LMFDB - Embedded newform 840.2.dd.a.577.11

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 = [48,0,0,0,0,0,0] 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			577.11
Character	$\chi$	$=$	840.577
Dual form			840.2.dd.a.313.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{3} +(1.81110 - 1.31145i) q^{5} +(2.33376 - 1.24643i) q^{7} +(0.866025 - 0.500000i) q^{9} +(0.574500 - 0.995063i) q^{11} +(-1.27881 - 1.27881i) q^{13} +(1.40996 - 1.73551i) q^{15} +(0.691585 + 2.58103i) q^{17} +(0.176794 + 0.306216i) q^{19} +(1.93164 - 1.80798i) q^{21} +(-3.28954 - 0.881430i) q^{23} +(1.56020 - 4.75035i) q^{25} +(0.707107 - 0.707107i) q^{27} +3.41202i q^{29} +(-5.20290 - 3.00390i) q^{31} +(0.297383 - 1.10985i) q^{33} +(2.59205 - 5.31801i) q^{35} +(-2.21989 + 8.28476i) q^{37} +(-1.56621 - 0.904252i) q^{39} +4.88449i q^{41} +(3.22090 - 3.22090i) q^{43} +(0.912737 - 2.04130i) q^{45} +(0.579607 + 0.155305i) q^{47} +(3.89284 - 5.81771i) q^{49} +(1.33604 + 2.31409i) q^{51} +(0.568994 + 2.12352i) q^{53} +(-0.264496 - 2.55559i) q^{55} +(0.250024 + 0.250024i) q^{57} +(-0.873096 + 1.51225i) q^{59} +(10.3298 - 5.96392i) q^{61} +(1.39788 - 2.24632i) q^{63} +(-3.99314 - 0.638961i) q^{65} +(-4.89311 + 1.31110i) q^{67} -3.40558 q^{69} -4.35856 q^{71} +(8.13710 - 2.18033i) q^{73} +(0.277556 - 4.99229i) q^{75} +(0.100469 - 3.03831i) q^{77} +(2.36967 - 1.36813i) q^{79} +(0.500000 - 0.866025i) q^{81} +(2.18195 + 2.18195i) q^{83} +(4.63743 + 3.76754i) q^{85} +(0.883096 + 3.29576i) q^{87} +(6.61849 + 11.4636i) q^{89} +(-4.57836 - 1.39048i) q^{91} +(-5.80308 - 1.55493i) q^{93} +(0.721779 + 0.322733i) q^{95} +(-11.2876 + 11.2876i) q^{97} -1.14900i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{11} + 16 q^{13} - 4 q^{15} - 4 q^{17} + 8 q^{19} - 24 q^{23} + 28 q^{25} + 12 q^{33} - 4 q^{37} - 12 q^{39} + 16 q^{43} - 4 q^{45} + 12 q^{47} - 12 q^{49} + 20 q^{53} - 56 q^{55} + 8 q^{57}+ \cdots + 44 q^{97}+O(q^{100}) $ 48 * q - 4 * q^11 + 16 * q^13 - 4 * q^15 - 4 * q^17 + 8 * q^19 - 24 * q^23 + 28 * q^25 + 12 * q^33 - 4 * q^37 - 12 * q^39 + 16 * q^43 - 4 * q^45 + 12 * q^47 - 12 * q^49 + 20 * q^53 - 56 * q^55 + 8 * q^57 + 8 * q^59 + 8 * q^63 + 12 * q^65 - 52 * q^67 - 8 * q^69 + 16 * q^71 - 4 * q^73 + 24 * q^75 + 8 * q^77 + 108 * q^79 + 24 * q^81 + 64 * q^83 + 32 * q^85 + 20 * q^87 + 64 * q^89 + 48 * q^91 - 24 * q^93 + 36 * q^95 + 44 * q^97

Character values

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

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

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
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$		0			0
$5$	1.81110	−	1.31145i	0.809950	−	0.586498i
$5$	1.81110	−	1.31145i	0.809950	−	0.586498i
$6$		0			0
$7$	2.33376	−	1.24643i	0.882077	−	0.471105i
$7$	2.33376	−	1.24643i	0.882077	−	0.471105i
$8$		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	$-0.330692\pi$
$13$	−1.27881	−	1.27881i	−0.354677	−	0.354677i	−0.861846	+	0.507170i	$0.830692\pi$
$14$		0			0
$15$	1.40996	−	1.73551i	0.364051	−	0.448107i
$16$		0			0
$17$	0.691585	+	2.58103i	0.167734	+	0.625992i	0.997676	+	0.0681418i	$0.0217070\pi$
$17$	0.691585	+	2.58103i	0.167734	+	0.625992i	−0.829942	+	0.557850i	$0.811626\pi$
$18$		0			0
$19$	0.176794	+	0.306216i	0.0405593	+	0.0702507i	0.885592	−	0.464463i	$-0.153753\pi$
$19$	0.176794	+	0.306216i	0.0405593	+	0.0702507i	−0.845033	+	0.534714i	$0.820419\pi$
$20$		0			0
$21$	1.93164	−	1.80798i	0.421518	−	0.394533i
$22$		0			0
$23$	−3.28954	−	0.881430i	−0.685917	−	0.183791i	−0.101003	−	0.994886i	$-0.532205\pi$
$23$	−3.28954	−	0.881430i	−0.685917	−	0.183791i	−0.584914	+	0.811095i	$0.698872\pi$
$24$		0			0
$25$	1.56020	−	4.75035i	0.312040	−	0.950069i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			3.41202i			0.633597i	0.948493	+	0.316798i	$0.102608\pi$
$29$			3.41202i			0.633597i	−0.948493	+	0.316798i	$0.897392\pi$
$30$		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
$33$	0.297383	−	1.10985i	0.0517677	−	0.193200i
$34$		0			0
$35$	2.59205	−	5.31801i	0.438136	−	0.898908i
$36$		0			0
$37$	−2.21989	+	8.28476i	−0.364948	+	1.36201i	0.502542	+	0.864553i	$0.332398\pi$
$37$	−2.21989	+	8.28476i	−0.364948	+	1.36201i	−0.867491	+	0.497453i	$0.834269\pi$
$38$		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	−0.417496	−	0.908679i	$-0.637092\pi$
$43$	3.22090	−	3.22090i	0.491183	−	0.491183i	0.908679	+	0.417496i	$0.137092\pi$
$44$		0			0
$45$	0.912737	−	2.04130i	0.136063	−	0.304299i
$46$		0			0
$47$	0.579607	+	0.155305i	0.0845444	+	0.0226536i	0.300843	−	0.953674i	$-0.402732\pi$
$47$	0.579607	+	0.155305i	0.0845444	+	0.0226536i	−0.216299	+	0.976327i	$0.569399\pi$
$48$		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
$53$	0.568994	+	2.12352i	0.0781574	+	0.291687i	0.993931	−	0.110008i	$-0.0350877\pi$
$53$	0.568994	+	2.12352i	0.0781574	+	0.291687i	−0.915773	+	0.401696i	$0.868421\pi$
$54$		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	−0.917246	−	0.398321i	$-0.869593\pi$
$59$	−0.873096	+	1.51225i	−0.113667	+	0.196878i	0.803579	+	0.595198i	$0.202927\pi$
$60$		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
$63$	1.39788	−	2.24632i	0.176116	−	0.283009i
$64$		0			0
$65$	−3.99314	−	0.638961i	−0.495288	−	0.0792533i
$66$		0			0
$67$	−4.89311	+	1.31110i	−0.597788	+	0.160177i	−0.545010	−	0.838429i	$-0.683474\pi$
