LMFDB - Embedded newform 416.2.ba.c.49.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(17,416)] 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("416.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.8607891481591137382656.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 6 x^{12} - 20 x^{10} + 48 x^{9} - 76 x^{8} + 96 x^{7} + \cdots + 256 $ x^16 - 3x^15 + 5x^14 - 6x^13 + 6x^12 - 20x^10 + 48x^9 - 76x^8 + 96x^7 - 80x^6 + 96x^4 - 192x^3 + 320x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.7
Root			$-0.0207305 - 1.41406i$ of defining polynomial
Character	$\chi$	$=$	416.49
Dual form			416.2.ba.c.17.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.95589 - 1.12924i) q^{3} +0.642566 q^{5} +(-0.306483 - 0.176948i) q^{7} +(1.05034 - 1.81925i) q^{9} +(1.15663 + 2.00334i) q^{11} +(3.23687 - 1.58829i) q^{13} +(1.25679 - 0.725608i) q^{15} +(3.34390 - 5.79180i) q^{17} +(-1.51026 + 2.61585i) q^{19} -0.799263 q^{21} +(-0.693517 - 1.20121i) q^{23} -4.58711 q^{25} +2.03107i q^{27} +(-5.85776 + 3.38198i) q^{29} -7.83867i q^{31} +(4.52449 + 2.61221i) q^{33} +(-0.196935 - 0.113701i) q^{35} +(2.54831 + 4.41379i) q^{37} +(4.53742 - 6.76172i) q^{39} +(-7.03170 + 4.05975i) q^{41} +(-0.0281959 - 0.0162789i) q^{43} +(0.674915 - 1.16899i) q^{45} +12.6079i q^{47} +(-3.43738 - 5.95372i) q^{49} -15.1042i q^{51} -3.40398i q^{53} +(0.743211 + 1.28728i) q^{55} +6.82176i q^{57} +(-2.40152 + 4.15956i) q^{59} +(8.23572 + 4.75490i) q^{61} +(-0.643824 + 0.371712i) q^{63} +(2.07990 - 1.02058i) q^{65} +(-2.24483 - 3.88815i) q^{67} +(-2.71289 - 1.56629i) q^{69} +(5.35176 + 3.08984i) q^{71} +6.24869i q^{73} +(-8.97189 + 5.17993i) q^{75} -0.818652i q^{77} -7.68780 q^{79} +(5.44459 + 9.43030i) q^{81} +16.7317 q^{83} +(2.14867 - 3.72161i) q^{85} +(-7.63810 + 13.2296i) q^{87} +(-1.37983 + 0.796643i) q^{89} +(-1.27309 - 0.0859734i) q^{91} +(-8.85170 - 15.3316i) q^{93} +(-0.970443 + 1.68086i) q^{95} +(-5.29486 - 3.05699i) q^{97} +4.85944 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 18 q^{7} + 2 q^{9} + 36 q^{15} + 8 q^{17} + 2 q^{23} - 12 q^{25} - 30 q^{33} + 14 q^{39} + 24 q^{41} - 14 q^{49} - 4 q^{55} + 6 q^{65} - 6 q^{71} - 32 q^{79} + 12 q^{81} - 34 q^{87} - 30 q^{89} - 28 q^{95}+ \cdots - 30 q^{97}+O(q^{100}) $ 16 * q - 18 * q^7 + 2 * q^9 + 36 * q^15 + 8 * q^17 + 2 * q^23 - 12 * q^25 - 30 * q^33 + 14 * q^39 + 24 * q^41 - 14 * q^49 - 4 * q^55 + 6 * q^65 - 6 * q^71 - 32 * q^79 + 12 * q^81 - 34 * q^87 - 30 * q^89 - 28 * q^95 - 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.95589	−	1.12924i	1.12924	−	0.651964i	0.185493	−	0.982646i	$-0.440612\pi$
$3$	1.95589	−	1.12924i	1.12924	−	0.651964i	0.943742	+	0.330681i	$0.107279\pi$
$4$		0			0
$5$	0.642566			0.287364			0.143682	−	0.989624i	$-0.454106\pi$
$5$	0.642566			0.287364			0.143682	+	0.989624i	$0.454106\pi$
$6$		0			0
$7$	−0.306483	−	0.176948i	−0.115840	−	0.0668800i	0.440961	−	0.897526i	$-0.354638\pi$
$7$	−0.306483	−	0.176948i	−0.115840	−	0.0668800i	−0.556800	+	0.830646i	$0.687971\pi$
$8$		0			0
$9$	1.05034	−	1.81925i	0.350115	−	0.606416i
$10$		0			0
$11$	1.15663	+	2.00334i	0.348737	+	0.604030i	0.986025	−	0.166595i	$-0.0532773\pi$
$11$	1.15663	+	2.00334i	0.348737	+	0.604030i	−0.637288	+	0.770625i	$0.719944\pi$
$12$		0			0
$13$	3.23687	−	1.58829i	0.897746	−	0.440513i
$13$	3.23687	−	1.58829i	0.897746	−	0.440513i
$14$		0			0
$15$	1.25679	−	0.725608i	0.324502	−	0.187351i
$16$		0			0
$17$	3.34390	−	5.79180i	0.811015	−	1.40472i	−0.101140	−	0.994872i	$-0.532249\pi$
$17$	3.34390	−	5.79180i	0.811015	−	1.40472i	0.912155	−	0.409846i	$-0.134418\pi$
$18$		0			0
$19$	−1.51026	+	2.61585i	−0.346478	+	0.600117i	−0.985621	−	0.168970i	$-0.945956\pi$
$19$	−1.51026	+	2.61585i	−0.346478	+	0.600117i	0.639143	+	0.769088i	$0.279289\pi$
$20$		0			0
$21$	−0.799263			−0.174413
$22$		0			0
$23$	−0.693517	−	1.20121i	−0.144608	−	0.250469i	0.784618	−	0.619979i	$-0.212859\pi$
$23$	−0.693517	−	1.20121i	−0.144608	−	0.250469i	−0.929227	+	0.369510i	$0.879526\pi$
$24$		0			0
$25$	−4.58711			−0.917422
$26$		0			0
$27$			2.03107i			0.390879i
$28$		0			0
$29$	−5.85776	+	3.38198i	−1.08776	+	0.628018i	−0.932979	−	0.359931i	$-0.882800\pi$
$29$	−5.85776	+	3.38198i	−1.08776	+	0.628018i	−0.154780	+	0.987949i	$0.549467\pi$
$30$		0			0
$31$		−	7.83867i		−	1.40787i	−0.710266	−	0.703933i	$-0.751425\pi$
$31$		−	7.83867i		−	1.40787i	0.710266	−	0.703933i	$-0.248575\pi$
$32$		0			0
$33$	4.52449	+	2.61221i	0.787612	+	0.454728i
$34$		0			0
$35$	−0.196935	−	0.113701i	−0.0332881	−	0.0192189i
$36$		0			0
$37$	2.54831	+	4.41379i	0.418939	+	0.725623i	0.995833	−	0.0911955i	$-0.0290688\pi$
$37$	2.54831	+	4.41379i	0.418939	+	0.725623i	−0.576894	+	0.816819i	$0.695735\pi$
$38$		0			0
$39$	4.53742	−	6.76172i	0.726568	−	1.08274i
$40$		0			0
$41$	−7.03170	+	4.05975i	−1.09817	+	0.634027i	−0.935739	−	0.352694i	$-0.885266\pi$
$41$	−7.03170	+	4.05975i	−1.09817	+	0.634027i	−0.162428	+	0.986720i	$0.551932\pi$
$42$		0			0
$43$	−0.0281959	−	0.0162789i	−0.00429983	−	0.00248251i	0.497849	−	0.867264i	$-0.334124\pi$
$43$	−0.0281959	−	0.0162789i	−0.00429983	−	0.00248251i	−0.502148	+	0.864781i	$0.667457\pi$
$44$		0			0
$45$	0.674915	−	1.16899i	0.100610	−	0.174262i
$46$		0			0
$47$			12.6079i			1.83905i	0.393036	+	0.919523i	$0.371425\pi$
$47$			12.6079i			1.83905i	−0.393036	+	0.919523i	$0.628575\pi$
$48$		0			0
$49$	−3.43738	−	5.95372i	−0.491054	−	0.850531i
$50$		0			0
$51$		−	15.1042i		−	2.11501i
$52$		0			0
$53$		−	3.40398i		−	0.467573i	−0.972288	−	0.233787i	$-0.924888\pi$
$53$		−	3.40398i		−	0.467573i	0.972288	−	0.233787i	$-0.0751117\pi$
$54$		0			0
$55$	0.743211	+	1.28728i	0.100215	+	0.173577i
$56$		0			0
$57$			6.82176i			0.903565i
$58$		0			0
$59$	−2.40152	+	4.15956i	−0.312652	+	0.541529i	−0.978936	−	0.204170i	$-0.934551\pi$
$59$	−2.40152	+	4.15956i	−0.312652	+	0.541529i	0.666284	+	0.745698i	$0.267884\pi$
$60$		0			0
$61$	8.23572	+	4.75490i	1.05448	+	0.608802i	0.923899	−	0.382636i	$-0.124984\pi$
$61$	8.23572	+	4.75490i	1.05448	+	0.608802i	0.130577	+	0.991438i	$0.458317\pi$
$62$		0			0
$63$	−0.643824	+	0.371712i	−0.0811142	+	0.0468313i
$64$		0			0
$65$	2.07990	−	1.02058i	0.257980	−	0.126588i
$66$		0			0
$67$	−2.24483	−	3.88815i	−0.274249	−	0.475013i	0.695696	−	0.718336i	$-0.255096\pi$
$67$	−2.24483	−	3.88815i	−0.274249	−	0.475013i	−0.969945	+	0.243323i	$0.921763\pi$
$68$		0			0
$69$	−2.71289	−	1.56629i	−0.326594	−	0.188559i
$70$		0			0
$71$	5.35176	+	3.08984i	0.635137	+	0.366696i	0.782739	−	0.622350i	$-0.213822\pi$
