LMFDB - Embedded newform 2548.2.bb.d.1733.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(569,2548)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2548.569"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-14,0,-6,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1733.3
Root			$1.75101i$ of defining polynomial
Character	$\chi$	$=$	2548.1733
Dual form			2548.2.bb.d.569.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.875503 - 1.51642i) q^{3} +(1.19976 - 0.692682i) q^{5} +(-0.0330100 + 0.0571750i) q^{9} +(-0.998442 + 0.576451i) q^{11} +(-1.65348 + 3.20406i) q^{13} +(-2.10079 - 1.21289i) q^{15} +1.56249 q^{17} +(7.26523 + 4.19458i) q^{19} +2.22134 q^{23} +(-1.54038 + 2.66802i) q^{25} -5.13741 q^{27} +(-1.43491 + 2.48533i) q^{29} +(5.75927 + 3.32512i) q^{31} +(1.74828 + 1.00937i) q^{33} -3.48068i q^{37} +(6.30631 - 0.297802i) q^{39} +(10.8758 + 6.27917i) q^{41} +(-3.07841 - 5.33196i) q^{43} +0.0914616i q^{45} +(6.41233 - 3.70216i) q^{47} +(-1.36797 - 2.36939i) q^{51} +(-5.61504 + 9.72553i) q^{53} +(-0.798593 + 1.38320i) q^{55} -14.6895i q^{57} +8.05559i q^{59} +(-0.829207 + 1.43623i) q^{61} +(0.235615 + 4.98944i) q^{65} +(3.21406 - 1.85564i) q^{67} +(-1.94479 - 3.36848i) q^{69} +(8.60538 - 4.96832i) q^{71} +(-2.85962 - 1.65100i) q^{73} +5.39444 q^{75} +(-2.32405 - 4.02538i) q^{79} +(4.59685 + 7.96198i) q^{81} -1.82551i q^{83} +(1.87462 - 1.08231i) q^{85} +5.02506 q^{87} -2.37681i q^{89} -11.6446i q^{93} +11.6220 q^{95} +(-6.53519 + 3.77309i) q^{97} -0.0761145i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} + 6 q^{15} - 4 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} + 30 q^{31} - 42 q^{33} - 18 q^{39} + 36 q^{41} + 6 q^{43} - 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 4 q^{61}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 + 6 * q^15 - 4 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 + 30 * q^31 - 42 * q^33 - 18 * q^39 + 36 * q^41 + 6 * q^43 - 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 4 * q^61 + 30 * q^65 - 24 * q^67 - 52 * q^69 + 36 * q^71 - 12 * q^73 + 20 * q^75 - 4 * q^79 + 42 * q^85 - 52 * q^87 + 60 * q^95 - 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.875503	−	1.51642i	−0.505472	−	0.875503i	−0.999980	−	0.00632977i	$-0.997985\pi$
$3$	−0.875503	−	1.51642i	−0.505472	−	0.875503i	0.494508	−	0.869173i	$-0.335348\pi$
$4$		0			0
$5$	1.19976	−	0.692682i	0.536549	−	0.309777i	−0.207130	−	0.978313i	$-0.566412\pi$
$5$	1.19976	−	0.692682i	0.536549	−	0.309777i	0.743679	+	0.668537i	$0.233079\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.0330100	+	0.0571750i	−0.0110033	+	0.0190583i
$10$		0			0
$11$	−0.998442	+	0.576451i	−0.301042	+	0.173806i	−0.642911	−	0.765941i	$-0.722273\pi$
$11$	−0.998442	+	0.576451i	−0.301042	+	0.173806i	0.341869	+	0.939748i	$0.388940\pi$
$12$		0			0
$13$	−1.65348	+	3.20406i	−0.458593	+	0.888647i
$13$	−1.65348	+	3.20406i	−0.458593	+	0.888647i
$14$		0			0
$15$	−2.10079	−	1.21289i	−0.542420	−	0.313167i
$16$		0			0
$17$	1.56249			0.378960			0.189480	−	0.981885i	$-0.439320\pi$
$17$	1.56249			0.378960			0.189480	+	0.981885i	$0.439320\pi$
$18$		0			0
$19$	7.26523	+	4.19458i	1.66676	+	0.962303i	0.969368	+	0.245612i	$0.0789888\pi$
$19$	7.26523	+	4.19458i	1.66676	+	0.962303i	0.697390	+	0.716692i	$0.254345\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.22134			0.463182			0.231591	−	0.972813i	$-0.425607\pi$
$23$	2.22134			0.463182			0.231591	+	0.972813i	$0.425607\pi$
$24$		0			0
$25$	−1.54038	+	2.66802i	−0.308077	+	0.533605i
$26$		0			0
$27$	−5.13741			−0.988696
$28$		0			0
$29$	−1.43491	+	2.48533i	−0.266455	+	0.461514i	−0.967944	−	0.251167i	$-0.919186\pi$
$29$	−1.43491	+	2.48533i	−0.266455	+	0.461514i	0.701489	+	0.712681i	$0.252519\pi$
$30$		0			0
$31$	5.75927	+	3.32512i	1.03440	+	0.597209i	0.918241	−	0.396022i	$-0.129610\pi$
$31$	5.75927	+	3.32512i	1.03440	+	0.597209i	0.116155	+	0.993231i	$0.462943\pi$
$32$		0			0
$33$	1.74828	+	1.00937i	0.304336	+	0.175708i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	3.48068i		−	0.572220i	−0.958197	−	0.286110i	$-0.907638\pi$
$37$		−	3.48068i		−	0.572220i	0.958197	−	0.286110i	$-0.0923623\pi$
$38$		0			0
$39$	6.30631	−	0.297802i	1.00982	−	0.0476864i
$40$		0			0
$41$	10.8758	+	6.27917i	1.69852	+	0.980641i	0.947167	+	0.320740i	$0.103932\pi$
$41$	10.8758	+	6.27917i	1.69852	+	0.980641i	0.751353	+	0.659901i	$0.229402\pi$
$42$		0			0
$43$	−3.07841	−	5.33196i	−0.469453	−	0.813116i	0.529937	−	0.848037i	$-0.322215\pi$
$43$	−3.07841	−	5.33196i	−0.469453	−	0.813116i	−0.999390	+	0.0349208i	$0.988882\pi$
$44$		0			0
$45$			0.0914616i			0.0136343i
$46$		0			0
$47$	6.41233	−	3.70216i	0.935334	−	0.540015i	0.0468394	−	0.998902i	$-0.485085\pi$
$47$	6.41233	−	3.70216i	0.935334	−	0.540015i	0.888495	+	0.458887i	$0.151752\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.36797	−	2.36939i	−0.191554	−	0.331781i
$52$		0			0
$53$	−5.61504	+	9.72553i	−0.771285	+	1.33590i	0.165574	+	0.986197i	$0.447052\pi$
$53$	−5.61504	+	9.72553i	−0.771285	+	1.33590i	−0.936859	+	0.349707i	$0.886281\pi$
$54$		0			0
$55$	−0.798593	+	1.38320i	−0.107682	+	0.186511i
$56$		0			0
$57$		−	14.6895i		−	1.94567i
$58$		0			0
$59$			8.05559i			1.04875i	0.851488	+	0.524374i	$0.175701\pi$
$59$			8.05559i			1.04875i	−0.851488	+	0.524374i	$0.824299\pi$
$60$		0			0
$61$	−0.829207	+	1.43623i	−0.106169	+	0.183890i	−0.914215	−	0.405229i	$-0.867192\pi$
$61$	−0.829207	+	1.43623i	−0.106169	+	0.183890i	0.808046	+	0.589119i	$0.200525\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.235615	+	4.98944i	0.0292245	+	0.618864i
$66$		0			0
$67$	3.21406	−	1.85564i	0.392660	−	0.226702i	−0.290652	−	0.956829i	$-0.593872\pi$
$67$	3.21406	−	1.85564i	0.392660	−	0.226702i	0.683312	+	0.730126i	$0.260539\pi$
$68$		0			0
$69$	−1.94479	−	3.36848i	−0.234125	−	0.405517i
$70$		0			0
$71$	8.60538	−	4.96832i	1.02127	−	0.589631i	0.106799	−	0.994281i	$-0.465940\pi$
$71$	8.60538	−	4.96832i	1.02127	−	0.589631i	0.914472	+	0.404650i	$0.132607\pi$
$72$		0			0
$73$	−2.85962	−	1.65100i	−0.334693	−	0.193235i	0.323230	−	0.946320i	$-0.395231\pi$
$73$	−2.85962	−	1.65100i	−0.334693	−	0.193235i	−0.657923	+	0.753086i	$0.728565\pi$
$74$		0			0
$75$	5.39444			0.622897
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.32405	−	4.02538i	−0.261477	−	0.452891i	0.705158	−	0.709050i	$-0.250876\pi$
