LMFDB - Embedded newform 567.2.ba.a.143.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(143,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.11
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00959490 + 0.0114348i) q^{2} +(0.347258 + 1.96940i) q^{4} +(-1.26073 + 1.05788i) q^{5} +(1.81613 + 1.92397i) q^{7} +(-0.0517058 - 0.0298524i) q^{8} -0.0245663i q^{10} +(-2.95219 + 3.51829i) q^{11} +(1.52751 - 4.19679i) q^{13} +(-0.0394257 + 0.00230675i) q^{14} +(-3.75751 + 1.36762i) q^{16} -3.77410 q^{17} +1.46832i q^{19} +(-2.52118 - 2.11552i) q^{20} +(-0.0119048 - 0.0675152i) q^{22} +(2.54129 - 6.98214i) q^{23} +(-0.397908 + 2.25665i) q^{25} +(0.0333330 + 0.0577345i) q^{26} +(-3.15839 + 4.24480i) q^{28} +(2.83246 + 7.78213i) q^{29} +(-8.27481 + 1.45907i) q^{31} +(0.0612550 - 0.168297i) q^{32} +(0.0362121 - 0.0431559i) q^{34} +(-4.32497 - 0.504358i) q^{35} +(0.397320 - 0.688178i) q^{37} +(-0.0167899 - 0.0140884i) q^{38} +(0.0967671 - 0.0170627i) q^{40} +(3.97658 + 1.44736i) q^{41} +(-0.303215 + 1.71962i) q^{43} +(-7.95407 - 4.59229i) q^{44} +(0.0554557 + 0.0960520i) q^{46} +(0.286275 - 1.62355i) q^{47} +(-0.403318 + 6.98837i) q^{49} +(-0.0219863 - 0.0262023i) q^{50} +(8.79559 + 1.55090i) q^{52} +(3.66888 + 2.11823i) q^{53} -7.55866i q^{55} +(-0.0364696 - 0.153696i) q^{56} +(-0.116164 - 0.0422802i) q^{58} +(10.8663 + 3.95501i) q^{59} +(2.96287 + 0.522435i) q^{61} +(0.0627118 - 0.108620i) q^{62} +(-3.99733 - 6.92357i) q^{64} +(2.51392 + 6.90693i) q^{65} +(-8.30643 + 6.96992i) q^{67} +(-1.31059 - 7.43270i) q^{68} +(0.0472649 - 0.0446158i) q^{70} +(-6.66808 + 3.84982i) q^{71} +(13.7076 - 7.91406i) q^{73} +(0.00405690 + 0.0111462i) q^{74} +(-2.89171 + 0.509886i) q^{76} +(-12.1307 + 0.709749i) q^{77} +(1.22109 + 1.02462i) q^{79} +(3.29043 - 5.69919i) q^{80} +(-0.0547050 + 0.0315840i) q^{82} +(4.61667 - 1.68033i) q^{83} +(4.75812 - 3.99254i) q^{85} +(-0.0167541 - 0.0199668i) q^{86} +(0.257675 - 0.0937859i) q^{88} +7.18505 q^{89} +(10.8487 - 4.68306i) q^{91} +(14.6331 + 2.58021i) q^{92} +(0.0158181 + 0.0188513i) q^{94} +(-1.55330 - 1.85115i) q^{95} +(1.56544 + 0.276029i) q^{97} +(-0.0760405 - 0.0716645i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−0.00959490	+	0.0114348i	−0.00678462	+	0.00808559i	−0.769426	−	0.638736i	$-0.779458\pi$
$2$	−0.00959490	+	0.0114348i	−0.00678462	+	0.00808559i	0.762641	+	0.646821i	$0.223902\pi$
$3$		0			0
$3$		0			0
$4$	0.347258	+	1.96940i	0.173629	+	0.984698i
$5$	−1.26073	+	1.05788i	−0.563815	+	0.473097i	−0.879587	−	0.475738i	$-0.842181\pi$
$5$	−1.26073	+	1.05788i	−0.563815	+	0.473097i	0.315772	+	0.948835i	$0.397737\pi$
$6$		0			0
$7$	1.81613	+	1.92397i	0.686434	+	0.727192i
$7$	1.81613	+	1.92397i	0.686434	+	0.727192i
$8$	−0.0517058	−	0.0298524i	−0.0182808	−	0.0105544i
$9$		0			0
$10$		−	0.0245663i		−	0.00776856i
$11$	−2.95219	+	3.51829i	−0.890120	+	1.06080i	0.107659	+	0.994188i	$0.465665\pi$
$11$	−2.95219	+	3.51829i	−0.890120	+	1.06080i	−0.997779	+	0.0666155i	$0.978780\pi$
$12$		0			0
$13$	1.52751	−	4.19679i	0.423654	−	1.16398i	−0.525946	−	0.850518i	$-0.676289\pi$
$13$	1.52751	−	4.19679i	0.423654	−	1.16398i	0.949600	−	0.313463i	$-0.101489\pi$
$14$	−0.0394257	+	0.00230675i	−0.0105370	+	0.000616504i
$15$		0			0
$16$	−3.75751	+	1.36762i	−0.939379	+	0.341906i
$17$	−3.77410			−0.915355			−0.457677	−	0.889118i	$-0.651318\pi$
$17$	−3.77410			−0.915355			−0.457677	+	0.889118i	$0.651318\pi$
$18$		0			0
$19$			1.46832i			0.336856i	0.985714	+	0.168428i	$0.0538690\pi$
$19$			1.46832i			0.336856i	−0.985714	+	0.168428i	$0.946131\pi$
$20$	−2.52118	−	2.11552i	−0.563752	−	0.473044i
$21$		0			0
$22$	−0.0119048	−	0.0675152i	−0.00253810	−	0.0143943i
$23$	2.54129	−	6.98214i	0.529896	−	1.45588i	−0.329297	−	0.944226i	$-0.606812\pi$
$23$	2.54129	−	6.98214i	0.529896	−	1.45588i	0.859193	−	0.511651i	$-0.170966\pi$
$24$		0			0
$25$	−0.397908	+	2.25665i	−0.0795815	+	0.451329i
$26$	0.0333330	+	0.0577345i	0.00653714	+	0.0113227i
$27$		0			0
$28$	−3.15839	+	4.24480i	−0.596880	+	0.802192i
$29$	2.83246	+	7.78213i	0.525975	+	1.44511i	0.863771	+	0.503885i	$0.168097\pi$
$29$	2.83246	+	7.78213i	0.525975	+	1.44511i	−0.337795	+	0.941220i	$0.609681\pi$
$30$		0			0
$31$	−8.27481	+	1.45907i	−1.48620	+	0.262057i	−0.857052	−	0.515229i	$-0.827707\pi$
$31$	−8.27481	+	1.45907i	−1.48620	+	0.262057i	−0.629147	+	0.777286i	$0.716596\pi$
$32$	0.0612550	−	0.168297i	0.0108284	−	0.0297509i
$33$		0			0
$34$	0.0362121	−	0.0431559i	0.00621033	−	0.00740118i
$35$	−4.32497	−	0.504358i	−0.731054	−	0.0852520i
$36$		0			0
$37$	0.397320	−	0.688178i	0.0653190	−	0.113136i	−0.831516	−	0.555500i	$-0.812527\pi$
$37$	0.397320	−	0.688178i	0.0653190	−	0.113136i	0.896835	+	0.442364i	$0.145860\pi$
$38$	−0.0167899	−	0.0140884i	−0.00272368	−	0.00228544i
$39$		0			0
$40$	0.0967671	−	0.0170627i	0.0153002	−	0.00269784i
$41$	3.97658	+	1.44736i	0.621037	+	0.226039i	0.633326	−	0.773885i	$-0.281689\pi$
$41$	3.97658	+	1.44736i	0.621037	+	0.226039i	−0.0122884	+	0.999924i	$0.503912\pi$
$42$		0			0
$43$	−0.303215	+	1.71962i	−0.0462399	+	0.262239i	−0.999160	−	0.0409825i	$-0.986951\pi$
$43$	−0.303215	+	1.71962i	−0.0462399	+	0.262239i	0.952920	+	0.303222i	$0.0980623\pi$
$44$	−7.95407	−	4.59229i	−1.19912	−	0.692313i
$45$		0			0
$46$	0.0554557	+	0.0960520i	0.00817649	+	0.0141621i
$47$	0.286275	−	1.62355i	0.0417575	−	0.236819i	−0.956785	−	0.290798i	$-0.906079\pi$
$47$	0.286275	−	1.62355i	0.0417575	−	0.236819i	0.998542	+	0.0539790i	$0.0171904\pi$
$48$		0			0
$49$	−0.403318	+	6.98837i	−0.0576169	+	0.998339i
$50$	−0.0219863	−	0.0262023i	−0.00310933	−	0.00370556i
$51$		0			0
$52$	8.79559	+	1.55090i	1.21973	+	0.215071i
$53$	3.66888	+	2.11823i	0.503959	+	0.290961i	0.730347	−	0.683076i	$-0.239358\pi$
$53$	3.66888	+	2.11823i	0.503959	+	0.290961i	−0.226388	+	0.974037i	$0.572692\pi$
$54$		0			0
$55$		−	7.55866i		−	1.01921i
$56$	−0.0364696	−	0.153696i	−0.00487346	−	0.0205385i
$57$		0			0
$58$	−0.116164	−	0.0422802i	−0.0152531	−	0.00555166i
$59$	10.8663	+	3.95501i	1.41467	+	0.514898i	0.932497	−	0.361178i	$-0.117625\pi$
$59$	10.8663	+	3.95501i	1.41467	+	0.514898i	0.482173	+	0.876076i	$0.339848\pi$
$60$		0			0
$61$	2.96287	+	0.522435i	0.379357	+	0.0668909i	0.360075	−	0.932923i	$-0.382751\pi$
$61$	2.96287	+	0.522435i	0.379357	+	0.0668909i	0.0192817	+	0.999814i	$0.493862\pi$
$62$	0.0627118	−	0.108620i	0.00796441	−	0.0137948i
$63$		0			0
$64$	−3.99733	−	6.92357i	−0.499666	−	0.865447i
$65$	2.51392	+	6.90693i	0.311813	+	0.856700i
$66$		0			0
$67$	−8.30643	+	6.96992i	−1.01479	+	0.851512i	−0.988964	−	0.148155i	$-0.952667\pi$
$67$	−8.30643	+	6.96992i	−1.01479	+	0.851512i	−0.0258279	+	0.999666i	$0.508222\pi$
$68$	−1.31059	−	7.43270i	−0.158932	−	0.901348i
$69$		0			0
$70$	0.0472649	−	0.0446158i	0.00564924	−	0.00533260i
$71$	−6.66808	+	3.84982i	−0.791355	+	0.456889i	−0.840439	−	0.541906i	$-0.817703\pi$
$71$	−6.66808	+	3.84982i	−0.791355	+	0.456889i	0.0490844	+	0.998795i	$0.484370\pi$
$72$		0			0
$73$	13.7076	−	7.91406i	1.60435	−	0.926271i	0.613745	−	0.789504i	$-0.289662\pi$
$73$	13.7076	−	7.91406i	1.60435	−	0.926271i	0.990603	−	0.136767i	$-0.0436712\pi$
$74$	0.00405690	+	0.0111462i	0.000471605	+	0.00129573i
$75$		0			0
$76$	−2.89171	+	0.509886i	−0.331701	+	0.0584879i
$77$	−12.1307	+	0.709749i	−1.38242	+	0.0808833i
$78$		0			0
$79$	1.22109	+	1.02462i	0.137384	+	0.115279i	0.708890	−	0.705319i	$-0.249196\pi$
$79$	1.22109	+	1.02462i	0.137384	+	0.115279i	−0.571506	+	0.820598i	$0.693641\pi$
$80$	3.29043	−	5.69919i	0.367881	−	0.637189i
$81$		0			0
$82$	−0.0547050	+	0.0315840i	−0.00604116	+	0.00348787i
$83$	4.61667	−	1.68033i	0.506745	−	0.184440i	−0.0759804	−	0.997109i	$-0.524209\pi$
