$-0.960540\pi$
$751$	−10.6625	+	18.4680i	−0.389079	+	0.673905i	0.603246	+	0.797555i	$0.293874\pi$
$752$		0			0
$753$	−14.8116			−0.539766
$754$		0			0
$755$	−15.0519			−0.547795
$756$		0			0
$757$	14.2627	−	24.7037i	0.518387	−	0.897873i	−0.481385	−	0.876509i	$-0.659866\pi$
$757$	14.2627	−	24.7037i	0.518387	−	0.897873i	0.999772	−	0.0213632i	$-0.00680064\pi$
$758$		0			0
$759$	55.6021			2.01823
$760$		0			0
$761$	15.5831	+	26.9907i	0.564886	+	0.978411i	0.997060	+	0.0766207i	$0.0244131\pi$
$761$	15.5831	+	26.9907i	0.564886	+	0.978411i	−0.432175	+	0.901790i	$0.642254\pi$
$762$		0			0
$763$	−1.04892	−	1.81678i	−0.0379734	−	0.0657718i
$764$		0			0
$765$	38.2678	−	66.2819i	1.38358	−	2.39643i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	13.1905	−	22.8467i	0.475663	−	0.823872i	−0.523949	−	0.851750i	$-0.675542\pi$
$769$	13.1905	−	22.8467i	0.475663	−	0.823872i	0.999611	+	0.0278779i	$0.00887497\pi$
$770$		0			0
$771$	27.2630	+	47.2209i	0.981853	+	1.70062i
$772$		0			0
$773$	−0.838478	−	1.45229i	−0.0301580	−	0.0522351i	0.850553	−	0.525890i	$-0.176268\pi$
$773$	−0.838478	−	1.45229i	−0.0301580	−	0.0522351i	−0.880710	+	0.473655i	$0.842934\pi$
$774$		0			0
$775$	−10.2121			−0.366828
$776$		0			0
$777$	−12.9928	+	22.5041i	−0.466113	+	0.807331i
$778$		0			0
$779$	−11.8170			−0.423388
$780$		0			0
$781$	−69.8563			−2.49966
$782$		0			0
$783$	15.7552	−	27.2888i	0.563044	−	0.975221i
$784$		0			0
$785$	−31.4644			−1.12301
$786$		0			0
$787$	2.29440	+	3.97403i	0.0817867	+	0.141659i	0.904017	−	0.427496i	$-0.140604\pi$
$787$	2.29440	+	3.97403i	0.0817867	+	0.141659i	−0.822231	+	0.569154i	$0.807271\pi$
$788$		0			0
$789$	−27.1742	−	47.0671i	−0.967427	−	1.67563i
$790$		0			0
$791$	4.63922	−	8.03536i	0.164952	−	0.285705i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−42.2482	+	73.1761i	−1.49839	+	2.59529i
$796$		0			0
$797$	−19.0303	−	32.9614i	−0.674086	−	1.16755i	−0.976735	−	0.214450i	$-0.931204\pi$
$797$	−19.0303	−	32.9614i	−0.674086	−	1.16755i	0.302649	−	0.953102i	$-0.402129\pi$
$798$		0			0
$799$	4.26755	+	7.39162i	0.150975	+	0.261497i
$800$		0			0
$801$	−36.1032			−1.27564
$802$		0			0
$803$	6.24914	−	10.8238i	0.220527	−	0.381964i
$804$		0			0
$805$	15.6407			0.551263
$806$		0			0
$807$	10.1250			0.356416
$808$		0			0
$809$	−23.5308	+	40.7565i	−0.827299	+	1.43292i	0.0728511	+	0.997343i	$0.476790\pi$
$809$	−23.5308	+	40.7565i	−0.827299	+	1.43292i	−0.900150	+	0.435581i	$0.856543\pi$
$810$		0			0
$811$	6.21744			0.218324			0.109162	−	0.994024i	$-0.465183\pi$
$811$	6.21744			0.218324			0.109162	+	0.994024i	$0.465183\pi$
$812$		0			0
$813$	4.41036	+	7.63897i	0.154678	+	0.267910i
$814$		0			0
$815$	1.45593	+	2.52174i	0.0509989	+	0.0883327i
$816$		0			0
$817$	−2.36509	+	4.09646i	−0.0827441	+	0.143317i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.84213	−	13.5830i	0.273692	−	0.474049i	−0.696112	−	0.717933i	$-0.745088\pi$