$79$	−2.32405	−	4.02538i	−0.261477	−	0.452891i	−0.966635	+	0.256160i	$0.917543\pi$
$80$		0			0
$81$	4.59685	+	7.96198i	0.510761	+	0.884664i
$82$		0			0
$83$		−	1.82551i		−	0.200376i	−0.994969	−	0.100188i	$-0.968056\pi$
$83$		−	1.82551i		−	0.200376i	0.994969	−	0.100188i	$-0.0319445\pi$
$84$		0			0
$85$	1.87462	−	1.08231i	0.203331	−	0.117393i
$86$		0			0
$87$	5.02506			0.538743
$88$		0			0
$89$		−	2.37681i		−	0.251941i	−0.992034	−	0.125970i	$-0.959796\pi$
$89$		−	2.37681i		−	0.251941i	0.992034	−	0.125970i	$-0.0402045\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		−	11.6446i		−	1.20749i
$94$		0			0
$95$	11.6220			1.19240
$96$		0			0
$97$	−6.53519	+	3.77309i	−0.663548	+	0.383099i	−0.793627	−	0.608404i	$-0.791810\pi$
$97$	−6.53519	+	3.77309i	−0.663548	+	0.383099i	0.130080	+	0.991504i	$0.458477\pi$
$98$		0			0
$99$		−	0.0761145i		−	0.00764980i
$100$		0			0
$101$	6.60026	+	11.4320i	0.656751	+	1.13753i	0.981452	+	0.191709i	$0.0614030\pi$
$101$	6.60026	+	11.4320i	0.656751	+	1.13753i	−0.324701	+	0.945817i	$0.605264\pi$
$102$		0			0
$103$	−2.95060	−	5.11059i	−0.290731	−	0.503562i	0.683251	−	0.730183i	$-0.260565\pi$
$103$	−2.95060	−	5.11059i	−0.290731	−	0.503562i	−0.973983	+	0.226621i	$0.927232\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.1927			0.985363			0.492682	−	0.870210i	$-0.336017\pi$
$107$	10.1927			0.985363			0.492682	+	0.870210i	$0.336017\pi$
$108$		0			0
$109$	−5.32481	−	3.07428i	−0.510024	−	0.294463i	0.222819	−	0.974860i	$-0.428474\pi$
$109$	−5.32481	−	3.07428i	−0.510024	−	0.294463i	−0.732844	+	0.680397i	$0.761807\pi$
$110$		0			0
$111$	−5.27816	+	3.04734i	−0.500980	+	0.289241i
$112$		0			0
$113$	−7.29876	−	12.6418i	−0.686609	−	1.18924i	−0.972928	−	0.231108i	$-0.925765\pi$
$113$	−7.29876	−	12.6418i	−0.686609	−	1.18924i	0.286319	−	0.958134i	$-0.407568\pi$
$114$		0			0
$115$	2.66508	−	1.53868i	0.248520	−	0.143483i
$116$		0			0
$117$	−0.128611	−	0.200304i	−0.0118901	−	0.0185181i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.83541	+	8.37517i	−0.439583	+	0.761380i
$122$		0			0
$123$		−	21.9897i		−	1.98275i
$124$		0			0
$125$			11.1948i			1.00129i
$126$		0			0
$127$	4.36114	−	7.55372i	0.386989	−	0.670284i	−0.605054	−	0.796184i	$-0.706849\pi$
$127$	4.36114	−	7.55372i	0.386989	−	0.670284i	0.992043	+	0.125900i	$0.0401818\pi$
$128$		0			0
$129$	−5.39031	+	9.33629i	−0.474590	+	0.822014i
$130$		0			0
$131$	−9.72166	−	16.8384i	−0.849385	−	1.47118i	−0.881758	−	0.471703i	$-0.843640\pi$
$131$	−9.72166	−	16.8384i	−0.849385	−	1.47118i	0.0323725	−	0.999476i	$-0.489694\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−6.16366	+	3.55859i	−0.530484	+	0.306275i
$136$		0			0
$137$			3.35460i			0.286602i	0.989679	+	0.143301i	$0.0457718\pi$
$137$			3.35460i			0.286602i	−0.989679	+	0.143301i	$0.954228\pi$
$138$		0			0
$139$	3.95629	+	6.85250i	0.335568	+	0.581222i	0.983594	−	0.180397i	$-0.0577383\pi$
$139$	3.95629	+	6.85250i	0.335568	+	0.581222i	−0.648025	+	0.761619i	$0.724405\pi$
$140$		0			0
$141$	−11.2280	−	6.48250i	−0.945570	−	0.545925i
$142$		0			0
$143$	−0.196079	−	4.15222i	−0.0163970	−	0.347226i
$144$		0			0
$145$			3.97573i			0.330167i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.04756	−	1.18216i	−0.167743	−	0.0968464i	0.413778	−	0.910378i	$-0.364209\pi$
$149$	−2.04756	−	1.18216i	−0.167743	−	0.0968464i	−0.581521	+	0.813531i	$0.697542\pi$
$150$		0			0
$151$	−10.0357	−	5.79414i	−0.816697	−	0.471520i	0.0325791	−	0.999469i	$-0.489628\pi$
$151$	−10.0357	−	5.79414i	−0.816697	−	0.471520i	−0.849276	+	0.527949i	$0.822961\pi$
$152$		0			0
$153$	−0.0515779	+	0.0893355i	−0.00416982	+	0.00722235i
$154$		0			0
$155$	9.21299			0.740005
$156$		0			0
$157$	4.51821	−	7.82577i	0.360592	−	0.624564i	−0.627466	−	0.778644i	$-0.715908\pi$
$157$	4.51821	−	7.82577i	0.360592	−	0.624564i	0.988058	+	0.154080i	$0.0492413\pi$
$158$		0			0
$159$	19.6639			1.55945
$160$		0			0
$161$		0			0
$162$		0			0
$163$	18.4945	+	10.6778i	1.44860	+	0.836351i	0.998398	−	0.0565755i	$-0.0180182\pi$
$163$	18.4945	+	10.6778i	1.44860	+	0.836351i	0.450203	+	0.892926i	$0.351352\pi$
$164$		0			0
$165$	2.79668			0.217721
$166$		0			0
$167$	−2.75508	−	1.59065i	−0.213194	−	0.123088i	0.389601	−	0.920984i	$-0.372613\pi$
$167$	−2.75508	−	1.59065i	−0.213194	−	0.123088i	−0.602795	+	0.797896i	$0.705946\pi$
$168$		0			0
$169$	−7.53201	−	10.5957i	−0.579385	−	0.815054i
$170$		0			0
$171$	−0.479650	+	0.276926i	−0.0366798	+	0.0211771i
$172$		0			0
$173$	2.66952	−	4.62374i	0.202960	−	0.351537i	−0.746521	−	0.665362i	$-0.768277\pi$
$173$	2.66952	−	4.62374i	0.202960	−	0.351537i	0.949481	+	0.313825i	$0.101611\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	12.2156	−	7.05269i	0.918182	−	0.530113i
$178$		0			0
$179$	4.92279	+	8.52652i	0.367947	+	0.637302i	0.989244	−	0.146272i	$-0.0467276\pi$
$179$	4.92279	+	8.52652i	0.367947	+	0.637302i	−0.621298	+	0.783575i	$0.713394\pi$
$180$		0			0
$181$	15.1253			1.12425			0.562127	−	0.827051i	$-0.309983\pi$
$181$	15.1253			1.12425			0.562127	+	0.827051i	$0.309983\pi$
$182$		0			0
$183$	2.90389			0.214662
$184$		0			0
$185$	−2.41100	−	4.17598i	−0.177260	−	0.307024i
$186$		0			0
$187$	−1.56006	+	0.900700i	−0.114083	+	0.0658657i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.0900	−	19.2084i	0.802443	−	1.38987i	−0.115561	−	0.993300i	$-0.536867\pi$
$191$	11.0900	−	19.2084i	0.802443	−	1.38987i	0.918004	−	0.396571i	$-0.129800\pi$
$192$		0			0
$193$	6.03781	−	3.48593i	0.434611	−	0.250923i	−0.266698	−	0.963780i	$-0.585933\pi$
$193$	6.03781	−	3.48593i	0.434611	−	0.250923i	0.701309	+	0.712857i	$0.252599\pi$
$194$		0			0
$195$	7.35978	−	4.72556i	0.527045	−	0.338404i
$196$		0			0
$197$	17.0895	+	9.86660i	1.21757	+	0.702966i	0.964398	−	0.264455i	$-0.0851919\pi$
$197$	17.0895	+	9.86660i	1.21757	+	0.702966i	0.253175	+	0.967421i	$0.418525\pi$
$198$		0			0
$199$	13.8039			0.978529			0.489265	−	0.872135i	$-0.337265\pi$
$199$	13.8039			0.978529			0.489265	+	0.872135i	$0.337265\pi$
$200$		0			0
$201$	−5.62784	−	3.24923i	−0.396957	−	0.229183i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	17.3978			1.21512
$206$		0			0
$207$	−0.0733265	+	0.127005i	−0.00509655	+	0.00882748i
$208$		0			0
$209$	−9.67188			−0.669018
$210$		0			0
$211$	4.73718	−	8.20504i	0.326121	−	0.564859i	−0.655617	−	0.755093i	$-0.727592\pi$
