LMFDB - Embedded newform 1148.2.i.d.165.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 14 x^{14} - 8 x^{13} + 136 x^{12} - 87 x^{11} + 706 x^{10} - 568 x^{9} + 2685 x^{8} + \cdots + 121 $ x^16 + 14x^14 - 8x^13 + 136x^12 - 87x^11 + 706x^10 - 568x^9 + 2685x^8 - 2100x^7 + 5529x^6 - 4919x^5 + 8145x^4 - 5182x^3 + 2775x^2 - 660x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.5
Root			$0.154058 - 0.266837i$ of defining polynomial
Character	$\chi$	$=$	1148.165
Dual form			1148.2.i.d.821.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.154058 + 0.266837i) q^{3} +(1.65062 + 2.85896i) q^{5} +(-2.57062 - 0.626020i) q^{7} +(1.45253 + 2.51586i) q^{9} +O(q^{10})$	\(q+(-0.154058 + 0.266837i) q^{3} +(1.65062 + 2.85896i) q^{5} +(-2.57062 - 0.626020i) q^{7} +(1.45253 + 2.51586i) q^{9} +(-0.758653 + 1.31403i) q^{11} +1.10922 q^{13} -1.01717 q^{15} +(-0.803385 + 1.39150i) q^{17} +(-0.440259 - 0.762551i) q^{19} +(0.563071 - 0.589494i) q^{21} +(-0.341030 - 0.590681i) q^{23} +(-2.94909 + 5.10798i) q^{25} -1.81945 q^{27} -1.88250 q^{29} +(-2.35704 + 4.08252i) q^{31} +(-0.233754 - 0.404874i) q^{33} +(-2.45336 - 8.38262i) q^{35} +(1.61068 + 2.78978i) q^{37} +(-0.170884 + 0.295981i) q^{39} +1.00000 q^{41} -9.57315 q^{43} +(-4.79516 + 8.30546i) q^{45} +(-2.39296 - 4.14472i) q^{47} +(6.21620 + 3.21852i) q^{49} +(-0.247537 - 0.428746i) q^{51} +(0.816086 - 1.41350i) q^{53} -5.00899 q^{55} +0.271303 q^{57} +(-0.505024 + 0.874727i) q^{59} +(0.190336 + 0.329671i) q^{61} +(-2.15893 - 7.37664i) q^{63} +(1.83090 + 3.17121i) q^{65} +(-4.24350 + 7.34995i) q^{67} +0.210154 q^{69} +7.90937 q^{71} +(-0.782304 + 1.35499i) q^{73} +(-0.908666 - 1.57385i) q^{75} +(2.77282 - 2.90293i) q^{77} +(4.20735 + 7.28734i) q^{79} +(-4.07729 + 7.06208i) q^{81} +1.55396 q^{83} -5.30433 q^{85} +(0.290015 - 0.502321i) q^{87} +(-6.96078 - 12.0564i) q^{89} +(-2.85138 - 0.694393i) q^{91} +(-0.726245 - 1.25789i) q^{93} +(1.45340 - 2.51736i) q^{95} +0.601041 q^{97} -4.40787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^9	$ 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.154058	+	0.266837i	−0.0889457	+	0.154058i	−0.907066	−	0.420989i	$-0.861683\pi$
$3$	−0.154058	+	0.266837i	−0.0889457	+	0.154058i	0.818120	+	0.575047i	$0.195016\pi$
$4$		0			0
$5$	1.65062	+	2.85896i	0.738180	+	1.27856i	0.953314	+	0.301980i	$0.0976477\pi$
$5$	1.65062	+	2.85896i	0.738180	+	1.27856i	−0.215134	+	0.976584i	$0.569019\pi$
$6$		0			0
$7$	−2.57062	−	0.626020i	−0.971604	−	0.236613i
$7$	−2.57062	−	0.626020i	−0.971604	−	0.236613i
$8$		0			0
$9$	1.45253	+	2.51586i	0.484177	+	0.838620i
$10$		0			0
$11$	−0.758653	+	1.31403i	−0.228743	+	0.396194i	−0.957436	−	0.288647i	$-0.906795\pi$
$11$	−0.758653	+	1.31403i	−0.228743	+	0.396194i	0.728693	+	0.684840i	$0.240128\pi$
$12$		0			0
$13$	1.10922			0.307642			0.153821	−	0.988099i	$-0.450842\pi$
$13$	1.10922			0.307642			0.153821	+	0.988099i	$0.450842\pi$
$14$		0			0
$15$	−1.01717			−0.262632
$16$		0			0
$17$	−0.803385	+	1.39150i	−0.194850	+	0.337489i	−0.946851	−	0.321672i	$-0.895755\pi$
$17$	−0.803385	+	1.39150i	−0.194850	+	0.337489i	0.752002	+	0.659161i	$0.229089\pi$
$18$		0			0
$19$	−0.440259	−	0.762551i	−0.101002	−	0.174941i	0.811096	−	0.584914i	$-0.198872\pi$
$19$	−0.440259	−	0.762551i	−0.101002	−	0.174941i	−0.912098	+	0.409972i	$0.865538\pi$
$20$		0			0
$21$	0.563071	−	0.589494i	0.122872	−	0.128638i
$22$		0			0
$23$	−0.341030	−	0.590681i	−0.0711097	−	0.123166i	0.828278	−	0.560317i	$-0.189321\pi$
$23$	−0.341030	−	0.590681i	−0.0711097	−	0.123166i	−0.899388	+	0.437151i	$0.855987\pi$
$24$		0			0
$25$	−2.94909	+	5.10798i	−0.589819	+	1.02160i
$26$		0			0
$27$	−1.81945			−0.350153
$28$		0			0
$29$	−1.88250			−0.349572			−0.174786	−	0.984606i	$-0.555923\pi$
$29$	−1.88250			−0.349572			−0.174786	+	0.984606i	$0.555923\pi$
$30$		0			0
$31$	−2.35704	+	4.08252i	−0.423337	+	0.733242i	−0.996264	−	0.0863651i	$-0.972475\pi$
$31$	−2.35704	+	4.08252i	−0.423337	+	0.733242i	0.572926	+	0.819607i	$0.305808\pi$
$32$		0			0
$33$	−0.233754	−	0.404874i	−0.0406913	−	0.0704794i
$34$		0			0
$35$	−2.45336	−	8.38262i	−0.414693	−	1.41692i
$36$		0			0
$37$	1.61068	+	2.78978i	0.264794	+	0.458636i	0.967510	−	0.252834i	$-0.0813628\pi$
$37$	1.61068	+	2.78978i	0.264794	+	0.458636i	−0.702716	+	0.711471i	$0.748029\pi$
$38$		0			0
$39$	−0.170884	+	0.295981i	−0.0273634	+	0.0473948i
$40$		0			0
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$		0			0
$43$	−9.57315			−1.45989			−0.729946	−	0.683505i	$-0.760455\pi$
$43$	−9.57315			−1.45989			−0.729946	+	0.683505i	$0.760455\pi$
$44$		0			0
$45$	−4.79516	+	8.30546i	−0.714820	+	1.23810i
$46$		0			0
$47$	−2.39296	−	4.14472i	−0.349049	−	0.604570i	0.637032	−	0.770837i	$-0.280162\pi$
$47$	−2.39296	−	4.14472i	−0.349049	−	0.604570i	−0.986081	+	0.166267i	$0.946829\pi$
$48$		0			0
$49$	6.21620	+	3.21852i	0.888028	+	0.459789i
$50$		0			0
$51$	−0.247537	−	0.428746i	−0.0346620	−	0.0600364i
$52$		0			0
$53$	0.816086	−	1.41350i	0.112098	−	0.194159i	−0.804518	−	0.593928i	$-0.797576\pi$
$53$	0.816086	−	1.41350i	0.112098	−	0.194159i	0.916616	+	0.399769i	$0.130910\pi$
$54$		0			0
$55$	−5.00899			−0.675412
$56$		0			0
$57$	0.271303			0.0359349
$58$		0			0
$59$	−0.505024	+	0.874727i	−0.0657485	+	0.113880i	−0.897026	−	0.441978i	$-0.854277\pi$
$59$	−0.505024	+	0.874727i	−0.0657485	+	0.113880i	0.831277	+	0.555858i	$0.187610\pi$
$60$		0			0
$61$	0.190336	+	0.329671i	0.0243700	+	0.0422101i	0.877953	−	0.478746i	$-0.158909\pi$
$61$	0.190336	+	0.329671i	0.0243700	+	0.0422101i	−0.853583	+	0.520957i	$0.825575\pi$
$62$		0			0
$63$	−2.15893	−	7.37664i	−0.272000	−	0.929369i
$64$		0			0
$65$	1.83090	+	3.17121i	0.227095	+	0.393340i
$66$		0			0
$67$	−4.24350	+	7.34995i	−0.518425	+	0.897939i	0.481345	+	0.876531i	$0.340148\pi$
$67$	−4.24350	+	7.34995i	−0.518425	+	0.897939i	−0.999771	+	0.0214082i	$0.993185\pi$
$68$		0			0
$69$	0.210154			0.0252996
$70$		0			0
$71$	7.90937			0.938669			0.469335	−	0.883020i	$-0.344494\pi$
$71$	7.90937			0.938669			0.469335	+	0.883020i	$0.344494\pi$
$72$		0			0
$73$	−0.782304	+	1.35499i	−0.0915618	+	0.158590i	−0.908168	−	0.418605i	$-0.862519\pi$
$73$	−0.782304	+	1.35499i	−0.0915618	+	0.158590i	0.816607	+	0.577195i	$0.195853\pi$
$74$		0			0
$75$	−0.908666	−	1.57385i	−0.104924	−	0.181733i
$76$		0			0
$77$	2.77282	−	2.90293i	0.315992	−	0.330820i
$78$		0			0