$67$	−4.89311	+	1.31110i	−0.597788	+	0.160177i	−0.0527781	+	0.998606i	$0.516808\pi$
$68$		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
$73$	8.13710	−	2.18033i	0.952375	−	0.255188i	0.251005	−	0.967986i	$-0.419239\pi$
$73$	8.13710	−	2.18033i	0.952375	−	0.255188i	0.701370	+	0.712797i	$0.252572\pi$
$74$		0			0
$75$	0.277556	−	4.99229i	0.0320494	−	0.576460i
$76$		0			0
$77$	0.100469	−	3.03831i	0.0114496	−	0.346247i
$78$		0			0
$79$	2.36967	−	1.36813i	0.266609	−	0.153927i	−0.360737	−	0.932668i	$-0.617475\pi$
$79$	2.36967	−	1.36813i	0.266609	−	0.153927i	0.627346	+	0.778741i	$0.284141\pi$
$80$		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	$-0.195833\pi$
$83$	2.18195	+	2.18195i	0.239500	+	0.239500i	−0.577143	+	0.816643i	$0.695833\pi$
$84$		0			0
$85$	4.63743	+	3.76754i	0.503000	+	0.408647i
$86$		0			0
$87$	0.883096	+	3.29576i	0.0946779	+	0.353343i
$88$		0			0
$89$	6.61849	+	11.4636i	0.701559	+	1.21513i	0.967919	+	0.251262i	$0.0808454\pi$
$89$	6.61849	+	11.4636i	0.701559	+	1.21513i	−0.266361	+	0.963873i	$0.585821\pi$
$90$		0			0
$91$	−4.57836	−	1.39048i	−0.479942	−	0.145762i
$92$		0			0
$93$	−5.80308	−	1.55493i	−0.601752	−	0.161239i
$94$		0			0
$95$	0.721779	+	0.322733i	0.0740529	+	0.0331117i
$96$		0			0
$97$	−11.2876	+	11.2876i	−1.14608	+	1.14608i	−0.158763	+	0.987317i	$0.550750\pi$
$97$	−11.2876	+	11.2876i	−1.14608	+	1.14608i	−0.987317	+	0.158763i	$0.949250\pi$
$98$		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
$103$	4.90272	−	18.2972i	0.483079	−	1.80288i	−0.105478	−	0.994422i	$-0.533637\pi$
$103$	4.90272	−	18.2972i	0.483079	−	1.80288i	0.588557	−	0.808455i	$-0.299696\pi$
$104$		0			0
$105$	1.12732	−	5.80768i	0.110016	−	0.566771i
$106$		0			0
$107$	0.280829	−	1.04807i	0.0271488	−	0.101321i	−0.951022	−	0.309123i	$-0.899964\pi$
$107$	0.280829	−	1.04807i	0.0271488	−	0.101321i	0.978171	+	0.207802i	$0.0666311\pi$
$108$		0			0
$109$	9.90626	+	5.71938i	0.948848	+	0.547818i	0.892723	−	0.450606i	$-0.148792\pi$
$109$	9.90626	+	5.71938i	0.948848	+	0.547818i	0.0561251	+	0.998424i	$0.482125\pi$
$110$		0			0
$111$			8.57701i			0.814094i
$112$		0			0
$113$	−11.7834	+	11.7834i	−1.10849	+	1.10849i	−0.115136	+	0.993350i	$0.536730\pi$
$113$	−11.7834	+	11.7834i	−1.10849	+	1.10849i	−0.993350	+	0.115136i	$0.963270\pi$
$114$		0			0
$115$	−7.11365	+	2.71771i	−0.663351	+	0.253427i
$116$		0			0
$117$	−1.74688	−	0.468075i	−0.161499	−	0.0432736i
$118$		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
$123$	1.26420	+	4.71805i	0.113989	+	0.425413i
$124$		0			0
$125$	−3.40416	−	10.6495i	−0.304477	−	0.952520i
$126$		0			0
$127$	−14.3921	−	14.3921i	−1.27709	−	1.27709i	−0.942290	−	0.334798i	$-0.891332\pi$
$127$	−14.3921	−	14.3921i	−1.27709	−	1.27709i	−0.334798	−	0.942290i	$-0.608668\pi$
$128$		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
$133$	0.794269	+	0.494273i	0.0688719	+	0.0428589i
$134$		0			0
$135$	0.353309	−	2.20798i	0.0304080	−	0.190033i
$136$		0			0
$137$	0.0736375	−	0.0197311i	0.00629128	−	0.00168574i	−0.255672	−	0.966764i	$-0.582297\pi$
$137$	0.0736375	−	0.0197311i	0.00629128	−	0.00168574i	0.261963	+	0.965078i	$0.415630\pi$
$138$		0			0
$139$	8.85468			0.751044			0.375522	−	0.926813i	$-0.377463\pi$
$139$	8.85468			0.751044			0.375522	+	0.926813i	$0.377463\pi$
$140$		0			0
$141$	0.600054			0.0505336
$142$		0			0
$143$	−2.00716	+	0.537818i	−0.167848	+	0.0449746i
$144$		0			0
$145$	4.47470	+	6.17953i	0.371603	+	0.513182i
$146$		0			0
$147$	2.25446	−	6.62702i	0.185945	−	0.546588i
$148$		0			0
$149$	−6.20060	+	3.57992i	−0.507973	+	0.293279i	−0.732000	−	0.681304i	$-0.761413\pi$
$149$	−6.20060	+	3.57992i	−0.507973	+	0.293279i	0.224027	+	0.974583i	$0.428080\pi$
$150$		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
$157$	−2.03270	−	7.58613i	−0.162227	−	0.605439i	−0.998378	−	0.0569392i	$-0.981866\pi$
$157$	−2.03270	−	7.58613i	−0.162227	−	0.605439i	0.836151	−	0.548500i	$-0.184801\pi$
$158$		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
$163$	0.801485	+	0.214757i	0.0627771	+	0.0168211i	0.290071	−	0.957005i	$-0.406321\pi$
$163$	0.801485	+	0.214757i	0.0627771	+	0.0168211i	−0.227294	+	0.973826i	$0.572988\pi$
$164$		0			0
$165$	−0.916919	−	2.40005i	−0.0713820	−	0.186844i
$166$		0			0
$167$	−13.9691	+	13.9691i	−1.08096	+	1.08096i	−0.0845414	+	0.996420i	$0.526943\pi$
$167$	−13.9691	+	13.9691i	−1.08096	+	1.08096i	−0.996420	+	0.0845414i	$0.973057\pi$
$168$		0			0
$169$		−	9.72931i		−	0.748409i
$170$		0			0
$171$	0.306216	+	0.176794i	0.0234169	+	0.0135198i
$172$		0			0
$173$	−3.09167	+	11.5383i	−0.235056	+	0.877240i	0.743068	+	0.669216i	$0.233370\pi$
$173$	−3.09167	+	11.5383i	−0.235056	+	0.877240i	−0.978124	+	0.208024i	$0.933297\pi$
$174$		0			0
$175$	−2.27984	−	13.0308i	−0.172339	−	0.985038i
$176$		0			0
$177$	−0.451948	+	1.68669i	−0.0339705	+	0.126780i
$178$		0			0
$179$	21.0178	+	12.1346i	1.57094	+	0.906985i	0.996053	+	0.0887556i	$0.0282890\pi$
$179$	21.0178	+	12.1346i	1.57094	+	0.906985i	0.574891	+	0.818230i	$0.305044\pi$
$180$		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
$185$	6.84459	+	17.9158i	0.503224	+	1.31720i
$186$		0			0
$187$	2.96560	+	0.794631i	0.216866	+	0.0581092i
$188$		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
$193$	0.763881	+	2.85084i	0.0549853	+	0.205208i	0.987954	−	0.154751i	$-0.0494574\pi$
$193$	0.763881	+	2.85084i	0.0549853	+	0.205208i	−0.932968	+	0.359959i	$0.882791\pi$