$83$	4.61667	−	1.68033i	0.506745	−	0.184440i	0.582725	+	0.812669i	$0.301986\pi$
$84$		0			0
$85$	4.75812	−	3.99254i	0.516091	−	0.433051i
$86$	−0.0167541	−	0.0199668i	−0.00180664	−	0.00215307i
$87$		0			0
$88$	0.257675	−	0.0937859i	0.0274682	−	0.00999761i
$89$	7.18505			0.761614			0.380807	−	0.924655i	$-0.375646\pi$
$89$	7.18505			0.761614			0.380807	+	0.924655i	$0.375646\pi$
$90$		0			0
$91$	10.8487	−	4.68306i	1.13725	−	0.490918i
$92$	14.6331	+	2.58021i	1.52561	+	0.269005i
$93$		0			0
$94$	0.0158181	+	0.0188513i	0.00163151	+	0.00194436i
$95$	−1.55330	−	1.85115i	−0.159365	−	0.189924i
$96$		0			0
$97$	1.56544	+	0.276029i	0.158946	+	0.0280265i	0.252555	−	0.967583i	$-0.418729\pi$
$97$	1.56544	+	0.276029i	0.158946	+	0.0280265i	−0.0936086	+	0.995609i	$0.529840\pi$
$98$	−0.0760405	−	0.0716645i	−0.00768125	−	0.00723921i
$99$		0			0
$100$	−4.58241			−0.458241
$101$	−2.17178	+	0.790462i	−0.216100	+	0.0786539i	−0.447802	−	0.894133i	$-0.647793\pi$
$101$	−2.17178	+	0.790462i	−0.216100	+	0.0786539i	0.231702	+	0.972787i	$0.425571\pi$
$102$		0			0
$103$	−0.351554	−	0.418965i	−0.0346396	−	0.0412819i	0.748447	−	0.663195i	$-0.230800\pi$
$103$	−0.351554	−	0.418965i	−0.0346396	−	0.0412819i	−0.783086	+	0.621913i	$0.786356\pi$
$104$	−0.204265	+	0.171399i	−0.0200299	+	0.0168070i
$105$		0			0
$106$	−0.0594239	+	0.0216285i	−0.00577176	+	0.00210075i
$107$	2.89299	−	1.67027i	0.279676	−	0.161471i	−0.353601	−	0.935397i	$-0.615043\pi$
$107$	2.89299	−	1.67027i	0.279676	−	0.161471i	0.633277	+	0.773925i	$0.281709\pi$
$108$		0			0
$109$	1.92585	−	3.33567i	0.184463	−	0.319499i	−0.758932	−	0.651169i	$-0.774279\pi$
$109$	1.92585	−	3.33567i	0.184463	−	0.319499i	0.943395	+	0.331670i	$0.107612\pi$
$110$	0.0864314	+	0.0725246i	0.00824091	+	0.00691495i
$111$		0			0
$112$	−9.45541	−	4.74556i	−0.893453	−	0.448413i
$113$	−4.52691	+	0.798216i	−0.425856	+	0.0750899i	−0.382469	−	0.923968i	$-0.624926\pi$
$113$	−4.52691	+	0.798216i	−0.425856	+	0.0750899i	−0.0433872	+	0.999058i	$0.513815\pi$
$114$		0			0
$115$	4.18237	+	11.4910i	0.390008	+	1.07154i
$116$	−14.3425	+	8.28065i	−1.33167	+	0.768839i
$117$		0			0
$118$	−0.149485	+	0.0863054i	−0.0137612	+	0.00794506i
$119$	−6.85428	−	7.26126i	−0.628330	−	0.665639i
$120$		0			0
$121$	−1.75277	−	9.94044i	−0.159343	−	0.903676i
$122$	−0.0344024	+	0.0288670i	−0.00311464	+	0.00261350i
$123$		0			0
$124$	−5.74698	−	15.7897i	−0.516094	−	1.41796i
$125$	−6.00001	−	10.3923i	−0.536657	−	0.929518i
$126$		0			0
$127$	2.63202	−	4.55879i	0.233554	−	0.404527i	−0.725298	−	0.688435i	$-0.758298\pi$
$127$	2.63202	−	4.55879i	0.233554	−	0.404527i	0.958851	+	0.283908i	$0.0916312\pi$
$128$	0.470277	+	0.0829224i	0.0415670	+	0.00732938i
$129$		0			0
$130$	−0.103100	−	0.0375253i	−0.00904246	−	0.00329119i
$131$	14.2240	+	5.17710i	1.24275	+	0.452325i	0.877947	−	0.478758i	$-0.158913\pi$
$131$	14.2240	+	5.17710i	1.24275	+	0.452325i	0.364807	+	0.931083i	$0.381135\pi$
$132$		0			0
$133$	−2.82500	+	2.66667i	−0.244959	+	0.231229i
$134$		−	0.161858i		−	0.0139824i
$135$		0			0
$136$	0.195143	+	0.112666i	0.0167334	+	0.00966102i
$137$	−3.51827	−	0.620365i	−0.300586	−	0.0530014i	0.0213213	−	0.999773i	$-0.493213\pi$
$137$	−3.51827	−	0.620365i	−0.300586	−	0.0530014i	−0.321907	+	0.946771i	$0.604324\pi$
$138$		0			0
$139$	−3.91305	−	4.66340i	−0.331901	−	0.395544i	0.574124	−	0.818768i	$-0.305343\pi$
$139$	−3.91305	−	4.66340i	−0.331901	−	0.395544i	−0.906025	+	0.423224i	$0.860898\pi$
$140$	−0.508600	−	8.69273i	−0.0429846	−	0.734670i
$141$		0			0
$142$	0.0199578	−	0.113186i	0.00167482	−	0.00949839i
$143$	10.2560	+	17.7640i	0.857652	+	1.48550i
$144$		0			0
$145$	−11.8035	−	6.81476i	−0.980228	−	0.565935i
$146$	−0.0410273	+	0.232677i	−0.00339544	+	0.0192565i
$147$		0			0
$148$	1.49327	+	0.543505i	0.122746	+	0.0446758i
$149$	19.9144	−	3.51144i	1.63145	−	0.287668i	0.718433	−	0.695596i	$-0.244860\pi$
$149$	19.9144	−	3.51144i	1.63145	−	0.287668i	0.913014	+	0.407928i	$0.133748\pi$
$150$		0			0
$151$	14.6511	+	12.2937i	1.19229	+	1.00045i	0.999817	+	0.0191488i	$0.00609564\pi$
$151$	14.6511	+	12.2937i	1.19229	+	1.00045i	0.192474	+	0.981302i	$0.438349\pi$
$152$	0.0438328	−	0.0759207i	0.00355531	−	0.00615798i
$153$		0			0
$154$	0.108277	−	0.145521i	0.00872518	−	0.0117264i
$155$	8.88877	−	10.5932i	0.713963	−	0.850868i
$156$		0			0
$157$	5.43336	−	14.9280i	0.433630	−	1.19139i	−0.509939	−	0.860211i	$-0.670332\pi$
$157$	5.43336	−	14.9280i	0.433630	−	1.19139i	0.943569	−	0.331177i	$-0.107446\pi$
$158$	−0.0234325	+	0.00413178i	−0.00186419	+	0.000328707i
$159$		0			0
$160$	0.100811	+	0.276977i	0.00796983	+	0.0218969i
$161$	18.0488	−	7.79114i	1.42244	−	0.614028i
$162$		0			0
$163$	8.71884	+	15.1015i	0.682912	+	1.18284i	0.974088	+	0.226169i	$0.0726202\pi$
$163$	8.71884	+	15.1015i	0.682912	+	1.18284i	−0.291176	+	0.956670i	$0.594046\pi$
$164$	−1.46952	+	8.33406i	−0.114750	+	0.650781i
$165$		0			0
$166$	−0.0250823	+	0.0689130i	−0.00194676	+	0.00534869i
$167$	−1.64317	−	9.31890i	−0.127153	−	0.721118i	−0.980006	−	0.198968i	$-0.936241\pi$
$167$	−1.64317	−	9.31890i	−0.127153	−	0.721118i	0.852853	−	0.522150i	$-0.174870\pi$
$168$		0			0
$169$	−5.32122	−	4.46503i	−0.409325	−	0.343464i
$170$			0.0927159i			0.00711099i
$171$		0			0
$172$	−3.49190			−0.266255
$173$	−1.42819	+	0.519819i	−0.108583	+	0.0395211i	−0.395740	−	0.918362i	$-0.629512\pi$
$173$	−1.42819	+	0.519819i	−0.108583	+	0.0395211i	0.287157	+	0.957883i	$0.407290\pi$
$174$		0			0
$175$	−5.06437	+	3.33281i	−0.382831	+	0.251937i
$176$	6.28122	−	17.2575i	0.473465	−	1.30083i
$177$		0			0
$178$	−0.0689398	+	0.0821592i	−0.00516726	+	0.00615810i
$179$		−	8.59347i		−	0.642306i	−0.947027	−	0.321153i	$-0.895930\pi$
$179$		−	8.59347i		−	0.642306i	0.947027	−	0.321153i	$-0.104070\pi$
$180$		0			0
$181$	−9.18805	−	5.30472i	−0.682942	−	0.394297i	0.118021	−	0.993011i	$-0.462345\pi$
$181$	−9.18805	−	5.30472i	−0.682942	−	0.394297i	−0.800963	+	0.598714i	$0.795678\pi$
$182$	−0.0505422	+	0.168985i	−0.00374644	+	0.0125260i
$183$		0			0
$184$	−0.339833	+	0.285154i	−0.0250528	+	0.0210218i
$185$	0.227095	+	1.28792i	0.0166964	+	0.0946898i
$186$		0			0
$187$	11.1419	−	13.2784i	0.814775	−	0.971011i
$188$	3.29682			0.240445
$189$		0			0
$190$	0.0360713			0.00261688
$191$	−6.31992	+	7.53179i	−0.457294	+	0.544981i	−0.944589	−	0.328256i	$-0.893539\pi$
$191$	−6.31992	+	7.53179i	−0.457294	+	0.544981i	0.487295	+	0.873237i	$0.337984\pi$
$192$		0			0
$193$	3.38821	+	19.2155i	0.243889	+	1.38316i	0.823059	+	0.567955i	$0.192265\pi$
$193$	3.38821	+	19.2155i	0.243889	+	1.38316i	−0.579171	+	0.815206i	$0.696623\pi$
$194$	−0.0181766	+	0.0152520i	−0.00130500	+	0.00109503i
$195$		0			0
$196$	−13.9029	+	1.63247i	−0.993066	+	0.116605i
$197$	3.74738	+	2.16355i	0.266990	+	0.154147i	0.627519	−	0.778601i	$-0.284070\pi$
$197$	3.74738	+	2.16355i	0.266990	+	0.154147i	−0.360529	+	0.932748i	$0.617404\pi$
$198$		0			0
$199$			1.69609i			0.120233i	0.998191	+	0.0601164i	$0.0191472\pi$
$199$			1.69609i			0.120233i	−0.998191	+	0.0601164i	$0.980853\pi$
$200$	0.0879404	−	0.104803i	0.00621832	−	0.00741071i
$201$		0			0
$202$	0.0117992	−	0.0324181i	0.000830191	−	0.00228093i
$203$	−9.82845	+	19.5830i	−0.689822	+	1.37445i
$204$		0			0
$205$	−6.54451	+	2.38201i	−0.457089	+	0.166367i
$206$	0.00816388			0.000568805
$207$		0			0
$208$			17.8586i			1.23827i
$209$	−5.16597	−	4.33477i	−0.357338	−	0.299842i
$210$		0			0
$211$	1.04647	+	5.93483i	0.0720420	+	0.408570i	0.999408	+	0.0344141i	$0.0109565\pi$
$211$	1.04647	+	5.93483i	0.0720420	+	0.408570i	−0.927366	+	0.374156i	$0.877932\pi$
$212$	−2.89758	+	7.96104i	−0.199007	+	0.546767i
$213$		0			0
$214$	−0.00865884	+	0.0491067i	−0.000591906	+	0.00335687i
