LMFDB - Embedded newform 1148.2.r.a.81.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(81,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("1148.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			81.15
Character	$\chi$	$=$	1148.81
Dual form			1148.2.r.a.737.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.294024 + 0.169755i) q^{3} +(-2.09216 - 3.62373i) q^{5} +(-0.0873039 + 2.64431i) q^{7} +(-1.44237 - 2.49825i) q^{9} +O(q^{10})$	\(q+(0.294024 + 0.169755i) q^{3} +(-2.09216 - 3.62373i) q^{5} +(-0.0873039 + 2.64431i) q^{7} +(-1.44237 - 2.49825i) q^{9} +(-3.02680 - 1.74752i) q^{11} +4.69474i q^{13} -1.42062i q^{15} +(0.513708 + 0.296589i) q^{17} +(0.364147 - 0.210240i) q^{19} +(-0.474554 + 0.762670i) q^{21} +(2.40916 + 4.17279i) q^{23} +(-6.25428 + 10.8327i) q^{25} -1.99792i q^{27} +5.24692i q^{29} +(-0.176817 + 0.306255i) q^{31} +(-0.593301 - 1.02763i) q^{33} +(9.76492 - 5.21596i) q^{35} +(1.33617 + 2.31431i) q^{37} +(-0.796955 + 1.38037i) q^{39} +(-3.27959 + 5.49948i) q^{41} -1.13438 q^{43} +(-6.03533 + 10.4535i) q^{45} +(2.07940 - 1.20054i) q^{47} +(-6.98476 - 0.461717i) q^{49} +(0.100695 + 0.174409i) q^{51} +(-5.65391 - 3.26429i) q^{53} +14.6244i q^{55} +0.142757 q^{57} +(0.0567409 - 0.0982782i) q^{59} +(1.54050 + 2.66823i) q^{61} +(6.73208 - 3.59596i) q^{63} +(17.0125 - 9.82216i) q^{65} +(5.74960 + 3.31954i) q^{67} +1.63587i q^{69} -8.06848i q^{71} +(-2.25368 + 3.90348i) q^{73} +(-3.67782 + 2.12339i) q^{75} +(4.88524 - 7.85123i) q^{77} +(-11.1141 + 6.41672i) q^{79} +(-3.98794 + 6.90732i) q^{81} +7.34427 q^{83} -2.48205i q^{85} +(-0.890689 + 1.54272i) q^{87} +(-5.69457 + 3.28776i) q^{89} +(-12.4144 - 0.409869i) q^{91} +(-0.103977 + 0.0600309i) q^{93} +(-1.52371 - 0.879714i) q^{95} +16.0169i q^{97} +10.0823i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^5 + 32 * q^9	$ 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) $ 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.294024	+	0.169755i	0.169755	+	0.0980079i	0.582470	−	0.812852i	$-0.302086\pi$
$3$	0.294024	+	0.169755i	0.169755	+	0.0980079i	−0.412715	+	0.910860i	$0.635420\pi$
$4$		0			0
$5$	−2.09216	−	3.62373i	−0.935643	−	1.62058i	−0.773483	−	0.633817i	$-0.781487\pi$
$5$	−2.09216	−	3.62373i	−0.935643	−	1.62058i	−0.162161	−	0.986764i	$-0.551846\pi$
$6$		0			0
$7$	−0.0873039	+	2.64431i	−0.0329978	+	0.999455i
$7$	−0.0873039	+	2.64431i	−0.0329978	+	0.999455i
$8$		0			0
$9$	−1.44237	−	2.49825i	−0.480789	−	0.832751i
$10$		0			0
$11$	−3.02680	−	1.74752i	−0.912614	−	0.526898i	−0.0313427	−	0.999509i	$-0.509978\pi$
$11$	−3.02680	−	1.74752i	−0.912614	−	0.526898i	−0.881271	+	0.472611i	$0.843312\pi$
$12$		0			0
$13$			4.69474i			1.30209i	0.759040	+	0.651044i	$0.225669\pi$
$13$			4.69474i			1.30209i	−0.759040	+	0.651044i	$0.774331\pi$
$14$		0			0
$15$		−	1.42062i		−	0.366802i
$16$		0			0
$17$	0.513708	+	0.296589i	0.124592	+	0.0719335i	0.561001	−	0.827815i	$-0.310416\pi$
$17$	0.513708	+	0.296589i	0.124592	+	0.0719335i	−0.436408	+	0.899749i	$0.643750\pi$
$18$		0			0
$19$	0.364147	−	0.210240i	0.0835411	−	0.0482325i	−0.457648	−	0.889134i	$-0.651308\pi$
$19$	0.364147	−	0.210240i	0.0835411	−	0.0482325i	0.541189	+	0.840901i	$0.317975\pi$
$20$		0			0
$21$	−0.474554	+	0.762670i	−0.103556	+	0.166428i
$22$		0			0
$23$	2.40916	+	4.17279i	0.502345	+	0.870087i	0.999996	+	0.00270972i	$0.000862532\pi$
$23$	2.40916	+	4.17279i	0.502345	+	0.870087i	−0.497651	+	0.867377i	$0.665804\pi$
$24$		0			0
$25$	−6.25428	+	10.8327i	−1.25086	+	2.16655i
$26$		0			0
$27$		−	1.99792i		−	0.384500i
$28$		0			0
$29$			5.24692i			0.974328i	0.873311	+	0.487164i	$0.161969\pi$
$29$			5.24692i			0.974328i	−0.873311	+	0.487164i	$0.838031\pi$
$30$		0			0
$31$	−0.176817	+	0.306255i	−0.0317572	+	0.0550051i	−0.881467	−	0.472245i	$-0.843444\pi$
$31$	−0.176817	+	0.306255i	−0.0317572	+	0.0550051i	0.849710	+	0.527250i	$0.176777\pi$
$32$		0			0
$33$	−0.593301	−	1.02763i	−0.103280	−	0.178887i
$34$		0			0
$35$	9.76492	−	5.21596i	1.65057	−	0.881658i
$36$		0			0
$37$	1.33617	+	2.31431i	0.219664	+	0.380470i	0.954705	−	0.297553i	$-0.0961705\pi$
$37$	1.33617	+	2.31431i	0.219664	+	0.380470i	−0.735041	+	0.678023i	$0.762837\pi$
$38$		0			0
$39$	−0.796955	+	1.38037i	−0.127615	+	0.221036i
$40$		0			0
$41$	−3.27959	+	5.49948i	−0.512186	+	0.858875i
$41$	−3.27959	+	5.49948i	−0.512186	+	0.858875i
$42$		0			0
$43$	−1.13438			−0.172992			−0.0864959	−	0.996252i	$-0.527567\pi$
$43$	−1.13438			−0.172992			−0.0864959	+	0.996252i	$0.527567\pi$
$44$		0			0
$45$	−6.03533	+	10.4535i	−0.899694	+	1.55832i
$46$		0			0
$47$	2.07940	−	1.20054i	0.303311	−	0.175117i	−0.340618	−	0.940202i	$-0.610636\pi$
$47$	2.07940	−	1.20054i	0.303311	−	0.175117i	0.643929	+	0.765085i	$0.277303\pi$
$48$		0			0
$49$	−6.98476	−	0.461717i	−0.997822	−	0.0659596i
$50$		0			0
$51$	0.100695	+	0.174409i	0.0141001	+	0.0244221i
$52$		0			0
$53$	−5.65391	−	3.26429i	−0.776624	−	0.448384i	0.0586085	−	0.998281i	$-0.481334\pi$
$53$	−5.65391	−	3.26429i	−0.776624	−	0.448384i	−0.835232	+	0.549897i	$0.814667\pi$
$54$		0			0
$55$			14.6244i			1.97195i
$56$		0			0
$57$	0.142757			0.0189087
$58$		0			0
$59$	0.0567409	−	0.0982782i	0.00738704	−	0.0127947i	−0.862308	−	0.506384i	$-0.830982\pi$
$59$	0.0567409	−	0.0982782i	0.00738704	−	0.0127947i	0.869695	+	0.493589i	$0.164315\pi$
$60$		0			0
$61$	1.54050	+	2.66823i	0.197241	+	0.341632i	0.947633	−	0.319361i	$-0.103468\pi$
$61$	1.54050	+	2.66823i	0.197241	+	0.341632i	−0.750392	+	0.660993i	$0.770135\pi$
$62$		0			0
$63$	6.73208	−	3.59596i	0.848162	−	0.453048i
$64$		0			0
$65$	17.0125	−	9.82216i	2.11014	−	1.21829i
$66$		0			0
$67$	5.74960	+	3.31954i	0.702426	+	0.405546i	0.808250	−	0.588839i	$-0.200415\pi$
$67$	5.74960	+	3.31954i	0.702426	+	0.405546i	−0.105824	+	0.994385i	$0.533748\pi$
$68$		0			0
$69$			1.63587i			0.196935i
$70$		0			0
$71$		−	8.06848i		−	0.957552i	−0.877937	−	0.478776i	$-0.841081\pi$
$71$		−	8.06848i		−	0.957552i	0.877937	−	0.478776i	$-0.158919\pi$
$72$		0			0
$73$	−2.25368	+	3.90348i	−0.263773	+	0.456868i	−0.967241	−	0.253858i	$-0.918300\pi$
$73$	−2.25368	+	3.90348i	−0.263773	+	0.456868i	0.703468	+	0.710727i	$0.251634\pi$
$74$		0			0
$75$	−3.67782	+	2.12339i	−0.424678	+	0.245188i
$76$		0			0
$77$	4.88524	−	7.85123i	0.556725	−	0.894731i
$78$		0			0
$79$	−11.1141	+	6.41672i	−1.25043	+	0.721937i	−0.971195	−	0.238285i	$-0.923415\pi$
