LMFDB - Embedded newform 864.2.bh.b.815.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(47,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 9, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bh (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			815.3
Character	$\chi$	$=$	864.815
Dual form			864.2.bh.b.335.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.59734 + 0.669704i) q^{3} +(-3.00936 + 1.09532i) q^{5} +(-4.58614 + 0.808660i) q^{7} +(2.10299 - 2.13949i) q^{9} +(0.303411 - 0.833616i) q^{11} +(-1.22056 + 1.45461i) q^{13} +(4.07344 - 3.76498i) q^{15} +(-4.03247 - 2.32815i) q^{17} +(0.171350 + 0.296787i) q^{19} +(6.78406 - 4.36306i) q^{21} +(-1.00156 + 5.68012i) q^{23} +(4.02633 - 3.37849i) q^{25} +(-1.92637 + 4.82588i) q^{27} +(4.16935 - 3.49850i) q^{29} +(7.80815 + 1.37679i) q^{31} +(0.0736241 + 1.53476i) q^{33} +(12.9156 - 7.45683i) q^{35} +(2.31812 + 1.33837i) q^{37} +(0.975496 - 3.14092i) q^{39} +(0.0346849 - 0.0413359i) q^{41} +(2.85915 + 1.04064i) q^{43} +(-3.98525 + 8.74195i) q^{45} +(-1.90179 - 10.7856i) q^{47} +(13.8009 - 5.02311i) q^{49} +(8.00039 + 1.01828i) q^{51} -1.27415 q^{53} +2.84099i q^{55} +(-0.472464 - 0.359316i) q^{57} +(-2.43399 - 6.68734i) q^{59} +(-8.19039 + 1.44419i) q^{61} +(-7.91450 + 11.5126i) q^{63} +(2.07985 - 5.71435i) q^{65} +(6.31205 + 5.29644i) q^{67} +(-2.20417 - 9.74384i) q^{69} +(-0.186788 + 0.323526i) q^{71} +(6.29550 + 10.9041i) q^{73} +(-4.16883 + 8.09304i) q^{75} +(-0.717374 + 4.06843i) q^{77} +(-2.54509 - 3.03312i) q^{79} +(-0.154829 - 8.99867i) q^{81} +(-8.90996 - 10.6185i) q^{83} +(14.6852 + 2.58940i) q^{85} +(-4.31692 + 8.38053i) q^{87} +(-6.35012 + 3.66624i) q^{89} +(4.42138 - 7.65805i) q^{91} +(-13.3943 + 3.02994i) q^{93} +(-0.840731 - 0.705457i) q^{95} +(-0.833364 - 0.303320i) q^{97} +(-1.14544 - 2.40223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67}+ \cdots + 12 q^{99}+O(q^{100}) $ 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$	$-1$

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
$3$	−1.59734	+	0.669704i	−0.922225	+	0.386654i
$3$	−1.59734	+	0.669704i	−0.922225	+	0.386654i
$4$		0			0
$5$	−3.00936	+	1.09532i	−1.34583	+	0.489842i	−0.911643	−	0.410982i	$-0.865186\pi$
$5$	−3.00936	+	1.09532i	−1.34583	+	0.489842i	−0.434185	+	0.900824i	$0.642964\pi$
$6$		0			0
$7$	−4.58614	+	0.808660i	−1.73340	+	0.305645i	−0.949155	−	0.314810i	$-0.898059\pi$
$7$	−4.58614	+	0.808660i	−1.73340	+	0.305645i	−0.784242	+	0.620455i	$0.786948\pi$
$8$		0			0
$9$	2.10299	−	2.13949i	0.700998	−	0.713163i
$10$		0			0
$11$	0.303411	−	0.833616i	0.0914819	−	0.251345i	−0.885510	−	0.464620i	$-0.846191\pi$
$11$	0.303411	−	0.833616i	0.0914819	−	0.251345i	0.976992	+	0.213275i	$0.0684132\pi$
$12$		0			0
$13$	−1.22056	+	1.45461i	−0.338523	+	0.403436i	−0.908270	−	0.418384i	$-0.862597\pi$
$13$	−1.22056	+	1.45461i	−0.338523	+	0.403436i	0.569747	+	0.821820i	$0.307041\pi$
$14$		0			0
$15$	4.07344	−	3.76498i	1.05176	−	0.972113i
$16$		0			0
$17$	−4.03247	−	2.32815i	−0.978017	−	0.564658i	−0.0763460	−	0.997081i	$-0.524325\pi$
$17$	−4.03247	−	2.32815i	−0.978017	−	0.564658i	−0.901671	+	0.432423i	$0.857659\pi$
$18$		0			0
$19$	0.171350	+	0.296787i	0.0393104	+	0.0680876i	0.885011	−	0.465570i	$-0.154151\pi$
$19$	0.171350	+	0.296787i	0.0393104	+	0.0680876i	−0.845701	+	0.533657i	$0.820817\pi$
$20$		0			0
$21$	6.78406	−	4.36306i	1.48040	−	0.952097i
$22$		0			0
$23$	−1.00156	+	5.68012i	−0.208839	+	1.18439i	0.682443	+	0.730939i	$0.260918\pi$
$23$	−1.00156	+	5.68012i	−0.208839	+	1.18439i	−0.891282	+	0.453449i	$0.850194\pi$
$24$		0			0
$25$	4.02633	−	3.37849i	0.805265	−	0.675698i
$26$		0			0
$27$	−1.92637	+	4.82588i	−0.370731	+	0.928740i
$28$		0			0
$29$	4.16935	−	3.49850i	0.774229	−	0.649655i	−0.167559	−	0.985862i	$-0.553589\pi$
$29$	4.16935	−	3.49850i	0.774229	−	0.649655i	0.941788	+	0.336207i	$0.109144\pi$
$30$		0			0
$31$	7.80815	+	1.37679i	1.40238	+	0.247278i	0.823123	−	0.567864i	$-0.192230\pi$
$31$	7.80815	+	1.37679i	1.40238	+	0.247278i	0.579262	+	0.815142i	$0.303341\pi$
$32$		0			0
$33$	0.0736241	+	1.53476i	0.0128163	+	0.267168i
$34$		0			0
$35$	12.9156	−	7.45683i	2.18314	−	1.26044i
$36$		0			0
$37$	2.31812	+	1.33837i	0.381097	+	0.220026i	0.678295	−	0.734789i	$-0.262719\pi$
$37$	2.31812	+	1.33837i	0.381097	+	0.220026i	−0.297199	+	0.954816i	$0.596052\pi$
$38$		0			0
$39$	0.975496	−	3.14092i	0.156204	−	0.502950i
$40$		0			0
$41$	0.0346849	−	0.0413359i	0.00541687	−	0.00645558i	−0.763329	−	0.646010i	$-0.776437\pi$
$41$	0.0346849	−	0.0413359i	0.00541687	−	0.00645558i	0.768746	+	0.639554i	$0.220881\pi$
$42$		0			0
$43$	2.85915	+	1.04064i	0.436016	+	0.158697i	0.550696	−	0.834706i	$-0.314362\pi$
$43$	2.85915	+	1.04064i	0.436016	+	0.158697i	−0.114681	+	0.993402i	$0.536584\pi$
$44$		0			0
$45$	−3.98525	+	8.74195i	−0.594086	+	1.30317i
$46$		0			0
$47$	−1.90179	−	10.7856i	−0.277404	−	1.57324i	−0.731219	−	0.682143i	$-0.761048\pi$
$47$	−1.90179	−	10.7856i	−0.277404	−	1.57324i	0.453814	−	0.891096i	$-0.350063\pi$
$48$		0			0
$49$	13.8009	−	5.02311i	1.97155	−	0.717587i
$50$		0			0
$51$	8.00039	+	1.01828i	1.12028	+	0.142588i
$52$		0			0
$53$	−1.27415			−0.175018			−0.0875092	−	0.996164i	$-0.527891\pi$
$53$	−1.27415			−0.175018			−0.0875092	+	0.996164i	$0.527891\pi$
$54$		0			0
$55$			2.84099i			0.383078i
$56$		0			0
$57$	−0.472464	−	0.359316i	−0.0625793	−	0.0475926i
$58$		0			0
$59$	−2.43399	−	6.68734i	−0.316879	−	0.870618i	−0.991223	−	0.132201i	$-0.957796\pi$
$59$	−2.43399	−	6.68734i	−0.316879	−	0.870618i	0.674344	−	0.738417i	$-0.264427\pi$
$60$		0			0
$61$	−8.19039	+	1.44419i	−1.04867	+	0.184909i	−0.671326	−	0.741163i	$-0.734275\pi$
$61$	−8.19039	+	1.44419i	−1.04867	+	0.184909i	−0.377347	+	0.926072i	$0.623164\pi$
$62$		0			0
$63$	−7.91450	+	11.5126i	−0.997134	+	1.45045i
$64$		0			0
$65$	2.07985	−	5.71435i	0.257974	−	0.708778i
$66$		0			0
$67$	6.31205	+	5.29644i	0.771139	+	0.647063i	0.941000	−	0.338405i	$-0.109887\pi$
$67$	6.31205	+	5.29644i	0.771139	+	0.647063i	−0.169861	+	0.985468i	$0.554332\pi$
$68$		0			0
$69$	−2.20417	−	9.74384i	−0.265351	−	1.17302i
$70$		0			0
$71$	−0.186788	+	0.323526i	−0.0221676	+	0.0383955i	−0.876896	−	0.480679i	$-0.840390\pi$
$71$	−0.186788	+	0.323526i	−0.0221676	+	0.0383955i	0.854729	+	0.519075i	$0.173723\pi$
$72$		0			0
$73$	6.29550	+	10.9041i	0.736832	+	1.27623i	0.953915	+	0.300077i	$0.0970125\pi$
$73$	6.29550	+	10.9041i	0.736832	+	1.27623i	−0.217083	+	0.976153i	$0.569654\pi$
$74$		0			0
$75$	−4.16883	+	8.09304i	−0.481375	+	0.934504i
$76$		0			0
$77$	−0.717374	+	4.06843i	−0.0817524	+	0.463641i
$78$		0			0
$79$	−2.54509	−	3.03312i	−0.286345	−	0.341252i	0.603628	−	0.797266i	$-0.293721\pi$
$79$	−2.54509	−	3.03312i	−0.286345	−	0.341252i	−0.889973	+	0.456014i	$0.849277\pi$
$80$		0			0
$81$	−0.154829	−	8.99867i	−0.0172032	−	0.999852i
