LMFDB - Embedded newform 840.2.bt.a.97.9

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

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.9
Character	$\chi$	$=$	840.97
Dual form			840.2.bt.a.433.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(-0.0188126 + 2.23599i) q^{5} +(-2.30215 - 1.30388i) q^{7} +1.00000i q^{9} -5.19499 q^{11} +(-0.817355 - 0.817355i) q^{13} +(-1.59439 + 1.56778i) q^{15} +(-0.550305 + 0.550305i) q^{17} -1.30741 q^{19} +(-0.705888 - 2.54985i) q^{21} +(-3.04663 + 3.04663i) q^{23} +(-4.99929 - 0.0841295i) q^{25} +(-0.707107 + 0.707107i) q^{27} +2.99042i q^{29} -3.89498i q^{31} +(-3.67341 - 3.67341i) q^{33} +(2.95876 - 5.12306i) q^{35} +(0.199077 + 0.199077i) q^{37} -1.15591i q^{39} -2.72993i q^{41} +(1.98342 - 1.98342i) q^{43} +(-2.23599 - 0.0188126i) q^{45} +(-4.41033 + 4.41033i) q^{47} +(3.59981 + 6.00344i) q^{49} -0.778249 q^{51} +(-1.09146 + 1.09146i) q^{53} +(0.0977312 - 11.6159i) q^{55} +(-0.924478 - 0.924478i) q^{57} +13.8935 q^{59} +10.9392i q^{61} +(1.30388 - 2.30215i) q^{63} +(1.84297 - 1.81222i) q^{65} +(-10.0506 - 10.0506i) q^{67} -4.30858 q^{69} -16.2833 q^{71} +(-5.32068 - 5.32068i) q^{73} +(-3.47554 - 3.59452i) q^{75} +(11.9597 + 6.77362i) q^{77} +8.15872i q^{79} -1.00000 q^{81} +(7.49447 + 7.49447i) q^{83} +(-1.22012 - 1.24083i) q^{85} +(-2.11455 + 2.11455i) q^{87} +16.5546 q^{89} +(0.815946 + 2.94740i) q^{91} +(2.75417 - 2.75417i) q^{93} +(0.0245958 - 2.92335i) q^{95} +(-9.70745 + 9.70745i) q^{97} -5.19499i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7} - 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} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 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 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * 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
$7$	−2.30215	−	1.30388i	−0.870132	−	0.492819i
$7$	−2.30215	−	1.30388i	−0.870132	−	0.492819i
$8$		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	0.584616	−	0.811310i	$-0.301245\pi$
$13$	−0.817355	−	0.817355i	−0.226693	−	0.226693i	−0.811310	+	0.584616i	$0.801245\pi$
$14$		0			0
$15$	−1.59439	+	1.56778i	−0.411669	+	0.404799i
$16$		0			0
$17$	−0.550305	+	0.550305i	−0.133469	+	0.133469i	−0.770685	−	0.637216i	$-0.780086\pi$
$17$	−0.550305	+	0.550305i	−0.133469	+	0.133469i	0.637216	+	0.770685i	$0.280086\pi$
$18$		0			0
$19$	−1.30741			−0.299940			−0.149970	−	0.988691i	$-0.547918\pi$
$19$	−1.30741			−0.299940			−0.149970	+	0.988691i	$0.547918\pi$
$20$		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	$-0.886256\pi$
$31$		−	3.89498i		−	0.699559i	0.936832	−	0.349780i	$-0.113744\pi$
$32$		0			0
$33$	−3.67341	−	3.67341i	−0.639459	−	0.639459i
$34$		0			0
$35$	2.95876	−	5.12306i	0.500122	−	0.865955i
$36$		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	$-0.931621\pi$
$41$		−	2.72993i		−	0.426344i	0.977015	−	0.213172i	$-0.0683795\pi$
$42$		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	−0.951369	−	0.308055i	$-0.900322\pi$
$47$	−4.41033	+	4.41033i	−0.643313	+	0.643313i	0.308055	+	0.951369i	$0.400322\pi$
$48$		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	$-0.140325\pi$
