LMFDB - Embedded newform 840.2.dd.b.73.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(73,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dd (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.12
Character	$\chi$	$=$	840.73
Dual form			840.2.dd.b.817.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{3} +(2.04130 - 0.912737i) q^{5} +(-1.24643 - 2.33376i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(0.574500 - 0.995063i) q^{11} +(1.27881 - 1.27881i) q^{13} +(1.40996 + 1.73551i) q^{15} +(2.58103 - 0.691585i) q^{17} +(-0.176794 - 0.306216i) q^{19} +(1.93164 - 1.80798i) q^{21} +(0.881430 - 3.28954i) q^{23} +(3.33382 - 3.72634i) q^{25} +(-0.707107 - 0.707107i) q^{27} -3.41202i q^{29} +(-5.20290 - 3.00390i) q^{31} +(1.10985 + 0.297383i) q^{33} +(-4.67444 - 3.62624i) q^{35} +(8.28476 + 2.21989i) q^{37} +(1.56621 + 0.904252i) q^{39} +4.88449i q^{41} +(3.22090 + 3.22090i) q^{43} +(-1.31145 + 1.81110i) q^{45} +(0.155305 - 0.579607i) q^{47} +(-3.89284 + 5.81771i) q^{49} +(1.33604 + 2.31409i) q^{51} +(-2.12352 + 0.568994i) q^{53} +(0.264496 - 2.55559i) q^{55} +(0.250024 - 0.250024i) q^{57} +(0.873096 - 1.51225i) q^{59} +(10.3298 - 5.96392i) q^{61} +(2.24632 + 1.39788i) q^{63} +(1.44321 - 3.77764i) q^{65} +(1.31110 + 4.89311i) q^{67} +3.40558 q^{69} -4.35856 q^{71} +(2.18033 + 8.13710i) q^{73} +(4.46223 + 2.25577i) q^{75} +(-3.03831 - 0.100469i) q^{77} +(-2.36967 + 1.36813i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-2.18195 + 2.18195i) q^{83} +(4.63743 - 3.76754i) q^{85} +(3.29576 - 0.883096i) q^{87} +(-6.61849 - 11.4636i) q^{89} +(-4.57836 - 1.39048i) q^{91} +(1.55493 - 5.80308i) q^{93} +(-0.640384 - 0.463712i) q^{95} +(11.2876 + 11.2876i) q^{97} +1.14900i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) $ 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$		0			0
$5$	2.04130	−	0.912737i	0.912898	−	0.408189i
$5$	2.04130	−	0.912737i	0.912898	−	0.408189i
$6$		0			0
$7$	−1.24643	−	2.33376i	−0.471105	−	0.882077i
$7$	−1.24643	−	2.33376i	−0.471105	−	0.882077i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	0.574500	−	0.995063i	0.173218	−	0.300023i	−0.766325	−	0.642453i	$-0.777917\pi$
$11$	0.574500	−	0.995063i	0.173218	−	0.300023i	0.939543	+	0.342430i	$0.111250\pi$
$12$		0			0
$13$	1.27881	−	1.27881i	0.354677	−	0.354677i	−0.507170	−	0.861846i	$-0.669308\pi$
$13$	1.27881	−	1.27881i	0.354677	−	0.354677i	0.861846	+	0.507170i	$0.169308\pi$
$14$		0			0
$15$	1.40996	+	1.73551i	0.364051	+	0.448107i
$16$		0			0
$17$	2.58103	−	0.691585i	0.625992	−	0.167734i	0.0681418	−	0.997676i	$-0.478293\pi$
$17$	2.58103	−	0.691585i	0.625992	−	0.167734i	0.557850	+	0.829942i	$0.311626\pi$
$18$		0			0
$19$	−0.176794	−	0.306216i	−0.0405593	−	0.0702507i	0.845033	−	0.534714i	$-0.179581\pi$
$19$	−0.176794	−	0.306216i	−0.0405593	−	0.0702507i	−0.885592	+	0.464463i	$0.846247\pi$
$20$		0			0
$21$	1.93164	−	1.80798i	0.421518	−	0.394533i
$22$		0			0
$23$	0.881430	−	3.28954i	0.183791	−	0.685917i	−0.811095	−	0.584914i	$-0.801128\pi$
$23$	0.881430	−	3.28954i	0.183791	−	0.685917i	0.994886	−	0.101003i	$-0.0322051\pi$
$24$		0			0
$25$	3.33382	−	3.72634i	0.666764	−	0.745269i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	3.41202i		−	0.633597i	−0.948493	−	0.316798i	$-0.897392\pi$
$29$		−	3.41202i		−	0.633597i	0.948493	−	0.316798i	$-0.102608\pi$
$30$		0			0
$31$	−5.20290	−	3.00390i	−0.934469	−	0.539516i	−0.0462467	−	0.998930i	$-0.514726\pi$
$31$	−5.20290	−	3.00390i	−0.934469	−	0.539516i	−0.888222	+	0.459414i	$0.848059\pi$
$32$		0			0
$33$	1.10985	+	0.297383i	0.193200	+	0.0517677i
$34$		0			0
$35$	−4.67444	−	3.62624i	−0.790125	−	0.612946i
$36$		0			0
$37$	8.28476	+	2.21989i	1.36201	+	0.364948i	0.864553	−	0.502542i	$-0.167602\pi$
$37$	8.28476	+	2.21989i	1.36201	+	0.364948i	0.497453	+	0.867491i	$0.334269\pi$
$38$		0			0
$39$	1.56621	+	0.904252i	0.250794	+	0.144796i
$40$		0			0
$41$			4.88449i			0.762829i	0.924404	+	0.381415i	$0.124563\pi$
$41$			4.88449i			0.762829i	−0.924404	+	0.381415i	$0.875437\pi$
$42$		0			0
$43$	3.22090	+	3.22090i	0.491183	+	0.491183i	0.908679	−	0.417496i	$-0.137092\pi$
$43$	3.22090	+	3.22090i	0.491183	+	0.491183i	−0.417496	+	0.908679i	$0.637092\pi$
$44$		0			0
$45$	−1.31145	+	1.81110i	−0.195499	+	0.269983i
$46$		0			0
$47$	0.155305	−	0.579607i	0.0226536	−	0.0845444i	−0.953674	−	0.300843i	$-0.902732\pi$
$47$	0.155305	−	0.579607i	0.0226536	−	0.0845444i	0.976327	+	0.216299i	$0.0693986\pi$
$48$		0			0
$49$	−3.89284	+	5.81771i	−0.556120	+	0.831102i
$50$		0			0
$51$	1.33604	+	2.31409i	0.187083	+	0.324037i
$52$		0			0
$53$	−2.12352	+	0.568994i	−0.291687	+	0.0781574i	−0.401696	−	0.915773i	$-0.631579\pi$
$53$	−2.12352	+	0.568994i	−0.291687	+	0.0781574i	0.110008	+	0.993931i	$0.464912\pi$
$54$		0			0
$55$	0.264496	−	2.55559i	0.0356646	−	0.344596i
$56$		0			0
$57$	0.250024	−	0.250024i	0.0331165	−	0.0331165i
$58$		0			0
$59$	0.873096	−	1.51225i	0.113667	−	0.196878i	−0.803579	−	0.595198i	$-0.797073\pi$
$59$	0.873096	−	1.51225i	0.113667	−	0.196878i	0.917246	+	0.398321i	$0.130407\pi$
$60$		0			0
$61$	10.3298	−	5.96392i	1.32260	−	0.763601i	0.338454	−	0.940983i	$-0.390096\pi$
$61$	10.3298	−	5.96392i	1.32260	−	0.763601i	0.984142	+	0.177381i	$0.0567626\pi$
$62$		0			0
$63$	2.24632	+	1.39788i	0.283009	+	0.176116i
$64$		0			0
$65$	1.44321	−	3.77764i	0.179009	−	0.468559i
$66$		0			0
$67$	1.31110	+	4.89311i	0.160177	+	0.597788i	0.998606	+	0.0527781i	$0.0168076\pi$
$67$	1.31110	+	4.89311i	0.160177	+	0.597788i	−0.838429	+	0.545010i	$0.816526\pi$
$68$		0			0
$69$	3.40558			0.409984
$70$		0			0
$71$	−4.35856			−0.517266			−0.258633	−	0.965976i	$-0.583272\pi$
$71$	−4.35856			−0.517266			−0.258633	+	0.965976i	$0.583272\pi$
$72$		0			0
$73$	2.18033	+	8.13710i	0.255188	+	0.952375i	0.967986	+	0.251005i	$0.0807612\pi$
$73$	2.18033	+	8.13710i	0.255188	+	0.952375i	−0.712797	+	0.701370i	$0.752572\pi$
$74$		0			0
$75$	4.46223	+	2.25577i	0.515254	+	0.260474i
$76$		0			0
$77$	−3.03831	−	0.100469i	−0.346247	−	0.0114496i
$78$		0			0
$79$	−2.36967	+	1.36813i	−0.266609	+	0.153927i	−0.627346	−	0.778741i	$-0.715859\pi$
$79$	−2.36967	+	1.36813i	−0.266609	+	0.153927i	0.360737	+	0.932668i	$0.382525\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	−2.18195	+	2.18195i	−0.239500	+	0.239500i	−0.816643	−	0.577143i	$-0.804167\pi$
$83$	−2.18195	+	2.18195i	−0.239500	+	0.239500i	0.577143	+	0.816643i	$0.304167\pi$
$84$		0			0
$85$	4.63743	−	3.76754i	0.503000	−	0.408647i
$86$		0			0
$87$	3.29576	−	0.883096i	0.353343	−	0.0946779i
$88$		0			0
$89$	−6.61849	−	11.4636i	−0.701559	−	1.21513i	−0.967919	−	0.251262i	$-0.919155\pi$