$194$		0			0
$195$	−4.02245	+	0.416312i	−0.288054	+	0.0298127i
$196$		0			0
$197$	−17.4032	−	17.4032i	−1.23993	−	1.23993i	−0.960029	−	0.279900i	$-0.909699\pi$
$197$	−17.4032	−	17.4032i	−1.23993	−	1.23993i	−0.279900	−	0.960029i	$-0.590301\pi$
$198$		0			0
$199$	−4.86369	+	8.42415i	−0.344778	+	0.597172i	−0.985313	−	0.170756i	$-0.945379\pi$
$199$	−4.86369	+	8.42415i	−0.344778	+	0.597172i	0.640536	+	0.767928i	$0.278712\pi$
$200$		0			0
$201$	−4.38704	+	2.53286i	−0.309438	+	0.178654i
$202$		0			0
$203$	4.25284	+	7.96283i	0.298491	+	0.558881i
$204$		0			0
$205$	6.40576	+	8.84632i	0.447398	+	0.617854i
$206$		0			0
$207$	−3.28954	+	0.881430i	−0.228639	+	0.0612636i
$208$		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
$213$	−4.21005	+	1.12808i	−0.288468	+	0.0772947i
$214$		0			0
$215$	1.60934	−	10.0574i	0.109756	−	0.685912i
$216$		0			0
$217$	−15.8864	−	0.525327i	−1.07844	−	0.0356615i
$218$		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	$-0.433060\pi$
$223$	−11.4869	−	11.4869i	−0.769218	−	0.769218i	−0.977969	+	0.208751i	$0.933060\pi$
$224$		0			0
$225$	−1.02400	−	4.89402i	−0.0682668	−	0.326268i
$226$		0			0
$227$	6.70018	+	25.0054i	0.444707	+	1.65967i	0.716710	+	0.697371i	$0.245647\pi$
$227$	6.70018	+	25.0054i	0.444707	+	1.65967i	−0.272003	+	0.962296i	$0.587686\pi$
$228$		0			0
$229$	7.75451	+	13.4312i	0.512433	+	0.887559i	0.999896	+	0.0144160i	$0.00458891\pi$
$229$	7.75451	+	13.4312i	0.512433	+	0.887559i	−0.487463	+	0.873143i	$0.662078\pi$
$230$		0			0
$231$	−0.689325	−	2.96078i	−0.0453543	−	0.194805i
$232$		0			0
$233$	−19.2121	−	5.14787i	−1.25863	−	0.337248i	−0.432963	−	0.901412i	$-0.642532\pi$
$233$	−19.2121	−	5.14787i	−1.25863	−	0.337248i	−0.825663	+	0.564164i	$0.809199\pi$
$234$		0			0
$235$	1.25340	−	0.478852i	0.0817631	−	0.0312368i
$236$		0			0
$237$	1.93483	−	1.93483i	0.125681	−	0.125681i
$238$		0			0
$239$		−	14.1939i		−	0.918125i	−0.888404	−	0.459063i	$-0.848185\pi$
$239$		−	14.1939i		−	0.918125i	0.888404	−	0.459063i	$-0.151815\pi$
$240$		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
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$		0			0
$245$	−0.579303	−	15.6418i	−0.0370103	−	0.999315i
$246$		0			0
$247$	0.165506	−	0.617675i	0.0105309	−	0.0393017i
$248$		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
$255$	5.45452	+	2.43891i	0.341575	+	0.152730i
$256$		0			0
$257$	11.5570	+	3.09670i	0.720908	+	0.193167i	0.600577	−	0.799567i	$-0.294938\pi$
$257$	11.5570	+	3.09670i	0.720908	+	0.193167i	0.120331	+	0.992734i	$0.461604\pi$
$258$		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
$263$	−4.32005	−	16.1226i	−0.266385	−	0.994164i	−0.961397	−	0.275165i	$-0.911267\pi$
$263$	−4.32005	−	16.1226i	−0.266385	−	0.994164i	0.695012	−	0.718999i	$-0.255399\pi$
$264$		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	−0.504881	−	0.863189i	$-0.668464\pi$
$269$	8.12029	−	14.0648i	0.495103	−	0.857543i	0.999984	+	0.00564562i	$0.00179707\pi$
$270$		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
$273$	−4.78224	−	0.158137i	−0.289434	−	0.00957089i
$274$		0			0
$275$	−3.83056	−	4.28157i	−0.230991	−	0.258188i
$276$		0			0
$277$	−17.9539	+	4.81074i	−1.07875	+	0.289049i	−0.754082	−	0.656780i	$-0.771918\pi$
$277$	−17.9539	+	4.81074i	−1.07875	+	0.289049i	−0.324665	+	0.945829i	$0.605251\pi$
$278$		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
$283$	−16.4542	+	4.40890i	−0.978102	+	0.262082i	−0.712245	−	0.701931i	$-0.752322\pi$
$283$	−16.4542	+	4.40890i	−0.978102	+	0.262082i	−0.265857	+	0.964012i	$0.585655\pi$
$284$		0			0
$285$	0.780714	+	0.124926i	0.0462455	+	0.00739996i
$286$		0			0
$287$	6.08816	+	11.3992i	0.359373	+	0.672874i
$288$		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	$-0.170956\pi$
$293$	5.94968	+	5.94968i	0.347584	+	0.347584i	−0.511625	+	0.859209i	$0.670956\pi$
$294$		0			0
$295$	0.401968	+	3.88386i	0.0234035	+	0.226127i
$296$		0			0
$297$	−0.297383	−	1.10985i	−0.0172559	−	0.0643999i
$298$		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
$303$	2.24897	+	0.602609i	0.129200	+	0.0346190i
$304$		0			0
$305$	10.8870	−	24.3483i	0.623387	−	1.39418i
$306$		0			0
$307$	−7.93464	+	7.93464i	−0.452854	+	0.452854i	−0.896301	−	0.443447i	$-0.853756\pi$
$307$	−7.93464	+	7.93464i	−0.452854	+	0.452854i	0.443447	+	0.896301i	$0.353756\pi$
$308$		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
$313$	2.93749	−	10.9629i	0.166037	−	0.619658i	−0.831869	−	0.554972i	$-0.812729\pi$
$313$	2.93749	−	10.9629i	0.166037	−	0.619658i	0.997906	−	0.0646855i	$-0.0206044\pi$
$314$		0			0
$315$	−0.414226	−	5.90156i	−0.0233390	−	0.332515i
$316$		0			0
$317$	5.40379	−	20.1672i	0.303507	−	1.13270i	−0.630716	−	0.776014i	$-0.717239\pi$
$317$	5.40379	−	20.1672i	0.303507	−	1.13270i	0.934223	−	0.356690i	$-0.116095\pi$
$318$		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
$325$	−8.06996	+	4.07958i	−0.447641	+	0.226294i
$326$		0			0
$327$	11.0490	+	2.96057i	0.611011	+	0.163720i
$328$		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
$333$	2.21989	+	8.28476i	0.121649	+	0.454002i
$334$		0			0
$335$	−7.14248	+	8.79162i	−0.390236	+	0.480337i
$336$		0			0
$337$	−21.6983	−	21.6983i	−1.18198	−	1.18198i	−0.979230	−	0.202752i	$-0.935011\pi$
$337$	−21.6983	−	21.6983i	−1.18198	−	1.18198i	−0.202752	−	0.979230i	$-0.564989\pi$
$338$		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