$82$		0			0
$83$	−8.90996	−	10.6185i	−0.977996	−	1.16553i	−0.986199	−	0.165563i	$-0.947056\pi$
$83$	−8.90996	−	10.6185i	−0.977996	−	1.16553i	0.00820363	−	0.999966i	$-0.497389\pi$
$84$		0			0
$85$	14.6852	+	2.58940i	1.59284	+	0.280860i
$86$		0			0
$87$	−4.31692	+	8.38053i	−0.462822	+	0.898487i
$88$		0			0
$89$	−6.35012	+	3.66624i	−0.673111	+	0.388621i	−0.797254	−	0.603644i	$-0.793715\pi$
$89$	−6.35012	+	3.66624i	−0.673111	+	0.388621i	0.124143	+	0.992264i	$0.460382\pi$
$90$		0			0
$91$	4.42138	−	7.65805i	0.463487	−	0.802782i
$92$		0			0
$93$	−13.3943	+	3.02994i	−1.38892	+	0.314191i
$94$		0			0
$95$	−0.840731	−	0.705457i	−0.0862572	−	0.0723783i
$96$		0			0
$97$	−0.833364	−	0.303320i	−0.0846153	−	0.0307975i	0.299366	−	0.954138i	$-0.403225\pi$
$97$	−0.833364	−	0.303320i	−0.0846153	−	0.0307975i	−0.383981	+	0.923341i	$0.625447\pi$
$98$		0			0
$99$	−1.14544	−	2.40223i	−0.115121	−	0.241434i
$100$		0			0
$101$	−1.09507	−	6.21046i	−0.108964	−	0.617964i	−0.989563	−	0.144102i	$-0.953971\pi$
$101$	−1.09507	−	6.21046i	−0.108964	−	0.617964i	0.880599	−	0.473862i	$-0.157140\pi$
$102$		0			0
$103$	−2.99018	−	8.21544i	−0.294631	−	0.809492i	−0.995374	−	0.0960778i	$-0.969370\pi$
$103$	−2.99018	−	8.21544i	−0.294631	−	0.809492i	0.700743	−	0.713414i	$-0.252852\pi$
$104$		0			0
$105$	−15.6368	+	20.5607i	−1.52599	+	2.00652i
$106$		0			0
$107$		−	3.23101i		−	0.312354i	−0.987729	−	0.156177i	$-0.950083\pi$
$107$		−	3.23101i		−	0.312354i	0.987729	−	0.156177i	$-0.0499170\pi$
$108$		0			0
$109$		−	10.8688i		−	1.04104i	−0.853849	−	0.520521i	$-0.825738\pi$
$109$		−	10.8688i		−	1.04104i	0.853849	−	0.520521i	$-0.174262\pi$
$110$		0			0
$111$	−4.59914	−	0.585375i	−0.436531	−	0.0555614i
$112$		0			0
$113$	3.71933	+	10.2188i	0.349885	+	0.961301i	0.982406	+	0.186758i	$0.0597979\pi$
$113$	3.71933	+	10.2188i	0.349885	+	0.961301i	−0.632521	+	0.774543i	$0.717980\pi$
$114$		0			0
$115$	−3.20749	−	18.1906i	−0.299100	−	1.69628i
$116$		0			0
$117$	0.545285	+	5.67041i	0.0504117	+	0.524230i
$118$		0			0
$119$	20.3761	+	7.41630i	1.86788	+	0.679851i
$120$		0			0
$121$	7.82363	+	6.56481i	0.711239	+	0.596801i
$122$		0			0
$123$	−0.0277209	+	0.0892561i	−0.00249950	+	0.00804795i
$124$		0			0
$125$	−0.409913	+	0.709991i	−0.0366638	+	0.0635035i
$126$		0			0
$127$	12.2372	−	7.06513i	1.08587	−	0.626929i	0.153399	−	0.988164i	$-0.450978\pi$
$127$	12.2372	−	7.06513i	1.08587	−	0.626929i	0.932475	+	0.361235i	$0.117645\pi$
$128$		0			0
$129$	−5.26395	+	0.252517i	−0.463465	+	0.0222329i
$130$		0			0
$131$	3.55599	+	0.627016i	0.310688	+	0.0547827i	0.326818	−	0.945087i	$-0.394024\pi$
$131$	3.55599	+	0.627016i	0.310688	+	0.0547827i	−0.0161302	+	0.999870i	$0.505135\pi$
$132$		0			0
$133$	−1.02583	−	1.22254i	−0.0889511	−	0.106008i
$134$		0			0
$135$	0.511290	−	16.6328i	0.0440049	−	1.43152i
$136$		0			0
$137$	−8.46244	−	10.0851i	−0.722995	−	0.861632i	0.271923	−	0.962319i	$-0.412340\pi$
$137$	−8.46244	−	10.0851i	−0.722995	−	0.861632i	−0.994918	+	0.100687i	$0.967896\pi$
$138$		0			0
$139$	−2.08259	+	11.8109i	−0.176643	+	1.00179i	0.759588	+	0.650405i	$0.225401\pi$
$139$	−2.08259	+	11.8109i	−0.176643	+	1.00179i	−0.936230	+	0.351387i	$0.885710\pi$
$140$		0			0
$141$	10.2609	+	15.9546i	0.864128	+	1.34362i
$142$		0			0
$143$	0.842252	+	1.45882i	0.0704327	+	0.121993i
$144$		0			0
$145$	−8.71512	+	15.0950i	−0.723751	+	1.25357i
$146$		0			0
$147$	−18.6807	+	17.2661i	−1.54076	+	1.42408i
$148$		0			0
$149$	6.78333	+	5.69189i	0.555712	+	0.466298i	0.876870	−	0.480728i	$-0.159628\pi$
$149$	6.78333	+	5.69189i	0.555712	+	0.466298i	−0.321158	+	0.947026i	$0.604072\pi$
$150$		0			0
$151$	−1.00187	+	2.75261i	−0.0815308	+	0.224004i	−0.973759	−	0.227580i	$-0.926919\pi$
$151$	−1.00187	+	2.75261i	−0.0815308	+	0.224004i	0.892229	+	0.451584i	$0.149141\pi$
$152$		0			0
$153$	−13.4613	+	3.73134i	−1.08828	+	0.301661i
$154$		0			0
$155$	−25.0056	+	4.40916i	−2.00850	+	0.354152i
$156$		0			0
$157$	−3.73399	−	10.2591i	−0.298005	−	0.818762i	−0.994833	−	0.101524i	$-0.967628\pi$
$157$	−3.73399	−	10.2591i	−0.298005	−	0.818762i	0.696828	−	0.717238i	$-0.254594\pi$
$158$		0			0
$159$	2.03526	−	0.853305i	0.161406	−	0.0676715i
$160$		0			0
$161$		−	26.8597i		−	2.11684i
$162$		0			0
$163$	0.983434			0.0770285			0.0385143	−	0.999258i	$-0.487737\pi$
$163$	0.983434			0.0770285			0.0385143	+	0.999258i	$0.487737\pi$
$164$		0			0
$165$	−1.90262	−	4.53802i	−0.148119	−	0.353284i
$166$		0			0
$167$	−1.50427	+	0.547510i	−0.116404	+	0.0423676i	−0.399565	−	0.916705i	$-0.630839\pi$
$167$	−1.50427	+	0.547510i	−0.116404	+	0.0423676i	0.283161	+	0.959072i	$0.408617\pi$
$168$		0			0
$169$	1.63131	+	9.25162i	0.125485	+	0.711663i
$170$		0			0
$171$	0.995320	+	0.257540i	0.0761141	+	0.0196946i
$172$		0			0
$173$	13.3229	+	4.84914i	1.01292	+	0.368673i	0.794554	−	0.607193i	$-0.207705\pi$
$173$	13.3229	+	4.84914i	1.01292	+	0.368673i	0.218367	+	0.975867i	$0.429927\pi$
$174$		0			0
$175$	−15.7332	+	18.7501i	−1.18932	+	1.41738i
$176$		0			0
$177$	8.36646	+	9.05191i	0.628861	+	0.680383i
$178$		0			0
$179$	5.27151	+	3.04351i	0.394011	+	0.227483i	0.683897	−	0.729579i	$-0.260284\pi$
$179$	5.27151	+	3.04351i	0.394011	+	0.227483i	−0.289885	+	0.957061i	$0.593617\pi$
$180$		0			0
$181$	−11.4059	+	6.58520i	−0.847795	+	0.489474i	−0.859906	−	0.510452i	$-0.829478\pi$
$181$	−11.4059	+	6.58520i	−0.847795	+	0.489474i	0.0121116	+	0.999927i	$0.496145\pi$
$182$		0			0
$183$	12.1157	−	7.79200i	0.895616	−	0.576001i
$184$		0			0
$185$	−8.44201	−	1.48855i	−0.620669	−	0.109441i
$186$		0			0
$187$	−3.16427	+	2.65514i	−0.231395	+	0.194163i
$188$		0			0
$189$	4.93213	−	23.6899i	0.358760	−	1.72319i
$190$		0			0
$191$	−16.3786	+	13.7433i	−1.18512	+	0.994431i	−0.185185	+	0.982704i	$0.559288\pi$
$191$	−16.3786	+	13.7433i	−1.18512	+	0.994431i	−0.999931	+	0.0117270i	$0.996267\pi$
$192$		0			0
$193$	3.64547	−	20.6745i	0.262407	−	1.48818i	−0.513912	−	0.857843i	$-0.671804\pi$
$193$	3.64547	−	20.6745i	0.262407	−	1.48818i	0.776319	−	0.630341i	$-0.217085\pi$
$194$		0			0
$195$	0.504686	+	10.5207i	0.0361413	+	0.753399i
$196$		0			0
$197$	−5.23281	−	9.06349i	−0.372822	−	0.645747i	0.617176	−	0.786825i	$-0.288277\pi$
$197$	−5.23281	−	9.06349i	−0.372822	−	0.645747i	−0.989999	+	0.141078i	$0.954943\pi$
$198$		0			0
$199$	−14.3685	−	8.29565i	−1.01855	−	0.588063i	−0.104870	−	0.994486i	$-0.533443\pi$
$199$	−14.3685	−	8.29565i	−1.01855	−	0.588063i	−0.913685	+	0.406423i	$0.866776\pi$
$200$		0			0
$201$	−13.6295	−	4.23301i	−0.961353	−	0.298574i
$202$		0			0
$203$	−16.2921	+	19.4162i	−1.14348	+	1.36275i
$204$		0			0
$205$	−0.0591036	+	0.162386i	−0.00412797	+	0.0113415i
$206$		0			0
$207$	10.0463	+	14.0881i	0.698265	+	0.979190i
$208$		0			0
$209$	0.299396	−	0.0527915i	0.0207096	−	0.00365167i
$210$		0			0
$211$	8.76523	−	3.19028i	0.603423	−	0.219628i	−0.0222000	−	0.999754i	$-0.507067\pi$
