LMFDB - Embedded newform 1824.2.bb.a.31.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1824,2,Mod(31,1824)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1824, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1824.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1824 = 2^{5} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1824.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.5647133287$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.11
Character	$\chi$	$=$	1824.31
Dual form			1824.2.bb.a.1471.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(0.0666287 + 0.115404i) q^{5} +1.13909i q^{7} +(-0.500000 + 0.866025i) q^{9} +2.16381i q^{11} +(-0.470939 - 0.271897i) q^{13} +(0.0666287 - 0.115404i) q^{15} +(-1.34935 - 2.33715i) q^{17} +(-3.12235 - 3.04154i) q^{19} +(0.986479 - 0.569544i) q^{21} +(-6.86977 - 3.96626i) q^{23} +(2.49112 - 4.31475i) q^{25} +1.00000 q^{27} +(2.69803 + 1.55771i) q^{29} +9.07735 q^{31} +(1.87392 - 1.08191i) q^{33} +(-0.131456 + 0.0758959i) q^{35} -4.99731i q^{37} +0.543793i q^{39} +(9.79815 - 5.65696i) q^{41} +(-8.56467 + 4.94482i) q^{43} -0.133257 q^{45} +(3.48636 + 2.01285i) q^{47} +5.70248 q^{49} +(-1.34935 + 2.33715i) q^{51} +(2.89540 + 1.67166i) q^{53} +(-0.249713 + 0.144172i) q^{55} +(-1.07288 + 4.22480i) q^{57} +(-5.90978 - 10.2360i) q^{59} +(3.59876 - 6.23323i) q^{61} +(-0.986479 - 0.569544i) q^{63} -0.0724644i q^{65} +(3.01280 - 5.21833i) q^{67} +7.93253i q^{69} +(2.69279 + 4.66405i) q^{71} +(-4.87607 - 8.44559i) q^{73} -4.98224 q^{75} -2.46477 q^{77} +(-5.57634 - 9.65851i) q^{79} +(-0.500000 - 0.866025i) q^{81} -8.00865i q^{83} +(0.179811 - 0.311442i) q^{85} -3.11541i q^{87} +(-10.5189 - 6.07310i) q^{89} +(0.309714 - 0.536441i) q^{91} +(-4.53868 - 7.86122i) q^{93} +(0.142969 - 0.562986i) q^{95} +(6.55667 - 3.78549i) q^{97} +(-1.87392 - 1.08191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) $ 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1824\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$799$	$1217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	0.0666287	+	0.115404i	0.0297972	+	0.0516103i	0.880539	−	0.473973i	$-0.157181\pi$
$5$	0.0666287	+	0.115404i	0.0297972	+	0.0516103i	−0.850742	+	0.525583i	$0.823847\pi$
$6$		0			0
$7$			1.13909i			0.430535i	0.976555	+	0.215267i	$0.0690623\pi$
$7$			1.13909i			0.430535i	−0.976555	+	0.215267i	$0.930938\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$			2.16381i			0.652414i	0.945298	+	0.326207i	$0.105771\pi$
$11$			2.16381i			0.652414i	−0.945298	+	0.326207i	$0.894229\pi$
$12$		0			0
$13$	−0.470939	−	0.271897i	−0.130615	−	0.0754106i	0.433269	−	0.901265i	$-0.357360\pi$
$13$	−0.470939	−	0.271897i	−0.130615	−	0.0754106i	−0.563884	+	0.825854i	$0.690693\pi$
$14$		0			0
$15$	0.0666287	−	0.115404i	0.0172034	−	0.0297972i
$16$		0			0
$17$	−1.34935	−	2.33715i	−0.327266	−	0.566841i	0.654702	−	0.755887i	$-0.272794\pi$
$17$	−1.34935	−	2.33715i	−0.327266	−	0.566841i	−0.981968	+	0.189046i	$0.939461\pi$
$18$		0			0
$19$	−3.12235	−	3.04154i	−0.716315	−	0.697777i
$19$	−3.12235	−	3.04154i	−0.716315	−	0.697777i
$20$		0			0
$21$	0.986479	−	0.569544i	0.215267	−	0.124285i
$22$		0			0
$23$	−6.86977	−	3.96626i	−1.43245	−	0.827023i	−0.435139	−	0.900363i	$-0.643301\pi$
$23$	−6.86977	−	3.96626i	−1.43245	−	0.827023i	−0.997307	+	0.0733405i	$0.976634\pi$
$24$		0			0
$25$	2.49112	−	4.31475i	0.498224	−	0.862950i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	2.69803	+	1.55771i	0.501011	+	0.289259i	0.729131	−	0.684374i	$-0.239925\pi$
$29$	2.69803	+	1.55771i	0.501011	+	0.289259i	−0.228120	+	0.973633i	$0.573258\pi$
$30$		0			0
$31$	9.07735			1.63034			0.815170	−	0.579221i	$-0.196643\pi$
$31$	9.07735			1.63034			0.815170	+	0.579221i	$0.196643\pi$
$32$		0			0
$33$	1.87392	−	1.08191i	0.326207	−	0.188336i
$34$		0			0
$35$	−0.131456	+	0.0758959i	−0.0222200	+	0.0128287i
$36$		0			0
$37$		−	4.99731i		−	0.821553i	−0.911736	−	0.410776i	$-0.865258\pi$
$37$		−	4.99731i		−	0.821553i	0.911736	−	0.410776i	$-0.134742\pi$
$38$		0			0
$39$			0.543793i			0.0870766i
$40$		0			0
$41$	9.79815	−	5.65696i	1.53021	−	0.883469i	0.530862	−	0.847458i	$-0.321868\pi$
$41$	9.79815	−	5.65696i	1.53021	−	0.883469i	0.999351	−	0.0360110i	$-0.0114651\pi$
$42$		0			0
$43$	−8.56467	+	4.94482i	−1.30610	+	0.754077i	−0.981443	−	0.191754i	$-0.938582\pi$
$43$	−8.56467	+	4.94482i	−1.30610	+	0.754077i	−0.324657	+	0.945832i	$0.605249\pi$
$44$		0			0
$45$	−0.133257			−0.0198648
$46$		0			0
$47$	3.48636	+	2.01285i	0.508539	+	0.293605i	0.732233	−	0.681055i	$-0.238478\pi$
$47$	3.48636	+	2.01285i	0.508539	+	0.293605i	−0.223694	+	0.974659i	$0.571812\pi$
$48$		0			0
$49$	5.70248			0.814640
$50$		0			0
$51$	−1.34935	+	2.33715i	−0.188947	+	0.327266i
$52$		0			0
$53$	2.89540	+	1.67166i	0.397714	+	0.229620i	0.685497	−	0.728075i	$-0.259585\pi$
$53$	2.89540	+	1.67166i	0.397714	+	0.229620i	−0.287783	+	0.957696i	$0.592918\pi$
$54$		0			0
$55$	−0.249713	+	0.144172i	−0.0336713	+	0.0194402i
$56$		0			0
$57$	−1.07288	+	4.22480i	−0.142106	+	0.559588i
$58$		0			0
$59$	−5.90978	−	10.2360i	−0.769387	−	1.33262i	−0.937896	−	0.346918i	$-0.887228\pi$
$59$	−5.90978	−	10.2360i	−0.769387	−	1.33262i	0.168508	−	0.985700i	$-0.446105\pi$
$60$		0			0
$61$	3.59876	−	6.23323i	0.460774	−	0.798083i	−0.538226	−	0.842800i	$-0.680905\pi$
$61$	3.59876	−	6.23323i	0.460774	−	0.798083i	0.999000	+	0.0447173i	$0.0142387\pi$
$62$		0			0
$63$	−0.986479	−	0.569544i	−0.124285	−	0.0717558i
$64$		0			0
$65$		−	0.0724644i		−	0.00898811i
$66$		0			0
$67$	3.01280	−	5.21833i	0.368072	−	0.637520i	−0.621192	−	0.783659i	$-0.713351\pi$
$67$	3.01280	−	5.21833i	0.368072	−	0.637520i	0.989264	+	0.146138i	$0.0466845\pi$
$68$		0			0
$69$			7.93253i			0.954964i
$70$		0			0
$71$	2.69279	+	4.66405i	0.319575	+	0.553521i	0.980399	−	0.197020i	$-0.0631264\pi$
$71$	2.69279	+	4.66405i	0.319575	+	0.553521i	−0.660824	+	0.750541i	$0.729793\pi$
$72$		0			0
$73$	−4.87607	−	8.44559i	−0.570700	−	0.988482i	−0.996494	−	0.0836617i	$-0.973338\pi$
$73$	−4.87607	−	8.44559i	−0.570700	−	0.988482i	0.425794	−	0.904820i	$-0.359995\pi$
$74$		0			0
$75$	−4.98224			−0.575300
$76$		0			0
$77$	−2.46477			−0.280887
$78$		0			0
$79$	−5.57634	−	9.65851i	−0.627388	−	1.08667i	−0.988074	−	0.153980i	$-0.950791\pi$