$59$	13.8935			1.80878			0.904392	+	0.426702i	$0.140325\pi$
$60$		0			0
$61$			10.9392i			1.40062i	0.713838	+	0.700311i	$0.246955\pi$
$61$			10.9392i			1.40062i	−0.713838	+	0.700311i	$0.753045\pi$
$62$		0			0
$63$	1.30388	−	2.30215i	0.164273	−	0.290044i
$64$		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	0.323492	−	0.946231i	$-0.395143\pi$
$73$	−5.32068	−	5.32068i	−0.622738	−	0.622738i	−0.946231	+	0.323492i	$0.895143\pi$
$74$		0			0
$75$	−3.47554	−	3.59452i	−0.401321	−	0.415060i
$76$		0			0
$77$	11.9597	+	6.77362i	1.36293	+	0.771926i
$78$		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	0.986484	−	0.163859i	$-0.0523943\pi$
$83$	7.49447	+	7.49447i	0.822625	+	0.822625i	−0.163859	+	0.986484i	$0.552394\pi$
$84$		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	$-0.159283\pi$
$89$	16.5546			1.75478			0.877390	+	0.479777i	$0.159283\pi$
$90$		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	−0.999898	−	0.0142566i	$-0.995462\pi$
$97$	−9.70745	+	9.70745i	−0.985642	+	0.985642i	0.0142566	+	0.999898i	$0.495462\pi$
$98$		0			0
$99$		−	5.19499i		−	0.522116i
$100$		0			0
$101$			17.3275i			1.72415i	0.506777	+	0.862077i	$0.330837\pi$
$101$			17.3275i			1.72415i	−0.506777	+	0.862077i	$0.669163\pi$
$102$		0			0
$103$	−9.94786	−	9.94786i	−0.980191	−	0.980191i	0.0196162	−	0.999808i	$-0.493756\pi$
$103$	−9.94786	−	9.94786i	−0.980191	−	0.980191i	−0.999808	+	0.0196162i	$0.993756\pi$
$104$		0			0
$105$	5.71471	−	1.53039i	0.557699	−	0.149351i
$106$		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	$0.202771\pi$
$131$			13.6157i			1.18961i	−0.803869	+	0.594806i	$0.797229\pi$
$132$		0			0
$133$	3.00986	+	1.70470i	0.260988	+	0.147816i
$134$		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	$-0.580958\pi$
$139$	−5.93270			−0.503205			−0.251603	+	0.967831i	$0.580958\pi$
$140$		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
$147$	−1.69962	+	6.79053i	−0.140183	+	0.560073i
$148$		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	−0.227844	−	0.973698i	$-0.573167\pi$
$157$	9.34553	−	9.34553i	0.745854	−	0.745854i	0.973698	+	0.227844i	$0.0731675\pi$
$158$		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	−0.980654	−	0.195749i	$-0.937286\pi$
$167$	−10.1432	+	10.1432i	−0.784905	+	0.784905i	0.195749	+	0.980654i	$0.437286\pi$
$168$		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	0.782262	−	0.622950i	$-0.214066\pi$
$173$	2.09542	+	2.09542i	0.159312	+	0.159312i	−0.622950	+	0.782262i	$0.714066\pi$
$174$		0			0
$175$	11.3994	+	6.71214i	0.861717	+	0.507390i
$176$		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	$0.114980\pi$
$181$			9.50946i			0.706832i	−0.935466	+	0.353416i	$0.885020\pi$
$182$		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	$-0.453880\pi$
$199$	4.07354			0.288766			0.144383	+	0.989522i	$0.453880\pi$
$200$		0			0
$201$		−	14.2136i		−	1.00255i
$202$		0			0
$203$	3.89914	−	6.88441i	0.273666	−	0.483191i
$204$		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
$217$	−5.07857	+	8.96684i	−0.344756	+	0.608709i
$218$		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	0.987972	−	0.154633i	$-0.0494194\pi$