$343$	1.83358	−	18.4293i	0.0990042	−	0.995087i
$344$		0			0
$345$	−6.16787	+	4.46625i	−0.332067	+	0.240455i
$346$		0			0
$347$	17.4004	−	4.66241i	0.934100	−	0.250291i	0.240498	−	0.970650i	$-0.422689\pi$
$347$	17.4004	−	4.66241i	0.934100	−	0.250291i	0.693602	+	0.720358i	$0.256023\pi$
$348$		0			0
$349$	−3.70297			−0.198216			−0.0991078	−	0.995077i	$-0.531599\pi$
$349$	−3.70297			−0.198216			−0.0991078	+	0.995077i	$0.531599\pi$
$350$		0			0
$351$	−1.80850			−0.0965308
$352$		0			0
$353$	19.1753	−	5.13800i	1.02060	−	0.273468i	0.290546	−	0.956861i	$-0.406163\pi$
$353$	19.1753	−	5.13800i	1.02060	−	0.273468i	0.730051	+	0.683393i	$0.239496\pi$
$354$		0			0
$355$	−7.89381	+	5.71604i	−0.418960	+	0.303376i
$356$		0			0
$357$	6.00234	+	3.73525i	0.317677	+	0.197690i
$358$		0			0
$359$	27.3891	−	15.8131i	1.44554	−	0.834583i	0.447328	−	0.894370i	$-0.352376\pi$
$359$	27.3891	−	15.8131i	1.44554	−	0.834583i	0.998211	+	0.0597871i	$0.0190422\pi$
$360$		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
$367$	5.61560	+	20.9577i	0.293132	+	1.09398i	0.942690	+	0.333671i	$0.108287\pi$
$367$	5.61560	+	20.9577i	0.293132	+	1.09398i	−0.649558	+	0.760312i	$0.725046\pi$
$368$		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
$373$	−21.9555	−	5.88296i	−1.13681	−	0.304608i	−0.359144	−	0.933282i	$-0.616931\pi$
$373$	−21.9555	−	5.88296i	−1.13681	−	0.304608i	−0.777669	+	0.628674i	$0.783598\pi$
$374$		0			0
$375$	−6.04446	−	9.40556i	−0.312134	−	0.485701i
$376$		0			0
$377$	4.36331	−	4.36331i	0.224722	−	0.224722i
$378$		0			0
$379$			19.0895i			0.980562i	0.871564	+	0.490281i	$0.163106\pi$
$379$			19.0895i			0.980562i	−0.871564	+	0.490281i	$0.836894\pi$
$380$		0			0
$381$	−17.6266	−	10.1767i	−0.903038	−	0.521369i
$382$		0			0
$383$	8.54737	−	31.8992i	0.436750	−	1.62997i	−0.300093	−	0.953910i	$-0.597018\pi$
$383$	8.54737	−	31.8992i	0.436750	−	1.62997i	0.736843	−	0.676064i	$-0.236316\pi$
$384$		0			0
$385$	−3.80263	−	5.63445i	−0.193800	−	0.287158i
$386$		0			0
$387$	1.17893	−	4.39984i	0.0599285	−	0.223656i
$388$		0			0
$389$	−16.0286	−	9.25414i	−0.812684	−	0.469204i	0.0352028	−	0.999380i	$-0.488792\pi$
$389$	−16.0286	−	9.25414i	−0.812684	−	0.469204i	−0.847887	+	0.530177i	$0.822126\pi$
$390$		0			0
$391$		−	9.09999i		−	0.460206i
$392$		0			0
$393$	−13.8912	+	13.8912i	−0.700718	+	0.700718i
$394$		0			0
$395$	2.49749	−	5.58554i	0.125662	−	0.281039i
$396$		0			0
$397$	15.2128	+	4.07627i	0.763511	+	0.204582i	0.619503	−	0.784994i	$-0.287334\pi$
$397$	15.2128	+	4.07627i	0.763511	+	0.204582i	0.144008	+	0.989577i	$0.454001\pi$
$398$		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
$403$	2.81210	+	10.4949i	0.140081	+	0.522788i
$404$		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	$-0.589813\pi$
$409$	14.0063	−	24.2597i	0.692568	−	1.19956i	0.970994	−	0.239105i	$-0.0768540\pi$
$410$		0			0
$411$	0.0660216	−	0.0381176i	0.00325661	−	0.00188020i
$412$		0			0
$413$	−0.152689	+	4.61747i	−0.00751331	+	0.227211i
$414$		0			0
$415$	6.81324	+	1.09022i	0.334449	+	0.0535167i
$416$		0			0
$417$	8.55297	−	2.29176i	0.418841	−	0.112228i
$418$		0			0
$419$	−32.1069			−1.56852			−0.784262	−	0.620430i	$-0.786958\pi$
$419$	−32.1069			−1.56852			−0.784262	+	0.620430i	$0.786958\pi$
$420$		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
$423$	0.579607	−	0.155305i	0.0281815	−	0.00755120i
$424$		0			0
$425$	13.3398	+	0.741651i	0.647075	+	0.0359754i
$426$		0			0
$427$	16.6737	−	26.7937i	0.806896	−	1.29664i
$428$		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	$-0.292600\pi$
$433$	−3.92665	−	3.92665i	−0.188703	−	0.188703i	−0.795135	+	0.606432i	$0.792600\pi$
$434$		0			0
$435$	5.92160	+	4.81083i	0.283919	+	0.230662i
$436$		0			0
$437$	−0.311663	−	1.16314i	−0.0149088	−	0.0556406i
$438$		0			0
$439$	10.3981	+	18.0101i	0.496275	+	0.859574i	0.999991	−	0.00429550i	$-0.00136730\pi$
$439$	10.3981	+	18.0101i	0.496275	+	0.859574i	−0.503715	+	0.863870i	$0.668034\pi$
$440$		0			0
$441$	0.462441	−	6.98471i	0.0220210	−	0.332605i
$442$		0			0
$443$	3.63941	+	0.975177i	0.172914	+	0.0463321i	0.344237	−	0.938883i	$-0.388138\pi$
$443$	3.63941	+	0.975177i	0.172914	+	0.0463321i	−0.171323	+	0.985215i	$0.554804\pi$
$444$		0			0
$445$	27.0207	+	12.0819i	1.28090	+	0.572736i
$446$		0			0
$447$	−5.06277	+	5.06277i	−0.239461	+	0.239461i
$448$		0			0
$449$		−	18.7981i		−	0.887135i	−0.896241	−	0.443568i	$-0.853713\pi$
$449$		−	18.7981i		−	0.887135i	0.896241	−	0.443568i	$-0.146287\pi$
$450$		0			0
$451$	4.86037	+	2.80614i	0.228866	+	0.132136i
$452$		0			0
$453$	0.819057	−	3.05676i	0.0384827	−	0.143619i
$454$		0			0
$455$	−10.1154	+	3.48598i	−0.474219	+	0.163425i
$456$		0			0
$457$	−1.91387	+	7.14267i	−0.0895272	+	0.334120i	−0.996133	−	0.0878586i	$-0.971998\pi$
$457$	−1.91387	+	7.14267i	−0.0895272	+	0.334120i	0.906606	+	0.421979i	$0.138664\pi$
$458$		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	−0.244157	−	0.969736i	$-0.578511\pi$
$463$	15.6126	−	15.6126i	0.725579	−	0.725579i	0.969736	+	0.244157i	$0.0785111\pi$
$464$		0			0
$465$	−12.5492	+	4.79431i	−0.581955	+	0.222331i
$466$		0			0
$467$	29.9871	+	8.03502i	1.38764	+	0.371816i	0.873889	−	0.486125i	$-0.161590\pi$
$467$	29.9871	+	8.03502i	1.38764	+	0.371816i	0.513748	+	0.857941i	$0.328257\pi$
$468$		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
$473$	−1.35459	−	5.05541i	−0.0622842	−	0.232448i