$79$	−11.1141	+	6.41672i	−1.25043	+	0.721937i	−0.279236	+	0.960222i	$0.590081\pi$
$80$		0			0
$81$	−3.98794	+	6.90732i	−0.443105	+	0.767480i
$82$		0			0
$83$	7.34427			0.806138			0.403069	−	0.915170i	$-0.367943\pi$
$83$	7.34427			0.806138			0.403069	+	0.915170i	$0.367943\pi$
$84$		0			0
$85$		−	2.48205i		−	0.269216i
$86$		0			0
$87$	−0.890689	+	1.54272i	−0.0954919	+	0.165397i
$88$		0			0
$89$	−5.69457	+	3.28776i	−0.603623	+	0.348502i	−0.770465	−	0.637482i	$-0.779976\pi$
$89$	−5.69457	+	3.28776i	−0.603623	+	0.348502i	0.166843	+	0.985984i	$0.446643\pi$
$90$		0			0
$91$	−12.4144	−	0.409869i	−1.30138	−	0.0429660i
$92$		0			0
$93$	−0.103977	+	0.0600309i	−0.0107819	+	0.00622491i
$94$		0			0
$95$	−1.52371	−	0.879714i	−0.156329	−	0.0902568i
$96$		0			0
$97$			16.0169i			1.62627i	0.582074	+	0.813136i	$0.302242\pi$
$97$			16.0169i			1.62627i	−0.582074	+	0.813136i	$0.697758\pi$
$98$		0			0
$99$			10.0823i			1.01331i
$100$		0			0
$101$	−4.47921	−	2.58607i	−0.445698	−	0.257324i	0.260313	−	0.965524i	$-0.416174\pi$
$101$	−4.47921	−	2.58607i	−0.445698	−	0.257324i	−0.706012	+	0.708200i	$0.749507\pi$
$102$		0			0
$103$	−4.68488	−	8.11445i	−0.461615	−	0.799541i	0.537427	−	0.843310i	$-0.319396\pi$
$103$	−4.68488	−	8.11445i	−0.461615	−	0.799541i	−0.999042	+	0.0437699i	$0.986063\pi$
$104$		0			0
$105$	3.75655	+	0.124025i	0.366602	+	0.0121036i
$106$		0			0
$107$	−7.68469	−	13.3103i	−0.742907	−	1.28675i	−0.951166	−	0.308678i	$-0.900113\pi$
$107$	−7.68469	−	13.3103i	−0.742907	−	1.28675i	0.208260	−	0.978074i	$-0.433220\pi$
$108$		0			0
$109$	−6.79035	−	3.92041i	−0.650397	−	0.375507i	0.138211	−	0.990403i	$-0.455865\pi$
$109$	−6.79035	−	3.92041i	−0.650397	−	0.375507i	−0.788608	+	0.614896i	$0.789198\pi$
$110$		0			0
$111$			0.907282i			0.0861154i
$112$		0			0
$113$	−12.6306			−1.18819			−0.594094	−	0.804395i	$-0.702489\pi$
$113$	−12.6306			−1.18819			−0.594094	+	0.804395i	$0.702489\pi$
$114$		0			0
$115$	10.0807	−	17.4603i	0.940031	−	1.62818i
$116$		0			0
$117$	11.7287	−	6.77154i	1.08431	−	0.626029i
$118$		0			0
$119$	−0.829123	+	1.33251i	−0.0760056	+	0.122151i
$120$		0			0
$121$	0.607671	+	1.05252i	0.0552428	+	0.0956834i
$122$		0			0
$123$	−1.89784	+	1.06025i	−0.171123	+	0.0955997i
$124$		0			0
$125$	31.4183			2.81014
$126$		0			0
$127$	−5.65473			−0.501777			−0.250888	−	0.968016i	$-0.580723\pi$
$127$	−5.65473			−0.501777			−0.250888	+	0.968016i	$0.580723\pi$
$128$		0			0
$129$	−0.333536	−	0.192567i	−0.0293662	−	0.0169546i
$130$		0			0
$131$	9.46402	+	16.3922i	0.826875	+	1.43219i	0.900477	+	0.434903i	$0.143217\pi$
$131$	9.46402	+	16.3922i	0.826875	+	1.43219i	−0.0736020	+	0.997288i	$0.523449\pi$
$132$		0			0
$133$	0.524149	+	0.981273i	0.0454495	+	0.0850871i
$134$		0			0
$135$	−7.23994	+	4.17998i	−0.623114	+	0.359755i
$136$		0			0
$137$	−15.0288	−	8.67688i	−1.28400	−	0.741316i	−0.306421	−	0.951896i	$-0.599131\pi$
$137$	−15.0288	−	8.67688i	−1.28400	−	0.741316i	−0.977577	+	0.210580i	$0.932465\pi$
$138$		0			0
$139$	−18.2679			−1.54946			−0.774730	−	0.632293i	$-0.782114\pi$
$139$	−18.2679			−1.54946			−0.774730	+	0.632293i	$0.782114\pi$
$140$		0			0
$141$	0.815190			0.0686514
$142$		0			0
$143$	8.20417	−	14.2100i	0.686067	−	1.18830i
$144$		0			0
$145$	19.0134	−	10.9774i	1.57898	−	0.911623i
$146$		0			0
$147$	−1.97531	−	1.32145i	−0.162921	−	0.108991i
$148$		0			0
$149$	14.1062	−	8.14421i	1.15562	−	0.667200i	0.205373	−	0.978684i	$-0.434159\pi$
$149$	14.1062	−	8.14421i	1.15562	−	0.667200i	0.950251	+	0.311484i	$0.100826\pi$
$150$		0			0
$151$	−8.44092	−	4.87336i	−0.686912	−	0.396589i	0.115542	−	0.993303i	$-0.463139\pi$
$151$	−8.44092	−	4.87336i	−0.686912	−	0.396589i	−0.802454	+	0.596714i	$0.796473\pi$
$152$		0			0
$153$		−	1.71116i		−	0.138339i
$154$		0			0
$155$	1.47972			0.118854
$156$		0			0
$157$	11.1066	+	6.41237i	0.886400	+	0.511763i	0.872763	−	0.488144i	$-0.162326\pi$
$157$	11.1066	+	6.41237i	0.886400	+	0.511763i	0.0136364	+	0.999907i	$0.495659\pi$
$158$		0			0
$159$	−1.10826	−	1.91956i	−0.0878904	−	0.152231i
$160$		0			0
$161$	−11.2445	+	6.00627i	−0.886189	+	0.473360i
$162$		0			0
$163$	−5.70745	−	9.88559i	−0.447042	−	0.774299i	0.551150	−	0.834406i	$-0.314189\pi$
$163$	−5.70745	−	9.88559i	−0.447042	−	0.774299i	−0.998192	+	0.0601069i	$0.980856\pi$
$164$		0			0
$165$	−2.48256	+	4.29992i	−0.193267	+	0.334749i
$166$		0			0
$167$			8.80882i			0.681647i	0.940127	+	0.340823i	$0.110706\pi$
$167$			8.80882i			0.681647i	−0.940127	+	0.340823i	$0.889294\pi$
$168$		0			0
$169$	−9.04061			−0.695432
$170$		0			0
$171$	−1.05047	−	0.606488i	−0.0803312	−	0.0463793i
$172$		0			0
$173$	5.68920	+	9.85398i	0.432542	+	0.749184i	0.997091	−	0.0762150i	$-0.0242835\pi$
$173$	5.68920	+	9.85398i	0.432542	+	0.749184i	−0.564550	+	0.825399i	$0.690950\pi$
$174$		0			0
$175$	−28.0991	−	17.4840i	−2.12409	−	1.32167i
$176$		0			0
$177$	0.0333664	−	0.0192641i	0.00250797	−	0.00144798i
$178$		0			0
$179$	−20.9361	−	12.0875i	−1.56484	−	0.903461i	−0.996755	−	0.0804918i	$-0.974351\pi$
$179$	−20.9361	−	12.0875i	−1.56484	−	0.903461i	−0.568086	−	0.822969i	$-0.692316\pi$
$180$		0			0
$181$		−	13.1837i		−	0.979940i	−0.871739	−	0.489970i	$-0.837008\pi$
$181$		−	13.1837i		−	0.979940i	0.871739	−	0.489970i	$-0.162992\pi$
$182$		0			0
$183$			1.04603i			0.0773249i
$184$		0			0
$185$	5.59095	−	9.68381i	0.411055	−	0.711968i
$186$		0			0
$187$	−1.03659	−	1.79543i	−0.0758032	−	0.131295i
$188$		0			0
$189$	5.28313	+	0.174426i	0.384291	+	0.0126877i
$190$		0			0
$191$	−14.8508	+	8.57414i	−1.07457	+	0.620403i	−0.929426	−	0.369008i	$-0.879698\pi$
$191$	−14.8508	+	8.57414i	−1.07457	+	0.620403i	−0.145143	+	0.989411i	$0.546364\pi$
$192$		0			0
$193$	20.8507	+	12.0382i	1.50087	+	0.866527i	0.999999	+	0.00100383i	$0.000319529\pi$
$193$	20.8507	+	12.0382i	1.50087	+	0.866527i	0.500869	+	0.865523i	$0.333014\pi$
$194$		0			0
$195$	6.66944			0.477608
$196$		0			0
$197$	9.46342			0.674241			0.337120	−	0.941462i	$-0.390547\pi$
$197$	9.46342			0.674241			0.337120	+	0.941462i	$0.390547\pi$
$198$		0			0
$199$	16.0359	+	9.25832i	1.13675	+	0.656305i	0.945625	−	0.325260i	$-0.105452\pi$
$199$	16.0359	+	9.25832i	1.13675	+	0.656305i	0.191129	+	0.981565i	$0.438785\pi$
$200$		0			0
$201$	1.12701	+	1.95205i	0.0794934	+	0.137687i
$202$		0			0
$203$	−13.8745	−	0.458076i	−0.973797	−	0.0321506i
$204$		0			0
$205$	26.7901	+	0.378552i	1.87110	+	0.0264392i
$206$		0			0
$207$	6.94979	−	12.0374i	0.483044	−	0.836656i
$208$		0			0