$71$	5.35176	+	3.08984i	0.635137	+	0.366696i	−0.147602	+	0.989047i	$0.547155\pi$
$72$		0			0
$73$			6.24869i			0.731354i	0.930742	+	0.365677i	$0.119162\pi$
$73$			6.24869i			0.731354i	−0.930742	+	0.365677i	$0.880838\pi$
$74$		0			0
$75$	−8.97189	+	5.17993i	−1.03599	+	0.598126i
$76$		0			0
$77$		−	0.818652i		−	0.0932941i
$78$		0			0
$79$	−7.68780			−0.864945			−0.432472	−	0.901647i	$-0.642359\pi$
$79$	−7.68780			−0.864945			−0.432472	+	0.901647i	$0.642359\pi$
$80$		0			0
$81$	5.44459	+	9.43030i	0.604954	+	1.04781i
$82$		0			0
$83$	16.7317			1.83654			0.918269	−	0.395957i	$-0.129587\pi$
$83$	16.7317			1.83654			0.918269	+	0.395957i	$0.129587\pi$
$84$		0			0
$85$	2.14867	−	3.72161i	0.233056	−	0.403666i
$86$		0			0
$87$	−7.63810	+	13.2296i	−0.818891	+	1.41836i
$88$		0			0
$89$	−1.37983	+	0.796643i	−0.146261	+	0.0844440i	−0.571345	−	0.820710i	$-0.693578\pi$
$89$	−1.37983	+	0.796643i	−0.146261	+	0.0844440i	0.425083	+	0.905154i	$0.360245\pi$
$90$		0			0
$91$	−1.27309	−	0.0859734i	−0.133456	−	0.00901246i
$92$		0			0
$93$	−8.85170	−	15.3316i	−0.917878	−	1.58981i
$94$		0			0
$95$	−0.970443	+	1.68086i	−0.0995653	+	0.172452i
$96$		0			0
$97$	−5.29486	−	3.05699i	−0.537611	−	0.310390i	0.206499	−	0.978447i	$-0.433793\pi$
$97$	−5.29486	−	3.05699i	−0.537611	−	0.310390i	−0.744110	+	0.668057i	$0.767126\pi$
$98$		0			0
$99$	4.85944			0.488392
$100$		0			0
$101$	−7.17483	+	4.14239i	−0.713922	+	0.412183i	−0.812511	−	0.582945i	$-0.801900\pi$
$101$	−7.17483	+	4.14239i	−0.713922	+	0.412183i	0.0985896	+	0.995128i	$0.468567\pi$
$102$		0			0
$103$	−11.5770			−1.14071			−0.570356	−	0.821397i	$-0.693195\pi$
$103$	−11.5770			−1.14071			−0.570356	+	0.821397i	$0.693195\pi$
$104$		0			0
$105$	−0.513579			−0.0501201
$106$		0			0
$107$	−8.91550	+	5.14737i	−0.861894	+	0.497615i	−0.864646	−	0.502381i	$-0.832457\pi$
$107$	−8.91550	+	5.14737i	−0.861894	+	0.497615i	0.00275201	+	0.999996i	$0.499124\pi$
$108$		0			0
$109$	−8.84423			−0.847123			−0.423562	−	0.905867i	$-0.639220\pi$
$109$	−8.84423			−0.847123			−0.423562	+	0.905867i	$0.639220\pi$
$110$		0			0
$111$	9.96842	+	5.75527i	0.946161	+	0.546266i
$112$		0			0
$113$	0.956864	−	1.65734i	0.0900142	−	0.155909i	−0.817503	−	0.575925i	$-0.804642\pi$
$113$	0.956864	−	1.65734i	0.0900142	−	0.155909i	0.907517	+	0.420016i	$0.137975\pi$
$114$		0			0
$115$	−0.445630	−	0.771855i	−0.0415553	−	0.0719758i
$116$		0			0
$117$	0.510329	−	7.55693i	0.0471799	−	0.698638i
$118$		0			0
$119$	−2.04969	+	1.18339i	−0.187895	+	0.108481i
$120$		0			0
$121$	2.82441	−	4.89203i	0.256765	−	0.444730i
$122$		0			0
$123$	−9.16883	+	15.8809i	−0.826725	+	1.43193i
$124$		0			0
$125$	−6.16035			−0.550998
$126$		0			0
$127$	−6.82376	−	11.8191i	−0.605511	−	1.04878i	−0.991970	−	0.126470i	$-0.959635\pi$
$127$	−6.82376	−	11.8191i	−0.605511	−	1.04878i	0.386459	−	0.922306i	$-0.373698\pi$
$128$		0			0
$129$	−0.0735308			−0.00647403
$130$		0			0
$131$		−	5.81035i		−	0.507653i	−0.967250	−	0.253826i	$-0.918311\pi$
$131$		−	5.81035i		−	0.507653i	0.967250	−	0.253826i	$-0.0816892\pi$
$132$		0			0
$133$	0.925738	−	0.534475i	0.0802717	−	0.0463449i
$134$		0			0
$135$			1.30510i			0.112325i
$136$		0			0
$137$	5.11297	+	2.95197i	0.436830	+	0.252204i	0.702252	−	0.711928i	$-0.252178\pi$
$137$	5.11297	+	2.95197i	0.436830	+	0.252204i	−0.265422	+	0.964132i	$0.585511\pi$
$138$		0			0
$139$	4.78695	+	2.76375i	0.406024	+	0.234418i	0.689080	−	0.724685i	$-0.258015\pi$
$139$	4.78695	+	2.76375i	0.406024	+	0.234418i	−0.283056	+	0.959103i	$0.591348\pi$
$140$		0			0
$141$	14.2372	+	24.6596i	1.19899	+	2.07672i
$142$		0			0
$143$	6.92575	+	4.64749i	0.579161	+	0.388643i
$144$		0			0
$145$	−3.76400	+	2.17314i	−0.312583	+	0.180470i
$146$		0			0
$147$	−13.4463	−	7.76322i	−1.10903	−	0.640299i
$148$		0			0
$149$	−6.65703	+	11.5303i	−0.545365	+	0.944600i	0.453219	+	0.891399i	$0.350276\pi$
$149$	−6.65703	+	11.5303i	−0.545365	+	0.944600i	−0.998584	+	0.0532004i	$0.983058\pi$
$150$		0			0
$151$		−	5.22848i		−	0.425487i	−0.977108	−	0.212744i	$-0.931760\pi$
$151$		−	5.22848i		−	0.425487i	0.977108	−	0.212744i	$-0.0682400\pi$
$152$		0			0
$153$	−7.02449	−	12.1668i	−0.567896	−	0.983625i
$154$		0			0
$155$		−	5.03686i		−	0.404570i
$156$		0			0
$157$		−	13.7313i		−	1.09588i	−0.836519	−	0.547938i	$-0.815413\pi$
$157$		−	13.7313i		−	1.09588i	0.836519	−	0.547938i	$-0.184587\pi$
$158$		0			0
$159$	−3.84390	−	6.65783i	−0.304841	−	0.528000i
$160$		0			0
$161$			0.490865i			0.0386856i
$162$		0			0
$163$	8.42963	−	14.6006i	0.660260	−	1.14360i	−0.320287	−	0.947320i	$-0.603779\pi$
$163$	8.42963	−	14.6006i	0.660260	−	1.14360i	0.980547	−	0.196283i	$-0.0628872\pi$
$164$		0			0
$165$	2.90728	+	1.67852i	0.226331	+	0.130673i
$166$		0			0
$167$	−6.98117	+	4.03058i	−0.540219	+	0.311895i	−0.745168	−	0.666877i	$-0.767631\pi$
$167$	−6.98117	+	4.03058i	−0.540219	+	0.311895i	0.204949	+	0.978773i	$0.434297\pi$
$168$		0			0
$169$	7.95466	−	10.2822i	0.611897	−	0.790938i
$170$		0			0
$171$	3.17259	+	5.49509i	0.242614	+	0.420220i
$172$		0			0
$173$	14.4482	+	8.34170i	1.09848	+	0.634208i	0.935821	−	0.352475i	$-0.114660\pi$
$173$	14.4482	+	8.34170i	1.09848	+	0.634208i	0.162659	+	0.986682i	$0.447993\pi$
$174$		0			0
$175$	1.40587	+	0.811679i	0.106274	+	0.0613572i
$176$		0			0
$177$			10.8475i			0.815351i
$178$		0			0
$179$	−10.2099	+	5.89469i	−0.763123	+	0.440590i	−0.830416	−	0.557144i	$-0.811897\pi$
$179$	−10.2099	+	5.89469i	−0.763123	+	0.440590i	0.0672926	+	0.997733i	$0.478564\pi$
$180$		0			0
$181$		−	5.65279i		−	0.420169i	−0.977683	−	0.210084i	$-0.932626\pi$
$181$		−	5.65279i		−	0.420169i	0.977683	−	0.210084i	$-0.0673739\pi$
$182$		0			0
$183$	21.4776			1.58767
$184$		0			0
$185$	1.63745	+	2.83615i	0.120388	+	0.208518i
$186$		0			0
$187$	15.4706			1.13132
$188$		0			0
$189$	0.359393	−	0.622487i	0.0261420	−	0.0452793i
$190$		0			0
$191$	5.60725	−	9.71203i	0.405726	−	0.702738i	−0.588680	−	0.808366i	$-0.700352\pi$
$191$	5.60725	−	9.71203i	0.405726	−	0.702738i	0.994406	+	0.105628i	$0.0336854\pi$
$192$		0			0
$193$	0.671819	−	0.387875i	0.0483586	−	0.0279198i	−0.475626	−	0.879648i	$-0.657778\pi$
$193$	0.671819	−	0.387875i	0.0483586	−	0.0279198i	0.523984	+	0.851728i	$0.324445\pi$
$194$		0			0
$195$	2.91559	−	4.34485i	0.208790	−	0.311141i
$196$		0			0
$197$	1.52807	+	2.64669i	0.108870	+	0.188569i	0.915313	−	0.402744i	$-0.131943\pi$
$197$	1.52807	+	2.64669i	0.108870	+	0.188569i	−0.806443	+	0.591312i	$0.798610\pi$
$198$		0			0
$199$	13.1258	−	22.7346i	0.930465	−	1.61161i	0.147938	−	0.988997i	$-0.452736\pi$
$199$	13.1258	−	22.7346i	0.930465	−	1.61161i	0.782527	−	0.622616i	$-0.213930\pi$