$211$	4.73718	−	8.20504i	0.326121	−	0.564859i	0.981739	+	0.190235i	$0.0609249\pi$
$212$		0			0
$213$	−15.0681	−	8.69955i	−1.03245	−	0.596083i
$214$		0			0
$215$	−7.38670	−	4.26471i	−0.503769	−	0.290851i
$216$		0			0
$217$		0			0
$218$		0			0
$219$			5.78182i			0.390699i
$220$		0			0
$221$	−2.58355	+	5.00632i	−0.173788	+	0.336762i
$222$		0			0
$223$	12.6335	+	7.29395i	0.846001	+	0.488439i	0.859300	−	0.511473i	$-0.170900\pi$
$223$	12.6335	+	7.29395i	0.846001	+	0.488439i	−0.0132984	+	0.999912i	$0.504233\pi$
$224$		0			0
$225$	−0.101696	−	0.176143i	−0.00677974	−	0.0117429i
$226$		0			0
$227$		−	7.16353i		−	0.475460i	−0.971331	−	0.237730i	$-0.923597\pi$
$227$		−	7.16353i		−	0.475460i	0.971331	−	0.237730i	$-0.0764033\pi$
$228$		0			0
$229$	10.6525	−	6.15024i	0.703939	−	0.406420i	−0.104874	−	0.994486i	$-0.533444\pi$
$229$	10.6525	−	6.15024i	0.703939	−	0.406420i	0.808813	+	0.588066i	$0.200110\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.40185	+	16.2845i	0.615936	+	1.06683i	0.990220	+	0.139518i	$0.0445553\pi$
$233$	9.40185	+	16.2845i	0.615936	+	1.06683i	−0.374284	+	0.927314i	$0.622111\pi$
$234$		0			0
$235$	5.12883	−	8.88340i	0.334568	−	0.579489i
$236$		0			0
$237$	−4.06943	+	7.04846i	−0.264338	+	0.457847i
$238$		0			0
$239$			1.60295i			0.103686i	0.998655	+	0.0518432i	$0.0165096\pi$
$239$			1.60295i			0.103686i	−0.998655	+	0.0518432i	$0.983490\pi$
$240$		0			0
$241$		−	18.3657i		−	1.18304i	−0.806291	−	0.591519i	$-0.798529\pi$
$241$		−	18.3657i		−	1.18304i	0.806291	−	0.591519i	$-0.201471\pi$
$242$		0			0
$243$	0.342988	−	0.594073i	0.0220027	−	0.0381098i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−25.4526	+	16.3426i	−1.61951	+	1.03985i
$248$		0			0
$249$	−2.76824	+	1.59824i	−0.175430	+	0.101285i
$250$		0			0
$251$	−7.18228	−	12.4401i	−0.453341	−	0.785210i	0.545250	−	0.838274i	$-0.316435\pi$
$251$	−7.18228	−	12.4401i	−0.453341	−	0.785210i	−0.998591	+	0.0530634i	$0.983101\pi$
$252$		0			0
$253$	−2.21788	+	1.28049i	−0.139437	+	0.0805040i
$254$		0			0
$255$	−3.28246	−	1.89513i	−0.205556	−	0.118678i
$256$		0			0
$257$	−17.3657			−1.08324			−0.541620	−	0.840624i	$-0.682189\pi$
$257$	−17.3657			−1.08324			−0.541620	+	0.840624i	$0.682189\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.0947325	−	0.164081i	−0.00586379	−	0.0101564i
$262$		0			0
$263$	−8.37095	−	14.4989i	−0.516175	−	0.894042i	−0.999824	−	0.0187793i	$-0.994022\pi$
$263$	−8.37095	−	14.4989i	−0.516175	−	0.894042i	0.483648	−	0.875262i	$-0.339311\pi$
$264$		0			0
$265$			15.5577i			0.955704i
$266$		0			0
$267$	−3.60422	+	2.08090i	−0.220575	+	0.127349i
$268$		0			0
$269$	24.7915			1.51156			0.755781	−	0.654824i	$-0.227257\pi$
$269$	24.7915			1.51156			0.755781	+	0.654824i	$0.227257\pi$
$270$		0			0
$271$			20.2317i			1.22899i	0.788922	+	0.614493i	$0.210639\pi$
$271$			20.2317i			1.22899i	−0.788922	+	0.614493i	$0.789361\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	3.55182i		−	0.214183i
$276$		0			0
$277$	−11.0533			−0.664127			−0.332064	−	0.943257i	$-0.607745\pi$
$277$	−11.0533			−0.664127			−0.332064	+	0.943257i	$0.607745\pi$
$278$		0			0
$279$	−0.380227	+	0.219524i	−0.0227636	+	0.0131426i
$280$		0			0
$281$		−	3.18955i		−	0.190273i	−0.995464	−	0.0951363i	$-0.969671\pi$
$281$		−	3.18955i		−	0.190273i	0.995464	−	0.0951363i	$-0.0303287\pi$
$282$		0			0
$283$	8.96481	+	15.5275i	0.532903	+	0.923015i	0.999262	+	0.0384190i	$0.0122322\pi$
$283$	8.96481	+	15.5275i	0.532903	+	0.923015i	−0.466359	+	0.884596i	$0.654435\pi$
$284$		0			0
$285$	−10.1751	−	17.6238i	−0.602723	−	1.04395i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−14.5586			−0.856389
$290$		0			0
$291$	11.4431	+	6.60670i	0.670809	+	0.387292i
$292$		0			0
$293$	−14.6945	+	8.48385i	−0.858460	+	0.495632i	−0.863496	−	0.504355i	$-0.831730\pi$
$293$	−14.6945	+	8.48385i	−0.858460	+	0.495632i	0.00503646	+	0.999987i	$0.498397\pi$
$294$		0			0
$295$	5.57996	+	9.66477i	0.324878	+	0.562705i
$296$		0			0
$297$	5.12941	−	2.96147i	0.297639	−	0.171842i
$298$		0			0
$299$	−3.67295	+	7.11732i	−0.212412	+	0.411605i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	11.5571	−	20.0175i	0.663938	−	1.14997i
$304$		0			0
$305$			2.29750i			0.131555i
$306$		0			0
$307$		−	26.9884i		−	1.54031i	−0.637857	−	0.770155i	$-0.720179\pi$
$307$		−	26.9884i		−	1.54031i	0.637857	−	0.770155i	$-0.279821\pi$
$308$		0			0
$309$	−5.16652	+	8.94868i	−0.293913	+	0.509072i
$310$		0			0
$311$	−14.1891	+	24.5762i	−0.804588	+	1.39359i	0.111981	+	0.993710i	$0.464280\pi$
$311$	−14.1891	+	24.5762i	−0.804588	+	1.39359i	−0.916569	+	0.399876i	$0.869053\pi$
$312$		0			0
$313$	8.33368	+	14.4344i	0.471047	+	0.815878i	0.999452	−	0.0331150i	$-0.0105428\pi$
$313$	8.33368	+	14.4344i	0.471047	+	0.815878i	−0.528404	+	0.848993i	$0.677209\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−24.8919	+	14.3713i	−1.39807	+	0.807175i	−0.994190	−	0.107638i	$-0.965671\pi$
$317$	−24.8919	+	14.3713i	−1.39807	+	0.807175i	−0.403878	+	0.914813i	$0.632338\pi$
$318$		0			0
$319$		−	3.30861i		−	0.185247i
$320$		0			0
$321$	−8.92372	−	15.4563i	−0.498073	−	0.862688i
$322$		0			0
$323$	11.3519	+	6.55401i	0.631635	+	0.364675i
$324$		0			0
$325$	−6.00152	−	9.34701i	−0.332904	−	0.518479i
$326$		0			0
$327$			10.7662i			0.595370i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−22.6827	−	13.0959i	−1.24675	−	0.719814i	−0.276293	−	0.961073i	$-0.589106\pi$
$331$	−22.6827	−	13.0959i	−1.24675	−	0.719814i	−0.970461	+	0.241260i	$0.922439\pi$
$332$		0			0
$333$	0.199008	+	0.114897i	0.0109056	+	0.00629633i
$334$		0			0
$335$	2.57073	−	4.45264i	0.140454	−	0.243274i
$336$		0			0
$337$	4.47831			0.243949			0.121975	−	0.992533i	$-0.461077\pi$
$337$	4.47831			0.243949			0.121975	+	0.992533i	$0.461077\pi$
$338$		0			0
$339$	−12.7802	+	22.1359i	−0.694123	+	1.20226i
$340$		0			0
$341$	−7.66707			−0.415195
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−4.66657	−	2.69424i	−0.251239	−	0.145053i
$346$		0			0
$347$	−26.9212			−1.44520			−0.722602	−	0.691264i	$-0.757054\pi$
$347$	−26.9212			−1.44520			−0.722602	+	0.691264i	$0.757054\pi$
$348$		0			0
$349$	17.9560	+	10.3669i	0.961164	+	0.554928i	0.896531	−	0.442981i	$-0.146079\pi$
$349$	17.9560	+	10.3669i	0.961164	+	0.554928i	0.0646328	+	0.997909i	$0.479412\pi$