$474$		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	−0.835789	−	0.549051i	$-0.814989\pi$
$479$	1.26060	−	2.18342i	0.0575982	−	0.0997630i	0.893387	+	0.449288i	$0.148322\pi$
$480$		0			0
$481$	13.4334	−	7.75578i	0.612511	−	0.353633i
$482$		0			0
$483$	−7.94780	+	4.24481i	−0.361637	+	0.193146i
$484$		0			0
$485$	−5.63989	+	35.2461i	−0.256094	+	1.60044i
$486$		0			0
$487$	−35.8967	+	9.61849i	−1.62663	+	0.435855i	−0.952941	−	0.303156i	$-0.901960\pi$
$487$	−35.8967	+	9.61849i	−1.62663	+	0.435855i	−0.673693	+	0.739011i	$0.735293\pi$
$488$		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
$493$	−8.80654	+	2.35970i	−0.396627	+	0.106276i
$494$		0			0
$495$	−1.50686	−	2.08096i	−0.0677281	−	0.0935321i
$496$		0			0
$497$	−10.1718	+	5.43263i	−0.456269	+	0.243687i
$498$		0			0
$499$	15.1839	−	8.76642i	0.679724	−	0.392439i	−0.120027	−	0.992771i	$-0.538298\pi$
$499$	15.1839	−	8.76642i	0.679724	−	0.392439i	0.799751	+	0.600332i	$0.204965\pi$
$500$		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	$-0.403587\pi$
$503$	−14.7170	−	14.7170i	−0.656199	−	0.656199i	−0.954478	+	0.298280i	$0.903587\pi$
$504$		0			0
$505$	5.17858	−	0.535967i	0.230444	−	0.0238502i
$506$		0			0
$507$	−2.51813	−	9.39780i	−0.111834	−	0.417371i
$508$		0			0
$509$	5.13342	+	8.89134i	0.227535	+	0.394102i	0.957077	−	0.289834i	$-0.0936001\pi$
$509$	5.13342	+	8.89134i	0.227535	+	0.394102i	−0.729542	+	0.683936i	$0.760267\pi$
$510$		0			0
$511$	16.2724	−	15.2307i	0.719848	−	0.673765i
$512$		0			0
$513$	0.341539	+	0.0915152i	0.0150793	+	0.00404049i
$514$		0			0
$515$	−15.1165	−	39.5678i	−0.666114	−	1.74357i
$516$		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
$523$	4.74130	−	17.6948i	0.207323	−	0.773738i	−0.781407	−	0.624022i	$-0.785497\pi$
$523$	4.74130	−	17.6948i	0.207323	−	0.773738i	0.988729	−	0.149716i	$-0.0478359\pi$
$524$		0			0
$525$	−5.57478	−	11.9967i	−0.243303	−	0.523581i
$526$		0			0
$527$	4.15490	−	15.5063i	0.180990	−	0.675465i
$528$		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
$535$	−0.865880	−	2.26646i	−0.0374352	−	0.0979875i
$536$		0			0
$537$	23.4423	+	6.28135i	1.01161	+	0.271060i
$538$		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
$543$	5.01819	+	18.7281i	0.215351	+	0.803701i
$544$		0			0
$545$	25.4420	−	2.63317i	1.08981	−	0.112793i
$546$		0			0
$547$	−5.18970	−	5.18970i	−0.221895	−	0.221895i	0.587401	−	0.809296i	$-0.300151\pi$
$547$	−5.18970	−	5.18970i	−0.221895	−	0.221895i	−0.809296	+	0.587401i	$0.800151\pi$
$548$		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
$553$	3.82497	−	6.14651i	0.162654	−	0.261376i
$554$		0			0
$555$	11.2483	+	15.5339i	0.477465	+	0.659376i
$556$		0			0
$557$	−15.2377	+	4.08292i	−0.645640	+	0.172999i	−0.566757	−	0.823885i	$-0.691802\pi$
$557$	−15.2377	+	4.08292i	−0.645640	+	0.172999i	−0.0788833	+	0.996884i	$0.525135\pi$
$558$		0			0
$559$	−8.23782			−0.348423
$560$		0			0
$561$	3.07022			0.129625
$562$		0			0
$563$	27.1328	−	7.27022i	1.14351	−	0.306403i	0.363150	−	0.931731i	$-0.381701\pi$
$563$	27.1328	−	7.27022i	1.14351	−	0.306403i	0.780362	+	0.625327i	$0.215035\pi$
$564$		0			0
$565$	−5.88761	+	36.7942i	−0.247694	+	1.54794i
$566$		0			0
$567$	0.0874408	−	2.64431i	0.00367217	−	0.111050i
$568$		0			0
$569$	−14.1303	+	8.15812i	−0.592372	+	0.342006i	−0.766035	−	0.642799i	$-0.777773\pi$
$569$	−14.1303	+	8.15812i	−0.592372	+	0.342006i	0.173663	+	0.984805i	$0.444440\pi$
$570$		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
$577$	−6.03993	−	22.5413i	−0.251446	−	0.938408i	−0.970033	−	0.242972i	$-0.921878\pi$
$577$	−6.03993	−	22.5413i	−0.251446	−	0.938408i	0.718588	−	0.695436i	$-0.244789\pi$
$578$		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
$583$	2.43992	+	0.653774i	0.101051	+	0.0270766i
$584$		0			0
$585$	−3.77764	+	1.44321i	−0.156186	+	0.0596695i
$586$		0			0
$587$	3.39180	−	3.39180i	0.139995	−	0.139995i	−0.633636	−	0.773631i	$-0.718438\pi$
$587$	3.39180	−	3.39180i	0.139995	−	0.139995i	0.773631	+	0.633636i	$0.218438\pi$
$588$		0			0
$589$		−	2.12428i		−	0.0875295i
$590$		0			0
$591$	−21.3145	−	12.3059i	−0.876762	−	0.506199i
$592$		0			0
$593$	4.11594	−	15.3609i	0.169021	−	0.630796i	−0.828472	−	0.560031i	$-0.810789\pi$
$593$	4.11594	−	15.3609i	0.169021	−	0.630796i	0.997493	−	0.0707654i	$-0.0225442\pi$
$594$		0			0
$595$	15.5186	+	3.01230i	0.636200	+	0.123492i
$596$		0			0
$597$	−2.51763	+	9.39592i	−0.103040	+	0.384549i
$598$		0			0
$599$	−26.4226	−	15.2551i	−1.07960	−	0.623307i	−0.148811	−	0.988866i	$-0.547545\pi$
$599$	−26.4226	−	15.2551i	−1.07960	−	0.623307i	−0.930788	+	0.365559i	$0.880878\pi$
$600$		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
$605$	19.7594	+	8.83512i	0.803333	+	0.359199i
$606$		0			0
$607$	−12.7273	−	3.41028i	−0.516587	−	0.138419i	−0.00889954	−	0.999960i	$-0.502833\pi$
$607$	−12.7273	−	3.41028i	−0.516587	−	0.138419i	−0.507687	+	0.861541i	$0.669500\pi$
$608$		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
$613$	6.91603	+	25.8110i	0.279336	+	1.04250i	0.952880	+	0.303348i	$0.0981045\pi$
$613$	6.91603	+	25.8110i	0.279336	+	1.04250i	−0.673544	+	0.739147i	$0.735229\pi$
$614$		0			0
$615$	8.47709	+	6.88696i	0.341829	+	0.277709i
$616$		0			0
$617$	−10.6207	−	10.6207i	−0.427574	−	0.427574i	0.460227	−	0.887801i	$-0.347768\pi$
$617$	−10.6207	−	10.6207i	−0.427574	−	0.427574i	−0.887801	+	0.460227i	$0.847768\pi$