$79$	−5.57634	−	9.65851i	−0.627388	−	1.08667i	0.360686	−	0.932687i	$-0.382542\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	8.00865i		−	0.879063i	−0.898227	−	0.439532i	$-0.855144\pi$
$83$		−	8.00865i		−	0.879063i	0.898227	−	0.439532i	$-0.144856\pi$
$84$		0			0
$85$	0.179811	−	0.311442i	0.0195032	−	0.0337806i
$86$		0			0
$87$		−	3.11541i		−	0.334007i
$88$		0			0
$89$	−10.5189	−	6.07310i	−1.11500	−	0.643747i	−0.174882	−	0.984589i	$-0.555954\pi$
$89$	−10.5189	−	6.07310i	−1.11500	−	0.643747i	−0.940120	+	0.340843i	$0.889288\pi$
$90$		0			0
$91$	0.309714	−	0.536441i	0.0324669	−	0.0562343i
$92$		0			0
$93$	−4.53868	−	7.86122i	−0.470639	−	0.815170i
$94$		0			0
$95$	0.142969	−	0.562986i	0.0146683	−	0.0577611i
$96$		0			0
$97$	6.55667	−	3.78549i	0.665729	−	0.384359i	−0.128728	−	0.991680i	$-0.541089\pi$
$97$	6.55667	−	3.78549i	0.665729	−	0.384359i	0.794456	+	0.607321i	$0.207756\pi$
$98$		0			0
$99$	−1.87392	−	1.08191i	−0.188336	−	0.108736i
$100$		0			0
$101$	−2.18711	+	3.78819i	−0.217626	+	0.376939i	−0.954082	−	0.299547i	$-0.903165\pi$
$101$	−2.18711	+	3.78819i	−0.217626	+	0.376939i	0.736456	+	0.676486i	$0.236498\pi$
$102$		0			0
$103$	5.51718			0.543624			0.271812	−	0.962350i	$-0.412377\pi$
$103$	5.51718			0.543624			0.271812	+	0.962350i	$0.412377\pi$
$104$		0			0
$105$	0.131456	+	0.0758959i	0.0128287	+	0.00740668i
$106$		0			0
$107$	−19.9863			−1.93215			−0.966074	−	0.258264i	$-0.916849\pi$
$107$	−19.9863			−1.93215			−0.966074	+	0.258264i	$0.916849\pi$
$108$		0			0
$109$	3.99108	−	2.30425i	0.382277	−	0.220707i	−0.296532	−	0.955023i	$-0.595830\pi$
$109$	3.99108	−	2.30425i	0.382277	−	0.220707i	0.678808	+	0.734316i	$0.262497\pi$
$110$		0			0
$111$	−4.32780	+	2.49866i	−0.410776	+	0.237162i
$112$		0			0
$113$			5.94873i			0.559609i	0.960057	+	0.279805i	$0.0902697\pi$
$113$			5.94873i			0.559609i	−0.960057	+	0.279805i	$0.909730\pi$
$114$		0			0
$115$		−	1.05707i		−	0.0985720i
$116$		0			0
$117$	0.470939	−	0.271897i	0.0435383	−	0.0251369i
$118$		0			0
$119$	2.66221	−	1.53703i	0.244045	−	0.140899i
$120$		0			0
$121$	6.31791			0.574355
$122$		0			0
$123$	−9.79815	−	5.65696i	−0.883469	−	0.510071i
$124$		0			0
$125$	1.33021			0.118977
$126$		0			0
$127$	−0.933764	+	1.61733i	−0.0828582	+	0.143515i	−0.904477	−	0.426523i	$-0.859738\pi$
$127$	−0.933764	+	1.61733i	−0.0828582	+	0.143515i	0.821618	+	0.570038i	$0.193072\pi$
$128$		0			0
$129$	8.56467	+	4.94482i	0.754077	+	0.435367i
$130$		0			0
$131$	−5.49593	+	3.17307i	−0.480181	+	0.277233i	−0.720492	−	0.693463i	$-0.756084\pi$
$131$	−5.49593	+	3.17307i	−0.480181	+	0.277233i	0.240311	+	0.970696i	$0.422751\pi$
$132$		0			0
$133$	3.46458	−	3.55663i	0.300417	−	0.308399i
$134$		0			0
$135$	0.0666287	+	0.115404i	0.00573448	+	0.00993242i
$136$		0			0
$137$	−4.45094	+	7.70926i	−0.380270	+	0.658646i	−0.991101	−	0.133115i	$-0.957502\pi$
$137$	−4.45094	+	7.70926i	−0.380270	+	0.658646i	0.610831	+	0.791761i	$0.290835\pi$
$138$		0			0
$139$	1.27779	+	0.737735i	0.108381	+	0.0625738i	0.553211	−	0.833041i	$-0.313402\pi$
$139$	1.27779	+	0.737735i	0.108381	+	0.0625738i	−0.444830	+	0.895615i	$0.646736\pi$
$140$		0			0
$141$		−	4.02571i		−	0.339026i
$142$		0			0
$143$	0.588334	−	1.01902i	0.0491989	−	0.0852151i
$144$		0			0
$145$			0.415152i			0.0344765i
$146$		0			0
$147$	−2.85124	−	4.93849i	−0.235166	−	0.407320i
$148$		0			0
$149$	4.28808	+	7.42718i	0.351293	+	0.608458i	0.986476	−	0.163904i	$-0.0524086\pi$
$149$	4.28808	+	7.42718i	0.351293	+	0.608458i	−0.635183	+	0.772362i	$0.719075\pi$
$150$		0			0
$151$	20.0691			1.63320			0.816601	−	0.577203i	$-0.195856\pi$
$151$	20.0691			1.63320			0.816601	+	0.577203i	$0.195856\pi$
$152$		0			0
$153$	2.69870			0.218177
$154$		0			0
$155$	0.604812	+	1.04756i	0.0485797	+	0.0841424i
$156$		0			0
$157$	−6.14060	−	10.6358i	−0.490073	−	0.848832i	0.509861	−	0.860257i	$-0.329697\pi$
$157$	−6.14060	−	10.6358i	−0.490073	−	0.848832i	−0.999935	+	0.0114245i	$0.996363\pi$
$158$		0			0
$159$		−	3.34332i		−	0.265143i
$160$		0			0
$161$	4.51792	−	7.82527i	0.356062	−	0.616718i
$162$		0			0
$163$			1.38088i			0.108159i	0.998537	+	0.0540796i	$0.0172225\pi$
$163$			1.38088i			0.108159i	−0.998537	+	0.0540796i	$0.982778\pi$
$164$		0			0
$165$	0.249713	+	0.144172i	0.0194402	+	0.0112238i
$166$		0			0
$167$	0.788293	−	1.36536i	0.0609999	−	0.105655i	−0.833913	−	0.551896i	$-0.813904\pi$
$167$	0.788293	−	1.36536i	0.0609999	−	0.105655i	0.894913	+	0.446241i	$0.147238\pi$
$168$		0			0
$169$	−6.35214	−	11.0022i	−0.488626	−	0.846326i
$170$		0			0
$171$	4.19522	−	1.18326i	0.320817	−	0.0904864i
$172$		0			0
$173$	−8.22439	+	4.74835i	−0.625289	+	0.361011i	−0.778925	−	0.627117i	$-0.784235\pi$
$173$	−8.22439	+	4.74835i	−0.625289	+	0.361011i	0.153636	+	0.988127i	$0.450902\pi$
$174$		0			0
$175$	4.91488	+	2.83761i	0.371530	+	0.214503i
$176$		0			0
$177$	−5.90978	+	10.2360i	−0.444206	+	0.769387i
$178$		0			0
$179$	−11.4361			−0.854777			−0.427388	−	0.904068i	$-0.640566\pi$
$179$	−11.4361			−0.854777			−0.427388	+	0.904068i	$0.640566\pi$
$180$		0			0
$181$	−18.4566	−	10.6559i	−1.37187	−	0.792047i	−0.380703	−	0.924697i	$-0.624318\pi$
$181$	−18.4566	−	10.6559i	−1.37187	−	0.792047i	−0.991163	+	0.132650i	$0.957651\pi$
$182$		0			0
$183$	−7.19751			−0.532055
$184$		0			0
$185$	0.576711	−	0.332964i	0.0424006	−	0.0244800i
$186$		0			0
$187$	5.05715	−	2.91975i	0.369815	−	0.213513i
$188$		0			0
$189$			1.13909i			0.0828564i
$190$		0			0
$191$		−	21.2564i		−	1.53806i	−0.639213	−	0.769029i	$-0.720740\pi$
$191$		−	21.2564i		−	1.53806i	0.639213	−	0.769029i	$-0.279260\pi$
$192$		0			0
$193$	−17.1611	+	9.90794i	−1.23528	+	0.713189i	−0.968126	−	0.250465i	$-0.919417\pi$
$193$	−17.1611	+	9.90794i	−1.23528	+	0.713189i	−0.267154	+	0.963654i	$0.586083\pi$
$194$		0			0
$195$	−0.0627561	+	0.0362322i	−0.00449405	+	0.00259464i
$196$		0			0
$197$	25.2387			1.79819			0.899093	−	0.437758i	$-0.144227\pi$
$197$	25.2387			1.79819			0.899093	+	0.437758i	$0.144227\pi$
$198$		0			0
$199$	0.237605	+	0.137181i	0.0168434	+	0.00972451i	0.508398	−	0.861122i	$-0.330238\pi$
$199$	0.237605	+	0.137181i	0.0168434	+	0.00972451i	−0.491555	+	0.870847i	$0.663571\pi$
$200$		0			0
$201$	−6.02561			−0.425013
$202$		0			0
$203$	−1.77436	+	3.07329i	−0.124536	+	0.215703i
$204$		0			0
$205$	1.30568	+	0.753832i	0.0911923	+	0.0526499i
$206$		0			0
$207$	6.86977	−	3.96626i	0.477482	−	0.275674i
$208$		0			0
