LMFDB - Embedded newform 1372.2.e.d.1353.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1372,2,Mod(361,1372)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1372.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1372, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1372 = 2^{2} \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1372.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,7,0,7,0,0,0,-9,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$10.9554751573$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 10 x^{10} - 7 x^{9} + 68 x^{8} - 44 x^{7} + 225 x^{6} - 77 x^{5} + 490 x^{4} + \cdots + 49 $ x^12 - x^11 + 10x^10 - 7x^9 + 68x^8 - 44x^7 + 225x^6 - 77x^5 + 490x^4 - 182x^3 + 343x^2 + 98x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1353.1
Root			$0.529947 - 0.917895i$ of defining polynomial
Character	$\chi$	$=$	1372.1353
Dual form			1372.2.e.d.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.653437 - 1.13179i) q^{3} +(0.483381 - 0.837240i) q^{5} +(0.646041 - 1.11898i) q^{9} +(1.89324 + 3.27919i) q^{11} +2.23352 q^{13} -1.26343 q^{15} +(1.22501 + 2.12179i) q^{17} +(4.11950 - 7.13518i) q^{19} +(-2.43732 + 4.22156i) q^{23} +(2.03269 + 3.52072i) q^{25} -5.60921 q^{27} +2.43817 q^{29} +(0.826242 + 1.43109i) q^{31} +(2.47423 - 4.28549i) q^{33} +(1.82386 - 3.15902i) q^{37} +(-1.45946 - 2.52787i) q^{39} +0.608796 q^{41} +3.24779 q^{43} +(-0.624567 - 1.08178i) q^{45} +(4.73365 - 8.19893i) q^{47} +(1.60094 - 2.77291i) q^{51} +(0.881856 + 1.52742i) q^{53} +3.66063 q^{55} -10.7673 q^{57} +(-0.302587 - 0.524095i) q^{59} +(4.20579 - 7.28465i) q^{61} +(1.07964 - 1.86999i) q^{65} +(-4.67472 - 8.09685i) q^{67} +6.37053 q^{69} -5.91185 q^{71} +(-5.29447 - 9.17030i) q^{73} +(2.65646 - 4.60113i) q^{75} +(-5.52311 + 9.56630i) q^{79} +(1.72714 + 2.99150i) q^{81} -12.9132 q^{83} +2.36859 q^{85} +(-1.59319 - 2.75948i) q^{87} +(7.97696 - 13.8165i) q^{89} +(1.07979 - 1.87026i) q^{93} +(-3.98257 - 6.89802i) q^{95} +9.28081 q^{97} +4.89245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 7 q^{3} + 7 q^{5} - 9 q^{9} - 3 q^{11} - 14 q^{13} + 22 q^{15} + 7 q^{19} - 11 q^{23} - 3 q^{25} - 56 q^{27} + 12 q^{29} + 14 q^{31} + 6 q^{37} - 5 q^{39} - 6 q^{43} + 21 q^{45} + 42 q^{47} + 17 q^{51}+ \cdots - 68 q^{99}+O(q^{100}) $ 12 * q + 7 * q^3 + 7 * q^5 - 9 * q^9 - 3 * q^11 - 14 * q^13 + 22 * q^15 + 7 * q^19 - 11 * q^23 - 3 * q^25 - 56 * q^27 + 12 * q^29 + 14 * q^31 + 6 * q^37 - 5 * q^39 - 6 * q^43 + 21 * q^45 + 42 * q^47 + 17 * q^51 + 17 * q^53 - 28 * q^55 - 12 * q^57 + 35 * q^59 + 7 * q^61 + 6 * q^65 + 14 * q^67 - 28 * q^69 - 56 * q^71 + 35 * q^75 - 6 * q^79 - 34 * q^81 - 98 * q^83 - 46 * q^85 + 21 * q^87 - 7 * q^89 + 14 * q^93 + 25 * q^95 + 42 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1372\mathbb{Z}\right)^\times$.

$n$	$687$	$689$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.653437	−	1.13179i	−0.377262	−	0.653437i	0.613401	−	0.789772i	$-0.289801\pi$
$3$	−0.653437	−	1.13179i	−0.377262	−	0.653437i	−0.990663	+	0.136335i	$0.956468\pi$
$4$		0			0
$5$	0.483381	−	0.837240i	0.216174	−	0.374425i	−0.737461	−	0.675390i	$-0.763975\pi$
$5$	0.483381	−	0.837240i	0.216174	−	0.374425i	0.953635	+	0.300965i	$0.0973087\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.646041	−	1.11898i	0.215347	−	0.372992i
$10$		0			0
$11$	1.89324	+	3.27919i	0.570834	+	0.988714i	0.996481	+	0.0838246i	$0.0267135\pi$
$11$	1.89324	+	3.27919i	0.570834	+	0.988714i	−0.425646	+	0.904890i	$0.639953\pi$
$12$		0			0
$13$	2.23352			0.619467			0.309734	−	0.950823i	$-0.399760\pi$
$13$	2.23352			0.619467			0.309734	+	0.950823i	$0.399760\pi$
$14$		0			0
$15$	−1.26343			−0.326217
$16$		0			0
$17$	1.22501	+	2.12179i	0.297110	+	0.514609i	0.975473	−	0.220117i	$-0.0706440\pi$
$17$	1.22501	+	2.12179i	0.297110	+	0.514609i	−0.678364	+	0.734726i	$0.737311\pi$
$18$		0			0
$19$	4.11950	−	7.13518i	0.945078	−	1.63692i	0.189483	−	0.981884i	$-0.439319\pi$
$19$	4.11950	−	7.13518i	0.945078	−	1.63692i	0.755595	−	0.655039i	$-0.227348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.43732	+	4.22156i	−0.508216	+	0.880255i	0.491739	+	0.870743i	$0.336361\pi$
$23$	−2.43732	+	4.22156i	−0.508216	+	0.880255i	−0.999955	+	0.00951279i	$0.996972\pi$
$24$		0			0
$25$	2.03269	+	3.52072i	0.406537	+	0.704143i
$26$		0			0
$27$	−5.60921			−1.07949
$28$		0			0
$29$	2.43817			0.452756			0.226378	−	0.974040i	$-0.427312\pi$
$29$	2.43817			0.452756			0.226378	+	0.974040i	$0.427312\pi$
$30$		0			0
$31$	0.826242	+	1.43109i	0.148397	+	0.257032i	0.930635	−	0.365948i	$-0.119255\pi$
$31$	0.826242	+	1.43109i	0.148397	+	0.257032i	−0.782238	+	0.622980i	$0.785922\pi$
$32$		0			0
$33$	2.47423	−	4.28549i	0.430708	−	0.746009i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.82386	−	3.15902i	0.299841	−	0.519340i	−0.676258	−	0.736665i	$-0.736400\pi$
$37$	1.82386	−	3.15902i	0.299841	−	0.519340i	0.976099	+	0.217324i	$0.0697330\pi$
$38$		0			0
$39$	−1.45946	−	2.52787i	−0.233701	−	0.404783i
$40$		0			0
$41$	0.608796			0.0950780			0.0475390	−	0.998869i	$-0.484862\pi$
$41$	0.608796			0.0950780			0.0475390	+	0.998869i	$0.484862\pi$
$42$		0			0
$43$	3.24779			0.495283			0.247641	−	0.968852i	$-0.420345\pi$
$43$	3.24779			0.495283			0.247641	+	0.968852i	$0.420345\pi$
$44$		0			0
$45$	−0.624567	−	1.08178i	−0.0931049	−	0.161263i
$46$		0			0
$47$	4.73365	−	8.19893i	0.690474	−	1.19594i	−0.281209	−	0.959647i	$-0.590735\pi$
$47$	4.73365	−	8.19893i	0.690474	−	1.19594i	0.971683	−	0.236290i	$-0.0759314\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.60094	−	2.77291i	0.224176	−	0.388285i
$52$		0			0
$53$	0.881856	+	1.52742i	0.121132	+	0.209807i	0.920214	−	0.391415i	$-0.128014\pi$
$53$	0.881856	+	1.52742i	0.121132	+	0.209807i	−0.799082	+	0.601222i	$0.794681\pi$
$54$		0			0
$55$	3.66063			0.493599
$56$		0			0
$57$	−10.7673			−1.42617
$58$		0			0
$59$	−0.302587	−	0.524095i	−0.0393934	−	0.0682314i	0.845656	−	0.533728i	$-0.179209\pi$
$59$	−0.302587	−	0.524095i	−0.0393934	−	0.0682314i	−0.885050	+	0.465496i	$0.845876\pi$
$60$		0			0
$61$	4.20579	−	7.28465i	0.538497	−	0.932703i	−0.460489	−	0.887666i	$-0.652326\pi$
$61$	4.20579	−	7.28465i	0.538497	−	0.932703i	0.998985	−	0.0450378i	$-0.0143408\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.07964	−	1.86999i	0.133913	−	0.231944i