$215$	−1.43687	−	2.48874i	−0.0979939	−	0.169730i
$216$		0			0
$217$	−17.8354	−	13.2706i	−1.21074	−	0.900868i
$218$	0.0196642	+	0.0540270i	0.00133183	+	0.00365917i
$219$		0			0
$220$	14.8860	−	2.62480i	1.00361	−	0.176964i
$221$	−5.76497	+	15.8391i	−0.387794	+	1.06546i
$222$		0			0
$223$	−0.590154	+	0.703318i	−0.0395196	+	0.0470976i	−0.785442	−	0.618935i	$-0.787564\pi$
$223$	−0.590154	+	0.703318i	−0.0395196	+	0.0470976i	0.745923	+	0.666033i	$0.232009\pi$
$224$	0.435045	−	0.187796i	0.0290676	−	0.0125477i
$225$		0			0
$226$	0.0343078	−	0.0594229i	0.00228212	−	0.00395275i
$227$	10.2102	+	8.56739i	0.677676	+	0.568638i	0.915326	−	0.402713i	$-0.131933\pi$
$227$	10.2102	+	8.56739i	0.677676	+	0.568638i	−0.237650	+	0.971351i	$0.576377\pi$
$228$		0			0
$229$	12.1287	−	2.13862i	0.801488	−	0.141324i	0.242123	−	0.970246i	$-0.422156\pi$
$229$	12.1287	−	2.13862i	0.801488	−	0.141324i	0.559365	+	0.828922i	$0.311045\pi$
$230$	−0.171526	−	0.0624303i	−0.0113101	−	0.00411653i
$231$		0			0
$232$	0.0858601	−	0.486937i	0.00563699	−	0.0319690i
$233$	−21.5947	−	12.4677i	−1.41472	−	0.816788i	−0.418891	−	0.908037i	$-0.637581\pi$
$233$	−21.5947	−	12.4677i	−1.41472	−	0.816788i	−0.995828	+	0.0912481i	$0.970914\pi$
$234$		0			0
$235$	1.35660	+	2.34970i	0.0884947	+	0.153277i
$236$	−4.01557	+	22.7734i	−0.261391	+	1.48242i
$237$		0			0
$238$	0.148797	−	0.00870590i	0.00964506	−	0.000564320i
$239$	−7.34853	−	8.75764i	−0.475337	−	0.566485i	0.474088	−	0.880477i	$-0.342778\pi$
$239$	−7.34853	−	8.75764i	−0.475337	−	0.566485i	−0.949425	+	0.313993i	$0.898333\pi$
$240$		0			0
$241$	−6.05886	−	1.06834i	−0.390286	−	0.0688179i	−0.0249379	−	0.999689i	$-0.507939\pi$
$241$	−6.05886	−	1.06834i	−0.390286	−	0.0688179i	−0.365348	+	0.930871i	$0.619050\pi$
$242$	0.130484	+	0.0753350i	0.00838784	+	0.00484272i
$243$		0			0
$244$			6.01649i			0.385166i
$245$	−6.88436	−	9.23710i	−0.439826	−	0.590137i
$246$		0			0
$247$	6.16224	+	2.24287i	0.392094	+	0.142711i
$248$	0.471412	+	0.171580i	0.0299347	+	0.0108953i
$249$		0			0
$250$	0.176403	+	0.0311046i	0.0111567	+	0.00196723i
$251$	−6.31801	+	10.9431i	−0.398789	+	0.690724i	−0.993577	−	0.113160i	$-0.963903\pi$
$251$	−6.31801	+	10.9431i	−0.398789	+	0.690724i	0.594787	+	0.803883i	$0.297236\pi$
$252$		0			0
$253$	17.0628	+	29.5536i	1.07273	+	1.85802i
$254$	0.0268747	+	0.0738376i	0.00168627	+	0.00463298i
$255$		0			0
$256$	12.2431	−	10.2731i	0.765191	−	0.642072i
$257$	2.59847	+	14.7367i	0.162088	+	0.919247i	0.952016	+	0.306048i	$0.0990068\pi$
$257$	2.59847	+	14.7367i	0.162088	+	0.919247i	−0.789928	+	0.613200i	$0.789882\pi$
$258$		0			0
$259$	2.04562	−	0.485392i	0.127109	−	0.0301608i
$260$	−12.7295	+	7.34939i	−0.789451	+	0.455790i
$261$		0			0
$262$	−0.195676	+	0.112974i	−0.0120889	+	0.00697955i
$263$	5.44968	+	14.9729i	0.336042	+	0.923267i	0.986505	+	0.163730i	$0.0523525\pi$
$263$	5.44968	+	14.9729i	0.336042	+	0.923267i	−0.650463	+	0.759538i	$0.725425\pi$
$264$		0			0
$265$	−6.86628	+	1.21071i	−0.421792	+	0.0743734i
$266$	−0.00338704	−	0.0578896i	−0.000207673	−	0.00354944i
$267$		0			0
$268$	−16.6110	−	13.9383i	−1.01468	−	0.851417i
$269$	4.94336	−	8.56215i	0.301402	−	0.522044i	−0.675052	−	0.737770i	$-0.735879\pi$
$269$	4.94336	−	8.56215i	0.301402	−	0.522044i	0.976454	+	0.215727i	$0.0692121\pi$
$270$		0			0
$271$	1.92889	−	1.11364i	0.117171	−	0.0676490i	−0.440269	−	0.897866i	$-0.645117\pi$
$271$	1.92889	−	1.11364i	0.117171	−	0.0676490i	0.557440	+	0.830217i	$0.311784\pi$
$272$	14.1812	−	5.16155i	0.859864	−	0.312965i
$273$		0			0
$274$	0.0408511	−	0.0342782i	0.00246791	−	0.00207082i
$275$	−6.76483	−	8.06201i	−0.407935	−	0.486158i
$276$		0			0
$277$	8.12965	−	2.95895i	0.488464	−	0.177786i	−0.0860344	−	0.996292i	$-0.527420\pi$
$277$	8.12965	−	2.95895i	0.488464	−	0.177786i	0.574498	+	0.818506i	$0.305197\pi$
$278$	0.0908701			0.00545003
$279$		0			0
$280$	0.208570	+	0.155189i	0.0124644	+	0.00927431i
$281$	−29.4759	−	5.19740i	−1.75839	−	0.310051i	−0.800958	−	0.598721i	$-0.795676\pi$
$281$	−29.4759	−	5.19740i	−1.75839	−	0.310051i	−0.957429	+	0.288670i	$0.906787\pi$
$282$		0			0
$283$	6.29451	+	7.50150i	0.374170	+	0.445918i	0.919965	−	0.392001i	$-0.128217\pi$
$283$	6.29451	+	7.50150i	0.374170	+	0.445918i	−0.545795	+	0.837918i	$0.683772\pi$
$284$	−9.89735	−	11.7952i	−0.587300	−	0.699917i
$285$		0			0
$286$	−0.301532	−	0.0531682i	−0.0178300	−	0.00314390i
$287$	4.43733	+	10.2794i	0.261927	+	0.606774i
$288$		0			0
$289$	−2.75614			−0.162126
$290$	0.191178	−	0.0695833i	0.0112264	−	0.00408607i
$291$		0			0
$292$	20.3460	+	24.2474i	1.19066	+	1.41897i
$293$	7.96197	−	6.68088i	0.465143	−	0.390301i	−0.379876	−	0.925037i	$-0.624033\pi$
$293$	7.96197	−	6.68088i	0.465143	−	0.390301i	0.845019	+	0.534736i	$0.179589\pi$
$294$		0			0
$295$	−17.8834	+	6.50901i	−1.04121	+	0.378969i
$296$	−0.0410875	+	0.0237219i	−0.00238816	+	0.00137881i
$297$		0			0
$298$	−0.150924	+	0.261408i	−0.00874278	+	0.0151429i
$299$	−25.4208	−	21.3306i	−1.47012	−	1.23358i
$300$		0			0
$301$	−3.85917	+	2.53968i	−0.222439	+	0.146385i
$302$	−0.281152	+	0.0495747i	−0.0161785	+	0.00285270i
$303$		0			0
$304$	−2.00811	−	5.51724i	−0.115173	−	0.316435i
$305$	−4.28805	+	2.47571i	−0.245533	+	0.141759i
$306$		0			0
$307$	−14.7821	+	8.53446i	−0.843660	+	0.487087i	−0.858507	−	0.512802i	$-0.828607\pi$
$307$	−14.7821	+	8.53446i	−0.843660	+	0.487087i	0.0148465	+	0.999890i	$0.495274\pi$
$308$	−5.61024	−	23.6436i	−0.319673	−	1.34722i
$309$		0			0
$310$	0.0358441	+	0.203282i	0.00203581	+	0.0115456i
$311$	−25.4810	+	21.3811i	−1.44489	+	1.21241i	−0.508690	+	0.860950i	$0.669870\pi$
$311$	−25.4810	+	21.3811i	−1.44489	+	1.21241i	−0.936203	+	0.351459i	$0.885686\pi$
$312$		0			0
$313$	0.334233	+	0.918298i	0.0188920	+	0.0519052i	0.948780	−	0.315937i	$-0.102319\pi$
$313$	0.334233	+	0.918298i	0.0188920	+	0.0519052i	−0.929888	+	0.367842i	$0.880097\pi$
$314$	0.118566	+	0.205362i	0.00669106	+	0.0115893i
$315$		0			0
$316$	−1.59384	+	2.76062i	−0.0896608	+	0.155297i
$317$	3.33535	+	0.588112i	0.187332	+	0.0330317i	0.266527	−	0.963827i	$-0.414124\pi$
$317$	3.33535	+	0.588112i	0.187332	+	0.0330317i	−0.0791950	+	0.996859i	$0.525235\pi$
$318$		0			0
$319$	−35.7417	−	13.0089i	−2.00115	−	0.728360i
$320$	12.3638	+	4.50007i	0.691159	+	0.251561i
$321$		0			0
$322$	−0.0840863	+	0.281138i	−0.00468595	+	0.0156672i
$323$		−	5.54159i		−	0.308343i
$324$		0			0
$325$	8.86287	+	5.11698i	0.491624	+	0.283839i
$326$	−0.256338	−	0.0451993i	−0.0141972	−	0.00250336i
$327$		0			0
$328$	−0.162405	−	0.193547i	−0.00896733	−	0.0106868i
$329$	3.64357	−	2.39779i	0.200877	−	0.132195i
$330$		0			0
$331$	1.05543	−	5.98565i	0.0580117	−	0.329001i	−0.941966	−	0.335709i	$-0.891024\pi$
$331$	1.05543	−	5.98565i	0.0580117	−	0.329001i	0.999978	+	0.00670803i	$0.00213525\pi$
$332$	4.91240	+	8.50853i	0.269603	+	0.466967i
$333$		0			0
$334$	0.122325	+	0.0706246i	0.00669335	+	0.00386441i
$335$	3.09883	−	17.5744i	0.169307	−	0.960190i
$336$		0			0
$337$	−16.0696	−	5.84885i	−0.875366	−	0.318607i	−0.135028	−	0.990842i	$-0.543112\pi$
$337$	−16.0696	−	5.84885i	−0.875366	−	0.318607i	−0.740338	+	0.672235i	$0.765335\pi$
$338$	0.102113	−	0.0180053i	0.00555422	−	0.000979359i
$339$		0			0
$340$	9.51518	+	7.98419i	0.516033	+	0.433003i
$341$	19.2954	−	33.4206i	1.04490	−	1.80983i
$342$		0			0
$343$	−14.1779	+	11.9158i	−0.765534	+	0.643395i
$344$	0.0670127	−	0.0798626i	0.00361308	−	0.00430590i
$345$		0			0
$346$	0.00775934	−	0.0213186i	0.000417144	−	0.00114610i
$347$	−20.7567	+	3.65996i	−1.11428	+	0.196477i	−0.700327	−	0.713822i	$-0.746962\pi$
$347$	−20.7567	+	3.65996i	−1.11428	+	0.196477i	−0.413950	+	0.910299i	$0.635851\pi$
