LMFDB - Embedded newform 740.2.i.a.121.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(121,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 204x^{10} + 727x^{8} + 1008x^{6} + 426x^{4} + 64x^{2} + 3 $ x^14 + 24x^12 + 204x^10 + 727x^8 + 1008x^6 + 426x^4 + 64x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$2.12787i$ of defining polynomial
Character	$\chi$	$=$	740.121
Dual form			740.2.i.a.581.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.795627 - 1.37807i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.53626 - 2.66088i) q^{7} +(0.233956 - 0.405224i) q^{9} +3.41859 q^{11} +(0.945375 + 1.63744i) q^{13} +(-0.795627 + 1.37807i) q^{15} +(1.96654 - 3.40615i) q^{17} +(-0.897417 - 1.55437i) q^{19} +(-2.44458 + 4.23414i) q^{21} -9.16334 q^{23} +(-0.500000 + 0.866025i) q^{25} -5.51833 q^{27} -2.24244 q^{29} -3.62938 q^{31} +(-2.71992 - 4.71105i) q^{33} +(-1.53626 + 2.66088i) q^{35} +(-6.03924 + 0.726378i) q^{37} +(1.50433 - 2.60558i) q^{39} +(3.30993 + 5.73297i) q^{41} +6.37644 q^{43} -0.467912 q^{45} -3.32122 q^{47} +(-1.22020 + 2.11345i) q^{49} -6.25853 q^{51} +(1.41367 - 2.44855i) q^{53} +(-1.70930 - 2.96059i) q^{55} +(-1.42802 + 2.47340i) q^{57} +(5.10819 - 8.84764i) q^{59} +(3.65748 + 6.33494i) q^{61} -1.43767 q^{63} +(0.945375 - 1.63744i) q^{65} +(-6.34541 - 10.9906i) q^{67} +(7.29060 + 12.6277i) q^{69} +(-2.10924 - 3.65331i) q^{71} +4.74475 q^{73} +1.59125 q^{75} +(-5.25185 - 9.09648i) q^{77} +(-0.346287 - 0.599786i) q^{79} +(3.68866 + 6.38895i) q^{81} +(-5.27689 + 9.13984i) q^{83} -3.93308 q^{85} +(1.78414 + 3.09023i) q^{87} +(-4.29386 + 7.43719i) q^{89} +(2.90469 - 5.03107i) q^{91} +(2.88763 + 5.00152i) q^{93} +(-0.897417 + 1.55437i) q^{95} -3.39878 q^{97} +(0.799801 - 1.38530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) $ 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.795627	−	1.37807i	−0.459355	−	0.795627i	0.539572	−	0.841940i	$-0.318586\pi$
$3$	−0.795627	−	1.37807i	−0.459355	−	0.795627i	−0.998927	+	0.0463129i	$0.985253\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.53626	−	2.66088i	−0.580652	−	1.00572i	−0.995402	−	0.0957839i	$-0.969464\pi$
$7$	−1.53626	−	2.66088i	−0.580652	−	1.00572i	0.414750	−	0.909935i	$-0.363869\pi$
$8$		0			0
$9$	0.233956	−	0.405224i	0.0779853	−	0.135075i
$10$		0			0
$11$	3.41859			1.03074			0.515372	−	0.856966i	$-0.327654\pi$
$11$	3.41859			1.03074			0.515372	+	0.856966i	$0.327654\pi$
$12$		0			0
$13$	0.945375	+	1.63744i	0.262200	+	0.454144i	0.966826	−	0.255435i	$-0.0822187\pi$
$13$	0.945375	+	1.63744i	0.262200	+	0.454144i	−0.704626	+	0.709579i	$0.748885\pi$
$14$		0			0
$15$	−0.795627	+	1.37807i	−0.205430	+	0.355815i
$16$		0			0
$17$	1.96654	−	3.40615i	0.476956	−	0.826112i	−0.522695	−	0.852520i	$-0.675073\pi$
$17$	1.96654	−	3.40615i	0.476956	−	0.826112i	0.999651	+	0.0264077i	$0.00840681\pi$
$18$		0			0
$19$	−0.897417	−	1.55437i	−0.205882	−	0.356597i	0.744532	−	0.667587i	$-0.232673\pi$
$19$	−0.897417	−	1.55437i	−0.205882	−	0.356597i	−0.950413	+	0.310990i	$0.899339\pi$
$20$		0			0
$21$	−2.44458	+	4.23414i	−0.533452	+	0.923965i
$22$		0			0
$23$	−9.16334			−1.91069			−0.955345	−	0.295494i	$-0.904516\pi$
$23$	−9.16334			−1.91069			−0.955345	+	0.295494i	$0.904516\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−5.51833			−1.06200
$28$		0			0
$29$	−2.24244			−0.416410			−0.208205	−	0.978085i	$-0.566762\pi$
$29$	−2.24244			−0.416410			−0.208205	+	0.978085i	$0.566762\pi$
$30$		0			0
$31$	−3.62938			−0.651855			−0.325928	−	0.945395i	$-0.605677\pi$
$31$	−3.62938			−0.651855			−0.325928	+	0.945395i	$0.605677\pi$
$32$		0			0
$33$	−2.71992	−	4.71105i	−0.473478	−	0.820088i
$34$		0			0
$35$	−1.53626	+	2.66088i	−0.259676	+	0.449771i
$36$		0			0
$37$	−6.03924	+	0.726378i	−0.992844	+	0.119416i
$37$	−6.03924	+	0.726378i	−0.992844	+	0.119416i
$38$		0			0
$39$	1.50433	−	2.60558i	0.240886	−	0.417227i
$40$		0			0
$41$	3.30993	+	5.73297i	0.516924	+	0.895339i	0.999807	+	0.0196541i	$0.00625650\pi$
$41$	3.30993	+	5.73297i	0.516924	+	0.895339i	−0.482882	+	0.875685i	$0.660410\pi$
$42$		0			0
$43$	6.37644			0.972398			0.486199	−	0.873848i	$-0.338383\pi$
$43$	6.37644			0.972398			0.486199	+	0.873848i	$0.338383\pi$
$44$		0			0
$45$	−0.467912			−0.0697522
$46$		0			0
$47$	−3.32122			−0.484449			−0.242225	−	0.970220i	$-0.577877\pi$
$47$	−3.32122			−0.484449			−0.242225	+	0.970220i	$0.577877\pi$
$48$		0			0
$49$	−1.22020	+	2.11345i	−0.174314	+	0.301921i
$50$		0			0
$51$	−6.25853			−0.876369
$52$		0			0
$53$	1.41367	−	2.44855i	0.194183	−	0.336334i	−0.752450	−	0.658650i	$-0.771128\pi$
$53$	1.41367	−	2.44855i	0.194183	−	0.336334i	0.946632	+	0.322316i	$0.104461\pi$
$54$		0			0
$55$	−1.70930	−	2.96059i	−0.230482	−	0.399206i
$56$		0			0
$57$	−1.42802	+	2.47340i	−0.189146	+	0.327610i
$58$		0			0
$59$	5.10819	−	8.84764i	0.665029	−	1.15186i	−0.314248	−	0.949341i	$-0.601752\pi$
$59$	5.10819	−	8.84764i	0.665029	−	1.15186i	0.979277	−	0.202523i	$-0.0649142\pi$
$60$		0			0
$61$	3.65748	+	6.33494i	0.468292	+	0.811106i	0.999343	−	0.0362336i	$-0.0115360\pi$
$61$	3.65748	+	6.33494i	0.468292	+	0.811106i	−0.531051	+	0.847340i	$0.678203\pi$
$62$		0			0
$63$	−1.43767			−0.181129
$64$		0			0
$65$	0.945375	−	1.63744i	0.117259	−	0.203099i
$66$		0			0
$67$	−6.34541	−	10.9906i	−0.775215	−	1.34271i	−0.934673	−	0.355508i	$-0.884308\pi$
$67$	−6.34541	−	10.9906i	−0.775215	−	1.34271i	0.159458	−	0.987205i	$-0.449025\pi$
$68$		0			0
$69$	7.29060	+	12.6277i	0.877685	+	1.52020i
$70$		0			0
$71$	−2.10924	−	3.65331i	−0.250321	−	0.433569i	0.713293	−	0.700866i	$-0.247203\pi$
$71$	−2.10924	−	3.65331i	−0.250321	−	0.433569i	−0.963614	+	0.267297i	$0.913869\pi$
$72$		0			0
$73$	4.74475			0.555331			0.277665	−	0.960678i	$-0.410439\pi$
$73$	4.74475			0.555331			0.277665	+	0.960678i	$0.410439\pi$
$74$		0			0
$75$	1.59125			0.183742
$76$		0			0
$77$	−5.25185	−	9.09648i	−0.598504	−	1.03664i
$78$		0			0
$79$	−0.346287	−	0.599786i	−0.0389603	−	0.0674813i	0.845888	−	0.533361i	$-0.179071\pi$
$79$	−0.346287	−	0.599786i	−0.0389603	−	0.0674813i	−0.884848	+	0.465880i	$0.845738\pi$
$80$		0			0
$81$	3.68866	+	6.38895i	0.409851	+	0.709883i
$82$		0			0
$83$	−5.27689	+	9.13984i	−0.579214	+	1.00323i	0.416356	+	0.909202i	$0.363307\pi$