$618$		0			0
$619$	−11.2987	+	19.5699i	−0.454132	+	0.786579i	−0.998638	−	0.0521778i	$-0.983384\pi$
$619$	−11.2987	+	19.5699i	−0.454132	+	0.786579i	0.544506	+	0.838757i	$0.316717\pi$
$620$		0			0
$621$	−2.94932	+	1.70279i	−0.118352	+	0.0683307i
$622$		0			0
$623$	29.7344	+	18.5037i	1.19128	+	0.741335i
$624$		0			0
$625$	−20.1316	−	14.8230i	−0.805263	−	0.592918i
$626$		0			0
$627$	0.392429	−	0.105151i	0.0156721	−	0.00419932i
$628$		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
$633$	−17.7552	+	4.75750i	−0.705707	+	0.189094i
$634$		0			0
$635$	−44.9400	−	7.19105i	−1.78339	−	0.285368i
$636$		0			0
$637$	−12.4179	+	2.46154i	−0.492015	+	0.0975298i
$638$		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	$-0.221179\pi$
$643$	3.24259	+	3.24259i	0.127875	+	0.127875i	−0.640273	+	0.768148i	$0.721179\pi$
$644$		0			0
$645$	−1.04856	−	10.1313i	−0.0412869	−	0.398919i
$646$		0			0
$647$	−2.68385	−	10.0163i	−0.105513	−	0.393780i	0.892890	−	0.450275i	$-0.148674\pi$
$647$	−2.68385	−	10.0163i	−0.105513	−	0.393780i	−0.998403	+	0.0564952i	$0.982007\pi$
$648$		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
$653$	−7.05023	−	1.88910i	−0.275897	−	0.0739263i	0.118218	−	0.992988i	$-0.462282\pi$
$653$	−7.05023	−	1.88910i	−0.275897	−	0.0739263i	−0.394114	+	0.919061i	$0.628949\pi$
$654$		0			0
$655$	−17.9308	+	40.1016i	−0.700616	+	1.56690i
$656$		0			0
$657$	5.95677	−	5.95677i	0.232396	−	0.232396i
$658$		0			0
$659$		−	11.8101i		−	0.460057i	−0.973184	−	0.230028i	$-0.926118\pi$
$659$		−	11.8101i		−	0.460057i	0.973184	−	0.230028i	$-0.0738819\pi$
$660$		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
$663$	1.25073	−	4.66781i	0.0485745	−	0.181283i
$664$		0			0
$665$	2.08672	−	0.146465i	0.0809195	−	0.00567967i
$666$		0			0
$667$	3.00746	−	11.2240i	0.116449	−	0.434594i
$668$		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	−0.872758	−	0.488153i	$-0.837671\pi$
$673$	−9.97751	+	9.97751i	−0.384605	+	0.384605i	0.488153	+	0.872758i	$0.337671\pi$
$674$		0			0
$675$	−2.25577	−	4.46223i	−0.0868248	−	0.171751i
$676$		0			0
$677$	−2.65481	−	0.711353i	−0.102033	−	0.0273395i	0.207442	−	0.978247i	$-0.433486\pi$
$677$	−2.65481	−	0.711353i	−0.102033	−	0.0273395i	−0.309474	+	0.950908i	$0.600153\pi$
$678$		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
$683$	12.2443	+	45.6962i	0.468513	+	1.74852i	0.644971	+	0.764207i	$0.276869\pi$
$683$	12.2443	+	45.6962i	0.468513	+	1.74852i	−0.176458	+	0.984308i	$0.556464\pi$
$684$		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
$693$	−1.43214	−	2.68149i	−0.0544027	−	0.101861i
$694$		0			0
$695$	16.0368	−	11.6125i	0.608309	−	0.440486i
$696$		0			0
$697$	−12.6070	+	3.37804i	−0.477525	+	0.127952i
$698$		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
$703$	−2.92939	+	0.784927i	−0.110484	+	0.0296041i
$704$		0			0
$705$	1.08676	−	0.786940i	0.0409297	−	0.0296379i
$706$		0			0
$707$	6.15674	+	0.203589i	0.231548	+	0.00765674i
$708$		0			0
$709$	−12.3526	+	7.13175i	−0.463910	+	0.267839i	−0.713687	−	0.700465i	$-0.752976\pi$
$709$	−12.3526	+	7.13175i	−0.463910	+	0.267839i	0.249777	+	0.968303i	$0.419643\pi$
$710$		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
$717$	−3.67364	−	13.7102i	−0.137195	−	0.512018i
$718$		0			0
$719$	−10.6678	−	18.4772i	−0.397843	−	0.689084i	0.595617	−	0.803269i	$-0.296908\pi$
$719$	−10.6678	−	18.4772i	−0.397843	−	0.689084i	−0.993459	+	0.114185i	$0.963574\pi$
$720$		0			0
$721$	−11.3644	−	48.8121i	−0.423231	−	1.81786i
$722$		0			0
$723$	4.99946	+	1.33960i	0.185932	+	0.0498203i
$724$		0			0
$725$	16.2083	+	5.32343i	0.601961	+	0.197707i
$726$		0			0
$727$	−23.3102	+	23.3102i	−0.864529	+	0.864529i	−0.991860	−	0.127331i	$-0.959359\pi$
$727$	−23.3102	+	23.3102i	−0.864529	+	0.864529i	0.127331	+	0.991860i	$0.459359\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	10.5408	+	6.08572i	0.389865	+	0.225089i
$732$		0			0
$733$	−4.74908	+	17.7238i	−0.175411	+	0.654644i	0.821070	+	0.570828i	$0.193378\pi$
$733$	−4.74908	+	17.7238i	−0.175411	+	0.654644i	−0.996481	+	0.0838162i	$0.973289\pi$
$734$		0			0
$735$	−4.60795	−	14.9588i	−0.169967	−	0.551765i
$736$		0			0
$737$	−1.50646	+	5.62218i	−0.0554911	+	0.207096i
$738$		0			0
$739$	−15.4768	−	8.93552i	−0.569322	−	0.328698i	0.187556	−	0.982254i	$-0.439943\pi$
$739$	−15.4768	−	8.93552i	−0.569322	−	0.328698i	−0.756879	+	0.653555i	$0.773277\pi$
$740$		0			0
$741$		−	0.639464i		−	0.0234913i
$742$		0			0
$743$	−33.6457	+	33.6457i	−1.23434	+	1.23434i	−0.272061	+	0.962280i	$0.587705\pi$
$743$	−33.6457	+	33.6457i	−1.23434	+	1.23434i	−0.962280	+	0.272061i	$0.912295\pi$
$744$		0			0
$745$	−6.53506	+	14.6154i	−0.239426	+	0.535467i
$746$		0			0
$747$	2.98059	+	0.798647i	0.109054	+	0.0292210i
$748$		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
$753$	5.59849	+	20.8938i	0.204020	+	0.761414i
$754$		0			0
$755$	−0.728479	−	7.03865i	−0.0265121	−	0.256163i
$756$		0			0
$757$	38.6362	+	38.6362i	1.40426	+	1.40426i	0.785889	+	0.618367i	$0.212206\pi$
$757$	38.6362	+	38.6362i	1.40426	+	1.40426i	0.618367	+	0.785889i	$0.287794\pi$
$758$		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
$763$	30.2476	+	1.00022i	1.09504	+	0.0362102i
$764$		0			0
$765$	5.89990	+	0.944070i	0.213311	+	0.0341329i
$766$		0			0
$767$	3.05039	−	0.817350i	0.110143	−	0.0295128i
$768$		0			0
$769$	19.4505			0.701404			0.350702	−	0.936487i	$-0.385943\pi$