$350$		0			0
$351$	8.49461	−	16.4606i	0.453409	−	0.878601i
$352$		0			0
$353$	9.78961	−	5.65204i	0.521049	−	0.300828i	−0.216315	−	0.976324i	$-0.569404\pi$
$353$	9.78961	−	5.65204i	0.521049	−	0.300828i	0.737364	+	0.675496i	$0.236070\pi$
$354$		0			0
$355$	6.88292	−	11.9216i	0.365308	−	0.632731i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.3678	−	8.87263i	0.811084	−	0.468279i	−0.0362484	−	0.999343i	$-0.511541\pi$
$359$	15.3678	−	8.87263i	0.811084	−	0.468279i	0.847332	+	0.531063i	$0.178207\pi$
$360$		0			0
$361$	25.6891	+	44.4948i	1.35206	+	2.34183i
$362$		0			0
$363$	16.9337			0.888786
$364$		0			0
$365$	−4.57447			−0.239439
$366$		0			0
$367$	−4.78155	−	8.28189i	−0.249595	−	0.432311i	0.713819	−	0.700331i	$-0.246964\pi$
$367$	−4.78155	−	8.28189i	−0.249595	−	0.432311i	−0.963413	+	0.268020i	$0.913631\pi$
$368$		0			0
$369$	−0.718022	+	0.414550i	−0.0373788	+	0.0215806i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5.94176	+	10.2914i	−0.307653	+	0.532870i	−0.977848	−	0.209314i	$-0.932877\pi$
$373$	−5.94176	+	10.2914i	−0.307653	+	0.532870i	0.670196	+	0.742184i	$0.266210\pi$
$374$		0			0
$375$	16.9760	−	9.80108i	0.876635	−	0.506125i
$376$		0			0
$377$	−5.59056	−	8.70697i	−0.287928	−	0.448432i
$378$		0			0
$379$	−14.9391	−	8.62512i	−0.767372	−	0.443042i	0.0645643	−	0.997914i	$-0.479434\pi$
$379$	−14.9391	−	8.62512i	−0.767372	−	0.443042i	−0.831936	+	0.554871i	$0.812768\pi$
$380$		0			0
$381$	−15.2728			−0.782448
$382$		0			0
$383$	11.2843	+	6.51499i	0.576600	+	0.332900i	0.759781	−	0.650179i	$-0.225306\pi$
$383$	11.2843	+	6.51499i	0.576600	+	0.332900i	−0.183181	+	0.983079i	$0.558639\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.406473			0.0206622
$388$		0			0
$389$	−12.0792	+	20.9218i	−0.612442	+	1.06078i	0.378386	+	0.925648i	$0.376479\pi$
$389$	−12.0792	+	20.9218i	−0.612442	+	1.06078i	−0.990828	+	0.135132i	$0.956854\pi$
$390$		0			0
$391$	3.47083			0.175528
$392$		0			0
$393$	−17.0227	+	29.4841i	−0.858680	+	1.48728i
$394$		0			0
$395$	−5.57661	−	3.21966i	−0.280590	−	0.161999i
$396$		0			0
$397$	−4.17021	−	2.40767i	−0.209297	−	0.120838i	0.391688	−	0.920098i	$-0.371891\pi$
$397$	−4.17021	−	2.40767i	−0.209297	−	0.120838i	−0.600985	+	0.799261i	$0.705225\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			8.02173i			0.400586i	0.979736	+	0.200293i	$0.0641894\pi$
$401$			8.02173i			0.400586i	−0.979736	+	0.200293i	$0.935811\pi$
$402$		0			0
$403$	−20.1767	+	12.9550i	−1.00507	+	0.645337i
$404$		0			0
$405$	11.0302	+	6.36831i	0.548097	+	0.316444i
$406$		0			0
$407$	2.00644	+	3.47526i	0.0994555	+	0.172262i
$408$		0			0
$409$		−	9.96745i		−	0.492859i	−0.969161	−	0.246429i	$-0.920743\pi$
$409$		−	9.96745i		−	0.492859i	0.969161	−	0.246429i	$-0.0792573\pi$
$410$		0			0
$411$	5.08696	−	2.93696i	0.250921	−	0.144869i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.26450	−	2.19018i	−0.0620719	−	0.107512i
$416$		0			0
$417$	6.92749	−	11.9988i	0.339241	−	0.587582i
$418$		0			0
$419$	14.8442	−	25.7109i	0.725187	−	1.25606i	−0.233710	−	0.972306i	$-0.575087\pi$
$419$	14.8442	−	25.7109i	0.725187	−	1.25606i	0.958897	−	0.283754i	$-0.0915800\pi$
$420$		0			0
$421$			13.1380i			0.640305i	0.947366	+	0.320152i	$0.103734\pi$
$421$			13.1380i			0.640305i	−0.947366	+	0.320152i	$0.896266\pi$
$422$		0			0
$423$			0.488833i			0.0237679i
$424$		0			0
$425$	−2.40684	+	4.16877i	−0.116749	+	0.202215i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−6.12482	+	3.93262i	−0.295709	+	0.189868i
$430$		0			0
$431$	12.4729	−	7.20126i	0.600800	−	0.346872i	−0.168556	−	0.985692i	$-0.553910\pi$
$431$	12.4729	−	7.20126i	0.600800	−	0.346872i	0.769356	+	0.638820i	$0.220577\pi$
$432$		0			0
$433$	−18.1596	−	31.4534i	−0.872695	−	1.51155i	−0.859198	−	0.511643i	$-0.829037\pi$
$433$	−18.1596	−	31.4534i	−0.872695	−	1.51155i	−0.0134964	−	0.999909i	$-0.504296\pi$
$434$		0			0
$435$	6.02886	−	3.48076i	0.289062	−	0.166890i
$436$		0			0
$437$	16.1386	+	9.31761i	0.772013	+	0.445722i
$438$		0			0
$439$	−20.5444			−0.980532			−0.490266	−	0.871573i	$-0.663100\pi$
$439$	−20.5444			−0.980532			−0.490266	+	0.871573i	$0.663100\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.6606	+	21.9287i	0.601521	+	1.04187i	0.992591	+	0.121504i	$0.0387719\pi$
$443$	12.6606	+	21.9287i	0.601521	+	1.04187i	−0.391070	+	0.920361i	$0.627895\pi$
$444$		0			0
$445$	−1.64637	−	2.85160i	−0.0780454	−	0.135179i
$446$		0			0
$447$			4.13994i			0.195812i
$448$		0			0
$449$	−29.0997	+	16.8007i	−1.37330	+	0.792876i	−0.991342	−	0.131303i	$-0.958084\pi$
$449$	−29.0997	+	16.8007i	−1.37330	+	0.792876i	−0.381959	+	0.924179i	$0.624751\pi$
$450$		0			0
$451$	−14.4785			−0.681767
$452$		0			0
$453$			20.2911i			0.953361i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	37.9955i		−	1.77735i	−0.458534	−	0.888677i	$-0.651625\pi$
$457$		−	37.9955i		−	1.77735i	0.458534	−	0.888677i	$-0.348375\pi$
$458$		0			0
$459$	−8.02717			−0.374676
$460$		0			0
$461$	−31.4812	+	18.1757i	−1.46623	+	0.846525i	−0.999287	−	0.0377645i	$-0.987976\pi$
$461$	−31.4812	+	18.1757i	−1.46623	+	0.846525i	−0.466938	+	0.884290i	$0.654643\pi$
$462$		0			0
$463$			35.3400i			1.64239i	0.570649	+	0.821194i	$0.306692\pi$
$463$			35.3400i			1.64239i	−0.570649	+	0.821194i	$0.693308\pi$
$464$		0			0
$465$	−8.06600	−	13.9707i	−0.374052	−	0.647877i
$466$		0			0
$467$	14.7859	+	25.6099i	0.684208	+	1.18508i	0.973685	+	0.227899i	$0.0731855\pi$
$467$	14.7859	+	25.6099i	0.684208	+	1.18508i	−0.289476	+	0.957185i	$0.593481\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−15.8228			−0.729077
$472$		0			0
$473$	6.14722	+	3.54910i	0.282650	+	0.163188i
$474$		0			0
$475$	−22.3825	+	12.9225i	−1.02698	+	0.592927i
$476$		0			0
$477$	−0.370705	−	0.642079i	−0.0169734	−	0.0293988i
$478$		0			0
$479$	−18.8339	+	10.8738i	−0.860545	+	0.496836i	−0.864195	−	0.503157i	$-0.832172\pi$
$479$	−18.8339	+	10.8738i	−0.860545	+	0.496836i	0.00364974	+	0.999993i	$0.498838\pi$
$480$		0			0
$481$	11.1523	+	5.75523i	0.508501	+	0.262416i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.22710	+	9.05361i	−0.237350	+	0.411103i
$486$		0			0
$487$		−	30.0473i		−	1.36157i	−0.732482	−	0.680786i	$-0.761638\pi$
$487$		−	30.0473i		−	1.36157i	0.732482	−	0.680786i	$-0.238362\pi$
$488$		0			0
$489$		−	37.3938i		−	1.69101i
$490$		0			0