$200$		0			0
$201$	−8.78128	−	5.06987i	−0.619384	−	0.357601i
$202$		0			0
$203$	2.39374			0.168007
$204$		0			0
$205$	−4.51833	+	2.60866i	−0.315574	+	0.182196i
$206$		0			0
$207$	−2.91373			−0.202518
$208$		0			0
$209$	−6.98726			−0.483319
$210$		0			0
$211$	10.9194	−	6.30433i	0.751724	−	0.434008i	−0.0745926	−	0.997214i	$-0.523766\pi$
$211$	10.9194	−	6.30433i	0.751724	−	0.434008i	0.826316	+	0.563206i	$0.190432\pi$
$212$		0			0
$213$	13.9566			0.956292
$214$		0			0
$215$	−0.0181177	−	0.0104603i	−0.00123562	−	0.000713384i
$216$		0			0
$217$	−1.38703	+	2.40241i	−0.0941581	+	0.163087i
$218$		0			0
$219$	7.05624	+	12.2218i	0.476816	+	0.825870i
$220$		0			0
$221$	1.62470	−	24.0584i	0.109289	−	1.61834i
$222$		0			0
$223$	14.8690	−	8.58464i	0.995704	−	0.574870i	0.0887299	−	0.996056i	$-0.471719\pi$
$223$	14.8690	−	8.58464i	0.995704	−	0.574870i	0.906975	+	0.421185i	$0.138386\pi$
$224$		0			0
$225$	−4.81804	+	8.34510i	−0.321203	+	0.556340i
$226$		0			0
$227$	2.30952	−	4.00021i	0.153289	−	0.265504i	−0.779146	−	0.626843i	$-0.784347\pi$
$227$	2.30952	−	4.00021i	0.153289	−	0.265504i	0.932435	+	0.361339i	$0.117680\pi$
$228$		0			0
$229$	22.9078			1.51379			0.756895	−	0.653537i	$-0.226716\pi$
$229$	22.9078			1.51379			0.756895	+	0.653537i	$0.226716\pi$
$230$		0			0
$231$	−0.924451	−	1.60120i	−0.0608244	−	0.105351i
$232$		0			0
$233$	24.6115			1.61236			0.806178	−	0.591674i	$-0.201533\pi$
$233$	24.6115			1.61236			0.806178	+	0.591674i	$0.201533\pi$
$234$		0			0
$235$			8.10138i			0.528476i
$236$		0			0
$237$	−15.0365	+	8.68133i	−0.976726	+	0.563913i
$238$		0			0
$239$			10.1001i			0.653319i	0.945142	+	0.326659i	$0.105923\pi$
$239$			10.1001i			0.653319i	−0.945142	+	0.326659i	$0.894077\pi$
$240$		0			0
$241$	−15.6591	−	9.04077i	−1.00869	−	0.582367i	−0.0978820	−	0.995198i	$-0.531207\pi$
$241$	−15.6591	−	9.04077i	−1.00869	−	0.582367i	−0.910808	+	0.412831i	$0.864540\pi$
$242$		0			0
$243$	16.0212	+	9.24983i	1.02776	+	0.593377i
$244$		0			0
$245$	−2.20874	−	3.82565i	−0.141111	−	0.244412i
$246$		0			0
$247$	−0.733789	+	10.8659i	−0.0466899	+	0.691381i
$248$		0			0
$249$	32.7253	−	18.8940i	2.07388	−	1.19736i
$250$		0			0
$251$	−13.3339	−	7.69835i	−0.841631	−	0.485916i	0.0161874	−	0.999869i	$-0.494847\pi$
$251$	−13.3339	−	7.69835i	−0.841631	−	0.485916i	−0.857818	+	0.513953i	$0.828181\pi$
$252$		0			0
$253$	1.60429	−	2.77871i	0.100861	−	0.174696i
$254$		0			0
$255$		−	9.70543i		−	0.607778i
$256$		0			0
$257$	0.569829	+	0.986973i	0.0355450	+	0.0615657i	0.883251	−	0.468901i	$-0.155350\pi$
$257$	0.569829	+	0.986973i	0.0355450	+	0.0615657i	−0.847706	+	0.530467i	$0.822017\pi$
$258$		0			0
$259$		−	1.80367i		−	0.112074i
$260$		0			0
$261$			14.2090i			0.879514i
$262$		0			0
$263$	−4.69352	−	8.12941i	−0.289415	−	0.501281i	0.684255	−	0.729242i	$-0.260127\pi$
$263$	−4.69352	−	8.12941i	−0.289415	−	0.501281i	−0.973670	+	0.227961i	$0.926794\pi$
$264$		0			0
$265$		−	2.18728i		−	0.134364i
$266$		0			0
$267$	−1.79920	+	3.11630i	−0.110109	+	0.190714i
$268$		0			0
$269$	16.5114	+	9.53286i	1.00672	+	0.581229i	0.910229	−	0.414105i	$-0.135906\pi$
$269$	16.5114	+	9.53286i	1.00672	+	0.581229i	0.0964886	+	0.995334i	$0.469239\pi$
$270$		0			0
$271$	−15.3555	+	8.86548i	−0.932778	+	0.538539i	−0.887689	−	0.460444i	$-0.847690\pi$
$271$	−15.3555	+	8.86548i	−0.932778	+	0.538539i	−0.0450887	+	0.998983i	$0.514357\pi$
$272$		0			0
$273$	−2.58711	+	1.26946i	−0.156579	+	0.0768313i
$274$		0			0
$275$	−5.30559	−	9.18955i	−0.319939	−	0.554151i
$276$		0			0
$277$	−22.4083	−	12.9374i	−1.34638	−	0.777334i	−0.358647	−	0.933473i	$-0.616762\pi$
$277$	−22.4083	−	12.9374i	−1.34638	−	0.777334i	−0.987735	+	0.156139i	$0.950095\pi$
$278$		0			0
$279$	−14.2605	−	8.23330i	−0.853753	−	0.492915i
$280$		0			0
$281$		−	0.736068i		−	0.0439101i	−0.999759	−	0.0219551i	$-0.993011\pi$
$281$		−	0.736068i		−	0.0439101i	0.999759	−	0.0219551i	$-0.00698908\pi$
$282$		0			0
$283$	−21.0813	+	12.1713i	−1.25315	+	0.723508i	−0.971734	−	0.236077i	$-0.924138\pi$
$283$	−21.0813	+	12.1713i	−1.25315	+	0.723508i	−0.281418	+	0.959585i	$0.590805\pi$
$284$		0			0
$285$			4.38343i			0.259652i
$286$		0			0
$287$	2.87346			0.169615
$288$		0			0
$289$	−13.8633	−	24.0120i	−0.815489	−	1.41247i
$290$		0			0
$291$	−13.8082			−0.809453
$292$		0			0
$293$	3.07441	−	5.32504i	0.179609	−	0.311092i	−0.762138	−	0.647415i	$-0.775850\pi$
$293$	3.07441	−	5.32504i	0.179609	−	0.311092i	0.941747	+	0.336323i	$0.109183\pi$
$294$		0			0
$295$	−1.54314	+	2.67279i	−0.0898449	+	0.155616i
$296$		0			0
$297$	−4.06893	+	2.34920i	−0.236103	+	0.136314i
$298$		0			0
$299$	−4.15269	−	2.78664i	−0.240156	−	0.161156i
$300$		0			0
$301$	0.00576103	+	0.00997839i	0.000332060	+	0.000575145i
$302$		0			0
$303$	−9.35546	+	16.2041i	−0.537457	+	0.930903i
$304$		0			0
$305$	5.29199	+	3.05533i	0.303019	+	0.174948i
$306$		0			0
$307$	11.7521			0.670727			0.335364	−	0.942089i	$-0.391141\pi$
$307$	11.7521			0.670727			0.335364	+	0.942089i	$0.391141\pi$
$308$		0			0
$309$	−22.6433	+	13.0731i	−1.28813	+	0.743704i
$310$		0			0
$311$	24.0980			1.36647			0.683235	−	0.730199i	$-0.260573\pi$
$311$	24.0980			1.36647			0.683235	+	0.730199i	$0.260573\pi$
$312$		0			0
$313$	−4.66324			−0.263582			−0.131791	−	0.991278i	$-0.542073\pi$
$313$	−4.66324			−0.263582			−0.131791	+	0.991278i	$0.542073\pi$
$314$		0			0
$315$	−0.413699	+	0.238849i	−0.0233093	+	0.0134576i
$316$		0			0
$317$	−20.2486			−1.13728			−0.568638	−	0.822588i	$-0.692529\pi$
$317$	−20.2486			−1.13728			−0.568638	+	0.822588i	$0.692529\pi$
$318$		0			0
$319$	−13.5505	−	7.82340i	−0.758684	−	0.438026i
$320$		0			0
$321$	−11.6252	+	20.1354i	−0.648854	+	1.12385i
$322$		0			0
$323$	10.1003	+	17.4943i	0.561997	+	0.973408i
$324$		0			0
$325$	−14.8479	+	7.28567i	−0.823612	+	0.404136i
$326$		0			0
$327$	−17.2984	+	9.98721i	−0.956602	+	0.552294i
$328$		0			0
$329$	2.23093	−	3.86409i	0.122995	−	0.213034i
$330$		0			0
$331$	1.39380	−	2.41414i	0.0766104	−	0.132693i	−0.825175	−	0.564877i	$-0.808924\pi$
$331$	1.39380	−	2.41414i	0.0766104	−	0.132693i	0.901785	+	0.432184i	$0.142257\pi$
$332$		0			0
$333$	10.7064			0.586707
$334$		0			0
$335$	−1.44245	−	2.49839i	−0.0788094	−	0.136502i
$336$		0			0
$337$	22.6505			1.23385			0.616926	−	0.787021i	$-0.288378\pi$
$337$	22.6505			1.23385			0.616926	+	0.787021i	$0.288378\pi$
$338$		0			0
$339$		−	4.32210i		−	0.234744i
$340$		0			0
$341$	15.7035	−	9.06644i	0.850394	−	0.490975i
$342$		0			0
$343$			4.91022i			0.265127i
$344$		0			0
$345$	−1.74321	−	1.00644i	−0.0938513	−	0.0541851i