$66$		0			0
$67$	−4.67472	−	8.09685i	−0.571108	−	0.989188i	−0.996453	−	0.0841562i	$-0.973181\pi$
$67$	−4.67472	−	8.09685i	−0.571108	−	0.989188i	0.425345	−	0.905031i	$-0.360153\pi$
$68$		0			0
$69$	6.37053			0.766922
$70$		0			0
$71$	−5.91185			−0.701608			−0.350804	−	0.936449i	$-0.614092\pi$
$71$	−5.91185			−0.701608			−0.350804	+	0.936449i	$0.614092\pi$
$72$		0			0
$73$	−5.29447	−	9.17030i	−0.619671	−	1.07330i	−0.989546	−	0.144220i	$-0.953933\pi$
$73$	−5.29447	−	9.17030i	−0.619671	−	1.07330i	0.369874	−	0.929082i	$-0.379401\pi$
$74$		0			0
$75$	2.65646	−	4.60113i	0.306742	−	0.531293i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−5.52311	+	9.56630i	−0.621398	+	1.07629i	0.367827	+	0.929894i	$0.380102\pi$
$79$	−5.52311	+	9.56630i	−0.621398	+	1.07629i	−0.989226	+	0.146399i	$0.953232\pi$
$80$		0			0
$81$	1.72714	+	2.99150i	0.191905	+	0.332389i
$82$		0			0
$83$	−12.9132			−1.41740			−0.708701	−	0.705509i	$-0.750719\pi$
$83$	−12.9132			−1.41740			−0.708701	+	0.705509i	$0.750719\pi$
$84$		0			0
$85$	2.36859			0.256910
$86$		0			0
$87$	−1.59319	−	2.75948i	−0.170808	−	0.295847i
$88$		0			0
$89$	7.97696	−	13.8165i	0.845556	−	1.46455i	−0.0395811	−	0.999216i	$-0.512602\pi$
$89$	7.97696	−	13.8165i	0.845556	−	1.46455i	0.885137	−	0.465330i	$-0.154064\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.07979	−	1.87026i	0.111969	−	0.193937i
$94$		0			0
$95$	−3.98257	−	6.89802i	−0.408603	−	0.707722i
$96$		0			0
$97$	9.28081			0.942324			0.471162	−	0.882047i	$-0.343835\pi$
$97$	9.28081			0.942324			0.471162	+	0.882047i	$0.343835\pi$
$98$		0			0
$99$	4.89245			0.491710
$100$		0			0
$101$	9.45150	+	16.3705i	0.940459	+	1.62892i	0.764597	+	0.644508i	$0.222938\pi$
$101$	9.45150	+	16.3705i	0.940459	+	1.62892i	0.175862	+	0.984415i	$0.443729\pi$
$102$		0			0
$103$	−2.54813	+	4.41349i	−0.251074	+	0.434874i	−0.963822	−	0.266547i	$-0.914117\pi$
$103$	−2.54813	+	4.41349i	−0.251074	+	0.434874i	0.712747	+	0.701421i	$0.247451\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.80989	−	4.86687i	0.271642	−	0.470498i	−0.697640	−	0.716448i	$-0.745767\pi$
$107$	2.80989	−	4.86687i	0.271642	−	0.470498i	0.969282	+	0.245950i	$0.0791000\pi$
$108$		0			0
$109$	−5.11617	−	8.86146i	−0.490040	−	0.848774i	0.509894	−	0.860237i	$-0.329685\pi$
$109$	−5.11617	−	8.86146i	−0.490040	−	0.848774i	−0.999934	+	0.0114629i	$0.996351\pi$
$110$		0			0
$111$	−4.76712			−0.452475
$112$		0			0
$113$	15.1691			1.42699			0.713494	−	0.700662i	$-0.247112\pi$
$113$	15.1691			1.42699			0.713494	+	0.700662i	$0.247112\pi$
$114$		0			0
$115$	2.35630	+	4.08124i	0.219726	+	0.380577i
$116$		0			0
$117$	1.44294	−	2.49925i	0.133400	−	0.231056i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.66874	+	2.89035i	−0.151704	+	0.262759i
$122$		0			0
$123$	−0.397810	−	0.689027i	−0.0358693	−	0.0621275i
$124$		0			0
$125$	8.76405			0.783881
$126$		0			0
$127$	3.20619			0.284503			0.142252	−	0.989831i	$-0.454566\pi$
$127$	3.20619			0.284503			0.142252	+	0.989831i	$0.454566\pi$
$128$		0			0
$129$	−2.12222	−	3.67580i	−0.186851	−	0.323636i
$130$		0			0
$131$	−2.75372	+	4.76958i	−0.240593	+	0.416720i	−0.960883	−	0.276953i	$-0.910675\pi$
$131$	−2.75372	+	4.76958i	−0.240593	+	0.416720i	0.720290	+	0.693673i	$0.244009\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.71138	+	4.69625i	−0.233359	+	0.404189i
$136$		0			0
$137$	−5.98185	−	10.3609i	−0.511064	−	0.885188i	−0.999918	−	0.0128228i	$-0.995918\pi$
$137$	−5.98185	−	10.3609i	−0.511064	−	0.885188i	0.488854	−	0.872366i	$-0.337415\pi$
$138$		0			0
$139$	−10.4025			−0.882325			−0.441162	−	0.897427i	$-0.645434\pi$
$139$	−10.4025			−0.882325			−0.441162	+	0.897427i	$0.645434\pi$
$140$		0			0
$141$	−12.3726			−1.04196
$142$		0			0
$143$	4.22860	+	7.32415i	0.353613	+	0.612476i
$144$		0			0
$145$	1.17856	−	2.04133i	0.0978743	−	0.169523i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.36252	−	14.4843i	0.685084	−	1.18660i	−0.288326	−	0.957532i	$-0.593099\pi$
$149$	8.36252	−	14.4843i	0.685084	−	1.18660i	0.973410	−	0.229069i	$-0.0735680\pi$
$150$		0			0
$151$	9.27503	+	16.0648i	0.754791	+	1.30734i	0.945478	+	0.325686i	$0.105595\pi$
$151$	9.27503	+	16.0648i	0.754791	+	1.30734i	−0.190687	+	0.981651i	$0.561071\pi$
$152$		0			0
$153$	3.16564			0.255926
$154$		0			0
$155$	1.59756			0.128319
$156$		0			0
$157$	−6.11381	−	10.5894i	−0.487935	−	0.845128i	0.511969	−	0.859004i	$-0.328916\pi$
$157$	−6.11381	−	10.5894i	−0.487935	−	0.845128i	−0.999904	+	0.0138760i	$0.995583\pi$
$158$		0			0
$159$	1.15247	−	1.99614i	0.0913972	−	0.158305i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−7.53806	+	13.0563i	−0.590427	+	1.02265i	0.403748	+	0.914870i	$0.367707\pi$
$163$	−7.53806	+	13.0563i	−0.590427	+	1.02265i	−0.994175	+	0.107779i	$0.965626\pi$
$164$		0			0
$165$	−2.39199	−	4.14305i	−0.186216	−	0.322536i
$166$		0			0
$167$	−8.55828			−0.662260			−0.331130	−	0.943585i	$-0.607430\pi$
$167$	−8.55828			−0.662260			−0.331130	+	0.943585i	$0.607430\pi$
$168$		0			0
$169$	−8.01139			−0.616261
$170$		0			0
$171$	−5.32273	−	9.21923i	−0.407039	−	0.705012i
$172$		0			0
$173$	−8.88041	+	15.3813i	−0.675165	+	1.16942i	0.301255	+	0.953544i	$0.402594\pi$
$173$	−8.88041	+	15.3813i	−0.675165	+	1.16942i	−0.976421	+	0.215877i	$0.930739\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.395443	+	0.684927i	−0.0297233	+	0.0514822i
$178$		0			0
$179$	7.03069	+	12.1775i	0.525498	+	0.910189i	0.999559	+	0.0296973i	$0.00945433\pi$
$179$	7.03069	+	12.1775i	0.525498	+	0.910189i	−0.474061	+	0.880492i	$0.657212\pi$
$180$		0			0
$181$	−3.14416			−0.233704			−0.116852	−	0.993149i	$-0.537280\pi$
$181$	−3.14416			−0.233704			−0.116852	+	0.993149i	$0.537280\pi$
$182$		0			0
$183$	−10.9929			−0.812617
$184$		0			0
$185$	−1.76324	−	3.05402i	−0.129636	−	0.224536i
$186$		0			0
$187$	−4.63850	+	8.03412i	−0.339201	+	0.587513i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.4797	−	18.1515i	0.758288	−	1.31339i	−0.185435	−	0.982656i	$-0.559369\pi$
$191$	10.4797	−	18.1515i	0.758288	−	1.31339i	0.943723	−	0.330737i	$-0.107297\pi$
$192$		0			0
$193$	2.42093	+	4.19318i	0.174262	+	0.301831i	0.939906	−	0.341434i	$-0.110913\pi$