$821$	7.84213	−	13.5830i	0.273692	−	0.474049i	0.969804	+	0.243884i	$0.0784217\pi$
$822$		0			0
$823$	12.6153	+	21.8503i	0.439741	+	0.761655i	0.997669	−	0.0682349i	$-0.0217367\pi$
$823$	12.6153	+	21.8503i	0.439741	+	0.761655i	−0.557928	+	0.829889i	$0.688403\pi$
$824$		0			0
$825$	−25.5846	−	44.3138i	−0.890740	−	1.54281i
$826$		0			0
$827$	−51.8582			−1.80328			−0.901642	−	0.432483i	$-0.857638\pi$
$827$	−51.8582			−1.80328			−0.901642	+	0.432483i	$0.857638\pi$
$828$		0			0
$829$	11.8596	−	20.5414i	0.411900	−	0.713432i	−0.583197	−	0.812331i	$-0.698198\pi$
$829$	11.8596	−	20.5414i	0.411900	−	0.713432i	0.995098	+	0.0988982i	$0.0315318\pi$
$830$		0			0
$831$	−27.1987			−0.943511
$832$		0			0
$833$	21.1333			0.732227
$834$		0			0
$835$	−3.93900	+	6.82255i	−0.136315	+	0.236104i
$836$		0			0
$837$	18.5767			0.642106
$838$		0			0
$839$	−6.51573	−	11.2856i	−0.224948	−	0.389621i	0.731356	−	0.681996i	$-0.238888\pi$
$839$	−6.51573	−	11.2856i	−0.224948	−	0.389621i	−0.956304	+	0.292375i	$0.905555\pi$
$840$		0			0
$841$	−3.95928	−	6.85767i	−0.136527	−	0.236471i
$842$		0			0
$843$	17.3116	−	29.9846i	0.596244	−	1.03273i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−27.0601	+	46.8695i	−0.929796	+	1.61045i
$848$		0			0
$849$	−20.3327	−	35.2173i	−0.697818	−	1.20866i
$850$		0			0
$851$	7.97189	+	13.8077i	0.273273	+	0.473323i
$852$		0			0
$853$	18.4155			0.630535			0.315267	−	0.949003i	$-0.397906\pi$
$853$	18.4155			0.630535			0.315267	+	0.949003i	$0.397906\pi$
$854$		0			0
$855$	11.3143	−	19.5970i	0.386941	−	0.670202i
$856$		0			0
$857$	−6.54288			−0.223500			−0.111750	−	0.993736i	$-0.535646\pi$
$857$	−6.54288			−0.223500			−0.111750	+	0.993736i	$0.535646\pi$
$858$		0			0
$859$	−38.9396			−1.32860			−0.664301	−	0.747465i	$-0.731271\pi$
$859$	−38.9396			−1.32860			−0.664301	+	0.747465i	$0.731271\pi$
$860$		0			0
$861$	17.9182	−	31.0352i	0.610650	−	1.05768i
$862$		0			0
$863$	−40.8732			−1.39134			−0.695670	−	0.718361i	$-0.744893\pi$
$863$	−40.8732			−1.39134			−0.695670	+	0.718361i	$0.744893\pi$
$864$		0			0
$865$	29.6775	+	51.4030i	1.00907	+	1.74776i
$866$		0			0
$867$	20.6060	+	35.6907i	0.699818	+	1.21212i
$868$		0			0
$869$	−37.0405	+	64.1560i	−1.25651	+	2.17634i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.14526	−	1.98365i	0.0387612	−	0.0671363i
$874$		0			0
$875$	5.42543	+	9.39712i	0.183413	+	0.317681i
$876$		0			0
$877$	−12.9717	−	22.4676i	−0.438022	−	0.758676i	0.559515	−	0.828820i	$-0.310987\pi$
$877$	−12.9717	−	22.4676i	−0.438022	−	0.758676i	−0.997537	+	0.0701443i	$0.977654\pi$
$878$		0			0
$879$	−39.4553			−1.33079
$880$		0			0
$881$	28.2787	−	48.9802i	0.952735	−	1.65019i	0.213266	−	0.976994i	$-0.431590\pi$
$881$	28.2787	−	48.9802i	0.952735	−	1.65019i	0.739469	−	0.673191i	$-0.235077\pi$
$882$		0			0
$883$	−11.4910			−0.386702			−0.193351	−	0.981130i	$-0.561936\pi$
$883$	−11.4910			−0.386702			−0.193351	+	0.981130i	$0.561936\pi$