$211$	8.76523	−	3.19028i	0.603423	−	0.219628i	0.625623	+	0.780126i	$0.284845\pi$
$212$		0			0
$213$	0.0816973	−	0.641874i	0.00559781	−	0.0439805i
$214$		0			0
$215$	−9.74405			−0.664539
$216$		0			0
$217$	−36.9226			−2.50647
$218$		0			0
$219$	−17.3586	−	13.2015i	−1.17298	−	0.892073i
$220$		0			0
$221$	8.30841	−	3.02402i	0.558884	−	0.203417i
$222$		0			0
$223$	18.4672	−	3.25626i	1.23665	−	0.218055i	0.483172	−	0.875525i	$-0.339485\pi$
$223$	18.4672	−	3.25626i	1.23665	−	0.218055i	0.753481	+	0.657470i	$0.228373\pi$
$224$		0			0
$225$	1.23910	−	15.7192i	0.0826067	−	1.04795i
$226$		0			0
$227$	−1.73323	+	4.76200i	−0.115038	+	0.316065i	−0.983828	−	0.179116i	$-0.942676\pi$
$227$	−1.73323	+	4.76200i	−0.115038	+	0.316065i	0.868790	+	0.495181i	$0.164898\pi$
$228$		0			0
$229$	−14.4905	+	17.2691i	−0.957559	+	1.14117i	0.0323508	+	0.999477i	$0.489701\pi$
$229$	−14.4905	+	17.2691i	−0.957559	+	1.14117i	−0.989910	+	0.141698i	$0.954744\pi$
$230$		0			0
$231$	−1.57875	−	6.97910i	−0.103874	−	0.459191i
$232$		0			0
$233$	4.93700	+	2.85038i	0.323434	+	0.186735i	0.652922	−	0.757425i	$-0.273543\pi$
$233$	4.93700	+	2.85038i	0.323434	+	0.186735i	−0.329488	+	0.944160i	$0.606876\pi$
$234$		0			0
$235$	17.5368	+	30.3747i	1.14398	+	1.98143i
$236$		0			0
$237$	6.09666	+	3.14047i	0.396020	+	0.203995i
$238$		0			0
$239$	3.99952	−	22.6824i	0.258707	−	1.46720i	−0.527667	−	0.849451i	$-0.676933\pi$
$239$	3.99952	−	22.6824i	0.258707	−	1.46720i	0.786374	−	0.617750i	$-0.211956\pi$
$240$		0			0
$241$	16.6164	−	13.9428i	1.07036	−	0.898137i	0.0752732	−	0.997163i	$-0.476017\pi$
$241$	16.6164	−	13.9428i	1.07036	−	0.898137i	0.995085	+	0.0990259i	$0.0315727\pi$
$242$		0			0
$243$	6.27375	+	14.2702i	0.402462	+	0.915437i
$244$		0			0
$245$	−36.0300	+	30.2327i	−2.30187	+	1.93150i
$246$		0			0
$247$	−0.640852	−	0.112999i	−0.0407764	−	0.00718999i
$248$		0			0
$249$	21.3435	+	10.9943i	1.35259	+	0.696735i
$250$		0			0
$251$	6.86745	−	3.96493i	0.433470	−	0.250264i	−0.267354	−	0.963598i	$-0.586149\pi$
$251$	6.86745	−	3.96493i	0.433470	−	0.250264i	0.700824	+	0.713334i	$0.252816\pi$
$252$		0			0
$253$	4.43115	+	2.55833i	0.278584	+	0.160841i
$254$		0			0
$255$	−25.1914	+	5.69859i	−1.57755	+	0.356860i
$256$		0			0
$257$	0.0798480	−	0.0951592i	0.00498078	−	0.00593587i	−0.763548	−	0.645751i	$-0.776545\pi$
$257$	0.0798480	−	0.0951592i	0.00498078	−	0.00593587i	0.768529	+	0.639815i	$0.220989\pi$
$258$		0			0
$259$	−11.7135	−	4.26337i	−0.727842	−	0.264913i
$260$		0			0
$261$	1.28312	−	16.2776i	0.0794229	−	1.00756i
$262$		0			0
$263$	−0.961362	−	5.45215i	−0.0592801	−	0.336194i	0.940715	−	0.339197i	$-0.110155\pi$
$263$	−0.961362	−	5.45215i	−0.0592801	−	0.336194i	−0.999995	+	0.00300271i	$0.999044\pi$
$264$		0			0
$265$	3.83439	−	1.39560i	0.235545	−	0.0857313i
$266$		0			0
$267$	7.68800	−	10.1089i	0.470498	−	0.618657i
$268$		0			0
$269$	5.59805			0.341319			0.170659	−	0.985330i	$-0.445410\pi$
$269$	5.59805			0.341319			0.170659	+	0.985330i	$0.445410\pi$
$270$		0			0
$271$			1.56554i			0.0951000i	0.998869	+	0.0475500i	$0.0151413\pi$
$271$			1.56554i			0.0951000i	−0.998869	+	0.0475500i	$0.984859\pi$
$272$		0			0
$273$	−1.93382	+	15.1935i	−0.117040	+	0.919555i
$274$		0			0
$275$	−1.59473	−	4.38148i	−0.0961657	−	0.264213i
$276$		0			0
$277$	27.6100	−	4.86839i	1.65893	−	0.292513i	0.735854	−	0.677140i	$-0.236781\pi$
$277$	27.6100	−	4.86839i	1.65893	−	0.292513i	0.923072	+	0.384627i	$0.125670\pi$
$278$		0			0
$279$	19.3661	−	13.8101i	1.15942	−	0.826787i
$280$		0			0
$281$	3.07719	−	8.45452i	0.183570	−	0.504354i	−0.813438	−	0.581651i	$-0.802407\pi$
$281$	3.07719	−	8.45452i	0.183570	−	0.504354i	0.997008	+	0.0772972i	$0.0246290\pi$
$282$		0			0
$283$	22.1256	+	18.5656i	1.31523	+	1.10361i	0.987293	+	0.158909i	$0.0507976\pi$
$283$	22.1256	+	18.5656i	1.31523	+	1.10361i	0.327936	+	0.944700i	$0.393647\pi$
$284$		0			0
$285$	1.81538	+	0.563815i	0.107534	+	0.0333975i
$286$		0			0
$287$	−0.125643	+	0.217620i	−0.00741648	+	0.0128457i
$288$		0			0
$289$	2.34052	+	4.05391i	0.137678	+	0.238465i
$290$		0			0
$291$	1.53430	−	0.0736019i	0.0899423	−	0.00431462i
$292$		0			0
$293$	3.10437	−	17.6058i	0.181359	−	1.02854i	−0.749185	−	0.662360i	$-0.769555\pi$
$293$	3.10437	−	17.6058i	0.181359	−	1.02854i	0.930545	−	0.366179i	$-0.119334\pi$
$294$		0			0
$295$	14.6495	+	17.4587i	0.852930	+	1.01648i
$296$		0			0
$297$	3.43844	+	3.07008i	0.199519	+	0.178144i
$298$		0			0
$299$	−7.03989	−	8.38981i	−0.407127	−	0.485196i
$300$		0			0
$301$	−13.9540	−	2.46046i	−0.804293	−	0.141819i
$302$		0			0
$303$	5.90837	+	9.18685i	0.339427	+	0.527771i
$304$		0			0
$305$	23.0660	−	13.3172i	1.32076	−	0.762540i
$306$		0			0
$307$	−2.66885	+	4.62258i	−0.152319	+	0.263825i	−0.932080	−	0.362253i	$-0.882008\pi$
$307$	−2.66885	+	4.62258i	−0.152319	+	0.263825i	0.779760	+	0.626078i	$0.215341\pi$
$308$		0			0
$309$	10.2782	+	11.1203i	0.584709	+	0.632613i
$310$		0			0
$311$	7.48203	+	6.27817i	0.424267	+	0.356002i	0.829783	−	0.558086i	$-0.188464\pi$
$311$	7.48203	+	6.27817i	0.424267	+	0.356002i	−0.405517	+	0.914088i	$0.632908\pi$
$312$		0			0
$313$	−20.9377	−	7.62069i	−1.18347	−	0.430747i	−0.326042	−	0.945355i	$-0.605715\pi$
$313$	−20.9377	−	7.62069i	−1.18347	−	0.430747i	−0.857425	+	0.514608i	$0.827937\pi$
$314$		0			0
$315$	11.2077	−	43.3145i	0.631480	−	2.44050i
$316$		0			0
$317$	−2.75422	−	15.6200i	−0.154692	−	0.877304i	−0.959067	−	0.283181i	$-0.908610\pi$
$317$	−2.75422	−	15.6200i	−0.154692	−	0.877304i	0.804374	−	0.594123i	$-0.202501\pi$
$318$		0			0
$319$	−1.65138	−	4.53712i	−0.0924593	−	0.254030i
$320$		0			0
$321$	2.16382	+	5.16103i	0.120773	+	0.288060i
$322$		0			0
$323$		−	1.59571i		−	0.0887877i
$324$		0			0
$325$			9.98038i			0.553612i
$326$		0			0
$327$	7.27887	+	17.3612i	0.402522	+	0.960075i
$328$		0			0
$329$	17.4437	+	47.9263i	0.961704	+	2.64226i
$330$		0			0
$331$	−4.91331	−	27.8648i	−0.270060	−	1.53159i	−0.754229	−	0.656611i	$-0.771989\pi$
$331$	−4.91331	−	27.8648i	−0.270060	−	1.53159i	0.484169	−	0.874974i	$-0.339122\pi$
$332$		0			0
$333$	7.73842	−	2.14501i	0.424063	−	0.117546i
$334$		0			0
$335$	−24.7965	−	9.02520i	−1.35478	−	0.493099i
$336$		0			0
$337$	−2.65131	−	2.22472i	−0.144426	−	0.121188i	0.567712	−	0.823227i	$-0.307829\pi$
$337$	−2.65131	−	2.22472i	−0.144426	−	0.121188i	−0.712138	+	0.702039i	$0.752273\pi$
$338$		0			0
$339$	−12.7846	−	13.8320i	−0.694363	−	0.751251i
$340$		0			0
$341$	3.51679	−	6.09126i	0.190445	−	0.329860i
$342$		0			0
$343$	−30.9999	+	17.8978i	−1.67383	+	0.966389i
$344$		0			0
$345$	17.3058	+	26.9085i	0.931710	+	1.44870i
$346$		0			0
$347$	21.3082	+	3.75721i	1.14388	+	0.201698i	0.713304	−	0.700854i	$-0.247198\pi$
$347$	21.3082	+	3.75721i	1.14388	+	0.201698i	0.430581	+	0.902552i	$0.358309\pi$
$348$		0			0
