LMFDB - Embedded newform 740.2.cc.a.17.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(17,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.cc (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	740.17
Dual form			740.2.cc.a.653.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.42609 + 0.998562i) q^{3} +(-1.41528 - 1.73118i) q^{5} +(0.136680 + 1.56226i) q^{7} +(0.0105581 - 0.0290083i) q^{9} +(2.07693 - 1.19912i) q^{11} +(-2.59943 + 0.946115i) q^{13} +(3.74701 + 1.05558i) q^{15} +(0.0137279 - 0.0377171i) q^{17} +(-2.33571 - 3.33574i) q^{19} +(-1.75493 - 2.09144i) q^{21} +(1.98130 - 3.43171i) q^{23} +(-0.993958 + 4.90021i) q^{25} +(-1.33786 - 4.99294i) q^{27} +(1.14194 - 4.26176i) q^{29} +(6.05569 - 6.05569i) q^{31} +(-1.76451 + 3.78399i) q^{33} +(2.51111 - 2.44765i) q^{35} +(-2.40978 - 5.58506i) q^{37} +(2.76228 - 3.94494i) q^{39} +(-1.99128 - 5.47099i) q^{41} -3.96556 q^{43} +(-0.0651612 + 0.0227768i) q^{45} +(6.78359 - 1.81766i) q^{47} +(4.47169 - 0.788479i) q^{49} +(0.0180856 + 0.0674963i) q^{51} +(-0.974499 + 11.1386i) q^{53} +(-5.01532 - 1.89845i) q^{55} +(6.66189 + 2.42473i) q^{57} +(1.14585 - 13.0971i) q^{59} +(0.941466 - 2.01898i) q^{61} +(0.0467615 + 0.0125297i) q^{63} +(5.31682 + 3.16106i) q^{65} +(0.962767 - 0.0842312i) q^{67} +(0.601256 + 6.87238i) q^{69} +(-0.221860 + 1.25823i) q^{71} +(-5.46509 - 5.46509i) q^{73} +(-3.47568 - 7.98069i) q^{75} +(2.15720 + 3.08080i) q^{77} +(-10.1851 + 0.891079i) q^{79} +(6.96461 + 5.84400i) q^{81} +(7.88711 - 3.67782i) q^{83} +(-0.0847239 + 0.0296149i) q^{85} +(2.62713 + 7.21797i) q^{87} +(0.000139453 + 1.22005e-5i) q^{89} +(-1.83336 - 3.93166i) q^{91} +(-2.58900 + 14.6830i) q^{93} +(-2.46908 + 8.76455i) q^{95} +(-0.902154 - 0.520859i) q^{97} +(-0.0128557 - 0.0729086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) $ 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Character values

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

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−1.42609	+	0.998562i	−0.823356	+	0.576520i	−0.907557	−	0.419929i	$-0.862055\pi$
$3$	−1.42609	+	0.998562i	−0.823356	+	0.576520i	0.0842012	+	0.996449i	$0.473166\pi$
$4$		0			0
$5$	−1.41528	−	1.73118i	−0.632933	−	0.774207i
$5$	−1.41528	−	1.73118i	−0.632933	−	0.774207i
$6$		0			0
$7$	0.136680	+	1.56226i	0.0516601	+	0.590478i	0.977270	+	0.211999i	$0.0679972\pi$
$7$	0.136680	+	1.56226i	0.0516601	+	0.590478i	−0.925610	+	0.378479i	$0.876447\pi$
$8$		0			0
$9$	0.0105581	−	0.0290083i	0.00351938	−	0.00966942i
$10$		0			0
$11$	2.07693	−	1.19912i	0.626218	−	0.361547i	−0.153068	−	0.988216i	$-0.548915\pi$
$11$	2.07693	−	1.19912i	0.626218	−	0.361547i	0.779286	+	0.626669i	$0.215582\pi$
$12$		0			0
$13$	−2.59943	+	0.946115i	−0.720952	+	0.262405i	−0.676330	−	0.736599i	$-0.736431\pi$
$13$	−2.59943	+	0.946115i	−0.720952	+	0.262405i	−0.0446223	+	0.999004i	$0.514208\pi$
$14$		0			0
$15$	3.74701	+	1.05558i	0.967475	+	0.272549i
$16$		0			0
$17$	0.0137279	−	0.0377171i	0.00332951	−	0.00914774i	−0.938017	−	0.346590i	$-0.887340\pi$
$17$	0.0137279	−	0.0377171i	0.00332951	−	0.00914774i	0.941346	+	0.337442i	$0.109562\pi$
$18$		0			0
$19$	−2.33571	−	3.33574i	−0.535849	−	0.765272i	0.456368	−	0.889791i	$-0.349150\pi$
$19$	−2.33571	−	3.33574i	−0.535849	−	0.765272i	−0.992217	+	0.124519i	$0.960261\pi$
$20$		0			0
$21$	−1.75493	−	2.09144i	−0.382957	−	0.456390i
$22$		0			0
$23$	1.98130	−	3.43171i	0.413129	−	0.715560i	−0.582101	−	0.813116i	$-0.697769\pi$
$23$	1.98130	−	3.43171i	0.413129	−	0.715560i	0.995230	+	0.0975562i	$0.0311026\pi$
$24$		0			0
$25$	−0.993958	+	4.90021i	−0.198792	+	0.980042i
$26$		0			0
$27$	−1.33786	−	4.99294i	−0.257470	−	0.960892i
$28$		0			0
$29$	1.14194	−	4.26176i	0.212052	−	0.791390i	−0.775131	−	0.631800i	$-0.782316\pi$
$29$	1.14194	−	4.26176i	0.212052	−	0.791390i	0.987183	−	0.159589i	$-0.0510170\pi$
$30$		0			0
$31$	6.05569	−	6.05569i	1.08763	−	1.08763i	0.0918632	−	0.995772i	$-0.470718\pi$
$31$	6.05569	−	6.05569i	1.08763	−	1.08763i	0.995772	−	0.0918632i	$-0.0292823\pi$
$32$		0			0
$33$	−1.76451	+	3.78399i	−0.307161	+	0.658709i
$34$		0			0
$35$	2.51111	−	2.44765i	0.424454	−	0.413728i
$36$		0			0
$37$	−2.40978	−	5.58506i	−0.396166	−	0.918179i
$37$	−2.40978	−	5.58506i	−0.396166	−	0.918179i
$38$		0			0
$39$	2.76228	−	3.94494i	0.442318	−	0.631696i
$40$		0			0
$41$	−1.99128	−	5.47099i	−0.310985	−	0.854425i	−0.992458	−	0.122582i	$-0.960883\pi$
$41$	−1.99128	−	5.47099i	−0.310985	−	0.854425i	0.681473	−	0.731843i	$-0.261340\pi$
$42$		0			0
$43$	−3.96556			−0.604742			−0.302371	−	0.953190i	$-0.597778\pi$
$43$	−3.96556			−0.604742			−0.302371	+	0.953190i	$0.597778\pi$
$44$		0			0
$45$	−0.0651612	+	0.0227768i	−0.00971366	+	0.00339537i
$46$		0			0
$47$	6.78359	−	1.81766i	0.989489	−	0.265133i	0.272453	−	0.962169i	$-0.412165\pi$
$47$	6.78359	−	1.81766i	0.989489	−	0.265133i	0.717036	+	0.697036i	$0.245498\pi$
$48$		0			0
$49$	4.47169	−	0.788479i	0.638813	−	0.112640i
$50$		0			0
$51$	0.0180856	+	0.0674963i	0.00253249	+	0.00945137i
$52$		0			0
$53$	−0.974499	+	11.1386i	−0.133858	+	1.53000i	0.571176	+	0.820828i	$0.306487\pi$
$53$	−0.974499	+	11.1386i	−0.133858	+	1.53000i	−0.705034	+	0.709174i	$0.749068\pi$
$54$		0			0
$55$	−5.01532	−	1.89845i	−0.676266	−	0.255987i
$56$		0			0
$57$	6.66189	+	2.42473i	0.882389	+	0.321163i
$58$		0			0
$59$	1.14585	−	13.0971i	0.149177	−	1.70510i	−0.440739	−	0.897635i	$-0.645283\pi$
$59$	1.14585	−	13.0971i	0.149177	−	1.70510i	0.589916	−	0.807465i	$-0.299161\pi$
$60$		0			0
$61$	0.941466	−	2.01898i	0.120542	−	0.258504i	−0.836773	−	0.547550i	$-0.815560\pi$
$61$	0.941466	−	2.01898i	0.120542	−	0.258504i	0.957315	+	0.289046i	$0.0933382\pi$
$62$		0			0
$63$	0.0467615	+	0.0125297i	0.00589139	+	0.00157859i
$64$		0			0
$65$	5.31682	+	3.16106i	0.659470	+	0.392081i
$66$		0			0
$67$	0.962767	−	0.0842312i	0.117621	−	0.0102905i	−0.0281934	−	0.999602i	$-0.508975\pi$
$67$	0.962767	−	0.0842312i	0.117621	−	0.0102905i	0.145814	+	0.989312i	$0.453420\pi$
$68$		0			0
$69$	0.601256	+	6.87238i	0.0723827	+	0.827338i
$70$		0			0
$71$	−0.221860	+	1.25823i	−0.0263300	+	0.149325i	−0.995138	−	0.0984860i	$-0.968600\pi$
$71$	−0.221860	+	1.25823i	−0.0263300	+	0.149325i	0.968808	+	0.247811i	$0.0797111\pi$
$72$		0			0
$73$	−5.46509	−	5.46509i	−0.639640	−	0.639640i	0.310827	−	0.950467i	$-0.399394\pi$
$73$	−5.46509	−	5.46509i	−0.639640	−	0.639640i	−0.950467	+	0.310827i	$0.899394\pi$
$74$		0			0
$75$	−3.47568	−	7.98069i	−0.401337	−	0.921530i
$76$		0			0
$77$	2.15720	+	3.08080i	0.245836	+	0.351090i
$78$		0			0
$79$	−10.1851	+	0.891079i	−1.14591	+	0.100254i	−0.644253	−	0.764812i	$-0.722832\pi$
$79$	−10.1851	+	0.891079i	−1.14591	+	0.100254i	−0.501658	+	0.865066i	$0.667276\pi$
$80$		0			0
$81$	6.96461	+	5.84400i	0.773846	+	0.649334i
$82$		0			0
$83$	7.88711	−	3.67782i	0.865722	−	0.403693i	0.0615605	−	0.998103i	$-0.480392\pi$
