LMFDB - Embedded newform 840.2.bt.b.97.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(97,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 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("840.97"); 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.bt (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0] 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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	840.97
Dual form			840.2.bt.b.433.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(0.0188126 - 2.23599i) q^{5} +(-1.30388 - 2.30215i) q^{7} +1.00000i q^{9} -5.19499 q^{11} +(0.817355 + 0.817355i) q^{13} +(-1.59439 + 1.56778i) q^{15} +(0.550305 - 0.550305i) q^{17} +1.30741 q^{19} +(-0.705888 + 2.54985i) q^{21} +(-3.04663 + 3.04663i) q^{23} +(-4.99929 - 0.0841295i) q^{25} +(0.707107 - 0.707107i) q^{27} +2.99042i q^{29} +3.89498i q^{31} +(3.67341 + 3.67341i) q^{33} +(-5.17212 + 2.87214i) q^{35} +(0.199077 + 0.199077i) q^{37} -1.15591i q^{39} +2.72993i q^{41} +(1.98342 - 1.98342i) q^{43} +(2.23599 + 0.0188126i) q^{45} +(4.41033 - 4.41033i) q^{47} +(-3.59981 + 6.00344i) q^{49} -0.778249 q^{51} +(-1.09146 + 1.09146i) q^{53} +(-0.0977312 + 11.6159i) q^{55} +(-0.924478 - 0.924478i) q^{57} -13.8935 q^{59} -10.9392i q^{61} +(2.30215 - 1.30388i) q^{63} +(1.84297 - 1.81222i) q^{65} +(-10.0506 - 10.0506i) q^{67} +4.30858 q^{69} -16.2833 q^{71} +(5.32068 + 5.32068i) q^{73} +(3.47554 + 3.59452i) q^{75} +(6.77362 + 11.9597i) q^{77} +8.15872i q^{79} -1.00000 q^{81} +(-7.49447 - 7.49447i) q^{83} +(-1.22012 - 1.24083i) q^{85} +(2.11455 - 2.11455i) q^{87} -16.5546 q^{89} +(0.815946 - 2.94740i) q^{91} +(2.75417 - 2.75417i) q^{93} +(0.0245958 - 2.92335i) q^{95} +(9.70745 - 9.70745i) q^{97} -5.19499i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{11} - 16 q^{13} + 4 q^{15} - 20 q^{17} - 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} + 4 q^{45} + 24 q^{47} - 36 q^{49} + 16 q^{53} - 28 q^{55} + 4 q^{57} - 8 q^{59} + 4 q^{63} + 24 q^{65}+ \cdots + 28 q^{97}+O(q^{100}) $ 24 * q - 8 * q^11 - 16 * q^13 + 4 * q^15 - 20 * q^17 - 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 + 4 * q^45 + 24 * q^47 - 36 * q^49 + 16 * q^53 - 28 * q^55 + 4 * q^57 - 8 * q^59 + 4 * q^63 + 24 * q^65 + 16 * q^67 + 8 * q^69 + 8 * q^71 + 28 * q^73 + 28 * q^77 - 24 * q^81 - 64 * q^83 - 20 * q^85 - 20 * q^87 - 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 + 28 * q^97

Character values

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

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

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	0.0188126	−	2.23599i	0.00841325	−	0.999965i
$5$	0.0188126	−	2.23599i	0.00841325	−	0.999965i
$6$		0			0
$7$	−1.30388	−	2.30215i	−0.492819	−	0.870132i
$7$	−1.30388	−	2.30215i	−0.492819	−	0.870132i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−5.19499			−1.56635			−0.783174	−	0.621803i	$-0.786400\pi$
$11$	−5.19499			−1.56635			−0.783174	+	0.621803i	$0.786400\pi$
$12$		0			0
$13$	0.817355	+	0.817355i	0.226693	+	0.226693i	0.811310	−	0.584616i	$-0.198755\pi$
$13$	0.817355	+	0.817355i	0.226693	+	0.226693i	−0.584616	+	0.811310i	$0.698755\pi$
$14$		0			0
$15$	−1.59439	+	1.56778i	−0.411669	+	0.404799i
$16$		0			0
$17$	0.550305	−	0.550305i	0.133469	−	0.133469i	−0.637216	−	0.770685i	$-0.719914\pi$
$17$	0.550305	−	0.550305i	0.133469	−	0.133469i	0.770685	+	0.637216i	$0.219914\pi$
$18$		0			0
$19$	1.30741			0.299940			0.149970	−	0.988691i	$-0.452082\pi$
$19$	1.30741			0.299940			0.149970	+	0.988691i	$0.452082\pi$
$20$		0			0
$21$	−0.705888	+	2.54985i	−0.154037	+	0.556422i
$22$		0			0
$23$	−3.04663	+	3.04663i	−0.635266	+	0.635266i	−0.949384	−	0.314118i	$-0.898291\pi$
$23$	−3.04663	+	3.04663i	−0.635266	+	0.635266i	0.314118	+	0.949384i	$0.398291\pi$
$24$		0			0
$25$	−4.99929	−	0.0841295i	−0.999858	−	0.0168259i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			2.99042i			0.555308i	0.960681	+	0.277654i	$0.0895568\pi$
$29$			2.99042i			0.555308i	−0.960681	+	0.277654i	$0.910443\pi$
$30$		0			0
$31$			3.89498i			0.699559i	0.936832	+	0.349780i	$0.113744\pi$
$31$			3.89498i			0.699559i	−0.936832	+	0.349780i	$0.886256\pi$
$32$		0			0
$33$	3.67341	+	3.67341i	0.639459	+	0.639459i
$34$		0			0
$35$	−5.17212	+	2.87214i	−0.874247	+	0.485481i
$36$		0			0
$37$	0.199077	+	0.199077i	0.0327281	+	0.0327281i	0.723281	−	0.690553i	$-0.242633\pi$
$37$	0.199077	+	0.199077i	0.0327281	+	0.0327281i	−0.690553	+	0.723281i	$0.742633\pi$
$38$		0			0
$39$		−	1.15591i		−	0.185094i
$40$		0			0
$41$			2.72993i			0.426344i	0.977015	+	0.213172i	$0.0683795\pi$
$41$			2.72993i			0.426344i	−0.977015	+	0.213172i	$0.931621\pi$
$42$		0			0
$43$	1.98342	−	1.98342i	0.302469	−	0.302469i	−0.539510	−	0.841979i	$-0.681391\pi$
$43$	1.98342	−	1.98342i	0.302469	−	0.302469i	0.841979	+	0.539510i	$0.181391\pi$
$44$		0			0
$45$	2.23599	+	0.0188126i	0.333322	+	0.00280442i
$46$		0			0
$47$	4.41033	−	4.41033i	0.643313	−	0.643313i	−0.308055	−	0.951369i	$-0.599678\pi$
$47$	4.41033	−	4.41033i	0.643313	−	0.643313i	0.951369	+	0.308055i	$0.0996781\pi$
$48$		0			0
$49$	−3.59981	+	6.00344i	−0.514259	+	0.857635i
$50$		0			0
$51$	−0.778249			−0.108977
$52$		0			0
$53$	−1.09146	+	1.09146i	−0.149923	+	0.149923i	−0.778084	−	0.628160i	$-0.783808\pi$
$53$	−1.09146	+	1.09146i	−0.149923	+	0.149923i	0.628160	+	0.778084i	$0.283808\pi$
$54$		0			0
$55$	−0.0977312	+	11.6159i	−0.0131781	+	1.56629i
$56$		0			0
$57$	−0.924478	−	0.924478i	−0.122450	−	0.122450i
$58$		0			0
$59$	−13.8935			−1.80878			−0.904392	−	0.426702i	$-0.859675\pi$
$59$	−13.8935			−1.80878			−0.904392	+	0.426702i	$0.859675\pi$
$60$		0			0
$61$		−	10.9392i		−	1.40062i	−0.713838	−	0.700311i	$-0.753045\pi$
$61$		−	10.9392i		−	1.40062i	0.713838	−	0.700311i	$-0.246955\pi$
$62$		0			0
$63$	2.30215	−	1.30388i	0.290044	−	0.164273i
$64$		0			0
$65$	1.84297	−	1.81222i	0.228593	−	0.224778i
$66$		0			0
$67$	−10.0506	−	10.0506i	−1.22787	−	1.22787i	−0.964767	−	0.263104i	$-0.915254\pi$
$67$	−10.0506	−	10.0506i	−1.22787	−	1.22787i	−0.263104	−	0.964767i	$-0.584746\pi$
$68$		0			0
$69$	4.30858			0.518692
$70$		0			0
$71$	−16.2833			−1.93247			−0.966233	−	0.257668i	$-0.917046\pi$
$71$	−16.2833			−1.93247			−0.966233	+	0.257668i	$0.917046\pi$
$72$		0			0
$73$	5.32068	+	5.32068i	0.622738	+	0.622738i	0.946231	−	0.323492i	$-0.104857\pi$