$346$		0			0
$347$	−2.15567	−	1.24457i	−0.115722	−	0.0668123i	0.441022	−	0.897496i	$-0.354616\pi$
$347$	−2.15567	−	1.24457i	−0.115722	−	0.0668123i	−0.556744	+	0.830684i	$0.687950\pi$
$348$		0			0
$349$	0.504568	+	0.873938i	0.0270089	+	0.0467808i	0.879214	−	0.476427i	$-0.158068\pi$
$349$	0.504568	+	0.873938i	0.0270089	+	0.0467808i	−0.852205	+	0.523208i	$0.824735\pi$
$350$		0			0
$351$	3.22593	+	6.57431i	0.172187	+	0.350911i
$352$		0			0
$353$	2.66110	−	1.53639i	0.141636	−	0.0817738i	−0.427507	−	0.904012i	$-0.640608\pi$
$353$	2.66110	−	1.53639i	0.141636	−	0.0817738i	0.569144	+	0.822238i	$0.307275\pi$
$354$		0			0
$355$	3.43886	+	1.98542i	0.182515	+	0.105375i
$356$		0			0
$357$	−2.67265	+	4.62917i	−0.141452	+	0.245002i
$358$		0			0
$359$		−	3.31798i		−	0.175116i	−0.996159	−	0.0875582i	$-0.972094\pi$
$359$		−	3.31798i		−	0.175116i	0.996159	−	0.0875582i	$-0.0279064\pi$
$360$		0			0
$361$	4.93822	+	8.55324i	0.259906	+	0.450171i
$362$		0			0
$363$		−	12.7577i		−	0.669606i
$364$		0			0
$365$			4.01519i			0.210165i
$366$		0			0
$367$	14.7079	+	25.4749i	0.767748	+	1.32978i	0.938782	+	0.344513i	$0.111956\pi$
$367$	14.7079	+	25.4749i	0.767748	+	1.32978i	−0.171034	+	0.985265i	$0.554711\pi$
$368$		0			0
$369$			17.0565i			0.887928i
$370$		0			0
$371$	−0.602327	+	1.04326i	−0.0312713	+	0.0541635i
$372$		0			0
$373$	−6.80078	−	3.92643i	−0.352131	−	0.203303i	0.313492	−	0.949591i	$-0.398501\pi$
$373$	−6.80078	−	3.92643i	−0.352131	−	0.203303i	−0.665624	+	0.746288i	$0.731834\pi$
$374$		0			0
$375$	−12.0490	+	6.95648i	−0.622206	+	0.359231i
$376$		0			0
$377$	−13.5892	+	20.2509i	−0.699882	+	1.04297i
$378$		0			0
$379$	2.12837	+	3.68644i	0.109327	+	0.189360i	0.915498	−	0.402323i	$-0.131797\pi$
$379$	2.12837	+	3.68644i	0.109327	+	0.189360i	−0.806171	+	0.591683i	$0.798464\pi$
$380$		0			0
$381$	−26.6931	−	15.4113i	−1.36753	−	0.789543i
$382$		0			0
$383$	−18.9596	−	10.9463i	−0.968790	−	0.559331i	−0.0699226	−	0.997552i	$-0.522275\pi$
$383$	−18.9596	−	10.9463i	−0.968790	−	0.559331i	−0.898867	+	0.438221i	$0.855609\pi$
$384$		0			0
$385$		−	0.526038i		−	0.0268094i
$386$		0			0
$387$	−0.0592307	+	0.0341969i	−0.00301087	+	0.00173833i
$388$		0			0
$389$		−	22.2842i		−	1.12985i	−0.825141	−	0.564926i	$-0.808905\pi$
$389$		−	22.2842i		−	1.12985i	0.825141	−	0.564926i	$-0.191095\pi$
$390$		0			0
$391$	−9.27621			−0.469118
$392$		0			0
$393$	−6.56125	−	11.3644i	−0.330971	−	0.573259i
$394$		0			0
$395$	−4.93991			−0.248554
$396$		0			0
$397$	11.3561	−	19.6694i	0.569948	−	0.987179i	−0.426622	−	0.904430i	$-0.640297\pi$
$397$	11.3561	−	19.6694i	0.569948	−	0.987179i	0.996570	−	0.0827491i	$-0.0263700\pi$
$398$		0			0
$399$	1.20710	−	2.09075i	0.0604304	−	0.104669i
$400$		0			0
$401$	−19.5220	+	11.2710i	−0.974883	+	0.562849i	−0.900721	−	0.434397i	$-0.856961\pi$
$401$	−19.5220	+	11.2710i	−0.974883	+	0.562849i	−0.0741618	+	0.997246i	$0.523628\pi$
$402$		0			0
$403$	−12.4501	−	25.3728i	−0.620183	−	1.26391i
$404$		0			0
$405$	3.49850	+	6.05959i	0.173842	+	0.301103i
$406$		0			0
$407$	−5.89489	+	10.2103i	−0.292199	+	0.506104i
$408$		0			0
$409$	10.0317	+	5.79180i	0.496035	+	0.286386i	0.727075	−	0.686558i	$-0.240879\pi$
$409$	10.0317	+	5.79180i	0.496035	+	0.286386i	−0.231039	+	0.972944i	$0.574213\pi$
$410$		0			0
$411$	13.3339			0.657712
$412$		0			0
$413$	1.47205	−	0.849888i	0.0724348	−	0.0418203i
$414$		0			0
$415$	10.7512			0.527755
$416$		0			0
$417$	12.4837			0.611329
$418$		0			0
$419$	−9.30144	+	5.37019i	−0.454405	+	0.262351i	−0.709689	−	0.704515i	$-0.751164\pi$
$419$	−9.30144	+	5.37019i	−0.454405	+	0.262351i	0.255284	+	0.966866i	$0.417831\pi$
$420$		0			0
$421$	38.0009			1.85205			0.926026	−	0.377459i	$-0.123202\pi$
$421$	38.0009			1.85205			0.926026	+	0.377459i	$0.123202\pi$
$422$		0			0
$423$	22.9368	+	13.2426i	1.11523	+	0.643877i
$424$		0			0
$425$	−15.3388	+	26.5676i	−0.744043	+	1.28872i
$426$		0			0
$427$	−1.68274	−	2.91459i	−0.0814333	−	0.141047i
$428$		0			0
$429$	18.7941	+	1.26919i	0.907390	+	0.0612772i
$430$		0			0
$431$	22.4367	−	12.9539i	1.08074	−	0.623965i	0.149643	−	0.988740i	$-0.452187\pi$
$431$	22.4367	−	12.9539i	1.08074	−	0.623965i	0.931096	+	0.364775i	$0.118854\pi$
$432$		0			0
$433$	1.04183	−	1.80451i	0.0500674	−	0.0867192i	−0.839906	−	0.542733i	$-0.817390\pi$
$433$	1.04183	−	1.80451i	0.0500674	−	0.0867192i	0.889973	+	0.456013i	$0.150723\pi$
$434$		0			0
$435$	−4.90798	+	8.50088i	−0.235320	+	0.407586i
$436$		0			0
$437$	4.18957			0.200414
$438$		0			0
$439$	10.2239	+	17.7083i	0.487961	+	0.845173i	0.999904	−	0.0138464i	$-0.00440760\pi$
$439$	10.2239	+	17.7083i	0.487961	+	0.845173i	−0.511943	+	0.859019i	$0.671074\pi$
$440$		0			0
$441$	−14.4417			−0.687701
$442$		0			0
$443$		−	24.7167i		−	1.17433i	−0.809468	−	0.587163i	$-0.800245\pi$
$443$		−	24.7167i		−	1.17433i	0.809468	−	0.587163i	$-0.199755\pi$
$444$		0			0
$445$	−0.886629	+	0.511896i	−0.0420303	+	0.0242662i
$446$		0			0
$447$			30.0694i			1.42223i
$448$		0			0
$449$	10.9531	+	6.32377i	0.516909	+	0.298437i	0.735669	−	0.677341i	$-0.236868\pi$
$449$	10.9531	+	6.32377i	0.516909	+	0.298437i	−0.218760	+	0.975779i	$0.570201\pi$
$450$		0			0
$451$	−16.2661	−	9.39126i	−0.765943	−	0.442217i
$452$		0			0
$453$	−5.90418	−	10.2263i	−0.277403	−	0.480475i
$454$		0			0
$455$	−0.818043	−	0.0552435i	−0.0383505	−	0.00258986i
$456$		0			0
$457$	−29.8239	+	17.2188i	−1.39510	+	0.805463i	−0.993874	−	0.110515i	$-0.964750\pi$
$457$	−29.8239	+	17.2188i	−1.39510	+	0.805463i	−0.401228	+	0.915978i	$0.631417\pi$
$458$		0			0
$459$	11.7636	+	6.79169i	0.549076	+	0.317009i
$460$		0			0
$461$	−6.67318	+	11.5583i	−0.310801	+	0.538323i	−0.978536	−	0.206076i	$-0.933931\pi$
$461$	−6.67318	+	11.5583i	−0.310801	+	0.538323i	0.667735	+	0.744399i	$0.267264\pi$
$462$		0			0
$463$		−	4.86497i		−	0.226094i	−0.993590	−	0.113047i	$-0.963939\pi$
$463$		−	4.86497i		−	0.226094i	0.993590	−	0.113047i	$-0.0360611\pi$
$464$		0			0
$465$	−5.68780	−	9.85155i	−0.263765	−	0.456855i
$466$		0			0
$467$			34.9985i			1.61954i	0.586749	+	0.809769i	$0.300408\pi$
$467$			34.9985i			1.61954i	−0.586749	+	0.809769i	$0.699592\pi$
$468$		0			0
$469$			1.58887i			0.0733671i
$470$		0			0
$471$	−15.5058	−	26.8569i	−0.714471	−	1.23750i
$472$		0			0
$473$		−	0.0753146i		−	0.00346297i
$474$		0			0
$475$	6.92774	−	11.9992i	0.317866	−	0.550561i
$476$		0			0
$477$	−6.19270	−	3.57535i	−0.283544	−	0.163704i
$478$		0			0
$479$	9.70423	−	5.60274i	0.443398	−	0.255996i	−0.261640	−	0.965166i	$-0.584263\pi$
$479$	9.70423	−	5.60274i	0.443398	−	0.255996i	0.705038	+	0.709170i	$0.250930\pi$