$769$	19.4505			0.701404			0.350702	+	0.936487i	$0.385943\pi$
$770$		0			0
$771$	11.9647			0.430899
$772$		0			0
$773$	24.2176	−	6.48908i	0.871046	−	0.233396i	0.204506	−	0.978865i	$-0.434441\pi$
$773$	24.2176	−	6.48908i	0.871046	−	0.233396i	0.666540	+	0.745469i	$0.267775\pi$
$774$		0			0
$775$	−22.3871	+	20.0289i	−0.804169	+	0.719460i
$776$		0			0
$777$	10.6906	+	20.0167i	0.383524	+	0.718094i
$778$		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
$787$	−5.44211	−	20.3102i	−0.193990	−	0.723982i	−0.992526	−	0.122034i	$-0.961058\pi$
$787$	−5.44211	−	20.3102i	−0.193990	−	0.723982i	0.798536	−	0.601948i	$-0.205608\pi$
$788$		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
$793$	−20.8365	−	5.58312i	−0.739926	−	0.198263i
$794$		0			0
$795$	4.48765	+	2.00659i	0.159161	+	0.0711663i
$796$		0			0
$797$	35.0360	−	35.0360i	1.24104	−	1.24104i	0.281469	−	0.959570i	$-0.409178\pi$
$797$	35.0360	−	35.0360i	1.24104	−	1.24104i	0.959570	−	0.281469i	$-0.0908217\pi$
$798$		0			0
$799$			1.60339i			0.0567239i
$800$		0			0
$801$	11.4636	+	6.61849i	0.405045	+	0.233853i
$802$		0			0
$803$	2.50520	−	9.34952i	0.0884065	−	0.329937i
$804$		0			0
$805$	−13.2141	+	15.2091i	−0.465736	+	0.536051i
$806$		0			0
$807$	4.20337	−	15.6872i	0.147966	−	0.552215i
$808$		0			0
$809$	−19.5041	−	11.2607i	−0.685726	−	0.395904i	0.116283	−	0.993216i	$-0.462902\pi$
$809$	−19.5041	−	11.2607i	−0.685726	−	0.395904i	−0.802009	+	0.597312i	$0.796235\pi$
$810$		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
$815$	1.73322	−	0.662159i	0.0607119	−	0.0231944i
$816$		0			0
$817$	1.55573	+	0.416856i	0.0544280	+	0.0145839i
$818$		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
$823$	5.42483	+	20.2458i	0.189098	+	0.705723i	0.993716	+	0.111930i	$0.0357033\pi$
$823$	5.42483	+	20.2458i	0.189098	+	0.705723i	−0.804618	+	0.593792i	$0.797630\pi$
$824$		0			0
$825$	−4.80819	−	3.14425i	−0.167400	−	0.109469i
$826$		0			0
$827$	10.1627	+	10.1627i	0.353391	+	0.353391i	0.861370	−	0.507979i	$-0.169607\pi$
$827$	10.1627	+	10.1627i	0.353391	+	0.353391i	−0.507979	+	0.861370i	$0.669607\pi$
$828$		0			0
$829$	5.76151	−	9.97922i	0.200105	−	0.346593i	−0.748457	−	0.663184i	$-0.769205\pi$
$829$	5.76151	−	9.97922i	0.200105	−	0.346593i	0.948562	+	0.316591i	$0.102538\pi$
$830$		0			0
$831$	−16.0971	+	9.29364i	−0.558400	+	0.322393i
$832$		0			0
$833$	17.7079	+	6.02410i	0.613544	+	0.208723i
$834$		0			0
$835$	−6.97972	+	43.6193i	−0.241543	+	1.50951i
$836$		0			0
$837$	−5.80308	+	1.55493i	−0.200584	+	0.0537463i
$838$		0			0
$839$	15.2304			0.525813			0.262907	−	0.964821i	$-0.415319\pi$
$839$	15.2304			0.525813			0.262907	+	0.964821i	$0.415319\pi$
$840$		0			0
$841$	17.3581			0.598555
$842$		0			0
$843$	−28.7884	+	7.71382i	−0.991524	+	0.265678i
$844$		0			0
$845$	−12.7595	−	17.6208i	−0.438940	−	0.606174i
$846$		0			0
$847$	21.7439	+	13.5312i	0.747129	+	0.464937i
$848$		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	$-0.188471\pi$
$853$	7.93430	+	7.93430i	0.271665	+	0.271665i	−0.558105	+	0.829770i	$0.688471\pi$
$854$		0			0
$855$	0.786445	−	0.0813947i	0.0268959	−	0.00278364i
$856$		0			0
$857$	6.13354	+	22.8907i	0.209518	+	0.781930i	0.988025	+	0.154295i	$0.0493105\pi$
$857$	6.13354	+	22.8907i	0.209518	+	0.781930i	−0.778507	+	0.627636i	$0.784023\pi$
$858$		0			0
$859$	−20.5470	−	35.5885i	−0.701055	−	1.21426i	−0.968096	−	0.250578i	$-0.919379\pi$
$859$	−20.5470	−	35.5885i	−0.701055	−	1.21426i	0.267041	−	0.963685i	$-0.413954\pi$
$860$		0			0
$861$	8.83104	+	9.43506i	0.300961	+	0.321546i
$862$		0			0
$863$	−15.8067	−	4.23539i	−0.538066	−	0.144174i	−0.0204557	−	0.999791i	$-0.506512\pi$
$863$	−15.8067	−	4.23539i	−0.538066	−	0.144174i	−0.517611	+	0.855616i	$0.673178\pi$
$864$		0			0
$865$	9.53254	+	24.9516i	0.324116	+	0.848381i
$866$		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
$873$	−4.13154	+	15.4191i	−0.139831	+	0.521858i
$874$		0			0
$875$	−21.2183	−	20.6103i	−0.717309	−	0.696755i
$876$		0			0
$877$	11.8762	−	44.3226i	0.401031	−	1.49667i	−0.410230	−	0.911982i	$-0.634552\pi$
$877$	11.8762	−	44.3226i	0.401031	−	1.49667i	0.811261	−	0.584685i	$-0.198782\pi$
$878$		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	−0.774162	−	0.632987i	$-0.781829\pi$
$883$	−4.19508	+	4.19508i	−0.141176	+	0.141176i	0.632987	+	0.774162i	$0.281829\pi$
$884$		0			0
$885$	1.39349	+	3.64748i	0.0468416	+	0.122609i
$886$		0			0
$887$	9.61172	+	2.57545i	0.322730	+	0.0864752i	0.416547	−	0.909114i	$-0.363240\pi$
$887$	9.61172	+	2.57545i	0.322730	+	0.0864752i	−0.0938170	+	0.995589i	$0.529907\pi$
$888$		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
$893$	0.0549140	+	0.204942i	0.00183763	+	0.00685812i
$894$		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
$903$	0.398297	−	12.0449i	0.0132545	−	0.400830i
$904$		0			0
$905$	25.4274	+	35.1151i	0.845236	+	1.16727i
$906$		0			0
$907$	−2.27984	+	0.610881i	−0.0757007	+	0.0202840i	−0.296471	−	0.955042i	$-0.595810\pi$
$907$	−2.27984	+	0.610881i	−0.0757007	+	0.0202840i	0.220770	+	0.975326i	$0.429143\pi$
$908$		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
$913$	3.42470	−	0.917645i	0.113341	−	0.0303696i
$914$		0			0
$915$	4.21421	−	26.3364i	0.139318	−	0.870655i
$916$		0			0
$917$	−27.4615	+	44.1291i	−0.906859	+	1.45727i
$918$		0			0
$919$	15.7670	−	9.10309i	0.520106	−	0.300283i	−0.216872	−	0.976200i	$-0.569585\pi$