$884$		0			0
$885$	72.8098			2.44748
$886$		0			0
$887$	2.25518	−	3.90608i	0.0757214	−	0.131153i	−0.825678	−	0.564141i	$-0.809207\pi$
$887$	2.25518	−	3.90608i	0.0757214	−	0.131153i	0.901400	+	0.432988i	$0.142541\pi$
$888$		0			0
$889$	−18.6722			−0.626244
$890$		0			0
$891$	−0.0697281	−	0.120773i	−0.00233598	−	0.00404604i
$892$		0			0
$893$	1.26175	+	2.18541i	0.0422228	+	0.0731321i
$894$		0			0
$895$	−25.7174	+	44.5439i	−0.859639	+	1.48894i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.8826	−	18.8491i	0.362953	−	0.628654i
$900$		0			0
$901$	−30.3025	−	52.4855i	−1.00952	−	1.74855i
$902$		0			0
$903$	−7.17241	−	12.4230i	−0.238683	−	0.413411i
$904$		0			0
$905$	−57.4312			−1.90908
$906$		0			0
$907$	−9.98374	+	17.2923i	−0.331505	+	0.574183i	−0.982807	−	0.184635i	$-0.940890\pi$
$907$	−9.98374	+	17.2923i	−0.331505	+	0.574183i	0.651303	+	0.758818i	$0.274223\pi$
$908$		0			0
$909$	32.1661			1.06688
$910$		0			0
$911$	4.73855			0.156995			0.0784975	−	0.996914i	$-0.474988\pi$
$911$	4.73855			0.156995			0.0784975	+	0.996914i	$0.474988\pi$
$912$		0			0
$913$	−0.125646	+	0.217625i	−0.00415827	+	0.00720233i
$914$		0			0
$915$	100.719			3.32968
$916$		0			0
$917$	−11.5625	−	20.0268i	−0.381827	−	0.661344i
$918$		0			0
$919$	6.00700	+	10.4044i	0.198153	+	0.343210i	0.947929	−	0.318480i	$-0.103172\pi$
$919$	6.00700	+	10.4044i	0.198153	+	0.343210i	−0.749777	+	0.661691i	$0.769839\pi$
$920$		0			0
$921$	−28.0127	+	48.5194i	−0.923049	+	1.59877i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	7.33632	−	12.7069i	0.241217	−	0.417800i
$926$		0			0
$927$	−2.94235	−	5.09631i	−0.0966396	−	0.167385i
$928$		0			0
$929$	12.6097	+	21.8406i	0.413710	+	0.716567i	0.995292	−	0.0969208i	$-0.0308994\pi$
$929$	12.6097	+	21.8406i	0.413710	+	0.716567i	−0.581582	+	0.813488i	$0.697566\pi$
$930$		0			0
$931$	6.24831			0.204780
$932$		0			0
$933$	30.2969	−	52.4757i	0.991875	−	1.71798i
$934$		0			0
$935$	101.069			3.30533
$936$		0			0
$937$	−9.69143			−0.316605			−0.158303	−	0.987391i	$-0.550602\pi$
$937$	−9.69143			−0.316605			−0.158303	+	0.987391i	$0.550602\pi$
$938$		0			0
$939$	1.99061	−	3.44783i	0.0649610	−	0.112516i
$940$		0			0
$941$	5.46117			0.178029			0.0890146	−	0.996030i	$-0.471628\pi$
$941$	5.46117			0.178029			0.0890146	+	0.996030i	$0.471628\pi$
$942$		0			0
$943$	−10.9940	−	19.0421i	−0.358013	−	0.620096i
$944$		0			0
$945$	13.0918	+	22.6757i	0.425876	+	0.737639i
$946$		0			0
$947$	−16.9306	+	29.3246i	−0.550170	+	0.952922i	0.448092	+	0.893987i	$0.352104\pi$
$947$	−16.9306	+	29.3246i	−0.550170	+	0.952922i	−0.998262	+	0.0589343i	$0.981230\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	13.5308	−	23.4360i	0.438766	−	0.759965i
$952$		0			0
$953$	23.7223	+	41.0882i	0.768440	+	1.33098i	0.938408	+	0.345528i	$0.112300\pi$
$953$	23.7223	+	41.0882i	0.768440	+	1.33098i	−0.169968	+	0.985450i	$0.554367\pi$