$89$	−6.61849	−	11.4636i	−0.701559	−	1.21513i	0.266361	−	0.963873i	$-0.414179\pi$
$90$		0			0
$91$	−4.57836	−	1.39048i	−0.479942	−	0.145762i
$92$		0			0
$93$	1.55493	−	5.80308i	0.161239	−	0.601752i
$94$		0			0
$95$	−0.640384	−	0.463712i	−0.0657020	−	0.0475759i
$96$		0			0
$97$	11.2876	+	11.2876i	1.14608	+	1.14608i	0.987317	+	0.158763i	$0.0507505\pi$
$97$	11.2876	+	11.2876i	1.14608	+	1.14608i	0.158763	+	0.987317i	$0.449250\pi$
$98$		0			0
$99$			1.14900i			0.115479i
$100$		0			0
$101$	2.01637	+	1.16415i	0.200636	+	0.115837i	0.596952	−	0.802277i	$-0.296378\pi$
$101$	2.01637	+	1.16415i	0.200636	+	0.115837i	−0.396316	+	0.918114i	$0.629712\pi$
$102$		0			0
$103$	18.2972	+	4.90272i	1.80288	+	0.483079i	0.994422	−	0.105478i	$-0.0336372\pi$
$103$	18.2972	+	4.90272i	1.80288	+	0.483079i	0.808455	+	0.588557i	$0.200304\pi$
$104$		0			0
$105$	2.29284	−	5.45370i	0.223759	−	0.532227i
$106$		0			0
$107$	−1.04807	−	0.280829i	−0.101321	−	0.0271488i	0.207802	−	0.978171i	$-0.433369\pi$
$107$	−1.04807	−	0.280829i	−0.101321	−	0.0271488i	−0.309123	+	0.951022i	$0.600036\pi$
$108$		0			0
$109$	−9.90626	−	5.71938i	−0.948848	−	0.547818i	−0.0561251	−	0.998424i	$-0.517875\pi$
$109$	−9.90626	−	5.71938i	−0.948848	−	0.547818i	−0.892723	+	0.450606i	$0.851208\pi$
$110$		0			0
$111$			8.57701i			0.814094i
$112$		0			0
$113$	−11.7834	−	11.7834i	−1.10849	−	1.10849i	−0.993350	−	0.115136i	$-0.963270\pi$
$113$	−11.7834	−	11.7834i	−1.10849	−	1.10849i	−0.115136	−	0.993350i	$-0.536730\pi$
$114$		0			0
$115$	−1.20322	−	7.51946i	−0.112201	−	0.701193i
$116$		0			0
$117$	−0.468075	+	1.74688i	−0.0432736	+	0.161499i
$118$		0			0
$119$	−4.83106	−	5.16149i	−0.442862	−	0.473153i
$120$		0			0
$121$	4.83990	+	8.38295i	0.439991	+	0.762087i
$122$		0			0
$123$	−4.71805	+	1.26420i	−0.425413	+	0.113989i
$124$		0			0
$125$	3.40416	−	10.6495i	0.304477	−	0.952520i
$126$		0			0
$127$	−14.3921	+	14.3921i	−1.27709	+	1.27709i	−0.334798	+	0.942290i	$0.608668\pi$
$127$	−14.3921	+	14.3921i	−1.27709	+	1.27709i	−0.942290	+	0.334798i	$0.891332\pi$
$128$		0			0
$129$	−2.27752	+	3.94479i	−0.200525	+	0.347319i
$130$		0			0
$131$	−17.0132	+	9.82256i	−1.48645	+	0.858201i	−0.999881	−	0.0154420i	$-0.995084\pi$
$131$	−17.0132	+	9.82256i	−1.48645	+	0.858201i	−0.486567	+	0.873643i	$0.661751\pi$
$132$		0			0
$133$	−0.494273	+	0.794269i	−0.0428589	+	0.0688719i
$134$		0			0
$135$	−2.08882	−	0.798015i	−0.179777	−	0.0686822i
$136$		0			0
$137$	−0.0197311	−	0.0736375i	−0.00168574	−	0.00629128i	0.965078	−	0.261963i	$-0.0843699\pi$
$137$	−0.0197311	−	0.0736375i	−0.00168574	−	0.00629128i	−0.966764	+	0.255672i	$0.917703\pi$
$138$		0			0
$139$	−8.85468			−0.751044			−0.375522	−	0.926813i	$-0.622537\pi$
$139$	−8.85468			−0.751044			−0.375522	+	0.926813i	$0.622537\pi$
$140$		0			0
$141$	0.600054			0.0505336
$142$		0			0
$143$	−0.537818	−	2.00716i	−0.0449746	−	0.167848i
$144$		0			0
$145$	−3.11428	−	6.96497i	−0.258627	−	0.578409i
$146$		0			0
$147$	−6.62702	−	2.25446i	−0.546588	−	0.185945i
$148$		0			0
$149$	6.20060	−	3.57992i	0.507973	−	0.293279i	−0.224027	−	0.974583i	$-0.571920\pi$
$149$	6.20060	−	3.57992i	0.507973	−	0.293279i	0.732000	+	0.681304i	$0.238587\pi$
$150$		0			0
$151$	1.58230	−	2.74062i	0.128766	−	0.223028i	−0.794433	−	0.607352i	$-0.792232\pi$
$151$	1.58230	−	2.74062i	0.128766	−	0.223028i	0.923199	+	0.384323i	$0.125565\pi$
$152$		0			0
$153$	−1.88945	+	1.88945i	−0.152753	+	0.152753i
$154$		0			0
$155$	−13.3625	−	1.38297i	−1.07330	−	0.111083i
$156$		0			0
$157$	−7.58613	+	2.03270i	−0.605439	+	0.162227i	−0.548500	−	0.836151i	$-0.684801\pi$
$157$	−7.58613	+	2.03270i	−0.605439	+	0.162227i	−0.0569392	+	0.998378i	$0.518134\pi$
$158$		0			0
$159$	−1.09921	−	1.90389i	−0.0871732	−	0.150988i
$160$		0			0
$161$	−8.77562	+	2.04313i	−0.691616	+	0.161021i
$162$		0			0
$163$	−0.214757	+	0.801485i	−0.0168211	+	0.0627771i	−0.973826	−	0.227294i	$-0.927012\pi$
$163$	−0.214757	+	0.801485i	−0.0168211	+	0.0627771i	0.957005	+	0.290071i	$0.0936789\pi$
$164$		0			0
$165$	2.53697	−	0.405952i	0.197503	−	0.0316033i
$166$		0			0
$167$	13.9691	+	13.9691i	1.08096	+	1.08096i	0.996420	+	0.0845414i	$0.0269425\pi$
$167$	13.9691	+	13.9691i	1.08096	+	1.08096i	0.0845414	+	0.996420i	$0.473057\pi$
$168$		0			0
$169$			9.72931i			0.748409i
$170$		0			0
$171$	0.306216	+	0.176794i	0.0234169	+	0.0135198i
$172$		0			0
$173$	−11.5383	−	3.09167i	−0.877240	−	0.235056i	−0.208024	−	0.978124i	$-0.566703\pi$
$173$	−11.5383	−	3.09167i	−0.877240	−	0.235056i	−0.669216	+	0.743068i	$0.733370\pi$
$174$		0			0
$175$	−12.8517	−	3.13571i	−0.971501	−	0.237037i
$176$		0			0
$177$	1.68669	+	0.451948i	0.126780	+	0.0339705i
$178$		0			0
$179$	−21.0178	−	12.1346i	−1.57094	−	0.906985i	−0.996053	−	0.0887556i	$-0.971711\pi$
$179$	−21.0178	−	12.1346i	−1.57094	−	0.906985i	−0.574891	−	0.818230i	$-0.694956\pi$
$180$		0			0
$181$			19.3888i			1.44116i	0.693374	+	0.720578i	$0.256124\pi$
$181$			19.3888i			1.44116i	−0.693374	+	0.720578i	$0.743876\pi$
$182$		0			0
$183$	8.43425	+	8.43425i	0.623478	+	0.623478i
$184$		0			0
$185$	18.9379	−	3.03034i	1.39234	−	0.222795i
$186$		0			0
$187$	0.794631	−	2.96560i	0.0581092	−	0.216866i
$188$		0			0
$189$	−0.768858	+	2.53157i	−0.0559262	+	0.184145i
$190$		0			0
$191$	2.77973	+	4.81464i	0.201135	+	0.348375i	0.948894	−	0.315594i	$-0.102204\pi$
$191$	2.77973	+	4.81464i	0.201135	+	0.348375i	−0.747760	+	0.663969i	$0.768870\pi$
$192$		0			0
$193$	−2.85084	+	0.763881i	−0.205208	+	0.0549853i	−0.359959	−	0.932968i	$-0.617209\pi$
$193$	−2.85084	+	0.763881i	−0.205208	+	0.0549853i	0.154751	+	0.987954i	$0.450543\pi$
$194$		0			0
$195$	4.02245	+	0.416312i	0.288054	+	0.0298127i
$196$		0			0
$197$	−17.4032	+	17.4032i	−1.23993	+	1.23993i	−0.279900	+	0.960029i	$0.590301\pi$
$197$	−17.4032	+	17.4032i	−1.23993	+	1.23993i	−0.960029	+	0.279900i	$0.909699\pi$
$198$		0			0
$199$	4.86369	−	8.42415i	0.344778	−	0.597172i	−0.640536	−	0.767928i	$-0.721288\pi$
$199$	4.86369	−	8.42415i	0.344778	−	0.597172i	0.985313	+	0.170756i	$0.0546210\pi$
$200$		0			0
$201$	−4.38704	+	2.53286i	−0.309438	+	0.178654i
$202$		0			0
$203$	−7.96283	+	4.25284i	−0.558881	+	0.298491i
$204$		0			0
$205$	4.45826	+	9.97071i	0.311378	+	0.696385i
$206$		0			0
$207$	0.881430	+	3.28954i	0.0612636	+	0.228639i
$208$		0			0
$209$	−0.406272			−0.0281024
$210$		0			0
$211$	−18.3816			−1.26544			−0.632720	−	0.774381i	$-0.718061\pi$
$211$	−18.3816			−1.26544			−0.632720	+	0.774381i	$0.718061\pi$
$212$		0			0
$213$	−1.12808	−	4.21005i	−0.0772947	−	0.288468i
$214$		0			0
$215$	9.51467	+	3.63500i	0.648895	+	0.247905i
$216$		0			0