$73$	5.32068	+	5.32068i	0.622738	+	0.622738i	−0.323492	+	0.946231i	$0.604857\pi$
$74$		0			0
$75$	3.47554	+	3.59452i	0.401321	+	0.415060i
$76$		0			0
$77$	6.77362	+	11.9597i	0.771926	+	1.36293i
$78$		0			0
$79$			8.15872i			0.917928i	0.888455	+	0.458964i	$0.151779\pi$
$79$			8.15872i			0.917928i	−0.888455	+	0.458964i	$0.848221\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−7.49447	−	7.49447i	−0.822625	−	0.822625i	0.163859	−	0.986484i	$-0.447606\pi$
$83$	−7.49447	−	7.49447i	−0.822625	−	0.822625i	−0.986484	+	0.163859i	$0.947606\pi$
$84$		0			0
$85$	−1.22012	−	1.24083i	−0.132341	−	0.134587i
$86$		0			0
$87$	2.11455	−	2.11455i	0.226703	−	0.226703i
$88$		0			0
$89$	−16.5546			−1.75478			−0.877390	−	0.479777i	$-0.840717\pi$
$89$	−16.5546			−1.75478			−0.877390	+	0.479777i	$0.840717\pi$
$90$		0			0
$91$	0.815946	−	2.94740i	0.0855343	−	0.308972i
$92$		0			0
$93$	2.75417	−	2.75417i	0.285594	−	0.285594i
$94$		0			0
$95$	0.0245958	−	2.92335i	0.00252347	−	0.299930i
$96$		0			0
$97$	9.70745	−	9.70745i	0.985642	−	0.985642i	−0.0142566	−	0.999898i	$-0.504538\pi$
$97$	9.70745	−	9.70745i	0.985642	−	0.985642i	0.999898	+	0.0142566i	$0.00453816\pi$
$98$		0			0
$99$		−	5.19499i		−	0.522116i
$100$		0			0
$101$		−	17.3275i		−	1.72415i	−0.506777	−	0.862077i	$-0.669163\pi$
$101$		−	17.3275i		−	1.72415i	0.506777	−	0.862077i	$-0.330837\pi$
$102$		0			0
$103$	9.94786	+	9.94786i	0.980191	+	0.980191i	0.999808	−	0.0196162i	$-0.00624444\pi$
$103$	9.94786	+	9.94786i	0.980191	+	0.980191i	−0.0196162	+	0.999808i	$0.506244\pi$
$104$		0			0
$105$	5.68815	+	1.62633i	0.555107	+	0.158713i
$106$		0			0
$107$	4.45880	+	4.45880i	0.431049	+	0.431049i	0.888985	−	0.457936i	$-0.151411\pi$
$107$	4.45880	+	4.45880i	0.431049	+	0.431049i	−0.457936	+	0.888985i	$0.651411\pi$
$108$		0			0
$109$			6.76993i			0.648442i	0.945981	+	0.324221i	$0.105102\pi$
$109$			6.76993i			0.648442i	−0.945981	+	0.324221i	$0.894898\pi$
$110$		0			0
$111$		−	0.281538i		−	0.0267224i
$112$		0			0
$113$	4.02997	−	4.02997i	0.379107	−	0.379107i	−0.491673	−	0.870780i	$-0.663614\pi$
$113$	4.02997	−	4.02997i	0.379107	−	0.379107i	0.870780	+	0.491673i	$0.163614\pi$
$114$		0			0
$115$	6.75491	+	6.86954i	0.629899	+	0.640588i
$116$		0			0
$117$	−0.817355	+	0.817355i	−0.0755645	+	0.0755645i
$118$		0			0
$119$	−1.98442	−	0.549356i	−0.181911	−	0.0503594i
$120$		0			0
$121$	15.9879			1.45344
$122$		0			0
$123$	1.93035	−	1.93035i	0.174054	−	0.174054i
$124$		0			0
$125$	−0.282162	+	11.1768i	−0.0252374	+	0.999681i
$126$		0			0
$127$	0.737538	+	0.737538i	0.0654459	+	0.0654459i	0.739072	−	0.673626i	$-0.235264\pi$
$127$	0.737538	+	0.737538i	0.0654459	+	0.0654459i	−0.673626	+	0.739072i	$0.735264\pi$
$128$		0			0
$129$	−2.80498			−0.246965
$130$		0			0
$131$		−	13.6157i		−	1.18961i	−0.803869	−	0.594806i	$-0.797229\pi$
$131$		−	13.6157i		−	1.18961i	0.803869	−	0.594806i	$-0.202771\pi$
$132$		0			0
$133$	−1.70470	−	3.00986i	−0.147816	−	0.260988i
$134$		0			0
$135$	−1.56778	−	1.59439i	−0.134933	−	0.137223i
$136$		0			0
$137$	−2.42049	−	2.42049i	−0.206797	−	0.206797i	0.596108	−	0.802904i	$-0.296713\pi$
$137$	−2.42049	−	2.42049i	−0.206797	−	0.206797i	−0.802904	+	0.596108i	$0.796713\pi$
$138$		0			0
$139$	5.93270			0.503205			0.251603	−	0.967831i	$-0.419042\pi$
$139$	5.93270			0.503205			0.251603	+	0.967831i	$0.419042\pi$
$140$		0			0
$141$	−6.23715			−0.525263
$142$		0			0
$143$	−4.24615	−	4.24615i	−0.355081	−	0.355081i
$144$		0			0
$145$	6.68655	+	0.0562577i	0.555288	+	0.00467194i
$146$		0			0
$147$	6.79053	−	1.69962i	0.560073	−	0.140183i
$148$		0			0
$149$			5.96507i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$149$			5.96507i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$150$		0			0
$151$	−7.86040			−0.639670			−0.319835	−	0.947473i	$-0.603628\pi$
$151$	−7.86040			−0.639670			−0.319835	+	0.947473i	$0.603628\pi$
$152$		0			0
$153$	0.550305	+	0.550305i	0.0444895	+	0.0444895i
$154$		0			0
$155$	8.70914	+	0.0732748i	0.699535	+	0.00588557i
$156$		0			0
$157$	−9.34553	+	9.34553i	−0.745854	+	0.745854i	−0.973698	−	0.227844i	$-0.926833\pi$
$157$	−9.34553	+	9.34553i	−0.745854	+	0.745854i	0.227844	+	0.973698i	$0.426833\pi$
$158$		0			0
$159$	1.54356			0.122412
$160$		0			0
$161$	10.9862	+	3.04138i	0.865836	+	0.239694i
$162$		0			0
$163$	10.7290	−	10.7290i	0.840364	−	0.840364i	−0.148542	−	0.988906i	$-0.547458\pi$
$163$	10.7290	−	10.7290i	0.840364	−	0.840364i	0.988906	+	0.148542i	$0.0474581\pi$
$164$		0			0
$165$	8.28281	−	8.14460i	0.644816	−	0.634056i
$166$		0			0
$167$	10.1432	−	10.1432i	0.784905	−	0.784905i	−0.195749	−	0.980654i	$-0.562714\pi$
$167$	10.1432	−	10.1432i	0.784905	−	0.784905i	0.980654	+	0.195749i	$0.0627139\pi$
$168$		0			0
$169$		−	11.6639i		−	0.897220i
$170$		0			0
$171$			1.30741i			0.0999801i
$172$		0			0
$173$	−2.09542	−	2.09542i	−0.159312	−	0.159312i	0.622950	−	0.782262i	$-0.285934\pi$
$173$	−2.09542	−	2.09542i	−0.159312	−	0.159312i	−0.782262	+	0.622950i	$0.785934\pi$
$174$		0			0
$175$	6.32478	+	11.6188i	0.478108	+	0.878301i
$176$		0			0
$177$	9.82421	+	9.82421i	0.738433	+	0.738433i
$178$		0			0
$179$		−	19.6465i		−	1.46845i	−0.678909	−	0.734223i	$-0.737547\pi$
$179$		−	19.6465i		−	1.46845i	0.678909	−	0.734223i	$-0.262453\pi$
$180$		0			0
$181$		−	9.50946i		−	0.706832i	−0.935466	−	0.353416i	$-0.885020\pi$
$181$		−	9.50946i		−	0.706832i	0.935466	−	0.353416i	$-0.114980\pi$
$182$		0			0
$183$	−7.73519	+	7.73519i	−0.571802	+	0.571802i
$184$		0			0
$185$	0.448880	−	0.441390i	0.0330023	−	0.0324516i
$186$		0			0
$187$	−2.85883	+	2.85883i	−0.209058	+	0.209058i
$188$		0			0
$189$	−2.54985	−	0.705888i	−0.185474	−	0.0513458i
$190$		0			0
$191$	14.3411			1.03768			0.518842	−	0.854870i	$-0.326363\pi$
$191$	14.3411			1.03768			0.518842	+	0.854870i	$0.326363\pi$
$192$		0			0
$193$	−2.94208	+	2.94208i	−0.211775	+	0.211775i	−0.805021	−	0.593246i	$-0.797846\pi$
$193$	−2.94208	+	2.94208i	−0.211775	+	0.211775i	0.593246	+	0.805021i	$0.297846\pi$
$194$		0			0
$195$	−2.58461	−	0.0217458i	−0.185088	−	0.00155725i
$196$		0			0
$197$	−8.66057	−	8.66057i	−0.617040	−	0.617040i	0.327731	−	0.944771i	$-0.393716\pi$
$197$	−8.66057	−	8.66057i	−0.617040	−	0.617040i	−0.944771	+	0.327731i	$0.893716\pi$
$198$		0			0
$199$	−4.07354			−0.288766			−0.144383	−	0.989522i	$-0.546120\pi$
$199$	−4.07354			−0.288766			−0.144383	+	0.989522i	$0.546120\pi$
$200$		0			0
$201$			14.2136i			1.00255i
$202$		0			0