$954$		0			0
$955$	4.80947	+	8.33025i	0.155631	+	0.269560i
$956$		0			0
$957$	109.057			3.52532
$958$		0			0
$959$	−0.713792	+	1.23632i	−0.0230495	+	0.0399230i
$960$		0			0
$961$	−18.1685			−0.586081
$962$		0			0
$963$	−21.6679			−0.698237
$964$		0			0
$965$	2.35690	−	4.08226i	0.0758712	−	0.131413i
$966$		0			0
$967$	−52.5163			−1.68881			−0.844406	−	0.535705i	$-0.820046\pi$
$967$	−52.5163			−1.68881			−0.844406	+	0.535705i	$0.820046\pi$
$968$		0			0
$969$	13.1340	+	22.7488i	0.421925	+	0.730796i
$970$		0			0
$971$	0.593523	+	1.02801i	0.0190471	+	0.0329905i	0.875392	−	0.483414i	$-0.160603\pi$
$971$	0.593523	+	1.02801i	0.0190471	+	0.0329905i	−0.856345	+	0.516405i	$0.827270\pi$
$972$		0			0
$973$	5.31067	−	9.19834i	0.170252	−	0.294885i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.0227	+	29.4842i	−0.544605	+	0.943284i	0.454026	+	0.890988i	$0.349987\pi$
$977$	−17.0227	+	29.4842i	−0.544605	+	0.943284i	−0.998632	+	0.0522959i	$0.983346\pi$
$978$		0			0
$979$	−23.8381	−	41.2888i	−0.761869	−	1.31960i
$980$		0			0
$981$	−2.82371	−	4.89081i	−0.0901541	−	0.156151i
$982$		0			0
$983$	−38.5338			−1.22904			−0.614518	−	0.788903i	$-0.710650\pi$
$983$	−38.5338			−1.22904			−0.614518	+	0.788903i	$0.710650\pi$
$984$		0			0
$985$	37.7585	−	65.3996i	1.20308	−	2.08380i
$986$		0			0
$987$	−7.65279			−0.243591
$988$		0			0
$989$	−8.80146			−0.279870
$990$		0			0
$991$	−22.1876	+	38.4301i	−0.704812	+	1.22077i	0.261947	+	0.965082i	$0.415636\pi$
$991$	−22.1876	+	38.4301i	−0.704812	+	1.22077i	−0.966759	+	0.255689i	$0.917698\pi$
$992$		0			0
$993$	−89.4814			−2.83961
$994$		0			0
$995$	28.1320	+	48.7260i	0.891844	+	1.54472i
$996$		0			0
$997$	14.6177	+	25.3187i	0.462949	+	0.801851i	0.999106	−	0.0422673i	$-0.0134581\pi$
$997$	14.6177	+	25.3187i	0.462949	+	0.801851i	−0.536158	+	0.844118i	$0.680125\pi$
$998$		0			0
$999$	−13.3455	+	23.1150i	−0.422232	+	0.731328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.i.j.529.3		6
13.2	odd	12		1352.2.o.g.361.5		12
13.3	even	3	inner	1352.2.i.j.1329.3		6
13.4	even	6		1352.2.a.i.1.1	✓	3
13.5	odd	4		1352.2.o.g.1161.5		12
13.6	odd	12		1352.2.f.e.337.1		6
13.7	odd	12		1352.2.f.e.337.2		6
13.8	odd	4		1352.2.o.g.1161.6		12
13.9	even	3		1352.2.a.j.1.1	yes	3
13.10	even	6		1352.2.i.i.1329.3		6
13.11	odd	12		1352.2.o.g.361.6		12
13.12	even	2		1352.2.i.i.529.3		6
52.7	even	12		2704.2.f.p.337.6		6
52.19	even	12		2704.2.f.p.337.5		6
52.35	odd	6		2704.2.a.bc.1.3		3
52.43	odd	6		2704.2.a.bb.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1352.2.a.i.1.1	✓	3	13.4	even	6
1352.2.a.j.1.1	yes	3	13.9	even	3
1352.2.f.e.337.1		6	13.6	odd	12
1352.2.f.e.337.2		6	13.7	odd	12
1352.2.i.i.529.3		6	13.12	even	2
1352.2.i.i.1329.3		6	13.10	even	6
1352.2.i.j.529.3		6	1.1	even	1	trivial
1352.2.i.j.1329.3		6	13.3	even	3	inner
1352.2.o.g.361.5		12	13.2	odd	12
1352.2.o.g.361.6		12	13.11	odd	12
1352.2.o.g.1161.5		12	13.5	odd	4