$217$	−0.525327	+	15.8864i	−0.0356615	+	1.07844i
$218$		0			0
$219$	−7.29552	+	4.21207i	−0.492986	+	0.284625i
$220$		0			0
$221$	2.41623	−	4.18504i	0.162533	−	0.281516i
$222$		0			0
$223$	11.4869	−	11.4869i	0.769218	−	0.769218i	−0.208751	−	0.977969i	$-0.566940\pi$
$223$	11.4869	−	11.4869i	0.769218	−	0.769218i	0.977969	+	0.208751i	$0.0669398\pi$
$224$		0			0
$225$	−1.02400	+	4.89402i	−0.0682668	+	0.326268i
$226$		0			0
$227$	25.0054	−	6.70018i	1.65967	−	0.444707i	0.697371	−	0.716710i	$-0.254353\pi$
$227$	25.0054	−	6.70018i	1.65967	−	0.444707i	0.962296	+	0.272003i	$0.0876862\pi$
$228$		0			0
$229$	−7.75451	−	13.4312i	−0.512433	−	0.887559i	−0.999896	−	0.0144160i	$-0.995411\pi$
$229$	−7.75451	−	13.4312i	−0.512433	−	0.887559i	0.487463	−	0.873143i	$-0.337922\pi$
$230$		0			0
$231$	−0.689325	−	2.96078i	−0.0453543	−	0.194805i
$232$		0			0
$233$	5.14787	−	19.2121i	0.337248	−	1.25863i	−0.564164	−	0.825663i	$-0.690801\pi$
$233$	5.14787	−	19.2121i	0.337248	−	1.25863i	0.901412	−	0.432963i	$-0.142532\pi$
$234$		0			0
$235$	−0.212004	−	1.32491i	−0.0138296	−	0.0864273i
$236$		0			0
$237$	−1.93483	−	1.93483i	−0.125681	−	0.125681i
$238$		0			0
$239$			14.1939i			0.918125i	0.888404	+	0.459063i	$0.151815\pi$
$239$			14.1939i			0.918125i	−0.888404	+	0.459063i	$0.848185\pi$
$240$		0			0
$241$	4.48239	+	2.58791i	0.288736	+	0.166702i	0.637372	−	0.770556i	$-0.280022\pi$
$241$	4.48239	+	2.58791i	0.288736	+	0.166702i	−0.348635	+	0.937258i	$0.613355\pi$
$242$		0			0
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$		0			0
$245$	−2.63641	+	15.4288i	−0.168434	+	0.985713i
$246$		0			0
$247$	−0.617675	−	0.165506i	−0.0393017	−	0.0105309i
$248$		0			0
$249$	−2.67233	−	1.54287i	−0.169352	−	0.0977753i
$250$		0			0
$251$			21.6309i			1.36533i	0.730732	+	0.682665i	$0.239179\pi$
$251$			21.6309i			1.36533i	−0.730732	+	0.682665i	$0.760821\pi$
$252$		0			0
$253$	−2.76692	−	2.76692i	−0.173955	−	0.173955i
$254$		0			0
$255$	4.83942	+	3.50430i	0.303056	+	0.219448i
$256$		0			0
$257$	3.09670	−	11.5570i	0.193167	−	0.720908i	−0.799567	−	0.600577i	$-0.794938\pi$
$257$	3.09670	−	11.5570i	0.193167	−	0.720908i	0.992734	−	0.120331i	$-0.0383957\pi$
$258$		0			0
$259$	−5.14565	−	22.1015i	−0.319735	−	1.37332i
$260$		0			0
$261$	1.70601	+	2.95490i	0.105599	+	0.182904i
$262$		0			0
$263$	16.1226	−	4.32005i	0.994164	−	0.266385i	0.275165	−	0.961397i	$-0.411267\pi$
$263$	16.1226	−	4.32005i	0.994164	−	0.266385i	0.718999	+	0.695012i	$0.244601\pi$
$264$		0			0
$265$	−3.81539	+	3.09970i	−0.234378	+	0.190413i
$266$		0			0
$267$	9.35996	−	9.35996i	0.572820	−	0.572820i
$268$		0			0
$269$	−8.12029	+	14.0648i	−0.495103	+	0.857543i	−0.999984	−	0.00564562i	$-0.998203\pi$
$269$	−8.12029	+	14.0648i	−0.495103	+	0.857543i	0.504881	+	0.863189i	$0.331536\pi$
$270$		0			0
$271$	8.94550	−	5.16469i	0.543400	−	0.313732i	−0.203055	−	0.979167i	$-0.565087\pi$
$271$	8.94550	−	5.16469i	0.543400	−	0.313732i	0.746456	+	0.665435i	$0.231754\pi$
$272$		0			0
$273$	0.158137	−	4.78224i	0.00957089	−	0.289434i
$274$		0			0
$275$	−1.79267	−	5.45814i	−0.108102	−	0.329139i
$276$		0			0
$277$	4.81074	+	17.9539i	0.289049	+	1.07875i	0.945829	+	0.324665i	$0.105251\pi$
$277$	4.81074	+	17.9539i	0.289049	+	1.07875i	−0.656780	+	0.754082i	$0.728082\pi$
$278$		0			0
$279$	6.00779			0.359677
$280$		0			0
$281$	−29.8039			−1.77795			−0.888976	−	0.457953i	$-0.848583\pi$
$281$	−29.8039			−1.77795			−0.888976	+	0.457953i	$0.848583\pi$
$282$		0			0
$283$	−4.40890	−	16.4542i	−0.262082	−	0.978102i	−0.964012	−	0.265857i	$-0.914345\pi$
$283$	−4.40890	−	16.4542i	−0.262082	−	0.978102i	0.701931	−	0.712245i	$-0.252322\pi$
$284$		0			0
$285$	0.282168	−	0.738581i	0.0167142	−	0.0437498i
$286$		0			0
$287$	11.3992	−	6.08816i	0.672874	−	0.359373i
$288$		0			0
$289$	−8.53900	+	4.92999i	−0.502294	+	0.290000i
$290$		0			0
$291$	−7.98152	+	13.8244i	−0.467885	+	0.810401i
$292$		0			0
$293$	−5.94968	+	5.94968i	−0.347584	+	0.347584i	−0.859209	−	0.511625i	$-0.829044\pi$
$293$	−5.94968	+	5.94968i	−0.347584	+	0.347584i	0.511625	+	0.859209i	$0.329044\pi$
$294$		0			0
$295$	0.401968	−	3.88386i	0.0234035	−	0.226127i
$296$		0			0
$297$	−1.10985	+	0.297383i	−0.0643999	+	0.0172559i
$298$		0			0
$299$	−3.07950	−	5.33386i	−0.178092	−	0.308465i
$300$		0			0
$301$	3.50218	−	11.5314i	0.201863	−	0.664660i
$302$		0			0
$303$	−0.602609	+	2.24897i	−0.0346190	+	0.129200i
$304$		0			0
$305$	15.6428	−	21.6026i	0.895702	−	1.23696i
$306$		0			0
$307$	7.93464	+	7.93464i	0.452854	+	0.452854i	0.896301	−	0.443447i	$-0.146244\pi$
$307$	7.93464	+	7.93464i	0.452854	+	0.452854i	−0.443447	+	0.896301i	$0.646244\pi$
$308$		0			0
$309$			18.9427i			1.07761i
$310$		0			0
$311$	16.3412	+	9.43457i	0.926622	+	0.534985i	0.885742	−	0.464179i	$-0.153650\pi$
$311$	16.3412	+	9.43457i	0.926622	+	0.534985i	0.0408802	+	0.999164i	$0.486984\pi$
$312$		0			0
$313$	10.9629	+	2.93749i	0.619658	+	0.166037i	0.554972	−	0.831869i	$-0.312729\pi$
$313$	10.9629	+	2.93749i	0.619658	+	0.166037i	0.0646855	+	0.997906i	$0.479396\pi$
$314$		0			0
$315$	5.86130	+	0.803196i	0.330247	+	0.0452549i
$316$		0			0
$317$	−20.1672	−	5.40379i	−1.13270	−	0.303507i	−0.356690	−	0.934223i	$-0.616095\pi$
$317$	−20.1672	−	5.40379i	−1.13270	−	0.303507i	−0.776014	+	0.630716i	$0.782761\pi$
$318$		0			0
$319$	−3.39518	−	1.96021i	−0.190093	−	0.109750i
$320$		0			0
$321$		−	1.08504i		−	0.0605611i
$322$		0			0
$323$	−0.668085	−	0.668085i	−0.0371732	−	0.0371732i
$324$		0			0
$325$	−0.501961	−	9.02858i	−0.0278438	−	0.500815i
$326$		0			0
$327$	2.96057	−	11.0490i	0.163720	−	0.611011i
$328$		0			0
$329$	−1.54624	+	0.359993i	−0.0852469	+	0.0198471i
$330$		0			0
$331$	6.68130	+	11.5723i	0.367237	+	0.636074i	0.989133	−	0.147027i	$-0.0469703\pi$
$331$	6.68130	+	11.5723i	0.367237	+	0.636074i	−0.621895	+	0.783101i	$0.713637\pi$
$332$		0			0
$333$	−8.28476	+	2.21989i	−0.454002	+	0.121649i
$334$		0			0
$335$	7.14248	+	8.79162i	0.390236	+	0.480337i
$336$		0			0
$337$	−21.6983	+	21.6983i	−1.18198	+	1.18198i	−0.202752	+	0.979230i	$0.564989\pi$
$337$	−21.6983	+	21.6983i	−1.18198	+	1.18198i	−0.979230	+	0.202752i	$0.935011\pi$
$338$		0			0
$339$	8.33210	−	14.4316i	0.452537	−	0.783818i
$340$		0			0
$341$	−5.97813	+	3.45148i	−0.323734	+	0.186908i
$342$		0			0
$343$	18.4293	+	1.83358i	0.995087	+	0.0990042i
$344$		0			0
$345$	6.95182	−	3.10840i	0.374273	−	0.167351i
$346$		0			0
$347$	−4.66241	−	17.4004i	−0.250291	−	0.934100i	−0.970650	−	0.240498i	$-0.922689\pi$
$347$	−4.66241	−	17.4004i	−0.250291	−	0.934100i	0.720358	−	0.693602i	$-0.243977\pi$
$348$		0			0
$349$	3.70297			0.198216			0.0991078	−	0.995077i	$-0.468401\pi$