$203$	6.88441	−	3.89914i	0.483191	−	0.273666i
$204$		0			0
$205$	6.10410	+	0.0513572i	0.426329	+	0.00358694i
$206$		0			0
$207$	−3.04663	−	3.04663i	−0.211755	−	0.211755i
$208$		0			0
$209$	−6.79198			−0.469811
$210$		0			0
$211$	24.2786			1.67141			0.835704	−	0.549180i	$-0.185060\pi$
$211$	24.2786			1.67141			0.835704	+	0.549180i	$0.185060\pi$
$212$		0			0
$213$	11.5140	+	11.5140i	0.788926	+	0.788926i
$214$		0			0
$215$	−4.39760	−	4.47222i	−0.299914	−	0.305003i
$216$		0			0
$217$	8.96684	−	5.07857i	0.608709	−	0.344756i
$218$		0			0
$219$		−	7.52458i		−	0.508464i
$220$		0			0
$221$	0.899588			0.0605129
$222$		0			0
$223$	−12.4444	−	12.4444i	−0.833339	−	0.833339i	0.154633	−	0.987972i	$-0.450581\pi$
$223$	−12.4444	−	12.4444i	−0.833339	−	0.833339i	−0.987972	+	0.154633i	$0.950581\pi$
$224$		0			0
$225$	0.0841295	−	4.99929i	0.00560864	−	0.333286i
$226$		0			0
$227$	−0.870542	+	0.870542i	−0.0577799	+	0.0577799i	−0.735406	−	0.677626i	$-0.763009\pi$
$227$	−0.870542	+	0.870542i	−0.0577799	+	0.0577799i	0.677626	+	0.735406i	$0.263009\pi$
$228$		0			0
$229$	−20.5096			−1.35531			−0.677655	−	0.735380i	$-0.737004\pi$
$229$	−20.5096			−1.35531			−0.677655	+	0.735380i	$0.737004\pi$
$230$		0			0
$231$	3.66708	−	13.2464i	0.241276	−	0.871551i
$232$		0			0
$233$	−2.49345	+	2.49345i	−0.163351	+	0.163351i	−0.784050	−	0.620698i	$-0.786849\pi$
$233$	−2.49345	+	2.49345i	−0.163351	+	0.163351i	0.620698	+	0.784050i	$0.286849\pi$
$234$		0			0
$235$	−9.77849	−	9.94443i	−0.637878	−	0.648703i
$236$		0			0
$237$	5.76909	−	5.76909i	0.374743	−	0.374743i
$238$		0			0
$239$			23.0468i			1.49078i	0.666631	+	0.745388i	$0.267736\pi$
$239$			23.0468i			1.49078i	−0.666631	+	0.745388i	$0.732264\pi$
$240$		0			0
$241$		−	20.7075i		−	1.33388i	−0.745109	−	0.666942i	$-0.767603\pi$
$241$		−	20.7075i		−	1.33388i	0.745109	−	0.666942i	$-0.232397\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	13.3559	+	8.16208i	0.853278	+	0.521456i
$246$		0			0
$247$	1.06862	+	1.06862i	0.0679945	+	0.0679945i
$248$		0			0
$249$			10.5988i			0.671670i
$250$		0			0
$251$			3.12576i			0.197296i	0.995122	+	0.0986481i	$0.0314518\pi$
$251$			3.12576i			0.197296i	−0.995122	+	0.0986481i	$0.968548\pi$
$252$		0			0
$253$	15.8272	−	15.8272i	0.995047	−	0.995047i
$254$		0			0
$255$	−0.0146409	+	1.74016i	−0.000916848	+	0.108973i
$256$		0			0
$257$	1.42680	−	1.42680i	0.0890016	−	0.0890016i	−0.661204	−	0.750206i	$-0.729954\pi$
$257$	1.42680	−	1.42680i	0.0890016	−	0.0890016i	0.750206	+	0.661204i	$0.229954\pi$
$258$		0			0
$259$	0.198734	−	0.717879i	0.0123487	−	0.0446068i
$260$		0			0
$261$	−2.99042			−0.185103
$262$		0			0
$263$	−8.20481	+	8.20481i	−0.505930	+	0.505930i	−0.913275	−	0.407344i	$-0.866455\pi$
$263$	−8.20481	+	8.20481i	−0.505930	+	0.505930i	0.407344	+	0.913275i	$0.366455\pi$
$264$		0			0
$265$	2.41996	+	2.46102i	0.148657	+	0.151179i
$266$		0			0
$267$	11.7058	+	11.7058i	0.716386	+	0.716386i
$268$		0			0
$269$	−9.63912			−0.587707			−0.293854	−	0.955850i	$-0.594938\pi$
$269$	−9.63912			−0.587707			−0.293854	+	0.955850i	$0.594938\pi$
$270$		0			0
$271$			26.5971i			1.61566i	0.589417	+	0.807829i	$0.299357\pi$
$271$			26.5971i			1.61566i	−0.589417	+	0.807829i	$0.700643\pi$
$272$		0			0
$273$	−2.66109	+	1.50717i	−0.161057	+	0.0912180i
$274$		0			0
$275$	25.9713	+	0.437052i	1.56613	+	0.0263552i
$276$		0			0
$277$	−19.9489	−	19.9489i	−1.19862	−	1.19862i	−0.974581	−	0.224034i	$-0.928077\pi$
$277$	−19.9489	−	19.9489i	−1.19862	−	1.19862i	−0.224034	−	0.974581i	$-0.571923\pi$
$278$		0			0
$279$	−3.89498			−0.233186
$280$		0			0
$281$	−15.0938			−0.900422			−0.450211	−	0.892922i	$-0.648651\pi$
$281$	−15.0938			−0.900422			−0.450211	+	0.892922i	$0.648651\pi$
$282$		0			0
$283$	−0.163056	−	0.163056i	−0.00969268	−	0.00969268i	0.702244	−	0.711937i	$-0.252182\pi$
$283$	−0.163056	−	0.163056i	−0.00969268	−	0.00969268i	−0.711937	+	0.702244i	$0.752182\pi$
$284$		0			0
$285$	−2.08452	+	2.04973i	−0.123476	+	0.121416i
$286$		0			0
$287$	6.28472	−	3.55950i	0.370976	−	0.210110i
$288$		0			0
$289$			16.3943i			0.964372i
$290$		0			0
$291$	−13.7284			−0.804773
$292$		0			0
$293$	14.0636	+	14.0636i	0.821606	+	0.821606i	0.986338	−	0.164732i	$-0.0526760\pi$
$293$	14.0636	+	14.0636i	0.821606	+	0.821606i	−0.164732	+	0.986338i	$0.552676\pi$
$294$		0			0
$295$	−0.261374	+	31.0658i	−0.0152178	+	1.80872i
$296$		0			0
$297$	−3.67341	+	3.67341i	−0.213153	+	0.213153i
$298$		0			0
$299$	−4.98035			−0.288021
$300$		0			0
$301$	−7.15228	−	1.98000i	−0.412251	−	0.114126i
$302$		0			0
$303$	−12.2524	+	12.2524i	−0.703883	+	0.703883i
$304$		0			0
$305$	−24.4599	−	0.205795i	−1.40057	−	0.0117838i
$306$		0			0
$307$	7.28161	−	7.28161i	0.415584	−	0.415584i	−0.468095	−	0.883678i	$-0.655059\pi$
$307$	7.28161	−	7.28161i	0.415584	−	0.415584i	0.883678	+	0.468095i	$0.155059\pi$
$308$		0			0
$309$		−	14.0684i		−	0.800323i
$310$		0			0
$311$			8.14282i			0.461737i	0.972985	+	0.230869i	$0.0741568\pi$
$311$			8.14282i			0.461737i	−0.972985	+	0.230869i	$0.925843\pi$
$312$		0			0
$313$	11.6844	+	11.6844i	0.660441	+	0.660441i	0.955484	−	0.295043i	$-0.0953340\pi$
$313$	11.6844	+	11.6844i	0.660441	+	0.660441i	−0.295043	+	0.955484i	$0.595334\pi$
$314$		0			0
$315$	−2.87214	−	5.17212i	−0.161827	−	0.291416i
$316$		0			0
$317$	−2.40116	−	2.40116i	−0.134863	−	0.134863i	0.636453	−	0.771316i	$-0.280401\pi$
$317$	−2.40116	−	2.40116i	−0.134863	−	0.134863i	−0.771316	+	0.636453i	$0.780401\pi$
$318$		0			0
$319$		−	15.5352i		−	0.869805i
$320$		0			0
$321$		−	6.30570i		−	0.351950i
$322$		0			0
$323$	0.719474	−	0.719474i	0.0400326	−	0.0400326i
$324$		0			0
$325$	−4.01743	−	4.15496i	−0.222847	−	0.230476i
$326$		0			0
$327$	4.78706	−	4.78706i	0.264725	−	0.264725i
$328$		0			0
$329$	−15.9038	−	4.40273i	−0.876804	−	0.242730i
$330$		0			0
$331$	19.9270			1.09529			0.547644	−	0.836711i	$-0.315525\pi$
$331$	19.9270			1.09529			0.547644	+	0.836711i	$0.315525\pi$
$332$		0			0
$333$	−0.199077	+	0.199077i	−0.0109094	+	0.0109094i
$334$		0			0
$335$	−22.6620	+	22.2839i	−1.23816	+	1.21750i
$336$		0			0
$337$	−14.2601	−	14.2601i	−0.776798	−	0.776798i	0.202487	−	0.979285i	$-0.435098\pi$
$337$	−14.2601	−	14.2601i	−0.776798	−	0.776798i	−0.979285	+	0.202487i	$0.935098\pi$
$338$		0			0
$339$	−5.69923			−0.309540
$340$		0			0
$341$		−	20.2344i		−	1.09575i
$342$		0			0
$343$	18.5146	+	0.459569i	0.999692	+	0.0248144i
$344$		0			0
