LMFDB - Embedded newform 1148.2.ba.a.701.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.20
Character	$\chi$	$=$	1148.701
Dual form			1148.2.ba.a.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.08866i q^{3} +(-1.11364 + 3.42744i) q^{5} +(-0.587785 + 0.809017i) q^{7} -6.53981 q^{9} +O(q^{10})$	\(q+3.08866i q^{3} +(-1.11364 + 3.42744i) q^{5} +(-0.587785 + 0.809017i) q^{7} -6.53981 q^{9} +(5.51230 - 1.79105i) q^{11} +(-3.99429 - 5.49767i) q^{13} +(-10.5862 - 3.43966i) q^{15} +(-5.22070 + 1.69631i) q^{17} +(-1.80765 + 2.48802i) q^{19} +(-2.49878 - 1.81547i) q^{21} +(-1.09184 + 0.793269i) q^{23} +(-6.46203 - 4.69494i) q^{25} -10.9333i q^{27} +(9.05917 + 2.94350i) q^{29} +(1.41863 + 4.36610i) q^{31} +(5.53195 + 17.0256i) q^{33} +(-2.11827 - 2.91555i) q^{35} +(-1.00424 + 3.09074i) q^{37} +(16.9804 - 12.3370i) q^{39} +(-6.06447 - 2.05480i) q^{41} +(-0.450967 + 0.327647i) q^{43} +(7.28300 - 22.4148i) q^{45} +(-0.526001 - 0.723978i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-5.23932 - 16.1250i) q^{51} +(5.67195 + 1.84293i) q^{53} +20.8876i q^{55} +(-7.68464 - 5.58322i) q^{57} +(0.983245 - 0.714369i) q^{59} +(-1.69686 - 1.23284i) q^{61} +(3.84400 - 5.29082i) q^{63} +(23.2911 - 7.56774i) q^{65} +(-14.1189 - 4.58751i) q^{67} +(-2.45014 - 3.37232i) q^{69} +(0.947422 - 0.307836i) q^{71} +6.86712 q^{73} +(14.5011 - 19.9590i) q^{75} +(-1.79105 + 5.51230i) q^{77} +7.78933i q^{79} +14.1497 q^{81} +0.588419 q^{83} -19.7827i q^{85} +(-9.09148 + 27.9807i) q^{87} +(-7.21580 + 9.93170i) q^{89} +6.79549 q^{91} +(-13.4854 + 4.38167i) q^{93} +(-6.51445 - 8.96638i) q^{95} +(13.0390 + 4.23662i) q^{97} +(-36.0494 + 11.7132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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
$3$			3.08866i			1.78324i	0.452787	+	0.891619i	$0.350430\pi$
$3$			3.08866i			1.78324i	−0.452787	+	0.891619i	$0.649570\pi$
$4$		0			0
$5$	−1.11364	+	3.42744i	−0.498036	+	1.53280i	0.314136	+	0.949378i	$0.398285\pi$
$5$	−1.11364	+	3.42744i	−0.498036	+	1.53280i	−0.812172	+	0.583418i	$0.801715\pi$
$6$		0			0
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$8$		0			0
$9$	−6.53981			−2.17994
$10$		0			0
$11$	5.51230	−	1.79105i	1.66202	−	0.540023i	0.680726	−	0.732538i	$-0.261664\pi$
$11$	5.51230	−	1.79105i	1.66202	−	0.540023i	0.981294	+	0.192515i	$0.0616642\pi$
$12$		0			0
$13$	−3.99429	−	5.49767i	−1.10782	−	1.52478i	−0.824594	−	0.565725i	$-0.808597\pi$
$13$	−3.99429	−	5.49767i	−1.10782	−	1.52478i	−0.283222	−	0.959054i	$-0.591403\pi$
$14$		0			0
$15$	−10.5862	−	3.43966i	−2.73334	−	0.888116i
$16$		0			0
$17$	−5.22070	+	1.69631i	−1.26621	+	0.411415i	−0.863702	−	0.504003i	$-0.831860\pi$
$17$	−5.22070	+	1.69631i	−1.26621	+	0.411415i	−0.402504	+	0.915418i	$0.631860\pi$
$18$		0			0
$19$	−1.80765	+	2.48802i	−0.414704	+	0.570791i	−0.964358	−	0.264601i	$-0.914760\pi$
$19$	−1.80765	+	2.48802i	−0.414704	+	0.570791i	0.549654	+	0.835392i	$0.314760\pi$
$20$		0			0
$21$	−2.49878	−	1.81547i	−0.545278	−	0.396168i
$22$		0			0
$23$	−1.09184	+	0.793269i	−0.227665	+	0.165408i	−0.695770	−	0.718265i	$-0.744937\pi$
$23$	−1.09184	+	0.793269i	−0.227665	+	0.165408i	0.468105	+	0.883673i	$0.344937\pi$
$24$		0			0
$25$	−6.46203	−	4.69494i	−1.29241	−	0.938988i
$26$		0			0
$27$		−	10.9333i		−	2.10411i
$28$		0			0
$29$	9.05917	+	2.94350i	1.68225	+	0.546595i	0.985345	−	0.170573i	$-0.0545618\pi$
$29$	9.05917	+	2.94350i	1.68225	+	0.546595i	0.696901	+	0.717168i	$0.254562\pi$
$30$		0			0
$31$	1.41863	+	4.36610i	0.254794	+	0.784176i	0.993870	+	0.110554i	$0.0352624\pi$
$31$	1.41863	+	4.36610i	0.254794	+	0.784176i	−0.739076	+	0.673622i	$0.764738\pi$
$32$		0			0
$33$	5.53195	+	17.0256i	0.962990	+	2.96378i
$34$		0			0
$35$	−2.11827	−	2.91555i	−0.358053	−	0.492818i
$36$		0			0
$37$	−1.00424	+	3.09074i	−0.165096	+	0.508115i	−0.999043	−	0.0437299i	$-0.986076\pi$
$37$	−1.00424	+	3.09074i	−0.165096	+	0.508115i	0.833947	+	0.551845i	$0.186076\pi$
$38$		0			0
$39$	16.9804	−	12.3370i	2.71904	−	1.97550i
$40$		0			0
$41$	−6.06447	−	2.05480i	−0.947111	−	0.320906i
$41$	−6.06447	−	2.05480i	−0.947111	−	0.320906i
$42$		0			0
$43$	−0.450967	+	0.327647i	−0.0687718	+	0.0499657i	−0.621640	−	0.783303i	$-0.713533\pi$
$43$	−0.450967	+	0.327647i	−0.0687718	+	0.0499657i	0.552868	+	0.833269i	$0.313533\pi$
$44$		0			0
$45$	7.28300	−	22.4148i	1.08569	−	3.34140i
$46$		0			0
$47$	−0.526001	−	0.723978i	−0.0767251	−	0.105603i	0.768930	−	0.639334i	$-0.220790\pi$
$47$	−0.526001	−	0.723978i	−0.0767251	−	0.105603i	−0.845655	+	0.533730i	$0.820790\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$		0			0
$51$	−5.23932	−	16.1250i	−0.733651	−	2.25795i
$52$		0			0
$53$	5.67195	+	1.84293i	0.779103	+	0.253146i	0.671457	−	0.741043i	$-0.265669\pi$
$53$	5.67195	+	1.84293i	0.779103	+	0.253146i	0.107646	+	0.994189i	$0.465669\pi$
$54$		0			0
$55$			20.8876i			2.81649i
$56$		0			0
$57$	−7.68464	−	5.58322i	−1.01786	−	0.739516i
$58$		0			0
$59$	0.983245	−	0.714369i	0.128008	−	0.0930029i	−0.521939	−	0.852983i	$-0.674791\pi$
$59$	0.983245	−	0.714369i	0.128008	−	0.0930029i	0.649947	+	0.759980i	$0.274791\pi$
$60$		0			0
$61$	−1.69686	−	1.23284i	−0.217261	−	0.157849i	0.473832	−	0.880615i	$-0.342870\pi$
$61$	−1.69686	−	1.23284i	−0.217261	−	0.157849i	−0.691093	+	0.722766i	$0.742870\pi$
$62$		0			0
$63$	3.84400	−	5.29082i	0.484299	−	0.666580i
$64$		0			0
$65$	23.2911	−	7.56774i	2.88891	−	0.938663i
$66$		0			0
$67$	−14.1189	−	4.58751i	−1.72490	−	0.560454i	−0.732203	−	0.681087i	$-0.761508\pi$
$67$	−14.1189	−	4.58751i	−1.72490	−	0.560454i	−0.992697	+	0.120633i	$0.961508\pi$
$68$		0			0
$69$	−2.45014	−	3.37232i	−0.294962	−	0.405980i
$70$		0			0
$71$	0.947422	−	0.307836i	0.112438	−	0.0365334i	−0.252257	−	0.967660i	$-0.581173\pi$
$71$	0.947422	−	0.307836i	0.112438	−	0.0365334i	0.364696	+	0.931127i	$0.381173\pi$
$72$		0			0
$73$	6.86712			0.803736			0.401868	−	0.915698i	$-0.368361\pi$
$73$	6.86712			0.803736			0.401868	+	0.915698i	$0.368361\pi$
$74$		0			0
$75$	14.5011	−	19.9590i	1.67444	−	2.30467i
$76$		0			0
$77$	−1.79105	+	5.51230i	−0.204110	+	0.628185i
$78$		0			0
$79$			7.78933i			0.876368i	0.898885	+	0.438184i	$0.144378\pi$
$79$			7.78933i			0.876368i	−0.898885	+	0.438184i	$0.855622\pi$
$80$		0			0
$81$	14.1497			1.57219
$82$		0			0
$83$	0.588419			0.0645874			0.0322937	−	0.999478i	$-0.489719\pi$
$83$	0.588419			0.0645874			0.0322937	+	0.999478i	$0.489719\pi$
$84$		0			0
$85$		−	19.7827i		−	2.14573i