1352.2.o.g.1161.6		12	13.8	odd	4
2704.2.a.bb.1.3		3	52.43	odd	6
2704.2.a.bc.1.3		3	52.35	odd	6
2704.2.f.p.337.5		6	52.19	even	12
2704.2.f.p.337.6		6	52.7	even	12

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:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40097 - 2.42655i) q^{3} +2.80194 q^{5} +(-0.900969 - 1.56052i) q^{7} +(-2.42543 - 4.20096i) q^{9} +O(q^{10})\)	\(q+(1.40097 - 2.42655i) q^{3} +2.80194 q^{5} +(-0.900969 - 1.56052i) q^{7} +(-2.42543 - 4.20096i) q^{9} +(3.20291 - 5.54760i) q^{11} +(3.92543 - 6.79904i) q^{15} +(2.81551 + 4.87661i) q^{17} +(0.832437 + 1.44182i) q^{19} -5.04892 q^{21} +(-1.54892 + 2.68280i) q^{23} +2.85086 q^{25} -5.18598 q^{27} +(-3.03803 + 5.26203i) q^{29} -3.58211 q^{31} +(-8.97434 - 15.5440i) q^{33} +(-2.52446 - 4.37249i) q^{35} +(2.57338 - 4.45722i) q^{37} +(-3.54892 + 6.14691i) q^{41} +(1.42058 + 2.46052i) q^{43} +(-6.79590 - 11.7708i) q^{45} +1.51573 q^{47} +(1.87651 - 3.25021i) q^{49} +15.7778 q^{51} -10.7627 q^{53} +(8.97434 - 15.5440i) q^{55} +4.66487 q^{57} +(4.63706 + 8.03163i) q^{59} +(6.41454 + 11.1103i) q^{61} +(-4.37047 + 7.56988i) q^{63} +(1.08546 - 1.88007i) q^{67} +(4.33997 + 7.51705i) q^{69} +(-5.45257 - 9.44414i) q^{71} +1.95108 q^{73} +(3.99396 - 6.91774i) q^{75} -11.5429 q^{77} -11.5646 q^{79} +(0.0108851 - 0.0188536i) q^{81} -0.0392287 q^{83} +(7.88889 + 13.6640i) q^{85} +(8.51238 + 14.7439i) q^{87} +(3.72132 - 6.44552i) q^{89} +(-5.01842 + 8.69215i) q^{93} +(2.33244 + 4.03990i) q^{95} +(0.236094 + 0.408928i) q^{97} -31.0737 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} + 8 q^{5} - q^{7} - q^{9}+O(q^{10}) \) 6 * q + 4 * q^3 + 8 * q^5 - q^7 - q^9	\( 6 q + 4 q^{3} + 8 q^{5} - q^{7} - q^{9} + 6 q^{11} + 10 q^{15} + 2 q^{17} + 6 q^{19} - 12 q^{21} + 9 q^{23} - 10 q^{25} - 2 q^{27} - 3 q^{29} - 10 q^{31} - 22 q^{33} - 6 q^{35} - 12 q^{37} - 3 q^{41} + 17 q^{43} - 13 q^{45} - 16 q^{47} + 16 q^{49} + 10 q^{51} - 30 q^{53} + 22 q^{55} + 30 q^{57} + 17 q^{59} + 28 q^{61} - 12 q^{63} + 17 q^{67} + 2 q^{69} - 7 q^{71} + 30 q^{73} + 5 q^{75} - 32 q^{77} - 26 q^{79} - 3 q^{81} - 26 q^{83} + 5 q^{85} + 4 q^{87} - 19 q^{89} - 2 q^{93} + 15 q^{95} - 5 q^{97} - 74 q^{99}+O(q^{100}) \) 6 * q + 4 * q^3 + 8 * q^5 - q^7 - q^9 + 6 * q^11 + 10 * q^15 + 2 * q^17 + 6 * q^19 - 12 * q^21 + 9 * q^23 - 10 * q^25 - 2 * q^27 - 3 * q^29 - 10 * q^31 - 22 * q^33 - 6 * q^35 - 12 * q^37 - 3 * q^41 + 17 * q^43 - 13 * q^45 - 16 * q^47 + 16 * q^49 + 10 * q^51 - 30 * q^53 + 22 * q^55 + 30 * q^57 + 17 * q^59 + 28 * q^61 - 12 * q^63 + 17 * q^67 + 2 * q^69 - 7 * q^71 + 30 * q^73 + 5 * q^75 - 32 * q^77 - 26 * q^79 - 3 * q^81 - 26 * q^83 + 5 * q^85 + 4 * q^87 - 19 * q^89 - 2 * q^93 + 15 * q^95 - 5 * q^97 - 74 * q^99

Introduction

L-functions

Modular forms

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Database

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