$193$	2.42093	+	4.19318i	0.174262	+	0.301831i	−0.765643	+	0.643265i	$0.777579\pi$
$194$		0			0
$195$	−2.82191			−0.202081
$196$		0			0
$197$	18.6607			1.32952			0.664759	−	0.747058i	$-0.268534\pi$
$197$	18.6607			1.32952			0.664759	+	0.747058i	$0.268534\pi$
$198$		0			0
$199$	−3.19746	−	5.53817i	−0.226662	−	0.392590i	0.730155	−	0.683282i	$-0.239448\pi$
$199$	−3.19746	−	5.53817i	−0.226662	−	0.392590i	−0.956817	+	0.290692i	$0.906115\pi$
$200$		0			0
$201$	−6.10927	+	10.5816i	−0.430914	+	0.746366i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.294280	−	0.509708i	0.0205534	−	0.0355996i
$206$		0			0
$207$	3.14921	+	5.45459i	0.218885	+	0.379120i
$208$		0			0
$209$	31.1969			2.15793
$210$		0			0
$211$	22.2657			1.53283			0.766417	−	0.642344i	$-0.222038\pi$
$211$	22.2657			1.53283			0.766417	+	0.642344i	$0.222038\pi$
$212$		0			0
$213$	3.86302	+	6.69095i	0.264690	+	0.458457i
$214$		0			0
$215$	1.56992	−	2.71918i	0.107067	−	0.185446i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−6.91921	+	11.9844i	−0.467557	+	0.809832i
$220$		0			0
$221$	2.73609	+	4.73905i	0.184050	+	0.318783i
$222$		0			0
$223$	−20.2710			−1.35745			−0.678724	−	0.734393i	$-0.737467\pi$
$223$	−20.2710			−1.35745			−0.678724	+	0.734393i	$0.737467\pi$
$224$		0			0
$225$	5.25279			0.350186
$226$		0			0
$227$	7.44311	+	12.8918i	0.494016	+	0.855661i	0.999976	−	0.00689568i	$-0.00219498\pi$
$227$	7.44311	+	12.8918i	0.494016	+	0.855661i	−0.505960	+	0.862557i	$0.668862\pi$
$228$		0			0
$229$	−5.32467	+	9.22260i	−0.351864	+	0.609447i	−0.986576	−	0.163302i	$-0.947785\pi$
$229$	−5.32467	+	9.22260i	−0.351864	+	0.609447i	0.634712	+	0.772749i	$0.281119\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.9958	+	22.5093i	−0.851381	+	1.47464i	0.0285809	+	0.999591i	$0.490901\pi$
$233$	−12.9958	+	22.5093i	−0.851381	+	1.47464i	−0.879962	+	0.475044i	$0.842432\pi$
$234$		0			0
$235$	−4.57631	−	7.92640i	−0.298526	−	0.517062i
$236$		0			0
$237$	14.4360			0.937720
$238$		0			0
$239$	−18.0618			−1.16832			−0.584162	−	0.811637i	$-0.698577\pi$
$239$	−18.0618			−1.16832			−0.584162	+	0.811637i	$0.698577\pi$
$240$		0			0
$241$	−5.67427	−	9.82812i	−0.365512	−	0.633085i	0.623347	−	0.781946i	$-0.285773\pi$
$241$	−5.67427	−	9.82812i	−0.365512	−	0.633085i	−0.988858	+	0.148861i	$0.952439\pi$
$242$		0			0
$243$	−6.15666	+	10.6636i	−0.394950	+	0.684073i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	9.20099	−	15.9366i	0.585445	−	1.01402i
$248$		0			0
$249$	8.43793	+	14.6149i	0.534732	+	0.926183i
$250$		0			0
$251$	−2.21702			−0.139937			−0.0699685	−	0.997549i	$-0.522290\pi$
$251$	−2.21702			−0.139937			−0.0699685	+	0.997549i	$0.522290\pi$
$252$		0			0
$253$	−18.4577			−1.16043
$254$		0			0
$255$	−1.54773	−	2.68074i	−0.0969224	−	0.167874i
$256$		0			0
$257$	−15.7130	+	27.2158i	−0.980153	+	1.69767i	−0.318391	+	0.947959i	$0.603143\pi$
$257$	−15.7130	+	27.2158i	−0.980153	+	1.69767i	−0.661761	+	0.749715i	$0.730191\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.57515	−	2.72825i	0.0974996	−	0.168874i
$262$		0			0
$263$	−3.26071	−	5.64771i	−0.201064	−	0.348253i	0.747808	−	0.663915i	$-0.231107\pi$
$263$	−3.26071	−	5.64771i	−0.201064	−	0.348253i	−0.948871	+	0.315663i	$0.897773\pi$
$264$		0			0
$265$	1.70509			0.104743
$266$		0			0
$267$	−20.8498			−1.27598
$268$		0			0
$269$	15.3654	+	26.6136i	0.936844	+	1.62266i	0.771313	+	0.636456i	$0.219600\pi$
$269$	15.3654	+	26.6136i	0.936844	+	1.62266i	0.165531	+	0.986205i	$0.447066\pi$
$270$		0			0
$271$	−5.85225	+	10.1364i	−0.355499	+	0.615742i	−0.987203	−	0.159467i	$-0.949022\pi$
$271$	−5.85225	+	10.1364i	−0.355499	+	0.615742i	0.631704	+	0.775209i	$0.282356\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.69674	+	13.3311i	−0.464131	+	0.803898i
$276$		0			0
$277$	14.2446	+	24.6724i	0.855874	+	1.48242i	0.875832	+	0.482617i	$0.160314\pi$
$277$	14.2446	+	24.6724i	0.855874	+	1.48242i	−0.0199572	+	0.999801i	$0.506353\pi$
$278$		0			0
$279$	2.13514			0.127828
$280$		0			0
$281$	−5.96553			−0.355874			−0.177937	−	0.984042i	$-0.556942\pi$
$281$	−5.96553			−0.355874			−0.177937	+	0.984042i	$0.556942\pi$
$282$		0			0
$283$	0.537836	+	0.931560i	0.0319711	+	0.0553755i	0.881568	−	0.472057i	$-0.156488\pi$
$283$	0.537836	+	0.931560i	0.0319711	+	0.0553755i	−0.849597	+	0.527432i	$0.823155\pi$
$284$		0			0
$285$	−5.20472	+	9.01484i	−0.308301	+	0.533993i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.49868	−	9.52399i	0.323452	−	0.560235i
$290$		0			0
$291$	−6.06442	−	10.5039i	−0.355503	−	0.615749i
$292$		0			0
$293$	−3.88129			−0.226747			−0.113374	−	0.993552i	$-0.536166\pi$
$293$	−3.88129			−0.226747			−0.113374	+	0.993552i	$0.536166\pi$
$294$		0			0
$295$	−0.585058			−0.0340634
$296$		0			0
$297$	−10.6196	−	18.3937i	−0.616212	−	1.06731i
$298$		0			0
$299$	−5.44380	+	9.42893i	−0.314823	+	0.545289i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	12.3519	−	21.3941i	0.709599	−	1.22906i
$304$		0			0
$305$	−4.06600	−	7.04251i	−0.232818	−	0.403253i
$306$		0			0
$307$	−21.6625			−1.23635			−0.618173	−	0.786042i	$-0.712127\pi$
$307$	−21.6625			−1.23635			−0.618173	+	0.786042i	$0.712127\pi$
$308$		0			0
$309$	6.66016			0.378883
$310$		0			0
$311$	4.86363	+	8.42405i	0.275791	+	0.477684i	0.970334	−	0.241767i	$-0.0777269\pi$
$311$	4.86363	+	8.42405i	0.275791	+	0.477684i	−0.694543	+	0.719451i	$0.744394\pi$
$312$		0			0
$313$	−5.11573	+	8.86071i	−0.289158	+	0.500837i	−0.973609	−	0.228222i	$-0.926709\pi$
$313$	−5.11573	+	8.86071i	−0.289158	+	0.500837i	0.684451	+	0.729059i	$0.260042\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.0918	+	17.4796i	−0.566815	+	0.981752i	0.430064	+	0.902799i	$0.358491\pi$
$317$	−10.0918	+	17.4796i	−0.566815	+	0.981752i	−0.996878	+	0.0789533i	$0.974842\pi$
$318$		0			0
$319$	4.61604	+	7.99522i	0.258449	+	0.447646i
$320$		0			0
$321$	−7.34433			−0.409921
$322$		0			0
$323$	20.1858			1.12317
$324$		0			0
$325$	4.54005	+	7.86359i	0.251836	+	0.436194i
$326$		0			0
$327$	−6.68619	+	11.5808i	−0.369747	+	0.640420i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	11.7824	−	20.4077i	0.647620	−	1.12171i	−0.336070	−	0.941837i	$-0.609098\pi$
$331$	11.7824	−	20.4077i	0.647620	−	1.12171i	0.983690	−	0.179874i	$-0.0575688\pi$
$332$		0			0
$333$	−2.35658	−	4.08171i	−0.129140	−	0.223677i
