LMFDB - Embedded newform 552.2.q.d.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	552.73
Dual form			552.2.q.d.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{3} +(1.92120 + 1.23468i) q^{5} +(0.378426 + 2.63201i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{3} +(1.92120 + 1.23468i) q^{5} +(0.378426 + 2.63201i) q^{7} +(0.841254 - 0.540641i) q^{9} +(-1.90442 + 4.17009i) q^{11} +(-0.246103 + 1.71169i) q^{13} +(2.19122 + 0.643401i) q^{15} +(-1.99661 - 2.30421i) q^{17} +(-1.69713 + 1.95859i) q^{19} +(1.10462 + 2.41878i) q^{21} +(4.51927 - 1.60506i) q^{23} +(0.0894893 + 0.195954i) q^{25} +(0.654861 - 0.755750i) q^{27} +(-5.02332 - 5.79722i) q^{29} +(1.10129 + 0.323369i) q^{31} +(-0.652424 + 4.53771i) q^{33} +(-2.52266 + 5.52384i) q^{35} +(7.40338 - 4.75787i) q^{37} +(0.246103 + 1.71169i) q^{39} +(4.83341 + 3.10624i) q^{41} +(4.05546 - 1.19079i) q^{43} +2.28373 q^{45} -2.43774 q^{47} +(-0.0678292 + 0.0199164i) q^{49} +(-2.56490 - 1.64836i) q^{51} +(-1.13221 - 7.87469i) q^{53} +(-8.80747 + 5.66022i) q^{55} +(-1.07658 + 2.35739i) q^{57} +(0.762525 - 5.30348i) q^{59} +(10.2607 + 3.01281i) q^{61} +(1.74133 + 2.00960i) q^{63} +(-2.58619 + 2.98463i) q^{65} +(6.67408 + 14.6142i) q^{67} +(3.88401 - 2.81326i) q^{69} +(-6.49235 - 14.2163i) q^{71} +(6.10673 - 7.04754i) q^{73} +(0.141071 + 0.162805i) q^{75} +(-11.6964 - 3.43437i) q^{77} +(-0.841256 + 5.85107i) q^{79} +(0.415415 - 0.909632i) q^{81} +(-3.82619 + 2.45894i) q^{83} +(-0.990920 - 6.89200i) q^{85} +(-6.45311 - 4.14716i) q^{87} +(4.57162 - 1.34235i) q^{89} -4.59831 q^{91} +1.14779 q^{93} +(-5.67873 + 1.66743i) q^{95} +(-9.16603 - 5.89065i) q^{97} +(0.652424 + 4.53771i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$		0			0
$5$	1.92120	+	1.23468i	0.859185	+	0.552165i	0.894427	−	0.447214i	$-0.147584\pi$
$5$	1.92120	+	1.23468i	0.859185	+	0.552165i	−0.0352420	+	0.999379i	$0.511220\pi$
$6$		0			0
$7$	0.378426	+	2.63201i	0.143032	+	0.994807i	0.927282	+	0.374363i	$0.122139\pi$
$7$	0.378426	+	2.63201i	0.143032	+	0.994807i	−0.784251	+	0.620444i	$0.786952\pi$
$8$		0			0
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$		0			0
$11$	−1.90442	+	4.17009i	−0.574203	+	1.25733i	0.370326	+	0.928902i	$0.379246\pi$
$11$	−1.90442	+	4.17009i	−0.574203	+	1.25733i	−0.944529	+	0.328427i	$0.893481\pi$
$12$		0			0
$13$	−0.246103	+	1.71169i	−0.0682568	+	0.474736i	0.926810	+	0.375530i	$0.122539\pi$
$13$	−0.246103	+	1.71169i	−0.0682568	+	0.474736i	−0.995067	+	0.0992060i	$0.968370\pi$
$14$		0			0
$15$	2.19122	+	0.643401i	0.565771	+	0.166125i
$16$		0			0
$17$	−1.99661	−	2.30421i	−0.484248	−	0.558852i	0.460071	−	0.887882i	$-0.347824\pi$
$17$	−1.99661	−	2.30421i	−0.484248	−	0.558852i	−0.944320	+	0.329030i	$0.893278\pi$
$18$		0			0
$19$	−1.69713	+	1.95859i	−0.389347	+	0.449331i	−0.916257	−	0.400590i	$-0.868805\pi$
$19$	−1.69713	+	1.95859i	−0.389347	+	0.449331i	0.526910	+	0.849921i	$0.323351\pi$
$20$		0			0
$21$	1.10462	+	2.41878i	0.241048	+	0.527821i
$22$		0			0
$23$	4.51927	−	1.60506i	0.942333	−	0.334677i
$23$	4.51927	−	1.60506i	0.942333	−	0.334677i
$24$		0			0
$25$	0.0894893	+	0.195954i	0.0178979	+	0.0391909i
$26$		0			0
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$		0			0
$29$	−5.02332	−	5.79722i	−0.932807	−	1.07652i	−0.996908	−	0.0785734i	$-0.974963\pi$
$29$	−5.02332	−	5.79722i	−0.932807	−	1.07652i	0.0641012	−	0.997943i	$-0.479582\pi$
$30$		0			0
$31$	1.10129	+	0.323369i	0.197798	+	0.0580789i	0.379131	−	0.925343i	$-0.376223\pi$
$31$	1.10129	+	0.323369i	0.197798	+	0.0580789i	−0.181333	+	0.983422i	$0.558041\pi$
$32$		0			0
$33$	−0.652424	+	4.53771i	−0.113572	+	0.789913i
$34$		0			0
$35$	−2.52266	+	5.52384i	−0.426407	+	0.933700i
$36$		0			0
$37$	7.40338	−	4.75787i	1.21711	−	0.782188i	0.235275	−	0.971929i	$-0.424401\pi$
$37$	7.40338	−	4.75787i	1.21711	−	0.782188i	0.981834	+	0.189741i	$0.0607647\pi$
$38$		0			0
$39$	0.246103	+	1.71169i	0.0394081	+	0.274089i
$40$		0			0
$41$	4.83341	+	3.10624i	0.754851	+	0.485113i	0.860601	−	0.509279i	$-0.170088\pi$
$41$	4.83341	+	3.10624i	0.754851	+	0.485113i	−0.105750	+	0.994393i	$0.533724\pi$
$42$		0			0
$43$	4.05546	−	1.19079i	0.618451	−	0.181594i	0.0425252	−	0.999095i	$-0.486460\pi$
$43$	4.05546	−	1.19079i	0.618451	−	0.181594i	0.575926	+	0.817502i	$0.304642\pi$
$44$		0			0
$45$	2.28373			0.340438
$46$		0			0
$47$	−2.43774			−0.355581			−0.177790	−	0.984068i	$-0.556895\pi$
$47$	−2.43774			−0.355581			−0.177790	+	0.984068i	$0.556895\pi$
$48$		0			0
$49$	−0.0678292	+	0.0199164i	−0.00968988	+	0.00284521i
$50$		0			0
$51$	−2.56490	−	1.64836i	−0.359158	−	0.230817i
$52$		0			0
$53$	−1.13221	−	7.87469i	−0.155521	−	1.08167i	−0.906762	−	0.421643i	$-0.861453\pi$
$53$	−1.13221	−	7.87469i	−0.155521	−	1.08167i	0.751241	−	0.660028i	$-0.229456\pi$
$54$		0			0
$55$	−8.80747	+	5.66022i	−1.18760	+	0.763224i
$56$		0			0
$57$	−1.07658	+	2.35739i	−0.142597	+	0.312243i
$58$		0			0
$59$	0.762525	−	5.30348i	0.0992723	−	0.690454i	−0.878030	−	0.478605i	$-0.841143\pi$
$59$	0.762525	−	5.30348i	0.0992723	−	0.690454i	0.977302	−	0.211849i	$-0.0679484\pi$
$60$		0			0
$61$	10.2607	+	3.01281i	1.31375	+	0.385751i	0.862232	−	0.506514i	$-0.169066\pi$
$61$	10.2607	+	3.01281i	1.31375	+	0.385751i	0.451514	+	0.892264i	$0.350884\pi$
$62$		0			0
$63$	1.74133	+	2.00960i	0.219386	+	0.253185i
$64$		0			0
$65$	−2.58619	+	2.98463i	−0.320778	+	0.370197i
$66$		0			0
$67$	6.67408	+	14.6142i	0.815369	+	1.78541i	0.582353	+	0.812936i	$0.302132\pi$
$67$	6.67408	+	14.6142i	0.815369	+	1.78541i	0.233016	+	0.972473i	$0.425141\pi$
$68$		0			0
$69$	3.88401	−	2.81326i	0.467580	−	0.338677i
$70$		0			0
$71$	−6.49235	−	14.2163i	−0.770501	−	1.68716i	−0.725548	−	0.688172i	$-0.758414\pi$
$71$	−6.49235	−	14.2163i	−0.770501	−	1.68716i	−0.0449529	−	0.998989i	$-0.514314\pi$
$72$		0			0
$73$	6.10673	−	7.04754i	0.714739	−	0.824852i	−0.275925	−	0.961179i	$-0.588984\pi$
$73$	6.10673	−	7.04754i	0.714739	−	0.824852i	0.990664	+	0.136327i	$0.0435297\pi$
$74$		0			0
$75$	0.141071	+	0.162805i	0.0162895	+	0.0187991i
$76$		0			0
$77$	−11.6964	−	3.43437i	−1.33293	−	0.391383i
$78$		0			0
$79$	−0.841256	+	5.85107i	−0.0946487	+	0.658296i	0.886168	+	0.463364i	$0.153358\pi$
$79$	−0.841256	+	5.85107i	−0.0946487	+	0.658296i	−0.980817	+	0.194932i	$0.937551\pi$
$80$		0			0
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$		0			0
$83$	−3.82619	+	2.45894i	−0.419979	+	0.269904i	−0.733516	−	0.679672i	$-0.762122\pi$
$83$	−3.82619	+	2.45894i	−0.419979	+	0.269904i	0.313537	+	0.949576i	$0.398486\pi$
$84$		0			0
$85$	−0.990920	−	6.89200i	−0.107480	−	0.747542i
$86$		0			0
$87$	−6.45311	−	4.14716i	−0.691846	−	0.444622i