$223$	12.4444	+	12.4444i	0.833339	+	0.833339i	−0.154633	+	0.987972i	$0.549419\pi$
$224$		0			0
$225$	0.0841295	−	4.99929i	0.00560864	−	0.333286i
$226$		0			0
$227$	0.870542	−	0.870542i	0.0577799	−	0.0577799i	−0.677626	−	0.735406i	$-0.736991\pi$
$227$	0.870542	−	0.870542i	0.0577799	−	0.0577799i	0.735406	+	0.677626i	$0.236991\pi$
$228$		0			0
$229$	20.5096			1.35531			0.677655	−	0.735380i	$-0.262996\pi$
$229$	20.5096			1.35531			0.677655	+	0.735380i	$0.262996\pi$
$230$		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	$0.232397\pi$
$241$			20.7075i			1.33388i	−0.745109	+	0.666942i	$0.767603\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−13.4914	+	7.93620i	−0.861931	+	0.507025i
$246$		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	$-0.968548\pi$
$251$		−	3.12576i		−	0.197296i	0.995122	−	0.0986481i	$-0.0314518\pi$
$252$		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	−0.750206	−	0.661204i	$-0.770046\pi$
$257$	−1.42680	+	1.42680i	−0.0890016	+	0.0890016i	0.661204	+	0.750206i	$0.270046\pi$
$258$		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	$-0.405062\pi$
$269$	9.63912			0.587707			0.293854	+	0.955850i	$0.405062\pi$
$270$		0			0
$271$		−	26.5971i		−	1.61566i	−0.589417	−	0.807829i	$-0.700643\pi$
$271$		−	26.5971i		−	1.61566i	0.589417	−	0.807829i	$-0.299357\pi$
$272$		0			0
$273$	−1.50717	+	2.66109i	−0.0912180	+	0.161057i
$274$		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	0.711937	−	0.702244i	$-0.247818\pi$
$283$	0.163056	+	0.163056i	0.00969268	+	0.00969268i	−0.702244	+	0.711937i	$0.747818\pi$
$284$		0			0
$285$	2.08452	−	2.04973i	0.123476	−	0.121416i
$286$		0			0
$287$	−3.55950	+	6.28472i	−0.210110	+	0.370976i
$288$		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	0.164732	−	0.986338i	$-0.447324\pi$
$293$	−14.0636	−	14.0636i	−0.821606	−	0.821606i	−0.986338	+	0.164732i	$0.947324\pi$
$294$		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	−0.883678	−	0.468095i	$-0.844941\pi$
$307$	−7.28161	+	7.28161i	−0.415584	+	0.415584i	0.468095	+	0.883678i	$0.344941\pi$
$308$		0			0
$309$		−	14.0684i		−	0.800323i
$310$		0			0
$311$		−	8.14282i		−	0.461737i	−0.972985	−	0.230869i	$-0.925843\pi$
$311$		−	8.14282i		−	0.461737i	0.972985	−	0.230869i	$-0.0741568\pi$
$312$		0			0
$313$	−11.6844	−	11.6844i	−0.660441	−	0.660441i	0.295043	−	0.955484i	$-0.404666\pi$
$313$	−11.6844	−	11.6844i	−0.660441	−	0.660441i	−0.955484	+	0.295043i	$0.904666\pi$
$314$		0			0
$315$	5.12306	+	2.95876i	0.288652	+	0.166707i
$316$		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
$343$	−0.459569	−	18.5146i	−0.0248144	−	0.999692i
$344$		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	$-0.402951\pi$
$349$	11.2159			0.600373			0.300186	+	0.953881i	$0.402951\pi$
$350$		0			0
$351$	1.15591			0.0616981
$352$		0			0
$353$	−25.4175	−	25.4175i	−1.35283	−	1.35283i	−0.882475	−	0.470360i	$-0.844124\pi$
$353$	−25.4175	−	25.4175i	−1.35283	−	1.35283i	−0.470360	−	0.882475i	$-0.655876\pi$
$354$		0			0
$355$	0.306330	−	36.4092i	0.0162583	−	1.93240i
$356$		0			0
$357$	1.79165	+	1.01474i	0.0948240	+	0.0537057i