$334$		0			0
$335$	−9.03867			−0.493835
$336$		0			0
$337$	17.6174			0.959680			0.479840	−	0.877356i	$-0.340695\pi$
$337$	17.6174			0.959680			0.479840	+	0.877356i	$0.340695\pi$
$338$		0			0
$339$	−9.91204	−	17.1682i	−0.538348	−	0.932446i
$340$		0			0
$341$	−3.12856	+	5.41882i	−0.169421	+	0.293445i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3.07939	−	5.33366i	0.165789	−	0.287155i
$346$		0			0
$347$	13.4143	+	23.2342i	0.720116	+	1.24728i	0.960953	+	0.276712i	$0.0892449\pi$
$347$	13.4143	+	23.2342i	0.720116	+	1.24728i	−0.240836	+	0.970566i	$0.577422\pi$
$348$		0			0
$349$	28.0841			1.50331			0.751654	−	0.659557i	$-0.229256\pi$
$349$	28.0841			1.50331			0.751654	+	0.659557i	$0.229256\pi$
$350$		0			0
$351$	−12.5283			−0.668710
$352$		0			0
$353$	5.91904	+	10.2521i	0.315039	+	0.545663i	0.979446	−	0.201708i	$-0.0646492\pi$
$353$	5.91904	+	10.2521i	0.315039	+	0.545663i	−0.664407	+	0.747371i	$0.731316\pi$
$354$		0			0
$355$	−2.85768	+	4.94964i	−0.151670	+	0.262700i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.27300	+	9.13310i	−0.278298	+	0.482027i	−0.970962	−	0.239234i	$-0.923104\pi$
$359$	−5.27300	+	9.13310i	−0.278298	+	0.482027i	0.692664	+	0.721261i	$0.256437\pi$
$360$		0			0
$361$	−24.4406	−	42.3323i	−1.28634	−	2.22801i
$362$		0			0
$363$	4.36168			0.228929
$364$		0			0
$365$	−10.2370			−0.535828
$366$		0			0
$367$	−11.5228	−	19.9581i	−0.601487	−	1.04181i	−0.992596	−	0.121462i	$-0.961242\pi$
$367$	−11.5228	−	19.9581i	−0.601487	−	1.04181i	0.391109	−	0.920344i	$-0.372092\pi$
$368$		0			0
$369$	0.393307	−	0.681228i	0.0204747	−	0.0354633i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−15.7484	+	27.2771i	−0.815424	+	1.41235i	0.0935999	+	0.995610i	$0.470163\pi$
$373$	−15.7484	+	27.2771i	−0.815424	+	1.41235i	−0.909023	+	0.416745i	$0.863171\pi$
$374$		0			0
$375$	−5.72675	−	9.91903i	−0.295728	−	0.512216i
$376$		0			0
$377$	5.44569			0.280467
$378$		0			0
$379$	24.2707			1.24670			0.623351	−	0.781942i	$-0.285771\pi$
$379$	24.2707			1.24670			0.623351	+	0.781942i	$0.285771\pi$
$380$		0			0
$381$	−2.09504	−	3.62872i	−0.107332	−	0.185905i
$382$		0			0
$383$	−2.48829	+	4.30984i	−0.127146	+	0.220223i	−0.922570	−	0.385831i	$-0.873915\pi$
$383$	−2.48829	+	4.30984i	−0.127146	+	0.220223i	0.795424	+	0.606053i	$0.207248\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.09820	−	3.63419i	0.106658	−	0.184736i
$388$		0			0
$389$	−6.98785	−	12.1033i	−0.354298	−	0.613662i	0.632700	−	0.774397i	$-0.281947\pi$
$389$	−6.98785	−	12.1033i	−0.354298	−	0.613662i	−0.986998	+	0.160735i	$0.948614\pi$
$390$		0			0
$391$	−11.9430			−0.603983
$392$		0			0
$393$	7.19752			0.363067
$394$		0			0
$395$	5.33953	+	9.24833i	0.268661	+	0.465334i
$396$		0			0
$397$	2.67606	−	4.63507i	0.134308	−	0.232628i	−0.791025	−	0.611784i	$-0.790452\pi$
$397$	2.67606	−	4.63507i	0.134308	−	0.232628i	0.925333	+	0.379156i	$0.123786\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.906693	+	1.57044i	−0.0452781	+	0.0784239i	−0.887776	−	0.460275i	$-0.847751\pi$
$401$	−0.906693	+	1.57044i	−0.0452781	+	0.0784239i	0.842498	+	0.538699i	$0.181084\pi$
$402$		0			0
$403$	1.84543	+	3.19638i	0.0919274	+	0.159223i
$404$		0			0
$405$	3.33947			0.165939
$406$		0			0
$407$	13.8121			0.684639
$408$		0			0
$409$	−16.9503	−	29.3588i	−0.838140	−	1.45170i	−0.891448	−	0.453123i	$-0.850310\pi$
$409$	−16.9503	−	29.3588i	−0.838140	−	1.45170i	0.0533078	−	0.998578i	$-0.483024\pi$
$410$		0			0
$411$	−7.81752	+	13.5403i	−0.385610	+	0.667896i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6.24197	+	10.8114i	−0.306406	+	0.530711i
$416$		0			0
$417$	6.79735	+	11.7734i	0.332868	+	0.576543i
$418$		0			0
$419$	15.6842			0.766226			0.383113	−	0.923702i	$-0.374852\pi$
$419$	15.6842			0.766226			0.383113	+	0.923702i	$0.374852\pi$
$420$		0			0
$421$	−1.36544			−0.0665477			−0.0332739	−	0.999446i	$-0.510593\pi$
$421$	−1.36544			−0.0665477			−0.0332739	+	0.999446i	$0.510593\pi$
$422$		0			0
$423$	−6.11626	−	10.5937i	−0.297383	−	0.515082i
$424$		0			0
$425$	−4.98014	+	8.62586i	−0.241572	+	0.418415i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	5.52624	−	9.57174i	0.266810	−	0.462128i
$430$		0			0
$431$	−13.9372	−	24.1399i	−0.671331	−	1.16278i	−0.977527	−	0.210811i	$-0.932390\pi$
$431$	−13.9372	−	24.1399i	−0.671331	−	1.16278i	0.306196	−	0.951969i	$-0.400944\pi$
$432$		0			0
$433$	−10.5777			−0.508334			−0.254167	−	0.967160i	$-0.581801\pi$
$433$	−10.5777			−0.508334			−0.254167	+	0.967160i	$0.581801\pi$
$434$		0			0
$435$	−3.08046			−0.147697
$436$		0			0
$437$	20.0811	+	34.7814i	0.960607	+	1.66382i
$438$		0			0
$439$	−14.7647	+	25.5732i	−0.704679	+	1.22054i	0.262128	+	0.965033i	$0.415576\pi$
$439$	−14.7647	+	25.5732i	−0.704679	+	1.22054i	−0.966807	+	0.255507i	$0.917758\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.73998	−	13.4060i	0.367737	−	0.636940i	−0.621474	−	0.783435i	$-0.713466\pi$
$443$	7.73998	−	13.4060i	0.367737	−	0.636940i	0.989211	+	0.146495i	$0.0467992\pi$
$444$		0			0
$445$	−7.71182	−	13.3573i	−0.365575	−	0.633195i
$446$		0			0
$447$	−21.8575			−1.03383
$448$		0			0
$449$	−36.5746			−1.72606			−0.863032	−	0.505149i	$-0.831438\pi$
$449$	−36.5746			−1.72606			−0.863032	+	0.505149i	$0.831438\pi$
$450$		0			0
$451$	1.15260	+	1.99636i	0.0542738	+	0.0940050i
$452$		0			0
$453$	12.1213	−	20.9947i	0.569508	−	0.986417i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.84871	−	6.66617i	0.180035	−	0.311830i	−0.761857	−	0.647745i	$-0.775712\pi$
$457$	3.84871	−	6.66617i	0.180035	−	0.311830i	0.941892	+	0.335915i	$0.109046\pi$
$458$		0			0
$459$	−6.87136	−	11.9015i	−0.320728	−	0.555517i
$460$		0			0
$461$	−13.4571			−0.626761			−0.313381	−	0.949628i	$-0.601462\pi$
$461$	−13.4571			−0.626761			−0.313381	+	0.949628i	$0.601462\pi$
$462$		0			0
$463$	−27.7916			−1.29158			−0.645792	−	0.763514i	$-0.723473\pi$
$463$	−27.7916			−1.29158			−0.645792	+	0.763514i	$0.723473\pi$
$464$		0			0
$465$	−1.04390	−	1.80809i	−0.0484099	−	0.0838483i
$466$		0			0
$467$	15.6279	−	27.0683i	0.723171	−	1.25257i	−0.236551	−	0.971619i	$-0.576017\pi$
$467$	15.6279	−	27.0683i	0.723171	−	1.25257i	0.959722	−	0.280950i	$-0.0906496\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−7.98997	+	13.8390i	−0.368159	+	0.637669i