$83$	7.88711	−	3.67782i	0.865722	−	0.403693i	0.804162	+	0.594410i	$0.202615\pi$
$84$		0			0
$85$	−0.0847239	+	0.0296149i	−0.00918960	+	0.00321218i
$86$		0			0
$87$	2.62713	+	7.21797i	0.281658	+	0.773848i
$88$		0			0
$89$	0.000139453	0	1.22005e-5i	1.47820e−5	0	1.29326e-6i	0.0871631	−	0.996194i	$-0.472220\pi$
$89$	0.000139453	0	1.22005e-5i	1.47820e−5	0	1.29326e-6i	−0.0871484	+	0.996195i	$0.527775\pi$
$90$		0			0
$91$	−1.83336	−	3.93166i	−0.192189	−	0.412150i
$92$		0			0
$93$	−2.58900	+	14.6830i	−0.268467	+	1.52255i
$94$		0			0
$95$	−2.46908	+	8.76455i	−0.253322	+	0.899224i
$96$		0			0
$97$	−0.902154	−	0.520859i	−0.0915999	−	0.0528852i	0.453500	−	0.891256i	$-0.350175\pi$
$97$	−0.902154	−	0.520859i	−0.0915999	−	0.0528852i	−0.545100	+	0.838371i	$0.683508\pi$
$98$		0			0
$99$	−0.0128557	−	0.0729086i	−0.00129205	−	0.00732759i
$100$		0			0
$101$	8.34072	+	4.81552i	0.829932	+	0.479162i	0.853830	−	0.520553i	$-0.174274\pi$
$101$	8.34072	+	4.81552i	0.829932	+	0.479162i	−0.0238971	+	0.999714i	$0.507607\pi$
$102$		0			0
$103$	1.54796	−	0.893714i	0.152525	−	0.0880603i	−0.421795	−	0.906691i	$-0.638600\pi$
$103$	1.54796	−	0.893714i	0.152525	−	0.0880603i	0.574320	+	0.818631i	$0.305267\pi$
$104$		0			0
$105$	−1.13694	+	5.99807i	−0.110954	+	0.585352i
$106$		0			0
$107$	−2.52760	−	1.17864i	−0.244352	−	0.113943i	0.296584	−	0.955007i	$-0.404152\pi$
$107$	−2.52760	−	1.17864i	−0.244352	−	0.113943i	−0.540937	+	0.841063i	$0.681930\pi$
$108$		0			0
$109$	−9.23197	−	6.46429i	−0.884262	−	0.619167i	0.0407230	−	0.999170i	$-0.487034\pi$
$109$	−9.23197	−	6.46429i	−0.884262	−	0.619167i	−0.924985	+	0.380004i	$0.875923\pi$
$110$		0			0
$111$	9.01361	+	5.55851i	0.855534	+	0.527590i
$112$		0			0
$113$	−11.9063	+	2.09939i	−1.12005	+	0.197494i	−0.702861	−	0.711327i	$-0.748094\pi$
$113$	−11.9063	+	2.09939i	−1.12005	+	0.197494i	−0.417185	+	0.908822i	$0.636983\pi$
$114$		0			0
$115$	−8.74499	+	1.42685i	−0.815474	+	0.133055i
$116$		0			0
$117$			0.0853942i			0.00789470i
$118$		0			0
$119$	0.0608001	+	0.0162913i	0.00557354	+	0.00149343i
$120$		0			0
$121$	−2.62424	+	4.54532i	−0.238568	+	0.413211i
$122$		0			0
$123$	8.30287	+	5.81373i	0.748644	+	0.524206i
$124$		0			0
$125$	9.88987	−	5.21446i	0.884577	−	0.466395i
$126$		0			0
$127$	−6.43910	−	0.563348i	−0.571378	−	0.0499891i	−0.202194	−	0.979346i	$-0.564807\pi$
$127$	−6.43910	−	0.563348i	−0.571378	−	0.0499891i	−0.369184	+	0.929356i	$0.620363\pi$
$128$		0			0
$129$	5.65526	−	3.95985i	0.497918	−	0.348646i
$130$		0			0
$131$	−1.76644	+	0.823703i	−0.154334	+	0.0719673i	−0.498251	−	0.867033i	$-0.666024\pi$
$131$	−1.76644	+	0.823703i	−0.154334	+	0.0719673i	0.343916	+	0.939000i	$0.388246\pi$
$132$		0			0
$133$	4.89204	−	4.10491i	0.424194	−	0.355941i
$134$		0			0
$135$	−6.75023	+	9.38249i	−0.580968	+	0.807516i
$136$		0			0
$137$	−4.75539	+	17.7473i	−0.406280	+	1.51626i	0.395403	+	0.918508i	$0.370605\pi$
$137$	−4.75539	+	17.7473i	−0.406280	+	1.51626i	−0.801683	+	0.597750i	$0.796062\pi$
$138$		0			0
$139$	−20.0764	−	7.30721i	−1.70286	−	0.619789i	−0.706711	−	0.707502i	$-0.749822\pi$
$139$	−20.0764	−	7.30721i	−1.70286	−	0.619789i	−0.996146	+	0.0877129i	$0.972044\pi$
$140$		0			0
$141$	−7.85900	+	9.36599i	−0.661847	+	0.788759i
$142$		0			0
$143$	−4.26433	+	5.08203i	−0.356601	+	0.424981i
$144$		0			0
$145$	−8.99404	+	4.05470i	−0.746914	+	0.336724i
$146$		0			0
$147$	−5.58970	+	5.58970i	−0.461031	+	0.461031i
$148$		0			0
$149$		−	19.5882i		−	1.60473i	−0.596835	−	0.802364i	$-0.703575\pi$
$149$		−	19.5882i		−	1.60473i	0.596835	−	0.802364i	$-0.296425\pi$
$150$		0			0
$151$	1.41804	+	0.250038i	0.115398	+	0.0203478i	0.231049	−	0.972942i	$-0.425784\pi$
$151$	1.41804	+	0.250038i	0.115398	+	0.0203478i	−0.115651	+	0.993290i	$0.536895\pi$
$152$		0			0
$153$	−0.000949167	0	0.000796446i	−7.67356e−5	0	6.43888e-5i
$154$		0			0
$155$	−19.0540	−	1.91298i	−1.53045	−	0.153654i
$156$		0			0
$157$	2.37646	+	5.09634i	0.189662	+	0.406732i	0.978028	−	0.208475i	$-0.0668500\pi$
$157$	2.37646	+	5.09634i	0.189662	+	0.406732i	−0.788365	+	0.615208i	$0.789072\pi$
$158$		0			0
$159$	−9.73283	−	16.8578i	−0.771864	−	1.33691i
$160$		0			0
$161$	5.63201	+	2.62625i	0.443865	+	0.206977i
$162$		0			0
$163$	0.503054	+	0.599517i	0.0394023	+	0.0469578i	0.785386	−	0.619007i	$-0.212465\pi$
$163$	0.503054	+	0.599517i	0.0394023	+	0.0469578i	−0.745983	+	0.665965i	$0.768020\pi$
$164$		0			0
$165$	9.04804	−	2.30074i	0.704389	−	0.179113i
$166$		0			0
$167$	6.77505	+	1.19462i	0.524269	+	0.0924428i	0.429518	−	0.903058i	$-0.358683\pi$
$167$	6.77505	+	1.19462i	0.524269	+	0.0924428i	0.0947511	+	0.995501i	$0.469794\pi$
$168$		0			0
$169$	−4.09667	+	3.43752i	−0.315129	+	0.264424i
$170$		0			0
$171$	−0.121425	+	0.0325357i	−0.00928560	+	0.00248807i
$172$		0			0
$173$	−11.9443	+	17.0583i	−0.908110	+	1.29692i	0.0464578	+	0.998920i	$0.485207\pi$
$173$	−11.9443	+	17.0583i	−0.908110	+	1.29692i	−0.954568	+	0.297995i	$0.903682\pi$
$174$		0			0
$175$	−7.79124	−	0.883058i	−0.588962	−	0.0667529i
$176$		0			0
$177$	11.4442	+	19.8219i	0.860199	+	1.48991i
$178$		0			0
$179$	9.08732	+	9.08732i	0.679218	+	0.679218i	0.959823	−	0.280605i	$-0.0905352\pi$
$179$	9.08732	+	9.08732i	0.679218	+	0.679218i	−0.280605	+	0.959823i	$0.590535\pi$
$180$		0			0
$181$	14.1431	−	5.14766i	1.05125	−	0.382623i	0.242114	−	0.970248i	$-0.422159\pi$
$181$	14.1431	−	5.14766i	1.05125	−	0.382623i	0.809133	+	0.587625i	$0.199937\pi$
$182$		0			0
$183$	0.673458	+	3.81937i	0.0497834	+	0.282336i
$184$		0			0
$185$	−6.25822	+	12.0762i	−0.460114	+	0.887860i
$186$		0			0
$187$	−0.0167153	−	0.0947971i	−0.00122234	−	0.00693225i
$188$		0			0
$189$	7.61740	−	2.77251i	0.554085	−	0.201670i
$190$		0			0
$191$	10.7672	+	10.7672i	0.779090	+	0.779090i	0.979676	−	0.200586i	$-0.0642845\pi$
$191$	10.7672	+	10.7672i	0.779090	+	0.779090i	−0.200586	+	0.979676i	$0.564285\pi$
$192$		0			0
$193$	−2.66304	−	4.61252i	−0.191690	−	0.332017i	0.754120	−	0.656736i	$-0.228063\pi$
$193$	−2.66304	−	4.61252i	−0.191690	−	0.332017i	−0.945810	+	0.324719i	$0.894730\pi$
$194$		0			0
$195$	−10.7388	+	0.801206i	−0.769021	+	0.0573755i
$196$		0			0
$197$	6.35339	−	9.07359i	0.452661	−	0.646466i	−0.526352	−	0.850267i	$-0.676441\pi$
$197$	6.35339	−	9.07359i	0.452661	−	0.646466i	0.979012	+	0.203801i	$0.0653294\pi$
$198$		0			0
$199$	19.0018	−	5.09152i	1.34700	−	0.360928i	0.487975	−	0.872857i	$-0.337736\pi$
$199$	19.0018	−	5.09152i	1.34700	−	0.360928i	0.859028	+	0.511929i	$0.171069\pi$
$200$		0			0
$201$	−1.28889	+	1.08150i	−0.0909111	+	0.0762834i
$202$		0			0
$203$	6.81405	+	1.20150i	0.478253	+	0.0843288i
$204$		0			0
$205$	−6.65304	+	11.1902i	−0.464668	+	0.781560i
$206$		0			0
$207$	−0.0786290	−	0.0937064i	−0.00546510	−	0.00651305i
$208$		0			0
$209$	−8.85105	−	4.12731i	−0.612240	−	0.285492i
$210$		0			0