$83$	−5.27689	+	9.13984i	−0.579214	+	1.00323i	−0.995570	+	0.0940261i	$0.970026\pi$
$84$		0			0
$85$	−3.93308			−0.426602
$86$		0			0
$87$	1.78414	+	3.09023i	0.191280	+	0.331307i
$88$		0			0
$89$	−4.29386	+	7.43719i	−0.455149	+	0.788341i	−0.998697	−	0.0510374i	$-0.983747\pi$
$89$	−4.29386	+	7.43719i	−0.455149	+	0.788341i	0.543548	+	0.839378i	$0.317081\pi$
$90$		0			0
$91$	2.90469	−	5.03107i	0.304494	−	0.527399i
$92$		0			0
$93$	2.88763	+	5.00152i	0.299433	+	0.518634i
$94$		0			0
$95$	−0.897417	+	1.55437i	−0.0920730	+	0.159475i
$96$		0			0
$97$	−3.39878			−0.345094			−0.172547	−	0.985001i	$-0.555200\pi$
$97$	−3.39878			−0.345094			−0.172547	+	0.985001i	$0.555200\pi$
$98$		0			0
$99$	0.799801	−	1.38530i	0.0803830	−	0.139227i
$100$		0			0
$101$	−4.86232			−0.483819			−0.241909	−	0.970299i	$-0.577774\pi$
$101$	−4.86232			−0.483819			−0.241909	+	0.970299i	$0.577774\pi$
$102$		0			0
$103$	15.3756			1.51500			0.757501	−	0.652834i	$-0.226420\pi$
$103$	15.3756			1.51500			0.757501	+	0.652834i	$0.226420\pi$
$104$		0			0
$105$	4.88916			0.477134
$106$		0			0
$107$	−2.68098	−	4.64360i	−0.259181	−	0.448914i	0.706842	−	0.707371i	$-0.250119\pi$
$107$	−2.68098	−	4.64360i	−0.259181	−	0.448914i	−0.966023	+	0.258458i	$0.916786\pi$
$108$		0			0
$109$	6.83392	−	11.8367i	0.654571	−	1.13375i	−0.327431	−	0.944875i	$-0.606183\pi$
$109$	6.83392	−	11.8367i	0.654571	−	1.13375i	0.982001	−	0.188874i	$-0.0604838\pi$
$110$		0			0
$111$	5.80597	+	7.74454i	0.551079	+	0.735079i
$112$		0			0
$113$	−0.661446	+	1.14566i	−0.0622236	+	0.107774i	−0.895459	−	0.445144i	$-0.853153\pi$
$113$	−0.661446	+	1.14566i	−0.0622236	+	0.107774i	0.833235	+	0.552918i	$0.186486\pi$
$114$		0			0
$115$	4.58167	+	7.93569i	0.427243	+	0.740007i
$116$		0			0
$117$	0.884705			0.0817910
$118$		0			0
$119$	−12.0845			−1.10778
$120$		0			0
$121$	0.686783			0.0624348
$122$		0			0
$123$	5.26694	−	9.12261i	0.474904	−	0.822558i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.22159	−	14.2402i	0.729548	−	1.26361i	−0.227527	−	0.973772i	$-0.573064\pi$
$127$	8.22159	−	14.2402i	0.729548	−	1.26361i	0.957075	−	0.289842i	$-0.0936028\pi$
$128$		0			0
$129$	−5.07327	−	8.78715i	−0.446676	−	0.773666i
$130$		0			0
$131$	0.854721	−	1.48042i	0.0746773	−	0.129345i	−0.826269	−	0.563276i	$-0.809541\pi$
$131$	0.854721	−	1.48042i	0.0746773	−	0.129345i	0.900946	+	0.433931i	$0.142874\pi$
$132$		0			0
$133$	−2.75733	+	4.77584i	−0.239091	+	0.414118i
$134$		0			0
$135$	2.75916	+	4.77901i	0.237471	+	0.411312i
$136$		0			0
$137$	8.81030			0.752715			0.376357	−	0.926475i	$-0.377177\pi$
$137$	8.81030			0.752715			0.376357	+	0.926475i	$0.377177\pi$
$138$		0			0
$139$	6.21342	−	10.7620i	0.527015	−	0.912817i	−0.472489	−	0.881337i	$-0.656644\pi$
$139$	6.21342	−	10.7620i	0.527015	−	0.912817i	0.999504	−	0.0314808i	$-0.0100223\pi$
$140$		0			0
$141$	2.64245	+	4.57686i	0.222534	+	0.385441i
$142$		0			0
$143$	3.23185	+	5.59774i	0.270261	+	0.468106i
$144$		0			0
$145$	1.12122	+	1.94201i	0.0931122	+	0.161275i
$146$		0			0
$147$	3.88330			0.320289
$148$		0			0
$149$	21.1302			1.73105			0.865527	−	0.500862i	$-0.166984\pi$
$149$	21.1302			1.73105			0.865527	+	0.500862i	$0.166984\pi$
$150$		0			0
$151$	6.83612	+	11.8405i	0.556315	+	0.963567i	0.997800	+	0.0662977i	$0.0211187\pi$
$151$	6.83612	+	11.8405i	0.556315	+	0.963567i	−0.441484	+	0.897269i	$0.645548\pi$
$152$		0			0
$153$	−0.920168	−	1.59378i	−0.0743911	−	0.128849i
$154$		0			0
$155$	1.81469	+	3.14313i	0.145759	+	0.252463i
$156$		0			0
$157$	5.87158	−	10.1699i	0.468603	−	0.811645i	−0.530753	−	0.847527i	$-0.678091\pi$
$157$	5.87158	−	10.1699i	0.468603	−	0.811645i	0.999356	+	0.0358821i	$0.0114241\pi$
$158$		0			0
$159$	−4.49902			−0.356795
$160$		0			0
$161$	14.0773	+	24.3826i	1.10945	+	1.92162i
$162$		0			0
$163$	11.2095	−	19.4154i	0.877993	−	1.52073i	0.0244524	−	0.999701i	$-0.492216\pi$
$163$	11.2095	−	19.4154i	0.877993	−	1.52073i	0.853540	−	0.521027i	$-0.174451\pi$
$164$		0			0
$165$	−2.71992	+	4.71105i	−0.211746	+	0.366755i
$166$		0			0
$167$	8.48577	+	14.6978i	0.656648	+	1.13735i	0.981478	+	0.191576i	$0.0613598\pi$
$167$	8.48577	+	14.6978i	0.656648	+	1.13735i	−0.324829	+	0.945773i	$0.605307\pi$
$168$		0			0
$169$	4.71253	−	8.16234i	0.362502	−	0.627873i
$170$		0			0
$171$	−0.839824			−0.0642230
$172$		0			0
$173$	−2.77348	+	4.80381i	−0.210864	+	0.365227i	−0.951985	−	0.306144i	$-0.900961\pi$
$173$	−2.77348	+	4.80381i	−0.210864	+	0.365227i	0.741121	+	0.671371i	$0.234294\pi$
$174$		0			0
$175$	3.07252			0.232261
$176$		0			0
$177$	−16.2568			−1.22194
$178$		0			0
$179$	−21.3631			−1.59675			−0.798375	−	0.602161i	$-0.794307\pi$
$179$	−21.3631			−1.59675			−0.798375	+	0.602161i	$0.794307\pi$
$180$		0			0
$181$	1.13711	+	1.96954i	0.0845209	+	0.146395i	0.905187	−	0.425014i	$-0.139731\pi$
$181$	1.13711	+	1.96954i	0.0845209	+	0.146395i	−0.820666	+	0.571408i	$0.806397\pi$
$182$		0			0
$183$	5.81998	−	10.0805i	0.430225	−	0.745172i
$184$		0			0
$185$	3.64868	+	4.86694i	0.268256	+	0.357825i
$186$		0			0
$187$	6.72280	−	11.6442i	0.491620	−	0.851510i
$188$		0			0
$189$	8.47760	+	14.6836i	0.616654	+	1.06808i
$190$		0			0
$191$	−16.2866			−1.17846			−0.589230	−	0.807965i	$-0.700569\pi$
$191$	−16.2866			−1.17846			−0.589230	+	0.807965i	$0.700569\pi$
$192$		0			0
$193$	−8.30630			−0.597900			−0.298950	−	0.954269i	$-0.596636\pi$
$193$	−8.30630			−0.597900			−0.298950	+	0.954269i	$0.596636\pi$
$194$		0			0
$195$	−3.00866			−0.215455
$196$		0			0
$197$	10.5862	−	18.3359i	0.754238	−	1.30638i	−0.191515	−	0.981490i	$-0.561340\pi$
$197$	10.5862	−	18.3359i	0.754238	−	1.30638i	0.945752	−	0.324888i	$-0.105327\pi$
$198$		0			0
$199$	−0.218524			−0.0154908			−0.00774539	−	0.999970i	$-0.502465\pi$
$199$	−0.218524			−0.0154908			−0.00774539	+	0.999970i	$0.502465\pi$
$200$		0			0
$201$	−10.0972	+	17.4888i	−0.712199	+	1.23356i
$202$		0			0
$203$	3.44497	+	5.96687i	0.241790	+	0.418792i
$204$		0			0
$205$	3.30993	−	5.73297i	0.231176	−	0.400408i
$206$		0			0
$207$	−2.14382	+	3.71320i	−0.149006	+	0.258086i
$208$		0			0
$209$	−3.06790	−	5.31376i	−0.212211	−	0.367561i
$210$		0			0
$211$	10.7208			0.738047			0.369024	−	0.929420i	$-0.379692\pi$