$472$		0			0
$473$	6.14885	+	10.6501i	0.282724	+	0.489693i
$474$		0			0
$475$	33.4946			1.53684
$476$		0			0
$477$	2.27886			0.104342
$478$		0			0
$479$	20.5651	+	35.6198i	0.939643	+	1.62751i	0.766138	+	0.642677i	$0.222176\pi$
$479$	20.5651	+	35.6198i	0.939643	+	1.62751i	0.173505	+	0.984833i	$0.444491\pi$
$480$		0			0
$481$	4.07364	−	7.05574i	0.185742	−	0.321714i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.48616	−	7.77027i	0.203706	−	0.352830i
$486$		0			0
$487$	−1.05975	−	1.83553i	−0.0480217	−	0.0831760i	0.841015	−	0.541011i	$-0.181958\pi$
$487$	−1.05975	−	1.83553i	−0.0480217	−	0.0831760i	−0.889037	+	0.457835i	$0.848625\pi$
$488$		0			0
$489$	19.7026			0.890982
$490$		0			0
$491$	27.0278			1.21975			0.609873	−	0.792499i	$-0.291220\pi$
$491$	27.0278			1.21975			0.609873	+	0.792499i	$0.291220\pi$
$492$		0			0
$493$	2.98679	+	5.17327i	0.134518	+	0.232992i
$494$		0			0
$495$	2.36492	−	4.09615i	0.106295	−	0.184108i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.9235	−	25.8482i	0.668065	−	1.15712i	−0.310379	−	0.950613i	$-0.600456\pi$
$499$	14.9235	−	25.8482i	0.668065	−	1.15712i	0.978444	−	0.206510i	$-0.0662107\pi$
$500$		0			0
$501$	5.59230	+	9.68614i	0.249845	+	0.432745i
$502$		0			0
$503$	−30.5276			−1.36116			−0.680580	−	0.732674i	$-0.738272\pi$
$503$	−30.5276			−1.36116			−0.680580	+	0.732674i	$0.738272\pi$
$504$		0			0
$505$	18.2747			0.813213
$506$		0			0
$507$	5.23494	+	9.06717i	0.232492	+	0.402687i
$508$		0			0
$509$	−6.38305	+	11.0558i	−0.282924	+	0.490038i	−0.972104	−	0.234552i	$-0.924638\pi$
$509$	−6.38305	+	11.0558i	−0.282924	+	0.490038i	0.689180	+	0.724590i	$0.257971\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−23.1071	+	40.0227i	−1.02020	+	1.76705i
$514$		0			0
$515$	2.46343	+	4.26679i	0.108552	+	0.188017i
$516$		0			0
$517$	35.8478			1.57659
$518$		0			0
$519$	23.2112			1.01886
$520$		0			0
$521$	−8.26051	−	14.3076i	−0.361900	−	0.626829i	0.626374	−	0.779523i	$-0.284538\pi$
$521$	−8.26051	−	14.3076i	−0.361900	−	0.626829i	−0.988273	+	0.152694i	$0.951205\pi$
$522$		0			0
$523$	5.21484	−	9.03237i	0.228029	−	0.394958i	−0.729195	−	0.684306i	$-0.760105\pi$
$523$	5.21484	−	9.03237i	0.228029	−	0.394958i	0.957224	+	0.289348i	$0.0934386\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.02432	+	3.50622i	−0.0881806	+	0.152733i
$528$		0			0
$529$	−0.381027	−	0.659958i	−0.0165664	−	0.0286938i
$530$		0			0
$531$	−0.781933			−0.0339330
$532$		0			0
$533$	1.35976			0.0588977
$534$		0			0
$535$	−2.71649	−	4.70510i	−0.117444	−	0.203419i
$536$		0			0
$537$	9.18822	−	15.9145i	0.396501	−	0.686760i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	13.2024	−	22.8672i	0.567614	−	0.983136i	−0.429187	−	0.903216i	$-0.641200\pi$
$541$	13.2024	−	22.8672i	0.567614	−	0.983136i	0.996801	−	0.0799208i	$-0.0254668\pi$
$542$		0			0
$543$	2.05451	+	3.55852i	0.0881675	+	0.152711i
$544$		0			0
$545$	−9.89223			−0.423736
$546$		0			0
$547$	−23.1444			−0.989584			−0.494792	−	0.869012i	$-0.664756\pi$
$547$	−23.1444			−0.989584			−0.494792	+	0.869012i	$0.664756\pi$
$548$		0			0
$549$	−5.43422	−	9.41235i	−0.231927	−	0.401709i
$550$		0			0
$551$	10.0440	−	17.3968i	0.427890	−	0.741127i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.30433	+	3.99122i	−0.0978135	+	0.169418i
$556$		0			0
$557$	−2.47537	−	4.28747i	−0.104885	−	0.181666i	0.808806	−	0.588075i	$-0.200114\pi$
$557$	−2.47537	−	4.28747i	−0.104885	−	0.181666i	−0.913691	+	0.406409i	$0.866781\pi$
$558$		0			0
$559$	7.25400			0.306811
$560$		0			0
$561$	12.1239			0.511870
$562$		0			0
$563$	6.28920	+	10.8932i	0.265058	+	0.459094i	0.967579	−	0.252569i	$-0.0812755\pi$
$563$	6.28920	+	10.8932i	0.265058	+	0.459094i	−0.702521	+	0.711663i	$0.747942\pi$
$564$		0			0
$565$	7.33244	−	12.7002i	0.308478	−	0.534300i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.25293	−	9.09834i	0.220214	−	0.381422i	−0.734659	−	0.678437i	$-0.762658\pi$
$569$	5.25293	−	9.09834i	0.220214	−	0.381422i	0.954873	+	0.297015i	$0.0959910\pi$
$570$		0			0
$571$	1.60966	+	2.78800i	0.0673620	+	0.116674i	0.897739	−	0.440527i	$-0.145208\pi$
$571$	1.60966	+	2.78800i	0.0673620	+	0.116674i	−0.830377	+	0.557201i	$0.811875\pi$
$572$		0			0
$573$	−27.3914			−1.14429
$574$		0			0
$575$	−19.8172			−0.826434
$576$		0			0
$577$	−12.8218	−	22.2080i	−0.533779	−	0.924533i	−0.999221	−	0.0394545i	$-0.987438\pi$
$577$	−12.8218	−	22.2080i	−0.533779	−	0.924533i	0.465442	−	0.885078i	$-0.345895\pi$
$578$		0			0
$579$	3.16385	−	5.47995i	0.131485	−	0.227739i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.33914	+	5.78356i	−0.138293	+	0.239530i
$584$		0			0
$585$	−1.39498	−	2.41618i	−0.0576755	−	0.0998968i
$586$		0			0
$587$	−13.6017			−0.561402			−0.280701	−	0.959795i	$-0.590567\pi$
$587$	−13.6017			−0.561402			−0.280701	+	0.959795i	$0.590567\pi$
$588$		0			0
$589$	13.6148			0.560989
$590$		0			0
$591$	−12.1936	−	21.1199i	−0.501577	−	0.868756i
$592$		0			0
$593$	15.9857	−	27.6881i	0.656455	−	1.13701i	−0.325071	−	0.945689i	$-0.605388\pi$
$593$	15.9857	−	27.6881i	0.656455	−	1.13701i	0.981527	−	0.191325i	$-0.0612783\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.17868	+	7.23768i	−0.171022	+	0.296219i
$598$		0			0
$599$	3.96809	+	6.87294i	0.162132	+	0.280821i	0.935633	−	0.352974i	$-0.114830\pi$
$599$	3.96809	+	6.87294i	0.162132	+	0.280821i	−0.773501	+	0.633795i	$0.781496\pi$
$600$		0			0
$601$	−2.41626			−0.0985612			−0.0492806	−	0.998785i	$-0.515693\pi$
$601$	−2.41626			−0.0985612			−0.0492806	+	0.998785i	$0.515693\pi$
$602$		0			0
$603$	−12.0802			−0.491945
$604$		0			0
$605$	1.61328	+	2.79428i	0.0655891	+	0.113604i
$606$		0			0
$607$	6.66779	−	11.5489i	0.270637	−	0.468757i	−0.698388	−	0.715719i	$-0.746099\pi$
$607$	6.66779	−	11.5489i	0.270637	−	0.468757i	0.969025	+	0.246962i	$0.0794323\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	10.5727	−	18.3125i	0.427726	−	0.740843i
$612$		0			0
$613$	12.3696	+	21.4247i	0.499602	+	0.865337i	1.00000		0.000458946i	$-0.000146087\pi$
$613$	12.3696	+	21.4247i	0.499602	+	0.865337i	−0.500397	+	0.865796i	$0.666813\pi$
$614$		0			0
$615$	−0.769174			−0.0310161
$616$		0			0
$617$	−13.6111			−0.547963			−0.273982	−	0.961735i	$-0.588341\pi$
$617$	−13.6111			−0.547963			−0.273982	+	0.961735i	$0.588341\pi$