$86$		0			0
$87$	−9.09148	+	27.9807i	−0.974708	+	2.99984i
$88$		0			0
$89$	−7.21580	+	9.93170i	−0.764874	+	1.05276i	0.231919	+	0.972735i	$0.425499\pi$
$89$	−7.21580	+	9.93170i	−0.764874	+	1.05276i	−0.996793	+	0.0800232i	$0.974501\pi$
$90$		0			0
$91$	6.79549			0.712361
$92$		0			0
$93$	−13.4854	+	4.38167i	−1.39837	+	0.454358i
$94$		0			0
$95$	−6.51445	−	8.96638i	−0.668369	−	0.919931i
$96$		0			0
$97$	13.0390	+	4.23662i	1.32391	+	0.430164i	0.883835	−	0.467798i	$-0.154953\pi$
$97$	13.0390	+	4.23662i	1.32391	+	0.430164i	0.440073	+	0.897962i	$0.354953\pi$
$98$		0			0
$99$	−36.0494	+	11.7132i	−3.62310	+	1.17722i
$100$		0			0
$101$	−7.80734	+	10.7459i	−0.776859	+	1.06926i	0.218762	+	0.975778i	$0.429798\pi$
$101$	−7.80734	+	10.7459i	−0.776859	+	1.06926i	−0.995621	+	0.0934771i	$0.970202\pi$
$102$		0			0
$103$	−3.74355	−	2.71985i	−0.368863	−	0.267994i	0.387877	−	0.921711i	$-0.373209\pi$
$103$	−3.74355	−	2.71985i	−0.368863	−	0.267994i	−0.756739	+	0.653717i	$0.773209\pi$
$104$		0			0
$105$	9.00514	−	6.54262i	0.878812	−	0.638494i
$106$		0			0
$107$	−5.40007	−	3.92338i	−0.522044	−	0.379287i	0.295329	−	0.955396i	$-0.404571\pi$
$107$	−5.40007	−	3.92338i	−0.522044	−	0.379287i	−0.817373	+	0.576108i	$0.804571\pi$
$108$		0			0
$109$			14.4780i			1.38675i	0.720579	+	0.693373i	$0.243876\pi$
$109$			14.4780i			1.38675i	−0.720579	+	0.693373i	$0.756124\pi$
$110$		0			0
$111$	−9.54624	−	3.10176i	−0.906089	−	0.294406i
$112$		0			0
$113$	−1.81046	−	5.57203i	−0.170314	−	0.524173i	0.829074	−	0.559138i	$-0.188868\pi$
$113$	−1.81046	−	5.57203i	−0.170314	−	0.524173i	−0.999389	+	0.0349655i	$0.988868\pi$
$114$		0			0
$115$	−1.50296	−	4.62563i	−0.140152	−	0.431343i
$116$		0			0
$117$	26.1219	+	35.9537i	2.41497	+	3.32392i
$118$		0			0
$119$	1.69631	−	5.22070i	0.155500	−	0.478581i
$120$		0			0
$121$	18.2784	−	13.2800i	1.66167	−	1.20727i
$122$		0			0
$123$	6.34657	−	18.7311i	0.572251	−	1.68892i
$124$		0			0
$125$	8.71025	−	6.32836i	0.779068	−	0.566026i
$126$		0			0
$127$	−1.64879	+	5.07444i	−0.146306	+	0.450284i	−0.997177	−	0.0750916i	$-0.976075\pi$
$127$	−1.64879	+	5.07444i	−0.146306	+	0.450284i	0.850871	+	0.525375i	$0.176075\pi$
$128$		0			0
$129$	−1.01199	−	1.39288i	−0.0891007	−	0.122637i
$130$		0			0
$131$	−3.23259	−	9.94890i	−0.282433	−	0.869240i	−0.987156	−	0.159757i	$-0.948929\pi$
$131$	−3.23259	−	9.94890i	−0.282433	−	0.869240i	0.704723	−	0.709482i	$-0.251071\pi$
$132$		0			0
$133$	−0.950339	−	2.92484i	−0.0824049	−	0.253616i
$134$		0			0
$135$	37.4731	+	12.1757i	3.22517	+	1.04792i
$136$		0			0
$137$		−	10.7209i		−	0.915945i	−0.888966	−	0.457972i	$-0.848576\pi$
$137$		−	10.7209i		−	0.915945i	0.888966	−	0.457972i	$-0.151424\pi$
$138$		0			0
$139$	−0.194030	−	0.140971i	−0.0164574	−	0.0119570i	0.579526	−	0.814954i	$-0.303238\pi$
$139$	−0.194030	−	0.140971i	−0.0164574	−	0.0119570i	−0.595984	+	0.802997i	$0.703238\pi$
$140$		0			0
$141$	2.23612	−	1.62464i	0.188315	−	0.136819i
$142$		0			0
$143$	−31.8643	−	23.1508i	−2.66463	−	1.93597i
$144$		0			0
$145$	−20.1773	+	27.7717i	−1.67564	+	2.30632i
$146$		0			0
$147$	2.93749	−	0.954448i	0.242280	−	0.0787215i
$148$		0			0
$149$	8.51263	+	2.76592i	0.697382	+	0.226593i	0.636189	−	0.771533i	$-0.280510\pi$
$149$	8.51263	+	2.76592i	0.697382	+	0.226593i	0.0611923	+	0.998126i	$0.480510\pi$
$150$		0			0
$151$	−6.28301	−	8.64782i	−0.511304	−	0.703750i	0.472834	−	0.881151i	$-0.343231\pi$
$151$	−6.28301	−	8.64782i	−0.511304	−	0.703750i	−0.984139	+	0.177402i	$0.943231\pi$
$152$		0			0
$153$	34.1424	−	11.0935i	2.76025	−	0.896859i
$154$		0			0
$155$	−16.5444			−1.32888
$156$		0			0
$157$	−5.66886	+	7.80252i	−0.452424	+	0.622709i	−0.972916	−	0.231158i	$-0.925749\pi$
$157$	−5.66886	+	7.80252i	−0.452424	+	0.622709i	0.520492	+	0.853867i	$0.325749\pi$
$158$		0			0
$159$	−5.69218	+	17.5187i	−0.451419	+	1.38933i
$160$		0			0
$161$		−	1.34959i		−	0.106363i
$162$		0			0
$163$	−6.26336			−0.490584			−0.245292	−	0.969449i	$-0.578884\pi$
$163$	−6.26336			−0.490584			−0.245292	+	0.969449i	$0.578884\pi$
$164$		0			0
$165$	−64.5148			−5.02247
$166$		0			0
$167$			0.0521509i			0.00403556i	0.999998	+	0.00201778i	$0.000642280\pi$
$167$			0.0521509i			0.00403556i	−0.999998	+	0.00201778i	$0.999358\pi$
$168$		0			0
$169$	−10.2528	+	31.5548i	−0.788676	+	2.42729i
$170$		0			0
$171$	11.8217	−	16.2712i	0.904028	−	1.24429i
$172$		0			0
$173$	5.63737			0.428601			0.214301	−	0.976768i	$-0.431253\pi$
$173$	5.63737			0.428601			0.214301	+	0.976768i	$0.431253\pi$
$174$		0			0
$175$	7.59658	−	2.46828i	0.574247	−	0.186584i
$176$		0			0
$177$	2.20644	+	3.03691i	0.165846	+	0.228268i
$178$		0			0
$179$	−16.1755	−	5.25574i	−1.20901	−	0.392832i	−0.365944	−	0.930637i	$-0.619254\pi$
$179$	−16.1755	−	5.25574i	−1.20901	−	0.392832i	−0.843069	+	0.537805i	$0.819254\pi$
$180$		0			0
$181$	8.83006	−	2.86906i	0.656333	−	0.213256i	0.0381286	−	0.999273i	$-0.487860\pi$
$181$	8.83006	−	2.86906i	0.656333	−	0.213256i	0.618205	+	0.786017i	$0.287860\pi$
$182$		0			0
$183$	3.80782	−	5.24102i	0.281482	−	0.387427i
$184$		0			0
$185$	−9.47495	−	6.88396i	−0.696612	−	0.506118i
$186$		0			0
$187$	−25.7399	+	18.7011i	−1.88229	+	1.36756i
$188$		0			0
$189$	8.84519	+	6.42641i	0.643393	+	0.467453i
$190$		0			0
$191$		−	2.62787i		−	0.190146i	−0.995470	−	0.0950730i	$-0.969692\pi$
$191$		−	2.62787i		−	0.190146i	0.995470	−	0.0950730i	$-0.0303084\pi$
$192$		0			0
$193$	−19.1014	−	6.20643i	−1.37495	−	0.446749i	−0.473945	−	0.880555i	$-0.657170\pi$
$193$	−19.1014	−	6.20643i	−1.37495	−	0.446749i	−0.901006	+	0.433806i	$0.857170\pi$
$194$		0			0
$195$	23.3742	+	71.9383i	1.67386	+	5.15161i
$196$		0			0
$197$	−1.44774	−	4.45569i	−0.103147	−	0.317455i	0.886144	−	0.463410i	$-0.153374\pi$
$197$	−1.44774	−	4.45569i	−0.103147	−	0.317455i	−0.989291	+	0.145955i	$0.953374\pi$
$198$		0			0
$199$	7.61905	+	10.4867i	0.540100	+	0.743384i	0.988627	−	0.150385i	$-0.0480514\pi$
$199$	7.61905	+	10.4867i	0.540100	+	0.743384i	−0.448528	+	0.893769i	$0.648051\pi$
$200$		0			0
$201$	14.1693	−	43.6085i	0.999423	−	3.07591i
$202$		0			0
$203$	−7.70619	+	5.59888i	−0.540869	+	0.392964i
$204$		0			0
$205$	13.7963	−	18.4973i	0.963578	−	1.29191i
$206$		0			0
$207$	7.14043	−	5.18783i	0.496294	−	0.360579i
$208$		0			0
$209$	−5.50814	+	16.9523i	−0.381006	+	1.17262i
$210$		0			0
$211$	9.17972	+	12.6348i	0.631958	+	0.869816i	0.998155	−	0.0607217i	$-0.0193402\pi$
$211$	9.17972	+	12.6348i	0.631958	+	0.869816i	−0.366197	+	0.930538i	$0.619340\pi$