$79$	4.20735	+	7.28734i	0.473364	+	0.819890i	0.999535	−	0.0304887i	$-0.00970637\pi$
$79$	4.20735	+	7.28734i	0.473364	+	0.819890i	−0.526172	+	0.850378i	$0.676373\pi$
$80$		0			0
$81$	−4.07729	+	7.06208i	−0.453033	+	0.784676i
$82$		0			0
$83$	1.55396			0.170570			0.0852848	−	0.996357i	$-0.472820\pi$
$83$	1.55396			0.170570			0.0852848	+	0.996357i	$0.472820\pi$
$84$		0			0
$85$	−5.30433			−0.575336
$86$		0			0
$87$	0.290015	−	0.502321i	0.0310929	−	0.0538544i
$88$		0			0
$89$	−6.96078	−	12.0564i	−0.737841	−	1.27798i	−0.953466	−	0.301502i	$-0.902512\pi$
$89$	−6.96078	−	12.0564i	−0.737841	−	1.27798i	0.215625	−	0.976476i	$-0.430821\pi$
$90$		0			0
$91$	−2.85138	−	0.694393i	−0.298906	−	0.0727922i
$92$		0			0
$93$	−0.726245	−	1.25789i	−0.0753081	−	0.130437i
$94$		0			0
$95$	1.45340	−	2.51736i	0.149116	−	0.258276i
$96$		0			0
$97$	0.601041			0.0610264			0.0305132	−	0.999534i	$-0.490286\pi$
$97$	0.601041			0.0610264			0.0305132	+	0.999534i	$0.490286\pi$
$98$		0			0
$99$	−4.40787			−0.443008
$100$		0			0
$101$	−1.89711	+	3.28590i	−0.188770	+	0.326959i	−0.944840	−	0.327531i	$-0.893783\pi$
$101$	−1.89711	+	3.28590i	−0.188770	+	0.326959i	0.756071	+	0.654490i	$0.227117\pi$
$102$		0			0
$103$	−0.260005	−	0.450341i	−0.0256190	−	0.0443734i	0.852932	−	0.522023i	$-0.174822\pi$
$103$	−0.260005	−	0.450341i	−0.0256190	−	0.0443734i	−0.878551	+	0.477649i	$0.841489\pi$
$104$		0			0
$105$	2.61475	+	0.636767i	0.255174	+	0.0621421i
$106$		0			0
$107$	4.67689	+	8.10061i	0.452132	+	0.783115i	0.998518	−	0.0544180i	$-0.0173304\pi$
$107$	4.67689	+	8.10061i	0.452132	+	0.783115i	−0.546387	+	0.837533i	$0.683997\pi$
$108$		0			0
$109$	−2.62674	+	4.54964i	−0.251596	+	0.435777i	−0.963965	−	0.266028i	$-0.914289\pi$
$109$	−2.62674	+	4.54964i	−0.251596	+	0.435777i	0.712370	+	0.701805i	$0.247622\pi$
$110$		0			0
$111$	−0.992554			−0.0942091
$112$		0			0
$113$	−0.945705			−0.0889644			−0.0444822	−	0.999010i	$-0.514164\pi$
$113$	−0.945705			−0.0889644			−0.0444822	+	0.999010i	$0.514164\pi$
$114$		0			0
$115$	1.12582	−	1.94998i	0.104983	−	0.181837i
$116$		0			0
$117$	1.61118	+	2.79064i	0.148953	+	0.257995i
$118$		0			0
$119$	2.93631	−	3.07410i	0.269171	−	0.281802i
$120$		0			0
$121$	4.34889	+	7.53250i	0.395354	+	0.684773i
$122$		0			0
$123$	−0.154058	+	0.266837i	−0.0138910	+	0.0240599i
$124$		0			0
$125$	−2.96513			−0.265210
$126$		0			0
$127$	11.5966			1.02903			0.514517	−	0.857480i	$-0.327971\pi$
$127$	11.5966			1.02903			0.514517	+	0.857480i	$0.327971\pi$
$128$		0			0
$129$	1.47482	−	2.55447i	0.129851	−	0.224909i
$130$		0			0
$131$	4.00973	+	6.94506i	0.350332	+	0.606793i	0.986308	−	0.164916i	$-0.0527354\pi$
$131$	4.00973	+	6.94506i	0.350332	+	0.606793i	−0.635976	+	0.771709i	$0.719402\pi$
$132$		0			0
$133$	0.654368	+	2.23584i	0.0567409	+	0.193872i
$134$		0			0
$135$	−3.00322	−	5.20173i	−0.258476	−	0.447694i
$136$		0			0
$137$	0.408613	−	0.707739i	0.0349102	−	0.0604662i	−0.848042	−	0.529928i	$-0.822219\pi$
$137$	0.408613	−	0.707739i	0.0349102	−	0.0604662i	0.882953	+	0.469462i	$0.155552\pi$
$138$		0			0
$139$	2.61528			0.221825			0.110912	−	0.993830i	$-0.464623\pi$
$139$	2.61528			0.221825			0.110912	+	0.993830i	$0.464623\pi$
$140$		0			0
$141$	1.47462			0.124186
$142$		0			0
$143$	−0.841512	+	1.45754i	−0.0703708	+	0.121886i
$144$		0			0
$145$	−3.10729	−	5.38199i	−0.258047	−	0.446950i
$146$		0			0
$147$	−1.81648	+	1.16287i	−0.149821	+	0.0959120i
$148$		0			0
$149$	8.00914	+	13.8722i	0.656134	+	1.13646i	0.981608	+	0.190907i	$0.0611428\pi$
$149$	8.00914	+	13.8722i	0.656134	+	1.13646i	−0.325474	+	0.945551i	$0.605524\pi$
$150$		0			0
$151$	4.83913	−	8.38161i	0.393802	−	0.682086i	−0.599145	−	0.800640i	$-0.704493\pi$
$151$	4.83913	−	8.38161i	0.393802	−	0.682086i	0.992948	+	0.118555i	$0.0378261\pi$
$152$		0			0
$153$	−4.66777			−0.377367
$154$		0			0
$155$	−15.5623			−1.25000
$156$		0			0
$157$	−4.39030	+	7.60422i	−0.350384	+	0.606883i	−0.986317	−	0.164862i	$-0.947282\pi$
$157$	−4.39030	+	7.60422i	−0.350384	+	0.606883i	0.635933	+	0.771744i	$0.280616\pi$
$158$		0			0
$159$	0.251450	+	0.435524i	0.0199413	+	0.0345393i
$160$		0			0
$161$	0.506881	+	1.73191i	0.0399478	+	0.136494i
$162$		0			0
$163$	5.79843	+	10.0432i	0.454168	+	0.786642i	0.998640	−	0.0521373i	$-0.0166034\pi$
$163$	5.79843	+	10.0432i	0.454168	+	0.786642i	−0.544472	+	0.838779i	$0.683270\pi$
$164$		0			0
$165$	0.771678	−	1.33658i	0.0600750	−	0.104053i
$166$		0			0
$167$	−3.23013			−0.249955			−0.124977	−	0.992160i	$-0.539886\pi$
$167$	−3.23013			−0.249955			−0.124977	+	0.992160i	$0.539886\pi$
$168$		0			0
$169$	−11.7696			−0.905356
$170$		0			0
$171$	1.27898	−	2.21526i	0.0978061	−	0.169405i
$172$		0			0
$173$	−4.92864	−	8.53666i	−0.374718	−	0.649030i	0.615567	−	0.788085i	$-0.288927\pi$
$173$	−4.92864	−	8.53666i	−0.374718	−	0.649030i	−0.990285	+	0.139054i	$0.955594\pi$
$174$		0			0
$175$	10.7787	−	11.2845i	0.814793	−	0.853028i
$176$		0			0
$177$	−0.155606	−	0.269518i	−0.0116961	−	0.0202582i
$178$		0			0
$179$	10.0473	−	17.4024i	0.750967	−	1.30071i	−0.196387	−	0.980526i	$-0.562921\pi$
$179$	10.0473	−	17.4024i	0.750967	−	1.30071i	0.947354	−	0.320187i	$-0.103746\pi$
$180$		0			0
$181$	3.60880			0.268240			0.134120	−	0.990965i	$-0.457179\pi$
$181$	3.60880			0.268240			0.134120	+	0.990965i	$0.457179\pi$
$182$		0			0
$183$	−0.117291			−0.00867042
$184$		0			0
$185$	−5.31723	+	9.20972i	−0.390931	+	0.677112i
$186$		0			0
$187$	−1.21898	−	2.11134i	−0.0891408	−	0.154396i
$188$		0			0
$189$	4.67712	+	1.13901i	0.340210	+	0.0828509i
$190$		0			0
$191$	9.77093	+	16.9238i	0.707000	+	1.22456i	0.965965	+	0.258673i	$0.0832853\pi$
$191$	9.77093	+	16.9238i	0.707000	+	1.22456i	−0.258965	+	0.965887i	$0.583381\pi$
$192$		0			0
$193$	13.4820	−	23.3516i	0.970459	−	1.68088i	0.276287	−	0.961075i	$-0.410896\pi$
$193$	13.4820	−	23.3516i	0.970459	−	1.68088i	0.694172	−	0.719809i	$-0.255771\pi$
$194$		0			0
$195$	−1.12826			−0.0807965
$196$		0			0
$197$	10.5882			0.754381			0.377191	−	0.926136i	$-0.376890\pi$
$197$	10.5882			0.754381			0.377191	+	0.926136i	$0.376890\pi$
$198$		0			0
$199$	9.92789	−	17.1956i	0.703770	−	1.21896i	−0.263364	−	0.964696i	$-0.584832\pi$
$199$	9.92789	−	17.1956i	0.703770	−	1.21896i	0.967134	−	0.254268i	$-0.0818346\pi$
$200$		0			0
$201$	−1.30749	−	2.26464i	−0.0922234	−	0.159736i
$202$		0			0
$203$	4.83920	+	1.17848i	0.339645	+	0.0827133i
$204$		0			0