$349$	13.6098	+	16.2195i	0.728514	+	0.868209i	0.995428	−	0.0955113i	$-0.0304486\pi$
$349$	13.6098	+	16.2195i	0.728514	+	0.868209i	−0.266915	+	0.963720i	$0.586004\pi$
$350$		0			0
$351$	−4.66850	−	8.69240i	−0.249186	−	0.463966i
$352$		0			0
$353$	−10.0326	−	11.9564i	−0.533980	−	0.636373i	0.429847	−	0.902902i	$-0.358568\pi$
$353$	−10.0326	−	11.9564i	−0.533980	−	0.636373i	−0.963827	+	0.266529i	$0.914123\pi$
$354$		0			0
$355$	0.207748	−	1.17820i	0.0110261	−	0.0625324i
$356$		0			0
$357$	−37.5143	+	1.79960i	−1.98547	+	0.0952449i
$358$		0			0
$359$	−2.44114	−	4.22817i	−0.128838	−	0.223154i	0.794389	−	0.607410i	$-0.207791\pi$
$359$	−2.44114	−	4.22817i	−0.128838	−	0.223154i	−0.923227	+	0.384256i	$0.874458\pi$
$360$		0			0
$361$	9.44128	−	16.3528i	0.496909	−	0.860672i
$362$		0			0
$363$	−16.8935	−	5.24672i	−0.886678	−	0.275381i
$364$		0			0
$365$	−30.8889	−	25.9189i	−1.61680	−	1.35666i
$366$		0			0
$367$	3.44230	−	9.45764i	0.179687	−	0.493685i	−0.816849	−	0.576852i	$-0.804281\pi$
$367$	3.44230	−	9.45764i	0.179687	−	0.493685i	0.996536	+	0.0831666i	$0.0265033\pi$
$368$		0			0
$369$	−0.0154955	−	0.161137i	−0.000806662	−	0.00838846i
$370$		0			0
$371$	5.84344	−	1.03036i	0.303376	−	0.0534935i
$372$		0			0
$373$	−0.511543	−	1.40545i	−0.0264867	−	0.0727717i	0.925745	−	0.378149i	$-0.123439\pi$
$373$	−0.511543	−	1.40545i	−0.0264867	−	0.0727717i	−0.952231	+	0.305378i	$0.901217\pi$
$374$		0			0
$375$	0.179288	−	1.40862i	0.00925839	−	0.0727407i
$376$		0			0
$377$			10.3349i			0.532275i
$378$		0			0
$379$	−26.4034			−1.35625			−0.678126	−	0.734945i	$-0.737208\pi$
$379$	−26.4034			−1.35625			−0.678126	+	0.734945i	$0.737208\pi$
$380$		0			0
$381$	−14.8154	+	19.4807i	−0.759015	+	0.998027i
$382$		0			0
$383$	14.7665	−	5.37456i	0.754532	−	0.274627i	0.0640204	−	0.997949i	$-0.479608\pi$
$383$	14.7665	−	5.37456i	0.754532	−	0.274627i	0.690511	+	0.723321i	$0.257386\pi$
$384$		0			0
$385$	−2.29739	−	13.0291i	−0.117086	−	0.664027i
$386$		0			0
$387$	8.23922	−	3.92864i	0.418823	−	0.199704i
$388$		0			0
$389$	19.0208	+	6.92300i	0.964393	+	0.351010i	0.775753	−	0.631036i	$-0.217370\pi$
$389$	19.0208	+	6.92300i	0.964393	+	0.351010i	0.188639	+	0.982046i	$0.439592\pi$
$390$		0			0
$391$	17.2629	−	20.5731i	0.873023	−	1.04043i
$392$		0			0
$393$	−6.10004	+	1.37990i	−0.307706	+	0.0696066i
$394$		0			0
$395$	10.9813	+	6.34007i	0.552530	+	0.319003i
$396$		0			0
$397$	23.8679	−	13.7801i	1.19789	−	0.691604i	0.237808	−	0.971312i	$-0.423571\pi$
$397$	23.8679	−	13.7801i	1.19789	−	0.691604i	0.960085	+	0.279708i	$0.0902376\pi$
$398$		0			0
$399$	2.45735	+	1.26581i	0.123021	+	0.0633698i
$400$		0			0
$401$	−6.68368	−	1.17851i	−0.333767	−	0.0588521i	0.00425323	−	0.999991i	$-0.498646\pi$
$401$	−6.68368	−	1.17851i	−0.333767	−	0.0588521i	−0.338020	+	0.941139i	$0.609757\pi$
$402$		0			0
$403$	−11.5330	+	9.67734i	−0.574500	+	0.482063i
$404$		0			0
$405$	10.3223	+	26.9107i	0.512922	+	1.33720i
$406$		0			0
$407$	1.81903	−	1.52635i	0.0901659	−	0.0756581i
$408$		0			0
$409$	−2.97274	+	16.8592i	−0.146992	+	0.833636i	0.818753	+	0.574145i	$0.194666\pi$
$409$	−2.97274	+	16.8592i	−0.146992	+	0.833636i	−0.965746	+	0.259490i	$0.916445\pi$
$410$		0			0
$411$	20.2715	+	10.4421i	0.999917	+	0.515070i
$412$		0			0
$413$	16.5704	+	28.7008i	0.815377	+	1.41227i
$414$		0			0
$415$	38.4439	+	22.1956i	1.88714	+	1.08954i
$416$		0			0
$417$	−4.58323	−	20.2608i	−0.224442	−	0.992177i
$418$		0			0
$419$	−0.999049	+	1.19062i	−0.0488067	+	0.0581656i	−0.789896	−	0.613241i	$-0.789865\pi$
$419$	−0.999049	+	1.19062i	−0.0488067	+	0.0581656i	0.741089	+	0.671407i	$0.234310\pi$
$420$		0			0
$421$	4.61578	−	12.6818i	0.224959	−	0.618071i	−0.774943	−	0.632031i	$-0.782222\pi$
$421$	4.61578	−	12.6818i	0.224959	−	0.618071i	0.999903	+	0.0139601i	$0.00444380\pi$
$422$		0			0
$423$	−27.0751	−	18.6132i	−1.31644	−	0.905003i
$424$		0			0
$425$	−24.1016	+	4.24977i	−1.16910	+	0.206144i
$426$		0			0
$427$	36.3944	−	13.2465i	1.76125	−	0.641042i
$428$		0			0
$429$	−2.32234	−	1.76618i	−0.112124	−	0.0852719i
$430$		0			0
$431$	32.6219			1.57134			0.785671	−	0.618644i	$-0.212318\pi$
$431$	32.6219			1.57134			0.785671	+	0.618644i	$0.212318\pi$
$432$		0			0
$433$	−20.4173			−0.981192			−0.490596	−	0.871387i	$-0.663221\pi$
$433$	−20.4173			−0.981192			−0.490596	+	0.871387i	$0.663221\pi$
$434$		0			0
$435$	3.81182	−	29.9485i	0.182763	−	1.43592i
$436$		0			0
$437$	−1.85740	+	0.676039i	−0.0888516	+	0.0323393i
$438$		0			0
$439$	−5.01912	+	0.885007i	−0.239550	+	0.0422391i	−0.292134	−	0.956377i	$-0.594365\pi$
$439$	−5.01912	+	0.885007i	−0.239550	+	0.0422391i	0.0525843	+	0.998616i	$0.483254\pi$
$440$		0			0
$441$	18.2763	−	40.0904i	0.870299	−	1.90907i
$442$		0			0
$443$	−6.33577	+	17.4074i	−0.301022	+	0.827050i	0.693301	+	0.720648i	$0.256155\pi$
$443$	−6.33577	+	17.4074i	−0.301022	+	0.827050i	−0.994323	+	0.106403i	$0.966067\pi$
$444$		0			0
$445$	15.0941	−	17.9885i	0.715529	−	0.852735i
$446$		0			0
$447$	−14.6472	−	4.54907i	−0.692787	−	0.215163i
$448$		0			0
$449$	16.4019	+	9.46962i	0.774052	+	0.446899i	0.834318	−	0.551283i	$-0.185862\pi$
$449$	16.4019	+	9.46962i	0.774052	+	0.446899i	−0.0602665	+	0.998182i	$0.519195\pi$
$450$		0			0
$451$	−0.0239344	−	0.0414557i	−0.00112703	−	0.00195207i
$452$		0			0
$453$	−0.243108	−	5.06781i	−0.0114222	−	0.238106i
$454$		0			0
$455$	−4.91753	+	27.8887i	−0.230537	+	1.30744i
$456$		0			0
$457$	−8.02025	+	6.72979i	−0.375172	+	0.314806i	−0.810803	−	0.585319i	$-0.800969\pi$
$457$	−8.02025	+	6.72979i	−0.375172	+	0.314806i	0.435632	+	0.900125i	$0.356525\pi$
$458$		0			0
$459$	19.0034	−	14.9753i	0.887002	−	0.698987i
$460$		0			0
$461$	18.6832	−	15.6771i	0.870163	−	0.730153i	−0.0939698	−	0.995575i	$-0.529956\pi$
$461$	18.6832	−	15.6771i	0.870163	−	0.730153i	0.964132	+	0.265422i	$0.0855113\pi$
$462$		0			0
$463$	−15.5149	−	2.73570i	−0.721039	−	0.127139i	−0.198925	−	0.980015i	$-0.563745\pi$
$463$	−15.5149	−	2.73570i	−0.721039	−	0.127139i	−0.522113	+	0.852876i	$0.674856\pi$
$464$		0			0
$465$	36.9896	−	23.7892i	1.71535	−	1.10320i
$466$		0			0
$467$	6.64718	−	3.83775i	0.307595	−	0.177590i	−0.338255	−	0.941055i	$-0.609837\pi$
$467$	6.64718	−	3.83775i	0.307595	−	0.177590i	0.645850	+	0.763465i	$0.276503\pi$
$468$		0			0
$469$	−33.2309	−	19.1859i	−1.53446	−	0.885922i
$470$		0			0
$471$	12.8350	+	13.8865i	0.591405	+	0.639858i
$472$		0			0
$473$	1.73499	−	2.06769i	0.0797751	−	0.0950723i
$474$		0			0
$475$	1.69260	+	0.616057i	0.0776619	+	0.0282666i
$476$		0			0
$477$	−2.67954	+	2.72604i	−0.122688	+	0.124817i
$478$		0			0
$479$	5.41592	+	30.7152i	0.247460	+	1.40341i	0.814710	+	0.579869i	$0.196896\pi$
$479$	5.41592	+	30.7152i	0.247460	+	1.40341i	−0.567250	+	0.823545i	$0.691993\pi$
$480$		0			0
$481$	−4.77621	+	1.73840i	−0.217776	+	0.0792641i
$482$		0			0
$483$	17.9881	+	42.9042i	0.818485	+	1.95221i