$209$	−1.46960			−0.101654
$210$		0			0
$211$		−	0.563983i		−	0.0388262i	−0.999812	−	0.0194131i	$-0.993820\pi$
$211$		−	0.563983i		−	0.0388262i	0.999812	−	0.0194131i	$-0.00617977\pi$
$212$		0			0
$213$	1.36966	−	2.37232i	0.0938477	−	0.162549i
$214$		0			0
$215$	2.37331	+	4.11070i	0.161859	+	0.280347i
$216$		0			0
$217$	−0.794397	−	0.494295i	−0.0539272	−	0.0335549i
$218$		0			0
$219$	−1.32527	+	0.765145i	−0.0895535	+	0.0517037i
$220$		0			0
$221$	−1.39241	+	2.41173i	−0.0936637	+	0.162230i
$222$		0			0
$223$	16.7194			1.11962			0.559808	−	0.828623i	$-0.310875\pi$
$223$	16.7194			1.11962			0.559808	+	0.828623i	$0.310875\pi$
$224$		0			0
$225$	36.0839			2.40559
$226$		0			0
$227$	4.19247	+	2.42052i	0.278264	+	0.160656i	0.632637	−	0.774448i	$-0.281972\pi$
$227$	4.19247	+	2.42052i	0.278264	+	0.160656i	−0.354373	+	0.935104i	$0.615306\pi$
$228$		0			0
$229$	−10.0330	+	5.79257i	−0.663001	+	0.382784i	−0.793419	−	0.608675i	$-0.791701\pi$
$229$	−10.0330	+	5.79257i	−0.663001	+	0.382784i	0.130419	+	0.991459i	$0.458368\pi$
$230$		0			0
$231$	2.76916	−	1.47916i	0.182197	−	0.0973213i
$232$		0			0
$233$	10.3937	−	6.00079i	0.680912	−	0.393125i	−0.119286	−	0.992860i	$-0.538061\pi$
$233$	10.3937	−	6.00079i	0.680912	−	0.393125i	0.800199	+	0.599735i	$0.204727\pi$
$234$		0			0
$235$	−8.70087	−	5.02345i	−0.567582	−	0.327694i
$236$		0			0
$237$	−4.35707			−0.283022
$238$		0			0
$239$		−	4.45645i		−	0.288264i	−0.989559	−	0.144132i	$-0.953961\pi$
$239$		−	4.45645i		−	0.288264i	0.989559	−	0.144132i	$-0.0460389\pi$
$240$		0			0
$241$	−11.4069	+	19.7573i	−0.734783	+	1.27268i	0.220035	+	0.975492i	$0.429383\pi$
$241$	−11.4069	+	19.7573i	−0.734783	+	1.27268i	−0.954818	+	0.297190i	$0.903951\pi$
$242$		0			0
$243$	−7.53586	+	4.35083i	−0.483425	+	0.279106i
$244$		0			0
$245$	12.9401	+	26.2769i	0.826713	+	1.67877i
$246$		0			0
$247$	0.987025	+	1.70958i	0.0628029	+	0.108778i
$248$		0			0
$249$	2.15939	+	1.24672i	0.136846	+	0.0790080i
$250$		0			0
$251$	17.0358			1.07529			0.537644	−	0.843172i	$-0.319314\pi$
$251$	17.0358			1.07529			0.537644	+	0.843172i	$0.319314\pi$
$252$		0			0
$253$		−	16.8403i		−	1.05874i
$254$		0			0
$255$	0.421340	−	0.729783i	0.0263853	−	0.0457008i
$256$		0			0
$257$	−24.3130	+	14.0371i	−1.51660	+	0.875612i	−0.516794	+	0.856110i	$0.672875\pi$
$257$	−24.3130	+	14.0371i	−1.51660	+	0.875612i	−0.999810	+	0.0195016i	$0.993792\pi$
$258$		0			0
$259$	−6.23640	+	3.33119i	−0.387511	+	0.206990i
$260$		0			0
$261$	13.1081	−	7.56798i	0.811372	−	0.468446i
$262$		0			0
$263$	22.0136	+	12.7096i	1.35742	+	0.783705i	0.989275	−	0.146065i	$-0.0466607\pi$
$263$	22.0136	+	12.7096i	1.35742	+	0.783705i	0.368142	+	0.929770i	$0.379994\pi$
$264$		0			0
$265$			27.3177i			1.67811i
$266$		0			0
$267$	−2.23245			−0.136624
$268$		0			0
$269$	10.4165	−	18.0418i	0.635103	−	1.10003i	−0.351391	−	0.936229i	$-0.614291\pi$
$269$	10.4165	−	18.0418i	0.635103	−	1.10003i	0.986493	−	0.163801i	$-0.0523755\pi$
$270$		0			0
$271$	−6.42979	−	11.1367i	−0.390582	−	0.676507i	0.601945	−	0.798538i	$-0.294393\pi$
$271$	−6.42979	−	11.1367i	−0.390582	−	0.676507i	−0.992526	+	0.122030i	$0.961059\pi$
$272$		0			0
$273$	−3.58054	−	2.22791i	−0.216704	−	0.134839i
$274$		0			0
$275$	37.8609	−	21.8590i	2.28310	−	1.31815i
$276$		0			0
$277$	14.9628	−	25.9162i	0.899025	−	1.55716i	0.0702814	−	0.997527i	$-0.477610\pi$
$277$	14.9628	−	25.9162i	0.899025	−	1.55716i	0.828743	−	0.559629i	$-0.189056\pi$
$278$		0			0
$279$	1.02014			0.0610740
$280$		0			0
$281$			11.4220i			0.681381i	0.940176	+	0.340690i	$0.110661\pi$
$281$			11.4220i			0.681381i	−0.940176	+	0.340690i	$0.889339\pi$
$282$		0			0
$283$	11.3348	−	19.6325i	0.673787	−	1.16703i	−0.303035	−	0.952979i	$-0.598000\pi$
$283$	11.3348	−	19.6325i	0.673787	−	1.16703i	0.976822	−	0.214054i	$-0.0686667\pi$
$284$		0			0
$285$	−0.298671	−	0.517314i	−0.0176918	−	0.0306430i
$286$		0			0
$287$	−14.2560	−	9.15238i	−0.841506	−	0.540248i
$288$		0			0
$289$	−8.32407	−	14.4177i	−0.489651	−	0.848101i
$290$		0			0
$291$	−2.71895	+	4.70936i	−0.159388	+	0.276067i
$292$		0			0
$293$		−	15.8416i		−	0.925474i	−0.886496	−	0.462737i	$-0.846867\pi$
$293$		−	15.8416i		−	0.925474i	0.886496	−	0.462737i	$-0.153133\pi$
$294$		0			0
$295$	−0.474845			−0.0276465
$296$		0			0
$297$	−3.49142	+	6.04731i	−0.202592	+	0.350900i
$298$		0			0
$299$	−19.5902	+	11.3104i	−1.13293	+	0.654097i
$300$		0			0
$301$	0.0990360	−	2.99966i	0.00570834	−	0.172897i
$302$		0			0
$303$	−0.877997	−	1.52074i	−0.0504396	−	0.0873640i
$304$		0			0
$305$	6.44597	−	11.1647i	0.369095	−	0.639291i
$306$		0			0
$307$	−17.7706			−1.01422			−0.507111	−	0.861881i	$-0.669286\pi$
$307$	−17.7706			−1.01422			−0.507111	+	0.861881i	$0.669286\pi$
$308$		0			0
$309$		−	3.18112i		−	0.180968i
$310$		0			0
$311$	27.1694	+	15.6862i	1.54063	+	0.889485i	0.998799	+	0.0489990i	$0.0156031\pi$
$311$	27.1694	+	15.6862i	1.54063	+	0.889485i	0.541834	+	0.840486i	$0.317730\pi$
$312$		0			0
$313$	−5.48992	+	3.16961i	−0.310309	+	0.179157i	−0.647065	−	0.762435i	$-0.724004\pi$
$313$	−5.48992	+	3.16961i	−0.310309	+	0.179157i	0.336756	+	0.941592i	$0.390670\pi$
$314$		0			0
$315$	−27.1154	−	16.8719i	−1.52778	−	0.950625i
$316$		0			0
$317$	−17.3736	+	10.0306i	−0.975797	+	0.563377i	−0.900999	−	0.433822i	$-0.857165\pi$
$317$	−17.3736	+	10.0306i	−0.975797	+	0.563377i	−0.0747986	+	0.997199i	$0.523831\pi$
$318$		0			0
$319$	9.16910	−	15.8814i	0.513371	−	0.889185i
$320$		0			0
$321$		−	5.21805i		−	0.291243i
$322$		0			0
$323$	0.249420			0.0138781
$324$		0			0
$325$	−50.8569	−	29.3623i	−2.82103	−	1.62873i
$326$		0			0
$327$	−1.33102	−	2.30539i	−0.0736054	−	0.127488i
$328$		0			0
$329$	2.99306	+	5.60338i	0.165013	+	0.308925i
$330$		0			0
$331$	16.7442	−	9.66729i	0.920347	−	0.531362i	0.0366010	−	0.999330i	$-0.488347\pi$
$331$	16.7442	−	9.66729i	0.920347	−	0.531362i	0.883746	+	0.467968i	$0.155014\pi$
$332$		0			0
$333$	3.85448	−	6.67616i	0.211224	−	0.365851i
$334$		0			0
$335$		−	27.7800i		−	1.51779i
$336$		0			0
$337$	−6.72087			−0.366109			−0.183055	−	0.983103i	$-0.558599\pi$
$337$	−6.72087			−0.366109			−0.183055	+	0.983103i	$0.558599\pi$
$338$		0			0
$339$	−3.71370	−	2.14411i	−0.201701	−	0.116452i
$340$		0			0
$341$	1.07038	−	0.617982i	0.0579641	−	0.0334656i
$342$		0			0
$343$	1.83072	−	18.4296i	0.0988496	−	0.995102i
$344$		0			0
$345$	5.92794	−	3.42250i	0.319150	−	0.184261i
$346$		0			0