$480$		0			0
$481$	15.2589	+	10.2394i	0.695747	+	0.466878i
$482$		0			0
$483$	0.554303	+	0.960080i	0.0252216	+	0.0436852i
$484$		0			0
$485$	−3.40229	−	1.96431i	−0.154490	−	0.0891949i
$486$		0			0
$487$	−15.3246	−	8.84766i	−0.694424	−	0.400926i	0.110843	−	0.993838i	$-0.464645\pi$
$487$	−15.3246	−	8.84766i	−0.694424	−	0.400926i	−0.805267	+	0.592912i	$0.797978\pi$
$488$		0			0
$489$		−	38.0762i		−	1.72186i
$490$		0			0
$491$	2.20922	−	1.27549i	0.0997007	−	0.0575622i	−0.449321	−	0.893371i	$-0.648334\pi$
$491$	2.20922	−	1.27549i	0.0997007	−	0.0575622i	0.549021	+	0.835808i	$0.315001\pi$
$492$		0			0
$493$			45.2360i			2.03733i
$494$		0			0
$495$	3.12251			0.140346
$496$		0			0
$497$	−1.09348	−	1.89396i	−0.0490493	−	0.0849559i
$498$		0			0
$499$	−20.8838			−0.934889			−0.467444	−	0.884022i	$-0.654825\pi$
$499$	−20.8838			−0.934889			−0.467444	+	0.884022i	$0.654825\pi$
$500$		0			0
$501$	−9.10294	+	15.7668i	−0.406689	+	0.704407i
$502$		0			0
$503$	4.58269	−	7.93745i	0.204332	−	0.353914i	−0.745588	−	0.666408i	$-0.767831\pi$
$503$	4.58269	−	7.93745i	0.204332	−	0.353914i	0.949920	+	0.312494i	$0.101164\pi$
$504$		0			0
$505$	−4.61030	+	2.66176i	−0.205155	+	0.118447i
$506$		0			0
$507$	3.94745	−	29.0935i	0.175312	−	1.29209i
$508$		0			0
$509$	−7.84874	−	13.5944i	−0.347889	−	0.602562i	0.637985	−	0.770049i	$-0.279768\pi$
$509$	−7.84874	−	13.5944i	−0.347889	−	0.602562i	−0.985874	+	0.167487i	$0.946435\pi$
$510$		0			0
$511$	1.10569	−	1.91511i	0.0489129	−	0.0847197i
$512$		0			0
$513$	−5.31297	−	3.06745i	−0.234574	−	0.135431i
$514$		0			0
$515$	−7.43896			−0.327800
$516$		0			0
$517$	−25.2579	+	14.5826i	−1.11084	+	0.641344i
$518$		0			0
$519$	37.6790			1.65392
$520$		0			0
$521$	16.1321			0.706761			0.353381	−	0.935480i	$-0.385032\pi$
$521$	16.1321			0.706761			0.353381	+	0.935480i	$0.385032\pi$
$522$		0			0
$523$	2.95531	−	1.70625i	0.129226	−	0.0746089i	−0.433993	−	0.900916i	$-0.642896\pi$
$523$	2.95531	−	1.70625i	0.129226	−	0.0746089i	0.563220	+	0.826307i	$0.309562\pi$
$524$		0			0
$525$	3.66631			0.160011
$526$		0			0
$527$	−45.4000	−	26.2117i	−1.97766	−	1.14180i
$528$		0			0
$529$	10.5381	−	18.2525i	0.458177	−	0.793586i
$530$		0			0
$531$	5.04485	+	8.73794i	0.218928	+	0.379194i
$532$		0			0
$533$	−16.3126	+	24.3093i	−0.706578	+	1.05295i
$534$		0			0
$535$	−5.72879	+	3.30752i	−0.247677	+	0.142997i
$536$		0			0
$537$	−13.3130	+	23.0587i	−0.574497	+	0.995058i
$538$		0			0
$539$	7.95155	−	13.7725i	0.342498	−	0.593223i
$540$		0			0
$541$	−9.17340			−0.394395			−0.197198	−	0.980364i	$-0.563184\pi$
$541$	−9.17340			−0.394395			−0.197198	+	0.980364i	$0.563184\pi$
$542$		0			0
$543$	−6.38333	−	11.0563i	−0.273935	−	0.474469i
$544$		0			0
$545$	−5.68300			−0.243433
$546$		0			0
$547$			21.0672i			0.900767i	0.892835	+	0.450384i	$0.148713\pi$
$547$			21.0672i			0.900767i	−0.892835	+	0.450384i	$0.851287\pi$
$548$		0			0
$549$	17.3007	−	9.98855i	0.738375	−	0.426301i
$550$		0			0
$551$		−	20.4307i		−	0.870378i
$552$		0			0
$553$	2.35618	+	1.36034i	0.100195	+	0.0578475i
$554$		0			0
$555$	6.40537	+	3.69814i	0.271893	+	0.156977i
$556$		0			0
$557$	9.56798	+	16.5722i	0.405408	+	0.702188i	0.994369	−	0.105974i	$-0.0337960\pi$
$557$	9.56798	+	16.5722i	0.405408	+	0.702188i	−0.588961	+	0.808162i	$0.700463\pi$
$558$		0			0
$559$	−0.117122	−	0.00790940i	−0.00495373	−	0.000334532i
$560$		0			0
$561$	30.2589	−	17.4700i	1.27753	−	0.737582i
$562$		0			0
$563$	5.53304	+	3.19450i	0.233190	+	0.134632i	0.612043	−	0.790825i	$-0.290348\pi$
$563$	5.53304	+	3.19450i	0.233190	+	0.134632i	−0.378853	+	0.925457i	$0.623681\pi$
$564$		0			0
$565$	0.614848	−	1.06495i	0.0258668	−	0.0448027i
$566$		0			0
$567$		−	3.85363i		−	0.161837i
$568$		0			0
$569$	0.966936	+	1.67478i	0.0405361	+	0.0702106i	0.885582	−	0.464484i	$-0.153760\pi$
$569$	0.966936	+	1.67478i	0.0405361	+	0.0702106i	−0.845046	+	0.534694i	$0.820427\pi$
$570$		0			0
$571$			36.9706i			1.54717i	0.633693	+	0.773585i	$0.281538\pi$
$571$			36.9706i			1.54717i	−0.633693	+	0.773585i	$0.718462\pi$
$572$		0			0
$573$		−	25.3276i		−	1.05808i
$574$		0			0
$575$	3.18124	+	5.51007i	0.132667	+	0.229786i
$576$		0			0
$577$		−	23.0494i		−	0.959558i	−0.877389	−	0.479779i	$-0.840717\pi$
$577$		−	23.0494i		−	0.959558i	0.877389	−	0.479779i	$-0.159283\pi$
$578$		0			0
$579$	0.876004	−	1.51728i	0.0364055	−	0.0630561i
$580$		0			0
$581$	−5.12796	−	2.96063i	−0.212744	−	0.122828i
$582$		0			0
$583$	6.81934	−	3.93715i	0.282428	−	0.163060i
$584$		0			0
$585$	0.327920	−	4.85582i	0.0135578	−	0.200763i
$586$		0			0
$587$	−14.3010	−	24.7701i	−0.590267	−	1.02237i	−0.994196	−	0.107583i	$-0.965689\pi$
$587$	−14.3010	−	24.7701i	−0.590267	−	1.02237i	0.403929	−	0.914790i	$-0.367644\pi$
$588$		0			0
$589$	20.5048	+	11.8384i	0.844885	+	0.487795i
$590$		0			0
$591$	5.97746	+	3.45109i	0.245880	+	0.141959i
$592$		0			0
$593$		−	32.2516i		−	1.32441i	−0.749321	−	0.662207i	$-0.769620\pi$
$593$		−	32.2516i		−	1.32441i	0.749321	−	0.662207i	$-0.230380\pi$
$594$		0			0
$595$	−1.31706	+	0.760406i	−0.0539943	+	0.0311736i
$596$		0			0
$597$		−	59.2886i		−	2.42652i
$598$		0			0
$599$	−22.6404			−0.925060			−0.462530	−	0.886604i	$-0.653058\pi$
$599$	−22.6404			−0.925060			−0.462530	+	0.886604i	$0.653058\pi$
$600$		0			0
$601$	−1.77121	−	3.06782i	−0.0722490	−	0.125139i	0.827638	−	0.561263i	$-0.189684\pi$
$601$	−1.77121	−	3.06782i	−0.0722490	−	0.125139i	−0.899887	+	0.436124i	$0.856351\pi$
$602$		0			0
$603$	−9.43136			−0.384075
$604$		0			0
$605$	1.81487	−	3.14345i	0.0737850	−	0.127799i
$606$		0			0
$607$	−9.01370	+	15.6122i	−0.365855	+	0.633679i	−0.988913	−	0.148496i	$-0.952557\pi$
$607$	−9.01370	+	15.6122i	−0.365855	+	0.633679i	0.623058	+	0.782176i	$0.285890\pi$
$608$		0			0
$609$	4.68189	−	2.70309i	0.189720	−	0.109535i
$610$		0			0
$611$	20.0250	+	40.8100i	0.810123	+	1.65100i
$612$		0			0
$613$	20.5202	+	35.5421i	0.828804	+	1.43553i	0.898977	+	0.437996i	$0.144312\pi$
$613$	20.5202	+	35.5421i	0.828804	+	1.43553i	−0.0701726	+	0.997535i	$0.522355\pi$
$614$		0			0
$615$	−5.89157	+	10.2045i	−0.237571	+	0.411485i
$616$		0			0
$617$	−4.18519	−	2.41632i	−0.168490	−	0.0972775i	0.413384	−	0.910557i	$-0.364347\pi$
$617$	−4.18519	−	2.41632i	−0.168490	−	0.0972775i	−0.581873	+	0.813279i	$0.697680\pi$
$618$		0			0
$619$	22.8273			0.917507			0.458754	−	0.888564i	$-0.348296\pi$
$619$	22.8273			0.917507			0.458754	+	0.888564i	$0.348296\pi$
$620$		0			0
$621$	2.43974	−	1.40858i	0.0979032	−	0.0565244i
$622$		0			0
$623$	0.563857			0.0225905