$358$		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	$0.538798\pi$
$367$	−21.3444	+	21.3444i	−1.11417	+	1.11417i	−0.992581	+	0.121587i	$0.961202\pi$
$368$		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	$0.0836313\pi$
$383$	23.9817	+	23.9817i	1.22541	+	1.22541i	0.259723	+	0.965683i	$0.416369\pi$
$384$		0			0
$385$	−15.3707	+	26.6142i	−0.783365	+	1.35639i
$386$		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	−0.716173	−	0.697923i	$-0.754108\pi$
$397$	−0.363615	+	0.363615i	−0.0182493	+	0.0182493i	0.697923	+	0.716173i	$0.254108\pi$
$398$		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	$-0.375000\pi$
$409$	15.4786			0.765369			0.382684	+	0.923879i	$0.375000\pi$
$410$		0			0
$411$		−	3.42309i		−	0.168849i
$412$		0			0
$413$	−31.9850	−	18.1155i	−1.57388	−	0.891403i
$414$		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	$-0.816116\pi$
$419$	−34.2957			−1.67546			−0.837728	+	0.546088i	$0.816116\pi$
$420$		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
$427$	14.2634	−	25.1837i	0.690253	−	1.21873i
$428$		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	$0.0465515\pi$
$433$	23.6189	+	23.6189i	1.13505	+	1.13505i	0.145725	+	0.989325i	$0.453449\pi$
$434$		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	$-0.594109\pi$
$439$	−12.2095			−0.582729			−0.291365	+	0.956612i	$0.594109\pi$
$440$		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
$455$	−6.60571	+	1.76900i	−0.309681	+	0.0829319i
$456$		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	$-0.774771\pi$
$461$		−	27.9120i		−	1.29999i	0.759939	−	0.649995i	$-0.225229\pi$
$462$		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	$0.587523\pi$
$467$	−26.6658	+	26.6658i	−1.23395	+	1.23395i	−0.962435	+	0.271511i	$0.912477\pi$
$468$		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	$-0.641516\pi$
$479$	−18.8257			−0.860166			−0.430083	+	0.902789i	$0.641516\pi$
$480$		0			0
$481$		−	0.325434i		−	0.0148385i
$482$		0			0
$483$	9.91901	+	5.61786i	0.451331	+	0.255621i
$484$		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
$497$	37.4865	+	21.2314i	1.68150	+	0.952356i
$498$		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	0.273286	−	0.961933i	$-0.411890\pi$
$503$	−15.4448	−	15.4448i	−0.688647	−	0.688647i	−0.961933	+	0.273286i	$0.911890\pi$
$504$		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	$-0.747124\pi$
$509$	−31.6165			−1.40138			−0.700689	+	0.713467i	$0.747124\pi$
$510$		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	$0.0200733\pi$
$521$			2.87693i			0.126041i	−0.998012	+	0.0630203i	$0.979927\pi$
$522$		0			0
$523$	29.2446	+	29.2446i	1.27878	+	1.27878i	0.941353	+	0.337424i	$0.109556\pi$
$523$	29.2446	+	29.2446i	1.27878	+	1.27878i	0.337424	+	0.941353i	$0.390444\pi$
$524$		0			0
$525$	3.31442	+	12.8068i	0.144653	+	0.558935i
$526$		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
$553$	10.6380	−	18.7826i	0.452372	−	0.798718i
$554$		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	0.726895	−	0.686749i	$-0.240963\pi$
$563$	0.952567	+	0.952567i	0.0401459	+	0.0401459i	−0.686749	+	0.726895i	$0.740963\pi$
$564$		0			0