$209$	6.58132	−	6.75618i	0.455240	−	0.467335i
$210$		0			0
$211$	−3.82416	−	6.62363i	−0.263266	−	0.455990i	0.703842	−	0.710356i	$-0.251466\pi$
$211$	−3.82416	−	6.62363i	−0.263266	−	0.455990i	−0.967108	+	0.254367i	$0.918133\pi$
$212$		0			0
$213$	2.69279	−	4.66405i	0.184507	−	0.319575i
$214$		0			0
$215$	−1.14131	−	0.658933i	−0.0778364	−	0.0449389i
$216$		0			0
$217$			10.3399i			0.701918i
$218$		0			0
$219$	−4.87607	+	8.44559i	−0.329494	+	0.570700i
$220$		0			0
$221$			1.46754i			0.0987172i
$222$		0			0
$223$	12.7679	+	22.1146i	0.855001	+	1.48091i	0.876644	+	0.481140i	$0.159777\pi$
$223$	12.7679	+	22.1146i	0.855001	+	1.48091i	−0.0216423	+	0.999766i	$0.506889\pi$
$224$		0			0
$225$	2.49112	+	4.31475i	0.166075	+	0.287650i
$226$		0			0
$227$	−3.95642			−0.262597			−0.131299	−	0.991343i	$-0.541915\pi$
$227$	−3.95642			−0.262597			−0.131299	+	0.991343i	$0.541915\pi$
$228$		0			0
$229$	26.1935			1.73091			0.865457	−	0.500983i	$-0.167028\pi$
$229$	26.1935			1.73091			0.865457	+	0.500983i	$0.167028\pi$
$230$		0			0
$231$	1.23239	+	2.13456i	0.0810851	+	0.140444i
$232$		0			0
$233$	1.09944	+	1.90429i	0.0720270	+	0.124754i	0.899790	−	0.436324i	$-0.143720\pi$
$233$	1.09944	+	1.90429i	0.0720270	+	0.124754i	−0.827763	+	0.561079i	$0.810387\pi$
$234$		0			0
$235$			0.536455i			0.0349945i
$236$		0			0
$237$	−5.57634	+	9.65851i	−0.362222	+	0.627388i
$238$		0			0
$239$			22.7569i			1.47202i	0.676971	+	0.736010i	$0.263292\pi$
$239$			22.7569i			1.47202i	−0.676971	+	0.736010i	$0.736708\pi$
$240$		0			0
$241$	13.6648	+	7.88937i	0.880227	+	0.508199i	0.870733	−	0.491756i	$-0.163645\pi$
$241$	13.6648	+	7.88937i	0.880227	+	0.508199i	0.00949354	+	0.999955i	$0.496978\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	0.379949	+	0.658090i	0.0242740	+	0.0420438i
$246$		0			0
$247$	0.643450	+	2.28133i	0.0409418	+	0.145158i
$248$		0			0
$249$	−6.93569	+	4.00432i	−0.439532	+	0.253764i
$250$		0			0
$251$	−6.83797	−	3.94790i	−0.431609	−	0.249189i	0.268423	−	0.963301i	$-0.413497\pi$
$251$	−6.83797	−	3.94790i	−0.431609	−	0.249189i	−0.700032	+	0.714112i	$0.746831\pi$
$252$		0			0
$253$	8.58225	−	14.8649i	0.539562	−	0.934548i
$254$		0			0
$255$	−0.359622			−0.0225204
$256$		0			0
$257$	−9.50522	−	5.48784i	−0.592919	−	0.342322i	0.173332	−	0.984863i	$-0.444547\pi$
$257$	−9.50522	−	5.48784i	−0.592919	−	0.342322i	−0.766251	+	0.642542i	$0.777880\pi$
$258$		0			0
$259$	5.69237			0.353707
$260$		0			0
$261$	−2.69803	+	1.55771i	−0.167004	+	0.0964196i
$262$		0			0
$263$	−0.351895	+	0.203167i	−0.0216988	+	0.0125278i	−0.510810	−	0.859694i	$-0.670654\pi$
$263$	−0.351895	+	0.203167i	−0.0216988	+	0.0125278i	0.489111	+	0.872221i	$0.337321\pi$
$264$		0			0
$265$			0.445522i			0.0273682i
$266$		0			0
$267$			12.1462i			0.743335i
$268$		0			0
$269$	−23.4610	+	13.5452i	−1.43044	+	0.825866i	−0.997154	−	0.0753896i	$-0.975980\pi$
$269$	−23.4610	+	13.5452i	−1.43044	+	0.825866i	−0.433288	+	0.901256i	$0.642647\pi$
$270$		0			0
$271$	24.8920	−	14.3714i	1.51208	−	0.872999i	0.512178	−	0.858879i	$-0.328839\pi$
$271$	24.8920	−	14.3714i	1.51208	−	0.872999i	0.999900	−	0.0141199i	$-0.00449464\pi$
$272$		0			0
$273$	−0.619428			−0.0374895
$274$		0			0
$275$	9.33631	+	5.39032i	0.563001	+	0.325049i
$276$		0			0
$277$	−2.31850			−0.139305			−0.0696527	−	0.997571i	$-0.522189\pi$
$277$	−2.31850			−0.139305			−0.0696527	+	0.997571i	$0.522189\pi$
$278$		0			0
$279$	−4.53868	+	7.86122i	−0.271723	+	0.470639i
$280$		0			0
$281$	−23.1691	−	13.3767i	−1.38215	−	0.797987i	−0.389740	−	0.920925i	$-0.627435\pi$
$281$	−23.1691	−	13.3767i	−1.38215	−	0.797987i	−0.992414	+	0.122938i	$0.960768\pi$
$282$		0			0
$283$	−0.437764	+	0.252743i	−0.0260224	+	0.0150240i	−0.512955	−	0.858416i	$-0.671449\pi$
$283$	−0.437764	+	0.252743i	−0.0260224	+	0.0150240i	0.486932	+	0.873440i	$0.338116\pi$
$284$		0			0
$285$	−0.559044	+	0.157678i	−0.0331149	+	0.00934006i
$286$		0			0
$287$	6.44378	+	11.1610i	0.380364	+	0.658810i
$288$		0			0
$289$	4.85850	−	8.41516i	0.285794	−	0.495010i
$290$		0			0
$291$	−6.55667	−	3.78549i	−0.384359	−	0.221910i
$292$		0			0
$293$			23.9043i			1.39650i	0.715852	+	0.698252i	$0.246039\pi$
$293$			23.9043i			1.39650i	−0.715852	+	0.698252i	$0.753961\pi$
$294$		0			0
$295$	0.787521	−	1.36403i	0.0458513	−	0.0794167i
$296$		0			0
$297$			2.16381i			0.125557i
$298$		0			0
$299$	2.15683	+	3.73573i	0.124733	+	0.216043i
$300$		0			0
$301$	−5.63258	−	9.75591i	−0.324656	−	0.562322i
$302$		0			0
$303$	4.37422			0.251293
$304$		0			0
$305$	0.959121			0.0549191
$306$		0			0
$307$	11.4005	+	19.7463i	0.650663	+	1.12698i	0.982962	+	0.183807i	$0.0588423\pi$
$307$	11.4005	+	19.7463i	0.650663	+	1.12698i	−0.332299	+	0.943174i	$0.607824\pi$
$308$		0			0
$309$	−2.75859	−	4.77802i	−0.156931	−	0.271812i
$310$		0			0
$311$		−	9.59548i		−	0.544110i	−0.962282	−	0.272055i	$-0.912297\pi$
$311$		−	9.59548i		−	0.544110i	0.962282	−	0.272055i	$-0.0877032\pi$
$312$		0			0
$313$	7.38895	−	12.7980i	0.417648	−	0.723387i	−0.578054	−	0.815998i	$-0.696188\pi$
$313$	7.38895	−	12.7980i	0.417648	−	0.723387i	0.995702	+	0.0926108i	$0.0295212\pi$
$314$		0			0
$315$		−	0.151792i		−	0.00855250i
$316$		0			0
$317$	7.31434	+	4.22293i	0.410814	+	0.237184i	0.691139	−	0.722721i	$-0.257109\pi$
$317$	7.31434	+	4.22293i	0.410814	+	0.237184i	−0.280325	+	0.959905i	$0.590442\pi$
$318$		0			0
$319$	−3.37059	+	5.83803i	−0.188717	+	0.326867i
$320$		0			0
$321$	9.99315	+	17.3086i	0.557763	+	0.966074i
$322$		0			0
$323$	−2.89537	+	11.4015i	−0.161103	+	0.634396i
$324$		0			0
$325$	−2.34633	+	1.35466i	−0.130151	+	0.0751427i
$326$		0			0
$327$	−3.99108	−	2.30425i	−0.220707	−	0.127426i
$328$		0			0
$329$	−2.29282	+	3.97128i	−0.126407	+	0.218944i
$330$		0			0
$331$	18.4435			1.01375			0.506873	−	0.862021i	$-0.330801\pi$
$331$	18.4435			1.01375			0.506873	+	0.862021i	$0.330801\pi$
$332$		0			0
$333$	4.32780	+	2.49866i	0.237162	+	0.136925i
$334$		0			0
$335$	0.802956			0.0438702
$336$		0			0
$337$	5.40196	−	3.11882i	0.294264	−	0.169893i	−0.345599	−	0.938382i	$-0.612324\pi$
$337$	5.40196	−	3.11882i	0.294264	−	0.169893i	0.639863	+	0.768489i	$0.278991\pi$
$338$		0			0
$339$	5.15175	−	2.97436i	0.279805	−	0.161545i
$340$		0			0
$341$			19.6417i			1.06366i
$342$		0			0
$343$			14.4692i			0.781265i
$344$		0			0
$345$	−0.915447	+	0.528534i	−0.0492860	+	0.0284553i