$211$	10.7208			0.738047			0.369024	+	0.929420i	$0.379692\pi$
$212$		0			0
$213$	−3.35634	+	5.81335i	−0.229973	+	0.398324i
$214$		0			0
$215$	−3.18822	−	5.52216i	−0.217435	−	0.376608i
$216$		0			0
$217$	5.57567	+	9.65735i	0.378501	+	0.655584i
$218$		0			0
$219$	−3.77505	−	6.53858i	−0.255094	−	0.441836i
$220$		0			0
$221$	7.43647			0.500231
$222$		0			0
$223$	−10.5363			−0.705563			−0.352782	−	0.935706i	$-0.614764\pi$
$223$	−10.5363			−0.705563			−0.352782	+	0.935706i	$0.614764\pi$
$224$		0			0
$225$	0.233956	+	0.405224i	0.0155971	+	0.0270149i
$226$		0			0
$227$	−6.61481	−	11.4572i	−0.439041	−	0.760441i	0.558575	−	0.829454i	$-0.311348\pi$
$227$	−6.61481	−	11.4572i	−0.439041	−	0.760441i	−0.997616	+	0.0690133i	$0.978015\pi$
$228$		0			0
$229$	−9.73906	−	16.8685i	−0.643575	−	1.11470i	−0.984629	−	0.174661i	$-0.944117\pi$
$229$	−9.73906	−	16.8685i	−0.643575	−	1.11470i	0.341054	−	0.940044i	$-0.389216\pi$
$230$		0			0
$231$	−8.35703	+	14.4748i	−0.549852	+	0.952372i
$232$		0			0
$233$	9.18392			0.601659			0.300829	−	0.953678i	$-0.402737\pi$
$233$	9.18392			0.601659			0.300829	+	0.953678i	$0.402737\pi$
$234$		0			0
$235$	1.66061	+	2.87626i	0.108326	+	0.187626i
$236$		0			0
$237$	−0.551030	+	0.954412i	−0.0357933	+	0.0619957i
$238$		0			0
$239$	−14.3816	+	24.9096i	−0.930267	+	1.61127i	−0.147405	+	0.989076i	$0.547092\pi$
$239$	−14.3816	+	24.9096i	−0.930267	+	1.61127i	−0.782863	+	0.622194i	$0.786241\pi$
$240$		0			0
$241$	4.95684	+	8.58550i	0.319298	+	0.553041i	0.980342	−	0.197307i	$-0.0632195\pi$
$241$	4.95684	+	8.58550i	0.319298	+	0.553041i	−0.661044	+	0.750348i	$0.729886\pi$
$242$		0			0
$243$	−2.40790	+	4.17060i	−0.154467	+	0.267544i
$244$		0			0
$245$	2.44040			0.155911
$246$		0			0
$247$	1.69679	−	2.93893i	0.107964	−	0.187000i
$248$		0			0
$249$	16.7937			1.06426
$250$		0			0
$251$	25.8573			1.63210			0.816048	−	0.577984i	$-0.196160\pi$
$251$	25.8573			1.63210			0.816048	+	0.577984i	$0.196160\pi$
$252$		0			0
$253$	−31.3257			−1.96943
$254$		0			0
$255$	3.12926	+	5.42004i	0.195962	+	0.339416i
$256$		0			0
$257$	−7.36563	+	12.7576i	−0.459455	+	0.795800i	−0.998932	−	0.0462004i	$-0.985289\pi$
$257$	−7.36563	+	12.7576i	−0.459455	+	0.795800i	0.539477	+	0.842000i	$0.318622\pi$
$258$		0			0
$259$	11.2107	+	14.9538i	0.696596	+	0.929184i
$260$		0			0
$261$	−0.524632	+	0.908689i	−0.0324739	+	0.0562464i
$262$		0			0
$263$	−7.37269	−	12.7699i	−0.454620	−	0.787424i	0.544047	−	0.839055i	$-0.316891\pi$
$263$	−7.37269	−	12.7699i	−0.454620	−	0.787424i	−0.998666	+	0.0516307i	$0.983558\pi$
$264$		0			0
$265$	−2.82734			−0.173682
$266$		0			0
$267$	13.6653			0.836300
$268$		0			0
$269$	−25.4861			−1.55391			−0.776957	−	0.629554i	$-0.783238\pi$
$269$	−25.4861			−1.55391			−0.776957	+	0.629554i	$0.783238\pi$
$270$		0			0
$271$	11.5506	−	20.0062i	0.701646	−	1.21529i	−0.266242	−	0.963906i	$-0.585782\pi$
$271$	11.5506	−	20.0062i	0.701646	−	1.21529i	0.967888	−	0.251381i	$-0.0808847\pi$
$272$		0			0
$273$	−9.24419			−0.559484
$274$		0			0
$275$	−1.70930	+	2.96059i	−0.103074	+	0.178530i
$276$		0			0
$277$	8.60893	+	14.9111i	0.517260	+	0.895921i	0.999799	+	0.0200466i	$0.00638145\pi$
$277$	8.60893	+	14.9111i	0.517260	+	0.895921i	−0.482539	+	0.875875i	$0.660285\pi$
$278$		0			0
$279$	−0.849115	+	1.47071i	−0.0508352	+	0.0880491i
$280$		0			0
$281$	−8.87242	+	15.3675i	−0.529284	+	0.916747i	0.470132	+	0.882596i	$0.344206\pi$
$281$	−8.87242	+	15.3675i	−0.529284	+	0.916747i	−0.999417	+	0.0341515i	$0.989127\pi$
$282$		0			0
$283$	−0.0985752	−	0.170737i	−0.00585969	−	0.0101493i	0.863081	−	0.505066i	$-0.168532\pi$
$283$	−0.0985752	−	0.170737i	−0.00585969	−	0.0101493i	−0.868940	+	0.494917i	$0.835199\pi$
$284$		0			0
$285$	2.85604			0.169177
$286$		0			0
$287$	10.1698	−	17.6147i	0.600307	−	1.03976i
$288$		0			0
$289$	0.765445	+	1.32579i	0.0450261	+	0.0779876i
$290$		0			0
$291$	2.70416	+	4.68374i	0.158521	+	0.274566i
$292$		0			0
$293$	2.17638	+	3.76961i	0.127146	+	0.220223i	0.922570	−	0.385831i	$-0.126085\pi$
$293$	2.17638	+	3.76961i	0.127146	+	0.220223i	−0.795424	+	0.606053i	$0.792752\pi$
$294$		0			0
$295$	−10.2164			−0.594820
$296$		0			0
$297$	−18.8649			−1.09465
$298$		0			0
$299$	−8.66280	−	15.0044i	−0.500983	−	0.867727i
$300$		0			0
$301$	−9.79588	−	16.9670i	−0.564625	−	0.977959i
$302$		0			0
$303$	3.86859	+	6.70059i	0.222245	+	0.384939i
$304$		0			0
$305$	3.65748	−	6.33494i	0.209427	−	0.362738i
$306$		0			0
$307$	−7.86608			−0.448941			−0.224470	−	0.974481i	$-0.572065\pi$
$307$	−7.86608			−0.448941			−0.224470	+	0.974481i	$0.572065\pi$
$308$		0			0
$309$	−12.2332	−	21.1886i	−0.695924	−	1.20538i
$310$		0			0
$311$	9.13790	−	15.8273i	0.518163	−	0.897485i	−0.481614	−	0.876383i	$-0.659949\pi$
$311$	9.13790	−	15.8273i	0.518163	−	0.897485i	0.999777	−	0.0211013i	$-0.00671726\pi$
$312$		0			0
$313$	7.14105	−	12.3687i	0.403636	−	0.699118i	−0.590526	−	0.807019i	$-0.701080\pi$
$313$	7.14105	−	12.3687i	0.403636	−	0.699118i	0.994162	+	0.107901i	$0.0344129\pi$
$314$		0			0
$315$	0.718835	+	1.24506i	0.0405018	+	0.0701511i
$316$		0			0
$317$	13.1300	−	22.7419i	0.737457	−	1.27731i	−0.216180	−	0.976354i	$-0.569360\pi$
$317$	13.1300	−	22.7419i	0.737457	−	1.27731i	0.953637	−	0.300959i	$-0.0973069\pi$
$318$		0			0
$319$	−7.66599			−0.429213
$320$		0			0
$321$	−4.26613	+	7.38915i	−0.238112	+	0.412422i
$322$		0			0
$323$	−7.05922			−0.392786
$324$		0			0
$325$	−1.89075			−0.104880
$326$		0			0
$327$	−21.7490			−1.20272
$328$		0			0
$329$	5.10226	+	8.83737i	0.281297	+	0.487220i
$330$		0			0
$331$	8.76995	−	15.1900i	0.482040	−	0.834918i	−0.517748	−	0.855533i	$-0.673229\pi$
$331$	8.76995	−	15.1900i	0.482040	−	0.834918i	0.999787	+	0.0206159i	$0.00656270\pi$
$332$		0			0
$333$	−1.11857	+	2.61718i	−0.0612973	+	0.143421i
$334$		0			0
$335$	−6.34541	+	10.9906i	−0.346687	+	0.600479i
$336$		0			0
$337$	7.22756	+	12.5185i	0.393710	+	0.681926i	0.992936	−	0.118654i	$-0.0378579\pi$
$337$	7.22756	+	12.5185i	0.393710	+	0.681926i	−0.599225	+	0.800580i	$0.704525\pi$
$338$		0			0
$339$	2.10506			0.114331
$340$		0			0
$341$	−12.4074			−0.671897
$342$		0			0
$343$	−14.0095			−0.756441
$344$		0			0
$345$	7.29060	−	12.6277i	0.392513	−	0.679852i
$346$		0			0