$348$		0			0
$349$	−2.22508	−	6.11336i	−0.119106	−	0.327240i	0.865785	−	0.500416i	$-0.166819\pi$
$349$	−2.22508	−	6.11336i	−0.119106	−	0.327240i	−0.984891	+	0.173175i	$0.944597\pi$
$350$	0.0104823	−	0.0898878i	0.000560302	−	0.00480471i
$351$		0			0
$352$	0.411279	+	0.712357i	0.0219213	+	0.0379687i
$353$	3.31542	−	18.8027i	0.176462	−	1.00077i	−0.759980	−	0.649946i	$-0.774791\pi$
$353$	3.31542	−	18.8027i	0.176462	−	1.00077i	0.936443	−	0.350821i	$-0.114097\pi$
$354$		0			0
$355$	4.33400	−	11.9076i	0.230025	−	0.631989i
$356$	2.49506	+	14.1502i	0.132238	+	0.749959i
$357$		0			0
$358$	0.0982642	+	0.0824534i	0.00519342	+	0.00435780i
$359$			20.1016i			1.06092i	0.847710	+	0.530460i	$0.177981\pi$
$359$			20.1016i			1.06092i	−0.847710	+	0.530460i	$0.822019\pi$
$360$		0			0
$361$	16.8440			0.886528
$362$	0.148817	−	0.0541648i	0.00782162	−	0.00284684i
$363$		0			0
$364$	12.9901	+	19.7391i	0.680865	+	1.03461i
$365$	−8.90941	+	24.4784i	−0.466340	+	1.28126i
$366$		0			0
$367$	0.397490	−	0.473710i	0.0207488	−	0.0247275i	−0.755570	−	0.655068i	$-0.772640\pi$
$367$	0.397490	−	0.473710i	0.0207488	−	0.0247275i	0.776319	+	0.630340i	$0.217085\pi$
$368$			29.7110i			1.54880i
$369$		0			0
$370$	−0.0169060	−	0.00976069i	−0.000878902	−	0.000507434i
$371$	2.58777	+	10.9058i	0.134350	+	0.566201i
$372$		0			0
$373$	24.6870	−	20.7149i	1.27825	−	1.07258i	0.284764	−	0.958598i	$-0.408085\pi$
$373$	24.6870	−	20.7149i	1.27825	−	1.07258i	0.993483	−	0.113979i	$-0.0363595\pi$
$374$	0.0449298	+	0.254809i	0.00232326	+	0.0131759i
$375$		0			0
$376$	−0.0632688	+	0.0754008i	−0.00326284	+	0.00388850i
$377$	36.9866			1.90491
$378$		0			0
$379$	8.60323			0.441918			0.220959	−	0.975283i	$-0.429081\pi$
$379$	8.60323			0.441918			0.220959	+	0.975283i	$0.429081\pi$
$380$	3.10626	−	3.70190i	0.159348	−	0.189903i
$381$		0			0
$382$	−0.0254852	−	0.144534i	−0.00130393	−	0.00739498i
$383$	−9.30459	+	7.80747i	−0.475442	+	0.398943i	−0.848775	−	0.528754i	$-0.822659\pi$
$383$	−9.30459	+	7.80747i	−0.475442	+	0.398943i	0.373333	+	0.927697i	$0.378215\pi$
$384$		0			0
$385$	14.5426	−	13.7275i	0.741161	−	0.699620i
$386$	−0.252234	−	0.145627i	−0.0128384	−	0.00741224i
$387$		0			0
$388$			3.17883i			0.161380i
$389$	20.6789	−	24.6442i	1.04846	−	1.24951i	0.0809437	−	0.996719i	$-0.474207\pi$
$389$	20.6789	−	24.6442i	1.04846	−	1.24951i	0.967521	−	0.252792i	$-0.0813489\pi$
$390$		0			0
$391$	−9.59110	+	26.3513i	−0.485043	+	1.33264i
$392$	0.229473	−	0.349299i	0.0115901	−	0.0176423i
$393$		0			0
$394$	−0.0606954	+	0.0220913i	−0.00305779	+	0.00111295i
$395$	−2.62339			−0.131997
$396$		0			0
$397$		−	11.5611i		−	0.580233i	−0.956991	−	0.290116i	$-0.906306\pi$
$397$		−	11.5611i		−	0.580233i	0.956991	−	0.290116i	$-0.0936940\pi$
$398$	−0.0193944	−	0.0162738i	−0.000972153	−	0.000815733i
$399$		0			0
$400$	−1.59110	−	9.02357i	−0.0795549	−	0.451179i
$401$	0.0353788	−	0.0972024i	0.00176673	−	0.00485406i	−0.938806	−	0.344446i	$-0.888067\pi$
$401$	0.0353788	−	0.0972024i	0.00176673	−	0.00485406i	0.940573	+	0.339592i	$0.110289\pi$
$402$		0			0
$403$	−6.51641	+	36.9564i	−0.324606	+	1.84093i
$404$	−2.31090	−	4.00259i	−0.114971	−	0.199136i
$405$		0			0
$406$	−0.129623	−	0.300282i	−0.00643310	−	0.0149028i
$407$	1.24824	+	3.42952i	0.0618731	+	0.169995i
$408$		0			0
$409$	−3.57697	+	0.630716i	−0.176870	+	0.0311869i	−0.261381	−	0.965236i	$-0.584178\pi$
$409$	−3.57697	+	0.630716i	−0.176870	+	0.0311869i	0.0845117	+	0.996422i	$0.473067\pi$
$410$	0.0355563	−	0.0976900i	0.00175600	−	0.00482457i
$411$		0			0
$412$	0.703029	−	0.837837i	0.0346357	−	0.0412773i
$413$	12.1253	+	28.0892i	0.596648	+	1.38218i
$414$		0			0
$415$	−4.04278	+	7.00230i	−0.198452	+	0.343730i
$416$	−0.612739	−	0.514149i	−0.0300420	−	0.0252082i
$417$		0			0
$418$	0.0991340	−	0.0174800i	0.00484880	−	0.000854974i
$419$	−37.3388	−	13.5902i	−1.82412	−	0.663926i	−0.994392	−	0.105761i	$-0.966272\pi$
$419$	−37.3388	−	13.5902i	−1.82412	−	0.663926i	−0.829730	−	0.558165i	$-0.811506\pi$
$420$		0			0
$421$	−1.45892	+	8.27397i	−0.0711036	+	0.403249i	0.928395	+	0.371594i	$0.121189\pi$
$421$	−1.45892	+	8.27397i	−0.0711036	+	0.403249i	−0.999499	+	0.0316544i	$0.989922\pi$
$422$	−0.0779040	−	0.0449779i	−0.00379231	−	0.00218949i
$423$		0			0
$424$	−0.126468	−	0.219049i	−0.00614184	−	0.0106380i
$425$	1.50174	−	8.51682i	0.0728453	−	0.413126i
$426$		0			0
$427$	4.37583	+	6.64929i	0.211761	+	0.321782i
$428$	4.29404	+	5.11744i	0.207560	+	0.247361i
$429$		0			0
$430$	0.0422447	+	0.00744889i	0.00203722	+	0.000359217i
$431$	4.45253	+	2.57067i	0.214471	+	0.123825i	0.603387	−	0.797448i	$-0.293817\pi$
$431$	4.45253	+	2.57067i	0.214471	+	0.123825i	−0.388917	+	0.921273i	$0.627151\pi$
$432$		0			0
$433$		−	19.5889i		−	0.941384i	−0.882298	−	0.470692i	$-0.844004\pi$
$433$		−	19.5889i		−	0.941384i	0.882298	−	0.470692i	$-0.155996\pi$
$434$	0.322875	−	0.0766129i	0.0154985	−	0.00367754i
$435$		0			0
$436$	7.23802	+	2.63442i	0.346638	+	0.126166i
$437$	10.2520	+	3.73143i	0.490421	+	0.178499i
$438$		0			0
$439$	−31.6846	−	5.58684i	−1.51222	−	0.266645i	−0.644851	−	0.764309i	$-0.723080\pi$
$439$	−31.6846	−	5.58684i	−1.51222	−	0.266645i	−0.867370	+	0.497663i	$0.834192\pi$
$440$	−0.225644	+	0.390827i	−0.0107572	+	0.0186319i
$441$		0			0
$442$	−0.125802	−	0.217896i	−0.00598380	−	0.0103643i
$443$	7.92834	+	21.7829i	0.376687	+	1.03494i	0.972721	+	0.231979i	$0.0745201\pi$
$443$	7.92834	+	21.7829i	0.376687	+	1.03494i	−0.596034	+	0.802959i	$0.703258\pi$
$444$		0			0
$445$	−9.05840	+	7.60090i	−0.429409	+	0.360317i
$446$	−0.00237980	−	0.0134965i	−0.000112687	−	0.000639079i
$447$		0			0
$448$	6.06106	−	20.2649i	0.286358	−	0.957425i
$449$	16.3545	−	9.44229i	0.771817	−	0.445609i	−0.0617051	−	0.998094i	$-0.519654\pi$
$449$	16.3545	−	9.44229i	0.771817	−	0.445609i	0.833523	+	0.552485i	$0.186321\pi$
$450$		0			0
$451$	−16.8318	+	9.71787i	−0.792581	+	0.457597i
$452$	−3.14401	−	8.63809i	−0.147882	−	0.406302i
$453$		0			0
$454$	−0.195932	+	0.0345481i	−0.00919554	+	0.00162142i
$455$	−8.72312	+	17.3806i	−0.408946	+	0.814816i
$456$		0			0
$457$	−14.1005	−	11.8318i	−0.659596	−	0.553467i	0.250370	−	0.968150i	$-0.419448\pi$
$457$	−14.1005	−	11.8318i	−0.659596	−	0.553467i	−0.909966	+	0.414684i	$0.863892\pi$
$458$	−0.0919191	+	0.159209i	−0.00429510	+	0.00743933i
$459$		0			0
$460$	−21.1779	+	12.2271i	−0.987425	+	0.570090i
$461$	15.0689	−	5.48464i	0.701830	−	0.255445i	0.0336380	−	0.999434i	$-0.489291\pi$
$461$	15.0689	−	5.48464i	0.701830	−	0.255445i	0.668192	+	0.743989i	$0.267068\pi$
$462$		0			0
$463$	27.7311	−	23.2691i	1.28877	−	1.08141i	0.296802	−	0.954939i	$-0.404080\pi$
$463$	27.7311	−	23.2691i	1.28877	−	1.08141i	0.991971	−	0.126469i	$-0.0403645\pi$
$464$	−21.2860	−	25.3677i	−0.988180	−	1.17767i
$465$		0			0
$466$	0.349765	−	0.127304i	0.0162025	−	0.00589724i
$467$	10.8654			0.502793			0.251396	−	0.967884i	$-0.419110\pi$
$467$	10.8654			0.502793			0.251396	+	0.967884i	$0.419110\pi$
$468$		0			0
$469$	−28.4955	−	3.32301i	−1.31580	−	0.153442i
$470$	−0.0398846	−	0.00703274i	−0.00183974	−	0.000324396i
$471$		0			0
$472$	−0.443784	−	0.528881i	−0.0204268	−	0.0243437i
$473$	−5.15496	−	6.14344i	−0.237025	−	0.282476i
$474$		0			0
$475$	−3.31348	−	0.584256i	−0.152033	−	0.0268075i
$476$	11.9201	−	16.0203i	0.546357	−	0.734290i
$477$		0			0
$478$	0.170650			0.00780534
$479$	−11.5834	+	4.21600i	−0.529257	+	0.192634i	−0.592807	−	0.805345i	$-0.701980\pi$
$479$	−11.5834	+	4.21600i	−0.529257	+	0.192634i	0.0635495	+	0.997979i	$0.479758\pi$
$480$		0			0
$481$	−2.28123	−	2.71867i	−0.104015	−	0.123961i
$482$	0.0703504	−	0.0590310i	0.00320437	−	0.00268879i
$483$		0			0
$484$	18.9680	−	6.90379i	0.862182	−	0.313809i