$88$		0			0
$89$	4.57162	−	1.34235i	0.484591	−	0.142289i	−0.0303064	−	0.999541i	$-0.509648\pi$
$89$	4.57162	−	1.34235i	0.484591	−	0.142289i	0.514897	+	0.857252i	$0.327830\pi$
$90$		0			0
$91$	−4.59831			−0.482034
$92$		0			0
$93$	1.14779			0.119020
$94$		0			0
$95$	−5.67873	+	1.66743i	−0.582626	+	0.171074i
$96$		0			0
$97$	−9.16603	−	5.89065i	−0.930669	−	0.598105i	−0.0149348	−	0.999888i	$-0.504754\pi$
$97$	−9.16603	−	5.89065i	−0.930669	−	0.598105i	−0.915735	+	0.401784i	$0.868390\pi$
$98$		0			0
$99$	0.652424	+	4.53771i	0.0655711	+	0.456057i
$100$		0			0
$101$	−7.43646	+	4.77912i	−0.739956	+	0.475541i	−0.855527	−	0.517759i	$-0.826767\pi$
$101$	−7.43646	+	4.77912i	−0.739956	+	0.475541i	0.115571	+	0.993299i	$0.463130\pi$
$102$		0			0
$103$	−1.38134	+	3.02471i	−0.136107	+	0.298033i	−0.965397	−	0.260786i	$-0.916018\pi$
$103$	−1.38134	+	3.02471i	−0.136107	+	0.298033i	0.829289	+	0.558820i	$0.188746\pi$
$104$		0			0
$105$	−0.864223	+	6.01080i	−0.0843395	+	0.586594i
$106$		0			0
$107$	−13.0919	−	3.84414i	−1.26565	−	0.371627i	−0.421052	−	0.907036i	$-0.638339\pi$
$107$	−13.0919	−	3.84414i	−1.26565	−	0.371627i	−0.844593	+	0.535409i	$0.820157\pi$
$108$		0			0
$109$	−1.32429	−	1.52831i	−0.126844	−	0.146385i	0.688775	−	0.724975i	$-0.258149\pi$
$109$	−1.32429	−	1.52831i	−0.126844	−	0.146385i	−0.815619	+	0.578590i	$0.803603\pi$
$110$		0			0
$111$	5.76305	−	6.65091i	0.547004	−	0.631277i
$112$		0			0
$113$	1.78410	+	3.90663i	0.167834	+	0.367504i	0.974796	−	0.223099i	$-0.0716172\pi$
$113$	1.78410	+	3.90663i	0.167834	+	0.367504i	−0.806962	+	0.590603i	$0.798890\pi$
$114$		0			0
$115$	10.6641	+	2.49621i	0.994435	+	0.232773i
$116$		0			0
$117$	0.718372	+	1.57302i	0.0664135	+	0.145425i
$118$		0			0
$119$	5.30913	−	6.12707i	0.486687	−	0.561667i
$120$		0			0
$121$	−6.55937	−	7.56992i	−0.596307	−	0.688174i
$122$		0			0
$123$	5.51275	+	1.61869i	0.497068	+	0.145952i
$124$		0			0
$125$	1.55503	−	10.8155i	0.139086	−	0.967365i
$126$		0			0
$127$	3.64707	−	7.98597i	0.323625	−	0.708640i	−0.675975	−	0.736925i	$-0.736277\pi$
$127$	3.64707	−	7.98597i	0.323625	−	0.708640i	0.999600	+	0.0282847i	$0.00900449\pi$
$128$		0			0
$129$	3.55570	−	2.28511i	0.313062	−	0.201193i
$130$		0			0
$131$	0.0499416	+	0.347351i	0.00436342	+	0.0303482i	0.991887	−	0.127124i	$-0.0405746\pi$
$131$	0.0499416	+	0.347351i	0.00436342	+	0.0303482i	−0.987523	+	0.157472i	$0.949666\pi$
$132$		0			0
$133$	−5.79726	−	3.72567i	−0.502686	−	0.323057i
$134$		0			0
$135$	2.19122	−	0.643401i	0.188590	−	0.0553751i
$136$		0			0
$137$	−6.59758			−0.563669			−0.281835	−	0.959463i	$-0.590943\pi$
$137$	−6.59758			−0.563669			−0.281835	+	0.959463i	$0.590943\pi$
$138$		0			0
$139$	−4.68361			−0.397259			−0.198629	−	0.980075i	$-0.563649\pi$
$139$	−4.68361			−0.397259			−0.198629	+	0.980075i	$0.563649\pi$
$140$		0			0
$141$	−2.33899	+	0.686790i	−0.196979	+	0.0578382i
$142$		0			0
$143$	−6.66920	−	4.28603i	−0.557706	−	0.358416i
$144$		0			0
$145$	−2.49308	−	17.3398i	−0.207039	−	1.43999i
$146$		0			0
$147$	−0.0594705	+	0.0382194i	−0.00490505	+	0.00315228i
$148$		0			0
$149$	1.81118	−	3.96592i	0.148377	−	0.324901i	−0.820820	−	0.571187i	$-0.806483\pi$
$149$	1.81118	−	3.96592i	0.148377	−	0.324901i	0.969197	+	0.246286i	$0.0792103\pi$
$150$		0			0
$151$	0.408413	−	2.84057i	0.0332361	−	0.231162i	−0.966432	−	0.256922i	$-0.917291\pi$
$151$	0.408413	−	2.84057i	0.0332361	−	0.231162i	0.999668	+	0.0257600i	$0.00820059\pi$
$152$		0			0
$153$	−2.92540	−	0.858975i	−0.236505	−	0.0694440i
$154$		0			0
$155$	1.71655	+	1.98100i	0.137876	+	0.159118i
$156$		0			0
$157$	2.76681	−	3.19307i	0.220816	−	0.254835i	−0.634523	−	0.772904i	$-0.718803\pi$
$157$	2.76681	−	3.19307i	0.220816	−	0.254835i	0.855339	+	0.518069i	$0.173349\pi$
$158$		0			0
$159$	−3.30490	−	7.23673i	−0.262096	−	0.573910i
$160$		0			0
$161$	5.93474	+	11.2874i	0.467723	+	0.889570i
$162$		0			0
$163$	3.53236	+	7.73480i	0.276676	+	0.605836i	0.996051	−	0.0887862i	$-0.0282988\pi$
$163$	3.53236	+	7.73480i	0.276676	+	0.605836i	−0.719375	+	0.694622i	$0.755572\pi$
$164$		0			0
$165$	−6.85604	+	7.91229i	−0.533742	+	0.615971i
$166$		0			0
$167$	−11.6311	−	13.4230i	−0.900042	−	1.03870i	−0.999048	−	0.0436174i	$-0.986112\pi$
$167$	−11.6311	−	13.4230i	−0.900042	−	1.03870i	0.0990059	−	0.995087i	$-0.468434\pi$
$168$		0			0
$169$	9.60411	+	2.82002i	0.738777	+	0.216925i
$170$		0			0
$171$	−0.368821	+	2.56520i	−0.0282044	+	0.196166i
$172$		0			0
$173$	−7.13558	+	15.6247i	−0.542508	+	1.18793i	0.417686	+	0.908592i	$0.362841\pi$
$173$	−7.13558	+	15.6247i	−0.542508	+	1.18793i	−0.960194	+	0.279335i	$0.909886\pi$
$174$		0			0
$175$	−0.481889	+	0.309691i	−0.0364274	+	0.0234105i
$176$		0			0
$177$	−0.762525	−	5.30348i	−0.0573149	−	0.398634i
$178$		0			0
$179$	6.74318	+	4.33358i	0.504009	+	0.323907i	0.767818	−	0.640668i	$-0.221343\pi$
$179$	6.74318	+	4.33358i	0.504009	+	0.323907i	−0.263809	+	0.964575i	$0.584979\pi$
$180$		0			0
$181$	−16.3840	+	4.81077i	−1.21781	+	0.357582i	−0.826637	−	0.562735i	$-0.809749\pi$
$181$	−16.3840	+	4.81077i	−1.21781	+	0.357582i	−0.391174	+	0.920317i	$0.627931\pi$
$182$		0			0
$183$	10.6939			0.790513
$184$		0			0
$185$	20.0978			1.47762
$186$		0			0
$187$	13.4111	−	3.93786i	0.980718	−	0.287965i
$188$		0			0
$189$	2.23696	+	1.43761i	0.162715	+	0.104570i
$190$		0			0
$191$	−2.00632	−	13.9543i	−0.145173	−	1.00970i	−0.923982	−	0.382436i	$-0.875085\pi$
$191$	−2.00632	−	13.9543i	−0.145173	−	1.00970i	0.778809	−	0.627261i	$-0.215824\pi$
$192$		0			0
$193$	−18.0079	+	11.5730i	−1.29624	+	0.833041i	−0.992797	−	0.119809i	$-0.961772\pi$
$193$	−18.0079	+	11.5730i	−1.29624	+	0.833041i	−0.303441	+	0.952850i	$0.598135\pi$
$194$		0			0
$195$	−1.64057	+	3.59234i	−0.117483	+	0.257253i
$196$		0			0
$197$	−3.64384	+	25.3434i	−0.259613	+	1.80565i	0.275974	+	0.961165i	$0.411000\pi$
$197$	−3.64384	+	25.3434i	−0.259613	+	1.80565i	−0.535587	+	0.844480i	$0.679910\pi$
$198$		0			0
$199$	−24.0826	−	7.07128i	−1.70717	−	0.501270i	−0.724916	−	0.688837i	$-0.758121\pi$
$199$	−24.0826	−	7.07128i	−1.70717	−	0.501270i	−0.982252	+	0.187568i	$0.939940\pi$
$200$		0			0
$201$	10.5210	+	12.1419i	0.742096	+	0.856425i
$202$		0			0
$203$	13.3574	−	15.4153i	0.937505	−	1.08194i
$204$		0			0
$205$	5.45071	+	11.9354i	0.380694	+	0.833604i
$206$		0			0
$207$	2.93409	−	3.79356i	0.203934	−	0.263671i
$208$		0			0
$209$	−4.93545	−	10.8071i	−0.341392	−	0.747545i
$210$		0			0
$211$	−8.99494	+	10.3807i	−0.619237	+	0.714638i	−0.975562	−	0.219724i	$-0.929484\pi$
$211$	−8.99494	+	10.3807i	−0.619237	+	0.714638i	0.356325	+	0.934362i	$0.384030\pi$
$212$		0			0
$213$	−10.2346	−	11.8113i	−0.701260	−	0.809297i