$347$	13.5011			0.724778			0.362389	−	0.932027i	$-0.381961\pi$
$347$	13.5011			0.724778			0.362389	+	0.932027i	$0.381961\pi$
$348$		0			0
$349$	5.98136	−	10.3600i	0.320175	−	0.554559i	−0.660349	−	0.750959i	$-0.729592\pi$
$349$	5.98136	−	10.3600i	0.320175	−	0.554559i	0.980524	+	0.196400i	$0.0629251\pi$
$350$		0			0
$351$	−5.21689	−	9.03592i	−0.278457	−	0.482302i
$352$		0			0
$353$	−2.27786	+	3.94536i	−0.121238	+	0.209990i	−0.920256	−	0.391317i	$-0.872020\pi$
$353$	−2.27786	+	3.94536i	−0.121238	+	0.209990i	0.799018	+	0.601307i	$0.205353\pi$
$354$		0			0
$355$	−2.10924	+	3.65331i	−0.111947	+	0.193898i
$356$		0			0
$357$	9.61473	+	16.6532i	0.508866	+	0.881381i
$358$		0			0
$359$	−7.14442			−0.377068			−0.188534	−	0.982067i	$-0.560374\pi$
$359$	−7.14442			−0.377068			−0.188534	+	0.982067i	$0.560374\pi$
$360$		0			0
$361$	7.88929	−	13.6646i	0.415226	−	0.719192i
$362$		0			0
$363$	−0.546423	−	0.946432i	−0.0286798	−	0.0496748i
$364$		0			0
$365$	−2.37237	−	4.10907i	−0.124176	−	0.215079i
$366$		0			0
$367$	14.4395	+	25.0099i	0.753735	+	1.30551i	0.946001	+	0.324165i	$0.105083\pi$
$367$	14.4395	+	25.0099i	0.753735	+	1.30551i	−0.192266	+	0.981343i	$0.561584\pi$
$368$		0			0
$369$	3.09751			0.161250
$370$		0			0
$371$	−8.68707			−0.451010
$372$		0			0
$373$	−13.7490	−	23.8140i	−0.711896	−	1.23304i	−0.964145	−	0.265378i	$-0.914503\pi$
$373$	−13.7490	−	23.8140i	−0.711896	−	1.23304i	0.252249	−	0.967662i	$-0.418830\pi$
$374$		0			0
$375$	−0.795627	−	1.37807i	−0.0410860	−	0.0711630i
$376$		0			0
$377$	−2.11995	−	3.67185i	−0.109183	−	0.189110i
$378$		0			0
$379$	3.68880	−	6.38919i	0.189481	−	0.328191i	−0.755596	−	0.655038i	$-0.772653\pi$
$379$	3.68880	−	6.38919i	0.189481	−	0.328191i	0.945077	+	0.326847i	$0.105986\pi$
$380$		0			0
$381$	−26.1653			−1.34049
$382$		0			0
$383$	10.4670	+	18.1293i	0.534837	+	0.926365i	0.999171	+	0.0407046i	$0.0129602\pi$
$383$	10.4670	+	18.1293i	0.534837	+	0.926365i	−0.464334	+	0.885660i	$0.653706\pi$
$384$		0			0
$385$	−5.25185	+	9.09648i	−0.267659	+	0.463600i
$386$		0			0
$387$	1.49181	−	2.58388i	0.0758328	−	0.131346i
$388$		0			0
$389$	−9.78686	−	16.9513i	−0.496213	−	0.859467i	0.503777	−	0.863834i	$-0.331943\pi$
$389$	−9.78686	−	16.9513i	−0.496213	−	0.859467i	−0.999990	+	0.00436684i	$0.998610\pi$
$390$		0			0
$391$	−18.0201	+	31.2117i	−0.911314	+	1.57844i
$392$		0			0
$393$	−2.72016			−0.137214
$394$		0			0
$395$	−0.346287	+	0.599786i	−0.0174236	+	0.0301785i
$396$		0			0
$397$	15.5500			0.780432			0.390216	−	0.920723i	$-0.372400\pi$
$397$	15.5500			0.780432			0.390216	+	0.920723i	$0.372400\pi$
$398$		0			0
$399$	8.77524			0.439311
$400$		0			0
$401$	−10.4214			−0.520421			−0.260210	−	0.965552i	$-0.583792\pi$
$401$	−10.4214			−0.520421			−0.260210	+	0.965552i	$0.583792\pi$
$402$		0			0
$403$	−3.43112	−	5.94288i	−0.170916	−	0.296036i
$404$		0			0
$405$	3.68866	−	6.38895i	0.183291	−	0.317469i
$406$		0			0
$407$	−20.6457	+	2.48319i	−1.02337	+	0.123087i
$408$		0			0
$409$	11.3454	−	19.6508i	0.560995	−	0.971671i	−0.436415	−	0.899745i	$-0.643752\pi$
$409$	11.3454	−	19.6508i	0.560995	−	0.971671i	0.997410	−	0.0719258i	$-0.0229145\pi$
$410$		0			0
$411$	−7.00971	−	12.1412i	−0.345763	−	0.598880i
$412$		0			0
$413$	−31.3900			−1.54460
$414$		0			0
$415$	10.5538			0.518065
$416$		0			0
$417$	−19.7743			−0.968349
$418$		0			0
$419$	−14.3953	+	24.9333i	−0.703254	+	1.21807i	0.264064	+	0.964505i	$0.414937\pi$
$419$	−14.3953	+	24.9333i	−0.703254	+	1.21807i	−0.967318	+	0.253567i	$0.918396\pi$
$420$		0			0
$421$	28.0292			1.36606			0.683030	−	0.730390i	$-0.260662\pi$
$421$	28.0292			1.36606			0.683030	+	0.730390i	$0.260662\pi$
$422$		0			0
$423$	−0.777019	+	1.34584i	−0.0377799	+	0.0654368i
$424$		0			0
$425$	1.96654	+	3.40615i	0.0953912	+	0.165222i
$426$		0			0
$427$	11.2377	−	19.4643i	0.543830	−	0.941942i
$428$		0			0
$429$	5.14270	−	8.90742i	0.248292	−	0.430054i
$430$		0			0
$431$	−6.21355	−	10.7622i	−0.299296	−	0.518396i	0.676679	−	0.736278i	$-0.263419\pi$
$431$	−6.21355	−	10.7622i	−0.299296	−	0.518396i	−0.975975	+	0.217882i	$0.930085\pi$
$432$		0			0
$433$	3.89461			0.187163			0.0935814	−	0.995612i	$-0.470168\pi$
$433$	3.89461			0.187163			0.0935814	+	0.995612i	$0.470168\pi$
$434$		0			0
$435$	1.78414	−	3.09023i	0.0855432	−	0.148165i
$436$		0			0
$437$	8.22334	+	14.2432i	0.393376	+	0.681347i
$438$		0			0
$439$	1.42944	+	2.47587i	0.0682236	+	0.118167i	0.898119	−	0.439752i	$-0.144934\pi$
$439$	1.42944	+	2.47587i	0.0682236	+	0.118167i	−0.829896	+	0.557918i	$0.811600\pi$
$440$		0			0
$441$	0.570946	+	0.988908i	0.0271879	+	0.0470909i
$442$		0			0
$443$	22.3986			1.06419			0.532095	−	0.846685i	$-0.321405\pi$
$443$	22.3986			1.06419			0.532095	+	0.846685i	$0.321405\pi$
$444$		0			0
$445$	8.58773			0.407097
$446$		0			0
$447$	−16.8118	−	29.1188i	−0.795169	−	1.37727i
$448$		0			0
$449$	−8.93201	−	15.4707i	−0.421528	−	0.730107i	0.574562	−	0.818461i	$-0.305173\pi$
$449$	−8.93201	−	15.4707i	−0.421528	−	0.730107i	−0.996089	+	0.0883542i	$0.971839\pi$
$450$		0			0
$451$	11.3153	+	19.5987i	0.532817	+	0.922866i
$452$		0			0
$453$	10.8780	−	18.8412i	0.511093	−	0.885239i
$454$		0			0
$455$	−5.80938			−0.272348
$456$		0			0
$457$	−14.6709	−	25.4107i	−0.686276	−	1.18866i	−0.973034	−	0.230661i	$-0.925911\pi$
$457$	−14.6709	−	25.4107i	−0.686276	−	1.18866i	0.286759	−	0.958003i	$-0.407422\pi$
$458$		0			0
$459$	−10.8520	+	18.7962i	−0.506528	+	0.877333i
$460$		0			0
$461$	−15.7560	+	27.2902i	−0.733830	+	1.27103i	0.221404	+	0.975182i	$0.428936\pi$
$461$	−15.7560	+	27.2902i	−0.733830	+	1.27103i	−0.955235	+	0.295849i	$0.904397\pi$
$462$		0			0
$463$	10.1893	+	17.6484i	0.473539	+	0.820193i	0.999541	−	0.0302900i	$-0.00964309\pi$
$463$	10.1893	+	17.6484i	0.473539	+	0.820193i	−0.526003	+	0.850483i	$0.676310\pi$
$464$		0			0
$465$	2.88763	−	5.00152i	0.133911	−	0.231940i
$466$		0			0
$467$	−12.6834			−0.586919			−0.293459	−	0.955972i	$-0.594807\pi$
$467$	−12.6834			−0.586919			−0.293459	+	0.955972i	$0.594807\pi$
$468$		0			0
$469$	−19.4964	+	33.7688i	−0.900261	+	1.55930i
$470$		0			0
$471$	−18.6864			−0.861022
$472$		0			0
$473$	21.7985			1.00229
$474$		0			0
$475$	1.79483			0.0823526
$476$		0			0
$477$	−0.661473	−	1.14571i	−0.0302868	−	0.0524582i