$618$		0			0
$619$	−6.72445	−	11.6471i	−0.270278	−	0.468136i	0.698655	−	0.715459i	$-0.253782\pi$
$619$	−6.72445	−	11.6471i	−0.270278	−	0.468136i	−0.968933	+	0.247323i	$0.920449\pi$
$620$		0			0
$621$	13.6714	−	23.6796i	0.548615	−	0.950229i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.92706	+	10.2660i	−0.237082	+	0.410639i
$626$		0			0
$627$	−20.3852	−	35.3082i	−0.814106	−	1.41007i
$628$		0			0
$629$	8.93703			0.356343
$630$		0			0
$631$	−34.2018			−1.36155			−0.680777	−	0.732491i	$-0.738358\pi$
$631$	−34.2018			−1.36155			−0.680777	+	0.732491i	$0.738358\pi$
$632$		0			0
$633$	−14.5492	−	25.2000i	−0.578280	−	1.00161i
$634$		0			0
$635$	1.54981	−	2.68435i	0.0615023	−	0.106525i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−3.81930	+	6.61522i	−0.151089	+	0.261694i
$640$		0			0
$641$	21.1280	+	36.5948i	0.834506	+	1.44541i	0.894432	+	0.447204i	$0.147580\pi$
$641$	21.1280	+	36.5948i	0.834506	+	1.44541i	−0.0599258	+	0.998203i	$0.519086\pi$
$642$		0			0
$643$	−21.6806			−0.855000			−0.427500	−	0.904015i	$-0.640606\pi$
$643$	−21.6806			−0.855000			−0.427500	+	0.904015i	$0.640606\pi$
$644$		0			0
$645$	−4.10337			−0.161570
$646$		0			0
$647$	16.7909	+	29.0826i	0.660117	+	1.14336i	0.980584	+	0.196097i	$0.0628268\pi$
$647$	16.7909	+	29.0826i	0.660117	+	1.14336i	−0.320467	+	0.947260i	$0.603840\pi$
$648$		0			0
$649$	1.14574	−	1.98448i	0.0449743	−	0.0778977i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.37144	+	4.10746i	−0.0928017	+	0.160737i	−0.908689	−	0.417474i	$-0.862916\pi$
$653$	−2.37144	+	4.10746i	−0.0928017	+	0.160737i	0.815887	+	0.578211i	$0.196249\pi$
$654$		0			0
$655$	2.66219	+	4.61105i	0.104020	+	0.180168i
$656$		0			0
$657$	−13.6818			−0.533777
$658$		0			0
$659$	−11.1917			−0.435968			−0.217984	−	0.975952i	$-0.569948\pi$
$659$	−11.1917			−0.435968			−0.217984	+	0.975952i	$0.569948\pi$
$660$		0			0
$661$	22.2191	+	38.4846i	0.864222	+	1.49688i	0.867817	+	0.496883i	$0.165522\pi$
$661$	22.2191	+	38.4846i	0.864222	+	1.49688i	−0.00359535	+	0.999994i	$0.501144\pi$
$662$		0			0
$663$	3.57573	−	6.19335i	0.138870	−	0.240530i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.94258	+	10.2929i	−0.230098	+	0.398541i
$668$		0			0
$669$	13.2458	+	22.9425i	0.512114	+	0.887007i
$670$		0			0
$671$	31.8504			1.22957
$672$		0			0
$673$	−29.0230			−1.11875			−0.559377	−	0.828913i	$-0.688960\pi$
$673$	−29.0230			−1.11875			−0.559377	+	0.828913i	$0.688960\pi$
$674$		0			0
$675$	−11.4018	−	19.7484i	−0.438854	−	0.760117i
$676$		0			0
$677$	1.39441	−	2.41519i	0.0535916	−	0.0928234i	−0.837985	−	0.545693i	$-0.816266\pi$
$677$	1.39441	−	2.41519i	0.0535916	−	0.0928234i	0.891577	+	0.452870i	$0.149600\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	9.72720	−	16.8480i	0.372747	−	0.645617i
$682$		0			0
$683$	2.85501	+	4.94503i	0.109244	+	0.189216i	0.915464	−	0.402399i	$-0.131824\pi$
$683$	2.85501	+	4.94503i	0.109244	+	0.189216i	−0.806220	+	0.591616i	$0.798490\pi$
$684$		0			0
$685$	−11.5660			−0.441916
$686$		0			0
$687$	13.9173			0.530980
$688$		0			0
$689$	1.96964	+	3.41152i	0.0750374	+	0.129969i
$690$		0			0
$691$	25.6527	−	44.4318i	0.975875	−	1.69027i	0.298859	−	0.954297i	$-0.403394\pi$
$691$	25.6527	−	44.4318i	0.975875	−	1.69027i	0.677016	−	0.735968i	$-0.263273\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.02835	+	8.70935i	−0.190736	+	0.330364i
$696$		0			0
$697$	0.745784	+	1.29174i	0.0282486	+	0.0489280i
$698$		0			0
$699$	33.9677			1.28477
$700$		0			0
$701$	30.6669			1.15827			0.579137	−	0.815230i	$-0.303390\pi$
$701$	30.6669			1.15827			0.579137	+	0.815230i	$0.303390\pi$
$702$		0			0
$703$	−15.0268	−	26.0272i	−0.566747	−	0.981634i
$704$		0			0
$705$	−5.98066	+	10.3588i	−0.225245	+	0.390135i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−13.6077	+	23.5693i	−0.511049	+	0.885162i	0.488869	+	0.872357i	$0.337409\pi$
$709$	−13.6077	+	23.5693i	−0.511049	+	0.885162i	−0.999918	+	0.0128053i	$0.995924\pi$
$710$		0			0
$711$	7.13630	+	12.3604i	0.267632	+	0.463553i
$712$		0			0
$713$	−8.05526			−0.301672
$714$		0			0
$715$	8.17609			0.305768
$716$		0			0
$717$	11.8023	+	20.4421i	0.440764	+	0.763425i
$718$		0			0
$719$	24.7463	−	42.8619i	0.922881	−	1.59848i	0.127948	−	0.991781i	$-0.459161\pi$
$719$	24.7463	−	42.8619i	0.922881	−	1.59848i	0.794933	−	0.606697i	$-0.207506\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−7.41555	+	12.8441i	−0.275787	+	0.477678i
$724$		0			0
$725$	4.95603	+	8.58409i	0.184062	+	0.318805i
$726$		0			0
$727$	34.1732			1.26742			0.633708	−	0.773573i	$-0.281532\pi$
$727$	34.1732			1.26742			0.633708	+	0.773573i	$0.281532\pi$
$728$		0			0
$729$	26.4548			0.979807
$730$		0			0
$731$	3.97858	+	6.89111i	0.147153	+	0.254877i
$732$		0			0
$733$	19.4898	−	33.7573i	0.719873	−	1.24686i	−0.241177	−	0.970481i	$-0.577534\pi$
$733$	19.4898	−	33.7573i	0.719873	−	1.24686i	0.961050	−	0.276375i	$-0.0891331\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	17.7008	−	30.6586i	0.652016	−	1.12932i
$738$		0			0
$739$	14.1386	+	24.4887i	0.520096	+	0.900833i	0.999727	+	0.0233626i	$0.00743722\pi$
$739$	14.1386	+	24.4887i	0.520096	+	0.900833i	−0.479631	+	0.877470i	$0.659229\pi$
$740$		0			0
$741$	−24.0491			−0.883464
$742$		0			0
$743$	27.4681			1.00771			0.503854	−	0.863789i	$-0.331915\pi$
$743$	27.4681			1.00771			0.503854	+	0.863789i	$0.331915\pi$
$744$		0			0
$745$	−8.08456	−	14.0029i	−0.296195	−	0.513025i
$746$		0			0
$747$	−8.34242	+	14.4495i	−0.305233	+	0.528679i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.100004	−	0.173212i	0.00364920	−	0.00632060i	−0.864195	−	0.503157i	$-0.832172\pi$
$751$	0.100004	−	0.173212i	0.00364920	−	0.00632060i	0.867844	+	0.496836i	$0.165505\pi$
$752$		0			0
$753$	1.44868	+	2.50919i	0.0527929	+	0.0914400i
$754$		0			0
$755$	17.9335			0.652666
$756$		0			0
$757$	−9.94418			−0.361427			−0.180714	−	0.983536i	$-0.557841\pi$
$757$	−9.94418			−0.361427			−0.180714	+	0.983536i	$0.557841\pi$
$758$		0			0
$759$	12.0610	+	20.8902i	0.437785	+	0.758267i
$760$		0			0
$761$	−2.93378	+	5.08145i	−0.106349	+	0.184202i	−0.914289	−	0.405063i	$-0.867250\pi$
$761$	−2.93378	+	5.08145i	−0.106349	+	0.184202i	0.807939	+	0.589266i	$0.200583\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.53021	−	2.65040i	0.0553248	−	0.0958253i