$214$		0			0
$215$	9.26157	+	2.71944i	0.631634	+	0.185464i
$216$		0			0
$217$	−0.434353	+	3.02099i	−0.0294858	+	0.205078i
$218$		0			0
$219$	3.87384	−	8.48253i	0.261770	−	0.573196i
$220$		0			0
$221$	4.43545	−	2.85049i	0.298361	−	0.191745i
$222$		0			0
$223$	−2.17025	−	15.0944i	−0.145331	−	1.01080i	−0.923734	−	0.383034i	$-0.874879\pi$
$223$	−2.17025	−	15.0944i	−0.145331	−	1.01080i	0.778404	−	0.627764i	$-0.216030\pi$
$224$		0			0
$225$	0.181224	+	0.116466i	0.0120816	+	0.00776438i
$226$		0			0
$227$	22.8920	−	6.72170i	1.51940	−	0.446135i	0.587610	−	0.809144i	$-0.300069\pi$
$227$	22.8920	−	6.72170i	1.51940	−	0.446135i	0.931785	+	0.363010i	$0.118251\pi$
$228$		0			0
$229$	15.2019			1.00457			0.502284	−	0.864703i	$-0.332493\pi$
$229$	15.2019			1.00457			0.502284	+	0.864703i	$0.332493\pi$
$230$		0			0
$231$	−12.1902			−0.802056
$232$		0			0
$233$	−9.58489	+	2.81438i	−0.627927	+	0.184376i	−0.580186	−	0.814484i	$-0.697020\pi$
$233$	−9.58489	+	2.81438i	−0.627927	+	0.184376i	−0.0477406	+	0.998860i	$0.515202\pi$
$234$		0			0
$235$	−4.68337	−	3.00982i	−0.305510	−	0.196339i
$236$		0			0
$237$	0.841256	+	5.85107i	0.0546455	+	0.380068i
$238$		0			0
$239$	17.7339	−	11.3969i	1.14711	−	0.737204i	0.178050	−	0.984022i	$-0.443021\pi$
$239$	17.7339	−	11.3969i	1.14711	−	0.737204i	0.969062	+	0.246818i	$0.0793849\pi$
$240$		0			0
$241$	−3.37068	+	7.38075i	−0.217124	+	0.475436i	−0.986583	−	0.163261i	$-0.947799\pi$
$241$	−3.37068	+	7.38075i	−0.217124	+	0.475436i	0.769459	+	0.638697i	$0.220526\pi$
$242$		0			0
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$		0			0
$245$	−0.154904	−	0.0454838i	−0.00989642	−	0.00290585i
$246$		0			0
$247$	−2.93482	−	3.38696i	−0.186738	−	0.215507i
$248$		0			0
$249$	−2.97844	+	3.43730i	−0.188751	+	0.217830i
$250$		0			0
$251$	12.5252	+	27.4264i	0.790583	+	1.73114i	0.674974	+	0.737842i	$0.264155\pi$
$251$	12.5252	+	27.4264i	0.790583	+	1.73114i	0.115610	+	0.993295i	$0.463118\pi$
$252$		0			0
$253$	−1.91334	+	21.9024i	−0.120291	+	1.37700i
$254$		0			0
$255$	−2.89248	−	6.33365i	−0.181134	−	0.396629i
$256$		0			0
$257$	−15.3516	+	17.7167i	−0.957609	+	1.10514i	0.0367771	+	0.999323i	$0.488291\pi$
$257$	−15.3516	+	17.7167i	−0.957609	+	1.10514i	−0.994386	+	0.105816i	$0.966255\pi$
$258$		0			0
$259$	15.3244	+	17.6853i	0.952212	+	1.09891i
$260$		0			0
$261$	−7.36010	−	2.16112i	−0.455579	−	0.133770i
$262$		0			0
$263$	0.445501	−	3.09853i	0.0274708	−	0.191063i	−0.971465	−	0.237182i	$-0.923776\pi$
$263$	0.445501	−	3.09853i	0.0274708	−	0.191063i	0.998936	+	0.0461187i	$0.0146853\pi$
$264$		0			0
$265$	7.54750	−	16.5267i	0.463639	−	1.01523i
$266$		0			0
$267$	4.00825	−	2.57595i	0.245301	−	0.157645i
$268$		0			0
$269$	−0.711178	−	4.94635i	−0.0433613	−	0.301584i	−0.999949	−	0.0101385i	$-0.996773\pi$
$269$	−0.711178	−	4.94635i	−0.0433613	−	0.301584i	0.956587	−	0.291446i	$-0.0941363\pi$
$270$		0			0
$271$	−5.62965	−	3.61795i	−0.341977	−	0.219775i	0.358367	−	0.933581i	$-0.383334\pi$
$271$	−5.62965	−	3.61795i	−0.341977	−	0.219775i	−0.700344	+	0.713806i	$0.746970\pi$
$272$		0			0
$273$	−4.41205	+	1.29549i	−0.267029	+	0.0784068i
$274$		0			0
$275$	−0.987572			−0.0595528
$276$		0			0
$277$	29.1628			1.75222			0.876112	−	0.482107i	$-0.160128\pi$
$277$	29.1628			1.75222			0.876112	+	0.482107i	$0.160128\pi$
$278$		0			0
$279$	1.10129	−	0.323369i	0.0659328	−	0.0193596i
$280$		0			0
$281$	16.5582	+	10.6413i	0.987777	+	0.634806i	0.931550	−	0.363612i	$-0.118457\pi$
$281$	16.5582	+	10.6413i	0.987777	+	0.634806i	0.0562268	+	0.998418i	$0.482093\pi$
$282$		0			0
$283$	3.93443	+	27.3646i	0.233878	+	1.62666i	0.681070	+	0.732218i	$0.261515\pi$
$283$	3.93443	+	27.3646i	0.233878	+	1.62666i	−0.447192	+	0.894438i	$0.647576\pi$
$284$		0			0
$285$	−4.97894	+	3.19977i	−0.294927	+	0.189538i
$286$		0			0
$287$	−6.34658	+	13.8971i	−0.374627	+	0.820318i
$288$		0			0
$289$	1.09642	−	7.62577i	0.0644953	−	0.448575i
$290$		0			0
$291$	−10.4543	−	3.06967i	−0.612844	−	0.179947i
$292$		0			0
$293$	8.53167	+	9.84607i	0.498425	+	0.575213i	0.948097	−	0.317980i	$-0.103005\pi$
$293$	8.53167	+	9.84607i	0.498425	+	0.575213i	−0.449672	+	0.893194i	$0.648459\pi$
$294$		0			0
$295$	8.01304	−	9.24754i	0.466537	−	0.538413i
$296$		0			0
$297$	1.90442	+	4.17009i	0.110505	+	0.241973i
$298$		0			0
$299$	1.63514	+	8.13058i	0.0945628	+	0.470204i
$300$		0			0
$301$	4.66886	+	10.2234i	0.269109	+	0.589266i
$302$		0			0
$303$	−5.78880	+	6.68063i	−0.332558	+	0.383792i
$304$		0			0
$305$	15.9929	+	18.4568i	0.915753	+	1.05683i
$306$		0			0
$307$	−21.1246	−	6.20274i	−1.20564	−	0.354009i	−0.383636	−	0.923484i	$-0.625328\pi$
$307$	−21.1246	−	6.20274i	−1.20564	−	0.354009i	−0.822009	+	0.569475i	$0.807147\pi$
$308$		0			0
$309$	−0.473225	+	3.29135i	−0.0269209	+	0.187239i
$310$		0			0
$311$	−5.13763	+	11.2498i	−0.291328	+	0.637919i	−0.997541	−	0.0700797i	$-0.977675\pi$
$311$	−5.13763	+	11.2498i	−0.291328	+	0.637919i	0.706213	+	0.707999i	$0.250402\pi$
$312$		0			0
$313$	15.1033	−	9.70633i	0.853692	−	0.548634i	−0.0390325	−	0.999238i	$-0.512428\pi$
$313$	15.1033	−	9.70633i	0.853692	−	0.548634i	0.892724	+	0.450604i	$0.148791\pi$
$314$		0			0
$315$	0.864223	+	6.01080i	0.0486935	+	0.338670i
$316$		0			0
$317$	−0.999649	−	0.642435i	−0.0561459	−	0.0360828i	0.512267	−	0.858826i	$-0.328806\pi$
$317$	−0.999649	−	0.642435i	−0.0561459	−	0.0360828i	−0.568413	+	0.822744i	$0.692442\pi$
$318$		0			0
$319$	33.7414	−	9.90737i	1.88916	−	0.554706i
$320$		0			0
$321$	−13.6446			−0.761569
$322$		0			0
$323$	7.90148			0.439650
$324$		0			0
$325$	−0.357436	+	0.104953i	−0.0198270	+	0.00582173i
$326$		0			0
$327$	−1.70122	−	1.09331i	−0.0940775	−	0.0604599i
$328$		0			0
$329$	−0.922504	−	6.41616i	−0.0508593	−	0.353734i
$330$		0			0
$331$	−20.3996	+	13.1100i	−1.12126	+	0.720591i	−0.963718	−	0.266921i	$-0.913994\pi$
$331$	−20.3996	+	13.1100i	−1.12126	+	0.720591i	−0.157543	+	0.987512i	$0.550357\pi$
$332$		0			0
$333$	3.65583	−	8.00514i	0.200338	−	0.438679i
$334$		0			0
$335$	−5.22161	+	36.3171i	−0.285287	+	1.98421i
$336$		0			0
$337$	−28.1809	−	8.27465i	−1.53511	−	0.450749i	−0.598500	−	0.801123i	$-0.704236\pi$
$337$	−28.1809	−	8.27465i	−1.53511	−	0.450749i	−0.936610	+	0.350374i	$0.886054\pi$
$338$		0			0
$339$	2.81245	+	3.24574i	0.152751	+	0.176285i
$340$		0			0
$341$	−3.44580	+	3.97667i	−0.186601	+	0.215349i
$342$		0			0
$343$	7.65426	+	16.7605i	0.413291	+	0.904981i
$344$		0			0
$345$	10.9354	−	0.609332i	0.588743	−	0.0328053i
$346$		0			0
$347$	3.97900	+	8.71279i	0.213604	+	0.467727i	0.985857	−	0.167588i	$-0.0535977\pi$
$347$	3.97900	+	8.71279i	0.213604	+	0.467727i	−0.772253	+	0.635315i	$0.780870\pi$
$348$		0			0