$624$		0			0
$625$	18.9771			0.759085
$626$		0			0
$627$	−13.6663	+	7.89026i	−0.545781	+	0.315107i
$628$		0			0
$629$	34.0851			1.35906
$630$		0			0
$631$	36.6267	+	21.1464i	1.45808	+	0.841825i	0.998917	−	0.0465243i	$-0.0148145\pi$
$631$	36.6267	+	21.1464i	1.45808	+	0.841825i	0.459167	+	0.888350i	$0.348148\pi$
$632$		0			0
$633$	14.2381	−	24.6612i	0.565915	−	0.980194i
$634$		0			0
$635$	−4.38472	−	7.59455i	−0.174002	−	0.301381i
$636$		0			0
$637$	−20.5826	−	13.8118i	−0.815512	−	0.547245i
$638$		0			0
$639$	11.2424	−	6.49079i	0.444741	−	0.256772i
$640$		0			0
$641$	19.4086	−	33.6167i	0.766593	−	1.32778i	−0.172807	−	0.984956i	$-0.555284\pi$
$641$	19.4086	−	33.6167i	0.766593	−	1.32778i	0.939400	−	0.342823i	$-0.111383\pi$
$642$		0			0
$643$	−6.67441	+	11.5604i	−0.263213	+	0.455898i	−0.967094	−	0.254420i	$-0.918116\pi$
$643$	−6.67441	+	11.5604i	−0.263213	+	0.455898i	0.703881	+	0.710318i	$0.251449\pi$
$644$		0			0
$645$	−0.0472484			−0.00186040
$646$		0			0
$647$	6.64954	+	11.5173i	0.261421	+	0.452794i	0.966620	−	0.256216i	$-0.0824757\pi$
$647$	6.64954	+	11.5173i	0.261421	+	0.452794i	−0.705199	+	0.709009i	$0.749142\pi$
$648$		0			0
$649$	−11.1107			−0.436133
$650$		0			0
$651$			6.26515i			0.245551i
$652$		0			0
$653$	2.37825	−	1.37308i	0.0930682	−	0.0537329i	−0.452744	−	0.891641i	$-0.649555\pi$
$653$	2.37825	−	1.37308i	0.0930682	−	0.0537329i	0.545812	+	0.837908i	$0.316221\pi$
$654$		0			0
$655$		−	3.73353i		−	0.145881i
$656$		0			0
$657$	11.3679	+	6.56327i	0.443505	+	0.256058i
$658$		0			0
$659$	42.8439	+	24.7359i	1.66896	+	0.963576i	0.968199	+	0.250181i	$0.0804901\pi$
$659$	42.8439	+	24.7359i	1.66896	+	0.963576i	0.700763	+	0.713394i	$0.252843\pi$
$660$		0			0
$661$	−18.2518	−	31.6131i	−0.709914	−	1.22961i	−0.964889	−	0.262660i	$-0.915400\pi$
$661$	−18.2518	−	31.6131i	−0.709914	−	1.22961i	0.254974	−	0.966948i	$-0.417933\pi$
$662$		0			0
$663$	−23.9899	−	48.8903i	−0.931689	−	1.89874i
$664$		0			0
$665$	0.594847	−	0.343435i	0.0230672	−	0.0133178i
$666$		0			0
$667$	8.12492	+	4.69093i	0.314598	+	0.181633i
$668$		0			0
$669$	19.3882	−	33.5813i	0.749590	−	1.29833i
$670$		0			0
$671$			21.9986i			0.849247i
$672$		0			0
$673$	12.8769	+	22.3034i	0.496368	+	0.859734i	0.999991	−	0.00418893i	$-0.00133338\pi$
$673$	12.8769	+	22.3034i	0.496368	+	0.859734i	−0.503623	+	0.863923i	$0.668000\pi$
$674$		0			0
$675$		−	9.31674i		−	0.358601i
$676$		0			0
$677$			26.6436i			1.02400i	0.858987	+	0.511998i	$0.171094\pi$
$677$			26.6436i			1.02400i	−0.858987	+	0.511998i	$0.828906\pi$
$678$		0			0
$679$	1.08185	+	1.87383i	0.0415177	+	0.0719108i
$680$		0			0
$681$		−	10.4320i		−	0.399755i
$682$		0			0
$683$	13.4138	−	23.2334i	0.513266	−	0.889003i	−0.486615	−	0.873616i	$-0.661769\pi$
$683$	13.4138	−	23.2334i	0.513266	−	0.889003i	0.999882	−	0.0153869i	$-0.00489798\pi$
$684$		0			0
$685$	3.28542	+	1.89684i	0.125529	+	0.0724744i
$686$		0			0
$687$	44.8052	−	25.8683i	1.70942	−	0.986936i
$688$		0			0
$689$	−5.40652	−	11.0183i	−0.205972	−	0.419762i
$690$		0			0
$691$	−6.27307	−	10.8653i	−0.238639	−	0.413335i	0.721685	−	0.692221i	$-0.243368\pi$
$691$	−6.27307	−	10.8653i	−0.238639	−	0.413335i	−0.960324	+	0.278887i	$0.910035\pi$
$692$		0			0
$693$	−1.48933	−	0.859867i	−0.0565751	−	0.0326636i
$694$		0			0
$695$	3.07593	+	1.77589i	0.116677	+	0.0673633i
$696$		0			0
$697$			54.3016i			2.05682i
$698$		0			0
$699$	48.1375	−	27.7922i	1.82073	−	1.05120i
$700$		0			0
$701$		−	4.96259i		−	0.187434i	−0.995599	−	0.0937171i	$-0.970125\pi$
$701$		−	4.96259i		−	0.187434i	0.995599	−	0.0937171i	$-0.0298749\pi$
$702$		0			0
$703$	−15.3944			−0.580612
$704$		0			0
$705$	9.14836	+	15.8454i	0.344547	+	0.596773i
$706$		0			0
$707$	2.93195			0.110267
$708$		0			0
$709$	−6.37556	+	11.0428i	−0.239439	+	0.414721i	−0.960554	−	0.278095i	$-0.910297\pi$
$709$	−6.37556	+	11.0428i	−0.239439	+	0.414721i	0.721114	+	0.692816i	$0.243630\pi$
$710$		0			0
$711$	−8.07483	+	13.9860i	−0.302830	+	0.524517i
$712$		0			0
$713$	−9.41587	+	5.43625i	−0.352627	+	0.203589i
$714$		0			0
$715$	4.45025	+	2.98632i	0.166430	+	0.111682i
$716$		0			0
$717$	11.4053	+	19.7546i	0.425941	+	0.737751i
$718$		0			0
$719$	16.5699	−	28.7000i	0.617955	−	1.07033i	−0.371904	−	0.928271i	$-0.621295\pi$
$719$	16.5699	−	28.7000i	0.617955	−	1.07033i	0.989858	−	0.142058i	$-0.0453719\pi$
$720$		0			0
$721$	3.54814	+	2.04852i	0.132140	+	0.0762908i
$722$		0			0
$723$	−40.8366			−1.51873
$724$		0			0
$725$	26.8702	−	15.5135i	0.997934	−	0.576158i
$726$		0			0
$727$	−10.2705			−0.380912			−0.190456	−	0.981696i	$-0.560997\pi$
$727$	−10.2705			−0.380912			−0.190456	+	0.981696i	$0.560997\pi$
$728$		0			0
$729$	9.11343			0.337534
$730$		0			0
$731$	−0.188568	+	0.108870i	−0.00697445	+	0.00402670i
$732$		0			0
$733$	−28.5069			−1.05293			−0.526463	−	0.850198i	$-0.676482\pi$
$733$	−28.5069			−1.05293			−0.526463	+	0.850198i	$0.676482\pi$
$734$		0			0
$735$	−8.64012	−	4.98838i	−0.318696	−	0.183999i
$736$		0			0
$737$	5.19287	−	8.99431i	0.191282	−	0.331310i
$738$		0			0
$739$	−5.94448	−	10.2961i	−0.218671	−	0.378750i	0.735731	−	0.677274i	$-0.236839\pi$
$739$	−5.94448	−	10.2961i	−0.218671	−	0.378750i	−0.954402	+	0.298524i	$0.903506\pi$
$740$		0			0
$741$	10.8350	+	22.0812i	0.398032	+	0.811172i
$742$		0			0
$743$	−27.5090	+	15.8823i	−1.00921	+	0.582665i	−0.910959	−	0.412497i	$-0.864657\pi$
$743$	−27.5090	+	15.8823i	−1.00921	+	0.582665i	−0.0982467	+	0.995162i	$0.531323\pi$
$744$		0			0
$745$	−4.27758	+	7.40898i	−0.156718	+	0.271444i
$746$		0			0
$747$	17.5740	−	30.4391i	0.642999	−	1.11371i
$748$		0			0
$749$	3.64326			0.133122
$750$		0			0
$751$	−16.0950	−	27.8773i	−0.587314	−	1.01726i	−0.994583	−	0.103949i	$-0.966852\pi$
$751$	−16.0950	−	27.8773i	−0.587314	−	1.01726i	0.407269	−	0.913308i	$-0.366481\pi$
$752$		0			0
$753$	−34.7730			−1.26720
$754$		0			0
$755$		−	3.35964i		−	0.122270i
$756$		0			0
$757$	−1.98947	+	1.14862i	−0.0723086	+	0.0417474i	−0.535718	−	0.844397i	$-0.679959\pi$
$757$	−1.98947	+	1.14862i	−0.0723086	+	0.0417474i	0.463410	+	0.886144i	$0.346626\pi$
$758$		0			0
$759$		−	7.24647i		−	0.263030i
$760$		0			0
$761$	−23.3130	−	13.4598i	−0.845095	−	0.487916i	0.0138981	−	0.999903i	$-0.495576\pi$
$761$	−23.3130	−	13.4598i	−0.845095	−	0.487916i	−0.858993	+	0.511988i	$0.828909\pi$
$762$		0			0
$763$	2.71060	+	1.56497i	0.0981304	+	0.0566556i
$764$		0			0
$765$	−4.51369	−	7.81795i	−0.163193	−	0.282659i
$766$		0			0
$767$	−1.16682	+	17.2783i	−0.0421316	+	0.623882i
$768$		0			0
$769$	−22.9461	+	13.2479i	−0.827457	+	0.477733i	−0.852981	−	0.521942i	$-0.825208\pi$