$345$	0.0810556	−	9.63394i	0.00436389	−	0.518674i
$346$		0			0
$347$	−10.8252	−	10.8252i	−0.581126	−	0.581126i	0.354087	−	0.935213i	$-0.384792\pi$
$347$	−10.8252	−	10.8252i	−0.581126	−	0.581126i	−0.935213	+	0.354087i	$0.884792\pi$
$348$		0			0
$349$	−11.2159			−0.600373			−0.300186	−	0.953881i	$-0.597049\pi$
$349$	−11.2159			−0.600373			−0.300186	+	0.953881i	$0.597049\pi$
$350$		0			0
$351$	1.15591			0.0616981
$352$		0			0
$353$	25.4175	+	25.4175i	1.35283	+	1.35283i	0.882475	+	0.470360i	$0.155876\pi$
$353$	25.4175	+	25.4175i	1.35283	+	1.35283i	0.470360	+	0.882475i	$0.344124\pi$
$354$		0			0
$355$	−0.306330	+	36.4092i	−0.0162583	+	1.93240i
$356$		0			0
$357$	1.01474	+	1.79165i	0.0537057	+	0.0948240i
$358$		0			0
$359$			28.3149i			1.49440i	0.664597	+	0.747202i	$0.268603\pi$
$359$			28.3149i			1.49440i	−0.664597	+	0.747202i	$0.731397\pi$
$360$		0			0
$361$	−17.2907			−0.910036
$362$		0			0
$363$	−11.3051	−	11.3051i	−0.593366	−	0.593366i
$364$		0			0
$365$	11.9971	−	11.7969i	0.627956	−	0.617477i
$366$		0			0
$367$	21.3444	−	21.3444i	1.11417	−	1.11417i	0.121587	−	0.992581i	$-0.461202\pi$
$367$	21.3444	−	21.3444i	1.11417	−	1.11417i	0.992581	−	0.121587i	$-0.0387983\pi$
$368$		0			0
$369$	−2.72993			−0.142115
$370$		0			0
$371$	3.93583	+	1.08958i	0.204338	+	0.0565680i
$372$		0			0
$373$	−4.99355	+	4.99355i	−0.258556	+	0.258556i	−0.824467	−	0.565911i	$-0.808525\pi$
$373$	−4.99355	+	4.99355i	−0.258556	+	0.258556i	0.565911	+	0.824467i	$0.308525\pi$
$374$		0			0
$375$	8.10270	−	7.70366i	0.418421	−	0.397815i
$376$		0			0
$377$	−2.44424	+	2.44424i	−0.125885	+	0.125885i
$378$		0			0
$379$		−	6.22172i		−	0.319588i	−0.987150	−	0.159794i	$-0.948917\pi$
$379$		−	6.22172i		−	0.319588i	0.987150	−	0.159794i	$-0.0510830\pi$
$380$		0			0
$381$		−	1.04304i		−	0.0534364i
$382$		0			0
$383$	−23.9817	−	23.9817i	−1.22541	−	1.22541i	−0.965683	−	0.259723i	$-0.916369\pi$
$383$	−23.9817	−	23.9817i	−1.22541	−	1.22541i	−0.259723	−	0.965683i	$-0.583631\pi$
$384$		0			0
$385$	26.8691	−	14.9207i	1.36938	−	0.760432i
$386$		0			0
$387$	1.98342	+	1.98342i	0.100823	+	0.100823i
$388$		0			0
$389$		−	13.0476i		−	0.661541i	−0.943711	−	0.330771i	$-0.892691\pi$
$389$		−	13.0476i		−	0.661541i	0.943711	−	0.330771i	$-0.107309\pi$
$390$		0			0
$391$			3.35315i			0.169576i
$392$		0			0
$393$	−9.62778	+	9.62778i	−0.485657	+	0.485657i
$394$		0			0
$395$	18.2428	+	0.153487i	0.917895	+	0.00772276i
$396$		0			0
$397$	0.363615	−	0.363615i	0.0182493	−	0.0182493i	−0.697923	−	0.716173i	$-0.745892\pi$
$397$	0.363615	−	0.363615i	0.0182493	−	0.0182493i	0.716173	+	0.697923i	$0.245892\pi$
$398$		0			0
$399$	−0.922885	+	3.33370i	−0.0462020	+	0.166894i
$400$		0			0
$401$	5.54793			0.277050			0.138525	−	0.990359i	$-0.455764\pi$
$401$	5.54793			0.277050			0.138525	+	0.990359i	$0.455764\pi$
$402$		0			0
$403$	−3.18358	+	3.18358i	−0.158585	+	0.158585i
$404$		0			0
$405$	−0.0188126	+	2.23599i	−0.000934806	+	0.111107i
$406$		0			0
$407$	−1.03420	−	1.03420i	−0.0512636	−	0.0512636i
$408$		0			0
$409$	−15.4786			−0.765369			−0.382684	−	0.923879i	$-0.625000\pi$
$409$	−15.4786			−0.765369			−0.382684	+	0.923879i	$0.625000\pi$
$410$		0			0
$411$			3.42309i			0.168849i
$412$		0			0
$413$	18.1155	+	31.9850i	0.891403	+	1.57388i
$414$		0			0
$415$	−16.8985	+	16.6166i	−0.829516	+	0.815675i
$416$		0			0
$417$	−4.19506	−	4.19506i	−0.205433	−	0.205433i
$418$		0			0
$419$	34.2957			1.67546			0.837728	−	0.546088i	$-0.183884\pi$
$419$	34.2957			1.67546			0.837728	+	0.546088i	$0.183884\pi$
$420$		0			0
$421$	−27.0249			−1.31711			−0.658556	−	0.752532i	$-0.728832\pi$
$421$	−27.0249			−1.31711			−0.658556	+	0.752532i	$0.728832\pi$
$422$		0			0
$423$	4.41033	+	4.41033i	0.214438	+	0.214438i
$424$		0			0
$425$	−2.79743	+	2.70484i	−0.135695	+	0.131204i
$426$		0			0
$427$	−25.1837	+	14.2634i	−1.21873	+	0.690253i
$428$		0			0
$429$			6.00496i			0.289922i
$430$		0			0
$431$	−17.0803			−0.822731			−0.411366	−	0.911470i	$-0.634948\pi$
$431$	−17.0803			−0.822731			−0.411366	+	0.911470i	$0.634948\pi$
$432$		0			0
$433$	−23.6189	−	23.6189i	−1.13505	−	1.13505i	−0.989325	−	0.145725i	$-0.953449\pi$
$433$	−23.6189	−	23.6189i	−1.13505	−	1.13505i	−0.145725	−	0.989325i	$-0.546551\pi$
$434$		0			0
$435$	−4.68833	−	4.76789i	−0.224788	−	0.228603i
$436$		0			0
$437$	−3.98319	+	3.98319i	−0.190542	+	0.190542i
$438$		0			0
$439$	12.2095			0.582729			0.291365	−	0.956612i	$-0.405891\pi$
$439$	12.2095			0.582729			0.291365	+	0.956612i	$0.405891\pi$
$440$		0			0
$441$	−6.00344	−	3.59981i	−0.285878	−	0.171420i
$442$		0			0
$443$	−10.4501	+	10.4501i	−0.496500	+	0.496500i	−0.910347	−	0.413847i	$-0.864185\pi$
$443$	−10.4501	+	10.4501i	−0.496500	+	0.496500i	0.413847	+	0.910347i	$0.364185\pi$
$444$		0			0
$445$	−0.311435	+	37.0158i	−0.0147634	+	1.75472i
$446$		0			0
$447$	4.21794	−	4.21794i	0.199502	−	0.199502i
$448$		0			0
$449$		−	27.4726i		−	1.29651i	−0.761423	−	0.648255i	$-0.775499\pi$
$449$		−	27.4726i		−	1.29651i	0.761423	−	0.648255i	$-0.224501\pi$
$450$		0			0
$451$		−	14.1820i		−	0.667803i
$452$		0			0
$453$	5.55814	+	5.55814i	0.261144	+	0.261144i
$454$		0			0
$455$	−6.57501	−	1.87989i	−0.308241	−	0.0881308i
$456$		0			0
$457$	−21.3864	−	21.3864i	−1.00042	−	1.00042i	−1.00000		0.000415123i	$-0.999868\pi$
$457$	−21.3864	−	21.3864i	−1.00042	−	1.00042i	−0.000415123	−	1.00000i	$-0.500132\pi$
$458$		0			0
$459$		−	0.778249i		−	0.0363255i
$460$		0			0
$461$			27.9120i			1.29999i	0.759939	+	0.649995i	$0.225229\pi$
$461$			27.9120i			1.29999i	−0.759939	+	0.649995i	$0.774771\pi$
$462$		0			0
$463$	−20.8693	+	20.8693i	−0.969877	+	0.969877i	−0.999559	−	0.0296827i	$-0.990550\pi$
$463$	−20.8693	+	20.8693i	−0.969877	+	0.969877i	0.0296827	+	0.999559i	$0.490550\pi$
$464$		0			0
$465$	−6.10648	−	6.21010i	−0.283181	−	0.287987i
$466$		0			0
$467$	26.6658	−	26.6658i	1.23395	−	1.23395i	0.271511	−	0.962435i	$-0.412477\pi$
$467$	26.6658	−	26.6658i	1.23395	−	1.23395i	0.962435	−	0.271511i	$-0.0875232\pi$
$468$		0			0
$469$	−10.0332	+	36.2426i	−0.463292	+	1.67353i
$470$		0			0
$471$	13.2166			0.608987
$472$		0			0
$473$	−10.3039	+	10.3039i	−0.473772	+	0.473772i
$474$		0			0
$475$	−6.53612	−	0.109992i	−0.299898	−	0.00504677i
$476$		0			0
$477$	−1.09146	−	1.09146i	−0.0499744	−	0.0499744i
$478$		0			0
$479$	18.8257			0.860166			0.430083	−	0.902789i	$-0.358484\pi$
$479$	18.8257			0.860166			0.430083	+	0.902789i	$0.358484\pi$
$480$		0			0