$349$	−1.39106	+	1.60537i	−0.0744619	+	0.0859337i	−0.791758	−	0.610835i	$-0.790834\pi$
$349$	−1.39106	+	1.60537i	−0.0744619	+	0.0859337i	0.717296	+	0.696768i	$0.245379\pi$
$350$		0			0
$351$	1.13244	+	1.30691i	0.0604453	+	0.0697576i
$352$		0			0
$353$	−17.3881	−	5.10561i	−0.925476	−	0.271744i	−0.215934	−	0.976408i	$-0.569280\pi$
$353$	−17.3881	−	5.10561i	−0.925476	−	0.271744i	−0.709542	+	0.704664i	$0.751098\pi$
$354$		0			0
$355$	5.07943	−	35.3282i	0.269588	−	1.87503i
$356$		0			0
$357$	3.36788	−	7.37463i	0.178247	−	0.390307i
$358$		0			0
$359$	15.5991	−	10.0249i	0.823287	−	0.529094i	−0.0598515	−	0.998207i	$-0.519063\pi$
$359$	15.5991	−	10.0249i	0.823287	−	0.529094i	0.883138	+	0.469113i	$0.155426\pi$
$360$		0			0
$361$	1.74815	+	12.1587i	0.0920080	+	0.639930i
$362$		0			0
$363$	−8.42636	−	5.41530i	−0.442269	−	0.284229i
$364$		0			0
$365$	20.4337	−	5.99987i	1.06955	−	0.314047i
$366$		0			0
$367$	20.2707			1.05812			0.529061	−	0.848584i	$-0.322544\pi$
$367$	20.2707			1.05812			0.529061	+	0.848584i	$0.322544\pi$
$368$		0			0
$369$	5.74548			0.299098
$370$		0			0
$371$	20.2978	−	5.95998i	1.05381	−	0.309426i
$372$		0			0
$373$	−4.72549	−	3.03689i	−0.244676	−	0.157244i	0.412555	−	0.910933i	$-0.364636\pi$
$373$	−4.72549	−	3.03689i	−0.244676	−	0.157244i	−0.657232	+	0.753689i	$0.728273\pi$
$374$		0			0
$375$	−1.55503	−	10.8155i	−0.0803014	−	0.558508i
$376$		0			0
$377$	11.1593	−	7.17163i	0.574732	−	0.369358i
$378$		0			0
$379$	10.2302	−	22.4011i	0.525492	−	1.15067i	−0.441826	−	0.897101i	$-0.645669\pi$
$379$	10.2302	−	22.4011i	0.525492	−	1.15067i	0.967318	−	0.253566i	$-0.0816036\pi$
$380$		0			0
$381$	1.24943	−	8.68998i	0.0640102	−	0.445201i
$382$		0			0
$383$	−3.72748	−	1.09449i	−0.190466	−	0.0559257i	0.185109	−	0.982718i	$-0.440736\pi$
$383$	−3.72748	−	1.09449i	−0.190466	−	0.0559257i	−0.375574	+	0.926792i	$0.622554\pi$
$384$		0			0
$385$	−18.2307	−	21.0394i	−0.929124	−	1.07227i
$386$		0			0
$387$	2.76788	−	3.19430i	0.140699	−	0.162375i
$388$		0			0
$389$	−11.6566	−	25.5244i	−0.591012	−	1.29414i	−0.934829	−	0.355099i	$-0.884447\pi$
$389$	−11.6566	−	25.5244i	−0.591012	−	1.29414i	0.343816	−	0.939037i	$-0.388280\pi$
$390$		0			0
$391$	−12.7216	−	7.20867i	−0.643358	−	0.364558i
$392$		0			0
$393$	0.145779	+	0.319211i	0.00735357	+	0.0161021i
$394$		0			0
$395$	−8.84040	+	10.2024i	−0.444809	+	0.513337i
$396$		0			0
$397$	17.7145	+	20.4436i	0.889063	+	1.02603i	0.999483	+	0.0321489i	$0.0102351\pi$
$397$	17.7145	+	20.4436i	0.889063	+	1.02603i	−0.110420	+	0.993885i	$0.535219\pi$
$398$		0			0
$399$	−6.61208	−	1.94148i	−0.331018	−	0.0971956i
$400$		0			0
$401$	−1.12636	+	7.83403i	−0.0562479	+	0.391213i	0.942177	+	0.335115i	$0.108775\pi$
$401$	−1.12636	+	7.83403i	−0.0562479	+	0.391213i	−0.998425	+	0.0560982i	$0.982134\pi$
$402$		0			0
$403$	−0.824539	+	1.80549i	−0.0410732	+	0.0899378i
$404$		0			0
$405$	1.92120	−	1.23468i	0.0954650	−	0.0613516i
$406$		0			0
$407$	5.74160	+	39.9337i	0.284601	+	1.97944i
$408$		0			0
$409$	−27.0593	−	17.3900i	−1.33800	−	0.859878i	−0.341210	−	0.939987i	$-0.610837\pi$
$409$	−27.0593	−	17.3900i	−1.33800	−	0.859878i	−0.996786	+	0.0801091i	$0.974473\pi$
$410$		0			0
$411$	−6.33033	+	1.85875i	−0.312252	+	0.0916855i
$412$		0			0
$413$	14.2474			0.701067
$414$		0			0
$415$	−10.3869			−0.509871
$416$		0			0
$417$	−4.49389	+	1.31953i	−0.220067	+	0.0646174i
$418$		0			0
$419$	−8.13577	−	5.22854i	−0.397458	−	0.255431i	0.326610	−	0.945159i	$-0.394094\pi$
$419$	−8.13577	−	5.22854i	−0.397458	−	0.255431i	−0.724068	+	0.689728i	$0.757730\pi$
$420$		0			0
$421$	−4.59917	−	31.9880i	−0.224150	−	1.55900i	−0.722098	−	0.691791i	$-0.756822\pi$
$421$	−4.59917	−	31.9880i	−0.224150	−	1.55900i	0.497948	−	0.867207i	$-0.334087\pi$
$422$		0			0
$423$	−2.05076	+	1.31794i	−0.0997112	+	0.0640805i
$424$		0			0
$425$	0.272844	−	0.597446i	0.0132349	−	0.0289804i
$426$		0			0
$427$	−4.04684	+	28.1464i	−0.195840	+	1.36210i
$428$		0			0
$429$	−7.60657	−	2.23349i	−0.367248	−	0.107834i
$430$		0			0
$431$	−15.6514	−	18.0626i	−0.753900	−	0.870047i	0.241040	−	0.970515i	$-0.422511\pi$
$431$	−15.6514	−	18.0626i	−0.753900	−	0.870047i	−0.994940	+	0.100468i	$0.967966\pi$
$432$		0			0
$433$	−10.9333	+	12.6177i	−0.525420	+	0.606367i	−0.954980	−	0.296672i	$-0.904123\pi$
$433$	−10.9333	+	12.6177i	−0.525420	+	0.606367i	0.429560	+	0.903038i	$0.358669\pi$
$434$		0			0
$435$	−7.27728	−	15.9350i	−0.348919	−	0.764025i
$436$		0			0
$437$	−4.52613	+	11.5754i	−0.216514	+	0.553725i
$438$		0			0
$439$	−10.5838	−	23.1754i	−0.505139	−	1.10610i	−0.974765	−	0.223235i	$-0.928338\pi$
$439$	−10.5838	−	23.1754i	−0.505139	−	1.10610i	0.469626	−	0.882866i	$-0.344389\pi$
$440$		0			0
$441$	−0.0462939	+	0.0534260i	−0.00220447	+	0.00254410i
$442$		0			0
$443$	−10.1209	−	11.6802i	−0.480860	−	0.554941i	0.462541	−	0.886598i	$-0.346938\pi$
$443$	−10.1209	−	11.6802i	−0.480860	−	0.554941i	−0.943400	+	0.331657i	$0.892392\pi$
$444$		0			0
$445$	10.4403	+	3.06556i	0.494920	+	0.145322i
$446$		0			0
$447$	0.620481	−	4.31554i	0.0293478	−	0.204118i
$448$		0			0
$449$	8.49848	−	18.6091i	0.401068	−	0.878216i	−0.596093	−	0.802915i	$-0.703281\pi$
$449$	8.49848	−	18.6091i	0.401068	−	0.878216i	0.997161	−	0.0753007i	$-0.0239917\pi$
$450$		0			0
$451$	−22.1581	+	14.2402i	−1.04339	+	0.670543i
$452$		0			0
$453$	−0.408413	−	2.84057i	−0.0191889	−	0.133462i
$454$		0			0
$455$	−8.83425	−	5.67743i	−0.414156	−	0.266162i
$456$		0			0
$457$	6.86581	−	2.01598i	0.321169	−	0.0943037i	−0.117174	−	0.993111i	$-0.537384\pi$
$457$	6.86581	−	2.01598i	0.321169	−	0.0943037i	0.438343	+	0.898808i	$0.355565\pi$
$458$		0			0
$459$	−3.04890			−0.142311
$460$		0			0
$461$	9.32069			0.434108			0.217054	−	0.976160i	$-0.430355\pi$
$461$	9.32069			0.434108			0.217054	+	0.976160i	$0.430355\pi$
$462$		0			0
$463$	−7.07182	+	2.07647i	−0.328655	+	0.0965019i	−0.441898	−	0.897065i	$-0.645695\pi$
$463$	−7.07182	+	2.07647i	−0.328655	+	0.0965019i	0.113242	+	0.993567i	$0.463876\pi$
$464$		0			0
$465$	2.20513	+	1.41715i	0.102260	+	0.0657187i
$466$		0			0
$467$	−0.556229	−	3.86866i	−0.0257392	−	0.179020i	0.972896	−	0.231242i	$-0.0742788\pi$
$467$	−0.556229	−	3.86866i	−0.0257392	−	0.179020i	−0.998636	+	0.0522217i	$0.983370\pi$
$468$		0			0
$469$	−35.9391	+	23.0967i	−1.65951	+	1.06650i
$470$		0			0
$471$	1.75515	−	3.84323i	0.0808728	−	0.177087i
$472$		0			0
$473$	−2.75758	+	19.1794i	−0.126794	+	0.881869i
$474$		0			0
$475$	−0.535668	−	0.157286i	−0.0245781	−	0.00721680i
$476$		0			0
$477$	−5.20985	−	6.01249i	−0.238543	−	0.275293i
$478$		0			0
$479$	6.41186	−	7.39968i	0.292966	−	0.338100i	−0.590117	−	0.807318i	$-0.700918\pi$