$346$		0			0
$347$	11.5686	−	6.67913i	0.621035	−	0.358555i	−0.156237	−	0.987720i	$-0.549936\pi$
$347$	11.5686	−	6.67913i	0.621035	−	0.358555i	0.777272	+	0.629165i	$0.216603\pi$
$348$		0			0
$349$	−27.1040			−1.45084			−0.725422	−	0.688305i	$-0.758355\pi$
$349$	−27.1040			−1.45084			−0.725422	+	0.688305i	$0.758355\pi$
$350$		0			0
$351$	−0.470939	−	0.271897i	−0.0251369	−	0.0145128i
$352$		0			0
$353$	5.50145			0.292812			0.146406	−	0.989225i	$-0.453229\pi$
$353$	5.50145			0.292812			0.146406	+	0.989225i	$0.453229\pi$
$354$		0			0
$355$	−0.358834	+	0.621519i	−0.0190449	+	0.0329868i
$356$		0			0
$357$	−2.66221	−	1.53703i	−0.140899	−	0.0813483i
$358$		0			0
$359$	3.30782	−	1.90977i	0.174580	−	0.100794i	−0.410164	−	0.912012i	$-0.634528\pi$
$359$	3.30782	−	1.90977i	0.174580	−	0.100794i	0.584744	+	0.811218i	$0.301195\pi$
$360$		0			0
$361$	0.498096	+	18.9935i	0.0262156	+	0.999656i
$362$		0			0
$363$	−3.15895	−	5.47147i	−0.165802	−	0.287178i
$364$		0			0
$365$	0.649771	−	1.12544i	0.0340106	−	0.0589081i
$366$		0			0
$367$	8.60002	+	4.96522i	0.448917	+	0.259183i	0.707373	−	0.706841i	$-0.249880\pi$
$367$	8.60002	+	4.96522i	0.448917	+	0.259183i	−0.258455	+	0.966023i	$0.583214\pi$
$368$		0			0
$369$			11.3139i			0.588979i
$370$		0			0
$371$	−1.90417	+	3.29812i	−0.0988595	+	0.171230i
$372$		0			0
$373$			2.17673i			0.112707i	0.998411	+	0.0563533i	$0.0179473\pi$
$373$			2.17673i			0.112707i	−0.998411	+	0.0563533i	$0.982053\pi$
$374$		0			0
$375$	−0.665104	−	1.15199i	−0.0343458	−	0.0594887i
$376$		0			0
$377$	−0.847070	−	1.46717i	−0.0436263	−	0.0755630i
$378$		0			0
$379$	2.19502			0.112751			0.0563753	−	0.998410i	$-0.482046\pi$
$379$	2.19502			0.112751			0.0563753	+	0.998410i	$0.482046\pi$
$380$		0			0
$381$	1.86753			0.0956764
$382$		0			0
$383$	12.1511	+	21.0464i	0.620893	+	1.07542i	0.989320	+	0.145762i	$0.0465632\pi$
$383$	12.1511	+	21.0464i	0.620893	+	1.07542i	−0.368427	+	0.929657i	$0.620103\pi$
$384$		0			0
$385$	−0.164225	−	0.284445i	−0.00836966	−	0.0144967i
$386$		0			0
$387$		−	9.88963i		−	0.502718i
$388$		0			0
$389$	0.588510	−	1.01933i	0.0298386	−	0.0516820i	−0.850720	−	0.525618i	$-0.823834\pi$
$389$	0.588510	−	1.01933i	0.0298386	−	0.0516820i	0.880559	+	0.473936i	$0.157167\pi$
$390$		0			0
$391$			21.4075i			1.08263i
$392$		0			0
$393$	5.49593	+	3.17307i	0.277233	+	0.160060i
$394$		0			0
$395$	0.743088	−	1.28707i	0.0373888	−	0.0647594i
$396$		0			0
$397$	−3.58104	−	6.20254i	−0.179727	−	0.311296i	0.762060	−	0.647506i	$-0.224188\pi$
$397$	−3.58104	−	6.20254i	−0.179727	−	0.311296i	−0.941787	+	0.336210i	$0.890855\pi$
$398$		0			0
$399$	−4.81242	−	1.22210i	−0.240922	−	0.0611815i
$400$		0			0
$401$	−12.2094	+	7.04908i	−0.609706	+	0.352014i	−0.772850	−	0.634588i	$-0.781170\pi$
$401$	−12.2094	+	7.04908i	−0.609706	+	0.352014i	0.163144	+	0.986602i	$0.447836\pi$
$402$		0			0
$403$	−4.27488	−	2.46810i	−0.212947	−	0.122945i
$404$		0			0
$405$	0.0666287	−	0.115404i	0.00331081	−	0.00573448i
$406$		0			0
$407$	10.8132			0.535993
$408$		0			0
$409$	−7.67460	−	4.43093i	−0.379484	−	0.219095i	0.298110	−	0.954532i	$-0.403644\pi$
$409$	−7.67460	−	4.43093i	−0.379484	−	0.219095i	−0.677594	+	0.735436i	$0.736977\pi$
$410$		0			0
$411$	8.90188			0.439097
$412$		0			0
$413$	11.6597	−	6.73175i	0.573738	−	0.331248i
$414$		0			0
$415$	0.924232	−	0.533605i	0.0453687	−	0.0261937i
$416$		0			0
$417$		−	1.47547i		−	0.0722541i
$418$		0			0
$419$			9.29685i			0.454181i	0.973874	+	0.227090i	$0.0729213\pi$
$419$			9.29685i			0.454181i	−0.973874	+	0.227090i	$0.927079\pi$
$420$		0			0
$421$	3.65737	−	2.11158i	0.178249	−	0.102912i	−0.408221	−	0.912883i	$-0.633851\pi$
$421$	3.65737	−	2.11158i	0.178249	−	0.102912i	0.586470	+	0.809971i	$0.300517\pi$
$422$		0			0
$423$	−3.48636	+	2.01285i	−0.169513	+	0.0978683i
$424$		0			0
$425$	−13.4456			−0.652207
$426$		0			0
$427$	7.10019	+	4.09930i	0.343602	+	0.198379i
$428$		0			0
$429$	−1.17667			−0.0568100
$430$		0			0
$431$	−2.30829	+	3.99808i	−0.111186	+	0.192581i	−0.916249	−	0.400610i	$-0.868798\pi$
$431$	−2.30829	+	3.99808i	−0.111186	+	0.192581i	0.805062	+	0.593190i	$0.202132\pi$
$432$		0			0
$433$	−0.122023	−	0.0704501i	−0.00586406	−	0.00338562i	0.497065	−	0.867713i	$-0.334411\pi$
$433$	−0.122023	−	0.0704501i	−0.00586406	−	0.00338562i	−0.502929	+	0.864328i	$0.667744\pi$
$434$		0			0
$435$	0.359532	−	0.207576i	0.0172382	−	0.00995250i
$436$		0			0
$437$	9.38626	+	33.2787i	0.449006	+	1.59194i
$438$		0			0
$439$	−0.422712	−	0.732158i	−0.0201749	−	0.0349440i	0.855762	−	0.517370i	$-0.173089\pi$
$439$	−0.422712	−	0.732158i	−0.0201749	−	0.0349440i	−0.875937	+	0.482426i	$0.839756\pi$
$440$		0			0
$441$	−2.85124	+	4.93849i	−0.135773	+	0.235166i
$442$		0			0
$443$	−14.6457	−	8.45573i	−0.695840	−	0.401744i	0.109956	−	0.993936i	$-0.464929\pi$
$443$	−14.6457	−	8.45573i	−0.695840	−	0.401744i	−0.805796	+	0.592193i	$0.798262\pi$
$444$		0			0
$445$		−	1.61857i		−	0.0767275i
$446$		0			0
$447$	4.28808	−	7.42718i	0.202819	−	0.351293i
$448$		0			0
$449$			37.5477i			1.77199i	0.463698	+	0.885993i	$0.346522\pi$
$449$			37.5477i			1.77199i	−0.463698	+	0.885993i	$0.653478\pi$
$450$		0			0
$451$	12.2406	+	21.2014i	0.576388	+	0.998333i
$452$		0			0
$453$	−10.0346	−	17.3804i	−0.471465	−	0.816601i
$454$		0			0
$455$	0.0825434			0.00386969
$456$		0			0
$457$	−36.3446			−1.70013			−0.850065	−	0.526677i	$-0.823438\pi$
$457$	−36.3446			−1.70013			−0.850065	+	0.526677i	$0.823438\pi$
$458$		0			0
$459$	−1.34935	−	2.33715i	−0.0629824	−	0.109089i
$460$		0			0
$461$	−4.85347	−	8.40646i	−0.226049	−	0.391528i	0.730585	−	0.682822i	$-0.239248\pi$
$461$	−4.85347	−	8.40646i	−0.226049	−	0.391528i	−0.956634	+	0.291294i	$0.905914\pi$
$462$		0			0
$463$		−	38.8906i		−	1.80740i	−0.428168	−	0.903699i	$-0.640841\pi$
$463$		−	38.8906i		−	1.80740i	0.428168	−	0.903699i	$-0.359159\pi$
$464$		0			0
$465$	0.604812	−	1.04756i	0.0280475	−	0.0485797i
$466$		0			0
$467$			12.8807i			0.596047i	0.954559	+	0.298023i	$0.0963273\pi$
$467$			12.8807i			0.596047i	−0.954559	+	0.298023i	$0.903673\pi$
$468$		0			0
$469$	5.94413	+	3.43185i	0.274475	+	0.158468i
$470$		0			0
$471$	−6.14060	+	10.6358i	−0.282944	+	0.490073i
$472$		0			0
$473$	−10.6997	−	18.5324i	−0.491971	−	0.852119i
$474$		0			0
$475$	−20.9016	+	5.89530i	−0.959032	+	0.270495i
$476$		0			0
$477$	−2.89540	+	1.67166i	−0.132571	+	0.0765401i