$349$	3.70297			0.198216			0.0991078	+	0.995077i	$0.468401\pi$
$350$		0			0
$351$	−1.80850			−0.0965308
$352$		0			0
$353$	5.13800	+	19.1753i	0.273468	+	1.02060i	0.956861	+	0.290546i	$0.0938370\pi$
$353$	5.13800	+	19.1753i	0.273468	+	1.02060i	−0.683393	+	0.730051i	$0.739496\pi$
$354$		0			0
$355$	−8.89714	+	3.97822i	−0.472211	+	0.211142i
$356$		0			0
$357$	3.73525	−	6.00234i	0.197690	−	0.317677i
$358$		0			0
$359$	−27.3891	+	15.8131i	−1.44554	+	0.834583i	−0.998211	−	0.0597871i	$-0.980958\pi$
$359$	−27.3891	+	15.8131i	−1.44554	+	0.834583i	−0.447328	+	0.894370i	$0.647624\pi$
$360$		0			0
$361$	9.43749	−	16.3462i	0.496710	−	0.860327i
$362$		0			0
$363$	−6.84465	+	6.84465i	−0.359251	+	0.359251i
$364$		0			0
$365$	11.8777	+	14.6202i	0.621709	+	0.765256i
$366$		0			0
$367$	20.9577	−	5.61560i	1.09398	−	0.293132i	0.333671	−	0.942690i	$-0.391713\pi$
$367$	20.9577	−	5.61560i	1.09398	−	0.293132i	0.760312	+	0.649558i	$0.225046\pi$
$368$		0			0
$369$	−2.44224	−	4.23009i	−0.127138	−	0.220210i
$370$		0			0
$371$	3.97470	+	4.24656i	0.206356	+	0.220470i
$372$		0			0
$373$	5.88296	−	21.9555i	0.304608	−	1.13681i	−0.628674	−	0.777669i	$-0.716402\pi$
$373$	5.88296	−	21.9555i	0.304608	−	1.13681i	0.933282	−	0.359144i	$-0.116931\pi$
$374$		0			0
$375$	11.1677	+	0.531873i	0.576697	+	0.0274658i
$376$		0			0
$377$	−4.36331	−	4.36331i	−0.224722	−	0.224722i
$378$		0			0
$379$		−	19.0895i		−	0.980562i	−0.871564	−	0.490281i	$-0.836894\pi$
$379$		−	19.0895i		−	0.980562i	0.871564	−	0.490281i	$-0.163106\pi$
$380$		0			0
$381$	−17.6266	−	10.1767i	−0.903038	−	0.521369i
$382$		0			0
$383$	31.8992	+	8.54737i	1.62997	+	0.436750i	0.953910	−	0.300093i	$-0.0970178\pi$
$383$	31.8992	+	8.54737i	1.62997	+	0.436750i	0.676064	+	0.736843i	$0.263684\pi$
$384$		0			0
$385$	−6.29380	+	2.56809i	−0.320762	+	0.130882i
$386$		0			0
$387$	−4.39984	−	1.17893i	−0.223656	−	0.0599285i
$388$		0			0
$389$	16.0286	+	9.25414i	0.812684	+	0.469204i	0.847887	−	0.530177i	$-0.177874\pi$
$389$	16.0286	+	9.25414i	0.812684	+	0.469204i	−0.0352028	+	0.999380i	$0.511208\pi$
$390$		0			0
$391$		−	9.09999i		−	0.460206i
$392$		0			0
$393$	−13.8912	−	13.8912i	−0.700718	−	0.700718i
$394$		0			0
$395$	−3.58847	+	4.95566i	−0.180556	+	0.249346i
$396$		0			0
$397$	4.07627	−	15.2128i	0.204582	−	0.763511i	−0.784994	−	0.619503i	$-0.787334\pi$
$397$	4.07627	−	15.2128i	0.204582	−	0.763511i	0.989577	−	0.144008i	$-0.0459991\pi$
$398$		0			0
$399$	−0.895132	−	0.271859i	−0.0448127	−	0.0136100i
$400$		0			0
$401$	−1.82724	−	3.16487i	−0.0912479	−	0.158046i	0.816789	−	0.576937i	$-0.195752\pi$
$401$	−1.82724	−	3.16487i	−0.0912479	−	0.158046i	−0.908036	+	0.418891i	$0.862419\pi$
$402$		0			0
$403$	−10.4949	+	2.81210i	−0.522788	+	0.140081i
$404$		0			0
$405$	0.230197	−	2.22419i	0.0114386	−	0.110521i
$406$		0			0
$407$	6.96853	−	6.96853i	0.345417	−	0.345417i
$408$		0			0
$409$	−14.0063	+	24.2597i	−0.692568	+	1.19956i	0.278426	+	0.960458i	$0.410187\pi$
$409$	−14.0063	+	24.2597i	−0.692568	+	1.19956i	−0.970994	+	0.239105i	$0.923146\pi$
$410$		0			0
$411$	0.0660216	−	0.0381176i	0.00325661	−	0.00188020i
$412$		0			0
$413$	−4.61747	−	0.152689i	−0.227211	−	0.00751331i
$414$		0			0
$415$	−2.46246	+	6.44555i	−0.120878	+	0.316400i
$416$		0			0
$417$	−2.29176	−	8.55297i	−0.112228	−	0.418841i
$418$		0			0
$419$	32.1069			1.56852			0.784262	−	0.620430i	$-0.213042\pi$
$419$	32.1069			1.56852			0.784262	+	0.620430i	$0.213042\pi$
$420$		0			0
$421$	30.9292			1.50740			0.753699	−	0.657219i	$-0.228267\pi$
$421$	30.9292			1.50740			0.753699	+	0.657219i	$0.228267\pi$
$422$		0			0
$423$	0.155305	+	0.579607i	0.00755120	+	0.0281815i
$424$		0			0
$425$	6.02761	−	11.9234i	0.292382	−	0.578371i
$426$		0			0
$427$	−26.7937	−	16.6737i	−1.29664	−	0.806896i
$428$		0			0
$429$	1.79957	−	1.03899i	0.0868843	−	0.0501627i
$430$		0			0
$431$	18.9761	−	32.8675i	0.914045	−	1.58317i	0.105751	−	0.994393i	$-0.466275\pi$
$431$	18.9761	−	32.8675i	0.914045	−	1.58317i	0.808294	−	0.588779i	$-0.200391\pi$
$432$		0			0
$433$	3.92665	−	3.92665i	0.188703	−	0.188703i	−0.606432	−	0.795135i	$-0.707400\pi$
$433$	3.92665	−	3.92665i	0.188703	−	0.188703i	0.795135	+	0.606432i	$0.207400\pi$
$434$		0			0
$435$	5.92160	−	4.81083i	0.283919	−	0.230662i
$436$		0			0
$437$	−1.16314	+	0.311663i	−0.0556406	+	0.0149088i
$438$		0			0
$439$	−10.3981	−	18.0101i	−0.496275	−	0.859574i	0.503715	−	0.863870i	$-0.331966\pi$
$439$	−10.3981	−	18.0101i	−0.496275	−	0.859574i	−0.999991	+	0.00429550i	$0.998633\pi$
$440$		0			0
$441$	0.462441	−	6.98471i	0.0220210	−	0.332605i
$442$		0			0
$443$	−0.975177	+	3.63941i	−0.0463321	+	0.172914i	−0.985215	−	0.171323i	$-0.945196\pi$
$443$	−0.975177	+	3.63941i	−0.0463321	+	0.172914i	0.938883	+	0.344237i	$0.111862\pi$
$444$		0			0
$445$	−23.9736	−	17.3596i	−1.13646	−	0.822926i
$446$		0			0
$447$	5.06277	+	5.06277i	0.239461	+	0.239461i
$448$		0			0
$449$			18.7981i			0.887135i	0.896241	+	0.443568i	$0.146287\pi$
$449$			18.7981i			0.887135i	−0.896241	+	0.443568i	$0.853713\pi$
$450$		0			0
$451$	4.86037	+	2.80614i	0.228866	+	0.132136i
$452$		0			0
$453$	3.05676	+	0.819057i	0.143619	+	0.0384827i
$454$		0			0
$455$	−10.6150	+	1.34044i	−0.497637	+	0.0628410i
$456$		0			0
$457$	7.14267	+	1.91387i	0.334120	+	0.0895272i	0.421979	−	0.906606i	$-0.361336\pi$
$457$	7.14267	+	1.91387i	0.334120	+	0.0895272i	−0.0878586	+	0.996133i	$0.528002\pi$
$458$		0			0
$459$	−2.31409	−	1.33604i	−0.108012	−	0.0623610i
$460$		0			0
$461$		−	17.6657i		−	0.822772i	−0.911461	−	0.411386i	$-0.865045\pi$
$461$		−	17.6657i		−	0.822772i	0.911461	−	0.411386i	$-0.134955\pi$
$462$		0			0
$463$	15.6126	+	15.6126i	0.725579	+	0.725579i	0.969736	−	0.244157i	$-0.0785111\pi$
$463$	15.6126	+	15.6126i	0.725579	+	0.725579i	−0.244157	+	0.969736i	$0.578511\pi$
$464$		0			0
$465$	−2.12261	−	13.2651i	−0.0984336	−	0.615154i
$466$		0			0
$467$	8.03502	−	29.9871i	0.371816	−	1.38764i	−0.486125	−	0.873889i	$-0.661590\pi$
$467$	8.03502	−	29.9871i	0.371816	−	1.38764i	0.857941	−	0.513748i	$-0.171743\pi$
$468$		0			0
$469$	9.78513	−	9.15870i	0.451835	−	0.422910i
$470$		0			0
$471$	−3.92687	−	6.80153i	−0.180941	−	0.313398i
$472$		0			0
$473$	5.05541	−	1.35459i	0.232448	−	0.0622842i
$474$		0			0
$475$	−1.73046	−	0.362074i	−0.0793991	−	0.0166131i
$476$		0			0
$477$	1.55452	−	1.55452i	0.0711767	−	0.0711767i
$478$		0			0
$479$	−1.26060	+	2.18342i	−0.0575982	+	0.0997630i	−0.893387	−	0.449288i	$-0.851678\pi$
$479$	−1.26060	+	2.18342i	−0.0575982	+	0.0997630i	0.835789	+	0.549051i	$0.185011\pi$
$480$		0			0
$481$	13.4334	−	7.75578i	0.612511	−	0.353633i
$482$		0			0