$479$	6.41186	−	7.39968i	0.292966	−	0.338100i	0.883083	+	0.469217i	$0.155464\pi$
$480$		0			0
$481$	6.32198	+	13.8432i	0.288257	+	0.631195i
$482$		0			0
$483$	8.87436	+	9.15815i	0.403797	+	0.416710i
$484$		0			0
$485$	−10.3367	−	22.6342i	−0.469365	−	1.02777i
$486$		0			0
$487$	−7.40740	+	8.54860i	−0.335661	+	0.387374i	−0.898339	−	0.439302i	$-0.855226\pi$
$487$	−7.40740	+	8.54860i	−0.335661	+	0.387374i	0.562678	+	0.826676i	$0.309771\pi$
$488$		0			0
$489$	5.56842	+	6.42630i	0.251813	+	0.290607i
$490$		0			0
$491$	−24.7044	−	7.25387i	−1.11489	−	0.327363i	−0.328140	−	0.944629i	$-0.606422\pi$
$491$	−24.7044	−	7.25387i	−1.11489	−	0.327363i	−0.786754	+	0.617266i	$0.788240\pi$
$492$		0			0
$493$	−3.32840	+	23.1495i	−0.149904	+	1.04260i
$494$		0			0
$495$	−4.34917	+	9.52336i	−0.195481	+	0.428043i
$496$		0			0
$497$	34.9605	−	22.4678i	1.56819	−	1.00782i
$498$		0			0
$499$	−4.66202	−	32.4251i	−0.208701	−	1.45155i	−0.777403	−	0.629003i	$-0.783463\pi$
$499$	−4.66202	−	32.4251i	−0.208701	−	1.45155i	0.568702	−	0.822544i	$-0.307446\pi$
$500$		0			0
$501$	−14.9417	−	9.60243i	−0.667545	−	0.429005i
$502$		0			0
$503$	19.9771	−	5.86581i	0.890735	−	0.261544i	0.195824	−	0.980639i	$-0.437262\pi$
$503$	19.9771	−	5.86581i	0.890735	−	0.261544i	0.694911	+	0.719096i	$0.255444\pi$
$504$		0			0
$505$	−20.1876			−0.898335
$506$		0			0
$507$	10.0096			0.444540
$508$		0			0
$509$	20.4103	−	5.99301i	0.904671	−	0.265635i	0.203875	−	0.978997i	$-0.434646\pi$
$509$	20.4103	−	5.99301i	0.904671	−	0.265635i	0.700796	+	0.713362i	$0.252828\pi$
$510$		0			0
$511$	20.8602	+	13.4060i	0.922799	+	0.593047i
$512$		0			0
$513$	0.368821	+	2.56520i	0.0162838	+	0.113257i
$514$		0			0
$515$	−6.38836	+	4.10555i	−0.281505	+	0.180912i
$516$		0			0
$517$	4.64247	−	10.1656i	0.204176	−	0.447082i
$518$		0			0
$519$	−2.44454	+	17.0022i	−0.107303	+	0.746312i
$520$		0			0
$521$	5.13935	+	1.50905i	0.225159	+	0.0661127i	0.392366	−	0.919809i	$-0.371657\pi$
$521$	5.13935	+	1.50905i	0.225159	+	0.0661127i	−0.167207	+	0.985922i	$0.553475\pi$
$522$		0			0
$523$	−29.6108	−	34.1726i	−1.29479	−	1.49427i	−0.761193	−	0.648525i	$-0.775386\pi$
$523$	−29.6108	−	34.1726i	−1.29479	−	1.49427i	−0.533595	−	0.845740i	$-0.679159\pi$
$524$		0			0
$525$	−0.375119	+	0.432910i	−0.0163715	+	0.0188938i
$526$		0			0
$527$	−1.45374	−	3.18325i	−0.0633260	−	0.138665i
$528$		0			0
$529$	17.8476	−	14.5074i	0.775982	−	0.630755i
$530$		0			0
$531$	−2.22580	−	4.87382i	−0.0965914	−	0.211506i
$532$		0			0
$533$	−6.50643	+	7.50882i	−0.281825	+	0.325243i
$534$		0			0
$535$	−20.4059	−	23.5497i	−0.882224	−	1.01814i
$536$		0			0
$537$	7.69094	+	2.25826i	0.331889	+	0.0974513i
$538$		0			0
$539$	0.0461216	−	0.320783i	0.00198660	−	0.0138171i
$540$		0			0
$541$	3.52068	−	7.70922i	0.151366	−	0.331445i	−0.818725	−	0.574185i	$-0.805319\pi$
$541$	3.52068	−	7.70922i	0.151366	−	0.331445i	0.970091	+	0.242740i	$0.0780462\pi$
$542$		0			0
$543$	−14.3650	+	9.23180i	−0.616459	+	0.396174i
$544$		0			0
$545$	−0.657246	−	4.57124i	−0.0281533	−	0.195811i
$546$		0			0
$547$	12.7677	+	8.20530i	0.545907	+	0.350833i	0.784345	−	0.620325i	$-0.212999\pi$
$547$	12.7677	+	8.20530i	0.545907	+	0.350833i	−0.238438	+	0.971158i	$0.576635\pi$
$548$		0			0
$549$	10.2607	−	3.01281i	0.437915	−	0.128584i
$550$		0			0
$551$	19.8796			0.846898
$552$		0			0
$553$	−15.7184			−0.668416
$554$		0			0
$555$	19.2837	−	5.66220i	0.818547	−	0.240347i
$556$		0			0
$557$	25.6320	+	16.4727i	1.08606	+	0.697971i	0.955950	−	0.293528i	$-0.0948295\pi$
$557$	25.6320	+	16.4727i	1.08606	+	0.697971i	0.130113	+	0.991499i	$0.458466\pi$
$558$		0			0
$559$	1.04020	+	7.23473i	0.0439956	+	0.305996i
$560$		0			0
$561$	11.7585	−	7.55670i	0.496442	−	0.319044i
$562$		0			0
$563$	−7.15695	+	15.6715i	−0.301629	+	0.660476i	−0.998384	−	0.0568338i	$-0.981899\pi$
$563$	−7.15695	+	15.6715i	−0.301629	+	0.660476i	0.696754	+	0.717310i	$0.254627\pi$
$564$		0			0
$565$	−1.39582	+	9.70818i	−0.0587228	+	0.408426i
$566$		0			0
$567$	2.55137	+	0.749149i	0.107147	+	0.0314613i
$568$		0			0
$569$	1.30394	+	1.50483i	0.0546641	+	0.0630858i	0.782423	−	0.622747i	$-0.213984\pi$
$569$	1.30394	+	1.50483i	0.0546641	+	0.0630858i	−0.727759	+	0.685833i	$0.759438\pi$
$570$		0			0
$571$	0.0843731	−	0.0973718i	0.00353090	−	0.00407488i	−0.753981	−	0.656896i	$-0.771869\pi$
$571$	0.0843731	−	0.0973718i	0.00353090	−	0.00407488i	0.757512	+	0.652821i	$0.226415\pi$
$572$		0			0
$573$	−5.85643	−	12.8238i	−0.244656	−	0.535722i
$574$		0			0
$575$	0.718944	+	0.741935i	0.0299820	+	0.0309408i
$576$		0			0
$577$	−14.0510	−	30.7675i	−0.584953	−	1.28087i	−0.938444	−	0.345430i	$-0.887733\pi$
$577$	−14.0510	−	30.7675i	−0.584953	−	1.28087i	0.353492	−	0.935438i	$-0.384994\pi$
$578$		0			0
$579$	−14.0180	+	16.1776i	−0.582567	+	0.672318i
$580$		0			0
$581$	−7.91990	−	9.14005i	−0.328573	−	0.379193i
$582$		0			0
$583$	34.9943	+	10.2753i	1.44932	+	0.425558i
$584$		0			0
$585$	−0.562033	+	3.90903i	−0.0232372	+	0.161618i
$586$		0			0
$587$	−4.65842	+	10.2005i	−0.192274	+	0.421021i	−0.981075	−	0.193627i	$-0.937975\pi$
$587$	−4.65842	+	10.2005i	−0.192274	+	0.421021i	0.788801	+	0.614648i	$0.210702\pi$
$588$		0			0
$589$	−2.50238	+	1.60818i	−0.103109	+	0.0662641i
$590$		0			0
$591$	3.64384	+	25.3434i	0.149887	+	1.04249i
$592$		0			0
$593$	−34.5384	−	22.1965i	−1.41832	−	0.911500i	−0.999995	−	0.00320409i	$-0.998980\pi$
$593$	−34.5384	−	22.1965i	−1.41832	−	0.911500i	−0.418327	−	0.908296i	$-0.637384\pi$
$594$		0			0
$595$	17.7648	−	5.21623i	0.728287	−	0.213844i
$596$		0			0
$597$	−25.0993			−1.02724
$598$		0			0
$599$	−13.8948			−0.567727			−0.283863	−	0.958865i	$-0.591616\pi$
$599$	−13.8948			−0.567727			−0.283863	+	0.958865i	$0.591616\pi$
$600$		0			0
$601$	36.4668	−	10.7076i	1.48751	−	0.436773i	0.565766	−	0.824566i	$-0.308581\pi$
$601$	36.4668	−	10.7076i	1.48751	−	0.436773i	0.921746	+	0.387793i	$0.126762\pi$
$602$		0			0
$603$	13.5156	+	8.68597i	0.550399	+	0.353720i
$604$		0			0
$605$	−3.25543	−	22.6420i	−0.132352	−	0.920528i
$606$		0			0
$607$	−7.82890	+	5.03133i	−0.317765	+	0.204215i	−0.689794	−	0.724006i	$-0.742299\pi$
$607$	−7.82890	+	5.03133i	−0.317765	+	0.204215i	0.372028	+	0.928221i	$0.378662\pi$
$608$		0			0
$609$	8.47335	−	18.5540i	0.343357	−	0.751848i
$610$		0			0
$611$	0.599936	−	4.17264i	0.0242708	−	0.168807i
$612$		0			0
$613$	−34.4865	−	10.1261i	−1.39290	−	0.408991i	−0.502657	−	0.864486i	$-0.667644\pi$
$613$	−34.4865	−	10.1261i	−1.39290	−	0.408991i	−0.890238	+	0.455495i	$0.849462\pi$
$614$		0			0
$615$	8.59251	+	9.91629i	0.346483	+	0.399863i
$616$		0			0
$617$	−12.3944	+	14.3039i	−0.498978	+	0.575851i	−0.948242	−	0.317548i	$-0.897141\pi$