$478$		0			0
$479$	−0.967512	−	0.558593i	−0.0442067	−	0.0255228i	0.477734	−	0.878505i	$-0.341458\pi$
$479$	−0.967512	−	0.558593i	−0.0442067	−	0.0255228i	−0.521940	+	0.852982i	$0.674792\pi$
$480$		0			0
$481$	−1.35875	+	2.35343i	−0.0619538	+	0.107307i
$482$		0			0
$483$	−9.03584			−0.411145
$484$		0			0
$485$	0.873724	+	0.504445i	0.0396738	+	0.0229057i
$486$		0			0
$487$	−12.7687			−0.578604			−0.289302	−	0.957238i	$-0.593423\pi$
$487$	−12.7687			−0.578604			−0.289302	+	0.957238i	$0.593423\pi$
$488$		0			0
$489$	1.19588	−	0.690442i	0.0540796	−	0.0312228i
$490$		0			0
$491$	25.2539	−	14.5803i	1.13969	−	0.658001i	0.193337	−	0.981132i	$-0.438069\pi$
$491$	25.2539	−	14.5803i	1.13969	−	0.658001i	0.946354	+	0.323132i	$0.104736\pi$
$492$		0			0
$493$		−	8.40758i		−	0.378658i
$494$		0			0
$495$		−	0.288344i		−	0.0129601i
$496$		0			0
$497$	−5.31276	+	3.06732i	−0.238310	+	0.137588i
$498$		0			0
$499$	34.8497	−	20.1205i	1.56009	−	0.900716i	0.562839	−	0.826567i	$-0.309709\pi$
$499$	34.8497	−	20.1205i	1.56009	−	0.900716i	0.997247	−	0.0741490i	$-0.0236240\pi$
$500$		0			0
$501$	−1.57659			−0.0704367
$502$		0			0
$503$	1.27674	+	0.737124i	0.0569269	+	0.0328667i	0.528193	−	0.849124i	$-0.322870\pi$
$503$	1.27674	+	0.737124i	0.0569269	+	0.0328667i	−0.471266	+	0.881991i	$0.656203\pi$
$504$		0			0
$505$	−0.582897			−0.0259386
$506$		0			0
$507$	−6.35214	+	11.0022i	−0.282109	+	0.488626i
$508$		0			0
$509$	7.24752	+	4.18436i	0.321241	+	0.185468i	0.651945	−	0.758266i	$-0.273953\pi$
$509$	7.24752	+	4.18436i	0.321241	+	0.185468i	−0.330705	+	0.943734i	$0.607286\pi$
$510$		0			0
$511$	9.62027	−	5.55427i	0.425576	−	0.245706i
$512$		0			0
$513$	−3.12235	−	3.04154i	−0.137855	−	0.134287i
$514$		0			0
$515$	0.367602	+	0.636706i	0.0161985	+	0.0280566i
$516$		0			0
$517$	−4.35544	+	7.54384i	−0.191552	+	0.331778i
$518$		0			0
$519$	8.22439	+	4.74835i	0.361011	+	0.208430i
$520$		0			0
$521$			2.75117i			0.120531i	0.998182	+	0.0602654i	$0.0191947\pi$
$521$			2.75117i			0.120531i	−0.998182	+	0.0602654i	$0.980805\pi$
$522$		0			0
$523$	−6.03753	+	10.4573i	−0.264003	+	0.457266i	−0.967302	−	0.253628i	$-0.918376\pi$
$523$	−6.03753	+	10.4573i	−0.264003	+	0.457266i	0.703299	+	0.710894i	$0.251709\pi$
$524$		0			0
$525$		−	5.67521i		−	0.247687i
$526$		0			0
$527$	−12.2485	−	21.2151i	−0.533555	−	0.924144i
$528$		0			0
$529$	19.9625	+	34.5760i	0.867934	+	1.50331i
$530$		0			0
$531$	11.8196			0.512925
$532$		0			0
$533$	−6.15244			−0.266492
$534$		0			0
$535$	−1.33166	−	2.30650i	−0.0575727	−	0.0997189i
$536$		0			0
$537$	5.71807	+	9.90398i	0.246753	+	0.427388i
$538$		0			0
$539$			12.3391i			0.531483i
$540$		0			0
$541$	−4.75097	+	8.22891i	−0.204260	+	0.353789i	−0.949897	−	0.312564i	$-0.898812\pi$
$541$	−4.75097	+	8.22891i	−0.204260	+	0.353789i	0.745637	+	0.666353i	$0.232145\pi$
$542$		0			0
$543$			21.3118i			0.914578i
$544$		0			0
$545$	0.531841	+	0.307059i	0.0227816	+	0.0131529i
$546$		0			0
$547$	12.0308	−	20.8380i	0.514400	−	0.890967i	−0.485461	−	0.874259i	$-0.661348\pi$
$547$	12.0308	−	20.8380i	0.514400	−	0.890967i	0.999860	−	0.0167082i	$-0.00531862\pi$
$548$		0			0
$549$	3.59876	+	6.23323i	0.153591	+	0.266028i
$550$		0			0
$551$	−3.68635	−	13.0699i	−0.157044	−	0.556794i
$552$		0			0
$553$	11.0019	−	6.35194i	0.467848	−	0.270112i
$554$		0			0
$555$	−0.576711	−	0.332964i	−0.0244800	−	0.0141335i
$556$		0			0
$557$	−20.7785	+	35.9894i	−0.880414	+	1.52492i	−0.0295327	+	0.999564i	$0.509402\pi$
$557$	−20.7785	+	35.9894i	−0.880414	+	1.52492i	−0.850881	+	0.525358i	$0.823931\pi$
$558$		0			0
$559$	5.37792			0.227462
$560$		0			0
$561$	−5.05715	−	2.91975i	−0.213513	−	0.123272i
$562$		0			0
$563$	4.78220			0.201546			0.100773	−	0.994909i	$-0.467868\pi$
$563$	4.78220			0.201546			0.100773	+	0.994909i	$0.467868\pi$
$564$		0			0
$565$	−0.686509	+	0.396356i	−0.0288816	+	0.0166748i
$566$		0			0
$567$	0.986479	−	0.569544i	0.0414282	−	0.0239186i
$568$		0			0
$569$		−	34.5515i		−	1.44847i	−0.689552	−	0.724236i	$-0.742193\pi$
$569$		−	34.5515i		−	1.44847i	0.689552	−	0.724236i	$-0.257807\pi$
$570$		0			0
$571$			28.6234i			1.19785i	0.800804	+	0.598926i	$0.204406\pi$
$571$			28.6234i			1.19785i	−0.800804	+	0.598926i	$0.795594\pi$
$572$		0			0
$573$	−18.4086	+	10.6282i	−0.769029	+	0.443999i
$574$		0			0
$575$	−34.2269	+	19.7609i	−1.42736	+	0.824086i
$576$		0			0
$577$	10.5896			0.440851			0.220426	−	0.975404i	$-0.429255\pi$
$577$	10.5896			0.440851			0.220426	+	0.975404i	$0.429255\pi$
$578$		0			0
$579$	17.1611	+	9.90794i	0.713189	+	0.411760i
$580$		0			0
$581$	9.12255			0.378467
$582$		0			0
$583$	−3.61716	+	6.26511i	−0.149808	+	0.259474i
$584$		0			0
$585$	0.0627561	+	0.0362322i	0.00259464	+	0.00149802i
$586$		0			0
$587$	22.9036	−	13.2234i	0.945335	−	0.545789i	0.0537062	−	0.998557i	$-0.482897\pi$
$587$	22.9036	−	13.2234i	0.945335	−	0.545789i	0.891629	+	0.452767i	$0.149563\pi$
$588$		0			0
$589$	−28.3426	−	27.6091i	−1.16784	−	1.13761i
$590$		0			0
$591$	−12.6194	−	21.8574i	−0.519091	−	0.899093i
$592$		0			0
$593$	11.6088	−	20.1070i	0.476714	−	0.825694i	−0.522930	−	0.852376i	$-0.675161\pi$
$593$	11.6088	−	20.1070i	0.476714	−	0.825694i	0.999644	+	0.0266823i	$0.00849424\pi$
$594$		0			0
$595$	0.354760	+	0.204821i	0.0145437	+	0.00839683i
$596$		0			0
$597$		−	0.274362i		−	0.0112289i
$598$		0			0
$599$	2.05563	−	3.56046i	0.0839908	−	0.145476i	−0.820970	−	0.570971i	$-0.806567\pi$
$599$	2.05563	−	3.56046i	0.0839908	−	0.145476i	0.904961	+	0.425495i	$0.139900\pi$
$600$		0			0
$601$			34.5056i			1.40751i	0.710442	+	0.703756i	$0.248495\pi$
$601$			34.5056i			1.40751i	−0.710442	+	0.703756i	$0.751505\pi$
$602$		0			0
$603$	3.01280	+	5.21833i	0.122691	+	0.212507i
$604$		0			0
$605$	0.420954	+	0.729113i	0.0171142	+	0.0296427i
$606$		0			0
$607$	−32.0668			−1.30155			−0.650776	−	0.759270i	$-0.725556\pi$
$607$	−32.0668			−1.30155			−0.650776	+	0.759270i	$0.725556\pi$
$608$		0			0
$609$	3.54873			0.143802
$610$		0			0
$611$	−1.09458	−	1.89586i	−0.0442818	−	0.0766984i
$612$		0			0
$613$	−12.6969	−	21.9917i	−0.512825	−	0.888238i	−0.999889	−	0.0148724i	$-0.995266\pi$
$613$	−12.6969	−	21.9917i	−0.512825	−	0.888238i	0.487065	−	0.873366i	$-0.338068\pi$
$614$		0			0
$615$		−	1.50766i		−	0.0607949i
$616$		0			0
$617$	18.2525	−	31.6143i	0.734820	−	1.27275i	−0.219982	−	0.975504i	$-0.570600\pi$