$484$		0			0
$485$	2.84013			0.128964
$486$		0			0
$487$		−	14.2176i		−	0.644263i	−0.946695	−	0.322131i	$-0.895601\pi$
$487$		−	14.2176i		−	0.644263i	0.946695	−	0.322131i	$-0.104399\pi$
$488$		0			0
$489$	−1.57088	+	0.658609i	−0.0710376	+	0.0297833i
$490$		0			0
$491$	−0.483056	−	1.32718i	−0.0218000	−	0.0598950i	0.928315	−	0.371794i	$-0.121257\pi$
$491$	−0.483056	−	1.32718i	−0.0218000	−	0.0598950i	−0.950115	+	0.311899i	$0.899035\pi$
$492$		0			0
$493$	−24.9578	+	4.40073i	−1.12404	+	0.198199i
$494$		0			0
$495$	6.07826	+	5.97458i	0.273197	+	0.268537i
$496$		0			0
$497$	0.595012	−	1.63478i	0.0266899	−	0.0733300i
$498$		0			0
$499$	−22.9472	−	19.2550i	−1.02726	−	0.861971i	−0.0367345	−	0.999325i	$-0.511696\pi$
$499$	−22.9472	−	19.2550i	−1.02726	−	0.861971i	−0.990522	+	0.137355i	$0.956140\pi$
$500$		0			0
$501$	2.03616	−	1.88198i	0.0909691	−	0.0840805i
$502$		0			0
$503$	4.40212	−	7.62469i	0.196281	−	0.339968i	−0.751039	−	0.660258i	$-0.770447\pi$
$503$	4.40212	−	7.62469i	0.196281	−	0.339968i	0.947320	+	0.320290i	$0.103780\pi$
$504$		0			0
$505$	10.0979	+	17.4901i	0.449351	+	0.778299i
$506$		0			0
$507$	−8.80160	−	13.6855i	−0.390893	−	0.607794i
$508$		0			0
$509$	−3.62638	+	20.5662i	−0.160737	+	0.911582i	0.792616	+	0.609722i	$0.208719\pi$
$509$	−3.62638	+	20.5662i	−0.160737	+	0.911582i	−0.953352	+	0.301860i	$0.902392\pi$
$510$		0			0
$511$	−37.6897	−	44.9169i	−1.66730	−	1.98701i
$512$		0			0
$513$	−1.76234	+	0.255191i	−0.0778093	+	0.0112670i
$514$		0			0
$515$	17.9971	+	21.4481i	0.793045	+	0.945114i
$516$		0			0
$517$	−9.56806	−	1.68711i	−0.420803	−	0.0741988i
$518$		0			0
$519$	−24.5287	+	1.17667i	−1.07669	+	0.0516499i
$520$		0			0
$521$	18.8404	−	10.8775i	0.825413	−	0.476552i	−0.0268665	−	0.999639i	$-0.508553\pi$
$521$	18.8404	−	10.8775i	0.825413	−	0.476552i	0.852280	+	0.523087i	$0.175220\pi$
$522$		0			0
$523$	−2.21522	+	3.83687i	−0.0968647	+	0.167775i	−0.910385	−	0.413761i	$-0.864215\pi$
$523$	−2.21522	+	3.83687i	−0.0968647	+	0.167775i	0.813521	+	0.581536i	$0.197548\pi$
$524$		0			0
$525$	12.5743	−	40.4870i	0.548788	−	1.76700i
$526$		0			0
$527$	−28.2807	−	23.7303i	−1.23193	−	1.03371i
$528$		0			0
$529$	−9.64774	−	3.51149i	−0.419467	−	0.152673i
$530$		0			0
$531$	−19.4262	−	8.85594i	−0.843024	−	0.384315i
$532$		0			0
$533$	0.0177924	+	0.100906i	0.000770676	+	0.00437072i
$534$		0			0
$535$	3.53899	+	9.72329i	0.153004	+	0.420375i
$536$		0			0
$537$	−10.4586	−	1.33117i	−0.451324	−	0.0574442i
$538$		0			0
$539$		−	13.0287i		−	0.561186i
$540$		0			0
$541$			37.3027i			1.60377i	0.597479	+	0.801884i	$0.296169\pi$
$541$			37.3027i			1.60377i	−0.597479	+	0.801884i	$0.703831\pi$
$542$		0			0
$543$	13.8090	−	18.1574i	0.592600	−	0.779208i
$544$		0			0
$545$	11.9048	+	32.7082i	0.509945	+	1.40106i
$546$		0			0
$547$	−3.56925	−	20.2422i	−0.152610	−	0.865496i	−0.960938	−	0.276763i	$-0.910738\pi$
$547$	−3.56925	−	20.2422i	−0.152610	−	0.865496i	0.808328	−	0.588733i	$-0.200373\pi$
$548$		0			0
$549$	−14.1345	+	20.5604i	−0.603247	+	0.877496i
$550$		0			0
$551$	1.75273	+	0.637941i	0.0746687	+	0.0271772i
$552$		0			0
$553$	14.1249	+	11.8522i	0.600651	+	0.504006i
$554$		0			0
$555$	14.4816	−	3.27591i	0.614712	−	0.139055i
$556$		0			0
$557$	−13.7564	+	23.8268i	−0.582877	+	1.00957i	0.412259	+	0.911067i	$0.364740\pi$
$557$	−13.7564	+	23.8268i	−0.582877	+	1.00957i	−0.995136	+	0.0985064i	$0.968593\pi$
$558$		0			0
$559$	−5.00349	+	2.88877i	−0.211625	+	0.122182i
$560$		0			0
$561$	3.27627	−	6.36029i	0.138324	−	0.268532i
$562$		0			0
$563$	28.2129	+	4.97470i	1.18903	+	0.209658i	0.732952	−	0.680280i	$-0.238142\pi$
$563$	28.2129	+	4.97470i	1.18903	+	0.209658i	0.456080	+	0.889939i	$0.349253\pi$
$564$		0			0
$565$	−22.3856	−	26.6781i	−0.941770	−	1.12236i
$566$		0			0
$567$	7.98693	+	41.1439i	0.335419	+	1.72788i
$568$		0			0
$569$	−4.16772	−	4.96689i	−0.174720	−	0.208223i	0.671577	−	0.740935i	$-0.265617\pi$
$569$	−4.16772	−	4.96689i	−0.174720	−	0.208223i	−0.846297	+	0.532712i	$0.821173\pi$
$570$		0			0
$571$	4.13866	−	23.4715i	0.173197	−	0.982252i	−0.767006	−	0.641639i	$-0.778255\pi$
$571$	4.13866	−	23.4715i	0.173197	−	0.982252i	0.940204	−	0.340612i	$-0.110634\pi$
$572$		0			0
$573$	16.9583	−	32.9216i	0.708444	−	1.37532i
$574$		0			0
$575$	15.1576	+	26.2538i	0.632117	+	1.09486i
$576$		0			0
$577$	9.82303	−	17.0140i	0.408938	−	0.708302i	−0.585833	−	0.810432i	$-0.699232\pi$
$577$	9.82303	−	17.0140i	0.408938	−	0.708302i	0.994771	+	0.102130i	$0.0325658\pi$
$578$		0			0
$579$	8.02273	+	35.4656i	0.333413	+	1.47390i
$580$		0			0
$581$	49.4491	+	41.4927i	2.05149	+	1.72141i
$582$		0			0
$583$	−0.386593	+	1.06215i	−0.0160110	+	0.0439899i
$584$		0			0
$585$	−7.85187	−	16.4671i	−0.324635	−	0.680830i
$586$		0			0
$587$	0.851961	−	0.150224i	0.0351642	−	0.00620040i	−0.156038	−	0.987751i	$-0.549872\pi$
$587$	0.851961	−	0.150224i	0.0351642	−	0.00620040i	0.191203	+	0.981551i	$0.438761\pi$
$588$		0			0
$589$	0.929313	+	2.55327i	0.0382917	+	0.105206i
$590$		0			0
$591$	14.4284	+	10.9731i	0.593507	+	0.451371i
$592$		0			0
$593$			14.5405i			0.597108i	0.954393	+	0.298554i	$0.0965044\pi$
$593$			14.5405i			0.597108i	−0.954393	+	0.298554i	$0.903496\pi$
$594$		0			0
$595$	−69.4424			−2.84686
$596$		0			0
$597$	28.5070	+	3.62835i	1.16671	+	0.148499i
$598$		0			0
$599$	−19.6014	+	7.13433i	−0.800892	+	0.291501i	−0.709856	−	0.704347i	$-0.751240\pi$
$599$	−19.6014	+	7.13433i	−0.800892	+	0.291501i	−0.0910360	+	0.995848i	$0.529018\pi$
$600$		0			0
$601$	−3.10434	−	17.6056i	−0.126629	−	0.718147i	−0.980327	−	0.197379i	$-0.936757\pi$
$601$	−3.10434	−	17.6056i	−0.126629	−	0.718147i	0.853699	−	0.520768i	$-0.174354\pi$
$602$		0			0
$603$	24.6059	−	2.36618i	1.00203	−	0.0963583i
$604$		0			0
$605$	−30.7347	−	11.1865i	−1.24954	−	0.454797i
$606$		0			0
$607$	11.4075	−	13.5950i	0.463017	−	0.551803i	−0.483126	−	0.875551i	$-0.660499\pi$
$607$	11.4075	−	13.5950i	0.463017	−	0.551803i	0.946143	+	0.323748i	$0.104943\pi$
$608$		0			0
$609$	13.0210	−	41.9252i	0.527636	−	1.69889i
$610$		0			0
$611$	18.0101	+	10.3981i	0.728609	+	0.420662i
$612$		0			0
$613$	−6.61359	+	3.81836i	−0.267120	+	0.154222i	−0.627578	−	0.778554i	$-0.715954\pi$
$613$	−6.61359	+	3.81836i	−0.267120	+	0.154222i	0.360458	+	0.932775i	$0.382620\pi$
$614$		0			0
$615$	−0.0143418	−	0.298967i	−0.000578315	−	0.0120555i
$616$		0			0
$617$	1.20638	+	0.212717i	0.0485669	+	0.00856365i	0.197879	−	0.980226i	$-0.436595\pi$
$617$	1.20638	+	0.212717i	0.0485669	+	0.00856365i	−0.149312	+	0.988790i	$0.547706\pi$
$618$		0			0
$619$	4.70712	−	3.94975i	0.189195	−	0.158754i	−0.543270	−	0.839558i	$-0.682814\pi$
$619$	4.70712	−	3.94975i	0.189195	−	0.158754i	0.732465	+	0.680804i	$0.238370\pi$
$620$		0			0
$621$	−25.4822	−	15.7754i	−1.02256	−	0.633047i
$622$		0			0
$623$	26.1578	−	21.9490i	1.04799	−	0.879367i
$624$		0			0