$565$	8.93514	+	9.08677i	0.375904	+	0.382283i
$566$		0			0
$567$	2.30215	+	1.30388i	0.0966813	+	0.0547577i
$568$		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	−0.0836224	−	0.996498i	$-0.526649\pi$
$577$	21.9280	−	21.9280i	0.912875	−	0.912875i	0.996498	+	0.0836224i	$0.0266490\pi$
$578$		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	−0.00583245	−	0.999983i	$-0.501857\pi$
$587$	24.0864	−	24.0864i	0.994151	−	0.994151i	0.999983	+	0.00583245i	$0.00185654\pi$
$588$		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	0.955369	−	0.295415i	$-0.0954579\pi$
$593$	16.0709	+	16.0709i	0.659954	+	0.659954i	−0.295415	+	0.955369i	$0.595458\pi$
$594$		0			0
$595$	1.19102	+	4.44746i	0.0488272	+	0.182328i
$596$		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	$-0.975196\pi$
$601$		−	3.81675i		−	0.155689i	0.996966	−	0.0778443i	$-0.0248037\pi$
$602$		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	−0.359814	−	0.933024i	$-0.617160\pi$
$607$	14.1224	−	14.1224i	0.573211	−	0.573211i	0.933024	+	0.359814i	$0.117160\pi$
$608$		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	$-0.575809\pi$
$619$	−11.7390			−0.471831			−0.235916	+	0.971774i	$0.575809\pi$
$620$		0			0
$621$		−	4.30858i		−	0.172897i
$622$		0			0
$623$	−38.1111	−	21.5851i	−1.52689	−	0.864789i
$624$		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
$637$	1.96462	−	7.84927i	0.0778411	−	0.310999i
$638$		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	0.965328	−	0.261041i	$-0.0840657\pi$
$643$	17.8589	+	17.8589i	0.704287	+	0.704287i	−0.261041	+	0.965328i	$0.584066\pi$
$644$		0			0
$645$	−0.0527690	+	6.27191i	−0.00207778	+	0.246956i
$646$		0			0
$647$	−9.02595	+	9.02595i	−0.354847	+	0.354847i	−0.861909	−	0.507062i	$-0.830731\pi$
$647$	−9.02595	+	9.02595i	−0.354847	+	0.354847i	0.507062	+	0.861909i	$0.330731\pi$
$648$		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	$-0.659761\pi$
$661$		−	45.0781i		−	1.75334i	0.481095	−	0.876668i	$-0.340239\pi$
$662$		0			0
$663$	0.636105	+	0.636105i	0.0247043	+	0.0247043i
$664$		0			0
$665$	−3.86832	+	6.69794i	−0.150007	+	0.259735i
$666$		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	−0.934976	−	0.354712i	$-0.884579\pi$
$677$	−15.0980	+	15.0980i	−0.580264	+	0.580264i	0.354712	+	0.934976i	$0.384579\pi$
$678$		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	$-0.962934\pi$
$691$		−	6.10818i		−	0.232366i	0.993228	−	0.116183i	$-0.0370659\pi$
$692$		0			0
$693$	−6.77362	+	11.9597i	−0.257309	+	0.454310i
$694$		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
$707$	22.5930	−	39.8906i	0.849696	−	1.50024i
$708$		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	$-0.618189\pi$
$719$	−19.4579			−0.725656			−0.362828	+	0.931856i	$0.618189\pi$
$720$		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	−0.987168	−	0.159686i	$-0.948952\pi$
$727$	−22.3113	+	22.3113i	−0.827481	+	0.827481i	0.159686	+	0.987168i	$0.448952\pi$
$728$		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	0.855979	−	0.517011i	$-0.172955\pi$
$733$	9.17722	+	9.17722i	0.338968	+	0.338968i	−0.517011	+	0.855979i	$0.672955\pi$
$734$		0			0