$211$	−1.93788	−	3.35650i	−0.133409	−	0.231071i	0.791580	−	0.611066i	$-0.209259\pi$
$211$	−1.93788	−	3.35650i	−0.133409	−	0.231071i	−0.924989	+	0.379995i	$0.875926\pi$
$212$		0			0
$213$	−0.940029	−	2.01590i	−0.0644097	−	0.138127i
$214$		0			0
$215$	5.61238	+	6.86509i	0.382761	+	0.468195i
$216$		0			0
$217$	10.2882	+	8.63286i	0.698411	+	0.586037i
$218$		0			0
$219$	13.2510	+	2.33650i	0.895416	+	0.157886i
$220$		0			0
$221$			0.111031i			0.00746877i
$222$		0			0
$223$	19.6240	−	19.6240i	1.31412	−	1.31412i	0.395766	−	0.918351i	$-0.370479\pi$
$223$	19.6240	−	19.6240i	1.31412	−	1.31412i	0.918351	−	0.395766i	$-0.129521\pi$
$224$		0			0
$225$	0.131652	+	0.0805701i	0.00877682	+	0.00537134i
$226$		0			0
$227$	−1.17459	+	1.39982i	−0.0779604	+	0.0929096i	−0.803615	−	0.595150i	$-0.797093\pi$
$227$	−1.17459	+	1.39982i	−0.0779604	+	0.0929096i	0.725654	+	0.688059i	$0.241537\pi$
$228$		0			0
$229$	−6.93291	+	8.26232i	−0.458139	+	0.545989i	−0.944820	−	0.327591i	$-0.893763\pi$
$229$	−6.93291	+	8.26232i	−0.458139	+	0.545989i	0.486680	+	0.873580i	$0.338208\pi$
$230$		0			0
$231$	−6.15274	−	2.23942i	−0.404821	−	0.147343i
$232$		0			0
$233$	3.17974	−	11.8669i	0.208312	−	0.777429i	−0.780103	−	0.625651i	$-0.784833\pi$
$233$	3.17974	−	11.8669i	0.208312	−	0.777429i	0.988415	−	0.151778i	$-0.0485000\pi$
$234$		0			0
$235$	−12.7474	−	9.17111i	−0.831548	−	0.598257i
$236$		0			0
$237$	13.6351	−	11.4412i	0.885694	−	0.743185i
$238$		0			0
$239$	−5.00091	+	2.33196i	−0.323482	+	0.150842i	−0.577575	−	0.816338i	$-0.696001\pi$
$239$	−5.00091	+	2.33196i	−0.323482	+	0.150842i	0.254093	+	0.967180i	$0.418223\pi$
$240$		0			0
$241$	3.53598	−	2.47592i	0.227773	−	0.159488i	−0.454120	−	0.890941i	$-0.650046\pi$
$241$	3.53598	−	2.47592i	0.227773	−	0.159488i	0.681892	+	0.731453i	$0.261157\pi$
$242$		0			0
$243$	−0.319577	−	0.0279593i	−0.0205008	−	0.00179359i
$244$		0			0
$245$	−7.69370	−	6.62537i	−0.491532	−	0.423279i
$246$		0			0
$247$	9.22752	+	6.46118i	0.587133	+	0.411115i
$248$		0			0
$249$	−7.57523	+	13.1207i	−0.480060	+	0.831489i
$250$		0			0
$251$	−6.10700	−	1.63636i	−0.385470	−	0.103286i	0.0608794	−	0.998145i	$-0.480610\pi$
$251$	−6.10700	−	1.63636i	−0.385470	−	0.103286i	−0.446349	+	0.894859i	$0.647276\pi$
$252$		0			0
$253$		−	9.50321i		−	0.597462i
$254$		0			0
$255$	0.0912520	−	0.126836i	0.00571442	−	0.00794276i
$256$		0			0
$257$	−7.43637	+	1.31123i	−0.463868	+	0.0817925i	−0.400698	−	0.916210i	$-0.631232\pi$
$257$	−7.43637	+	1.31123i	−0.463868	+	0.0817925i	−0.0631704	+	0.998003i	$0.520121\pi$
$258$		0			0
$259$	8.39594	−	4.52807i	0.521698	−	0.281360i
$260$		0			0
$261$	−0.111570	−	0.0781219i	−0.00690599	−	0.00483563i
$262$		0			0
$263$	21.6511	+	10.0961i	1.33506	+	0.622549i	0.953388	−	0.301748i	$-0.0975702\pi$
$263$	21.6511	+	10.0961i	1.33506	+	0.622549i	0.381673	+	0.924297i	$0.375348\pi$
$264$		0			0
$265$	20.6621	−	14.0772i	1.26926	−	0.864755i
$266$		0			0
$267$	−0.000211056	0	0.000121853i	−1.29164e−5	0	7.45730e-6i
$268$		0			0
$269$	6.82799	+	3.94214i	0.416310	+	0.240357i	0.693497	−	0.720459i	$-0.256069\pi$
$269$	6.82799	+	3.94214i	0.416310	+	0.240357i	−0.277187	+	0.960816i	$0.589402\pi$
$270$		0			0
$271$	0.582593	+	3.30405i	0.0353900	+	0.200707i	0.997376	−	0.0723908i	$-0.0230629\pi$
$271$	0.582593	+	3.30405i	0.0353900	+	0.200707i	−0.961986	+	0.273098i	$0.911952\pi$
$272$		0			0
$273$	6.54056	+	3.77619i	0.395853	+	0.228546i
$274$		0			0
$275$	3.81154	+	11.3693i	0.229844	+	0.685592i
$276$		0			0
$277$	−1.79190	+	10.1624i	−0.107665	+	0.610597i	0.882458	+	0.470392i	$0.155887\pi$
$277$	−1.79190	+	10.1624i	−0.107665	+	0.610597i	−0.990122	+	0.140205i	$0.955224\pi$
$278$		0			0
$279$	−0.111728	−	0.239602i	−0.00668900	−	0.0143446i
$280$		0			0
$281$	−17.3751	−	1.52012i	−1.03651	−	0.0906828i	−0.443821	−	0.896115i	$-0.646378\pi$
$281$	−17.3751	−	1.52012i	−1.03651	−	0.0906828i	−0.592688	+	0.805432i	$0.701933\pi$
$282$		0			0
$283$	−5.99868	−	16.4812i	−0.356585	−	0.979708i	−0.980206	−	0.197982i	$-0.936561\pi$
$283$	−5.99868	−	16.4812i	−0.356585	−	0.979708i	0.623621	−	0.781727i	$-0.285661\pi$
$284$		0			0
$285$	−5.23081	−	14.9646i	−0.309846	−	0.886426i
$286$		0			0
$287$	8.27492	−	3.85866i	0.488453	−	0.227769i
$288$		0			0
$289$	13.0215	+	10.9264i	0.765972	+	0.642727i
$290$		0			0
$291$	1.80667	−	0.158063i	0.105909	−	0.00926581i
$292$		0			0
$293$	−8.86675	−	12.6630i	−0.518001	−	0.739782i	0.471883	−	0.881661i	$-0.343574\pi$
$293$	−8.86675	−	12.6630i	−0.518001	−	0.739782i	−0.989884	+	0.141879i	$0.954686\pi$
$294$		0			0
$295$	−24.2952	+	16.5524i	−1.41452	+	0.963720i
$296$		0			0
$297$	−8.76575	−	8.76575i	−0.508640	−	0.508640i
$298$		0			0
$299$	−1.90345	+	10.7950i	−0.110079	+	0.624292i
$300$		0			0
$301$	−0.542011	−	6.19522i	−0.0312410	−	0.357086i
$302$		0			0
$303$	−16.7032	+	1.46134i	−0.959576	+	0.0839520i
$304$		0			0
$305$	−4.82766	+	1.22758i	−0.276431	+	0.0702910i
$306$		0			0
$307$	−19.6533	−	5.26608i	−1.12167	−	0.300551i	−0.350112	−	0.936708i	$-0.613857\pi$
$307$	−19.6533	−	5.26608i	−1.12167	−	0.300551i	−0.771560	+	0.636157i	$0.780523\pi$
$308$		0			0
$309$	−1.31511	+	2.82025i	−0.0748137	+	0.160439i
$310$		0			0
$311$	0.650807	−	7.43875i	0.0369039	−	0.421813i	−0.955161	−	0.296087i	$-0.904318\pi$
$311$	0.650807	−	7.43875i	0.0369039	−	0.421813i	0.992065	−	0.125726i	$-0.0401262\pi$
$312$		0			0
$313$	−29.4252	−	10.7099i	−1.66321	−	0.605359i	−0.672349	−	0.740235i	$-0.734714\pi$
$313$	−29.4252	−	10.7099i	−1.66321	−	0.605359i	−0.990863	+	0.134875i	$0.956937\pi$
$314$		0			0
$315$	−0.0444895	−	0.0986855i	−0.00250670	−	0.00556030i
$316$		0			0
$317$	0.626337	−	7.15907i	0.0351786	−	0.402093i	−0.958107	−	0.286409i	$-0.907538\pi$
$317$	0.626337	−	7.15907i	0.0351786	−	0.402093i	0.993286	−	0.115684i	$-0.0369061\pi$
$318$		0			0
$319$	−2.73863	−	10.2207i	−0.153334	−	0.572249i
$320$		0			0
$321$	4.78154	−	0.843114i	0.266879	−	0.0470580i
$322$		0			0
$323$	−0.157879	+	0.0423036i	−0.00878463	+	0.00235383i
$324$		0			0
$325$	−2.05244	−	13.6782i	−0.113849	−	0.758727i
$326$		0			0
$327$	19.6206			1.08502
$328$		0			0
$329$	3.76683	+	10.3493i	0.207672	+	0.570574i
$330$		0			0
$331$	9.11428	−	13.0165i	0.500966	−	0.715454i	−0.486431	−	0.873719i	$-0.661701\pi$
$331$	9.11428	−	13.0165i	0.500966	−	0.715454i	0.987397	+	0.158266i	$0.0505902\pi$
$332$		0			0
$333$	−0.187456	+	0.0109357i	−0.0102725	+	0.000599275i
$334$		0			0
$335$	−1.50841	−	1.54751i	−0.0824130	−	0.0845496i
$336$		0			0
$337$	5.18652	−	11.1225i	0.282528	−	0.605883i	−0.712914	−	0.701251i	$-0.752625\pi$
$337$	5.18652	−	11.1225i	0.282528	−	0.605883i	0.995442	+	0.0953684i	$0.0304029\pi$
$338$		0			0
$339$	14.8831	−	14.8831i	0.808337	−	0.808337i
$340$		0			0
$341$	5.31577	−	19.8387i	0.287865	−	1.07433i
$342$		0			0
$343$	4.68420	+	17.4817i	0.252923	+	0.943922i
$344$		0			0
$345$	11.0464	−	10.7672i	0.594717	−	0.579688i
$346$		0			0