$212$		0			0
$213$	0.950800	+	2.92626i	0.0651477	+	0.200504i
$214$		0			0
$215$	−0.620773	−	1.91054i	−0.0423363	−	0.130298i
$216$		0			0
$217$	−4.36610	−	1.41863i	−0.296390	−	0.0963031i
$218$		0			0
$219$			21.2102i			1.43325i
$220$		0			0
$221$	30.1787	+	21.9261i	2.03004	+	1.47491i
$222$		0			0
$223$	−5.61478	+	4.07938i	−0.375994	+	0.273175i	−0.759692	−	0.650283i	$-0.774650\pi$
$223$	−5.61478	+	4.07938i	−0.375994	+	0.273175i	0.383698	+	0.923459i	$0.374650\pi$
$224$		0			0
$225$	42.2605	+	30.7040i	2.81736	+	2.04694i
$226$		0			0
$227$	−6.24608	+	8.59699i	−0.414567	+	0.570602i	−0.964325	−	0.264722i	$-0.914720\pi$
$227$	−6.24608	+	8.59699i	−0.414567	+	0.570602i	0.549758	+	0.835324i	$0.314720\pi$
$228$		0			0
$229$	−5.60206	+	1.82022i	−0.370195	+	0.120284i	−0.488205	−	0.872729i	$-0.662348\pi$
$229$	−5.60206	+	1.82022i	−0.370195	+	0.120284i	0.118011	+	0.993012i	$0.462348\pi$
$230$		0			0
$231$	−17.0256	−	5.53195i	−1.12020	−	0.363976i
$232$		0			0
$233$	16.1101	+	22.1737i	1.05541	+	1.45265i	0.884024	+	0.467441i	$0.154824\pi$
$233$	16.1101	+	22.1737i	1.05541	+	1.45265i	0.171385	+	0.985204i	$0.445176\pi$
$234$		0			0
$235$	3.06717	−	0.996583i	0.200080	−	0.0650099i
$236$		0			0
$237$	−24.0586			−1.56277
$238$		0			0
$239$	7.49791	−	10.3200i	0.484999	−	0.667544i	−0.494457	−	0.869202i	$-0.664633\pi$
$239$	7.49791	−	10.3200i	0.484999	−	0.667544i	0.979456	+	0.201658i	$0.0646329\pi$
$240$		0			0
$241$	3.29045	−	10.1270i	0.211957	−	0.652336i	−0.787399	−	0.616444i	$-0.788573\pi$
$241$	3.29045	−	10.1270i	0.211957	−	0.652336i	0.999356	−	0.0358920i	$-0.0114272\pi$
$242$		0			0
$243$			10.9037i			0.699475i
$244$		0			0
$245$	3.60382			0.230240
$246$		0			0
$247$	20.8986			1.32975
$248$		0			0
$249$			1.81743i			0.115175i
$250$		0			0
$251$	5.03354	−	15.4916i	0.317714	−	0.977823i	−0.656909	−	0.753970i	$-0.728136\pi$
$251$	5.03354	−	15.4916i	0.317714	−	0.977823i	0.974623	−	0.223853i	$-0.0718636\pi$
$252$		0			0
$253$	−4.59777	+	6.32828i	−0.289059	+	0.397856i
$254$		0			0
$255$	61.1020			3.82635
$256$		0			0
$257$	5.42559	−	1.76288i	0.338439	−	0.109965i	−0.134867	−	0.990864i	$-0.543061\pi$
$257$	5.42559	−	1.76288i	0.338439	−	0.109965i	0.473306	+	0.880898i	$0.343061\pi$
$258$		0			0
$259$	−1.91018	−	2.62914i	−0.118693	−	0.163367i
$260$		0			0
$261$	−59.2453	−	19.2499i	−3.66719	−	1.19154i
$262$		0			0
$263$	−6.07699	+	1.97453i	−0.374723	+	0.121755i	−0.490323	−	0.871541i	$-0.663121\pi$
$263$	−6.07699	+	1.97453i	−0.374723	+	0.121755i	0.115600	+	0.993296i	$0.463121\pi$
$264$		0			0
$265$	−12.6330	+	17.3879i	−0.776042	+	1.06813i
$266$		0			0
$267$	−30.6756	−	22.2871i	−1.87732	−	1.36395i
$268$		0			0
$269$	−6.12042	+	4.44675i	−0.373169	+	0.271123i	−0.758524	−	0.651645i	$-0.774079\pi$
$269$	−6.12042	+	4.44675i	−0.373169	+	0.271123i	0.385355	+	0.922768i	$0.374079\pi$
$270$		0			0
$271$	25.7073	+	18.6774i	1.56161	+	1.13457i	0.934678	+	0.355497i	$0.115688\pi$
$271$	25.7073	+	18.6774i	1.56161	+	1.13457i	0.626929	+	0.779077i	$0.284312\pi$
$272$		0			0
$273$			20.9890i			1.27031i
$274$		0			0
$275$	−44.0296	−	14.3061i	−2.65508	−	0.862688i
$276$		0			0
$277$	1.57383	+	4.84374i	0.0945620	+	0.291032i	0.987139	−	0.159862i	$-0.0511051\pi$
$277$	1.57383	+	4.84374i	0.0945620	+	0.291032i	−0.892577	+	0.450894i	$0.851105\pi$
$278$		0			0
$279$	−9.27759	−	28.5535i	−0.555435	−	1.70945i
$280$		0			0
$281$	−6.02831	−	8.29726i	−0.359619	−	0.494973i	0.590424	−	0.807094i	$-0.298961\pi$
$281$	−6.02831	−	8.29726i	−0.359619	−	0.494973i	−0.950043	+	0.312120i	$0.898961\pi$
$282$		0			0
$283$	4.86290	−	14.9665i	0.289069	−	0.889664i	−0.696080	−	0.717964i	$-0.745074\pi$
$283$	4.86290	−	14.9665i	0.289069	−	0.889664i	0.985149	−	0.171700i	$-0.0549259\pi$
$284$		0			0
$285$	27.6941	−	20.1209i	1.64046	−	1.19186i
$286$		0			0
$287$	5.22697	−	3.69848i	0.308539	−	0.218314i
$288$		0			0
$289$	10.6250	−	7.71948i	0.624997	−	0.454087i
$290$		0			0
$291$	−13.0855	+	40.2730i	−0.767085	+	2.36084i
$292$		0			0
$293$	6.17093	+	8.49355i	0.360509	+	0.496199i	0.950291	−	0.311365i	$-0.100786\pi$
$293$	6.17093	+	8.49355i	0.360509	+	0.496199i	−0.589781	+	0.807563i	$0.700786\pi$
$294$		0			0
$295$	1.35347	+	4.16556i	0.0788022	+	0.242528i
$296$		0			0
$297$	−19.5821	−	60.2674i	−1.13627	−	3.49707i
$298$		0			0
$299$	8.72226	+	2.83403i	0.504421	+	0.163896i
$300$		0			0
$301$		−	0.557426i		−	0.0321295i
$302$		0			0
$303$	−33.1904	−	24.1142i	−1.90674	−	1.38533i
$304$		0			0
$305$	6.11518	−	4.44294i	0.350154	−	0.254402i
$306$		0			0
$307$	11.0682	+	8.04153i	0.631697	+	0.458955i	0.856988	−	0.515337i	$-0.172333\pi$
$307$	11.0682	+	8.04153i	0.631697	+	0.458955i	−0.225291	+	0.974292i	$0.572333\pi$
$308$		0			0
$309$	8.40067	−	11.5625i	0.477898	−	0.657770i
$310$		0			0
$311$	13.0821	−	4.25063i	0.741818	−	0.241031i	0.0863610	−	0.996264i	$-0.472476\pi$
$311$	13.0821	−	4.25063i	0.741818	−	0.241031i	0.655457	+	0.755233i	$0.272476\pi$
$312$		0			0
$313$	−18.8526	−	6.12558i	−1.06561	−	0.346238i	−0.276835	−	0.960918i	$-0.589285\pi$
$313$	−18.8526	−	6.12558i	−1.06561	−	0.346238i	−0.788777	+	0.614679i	$0.789285\pi$
$314$		0			0
$315$	13.8531	+	19.0671i	0.780533	+	1.07431i
$316$		0			0
$317$	−17.4330	+	5.66433i	−0.979136	+	0.318140i	−0.754498	−	0.656302i	$-0.772120\pi$
$317$	−17.4330	+	5.66433i	−0.979136	+	0.318140i	−0.224637	+	0.974442i	$0.572120\pi$
$318$		0			0
$319$	55.2088			3.09110
$320$		0			0
$321$	12.1180	−	16.6790i	0.676359	−	0.930929i
$322$		0			0
$323$	5.21676	−	16.0555i	0.290268	−	0.893354i
$324$		0			0
$325$			54.2791i			3.01086i
$326$		0			0
$327$	−44.7177			−2.47290
$328$		0			0
$329$	0.894886			0.0493367
$330$		0			0
$331$			10.7100i			0.588673i	0.955702	+	0.294336i	$0.0950986\pi$
$331$			10.7100i			0.588673i	−0.955702	+	0.294336i	$0.904901\pi$
$332$		0			0
$333$	6.56756	−	20.2129i	0.359900	−	1.10766i
$334$		0			0
$335$	31.4468	−	43.2828i	1.71812	−	2.36479i
$336$		0			0
$337$	3.51109			0.191261			0.0956306	−	0.995417i	$-0.469513\pi$
$337$	3.51109			0.191261			0.0956306	+	0.995417i	$0.469513\pi$
$338$		0			0
$339$	17.2101	−	5.59190i	0.934724	−	0.303710i
$340$		0			0
$341$	15.6399	+	21.5264i	0.846946	+	1.16572i
$342$		0			0
$343$	0.951057	+	0.309017i	0.0513522	+	0.0166853i
$344$		0			0
$345$	14.2870	−	4.64213i	0.769186	−	0.249924i
$346$		0			0
$347$	−14.7538	+	20.3069i	−0.792027	+	1.09013i	0.201826	+	0.979421i	$0.435312\pi$