$617$	18.2525	−	31.6143i	0.734820	−	1.27275i	0.954802	−	0.297242i	$-0.0960667\pi$
$618$		0			0
$619$		−	3.93133i		−	0.158014i	−0.996874	−	0.0790068i	$-0.974825\pi$
$619$		−	3.93133i		−	0.158014i	0.996874	−	0.0790068i	$-0.0251749\pi$
$620$		0			0
$621$	−6.86977	−	3.96626i	−0.275674	−	0.159161i
$622$		0			0
$623$	6.91779	−	11.9820i	0.277155	−	0.480047i
$624$		0			0
$625$	−12.3670	−	21.4202i	−0.494679	−	0.856809i
$626$		0			0
$627$	−9.14168	−	2.32150i	−0.365084	−	0.0927119i
$628$		0			0
$629$	−11.6794	+	6.74313i	−0.465690	+	0.268866i
$630$		0			0
$631$	−8.65919	−	4.99939i	−0.344717	−	0.199022i	0.317639	−	0.948212i	$-0.397110\pi$
$631$	−8.65919	−	4.99939i	−0.344717	−	0.199022i	−0.662356	+	0.749189i	$0.730443\pi$
$632$		0			0
$633$	−3.82416	+	6.62363i	−0.151997	+	0.263266i
$634$		0			0
$635$	−0.248862			−0.00987578
$636$		0			0
$637$	−2.68552	−	1.55049i	−0.106404	−	0.0614325i
$638$		0			0
$639$	−5.38558			−0.213050
$640$		0			0
$641$	13.5929	−	7.84787i	0.536888	−	0.309972i	−0.206929	−	0.978356i	$-0.566347\pi$
$641$	13.5929	−	7.84787i	0.536888	−	0.309972i	0.743817	+	0.668384i	$0.233014\pi$
$642$		0			0
$643$	−2.43842	+	1.40782i	−0.0961619	+	0.0555191i	−0.547310	−	0.836930i	$-0.684348\pi$
$643$	−2.43842	+	1.40782i	−0.0961619	+	0.0555191i	0.451148	+	0.892449i	$0.351015\pi$
$644$		0			0
$645$			1.31787i			0.0518909i
$646$		0			0
$647$			12.5145i			0.491995i	0.969271	+	0.245997i	$0.0791154\pi$
$647$			12.5145i			0.491995i	−0.969271	+	0.245997i	$0.920885\pi$
$648$		0			0
$649$	22.1489	−	12.7877i	0.869419	−	0.501960i
$650$		0			0
$651$	8.95462	−	5.16995i	0.350959	−	0.202626i
$652$		0			0
$653$	−27.2687			−1.06711			−0.533553	−	0.845766i	$-0.679144\pi$
$653$	−27.2687			−1.06711			−0.533553	+	0.845766i	$0.679144\pi$
$654$		0			0
$655$	−0.732373	−	0.422835i	−0.0286162	−	0.0165215i
$656$		0			0
$657$	9.75213			0.380467
$658$		0			0
$659$	−3.91399	+	6.77923i	−0.152467	+	0.264081i	−0.932134	−	0.362114i	$-0.882055\pi$
$659$	−3.91399	+	6.77923i	−0.152467	+	0.264081i	0.779667	+	0.626195i	$0.215389\pi$
$660$		0			0
$661$	31.0066	+	17.9017i	1.20602	+	0.696294i	0.961887	−	0.273449i	$-0.0881644\pi$
$661$	31.0066	+	17.9017i	1.20602	+	0.696294i	0.244130	+	0.969743i	$0.421498\pi$
$662$		0			0
$663$	1.27092	−	0.733769i	0.0493586	−	0.0284972i
$664$		0			0
$665$	0.641290	+	0.162854i	0.0248682	+	0.00631520i
$666$		0			0
$667$	−12.3565	−	21.4022i	−0.478447	−	0.828695i
$668$		0			0
$669$	12.7679	−	22.1146i	0.493635	−	0.855001i
$670$		0			0
$671$	13.4875	+	7.78704i	0.520681	+	0.300615i
$672$		0			0
$673$			10.3482i			0.398895i	0.979908	+	0.199448i	$0.0639148\pi$
$673$			10.3482i			0.398895i	−0.979908	+	0.199448i	$0.936085\pi$
$674$		0			0
$675$	2.49112	−	4.31475i	0.0958833	−	0.166075i
$676$		0			0
$677$			35.9710i			1.38248i	0.722626	+	0.691239i	$0.242935\pi$
$677$			35.9710i			1.38248i	−0.722626	+	0.691239i	$0.757065\pi$
$678$		0			0
$679$	4.31201	+	7.46862i	0.165480	+	0.286619i
$680$		0			0
$681$	1.97821	+	3.42636i	0.0758052	+	0.131299i
$682$		0			0
$683$	33.9887			1.30054			0.650270	−	0.759703i	$-0.274656\pi$
$683$	33.9887			1.30054			0.650270	+	0.759703i	$0.274656\pi$
$684$		0			0
$685$	−1.18624			−0.0453239
$686$		0			0
$687$	−13.0967	−	22.6842i	−0.499672	−	0.865457i
$688$		0			0
$689$	−0.909038	−	1.57450i	−0.0346316	−	0.0599836i
$690$		0			0
$691$			0.422716i			0.0160809i	0.999968	+	0.00804045i	$0.00255938\pi$
$691$			0.422716i			0.0160809i	−0.999968	+	0.00804045i	$0.997441\pi$
$692$		0			0
$693$	1.23239	−	2.13456i	0.0468145	−	0.0810851i
$694$		0			0
$695$			0.196617i			0.00745811i
$696$		0			0
$697$	−26.4423	−	15.2665i	−1.00157	−	0.578259i
$698$		0			0
$699$	1.09944	−	1.90429i	0.0415848	−	0.0720270i
$700$		0			0
$701$	−5.22559	−	9.05099i	−0.197368	−	0.341851i	0.750306	−	0.661090i	$-0.229906\pi$
$701$	−5.22559	−	9.05099i	−0.197368	−	0.341851i	−0.947674	+	0.319239i	$0.896573\pi$
$702$		0			0
$703$	−15.1995	+	15.6033i	−0.573260	+	0.588491i
$704$		0			0
$705$	0.464584	−	0.268228i	0.0174972	−	0.0101020i
$706$		0			0
$707$	−4.31508	−	2.49131i	−0.162285	−	0.0936954i
$708$		0			0
$709$	−8.38163	+	14.5174i	−0.314779	+	0.545213i	−0.979390	−	0.201976i	$-0.935264\pi$
$709$	−8.38163	+	14.5174i	−0.314779	+	0.545213i	0.664612	+	0.747189i	$0.268597\pi$
$710$		0			0
$711$	11.1527			0.418258
$712$		0			0
$713$	−62.3593	−	36.0032i	−2.33537	−	1.34833i
$714$		0			0
$715$	0.156800			0.00586397
$716$		0			0
$717$	19.7080	−	11.3784i	0.736010	−	0.424935i
$718$		0			0
$719$	−28.0698	+	16.2061i	−1.04683	+	0.604387i	−0.921760	−	0.387761i	$-0.873249\pi$
$719$	−28.0698	+	16.2061i	−1.04683	+	0.604387i	−0.125069	+	0.992148i	$0.539915\pi$
$720$		0			0
$721$			6.28455i			0.234049i
$722$		0			0
$723$		−	15.7787i		−	0.586818i
$724$		0			0
$725$	13.4422	−	7.76087i	0.499232	−	0.288232i
$726$		0			0
$727$	−20.2719	+	11.7040i	−0.751845	+	0.434078i	−0.826360	−	0.563142i	$-0.809592\pi$
$727$	−20.2719	+	11.7040i	−0.751845	+	0.434078i	0.0745152	+	0.997220i	$0.476259\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	23.1135	+	13.3446i	0.854884	+	0.493568i
$732$		0			0
$733$	40.4992			1.49587			0.747937	−	0.663770i	$-0.231045\pi$
$733$	40.4992			1.49587			0.747937	+	0.663770i	$0.231045\pi$
$734$		0			0
$735$	0.379949	−	0.658090i	0.0140146	−	0.0242740i
$736$		0			0
$737$	11.2915	+	6.51915i	0.415927	+	0.240136i
$738$		0			0
$739$	−2.45801	+	1.41914i	−0.0904195	+	0.0522037i	−0.544528	−	0.838743i	$-0.683291\pi$
$739$	−2.45801	+	1.41914i	−0.0904195	+	0.0522037i	0.454108	+	0.890946i	$0.349958\pi$
$740$		0			0
$741$	1.65397	−	1.69791i	0.0607600	−	0.0623743i
$742$		0			0
$743$	−26.3118	−	45.5733i	−0.965285	−	1.67192i	−0.708847	−	0.705363i	$-0.750784\pi$
$743$	−26.3118	−	45.5733i	−0.965285	−	1.67192i	−0.256439	−	0.966560i	$-0.582549\pi$
$744$		0			0
$745$	−0.571418	+	0.989726i	−0.0209351	+	0.0362607i
$746$		0			0
$747$	6.93569	+	4.00432i	0.253764	+	0.146511i
$748$		0			0
$749$		−	22.7662i		−	0.831857i
$750$		0			0
$751$	0.975634	−	1.68985i	0.0356014	−	0.0616634i	−0.847676	−	0.530515i	$-0.821999\pi$
$751$	0.975634	−	1.68985i	0.0356014	−	0.0616634i	0.883277	+	0.468851i	$0.155332\pi$
$752$		0			0
$753$			7.89580i			0.287739i
$754$		0			0
$755$	1.33718	+	2.31606i	0.0486649	+	0.0842901i
$756$		0			0
$757$	26.3408	+	45.6236i	0.957372	+	1.65822i	0.728845	+	0.684679i	$0.240058\pi$