$478$		0			0
$479$	−10.0337	+	17.3788i	−0.458450	+	0.794059i	−0.998879	−	0.0473304i	$-0.984929\pi$
$479$	−10.0337	+	17.3788i	−0.458450	+	0.794059i	0.540429	+	0.841390i	$0.318262\pi$
$480$		0			0
$481$	−6.89874	−	9.20218i	−0.314556	−	0.419583i
$482$		0			0
$483$	22.4005	−	38.7989i	1.01926	−	1.76541i
$484$		0			0
$485$	1.69939	+	2.94343i	0.0771653	+	0.133654i
$486$		0			0
$487$	−11.5540			−0.523560			−0.261780	−	0.965128i	$-0.584309\pi$
$487$	−11.5540			−0.523560			−0.261780	+	0.965128i	$0.584309\pi$
$488$		0			0
$489$	−35.6742			−1.61324
$490$		0			0
$491$	15.9933			0.721766			0.360883	−	0.932611i	$-0.382475\pi$
$491$	15.9933			0.721766			0.360883	+	0.932611i	$0.382475\pi$
$492$		0			0
$493$	−4.40984	+	7.63807i	−0.198609	+	0.344002i
$494$		0			0
$495$	−1.59960			−0.0718967
$496$		0			0
$497$	−6.48070	+	11.2249i	−0.290699	+	0.503505i
$498$		0			0
$499$	14.1135	+	24.4453i	0.631806	+	1.09432i	0.987182	+	0.159597i	$0.0510194\pi$
$499$	14.1135	+	24.4453i	0.631806	+	1.09432i	−0.355376	+	0.934723i	$0.615647\pi$
$500$		0			0
$501$	13.5030	−	23.3879i	0.603270	−	1.04489i
$502$		0			0
$503$	−9.18647	+	15.9114i	−0.409605	+	0.709456i	−0.994845	−	0.101404i	$-0.967667\pi$
$503$	−9.18647	+	15.9114i	−0.409605	+	0.709456i	0.585241	+	0.810860i	$0.301000\pi$
$504$		0			0
$505$	2.43116	+	4.21089i	0.108185	+	0.187382i
$506$		0			0
$507$	−14.9977			−0.666070
$508$		0			0
$509$	19.2792	−	33.3925i	0.854535	−	1.48010i	−0.0225407	−	0.999746i	$-0.507176\pi$
$509$	19.2792	−	33.3925i	0.854535	−	1.48010i	0.877076	−	0.480352i	$-0.159491\pi$
$510$		0			0
$511$	−7.28918	−	12.6252i	−0.322454	−	0.558507i
$512$		0			0
$513$	4.95224	+	8.57753i	0.218647	+	0.378707i
$514$		0			0
$515$	−7.68779	−	13.3156i	−0.338765	−	0.586758i
$516$		0			0
$517$	−11.3539			−0.499344
$518$		0			0
$519$	8.82663			0.387446
$520$		0			0
$521$	−9.99608	−	17.3137i	−0.437936	−	0.758527i	0.559594	−	0.828767i	$-0.310957\pi$
$521$	−9.99608	−	17.3137i	−0.437936	−	0.758527i	−0.997530	+	0.0702393i	$0.977624\pi$
$522$		0			0
$523$	12.9249	+	22.3865i	0.565165	+	0.978894i	0.997034	+	0.0769583i	$0.0245208\pi$
$523$	12.9249	+	22.3865i	0.565165	+	0.978894i	−0.431869	+	0.901936i	$0.642146\pi$
$524$		0			0
$525$	−2.44458	−	4.23414i	−0.106690	−	0.184793i
$526$		0			0
$527$	−7.13731	+	12.3622i	−0.310906	+	0.538506i
$528$		0			0
$529$	60.9669			2.65073
$530$		0			0
$531$	−2.39018	−	4.13992i	−0.103725	−	0.179657i
$532$		0			0
$533$	−6.25825	+	10.8396i	−0.271075	+	0.469516i
$534$		0			0
$535$	−2.68098	+	4.64360i	−0.115909	+	0.200760i
$536$		0			0
$537$	16.9970	+	29.4397i	0.733475	+	1.27042i
$538$		0			0
$539$	−4.17137	+	7.22502i	−0.179674	+	0.311204i
$540$		0			0
$541$	−25.6404			−1.10237			−0.551183	−	0.834384i	$-0.685824\pi$
$541$	−25.6404			−1.10237			−0.551183	+	0.834384i	$0.685824\pi$
$542$		0			0
$543$	1.80944	−	3.13403i	0.0776503	−	0.134494i
$544$		0			0
$545$	−13.6678			−0.585466
$546$		0			0
$547$	−21.7589			−0.930345			−0.465173	−	0.885220i	$-0.654008\pi$
$547$	−21.7589			−0.930345			−0.465173	+	0.885220i	$0.654008\pi$
$548$		0			0
$549$	3.42276			0.146080
$550$		0			0
$551$	2.01240	+	3.48558i	0.0857312	+	0.148491i
$552$		0			0
$553$	−1.06397	+	1.84286i	−0.0452448	+	0.0783663i
$554$		0			0
$555$	3.80398	−	8.90039i	0.161470	−	0.377801i
$556$		0			0
$557$	8.15805	−	14.1302i	0.345668	−	0.598714i	−0.639807	−	0.768535i	$-0.720986\pi$
$557$	8.15805	−	14.1302i	0.345668	−	0.598714i	0.985475	+	0.169822i	$0.0543191\pi$
$558$		0			0
$559$	6.02813	+	10.4410i	0.254963	+	0.441608i
$560$		0			0
$561$	−21.3954			−0.903313
$562$		0			0
$563$	−5.14741			−0.216938			−0.108469	−	0.994100i	$-0.534595\pi$
$563$	−5.14741			−0.216938			−0.108469	+	0.994100i	$0.534595\pi$
$564$		0			0
$565$	1.32289			0.0556545
$566$		0			0
$567$	11.3335	−	19.6302i	0.475962	−	0.824391i
$568$		0			0
$569$	22.8603			0.958353			0.479176	−	0.877719i	$-0.340935\pi$
$569$	22.8603			0.958353			0.479176	+	0.877719i	$0.340935\pi$
$570$		0			0
$571$	3.29158	−	5.70119i	0.137748	−	0.238587i	−0.788896	−	0.614527i	$-0.789347\pi$
$571$	3.29158	−	5.70119i	0.137748	−	0.238587i	0.926644	+	0.375940i	$0.122680\pi$
$572$		0			0
$573$	12.9581	+	22.4441i	0.541332	+	0.937615i
$574$		0			0
$575$	4.58167	−	7.93569i	0.191069	−	0.330941i
$576$		0			0
$577$	−16.0852	+	27.8603i	−0.669634	+	1.15984i	0.308373	+	0.951266i	$0.400216\pi$
$577$	−16.0852	+	27.8603i	−0.669634	+	1.15984i	−0.978007	+	0.208574i	$0.933118\pi$
$578$		0			0
$579$	6.60871	+	11.4466i	0.274649	+	0.475706i
$580$		0			0
$581$	32.4267			1.34529
$582$		0			0
$583$	4.83276	−	8.37059i	0.200153	−	0.346675i
$584$		0			0
$585$	−0.442352	−	0.766177i	−0.0182890	−	0.0316775i
$586$		0			0
$587$	9.72391	+	16.8423i	0.401349	+	0.695157i	0.993889	−	0.110384i	$-0.0352082\pi$
$587$	9.72391	+	16.8423i	0.401349	+	0.695157i	−0.592540	+	0.805541i	$0.701875\pi$
$588$		0			0
$589$	3.25706	+	5.64140i	0.134205	+	0.232450i
$590$		0			0
$591$	−33.6907			−1.38585
$592$		0			0
$593$	23.7692			0.976082			0.488041	−	0.872821i	$-0.337712\pi$
$593$	23.7692			0.976082			0.488041	+	0.872821i	$0.337712\pi$
$594$		0			0
$595$	6.04224	+	10.4655i	0.247708	+	0.429042i
$596$		0			0
$597$	0.173864	+	0.301141i	0.00711577	+	0.0123249i
$598$		0			0
$599$	−4.03233	−	6.98419i	−0.164756	−	0.285366i	0.771812	−	0.635850i	$-0.219350\pi$
$599$	−4.03233	−	6.98419i	−0.164756	−	0.285366i	−0.936569	+	0.350484i	$0.886017\pi$
$600$		0			0
$601$	15.0641	−	26.0918i	0.614478	−	1.06431i	−0.375998	−	0.926620i	$-0.622700\pi$
$601$	15.0641	−	26.0918i	0.614478	−	1.06431i	0.990476	−	0.137686i	$-0.0439666\pi$
$602$		0			0
$603$	−5.93819			−0.241822
$604$		0			0
$605$	−0.343391	−	0.594771i	−0.0139608	−	0.0241809i
$606$		0			0
$607$	2.52778	−	4.37825i	0.102599	−	0.177708i	−0.810155	−	0.586215i	$-0.800617\pi$
$607$	2.52778	−	4.37825i	0.102599	−	0.177708i	0.912755	+	0.408508i	$0.133951\pi$
$608$		0			0
$609$	5.48182	−	9.49480i	0.222135	−	0.384749i
$610$		0			0
$611$	−3.13980	−	5.43829i	−0.127023	−	0.220010i
$612$		0			0
$613$	−22.6931	+	39.3056i	−0.916565	+	1.58754i	−0.111971	+	0.993712i	$0.535716\pi$
$613$	−22.6931	+	39.3056i	−0.916565	+	1.58754i	−0.804594	+	0.593825i	$0.797617\pi$
$614$		0			0
$615$	−10.5339			−0.424767
$616$		0			0