$625$	−4.10756	+	23.2951i	−0.164302	+	0.931805i
$626$		0			0
$627$	−0.442882	+	0.284832i	−0.0176870	+	0.0113751i
$628$		0			0
$629$	−6.23183	−	10.7938i	−0.248479	−	0.430379i
$630$		0			0
$631$	−4.14675	−	2.39413i	−0.165080	−	0.0953088i	0.415184	−	0.909737i	$-0.363717\pi$
$631$	−4.14675	−	2.39413i	−0.165080	−	0.0953088i	−0.580264	+	0.814429i	$0.697051\pi$
$632$		0			0
$633$	−11.8645	+	10.9661i	−0.471572	+	0.435862i
$634$		0			0
$635$	−29.0875	+	34.6652i	−1.15430	+	1.37565i
$636$		0			0
$637$	−9.53816	+	26.2059i	−0.377916	+	1.03832i
$638$		0			0
$639$	0.299367	+	1.08000i	0.0118428	+	0.0427243i
$640$		0			0
$641$	7.66053	−	1.35076i	0.302573	−	0.0533517i	−0.0203006	−	0.999794i	$-0.506462\pi$
$641$	7.66053	−	1.35076i	0.302573	−	0.0533517i	0.322873	+	0.946442i	$0.395351\pi$
$642$		0			0
$643$	−22.0412	+	8.02234i	−0.869220	+	0.316370i	−0.737851	−	0.674964i	$-0.764159\pi$
$643$	−22.0412	+	8.02234i	−0.869220	+	0.316370i	−0.131369	+	0.991334i	$0.541937\pi$
$644$		0			0
$645$	15.5646	−	6.52563i	0.612854	−	0.256946i
$646$		0			0
$647$	−11.2669			−0.442948			−0.221474	−	0.975166i	$-0.571087\pi$
$647$	−11.2669			−0.442948			−0.221474	+	0.975166i	$0.571087\pi$
$648$		0			0
$649$	−6.31318			−0.247814
$650$		0			0
$651$	58.9779	−	24.7272i	2.31153	−	0.969135i
$652$		0			0
$653$	−36.3675	+	13.2367i	−1.42317	+	0.517991i	−0.934965	−	0.354739i	$-0.884570\pi$
$653$	−36.3675	+	13.2367i	−1.42317	+	0.517991i	−0.488203	+	0.872730i	$0.662347\pi$
$654$		0			0
$655$	−11.3880	+	2.00802i	−0.444968	+	0.0784598i
$656$		0			0
$657$	36.5686	+	9.46215i	1.42668	+	0.369154i
$658$		0			0
$659$	11.6740	−	32.0740i	0.454753	−	1.24942i	−0.474590	−	0.880207i	$-0.657404\pi$
$659$	11.6740	−	32.0740i	0.454753	−	1.24942i	0.929343	−	0.369217i	$-0.120374\pi$
$660$		0			0
$661$	32.5831	−	38.8310i	1.26734	−	1.51035i	0.505083	−	0.863071i	$-0.331462\pi$
$661$	32.5831	−	38.8310i	1.26734	−	1.51035i	0.762252	−	0.647281i	$-0.224094\pi$
$662$		0			0
$663$	−11.2462	+	10.3946i	−0.436765	+	0.403691i
$664$		0			0
$665$	4.42618	+	2.55546i	0.171640	+	0.0990964i
$666$		0			0
$667$	15.6961	+	27.1864i	0.607754	+	1.05266i
$668$		0			0
$669$	−27.3176	+	17.5689i	−1.05616	+	0.679252i
$670$		0			0
$671$	−1.28116	+	7.26582i	−0.0494587	+	0.280494i
$672$		0			0
$673$	17.6716	−	14.8283i	0.681191	−	0.571587i	−0.235163	−	0.971956i	$-0.575562\pi$
$673$	17.6716	−	14.8283i	0.681191	−	0.571587i	0.916354	+	0.400369i	$0.131118\pi$
$674$		0			0
$675$	8.54795	+	25.9388i	0.329011	+	0.998384i
$676$		0			0
$677$	32.2459	−	27.0575i	1.23931	−	1.03991i	0.241733	−	0.970343i	$-0.422284\pi$
$677$	32.2459	−	27.0575i	1.23931	−	1.03991i	0.997578	−	0.0695623i	$-0.0221603\pi$
$678$		0			0
$679$	4.06720	+	0.717158i	0.156085	+	0.0275220i
$680$		0			0
$681$	−0.420576	−	8.76729i	−0.0161165	−	0.335963i
$682$		0			0
$683$	−34.0757	+	19.6736i	−1.30387	+	0.752789i	−0.981065	−	0.193676i	$-0.937959\pi$
$683$	−34.0757	+	19.6736i	−1.30387	+	0.752789i	−0.322804	+	0.946466i	$0.604625\pi$
$684$		0			0
$685$	36.5130	+	21.0808i	1.39509	+	0.805456i
$686$		0			0
$687$	11.5811	−	37.2890i	0.441846	−	1.42266i
$688$		0			0
$689$	1.55518	−	1.85340i	0.0592478	−	0.0706087i
$690$		0			0
$691$	−34.6497	−	12.6115i	−1.31814	−	0.479762i	−0.415276	−	0.909696i	$-0.636315\pi$
$691$	−34.6497	−	12.6115i	−1.31814	−	0.479762i	−0.902861	+	0.429933i	$0.858537\pi$
$692$		0			0
$693$	7.19573	+	10.0907i	0.273343	+	0.383314i
$694$		0			0
$695$	−6.66949	−	37.8245i	−0.252988	−	1.43477i
$696$		0			0
$697$	−0.236102	+	0.0859340i	−0.00894299	+	0.00325498i
$698$		0			0
$699$	−9.79498	−	1.24670i	−0.370480	−	0.0471545i
$700$		0			0
$701$	−6.58502			−0.248713			−0.124356	−	0.992238i	$-0.539687\pi$
$701$	−6.58502			−0.248713			−0.124356	+	0.992238i	$0.539687\pi$
$702$		0			0
$703$			0.917317i			0.0345973i
$704$		0			0
$705$	−48.3543	−	36.7742i	−1.82113	−	1.38500i
$706$		0			0
$707$	10.0443	+	27.5965i	0.377755	+	1.03787i
$708$		0			0
$709$	−11.2866	+	1.99013i	−0.423876	+	0.0747408i	−0.381517	−	0.924362i	$-0.624598\pi$
$709$	−11.2866	+	1.99013i	−0.423876	+	0.0747408i	−0.0423588	+	0.999102i	$0.513487\pi$
$710$		0			0
$711$	−11.8416	−	0.933440i	−0.444095	−	0.0350067i
$712$		0			0
$713$	−15.6406	+	42.9723i	−0.585746	+	1.60932i
$714$		0			0
$715$	−4.13252	−	3.46760i	−0.154548	−	0.129681i
$716$		0			0
$717$	8.80188	+	38.9100i	0.328712	+	1.45312i
$718$		0			0
$719$	−14.6250	+	25.3313i	−0.545421	+	0.944697i	0.453159	+	0.891430i	$0.350297\pi$
$719$	−14.6250	+	25.3313i	−0.545421	+	0.944697i	−0.998580	+	0.0532673i	$0.983036\pi$
$720$		0			0
$721$	20.3569	+	35.2591i	0.758129	+	1.31312i
$722$		0			0
$723$	−17.2045	+	33.3995i	−0.639843	+	1.24214i
$724$		0			0
$725$	4.96752	−	28.1722i	0.184489	−	1.04629i
$726$		0			0
$727$	32.7533	+	39.0339i	1.21475	+	1.44769i	0.858125	+	0.513440i	$0.171629\pi$
$727$	32.7533	+	39.0339i	1.21475	+	1.44769i	0.356628	+	0.934246i	$0.383926\pi$
$728$		0			0
$729$	−19.5782	−	18.5929i	−0.725117	−	0.688626i
$730$		0			0
$731$	−9.10664	−	10.8529i	−0.336821	−	0.401408i
$732$		0			0
$733$	2.54100	+	0.448046i	0.0938538	+	0.0165490i	0.220378	−	0.975415i	$-0.429271\pi$
$733$	2.54100	+	0.448046i	0.0938538	+	0.0165490i	−0.126524	+	0.991964i	$0.540382\pi$
$734$		0			0
$735$	37.3052	−	72.4213i	1.37602	−	2.67130i
$736$		0			0
$737$	6.33034	−	3.65482i	0.233181	−	0.134627i
$738$		0			0
$739$	−3.86165	+	6.68857i	−0.142053	+	0.246043i	−0.928270	−	0.371908i	$-0.878704\pi$
$739$	−3.86165	+	6.68857i	−0.142053	+	0.246043i	0.786217	+	0.617951i	$0.212037\pi$
$740$		0			0
$741$	1.09934	−	0.248682i	0.0403851	−	0.00913557i
$742$		0			0
$743$	9.80501	+	8.22738i	0.359711	+	0.301833i	0.804676	−	0.593715i	$-0.202339\pi$
$743$	9.80501	+	8.22738i	0.359711	+	0.301833i	−0.444965	+	0.895548i	$0.646784\pi$
$744$		0			0
$745$	−26.6479	−	9.69906i	−0.976305	−	0.355346i
$746$		0			0
$747$	−41.4557	−	3.26783i	−1.51679	−	0.119564i
$748$		0			0
$749$	2.61279	+	14.8179i	0.0954693	+	0.541433i
$750$		0			0
$751$	15.0834	+	41.4413i	0.550401	+	1.51221i	0.833165	+	0.553025i	$0.186527\pi$
$751$	15.0834	+	41.4413i	0.550401	+	1.51221i	−0.282763	+	0.959190i	$0.591251\pi$
$752$		0			0
$753$	−8.31434	+	10.9325i	−0.302991	+	0.398402i
$754$		0			0
$755$		−	9.38096i		−	0.341408i
$756$		0			0
$757$		−	27.9094i		−	1.01438i	−0.861833	−	0.507192i	$-0.830684\pi$
$757$		−	27.9094i		−	1.01438i	0.861833	−	0.507192i	$-0.169316\pi$
$758$		0			0
$759$	−8.79138	−	1.11896i	−0.319107	−	0.0406157i
$760$		0			0
$761$	−7.20399	−	19.7928i	−0.261145	−	0.717489i	−0.999091	−	0.0426294i	$-0.986427\pi$
$761$	−7.20399	−	19.7928i	−0.261145	−	0.717489i	0.737946	−	0.674859i	$-0.235796\pi$
$762$		0			0
$763$	8.78916	+	49.8458i	0.318189	+	1.80454i
$764$		0			0
$765$	36.4229	−	25.9734i	1.31687	−	0.939070i
$766$		0			0
$767$	12.6983	+	4.62181i	0.458509	+	0.166884i
$768$		0			0