$347$	−23.2089	−	13.3996i	−1.24592	−	0.719331i	−0.275625	−	0.961265i	$-0.588885\pi$
$347$	−23.2089	−	13.3996i	−1.24592	−	0.719331i	−0.970293	+	0.241935i	$0.922218\pi$
$348$		0			0
$349$	−2.09042			−0.111897			−0.0559487	−	0.998434i	$-0.517818\pi$
$349$	−2.09042			−0.111897			−0.0559487	+	0.998434i	$0.517818\pi$
$350$		0			0
$351$	9.37973			0.500653
$352$		0			0
$353$	−13.8452	+	23.9805i	−0.736904	+	1.27636i	0.216978	+	0.976176i	$0.430380\pi$
$353$	−13.8452	+	23.9805i	−0.736904	+	1.27636i	−0.953883	+	0.300179i	$0.902953\pi$
$354$		0			0
$355$	−29.2380	+	16.8806i	−1.55179	+	0.895927i
$356$		0			0
$357$	−0.469982	+	0.251042i	−0.0248741	+	0.0132866i
$358$		0			0
$359$	−11.4361	−	19.8080i	−0.603576	−	1.04542i	−0.992275	−	0.124060i	$-0.960409\pi$
$359$	−11.4361	−	19.8080i	−0.603576	−	1.04542i	0.388699	−	0.921365i	$-0.372925\pi$
$360$		0			0
$361$	−9.41160	+	16.3014i	−0.495347	+	0.857967i
$362$		0			0
$363$			0.412620i			0.0216569i
$364$		0			0
$365$	18.8602			0.987190
$366$		0			0
$367$	15.0035	−	25.9869i	0.783178	−	1.35650i	−0.146904	−	0.989151i	$-0.546931\pi$
$367$	15.0035	−	25.9869i	0.783178	−	1.35650i	0.930081	−	0.367353i	$-0.119736\pi$
$368$		0			0
$369$	18.4695	+	0.260979i	0.961482	+	0.0135860i
$370$		0			0
$371$	9.12539	−	14.6657i	0.473767	−	0.761405i
$372$		0			0
$373$	−14.8866	−	25.7843i	−0.770796	−	1.33506i	−0.937127	−	0.348989i	$-0.886525\pi$
$373$	−14.8866	−	25.7843i	−0.770796	−	1.33506i	0.166330	−	0.986070i	$-0.446808\pi$
$374$		0			0
$375$	9.23773	+	5.33340i	0.477034	+	0.275416i
$376$		0			0
$377$	−24.6329			−1.26866
$378$		0			0
$379$	32.7944			1.68454			0.842268	−	0.539059i	$-0.181220\pi$
$379$	32.7944			1.68454			0.842268	+	0.539059i	$0.181220\pi$
$380$		0			0
$381$	−1.66263	−	0.959918i	−0.0851790	−	0.0491781i
$382$		0			0
$383$	−19.8601	+	11.4662i	−1.01480	+	0.585896i	−0.912594	−	0.408867i	$-0.865924\pi$
$383$	−19.8601	+	11.4662i	−1.01480	+	0.585896i	−0.102208	+	0.994763i	$0.532591\pi$
$384$		0			0
$385$	−38.6715	−	1.27677i	−1.97088	−	0.0650701i
$386$		0			0
$387$	1.63620	+	2.83397i	0.0831725	+	0.144059i
$388$		0			0
$389$	−6.17937	+	10.7030i	−0.313306	+	0.542662i	−0.979076	−	0.203495i	$-0.934770\pi$
$389$	−6.17937	+	10.7030i	−0.313306	+	0.542662i	0.665770	+	0.746157i	$0.268103\pi$
$390$		0			0
$391$			2.85813i			0.144542i
$392$		0			0
$393$			6.42625i			0.324161i
$394$		0			0
$395$	46.5049	+	26.8496i	2.33992	+	1.35095i
$396$		0			0
$397$	−25.5979	+	14.7789i	−1.28472	+	0.741733i	−0.977707	−	0.209972i	$-0.932663\pi$
$397$	−25.5979	+	14.7789i	−1.28472	+	0.741733i	−0.307013	+	0.951705i	$0.599329\pi$
$398$		0			0
$399$	−0.0124633	+	0.377494i	−0.000623943	+	0.0188984i
$400$		0			0
$401$	−8.24277	−	14.2769i	−0.411624	−	0.712954i	0.583443	−	0.812154i	$-0.301705\pi$
$401$	−8.24277	−	14.2769i	−0.411624	−	0.712954i	−0.995068	+	0.0992000i	$0.968372\pi$
$402$		0			0
$403$	−1.43779	−	0.830108i	−0.0716214	−	0.0413506i
$404$		0			0
$405$	33.3737			1.65835
$406$		0			0
$407$		−	9.33992i		−	0.462962i
$408$		0			0
$409$	−5.06901	+	8.77979i	−0.250647	+	0.434133i	−0.963704	−	0.266973i	$-0.913977\pi$
$409$	−5.06901	+	8.77979i	−0.250647	+	0.434133i	0.713057	+	0.701106i	$0.247310\pi$
$410$		0			0
$411$	−2.94588	−	5.10242i	−0.145310	−	0.251684i
$412$		0			0
$413$	0.254924	+	0.158621i	0.0125440	+	0.00780522i
$414$		0			0
$415$	−15.3654	−	26.6137i	−0.754258	−	1.30641i
$416$		0			0
$417$	−5.37119	−	3.10106i	−0.263028	−	0.151859i
$418$		0			0
$419$	−15.1068			−0.738018			−0.369009	−	0.929426i	$-0.620303\pi$
$419$	−15.1068			−0.738018			−0.369009	+	0.929426i	$0.620303\pi$
$420$		0			0
$421$			28.1611i			1.37249i	0.727370	+	0.686245i	$0.240742\pi$
$421$			28.1611i			1.37249i	−0.727370	+	0.686245i	$0.759258\pi$
$422$		0			0
$423$	−5.99851	−	3.46324i	−0.291657	−	0.168388i
$424$		0			0
$425$	−6.42575	+	3.70991i	−0.311695	+	0.179957i
$426$		0			0
$427$	−7.19012	+	3.84062i	−0.347954	+	0.185861i
$428$		0			0
$429$	4.82444	−	2.78539i	0.232926	−	0.134480i
$430$		0			0
$431$	−14.6842	+	25.4339i	−0.707315	+	1.22511i	0.258534	+	0.966002i	$0.416760\pi$
$431$	−14.6842	+	25.4339i	−0.707315	+	1.22511i	−0.965850	+	0.259104i	$0.916573\pi$
$432$		0			0
$433$	−5.54692			−0.266568			−0.133284	−	0.991078i	$-0.542552\pi$
$433$	−5.54692			−0.266568			−0.133284	+	0.991078i	$0.542552\pi$
$434$		0			0
$435$	7.45386			0.357385
$436$		0			0
$437$	1.75458	+	1.01301i	0.0839329	+	0.0484587i
$438$		0			0
$439$	27.8508	−	16.0797i	1.32925	−	0.767442i	0.344065	−	0.938946i	$-0.388196\pi$
$439$	27.8508	−	16.0797i	1.32925	−	0.767442i	0.985183	+	0.171504i	$0.0548628\pi$
$440$		0			0
$441$	8.92109	+	18.1156i	0.424814	+	0.862650i
$442$		0			0
$443$	13.6302	+	23.6082i	0.647591	+	1.12166i	0.983697	+	0.179837i	$0.0575569\pi$
$443$	13.6302	+	23.6082i	0.647591	+	1.12166i	−0.336105	+	0.941824i	$0.609110\pi$
$444$		0			0
$445$	23.8279	+	13.7571i	1.12955	+	0.652147i
$446$		0			0
$447$	5.53007			0.261564
$448$		0			0
$449$	−4.00100			−0.188819			−0.0944095	−	0.995533i	$-0.530096\pi$
$449$	−4.00100			−0.188819			−0.0944095	+	0.995533i	$0.530096\pi$
$450$		0			0
$451$	19.5371	−	10.9147i	0.919967	−	0.513951i
$452$		0			0
$453$	−1.65455	−	2.86577i	−0.0777377	−	0.134646i
$454$		0			0
$455$	24.4876	+	45.8438i	1.14800	+	2.14919i
$456$		0			0
$457$	14.3377	−	8.27785i	0.670687	−	0.387222i	−0.125650	−	0.992075i	$-0.540102\pi$
$457$	14.3377	−	8.27785i	0.670687	−	0.387222i	0.796337	+	0.604853i	$0.206768\pi$
$458$		0			0
$459$	0.592563	−	1.02635i	0.0276585	−	0.0479059i
$460$		0			0
$461$	−1.76219			−0.0820732			−0.0410366	−	0.999158i	$-0.513066\pi$
$461$	−1.76219			−0.0820732			−0.0410366	+	0.999158i	$0.513066\pi$
$462$		0			0
$463$			40.0312i			1.86041i	0.367042	+	0.930204i	$0.380371\pi$
$463$			40.0312i			1.86041i	−0.367042	+	0.930204i	$0.619629\pi$
$464$		0			0
$465$	0.435072	+	0.251189i	0.0201760	+	0.0116486i
$466$		0			0
$467$	10.2164	+	17.6953i	0.472758	+	0.818841i	0.999514	−	0.0311756i	$-0.00992511\pi$
$467$	10.2164	+	17.6953i	0.472758	+	0.818841i	−0.526756	+	0.850017i	$0.676592\pi$
$468$		0			0
$469$	−9.27985	+	14.9139i	−0.428504	+	0.688661i
$470$		0			0
$471$	2.17706	+	3.77078i	0.100314	+	0.173748i
$472$		0			0
$473$	3.43355	+	1.98236i	0.157875	+	0.0911490i
$474$		0			0
$475$			5.25961i			0.241328i
$476$		0			0
$477$			18.8332i			0.862312i
$478$		0			0
$479$	−14.9075	−	8.60685i	−0.681141	−	0.393257i	0.119144	−	0.992877i	$-0.461985\pi$
$479$	−14.9075	−	8.60685i	−0.681141	−	0.393257i	−0.800285	+	0.599620i	$0.795318\pi$