$485$	−2.26560	+	1.30805i	−0.102876	+	0.0593953i
$486$		0			0
$487$	9.66499	−	16.7403i	0.437963	−	0.758574i	−0.559570	−	0.828783i	$-0.689034\pi$
$487$	9.66499	−	16.7403i	0.437963	−	0.758574i	0.997532	+	0.0702097i	$0.0223669\pi$
$488$	−0.137602	−	0.115462i	−0.00622894	−	0.00522670i
$489$		0			0
$490$	0.171679	+	0.00990806i	0.00775565	+	0.000447600i
$491$	32.7847	−	5.78082i	1.47955	−	0.260885i	0.625153	−	0.780502i	$-0.285037\pi$
$491$	32.7847	−	5.78082i	1.47955	−	0.260885i	0.854399	+	0.519617i	$0.173926\pi$
$492$		0			0
$493$	−10.6900	−	29.3706i	−0.481454	−	1.32278i
$494$	−0.0847727	+	0.0489436i	−0.00381411	+	0.00220207i
$495$		0			0
$496$	29.0973	−	16.7993i	1.30651	−	0.754311i
$497$	−19.5170	−	5.83740i	−0.875459	−	0.261843i
$498$		0			0
$499$	−3.49591	−	19.8263i	−0.156498	−	0.887546i	−0.957403	−	0.288755i	$-0.906759\pi$
$499$	−3.49591	−	19.8263i	−0.156498	−	0.887546i	0.800905	−	0.598792i	$-0.204352\pi$
$500$	18.3831	−	15.4252i	0.822115	−	0.689837i
$501$		0			0
$502$	−0.0645112	−	0.177243i	−0.00287927	−	0.00791074i
$503$	5.39577	+	9.34574i	0.240585	+	0.416706i	0.960881	−	0.276961i	$-0.0893273\pi$
$503$	5.39577	+	9.34574i	0.240585	+	0.416706i	−0.720296	+	0.693667i	$0.755994\pi$
$504$		0			0
$505$	1.90181	−	3.29403i	0.0846294	−	0.146582i
$506$	−0.501654	−	0.0884552i	−0.0223013	−	0.00393231i
$507$		0			0
$508$	9.89205	+	3.60041i	0.438889	+	0.159742i
$509$	32.3031	+	11.7574i	1.43181	+	0.521136i	0.937449	−	0.348122i	$-0.113180\pi$
$509$	32.3031	+	11.7574i	1.43181	+	0.521136i	0.494360	+	0.869258i	$0.335403\pi$
$510$		0			0
$511$	40.1212	+	11.9999i	1.77486	+	0.530846i
$512$			1.19363i			0.0527514i
$513$		0			0
$514$	−0.193442	−	0.111684i	−0.00853237	−	0.00492616i
$515$	0.886427	+	0.156301i	0.0390607	+	0.00688745i
$516$		0			0
$517$	4.86697	+	5.80022i	0.214049	+	0.255094i
$518$	−0.0140772	+	0.0280484i	−0.000618515	+	0.00123238i
$519$		0			0
$520$	0.0762041	−	0.432175i	0.00334177	−	0.0189521i
$521$	−16.4187	−	28.4380i	−0.719317	−	1.24589i	−0.961271	−	0.275605i	$-0.911122\pi$
$521$	−16.4187	−	28.4380i	−0.719317	−	1.24589i	0.241954	−	0.970288i	$-0.422212\pi$
$522$		0			0
$523$	2.01194	+	1.16159i	0.0879760	+	0.0507929i	0.543343	−	0.839511i	$-0.317158\pi$
$523$	2.01194	+	1.16159i	0.0879760	+	0.0507929i	−0.455367	+	0.890304i	$0.650492\pi$
$524$	−5.25638	+	29.8104i	−0.229626	+	1.30227i
$525$		0			0
$526$	−0.223500	−	0.0813475i	−0.00974508	−	0.00354692i
$527$	31.2300	−	5.50669i	1.36040	−	0.239875i
$528$		0			0
$529$	−24.6732	−	20.7032i	−1.07275	−	0.900141i
$530$	0.0520371	−	0.0901309i	0.00226035	−	0.00391504i
$531$		0			0
$532$	−6.23273	−	4.63753i	−0.270223	−	0.201063i
$533$	12.1485	−	14.4780i	0.526210	−	0.627113i
$534$		0			0
$535$	−1.88034	+	5.16619i	−0.0812941	+	0.223354i
$536$	0.637559	−	0.112419i	0.0275384	−	0.00485576i
$537$		0			0
$538$	0.0504750	+	0.138679i	0.00217613	+	0.00597888i
$539$	−23.3964	−	22.0500i	−1.00776	−	0.949761i
$540$		0			0
$541$	9.54866	+	16.5388i	0.410529	+	0.711057i	0.994948	−	0.100395i	$-0.0320108\pi$
$541$	9.54866	+	16.5388i	0.410529	+	0.711057i	−0.584419	+	0.811452i	$0.698677\pi$
$542$	−0.00577323	+	0.0327416i	−0.000247982	+	0.00140637i
$543$		0			0
$544$	−0.231183	+	0.635169i	−0.00991187	+	0.0272326i
$545$	1.10075	+	6.24269i	0.0471511	+	0.267407i
$546$		0			0
$547$	18.5854	+	15.5950i	0.794655	+	0.666795i	0.946893	−	0.321549i	$-0.104204\pi$
$547$	18.5854	+	15.5950i	0.794655	+	0.666795i	−0.152238	+	0.988344i	$0.548648\pi$
$548$		−	7.14428i		−	0.305189i
$549$		0			0
$550$	0.157095			0.00669855
$551$	−11.4267	+	4.15896i	−0.486792	+	0.177178i
$552$		0			0
$553$	0.246332	+	4.21019i	0.0104751	+	0.179035i
$554$	−0.0441683	+	0.121351i	−0.00187653	+	0.00515573i
$555$		0			0
$556$	7.82524	−	9.32575i	0.331864	−	0.395500i
$557$			16.5691i			0.702055i	0.936365	+	0.351028i	$0.114168\pi$
$557$			16.5691i			0.702055i	−0.936365	+	0.351028i	$0.885832\pi$
$558$		0			0
$559$	6.75372	+	3.89926i	0.285652	+	0.164921i
$560$	16.9409	−	4.01980i	0.715885	−	0.169868i
$561$		0			0
$562$	0.342250	−	0.287181i	0.0144369	−	0.0121140i
$563$	−6.89101	−	39.0809i	−0.290422	−	1.64706i	−0.685250	−	0.728308i	$-0.740307\pi$
$563$	−6.89101	−	39.0809i	−0.290422	−	1.64706i	0.394829	−	0.918755i	$-0.370804\pi$
$564$		0			0
$565$	4.86279	−	5.79525i	0.204579	−	0.243808i
$566$	−0.146173			−0.00614411
$567$		0			0
$568$	0.459704			0.0192888
$569$	−4.54173	+	5.41262i	−0.190399	+	0.226909i	−0.852796	−	0.522244i	$-0.825095\pi$
$569$	−4.54173	+	5.41262i	−0.190399	+	0.226909i	0.662397	+	0.749153i	$0.269539\pi$
$570$		0			0
$571$	−3.80649	−	21.5877i	−0.159297	−	0.903417i	−0.954752	−	0.297404i	$-0.903879\pi$
$571$	−3.80649	−	21.5877i	−0.159297	−	0.903417i	0.795455	−	0.606013i	$-0.207232\pi$
$572$	−31.4228	+	26.3668i	−1.31385	+	1.10245i
$573$		0			0
$574$	−0.160118	−	0.0478901i	−0.00668321	−	0.00199889i
$575$	14.7450	+	8.51305i	0.614910	+	0.355019i
$576$		0			0
$577$			4.42356i			0.184155i	0.995752	+	0.0920775i	$0.0293508\pi$
$577$			4.42356i			0.184155i	−0.995752	+	0.0920775i	$0.970649\pi$
$578$	0.0264449	−	0.0315158i	0.00109996	−	0.00131088i
$579$		0			0
$580$	9.32210	−	25.6122i	0.387079	−	1.06349i
$581$	11.6174	+	5.83062i	0.481970	+	0.241895i
$582$		0			0
$583$	−18.2838	+	6.65475i	−0.757236	+	0.275611i
$584$	−0.945014			−0.0391050
$585$		0			0
$586$			0.155146i			0.00640900i
$587$	−28.2005	−	23.6630i	−1.16396	−	0.976677i	−0.164007	−	0.986459i	$-0.552442\pi$
$587$	−28.2005	−	23.6630i	−1.16396	−	0.976677i	−0.999952	+	0.00978187i	$0.996886\pi$
$588$		0			0
$589$	−2.14239	−	12.1501i	−0.0882755	−	0.500635i
$590$	0.0971600	−	0.266945i	0.00400001	−	0.0109899i
$591$		0			0
$592$	−0.551766	+	3.12922i	−0.0226775	+	0.128610i
$593$	−15.9700	−	27.6608i	−0.655809	−	1.13589i	−0.981690	−	0.190484i	$-0.938994\pi$
$593$	−15.9700	−	27.6608i	−0.655809	−	1.13589i	0.325882	−	0.945411i	$-0.394339\pi$
$594$		0			0
$595$	16.3229	+	1.90350i	0.669174	+	0.0780359i
$596$	13.8308	+	37.9999i	0.566533	+	1.55654i
$597$		0			0
$598$	0.487819	−	0.0860157i	0.0199484	−	0.00351744i
$599$	13.1453	−	36.1165i	0.537104	−	1.47568i	−0.313353	−	0.949637i	$-0.601452\pi$
$599$	13.1453	−	36.1165i	0.537104	−	1.47568i	0.850457	−	0.526044i	$-0.176325\pi$
$600$		0			0
$601$	11.7434	−	13.9953i	0.479025	−	0.570880i	−0.471366	−	0.881938i	$-0.656239\pi$
$601$	11.7434	−	13.9953i	0.479025	−	0.570880i	0.950391	+	0.311058i	$0.100683\pi$
$602$	0.00798775	−	0.0684967i	0.000325557	−	0.00279172i
$603$		0			0
$604$	−19.1235	+	33.1229i	−0.778126	+	1.34775i
$605$	12.7255	+	10.6780i	0.517366	+	0.434122i
$606$		0			0
$607$	19.1650	−	3.37930i	0.777883	−	0.137162i	0.229410	−	0.973330i	$-0.426320\pi$
$607$	19.1650	−	3.37930i	0.777883	−	0.137162i	0.548473	+	0.836168i	$0.315209\pi$
$608$	0.247113	+	0.0899419i	0.0100218	+	0.00364763i
$609$		0			0
$610$	0.0128343	−	0.0727870i	0.000519646	−	0.00294706i
$611$	−6.37641	−	3.68142i	−0.257962	−	0.148934i
$612$		0			0
$613$	−13.2018	−	22.8662i	−0.533217	−	0.923559i	−0.999247	−	0.0387902i	$-0.987650\pi$
$613$	−13.2018	−	22.8662i	−0.533217	−	0.923559i	0.466030	−	0.884769i	$-0.345684\pi$
$614$	0.0442435	−	0.250917i	0.00178552	−	0.0101262i
$615$		0			0
$616$	0.648413	+	0.325430i	0.0261253	+	0.0131120i
$617$	−16.7822	−	20.0003i	−0.675628	−	0.805182i	0.313910	−	0.949453i	$-0.398361\pi$
$617$	−16.7822	−	20.0003i	−0.675628	−	0.805182i	−0.989538	+	0.144271i	$0.953916\pi$
$618$		0			0
$619$	−27.6159	−	4.86943i	−1.10998	−	0.195719i	−0.411541	−	0.911391i	$-0.635009\pi$
$619$	−27.6159	−	4.86943i	−1.10998	−	0.195719i	−0.698436	+	0.715672i	$0.746120\pi$
$620$	23.9489	+	13.8269i	0.961813	+	0.555303i
$621$		0			0
$622$		−	0.496518i		−	0.0199085i