$481$			0.325434i			0.0148385i
$482$		0			0
$483$	−5.61786	−	9.91901i	−0.255621	−	0.451331i
$484$		0			0
$485$	−21.5231	−	21.8884i	−0.977314	−	0.993899i
$486$		0			0
$487$	−3.79308	−	3.79308i	−0.171881	−	0.171881i	0.615924	−	0.787805i	$-0.288783\pi$
$487$	−3.79308	−	3.79308i	−0.171881	−	0.171881i	−0.787805	+	0.615924i	$0.788783\pi$
$488$		0			0
$489$	−15.1732			−0.686154
$490$		0			0
$491$	−31.0544			−1.40146			−0.700732	−	0.713425i	$-0.747143\pi$
$491$	−31.0544			−1.40146			−0.700732	+	0.713425i	$0.747143\pi$
$492$		0			0
$493$	1.64564	+	1.64564i	0.0741161	+	0.0741161i
$494$		0			0
$495$	−11.6159	−	0.0977312i	−0.522097	−	0.00439269i
$496$		0			0
$497$	21.2314	+	37.4865i	0.952356	+	1.68150i
$498$		0			0
$499$			19.4573i			0.871029i	0.900182	+	0.435514i	$0.143434\pi$
$499$			19.4573i			0.871029i	−0.900182	+	0.435514i	$0.856566\pi$
$500$		0			0
$501$	−14.3447			−0.640872
$502$		0			0
$503$	15.4448	+	15.4448i	0.688647	+	0.688647i	0.961933	−	0.273286i	$-0.0881104\pi$
$503$	15.4448	+	15.4448i	0.688647	+	0.688647i	−0.273286	+	0.961933i	$0.588110\pi$
$504$		0			0
$505$	−38.7442	−	0.325976i	−1.72409	−	0.0145057i
$506$		0			0
$507$	−8.24760	+	8.24760i	−0.366289	+	0.366289i
$508$		0			0
$509$	31.6165			1.40138			0.700689	−	0.713467i	$-0.252876\pi$
$509$	31.6165			1.40138			0.700689	+	0.713467i	$0.252876\pi$
$510$		0			0
$511$	5.31151	−	19.1865i	0.234967	−	0.848762i
$512$		0			0
$513$	0.924478	−	0.924478i	0.0408167	−	0.0408167i
$514$		0			0
$515$	22.4304	−	22.0561i	0.988403	−	0.971910i
$516$		0			0
$517$	−22.9116	+	22.9116i	−1.00765	+	1.00765i
$518$		0			0
$519$			2.96337i			0.130078i
$520$		0			0
$521$		−	2.87693i		−	0.126041i	−0.998012	−	0.0630203i	$-0.979927\pi$
$521$		−	2.87693i		−	0.126041i	0.998012	−	0.0630203i	$-0.0200733\pi$
$522$		0			0
$523$	−29.2446	−	29.2446i	−1.27878	−	1.27878i	−0.941353	−	0.337424i	$-0.890444\pi$
$523$	−29.2446	−	29.2446i	−1.27878	−	1.27878i	−0.337424	−	0.941353i	$-0.609556\pi$
$524$		0			0
$525$	3.74346	−	12.6880i	0.163378	−	0.553752i
$526$		0			0
$527$	2.14343	+	2.14343i	0.0933692	+	0.0933692i
$528$		0			0
$529$			4.43613i			0.192875i
$530$		0			0
$531$		−	13.8935i		−	0.602928i
$532$		0			0
$533$	−2.23132	+	2.23132i	−0.0966494	+	0.0966494i
$534$		0			0
$535$	10.0537	−	9.88595i	0.434660	−	0.427407i
$536$		0			0
$537$	−13.8921	+	13.8921i	−0.599490	+	0.599490i
$538$		0			0
$539$	18.7010	−	31.1878i	0.805508	−	1.34335i
$540$		0			0
$541$	−1.43266			−0.0615950			−0.0307975	−	0.999526i	$-0.509805\pi$
$541$	−1.43266			−0.0615950			−0.0307975	+	0.999526i	$0.509805\pi$
$542$		0			0
$543$	−6.72420	+	6.72420i	−0.288563	+	0.288563i
$544$		0			0
$545$	15.1375	+	0.127360i	0.648419	+	0.00545551i
$546$		0			0
$547$	2.35459	+	2.35459i	0.100675	+	0.100675i	0.755650	−	0.654975i	$-0.227321\pi$
$547$	2.35459	+	2.35459i	0.100675	+	0.100675i	−0.654975	+	0.755650i	$0.727321\pi$
$548$		0			0
$549$	10.9392			0.466874
$550$		0			0
$551$			3.90971i			0.166559i
$552$		0			0
$553$	18.7826	−	10.6380i	0.798718	−	0.452372i
$554$		0			0
$555$	−0.629516	−	0.00529646i	−0.0267214	−	0.000224822i
$556$		0			0
$557$	23.6125	+	23.6125i	1.00050	+	1.00050i	1.00000		0.000495740i	$0.000157799\pi$
$557$	23.6125	+	23.6125i	1.00050	+	1.00050i	0.000495740		1.00000i	$0.499842\pi$
$558$		0			0
$559$	3.24232			0.137135
$560$		0			0
$561$	4.04299			0.170695
$562$		0			0
$563$	−0.952567	−	0.952567i	−0.0401459	−	0.0401459i	0.686749	−	0.726895i	$-0.259037\pi$
$563$	−0.952567	−	0.952567i	−0.0401459	−	0.0401459i	−0.726895	+	0.686749i	$0.759037\pi$
$564$		0			0
$565$	−8.93514	−	9.08677i	−0.375904	−	0.382283i
$566$		0			0
$567$	1.30388	+	2.30215i	0.0547577	+	0.0966813i
$568$		0			0
$569$		−	47.6344i		−	1.99694i	−0.0553320	−	0.998468i	$-0.517622\pi$
$569$		−	47.6344i		−	1.99694i	0.0553320	−	0.998468i	$-0.482378\pi$
$570$		0			0
$571$	26.5737			1.11208			0.556038	−	0.831157i	$-0.312321\pi$
$571$	26.5737			1.11208			0.556038	+	0.831157i	$0.312321\pi$
$572$		0			0
$573$	−10.1407	−	10.1407i	−0.423633	−	0.423633i
$574$		0			0
$575$	15.4873	−	14.9747i	0.645865	−	0.624487i
$576$		0			0
$577$	−21.9280	+	21.9280i	−0.912875	+	0.912875i	−0.996498	−	0.0836224i	$-0.973351\pi$
$577$	−21.9280	+	21.9280i	−0.912875	+	0.912875i	0.0836224	+	0.996498i	$0.473351\pi$
$578$		0			0
$579$	4.16073			0.172914
$580$		0			0
$581$	−7.48155	+	27.0253i	−0.310387	+	1.12120i
$582$		0			0
$583$	5.67011	−	5.67011i	0.234832	−	0.234832i
$584$		0			0
$585$	1.81222	+	1.84297i	0.0749260	+	0.0761975i
$586$		0			0
$587$	−24.0864	+	24.0864i	−0.994151	+	0.994151i	−0.999983	−	0.00583245i	$-0.998143\pi$
$587$	−24.0864	+	24.0864i	−0.994151	+	0.994151i	0.00583245	+	0.999983i	$0.498143\pi$
$588$		0			0
$589$			5.09234i			0.209826i
$590$		0			0
$591$			12.2479i			0.503811i
$592$		0			0
$593$	−16.0709	−	16.0709i	−0.659954	−	0.659954i	0.295415	−	0.955369i	$-0.404542\pi$
$593$	−16.0709	−	16.0709i	−0.659954	−	0.659954i	−0.955369	+	0.295415i	$0.904542\pi$
$594$		0			0
$595$	−1.26569	+	4.42680i	−0.0518881	+	0.181481i
$596$		0			0
$597$	2.88043	+	2.88043i	0.117888	+	0.117888i
$598$		0			0
$599$			7.55382i			0.308641i	0.988021	+	0.154320i	$0.0493188\pi$
$599$			7.55382i			0.308641i	−0.988021	+	0.154320i	$0.950681\pi$
$600$		0			0
$601$			3.81675i			0.155689i	0.996966	+	0.0778443i	$0.0248037\pi$
$601$			3.81675i			0.155689i	−0.996966	+	0.0778443i	$0.975196\pi$
$602$		0			0
$603$	10.0506	−	10.0506i	0.409291	−	0.409291i
$604$		0			0
$605$	0.300774	−	35.7487i	0.0122282	−	1.45339i
$606$		0			0
$607$	−14.1224	+	14.1224i	−0.573211	+	0.573211i	−0.933024	−	0.359814i	$-0.882840\pi$
$607$	−14.1224	+	14.1224i	−0.573211	+	0.573211i	0.359814	+	0.933024i	$0.382840\pi$
$608$		0			0
$609$	−7.62512	−	2.11090i	−0.308986	−	0.0855381i
$610$		0			0
$611$	7.20961			0.291670
$612$		0			0
$613$	21.4072	−	21.4072i	0.864628	−	0.864628i	−0.127243	−	0.991872i	$-0.540613\pi$
$613$	21.4072	−	21.4072i	0.864628	−	0.864628i	0.991872	+	0.127243i	$0.0406129\pi$
$614$		0			0
$615$	−4.27994	−	4.35257i	−0.172584	−	0.175512i
$616$		0			0
$617$	1.82038	+	1.82038i	0.0732859	+	0.0732859i	0.742800	−	0.669514i	$-0.233497\pi$
$617$	1.82038	+	1.82038i	0.0732859	+	0.0732859i	−0.669514	+	0.742800i	$0.733497\pi$
$618$		0			0
$619$	11.7390			0.471831			0.235916	−	0.971774i	$-0.424191\pi$
$619$	11.7390			0.471831			0.235916	+	0.971774i	$0.424191\pi$
$620$		0			0
$621$			4.30858i			0.172897i
$622$		0			0