$480$		0			0
$481$	−10.8651	+	6.27295i	−0.495405	+	0.286022i
$482$		0			0
$483$	−4.32574	−	0.142817i	−0.196828	−	0.00649842i
$484$		0			0
$485$	58.0410	−	33.5100i	2.63551	−	1.52161i
$486$		0			0
$487$	−15.8130	+	27.3890i	−0.716558	+	1.24111i	0.245798	+	0.969321i	$0.420950\pi$
$487$	−15.8130	+	27.3890i	−0.716558	+	1.24111i	−0.962356	+	0.271793i	$0.912383\pi$
$488$		0			0
$489$		−	3.87547i		−	0.175255i
$490$		0			0
$491$	−17.6941			−0.798524			−0.399262	−	0.916837i	$-0.630734\pi$
$491$	−17.6941			−0.798524			−0.399262	+	0.916837i	$0.630734\pi$
$492$		0			0
$493$	−1.55618	+	2.69538i	−0.0700868	+	0.121394i
$494$		0			0
$495$	36.5354	−	21.0938i	1.64215	−	0.948094i
$496$		0			0
$497$	21.3356	+	0.704409i	0.957031	+	0.0315971i
$498$		0			0
$499$	−12.4272	+	7.17486i	−0.556319	+	0.321191i	−0.751667	−	0.659543i	$-0.770750\pi$
$499$	−12.4272	+	7.17486i	−0.556319	+	0.321191i	0.195348	+	0.980734i	$0.437416\pi$
$500$		0			0
$501$	−1.49534	+	2.59000i	−0.0668068	+	0.115713i
$502$		0			0
$503$		−	5.34019i		−	0.238107i	−0.992888	−	0.119054i	$-0.962014\pi$
$503$		−	5.34019i		−	0.238107i	0.992888	−	0.119054i	$-0.0379860\pi$
$504$		0			0
$505$			21.6420i			0.963054i
$506$		0			0
$507$	−2.65816	−	1.53469i	−0.118053	−	0.0681578i
$508$		0			0
$509$	25.9828	−	15.0012i	1.15167	−	0.664915i	0.202374	−	0.979308i	$-0.435134\pi$
$509$	25.9828	−	15.0012i	1.15167	−	0.664915i	0.949293	+	0.314393i	$0.101801\pi$
$510$		0			0
$511$	−10.1253	−	6.30021i	−0.447916	−	0.278705i
$512$		0			0
$513$	−0.420044	−	0.727538i	−0.0185454	−	0.0321216i
$514$		0			0
$515$	−19.6031	+	33.9535i	−0.863814	+	1.49617i
$516$		0			0
$517$	−8.39189			−0.369075
$518$		0			0
$519$			3.86307i			0.169570i
$520$		0			0
$521$	28.9614	+	16.7209i	1.26882	+	0.732555i	0.974765	−	0.223232i	$-0.0716608\pi$
$521$	28.9614	+	16.7209i	1.26882	+	0.732555i	0.294058	+	0.955788i	$0.404994\pi$
$522$		0			0
$523$	6.89239	+	11.9380i	0.301383	+	0.522011i	0.976450	−	0.215746i	$-0.0692183\pi$
$523$	6.89239	+	11.9380i	0.301383	+	0.522011i	−0.675066	+	0.737757i	$0.735885\pi$
$524$		0			0
$525$	−5.29381	−	9.91067i	−0.231041	−	0.432537i
$526$		0			0
$527$	−0.181664	+	0.104884i	−0.00791341	+	0.00456881i
$528$		0			0
$529$	−0.108116	+	0.187263i	−0.00470070	+	0.00814185i
$530$		0			0
$531$	−0.327365			−0.0142064
$532$		0			0
$533$	−25.8186	−	15.3968i	−1.11833	−	0.666911i
$534$		0			0
$535$	−32.1552	+	55.6945i	−1.39019	+	2.40788i
$536$		0			0
$537$	−4.10382	−	7.10802i	−0.177093	−	0.306734i
$538$		0			0
$539$	20.3346	+	13.6035i	0.875873	+	0.585946i
$540$		0			0
$541$	10.1515	+	17.5830i	0.436448	+	0.755951i	0.997413	−	0.0718893i	$-0.0229028\pi$
$541$	10.1515	+	17.5830i	0.436448	+	0.755951i	−0.560964	+	0.827840i	$0.689569\pi$
$542$		0			0
$543$	2.23800	−	3.87634i	0.0960419	−	0.166350i
$544$		0			0
$545$			32.8085i			1.40536i
$546$		0			0
$547$		−	4.94543i		−	0.211451i	−0.994395	−	0.105726i	$-0.966283\pi$
$547$		−	4.94543i		−	0.211451i	0.994395	−	0.105726i	$-0.0337165\pi$
$548$		0			0
$549$	4.44394	−	7.69714i	0.189663	−	0.328506i
$550$		0			0
$551$	1.10311	+	1.91065i	0.0469942	+	0.0813964i
$552$		0			0
$553$	−15.9975	−	29.9493i	−0.680282	−	1.27357i
$554$		0			0
$555$	3.28774	−	1.89818i	0.139557	−	0.0805733i
$556$		0			0
$557$	3.65247	+	2.10875i	0.154760	+	0.0893507i	0.575380	−	0.817886i	$-0.304854\pi$
$557$	3.65247	+	2.10875i	0.154760	+	0.0893507i	−0.420620	+	0.907237i	$0.638187\pi$
$558$		0			0
$559$		−	5.32563i		−	0.225250i
$560$		0			0
$561$		−	0.703867i		−	0.0297173i
$562$		0			0
$563$	−0.289260	−	0.167004i	−0.0121909	−	0.00703839i	0.493892	−	0.869523i	$-0.335574\pi$
$563$	−0.289260	−	0.167004i	−0.0121909	−	0.00703839i	−0.506083	+	0.862485i	$0.668907\pi$
$564$		0			0
$565$	26.4253	+	45.7700i	1.11172	+	1.92556i
$566$		0			0
$567$	−17.9169	−	11.1484i	−0.752441	−	0.468189i
$568$		0			0
$569$	−22.1104	−	38.2964i	−0.926917	−	1.60547i	−0.788449	−	0.615101i	$-0.789115\pi$
$569$	−22.1104	−	38.2964i	−0.926917	−	1.60547i	−0.138469	−	0.990367i	$-0.544218\pi$
$570$		0			0
$571$	−6.59195	−	3.80587i	−0.275865	−	0.159271i	0.355685	−	0.934606i	$-0.384248\pi$
$571$	−6.59195	−	3.80587i	−0.275865	−	0.159271i	−0.631550	+	0.775335i	$0.717581\pi$
$572$		0			0
$573$	−5.82200			−0.243218
$574$		0			0
$575$	−60.2703			−2.51345
$576$		0			0
$577$	0.367907	+	0.212411i	0.0153162	+	0.00884280i	0.507639	−	0.861570i	$-0.330519\pi$
$577$	0.367907	+	0.212411i	0.0153162	+	0.00884280i	−0.492322	+	0.870413i	$0.663852\pi$
$578$		0			0
$579$	4.08708	+	7.07902i	0.169853	+	0.294194i
$580$		0			0
$581$	−0.641183	+	19.4205i	−0.0266008	+	0.805699i
$582$		0			0
$583$	11.4088	+	19.7607i	0.472505	+	0.818403i
$584$		0			0
$585$	−49.0765	−	28.3343i	−2.02906	−	1.17148i
$586$		0			0
$587$			33.5213i			1.38357i	0.722103	+	0.691785i	$0.243176\pi$
$587$			33.5213i			1.38357i	−0.722103	+	0.691785i	$0.756824\pi$
$588$		0			0
$589$			0.148696i			0.00612691i
$590$		0			0
$591$	2.78247	+	1.60646i	0.114456	+	0.0660809i
$592$		0			0
$593$	−39.4301	+	22.7650i	−1.61920	+	0.934847i	−0.632075	+	0.774907i	$0.717797\pi$
$593$	−39.4301	+	22.7650i	−1.61920	+	0.934847i	−0.987127	+	0.159940i	$0.948870\pi$
$594$		0			0
$595$	6.56332	+	0.216693i	0.269070	+	0.00888354i
$596$		0			0
$597$	3.14329	+	5.44433i	0.128646	+	0.222822i
$598$		0			0
$599$	3.01805	−	5.22741i	0.123314	−	0.213586i	−0.797759	−	0.602977i	$-0.793981\pi$
$599$	3.01805	−	5.22741i	0.123314	−	0.213586i	0.921073	+	0.389391i	$0.127314\pi$
$600$		0			0
$601$		−	1.91508i		−	0.0781177i	−0.999237	−	0.0390588i	$-0.987564\pi$
$601$		−	1.91508i		−	0.0781177i	0.999237	−	0.0390588i	$-0.0124360\pi$
$602$		0			0
$603$		−	19.1520i		−	0.779928i
$604$		0			0
$605$	2.54269	−	4.40407i	0.103375	−	0.179051i
$606$		0			0
$607$	−15.5421	−	26.9198i	−0.630836	−	1.09264i	−0.987381	−	0.158362i	$-0.949379\pi$
$607$	−15.5421	−	26.9198i	−0.630836	−	1.09264i	0.356545	−	0.934278i	$-0.383955\pi$
$608$		0			0
$609$	−4.00167	−	2.48994i	−0.162156	−	0.100898i
$610$		0			0
$611$	5.63623	+	9.76224i	0.228017	+	0.394938i
$612$		0			0
$613$	−12.2562	+	21.2283i	−0.495021	+	0.857402i	−0.999984	−	0.00573943i	$-0.998173\pi$
$613$	−12.2562	+	21.2283i	−0.495021	+	0.857402i	0.504962	+	0.863141i	$0.331506\pi$
$614$		0			0
$615$	7.81266	+	4.65905i	0.315037	+	0.187871i
$616$		0			0
$617$	−7.04873			−0.283771			−0.141886	−	0.989883i	$-0.545316\pi$
$617$	−7.04873			−0.283771			−0.141886	+	0.989883i	$0.545316\pi$