$483$	−4.24481	−	7.94780i	−0.193146	−	0.361637i
$484$		0			0
$485$	33.3439	+	12.7387i	1.51407	+	0.578437i
$486$		0			0
$487$	9.61849	+	35.8967i	0.435855	+	1.62663i	0.739011	+	0.673693i	$0.235293\pi$
$487$	9.61849	+	35.8967i	0.435855	+	1.62663i	−0.303156	+	0.952941i	$0.598040\pi$
$488$		0			0
$489$	−0.829758			−0.0375230
$490$		0			0
$491$	−2.60684			−0.117645			−0.0588225	−	0.998268i	$-0.518735\pi$
$491$	−2.60684			−0.117645			−0.0588225	+	0.998268i	$0.518735\pi$
$492$		0			0
$493$	−2.35970	−	8.80654i	−0.106276	−	0.396627i
$494$		0			0
$495$	1.04873	+	2.34545i	0.0471371	+	0.105420i
$496$		0			0
$497$	5.43263	+	10.1718i	0.243687	+	0.456269i
$498$		0			0
$499$	−15.1839	+	8.76642i	−0.679724	+	0.392439i	−0.799751	−	0.600332i	$-0.795035\pi$
$499$	−15.1839	+	8.76642i	−0.679724	+	0.392439i	0.120027	+	0.992771i	$0.461702\pi$
$500$		0			0
$501$	−9.87765	+	17.1086i	−0.441301	+	0.764355i
$502$		0			0
$503$	14.7170	−	14.7170i	0.656199	−	0.656199i	−0.298280	−	0.954478i	$-0.596413\pi$
$503$	14.7170	−	14.7170i	0.656199	−	0.656199i	0.954478	+	0.298280i	$0.0964129\pi$
$504$		0			0
$505$	5.17858	+	0.535967i	0.230444	+	0.0238502i
$506$		0			0
$507$	−9.39780	+	2.51813i	−0.417371	+	0.111834i
$508$		0			0
$509$	−5.13342	−	8.89134i	−0.227535	−	0.394102i	0.729542	−	0.683936i	$-0.239733\pi$
$509$	−5.13342	−	8.89134i	−0.227535	−	0.394102i	−0.957077	+	0.289834i	$0.906400\pi$
$510$		0			0
$511$	16.2724	−	15.2307i	0.719848	−	0.673765i
$512$		0			0
$513$	−0.0915152	+	0.341539i	−0.00404049	+	0.0150793i
$514$		0			0
$515$	41.8250	−	6.69261i	1.84303	−	0.294912i
$516$		0			0
$517$	−0.487523	−	0.487523i	−0.0214412	−	0.0214412i
$518$		0			0
$519$		−	11.9453i		−	0.524341i
$520$		0			0
$521$	19.2739	+	11.1278i	0.844404	+	0.487517i	0.858759	−	0.512380i	$-0.171236\pi$
$521$	19.2739	+	11.1278i	0.844404	+	0.487517i	−0.0143550	+	0.999897i	$0.504570\pi$
$522$		0			0
$523$	17.6948	+	4.74130i	0.773738	+	0.207323i	0.624022	−	0.781407i	$-0.285497\pi$
$523$	17.6948	+	4.74130i	0.773738	+	0.207323i	0.149716	+	0.988729i	$0.452164\pi$
$524$		0			0
$525$	−0.297412	−	13.2254i	−0.0129801	−	0.577204i
$526$		0			0
$527$	−15.5063	−	4.15490i	−0.675465	−	0.180990i
$528$		0			0
$529$	9.87443	+	5.70100i	0.429323	+	0.247870i
$530$		0			0
$531$			1.74619i			0.0757783i
$532$		0			0
$533$	6.24631	+	6.24631i	0.270558	+	0.270558i
$534$		0			0
$535$	−2.39575	+	0.383355i	−0.103577	+	0.0165739i
$536$		0			0
$537$	6.28135	−	23.4423i	0.271060	−	1.01161i
$538$		0			0
$539$	3.55256	+	7.21590i	0.153019	+	0.310811i
$540$		0			0
$541$	4.99183	+	8.64610i	0.214615	+	0.371725i	0.953154	−	0.302487i	$-0.0978169\pi$
$541$	4.99183	+	8.64610i	0.214615	+	0.371725i	−0.738538	+	0.674212i	$0.764484\pi$
$542$		0			0
$543$	−18.7281	+	5.01819i	−0.803701	+	0.215351i
$544$		0			0
$545$	−25.4420	−	2.63317i	−1.08981	−	0.112793i
$546$		0			0
$547$	−5.18970	+	5.18970i	−0.221895	+	0.221895i	−0.809296	−	0.587401i	$-0.800151\pi$
$547$	−5.18970	+	5.18970i	−0.221895	+	0.221895i	0.587401	+	0.809296i	$0.300151\pi$
$548$		0			0
$549$	−5.96392	+	10.3298i	−0.254534	+	0.440866i
$550$		0			0
$551$	−1.04482	+	0.603224i	−0.0445106	+	0.0256982i
$552$		0			0
$553$	6.14651	+	3.82497i	0.261376	+	0.162654i
$554$		0			0
$555$	7.82856	+	17.5083i	0.332304	+	0.743185i
$556$		0			0
$557$	4.08292	+	15.2377i	0.172999	+	0.645640i	0.996884	+	0.0788833i	$0.0251354\pi$
$557$	4.08292	+	15.2377i	0.172999	+	0.645640i	−0.823885	+	0.566757i	$0.808198\pi$
$558$		0			0
$559$	8.23782			0.348423
$560$		0			0
$561$	3.07022			0.129625
$562$		0			0
$563$	7.27022	+	27.1328i	0.306403	+	1.14351i	0.931731	+	0.363150i	$0.118299\pi$
$563$	7.27022	+	27.1328i	0.306403	+	1.14351i	−0.625327	+	0.780362i	$0.715035\pi$
$564$		0			0
$565$	−34.8085	−	13.2983i	−1.46441	−	0.559463i
$566$		0			0
$567$	−2.64431	−	0.0874408i	−0.111050	−	0.00367217i
$568$		0			0
$569$	14.1303	−	8.15812i	0.592372	−	0.342006i	−0.173663	−	0.984805i	$-0.555560\pi$
$569$	14.1303	−	8.15812i	0.592372	−	0.342006i	0.766035	+	0.642799i	$0.222227\pi$
$570$		0			0
$571$	8.17973	−	14.1677i	0.342311	−	0.592900i	−0.642550	−	0.766243i	$-0.722124\pi$
$571$	8.17973	−	14.1677i	0.342311	−	0.592900i	0.984861	+	0.173343i	$0.0554570\pi$
$572$		0			0
$573$	−3.93114	+	3.93114i	−0.164226	+	0.164226i
$574$		0			0
$575$	−9.31943	−	14.2512i	−0.388647	−	0.594318i
$576$		0			0
$577$	−22.5413	+	6.03993i	−0.938408	+	0.251446i	−0.695436	−	0.718588i	$-0.744789\pi$
$577$	−22.5413	+	6.03993i	−0.938408	+	0.251446i	−0.242972	+	0.970033i	$0.578122\pi$
$578$		0			0
$579$	−1.47570	−	2.55599i	−0.0613282	−	0.106223i
$580$		0			0
$581$	7.81176	+	2.37249i	0.324087	+	0.0984276i
$582$		0			0
$583$	−0.653774	+	2.43992i	−0.0270766	+	0.101051i
$584$		0			0
$585$	0.638961	+	3.99314i	0.0264178	+	0.165096i
$586$		0			0
$587$	−3.39180	−	3.39180i	−0.139995	−	0.139995i	0.633636	−	0.773631i	$-0.281562\pi$
$587$	−3.39180	−	3.39180i	−0.139995	−	0.139995i	−0.773631	+	0.633636i	$0.781562\pi$
$588$		0			0
$589$			2.12428i			0.0875295i
$590$		0			0
$591$	−21.3145	−	12.3059i	−0.876762	−	0.506199i
$592$		0			0
$593$	15.3609	+	4.11594i	0.630796	+	0.169021i	0.560031	−	0.828472i	$-0.310789\pi$
$593$	15.3609	+	4.11594i	0.630796	+	0.169021i	0.0707654	+	0.997493i	$0.477456\pi$
$594$		0			0
$595$	−14.5727	−	6.12666i	−0.597424	−	0.251169i
$596$		0			0
$597$	9.39592	+	2.51763i	0.384549	+	0.103040i
$598$		0			0
$599$	26.4226	+	15.2551i	1.07960	+	0.623307i	0.930788	−	0.365559i	$-0.119122\pi$
$599$	26.4226	+	15.2551i	1.07960	+	0.623307i	0.148811	+	0.988866i	$0.452455\pi$
$600$		0			0
$601$			41.7609i			1.70346i	0.523980	+	0.851731i	$0.324447\pi$
$601$			41.7609i			1.70346i	−0.523980	+	0.851731i	$0.675553\pi$
$602$		0			0
$603$	−3.58200	−	3.58200i	−0.145871	−	0.145871i
$604$		0			0
$605$	17.5311	+	12.6946i	0.712742	+	0.516108i
$606$		0			0
$607$	−3.41028	+	12.7273i	−0.138419	+	0.516587i	0.861541	+	0.507687i	$0.169500\pi$
$607$	−3.41028	+	12.7273i	−0.138419	+	0.516587i	−0.999960	+	0.00889954i	$0.997167\pi$
$608$		0			0
$609$	−6.16886	−	6.59079i	−0.249975	−	0.267072i
$610$		0			0
$611$	−0.542600	−	0.939810i	−0.0219512	−	0.0380206i
$612$		0			0
$613$	−25.8110	+	6.91603i	−1.04250	+	0.279336i	−0.739147	−	0.673544i	$-0.764771\pi$
$613$	−25.8110	+	6.91603i	−1.04250	+	0.279336i	−0.303348	+	0.952880i	$0.598105\pi$
$614$		0			0
$615$	−8.47709	+	6.88696i	−0.341829	+	0.277709i
$616$		0			0
$617$	−10.6207	+	10.6207i	−0.427574	+	0.427574i	−0.887801	−	0.460227i	$-0.847768\pi$
$617$	−10.6207	+	10.6207i	−0.427574	+	0.427574i	0.460227	+	0.887801i	$0.347768\pi$
$618$		0			0
$619$	11.2987	−	19.5699i	0.454132	−	0.786579i	−0.544506	−	0.838757i	$-0.683283\pi$