$205$	1.65062	+	2.85896i	0.115284	+	0.199678i
$206$		0			0
$207$	0.990714	−	1.71597i	0.0688594	−	0.119268i
$208$		0			0
$209$	1.33602			0.0924142
$210$		0			0
$211$	9.05365			0.623279			0.311639	−	0.950200i	$-0.399122\pi$
$211$	9.05365			0.623279			0.311639	+	0.950200i	$0.399122\pi$
$212$		0			0
$213$	−1.21850	+	2.11051i	−0.0834906	+	0.144610i
$214$		0			0
$215$	−15.8016	−	27.3692i	−1.07766	−	1.86657i
$216$		0			0
$217$	8.61480	−	9.01906i	0.584811	−	0.612253i
$218$		0			0
$219$	−0.241041	−	0.417495i	−0.0162880	−	0.0282117i
$220$		0			0
$221$	−0.891130	+	1.54348i	−0.0599439	+	0.103826i
$222$		0			0
$223$	−11.4325			−0.765580			−0.382790	−	0.923835i	$-0.625037\pi$
$223$	−11.4325			−0.765580			−0.382790	+	0.923835i	$0.625037\pi$
$224$		0			0
$225$	−17.1346			−1.14231
$226$		0			0
$227$	10.6489	−	18.4444i	0.706792	−	1.22420i	−0.259249	−	0.965811i	$-0.583475\pi$
$227$	10.6489	−	18.4444i	0.706792	−	1.22420i	0.966041	−	0.258389i	$-0.0831918\pi$
$228$		0			0
$229$	10.5563	+	18.2841i	0.697583	+	1.20825i	0.969302	+	0.245873i	$0.0790745\pi$
$229$	10.5563	+	18.2841i	0.697583	+	1.20825i	−0.271719	+	0.962377i	$0.587592\pi$
$230$		0			0
$231$	0.347434	+	1.18711i	0.0228595	+	0.0781062i
$232$		0			0
$233$	−11.3391	−	19.6399i	−0.742849	−	1.28665i	−0.951193	−	0.308597i	$-0.900141\pi$
$233$	−11.3391	−	19.6399i	−0.742849	−	1.28665i	0.208344	−	0.978056i	$-0.433193\pi$
$234$		0			0
$235$	7.89973	−	13.6827i	0.515322	−	0.892563i
$236$		0			0
$237$	−2.59271			−0.168415
$238$		0			0
$239$	17.7226			1.14638			0.573191	−	0.819422i	$-0.305705\pi$
$239$	17.7226			1.14638			0.573191	+	0.819422i	$0.305705\pi$
$240$		0			0
$241$	10.0857	−	17.4689i	0.649675	−	1.12527i	−0.333526	−	0.942741i	$-0.608238\pi$
$241$	10.0857	−	17.4689i	0.649675	−	1.12527i	0.983200	−	0.182529i	$-0.0584283\pi$
$242$		0			0
$243$	−3.98546	−	6.90302i	−0.255667	−	0.442829i
$244$		0			0
$245$	1.05896	+	23.0844i	0.0676547	+	1.47481i
$246$		0			0
$247$	−0.488344	−	0.845836i	−0.0310726	−	0.0538193i
$248$		0			0
$249$	−0.239401	+	0.414655i	−0.0151714	+	0.0262777i
$250$		0			0
$251$	−16.5113			−1.04219			−0.521093	−	0.853500i	$-0.674476\pi$
$251$	−16.5113			−1.04219			−0.521093	+	0.853500i	$0.674476\pi$
$252$		0			0
$253$	1.03489			0.0650632
$254$		0			0
$255$	0.817178	−	1.41539i	0.0511736	−	0.0886354i
$256$		0			0
$257$	−8.56844	−	14.8410i	−0.534485	−	0.925755i	−0.999188	−	0.0402885i	$-0.987172\pi$
$257$	−8.56844	−	14.8410i	−0.534485	−	0.925755i	0.464703	−	0.885467i	$-0.346161\pi$
$258$		0			0
$259$	−2.39399	−	8.17978i	−0.148755	−	0.508267i
$260$		0			0
$261$	−2.73439	−	4.73611i	−0.169255	−	0.293158i
$262$		0			0
$263$	8.62215	−	14.9340i	0.531665	−	0.920870i	−0.467652	−	0.883913i	$-0.654900\pi$
$263$	8.62215	−	14.9340i	0.531665	−	0.920870i	0.999317	−	0.0369575i	$-0.0117666\pi$
$264$		0			0
$265$	5.38819			0.330994
$266$		0			0
$267$	4.28947			0.262511
$268$		0			0
$269$	7.25363	−	12.5637i	0.442262	−	0.766020i	−0.555595	−	0.831453i	$-0.687510\pi$
$269$	7.25363	−	12.5637i	0.442262	−	0.766020i	0.997857	+	0.0654330i	$0.0208429\pi$
$270$		0			0
$271$	11.9390	+	20.6789i	0.725240	+	1.25615i	0.958875	+	0.283829i	$0.0916047\pi$
$271$	11.9390	+	20.6789i	0.725240	+	1.25615i	−0.233635	+	0.972324i	$0.575062\pi$
$272$		0			0
$273$	0.624569	−	0.653877i	0.0378007	−	0.0395745i
$274$		0			0
$275$	−4.47468	−	7.75037i	−0.269833	−	0.467365i
$276$		0			0
$277$	7.81755	−	13.5404i	0.469711	−	0.813563i	−0.529689	−	0.848192i	$-0.677691\pi$
$277$	7.81755	−	13.5404i	0.469711	−	0.813563i	0.999400	+	0.0346285i	$0.0110248\pi$
$278$		0			0
$279$	−13.6947			−0.819881
$280$		0			0
$281$	5.17005			0.308419			0.154210	−	0.988038i	$-0.450717\pi$
$281$	5.17005			0.308419			0.154210	+	0.988038i	$0.450717\pi$
$282$		0			0
$283$	5.03055	−	8.71317i	0.299035	−	0.517944i	−0.676880	−	0.736093i	$-0.736668\pi$
$283$	5.03055	−	8.71317i	0.299035	−	0.517944i	0.975916	+	0.218149i	$0.0700018\pi$
$284$		0			0
$285$	0.447817	+	0.775643i	0.0265264	+	0.0459451i
$286$		0			0
$287$	−2.57062	−	0.626020i	−0.151739	−	0.0369528i
$288$		0			0
$289$	7.20914	+	12.4866i	0.424067	+	0.734506i
$290$		0			0
$291$	−0.0925954	+	0.160380i	−0.00542804	+	0.00940164i
$292$		0			0
$293$	−9.32341			−0.544680			−0.272340	−	0.962201i	$-0.587797\pi$
$293$	−9.32341			−0.544680			−0.272340	+	0.962201i	$0.587797\pi$
$294$		0			0
$295$	−3.33441			−0.194137
$296$		0			0
$297$	1.38033	−	2.39080i	0.0800950	−	0.138729i
$298$		0			0
$299$	−0.378277	−	0.655195i	−0.0218763	−	0.0378909i
$300$		0			0
$301$	24.6089	+	5.99298i	1.41844	+	0.345430i
$302$		0			0
$303$	−0.584532	−	1.01244i	−0.0335805	−	0.0581631i
$304$		0			0
$305$	−0.628344	+	1.08832i	−0.0359789	+	0.0623172i
$306$		0			0
$307$	−10.3822			−0.592544			−0.296272	−	0.955104i	$-0.595743\pi$
$307$	−10.3822			−0.592544			−0.296272	+	0.955104i	$0.595743\pi$
$308$		0			0
$309$	0.160224			0.00911480
$310$		0			0
$311$	−15.8767	+	27.4992i	−0.900284	+	1.55934i	−0.0731596	+	0.997320i	$0.523308\pi$
$311$	−15.8767	+	27.4992i	−0.900284	+	1.55934i	−0.827125	+	0.562018i	$0.810025\pi$
$312$		0			0
$313$	12.2599	+	21.2348i	0.692971	+	1.20026i	0.970860	+	0.239647i	$0.0770319\pi$
$313$	12.2599	+	21.2348i	0.692971	+	1.20026i	−0.277889	+	0.960613i	$0.589635\pi$
$314$		0			0
$315$	17.5259	−	18.3483i	0.987474	−	1.03381i
$316$		0			0
$317$	3.94727	+	6.83687i	0.221701	+	0.383997i	0.955325	−	0.295559i	$-0.0955058\pi$
$317$	3.94727	+	6.83687i	0.221701	+	0.383997i	−0.733624	+	0.679556i	$0.762173\pi$
$318$		0			0
$319$	1.42816	−	2.47365i	0.0799619	−	0.138498i
$320$		0			0
$321$	−2.88206			−0.160861
$322$		0			0
$323$	1.41479			0.0787211
$324$		0			0
$325$	−3.27119	+	5.66587i	−0.181453	+	0.314286i
$326$		0			0
$327$	−0.809342	−	1.40182i	−0.0447567	−	0.0775209i
$328$		0			0
$329$	3.55671	+	12.1526i	0.196088	+	0.669992i
$330$		0			0
$331$	7.06349	+	12.2343i	0.388244	+	0.672459i	0.992213	−	0.124549i	$-0.0397484\pi$
$331$	7.06349	+	12.2343i	0.388244	+	0.672459i	−0.603969	+	0.797008i	$0.706415\pi$
$332$		0			0
$333$	−4.67912	+	8.10448i	−0.256414	+	0.444123i
$334$		0			0
$335$	−28.0176			−1.53076
$336$		0			0
$337$	16.5644			0.902319			0.451160	−	0.892443i	$-0.351011\pi$
$337$	16.5644			0.902319			0.451160	+	0.892443i	$0.351011\pi$
$338$		0			0
$339$	0.145694	−	0.252349i	0.00791300	−	0.0137057i
$340$		0			0
$341$	−3.57636	−	6.19443i	−0.193671	−	0.335447i
$342$		0			0