$491$	−20.0899	+	34.7967i	−0.906643	+	1.57035i	−0.0879471	+	0.996125i	$0.528031\pi$
$491$	−20.0899	+	34.7967i	−0.906643	+	1.57035i	−0.818696	+	0.574227i	$0.805303\pi$
$492$		0			0
$493$	−2.24203	+	3.88331i	−0.100976	+	0.174895i
$494$		0			0
$495$	−0.0527231	−	0.0913191i	−0.00236973	−	0.00410449i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−10.1671	+	5.86999i	−0.455143	+	0.262777i	−0.710000	−	0.704202i	$-0.751305\pi$
$499$	−10.1671	+	5.86999i	−0.455143	+	0.262777i	0.254857	+	0.966979i	$0.417972\pi$
$500$		0			0
$501$			5.57046i			0.248870i
$502$		0			0
$503$	16.6965	+	28.9191i	0.744459	+	1.28944i	0.950447	+	0.310886i	$0.100626\pi$
$503$	16.6965	+	28.9191i	0.744459	+	1.28944i	−0.205989	+	0.978554i	$0.566041\pi$
$504$		0			0
$505$	15.8375	+	9.14376i	0.704758	+	0.406892i
$506$		0			0
$507$	−9.47319	+	20.6982i	−0.420719	+	0.919240i
$508$		0			0
$509$			20.7826i			0.921172i	0.887615	+	0.460586i	$0.152361\pi$
$509$			20.7826i			0.921172i	−0.887615	+	0.460586i	$0.847639\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−37.3245	−	21.5493i	−1.64792	−	0.951425i
$514$		0			0
$515$	−7.08003	−	4.08766i	−0.311983	−	0.180124i
$516$		0			0
$517$	−4.26822	+	7.39278i	−0.187716	+	0.325134i
$518$		0			0
$519$	−9.34869			−0.410362
$520$		0			0
$521$	−3.75119	+	6.49726i	−0.164343	+	0.284650i	−0.936422	−	0.350877i	$-0.885884\pi$
$521$	−3.75119	+	6.49726i	−0.164343	+	0.284650i	0.772079	+	0.635527i	$0.219217\pi$
$522$		0			0
$523$	7.32578			0.320334			0.160167	−	0.987090i	$-0.448797\pi$
$523$	7.32578			0.320334			0.160167	+	0.987090i	$0.448797\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.99882	+	5.19547i	0.391995	+	0.226318i
$528$		0			0
$529$	−18.0656			−0.785462
$530$		0			0
$531$	−0.460578	−	0.265915i	−0.0199874	−	0.0115397i
$532$		0			0
$533$	−38.1018	+	24.4644i	−1.65037	+	1.05967i
$534$		0			0
$535$	12.2288	−	7.06028i	0.528696	−	0.305243i
$536$		0			0
$537$	8.61983	−	14.9300i	0.371973	−	0.644277i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−10.1260	+	5.84622i	−0.435349	+	0.251349i	−0.701623	−	0.712549i	$-0.747541\pi$
$541$	−10.1260	+	5.84622i	−0.435349	+	0.251349i	0.266274	+	0.963897i	$0.414207\pi$
$542$		0			0
$543$	−13.2422	−	22.9362i	−0.568278	−	0.984287i
$544$		0			0
$545$	−8.51799			−0.364871
$546$		0			0
$547$	5.10513			0.218280			0.109140	−	0.994026i	$-0.465190\pi$
$547$	5.10513			0.218280			0.109140	+	0.994026i	$0.465190\pi$
$548$		0			0
$549$	−0.0547442	−	0.0948197i	−0.00233643	−	0.00404681i
$550$		0			0
$551$	−20.8498	+	12.0377i	−0.888233	+	0.512822i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.22168	+	7.31216i	−0.179200	+	0.310384i
$556$		0			0
$557$	−10.8544	+	6.26679i	−0.459916	+	0.265532i	−0.712009	−	0.702171i	$-0.752214\pi$
$557$	−10.8544	+	6.26679i	−0.459916	+	0.265532i	0.252093	+	0.967703i	$0.418881\pi$
$558$		0			0
$559$	22.1740	−	1.04712i	0.937860	−	0.0442884i
$560$		0			0
$561$	2.73167	+	1.57713i	0.115331	+	0.0665865i
$562$		0			0
$563$	−3.90630			−0.164631			−0.0823155	−	0.996606i	$-0.526232\pi$
$563$	−3.90630			−0.164631			−0.0823155	+	0.996606i	$0.526232\pi$
$564$		0			0
$565$	−17.5135	−	10.1114i	−0.736799	−	0.425391i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	46.1329			1.93399			0.966996	−	0.254793i	$-0.0820073\pi$
$569$	46.1329			1.93399			0.966996	+	0.254793i	$0.0820073\pi$
$570$		0			0
$571$	15.0580	−	26.0812i	0.630157	−	1.09146i	−0.357362	−	0.933966i	$-0.616324\pi$
$571$	15.0580	−	26.0812i	0.630157	−	1.09146i	0.987519	−	0.157499i	$-0.0503430\pi$
$572$		0			0
$573$	−38.8372			−1.62245
$574$		0			0
$575$	−3.42172	+	5.92660i	−0.142696	+	0.247156i
$576$		0			0
$577$	−22.1962	−	12.8150i	−0.924042	−	0.533496i	−0.0391195	−	0.999235i	$-0.512455\pi$
$577$	−22.1962	−	12.8150i	−0.924042	−	0.533496i	−0.884922	+	0.465739i	$0.845789\pi$
$578$		0			0
$579$	−10.5722	−	6.10388i	−0.439367	−	0.253669i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		−	12.9472i		−	0.536217i
$584$		0			0
$585$	−0.293049	−	0.151230i	−0.0121161	−	0.00625259i
$586$		0			0
$587$	11.4147	+	6.59025i	0.471133	+	0.272009i	0.716714	−	0.697367i	$-0.245645\pi$
$587$	11.4147	+	6.59025i	0.471133	+	0.272009i	−0.245581	+	0.969376i	$0.578979\pi$
$588$		0			0
$589$	27.8950	+	48.3155i	1.14939	+	1.99081i
$590$		0			0
$591$		−	34.5529i		−	1.42132i
$592$		0			0
$593$	5.66124	−	3.26852i	0.232479	−	0.134222i	−0.379236	−	0.925300i	$-0.623813\pi$
$593$	5.66124	−	3.26852i	0.232479	−	0.134222i	0.611715	+	0.791078i	$0.290480\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.0853	−	20.9324i	−0.494619	−	0.856705i
$598$		0			0
$599$	−6.21222	+	10.7599i	−0.253824	+	0.439637i	−0.964576	−	0.263807i	$-0.915022\pi$
$599$	−6.21222	+	10.7599i	−0.253824	+	0.439637i	0.710751	+	0.703444i	$0.248355\pi$
$600$		0			0
$601$	9.27019	−	16.0564i	0.378139	−	0.654956i	−0.612653	−	0.790352i	$-0.709898\pi$
$601$	9.27019	−	16.0564i	0.378139	−	0.654956i	0.990791	+	0.135397i	$0.0432309\pi$
$602$		0			0
$603$			0.245018i			0.00997792i
$604$		0			0
$605$			13.3976i			0.544690i
$606$		0			0
$607$	−7.87226	+	13.6351i	−0.319525	+	0.553434i	−0.980389	−	0.197072i	$-0.936857\pi$
$607$	−7.87226	+	13.6351i	−0.319525	+	0.553434i	0.660864	+	0.750506i	$0.270190\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.25929	+	26.6669i	0.0509453	+	1.07883i
$612$		0			0
$613$	−16.6796	+	9.62996i	−0.673682	+	0.388950i	−0.797470	−	0.603358i	$-0.793829\pi$
$613$	−16.6796	+	9.62996i	−0.673682	+	0.388950i	0.123788	+	0.992309i	$0.460496\pi$
$614$		0			0
$615$	−15.2319	−	26.3824i	−0.614208	−	1.06384i
$616$		0			0
$617$	37.5872	−	21.7010i	1.51320	−	0.873649i	0.513323	−	0.858195i	$-0.328414\pi$
$617$	37.5872	−	21.7010i	1.51320	−	0.873649i	0.999881	−	0.0154532i	$-0.00491911\pi$
$618$		0			0
$619$	−11.5943	−	6.69400i	−0.466016	−	0.269054i	0.248555	−	0.968618i	$-0.420044\pi$
$619$	−11.5943	−	6.69400i	−0.466016	−	0.269054i	−0.714570	+	0.699564i	$0.753378\pi$
$620$		0			0
$621$	−11.4120			−0.457946
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.0525074	+	0.0909454i	0.00210029	+	0.00363782i
$626$		0			0
$627$	8.46776	+	14.6666i	0.338170	+	0.585727i
$628$		0			0
$629$		−	5.43854i		−	0.216849i
$630$		0			0
$631$	13.1568	−	7.59606i	0.523762	−	0.302394i	−0.214710	−	0.976678i	$-0.568881\pi$
$631$	13.1568	−	7.59606i	0.523762	−	0.302394i	0.738473	+	0.674283i	$0.235547\pi$