$769$	−9.76794	−	8.19627i	−0.352241	−	0.295565i	0.449448	−	0.893306i	$-0.351621\pi$
$769$	−9.76794	−	8.19627i	−0.352241	−	0.295565i	−0.801689	+	0.597741i	$0.796065\pi$
$770$		0			0
$771$	−0.0638161	+	0.205476i	−0.00229828	+	0.00740004i
$772$		0			0
$773$	24.3894	−	42.2437i	0.877226	−	1.51940i	0.0228536	−	0.999739i	$-0.492725\pi$
$773$	24.3894	−	42.2437i	0.877226	−	1.51940i	0.854372	−	0.519661i	$-0.173942\pi$
$774$		0			0
$775$	36.0896	−	20.8363i	1.29638	−	0.748463i
$776$		0			0
$777$	21.5656	−	1.03453i	0.773663	−	0.0371134i
$778$		0			0
$779$	0.0182112	+	0.00321113i	0.000652484	+	0.000115051i
$780$		0			0
$781$	0.213023	+	0.253871i	0.00762256	+	0.00908421i
$782$		0			0
$783$	8.85160	+	26.8602i	0.316330	+	0.959905i
$784$		0			0
$785$	22.4739	+	26.7833i	0.802127	+	0.955938i
$786$		0			0
$787$	4.56672	−	25.8991i	0.162786	−	0.923205i	−0.788532	−	0.614994i	$-0.789159\pi$
$787$	4.56672	−	25.8991i	0.162786	−	0.923205i	0.951318	−	0.308211i	$-0.0997304\pi$
$788$		0			0
$789$	5.18695	+	8.06512i	0.184660	+	0.287126i
$790$		0			0
$791$	−25.3209	−	43.8570i	−0.900306	−	1.55938i
$792$		0			0
$793$	7.89615	−	13.6765i	0.280401	−	0.485668i
$794$		0			0
$795$	−5.19019	+	4.79716i	−0.184077	+	0.170138i
$796$		0			0
$797$	−27.3124	−	22.9179i	−0.967456	−	0.811792i	0.0146935	−	0.999892i	$-0.495323\pi$
$797$	−27.3124	−	22.9179i	−0.967456	−	0.811792i	−0.982150	+	0.188100i	$0.939767\pi$
$798$		0			0
$799$	−17.4415	+	47.9201i	−0.617036	+	1.69529i
$800$		0			0
$801$	−5.51037	+	21.2961i	−0.194700	+	0.752460i
$802$		0			0
$803$	11.0000	−	1.93959i	0.388180	−	0.0684467i
$804$		0			0
$805$	29.4200	+	80.8307i	1.03692	+	2.84891i
$806$		0			0
$807$	−8.94199	+	3.74903i	−0.314773	+	0.131972i
$808$		0			0
$809$			41.4917i			1.45877i	0.684103	+	0.729385i	$0.260194\pi$
$809$			41.4917i			1.45877i	−0.684103	+	0.729385i	$0.739806\pi$
$810$		0			0
$811$	−29.0442			−1.01988			−0.509940	−	0.860210i	$-0.670333\pi$
$811$	−29.0442			−1.01988			−0.509940	+	0.860210i	$0.670333\pi$
$812$		0			0
$813$	−1.04845	−	2.50071i	−0.0367708	−	0.0877036i
$814$		0			0
$815$	−2.95951	+	1.07717i	−0.103667	+	0.0377318i
$816$		0			0
$817$	0.181065	+	1.02687i	0.00633467	+	0.0359257i
$818$		0			0
$819$	−7.08619	−	25.5643i	−0.247611	−	0.893290i
$820$		0			0
$821$	−47.7187	−	17.3682i	−1.66539	−	0.606153i	−0.674196	−	0.738552i	$-0.735510\pi$
$821$	−47.7187	−	17.3682i	−1.66539	−	0.606153i	−0.991197	+	0.132399i	$0.957732\pi$
$822$		0			0
$823$	10.2372	−	12.2002i	0.356847	−	0.425274i	−0.557518	−	0.830165i	$-0.688246\pi$
$823$	10.2372	−	12.2002i	0.356847	−	0.425274i	0.914365	+	0.404891i	$0.132691\pi$
$824$		0			0
$825$	5.48162	+	5.93072i	0.190845	+	0.206481i
$826$		0			0
$827$	−26.8166	−	15.4826i	−0.932504	−	0.538381i	−0.0449012	−	0.998991i	$-0.514297\pi$
$827$	−26.8166	−	15.4826i	−0.932504	−	0.538381i	−0.887603	+	0.460610i	$0.847631\pi$
$828$		0			0
$829$	−5.02207	+	2.89949i	−0.174424	+	0.100704i	−0.584670	−	0.811271i	$-0.698776\pi$
$829$	−5.02207	+	2.89949i	−0.174424	+	0.100704i	0.410246	+	0.911975i	$0.365443\pi$
$830$		0			0
$831$	−40.8422	+	26.2670i	−1.41680	+	0.911193i
$832$		0			0
$833$	−67.3461	−	11.8749i	−2.33340	−	0.411442i
$834$		0			0
$835$	3.92720	−	3.29531i	0.135906	−	0.114039i
$836$		0			0
$837$	−21.6856	+	35.0289i	−0.749565	+	1.21078i
$838$		0			0
$839$	11.9037	−	9.98841i	0.410962	−	0.344838i	−0.413750	−	0.910390i	$-0.635781\pi$
$839$	11.9037	−	9.98841i	0.410962	−	0.344838i	0.824712	+	0.565552i	$0.191337\pi$
$840$		0			0
$841$	0.108181	−	0.613526i	0.00373038	−	0.0211561i
$842$		0			0
$843$	0.746695	+	15.5655i	0.0257175	+	0.536106i
$844$		0			0
$845$	−15.0427	−	26.0547i	−0.517484	−	0.896309i
$846$		0			0
$847$	−41.1889	−	23.7804i	−1.41527	−	0.817106i
$848$		0			0
$849$	−47.7755	−	14.8380i	−1.63965	−	0.509237i
$850$		0			0
$851$	−9.92382	+	11.8268i	−0.340184	+	0.405416i
$852$		0			0
$853$	5.27000	−	14.4792i	0.180441	−	0.495758i	−0.816189	−	0.577785i	$-0.803917\pi$
$853$	5.27000	−	14.4792i	0.180441	−	0.495758i	0.996630	+	0.0820269i	$0.0261393\pi$
$854$		0			0
$855$	−3.27737	+	0.315163i	−0.112084	+	0.0107783i
$856$		0			0
$857$	−43.4090	+	7.65418i	−1.48282	+	0.261462i	−0.855706	−	0.517463i	$-0.826877\pi$
$857$	−43.4090	+	7.65418i	−1.48282	+	0.261462i	−0.627118	+	0.778924i	$0.715766\pi$
$858$		0			0
$859$	−49.6251	+	18.0621i	−1.69319	+	0.616270i	−0.995021	−	0.0996665i	$-0.968222\pi$
$859$	−49.6251	+	18.0621i	−1.69319	+	0.616270i	−0.698166	+	0.715936i	$0.746000\pi$
$860$		0			0
$861$	0.0549538	−	0.431757i	0.00187282	−	0.0147143i
$862$		0			0
$863$	−51.1622			−1.74158			−0.870791	−	0.491653i	$-0.836393\pi$
$863$	−51.1622			−1.74158			−0.870791	+	0.491653i	$0.836393\pi$
$864$		0			0
$865$	−45.4048			−1.54381
$866$		0			0
$867$	−6.45353	−	4.90801i	−0.219173	−	0.166685i
$868$		0			0
$869$	−3.30066	+	1.20134i	−0.111967	+	0.0407527i
$870$		0			0
$871$	−15.4085	+	2.71693i	−0.522097	+	0.0920597i
$872$		0			0
$873$	−2.40151	+	1.14509i	−0.0812788	+	0.0387556i
$874$		0			0
$875$	1.30578	−	3.58759i	0.0441433	−	0.121283i
$876$		0			0
$877$	−21.3535	+	25.4481i	−0.721055	+	0.859320i	−0.994733	−	0.102501i	$-0.967315\pi$
$877$	−21.3535	+	25.4481i	−0.721055	+	0.859320i	0.273678	+	0.961822i	$0.411760\pi$
$878$		0			0
$879$	6.83190	+	30.2014i	0.230434	+	1.01867i
$880$		0			0
$881$	−24.0135	−	13.8642i	−0.809034	−	0.467096i	0.0375862	−	0.999293i	$-0.488033\pi$
$881$	−24.0135	−	13.8642i	−0.809034	−	0.467096i	−0.846620	+	0.532197i	$0.821366\pi$
$882$		0			0
$883$	−7.38127	−	12.7847i	−0.248400	−	0.430241i	0.714682	−	0.699449i	$-0.246571\pi$
$883$	−7.38127	−	12.7847i	−0.248400	−	0.430241i	−0.963082	+	0.269208i	$0.913238\pi$
$884$		0			0
$885$	−35.0924	−	18.0766i	−1.17962	−	0.607637i
$886$		0			0
$887$	3.08832	−	17.5147i	0.103695	−	0.588086i	−0.888038	−	0.459770i	$-0.847932\pi$
$887$	3.08832	−	17.5147i	0.103695	−	0.588086i	0.991733	−	0.128316i	$-0.0409572\pi$
$888$		0			0
$889$	−50.4081	+	42.2974i	−1.69063	+	1.41861i
$890$		0			0
$891$	−7.54841	−	2.60123i	−0.252881	−	0.0871445i
$892$		0			0
$893$	2.87515	−	2.41254i	0.0962132	−	0.0807324i
$894$		0			0
$895$	−19.1975	−	3.38504i	−0.641702	−	0.113149i
$896$		0			0
$897$	16.8638	+	8.68675i	0.563066	+	0.290042i
$898$		0			0
$899$	37.3716	−	21.5765i	1.24641	−	0.719616i
$900$		0			0
$901$	5.13798	+	2.96642i	0.171171	+	0.0988256i
$902$		0			0
$903$	23.9370	−	5.41483i	0.796574	−	0.180194i
$904$		0			0
$905$	27.1116	−	32.3104i	0.901221	−	1.07403i
$906$		0			0
$907$	33.8368	+	12.3156i	1.12353	+	0.408932i	0.835940	−	0.548821i	$-0.184923\pi$
$907$	33.8368	+	12.3156i	1.12353	+	0.408932i	0.287591	+	0.957753i	$0.407146\pi$
$908$		0			0
$909$	−15.5901	−	10.7177i	−0.517093	−	0.355483i
$910$		0			0
$911$	−0.0484884	−	0.274992i	−0.00160649	−	0.00911088i	0.983994	−	0.178202i	$-0.0570280\pi$
$911$	−0.0484884	−	0.274992i	−0.00160649	−	0.00911088i	−0.985600	+	0.169091i	$0.945917\pi$