$617$	−12.3944	+	14.3039i	−0.498978	+	0.575851i	0.449264	+	0.893399i	$0.351686\pi$
$618$		0			0
$619$	5.02572	+	11.0048i	0.202001	+	0.442320i	0.983337	−	0.181790i	$-0.0581891\pi$
$619$	5.02572	+	11.0048i	0.202001	+	0.442320i	−0.781337	+	0.624110i	$0.785462\pi$
$620$		0			0
$621$	1.74647	−	4.46652i	0.0700835	−	0.179235i
$622$		0			0
$623$	5.26310	+	11.5246i	0.210862	+	0.461722i
$624$		0			0
$625$	17.0465	−	19.6727i	0.681859	−	0.786908i
$626$		0			0
$627$	−7.78025	−	8.97889i	−0.310713	−	0.358582i
$628$		0			0
$629$	−25.7448	−	7.55934i	−1.02651	−	0.301411i
$630$		0			0
$631$	−3.77021	+	26.2224i	−0.150090	+	1.04390i	0.765976	+	0.642869i	$0.222256\pi$
$631$	−3.77021	+	26.2224i	−0.150090	+	1.04390i	−0.916066	+	0.401028i	$0.868653\pi$
$632$		0			0
$633$	−5.70600	+	12.4944i	−0.226793	+	0.496607i
$634$		0			0
$635$	16.8668	−	10.8397i	0.669340	−	0.430158i
$636$		0			0
$637$	−0.0173977	−	0.121004i	−0.000689323	−	0.00479434i
$638$		0			0
$639$	−13.1476	−	8.44946i	−0.520111	−	0.334255i
$640$		0			0
$641$	7.37655	−	2.16595i	0.291356	−	0.0855499i	−0.132788	−	0.991144i	$-0.542393\pi$
$641$	7.37655	−	2.16595i	0.291356	−	0.0855499i	0.424145	+	0.905594i	$0.360575\pi$
$642$		0			0
$643$	−10.8542			−0.428048			−0.214024	−	0.976828i	$-0.568657\pi$
$643$	−10.8542			−0.428048			−0.214024	+	0.976828i	$0.568657\pi$
$644$		0			0
$645$	9.65256			0.380069
$646$		0			0
$647$	15.4575	−	4.53873i	0.607697	−	0.178436i	0.0366156	−	0.999329i	$-0.488342\pi$
$647$	15.4575	−	4.53873i	0.607697	−	0.178436i	0.571081	+	0.820893i	$0.306524\pi$
$648$		0			0
$649$	20.6638	+	13.2798i	0.811125	+	0.521278i
$650$		0			0
$651$	0.434353	+	3.02099i	0.0170236	+	0.118402i
$652$		0			0
$653$	−41.1474	+	26.4438i	−1.61022	+	1.03483i	−0.648344	+	0.761348i	$0.724538\pi$
$653$	−41.1474	+	26.4438i	−1.61022	+	1.03483i	−0.961878	+	0.273479i	$0.911826\pi$
$654$		0			0
$655$	−0.332919	+	0.728992i	−0.0130082	+	0.0284841i
$656$		0			0
$657$	1.32712	−	9.23032i	0.0517759	−	0.360109i
$658$		0			0
$659$	−26.7961	−	7.86805i	−1.04383	−	0.306496i	−0.285507	−	0.958377i	$-0.592162\pi$
$659$	−26.7961	−	7.86805i	−1.04383	−	0.306496i	−0.758321	+	0.651881i	$0.773980\pi$
$660$		0			0
$661$	20.5437	+	23.7087i	0.799057	+	0.922161i	0.998329	−	0.0577830i	$-0.0184032\pi$
$661$	20.5437	+	23.7087i	0.799057	+	0.922161i	−0.199272	+	0.979944i	$0.563858\pi$
$662$		0			0
$663$	3.45271	−	3.98464i	0.134092	−	0.154750i
$664$		0			0
$665$	−6.53767	−	14.3155i	−0.253520	−	0.555131i
$666$		0			0
$667$	−32.0066	−	18.1365i	−1.23930	−	0.702248i
$668$		0			0
$669$	−6.33493	−	13.8716i	−0.244923	−	0.536306i
$670$		0			0
$671$	−32.1043	+	37.0503i	−1.23937	+	1.43031i
$672$		0			0
$673$	26.0490	+	30.0622i	1.00412	+	1.15881i	0.987286	+	0.158954i	$0.0508123\pi$
$673$	26.0490	+	30.0622i	1.00412	+	1.15881i	0.0168310	+	0.999858i	$0.494642\pi$
$674$		0			0
$675$	0.206695	+	0.0606913i	0.00795571	+	0.00233601i
$676$		0			0
$677$	1.87722	−	13.0564i	0.0721475	−	0.501797i	−0.921421	−	0.388565i	$-0.872971\pi$
$677$	1.87722	−	13.0564i	0.0721475	−	0.501797i	0.993569	−	0.113231i	$-0.0361201\pi$
$678$		0			0
$679$	12.0356	−	26.3543i	0.461884	−	1.01138i
$680$		0			0
$681$	20.0710	−	12.8988i	0.769122	−	0.494285i
$682$		0			0
$683$	5.45627	+	37.9492i	0.208778	+	1.45208i	0.777152	+	0.629313i	$0.216664\pi$
$683$	5.45627	+	37.9492i	0.208778	+	1.45208i	−0.568373	+	0.822771i	$0.692427\pi$
$684$		0			0
$685$	−12.6752	−	8.14588i	−0.484296	−	0.311238i
$686$		0			0
$687$	14.5861	−	4.28286i	0.556494	−	0.163401i
$688$		0			0
$689$	13.7576			0.524124
$690$		0			0
$691$	27.4084			1.04266			0.521331	−	0.853354i	$-0.325436\pi$
$691$	27.4084			1.04266			0.521331	+	0.853354i	$0.325436\pi$
$692$		0			0
$693$	−11.6964	+	3.43437i	−0.444310	+	0.130461i
$694$		0			0
$695$	−8.99813	−	5.78275i	−0.341319	−	0.219352i
$696$		0			0
$697$	−2.49299	−	17.3391i	−0.0944287	−	0.656766i
$698$		0			0
$699$	−8.40373	+	5.40075i	−0.317858	+	0.204275i
$700$		0			0
$701$	5.84805	−	12.8055i	0.220878	−	0.483655i	−0.766459	−	0.642293i	$-0.777983\pi$
$701$	5.84805	−	12.8055i	0.220878	−	0.483655i	0.987337	+	0.158638i	$0.0507103\pi$
$702$		0			0
$703$	−3.24578	+	22.5749i	−0.122417	+	0.851427i
$704$		0			0
$705$	−5.34163	−	1.56844i	−0.201177	−	0.0590710i
$706$		0			0
$707$	−15.3929	−	17.7643i	−0.578908	−	0.668096i
$708$		0			0
$709$	−12.2640	+	14.1534i	−0.460584	+	0.531542i	−0.937769	−	0.347261i	$-0.887112\pi$
$709$	−12.2640	+	14.1534i	−0.460584	+	0.531542i	0.477185	+	0.878803i	$0.341657\pi$
$710$		0			0
$711$	2.45562	+	5.37705i	0.0920928	+	0.201655i
$712$		0			0
$713$	5.49607	−	0.306246i	0.205830	−	0.0114690i
$714$		0			0
$715$	−7.52097	−	16.4686i	−0.281268	−	0.615892i
$716$		0			0
$717$	13.8047	−	15.9315i	0.515546	−	0.594971i
$718$		0			0
$719$	−8.16681	−	9.42501i	−0.304571	−	0.351493i	0.582746	−	0.812655i	$-0.301978\pi$
$719$	−8.16681	−	9.42501i	−0.304571	−	0.351493i	−0.887316	+	0.461161i	$0.847433\pi$
$720$		0			0
$721$	−8.48380	−	2.49107i	−0.315953	−	0.0927723i
$722$		0			0
$723$	−1.15474	+	8.03141i	−0.0429453	+	0.298691i
$724$		0			0
$725$	0.686457	−	1.50313i	0.0254944	−	0.0558249i
$726$		0			0
$727$	−24.6161	+	15.8198i	−0.912959	+	0.586723i	−0.910607	−	0.413274i	$-0.864385\pi$
$727$	−24.6161	+	15.8198i	−0.912959	+	0.586723i	−0.00235247	+	0.999997i	$0.500749\pi$
$728$		0			0
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$		0			0
$731$	−10.8410	−	6.96708i	−0.400968	−	0.257687i
$732$		0			0
$733$	24.6789	−	7.24639i	0.911537	−	0.267652i	0.207850	−	0.978161i	$-0.433354\pi$
$733$	24.6789	−	7.24639i	0.911537	−	0.267652i	0.703688	+	0.710509i	$0.251535\pi$
$734$		0			0
$735$	−0.161443			−0.00595492
$736$		0			0
$737$	−73.6527			−2.71303
$738$		0			0
$739$	41.4600	−	12.1738i	1.52513	−	0.447819i	0.591576	−	0.806249i	$-0.298506\pi$
$739$	41.4600	−	12.1738i	1.52513	−	0.447819i	0.933557	+	0.358430i	$0.116688\pi$
$740$		0			0
$741$	−3.77015	−	2.42293i	−0.138500	−	0.0890086i
$742$		0			0
$743$	−3.18052	−	22.1210i	−0.116682	−	0.811540i	−0.961168	−	0.275963i	$-0.911003\pi$
$743$	−3.18052	−	22.1210i	−0.116682	−	0.811540i	0.844486	−	0.535577i	$-0.179906\pi$
$744$		0			0
$745$	8.37626	−	5.38310i	0.306882	−	0.197221i
$746$		0			0
$747$	−1.88939	+	4.13719i	−0.0691292	+	0.151372i
$748$		0			0
$749$	5.16349	−	35.9129i	0.188670	−	1.31223i
$750$		0			0
$751$	−11.6763	−	3.42848i	−0.426075	−	0.125107i	0.0616629	−	0.998097i	$-0.480360\pi$
$751$	−11.6763	−	3.42848i	−0.426075	−	0.125107i	−0.487738	+	0.872990i	$0.662178\pi$
$752$		0			0
$753$	19.7447	+	22.7866i	0.719538	+	0.830391i
$754$		0			0
$755$	4.29183	−	4.95304i	0.156196	−	0.180259i
$756$		0			0
$757$	13.2656	+	29.0475i	0.482145	+	1.05575i	0.981868	+	0.189566i	$0.0607080\pi$