$632$		0			0
$633$	−16.5897			−0.659380
$634$		0			0
$635$		−	12.0835i		−	0.479520i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			0.656016i			0.0259516i
$640$		0			0
$641$	35.9342			1.41932			0.709658	−	0.704546i	$-0.248849\pi$
$641$	35.9342			1.41932			0.709658	+	0.704546i	$0.248849\pi$
$642$		0			0
$643$	7.72476	−	4.45989i	0.304635	−	0.175881i	−0.339888	−	0.940466i	$-0.610389\pi$
$643$	7.72476	−	4.45989i	0.304635	−	0.175881i	0.644523	+	0.764585i	$0.277056\pi$
$644$		0			0
$645$			14.9351i			0.588068i
$646$		0			0
$647$	4.88360	+	8.45865i	0.191994	+	0.332544i	0.945911	−	0.324426i	$-0.105171\pi$
$647$	4.88360	+	8.45865i	0.191994	+	0.332544i	−0.753917	+	0.656970i	$0.771838\pi$
$648$		0			0
$649$	−4.64365	−	8.04304i	−0.182279	−	0.315717i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	16.5372			0.647149			0.323575	−	0.946203i	$-0.395115\pi$
$653$	16.5372			0.647149			0.323575	+	0.946203i	$0.395115\pi$
$654$		0			0
$655$	−23.3273	−	13.4680i	−0.911473	−	0.526239i
$656$		0			0
$657$	0.188792	−	0.108999i	0.00736547	−	0.00425245i
$658$		0			0
$659$	−7.82010	−	13.5448i	−0.304628	−	0.527631i	0.672550	−	0.740051i	$-0.265199\pi$
$659$	−7.82010	−	13.5448i	−0.304628	−	0.527631i	−0.977178	+	0.212420i	$0.931865\pi$
$660$		0			0
$661$	21.9320	−	12.6624i	0.853056	−	0.492512i	−0.00862494	−	0.999963i	$-0.502745\pi$
$661$	21.9320	−	12.6624i	0.853056	−	0.492512i	0.861681	+	0.507451i	$0.169412\pi$
$662$		0			0
$663$	9.85357	−	0.465313i	0.382681	−	0.0180713i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.18742	+	5.52077i	−0.123417	+	0.213765i
$668$		0			0
$669$		−	25.5435i		−	0.987568i
$670$		0			0
$671$		−	1.91199i		−	0.0738114i
$672$		0			0
$673$	−4.08919	+	7.08268i	−0.157627	+	0.273017i	−0.934012	−	0.357241i	$-0.883718\pi$
$673$	−4.08919	+	7.08268i	−0.157627	+	0.273017i	0.776386	+	0.630258i	$0.217051\pi$
$674$		0			0
$675$	7.91359	−	13.7067i	0.304594	−	0.527573i
$676$		0			0
$677$	−22.4808	−	38.9379i	−0.864007	−	1.49650i	−0.868030	−	0.496512i	$-0.834614\pi$
$677$	−22.4808	−	38.9379i	−0.864007	−	1.49650i	0.00402279	−	0.999992i	$-0.498720\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−10.8629	+	6.27169i	−0.416267	+	0.240332i
$682$		0			0
$683$			20.4486i			0.782444i	0.920296	+	0.391222i	$0.127947\pi$
$683$			20.4486i			0.782444i	−0.920296	+	0.391222i	$0.872053\pi$
$684$		0			0
$685$	2.32367	+	4.02471i	0.0887827	+	0.153776i
$686$		0			0
$687$	−18.6526	−	10.7691i	−0.711643	−	0.410867i
$688$		0			0
$689$	−21.8768	−	34.0719i	−0.833441	−	1.29804i
$690$		0			0
$691$			33.7107i			1.28242i	0.767367	+	0.641208i	$0.221567\pi$
$691$			33.7107i			1.28242i	−0.767367	+	0.641208i	$0.778433\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.49320	+	5.48090i	0.360098	+	0.207902i
$696$		0			0
$697$	16.9934	+	9.81115i	0.643671	+	0.371624i
$698$		0			0
$699$	16.4627	−	28.5142i	0.622676	−	1.07851i
$700$		0			0
$701$	−29.6172			−1.11862			−0.559312	−	0.828957i	$-0.688935\pi$
$701$	−29.6172			−1.11862			−0.559312	+	0.828957i	$0.688935\pi$
$702$		0			0
$703$	14.6000	−	25.2879i	0.550649	−	0.953753i
$704$		0			0
$705$	−17.9612			−0.676459
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−8.59653	−	4.96321i	−0.322849	−	0.186397i	0.329813	−	0.944046i	$-0.393014\pi$
$709$	−8.59653	−	4.96321i	−0.322849	−	0.186397i	−0.652662	+	0.757649i	$0.726348\pi$
$710$		0			0
$711$	0.306868			0.0115085
$712$		0			0
$713$	12.7933	+	7.38623i	0.479114	+	0.276616i
$714$		0			0
$715$	−3.11141	−	4.84584i	−0.116360	−	0.181224i
$716$		0			0
$717$	2.43074	−	1.40339i	0.0907778	−	0.0524106i
$718$		0			0
$719$	−10.3425	+	17.9138i	−0.385711	+	0.668071i	−0.991868	−	0.127274i	$-0.959377\pi$
$719$	−10.3425	+	17.9138i	−0.385711	+	0.668071i	0.606157	+	0.795345i	$0.292710\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−27.8500	+	16.0792i	−1.03575	+	0.597992i
$724$		0			0
$725$	−4.42061	−	7.65673i	−0.164177	−	0.284364i
$726$		0			0
$727$	4.83449			0.179301			0.0896506	−	0.995973i	$-0.471425\pi$
$727$	4.83449			0.179301			0.0896506	+	0.995973i	$0.471425\pi$
$728$		0			0
$729$	26.3800			0.977035
$730$		0			0
$731$	−4.80999	−	8.33115i	−0.177904	−	0.308139i
$732$		0			0
$733$	11.0018	−	6.35187i	0.406359	−	0.234612i	−0.282865	−	0.959160i	$-0.591285\pi$
$733$	11.0018	−	6.35187i	0.406359	−	0.234612i	0.689224	+	0.724548i	$0.257951\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.13937	+	3.70549i	−0.0788046	+	0.136494i
$738$		0			0
$739$	2.23852	−	1.29241i	0.0823451	−	0.0475420i	−0.458262	−	0.888817i	$-0.651528\pi$
$739$	2.23852	−	1.29241i	0.0823451	−	0.0475420i	0.540607	+	0.841275i	$0.318195\pi$
$740$		0			0
$741$	47.0660	+	24.2888i	1.72901	+	0.892270i
$742$		0			0
$743$	9.98318	+	5.76379i	0.366247	+	0.211453i	0.671818	−	0.740717i	$-0.265514\pi$
$743$	9.98318	+	5.76379i	0.366247	+	0.211453i	−0.305570	+	0.952169i	$0.598847\pi$
$744$		0			0
$745$	−3.27544			−0.120003
$746$		0			0
$747$	0.104374	+	0.0602602i	0.00381884	+	0.00220481i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.00538			0.255630			0.127815	−	0.991798i	$-0.459204\pi$
$751$	7.00538			0.255630			0.127815	+	0.991798i	$0.459204\pi$
$752$		0			0
$753$	−12.5762	+	21.7826i	−0.458302	+	0.793803i
$754$		0			0
$755$	−16.0540			−0.584264
$756$		0			0
$757$	8.60091	−	14.8972i	0.312605	−	0.541449i	−0.666320	−	0.745666i	$-0.732132\pi$
$757$	8.60091	−	14.8972i	0.312605	−	0.541449i	0.978926	+	0.204217i	$0.0654649\pi$
$758$		0			0
$759$	3.88352	+	2.24215i	0.140963	+	0.0813850i
$760$		0			0
$761$	−29.9238	−	17.2765i	−1.08474	−	0.626274i	−0.152567	−	0.988293i	$-0.548754\pi$
$761$	−29.9238	−	17.2765i	−1.08474	−	0.626274i	−0.932170	+	0.362020i	$0.882087\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$			0.142908i			0.00516686i
$766$		0			0
$767$	−25.8106	−	13.3198i	−0.931967	−	0.480948i
$768$		0			0
$769$	9.48253	+	5.47474i	0.341949	+	0.197424i	0.661133	−	0.750268i	$-0.270076\pi$
$769$	9.48253	+	5.47474i	0.341949	+	0.197424i	−0.319185	+	0.947693i	$0.603409\pi$
$770$		0			0
$771$	15.2037	+	26.3335i	0.547547	+	0.948379i
$772$		0			0
$773$			22.0036i			0.791413i	0.918377	+	0.395707i	$0.129500\pi$
$773$			22.0036i			0.791413i	−0.918377	+	0.395707i	$0.870500\pi$
$774$		0			0
$775$	−17.7430	+	10.2439i	−0.637347	+	0.367973i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	52.6770	+	91.2392i	1.88735	+	3.26898i