$347$	17.0603	−	29.5494i	0.915847	−	1.58629i	0.110191	−	0.993910i	$-0.464854\pi$
$347$	17.0603	−	29.5494i	0.915847	−	1.58629i	0.805656	−	0.592384i	$-0.201813\pi$
$348$		0			0
$349$	−19.3414	−	23.0502i	−1.03532	−	1.23385i	−0.971784	−	0.235872i	$-0.924205\pi$
$349$	−19.3414	−	23.0502i	−1.03532	−	1.23385i	−0.0635399	−	0.997979i	$-0.520239\pi$
$350$		0			0
$351$	8.20156	+	11.7130i	0.437767	+	0.625196i
$352$		0			0
$353$	3.71258	−	10.2002i	0.197601	−	0.542904i	−0.800831	−	0.598891i	$-0.795608\pi$
$353$	3.71258	−	10.2002i	0.197601	−	0.542904i	0.998431	+	0.0559870i	$0.0178306\pi$
$354$		0			0
$355$	2.49222	−	1.39667i	0.132273	−	0.0741277i
$356$		0			0
$357$	−0.102975	+	0.0374797i	−0.00545000	+	0.00198364i
$358$		0			0
$359$	−12.0543	+	6.95955i	−0.636201	+	0.367311i	−0.783150	−	0.621833i	$-0.786388\pi$
$359$	−12.0543	+	6.95955i	−0.636201	+	0.367311i	0.146949	+	0.989144i	$0.453055\pi$
$360$		0			0
$361$	0.826751	−	2.27148i	0.0435132	−	0.119552i
$362$		0			0
$363$	−0.796368	−	9.10253i	−0.0417985	−	0.477759i
$364$		0			0
$365$	−1.72641	+	17.1957i	−0.0903642	+	0.900063i
$366$		0			0
$367$	−19.9455	+	13.9660i	−1.04115	+	0.729019i	−0.963431	−	0.267957i	$-0.913652\pi$
$367$	−19.9455	+	13.9660i	−1.04115	+	0.729019i	−0.0777161	+	0.996976i	$0.524763\pi$
$368$		0			0
$369$	−0.179728			−0.00935627
$370$		0			0
$371$	−17.5345			−0.910347
$372$		0			0
$373$	1.90588	−	1.33451i	0.0986828	−	0.0690984i	−0.523194	−	0.852214i	$-0.675260\pi$
$373$	1.90588	−	1.33451i	0.0986828	−	0.0690984i	0.621876	+	0.783115i	$0.286371\pi$
$374$		0			0
$375$	−8.89692	+	17.3119i	−0.459435	+	0.893985i
$376$		0			0
$377$	1.06374	+	12.1586i	0.0547852	+	0.626198i
$378$		0			0
$379$	4.18735	−	11.5047i	0.215090	−	0.590955i	−0.784484	−	0.620149i	$-0.787072\pi$
$379$	4.18735	−	11.5047i	0.215090	−	0.590955i	0.999574	+	0.0291946i	$0.00929425\pi$
$380$		0			0
$381$	9.74530	−	5.62645i	0.499267	−	0.288252i
$382$		0			0
$383$	1.60400	−	0.583808i	0.0819605	−	0.0298312i	−0.300714	−	0.953714i	$-0.597225\pi$
$383$	1.60400	−	0.583808i	0.0819605	−	0.0298312i	0.382675	+	0.923883i	$0.375003\pi$
$384$		0			0
$385$	2.28037	−	8.09470i	0.116219	−	0.412544i
$386$		0			0
$387$	−0.0418689	+	0.115034i	−0.00212832	+	0.00584750i
$388$		0			0
$389$	−6.98479	−	9.97531i	−0.354143	−	0.505768i	0.602069	−	0.798444i	$-0.294343\pi$
$389$	−6.98479	−	9.97531i	−0.354143	−	0.505768i	−0.956212	+	0.292676i	$0.905454\pi$
$390$		0			0
$391$	−0.102235	−	0.121839i	−0.00517025	−	0.00616166i
$392$		0			0
$393$	1.69659	−	2.93858i	0.0855815	−	0.148232i
$394$		0			0
$395$	15.9574	+	16.3711i	0.802902	+	0.823718i
$396$		0			0
$397$	6.12157	+	22.8460i	0.307233	+	1.14661i	0.931006	+	0.365004i	$0.118932\pi$
$397$	6.12157	+	22.8460i	0.307233	+	1.14661i	−0.623773	+	0.781606i	$0.714401\pi$
$398$		0			0
$399$	−2.87751	+	10.7390i	−0.144055	+	0.537622i
$400$		0			0
$401$	−22.9473	+	22.9473i	−1.14593	+	1.14593i	−0.158589	+	0.987345i	$0.550695\pi$
$401$	−22.9473	+	22.9473i	−1.14593	+	1.14593i	−0.987345	+	0.158589i	$0.949305\pi$
$402$		0			0
$403$	−10.0120	+	21.4707i	−0.498732	+	1.06953i
$404$		0			0
$405$	0.260128	−	20.3279i	0.0129259	−	1.01010i
$406$		0			0
$407$	−11.7021	−	8.71017i	−0.580051	−	0.431747i
$408$		0			0
$409$	−11.4320	+	16.3265i	−0.565274	+	0.807294i	−0.995433	−	0.0954584i	$-0.969568\pi$
$409$	−11.4320	+	16.3265i	−0.565274	+	0.807294i	0.430160	+	0.902753i	$0.358457\pi$
$410$		0			0
$411$	−10.9402	−	30.0579i	−0.539640	−	1.48265i
$412$		0			0
$413$	20.6177			1.01453
$414$		0			0
$415$	−17.5294	−	8.44884i	−0.860486	−	0.414737i
$416$		0			0
$417$	35.9275	−	9.62675i	1.75938	−	0.471424i
$418$		0			0
$419$	17.0399	−	3.00459i	0.832453	−	0.146784i	0.258850	−	0.965918i	$-0.416656\pi$
$419$	17.0399	−	3.00459i	0.832453	−	0.146784i	0.573603	+	0.819134i	$0.305545\pi$
$420$		0			0
$421$	5.95528	+	22.2254i	0.290243	+	1.08320i	0.944922	+	0.327294i	$0.106137\pi$
$421$	5.95528	+	22.2254i	0.290243	+	1.08320i	−0.654680	+	0.755906i	$0.727196\pi$
$422$		0			0
$423$	0.0188950	−	0.215971i	0.000918709	−	0.0105009i
$424$		0			0
$425$	0.171177	+	0.104759i	0.00830329	+	0.00508155i
$426$		0			0
$427$	3.28285	+	1.19486i	0.158868	+	0.0578232i
$428$		0			0
$429$	1.00661	−	11.5057i	0.0485998	−	0.555498i
$430$		0			0
$431$	14.3958	−	30.8719i	0.693422	−	1.48705i	−0.171522	−	0.985180i	$-0.554869\pi$
$431$	14.3958	−	30.8719i	0.693422	−	1.48705i	0.864944	−	0.501868i	$-0.167354\pi$
$432$		0			0
$433$	−10.2748	−	2.75313i	−0.493776	−	0.132307i	0.00333379	−	0.999994i	$-0.498939\pi$
$433$	−10.2748	−	2.75313i	−0.493776	−	0.132307i	−0.497110	+	0.867687i	$0.665605\pi$
$434$		0			0
$435$	8.77747	−	14.7635i	0.420848	−	0.707855i
$436$		0			0
$437$	−16.0750	+	1.40638i	−0.768973	+	0.0672764i
$438$		0			0
$439$	3.58928	+	41.0256i	0.171307	+	1.95805i	0.269819	+	0.962911i	$0.413036\pi$
$439$	3.58928	+	41.0256i	0.171307	+	1.95805i	−0.0985121	+	0.995136i	$0.531408\pi$
$440$		0			0
$441$	0.0243403	−	0.138041i	0.00115906	−	0.00657337i
$442$		0			0
$443$	12.2460	+	12.2460i	0.581826	+	0.581826i	0.935405	−	0.353579i	$-0.115035\pi$
$443$	12.2460	+	12.2460i	0.581826	+	0.581826i	−0.353579	+	0.935405i	$0.615035\pi$
$444$		0			0
$445$	−0.000176244	0	0.000258685i	−8.35476e−6	0	1.22628e-5i
$446$		0			0
$447$	19.5600	+	27.9346i	0.925158	+	1.32126i
$448$		0			0
$449$	9.22806	−	0.807351i	0.435499	−	0.0381012i	0.132701	−	0.991156i	$-0.457635\pi$
$449$	9.22806	−	0.807351i	0.435499	−	0.0381012i	0.302798	+	0.953055i	$0.402079\pi$
$450$		0			0
$451$	−10.6961	−	8.97508i	−0.503659	−	0.422620i
$452$		0			0
$453$	−2.27193	+	1.05942i	−0.106745	+	0.0497759i
$454$		0			0
$455$	−4.21168	+	8.73829i	−0.197447	+	0.409657i
$456$		0			0
$457$	−11.3366	−	31.1469i	−0.530302	−	1.45699i	−0.858713	−	0.512457i	$-0.828736\pi$
$457$	−11.3366	−	31.1469i	−0.530302	−	1.45699i	0.328412	−	0.944535i	$-0.393487\pi$
$458$		0			0
$459$	−0.206685	−	0.0180826i	−0.00964725	−	0.000844025i
$460$		0			0
$461$	6.12188	+	13.1284i	0.285124	+	0.611451i	0.995748	−	0.0921213i	$-0.0293647\pi$
$461$	6.12188	+	13.1284i	0.285124	+	0.611451i	−0.710623	+	0.703573i	$0.751587\pi$
$462$		0			0
$463$	0.726498	−	4.12018i	0.0337632	−	0.191481i	−0.963261	−	0.268566i	$-0.913450\pi$
$463$	0.726498	−	4.12018i	0.0337632	−	0.191481i	0.997025	+	0.0770852i	$0.0245614\pi$
$464$		0			0
$465$	29.0830	−	16.2985i	1.34869	−	0.755825i
$466$		0			0
$467$	4.24407	+	2.45032i	0.196392	+	0.113387i	0.594972	−	0.803747i	$-0.297163\pi$
$467$	4.24407	+	2.45032i	0.196392	+	0.113387i	−0.398579	+	0.917134i	$0.630497\pi$
$468$		0			0
$469$	0.263182	+	1.49258i	0.0121526	+	0.0689208i
$470$		0			0
$471$	−8.47808	−	4.89482i	−0.390649	−	0.225541i
$472$		0			0
$473$	−8.23618	+	4.75516i	−0.378700	+	0.218643i
$474$		0			0
$475$	18.6674	−	8.12989i	0.856521	−	0.373025i
$476$		0			0
$477$	0.312822	+	0.145871i	0.0143231	+	0.00667899i
$478$		0			0