$617$	−13.4068	+	23.2212i	−0.539736	+	0.934851i	0.459181	+	0.888342i	$0.348143\pi$
$617$	−13.4068	+	23.2212i	−0.539736	+	0.934851i	−0.998918	+	0.0465084i	$0.985191\pi$
$618$		0			0
$619$	−30.6521			−1.23201			−0.616006	−	0.787741i	$-0.711250\pi$
$619$	−30.6521			−1.23201			−0.616006	+	0.787741i	$0.711250\pi$
$620$		0			0
$621$	50.5663			2.02916
$622$		0			0
$623$	26.3860			1.05713
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−4.88181	+	8.45555i	−0.194961	+	0.337682i
$628$		0			0
$629$	−9.40225	+	21.9990i	−0.374892	+	0.877157i
$630$		0			0
$631$	4.31031	−	7.46567i	0.171591	−	0.297204i	−0.767385	−	0.641186i	$-0.778443\pi$
$631$	4.31031	−	7.46567i	0.171591	−	0.297204i	0.938976	+	0.343982i	$0.111776\pi$
$632$		0			0
$633$	−8.52972	−	14.7739i	−0.339026	−	0.587210i
$634$		0			0
$635$	−16.4432			−0.652527
$636$		0			0
$637$	−4.61419			−0.182821
$638$		0			0
$639$	−1.97388			−0.0780855
$640$		0			0
$641$	6.56516	−	11.3712i	0.259308	−	0.449135i	−0.706749	−	0.707465i	$-0.749839\pi$
$641$	6.56516	−	11.3712i	0.259308	−	0.449135i	0.966057	+	0.258330i	$0.0831722\pi$
$642$		0			0
$643$	20.1992			0.796577			0.398289	−	0.917260i	$-0.369604\pi$
$643$	20.1992			0.796577			0.398289	+	0.917260i	$0.369604\pi$
$644$		0			0
$645$	−5.07327	+	8.78715i	−0.199760	+	0.345994i
$646$		0			0
$647$	18.4800	+	32.0083i	0.726524	+	1.25838i	0.958344	+	0.285617i	$0.0921986\pi$
$647$	18.4800	+	32.0083i	0.726524	+	1.25838i	−0.231820	+	0.972759i	$0.574468\pi$
$648$		0			0
$649$	17.4628	−	30.2465i	0.685475	−	1.18728i
$650$		0			0
$651$	8.87231	−	15.3673i	0.347733	−	0.602292i
$652$		0			0
$653$	1.51371	+	2.62183i	0.0592362	+	0.102600i	0.894123	−	0.447822i	$-0.147800\pi$
$653$	1.51371	+	2.62183i	0.0592362	+	0.102600i	−0.834887	+	0.550422i	$0.814467\pi$
$654$		0			0
$655$	−1.70944			−0.0667934
$656$		0			0
$657$	1.11006	−	1.92269i	0.0433077	−	0.0750111i
$658$		0			0
$659$	6.10755	+	10.5786i	0.237916	+	0.412083i	0.960116	−	0.279601i	$-0.0902023\pi$
$659$	6.10755	+	10.5786i	0.237916	+	0.412083i	−0.722200	+	0.691684i	$0.756869\pi$
$660$		0			0
$661$	−5.69340	−	9.86126i	−0.221448	−	0.383558i	0.733800	−	0.679365i	$-0.237745\pi$
$661$	−5.69340	−	9.86126i	−0.221448	−	0.383558i	−0.955248	+	0.295807i	$0.904411\pi$
$662$		0			0
$663$	−5.91666	−	10.2479i	−0.229784	−	0.397997i
$664$		0			0
$665$	5.51467			0.213850
$666$		0			0
$667$	20.5482			0.795631
$668$		0			0
$669$	8.38296	+	14.5197i	0.324104	+	0.561365i
$670$		0			0
$671$	12.5034	+	21.6566i	0.482690	+	0.836044i
$672$		0			0
$673$	−15.0026	−	25.9852i	−0.578306	−	1.00166i	−0.995674	−	0.0929179i	$-0.970381\pi$
$673$	−15.0026	−	25.9852i	−0.578306	−	1.00166i	0.417368	−	0.908738i	$-0.362953\pi$
$674$		0			0
$675$	2.75916	−	4.77901i	0.106200	−	0.183944i
$676$		0			0
$677$	−7.25195			−0.278715			−0.139358	−	0.990242i	$-0.544504\pi$
$677$	−7.25195			−0.278715			−0.139358	+	0.990242i	$0.544504\pi$
$678$		0			0
$679$	5.22142	+	9.04376i	0.200380	+	0.347068i
$680$		0			0
$681$	−10.5258	+	18.2313i	−0.403351	+	0.698625i
$682$		0			0
$683$	−0.482627	+	0.835935i	−0.0184672	+	0.0319862i	−0.875111	−	0.483922i	$-0.839212\pi$
$683$	−0.482627	+	0.835935i	−0.0184672	+	0.0319862i	0.856644	+	0.515908i	$0.172545\pi$
$684$		0			0
$685$	−4.40515	−	7.62994i	−0.168312	−	0.291525i
$686$		0			0
$687$	−15.4973	+	26.8421i	−0.591259	+	1.02409i
$688$		0			0
$689$	5.34579			0.203659
$690$		0			0
$691$	−6.44091	+	11.1560i	−0.245024	+	0.424394i	−0.962138	−	0.272562i	$-0.912129\pi$
$691$	−6.44091	+	11.1560i	−0.245024	+	0.424394i	0.717114	+	0.696955i	$0.245462\pi$
$692$		0			0
$693$	−4.91481			−0.186698
$694$		0			0
$695$	−12.4268			−0.471377
$696$		0			0
$697$	26.0364			0.986201
$698$		0			0
$699$	−7.30697	−	12.6561i	−0.276375	−	0.478696i
$700$		0			0
$701$	16.2997	−	28.2319i	0.615631	−	1.06630i	−0.374642	−	0.927169i	$-0.622234\pi$
$701$	16.2997	−	28.2319i	0.615631	−	1.06630i	0.990273	−	0.139135i	$-0.0444322\pi$
$702$		0			0
$703$	6.54877	+	8.73535i	0.246992	+	0.329460i
$704$		0			0
$705$	2.64245	−	4.57686i	0.0995204	−	0.172374i
$706$		0			0
$707$	7.46979	+	12.9381i	0.280930	+	0.486586i
$708$		0			0
$709$	34.3877			1.29146			0.645728	−	0.763567i	$-0.276554\pi$
$709$	34.3877			1.29146			0.645728	+	0.763567i	$0.276554\pi$
$710$		0			0
$711$	−0.324064			−0.0121533
$712$		0			0
$713$	33.2572			1.24549
$714$		0			0
$715$	3.23185	−	5.59774i	0.120864	−	0.209343i
$716$		0			0
$717$	45.7695			1.70929
$718$		0			0
$719$	−4.48338	+	7.76545i	−0.167202	+	0.289602i	−0.937435	−	0.348160i	$-0.886807\pi$
$719$	−4.48338	+	7.76545i	−0.167202	+	0.289602i	0.770233	+	0.637763i	$0.220140\pi$
$720$		0			0
$721$	−23.6209	−	40.9126i	−0.879689	−	1.52367i
$722$		0			0
$723$	7.88759	−	13.6617i	0.293343	−	0.508085i
$724$		0			0
$725$	1.12122	−	1.94201i	0.0416410	−	0.0721244i
$726$		0			0
$727$	12.4286	+	21.5270i	0.460951	+	0.798391i	0.999009	−	0.0445175i	$-0.0141750\pi$
$727$	12.4286	+	21.5270i	0.460951	+	0.798391i	−0.538058	+	0.842908i	$0.680842\pi$
$728$		0			0
$729$	29.7951			1.10352
$730$		0			0
$731$	12.5395	−	21.7191i	0.463791	−	0.803309i
$732$		0			0
$733$	4.10956	+	7.11796i	0.151790	+	0.262908i	0.931886	−	0.362752i	$-0.118163\pi$
$733$	4.10956	+	7.11796i	0.151790	+	0.262908i	−0.780096	+	0.625660i	$0.784830\pi$
$734$		0			0
$735$	−1.94165	−	3.36303i	−0.0716188	−	0.124047i
$736$		0			0
$737$	−21.6924	−	37.5723i	−0.799049	−	1.38399i
$738$		0			0
$739$	38.8470			1.42901			0.714506	−	0.699630i	$-0.246652\pi$
$739$	38.8470			1.42901			0.714506	+	0.699630i	$0.246652\pi$
$740$		0			0
$741$	−5.40005			−0.198376
$742$		0			0
$743$	−4.93828	−	8.55335i	−0.181168	−	0.313792i	0.761111	−	0.648622i	$-0.224654\pi$
$743$	−4.93828	−	8.55335i	−0.181168	−	0.313792i	−0.942278	+	0.334830i	$0.891321\pi$
$744$		0			0
$745$	−10.5651	−	18.2993i	−0.387075	−	0.670434i
$746$		0			0
$747$	2.46912	+	4.27664i	0.0903404	+	0.156474i
$748$		0			0
$749$	−8.23739	+	14.2676i	−0.300988	+	0.521326i
$750$		0			0
$751$	15.9259			0.581146			0.290573	−	0.956853i	$-0.406154\pi$
$751$	15.9259			0.581146			0.290573	+	0.956853i	$0.406154\pi$
$752$		0			0
$753$	−20.5727	−	35.6330i	−0.749712	−	1.29854i
$754$		0			0
$755$	6.83612	−	11.8405i	0.248792	−	0.430920i
$756$		0			0