$757$	13.2656	+	29.0475i	0.482145	+	1.05575i	−0.499723	+	0.866185i	$0.666565\pi$
$758$		0			0
$759$	4.33479	+	21.5543i	0.157343	+	0.782371i
$760$		0			0
$761$	13.9210	+	30.4828i	0.504637	+	1.10500i	0.974934	+	0.222493i	$0.0714196\pi$
$761$	13.9210	+	30.4828i	0.504637	+	1.10500i	−0.470297	+	0.882508i	$0.655853\pi$
$762$		0			0
$763$	3.52138	−	4.06389i	0.127482	−	0.147123i
$764$		0			0
$765$	−4.55971	−	5.26219i	−0.164857	−	0.190255i
$766$		0			0
$767$	8.89023	+	2.61041i	0.321007	+	0.0942563i
$768$		0			0
$769$	−5.57273	+	38.7592i	−0.200958	+	1.39769i	0.600493	+	0.799630i	$0.294971\pi$
$769$	−5.57273	+	38.7592i	−0.200958	+	1.39769i	−0.801451	+	0.598061i	$0.795938\pi$
$770$		0			0
$771$	−9.73841	+	21.3241i	−0.350720	+	0.767970i
$772$		0			0
$773$	20.9969	−	13.4939i	0.755207	−	0.485342i	−0.105515	−	0.994418i	$-0.533649\pi$
$773$	20.9969	−	13.4939i	0.755207	−	0.485342i	0.860722	+	0.509076i	$0.170013\pi$
$774$		0			0
$775$	0.0351885	+	0.244742i	0.00126401	+	0.00879138i
$776$		0			0
$777$	19.6862	+	12.6515i	0.706238	+	0.453871i
$778$		0			0
$779$	−14.2867	+	4.19497i	−0.511876	+	0.150300i
$780$		0			0
$781$	71.6472			2.56374
$782$		0			0
$783$	−7.67082			−0.274133
$784$		0			0
$785$	9.25801	−	2.71840i	0.330432	−	0.0970237i
$786$		0			0
$787$	37.7028	+	24.2301i	1.34396	+	0.863710i	0.997239	−	0.0742587i	$-0.0236591\pi$
$787$	37.7028	+	24.2301i	1.34396	+	0.863710i	0.346720	+	0.937969i	$0.387295\pi$
$788$		0			0
$789$	−0.445501	−	3.09853i	−0.0158603	−	0.110311i
$790$		0			0
$791$	−9.60714	+	6.17413i	−0.341590	+	0.219527i
$792$		0			0
$793$	−7.68217	+	16.8216i	−0.272802	+	0.597353i
$794$		0			0
$795$	2.58566	−	17.9837i	0.0917039	−	0.637815i
$796$		0			0
$797$	36.3094	+	10.6614i	1.28615	+	0.377647i	0.852164	−	0.523275i	$-0.175290\pi$
$797$	36.3094	+	10.6614i	1.28615	+	0.377647i	0.433982	+	0.900921i	$0.357108\pi$
$798$		0			0
$799$	4.86721	+	5.61706i	0.172189	+	0.198717i
$800$		0			0
$801$	3.12016	−	3.60086i	0.110246	−	0.127230i
$802$		0			0
$803$	17.7591	+	38.8871i	0.626706	+	1.37229i
$804$		0			0
$805$	−2.53448	+	29.0127i	−0.0893287	+	1.02256i
$806$		0			0
$807$	−2.07592	−	4.54563i	−0.0730758	−	0.160014i
$808$		0			0
$809$	−9.49764	+	10.9609i	−0.333919	+	0.385363i	−0.897734	−	0.440538i	$-0.854788\pi$
$809$	−9.49764	+	10.9609i	−0.333919	+	0.385363i	0.563815	+	0.825901i	$0.309333\pi$
$810$		0			0
$811$	−2.27878	−	2.62985i	−0.0800188	−	0.0923466i	0.714328	−	0.699811i	$-0.246732\pi$
$811$	−2.27878	−	2.62985i	−0.0800188	−	0.0923466i	−0.794347	+	0.607464i	$0.792187\pi$
$812$		0			0
$813$	−6.42090	−	1.88535i	−0.225191	−	0.0661220i
$814$		0			0
$815$	−2.76362	+	19.2214i	−0.0968053	+	0.673296i
$816$		0			0
$817$	−4.55035	+	9.96389i	−0.159197	+	0.348592i
$818$		0			0
$819$	−3.86834	+	2.48603i	−0.135171	+	0.0868691i
$820$		0			0
$821$	−5.43073	−	37.7715i	−0.189534	−	1.31824i	−0.833218	−	0.552945i	$-0.813504\pi$
$821$	−5.43073	−	37.7715i	−0.189534	−	1.31824i	0.643684	−	0.765291i	$-0.277405\pi$
$822$		0			0
$823$	25.3708	+	16.3049i	0.884372	+	0.568351i	0.902117	−	0.431491i	$-0.142012\pi$
$823$	25.3708	+	16.3049i	0.884372	+	0.568351i	−0.0177452	+	0.999843i	$0.505649\pi$
$824$		0			0
$825$	−0.947568	+	0.278231i	−0.0329901	+	0.00968676i
$826$		0			0
$827$	−41.2905			−1.43581			−0.717905	−	0.696141i	$-0.754899\pi$
$827$	−41.2905			−1.43581			−0.717905	+	0.696141i	$0.754899\pi$
$828$		0			0
$829$	47.8835			1.66306			0.831532	−	0.555477i	$-0.187464\pi$
$829$	47.8835			1.66306			0.831532	+	0.555477i	$0.187464\pi$
$830$		0			0
$831$	27.9815	−	8.21612i	0.970668	−	0.285014i
$832$		0			0
$833$	0.181320	+	0.116527i	0.00628236	+	0.00403743i
$834$		0			0
$835$	−5.77254	−	40.1489i	−0.199767	−	1.38941i
$836$		0			0
$837$	0.965581	−	0.620541i	0.0333754	−	0.0214490i
$838$		0			0
$839$	13.6188	−	29.8210i	0.470174	−	1.02954i	−0.514876	−	0.857265i	$-0.672162\pi$
$839$	13.6188	−	29.8210i	0.470174	−	1.02954i	0.985049	−	0.172272i	$-0.0551108\pi$
$840$		0			0
$841$	−4.24689	+	29.5378i	−0.146444	+	1.01854i
$842$		0			0
$843$	18.8854	+	5.54527i	0.650449	+	0.190989i
$844$		0			0
$845$	14.9696	+	17.2758i	0.514968	+	0.594305i
$846$		0			0
$847$	17.4419	−	20.1290i	0.599310	−	0.691641i
$848$		0			0
$849$	11.4846	+	25.1477i	0.394149	+	0.863066i
$850$		0			0
$851$	25.8213	−	33.3849i	0.885141	−	1.14442i
$852$		0			0
$853$	5.41389	+	11.8548i	0.185368	+	0.405900i	0.979387	−	0.201994i	$-0.0647420\pi$
$853$	5.41389	+	11.8548i	0.185368	+	0.405900i	−0.794019	+	0.607893i	$0.792015\pi$
$854$		0			0
$855$	−3.87578	+	4.47288i	−0.132549	+	0.152969i
$856$		0			0
$857$	29.9948	+	34.6158i	1.02460	+	1.18245i	0.983054	+	0.183317i	$0.0586834\pi$
$857$	29.9948	+	34.6158i	1.02460	+	1.18245i	0.0415477	+	0.999137i	$0.486771\pi$
$858$		0			0
$859$	17.6706	+	5.18857i	0.602915	+	0.177032i	0.568924	−	0.822390i	$-0.307360\pi$
$859$	17.6706	+	5.18857i	0.602915	+	0.177032i	0.0339912	+	0.999422i	$0.489178\pi$
$860$		0			0
$861$	−2.17424	+	15.1222i	−0.0740979	+	0.515362i
$862$		0			0
$863$	5.05264	−	11.0637i	0.171994	−	0.376614i	−0.803931	−	0.594723i	$-0.797262\pi$
$863$	5.05264	−	11.0637i	0.171994	−	0.376614i	0.975924	+	0.218109i	$0.0699889\pi$
$864$		0			0
$865$	−33.0004	+	21.2080i	−1.12205	+	0.721095i
$866$		0			0
$867$	−1.09642	−	7.62577i	−0.0372364	−	0.258985i
$868$		0			0
$869$	−22.7974	−	14.6510i	−0.773348	−	0.497000i
$870$		0			0
$871$	−26.6574	+	7.82733i	−0.903253	+	0.265219i
$872$		0			0
$873$	−10.8957			−0.368763
$874$		0			0
$875$	29.0549			0.982235
$876$		0			0
$877$	−46.0155	+	13.5114i	−1.55383	+	0.456247i	−0.942243	−	0.334929i	$-0.891288\pi$
$877$	−46.0155	+	13.5114i	−1.55383	+	0.456247i	−0.611589	+	0.791175i	$0.709470\pi$
$878$		0			0
$879$	10.9600	+	7.04358i	0.369673	+	0.237574i
$880$		0			0
$881$	−1.65041	−	11.4789i	−0.0556039	−	0.386733i	−0.998552	−	0.0537939i	$-0.982869\pi$
$881$	−1.65041	−	11.4789i	−0.0556039	−	0.386733i	0.942948	−	0.332940i	$-0.108040\pi$
$882$		0			0
$883$	−17.1384	+	11.0142i	−0.576754	+	0.370657i	−0.796261	−	0.604954i	$-0.793192\pi$
$883$	−17.1384	+	11.0142i	−0.576754	+	0.370657i	0.219507	+	0.975611i	$0.429555\pi$
$884$		0			0
$885$	5.08312	−	11.1305i	0.170867	−	0.374147i
$886$		0			0
$887$	−4.19871	+	29.2027i	−0.140979	+	0.980529i	0.789387	+	0.613896i	$0.210399\pi$
$887$	−4.19871	+	29.2027i	−0.140979	+	0.980529i	−0.930366	+	0.366633i	$0.880510\pi$
$888$		0			0
$889$	22.3993	+	6.57703i	0.751249	+	0.220587i
$890$		0			0
$891$	3.00212	+	3.46463i	0.100575	+	0.116070i
$892$		0			0
$893$	4.13715	−	4.77452i	0.138444	−	0.159773i
$894$		0			0
$895$	7.60439	+	16.6513i	0.254187	+	0.556592i
$896$		0			0