$479$	−6.28596	−	4.40148i	−0.287213	−	0.201109i	0.421087	−	0.907020i	$-0.361649\pi$
$479$	−6.28596	−	4.40148i	−0.287213	−	0.201109i	−0.708300	+	0.705912i	$0.750538\pi$
$480$		0			0
$481$	11.5482	+	12.2381i	0.526552	+	0.558007i
$482$		0			0
$483$	−10.6542	+	1.87863i	−0.484785	+	0.0854807i
$484$		0			0
$485$	0.375102	+	2.29895i	0.0170325	+	0.104390i
$486$		0			0
$487$		−	18.0724i		−	0.818939i	−0.912324	−	0.409469i	$-0.865714\pi$
$487$		−	18.0724i		−	0.818939i	0.912324	−	0.409469i	$-0.134286\pi$
$488$		0			0
$489$	−1.31606	−	0.352636i	−0.0595142	−	0.0159468i
$490$		0			0
$491$	5.09853	−	8.83092i	0.230094	−	0.398534i	−0.727742	−	0.685851i	$-0.759430\pi$
$491$	5.09853	−	8.83092i	0.230094	−	0.398534i	0.957835	+	0.287317i	$0.0927635\pi$
$492$		0			0
$493$	−0.145065	−	0.101576i	−0.00653340	−	0.00457474i
$494$		0			0
$495$	−0.108023	+	0.125442i	−0.00485528	+	0.00563819i
$496$		0			0
$497$	−1.99601	−	0.174628i	−0.0895331	−	0.00783313i
$498$		0			0
$499$	−4.99005	+	3.49407i	−0.223385	+	0.156416i	−0.679912	−	0.733294i	$-0.737982\pi$
$499$	−4.99005	+	3.49407i	−0.223385	+	0.156416i	0.456527	+	0.889710i	$0.349093\pi$
$500$		0			0
$501$	−10.8548	+	5.06166i	−0.484955	+	0.226138i
$502$		0			0
$503$	30.7488	−	25.8013i	1.37102	−	1.15042i	0.398617	−	0.917117i	$-0.369490\pi$
$503$	30.7488	−	25.8013i	1.37102	−	1.15042i	0.972404	−	0.233305i	$-0.0749542\pi$
$504$		0			0
$505$	−3.46794	−	21.2546i	−0.154322	−	0.945816i
$506$		0			0
$507$	2.40967	−	8.99300i	0.107017	−	0.399393i
$508$		0			0
$509$	14.3850	+	5.23570i	0.637602	+	0.232068i	0.640537	−	0.767928i	$-0.278712\pi$
$509$	14.3850	+	5.23570i	0.637602	+	0.232068i	−0.00293469	+	0.999996i	$0.500934\pi$
$510$		0			0
$511$	7.79090	−	9.28484i	0.344649	−	0.410737i
$512$		0			0
$513$	−13.5303	+	16.1248i	−0.597379	+	0.711928i
$514$		0			0
$515$	−3.73798	−	1.41494i	−0.164715	−	0.0623495i
$516$		0			0
$517$	11.9095	−	11.9095i	0.523777	−	0.523777i
$518$		0			0
$519$		−	36.2538i		−	1.59137i
$520$		0			0
$521$	−21.8352	−	3.85013i	−0.956617	−	0.168677i	−0.326517	−	0.945191i	$-0.605875\pi$
$521$	−21.8352	−	3.85013i	−0.956617	−	0.168677i	−0.630100	+	0.776514i	$0.716986\pi$
$522$		0			0
$523$	−14.3297	−	12.0240i	−0.626593	−	0.525774i	0.273275	−	0.961936i	$-0.411893\pi$
$523$	−14.3297	−	12.0240i	−0.626593	−	0.525774i	−0.899868	+	0.436162i	$0.856337\pi$
$524$		0			0
$525$	11.9928	−	6.52071i	0.523410	−	0.284587i
$526$		0			0
$527$	−0.145271	−	0.311535i	−0.00632812	−	0.0135707i
$528$		0			0
$529$	3.64893	+	6.32013i	0.158649	+	0.274788i
$530$		0			0
$531$	−0.367827	−	0.171520i	−0.0159623	−	0.00744335i
$532$		0			0
$533$	10.3524	+	12.3375i	0.448411	+	0.534395i
$534$		0			0
$535$	1.53683	+	6.04383i	0.0664429	+	0.261298i
$536$		0			0
$537$	−22.0336	−	3.88512i	−0.950821	−	0.167655i
$538$		0			0
$539$	8.34190	−	6.99969i	0.359311	−	0.301498i
$540$		0			0
$541$	−5.89330	+	1.57911i	−0.253373	+	0.0678910i	−0.383270	−	0.923636i	$-0.625202\pi$
$541$	−5.89330	+	1.57911i	−0.253373	+	0.0678910i	0.129897	+	0.991528i	$0.458535\pi$
$542$		0			0
$543$	−15.0291	+	21.4638i	−0.644961	+	0.921100i
$544$		0			0
$545$	1.87498	+	25.1310i	0.0803155	+	1.07649i
$546$		0			0
$547$	−4.89040	−	8.47042i	−0.209098	−	0.362169i	0.742332	−	0.670032i	$-0.233720\pi$
$547$	−4.89040	−	8.47042i	−0.209098	−	0.362169i	−0.951431	+	0.307863i	$0.900386\pi$
$548$		0			0
$549$	−0.0486270	−	0.0486270i	−0.00207535	−	0.00207535i
$550$		0			0
$551$	−16.8834	+	6.14505i	−0.719257	+	0.261788i
$552$		0			0
$553$	−2.78419	−	15.7899i	−0.118396	−	0.671456i
$554$		0			0
$555$	−3.13402	−	23.4710i	−0.133032	−	0.996289i
$556$		0			0
$557$	−1.74396	−	9.89048i	−0.0738939	−	0.419073i	−0.999205	−	0.0398645i	$-0.987307\pi$
$557$	−1.74396	−	9.89048i	−0.0738939	−	0.419073i	0.925311	−	0.379209i	$-0.123804\pi$
$558$		0			0
$559$	10.3082	−	3.75187i	0.435990	−	0.158687i
$560$		0			0
$561$	0.118498	+	0.118498i	0.00500300	+	0.00500300i
$562$		0			0
$563$	11.8422	+	20.5113i	0.499089	+	0.864447i	0.999999	−	0.00105195i	$-0.000334845\pi$
$563$	11.8422	+	20.5113i	0.499089	+	0.864447i	−0.500911	+	0.865499i	$0.667002\pi$
$564$		0			0
$565$	20.4851	+	17.6406i	0.861815	+	0.742146i
$566$		0			0
$567$	−8.17791	+	11.6793i	−0.343440	+	0.490483i
$568$		0			0
$569$	32.3542	−	8.66928i	1.35636	−	0.363435i	0.493881	−	0.869530i	$-0.335578\pi$
$569$	32.3542	−	8.66928i	1.35636	−	0.363435i	0.862478	+	0.506094i	$0.168911\pi$
$570$		0			0
$571$	−1.85227	+	1.55424i	−0.0775151	+	0.0650429i	−0.680722	−	0.732542i	$-0.738334\pi$
$571$	−1.85227	+	1.55424i	−0.0775151	+	0.0650429i	0.603207	+	0.797585i	$0.293889\pi$
$572$		0			0
$573$	−26.1069	−	4.60334i	−1.09063	−	0.192307i
$574$		0			0
$575$	14.8468	+	13.1197i	0.619152	+	0.547131i
$576$		0			0
$577$	−25.0785	−	29.8873i	−1.04403	−	1.24423i	−0.969004	−	0.247045i	$-0.920541\pi$
$577$	−25.0785	−	29.8873i	−1.04403	−	1.24423i	−0.0750259	−	0.997182i	$-0.523904\pi$
$578$		0			0
$579$	8.40364	+	3.91868i	0.349243	+	0.162855i
$580$		0			0
$581$	6.82370	+	11.8190i	0.283095	+	0.490335i
$582$		0			0
$583$	11.3325	+	24.3026i	0.469343	+	1.00651i
$584$		0			0
$585$	0.147833	−	0.120857i	0.00611213	−	0.00499681i
$586$		0			0
$587$	−4.60693	−	3.86567i	−0.190148	−	0.159553i	0.542744	−	0.839898i	$-0.317385\pi$
$587$	−4.60693	−	3.86567i	−0.190148	−	0.159553i	−0.732892	+	0.680345i	$0.761830\pi$
$588$		0			0
$589$	−34.3446	−	6.05588i	−1.41515	−	0.249528i
$590$		0			0
$591$			19.2840i			0.793240i
$592$		0			0
$593$	17.3366	−	17.3366i	0.711927	−	0.711927i	−0.255011	−	0.966938i	$-0.582079\pi$
$593$	17.3366	−	17.3366i	0.711927	−	0.711927i	0.966938	+	0.255011i	$0.0820790\pi$
$594$		0			0
$595$	−0.0578461	−	0.128313i	−0.00237146	−	0.00526031i
$596$		0			0
$597$	−22.0142	+	26.2355i	−0.900980	+	1.07375i
$598$		0			0
$599$	−6.11123	+	7.28308i	−0.249698	+	0.297578i	−0.876305	−	0.481757i	$-0.839999\pi$
$599$	−6.11123	+	7.28308i	−0.249698	+	0.297578i	0.626607	+	0.779336i	$0.284443\pi$
$600$		0			0
$601$	45.6107	+	16.6009i	1.86050	+	0.677167i	0.978615	+	0.205702i	$0.0659479\pi$
$601$	45.6107	+	16.6009i	1.86050	+	0.677167i	0.881885	+	0.471464i	$0.156274\pi$
$602$		0			0
$603$	0.00772164	−	0.0288175i	0.000314449	−	0.00117354i
$604$		0			0
$605$	11.5828	−	1.88988i	0.470908	−	0.0768344i
$606$		0			0
$607$	−9.83742	+	8.25458i	−0.399289	+	0.335043i	−0.820219	−	0.572050i	$-0.806148\pi$
$607$	−9.83742	+	8.25458i	−0.399289	+	0.335043i	0.420930	+	0.907093i	$0.361704\pi$
$608$		0			0
$609$	−10.9172	+	5.09080i	−0.442389	+	0.206290i
$610$		0			0
$611$	−15.9138	+	11.1429i	−0.643802	+	0.450795i
$612$		0			0
$613$	−1.99094	−	0.174185i	−0.0804134	−	0.00703526i	0.0468780	−	0.998901i	$-0.485073\pi$
$613$	−1.99094	−	0.174185i	−0.0804134	−	0.00703526i	−0.127291	+	0.991865i	$0.540628\pi$
$614$		0			0
$615$	−1.68629	−	22.6018i	−0.0679977	−	0.911393i
$616$		0			0
$617$	−13.3945	−	9.37896i	−0.539244	−	0.377583i	0.271994	−	0.962299i	$-0.412317\pi$