$343$	−13.9646	−	12.1651i	−0.754020	−	0.656852i
$344$		0			0
$345$	0.346885	+	0.600822i	0.0186756	+	0.0323472i
$346$		0			0
$347$	6.55077	−	11.3463i	0.351664	−	0.609100i	−0.634877	−	0.772613i	$-0.718949\pi$
$347$	6.55077	−	11.3463i	0.351664	−	0.609100i	0.986541	+	0.163513i	$0.0522827\pi$
$348$		0			0
$349$	22.0563			1.18065			0.590324	−	0.807167i	$-0.299000\pi$
$349$	22.0563			1.18065			0.590324	+	0.807167i	$0.299000\pi$
$350$		0			0
$351$	−2.01817			−0.107722
$352$		0			0
$353$	−10.3016	+	17.8429i	−0.548298	+	0.949680i	0.450094	+	0.892981i	$0.351391\pi$
$353$	−10.3016	+	17.8429i	−0.548298	+	0.949680i	−0.998391	+	0.0566982i	$0.981943\pi$
$354$		0			0
$355$	13.0554	+	22.6125i	0.692907	+	1.20015i
$356$		0			0
$357$	0.367919	+	1.25711i	0.0194724	+	0.0665331i
$358$		0			0
$359$	7.59149	+	13.1489i	0.400664	+	0.693970i	0.993806	−	0.111128i	$-0.0354462\pi$
$359$	7.59149	+	13.1489i	0.400664	+	0.693970i	−0.593142	+	0.805098i	$0.702113\pi$
$360$		0			0
$361$	9.11234	−	15.7830i	0.479597	−	0.830686i
$362$		0			0
$363$	−2.67993			−0.140660
$364$		0			0
$365$	−5.16515			−0.270356
$366$		0			0
$367$	−0.514154	+	0.890542i	−0.0268386	+	0.0464859i	−0.879133	−	0.476577i	$-0.841877\pi$
$367$	−0.514154	+	0.890542i	−0.0268386	+	0.0464859i	0.852294	+	0.523063i	$0.175211\pi$
$368$		0			0
$369$	1.45253	+	2.51586i	0.0756158	+	0.130970i
$370$		0			0
$371$	−2.98273	+	3.12269i	−0.154856	+	0.162122i
$372$		0			0
$373$	12.5362	+	21.7133i	0.649098	+	1.12427i	0.983339	+	0.181784i	$0.0581870\pi$
$373$	12.5362	+	21.7133i	0.649098	+	1.12427i	−0.334240	+	0.942488i	$0.608480\pi$
$374$		0			0
$375$	0.456804	−	0.791207i	0.0235892	−	0.0408578i
$376$		0			0
$377$	−2.08810			−0.107543
$378$		0			0
$379$	7.20297			0.369992			0.184996	−	0.982739i	$-0.440773\pi$
$379$	7.20297			0.369992			0.184996	+	0.982739i	$0.440773\pi$
$380$		0			0
$381$	−1.78656	+	3.09441i	−0.0915281	+	0.158531i
$382$		0			0
$383$	5.49408	+	9.51602i	0.280734	+	0.486246i	0.971566	−	0.236770i	$-0.0760887\pi$
$383$	5.49408	+	9.51602i	0.280734	+	0.486246i	−0.690831	+	0.723016i	$0.742755\pi$
$384$		0			0
$385$	12.8762	+	3.13573i	0.656233	+	0.159812i
$386$		0			0
$387$	−13.9053	−	24.0847i	−0.706846	−	1.22429i
$388$		0			0
$389$	−3.41410	+	5.91339i	−0.173102	+	0.299821i	−0.939503	−	0.342542i	$-0.888712\pi$
$389$	−3.41410	+	5.91339i	−0.173102	+	0.299821i	0.766401	+	0.642362i	$0.222046\pi$
$390$		0			0
$391$	1.09591			0.0554227
$392$		0			0
$393$	−2.47093			−0.124642
$394$		0			0
$395$	−13.8895	+	24.0573i	−0.698855	+	1.21045i
$396$		0			0
$397$	−0.912292	−	1.58014i	−0.0457866	−	0.0793048i	0.842224	−	0.539128i	$-0.181246\pi$
$397$	−0.912292	−	1.58014i	−0.0457866	−	0.0793048i	−0.888010	+	0.459823i	$0.847913\pi$
$398$		0			0
$399$	−0.697416	−	0.169841i	−0.0349145	−	0.00850268i
$400$		0			0
$401$	−0.255005	−	0.441682i	−0.0127344	−	0.0220566i	0.859588	−	0.510988i	$-0.170720\pi$
$401$	−0.255005	−	0.441682i	−0.0127344	−	0.0220566i	−0.872322	+	0.488931i	$0.837387\pi$
$402$		0			0
$403$	−2.61448	+	4.52841i	−0.130236	+	0.225576i
$404$		0			0
$405$	−26.9203			−1.33768
$406$		0			0
$407$	−4.88778			−0.242278
$408$		0			0
$409$	−11.7233	+	20.3054i	−0.579681	+	1.00404i	0.415835	+	0.909440i	$0.363490\pi$
$409$	−11.7233	+	20.3054i	−0.579681	+	1.00404i	−0.995516	+	0.0945969i	$0.969844\pi$
$410$		0			0
$411$	0.125901	+	0.218066i	0.00621022	+	0.0107564i
$412$		0			0
$413$	1.84582	−	1.93244i	0.0908270	−	0.0950890i
$414$		0			0
$415$	2.56500	+	4.44272i	0.125911	+	0.218084i
$416$		0			0
$417$	−0.402906	+	0.697853i	−0.0197304	+	0.0341740i
$418$		0			0
$419$	−38.8743			−1.89913			−0.949566	−	0.313567i	$-0.898476\pi$
$419$	−38.8743			−1.89913			−0.949566	+	0.313567i	$0.898476\pi$
$420$		0			0
$421$	3.62394			0.176620			0.0883101	−	0.996093i	$-0.471853\pi$
$421$	3.62394			0.176620			0.0883101	+	0.996093i	$0.471853\pi$
$422$		0			0
$423$	6.95170	−	12.0407i	0.338003	−	0.585438i
$424$		0			0
$425$	−4.73852	−	8.20735i	−0.229852	−	0.398115i
$426$		0			0
$427$	−0.282901	−	0.966614i	−0.0136905	−	0.0467777i
$428$		0			0
$429$	−0.259284	−	0.449093i	−0.0125184	−	0.0216824i
$430$		0			0
$431$	4.18897	−	7.25551i	0.201776	−	0.349486i	−0.747325	−	0.664459i	$-0.768662\pi$
$431$	4.18897	−	7.25551i	0.201776	−	0.349486i	0.949101	+	0.314973i	$0.101995\pi$
$432$		0			0
$433$	−5.27478			−0.253490			−0.126745	−	0.991935i	$-0.540453\pi$
$433$	−5.27478			−0.253490			−0.126745	+	0.991935i	$0.540453\pi$
$434$		0			0
$435$	1.91482			0.0918085
$436$		0			0
$437$	−0.300283	+	0.520106i	−0.0143645	+	0.0248800i
$438$		0			0
$439$	−14.2851	−	24.7425i	−0.681790	−	1.18090i	−0.974434	−	0.224674i	$-0.927868\pi$
$439$	−14.2851	−	24.7425i	−0.681790	−	1.18090i	0.292644	−	0.956221i	$-0.405465\pi$
$440$		0			0
$441$	0.931879	+	20.3141i	0.0443752	+	0.967337i
$442$		0			0
$443$	6.16550	+	10.6790i	0.292932	+	0.507372i	0.974502	−	0.224380i	$-0.0720358\pi$
$443$	6.16550	+	10.6790i	0.292932	+	0.507372i	−0.681570	+	0.731753i	$0.738702\pi$
$444$		0			0
$445$	22.9792	−	39.8011i	1.08932	−	1.88676i
$446$		0			0
$447$	−4.93550			−0.233441
$448$		0			0
$449$	−36.7971			−1.73656			−0.868280	−	0.496074i	$-0.834775\pi$
$449$	−36.7971			−1.73656			−0.868280	+	0.496074i	$0.834775\pi$
$450$		0			0
$451$	−0.758653	+	1.31403i	−0.0357236	+	0.0618751i
$452$		0			0
$453$	1.49102	+	2.58252i	0.0700541	+	0.121337i
$454$		0			0
$455$	−2.72131	−	9.29816i	−0.127577	−	0.435905i
$456$		0			0
$457$	−2.23189	−	3.86575i	−0.104404	−	0.180832i	0.809091	−	0.587684i	$-0.199960\pi$
$457$	−2.23189	−	3.86575i	−0.104404	−	0.180832i	−0.913494	+	0.406851i	$0.866627\pi$
$458$		0			0
$459$	1.46172	−	2.53177i	0.0682272	−	0.118173i
$460$		0			0
$461$	10.8591			0.505757			0.252878	−	0.967498i	$-0.418623\pi$
$461$	10.8591			0.505757			0.252878	+	0.967498i	$0.418623\pi$
$462$		0			0
$463$	17.7680			0.825747			0.412874	−	0.910788i	$-0.364525\pi$
$463$	17.7680			0.825747			0.412874	+	0.910788i	$0.364525\pi$
$464$		0			0
$465$	2.39751	−	4.15261i	0.111182	−	0.192573i
$466$		0			0
$467$	1.82658	+	3.16373i	0.0845242	+	0.146400i	0.905188	−	0.425011i	$-0.139730\pi$
$467$	1.82658	+	3.16373i	0.0845242	+	0.146400i	−0.820664	+	0.571411i	$0.806396\pi$
$468$		0			0
$469$	15.5096	−	16.2374i	0.716169	−	0.749775i
$470$		0			0
$471$	−1.35273	−	2.34299i	−0.0623303	−	0.107959i
$472$		0			0
$473$	7.26270	−	12.5794i	0.333939	−	0.578400i
$474$		0			0
$475$	5.19346			0.238292
$476$		0			0