$766$		0			0
$767$	−0.675833	−	1.17058i	−0.0244029	−	0.0422671i
$768$		0			0
$769$	12.9114			0.465596			0.232798	−	0.972525i	$-0.425212\pi$
$769$	12.9114			0.465596			0.232798	+	0.972525i	$0.425212\pi$
$770$		0			0
$771$	41.0699			1.47910
$772$		0			0
$773$	19.9558	+	34.5645i	0.717760	+	1.24320i	0.961885	+	0.273453i	$0.0881659\pi$
$773$	19.9558	+	34.5645i	0.717760	+	1.24320i	−0.244125	+	0.969744i	$0.578501\pi$
$774$		0			0
$775$	−3.35898	+	5.81793i	−0.120658	+	0.208986i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.50794	−	4.34387i	0.0898561	−	0.155635i
$780$		0			0
$781$	−11.1926	−	19.3861i	−0.400502	−	0.693690i
$782$		0			0
$783$	−13.6762			−0.488747
$784$		0			0
$785$	−11.8212			−0.421916
$786$		0			0
$787$	−5.59497	−	9.69077i	−0.199439	−	0.345439i	0.748908	−	0.662674i	$-0.230579\pi$
$787$	−5.59497	−	9.69077i	−0.199439	−	0.345439i	−0.948347	+	0.317236i	$0.897245\pi$
$788$		0			0
$789$	−4.26133	+	7.38084i	−0.151707	+	0.262765i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	9.39372	−	16.2704i	0.333581	−	0.577779i
$794$		0			0
$795$	−1.11417	−	1.92980i	−0.0395155	−	0.0684428i
$796$		0			0
$797$	−27.4646			−0.972846			−0.486423	−	0.873723i	$-0.661699\pi$
$797$	−27.4646			−0.972846			−0.486423	+	0.873723i	$0.661699\pi$
$798$		0			0
$799$	23.1952			0.820586
$800$		0			0
$801$	−10.3069	−	17.8520i	−0.364176	−	0.630771i
$802$		0			0
$803$	20.0475	−	34.7232i	0.707459	−	1.22536i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	20.0806	−	34.7806i	0.706871	−	1.22434i
$808$		0			0
$809$	−19.4532	−	33.6939i	−0.683938	−	1.18462i	−0.973769	−	0.227538i	$-0.926932\pi$
$809$	−19.4532	−	33.6939i	−0.683938	−	1.18462i	0.289831	−	0.957078i	$-0.406401\pi$
$810$		0			0
$811$	−24.3485			−0.854992			−0.427496	−	0.904017i	$-0.640604\pi$
$811$	−24.3485			−0.854992			−0.427496	+	0.904017i	$0.640604\pi$
$812$		0			0
$813$	15.2963			0.536465
$814$		0			0
$815$	7.28751	+	12.6223i	0.255270	+	0.442141i
$816$		0			0
$817$	13.3793	−	23.1735i	0.468081	−	0.810740i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.18816	+	2.05795i	−0.0414670	+	0.0718230i	−0.886014	−	0.463658i	$-0.846536\pi$
$821$	−1.18816	+	2.05795i	−0.0414670	+	0.0718230i	0.844547	+	0.535481i	$0.179870\pi$
$822$		0			0
$823$	4.35915	+	7.55027i	0.151951	+	0.263186i	0.931944	−	0.362601i	$-0.118111\pi$
$823$	4.35915	+	7.55027i	0.151951	+	0.263186i	−0.779994	+	0.625787i	$0.784778\pi$
$824$		0			0
$825$	20.1173			0.700396
$826$		0			0
$827$	−37.7669			−1.31328			−0.656642	−	0.754202i	$-0.728024\pi$
$827$	−37.7669			−1.31328			−0.656642	+	0.754202i	$0.728024\pi$
$828$		0			0
$829$	7.66959	+	13.2841i	0.266376	+	0.461377i	0.967923	−	0.251246i	$-0.0808404\pi$
$829$	7.66959	+	13.2841i	0.266376	+	0.461377i	−0.701547	+	0.712623i	$0.747507\pi$
$830$		0			0
$831$	18.6159	−	32.2436i	0.645778	−	1.11852i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−4.13691	+	7.16533i	−0.143164	+	0.247967i
$836$		0			0
$837$	−4.63456	−	8.02730i	−0.160194	−	0.277464i
$838$		0			0
$839$	44.2930			1.52916			0.764582	−	0.644526i	$-0.222945\pi$
$839$	44.2930			1.52916			0.764582	+	0.644526i	$0.222945\pi$
$840$		0			0
$841$	−23.0553			−0.795012
$842$		0			0
$843$	3.89810	+	6.75170i	0.134258	+	0.232541i
$844$		0			0
$845$	−3.87255	+	6.70745i	−0.133220	+	0.230743i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.702884	−	1.21743i	0.0241229	−	0.0417821i
$850$		0			0
$851$	8.89066	+	15.3991i	0.304768	+	0.527874i
$852$		0			0
$853$	−28.4674			−0.974706			−0.487353	−	0.873205i	$-0.662038\pi$
$853$	−28.4674			−0.974706			−0.487353	+	0.873205i	$0.662038\pi$
$854$		0			0
$855$	−10.2916			−0.351966
$856$		0			0
$857$	−12.2048	−	21.1394i	−0.416909	−	0.722108i	0.578717	−	0.815528i	$-0.303553\pi$
$857$	−12.2048	−	21.1394i	−0.416909	−	0.722108i	−0.995627	+	0.0934199i	$0.970220\pi$
$858$		0			0
$859$	−2.09041	+	3.62069i	−0.0713237	+	0.123536i	−0.899482	−	0.436958i	$-0.856056\pi$
$859$	−2.09041	+	3.62069i	−0.0713237	+	0.123536i	0.828158	+	0.560495i	$0.189389\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.8316	+	43.0096i	−0.845277	+	1.46406i	0.0401029	+	0.999196i	$0.487231\pi$
$863$	−24.8316	+	43.0096i	−0.845277	+	1.46406i	−0.885380	+	0.464868i	$0.846102\pi$
$864$		0			0
$865$	8.58524	+	14.8701i	0.291907	+	0.505598i
$866$		0			0
$867$	−14.3722			−0.488104
$868$		0			0
$869$	−41.8264			−1.41886
$870$		0			0
$871$	−10.4411	−	18.0845i	−0.353782	−	0.612769i
$872$		0			0
$873$	5.99578	−	10.3850i	0.202926	−	0.351479i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.81217	−	6.60288i	0.128728	−	0.222963i	−0.794456	−	0.607322i	$-0.792244\pi$
$877$	3.81217	−	6.60288i	0.128728	−	0.222963i	0.923184	+	0.384358i	$0.125577\pi$
$878$		0			0
$879$	2.53617	+	4.39278i	0.0855431	+	0.148165i
$880$		0			0
$881$	−23.6086			−0.795393			−0.397697	−	0.917517i	$-0.630190\pi$
$881$	−23.6086			−0.795393			−0.397697	+	0.917517i	$0.630190\pi$
$882$		0			0
$883$	−1.58826			−0.0534491			−0.0267245	−	0.999643i	$-0.508508\pi$
$883$	−1.58826			−0.0534491			−0.0267245	+	0.999643i	$0.508508\pi$
$884$		0			0
$885$	0.382299	+	0.662160i	0.0128508	+	0.0222583i
$886$		0			0
$887$	3.66635	−	6.35031i	0.123104	−	0.213223i	−0.797886	−	0.602808i	$-0.794048\pi$
$887$	3.66635	−	6.35031i	0.123104	−	0.213223i	0.920990	+	0.389586i	$0.127382\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−6.53980	+	11.3273i	−0.219092	+	0.379478i
$892$		0			0
$893$	−39.0006	−	67.5509i	−1.30510	−	2.26051i
$894$		0			0
$895$	13.5940			0.454397
$896$		0			0
$897$	14.2287			0.475083
$898$		0			0
$899$	2.01452	+	3.48924i	0.0671879	+	0.116373i
$900$		0			0
$901$	−2.16057	+	3.74222i	−0.0719791	+	0.124671i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.51983	+	2.63242i	−0.0505207	+	0.0875045i
$906$		0			0
$907$	−13.6499	−	23.6424i	−0.453239	−	0.785033i	0.545346	−	0.838211i	$-0.316398\pi$
$907$	−13.6499	−	23.6424i	−0.453239	−	0.785033i	−0.998585	+	0.0531781i	$0.983065\pi$
$908$		0			0
$909$	24.4242			0.810100
$910$		0			0
$911$	−13.1608			−0.436036			−0.218018	−	0.975945i	$-0.569959\pi$
$911$	−13.1608			−0.436036			−0.218018	+	0.975945i	$0.569959\pi$
$912$		0			0
$913$	−24.4477	−	42.3447i	−0.809102	−	1.40141i
$914$		0			0