$618$		0			0
$619$	−0.673139	+	1.16591i	−0.0270557	+	0.0468619i	−0.879236	−	0.476386i	$-0.841946\pi$
$619$	−0.673139	+	1.16591i	−0.0270557	+	0.0468619i	0.852181	+	0.523248i	$0.175280\pi$
$620$		0			0
$621$	8.33691	−	4.81332i	0.334549	−	0.193152i
$622$		0			0
$623$	−8.19670	−	15.3452i	−0.328394	−	0.614794i
$624$		0			0
$625$	−34.4607	−	59.6877i	−1.37843	−	2.38751i
$626$		0			0
$627$	−0.432097	−	0.249471i	−0.0172563	−	0.00996293i
$628$		0			0
$629$			1.58517i			0.0632049i
$630$		0			0
$631$	29.5849			1.17776			0.588879	−	0.808222i	$-0.299570\pi$
$631$	29.5849			1.17776			0.588879	+	0.808222i	$0.299570\pi$
$632$		0			0
$633$	0.0957388	−	0.165824i	0.00380527	−	0.00659093i
$634$		0			0
$635$	11.8306	+	20.4912i	0.469484	+	0.813170i
$636$		0			0
$637$	2.16764	−	32.7916i	0.0858852	−	1.29925i
$638$		0			0
$639$	−20.1571	+	11.6377i	−0.797402	+	0.460380i
$640$		0			0
$641$	28.6214	+	16.5246i	1.13048	+	0.652681i	0.944055	−	0.329789i	$-0.106977\pi$
$641$	28.6214	+	16.5246i	1.13048	+	0.652681i	0.186422	+	0.982470i	$0.440311\pi$
$642$		0			0
$643$			14.2295i			0.561155i	0.959831	+	0.280578i	$0.0905260\pi$
$643$			14.2295i			0.561155i	−0.959831	+	0.280578i	$0.909474\pi$
$644$		0			0
$645$			1.61152i			0.0634537i
$646$		0			0
$647$	4.63959	−	8.03601i	0.182401	−	0.315928i	−0.760297	−	0.649576i	$-0.774946\pi$
$647$	4.63959	−	8.03601i	0.182401	−	0.315928i	0.942698	+	0.333648i	$0.108280\pi$
$648$		0			0
$649$	−0.343487	+	0.198312i	−0.0134830	+	0.00778443i
$650$		0			0
$651$	−0.149663	−	0.280187i	−0.00586575	−	0.0109814i
$652$		0			0
$653$	−14.5493	+	8.40002i	−0.569356	+	0.328718i	−0.756892	−	0.653540i	$-0.773283\pi$
$653$	−14.5493	+	8.40002i	−0.569356	+	0.328718i	0.187536	+	0.982258i	$0.439950\pi$
$654$		0			0
$655$	39.6005	−	68.5901i	1.54732	−	2.68004i
$656$		0			0
$657$	13.0025			0.507277
$658$		0			0
$659$		−	1.20966i		−	0.0471216i	−0.999722	−	0.0235608i	$-0.992500\pi$
$659$		−	1.20966i		−	0.0471216i	0.999722	−	0.0235608i	$-0.00750033\pi$
$660$		0			0
$661$	−21.3689	+	37.0120i	−0.831153	+	1.43960i	0.0659721	+	0.997821i	$0.478985\pi$
$661$	−21.3689	+	37.0120i	−0.831153	+	1.43960i	−0.897125	+	0.441777i	$0.854348\pi$
$662$		0			0
$663$	−0.818804	+	0.472737i	−0.0317997	+	0.0183596i
$664$		0			0
$665$	2.45926	−	3.95236i	0.0953661	−	0.153266i
$666$		0			0
$667$	−21.8943	+	12.6407i	−0.847750	+	0.489449i
$668$		0			0
$669$	4.91591	+	2.83820i	0.190060	+	0.109731i
$670$		0			0
$671$		−	10.7683i		−	0.415704i
$672$		0			0
$673$			11.2114i			0.432169i	0.976375	+	0.216085i	$0.0693287\pi$
$673$			11.2114i			0.432169i	−0.976375	+	0.216085i	$0.930671\pi$
$674$		0			0
$675$	21.6430	+	12.4956i	0.833039	+	0.480955i
$676$		0			0
$677$	−12.2563	−	21.2286i	−0.471049	−	0.815880i	0.528403	−	0.848994i	$-0.322791\pi$
$677$	−12.2563	−	21.2286i	−0.471049	−	0.815880i	−0.999452	+	0.0331133i	$0.989458\pi$
$678$		0			0
$679$	−42.3537	−	1.39834i	−1.62539	−	0.0536634i
$680$		0			0
$681$	0.821791	+	1.42338i	0.0314911	+	0.0545442i
$682$		0			0
$683$	−22.2539	−	12.8483i	−0.851522	−	0.491627i	0.00964183	−	0.999954i	$-0.496931\pi$
$683$	−22.2539	−	12.8483i	−0.851522	−	0.491627i	−0.861164	+	0.508327i	$0.830264\pi$
$684$		0			0
$685$			72.6138i			2.77443i
$686$		0			0
$687$	−3.93326			−0.150063
$688$		0			0
$689$	15.3250	−	26.5436i	0.583835	−	1.01123i
$690$		0			0
$691$	17.7856	−	10.2685i	0.676597	−	0.390633i	−0.121975	−	0.992533i	$-0.538923\pi$
$691$	17.7856	−	10.2685i	0.676597	−	0.390633i	0.798572	+	0.601900i	$0.205589\pi$
$692$		0			0
$693$	−26.6607	−	0.880222i	−1.01275	−	0.0334369i
$694$		0			0
$695$	38.2193	+	66.1978i	1.44974	+	2.51103i
$696$		0			0
$697$	−3.31584	+	1.85243i	−0.125596	+	0.0701660i
$698$		0			0
$699$	4.07465			0.154117
$700$		0			0
$701$	4.12245			0.155703			0.0778513	−	0.996965i	$-0.475194\pi$
$701$	4.12245			0.155703			0.0778513	+	0.996965i	$0.475194\pi$
$702$		0			0
$703$	0.973121	+	0.561832i	0.0367020	+	0.0211899i
$704$		0			0
$705$	−1.70551	−	2.95403i	−0.0642332	−	0.111255i
$706$		0			0
$707$	7.22944	−	11.6187i	0.271891	−	0.436965i
$708$		0			0
$709$	−0.781214	+	0.451034i	−0.0293391	+	0.0169389i	−0.514598	−	0.857432i	$-0.672059\pi$
$709$	−0.781214	+	0.451034i	−0.0293391	+	0.0169389i	0.485259	+	0.874371i	$0.338725\pi$
$710$		0			0
$711$	32.0612	+	18.5105i	1.20239	+	0.694199i
$712$		0			0
$713$	−1.70392			−0.0638122
$714$		0			0
$715$	−68.6578			−2.56766
$716$		0			0
$717$	0.756503	−	1.31030i	0.0282521	−	0.0489341i
$718$		0			0
$719$	−4.58744	+	2.64856i	−0.171083	+	0.0987747i	−0.583096	−	0.812403i	$-0.698159\pi$
$719$	−4.58744	+	2.64856i	−0.171083	+	0.0987747i	0.412014	+	0.911178i	$0.364826\pi$
$720$		0			0
$721$	21.8661	−	11.6799i	0.814337	−	0.434981i
$722$		0			0
$723$	−6.70780	+	3.87275i	−0.249466	+	0.144029i
$724$		0			0
$725$	−56.8385	−	32.8157i	−2.11093	−	1.21874i
$726$		0			0
$727$		−	32.9678i		−	1.22271i	−0.791357	−	0.611354i	$-0.790625\pi$
$727$		−	32.9678i		−	1.22271i	0.791357	−	0.611354i	$-0.209375\pi$
$728$		0			0
$729$	20.9734			0.776791
$730$		0			0
$731$	−0.582741	−	0.336446i	−0.0215535	−	0.0124439i
$732$		0			0
$733$	−1.53214	−	2.65374i	−0.0565908	−	0.0980182i	0.836342	−	0.548208i	$-0.184690\pi$
$733$	−1.53214	−	2.65374i	−0.0565908	−	0.0980182i	−0.892933	+	0.450190i	$0.851356\pi$
$734$		0			0
$735$	−0.655924	+	9.92267i	−0.0241941	+	0.366003i
$736$		0			0
$737$	−11.6019	−	20.0951i	−0.427363	−	0.740214i
$738$		0			0
$739$	−17.0637	+	29.5552i	−0.627697	+	1.08720i	0.360315	+	0.932831i	$0.382669\pi$
$739$	−17.0637	+	29.5552i	−0.627697	+	1.08720i	−0.988013	+	0.154373i	$0.950664\pi$
$740$		0			0
$741$			0.670209i			0.0246207i
$742$		0			0
$743$	−21.8675			−0.802242			−0.401121	−	0.916025i	$-0.631379\pi$
$743$	−21.8675			−0.802242			−0.401121	+	0.916025i	$0.631379\pi$
$744$		0			0
$745$	−59.0249	−	34.0780i	−2.16250	−	1.24852i
$746$		0			0
$747$	−10.5931	−	18.3478i	−0.387582	−	0.671312i
$748$		0			0
$749$	35.8674	−	19.1587i	1.31057	−	0.700042i
$750$		0			0
$751$	12.1252	−	7.00051i	0.442457	−	0.255452i	−0.262183	−	0.965018i	$-0.584442\pi$
$751$	12.1252	−	7.00051i	0.442457	−	0.255452i	0.704639	+	0.709566i	$0.251109\pi$
$752$		0			0
$753$	5.00892	+	2.89190i	0.182535	+	0.105387i
$754$		0			0
$755$			40.7835i			1.48426i
$756$		0			0
$757$			18.5806i			0.675323i	0.941268	+	0.337662i	$0.109636\pi$
$757$			18.5806i			0.675323i	−0.941268	+	0.337662i	$0.890364\pi$
$758$		0			0