$619$	11.2987	−	19.5699i	0.454132	−	0.786579i	0.998638	+	0.0521778i	$0.0166162\pi$
$620$		0			0
$621$	−2.94932	+	1.70279i	−0.118352	+	0.0683307i
$622$		0			0
$623$	−18.5037	+	29.7344i	−0.741335	+	1.19128i
$624$		0			0
$625$	−2.77128	−	24.8459i	−0.110851	−	0.993837i
$626$		0			0
$627$	−0.105151	−	0.392429i	−0.00419932	−	0.0156721i
$628$		0			0
$629$	22.9185			0.913819
$630$		0			0
$631$	7.18933			0.286203			0.143101	−	0.989708i	$-0.454293\pi$
$631$	7.18933			0.286203			0.143101	+	0.989708i	$0.454293\pi$
$632$		0			0
$633$	−4.75750	−	17.7552i	−0.189094	−	0.705707i
$634$		0			0
$635$	−16.2423	+	42.5147i	−0.644558	+	1.68714i
$636$		0			0
$637$	2.46154	+	12.4179i	0.0975298	+	0.492015i
$638$		0			0
$639$	3.77463	−	2.17928i	0.149322	−	0.0862110i
$640$		0			0
$641$	4.87266	−	8.43969i	0.192458	−	0.333348i	−0.753606	−	0.657326i	$-0.771687\pi$
$641$	4.87266	−	8.43969i	0.192458	−	0.333348i	0.946064	+	0.323979i	$0.105021\pi$
$642$		0			0
$643$	−3.24259	+	3.24259i	−0.127875	+	0.127875i	−0.768148	−	0.640273i	$-0.778821\pi$
$643$	−3.24259	+	3.24259i	−0.127875	+	0.127875i	0.640273	+	0.768148i	$0.278821\pi$
$644$		0			0
$645$	−1.04856	+	10.1313i	−0.0412869	+	0.398919i
$646$		0			0
$647$	−10.0163	+	2.68385i	−0.393780	+	0.105513i	−0.450275	−	0.892890i	$-0.648674\pi$
$647$	−10.0163	+	2.68385i	−0.393780	+	0.105513i	0.0564952	+	0.998403i	$0.482007\pi$
$648$		0			0
$649$	−1.00319	−	1.73757i	−0.0393786	−	0.0682057i
$650$		0			0
$651$	−15.4811	+	3.60429i	−0.606752	+	0.141263i
$652$		0			0
$653$	1.88910	−	7.05023i	0.0739263	−	0.275897i	−0.919061	−	0.394114i	$-0.871051\pi$
$653$	1.88910	−	7.05023i	0.0739263	−	0.275897i	0.992988	+	0.118218i	$0.0377180\pi$
$654$		0			0
$655$	−25.7636	+	35.5794i	−1.00667	+	1.39020i
$656$		0			0
$657$	−5.95677	−	5.95677i	−0.232396	−	0.232396i
$658$		0			0
$659$			11.8101i			0.460057i	0.973184	+	0.230028i	$0.0738819\pi$
$659$			11.8101i			0.460057i	−0.973184	+	0.230028i	$0.926118\pi$
$660$		0			0
$661$	−35.2128	−	20.3301i	−1.36962	−	0.790750i	−0.378740	−	0.925503i	$-0.623643\pi$
$661$	−35.2128	−	20.3301i	−1.36962	−	0.790750i	−0.990879	+	0.134753i	$0.956976\pi$
$662$		0			0
$663$	4.66781	+	1.25073i	0.181283	+	0.0485745i
$664$		0			0
$665$	−0.284000	+	2.07248i	−0.0110130	+	0.0803675i
$666$		0			0
$667$	−11.2240	−	3.00746i	−0.434594	−	0.116449i
$668$		0			0
$669$	14.0685	+	8.12245i	0.543919	+	0.314032i
$670$		0			0
$671$		−	13.7051i		−	0.529079i
$672$		0			0
$673$	−9.97751	−	9.97751i	−0.384605	−	0.384605i	0.488153	−	0.872758i	$-0.337671\pi$
$673$	−9.97751	−	9.97751i	−0.384605	−	0.384605i	−0.872758	+	0.488153i	$0.837671\pi$
$674$		0			0
$675$	−4.99229	+	0.277556i	−0.192153	+	0.0106831i
$676$		0			0
$677$	−0.711353	+	2.65481i	−0.0273395	+	0.102033i	−0.978247	−	0.207442i	$-0.933486\pi$
$677$	−0.711353	+	2.65481i	−0.0273395	+	0.102033i	0.950908	+	0.309474i	$0.100153\pi$
$678$		0			0
$679$	12.2733	−	40.4116i	0.471007	−	1.55085i
$680$		0			0
$681$	12.9438	+	22.4192i	0.496006	+	0.859107i
$682$		0			0
$683$	−45.6962	+	12.2443i	−1.74852	+	0.468513i	−0.984308	−	0.176458i	$-0.943536\pi$
$683$	−45.6962	+	12.2443i	−1.74852	+	0.468513i	−0.764207	+	0.644971i	$0.776869\pi$
$684$		0			0
$685$	−0.107489	−	0.132307i	−0.00410694	−	0.00505519i
$686$		0			0
$687$	10.9665	−	10.9665i	0.418400	−	0.418400i
$688$		0			0
$689$	−1.98793	+	3.44320i	−0.0757341	+	0.131175i
$690$		0			0
$691$	−27.4191	+	15.8304i	−1.04307	+	0.602219i	−0.920702	−	0.390266i	$-0.872383\pi$
$691$	−27.4191	+	15.8304i	−1.04307	+	0.602219i	−0.122371	+	0.992484i	$0.539050\pi$
$692$		0			0
$693$	2.68149	−	1.43214i	0.101861	−	0.0544027i
$694$		0			0
$695$	−18.0751	+	8.08200i	−0.685627	+	0.306568i
$696$		0			0
$697$	3.37804	+	12.6070i	0.127952	+	0.477525i
$698$		0			0
$699$	19.8898			0.752302
$700$		0			0
$701$	−2.81268			−0.106233			−0.0531167	−	0.998588i	$-0.516916\pi$
$701$	−2.81268			−0.106233			−0.0531167	+	0.998588i	$0.516916\pi$
$702$		0			0
$703$	−0.784927	−	2.92939i	−0.0296041	−	0.110484i
$704$		0			0
$705$	1.22489	−	0.547691i	0.0461320	−	0.0206272i
$706$		0			0
$707$	0.203589	−	6.15674i	0.00765674	−	0.231548i
$708$		0			0
$709$	12.3526	−	7.13175i	0.463910	−	0.267839i	−0.249777	−	0.968303i	$-0.580357\pi$
$709$	12.3526	−	7.13175i	0.463910	−	0.267839i	0.713687	+	0.700465i	$0.247024\pi$
$710$		0			0
$711$	1.36813	−	2.36967i	0.0513090	−	0.0888697i
$712$		0			0
$713$	−14.4674	+	14.4674i	−0.541810	+	0.541810i
$714$		0			0
$715$	−2.92986	−	3.60634i	−0.109571	−	0.134870i
$716$		0			0
$717$	−13.7102	+	3.67364i	−0.512018	+	0.137195i
$718$		0			0
$719$	10.6678	+	18.4772i	0.397843	+	0.689084i	0.993459	−	0.114185i	$-0.0364257\pi$
$719$	10.6678	+	18.4772i	0.397843	+	0.689084i	−0.595617	+	0.803269i	$0.703092\pi$
$720$		0			0
$721$	−11.3644	−	48.8121i	−0.423231	−	1.81786i
$722$		0			0
$723$	−1.33960	+	4.99946i	−0.0498203	+	0.185932i
$724$		0			0
$725$	−12.7144	−	11.3751i	−0.472200	−	0.422460i
$726$		0			0
$727$	23.3102	+	23.3102i	0.864529	+	0.864529i	0.991860	−	0.127331i	$-0.0406411\pi$
$727$	23.3102	+	23.3102i	0.864529	+	0.864529i	−0.127331	+	0.991860i	$0.540641\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	10.5408	+	6.08572i	0.389865	+	0.225089i
$732$		0			0
$733$	−17.7238	−	4.74908i	−0.654644	−	0.175411i	−0.0838162	−	0.996481i	$-0.526711\pi$
$733$	−17.7238	−	4.74908i	−0.654644	−	0.175411i	−0.570828	+	0.821070i	$0.693378\pi$
$734$		0			0
$735$	−15.5855	+	1.44670i	−0.574879	+	0.0533624i
$736$		0			0
$737$	5.62218	+	1.50646i	0.207096	+	0.0554911i
$738$		0			0
$739$	15.4768	+	8.93552i	0.569322	+	0.328698i	0.756879	−	0.653555i	$-0.226723\pi$
$739$	15.4768	+	8.93552i	0.569322	+	0.328698i	−0.187556	+	0.982254i	$0.560057\pi$
$740$		0			0
$741$		−	0.639464i		−	0.0234913i
$742$		0			0
$743$	−33.6457	−	33.6457i	−1.23434	−	1.23434i	−0.962280	−	0.272061i	$-0.912295\pi$
$743$	−33.6457	−	33.6457i	−1.23434	−	1.23434i	−0.272061	−	0.962280i	$-0.587705\pi$
$744$		0			0
$745$	9.38977	−	12.9672i	0.344015	−	0.475082i
$746$		0			0
$747$	0.798647	−	2.98059i	0.0292210	−	0.109054i
$748$		0			0
$749$	0.650955	+	2.79597i	0.0237854	+	0.102163i
$750$		0			0
$751$	−16.9005	−	29.2726i	−0.616709	−	1.06817i	−0.990082	−	0.140491i	$-0.955132\pi$
$751$	−16.9005	−	29.2726i	−0.616709	−	1.06817i	0.373373	−	0.927681i	$-0.378201\pi$
$752$		0			0
$753$	−20.8938	+	5.59849i	−0.761414	+	0.204020i
$754$		0			0
$755$	0.728479	−	7.03865i	0.0265121	−	0.256163i
$756$		0			0
$757$	38.6362	−	38.6362i	1.40426	−	1.40426i	0.618367	−	0.785889i	$-0.287794\pi$
$757$	38.6362	−	38.6362i	1.40426	−	1.40426i	0.785889	−	0.618367i	$-0.212206\pi$
$758$		0			0
$759$	1.95651	−	3.38877i	0.0710167	−	0.123005i