$623$	21.5851	+	38.1111i	0.864789	+	1.52689i
$624$		0			0
$625$	24.9858	+	0.841176i	0.999434	+	0.0336471i
$626$		0			0
$627$	4.80265	+	4.80265i	0.191799	+	0.191799i
$628$		0			0
$629$	0.219106			0.00873635
$630$		0			0
$631$	16.0788			0.640085			0.320043	−	0.947403i	$-0.396303\pi$
$631$	16.0788			0.640085			0.320043	+	0.947403i	$0.396303\pi$
$632$		0			0
$633$	−17.1676	−	17.1676i	−0.682349	−	0.682349i
$634$		0			0
$635$	1.66300	−	1.63525i	0.0659942	−	0.0648930i
$636$		0			0
$637$	−7.84927	+	1.96462i	−0.310999	+	0.0778411i
$638$		0			0
$639$		−	16.2833i		−	0.644156i
$640$		0			0
$641$	−7.16795			−0.283117			−0.141559	−	0.989930i	$-0.545211\pi$
$641$	−7.16795			−0.283117			−0.141559	+	0.989930i	$0.545211\pi$
$642$		0			0
$643$	−17.8589	−	17.8589i	−0.704287	−	0.704287i	0.261041	−	0.965328i	$-0.415934\pi$
$643$	−17.8589	−	17.8589i	−0.704287	−	0.704287i	−0.965328	+	0.261041i	$0.915934\pi$
$644$		0			0
$645$	−0.0527690	+	6.27191i	−0.00207778	+	0.246956i
$646$		0			0
$647$	9.02595	−	9.02595i	0.354847	−	0.354847i	−0.507062	−	0.861909i	$-0.669269\pi$
$647$	9.02595	−	9.02595i	0.354847	−	0.354847i	0.861909	+	0.507062i	$0.169269\pi$
$648$		0			0
$649$	72.1767			2.83318
$650$		0			0
$651$	−9.93161	−	2.74942i	−0.389250	−	0.107758i
$652$		0			0
$653$	−1.90663	+	1.90663i	−0.0746123	+	0.0746123i	−0.743428	−	0.668816i	$-0.766801\pi$
$653$	−1.90663	+	1.90663i	−0.0746123	+	0.0746123i	0.668816	+	0.743428i	$0.266801\pi$
$654$		0			0
$655$	−30.4446	−	0.256147i	−1.18957	−	0.0100085i
$656$		0			0
$657$	−5.32068	+	5.32068i	−0.207579	+	0.207579i
$658$		0			0
$659$			42.8056i			1.66747i	0.552165	+	0.833735i	$0.313802\pi$
$659$			42.8056i			1.66747i	−0.552165	+	0.833735i	$0.686198\pi$
$660$		0			0
$661$			45.0781i			1.75334i	0.481095	+	0.876668i	$0.340239\pi$
$661$			45.0781i			1.75334i	−0.481095	+	0.876668i	$0.659761\pi$
$662$		0			0
$663$	−0.636105	−	0.636105i	−0.0247043	−	0.0247043i
$664$		0			0
$665$	−6.76208	+	3.75507i	−0.262222	+	0.145615i
$666$		0			0
$667$	−9.11070	−	9.11070i	−0.352768	−	0.352768i
$668$		0			0
$669$			17.5991i			0.680419i
$670$		0			0
$671$			56.8290i			2.19386i
$672$		0			0
$673$	22.0502	−	22.0502i	0.849974	−	0.849974i	−0.140155	−	0.990130i	$-0.544760\pi$
$673$	22.0502	−	22.0502i	0.849974	−	0.849974i	0.990130	+	0.140155i	$0.0447602\pi$
$674$		0			0
$675$	−3.59452	+	3.47554i	−0.138353	+	0.133774i
$676$		0			0
$677$	15.0980	−	15.0980i	0.580264	−	0.580264i	−0.354712	−	0.934976i	$-0.615421\pi$
$677$	15.0980	−	15.0980i	0.580264	−	0.580264i	0.934976	+	0.354712i	$0.115421\pi$
$678$		0			0
$679$	−35.0053	−	9.69071i	−1.34338	−	0.371895i
$680$		0			0
$681$	1.23113			0.0471771
$682$		0			0
$683$	4.73943	−	4.73943i	0.181349	−	0.181349i	−0.610594	−	0.791944i	$-0.709069\pi$
$683$	4.73943	−	4.73943i	0.181349	−	0.181349i	0.791944	+	0.610594i	$0.209069\pi$
$684$		0			0
$685$	−5.45773	+	5.36666i	−0.208529	+	0.205049i
$686$		0			0
$687$	14.5025	+	14.5025i	0.553303	+	0.553303i
$688$		0			0
$689$	−1.78422			−0.0679733
$690$		0			0
$691$			6.10818i			0.232366i	0.993228	+	0.116183i	$0.0370659\pi$
$691$			6.10818i			0.232366i	−0.993228	+	0.116183i	$0.962934\pi$
$692$		0			0
$693$	−11.9597	+	6.77362i	−0.454310	+	0.257309i
$694$		0			0
$695$	0.111610	−	13.2655i	0.00423359	−	0.503188i
$696$		0			0
$697$	1.50230	+	1.50230i	0.0569035	+	0.0569035i
$698$		0			0
$699$	3.52627			0.133376
$700$		0			0
$701$	28.4319			1.07386			0.536929	−	0.843628i	$-0.319584\pi$
$701$	28.4319			1.07386			0.536929	+	0.843628i	$0.319584\pi$
$702$		0			0
$703$	0.260276	+	0.260276i	0.00981648	+	0.00981648i
$704$		0			0
$705$	−0.117337	+	13.9462i	−0.00441917	+	0.525245i
$706$		0			0
$707$	−39.8906	+	22.5930i	−1.50024	+	0.849696i
$708$		0			0
$709$			11.7255i			0.440359i	0.975459	+	0.220180i	$0.0706643\pi$
$709$			11.7255i			0.440359i	−0.975459	+	0.220180i	$0.929336\pi$
$710$		0			0
$711$	−8.15872			−0.305976
$712$		0			0
$713$	−11.8666	−	11.8666i	−0.444406	−	0.444406i
$714$		0			0
$715$	−9.57422	+	9.41445i	−0.358055	+	0.352081i
$716$		0			0
$717$	16.2966	−	16.2966i	0.608607	−	0.608607i
$718$		0			0
$719$	19.4579			0.725656			0.362828	−	0.931856i	$-0.381811\pi$
$719$	19.4579			0.725656			0.362828	+	0.931856i	$0.381811\pi$
$720$		0			0
$721$	9.93071	−	35.8723i	0.369839	−	1.33595i
$722$		0			0
$723$	−14.6424	+	14.6424i	−0.544556	+	0.544556i
$724$		0			0
$725$	0.251583	−	14.9500i	0.00934356	−	0.555229i
$726$		0			0
$727$	22.3113	−	22.3113i	0.827481	−	0.827481i	−0.159686	−	0.987168i	$-0.551048\pi$
$727$	22.3113	−	22.3113i	0.827481	−	0.827481i	0.987168	+	0.159686i	$0.0510483\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	2.18297i		−	0.0807402i
$732$		0			0
$733$	−9.17722	−	9.17722i	−0.338968	−	0.338968i	0.517011	−	0.855979i	$-0.327045\pi$
$733$	−9.17722	−	9.17722i	−0.338968	−	0.338968i	−0.855979	+	0.517011i	$0.827045\pi$
$734$		0			0
$735$	−3.67259	−	15.2155i	−0.135466	−	0.561233i
$736$		0			0
$737$	52.2125	+	52.2125i	1.92327	+	1.92327i
$738$		0			0
$739$		−	18.5498i		−	0.682366i	−0.939997	−	0.341183i	$-0.889172\pi$
$739$		−	18.5498i		−	0.682366i	0.939997	−	0.341183i	$-0.110828\pi$
$740$		0			0
$741$		−	1.51125i		−	0.0555173i
$742$		0			0
$743$	25.0521	−	25.0521i	0.919072	−	0.919072i	−0.0778896	−	0.996962i	$-0.524818\pi$
$743$	25.0521	−	25.0521i	0.919072	−	0.919072i	0.996962	+	0.0778896i	$0.0248182\pi$
$744$		0			0
$745$	13.3378	+	0.112218i	0.488660	+	0.00411137i
$746$		0			0
$747$	7.49447	−	7.49447i	0.274208	−	0.274208i
$748$		0			0
$749$	4.45112	−	16.0786i	0.162640	−	0.587498i
$750$		0			0
$751$	2.07100			0.0755720			0.0377860	−	0.999286i	$-0.487969\pi$
$751$	2.07100			0.0755720			0.0377860	+	0.999286i	$0.487969\pi$
$752$		0			0
$753$	2.21025	−	2.21025i	0.0805459	−	0.0805459i
$754$		0			0
$755$	−0.147875	+	17.5758i	−0.00538171	+	0.639648i
$756$		0			0
$757$	2.35793	+	2.35793i	0.0857003	+	0.0857003i	0.748657	−	0.662957i	$-0.230699\pi$
$757$	2.35793	+	2.35793i	0.0857003	+	0.0857003i	−0.662957	+	0.748657i	$0.730699\pi$
$758$		0			0
$759$	−22.3830			−0.812452
$760$		0			0
$761$		−	26.2514i		−	0.951614i	−0.879550	−	0.475807i	$-0.842156\pi$
$761$		−	26.2514i		−	0.951614i	0.879550	−	0.475807i	$-0.157844\pi$
$762$		0			0
$763$	15.5854	−	8.82715i	0.564230	−	0.319564i
$764$		0			0
$765$	1.24083	−	1.22012i	0.0448622	−	0.0441136i
$766$		0			0
$767$	−11.3559	−	11.3559i	−0.410039	−	0.410039i
$768$		0			0
$769$	36.8140			1.32755			0.663773	−	0.747934i	$-0.268954\pi$