$759$	2.85871	−	4.95144i	0.103765	−	0.179726i
$760$		0			0
$761$	−7.88037	−	13.6492i	−0.285663	−	0.494783i	0.687107	−	0.726557i	$-0.258881\pi$
$761$	−7.88037	−	13.6492i	−0.285663	−	0.494783i	−0.972770	+	0.231773i	$0.925547\pi$
$762$		0			0
$763$	10.9596	−	17.6135i	0.396764	−	0.637652i
$764$		0			0
$765$	−6.20079	+	3.58003i	−0.224190	+	0.129436i
$766$		0			0
$767$	0.461391	+	0.266384i	0.0166599	+	0.00961857i
$768$		0			0
$769$	6.52930			0.235453			0.117726	−	0.993046i	$-0.462439\pi$
$769$	6.52930			0.235453			0.117726	+	0.993046i	$0.462439\pi$
$770$		0			0
$771$	−9.53147			−0.343268
$772$		0			0
$773$	19.4930	+	11.2543i	0.701113	+	0.404788i	0.807762	−	0.589509i	$-0.200679\pi$
$773$	19.4930	+	11.2543i	0.701113	+	0.404788i	−0.106649	+	0.994297i	$0.534012\pi$
$774$		0			0
$775$	−2.21172	−	3.83082i	−0.0794474	−	0.137607i
$776$		0			0
$777$	−2.39913	−	0.0792092i	−0.0860685	−	0.00284161i
$778$		0			0
$779$	−0.0380406	+	2.69212i	−0.00136294	+	0.0964553i
$780$		0			0
$781$	−14.0998	+	24.4217i	−0.504532	+	0.873875i
$782$		0			0
$783$	10.4829			0.374629
$784$		0			0
$785$		−	53.6629i		−	1.91531i
$786$		0			0
$787$	17.4455	−	30.2165i	0.621865	−	1.07710i	−0.367273	−	0.930113i	$-0.619709\pi$
$787$	17.4455	−	30.2165i	0.621865	−	1.07710i	0.989138	−	0.146988i	$-0.0469580\pi$
$788$		0			0
$789$	4.31502	+	7.47383i	0.153619	+	0.266075i
$790$		0			0
$791$	1.10270	−	33.3993i	0.0392076	−	1.18754i
$792$		0			0
$793$	−12.5267	+	7.23227i	−0.444835	+	0.256825i
$794$		0			0
$795$	−4.63730	+	8.03204i	−0.164468	+	0.284867i
$796$		0			0
$797$	30.0410			1.06411			0.532053	−	0.846711i	$-0.321421\pi$
$797$	30.0410			1.06411			0.532053	+	0.846711i	$0.321421\pi$
$798$		0			0
$799$	1.42427			0.0503871
$800$		0			0
$801$	16.4273	+	9.48431i	0.580430	+	0.335112i
$802$		0			0
$803$	13.6429	−	7.87671i	0.481446	−	0.277963i
$804$		0			0
$805$	45.2904	+	28.1809i	1.59628	+	0.993246i
$806$		0			0
$807$	6.12537	−	3.53649i	0.215623	−	0.124490i
$808$		0			0
$809$	−32.7648	−	18.9168i	−1.15195	−	0.665079i	−0.202589	−	0.979264i	$-0.564935\pi$
$809$	−32.7648	−	18.9168i	−1.15195	−	0.665079i	−0.949362	+	0.314185i	$0.898269\pi$
$810$		0			0
$811$	11.5682			0.406215			0.203107	−	0.979156i	$-0.434896\pi$
$811$	11.5682			0.406215			0.203107	+	0.979156i	$0.434896\pi$
$812$		0			0
$813$		−	4.36595i		−	0.153120i
$814$		0			0
$815$	−23.8818	+	41.3645i	−0.836544	+	1.44894i
$816$		0			0
$817$	−0.413082	+	0.238493i	−0.0144519	+	0.00834382i
$818$		0			0
$819$	16.8821	+	31.6054i	0.589908	+	1.10438i
$820$		0			0
$821$	15.3163	+	26.5287i	0.534544	+	0.925857i	0.999185	+	0.0403581i	$0.0128499\pi$
$821$	15.3163	+	26.5287i	0.534544	+	0.925857i	−0.464641	+	0.885499i	$0.653817\pi$
$822$		0			0
$823$	16.8684	+	9.73895i	0.587994	+	0.339479i	0.764304	−	0.644856i	$-0.223083\pi$
$823$	16.8684	+	9.73895i	0.587994	+	0.339479i	−0.176310	+	0.984335i	$0.556416\pi$
$824$		0			0
$825$	14.8427			0.516756
$826$		0			0
$827$		−	30.2885i		−	1.05324i	−0.850102	−	0.526618i	$-0.823460\pi$
$827$		−	30.2885i		−	1.05324i	0.850102	−	0.526618i	$-0.176540\pi$
$828$		0			0
$829$	−4.92108	+	8.52356i	−0.170916	+	0.296035i	−0.938740	−	0.344625i	$-0.888006\pi$
$829$	−4.92108	+	8.52356i	−0.170916	+	0.296035i	0.767824	+	0.640661i	$0.221339\pi$
$830$		0			0
$831$	8.79881	−	5.08000i	0.305227	−	0.176223i
$832$		0			0
$833$	−3.45118	−	2.30879i	−0.119576	−	0.0799949i
$834$		0			0
$835$	31.9208	−	18.4295i	1.10466	−	0.637778i
$836$		0			0
$837$	0.611874	+	0.353266i	0.0211495	+	0.0122107i
$838$		0			0
$839$		−	7.67304i		−	0.264903i	−0.991190	−	0.132451i	$-0.957715\pi$
$839$		−	7.67304i		−	0.264903i	0.991190	−	0.132451i	$-0.0422848\pi$
$840$		0			0
$841$	1.46988			0.0506855
$842$		0			0
$843$	−1.93894	+	3.35835i	−0.0667807	+	0.115668i
$844$		0			0
$845$	18.9144	+	32.7607i	0.650676	+	1.12700i
$846$		0			0
$847$	−2.83623	+	1.51498i	−0.0974541	+	0.0520554i
$848$		0			0
$849$	6.66543	−	3.84829i	0.228757	−	0.132073i
$850$		0			0
$851$	−6.43808	+	11.1511i	−0.220694	+	0.382254i
$852$		0			0
$853$	23.4075			0.801459			0.400729	−	0.916196i	$-0.368757\pi$
$853$	23.4075			0.801459			0.400729	+	0.916196i	$0.368757\pi$
$854$		0			0
$855$			5.07548i			0.173578i
$856$		0			0
$857$	−1.29565	+	2.24414i	−0.0442587	+	0.0766583i	−0.887306	−	0.461181i	$-0.847426\pi$
$857$	−1.29565	+	2.24414i	−0.0442587	+	0.0766583i	0.843047	+	0.537839i	$0.180759\pi$
$858$		0			0
$859$	−13.1249	−	22.7329i	−0.447814	−	0.775637i	0.550429	−	0.834882i	$-0.314464\pi$
$859$	−13.1249	−	22.7329i	−0.447814	−	0.775637i	−0.998243	+	0.0592446i	$0.981131\pi$
$860$		0			0
$861$	−2.63795	−	5.11104i	−0.0899010	−	0.174184i
$862$		0			0
$863$	−5.23479	−	9.06692i	−0.178194	−	0.308642i	0.763068	−	0.646318i	$-0.223692\pi$
$863$	−5.23479	−	9.06692i	−0.178194	−	0.308642i	−0.941262	+	0.337677i	$0.890359\pi$
$864$		0			0
$865$	23.8054	−	41.2322i	0.809409	−	1.40194i
$866$		0			0
$867$		−	5.65220i		−	0.191959i
$868$		0			0
$869$	44.8534			1.52155
$870$		0			0
$871$	−15.5844	+	26.9929i	−0.528056	+	0.914620i
$872$		0			0
$873$	40.0143	−	23.1023i	1.35428	−	0.781894i
$874$		0			0
$875$	−2.74294	+	83.0797i	−0.0927283	+	2.80861i
$876$		0			0
$877$	4.03604	+	6.99063i	0.136287	+	0.236057i	0.926089	−	0.377306i	$-0.123150\pi$
$877$	4.03604	+	6.99063i	0.136287	+	0.236057i	−0.789801	+	0.613363i	$0.789816\pi$
$878$		0			0
$879$	2.68918	−	4.65780i	0.0907038	−	0.157104i
$880$		0			0
$881$	−31.3701			−1.05688			−0.528442	−	0.848969i	$-0.677224\pi$
$881$	−31.3701			−1.05688			−0.528442	+	0.848969i	$0.677224\pi$
$882$		0			0
$883$		−	9.24853i		−	0.311238i	−0.987817	−	0.155619i	$-0.950263\pi$
$883$		−	9.24853i		−	0.311238i	0.987817	−	0.155619i	$-0.0497372\pi$
$884$		0			0
$885$	−0.139616	−	0.0806072i	−0.00469313	−	0.00270958i
$886$		0			0
$887$	44.6503	−	25.7789i	1.49921	−	0.865569i	0.499211	−	0.866481i	$-0.333623\pi$
$887$	44.6503	−	25.7789i	1.49921	−	0.865569i	1.00000		0.000911288i	$0.000290072\pi$
$888$		0			0
$889$	0.493680	−	14.9529i	0.0165575	−	0.501503i
$890$		0			0
$891$	24.1414	−	13.9380i	0.808767	−	0.466942i
$892$		0			0
$893$	0.504804	−	0.874347i	0.0168926	−	0.0292589i
$894$		0			0
$895$			101.156i			3.38127i
$896$		0			0
$897$	−7.67997			−0.256427
$898$		0			0
$899$	−1.60690	−	0.927741i	−0.0535930	−	0.0309419i
$900$		0			0
$901$	−1.93630	−	3.35378i	−0.0645077	−	0.111731i
$902$		0			0
$903$	0.538325	−	0.865160i	0.0179143	−	0.0287907i
$904$		0			0
$905$	−47.7744	+	27.5825i	−1.58807	+	0.916875i