$347$	−14.7538	+	20.3069i	−0.792027	+	1.09013i	−0.993853	+	0.110710i	$0.964688\pi$
$348$		0			0
$349$	5.63687	+	4.09543i	0.301735	+	0.219223i	0.728342	−	0.685214i	$-0.240291\pi$
$349$	5.63687	+	4.09543i	0.301735	+	0.219223i	−0.426607	+	0.904437i	$0.640291\pi$
$350$		0			0
$351$	−60.1074	+	43.6706i	−3.20830	+	2.33096i
$352$		0			0
$353$	−19.4333	−	14.1191i	−1.03433	−	0.751484i	−0.0651587	−	0.997875i	$-0.520755\pi$
$353$	−19.4333	−	14.1191i	−1.03433	−	0.751484i	−0.969171	+	0.246391i	$0.920755\pi$
$354$		0			0
$355$			3.59005i			0.190540i
$356$		0			0
$357$	16.1250	+	5.23932i	0.853423	+	0.277294i
$358$		0			0
$359$	8.99676	+	27.6892i	0.474831	+	1.46138i	0.846186	+	0.532888i	$0.178893\pi$
$359$	8.99676	+	27.6892i	0.474831	+	1.46138i	−0.371355	+	0.928491i	$0.621107\pi$
$360$		0			0
$361$	2.94869	+	9.07512i	0.155194	+	0.477638i
$362$		0			0
$363$	41.0174	+	56.4556i	2.15286	+	2.96315i
$364$		0			0
$365$	−7.64751	+	23.5366i	−0.400289	+	1.23196i
$366$		0			0
$367$	−25.8398	+	18.7737i	−1.34882	+	0.979978i	−0.349755	+	0.936841i	$0.613735\pi$
$367$	−25.8398	+	18.7737i	−1.34882	+	0.979978i	−0.999069	+	0.0431371i	$0.986265\pi$
$368$		0			0
$369$	39.6605	+	13.4380i	2.06464	+	0.699554i
$370$		0			0
$371$	−4.82485	+	3.50546i	−0.250494	+	0.181994i
$372$		0			0
$373$	−10.2834	+	31.6489i	−0.532452	+	1.63872i	0.216638	+	0.976252i	$0.430491\pi$
$373$	−10.2834	+	31.6489i	−0.532452	+	1.63872i	−0.749090	+	0.662468i	$0.769509\pi$
$374$		0			0
$375$	19.5462	+	26.9030i	1.00936	+	1.38926i
$376$		0			0
$377$	−20.0026	−	61.5615i	−1.03018	−	3.17058i
$378$		0			0
$379$	1.48106	+	4.55822i	0.0760767	+	0.234140i	0.981862	−	0.189597i	$-0.0607181\pi$
$379$	1.48106	+	4.55822i	0.0760767	+	0.234140i	−0.905785	+	0.423737i	$0.860718\pi$
$380$		0			0
$381$	−15.6732	−	5.09253i	−0.802963	−	0.260898i
$382$		0			0
$383$		−	18.9334i		−	0.967453i	−0.875219	−	0.483727i	$-0.839283\pi$
$383$		−	18.9334i		−	0.967453i	0.875219	−	0.483727i	$-0.160717\pi$
$384$		0			0
$385$	−16.8985	−	12.2774i	−0.861225	−	0.625717i
$386$		0			0
$387$	2.94924	−	2.14275i	0.149918	−	0.108922i
$388$		0			0
$389$	−9.70335	−	7.04990i	−0.491979	−	0.357444i	0.313966	−	0.949434i	$-0.398342\pi$
$389$	−9.70335	−	7.04990i	−0.491979	−	0.357444i	−0.805945	+	0.591990i	$0.798342\pi$
$390$		0			0
$391$	4.35455	−	5.99352i	0.220219	−	0.303105i
$392$		0			0
$393$	30.7288	−	9.98438i	1.55006	−	0.503645i
$394$		0			0
$395$	−26.6974	−	8.67452i	−1.34329	−	0.436463i
$396$		0			0
$397$	−9.57860	−	13.1838i	−0.480736	−	0.661677i	0.497910	−	0.867229i	$-0.334101\pi$
$397$	−9.57860	−	13.1838i	−0.480736	−	0.661677i	−0.978646	+	0.205552i	$0.934101\pi$
$398$		0			0
$399$	9.03384	−	2.93527i	0.452258	−	0.146947i
$400$		0			0
$401$	18.8536			0.941506			0.470753	−	0.882265i	$-0.343982\pi$
$401$	18.8536			0.941506			0.470753	+	0.882265i	$0.343982\pi$
$402$		0			0
$403$	18.3370	−	25.2387i	0.913429	−	1.25723i
$404$		0			0
$405$	−15.7577	+	48.4971i	−0.783005	+	2.40984i
$406$		0			0
$407$			18.8357i			0.933653i
$408$		0			0
$409$	38.0194			1.87994			0.939969	−	0.341261i	$-0.110854\pi$
$409$	38.0194			1.87994			0.939969	+	0.341261i	$0.110854\pi$
$410$		0			0
$411$	33.1131			1.63335
$412$		0			0
$413$			1.21536i			0.0598038i
$414$		0			0
$415$	−0.655288	+	2.01677i	−0.0321668	+	0.0989993i
$416$		0			0
$417$	0.435411	−	0.599292i	0.0213222	−	0.0293474i
$418$		0			0
$419$	−30.1308			−1.47199			−0.735994	−	0.676988i	$-0.763285\pi$
$419$	−30.1308			−1.47199			−0.735994	+	0.676988i	$0.763285\pi$
$420$		0			0
$421$	22.7417	−	7.38921i	1.10836	−	0.360128i	0.303046	−	0.952976i	$-0.401996\pi$
$421$	22.7417	−	7.38921i	1.10836	−	0.360128i	0.805314	+	0.592848i	$0.201996\pi$
$422$		0			0
$423$	3.43995	+	4.73468i	0.167256	+	0.230208i
$424$		0			0
$425$	41.7004	+	13.5493i	2.02277	+	0.657237i
$426$		0			0
$427$	1.99478	−	0.648143i	0.0965341	−	0.0313658i
$428$		0			0
$429$	71.5049	−	98.4181i	3.45229	−	4.75167i
$430$		0			0
$431$	21.0717	+	15.3095i	1.01499	+	0.737434i	0.965250	−	0.261329i	$-0.0841606\pi$
$431$	21.0717	+	15.3095i	1.01499	+	0.737434i	0.0497403	+	0.998762i	$0.484161\pi$
$432$		0			0
$433$	12.9391	−	9.40080i	0.621813	−	0.451774i	−0.231741	−	0.972777i	$-0.574442\pi$
$433$	12.9391	−	9.40080i	0.621813	−	0.451774i	0.853554	+	0.521004i	$0.174442\pi$
$434$		0			0
$435$	−85.7774	−	62.3209i	−4.11271	−	2.98806i
$436$		0			0
$437$		−	4.15048i		−	0.198544i
$438$		0			0
$439$	−11.7978	−	3.83335i	−0.563080	−	0.182956i	0.0136267	−	0.999907i	$-0.495662\pi$
$439$	−11.7978	−	3.83335i	−0.563080	−	0.182956i	−0.576706	+	0.816951i	$0.695662\pi$
$440$		0			0
$441$	2.02091	+	6.21973i	0.0962339	+	0.296178i
$442$		0			0
$443$	12.2867	+	37.8147i	0.583760	+	1.79663i	0.604194	+	0.796838i	$0.293495\pi$
$443$	12.2867	+	37.8147i	0.583760	+	1.79663i	−0.0204335	+	0.999791i	$0.506505\pi$
$444$		0			0
$445$	−26.0044	−	35.7921i	−1.23273	−	1.69671i
$446$		0			0
$447$	−8.54298	+	26.2926i	−0.404069	+	1.24360i
$448$		0			0
$449$	−9.38106	+	6.81574i	−0.442719	+	0.321654i	−0.786715	−	0.617317i	$-0.788220\pi$
$449$	−9.38106	+	6.81574i	−0.442719	+	0.321654i	0.343995	+	0.938971i	$0.388220\pi$
$450$		0			0
$451$	−37.1094	−	0.464873i	−1.74741	−	0.0218900i
$452$		0			0
$453$	26.7102	−	19.4061i	1.25495	−	0.911777i
$454$		0			0
$455$	−7.56774	+	23.2911i	−0.354781	+	1.09190i
$456$		0			0
$457$	23.0394	+	31.7110i	1.07774	+	1.48338i	0.861989	+	0.506926i	$0.169218\pi$
$457$	23.0394	+	31.7110i	1.07774	+	1.48338i	0.215746	+	0.976450i	$0.430782\pi$
$458$		0			0
$459$	18.5462	+	57.0793i	0.865662	+	2.66423i
$460$		0			0
$461$	−11.1474	−	34.3081i	−0.519185	−	1.59789i	−0.775536	−	0.631304i	$-0.782520\pi$
$461$	−11.1474	−	34.3081i	−0.519185	−	1.59789i	0.256350	−	0.966584i	$-0.417480\pi$
$462$		0			0
$463$	−18.9673	−	6.16284i	−0.881484	−	0.286411i	−0.166911	−	0.985972i	$-0.553379\pi$
$463$	−18.9673	−	6.16284i	−0.881484	−	0.286411i	−0.714573	+	0.699561i	$0.753379\pi$
$464$		0			0
$465$		−	51.1000i		−	2.36970i
$466$		0			0
$467$	12.2415	+	8.89400i	0.566471	+	0.411565i	0.833821	−	0.552034i	$-0.186148\pi$
$467$	12.2415	+	8.89400i	0.566471	+	0.411565i	−0.267351	+	0.963599i	$0.586148\pi$
$468$		0			0
$469$	12.0103	−	8.72597i	0.554583	−	0.402928i
$470$		0			0
$471$	−24.0993	−	17.5092i	−1.11044	−	0.806780i
$472$		0			0
$473$	−1.89903	+	2.61379i	−0.0873176	+	0.120182i
$474$		0			0
$475$	23.3622	−	7.59085i	1.07193	−	0.348292i
$476$		0			0
$477$	−37.0935	−	12.0524i	−1.69839	−	0.551842i
$478$		0			0