$735$	−15.1516	−	3.92809i	−0.558874	−	0.144890i
$736$		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	$0.157844\pi$
$761$			26.2514i			0.951614i	−0.879550	+	0.475807i	$0.842156\pi$
$762$		0			0
$763$	8.82715	−	15.5854i	0.319564	−	0.564230i
$764$		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	$-0.731046\pi$
$769$	−36.8140			−1.32755			−0.663773	+	0.747934i	$0.731046\pi$
$770$		0			0
$771$	−2.01780			−0.0726695
$772$		0			0
$773$	2.82574	+	2.82574i	0.101635	+	0.101635i	0.756096	−	0.654461i	$-0.227104\pi$
$773$	2.82574	+	2.82574i	0.101635	+	0.101635i	−0.654461	+	0.756096i	$0.727104\pi$
$774$		0			0
$775$	−0.327683	+	19.4722i	−0.0117707	+	0.699460i
$776$		0			0
$777$	0.367091	−	0.648143i	0.0131693	−	0.0232520i
$778$		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	−0.247757	−	0.968822i	$-0.579693\pi$
$787$	20.2284	−	20.2284i	0.721065	−	0.721065i	0.968822	+	0.247757i	$0.0796934\pi$
$788$		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	$0.604010\pi$
$797$	−35.7989	+	35.7989i	−1.26806	+	1.26806i	−0.947089	+	0.320972i	$0.895990\pi$
$798$		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
$805$	6.59380	+	24.6223i	0.232401	+	0.867822i
$806$		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	$0.144244\pi$
$811$			24.9358i			0.875613i	−0.899069	+	0.437806i	$0.855756\pi$
$812$		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	$-0.352312\pi$
$829$	25.7696			0.895014			0.447507	+	0.894280i	$0.352312\pi$
$830$		0			0
$831$		−	28.2121i		−	0.978665i
$832$		0			0
$833$	−5.28472	−	1.32273i	−0.183105	−	0.0458299i
$834$		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	$-0.600662\pi$
$839$	−18.0163			−0.621990			−0.310995	+	0.950411i	$0.600662\pi$
$840$		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
$847$	−36.8066	−	20.8462i	−1.26469	−	0.716285i
$848$		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	0.936074	−	0.351803i	$-0.114431\pi$
$853$	17.0643	+	17.0643i	0.584271	+	0.584271i	−0.351803	+	0.936074i	$0.614431\pi$
$854$		0			0
$855$	2.92335	+	0.0245958i	0.0999766	+	0.000841158i
$856$		0			0
$857$	−4.20254	+	4.20254i	−0.143556	+	0.143556i	−0.775232	−	0.631676i	$-0.782367\pi$
$857$	−4.20254	+	4.20254i	−0.143556	+	0.143556i	0.631676	+	0.775232i	$0.282367\pi$
$858$		0			0
$859$	31.7205			1.08229			0.541145	−	0.840929i	$-0.317991\pi$
$859$	31.7205			1.08229			0.541145	+	0.840929i	$0.317991\pi$
$860$		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
$875$	−15.2227	+	25.3627i	−0.514622	+	0.857417i
$876$		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	$-0.828729\pi$
$881$		−	30.4222i		−	1.02495i	0.858702	−	0.512475i	$-0.171271\pi$
$882$		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	−0.769651	−	0.638465i	$-0.779570\pi$
$887$	−3.90707	+	3.90707i	−0.131187	+	0.131187i	0.638465	+	0.769651i	$0.279570\pi$
$888$		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
$903$	−6.45750	−	3.65735i	−0.214892	−	0.121709i
$904$		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
$917$	17.7532	−	31.3455i	0.586263	−	1.03512i
$918$		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	$-0.436169\pi$