$897$	3.85956	+	7.34056i	0.128867	+	0.245094i
$898$		0			0
$899$	−3.65751	−	8.00884i	−0.121985	−	0.267110i
$900$		0			0
$901$	−15.8843	+	18.3315i	−0.529184	+	0.610711i
$902$		0			0
$903$	7.36000	+	8.49390i	0.244926	+	0.282659i
$904$		0			0
$905$	−37.4166	−	10.9865i	−1.24377	−	0.365203i
$906$		0			0
$907$	6.81379	−	47.3909i	0.226248	−	1.57359i	−0.487459	−	0.873146i	$-0.662076\pi$
$907$	6.81379	−	47.3909i	0.226248	−	1.57359i	0.713707	−	0.700444i	$-0.247015\pi$
$908$		0			0
$909$	−3.67216	+	8.04091i	−0.121798	+	0.266700i
$910$		0			0
$911$	−37.6247	+	24.1799i	−1.24656	+	0.801116i	−0.986386	−	0.164446i	$-0.947417\pi$
$911$	−37.6247	+	24.1799i	−1.24656	+	0.801116i	−0.260175	+	0.965562i	$0.583780\pi$
$912$		0			0
$913$	−2.96735	−	20.6384i	−0.0982051	−	0.683032i
$914$		0			0
$915$	20.5450	+	13.2035i	0.679197	+	0.436493i
$916$		0			0
$917$	−0.895333	+	0.262894i	−0.0295665	+	0.00868151i
$918$		0			0
$919$	15.1051			0.498273			0.249136	−	0.968468i	$-0.419853\pi$
$919$	15.1051			0.498273			0.249136	+	0.968468i	$0.419853\pi$
$920$		0			0
$921$	−22.0164			−0.725466
$922$		0			0
$923$	25.9316	−	7.61420i	0.853548	−	0.250624i
$924$		0			0
$925$	1.59485	+	1.02495i	0.0524383	+	0.0337000i
$926$		0			0
$927$	0.473225	+	3.29135i	0.0155428	+	0.108102i
$928$		0			0
$929$	23.4545	−	15.0733i	0.769517	−	0.494539i	−0.0960223	−	0.995379i	$-0.530612\pi$
$929$	23.4545	−	15.0733i	0.769517	−	0.494539i	0.865540	+	0.500840i	$0.166976\pi$
$930$		0			0
$931$	0.0761065	−	0.166650i	0.00249429	−	0.00546174i
$932$		0			0
$933$	−1.76007	+	12.2416i	−0.0576222	+	0.400771i
$934$		0			0
$935$	30.6274	+	8.99301i	1.00162	+	0.294103i
$936$		0			0
$937$	−37.7275	−	43.5399i	−1.23250	−	1.42238i	−0.871913	−	0.489661i	$-0.837121\pi$
$937$	−37.7275	−	43.5399i	−1.23250	−	1.42238i	−0.360590	−	0.932724i	$-0.617425\pi$
$938$		0			0
$939$	11.7570	−	13.5683i	0.383674	−	0.442783i
$940$		0			0
$941$	20.4813	+	44.8477i	0.667670	+	1.46199i	0.875198	+	0.483765i	$0.160731\pi$
$941$	20.4813	+	44.8477i	0.667670	+	1.46199i	−0.207528	+	0.978229i	$0.566542\pi$
$942$		0			0
$943$	26.8292	+	6.28006i	0.873678	+	0.204507i
$944$		0			0
$945$	2.52266	+	5.52384i	0.0820620	+	0.179691i
$946$		0			0
$947$	−22.9779	+	26.5179i	−0.746680	+	0.861715i	−0.994242	−	0.107157i	$-0.965825\pi$
$947$	−22.9779	+	26.5179i	−0.746680	+	0.861715i	0.247562	+	0.968872i	$0.420371\pi$
$948$		0			0
$949$	10.5603	+	12.1872i	0.342802	+	0.395614i
$950$		0			0
$951$	−1.14015	−	0.334778i	−0.0369719	−	0.0108559i
$952$		0			0
$953$	0.340098	−	2.36544i	0.0110169	−	0.0766240i	−0.983571	−	0.180520i	$-0.942222\pi$
$953$	0.340098	−	2.36544i	0.0110169	−	0.0766240i	0.994588	+	0.103896i	$0.0331310\pi$
$954$		0			0
$955$	13.3745	−	29.2861i	0.432789	−	0.947676i
$956$		0			0
$957$	29.5834	−	19.0121i	0.956296	−	0.614574i
$958$		0			0
$959$	−2.49670	−	17.3649i	−0.0806225	−	0.560742i
$960$		0			0
$961$	−24.9706	−	16.0476i	−0.805502	−	0.517665i
$962$		0			0
$963$	−13.0919	+	3.84414i	−0.421882	+	0.123876i
$964$		0			0
$965$	−48.8856			−1.57368
$966$		0			0
$967$	−37.4419			−1.20405			−0.602026	−	0.798477i	$-0.705640\pi$
$967$	−37.4419			−1.20405			−0.602026	+	0.798477i	$0.705640\pi$
$968$		0			0
$969$	7.58142	−	2.22611i	0.243550	−	0.0715128i
$970$		0			0
$971$	−39.7745	−	25.5615i	−1.27643	−	0.820309i	−0.285983	−	0.958235i	$-0.592320\pi$
$971$	−39.7745	−	25.5615i	−1.27643	−	0.820309i	−0.990443	+	0.137926i	$0.955956\pi$
$972$		0			0
$973$	−1.77240	−	12.3273i	−0.0568206	−	0.395196i
$974$		0			0
$975$	−0.313389	+	0.201403i	−0.0100365	+	0.00645005i
$976$		0			0
$977$	−12.4140	+	27.1829i	−0.397159	+	0.869657i	0.600391	+	0.799706i	$0.295011\pi$
$977$	−12.4140	+	27.1829i	−0.397159	+	0.869657i	−0.997550	+	0.0699507i	$0.977716\pi$
$978$		0			0
$979$	−3.10855	+	21.6205i	−0.0993497	+	0.690993i
$980$		0			0
$981$	−1.94033	−	0.569731i	−0.0619498	−	0.0181901i
$982$		0			0
$983$	16.7460	+	19.3259i	0.534114	+	0.616400i	0.957108	−	0.289732i	$-0.0935663\pi$
$983$	16.7460	+	19.3259i	0.534114	+	0.616400i	−0.422994	+	0.906132i	$0.639021\pi$
$984$		0			0
$985$	−38.2915	+	44.1907i	−1.22007	+	1.40803i
$986$		0			0
$987$	−2.69278	−	5.89636i	−0.0857120	−	0.187683i
$988$		0			0
$989$	16.4164	−	11.8907i	0.522012	−	0.378103i
$990$		0			0
$991$	0.990728	+	2.16939i	0.0314715	+	0.0689130i	0.924715	−	0.380660i	$-0.124303\pi$
$991$	0.990728	+	2.16939i	0.0314715	+	0.0689130i	−0.893243	+	0.449573i	$0.851576\pi$
$992$		0			0
$993$	−15.8797	+	18.3262i	−0.503928	+	0.581564i
$994$		0			0
$995$	−37.5366	−	43.3195i	−1.18999	−	1.37332i
$996$		0			0
$997$	3.22836	+	0.947932i	0.102243	+	0.0300213i	0.332454	−	0.943119i	$-0.392123\pi$
$997$	3.22836	+	0.947932i	0.102243	+	0.0300213i	−0.230211	+	0.973141i	$0.573942\pi$
$998$		0			0
$999$	1.25243	−	8.71084i	0.0396251	−	0.275599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.d.73.3	✓	30
23.6	even	11	inner	552.2.q.d.121.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.d.73.3	✓	30	1.1	even	1	trivial
552.2.q.d.121.3	yes	30	23.6	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{3} +(1.92120 + 1.23468i) q^{5} +(0.378426 + 2.63201i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{3} +(1.92120 + 1.23468i) q^{5} +(0.378426 + 2.63201i) q^{7} +(0.841254 - 0.540641i) q^{9} +(-1.90442 + 4.17009i) q^{11} +(-0.246103 + 1.71169i) q^{13} +(2.19122 + 0.643401i) q^{15} +(-1.99661 - 2.30421i) q^{17} +(-1.69713 + 1.95859i) q^{19} +(1.10462 + 2.41878i) q^{21} +(4.51927 - 1.60506i) q^{23} +(0.0894893 + 0.195954i) q^{25} +(0.654861 - 0.755750i) q^{27} +(-5.02332 - 5.79722i) q^{29} +(1.10129 + 0.323369i) q^{31} +(-0.652424 + 4.53771i) q^{33} +(-2.52266 + 5.52384i) q^{35} +(7.40338 - 4.75787i) q^{37} +(0.246103 + 1.71169i) q^{39} +(4.83341 + 3.10624i) q^{41} +(4.05546 - 1.19079i) q^{43} +2.28373 q^{45} -2.43774 q^{47} +(-0.0678292 + 0.0199164i) q^{49} +(-2.56490 - 1.64836i) q^{51} +(-1.13221 - 7.87469i) q^{53} +(-8.80747 + 5.66022i) q^{55} +(-1.07658 + 2.35739i) q^{57} +(0.762525 - 5.30348i) q^{59} +(10.2607 + 3.01281i) q^{61} +(1.74133 + 2.00960i) q^{63} +(-2.58619 + 2.98463i) q^{65} +(6.67408 + 14.6142i) q^{67} +(3.88401 - 2.81326i) q^{69} +(-6.49235 - 14.2163i) q^{71} +(6.10673 - 7.04754i) q^{73} +(0.141071 + 0.162805i) q^{75} +(-11.6964 - 3.43437i) q^{77} +(-0.841256 + 5.85107i) q^{79} +(0.415415 - 0.909632i) q^{81} +(-3.82619 + 2.45894i) q^{83} +(-0.990920 - 6.89200i) q^{85} +(-6.45311 - 4.14716i) q^{87} +(4.57162 - 1.34235i) q^{89} -4.59831 q^{91} +1.14779 q^{93} +(-5.67873 + 1.66743i) q^{95} +(-9.16603 - 5.89065i) q^{97} +(0.652424 + 4.53771i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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