$479$	12.1346	+	16.7019i	0.554445	+	0.763128i	0.990607	−	0.136740i	$-0.0436626\pi$
$479$	12.1346	+	16.7019i	0.554445	+	0.763128i	−0.436162	+	0.899868i	$0.643663\pi$
$480$		0			0
$481$	21.0031	−	6.82432i	0.957659	−	0.311162i
$482$		0			0
$483$	4.16842			0.189670
$484$		0			0
$485$	−29.0415	+	39.9722i	−1.31871	+	1.81504i
$486$		0			0
$487$	−3.47164	+	10.6846i	−0.157315	+	0.484165i	−0.998388	−	0.0567560i	$-0.981924\pi$
$487$	−3.47164	+	10.6846i	−0.157315	+	0.484165i	0.841073	+	0.540921i	$0.181924\pi$
$488$		0			0
$489$		−	19.3454i		−	0.874828i
$490$		0			0
$491$	−35.1870			−1.58797			−0.793984	−	0.607939i	$-0.791997\pi$
$491$	−35.1870			−1.58797			−0.793984	+	0.607939i	$0.791997\pi$
$492$		0			0
$493$	−52.2883			−2.35495
$494$		0			0
$495$		−	136.601i		−	6.13977i
$496$		0			0
$497$	−0.307836	+	0.947422i	−0.0138083	+	0.0424977i
$498$		0			0
$499$	13.7594	−	18.9382i	0.615957	−	0.847792i	−0.381094	−	0.924536i	$-0.624453\pi$
$499$	13.7594	−	18.9382i	0.615957	−	0.847792i	0.997051	+	0.0767445i	$0.0244526\pi$
$500$		0			0
$501$	−0.161076			−0.00719636
$502$		0			0
$503$	18.2318	−	5.92387i	0.812915	−	0.264132i	0.127083	−	0.991892i	$-0.459439\pi$
$503$	18.2318	−	5.92387i	0.812915	−	0.264132i	0.685832	+	0.727760i	$0.259439\pi$
$504$		0			0
$505$	−28.1362	−	38.7262i	−1.25205	−	1.72329i
$506$		0			0
$507$	−97.4621	−	31.6673i	−4.32844	−	1.40640i
$508$		0			0
$509$	−19.8817	+	6.45995i	−0.881240	+	0.286332i	−0.714472	−	0.699664i	$-0.753333\pi$
$509$	−19.8817	+	6.45995i	−0.881240	+	0.286332i	−0.166768	+	0.985996i	$0.553333\pi$
$510$		0			0
$511$	−4.03639	+	5.55562i	−0.178560	+	0.245766i
$512$		0			0
$513$	27.2022	+	19.7635i	1.20101	+	0.872582i
$514$		0			0
$515$	13.4911	−	9.80183i	0.594487	−	0.431920i
$516$		0			0
$517$	−4.19616	−	3.04869i	−0.184547	−	0.134081i
$518$		0			0
$519$			17.4119i			0.764297i
$520$		0			0
$521$	−0.190173	−	0.0617910i	−0.00833164	−	0.00270711i	0.304848	−	0.952401i	$-0.401394\pi$
$521$	−0.190173	−	0.0617910i	−0.00833164	−	0.00270711i	−0.313180	+	0.949694i	$0.601394\pi$
$522$		0			0
$523$	−0.987891	−	3.04042i	−0.0431975	−	0.132948i	0.927132	−	0.374735i	$-0.122266\pi$
$523$	−0.987891	−	3.04042i	−0.0431975	−	0.132948i	−0.970329	+	0.241787i	$0.922266\pi$
$524$		0			0
$525$	7.62366	+	23.4632i	0.332724	+	1.02402i
$526$		0			0
$527$	−14.8125	−	20.3877i	−0.645243	−	0.888101i
$528$		0			0
$529$	−6.54455	+	20.1421i	−0.284546	+	0.875741i
$530$		0			0
$531$	−6.43023	+	4.67184i	−0.279048	+	0.202741i
$532$		0			0
$533$	12.9266	+	41.5479i	0.559915	+	1.79964i
$534$		0			0
$535$	19.4609	−	14.1391i	0.841366	−	0.611289i
$536$		0			0
$537$	16.2332	−	49.9606i	0.700513	−	2.15596i
$538$		0			0
$539$	−3.40679	−	4.68904i	−0.146741	−	0.201971i
$540$		0			0
$541$	5.86917	+	18.0634i	0.252335	+	0.776608i	0.994343	+	0.106217i	$0.0338738\pi$
$541$	5.86917	+	18.0634i	0.252335	+	0.776608i	−0.742008	+	0.670391i	$0.766126\pi$
$542$		0			0
$543$	8.86155	+	27.2730i	0.380285	+	1.17040i
$544$		0			0
$545$	−49.6226	−	16.1234i	−2.12560	−	0.690649i
$546$		0			0
$547$		−	18.6830i		−	0.798827i	−0.916771	−	0.399414i	$-0.869214\pi$
$547$		−	18.6830i		−	0.798827i	0.916771	−	0.399414i	$-0.130786\pi$
$548$		0			0
$549$	11.0971	+	8.06254i	0.473614	+	0.344101i
$550$		0			0
$551$	−23.6993	+	17.2186i	−1.00963	+	0.733536i
$552$		0			0
$553$	−6.30170	−	4.57845i	−0.267976	−	0.194696i
$554$		0			0
$555$	21.2622	−	29.2649i	0.902529	−	1.24223i
$556$		0			0
$557$	33.0912	−	10.7520i	1.40212	−	0.455576i	0.492244	−	0.870457i	$-0.336177\pi$
$557$	33.0912	−	10.7520i	1.40212	−	0.455576i	0.909876	+	0.414881i	$0.136177\pi$
$558$		0			0
$559$	3.60259	+	1.17055i	0.152373	+	0.0495090i
$560$		0			0
$561$	−57.7613	−	79.5017i	−2.43869	−	3.35656i
$562$		0			0
$563$	−0.130119	+	0.0422783i	−0.00548387	+	0.00178182i	−0.311758	−	0.950162i	$-0.600918\pi$
$563$	−0.130119	+	0.0422783i	−0.00548387	+	0.00178182i	0.306274	+	0.951943i	$0.400918\pi$
$564$		0			0
$565$	21.1140			0.888272
$566$		0			0
$567$	−8.31697	+	11.4473i	−0.349280	+	0.480743i
$568$		0			0
$569$	−6.37158	+	19.6097i	−0.267110	+	0.822081i	0.724089	+	0.689706i	$0.242260\pi$
$569$	−6.37158	+	19.6097i	−0.267110	+	0.822081i	−0.991200	+	0.132375i	$0.957740\pi$
$570$		0			0
$571$			12.8896i			0.539415i	0.962942	+	0.269707i	$0.0869269\pi$
$571$			12.8896i			0.539415i	−0.962942	+	0.269707i	$0.913073\pi$
$572$		0			0
$573$	8.11659			0.339075
$574$		0			0
$575$	10.7799			0.449552
$576$		0			0
$577$			16.8202i			0.700232i	0.936706	+	0.350116i	$0.113858\pi$
$577$			16.8202i			0.700232i	−0.936706	+	0.350116i	$0.886142\pi$
$578$		0			0
$579$	19.1695	−	58.9978i	0.796659	−	2.45186i
$580$		0			0
$581$	−0.345864	+	0.476041i	−0.0143489	+	0.0197495i
$582$		0			0
$583$	34.5663			1.43159
$584$		0			0
$585$	−152.319	+	49.4916i	−6.29763	+	2.04623i
$586$		0			0
$587$	−11.8657	−	16.3318i	−0.489751	−	0.674085i	0.490591	−	0.871390i	$-0.336781\pi$
$587$	−11.8657	−	16.3318i	−0.489751	−	0.674085i	−0.980342	+	0.197305i	$0.936781\pi$
$588$		0			0
$589$	−13.4274	−	4.36281i	−0.553264	−	0.179767i
$590$		0			0
$591$	13.7621	−	4.47158i	0.566097	−	0.183936i
$592$		0			0
$593$	1.64751	−	2.26760i	0.0676550	−	0.0931192i	−0.773849	−	0.633371i	$-0.781671\pi$
$593$	1.64751	−	2.26760i	0.0676550	−	0.0931192i	0.841504	+	0.540251i	$0.181671\pi$
$594$		0			0
$595$	16.0045	+	11.6280i	0.656122	+	0.476700i
$596$		0			0
$597$	−32.3899	+	23.5326i	−1.32563	+	0.963126i
$598$		0			0
$599$	24.9662	+	18.1390i	1.02009	+	0.741139i	0.966302	−	0.257413i	$-0.0828700\pi$
$599$	24.9662	+	18.1390i	1.02009	+	0.741139i	0.0537894	+	0.998552i	$0.482870\pi$
$600$		0			0
$601$			7.74140i			0.315778i	0.987457	+	0.157889i	$0.0504689\pi$
$601$			7.74140i			0.315778i	−0.987457	+	0.157889i	$0.949531\pi$
$602$		0			0
$603$	92.3350	+	30.0015i	3.76017	+	1.22175i
$604$		0			0
$605$	25.1608	+	77.4371i	1.02293	+	3.14827i
$606$		0			0
$607$	4.24158	+	13.0543i	0.172161	+	0.529856i	0.999492	−	0.0318577i	$-0.0101423\pi$
$607$	4.24158	+	13.0543i	0.172161	+	0.529856i	−0.827332	+	0.561713i	$0.810142\pi$
$608$		0			0
$609$	−17.2930	−	23.8018i	−0.700748	−	0.964497i
$610$		0			0
$611$	−1.87919	+	5.78356i	−0.0760240	+	0.233978i
$612$		0			0
$613$	−32.5332	+	23.6368i	−1.31400	+	0.954679i	−0.314017	+	0.949417i	$0.601675\pi$
$613$	−32.5332	+	23.6368i	−1.31400	+	0.954679i	−0.999986	+	0.00526211i	$0.998325\pi$
$614$		0			0
$615$	57.1318	+	42.6122i	2.30377	+	1.71829i
$616$		0			0
$617$	12.3053	−	8.94035i	0.495394	−	0.359925i	−0.311861	−	0.950128i	$-0.600952\pi$