$929$	12.1425			0.398381			0.199191	+	0.979961i	$0.436169\pi$
$930$		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	−0.868582	−	0.495546i	$-0.834968\pi$
$937$	−11.4188	+	11.4188i	−0.373036	+	0.373036i	0.495546	+	0.868582i	$0.334968\pi$
$938$		0			0
$939$		−	16.5242i		−	0.539248i
$940$		0			0
$941$			21.2998i			0.694353i	0.937800	+	0.347176i	$0.112860\pi$
$941$			21.2998i			0.694353i	−0.937800	+	0.347176i	$0.887140\pi$
$942$		0			0
$943$	8.31709	+	8.31709i	0.270842	+	0.270842i
$944$		0			0
$945$	1.53039	+	5.71471i	0.0497835	+	0.185900i
$946$		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	$-0.962997\pi$
$971$		−	7.22848i		−	0.231973i	0.993251	−	0.115986i	$-0.0370029\pi$
$972$		0			0
$973$	13.6580	+	7.73551i	0.437855	+	0.247989i
$974$		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	0.600213	−	0.799840i	$-0.295082\pi$
$983$	−6.25887	−	6.25887i	−0.199627	−	0.199627i	−0.799840	+	0.600213i	$0.795082\pi$
$984$		0			0
$985$	19.5279	−	19.2020i	0.622209	−	0.611827i
$986$		0			0
$987$	14.3589	+	8.13248i	0.457048	+	0.258860i
$988$		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	−0.0262684	−	0.999655i	$-0.508362\pi$
$997$	30.7350	−	30.7350i	0.973386	−	0.973386i	0.999655	+	0.0262684i	$0.00836247\pi$
$998$		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.a.97.9	✓	24
4.3	odd	2		1680.2.cz.f.97.6		24
5.3	odd	4		840.2.bt.b.433.4	yes	24
7.6	odd	2		840.2.bt.b.97.4	yes	24
20.3	even	4		1680.2.cz.e.433.7		24
28.27	even	2		1680.2.cz.e.97.7		24
35.13	even	4	inner	840.2.bt.a.433.9	yes	24
140.83	odd	4		1680.2.cz.f.433.6		24

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-0.0188126 + 2.23599i) q^{5} +(-2.30215 - 1.30388i) q^{7} +1.00000i q^{9} -5.19499 q^{11} +(-0.817355 - 0.817355i) q^{13} +(-1.59439 + 1.56778i) q^{15} +(-0.550305 + 0.550305i) q^{17} -1.30741 q^{19} +(-0.705888 - 2.54985i) q^{21} +(-3.04663 + 3.04663i) q^{23} +(-4.99929 - 0.0841295i) q^{25} +(-0.707107 + 0.707107i) q^{27} +2.99042i q^{29} -3.89498i q^{31} +(-3.67341 - 3.67341i) q^{33} +(2.95876 - 5.12306i) q^{35} +(0.199077 + 0.199077i) q^{37} -1.15591i q^{39} -2.72993i q^{41} +(1.98342 - 1.98342i) q^{43} +(-2.23599 - 0.0188126i) q^{45} +(-4.41033 + 4.41033i) q^{47} +(3.59981 + 6.00344i) q^{49} -0.778249 q^{51} +(-1.09146 + 1.09146i) q^{53} +(0.0977312 - 11.6159i) q^{55} +(-0.924478 - 0.924478i) q^{57} +13.8935 q^{59} +10.9392i q^{61} +(1.30388 - 2.30215i) q^{63} +(1.84297 - 1.81222i) q^{65} +(-10.0506 - 10.0506i) q^{67} -4.30858 q^{69} -16.2833 q^{71} +(-5.32068 - 5.32068i) q^{73} +(-3.47554 - 3.59452i) q^{75} +(11.9597 + 6.77362i) q^{77} +8.15872i q^{79} -1.00000 q^{81} +(7.49447 + 7.49447i) q^{83} +(-1.22012 - 1.24083i) q^{85} +(-2.11455 + 2.11455i) q^{87} +16.5546 q^{89} +(0.815946 + 2.94740i) q^{91} +(2.75417 - 2.75417i) q^{93} +(0.0245958 - 2.92335i) q^{95} +(-9.70745 + 9.70745i) q^{97} -5.19499i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 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 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * 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

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