$623$	13.0490	+	13.8238i	0.522797	+	0.553839i
$624$		0			0
$625$	7.79185	+	2.83600i	0.311674	+	0.113440i
$626$	−0.0137074	−	0.00498910i	−0.000547859	−	0.000199405i
$627$		0			0
$628$	31.2860	+	5.51657i	1.24845	+	0.220135i
$629$	−1.49953	+	2.59725i	−0.0597900	+	0.103559i
$630$		0			0
$631$	−19.6263	−	33.9938i	−0.781312	−	1.35327i	−0.931178	−	0.364565i	$-0.881218\pi$
$631$	−19.6263	−	33.9938i	−0.781312	−	1.35327i	0.149866	−	0.988706i	$-0.452116\pi$
$632$	−0.0325503	−	0.0894312i	−0.00129478	−	0.00355738i
$633$		0			0
$634$	−0.0387273	+	0.0324960i	−0.00153806	+	0.00129058i
$635$	1.50438	+	8.53175i	0.0596994	+	0.338572i
$636$		0			0
$637$	28.7127	+	12.3674i	1.13764	+	0.490016i
$638$	0.491692	−	0.283879i	0.0194663	−	0.0112389i
$639$		0			0
$640$	−0.680613	+	0.392952i	−0.0269036	+	0.0155328i
$641$	−10.2351	−	28.1208i	−0.404263	−	1.11070i	−0.960160	−	0.279452i	$-0.909847\pi$
$641$	−10.2351	−	28.1208i	−0.404263	−	1.11070i	0.555897	−	0.831251i	$-0.312375\pi$
$642$		0			0
$643$	1.69315	−	0.298548i	0.0667714	−	0.0117736i	−0.140163	−	0.990128i	$-0.544763\pi$
$643$	1.69315	−	0.298548i	0.0667714	−	0.0117736i	0.206934	+	0.978355i	$0.433651\pi$
$644$	21.6114	+	32.8396i	0.851609	+	1.29406i
$645$		0			0
$646$	0.0633668	+	0.0531710i	0.00249313	+	0.00209199i
$647$	−23.2767	+	40.3164i	−0.915102	+	1.58500i	−0.108350	+	0.994113i	$0.534557\pi$
$647$	−23.2767	+	40.3164i	−0.915102	+	1.58500i	−0.806752	+	0.590890i	$0.798777\pi$
$648$		0			0
$649$	−45.9942	+	26.5548i	−1.80543	+	1.04237i
$650$	−0.143550	+	0.0522479i	−0.00563049	+	0.00204933i
$651$		0			0
$652$	−26.7131	+	22.4150i	−1.04617	+	0.877837i
$653$	12.3612	+	14.7315i	0.483730	+	0.576487i	0.951611	−	0.307305i	$-0.0994271\pi$
$653$	12.3612	+	14.7315i	0.483730	+	0.576487i	−0.467882	+	0.883791i	$0.654983\pi$
$654$		0			0
$655$	−23.4093	+	8.52029i	−0.914677	+	0.332915i
$656$	−16.9215			−0.660673
$657$		0			0
$658$	−0.00754150	+	0.0646699i	−0.000293998	+	0.00252110i
$659$	−20.4588	−	3.60744i	−0.796962	−	0.140526i	−0.239683	−	0.970851i	$-0.577043\pi$
$659$	−20.4588	−	3.60744i	−0.796962	−	0.140526i	−0.557279	+	0.830325i	$0.688155\pi$
$660$		0			0
$661$	9.07299	+	10.8128i	0.352898	+	0.420568i	0.913066	−	0.407811i	$-0.133708\pi$
$661$	9.07299	+	10.8128i	0.352898	+	0.420568i	−0.560168	+	0.828379i	$0.689263\pi$
$662$	0.0583176	+	0.0695003i	0.00226658	+	0.00270120i
$663$		0			0
$664$	−0.288870	−	0.0509356i	−0.0112103	−	0.00197668i
$665$	0.740559	−	6.35045i	0.0287177	−	0.246260i
$666$		0			0
$667$	61.5341			2.38261
$668$	17.7820	−	6.47212i	0.688006	−	0.250414i
$669$		0			0
$670$	0.171226	+	0.204059i	0.00661502	+	0.00788347i
$671$	−10.5850	+	8.88191i	−0.408631	+	0.342882i
$672$		0			0
$673$	−6.36430	+	2.31642i	−0.245326	+	0.0892913i	−0.461757	−	0.887007i	$-0.652781\pi$
$673$	−6.36430	+	2.31642i	−0.245326	+	0.0892913i	0.216431	+	0.976298i	$0.430558\pi$
$674$	0.221066	−	0.127633i	0.00851515	−	0.00491623i
$675$		0			0
$676$	6.94558	−	12.0301i	0.267138	−	0.462696i
$677$	−24.1811	−	20.2904i	−0.929356	−	0.779823i	0.0463453	−	0.998925i	$-0.485243\pi$
$677$	−24.1811	−	20.2904i	−0.929356	−	0.779823i	−0.975702	+	0.219103i	$0.929687\pi$
$678$		0			0
$679$	2.31198	+	3.51317i	0.0887255	+	0.134823i
$680$	−0.365209	+	0.0643962i	−0.0140051	+	0.00246948i
$681$		0			0
$682$	0.197019	+	0.541306i	0.00754425	+	0.0207277i
$683$	21.2271	−	12.2555i	0.812233	−	0.468943i	−0.0354979	−	0.999370i	$-0.511302\pi$
$683$	21.2271	−	12.2555i	0.812233	−	0.468943i	0.847731	+	0.530427i	$0.177968\pi$
$684$		0			0
$685$	5.09185	−	2.93978i	0.194550	−	0.112323i
$686$	−0.000219288	−	0.276452i	−8.37245e−6	−	0.0105550i
$687$		0			0
$688$	−1.21246	−	6.87618i	−0.0462244	−	0.262152i
$689$	14.4940	−	12.1619i	0.552178	−	0.463332i
$690$		0			0
$691$	−9.24106	−	25.3896i	−0.351547	−	0.965866i	−0.981874	−	0.189537i	$-0.939301\pi$
$691$	−9.24106	−	25.3896i	−0.351547	−	0.965866i	0.630327	−	0.776330i	$-0.282921\pi$
$692$	−1.51968	−	2.63216i	−0.0577695	−	0.100060i
$693$		0			0
$694$	0.157307	−	0.272465i	0.00597131	−	0.0103426i
$695$	9.86660	+	1.73975i	0.374261	+	0.0659924i
$696$		0			0
$697$	−15.0080	−	5.46247i	−0.568469	−	0.206906i
$698$	0.0912541	+	0.0332138i	0.00345402	+	0.00125716i
$699$		0			0
$700$	−8.32226	−	8.81641i	−0.314552	−	0.333229i
$701$			28.6921i			1.08369i	0.840479	+	0.541843i	$0.182273\pi$
$701$			28.6921i			1.08369i	−0.840479	+	0.541843i	$0.817727\pi$
$702$		0			0
$703$	1.01047	+	0.583393i	0.0381104	+	0.0220031i
$704$	36.1600	+	6.37598i	1.36283	+	0.240304i
$705$		0			0
$706$	0.183193	+	0.218321i	0.00689457	+	0.00821662i
$707$	−5.46506	−	2.74285i	−0.205535	−	0.103155i
$708$		0			0
$709$	−6.60874	+	37.4800i	−0.248196	+	1.40759i	0.564754	+	0.825259i	$0.308971\pi$
$709$	−6.60874	+	37.4800i	−0.248196	+	1.40759i	−0.812950	+	0.582333i	$0.802140\pi$
$710$	0.0945759	+	0.163810i	0.00354937	+	0.00614769i
$711$		0			0
$712$	−0.371509	−	0.214491i	−0.0139229	−	0.00803838i
$713$	−10.8413	+	61.4838i	−0.406008	+	2.30259i
$714$		0			0
$715$	−31.7221	−	11.5459i	−1.18634	−	0.431793i
$716$	16.9239	−	2.98415i	0.632477	−	0.111523i
$717$		0			0
$718$	−0.229857	−	0.192873i	−0.00857817	−	0.00719794i
$719$	6.16159	−	10.6722i	0.229789	−	0.398005i	−0.727957	−	0.685623i	$-0.759530\pi$
$719$	6.16159	−	10.6722i	0.229789	−	0.398005i	0.957745	+	0.287618i	$0.0928632\pi$
$720$		0			0
$721$	0.167608	−	1.43728i	0.00624205	−	0.0535269i
$722$	−0.161617	+	0.192607i	−0.00601475	+	0.00716810i
$723$		0			0
$724$	7.25648	−	19.9370i	0.269685	−	0.740953i
$725$	−18.6886	+	3.29530i	−0.694076	+	0.122384i
$726$		0			0
$727$	9.28805	+	25.5187i	0.344475	+	0.946437i	0.984079	+	0.177732i	$0.0568761\pi$
$727$	9.28805	+	25.5187i	0.344475	+	0.946437i	−0.639604	+	0.768705i	$0.720902\pi$
$728$	−0.700739	−	0.0817168i	−0.0259711	−	0.00302863i
$729$		0			0
$730$	−0.194420	−	0.336745i	−0.00719579	−	0.0124635i
$731$	1.14437	−	6.49002i	0.0423259	−	0.240042i
$732$		0			0
$733$	−15.7087	+	43.1594i	−0.580216	+	1.59413i	0.207597	+	0.978214i	$0.433436\pi$
$733$	−15.7087	+	43.1594i	−0.580216	+	1.59413i	−0.787813	+	0.615915i	$0.788786\pi$
$734$	0.00160288	+	0.00909040i	5.91635e−5	+	0.000335533i
$735$		0			0
$736$	−1.01940	−	0.855382i	−0.0375757	−	0.0315298i
$737$		−	49.8010i		−	1.83444i
$738$		0			0
$739$	27.6265			1.01626			0.508129	−	0.861281i	$-0.330337\pi$
$739$	27.6265			1.01626			0.508129	+	0.861281i	$0.330337\pi$
$740$	−2.45757	+	0.894481i	−0.0903419	+	0.0328818i
$741$		0			0
$742$	−0.149534	−	0.0750495i	−0.00548958	−	0.00275515i
$743$	−3.93643	+	10.8153i	−0.144414	+	0.396773i	−0.990719	−	0.135925i	$-0.956600\pi$
$743$	−3.93643	+	10.8153i	−0.144414	+	0.396773i	0.846306	+	0.532698i	$0.178822\pi$
$744$		0			0
$745$	−21.3919	+	25.4939i	−0.783740	+	0.934025i
$746$			0.481047i			0.0176124i
$747$		0			0
$748$	30.0195	+	17.3318i	1.09762	+	0.633712i
$749$	8.46761	+	2.53260i	0.309400	+	0.0925391i
$750$		0			0
$751$	−8.89746	+	7.46586i	−0.324673	+	0.272433i	−0.790525	−	0.612430i	$-0.790192\pi$
$751$	−8.89746	+	7.46586i	−0.324673	+	0.272433i	0.465852	+	0.884863i	$0.345748\pi$
$752$	1.14472	+	6.49202i	0.0417436	+	0.236740i
$753$		0			0
$754$	−0.354883	+	0.422933i	−0.0129241	+	0.0154023i
$755$	−31.4764			−1.14554
$756$		0			0
$757$	25.0813			0.911595			0.455798	−	0.890083i	$-0.349354\pi$
$757$	25.0813			0.911595			0.455798	+	0.890083i	$0.349354\pi$
$758$	−0.0825471	+	0.0983759i	−0.00299825	+	0.00357317i
$759$		0			0
$760$	0.0250534	+	0.142085i	0.000908784	+	0.00515397i
$761$	19.9698	−	16.7566i	0.723904	−	0.607428i	−0.204558	−	0.978854i	$-0.565576\pi$
$761$	19.9698	−	16.7566i	0.723904	−	0.607428i	0.928462	+	0.371427i	$0.121131\pi$
$762$		0			0
$763$	9.91533	−	2.35274i	0.358959	−	0.0851751i