$477$	4.74156			0.217101
$478$		0			0
$479$	−0.922793	+	1.59833i	−0.0421635	+	0.0730293i	−0.886337	−	0.463041i	$-0.846758\pi$
$479$	−0.922793	+	1.59833i	−0.0421635	+	0.0730293i	0.844174	+	0.536070i	$0.180092\pi$
$480$		0			0
$481$	1.78659	+	3.09447i	0.0814617	+	0.141096i
$482$		0			0
$483$	−0.540227	−	0.131561i	−0.0245812	−	0.00598622i
$484$		0			0
$485$	0.992090	+	1.71835i	0.0450485	+	0.0780263i
$486$		0			0
$487$	−3.49011	+	6.04504i	−0.158152	+	0.273927i	−0.934202	−	0.356744i	$-0.883887\pi$
$487$	−3.49011	+	6.04504i	−0.158152	+	0.273927i	0.776050	+	0.630671i	$0.217220\pi$
$488$		0			0
$489$	−3.57319			−0.161585
$490$		0			0
$491$	4.53099			0.204481			0.102240	−	0.994760i	$-0.467399\pi$
$491$	4.53099			0.204481			0.102240	+	0.994760i	$0.467399\pi$
$492$		0			0
$493$	1.51237	−	2.61951i	0.0681138	−	0.117977i
$494$		0			0
$495$	−7.27572	−	12.6019i	−0.327019	−	0.566414i
$496$		0			0
$497$	−20.3320	−	4.95142i	−0.912015	−	0.222102i
$498$		0			0
$499$	−14.4006	−	24.9425i	−0.644659	−	1.11658i	−0.984380	−	0.176055i	$-0.943666\pi$
$499$	−14.4006	−	24.9425i	−0.644659	−	1.11658i	0.339722	−	0.940526i	$-0.389667\pi$
$500$		0			0
$501$	0.497629	−	0.861918i	0.0222324	−	0.0385077i
$502$		0			0
$503$	−12.0511			−0.537330			−0.268665	−	0.963234i	$-0.586583\pi$
$503$	−12.0511			−0.537330			−0.268665	+	0.963234i	$0.586583\pi$
$504$		0			0
$505$	−12.5256			−0.557384
$506$		0			0
$507$	1.81321	−	3.14057i	0.0805275	−	0.139478i
$508$		0			0
$509$	−7.63542	−	13.2249i	−0.338434	−	0.586185i	0.645704	−	0.763587i	$-0.276564\pi$
$509$	−7.63542	−	13.2249i	−0.338434	−	0.586185i	−0.984138	+	0.177403i	$0.943230\pi$
$510$		0			0
$511$	2.85926	−	2.99343i	0.126486	−	0.132422i
$512$		0			0
$513$	0.801029	+	1.38742i	0.0353663	+	0.0612562i
$514$		0			0
$515$	0.858338	−	1.48668i	0.0378229	−	0.0655112i
$516$		0			0
$517$	7.26170			0.319369
$518$		0			0
$519$	3.03720			0.133318
$520$		0			0
$521$	−11.0877	+	19.2045i	−0.485761	+	0.841363i	−0.999866	−	0.0163643i	$-0.994791\pi$
$521$	−11.0877	+	19.2045i	−0.485761	+	0.841363i	0.514105	+	0.857727i	$0.328124\pi$
$522$		0			0
$523$	17.0390	+	29.5123i	0.745062	+	1.29048i	0.950166	+	0.311745i	$0.100913\pi$
$523$	17.0390	+	29.5123i	0.745062	+	1.29048i	−0.205104	+	0.978740i	$0.565753\pi$
$524$		0			0
$525$	1.35057	+	4.61463i	0.0589438	+	0.201399i
$526$		0			0
$527$	−3.78723	−	6.55967i	−0.164974	−	0.285744i
$528$		0			0
$529$	11.2674	−	19.5157i	0.489887	−	0.848509i
$530$		0			0
$531$	−2.93425			−0.127336
$532$		0			0
$533$	1.10922			0.0480456
$534$		0			0
$535$	−15.4395	+	26.7420i	−0.667509	+	1.15616i
$536$		0			0
$537$	3.09573	+	5.36196i	0.133591	+	0.231386i
$538$		0			0
$539$	−8.94516	+	5.72650i	−0.385295	+	0.246658i
$540$		0			0
$541$	14.6876	+	25.4397i	0.631470	+	1.09374i	0.987251	+	0.159169i	$0.0508815\pi$
$541$	14.6876	+	25.4397i	0.631470	+	1.09374i	−0.355781	+	0.934569i	$0.615785\pi$
$542$		0			0
$543$	−0.555966	+	0.962962i	−0.0238588	+	0.0413246i
$544$		0			0
$545$	−17.3430			−0.742892
$546$		0			0
$547$	−4.60982			−0.197102			−0.0985509	−	0.995132i	$-0.531421\pi$
$547$	−4.60982			−0.197102			−0.0985509	+	0.995132i	$0.531421\pi$
$548$		0			0
$549$	−0.552938	+	0.957716i	−0.0235988	+	0.0408743i
$550$		0			0
$551$	0.828788	+	1.43550i	0.0353075	+	0.0611545i
$552$		0			0
$553$	−6.25348	−	21.3669i	−0.265925	−	0.908612i
$554$		0			0
$555$	−1.63833	−	2.83767i	−0.0695432	−	0.120452i
$556$		0			0
$557$	0.576847	−	0.999128i	0.0244418	−	0.0423344i	−0.853546	−	0.521018i	$-0.825552\pi$
$557$	0.576847	−	0.999128i	0.0244418	−	0.0423344i	0.877988	+	0.478683i	$0.158886\pi$
$558$		0			0
$559$	−10.6187			−0.449124
$560$		0			0
$561$	0.751178			0.0317147
$562$		0			0
$563$	0.326283	−	0.565138i	0.0137512	−	0.0238177i	−0.859068	−	0.511862i	$-0.828956\pi$
$563$	0.326283	−	0.565138i	0.0137512	−	0.0238177i	0.872819	+	0.488044i	$0.162289\pi$
$564$		0			0
$565$	−1.56100	−	2.70373i	−0.0656717	−	0.113747i
$566$		0			0
$567$	14.9022	−	15.6015i	0.625833	−	0.655200i
$568$		0			0
$569$	2.28233	+	3.95312i	0.0956804	+	0.165723i	0.909892	−	0.414844i	$-0.136164\pi$
$569$	2.28233	+	3.95312i	0.0956804	+	0.165723i	−0.814212	+	0.580568i	$0.802831\pi$
$570$		0			0
$571$	−16.3261	+	28.2776i	−0.683226	+	1.18338i	0.290765	+	0.956794i	$0.406090\pi$
$571$	−16.3261	+	28.2776i	−0.683226	+	1.18338i	−0.973991	+	0.226587i	$0.927243\pi$
$572$		0			0
$573$	−6.02118			−0.251538
$574$		0			0
$575$	4.02292			0.167767
$576$		0			0
$577$	7.97711	−	13.8168i	0.332091	−	0.575199i	−0.650830	−	0.759223i	$-0.725579\pi$
$577$	7.97711	−	13.8168i	0.332091	−	0.575199i	0.982922	+	0.184024i	$0.0589125\pi$
$578$		0			0
$579$	4.15405	+	7.19502i	0.172636	+	0.299015i
$580$		0			0
$581$	−3.99465	−	0.972812i	−0.165726	−	0.0403590i
$582$		0			0
$583$	1.23825	+	2.14472i	0.0512832	+	0.0888250i
$584$		0			0
$585$	−5.31888	+	9.21257i	−0.219909	+	0.380893i
$586$		0			0
$587$	7.90734			0.326371			0.163185	−	0.986595i	$-0.447823\pi$
$587$	7.90734			0.326371			0.163185	+	0.986595i	$0.447823\pi$
$588$		0			0
$589$	4.15084			0.171032
$590$		0			0
$591$	−1.63121	+	2.82534i	−0.0670990	+	0.116219i
$592$		0			0
$593$	−13.5960	−	23.5489i	−0.558320	−	0.967039i	−0.997637	−	0.0687069i	$-0.978113\pi$
$593$	−13.5960	−	23.5489i	−0.558320	−	0.967039i	0.439317	−	0.898332i	$-0.355221\pi$
$594$		0			0
$595$	13.6354	+	3.32062i	0.558999	+	0.136132i
$596$		0			0
$597$	3.05895	+	5.29826i	0.125195	+	0.216843i
$598$		0			0
$599$	−12.0440	+	20.8609i	−0.492105	+	0.852351i	−0.999959	−	0.00909221i	$-0.997106\pi$
$599$	−12.0440	+	20.8609i	−0.492105	+	0.852351i	0.507853	+	0.861444i	$0.330439\pi$
$600$		0			0
$601$	−13.6546			−0.556984			−0.278492	−	0.960439i	$-0.589835\pi$
$601$	−13.6546			−0.556984			−0.278492	+	0.960439i	$0.589835\pi$
$602$		0			0
$603$	−24.6552			−1.00404
$604$		0			0
$605$	−14.3567	+	24.8666i	−0.583684	+	1.01097i
$606$		0			0
$607$	−7.69501	−	13.3282i	−0.312331	−	0.540973i	0.666536	−	0.745473i	$-0.267776\pi$
$607$	−7.69501	−	13.3282i	−0.312331	−	0.540973i	−0.978867	+	0.204500i	$0.934443\pi$
$608$		0			0
$609$	−1.05998	+	1.10972i	−0.0429526	+	0.0449682i
$610$		0			0
$611$	−2.65431	−	4.59741i	−0.107382	−	0.185991i
$612$		0			0
$613$	−5.39436	+	9.34331i	−0.217876	+	0.377373i	−0.954159	−	0.299302i	$-0.903246\pi$
$613$	−5.39436	+	9.34331i	−0.217876	+	0.377373i	0.736282	+	0.676675i	$0.236580\pi$
$614$		0			0
$615$	−1.01717			−0.0410162