$760$		0			0
$761$	−1.25087	+	0.722188i	−0.0453439	+	0.0261793i	−0.522501	−	0.852639i	$-0.675001\pi$
$761$	−1.25087	+	0.722188i	−0.0453439	+	0.0261793i	0.477157	+	0.878818i	$0.341667\pi$
$762$		0			0
$763$	−1.00022	+	30.2476i	−0.0362102	+	1.09504i
$764$		0			0
$765$	−2.13236	+	5.58150i	−0.0770957	+	0.201799i
$766$		0			0
$767$	−0.817350	−	3.05039i	−0.0295128	−	0.110143i
$768$		0			0
$769$	−19.4505			−0.701404			−0.350702	−	0.936487i	$-0.614057\pi$
$769$	−19.4505			−0.701404			−0.350702	+	0.936487i	$0.614057\pi$
$770$		0			0
$771$	11.9647			0.430899
$772$		0			0
$773$	6.48908	+	24.2176i	0.233396	+	0.871046i	0.978865	+	0.204506i	$0.0655588\pi$
$773$	6.48908	+	24.2176i	0.233396	+	0.871046i	−0.745469	+	0.666540i	$0.767775\pi$
$774$		0			0
$775$	−28.5391	+	9.37335i	−1.02515	+	0.336701i
$776$		0			0
$777$	20.0167	−	10.6906i	0.718094	−	0.383524i
$778$		0			0
$779$	1.49571	−	0.863547i	0.0535893	−	0.0309398i
$780$		0			0
$781$	−2.50399	+	4.33704i	−0.0895999	+	0.155192i
$782$		0			0
$783$	−2.41266	+	2.41266i	−0.0862216	+	0.0862216i
$784$		0			0
$785$	−13.6302	+	11.0735i	−0.486484	+	0.395230i
$786$		0			0
$787$	−20.3102	+	5.44211i	−0.723982	+	0.193990i	−0.601948	−	0.798536i	$-0.705608\pi$
$787$	−20.3102	+	5.44211i	−0.723982	+	0.193990i	−0.122034	+	0.992526i	$0.538942\pi$
$788$		0			0
$789$	8.34569	+	14.4552i	0.297114	+	0.514617i
$790$		0			0
$791$	−12.8124	+	42.1866i	−0.455557	+	1.49998i
$792$		0			0
$793$	5.58312	−	20.8365i	0.198263	−	0.739926i
$794$		0			0
$795$	−3.98158	−	2.88313i	−0.141212	−	0.102254i
$796$		0			0
$797$	−35.0360	−	35.0360i	−1.24104	−	1.24104i	−0.959570	−	0.281469i	$-0.909178\pi$
$797$	−35.0360	−	35.0360i	−1.24104	−	1.24104i	−0.281469	−	0.959570i	$-0.590822\pi$
$798$		0			0
$799$		−	1.60339i		−	0.0567239i
$800$		0			0
$801$	11.4636	+	6.61849i	0.405045	+	0.233853i
$802$		0			0
$803$	9.34952	+	2.50520i	0.329937	+	0.0884065i
$804$		0			0
$805$	−16.0489	+	12.1805i	−0.565648	+	0.429306i
$806$		0			0
$807$	−15.6872	−	4.20337i	−0.552215	−	0.147966i
$808$		0			0
$809$	19.5041	+	11.2607i	0.685726	+	0.395904i	0.802009	−	0.597312i	$-0.203765\pi$
$809$	19.5041	+	11.2607i	0.685726	+	0.395904i	−0.116283	+	0.993216i	$0.537098\pi$
$810$		0			0
$811$		−	30.3063i		−	1.06420i	−0.846682	−	0.532099i	$-0.821403\pi$
$811$		−	30.3063i		−	1.06420i	0.846682	−	0.532099i	$-0.178597\pi$
$812$		0			0
$813$	7.30397	+	7.30397i	0.256161	+	0.256161i
$814$		0			0
$815$	0.293161	+	1.83209i	0.0102690	+	0.0641753i
$816$		0			0
$817$	0.416856	−	1.55573i	0.0145839	−	0.0544280i
$818$		0			0
$819$	4.66022	−	1.08499i	0.162841	−	0.0379125i
$820$		0			0
$821$	3.85389	+	6.67513i	0.134502	+	0.232964i	0.925407	−	0.378975i	$-0.123723\pi$
$821$	3.85389	+	6.67513i	0.134502	+	0.232964i	−0.790905	+	0.611939i	$0.790390\pi$
$822$		0			0
$823$	−20.2458	+	5.42483i	−0.705723	+	0.189098i	−0.593792	−	0.804618i	$-0.702370\pi$
$823$	−20.2458	+	5.42483i	−0.705723	+	0.189098i	−0.111930	+	0.993716i	$0.535703\pi$
$824$		0			0
$825$	4.80819	−	3.14425i	0.167400	−	0.109469i
$826$		0			0
$827$	10.1627	−	10.1627i	0.353391	−	0.353391i	−0.507979	−	0.861370i	$-0.669607\pi$
$827$	10.1627	−	10.1627i	0.353391	−	0.353391i	0.861370	+	0.507979i	$0.169607\pi$
$828$		0			0
$829$	−5.76151	+	9.97922i	−0.200105	+	0.346593i	−0.948562	−	0.316591i	$-0.897462\pi$
$829$	−5.76151	+	9.97922i	−0.200105	+	0.346593i	0.748457	+	0.663184i	$0.230795\pi$
$830$		0			0
$831$	−16.0971	+	9.29364i	−0.558400	+	0.322393i
$832$		0			0
$833$	−6.02410	+	17.7079i	−0.208723	+	0.613544i
$834$		0			0
$835$	41.2653	+	15.7650i	1.42804	+	0.545571i
$836$		0			0
$837$	1.55493	+	5.80308i	0.0537463	+	0.200584i
$838$		0			0
$839$	−15.2304			−0.525813			−0.262907	−	0.964821i	$-0.584681\pi$
$839$	−15.2304			−0.525813			−0.262907	+	0.964821i	$0.584681\pi$
$840$		0			0
$841$	17.3581			0.598555
$842$		0			0
$843$	−7.71382	−	28.7884i	−0.265678	−	0.991524i
$844$		0			0
$845$	8.88031	+	19.8605i	0.305492	+	0.683221i
$846$		0			0
$847$	13.5312	−	21.7439i	0.464937	−	0.747129i
$848$		0			0
$849$	14.7525	−	8.51734i	0.506303	−	0.292314i
$850$		0			0
$851$	14.6049	−	25.2964i	0.500648	−	0.867148i
$852$		0			0
$853$	−7.93430	+	7.93430i	−0.271665	+	0.271665i	−0.829770	−	0.558105i	$-0.811529\pi$
$853$	−7.93430	+	7.93430i	−0.271665	+	0.271665i	0.558105	+	0.829770i	$0.311529\pi$
$854$		0			0
$855$	0.786445	+	0.0813947i	0.0268959	+	0.00278364i
$856$		0			0
$857$	22.8907	−	6.13354i	0.781930	−	0.209518i	0.154295	−	0.988025i	$-0.450689\pi$
$857$	22.8907	−	6.13354i	0.781930	−	0.209518i	0.627636	+	0.778507i	$0.284023\pi$
$858$		0			0
$859$	20.5470	+	35.5885i	0.701055	+	1.21426i	0.968096	+	0.250578i	$0.0806208\pi$
$859$	20.5470	+	35.5885i	0.701055	+	1.21426i	−0.267041	+	0.963685i	$0.586046\pi$
$860$		0			0
$861$	8.83104	+	9.43506i	0.300961	+	0.321546i
$862$		0			0
$863$	4.23539	−	15.8067i	0.144174	−	0.538066i	−0.855616	−	0.517611i	$-0.826822\pi$
$863$	4.23539	−	15.8067i	0.144174	−	0.538066i	0.999791	−	0.0204557i	$-0.00651171\pi$
$864$		0			0
$865$	−26.3750	+	4.22039i	−0.896777	+	0.143497i
$866$		0			0
$867$	−6.97206	−	6.97206i	−0.236784	−	0.236784i
$868$		0			0
$869$			3.14397i			0.106652i
$870$		0			0
$871$	7.93398	+	4.58069i	0.268833	+	0.155211i
$872$		0			0
$873$	−15.4191	−	4.13154i	−0.521858	−	0.139831i
$874$		0			0
$875$	−29.0964	+	5.32934i	−0.983636	+	0.180165i
$876$		0			0
$877$	−44.3226	−	11.8762i	−1.49667	−	0.401031i	−0.584685	−	0.811261i	$-0.698782\pi$
$877$	−44.3226	−	11.8762i	−1.49667	−	0.401031i	−0.911982	+	0.410230i	$0.865448\pi$
$878$		0			0
$879$	−7.28684	−	4.20706i	−0.245779	−	0.141901i
$880$		0			0
$881$			4.45125i			0.149967i	0.997185	+	0.0749833i	$0.0238903\pi$
$881$			4.45125i			0.149967i	−0.997185	+	0.0749833i	$0.976110\pi$
$882$		0			0
$883$	−4.19508	−	4.19508i	−0.141176	−	0.141176i	0.632987	−	0.774162i	$-0.281829\pi$
$883$	−4.19508	−	4.19508i	−0.141176	−	0.141176i	−0.774162	+	0.632987i	$0.781829\pi$
$884$		0			0
$885$	3.85556	−	0.616946i	0.129603	−	0.0207384i
$886$		0			0
$887$	2.57545	−	9.61172i	0.0864752	−	0.322730i	−0.909114	−	0.416547i	$-0.863240\pi$
$887$	2.57545	−	9.61172i	0.0864752	−	0.322730i	0.995589	+	0.0938170i	$0.0299069\pi$
$888$		0			0
$889$	51.5262	+	15.6489i	1.72813	+	0.524847i
$890$		0			0
$891$	−0.574500	−	0.995063i	−0.0192465	−	0.0333359i
$892$		0			0
$893$	−0.204942	+	0.0549140i	−0.00685812	+	0.00183763i
$894$		0			0
$895$	−53.9794	−	5.58671i	−1.80433	−	0.186743i
$896$		0			0
$897$	4.35508	−	4.35508i	0.145412	−	0.145412i
$898$		0			0
$899$	−10.2494	+	17.7524i	−0.341835	+	0.592076i
$900$		0			0
$901$	−5.08735	+	2.93719i	−0.169484	+	0.0978518i