$764$	−17.0277	−	9.83096i	−0.616041	−	0.355672i
$765$		0			0
$766$		−	0.181308i		−	0.00655091i
$767$	33.1967	−	39.5623i	1.19866	−	1.42851i
$768$		0			0
$769$	−3.57920	+	9.83378i	−0.129069	+	0.354615i	−0.987348	−	0.158569i	$-0.949312\pi$
$769$	−3.57920	+	9.83378i	−0.129069	+	0.354615i	0.858279	+	0.513184i	$0.171534\pi$
$770$	0.0174359	+	0.298006i	0.000628347	+	0.0107394i
$771$		0			0
$772$	−36.6663	+	13.3455i	−1.31965	+	0.480314i
$773$	−28.1877			−1.01384			−0.506921	−	0.861993i	$-0.669216\pi$
$773$	−28.1877			−1.01384			−0.506921	+	0.861993i	$0.669216\pi$
$774$		0			0
$775$		−	19.2539i		−	0.691620i
$776$	−0.0727022	−	0.0610044i	−0.00260986	−	0.00218993i
$777$		0			0
$778$	0.0833881	+	0.472917i	0.00298961	+	0.0169549i
$779$	−2.12518	+	5.83889i	−0.0761426	+	0.209200i
$780$		0			0
$781$	6.14069	−	34.8256i	0.219731	−	1.24616i
$782$	−0.209295	−	0.362510i	−0.00748439	−	0.0129633i
$783$		0			0
$784$	−8.04199	−	26.8105i	−0.287214	−	0.957518i
$785$	8.94204	+	24.5680i	0.319155	+	0.876871i
$786$		0			0
$787$	−34.6191	+	6.10428i	−1.23404	+	0.217594i	−0.752359	−	0.658754i	$-0.771084\pi$
$787$	−34.6191	+	6.10428i	−1.23404	+	0.217594i	−0.481679	+	0.876348i	$0.659973\pi$
$788$	−2.95958	+	8.13139i	−0.105431	+	0.289669i
$789$		0			0
$790$	0.0251711	−	0.0299978i	0.000895548	−	0.00106727i
$791$	−9.75722	−	7.25997i	−0.346927	−	0.258135i
$792$		0			0
$793$	6.71836	−	11.6365i	0.238576	−	0.413226i
$794$	0.132198	+	0.110927i	0.00469153	+	0.00393666i
$795$		0			0
$796$	−3.34028	+	0.588981i	−0.118393	+	0.0208759i
$797$	−3.03842	−	1.10589i	−0.107626	−	0.0391728i	0.287646	−	0.957737i	$-0.407127\pi$
$797$	−3.03842	−	1.10589i	−0.107626	−	0.0391728i	−0.395272	+	0.918564i	$0.629350\pi$
$798$		0			0
$799$	−1.08043	+	6.12744i	−0.0382229	+	0.216773i
$800$	0.355412	+	0.205197i	0.0125657	+	0.00725482i
$801$		0			0
$802$	0.000772030		0.00133719i	2.72613e−5		4.72180e-5i
$803$	−12.6234	+	71.5910i	−0.445471	+	2.52639i
$804$		0			0
$805$	−14.5125	+	28.9159i	−0.511499	+	1.01915i
$806$	−0.360063	−	0.429107i	−0.0126827	−	0.0151146i
$807$		0			0
$808$	0.135891	+	0.0239612i	0.00478061	+	0.000842951i
$809$	−6.10355	−	3.52388i	−0.214589	−	0.123893i	0.388853	−	0.921300i	$-0.372871\pi$
$809$	−6.10355	−	3.52388i	−0.214589	−	0.123893i	−0.603442	+	0.797407i	$0.706205\pi$
$810$		0			0
$811$			27.1164i			0.952186i	0.879395	+	0.476093i	$0.157947\pi$
$811$			27.1164i			0.952186i	−0.879395	+	0.476093i	$0.842053\pi$
$812$	−41.9796	−	12.5558i	−1.47320	−	0.440621i
$813$		0			0
$814$	−0.0511925	−	0.0186325i	−0.00179429	−	0.000653070i
$815$	−26.9676	−	9.81540i	−0.944634	−	0.343819i
$816$		0			0
$817$	−2.52495	−	0.445217i	−0.0883369	−	0.0155762i
$818$	0.0271086	−	0.0469534i	0.000947829	−	0.00164169i
$819$		0			0
$820$	−6.96375	−	12.0616i	−0.243185	−	0.421208i
$821$	13.1798	+	36.2112i	0.459978	+	1.26378i	0.925502	+	0.378743i	$0.123644\pi$
$821$	13.1798	+	36.2112i	0.459978	+	1.26378i	−0.465524	+	0.885035i	$0.654134\pi$
$822$		0			0
$823$	24.4459	−	20.5125i	0.852130	−	0.715022i	−0.108128	−	0.994137i	$-0.534486\pi$
$823$	24.4459	−	20.5125i	0.852130	−	0.715022i	0.960258	+	0.279115i	$0.0900412\pi$
$824$	0.00567026	+	0.0321576i	0.000197533	+	0.00112026i
$825$		0			0
$826$	−0.437535	−	0.130863i	−0.0152238	−	0.00455331i
$827$	−19.5503	+	11.2874i	−0.679831	+	0.392501i	−0.799791	−	0.600278i	$-0.795057\pi$
$827$	−19.5503	+	11.2874i	−0.679831	+	0.392501i	0.119960	+	0.992779i	$0.461723\pi$
$828$		0			0
$829$	−28.8216	+	16.6401i	−1.00101	+	0.577936i	−0.908548	−	0.417780i	$-0.862808\pi$
$829$	−28.8216	+	16.6401i	−1.00101	+	0.577936i	−0.0924662	+	0.995716i	$0.529475\pi$
$830$	−0.0412795	−	0.113415i	−0.00143283	−	0.00393668i
$831$		0			0
$832$	−35.1628	+	6.20014i	−1.21905	+	0.214951i
$833$	1.52217	−	26.3748i	0.0527399	−	0.913834i
$834$		0			0
$835$	11.9298	+	10.0103i	0.412849	+	0.346422i
$836$	6.74295	−	11.6791i	0.233210	−	0.403931i
$837$		0			0
$838$	0.513663	−	0.296564i	0.0177442	−	0.0102446i
$839$	28.7046	−	10.4476i	0.990993	−	0.360692i	0.204888	−	0.978785i	$-0.434317\pi$
$839$	28.7046	−	10.4476i	0.990993	−	0.360692i	0.786105	+	0.618093i	$0.212095\pi$
$840$		0			0
$841$	−30.3234	+	25.4443i	−1.04563	+	0.877391i
$842$	−0.0806126	−	0.0960703i	−0.00277809	−	0.00331080i
$843$		0			0
$844$	−11.3246	+	4.12183i	−0.389810	+	0.141879i
$845$	11.4321			0.393275
$846$		0			0
$847$	15.9418	−	21.4254i	0.547768	−	0.736187i
$848$	−16.6828	−	2.94163i	−0.572890	−	0.101016i
$849$		0			0
$850$	0.0829786	+	0.0988901i	0.00284614	+	0.00339190i
$851$	−3.79525	−	4.52301i	−0.130100	−	0.155047i
$852$		0			0
$853$	39.5220	+	6.96880i	1.35321	+	0.238607i	0.802780	−	0.596275i	$-0.203353\pi$
$853$	39.5220	+	6.96880i	1.35321	+	0.238607i	0.550429	+	0.834882i	$0.314464\pi$
$854$	−0.118019	−	0.0137628i	−0.00403851	−	0.000470952i
$855$		0			0
$856$	−0.199446			−0.00681693
$857$	−28.0069	+	10.1937i	−0.956698	+	0.348209i	−0.772739	−	0.634724i	$-0.781114\pi$
$857$	−28.0069	+	10.1937i	−0.956698	+	0.348209i	−0.183959	+	0.982934i	$0.558891\pi$
$858$		0			0
$859$	31.5023	+	37.5429i	1.07484	+	1.28095i	0.957680	+	0.287835i	$0.0929356\pi$
$859$	31.5023	+	37.5429i	1.07484	+	1.28095i	0.117163	+	0.993113i	$0.462620\pi$
$860$	4.40234	−	3.69401i	0.150119	−	0.125965i
$861$		0			0
$862$	−0.0721165	+	0.0262483i	−0.00245630	+	0.000894019i
$863$	−16.1553	+	9.32725i	−0.549932	+	0.317503i	−0.749095	−	0.662463i	$-0.769511\pi$
$863$	−16.1553	+	9.32725i	−0.549932	+	0.317503i	0.199163	+	0.979966i	$0.436178\pi$
$864$		0			0
$865$	1.25066	−	2.16620i	0.0425236	−	0.0736530i
$866$	0.223995	+	0.187954i	0.00761165	+	0.00638693i
$867$		0			0
$868$	19.9416	−	39.7332i	0.676863	−	1.34863i
$869$	−7.20980	+	1.27128i	−0.244576	+	0.0431253i
$870$		0			0
$871$	16.5632	+	45.5070i	0.561222	+	1.54195i
$872$	−0.199155	+	0.114982i	−0.00674424	+	0.00389379i
$873$		0			0
$874$	−0.141035	+	0.0814267i	−0.00477059	+	0.00275430i
$875$	9.09770	−	30.4177i	0.307558	−	1.02831i
$876$		0			0
$877$	−0.106352	−	0.603150i	−0.00359124	−	0.0203669i	0.982959	−	0.183822i	$-0.0588471\pi$
$877$	−0.106352	−	0.603150i	−0.00359124	−	0.0203669i	−0.986551	+	0.163455i	$0.947736\pi$
$878$	0.367894	−	0.308700i	0.0124158	−	0.0104181i
$879$		0			0
$880$	10.3374	+	28.4018i	0.348474	+	0.957424i
$881$	24.2819	+	42.0575i	0.818079	+	1.41695i	0.907096	+	0.420924i	$0.138294\pi$
$881$	24.2819	+	42.0575i	0.818079	+	1.41695i	−0.0890174	+	0.996030i	$0.528373\pi$
$882$		0			0
$883$	−10.4471	+	18.0949i	−0.351573	+	0.608943i	−0.986525	−	0.163609i	$-0.947686\pi$
$883$	−10.4471	+	18.0949i	−0.351573	+	0.608943i	0.634952	+	0.772551i	$0.281020\pi$
$884$	−33.1955	−	5.85326i	−1.11648	−	0.196866i
$885$		0			0
$886$	−0.325154	−	0.118346i	−0.0109238	−	0.00397592i
$887$	−10.6701	−	3.88359i	−0.358266	−	0.130398i	0.156615	−	0.987660i	$-0.449942\pi$
$887$	−10.6701	−	3.88359i	−0.358266	−	0.130398i	−0.514881	+	0.857261i	$0.672164\pi$
$888$		0			0
$889$	13.5511	−	3.21545i	0.454488	−	0.107843i
$890$		−	0.176510i		−	0.00591664i
$891$		0			0
$892$	−1.59005	−	0.918014i	−0.0532387	−	0.0307374i
$893$	2.38389	+	0.420344i	0.0797738	+	0.0140663i
$894$		0			0
$895$	9.09083	+	10.8340i	0.303873	+	0.362142i
$896$	0.694545	+	1.05540i	0.0232031	+	0.0352583i
$897$		0			0
$898$	−0.0489497	+	0.277608i	−0.00163347	+	0.00926389i
$899$	−34.7928	−	60.2629i	−1.16040	−	2.00988i
$900$		0			0
$901$	−13.8467	−	7.99441i	−0.461301	−	0.266332i
$902$	0.0503784	−	0.285710i	0.00167742	−	0.00951310i
$903$		0			0
$904$	0.257896	+	0.0938665i	0.00857750	+	0.00312195i
$905$	17.1954	−	3.03201i	0.571594	−	0.100787i
$906$		0			0
$907$	31.2356	+	26.2098i	1.03716	+	0.870281i	0.991686	−	0.128685i	$-0.0410755\pi$