$616$		0			0
$617$	−26.2621			−1.05727			−0.528637	−	0.848848i	$-0.677297\pi$
$617$	−26.2621			−1.05727			−0.528637	+	0.848848i	$0.677297\pi$
$618$		0			0
$619$	−8.01284	+	13.8787i	−0.322063	+	0.557830i	−0.980914	−	0.194444i	$-0.937710\pi$
$619$	−8.01284	+	13.8787i	−0.322063	+	0.557830i	0.658850	+	0.752274i	$0.271043\pi$
$620$		0			0
$621$	0.620487	+	1.07471i	0.0248993	+	0.0431268i
$622$		0			0
$623$	10.3460	+	35.3501i	0.414503	+	1.41627i
$624$		0			0
$625$	9.85116	+	17.0627i	0.394046	+	0.682508i
$626$		0			0
$627$	−0.205825	+	0.356499i	−0.00821984	+	0.0142372i
$628$		0			0
$629$	−5.17598			−0.206380
$630$		0			0
$631$	−3.37257			−0.134260			−0.0671299	−	0.997744i	$-0.521384\pi$
$631$	−3.37257			−0.134260			−0.0671299	+	0.997744i	$0.521384\pi$
$632$		0			0
$633$	−1.39479	+	2.41585i	−0.0554379	+	0.0960213i
$634$		0			0
$635$	19.1416	+	33.1543i	0.759612	+	1.31569i
$636$		0			0
$637$	6.89512	+	3.57004i	0.273195	+	0.141450i
$638$		0			0
$639$	11.4886	+	19.8989i	0.454482	+	0.787187i
$640$		0			0
$641$	−17.7318	+	30.7124i	−0.700365	+	1.21307i	0.267973	+	0.963426i	$0.413646\pi$
$641$	−17.7318	+	30.7124i	−0.700365	+	1.21307i	−0.968338	+	0.249642i	$0.919687\pi$
$642$		0			0
$643$	30.4094			1.19923			0.599615	−	0.800288i	$-0.295320\pi$
$643$	30.4094			1.19923			0.599615	+	0.800288i	$0.295320\pi$
$644$		0			0
$645$	9.73750			0.383414
$646$		0			0
$647$	−15.2904	+	26.4837i	−0.601126	+	1.04118i	0.391524	+	0.920168i	$0.371948\pi$
$647$	−15.2904	+	26.4837i	−0.601126	+	1.04118i	−0.992651	+	0.121014i	$0.961385\pi$
$648$		0			0
$649$	−0.766276	−	1.32723i	−0.0300790	−	0.0520983i
$650$		0			0
$651$	1.07943	+	3.68821i	0.0423064	+	0.144552i
$652$		0			0
$653$	23.5832	+	40.8473i	0.922882	+	1.59848i	0.794933	+	0.606697i	$0.207506\pi$
$653$	23.5832	+	40.8473i	0.922882	+	1.59848i	0.127949	+	0.991781i	$0.459161\pi$
$654$		0			0
$655$	−13.2371	+	22.9273i	−0.517216	+	0.895844i
$656$		0			0
$657$	−4.54529			−0.177329
$658$		0			0
$659$	2.62840			0.102388			0.0511940	−	0.998689i	$-0.483697\pi$
$659$	2.62840			0.102388			0.0511940	+	0.998689i	$0.483697\pi$
$660$		0			0
$661$	−11.8567	+	20.5363i	−0.461171	+	0.798771i	−0.999020	−	0.0442702i	$-0.985904\pi$
$661$	−11.8567	+	20.5363i	−0.461171	+	0.798771i	0.537849	+	0.843041i	$0.319237\pi$
$662$		0			0
$663$	−0.274572	−	0.475573i	−0.0106635	−	0.0184697i
$664$		0			0
$665$	−5.31207	+	5.56134i	−0.205993	+	0.215659i
$666$		0			0
$667$	0.641989	+	1.11196i	0.0248579	+	0.0430552i
$668$		0			0
$669$	1.76128	−	3.05063i	0.0680950	−	0.117944i
$670$		0			0
$671$	−0.577595			−0.0222978
$672$		0			0
$673$	−22.4850			−0.866734			−0.433367	−	0.901218i	$-0.642675\pi$
$673$	−22.4850			−0.866734			−0.433367	+	0.901218i	$0.642675\pi$
$674$		0			0
$675$	5.36573	−	9.29371i	0.206527	−	0.357715i
$676$		0			0
$677$	−12.7416	−	22.0691i	−0.489699	−	0.848183i	0.510231	−	0.860037i	$-0.329560\pi$
$677$	−12.7416	−	22.0691i	−0.489699	−	0.848183i	−0.999930	+	0.0118544i	$0.996227\pi$
$678$		0			0
$679$	−1.54505	−	0.376264i	−0.0592935	−	0.0144397i
$680$		0			0
$681$	3.28111	+	5.68304i	0.125732	+	0.217775i
$682$		0			0
$683$	−5.03771	+	8.72556i	−0.192762	+	0.333874i	−0.946165	−	0.323686i	$-0.895078\pi$
$683$	−5.03771	+	8.72556i	−0.192762	+	0.333874i	0.753402	+	0.657560i	$0.228411\pi$
$684$		0			0
$685$	2.69786			0.103080
$686$		0			0
$687$	−6.50518			−0.248188
$688$		0			0
$689$	0.905217	−	1.56788i	0.0344860	−	0.0597316i
$690$		0			0
$691$	10.5034	+	18.1925i	0.399569	+	0.692074i	0.993673	−	0.112315i	$-0.0358265\pi$
$691$	10.5034	+	18.1925i	0.399569	+	0.692074i	−0.594104	+	0.804388i	$0.702493\pi$
$692$		0			0
$693$	11.3310	+	2.75942i	0.430428	+	0.104822i
$694$		0			0
$695$	4.31683	+	7.47697i	0.163747	+	0.283618i
$696$		0			0
$697$	−0.803385	+	1.39150i	−0.0304304	+	0.0527070i
$698$		0			0
$699$	6.98754			0.264293
$700$		0			0
$701$	48.8524			1.84513			0.922564	−	0.385844i	$-0.126090\pi$
$701$	48.8524			1.84513			0.922564	+	0.385844i	$0.126090\pi$
$702$		0			0
$703$	1.41823	−	2.45645i	0.0534896	−	0.0926467i
$704$		0			0
$705$	2.43404	+	4.21588i	0.0916712	+	0.158779i
$706$		0			0
$707$	6.93380	−	7.25917i	0.260772	−	0.273009i
$708$		0			0
$709$	−20.5357	−	35.5689i	−0.771234	−	1.33582i	−0.936887	−	0.349633i	$-0.886306\pi$
$709$	−20.5357	−	35.5689i	−0.771234	−	1.33582i	0.165652	−	0.986184i	$-0.447027\pi$
$710$		0			0
$711$	−12.2226	+	21.1702i	−0.458384	+	0.793944i
$712$		0			0
$713$	3.21529			0.120414
$714$		0			0
$715$	−5.55607			−0.207785
$716$		0			0
$717$	−2.73032	+	4.72906i	−0.101966	+	0.176610i
$718$		0			0
$719$	−17.5858	−	30.4596i	−0.655841	−	1.13595i	−0.981682	−	0.190525i	$-0.938981\pi$
$719$	−17.5858	−	30.4596i	−0.655841	−	1.13595i	0.325841	−	0.945424i	$-0.394352\pi$
$720$		0			0
$721$	0.386451	+	1.32043i	0.0143922	+	0.0491752i
$722$		0			0
$723$	3.10756	+	5.38246i	0.115572	+	0.200176i
$724$		0			0
$725$	5.55167	−	9.61577i	0.206184	−	0.357121i
$726$		0			0
$727$	−31.0287			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$727$	−31.0287			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$728$		0			0
$729$	−22.0078			−0.815103
$730$		0			0
$731$	7.69092	−	13.3211i	0.284459	−	0.492698i
$732$		0			0
$733$	−1.36053	−	2.35650i	−0.0502522	−	0.0870393i	0.839805	−	0.542888i	$-0.182669\pi$
$733$	−1.36053	−	2.35650i	−0.0502522	−	0.0870393i	−0.890057	+	0.455849i	$0.849336\pi$
$734$		0			0
$735$	−6.32292	−	3.27378i	−0.233224	−	0.120755i
$736$		0			0
$737$	−6.43868	−	11.1521i	−0.237172	−	0.410794i
$738$		0			0
$739$	−10.5210	+	18.2230i	−0.387022	+	0.670342i	−0.992048	−	0.125864i	$-0.959830\pi$
$739$	−10.5210	+	18.2230i	−0.387022	+	0.670342i	0.605025	+	0.796206i	$0.293163\pi$
$740$		0			0
$741$	0.300934			0.0110551
$742$		0			0
$743$	30.2470			1.10965			0.554827	−	0.831966i	$-0.312785\pi$
$743$	30.2470			1.10965			0.554827	+	0.831966i	$0.312785\pi$
$744$		0			0
$745$	−26.4401	+	45.7956i	−0.968690	+	1.67782i
$746$		0			0
$747$	2.25718	+	3.90955i	0.0825859	+	0.143043i
$748$		0			0
$749$	−6.95137	−	23.7514i	−0.253997	−	0.867858i
$750$		0			0
$751$	23.5426	+	40.7770i	0.859083	+	1.48798i	0.872805	+	0.488070i	$0.162299\pi$
$751$	23.5426	+	40.7770i	0.859083	+	1.48798i	−0.0137216	+	0.999906i	$0.504368\pi$
$752$		0			0
$753$	2.54371	−	4.40584i	0.0926980	−	0.160558i
$754$		0			0
$755$	31.9502			1.16279
$756$		0			0
$757$	−20.1878			−0.733738			−0.366869	−	0.930273i	$-0.619570\pi$