$915$	−5.31374	+	9.20368i	−0.175667	+	0.304264i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−3.11792	+	5.40040i	−0.102851	+	0.178143i	−0.912858	−	0.408277i	$-0.866130\pi$
$919$	−3.11792	+	5.40040i	−0.102851	+	0.178143i	0.810007	+	0.586420i	$0.199463\pi$
$920$		0			0
$921$	14.1551	+	24.5174i	0.466427	+	0.807875i
$922$		0			0
$923$	−13.2042			−0.434623
$924$		0			0
$925$	14.8294			0.487587
$926$		0			0
$927$	3.29239	+	5.70258i	0.108136	+	0.187297i
$928$		0			0
$929$	−21.6686	+	37.5311i	−0.710923	+	1.23135i	0.253588	+	0.967312i	$0.418389\pi$
$929$	−21.6686	+	37.5311i	−0.710923	+	1.23135i	−0.964511	+	0.264042i	$0.914944\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	6.35615	−	11.0092i	0.208091	−	0.360424i
$934$		0			0
$935$	4.48432	+	7.76708i	0.146653	+	0.254011i
$936$		0			0
$937$	−47.4200			−1.54914			−0.774572	−	0.632486i	$-0.782035\pi$
$937$	−47.4200			−1.54914			−0.774572	+	0.632486i	$0.782035\pi$
$938$		0			0
$939$	13.3712			0.436354
$940$		0			0
$941$	18.9537	+	32.8288i	0.617874	+	1.07019i	0.989873	+	0.141955i	$0.0453390\pi$
$941$	18.9537	+	32.8288i	0.617874	+	1.07019i	−0.372000	+	0.928233i	$0.621328\pi$
$942$		0			0
$943$	−1.48383	+	2.57007i	−0.0483201	+	0.0836929i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.2538	+	42.0088i	−0.788142	+	1.36510i	0.138962	+	0.990298i	$0.455624\pi$
$947$	−24.2538	+	42.0088i	−0.788142	+	1.36510i	−0.927104	+	0.374805i	$0.877710\pi$
$948$		0			0
$949$	−11.8253	−	20.4820i	−0.383866	−	0.664875i
$950$		0			0
$951$	26.3775			0.855351
$952$		0			0
$953$	33.8440			1.09631			0.548157	−	0.836376i	$-0.315330\pi$
$953$	33.8440			1.09631			0.548157	+	0.836376i	$0.315330\pi$
$954$		0			0
$955$	−10.1314	−	17.5481i	−0.327845	−	0.567844i
$956$		0			0
$957$	6.03258	−	10.4487i	0.195006	−	0.337760i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	14.1346	−	24.4819i	0.455956	−	0.789740i
$962$		0			0
$963$	−3.63060	−	6.28839i	−0.116994	−	0.202640i
$964$		0			0
$965$	4.68093			0.150684
$966$		0			0
$967$	28.6546			0.921471			0.460735	−	0.887538i	$-0.347586\pi$
$967$	28.6546			0.921471			0.460735	+	0.887538i	$0.347586\pi$
$968$		0			0
$969$	−13.1901	−	22.8460i	−0.423728	−	0.733919i
$970$		0			0
$971$	−19.2384	+	33.3220i	−0.617391	+	1.06935i	0.372569	+	0.928004i	$0.378477\pi$
$971$	−19.2384	+	33.3220i	−0.617391	+	1.06935i	−0.989960	+	0.141348i	$0.954856\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	5.93327	−	10.2767i	0.190017	−	0.329118i
$976$		0			0
$977$	−3.43627	−	5.95179i	−0.109936	−	0.190414i	0.805808	−	0.592177i	$-0.201731\pi$
$977$	−3.43627	−	5.95179i	−0.109936	−	0.190414i	−0.915744	+	0.401762i	$0.868398\pi$
$978$		0			0
$979$	60.4093			1.93069
$980$		0			0
$981$	−13.2210			−0.422114
$982$		0			0
$983$	−5.97653	−	10.3517i	−0.190622	−	0.330167i	0.754835	−	0.655915i	$-0.227717\pi$
$983$	−5.97653	−	10.3517i	−0.190622	−	0.330167i	−0.945456	+	0.325748i	$0.894384\pi$
$984$		0			0
$985$	9.02021	−	15.6235i	0.287408	−	0.497805i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.91588	+	13.7107i	−0.251710	+	0.435975i
$990$		0			0
$991$	14.5774	+	25.2488i	0.463066	+	0.802054i	0.999112	−	0.0421347i	$-0.0134159\pi$
$991$	14.5774	+	25.2488i	0.463066	+	0.802054i	−0.536046	+	0.844189i	$0.680083\pi$
$992$		0			0
$993$	−30.7962			−0.977289
$994$		0			0
$995$	−6.18236			−0.195994
$996$		0			0
$997$	1.49686	+	2.59263i	0.0474059	+	0.0821094i	0.888755	−	0.458383i	$-0.151571\pi$
$997$	1.49686	+	2.59263i	0.0474059	+	0.0821094i	−0.841349	+	0.540493i	$0.818238\pi$
$998$		0			0
$999$	−10.2304	+	17.7196i	−0.323676	+	0.560624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1372.2.e.d.1353.1		12
7.2	even	3		1372.2.a.a.1.6	✓	6
7.3	odd	6		1372.2.e.a.361.6		12
7.4	even	3	inner	1372.2.e.d.361.1		12
7.5	odd	6		1372.2.a.d.1.1	yes	6
7.6	odd	2		1372.2.e.a.1353.6		12
28.19	even	6		5488.2.a.g.1.6		6
28.23	odd	6		5488.2.a.q.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1372.2.a.a.1.6	✓	6	7.2	even	3
1372.2.a.d.1.1	yes	6	7.5	odd	6
1372.2.e.a.361.6		12	7.3	odd	6
1372.2.e.a.1353.6		12	7.6	odd	2
1372.2.e.d.361.1		12	7.4	even	3	inner
1372.2.e.d.1353.1		12	1.1	even	1	trivial
5488.2.a.g.1.6		6	28.19	even	6
5488.2.a.q.1.1		6	28.23	odd	6

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1372 = 2^{2} \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1372.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.653437 - 1.13179i) q^{3} +(0.483381 - 0.837240i) q^{5} +(0.646041 - 1.11898i) q^{9} +(1.89324 + 3.27919i) q^{11} +2.23352 q^{13} -1.26343 q^{15} +(1.22501 + 2.12179i) q^{17} +(4.11950 - 7.13518i) q^{19} +(-2.43732 + 4.22156i) q^{23} +(2.03269 + 3.52072i) q^{25} -5.60921 q^{27} +2.43817 q^{29} +(0.826242 + 1.43109i) q^{31} +(2.47423 - 4.28549i) q^{33} +(1.82386 - 3.15902i) q^{37} +(-1.45946 - 2.52787i) q^{39} +0.608796 q^{41} +3.24779 q^{43} +(-0.624567 - 1.08178i) q^{45} +(4.73365 - 8.19893i) q^{47} +(1.60094 - 2.77291i) q^{51} +(0.881856 + 1.52742i) q^{53} +3.66063 q^{55} -10.7673 q^{57} +(-0.302587 - 0.524095i) q^{59} +(4.20579 - 7.28465i) q^{61} +(1.07964 - 1.86999i) q^{65} +(-4.67472 - 8.09685i) q^{67} +6.37053 q^{69} -5.91185 q^{71} +(-5.29447 - 9.17030i) q^{73} +(2.65646 - 4.60113i) q^{75} +(-5.52311 + 9.56630i) q^{79} +(1.72714 + 2.99150i) q^{81} -12.9132 q^{83} +2.36859 q^{85} +(-1.59319 - 2.75948i) q^{87} +(7.97696 - 13.8165i) q^{89} +(1.07979 - 1.87026i) q^{93} +(-3.98257 - 6.89802i) q^{95} +9.28081 q^{97} +4.89245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 7 q^{3} + 7 q^{5} - 9 q^{9} - 3 q^{11} - 14 q^{13} + 22 q^{15} + 7 q^{19} - 11 q^{23} - 3 q^{25} - 56 q^{27} + 12 q^{29} + 14 q^{31} + 6 q^{37} - 5 q^{39} - 6 q^{43} + 21 q^{45} + 42 q^{47} + 17 q^{51}+ \cdots - 68 q^{99}+O(q^{100}) \) 12 * q + 7 * q^3 + 7 * q^5 - 9 * q^9 - 3 * q^11 - 14 * q^13 + 22 * q^15 + 7 * q^19 - 11 * q^23 - 3 * q^25 - 56 * q^27 + 12 * q^29 + 14 * q^31 + 6 * q^37 - 5 * q^39 - 6 * q^43 + 21 * q^45 + 42 * q^47 + 17 * q^51 + 17 * q^53 - 28 * q^55 - 12 * q^57 + 35 * q^59 + 7 * q^61 + 6 * q^65 + 14 * q^67 - 28 * q^69 - 56 * q^71 + 35 * q^75 - 6 * q^79 - 34 * q^81 - 98 * q^83 - 46 * q^85 + 21 * q^87 - 7 * q^89 + 14 * q^93 + 25 * q^95 + 42 * q^97 - 68 * q^99

Introduction

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