$769$	36.8140			1.32755			0.663773	+	0.747934i	$0.268954\pi$
$770$		0			0
$771$	−2.01780			−0.0726695
$772$		0			0
$773$	−2.82574	−	2.82574i	−0.101635	−	0.101635i	0.654461	−	0.756096i	$-0.272896\pi$
$773$	−2.82574	−	2.82574i	−0.101635	−	0.101635i	−0.756096	+	0.654461i	$0.772896\pi$
$774$		0			0
$775$	0.327683	−	19.4722i	0.0117707	−	0.699460i
$776$		0			0
$777$	−0.648143	+	0.367091i	−0.0232520	+	0.0131693i
$778$		0			0
$779$			3.56914i			0.127878i
$780$		0			0
$781$	84.5913			3.02691
$782$		0			0
$783$	2.11455	+	2.11455i	0.0755678	+	0.0755678i
$784$		0			0
$785$	20.7207	+	21.0723i	0.739553	+	0.752103i
$786$		0			0
$787$	−20.2284	+	20.2284i	−0.721065	+	0.721065i	−0.968822	−	0.247757i	$-0.920307\pi$
$787$	−20.2284	+	20.2284i	−0.721065	+	0.721065i	0.247757	+	0.968822i	$0.420307\pi$
$788$		0			0
$789$	11.6034			0.413090
$790$		0			0
$791$	−14.5322	−	4.02302i	−0.516705	−	0.143042i
$792$		0			0
$793$	8.94121	−	8.94121i	0.317512	−	0.317512i
$794$		0			0
$795$	0.0290383	−	3.45137i	0.00102988	−	0.122408i
$796$		0			0
$797$	35.7989	−	35.7989i	1.26806	−	1.26806i	0.320972	−	0.947089i	$-0.395990\pi$
$797$	35.7989	−	35.7989i	1.26806	−	1.26806i	0.947089	−	0.320972i	$-0.104010\pi$
$798$		0			0
$799$		−	4.85406i		−	0.171724i
$800$		0			0
$801$		−	16.5546i		−	0.584927i
$802$		0			0
$803$	−27.6409	−	27.6409i	−0.975425	−	0.975425i
$804$		0			0
$805$	7.00716	−	24.5079i	0.246970	−	0.863789i
$806$		0			0
$807$	6.81588	+	6.81588i	0.239930	+	0.239930i
$808$		0			0
$809$			30.7500i			1.08111i	0.841308	+	0.540556i	$0.181786\pi$
$809$			30.7500i			1.08111i	−0.841308	+	0.540556i	$0.818214\pi$
$810$		0			0
$811$		−	24.9358i		−	0.875613i	−0.899069	−	0.437806i	$-0.855756\pi$
$811$		−	24.9358i		−	0.875613i	0.899069	−	0.437806i	$-0.144244\pi$
$812$		0			0
$813$	18.8070	−	18.8070i	0.659590	−	0.659590i
$814$		0			0
$815$	−23.7882	−	24.1919i	−0.833264	−	0.847404i
$816$		0			0
$817$	2.59315	−	2.59315i	0.0907227	−	0.0907227i
$818$		0			0
$819$	2.94740	+	0.815946i	0.102991	+	0.0285114i
$820$		0			0
$821$	−19.5635			−0.682770			−0.341385	−	0.939924i	$-0.610896\pi$
$821$	−19.5635			−0.682770			−0.341385	+	0.939924i	$0.610896\pi$
$822$		0			0
$823$	18.2254	−	18.2254i	0.635297	−	0.635297i	−0.314094	−	0.949392i	$-0.601701\pi$
$823$	18.2254	−	18.2254i	0.635297	−	0.635297i	0.949392	+	0.314094i	$0.101701\pi$
$824$		0			0
$825$	−18.0554	−	18.6735i	−0.628609	−	0.650128i
$826$		0			0
$827$	19.7863	+	19.7863i	0.688038	+	0.688038i	0.961798	−	0.273760i	$-0.0882675\pi$
$827$	19.7863	+	19.7863i	0.688038	+	0.688038i	−0.273760	+	0.961798i	$0.588268\pi$
$828$		0			0
$829$	−25.7696			−0.895014			−0.447507	−	0.894280i	$-0.647688\pi$
$829$	−25.7696			−0.895014			−0.447507	+	0.894280i	$0.647688\pi$
$830$		0			0
$831$			28.2121i			0.978665i
$832$		0			0
$833$	1.32273	+	5.28472i	0.0458299	+	0.183105i
$834$		0			0
$835$	−22.4893	−	22.8709i	−0.778273	−	0.791481i
$836$		0			0
$837$	2.75417	+	2.75417i	0.0951980	+	0.0951980i
$838$		0			0
$839$	18.0163			0.621990			0.310995	−	0.950411i	$-0.399338\pi$
$839$	18.0163			0.621990			0.310995	+	0.950411i	$0.399338\pi$
$840$		0			0
$841$	20.0574			0.691633
$842$		0			0
$843$	10.6729	+	10.6729i	0.367596	+	0.367596i
$844$		0			0
$845$	−26.0803	−	0.219428i	−0.897188	−	0.00754854i
$846$		0			0
$847$	−20.8462	−	36.8066i	−0.716285	−	1.26469i
$848$		0			0
$849$			0.230596i			0.00791404i
$850$		0			0
$851$	−1.21303			−0.0415821
$852$		0			0
$853$	−17.0643	−	17.0643i	−0.584271	−	0.584271i	0.351803	−	0.936074i	$-0.385569\pi$
$853$	−17.0643	−	17.0643i	−0.584271	−	0.584271i	−0.936074	+	0.351803i	$0.885569\pi$
$854$		0			0
$855$	2.92335	+	0.0245958i	0.0999766	+	0.000841158i
$856$		0			0
$857$	4.20254	−	4.20254i	0.143556	−	0.143556i	−0.631676	−	0.775232i	$-0.717633\pi$
$857$	4.20254	−	4.20254i	0.143556	−	0.143556i	0.775232	+	0.631676i	$0.217633\pi$
$858$		0			0
$859$	−31.7205			−1.08229			−0.541145	−	0.840929i	$-0.682009\pi$
$859$	−31.7205			−1.08229			−0.541145	+	0.840929i	$0.682009\pi$
$860$		0			0
$861$	−6.96091	−	1.92703i	−0.237227	−	0.0656729i
$862$		0			0
$863$	23.4690	−	23.4690i	0.798894	−	0.798894i	−0.184027	−	0.982921i	$-0.558913\pi$
$863$	23.4690	−	23.4690i	0.798894	−	0.798894i	0.982921	+	0.184027i	$0.0589134\pi$
$864$		0			0
$865$	−4.72476	+	4.64592i	−0.160647	+	0.157966i
$866$		0			0
$867$	11.5925	−	11.5925i	0.393703	−	0.393703i
$868$		0			0
$869$		−	42.3845i		−	1.43779i
$870$		0			0
$871$		−	16.4297i		−	0.556701i
$872$		0			0
$873$	9.70745	+	9.70745i	0.328547	+	0.328547i
$874$		0			0
$875$	26.0986	−	13.9236i	0.882292	−	0.470702i
$876$		0			0
$877$	−15.6871	−	15.6871i	−0.529715	−	0.529715i	0.390773	−	0.920487i	$-0.372208\pi$
$877$	−15.6871	−	15.6871i	−0.529715	−	0.529715i	−0.920487	+	0.390773i	$0.872208\pi$
$878$		0			0
$879$		−	19.8890i		−	0.670839i
$880$		0			0
$881$			30.4222i			1.02495i	0.858702	+	0.512475i	$0.171271\pi$
$881$			30.4222i			1.02495i	−0.858702	+	0.512475i	$0.828729\pi$
$882$		0			0
$883$	−25.2219	+	25.2219i	−0.848786	+	0.848786i	−0.989982	−	0.141196i	$-0.954905\pi$
$883$	−25.2219	+	25.2219i	−0.848786	+	0.848786i	0.141196	+	0.989982i	$0.454905\pi$
$884$		0			0
$885$	22.1517	−	21.7820i	0.744620	−	0.732194i
$886$		0			0
$887$	3.90707	−	3.90707i	0.131187	−	0.131187i	−0.638465	−	0.769651i	$-0.720430\pi$
$887$	3.90707	−	3.90707i	0.131187	−	0.131187i	0.769651	+	0.638465i	$0.220430\pi$
$888$		0			0
$889$	0.736267	−	2.65958i	0.0246936	−	0.0891996i
$890$		0			0
$891$	5.19499			0.174039
$892$		0			0
$893$	5.76611	−	5.76611i	0.192956	−	0.192956i
$894$		0			0
$895$	−43.9293	−	0.369601i	−1.46839	−	0.0123544i
$896$		0			0
$897$	3.52164	+	3.52164i	0.117584	+	0.117584i
$898$		0			0
$899$	−11.6476			−0.388471
$900$		0			0
$901$			1.20127i			0.0400201i
$902$		0			0
$903$	3.65735	+	6.45750i	0.121709	+	0.214892i
$904$		0			0
$905$	−21.2630	−	0.178898i	−0.706807	−	0.00594676i
$906$		0			0
$907$	27.4534	+	27.4534i	0.911576	+	0.911576i	0.996396	−	0.0848205i	$-0.0270317\pi$
$907$	27.4534	+	27.4534i	0.911576	+	0.911576i	−0.0848205	+	0.996396i	$0.527032\pi$
$908$		0			0
$909$	17.3275			0.574718
$910$		0			0
$911$	32.7134			1.08384			0.541922	−	0.840429i	$-0.317697\pi$
$911$	32.7134			1.08384			0.541922	+	0.840429i	$0.317697\pi$
$912$		0			0
$913$	38.9337	+	38.9337i	1.28852	+	1.28852i
$914$		0			0
$915$	17.1503	+	17.4413i	0.566971	+	0.576592i
$916$		0			0
$917$	−31.3455	+	17.7532i	−1.03512	+	0.586263i