$757$	−20.1878			−0.733738			−0.366869	+	0.930273i	$0.619570\pi$
$758$		0			0
$759$	−0.159434	+	0.276148i	−0.00578709	+	0.0100235i
$760$		0			0
$761$	−25.6088	−	44.3558i	−0.928320	−	1.60790i	−0.786133	−	0.618057i	$-0.787920\pi$
$761$	−25.6088	−	44.3558i	−0.928320	−	1.60790i	−0.142187	−	0.989840i	$-0.545413\pi$
$762$		0			0
$763$	9.60052	−	10.0510i	0.347562	−	0.363871i
$764$		0			0
$765$	−7.70472	−	13.3450i	−0.278565	−	0.482488i
$766$		0			0
$767$	−0.560182	+	0.970263i	−0.0202270	+	0.0350342i
$768$		0			0
$769$	0.804472			0.0290100			0.0145050	−	0.999895i	$-0.495383\pi$
$769$	0.804472			0.0290100			0.0145050	+	0.999895i	$0.495383\pi$
$770$		0			0
$771$	5.28017			0.190160
$772$		0			0
$773$	20.0054	−	34.6503i	0.719543	−	1.24628i	−0.241638	−	0.970366i	$-0.577685\pi$
$773$	20.0054	−	34.6503i	0.719543	−	1.24628i	0.961181	−	0.275919i	$-0.0889820\pi$
$774$		0			0
$775$	−13.9023	−	24.0795i	−0.499385	−	0.864960i
$776$		0			0
$777$	2.55148	+	0.621359i	0.0915339	+	0.0222911i
$778$		0			0
$779$	−0.440259	−	0.762551i	−0.0157739	−	0.0273212i
$780$		0			0
$781$	−6.00047	+	10.3931i	−0.214714	+	0.371895i
$782$		0			0
$783$	3.42511			0.122404
$784$		0			0
$785$	−28.9869			−1.03459
$786$		0			0
$787$	22.5922	−	39.1309i	0.805326	−	1.39487i	−0.110745	−	0.993849i	$-0.535324\pi$
$787$	22.5922	−	39.1309i	0.805326	−	1.39487i	0.916071	−	0.401016i	$-0.131343\pi$
$788$		0			0
$789$	2.65663	+	4.60142i	0.0945785	+	0.163815i
$790$		0			0
$791$	2.43105	+	0.592030i	0.0864382	+	0.0210502i
$792$		0			0
$793$	0.211124	+	0.365677i	0.00749723	+	0.0129856i
$794$		0			0
$795$	−0.830096	+	1.43777i	−0.0294405	+	0.0509924i
$796$		0			0
$797$	42.7382			1.51386			0.756932	−	0.653494i	$-0.226697\pi$
$797$	42.7382			1.51386			0.756932	+	0.653494i	$0.226697\pi$
$798$		0			0
$799$	7.68987			0.272048
$800$		0			0
$801$	20.2215	−	35.0247i	0.714492	−	1.23754i
$802$		0			0
$803$	−1.18699	−	2.05594i	−0.0418881	−	0.0725524i
$804$		0			0
$805$	−4.11479	+	4.30788i	−0.145027	+	0.151833i
$806$		0			0
$807$	2.23497	+	3.87108i	0.0786746	+	0.136268i
$808$		0			0
$809$	−6.50819	+	11.2725i	−0.228816	+	0.396321i	−0.957457	−	0.288575i	$-0.906819\pi$
$809$	−6.50819	+	11.2725i	−0.228816	+	0.396321i	0.728642	+	0.684895i	$0.240152\pi$
$810$		0			0
$811$	−21.9400			−0.770418			−0.385209	−	0.922829i	$-0.625871\pi$
$811$	−21.9400			−0.770418			−0.385209	+	0.922829i	$0.625871\pi$
$812$		0			0
$813$	−7.35719			−0.258028
$814$		0			0
$815$	−19.1420	+	33.1549i	−0.670515	+	1.16137i
$816$		0			0
$817$	4.21466	+	7.30001i	0.147452	+	0.255395i
$818$		0			0
$819$	−2.39473	−	8.18230i	−0.0836786	−	0.285913i
$820$		0			0
$821$	13.7541	+	23.8227i	0.480020	+	0.831419i	0.999737	−	0.0229191i	$-0.00729603\pi$
$821$	13.7541	+	23.8227i	0.480020	+	0.831419i	−0.519717	+	0.854338i	$0.673963\pi$
$822$		0			0
$823$	14.9484	−	25.8914i	0.521068	−	0.902516i	−0.478632	−	0.878016i	$-0.658867\pi$
$823$	14.9484	−	25.8914i	0.521068	−	0.902516i	0.999700	−	0.0245003i	$-0.00779946\pi$
$824$		0			0
$825$	2.75745			0.0960020
$826$		0			0
$827$	8.18193			0.284513			0.142257	−	0.989830i	$-0.454564\pi$
$827$	8.18193			0.284513			0.142257	+	0.989830i	$0.454564\pi$
$828$		0			0
$829$	28.1775	−	48.8048i	0.978643	−	1.69506i	0.311297	−	0.950313i	$-0.399237\pi$
$829$	28.1775	−	48.8048i	0.978643	−	1.69506i	0.667346	−	0.744747i	$-0.267430\pi$
$830$		0			0
$831$	2.40872	+	4.17202i	0.0835575	+	0.144726i
$832$		0			0
$833$	−9.47259	+	6.06415i	−0.328206	+	0.210110i
$834$		0			0
$835$	−5.33172	−	9.23480i	−0.184512	−	0.319583i
$836$		0			0
$837$	4.28852	−	7.42794i	0.148233	−	0.256747i
$838$		0			0
$839$	26.0609			0.899724			0.449862	−	0.893098i	$-0.351473\pi$
$839$	26.0609			0.899724			0.449862	+	0.893098i	$0.351473\pi$
$840$		0			0
$841$	−25.4562			−0.877800
$842$		0			0
$843$	−0.796490	+	1.37956i	−0.0274326	+	0.0475146i
$844$		0			0
$845$	−19.4272	−	33.6489i	−0.668316	−	1.15756i
$846$		0			0
$847$	−6.46386	−	22.0857i	−0.222101	−	0.758874i
$848$		0			0
$849$	1.55000	+	2.68468i	0.0531958	+	0.0921378i
$850$		0			0
$851$	1.09858	−	1.90279i	0.0376588	−	0.0652269i
$852$		0			0
$853$	34.0375			1.16542			0.582712	−	0.812679i	$-0.301992\pi$
$853$	34.0375			1.16542			0.582712	+	0.812679i	$0.301992\pi$
$854$		0			0
$855$	8.44445			0.288794
$856$		0			0
$857$	20.0241	−	34.6828i	0.684011	−	1.18474i	−0.289735	−	0.957107i	$-0.593567\pi$
$857$	20.0241	−	34.6828i	0.684011	−	1.18474i	0.973746	−	0.227636i	$-0.0730995\pi$
$858$		0			0
$859$	12.7420	+	22.0698i	0.434752	+	0.753013i	0.997275	−	0.0737687i	$-0.0235026\pi$
$859$	12.7420	+	22.0698i	0.434752	+	0.753013i	−0.562523	+	0.826781i	$0.690169\pi$
$860$		0			0
$861$	0.563071	−	0.589494i	0.0191894	−	0.0200899i
$862$		0			0
$863$	0.373653	+	0.647186i	0.0127193	+	0.0220305i	0.872315	−	0.488944i	$-0.162618\pi$
$863$	0.373653	+	0.647186i	0.0127193	+	0.0220305i	−0.859596	+	0.510975i	$0.829285\pi$
$864$		0			0
$865$	16.2706	−	28.1816i	0.553218	−	0.958202i
$866$		0			0
$867$	−4.44252			−0.150876
$868$		0			0
$869$	−12.7677			−0.433114
$870$		0			0
$871$	−4.70696	+	8.15270i	−0.159489	+	0.276244i
$872$		0			0
$873$	0.873031	+	1.51213i	0.0295476	+	0.0511780i
$874$		0			0
$875$	7.62224	+	1.85623i	0.257679	+	0.0627521i
$876$		0			0
$877$	−8.27010	−	14.3242i	−0.279262	−	0.483695i	0.691940	−	0.721955i	$-0.256756\pi$
$877$	−8.27010	−	14.3242i	−0.279262	−	0.483695i	−0.971201	+	0.238260i	$0.923423\pi$
$878$		0			0
$879$	1.43635	−	2.48783i	0.0484469	−	0.0839125i
$880$		0			0
$881$	−50.7950			−1.71133			−0.855663	−	0.517533i	$-0.826850\pi$
$881$	−50.7950			−1.71133			−0.855663	+	0.517533i	$0.826850\pi$
$882$		0			0
$883$	−26.1612			−0.880394			−0.440197	−	0.897901i	$-0.645091\pi$
$883$	−26.1612			−0.880394			−0.440197	+	0.897901i	$0.645091\pi$
$884$		0			0
$885$	0.513694	−	0.889744i	0.0172676	−	0.0299084i
$886$		0			0
$887$	−17.7641	−	30.7684i	−0.596461	−	1.03310i	−0.993339	−	0.115229i	$-0.963240\pi$
$887$	−17.7641	−	30.7684i	−0.596461	−	1.03310i	0.396878	−	0.917871i	$-0.370094\pi$
$888$		0			0
$889$	−29.8105	−	7.25972i	−0.999813	−	0.243483i
$890$		0			0
$891$	−6.18650	−	10.7153i	−0.207256	−	0.358977i
$892$		0			0
$893$	−2.10704	+	3.64951i	−0.0705095	+	0.122126i
$894$		0			0
$895$	66.3368			2.21740
$896$		0			0
$897$	0.233107			0.00778321
$898$		0			0
$899$	4.43713	−	7.68534i	0.147987	−	0.256320i
$900$		0			0
$901$	1.31126	+	2.27117i	0.0436845	+	0.0756637i