$919$	15.7670	−	9.10309i	0.520106	−	0.300283i	0.736978	+	0.675917i	$0.236252\pi$
$920$		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
$927$	−4.90272	−	18.2972i	−0.161026	−	0.600959i
$928$		0			0
$929$	18.4222	+	31.9082i	0.604414	+	1.04688i	0.992144	+	0.125103i	$0.0399260\pi$
$929$	18.4222	+	31.9082i	0.604414	+	1.04688i	−0.387730	+	0.921773i	$0.626741\pi$
$930$		0			0
$931$	2.46971	+	0.163513i	0.0809413	+	0.00535893i
$932$		0			0
$933$	18.2262	+	4.88369i	0.596699	+	0.159885i
$934$		0			0
$935$	6.41314	−	2.45008i	0.209732	−	0.0801262i
$936$		0			0
$937$	−27.4546	+	27.4546i	−0.896902	+	0.896902i	−0.995161	−	0.0982591i	$-0.968673\pi$
$937$	−27.4546	+	27.4546i	−0.896902	+	0.896902i	0.0982591	+	0.995161i	$0.468673\pi$
$938$		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
$943$	4.30533	−	16.0677i	0.140201	−	0.523237i
$944$		0			0
$945$	−1.92755	−	5.59326i	−0.0627031	−	0.181949i
$946$		0			0
$947$	8.88381	−	33.1548i	0.288685	−	1.07739i	−0.657419	−	0.753525i	$-0.728352\pi$
$947$	8.88381	−	33.1548i	0.288685	−	1.07739i	0.946104	−	0.323862i	$-0.104981\pi$
$948$		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	−0.999662	−	0.0260068i	$-0.991721\pi$
$953$	−30.0574	+	30.0574i	−0.973655	+	0.973655i	0.0260068	+	0.999662i	$0.491721\pi$
$954$		0			0
$955$	11.3486	+	5.07434i	0.367230	+	0.164202i
$956$		0			0
$957$	3.78683	+	1.01468i	0.122411	+	0.0327999i
$958$		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
$963$	−0.280829	−	1.04807i	−0.00904960	−	0.0337736i
$964$		0			0
$965$	5.12220	+	4.16138i	0.164890	+	0.133960i
$966$		0			0
$967$	−37.5319	−	37.5319i	−1.20694	−	1.20694i	−0.972012	−	0.234931i	$-0.924514\pi$
$967$	−37.5319	−	37.5319i	−1.20694	−	1.20694i	−0.234931	−	0.972012i	$-0.575486\pi$
$968$		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
$973$	20.6647	−	11.0367i	0.662479	−	0.353821i
$974$		0			0
$975$	−6.73911	+	6.02923i	−0.215824	+	0.193090i
$976$		0			0
$977$	54.2472	−	14.5355i	1.73552	−	0.465031i	0.754078	−	0.656785i	$-0.228084\pi$
$977$	54.2472	−	14.5355i	1.73552	−	0.465031i	0.981443	+	0.191754i	$0.0614175\pi$
$978$		0			0
$979$	15.2093			0.486091
$980$		0			0
$981$	11.4388			0.365212
$982$		0			0
$983$	−48.5203	+	13.0010i	−1.54756	+	0.414667i	−0.928698	−	0.370836i	$-0.879071\pi$
$983$	−48.5203	+	13.0010i	−1.54756	+	0.414667i	−0.618858	+	0.785503i	$0.712404\pi$
$984$		0			0
$985$	−54.3426	−	8.69560i	−1.73150	−	0.277065i
$986$		0			0
$987$	1.40038	−	0.747923i	0.0445745	−	0.0238066i
$988$		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
$997$	3.31265	+	12.3630i	0.104913	+	0.391540i	0.998335	−	0.0576775i	$-0.0183695\pi$
$997$	3.31265	+	12.3630i	0.104913	+	0.391540i	−0.893422	+	0.449217i	$0.851703\pi$
$998$		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.a.577.11	yes	48
5.3	odd	4		840.2.dd.b.73.12	yes	48
7.5	odd	6		840.2.dd.b.817.12	yes	48
35.33	even	12	inner	840.2.dd.a.313.11	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dd.a.313.11	✓	48	35.33	even	12	inner
840.2.dd.a.577.11	yes	48	1.1	even	1	trivial
840.2.dd.b.73.12	yes	48	5.3	odd	4
840.2.dd.b.817.12	yes	48	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{3} +(1.81110 - 1.31145i) q^{5} +(2.33376 - 1.24643i) q^{7} +(0.866025 - 0.500000i) q^{9} +(0.574500 - 0.995063i) q^{11} +(-1.27881 - 1.27881i) q^{13} +(1.40996 - 1.73551i) q^{15} +(0.691585 + 2.58103i) q^{17} +(0.176794 + 0.306216i) q^{19} +(1.93164 - 1.80798i) q^{21} +(-3.28954 - 0.881430i) q^{23} +(1.56020 - 4.75035i) q^{25} +(0.707107 - 0.707107i) q^{27} +3.41202i q^{29} +(-5.20290 - 3.00390i) q^{31} +(0.297383 - 1.10985i) q^{33} +(2.59205 - 5.31801i) q^{35} +(-2.21989 + 8.28476i) q^{37} +(-1.56621 - 0.904252i) q^{39} +4.88449i q^{41} +(3.22090 - 3.22090i) q^{43} +(0.912737 - 2.04130i) q^{45} +(0.579607 + 0.155305i) q^{47} +(3.89284 - 5.81771i) q^{49} +(1.33604 + 2.31409i) q^{51} +(0.568994 + 2.12352i) q^{53} +(-0.264496 - 2.55559i) q^{55} +(0.250024 + 0.250024i) q^{57} +(-0.873096 + 1.51225i) q^{59} +(10.3298 - 5.96392i) q^{61} +(1.39788 - 2.24632i) q^{63} +(-3.99314 - 0.638961i) q^{65} +(-4.89311 + 1.31110i) q^{67} -3.40558 q^{69} -4.35856 q^{71} +(8.13710 - 2.18033i) q^{73} +(0.277556 - 4.99229i) q^{75} +(0.100469 - 3.03831i) q^{77} +(2.36967 - 1.36813i) q^{79} +(0.500000 - 0.866025i) q^{81} +(2.18195 + 2.18195i) q^{83} +(4.63743 + 3.76754i) q^{85} +(0.883096 + 3.29576i) q^{87} +(6.61849 + 11.4636i) q^{89} +(-4.57836 - 1.39048i) q^{91} +(-5.80308 - 1.55493i) q^{93} +(0.721779 + 0.322733i) q^{95} +(-11.2876 + 11.2876i) q^{97} -1.14900i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{11} + 16 q^{13} - 4 q^{15} - 4 q^{17} + 8 q^{19} - 24 q^{23} + 28 q^{25} + 12 q^{33} - 4 q^{37} - 12 q^{39} + 16 q^{43} - 4 q^{45} + 12 q^{47} - 12 q^{49} + 20 q^{53} - 56 q^{55} + 8 q^{57}+ \cdots + 44 q^{97}+O(q^{100}) \) 48 * q - 4 * q^11 + 16 * q^13 - 4 * q^15 - 4 * q^17 + 8 * q^19 - 24 * q^23 + 28 * q^25 + 12 * q^33 - 4 * q^37 - 12 * q^39 + 16 * q^43 - 4 * q^45 + 12 * q^47 - 12 * q^49 + 20 * q^53 - 56 * q^55 + 8 * q^57 + 8 * q^59 + 8 * q^63 + 12 * q^65 - 52 * q^67 - 8 * q^69 + 16 * q^71 - 4 * q^73 + 24 * q^75 + 8 * q^77 + 108 * q^79 + 24 * q^81 + 64 * q^83 + 32 * q^85 + 20 * q^87 + 64 * q^89 + 48 * q^91 - 24 * q^93 + 36 * q^95 + 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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