$912$		0			0
$913$	−11.5551	+	4.20572i	−0.382418	+	0.139189i
$914$		0			0
$915$	−27.9258	+	36.7195i	−0.923197	+	1.21391i
$916$		0			0
$917$	−16.8153			−0.555290
$918$		0			0
$919$		−	19.5234i		−	0.644017i	−0.946737	−	0.322008i	$-0.895642\pi$
$919$		−	19.5234i		−	0.644017i	0.946737	−	0.322008i	$-0.104358\pi$
$920$		0			0
$921$	1.16730	−	9.17118i	0.0384639	−	0.302201i
$922$		0			0
$923$	−0.242618	−	0.666587i	−0.00798586	−	0.0219410i
$924$		0			0
$925$	13.8552	−	2.44304i	0.455555	−	0.0803267i
$926$		0			0
$927$	−23.8652	−	10.8796i	−0.783835	−	0.357332i
$928$		0			0
$929$	−12.7507	+	35.0323i	−0.418338	+	1.14937i	0.534308	+	0.845290i	$0.320572\pi$
$929$	−12.7507	+	35.0323i	−0.418338	+	1.14937i	−0.952645	+	0.304083i	$0.901650\pi$
$930$		0			0
$931$	3.85557	+	3.23521i	0.126361	+	0.106030i
$932$		0			0
$933$	−16.1559	−	5.01763i	−0.528919	−	0.164270i
$934$		0			0
$935$	6.61423	−	11.4562i	0.216308	−	0.374657i
$936$		0			0
$937$	−1.65449	−	2.86566i	−0.0540499	−	0.0936171i	0.837735	−	0.546078i	$-0.183880\pi$
$937$	−1.65449	−	2.86566i	−0.0540499	−	0.0936171i	−0.891784	+	0.452461i	$0.850546\pi$
$938$		0			0
$939$	38.5482	−	1.84920i	1.25797	−	0.0603462i
$940$		0			0
$941$	−8.25196	+	46.7992i	−0.269006	+	1.52561i	0.488373	+	0.872635i	$0.337591\pi$
$941$	−8.25196	+	46.7992i	−0.269006	+	1.52561i	−0.757379	+	0.652975i	$0.773521\pi$
$942$		0			0
$943$	0.200054	+	0.238415i	0.00651465	+	0.00776386i
$944$		0			0
$945$	11.1054	+	76.6938i	0.361260	+	2.49485i
$946$		0			0
$947$	−15.7887	−	18.8162i	−0.513063	−	0.611444i	0.445863	−	0.895101i	$-0.352897\pi$
$947$	−15.7887	−	18.8162i	−0.513063	−	0.611444i	−0.958926	+	0.283657i	$0.908452\pi$
$948$		0			0
$949$	−23.5453	−	4.15167i	−0.764312	−	0.134769i
$950$		0			0
$951$	14.8602	+	23.1059i	0.481874	+	0.749259i
$952$		0			0
$953$	−5.53399	+	3.19505i	−0.179264	+	0.103498i	−0.586947	−	0.809626i	$-0.699670\pi$
$953$	−5.53399	+	3.19505i	−0.179264	+	0.103498i	0.407683	+	0.913124i	$0.366337\pi$
$954$		0			0
$955$	34.2360	−	59.2984i	1.10785	−	1.91885i
$956$		0			0
$957$	5.67634	+	6.14139i	0.183490	+	0.198523i
$958$		0			0
$959$	46.9654	+	39.4086i	1.51659	+	1.27257i
$960$		0			0
$961$	29.9411	+	10.8977i	0.965843	+	0.351538i
$962$		0			0
$963$	−6.91272	−	6.79480i	−0.222759	−	0.218959i
$964$		0			0
$965$	11.6746	+	66.2101i	0.375819	+	2.13138i
$966$		0			0
$967$	7.29798	+	20.0510i	0.234687	+	0.644798i	0.999999	+	0.00113855i	$0.000362411\pi$
$967$	7.29798	+	20.0510i	0.234687	+	0.644798i	−0.765312	+	0.643659i	$0.777415\pi$
$968$		0			0
$969$	1.06865	+	2.54889i	0.0343301	+	0.0818823i
$970$		0			0
$971$			18.8858i			0.606074i	0.952979	+	0.303037i	$0.0980006\pi$
$971$			18.8858i			0.606074i	−0.952979	+	0.303037i	$0.901999\pi$
$972$		0			0
$973$		−	55.8507i		−	1.79049i
$974$		0			0
$975$	−6.68390	−	15.9421i	−0.214056	−	0.510555i
$976$		0			0
$977$	−12.8528	−	35.3129i	−0.411199	−	1.12976i	−0.956554	−	0.291555i	$-0.905827\pi$
$977$	−12.8528	−	35.3129i	−0.411199	−	1.12976i	0.545355	−	0.838205i	$-0.316395\pi$
$978$		0			0
$979$	1.12954	+	6.40593i	0.0361002	+	0.204735i
$980$		0			0
$981$	−23.2537	−	22.8570i	−0.742432	−	0.729768i
$982$		0			0
$983$	0.0615360	+	0.0223973i	0.00196269	+	0.000714362i	0.343001	−	0.939335i	$-0.388556\pi$
$983$	0.0615360	+	0.0223973i	0.00196269	+	0.000714362i	−0.341039	+	0.940049i	$0.610779\pi$
$984$		0			0
$985$	25.6749	+	21.5438i	0.818069	+	0.686441i
$986$		0			0
$987$	−59.9600	−	64.8724i	−1.90855	−	2.06491i
$988$		0			0
$989$	−8.77459	+	15.1980i	−0.279016	+	0.483269i
$990$		0			0
$991$	−2.32285	+	1.34110i	−0.0737876	+	0.0426013i	−0.536440	−	0.843939i	$-0.680231\pi$
$991$	−2.32285	+	1.34110i	−0.0737876	+	0.0426013i	0.462652	+	0.886540i	$0.346898\pi$
$992$		0			0
$993$	26.5094	+	41.2191i	0.841249	+	1.30805i
$994$		0			0
$995$	52.3264	+	9.22655i	1.65886	+	0.292501i
$996$		0			0
$997$	6.81445	+	8.12114i	0.215816	+	0.257199i	0.863081	−	0.505066i	$-0.168532\pi$
$997$	6.81445	+	8.12114i	0.215816	+	0.257199i	−0.647265	+	0.762265i	$0.724087\pi$
$998$		0			0
$999$	−10.9244	+	8.60876i	−0.345632	+	0.272369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.815.3		192
4.3	odd	2		216.2.v.b.59.25	yes	192
8.3	odd	2	inner	864.2.bh.b.815.4		192
8.5	even	2		216.2.v.b.59.24	yes	192
12.11	even	2		648.2.v.b.611.8		192
24.5	odd	2		648.2.v.b.611.9		192
27.11	odd	18	inner	864.2.bh.b.335.4		192
108.11	even	18		216.2.v.b.11.24	✓	192
108.43	odd	18		648.2.v.b.35.9		192
216.11	even	18	inner	864.2.bh.b.335.3		192
216.173	odd	18		216.2.v.b.11.25	yes	192
216.205	even	18		648.2.v.b.35.8		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.24	✓	192	108.11	even	18
216.2.v.b.11.25	yes	192	216.173	odd	18
216.2.v.b.59.24	yes	192	8.5	even	2
216.2.v.b.59.25	yes	192	4.3	odd	2
648.2.v.b.35.8		192	216.205	even	18
648.2.v.b.35.9		192	108.43	odd	18
648.2.v.b.611.8		192	12.11	even	2
648.2.v.b.611.9		192	24.5	odd	2
864.2.bh.b.335.3		192	216.11	even	18	inner
864.2.bh.b.335.4		192	27.11	odd	18	inner
864.2.bh.b.815.3		192	1.1	even	1	trivial
864.2.bh.b.815.4		192	8.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bh (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59734 + 0.669704i) q^{3} +(-3.00936 + 1.09532i) q^{5} +(-4.58614 + 0.808660i) q^{7} +(2.10299 - 2.13949i) q^{9} +(0.303411 - 0.833616i) q^{11} +(-1.22056 + 1.45461i) q^{13} +(4.07344 - 3.76498i) q^{15} +(-4.03247 - 2.32815i) q^{17} +(0.171350 + 0.296787i) q^{19} +(6.78406 - 4.36306i) q^{21} +(-1.00156 + 5.68012i) q^{23} +(4.02633 - 3.37849i) q^{25} +(-1.92637 + 4.82588i) q^{27} +(4.16935 - 3.49850i) q^{29} +(7.80815 + 1.37679i) q^{31} +(0.0736241 + 1.53476i) q^{33} +(12.9156 - 7.45683i) q^{35} +(2.31812 + 1.33837i) q^{37} +(0.975496 - 3.14092i) q^{39} +(0.0346849 - 0.0413359i) q^{41} +(2.85915 + 1.04064i) q^{43} +(-3.98525 + 8.74195i) q^{45} +(-1.90179 - 10.7856i) q^{47} +(13.8009 - 5.02311i) q^{49} +(8.00039 + 1.01828i) q^{51} -1.27415 q^{53} +2.84099i q^{55} +(-0.472464 - 0.359316i) q^{57} +(-2.43399 - 6.68734i) q^{59} +(-8.19039 + 1.44419i) q^{61} +(-7.91450 + 11.5126i) q^{63} +(2.07985 - 5.71435i) q^{65} +(6.31205 + 5.29644i) q^{67} +(-2.20417 - 9.74384i) q^{69} +(-0.186788 + 0.323526i) q^{71} +(6.29550 + 10.9041i) q^{73} +(-4.16883 + 8.09304i) q^{75} +(-0.717374 + 4.06843i) q^{77} +(-2.54509 - 3.03312i) q^{79} +(-0.154829 - 8.99867i) q^{81} +(-8.90996 - 10.6185i) q^{83} +(14.6852 + 2.58940i) q^{85} +(-4.31692 + 8.38053i) q^{87} +(-6.35012 + 3.66624i) q^{89} +(4.42138 - 7.65805i) q^{91} +(-13.3943 + 3.02994i) q^{93} +(-0.840731 - 0.705457i) q^{95} +(-0.833364 - 0.303320i) q^{97} +(-1.14544 - 2.40223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67}+ \cdots + 12 q^{99}+O(q^{100}) \) 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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