$780$		0			0
$781$	−5.72798	+	9.92115i	−0.204963	+	0.355007i
$782$		0			0
$783$	7.37171	−	12.7682i	0.263443	−	0.456297i
$784$		0			0
$785$		−	12.5187i		−	0.446812i
$786$		0			0
$787$			39.3231i			1.40172i	0.713300	+	0.700859i	$0.247200\pi$
$787$			39.3231i			1.40172i	−0.713300	+	0.700859i	$0.752800\pi$
$788$		0			0
$789$	−14.6576	+	25.3877i	−0.521824	+	0.903826i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.23068	−	5.03160i	−0.114725	−	0.178677i
$794$		0			0
$795$	23.5920	−	13.6208i	0.836721	−	0.483081i
$796$		0			0
$797$	−27.2620	−	47.2192i	−0.965669	−	1.67259i	−0.707806	−	0.706407i	$-0.750315\pi$
$797$	−27.2620	−	47.2192i	−0.965669	−	1.67259i	−0.257863	−	0.966181i	$-0.583018\pi$
$798$		0			0
$799$	10.0192	−	5.78460i	0.354454	−	0.204644i
$800$		0			0
$801$	0.135894	+	0.0784583i	0.00480157	+	0.00277219i
$802$		0			0
$803$	3.80688			0.134342
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−21.7050	−	37.5942i	−0.764052	−	1.32338i
$808$		0			0
$809$	−1.56318	−	2.70751i	−0.0549586	−	0.0951911i	0.837237	−	0.546840i	$-0.184169\pi$
$809$	−1.56318	−	2.70751i	−0.0549586	−	0.0951911i	−0.892196	+	0.451649i	$0.850836\pi$
$810$		0			0
$811$		−	4.48741i		−	0.157574i	−0.996891	−	0.0787872i	$-0.974895\pi$
$811$		−	4.48741i		−	0.157574i	0.996891	−	0.0787872i	$-0.0251048\pi$
$812$		0			0
$813$	30.6796	−	17.7129i	1.07598	−	0.621218i
$814$		0			0
$815$	29.5853			1.03633
$816$		0			0
$817$		−	51.6506i		−	1.80702i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			24.6872i			0.861589i	0.902450	+	0.430795i	$0.141767\pi$
$821$			24.6872i			0.861589i	−0.902450	+	0.430795i	$0.858233\pi$
$822$		0			0
$823$	11.0134			0.383904			0.191952	−	0.981404i	$-0.438518\pi$
$823$	11.0134			0.383904			0.191952	+	0.981404i	$0.438518\pi$
$824$		0			0
$825$	−5.38604	+	3.10963i	−0.187518	+	0.108263i
$826$		0			0
$827$			23.8575i			0.829605i	0.909911	+	0.414803i	$0.136149\pi$
$827$			23.8575i			0.829605i	−0.909911	+	0.414803i	$0.863851\pi$
$828$		0			0
$829$	10.2157	+	17.6941i	0.354806	+	0.614541i	0.987085	−	0.160199i	$-0.0512137\pi$
$829$	10.2157	+	17.6941i	0.354806	+	0.614541i	−0.632279	+	0.774741i	$0.717880\pi$
$830$		0			0
$831$	9.67718	+	16.7614i	0.335697	+	0.581445i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−4.40725			−0.152519
$836$		0			0
$837$	−29.5878	−	17.0825i	−1.02270	−	0.590458i
$838$		0			0
$839$	21.0080	−	12.1290i	0.725276	−	0.418738i	−0.0914153	−	0.995813i	$-0.529139\pi$
$839$	21.0080	−	12.1290i	0.725276	−	0.418738i	0.816692	+	0.577074i	$0.195806\pi$
$840$		0			0
$841$	10.3821	+	17.9823i	0.358003	+	0.620080i
$842$		0			0
$843$	−4.83668	+	2.79246i	−0.166584	+	0.0961775i
$844$		0			0
$845$	−16.3760	−	7.49501i	−0.563353	−	0.257836i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	15.6974	−	27.1888i	0.538734	−	0.933115i
$850$		0			0
$851$		−	7.73178i		−	0.265042i
$852$		0			0
$853$		−	51.8470i		−	1.77521i	−0.460608	−	0.887604i	$-0.652369\pi$
$853$		−	51.8470i		−	1.77521i	0.460608	−	0.887604i	$-0.347631\pi$
$854$		0			0
$855$	−0.383643	+	0.664490i	−0.0131203	+	0.0227251i
$856$		0			0
$857$	13.4527	−	23.3008i	0.459536	−	0.795939i	−0.539401	−	0.842049i	$-0.681349\pi$
$857$	13.4527	−	23.3008i	0.459536	−	0.795939i	0.998936	+	0.0461102i	$0.0146825\pi$
$858$		0			0
$859$	−16.7255	−	28.9694i	−0.570665	−	0.988422i	−0.996498	−	0.0836195i	$-0.973352\pi$
$859$	−16.7255	−	28.9694i	−0.570665	−	0.988422i	0.425832	−	0.904802i	$-0.359981\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.14724	+	2.97176i	−0.175214	+	0.101160i	−0.585042	−	0.811003i	$-0.698922\pi$
$863$	−5.14724	+	2.97176i	−0.175214	+	0.101160i	0.409828	+	0.912163i	$0.365589\pi$
$864$		0			0
$865$		−	7.39651i		−	0.251489i
$866$		0			0
$867$	12.7461	+	22.0769i	0.432881	+	0.749771i
$868$		0			0
$869$	4.64087	+	2.67941i	0.157431	+	0.0908926i
$870$		0			0
$871$	0.631194	+	13.3663i	0.0213872	+	0.452900i
$872$		0			0
$873$		−	0.498199i		−	0.0168615i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−43.0073	−	24.8303i	−1.45225	−	0.838458i	−0.453643	−	0.891184i	$-0.649876\pi$
$877$	−43.0073	−	24.8303i	−1.45225	−	0.838458i	−0.998609	+	0.0527255i	$0.983209\pi$
$878$		0			0
$879$	25.7301	+	14.8553i	0.867854	+	0.501056i
$880$		0			0
$881$	−10.6452	+	18.4381i	−0.358647	+	0.621195i	−0.987735	−	0.156139i	$-0.950095\pi$
$881$	−10.6452	+	18.4381i	−0.358647	+	0.621195i	0.629088	+	0.777334i	$0.283428\pi$
$882$		0			0
$883$	−32.8053			−1.10399			−0.551993	−	0.833848i	$-0.686133\pi$
$883$	−32.8053			−1.10399			−0.551993	+	0.833848i	$0.686133\pi$
$884$		0			0
$885$	9.77054	−	16.9231i	0.328433	−	0.568863i
$886$		0			0
$887$	−17.2358			−0.578721			−0.289361	−	0.957220i	$-0.593443\pi$
$887$	−17.2358			−0.578721			−0.289361	+	0.957220i	$0.593443\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−9.17938	−	5.29972i	−0.307521	−	0.177547i
$892$		0			0
$893$	62.1161			2.07863
$894$		0			0
$895$	11.8123	+	6.81985i	0.394843	+	0.227963i
$896$		0			0
$897$	14.0085	−	0.661520i	0.467730	−	0.0220875i
$898$		0			0
$899$	−16.5280	+	9.54247i	−0.551241	+	0.318259i
$900$		0			0
$901$	−8.77345	+	15.1961i	−0.292286	+	0.506254i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	18.1467	−	10.4770i	0.603217	−	0.348267i
$906$		0			0
$907$	−17.3178	−	29.9953i	−0.575028	−	0.995978i	−0.996039	−	0.0889223i	$-0.971658\pi$
$907$	−17.3178	−	29.9953i	−0.575028	−	0.995978i	0.421010	−	0.907056i	$-0.361676\pi$
$908$		0			0
$909$	−0.871499			−0.0289058
$910$		0			0
$911$	−7.85153			−0.260133			−0.130066	−	0.991505i	$-0.541519\pi$
$911$	−7.85153			−0.260133			−0.130066	+	0.991505i	$0.541519\pi$
$912$		0			0
$913$	1.05232	+	1.82267i	0.0348267	+	0.0603216i
$914$		0			0
$915$	3.48397	−	2.01147i	0.115177	−	0.0664972i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.3659	−	31.8106i	0.605834	−	1.04934i	−0.386085	−	0.922463i	$-0.626173\pi$
$919$	18.3659	−	31.8106i	0.605834	−	1.04934i	0.991919	−	0.126872i	$-0.0404937\pi$
$920$		0			0
$921$	−40.9256	+	23.6284i	−1.34854	+	0.778583i
$922$		0			0
$923$	1.68997	+	35.7872i	0.0556260	+	1.17795i
$924$		0			0
$925$	9.28654	+	5.36159i	0.305339	+	0.176288i
$926$		0			0
$927$	0.389597			0.0127961
$928$		0			0
$929$	−28.6355	−	16.5327i	−0.939501	−	0.542421i	−0.0496975	−	0.998764i	$-0.515826\pi$