$918$		0			0
$919$			13.8174i			0.455793i	0.973685	+	0.227897i	$0.0731848\pi$
$919$			13.8174i			0.455793i	−0.973685	+	0.227897i	$0.926815\pi$
$920$		0			0
$921$	−10.2978			−0.339323
$922$		0			0
$923$	−13.3092	−	13.3092i	−0.438077	−	0.438077i
$924$		0			0
$925$	−0.978498	−	1.01199i	−0.0321728	−	0.0332742i
$926$		0			0
$927$	−9.94786	+	9.94786i	−0.326730	+	0.326730i
$928$		0			0
$929$	−12.1425			−0.398381			−0.199191	−	0.979961i	$-0.563831\pi$
$929$	−12.1425			−0.398381			−0.199191	+	0.979961i	$0.563831\pi$
$930$		0			0
$931$	−4.70643	+	7.84896i	−0.154247	+	0.257239i
$932$		0			0
$933$	5.75785	−	5.75785i	0.188503	−	0.188503i
$934$		0			0
$935$	6.33852	+	6.44609i	0.207292	+	0.210810i
$936$		0			0
$937$	11.4188	−	11.4188i	0.373036	−	0.373036i	−0.495546	−	0.868582i	$-0.665032\pi$
$937$	11.4188	−	11.4188i	0.373036	−	0.373036i	0.868582	+	0.495546i	$0.165032\pi$
$938$		0			0
$939$		−	16.5242i		−	0.539248i
$940$		0			0
$941$		−	21.2998i		−	0.694353i	−0.937800	−	0.347176i	$-0.887140\pi$
$941$		−	21.2998i		−	0.694353i	0.937800	−	0.347176i	$-0.112860\pi$
$942$		0			0
$943$	−8.31709	−	8.31709i	−0.270842	−	0.270842i
$944$		0			0
$945$	−1.62633	+	5.68815i	−0.0529044	+	0.185036i
$946$		0			0
$947$	−38.6453	−	38.6453i	−1.25580	−	1.25580i	−0.953078	−	0.302726i	$-0.902103\pi$
$947$	−38.6453	−	38.6453i	−1.25580	−	1.25580i	−0.302726	−	0.953078i	$-0.597897\pi$
$948$		0			0
$949$			8.69776i			0.282341i
$950$		0			0
$951$			3.39576i			0.110115i
$952$		0			0
$953$	−12.2652	+	12.2652i	−0.397308	+	0.397308i	−0.877283	−	0.479974i	$-0.840646\pi$
$953$	−12.2652	+	12.2652i	−0.397308	+	0.397308i	0.479974	+	0.877283i	$0.340646\pi$
$954$		0			0
$955$	0.269793	−	32.0665i	0.00873030	−	1.03765i
$956$		0			0
$957$	−10.9851	+	10.9851i	−0.355096	+	0.355096i
$958$		0			0
$959$	−2.41632	+	8.72836i	−0.0780270	+	0.281854i
$960$		0			0
$961$	15.8291			0.510617
$962$		0			0
$963$	−4.45880	+	4.45880i	−0.143683	+	0.143683i
$964$		0			0
$965$	6.52311	+	6.63380i	0.209986	+	0.213550i
$966$		0			0
$967$	−2.52230	−	2.52230i	−0.0811116	−	0.0811116i	0.665387	−	0.746499i	$-0.268267\pi$
$967$	−2.52230	−	2.52230i	−0.0811116	−	0.0811116i	−0.746499	+	0.665387i	$0.768267\pi$
$968$		0			0
$969$	−1.01749			−0.0326865
$970$		0			0
$971$			7.22848i			0.231973i	0.993251	+	0.115986i	$0.0370029\pi$
$971$			7.22848i			0.231973i	−0.993251	+	0.115986i	$0.962997\pi$
$972$		0			0
$973$	−7.73551	−	13.6580i	−0.247989	−	0.437855i
$974$		0			0
$975$	−0.0972465	+	5.77875i	−0.00311438	+	0.185068i
$976$		0			0
$977$	11.4690	+	11.4690i	0.366925	+	0.366925i	0.866355	−	0.499429i	$-0.166457\pi$
$977$	11.4690	+	11.4690i	0.366925	+	0.366925i	−0.499429	+	0.866355i	$0.666457\pi$
$978$		0			0
$979$	86.0008			2.74860
$980$		0			0
$981$	−6.76993			−0.216147
$982$		0			0
$983$	6.25887	+	6.25887i	0.199627	+	0.199627i	0.799840	−	0.600213i	$-0.204918\pi$
$983$	6.25887	+	6.25887i	0.199627	+	0.199627i	−0.600213	+	0.799840i	$0.704918\pi$
$984$		0			0
$985$	−19.5279	+	19.2020i	−0.622209	+	0.611827i
$986$		0			0
$987$	8.13248	+	14.3589i	0.258860	+	0.457048i
$988$		0			0
$989$			12.0855i			0.384296i
$990$		0			0
$991$	26.2928			0.835219			0.417609	−	0.908627i	$-0.362868\pi$
$991$	26.2928			0.835219			0.417609	+	0.908627i	$0.362868\pi$
$992$		0			0
$993$	−14.0905	−	14.0905i	−0.447149	−	0.447149i
$994$		0			0
$995$	−0.0766340	+	9.10840i	−0.00242946	+	0.288756i
$996$		0			0
$997$	−30.7350	+	30.7350i	−0.973386	+	0.973386i	−0.999655	−	0.0262684i	$-0.991638\pi$
$997$	−30.7350	+	30.7350i	−0.973386	+	0.973386i	0.0262684	+	0.999655i	$0.491638\pi$
$998$		0			0
$999$	0.281538			0.00890746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bt.b.97.4	yes	24
4.3	odd	2		1680.2.cz.e.97.7		24
5.3	odd	4		840.2.bt.a.433.9	yes	24
7.6	odd	2		840.2.bt.a.97.9	✓	24
20.3	even	4		1680.2.cz.f.433.6		24
28.27	even	2		1680.2.cz.f.97.6		24
35.13	even	4	inner	840.2.bt.b.433.4	yes	24
140.83	odd	4		1680.2.cz.e.433.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.9	✓	24	7.6	odd	2
840.2.bt.a.433.9	yes	24	5.3	odd	4
840.2.bt.b.97.4	yes	24	1.1	even	1	trivial
840.2.bt.b.433.4	yes	24	35.13	even	4	inner
1680.2.cz.e.97.7		24	4.3	odd	2
1680.2.cz.e.433.7		24	140.83	odd	4
1680.2.cz.f.97.6		24	28.27	even	2
1680.2.cz.f.433.6		24	20.3	even	4

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.bt (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(0.0188126 - 2.23599i) q^{5} +(-1.30388 - 2.30215i) q^{7} +1.00000i q^{9} -5.19499 q^{11} +(0.817355 + 0.817355i) q^{13} +(-1.59439 + 1.56778i) q^{15} +(0.550305 - 0.550305i) q^{17} +1.30741 q^{19} +(-0.705888 + 2.54985i) q^{21} +(-3.04663 + 3.04663i) q^{23} +(-4.99929 - 0.0841295i) q^{25} +(0.707107 - 0.707107i) q^{27} +2.99042i q^{29} +3.89498i q^{31} +(3.67341 + 3.67341i) q^{33} +(-5.17212 + 2.87214i) q^{35} +(0.199077 + 0.199077i) q^{37} -1.15591i q^{39} +2.72993i q^{41} +(1.98342 - 1.98342i) q^{43} +(2.23599 + 0.0188126i) q^{45} +(4.41033 - 4.41033i) q^{47} +(-3.59981 + 6.00344i) q^{49} -0.778249 q^{51} +(-1.09146 + 1.09146i) q^{53} +(-0.0977312 + 11.6159i) q^{55} +(-0.924478 - 0.924478i) q^{57} -13.8935 q^{59} -10.9392i q^{61} +(2.30215 - 1.30388i) q^{63} +(1.84297 - 1.81222i) q^{65} +(-10.0506 - 10.0506i) q^{67} +4.30858 q^{69} -16.2833 q^{71} +(5.32068 + 5.32068i) q^{73} +(3.47554 + 3.59452i) q^{75} +(6.77362 + 11.9597i) q^{77} +8.15872i q^{79} -1.00000 q^{81} +(-7.49447 - 7.49447i) q^{83} +(-1.22012 - 1.24083i) q^{85} +(2.11455 - 2.11455i) q^{87} -16.5546 q^{89} +(0.815946 - 2.94740i) q^{91} +(2.75417 - 2.75417i) q^{93} +(0.0245958 - 2.92335i) q^{95} +(9.70745 - 9.70745i) q^{97} -5.19499i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{11} - 16 q^{13} + 4 q^{15} - 20 q^{17} - 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} + 4 q^{45} + 24 q^{47} - 36 q^{49} + 16 q^{53} - 28 q^{55} + 4 q^{57} - 8 q^{59} + 4 q^{63} + 24 q^{65}+ \cdots + 28 q^{97}+O(q^{100}) \) 24 * q - 8 * q^11 - 16 * q^13 + 4 * q^15 - 20 * q^17 - 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 + 4 * q^45 + 24 * q^47 - 36 * q^49 + 16 * q^53 - 28 * q^55 + 4 * q^57 - 8 * q^59 + 4 * q^63 + 24 * q^65 + 16 * q^67 + 8 * q^69 + 8 * q^71 + 28 * q^73 + 28 * q^77 - 24 * q^81 - 64 * q^83 - 20 * q^85 - 20 * q^87 - 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 + 28 * q^97

Introduction

L-functions

Modular forms

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