$907$	31.2356	+	26.2098i	1.03716	+	0.870281i	0.0454747	+	0.998965i	$0.485520\pi$
$908$	−13.3270	+	23.0831i	−0.442272	+	0.766038i
$909$		0			0
$910$	−0.115046	−	0.266512i	−0.00381373	−	0.00883479i
$911$	22.9670	−	27.3710i	0.760931	−	0.906843i	−0.236975	−	0.971516i	$-0.576156\pi$
$911$	22.9670	−	27.3710i	0.760931	−	0.906843i	0.997907	+	0.0646730i	$0.0206004\pi$
$912$		0			0
$913$	−7.71741	+	21.2034i	−0.255409	+	0.701730i
$914$	0.270587	−	0.0477117i	0.00895021	−	0.00157816i
$915$		0			0
$916$	8.42357	+	23.1436i	0.278323	+	0.764685i
$917$	15.8720	+	36.7688i	0.524141	+	1.21421i
$918$		0			0
$919$	−13.2691	−	22.9827i	−0.437706	−	0.758129i	0.559806	−	0.828624i	$-0.310876\pi$
$919$	−13.2691	−	22.9827i	−0.437706	−	0.758129i	−0.997512	+	0.0704945i	$0.977542\pi$
$920$	0.126780	−	0.719003i	0.00417980	−	0.0237048i
$921$		0			0
$922$	−0.0818693	+	0.224934i	−0.00269622	+	0.00740781i
$923$	5.97134	+	33.8652i	0.196549	+	1.11469i
$924$		0			0
$925$	1.39488	+	1.17044i	0.0458633	+	0.0384839i
$926$			0.540363i			0.0177574i
$927$		0			0
$928$	1.48321			0.0486887
$929$	11.5826	−	4.21571i	0.380011	−	0.138313i	−0.144950	−	0.989439i	$-0.546302\pi$
$929$	11.5826	−	4.21571i	0.380011	−	0.138313i	0.524961	+	0.851126i	$0.324080\pi$
$930$		0			0
$931$	−10.2612	−	0.592201i	−0.336296	−	0.0194086i
$932$	17.0550	−	46.8581i	0.558654	−	1.53489i
$933$		0			0
$934$	−0.104253	+	0.124244i	−0.00341126	+	0.00406538i
$935$			28.5272i			0.932938i
$936$		0			0
$937$	−32.0189	−	18.4861i	−1.04601	−	0.603915i	−0.124481	−	0.992222i	$-0.539727\pi$
$937$	−32.0189	−	18.4861i	−1.04601	−	0.603915i	−0.921530	+	0.388307i	$0.873060\pi$
$938$	0.311409	−	0.293955i	0.0101679	−	0.00959798i
$939$		0			0
$940$	−4.15639	+	3.48763i	−0.135567	+	0.113754i
$941$	−7.49093	−	42.4832i	−0.244197	−	1.38491i	−0.822349	−	0.568983i	$-0.807337\pi$
$941$	−7.49093	−	42.4832i	−0.244197	−	1.38491i	0.578152	−	0.815929i	$-0.303774\pi$
$942$		0			0
$943$	20.2113	−	24.0869i	0.658171	−	0.784377i
$944$	−46.2392			−1.50496
$945$		0			0
$946$	0.119710			0.00389211
$947$	−21.1385	+	25.1919i	−0.686909	+	0.818626i	−0.990978	−	0.134024i	$-0.957210\pi$
$947$	−21.1385	+	25.1919i	−0.686909	+	0.818626i	0.304069	+	0.952650i	$0.401655\pi$
$948$		0			0
$949$	−12.2753	−	69.6166i	−0.398473	−	2.25985i
$950$	0.0384733	−	0.0322830i	0.00124824	−	0.00104740i
$951$		0			0
$952$	0.137640	+	0.580066i	0.00446094	+	0.0188000i
$953$	−39.0374	−	22.5383i	−1.26455	−	0.730086i	−0.290595	−	0.956846i	$-0.593853\pi$
$953$	−39.0374	−	22.5383i	−1.26455	−	0.730086i	−0.973951	+	0.226760i	$0.927187\pi$
$954$		0			0
$955$		−	16.1812i		−	0.523613i
$956$	14.6954	−	17.5133i	0.475284	−	0.566421i
$957$		0			0
$958$	0.0629322	−	0.172905i	0.00203325	−	0.00558630i
$959$	−5.19608	−	7.89570i	−0.167790	−	0.254965i
$960$		0			0
$961$	37.2131	−	13.5445i	1.20042	−	0.436918i
$962$	0.0529755			0.00170800
$963$		0			0
$964$		−	12.3033i		−	0.396262i
$965$	−24.5992	−	20.6412i	−0.791878	−	0.664464i
$966$		0			0
$967$	0.795684	+	4.51255i	0.0255875	+	0.145114i	0.994925	−	0.100619i	$-0.0320824\pi$
$967$	0.795684	+	4.51255i	0.0255875	+	0.145114i	−0.969338	+	0.245733i	$0.920971\pi$
$968$	−0.206117	+	0.566303i	−0.00662486	+	0.0182017i
$969$		0			0
$970$	0.00678103	−	0.0384572i	0.000217726	−	0.00123478i
$971$	8.12033	+	14.0648i	0.260594	+	0.451362i	0.966400	−	0.257043i	$-0.0827483\pi$
$971$	8.12033	+	14.0648i	0.260594	+	0.451362i	−0.705806	+	0.708405i	$0.749415\pi$
$972$		0			0
$973$	1.86560	−	15.9979i	0.0598085	−	0.512871i
$974$	0.0986861	+	0.271138i	0.00316211	+	0.00868782i
$975$		0			0
$976$	−11.8475	+	2.08904i	−0.379230	+	0.0668685i
$977$	−2.94829	+	8.10036i	−0.0943241	+	0.259153i	−0.977878	−	0.209176i	$-0.932922\pi$
$977$	−2.94829	+	8.10036i	−0.0943241	+	0.259153i	0.883554	+	0.468330i	$0.155144\pi$
$978$		0			0
$979$	−21.2117	+	25.2791i	−0.677927	+	0.807922i
$980$	15.8009	−	16.7657i	0.504740	−	0.535560i
$981$		0			0
$982$	−0.248463	+	0.430351i	−0.00792878	+	0.0137331i
$983$	17.4896	+	14.6755i	0.557831	+	0.468076i	0.877583	−	0.479425i	$-0.159155\pi$
$983$	17.4896	+	14.6755i	0.557831	+	0.468076i	−0.319751	+	0.947501i	$0.603599\pi$
$984$		0			0
$985$	−7.01321	+	1.23662i	−0.223459	+	0.0394019i
$986$	0.438415	+	0.159570i	0.0139620	+	0.00508174i
$987$		0			0
$988$	−2.27722	+	12.9147i	−0.0724480	+	0.410873i
$989$	11.2361	+	6.48715i	0.357286	+	0.206279i
$990$		0			0
$991$	7.45798	+	12.9176i	0.236910	+	0.410341i	0.959826	−	0.280595i	$-0.0905319\pi$
$991$	7.45798	+	12.9176i	0.236910	+	0.410341i	−0.722916	+	0.690936i	$0.757199\pi$
$992$	−0.261316	+	1.48200i	−0.00829680	+	0.0470535i
$993$		0			0
$994$	0.254013	−	0.167163i	0.00805681	−	0.00530210i
$995$	−1.79426	−	2.13831i	−0.0568818	−	0.0677891i
$996$		0			0
$997$	−2.28470	−	0.402855i	−0.0723573	−	0.0127585i	0.137352	−	0.990522i	$-0.456141\pi$
$997$	−2.28470	−	0.402855i	−0.0723573	−	0.0127585i	−0.209710	+	0.977764i	$0.567252\pi$
$998$	0.260252	+	0.150256i	0.00823812	+	0.00475628i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.11		132
3.2	odd	2		189.2.ba.a.101.12	✓	132
7.5	odd	6		567.2.bd.a.467.12		132
21.5	even	6		189.2.bd.a.47.11	yes	132
27.4	even	9		189.2.bd.a.185.11	yes	132
27.23	odd	18		567.2.bd.a.17.12		132
189.131	even	18	inner	567.2.ba.a.341.11		132
189.166	odd	18		189.2.ba.a.131.12	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.12	✓	132	3.2	odd	2
189.2.ba.a.131.12	yes	132	189.166	odd	18
189.2.bd.a.47.11	yes	132	21.5	even	6
189.2.bd.a.185.11	yes	132	27.4	even	9
567.2.ba.a.143.11		132	1.1	even	1	trivial
567.2.ba.a.341.11		132	189.131	even	18	inner
567.2.bd.a.17.12		132	27.23	odd	18
567.2.bd.a.467.12		132	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.00959490 + 0.0114348i) q^{2} +(0.347258 + 1.96940i) q^{4} +(-1.26073 + 1.05788i) q^{5} +(1.81613 + 1.92397i) q^{7} +(-0.0517058 - 0.0298524i) q^{8} -0.0245663i q^{10} +(-2.95219 + 3.51829i) q^{11} +(1.52751 - 4.19679i) q^{13} +(-0.0394257 + 0.00230675i) q^{14} +(-3.75751 + 1.36762i) q^{16} -3.77410 q^{17} +1.46832i q^{19} +(-2.52118 - 2.11552i) q^{20} +(-0.0119048 - 0.0675152i) q^{22} +(2.54129 - 6.98214i) q^{23} +(-0.397908 + 2.25665i) q^{25} +(0.0333330 + 0.0577345i) q^{26} +(-3.15839 + 4.24480i) q^{28} +(2.83246 + 7.78213i) q^{29} +(-8.27481 + 1.45907i) q^{31} +(0.0612550 - 0.168297i) q^{32} +(0.0362121 - 0.0431559i) q^{34} +(-4.32497 - 0.504358i) q^{35} +(0.397320 - 0.688178i) q^{37} +(-0.0167899 - 0.0140884i) q^{38} +(0.0967671 - 0.0170627i) q^{40} +(3.97658 + 1.44736i) q^{41} +(-0.303215 + 1.71962i) q^{43} +(-7.95407 - 4.59229i) q^{44} +(0.0554557 + 0.0960520i) q^{46} +(0.286275 - 1.62355i) q^{47} +(-0.403318 + 6.98837i) q^{49} +(-0.0219863 - 0.0262023i) q^{50} +(8.79559 + 1.55090i) q^{52} +(3.66888 + 2.11823i) q^{53} -7.55866i q^{55} +(-0.0364696 - 0.153696i) q^{56} +(-0.116164 - 0.0422802i) q^{58} +(10.8663 + 3.95501i) q^{59} +(2.96287 + 0.522435i) q^{61} +(0.0627118 - 0.108620i) q^{62} +(-3.99733 - 6.92357i) q^{64} +(2.51392 + 6.90693i) q^{65} +(-8.30643 + 6.96992i) q^{67} +(-1.31059 - 7.43270i) q^{68} +(0.0472649 - 0.0446158i) q^{70} +(-6.66808 + 3.84982i) q^{71} +(13.7076 - 7.91406i) q^{73} +(0.00405690 + 0.0111462i) q^{74} +(-2.89171 + 0.509886i) q^{76} +(-12.1307 + 0.709749i) q^{77} +(1.22109 + 1.02462i) q^{79} +(3.29043 - 5.69919i) q^{80} +(-0.0547050 + 0.0315840i) q^{82} +(4.61667 - 1.68033i) q^{83} +(4.75812 - 3.99254i) q^{85} +(-0.0167541 - 0.0199668i) q^{86} +(0.257675 - 0.0937859i) q^{88} +7.18505 q^{89} +(10.8487 - 4.68306i) q^{91} +(14.6331 + 2.58021i) q^{92} +(0.0158181 + 0.0188513i) q^{94} +(-1.55330 - 1.85115i) q^{95} +(1.56544 + 0.276029i) q^{97} +(-0.0760405 - 0.0716645i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more