$902$		0			0
$903$	12.0449	+	0.398297i	0.400830	+	0.0132545i
$904$		0			0
$905$	17.6969	+	39.5783i	0.588264	+	1.31563i
$906$		0			0
$907$	0.610881	+	2.27984i	0.0202840	+	0.0757007i	0.975326	−	0.220770i	$-0.0708570\pi$
$907$	0.610881	+	2.27984i	0.0202840	+	0.0757007i	−0.955042	+	0.296471i	$0.904190\pi$
$908$		0			0
$909$	−2.32830			−0.0772249
$910$		0			0
$911$	−8.72272			−0.288997			−0.144498	−	0.989505i	$-0.546157\pi$
$911$	−8.72272			−0.288997			−0.144498	+	0.989505i	$0.546157\pi$
$912$		0			0
$913$	0.917645	+	3.42470i	0.0303696	+	0.113341i
$914$		0			0
$915$	24.9151	+	9.51859i	0.823668	+	0.314675i
$916$		0			0
$917$	44.1291	+	27.4615i	1.45727	+	0.906859i
$918$		0			0
$919$	−15.7670	+	9.10309i	−0.520106	+	0.300283i	−0.736978	−	0.675917i	$-0.763748\pi$
$919$	−15.7670	+	9.10309i	−0.520106	+	0.300283i	0.216872	+	0.976200i	$0.430415\pi$
$920$		0			0
$921$	−5.61064	+	9.71792i	−0.184877	+	0.320216i
$922$		0			0
$923$	−5.57375	+	5.57375i	−0.183462	+	0.183462i
$924$		0			0
$925$	35.8920	−	23.4711i	1.18012	−	0.771726i
$926$		0			0
$927$	−18.2972	+	4.90272i	−0.600959	+	0.161026i
$928$		0			0
$929$	−18.4222	−	31.9082i	−0.604414	−	1.04688i	−0.992144	−	0.125103i	$-0.960074\pi$
$929$	−18.4222	−	31.9082i	−0.604414	−	1.04688i	0.387730	−	0.921773i	$-0.373259\pi$
$930$		0			0
$931$	2.46971	+	0.163513i	0.0809413	+	0.00535893i
$932$		0			0
$933$	−4.88369	+	18.2262i	−0.159885	+	0.596699i
$934$		0			0
$935$	−1.08474	−	6.77898i	−0.0354747	−	0.221696i
$936$		0			0
$937$	27.4546	+	27.4546i	0.896902	+	0.896902i	0.995161	−	0.0982591i	$-0.0313274\pi$
$937$	27.4546	+	27.4546i	0.896902	+	0.896902i	−0.0982591	+	0.995161i	$0.531327\pi$
$938$		0			0
$939$			11.3496i			0.370380i
$940$		0			0
$941$	−32.1092	−	18.5382i	−1.04673	−	0.604329i	−0.124997	−	0.992157i	$-0.539892\pi$
$941$	−32.1092	−	18.5382i	−1.04673	−	0.604329i	−0.921732	+	0.387828i	$0.873225\pi$
$942$		0			0
$943$	16.0677	+	4.30533i	0.523237	+	0.140201i
$944$		0			0
$945$	0.741190	+	5.86947i	0.0241109	+	0.190934i
$946$		0			0
$947$	−33.1548	−	8.88381i	−1.07739	−	0.288685i	−0.323862	−	0.946104i	$-0.604981\pi$
$947$	−33.1548	−	8.88381i	−1.07739	−	0.288685i	−0.753525	+	0.657419i	$0.771648\pi$
$948$		0			0
$949$	13.1940	+	7.61755i	0.428295	+	0.247276i
$950$		0			0
$951$		−	20.8786i		−	0.677036i
$952$		0			0
$953$	−30.0574	−	30.0574i	−0.973655	−	0.973655i	0.0260068	−	0.999662i	$-0.491721\pi$
$953$	−30.0574	−	30.0574i	−0.973655	−	0.973655i	−0.999662	+	0.0260068i	$0.991721\pi$
$954$		0			0
$955$	10.0688	+	7.29097i	0.325818	+	0.235930i
$956$		0			0
$957$	1.01468	−	3.78683i	0.0327999	−	0.122411i
$958$		0			0
$959$	−0.147259	+	0.137831i	−0.00475523	+	0.00445081i
$960$		0			0
$961$	2.54680	+	4.41118i	0.0821547	+	0.142296i
$962$		0			0
$963$	1.04807	−	0.280829i	0.0337736	−	0.00904960i
$964$		0			0
$965$	−5.12220	+	4.16138i	−0.164890	+	0.133960i
$966$		0			0
$967$	−37.5319	+	37.5319i	−1.20694	+	1.20694i	−0.234931	+	0.972012i	$0.575486\pi$
$967$	−37.5319	+	37.5319i	−1.20694	+	1.20694i	−0.972012	+	0.234931i	$0.924514\pi$
$968$		0			0
$969$	0.472407	−	0.818233i	0.0151759	−	0.0262854i
$970$		0			0
$971$	−33.5821	+	19.3886i	−1.07770	+	0.622210i	−0.930275	−	0.366863i	$-0.880432\pi$
$971$	−33.5821	+	19.3886i	−1.07770	+	0.622210i	−0.147425	+	0.989073i	$0.547098\pi$
$972$		0			0
$973$	11.0367	+	20.6647i	0.353821	+	0.662479i
$974$		0			0
$975$	8.59102	−	2.82162i	0.275133	−	0.0903643i
$976$		0			0
$977$	−14.5355	−	54.2472i	−0.465031	−	1.73552i	−0.656785	−	0.754078i	$-0.728084\pi$
$977$	−14.5355	−	54.2472i	−0.465031	−	1.73552i	0.191754	−	0.981443i	$-0.438582\pi$
$978$		0			0
$979$	−15.2093			−0.486091
$980$		0			0
$981$	11.4388			0.365212
$982$		0			0
$983$	−13.0010	−	48.5203i	−0.414667	−	1.54756i	−0.785503	−	0.618858i	$-0.787596\pi$
$983$	−13.0010	−	48.5203i	−0.414667	−	1.54756i	0.370836	−	0.928698i	$-0.379071\pi$
$984$		0			0
$985$	−19.6407	+	51.4098i	−0.625804	+	1.63805i
$986$		0			0
$987$	−0.747923	−	1.40038i	−0.0238066	−	0.0445745i
$988$		0			0
$989$	13.4343	−	7.75629i	0.427186	−	0.246636i
$990$		0			0
$991$	3.53895	−	6.12964i	0.112418	−	0.194714i	−0.804326	−	0.594188i	$-0.797474\pi$
$991$	3.53895	−	6.12964i	0.112418	−	0.194714i	0.916745	+	0.399473i	$0.130807\pi$
$992$		0			0
$993$	−9.44878	+	9.44878i	−0.299848	+	0.299848i
$994$		0			0
$995$	2.23921	−	21.6355i	0.0709877	−	0.685891i
$996$		0			0
$997$	12.3630	−	3.31265i	0.391540	−	0.104913i	−0.0576775	−	0.998335i	$-0.518370\pi$
$997$	12.3630	−	3.31265i	0.391540	−	0.104913i	0.449217	+	0.893422i	$0.351703\pi$
$998$		0			0
$999$	−4.28851	−	7.42791i	−0.135682	−	0.235009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dd.b.73.12	yes	48
5.2	odd	4		840.2.dd.a.577.11	yes	48
7.5	odd	6		840.2.dd.a.313.11	✓	48
35.12	even	12	inner	840.2.dd.b.817.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dd.a.313.11	✓	48	7.5	odd	6
840.2.dd.a.577.11	yes	48	5.2	odd	4
840.2.dd.b.73.12	yes	48	1.1	even	1	trivial
840.2.dd.b.817.12	yes	48	35.12	even	12	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{3} +(2.04130 - 0.912737i) q^{5} +(-1.24643 - 2.33376i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(0.574500 - 0.995063i) q^{11} +(1.27881 - 1.27881i) q^{13} +(1.40996 + 1.73551i) q^{15} +(2.58103 - 0.691585i) q^{17} +(-0.176794 - 0.306216i) q^{19} +(1.93164 - 1.80798i) q^{21} +(0.881430 - 3.28954i) q^{23} +(3.33382 - 3.72634i) q^{25} +(-0.707107 - 0.707107i) q^{27} -3.41202i q^{29} +(-5.20290 - 3.00390i) q^{31} +(1.10985 + 0.297383i) q^{33} +(-4.67444 - 3.62624i) q^{35} +(8.28476 + 2.21989i) q^{37} +(1.56621 + 0.904252i) q^{39} +4.88449i q^{41} +(3.22090 + 3.22090i) q^{43} +(-1.31145 + 1.81110i) q^{45} +(0.155305 - 0.579607i) q^{47} +(-3.89284 + 5.81771i) q^{49} +(1.33604 + 2.31409i) q^{51} +(-2.12352 + 0.568994i) q^{53} +(0.264496 - 2.55559i) q^{55} +(0.250024 - 0.250024i) q^{57} +(0.873096 - 1.51225i) q^{59} +(10.3298 - 5.96392i) q^{61} +(2.24632 + 1.39788i) q^{63} +(1.44321 - 3.77764i) q^{65} +(1.31110 + 4.89311i) q^{67} +3.40558 q^{69} -4.35856 q^{71} +(2.18033 + 8.13710i) q^{73} +(4.46223 + 2.25577i) q^{75} +(-3.03831 - 0.100469i) q^{77} +(-2.36967 + 1.36813i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-2.18195 + 2.18195i) q^{83} +(4.63743 - 3.76754i) q^{85} +(3.29576 - 0.883096i) q^{87} +(-6.61849 - 11.4636i) q^{89} +(-4.57836 - 1.39048i) q^{91} +(1.55493 - 5.80308i) q^{93} +(-0.640384 - 0.463712i) q^{95} +(11.2876 + 11.2876i) q^{97} +1.14900i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) \) 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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