$902$		0			0
$903$	−5.39036	+	5.64331i	−0.179380	+	0.187798i
$904$		0			0
$905$	5.95676	+	10.3174i	0.198009	+	0.342962i
$906$		0			0
$907$	−14.5243	+	25.1569i	−0.482273	+	0.835321i	−0.999793	−	0.0203503i	$-0.993522\pi$
$907$	−14.5243	+	25.1569i	−0.482273	+	0.835321i	0.517520	+	0.855671i	$0.326855\pi$
$908$		0			0
$909$	−11.0225			−0.365592
$910$		0			0
$911$	10.5596			0.349855			0.174927	−	0.984581i	$-0.444031\pi$
$911$	10.5596			0.349855			0.174927	+	0.984581i	$0.444031\pi$
$912$		0			0
$913$	−1.17892	+	2.04195i	−0.0390165	+	0.0675786i
$914$		0			0
$915$	−0.193603	−	0.335331i	−0.00640033	−	0.0110857i
$916$		0			0
$917$	−5.95976	−	20.3633i	−0.196809	−	0.672455i
$918$		0			0
$919$	−7.75415	−	13.4306i	−0.255786	−	0.443034i	0.709323	−	0.704884i	$-0.249001\pi$
$919$	−7.75415	−	13.4306i	−0.255786	−	0.443034i	−0.965109	+	0.261850i	$0.915668\pi$
$920$		0			0
$921$	1.59947	−	2.77036i	0.0527042	−	0.0912864i
$922$		0			0
$923$	8.77322			0.288774
$924$		0			0
$925$	−19.0002			−0.624721
$926$		0			0
$927$	0.755330	−	1.30827i	0.0248083	−	0.0429692i
$928$		0			0
$929$	−2.55325	−	4.42236i	−0.0837694	−	0.145093i	0.821097	−	0.570789i	$-0.193363\pi$
$929$	−2.55325	−	4.42236i	−0.0837694	−	0.145093i	−0.904866	+	0.425696i	$0.860029\pi$
$930$		0			0
$931$	−0.282450	−	6.15715i	−0.00925693	−	0.201793i
$932$		0			0
$933$	−4.89188	−	8.47298i	−0.160153	−	0.277393i
$934$		0			0
$935$	4.02415	−	6.97003i	0.131604	−	0.227944i
$936$		0			0
$937$	−6.24701			−0.204081			−0.102040	−	0.994780i	$-0.532537\pi$
$937$	−6.24701			−0.204081			−0.102040	+	0.994780i	$0.532537\pi$
$938$		0			0
$939$	−7.55497			−0.246547
$940$		0			0
$941$	15.1867	−	26.3042i	0.495073	−	0.857491i	−0.504911	−	0.863171i	$-0.668475\pi$
$941$	15.1867	−	26.3042i	0.495073	−	0.857491i	0.999984	+	0.00568029i	$0.00180810\pi$
$942$		0			0
$943$	−0.341030	−	0.590681i	−0.0111055	−	0.0192352i
$944$		0			0
$945$	4.46376	+	15.2518i	0.145206	+	0.496140i
$946$		0			0
$947$	−21.0502	−	36.4599i	−0.684038	−	1.18479i	−0.973738	−	0.227671i	$-0.926889\pi$
$947$	−21.0502	−	36.4599i	−0.684038	−	1.18479i	0.289700	−	0.957117i	$-0.406444\pi$
$948$		0			0
$949$	−0.867746	+	1.50298i	−0.0281682	+	0.0487888i
$950$		0			0
$951$	−2.43244			−0.0788773
$952$		0			0
$953$	−48.9720			−1.58636			−0.793180	−	0.608988i	$-0.791576\pi$
$953$	−48.9720			−1.58636			−0.793180	+	0.608988i	$0.791576\pi$
$954$		0			0
$955$	−32.2562	+	55.8694i	−1.04379	+	1.80789i
$956$		0			0
$957$	0.440042	+	0.762175i	0.0142245	+	0.0246376i
$958$		0			0
$959$	−1.49345	+	1.56353i	−0.0482260	+	0.0504890i
$960$		0			0
$961$	4.38870	+	7.60145i	0.141571	+	0.245208i
$962$		0			0
$963$	−13.5867	+	23.5328i	−0.437824	+	0.758333i
$964$		0			0
$965$	89.0150			2.86549
$966$		0			0
$967$	33.8769			1.08941			0.544704	−	0.838628i	$-0.316642\pi$
$967$	33.8769			1.08941			0.544704	+	0.838628i	$0.316642\pi$
$968$		0			0
$969$	−0.217960	+	0.377519i	−0.00700190	+	0.0121276i
$970$		0			0
$971$	0.471648	+	0.816918i	0.0151359	+	0.0262161i	0.873494	−	0.486835i	$-0.161849\pi$
$971$	0.471648	+	0.816918i	0.0151359	+	0.0262161i	−0.858358	+	0.513051i	$0.828515\pi$
$972$		0			0
$973$	−6.72289	−	1.63722i	−0.215526	−	0.0524867i
$974$		0			0
$975$	−1.00791	−	1.74575i	−0.0322789	−	0.0559087i
$976$		0			0
$977$	8.55072	−	14.8103i	0.273562	−	0.473823i	−0.696210	−	0.717839i	$-0.745132\pi$
$977$	8.55072	−	14.8103i	0.273562	−	0.473823i	0.969771	+	0.244016i	$0.0784649\pi$
$978$		0			0
$979$	21.1233			0.675103
$980$		0			0
$981$	−15.2617			−0.487268
$982$		0			0
$983$	−0.942761	+	1.63291i	−0.0300694	+	0.0520817i	−0.880668	−	0.473733i	$-0.842906\pi$
$983$	−0.942761	+	1.63291i	−0.0300694	+	0.0520817i	0.850599	+	0.525815i	$0.176239\pi$
$984$		0			0
$985$	17.4772	+	30.2714i	0.556869	+	0.964526i
$986$		0			0
$987$	−3.79069	−	0.923143i	−0.120659	−	0.0293839i
$988$		0			0
$989$	3.26473	+	5.65468i	0.103812	+	0.179808i
$990$		0			0
$991$	−11.4626	+	19.8538i	−0.364122	+	0.630678i	−0.988635	−	0.150337i	$-0.951964\pi$
$991$	−11.4626	+	19.8538i	−0.364122	+	0.630678i	0.624513	+	0.781015i	$0.285298\pi$
$992$		0			0
$993$	−4.35276			−0.138131
$994$		0			0
$995$	65.5487			2.07803
$996$		0			0
$997$	24.1129	−	41.7648i	0.763663	−	1.32270i	−0.177287	−	0.984159i	$-0.556732\pi$
$997$	24.1129	−	41.7648i	0.763663	−	1.32270i	0.940950	−	0.338544i	$-0.109935\pi$
$998$		0			0
$999$	−2.93055	−	5.07586i	−0.0927184	−	0.160593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.d.165.5	✓	16
7.2	even	3	inner	1148.2.i.d.821.5	yes	16
7.3	odd	6		8036.2.a.n.1.5		8
7.4	even	3		8036.2.a.m.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.d.165.5	✓	16	1.1	even	1	trivial
1148.2.i.d.821.5	yes	16	7.2	even	3	inner
8036.2.a.m.1.4		8	7.4	even	3
8036.2.a.n.1.5		8	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.154058 + 0.266837i) q^{3} +(1.65062 + 2.85896i) q^{5} +(-2.57062 - 0.626020i) q^{7} +(1.45253 + 2.51586i) q^{9} +O(q^{10})\)	\(q+(-0.154058 + 0.266837i) q^{3} +(1.65062 + 2.85896i) q^{5} +(-2.57062 - 0.626020i) q^{7} +(1.45253 + 2.51586i) q^{9} +(-0.758653 + 1.31403i) q^{11} +1.10922 q^{13} -1.01717 q^{15} +(-0.803385 + 1.39150i) q^{17} +(-0.440259 - 0.762551i) q^{19} +(0.563071 - 0.589494i) q^{21} +(-0.341030 - 0.590681i) q^{23} +(-2.94909 + 5.10798i) q^{25} -1.81945 q^{27} -1.88250 q^{29} +(-2.35704 + 4.08252i) q^{31} +(-0.233754 - 0.404874i) q^{33} +(-2.45336 - 8.38262i) q^{35} +(1.61068 + 2.78978i) q^{37} +(-0.170884 + 0.295981i) q^{39} +1.00000 q^{41} -9.57315 q^{43} +(-4.79516 + 8.30546i) q^{45} +(-2.39296 - 4.14472i) q^{47} +(6.21620 + 3.21852i) q^{49} +(-0.247537 - 0.428746i) q^{51} +(0.816086 - 1.41350i) q^{53} -5.00899 q^{55} +0.271303 q^{57} +(-0.505024 + 0.874727i) q^{59} +(0.190336 + 0.329671i) q^{61} +(-2.15893 - 7.37664i) q^{63} +(1.83090 + 3.17121i) q^{65} +(-4.24350 + 7.34995i) q^{67} +0.210154 q^{69} +7.90937 q^{71} +(-0.782304 + 1.35499i) q^{73} +(-0.908666 - 1.57385i) q^{75} +(2.77282 - 2.90293i) q^{77} +(4.20735 + 7.28734i) q^{79} +(-4.07729 + 7.06208i) q^{81} +1.55396 q^{83} -5.30433 q^{85} +(0.290015 - 0.502321i) q^{87} +(-6.96078 - 12.0564i) q^{89} +(-2.85138 - 0.694393i) q^{91} +(-0.726245 - 1.25789i) q^{93} +(1.45340 - 2.51736i) q^{95} +0.601041 q^{97} -4.40787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^9	\( 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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