$617$	−13.3945	−	9.37896i	−0.539244	−	0.377583i	−0.811238	+	0.584716i	$0.801206\pi$
$618$		0			0
$619$	−20.6243	+	35.7223i	−0.828959	+	1.43580i	0.0698962	+	0.997554i	$0.477733\pi$
$619$	−20.6243	+	35.7223i	−0.828959	+	1.43580i	−0.898855	+	0.438245i	$0.855600\pi$
$620$		0			0
$621$	−19.7850	−	5.30138i	−0.793945	−	0.212737i
$622$		0			0
$623$		0	0.000219529i		0	8.79524e-6i
$624$		0			0
$625$	−23.0241	−	9.74120i	−0.920964	−	0.389648i
$626$		0			0
$627$	16.7438	−	2.95239i	0.668683	−	0.117907i
$628$		0			0
$629$	−0.243734	+	0.0142189i	−0.00971830	+	0.000566943i
$630$		0			0
$631$	20.6786	+	14.4793i	0.823201	+	0.576412i	0.907511	−	0.420028i	$-0.137980\pi$
$631$	20.6786	+	14.4793i	0.823201	+	0.576412i	−0.0843099	+	0.996440i	$0.526869\pi$
$632$		0			0
$633$	6.11527	+	2.85160i	0.243060	+	0.113341i
$634$		0			0
$635$	8.13788	+	11.9445i	0.322942	+	0.474004i
$636$		0			0
$637$	−10.8779	+	6.28033i	−0.430996	+	0.248836i
$638$		0			0
$639$	0.0341567	+	0.0197204i	0.00135122	+	0.000780127i
$640$		0			0
$641$	2.26143	+	12.8252i	0.0893210	+	0.506565i	0.996340	+	0.0854755i	$0.0272409\pi$
$641$	2.26143	+	12.8252i	0.0893210	+	0.506565i	−0.907019	+	0.421089i	$0.861648\pi$
$642$		0			0
$643$	−11.3122	−	6.53112i	−0.446111	−	0.257562i	0.260076	−	0.965588i	$-0.416253\pi$
$643$	−11.3122	−	6.53112i	−0.446111	−	0.257562i	−0.706186	+	0.708026i	$0.749586\pi$
$644$		0			0
$645$	−14.8590	−	4.18595i	−0.585072	−	0.164822i
$646$		0			0
$647$	−7.72845	+	43.8302i	−0.303837	+	1.72314i	0.325092	+	0.945682i	$0.394605\pi$
$647$	−7.72845	+	43.8302i	−0.303837	+	1.72314i	−0.628929	+	0.777462i	$0.716507\pi$
$648$		0			0
$649$	−13.3251	−	28.5758i	−0.523057	−	1.12170i
$650$		0			0
$651$	−23.2924	−	2.03782i	−0.912903	−	0.0798687i
$652$		0			0
$653$	7.09874	+	19.5036i	0.277795	+	0.763236i	0.997612	+	0.0690713i	$0.0220036\pi$
$653$	7.09874	+	19.5036i	0.277795	+	0.763236i	−0.719817	+	0.694164i	$0.755774\pi$
$654$		0			0
$655$	3.92598	+	1.89225i	0.153401	+	0.0739362i
$656$		0			0
$657$	−0.216234	+	0.100832i	−0.00843609	+	0.00393381i
$658$		0			0
$659$	26.9546	+	22.6176i	1.05000	+	0.881057i	0.993094	−	0.117322i	$-0.0374309\pi$
$659$	26.9546	+	22.6176i	1.05000	+	0.881057i	0.0569094	+	0.998379i	$0.481875\pi$
$660$		0			0
$661$	50.6942	−	4.43517i	1.97178	−	0.172508i	0.973383	−	0.229183i	$-0.0736055\pi$
$661$	50.6942	−	4.43517i	1.97178	−	0.172508i	0.998393	+	0.0566751i	$0.0180499\pi$
$662$		0			0
$663$	−0.110871	−	0.158341i	−0.00430589	−	0.00614945i
$664$		0			0
$665$	−14.0300	−	2.65940i	−0.544058	−	0.103127i
$666$		0			0
$667$	−12.3626	−	12.3626i	−0.478682	−	0.478682i
$668$		0			0
$669$	−8.38987	+	47.5813i	−0.324371	+	1.83960i
$670$		0			0
$671$	−0.465633	−	5.32221i	−0.0179756	−	0.205462i
$672$		0			0
$673$	23.0690	−	2.01828i	0.889244	−	0.0777988i	0.366629	−	0.930367i	$-0.380512\pi$
$673$	23.0690	−	2.01828i	0.889244	−	0.0777988i	0.522615	+	0.852569i	$0.324956\pi$
$674$		0			0
$675$	25.7962	−	1.59299i	0.992898	−	0.0613144i
$676$		0			0
$677$	−30.1852	−	8.08809i	−1.16011	−	0.310850i	−0.373100	−	0.927791i	$-0.621705\pi$
$677$	−30.1852	−	8.08809i	−1.16011	−	0.310850i	−0.787010	+	0.616941i	$0.788372\pi$
$678$		0			0
$679$	0.690409	−	1.48059i	0.0264955	−	0.0568197i
$680$		0			0
$681$	0.277268	−	3.16918i	0.0106249	−	0.121443i
$682$		0			0
$683$	0.760676	+	0.276864i	0.0291065	+	0.0105939i	0.356532	−	0.934283i	$-0.383959\pi$
$683$	0.760676	+	0.276864i	0.0291065	+	0.0105939i	−0.327426	+	0.944877i	$0.606181\pi$
$684$		0			0
$685$	37.4540	−	16.8851i	1.43104	−	0.645145i
$686$		0			0
$687$	1.63654	−	18.7058i	0.0624380	−	0.713670i
$688$		0			0
$689$	−8.00524	−	29.8759i	−0.304975	−	1.13818i
$690$		0			0
$691$	−35.4237	+	6.24616i	−1.34758	+	0.237615i	−0.800434	−	0.599420i	$-0.795398\pi$
$691$	−35.4237	+	6.24616i	−1.34758	+	0.237615i	−0.547148	+	0.837036i	$0.684287\pi$
$692$		0			0
$693$	0.112145	−	0.0300491i	0.00426003	−	0.00114147i
$694$		0			0
$695$	15.7637	+	45.0976i	0.597950	+	1.71065i
$696$		0			0
$697$	−0.233686			−0.00885148
$698$		0			0
$699$	7.31527	+	20.0985i	0.276689	+	0.760197i
$700$		0			0
$701$	−7.61353	+	10.8732i	−0.287559	+	0.410677i	−0.936778	−	0.349925i	$-0.886207\pi$
$701$	−7.61353	+	10.8732i	−0.287559	+	0.410677i	0.649219	+	0.760602i	$0.275096\pi$
$702$		0			0
$703$	−13.0018	+	21.0835i	−0.490371	+	0.795180i
$704$		0			0
$705$	27.3369	+	0.349819i	1.02957	+	0.0131750i
$706$		0			0
$707$	−6.38307	+	13.6885i	−0.240060	+	0.514810i
$708$		0			0
$709$	−18.8743	+	18.8743i	−0.708839	+	0.708839i	−0.966291	−	0.257452i	$-0.917117\pi$
$709$	−18.8743	+	18.8743i	−0.708839	+	0.708839i	0.257452	+	0.966291i	$0.417117\pi$
$710$		0			0
$711$	−0.0816869	+	0.304860i	−0.00306350	+	0.0114331i
$712$		0			0
$713$	−8.78324	−	32.7795i	−0.328935	−	1.22760i
$714$		0			0
$715$	14.8331	+	0.189814i	0.554728	+	0.00709863i
$716$		0			0
$717$	4.80315	−	8.31931i	0.179377	−	0.310690i
$718$		0			0
$719$	−0.701922	−	0.836519i	−0.0261773	−	0.0311969i	0.752797	−	0.658253i	$-0.228704\pi$
$719$	−0.701922	−	0.836519i	−0.0261773	−	0.0311969i	−0.778974	+	0.627056i	$0.784260\pi$
$720$		0			0
$721$	1.60779	+	2.29616i	0.0598771	+	0.0855133i
$722$		0			0
$723$	−2.57028	+	7.06179i	−0.0955898	+	0.262631i
$724$		0			0
$725$	19.7485	+	9.83174i	0.733441	+	0.365142i
$726$		0			0
$727$	−35.4430	+	12.9002i	−1.31451	+	0.478441i	−0.901694	−	0.432375i	$-0.857676\pi$
$727$	−35.4430	+	12.9002i	−1.31451	+	0.478441i	−0.412812	+	0.910816i	$0.635453\pi$
$728$		0			0
$729$	−23.1372	+	13.3582i	−0.856932	+	0.494750i
$730$		0			0
$731$	−0.0544388	+	0.149569i	−0.00201349	+	0.00553202i
$732$		0			0
$733$	4.56292	+	52.1544i	0.168535	+	1.92637i	0.338593	+	0.940933i	$0.390049\pi$
$733$	4.56292	+	52.1544i	0.168535	+	1.92637i	−0.170058	+	0.985434i	$0.554396\pi$
$734$		0			0
$735$	17.5878	+	1.76577i	0.648735	+	0.0651315i
$736$		0			0
$737$	1.89860	−	1.32941i	0.0699357	−	0.0489695i
$738$		0			0
$739$	1.76773			0.0650270			0.0325135	−	0.999471i	$-0.489649\pi$
$739$	1.76773			0.0650270			0.0325135	+	0.999471i	$0.489649\pi$
$740$		0			0
$741$	−19.6112			−0.720435
$742$		0			0
$743$	25.2479	−	17.6788i	0.926257	−	0.648572i	−0.00997657	−	0.999950i	$-0.503176\pi$
$743$	25.2479	−	17.6788i	0.926257	−	0.648572i	0.936234	+	0.351378i	$0.114287\pi$
$744$		0			0
$745$	−33.9107	+	27.7228i	−1.24239	+	1.01569i
$746$		0			0
$747$	−0.0234139	−	0.267622i	−0.000856670	−	0.00979179i
$748$		0			0
$749$	1.49587	−	4.10986i	0.0546577	−	0.150171i
$750$		0			0
$751$	−42.6302	+	24.6126i	−1.55560	+	0.898125i	−0.557928	+	0.829889i	$0.688404\pi$
$751$	−42.6302	+	24.6126i	−1.55560	+	0.898125i	−0.997669	+	0.0682357i	$0.978263\pi$
$752$		0			0
$753$	10.3432	−	3.76460i	0.376926	−	0.137190i
$754$		0			0
$755$	−1.57406	−	2.80875i	−0.0572860	−	0.102221i
$756$		0			0
$757$	−3.13052	+	8.60103i	−0.113781	+	0.312610i	−0.983492	−	0.180951i	$-0.942083\pi$