$757$	26.3408	+	45.6236i	0.957372	+	1.65822i	0.228527	+	0.973538i	$0.426609\pi$
$758$		0			0
$759$	−17.1645			−0.623032
$760$		0			0
$761$	34.3255			1.24430			0.622148	−	0.782899i	$-0.286260\pi$
$761$	34.3255			1.24430			0.622148	+	0.782899i	$0.286260\pi$
$762$		0			0
$763$	2.62475	+	4.54620i	0.0950222	+	0.164583i
$764$		0			0
$765$	0.179811	+	0.311442i	0.00650108	+	0.0112602i
$766$		0			0
$767$			6.42739i			0.232080i
$768$		0			0
$769$	−5.97163	+	10.3432i	−0.215343	+	0.372984i	−0.953378	−	0.301777i	$-0.902420\pi$
$769$	−5.97163	+	10.3432i	−0.215343	+	0.372984i	0.738036	+	0.674761i	$0.235753\pi$
$770$		0			0
$771$			10.9757i			0.395279i
$772$		0			0
$773$	29.2496	+	16.8873i	1.05204	+	0.607393i	0.923219	−	0.384275i	$-0.125549\pi$
$773$	29.2496	+	16.8873i	1.05204	+	0.607393i	0.128817	+	0.991668i	$0.458882\pi$
$774$		0			0
$775$	22.6128	−	39.1665i	0.812275	−	1.40690i
$776$		0			0
$777$	−2.84619	−	4.92974i	−0.102106	−	0.176853i
$778$		0			0
$779$	−47.7991	−	12.1384i	−1.71258	−	0.434905i
$780$		0			0
$781$	−10.0921	+	5.82670i	−0.361125	+	0.208496i
$782$		0			0
$783$	2.69803	+	1.55771i	0.0964196	+	0.0556679i
$784$		0			0
$785$	0.818280	−	1.41730i	0.0292057	−	0.0505857i
$786$		0			0
$787$	−29.0693			−1.03621			−0.518105	−	0.855317i	$-0.673362\pi$
$787$	−29.0693			−1.03621			−0.518105	+	0.855317i	$0.673362\pi$
$788$		0			0
$789$	0.351895	+	0.203167i	0.0125278	+	0.00723293i
$790$		0			0
$791$	−6.77613			−0.240931
$792$		0			0
$793$	−3.38959	+	1.95698i	−0.120368	+	0.0694944i
$794$		0			0
$795$	0.385833	−	0.222761i	0.0136841	−	0.00790052i
$796$		0			0
$797$		−	4.35049i		−	0.154102i	−0.997027	−	0.0770511i	$-0.975450\pi$
$797$		−	4.35049i		−	0.154102i	0.997027	−	0.0770511i	$-0.0245505\pi$
$798$		0			0
$799$		−	10.8642i		−	0.384348i
$800$		0			0
$801$	10.5189	−	6.07310i	0.371667	−	0.214582i
$802$		0			0
$803$	18.2747	−	10.5509i	0.644900	−	0.372333i
$804$		0			0
$805$	1.20409			0.0424387
$806$		0			0
$807$	23.4610	+	13.5452i	0.825866	+	0.476814i
$808$		0			0
$809$	−3.33563			−0.117275			−0.0586373	−	0.998279i	$-0.518676\pi$
$809$	−3.33563			−0.117275			−0.0586373	+	0.998279i	$0.518676\pi$
$810$		0			0
$811$	15.6319	−	27.0752i	0.548909	−	0.950739i	−0.449440	−	0.893310i	$-0.648377\pi$
$811$	15.6319	−	27.0752i	0.548909	−	0.950739i	0.998350	−	0.0574283i	$-0.0182900\pi$
$812$		0			0
$813$	−24.8920	−	14.3714i	−0.872999	−	0.504026i
$814$		0			0
$815$	−0.159360	+	0.0920064i	−0.00558213	+	0.00322284i
$816$		0			0
$817$	41.7817	+	10.6103i	1.46176	+	0.371209i
$818$		0			0
$819$	0.309714	+	0.536441i	0.0108223	+	0.0187448i
$820$		0			0
$821$	18.1392	−	31.4179i	0.633061	−	1.09649i	−0.353862	−	0.935298i	$-0.615132\pi$
$821$	18.1392	−	31.4179i	0.633061	−	1.09649i	0.986922	−	0.161196i	$-0.0515351\pi$
$822$		0			0
$823$	−31.3786	−	18.1164i	−1.09379	−	0.631499i	−0.159206	−	0.987245i	$-0.550893\pi$
$823$	−31.3786	−	18.1164i	−1.09379	−	0.631499i	−0.934582	+	0.355747i	$0.884227\pi$
$824$		0			0
$825$		−	10.7806i		−	0.375334i
$826$		0			0
$827$	20.9495	−	36.2856i	0.728485	−	1.26177i	−0.229038	−	0.973417i	$-0.573558\pi$
$827$	20.9495	−	36.2856i	0.728485	−	1.26177i	0.957523	−	0.288356i	$-0.0931086\pi$
$828$		0			0
$829$			6.25554i			0.217264i	0.994082	+	0.108632i	$0.0346470\pi$
$829$			6.25554i			0.217264i	−0.994082	+	0.108632i	$0.965353\pi$
$830$		0			0
$831$	1.15925	+	2.00788i	0.0402140	+	0.0696527i
$832$		0			0
$833$	−7.69465	−	13.3275i	−0.266604	−	0.461771i
$834$		0			0
$835$	0.210092			0.00727052
$836$		0			0
$837$	9.07735			0.313759
$838$		0			0
$839$	−28.0867	−	48.6476i	−0.969660	−	1.67950i	−0.696536	−	0.717521i	$-0.745277\pi$
$839$	−28.0867	−	48.6476i	−0.969660	−	1.67950i	−0.273124	−	0.961979i	$-0.588057\pi$
$840$		0			0
$841$	−9.64710	−	16.7093i	−0.332659	−	0.576182i
$842$		0			0
$843$			26.7534i			0.921436i
$844$		0			0
$845$	0.846470	−	1.46613i	0.0291194	−	0.0504364i
$846$		0			0
$847$			7.19665i			0.247280i
$848$		0			0
$849$	0.437764	+	0.252743i	0.0150240	+	0.00867412i
$850$		0			0
$851$	−19.8206	+	34.3304i	−0.679443	+	1.17683i
$852$		0			0
$853$	−13.1491	−	22.7750i	−0.450217	−	0.779800i	0.548182	−	0.836359i	$-0.315320\pi$
$853$	−13.1491	−	22.7750i	−0.450217	−	0.779800i	−0.998399	+	0.0565597i	$0.981987\pi$
$854$		0			0
$855$	0.416076	+	0.405307i	0.0142295	+	0.0138612i
$856$		0			0
$857$	8.91649	−	5.14794i	0.304581	−	0.175850i	−0.339918	−	0.940455i	$-0.610399\pi$
$857$	8.91649	−	5.14794i	0.304581	−	0.175850i	0.644499	+	0.764605i	$0.277066\pi$
$858$		0			0
$859$	30.9500	+	17.8690i	1.05600	+	0.609682i	0.924323	−	0.381611i	$-0.124631\pi$
$859$	30.9500	+	17.8690i	1.05600	+	0.609682i	0.131677	+	0.991293i	$0.457964\pi$
$860$		0			0
$861$	6.44378	−	11.1610i	0.219603	−	0.380364i
$862$		0			0
$863$	−39.2657			−1.33662			−0.668310	−	0.743883i	$-0.732982\pi$
$863$	−39.2657			−1.33662			−0.668310	+	0.743883i	$0.732982\pi$
$864$		0			0
$865$	−1.09596	−	0.632753i	−0.0372638	−	0.0215142i
$866$		0			0
$867$	−9.71700			−0.330006
$868$		0			0
$869$	20.8992	−	12.0662i	0.708957	−	0.409317i
$870$		0			0
$871$	−2.83769	+	1.63834i	−0.0961515	+	0.0555131i
$872$		0			0
$873$			7.57099i			0.256239i
$874$		0			0
$875$			1.51522i			0.0512239i
$876$		0			0
$877$	−44.5622	+	25.7280i	−1.50476	+	0.868772i	−0.504773	+	0.863252i	$0.668424\pi$
$877$	−44.5622	+	25.7280i	−1.50476	+	0.868772i	−0.999985	+	0.00552053i	$0.998243\pi$
$878$		0			0
$879$	20.7017	−	11.9522i	0.698252	−	0.403136i
$880$		0			0
$881$	27.8313			0.937661			0.468831	−	0.883288i	$-0.344675\pi$
$881$	27.8313			0.937661			0.468831	+	0.883288i	$0.344675\pi$
$882$		0			0
$883$	−24.2664	−	14.0102i	−0.816631	−	0.471482i	0.0326226	−	0.999468i	$-0.489614\pi$
$883$	−24.2664	−	14.0102i	−0.816631	−	0.471482i	−0.849253	+	0.527986i	$0.822947\pi$
$884$		0			0
$885$	−1.57504			−0.0529445
$886$		0			0
$887$	−23.1470	+	40.0918i	−0.777201	+	1.34615i	0.156348	+	0.987702i	$0.450028\pi$
$887$	−23.1470	+	40.0918i	−0.777201	+	1.34615i	−0.933549	+	0.358450i	$0.883306\pi$
$888$		0			0
$889$	−1.84228	−	1.06364i	−0.0617880	−	0.0356733i
$890$		0			0
$891$	1.87392	−	1.08191i	0.0627786	−	0.0362452i
$892$		0			0
$893$	−4.76347	−	16.8887i	−0.159403	−	0.565160i
$894$		0			0
$895$	−0.761974	−	1.31978i	−0.0254700	−	0.0441153i
$896$		0			0
$897$	2.15683	−	3.73573i	0.0720144	−	0.124733i
$898$		0			0
$899$	24.4909	+	14.1399i	0.816819	+	0.471590i
$900$		0			0