$617$	12.3053	−	8.94035i	0.495394	−	0.359925i	0.807255	+	0.590203i	$0.200952\pi$
$618$		0			0
$619$	1.22364	−	3.76599i	0.0491824	−	0.151368i	−0.923449	−	0.383721i	$-0.874642\pi$
$619$	1.22364	−	3.76599i	0.0491824	−	0.151368i	0.972632	+	0.232353i	$0.0746424\pi$
$620$		0			0
$621$	8.67302	+	11.9374i	0.348036	+	0.479031i
$622$		0			0
$623$	−3.79357	−	11.6754i	−0.151986	−	0.467766i
$624$		0			0
$625$	−0.351415	−	1.08154i	−0.0140566	−	0.0432617i
$626$		0			0
$627$	−52.3599	−	17.0128i	−2.09105	−	0.679424i
$628$		0			0
$629$		−	17.8393i		−	0.711301i
$630$		0			0
$631$	−4.35000	−	3.16046i	−0.173171	−	0.125816i	0.497824	−	0.867278i	$-0.334133\pi$
$631$	−4.35000	−	3.16046i	−0.173171	−	0.125816i	−0.670995	+	0.741462i	$0.734133\pi$
$632$		0			0
$633$	−39.0246	+	28.3530i	−1.55109	+	1.12693i
$634$		0			0
$635$	−15.5562	−	11.3022i	−0.617327	−	0.448515i
$636$		0			0
$637$	−3.99429	+	5.49767i	−0.158260	+	0.217826i
$638$		0			0
$639$	−6.19596	+	2.01319i	−0.245108	+	0.0796405i
$640$		0			0
$641$	0.838232	+	0.272358i	0.0331082	+	0.0107575i	0.325524	−	0.945534i	$-0.394459\pi$
$641$	0.838232	+	0.272358i	0.0331082	+	0.0107575i	−0.292416	+	0.956291i	$0.594459\pi$
$642$		0			0
$643$	−6.28415	−	8.64939i	−0.247823	−	0.341099i	0.666925	−	0.745125i	$-0.267610\pi$
$643$	−6.28415	−	8.64939i	−0.247823	−	0.341099i	−0.914747	+	0.404027i	$0.867610\pi$
$644$		0			0
$645$	5.90101	−	1.91735i	0.232352	−	0.0754958i
$646$		0			0
$647$	48.0227			1.88797			0.943984	−	0.329991i	$-0.107046\pi$
$647$	48.0227			1.88797			0.943984	+	0.329991i	$0.107046\pi$
$648$		0			0
$649$	4.14046	−	5.69886i	0.162527	−	0.223700i
$650$		0			0
$651$	4.38167	−	13.4854i	0.171731	−	0.528535i
$652$		0			0
$653$			3.12266i			0.122199i	0.998132	+	0.0610995i	$0.0194607\pi$
$653$			3.12266i			0.122199i	−0.998132	+	0.0610995i	$0.980539\pi$
$654$		0			0
$655$	37.6992			1.47303
$656$		0			0
$657$	−44.9097			−1.75209
$658$		0			0
$659$		−	29.1705i		−	1.13632i	−0.822918	−	0.568161i	$-0.807655\pi$
$659$		−	29.1705i		−	1.13632i	0.822918	−	0.568161i	$-0.192345\pi$
$660$		0			0
$661$	−2.21650	+	6.82169i	−0.0862120	+	0.265333i	−0.984864	−	0.173329i	$-0.944548\pi$
$661$	−2.21650	+	6.82169i	−0.0862120	+	0.265333i	0.898652	+	0.438662i	$0.144548\pi$
$662$		0			0
$663$	−67.7223	+	93.2118i	−2.63012	+	3.62005i
$664$		0			0
$665$	11.0831			0.429782
$666$		0			0
$667$	−12.2262	+	3.97252i	−0.473399	+	0.153817i
$668$		0			0
$669$	−12.5998	−	17.3421i	−0.487137	−	0.670486i
$670$		0			0
$671$	−11.5617	−	3.75662i	−0.446334	−	0.145023i
$672$		0			0
$673$	−36.3011	+	11.7949i	−1.39931	+	0.454662i	−0.908966	−	0.416870i	$-0.863127\pi$
$673$	−36.3011	+	11.7949i	−1.39931	+	0.454662i	−0.490339	+	0.871532i	$0.663127\pi$
$674$		0			0
$675$	−51.3310	+	70.6511i	−1.97573	+	2.71936i
$676$		0			0
$677$	35.1359	+	25.5277i	1.35038	+	0.981109i	0.998992	+	0.0448799i	$0.0142905\pi$
$677$	35.1359	+	25.5277i	1.35038	+	0.981109i	0.351389	+	0.936230i	$0.385709\pi$
$678$		0			0
$679$	−11.0916	+	8.05854i	−0.425657	+	0.309258i
$680$		0			0
$681$	−26.5532	−	19.2920i	−1.01752	−	0.739271i
$682$		0			0
$683$		−	50.0871i		−	1.91653i	−0.285880	−	0.958265i	$-0.592286\pi$
$683$		−	50.0871i		−	1.91653i	0.285880	−	0.958265i	$-0.407714\pi$
$684$		0			0
$685$	36.7451	+	11.9392i	1.40396	+	0.456173i
$686$		0			0
$687$	−5.62204	−	17.3028i	−0.214494	−	0.660145i
$688$		0			0
$689$	−12.5236	−	38.5437i	−0.477112	−	1.46840i
$690$		0			0
$691$	−11.3452	−	15.6153i	−0.431592	−	0.594036i	0.536726	−	0.843757i	$-0.319661\pi$
$691$	−11.3452	−	15.6153i	−0.431592	−	0.594036i	−0.968318	+	0.249721i	$0.919661\pi$
$692$		0			0
$693$	11.7132	−	36.0494i	0.444946	−	1.36940i
$694$		0			0
$695$	0.699248	−	0.508034i	0.0265240	−	0.0192708i
$696$		0			0
$697$	35.1464	+	0.440281i	1.33126	+	0.0166768i
$698$		0			0
$699$	−68.4869	+	49.7586i	−2.59041	+	1.88204i
$700$		0			0
$701$	7.83745	−	24.1212i	0.296016	−	0.911045i	−0.686862	−	0.726788i	$-0.741012\pi$
$701$	7.83745	−	24.1212i	0.296016	−	0.911045i	0.982878	−	0.184257i	$-0.0589878\pi$
$702$		0			0
$703$	−5.87451	−	8.08556i	−0.221561	−	0.304953i
$704$		0			0
$705$	3.07810	+	9.47343i	0.115928	+	0.356790i
$706$		0			0
$707$	−4.10456	−	12.6325i	−0.154368	−	0.475096i
$708$		0			0
$709$	7.05474	+	2.29223i	0.264946	+	0.0860863i	0.438478	−	0.898742i	$-0.355518\pi$
$709$	7.05474	+	2.29223i	0.264946	+	0.0860863i	−0.173531	+	0.984828i	$0.555518\pi$
$710$		0			0
$711$		−	50.9407i		−	1.91043i
$712$		0			0
$713$	−5.01242	−	3.64174i	−0.187717	−	0.136384i
$714$		0			0
$715$	114.833	−	83.4313i	4.29452	−	3.12015i
$716$		0			0
$717$	31.8749	+	23.1585i	1.19039	+	0.864869i
$718$		0			0
$719$	10.5848	−	14.5687i	0.394747	−	0.543323i	−0.564669	−	0.825318i	$-0.690996\pi$
$719$	10.5848	−	14.5687i	0.394747	−	0.543323i	0.959416	+	0.281995i	$0.0909961\pi$
$720$		0			0
$721$	4.40080	−	1.42991i	0.163894	−	0.0532525i
$722$		0			0
$723$	31.2788	+	10.1631i	1.16327	+	0.377969i
$724$		0			0
$725$	−44.7211	−	61.5533i	−1.66090	−	2.28603i
$726$		0			0
$727$	−9.90835	+	3.21942i	−0.367480	+	0.119402i	−0.486935	−	0.873438i	$-0.661885\pi$
$727$	−9.90835	+	3.21942i	−0.367480	+	0.119402i	0.119455	+	0.992840i	$0.461885\pi$
$728$		0			0
$729$	8.77112			0.324856
$730$		0			0
$731$	1.79857	−	2.47552i	0.0665227	−	0.0915606i
$732$		0			0
$733$	10.3805	−	31.9479i	0.383413	−	1.18002i	−0.554212	−	0.832375i	$-0.686980\pi$
$733$	10.3805	−	31.9479i	0.383413	−	1.18002i	0.937625	−	0.347648i	$-0.113020\pi$
$734$		0			0
$735$			11.1310i			0.410572i
$736$		0			0
$737$	−86.0442			−3.16948
$738$		0			0
$739$	−15.7297			−0.578626			−0.289313	−	0.957234i	$-0.593427\pi$
$739$	−15.7297			−0.578626			−0.289313	+	0.957234i	$0.593427\pi$
$740$		0			0
$741$			64.5486i			2.37125i
$742$		0			0
$743$	4.37989	−	13.4799i	0.160683	−	0.494531i	−0.838010	−	0.545656i	$-0.816281\pi$
$743$	4.37989	−	13.4799i	0.160683	−	0.494531i	0.998692	+	0.0511250i	$0.0162807\pi$
$744$		0			0
$745$	−18.9600	+	26.0962i	−0.694642	+	0.956092i
$746$		0			0
$747$	−3.84815			−0.140796
$748$		0			0
$749$	6.34816	−	2.06264i	0.231957	−	0.0753673i
$750$		0			0
$751$	−8.06974	−	11.1071i	−0.294469	−	0.405302i	0.635990	−	0.771697i	$-0.280592\pi$
$751$	−8.06974	−	11.1071i	−0.294469	−	0.405302i	−0.930459	+	0.366395i	$0.880592\pi$
$752$		0			0
$753$	47.8483	+	15.5469i	1.74369	+	0.566559i
$754$		0			0
$755$	36.6369	−	11.9040i	1.33335	−	0.433232i
$756$		0			0
$757$	8.09793	−	11.1458i	0.294324	−	0.405103i	−0.636088	−	0.771616i	$-0.719449\pi$