$929$	−28.6355	−	16.5327i	−0.939501	−	0.542421i	−0.889804	+	0.456343i	$0.849159\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	49.6902			1.62679
$934$		0			0
$935$	−1.24780	+	2.16125i	−0.0408073	+	0.0706803i
$936$		0			0
$937$	−45.8626			−1.49826			−0.749132	−	0.662421i	$-0.769529\pi$
$937$	−45.8626			−1.49826			−0.749132	+	0.662421i	$0.769529\pi$
$938$		0			0
$939$	14.5923	−	25.2746i	0.476202	−	0.824806i
$940$		0			0
$941$	5.00328	+	2.88864i	0.163102	+	0.0941671i	0.579329	−	0.815094i	$-0.303315\pi$
$941$	5.00328	+	2.88864i	0.163102	+	0.0941671i	−0.416227	+	0.909261i	$0.636648\pi$
$942$		0			0
$943$	24.1590	+	13.9482i	0.786724	+	0.454215i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			0.0562941i			0.00182931i	1.00000		0.000914656i	$0.000291144\pi$
$947$			0.0562941i			0.00182931i	−1.00000		0.000914656i	$0.999709\pi$
$948$		0			0
$949$	10.0182	−	6.43249i	0.325205	−	0.208807i
$950$		0			0
$951$	43.5858	+	25.1643i	1.41337	+	0.816008i
$952$		0			0
$953$	−20.0778	−	34.7758i	−0.650385	−	1.12650i	−0.983030	−	0.183447i	$-0.941274\pi$
$953$	−20.0778	−	34.7758i	−0.650385	−	1.12650i	0.332645	−	0.943052i	$-0.392059\pi$
$954$		0			0
$955$		−	30.7273i		−	0.994312i
$956$		0			0
$957$	−5.01723	+	2.89670i	−0.162184	+	0.0936369i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	6.61283	+	11.4538i	0.213317	+	0.369476i
$962$		0			0
$963$	−0.336460	+	0.582766i	−0.0108423	+	0.0187794i
$964$		0			0
$965$	4.82928	−	8.36456i	0.155460	−	0.269265i
$966$		0			0
$967$		−	32.3647i		−	1.04078i	−0.853929	−	0.520390i	$-0.825787\pi$
$967$		−	32.3647i		−	1.04078i	0.853929	−	0.520390i	$-0.174213\pi$
$968$		0			0
$969$		−	22.9522i		−	0.737331i
$970$		0			0
$971$	15.3459	−	26.5799i	0.492473	−	0.852989i	−0.507489	−	0.861658i	$-0.669426\pi$
$971$	15.3459	−	26.5799i	0.492473	−	0.852989i	0.999962	+	0.00866935i	$0.00275957\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−8.91960	+	17.2841i	−0.285656	+	0.553535i
$976$		0			0
$977$	−4.87565	+	2.81496i	−0.155986	+	0.0900585i	−0.575961	−	0.817477i	$-0.695372\pi$
$977$	−4.87565	+	2.81496i	−0.155986	+	0.0900585i	0.419975	+	0.907536i	$0.362039\pi$
$978$		0			0
$979$	1.37011	+	2.37310i	0.0437890	+	0.0758447i
$980$		0			0
$981$	0.351544	−	0.202964i	0.0112239	−	0.00648014i
$982$		0			0
$983$	5.77088	+	3.33182i	0.184062	+	0.106268i	0.589200	−	0.807987i	$-0.299443\pi$
$983$	5.77088	+	3.33182i	0.184062	+	0.106268i	−0.405138	+	0.914256i	$0.632776\pi$
$984$		0			0
$985$	27.3376			0.871050
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.83820	−	11.8441i	−0.217442	−	0.376621i
$990$		0			0
$991$	26.4156	+	45.7532i	0.839120	+	1.45340i	0.890631	+	0.454726i	$0.150263\pi$
$991$	26.4156	+	45.7532i	0.839120	+	1.45340i	−0.0515115	+	0.998672i	$0.516404\pi$
$992$		0			0
$993$			45.8618i			1.45538i
$994$		0			0
$995$	16.5613	−	9.56167i	0.525029	−	0.303125i
$996$		0			0
$997$	−14.6367			−0.463548			−0.231774	−	0.972770i	$-0.574453\pi$
$997$	−14.6367			−0.463548			−0.231774	+	0.972770i	$0.574453\pi$
$998$		0			0
$999$			17.8817i			0.565752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bb.d.1733.3		16
7.2	even	3		2548.2.bq.e.1941.6		16
7.3	odd	6		2548.2.u.c.589.6		16
7.4	even	3		364.2.u.a.225.3	✓	16
7.5	odd	6		2548.2.bq.c.1941.3		16
7.6	odd	2		2548.2.bb.c.1733.6		16
13.10	even	6		2548.2.bq.e.361.6		16
21.11	odd	6		3276.2.cf.c.2773.3		16
28.11	odd	6		1456.2.cc.f.225.6		16
91.4	even	6		4732.2.g.k.337.11		16
91.10	odd	6		2548.2.u.c.1765.6		16
91.23	even	6	inner	2548.2.bb.d.569.3		16
91.32	odd	12		4732.2.a.s.1.6		8
91.46	odd	12		4732.2.a.t.1.6		8
91.62	odd	6		2548.2.bq.c.361.3		16
91.74	even	3		4732.2.g.k.337.12		16
91.75	odd	6		2548.2.bb.c.569.6		16
91.88	even	6		364.2.u.a.309.3	yes	16
273.179	odd	6		3276.2.cf.c.1765.6		16
364.179	odd	6		1456.2.cc.f.673.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.3	✓	16	7.4	even	3
364.2.u.a.309.3	yes	16	91.88	even	6
1456.2.cc.f.225.6		16	28.11	odd	6
1456.2.cc.f.673.6		16	364.179	odd	6
2548.2.u.c.589.6		16	7.3	odd	6
2548.2.u.c.1765.6		16	91.10	odd	6
2548.2.bb.c.569.6		16	91.75	odd	6
2548.2.bb.c.1733.6		16	7.6	odd	2
2548.2.bb.d.569.3		16	91.23	even	6	inner
2548.2.bb.d.1733.3		16	1.1	even	1	trivial
2548.2.bq.c.361.3		16	91.62	odd	6
2548.2.bq.c.1941.3		16	7.5	odd	6
2548.2.bq.e.361.6		16	13.10	even	6
2548.2.bq.e.1941.6		16	7.2	even	3
3276.2.cf.c.1765.6		16	273.179	odd	6
3276.2.cf.c.2773.3		16	21.11	odd	6
4732.2.a.s.1.6		8	91.32	odd	12
4732.2.a.t.1.6		8	91.46	odd	12
4732.2.g.k.337.11		16	91.4	even	6
4732.2.g.k.337.12		16	91.74	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.875503 - 1.51642i) q^{3} +(1.19976 - 0.692682i) q^{5} +(-0.0330100 + 0.0571750i) q^{9} +(-0.998442 + 0.576451i) q^{11} +(-1.65348 + 3.20406i) q^{13} +(-2.10079 - 1.21289i) q^{15} +1.56249 q^{17} +(7.26523 + 4.19458i) q^{19} +2.22134 q^{23} +(-1.54038 + 2.66802i) q^{25} -5.13741 q^{27} +(-1.43491 + 2.48533i) q^{29} +(5.75927 + 3.32512i) q^{31} +(1.74828 + 1.00937i) q^{33} -3.48068i q^{37} +(6.30631 - 0.297802i) q^{39} +(10.8758 + 6.27917i) q^{41} +(-3.07841 - 5.33196i) q^{43} +0.0914616i q^{45} +(6.41233 - 3.70216i) q^{47} +(-1.36797 - 2.36939i) q^{51} +(-5.61504 + 9.72553i) q^{53} +(-0.798593 + 1.38320i) q^{55} -14.6895i q^{57} +8.05559i q^{59} +(-0.829207 + 1.43623i) q^{61} +(0.235615 + 4.98944i) q^{65} +(3.21406 - 1.85564i) q^{67} +(-1.94479 - 3.36848i) q^{69} +(8.60538 - 4.96832i) q^{71} +(-2.85962 - 1.65100i) q^{73} +5.39444 q^{75} +(-2.32405 - 4.02538i) q^{79} +(4.59685 + 7.96198i) q^{81} -1.82551i q^{83} +(1.87462 - 1.08231i) q^{85} +5.02506 q^{87} -2.37681i q^{89} -11.6446i q^{93} +11.6220 q^{95} +(-6.53519 + 3.77309i) q^{97} -0.0761145i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} + 6 q^{15} - 4 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} + 30 q^{31} - 42 q^{33} - 18 q^{39} + 36 q^{41} + 6 q^{43} - 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 4 q^{61}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 + 6 * q^15 - 4 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 + 30 * q^31 - 42 * q^33 - 18 * q^39 + 36 * q^41 + 6 * q^43 - 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 4 * q^61 + 30 * q^65 - 24 * q^67 - 52 * q^69 + 36 * q^71 - 12 * q^73 + 20 * q^75 - 4 * q^79 + 42 * q^85 - 52 * q^87 + 60 * q^95 - 42 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more