$769$	−22.9461	+	13.2479i	−0.827457	+	0.477733i	0.0255242	+	0.999674i	$0.491875\pi$
$770$		0			0
$771$	2.22905	+	1.28694i	0.0802772	+	0.0463481i
$772$		0			0
$773$	−23.1594	+	40.1133i	−0.832986	+	1.44277i	0.0626740	+	0.998034i	$0.480037\pi$
$773$	−23.1594	+	40.1133i	−0.832986	+	1.44277i	−0.895660	+	0.444740i	$0.853296\pi$
$774$		0			0
$775$			35.9568i			1.29161i
$776$		0			0
$777$	−2.03677	−	3.52778i	−0.0730686	−	0.126558i
$778$		0			0
$779$		−	24.5252i		−	0.878705i
$780$		0			0
$781$			14.2952i			0.511523i
$782$		0			0
$783$	−6.86904	−	11.8975i	−0.245479	−	0.425183i
$784$		0			0
$785$		−	8.82325i		−	0.314915i
$786$		0			0
$787$	−25.1049	+	43.4830i	−0.894893	+	1.55000i	−0.0609564	+	0.998140i	$0.519415\pi$
$787$	−25.1049	+	43.4830i	−0.894893	+	1.55000i	−0.833937	+	0.551860i	$0.813918\pi$
$788$		0			0
$789$	−18.3600	−	10.6002i	−0.653634	−	0.377376i
$790$		0			0
$791$	−0.586524	+	0.338630i	−0.0208544	+	0.0120403i
$792$		0			0
$793$	34.2101	+	2.31025i	1.21484	+	0.0820396i
$794$		0			0
$795$	−2.46996	−	4.27809i	−0.0876004	−	0.151728i
$796$		0			0
$797$	32.7238	+	18.8931i	1.15914	+	0.669228i	0.951097	−	0.308892i	$-0.0999581\pi$
$797$	32.7238	+	18.8931i	1.15914	+	0.669228i	0.208041	+	0.978120i	$0.433291\pi$
$798$		0			0
$799$	73.0223	+	42.1594i	2.58334	+	1.49149i
$800$		0			0
$801$			3.34700i			0.118260i
$802$		0			0
$803$	−12.5183	+	7.22742i	−0.441760	+	0.255050i
$804$		0			0
$805$			0.315413i			0.0111169i
$806$		0			0
$807$	43.0594			1.51576
$808$		0			0
$809$	8.93101	+	15.4690i	0.313998	+	0.543860i	0.979224	−	0.202782i	$-0.0649983\pi$
$809$	8.93101	+	15.4690i	0.313998	+	0.543860i	−0.665226	+	0.746642i	$0.731665\pi$
$810$		0			0
$811$	−29.2622			−1.02754			−0.513768	−	0.857929i	$-0.671751\pi$
$811$	−29.2622			−1.02754			−0.513768	+	0.857929i	$0.671751\pi$
$812$		0			0
$813$	−20.0224	+	34.6798i	−0.702217	+	1.21628i
$814$		0			0
$815$	5.41659	−	9.38181i	0.189735	−	0.328631i
$816$		0			0
$817$	0.0851663	−	0.0491708i	0.00297959	−	0.00172027i
$818$		0			0
$819$	−1.49359	+	2.22576i	−0.0521902	+	0.0777745i
$820$		0			0
$821$	−14.1150	−	24.4479i	−0.492618	−	0.853239i	0.507346	−	0.861742i	$-0.330627\pi$
$821$	−14.1150	−	24.4479i	−0.492618	−	0.853239i	−0.999964	+	0.00850342i	$0.997293\pi$
$822$		0			0
$823$	16.9117	−	29.2919i	0.589505	−	1.02105i	−0.404792	−	0.914409i	$-0.632656\pi$
$823$	16.9117	−	29.2919i	0.589505	−	1.02105i	0.994297	−	0.106644i	$-0.0340106\pi$
$824$		0			0
$825$	−20.7543	−	11.9825i	−0.722573	−	0.417178i
$826$		0			0
$827$	−55.5280			−1.93090			−0.965449	−	0.260591i	$-0.916082\pi$
$827$	−55.5280			−1.93090			−0.965449	+	0.260591i	$0.916082\pi$
$828$		0			0
$829$	2.15990	−	1.24702i	0.0750165	−	0.0433108i	−0.462023	−	0.886868i	$-0.652876\pi$
$829$	2.15990	−	1.24702i	0.0750165	−	0.0433108i	0.537039	+	0.843557i	$0.319543\pi$
$830$		0			0
$831$	−58.4376			−2.02718
$832$		0			0
$833$	−45.9770			−1.59301
$834$		0			0
$835$	−4.48586	+	2.58991i	−0.155239	+	0.0896276i
$836$		0			0
$837$	15.9209			0.550306
$838$		0			0
$839$	−17.3429	−	10.0129i	−0.598744	−	0.345685i	0.169803	−	0.985478i	$-0.445687\pi$
$839$	−17.3429	−	10.0129i	−0.598744	−	0.345685i	−0.768547	+	0.639793i	$0.779020\pi$
$840$		0			0
$841$	8.37560	−	14.5070i	0.288814	−	0.500240i
$842$		0			0
$843$	−0.831194	−	1.43967i	−0.0286278	−	0.0495849i
$844$		0			0
$845$	5.11139	−	6.60698i	0.175837	−	0.227287i
$846$		0			0
$847$	−1.73127	+	0.999548i	−0.0594870	+	0.0343449i
$848$		0			0
$849$	−27.4885	+	47.6115i	−0.943403	+	1.63402i
$850$		0			0
$851$	3.53459	−	6.12209i	0.121164	−	0.209862i
$852$		0			0
$853$	−12.6665			−0.433692			−0.216846	−	0.976206i	$-0.569577\pi$
$853$	−12.6665			−0.433692			−0.216846	+	0.976206i	$0.569577\pi$
$854$		0			0
$855$	2.03860	+	3.53095i	0.0697185	+	0.120756i
$856$		0			0
$857$	−21.2258			−0.725059			−0.362530	−	0.931972i	$-0.618087\pi$
$857$	−21.2258			−0.725059			−0.362530	+	0.931972i	$0.618087\pi$
$858$		0			0
$859$		−	33.6456i		−	1.14797i	−0.818865	−	0.573986i	$-0.805396\pi$
$859$		−	33.6456i		−	1.14797i	0.818865	−	0.573986i	$-0.194604\pi$
$860$		0			0
$861$	5.62017	−	3.24481i	0.191535	−	0.110583i
$862$		0			0
$863$			31.3083i			1.06575i	0.846195	+	0.532874i	$0.178888\pi$
$863$			31.3083i			1.06575i	−0.846195	+	0.532874i	$0.821112\pi$
$864$		0			0
$865$	9.28395	+	5.36009i	0.315664	+	0.182248i
$866$		0			0
$867$	−54.2303	−	31.3099i	−1.84176	−	1.06334i
$868$		0			0
$869$	−8.89194	−	15.4013i	−0.301638	−	0.522453i
$870$		0			0
$871$	−13.4417	−	9.02001i	−0.455456	−	0.305631i
$872$		0			0
$873$	−11.1228	+	6.42178i	−0.376451	+	0.217344i
$874$		0			0
$875$	1.88804	+	1.09006i	0.0638274	+	0.0368507i
$876$		0			0
$877$	6.94228	−	12.0244i	0.234424	−	0.406035i	−0.724681	−	0.689085i	$-0.758013\pi$
$877$	6.94228	−	12.0244i	0.234424	−	0.406035i	0.959105	+	0.283050i	$0.0913462\pi$
$878$		0			0
$879$		−	13.8869i		−	0.468395i
$880$		0			0
$881$	10.4302	+	18.0656i	0.351401	+	0.608645i	0.986495	−	0.163790i	$-0.0523719\pi$
$881$	10.4302	+	18.0656i	0.351401	+	0.608645i	−0.635094	+	0.772435i	$0.719039\pi$
$882$		0			0
$883$			22.9456i			0.772181i	0.922461	+	0.386091i	$0.126175\pi$
$883$			22.9456i			0.772181i	−0.922461	+	0.386091i	$0.873825\pi$
$884$		0			0
$885$			6.97025i			0.234303i
$886$		0			0
$887$	13.4138	+	23.2335i	0.450393	+	0.780103i	0.998410	−	0.0563635i	$-0.0179506\pi$
$887$	13.4138	+	23.2335i	0.450393	+	0.780103i	−0.548017	+	0.836467i	$0.684617\pi$
$888$		0			0
$889$			4.82980i			0.161986i
$890$		0			0
$891$	−12.5947	+	21.8147i	−0.421940	+	0.730821i
$892$		0			0
$893$	−32.9803	−	19.0412i	−1.10364	−	0.637189i
$894$		0			0
$895$	−6.56053	+	3.78772i	−0.219294	+	0.126610i
$896$		0			0
$897$	−11.2690	−	0.761010i	−0.376261	−	0.0254094i
$898$		0			0
$899$	26.5102	+	45.9171i	0.884166	+	1.53142i
$900$		0			0
$901$	−19.7152	−	11.3826i	−0.656809	−	0.379209i
$902$		0			0
$903$	0.0225359	+	0.0130111i	0.000749948	+	0.000432983i
$904$		0			0
$905$		−	3.63229i		−	0.120741i
$906$		0			0
$907$	11.0322	−	6.36945i	0.366318	−	0.211494i	−0.305531	−	0.952182i	$-0.598834\pi$
$907$	11.0322	−	6.36945i	0.366318	−	0.211494i	0.671849	+	0.740688i	$0.265500\pi$
$908$		0			0
$909$			17.4037i			0.577245i
$910$		0			0
$911$	−34.5498			−1.14469			−0.572343	−	0.820014i	$-0.693965\pi$
$911$	−34.5498			−1.14469			−0.572343	+	0.820014i	$0.693965\pi$
$912$		0			0
$913$	19.3523	+	33.5192i	0.640469	+	1.10932i
$914$		0			0
$915$	13.8008			0.456239
$916$		0			0
$917$	−1.02813	+	1.78077i	−0.0339518	+	0.0588063i
$918$		0			0
$919$	−2.65896	+	4.60545i	−0.0877109	+	0.151920i	−0.906543	−	0.422113i	$-0.861288\pi$