$757$	8.09793	−	11.1458i	0.294324	−	0.405103i	0.930413	+	0.366513i	$0.119449\pi$
$758$		0			0
$759$	−19.5459	−	14.2009i	−0.709471	−	0.515461i
$760$		0			0
$761$	−7.97524	+	5.79435i	−0.289102	+	0.210045i	−0.722878	−	0.690976i	$-0.757181\pi$
$761$	−7.97524	+	5.79435i	−0.289102	+	0.210045i	0.433776	+	0.901021i	$0.357181\pi$
$762$		0			0
$763$	−11.7130	−	8.50998i	−0.424039	−	0.308082i
$764$		0			0
$765$			129.375i			4.67756i
$766$		0			0
$767$	−7.85473	−	2.55216i	−0.283618	−	0.0921530i
$768$		0			0
$769$	9.42688	+	29.0130i	0.339942	+	1.04623i	0.964236	+	0.265045i	$0.0853867\pi$
$769$	9.42688	+	29.0130i	0.339942	+	1.04623i	−0.624294	+	0.781189i	$0.714613\pi$
$770$		0			0
$771$	5.44493	+	16.7578i	0.196095	+	0.603517i
$772$		0			0
$773$	16.9674	+	23.3537i	0.610276	+	0.839973i	0.996600	−	0.0823902i	$-0.0262554\pi$
$773$	16.9674	+	23.3537i	0.610276	+	0.839973i	−0.386324	+	0.922363i	$0.626255\pi$
$774$		0			0
$775$	11.3314	−	34.8743i	0.407034	−	1.25272i
$776$		0			0
$777$	8.12052	−	5.89990i	0.291322	−	0.211658i
$778$		0			0
$779$	16.0748	−	11.3742i	0.575941	−	0.407522i
$780$		0			0
$781$	4.67112	−	3.39377i	0.167146	−	0.121439i
$782$		0			0
$783$	32.1821	−	99.0463i	1.15009	−	3.53963i
$784$		0			0
$785$	−20.4295	−	28.1189i	−0.729162	−	1.00361i
$786$		0			0
$787$	3.10451	+	9.55471i	0.110664	+	0.340589i	0.991018	−	0.133728i	$-0.0426950\pi$
$787$	3.10451	+	9.55471i	0.110664	+	0.340589i	−0.880354	+	0.474317i	$0.842695\pi$
$788$		0			0
$789$	−6.09866	−	18.7697i	−0.217118	−	0.668220i
$790$		0			0
$791$	5.57203	+	1.81046i	0.198119	+	0.0643727i
$792$		0			0
$793$			14.2531i			0.506142i
$794$		0			0
$795$	−53.7053	−	39.0192i	−1.90473	−	1.38387i
$796$		0			0
$797$	−6.87960	+	4.99832i	−0.243688	+	0.177050i	−0.702925	−	0.711264i	$-0.748123\pi$
$797$	−6.87960	+	4.99832i	−0.243688	+	0.177050i	0.459237	+	0.888314i	$0.348123\pi$
$798$		0			0
$799$	3.97418	+	2.88741i	0.140597	+	0.102149i
$800$		0			0
$801$	47.1900	−	64.9514i	1.66738	−	2.29495i
$802$		0			0
$803$	37.8536	−	12.2994i	1.33583	−	0.434036i
$804$		0			0
$805$	4.62563	+	1.50296i	0.163032	+	0.0529724i
$806$		0			0
$807$	−13.7345	−	18.9039i	−0.483477	−	0.665448i
$808$		0			0
$809$	5.49185	−	1.78441i	0.193083	−	0.0627365i	−0.210879	−	0.977512i	$-0.567633\pi$
$809$	5.49185	−	1.78441i	0.193083	−	0.0627365i	0.403962	+	0.914776i	$0.367633\pi$
$810$		0			0
$811$	32.2439			1.13224			0.566118	−	0.824324i	$-0.308445\pi$
$811$	32.2439			1.13224			0.566118	+	0.824324i	$0.308445\pi$
$812$		0			0
$813$	−57.6882	+	79.4010i	−2.02321	+	2.78471i
$814$		0			0
$815$	6.97514	−	21.4673i	0.244328	−	0.751965i
$816$		0			0
$817$		−	1.71429i		−	0.0599753i
$818$		0			0
$819$	−44.4412			−1.55290
$820$		0			0
$821$	6.96747			0.243166			0.121583	−	0.992581i	$-0.461203\pi$
$821$	6.96747			0.243166			0.121583	+	0.992581i	$0.461203\pi$
$822$		0			0
$823$			8.25033i			0.287588i	0.989608	+	0.143794i	$0.0459303\pi$
$823$			8.25033i			0.287588i	−0.989608	+	0.143794i	$0.954070\pi$
$824$		0			0
$825$	44.1866	−	135.992i	1.53838	−	4.73464i
$826$		0			0
$827$	27.6976	−	38.1225i	0.963141	−	1.32565i	0.0177044	−	0.999843i	$-0.494364\pi$
$827$	27.6976	−	38.1225i	0.963141	−	1.32565i	0.945437	−	0.325806i	$-0.105636\pi$
$828$		0			0
$829$	−8.56730			−0.297555			−0.148777	−	0.988871i	$-0.547534\pi$
$829$	−8.56730			−0.297555			−0.148777	+	0.988871i	$0.547534\pi$
$830$		0			0
$831$	−14.9607	+	4.86101i	−0.518979	+	0.168627i
$832$		0			0
$833$	3.22657	+	4.44099i	0.111794	+	0.153871i
$834$		0			0
$835$	−0.178744	−	0.0580774i	−0.00618569	−	0.00200985i
$836$		0			0
$837$	47.7358	−	15.5103i	1.64999	−	0.536114i
$838$		0			0
$839$	−19.7018	+	27.1172i	−0.680182	+	0.936190i	−0.999936	−	0.0113108i	$-0.996400\pi$
$839$	−19.7018	+	27.1172i	−0.680182	+	0.936190i	0.319754	+	0.947500i	$0.396400\pi$
$840$		0			0
$841$	49.9429	+	36.2856i	1.72217	+	1.25123i
$842$		0			0
$843$	25.6274	−	18.6194i	0.882655	−	0.641286i
$844$		0			0
$845$	−96.7342	−	70.2815i	−3.32776	−	2.41776i
$846$		0			0
$847$			22.5933i			0.776315i
$848$		0			0
$849$	46.2263	+	15.0198i	1.58648	+	0.515479i
$850$		0			0
$851$	−1.35532	−	4.17123i	−0.0464596	−	0.142988i
$852$		0			0
$853$	5.07934	+	15.6326i	0.173913	+	0.535250i	0.999582	−	0.0289048i	$-0.00920197\pi$
$853$	5.07934	+	15.6326i	0.173913	+	0.535250i	−0.825669	+	0.564155i	$0.809202\pi$
$854$		0			0
$855$	42.6033	+	58.6384i	1.45700	+	2.00539i
$856$		0			0
$857$	9.36135	−	28.8113i	0.319778	−	0.984174i	−0.653965	−	0.756524i	$-0.726896\pi$
$857$	9.36135	−	28.8113i	0.319778	−	0.984174i	0.973743	−	0.227650i	$-0.0731041\pi$
$858$		0			0
$859$	8.73587	−	6.34698i	0.298064	−	0.216556i	−0.428694	−	0.903450i	$-0.641026\pi$
$859$	8.73587	−	6.34698i	0.298064	−	0.216556i	0.726758	+	0.686893i	$0.241026\pi$
$860$		0			0
$861$	11.4233	+	16.1443i	0.389306	+	0.550197i
$862$		0			0
$863$	25.9628	−	18.8631i	0.883785	−	0.642108i	−0.0504648	−	0.998726i	$-0.516070\pi$
$863$	25.9628	−	18.8631i	0.883785	−	0.642108i	0.934250	+	0.356618i	$0.116070\pi$
$864$		0			0
$865$	−6.27800	+	19.3217i	−0.213459	+	0.656958i
$866$		0			0
$867$	23.8428	+	32.8169i	0.809745	+	1.11452i
$868$		0			0
$869$	13.9511	+	42.9371i	0.473259	+	1.45654i
$870$		0			0
$871$	31.1744	+	95.9450i	1.05630	+	3.25097i
$872$		0			0
$873$	−85.2725	−	27.7067i	−2.88604	−	0.937730i
$874$		0			0
$875$			10.7665i			0.363973i
$876$		0			0
$877$	25.2274	+	18.3288i	0.851870	+	0.618920i	0.925661	−	0.378354i	$-0.123510\pi$
$877$	25.2274	+	18.3288i	0.851870	+	0.618920i	−0.0737910	+	0.997274i	$0.523510\pi$
$878$		0			0
$879$	−26.2337	+	19.0599i	−0.884840	+	0.642874i
$880$		0			0
$881$	16.8844	+	12.2672i	0.568849	+	0.413293i	0.834687	−	0.550725i	$-0.185649\pi$
$881$	16.8844	+	12.2672i	0.568849	+	0.413293i	−0.265838	+	0.964018i	$0.585649\pi$
$882$		0			0
$883$	3.86804	−	5.32390i	0.130170	−	0.179163i	−0.738957	−	0.673752i	$-0.764681\pi$
$883$	3.86804	−	5.32390i	0.130170	−	0.179163i	0.869127	+	0.494589i	$0.164681\pi$
$884$		0			0
$885$	−12.8660	+	4.18041i	−0.432486	+	0.140523i
$886$		0			0
$887$	18.9929	+	6.17118i	0.637721	+	0.207208i	0.609992	−	0.792407i	$-0.291173\pi$
$887$	18.9929	+	6.17118i	0.637721	+	0.207208i	0.0277286	+	0.999615i	$0.491173\pi$
$888$		0			0
$889$	−3.13618	−	4.31658i	−0.105184	−	0.144773i
$890$		0			0
$891$	77.9973	−	25.3428i	2.61301	−	0.849017i
$892$		0			0
$893$	2.75210			0.0920955
$894$		0			0
$895$	36.0274	−	49.5875i	1.20426	−	1.65753i
$896$		0			0