$757$	−3.13052	+	8.60103i	−0.113781	+	0.312610i	0.869712	+	0.493560i	$0.164305\pi$
$758$		0			0
$759$	9.48955	+	13.5525i	0.344449	+	0.491924i
$760$		0			0
$761$	−6.80727	−	8.11259i	−0.246764	−	0.294081i	0.628418	−	0.777876i	$-0.283703\pi$
$761$	−6.80727	−	8.11259i	−0.246764	−	0.294081i	−0.875182	+	0.483794i	$0.839258\pi$
$762$		0			0
$763$	8.83706	−	15.3062i	0.319923	−	0.554123i
$764$		0			0
$765$	−3.54514e−5		0.00277037i	−1.28175e−6		0.000100163i
$766$		0			0
$767$	9.41283	+	35.1292i	0.339878	+	1.26844i
$768$		0			0
$769$	−6.35322	+	23.7105i	−0.229103	+	0.855024i	0.751616	+	0.659601i	$0.229275\pi$
$769$	−6.35322	+	23.7105i	−0.229103	+	0.855024i	−0.980719	+	0.195423i	$0.937392\pi$
$770$		0			0
$771$	9.29562	−	9.29562i	0.334774	−	0.334774i
$772$		0			0
$773$	20.5187	−	44.0026i	0.738008	−	1.58266i	−0.0727975	−	0.997347i	$-0.523193\pi$
$773$	20.5187	−	44.0026i	0.738008	−	1.58266i	0.810805	−	0.585316i	$-0.199030\pi$
$774$		0			0
$775$	23.6551	+	35.6933i	0.849715	+	1.28214i
$776$		0			0
$777$	−7.45184	+	14.8413i	−0.267333	+	0.532429i
$778$		0			0
$779$	−13.5988	+	19.4210i	−0.487226	+	0.695831i
$780$		0			0
$781$	1.04798	+	2.87930i	0.0374996	+	0.103029i
$782$		0			0
$783$	−22.8065			−0.815038
$784$		0			0
$785$	5.45932	−	11.3268i	0.194851	−	0.404272i
$786$		0			0
$787$	−6.01205	+	1.61092i	−0.214306	+	0.0574232i	−0.364375	−	0.931252i	$-0.618717\pi$
$787$	−6.01205	+	1.61092i	−0.214306	+	0.0574232i	0.150068	+	0.988676i	$0.452051\pi$
$788$		0			0
$789$	−40.9580	+	7.22199i	−1.45814	+	0.257110i
$790$		0			0
$791$	−4.90713	−	18.3137i	−0.174478	−	0.651159i
$792$		0			0
$793$	−0.537087	+	6.13894i	−0.0190725	+	0.218000i
$794$		0			0
$795$	−15.4091	+	40.7077i	−0.546504	+	1.44375i
$796$		0			0
$797$	−8.24596	−	3.00128i	−0.292087	−	0.106311i	0.191821	−	0.981430i	$-0.438561\pi$
$797$	−8.24596	−	3.00128i	−0.292087	−	0.106311i	−0.483908	+	0.875119i	$0.660783\pi$
$798$		0			0
$799$	0.0245677	−	0.280810i	0.000869143	−	0.00993435i
$800$		0			0
$801$	1.82628e−6	0	3.91647e-6i	6.45285e−8	0	1.38382e-7i
$802$		0			0
$803$	−17.9039	−	4.79733i	−0.631814	−	0.169294i
$804$		0			0
$805$	−3.42437	−	13.4669i	−0.120693	−	0.474646i
$806$		0			0
$807$	−13.6738	+	1.19630i	−0.481341	+	0.0421119i
$808$		0			0
$809$	1.58905	+	18.1630i	0.0558681	+	0.638576i	0.971576	+	0.236730i	$0.0760756\pi$
$809$	1.58905	+	18.1630i	0.0558681	+	0.638576i	−0.915707	+	0.401846i	$0.868369\pi$
$810$		0			0
$811$	−4.63654	+	26.2951i	−0.162811	+	0.923346i	0.788482	+	0.615058i	$0.210867\pi$
$811$	−4.63654	+	26.2951i	−0.162811	+	0.923346i	−0.951293	+	0.308288i	$0.900244\pi$
$812$		0			0
$813$	−4.13013	−	4.13013i	−0.144850	−	0.144850i
$814$		0			0
$815$	0.325907	−	1.71936i	0.0114160	−	0.0602266i
$816$		0			0
$817$	9.26240	+	13.2281i	0.324050	+	0.462792i
$818$		0			0
$819$	−0.133408	+	0.0116717i	−0.00466164	+	0.000407841i
$820$		0			0
$821$	12.0240	+	10.0894i	0.419642	+	0.352121i	0.828027	−	0.560688i	$-0.189463\pi$
$821$	12.0240	+	10.0894i	0.419642	+	0.352121i	−0.408385	+	0.912810i	$0.633908\pi$
$822$		0			0
$823$	−9.64786	+	4.49887i	−0.336303	+	0.156821i	−0.583432	−	0.812162i	$-0.698291\pi$
$823$	−9.64786	+	4.49887i	−0.336303	+	0.156821i	0.247129	+	0.968983i	$0.420513\pi$
$824$		0			0
$825$	−16.7885	−	12.4076i	−0.584501	−	0.431976i
$826$		0			0
$827$	−3.17620	−	8.72653i	−0.110447	−	0.303451i	0.872139	−	0.489258i	$-0.162732\pi$
$827$	−3.17620	−	8.72653i	−0.110447	−	0.303451i	−0.982586	+	0.185807i	$0.940510\pi$
$828$		0			0
$829$	7.40002	+	0.647418i	0.257013	+	0.0224858i	0.214934	−	0.976629i	$-0.431046\pi$
$829$	7.40002	+	0.647418i	0.257013	+	0.0224858i	0.0420792	+	0.999114i	$0.486602\pi$
$830$		0			0
$831$	−7.59233	−	16.2818i	−0.263375	−	0.564809i
$832$		0			0
$833$	0.0316478	−	0.179483i	0.00109653	−	0.00621873i
$834$		0			0
$835$	−7.52050	−	13.4196i	−0.260258	−	0.464403i
$836$		0			0
$837$	−38.3374	−	22.1341i	−1.32513	−	0.765066i
$838$		0			0
$839$	−9.30519	−	52.7723i	−0.321251	−	1.82190i	−0.534809	−	0.844973i	$-0.679616\pi$
$839$	−9.30519	−	52.7723i	−0.321251	−	1.82190i	0.213558	−	0.976930i	$-0.431495\pi$
$840$		0			0
$841$	8.25612	+	4.76667i	0.284694	+	0.164368i
$842$		0			0
$843$	26.2964	−	15.1822i	0.905696	−	0.522904i
$844$		0			0
$845$	11.7489	+	2.22702i	0.404175	+	0.0766118i
$846$		0			0
$847$	−7.45964	−	3.47849i	−0.256316	−	0.119522i
$848$		0			0
$849$	25.0122	+	17.5138i	0.858418	+	0.601070i
$850$		0			0
$851$	−23.9408	−	2.79600i	−0.820680	−	0.0958455i
$852$		0			0
$853$	18.9964	−	3.34958i	0.650424	−	0.114687i	0.161305	−	0.986905i	$-0.448430\pi$
$853$	18.9964	−	3.34958i	0.650424	−	0.114687i	0.489119	+	0.872217i	$0.337319\pi$
$854$		0			0
$855$	0.228176	+	0.164161i	0.00780344	+	0.00561419i
$856$		0			0
$857$		−	45.5118i		−	1.55465i	−0.629097	−	0.777327i	$-0.716575\pi$
$857$		−	45.5118i		−	1.55465i	0.629097	−	0.777327i	$-0.283425\pi$
$858$		0			0
$859$	47.0225	+	12.5996i	1.60439	+	0.429894i	0.946363	−	0.323105i	$-0.104727\pi$
$859$	47.0225	+	12.5996i	1.60439	+	0.429894i	0.658022	+	0.752999i	$0.271393\pi$
$860$		0			0
$861$	−7.94770	+	13.7658i	−0.270857	+	0.469138i
$862$		0			0
$863$	22.7181	+	15.9074i	0.773335	+	0.541495i	0.892321	−	0.451401i	$-0.149076\pi$
$863$	22.7181	+	15.9074i	0.773335	+	0.541495i	−0.118987	+	0.992896i	$0.537965\pi$
$864$		0			0
$865$	46.4355	−	3.46448i	1.57885	−	0.117796i
$866$		0			0
$867$	−29.4806	−	2.57921i	−1.00121	−	0.0875947i
$868$		0			0
$869$	−20.0852	+	14.0638i	−0.681343	+	0.477082i
$870$		0			0
$871$	−2.42295	+	1.12984i	−0.0820987	+	0.0382832i
$872$		0			0
$873$	−0.0246343	+	0.0206706i	−0.000833744	+	0.000699595i
$874$		0			0
$875$	9.49806	+	14.7378i	0.321093	+	0.498229i
$876$		0			0
$877$	7.69526	−	28.7191i	0.259851	−	0.969775i	−0.705477	−	0.708733i	$-0.749267\pi$
$877$	7.69526	−	28.7191i	0.259851	−	0.969775i	0.965327	−	0.261042i	$-0.0840663\pi$
$878$		0			0
$879$	25.2896	+	9.20467i	0.852998	+	0.310466i
$880$		0			0
$881$	12.2312	−	14.5766i	0.412079	−	0.491097i	−0.519584	−	0.854419i	$-0.673913\pi$
$881$	12.2312	−	14.5766i	0.412079	−	0.491097i	0.931663	+	0.363322i	$0.118358\pi$
$882$		0			0
$883$	−21.9253	+	26.1296i	−0.737846	+	0.879330i	−0.996234	−	0.0867110i	$-0.972364\pi$
$883$	−21.9253	+	26.1296i	−0.737846	+	0.879330i	0.258388	+	0.966041i	$0.416809\pi$
$884$		0			0
$885$	18.1185	−	47.8656i	0.609048	−	1.60898i
$886$		0			0
$887$	−22.8920	+	22.8920i	−0.768638	+	0.768638i	−0.977867	−	0.209229i	$-0.932905\pi$
$887$	−22.8920	+	22.8920i	−0.768638	+	0.768638i	0.209229	+	0.977867i	$0.432905\pi$
$888$		0			0
$889$		−	10.1365i		−	0.339968i
$890$		0			0
$891$	21.4726	+	3.78621i	0.719361	+	0.126843i
$892$		0			0
$893$	−21.9078	−	18.3828i	−0.733116	−	0.615157i
$894$		0			0
$895$	2.87066	−	28.5929i	0.0959555	−	0.955754i
$896$		0			0
$897$	−8.06499	−	17.2954i	−0.269282	−	0.577477i
$898$		0			0
$899$	−18.8927	−	32.7232i	−0.630108	−	1.09138i
$900$		0			0