$906$		0			0
$907$	0.133323	−	0.230922i	0.00442692	−	0.00766764i	−0.863803	−	0.503829i	$-0.831924\pi$
$907$	0.133323	−	0.230922i	0.00442692	−	0.00766764i	0.868230	+	0.496161i	$0.165258\pi$
$908$		0			0
$909$			14.9203i			0.494874i
$910$		0			0
$911$	50.9639			1.68851			0.844255	−	0.535942i	$-0.180044\pi$
$911$	50.9639			1.68851			0.844255	+	0.535942i	$0.180044\pi$
$912$		0			0
$913$	−22.2296	−	12.8343i	−0.735693	−	0.424753i
$914$		0			0
$915$	3.79054	−	2.18847i	0.125311	−	0.0723485i
$916$		0			0
$917$	−44.1722	+	23.5947i	−1.45870	+	0.779166i
$918$		0			0
$919$	−47.0626	+	27.1716i	−1.55245	+	0.896309i	−0.554511	+	0.832176i	$0.687095\pi$
$919$	−47.0626	+	27.1716i	−1.55245	+	0.896309i	−0.997941	+	0.0641328i	$0.979572\pi$
$920$		0			0
$921$	−5.22498	−	3.01664i	−0.172169	−	0.0994017i
$922$		0			0
$923$	37.8794			1.24682
$924$		0			0
$925$	−33.4270			−1.09907
$926$		0			0
$927$	−13.5146	+	23.4080i	−0.443879	+	0.768820i
$928$		0			0
$929$	2.77731	−	1.60348i	0.0911207	−	0.0526085i	−0.453747	−	0.891130i	$-0.649913\pi$
$929$	2.77731	−	1.60348i	0.0911207	−	0.0526085i	0.544868	+	0.838522i	$0.316580\pi$
$930$		0			0
$931$	−2.64055	+	1.30035i	−0.0865405	+	0.0426171i
$932$		0			0
$933$	5.32562	+	9.22425i	0.174353	+	0.301988i
$934$		0			0
$935$	−4.33744	+	7.51267i	−0.141850	+	0.245691i
$936$		0			0
$937$		−	9.33380i		−	0.304922i	−0.988309	−	0.152461i	$-0.951280\pi$
$937$		−	9.33380i		−	0.304922i	0.988309	−	0.152461i	$-0.0487198\pi$
$938$		0			0
$939$	−2.15222			−0.0702352
$940$		0			0
$941$	25.8479	−	44.7698i	0.842616	−	1.45945i	−0.0450599	−	0.998984i	$-0.514348\pi$
$941$	25.8479	−	44.7698i	0.842616	−	1.45945i	0.887676	−	0.460469i	$-0.152319\pi$
$942$		0			0
$943$	−30.8492	−	0.435910i	−1.00459	−	0.0141952i
$944$		0			0
$945$	−10.4211	−	19.5096i	−0.338998	−	0.634646i
$946$		0			0
$947$	−0.340654	−	0.590030i	−0.0110698	−	0.0191734i	0.860437	−	0.509556i	$-0.170190\pi$
$947$	−0.340654	−	0.590030i	−0.0110698	−	0.0191734i	−0.871507	+	0.490383i	$0.836857\pi$
$948$		0			0
$949$	−18.3259	−	10.5804i	−0.594883	−	0.343456i
$950$		0			0
$951$	−6.81099			−0.220862
$952$		0			0
$953$	22.1209			0.716566			0.358283	−	0.933613i	$-0.383362\pi$
$953$	22.1209			0.716566			0.358283	+	0.933613i	$0.383362\pi$
$954$		0			0
$955$	62.1408	+	35.8770i	2.01083	+	1.16095i
$956$		0			0
$957$	5.39187	−	3.11300i	0.174294	−	0.100629i
$958$		0			0
$959$	24.2564	−	38.9833i	0.783281	−	1.25884i
$960$		0			0
$961$	15.4375	+	26.7385i	0.497983	+	0.862532i
$962$		0			0
$963$	−22.1683	+	38.3966i	−0.714362	+	1.23731i
$964$		0			0
$965$		−	100.743i		−	3.24304i
$966$		0			0
$967$		−	8.55641i		−	0.275156i	−0.990491	−	0.137578i	$-0.956068\pi$
$967$		−	8.55641i		−	0.275156i	0.990491	−	0.137578i	$-0.0439317\pi$
$968$		0			0
$969$	0.0733355	+	0.0423403i	0.00235588	+	0.00136017i
$970$		0			0
$971$	32.5630	−	18.8003i	1.04500	−	0.603329i	0.123752	−	0.992313i	$-0.460507\pi$
$971$	32.5630	−	18.8003i	1.04500	−	0.603329i	0.921244	+	0.388984i	$0.127174\pi$
$972$		0			0
$973$	1.59486	−	48.3059i	0.0511287	−	1.54862i
$974$		0			0
$975$	−9.96877	−	17.2664i	−0.319256	−	0.552968i
$976$		0			0
$977$	−23.2023	−	13.3959i	−0.742308	−	0.428572i	0.0805997	−	0.996747i	$-0.474316\pi$
$977$	−23.2023	−	13.3959i	−0.742308	−	0.428572i	−0.822908	+	0.568175i	$0.807650\pi$
$978$		0			0
$979$	22.9817			0.734499
$980$		0			0
$981$			22.6187i			0.722159i
$982$		0			0
$983$	6.65553	−	11.5277i	0.212278	−	0.367677i	−0.740149	−	0.672443i	$-0.765245\pi$
$983$	6.65553	−	11.5277i	0.212278	−	0.367677i	0.952427	+	0.304766i	$0.0985783\pi$
$984$		0			0
$985$	−19.7990	−	34.2929i	−0.630849	−	1.09266i
$986$		0			0
$987$	−0.0711692	+	2.15561i	−0.00226534	+	0.0686140i
$988$		0			0
$989$	−2.73291	−	4.73354i	−0.0869015	−	0.150518i
$990$		0			0
$991$	−38.1601	−	22.0317i	−1.21219	−	0.699861i	−0.248958	−	0.968514i	$-0.580088\pi$
$991$	−38.1601	−	22.0317i	−1.21219	−	0.699861i	−0.963237	+	0.268653i	$0.913421\pi$
$992$		0			0
$993$	6.56427			0.208311
$994$		0			0
$995$		−	77.4796i		−	2.45627i
$996$		0			0
$997$	50.4632	+	29.1350i	1.59819	+	0.922713i	0.991837	+	0.127515i	$0.0407000\pi$
$997$	50.4632	+	29.1350i	1.59819	+	0.922713i	0.606349	+	0.795198i	$0.292633\pi$
$998$		0			0
$999$	4.62381	−	2.66956i	0.146291	−	0.0844610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.81.15	yes	56
7.2	even	3	inner	1148.2.r.a.737.14	yes	56
41.40	even	2	inner	1148.2.r.a.81.14	✓	56
287.163	even	6	inner	1148.2.r.a.737.15	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.14	✓	56	41.40	even	2	inner
1148.2.r.a.81.15	yes	56	1.1	even	1	trivial
1148.2.r.a.737.14	yes	56	7.2	even	3	inner
1148.2.r.a.737.15	yes	56	287.163	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.294024 + 0.169755i) q^{3} +(-2.09216 - 3.62373i) q^{5} +(-0.0873039 + 2.64431i) q^{7} +(-1.44237 - 2.49825i) q^{9} +O(q^{10})\)	\(q+(0.294024 + 0.169755i) q^{3} +(-2.09216 - 3.62373i) q^{5} +(-0.0873039 + 2.64431i) q^{7} +(-1.44237 - 2.49825i) q^{9} +(-3.02680 - 1.74752i) q^{11} +4.69474i q^{13} -1.42062i q^{15} +(0.513708 + 0.296589i) q^{17} +(0.364147 - 0.210240i) q^{19} +(-0.474554 + 0.762670i) q^{21} +(2.40916 + 4.17279i) q^{23} +(-6.25428 + 10.8327i) q^{25} -1.99792i q^{27} +5.24692i q^{29} +(-0.176817 + 0.306255i) q^{31} +(-0.593301 - 1.02763i) q^{33} +(9.76492 - 5.21596i) q^{35} +(1.33617 + 2.31431i) q^{37} +(-0.796955 + 1.38037i) q^{39} +(-3.27959 + 5.49948i) q^{41} -1.13438 q^{43} +(-6.03533 + 10.4535i) q^{45} +(2.07940 - 1.20054i) q^{47} +(-6.98476 - 0.461717i) q^{49} +(0.100695 + 0.174409i) q^{51} +(-5.65391 - 3.26429i) q^{53} +14.6244i q^{55} +0.142757 q^{57} +(0.0567409 - 0.0982782i) q^{59} +(1.54050 + 2.66823i) q^{61} +(6.73208 - 3.59596i) q^{63} +(17.0125 - 9.82216i) q^{65} +(5.74960 + 3.31954i) q^{67} +1.63587i q^{69} -8.06848i q^{71} +(-2.25368 + 3.90348i) q^{73} +(-3.67782 + 2.12339i) q^{75} +(4.88524 - 7.85123i) q^{77} +(-11.1141 + 6.41672i) q^{79} +(-3.98794 + 6.90732i) q^{81} +7.34427 q^{83} -2.48205i q^{85} +(-0.890689 + 1.54272i) q^{87} +(-5.69457 + 3.28776i) q^{89} +(-12.4144 - 0.409869i) q^{91} +(-0.103977 + 0.0600309i) q^{93} +(-1.52371 - 0.879714i) q^{95} +16.0169i q^{97} +10.0823i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^5 + 32 * q^9	\( 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) \) 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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