$919$	−2.65896	+	4.60545i	−0.0877109	+	0.151920i	0.818832	+	0.574033i	$0.194622\pi$
$920$		0			0
$921$	22.9858	−	13.2709i	0.757409	−	0.437290i
$922$		0			0
$923$	22.2305	+	1.50126i	0.731726	+	0.0494144i
$924$		0			0
$925$	−11.6894	−	20.2466i	−0.384344	−	0.665703i
$926$		0			0
$927$	−12.1598	+	21.0614i	−0.399380	+	0.691747i
$928$		0			0
$929$	5.19280	+	2.99807i	0.170370	+	0.0983633i	0.582760	−	0.812644i	$-0.301973\pi$
$929$	5.19280	+	2.99807i	0.170370	+	0.0983633i	−0.412390	+	0.911007i	$0.635306\pi$
$930$		0			0
$931$	20.7654			0.680558
$932$		0			0
$933$	47.1330	−	27.2123i	1.54307	−	0.890889i
$934$		0			0
$935$	9.94089			0.325102
$936$		0			0
$937$	−18.5525			−0.606085			−0.303043	−	0.952977i	$-0.598002\pi$
$937$	−18.5525			−0.606085			−0.303043	+	0.952977i	$0.598002\pi$
$938$		0			0
$939$	−9.12080	+	5.26590i	−0.297646	+	0.171846i
$940$		0			0
$941$	−35.5592			−1.15920			−0.579599	−	0.814902i	$-0.696791\pi$
$941$	−35.5592			−1.15920			−0.579599	+	0.814902i	$0.696791\pi$
$942$		0			0
$943$	9.75321	+	5.63102i	0.317608	+	0.183371i
$944$		0			0
$945$	0.230934	−	0.399989i	0.00751227	−	0.0130116i
$946$		0			0
$947$	−3.28589	−	5.69133i	−0.106777	−	0.184944i	0.807686	−	0.589613i	$-0.200720\pi$
$947$	−3.28589	−	5.69133i	−0.106777	−	0.184944i	−0.914463	+	0.404670i	$0.867386\pi$
$948$		0			0
$949$	9.92474	+	20.2262i	0.322171	+	0.656570i
$950$		0			0
$951$	−39.6041	+	22.8655i	−1.28425	+	0.741463i
$952$		0			0
$953$	20.4231	−	35.3738i	0.661568	−	1.14587i	−0.318635	−	0.947877i	$-0.603225\pi$
$953$	20.4231	−	35.3738i	0.661568	−	1.14587i	0.980204	−	0.197992i	$-0.0634422\pi$
$954$		0			0
$955$	3.60302	−	6.24062i	0.116591	−	0.201942i
$956$		0			0
$957$	−35.3378			−1.14231
$958$		0			0
$959$	−1.04469	−	1.80946i	−0.0337348	−	0.0584304i
$960$		0			0
$961$	−30.4447			−0.982088
$962$		0			0
$963$			21.6260i			0.696889i
$964$		0			0
$965$	0.431688	−	0.249235i	0.0138965	−	0.00802316i
$966$		0			0
$967$		−	35.6793i		−	1.14737i	−0.819076	−	0.573684i	$-0.805514\pi$
$967$		−	35.6793i		−	1.14737i	0.819076	−	0.573684i	$-0.194486\pi$
$968$		0			0
$969$	39.5103	+	22.8113i	1.26925	+	0.732804i
$970$		0			0
$971$	−21.6109	−	12.4770i	−0.693526	−	0.400407i	0.111406	−	0.993775i	$-0.464465\pi$
$971$	−21.6109	−	12.4770i	−0.693526	−	0.400407i	−0.804932	+	0.593368i	$0.797798\pi$
$972$		0			0
$973$	−0.978078	−	1.69408i	−0.0313557	−	0.0543098i
$974$		0			0
$975$	−20.8136	+	31.0167i	−0.666569	+	0.993330i
$976$		0			0
$977$	−20.5257	+	11.8505i	−0.656676	+	0.379132i	−0.791009	−	0.611804i	$-0.790444\pi$
$977$	−20.5257	+	11.8505i	−0.656676	+	0.379132i	0.134333	+	0.990936i	$0.457111\pi$
$978$		0			0
$979$	−3.19190	−	1.84284i	−0.102014	−	0.0588975i
$980$		0			0
$981$	−9.28948	+	16.0899i	−0.296590	+	0.513710i
$982$		0			0
$983$		−	9.34592i		−	0.298089i	−0.988831	−	0.149044i	$-0.952380\pi$
$983$		−	9.34592i		−	0.298089i	0.988831	−	0.149044i	$-0.0476197\pi$
$984$		0			0
$985$	0.981882	+	1.70067i	0.0312854	+	0.0541879i
$986$		0			0
$987$		−	10.0770i		−	0.320754i
$988$		0			0
$989$			0.0451588i			0.00143597i
$990$		0			0
$991$	20.9332	+	36.2573i	0.664964	+	1.15175i	0.979295	+	0.202438i	$0.0648863\pi$
$991$	20.9332	+	36.2573i	0.664964	+	1.15175i	−0.314332	+	0.949313i	$0.601780\pi$
$992$		0			0
$993$		−	6.29573i		−	0.199789i
$994$		0			0
$995$	8.43421	−	14.6085i	0.267382	−	0.463120i
$996$		0			0
$997$	−13.3093	−	7.68412i	−0.421509	−	0.243359i	0.274213	−	0.961669i	$-0.411583\pi$
$997$	−13.3093	−	7.68412i	−0.421509	−	0.243359i	−0.695723	+	0.718310i	$0.744916\pi$
$998$		0			0
$999$	−8.96472	+	5.17579i	−0.283631	+	0.163755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.ba.c.49.7		16
4.3	odd	2		104.2.s.c.101.7	yes	16
8.3	odd	2		104.2.s.c.101.4	yes	16
8.5	even	2	inner	416.2.ba.c.49.2		16
12.11	even	2		936.2.dg.d.829.2		16
13.4	even	6	inner	416.2.ba.c.17.2		16
24.11	even	2		936.2.dg.d.829.5		16
52.43	odd	6		104.2.s.c.69.4	✓	16
104.43	odd	6		104.2.s.c.69.7	yes	16
104.69	even	6	inner	416.2.ba.c.17.7		16
156.95	even	6		936.2.dg.d.901.5		16
312.251	even	6		936.2.dg.d.901.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.s.c.69.4	✓	16	52.43	odd	6
104.2.s.c.69.7	yes	16	104.43	odd	6
104.2.s.c.101.4	yes	16	8.3	odd	2
104.2.s.c.101.7	yes	16	4.3	odd	2
416.2.ba.c.17.2		16	13.4	even	6	inner
416.2.ba.c.17.7		16	104.69	even	6	inner
416.2.ba.c.49.2		16	8.5	even	2	inner
416.2.ba.c.49.7		16	1.1	even	1	trivial
936.2.dg.d.829.2		16	12.11	even	2
936.2.dg.d.829.5		16	24.11	even	2
936.2.dg.d.901.2		16	312.251	even	6
936.2.dg.d.901.5		16	156.95	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.95589 - 1.12924i) q^{3} +0.642566 q^{5} +(-0.306483 - 0.176948i) q^{7} +(1.05034 - 1.81925i) q^{9} +(1.15663 + 2.00334i) q^{11} +(3.23687 - 1.58829i) q^{13} +(1.25679 - 0.725608i) q^{15} +(3.34390 - 5.79180i) q^{17} +(-1.51026 + 2.61585i) q^{19} -0.799263 q^{21} +(-0.693517 - 1.20121i) q^{23} -4.58711 q^{25} +2.03107i q^{27} +(-5.85776 + 3.38198i) q^{29} -7.83867i q^{31} +(4.52449 + 2.61221i) q^{33} +(-0.196935 - 0.113701i) q^{35} +(2.54831 + 4.41379i) q^{37} +(4.53742 - 6.76172i) q^{39} +(-7.03170 + 4.05975i) q^{41} +(-0.0281959 - 0.0162789i) q^{43} +(0.674915 - 1.16899i) q^{45} +12.6079i q^{47} +(-3.43738 - 5.95372i) q^{49} -15.1042i q^{51} -3.40398i q^{53} +(0.743211 + 1.28728i) q^{55} +6.82176i q^{57} +(-2.40152 + 4.15956i) q^{59} +(8.23572 + 4.75490i) q^{61} +(-0.643824 + 0.371712i) q^{63} +(2.07990 - 1.02058i) q^{65} +(-2.24483 - 3.88815i) q^{67} +(-2.71289 - 1.56629i) q^{69} +(5.35176 + 3.08984i) q^{71} +6.24869i q^{73} +(-8.97189 + 5.17993i) q^{75} -0.818652i q^{77} -7.68780 q^{79} +(5.44459 + 9.43030i) q^{81} +16.7317 q^{83} +(2.14867 - 3.72161i) q^{85} +(-7.63810 + 13.2296i) q^{87} +(-1.37983 + 0.796643i) q^{89} +(-1.27309 - 0.0859734i) q^{91} +(-8.85170 - 15.3316i) q^{93} +(-0.970443 + 1.68086i) q^{95} +(-5.29486 - 3.05699i) q^{97} +4.85944 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 18 q^{7} + 2 q^{9} + 36 q^{15} + 8 q^{17} + 2 q^{23} - 12 q^{25} - 30 q^{33} + 14 q^{39} + 24 q^{41} - 14 q^{49} - 4 q^{55} + 6 q^{65} - 6 q^{71} - 32 q^{79} + 12 q^{81} - 34 q^{87} - 30 q^{89} - 28 q^{95}+ \cdots - 30 q^{97}+O(q^{100}) \) 16 * q - 18 * q^7 + 2 * q^9 + 36 * q^15 + 8 * q^17 + 2 * q^23 - 12 * q^25 - 30 * q^33 + 14 * q^39 + 24 * q^41 - 14 * q^49 - 4 * q^55 + 6 * q^65 - 6 * q^71 - 32 * q^79 + 12 * q^81 - 34 * q^87 - 30 * q^89 - 28 * q^95 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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