$897$	−8.75336	+	26.9401i	−0.292266	+	0.899503i
$898$		0			0
$899$			43.7290i			1.45845i
$900$		0			0
$901$	−32.7377			−1.09065
$902$		0			0
$903$	1.72170			0.0572945
$904$		0			0
$905$			33.4596i			1.11223i
$906$		0			0
$907$	−2.79856	+	8.61308i	−0.0929246	+	0.285993i	−0.986707	−	0.162508i	$-0.948042\pi$
$907$	−2.79856	+	8.61308i	−0.0929246	+	0.285993i	0.893783	+	0.448500i	$0.148042\pi$
$908$		0			0
$909$	51.0585	−	70.2760i	1.69350	−	2.33091i
$910$		0			0
$911$	1.08614			0.0359855			0.0179928	−	0.999838i	$-0.494272\pi$
$911$	1.08614			0.0359855			0.0179928	+	0.999838i	$0.494272\pi$
$912$		0			0
$913$	3.24354	−	1.05389i	0.107346	−	0.0348787i
$914$		0			0
$915$	13.7227	+	18.8877i	0.453659	+	0.624408i
$916$		0			0
$917$	9.94890	+	3.23259i	0.328542	+	0.106750i
$918$		0			0
$919$	−47.1185	+	15.3097i	−1.55430	+	0.505022i	−0.955277	−	0.295712i	$-0.904443\pi$
$919$	−47.1185	+	15.3097i	−1.55430	+	0.505022i	−0.599020	+	0.800734i	$0.704443\pi$
$920$		0			0
$921$	−24.8375	+	34.1860i	−0.818425	+	1.12647i
$922$		0			0
$923$	−5.47666	−	3.97902i	−0.180266	−	0.130971i
$924$		0			0
$925$	21.0003	−	15.2576i	0.690486	−	0.501667i
$926$		0			0
$927$	24.4821	+	17.7873i	0.804097	+	0.584211i
$928$		0			0
$929$			29.7704i			0.976735i	0.872638	+	0.488367i	$0.162407\pi$
$929$			29.7704i			0.976735i	−0.872638	+	0.488367i	$0.837593\pi$
$930$		0			0
$931$	2.92484	+	0.950339i	0.0958579	+	0.0311461i
$932$		0			0
$933$	13.1287	+	40.4061i	0.429816	+	1.32284i
$934$		0			0
$935$	−35.4319	−	109.048i	−1.15875	−	3.56625i
$936$		0			0
$937$	27.4424	+	37.7712i	0.896503	+	1.23393i	0.971570	+	0.236752i	$0.0760828\pi$
$937$	27.4424	+	37.7712i	0.896503	+	1.23393i	−0.0750674	+	0.997178i	$0.523917\pi$
$938$		0			0
$939$	18.9198	−	58.2292i	0.617425	−	1.90024i
$940$		0			0
$941$	38.7081	−	28.1231i	1.26185	−	0.916786i	0.263001	−	0.964796i	$-0.415288\pi$
$941$	38.7081	−	28.1231i	1.26185	−	0.916786i	0.998847	+	0.0480096i	$0.0152878\pi$
$942$		0			0
$943$	8.25145	−	2.56724i	0.268704	−	0.0836009i
$944$		0			0
$945$	−31.8765	+	23.1596i	−1.03694	+	0.753382i
$946$		0			0
$947$	8.60547	−	26.4849i	0.279640	−	0.860644i	−0.708314	−	0.705897i	$-0.750544\pi$
$947$	8.60547	−	26.4849i	0.279640	−	0.860644i	0.987954	−	0.154746i	$-0.0494560\pi$
$948$		0			0
$949$	−27.4293	−	37.7532i	−0.890392	−	1.22552i
$950$		0			0
$951$	−17.4952	−	53.8446i	−0.567320	−	1.74603i
$952$		0			0
$953$	−1.94326	−	5.98075i	−0.0629485	−	0.193735i	0.914636	−	0.404278i	$-0.132477\pi$
$953$	−1.94326	−	5.98075i	−0.0629485	−	0.193735i	−0.977585	+	0.210542i	$0.932477\pi$
$954$		0			0
$955$	9.00685	+	2.92650i	0.291455	+	0.0946994i
$956$		0			0
$957$			170.521i			5.51217i
$958$		0			0
$959$	8.67336	+	6.30156i	0.280077	+	0.203488i
$960$		0			0
$961$	8.02918	−	5.83354i	0.259006	−	0.188179i
$962$		0			0
$963$	35.3154	+	25.6581i	1.13802	+	0.826822i
$964$		0			0
$965$	42.5443	−	58.5572i	1.36955	−	1.88502i
$966$		0			0
$967$	−38.2660	+	12.4334i	−1.23055	+	0.399830i	−0.850914	−	0.525306i	$-0.823951\pi$
$967$	−38.2660	+	12.4334i	−1.23055	+	0.399830i	−0.379637	+	0.925136i	$0.623951\pi$
$968$		0			0
$969$	49.5901	+	16.1128i	1.59306	+	0.517618i
$970$		0			0
$971$	33.1026	+	45.5618i	1.06231	+	1.46215i	0.877624	+	0.479350i	$0.159128\pi$
$971$	33.1026	+	45.5618i	1.06231	+	1.46215i	0.184689	+	0.982797i	$0.440872\pi$
$972$		0			0
$973$	0.228096	−	0.0741128i	0.00731241	−	0.00237595i
$974$		0			0
$975$	−167.650			−5.36908
$976$		0			0
$977$	−8.55920	+	11.7807i	−0.273833	+	0.376899i	−0.923679	−	0.383167i	$-0.874833\pi$
$977$	−8.55920	+	11.7807i	−0.273833	+	0.376899i	0.649846	+	0.760066i	$0.274833\pi$
$978$		0			0
$979$	−21.9874	+	67.6704i	−0.702722	+	2.16276i
$980$		0			0
$981$		−	94.6837i		−	3.02302i
$982$		0			0
$983$	13.1894			0.420675			0.210338	−	0.977629i	$-0.432544\pi$
$983$	13.1894			0.420675			0.210338	+	0.977629i	$0.432544\pi$
$984$		0			0
$985$	16.8839			0.537964
$986$		0			0
$987$			2.76400i			0.0879790i
$988$		0			0
$989$	0.232472	−	0.715477i	0.00739219	−	0.0227508i
$990$		0			0
$991$	18.6328	−	25.6459i	0.591891	−	0.814669i	−0.403045	−	0.915180i	$-0.632048\pi$
$991$	18.6328	−	25.6459i	0.591891	−	0.814669i	0.994936	+	0.100512i	$0.0320480\pi$
$992$		0			0
$993$	−33.0794			−1.04974
$994$		0			0
$995$	−44.4274	+	14.4353i	−1.40844	+	0.457631i
$996$		0			0
$997$	22.8276	+	31.4195i	0.722957	+	0.995064i	0.999420	+	0.0340401i	$0.0108374\pi$
$997$	22.8276	+	31.4195i	0.722957	+	0.995064i	−0.276464	+	0.961024i	$0.589163\pi$
$998$		0			0
$999$	33.7919	+	10.9796i	1.06913	+	0.347381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.701.20	yes	80
41.31	even	10	inner	1148.2.ba.a.113.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.1	✓	80	41.31	even	10	inner
1148.2.ba.a.701.20	yes	80	1.1	even	1	trivial

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.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+3.08866i q^{3} +(-1.11364 + 3.42744i) q^{5} +(-0.587785 + 0.809017i) q^{7} -6.53981 q^{9} +O(q^{10})\)	\(q+3.08866i q^{3} +(-1.11364 + 3.42744i) q^{5} +(-0.587785 + 0.809017i) q^{7} -6.53981 q^{9} +(5.51230 - 1.79105i) q^{11} +(-3.99429 - 5.49767i) q^{13} +(-10.5862 - 3.43966i) q^{15} +(-5.22070 + 1.69631i) q^{17} +(-1.80765 + 2.48802i) q^{19} +(-2.49878 - 1.81547i) q^{21} +(-1.09184 + 0.793269i) q^{23} +(-6.46203 - 4.69494i) q^{25} -10.9333i q^{27} +(9.05917 + 2.94350i) q^{29} +(1.41863 + 4.36610i) q^{31} +(5.53195 + 17.0256i) q^{33} +(-2.11827 - 2.91555i) q^{35} +(-1.00424 + 3.09074i) q^{37} +(16.9804 - 12.3370i) q^{39} +(-6.06447 - 2.05480i) q^{41} +(-0.450967 + 0.327647i) q^{43} +(7.28300 - 22.4148i) q^{45} +(-0.526001 - 0.723978i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-5.23932 - 16.1250i) q^{51} +(5.67195 + 1.84293i) q^{53} +20.8876i q^{55} +(-7.68464 - 5.58322i) q^{57} +(0.983245 - 0.714369i) q^{59} +(-1.69686 - 1.23284i) q^{61} +(3.84400 - 5.29082i) q^{63} +(23.2911 - 7.56774i) q^{65} +(-14.1189 - 4.58751i) q^{67} +(-2.45014 - 3.37232i) q^{69} +(0.947422 - 0.307836i) q^{71} +6.86712 q^{73} +(14.5011 - 19.9590i) q^{75} +(-1.79105 + 5.51230i) q^{77} +7.78933i q^{79} +14.1497 q^{81} +0.588419 q^{83} -19.7827i q^{85} +(-9.09148 + 27.9807i) q^{87} +(-7.21580 + 9.93170i) q^{89} +6.79549 q^{91} +(-13.4854 + 4.38167i) q^{93} +(-6.51445 - 8.96638i) q^{95} +(13.0390 + 4.23662i) q^{97} +(-36.0494 + 11.7132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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