$757$	11.2887	−	19.5526i	0.410294	−	0.710650i	−0.584628	−	0.811302i	$-0.698759\pi$
$757$	11.2887	−	19.5526i	0.410294	−	0.710650i	0.994922	+	0.100652i	$0.0320928\pi$
$758$		0			0
$759$	24.9236	+	43.1689i	0.904670	+	1.56693i
$760$		0			0
$761$	6.99144	−	12.1095i	0.253440	−	0.438970i	−0.711031	−	0.703161i	$-0.751771\pi$
$761$	6.99144	−	12.1095i	0.253440	−	0.438970i	0.964471	+	0.264190i	$0.0851048\pi$
$762$		0			0
$763$	−41.9947			−1.52031
$764$		0			0
$765$	−0.920168	+	1.59378i	−0.0332687	+	0.0576231i
$766$		0			0
$767$	19.3166			0.697482
$768$		0			0
$769$	45.0764			1.62550			0.812749	−	0.582614i	$-0.197970\pi$
$769$	45.0764			1.62550			0.812749	+	0.582614i	$0.197970\pi$
$770$		0			0
$771$	23.4412			0.844213
$772$		0			0
$773$	20.1815	+	34.9554i	0.725878	+	1.25726i	0.958612	+	0.284717i	$0.0918996\pi$
$773$	20.1815	+	34.9554i	0.725878	+	1.25726i	−0.232734	+	0.972540i	$0.574767\pi$
$774$		0			0
$775$	1.81469	−	3.14313i	0.0651855	−	0.112905i
$776$		0			0
$777$	11.6878	−	27.3467i	0.419298	−	0.981056i
$778$		0			0
$779$	5.94078	−	10.2897i	0.212850	−	0.368668i
$780$		0			0
$781$	−7.21064	−	12.4892i	−0.258017	−	0.446899i
$782$		0			0
$783$	12.3745			0.442229
$784$		0			0
$785$	−11.7432			−0.419131
$786$		0			0
$787$	−24.6222			−0.877687			−0.438843	−	0.898564i	$-0.644612\pi$
$787$	−24.6222			−0.877687			−0.438843	+	0.898564i	$0.644612\pi$
$788$		0			0
$789$	−11.7318	+	20.3201i	−0.417664	+	0.723415i
$790$		0			0
$791$	4.06461			0.144521
$792$		0			0
$793$	−6.91538	+	11.9778i	−0.245572	+	0.425344i
$794$		0			0
$795$	2.24951	+	3.89626i	0.0797818	+	0.138186i
$796$		0			0
$797$	−16.8182	+	29.1301i	−0.595733	+	1.03184i	0.397710	+	0.917511i	$0.369805\pi$
$797$	−16.8182	+	29.1301i	−0.595733	+	1.03184i	−0.993443	+	0.114328i	$0.963528\pi$
$798$		0			0
$799$	−6.53131	+	11.3126i	−0.231061	+	0.400209i
$800$		0			0
$801$	2.00915	+	3.47995i	0.0709898	+	0.122958i
$802$		0			0
$803$	16.2204			0.572404
$804$		0			0
$805$	14.0773	−	24.3826i	0.496159	−	0.859373i
$806$		0			0
$807$	20.2774	+	35.1215i	0.713798	+	1.23634i
$808$		0			0
$809$	−13.5087	−	23.3977i	−0.474939	−	0.822618i	0.524649	−	0.851319i	$-0.324197\pi$
$809$	−13.5087	−	23.3977i	−0.474939	−	0.822618i	−0.999588	+	0.0287002i	$0.990863\pi$
$810$		0			0
$811$	−7.94033	−	13.7531i	−0.278823	−	0.482935i	0.692270	−	0.721639i	$-0.256611\pi$
$811$	−7.94033	−	13.7531i	−0.278823	−	0.482935i	−0.971092	+	0.238704i	$0.923278\pi$
$812$		0			0
$813$	−36.7597			−1.28922
$814$		0			0
$815$	−22.4189			−0.785301
$816$		0			0
$817$	−5.72232	−	9.91136i	−0.200199	−	0.346754i
$818$		0			0
$819$	−1.35914	−	2.35410i	−0.0474921	−	0.0822588i
$820$		0			0
$821$	−1.68973	−	2.92670i	−0.0589720	−	0.102142i	0.835032	−	0.550201i	$-0.185449\pi$
$821$	−1.68973	−	2.92670i	−0.0589720	−	0.102142i	−0.894004	+	0.448059i	$0.852116\pi$
$822$		0			0
$823$	−4.39961	+	7.62035i	−0.153361	+	0.265629i	−0.932461	−	0.361271i	$-0.882343\pi$
$823$	−4.39961	+	7.62035i	−0.153361	+	0.265629i	0.779100	+	0.626900i	$0.215676\pi$
$824$		0			0
$825$	5.43985			0.189391
$826$		0			0
$827$	11.9558	+	20.7080i	0.415743	+	0.720088i	0.995506	−	0.0946972i	$-0.0301883\pi$
$827$	11.9558	+	20.7080i	0.415743	+	0.720088i	−0.579763	+	0.814785i	$0.696855\pi$
$828$		0			0
$829$	−8.64171	+	14.9679i	−0.300139	+	0.519856i	−0.976167	−	0.217020i	$-0.930366\pi$
$829$	−8.64171	+	14.9679i	−0.300139	+	0.519856i	0.676028	+	0.736876i	$0.263700\pi$
$830$		0			0
$831$	13.6990	−	23.7273i	0.475213	−	0.823092i
$832$		0			0
$833$	4.79914	+	8.31236i	0.166280	+	0.288006i
$834$		0			0
$835$	8.48577	−	14.6978i	0.293662	−	0.508638i
$836$		0			0
$837$	20.0281			0.692272
$838$		0			0
$839$	−17.3961	+	30.1309i	−0.600579	+	1.04023i	0.392154	+	0.919900i	$0.371730\pi$
$839$	−17.3961	+	30.1309i	−0.600579	+	1.04023i	−0.992733	+	0.120334i	$0.961603\pi$
$840$		0			0
$841$	−23.9715			−0.826602
$842$		0			0
$843$	28.2365			0.972518
$844$		0			0
$845$	−9.42506			−0.324232
$846$		0			0
$847$	−1.05508	−	1.82745i	−0.0362529	−	0.0627919i
$848$		0			0
$849$	−0.156858	+	0.271686i	−0.00538336	+	0.00932425i
$850$		0			0
$851$	55.3396	−	6.65605i	1.89702	−	0.228166i
$852$		0			0
$853$	13.3714	−	23.1599i	0.457827	−	0.792979i	−0.541019	−	0.841010i	$-0.681961\pi$
$853$	13.3714	−	23.1599i	0.457827	−	0.792979i	0.998846	+	0.0480311i	$0.0152947\pi$
$854$		0			0
$855$	0.419912	+	0.727309i	0.0143607	+	0.0248734i
$856$		0			0
$857$	−30.6784			−1.04795			−0.523976	−	0.851733i	$-0.675552\pi$
$857$	−30.6784			−1.04795			−0.523976	+	0.851733i	$0.675552\pi$
$858$		0			0
$859$	18.0066			0.614376			0.307188	−	0.951649i	$-0.400612\pi$
$859$	18.0066			0.614376			0.307188	+	0.951649i	$0.400612\pi$
$860$		0			0
$861$	−32.3656			−1.10302
$862$		0			0
$863$	7.59673	−	13.1579i	0.258596	−	0.447901i	−0.707270	−	0.706943i	$-0.750074\pi$
$863$	7.59673	−	13.1579i	0.258596	−	0.447901i	0.965866	+	0.259042i	$0.0834069\pi$
$864$		0			0
$865$	5.54697			0.188603
$866$		0			0
$867$	1.21802	−	2.10967i	0.0413660	−	0.0716480i
$868$		0			0
$869$	−1.18381	−	2.05043i	−0.0401581	−	0.0695559i
$870$		0			0
$871$	11.9976	−	20.7804i	0.406523	−	0.704118i
$872$		0			0
$873$	−0.795165	+	1.37727i	−0.0269123	+	0.0466134i
$874$		0			0
$875$	−1.53626	−	2.66088i	−0.0519351	−	0.0899543i
$876$		0			0
$877$	−45.7605			−1.54522			−0.772611	−	0.634880i	$-0.781049\pi$
$877$	−45.7605			−1.54522			−0.772611	+	0.634880i	$0.781049\pi$
$878$		0			0
$879$	3.46318	−	5.99840i	0.116810	−	0.202321i
$880$		0			0
$881$	−6.62702	−	11.4783i	−0.223270	−	0.386715i	0.732529	−	0.680736i	$-0.238340\pi$
$881$	−6.62702	−	11.4783i	−0.223270	−	0.386715i	−0.955799	+	0.294021i	$0.905006\pi$
$882$		0			0
$883$	11.2805	+	19.5384i	0.379618	+	0.657518i	0.991007	−	0.133813i	$-0.0427220\pi$
$883$	11.2805	+	19.5384i	0.379618	+	0.657518i	−0.611388	+	0.791331i	$0.709389\pi$
$884$		0			0
$885$	8.12842	+	14.0788i	0.273234	+	0.473255i
$886$		0			0
$887$	42.7077			1.43398			0.716992	−	0.697081i	$-0.245518\pi$
$887$	42.7077			1.43398			0.716992	+	0.697081i	$0.245518\pi$
$888$		0			0
$889$	−50.5220			−1.69445
$890$		0			0
$891$	12.6100	+	21.8412i	0.422452	+	0.731708i
$892$		0			0
$893$	2.98052	+	5.16241i	0.0997392	+	0.172753i
$894$		0			0
$895$	10.6815	+	18.5009i	0.357044	+	0.618418i