$901$	0.406737	+	0.189665i	0.0135504	+	0.00631865i
$902$		0			0
$903$	6.95927	+	8.29373i	0.231590	+	0.275998i
$904$		0			0
$905$	−28.9280	−	17.1988i	−0.961598	−	0.571708i
$906$		0			0
$907$	−19.3243	−	3.40740i	−0.641654	−	0.113141i	−0.156652	−	0.987654i	$-0.550070\pi$
$907$	−19.3243	−	3.40740i	−0.641654	−	0.113141i	−0.485002	+	0.874513i	$0.661181\pi$
$908$		0			0
$909$	0.227752	−	0.191107i	0.00755407	−	0.00633862i
$910$		0			0
$911$	40.4885	−	10.8489i	1.34145	−	0.359439i	0.484475	−	0.874805i	$-0.339011\pi$
$911$	40.4885	−	10.8489i	1.34145	−	0.359439i	0.856970	+	0.515366i	$0.172344\pi$
$912$		0			0
$913$	11.9708	−	17.0961i	0.396177	−	0.565799i
$914$		0			0
$915$	5.65888	−	6.57136i	0.187077	−	0.217242i
$916$		0			0
$917$	−1.52827	−	2.64705i	−0.0504680	−	0.0874132i
$918$		0			0
$919$	32.4218	+	32.4218i	1.06950	+	1.06950i	0.997398	+	0.0720987i	$0.0229696\pi$
$919$	32.4218	+	32.4218i	1.06950	+	1.06950i	0.0720987	+	0.997398i	$0.477030\pi$
$920$		0			0
$921$	33.2859	−	12.1151i	1.09681	−	0.399206i
$922$		0			0
$923$	−0.613723	−	3.48059i	−0.0202009	−	0.114565i
$924$		0			0
$925$	29.7632	−	6.25713i	0.978608	−	0.205733i
$926$		0			0
$927$	−0.00958153	−	0.0543396i	−0.000314699	−	0.00178475i
$928$		0			0
$929$	31.1447	−	11.3357i	1.02182	−	0.371913i	0.223861	−	0.974621i	$-0.428134\pi$
$929$	31.1447	−	11.3357i	1.02182	−	0.371913i	0.797962	+	0.602708i	$0.205911\pi$
$930$		0			0
$931$	−13.0747	−	13.0747i	−0.428508	−	0.428508i
$932$		0			0
$933$	6.49994	+	11.2582i	0.212799	+	0.368578i
$934$		0			0
$935$	−0.140454	+	0.163102i	−0.00459333	+	0.00533400i
$936$		0			0
$937$	24.8487	−	35.4876i	0.811772	−	1.15933i	−0.172904	−	0.984939i	$-0.555315\pi$
$937$	24.8487	−	35.4876i	0.811772	−	1.15933i	0.984676	−	0.174392i	$-0.0557960\pi$
$938$		0			0
$939$	52.6576	−	14.1096i	1.71842	−	0.460448i
$940$		0			0
$941$	−29.5022	+	24.7553i	−0.961745	+	0.807000i	−0.981236	−	0.192810i	$-0.938240\pi$
$941$	−29.5022	+	24.7553i	−0.961745	+	0.807000i	0.0194909	+	0.999810i	$0.493795\pi$
$942$		0			0
$943$	−22.7201	−	4.00617i	−0.739869	−	0.130459i
$944$		0			0
$945$	−15.5805	−	9.26321i	−0.506833	−	0.301332i
$946$		0			0
$947$	19.1609	+	22.8351i	0.622647	+	0.742042i	0.981523	−	0.191344i	$-0.0612845\pi$
$947$	19.1609	+	22.8351i	0.622647	+	0.742042i	−0.358876	+	0.933385i	$0.616840\pi$
$948$		0			0
$949$	19.3767	+	9.03551i	0.628995	+	0.293305i
$950$		0			0
$951$	6.25556	+	10.8349i	0.202850	+	0.351347i
$952$		0			0
$953$	−13.2160	−	28.3418i	−0.428108	−	0.918080i	−0.995512	−	0.0946400i	$-0.969830\pi$
$953$	−13.2160	−	28.3418i	−0.428108	−	0.918080i	0.567404	−	0.823440i	$-0.307948\pi$
$954$		0			0
$955$	3.40134	−	33.8787i	0.110065	−	1.09629i
$956$		0			0
$957$	14.1115	+	11.8410i	0.456161	+	0.382765i
$958$		0			0
$959$	−28.3759	−	5.00343i	−0.916305	−	0.161569i
$960$		0			0
$961$		−	42.3429i		−	1.36590i
$962$		0			0
$963$	−0.0608770	+	0.0608770i	−0.00196174	+	0.00196174i
$964$		0			0
$965$	−4.21615	+	11.1382i	−0.135723	+	0.358552i
$966$		0			0
$967$	9.31200	−	11.0976i	0.299454	−	0.356875i	−0.595246	−	0.803544i	$-0.702945\pi$
$967$	9.31200	−	11.0976i	0.299454	−	0.356875i	0.894699	+	0.446669i	$0.147390\pi$
$968$		0			0
$969$	0.182908	−	0.217981i	0.00587584	−	0.00700255i
$970$		0			0
$971$	−52.8954	−	19.2524i	−1.69749	−	0.617838i	−0.701959	−	0.712218i	$-0.747691\pi$
$971$	−52.8954	−	19.2524i	−1.69749	−	0.617838i	−0.995536	+	0.0943801i	$0.969913\pi$
$972$		0			0
$973$	8.67170	−	32.3632i	0.278002	−	1.03752i
$974$		0			0
$975$	16.5854	+	17.4568i	0.531159	+	0.559066i
$976$		0			0
$977$	−8.43458	+	7.07746i	−0.269846	+	0.226428i	−0.767662	−	0.640855i	$-0.778580\pi$
$977$	−8.43458	+	7.07746i	−0.269846	+	0.226428i	0.497816	+	0.867283i	$0.334136\pi$
$978$		0			0
$979$	0.000304264	0	0.000141880i	9.72431e−6	0	4.53452e-6i
$980$		0			0
$981$	−0.284990	+	0.199552i	−0.00909904	+	0.00637122i
$982$		0			0
$983$	8.73550	+	0.764257i	0.278619	+	0.0243760i	0.225609	−	0.974218i	$-0.427563\pi$
$983$	8.73550	+	0.764257i	0.278619	+	0.0243760i	0.0530102	+	0.998594i	$0.483118\pi$
$984$		0			0
$985$	−24.6998	+	1.84282i	−0.787002	+	0.0587171i
$986$		0			0
$987$	−15.7062	−	10.9976i	−0.499935	−	0.350059i
$988$		0			0
$989$	−7.85694	+	13.6086i	−0.249836	+	0.432729i
$990$		0			0
$991$	−15.2136	−	4.07648i	−0.483277	−	0.129494i	0.00895133	−	0.999960i	$-0.497151\pi$
$991$	−15.2136	−	4.07648i	−0.483277	−	0.129494i	−0.492228	+	0.870466i	$0.663817\pi$
$992$		0			0
$993$			27.6640i			0.877890i
$994$		0			0
$995$	−35.7072	−	25.6896i	−1.13200	−	0.814415i
$996$		0			0
$997$	48.9120	−	8.62451i	1.54906	−	0.273141i	0.667282	−	0.744805i	$-0.267458\pi$
$997$	48.9120	−	8.62451i	1.54906	−	0.273141i	0.881778	+	0.471664i	$0.156347\pi$
$998$		0			0
$999$	−24.6620	+	19.5039i	−0.780270	+	0.617077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.cc.a.17.5	✓	228
5.3	odd	4		740.2.ch.a.313.5	yes	228
37.24	odd	36		740.2.ch.a.357.5	yes	228
185.98	even	36	inner	740.2.cc.a.653.5	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.cc.a.17.5	✓	228	1.1	even	1	trivial
740.2.cc.a.653.5	yes	228	185.98	even	36	inner
740.2.ch.a.313.5	yes	228	5.3	odd	4
740.2.ch.a.357.5	yes	228	37.24	odd	36

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.cc (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42609 + 0.998562i) q^{3} +(-1.41528 - 1.73118i) q^{5} +(0.136680 + 1.56226i) q^{7} +(0.0105581 - 0.0290083i) q^{9} +(2.07693 - 1.19912i) q^{11} +(-2.59943 + 0.946115i) q^{13} +(3.74701 + 1.05558i) q^{15} +(0.0137279 - 0.0377171i) q^{17} +(-2.33571 - 3.33574i) q^{19} +(-1.75493 - 2.09144i) q^{21} +(1.98130 - 3.43171i) q^{23} +(-0.993958 + 4.90021i) q^{25} +(-1.33786 - 4.99294i) q^{27} +(1.14194 - 4.26176i) q^{29} +(6.05569 - 6.05569i) q^{31} +(-1.76451 + 3.78399i) q^{33} +(2.51111 - 2.44765i) q^{35} +(-2.40978 - 5.58506i) q^{37} +(2.76228 - 3.94494i) q^{39} +(-1.99128 - 5.47099i) q^{41} -3.96556 q^{43} +(-0.0651612 + 0.0227768i) q^{45} +(6.78359 - 1.81766i) q^{47} +(4.47169 - 0.788479i) q^{49} +(0.0180856 + 0.0674963i) q^{51} +(-0.974499 + 11.1386i) q^{53} +(-5.01532 - 1.89845i) q^{55} +(6.66189 + 2.42473i) q^{57} +(1.14585 - 13.0971i) q^{59} +(0.941466 - 2.01898i) q^{61} +(0.0467615 + 0.0125297i) q^{63} +(5.31682 + 3.16106i) q^{65} +(0.962767 - 0.0842312i) q^{67} +(0.601256 + 6.87238i) q^{69} +(-0.221860 + 1.25823i) q^{71} +(-5.46509 - 5.46509i) q^{73} +(-3.47568 - 7.98069i) q^{75} +(2.15720 + 3.08080i) q^{77} +(-10.1851 + 0.891079i) q^{79} +(6.96461 + 5.84400i) q^{81} +(7.88711 - 3.67782i) q^{83} +(-0.0847239 + 0.0296149i) q^{85} +(2.62713 + 7.21797i) q^{87} +(0.000139453 + 1.22005e-5i) q^{89} +(-1.83336 - 3.93166i) q^{91} +(-2.58900 + 14.6830i) q^{93} +(-2.46908 + 8.76455i) q^{95} +(-0.902154 - 0.520859i) q^{97} +(-0.0128557 - 0.0729086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) \) 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more