$901$		−	9.02263i		−	0.300587i
$902$		0			0
$903$	−5.63258	+	9.75591i	−0.187441	+	0.324656i
$904$		0			0
$905$		−	2.83996i		−	0.0944033i
$906$		0			0
$907$	5.66770	+	9.81674i	0.188193	+	0.325959i	0.944648	−	0.328086i	$-0.106404\pi$
$907$	5.66770	+	9.81674i	0.188193	+	0.325959i	−0.756455	+	0.654046i	$0.773070\pi$
$908$		0			0
$909$	−2.18711	−	3.78819i	−0.0725419	−	0.125646i
$910$		0			0
$911$	36.1154			1.19656			0.598279	−	0.801288i	$-0.295851\pi$
$911$	36.1154			1.19656			0.598279	+	0.801288i	$0.295851\pi$
$912$		0			0
$913$	17.3292			0.573513
$914$		0			0
$915$	−0.479561	−	0.830623i	−0.0158538	−	0.0274596i
$916$		0			0
$917$	−3.61441	−	6.26034i	−0.119358	−	0.206735i
$918$		0			0
$919$			3.08334i			0.101710i	0.998706	+	0.0508550i	$0.0161946\pi$
$919$			3.08334i			0.101710i	−0.998706	+	0.0508550i	$0.983805\pi$
$920$		0			0
$921$	11.4005	−	19.7463i	0.375660	−	0.650663i
$922$		0			0
$923$		−	2.92864i		−	0.0963975i
$924$		0			0
$925$	−21.5621	−	12.4489i	−0.708959	−	0.409317i
$926$		0			0
$927$	−2.75859	+	4.77802i	−0.0906040	+	0.156931i
$928$		0			0
$929$	4.35429	+	7.54185i	0.142860	+	0.247440i	0.928572	−	0.371151i	$-0.121037\pi$
$929$	4.35429	+	7.54185i	0.142860	+	0.247440i	−0.785713	+	0.618592i	$0.787704\pi$
$930$		0			0
$931$	−17.8051	−	17.3443i	−0.583539	−	0.568437i
$932$		0			0
$933$	−8.30993	+	4.79774i	−0.272055	+	0.157071i
$934$		0			0
$935$	0.673902	+	0.389078i	0.0220390	+	0.0127242i
$936$		0			0
$937$	−4.56917	+	7.91404i	−0.149268	+	0.258540i	−0.930957	−	0.365128i	$-0.881025\pi$
$937$	−4.56917	+	7.91404i	−0.149268	+	0.258540i	0.781689	+	0.623668i	$0.214358\pi$
$938$		0			0
$939$	−14.7779			−0.482258
$940$		0			0
$941$	10.3359	+	5.96744i	0.336941	+	0.194533i	0.658919	−	0.752214i	$-0.271014\pi$
$941$	10.3359	+	5.96744i	0.336941	+	0.194533i	−0.321977	+	0.946747i	$0.604347\pi$
$942$		0			0
$943$	−89.7480			−2.92260
$944$		0			0
$945$	−0.131456	+	0.0758959i	−0.00427625	+	0.00246889i
$946$		0			0
$947$	24.3207	−	14.0416i	0.790317	−	0.456290i	−0.0497573	−	0.998761i	$-0.515845\pi$
$947$	24.3207	−	14.0416i	0.790317	−	0.456290i	0.840074	+	0.542472i	$0.182511\pi$
$948$		0			0
$949$			5.30314i			0.172147i
$950$		0			0
$951$		−	8.44587i		−	0.273876i
$952$		0			0
$953$	5.58722	−	3.22578i	0.180988	−	0.104493i	−0.406769	−	0.913531i	$-0.633345\pi$
$953$	5.58722	−	3.22578i	0.180988	−	0.104493i	0.587757	+	0.809038i	$0.300011\pi$
$954$		0			0
$955$	2.45308	−	1.41629i	0.0793797	−	0.0458299i
$956$		0			0
$957$	6.74117			0.217911
$958$		0			0
$959$	−8.78152	−	5.07001i	−0.283570	−	0.163719i
$960$		0			0
$961$	51.3983			1.65801
$962$		0			0
$963$	9.99315	−	17.3086i	0.322025	−	0.557763i
$964$		0			0
$965$	−2.28684	−	1.32031i	−0.0736159	−	0.0425021i
$966$		0			0
$967$	−22.2852	+	12.8663i	−0.716643	+	0.413754i	−0.813516	−	0.581543i	$-0.802449\pi$
$967$	−22.2852	+	12.8663i	−0.716643	+	0.413754i	0.0968730	+	0.995297i	$0.469116\pi$
$968$		0			0
$969$	11.3217	−	3.19328i	0.363704	−	0.102583i
$970$		0			0
$971$	−1.98657	−	3.44084i	−0.0637521	−	0.110422i	0.832388	−	0.554194i	$-0.186973\pi$
$971$	−1.98657	−	3.44084i	−0.0637521	−	0.110422i	−0.896140	+	0.443772i	$0.853640\pi$
$972$		0			0
$973$	−0.840345	+	1.45552i	−0.0269402	+	0.0466618i
$974$		0			0
$975$	2.34633	+	1.35466i	0.0751427	+	0.0433837i
$976$		0			0
$977$		−	20.3592i		−	0.651349i	−0.945482	−	0.325675i	$-0.894409\pi$
$977$		−	20.3592i		−	0.651349i	0.945482	−	0.325675i	$-0.105591\pi$
$978$		0			0
$979$	13.1410	−	22.7610i	0.419990	−	0.727444i
$980$		0			0
$981$			4.60851i			0.147138i
$982$		0			0
$983$	16.0763	+	27.8450i	0.512755	+	0.888117i	0.999891	+	0.0147910i	$0.00470830\pi$
$983$	16.0763	+	27.8450i	0.512755	+	0.888117i	−0.487136	+	0.873326i	$0.661958\pi$
$984$		0			0
$985$	1.68162	+	2.91266i	0.0535810	+	0.0928050i
$986$		0			0
$987$	4.58563			0.145962
$988$		0			0
$989$	78.4498			2.49456
$990$		0			0
$991$	−5.54930	−	9.61167i	−0.176279	−	0.305325i	0.764324	−	0.644832i	$-0.223073\pi$
$991$	−5.54930	−	9.61167i	−0.176279	−	0.305325i	−0.940603	+	0.339508i	$0.889740\pi$
$992$		0			0
$993$	−9.22175	−	15.9725i	−0.292643	−	0.506873i
$994$		0			0
$995$			0.0365608i			0.00115905i
$996$		0			0
$997$	20.6751	−	35.8103i	0.654786	−	1.13412i	−0.327161	−	0.944968i	$-0.606092\pi$
$997$	20.6751	−	35.8103i	0.654786	−	1.13412i	0.981947	−	0.189154i	$-0.0605746\pi$
$998$		0			0
$999$		−	4.99731i		−	0.158108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1824.2.bb.a.31.11	✓	40
4.3	odd	2		1824.2.bb.b.31.11	yes	40
19.8	odd	6		1824.2.bb.b.1471.11	yes	40
76.27	even	6	inner	1824.2.bb.a.1471.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1824.2.bb.a.31.11	✓	40	1.1	even	1	trivial
1824.2.bb.a.1471.11	yes	40	76.27	even	6	inner
1824.2.bb.b.31.11	yes	40	4.3	odd	2
1824.2.bb.b.1471.11	yes	40	19.8	odd	6

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:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(0.0666287 + 0.115404i) q^{5} +1.13909i q^{7} +(-0.500000 + 0.866025i) q^{9} +2.16381i q^{11} +(-0.470939 - 0.271897i) q^{13} +(0.0666287 - 0.115404i) q^{15} +(-1.34935 - 2.33715i) q^{17} +(-3.12235 - 3.04154i) q^{19} +(0.986479 - 0.569544i) q^{21} +(-6.86977 - 3.96626i) q^{23} +(2.49112 - 4.31475i) q^{25} +1.00000 q^{27} +(2.69803 + 1.55771i) q^{29} +9.07735 q^{31} +(1.87392 - 1.08191i) q^{33} +(-0.131456 + 0.0758959i) q^{35} -4.99731i q^{37} +0.543793i q^{39} +(9.79815 - 5.65696i) q^{41} +(-8.56467 + 4.94482i) q^{43} -0.133257 q^{45} +(3.48636 + 2.01285i) q^{47} +5.70248 q^{49} +(-1.34935 + 2.33715i) q^{51} +(2.89540 + 1.67166i) q^{53} +(-0.249713 + 0.144172i) q^{55} +(-1.07288 + 4.22480i) q^{57} +(-5.90978 - 10.2360i) q^{59} +(3.59876 - 6.23323i) q^{61} +(-0.986479 - 0.569544i) q^{63} -0.0724644i q^{65} +(3.01280 - 5.21833i) q^{67} +7.93253i q^{69} +(2.69279 + 4.66405i) q^{71} +(-4.87607 - 8.44559i) q^{73} -4.98224 q^{75} -2.46477 q^{77} +(-5.57634 - 9.65851i) q^{79} +(-0.500000 - 0.866025i) q^{81} -8.00865i q^{83} +(0.179811 - 0.311442i) q^{85} -3.11541i q^{87} +(-10.5189 - 6.07310i) q^{89} +(0.309714 - 0.536441i) q^{91} +(-4.53868 - 7.86122i) q^{93} +(0.142969 - 0.562986i) q^{95} +(6.55667 - 3.78549i) q^{97} +(-1.87392 - 1.08191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) \) 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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