$896$		0			0
$897$	−13.7847	+	23.8758i	−0.460258	+	0.797190i
$898$		0			0
$899$	8.13866			0.271439
$900$		0			0
$901$	−5.56008	−	9.63033i	−0.185233	−	0.320833i
$902$		0			0
$903$	−15.5877	+	26.9987i	−0.518727	+	0.898462i
$904$		0			0
$905$	1.13711	−	1.96954i	0.0377989	−	0.0654696i
$906$		0			0
$907$	19.8574	+	34.3941i	0.659356	+	1.14204i	0.980783	+	0.195103i	$0.0625042\pi$
$907$	19.8574	+	34.3941i	0.659356	+	1.14204i	−0.321427	+	0.946934i	$0.604162\pi$
$908$		0			0
$909$	−1.13757	+	1.97033i	−0.0377308	+	0.0653516i
$910$		0			0
$911$	−46.3504			−1.53566			−0.767828	−	0.640656i	$-0.778662\pi$
$911$	−46.3504			−1.53566			−0.767828	+	0.640656i	$0.778662\pi$
$912$		0			0
$913$	−18.0395	+	31.2454i	−0.597022	+	1.03407i
$914$		0			0
$915$	−11.6400			−0.384805
$916$		0			0
$917$	−5.25230			−0.173446
$918$		0			0
$919$	−23.2723			−0.767683			−0.383841	−	0.923399i	$-0.625399\pi$
$919$	−23.2723			−0.767683			−0.383841	+	0.923399i	$0.625399\pi$
$920$		0			0
$921$	6.25846	+	10.8400i	0.206223	+	0.357189i
$922$		0			0
$923$	3.98805	−	6.90751i	0.131268	−	0.227363i
$924$		0			0
$925$	2.39056	−	5.59332i	0.0786010	−	0.183907i
$926$		0			0
$927$	3.59721	−	6.23055i	0.118148	−	0.204638i
$928$		0			0
$929$	−21.8368	−	37.8224i	−0.716442	−	1.24091i	−0.962401	−	0.271633i	$-0.912436\pi$
$929$	−21.8368	−	37.8224i	−0.716442	−	1.24091i	0.245959	−	0.969280i	$-0.420897\pi$
$930$		0			0
$931$	4.38011			0.143552
$932$		0			0
$933$	−29.0814			−0.952084
$934$		0			0
$935$	−13.4456			−0.439718
$936$		0			0
$937$	−11.4758	+	19.8766i	−0.374897	+	0.649341i	−0.990312	−	0.138863i	$-0.955655\pi$
$937$	−11.4758	+	19.8766i	−0.374897	+	0.649341i	0.615414	+	0.788204i	$0.288989\pi$
$938$		0			0
$939$	−22.7264			−0.741649
$940$		0			0
$941$	−17.7649	+	30.7696i	−0.579118	+	1.00306i	0.416463	+	0.909153i	$0.363270\pi$
$941$	−17.7649	+	30.7696i	−0.579118	+	1.00306i	−0.995581	+	0.0939088i	$0.970064\pi$
$942$		0			0
$943$	−30.3300	−	52.5332i	−0.987682	−	1.71072i
$944$		0			0
$945$	8.47760	−	14.6836i	0.275776	−	0.477658i
$946$		0			0
$947$	−23.3398	+	40.4257i	−0.758440	+	1.31366i	0.185205	+	0.982700i	$0.440705\pi$
$947$	−23.3398	+	40.4257i	−0.758440	+	1.31366i	−0.943646	+	0.330957i	$0.892628\pi$
$948$		0			0
$949$	4.48557	+	7.76923i	0.145608	+	0.252200i
$950$		0			0
$951$	−41.7865			−1.35502
$952$		0			0
$953$	−2.71628	+	4.70473i	−0.0879888	+	0.152401i	−0.906661	−	0.421860i	$-0.861377\pi$
$953$	−2.71628	+	4.70473i	−0.0879888	+	0.152401i	0.818672	+	0.574261i	$0.194711\pi$
$954$		0			0
$955$	8.14332	+	14.1046i	0.263512	+	0.456416i
$956$		0			0
$957$	6.09926	+	10.5642i	0.197161	+	0.341493i
$958$		0			0
$959$	−13.5349	−	23.4432i	−0.437066	−	0.757020i
$960$		0			0
$961$	−17.8276			−0.575084
$962$		0			0
$963$	−2.50893			−0.0808491
$964$		0			0
$965$	4.15315	+	7.19347i	0.133695	+	0.231566i
$966$		0			0
$967$	7.09769	+	12.2936i	0.228246	+	0.395334i	0.957288	−	0.289135i	$-0.0933675\pi$
$967$	7.09769	+	12.2936i	0.228246	+	0.395334i	−0.729042	+	0.684469i	$0.760034\pi$
$968$		0			0
$969$	5.61651	+	9.72807i	0.180428	+	0.312511i
$970$		0			0
$971$	20.4125	−	35.3554i	0.655067	−	1.13461i	−0.326810	−	0.945090i	$-0.605974\pi$
$971$	20.4125	−	35.3554i	0.655067	−	1.13461i	0.981877	−	0.189519i	$-0.0606929\pi$
$972$		0			0
$973$	−38.1818			−1.22405
$974$		0			0
$975$	1.50433	+	2.60558i	0.0481772	+	0.0834453i
$976$		0			0
$977$	−5.36367	+	9.29015i	−0.171599	+	0.297218i	−0.938979	−	0.343974i	$-0.888227\pi$
$977$	−5.36367	+	9.29015i	−0.171599	+	0.297218i	0.767380	+	0.641193i	$0.221560\pi$
$978$		0			0
$979$	−14.6790	+	25.4247i	−0.469142	+	0.812578i
$980$		0			0
$981$	−3.19767	−	5.53853i	−0.102094	−	0.176832i
$982$		0			0
$983$	−11.8899	+	20.5939i	−0.379229	+	0.656845i	−0.990950	−	0.134229i	$-0.957144\pi$
$983$	−11.8899	+	20.5939i	−0.379229	+	0.656845i	0.611721	+	0.791074i	$0.290478\pi$
$984$		0			0
$985$	−21.1725			−0.674611
$986$		0			0
$987$	8.11899	−	14.0625i	0.258430	−	0.447614i
$988$		0			0
$989$	−58.4295			−1.85795
$990$		0			0
$991$	−40.0740			−1.27299			−0.636496	−	0.771280i	$-0.719617\pi$
$991$	−40.0740			−1.27299			−0.636496	+	0.771280i	$0.719617\pi$
$992$		0			0
$993$	−27.9104			−0.885710
$994$		0			0
$995$	0.109262	+	0.189248i	0.00346384	+	0.00599955i
$996$		0			0
$997$	3.21670	−	5.57148i	0.101874	−	0.176451i	−0.810583	−	0.585624i	$-0.800850\pi$
$997$	3.21670	−	5.57148i	0.101874	−	0.176451i	0.912457	+	0.409173i	$0.134183\pi$
$998$		0			0
$999$	33.3265	−	4.00839i	1.05440	−	0.126820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.i.a.121.3	✓	14
37.26	even	3	inner	740.2.i.a.581.3	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.i.a.121.3	✓	14	1.1	even	1	trivial
740.2.i.a.581.3	yes	14	37.26	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.795627 - 1.37807i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.53626 - 2.66088i) q^{7} +(0.233956 - 0.405224i) q^{9} +3.41859 q^{11} +(0.945375 + 1.63744i) q^{13} +(-0.795627 + 1.37807i) q^{15} +(1.96654 - 3.40615i) q^{17} +(-0.897417 - 1.55437i) q^{19} +(-2.44458 + 4.23414i) q^{21} -9.16334 q^{23} +(-0.500000 + 0.866025i) q^{25} -5.51833 q^{27} -2.24244 q^{29} -3.62938 q^{31} +(-2.71992 - 4.71105i) q^{33} +(-1.53626 + 2.66088i) q^{35} +(-6.03924 + 0.726378i) q^{37} +(1.50433 - 2.60558i) q^{39} +(3.30993 + 5.73297i) q^{41} +6.37644 q^{43} -0.467912 q^{45} -3.32122 q^{47} +(-1.22020 + 2.11345i) q^{49} -6.25853 q^{51} +(1.41367 - 2.44855i) q^{53} +(-1.70930 - 2.96059i) q^{55} +(-1.42802 + 2.47340i) q^{57} +(5.10819 - 8.84764i) q^{59} +(3.65748 + 6.33494i) q^{61} -1.43767 q^{63} +(0.945375 - 1.63744i) q^{65} +(-6.34541 - 10.9906i) q^{67} +(7.29060 + 12.6277i) q^{69} +(-2.10924 - 3.65331i) q^{71} +4.74475 q^{73} +1.59125 q^{75} +(-5.25185 - 9.09648i) q^{77} +(-0.346287 - 0.599786i) q^{79} +(3.68866 + 6.38895i) q^{81} +(-5.27689 + 9.13984i) q^{83} -3.93308 q^{85} +(1.78414 + 3.09023i) q^{87} +(-4.29386 + 7.43719i) q^{89} +(2.90469 - 5.03107i) q^{91} +(2.88763 + 5.00152i) q^{93} +(-0.897417 + 1.55437i) q^{95} -3.39878 q^{97} +(0.799801 - 1.38530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) \) 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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